diff --git a/-1BnXEwHUok.txt b/-1BnXEwHUok.txt new file mode 100644 index 0000000000000000000000000000000000000000..157b90247c82f17ceee53c8ec11d5ee454a70d47 --- /dev/null +++ b/-1BnXEwHUok.txt @@ -0,0 +1,8227 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer high quality educational + + align:start position:0% +to offer high quality educational + + + align:start position:0% +to offer high quality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT + + align:start position:0% +hundreds of MIT courses visit MIT + + + align:start position:0% +hundreds of MIT courses visit MIT +opencourseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu so today + + align:start position:0% +ocw.mit.edu so today + + + align:start position:0% +ocw.mit.edu so today +we're going to move on to a fairly + + align:start position:0% +we're going to move on to a fairly + + + align:start position:0% +we're going to move on to a fairly +different world than the world we've + + align:start position:0% +different world than the world we've + + + align:start position:0% +different world than the world we've +been living in and this will be a world + + align:start position:0% +been living in and this will be a world + + + align:start position:0% +been living in and this will be a world +we'll be living in for quite a few + + align:start position:0% +we'll be living in for quite a few + + + align:start position:0% +we'll be living in for quite a few +lectures but before I do that I want to + + align:start position:0% +lectures but before I do that I want to + + + align:start position:0% +lectures but before I do that I want to +get back to just finish up something + + align:start position:0% +get back to just finish up something + + + align:start position:0% +get back to just finish up something +that Professor Grimson started you may + + align:start position:0% +that Professor Grimson started you may + + + align:start position:0% +that Professor Grimson started you may +recall he talked about family trees and + + align:start position:0% +recall he talked about family trees and + + + align:start position:0% +recall he talked about family trees and +raised the question was it actually + + align:start position:0% +raised the question was it actually + + + align:start position:0% +raised the question was it actually +possible to represent all ancestral + + align:start position:0% +possible to represent all ancestral + + + align:start position:0% +possible to represent all ancestral +relationships as a tree well as a + + align:start position:0% +relationships as a tree well as a + + + align:start position:0% +relationships as a tree well as a +counter example I'm sure some of you are + + align:start position:0% +counter example I'm sure some of you are + + + align:start position:0% +counter example I'm sure some of you are +familiar with edus + + align:start position:0% +familiar with edus + + + align:start position:0% +familiar with edus +Rex uh for those of you who are not I'm + + align:start position:0% +Rex uh for those of you who are not I'm + + + align:start position:0% +Rex uh for those of you who are not I'm +happy to give you a plot summary at the + + align:start position:0% +happy to give you a plot summary at the + + + align:start position:0% +happy to give you a plot summary at the +end of the lecture it's a rather bizarre + + align:start position:0% +end of the lecture it's a rather bizarre + + + align:start position:0% +end of the lecture it's a rather bizarre +plot but it was captured in a wonderful + + align:start position:0% +plot but it was captured in a wonderful + + + align:start position:0% +plot but it was captured in a wonderful +song by Tom + + align:start position:0% +song by Tom + + + align:start position:0% +song by Tom +Lair uh to the short story is edus ended + + align:start position:0% +Lair uh to the short story is edus ended + + + align:start position:0% +Lair uh to the short story is edus ended +up marrying his mother and having four + + align:start position:0% +up marrying his mother and having four + + + align:start position:0% +up marrying his mother and having four +children um and Tom Lair if you've never + + align:start position:0% +children um and Tom Lair if you've never + + + align:start position:0% +children um and Tom Lair if you've never +heard of Tom Lair you're missing one of + + align:start position:0% +heard of Tom Lair you're missing one of + + + align:start position:0% +heard of Tom Lair you're missing one of +the world's funniest + + align:start position:0% +the world's funniest + + + align:start position:0% +the world's funniest +songwriters and he had a wonderful song + + align:start position:0% +songwriters and he had a wonderful song + + + align:start position:0% +songwriters and he had a wonderful song +called edus Rex and I recommend this + + align:start position:0% +called edus Rex and I recommend this + + + align:start position:0% +called edus Rex and I recommend this +YouTube as a way to go and listen to + + align:start position:0% +YouTube as a way to go and listen to + + + align:start position:0% +YouTube as a way to go and listen to +it and uh you can gather from uh the + + align:start position:0% +it and uh you can gather from uh the + + + align:start position:0% +it and uh you can gather from uh the +quote what the story is about I also + + align:start position:0% +quote what the story is about I also + + + align:start position:0% +quote what the story is about I also +recommend the play by the way it it's + + align:start position:0% +recommend the play by the way it it's + + + align:start position:0% +recommend the play by the way it it's +really uh kind of appalling what goes on + + align:start position:0% +really uh kind of appalling what goes on + + + align:start position:0% +really uh kind of appalling what goes on +but it's + + align:start position:0% +but it's + + + align:start position:0% +but it's +beautiful all right back to the main + + align:start position:0% +beautiful all right back to the main + + + align:start position:0% +beautiful all right back to the main +topic here's the uh the relevant + + align:start position:0% +topic here's the uh the relevant + + + align:start position:0% +topic here's the uh the relevant +reading uh a small bit from from later + + align:start position:0% +reading uh a small bit from from later + + + align:start position:0% +reading uh a small bit from from later +in the book and then chapter 14 you may + + align:start position:0% +in the book and then chapter 14 you may + + + align:start position:0% +in the book and then chapter 14 you may +notice that we're not actually going + + align:start position:0% +notice that we're not actually going + + + align:start position:0% +notice that we're not actually going +through the book in Order and the reason + + align:start position:0% +through the book in Order and the reason + + + align:start position:0% +through the book in Order and the reason +we're not doing that is because we're + + align:start position:0% +we're not doing that is because we're + + + align:start position:0% +we're not doing that is because we're +trying to get you information you need + + align:start position:0% +trying to get you information you need + + + align:start position:0% +trying to get you information you need +in time to do problem + + align:start position:0% +in time to do problem + + + align:start position:0% +in time to do problem +sets all + + align:start position:0% +sets all + + + align:start position:0% +sets all +right so the topic of today is really + + align:start position:0% +right so the topic of today is really + + + align:start position:0% +right so the topic of today is really +uncertainty and the fact that the world + + align:start position:0% +uncertainty and the fact that the world + + + align:start position:0% +uncertainty and the fact that the world +is + + align:start position:0% +is + + + align:start position:0% +is +really annoyingly hard to understand + + align:start position:0% +really annoyingly hard to understand + + + align:start position:0% +really annoyingly hard to understand +um this is signpost related to 602 but + + align:start position:0% +um this is signpost related to 602 but + + + align:start position:0% +um this is signpost related to 602 but +we won't go into too much detail about + + align:start position:0% +we won't go into too much detail about + + + align:start position:0% +we won't go into too much detail about +it um we'd rather things were certain + + align:start position:0% +it um we'd rather things were certain + + + align:start position:0% +it um we'd rather things were certain +but in fact they usually are + + align:start position:0% +but in fact they usually are + + + align:start position:0% +but in fact they usually are +not and this is a place where 6 + + align:start position:0% +not and this is a place where 6 + + + align:start position:0% +not and this is a place where 6 +uh2 diverges from the typical + + align:start position:0% +uh2 diverges from the typical + + + align:start position:0% +uh2 diverges from the typical +introductory computer science course + + align:start position:0% +introductory computer science course + + + align:start position:0% +introductory computer science course +which focuses on things that are + + align:start position:0% +which focuses on things that are + + + align:start position:0% +which focuses on things that are +functional given an input you always get + + align:start position:0% +functional given an input you always get + + + align:start position:0% +functional given an input you always get +the same output it's + + align:start position:0% +the same output it's + + + align:start position:0% +the same output it's +predictable and we like to do that + + align:start position:0% +predictable and we like to do that + + + align:start position:0% +predictable and we like to do that +because that's easier to teach but in + + align:start position:0% +because that's easier to teach but in + + + align:start position:0% +because that's easier to teach but in +fact for reasons we'll be talking about + + align:start position:0% +fact for reasons we'll be talking about + + + align:start position:0% +fact for reasons we'll be talking about +it's not nearly as + + align:start position:0% +it's not nearly as + + + align:start position:0% +it's not nearly as +useful if you're trying to actually + + align:start position:0% +useful if you're trying to actually + + + align:start position:0% +useful if you're trying to actually +write computations that help you + + align:start position:0% +write computations that help you + + + align:start position:0% +write computations that help you +understand the world you have to face + + align:start position:0% +understand the world you have to face + + + align:start position:0% +understand the world you have to face +uncertainty + + align:start position:0% +uncertainty + + + align:start position:0% +uncertainty +headon + + align:start position:0% +headon + + + align:start position:0% +headon +um an analogy is for many years people + + align:start position:0% +um an analogy is for many years people + + + align:start position:0% +um an analogy is for many years people +believed in Newtonian mechanics + + align:start position:0% +believed in Newtonian mechanics + + + align:start position:0% +believed in Newtonian mechanics +um I guess they still do in in 801 maybe + + align:start position:0% +um I guess they still do in in 801 maybe + + + align:start position:0% +um I guess they still do in in 801 maybe +that every effect has a + + align:start position:0% +that every effect has a + + + align:start position:0% +that every effect has a +cause an apple falls from the tree + + align:start position:0% +cause an apple falls from the tree + + + align:start position:0% +cause an apple falls from the tree +because of gravity and you know where + + align:start position:0% +because of gravity and you know where + + + align:start position:0% +because of gravity and you know where +it's going to land and the world can be + + align:start position:0% +it's going to land and the world can be + + + align:start position:0% +it's going to land and the world can be +understood causally and people believe + + align:start position:0% +understood causally and people believe + + + align:start position:0% +understood causally and people believe +this really for quite a long time um + + align:start position:0% +this really for quite a long time um + + + align:start position:0% +this really for quite a long time um +most of + + align:start position:0% +most of + + + align:start position:0% +most of +History until the early part of the 20th + + align:start position:0% +History until the early part of the 20th + + + align:start position:0% +History until the early part of the 20th +century when the so-called Copenhagen + + align:start position:0% +century when the so-called Copenhagen + + + align:start position:0% +century when the so-called Copenhagen +Doctrine was was uh put + + align:start position:0% +Doctrine was was uh put + + + align:start position:0% +Doctrine was was uh put +forth + + align:start position:0% +forth + + + align:start position:0% +forth +um the doctrine there from bour and + + align:start position:0% +um the doctrine there from bour and + + + align:start position:0% +um the doctrine there from bour and +Heisenberg two very famous physicists + + align:start position:0% +Heisenberg two very famous physicists + + + align:start position:0% +Heisenberg two very famous physicists +was one of what they called causal + + align:start position:0% +was one of what they called causal + + + align:start position:0% +was one of what they called causal +non-determinism and their assertion was + + align:start position:0% +non-determinism and their assertion was + + + align:start position:0% +non-determinism and their assertion was +that the world at its very most + + align:start position:0% +that the world at its very most + + + align:start position:0% +that the world at its very most +fundamental + + align:start position:0% +fundamental + + + align:start position:0% +fundamental +level uh behaves in a way that you + + align:start position:0% +level uh behaves in a way that you + + + align:start position:0% +level uh behaves in a way that you +cannot predict it's okay to make a + + align:start position:0% +cannot predict it's okay to make a + + + align:start position:0% +cannot predict it's okay to make a +statement that X is highly likely to + + align:start position:0% +statement that X is highly likely to + + + align:start position:0% +statement that X is highly likely to +occur almost certain to occur but for no + + align:start position:0% +occur almost certain to occur but for no + + + align:start position:0% +occur almost certain to occur but for no +case can you make the statement X will + + align:start position:0% +case can you make the statement X will + + + align:start position:0% +case can you make the statement X will +occur nothing has a probability of + + align:start position:0% +occur nothing has a probability of + + + align:start position:0% +occur nothing has a probability of +one um this was hard for us to imagine + + align:start position:0% +one um this was hard for us to imagine + + + align:start position:0% +one um this was hard for us to imagine +today when we all know quantum mechanics + + align:start position:0% +today when we all know quantum mechanics + + + align:start position:0% +today when we all know quantum mechanics +but at the turn of the century this was + + align:start position:0% +but at the turn of the century this was + + + align:start position:0% +but at the turn of the century this was +a shocking statement and two other very + + align:start position:0% +a shocking statement and two other very + + + align:start position:0% +a shocking statement and two other very +well-known physics physicists Albert + + align:start position:0% +well-known physics physicists Albert + + + align:start position:0% +well-known physics physicists Albert +Einstein and shringer basically said no + + align:start position:0% +Einstein and shringer basically said no + + + align:start position:0% +Einstein and shringer basically said no +this is wrong Bor Heisenberg you guys + + align:start position:0% +this is wrong Bor Heisenberg you guys + + + align:start position:0% +this is wrong Bor Heisenberg you guys +are ID idiots it's just not true they + + align:start position:0% +are ID idiots it's just not true they + + + align:start position:0% +are ID idiots it's just not true they +probably didn't call them idiots and + + align:start position:0% +probably didn't call them idiots and + + + align:start position:0% +probably didn't call them idiots and +this is most exemplified by Einstein's + + align:start position:0% +this is most exemplified by Einstein's + + + align:start position:0% +this is most exemplified by Einstein's +famous quote that God does not play + + align:start position:0% +famous quote that God does not play + + + align:start position:0% +famous quote that God does not play +dice uh which is indicative of the fact + + align:start position:0% +dice uh which is indicative of the fact + + + align:start position:0% +dice uh which is indicative of the fact +that this was actually a discussion that + + align:start position:0% +that this was actually a discussion that + + + align:start position:0% +that this was actually a discussion that +permeated not just the world of physics + + align:start position:0% +permeated not just the world of physics + + + align:start position:0% +permeated not just the world of physics +but Society in general people really + + align:start position:0% +but Society in general people really + + + align:start position:0% +but Society in general people really +turned it into literally a religious + + align:start position:0% +turned it into literally a religious + + + align:start position:0% +turned it into literally a religious +issue as did + + align:start position:0% +issue as did + + + align:start position:0% +issue as did +Einstein well so now we should ask the + + align:start position:0% +Einstein well so now we should ask the + + + align:start position:0% +Einstein well so now we should ask the +question does it really matter and to + + align:start position:0% +question does it really matter and to + + + align:start position:0% +question does it really matter and to +illustrate that I need two coins I + + align:start position:0% +illustrate that I need two coins I + + + align:start position:0% +illustrate that I need two coins I +forgot to bring any coins with me do + + align:start position:0% +forgot to bring any coins with me do + + + align:start position:0% +forgot to bring any coins with me do +anyone got a coin they can lend + + align:start position:0% +anyone got a coin they can lend + + + align:start position:0% +anyone got a coin they can lend +me all + + align:start position:0% +me all + + + align:start position:0% +me all +right now this is where I see how much + + align:start position:0% +right now this is where I see how much + + + align:start position:0% +right now this is where I see how much +the students trust me do I get a penny + + align:start position:0% +the students trust me do I get a penny + + + align:start position:0% +the students trust me do I get a penny +do I get a silver dollar all right so + + align:start position:0% +do I get a silver dollar all right so + + + align:start position:0% +do I get a silver dollar all right so +what have we got + + align:start position:0% +what have we got + + + align:start position:0% +what have we got +here all right this is someone who's + + align:start position:0% +here all right this is someone who's + + + align:start position:0% +here all right this is someone who's +entrusting me with two quarters not so + + align:start position:0% +entrusting me with two quarters not so + + + align:start position:0% +entrusting me with two quarters not so +bad um so we'll take these two quarters + + align:start position:0% +bad um so we'll take these two quarters + + + align:start position:0% +bad um so we'll take these two quarters +and we'll shake them up up and we'll put + + align:start position:0% +and we'll shake them up up and we'll put + + + align:start position:0% +and we'll shake them up up and we'll put +them down on the + + align:start position:0% +them down on the + + + align:start position:0% +them down on the +table um and now we'll ask a + + align:start position:0% +table um and now we'll ask a + + + align:start position:0% +table um and now we'll ask a +question do we have two heads two tails + + align:start position:0% +question do we have two heads two tails + + + align:start position:0% +question do we have two heads two tails +or one head and one + + align:start position:0% +or one head and one + + + align:start position:0% +or one head and one +tail so who thinks we have two + + align:start position:0% +tail so who thinks we have two + + + align:start position:0% +tail so who thinks we have two +heads who thinks we have two + + align:start position:0% +heads who thinks we have two + + + align:start position:0% +heads who thinks we have two +taals who thinks we have one of each all + + align:start position:0% +taals who thinks we have one of each all + + + align:start position:0% +taals who thinks we have one of each all +right well clearly everyone except a few + + align:start position:0% +right well clearly everyone except a few + + + align:start position:0% +right well clearly everyone except a few +people for example the Indians fan who + + align:start position:0% +people for example the Indians fan who + + + align:start position:0% +people for example the Indians fan who +clearly believe in the counterfactual + + align:start position:0% + + + + align:start position:0% + +um made the most probabilistic + + align:start position:0% +um made the most probabilistic + + + align:start position:0% +um made the most probabilistic +decision um but in fact there's no + + align:start position:0% +decision um but in fact there's no + + + align:start position:0% +decision um but in fact there's no +non-determinism here I know the answer + + align:start position:0% +non-determinism here I know the answer + + + align:start position:0% +non-determinism here I know the answer +right and so in some sense it doesn't + + align:start position:0% +right and so in some sense it doesn't + + + align:start position:0% +right and so in some sense it doesn't +matter whether it's deterministic + + align:start position:0% +matter whether it's deterministic + + + align:start position:0% +matter whether it's deterministic +because in fact it's not causally + + align:start position:0% +because in fact it's not causally + + + align:start position:0% +because in fact it's not causally +non-deterministic the answer is quite + + align:start position:0% +non-deterministic the answer is quite + + + align:start position:0% +non-deterministic the answer is quite +clear but you don't know the + + align:start position:0% +clear but you don't know the + + + align:start position:0% +clear but you don't know the +answer and so + + align:start position:0% +answer and so + + + align:start position:0% +answer and so +whether or not the world is inherently + + align:start position:0% +whether or not the world is inherently + + + align:start position:0% +whether or not the world is inherently +unpredictable the fact that we never + + align:start position:0% +unpredictable the fact that we never + + + align:start position:0% +unpredictable the fact that we never +have complete knowledge of the + + align:start position:0% +have complete knowledge of the + + + align:start position:0% +have complete knowledge of the +world suggest that we might as well + + align:start position:0% +world suggest that we might as well + + + align:start position:0% +world suggest that we might as well +treat it as inherently + + align:start position:0% +treat it as inherently + + + align:start position:0% +treat it as inherently +unpredictable okay and so this is called + + align:start position:0% +unpredictable okay and so this is called + + + align:start position:0% +unpredictable okay and so this is called +predictive + + align:start position:0% +predictive + + + align:start position:0% +predictive +non-determinism and this really is + + align:start position:0% +non-determinism and this really is + + + align:start position:0% +non-determinism and this really is +what's going to underline pretty much + + align:start position:0% +what's going to underline pretty much + + + align:start position:0% +what's going to underline pretty much +everything else we're going to be doing + + align:start position:0% +everything else we're going to be doing + + + align:start position:0% +everything else we're going to be doing +here all + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +no comments about that all + + align:start position:0% +no comments about that all + + + align:start position:0% +no comments about that all +right I wouldn't do that to + + align:start position:0% +right I wouldn't do that to + + + align:start position:0% +right I wouldn't do that to +you thank + + align:start position:0% +you thank + + + align:start position:0% +you thank +you I know you were wishing to get + + align:start position:0% +you I know you were wishing to get + + + align:start position:0% +you I know you were wishing to get +interest on the money but you don't get + + align:start position:0% + + + + align:start position:0% + +any yeah all + + align:start position:0% +any yeah all + + + align:start position:0% +any yeah all +right what was + + align:start position:0% +right what was + + + align:start position:0% +right what was +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +that all right so when we think about + + align:start position:0% +that all right so when we think about + + + align:start position:0% +that all right so when we think about +non-determinism in computation we use + + align:start position:0% +non-determinism in computation we use + + + align:start position:0% +non-determinism in computation we use +the word stochastic + + align:start position:0% +the word stochastic + + + align:start position:0% +the word stochastic +process and that's any process that's + + align:start position:0% +process and that's any process that's + + + align:start position:0% +process and that's any process that's +ongoing in which the next state depends + + align:start position:0% +ongoing in which the next state depends + + + align:start position:0% +ongoing in which the next state depends +upon the previous States in some random + + align:start position:0% +upon the previous States in some random + + + align:start position:0% +upon the previous States in some random +element so typically up till now when + + align:start position:0% +element so typically up till now when + + + align:start position:0% +element so typically up till now when +we've written code what one line of code + + align:start position:0% +we've written code what one line of code + + + align:start position:0% +we've written code what one line of code +did depended only on what the previous + + align:start position:0% +did depended only on what the previous + + + align:start position:0% +did depended only on what the previous +lines of code did there was no + + align:start position:0% +lines of code did there was no + + + align:start position:0% +lines of code did there was no +Randomness here we're going to have + + align:start position:0% +Randomness here we're going to have + + + align:start position:0% +Randomness here we're going to have +Randomness and we can see the difference + + align:start position:0% +Randomness and we can see the difference + + + align:start position:0% +Randomness and we can see the difference +if we look at these two specifications + + align:start position:0% +if we look at these two specifications + + + align:start position:0% +if we look at these two specifications +of rolling a + + align:start position:0% +of rolling a + + + align:start position:0% +of rolling a +die the first one returns an in between + + align:start position:0% +die the first one returns an in between + + + align:start position:0% +die the first one returns an in between +one and six is what I'll call + + align:start position:0% +one and six is what I'll call + + + align:start position:0% +one and six is what I'll call +underdetermined by that I mean you can't + + align:start position:0% +underdetermined by that I mean you can't + + + align:start position:0% +underdetermined by that I mean you can't +tell what it's going to return maybe it + + align:start position:0% +tell what it's going to return maybe it + + + align:start position:0% +tell what it's going to return maybe it +will return a different number each time + + align:start position:0% +will return a different number each time + + + align:start position:0% +will return a different number each time +you call it but it's not required to + + align:start position:0% +you call it but it's not required to + + + align:start position:0% +you call it but it's not required to +maybe it will return three every time + + align:start position:0% +maybe it will return three every time + + + align:start position:0% +maybe it will return three every time +you call it the second specification + + align:start position:0% +you call it the second specification + + + align:start position:0% +you call it the second specification +requires Randomness it says it returns a + + align:start position:0% +requires Randomness it says it returns a + + + align:start position:0% +requires Randomness it says it returns a +randomly chosen in so it requires a + + align:start position:0% +randomly chosen in so it requires a + + + align:start position:0% +randomly chosen in so it requires a +stochastic + + align:start position:0% +stochastic + + + align:start position:0% +stochastic +implementation all right let's look at + + align:start position:0% +implementation all right let's look at + + + align:start position:0% +implementation all right let's look at +how we Implement a random process in + + align:start position:0% +how we Implement a random process in + + + align:start position:0% +how we Implement a random process in +Python we start by importing the library + + align:start position:0% +Python we start by importing the library + + + align:start position:0% +Python we start by importing the library +random um this is not to say you can + + align:start position:0% +random um this is not to say you can + + + align:start position:0% +random um this is not to say you can +report any random Library you want it's + + align:start position:0% +report any random Library you want it's + + + align:start position:0% +report any random Library you want it's +to say you report the library called + + align:start position:0% +to say you report the library called + + + align:start position:0% +to say you report the library called +random let me get my pen out of + + align:start position:0% + + + + align:start position:0% + +here and we'll use that a lot and then + + align:start position:0% +here and we'll use that a lot and then + + + align:start position:0% +here and we'll use that a lot and then +we're going to use the function in + + align:start position:0% +we're going to use the function in + + + align:start position:0% +we're going to use the function in +random called random. + + align:start position:0% +random called random. + + + align:start position:0% +random called random. +Choice it takes as an argument a + + align:start position:0% +Choice it takes as an argument a + + + align:start position:0% +Choice it takes as an argument a +sequence in this case a list and + + align:start position:0% +sequence in this case a list and + + + align:start position:0% +sequence in this case a list and +randomly chooses one member of the list + + align:start position:0% +randomly chooses one member of the list + + + align:start position:0% +randomly chooses one member of the list +and it chooses it + + align:start position:0% + + + + align:start position:0% + +uniformly it's a uniform + + align:start position:0% +uniformly it's a uniform + + + align:start position:0% +uniformly it's a uniform +distribution and what that means is that + + align:start position:0% +distribution and what that means is that + + + align:start position:0% +distribution and what that means is that +it's equally probable that it will + + align:start position:0% +it's equally probable that it will + + + align:start position:0% +it's equally probable that it will +choose any number in that list each time + + align:start position:0% +choose any number in that list each time + + + align:start position:0% +choose any number in that list each time +you call + + align:start position:0% +you call + + + align:start position:0% +you call +it we'll later look at distributions + + align:start position:0% +it we'll later look at distributions + + + align:start position:0% +it we'll later look at distributions +that are not uniform not equally + + align:start position:0% +that are not uniform not equally + + + align:start position:0% +that are not uniform not equally +probable where things are weighted but + + align:start position:0% +probable where things are weighted but + + + align:start position:0% +probable where things are weighted but +here it's quite simple it's just + + align:start position:0% + + + + align:start position:0% + +uniform and then we can test it using a + + align:start position:0% +uniform and then we can test it using a + + + align:start position:0% +uniform and then we can test it using a +test roll takes some number of N and uh + + align:start position:0% +test roll takes some number of N and uh + + + align:start position:0% +test roll takes some number of N and uh +rolls the die that many times and + + align:start position:0% +rolls the die that many times and + + + align:start position:0% +rolls the die that many times and +creates a string telling us what we + + align:start position:0% + + + + align:start position:0% + +got + + align:start position:0% +got + + + align:start position:0% +got +so let's consider running this on say + + align:start position:0% +so let's consider running this on say + + + align:start position:0% +so let's consider running this on say +test roll of + + align:start position:0% +test roll of + + + align:start position:0% +test roll of +five and we'll ask the question if we + + align:start position:0% +five and we'll ask the question if we + + + align:start position:0% +five and we'll ask the question if we +run it how probable is + + align:start position:0% +run it how probable is + + + align:start position:0% +run it how probable is +it that it's going to return a string of + + align:start position:0% +it that it's going to return a string of + + + align:start position:0% +it that it's going to return a string of +five + + align:start position:0% + + + + align:start position:0% + +ones how do we do that now I know how + + align:start position:0% +ones how do we do that now I know how + + + align:start position:0% +ones how do we do that now I know how +many people here are either in 6041 or + + align:start position:0% +many people here are either in 6041 or + + + align:start position:0% +many people here are either in 6041 or +have taken 6041 raise your + + align:start position:0% +have taken 6041 raise your + + + align:start position:0% +have taken 6041 raise your +hand oh good so very few of you know + + align:start position:0% +hand oh good so very few of you know + + + align:start position:0% +hand oh good so very few of you know +probability that + + align:start position:0% +probability that + + + align:start position:0% +probability that +helps all right so how do we think about + + align:start position:0% +helps all right so how do we think about + + + align:start position:0% +helps all right so how do we think about +that question well + + align:start position:0% +that question well + + + align:start position:0% +that question well +probability to me at least is all about + + align:start position:0% +probability to me at least is all about + + + align:start position:0% +probability to me at least is all about +counting especially discret probability + + align:start position:0% +counting especially discret probability + + + align:start position:0% +counting especially discret probability +which is what we're looking at + + align:start position:0% +which is what we're looking at + + + align:start position:0% +which is what we're looking at +here what you do is you start by + + align:start position:0% +here what you do is you start by + + + align:start position:0% +here what you do is you start by +counting the number of events that have + + align:start position:0% +counting the number of events that have + + + align:start position:0% +counting the number of events that have +the property of + + align:start position:0% + + + + align:start position:0% + +Interest + + align:start position:0% +Interest + + + align:start position:0% +Interest +and the number of possible events and + + align:start position:0% +and the number of possible events and + + + align:start position:0% +and the number of possible events and +divide one by the + + align:start position:0% +divide one by the + + + align:start position:0% +divide one by the +other so if we think about rolling a die + + align:start position:0% +other so if we think about rolling a die + + + align:start position:0% +other so if we think about rolling a die +five + + align:start position:0% +five + + + align:start position:0% +five +times we can enumerate all of the + + align:start position:0% +times we can enumerate all of the + + + align:start position:0% +times we can enumerate all of the +possible outcomes of five + + align:start position:0% +possible outcomes of five + + + align:start position:0% +possible outcomes of five +roles so if we look at that what are the + + align:start position:0% +roles so if we look at that what are the + + + align:start position:0% +roles so if we look at that what are the +outcomes well I could get five + + align:start position:0% +outcomes well I could get five + + + align:start position:0% +outcomes well I could get five +ones I could get five ones four ones and + + align:start position:0% +ones I could get five ones four ones and + + + align:start position:0% +ones I could get five ones four ones and +a two or four ones and a three skip a + + align:start position:0% +a two or four ones and a three skip a + + + align:start position:0% +a two or four ones and a three skip a +few the next one would be three ones a + + align:start position:0% +few the next one would be three ones a + + + align:start position:0% +few the next one would be three ones a +two and a one then a two and a two and + + align:start position:0% +two and a one then a two and a two and + + + align:start position:0% +two and a one then a two and a two and +finally at the end all + + align:start position:0% +finally at the end all + + + align:start position:0% +finally at the end all +sixes right + + align:start position:0% +sixes right + + + align:start position:0% +sixes right +so remember we looked before at when we + + align:start position:0% +so remember we looked before at when we + + + align:start position:0% +so remember we looked before at when we +were looking at optimization problems + + align:start position:0% +were looking at optimization problems + + + align:start position:0% +were looking at optimization problems +about binary numbers and we said we + + align:start position:0% +about binary numbers and we said we + + + align:start position:0% +about binary numbers and we said we +could look at all the possible choices + + align:start position:0% +could look at all the possible choices + + + align:start position:0% +could look at all the possible choices +of items in the knapsack by a vector of + + align:start position:0% +of items in the knapsack by a vector of + + + align:start position:0% +of items in the knapsack by a vector of +zeros and ones we said how many possible + + align:start position:0% +zeros and ones we said how many possible + + + align:start position:0% +zeros and ones we said how many possible +choices are are there well that depended + + align:start position:0% +choices are are there well that depended + + + align:start position:0% +choices are are there well that depended +on how many binary numbers you could get + + align:start position:0% +on how many binary numbers you could get + + + align:start position:0% +on how many binary numbers you could get +in that number of digits well here we're + + align:start position:0% +in that number of digits well here we're + + + align:start position:0% +in that number of digits well here we're +doing the same thing but instead of base + + align:start position:0% +doing the same thing but instead of base + + + align:start position:0% +doing the same thing but instead of base +two it's base + + align:start position:0% + + + + align:start position:0% + +six and so the number of possible + + align:start position:0% +six and so the number of possible + + + align:start position:0% +six and so the number of possible +outcomes of five roles is quite + + align:start position:0% + + + + align:start position:0% + +High how many of those are five ones + + align:start position:0% +High how many of those are five ones + + + align:start position:0% +High how many of those are five ones +only one of them + + align:start position:0% +only one of them + + + align:start position:0% +only one of them +right so in order to get the probability + + align:start position:0% +right so in order to get the probability + + + align:start position:0% +right so in order to get the probability +of five + + align:start position:0% +of five + + + align:start position:0% +of five +ones I divide one by 6 to the + + align:start position:0% + + + + align:start position:0% + +5th does that make sense to + + align:start position:0% +5th does that make sense to + + + align:start position:0% +5th does that make sense to +everybody so in fact we see it's highly + + align:start position:0% +everybody so in fact we see it's highly + + + align:start position:0% +everybody so in fact we see it's highly +unlikely probability of five runs is + + align:start position:0% +unlikely probability of five runs is + + + align:start position:0% +unlikely probability of five runs is +quite + + align:start position:0% +quite + + + align:start position:0% +quite +small now suppose we were to ask about + + align:start position:0% +small now suppose we were to ask about + + + align:start position:0% +small now suppose we were to ask about +the probability of something + + align:start position:0% +the probability of something + + + align:start position:0% +the probability of something +else instead of 51 say 5 + + align:start position:0% +else instead of 51 say 5 + + + align:start position:0% +else instead of 51 say 5 +three 4 + + align:start position:0% + + + + align:start position:0% + +21 kind of looks more likely than that + + align:start position:0% +21 kind of looks more likely than that + + + align:start position:0% +21 kind of looks more likely than that +than five ones in a row but of course it + + align:start position:0% +than five ones in a row but of course it + + + align:start position:0% +than five ones in a row but of course it +isn't right any specific combination is + + align:start position:0% +isn't right any specific combination is + + + align:start position:0% +isn't right any specific combination is +equally + + align:start position:0% +equally + + + align:start position:0% +equally +probable and there are a lot of + + align:start position:0% +probable and there are a lot of + + + align:start position:0% +probable and there are a lot of +them so this is all the probability + + align:start position:0% +them so this is all the probability + + + align:start position:0% +them so this is all the probability +we're going to think about we could + + align:start position:0% +we're going to think about we could + + + align:start position:0% +we're going to think about we could +think about this way as simply a matter + + align:start position:0% +think about this way as simply a matter + + + align:start position:0% +think about this way as simply a matter +of counting the number of possible + + align:start position:0% +of counting the number of possible + + + align:start position:0% +of counting the number of possible +events the number of events that have + + align:start position:0% +events the number of events that have + + + align:start position:0% +events the number of events that have +their property of interest in this case + + align:start position:0% +their property of interest in this case + + + align:start position:0% +their property of interest in this case +being all ones and then simple + + align:start position:0% +being all ones and then simple + + + align:start position:0% +being all ones and then simple +division + + align:start position:0% +division + + + align:start position:0% +division +given that framework there are three + + align:start position:0% +given that framework there are three + + + align:start position:0% +given that framework there are three +basic facts about probability we're + + align:start position:0% +basic facts about probability we're + + + align:start position:0% +basic facts about probability we're +going to be using a lot + + align:start position:0% +going to be using a lot + + + align:start position:0% +going to be using a lot +of so one + + align:start position:0% +of so one + + + align:start position:0% +of so one +probabilities always range from zero to + + align:start position:0% +probabilities always range from zero to + + + align:start position:0% +probabilities always range from zero to +one how do we know that well we've got a + + align:start position:0% +one how do we know that well we've got a + + + align:start position:0% +one how do we know that well we've got a +fraction right and we the denominator is + + align:start position:0% +fraction right and we the denominator is + + + align:start position:0% +fraction right and we the denominator is +all possible + + align:start position:0% +all possible + + + align:start position:0% +all possible +events the numerator is the subset of + + align:start position:0% +events the numerator is the subset of + + + align:start position:0% +events the numerator is the subset of +that that's of Interest + + align:start position:0% +that that's of Interest + + + align:start position:0% +that that's of Interest +so it has to range from zero to the + + align:start position:0% +so it has to range from zero to the + + + align:start position:0% +so it has to range from zero to the +denominator and that tells us that the + + align:start position:0% +denominator and that tells us that the + + + align:start position:0% +denominator and that tells us that the +fraction has to range from 0 to + + align:start position:0% +fraction has to range from 0 to + + + align:start position:0% +fraction has to range from 0 to +one so one says it's always going to + + align:start position:0% +one so one says it's always going to + + + align:start position:0% +one so one says it's always going to +happen zero + + align:start position:0% + + + + align:start position:0% + +never so if the probability of event + + align:start position:0% +never so if the probability of event + + + align:start position:0% +never so if the probability of event +occurring is P what's the probability of + + align:start position:0% +occurring is P what's the probability of + + + align:start position:0% +occurring is P what's the probability of +it not + + align:start position:0% +it not + + + align:start position:0% +it not +occurring this follows from the first + + align:start position:0% +occurring this follows from the first + + + align:start position:0% +occurring this follows from the first +bullet it's simply going to be + + align:start position:0% + + + + align:start position:0% + +one minus + + align:start position:0% +one minus + + + align:start position:0% +one minus +P this is a trick that we'll find we use + + align:start position:0% +P this is a trick that we'll find we use + + + align:start position:0% +P this is a trick that we'll find we use +a lot because it's often the case when + + align:start position:0% +a lot because it's often the case when + + + align:start position:0% +a lot because it's often the case when +you want to compute the probability of + + align:start position:0% +you want to compute the probability of + + + align:start position:0% +you want to compute the probability of +something happening it's easier to + + align:start position:0% +something happening it's easier to + + + align:start position:0% +something happening it's easier to +compute the probability of it's not + + align:start position:0% +compute the probability of it's not + + + align:start position:0% +compute the probability of it's not +happening and subtract it from one and + + align:start position:0% +happening and subtract it from one and + + + align:start position:0% +happening and subtract it from one and +we'll see an example of that later + + align:start position:0% + + + + align:start position:0% + +today now here's the Big + + align:start position:0% +today now here's the Big + + + align:start position:0% +today now here's the Big +E when events are independent of each + + align:start position:0% +E when events are independent of each + + + align:start position:0% +E when events are independent of each +other the probability of all of the + + align:start position:0% +other the probability of all of the + + + align:start position:0% +other the probability of all of the +events occurring is equal to the product + + align:start position:0% +events occurring is equal to the product + + + align:start position:0% +events occurring is equal to the product +of the probabilities of each of the + + align:start position:0% +of the probabilities of each of the + + + align:start position:0% +of the probabilities of each of the +events + + align:start position:0% + + + + align:start position:0% + +occurring so if the probability of + + align:start position:0% +occurring so if the probability of + + + align:start position:0% +occurring so if the probability of +a is + + align:start position:0% +a is + + + align:start position:0% +a is +0.5 and the probability of B is + + align:start position:0% +0.5 and the probability of B is + + + align:start position:0% +0.5 and the probability of B is +04 the probability of a and B is + + align:start position:0% + + + + align:start position:0% + +what 05 time4 you guys can figure that + + align:start position:0% +what 05 time4 you guys can figure that + + + align:start position:0% +what 05 time4 you guys can figure that +out I think it's 0. + + align:start position:0% +out I think it's 0. + + + align:start position:0% +out I think it's 0. +2 so you'd expect that right that it + + align:start position:0% +2 so you'd expect that right that it + + + align:start position:0% +2 so you'd expect that right that it +should be much smaller than either of + + align:start position:0% +should be much smaller than either of + + + align:start position:0% +should be much smaller than either of +the first two + + align:start position:0% +the first two + + + align:start position:0% +the first two +probabilities this is the most common + + align:start position:0% +probabilities this is the most common + + + align:start position:0% +probabilities this is the most common +rule it's something we use all the time + + align:start position:0% +rule it's something we use all the time + + + align:start position:0% +rule it's something we use all the time +in probabilties the so-called + + align:start position:0% +in probabilties the so-called + + + align:start position:0% +in probabilties the so-called +multiplicative + + align:start position:0% +multiplicative + + + align:start position:0% +multiplicative +law we have to be careful about it + + align:start position:0% +law we have to be careful about it + + + align:start position:0% +law we have to be careful about it +however in that it only holds if the + + align:start position:0% +however in that it only holds if the + + + align:start position:0% +however in that it only holds if the +events are actually + + align:start position:0% +events are actually + + + align:start position:0% +events are actually +independent two events are + + align:start position:0% +independent two events are + + + align:start position:0% +independent two events are +independent if the outcome of one has no + + align:start position:0% +independent if the outcome of one has no + + + align:start position:0% +independent if the outcome of one has no +influence in the outcome of the + + align:start position:0% + + + + align:start position:0% + +other so when we rolled the die we + + align:start position:0% +other so when we rolled the die we + + + align:start position:0% +other so when we rolled the die we +assumed that the first role the outcome + + align:start position:0% +assumed that the first role the outcome + + + align:start position:0% +assumed that the first role the outcome +was independent of the or the second + + align:start position:0% +was independent of the or the second + + + align:start position:0% +was independent of the or the second +role was independent of the first role + + align:start position:0% +role was independent of the first role + + + align:start position:0% +role was independent of the first role +dependent of the fourth rle when we + + align:start position:0% +dependent of the fourth rle when we + + + align:start position:0% +dependent of the fourth rle when we +looked at the two coins we assumed that + + align:start position:0% +looked at the two coins we assumed that + + + align:start position:0% +looked at the two coins we assumed that +heads and taals of the each coin was + + align:start position:0% +heads and taals of the each coin was + + + align:start position:0% +heads and taals of the each coin was +independent of the other + + align:start position:0% +independent of the other + + + align:start position:0% +independent of the other +coin I didn't for example look at one + + align:start position:0% +coin I didn't for example look at one + + + align:start position:0% +coin I didn't for example look at one +coin and make sure that the other one + + align:start position:0% +coin and make sure that the other one + + + align:start position:0% +coin and make sure that the other one +was + + align:start position:0% + + + + align:start position:0% + +different the danger here is that people + + align:start position:0% +different the danger here is that people + + + align:start position:0% +different the danger here is that people +often compute probabilities assuming + + align:start position:0% +often compute probabilities assuming + + + align:start position:0% +often compute probabilities assuming +Independence when you don't actually + + align:start position:0% +Independence when you don't actually + + + align:start position:0% +Independence when you don't actually +have + + align:start position:0% +have + + + align:start position:0% +have +Independence so let's look at an + + align:start position:0% +Independence so let's look at an + + + align:start position:0% +Independence so let's look at an +example um for those of you familiar + + align:start position:0% +example um for those of you familiar + + + align:start position:0% +example um for those of you familiar +with American + + align:start position:0% +with American + + + align:start position:0% +with American +football uh the B the New England + + align:start position:0% +football uh the B the New England + + + align:start position:0% +football uh the B the New England +Patriots and the Denver Broncos are two + + align:start position:0% +Patriots and the Denver Broncos are two + + + align:start position:0% +Patriots and the Denver Broncos are two +prominent + + align:start position:0% +prominent + + + align:start position:0% +prominent +teams and let's look at Computing the + + align:start position:0% +teams and let's look at Computing the + + + align:start position:0% +teams and let's look at Computing the +probability of one of whether one of + + align:start position:0% +probability of one of whether one of + + + align:start position:0% +probability of one of whether one of +them will lose on a given + + align:start position:0% +them will lose on a given + + + align:start position:0% +them will lose on a given +Sunday so the Patriots have a winning + + align:start position:0% +Sunday so the Patriots have a winning + + + align:start position:0% +Sunday so the Patriots have a winning +percentage of seven of eight they've won + + align:start position:0% +percentage of seven of eight they've won + + + align:start position:0% +percentage of seven of eight they've won +seven of their eight games so far and + + align:start position:0% +seven of their eight games so far and + + + align:start position:0% +seven of their eight games so far and +the Broncos six of + + align:start position:0% +the Broncos six of + + + align:start position:0% +the Broncos six of +eight the probability of both winning + + align:start position:0% +eight the probability of both winning + + + align:start position:0% +eight the probability of both winning +next Sunday we assuming that this is + + align:start position:0% +next Sunday we assuming that this is + + + align:start position:0% +next Sunday we assuming that this is +indicative of how good they are we can + + align:start position:0% +indicative of how good they are we can + + + align:start position:0% +indicative of how good they are we can +get with the multiplicative rule so it's + + align:start position:0% +get with the multiplicative rule so it's + + + align:start position:0% +get with the multiplicative rule so it's +7 over8 * 6 over8 or 42 over + + align:start position:0% +7 over8 * 6 over8 or 42 over + + + align:start position:0% +7 over8 * 6 over8 or 42 over +64 uh we could simplify that fraction I + + align:start position:0% +64 uh we could simplify that fraction I + + + align:start position:0% +64 uh we could simplify that fraction I +suppose all right does that make sense + + align:start position:0% +suppose all right does that make sense + + + align:start position:0% +suppose all right does that make sense +so this is probably a pretty good + + align:start position:0% +so this is probably a pretty good + + + align:start position:0% +so this is probably a pretty good +estimate of both of them winning next + + align:start position:0% +estimate of both of them winning next + + + align:start position:0% +estimate of both of them winning next +Sunday so the probability of at least + + align:start position:0% +Sunday so the probability of at least + + + align:start position:0% +Sunday so the probability of at least +one of them + + align:start position:0% +one of them + + + align:start position:0% +one of them +losing is one minus + + align:start position:0% +losing is one minus + + + align:start position:0% +losing is one minus +that so here's an example of why we + + align:start position:0% +that so here's an example of why we + + + align:start position:0% +that so here's an example of why we +often use the one minus rule right + + align:start position:0% +often use the one minus rule right + + + align:start position:0% +often use the one minus rule right +because we could compute the probability + + align:start position:0% +because we could compute the probability + + + align:start position:0% +because we could compute the probability +of both of them winning by simply + + align:start position:0% +of both of them winning by simply + + + align:start position:0% +of both of them winning by simply +multiplying we then we subtract that + + align:start position:0% +multiplying we then we subtract that + + + align:start position:0% +multiplying we then we subtract that +from + + align:start position:0% +from + + + align:start position:0% +from +one however what about Sunday December + + align:start position:0% +one however what about Sunday December + + + align:start position:0% +one however what about Sunday December +18th what's the + + align:start position:0% +18th what's the + + + align:start position:0% +18th what's the +probability well as it + + align:start position:0% +probability well as it + + + align:start position:0% +probability well as it +happens that day the Patriots are + + align:start position:0% +happens that day the Patriots are + + + align:start position:0% +happens that day the Patriots are +playing the + + align:start position:0% + + + + align:start position:0% + +Broncos so now suddenly the outcomes are + + align:start position:0% +Broncos so now suddenly the outcomes are + + + align:start position:0% +Broncos so now suddenly the outcomes are +not + + align:start position:0% +not + + + align:start position:0% +not +independent the probability of one of + + align:start position:0% +independent the probability of one of + + + align:start position:0% +independent the probability of one of +them losing is influenced by the + + align:start position:0% +them losing is influenced by the + + + align:start position:0% +them losing is influenced by the +probability of the other + + align:start position:0% +probability of the other + + + align:start position:0% +probability of the other +winning right so you would expect the + + align:start position:0% +winning right so you would expect the + + + align:start position:0% +winning right so you would expect the +probability of one of them losing is + + align:start position:0% +probability of one of them losing is + + + align:start position:0% +probability of one of them losing is +much closer to one than 22 over 64 which + + align:start position:0% +much closer to one than 22 over 64 which + + + align:start position:0% +much closer to one than 22 over 64 which +is about a + + align:start position:0% +is about a + + + align:start position:0% +is about a +third all right + + align:start position:0% +third all right + + + align:start position:0% +third all right +so in this case it's easy but as we'll + + align:start position:0% +so in this case it's easy but as we'll + + + align:start position:0% +so in this case it's easy but as we'll +see as we get through the term there are + + align:start position:0% +see as we get through the term there are + + + align:start position:0% +see as we get through the term there are +lots of cases where you have to work + + align:start position:0% +lots of cases where you have to work + + + align:start position:0% +lots of cases where you have to work +pretty hard to understand whether or not + + align:start position:0% +pretty hard to understand whether or not + + + align:start position:0% +pretty hard to understand whether or not +two events really are independent and if + + align:start position:0% +two events really are independent and if + + + align:start position:0% +two events really are independent and if +you get it wrong you get a totally bogus + + align:start position:0% +you get it wrong you get a totally bogus + + + align:start position:0% +you get it wrong you get a totally bogus +answer right a third versus one is a + + align:start position:0% +answer right a third versus one is a + + + align:start position:0% +answer right a third versus one is a +pretty big + + align:start position:0% +pretty big + + + align:start position:0% +pretty big +difference by the way as it happens the + + align:start position:0% +difference by the way as it happens the + + + align:start position:0% +difference by the way as it happens the +probability of the Broncos losing is + + align:start position:0% +probability of the Broncos losing is + + + align:start position:0% +probability of the Broncos losing is +about + + align:start position:0% + + + + align:start position:0% + +one all + + align:start position:0% +one all + + + align:start position:0% +one all +right let's let's let's go look at some + + align:start position:0% +right let's let's let's go look at some + + + align:start position:0% +right let's let's let's go look at some +code + + align:start position:0% +code + + + align:start position:0% +code +um and we'll go back to our our dice + + align:start position:0% +um and we'll go back to our our dice + + + align:start position:0% +um and we'll go back to our our dice +because it's much easier to simulate + + align:start position:0% +because it's much easier to simulate + + + align:start position:0% +because it's much easier to simulate +dice games than it is to simulate uh + + align:start position:0% +dice games than it is to simulate uh + + + align:start position:0% +dice games than it is to simulate uh +football + + align:start position:0% +football + + + align:start position:0% +football +games + + align:start position:0% +games + + + align:start position:0% +games +um so here it is and we're going to talk + + align:start position:0% +um so here it is and we're going to talk + + + align:start position:0% +um so here it is and we're going to talk +a lot about + + align:start position:0% +a lot about + + + align:start position:0% +a lot about +simulations so here rather than rolling + + align:start position:0% +simulations so here rather than rolling + + + align:start position:0% +simulations so here rather than rolling +the die I've written a program to do + + align:start position:0% +the die I've written a program to do + + + align:start position:0% +the die I've written a program to do +it + + align:start position:0% +it + + + align:start position:0% +it +um we've already seen the code for + + align:start position:0% +um we've already seen the code for + + + align:start position:0% +um we've already seen the code for +rolling a d and so to run the + + align:start position:0% +rolling a d and so to run the + + + align:start position:0% +rolling a d and so to run the +simulation um typically what we're doing + + align:start position:0% +simulation um typically what we're doing + + + align:start position:0% +simulation um typically what we're doing +here is I'm giving you the + + align:start position:0% +here is I'm giving you the + + + align:start position:0% +here is I'm giving you the +goal for example are we going to get + + align:start position:0% +goal for example are we going to get + + + align:start position:0% +goal for example are we going to get +five ones the number of + + align:start position:0% +five ones the number of + + + align:start position:0% +five ones the number of +Trials each + + align:start position:0% +Trials each + + + align:start position:0% +Trials each +trial in this case will be say of length + + align:start position:0% +trial in this case will be say of length + + + align:start position:0% +trial in this case will be say of length +five so I'm going to roll the same die + + align:start position:0% +five so I'm going to roll the same die + + + align:start position:0% +five so I'm going to roll the same die +five + + align:start position:0% +five + + + align:start position:0% +five +times say a thousand different + + align:start position:0% +times say a thousand different + + + align:start position:0% +times say a thousand different +times and then just some text as to what + + align:start position:0% +times and then just some text as to what + + + align:start position:0% +times and then just some text as to what +I'm going to + + align:start position:0% +I'm going to + + + align:start position:0% +I'm going to +print almost almost all the simulations + + align:start position:0% +print almost almost all the simulations + + + align:start position:0% +print almost almost all the simulations +we look at are going to start with lines + + align:start position:0% +we look at are going to start with lines + + + align:start position:0% +we look at are going to start with lines +that look a lot like + + align:start position:0% +that look a lot like + + + align:start position:0% +that look a lot like +that we're going to initialize some + + align:start position:0% +that we're going to initialize some + + + align:start position:0% +that we're going to initialize some +variable and then we're going to run + + align:start position:0% +variable and then we're going to run + + + align:start position:0% +variable and then we're going to run +some number of + + align:start position:0% + + + + align:start position:0% + +Trials so in this + + align:start position:0% +Trials so in this + + + align:start position:0% +Trials so in this +case we're going to get from the length + + align:start position:0% +case we're going to get from the length + + + align:start position:0% +case we're going to get from the length +of the goal so if the goal is five ones + + align:start position:0% +of the goal so if the goal is five ones + + + align:start position:0% +of the goal so if the goal is five ones +then we're going to roll the die five + + align:start position:0% +then we're going to roll the die five + + + align:start position:0% +then we're going to roll the die five +times if it's 10 runs we'll roll the die + + align:start position:0% +times if it's 10 runs we'll roll the die + + + align:start position:0% +times if it's 10 runs we'll roll the die +10 times + + align:start position:0% +10 times + + + align:start position:0% +10 times +so this is essentially one + + align:start position:0% +so this is essentially one + + + align:start position:0% +so this is essentially one +trial one attempt + + align:start position:0% + + + + align:start position:0% + +right and then we'll check the result + + align:start position:0% +right and then we'll check the result + + + align:start position:0% +right and then we'll check the result +and if it has the property we want in + + align:start position:0% +and if it has the property we want in + + + align:start position:0% +and if it has the property we want in +this + + align:start position:0% +this + + + align:start position:0% +this +case it's equal to the goal then we're + + align:start position:0% +case it's equal to the goal then we're + + + align:start position:0% +case it's equal to the goal then we're +going to increment the total which we + + align:start position:0% +going to increment the total which we + + + align:start position:0% +going to increment the total which we +initialized up here by + + align:start position:0% +initialized up here by + + + align:start position:0% +initialized up here by +one so we'll keep track which is just + + align:start position:0% +one so we'll keep track which is just + + + align:start position:0% +one so we'll keep track which is just +the counting the number of Tri FES that + + align:start position:0% +the counting the number of Tri FES that + + + align:start position:0% +the counting the number of Tri FES that +actually meet the goal and then when + + align:start position:0% +actually meet the goal and then when + + + align:start position:0% +actually meet the goal and then when +we're + + align:start position:0% +we're + + + align:start position:0% +we're +done what we're going to do is divide + + align:start position:0% +done what we're going to do is divide + + + align:start position:0% +done what we're going to do is divide +the number that met the goal by the + + align:start position:0% +the number that met the goal by the + + + align:start position:0% +the number that met the goal by the +number of + + align:start position:0% +number of + + + align:start position:0% +number of +Trials exactly the counting argument we + + align:start position:0% +Trials exactly the counting argument we + + + align:start position:0% +Trials exactly the counting argument we +just looked at and then we'll print the + + align:start position:0% + + + + align:start position:0% + +result almost every simulation we look + + align:start position:0% +result almost every simulation we look + + + align:start position:0% +result almost every simulation we look +at is going to have this structure + + align:start position:0% +at is going to have this structure + + + align:start position:0% +at is going to have this structure +there'll be an outer loop which is the + + align:start position:0% +there'll be an outer loop which is the + + + align:start position:0% +there'll be an outer loop which is the +number of + + align:start position:0% +number of + + + align:start position:0% +number of +Trials and then inside maybe we'll have + + align:start position:0% +Trials and then inside maybe we'll have + + + align:start position:0% +Trials and then inside maybe we'll have +a loop or maybe it won't will be a + + align:start position:0% +a loop or maybe it won't will be a + + + align:start position:0% +a loop or maybe it won't will be a +single trial we'll sum up the results + + align:start position:0% +single trial we'll sum up the results + + + align:start position:0% +single trial we'll sum up the results +and then we'll divide by the number of + + align:start position:0% +and then we'll divide by the number of + + + align:start position:0% +and then we'll divide by the number of +Trials all right let's run + + align:start position:0% + + + + align:start position:0% + +it all + + align:start position:0% +it all + + + align:start position:0% +it all +right + + align:start position:0% +right + + + align:start position:0% +right +so a couple of things are going to go on + + align:start position:0% +so a couple of things are going to go on + + + align:start position:0% +so a couple of things are going to go on +here if you look at the + + align:start position:0% + + + + align:start position:0% + +code AS we've looked at it before what + + align:start position:0% +code AS we've looked at it before what + + + align:start position:0% +code AS we've looked at it before what +you're seeing is I'm Computing the + + align:start position:0% +you're seeing is I'm Computing the + + + align:start position:0% +you're seeing is I'm Computing the +estimated probability by the simulation + + align:start position:0% +estimated probability by the simulation + + + align:start position:0% +estimated probability by the simulation +and I'm comparing it to the actual + + align:start position:0% +and I'm comparing it to the actual + + + align:start position:0% +and I'm comparing it to the actual +probability which we've already seen how + + align:start position:0% +probability which we've already seen how + + + align:start position:0% +probability which we've already seen how +to + + align:start position:0% +to + + + align:start position:0% +to +compute so if you look at it there are a + + align:start position:0% +compute so if you look at it there are a + + + align:start position:0% +compute so if you look at it there are a +couple of things to look + + align:start position:0% +couple of things to look + + + align:start position:0% +couple of things to look +at uh the estimated probability is + + align:start position:0% +at uh the estimated probability is + + + align:start position:0% +at uh the estimated probability is +pretty close to the actual probability + + align:start position:0% +pretty close to the actual probability + + + align:start position:0% +pretty close to the actual probability +but not the + + align:start position:0% +but not the + + + align:start position:0% +but not the +same let's go back to the + + align:start position:0% +same let's go back to the + + + align:start position:0% +same let's go back to the +PowerPoint + + align:start position:0% + + + + align:start position:0% + +here are the + + align:start position:0% +here are the + + + align:start position:0% +here are the +results and there at least two question + + align:start position:0% +results and there at least two question + + + align:start position:0% +results and there at least two question +raised by this result first of all how + + align:start position:0% +raised by this result first of all how + + + align:start position:0% +raised by this result first of all how +did I know that this is what would get + + align:start position:0% +did I know that this is what would get + + + align:start position:0% +did I know that this is what would get +printed remember this is + + align:start position:0% +printed remember this is + + + align:start position:0% +printed remember this is +random how did I know that the estimate + + align:start position:0% +random how did I know that the estimate + + + align:start position:0% +random how did I know that the estimate +well there's nothing random about the + + align:start position:0% +well there's nothing random about the + + + align:start position:0% +well there's nothing random about the +actual + + align:start position:0% +actual + + + align:start position:0% +actual +probability but how did I know that the + + align:start position:0% +probability but how did I know that the + + + align:start position:0% +probability but how did I know that the +estimated probability would be zero and + + align:start position:0% +estimated probability would be zero and + + + align:start position:0% +estimated probability would be zero and +why did it print it twice cuz I messed + + align:start position:0% +why did it print it twice cuz I messed + + + align:start position:0% +why did it print it twice cuz I messed +up the PowerPoint any rate so how do I + + align:start position:0% +up the PowerPoint any rate so how do I + + + align:start position:0% +up the PowerPoint any rate so how do I +know what would get + + align:start position:0% +know what would get + + + align:start position:0% +know what would get +printed + + align:start position:0% +printed + + + align:start position:0% +printed +well a + + align:start position:0% +well a + + + align:start position:0% +well a +confession random + + align:start position:0% +confession random + + + align:start position:0% +confession random +do choice is not actually random in fact + + align:start position:0% +do choice is not actually random in fact + + + align:start position:0% +do choice is not actually random in fact +nothing we can do in a computer is + + align:start position:0% +nothing we can do in a computer is + + + align:start position:0% +nothing we can do in a computer is +actually random you can prove that it's + + align:start position:0% +actually random you can prove that it's + + + align:start position:0% +actually random you can prove that it's +impossible to build a computer that + + align:start position:0% +impossible to build a computer that + + + align:start position:0% +impossible to build a computer that +actually generates truly random numbers + + align:start position:0% +actually generates truly random numbers + + + align:start position:0% +actually generates truly random numbers +what they do instead is generate numbers + + align:start position:0% +what they do instead is generate numbers + + + align:start position:0% +what they do instead is generate numbers +that are called pseudo + + align:start position:0% + + + + align:start position:0% + +random how do they do + + align:start position:0% +random how do they do + + + align:start position:0% +random how do they do +that they have an algorithm that given + + align:start position:0% +that they have an algorithm that given + + + align:start position:0% +that they have an algorithm that given +one number generates the next number in + + align:start position:0% +one number generates the next number in + + + align:start position:0% +one number generates the next number in +a + + align:start position:0% +a + + + align:start position:0% +a +sequence and they start that algorithm + + align:start position:0% +sequence and they start that algorithm + + + align:start position:0% +sequence and they start that algorithm +with a + + align:start position:0% +with a + + + align:start position:0% +with a +seed + + align:start position:0% + + + + align:start position:0% + +now typically they get that seed by + + align:start position:0% +now typically they get that seed by + + + align:start position:0% +now typically they get that seed by +reading the clock of the + + align:start position:0% +reading the clock of the + + + align:start position:0% +reading the clock of the +computer so most computers have a clock + + align:start position:0% +computer so most computers have a clock + + + align:start position:0% +computer so most computers have a clock +that say keeps track of the number of + + align:start position:0% +that say keeps track of the number of + + + align:start position:0% +that say keeps track of the number of +microsc since January 1st + + align:start position:0% +microsc since January 1st + + + align:start position:0% +microsc since January 1st +1978 I don't know if that's still true + + align:start position:0% +1978 I don't know if that's still true + + + align:start position:0% +1978 I don't know if that's still true +that's what Unix used to do um so the + + align:start position:0% +that's what Unix used to do um so the + + + align:start position:0% +that's what Unix used to do um so the +notion is you start your program there's + + align:start position:0% +notion is you start your program there's + + + align:start position:0% +notion is you start your program there's +no way of knowing how many micros + + align:start position:0% +no way of knowing how many micros + + + align:start position:0% +no way of knowing how many micros +seconds have + + align:start position:0% +seconds have + + + align:start position:0% +seconds have +elapsed and so you're getting a random + + align:start position:0% +elapsed and so you're getting a random + + + align:start position:0% +elapsed and so you're getting a random +number to start the + + align:start position:0% +number to start the + + + align:start position:0% +number to start the +process since you don't know where it + + align:start position:0% +process since you don't know where it + + + align:start position:0% +process since you don't know where it +starts you don't know what the second + + align:start position:0% +starts you don't know what the second + + + align:start position:0% +starts you don't know what the second +number is you don't know what the third + + align:start position:0% +number is you don't know what the third + + + align:start position:0% +number is you don't know what the third +number is you don't know what the fourth + + align:start position:0% +number is you don't know what the fourth + + + align:start position:0% +number is you don't know what the fourth +number is and so it's predictably + + align:start position:0% +number is and so it's predictably + + + align:start position:0% +number is and so it's predictably +non-deterministic because you don't know + + align:start position:0% +non-deterministic because you don't know + + + align:start position:0% +non-deterministic because you don't know +what the seed is going to + + align:start position:0% +what the seed is going to + + + align:start position:0% +what the seed is going to +be now you can imagine that this makes + + align:start position:0% +be now you can imagine that this makes + + + align:start position:0% +be now you can imagine that this makes +programs really hard to + + align:start position:0% +programs really hard to + + + align:start position:0% +programs really hard to +debug every time you run it you + + align:start position:0% +debug every time you run it you + + + align:start position:0% +debug every time you run it you +something different could happen now + + align:start position:0% +something different could happen now + + + align:start position:0% +something different could happen now +we'll see often you want them to to be + + align:start position:0% +we'll see often you want them to to be + + + align:start position:0% +we'll see often you want them to to be +unpredictable but for now we want them + + align:start position:0% +unpredictable but for now we want them + + + align:start position:0% +unpredictable but for now we want them +to be predictable makes it easier to + + align:start position:0% +to be predictable makes it easier to + + + align:start position:0% +to be predictable makes it easier to +prepare PowerPoint so what you have if + + align:start position:0% +prepare PowerPoint so what you have if + + + align:start position:0% +prepare PowerPoint so what you have if +we go is a + + align:start position:0% + + + + align:start position:0% + +command you can call + + align:start position:0% +command you can call + + + align:start position:0% +command you can call +random. + + align:start position:0% +random. + + + align:start position:0% +random. +seed and give it a value and say I don't + + align:start position:0% +seed and give it a value and say I don't + + + align:start position:0% +seed and give it a value and say I don't +want you to just choose some random seed + + align:start position:0% +want you to just choose some random seed + + + align:start position:0% +want you to just choose some random seed +I want you to use zero as the + + align:start position:0% +I want you to use zero as the + + + align:start position:0% +I want you to use zero as the +seed for the same seed you always get + + align:start position:0% +seed for the same seed you always get + + + align:start position:0% +seed for the same seed you always get +the same sequence of random + + align:start position:0% +the same sequence of random + + + align:start position:0% +the same sequence of random +values and so what I've done is I've set + + align:start position:0% +values and so what I've done is I've set + + + align:start position:0% +values and so what I've done is I've set +the seed to be I think zero in this case + + align:start position:0% +the seed to be I think zero in this case + + + align:start position:0% +the seed to be I think zero in this case +not because there's anything magic about + + align:start position:0% +not because there's anything magic about + + + align:start position:0% +not because there's anything magic about +zero it's just sort of habit but it made + + align:start position:0% +zero it's just sort of habit but it made + + + align:start position:0% +zero it's just sort of habit but it made +it + + align:start position:0% +it + + + align:start position:0% +it +predictable as you write programs with + + align:start position:0% +predictable as you write programs with + + + align:start position:0% +predictable as you write programs with +Randomness in when you're debugging it + + align:start position:0% +Randomness in when you're debugging it + + + align:start position:0% +Randomness in when you're debugging it +you will almost surely want to start by + + align:start position:0% +you will almost surely want to start by + + + align:start position:0% +you will almost surely want to start by +setting random. seed to a value so you + + align:start position:0% +setting random. seed to a value so you + + + align:start position:0% +setting random. seed to a value so you +get the same answer but make sure you + + align:start position:0% +get the same answer but make sure you + + + align:start position:0% +get the same answer but make sure you +debug it with more than one value of + + align:start position:0% +debug it with more than one value of + + + align:start position:0% +debug it with more than one value of +this so you didn't just get lucky with + + align:start position:0% +this so you didn't just get lucky with + + + align:start position:0% +this so you didn't just get lucky with +your seed all right so that's how I knew + + align:start position:0% +your seed all right so that's how I knew + + + align:start position:0% +your seed all right so that's how I knew +would how what would get printed the + + align:start position:0% +would how what would get printed the + + + align:start position:0% +would how what would get printed the +next + + align:start position:0% + + + + align:start position:0% + +question is why did the simulation give + + align:start position:0% +question is why did the simulation give + + + align:start position:0% +question is why did the simulation give +me the wrong + + align:start position:0% +me the wrong + + + align:start position:0% +me the wrong +answer the actual probability is three Z + + align:start position:0% +answer the actual probability is three Z + + + align:start position:0% +answer the actual probability is three Z +and + + align:start position:0% +and + + + align:start position:0% +and +1286 but it estimated the probability of + + align:start position:0% +1286 but it estimated the probability of + + + align:start position:0% +1286 but it estimated the probability of +zero why is it + + align:start position:0% + + + + align:start position:0% + +wrong well let's think about this I ran + + align:start position:0% +wrong well let's think about this I ran + + + align:start position:0% +wrong well let's think about this I ran +a th + + align:start position:0% +a th + + + align:start position:0% +a th +trials what does it mean to say the + + align:start position:0% +trials what does it mean to say the + + + align:start position:0% +trials what does it mean to say the +probability is zero it means it tried it + + align:start position:0% +probability is zero it means it tried it + + + align:start position:0% +probability is zero it means it tried it +a thousand times and didn't ever get a + + align:start position:0% +a thousand times and didn't ever get a + + + align:start position:0% +a thousand times and didn't ever get a +sequence of five + + align:start position:0% +sequence of five + + + align:start position:0% +sequence of five +ones so the numerator of the division at + + align:start position:0% +ones so the numerator of the division at + + + align:start position:0% +ones so the numerator of the division at +the bottom was + + align:start position:0% +the bottom was + + + align:start position:0% +the bottom was +Zero hence the answer is zero is this + + align:start position:0% +Zero hence the answer is zero is this + + + align:start position:0% +Zero hence the answer is zero is this +surprising well no because if that's the + + align:start position:0% +surprising well no because if that's the + + + align:start position:0% +surprising well no because if that's the +actual + + align:start position:0% +actual + + + align:start position:0% +actual +probability of getting five ones it's + + align:start position:0% +probability of getting five ones it's + + + align:start position:0% +probability of getting five ones it's +not very shocking that in a thousand + + align:start position:0% +not very shocking that in a thousand + + + align:start position:0% +not very shocking that in a thousand +trials I it never happened + + align:start position:0% +trials I it never happened + + + align:start position:0% +trials I it never happened +right you know it's not a surprising + + align:start position:0% +right you know it's not a surprising + + + align:start position:0% +right you know it's not a surprising +result and so we have to be careful when + + align:start position:0% +result and so we have to be careful when + + + align:start position:0% +result and so we have to be careful when +we run these things to understand the + + align:start position:0% +we run these things to understand the + + + align:start position:0% +we run these things to understand the +difference between what's in this case + + align:start position:0% +difference between what's in this case + + + align:start position:0% +difference between what's in this case +an actual probability and what + + align:start position:0% +an actual probability and what + + + align:start position:0% +an actual probability and what +statisticians call a sample + + align:start position:0% + + + + align:start position:0% + +probability so what we got with the + + align:start position:0% +probability so what we got with the + + + align:start position:0% +probability so what we got with the +sample with zero so what's the obvious + + align:start position:0% +sample with zero so what's the obvious + + + align:start position:0% +sample with zero so what's the obvious +thing to + + align:start position:0% +thing to + + + align:start position:0% +thing to +do if you're doing a simulation of an + + align:start position:0% +do if you're doing a simulation of an + + + align:start position:0% +do if you're doing a simulation of an +event and the event is pretty + + align:start position:0% +event and the event is pretty + + + align:start position:0% +event and the event is pretty +rare you want to try it on a very large + + align:start position:0% +rare you want to try it on a very large + + + align:start position:0% +rare you want to try it on a very large +number of Trials so let's go back to our + + align:start position:0% + + + + align:start position:0% + +code and we'll change it to instead of a + + align:start position:0% +code and we'll change it to instead of a + + + align:start position:0% +code and we'll change it to instead of a +thousand a + + align:start position:0% +thousand a + + + align:start position:0% +thousand a +million + + align:start position:0% +million + + + align:start position:0% +million +you can see up here by the way where I + + align:start position:0% +you can see up here by the way where I + + + align:start position:0% +you can see up here by the way where I +set their + + align:start position:0% +set their + + + align:start position:0% +set their +seed now let's run + + align:start position:0% + + + + align:start position:0% + +it we did a lot better if we look at + + align:start position:0% +it we did a lot better if we look at + + + align:start position:0% +it we did a lot better if we look at +here our estimated probability it's uh + + align:start position:0% +here our estimated probability it's uh + + + align:start position:0% +here our estimated probability it's uh +30 is1 128 still not quite the actual + + align:start position:0% +30 is1 128 still not quite the actual + + + align:start position:0% +30 is1 128 still not quite the actual +probability but darn + + align:start position:0% +probability but darn + + + align:start position:0% +probability but darn +close and maybe if IID done 10 million + + align:start position:0% +close and maybe if IID done 10 million + + + align:start position:0% +close and maybe if IID done 10 million +it would have been even + + align:start position:0% + + + + align:start position:0% + +closer so if you're writing a simulation + + align:start position:0% +closer so if you're writing a simulation + + + align:start position:0% +closer so if you're writing a simulation +to compute the probability of an event + + align:start position:0% +to compute the probability of an event + + + align:start position:0% +to compute the probability of an event +and the event is moderately rare then + + align:start position:0% +and the event is moderately rare then + + + align:start position:0% +and the event is moderately rare then +you better run a lot of Trials before + + align:start position:0% +you better run a lot of Trials before + + + align:start position:0% +you better run a lot of Trials before +you believe your estimated + + align:start position:0% +you believe your estimated + + + align:start position:0% +you believe your estimated +probability uh in a week or so we'll + + align:start position:0% +probability uh in a week or so we'll + + + align:start position:0% +probability uh in a week or so we'll +actually look at that more + + align:start position:0% +actually look at that more + + + align:start position:0% +actually look at that more +mathematically and say what is a lot how + + align:start position:0% +mathematically and say what is a lot how + + + align:start position:0% +mathematically and say what is a lot how +do we know what is + + align:start position:0% + + + + align:start position:0% + +enough all right what are the morals + + align:start position:0% +enough all right what are the morals + + + align:start position:0% +enough all right what are the morals +here moral one I've just told you takes + + align:start position:0% +here moral one I've just told you takes + + + align:start position:0% +here moral one I've just told you takes +a lot of Trials to get a good estimate + + align:start position:0% +a lot of Trials to get a good estimate + + + align:start position:0% +a lot of Trials to get a good estimate +of the frequency of a rare + + align:start position:0% +of the frequency of a rare + + + align:start position:0% +of the frequency of a rare +event moral + + align:start position:0% +event moral + + + align:start position:0% +event moral +two we should always if we're getting an + + align:start position:0% +two we should always if we're getting an + + + align:start position:0% +two we should always if we're getting an +estimated probability + + align:start position:0% +estimated probability + + + align:start position:0% +estimated probability +know that and probably say that and not + + align:start position:0% +know that and probably say that and not + + + align:start position:0% +know that and probably say that and not +confuse it with the actual + + align:start position:0% +confuse it with the actual + + + align:start position:0% +confuse it with the actual +probability the third moral here is it + + align:start position:0% +probability the third moral here is it + + + align:start position:0% +probability the third moral here is it +was kind of stupid to do a simulation + + align:start position:0% +was kind of stupid to do a simulation + + + align:start position:0% +was kind of stupid to do a simulation +since it was a very simple closed form + + align:start position:0% +since it was a very simple closed form + + + align:start position:0% +since it was a very simple closed form +answer that we could compute that would + + align:start position:0% +answer that we could compute that would + + + align:start position:0% +answer that we could compute that would +really tell us what the actual + + align:start position:0% +really tell us what the actual + + + align:start position:0% +really tell us what the actual +probability is why even bother with the + + align:start position:0% +probability is why even bother with the + + + align:start position:0% +probability is why even bother with the +simulation well we're going to see why + + align:start position:0% +simulation well we're going to see why + + + align:start position:0% +simulation well we're going to see why +now cuz simulations can be very + + align:start position:0% +now cuz simulations can be very + + + align:start position:0% +now cuz simulations can be very +useful but let's look at another + + align:start position:0% +useful but let's look at another + + + align:start position:0% +useful but let's look at another +problem um this is a famous birthday + + align:start position:0% +problem um this is a famous birthday + + + align:start position:0% +problem um this is a famous birthday +problem some of you have seen it what's + + align:start position:0% +problem some of you have seen it what's + + + align:start position:0% +problem some of you have seen it what's +the probability of at least two people + + align:start position:0% +the probability of at least two people + + + align:start position:0% +the probability of at least two people +in a group having the same + + align:start position:0% +in a group having the same + + + align:start position:0% +in a group having the same +birthday there's a URL at the bottom + + align:start position:0% +birthday there's a URL at the bottom + + + align:start position:0% +birthday there's a URL at the bottom +that's pointing to a Google form I'd + + align:start position:0% +that's pointing to a Google form I'd + + + align:start position:0% +that's pointing to a Google form I'd +like please all of you who have a + + align:start position:0% +like please all of you who have a + + + align:start position:0% +like please all of you who have a +Computing device to go to it and fill + + align:start position:0% +Computing device to go to it and fill + + + align:start position:0% +Computing device to go to it and fill +out your + + align:start position:0% +out your + + + align:start position:0% +out your +birthday it's it's Anonymous so we won't + + align:start position:0% +birthday it's it's Anonymous so we won't + + + align:start position:0% +birthday it's it's Anonymous so we won't +know how old you are don't worry + + align:start position:0% +know how old you are don't worry + + + align:start position:0% +know how old you are don't worry +actually it's only the date it's not the + + align:start position:0% +actually it's only the date it's not the + + + align:start position:0% +actually it's only the date it's not the +year all right + + align:start position:0% +year all right + + + align:start position:0% +year all right +so Suppose there were 367 people in the + + align:start position:0% +so Suppose there were 367 people in the + + + align:start position:0% +so Suppose there were 367 people in the +group roughly the number of people who + + align:start position:0% +group roughly the number of people who + + + align:start position:0% +group roughly the number of people who +took the uh 601 600 midterm all right um + + align:start position:0% +took the uh 601 600 midterm all right um + + + align:start position:0% +took the uh 601 600 midterm all right um +if there're 367 people what's the + + align:start position:0% +if there're 367 people what's the + + + align:start position:0% +if there're 367 people what's the +probability of at least two of them + + align:start position:0% +probability of at least two of them + + + align:start position:0% +probability of at least two of them +sharing a + + align:start position:0% + + + + align:start position:0% + +birthday one by something called the + + align:start position:0% +birthday one by something called the + + + align:start position:0% +birthday one by something called the +pigeon hole principle right you got some + + align:start position:0% +pigeon hole principle right you got some + + + align:start position:0% +pigeon hole principle right you got some +number of holes and if you have more + + align:start position:0% +number of holes and if you have more + + + align:start position:0% +number of holes and if you have more +pigeons than holes two pigeons have to + + align:start position:0% +pigeons than holes two pigeons have to + + + align:start position:0% +pigeons than holes two pigeons have to +share a + + align:start position:0% +share a + + + align:start position:0% +share a +hole what about smaller + + align:start position:0% +hole what about smaller + + + align:start position:0% +hole what about smaller +numbers well if we make a simplifying + + align:start position:0% +numbers well if we make a simplifying + + + align:start position:0% +numbers well if we make a simplifying +assumption that each birth date is + + align:start position:0% +assumption that each birth date is + + + align:start position:0% +assumption that each birth date is +equally likely then there's actually a + + align:start position:0% +equally likely then there's actually a + + + align:start position:0% +equally likely then there's actually a +nice closed form solution for + + align:start position:0% + + + + align:start position:0% + +it again this is a question where it's + + align:start position:0% +it again this is a question where it's + + + align:start position:0% +it again this is a question where it's +easier to compute the opposite of what + + align:start position:0% +easier to compute the opposite of what + + + align:start position:0% +easier to compute the opposite of what +you're trying to do and subtract it from + + align:start position:0% +you're trying to do and subtract it from + + + align:start position:0% +you're trying to do and subtract it from +one and so + + align:start position:0% +one and so + + + align:start position:0% +one and so +this fraction is giving the probability + + align:start position:0% +this fraction is giving the probability + + + align:start position:0% +this fraction is giving the probability +of two people not sharing a + + align:start position:0% +of two people not sharing a + + + align:start position:0% +of two people not sharing a +birthday uh the proof that this is right + + align:start position:0% +birthday uh the proof that this is right + + + align:start position:0% +birthday uh the proof that this is right +is a little bit elaborate but you can + + align:start position:0% +is a little bit elaborate but you can + + + align:start position:0% +is a little bit elaborate but you can +trust me it's + + align:start position:0% +trust me it's + + + align:start position:0% +trust me it's +accurate but it's a formula and it's not + + align:start position:0% +accurate but it's a formula and it's not + + + align:start position:0% +accurate but it's a formula and it's not +that complicated a formula though + + align:start position:0% +that complicated a formula though + + + align:start position:0% +that complicated a formula though +numbers like 366 factorial are + + align:start position:0% +numbers like 366 factorial are + + + align:start position:0% +numbers like 366 factorial are +big all + + align:start position:0% + + + + align:start position:0% + +right so let's approximate a solution + + align:start position:0% +right so let's approximate a solution + + + align:start position:0% +right so let's approximate a solution +solution we'll write a simulation and + + align:start position:0% +solution we'll write a simulation and + + + align:start position:0% +solution we'll write a simulation and +see if we get the same answer that that + + align:start position:0% +see if we get the same answer that that + + + align:start position:0% +see if we get the same answer that that +formula gave + + align:start position:0% +formula gave + + + align:start position:0% +formula gave +us so here's the code for + + align:start position:0% +us so here's the code for + + + align:start position:0% +us so here's the code for +that uh two arguments the number of + + align:start position:0% +that uh two arguments the number of + + + align:start position:0% +that uh two arguments the number of +people in the + + align:start position:0% +people in the + + + align:start position:0% +people in the +group and the number that we asking do + + align:start position:0% +group and the number that we asking do + + + align:start position:0% +group and the number that we asking do +they have the same + + align:start position:0% +they have the same + + + align:start position:0% +they have the same +birthday so since I'm assuming for now + + align:start position:0% +birthday so since I'm assuming for now + + + align:start position:0% +birthday so since I'm assuming for now +that every birthday is equally likely + + align:start position:0% +that every birthday is equally likely + + + align:start position:0% +that every birthday is equally likely +the possible dates range from 1 to + + align:start position:0% +the possible dates range from 1 to + + + align:start position:0% +the possible dates range from 1 to +366 because some years have of February + + align:start position:0% + + + + align:start position:0% + +29th I'll keep track of the number of + + align:start position:0% +29th I'll keep track of the number of + + + align:start position:0% +29th I'll keep track of the number of +people born in each date by starting + + align:start position:0% +people born in each date by starting + + + align:start position:0% +people born in each date by starting +with + + align:start position:0% +with + + + align:start position:0% +with +none and then for p in the range of + + align:start position:0% +none and then for p in the range of + + + align:start position:0% +none and then for p in the range of +number of people I'll make a random + + align:start position:0% +number of people I'll make a random + + + align:start position:0% +number of people I'll make a random +choice of the possible + + align:start position:0% +choice of the possible + + + align:start position:0% +choice of the possible +dates and increment that element of the + + align:start position:0% +dates and increment that element of the + + + align:start position:0% +dates and increment that element of the +list by + + align:start position:0% +list by + + + align:start position:0% +list by +one and then at the end we can say look + + align:start position:0% +one and then at the end we can say look + + + align:start position:0% +one and then at the end we can say look +at the maximum number of + + align:start position:0% +at the maximum number of + + + align:start position:0% +at the maximum number of +birthdays and see if it's greater than + + align:start position:0% +birthdays and see if it's greater than + + + align:start position:0% +birthdays and see if it's greater than +or equal to the number of + + align:start position:0% +or equal to the number of + + + align:start position:0% +or equal to the number of +same so that tells us + + align:start position:0% + + + + align:start position:0% + +that and then we can actually look at + + align:start position:0% +that and then we can actually look at + + + align:start position:0% +that and then we can actually look at +the birthday problem number of people + + align:start position:0% +the birthday problem number of people + + + align:start position:0% +the birthday problem number of people +the number of same and as usual the + + align:start position:0% +the number of same and as usual the + + + align:start position:0% +the number of same and as usual the +number of + + align:start position:0% + + + + align:start position:0% + +Trials so number of hits is zero for T + + align:start position:0% +Trials so number of hits is zero for T + + + align:start position:0% +Trials so number of hits is zero for T +and range number of Trials if same data + + align:start position:0% +and range number of Trials if same data + + + align:start position:0% +and range number of Trials if same data +is + + align:start position:0% +is + + + align:start position:0% +is +true then we'll increment the number of + + align:start position:0% +true then we'll increment the number of + + + align:start position:0% +true then we'll increment the number of +hints by one and then as usual divide by + + align:start position:0% +hints by one and then as usual divide by + + + align:start position:0% +hints by one and then as usual divide by +the number of Trials + + align:start position:0% +the number of Trials + + + align:start position:0% +the number of Trials +and we'll try it for people in uh for 10 + + align:start position:0% +and we'll try it for people in uh for 10 + + + align:start position:0% +and we'll try it for people in uh for 10 +20 40 and 100 + + align:start position:0% +20 40 and 100 + + + align:start position:0% +20 40 and 100 +people um and then just we'll print the + + align:start position:0% +people um and then just we'll print the + + + align:start position:0% +people um and then just we'll print the +estimated probability and the actual + + align:start position:0% +estimated probability and the actual + + + align:start position:0% +estimated probability and the actual +probability + + align:start position:0% +probability + + + align:start position:0% +probability +computed using that formula I showed you + + align:start position:0% +computed using that formula I showed you + + + align:start position:0% +computed using that formula I showed you +I've not shown you but I've imported a + + align:start position:0% +I've not shown you but I've imported a + + + align:start position:0% +I've not shown you but I've imported a +library called math because it is a + + align:start position:0% +library called math because it is a + + + align:start position:0% +library called math because it is a +factorial implementation that's way + + align:start position:0% +factorial implementation that's way + + + align:start position:0% +factorial implementation that's way +faster than the recursive one that we've + + align:start position:0% +faster than the recursive one that we've + + + align:start position:0% +faster than the recursive one that we've +seen before all right let's run + + align:start position:0% + + + + align:start position:0% + +it and we'll see what we get so for 10 + + align:start position:0% +it and we'll see what we get so for 10 + + + align:start position:0% +it and we'll see what we get so for 10 +the estimated proba ility is + + align:start position:0% +the estimated proba ility is + + + align:start position:0% +the estimated proba ility is +.11 now so as you can see the + + align:start position:0% +.11 now so as you can see the + + + align:start position:0% +.11 now so as you can see the +estimates are really uh pretty + + align:start position:0% +estimates are really uh pretty + + + align:start position:0% +estimates are really uh pretty +good once again we have this business + + align:start position:0% +good once again we have this business + + + align:start position:0% +good once again we have this business +that for 100 we're estimating one when + + align:start position:0% +that for 100 we're estimating one when + + + align:start position:0% +that for 100 we're estimating one when +the real answer is point many many many + + align:start position:0% +the real answer is point many many many + + + align:start position:0% +the real answer is point many many many +nines but again this is sample + + align:start position:0% +nines but again this is sample + + + align:start position:0% +nines but again this is sample +probability just means in the number of + + align:start position:0% +probability just means in the number of + + + align:start position:0% +probability just means in the number of +Trials we did um everyone for 100 people + + align:start position:0% +Trials we did um everyone for 100 people + + + align:start position:0% +Trials we did um everyone for 100 people +there is a shared birthday this is a + + align:start position:0% +there is a shared birthday this is a + + + align:start position:0% +there is a shared birthday this is a +number that usually surprises people as + + align:start position:0% +number that usually surprises people as + + + align:start position:0% +number that usually surprises people as +to why with 100 people the probability + + align:start position:0% +to why with 100 people the probability + + + align:start position:0% +to why with 100 people the probability +is so + + align:start position:0% +is so + + + align:start position:0% +is so +high but we could work out the formula + + align:start position:0% +high but we could work out the formula + + + align:start position:0% +high but we could work out the formula +and see it and as you can see the + + align:start position:0% +and see it and as you can see the + + + align:start position:0% +and see it and as you can see the +estimates are pretty good from my + + align:start position:0% + + + + align:start position:0% + +simulation all right + + align:start position:0% +simulation all right + + + align:start position:0% +simulation all right +now now we're going to see why we did a + + align:start position:0% +now now we're going to see why we did a + + + align:start position:0% +now now we're going to see why we did a +simulation in the first place suppose we + + align:start position:0% +simulation in the first place suppose we + + + align:start position:0% +simulation in the first place suppose we +want the probability of three people + + align:start position:0% +want the probability of three people + + + align:start position:0% +want the probability of three people +sharing a birthday instead of + + align:start position:0% + + + + align:start position:0% + +two it's pretty easy to see how we + + align:start position:0% +two it's pretty easy to see how we + + + align:start position:0% +two it's pretty easy to see how we +change the simulation right I even made + + align:start position:0% +change the simulation right I even made + + + align:start position:0% +change the simulation right I even made +it a parameter I just changed the number + + align:start position:0% +it a parameter I just changed the number + + + align:start position:0% +it a parameter I just changed the number +two to a number three the math on the + + align:start position:0% +two to a number three the math on the + + + align:start position:0% +two to a number three the math on the +other hand is + + align:start position:0% + + + + align:start position:0% + +ugly why is the math so much uglier for + + align:start position:0% +ugly why is the math so much uglier for + + + align:start position:0% +ugly why is the math so much uglier for +three than for + + align:start position:0% +three than for + + + align:start position:0% +three than for +two because for two the complimentary + + align:start position:0% +two because for two the complimentary + + + align:start position:0% +two because for two the complimentary +problem the number we're subtracting + + align:start position:0% +problem the number we're subtracting + + + align:start position:0% +problem the number we're subtracting +from one is simply the question of are + + align:start position:0% +from one is simply the question of are + + + align:start position:0% +from one is simply the question of are +all birthdays + + align:start position:0% +all birthdays + + + align:start position:0% +all birthdays +different so did two people share a + + align:start position:0% +different so did two people share a + + + align:start position:0% +different so did two people share a +birthday is one minus or off does + + align:start position:0% +birthday is one minus or off does + + + align:start position:0% +birthday is one minus or off does +everybody have a different + + align:start position:0% +everybody have a different + + + align:start position:0% +everybody have a different +birthday on the other hand for three + + align:start position:0% +birthday on the other hand for three + + + align:start position:0% +birthday on the other hand for three +people the complimentary problem is a + + align:start position:0% +people the complimentary problem is a + + + align:start position:0% +people the complimentary problem is a +complicated disjunct a bunch of ores + + align:start position:0% +complicated disjunct a bunch of ores + + + align:start position:0% +complicated disjunct a bunch of ores +either all birthdays are distinct or two + + align:start position:0% +either all birthdays are distinct or two + + + align:start position:0% +either all birthdays are distinct or two +people share a birthday and the rest are + + align:start position:0% +people share a birthday and the rest are + + + align:start position:0% +people share a birthday and the rest are +distinct or + + align:start position:0% +distinct or + + + align:start position:0% +distinct or +there are two groups of two people + + align:start position:0% +there are two groups of two people + + + align:start position:0% +there are two groups of two people +sharing a birthday and everything is + + align:start position:0% +sharing a birthday and everything is + + + align:start position:0% +sharing a birthday and everything is +distinct so you can see here there's a + + align:start position:0% +distinct so you can see here there's a + + + align:start position:0% +distinct so you can see here there's a +lot of + + align:start position:0% +lot of + + + align:start position:0% +lot of +possibilities and so it's one minus now + + align:start position:0% +possibilities and so it's one minus now + + + align:start position:0% +possibilities and so it's one minus now +a very complicated formula and in fact + + align:start position:0% +a very complicated formula and in fact + + + align:start position:0% +a very complicated formula and in fact +if you try and look how to do this most + + align:start position:0% +if you try and look how to do this most + + + align:start position:0% +if you try and look how to do this most +people will tell you don't bother here's + + align:start position:0% +people will tell you don't bother here's + + + align:start position:0% +people will tell you don't bother here's +a kind of a good + + align:start position:0% +a kind of a good + + + align:start position:0% +a kind of a good +approximation but the math gets very + + align:start position:0% + + + + align:start position:0% + +hairy in conrast changing the + + align:start position:0% +hairy in conrast changing the + + + align:start position:0% +hairy in conrast changing the +stimulation is dead easy we can do + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +whoops so if we come over here for the + + align:start position:0% + + + + align:start position:0% + +code all I have to do is change this two + + align:start position:0% +code all I have to do is change this two + + + align:start position:0% +code all I have to do is change this two +to a + + align:start position:0% + + + + align:start position:0% + +three and I'm going to leave in this + + align:start position:0% +three and I'm going to leave in this + + + align:start position:0% +three and I'm going to leave in this +code which is the wrong code the + + align:start position:0% +code which is the wrong code the + + + align:start position:0% +code which is the wrong code the +Computing the actual probability now for + + align:start position:0% +Computing the actual probability now for + + + align:start position:0% +Computing the actual probability now for +two people sharing rather than three + + align:start position:0% +two people sharing rather than three + + + align:start position:0% +two people sharing rather than three +because I want to make it easy for you + + align:start position:0% +because I want to make it easy for you + + + align:start position:0% +because I want to make it easy for you +to see the difference between what + + align:start position:0% +to see the difference between what + + + align:start position:0% +to see the difference between what +happens when we look at three shared + + align:start position:0% +happens when we look at three shared + + + align:start position:0% +happens when we look at three shared +rather than two + + align:start position:0% + + + + align:start position:0% + +shared and I get invalid + + align:start position:0% +shared and I get invalid + + + align:start position:0% +shared and I get invalid +syntax that's not good + + align:start position:0% +syntax that's not good + + + align:start position:0% +syntax that's not good +good that's what happens when I type in + + align:start position:0% +good that's what happens when I type in + + + align:start position:0% +good that's what happens when I type in +real + + align:start position:0% + + + + align:start position:0% + +time why do I have invalid + + align:start position:0% +time why do I have invalid + + + align:start position:0% +time why do I have invalid +syntax + + align:start position:0% +syntax + + + align:start position:0% +syntax +pardon one person at + + align:start position:0% + + + + align:start position:0% + +Anna + + align:start position:0% +Anna + + + align:start position:0% +Anna +oh that's not a good + + align:start position:0% + + + + align:start position:0% + +line + + align:start position:0% + + + + align:start position:0% + +so now we + + align:start position:0% +so now we + + + align:start position:0% +so now we +see that if we get say to n equals + + align:start position:0% +see that if we get say to n equals + + + align:start position:0% +see that if we get say to n equals +100 um for two you'll remember it was + + align:start position:0% +100 um for two you'll remember it was + + + align:start position:0% +100 um for two you'll remember it was +099 but for three it's only + + align:start position:0% +099 but for three it's only + + + align:start position:0% +099 but for three it's only +63 so we see going from two sharing to + + align:start position:0% +63 so we see going from two sharing to + + + align:start position:0% +63 so we see going from two sharing to +three sharing gets us a radically + + align:start position:0% +three sharing gets us a radically + + + align:start position:0% +three sharing gets us a radically +different answer not + + align:start position:0% +different answer not + + + align:start position:0% +different answer not +surprisingly um but we also in the real + + align:start position:0% +surprisingly um but we also in the real + + + align:start position:0% +surprisingly um but we also in the real +thing I wanted you to see is how easy it + + align:start position:0% +thing I wanted you to see is how easy it + + + align:start position:0% +thing I wanted you to see is how easy it +was to answer this question the + + align:start position:0% +was to answer this question the + + + align:start position:0% +was to answer this question the +simulation and that's a primary reason + + align:start position:0% +simulation and that's a primary reason + + + align:start position:0% +simulation and that's a primary reason +we use simulations to get probabilistic + + align:start position:0% +we use simulations to get probabilistic + + + align:start position:0% +we use simulations to get probabilistic +questions rather than sitting down and a + + align:start position:0% +questions rather than sitting down and a + + + align:start position:0% +questions rather than sitting down and a +pencil and paper and doing fancy + + align:start position:0% +pencil and paper and doing fancy + + + align:start position:0% +pencil and paper and doing fancy +probability + + align:start position:0% +probability + + + align:start position:0% +probability +calculations because it's often way + + align:start position:0% +calculations because it's often way + + + align:start position:0% +calculations because it's often way +easier to do a + + align:start position:0% +easier to do a + + + align:start position:0% +easier to do a +simulation we can see that in Spades if + + align:start position:0% +simulation we can see that in Spades if + + + align:start position:0% +simulation we can see that in Spades if +we look at the next + + align:start position:0% + + + + align:start position:0% + +question let's think about this + + align:start position:0% +question let's think about this + + + align:start position:0% +question let's think about this +assumption that all birthdays are + + align:start position:0% +assumption that all birthdays are + + + align:start position:0% +assumption that all birthdays are +equally + + align:start position:0% +equally + + + align:start position:0% +equally +likely well as you can see this is a + + align:start position:0% +likely well as you can see this is a + + + align:start position:0% +likely well as you can see this is a +chart of how common birth dates are in + + align:start position:0% +chart of how common birth dates are in + + + align:start position:0% +chart of how common birth dates are in +the US a heat + + align:start position:0% +the US a heat + + + align:start position:0% +the US a heat +map + + align:start position:0% +map + + + align:start position:0% +map +and you'll see for example that February + + align:start position:0% +and you'll see for example that February + + + align:start position:0% +and you'll see for example that February +29th is a quite an uncommon + + align:start position:0% +29th is a quite an uncommon + + + align:start position:0% +29th is a quite an uncommon +birthday so we should probably treat + + align:start position:0% +birthday so we should probably treat + + + align:start position:0% +birthday so we should probably treat +that differently um somewhat + + align:start position:0% +that differently um somewhat + + + align:start position:0% +that differently um somewhat +surprisingly you'll see that July 4th is + + align:start position:0% +surprisingly you'll see that July 4th is + + + align:start position:0% +surprisingly you'll see that July 4th is +a very uncommon birthday as well + + align:start position:0% +a very uncommon birthday as well + + + align:start position:0% +a very uncommon birthday as well +it's easy to understand why February + + align:start position:0% +it's easy to understand why February + + + align:start position:0% +it's easy to understand why February +29th the only thing I can figure out for + + align:start position:0% +29th the only thing I can figure out for + + + align:start position:0% +29th the only thing I can figure out for +July 4th is Obstetricians don't like + + align:start position:0% +July 4th is Obstetricians don't like + + + align:start position:0% +July 4th is Obstetricians don't like +working on + + align:start position:0% +working on + + + align:start position:0% +working on +holidays and so they induce labor + + align:start position:0% +holidays and so they induce labor + + + align:start position:0% +holidays and so they induce labor +sometime around the 2 or so to the third + + align:start position:0% +sometime around the 2 or so to the third + + + align:start position:0% +sometime around the 2 or so to the third +so they don't have to come to work on + + align:start position:0% +so they don't have to come to work on + + + align:start position:0% +so they don't have to come to work on +the fourth of the + + align:start position:0% +the fourth of the + + + align:start position:0% +the fourth of the +5th sounds a horrible thought but I + + align:start position:0% +5th sounds a horrible thought but I + + + align:start position:0% +5th sounds a horrible thought but I +can't think of any other explanation for + + align:start position:0% +can't think of any other explanation for + + + align:start position:0% +can't think of any other explanation for +this + + align:start position:0% +this + + + align:start position:0% +this +anomaly um you'll probably if you look + + align:start position:0% +anomaly um you'll probably if you look + + + align:start position:0% +anomaly um you'll probably if you look +at it see Christmas day is not so common + + align:start position:0% +at it see Christmas day is not so common + + + align:start position:0% +at it see Christmas day is not so common +either um so now the question question + + align:start position:0% +either um so now the question question + + + align:start position:0% +either um so now the question question +which we can answer since you've all + + align:start position:0% +which we can answer since you've all + + + align:start position:0% +which we can answer since you've all +filled out this form is how exceptional + + align:start position:0% +filled out this form is how exceptional + + + align:start position:0% +filled out this form is how exceptional +are MIT students we like to think that + + align:start position:0% +are MIT students we like to think that + + + align:start position:0% +are MIT students we like to think that +you're different in every respect so are + + align:start position:0% +you're different in every respect so are + + + align:start position:0% +you're different in every respect so are +your birthdays distributed differently + + align:start position:0% +your birthdays distributed differently + + + align:start position:0% +your birthdays distributed differently +than other dates um have we got that + + align:start position:0% +than other dates um have we got that + + + align:start position:0% +than other dates um have we got that +data all right so now we'll go look at + + align:start position:0% + + + + align:start position:0% + +that we should have a heat map for you + + align:start position:0% +that we should have a heat map for you + + + align:start position:0% +that we should have a heat map for you +guys + + align:start position:0% +guys + + + align:start position:0% +guys +I this + + align:start position:0% +I this + + + align:start position:0% +I this +one + + align:start position:0% +one + + + align:start position:0% +one +I all the February 31 thank you for + + align:start position:0% +I all the February 31 thank you for + + + align:start position:0% +I all the February 31 thank you for +those + + align:start position:0% + + + + align:start position:0% + +sub yeah all right so here it is and we + + align:start position:0% +sub yeah all right so here it is and we + + + align:start position:0% +sub yeah all right so here it is and we +can see that + + align:start position:0% +can see that + + + align:start position:0% +can see that +uh well they don't seem to be banded + + align:start position:0% +uh well they don't seem to be banded + + + align:start position:0% +uh well they don't seem to be banded +quite as much in in the summer + + align:start position:0% +quite as much in in the summer + + + align:start position:0% +quite as much in in the summer +months probably says more about your + + align:start position:0% +months probably says more about your + + + align:start position:0% +months probably says more about your +parents than it does about you + + align:start position:0% +parents than it does about you + + + align:start position:0% +parents than it does about you +um but you can see that indeed we do + + align:start position:0% +um but you can see that indeed we do + + + align:start position:0% +um but you can see that indeed we do +have wow wow we have a day where there + + align:start position:0% +have wow wow we have a day where there + + + align:start position:0% +have wow wow we have a day where there +are five birthdays that look like or no + + align:start position:0% +are five birthdays that look like or no + + + align:start position:0% +are five birthdays that look like or no +feary + + align:start position:0% + + + + align:start position:0% + +wow you want to raise your hand if + + align:start position:0% +wow you want to raise your hand if + + + align:start position:0% +wow you want to raise your hand if +you're born on February + + align:start position:0% + + + + align:start position:0% + +12th + + align:start position:0% +12th + + + align:start position:0% +12th +aha all right so you are exceptional and + + align:start position:0% +aha all right so you are exceptional and + + + align:start position:0% +aha all right so you are exceptional and +that you lie about when you're + + align:start position:0% +that you lie about when you're + + + align:start position:0% +that you lie about when you're +born + + align:start position:0% +born + + + align:start position:0% +born +but if you hadn't lied I think we would + + align:start position:0% +but if you hadn't lied I think we would + + + align:start position:0% +but if you hadn't lied I think we would +have still seen the probabilities would + + align:start position:0% +have still seen the probabilities would + + + align:start position:0% +have still seen the probabilities would +hold how many people were there do we + + align:start position:0% + + + + align:start position:0% + +know 146 112 unique + + align:start position:0% +know 146 112 unique + + + align:start position:0% +know 146 112 unique +birthdays 146 people 112 unique + + align:start position:0% +birthdays 146 people 112 unique + + + align:start position:0% +birthdays 146 people 112 unique +birthdays so + + align:start position:0% +birthdays so + + + align:start position:0% +birthdays so +indeed the probability does + + align:start position:0% +indeed the probability does + + + align:start position:0% +indeed the probability does +work + + align:start position:0% + + + + align:start position:0% + +okay so we know you're exceptional in a + + align:start position:0% +okay so we know you're exceptional in a + + + align:start position:0% +okay so we know you're exceptional in a +funny way + + align:start position:0% +funny way + + + align:start position:0% +funny way +well you can imagine how hard it would + + align:start position:0% +well you can imagine how hard it would + + + align:start position:0% +well you can imagine how hard it would +be to adjust the analytic model to + + align:start position:0% +be to adjust the analytic model to + + + align:start position:0% +be to adjust the analytic model to +account for a weird distribution of + + align:start position:0% +account for a weird distribution of + + + align:start position:0% +account for a weird distribution of +birth + + align:start position:0% +birth + + + align:start position:0% +birth +dates uh but again adjusting the + + align:start position:0% +dates uh but again adjusting the + + + align:start position:0% +dates uh but again adjusting the +simulation model is + + align:start position:0% +simulation model is + + + align:start position:0% +simulation model is +easy um I could have gone back to that + + align:start position:0% +easy um I could have gone back to that + + + align:start position:0% +easy um I could have gone back to that +heat map I showed you of birthdays in + + align:start position:0% +heat map I showed you of birthdays in + + + align:start position:0% +heat map I showed you of birthdays in +the US and gotten a separate probability + + align:start position:0% +the US and gotten a separate probability + + + align:start position:0% +the US and gotten a separate probability +for each day but I was too + + align:start position:0% +for each day but I was too + + + align:start position:0% +for each day but I was too +lazy and instead what I + + align:start position:0% +lazy and instead what I + + + align:start position:0% +lazy and instead what I +observed was that we had this a few days + + align:start position:0% +observed was that we had this a few days + + + align:start position:0% +observed was that we had this a few days +like February 29th highly + + align:start position:0% +like February 29th highly + + + align:start position:0% +like February 29th highly +unlikely and this band in the middle of + + align:start position:0% +unlikely and this band in the middle of + + + align:start position:0% +unlikely and this band in the middle of +people who were conceived in the late + + align:start position:0% +people who were conceived in the late + + + align:start position:0% +people who were conceived in the late +fall and early + + align:start position:0% +fall and early + + + align:start position:0% +fall and early +winter so what I + + align:start position:0% +winter so what I + + + align:start position:0% +winter so what I +did is I duplicated some + + align:start position:0% +did is I duplicated some + + + align:start position:0% +did is I duplicated some +dates so the 58th day of the year + + align:start position:0% +dates so the 58th day of the year + + + align:start position:0% +dates so the 58th day of the year +February 29th occurs only once + + align:start position:0% + + + + align:start position:0% + +the dates before that I said let's May + + align:start position:0% +the dates before that I said let's May + + + align:start position:0% +the dates before that I said let's May +pretend they occur four times what only + + align:start position:0% +pretend they occur four times what only + + + align:start position:0% +pretend they occur four times what only +matters here is not how often they occur + + align:start position:0% +matters here is not how often they occur + + + align:start position:0% +matters here is not how often they occur +but the relative + + align:start position:0% +but the relative + + + align:start position:0% +but the relative +frequency + + align:start position:0% +frequency + + + align:start position:0% +frequency +um and + + align:start position:0% +um and + + + align:start position:0% +um and +then the dates after that occur four + + align:start position:0% +then the dates after that occur four + + + align:start position:0% +then the dates after that occur four +times except for the dates in that band + + align:start position:0% +times except for the dates in that band + + + align:start position:0% +times except for the dates in that band +which is going to have occur yet more + + align:start position:0% +which is going to have occur yet more + + + align:start position:0% +which is going to have occur yet more +often so now and don't worry about the + + align:start position:0% +often so now and don't worry about the + + + align:start position:0% +often so now and don't worry about the +exact details here but what I'm doing is + + align:start position:0% +exact details here but what I'm doing is + + + align:start position:0% +exact details here but what I'm doing is +simply adjusting the simulation to + + align:start position:0% +simply adjusting the simulation to + + + align:start position:0% +simply adjusting the simulation to +change the probability of each date + + align:start position:0% +change the probability of each date + + + align:start position:0% +change the probability of each date +getting chosen by same + + align:start position:0% + + + + align:start position:0% + +date and then I can run the simulation + + align:start position:0% +date and then I can run the simulation + + + align:start position:0% +date and then I can run the simulation +model and again with a very small change + + align:start position:0% +model and again with a very small change + + + align:start position:0% +model and again with a very small change +to + + align:start position:0% +to + + + align:start position:0% +to +code I've modeled something that's + + align:start position:0% +code I've modeled something that's + + + align:start position:0% +code I've modeled something that's +mathematically enormously complex I have + + align:start position:0% +mathematically enormously complex I have + + + align:start position:0% +mathematically enormously complex I have +no idea to actually do this + + align:start position:0% +no idea to actually do this + + + align:start position:0% +no idea to actually do this +probability + + align:start position:0% +probability + + + align:start position:0% +probability +mathematically but the code is as you + + align:start position:0% +mathematically but the code is as you + + + align:start position:0% +mathematically but the code is as you +can see quite straight + + align:start position:0% + + + + align:start position:0% + +forward so let's go to that + + align:start position:0% + + + + align:start position:0% + +here so what I'm going to do is comment + + align:start position:0% +here so what I'm going to do is comment + + + align:start position:0% +here so what I'm going to do is comment +this one + + align:start position:0% + + + + align:start position:0% + +out and uncomment this more + + align:start position:0% +out and uncomment this more + + + align:start position:0% +out and uncomment this more +complicated set of + + align:start position:0% + + + + align:start position:0% + +dates + + align:start position:0% + + + + align:start position:0% + +and see what we + + align:start position:0% + + + + align:start position:0% + +get and again it changes quite + + align:start position:0% +get and again it changes quite + + + align:start position:0% +get and again it changes quite +dramatically you might remember before + + align:start position:0% +dramatically you might remember before + + + align:start position:0% +dramatically you might remember before +it was around I think 6 something for + + align:start position:0% +it was around I think 6 something for + + + align:start position:0% +it was around I think 6 something for +100 and now it's + + align:start position:0% +100 and now it's + + + align:start position:0% +100 and now it's +75 so getting away from the notion that + + align:start position:0% +75 so getting away from the notion that + + + align:start position:0% +75 so getting away from the notion that +birthdays are uniformly distributed to + + align:start position:0% +birthdays are uniformly distributed to + + + align:start position:0% +birthdays are uniformly distributed to +saying some birthdays are more common + + align:start position:0% +saying some birthdays are more common + + + align:start position:0% +saying some birthdays are more common +than others again dramatically changes + + align:start position:0% +than others again dramatically changes + + + align:start position:0% +than others again dramatically changes +the + + align:start position:0% +the + + + align:start position:0% +the +answer and we can easily look at + + align:start position:0% + + + + align:start position:0% + +that so that gets us to the big topic of + + align:start position:0% +that so that gets us to the big topic of + + + align:start position:0% +that so that gets us to the big topic of +simulation + + align:start position:0% +simulation + + + align:start position:0% +simulation +models it's a program that describes a + + align:start position:0% +models it's a program that describes a + + + align:start position:0% +models it's a program that describes a +computation that provides information + + align:start position:0% +computation that provides information + + + align:start position:0% +computation that provides information +about the possible behaviors of a system + + align:start position:0% +about the possible behaviors of a system + + + align:start position:0% +about the possible behaviors of a system +I say possible behaviors because I'm + + align:start position:0% +I say possible behaviors because I'm + + + align:start position:0% +I say possible behaviors because I'm +particularly interested in stochastic + + align:start position:0% + + + + align:start position:0% + +systems they're descriptive not + + align:start position:0% +systems they're descriptive not + + + align:start position:0% +systems they're descriptive not +prescriptive in the sense that they + + align:start position:0% +prescriptive in the sense that they + + + align:start position:0% +prescriptive in the sense that they +describe the possible outcomes they + + align:start position:0% +describe the possible outcomes they + + + align:start position:0% +describe the possible outcomes they +don't tell you how to achieve a possible + + align:start position:0% +don't tell you how to achieve a possible + + + align:start position:0% +don't tell you how to achieve a possible +outcomes this is different from what we + + align:start position:0% +outcomes this is different from what we + + + align:start position:0% +outcomes this is different from what we +looked at earlier in the course where we + + align:start position:0% +looked at earlier in the course where we + + + align:start position:0% +looked at earlier in the course where we +looked at optimization + + align:start position:0% +looked at optimization + + + align:start position:0% +looked at optimization +models so optimization model is + + align:start position:0% +models so optimization model is + + + align:start position:0% +models so optimization model is +prescriptive it tells you how to achieve + + align:start position:0% +prescriptive it tells you how to achieve + + + align:start position:0% +prescriptive it tells you how to achieve +an effect how to get the most value out + + align:start position:0% +an effect how to get the most value out + + + align:start position:0% +an effect how to get the most value out +of your + + align:start position:0% +of your + + + align:start position:0% +of your +knapsack how to find the shortest path + + align:start position:0% +knapsack how to find the shortest path + + + align:start position:0% +knapsack how to find the shortest path +from A to B in a + + align:start position:0% +from A to B in a + + + align:start position:0% +from A to B in a +graph in contrast to simulation model + + align:start position:0% +graph in contrast to simulation model + + + align:start position:0% +graph in contrast to simulation model +says if I do this here's what happens it + + align:start position:0% +says if I do this here's what happens it + + + align:start position:0% +says if I do this here's what happens it +doesn't tell you how to make something + + align:start position:0% +doesn't tell you how to make something + + + align:start position:0% +doesn't tell you how to make something +happen so it's very different and it's + + align:start position:0% +happen so it's very different and it's + + + align:start position:0% +happen so it's very different and it's +why we need both why we we need + + align:start position:0% +why we need both why we we need + + + align:start position:0% +why we need both why we we need +optimization models and we need + + align:start position:0% +optimization models and we need + + + align:start position:0% +optimization models and we need +simulation + + align:start position:0% +simulation + + + align:start position:0% +simulation +models we have to remember that a + + align:start position:0% +models we have to remember that a + + + align:start position:0% +models we have to remember that a +simulation model is only an + + align:start position:0% +simulation model is only an + + + align:start position:0% +simulation model is only an +approximation to reality you know I put + + align:start position:0% +approximation to reality you know I put + + + align:start position:0% +approximation to reality you know I put +in an approximation to the distribution + + align:start position:0% +in an approximation to the distribution + + + align:start position:0% +in an approximation to the distribution +of birth dates but it wasn't quite + + align:start position:0% +of birth dates but it wasn't quite + + + align:start position:0% +of birth dates but it wasn't quite +right and as the very famous + + align:start position:0% +right and as the very famous + + + align:start position:0% +right and as the very famous +statistician George Bach said all models + + align:start position:0% +statistician George Bach said all models + + + align:start position:0% +statistician George Bach said all models +are wrong but some are actually very + + align:start position:0% +are wrong but some are actually very + + + align:start position:0% +are wrong but some are actually very +useful in the next lecture we'll look at + + align:start position:0% +useful in the next lecture we'll look at + + + align:start position:0% +useful in the next lecture we'll look at +a useful class of + + align:start position:0% +a useful class of + + + align:start position:0% +a useful class of +models when do we use + + align:start position:0% +models when do we use + + + align:start position:0% +models when do we use +simulations typically as we've just + + align:start position:0% +simulations typically as we've just + + + align:start position:0% +simulations typically as we've just +shown to model systems that are + + align:start position:0% +shown to model systems that are + + + align:start position:0% +shown to model systems that are +mathematically + + align:start position:0% +mathematically + + + align:start position:0% +mathematically +intractable like the birthday problem we + + align:start position:0% +intractable like the birthday problem we + + + align:start position:0% +intractable like the birthday problem we +just looked + + align:start position:0% +just looked + + + align:start position:0% +just looked +at uh in other situations to extract + + align:start position:0% +at uh in other situations to extract + + + align:start position:0% +at uh in other situations to extract +intermediate results something that + + align:start position:0% +intermediate results something that + + + align:start position:0% +intermediate results something that +happens along the way to the + + align:start position:0% +happens along the way to the + + + align:start position:0% +happens along the way to the +answer and as I hope you've seen that + + align:start position:0% +answer and as I hope you've seen that + + + align:start position:0% +answer and as I hope you've seen that +simulations are used because we can play + + align:start position:0% +simulations are used because we can play + + + align:start position:0% +simulations are used because we can play +what if games by successively ref + + align:start position:0% +what if games by successively ref + + + align:start position:0% +what if games by successively ref +finding it we started with a simple + + align:start position:0% +finding it we started with a simple + + + align:start position:0% +finding it we started with a simple +simulation that assumed that we only + + align:start position:0% +simulation that assumed that we only + + + align:start position:0% +simulation that assumed that we only +asked the question of did two people + + align:start position:0% +asked the question of did two people + + + align:start position:0% +asked the question of did two people +share a + + align:start position:0% +share a + + + align:start position:0% +share a +birthday we showed how we could change + + align:start position:0% +birthday we showed how we could change + + + align:start position:0% +birthday we showed how we could change +it to ask to three people share a + + align:start position:0% +it to ask to three people share a + + + align:start position:0% +it to ask to three people share a +birthday we then saw that we could + + align:start position:0% +birthday we then saw that we could + + + align:start position:0% +birthday we then saw that we could +change it to assume a different + + align:start position:0% +change it to assume a different + + + align:start position:0% +change it to assume a different +distribution of birth dates in in the + + align:start position:0% +distribution of birth dates in in the + + + align:start position:0% +distribution of birth dates in in the +group and so we can start with something + + align:start position:0% +group and so we can start with something + + + align:start position:0% +group and so we can start with something +simple and we get it ever more complex + + align:start position:0% +simple and we get it ever more complex + + + align:start position:0% +simple and we get it ever more complex +to answer questions what if + + align:start position:0% + + + + align:start position:0% + +we're going to start in the next lecture + + align:start position:0% +we're going to start in the next lecture + + + align:start position:0% +we're going to start in the next lecture +by producing a Samu simulation of random + + align:start position:0% +by producing a Samu simulation of random + + + align:start position:0% +by producing a Samu simulation of random +of a random walk and with that I'll stop + + align:start position:0% +of a random walk and with that I'll stop + + + align:start position:0% +of a random walk and with that I'll stop +and see you guys + + align:start position:0% + + + + align:start position:0% + +soon \ No newline at end of file diff --git a/-GXIkn_ecKY.txt b/-GXIkn_ecKY.txt new file mode 100644 index 0000000000000000000000000000000000000000..e361b03376697698c0f7cf7f27aea161f1709775 --- /dev/null +++ b/-GXIkn_ecKY.txt @@ -0,0 +1,3003 @@ +align:start position:0% + +hi everybody I'm rumen and today I will + + align:start position:0% +hi everybody I'm rumen and today I will + + + align:start position:0% +hi everybody I'm rumen and today I will +talk about three things optical trapping + + align:start position:0% +talk about three things optical trapping + + + align:start position:0% +talk about three things optical trapping +the Boltzmann constant and Brownian + + align:start position:0% +the Boltzmann constant and Brownian + + + align:start position:0% +the Boltzmann constant and Brownian +motion the goal of the lab is to extract + + align:start position:0% +motion the goal of the lab is to extract + + + align:start position:0% +motion the goal of the lab is to extract +Boltzmann's constant out of Brownian + + align:start position:0% +Boltzmann's constant out of Brownian + + + align:start position:0% +Boltzmann's constant out of Brownian +motion and there are two key components + + align:start position:0% +motion and there are two key components + + + align:start position:0% +motion and there are two key components +to think about first one is the + + align:start position:0% +to think about first one is the + + + align:start position:0% +to think about first one is the +Boltzmann constant which is prevalent in + + align:start position:0% +Boltzmann constant which is prevalent in + + + align:start position:0% +Boltzmann constant which is prevalent in +different types of science for example + + align:start position:0% +different types of science for example + + + align:start position:0% +different types of science for example +we can have it in biophysics where + + align:start position:0% +we can have it in biophysics where + + + align:start position:0% +we can have it in biophysics where +people use the Boltzmann constant to try + + align:start position:0% +people use the Boltzmann constant to try + + + align:start position:0% +people use the Boltzmann constant to try +to understand forces in a cellular level + + align:start position:0% +to understand forces in a cellular level + + + align:start position:0% +to understand forces in a cellular level +we have it in thermodynamics with the + + align:start position:0% +we have it in thermodynamics with the + + + align:start position:0% +we have it in thermodynamics with the +famous equipartition theorem how does + + align:start position:0% +famous equipartition theorem how does + + + align:start position:0% +famous equipartition theorem how does +this relate to the Brownian motion the + + align:start position:0% +this relate to the Brownian motion the + + + align:start position:0% +this relate to the Brownian motion the +key thing is to think about length + + align:start position:0% +key thing is to think about length + + + align:start position:0% +key thing is to think about length +scales Brownian motion is relevant in + + align:start position:0% +scales Brownian motion is relevant in + + + align:start position:0% +scales Brownian motion is relevant in +terms of microns and at the same time if + + align:start position:0% +terms of microns and at the same time if + + + align:start position:0% +terms of microns and at the same time if +we look at the cellular level for + + align:start position:0% +we look at the cellular level for + + + align:start position:0% +we look at the cellular level for +example if we look at our hair we have + + align:start position:0% +example if we look at our hair we have + + + align:start position:0% +example if we look at our hair we have +micron sized hair all right so there are + + align:start position:0% +micron sized hair all right so there are + + + align:start position:0% +micron sized hair all right so there are +different ways to measure the + + align:start position:0% +different ways to measure the + + + align:start position:0% +different ways to measure the +Boltzmann's constant some people measure + + align:start position:0% +Boltzmann's constant some people measure + + + align:start position:0% +Boltzmann's constant some people measure +the speed of sound in argon gas others + + align:start position:0% +the speed of sound in argon gas others + + + align:start position:0% +the speed of sound in argon gas others +do optical trapping in air we will do + + align:start position:0% +do optical trapping in air we will do + + + align:start position:0% +do optical trapping in air we will do +slightly different optical trapping as + + align:start position:0% +slightly different optical trapping as + + + align:start position:0% +slightly different optical trapping as +you will see but the consensus among the + + align:start position:0% +you will see but the consensus among the + + + align:start position:0% +you will see but the consensus among the +scientific community is that it is + + align:start position:0% +scientific community is that it is + + + align:start position:0% +scientific community is that it is +challenging our plan is to prepare + + align:start position:0% +challenging our plan is to prepare + + + align:start position:0% +challenging our plan is to prepare +Brownian particles and control their + + align:start position:0% +Brownian particles and control their + + + align:start position:0% +Brownian particles and control their +Brownian motion we take glass beads of + + align:start position:0% +Brownian motion we take glass beads of + + + align:start position:0% +Brownian motion we take glass beads of +their spherical glass beads of diameter + + align:start position:0% +their spherical glass beads of diameter + + + align:start position:0% +their spherical glass beads of diameter +of 3.2 microns and the main to is to + + align:start position:0% +of 3.2 microns and the main to is to + + + align:start position:0% +of 3.2 microns and the main to is to +concentrate a highly focused lasers on + + align:start position:0% +concentrate a highly focused lasers on + + + align:start position:0% +concentrate a highly focused lasers on +top of these beads there's interesting + + align:start position:0% +top of these beads there's interesting + + + align:start position:0% +top of these beads there's interesting +physics going on light carries momentum + + align:start position:0% +physics going on light carries momentum + + + align:start position:0% +physics going on light carries momentum +versa generates force we have that the + + align:start position:0% +versa generates force we have that the + + + align:start position:0% +versa generates force we have that the +net gradient force opposes the motion of + + align:start position:0% +net gradient force opposes the motion of + + + align:start position:0% +net gradient force opposes the motion of +the beam while the net scattering force + + align:start position:0% +the beam while the net scattering force + + + align:start position:0% +the beam while the net scattering force +goes along the motion of the beam and + + align:start position:0% +goes along the motion of the beam and + + + align:start position:0% +goes along the motion of the beam and +when these two forces balance each other + + align:start position:0% +when these two forces balance each other + + + align:start position:0% +when these two forces balance each other +we have a beat that is at the center + + align:start position:0% +we have a beat that is at the center + + + align:start position:0% +we have a beat that is at the center +when you push this beat a little bit to + + align:start position:0% +when you push this beat a little bit to + + + align:start position:0% +when you push this beat a little bit to +the left or to the right then we have + + align:start position:0% +the left or to the right then we have + + + align:start position:0% +the left or to the right then we have +that the gradient forces are pulling + + align:start position:0% +that the gradient forces are pulling + + + align:start position:0% +that the gradient forces are pulling +back in the center and essentially we + + align:start position:0% +back in the center and essentially we + + + align:start position:0% +back in the center and essentially we +observe a simple harmonic motion in a + + align:start position:0% +observe a simple harmonic motion in a + + + align:start position:0% +observe a simple harmonic motion in a +more concrete example what we did is we + + align:start position:0% +more concrete example what we did is we + + + align:start position:0% +more concrete example what we did is we +took samples and we can find everything + + align:start position:0% +took samples and we can find everything + + + align:start position:0% +took samples and we can find everything +into a two-dimensional plane this is + + align:start position:0% +into a two-dimensional plane this is + + + align:start position:0% +into a two-dimensional plane this is +very important we have two directions + + align:start position:0% +very important we have two directions + + + align:start position:0% +very important we have two directions +the X direction in the Y direction for + + align:start position:0% +the X direction in the Y direction for + + + align:start position:0% +the X direction in the Y direction for +the beads we put them into water and + + align:start position:0% +the beads we put them into water and + + + align:start position:0% +the beads we put them into water and +source of Brownian motion comes from the + + align:start position:0% +source of Brownian motion comes from the + + + align:start position:0% +source of Brownian motion comes from the +collisions between our bead with the + + align:start position:0% +collisions between our bead with the + + + align:start position:0% +collisions between our bead with the +molecules into the water + + align:start position:0% +molecules into the water + + + align:start position:0% +molecules into the water +these are thermal collisions that + + align:start position:0% +these are thermal collisions that + + + align:start position:0% +these are thermal collisions that +generate Brownian motion as you can see + + align:start position:0% +generate Brownian motion as you can see + + + align:start position:0% +generate Brownian motion as you can see +this lonely beat has its Brownian motion + + align:start position:0% +this lonely beat has its Brownian motion + + + align:start position:0% +this lonely beat has its Brownian motion +what's interesting is when we shine + + align:start position:0% +what's interesting is when we shine + + + align:start position:0% +what's interesting is when we shine +light on top of a beat we trap this beat + + align:start position:0% +light on top of a beat we trap this beat + + + align:start position:0% +light on top of a beat we trap this beat +and we can find the Brownian motion so + + align:start position:0% +and we can find the Brownian motion so + + + align:start position:0% +and we can find the Brownian motion so +it's feasible to measure the motion and + + align:start position:0% +it's feasible to measure the motion and + + + align:start position:0% +it's feasible to measure the motion and +the theory behind this is very beautiful + + align:start position:0% +the theory behind this is very beautiful + + + align:start position:0% +the theory behind this is very beautiful +it's about the equipartition theorem + + align:start position:0% +it's about the equipartition theorem + + + align:start position:0% +it's about the equipartition theorem +which relates the kinetic energy coming + + align:start position:0% +which relates the kinetic energy coming + + + align:start position:0% +which relates the kinetic energy coming +from the simple harmonic motion on the + + align:start position:0% +from the simple harmonic motion on the + + + align:start position:0% +from the simple harmonic motion on the +left-hand side with the thermal energy + + align:start position:0% +left-hand side with the thermal energy + + + align:start position:0% +left-hand side with the thermal energy +of due to the degrees of freedom now let + + align:start position:0% +of due to the degrees of freedom now let + + + align:start position:0% +of due to the degrees of freedom now let +us recall that we have a two-dimensional + + align:start position:0% +us recall that we have a two-dimensional + + + align:start position:0% +us recall that we have a two-dimensional +confinement so we have a direction in X + + align:start position:0% +confinement so we have a direction in X + + + align:start position:0% +confinement so we have a direction in X +and direction in Y so it means that in + + align:start position:0% +and direction in Y so it means that in + + + align:start position:0% +and direction in Y so it means that in +each of the directions we have one + + align:start position:0% +each of the directions we have one + + + align:start position:0% +each of the directions we have one +degree of freedom which is correlated + + align:start position:0% +degree of freedom which is correlated + + + align:start position:0% +degree of freedom which is correlated +with this equipartition theorem now an + + align:start position:0% +with this equipartition theorem now an + + + align:start position:0% +with this equipartition theorem now an +interesting thing about the statistical + + align:start position:0% +interesting thing about the statistical + + + align:start position:0% +interesting thing about the statistical +motion of the molecules is that we have + + align:start position:0% +motion of the molecules is that we have + + + align:start position:0% +motion of the molecules is that we have +the simple harmonic motion however the + + align:start position:0% +the simple harmonic motion however the + + + align:start position:0% +the simple harmonic motion however the +things are moving into water so there is + + align:start position:0% +things are moving into water so there is + + + align:start position:0% +things are moving into water so there is +a drag force that dominates so we + + align:start position:0% +a drag force that dominates so we + + + align:start position:0% +a drag force that dominates so we +simplify the left hand side what is very + + align:start position:0% +simplify the left hand side what is very + + + align:start position:0% +simplify the left hand side what is very +interesting is the F factor which comes + + align:start position:0% +interesting is the F factor which comes + + + align:start position:0% +interesting is the F factor which comes +from the collisions between the beat + + align:start position:0% +from the collisions between the beat + + + align:start position:0% +from the collisions between the beat +with the molecules this generates + + align:start position:0% +with the molecules this generates + + + align:start position:0% +with the molecules this generates +forcing and driving of the simple + + align:start position:0% +forcing and driving of the simple + + + align:start position:0% +forcing and driving of the simple +harmonic motion I like to point out one + + align:start position:0% +harmonic motion I like to point out one + + + align:start position:0% +harmonic motion I like to point out one +thing about the scales of the forces we + + align:start position:0% +thing about the scales of the forces we + + + align:start position:0% +thing about the scales of the forces we +have Pico Newton's which is relevant for + + align:start position:0% +have Pico Newton's which is relevant for + + + align:start position:0% +have Pico Newton's which is relevant for +optical trapping and for Brownian motion + + align:start position:0% +optical trapping and for Brownian motion + + + align:start position:0% +optical trapping and for Brownian motion +this is the first observation that we + + align:start position:0% +this is the first observation that we + + + align:start position:0% +this is the first observation that we +did and actually Einstein this operation + + align:start position:0% +did and actually Einstein this operation + + + align:start position:0% +did and actually Einstein this operation +a long time ago he observed the white + + align:start position:0% +a long time ago he observed the white + + + align:start position:0% +a long time ago he observed the white +noise essentially the collisions they + + align:start position:0% +noise essentially the collisions they + + + align:start position:0% +noise essentially the collisions they +generate uncorrelated forcing and we can + + align:start position:0% +generate uncorrelated forcing and we can + + + align:start position:0% +generate uncorrelated forcing and we can +think of it as something that is not + + align:start position:0% +think of it as something that is not + + + align:start position:0% +think of it as something that is not +biased with any distribution is just + + align:start position:0% +biased with any distribution is just + + + align:start position:0% +biased with any distribution is just +uniform as you can see on these slides + + align:start position:0% +uniform as you can see on these slides + + + align:start position:0% +uniform as you can see on these slides +we have the position plotted in terms of + + align:start position:0% +we have the position plotted in terms of + + + align:start position:0% +we have the position plotted in terms of +and it exhibits a uniform distribution + + align:start position:0% +and it exhibits a uniform distribution + + + align:start position:0% +and it exhibits a uniform distribution +of the spectrum another thing that I + + align:start position:0% +of the spectrum another thing that I + + + align:start position:0% +of the spectrum another thing that I +would like to point out is to look at + + align:start position:0% +would like to point out is to look at + + + align:start position:0% +would like to point out is to look at +this plot of fluctuations in X&Y and the + + align:start position:0% +this plot of fluctuations in X&Y and the + + + align:start position:0% +this plot of fluctuations in X&Y and the +power which is linear with the current + + align:start position:0% +power which is linear with the current + + + align:start position:0% +power which is linear with the current +of the lasers as you can see as the + + align:start position:0% +of the lasers as you can see as the + + + align:start position:0% +of the lasers as you can see as the +power becomes big this means that we are + + align:start position:0% +power becomes big this means that we are + + + align:start position:0% +power becomes big this means that we are +trapping more so we have less + + align:start position:0% +trapping more so we have less + + + align:start position:0% +trapping more so we have less +fluctuations which is something as + + align:start position:0% +fluctuations which is something as + + + align:start position:0% +fluctuations which is something as +expected all right so let's figure out + + align:start position:0% +expected all right so let's figure out + + + align:start position:0% +expected all right so let's figure out +what we want to do with this lab we have + + align:start position:0% +what we want to do with this lab we have + + + align:start position:0% +what we want to do with this lab we have +the equipartition theorem and + + align:start position:0% +the equipartition theorem and + + + align:start position:0% +the equipartition theorem and +essentially we have three components + + align:start position:0% +essentially we have three components + + + align:start position:0% +essentially we have three components +that we would like to measure in order + + align:start position:0% +that we would like to measure in order + + + align:start position:0% +that we would like to measure in order +to extract Kb we need to find the + + align:start position:0% +to extract Kb we need to find the + + + align:start position:0% +to extract Kb we need to find the +fluctuations which I just presented to + + align:start position:0% +fluctuations which I just presented to + + + align:start position:0% +fluctuations which I just presented to +you we need to find the stiffness + + align:start position:0% +you we need to find the stiffness + + + align:start position:0% +you we need to find the stiffness +coefficient alpha which is related to + + align:start position:0% +coefficient alpha which is related to + + + align:start position:0% +coefficient alpha which is related to +the spring constant of motion and then + + align:start position:0% +the spring constant of motion and then + + + align:start position:0% +the spring constant of motion and then +we need to measure the temperature T the + + align:start position:0% +we need to measure the temperature T the + + + align:start position:0% +we need to measure the temperature T the +apparatus that we use has two main + + align:start position:0% +apparatus that we use has two main + + + align:start position:0% +apparatus that we use has two main +components the two components are + + align:start position:0% +components the two components are + + + align:start position:0% +components the two components are +concerned with the two types of light + + align:start position:0% +concerned with the two types of light + + + align:start position:0% +concerned with the two types of light +that we use in our experiment we use a + + align:start position:0% +that we use in our experiment we use a + + + align:start position:0% +that we use in our experiment we use a +laser that shines on top of the confined + + align:start position:0% +laser that shines on top of the confined + + + align:start position:0% +laser that shines on top of the confined +two-dimensional samples and tries to + + align:start position:0% +two-dimensional samples and tries to + + + align:start position:0% +two-dimensional samples and tries to +trap a beat the scatter light from the + + align:start position:0% +trap a beat the scatter light from the + + + align:start position:0% +trap a beat the scatter light from the +laser goes into a QP D a quadrant photo + + align:start position:0% +laser goes into a QP D a quadrant photo + + + align:start position:0% +laser goes into a QP D a quadrant photo +detector which is an ultra-fast camera + + align:start position:0% +detector which is an ultra-fast camera + + + align:start position:0% +detector which is an ultra-fast camera +that manages to quickly digitalize the + + align:start position:0% +that manages to quickly digitalize the + + + align:start position:0% +that manages to quickly digitalize the +content and give us the position of the + + align:start position:0% +content and give us the position of the + + + align:start position:0% +content and give us the position of the +scattered light so when we trap the beat + + align:start position:0% +scattered light so when we trap the beat + + + align:start position:0% +scattered light so when we trap the beat +we know where it is by observing the + + align:start position:0% +we know where it is by observing the + + + align:start position:0% +we know where it is by observing the +feedback from the QPD the other + + align:start position:0% +feedback from the QPD the other + + + align:start position:0% +feedback from the QPD the other +interesting part of the apparatus is the + + align:start position:0% +interesting part of the apparatus is the + + + align:start position:0% +interesting part of the apparatus is the +LED light which illuminates the sample + + align:start position:0% +LED light which illuminates the sample + + + align:start position:0% +LED light which illuminates the sample +and then it brings it to the CCD camera + + align:start position:0% +and then it brings it to the CCD camera + + + align:start position:0% +and then it brings it to the CCD camera +and this is very important so the CCD + + align:start position:0% +and this is very important so the CCD + + + align:start position:0% +and this is very important so the CCD +camera is very slow it cannot measure + + align:start position:0% +camera is very slow it cannot measure + + + align:start position:0% +camera is very slow it cannot measure +Brownian motion what it can do is it can + + align:start position:0% +Brownian motion what it can do is it can + + + align:start position:0% +Brownian motion what it can do is it can +tell us where are the beats it can allow + + align:start position:0% +tell us where are the beats it can allow + + + align:start position:0% +tell us where are the beats it can allow +us to look at the water and like find + + align:start position:0% +us to look at the water and like find + + + align:start position:0% +us to look at the water and like find +the beats we want to trap so these two + + align:start position:0% +the beats we want to trap so these two + + + align:start position:0% +the beats we want to trap so these two +components in combination are crucial + + align:start position:0% +components in combination are crucial + + + align:start position:0% +components in combination are crucial +for the success of our research there is + + align:start position:0% +for the success of our research there is + + + align:start position:0% +for the success of our research there is +interesting electronics coming behind + + align:start position:0% +interesting electronics coming behind + + + align:start position:0% +interesting electronics coming behind +this essentially the signals from the + + align:start position:0% +this essentially the signals from the + + + align:start position:0% +this essentially the signals from the +QPD and from the stage position where we + + align:start position:0% +QPD and from the stage position where we + + + align:start position:0% +QPD and from the stage position where we +put our sample are + + align:start position:0% +put our sample are + + + align:start position:0% +put our sample are +given in terms of volts so a natural + + align:start position:0% +given in terms of volts so a natural + + + align:start position:0% +given in terms of volts so a natural +question that arises is how are we going + + align:start position:0% +question that arises is how are we going + + + align:start position:0% +question that arises is how are we going +to remember what is important there are + + align:start position:0% +to remember what is important there are + + + align:start position:0% +to remember what is important there are +two important things that would like to + + align:start position:0% +two important things that would like to + + + align:start position:0% +two important things that would like to +keep track of two positions the first + + align:start position:0% +keep track of two positions the first + + + align:start position:0% +keep track of two positions the first +one is the position of the stage that + + align:start position:0% +one is the position of the stage that + + + align:start position:0% +one is the position of the stage that +gives us a relative point of + + align:start position:0% +gives us a relative point of + + + align:start position:0% +gives us a relative point of +consideration and the second one is the + + align:start position:0% +consideration and the second one is the + + + align:start position:0% +consideration and the second one is the +position of the QPD which as you can + + align:start position:0% +position of the QPD which as you can + + + align:start position:0% +position of the QPD which as you can +recall it measures the place of the beat + + align:start position:0% +recall it measures the place of the beat + + + align:start position:0% +recall it measures the place of the beat +that we have trapped these inputs are + + align:start position:0% +that we have trapped these inputs are + + + align:start position:0% +that we have trapped these inputs are +given in terms of volts so the natural + + align:start position:0% +given in terms of volts so the natural + + + align:start position:0% +given in terms of volts so the natural +thing to do is to find a calibration + + align:start position:0% +thing to do is to find a calibration + + + align:start position:0% +thing to do is to find a calibration +that converts these volts into actual + + align:start position:0% +that converts these volts into actual + + + align:start position:0% +that converts these volts into actual +distances here you can see how we do + + align:start position:0% +distances here you can see how we do + + + align:start position:0% +distances here you can see how we do +this we plot the stage X or position you + + align:start position:0% +this we plot the stage X or position you + + + align:start position:0% +this we plot the stage X or position you +can we can plot the stage Y it's + + align:start position:0% +can we can plot the stage Y it's + + + align:start position:0% +can we can plot the stage Y it's +completely analogous to the to the QPD + + align:start position:0% +completely analogous to the to the QPD + + + align:start position:0% +completely analogous to the to the QPD +positions here and the conversion factor + + align:start position:0% +positions here and the conversion factor + + + align:start position:0% +positions here and the conversion factor +hides along these slopes here well as + + align:start position:0% +hides along these slopes here well as + + + align:start position:0% +hides along these slopes here well as +you can see we have two different slopes + + align:start position:0% +you can see we have two different slopes + + + align:start position:0% +you can see we have two different slopes +here with different absolute values so + + align:start position:0% +here with different absolute values so + + + align:start position:0% +here with different absolute values so +this type of measurement is prone to + + align:start position:0% +this type of measurement is prone to + + + align:start position:0% +this type of measurement is prone to +errors how we approach this problem is + + align:start position:0% +errors how we approach this problem is + + + align:start position:0% +errors how we approach this problem is +that we fought by choosing more data + + align:start position:0% +that we fought by choosing more data + + + align:start position:0% +that we fought by choosing more data +points and trying to increase the + + align:start position:0% +points and trying to increase the + + + align:start position:0% +points and trying to increase the +statistic thus hopefully reducing the + + align:start position:0% +statistic thus hopefully reducing the + + + align:start position:0% +statistic thus hopefully reducing the +systematics of this measurement the + + align:start position:0% +systematics of this measurement the + + + align:start position:0% +systematics of this measurement the +second step is to start getting the + + align:start position:0% +second step is to start getting the + + + align:start position:0% +second step is to start getting the +components that we need in order to + + align:start position:0% +components that we need in order to + + + align:start position:0% +components that we need in order to +extract KB is to measure the stiffness + + align:start position:0% +extract KB is to measure the stiffness + + + align:start position:0% +extract KB is to measure the stiffness +coefficient alpha now the main idea is + + align:start position:0% +coefficient alpha now the main idea is + + + align:start position:0% +coefficient alpha now the main idea is +to take the equation of motion and to + + align:start position:0% +to take the equation of motion and to + + + align:start position:0% +to take the equation of motion and to +make a Fourier transform in order to get + + align:start position:0% +make a Fourier transform in order to get + + + align:start position:0% +make a Fourier transform in order to get +the positions in terms of frequencies + + align:start position:0% +the positions in terms of frequencies + + + align:start position:0% +the positions in terms of frequencies +there is mathematics behind this and + + align:start position:0% +there is mathematics behind this and + + + align:start position:0% +there is mathematics behind this and +essentially the power spectral + + align:start position:0% +essentially the power spectral + + + align:start position:0% +essentially the power spectral +distribution and as the distribution of + + align:start position:0% +distribution and as the distribution of + + + align:start position:0% +distribution and as the distribution of +this motion here that we expect obtains + + align:start position:0% +this motion here that we expect obtains + + + align:start position:0% +this motion here that we expect obtains +this form here from where we can extract + + align:start position:0% +this form here from where we can extract + + + align:start position:0% +this form here from where we can extract +the characteristic frequency F naught + + align:start position:0% +the characteristic frequency F naught + + + align:start position:0% +the characteristic frequency F naught +and F naught gives us alpha which is + + align:start position:0% +and F naught gives us alpha which is + + + align:start position:0% +and F naught gives us alpha which is +what we really need this is a log-log + + align:start position:0% +what we really need this is a log-log + + + align:start position:0% +what we really need this is a log-log +plot as you can see here another thing I + + align:start position:0% +plot as you can see here another thing I + + + align:start position:0% +plot as you can see here another thing I +would like to mention is look at the + + align:start position:0% +would like to mention is look at the + + + align:start position:0% +would like to mention is look at the +proportionality here as we increase the + + align:start position:0% +proportionality here as we increase the + + + align:start position:0% +proportionality here as we increase the +power we also increase the stiffness + + align:start position:0% +power we also increase the stiffness + + + align:start position:0% +power we also increase the stiffness +coefficient alpha because we trap more + + align:start position:0% +coefficient alpha because we trap more + + + align:start position:0% +coefficient alpha because we trap more +closely so it means that F nost has to + + align:start position:0% +closely so it means that F nost has to + + + align:start position:0% +closely so it means that F nost has to +increase and indeed when we increase the + + align:start position:0% +increase and indeed when we increase the + + + align:start position:0% +increase and indeed when we increase the +power we are shifting F naught to the + + align:start position:0% +power we are shifting F naught to the + + + align:start position:0% +power we are shifting F naught to the +right having all these components + + align:start position:0% +right having all these components + + + align:start position:0% +right having all these components +we can put this into the big picture and + + align:start position:0% +we can put this into the big picture and + + + align:start position:0% +we can put this into the big picture and +the big picture is the extraction of KB + + align:start position:0% +the big picture is the extraction of KB + + + align:start position:0% +the big picture is the extraction of KB +over here I showed you x squared the + + align:start position:0% +over here I showed you x squared the + + + align:start position:0% +over here I showed you x squared the +fluctuations I showed you alpha we can + + align:start position:0% +fluctuations I showed you alpha we can + + + align:start position:0% +fluctuations I showed you alpha we can +measure the temperature T and then we + + align:start position:0% +measure the temperature T and then we + + + align:start position:0% +measure the temperature T and then we +can get Kb the essence of this + + align:start position:0% +can get Kb the essence of this + + + align:start position:0% +can get Kb the essence of this +measurement is to look at the inverse + + align:start position:0% +measurement is to look at the inverse + + + align:start position:0% +measurement is to look at the inverse +proportionality between fluctuations and + + align:start position:0% +proportionality between fluctuations and + + + align:start position:0% +proportionality between fluctuations and +trap stiffness then we can make a fit + + align:start position:0% +trap stiffness then we can make a fit + + + align:start position:0% +trap stiffness then we can make a fit +with a reasonable chi-square probability + + align:start position:0% +with a reasonable chi-square probability + + + align:start position:0% +with a reasonable chi-square probability +and from here we can extract Kb the + + align:start position:0% +and from here we can extract Kb the + + + align:start position:0% +and from here we can extract Kb the +result is presented on the slide we also + + align:start position:0% +result is presented on the slide we also + + + align:start position:0% +result is presented on the slide we also +show you the measurement that we extract + + align:start position:0% +show you the measurement that we extract + + + align:start position:0% +show you the measurement that we extract +from literature our result is within two + + align:start position:0% +from literature our result is within two + + + align:start position:0% +from literature our result is within two +sigma of the accepted value of KB + + align:start position:0% +sigma of the accepted value of KB + + + align:start position:0% +sigma of the accepted value of KB +actually we're very close to 1 Sigma + + align:start position:0% +actually we're very close to 1 Sigma + + + align:start position:0% +actually we're very close to 1 Sigma +from the accepted value of KB what is + + align:start position:0% +from the accepted value of KB what is + + + align:start position:0% +from the accepted value of KB what is +driving this like unfortunate outcome + + align:start position:0% +driving this like unfortunate outcome + + + align:start position:0% +driving this like unfortunate outcome +the thing that drives this unfortunate + + align:start position:0% +the thing that drives this unfortunate + + + align:start position:0% +the thing that drives this unfortunate +outcome is the systematic errors on our + + align:start position:0% +outcome is the systematic errors on our + + + align:start position:0% +outcome is the systematic errors on our +picture this is our starting error this + + align:start position:0% +picture this is our starting error this + + + align:start position:0% +picture this is our starting error this +is the uncertainty in KB and there are + + align:start position:0% +is the uncertainty in KB and there are + + + align:start position:0% +is the uncertainty in KB and there are +different factors that contribute it to + + align:start position:0% +different factors that contribute it to + + + align:start position:0% +different factors that contribute it to +this as you saw the calibration is very + + align:start position:0% +this as you saw the calibration is very + + + align:start position:0% +this as you saw the calibration is very +difficult + + align:start position:0% +difficult + + + align:start position:0% +difficult +we have error from the laser hitting the + + align:start position:0% +we have error from the laser hitting the + + + align:start position:0% +we have error from the laser hitting the +water and changing the temperature we + + align:start position:0% +water and changing the temperature we + + + align:start position:0% +water and changing the temperature we +have systematic error of the electronics + + align:start position:0% +have systematic error of the electronics + + + align:start position:0% +have systematic error of the electronics +which we safely ignore because the first + + align:start position:0% +which we safely ignore because the first + + + align:start position:0% +which we safely ignore because the first +two factors dominate this our + + align:start position:0% +two factors dominate this our + + + align:start position:0% +two factors dominate this our +electronics were very precise and then + + align:start position:0% +electronics were very precise and then + + + align:start position:0% +electronics were very precise and then +we have the statistical uncertainties + + align:start position:0% +we have the statistical uncertainties + + + align:start position:0% +we have the statistical uncertainties +that we use which correspond to some + + align:start position:0% +that we use which correspond to some + + + align:start position:0% +that we use which correspond to some +error propagating tricks okay now let's + + align:start position:0% +error propagating tricks okay now let's + + + align:start position:0% +error propagating tricks okay now let's +do our investigation the first one is + + align:start position:0% +do our investigation the first one is + + + align:start position:0% +do our investigation the first one is +about the calibration as you can see all + + align:start position:0% +about the calibration as you can see all + + + align:start position:0% +about the calibration as you can see all +of these slopes should be valid but + + align:start position:0% +of these slopes should be valid but + + + align:start position:0% +of these slopes should be valid but +they're actually not so what we do is we + + align:start position:0% +they're actually not so what we do is we + + + align:start position:0% +they're actually not so what we do is we +take them into account we average them + + align:start position:0% +take them into account we average them + + + align:start position:0% +take them into account we average them +then we take more data points we average + + align:start position:0% +then we take more data points we average + + + align:start position:0% +then we take more data points we average +again and then we propagate the errors + + align:start position:0% +again and then we propagate the errors + + + align:start position:0% +again and then we propagate the errors +in order to reduce the systematics the + + align:start position:0% +in order to reduce the systematics the + + + align:start position:0% +in order to reduce the systematics the +second one is due to the heating of the + + align:start position:0% +second one is due to the heating of the + + + align:start position:0% +second one is due to the heating of the +laser essentially what happens is when + + align:start position:0% +laser essentially what happens is when + + + align:start position:0% +laser essentially what happens is when +the laser hits the water it starts + + align:start position:0% +the laser hits the water it starts + + + align:start position:0% +the laser hits the water it starts +heating the vicinity and this is + + align:start position:0% +heating the vicinity and this is + + + align:start position:0% +heating the vicinity and this is +unfortunate because yes we can measure + + align:start position:0% +unfortunate because yes we can measure + + + align:start position:0% +unfortunate because yes we can measure +the room temperature by using the therm + + align:start position:0% +the room temperature by using the therm + + + align:start position:0% +the room temperature by using the therm +but actual uncertainty on the + + align:start position:0% +but actual uncertainty on the + + + align:start position:0% +but actual uncertainty on the +temperature is much bigger because we + + align:start position:0% +temperature is much bigger because we + + + align:start position:0% +temperature is much bigger because we +have extra heating due to the laser we + + align:start position:0% +have extra heating due to the laser we + + + align:start position:0% +have extra heating due to the laser we +tried elegantly to to avoid this by + + align:start position:0% +tried elegantly to to avoid this by + + + align:start position:0% +tried elegantly to to avoid this by +moving the laser constantly so that it + + align:start position:0% +moving the laser constantly so that it + + + align:start position:0% +moving the laser constantly so that it +doesn't stay in one place and heat up a + + align:start position:0% +doesn't stay in one place and heat up a + + + align:start position:0% +doesn't stay in one place and heat up a +lot but it's very hard to quantify how + + align:start position:0% +lot but it's very hard to quantify how + + + align:start position:0% +lot but it's very hard to quantify how +exactly it heats up the water and the + + align:start position:0% +exactly it heats up the water and the + + + align:start position:0% +exactly it heats up the water and the +third one is it's concerned with our fit + + align:start position:0% +third one is it's concerned with our fit + + + align:start position:0% +third one is it's concerned with our fit +with fluctuations in terms of the trap + + align:start position:0% +with fluctuations in terms of the trap + + + align:start position:0% +with fluctuations in terms of the trap +stiffness initially when we did the fit + + align:start position:0% +stiffness initially when we did the fit + + + align:start position:0% +stiffness initially when we did the fit +we with the PhD method we get a + + align:start position:0% +we with the PhD method we get a + + + align:start position:0% +we with the PhD method we get a +probability of chi-square equals 0 and + + align:start position:0% +probability of chi-square equals 0 and + + + align:start position:0% +probability of chi-square equals 0 and +then we quickly realize that essentially + + align:start position:0% +then we quickly realize that essentially + + + align:start position:0% +then we quickly realize that essentially +what we need to do is take into account + + align:start position:0% +what we need to do is take into account + + + align:start position:0% +what we need to do is take into account +the horizontal errors and here what we + + align:start position:0% +the horizontal errors and here what we + + + align:start position:0% +the horizontal errors and here what we +do is we transform the horizontal errors + + align:start position:0% +do is we transform the horizontal errors + + + align:start position:0% +do is we transform the horizontal errors +into the vertical errors and this thing + + align:start position:0% +into the vertical errors and this thing + + + align:start position:0% +into the vertical errors and this thing +we can do by using adding addition in + + align:start position:0% +we can do by using adding addition in + + + align:start position:0% +we can do by using adding addition in +quadrature and propagation of the errors + + align:start position:0% +quadrature and propagation of the errors + + + align:start position:0% +quadrature and propagation of the errors +which gave us a reasonable realistic + + align:start position:0% +which gave us a reasonable realistic + + + align:start position:0% +which gave us a reasonable realistic +chi-squared of 0.33 in conclusion I'll + + align:start position:0% +chi-squared of 0.33 in conclusion I'll + + + align:start position:0% +chi-squared of 0.33 in conclusion I'll +start with limitations as you saw it's + + align:start position:0% +start with limitations as you saw it's + + + align:start position:0% +start with limitations as you saw it's +very hard to distinguish between + + align:start position:0% +very hard to distinguish between + + + align:start position:0% +very hard to distinguish between +systematic errors and statistical + + align:start position:0% +systematic errors and statistical + + + align:start position:0% +systematic errors and statistical +uncertainties the reason for this is as + + align:start position:0% +uncertainties the reason for this is as + + + align:start position:0% +uncertainties the reason for this is as +you saw is that we are fighting with the + + align:start position:0% +you saw is that we are fighting with the + + + align:start position:0% +you saw is that we are fighting with the +systematics by introducing more + + align:start position:0% +systematics by introducing more + + + align:start position:0% +systematics by introducing more +statistics and everything mixes up in + + align:start position:0% +statistics and everything mixes up in + + + align:start position:0% +statistics and everything mixes up in +the propagation of errors the second + + align:start position:0% +the propagation of errors the second + + + align:start position:0% +the propagation of errors the second +thing that it was very difficult in this + + align:start position:0% +thing that it was very difficult in this + + + align:start position:0% +thing that it was very difficult in this +lab is that we need to move the laser + + align:start position:0% +lab is that we need to move the laser + + + align:start position:0% +lab is that we need to move the laser +constantly so one of the one of the + + align:start position:0% +constantly so one of the one of the + + + align:start position:0% +constantly so one of the one of the +people working on this topic has to keep + + align:start position:0% +people working on this topic has to keep + + + align:start position:0% +people working on this topic has to keep +track of where the laser is and whether + + align:start position:0% +track of where the laser is and whether + + + align:start position:0% +track of where the laser is and whether +you're trapping things that you may not + + align:start position:0% +you're trapping things that you may not + + + align:start position:0% +you're trapping things that you may not +want to trap the third thing is to the + + align:start position:0% +want to trap the third thing is to the + + + align:start position:0% +want to trap the third thing is to the +need to find better ways of calibration + + align:start position:0% +need to find better ways of calibration + + + align:start position:0% +need to find better ways of calibration +and there are people who are actively + + align:start position:0% +and there are people who are actively + + + align:start position:0% +and there are people who are actively +working on this on this topic here as + + align:start position:0% +working on this on this topic here as + + + align:start position:0% +working on this on this topic here as +you saw the main source of error came + + align:start position:0% +you saw the main source of error came + + + align:start position:0% +you saw the main source of error came +from the calibration actually but the + + align:start position:0% +from the calibration actually but the + + + align:start position:0% +from the calibration actually but the +process is that we can give a reasonable + + align:start position:0% +process is that we can give a reasonable + + + align:start position:0% +process is that we can give a reasonable +estimate to the Boltzmann constant and + + align:start position:0% +estimate to the Boltzmann constant and + + + align:start position:0% +estimate to the Boltzmann constant and +at the same time we can have a lot of + + align:start position:0% +at the same time we can have a lot of + + + align:start position:0% +at the same time we can have a lot of +fun while doing so I would like to thank + + align:start position:0% +fun while doing so I would like to thank + + + align:start position:0% +fun while doing so I would like to thank +to my partner Emma and I think + + align:start position:0% +to my partner Emma and I think + + + align:start position:0% +to my partner Emma and I think +collaboration is very important for + + align:start position:0% +collaboration is very important for + + + align:start position:0% +collaboration is very important for +Jayla and more specifically for this + + align:start position:0% +Jayla and more specifically for this + + + align:start position:0% +Jayla and more specifically for this +particular experiment this experiment is + + align:start position:0% +particular experiment this experiment is + + + align:start position:0% +particular experiment this experiment is +impossible to be done without a partner + + align:start position:0% +impossible to be done without a partner + + + align:start position:0% +impossible to be done without a partner +because it's very difficult it's very + + align:start position:0% +because it's very difficult it's very + + + align:start position:0% +because it's very difficult it's very +difficult to keep track of where you + + align:start position:0% +difficult to keep track of where you + + + align:start position:0% +difficult to keep track of where you +want to put + + align:start position:0% +want to put + + + align:start position:0% +want to put +and also what is going on around the + + align:start position:0% +and also what is going on around the + + + align:start position:0% +and also what is going on around the +laser well one of the people who is + + align:start position:0% +laser well one of the people who is + + + align:start position:0% +laser well one of the people who is +moving the laser the other one should be + + align:start position:0% +moving the laser the other one should be + + + align:start position:0% +moving the laser the other one should be +looking looking at the CCD camera and + + align:start position:0% +looking looking at the CCD camera and + + + align:start position:0% +looking looking at the CCD camera and +like telling where are we going on like + + align:start position:0% +like telling where are we going on like + + + align:start position:0% +like telling where are we going on like +what are we actually trapping like what + + align:start position:0% +what are we actually trapping like what + + + align:start position:0% +what are we actually trapping like what +do we want to avoid like we don't want + + align:start position:0% +do we want to avoid like we don't want + + + align:start position:0% +do we want to avoid like we don't want +these guys in our picture I also like to + + align:start position:0% +these guys in our picture I also like to + + + align:start position:0% +these guys in our picture I also like to +thank the staff of this class for their + + align:start position:0% +thank the staff of this class for their + + + align:start position:0% +thank the staff of this class for their +useful feedback and their valuable help + + align:start position:0% +useful feedback and their valuable help + + + align:start position:0% +useful feedback and their valuable help +and finally for your attention yeah so + + align:start position:0% +and finally for your attention yeah so + + + align:start position:0% +and finally for your attention yeah so +we have a lot of this should be trap + + align:start position:0% +we have a lot of this should be trap + + + align:start position:0% +we have a lot of this should be trap +stiffness versus the this is the current + + align:start position:0% +stiffness versus the this is the current + + + align:start position:0% +stiffness versus the this is the current +and here actually I haven't shown that + + align:start position:0% +and here actually I haven't shown that + + + align:start position:0% +and here actually I haven't shown that +it's like the trap stiffness defers + + align:start position:0% +it's like the trap stiffness defers + + + align:start position:0% +it's like the trap stiffness defers +whether you look in the X direction or + + align:start position:0% +whether you look in the X direction or + + + align:start position:0% +whether you look in the X direction or +the Y direction the actual measurements + + align:start position:0% +the Y direction the actual measurements + + + align:start position:0% +the Y direction the actual measurements +are analog is because the mathematics is + + align:start position:0% +are analog is because the mathematics is + + + align:start position:0% +are analog is because the mathematics is +the same but as you can see here we have + + align:start position:0% +the same but as you can see here we have + + + align:start position:0% +the same but as you can see here we have +different data points for the two cases + + align:start position:0% +different data points for the two cases + + + align:start position:0% +different data points for the two cases +we account this into our considerations + + align:start position:0% +we account this into our considerations + + + align:start position:0% +we account this into our considerations +yes yes + + align:start position:0% + + + + align:start position:0% + +mmm + + align:start position:0% + + + + align:start position:0% + +well I mean the air case well I mean + + align:start position:0% +well I mean the air case well I mean + + + align:start position:0% +well I mean the air case well I mean +everything boils down to this this + + align:start position:0% +everything boils down to this this + + + align:start position:0% +everything boils down to this this +consideration here okay let me just find + + align:start position:0% +consideration here okay let me just find + + + align:start position:0% +consideration here okay let me just find +my explanation it boils down to the the + + align:start position:0% +my explanation it boils down to the the + + + align:start position:0% +my explanation it boils down to the the +viscosity that dominates so in our case + + align:start position:0% +viscosity that dominates so in our case + + + align:start position:0% +viscosity that dominates so in our case +we have the viscosity of water that + + align:start position:0% +we have the viscosity of water that + + + align:start position:0% +we have the viscosity of water that +dominates when you look in different + + align:start position:0% +dominates when you look in different + + + align:start position:0% +dominates when you look in different +mediums you might have different types + + align:start position:0% +mediums you might have different types + + + align:start position:0% +mediums you might have different types +of viscosity which would change the + + align:start position:0% +of viscosity which would change the + + + align:start position:0% +of viscosity which would change the +motions so I have the paper I I didn't + + align:start position:0% +motions so I have the paper I I didn't + + + align:start position:0% +motions so I have the paper I I didn't +actually read through the whole details + + align:start position:0% +actually read through the whole details + + + align:start position:0% +actually read through the whole details +of the how exactly the mathematics + + align:start position:0% +of the how exactly the mathematics + + + align:start position:0% +of the how exactly the mathematics +changes probably does also probably and + + align:start position:0% +changes probably does also probably and + + + align:start position:0% +changes probably does also probably and +other issues that are that may not arise + + align:start position:0% +other issues that are that may not arise + + + align:start position:0% +other issues that are that may not arise +or may arise is the laser like in this + + align:start position:0% +or may arise is the laser like in this + + + align:start position:0% +or may arise is the laser like in this +case like laser like heats up the the + + align:start position:0% +case like laser like heats up the the + + + align:start position:0% +case like laser like heats up the the +water but I don't know how exactly the + + align:start position:0% +water but I don't know how exactly the + + + align:start position:0% +water but I don't know how exactly the +laser would react with the air maybe + + align:start position:0% +laser would react with the air maybe + + + align:start position:0% +laser would react with the air maybe +it's going to heat up a little bit but + + align:start position:0% +it's going to heat up a little bit but + + + align:start position:0% +it's going to heat up a little bit but +how is this heat by going to be + + align:start position:0% +how is this heat by going to be + + + align:start position:0% +how is this heat by going to be +distributed in space I'm not very + + align:start position:0% +distributed in space I'm not very + + + align:start position:0% +distributed in space I'm not very +knowledgeable of this as it now + + align:start position:0% + + + + align:start position:0% + +so the equipartition theorem it breaks + + align:start position:0% +so the equipartition theorem it breaks + + + align:start position:0% +so the equipartition theorem it breaks +into components it breaks into the + + align:start position:0% +into components it breaks into the + + + align:start position:0% +into components it breaks into the +component of X where we have one degree + + align:start position:0% +component of X where we have one degree + + + align:start position:0% +component of X where we have one degree +of freedom and it breaks into the + + align:start position:0% +of freedom and it breaks into the + + + align:start position:0% +of freedom and it breaks into the +component of Y where have another degree + + align:start position:0% +component of Y where have another degree + + + align:start position:0% +component of Y where have another degree +of freedom + + align:start position:0% +of freedom + + + align:start position:0% +of freedom +each of these considerations is + + align:start position:0% +each of these considerations is + + + align:start position:0% +each of these considerations is +concerned only with in one movement so + + align:start position:0% +concerned only with in one movement so + + + align:start position:0% +concerned only with in one movement so +for the okay well you can think about it + + align:start position:0% +for the okay well you can think about it + + + align:start position:0% +for the okay well you can think about it +in this way we have two degrees of + + align:start position:0% +in this way we have two degrees of + + + align:start position:0% +in this way we have two degrees of +freedom in total but in the actual + + align:start position:0% +freedom in total but in the actual + + + align:start position:0% +freedom in total but in the actual +directions that are useful for our + + align:start position:0% +directions that are useful for our + + + align:start position:0% +directions that are useful for our +considerations we have only one degree + + align:start position:0% +considerations we have only one degree + + + align:start position:0% +considerations we have only one degree +of freedom so yeah well I think this is + + align:start position:0% +of freedom so yeah well I think this is + + + align:start position:0% +of freedom so yeah well I think this is +for this this is 3.2 microns and this + + align:start position:0% +for this this is 3.2 microns and this + + + align:start position:0% +for this this is 3.2 microns and this +like later on like you might you saw the + + align:start position:0% +like later on like you might you saw the + + + align:start position:0% +like later on like you might you saw the +1 microns + + align:start position:0% +1 microns + + + align:start position:0% +1 microns +I think our data is concerned with the + + align:start position:0% +I think our data is concerned with the + + + align:start position:0% +I think our data is concerned with the +3.2 microns we didn't I like my results + + align:start position:0% +3.2 microns we didn't I like my results + + + align:start position:0% +3.2 microns we didn't I like my results +are not related with the micron 1 micron + + align:start position:0% +are not related with the micron 1 micron + + + align:start position:0% +are not related with the micron 1 micron +we just played with it and try this we + + align:start position:0% +we just played with it and try this we + + + align:start position:0% +we just played with it and try this we +also tried the trapping cells from + + align:start position:0% +also tried the trapping cells from + + + align:start position:0% +also tried the trapping cells from +onions it was very fun to play with but + + align:start position:0% +onions it was very fun to play with but + + + align:start position:0% +onions it was very fun to play with but +unfortunately we couldn't get any like + + align:start position:0% +unfortunately we couldn't get any like + + + align:start position:0% +unfortunately we couldn't get any like +valuable quantitative results there so + + align:start position:0% +valuable quantitative results there so + + + align:start position:0% +valuable quantitative results there so +even though it's quite a lot of fun we + + align:start position:0% +even though it's quite a lot of fun we + + + align:start position:0% +even though it's quite a lot of fun we +have some clips it's not worth for this + + align:start position:0% +have some clips it's not worth for this + + + align:start position:0% +have some clips it's not worth for this +presentation which concentrates on the + + align:start position:0% +presentation which concentrates on the + + + align:start position:0% +presentation which concentrates on the +KB + + align:start position:0% + + + + align:start position:0% + +[Applause] \ No newline at end of file diff --git a/-S5GwNe0xXg.txt b/-S5GwNe0xXg.txt new file mode 100644 index 0000000000000000000000000000000000000000..e73d1505cfe981a60a2288de2bec559c94be9492 --- /dev/null +++ b/-S5GwNe0xXg.txt @@ -0,0 +1,2339 @@ +FEMALE SPEAKER: The following +content is provided under a + +Creative Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation or to view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: Hi. + +Our subject matter today +concerns that phase of + +calculus known as the +'indefinite integral', or the + +'antiderivative'. + +In terms of the concepts that +we've talked about so far in + +our course, and keeping in mind +that one concept with + +many applications is +educationally more meaningful + +than many concepts each with one +application, I prefer to + +call today's lesson the inverse +derivative, or inverse + +differentiation. + +And again, bring into play a +very well-known feature of our + +course, namely, our discussion +of inverse functions. + +Now, you see, the only problem +that comes up in this context + +is a rather simple one and that +is that all the time that + +we've been taking a derivative, +we may not have + +realized that we were using the +idea of a function in a + +rather different way. + +Namely, noticed that by taking +a derivative, we had a rule + +which told us how, given a +particular function, to assign + +to it a new function called +its 'derivative'. + +In other words, what we could +have done is to have + +visualized a different function +machine, which I will + +call the 'D-machine'. + +Hopefully, the 'D' will suggest +differentiation, where + +the domain of my the machine-- + +in other words, the input of +my 'D-machine' will be + +differentiable functions and the +output, you see, the image + +of my 'D-machine' will +be the derivative of + +that particular function. + +So in other words then, if we +want to use our typical + +notation, what we're +saying is that the + +'D-machine' does what? + +Given a differentiable function +as its input, the + +output will be the derivative +'f prime'. + +Now again, we're used to talking +about the derivative + +with respect to a +given variable. + +Unless otherwise specified, +the variable is 'x'. + +And so, perhaps with that in +mind, maybe it would be more + +suggestive if I were to do +something like this to + +indicate, you see, that the +input is 'f of x' and the + +output is 'f prime of x'. + +Now, you may recall also that +long before we started dealing + +with functions of real +variables, we discussed + +functions in general +in terms of circle + +diagrams and the like. + +In this respect, notice that +we can think of our + +'D-machine' as operating on a +particular domain, the domain + +being what? + +The set of all differentiable +functions. + +And the range, or the image, +will also be what? + +All functions which +are derivatives of + +differentiable functions. + +Now, what kind of a +function is 'D'? + +Don't lose track of the +fact that things like + +one-to-oneness and ontoness are +concepts that transcend + +dealing with numbers. + +They apply whenever +we're dealing with + +any kind of a function. + +The idea is something +like this. + +If 'x squared' were to go into +the 'D-machine', the output + +would be '2x'. + +See? 'x squared' is +mapped into '2x'. + +'x cubed' is mapped into +'3 x squared'. + +See, the derivative of 'x cubed' +with respect to 'x' is + +'3 x squared'. + +'x squared plus 7', also +mapped into '2x'. + +In other words, without going +any further, notice that + +whatever 'D' is, 'D' +is not 1 to 1. + +You see, two different functions +can have the same + +derivative. + +In fact, many different +functions can have the same + +derivative. + +For example, once we know that +the derivative of 'x squared' + +is '2x', we certainly know +that the derivative of 'x + +squared' plus any constant +is also '2x'. + +In other words then, we cannot +make an inverse function + +machine as things stand here. + +And why is that? + +To have an inverse function, +what you must be able to do is + +to reverse arrowheads and +still have a function. + +Notice that, in a way, 'D +inverse' would be a little bit + +of a tricky thing to +talk about here. + +But let's pretend that +we could anyway. + +In other words, what would go +wrong if we tried to build a + +'D' inverse machine? + +Well, in terms of the example +that we're talking about, if + +the input to the D inverse +machine happened to be '2x', + +then there would be infinitely +many different outputs that + +we're sure of. + +Namely what? + +Every function of the form +'x squared plus c' + +where 'c' is a constant. + +And what do I mean, we can +be sure of that many? + +You see, all I know going back +to this diagram here is that + +every function of the form 'x +squared plus c' will map into + +'2x' under the derivative +function. + +The other question that comes +up is, how do you know that + +you can find a function whose +derivative is '2x' that comes + +from a function which doesn't +have the form 'x + +squared plus c'? + +How do you know there isn't some +other function 'f of x' + +which has the property that +'f of x' maps into '2x'? + +In other words, the derivative +of 'f of x' is '2x' even + +though 'f of x' does not have +the form 'x squared plus c'. + +And this is exactly where the +mean value theorem comes in to + +help us over here. + +You see, what we're saying here +is, suppose that 'D' of + +'f of x' is '2x'. + +All we know is that when you +run 'f of x' through the + +'D-machine', you wind +up with '2x'. + +What does that mean? + +'f prime of x' is '2x'. + +Well, we know the derivative of +'x squared' is also '2x'. + +Therefore, whatever 'f of x' +is by the corollary to the + +mean value theorem that we've +studied before, since 'f of x' + +and 'x squared' have identical +derivatives, namely, they're + +both '2x', it means that they +must differ by a constant. + +In other words, 'f of x' minus +'x squared' is a constant. + +But to say that 'f of x' minus +'x squared' is a constant is + +the same as saying that 'f of +x' belongs to the family 'x + +squared plus c'. + +In other words, 'f +of x' equals 'x + +squared' plus a constant. + +What the mean value theorem +tells us is not only does + +every function of the form 'x +squared plus c' have its + +derivative equal to '2x' but +that every function whose + +derivative is '2x' has the +form 'x squared plus c'. + +To generalize this, consider +the following. + +Suppose we're given +'f of x', OK? + +And we now say, look, every +time you differentiate a + +function, if you add on a +constant, you don't change + +anything, meaning what? + +The derivative of +a constant is 0. + +In other words, what we're +saying is, if the derivative + +of 'f of x' is 'f prime of x', +any function of the form 'f of + +x' plus 'c' will have +the same derivative. + +And not only that, the only +function whose derivative is + +'f prime of x' must +be one of these. + +That's what this 'e +sub f' stands for. + +You see, what I'm really saying +here is that certainly + +when you change the constant, +you change the function. + +The point is, with respect +to the thing called the + +derivative, you cannot tell +the difference between two + +functions just by looking at +their derivatives if they + +differ by a constant. + +In other words, with respect +to differentiation, two + +functions which differ by a +constant are equivalent and + +that's why I invented this +notation, 'e of f'. + +All I'm saying is that if we +visualize now that the input + +of the 'D-machine' is not +individual functions but whole + +classes of functions-- + +in other words, such that they +differ only by a constant, + +then you see there is a +one-to-one correspondence + +between the input +and the output. + +Now that's a subtle point. + +It's a point which I'm sure +most of you will grasp. + +But more importantly, the +important thing is simply that + +once we've seen one function +with a given derivative, in a + +manner of speaking, we've +seen them all. + +In other words, we only have +enough leeway as to fool + +around with an arbitrary +constant. + +So let's generalize again. + +What do we mean by 'D inverse' +of 'f of x'? + +We mean what? + +The set of all function 'g of +x' whose derivative with + +respect to 'x' is the +given 'f of x'. + +See, that's exactly what the +inverse function means. + +And by the way, notice that +this tells me my set + +implicitly. + +Let me put that in parentheses +over here. + +Namely, suppose somebody says, +does 'g of x' belong to this + +particular set called +'D inverse'? + +All I have to do is +differentiate the given 'g' + +and see if I get 'f'. + +If I do, 'G' belongs +to the set. + +If I don't, it doesn't +belong to the set. + +But as we've so often stressed +about inverse functions, + +notice that the test to see +whether something belongs to + +'D inverse', it's sufficient to +know how to differentiate. + +By the way, to summarize what +we did before, to list this + +thing explicitly, notice that +what we're saying is, to find + +the set of all functions whose +derivative is little 'f of x', + +all we have to do is what? + +Find one function, capital +'F', whose derivative is + +little 'f'. + +And then our set, explicitly, +is what? + +The set of all functions of the +form capital 'F of x' plus + +'c' where 'c' is an arbitrary +constant. + +Now, I'm sure this +concept is not + +difficult for you to grasp. + +For those of you who have been +through calculus before, as + +our course is intended to be for +this type of person too, + +you see, you may not be familiar +with the notation, + +the 'D inverse' notation, which +I want to stress here. + +But the concept, I hope, is +clear in its own right. + +Now of course, you see, the +problem that comes up is that + +it's much easier to +differentiate a function than + +it is to be given a function and +then have to try to find + +what you have to differentiate +to get it. + +Without meaning it as +facetiously as it may sound, I + +use this in on many occasions, +I prefer to say is much + +easier, you see, to scramble an +egg than to unscramble one. + +Told what to differentiate, +that's easy enough to do. + +Given the derivative, that +may not be so easy. + +Let's look in terms +of an example. + +But this is, again, a very +nice teachers trick. + +To get the right answer, you +start with the answer and then + +work to the problem. + +I'll start with the function 'h +of x' equals 'x' times the + +'square root of 'x +squared plus 1''. + +Or written more conveniently in +exponential notation, 'x' + +times ''x squared plus +1' to the 1/2'. + +Let me differentiate that. + +Remember, this is a product. + +The derivative of a +product is what? + +It's the first factor which is +'x' times the derivative of + +the second. + +That means what? + +I bring the 1/2 down to a +power 1 less, times the + +derivative of what's inside +with respect to 'x'. + +See, the some old chain +rule again. + +That's '2x'. + +Then what? + +Plus the second factor, 'x +squared plus 1' to the 1/2 + +times the derivative of the +first with respect to 'x', + +which is 1. + +At any rate, simplifying, +bringing the minus 1/2 power + +into the denominator, then +putting everything over a + +common denominator, I wind up +with the fact that 'h prime of + +x' is '2 x squared plus 1' over +the 'square root of 'x + +squared plus 1''. + +I hope I haven't made a +careless error here. + +But again, one of the beauties +of the new mathematics is that + +it's the method that's +important, OK? + +Now, at any rate, +what do I know? + +Starting with 'h of x' equaling +'x' times the 'square + +root of 'x squared plus 1'', I +now know that its derivative + +is '2 x squared plus 1' over +the 'square root of 'x + +squared plus 1''. + +Let's write that in terms of +our 'D inverse' notation. + +Namely, what we're saying is +that 'x' times the 'square + +root of 'x squared plus 1'' +has the property that its + +derivative is '2 x squared plus +1' over the 'square root + +of 'x squared plus 1''. + +Consequently, every function +which has the property that + +its derivative is '2 x squared +plus 1' over the 'square root + +of 'x squared plus 1'' must +come from this family. + +You see? + +Everything of this form +we'll have its + +derivative equal to this. + +And secondly, any other function +cannot have its + +derivative equal to this by +our corollary to the mean + +value theorem. + +Now you see, what +I'm saying is-- + +and here's the beauty of what we +mean by inverse operations + +and the like. + +It's conceivable that you +might not have been + +sophisticated enough at this +stage in the game to have been + +able to deduce this had +we been given this. + +Notice that my cute trick was I +started with this, found out + +what the derivative +was, and then just + +inverted the emphasis. + +A change in emphasis again. + +However, notice the following. + +Suppose you weren't +able to find this. + +And somebody said to you, I +wonder if 'x' times the + +'square root of 'x squared plus +1'' is a function whose + +derivative is equal to this. + +And all I'm saying, without +going through the work again + +because I've already done that, +is to simply observe + +that even if you did not know +this explicit representation, + +by definition, 'D inverse' of '2 +x squared plus 1' over the + +'square root of 'x squared +plus 1'' is simply what? + +The set of all functions 'g of +x' such that 'g prime of x' is + +equal to '2 x squared plus 1' +over the 'square root of 'x + +squared plus 1''. + +In other words, given any +function at all, I could + +differentiate it. + +If the derivative came +out to be this, + +then I have a solution. + +It belongs to the +solution set. + +Otherwise, it doesn't. + +But again, notice that's to +solve any 'D inverse' problem, + +it's sufficient to understand a + +corresponding derivative property. + +In fact, maybe now is a good +time to show how we get + +certain recipes for 'D +inverse' type things. + +Let me just write down +a typical one. + +You see, 'D inverse of 'x to the +n'' is 'x to the 'n + 1'' + +over 'n + 1' plus a constant. + +And of course, observe that as +soon as you see something like + +this, you have to beware of +'n' equals negative 1. + +Otherwise we have +a 0 denominator. + +Now, a person says, this doesn't +look familiar to me. + +Again, keep in mind what +D inverse means. + +Essentially, to say this is just +a switch in emphasis from + +saying what? + +That if you run the family of +functions 'x to the 'n + 1'' + +over 'n + 1' plus a constant +through your 'D-machine', you + +get 'x to the n'. + +Or more familiarly, what? + +The derivative of any member in +this family is 'x to the n' + +provided that 'n' is not +equal to minus 1. + +Now again, this may look a +little bit abstract to you. + +So to avoid this problem, +let's just do a concrete + +illustration. + +Let's pick a particular +value of 'n' and + +work with this thing. + +Let's suppose we're told to +determine 'D inverse' + +of 'x to the 7th'. + +What does that mean? + +What it really means is, let's +find a function whose + +derivative is 'x to the 7th'. + +And why do I say let's +find a function? + +Because once I find a function, +all I have to do is + +tack on arbitrary constants and +the family that I get that + +way is the unique family of +functions which have this + +particular derivative. + +So I play the detective game. + +I know from differential +calculus that if I + +differentiate 'x' to the 8th +power, I'll wind up with the + +exponent 7, at least. + +In other words, the derivative +of 'x' to the 8th power. + +'D of 'x to the 8th'' is +'8 'x to the 7th''. + +Well, what answer did +I want to get? + +I wanted to get 'x to the 7th', +not '8 'x to the 7th''. + +So I fudge this thing +a little bit. + +I say, evidently what I should +have done was to have started + +with 1/8 as much. + +In other words, multiplying +equals by equals, I multiply + +both sides of this equation by +1/8 and I wind up with '1/8 D + +'x to the 8th'' equals +'x to the 7th'. + +And now comes a very +crucial step. + +And let me write that down +because I think it's something + +that we should pay very +close attention to. + +And that is that the derivative +has the property + +that if you want to +differentiate a constant times + +a function, you can take the +constant out and differentiate + +just the function. + +This is a very crucial point +because you see-- + +and by the way, notice that in +general, not all functions + +have this property. + +For example, if you're squaring +something, if you + +double the number that's being +squared, the output is 4 times + +as much because twice +something squared + +is 4 times as much. + +In other words, in general, +you do not say that if you + +double the input, you're going +to double the output. + +Not every function has +that property. + +But the function called 'D', the +derivative, does have this + +particular property. + +And you see, with that +in mind, I can + +bring this 1/8 inside. + +This is the key step, that 1/8 +times the derivative of 'x to + +the 8th' is a derivative of +''1/8' x to the 8th'. + +That's this key step +over here. + +And now, you see, putting all +this together, I find what? + +That the derivative of +''1/8' x to the 8th' + +is 'x to the 7th'. + +And therefore, since I found one +function whose derivative + +is 'x to the 7th', I have, in +a sense, found them all, + +namely, ''1/8' x to +the 8th' plus 'c'. + +In other words, that's what I +call the equivalent class of + +''1/8' x to the 8th'. + +All the functions that differ +from ''1/8' x to + +the 8th' by a constant. + +And again, to emphasize this +very important point, let me + +again mention, beware of +non-constant factors. + +Let me give you a +for instance. + +Let's suppose I take almost +the same problem. + +And that almost as +a big almost. + +Let's suppose I say, let me +find all functions whose + +derivative, say, is 'x squared +plus 1' to the 7th power. + +In other words, still something +to the 7th power. + +So I argue something like, +well, since whenever I + +differentiate I reduce the +exponent by 1, to wind up with + +a 7th power, maybe +I should have + +started with an 8th power. + +So I say, OK, that's +what I'll do. + +I'll start with an 8th power. + +So I say, OK, what is the +derivative of 'x squared plus + +1' to the 8th power? + +Now notice I know how to +differentiate, hopefully. + +And again, let me make this +point very strongly. + +There is no sense studying +inverse functions if we don't + +know the original +function itself. + +Because the whole purpose of the +inverse function, or the + +whole strategy behind it, is to +reduce it to the original + +function, namely, to switch +the emphasis. + +So at any rate, I differentiate +'x squared plus + +1' to the 8th power. + +I get '8 'x squared plus +1' to the 7th'. + +But now, by the chain rule, I +must remember that this part + +was only the derivative with +respect to 'x squared plus 1'. + +The correction factor is what? + +The derivative of what's inside +with respect to 'x'. + +That's '2x'. + +And so I wind up with that if +I differentiate ''x squared + +plus 1' to the 8th', I get '16x' +times ''x squared plus + +1' to the 7th'. + +Now, how much did +I want to get? + +I wanted to get just ''x squared +plus 1' to the 7th'. + +That put me off by a +factor of '16x'. + +Now I say, OK, I'll +fix that up. + +Namely, I'll divide both sides +by '16x', assuming, of course, + +that 'x' is not 0. + +And this, by the way, +is perfectly valid. + +I can now go from here to here +and say, look, '1 over 16x' + +times the derivative of ''x +squared plus 1' to the 8th' + +with respect to 'x' is ''x +squared plus 1' to the 7th'. + +However, notice that I cannot +take this factor and bring it + +inside here. + +And again, as I so often have +said, also, of course I can + +bring it inside here. + +I just did. + +What I mean is, I don't +get the right answer. + +And what's the best proof that +I don't get the right answer? + +Very, very simple. + +Take this function, +differentiate it, and see if + +you get ''x squared plus +1' to the 7th'. + +You won't, unless you +differentiate incorrectly. + +Don't be like the person who +just differentiates, brings + +the 8 down, replaces this by +1 less, multiplies by a + +derivative of what's inside, +and cancels everything out. + +Notice that the expression +inside the brackets that I've + +just circled is a quotient. + +And the derivative of a quotient +is obtained in a very + +special way. + +The denominator times the +derivative of the numerator + +minus the numerator times the +derivative of the denominator + +over the square of +the denominator. + +And all I'm saying is, you won't +get ''x squared plus 1' + +to the 7th' power +if you do that. + +Again, notice that you do not +have to know the right answer + +in order to see what answer +is wrong, OK? + +So this would be +a wrong answer. + +By the way, this would also be +a wrong answer because we've + +already seen that the derivative +of ''1/8' x squared + +plus 1' to the 8th +power is what? + +You bring the 8 down, which +kills off the 1/8. + +You replace this to a power of +one less, which gives you ''x + +squared plus 1' to the 7th'. + +But the correction factor here +is you must also multiply by a + +derivative of what's inside +with respect to 'x'. + +And that's to '2x'. + +In other words, you do +not get ''x squared + +plus 1' to the 7th'. + +What you do get is what? ''x +squared plus 1' to the 7th' + +times '2x'. + +And the question that may now +come up is, how come this + +worked when you were raising +'x' to the 8th power but it + +didn't work when you were +raising 'x squared plus 1' to + +the 8th power? + +Again, as always in these +cases, the answer is + +immediately available in +terms of derivatives. + +We can talk, in fact, about +the inverse chain rule. + +That when we really +talked about 'D'-- + +remember, we mentioned this at +the very beginning of the + +lecture, that the variable +inside the parentheses was the + +one with respect to which you +were differentiating. + +In other words, what we saw was +that if you wanted to get + +something to the 7th power, what +you had to differentiate + +was 1/8 that same something to +the 8th power if you were + +differentiating with respect +to that same variable. + +In other words, what would have +been ''x squared plus 1' + +to the 7th' would +have been what? + +If you would differentiating +not with respect to 'x' but + +with respect to 'x +squared plus 1'. + +See, what we really wanted when +we wrote this down was + +the derivative with +respect to 'x'. + +And even though this notation +may look a little bit strange + +to you, observe that once you +get used to the notation, this + +is just another way of talking +about the chain rule. + +Namely, to find the derivative +of this with respect to 'x', + +you first take the derivative +with respect to 'x squared + +plus 1' and then multiply that +by the derivative of 'x + +squared plus 1' with +respect to 'x'. + +And if we do that, you see, we +get the answer that we've + +talked about before. + +In other words, what we could +say is that the function that + +you have to differentiate to get +''x squared plus 1' to the + +7th' times '2x' is ''1/8' x +squared plus 1' to the 8th' + +plus a constant. + +And how do I know that? + +Well, the way I know that +is simply what? + +In terms of inverse functions, +I started with ''1/8' x + +squared plus 1' to the 8th', +differentiated it and found + +out I got ''x squared plus 1' +to the 7th' times '2x'. + +And so this became the recipe. + +And again, a rather interesting +aside, if you look + +at this, and look at this, it +would appear at first glance + +that the top one should be a +more difficult problem than + +the bottom one. + +The reason being that the input +seems more simple in the + +bottom one. + +Yet, the interesting point is +that the '2x', which seems to + +make this thing more +complicated, is precisely the + +factor you need by the chain +rule to make this thing work. + +Because when you differentiate +'x squared plus 1' to the 8th + +power, you're going to +get a factor of '2x' + +by the chain rule. + +Now again, the main aim of the +lectures is not to take the + +place of the computational +drill supplied in our + +exercises and in the +text but to give + +you sort of an insight. + +And they'll be plenty of drill +on the mechanics of this in + +our exercises on this section. + +Let me just at least continue +on with the + +concept of our recipes. + +For example, here's +another one. + +And this one says what? + +That if you run the sum of two +functions through the 'D + +inverse' machine, the output is +the same as if you sent the + +functions through separately +and then added them up, OK? + +I'll talk about that in +more detail later. + +Again, all I want to see is +that this is the analogous + +result of, again, a beautiful +property of the derivative. + +And that is that the derivative +of a sum is the sum + +of the derivatives. + +And how does that +work over here? + +Again, a very interesting +property throughout advanced + +calculus, linear algebra +and the like. + +These properties are +very, very special. + +And we'll have occasion, as the +course goes on, to talk + +about them more. + +For the time being, rather than +have you get lost in the + +maze of details, let me work +a specific illustration. + +Let's suppose I would like to +find the family of functions + +whose derivative is 'x to the +5th' plus 'x cubed', OK? + +Now, what I'm saying is this. + +By my previous result, I +certainly know how to find the + +function whose derivative is 'x +to the 5th', namely, ''1/6' + +x to the 6th'. + +I also know how to find the +function whose derivative is + +'x cubed', namely, '1/4' +x to the 4th'. + +Putting these two steps together +and say equals added + +to equals are equal, I can +conclude that 'D of ''1/6' x + +to the sixth'' plus 'D of ''1/4' +x to the fourth'' is 'x + +to the 5th' plus 'x cubed'. + +Now, the key step is that since +the derivative of a sum + +is the sum of the derivatives, +I can say that the sum of + +these two derivatives is the +derivative of the sum of the + +two functions. + +Namely, that this is what? + +'D of ''1/6' x to the 6th'' plus +''1/4' x to the 4th', a + +very important power and +property of the derivative. + +Therefore, have I found one +function whose derivative is + +'x to the 5th' plus 'x cubed'? + +The answer is yes. ''1/6' +x to the 6th' plus + +''1/4' x to the 4th'. + +Therefore, what is the family +of all functions whose + +derivative is 'x 5th' +plus 'x cubed'? + +And again, as before, the +answer is, take your one + +solution that you found, tack on +an arbitrary constant, and + +I suppose, technically speaking, +I should put the + +braces in here to indicate +that my solution is an + +infinite set, all belonging +to one family called an + +equivalent set of functions +because they have the same + +derivative. + +Well, let's continue +on and do a little + +bit more harder stuff. + +Remember, we talked about +implicit differentiation. + +Well, is there an analogue +to implicit 'D inverses'? + +You see, notice that in every +problem so far, when I wrote + +'D inverse', I was essentially +telling you explicitly what + +came out of the 'D-machine'. + +Now, suppose I twist the +emphasis a little bit. + +Suppose I tell you, look, I run +a certain function through + +the 'D-machine'. + +In other words, I form +its derivative. + +What the output is, is the +square of the reciprocal of + +the function. + +In other words, if 'g of x' +comes in, '1 over 'g of x'' + +squared comes out. + +And now the question is, what +is the function 'g of x'? + +And again, notice that if we +don't know what the right 'g + +of x', is you can certainly test +a given 'g of x' to see + +whether it's right or not. + +Namely, what could you do? + +You differentiate 'g of x', see +what you get, and if what + +you get isn't 1 over the square +of 'g of x', you've got + +the wrong answer. + +But the question that comes up +is, given this type of a + +problem, how do we handle it? + +See? + +In other words, where does the +inverse idea come in here? + +The implicit relationship that +'g of x' is determined by this + +particular property. + +And again, notice how we use +properties of derivatives. + +We're given that 'g prime of x' +is a synonym, identity, for + +'1 over 'g squared of x'. + +We can cross-multiply and we get +'g squared of x' times 'g + +prime of x' is identically +one. + +Now, if you're clever about +this-- and remember, notice + +this very, very importantly. + +For example, ordinary division +is the inverse of ordinary + +multiplication. + +Notice that to be really cute +in division, you have to be + +pretty cute in multiplication. + +Since all you're doing is +changing the emphasis, notice + +that to handle hard problems in +antiderivatives, you have + +to be able to handle tough +derivative problems. + +What I'm driving at is, you look +at something like this + +and begin to wonder, do you +know a function whose + +derivative is this? + +See? + +The idea is, if you're familiar +with your chain rule, + +what is the derivative +of 'g cubed of x'? + +To differentiate 'g cubed', +what do you do? + +You bring the 3 down to a +power 1 less times the + +derivative of 'g of x' +with respect to 'x'. + +That's your chain rule. + +That's 'g prime of x'. + +In other words, if you're clever +enough to see this, + +what you say here is, OK, now +I multiply both sides by 3. + +The left hand side is just the +derivative of 'g cubed of x'. + +The right hand side is the +derivative off '3x'. + +Therefore, whatever g of x +is, its cube has the same + +derivative with respect +to 'x' as '3x'. + +And we've already learned that +if two functions have + +identical derivatives, +they differ + +by, at most, a constant. + +Consequently, 'g cubed +of x' must equal + +'3x' plus some constant. + +In other words, 'g of x' is the +cube root of '3x plus c'. + +Now, time is running short in +terms of other things that I + +want to teach you in +today's lesson. + +Let me leave this, then, +just for you to check. + +Simply differentiate the cube +root of '3x plus c'. + +And make sure that when you get +that derivative, it does + +turn out to be '1 over +'g of x' squared'. + +As I say, it's a straightforward +demonstration. + +I leave the details to you. + +But the point that's really +important is that whenever you + +do get an answer-- + +the hard part is to +get the answer. + +Whenever you do get the answer, +you can check by means + +of just taking a derivative. + +Now, with all of this talk about +'D inverse' in mind, let + +me now go back to the more +traditional notation, the + +notation that you'll find in +most textbooks, the notation + +that, as I say, if you've had +calculus before, most likely, + +you're more familiar with. + +And that is the following, that +when we write 'D inverse' + +of 'f of x', the average +textbook writes + +a symbol like this. + +It's called the 'integral' +of 'f of x'. + +I will have later lectures to +bemoan this choice of notation + +from a different +point of view. + +But for the time being, all +we're saying is, instead of + +writing 'D inverse'-- + +again, what's in the name? + +Just use this particular +notation. + +That when you see this +particular thing, perhaps read + +this as what? + +That this particular symbol is a +code to tell you to find all + +functions whose derivative +is 'f of x'. + +And by the way, to summarize +the results that we've + +obtained so far, let me just +rewrite some of these basic + +results in terms of the more +traditional notation. + +When you write this, this is +called the 'indefinite + +integral' and what we're saying +is the indefinite + +integral of ''x to the n' dx' is +'x to the 'n + 1'' over 'n + ++ 1' plus a constant when it +is not equal to minus 1. + +The integral of a sum is the +sum of the integrals. + +And the integral of a constant +times a function is a constant + +times the integral. + +All this says is what? + +That this is a consequent of the +fact that the derivative + +of the sum is the sum +of the derivatives. + +This is a consequent of the fact +that the derivative of a + +constant times a function is +the constant times the + +derivative of the function. + +And again, all this is, same +thing we were talking about + +before only with the 'D inverse' +notation replaced by + +the more common indefinite +integral. + +Now, we come to one more problem +which will finish us + +up for the day, once we get +through talking about it. + +And that's this. + +If all this means is find the +functions whose derivative is + +'f of x', why write this +notation here? + +Why couldn't we have just +written, for example, the + +so-called integral sign with +a little 'x' underneath? + +You see, we've talked about +misleading notations before. + +You see, in terms of our +differential notation, when + +you see ''f of x' dx', you have +every right to think of a + +differential. + +Now, in all fairness, the +chances are that this notation + +would not have been invented +if there weren't some + +connection between derivatives +and differentials. + +So let me mention this point. + +Going back as if we were +starting the lecture all over + +again, could I have invented a +different machine, which I'll + +call the 'script D- machine'? + +In other words, I don't want +to call it the same + +'D-machine' as before because +now it's going to have a + +different set of outputs. + +You see, now the input +will still be + +differentiable functions. + +But the output, instead of being +the derivative of the + +function, will be the +differential of the function. + +For example, before, +we said what? + +If 'x squared' goes in, the +output would be '2x'. + +With the script 'D-machine', the +output would be '2x dx'. + +Now, even though these machines +are different because + +one machine gives you a +differential as an output and + +the other gives you a derivative +as an output, + +notice that they +are equivalent. + +Namely, knowing the +differential, we can pin down + +the function the same as when +we knew the derivative. + +Now, the question that comes up +is, why should we use this + +particular type of notation? + +And to use the examples that are +most prevalent in the text + +and also in our notes, let me +give you the same problem that + +we've done before, +but now from a + +different point of view. + +Suppose we're still given the +problem 'g prime of x' equals + +'1 over 'g of x' squared'. + +We say, OK, let 'y' +equal 'g of x'. + +When we do that, this problem +now translates into what? + +'dy dx' equals '1 over +'y squared''. + +Now, if we allow ourselves to +use the differential notation, + +which we justified in previous +lectures, this says what? + +Cross-multiplying ''y squared' +dy' equals 'dx'. + +Notice, by the way, that 'y' is +implicitly a differentiable + +function of 'x'. + +So what we're saying over here +is, look, here are two + +functions which have the same +differential, therefore, if we + +integrate them, they differ +by a constant. + +Well, to mimic what we were +doing before, let's just say-- + +let's see, this, I +think, I have a + +little bit twisted here. + +If ''y squared' dy' equals +'3x', '3 'y squared' dy' + +equals '3dx'. + +If the differentials are equal, +then the functions + +differ by a constant. + +But 'y cubed' is the function +whose differential is '3 'y + +squared' dy'. + +'3x' is the function whose +differential is '3dx'. + +And we wind up with 'y cubed' +equals '3x + c', or, 'y' + +equals the 'cube root +of '3x + c''. + +By the way, let me just pull +this board down so that we can + +make a little bit of +a comparison here. + +You see, notice that in using +this differential notation, + +which allowed us to use some +nice algebraic devices and + +didn't seem quite as difficult +for us to recognize certain + +things, I hope you notice +that there seems to be a + +correspondence between the steps +that we had here and the + +steps that took place +over here. + +In other words, having done at +the so-called rigorous way, + +notice that differentials +give us a very nice, + +intuitively-simpler technique +for solving certain types of + +problems when we have implicit +relationships + +between 'y' and 'x'. + +And so, just to illustrate +this in terms of one more + +problem, let's take one that's +fairly geometric. + +Let's suppose we're given +the following problem. + +'dy dx' is 'minus x' over 'y' +and we know that when 'x' + +equals 3, 'y' equals 4. + +Using the language of +differentials, what we would + +do over here is we would +cross-multiply. + +Whatever you want to do. + +we recognize that, to get '2y', +you must differentiate + +'y squared'. + +This is a step you don't +really need. + +I don't care how you +want to do this. + +All I'm saying is that from this +step, I can get to here. + +Recognizing that y squared has +'2y dy' as its differential + +and that ''minus 'x squared'' +has 'minus 2x dx' as its + +differential, I know that 'y +squared' is equal to ''minus + +'x squared'' plus a constant. + +I transpose. + +I get that 'x squared' plus +'y squared' is a constant. + +Knowing that when 'x' equals +3, 'y' equals 4, I can + +determine that the constant must +be 25 when 'x' equals 3 + +and 'y' is 4. + +But since it's a constant, if +it's 25 when 'x' equals 3 and + +'y' equals 4, it's +25 everyplace. + +And again, if you want a +geometric interpretation of + +this, the circle centered at the +origin with radius equal + +to 5 is the only curve in the +whole world whose derivative + +at any given point is the +negative of the x-coordinate + +over the y-coordinate +and passes through + +the point (3 , 4). + +And if you want to see that +geometrically, let me just + +take a second here. + +You see, notice that any point +on the circle (x , y), notice + +that the tangent line to the +curve, which has slope 'dy + +dx', is what? + +Perpendicular to the +radius, again. + +The radius has slope +'y' over 'x'. + +And to be perpendicular-- + +if two lines are perpendicular, +their slopes + +are negative reciprocals. + +This is this particular +problem. + +And now, all I wanted to show +you is that if you're nervous + +about differentials and you +don't like to use them, notice + +that the same problem could +have been stated without + +differentials. + +Namely, we are thinking of a +function which we'll call 'g + +of x' such that the derivative +of 'g of x' is 'minus + +x' over 'g of x'. + +In other words, if the input of +the 'D-machine' is 'g', the + +output is 'minus x' over 'g'. + +And we also know that when 'x' +equals 3, the output is 4. + +So to 'g' of 3 equals 4. + +And without going through the +great details here, let's just + +notice that we could + +cross-multiply the same as before. + +We could multiply both sides +by 2, the same as before. + +We could recognize that the +left-hand side was the + +derivative of ''g of x' +squared', that the right-hand + +side is the derivative of +'minus 'x squared''. + +Therefore, since they have the +same identical derivatives, + +they must differ +by a constant. + +OK. + +We actually have plus or minus +here, but notice the fact that + +when the input is 3, the output +is 4 means that we're + +on the positive branch of +the curve, et cetera. + +I say et cetera not because +these points aren't important + +but because every point that +comes up now has already been + +discussed under the heading +of differential calculus. + +In other words, that the inverse +of differentiation can + +be handled very, very neatly +just by knowing + +differentiation with a +switch in emphasis. + +Why do we want to know this +particular topic? + +Well, because in many cases, to +look at it geometrically, + +in the past, we were +given the curve. + +We wanted to find out +what the slope was. + +In many physical applications, +we are, in a sense, told what + +the slope is and have to figure +out what the curve is. + +Hence the motivation. + +Well, at any rate, there'll be +more about this in the text + +and in our exercises. + +So until next time, good bye. + +MALE SPEAKER: Funding for the +publication of this video was + +provided by the Gabriella and +Paul Rosenbaum Foundation. + +Help OCW continue to provide +free and open access to MIT + +courses by making a donation +at ocw.mit.edu/donate. \ No newline at end of file diff --git a/-XGDKoWi0Zg.txt b/-XGDKoWi0Zg.txt new file mode 100644 index 0000000000000000000000000000000000000000..81020faed24733978eb1a18fb0ee1e57b365fc4e --- /dev/null +++ b/-XGDKoWi0Zg.txt @@ -0,0 +1,16355 @@ +align:start position:0% + +okay uh so uh let me get started uh + + align:start position:0% +okay uh so uh let me get started uh + + + align:start position:0% +okay uh so uh let me get started uh +today uh I'm going to be talking about + + align:start position:0% +today uh I'm going to be talking about + + + align:start position:0% +today uh I'm going to be talking about +auctions and let me sort of say that + + align:start position:0% +auctions and let me sort of say that + + + align:start position:0% +auctions and let me sort of say that +this lecture is going to be a you know + + align:start position:0% +this lecture is going to be a you know + + + align:start position:0% +this lecture is going to be a you know +there's a lot of math on the slides this + + align:start position:0% +there's a lot of math on the slides this + + + align:start position:0% +there's a lot of math on the slides this +you know I like to have lectures where + + align:start position:0% +you know I like to have lectures where + + + align:start position:0% +you know I like to have lectures where +sort of you sort of watch everything and + + align:start position:0% +sort of you sort of watch everything and + + + align:start position:0% +sort of you sort of watch everything and +you understand understand it today there + + align:start position:0% +you understand understand it today there + + + align:start position:0% +you understand understand it today there +are going to be sort of some of those + + align:start position:0% +are going to be sort of some of those + + + align:start position:0% +are going to be sort of some of those +slides that you'd sort of just look at + + align:start position:0% +slides that you'd sort of just look at + + + align:start position:0% +slides that you'd sort of just look at +them at home afterwards to try to get + + align:start position:0% +them at home afterwards to try to get + + + align:start position:0% +them at home afterwards to try to get +how I'm doing some of the derivations + + align:start position:0% +how I'm doing some of the derivations + + + align:start position:0% +how I'm doing some of the derivations +but um you know anyway you know we're + + align:start position:0% +but um you know anyway you know we're + + + align:start position:0% +but um you know anyway you know we're +used to and I think we've been almost + + align:start position:0% +used to and I think we've been almost + + + align:start position:0% +used to and I think we've been almost +all the Cs we've been sort of talking + + align:start position:0% +all the Cs we've been sort of talking + + + align:start position:0% +all the Cs we've been sort of talking +about firms and the firms have been + + align:start position:0% +about firms and the firms have been + + + align:start position:0% +about firms and the firms have been +setting prices and the the firms have + + align:start position:0% +setting prices and the the firms have + + + align:start position:0% +setting prices and the the firms have +been setting prices to maximize profits + + align:start position:0% +been setting prices to maximize profits + + + align:start position:0% +been setting prices to maximize profits +or some kind of oligopoly + + align:start position:0% +or some kind of oligopoly + + + align:start position:0% +or some kind of oligopoly +competition you know there are many real + + align:start position:0% +competition you know there are many real + + + align:start position:0% +competition you know there are many real +world applications where firms do not + + align:start position:0% +world applications where firms do not + + + align:start position:0% +world applications where firms do not +set prices and in fir instead firms use + + align:start position:0% +set prices and in fir instead firms use + + + align:start position:0% +set prices and in fir instead firms use +auctions uh as a mechanism + + align:start position:0% +auctions uh as a mechanism + + + align:start position:0% +auctions uh as a mechanism +uh to to set prices you know three of + + align:start position:0% +uh to to set prices you know three of + + + align:start position:0% +uh to to set prices you know three of +the sort of biggest applications uh + + align:start position:0% +the sort of biggest applications uh + + + align:start position:0% +the sort of biggest applications uh +government procurement like you know + + align:start position:0% +government procurement like you know + + + align:start position:0% +government procurement like you know +whenever the government is sort of + + align:start position:0% +whenever the government is sort of + + + align:start position:0% +whenever the government is sort of +hiring contractors to pave roads or fix + + align:start position:0% +hiring contractors to pave roads or fix + + + align:start position:0% +hiring contractors to pave roads or fix +Bridges or things like that these are + + align:start position:0% +Bridges or things like that these are + + + align:start position:0% +Bridges or things like that these are +usually done through procurement + + align:start position:0% +usually done through procurement + + + align:start position:0% +usually done through procurement +auctions where the government sort of + + align:start position:0% +auctions where the government sort of + + + align:start position:0% +auctions where the government sort of +asks firms to submit bids for how much + + align:start position:0% +asks firms to submit bids for how much + + + align:start position:0% +asks firms to submit bids for how much +they would need to charge to pay a road + + align:start position:0% +they would need to charge to pay a road + + + align:start position:0% +they would need to charge to pay a road +and then and then the uh choose the + + align:start position:0% +and then and then the uh choose the + + + align:start position:0% +and then and then the uh choose the +winning bidder to be the lowest bidder + + align:start position:0% +winning bidder to be the lowest bidder + + + align:start position:0% +winning bidder to be the lowest bidder +um uh in financial markets you know the + + align:start position:0% +um uh in financial markets you know the + + + align:start position:0% +um uh in financial markets you know the +US auction treasury bills and treasury + + align:start position:0% +US auction treasury bills and treasury + + + align:start position:0% +US auction treasury bills and treasury +bills are trillions of dollars and so + + align:start position:0% +bills are trillions of dollars and so + + + align:start position:0% +bills are trillions of dollars and so +they're trillions of dollars in auctions + + align:start position:0% +they're trillions of dollars in auctions + + + align:start position:0% +they're trillions of dollars in auctions +and that thing um online + + align:start position:0% +and that thing um online + + + align:start position:0% +and that thing um online +advertising uh is also absolutely + + align:start position:0% +advertising uh is also absolutely + + + align:start position:0% +advertising uh is also absolutely +enormous if you know every every time + + align:start position:0% +enormous if you know every every time + + + align:start position:0% +enormous if you know every every time +you're looking at a computer screen and + + align:start position:0% +you're looking at a computer screen and + + + align:start position:0% +you're looking at a computer screen and +you see sort of some ads on the page or + + align:start position:0% +you see sort of some ads on the page or + + + align:start position:0% +you see sort of some ads on the page or +whatever whether it's a news site or or + + align:start position:0% +whatever whether it's a news site or or + + + align:start position:0% +whatever whether it's a news site or or +a search engine or whatever almost all + + align:start position:0% +a search engine or whatever almost all + + + align:start position:0% +a search engine or whatever almost all +those ads these days are being auctioned + + align:start position:0% +those ads these days are being auctioned + + + align:start position:0% +those ads these days are being auctioned +off rather than being sold because it's + + align:start position:0% +off rather than being sold because it's + + + align:start position:0% +off rather than being sold because it's +just very hard to know what the price is + + align:start position:0% +just very hard to know what the price is + + + align:start position:0% +just very hard to know what the price is +what is it worth to sort of show you and + + align:start position:0% +what is it worth to sort of show you and + + + align:start position:0% +what is it worth to sort of show you and +AD at a particular point in time and so + + align:start position:0% +AD at a particular point in time and so + + + align:start position:0% +AD at a particular point in time and so +there sort of auction mechanisms are + + align:start position:0% +there sort of auction mechanisms are + + + align:start position:0% +there sort of auction mechanisms are +setting the prices um you know there + + align:start position:0% +setting the prices um you know there + + + align:start position:0% +setting the prices um you know there +have been uh lots of academic research + + align:start position:0% +have been uh lots of academic research + + + align:start position:0% +have been uh lots of academic research +in the past few decades I think one of + + align:start position:0% +in the past few decades I think one of + + + align:start position:0% +in the past few decades I think one of +the reasons why people in IO like this + + align:start position:0% +the reasons why people in IO like this + + + align:start position:0% +the reasons why people in IO like this +is because you know we always like to + + align:start position:0% +is because you know we always like to + + + align:start position:0% +is because you know we always like to +sort of like write down models and have + + align:start position:0% +sort of like write down models and have + + + align:start position:0% +sort of like write down models and have +these sort of mathematical models that + + align:start position:0% +these sort of mathematical models that + + + align:start position:0% +these sort of mathematical models that +shed Clarity on something and often in + + align:start position:0% +shed Clarity on something and often in + + + align:start position:0% +shed Clarity on something and often in +many other applications we're sort of + + align:start position:0% +many other applications we're sort of + + + align:start position:0% +many other applications we're sort of +making up the model and making up the + + align:start position:0% +making up the model and making up the + + + align:start position:0% +making up the model and making up the +game that people are playing in auctions + + align:start position:0% +game that people are playing in auctions + + + align:start position:0% +game that people are playing in auctions +it's very clear that there is a real + + align:start position:0% +it's very clear that there is a real + + + align:start position:0% +it's very clear that there is a real +game and you can see the game that + + align:start position:0% +game and you can see the game that + + + align:start position:0% +game and you can see the game that +people are playing it helps you could + + align:start position:0% +people are playing it helps you could + + + align:start position:0% +people are playing it helps you could +sort of do this nice connection between + + align:start position:0% +sort of do this nice connection between + + + align:start position:0% +sort of do this nice connection between +Theory and empirics and in terms of you + + align:start position:0% +Theory and empirics and in terms of you + + + align:start position:0% +Theory and empirics and in terms of you +know what's happened in IO this really + + align:start position:0% +know what's happened in IO this really + + + align:start position:0% +know what's happened in IO this really +sort of grew in the um I guess that was + + align:start position:0% +sort of grew in the um I guess that was + + + align:start position:0% +sort of grew in the um I guess that was +in the 1990s or early 2000s when uh you + + align:start position:0% +in the 1990s or early 2000s when uh you + + + align:start position:0% +in the 1990s or early 2000s when uh you +know formerly you know the sort of + + align:start position:0% +know formerly you know the sort of + + + align:start position:0% +know formerly you know the sort of +Airwaves that are used for cell phone + + align:start position:0% +Airwaves that are used for cell phone + + + align:start position:0% +Airwaves that are used for cell phone +signals and for TV licenses and things + + align:start position:0% +signals and for TV licenses and things + + + align:start position:0% +signals and for TV licenses and things +like that in the old days those were + + align:start position:0% +like that in the old days those were + + + align:start position:0% +like that in the old days those were +simply given away by the government and + + align:start position:0% +simply given away by the government and + + + align:start position:0% +simply given away by the government and +if you the government gave you one of + + align:start position:0% +if you the government gave you one of + + + align:start position:0% +if you the government gave you one of +the three licenses to to conduct + + align:start position:0% +the three licenses to to conduct + + + align:start position:0% +the three licenses to to conduct +television in a city you would make + + align:start position:0% +television in a city you would make + + + align:start position:0% +television in a city you would make +enormous amounts of money + + align:start position:0% +enormous amounts of money + + + align:start position:0% +enormous amounts of money +um at some point the government decided + + align:start position:0% +um at some point the government decided + + + align:start position:0% +um at some point the government decided +to shift and sort of auction off the + + align:start position:0% +to shift and sort of auction off the + + + align:start position:0% +to shift and sort of auction off the +right to provide cellular telephone + + align:start position:0% +right to provide cellular telephone + + + align:start position:0% +right to provide cellular telephone +service or auction off the right to to + + align:start position:0% +service or auction off the right to to + + + align:start position:0% +service or auction off the right to to +send TV signals over the air you know + + align:start position:0% +send TV signals over the air you know + + + align:start position:0% +send TV signals over the air you know +those auctions raised tens of billions + + align:start position:0% +those auctions raised tens of billions + + + align:start position:0% +those auctions raised tens of billions +of dollars therefore people wanted to + + align:start position:0% +of dollars therefore people wanted to + + + align:start position:0% +of dollars therefore people wanted to +hire lots of auction theorists to to + + align:start position:0% +hire lots of auction theorists to to + + + align:start position:0% +hire lots of auction theorists to to +work on the auctions and design the + + align:start position:0% +work on the auctions and design the + + + align:start position:0% +work on the auctions and design the +auctions for them they raised a lot of + + align:start position:0% +auctions for them they raised a lot of + + + align:start position:0% +auctions for them they raised a lot of +interest more recently the sort of + + align:start position:0% +interest more recently the sort of + + + align:start position:0% +interest more recently the sort of +online advertising example again it's + + align:start position:0% +online advertising example again it's + + + align:start position:0% +online advertising example again it's +it's just there's uh you know + + align:start position:0% +it's just there's uh you know + + + align:start position:0% +it's just there's uh you know +tremendously complex auctions that you + + align:start position:0% +tremendously complex auctions that you + + + align:start position:0% +tremendously complex auctions that you +can run to auction advertise Ing and it + + align:start position:0% +can run to auction advertise Ing and it + + + align:start position:0% +can run to auction advertise Ing and it +spurred a lot of interest there's also + + align:start position:0% +spurred a lot of interest there's also + + + align:start position:0% +spurred a lot of interest there's also +been a big literature on structural + + align:start position:0% +been a big literature on structural + + + align:start position:0% +been a big literature on structural +estimation of auctions and uh mostly + + align:start position:0% +estimation of auctions and uh mostly + + + align:start position:0% +estimation of auctions and uh mostly +tobas is going to do that on on in uh uh + + align:start position:0% +tobas is going to do that on on in uh uh + + + align:start position:0% +tobas is going to do that on on in uh uh +in Wednesday's lecture okay so I'm going + + align:start position:0% +in Wednesday's lecture okay so I'm going + + + align:start position:0% +in Wednesday's lecture okay so I'm going +to start with what's not a great model + + align:start position:0% +to start with what's not a great model + + + align:start position:0% +to start with what's not a great model +for applications but it's sort of a + + align:start position:0% +for applications but it's sort of a + + + align:start position:0% +for applications but it's sort of a +great model for solving the model and + + align:start position:0% +great model for solving the model and + + + align:start position:0% +great model for solving the model and +getting insights from it so it's sort of + + align:start position:0% +getting insights from it so it's sort of + + + align:start position:0% +getting insights from it so it's sort of +a special case but I I will sort of do a + + align:start position:0% +a special case but I I will sort of do a + + + align:start position:0% +a special case but I I will sort of do a +lot of my analysis in the independent + + align:start position:0% +lot of my analysis in the independent + + + align:start position:0% +lot of my analysis in the independent +private values model so here we have um + + align:start position:0% +private values model so here we have um + + + align:start position:0% +private values model so here we have um +biders indexed by I equals 1 to n + + align:start position:0% +biders indexed by I equals 1 to n + + + align:start position:0% +biders indexed by I equals 1 to n +there's one object to be sold um so you + + align:start position:0% +there's one object to be sold um so you + + + align:start position:0% +there's one object to be sold um so you +can think of this as people they're you + + align:start position:0% +can think of this as people they're you + + + align:start position:0% +can think of this as people they're you +know at a charity fundraiser and they're + + align:start position:0% +know at a charity fundraiser and they're + + + align:start position:0% +know at a charity fundraiser and they're +auctioning off a bottle of wine and + + align:start position:0% +auctioning off a bottle of wine and + + + align:start position:0% +auctioning off a bottle of wine and +whoever wins the auction is going to + + align:start position:0% +whoever wins the auction is going to + + + align:start position:0% +whoever wins the auction is going to +take the bottle of wine and drink it or + + align:start position:0% +take the bottle of wine and drink it or + + + align:start position:0% +take the bottle of wine and drink it or +something like that um each bidder + + align:start position:0% +something like that um each bidder + + + align:start position:0% +something like that um each bidder +observes a signal SI that relates to + + align:start position:0% +observes a signal SI that relates to + + + align:start position:0% +observes a signal SI that relates to +their value we're going to assume that + + align:start position:0% +their value we're going to assume that + + + align:start position:0% +their value we're going to assume that +these signals are independent across + + align:start position:0% +these signals are independent across + + + align:start position:0% +these signals are independent across +biders the term private values means + + align:start position:0% +biders the term private values means + + + align:start position:0% +biders the term private values means +that I know what the good is is worth to + + align:start position:0% +that I know what the good is is worth to + + + align:start position:0% +that I know what the good is is worth to +me my value is a function only of my own + + align:start position:0% +me my value is a function only of my own + + + align:start position:0% +me my value is a function only of my own +signal not of everybody else's signal so + + align:start position:0% +signal not of everybody else's signal so + + + align:start position:0% +signal not of everybody else's signal so +I know I'm an expert in wine I see the + + align:start position:0% +I know I'm an expert in wine I see the + + + align:start position:0% +I know I'm an expert in wine I see the +wine I see the label I just know how + + align:start position:0% +wine I see the label I just know how + + + align:start position:0% +wine I see the label I just know how +much I'm going to enjoy drinking that + + align:start position:0% +much I'm going to enjoy drinking that + + + align:start position:0% +much I'm going to enjoy drinking that +bottle of wine so my value depends only + + align:start position:0% +bottle of wine so my value depends only + + + align:start position:0% +bottle of wine so my value depends only +on my own uh signal um once you make the + + align:start position:0% +on my own uh signal um once you make the + + + align:start position:0% +on my own uh signal um once you make the +sort of decision that once once you have + + align:start position:0% +sort of decision that once once you have + + + align:start position:0% +sort of decision that once once you have +the private values model where your + + align:start position:0% +the private values model where your + + + align:start position:0% +the private values model where your +value only depends on your own signal + + align:start position:0% +value only depends on your own signal + + + align:start position:0% +value only depends on your own signal +it's without without loss of generality + + align:start position:0% +it's without without loss of generality + + + align:start position:0% +it's without without loss of generality +just sort of say the signal is your + + align:start position:0% +just sort of say the signal is your + + + align:start position:0% +just sort of say the signal is your +value um so that's what we're going to + + align:start position:0% +value um so that's what we're going to + + + align:start position:0% +value um so that's what we're going to +typically do is everyone just observes + + align:start position:0% +typically do is everyone just observes + + + align:start position:0% +typically do is everyone just observes +their own value uh we're going to assume + + align:start position:0% +their own value uh we're going to assume + + + align:start position:0% +their own value uh we're going to assume +that bidder is a risk neutral that is + + align:start position:0% +that bidder is a risk neutral that is + + + align:start position:0% +that bidder is a risk neutral that is +you get a value of s minus P if you win + + align:start position:0% +you get a value of s minus P if you win + + + align:start position:0% +you get a value of s minus P if you win +the auction at a price of P if you were + + align:start position:0% +the auction at a price of P if you were + + + align:start position:0% +the auction at a price of P if you were +to lose and be forced to pay P either as + + align:start position:0% +to lose and be forced to pay P either as + + + align:start position:0% +to lose and be forced to pay P either as +an entry fee or something else then your + + align:start position:0% +an entry fee or something else then your + + + align:start position:0% +an entry fee or something else then your +utility would be negative P okay and the + + align:start position:0% +utility would be negative P okay and the + + + align:start position:0% +utility would be negative P okay and the +biders are only going to observe their + + align:start position:0% +biders are only going to observe their + + + align:start position:0% +biders are only going to observe their +signal um this is also a model that + + align:start position:0% +signal um this is also a model that + + + align:start position:0% +signal um this is also a model that +people use for procurement auctions if + + align:start position:0% +people use for procurement auctions if + + + align:start position:0% +people use for procurement auctions if +you think about it like you have a um uh + + align:start position:0% +you think about it like you have a um uh + + + align:start position:0% +you think about it like you have a um uh +government is inviting contractors to + + align:start position:0% +government is inviting contractors to + + + align:start position:0% +government is inviting contractors to +bid on repaving Memorial Drive you can + + align:start position:0% +bid on repaving Memorial Drive you can + + + align:start position:0% +bid on repaving Memorial Drive you can +think of the S as the amount of money + + align:start position:0% +think of the S as the amount of money + + + align:start position:0% +think of the S as the amount of money +that will cost uh The Firm to do the + + align:start position:0% +that will cost uh The Firm to do the + + + align:start position:0% +that will cost uh The Firm to do the +paving job so that's uh and so and S is + + align:start position:0% +paving job so that's uh and so and S is + + + align:start position:0% +paving job so that's uh and so and S is +obviously a big negative number that + + align:start position:0% +obviously a big negative number that + + + align:start position:0% +obviously a big negative number that +like if you're asked to PVE a road it + + align:start position:0% +like if you're asked to PVE a road it + + + align:start position:0% +like if you're asked to PVE a road it +will cost you $2.7 million so that s is + + align:start position:0% +will cost you $2.7 million so that s is + + + align:start position:0% +will cost you $2.7 million so that s is +therefore for negative $2.7 million and + + align:start position:0% +therefore for negative $2.7 million and + + + align:start position:0% +therefore for negative $2.7 million and +then what you're bidding is you're + + align:start position:0% +then what you're bidding is you're + + + align:start position:0% +then what you're bidding is you're +bidding a price uh the price is going to + + align:start position:0% +bidding a price uh the price is going to + + + align:start position:0% +bidding a price uh the price is going to +be negative like the price could be $3 + + align:start position:0% +be negative like the price could be $3 + + + align:start position:0% +be negative like the price could be $3 +million and so if the if the price of of + + align:start position:0% +million and so if the if the price of of + + + align:start position:0% +million and so if the if the price of of +the of getting getting the contract is3 + + align:start position:0% +the of getting getting the contract is3 + + + align:start position:0% +the of getting getting the contract is3 +million your cost is -2.7 million you + + align:start position:0% +million your cost is -2.7 million you + + + align:start position:0% +million your cost is -2.7 million you +get 300,000 in + + align:start position:0% +get 300,000 in + + + align:start position:0% +get 300,000 in +profits + + align:start position:0% +profits + + + align:start position:0% +profits +um okay first auction that's considered + + align:start position:0% +um okay first auction that's considered + + + align:start position:0% +um okay first auction that's considered +Always by theorists not so often used in + + align:start position:0% +Always by theorists not so often used in + + + align:start position:0% +Always by theorists not so often used in +practice is the second price sealed bid + + align:start position:0% +practice is the second price sealed bid + + + align:start position:0% +practice is the second price sealed bid +auction uh in the second price sealed + + align:start position:0% +auction uh in the second price sealed + + + align:start position:0% +auction uh in the second price sealed +bit auction what you would do is you'd + + align:start position:0% +bit auction what you would do is you'd + + + align:start position:0% +bit auction what you would do is you'd +have every contractor say I will pay the + + align:start position:0% +have every contractor say I will pay the + + + align:start position:0% +have every contractor say I will pay the +road for 2.5 million I will have pay the + + align:start position:0% +road for 2.5 million I will have pay the + + + align:start position:0% +road for 2.5 million I will have pay the +road for 2.7 I would do it for 2.8 + + align:start position:0% +road for 2.7 I would do it for 2.8 + + + align:start position:0% +road for 2.7 I would do it for 2.8 +everyone just puts their bid in an + + align:start position:0% +everyone just puts their bid in an + + + align:start position:0% +everyone just puts their bid in an +envelope seals it they're all handed in + + align:start position:0% +envelope seals it they're all handed in + + + align:start position:0% +envelope seals it they're all handed in +and then on the day of the auction all + + align:start position:0% +and then on the day of the auction all + + + align:start position:0% +and then on the day of the auction all +the envelopes are opened Whoever has bid + + align:start position:0% +the envelopes are opened Whoever has bid + + + align:start position:0% +the envelopes are opened Whoever has bid +well in the bidding for a positive price + + align:start position:0% +well in the bidding for a positive price + + + align:start position:0% +well in the bidding for a positive price +whoever bids the highest amount is going + + align:start position:0% +whoever bids the highest amount is going + + + align:start position:0% +whoever bids the highest amount is going +to win but instead of paying what they + + align:start position:0% +to win but instead of paying what they + + + align:start position:0% +to win but instead of paying what they +bid they pay the second highest bid so + + align:start position:0% +bid they pay the second highest bid so + + + align:start position:0% +bid they pay the second highest bid so +if the you know we're bidding for a + + align:start position:0% +if the you know we're bidding for a + + + align:start position:0% +if the you know we're bidding for a +painting and you know + + align:start position:0% +painting and you know + + + align:start position:0% +painting and you know +the bids are 2.4 million 2.3 million 2.2 + + align:start position:0% +the bids are 2.4 million 2.3 million 2.2 + + + align:start position:0% +the bids are 2.4 million 2.3 million 2.2 +million you open the envelopes this + + align:start position:0% +million you open the envelopes this + + + align:start position:0% +million you open the envelopes this +person gets the good but they only pay + + align:start position:0% +person gets the good but they only pay + + + align:start position:0% +person gets the good but they only pay +the second highest bid instead of paying + + align:start position:0% +the second highest bid instead of paying + + + align:start position:0% +the second highest bid instead of paying +what they bid okay um why do we do that + + align:start position:0% +what they bid okay um why do we do that + + + align:start position:0% +what they bid okay um why do we do that +it turns out it it becomes a very easy + + align:start position:0% +it turns out it it becomes a very easy + + + align:start position:0% +it turns out it it becomes a very easy +auction to analyze and so it's it's a + + align:start position:0% +auction to analyze and so it's it's a + + + align:start position:0% +auction to analyze and so it's it's a +very nice mechanism in that sense um + + align:start position:0% +very nice mechanism in that sense um + + + align:start position:0% +very nice mechanism in that sense um +proposition in the second price seal bid + + align:start position:0% +proposition in the second price seal bid + + + align:start position:0% +proposition in the second price seal bid +auction it's a weekly dominant strategy + + align:start position:0% +auction it's a weekly dominant strategy + + + align:start position:0% +auction it's a weekly dominant strategy +to bid your true value so you don't have + + align:start position:0% +to bid your true value so you don't have + + + align:start position:0% +to bid your true value so you don't have +to think strategically about what other + + align:start position:0% +to think strategically about what other + + + align:start position:0% +to think strategically about what other +people are bidding what's the good Worth + + align:start position:0% +people are bidding what's the good Worth + + + align:start position:0% +people are bidding what's the good Worth +to them you just have this dominant + + align:start position:0% +to them you just have this dominant + + + align:start position:0% +to them you just have this dominant +strategy which is just to write down + + align:start position:0% +strategy which is just to write down + + + align:start position:0% +strategy which is just to write down +your own value um bid that and and + + align:start position:0% +your own value um bid that and and + + + align:start position:0% +your own value um bid that and and +that's a that's sort of a dominant + + align:start position:0% +that's a that's sort of a dominant + + + align:start position:0% +that's a that's sort of a dominant +strategy equilibrium okay um a good way + + align:start position:0% +strategy equilibrium okay um a good way + + + align:start position:0% +strategy equilibrium okay um a good way +to think about that is to just think + + align:start position:0% +to think about that is to just think + + + align:start position:0% +to think about that is to just think +about what are the deviations you could + + align:start position:0% +about what are the deviations you could + + + align:start position:0% +about what are the deviations you could +do so suppose your value is Si you + + align:start position:0% +do so suppose your value is Si you + + + align:start position:0% +do so suppose your value is Si you +consider writing down something that's + + align:start position:0% +consider writing down something that's + + + align:start position:0% +consider writing down something that's +other different from your value and let + + align:start position:0% +other different from your value and let + + + align:start position:0% +other different from your value and let +B hat be the largest value written down + + align:start position:0% +B hat be the largest value written down + + + align:start position:0% +B hat be the largest value written down +by everybody + + align:start position:0% +by everybody + + + align:start position:0% +by everybody +else okay you know there's six possible + + align:start position:0% +else okay you know there's six possible + + + align:start position:0% +else okay you know there's six possible +orderings of B S and B + + align:start position:0% +orderings of B S and B + + + align:start position:0% +orderings of B S and B +hat in the middle cases here I have the + + align:start position:0% +hat in the middle cases here I have the + + + align:start position:0% +hat in the middle cases here I have the +cases where sorry in the first top and + + align:start position:0% +cases where sorry in the first top and + + + align:start position:0% +cases where sorry in the first top and +bottom cases in the top and bottom cases + + align:start position:0% +bottom cases in the top and bottom cases + + + align:start position:0% +bottom cases in the top and bottom cases +when somebody else has written down a + + align:start position:0% +when somebody else has written down a + + + align:start position:0% +when somebody else has written down a +number that's bigger than both your + + align:start position:0% +number that's bigger than both your + + + align:start position:0% +number that's bigger than both your +value and the number you wrote down well + + align:start position:0% +value and the number you wrote down well + + + align:start position:0% +value and the number you wrote down well +then you lose whether you wrote down SI + + align:start position:0% +then you lose whether you wrote down SI + + + align:start position:0% +then you lose whether you wrote down SI +or wrote down bi and your value is zero + + align:start position:0% +or wrote down bi and your value is zero + + + align:start position:0% +or wrote down bi and your value is zero +either way the other case is if everyone + + align:start position:0% +either way the other case is if everyone + + + align:start position:0% +either way the other case is if everyone +El everyone else bid lower numbers + + align:start position:0% +El everyone else bid lower numbers + + + align:start position:0% +El everyone else bid lower numbers +things that are lower both than your + + align:start position:0% +things that are lower both than your + + + align:start position:0% +things that are lower both than your +value and the thing you wrote down in + + align:start position:0% +value and the thing you wrote down in + + + align:start position:0% +value and the thing you wrote down in +this case you're going to win the + + align:start position:0% +this case you're going to win the + + + align:start position:0% +this case you're going to win the +auction whether you wrote down bi or Si + + align:start position:0% +auction whether you wrote down bi or Si + + + align:start position:0% +auction whether you wrote down bi or Si +and you're going to pay B hat either way + + align:start position:0% +and you're going to pay B hat either way + + + align:start position:0% +and you're going to pay B hat either way +so the fact that you've done something + + align:start position:0% +so the fact that you've done something + + + align:start position:0% +so the fact that you've done something +different from writing down SI also + + align:start position:0% +different from writing down SI also + + + align:start position:0% +different from writing down SI also +doesn't make a difference the two cases + + align:start position:0% +doesn't make a difference the two cases + + + align:start position:0% +doesn't make a difference the two cases +where writing something different from + + align:start position:0% +where writing something different from + + + align:start position:0% +where writing something different from +SI does make a difference is here and + + align:start position:0% +SI does make a difference is here and + + + align:start position:0% +SI does make a difference is here and +here you know suppose that your value is + + align:start position:0% +here you know suppose that your value is + + + align:start position:0% +here you know suppose that your value is +Si someone else wrote down a number + + align:start position:0% +Si someone else wrote down a number + + + align:start position:0% +Si someone else wrote down a number +that's bigger than your value and you + + align:start position:0% +that's bigger than your value and you + + + align:start position:0% +that's bigger than your value and you +write down something even bigger well + + align:start position:0% +write down something even bigger well + + + align:start position:0% +write down something even bigger well +then if you'd written down your true + + align:start position:0% +then if you'd written down your true + + + align:start position:0% +then if you'd written down your true +value you would have lost now that you + + align:start position:0% +value you would have lost now that you + + + align:start position:0% +value you would have lost now that you +win you you you get the object and you + + align:start position:0% +win you you you get the object and you + + + align:start position:0% +win you you you get the object and you +pay B hat which is more than it's worth + + align:start position:0% +pay B hat which is more than it's worth + + + align:start position:0% +pay B hat which is more than it's worth +to you so you end up Los regretting that + + align:start position:0% +to you so you end up Los regretting that + + + align:start position:0% +to you so you end up Los regretting that +you won because you paid some bid + + align:start position:0% +you won because you paid some bid + + + align:start position:0% +you won because you paid some bid +something more than it's worth and then + + align:start position:0% +something more than it's worth and then + + + align:start position:0% +something more than it's worth and then +the final case + + align:start position:0% +the final case + + + align:start position:0% +the final case +is I would have won if I'd bid SI but I + + align:start position:0% +is I would have won if I'd bid SI but I + + + align:start position:0% +is I would have won if I'd bid SI but I +write down something lower and then I + + align:start position:0% +write down something lower and then I + + + align:start position:0% +write down something lower and then I +lose and so here instead of getting + + align:start position:0% +lose and so here instead of getting + + + align:start position:0% +lose and so here instead of getting +utility SI minus B hat I get utility + + align:start position:0% +utility SI minus B hat I get utility + + + align:start position:0% +utility SI minus B hat I get utility +zero so in all six cases I'm weakly + + align:start position:0% +zero so in all six cases I'm weakly + + + align:start position:0% +zero so in all six cases I'm weakly +worse off and in two of them I'm + + align:start position:0% +worse off and in two of them I'm + + + align:start position:0% +worse off and in two of them I'm +strictly worse off so just writing down + + align:start position:0% +strictly worse off so just writing down + + + align:start position:0% +strictly worse off so just writing down +my true value is is an OP optimal + + align:start position:0% +my true value is is an OP optimal + + + align:start position:0% +my true value is is an OP optimal +strategy um it's not the unique + + align:start position:0% +strategy um it's not the unique + + + align:start position:0% +strategy um it's not the unique +equilibrium um for instance you could + + align:start position:0% +equilibrium um for instance you could + + + align:start position:0% +equilibrium um for instance you could +have one person bid in this model one + + align:start position:0% +have one person bid in this model one + + + align:start position:0% +have one person bid in this model one +person bids s uper bar and everybody + + align:start position:0% +person bids s uper bar and everybody + + + align:start position:0% +person bids s uper bar and everybody +else bids zero and then all the biders + + align:start position:0% +else bids zero and then all the biders + + + align:start position:0% +else bids zero and then all the biders +bidding zero are happy to bid zero + + align:start position:0% +bidding zero are happy to bid zero + + + align:start position:0% +bidding zero are happy to bid zero +because they can't win unless they bid s + + align:start position:0% +because they can't win unless they bid s + + + align:start position:0% +because they can't win unless they bid s +upper bar which is more than it's worth + + align:start position:0% +upper bar which is more than it's worth + + + align:start position:0% +upper bar which is more than it's worth +to them the person biding s uper bar is + + align:start position:0% +to them the person biding s uper bar is + + + align:start position:0% +to them the person biding s uper bar is +happy to bit s uper bar because he's + + align:start position:0% +happy to bit s uper bar because he's + + + align:start position:0% +happy to bit s uper bar because he's +going to get it at a price of zero uh + + align:start position:0% +going to get it at a price of zero uh + + + align:start position:0% +going to get it at a price of zero uh +usually we don't pay attention to those + + align:start position:0% +usually we don't pay attention to those + + + align:start position:0% +usually we don't pay attention to those +equilibria so usually we think about + + align:start position:0% +equilibria so usually we think about + + + align:start position:0% +equilibria so usually we think about +this equilibrium of this game where + + align:start position:0% +this equilibrium of this game where + + + align:start position:0% +this equilibrium of this game where +everyone just plays their dominant + + align:start position:0% +everyone just plays their dominant + + + align:start position:0% +everyone just plays their dominant +strategy uh and that's an equ and that's + + align:start position:0% +strategy uh and that's an equ and that's + + + align:start position:0% +strategy uh and that's an equ and that's +that's what they do it it is the unique + + align:start position:0% +that's what they do it it is the unique + + + align:start position:0% +that's what they do it it is the unique +uh symmetric equilibrium if if you have + + align:start position:0% + + + + align:start position:0% + +distributions one thing that's nice + + align:start position:0% +distributions one thing that's nice + + + align:start position:0% +distributions one thing that's nice +about sort of this dominant strategy is + + align:start position:0% +about sort of this dominant strategy is + + + align:start position:0% +about sort of this dominant strategy is +now it's easy to figure out how much + + align:start position:0% +now it's easy to figure out how much + + + align:start position:0% +now it's easy to figure out how much +revenue the seller makes from this + + align:start position:0% +revenue the seller makes from this + + + align:start position:0% +revenue the seller makes from this +auction so the amount the seller makes + + align:start position:0% +auction so the amount the seller makes + + + align:start position:0% +auction so the amount the seller makes +I'm going to write SN minus one colon n + + align:start position:0% +I'm going to write SN minus one colon n + + + align:start position:0% +I'm going to write SN minus one colon n +for the N minus first order statistic of + + align:start position:0% +for the N minus first order statistic of + + + align:start position:0% +for the N minus first order statistic of +n draws from this distribution so this + + align:start position:0% +n draws from this distribution so this + + + align:start position:0% +n draws from this distribution so this +is the n minus first highest so because + + align:start position:0% +is the n minus first highest so because + + + align:start position:0% +is the n minus first highest so because +whatever the bids are you always get the + + align:start position:0% +whatever the bids are you always get the + + + align:start position:0% +whatever the bids are you always get the +you know second second highest sort of + + align:start position:0% +you know second second highest sort of + + + align:start position:0% +you know second second highest sort of +our n minus first lowest bid we just + + align:start position:0% +our n minus first lowest bid we just + + + align:start position:0% +our n minus first lowest bid we just +need to compute the expected value of + + align:start position:0% +need to compute the expected value of + + + align:start position:0% +need to compute the expected value of +this second highest draw from the + + align:start position:0% +this second highest draw from the + + + align:start position:0% +this second highest draw from the +distribution + + align:start position:0% +distribution + + + align:start position:0% +distribution +and good way to think about that + + align:start position:0% + + + + align:start position:0% + +is you know how is it going to be that + + align:start position:0% +is you know how is it going to be that + + + align:start position:0% +is you know how is it going to be that +the second highest bid is exactly 2.3 + + align:start position:0% +the second highest bid is exactly 2.3 + + + align:start position:0% +the second highest bid is exactly 2.3 +million the way that's going to happen + + align:start position:0% +million the way that's going to happen + + + align:start position:0% +million the way that's going to happen +is you know suppose we have one bidder + + align:start position:0% +is you know suppose we have one bidder + + + align:start position:0% +is you know suppose we have one bidder +like bidder number three + + align:start position:0% +like bidder number three + + + align:start position:0% +like bidder number three +who has a higher value than this one + + align:start position:0% +who has a higher value than this one + + + align:start position:0% +who has a higher value than this one +bidder who bids exactly this or within + + align:start position:0% +bidder who bids exactly this or within + + + align:start position:0% +bidder who bids exactly this or within +DX of this and then you have all the + + align:start position:0% +DX of this and then you have all the + + + align:start position:0% +DX of this and then you have all the +rest of the biders down here okay there + + align:start position:0% +rest of the biders down here okay there + + + align:start position:0% +rest of the biders down here okay there +are many ways this can happen it doesn't + + align:start position:0% +are many ways this can happen it doesn't + + + align:start position:0% +are many ways this can happen it doesn't +have to be bidder three up here and + + align:start position:0% +have to be bidder three up here and + + + align:start position:0% +have to be bidder three up here and +bidder seven here it could be bidder + + align:start position:0% +bidder seven here it could be bidder + + + align:start position:0% +bidder seven here it could be bidder +four here and bit nine here it could be + + align:start position:0% +four here and bit nine here it could be + + + align:start position:0% +four here and bit nine here it could be +bidder one here bit two here but for + + align:start position:0% +bidder one here bit two here but for + + + align:start position:0% +bidder one here bit two here but for +this particular + + align:start position:0% +this particular + + + align:start position:0% +this particular +configuration the probability that + + align:start position:0% +configuration the probability that + + + align:start position:0% +configuration the probability that +bidder three is above this point x is 1 + + align:start position:0% +bidder three is above this point x is 1 + + + align:start position:0% +bidder three is above this point x is 1 +- capital F + + align:start position:0% +- capital F + + + align:start position:0% +- capital F +ofx the probability that bitter 7 is in + + align:start position:0% +ofx the probability that bitter 7 is in + + + align:start position:0% +ofx the probability that bitter 7 is in +this tiny interval is f ofx + + align:start position:0% +this tiny interval is f ofx + + + align:start position:0% +this tiny interval is f ofx +DX um because he has to be an interval + + align:start position:0% +DX um because he has to be an interval + + + align:start position:0% +DX um because he has to be an interval +DX around this and then the probability + + align:start position:0% +DX around this and then the probability + + + align:start position:0% +DX around this and then the probability +that all the rest of the people are here + + align:start position:0% +that all the rest of the people are here + + + align:start position:0% +that all the rest of the people are here +is f ofx uh to the N minus + + align:start position:0% +is f ofx uh to the N minus + + + align:start position:0% +is f ofx uh to the N minus +2 so the total probability of a + + align:start position:0% +2 so the total probability of a + + + align:start position:0% +2 so the total probability of a +configuration like this with the second + + align:start position:0% +configuration like this with the second + + + align:start position:0% +configuration like this with the second +highest bid is X is just uh n * n minus + + align:start position:0% +highest bid is X is just uh n * n minus + + + align:start position:0% +highest bid is X is just uh n * n minus +one time this time this time that + + align:start position:0% +one time this time this time that + + + align:start position:0% +one time this time this time that +because they n people who could be the + + align:start position:0% +because they n people who could be the + + + align:start position:0% +because they n people who could be the +high bidder n minus one who could then + + align:start position:0% +high bidder n minus one who could then + + + align:start position:0% +high bidder n minus one who could then +be the second highest bidder so this + + align:start position:0% +be the second highest bidder so this + + + align:start position:0% +be the second highest bidder so this +thing here n n minus 1 capital f ofx n + + align:start position:0% +thing here n n minus 1 capital f ofx n + + + align:start position:0% +thing here n n minus 1 capital f ofx n +minus 2 little f ofx 1 - F ofx DX that's + + align:start position:0% +minus 2 little f ofx 1 - F ofx DX that's + + + align:start position:0% +minus 2 little f ofx 1 - F ofx DX that's +the density of the second highest value + + align:start position:0% +the density of the second highest value + + + align:start position:0% +the density of the second highest value +and so the expected second highest value + + align:start position:0% +and so the expected second highest value + + + align:start position:0% +and so the expected second highest value +is just integrate x times that + + align:start position:0% +is just integrate x times that + + + align:start position:0% +is just integrate x times that +density + + align:start position:0% +density + + + align:start position:0% +density +okay so just as an example here I do + + align:start position:0% +okay so just as an example here I do + + + align:start position:0% +okay so just as an example here I do +this for the uniform distribution and + + align:start position:0% +this for the uniform distribution and + + + align:start position:0% +this for the uniform distribution and +the uniform distribution ution this says + + align:start position:0% +the uniform distribution ution this says + + + align:start position:0% +the uniform distribution ution this says +that an auction with n biders raises n + + align:start position:0% +that an auction with n biders raises n + + + align:start position:0% +that an auction with n biders raises n +minus1 over n+ one as + + align:start position:0% +minus1 over n+ one as + + + align:start position:0% +minus1 over n+ one as +Revenue um so you know the revenue from + + align:start position:0% +Revenue um so you know the revenue from + + + align:start position:0% +Revenue um so you know the revenue from +a second price seal bid auction goes to + + align:start position:0% +a second price seal bid auction goes to + + + align:start position:0% +a second price seal bid auction goes to +one as number of biders goes to Infinity + + align:start position:0% +one as number of biders goes to Infinity + + + align:start position:0% +one as number of biders goes to Infinity +because the second highest value is + + align:start position:0% +because the second highest value is + + + align:start position:0% +because the second highest value is +almost almost the first value which is + + align:start position:0% +almost almost the first value which is + + + align:start position:0% +almost almost the first value which is +almost the top anyway um and this + + align:start position:0% +almost the top anyway um and this + + + align:start position:0% +almost the top anyway um and this +density calculation it you know it's an + + align:start position:0% +density calculation it you know it's an + + + align:start position:0% +density calculation it you know it's an +example of just sort of the how you + + align:start position:0% +example of just sort of the how you + + + align:start position:0% +example of just sort of the how you +compute a Ki order statistic which is + + align:start position:0% +compute a Ki order statistic which is + + + align:start position:0% +compute a Ki order statistic which is +you have um + + align:start position:0% +you have um + + + align:start position:0% +you have um +n minus1 choose K minus one possible + + align:start position:0% +n minus1 choose K minus one possible + + + align:start position:0% +n minus1 choose K minus one possible +groups of people who can be above + + align:start position:0% +groups of people who can be above + + + align:start position:0% +groups of people who can be above +x uh who can be sorry below x uh F ofx + + align:start position:0% +x uh who can be sorry below x uh F ofx + + + align:start position:0% +x uh who can be sorry below x uh F ofx +to the K minus one is then the + + align:start position:0% +to the K minus one is then the + + + align:start position:0% +to the K minus one is then the +probability that each of them has a + + align:start position:0% +probability that each of them has a + + + align:start position:0% +probability that each of them has a +value below x 1 minus F ofx the N minus + + align:start position:0% +value below x 1 minus F ofx the N minus + + + align:start position:0% +value below x 1 minus F ofx the N minus +K is the probability that everybody else + + align:start position:0% +K is the probability that everybody else + + + align:start position:0% +K is the probability that everybody else +is above X and then you have uh F ofx DX + + align:start position:0% +is above X and then you have uh F ofx DX + + + align:start position:0% +is above X and then you have uh F ofx DX +is the probability that someone has a + + align:start position:0% +is the probability that someone has a + + + align:start position:0% +is the probability that someone has a +value exactly X + + align:start position:0% +value exactly X + + + align:start position:0% +value exactly X +okay and so computing expected values of + + align:start position:0% +okay and so computing expected values of + + + align:start position:0% +okay and so computing expected values of +auctions revenues you're often Computing + + align:start position:0% +auctions revenues you're often Computing + + + align:start position:0% +auctions revenues you're often Computing +these order statistics and when the + + align:start position:0% +these order statistics and when the + + + align:start position:0% +these order statistics and when the +draws are independent and people bid + + align:start position:0% +draws are independent and people bid + + + align:start position:0% +draws are independent and people bid +truthfully that's a fairly easy + + align:start position:0% +truthfully that's a fairly easy + + + align:start position:0% +truthfully that's a fairly easy +calculation to do okay you know a second + + align:start position:0% +calculation to do okay you know a second + + + align:start position:0% +calculation to do okay you know a second +auction that's you know second price + + align:start position:0% +auction that's you know second price + + + align:start position:0% +auction that's you know second price +steel bid auctions are this + + align:start position:0% +steel bid auctions are this + + + align:start position:0% +steel bid auctions are this +nice uh economic gain nice sort of model + + align:start position:0% +nice uh economic gain nice sort of model + + + align:start position:0% +nice uh economic gain nice sort of model +because they're very simple uh in + + align:start position:0% +because they're very simple uh in + + + align:start position:0% +because they're very simple uh in +practice we don't see auctions conducted + + align:start position:0% +practice we don't see auctions conducted + + + align:start position:0% +practice we don't see auctions conducted +that way uh in practice what you often + + align:start position:0% +that way uh in practice what you often + + + align:start position:0% +that way uh in practice what you often +see is auctions conducted with an oral + + align:start position:0% +see is auctions conducted with an oral + + + align:start position:0% +see is auctions conducted with an oral +ascending bid process where like you + + align:start position:0% +ascending bid process where like you + + + align:start position:0% +ascending bid process where like you +know you anyway you probably haven't + + align:start position:0% +know you anyway you probably haven't + + + align:start position:0% +know you anyway you probably haven't +been there but you know you watch people + + align:start position:0% +been there but you know you watch people + + + align:start position:0% +been there but you know you watch people +do sort of auctions uh on TV for like + + align:start position:0% +do sort of auctions uh on TV for like + + + align:start position:0% +do sort of auctions uh on TV for like +paintings and it's always people with + + align:start position:0% +paintings and it's always people with + + + align:start position:0% +paintings and it's always people with +paddles up in the air who will bid 1 + + align:start position:0% +paddles up in the air who will bid 1 + + + align:start position:0% +paddles up in the air who will bid 1 +million 1.1 do I hear 1.2 people just + + align:start position:0% +million 1.1 do I hear 1.2 people just + + + align:start position:0% +million 1.1 do I hear 1.2 people just +keep raising their hand every time they + + align:start position:0% +keep raising their hand every time they + + + align:start position:0% +keep raising their hand every time they +want to bid higher and then they sort of + + align:start position:0% +want to bid higher and then they sort of + + + align:start position:0% +want to bid higher and then they sort of +keep bidding higher until the until like + + align:start position:0% +keep bidding higher until the until like + + + align:start position:0% +keep bidding higher until the until like +you know the guy says you know going + + align:start position:0% +you know the guy says you know going + + + align:start position:0% +you know the guy says you know going +going gone because it's no one else is + + align:start position:0% +going gone because it's no one else is + + + align:start position:0% +going gone because it's no one else is +willing to bid more than the current bid + + align:start position:0% +willing to bid more than the current bid + + + align:start position:0% +willing to bid more than the current bid +amount um analyzing that kind of game + + align:start position:0% +amount um analyzing that kind of game + + + align:start position:0% +amount um analyzing that kind of game +where people keep raising their hand + + align:start position:0% +where people keep raising their hand + + + align:start position:0% +where people keep raising their hand +would be a very complicated extensive + + align:start position:0% +would be a very complicated extensive + + + align:start position:0% +would be a very complicated extensive +form so what people do instead is is + + align:start position:0% +form so what people do instead is is + + + align:start position:0% +form so what people do instead is is +simplify to this What's called the + + align:start position:0% +simplify to this What's called the + + + align:start position:0% +simplify to this What's called the +button auction design which is the + + align:start position:0% +button auction design which is the + + + align:start position:0% +button auction design which is the +is going up and the bidder keeps call + + align:start position:0% +is going up and the bidder keeps call + + + align:start position:0% +is going up and the bidder keeps call +the auctioner keeps calling out higher + + align:start position:0% +the auctioner keeps calling out higher + + + align:start position:0% +the auctioner keeps calling out higher +and higher numbers and you just hold + + align:start position:0% +and higher numbers and you just hold + + + align:start position:0% +and higher numbers and you just hold +your finger on the button as long as you + + align:start position:0% +your finger on the button as long as you + + + align:start position:0% +your finger on the button as long as you +still want to buy the good at that price + + align:start position:0% +still want to buy the good at that price + + + align:start position:0% +still want to buy the good at that price +and then once you take your finger off + + align:start position:0% +and then once you take your finger off + + + align:start position:0% +and then once you take your finger off +the button you're out of the bidding and + + align:start position:0% +the button you're out of the bidding and + + + align:start position:0% +the button you're out of the bidding and +you've dropped out forever so it's like + + align:start position:0% +you've dropped out forever so it's like + + + align:start position:0% +you've dropped out forever so it's like +you know who's in who's in who's in and + + align:start position:0% +you know who's in who's in who's in and + + + align:start position:0% +you know who's in who's in who's in and +then you just take your finger off and + + align:start position:0% +then you just take your finger off and + + + align:start position:0% +then you just take your finger off and +you're out permanently that's nice + + align:start position:0% +you're out permanently that's nice + + + align:start position:0% +you're out permanently that's nice +because it can converts it to sort of a + + align:start position:0% +because it can converts it to sort of a + + + align:start position:0% +because it can converts it to sort of a +basic like one-dimensional strategy + + align:start position:0% +basic like one-dimensional strategy + + + align:start position:0% +basic like one-dimensional strategy +space which is I just choose at what + + align:start position:0% +space which is I just choose at what + + + align:start position:0% +space which is I just choose at what +point do I drop out of the + + align:start position:0% +point do I drop out of the + + + align:start position:0% +point do I drop out of the +auction okay and thinking about that + + align:start position:0% +auction okay and thinking about that + + + align:start position:0% +auction okay and thinking about that +game of at what point or what if I was + + align:start position:0% +game of at what point or what if I was + + + align:start position:0% +game of at what point or what if I was +giving instructions to a computer at + + align:start position:0% +giving instructions to a computer at + + + align:start position:0% +giving instructions to a computer at +what point should you drop out of the + + align:start position:0% +what point should you drop out of the + + + align:start position:0% +what point should you drop out of the +bidding um it's clear that in some sense + + align:start position:0% +bidding um it's clear that in some sense + + + align:start position:0% +bidding um it's clear that in some sense +this game is the second price sealed bid + + align:start position:0% +this game is the second price sealed bid + + + align:start position:0% +this game is the second price sealed bid +auction just in a different form so a + + align:start position:0% +auction just in a different form so a + + + align:start position:0% +auction just in a different form so a +perfect beas and equilibrium of this + + align:start position:0% +perfect beas and equilibrium of this + + + align:start position:0% +perfect beas and equilibrium of this +button auction model is just everybody + + align:start position:0% +button auction model is just everybody + + + align:start position:0% +button auction model is just everybody +drops out uh when the Val when the uh + + align:start position:0% +drops out uh when the Val when the uh + + + align:start position:0% +drops out uh when the Val when the uh +Auctioneer gets to their true value so + + align:start position:0% +Auctioneer gets to their true value so + + + align:start position:0% +Auctioneer gets to their true value so +as long as he's saying I will you know + + align:start position:0% +as long as he's saying I will you know + + + align:start position:0% +as long as he's saying I will you know +like if if the good is worth 2.4 million + + align:start position:0% +like if if the good is worth 2.4 million + + + align:start position:0% +like if if the good is worth 2.4 million +to you as long as he's saying 2 million + + align:start position:0% +to you as long as he's saying 2 million + + + align:start position:0% +to you as long as he's saying 2 million +21 23 you keep your finger on the button + + align:start position:0% +21 23 you keep your finger on the button + + + align:start position:0% +21 23 you keep your finger on the button +and as soon as he sort of gets to 24 you + + align:start position:0% +and as soon as he sort of gets to 24 you + + + align:start position:0% +and as soon as he sort of gets to 24 you +take your finger off the button and say + + align:start position:0% +take your finger off the button and say + + + align:start position:0% +take your finger off the button and say +I don't want it anymore okay + + align:start position:0% + + + + align:start position:0% + +um why is this true you know I think + + align:start position:0% +um why is this true you know I think + + + align:start position:0% +um why is this true you know I think +this one is actually it's even more + + align:start position:0% +this one is actually it's even more + + + align:start position:0% +this one is actually it's even more +obvious than the second price sealed bit + + align:start position:0% +obvious than the second price sealed bit + + + align:start position:0% +obvious than the second price sealed bit +auction like you know if if what's my + + align:start position:0% +auction like you know if if what's my + + + align:start position:0% +auction like you know if if what's my +dominant strategy as long as I want to + + align:start position:0% +dominant strategy as long as I want to + + + align:start position:0% +dominant strategy as long as I want to +win I say I keep saying I'm in as soon + + align:start position:0% +win I say I keep saying I'm in as soon + + + align:start position:0% +win I say I keep saying I'm in as soon +as I don't want to pay what's being + + align:start position:0% +as I don't want to pay what's being + + + align:start position:0% +as I don't want to pay what's being +charged I drop out um so it's same + + align:start position:0% +charged I drop out um so it's same + + + align:start position:0% +charged I drop out um so it's same +argument as a second price steal bid + + align:start position:0% +argument as a second price steal bid + + + align:start position:0% +argument as a second price steal bid +auction dropping out earlier you know + + align:start position:0% +auction dropping out earlier you know + + + align:start position:0% +auction dropping out earlier you know +could only cost me make me lose + + align:start position:0% +could only cost me make me lose + + + align:start position:0% +could only cost me make me lose +something that I would want to have + + align:start position:0% +something that I would want to have + + + align:start position:0% +something that I would want to have +bought and bidding past my value all I + + align:start position:0% +bought and bidding past my value all I + + + align:start position:0% +bought and bidding past my value all I +can do is lose and and and end up paying + + align:start position:0% +can do is lose and and and end up paying + + + align:start position:0% +can do is lose and and and end up paying +more than I wanted to get for it so um + + align:start position:0% +more than I wanted to get for it so um + + + align:start position:0% +more than I wanted to get for it so um +you know the game is still the same we + + align:start position:0% +you know the game is still the same we + + + align:start position:0% +you know the game is still the same we +get the second second highest price um + + align:start position:0% +get the second second highest price um + + + align:start position:0% +get the second second highest price um +you know in practice what's sort of + + align:start position:0% +you know in practice what's sort of + + + align:start position:0% +you know in practice what's sort of +funny is if you run second price sealed + + align:start position:0% +funny is if you run second price sealed + + + align:start position:0% +funny is if you run second price sealed +bit auction game um models people often + + align:start position:0% +bit auction game um models people often + + + align:start position:0% +bit auction game um models people often +get it wrong like people understand that + + align:start position:0% +get it wrong like people understand that + + + align:start position:0% +get it wrong like people understand that +I won't actually people understand like + + align:start position:0% +I won't actually people understand like + + + align:start position:0% +I won't actually people understand like +I won't actually need to pay what I bid + + align:start position:0% +I won't actually need to pay what I bid + + + align:start position:0% +I won't actually need to pay what I bid +I'll probably have to pay something less + + align:start position:0% +I'll probably have to pay something less + + + align:start position:0% +I'll probably have to pay something less +they don't sort of do that full + + align:start position:0% +they don't sort of do that full + + + align:start position:0% +they don't sort of do that full +consideration of the six cases and say + + align:start position:0% +consideration of the six cases and say + + + align:start position:0% +consideration of the six cases and say +okay I should still bid exactly what + + align:start position:0% +okay I should still bid exactly what + + + align:start position:0% +okay I should still bid exactly what +it's worth and you you'll see in second + + align:start position:0% +it's worth and you you'll see in second + + + align:start position:0% +it's worth and you you'll see in second +price experiments people over bid and + + align:start position:0% +price experiments people over bid and + + + align:start position:0% +price experiments people over bid and +second price deal bid auctions they + + align:start position:0% +second price deal bid auctions they + + + align:start position:0% +second price deal bid auctions they +realize okay I'm probably not going to + + align:start position:0% +realize okay I'm probably not going to + + + align:start position:0% +realize okay I'm probably not going to +have to pay what I bid so therefore I + + align:start position:0% +have to pay what I bid so therefore I + + + align:start position:0% +have to pay what I bid so therefore I +can bid more than it's actually Worth to + + align:start position:0% +can bid more than it's actually Worth to + + + align:start position:0% +can bid more than it's actually Worth to +me and I probably won't have to pay that + + align:start position:0% +me and I probably won't have to pay that + + + align:start position:0% +me and I probably won't have to pay that +somehow the sort of conditioning logic + + align:start position:0% +somehow the sort of conditioning logic + + + align:start position:0% +somehow the sort of conditioning logic +doesn't make it through um uh but in in + + align:start position:0% +doesn't make it through um uh but in in + + + align:start position:0% +doesn't make it through um uh but in in +practice I would say uh in practice + + align:start position:0% +practice I would say uh in practice + + + align:start position:0% +practice I would say uh in practice +people will tend to + + align:start position:0% +people will tend to + + + align:start position:0% +people will tend to +do um first price seal we'll tend to do + + align:start position:0% +do um first price seal we'll tend to do + + + align:start position:0% +do um first price seal we'll tend to do +auctions of this variety rather than + + align:start position:0% +auctions of this variety rather than + + + align:start position:0% +auctions of this variety rather than +second price sealed B auction one thing + + align:start position:0% +second price sealed B auction one thing + + + align:start position:0% +second price sealed B auction one thing +that is different about the auction from + + align:start position:0% +that is different about the auction from + + + align:start position:0% +that is different about the auction from +the auctioneers perspective is the + + align:start position:0% +the auctioneers perspective is the + + + align:start position:0% +the auctioneers perspective is the +information that's revealed about the + + align:start position:0% +information that's revealed about the + + + align:start position:0% +information that's revealed about the +bids uh in this auction when you open + + align:start position:0% +bids uh in this auction when you open + + + align:start position:0% +bids uh in this auction when you open +the envelopes you learn what the good + + align:start position:0% +the envelopes you learn what the good + + + align:start position:0% +the envelopes you learn what the good +was worth to + + align:start position:0% +was worth to + + + align:start position:0% +was worth to +everyone and you may learn how much + + align:start position:0% +everyone and you may learn how much + + + align:start position:0% +everyone and you may learn how much +Surplus went to the leading bidder + + align:start position:0% +Surplus went to the leading bidder + + + align:start position:0% +Surplus went to the leading bidder +because the second highest bidder had a + + align:start position:0% +because the second highest bidder had a + + + align:start position:0% +because the second highest bidder had a +value much below the highest bidder um + + align:start position:0% +value much below the highest bidder um + + + align:start position:0% +value much below the highest bidder um +whereas in this auction you never learn + + align:start position:0% +whereas in this auction you never learn + + + align:start position:0% +whereas in this auction you never learn +you know you learn when everybody else + + align:start position:0% +you know you learn when everybody else + + + align:start position:0% +you know you learn when everybody else +drops out you never learn the value of + + align:start position:0% +drops out you never learn the value of + + + align:start position:0% +drops out you never learn the value of +the highest bidder um there were some + + align:start position:0% +the highest bidder um there were some + + + align:start position:0% +the highest bidder um there were some +cases like there was like the famous you + + align:start position:0% +cases like there was like the famous you + + + align:start position:0% +cases like there was like the famous you +know Spectrum auction case where there + + align:start position:0% +know Spectrum auction case where there + + + align:start position:0% +know Spectrum auction case where there +were auctioning off I think it was + + align:start position:0% +were auctioning off I think it was + + + align:start position:0% +were auctioning off I think it was +cellular telephone Serv right to connect + + align:start position:0% +cellular telephone Serv right to connect + + + align:start position:0% +cellular telephone Serv right to connect +cellular telephone service in some small + + align:start position:0% +cellular telephone service in some small + + + align:start position:0% +cellular telephone service in some small +town in New Zealand that basically only + + align:start position:0% +town in New Zealand that basically only + + + align:start position:0% +town in New Zealand that basically only +one person wanted to provide the service + + align:start position:0% +one person wanted to provide the service + + + align:start position:0% +one person wanted to provide the service +there and like you know I'll make up + + align:start position:0% +there and like you know I'll make up + + + align:start position:0% +there and like you know I'll make up +these numbers I'm completely wrong there + + align:start position:0% +these numbers I'm completely wrong there + + + align:start position:0% +these numbers I'm completely wrong there +you know something like the you know + + align:start position:0% +you know something like the you know + + + align:start position:0% +you know something like the you know +High first person submitted uh $37 + + align:start position:0% +High first person submitted uh $37 + + + align:start position:0% +High first person submitted uh $37 +million and the second one submitted + + align:start position:0% +million and the second one submitted + + + align:start position:0% +million and the second one submitted +$115,000 and then everyone else + + align:start position:0% +$115,000 and then everyone else + + + align:start position:0% +$115,000 and then everyone else +submitted zero and then they open up the + + align:start position:0% +submitted zero and then they open up the + + + align:start position:0% +submitted zero and then they open up the +envelopes and they're like okay your + + align:start position:0% +envelopes and they're like okay your + + + align:start position:0% +envelopes and they're like okay your +brilliant auction design says we give it + + align:start position:0% +brilliant auction design says we give it + + + align:start position:0% +brilliant auction design says we give it +to the bidder number one who was willing + + align:start position:0% +to the bidder number one who was willing + + + align:start position:0% +to the bidder number one who was willing +pay 37 million we charge him $155,000 + + align:start position:0% +pay 37 million we charge him $155,000 + + + align:start position:0% +pay 37 million we charge him $155,000 +and you know everyone's like that was + + align:start position:0% +and you know everyone's like that was + + + align:start position:0% +and you know everyone's like that was +the worst auction design in history how + + align:start position:0% +the worst auction design in history how + + + align:start position:0% +the worst auction design in history how +could you have recommended that + + align:start position:0% +could you have recommended that + + + align:start position:0% +could you have recommended that +obviously if we' done the oral ascending + + align:start position:0% +obviously if we' done the oral ascending + + + align:start position:0% +obviously if we' done the oral ascending +auction all we would have seen is that + + align:start position:0% +auction all we would have seen is that + + + align:start position:0% +auction all we would have seen is that +like only two people show up and first + + align:start position:0% +like only two people show up and first + + + align:start position:0% +like only two people show up and first +one of them puts his hand out to 15,000 + + align:start position:0% +one of them puts his hand out to 15,000 + + + align:start position:0% +one of them puts his hand out to 15,000 +we're like okay it's not worth providing + + align:start position:0% +we're like okay it's not worth providing + + + align:start position:0% +we're like okay it's not worth providing +service in this town you know that was a + + align:start position:0% +service in this town you know that was a + + + align:start position:0% +service in this town you know that was a +reasonable price that we got uh and so + + align:start position:0% +reasonable price that we got uh and so + + + align:start position:0% +reasonable price that we got uh and so +and practice that sort of expost + + align:start position:0% +and practice that sort of expost + + + align:start position:0% +and practice that sort of expost +embarrassment of the auctioneer may be a + + align:start position:0% +embarrassment of the auctioneer may be a + + + align:start position:0% +embarrassment of the auctioneer may be a +factor that leads us not to do the + + align:start position:0% +factor that leads us not to do the + + + align:start position:0% +factor that leads us not to do the +second price sealed bid + + align:start position:0% +second price sealed bid + + + align:start position:0% +second price sealed bid +mechanism um + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um you know another mechanism that we + + align:start position:0% +um you know another mechanism that we + + + align:start position:0% +um you know another mechanism that we +see even more often in practice um is + + align:start position:0% +see even more often in practice um is + + + align:start position:0% +see even more often in practice um is +the first price sealed bid mechanism so + + align:start position:0% +the first price sealed bid mechanism so + + + align:start position:0% +the first price sealed bid mechanism so +the first price sealed bid mechanism + + align:start position:0% +the first price sealed bid mechanism + + + align:start position:0% +the first price sealed bid mechanism +would be like the second price sealed + + align:start position:0% +would be like the second price sealed + + + align:start position:0% +would be like the second price sealed +bid you know you're running your + + align:start position:0% +bid you know you're running your + + + align:start position:0% +bid you know you're running your +procurement auction you ask all the + + align:start position:0% +procurement auction you ask all the + + + align:start position:0% +procurement auction you ask all the +biders to bid what price they would they + + align:start position:0% +biders to bid what price they would they + + + align:start position:0% +biders to bid what price they would they +would need you would need to give them + + align:start position:0% +would need you would need to give them + + + align:start position:0% +would need you would need to give them +to get them to pave the road they all + + align:start position:0% +to get them to pave the road they all + + + align:start position:0% +to get them to pave the road they all +submit their bids and then um the + + align:start position:0% +submit their bids and then um the + + + align:start position:0% +submit their bids and then um the +highest bidder wins and actually pays + + align:start position:0% +highest bidder wins and actually pays + + + align:start position:0% +highest bidder wins and actually pays +the bid so here or if we're buying + + align:start position:0% +the bid so here or if we're buying + + + align:start position:0% +the bid so here or if we're buying +something I write down I'm willing to + + align:start position:0% +something I write down I'm willing to + + + align:start position:0% +something I write down I'm willing to +pay 2.4 million for the painting someone + + align:start position:0% +pay 2.4 million for the painting someone + + + align:start position:0% +pay 2.4 million for the painting someone +else writes down 2.3 2.2 we open the + + align:start position:0% +else writes down 2.3 2.2 we open the + + + align:start position:0% +else writes down 2.3 2.2 we open the +envelopes if I wrote down I'm willing to + + align:start position:0% +envelopes if I wrote down I'm willing to + + + align:start position:0% +envelopes if I wrote down I'm willing to +pay 2.4 million you charge me 2.4 + + align:start position:0% +pay 2.4 million you charge me 2.4 + + + align:start position:0% +pay 2.4 million you charge me 2.4 +million okay um what's the equilibrium + + align:start position:0% +million okay um what's the equilibrium + + + align:start position:0% +million okay um what's the equilibrium +of this game you know here this is a + + align:start position:0% +of this game you know here this is a + + + align:start position:0% +of this game you know here this is a +game where you have to shade your bids + + align:start position:0% +game where you have to shade your bids + + + align:start position:0% +game where you have to shade your bids +you can't bid what the good is truly + + align:start position:0% +you can't bid what the good is truly + + + align:start position:0% +you can't bid what the good is truly +worth to you because some sense bidding + + align:start position:0% +worth to you because some sense bidding + + + align:start position:0% +worth to you because some sense bidding +what the good is worth to you is a is a + + align:start position:0% +what the good is worth to you is a is a + + + align:start position:0% +what the good is worth to you is a is a +weekly dominated strategy like if if I'm + + align:start position:0% +weekly dominated strategy like if if I'm + + + align:start position:0% +weekly dominated strategy like if if I'm +willing to pay actly 2.4 million and at + + align:start position:0% +willing to pay actly 2.4 million and at + + + align:start position:0% +willing to pay actly 2.4 million and at +any higher price I wouldn't want it if I + + align:start position:0% +any higher price I wouldn't want it if I + + + align:start position:0% +any higher price I wouldn't want it if I +bid 2.4 million then if I lose I get + + align:start position:0% +bid 2.4 million then if I lose I get + + + align:start position:0% +bid 2.4 million then if I lose I get +zero utility and if I win I get zero + + align:start position:0% +zero utility and if I win I get zero + + + align:start position:0% +zero utility and if I win I get zero +utility because I bid exactly everything + + align:start position:0% +utility because I bid exactly everything + + + align:start position:0% +utility because I bid exactly everything +that the good was worth to me I get zero + + align:start position:0% +that the good was worth to me I get zero + + + align:start position:0% +that the good was worth to me I get zero +Surplus um so what do you do you know + + align:start position:0% +Surplus um so what do you do you know + + + align:start position:0% +Surplus um so what do you do you know +it's like Monopoly pricing where you + + align:start position:0% +it's like Monopoly pricing where you + + + align:start position:0% +it's like Monopoly pricing where you +shade your bid and you decide I'm going + + align:start position:0% +shade your bid and you decide I'm going + + + align:start position:0% +shade your bid and you decide I'm going +to bid less than my True Value as I go + + align:start position:0% +to bid less than my True Value as I go + + + align:start position:0% +to bid less than my True Value as I go +further and further down below my True + + align:start position:0% +further and further down below my True + + + align:start position:0% +further and further down below my True +Value I get more profit if I am chosen + + align:start position:0% +Value I get more profit if I am chosen + + + align:start position:0% +Value I get more profit if I am chosen +as a winner but it's less and less + + align:start position:0% +as a winner but it's less and less + + + align:start position:0% +as a winner but it's less and less +likely I'm going to win so it's kind of + + align:start position:0% +likely I'm going to win so it's kind of + + + align:start position:0% +likely I'm going to win so it's kind of +like the monopolist raising price above + + align:start position:0% +like the monopolist raising price above + + + align:start position:0% +like the monopolist raising price above +cost I get more and more profit if I do + + align:start position:0% +cost I get more and more profit if I do + + + align:start position:0% +cost I get more and more profit if I do +make the sale but it's less and less + + align:start position:0% +make the sale but it's less and less + + + align:start position:0% +make the sale but it's less and less +likely that I make the sale and you make + + align:start position:0% +likely that I make the sale and you make + + + align:start position:0% +likely that I make the sale and you make +that tradeoff of probability of winning + + align:start position:0% +that tradeoff of probability of winning + + + align:start position:0% +that tradeoff of probability of winning +times Surplus if I versus Surplus if I + + align:start position:0% +times Surplus if I versus Surplus if I + + + align:start position:0% +times Surplus if I versus Surplus if I +win okay um so let's think about what + + align:start position:0% +win okay um so let's think about what + + + align:start position:0% +win okay um so let's think about what +the equilibrium would look like so + + align:start position:0% +the equilibrium would look like so + + + align:start position:0% +the equilibrium would look like so +suppose we had a symmetric equilibrium + + align:start position:0% +suppose we had a symmetric equilibrium + + + align:start position:0% +suppose we had a symmetric equilibrium +everyone's using these strictly + + align:start position:0% +everyone's using these strictly + + + align:start position:0% +everyone's using these strictly +increasing strategies B star of s the + + align:start position:0% +increasing strategies B star of s the + + + align:start position:0% +increasing strategies B star of s the +higher is my value or signal s the + + align:start position:0% +higher is my value or signal s the + + + align:start position:0% +higher is my value or signal s the +higher I bid um my payoff if I bid bi + + align:start position:0% +higher I bid um my payoff if I bid bi + + + align:start position:0% +higher I bid um my payoff if I bid bi +and everyone else uses B Star is I get S + + align:start position:0% +and everyone else uses B Star is I get S + + + align:start position:0% +and everyone else uses B Star is I get S +minus bi is my prize I get that bit I + + align:start position:0% +minus bi is my prize I get that bit I + + + align:start position:0% +minus bi is my prize I get that bit I +get that prize if everybody else bids + + align:start position:0% +get that prize if everybody else bids + + + align:start position:0% +get that prize if everybody else bids +less than you know B star of SJ is less + + align:start position:0% +less than you know B star of SJ is less + + + align:start position:0% +less than you know B star of SJ is less +than bi for all J so I win if everybody + + align:start position:0% +than bi for all J so I win if everybody + + + align:start position:0% +than bi for all J so I win if everybody +else bids less than the amount that I + + align:start position:0% +else bids less than the amount that I + + + align:start position:0% +else bids less than the amount that I +bid um so that tells me that + + align:start position:0% +bid um so that tells me that + + + align:start position:0% +bid um so that tells me that +maximization problem would be that my + + align:start position:0% +maximization problem would be that my + + + align:start position:0% +maximization problem would be that my +optimal bid has to be the maximizer of + + align:start position:0% +optimal bid has to be the maximizer of + + + align:start position:0% +optimal bid has to be the maximizer of +sius bi + + align:start position:0% +sius bi + + + align:start position:0% +sius bi +time F the nus1 of you know so the + + align:start position:0% + + + + align:start position:0% + +probability that uh B star of + + align:start position:0% +probability that uh B star of + + + align:start position:0% +probability that uh B star of +SJ is less than or equal to bi is just + + align:start position:0% +SJ is less than or equal to bi is just + + + align:start position:0% +SJ is less than or equal to bi is just +the probability that SJ is less than or + + align:start position:0% +the probability that SJ is less than or + + + align:start position:0% +the probability that SJ is less than or +equal to B Star inverse of + + align:start position:0% +equal to B Star inverse of + + + align:start position:0% +equal to B Star inverse of +bi right so the probability that every + + align:start position:0% +bi right so the probability that every + + + align:start position:0% +bi right so the probability that every +everybody else's signal is below B Star + + align:start position:0% +everybody else's signal is below B Star + + + align:start position:0% +everybody else's signal is below B Star +inverse of bi is just F the F uh F of B + + align:start position:0% +inverse of bi is just F the F uh F of B + + + align:start position:0% +inverse of bi is just F the F uh F of B +inverse of bi raised to the N minus one + + align:start position:0% +inverse of bi raised to the N minus one + + + align:start position:0% +inverse of bi raised to the N minus one +power okay and a trick for simplifying + + align:start position:0% +power okay and a trick for simplifying + + + align:start position:0% +power okay and a trick for simplifying +the analysis of this that you would + + align:start position:0% +the analysis of this that you would + + + align:start position:0% +the analysis of this that you would +think shouldn't work but this is kind of + + align:start position:0% +think shouldn't work but this is kind of + + + align:start position:0% +think shouldn't work but this is kind of +like what we do in mechanism design + + align:start position:0% +like what we do in mechanism design + + + align:start position:0% +like what we do in mechanism design +often is instead of thinking about + + align:start position:0% +often is instead of thinking about + + + align:start position:0% +often is instead of thinking about +people choosing their + + align:start position:0% +people choosing their + + + align:start position:0% +people choosing their +bid think of people + + align:start position:0% +bid think of people + + + align:start position:0% +bid think of people +choosing pretending to be some other + + align:start position:0% +choosing pretending to be some other + + + align:start position:0% +choosing pretending to be some other +type and bidding like some other person + + align:start position:0% +type and bidding like some other person + + + align:start position:0% +type and bidding like some other person +with some other value bids in this um so + + align:start position:0% +with some other value bids in this um so + + + align:start position:0% +with some other value bids in this um so +if I'm thinking about what type S do I + + align:start position:0% +if I'm thinking about what type S do I + + + align:start position:0% +if I'm thinking about what type S do I +want to + + align:start position:0% +want to + + + align:start position:0% +want to +imitate I'm then going to sort of + + align:start position:0% +imitate I'm then going to sort of + + + align:start position:0% +imitate I'm then going to sort of +imitate Type S by choosing B star of + + align:start position:0% +imitate Type S by choosing B star of + + + align:start position:0% +imitate Type S by choosing B star of +s and then my value is going to be my + + align:start position:0% +s and then my value is going to be my + + + align:start position:0% +s and then my value is going to be my +price I'm going to win s I'm going to + + align:start position:0% +price I'm going to win s I'm going to + + + align:start position:0% +price I'm going to win s I'm going to +get a payoff of s minus B star of s if + + align:start position:0% +get a payoff of s minus B star of s if + + + align:start position:0% +get a payoff of s minus B star of s if +everyone else's value is less than S so + + align:start position:0% +everyone else's value is less than S so + + + align:start position:0% +everyone else's value is less than S so +if I bid like the bidder who has Type S + + align:start position:0% +if I bid like the bidder who has Type S + + + align:start position:0% +if I bid like the bidder who has Type S +then I win whenever every body else's + + align:start position:0% +then I win whenever every body else's + + + align:start position:0% +then I win whenever every body else's +type is less than S and so I've + + align:start position:0% +type is less than S and so I've + + + align:start position:0% +type is less than S and so I've +eliminated this inverse function here + + align:start position:0% +eliminated this inverse function here + + + align:start position:0% +eliminated this inverse function here +and I've got my Pro my payoff function + + align:start position:0% +and I've got my Pro my payoff function + + + align:start position:0% +and I've got my Pro my payoff function +I'm trying to maximize is s minus B star + + align:start position:0% +I'm trying to maximize is s minus B star + + + align:start position:0% +I'm trying to maximize is s minus B star +of s * F the N minus one of + + align:start position:0% +of s * F the N minus one of + + + align:start position:0% +of s * F the N minus one of +s so on the bottom line of that screen + + align:start position:0% +s so on the bottom line of that screen + + + align:start position:0% +s so on the bottom line of that screen +I've taken the first order condition + + align:start position:0% +I've taken the first order condition + + + align:start position:0% +I've taken the first order condition +differentiating this with respect to S + + align:start position:0% +differentiating this with respect to S + + + align:start position:0% +differentiating this with respect to S +um and differentiating this with respect + + align:start position:0% +um and differentiating this with respect + + + align:start position:0% +um and differentiating this with respect +to S and setting it equal to zero at s + + align:start position:0% +to S and setting it equal to zero at s + + + align:start position:0% +to S and setting it equal to zero at s +equal + + align:start position:0% +equal + + + align:start position:0% +equal +SI okay and so the derivative of this + + align:start position:0% +SI okay and so the derivative of this + + + align:start position:0% +SI okay and so the derivative of this +with respect to s + + align:start position:0% +with respect to s + + + align:start position:0% +with respect to s +is uh this term times the derivative of + + align:start position:0% +is uh this term times the derivative of + + + align:start position:0% +is uh this term times the derivative of +this one which is nus1 f the N minus 2 + + align:start position:0% +this one which is nus1 f the N minus 2 + + + align:start position:0% +this one which is nus1 f the N minus 2 +of si uh times little F of Si and then + + align:start position:0% +of si uh times little F of Si and then + + + align:start position:0% +of si uh times little F of Si and then +plus this times the derivative of this + + align:start position:0% +plus this times the derivative of this + + + align:start position:0% +plus this times the derivative of this +which is just minus B Star Prime + + align:start position:0% +which is just minus B Star Prime + + + align:start position:0% +which is just minus B Star Prime +evaluated SI so that's the first order + + align:start position:0% +evaluated SI so that's the first order + + + align:start position:0% +evaluated SI so that's the first order +condition for my maximization when I'm + + align:start position:0% +condition for my maximization when I'm + + + align:start position:0% +condition for my maximization when I'm +thinking about which type do I want to + + align:start position:0% +thinking about which type do I want to + + + align:start position:0% +thinking about which type do I want to +copy and noting that the type I copy has + + align:start position:0% +copy and noting that the type I copy has + + + align:start position:0% +copy and noting that the type I copy has +to be + + align:start position:0% +to be + + + align:start position:0% +to be +me okay some you know right what's the + + align:start position:0% +me okay some you know right what's the + + + align:start position:0% +me okay some you know right what's the +sort of trick here is that I know the + + align:start position:0% +sort of trick here is that I know the + + + align:start position:0% +sort of trick here is that I know the +equilibrium I know the equilibrium is + + align:start position:0% +equilibrium I know the equilibrium is + + + align:start position:0% +equilibrium I know the equilibrium is +SAR equals SI and so because you know + + align:start position:0% +SAR equals SI and so because you know + + + align:start position:0% +SAR equals SI and so because you know +the equilibrium is the identity uh that + + align:start position:0% +the equilibrium is the identity uh that + + + align:start position:0% +the equilibrium is the identity uh that +simplifies what the expression is for + + align:start position:0% +simplifies what the expression is for + + + align:start position:0% +simplifies what the expression is for +the the first organis evaluated at the + + align:start position:0% +the the first organis evaluated at the + + + align:start position:0% +the the first organis evaluated at the +equilibrium and now in the next three + + align:start position:0% +equilibrium and now in the next three + + + align:start position:0% +equilibrium and now in the next three +slides I'm going to do like three + + align:start position:0% +slides I'm going to do like three + + + align:start position:0% +slides I'm going to do like three +different rewritings of this + + align:start position:0% +different rewritings of this + + + align:start position:0% +different rewritings of this +um one rewriting I'm going to do is just + + align:start position:0% +um one rewriting I'm going to do is just + + + align:start position:0% +um one rewriting I'm going to do is just +think of myself as solving this for the + + align:start position:0% +think of myself as solving this for the + + + align:start position:0% +think of myself as solving this for the +bid so I'm going to solve this equation + + align:start position:0% +bid so I'm going to solve this equation + + + align:start position:0% +bid so I'm going to solve this equation +for B Star and I'm going to do that by + + align:start position:0% +for B Star and I'm going to do that by + + + align:start position:0% +for B Star and I'm going to do that by +just taking this expression B Star and N + + align:start position:0% +just taking this expression B Star and N + + + align:start position:0% +just taking this expression B Star and N +minus one f f to the N minus 2 little f + + align:start position:0% +minus one f f to the N minus 2 little f + + + align:start position:0% +minus one f f to the N minus 2 little f +move it to the other side and then + + align:start position:0% +move it to the other side and then + + + align:start position:0% +move it to the other side and then +divide by this uh and see what's left + + align:start position:0% +divide by this uh and see what's left + + + align:start position:0% +divide by this uh and see what's left +and what you get is the optimal bid is + + align:start position:0% +and what you get is the optimal bid is + + + align:start position:0% +and what you get is the optimal bid is +your true value minus a mark down so + + align:start position:0% +your true value minus a mark down so + + + align:start position:0% +your true value minus a mark down so +this is an expression for how much you + + align:start position:0% +this is an expression for how much you + + + align:start position:0% +this is an expression for how much you +shade your bid + + align:start position:0% +shade your bid + + + align:start position:0% +shade your bid +um if I look at the denominate the + + align:start position:0% +um if I look at the denominate the + + + align:start position:0% +um if I look at the denominate the +numerator you'll see that the numerator + + align:start position:0% +numerator you'll see that the numerator + + + align:start position:0% +numerator you'll see that the numerator +this F to the N minus one of Si that's + + align:start position:0% +this F to the N minus one of Si that's + + + align:start position:0% +this F to the N minus one of Si that's +just the probability that everyone else + + align:start position:0% +just the probability that everyone else + + + align:start position:0% +just the probability that everyone else +uh bids less than I bid um because + + align:start position:0% +uh bids less than I bid um because + + + align:start position:0% +uh bids less than I bid um because +that's the probability that everyone + + align:start position:0% +that's the probability that everyone + + + align:start position:0% +that's the probability that everyone +else has a lower type than I + + align:start position:0% +else has a lower type than I + + + align:start position:0% +else has a lower type than I +do so this is the probability that + + align:start position:0% +do so this is the probability that + + + align:start position:0% +do so this is the probability that +everyone else bids less than what I than + + align:start position:0% +everyone else bids less than what I than + + + align:start position:0% +everyone else bids less than what I than +what I'm bidding in + + align:start position:0% +what I'm bidding in + + + align:start position:0% +what I'm bidding in +equilibrium and then the denominator is + + align:start position:0% +equilibrium and then the denominator is + + + align:start position:0% +equilibrium and then the denominator is +just the derivative of the numerator + + align:start position:0% +just the derivative of the numerator + + + align:start position:0% +just the derivative of the numerator +with the change of variables formula so + + align:start position:0% +with the change of variables formula so + + + align:start position:0% +with the change of variables formula so +you different differentiate that this G + + align:start position:0% +you different differentiate that this G + + + align:start position:0% +you different differentiate that this G +with respect to this this is what you + + align:start position:0% +with respect to this this is what you + + + align:start position:0% +with respect to this this is what you +get and then you have a one over B Star + + align:start position:0% +get and then you have a one over B Star + + + align:start position:0% +get and then you have a one over B Star +Prime from a change of variables formula + + align:start position:0% +Prime from a change of variables formula + + + align:start position:0% +Prime from a change of variables formula +so what we get is that um + + align:start position:0% +so what we get is that um + + + align:start position:0% +so what we get is that um +the what you do in a second price steal + + align:start position:0% +the what you do in a second price steal + + + align:start position:0% +the what you do in a second price steal +bid auction is you mark down your bid + + align:start position:0% +bid auction is you mark down your bid + + + align:start position:0% +bid auction is you mark down your bid +you mark it down by the ratio of the CDF + + align:start position:0% +you mark it down by the ratio of the CDF + + + align:start position:0% +you mark it down by the ratio of the CDF +of the bid + + align:start position:0% +of the bid + + + align:start position:0% +of the bid +distribution the highest bid + + align:start position:0% +distribution the highest bid + + + align:start position:0% +distribution the highest bid +distribution evaluated at SI divided by + + align:start position:0% +distribution evaluated at SI divided by + + + align:start position:0% +distribution evaluated at SI divided by +the PDF of the highest bid + + align:start position:0% +the PDF of the highest bid + + + align:start position:0% +the PDF of the highest bid +distribution okay + + align:start position:0% +distribution okay + + + align:start position:0% +distribution okay +so you know when do you shade your bids + + align:start position:0% +so you know when do you shade your bids + + + align:start position:0% +so you know when do you shade your bids +more you're more aggressive in shading + + align:start position:0% +more you're more aggressive in shading + + + align:start position:0% +more you're more aggressive in shading +your bids if the probability of winning + + align:start position:0% +your bids if the probability of winning + + + align:start position:0% +your bids if the probability of winning +is higher and the density of the bid + + align:start position:0% +is higher and the density of the bid + + + align:start position:0% +is higher and the density of the bid +dist rival bid distribution is lower + + align:start position:0% +dist rival bid distribution is lower + + + align:start position:0% +dist rival bid distribution is lower +because the sort of you know dens this + + align:start position:0% +because the sort of you know dens this + + + align:start position:0% +because the sort of you know dens this +is kind of like an inverse elasticity + + align:start position:0% +is kind of like an inverse elasticity + + + align:start position:0% +is kind of like an inverse elasticity +rule for markups you know the the more + + align:start position:0% +rule for markups you know the the more + + + align:start position:0% +rule for markups you know the the more +biders there are who are bidding around + + align:start position:0% +biders there are who are bidding around + + + align:start position:0% +biders there are who are bidding around +almost exactly bar star of Si the more + + align:start position:0% +almost exactly bar star of Si the more + + + align:start position:0% +almost exactly bar star of Si the more +you don't want to shade your bid because + + align:start position:0% +you don't want to shade your bid because + + + align:start position:0% +you don't want to shade your bid because +if you shade your bid you're likely to + + align:start position:0% +if you shade your bid you're likely to + + + align:start position:0% +if you shade your bid you're likely to +lose but if this density is low then + + align:start position:0% +lose but if this density is low then + + + align:start position:0% +lose but if this density is low then +every extra bit of shading you do has + + align:start position:0% +every extra bit of shading you do has + + + align:start position:0% +every extra bit of shading you do has +very little there's very little demand + + align:start position:0% +very little there's very little demand + + + align:start position:0% +very little there's very little demand +elasticity there's very little impact on + + align:start position:0% +elasticity there's very little impact on + + + align:start position:0% +elasticity there's very little impact on +your probability of winning so then you + + align:start position:0% +your probability of winning so then you + + + align:start position:0% +your probability of winning so then you +shade more aggressively and so you know + + align:start position:0% +shade more aggressively and so you know + + + align:start position:0% +shade more aggressively and so you know +bid shading is based on How likely you + + align:start position:0% +bid shading is based on How likely you + + + align:start position:0% +bid shading is based on How likely you +are to win which gives you the + + align:start position:0% +are to win which gives you the + + + align:start position:0% +are to win which gives you the +inframarginal gains from from lowering + + align:start position:0% +inframarginal gains from from lowering + + + align:start position:0% +inframarginal gains from from lowering +the bid and then the g is how much + + align:start position:0% +the bid and then the g is how much + + + align:start position:0% +the bid and then the g is how much +what's the increased probability of + + align:start position:0% +what's the increased probability of + + + align:start position:0% +what's the increased probability of +losing and so I mark down uh based on + + align:start position:0% +losing and so I mark down uh based on + + + align:start position:0% +losing and so I mark down uh based on +those ratios okay uh and this expression + + align:start position:0% +those ratios okay uh and this expression + + + align:start position:0% +those ratios okay uh and this expression +I I did it because Tobias is going to be + + align:start position:0% +I I did it because Tobias is going to be + + + align:start position:0% +I I did it because Tobias is going to be +lecturing on Wednesday this is also sort + + align:start position:0% +lecturing on Wednesday this is also sort + + + align:start position:0% +lecturing on Wednesday this is also sort +of very very big part of the structural + + align:start position:0% +of very very big part of the structural + + + align:start position:0% +of very very big part of the structural +estimation of auction models because you + + align:start position:0% +estimation of auction models because you + + + align:start position:0% +estimation of auction models because you +know this is just the CDF of the bid + + align:start position:0% +know this is just the CDF of the bid + + + align:start position:0% +know this is just the CDF of the bid +rival bid distribution this is the PDF + + align:start position:0% +rival bid distribution this is the PDF + + + align:start position:0% +rival bid distribution this is the PDF +of the Rival bid distribution these are + + align:start position:0% +of the Rival bid distribution these are + + + align:start position:0% +of the Rival bid distribution these are +estimable objects that sort of basic + + align:start position:0% +estimable objects that sort of basic + + + align:start position:0% +estimable objects that sort of basic +Insight of structural estimation of + + align:start position:0% +Insight of structural estimation of + + + align:start position:0% +Insight of structural estimation of +auctions is this is observable this is + + align:start position:0% +auctions is this is observable this is + + + align:start position:0% +auctions is this is observable this is +observable this is observable so that's + + align:start position:0% +observable this is observable so that's + + + align:start position:0% +observable this is observable so that's +how you can back out people's values + + align:start position:0% +how you can back out people's values + + + align:start position:0% +how you can back out people's values +okay anyway Tobias will do that in much + + align:start position:0% +okay anyway Tobias will do that in much + + + align:start position:0% +okay anyway Tobias will do that in much +more detail on + + align:start position:0% +more detail on + + + align:start position:0% +more detail on +Wednesday second thing I'm going to do + + align:start position:0% +Wednesday second thing I'm going to do + + + align:start position:0% +Wednesday second thing I'm going to do +with that first order condition is I'm + + align:start position:0% +with that first order condition is I'm + + + align:start position:0% +with that first order condition is I'm +actually going to solve this auction and + + align:start position:0% +actually going to solve this auction and + + + align:start position:0% +actually going to solve this auction and +again this is something that it should + + align:start position:0% +again this is something that it should + + + align:start position:0% +again this is something that it should +not work but the model is sort of + + align:start position:0% +not work but the model is sort of + + + align:start position:0% +not work but the model is sort of +elegantly designed so that it does work + + align:start position:0% +elegantly designed so that it does work + + + align:start position:0% +elegantly designed so that it does work +so this was our first order condition + + align:start position:0% +so this was our first order condition + + + align:start position:0% +so this was our first order condition +that determined the optimal + + align:start position:0% +that determined the optimal + + + align:start position:0% +that determined the optimal +bid I'm going to rearrange it by putting + + align:start position:0% +bid I'm going to rearrange it by putting + + + align:start position:0% +bid I'm going to rearrange it by putting +all the things with negative signs on + + align:start position:0% +all the things with negative signs on + + + align:start position:0% +all the things with negative signs on +the left side so I put the B Star Prime + + align:start position:0% +the left side so I put the B Star Prime + + + align:start position:0% +the left side so I put the B Star Prime +term on the left side and I put this bar + + align:start position:0% +term on the left side and I put this bar + + + align:start position:0% +term on the left side and I put this bar +star times this stuff on the left + + align:start position:0% +star times this stuff on the left + + + align:start position:0% +star times this stuff on the left +side so I get B star of Si times this uh + + align:start position:0% +side so I get B star of Si times this uh + + + align:start position:0% +side so I get B star of Si times this uh +uh order statistic plus b star prime + + align:start position:0% +uh order statistic plus b star prime + + + align:start position:0% +uh order statistic plus b star prime +time that CDF equals SI times this + + align:start position:0% +time that CDF equals SI times this + + + align:start position:0% +time that CDF equals SI times this +density and then you look at that + + align:start position:0% +density and then you look at that + + + align:start position:0% +density and then you look at that +expression and you're like wow I can + + align:start position:0% +expression and you're like wow I can + + + align:start position:0% +expression and you're like wow I can +integrate both sides of that um the left + + align:start position:0% +integrate both sides of that um the left + + + align:start position:0% +integrate both sides of that um the left +side's an exact derivative right it's a + + align:start position:0% +side's an exact derivative right it's a + + + align:start position:0% +side's an exact derivative right it's a +derivative of this expression B Star * F + + align:start position:0% +derivative of this expression B Star * F + + + align:start position:0% +derivative of this expression B Star * F +the N minus one because this is B Star + + align:start position:0% +the N minus one because this is B Star + + + align:start position:0% +the N minus one because this is B Star +time the derivative of f the n minus1 + + align:start position:0% +time the derivative of f the n minus1 + + + align:start position:0% +time the derivative of f the n minus1 +and this is f nus1 * bar star Prime + + align:start position:0% +and this is f nus1 * bar star Prime + + + align:start position:0% +and this is f nus1 * bar star Prime +so B Star * F the N + + align:start position:0% +so B Star * F the N + + + align:start position:0% +so B Star * F the N +minus1 is the integral from s lower bar + + align:start position:0% +minus1 is the integral from s lower bar + + + align:start position:0% +minus1 is the integral from s lower bar +to SI of this uh density on the right + + align:start position:0% +to SI of this uh density on the right + + + align:start position:0% +to SI of this uh density on the right +side and then again skipping steps you + + align:start position:0% +side and then again skipping steps you + + + align:start position:0% +side and then again skipping steps you +can integrate this expression on the + + align:start position:0% +can integrate this expression on the + + + align:start position:0% +can integrate this expression on the +right side by parts that's a trick + + align:start position:0% +right side by parts that's a trick + + + align:start position:0% +right side by parts that's a trick +someone found a while ago and you can + + align:start position:0% +someone found a while ago and you can + + + align:start position:0% +someone found a while ago and you can +get a closed form for expression which + + align:start position:0% +get a closed form for expression which + + + align:start position:0% +get a closed form for expression which +is your bid is your markup your your bid + + align:start position:0% +is your bid is your markup your your bid + + + align:start position:0% +is your bid is your markup your your bid +is your value minus this mark down which + + align:start position:0% +is your value minus this mark down which + + + align:start position:0% +is your value minus this mark down which +is the integral from S Bar to SI F the + + align:start position:0% +is the integral from S Bar to SI F the + + + align:start position:0% +is the integral from S Bar to SI F the +nus one of X DX over capital F the nus + + align:start position:0% +nus one of X DX over capital F the nus + + + align:start position:0% +nus one of X DX over capital F the nus +one of s okay so this first price seal + + align:start position:0% +one of s okay so this first price seal + + + align:start position:0% +one of s okay so this first price seal +bit auction is + + align:start position:0% +bit auction is + + + align:start position:0% +bit auction is +solvable all the only thing you need to + + align:start position:0% +solvable all the only thing you need to + + + align:start position:0% +solvable all the only thing you need to +plug in is what is the distribution of + + align:start position:0% +plug in is what is the distribution of + + + align:start position:0% +plug in is what is the distribution of +of the values is it a uniform + + align:start position:0% +of the values is it a uniform + + + align:start position:0% +of the values is it a uniform +distribution is it an exponential + + align:start position:0% +distribution is it an exponential + + + align:start position:0% +distribution is it an exponential +distribution any distribution for which + + align:start position:0% +distribution any distribution for which + + + align:start position:0% +distribution any distribution for which +you can do this integral of f to the N + + align:start position:0% +you can do this integral of f to the N + + + align:start position:0% +you can do this integral of f to the N +minus one you can just get a nice closed + + align:start position:0% +minus one you can just get a nice closed + + + align:start position:0% +minus one you can just get a nice closed +form solution for what an auction will + + align:start position:0% +form solution for what an auction will + + + align:start position:0% +form solution for what an auction will +be + + align:start position:0% +be + + + align:start position:0% +be +for instance down here I did it for the + + align:start position:0% +for instance down here I did it for the + + + align:start position:0% +for instance down here I did it for the +uniform + + align:start position:0% +uniform + + + align:start position:0% +uniform +distribution in the uniform distribution + + align:start position:0% +distribution in the uniform distribution + + + align:start position:0% +distribution in the uniform distribution +f ofx is just X and so it's just the + + align:start position:0% +f ofx is just X and so it's just the + + + align:start position:0% +f ofx is just X and so it's just the +integral X the N minus1 DX that + + align:start position:0% +integral X the N minus1 DX that + + + align:start position:0% +integral X the N minus1 DX that +integrates to X the N / n you evaluate + + align:start position:0% +integrates to X the N / n you evaluate + + + align:start position:0% +integrates to X the N / n you evaluate +that and this tells me that the optimal + + align:start position:0% +that and this tells me that the optimal + + + align:start position:0% +that and this tells me that the optimal +bid with uniform distributions is nus + + align:start position:0% +bid with uniform distributions is nus + + + align:start position:0% +bid with uniform distributions is nus +one/ n times your value so as the number + + align:start position:0% +one/ n times your value so as the number + + + align:start position:0% +one/ n times your value so as the number +of bids gets large you know you're + + align:start position:0% +of bids gets large you know you're + + + align:start position:0% +of bids gets large you know you're +you're always shading your value and + + align:start position:0% +you're always shading your value and + + + align:start position:0% +you're always shading your value and +with a uniform distribution you're sh + + align:start position:0% +with a uniform distribution you're sh + + + align:start position:0% +with a uniform distribution you're sh +your value in a linear way with n bids + + align:start position:0% +your value in a linear way with n bids + + + align:start position:0% +your value in a linear way with n bids +you just bid n minus one/ n times your + + align:start position:0% +you just bid n minus one/ n times your + + + align:start position:0% +you just bid n minus one/ n times your +value so if there's n is two you bid + + align:start position:0% +value so if there's n is two you bid + + + align:start position:0% +value so if there's n is two you bid +half your value n is three you bid 2/3 + + align:start position:0% +half your value n is three you bid 2/3 + + + align:start position:0% +half your value n is three you bid 2/3 +of your value and as 10 you bid 90% of + + align:start position:0% +of your value and as 10 you bid 90% of + + + align:start position:0% +of your value and as 10 you bid 90% of +your + + align:start position:0% + + + + align:start position:0% + +value okay but you know it's nothing + + align:start position:0% +value okay but you know it's nothing + + + align:start position:0% +value okay but you know it's nothing +special about the uniform distribution + + align:start position:0% +special about the uniform distribution + + + align:start position:0% +special about the uniform distribution +you can solve this model however you do + + align:start position:0% +you can solve this model however you do + + + align:start position:0% +you can solve this model however you do +this + + align:start position:0% +this + + + align:start position:0% +this +okay um + + align:start position:0% + + + + align:start position:0% + +another um thing that you get from this + + align:start position:0% +another um thing that you get from this + + + align:start position:0% +another um thing that you get from this +is a proposition that helps you + + align:start position:0% +is a proposition that helps you + + + align:start position:0% +is a proposition that helps you +understand why the auction rise of + + align:start position:0% +understand why the auction rise of + + + align:start position:0% +understand why the auction rise of +Revenue it does the optimal bid + + align:start position:0% +Revenue it does the optimal bid + + + align:start position:0% +Revenue it does the optimal bid +expression I wrote down the previous + + align:start position:0% +expression I wrote down the previous + + + align:start position:0% +expression I wrote down the previous +page is just I bid the expected second + + align:start position:0% +page is just I bid the expected second + + + align:start position:0% +page is just I bid the expected second +highest value conditional on having the + + align:start position:0% +highest value conditional on having the + + + align:start position:0% +highest value conditional on having the +highest value so I just I know my signal + + align:start position:0% +highest value so I just I know my signal + + + align:start position:0% +highest value so I just I know my signal +I do the thought experiment if I did + + align:start position:0% +I do the thought experiment if I did + + + align:start position:0% +I do the thought experiment if I did +have the highest value so everyone + + align:start position:0% +have the highest value so everyone + + + align:start position:0% +have the highest value so everyone +else's value was less than mine what + + align:start position:0% +else's value was less than mine what + + + align:start position:0% +else's value was less than mine what +would be the second highest value I bid + + align:start position:0% +would be the second highest value I bid + + + align:start position:0% +would be the second highest value I bid +the expectation of + + align:start position:0% +the expectation of + + + align:start position:0% +the expectation of +that okay + + align:start position:0% +that okay + + + align:start position:0% +that okay +um why is that true I don't have great + + align:start position:0% +um why is that true I don't have great + + + align:start position:0% +um why is that true I don't have great +intuition but it it's easy to see it + + align:start position:0% +intuition but it it's easy to see it + + + align:start position:0% +intuition but it it's easy to see it +mathematically so you know + + align:start position:0% +mathematically so you know + + + align:start position:0% +mathematically so you know +the you know on the previous SL I had + + align:start position:0% +the you know on the previous SL I had + + + align:start position:0% +the you know on the previous SL I had +this expression for the the I had this + + align:start position:0% +this expression for the the I had this + + + align:start position:0% +this expression for the the I had this +thing I sort of recognized both sides + + align:start position:0% +thing I sort of recognized both sides + + + align:start position:0% +thing I sort of recognized both sides +were derivatives and I got this + + align:start position:0% +were derivatives and I got this + + + align:start position:0% +were derivatives and I got this +expression for B star of s as an + + align:start position:0% +expression for B star of s as an + + + align:start position:0% +expression for B star of s as an +integral so that gives me bar star of s + + align:start position:0% +integral so that gives me bar star of s + + + align:start position:0% +integral so that gives me bar star of s +is this integral of this density on the + + align:start position:0% +is this integral of this density on the + + + align:start position:0% +is this integral of this density on the +top and F the nus1 on the bottom but if + + align:start position:0% +top and F the nus1 on the bottom but if + + + align:start position:0% +top and F the nus1 on the bottom but if +you look at what this density is n-1 f + + align:start position:0% +you look at what this density is n-1 f + + + align:start position:0% +you look at what this density is n-1 f +nus 2 little F ofx DX that's the density + + align:start position:0% +nus 2 little F ofx DX that's the density + + + align:start position:0% +nus 2 little F ofx DX that's the density +of the highest of n minus one draws from + + align:start position:0% +of the highest of n minus one draws from + + + align:start position:0% +of the highest of n minus one draws from +F and so I'm + + align:start position:0% +F and so I'm + + + align:start position:0% +F and so I'm +integrating x times the density of the + + align:start position:0% +integrating x times the density of the + + + align:start position:0% +integrating x times the density of the +highest of n minus one draws from X from + + align:start position:0% +highest of n minus one draws from X from + + + align:start position:0% +highest of n minus one draws from X from +s lower bar up to capital S and then I'm + + align:start position:0% +s lower bar up to capital S and then I'm + + + align:start position:0% +s lower bar up to capital S and then I'm +dividing by F the nus one of X so when I + + align:start position:0% +dividing by F the nus one of X so when I + + + align:start position:0% +dividing by F the nus one of X so when I +divide by F the nus1 of X this this is + + align:start position:0% +divide by F the nus1 of X this this is + + + align:start position:0% +divide by F the nus1 of X this this is +giving me this density conditional on + + align:start position:0% +giving me this density conditional on + + + align:start position:0% +giving me this density conditional on +the highest value being less than + + align:start position:0% +the highest value being less than + + + align:start position:0% +the highest value being less than +SI and so this is just the expected + + align:start position:0% +SI and so this is just the expected + + + align:start position:0% +SI and so this is just the expected +second highest bid conditional on the + + align:start position:0% +second highest bid conditional on the + + + align:start position:0% +second highest bid conditional on the +second highest bid being less than + + align:start position:0% + + + + align:start position:0% + +SI so you know third way to think about + + align:start position:0% +SI so you know third way to think about + + + align:start position:0% +SI so you know third way to think about +bidding so you can thought about + + align:start position:0% +bidding so you can thought about + + + align:start position:0% +bidding so you can thought about +thinking about bidding in terms of + + align:start position:0% +thinking about bidding in terms of + + + align:start position:0% +thinking about bidding in terms of +markups it turns out that a way to think + + align:start position:0% +markups it turns out that a way to think + + + align:start position:0% +markups it turns out that a way to think +about what the markups imply is that the + + align:start position:0% +about what the markups imply is that the + + + align:start position:0% +about what the markups imply is that the +way you bid is you just take your value + + align:start position:0% +way you bid is you just take your value + + + align:start position:0% +way you bid is you just take your value +think about what the second highest + + align:start position:0% +think about what the second highest + + + align:start position:0% +think about what the second highest +value would be and you bid that uh in + + align:start position:0% +value would be and you bid that uh in + + + align:start position:0% +value would be and you bid that uh in +expectation so cor lary of that + + align:start position:0% +expectation so cor lary of that + + + align:start position:0% +expectation so cor lary of that +observation is that first and second + + align:start position:0% +observation is that first and second + + + align:start position:0% +observation is that first and second +price auctions yield exactly the same + + align:start position:0% +price auctions yield exactly the same + + + align:start position:0% +price auctions yield exactly the same +expected Revenue to the seller right the + + align:start position:0% +expected Revenue to the seller right the + + + align:start position:0% +expected Revenue to the seller right the +second price auction clearly you're + + align:start position:0% +second price auction clearly you're + + + align:start position:0% +second price auction clearly you're +always getting the second highest value + + align:start position:0% +always getting the second highest value + + + align:start position:0% +always getting the second highest value +as your Revenue so it's just the + + align:start position:0% +as your Revenue so it's just the + + + align:start position:0% +as your Revenue so it's just the +expected second highest value is the + + align:start position:0% +expected second highest value is the + + + align:start position:0% +expected second highest value is the +revenue in the first price sealed bit + + align:start position:0% +revenue in the first price sealed bit + + + align:start position:0% +revenue in the first price sealed bit +auction what you're getting is the + + align:start position:0% +auction what you're getting is the + + + align:start position:0% +auction what you're getting is the +expectation over the you always sell it + + align:start position:0% +expectation over the you always sell it + + + align:start position:0% +expectation over the you always sell it +to the high value person + + align:start position:0% +to the high value person + + + align:start position:0% +to the high value person +so I'm getting the expectation over the + + align:start position:0% +so I'm getting the expectation over the + + + align:start position:0% +so I'm getting the expectation over the +value of the high value person of the + + align:start position:0% +value of the high value person of the + + + align:start position:0% +value of the high value person of the +expected second the expected highest of + + align:start position:0% +expected second the expected highest of + + + align:start position:0% +expected second the expected highest of +and the expected second highest value + + align:start position:0% +and the expected second highest value + + + align:start position:0% +and the expected second highest value +conditional on the second highest value + + align:start position:0% +conditional on the second highest value + + + align:start position:0% +conditional on the second highest value +being less than that level and so + + align:start position:0% +being less than that level and so + + + align:start position:0% +being less than that level and so +iterated expectation says that's just + + align:start position:0% +iterated expectation says that's just + + + align:start position:0% +iterated expectation says that's just +another way to compute the expected + + align:start position:0% +another way to compute the expected + + + align:start position:0% +another way to compute the expected +second highest value I just condition on + + align:start position:0% +second highest value I just condition on + + + align:start position:0% +second highest value I just condition on +the highest value and say what's the + + align:start position:0% +the highest value and say what's the + + + align:start position:0% +the highest value and say what's the +expected second highest value + + align:start position:0% +expected second highest value + + + align:start position:0% +expected second highest value +conditional on that being the highest + + align:start position:0% +conditional on that being the highest + + + align:start position:0% +conditional on that being the highest +value and then I integrate out overall + + align:start position:0% +value and then I integrate out overall + + + align:start position:0% +value and then I integrate out overall +possible highest values that is the + + align:start position:0% +possible highest values that is the + + + align:start position:0% +possible highest values that is the +expected second highest value so because + + align:start position:0% +expected second highest value so because + + + align:start position:0% +expected second highest value so because +everyone's bidding expected second + + align:start position:0% +everyone's bidding expected second + + + align:start position:0% +everyone's bidding expected second +highest + + align:start position:0% +highest + + + align:start position:0% +highest +values conditional on winning you get + + align:start position:0% +values conditional on winning you get + + + align:start position:0% +values conditional on winning you get +the same expected second highest value + + align:start position:0% +the same expected second highest value + + + align:start position:0% +the same expected second highest value +as the + + align:start position:0% +as the + + + align:start position:0% +as the +revenue so this is a you know special + + align:start position:0% +revenue so this is a you know special + + + align:start position:0% +revenue so this is a you know special +case of What's called the revenue + + align:start position:0% +case of What's called the revenue + + + align:start position:0% +case of What's called the revenue +equivalence theorem that you have these + + align:start position:0% +equivalence theorem that you have these + + + align:start position:0% +equivalence theorem that you have these +sort of seemingly different auction + + align:start position:0% +sort of seemingly different auction + + + align:start position:0% +sort of seemingly different auction +mechanisms one where people bid + + align:start position:0% +mechanisms one where people bid + + + align:start position:0% +mechanisms one where people bid +truthfully one where people shade bids + + align:start position:0% +truthfully one where people shade bids + + + align:start position:0% +truthfully one where people shade bids +and somehow they raise exactly the same + + align:start position:0% +and somehow they raise exactly the same + + + align:start position:0% +and somehow they raise exactly the same +Revenue um I would say you know this is + + align:start position:0% +Revenue um I would say you know this is + + + align:start position:0% +Revenue um I would say you know this is +actually you know one of the most + + align:start position:0% +actually you know one of the most + + + align:start position:0% +actually you know one of the most +misunderstood things and you know like + + align:start position:0% +misunderstood things and you know like + + + align:start position:0% +misunderstood things and you know like +can like you talk to people who are + + align:start position:0% +can like you talk to people who are + + + align:start position:0% +can like you talk to people who are +doing like um selling auctions online + + align:start position:0% +doing like um selling auctions online + + + align:start position:0% +doing like um selling auctions online +which are often sold through second + + align:start position:0% +which are often sold through second + + + align:start position:0% +which are often sold through second +price mechanisms and just you know at + + align:start position:0% +price mechanisms and just you know at + + + align:start position:0% +price mechanisms and just you know at +every company that does this like you + + align:start position:0% +every company that does this like you + + + align:start position:0% +every company that does this like you +know many times per year every year some + + align:start position:0% +know many times per year every year some + + + align:start position:0% +know many times per year every year some +executive comes up and realizes wait + + align:start position:0% +executive comes up and realizes wait + + + align:start position:0% +executive comes up and realizes wait +people are bidding this and we're only + + align:start position:0% +people are bidding this and we're only + + + align:start position:0% +people are bidding this and we're only +charging them the second highest value I + + align:start position:0% +charging them the second highest value I + + + align:start position:0% +charging them the second highest value I +can get this sort of one over n thing + + align:start position:0% +can get this sort of one over n thing + + + align:start position:0% +can get this sort of one over n thing +there's this big gap that's $42 million + + align:start position:0% +there's this big gap that's $42 million + + + align:start position:0% +there's this big gap that's $42 million +we should switch to a first price + + align:start position:0% +we should switch to a first price + + + align:start position:0% +we should switch to a first price +auction instead of a second price + + align:start position:0% +auction instead of a second price + + + align:start position:0% +auction instead of a second price +auction and obviously the sort of + + align:start position:0% +auction and obviously the sort of + + + align:start position:0% +auction and obviously the sort of +mistake in that reasoning is like you + + align:start position:0% +mistake in that reasoning is like you + + + align:start position:0% +mistake in that reasoning is like you +yes if you had the same bids and you + + align:start position:0% +yes if you had the same bids and you + + + align:start position:0% +yes if you had the same bids and you +change the rule you would get more money + + align:start position:0% +change the rule you would get more money + + + align:start position:0% +change the rule you would get more money +but when you change the rules people + + align:start position:0% +but when you change the rules people + + + align:start position:0% +but when you change the rules people +will just start shading their bids they + + align:start position:0% +will just start shading their bids they + + + align:start position:0% +will just start shading their bids they +will bid less you'll raise exactly the + + align:start position:0% +will bid less you'll raise exactly the + + + align:start position:0% +will bid less you'll raise exactly the +same mechanism in same Revenue with a + + align:start position:0% +same mechanism in same Revenue with a + + + align:start position:0% +same mechanism in same Revenue with a +first or second price mechanism we often + + align:start position:0% +first or second price mechanism we often + + + align:start position:0% +first or second price mechanism we often +think second price mechanisms are better + + align:start position:0% +think second price mechanisms are better + + + align:start position:0% +think second price mechanisms are better +because in second price mechanisms + + align:start position:0% +because in second price mechanisms + + + align:start position:0% +because in second price mechanisms +people can think about how much to bid + + align:start position:0% +people can think about how much to bid + + + align:start position:0% +people can think about how much to bid +which is just what's it worth to me + + align:start position:0% +which is just what's it worth to me + + + align:start position:0% +which is just what's it worth to me +whereas in the first price mechanism + + align:start position:0% +whereas in the first price mechanism + + + align:start position:0% +whereas in the first price mechanism +they have to do this complicated + + align:start position:0% +they have to do this complicated + + + align:start position:0% +they have to do this complicated +reasoning about bid shading and what + + align:start position:0% +reasoning about bid shading and what + + + align:start position:0% +reasoning about bid shading and what +would be the expected second highest bid + + align:start position:0% +would be the expected second highest bid + + + align:start position:0% +would be the expected second highest bid +given what I know it's putting all that + + align:start position:0% +given what I know it's putting all that + + + align:start position:0% +given what I know it's putting all that +work on the firms is not doing you any + + align:start position:0% +work on the firms is not doing you any + + + align:start position:0% +work on the firms is not doing you any +good okay so + + align:start position:0% +good okay so + + + align:start position:0% +good okay so +um anyway you know uh Revenue + + align:start position:0% +um anyway you know uh Revenue + + + align:start position:0% +um anyway you know uh Revenue +equivalence theorem and I'm going to go + + align:start position:0% +equivalence theorem and I'm going to go + + + align:start position:0% +equivalence theorem and I'm going to go +through this quickly consider more + + align:start position:0% +through this quickly consider more + + + align:start position:0% +through this quickly consider more +General auction mechanism imagine you + + align:start position:0% +General auction mechanism imagine you + + + align:start position:0% +General auction mechanism imagine you +had some any game the bidders just + + align:start position:0% +had some any game the bidders just + + + align:start position:0% +had some any game the bidders just +submit bids B1 through BN the good is + + align:start position:0% +submit bids B1 through BN the good is + + + align:start position:0% +submit bids B1 through BN the good is +allocated to biders with some + + align:start position:0% +allocated to biders with some + + + align:start position:0% +allocated to biders with some +probability that depends on what all the + + align:start position:0% +probability that depends on what all the + + + align:start position:0% +probability that depends on what all the +bids are and the payments are some + + align:start position:0% +bids are and the payments are some + + + align:start position:0% +bids are and the payments are some +function of what all the bids are so the + + align:start position:0% +function of what all the bids are so the + + + align:start position:0% +function of what all the bids are so the +first price sealed bid auction would fit + + align:start position:0% +first price sealed bid auction would fit + + + align:start position:0% +first price sealed bid auction would fit +this you know you give it with + + align:start position:0% +this you know you give it with + + + align:start position:0% +this you know you give it with +probability one to the person with the + + align:start position:0% +probability one to the person with the + + + align:start position:0% +probability one to the person with the +highest bid and they pay their bid the + + align:start position:0% +highest bid and they pay their bid the + + + align:start position:0% +highest bid and they pay their bid the +um second price auction is again you + + align:start position:0% +um second price auction is again you + + + align:start position:0% +um second price auction is again you +give it to the person who had the + + align:start position:0% +give it to the person who had the + + + align:start position:0% +give it to the person who had the +highest bid but they pay the second + + align:start position:0% +highest bid but they pay the second + + + align:start position:0% +highest bid but they pay the second +highest of these numbers + + align:start position:0% +highest of these numbers + + + align:start position:0% +highest of these numbers +but it's a general class of auction + + align:start position:0% +but it's a general class of auction + + + align:start position:0% +but it's a general class of auction +mechanisms theorem is consider the + + align:start position:0% +mechanisms theorem is consider the + + + align:start position:0% +mechanisms theorem is consider the +symmetric independent private values + + align:start position:0% +symmetric independent private values + + + align:start position:0% +symmetric independent private values +model suppose that a general auction + + align:start position:0% +model suppose that a general auction + + + align:start position:0% +model suppose that a general auction +mechanism has an equilibrium bidding + + align:start position:0% +mechanism has an equilibrium bidding + + + align:start position:0% +mechanism has an equilibrium bidding +function in which the object is awarded + + align:start position:0% +function in which the object is awarded + + + align:start position:0% +function in which the object is awarded +to the bidder with the highest value and + + align:start position:0% +to the bidder with the highest value and + + + align:start position:0% +to the bidder with the highest value and +a bidder with value s lower bar gets + + align:start position:0% +a bidder with value s lower bar gets + + + align:start position:0% +a bidder with value s lower bar gets +zero um Surplus then in equilibrium the + + align:start position:0% +zero um Surplus then in equilibrium the + + + align:start position:0% +zero um Surplus then in equilibrium the +seller's expected revenue is the same + + align:start position:0% +seller's expected revenue is the same + + + align:start position:0% +seller's expected revenue is the same +thing we've just seen the expected + + align:start position:0% +thing we've just seen the expected + + + align:start position:0% +thing we've just seen the expected +second highest value and not only are + + align:start position:0% +second highest value and not only are + + + align:start position:0% +second highest value and not only are +the auctions equivalent in terms of + + align:start position:0% +the auctions equivalent in terms of + + + align:start position:0% +the auctions equivalent in terms of +Revenue they're equivalent from the + + align:start position:0% +Revenue they're equivalent from the + + + align:start position:0% +Revenue they're equivalent from the +bidder perspective and that the expected + + align:start position:0% +bidder perspective and that the expected + + + align:start position:0% +bidder perspective and that the expected +utility of a bidder who has Type SI is + + align:start position:0% +utility of a bidder who has Type SI is + + + align:start position:0% +utility of a bidder who has Type SI is +just the integral from s lower bar to SI + + align:start position:0% +just the integral from s lower bar to SI + + + align:start position:0% +just the integral from s lower bar to SI +F to the N minus one of X DX you'll hear + + align:start position:0% +F to the N minus one of X DX you'll hear + + + align:start position:0% +F to the N minus one of X DX you'll hear +people refer to this as the information + + align:start position:0% +people refer to this as the information + + + align:start position:0% +people refer to this as the information +rent of the bidder but in any mechanism + + align:start position:0% +rent of the bidder but in any mechanism + + + align:start position:0% +rent of the bidder but in any mechanism +you choose that's has these two natural + + align:start position:0% +you choose that's has these two natural + + + align:start position:0% +you choose that's has these two natural +properties you always raise the same + + align:start position:0% +properties you always raise the same + + + align:start position:0% +properties you always raise the same +revenue and you raise the same Revenue + + align:start position:0% +revenue and you raise the same Revenue + + + align:start position:0% +revenue and you raise the same Revenue +because you always maximize gross + + align:start position:0% +because you always maximize gross + + + align:start position:0% +because you always maximize gross +Surplus and you give away this much + + align:start position:0% +Surplus and you give away this much + + + align:start position:0% +Surplus and you give away this much +Surplus to a bidder of type SI so + + align:start position:0% +Surplus to a bidder of type SI so + + + align:start position:0% +Surplus to a bidder of type SI so +they're strongly equivalent in that they + + align:start position:0% +they're strongly equivalent in that they + + + align:start position:0% +they're strongly equivalent in that they +raise the same revenue for the seller + + align:start position:0% +raise the same revenue for the seller + + + align:start position:0% +raise the same revenue for the seller +and they give the same expected utility + + align:start position:0% +and they give the same expected utility + + + align:start position:0% +and they give the same expected utility +for a buyer and expected utility even + + align:start position:0% +for a buyer and expected utility even + + + align:start position:0% +for a buyer and expected utility even +conditional on knowing your type it's + + align:start position:0% +conditional on knowing your type it's + + + align:start position:0% +conditional on knowing your type it's +always the same + + align:start position:0% + + + + align:start position:0% + +um and you know the thing I gave earlier + + align:start position:0% +um and you know the thing I gave earlier + + + align:start position:0% +um and you know the thing I gave earlier +on first and second price auctions is a + + align:start position:0% +on first and second price auctions is a + + + align:start position:0% +on first and second price auctions is a +special case of this because of first + + align:start position:0% +special case of this because of first + + + align:start position:0% +special case of this because of first +and second price auction games I gave + + align:start position:0% +and second price auction games I gave + + + align:start position:0% +and second price auction games I gave +you know the option the object was + + align:start position:0% +you know the option the object was + + + align:start position:0% +you know the option the object was +always being awarded in equilibrium to + + align:start position:0% +always being awarded in equilibrium to + + + align:start position:0% +always being awarded in equilibrium to +the bidder with the highest value + + align:start position:0% +the bidder with the highest value + + + align:start position:0% +the bidder with the highest value +whether in the second price auction + + align:start position:0% +whether in the second price auction + + + align:start position:0% +whether in the second price auction +because you stated your value or in the + + align:start position:0% +because you stated your value or in the + + + align:start position:0% +because you stated your value or in the +first price auction because you bid n + + align:start position:0% +first price auction because you bid n + + + align:start position:0% +first price auction because you bid n +minus one over n times your value and + + align:start position:0% +minus one over n times your value and + + + align:start position:0% +minus one over n times your value and +then also a bidder with the lowest value + + align:start position:0% +then also a bidder with the lowest value + + + align:start position:0% +then also a bidder with the lowest value +was going to get zero profits because + + align:start position:0% +was going to get zero profits because + + + align:start position:0% +was going to get zero profits because +they they win with probability zero yes + + align:start position:0% +they they win with probability zero yes + + + align:start position:0% +they they win with probability zero yes +isn't the second condition more of a + + align:start position:0% +isn't the second condition more of a + + + align:start position:0% +isn't the second condition more of a +result is about the whole notion of like + + align:start position:0% +result is about the whole notion of like + + + align:start position:0% +result is about the whole notion of like +the revenue equivalence theem is like + + align:start position:0% +the revenue equivalence theem is like + + + align:start position:0% +the revenue equivalence theem is like +you can set s lower bars value to + + align:start position:0% +you can set s lower bars value to + + + align:start position:0% +you can set s lower bars value to +whatever you + + align:start position:0% +whatever you + + + align:start position:0% +whatever you +want and then it comes out and then you + + align:start position:0% +want and then it comes out and then you + + + align:start position:0% +want and then it comes out and then you +argue well in this case we just keep + + align:start position:0% +argue well in this case we just keep + + + align:start position:0% +argue well in this case we just keep +lowering it so well so I guess you're + + align:start position:0% +lowering it so well so I guess you're + + + align:start position:0% +lowering it so well so I guess you're +thinking about optimal like you know + + align:start position:0% +thinking about optimal like you know + + + align:start position:0% +thinking about optimal like you know +like if you're think about optimal like + + align:start position:0% +like if you're think about optimal like + + + align:start position:0% +like if you're think about optimal like +you could design mechanisms with the S + + align:start position:0% +you could design mechanisms with the S + + + align:start position:0% +you could design mechanisms with the S +lower bar type gets positive Surplus and + + align:start position:0% +lower bar type gets positive Surplus and + + + align:start position:0% +lower bar type gets positive Surplus and +then you wouldn't want to use such those + + align:start position:0% +then you wouldn't want to use such those + + + align:start position:0% +then you wouldn't want to use such those +mechanisms would provide less Surplus to + + align:start position:0% +mechanisms would provide less Surplus to + + + align:start position:0% +mechanisms would provide less Surplus to +the SE less Revenue to the seller and + + align:start position:0% +the SE less Revenue to the seller and + + + align:start position:0% +the SE less Revenue to the seller and +more Surplus to the buyer so we sort of + + align:start position:0% +more Surplus to the buyer so we sort of + + + align:start position:0% +more Surplus to the buyer so we sort of +tend to think of these as the mechanisms + + align:start position:0% +tend to think of these as the mechanisms + + + align:start position:0% +tend to think of these as the mechanisms +you would normally think someone would + + align:start position:0% +you would normally think someone would + + + align:start position:0% +you would normally think someone would +choose and if you choose a mechanism to + + align:start position:0% +choose and if you choose a mechanism to + + + align:start position:0% +choose and if you choose a mechanism to +make sure the SL bar type gets zero + + align:start position:0% +make sure the SL bar type gets zero + + + align:start position:0% +make sure the SL bar type gets zero +Surplus then these things are going to + + align:start position:0% +Surplus then these things are going to + + + align:start position:0% +Surplus then these things are going to +hold yeah there are there are worse + + align:start position:0% +hold yeah there are there are worse + + + align:start position:0% +hold yeah there are there are worse +mechanisms that give positive Surplus + + align:start position:0% +mechanisms that give positive Surplus + + + align:start position:0% +mechanisms that give positive Surplus +the SL bar types um there are better + + align:start position:0% +the SL bar types um there are better + + + align:start position:0% +the SL bar types um there are better +mechanisms that give negative Surplus + + align:start position:0% +mechanisms that give negative Surplus + + + align:start position:0% +mechanisms that give negative Surplus +the bar types but then how do you get + + align:start position:0% +the bar types but then how do you get + + + align:start position:0% +the bar types but then how do you get +the SL bar types to participate in them + + align:start position:0% +the SL bar types to participate in them + + + align:start position:0% +the SL bar types to participate in them +um so in some sense you know this + + align:start position:0% +um so in some sense you know this + + + align:start position:0% +um so in some sense you know this +theorem says that you know and sometimes + + align:start position:0% +theorem says that you know and sometimes + + + align:start position:0% +theorem says that you know and sometimes +I really don't like it as because it it + + align:start position:0% +I really don't like it as because it it + + + align:start position:0% +I really don't like it as because it it +sort of makes you think the field of + + align:start position:0% +sort of makes you think the field of + + + align:start position:0% +sort of makes you think the field of +auction design is completely irrelevant + + align:start position:0% +auction design is completely irrelevant + + + align:start position:0% +auction design is completely irrelevant +because it says that all auctions work + + align:start position:0% +because it says that all auctions work + + + align:start position:0% +because it says that all auctions work +out the same um and and the reason why + + align:start position:0% +out the same um and and the reason why + + + align:start position:0% +out the same um and and the reason why +it's it's sort of a you know let me see + + align:start position:0% +it's it's sort of a you know let me see + + + align:start position:0% +it's it's sort of a you know let me see +so I have a proof here again Alex does a + + align:start position:0% +so I have a proof here again Alex does a + + + align:start position:0% +so I have a proof here again Alex does a +proof in 124 if you want to see one + + align:start position:0% +proof in 124 if you want to see one + + + align:start position:0% +proof in 124 if you want to see one +there's there's a proof um oh actually + + align:start position:0% +there's there's a proof um oh actually + + + align:start position:0% +there's there's a proof um oh actually +before I get the comments on let let me + + align:start position:0% +before I get the comments on let let me + + + align:start position:0% +before I get the comments on let let me +just sort of just just do one + + align:start position:0% +just sort of just just do one + + + align:start position:0% +just sort of just just do one +application of the revenue equivalence + + align:start position:0% +application of the revenue equivalence + + + align:start position:0% +application of the revenue equivalence +theorem um you know Revenue equivalence + + align:start position:0% +theorem um you know Revenue equivalence + + + align:start position:0% +theorem um you know Revenue equivalence +theorem can also be a tool for solving + + align:start position:0% +theorem can also be a tool for solving + + + align:start position:0% +theorem can also be a tool for solving +um auctions so here's an example an all + + align:start position:0% +um auctions so here's an example an all + + + align:start position:0% +um auctions so here's an example an all +pay auction in the all pay auction + + align:start position:0% +pay auction in the all pay auction + + + align:start position:0% +pay auction in the all pay auction +biders submit bids B1 through BN the + + align:start position:0% +biders submit bids B1 through BN the + + + align:start position:0% +biders submit bids B1 through BN the +high value biders is awarded the object + + align:start position:0% +high value biders is awarded the object + + + align:start position:0% +high value biders is awarded the object +but everyone pays what they bid win or + + align:start position:0% +but everyone pays what they bid win or + + + align:start position:0% +but everyone pays what they bid win or +lose so in this case you know it's kind + + align:start position:0% +lose so in this case you know it's kind + + + align:start position:0% +lose so in this case you know it's kind +of like buying lottery tickets or raffle + + align:start position:0% +of like buying lottery tickets or raffle + + + align:start position:0% +of like buying lottery tickets or raffle +tickets um but we just all submit our + + align:start position:0% +tickets um but we just all submit our + + + align:start position:0% +tickets um but we just all submit our +bids everyone actually has to pay their + + align:start position:0% +bids everyone actually has to pay their + + + align:start position:0% +bids everyone actually has to pay their +bid win or lose and then whoever bid the + + align:start position:0% +bid win or lose and then whoever bid the + + + align:start position:0% +bid win or lose and then whoever bid the +highest amount gets the object + + align:start position:0% +highest amount gets the object + + + align:start position:0% +highest amount gets the object +um you know you can think of it as like + + align:start position:0% +um you know you can think of it as like + + + align:start position:0% +um you know you can think of it as like +you know there are examples like + + align:start position:0% +you know there are examples like + + + align:start position:0% +you know there are examples like +lobbying like imagine the sort of you + + align:start position:0% +lobbying like imagine the sort of you + + + align:start position:0% +lobbying like imagine the sort of you +know you're trying to win the rights to + + align:start position:0% +know you're trying to win the rights to + + + align:start position:0% +know you're trying to win the rights to +hold the next World Cup in Cutter you + + align:start position:0% +hold the next World Cup in Cutter you + + + align:start position:0% +hold the next World Cup in Cutter you +know you all submit Bri everyone every + + align:start position:0% +know you all submit Bri everyone every + + + align:start position:0% +know you all submit Bri everyone every +country who wants the World Cup submits + + align:start position:0% +country who wants the World Cup submits + + + align:start position:0% +country who wants the World Cup submits +bribes to FIFA whoever submits the + + align:start position:0% +bribes to FIFA whoever submits the + + + align:start position:0% +bribes to FIFA whoever submits the +highest bribe is going to win if you + + align:start position:0% +highest bribe is going to win if you + + + align:start position:0% +highest bribe is going to win if you +submit the second highest bribe you + + align:start position:0% +submit the second highest bribe you + + + align:start position:0% +submit the second highest bribe you +don't get your bribe back you know + + align:start position:0% +don't get your bribe back you know + + + align:start position:0% +don't get your bribe back you know +you've you've given the millions of + + align:start position:0% +you've you've given the millions of + + + align:start position:0% +you've you've given the millions of +dollars to whatever person second + + align:start position:0% +dollars to whatever person second + + + align:start position:0% +dollars to whatever person second +highest you know like we all pay our + + align:start position:0% +highest you know like we all pay our + + + align:start position:0% +highest you know like we all pay our +bribes and then the highest bribe wins + + align:start position:0% +bribes and then the highest bribe wins + + + align:start position:0% +bribes and then the highest bribe wins +okay um this again would be an auction + + align:start position:0% +okay um this again would be an auction + + + align:start position:0% +okay um this again would be an auction +that the revenue equivalence theorem + + align:start position:0% +that the revenue equivalence theorem + + + align:start position:0% +that the revenue equivalence theorem +would apply to uh and so because the + + align:start position:0% +would apply to uh and so because the + + + align:start position:0% +would apply to uh and so because the +revenue equivalence theorem + + align:start position:0% +revenue equivalence theorem + + + align:start position:0% +revenue equivalence theorem +applies we know that a bidder of type SI + + align:start position:0% +applies we know that a bidder of type SI + + + align:start position:0% +applies we know that a bidder of type SI +gets this much + + align:start position:0% +gets this much + + + align:start position:0% +gets this much +Surplus integral of s lower bar to s f + + align:start position:0% +Surplus integral of s lower bar to s f + + + align:start position:0% +Surplus integral of s lower bar to s f +the nus one of X DX but in the all pay + + align:start position:0% +the nus one of X DX but in the all pay + + + align:start position:0% +the nus one of X DX but in the all pay +off auction it's also an easy expression + + align:start position:0% +off auction it's also an easy expression + + + align:start position:0% +off auction it's also an easy expression +for your expected utility your expected + + align:start position:0% +for your expected utility your expected + + + align:start position:0% +for your expected utility your expected +utility in equilibrium is just your + + align:start position:0% +utility in equilibrium is just your + + + align:start position:0% +utility in equilibrium is just your +value times the probability that well El + + align:start position:0% +value times the probability that well El + + + align:start position:0% +value times the probability that well El +has a lower value minus what you bid so + + align:start position:0% +has a lower value minus what you bid so + + + align:start position:0% +has a lower value minus what you bid so +if this minus this equals this we get a + + align:start position:0% +if this minus this equals this we get a + + + align:start position:0% +if this minus this equals this we get a +markdown rule for your bid your bid is + + align:start position:0% +markdown rule for your bid your bid is + + + align:start position:0% +markdown rule for your bid your bid is +the expected Surplus you're going to get + + align:start position:0% +the expected Surplus you're going to get + + + align:start position:0% +the expected Surplus you're going to get +from winning when you have the highest + + align:start position:0% +from winning when you have the highest + + + align:start position:0% +from winning when you have the highest +value minus uh your information rent and + + align:start position:0% +value minus uh your information rent and + + + align:start position:0% +value minus uh your information rent and +so the revenue equivalence theorem once + + align:start position:0% +so the revenue equivalence theorem once + + + align:start position:0% +so the revenue equivalence theorem once +you know it can be a tool for actually + + align:start position:0% +you know it can be a tool for actually + + + align:start position:0% +you know it can be a tool for actually +computing + + align:start position:0% +computing + + + align:start position:0% +computing +equilibria of other auctions because you + + align:start position:0% +equilibria of other auctions because you + + + align:start position:0% +equilibria of other auctions because you +know that the equilibrium must be such + + align:start position:0% +know that the equilibrium must be such + + + align:start position:0% +know that the equilibrium must be such +that people get exactly that Surplus and + + align:start position:0% +that people get exactly that Surplus and + + + align:start position:0% +that people get exactly that Surplus and +sometimes you can figure out this case + + align:start position:0% +sometimes you can figure out this case + + + align:start position:0% +sometimes you can figure out this case +you can sort of figure out what the bids + + align:start position:0% +you can sort of figure out what the bids + + + align:start position:0% +you can sort of figure out what the bids +must be I want to get that Surplus okay + + align:start position:0% +must be I want to get that Surplus okay + + + align:start position:0% +must be I want to get that Surplus okay +so anyway it it you know it's a it's a + + align:start position:0% +so anyway it it you know it's a it's a + + + align:start position:0% +so anyway it it you know it's a it's a +beautiful + + align:start position:0% +beautiful + + + align:start position:0% +beautiful +theorem in practice it's really not a + + align:start position:0% +theorem in practice it's really not a + + + align:start position:0% +theorem in practice it's really not a +good it sort of has that basic thing to + + align:start position:0% +good it sort of has that basic thing to + + + align:start position:0% +good it sort of has that basic thing to +think about like we have to think about + + align:start position:0% +think about like we have to think about + + + align:start position:0% +think about like we have to think about +people bidding strategically and + + align:start position:0% +people bidding strategically and + + + align:start position:0% +people bidding strategically and +markdowns um there is an enormous field + + align:start position:0% +markdowns um there is an enormous field + + + align:start position:0% +markdowns um there is an enormous field +of auction design + + align:start position:0% +of auction design + + + align:start position:0% +of auction design +despite this and that's + + align:start position:0% +despite this and that's + + + align:start position:0% +despite this and that's +because the revenue equivalence theorem + + align:start position:0% +because the revenue equivalence theorem + + + align:start position:0% +because the revenue equivalence theorem +really doesn't cover the interesting + + align:start position:0% +really doesn't cover the interesting + + + align:start position:0% +really doesn't cover the interesting +cases um you + + align:start position:0% +cases um you + + + align:start position:0% +cases um you +know many of the assumptions in revenue + + align:start position:0% +know many of the assumptions in revenue + + + align:start position:0% +know many of the assumptions in revenue +theor revenue equivalence theorem uh are + + align:start position:0% +theor revenue equivalence theorem uh are + + + align:start position:0% +theor revenue equivalence theorem uh are +just not going to be hold in practice + + align:start position:0% +just not going to be hold in practice + + + align:start position:0% +just not going to be hold in practice +you know one is the biders are assumed + + align:start position:0% +you know one is the biders are assumed + + + align:start position:0% +you know one is the biders are assumed +to be risk-neutral if you're talking + + align:start position:0% +to be risk-neutral if you're talking + + + align:start position:0% +to be risk-neutral if you're talking +about biders you know bidding on on + + align:start position:0% +about biders you know bidding on on + + + align:start position:0% +about biders you know bidding on on +Paving contracts they have businesses to + + align:start position:0% +Paving contracts they have businesses to + + + align:start position:0% +Paving contracts they have businesses to +run they have employees who are going to + + align:start position:0% +run they have employees who are going to + + + align:start position:0% +run they have employees who are going to +be idle they can't it's not a long run + + align:start position:0% +be idle they can't it's not a long run + + + align:start position:0% +be idle they can't it's not a long run +thing they can't can't be completely + + align:start position:0% +thing they can't can't be completely + + + align:start position:0% +thing they can't can't be completely +risk + + align:start position:0% +risk + + + align:start position:0% +risk +neutral um third one values are + + align:start position:0% +neutral um third one values are + + + align:start position:0% +neutral um third one values are +independent you know even if I was + + align:start position:0% +independent you know even if I was + + + align:start position:0% +independent you know even if I was +having a hard time I also have a hard + + align:start position:0% +having a hard time I also have a hard + + + align:start position:0% +having a hard time I also have a hard +time thinking of cases where the signals + + align:start position:0% +time thinking of cases where the signals + + + align:start position:0% +time thinking of cases where the signals +are actually going to be independent you + + align:start position:0% +are actually going to be independent you + + + align:start position:0% +are actually going to be independent you +know like so okay it could be that I + + align:start position:0% +know like so okay it could be that I + + + align:start position:0% +know like so okay it could be that I +actually know exactly how much I like + + align:start position:0% +actually know exactly how much I like + + + align:start position:0% +actually know exactly how much I like +this bottle of wine I just have a + + align:start position:0% +this bottle of wine I just have a + + + align:start position:0% +this bottle of wine I just have a +valuation for it I'm bidding for this + + align:start position:0% +valuation for it I'm bidding for this + + + align:start position:0% +valuation for it I'm bidding for this +value of wine against somebody else but + + align:start position:0% +value of wine against somebody else but + + + align:start position:0% +value of wine against somebody else but +in practice if somebody else looked at + + align:start position:0% +in practice if somebody else looked at + + + align:start position:0% +in practice if somebody else looked at +that bottle of wine and they like it a + + align:start position:0% +that bottle of wine and they like it a + + + align:start position:0% +that bottle of wine and they like it a +lot it's probably they know something + + align:start position:0% +lot it's probably they know something + + + align:start position:0% +lot it's probably they know something +about how good it is if the wine + + align:start position:0% +about how good it is if the wine + + + align:start position:0% +about how good it is if the wine +actually tastes good their signal is + + align:start position:0% +actually tastes good their signal is + + + align:start position:0% +actually tastes good their signal is +going to tell me something about how + + align:start position:0% +going to tell me something about how + + + align:start position:0% +going to tell me something about how +much I'm going to enjoy that bottle of + + align:start position:0% +much I'm going to enjoy that bottle of + + + align:start position:0% +much I'm going to enjoy that bottle of +wine if it's a painting I intend to hang + + align:start position:0% +wine if it's a painting I intend to hang + + + align:start position:0% +wine if it's a painting I intend to hang +on my wall I know how much I like the + + align:start position:0% +on my wall I know how much I like the + + + align:start position:0% +on my wall I know how much I like the +painting but the fact that someone else + + align:start position:0% +painting but the fact that someone else + + + align:start position:0% +painting but the fact that someone else +is willing to pay a lot for the painting + + align:start position:0% +is willing to pay a lot for the painting + + + align:start position:0% +is willing to pay a lot for the painting +I also have the option of selling it to + + align:start position:0% +I also have the option of selling it to + + + align:start position:0% +I also have the option of selling it to +them later so if there are a lot of + + align:start position:0% +them later so if there are a lot of + + + align:start position:0% +them later so if there are a lot of +other people who like this painting then + + align:start position:0% +other people who like this painting then + + + align:start position:0% +other people who like this painting then +I that painting is more valuable to me + + align:start position:0% +I that painting is more valuable to me + + + align:start position:0% +I that painting is more valuable to me +because of the option value of selling + + align:start position:0% +because of the option value of selling + + + align:start position:0% +because of the option value of selling +it you know if if um many many cases if + + align:start position:0% +it you know if if um many many cases if + + + align:start position:0% +it you know if if um many many cases if +I know that other you know right if if + + align:start position:0% +I know that other you know right if if + + + align:start position:0% +I know that other you know right if if +if this is a good object we're all going + + align:start position:0% +if this is a good object we're all going + + + align:start position:0% +if this is a good object we're all going +to like it a lot if this is a bad object + + align:start position:0% +to like it a lot if this is a bad object + + + align:start position:0% +to like it a lot if this is a bad object +we're not going to like it a lot and so + + align:start position:0% +we're not going to like it a lot and so + + + align:start position:0% +we're not going to like it a lot and so +both the values are independent and the + + align:start position:0% +both the values are independent and the + + + align:start position:0% +both the values are independent and the +values only depend on my signal rather + + align:start position:0% +values only depend on my signal rather + + + align:start position:0% +values only depend on my signal rather +than on other people signals as well + + align:start position:0% +than on other people signals as well + + + align:start position:0% +than on other people signals as well +those two things just don't seem + + align:start position:0% +those two things just don't seem + + + align:start position:0% +those two things just don't seem +realistic for many applications because + + align:start position:0% +realistic for many applications because + + + align:start position:0% +realistic for many applications because +the fact that other people value + + align:start position:0% +the fact that other people value + + + align:start position:0% +the fact that other people value +something tells you something inherent + + align:start position:0% +something tells you something inherent + + + align:start position:0% +something tells you something inherent +about the object itself that then tells + + align:start position:0% +about the object itself that then tells + + + align:start position:0% +about the object itself that then tells +you something about my + + align:start position:0% +you something about my + + + align:start position:0% +you something about my +value okay or even just that I like it + + align:start position:0% +value okay or even just that I like it + + + align:start position:0% +value okay or even just that I like it +means that this is an unusually bottle + + align:start position:0% +means that this is an unusually bottle + + + align:start position:0% +means that this is an unusually bottle +Vine that I unusually like someone else + + align:start position:0% +Vine that I unusually like someone else + + + align:start position:0% +Vine that I unusually like someone else +probably has the same tastes um um then + + align:start position:0% +probably has the same tastes um um then + + + align:start position:0% +probably has the same tastes um um then +the second limitation is um the set of + + align:start position:0% +the second limitation is um the set of + + + align:start position:0% +the second limitation is um the set of +mechanisms that it considers it only + + align:start position:0% +mechanisms that it considers it only + + + align:start position:0% +mechanisms that it considers it only +considers mechanisms where you always + + align:start position:0% +considers mechanisms where you always + + + align:start position:0% +considers mechanisms where you always +allocate the good to to the high value + + align:start position:0% +allocate the good to to the high value + + + align:start position:0% +allocate the good to to the high value +bidder it doesn't let you not allocate + + align:start position:0% +bidder it doesn't let you not allocate + + + align:start position:0% +bidder it doesn't let you not allocate +the good okay so just sort of some + + align:start position:0% +the good okay so just sort of some + + + align:start position:0% +the good okay so just sort of some +examples of things people in Iowa have + + align:start position:0% +examples of things people in Iowa have + + + align:start position:0% +examples of things people in Iowa have +noted about how you would bid + + align:start position:0% +noted about how you would bid + + + align:start position:0% +noted about how you would bid +differently so suppose biders are risk + + align:start position:0% +differently so suppose biders are risk + + + align:start position:0% +differently so suppose biders are risk +averse they get utility U of S minus P + + align:start position:0% +averse they get utility U of S minus P + + + align:start position:0% +averse they get utility U of S minus P +if they win and U of minus P if they + + align:start position:0% +if they win and U of minus P if they + + + align:start position:0% +if they win and U of minus P if they +lose so this is our small construction + + align:start position:0% +lose so this is our small construction + + + align:start position:0% +lose so this is our small construction +company that cares about its its it its + + align:start position:0% +company that cares about its its it its + + + align:start position:0% +company that cares about its its it its +revenues in a nonlinear + + align:start position:0% +revenues in a nonlinear + + + align:start position:0% +revenues in a nonlinear +way in this game uh Revenue equivalence + + align:start position:0% +way in this game uh Revenue equivalence + + + align:start position:0% +way in this game uh Revenue equivalence +theorem doesn't hold anymore and the + + align:start position:0% +theorem doesn't hold anymore and the + + + align:start position:0% +theorem doesn't hold anymore and the +first price auction raises more Revenue + + align:start position:0% +first price auction raises more Revenue + + + align:start position:0% +first price auction raises more Revenue +than a second price + + align:start position:0% +than a second price + + + align:start position:0% +than a second price +auction you know why would that be + + align:start position:0% +auction you know why would that be + + + align:start position:0% +auction you know why would that be +imagine you're in a first price auction + + align:start position:0% +imagine you're in a first price auction + + + align:start position:0% +imagine you're in a first price auction +and you know compare the equili of the + + align:start position:0% +and you know compare the equili of the + + + align:start position:0% +and you know compare the equili of the +first price auction where you bid n + + align:start position:0% +first price auction where you bid n + + + align:start position:0% +first price auction where you bid n +minus one over n * V to the equival of + + align:start position:0% +minus one over n * V to the equival of + + + align:start position:0% +minus one over n * V to the equival of +the second price auction where you bid V + + align:start position:0% +the second price auction where you bid V + + + align:start position:0% +the second price auction where you bid V +okay those two auctions have exactly the + + align:start position:0% +okay those two auctions have exactly the + + + align:start position:0% +okay those two auctions have exactly the +same expected Surplus in dollars to the + + align:start position:0% +same expected Surplus in dollars to the + + + align:start position:0% +same expected Surplus in dollars to the +winning to the to to to the bidder that + + align:start position:0% +winning to the to to to the bidder that + + + align:start position:0% +winning to the to to to the bidder that +was the revenue equivalence theorem said + + align:start position:0% +was the revenue equivalence theorem said + + + align:start position:0% +was the revenue equivalence theorem said +but if in an au if in a first price + + align:start position:0% +but if in an au if in a first price + + + align:start position:0% +but if in an au if in a first price +auction I raise my bid a little bit I'm + + align:start position:0% +auction I raise my bid a little bit I'm + + + align:start position:0% +auction I raise my bid a little bit I'm +increasing the probability that I + + align:start position:0% +increasing the probability that I + + + align:start position:0% +increasing the probability that I +win uh which is reducing the probability + + align:start position:0% +win uh which is reducing the probability + + + align:start position:0% +win uh which is reducing the probability +of the bad state where I get zero and + + align:start position:0% +of the bad state where I get zero and + + + align:start position:0% +of the bad state where I get zero and +it's lowering my Surplus in the good + + align:start position:0% +it's lowering my Surplus in the good + + + align:start position:0% +it's lowering my Surplus in the good +states where I do win so what it's doing + + align:start position:0% +states where I do win so what it's doing + + + align:start position:0% +states where I do win so what it's doing +is it's to first order it's not changing + + align:start position:0% +is it's to first order it's not changing + + + align:start position:0% +is it's to first order it's not changing +your expected payment by the revenue + + align:start position:0% +your expected payment by the revenue + + + align:start position:0% +your expected payment by the revenue +equivalence theorem but it's reducing + + align:start position:0% +equivalence theorem but it's reducing + + + align:start position:0% +equivalence theorem but it's reducing +the variance in your payment by sort of + + align:start position:0% +the variance in your payment by sort of + + + align:start position:0% +the variance in your payment by sort of +increasing the probability of winning a + + align:start position:0% +increasing the probability of winning a + + + align:start position:0% +increasing the probability of winning a +small amount instead of a lower + + align:start position:0% +small amount instead of a lower + + + align:start position:0% +small amount instead of a lower +probability of winning a bigger amount + + align:start position:0% +probability of winning a bigger amount + + + align:start position:0% +probability of winning a bigger amount +and so in the first price deal bid + + align:start position:0% +and so in the first price deal bid + + + align:start position:0% +and so in the first price deal bid +auction if everyone else was bidding bar + + align:start position:0% +auction if everyone else was bidding bar + + + align:start position:0% +auction if everyone else was bidding bar +star of of Si you would raise your bid + + align:start position:0% +star of of Si you would raise your bid + + + align:start position:0% +star of of Si you would raise your bid +in the first price seal bid auction + + align:start position:0% +in the first price seal bid auction + + + align:start position:0% +in the first price seal bid auction +second price seal bid auction is is is + + align:start position:0% +second price seal bid auction is is is + + + align:start position:0% +second price seal bid auction is is is +unchanged you always have still have the + + align:start position:0% +unchanged you always have still have the + + + align:start position:0% +unchanged you always have still have the +same dominant strategy so with risk + + align:start position:0% +same dominant strategy so with risk + + + align:start position:0% +same dominant strategy so with risk +averse biders first price auctions raise + + align:start position:0% +averse biders first price auctions raise + + + align:start position:0% +averse biders first price auctions raise +more Revenue than second price auctions + + align:start position:0% +more Revenue than second price auctions + + + align:start position:0% +more Revenue than second price auctions +uh second example is if you have + + align:start position:0% +uh second example is if you have + + + align:start position:0% +uh second example is if you have +auctions with positively correlated + + align:start position:0% +auctions with positively correlated + + + align:start position:0% +auctions with positively correlated +values in auctions with a bidder's + + align:start position:0% +values in auctions with a bidder's + + + align:start position:0% +values in auctions with a bidder's +values are positively correlated uh + + align:start position:0% +values are positively correlated uh + + + align:start position:0% +values are positively correlated uh +second price auctions raise more + + align:start position:0% +second price auctions raise more + + + align:start position:0% +second price auctions raise more +expected Revenue than first price + + align:start position:0% +expected Revenue than first price + + + align:start position:0% +expected Revenue than first price +auctions and and there is sort of a big + + align:start position:0% +auctions and and there is sort of a big + + + align:start position:0% +auctions and and there is sort of a big +literature on auction design and a big + + align:start position:0% +literature on auction design and a big + + + align:start position:0% +literature on auction design and a big +set of people who are professional + + align:start position:0% +set of people who are professional + + + align:start position:0% +set of people who are professional +auction designers because to the extent + + align:start position:0% +auction designers because to the extent + + + align:start position:0% +auction designers because to the extent +that every auction differs from uh + + align:start position:0% +that every auction differs from uh + + + align:start position:0% +that every auction differs from uh +independent private values in some + + align:start position:0% +independent private values in some + + + align:start position:0% +independent private values in some +direction you're going to think about + + align:start position:0% +direction you're going to think about + + + align:start position:0% +direction you're going to think about +all these results of been shown about + + align:start position:0% +all these results of been shown about + + + align:start position:0% +all these results of been shown about +when first and second or all pay + + align:start position:0% +when first and second or all pay + + + align:start position:0% +when first and second or all pay +auctions do better and pick out an + + align:start position:0% +auctions do better and pick out an + + + align:start position:0% +auctions do better and pick out an +auction that works well in that + + align:start position:0% +auction that works well in that + + + align:start position:0% +auction that works well in that +circumstance uh a second Stark example + + align:start position:0% +circumstance uh a second Stark example + + + align:start position:0% +circumstance uh a second Stark example +of what this Revenue equivalent serum + + align:start position:0% +of what this Revenue equivalent serum + + + align:start position:0% +of what this Revenue equivalent serum +doesn't do is you know think about the + + align:start position:0% +doesn't do is you know think about the + + + align:start position:0% +doesn't do is you know think about the +case where there's n equals one there's + + align:start position:0% +case where there's n equals one there's + + + align:start position:0% +case where there's n equals one there's +one bidder that bidder has a value + + align:start position:0% +one bidder that bidder has a value + + + align:start position:0% +one bidder that bidder has a value +that's uniform uniformly distributed on + + align:start position:0% +that's uniform uniformly distributed on + + + align:start position:0% +that's uniform uniformly distributed on +01 this is this is the classic Monopoly + + align:start position:0% +01 this is this is the classic Monopoly + + + align:start position:0% +01 this is this is the classic Monopoly +pricing problem that I started in + + align:start position:0% +pricing problem that I started in + + + align:start position:0% +pricing problem that I started in +lecture one with um + + align:start position:0% +lecture one with um + + + align:start position:0% +lecture one with um +what does a revenue equivalence theorem + + align:start position:0% +what does a revenue equivalence theorem + + + align:start position:0% +what does a revenue equivalence theorem +consider it considers mechanisms that + + align:start position:0% +consider it considers mechanisms that + + + align:start position:0% +consider it considers mechanisms that +always sell the good well so if you have + + align:start position:0% +always sell the good well so if you have + + + align:start position:0% +always sell the good well so if you have +to always sell the good and the and the + + align:start position:0% +to always sell the good and the and the + + + align:start position:0% +to always sell the good and the and the +bidder has a value V that's drawn + + align:start position:0% +bidder has a value V that's drawn + + + align:start position:0% +bidder has a value V that's drawn +uniform 01 the only mechanism that + + align:start position:0% +uniform 01 the only mechanism that + + + align:start position:0% +uniform 01 the only mechanism that +always sells the good is to sell it for + + align:start position:0% +always sells the good is to sell it for + + + align:start position:0% +always sells the good is to sell it for +a price of zero you I started this class + + align:start position:0% +a price of zero you I started this class + + + align:start position:0% +a price of zero you I started this class +with a thing to do in this model is to + + align:start position:0% +with a thing to do in this model is to + + + align:start position:0% +with a thing to do in this model is to +set a price of a half rather than a + + align:start position:0% +set a price of a half rather than a + + + align:start position:0% +set a price of a half rather than a +price of zero because that maximizes + + align:start position:0% +price of zero because that maximizes + + + align:start position:0% +price of zero because that maximizes +probability of selling times value if + + align:start position:0% +probability of selling times value if + + + align:start position:0% +probability of selling times value if +you do sell but if you have to sell with + + align:start position:0% +you do sell but if you have to sell with + + + align:start position:0% +you do sell but if you have to sell with +probability one all you can do is give + + align:start position:0% +probability one all you can do is give + + + align:start position:0% +probability one all you can do is give +the object away for free so Revenue + + align:start position:0% +the object away for free so Revenue + + + align:start position:0% +the object away for free so Revenue +equivalent + + align:start position:0% +equivalent + + + align:start position:0% +equivalent +theorem mechanisms always give the + + align:start position:0% +theorem mechanisms always give the + + + align:start position:0% +theorem mechanisms always give the +object away for free to the SL lower bar + + align:start position:0% +object away for free to the SL lower bar + + + align:start position:0% +object away for free to the SL lower bar +type um you know so you you can charge + + align:start position:0% +type um you know so you you can charge + + + align:start position:0% +type um you know so you you can charge +it you can charge s lower bar but they + + align:start position:0% +it you can charge s lower bar but they + + + align:start position:0% +it you can charge s lower bar but they +always give away the good with + + align:start position:0% +always give away the good with + + + align:start position:0% +always give away the good with +probability one which means you're + + align:start position:0% +probability one which means you're + + + align:start position:0% +probability one which means you're +always giving away that Surplus that we + + align:start position:0% +always giving away that Surplus that we + + + align:start position:0% +always giving away that Surplus that we +were in Monopoly pricing where I was + + align:start position:0% +were in Monopoly pricing where I was + + + align:start position:0% +were in Monopoly pricing where I was +telling you you don't want to give + + align:start position:0% +telling you you don't want to give + + + align:start position:0% +telling you you don't want to give +away so Revenue equivalence theorem is + + align:start position:0% +away so Revenue equivalence theorem is + + + align:start position:0% +away so Revenue equivalence theorem is +considering this sort of class limited + + align:start position:0% +considering this sort of class limited + + + align:start position:0% +considering this sort of class limited +class of mechanisms which don't include + + align:start position:0% +class of mechanisms which don't include + + + align:start position:0% +class of mechanisms which don't include +the mechanisms you would actually want + + align:start position:0% +the mechanisms you would actually want + + + align:start position:0% +the mechanisms you would actually want +to use + + align:start position:0% + + + + align:start position:0% + +so let me just think about Reserve + + align:start position:0% +so let me just think about Reserve + + + align:start position:0% +so let me just think about Reserve +prices you know how would what's your + + align:start position:0% +prices you know how would what's your + + + align:start position:0% +prices you know how would what's your +intuition for like you know if we now go + + align:start position:0% +intuition for like you know if we now go + + + align:start position:0% +intuition for like you know if we now go +into an auction do I want to set a + + align:start position:0% +into an auction do I want to set a + + + align:start position:0% +into an auction do I want to set a +reserve price in my auction or do I not + + align:start position:0% +reserve price in my auction or do I not + + + align:start position:0% +reserve price in my auction or do I not +want to set a reserve price in my + + align:start position:0% +want to set a reserve price in my + + + align:start position:0% +want to set a reserve price in my +auction or how you know like with one + + align:start position:0% +auction or how you know like with one + + + align:start position:0% +auction or how you know like with one +bidder you know you need a reserve price + + align:start position:0% +bidder you know you need a reserve price + + + align:start position:0% +bidder you know you need a reserve price +you want it set it equal to a half what + + align:start position:0% +you want it set it equal to a half what + + + align:start position:0% +you want it set it equal to a half what +would I do with n biders um two + + align:start position:0% +would I do with n biders um two + + + align:start position:0% +would I do with n biders um two +intuitions you might have is that the + + align:start position:0% +intuitions you might have is that the + + + align:start position:0% +intuitions you might have is that the +more biders there are the less need + + align:start position:0% +more biders there are the less need + + + align:start position:0% +more biders there are the less need +there is to set a reserve price because + + align:start position:0% +there is to set a reserve price because + + + align:start position:0% +there is to set a reserve price because +the competition is going to set the + + align:start position:0% +the competition is going to set the + + + align:start position:0% +the competition is going to set the +reserve PR Reserve kind of Reserve + + align:start position:0% +reserve PR Reserve kind of Reserve + + + align:start position:0% +reserve PR Reserve kind of Reserve +equivalent for me but then on the + + align:start position:0% +equivalent for me but then on the + + + align:start position:0% +equivalent for me but then on the +alternate side um you know the more + + align:start position:0% +alternate side um you know the more + + + align:start position:0% +alternate side um you know the more +biders there are the less chance of the + + align:start position:0% +biders there are the less chance of the + + + align:start position:0% +biders there are the less chance of the +reserve price is binding so the downside + + align:start position:0% +reserve price is binding so the downside + + + align:start position:0% +reserve price is binding so the downside +of the reserve that don't sell the good + + align:start position:0% +of the reserve that don't sell the good + + + align:start position:0% +of the reserve that don't sell the good +also goes away um so it turns out the + + align:start position:0% +also goes away um so it turns out the + + + align:start position:0% +also goes away um so it turns out the +theorem is in a a second price sealed + + align:start position:0% +theorem is in a a second price sealed + + + align:start position:0% +theorem is in a a second price sealed +bid auction you set you always set the + + align:start position:0% +bid auction you set you always set the + + + align:start position:0% +bid auction you set you always set the +Monopoly price as a reserve so what you + + align:start position:0% +Monopoly price as a reserve so what you + + + align:start position:0% +Monopoly price as a reserve so what you +want to do is regardless of how many + + align:start position:0% +want to do is regardless of how many + + + align:start position:0% +want to do is regardless of how many +biders there are you just set a reserve + + align:start position:0% +biders there are you just set a reserve + + + align:start position:0% +biders there are you just set a reserve +price equal to the Monopoly + + align:start position:0% +price equal to the Monopoly + + + align:start position:0% +price equal to the Monopoly +price and I say that like you know I I + + align:start position:0% +price and I say that like you know I I + + + align:start position:0% +price and I say that like you know I I +just before these bids are drawn I just + + align:start position:0% +just before these bids are drawn I just + + + align:start position:0% +just before these bids are drawn I just +think X Ane what would the Monopoly + + align:start position:0% +think X Ane what would the Monopoly + + + align:start position:0% +think X Ane what would the Monopoly +price be to a single bidder I say I + + align:start position:0% +price be to a single bidder I say I + + + align:start position:0% +price be to a single bidder I say I +announc in advance this is the reserve + + align:start position:0% +announc in advance this is the reserve + + + align:start position:0% +announc in advance this is the reserve +if you want the good you must bid at + + align:start position:0% +if you want the good you must bid at + + + align:start position:0% +if you want the good you must bid at +least that Reserve you know you you have + + align:start position:0% +least that Reserve you know you you have + + + align:start position:0% +least that Reserve you know you you have +you can't get the good unless unless you + + align:start position:0% +you can't get the good unless unless you + + + align:start position:0% +you can't get the good unless unless you +bid at least that Reserve or the sale + + align:start position:0% +bid at least that Reserve or the sale + + + align:start position:0% +bid at least that Reserve or the sale +price will always be at least the + + align:start position:0% +price will always be at least the + + + align:start position:0% +price will always be at least the +reserve if you're the only one who bids + + align:start position:0% +reserve if you're the only one who bids + + + align:start position:0% +reserve if you're the only one who bids +above the reserve price okay and you + + align:start position:0% +above the reserve price okay and you + + + align:start position:0% +above the reserve price okay and you +know simple reasoning for that is + + align:start position:0% +know simple reasoning for that is + + + align:start position:0% +know simple reasoning for that is +think about a relaxed problem where the + + align:start position:0% +think about a relaxed problem where the + + + align:start position:0% +think about a relaxed problem where the +seller actually gets to choose a reserve + + align:start position:0% +seller actually gets to choose a reserve + + + align:start position:0% +seller actually gets to choose a reserve +price not in advance before conducting + + align:start position:0% +price not in advance before conducting + + + align:start position:0% +price not in advance before conducting +the auction but after observing where + + align:start position:0% +the auction but after observing where + + + align:start position:0% +the auction but after observing where +the second highest bidder dropped out so + + align:start position:0% +the second highest bidder dropped out so + + + align:start position:0% +the second highest bidder dropped out so +you had n biders n minus one of them + + align:start position:0% +you had n biders n minus one of them + + + align:start position:0% +you had n biders n minus one of them +have dropped out and suppose you can + + align:start position:0% +have dropped out and suppose you can + + + align:start position:0% +have dropped out and suppose you can +cheat and after the N minus first bidder + + align:start position:0% +cheat and after the N minus first bidder + + + align:start position:0% +cheat and after the N minus first bidder +has dropped out so someone dropped out + + align:start position:0% +has dropped out so someone dropped out + + + align:start position:0% +has dropped out so someone dropped out +at 2.3 million I now know that this guy + + align:start position:0% +at 2.3 million I now know that this guy + + + align:start position:0% +at 2.3 million I now know that this guy +is willing to pay at least 2.3 million + + align:start position:0% +is willing to pay at least 2.3 million + + + align:start position:0% +is willing to pay at least 2.3 million +and I think what's the reserve price + + align:start position:0% +and I think what's the reserve price + + + align:start position:0% +and I think what's the reserve price +just for him okay so it's a customized + + align:start position:0% +just for him okay so it's a customized + + + align:start position:0% +just for him okay so it's a customized +Reserve price well you know the pro + + align:start position:0% +Reserve price well you know the pro + + + align:start position:0% +Reserve price well you know the pro +once you know so I have I have these end + + align:start position:0% +once you know so I have I have these end + + + align:start position:0% +once you know so I have I have these end +draws from this distribution I know that + + align:start position:0% +draws from this distribution I know that + + + align:start position:0% +draws from this distribution I know that +n minus one of the draws are down here + + align:start position:0% +n minus one of the draws are down here + + + align:start position:0% +n minus one of the draws are down here +below this value this sort of Dropout + + align:start position:0% +below this value this sort of Dropout + + + align:start position:0% +below this value this sort of Dropout +Point s n minus1 col n what's my + + align:start position:0% +Point s n minus1 col n what's my + + + align:start position:0% +Point s n minus1 col n what's my +posterior on the value of the remaining + + align:start position:0% +posterior on the value of the remaining + + + align:start position:0% +posterior on the value of the remaining +bidder my posterior on the value of the + + align:start position:0% +bidder my posterior on the value of the + + + align:start position:0% +bidder my posterior on the value of the +remaining bidder is just that it's a + + align:start position:0% +remaining bidder is just that it's a + + + align:start position:0% +remaining bidder is just that it's a +single draw from the upper tail of the + + align:start position:0% +single draw from the upper tail of the + + + align:start position:0% +single draw from the upper tail of the +distribution I started from + + align:start position:0% +distribution I started from + + + align:start position:0% +distribution I started from +so the if I set a reserve price of R + + align:start position:0% +so the if I set a reserve price of R + + + align:start position:0% +so the if I set a reserve price of R +which is bigger than this um the + + align:start position:0% +which is bigger than this um the + + + align:start position:0% +which is bigger than this um the +probability I'm going to sell the good + + align:start position:0% +probability I'm going to sell the good + + + align:start position:0% +probability I'm going to sell the good +is just 1us F of R over 1 minus F of uh + + align:start position:0% +is just 1us F of R over 1 minus F of uh + + + align:start position:0% +is just 1us F of R over 1 minus F of uh +SN minus one Co n it's just it's just a + + align:start position:0% +SN minus one Co n it's just it's just a + + + align:start position:0% +SN minus one Co n it's just it's just a +single draw from the distribution + + align:start position:0% +single draw from the distribution + + + align:start position:0% +single draw from the distribution +conditional on the value being at least + + align:start position:0% +conditional on the value being at least + + + align:start position:0% +conditional on the value being at least +this and so this is the inverse CDF of + + align:start position:0% +this and so this is the inverse CDF of + + + align:start position:0% +this and so this is the inverse CDF of +that this is the sort of upper upper + + align:start position:0% +that this is the sort of upper upper + + + align:start position:0% +that this is the sort of upper upper +tail CDF of that right so the expected + + align:start position:0% +tail CDF of that right so the expected + + + align:start position:0% +tail CDF of that right so the expected +profit that I'm going to get is just R * + + align:start position:0% +profit that I'm going to get is just R * + + + align:start position:0% +profit that I'm going to get is just R * +1 - F of R ided this which is just a + + align:start position:0% +1 - F of R ided this which is just a + + + align:start position:0% +1 - F of R ided this which is just a +constant so if you think about how do I + + align:start position:0% +constant so if you think about how do I + + + align:start position:0% +constant so if you think about how do I +maximize this expression R * 1 minus F + + align:start position:0% +maximize this expression R * 1 minus F + + + align:start position:0% +maximize this expression R * 1 minus F +of R time is constant I just maximize + + align:start position:0% +of R time is constant I just maximize + + + align:start position:0% +of R time is constant I just maximize +that by maximizing R * 1 minus F of R + + align:start position:0% +that by maximizing R * 1 minus F of R + + + align:start position:0% +that by maximizing R * 1 minus F of R +which is the Monopoly pricing problem + + align:start position:0% +which is the Monopoly pricing problem + + + align:start position:0% +which is the Monopoly pricing problem +for One + + align:start position:0% +for One + + + align:start position:0% +for One +customer and so if the + + align:start position:0% + + + + align:start position:0% + +you know so I have this Monopoly profit + + align:start position:0% +you know so I have this Monopoly profit + + + align:start position:0% +you know so I have this Monopoly profit +when I use a price of R you know + + align:start position:0% +when I use a price of R you know + + + align:start position:0% +when I use a price of R you know +Monopoly profits like this if s n minus + + align:start position:0% +Monopoly profits like this if s n minus + + + align:start position:0% +Monopoly profits like this if s n minus +one colon n is here if some everyone + + align:start position:0% +one colon n is here if some everyone + + + align:start position:0% +one colon n is here if some everyone +else has dropped out low I'm below the + + align:start position:0% +else has dropped out low I'm below the + + + align:start position:0% +else has dropped out low I'm below the +sort of X anti- Monopoly price then I + + align:start position:0% +sort of X anti- Monopoly price then I + + + align:start position:0% +sort of X anti- Monopoly price then I +would want to use the Monopoly price as + + align:start position:0% +would want to use the Monopoly price as + + + align:start position:0% +would want to use the Monopoly price as +a reserve because it's going to raise + + align:start position:0% +a reserve because it's going to raise + + + align:start position:0% +a reserve because it's going to raise +more + + align:start position:0% +more + + + align:start position:0% +more +Revenue whereas if SN minus one col n + + align:start position:0% +Revenue whereas if SN minus one col n + + + align:start position:0% +Revenue whereas if SN minus one col n +was up here if everybody's bid really + + align:start position:0% +was up here if everybody's bid really + + + align:start position:0% +was up here if everybody's bid really +high well above the Monopoly price then + + align:start position:0% +high well above the Monopoly price then + + + align:start position:0% +high well above the Monopoly price then +I don't want to use the reserve price + + align:start position:0% +I don't want to use the reserve price + + + align:start position:0% +I don't want to use the reserve price +anymore because anything reserve price I + + align:start position:0% +anymore because anything reserve price I + + + align:start position:0% +anymore because anything reserve price I +do is just decreasing my Revenue um but + + align:start position:0% +do is just decreasing my Revenue um but + + + align:start position:0% +do is just decreasing my Revenue um but +in either case just setting this in the + + align:start position:0% +in either case just setting this in the + + + align:start position:0% +in either case just setting this in the +low case this is The Binding Reserve you + + align:start position:0% +low case this is The Binding Reserve you + + + align:start position:0% +low case this is The Binding Reserve you +want in the high case you don't want a + + align:start position:0% +want in the high case you don't want a + + + align:start position:0% +want in the high case you don't want a +reserve and this is a non-binding + + align:start position:0% +reserve and this is a non-binding + + + align:start position:0% +reserve and this is a non-binding +reserve so X poost it's always optimal + + align:start position:0% +reserve so X poost it's always optimal + + + align:start position:0% +reserve so X poost it's always optimal +to set PM as the reserve and so X anti + + align:start position:0% +to set PM as the reserve and so X anti + + + align:start position:0% +to set PM as the reserve and so X anti +it's always optimal to set PM is the + + align:start position:0% +it's always optimal to set PM is the + + + align:start position:0% +it's always optimal to set PM is the +reserve so what you do in a second price + + align:start position:0% +reserve so what you do in a second price + + + align:start position:0% +reserve so what you do in a second price +deal bit auction is you Monopoly price + + align:start position:0% +deal bit auction is you Monopoly price + + + align:start position:0% +deal bit auction is you Monopoly price +uh as a reserve and then and then that + + align:start position:0% +uh as a reserve and then and then that + + + align:start position:0% +uh as a reserve and then and then that +is that is sort of the fully optimal + + align:start position:0% +is that is sort of the fully optimal + + + align:start position:0% +is that is sort of the fully optimal +mechanism uh so obviously if you're + + align:start position:0% +mechanism uh so obviously if you're + + + align:start position:0% +mechanism uh so obviously if you're +thinking about auction design you need + + align:start position:0% +thinking about auction design you need + + + align:start position:0% +thinking about auction design you need +to think about what is that expected + + align:start position:0% +to think about what is that expected + + + align:start position:0% +to think about what is that expected +xane monop Monopoly price because that + + align:start position:0% +xane monop Monopoly price because that + + + align:start position:0% +xane monop Monopoly price because that +that sort of can be you know the as the + + align:start position:0% +that sort of can be you know the as the + + + align:start position:0% +that sort of can be you know the as the +number of biders goes up the value of + + align:start position:0% +number of biders goes up the value of + + + align:start position:0% +number of biders goes up the value of +that monopo the value of Reserve prices + + align:start position:0% +that monopo the value of Reserve prices + + + align:start position:0% +that monopo the value of Reserve prices +do go down because they're probably not + + align:start position:0% +do go down because they're probably not + + + align:start position:0% +do go down because they're probably not +going to be reant anyway but you still + + align:start position:0% +going to be reant anyway but you still + + + align:start position:0% +going to be reant anyway but you still +want the high reserve + + align:start position:0% +want the high reserve + + + align:start position:0% +want the high reserve +price and competition doesn't mean don't + + align:start position:0% +price and competition doesn't mean don't + + + align:start position:0% +price and competition doesn't mean don't +use Reserve prices + + align:start position:0% +use Reserve prices + + + align:start position:0% +use Reserve prices +um some comments here um you know + + align:start position:0% +um some comments here um you know + + + align:start position:0% +um some comments here um you know +Reserve prices are positive even if the + + align:start position:0% +Reserve prices are positive even if the + + + align:start position:0% +Reserve prices are positive even if the +seller doesn't have any value um Reserve + + align:start position:0% +seller doesn't have any value um Reserve + + + align:start position:0% +seller doesn't have any value um Reserve +prices do reduce social welfare so this + + align:start position:0% +prices do reduce social welfare so this + + + align:start position:0% +prices do reduce social welfare so this +is a inefficiency of auction mechanisms + + align:start position:0% +is a inefficiency of auction mechanisms + + + align:start position:0% +is a inefficiency of auction mechanisms +is you use Reserve prices they create + + align:start position:0% +is you use Reserve prices they create + + + align:start position:0% +is you use Reserve prices they create +dead weight loss now they only create + + align:start position:0% +dead weight loss now they only create + + + align:start position:0% +dead weight loss now they only create +dead weight loss if people don't if if + + align:start position:0% +dead weight loss if people don't if if + + + align:start position:0% +dead weight loss if people don't if if +all the biders have values below the + + align:start position:0% +all the biders have values below the + + + align:start position:0% +all the biders have values below the +reserve price so there's it's less of an + + align:start position:0% +reserve price so there's it's less of an + + + align:start position:0% +reserve price so there's it's less of an +issue but it's still it's still a social + + align:start position:0% +issue but it's still it's still a social + + + align:start position:0% +issue but it's still it's still a social +loss um + + align:start position:0% +loss um + + + align:start position:0% +loss um +the above analysis ignores entry if you + + align:start position:0% +the above analysis ignores entry if you + + + align:start position:0% +the above analysis ignores entry if you +think about biders like in the paving + + align:start position:0% +think about biders like in the paving + + + align:start position:0% +think about biders like in the paving +contract Paving Memorial Drive + + align:start position:0% +contract Paving Memorial Drive + + + align:start position:0% +contract Paving Memorial Drive +application it's going to take biders + + align:start position:0% +application it's going to take biders + + + align:start position:0% +application it's going to take biders +quite a long time to put together their + + align:start position:0% +quite a long time to put together their + + + align:start position:0% +quite a long time to put together their +bids and figure out exactly how much is + + align:start position:0% +bids and figure out exactly how much is + + + align:start position:0% +bids and figure out exactly how much is +going to cost them to do the job they're + + align:start position:0% +going to cost them to do the job they're + + + align:start position:0% +going to cost them to do the job they're +going to exert a lot of effort to submit + + align:start position:0% +going to exert a lot of effort to submit + + + align:start position:0% +going to exert a lot of effort to submit +a bid if you put in a high reserve price + + align:start position:0% +a bid if you put in a high reserve price + + + align:start position:0% +a bid if you put in a high reserve price +then they know that their Surplus is + + align:start position:0% +then they know that their Surplus is + + + align:start position:0% +then they know that their Surplus is +going to be low that's going to make you + + align:start position:0% +going to be low that's going to make you + + + align:start position:0% +going to be low that's going to make you +want to spend less time entering the + + align:start position:0% +want to spend less time entering the + + + align:start position:0% +want to spend less time entering the +auction entering you know like entry + + align:start position:0% +auction entering you know like entry + + + align:start position:0% +auction entering you know like entry +costs can make reserve price is not as + + align:start position:0% +costs can make reserve price is not as + + + align:start position:0% +costs can make reserve price is not as +as good of an idea as you think because + + align:start position:0% +as good of an idea as you think because + + + align:start position:0% +as good of an idea as you think because +if you put in a high entry if there's a + + align:start position:0% +if you put in a high entry if there's a + + + align:start position:0% +if you put in a high entry if there's a +high reserve price and therefore people + + align:start position:0% +high reserve price and therefore people + + + align:start position:0% +high reserve price and therefore people +don't enter the auction then attracting + + align:start position:0% +don't enter the auction then attracting + + + align:start position:0% +don't enter the auction then attracting +fewer biders is going to be a cost + + align:start position:0% +fewer biders is going to be a cost + + + align:start position:0% +fewer biders is going to be a cost +there's a theorem in a bu clumper paper + + align:start position:0% +there's a theorem in a bu clumper paper + + + align:start position:0% +there's a theorem in a bu clumper paper +showing that even an Exane sense if you + + align:start position:0% +showing that even an Exane sense if you + + + align:start position:0% +showing that even an Exane sense if you +attract one fewer bidder in expectation + + align:start position:0% +attract one fewer bidder in expectation + + + align:start position:0% +attract one fewer bidder in expectation +then you're you'd be you're actually + + align:start position:0% +then you're you'd be you're actually + + + align:start position:0% +then you're you'd be you're actually +worse off from having used the optimal + + align:start position:0% +worse off from having used the optimal + + + align:start position:0% +worse off from having used the optimal +reserve price um and then another + + align:start position:0% +reserve price um and then another + + + align:start position:0% +reserve price um and then another +comment on reserve prices is there can + + align:start position:0% +comment on reserve prices is there can + + + align:start position:0% +comment on reserve prices is there can +be commitment problems in setting + + align:start position:0% +be commitment problems in setting + + + align:start position:0% +be commitment problems in setting +Reserve price you know we sort of say + + align:start position:0% +Reserve price you know we sort of say + + + align:start position:0% +Reserve price you know we sort of say +we're only going to pay at most 2.1 + + align:start position:0% +we're only going to pay at most 2.1 + + + align:start position:0% +we're only going to pay at most 2.1 +million to repay Memorial Drive because + + align:start position:0% +million to repay Memorial Drive because + + + align:start position:0% +million to repay Memorial Drive because +it's got all these potholes in it + + align:start position:0% +it's got all these potholes in it + + + align:start position:0% +it's got all these potholes in it +everyone bids that it's going to take + + align:start position:0% +everyone bids that it's going to take + + + align:start position:0% +everyone bids that it's going to take +more than 2.1 million to do the work + + align:start position:0% +more than 2.1 million to do the work + + + align:start position:0% +more than 2.1 million to do the work +what do you do then like you know or if + + align:start position:0% +what do you do then like you know or if + + + align:start position:0% +what do you do then like you know or if +it's a bridge that's falling down like + + align:start position:0% +it's a bridge that's falling down like + + + align:start position:0% +it's a bridge that's falling down like +we're only going to pay 2.1 million to + + align:start position:0% +we're only going to pay 2.1 million to + + + align:start position:0% +we're only going to pay 2.1 million to +replace this bridge if everyone else + + align:start position:0% +replace this bridge if everyone else + + + align:start position:0% +replace this bridge if everyone else +bids more than that what do you do do + + align:start position:0% +bids more than that what do you do do + + + align:start position:0% +bids more than that what do you do do +you sort of really commit okay I'm never + + align:start position:0% +you sort of really commit okay I'm never + + + align:start position:0% +you sort of really commit okay I'm never +going to re fix that bridge or repay + + align:start position:0% +going to re fix that bridge or repay + + + align:start position:0% +going to re fix that bridge or repay +that road you know you're going to want + + align:start position:0% +that road you know you're going to want + + + align:start position:0% +that road you know you're going to want +to then sort of put on bid say okay I + + align:start position:0% +to then sort of put on bid say okay I + + + align:start position:0% +to then sort of put on bid say okay I +guess 2.1 million was too low now I'll + + align:start position:0% +guess 2.1 million was too low now I'll + + + align:start position:0% +guess 2.1 million was too low now I'll +have reserve of 2.3 million you know + + align:start position:0% +have reserve of 2.3 million you know + + + align:start position:0% +have reserve of 2.3 million you know +Reserve prices only work if you can + + align:start position:0% +Reserve prices only work if you can + + + align:start position:0% +Reserve prices only work if you can +commit to them they don't work if you + + align:start position:0% +commit to them they don't work if you + + + align:start position:0% +commit to them they don't work if you +undo them later + + align:start position:0% +undo them later + + + align:start position:0% +undo them later +on okay so then the final Theory topic + + align:start position:0% +on okay so then the final Theory topic + + + align:start position:0% +on okay so then the final Theory topic +I'm going to do I'll skip the next one + + align:start position:0% +I'm going to do I'll skip the next one + + + align:start position:0% +I'm going to do I'll skip the next one +after it is uh common value + + align:start position:0% +after it is uh common value + + + align:start position:0% +after it is uh common value +auctions you know more General model of + + align:start position:0% +auctions you know more General model of + + + align:start position:0% +auctions you know more General model of +auctions is that your your value depends + + align:start position:0% +auctions is that your your value depends + + + align:start position:0% +auctions is that your your value depends +on your signal and everybody else's + + align:start position:0% +on your signal and everybody else's + + + align:start position:0% +on your signal and everybody else's +signal so imagine you have these signals + + align:start position:0% +signal so imagine you have these signals + + + align:start position:0% +signal so imagine you have these signals +that have joint density at F and your + + align:start position:0% +that have joint density at F and your + + + align:start position:0% +that have joint density at F and your +expected value depends on your signal + + align:start position:0% +expected value depends on your signal + + + align:start position:0% +expected value depends on your signal +and everybody else's + + align:start position:0% +and everybody else's + + + align:start position:0% +and everybody else's +signal uh a special case of this is a + + align:start position:0% +signal uh a special case of this is a + + + align:start position:0% +signal uh a special case of this is a +pure common values model so suppose the + + align:start position:0% +pure common values model so suppose the + + + align:start position:0% +pure common values model so suppose the +object has value V to all biders uh and + + align:start position:0% +object has value V to all biders uh and + + + align:start position:0% +object has value V to all biders uh and +we get signals which are V plus Epsilon + + align:start position:0% +we get signals which are V plus Epsilon + + + align:start position:0% +we get signals which are V plus Epsilon +so I'm going to talk about empirical + + align:start position:0% +so I'm going to talk about empirical + + + align:start position:0% +so I'm going to talk about empirical +paper about like oil drilling so imagine + + align:start position:0% +paper about like oil drilling so imagine + + + align:start position:0% +paper about like oil drilling so imagine +you're bidding for the right to drill + + align:start position:0% +you're bidding for the right to drill + + + align:start position:0% +you're bidding for the right to drill +for oil on some tract of land + + align:start position:0% +for oil on some tract of land + + + align:start position:0% +for oil on some tract of land +offshore the value of winning that + + align:start position:0% +offshore the value of winning that + + + align:start position:0% +offshore the value of winning that +auction is the amount of oil that you're + + align:start position:0% +auction is the amount of oil that you're + + + align:start position:0% +auction is the amount of oil that you're +going to get to extract back from that + + align:start position:0% +going to get to extract back from that + + + align:start position:0% +going to get to extract back from that +well and you know we all hire geologists + + align:start position:0% +well and you know we all hire geologists + + + align:start position:0% +well and you know we all hire geologists +and all of our geologists do sort of + + align:start position:0% +and all of our geologists do sort of + + + align:start position:0% +and all of our geologists do sort of +Sonic testing or whatever they + + align:start position:0% +Sonic testing or whatever they + + + align:start position:0% +Sonic testing or whatever they +geologists do and then they try to + + align:start position:0% +geologists do and then they try to + + + align:start position:0% +geologists do and then they try to +estimate what's the probability that + + align:start position:0% +estimate what's the probability that + + + align:start position:0% +estimate what's the probability that +there's oil if there is oil how much is + + align:start position:0% +there's oil if there is oil how much is + + + align:start position:0% +there's oil if there is oil how much is +there and come up with an estimate of + + align:start position:0% +there and come up with an estimate of + + + align:start position:0% +there and come up with an estimate of +the value and suppose they all get these + + align:start position:0% +the value and suppose they all get these + + + align:start position:0% +the value and suppose they all get these +values V plus Epsilon + + align:start position:0% +values V plus Epsilon + + + align:start position:0% +values V plus Epsilon +I um you the bidder's expected value + + align:start position:0% +I um you the bidder's expected value + + + align:start position:0% +I um you the bidder's expected value +given all signals is what's my expected + + align:start position:0% +given all signals is what's my expected + + + align:start position:0% +given all signals is what's my expected +value given my signal and what everybody + + align:start position:0% +value given my signal and what everybody + + + align:start position:0% +value given my signal and what everybody +else's geologist said but I only observe + + align:start position:0% +else's geologist said but I only observe + + + align:start position:0% +else's geologist said but I only observe +ve um I only observe my own signal so + + align:start position:0% +ve um I only observe my own signal so + + + align:start position:0% +ve um I only observe my own signal so +imagine we have this pure common values + + align:start position:0% +imagine we have this pure common values + + + align:start position:0% +imagine we have this pure common values +auction where we just there's this + + align:start position:0% +auction where we just there's this + + + align:start position:0% +auction where we just there's this +common value that everyone has for + + align:start position:0% +common value that everyone has for + + + align:start position:0% +common value that everyone has for +winning we all submit our bids and then + + align:start position:0% +winning we all submit our bids and then + + + align:start position:0% +winning we all submit our bids and then +I find out that I've won the bidding + + align:start position:0% +I find out that I've won the bidding + + + align:start position:0% +I find out that I've won the bidding +when I find out that one in the bidding + + align:start position:0% +when I find out that one in the bidding + + + align:start position:0% +when I find out that one in the bidding +what I what I'm learning is that my + + align:start position:0% +what I what I'm learning is that my + + + align:start position:0% +what I what I'm learning is that my +geologist was more optimistic than + + align:start position:0% +geologist was more optimistic than + + + align:start position:0% +geologist was more optimistic than +everybody else's geologists and so + + align:start position:0% +everybody else's geologists and so + + + align:start position:0% +everybody else's geologists and so +particular if there n other geologists + + align:start position:0% +particular if there n other geologists + + + align:start position:0% +particular if there n other geologists +you know and n is a large number I've + + align:start position:0% +you know and n is a large number I've + + + align:start position:0% +you know and n is a large number I've +learned that my guy was out in the tales + + align:start position:0% +learned that my guy was out in the tales + + + align:start position:0% +learned that my guy was out in the tales +and how he read the seism graph + + align:start position:0% +and how he read the seism graph + + + align:start position:0% +and how he read the seism graph +um which then tells me that you know I + + align:start position:0% +um which then tells me that you know I + + + align:start position:0% +um which then tells me that you know I +now like this is what people call the + + align:start position:0% +now like this is what people call the + + + align:start position:0% +now like this is what people call the +Winner's curse that once I've learned + + align:start position:0% +Winner's curse that once I've learned + + + align:start position:0% +Winner's curse that once I've learned +that I win the auction I now think the + + align:start position:0% +that I win the auction I now think the + + + align:start position:0% +that I win the auction I now think the +good is worth much less than I thought + + align:start position:0% +good is worth much less than I thought + + + align:start position:0% +good is worth much less than I thought +when I was submitting my bid because + + align:start position:0% +when I was submitting my bid because + + + align:start position:0% +when I was submitting my bid because +I've learned that everybody else's + + align:start position:0% +I've learned that everybody else's + + + align:start position:0% +I've learned that everybody else's +estimate was lower than mine okay um now + + align:start position:0% +estimate was lower than mine okay um now + + + align:start position:0% +estimate was lower than mine okay um now +you know in a rational model it's not + + align:start position:0% +you know in a rational model it's not + + + align:start position:0% +you know in a rational model it's not +like biders get Negative value because + + align:start position:0% +like biders get Negative value because + + + align:start position:0% +like biders get Negative value because +of the winners curse you know in a + + align:start position:0% +of the winners curse you know in a + + + align:start position:0% +of the winners curse you know in a +rational model what biders do is they + + align:start position:0% +rational model what biders do is they + + + align:start position:0% +rational model what biders do is they +account for this in the winning they're + + align:start position:0% +account for this in the winning they're + + + align:start position:0% +account for this in the winning they're +like okay this I think there's like $50 + + align:start position:0% +like okay this I think there's like $50 + + + align:start position:0% +like okay this I think there's like $50 +million worth of oil there but what + + align:start position:0% +million worth of oil there but what + + + align:start position:0% +million worth of oil there but what +would I think if I learned that + + align:start position:0% +would I think if I learned that + + + align:start position:0% +would I think if I learned that +everybody else's geologist thought there + + align:start position:0% +everybody else's geologist thought there + + + align:start position:0% +everybody else's geologist thought there +was less oil than than mine thought + + align:start position:0% +was less oil than than mine thought + + + align:start position:0% +was less oil than than mine thought +there was and so what you bid is you bid + + align:start position:0% +there was and so what you bid is you bid + + + align:start position:0% +there was and so what you bid is you bid +based + + align:start position:0% +based + + + align:start position:0% +based +on what you think the probab what you + + align:start position:0% +on what you think the probab what you + + + align:start position:0% +on what you think the probab what you +think the value is conditional on + + align:start position:0% +think the value is conditional on + + + align:start position:0% +think the value is conditional on +learning that everybody else's geologist + + align:start position:0% +learning that everybody else's geologist + + + align:start position:0% +learning that everybody else's geologist +was less optimistic than yours right so + + align:start position:0% +was less optimistic than yours right so + + + align:start position:0% +was less optimistic than yours right so +what you bid on is you're not bidding + + align:start position:0% +what you bid on is you're not bidding + + + align:start position:0% +what you bid on is you're not bidding +based on your like so in a second price + + align:start position:0% +based on your like so in a second price + + + align:start position:0% +based on your like so in a second price +seal bid auction I'm not bidding what's + + align:start position:0% +seal bid auction I'm not bidding what's + + + align:start position:0% +seal bid auction I'm not bidding what's +my expected value conditional on my + + align:start position:0% +my expected value conditional on my + + + align:start position:0% +my expected value conditional on my +signal I'm bidding my what's my expected + + align:start position:0% +signal I'm bidding my what's my expected + + + align:start position:0% +signal I'm bidding my what's my expected +value conditional on my signal and on SJ + + align:start position:0% +value conditional on my signal and on SJ + + + align:start position:0% +value conditional on my signal and on SJ +less than or equal to SI for all J and + + align:start position:0% +less than or equal to SI for all J and + + + align:start position:0% +less than or equal to SI for all J and +actually in terms of like SJ equal SI + + align:start position:0% +actually in terms of like SJ equal SI + + + align:start position:0% +actually in terms of like SJ equal SI +for some J but it's more complicated but + + align:start position:0% +for some J but it's more complicated but + + + align:start position:0% +for some J but it's more complicated but +anyway what I'm bidding on I'm bidding + + align:start position:0% +anyway what I'm bidding on I'm bidding + + + align:start position:0% +anyway what I'm bidding on I'm bidding +on what do I think it's worth knowing + + align:start position:0% +on what do I think it's worth knowing + + + align:start position:0% +on what do I think it's worth knowing +that everybody + + align:start position:0% +that everybody + + + align:start position:0% +that everybody +else is bidding is has a worse signal + + align:start position:0% +else is bidding is has a worse signal + + + align:start position:0% +else is bidding is has a worse signal +than I do and actually knowing that it + + align:start position:0% +than I do and actually knowing that it + + + align:start position:0% +than I do and actually knowing that it +actually matters what I bid so there's + + align:start position:0% +actually matters what I bid so there's + + + align:start position:0% +actually matters what I bid so there's +somebody else who's very close to + + align:start position:0% +somebody else who's very close to + + + align:start position:0% +somebody else who's very close to +me + + align:start position:0% +me + + + align:start position:0% +me +um but so what rational players will do + + align:start position:0% +um but so what rational players will do + + + align:start position:0% +um but so what rational players will do +is they avoid the Winner's curse by just + + align:start position:0% +is they avoid the Winner's curse by just + + + align:start position:0% +is they avoid the Winner's curse by just +down weting their bids based on the + + align:start position:0% +down weting their bids based on the + + + align:start position:0% +down weting their bids based on the +amount of winners curse they expect to + + align:start position:0% +amount of winners curse they expect to + + + align:start position:0% +amount of winners curse they expect to +occur on once they learn that they + + align:start position:0% +occur on once they learn that they + + + align:start position:0% +occur on once they learn that they +one okay so what I want to do is is + + align:start position:0% +one okay so what I want to do is is + + + align:start position:0% +one okay so what I want to do is is +finish today with uh one empirical paper + + align:start position:0% +finish today with uh one empirical paper + + + align:start position:0% +finish today with uh one empirical paper +um so this is about Winter's curses and + + align:start position:0% +um so this is about Winter's curses and + + + align:start position:0% +um so this is about Winter's curses and +auction so paper Hendricks and Porter + + align:start position:0% +auction so paper Hendricks and Porter + + + align:start position:0% +auction so paper Hendricks and Porter +empirical study of an auction with + + align:start position:0% +empirical study of an auction with + + + align:start position:0% +empirical study of an auction with +asymmetric information + + align:start position:0% +asymmetric information + + + align:start position:0% +asymmetric information +uh this is about us auctions of uh + + align:start position:0% +uh this is about us auctions of uh + + + align:start position:0% +uh this is about us auctions of uh +leases to drill for oil and uh Waters + + align:start position:0% +leases to drill for oil and uh Waters + + + align:start position:0% +leases to drill for oil and uh Waters +off the US Coast um you know in + + align:start position:0% +off the US Coast um you know in + + + align:start position:0% +off the US Coast um you know in +the most of this oil drilling that + + align:start position:0% +the most of this oil drilling that + + + align:start position:0% +the most of this oil drilling that +they're talking about is if you go to + + align:start position:0% +they're talking about is if you go to + + + align:start position:0% +they're talking about is if you go to +the sort of gulf coast of the United + + align:start position:0% +the sort of gulf coast of the United + + + align:start position:0% +the sort of gulf coast of the United +States off the coast of Texas Louisiana + + align:start position:0% +States off the coast of Texas Louisiana + + + align:start position:0% +States off the coast of Texas Louisiana +there are many many many um offshore oil + + align:start position:0% +there are many many many um offshore oil + + + align:start position:0% +there are many many many um offshore oil +wells um and relatively shallow water + + align:start position:0% +wells um and relatively shallow water + + + align:start position:0% +wells um and relatively shallow water +where the government has auctioned off + + align:start position:0% +where the government has auctioned off + + + align:start position:0% +where the government has auctioned off +the right to drill for oil um the US + + align:start position:0% +the right to drill for oil um the US + + + align:start position:0% +the right to drill for oil um the US +government auctions off two different + + align:start position:0% +government auctions off two different + + + align:start position:0% +government auctions off two different +types of offshore oil leases one are + + align:start position:0% +types of offshore oil leases one are + + + align:start position:0% +types of offshore oil leases one are +what are called Wildcat tracks uh + + align:start position:0% +what are called Wildcat tracks uh + + + align:start position:0% +what are called Wildcat tracks uh +Wildcat tracts are 5,000 rough roughly + + align:start position:0% +Wildcat tracts are 5,000 rough roughly + + + align:start position:0% +Wildcat tracts are 5,000 rough roughly +5,000 acre plots that don't abut any + + align:start position:0% +5,000 acre plots that don't abut any + + + align:start position:0% +5,000 acre plots that don't abut any +other Drilling and about 35% of those + + align:start position:0% +other Drilling and about 35% of those + + + align:start position:0% +other Drilling and about 35% of those +that are 35% of those Wildcats tracks + + align:start position:0% +that are 35% of those Wildcats tracks + + + align:start position:0% +that are 35% of those Wildcats tracks +that are bought end up producing any oil + + align:start position:0% +that are bought end up producing any oil + + + align:start position:0% +that are bought end up producing any oil +uh the others either the company doesn't + + align:start position:0% +uh the others either the company doesn't + + + align:start position:0% +uh the others either the company doesn't +drill them because doing a more detailed + + align:start position:0% +drill them because doing a more detailed + + + align:start position:0% +drill them because doing a more detailed +Geological Survey after they've won the + + align:start position:0% +Geological Survey after they've won the + + + align:start position:0% +Geological Survey after they've won the +auction they decide it's not even worth + + align:start position:0% +auction they decide it's not even worth + + + align:start position:0% +auction they decide it's not even worth +drilling or they drill a hole and they + + align:start position:0% +drilling or they drill a hole and they + + + align:start position:0% +drilling or they drill a hole and they +spend millions of dollars drilling + + align:start position:0% +spend millions of dollars drilling + + + align:start position:0% +spend millions of dollars drilling +underground and then they don't find oil + + align:start position:0% +underground and then they don't find oil + + + align:start position:0% +underground and then they don't find oil +when they drill okay um the second type + + align:start position:0% +when they drill okay um the second type + + + align:start position:0% +when they drill okay um the second type +of auctions that things that are + + align:start position:0% +of auctions that things that are + + + align:start position:0% +of auctions that things that are +auctioned is that so like you know I'll + + align:start position:0% +auctioned is that so like you know I'll + + + align:start position:0% +auctioned is that so like you know I'll +just out go out here in the Gulf of + + align:start position:0% +just out go out here in the Gulf of + + + align:start position:0% +just out go out here in the Gulf of +Mexico and they'll just auction off + + align:start position:0% +Mexico and they'll just auction off + + + align:start position:0% +Mexico and they'll just auction off +right to drill here but then sometimes + + align:start position:0% +right to drill here but then sometimes + + + align:start position:0% +right to drill here but then sometimes +what happens is you auction have the + + align:start position:0% +what happens is you auction have the + + + align:start position:0% +what happens is you auction have the +right to drill on this tract and there + + align:start position:0% +right to drill on this tract and there + + + align:start position:0% +right to drill on this tract and there +is oil there and if there is oil there + + align:start position:0% +is oil there and if there is oil there + + + align:start position:0% +is oil there and if there is oil there +then immediately people tend to want to + + align:start position:0% +then immediately people tend to want to + + + align:start position:0% +then immediately people tend to want to +drill here or here or here or here or + + align:start position:0% +drill here or here or here or here or + + + align:start position:0% +drill here or here or here or here or +here um because if you know there's oil + + align:start position:0% +here um because if you know there's oil + + + align:start position:0% +here um because if you know there's oil +here there's probably oil nearby also so + + align:start position:0% +here there's probably oil nearby also so + + + align:start position:0% +here there's probably oil nearby also so +they ALS auction off with these called + + align:start position:0% +they ALS auction off with these called + + + align:start position:0% +they ALS auction off with these called +drainage tracts they're smaller plots + + align:start position:0% +drainage tracts they're smaller plots + + + align:start position:0% +drainage tracts they're smaller plots +that are adjacent to a previously + + align:start position:0% +that are adjacent to a previously + + + align:start position:0% +that are adjacent to a previously +drilled Wildcat tract and so when people + + align:start position:0% +drilled Wildcat tract and so when people + + + align:start position:0% +drilled Wildcat tract and so when people +buy drainage tracts it's more likely + + align:start position:0% +buy drainage tracts it's more likely + + + align:start position:0% +buy drainage tracts it's more likely +that there's going to be oil there it's + + align:start position:0% +that there's going to be oil there it's + + + align:start position:0% +that there's going to be oil there it's +much less risky much higher expected uh + + align:start position:0% +much less risky much higher expected uh + + + align:start position:0% +much less risky much higher expected uh +amount of oil because you know there's + + align:start position:0% +amount of oil because you know there's + + + align:start position:0% +amount of oil because you know there's +oil right right next door okay um + + align:start position:0% +oil right right next door okay um + + + align:start position:0% +oil right right next door okay um +okay here's just a map um you know + + align:start position:0% +okay here's just a map um you know + + + align:start position:0% +okay here's just a map um you know +showing here's random Wildcat tra that + + align:start position:0% +showing here's random Wildcat tra that + + + align:start position:0% +showing here's random Wildcat tra that +someone is is planning to drill on this + + align:start position:0% +someone is is planning to drill on this + + + align:start position:0% +someone is is planning to drill on this +would be an area where say this tract + + align:start position:0% +would be an area where say this tract + + + align:start position:0% +would be an area where say this tract +was drilled they had oil and then they + + align:start position:0% +was drilled they had oil and then they + + + align:start position:0% +was drilled they had oil and then they +started auctioning off all these little + + align:start position:0% +started auctioning off all these little + + + align:start position:0% +started auctioning off all these little +wild all these little drainage tracks + + align:start position:0% +wild all these little drainage tracks + + + align:start position:0% +wild all these little drainage tracks +around it where people can think if + + align:start position:0% +around it where people can think if + + + align:start position:0% +around it where people can think if +there's oil here there's probably oil + + align:start position:0% +there's oil here there's probably oil + + + align:start position:0% +there's oil here there's probably oil +here at all these other places + + align:start position:0% + + + + align:start position:0% + +nearby and asymmetric information that + + align:start position:0% +nearby and asymmetric information that + + + align:start position:0% +nearby and asymmetric information that +they the winners curse note is that this + + align:start position:0% +they the winners curse note is that this + + + align:start position:0% +they the winners curse note is that this +auction is very asymmetric auction and + + align:start position:0% +auction is very asymmetric auction and + + + align:start position:0% +auction is very asymmetric auction and +that there's one firm that + + align:start position:0% +that there's one firm that + + + align:start position:0% +that there's one firm that +has a whale in the ground at this + + align:start position:0% +has a whale in the ground at this + + + align:start position:0% +has a whale in the ground at this +location that knows something about the + + align:start position:0% +location that knows something about the + + + align:start position:0% +location that knows something about the +oil that they're pumping out of it and + + align:start position:0% +oil that they're pumping out of it and + + + align:start position:0% +oil that they're pumping out of it and +then there're all these people around + + align:start position:0% +then there're all these people around + + + align:start position:0% +then there're all these people around +here who don't have the same information + + align:start position:0% +here who don't have the same information + + + align:start position:0% +here who don't have the same information +that this person with the wild cat tract + + align:start position:0% +that this person with the wild cat tract + + + align:start position:0% +that this person with the wild cat tract +is here in particular you know the way + + align:start position:0% +is here in particular you know the way + + + align:start position:0% +is here in particular you know the way +um my understanding of oil drilling uh + + align:start position:0% +um my understanding of oil drilling uh + + + align:start position:0% +um my understanding of oil drilling uh +is you know oil oil drilling is a fairly + + align:start position:0% +is you know oil oil drilling is a fairly + + + align:start position:0% +is you know oil oil drilling is a fairly +sophisticated thing so you've got this + + align:start position:0% +sophisticated thing so you've got this + + + align:start position:0% +sophisticated thing so you've got this +thing that's + + align:start position:0% +thing that's + + + align:start position:0% +thing that's +underwater I've got my well here that + + align:start position:0% +underwater I've got my well here that + + + align:start position:0% +underwater I've got my well here that +I'm drilling down I'm going underwater + + align:start position:0% +I'm drilling down I'm going underwater + + + align:start position:0% +I'm drilling down I'm going underwater +and then I'm drilling into the ground on + + align:start position:0% +and then I'm drilling into the ground on + + + align:start position:0% +and then I'm drilling into the ground on +my wild cat TR you know so I own this + + align:start position:0% +my wild cat TR you know so I own this + + + align:start position:0% +my wild cat TR you know so I own this +Wildcat tract + + align:start position:0% +Wildcat tract + + + align:start position:0% +Wildcat tract +okay you can actually send a drill bit + + align:start position:0% +okay you can actually send a drill bit + + + align:start position:0% +okay you can actually send a drill bit +diagonally underground so you don't have + + align:start position:0% +diagonally underground so you don't have + + + align:start position:0% +diagonally underground so you don't have +to drill a straight hole you can sort of + + align:start position:0% +to drill a straight hole you can sort of + + + align:start position:0% +to drill a straight hole you can sort of +drill like this you can drill like + + align:start position:0% +drill like this you can drill like + + + align:start position:0% +drill like this you can drill like +this and so imagine that you know this + + align:start position:0% +this and so imagine that you know this + + + align:start position:0% +this and so imagine that you know this +firm is here they're producing a ton of + + align:start position:0% +firm is here they're producing a ton of + + + align:start position:0% +firm is here they're producing a ton of +oil from a well that you know on the + + align:start position:0% +oil from a well that you know on the + + + align:start position:0% +oil from a well that you know on the +surface is up there + + align:start position:0% +surface is up there + + + align:start position:0% +surface is up there +and + + align:start position:0% +and + + + align:start position:0% +and +then they propose that they there's an + + align:start position:0% +then they propose that they there's an + + + align:start position:0% +then they propose that they there's an +auction going to be conducted not only + + align:start position:0% +auction going to be conducted not only + + + align:start position:0% +auction going to be conducted not only +for this Wildcat tra but for this dra so + + align:start position:0% +for this Wildcat tra but for this dra so + + + align:start position:0% +for this Wildcat tra but for this dra so +this the Wildcat tract there's a + + align:start position:0% +this the Wildcat tract there's a + + + align:start position:0% +this the Wildcat tract there's a +drainage tract here there's a drainage + + align:start position:0% +drainage tract here there's a drainage + + + align:start position:0% +drainage tract here there's a drainage +tract here and you're going to bid + + align:start position:0% +tract here and you're going to bid + + + align:start position:0% +tract here and you're going to bid +against Exxon Mobile who's got their + + align:start position:0% +against Exxon Mobile who's got their + + + align:start position:0% +against Exxon Mobile who's got their +pipe in the ground pumping a ton of oil + + align:start position:0% +pipe in the ground pumping a ton of oil + + + align:start position:0% +pipe in the ground pumping a ton of oil +out of this Wildcat tract and let's + + align:start position:0% +out of this Wildcat tract and let's + + + align:start position:0% +out of this Wildcat tract and let's +suppose that you're bidding against them + + align:start position:0% +suppose that you're bidding against them + + + align:start position:0% +suppose that you're bidding against them +you're like okay I'm going to bid for + + align:start position:0% +you're like okay I'm going to bid for + + + align:start position:0% +you're like okay I'm going to bid for +this drainage tract and what you learn + + align:start position:0% +this drainage tract and what you learn + + + align:start position:0% +this drainage tract and what you learn +is that they didn't bid for that + + align:start position:0% +is that they didn't bid for that + + + align:start position:0% +is that they didn't bid for that +drainage tract they bid for that + + align:start position:0% +drainage tract they bid for that + + + align:start position:0% +drainage tract they bid for that +drainage tract as soon as you learn that + + align:start position:0% +drainage tract as soon as you learn that + + + align:start position:0% +drainage tract as soon as you learn that +Exon Mobile bid this drainage tract you + + align:start position:0% +Exon Mobile bid this drainage tract you + + + align:start position:0% +Exon Mobile bid this drainage tract you +think it must be that they what they did + + align:start position:0% +think it must be that they what they did + + + align:start position:0% +think it must be that they what they did +is they drilled thing down here and they + + align:start position:0% +is they drilled thing down here and they + + + align:start position:0% +is they drilled thing down here and they +went diagonally that way so they think + + align:start position:0% +went diagonally that way so they think + + + align:start position:0% +went diagonally that way so they think +there's oil over here I've just won this + + align:start position:0% +there's oil over here I've just won this + + + align:start position:0% +there's oil over here I've just won this +drainage tract do I even want to drill + + align:start position:0% +drainage tract do I even want to drill + + + align:start position:0% +drainage tract do I even want to drill +it once I've learned that xon mobile + + align:start position:0% +it once I've learned that xon mobile + + + align:start position:0% +it once I've learned that xon mobile +didn't didn't want this one okay um + + align:start position:0% +didn't didn't want this one okay um + + + align:start position:0% +didn't didn't want this one okay um +anyway so that that creates the sort of + + align:start position:0% +anyway so that that creates the sort of + + + align:start position:0% +anyway so that that creates the sort of +potential for a severe Winner's curse + + align:start position:0% +potential for a severe Winner's curse + + + align:start position:0% +potential for a severe Winner's curse +and that the person who has the pipe in + + align:start position:0% +and that the person who has the pipe in + + + align:start position:0% +and that the person who has the pipe in +the ground knows much more about the oil + + align:start position:0% +the ground knows much more about the oil + + + align:start position:0% +the ground knows much more about the oil +pressure and about where the oil is + + align:start position:0% +pressure and about where the oil is + + + align:start position:0% +pressure and about where the oil is +coming from than all the firms who are + + align:start position:0% +coming from than all the firms who are + + + align:start position:0% +coming from than all the firms who are +just able to observe that they've got a + + align:start position:0% +just able to observe that they've got a + + + align:start position:0% +just able to observe that they've got a +rig set up here in the middle of the + + align:start position:0% +rig set up here in the middle of the + + + align:start position:0% +rig set up here in the middle of the +ocean + + align:start position:0% + + + + align:start position:0% + +somewhere one thing that's interesting + + align:start position:0% +somewhere one thing that's interesting + + + align:start position:0% +somewhere one thing that's interesting +about this is so these these drainage + + align:start position:0% +about this is so these these drainage + + + align:start position:0% +about this is so these these drainage +tracts if you look at the um fraction + + align:start position:0% +tracts if you look at the um fraction + + + align:start position:0% +tracts if you look at the um fraction +that are productive and I guess it's + + align:start position:0% +that are productive and I guess it's + + + align:start position:0% +that are productive and I guess it's +even really hard to see this um so you + + align:start position:0% +even really hard to see this um so you + + + align:start position:0% +even really hard to see this um so you +know there were th this data said there + + align:start position:0% +know there were th this data said there + + + align:start position:0% +know there were th this data said there +were 1,56 Wildcat tracks only 385 had + + align:start position:0% +were 1,56 Wildcat tracks only 385 had + + + align:start position:0% +were 1,56 Wildcat tracks only 385 had +oil there were 144 drainage tracks 86 + + align:start position:0% +oil there were 144 drainage tracks 86 + + + align:start position:0% +oil there were 144 drainage tracks 86 +had oil so it's much higher fraction + + align:start position:0% +had oil so it's much higher fraction + + + align:start position:0% +had oil so it's much higher fraction +have oil the average value of the oil + + align:start position:0% +have oil the average value of the oil + + + align:start position:0% +have oil the average value of the oil +taken out of them these tracts have an + + align:start position:0% +taken out of them these tracts have an + + + align:start position:0% +taken out of them these tracts have an +average of 5.27 I guess it must be + + align:start position:0% +average of 5.27 I guess it must be + + + align:start position:0% +average of 5.27 I guess it must be +millions of something or other dollars + + align:start position:0% +millions of something or other dollars + + + align:start position:0% +millions of something or other dollars +in oil the drainage tracks have $1 13.5 + + align:start position:0% +in oil the drainage tracks have $1 13.5 + + + align:start position:0% +in oil the drainage tracks have $1 13.5 +million of value in on average yet + + align:start position:0% +million of value in on average yet + + + align:start position:0% +million of value in on average yet +somehow the Wildcat tracks attract three + + align:start position:0% +somehow the Wildcat tracks attract three + + + align:start position:0% +somehow the Wildcat tracks attract three +and a half bids per auction the drain + + align:start position:0% +and a half bids per auction the drain + + + align:start position:0% +and a half bids per auction the drain +tracks attract only 2.7 bids per auction + + align:start position:0% +tracks attract only 2.7 bids per auction + + + align:start position:0% +tracks attract only 2.7 bids per auction +so these you have these much more + + align:start position:0% +so these you have these much more + + + align:start position:0% +so these you have these much more +valuable tracks that are much lower risk + + align:start position:0% +valuable tracks that are much lower risk + + + align:start position:0% +valuable tracks that are much lower risk +and yet attract fewer biders than the + + align:start position:0% +and yet attract fewer biders than the + + + align:start position:0% +and yet attract fewer biders than the +Wildcat tracts and as a result + + align:start position:0% +Wildcat tracts and as a result + + + align:start position:0% +Wildcat tracts and as a result +unsurprisingly the average profits + + align:start position:0% +unsurprisingly the average profits + + + align:start position:0% +unsurprisingly the average profits +earned by the winning bidder are much + + align:start position:0% +earned by the winning bidder are much + + + align:start position:0% +earned by the winning bidder are much +higher in bidding for drainage tracks + + align:start position:0% +higher in bidding for drainage tracks + + + align:start position:0% +higher in bidding for drainage tracks +than bidding for Wildcat + + align:start position:0% +than bidding for Wildcat + + + align:start position:0% +than bidding for Wildcat +tracks and you know Hendrick and por + + align:start position:0% +tracks and you know Hendrick and por + + + align:start position:0% +tracks and you know Hendrick and por +sort to note isn't this sort of + + align:start position:0% +sort to note isn't this sort of + + + align:start position:0% +sort to note isn't this sort of +initially seem like a puzzle that why + + align:start position:0% +initially seem like a puzzle that why + + + align:start position:0% +initially seem like a puzzle that why +would the drainage tracts that are so + + align:start position:0% +would the drainage tracts that are so + + + align:start position:0% +would the drainage tracts that are so +much more reliable and so much more + + align:start position:0% +much more reliable and so much more + + + align:start position:0% +much more reliable and so much more +profitable have fewer biders and much + + align:start position:0% +profitable have fewer biders and much + + + align:start position:0% +profitable have fewer biders and much +higher profits than the sort of Wildcat + + align:start position:0% +higher profits than the sort of Wildcat + + + align:start position:0% +higher profits than the sort of Wildcat +ones where it's highly risky and they + + align:start position:0% +ones where it's highly risky and they + + + align:start position:0% +ones where it's highly risky and they +suggest that you know this is a natural + + align:start position:0% +suggest that you know this is a natural + + + align:start position:0% +suggest that you know this is a natural +consequence of the Winner's curse that + + align:start position:0% +consequence of the Winner's curse that + + + align:start position:0% +consequence of the Winner's curse that +the winner because the Winter's curse is + + align:start position:0% +the winner because the Winter's curse is + + + align:start position:0% +the winner because the Winter's curse is +so severe everybody's afraid to bid + + align:start position:0% +so severe everybody's afraid to bid + + + align:start position:0% +so severe everybody's afraid to bid +against the incumbent who's already + + align:start position:0% +against the incumbent who's already + + + align:start position:0% +against the incumbent who's already +extracting the oil from the Wildcat + + align:start position:0% +extracting the oil from the Wildcat + + + align:start position:0% +extracting the oil from the Wildcat +tract and therefore the incumbents earn + + align:start position:0% +tract and therefore the incumbents earn + + + align:start position:0% +tract and therefore the incumbents earn +high profits on these tracks and other + + align:start position:0% +high profits on these tracks and other + + + align:start position:0% +high profits on these tracks and other +people just tend to stay away because + + align:start position:0% +people just tend to stay away because + + + align:start position:0% +people just tend to stay away because +they're afraid of the Winner's + + align:start position:0% + + + + align:start position:0% + +curse so it's a nice idea but in some + + align:start position:0% +curse so it's a nice idea but in some + + + align:start position:0% +curse so it's a nice idea but in some +ways you know I I think I wanted to + + align:start position:0% +ways you know I I think I wanted to + + + align:start position:0% +ways you know I I think I wanted to +cover Hendrick's importer is it's just + + align:start position:0% +cover Hendrick's importer is it's just + + + align:start position:0% +cover Hendrick's importer is it's just +it's a really beautiful example of how + + align:start position:0% +it's a really beautiful example of how + + + align:start position:0% +it's a really beautiful example of how +you can write a reduced form uh + + align:start position:0% +you can write a reduced form uh + + + align:start position:0% +you can write a reduced form uh +empirical IO paper in that they start + + align:start position:0% +empirical IO paper in that they start + + + align:start position:0% +empirical IO paper in that they start +with this sort of simple idea of you + + align:start position:0% +with this sort of simple idea of you + + + align:start position:0% +with this sort of simple idea of you +know people are afraid of the Winner's + + align:start position:0% +know people are afraid of the Winner's + + + align:start position:0% +know people are afraid of the Winner's +curse therefore they bid less and what + + align:start position:0% +curse therefore they bid less and what + + + align:start position:0% +curse therefore they bid less and what +they try to do is sort of build that out + + align:start position:0% +they try to do is sort of build that out + + + align:start position:0% +they try to do is sort of build that out +is like write down a model and then + + align:start position:0% +is like write down a model and then + + + align:start position:0% +is like write down a model and then +think of seven different implications of + + align:start position:0% +think of seven different implications of + + + align:start position:0% +think of seven different implications of +the model that are not obvious from when + + align:start position:0% +the model that are not obvious from when + + + align:start position:0% +the model that are not obvious from when +you just State the model and then think + + align:start position:0% +you just State the model and then think + + + align:start position:0% +you just State the model and then think +about are those implications all true + + align:start position:0% +about are those implications all true + + + align:start position:0% +about are those implications all true +and use that to decide is the asymmetric + + align:start position:0% +and use that to decide is the asymmetric + + + align:start position:0% +and use that to decide is the asymmetric +information really the explanation here + + align:start position:0% +information really the explanation here + + + align:start position:0% +information really the explanation here +or could there be some different + + align:start position:0% +or could there be some different + + + align:start position:0% +or could there be some different +explanation they don't work out what the + + align:start position:0% +explanation they don't work out what the + + + align:start position:0% +explanation they don't work out what the +alternate explanations are but the sort + + align:start position:0% +alternate explanations are but the sort + + + align:start position:0% +alternate explanations are but the sort +of thought is like if I have my one + + align:start position:0% +of thought is like if I have my one + + + align:start position:0% +of thought is like if I have my one +explanation my one explanation makes + + align:start position:0% +explanation my one explanation makes + + + align:start position:0% +explanation my one explanation makes +seven different predictions I can then + + align:start position:0% +seven different predictions I can then + + + align:start position:0% +seven different predictions I can then +test my seven different predictions if + + align:start position:0% +test my seven different predictions if + + + align:start position:0% +test my seven different predictions if +they seem to hold then I think this is a + + align:start position:0% +they seem to hold then I think this is a + + + align:start position:0% +they seem to hold then I think this is a +good explanation for this so here's a + + align:start position:0% +good explanation for this so here's a + + + align:start position:0% +good explanation for this so here's a +very simple model so they + + align:start position:0% +very simple model so they + + + align:start position:0% +very simple model so they +have you know they have a wildcat track + + align:start position:0% +have you know they have a wildcat track + + + align:start position:0% +have you know they have a wildcat track +that has one informed person who's + + align:start position:0% +that has one informed person who's + + + align:start position:0% +that has one informed person who's +drilling on the Wildcat tra and then + + align:start position:0% +drilling on the Wildcat tra and then + + + align:start position:0% +drilling on the Wildcat tra and then +there's a single drainage track nearby + + align:start position:0% +there's a single drainage track nearby + + + align:start position:0% +there's a single drainage track nearby +they're going to assume the drain of + + align:start position:0% +they're going to assume the drain of + + + align:start position:0% +they're going to assume the drain of +tract has value v um to the person who + + align:start position:0% +tract has value v um to the person who + + + align:start position:0% +tract has value v um to the person who +is already drilling the Wildcat tract + + align:start position:0% +is already drilling the Wildcat tract + + + align:start position:0% +is already drilling the Wildcat tract +and V minus C to the others so the + + align:start position:0% +and V minus C to the others so the + + + align:start position:0% +and V minus C to the others so the +option is not only does xon mobile have + + align:start position:0% +option is not only does xon mobile have + + + align:start position:0% +option is not only does xon mobile have +an informational Advantage xon mobile + + align:start position:0% +an informational Advantage xon mobile + + + align:start position:0% +an informational Advantage xon mobile +would get V if they win the drainage + + align:start position:0% +would get V if they win the drainage + + + align:start position:0% +would get V if they win the drainage +tract whereas a rival would only get V + + align:start position:0% +tract whereas a rival would only get V + + + align:start position:0% +tract whereas a rival would only get V +minus C and the thought is that the + + align:start position:0% +minus C and the thought is that the + + + align:start position:0% +minus C and the thought is that the +rivals are getting less value because + + align:start position:0% +rivals are getting less value because + + + align:start position:0% +rivals are getting less value because +when you already have a platform nearby + + align:start position:0% +when you already have a platform nearby + + + align:start position:0% +when you already have a platform nearby +there's economies of scale and building + + align:start position:0% +there's economies of scale and building + + + align:start position:0% +there's economies of scale and building +a second platform here and so there's a + + align:start position:0% +a second platform here and so there's a + + + align:start position:0% +a second platform here and so there's a +cost Advantage as well that might + + align:start position:0% +cost Advantage as well that might + + + align:start position:0% +cost Advantage as well that might +explain why Exxon Mobile will bid more + + align:start position:0% +explain why Exxon Mobile will bid more + + + align:start position:0% +explain why Exxon Mobile will bid more +um + + align:start position:0% +um + + + align:start position:0% +um +we have n uninformed bidders the + + align:start position:0% +we have n uninformed bidders the + + + align:start position:0% +we have n uninformed bidders the +uninformed biders do get some signal + + align:start position:0% +uninformed biders do get some signal + + + align:start position:0% +uninformed biders do get some signal +they get some signal Z from their you + + align:start position:0% +they get some signal Z from their you + + + align:start position:0% +they get some signal Z from their you +know which can be the signal from their + + align:start position:0% +know which can be the signal from their + + + align:start position:0% +know which can be the signal from their +geologists it could be the signal from + + align:start position:0% +geologists it could be the signal from + + + align:start position:0% +geologists it could be the signal from +you know Exxon Mobile does have to + + align:start position:0% +you know Exxon Mobile does have to + + + align:start position:0% +you know Exxon Mobile does have to +report how much oil they're pulling out + + align:start position:0% +report how much oil they're pulling out + + + align:start position:0% +report how much oil they're pulling out +of that well because they pay royalties + + align:start position:0% +of that well because they pay royalties + + + align:start position:0% +of that well because they pay royalties +and they're going to assume that this + + align:start position:0% +and they're going to assume that this + + + align:start position:0% +and they're going to assume that this +satisfies the expected value is bigger + + align:start position:0% +satisfies the expected value is bigger + + + align:start position:0% +satisfies the expected value is bigger +than the government's reserve price the + + align:start position:0% +than the government's reserve price the + + + align:start position:0% +than the government's reserve price the +expected value is increasing in the + + align:start position:0% +expected value is increasing in the + + + align:start position:0% +expected value is increasing in the +quality of their signal but there's + + align:start position:0% +quality of their signal but there's + + + align:start position:0% +quality of their signal but there's +always some probability that the value + + align:start position:0% +always some probability that the value + + + align:start position:0% +always some probability that the value +will be less than the reserve price no + + align:start position:0% +will be less than the reserve price no + + + align:start position:0% +will be less than the reserve price no +matter how positive the signal + + align:start position:0% +matter how positive the signal + + + align:start position:0% +matter how positive the signal +is okay and then you have the one + + align:start position:0% +is okay and then you have the one + + + align:start position:0% +is okay and then you have the one +informed firm that both sees the True + + align:start position:0% +informed firm that both sees the True + + + align:start position:0% +informed firm that both sees the True +Value actually fully knows how much oil + + align:start position:0% +Value actually fully knows how much oil + + + align:start position:0% +Value actually fully knows how much oil +is under the drainage tract and sees the + + align:start position:0% +is under the drainage tract and sees the + + + align:start position:0% +is under the drainage tract and sees the +signal that the uninformed biders are + + align:start position:0% +signal that the uninformed biders are + + + align:start position:0% +signal that the uninformed biders are +relying on and then they think about a + + align:start position:0% +relying on and then they think about a + + + align:start position:0% +relying on and then they think about a +first price sealed bid auction with the + + align:start position:0% +first price sealed bid auction with the + + + align:start position:0% +first price sealed bid auction with the +reservation price of + + align:start position:0% + + + + align:start position:0% + +R you know observation like we've done a + + align:start position:0% +R you know observation like we've done a + + + align:start position:0% +R you know observation like we've done a +few times in this class this is not a + + align:start position:0% +few times in this class this is not a + + + align:start position:0% +few times in this class this is not a +game that can have a pure strategy + + align:start position:0% +game that can have a pure strategy + + + align:start position:0% +game that can have a pure strategy +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +okay because in a pure strategy + + align:start position:0% +okay because in a pure strategy + + + align:start position:0% +okay because in a pure strategy +equilibrium in some sense The Firm + + align:start position:0% +equilibrium in some sense The Firm + + + align:start position:0% +equilibrium in some sense The Firm +playing the the uninformed guys are just + + align:start position:0% +playing the the uninformed guys are just + + + align:start position:0% +playing the the uninformed guys are just +too vulnerable when they play Pure + + align:start position:0% +too vulnerable when they play Pure + + + align:start position:0% +too vulnerable when they play Pure +strategy equilibrium so you know you you + + align:start position:0% +strategy equilibrium so you know you you + + + align:start position:0% +strategy equilibrium so you know you you +can't have an equilibrium where the + + align:start position:0% +can't have an equilibrium where the + + + align:start position:0% +can't have an equilibrium where the +uninformed bidders are not bidding + + align:start position:0% +uninformed bidders are not bidding + + + align:start position:0% +uninformed bidders are not bidding +because if the uninformed guys were not + + align:start position:0% +because if the uninformed guys were not + + + align:start position:0% +because if the uninformed guys were not +bidding the informed guy would just bid + + align:start position:0% +bidding the informed guy would just bid + + + align:start position:0% +bidding the informed guy would just bid +R and then bidding R plus Epsilon would + + align:start position:0% +R and then bidding R plus Epsilon would + + + align:start position:0% +R and then bidding R plus Epsilon would +be a profitable deviation for the + + align:start position:0% +be a profitable deviation for the + + + align:start position:0% +be a profitable deviation for the +uninformed biders because on average the + + align:start position:0% +uninformed biders because on average the + + + align:start position:0% +uninformed biders because on average the +tracks are worth a lot so you can't have + + align:start position:0% +tracks are worth a lot so you can't have + + + align:start position:0% +tracks are worth a lot so you can't have +the uninformed biders not bidding + + align:start position:0% +the uninformed biders not bidding + + + align:start position:0% +the uninformed biders not bidding +because then the informed bidder would + + align:start position:0% +because then the informed bidder would + + + align:start position:0% +because then the informed bidder would +bid R and then the uninformed guys would + + align:start position:0% +bid R and then the uninformed guys would + + + align:start position:0% +bid R and then the uninformed guys would +wish they were b r plus Epsilon and so + + align:start position:0% +wish they were b r plus Epsilon and so + + + align:start position:0% +wish they were b r plus Epsilon and so +that can't be an + + align:start position:0% +that can't be an + + + align:start position:0% +that can't be an +equilibrium uh you also can't have an + + align:start position:0% +equilibrium uh you also can't have an + + + align:start position:0% +equilibrium uh you also can't have an +equilibrium where the uninformed guys + + align:start position:0% +equilibrium where the uninformed guys + + + align:start position:0% +equilibrium where the uninformed guys +are following some pure strategy that's + + align:start position:0% +are following some pure strategy that's + + + align:start position:0% +are following some pure strategy that's +you know some function B uninformed of z + + align:start position:0% +you know some function B uninformed of z + + + align:start position:0% +you know some function B uninformed of z +um because if they were playing this + + align:start position:0% +um because if they were playing this + + + align:start position:0% +um because if they were playing this +pure strategy then what would the + + align:start position:0% +pure strategy then what would the + + + align:start position:0% +pure strategy then what would the +incumbent do if the value was bigger + + align:start position:0% +incumbent do if the value was bigger + + + align:start position:0% +incumbent do if the value was bigger +than what they're bidding the incumbent + + align:start position:0% +than what they're bidding the incumbent + + + align:start position:0% +than what they're bidding the incumbent +would take it and if the value was less + + align:start position:0% +would take it and if the value was less + + + align:start position:0% +would take it and if the value was less +than what they're bidding the incumbent + + align:start position:0% +than what they're bidding the incumbent + + + align:start position:0% +than what they're bidding the incumbent +will leave it to them so basically if + + align:start position:0% +will leave it to them so basically if + + + align:start position:0% +will leave it to them so basically if +they're playing pure strategy they + + align:start position:0% +they're playing pure strategy they + + + align:start position:0% +they're playing pure strategy they +always lose because either the incumbent + + align:start position:0% +always lose because either the incumbent + + + align:start position:0% +always lose because either the incumbent +it's a good tract and the incumbent + + align:start position:0% +it's a good tract and the incumbent + + + align:start position:0% +it's a good tract and the incumbent +takes it from them or it's a bad tract + + align:start position:0% +takes it from them or it's a bad tract + + + align:start position:0% +takes it from them or it's a bad tract +the incumbent leaves it with them so you + + align:start position:0% +the incumbent leaves it with them so you + + + align:start position:0% +the incumbent leaves it with them so you +can't have any of these equilibria what + + align:start position:0% +can't have any of these equilibria what + + + align:start position:0% +can't have any of these equilibria what +do you get you know like in these models + + align:start position:0% +do you get you know like in these models + + + align:start position:0% +do you get you know like in these models +of search you get a mixed strategy + + align:start position:0% +of search you get a mixed strategy + + + align:start position:0% +of search you get a mixed strategy +equilibria so the uninformed biders are + + align:start position:0% +equilibria so the uninformed biders are + + + align:start position:0% +equilibria so the uninformed biders are +going to mix sometimes they're going to + + align:start position:0% +going to mix sometimes they're going to + + + align:start position:0% +going to mix sometimes they're going to +bid exactly zero and sometimes they're + + align:start position:0% +bid exactly zero and sometimes they're + + + align:start position:0% +bid exactly zero and sometimes they're +going to mix over the interval from R to + + align:start position:0% +going to mix over the interval from R to + + + align:start position:0% +going to mix over the interval from R to +Z and their mixing is going to be such + + align:start position:0% +Z and their mixing is going to be such + + + align:start position:0% +Z and their mixing is going to be such +that it forces the incumbent to play + + align:start position:0% +that it forces the incumbent to play + + + align:start position:0% +that it forces the incumbent to play +it's optimal for the incumbent to play a + + align:start position:0% +it's optimal for the incumbent to play a + + + align:start position:0% +it's optimal for the incumbent to play a +strategy which is if there's no oil bid + + align:start position:0% +strategy which is if there's no oil bid + + + align:start position:0% +strategy which is if there's no oil bid +zero if v a little bit bigger than the + + align:start position:0% +zero if v a little bit bigger than the + + + align:start position:0% +zero if v a little bit bigger than the +reserve price and Z is not too big then + + align:start position:0% +reserve price and Z is not too big then + + + align:start position:0% +reserve price and Z is not too big then +just bid exactly the reserve price and + + align:start position:0% +just bid exactly the reserve price and + + + align:start position:0% +just bid exactly the reserve price and +then as the either the value gets larger + + align:start position:0% +then as the either the value gets larger + + + align:start position:0% +then as the either the value gets larger +or Z gets bigger start to increase your + + align:start position:0% +or Z gets bigger start to increase your + + + align:start position:0% +or Z gets bigger start to increase your +bid and bid above the reserve price okay + + align:start position:0% +bid and bid above the reserve price okay + + + align:start position:0% +bid and bid above the reserve price okay +so the incumbent is you know if I think + + align:start position:0% +so the incumbent is you know if I think + + + align:start position:0% +so the incumbent is you know if I think +about what the incumbent bid + + align:start position:0% +about what the incumbent bid + + + align:start position:0% +about what the incumbent bid +distribution looks like uh sometimes I + + align:start position:0% +distribution looks like uh sometimes I + + + align:start position:0% +distribution looks like uh sometimes I +see the incumbent bidding exactly zero + + align:start position:0% +see the incumbent bidding exactly zero + + + align:start position:0% +see the incumbent bidding exactly zero +sry bidding exactly zero just not even + + align:start position:0% +sry bidding exactly zero just not even + + + align:start position:0% +sry bidding exactly zero just not even +bidding sometimes I see the incumbent + + align:start position:0% +bidding sometimes I see the incumbent + + + align:start position:0% +bidding sometimes I see the incumbent +bidding the reserve price and then + + align:start position:0% +bidding the reserve price and then + + + align:start position:0% +bidding the reserve price and then +there's going to be some you know + + align:start position:0% +there's going to be some you know + + + align:start position:0% +there's going to be some you know +density of bids where the incumbent bids + + align:start position:0% +density of bids where the incumbent bids + + + align:start position:0% +density of bids where the incumbent bids +more if if it knows the attct is highly + + align:start position:0% +more if if it knows the attct is highly + + + align:start position:0% +more if if it knows the attct is highly +valuable and looks attractive it's going + + align:start position:0% +valuable and looks attractive it's going + + + align:start position:0% +valuable and looks attractive it's going +to bit a higher amount okay and what are + + align:start position:0% +to bit a higher amount okay and what are + + + align:start position:0% +to bit a higher amount okay and what are +the so this is what the incumbent + + align:start position:0% +the so this is what the incumbent + + + align:start position:0% +the so this is what the incumbent +does what are the uninformed guys do the + + align:start position:0% +does what are the uninformed guys do the + + + align:start position:0% +does what are the uninformed guys do the +uninformed guys are playing sort of a + + align:start position:0% +uninformed guys are playing sort of a + + + align:start position:0% +uninformed guys are playing sort of a +corresponding mixture they don't know + + align:start position:0% +corresponding mixture they don't know + + + align:start position:0% +corresponding mixture they don't know +anything thing but sometimes they bid + + align:start position:0% +anything thing but sometimes they bid + + + align:start position:0% +anything thing but sometimes they bid +zero and then they also bid over some + + align:start position:0% +zero and then they also bid over some + + + align:start position:0% +zero and then they also bid over some +distribution of higher + + align:start position:0% + + + + align:start position:0% + +values be more realistic maybe they're + + align:start position:0% +values be more realistic maybe they're + + + align:start position:0% +values be more realistic maybe they're +they bid zero a lot because they're + + align:start position:0% + + + + align:start position:0% + +scared okay so anyway you know Hendrix + + align:start position:0% +scared okay so anyway you know Hendrix + + + align:start position:0% +scared okay so anyway you know Hendrix +and Porter solved for that + + align:start position:0% +and Porter solved for that + + + align:start position:0% +and Porter solved for that +equilibrium uh and you know very nice + + align:start position:0% +equilibrium uh and you know very nice + + + align:start position:0% +equilibrium uh and you know very nice +feature is that they have sort of many + + align:start position:0% +feature is that they have sort of many + + + align:start position:0% +feature is that they have sort of many +different predictions they can derive in + + align:start position:0% +different predictions they can derive in + + + align:start position:0% +different predictions they can derive in +this model so the first one is that in + + align:start position:0% +this model so the first one is that in + + + align:start position:0% +this model so the first one is that in +this + + align:start position:0% +this + + + align:start position:0% +this +equilibrium uh the + + align:start position:0% +equilibrium uh the + + + align:start position:0% +equilibrium uh the +incumbents bid zero with a smaller + + align:start position:0% +incumbents bid zero with a smaller + + + align:start position:0% +incumbents bid zero with a smaller +probability than the probability that + + align:start position:0% +probability than the probability that + + + align:start position:0% +probability than the probability that +the uh entr the uninformed guys bid zero + + align:start position:0% +the uh entr the uninformed guys bid zero + + + align:start position:0% +the uh entr the uninformed guys bid zero +so bidding zero bids by the incumbent + + align:start position:0% +so bidding zero bids by the incumbent + + + align:start position:0% +so bidding zero bids by the incumbent +are less common than zero bids by the + + align:start position:0% +are less common than zero bids by the + + + align:start position:0% +are less common than zero bids by the +the disadvantaged + + align:start position:0% +the disadvantaged + + + align:start position:0% +the disadvantaged +entrance uh the informed bidder wins the + + align:start position:0% +entrance uh the informed bidder wins the + + + align:start position:0% +entrance uh the informed bidder wins the +auction at least half the + + align:start position:0% +auction at least half the + + + align:start position:0% +auction at least half the +time uh the uninformed biders are + + align:start position:0% +time uh the uninformed biders are + + + align:start position:0% +time uh the uninformed biders are +earning zero profits because they're + + align:start position:0% +earning zero profits because they're + + + align:start position:0% +earning zero profits because they're +mixing and they're mixing with zero in + + align:start position:0% +mixing and they're mixing with zero in + + + align:start position:0% +mixing and they're mixing with zero in +the equilibrium support so sometimes the + + align:start position:0% +the equilibrium support so sometimes the + + + align:start position:0% +the equilibrium support so sometimes the +equ they do bid zero uh and so profits + + align:start position:0% +equ they do bid zero uh and so profits + + + align:start position:0% +equ they do bid zero uh and so profits +are zero in + + align:start position:0% +are zero in + + + align:start position:0% +are zero in +expectation in the bad news case where + + align:start position:0% +expectation in the bad news case where + + + align:start position:0% +expectation in the bad news case where +they bid something and the informed + + align:start position:0% +they bid something and the informed + + + align:start position:0% +they bid something and the informed +bidder bids zero then their profits are + + align:start position:0% +bidder bids zero then their profits are + + + align:start position:0% +bidder bids zero then their profits are +negative and in the good news case where + + align:start position:0% +negative and in the good news case where + + + align:start position:0% +negative and in the good news case where +the informed bidder bids at least are + + align:start position:0% +the informed bidder bids at least are + + + align:start position:0% +the informed bidder bids at least are +then their profits are positive in + + align:start position:0% +then their profits are positive in + + + align:start position:0% +then their profits are positive in +expectation because they're they have + + align:start position:0% +expectation because they're they have + + + align:start position:0% +expectation because they're they have +zero expected profits in the bad news + + align:start position:0% +zero expected profits in the bad news + + + align:start position:0% +zero expected profits in the bad news +case they get Negative profits they must + + align:start position:0% +case they get Negative profits they must + + + align:start position:0% +case they get Negative profits they must +get positive profits in the good news + + align:start position:0% +get positive profits in the good news + + + align:start position:0% +get positive profits in the good news +case + + align:start position:0% +case + + + align:start position:0% +case +okay uh the incumbent earns positive + + align:start position:0% +okay uh the incumbent earns positive + + + align:start position:0% +okay uh the incumbent earns positive +profits uh you know much less obvious + + align:start position:0% +profits uh you know much less obvious + + + align:start position:0% +profits uh you know much less obvious +statement is that uh when the cost C is + + align:start position:0% +statement is that uh when the cost C is + + + align:start position:0% +statement is that uh when the cost C is +close to zero so the two firms don't + + align:start position:0% +close to zero so the two firms don't + + + align:start position:0% +close to zero so the two firms don't +have big cost + + align:start position:0% +have big cost + + + align:start position:0% +have big cost +differences um the X anti-bid + + align:start position:0% +differences um the X anti-bid + + + align:start position:0% +differences um the X anti-bid +distributions of the incumbents and the + + align:start position:0% +distributions of the incumbents and the + + + align:start position:0% +distributions of the incumbents and the +entrance or and the uninformed biders uh + + align:start position:0% +entrance or and the uninformed biders uh + + + align:start position:0% +entrance or and the uninformed biders uh +converge to each other so as a v as a v + + align:start position:0% +converge to each other so as a v as a v + + + align:start position:0% +converge to each other so as a v as a v +c goes to zero you know this is a bid + + align:start position:0% +c goes to zero you know this is a bid + + + align:start position:0% +c goes to zero you know this is a bid +distribution that comes from bidding + + align:start position:0% +distribution that comes from bidding + + + align:start position:0% +distribution that comes from bidding +based on what you know about the value + + align:start position:0% +based on what you know about the value + + + align:start position:0% +based on what you know about the value +this is one that comes purely from + + align:start position:0% +this is one that comes purely from + + + align:start position:0% +this is one that comes purely from +randomization but these two + + align:start position:0% +randomization but these two + + + align:start position:0% +randomization but these two +distributions approach each other as C + + align:start position:0% +distributions approach each other as C + + + align:start position:0% +distributions approach each other as C +goes to zero and and when in the C + + align:start position:0% +goes to zero and and when in the C + + + align:start position:0% +goes to zero and and when in the C +equals Z Limit these two distributions + + align:start position:0% +equals Z Limit these two distributions + + + align:start position:0% +equals Z Limit these two distributions +would be + + align:start position:0% +would be + + + align:start position:0% +would be +identical um okay uh the incumbent bid + + align:start position:0% +identical um okay uh the incumbent bid + + + align:start position:0% +identical um okay uh the incumbent bid +is independent of the number of of rival + + align:start position:0% +is independent of the number of of rival + + + align:start position:0% +is independent of the number of of rival +bids um that's another property of the + + align:start position:0% +bids um that's another property of the + + + align:start position:0% +bids um that's another property of the +mixing uh and that the incumbent's bid + + align:start position:0% +mixing uh and that the incumbent's bid + + + align:start position:0% +mixing uh and that the incumbent's bid +is an increasing function of the true + + align:start position:0% +is an increasing function of the true + + + align:start position:0% +is an increasing function of the true +value of the tract and of the signal + + align:start position:0% +value of the tract and of the signal + + + align:start position:0% +value of the tract and of the signal +that's available um when when people are + + align:start position:0% +that's available um when when people are + + + align:start position:0% +that's available um when when people are +bidding on the tract um and it's it's a + + align:start position:0% +bidding on the tract um and it's it's a + + + align:start position:0% +bidding on the tract um and it's it's a +increasing function of the True Value + + align:start position:0% +increasing function of the True Value + + + align:start position:0% +increasing function of the True Value +because the more it's worth winning the + + align:start position:0% +because the more it's worth winning the + + + align:start position:0% +because the more it's worth winning the +more aggressive you want to be it's a + + align:start position:0% +more aggressive you want to be it's a + + + align:start position:0% +more aggressive you want to be it's a +increasing function of Z because if you + + align:start position:0% +increasing function of Z because if you + + + align:start position:0% +increasing function of Z because if you +know the opponents are getting better + + align:start position:0% +know the opponents are getting better + + + align:start position:0% +know the opponents are getting better +signals they're more likely to enter you + + align:start position:0% +signals they're more likely to enter you + + + align:start position:0% +signals they're more likely to enter you +bid more + + align:start position:0% + + + + align:start position:0% + +aggressively and and then what Hendrix + + align:start position:0% +aggressively and and then what Hendrix + + + align:start position:0% +aggressively and and then what Hendrix +and Porter do is they you know get this + + align:start position:0% +and Porter do is they you know get this + + + align:start position:0% +and Porter do is they you know get this +drain this data set it's a you know + + align:start position:0% +drain this data set it's a you know + + + align:start position:0% +drain this data set it's a you know +somewhat historic paper they got + + align:start position:0% +somewhat historic paper they got + + + align:start position:0% +somewhat historic paper they got +information on 114 drainage tracks + + align:start position:0% +information on 114 drainage tracks + + + align:start position:0% +information on 114 drainage tracks +auction between 1959 and + + align:start position:0% +auction between 1959 and + + + align:start position:0% +auction between 1959 and +1969 all of them are adjacent to a + + align:start position:0% +1969 all of them are adjacent to a + + + align:start position:0% +1969 all of them are adjacent to a +wildcat tract on which they have + + align:start position:0% +wildcat tract on which they have + + + align:start position:0% +wildcat tract on which they have +production data and so one of the nice + + align:start position:0% +production data and so one of the nice + + + align:start position:0% +production data and so one of the nice +things about going back historically is + + align:start position:0% +things about going back historically is + + + align:start position:0% +things about going back historically is +they're doing this far enough after the + + align:start position:0% +they're doing this far enough after the + + + align:start position:0% +they're doing this far enough after the +time all these auctions occurred that + + align:start position:0% +time all these auctions occurred that + + + align:start position:0% +time all these auctions occurred that +they can observe all the production that + + align:start position:0% +they can observe all the production that + + + align:start position:0% +they can observe all the production that +occurred over the lifetime of the wells + + align:start position:0% +occurred over the lifetime of the wells + + + align:start position:0% +occurred over the lifetime of the wells +so the you know Wells are are being + + align:start position:0% +so the you know Wells are are being + + + align:start position:0% +so the you know Wells are are being +drilled over the next 5 years after + + align:start position:0% +drilled over the next 5 years after + + + align:start position:0% +drilled over the next 5 years after +their auction and then they're producing + + align:start position:0% +their auction and then they're producing + + + align:start position:0% +their auction and then they're producing +oil after some number of years but + + align:start position:0% +oil after some number of years but + + + align:start position:0% +oil after some number of years but +they're sort of able to run out to when + + align:start position:0% +they're sort of able to run out to when + + + align:start position:0% +they're sort of able to run out to when +all the oil got produced and what the + + align:start position:0% +all the oil got produced and what the + + + align:start position:0% +all the oil got produced and what the +how how valuable things were + + align:start position:0% +how how valuable things were + + + align:start position:0% +how how valuable things were +exposed + + align:start position:0% +exposed + + + align:start position:0% +exposed +um anyway the data include um data + + align:start position:0% +um anyway the data include um data + + + align:start position:0% +um anyway the data include um data +include the sort of uh you know bids by + + align:start position:0% +include the sort of uh you know bids by + + + align:start position:0% +include the sort of uh you know bids by +all the bids by all the participants the + + align:start position:0% +all the bids by all the participants the + + + align:start position:0% +all the bids by all the participants the +number of neighbors bidding the number + + align:start position:0% +number of neighbors bidding the number + + + align:start position:0% +number of neighbors bidding the number +of non- neighbors bidding uh the expost + + align:start position:0% +of non- neighbors bidding uh the expost + + + align:start position:0% +of non- neighbors bidding uh the expost +profitability of the track the gross + + align:start position:0% +profitability of the track the gross + + + align:start position:0% +profitability of the track the gross +profits of the adjacent tract and things + + align:start position:0% +profits of the adjacent tract and things + + + align:start position:0% +profits of the adjacent tract and things +like that + + align:start position:0% + + + + align:start position:0% + +one of the interesting design features + + align:start position:0% +one of the interesting design features + + + align:start position:0% +one of the interesting design features +the US government chose is you know + + align:start position:0% +the US government chose is you know + + + align:start position:0% +the US government chose is you know +imagine sometimes you may have um this + + align:start position:0% +imagine sometimes you may have um this + + + align:start position:0% +imagine sometimes you may have um this +situation you know so imagine you have + + align:start position:0% +situation you know so imagine you have + + + align:start position:0% +situation you know so imagine you have +uh Exxon Mobile here and you have uh BP + + align:start position:0% +uh Exxon Mobile here and you have uh BP + + + align:start position:0% +uh Exxon Mobile here and you have uh BP +here + + align:start position:0% +here + + + align:start position:0% +here +um and then there's a drainage track + + align:start position:0% +um and then there's a drainage track + + + align:start position:0% +um and then there's a drainage track +right here the one case you think okay + + align:start position:0% +right here the one case you think okay + + + align:start position:0% +right here the one case you think okay +then you're going to get a lot of + + align:start position:0% +then you're going to get a lot of + + + align:start position:0% +then you're going to get a lot of +competition if Exon Mobile's got this + + align:start position:0% +competition if Exon Mobile's got this + + + align:start position:0% +competition if Exon Mobile's got this +BP's got this they're both producing oil + + align:start position:0% +BP's got this they're both producing oil + + + align:start position:0% +BP's got this they're both producing oil +and there's this little area in between + + align:start position:0% +and there's this little area in between + + + align:start position:0% +and there's this little area in between +um rules of the US government set up for + + align:start position:0% +um rules of the US government set up for + + + align:start position:0% +um rules of the US government set up for +this is that Exon Mobile and BP in that + + align:start position:0% +this is that Exon Mobile and BP in that + + + align:start position:0% +this is that Exon Mobile and BP in that +situation can form a joint venture and + + align:start position:0% +situation can form a joint venture and + + + align:start position:0% +situation can form a joint venture and +bid together jointly on the track rather + + align:start position:0% +bid together jointly on the track rather + + + align:start position:0% +bid together jointly on the track rather +than competing with each other um so in + + align:start position:0% +than competing with each other um so in + + + align:start position:0% +than competing with each other um so in +most cases in the data set where this + + align:start position:0% +most cases in the data set where this + + + align:start position:0% +most cases in the data set where this +occurs lo and behold the firms do form + + align:start position:0% +occurs lo and behold the firms do form + + + align:start position:0% +occurs lo and behold the firms do form +the joint venture and bid together um so + + align:start position:0% +the joint venture and bid together um so + + + align:start position:0% +the joint venture and bid together um so +mostly they have one incumbent + + align:start position:0% +mostly they have one incumbent + + + align:start position:0% +mostly they have one incumbent +tract um anyway so then testing + + align:start position:0% +tract um anyway so then testing + + + align:start position:0% +tract um anyway so then testing +predictions of the model um you know + + align:start position:0% +predictions of the model um you know + + + align:start position:0% +predictions of the model um you know +prediction one that the neighbors are + + align:start position:0% +prediction one that the neighbors are + + + align:start position:0% +prediction one that the neighbors are +supposed to bid much higher fraction + + align:start position:0% +supposed to bid much higher fraction + + + align:start position:0% +supposed to bid much higher fraction +time than the non- neighbors that's + + align:start position:0% +time than the non- neighbors that's + + + align:start position:0% +time than the non- neighbors that's +borne out in the data the neighbors are + + align:start position:0% +borne out in the data the neighbors are + + + align:start position:0% +borne out in the data the neighbors are +bidding 83% the non- neighbors + + align:start position:0% +bidding 83% the non- neighbors + + + align:start position:0% +bidding 83% the non- neighbors +68% um the incumbents are supposed to + + align:start position:0% +68% um the incumbents are supposed to + + + align:start position:0% +68% um the incumbents are supposed to +win more than half the time they're + + align:start position:0% +win more than half the time they're + + + align:start position:0% +win more than half the time they're +winning 52% of the time I don't know if + + align:start position:0% +winning 52% of the time I don't know if + + + align:start position:0% +winning 52% of the time I don't know if +that's such great + + align:start position:0% +that's such great + + + align:start position:0% +that's such great +confirmation uh the uninformed biders + + align:start position:0% +confirmation uh the uninformed biders + + + align:start position:0% +confirmation uh the uninformed biders +are supposed to get Negative profits if + + align:start position:0% +are supposed to get Negative profits if + + + align:start position:0% +are supposed to get Negative profits if +the neighbor enter if the incumbent + + align:start position:0% +the neighbor enter if the incumbent + + + align:start position:0% +the neighbor enter if the incumbent +enters negative profits otherwise you + + align:start position:0% +enters negative profits otherwise you + + + align:start position:0% +enters negative profits otherwise you +know that's one of the sort of clear + + align:start position:0% +know that's one of the sort of clear + + + align:start position:0% +know that's one of the sort of clear +things in the data + + align:start position:0% +things in the data + + + align:start position:0% +things in the data +that you know when this are when + + align:start position:0% +that you know when this are when + + + align:start position:0% +that you know when this are when +auctions were the non Neighbors when you + + align:start position:0% +auctions were the non Neighbors when you + + + align:start position:0% +auctions were the non Neighbors when you +compare them situations where the the + + align:start position:0% +compare them situations where the the + + + align:start position:0% +compare them situations where the the +incumbent bid and the incumbent didn't + + align:start position:0% +incumbent bid and the incumbent didn't + + + align:start position:0% +incumbent bid and the incumbent didn't +bid when the incumbent didn't bid you + + align:start position:0% +bid when the incumbent didn't bid you + + + align:start position:0% +bid when the incumbent didn't bid you +get very negative profits when the + + align:start position:0% +get very negative profits when the + + + align:start position:0% +get very negative profits when the +incumbent did bid you get positive + + align:start position:0% +incumbent did bid you get positive + + + align:start position:0% +incumbent did bid you get positive +profits + + align:start position:0% + + + + align:start position:0% + +um uh the incumbents are earning a lot + + align:start position:0% +um uh the incumbents are earning a lot + + + align:start position:0% +um uh the incumbents are earning a lot +of money uh that was also uh very clear + + align:start position:0% +of money uh that was also uh very clear + + + align:start position:0% +of money uh that was also uh very clear +in this table the incumbent wind tracks + + align:start position:0% +in this table the incumbent wind tracks + + + align:start position:0% +in this table the incumbent wind tracks +are very high positive profits whereas + + align:start position:0% +are very high positive profits whereas + + + align:start position:0% +are very high positive profits whereas +these are sort of essentially zero on + + align:start position:0% +these are sort of essentially zero on + + + align:start position:0% +these are sort of essentially zero on +average + + align:start position:0% +average + + + align:start position:0% +average +um uh you know the bottom part of the + + align:start position:0% +um uh you know the bottom part of the + + + align:start position:0% +um uh you know the bottom part of the +paper is where it sort of seem you know + + align:start position:0% +paper is where it sort of seem you know + + + align:start position:0% +paper is where it sort of seem you know +this starts to seem less um high-tech + + align:start position:0% +this starts to seem less um high-tech + + + align:start position:0% +this starts to seem less um high-tech +econometrically than you would expect + + align:start position:0% +econometrically than you would expect + + + align:start position:0% +econometrically than you would expect +today you know we're trying to see + + align:start position:0% +today you know we're trying to see + + + align:start position:0% +today you know we're trying to see +whether these two distributions are ex + + align:start position:0% +whether these two distributions are ex + + + align:start position:0% +whether these two distributions are ex +anti identical rather than sort of doing + + align:start position:0% +anti identical rather than sort of doing + + + align:start position:0% +anti identical rather than sort of doing +some kind of non-parametric estimation + + align:start position:0% +some kind of non-parametric estimation + + + align:start position:0% +some kind of non-parametric estimation +of the densities of those distributions + + align:start position:0% +of the densities of those distributions + + + align:start position:0% +of the densities of those distributions +they're just running some regressions + + align:start position:0% +they're just running some regressions + + + align:start position:0% +they're just running some regressions +and asking whether + + align:start position:0% +and asking whether + + + align:start position:0% +and asking whether +the whether the epsilons seem to have + + align:start position:0% +the whether the epsilons seem to have + + + align:start position:0% +the whether the epsilons seem to have +similar variances and whether the sort + + align:start position:0% +similar variances and whether the sort + + + align:start position:0% +similar variances and whether the sort +of bids seem to be similarly related to + + align:start position:0% +of bids seem to be similarly related to + + + align:start position:0% +of bids seem to be similarly related to +the number of once you control for the + + align:start position:0% +the number of once you control for the + + + align:start position:0% +the number of once you control for the +Acres the number of neighbors the values + + align:start position:0% +Acres the number of neighbors the values + + + align:start position:0% +Acres the number of neighbors the values +things like that um so I won't I don't + + align:start position:0% +things like that um so I won't I don't + + + align:start position:0% +things like that um so I won't I don't +really know whether that's really great + + align:start position:0% +really know whether that's really great + + + align:start position:0% +really know whether that's really great +verification um then my prediction six + + align:start position:0% +verification um then my prediction six + + + align:start position:0% +verification um then my prediction six +was that the you know the incumbent bid + + align:start position:0% +was that the you know the incumbent bid + + + align:start position:0% +was that the you know the incumbent bid +doesn't depend on the number of of + + align:start position:0% +doesn't depend on the number of of + + + align:start position:0% +doesn't depend on the number of of +non-incumbents bidding that's sort of + + align:start position:0% +non-incumbents bidding that's sort of + + + align:start position:0% +non-incumbents bidding that's sort of +also held out in a in a regression and + + align:start position:0% +also held out in a in a regression and + + + align:start position:0% +also held out in a in a regression and +then to check that your sort of your the + + align:start position:0% +then to check that your sort of your the + + + align:start position:0% +then to check that your sort of your the +incumbent bid goes up in the um true in + + align:start position:0% +incumbent bid goes up in the um true in + + + align:start position:0% +incumbent bid goes up in the um true in +in the v and the Z they show the + + align:start position:0% +in the v and the Z they show the + + + align:start position:0% +in the v and the Z they show the +incumbent bid does increase in the true + + align:start position:0% +incumbent bid does increase in the true + + + align:start position:0% +incumbent bid does increase in the true +value of oil that's eventually taken out + + align:start position:0% +value of oil that's eventually taken out + + + align:start position:0% +value of oil that's eventually taken out +of the tract 20 years later and also in + + align:start position:0% +of the tract 20 years later and also in + + + align:start position:0% +of the tract 20 years later and also in +the sort of amount of money that comes + + align:start position:0% +the sort of amount of money that comes + + + align:start position:0% +the sort of amount of money that comes +out of the Wildcat tract which is the + + align:start position:0% +out of the Wildcat tract which is the + + + align:start position:0% +out of the Wildcat tract which is the +observable thing that everyone else can + + align:start position:0% + + + + align:start position:0% + +see so is that my last slide or do I + + align:start position:0% +see so is that my last slide or do I + + + align:start position:0% +see so is that my last slide or do I +have more + + align:start position:0% +have more + + + align:start position:0% +have more +um nope that's it so so anyway you know + + align:start position:0% +um nope that's it so so anyway you know + + + align:start position:0% +um nope that's it so so anyway you know +I think it's just it's a very very nice + + align:start position:0% +I think it's just it's a very very nice + + + align:start position:0% +I think it's just it's a very very nice +example of how you sort of think about + + align:start position:0% +example of how you sort of think about + + + align:start position:0% +example of how you sort of think about +this idea of writing reduced form iio + + align:start position:0% +this idea of writing reduced form iio + + + align:start position:0% +this idea of writing reduced form iio +where you just here's my model here's a + + align:start position:0% +where you just here's my model here's a + + + align:start position:0% +where you just here's my model here's a +bunch of predictions that are not + + align:start position:0% +bunch of predictions that are not + + + align:start position:0% +bunch of predictions that are not +completely obvious and then I'm going to + + align:start position:0% +completely obvious and then I'm going to + + + align:start position:0% +completely obvious and then I'm going to +sort of like look at say as many sort of + + align:start position:0% +sort of like look at say as many sort of + + + align:start position:0% +sort of like look at say as many sort of +more nuanced predictions as I can find + + align:start position:0% +more nuanced predictions as I can find + + + align:start position:0% +more nuanced predictions as I can find +that they're true and it seems like make + + align:start position:0% +that they're true and it seems like make + + + align:start position:0% +that they're true and it seems like make +a pretty convincing case that we do + + align:start position:0% +a pretty convincing case that we do + + + align:start position:0% +a pretty convincing case that we do +badly in these auctions because of the + + align:start position:0% +badly in these auctions because of the + + + align:start position:0% +badly in these auctions because of the +asymmetric information can I say that + + align:start position:0% +asymmetric information can I say that + + + align:start position:0% +asymmetric information can I say that +like you know and sometimes people have + + align:start position:0% +like you know and sometimes people have + + + align:start position:0% +like you know and sometimes people have +criticized the US government saying well + + align:start position:0% +criticized the US government saying well + + + align:start position:0% +criticized the US government saying well +why on Earth would you + + align:start position:0% +why on Earth would you + + + align:start position:0% +why on Earth would you +give BP and Exon mobile the ability to + + align:start position:0% +give BP and Exon mobile the ability to + + + align:start position:0% +give BP and Exon mobile the ability to +jointly bid here one way to think about + + align:start position:0% +jointly bid here one way to think about + + + align:start position:0% +jointly bid here one way to think about +this is though maybe that's actually not + + align:start position:0% +this is though maybe that's actually not + + + align:start position:0% +this is though maybe that's actually not +so stupid maybe what maybe what we want + + align:start position:0% +so stupid maybe what maybe what we want + + + align:start position:0% +so stupid maybe what maybe what we want +to do on the Wildcat tracks is some + + align:start position:0% +to do on the Wildcat tracks is some + + + align:start position:0% +to do on the Wildcat tracks is some +sense it's fine to have adverse + + align:start position:0% +sense it's fine to have adverse + + + align:start position:0% +sense it's fine to have adverse +selection on the Wildcat tracks give all + + align:start position:0% +selection on the Wildcat tracks give all + + + align:start position:0% +selection on the Wildcat tracks give all +the money away to the person who has the + + align:start position:0% +the money away to the person who has the + + + align:start position:0% +the money away to the person who has the +initial sorry give all the drainage + + align:start position:0% +initial sorry give all the drainage + + + align:start position:0% +initial sorry give all the drainage +track profits away to the person who + + align:start position:0% +track profits away to the person who + + + align:start position:0% +track profits away to the person who +drilled the initial Wildcat tracks + + align:start position:0% +drilled the initial Wildcat tracks + + + align:start position:0% +drilled the initial Wildcat tracks +because the Wildcat tracks again were + + align:start position:0% +because the Wildcat tracks again were + + + align:start position:0% +because the Wildcat tracks again were +out here in the middle of nowhere there + + align:start position:0% +out here in the middle of nowhere there + + + align:start position:0% +out here in the middle of nowhere there +it's a symmetric auction model so in + + align:start position:0% +it's a symmetric auction model so in + + + align:start position:0% +it's a symmetric auction model so in +some sense what you're doing is just + + align:start position:0% +some sense what you're doing is just + + + align:start position:0% +some sense what you're doing is just +increasing the prize you get from the + + align:start position:0% +increasing the prize you get from the + + + align:start position:0% +increasing the prize you get from the +symmetric auction model to be you get + + align:start position:0% +symmetric auction model to be you get + + + align:start position:0% +symmetric auction model to be you get +the prize which is all the oil here plus + + align:start position:0% +the prize which is all the oil here plus + + + align:start position:0% +the prize which is all the oil here plus +the advantage on the surrounding + + align:start position:0% +the advantage on the surrounding + + + align:start position:0% +the advantage on the surrounding +drainage tracts and so in some sense if + + align:start position:0% +drainage tracts and so in some sense if + + + align:start position:0% +drainage tracts and so in some sense if +we just sort of always give you this big + + align:start position:0% +we just sort of always give you this big + + + align:start position:0% +we just sort of always give you this big +secondary prize that just gets competed + + align:start position:0% +secondary prize that just gets competed + + + align:start position:0% +secondary prize that just gets competed +away in the bidding for the initial + + align:start position:0% +away in the bidding for the initial + + + align:start position:0% +away in the bidding for the initial +Wildcat tracks and we can use sort of + + align:start position:0% +Wildcat tracks and we can use sort of + + + align:start position:0% +Wildcat tracks and we can use sort of +the competition for the Wildcat tracts + + align:start position:0% +the competition for the Wildcat tracts + + + align:start position:0% +the competition for the Wildcat tracts +as the sensible way to try to raise + + align:start position:0% +as the sensible way to try to raise + + + align:start position:0% +as the sensible way to try to raise +revenue not worrying so much about + + align:start position:0% +revenue not worrying so much about + + + align:start position:0% +revenue not worrying so much about +trying to get the the hard to get + + align:start position:0% +trying to get the the hard to get + + + align:start position:0% +trying to get the the hard to get +drainage tract revenue from the firms + + align:start position:0% +drainage tract revenue from the firms + + + align:start position:0% +drainage tract revenue from the firms +and just sort of bundle it in with the + + align:start position:0% +and just sort of bundle it in with the + + + align:start position:0% +and just sort of bundle it in with the +initial Wildcat revenue and then let + + align:start position:0% +initial Wildcat revenue and then let + + + align:start position:0% +initial Wildcat revenue and then let +them bid symmetrically in that case + + align:start position:0% +them bid symmetrically in that case + + + align:start position:0% +them bid symmetrically in that case +okay \ No newline at end of file diff --git a/-Y8pOF1AgUY.txt b/-Y8pOF1AgUY.txt new file mode 100644 index 0000000000000000000000000000000000000000..c7ca896f91088824dc6d6f748fa0c21a29c0048c --- /dev/null +++ b/-Y8pOF1AgUY.txt @@ -0,0 +1,651 @@ +align:start position:0% + +for 5111 we created this video series um + + align:start position:0% +for 5111 we created this video series um + + + align:start position:0% +for 5111 we created this video series um +and we call it behind the scenes at MIT + + align:start position:0% +and we call it behind the scenes at MIT + + + align:start position:0% +and we call it behind the scenes at MIT +and there are two kinds of videos um one + + align:start position:0% +and there are two kinds of videos um one + + + align:start position:0% +and there are two kinds of videos um one +where undergrads graduate students + + align:start position:0% +where undergrads graduate students + + + align:start position:0% +where undergrads graduate students +postdocs one other faculty member are + + align:start position:0% +postdocs one other faculty member are + + + align:start position:0% +postdocs one other faculty member are +talking about how the basic chemical + + align:start position:0% +talking about how the basic chemical + + + align:start position:0% +talking about how the basic chemical +principles we're learning about in the + + align:start position:0% +principles we're learning about in the + + + align:start position:0% +principles we're learning about in the +class are used in their laboratory or by + + align:start position:0% +class are used in their laboratory or by + + + align:start position:0% +class are used in their laboratory or by +them and how those chemical principles + + align:start position:0% +them and how those chemical principles + + + align:start position:0% +them and how those chemical principles +will make the world a better place my + + align:start position:0% +will make the world a better place my + + + align:start position:0% +will make the world a better place my +name is Darcy Wanger and I work as a + + align:start position:0% +name is Darcy Wanger and I work as a + + + align:start position:0% +name is Darcy Wanger and I work as a +graduate student in the bendi lab at MIT + + align:start position:0% +graduate student in the bendi lab at MIT + + + align:start position:0% +graduate student in the bendi lab at MIT +I work with Quantum dots in my research + + align:start position:0% +I work with Quantum dots in my research + + + align:start position:0% +I work with Quantum dots in my research +Quantum dots are really really tiny + + align:start position:0% +Quantum dots are really really tiny + + + align:start position:0% +Quantum dots are really really tiny +particles of a semiconductor people in + + align:start position:0% +particles of a semiconductor people in + + + align:start position:0% +particles of a semiconductor people in +our lab are working to make Quantum dots + + align:start position:0% +our lab are working to make Quantum dots + + + align:start position:0% +our lab are working to make Quantum dots +bind to a tumor so when a doctor goes in + + align:start position:0% +bind to a tumor so when a doctor goes in + + + align:start position:0% +bind to a tumor so when a doctor goes in +to remove a tumor they can see just + + align:start position:0% +to remove a tumor they can see just + + + align:start position:0% +to remove a tumor they can see just +shining a UV light on it and see whether + + align:start position:0% +shining a UV light on it and see whether + + + align:start position:0% +shining a UV light on it and see whether +it's all gone when they've taken out the + + align:start position:0% +it's all gone when they've taken out the + + + align:start position:0% +it's all gone when they've taken out the +tumor it was interesting because I've + + align:start position:0% +tumor it was interesting because I've + + + align:start position:0% +tumor it was interesting because I've +talked to some of the students in the + + align:start position:0% +talked to some of the students in the + + + align:start position:0% +talked to some of the students in the +class about their sort of perceptions of + + align:start position:0% +class about their sort of perceptions of + + + align:start position:0% +class about their sort of perceptions of +things and then after they had watch the + + align:start position:0% +things and then after they had watch the + + + align:start position:0% +things and then after they had watch the +videos sort of what they thought and a + + align:start position:0% +videos sort of what they thought and a + + + align:start position:0% +videos sort of what they thought and a +lot of students actually said you know I + + align:start position:0% +lot of students actually said you know I + + + align:start position:0% +lot of students actually said you know I +was wondering you're learning this and + + align:start position:0% +was wondering you're learning this and + + + align:start position:0% +was wondering you're learning this and +you know it's good it builds character + + align:start position:0% +you know it's good it builds character + + + align:start position:0% +you know it's good it builds character +to learn something that could be + + align:start position:0% +to learn something that could be + + + align:start position:0% +to learn something that could be +challenging um but wondered you know am + + align:start position:0% +challenging um but wondered you know am + + + align:start position:0% +challenging um but wondered you know am +I ever going to use this for anything + + align:start position:0% +I ever going to use this for anything + + + align:start position:0% +I ever going to use this for anything +and then they started watching these + + align:start position:0% +and then they started watching these + + + align:start position:0% +and then they started watching these +videos and seeing this and they're like + + align:start position:0% +videos and seeing this and they're like + + + align:start position:0% +videos and seeing this and they're like +oh yes this is used all the time it + + align:start position:0% +oh yes this is used all the time it + + + align:start position:0% +oh yes this is used all the time it +could be used in my undergraduate + + align:start position:0% +could be used in my undergraduate + + + align:start position:0% +could be used in my undergraduate +research you know people are doing this + + align:start position:0% +research you know people are doing this + + + align:start position:0% +research you know people are doing this +this is this is a subject that people + + align:start position:0% +this is this is a subject that people + + + align:start position:0% +this is this is a subject that people +are actively learning new things and I + + align:start position:0% +are actively learning new things and I + + + align:start position:0% +are actively learning new things and I +feel like this is a question for a lot + + align:start position:0% +feel like this is a question for a lot + + + align:start position:0% +feel like this is a question for a lot +of intro classes because you have these + + align:start position:0% +of intro classes because you have these + + + align:start position:0% +of intro classes because you have these +thick textbooks and you sort of feel + + align:start position:0% +thick textbooks and you sort of feel + + + align:start position:0% +thick textbooks and you sort of feel +like everything that could have been + + align:start position:0% +like everything that could have been + + + align:start position:0% +like everything that could have been +learned seems like it's all there like + + align:start position:0% +learned seems like it's all there like + + + align:start position:0% +learned seems like it's all there like +you know know volume two like what it's + + align:start position:0% +you know know volume two like what it's + + + align:start position:0% +you know know volume two like what it's +uh there three laws of thermodynamics or + + align:start position:0% +uh there three laws of thermodynamics or + + + align:start position:0% +uh there three laws of thermodynamics or +people trying to find a fourth law like + + align:start position:0% +people trying to find a fourth law like + + + align:start position:0% +people trying to find a fourth law like +what what is someone who do chemistry + + align:start position:0% +what what is someone who do chemistry + + + align:start position:0% +what what is someone who do chemistry +research what are they actually doing + + align:start position:0% +research what are they actually doing + + + align:start position:0% +research what are they actually doing +discovering know we know what the + + align:start position:0% +discovering know we know what the + + + align:start position:0% +discovering know we know what the +electrons are already um and so this + + align:start position:0% +electrons are already um and so this + + + align:start position:0% +electrons are already um and so this +gave people a sense of what people were + + align:start position:0% +gave people a sense of what people were + + + align:start position:0% +gave people a sense of what people were +using chemistry for now what were those + + align:start position:0% +using chemistry for now what were those + + + align:start position:0% +using chemistry for now what were those +current questions and when I was a high + + align:start position:0% +current questions and when I was a high + + + align:start position:0% +current questions and when I was a high +school teacher originally that was + + align:start position:0% +school teacher originally that was + + + align:start position:0% +school teacher originally that was +really what I wanted like what are + + align:start position:0% +really what I wanted like what are + + + align:start position:0% +really what I wanted like what are +people doing now what are the key + + align:start position:0% +people doing now what are the key + + + align:start position:0% +people doing now what are the key +questions if I was studying chemistry + + align:start position:0% +questions if I was studying chemistry + + + align:start position:0% +questions if I was studying chemistry +what would I be doing and I want to help + + align:start position:0% +what would I be doing and I want to help + + + align:start position:0% +what would I be doing and I want to help +create this material so other people can + + align:start position:0% +create this material so other people can + + + align:start position:0% +create this material so other people can +see that because you know for some + + align:start position:0% +see that because you know for some + + + align:start position:0% +see that because you know for some +people they're like if you know you tell + + align:start position:0% +people they're like if you know you tell + + + align:start position:0% +people they're like if you know you tell +you miss hard and it's a challenge to + + align:start position:0% +you miss hard and it's a challenge to + + + align:start position:0% +you miss hard and it's a challenge to +learn they'll just learn it and they + + align:start position:0% +learn they'll just learn it and they + + + align:start position:0% +learn they'll just learn it and they +don't you know if they don't use it it + + align:start position:0% +don't you know if they don't use it it + + + align:start position:0% +don't you know if they don't use it it +could be like Latin it builds character + + align:start position:0% +could be like Latin it builds character + + + align:start position:0% +could be like Latin it builds character +it's fine it's a dead language but okay + + align:start position:0% +it's fine it's a dead language but okay + + + align:start position:0% +it's fine it's a dead language but okay +I'm going to get in there but then for + + align:start position:0% +I'm going to get in there but then for + + + align:start position:0% +I'm going to get in there but then for +other people they really want to know + + align:start position:0% +other people they really want to know + + + align:start position:0% +other people they really want to know +that this is going to be useful and if + + align:start position:0% +that this is going to be useful and if + + + align:start position:0% +that this is going to be useful and if +they're going to really invest in it + + align:start position:0% +they're going to really invest in it + + + align:start position:0% +they're going to really invest in it +they want to know that it's important + + align:start position:0% +they want to know that it's important + + + align:start position:0% +they want to know that it's important +and they can do things and MIT students + + align:start position:0% +and they can do things and MIT students + + + align:start position:0% +and they can do things and MIT students +and I think so many people out there + + align:start position:0% +and I think so many people out there + + + align:start position:0% +and I think so many people out there +want to make the world a better place + + align:start position:0% +want to make the world a better place + + + align:start position:0% +want to make the world a better place +there are a lot of really wonderful + + align:start position:0% +there are a lot of really wonderful + + + align:start position:0% +there are a lot of really wonderful +human beings and they need the tools and + + align:start position:0% +human beings and they need the tools and + + + align:start position:0% +human beings and they need the tools and +they want to do something that's + + align:start position:0% +they want to do something that's + + + align:start position:0% +they want to do something that's +important so I want to create those + + align:start position:0% +important so I want to create those + + + align:start position:0% +important so I want to create those +tools for them to learn this that they + + align:start position:0% +tools for them to learn this that they + + + align:start position:0% +tools for them to learn this that they +can apply it and do something and they + + align:start position:0% +can apply it and do something and they + + + align:start position:0% +can apply it and do something and they +can see the power of + + align:start position:0% + + + + align:start position:0% + +chemistry \ No newline at end of file diff --git a/-cK1og4ElKE.txt b/-cK1og4ElKE.txt new file mode 100644 index 0000000000000000000000000000000000000000..d541f4a6a1348de96d4f17f09663702dd6464b3c --- /dev/null +++ b/-cK1og4ElKE.txt @@ -0,0 +1,4438 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation, or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare, at + +ocw.mit.edu. + +PROFESSOR: Good afternoon. + +In the last lecture we talked +about the remarkable human + +brain, and how it empowers our +thoughts, or feelings, or + +desires, or actions in the +world, and how we began to + +understand this remarkable +complexity, or at least grasp + +something of the complexity. + +How we understand the potential +for things like + +moral character, +and judgments. + +The case of Phineas Gage, to +produce language, to speak our + +feelings and thoughts that's +blocked in a patient like + +Broca's patient, with +Broca's aphasia. + +We talked about the fact that +split brain patients show us + +not only to the left and right +hemispheres of the human brain + +mediate separate mental +abilities, but that they also + +seem to have almost independent +forms of + +consciousness, or they +don't have to be + +aware of one another. + +And so my focus today is to say +we would learn from very + +unusual clinical cases. + +And I'm going to focus today on +tools we have to study the + +typical human brain. + +And what is it that we can do to +understand how your brain-- + +without having a + +hemispherectomy or a big stroke-- + +how does it operate, and what +are the principles of human + +brain function they gave +rise to the human mind? + +So what are the ways we can +learn about the human brain? + +And one thing we can't do is +when animal researchers can + +do, we can't literally go inside +the brain except in + +very rare clinical situations. + +I'll talk about them, but it's +a rare source of evidence. + +So there's a million ways in +which are trying to understand + +which part of the brain is which +part of the mind, and we + +talked about the fact that +phronology was a big misstep + +in assigning the functions of +mental life to different parts + +of the brain. + +And so we hope we can do +a bit better than that. + +And I'm going to review with +you today some of the core + +methods, and there's +a number of them + +studying the human brain. + +The reason there's a number +is none of them + +are the magic answer. + +All of them are limited in their +own ways, and we sort of + +need all of them to begin +to grasp how your + +brain makes your mind. + +There's three huge ways in which +we now have the human + +brain organized. + +Lesions, injuries to the brain, +stimulation when you're + +allowed to stimulate +the brain-- + +rarer, but we'll talk +about that. + +And the most common, the one you +see all the time in books + +and magazines, recording, +functional MRI, EEG, methods + +where we record brain +activity, and try to + +understand how that relates to +the life of the human mind. + +And so we're going to go through +these things a little + +bit and show you how they're +applied in some ways that I + +hope that you'll find +interesting. + +We'll come back to many of these +things as we go through + +the semester, and as we talk +about aging, or child + +development, or personality, +or other + +topics, social cognition. + +We'll use these tools to +understand the brain bases of + +those kinds of aspects +of our mental lives. + +So what's a big injury +you can have? + +You can have a stroke, where +tissue in the brain no longer + +receives its vascular supply +that it depends on so greatly. + +And a lot of different things +like hypoxia, lack of oxygen, + +the brain is very sensitive +to oxygen. + +Tumors can grow, you could have +degenerative disorders + +like Alzheimer's, Huntington's, +Parkinson's, and + +others, epilepsy. + +So there's lots of different +ways in which you can end up + +with brain injury, and +ultimately neuronal death. + +What's the strength of this +form of evidence? + +Well first of all, +it's causal. + +We've talked about the +difference between causal and + +correlational sources of +evidence, causal ones be more + +powerful for scientific +explanation. + +A certain part of the brain is +injured in you no longer can + +speak, you change your +character, you no longer can + +make memories. + +We're pretty sure that part of +the brain in some way is + +required, or causal, for +that part of your + +mental life to operate. + +The deficits you see following +brain injuries can be amazing, + +we talked about Phineas Gage +changing his character, unable + +to produce language, unable +to make new memories. + +We'll talk a little bit about +patients with Prosopagnosia, + +it's a good big word to go home +on spring break and if + +your parents ask what have you +learned about, you say + +Prosopagnosia. + +That just means a deficit +in recognizing faces. + +Patients with Prosopagnosia will +be unable to recognize + +their own spouse +by their face. + +They'll recognize it by the +voice, by the physical + +movements, but not +by their face. + +We learn amazing things about +the brain that until it + +happens we didn't know that +could happen, what people like + +to call counterintuitive. + +So we'll talk later in the +course in a couple times about + +blindsight, patients who say, +I see nothing, but their + +behavior shows some part of +their brain sees something. + +We'll talk about category +specific deficits where + +patients all of the sudden can +no longer name living things, + +but they can name nonliving +things. + +So you wouldn't have +thought of that if + +you didn't see that. + +And we get separations +in the brain + +between different things. + +We talked about the difference +between the left hemisphere + +being important for +local features, + +the right for global. + +The left thinking in terms of +functional things in the + +world, the right in terms +of appearances. + +We talked about that already. + +We'll talk about other things, +the hippocampus is important + +for knowing that, knowing a +piece of information but the + +Basal Ganglia is important for +learning how to do things, + +mental skills and +physical skills. + +We'll come back to all of those, +it gives us way to + +organize things. + +Much of our most solid +understanding of the human + +brain still comes from +the history of + +neurology and lesions. + +But what are its limitations? + +First, brain injuries don't +follow anatomical boundaries, + +they sort of crossover things +depending on the injury. + +So they're not going to +selectively damage one part of + +the brain and not touch an +adjacent one they could be + +doing something different. + +People can be variable +in their response. + +Nearby systems, if you have two +things in the brain that + +are next door to one another, +do quite different things. + +Injuries are likely to injure +them both, and you will have a + +wrong conclusion about +the architecture + +of the human brain. + +When we test a patient and ask +them to do things after a + +brain injury, we don't really +test the part of the brain + +that's not there. + +We really test a part of the +brain that is there, people do + +the best they can. + +So there's secondary +degeneration to an injury, + +there's recovery from +injury, there's + +compensation from an injury. + +When you test a patient with a +brain injury, you're testing + +what the rest of the brain can +do in the absence of one of + +its companions. + +And finally can offer +limited views of + +normal brain function. + +Let me pick one and we'll +come back in the course. + +We're very interested in +variation in people-- + +individuality-- + +what's the neurology +of individuality? + +That's very hard to study in +lesion cases, because we don't + +see enough of a lesion. + +we don't have enough Phineas +Gages to ask would that injury + +look different if you grew up in +one culture or another, if + +you were outgoing versus shy. + +Those kinds of things +are very hard to + +answer patient by patient. + +But we can test large groups of +people with imaging and ask + +what's the influence of +culture on your brain + +organization? + +What's the influence of +personality on how your + +brain's organized? + +And you'll see later on in the +semester evidence about those + +sorts of things. + +So let's go back to Paul Broca, +the neurologist who + +they gave a name to Broca's +area, because he sought a + +patient like this, +like [INAUDIBLE]. + +That this patient had a big +injury in this area could no + +longer speak. + +And every course you ever take +about the brain almost will + +include a discussion +about Broca's area. + +So I'm going to warp your world +in a very narrow way, + +but maybe a shocking way, and +tell you we don't even know + +how to think about Broca's +area once we get more + +scientific than that. + +So because this is MIT +so we're willing to + +tell the truth, OK. + +So some years later Nina +Dronkers said the following + +thing, she studied a large +group of patients who had + +Broca's aphasia by behavior. + +That is they had trouble +speaking, but the + +comprehension was pretty good. + +And then she made maps of +their injuries and she + +overlaid those maps. + +And she said who has Broca's +aphasia, and if you have + +Broca's aphasia, what's the +one part of the brain that + +every patient with Broca's +aphasia has damage to. + +Because these patients-- + +what you see on these maps is, +some patients have damage + +here, or here, or here. + +But you line them all up and you +say, what's the one spot + +that you have to have injured +to have Broca's aphasia? + +And it's not this area that you +saw in the picture, it's + +this area, in yellow, an area +called the Precentral Gyrus of + +the Insula. + +The Insula is a fascinating, +mysterious little structure-- + +you have one on the left, +and one on the right-- + +that runs along from the +temporal lobe, up to the + +frontal cortex. + +Just a couple years ago there +was a paper reporting that + +patients who had stroke in +posterior insula instantly + +gave up smoking, and never +wanted to smoke again. + +There's huge research efforts +to help people quit smoking, + +just because it's such a +difficult health problem. + +Nobody is doing insula lesions +to help people + +stop smoking, OK. + +But it just stopped the smoking, +and their desire to + +smoke, just like that. + +This is now more towards the +front of the brain, this is + +not what anybody in a book or +a course will tell you is + +Broca's area, that's out here. + +But it turns out this is the hot +spot, and you could say, + +well what about the +original patient? + +So kind of creatively Nina +Dronkers went back and they + +did an MRI of the brain of the +deceased original Broca's + +aphasic patient. + +They still had his brain, they +put it in a scanner and they + +ran a structural MRI. + +And what they found was sure +enough he had damage way + +inside the exterior limit of +this damage, in as well as in + +white matter that +connects to it. + +So even now imaging evidence +lets us rediscover what is the + +true basis of your ability +to speak, or its + +vulnerability to injury. + +And it turns out not +to be exactly what + +Broca thought it was. + +He saw big lesion and he said, +this is the part of matters. + +It turns out, as far as we +understand, it's a slightly + +different part that he thought +was just at the + +edge and not important. + +So we can get better even going +back to 150 years of + +imaging a brain, we don't have +many of those brains around. + +Stimulation, so you like to go +in the brain is stimulate. + +People who do animal work will +go in and stimulate a neuron + +and see what happens. + +It's rare, you only get into the +patient's brain when they + +have a neurosurgical procedure +and they're considering a + +resection, or removal +of tissue. + +You can also do recordings +by putting grids on + +top of those brains. + +And Penfield did famous studies +for patients with + +epilepsy, where he would +stimulate and map things that + +contributed a lot to our +thinking about the brain. + +But that's a rare source of +evidence, as you can imagine. + +Another one that's much more +common-- there's one of these + +devices down the street +in building 46-- + +is Transcranial Magnetic +Stimulation, or TMS. + +So this is one in which people +are allowed ethically, and + +responsibly to give you a +virtual lesion for a few + +moments, if you volunteer +to do so. + +So they put some sort of +wire, there's different + +configurations, over your head +in a targeted location. + +It generates a magnetic field +that passes through the skull + +and induces a current. + +And what happens is the +current drives lots + +of neurons to fire. + +Turns out, this is kind of +interesting, if all your + +neurons are firing at the same +moment, in one sense it's as + +if none of them were, because +there's no information. + +There's a lot of different ways +you could think about + +that, but for example if on your +300 channel television + +you had all the channels on +simultaneously on the same + +screen, it wouldn't be +very easy to watch, + +something like that. + +All the neurons firing pretty +much wipes out the + +function of that area. + +People do feel a little bit of +a physical sensation, if + +you're prone to epilepsy it's +not a good idea to try this, + +so it does require some +careful supervision + +experimentally. + +But you can do this with healthy +people, and if for + +example you do it on this side +of the motor cortex, people + +twitch or say they felt +somebody touch them. + +Nobody touched them, but the +part of the brain that codes + +for touch just got turned on. + +If you put it on the occipital +cortex, visual cortex, and you + +turn on at a certain moment, +you could put a word up and + +word down, and the person will +say they saw nothing. + +You'll make them functionally, +cortically + +blind for a few moments. + +People have done experiments +like this to suppress + +activity, to enhance activity, +sometimes it makes people even + +faster, like naming pictures. + +And it's also been used there's +still experimental + +studies of whether it can be +helpful for treatments of + +neuropsychiatric disorders. + +It's not invasive, in a sense of +you're not going literally + +inside, you have a causal thing +because turning the + +brain on or off. + +It's not very well targeted, it +can't go into subcortical + +areas, but it's a very +interesting tool. + +Let's talk about recording brain +structure for a moment. + +It's really important to +separate this concept between + +recording structure, which is +a picture of anatomy, or + +function, which is a picture +of physiology. + +So there's old ones angiography, +and things like + +that, I'll show you two. + +Computed Tomography, and MR +and a really cool measure + +called Diffusion +Tensor Imaging. + +And then, dysfunctional +measures, and we'll talk about + +those, EEG, PET, fMRI, MEG. + +So here's some different +images you can + +get from the brain. + +This is a post-mortem brain, +this is a cut brain, here's + +the front, here's the back. + +If a brain was open in +front of you, this is + +what you would see. + +So here's an MRI, Magnetic +Resonance Imaging, and it's + +pretty good, and I'll show you +some more pictures, in showing + +you lots of information. + +Not as good as if you were in +there, but pretty good. + +Here's a CT scan, Computed +Tomography. + +It's not as good, it's +more blurry. + +And this thing that looks really +sad, it looks like get + +your camera to focus, that's +actually the quality of the + +picture that we see that +underlies maybe the most + +widely used tool these days for +understanding the human + +mind and brain, Functional +Magnetic Resonance Imaging. + +It's a very smudgy picture, +but it has some really + +interesting properties. + +So here's the kind of thing you +go into for an MRI, both + +structural or functional. + +Some of you have almost +certainly been participants in + +research or experiments, +or studies, stick up + +your hand if you have. + +Oh, a lot of you, OK, so you'll +speak up on this, is it + +quiet or noisy? + +It's super noisy, so you have +to have ear plugs in. + +And this is why people doing +experiments with this + +Functional MRI want to do +visual studies, because + +auditory ones are tricky. + +So Tyler, your head TA, likes +auditory stuff, it's 10 times + +harder to pull off those +experiments. + +Everybody tries to do visual +stuff, so you don't have the + +noise problem. + +But you get some beautiful +pictures, here's Computed + +Tomography. + +And here's an MRI structural +scan from the brain, the + +ventricles, here's +Basal Ganglia. + +With an MRI, beautifully you can +see the difference between + +white and gray matter. + +I'm always impressed that +the gray matter is + +just this thin ribbon. + +Cortex really means bark, +it's just like + +the bark on our tree. + +And when you look at the brain +this way, look at how much + +white matter there is. + +Here's your frontal cortex, look +at all that white matter + +and then this thin, cortical +mantle, or ribbon, or bark. + +That's what we think of as the +smarts of language, and social + +planning, and things +like that. + +So that's a structural +picture. + +And then these two pictures +are sort of fun. + +This is just recorded down the +street, we're going to fly + +through your brain from +one ear to the other. + +And you get amazing resolution, +it's not the same + +thing like being inside +the brain. + +There's things that you don't +see, we know that, + +but you see a lot. + +Isn't that cool? + +Let's examine what +you can see now. + +Only about 40 years ago, you +would have to have a person + +die to see this. + +This is a patient with +Huntington's disease, we'll + +come back and talk about +that disorder. + +Here's a healthy person, +top of the brain. + +This is the caudate here, part +of the Basal Ganglia. + +And you could see in a patient +who has passed away that part + +of the brain is completely +withered away in + +Huntington's disease. + +You would have to wait until +person passed away to see + +something like that. + +Here's a healthy person +top of the brain, + +again lining the ventricle. + +This is the caudate. + +And here in a living +Huntington's patients you can + +see the great withering away. + +Some of cortex 2 in later +stage of disease, but + +especially in the +Basal Ganglia. + +Here's a healthy older person, +about 70 years of age, top of + +the brain, bottom of the +brain, the ventricle. + +Here's on the left and right +of the hippocampus, the + +structure we'll talk about, +without which you can cannot + +learn any new fact, +or remember any + +event in your life. + +So powerful for almost every +sense of learning. + +And look what happens the +structure in the same aged + +patient with Alzheimer's +disease. + +It's virtually gone, it's +greatly weathered. + +You see it's much wider here, +because the tissue's greatly + +shrunk in the Alzheimer's +patient. + +So we can see these kinds of +changes in living people, for + +both research purposes and +clinical purposes. + +Here's one that's more cheerful, +and more reflecting + +your experience. + +Here are studies of brain +changes from age four to 21. + +So they follow a large number +of people at NIH + +from age four to 21. + +And what this shows is this +color coding is the thickness + +of the cortex. + +And you might imagine that as +you get older, and smarter and + +go through grade school, and +middle school, and high + +school, and MIT college, and +as you head towards grad + +school, your brain will +get thicker, and + +thicker with cortex. + +It's exactly the opposite. + +Ever since you were about five +years old, you've been + +shedding neurons by the +millions, and connections + +among them by the trillions. + +And you're still going +to do that until your + +probably about 22 or 23. + +Then you peak, and you decline +and become faculty members. + +But that's really interesting, +we'll come back to this, that + +what happens as your brain +get smart, experienced, + +knowledgeable, all the +differences between you now, + +if you're 17, 18, 19, 20, and +when you were four, it all + +goes with your cortex +getting thinner. + +And we'll come back to that +and how people think about + +that, but let's see if I can +get this next movie to run. + +There's also an ordering-- and +we'll come back this but I + +want to show you this movie. + +So the more blue you are, the +thinner you are, the more + +advanced you are in terms +of ultimate young adult + +development. + +Here's visual cortex, +vision coming in. + +This is Somatomotor Cortex, how +you feel, your body, and + +how you move yourself. + +And what you see is, as you go +from age four to 21, the blue + +spreads, that spreading is your +brain maturing in higher + +thought areas. + +So we're going to review your +life on average right now, + +here you go. + +And now you're ready +to graduate. + +It's kind of an amazing story +of fantastic brain changes + +that move you from what you +could do and not do at four, + +to what you can do and +not do at age 21. + +And we couldn't see these +things, we couldn't begin to + +see these things, until just +a few years ago in any + +scientific sense. + +All these things are like +miraculous sources of + +information. + +So let's pick another +thing, and we'll tie + +it to school work. + +Here's the structure we +said, the hippocampus. + +So important for the formation +of new memories on an everyday + +basis, everything that's +important and that you learn. + +So here's a fun study they +took, and as you hear it, + +think about its scientific +limitation, but it's fun as + +students to think about. + +They looked at students in +medical school in Germany. + +They looked at the measure of +an anatomic thickness of the + +hippocampus before and after +they studied like crazy for a + +huge exam over some +number of periods. + +This is the difference between +the two, and what they're + +showing you is that as you +study, your hippocampus got + +thicker as you crammed +for your test. + +So will there be a day where +instead of having to give you + +tests we could just measure +the thickness of your + +hippocampus to know how much +you studied, and you could + +just zoom in and out of a +scanner, I don't know. + +But one cool thing about it is +it's showing you that we can + +see structural changes not just +on a giant scale from + +when you're four to 21, but from +some number of months of + +experience, we can see a +physical change in your brain. + +Now that's trivial for animal +researchers, they can show + +amazing things in seconds, but +you see the human brain + +physically changing. + +So let's take a look at another +one, slightly more + +controlled, we'll look +at two more examples. + +London taxi cab drivers. + +If you've travelled in various +cities, and have gone in + +various taxis, you may have +had better or worse + +experiences whether the taxi +driver knows where he or she + +is going exactly. + +London is famous for having a +very high code, taxi drivers + +have to take big exams to get +their official taxi license, + +they create a very +demanding thing. + +And when they ask this in the +hippocampus if you learn lots + +of routes, if you know tons of +routes in London, what happens + +to the hippocampus as +it's memorizing all + +these special routes? + +And what they saw, that taxi +drivers had bigger hippocampi, + +and the longer they drove, +the bigger it was. + +So is this a causal or + +correlational source of evidence? + +It's correlational right? + +So let's start with this, they +have bigger hippocampi, and + +now maybe that's simply +because, what? + +Maybe somebody who has an +awesome hippocampus is ready + +to go to be a taxi driver. + +Maybe they pass the test, and +the one who got lost all the + +time, and was driving to the +wrong airport and stuff, small + +hippocampus, never became +a taxi driver. + +So the size of the hippocampus +is the cause of your success, + +not the consequence. + +Because the longer you drove, +the bigger it got, that kind + +of goes with that. + +But you could do a causal +experiment this way. + +They taught people to juggle +three balls, they practiced + +every day for three months. + +Three months juggling +every day. + +What you see in yellow are parts +of the brain-- that's a + +statistical map-- + +parts of the brain that +significantly got thicker in + +three months of practice. + +So they could compare directly +before and after, it's a + +causal experiment. + +And these are areas that are +involved in the visual motion, + +and it makes sense that areas +involved in visual motion + +would somehow change. + +But the fact that we can see +three months of experience + +change the structure of your +brain, it's kind of remarkable + +in they way that we can measure +and scientifically + +scrutinize. + +You might be curious if you did +three months of this and + +you were a pretty good juggler, +you're impressing + +your friends at parties, your +brain scan is different. + +What do you think happened-- + +they followed these people +up-- after the juggling + +requirements stopped? + +They kind of stop, most of the +people, they were too busy. + +They would show off here and +there, but that was it. + +They measured their brain's +again about six months later, + +and this change was gone. + +It came in, and it went out +with the activity, it's + +activity dependent. + +So depending on what you do, +you could think about every + +activity you do-- mental and +physical that you do-- is + +constantly slightly changing +your brain. + +And if you do a lot of it, +you're fundamentally changing + +it like in these individuals. + +But if you stop doing it you +go right back to where you + +were, because you're going to +be doing something else. + +And another fun measure that's +kind of beautiful and + +intriguing is Diffusion +Tensor Imaging. + +Now every [INAUDIBLE] we talked +about so far has been + +gray matter of the brain, +the neurons and then the + +circuits they form. + +We're going to turn to white +matter, which is the + +myelinated axons that are +the super conducting + +highways of the brain. + +And what Diffusion Tensor +Imaging does, it shows you + +something about the organization +of that white + +matter, measuring directly the +movement of water at very, + +very tiny distances. + +This is a cross-section of +a myelinated nerve fiber. + +Those are the fibers that are +covered with white matter that + +have to go some distance. + +And the myelin protects the +quality and speed of that + +signal through your brain. + +And you could see at the level +of, if you're a tiny, tiny + +drop of water, or smaller than +that, this is a pretty big + +bump in the road. + +So imagine you're a little drop +of water moving a little + +bit, and you bump up against the +myelin, you go oh, can't + +go that way, and you go +back this way, and + +you go with the flow. + +You go parallel with a myelin, +it's hard to cross it at that + +microscopic scale. + +But we can measure that movement +in areas where it's + +highly constrained, and that's +a property of the water. + +Here cerebral spinal fluid, +things can go anywhere. + +Here's where there's a lot of +white matter, and the water + +tends to flow along parallel +with the white matter, just + +for physical reasons it +can't cross it over. + +And here for example, is a +statistical map comparing this + +measure of white matter +organization between adults, + +who either in their childhood +had a diagnosis of dyslexia, + +reading was difficult for +these individuals. + +Or people who typical reading +development, where you learned + +to read and wasn't particularly +difficult. + +And you can see that in this +area around the Temporal + +Parietal Cortex, there's a +significant difference. + +But we can do one more thing. + +These are reading scores this +way, this is the measure of + +the white matter organization +from the + +Diffusion Tensor Imaging. + +Each of these as an individual +person now. + +So the open dots are the people +who had typical reading + +development. + +The filled dots are the people +who had poor development, and + +you can see it's pretty +continuous. + +Even in the people with the open +circles who never had a + +problem, the better they +read, the more the + +organization is here. + +So this is not just the +difference between good and + +bad readers, it's a difference +between really good readers, + +and medium readers, and poor +readers, right, continuous. + +So now, cause or effect? + +Were those of you who at three, +who had awesome myelin, + +were you going, reading's +a snap. + +I love this stuff, where's +War and Peace, mom? + +Or, were you like the jugglers, +and you were reading + +a lot, and you were exercising +this part of the brain, and + +altered its physical +structure. + +And the answer is +we don't know. + +How could we know? + +How could we know? + +If you were scientists and were +given a pot of money to + +do this, how could you know? + +Well-- + +yeah? + +AUDIENCE: Track the entire +lives of multiple people. + +PROFESSOR: Yeah, do a +longitudinal study and start + +like, before people read. + +And you could see is +it different then? + +Are we born to be big readers, +or by being big readers do we + +alter the architecture +our brain. + +What's the effort, and what's +the talent, or what's the + +predisposition at birth, and +what's the time you put in + +creating this part. + +We don't know that yet, but we +have a place to look at that. + +And then you can create these +kinds of beautiful pictures, + +and I'll say a word +about this. + +So this is an individual +person's white matter + +organization. + +So we could take this picture +of you, or anybody you know + +who wants to go in a scanner. + +And what's color coded here in +blue are fibers that are + +running up or down, we can't +tell with the fibers which + +direction they're going, +but we can tell other + +orientations. + +Up and down, left and right in +red, up and down in blue, and + +green is front to back. + +Pretty cool, huh? + +I can tell you that I'll +say a word about this. + +Should we do that again? + +I like it, but I work +in this area. + +This is fantastic, this is an +individual person's white + +matter organization. + +As information is flowing around +in your mind, here's + +the paths that it's flowing +around in as you just do + +anything that's interesting +in your feelings + +or thoughts or anything. + +It's fantastic. + +I can tell you that the +algorithms that are used to + +create these maps, there's +some debate + +about the better ones. + +So the last steps of this are +a bit debated, and a bit + +depending on how cool you are +as a visual engineer. + +But there's a lot of things +that's right about Diffusion + +Tensor Imaging, there's +a lot of things that + +are right about it. + +Function, so most of all we're +interested in structure, not + +just for itself, but how is it +makes your mind do the things + +you could do. + +And when we think about +different functional measures + +that are available to +neuroscientists or + +psychologists, we often think +in two dimensions, Spatial + +Resolution, and Temporal +Resolution. + +How precise are we where we are, +and what's the time scale + +that we're measuring in, +milliseconds, are we averaging + +over many seconds, many hours. + +We know mental operations, +roughly speaking, occur at the + +millisecond level, or maybe +10 milliseconds. + +There's no answer to that, but +we know lots of things happen + +that fast in the mind. + +So if you look at this here you +can see that, for example, + +if you're in animal work, +looking at size, you can get + +down to the Synapse +or the Dendrite. + +We can't touch that in humans, +we can't touch + +that cellular stuff. + +And it's not until we get up +to here, which is like big + +patches of the brain, that we +can state things about people. + +That's why it's always going +to be fundamental in + +neuroscience to link the human +work to the animal work, + +because we can't get to the +neurons or anything like that + +in a person almost ever. + +That has to come from animal +work, where you can do + +invasive work. + +So we have to look at +a pretty big patches + +of the human brain. + +How about time? + +Well, we can get down to +milliseconds in time in the + +human brain. + +Functional things like PET and +MRI are here and in the order + +of multiple seconds, I'll +come back to this. + +But you can see all these +things have strengths. + +Now you don't always want to be +down to a single synapse, + +it's not clear that we would +understand much of the + +organization of the brain at +the level of the synapse. + +There's things happening in the +synapse, but a thing like + +knowledge, or love, or something +like that probably + +we can't study at the level +of the synapse. + +Effectively, yet. + +Bigger units are probably +more interpretable. + +So here's a fun one, EEG's, +Electroencephalography. + +So they put on your head some +sort of a cap with electrodes, + +and they measure changes in +electrical activity that are + +being picked up through +the skull. + +And you're picking up huge +changes in hundreds of + +thousands of neurons, but +you're able to do it + +millisecond by millisecond +at the speed of thought. + +The same electrical signal for +EEG and ERP, that evoke + +response potentials, with EEG +you just watch it over time. + +So you can see these different +rhythms that go with a person + +in coma, or in deep sleep, +asleep, drowsy, relaxed. + +You can see these characteristic +rhythms that + +people can measure. + +If you do an experiment, you can +time lock these moment by + +moment to some stimulus or +task you give the person. + +So here we're going to time lock +these, and then you get a + +thing like this that says, +here's a response, maybe the + +first moment after I see a word, +a second moment after I + +see a word or something +like that. + +So you can time lock +large electrical + +responses in the brain. + +And you get some studies like +this, and we'll come back to + +this, but here's a fun one +in language for example. + +You read a sentence like, It was +his first day at work, OK + +that's the baseline condition in +purple, not a particularly + +exciting sentence. + +Although, your first day at +work is actually pretty + +interesting-- but to +read the sentence. + +How about this one: He spread +the warm bread with socks. + +You go, Socks? + +I'm shocked, that makes +no sense at all. + +What happens as you read it, +here's in broken blue line, + +you go wow, and that's +called the N400. + +But that's kind of cool, that's +400 milliseconds after + +you saw that word you said, I +get it's socks but it doesn't + +make sense. + +So you're violating semantics. + +And then they have to do +a control experiment. + +And a lot of psychology, in a +course like this, we can't + +devote enough time to this. + +But I can tell you high quality +research in psychology + +is high quality thoughtfulness +like in any other field. + +You could say, well maybe it's +not the word "socks" that's + +bothering you, maybe just +because it's odd, just like a + +weirded out signal, it's +a weirded out signal. + +So they do this, She put on +her high-heeled shoes, but + +they put shoes in big print +that you didn't expect. + +So now you're weirded out, +but it makes sense. + +So what happens in your +mind, you a very + +different response here. + +So here the meaning is wrong, +here the size is wrong. + +And see you can read a person's +mind in this sense, + +millisecond by millisecond as +they understand something like + +a sentence. + +You can do it with babies, +which is pretty cute, and + +incredibly exciting too. + +So we can measure to +the milliseconds. + +Lots of people can take doing +it, it's relatively + +inexpensive. + +Why don't we just run +around and do that? + +And we do that at MIT, and lots +of places do this too. + +Well, Spatial Resolution is +really problematic, we don't + +know where in the brain +the signals are + +really coming from. + +We know where the electrode +is on the head, but that's + +picking up a lot of stuff below +it, we don't know where + +the brain is coming from. + +The way I think about it a +little bit, imagine you went + +to a football game, and you +were on the outside of the + +stadium, and you heard big +cheering on the side that you + +knew was MIT. + +You might think something good +happened to MIT, then you hear + +big cheering on the side where +CalTech team is sitting, and + +there's fans, it'd be +the usual Rose Bowl. + +You might figure something good +happened at CalTech, but + +you don't really know exactly +what happened, and exactly + +where it happened. + +So we don't know where the +signals are coming from in a + +very precise way. + +There's another method that's +sort of very intriguing too, + +and we're just installing it +at MIT, and you could be + +amongst the first generation +of participants, if you so + +choose to be. + +This is called +Magnetoencephalography, active + +neurons produce small +magnetic fields. + +You can use a superconducting +quantum device to measure this + +tiny, tiny change to the +magnetic field, they're + +secondary to the +neurons firing. + +These signals are problematic +to measure because they're + +estimated to be 100 million +times smaller than the earth's + +magnetic field. + +And all these measures we have +in human brain function, all + +of them, the signal is terrible +compared to the + +noise, it's terrible compared +to the noise. + +And MEG might be the worst, +there's a number of places + +that installed MEG, and had to +take it out because the local + +traffic on the road was too big +relative to the difference + +between the earth's magnetic +field in the signal they get. + +Signal to noise is terrible in +every noninvasive human brain + +measure we have. + +But you get something +beautiful. + +Now, any mental thought we have +of any interest of any + +kind, we pretty much understand +to be the property + +not of a single part of the +brain doing its thing, but a + +remarkable concert, different +parts of your brain playing or + +interacting with one another. + +It's a symphony orchestra doing +anything interesting in + +the human mind, and MEG can +show that beautifully. + +So here's an individual's +structural MRI that's been + +inflated, they've sort of blown +it out like a balloon so + +it's sort of easy to look at. + +And what you're going to see now +from Dale & Halgren in an + +MEG measurement millisecond by +millisecond of what your brain + +does, roughly speaking, when +you read a single word, OK + +here we go. + +See, back and forth, back and +forth, and there's all this + +interaction feeding forward from +when you see it, feeding + +being backward from parts of +your brain that say, I think I + +know what it is, let's +double check. + +Back and forth, back +and forth. + +Let me do it one more time, +because I think + +it's just so cool. + +Anything interesting that your +brain does is an incredibly + +complicated millisecond by +millisecond interaction + +between large scale +brain networks. + +So here we go again, reading a +single word, arrives in the + +back of the brain, front's +thinking about back, front, + +back, front, back front. + +We read the word. + +It's just amazing, and MEG is +one of the better measures for + +us to see this time based +way in which your mind + +accomplishes things. + +The strengths are it has great +temporal resolution, + +noninvasive, Spatial Resolution +is it maybe better + +than EEG, or perhaps better, not +as good as a fMRI, we'll + +come to that. + +And it only can measure neurons +in the cortex that are + +parallel to the skull, so we +can't see lots of things like + +support local structures +like the hippocampus. + +So now we're moving to the +measures that you most often + +see, but these other ones +all help us a lot. + +And they are all derived from +the following things. + +Sadly, for PET or fMRI, the most +widely used studies to + +understand how your mind works, +we can't interrogate + +the neurons to compute your +mind, we can't, they're off + +bounds to us. + +The other measures you just +saw are based on neurons. + +What we have to do is we have to +look for gossipy neighbors, + +that is the vasculature that +surrounds and supports the + +neurons that compute the mind. + +And we know the neurons require +oxygen and glucose, + +metabolically to do their +work, the cellular life. + +And the brain area's active, +there's increased blood flow, + +and increased energy supplies +that come to that. + +So it's all the sort of +inference by the secondary + +consequence of neurons +doing their business. + +So the brain is about 3 and 1/2 +pounds, it's about 2% of + +your total body mass. + +So it has a tenfold, 20% extra +demand of body oxygen, your + +brain cries out for oxygen +at every moment. + +So 2% of your body, but 20% +of the oxygen demand. + +And it's so sensitive that only +10 minutes of loss of + +oxygen can often cause +irreversible brain damage, + +especially in structures +like the hippocampus. + +The first discovery that blood +changes that are going with + +brain changes, blood changes +that are the sort of the + +echoes, if you will, a secondary +consequence, is low + +tech character current +machines. + +This is work from Angelo Mosso +in the late 1880's, and he saw + +a patient who had a unusual sort +of malformation, so he + +had almost no skull here. + +And he put on it something that +measured the pressure + +there, and he also measured-- +and what's shown here in red + +is this pressure as a control +thing, that's pretty clever-- + +pulses of blood in the forearm, +so those are in blue. + +That's the control, that's not +just blood everywhere. + +And what he did is, the guy's +still sitting there, nothing + +happening, and he noticed that +when the church bells rang + +nearby, boom, this device picked +up increased pressure + +over this part of the head. + +That's pretty cool, it has to +be blood, it's not neurons, + +OK, it's blood. + +But now he has the signature of +mental life in your brain, + +the blood consequence +of a thought, which + +is I hear the Church. + +They asked the guy, does it have +to be something that you + +hear, he says, did you +make your prayers + +today, your Ave Maria? + +Again nothing happening +peripherally, but boom, as he + +gives his answer, a change +in blood pressure there. + +Or do math problem, boom, +a change there. + +So all of the sudden, blood +changes of a part of the brain + +become the witness to that part +of the brain supporting + +the mental operations +to do that task. + +And here's a PET study, the +first weighted Positron + +Emission Tomography, which is +basically used to measure + +local brain activity by looking +at the consequences of + +photons disintegrating as +they're measured in this sort + +of a device. + +And here's the way they use this +task to discover which + +parts to map the neural +organization + +of the human mind. + +So I need somebody who's willing +to do a task at their + +seat, and it's just going to be +reading words, or coming up + +with words. + +OK, thanks. + +Here you go, ready? + +Look at that, in our field we +call that fixation, you're + +just looking, OK, +just looking. + +Alright, good job. + +Ready for something else? + +Alright, now just look +at these things, + +OK, you see the words? + +The technical word is reading. + +Alright, now imagine we did one +more thing with you-- and + +actually if you were +in a PET scanner + +here's what would happen. + +If in a PET scanner, you'd be +sitting down there like that, + +there'd be a physician in their +lab coat like this. + +There'd be physicist in the +basement making up some sort + +of a tracer they're going +to inject into you + +every round of this. + +Because that's what they need to +sort of track this, and it + +comes up an elevator, and people +take turns running down + +the hall with it, because it has +a pretty short half-life. + +The shortness of its half-life +is what makes you able to do + +these multiple measures. + +This is a pretty big deal +process, and in fact the one + +or two PET sessions I ever +attended, you would rotate who + +would run down the field with +the radioactive substance, so + +you would share the radioactive +substance. + +So now you've done that, and +you feel like, I'm doing + +pretty good. + +So now they come and +they say, are you + +ready for another injection? + +They have a catheter running +into your arm, and they inject + +you again, here comes the +radioactive stuff, the oxygen. + +And now they ask you to read the +words aloud presented one + +at a time, why don't you +just read aloud one + +at a time, go ahead. + +AUDIENCE: Rose, cat, +apple, pen, plane. + +PROFESSOR: OK, and they say +thank you very much, and we're + +going to do one more injection +if that's OK with you, of + +radioactive substance. + +And now we're going to ask you +to do one thing, and this is + +harder, as you see each word +tell us a verb that describes + +what you might do with that +object, or what a person might + +do, so go ahead, for +rose tell us. + +AUDIENCE: Smell, pet, +eat, write, fly. + +PROFESSOR: Perfect. + +Yeah, I can tell you that in the +experiment they present a + +lot of these, and a lot of +subjects after while just go + +use, use, use, use, hold, +hold, hold, hold. + +But you did a good job, OK. + +This is just looking at +something, this is looking at + +a word, which is reading. + +Now don't forget, we're the only +species that ever read, + +reading has been around in our +culture only for about 700 + +years on any scale, and reading +is an incredible thing + +to work correctly. + +And you saw the whole brain +flicker to get it right. + +But now you're going to say +the word in the next + +condition, so you're not just +looking at the word, but + +you're also saying it. + +And now finally you're not only +saying a word and looking + +at it, but you are thinking +about it to come up with + +smell, or pet. + +So they say, what we're going +to do is we're going to do a + +hierarchy of your mind, just +looking, reading, reading and + +talking, reading and talking +and thinking. + +And by comparing those different +conditions, we'll + +subtract them against each +other, and pull out the part + +of your mind that sees a word, +that speaks a word, and that + +thinks about a word, +and we'll separate + +those out in the brain. + +So basically the subtraction +method. + +So when we compare looking at +fixation versus looking at + +words, we'll see what part of +your brain discovers that it's + +a word, knows how to read words, +looking at words versus + +repeating them. + +We'll discover the basis of +speech, speaking a word versus + +coming up with the verb, +thinking about stuff, their + +meaning, and coming +up with an answer. + +So again the idea is if you're +saying something like pet for + +the cat, you're doing +all these things. + +Or you might just be reading +it aloud, and + +we'll subtract them. + +In both these conditions, here +you saw a word and read it, + +here you saw a word and came +up and produced a verb, you + +subtract these two and +you end up with a + +statistical image like this. + +This is not a raw image of +blood, all these you ever see + +those are statistics of the +areas that differed by some + +statistical criterion between +one condition and another. + +They're all statistics, they're +not blood, or raw + +blood, that underlies it, but +what you see is a statistic, + +and here's the statistic. + +Now in both of these cases, +you saw the word. + +In this case you simply read it, +in this case you read it + +in your head and you came +up with a verb. + +But why don't we see +anything back here? + +Why don't we see the seeing of +the word, even though the + +seeing occurred in +those conditions? + +Why isn't it visible in +this brain picture? + +Because it's been +subtracted out. + +So always in these brain imaging +experiments, for + +reasons I'm about to tell you, +we almost always have to do + +some kind of subtraction. + +And I'll tell you why, but that +subtraction is very big. + +Because what you subtract out, +that's the heart of the + +experiment, and your decision +about what's a legitimate + +subtraction. + +And the reason we have to +do it is this, look + +at these two things. + +Here's one condition, and here's +the other condition. + +Do you see that they look +pretty similar? + +Again, signal to noise. + +Your brain is busy all the time, +now we ask you to do + +something and see +the difference. + +And the difference is very tiny +by the way we measure it. + +It's not tiny mentally, it's +not tiny in terms of the + +consequences for civilization +in the world. + +It's tiny because of the weird +way we have to measure it. + +I can tell you that if I've +put on an optimal + +checkerboard, the +psychophysicists have said, + +this turns on your +visual cortex. + +I'll get about a 3% to 5% change +in your brain signal. + +If you wave your arm, I can get +3% to 5% signal change in + +your cortex here. + +If I ask you to do everything +in between seeing something + +and moving your lips or hand, +everything about thought, + +emotion, memory, desire, +motivation, everything that's + +big in our life will get +something like that one tenth + +of 1% of the signal change. + +One tenth of 1% of the +signal change. + +Yeah, Tyler's like yeah, that +means you have to test a lot + +of subjects, and work 40 +years on your Ph.D. + +So we have to do that +subtraction, because if we + +just take a picture of what's +going on in your head, it's so + +much that we can't tell what's +going on at all. + +And if we have you do something +that's pretty big, + +like seeing like a really +provocative picture, we'll + +just get one tenth of 1% +of the signal change. + +So we have to do the subtraction +to have a hint. + +And then we do one other weird +thing, we don't have to but we + +often do it. + +We want to average people to +make some general statement + +about humanity, as far as we can +do it, based on the 10 MIT + +students we test. + +So we scrunch everybody's +brain into common space, + +everybody's brain's a little +bit different, like their + +bodies are a little +bit different. + +We scrunch everybody to line +them all up so we have a + +common physical space. + +So by the time you see this +picture, it's a statistic on + +an average of people in +most cases, but you + +get an amazing story. + +Which up until these +pictures-- + +about the late 1980s, it was +unimaginable that you could go + +inside a living person's brain, +and see what it is that + +allows you to hear a word in +auditory cortex, to see a word + +in visual cortex, to move your +mouth to speak, or to think, + +what's the verb that goes +with that word? + +Unimaginable at your-- + +OK, now I have to do the quick +math, but you'll help me out-- + +what year were you born in? + +'82? + +'92? + +I know, at my age it +all blends. '92? + +OK, so just a year or two before +you were born-- this + +was 5 years before you were-- +unimaginable that you could + +see such a picture. + +When I was a graduate student at +Harvard, and the people at + +Washington St. Louis +University-- + +who did the first of these-- + +did an incredible service +to the field. + +Here we saw, oh my gosh, it was +like landing on the moon. + +Going inside the human brain, +and knowing which part of the + +brain endows us with +human capacities. + +Now, we can be appreciative +or we can be skeptical + +scientists, and we can say this, +let's pick this one. + +Let's compare seeing a +word like "board," + +versus seeing a fixation. + +We do that subtraction, and +that's seeing a word. + +Just by common sense, what's +wrong with this comparison? + +It's OK it's not terrible. + +How can you control it better? + +To understand what this part of +the brain is really doing? + +I heard something? + +Well partly it's a meaningful +word, versus something that + +doesn't mean anything +to a plus. + +But what else could you say +is different between them? + +Yeah? + +[INAUDIBLE] + +GUEST SPEAKER: [INAUDIBLE] + +PROFESSOR: In this case, oh my +gosh, yes, and I'll come back + +to that, but let me not do +that one for the moment, + +because that's a giant story +which I can't fit in today. + +Yes your mind can be +all over the place. + +So that's definitely the case, +so that's a good one. + +Yeah? + +GUEST SPEAKER: You could replace +the plus, which is + +like really small, +with [INAUDIBLE] + +PROFESSOR: Yeah, that's perfect, +OK that's the way I + +was going-- the other one's +great too, two great comments. + +Yeah you could say like, maybe +this is a part of your brain + +it goes with five things, +or something this + +big versus this big. + +No you go, that's not so +interesting, the part of your + +brain that looks at something +this big, versus this big. + +But that's just as legitimate +a conclusion here. + +How about this, five different +things, versus only this. + +There's a lot of different ways +in which you could say, + +what is the mental operation +that I've discovered in the + +human brain and mind, it all +comes down to the comparison. + +So here's what they did to +try to do a better job. + +They showed you a more +complicated thing that doesn't + +mean anything. + +A bunch of letters that you +can't pronounce, a bunch of + +letters that you can pronounce, +but it's not a real + +word, and here's the +real world itself. + +So if you want to say, what do +you think this part of the + +mind is doing? + +What part the mind does this +part of the brain allow to + +happen in humans, and only +humans on this planet? + +And every word you ever read +only happens because this part + +of the brain does +what it does. + +What is that part of +the brain doing? + +Is it just simply responding +too complicated + +things, five of them? + +No, not much, a little +bit, but not much. + +How about letters, letters are +pretty interesting, but there + +can't be a word by English, +you can't pronounce this. + +Not too interested? + +A word, a set of letters you've +never seen together + +before, but you can pronounce +by the rules of English. + +Boom. + +That's what I do, says this +part of the brain, + +that's what I do. + +I say, I see something, and it's +possibly a word and I can + +say it by the rules +of English. + +And by the way, if it's +a word I've done + +before, I do that too. + +I'm pretty flexible, I can do +new words, I can do words I've + +known before. + +It matches what you see with +language, that's reading. + +Only our species can take our +visual system, and the + +language you learn as a child, +and put them together, and + +allow our civilization +to read. + +And this is a part of the brain +where those roads meet. + +And by the way, we talked about +local and global, the + +forest and the trees. + +And consistent with what we +talked about the split brain + +patients, looking at global +stuff right hemisphere, if + +you're looking at local stuff, +left hemisphere. + +So we like it when the +information we have from + +split-brain patients, or stroke +patients aligns with + +healthy people doing a task +as they typically do. + +Because then we sort of believe +there's something + +right about that. + +So PET, pretty good spatial +resolution, I mean, depends + +what you mean by good. + +My neuroscience colleagues +dismiss everything we ever do + +as sort of pathetically +imprecise. + +But 5 to 10 millimeters, +not as good as fMRI. + +The temporal resolution is very +poor we can only take one + +picture that lasts about +a minute, and averages + +everything across that. + +You have to inject people with +radioactive stuff, and it's + +correlational. + +But it has one other thing +that's really, really + +interesting, Positron +Emission Tomography. + +Because you're injecting a +radioactive label, you can + +create different kinds of labels +that go to different + +parts of the brain. + +So here's Parkinson's disease, +which involves damage the + +Substantia nigra, and +the Basal Ganglia. + +Here's a healthy persons +Substantia nigra, and here's a + +person with Parkinson's disease, +where these cells + +have died away. + +Typically, at least 80% of these +have to die before a + +person shows Parkinson's disease +symptoms clinically. + +Here's an injection of +radioactive stuff using PET + +that binds to Dopamine +receiving neurons. + +And you can see that in the +living Parkinson's patient, + +this tremendous reduction +in these + +receptors waiting for Dopamine. + +In a living patient + +specifically Dopamine receptors. + +So that's a disease. + +Here's why video games are +taking over the world. + +Oh no, not yet. + +We can do one more thing. + +We can track the disease from a +typical person, to a person + +with moderate Parkinson's +disease or severe. + +Within the disease, we +can see differences. + +But here's why video games are +taking over the world, because + +if we take a healthy person, +young adults, give them this + +kind of Dopamine binding tracer, +and have them play a + +video game, two things happen. + +A, the parts of your brain that +are involved in reward, + +Dopamine, is the strongest +to reward + +neurotransmitter that we know. + +Things go crazy, and what this +graph is showing you is the + +better you do, the more +rewarded you are. + +This is why you will go for the +next level, because to get + +that dopamine fix, you +got to keep going. + +And we think these reward +mechanisms underlie + +everything, in many ways they +relate to everything. + +Why do you do whatever you do, +because at some level, in some + +way, you find it rewarding. + +And the data is very compelling +that way. + +The last method I'll talk about +is functional MRI, and + +it's the one that's most +widely visible. + +So you sit in a scanner, stimula +are presented to you + +to perform a task. + +We do a lot of stuff in our +lab with children, we show + +them how the frog would do it. + +For those of you who've done a +functional MRI experiment, + +because there were so many +hands that were put up. + +Do any of you want to say a +word about your experience + +doing that? + +What was it like, easy, +huge fun, recommend, + +no, not so much fun. + +It will vary a little bit. + +We said noisy. + +Some people find it +claustrophobic. + +GUEST SPEAKER: I dont know, I +didn't really do anything. + +I just had to sit there for a +really long time and not move. + +PROFESSOR: Oh, so they didn't +ask you to do a task, maybe. + +GUEST SPEAKER: Well, for +a big part of it, I + +was watching a movie. + +PROFESSOR: So for the student +they were watching a movie not + +doing anything, + +GUEST SPEAKER: [INAUDIBLE] + +PROFESSOR: You were doing +yes or no clicks. + +So that would be typical +functional MRI kind of + +experiment, some of them are +more obnoxious, some are less, + +some are funny, some +are not as funny. + +Any other experiences? + +Was it comfortable, not so +comfortable, medium. + +Anybody else want to share? + +No, OK. + +OK. + +So how does this work? + +Functional MRI takes advantage +of MRI but it focuses on + +hemoglobin, the stuff that +carries oxygen in your blood. + +And it rests on the fact that +after oxygen has been + +extracted it's more sensitive +to the magnetic field than + +oxygenated hemoglobin. + +So it's like this. + +Here's basically capillaries and +veins, arteries and veins. + +And as you go through the +capillary bed, the smallest + +vessels, neurons are extracting +oxygen to support + +their physical life. + +What happens when this part of +the brain gets active, is that + +more oxygen is extracted to +support the active neurons. + +So we call this BOLD effect, +blood oxygen level dependent. + +So we're measuring the change in +blood, changes the ratio of + +oxygenated to deoxygenated +hemoglobins, that changes the + +magnetic field as +we measure it. + +And that's what we directly +measure, not the neurons. + +So if the neurons are using up +oxygen, why does the BOLD + +signal increase, why does +this ratio go up? + +Because intuitively you'd +think it would go down, + +because oxygen is being +extracted at a higher rate. + +If you look at oxygen being +extracted, right after + +something happens, 10 +seconds, there's an + +initial dip of oxygen. + +That's the neurons extracting +oxygen to replenish themselves + +from their activity, their +activity has been to give your + +mind its life. + +Then what happens is there's +this vast oversupply for much + +longer time. + +Intuitively, it's as if we +said it's so important to + +metabolically support the +neurons that make up our + +minds, that if some areas +demanding a lot of blood, we + +send over way too much extra +as soon as we can, from a + +distance to make sure +everything's OK. + +And because our measurement is +so sad, we almost can never + +measure this initial dip. + +We almost always measure the +sustained oversupply of oxygen + +to that part of the brain. + +So you could say it's such +a house of cards. + +The oversupply of the blood +going to a part of the brain + +changes the balance of +oxygenated to deoxygenated + +hemoglobin that changes +the magnetic property. + +And that's how we try to figure +out what that part of + +the brain is doing +for your mind. + +But it works pretty well +in some cases. + +Decent Spatial Resolution, no +injection, you can zoom in a + +scanner and do a lot of +different things. + +Modest Temporal Resolution, +because it's not milliseconds, + +it's always on the order of +seconds, that's correlational, + +not causal. + +But you get some amazing +results, I'm just going to + +present to you two or three. + +So here's one, a thing we're +very interested about humans + +is empathy. + +How much we understand and feel +other people's happiness, + +or sadness, or pain. + +So the "observation or +imagination of another person + +in a particular emotional state +automatically activates + +a representation of that state +in the observer," empathy. + +And how do we understand how +another person feels, and we + +think that's a big thing +in how we relate to + +one another as humans. + +So Tania Singer did the +following experiment, we + +talked about this +before a little + +bit, embodied cognition. + +That we understand others out +there by the feelings + +we know within us. + +We don't know their feelings, +but we know our + +feelings inside us. + +So here's what she did, she +brought in pairs of people who + +were friends, or romantic +partners. + +And she either had them get +some pain, it was a shock, + +within ethical boundaries, but +not pleasant, that's the pain. + +Or, you got to watch through a +video camera, while you're + +being imaged, your partner +getting the shock. + +So think about somebody you +care about and think about + +them getting something painful, +and how you would + +feel at that moment. + +And they asked in the brain, +what's similar and dissimilar, + +and we'll focus on what's +similar right now, between + +feeling pain yourself, and +observing pain in somebody you + +care about, emphasizing with the +pain you see them having. + +And what they found is two +areas, something of an + +Anterior Cingulate, and +something in the Insula, which + +we talked about before, where +there was a lot of overlap. + +So this phrase, I'm feeling your +pain, in your brain when + +you feel for somebody else's +pain in this physical sense, + +you turn on some of the same +brain areas as when you feel + +physical pain directly. + +It's as if the basis to imagine +another person's + +feelings is the feelings you +know so well yourself. + +And this is literally shown +now by the brain imaging. + +It could've been a story, a +metaphor, an argument, this is + +scientific evidence that +supports that likelihood. + +So we're going to expend it +in a slightly fun way. + +There's been a lot of study in +neuroeconomics thinking about + +how we think about, for example, +things like trust. + +So one game, and there's a +number of them, is called the + +ultimatum game. + +And many people probably +know this, but let me + +remind you of this. + +This version of it has +two players, a + +proposer, and a responder. + +And what they do is they give +to proposer a certain amount + +of money, and the proposer is +allowed to make an offer to + +the responder. + +If the responder says, No, +nobody gets any money. + +Usually people offered about +50%, so let's make this + +concrete just for a moment. + +Can I pick you for a second? + +You can decline. + +Imagine if Tyler came over to +me and give me $10, and I + +said, how would you feel if I +gave you five and I kept five. + +What do you think? + +Might you go for It? + +GUEST SPEAKER: Yeah, sure. + +PROFESSOR: I mean, you go, I'm +$5 dollars ahead, you're $5 + +ahead, Tyler won't eat this +month because graduate student + +stipends are modest, but it's +a zero sum game in the end. + +So now Tyler comes over hands +me 10 more dollars, and I + +offer you one. + +What's your first feeling +assuming that I wasn't your + +teacher grading you? + +He saw me get ten, +I say here's one. + +What's your feeling? + +Think about it just for-- + +GUEST SPEAKER: You'd feel +kind of cheated. + +PROFESSOR: --yeah. + +You don't have to, by purely +economic perspective, would + +you be ahead by taking +that dollar? + +Yeah. + +A dollar's a dollar, $2 +is $2, but people + +have a sense of fairness. + +Even to their own detriment, +if you offer $2 and lower. + +Even knowing that you're just +ruining $1 or two you would've + +gotten for nothing, except +saying yes, people half the + +time will say no. + +It's like, you are so unfair-- + +you were saying to me, I would +never say this to you-- you + +are so unfair, that we're going +to take us both down, + +rather than you have the +pleasure of the $8. + +OK It's so unfair, +that my sense + +of fairness is disturbed. + +It's an interesting way to +think about it, imagine a + +friend of yours is handed $10, +and they offer you half, and + +if you say no, nobody +gets anything, so + +it's a trust game. + +They had the people in the +scanner playing this game with + +two people they saw on +a video monitor. + +The two people they're playing +with are set up. + +The person in the scanner is +the real participant, the + +people out there they see, +are confederates, + +they're play actors. + +And one is a fair person, here's +$5, thank you, here's + +$5, thank you. + +Here's $6, oh, you're awesome, +we can get along, And then + +there's an unfair player, +here's $1. + +And you go, why is +this guy a jerk? + +How about $2? + +And after a while, you go the +fair player was very decent, + +this unfair player-- + +who you believe is part of the +experiment, but is a set up-- + +and you're just thinking, why +is this person such a jerk? + +They're constantly getting $10, +and constantly giving me + +one or two. + +No, no, no thank you. + +Now, you get a shock, and you +see these two strangers, one + +of whom was a wonderful, fair +player, and one of whom was an + +absurdly unfair player. + +You see them get a shock. + +And they had both men and women +in the scanner watching + +these things happen. + +And here's what happened, +and it's kind of + +funny, but you know. + +For the women they had overlap +again between the parts of the + +brain to turn on in here in the +insula, when they got a + +shock, and when either the fair +player got a shock, or + +the unfair player. + +They felt bad for both +by this measure. + +Look at the men in the study. + +I feel bad if the fair guy gets +it, but this part of the + +brain's like, yeah, give +it to 'em, can + +you push up the voltage? + +It just came out this way, +whether it would work that way + +under all circumstances, all +ages, all societies, other + +groups of men and women, +don't know. + +But in this sample in +the United Kingdom, + +the men had no empathy. + +It's worse than that, it's +worse than they had no + +empathy, let me show you this. + +If they asked to indicate their + +desire for revenge against-- + +this is a behavioral response-- +their desire for + +revenge against the +bad player. + +I don't think they pursued the +unfair player down the street, + +but just that feeling. + +And the women said, a little +bit, the men said yes, if only + +I could take down this person, +that would be great. + +And here's the amazing thing, +we'll come back to the + +structure called a nucleus +accumbens. + +It sits in the bottom of +the Basal Ganglia. + +It's the structure that in the +human brain is most identified + +with reward and pleasure, most +identified with reward and + +pleasure by fMRI imaging. + +Look at the nucleus +accumbens when the + +unfair player gets zapped. + +The women, nothing much, the +men boom, big reward. + +Revenge is rewarding +in their brain. + +No sympathy, and lots of revenge +satisfaction for the + +unfair player. + +Now you can decide on your own +life who this applies to or + +not, but it's sort +of fun to explore + +these different things. + +How we form ideas about empathy, +trust, whether they + +are in a society +we grow up in. + +Somewhat different on average +men and women, huge ranges + +within men huge ranges +within women. + +So it's a sort of fun +thing to explore. + +Let me end with something that's +much more difficult and + +disturbing, but another place +where imaging is giving us + +insights that you could not +imagined having some time ago. + +So this is a very difficult +case, I don't know if any of + +you gone through it, I don't +wish it for you. + +Some of you probably have, and +many of you will at sometime + +in your life, when you have to +make an end of life decision. + +And amongst the most famous of +these cases was Terry Schiavo. + +Now I don't know that name even +rings a bell for you, but + +it got very, very famous amongst +these kinds of cases. + +So she had a cardiac arrest, +she had took a lot of diet + +pills, and that may +have contributed. + +In February 25, 1990, she went +into a coma, and then a + +vegetative state. + +So a vegetative state is when +a person seems to be kind of + +awake, but when you talk with +them, they're not very aware, + +they're not responsive, they're +not noticing, they're + +not talking. + +But their eyes are open, and +they're awake, their eyes are + +not closed, so that's +what she is. + +And they put in her a feeding +tube, because without that she + +wouldn't live, she couldn't +eat and feed herself. + +It was a heartbreaking +difference of opinion between + +her husband and her parents. + +Her husband petitioned some +years later, actually eight + +years later, to remove +the feeding tube and + +let her pass away. + +The parents opposed that, they +said that's not her wishes, + +she would want to keep on going +with the feeding tube. + +The husband said no, I don't +believe that's her wishes. + +So you have this very tragic +confrontation between the + +parents who loved her, and the +husband who presumably loved + +her having different ideas about +what to do with her, + +whether to end her +life or not. + +So finally her tube was removed, +but then the parents + +went to court, and a judge +reversed it, and they + +put the tube back. + +She became, sadly, kind of +back and forth, living + +nonliving, on judicial +decisions. + +Her case became particularly +famous, for a bunch of + +reasons, and it went back and +forth from court, to court. + +Moving up in the state courts, +and there were several US + +Supreme Court decisions about +whether to remove the tube, or + +keep the tube in. + +And it's a tragic thing, it's +a tragic choice between the + +parents and the husband. + +It got to the US Congress, +in the US Senate. + +President Bush signed a bill +to keep her alive. + +Everybody got involved, with +various opinions, finally the + +Supreme Court made a series +of decisions. + +It was disconnected in +2005, and she died in + +March 31 of that year. + +So tragic difficult decision, +and a tragic family situation + +that became kind +of a political, + +and judicial football. + +So what's going on in the mind +of somebody like this, and how + +could we even begin to interpret +it for a person who + +can't speak for themselves +and can't respond. + +So let me tell you about +a different case, we + +don't know her case. + +So, again a vegetative state is +one where you appear to be + +awake, but there's no +sign of awareness. + +Eyes are open, but the person's +not talking or + +responding to anything +in their environment. + +So here's a different woman, 23 +years old, in 2005 she had + +a road traffic accident, severe +traumatic brain injury. + +Five months later she's +un-responsive, but she has + +preserved sleep-wake, like +she's waking up going to + +sleep, waking up +going to sleep. + +Eyes open, but un-responsive +in every other way. + +They put her into an fMRI +scanner, as well as healthy + +comparison people, and +they have them do to + +mental imagery tasks. + +they read instructions to her. + +But you go into scanner, and +you're told to imagine two + +different things. + +Playing tennis, so imagine in +your mind's eye you playing + +tennis for a moment, +imagine that. + +Or imagine visiting all the +rooms of your house starting + +with your front door, in the +house that you are living in + +now, or where you grew up. + +Imagine those two things +in your mind. + +First of all, just a pure +cognitive neuroscience level, + +and we'll come back to that, +imagination is a really + +interesting thing. + +And it turns out when we imagine +things, again we use + +the parts of our brain that +does them, imagination is + +perception run backwards. + +We can see imagination +in the human brain. + +And depending on what you're +imagining, you use the same + +systems that you see with. + +If you imagine something you're +looking at, it will + +turn on your visual system, +it's even more + +specific than that. + +So let's first look at what +happens with the controls. + +When they imagine they're +playing tennis, they turn on + +the supplementary motor area, +that's a part of your brain + +that plans your physical +movements. + +You're not moving, but you're +thinking about it, this is + +imagination of movement. + +When you plan a movement., +you turn that on. + +When you go around your house, +you turn on spatial areas that + +are in the parahippocampal +cortex, and similar areas, + +parietal cortex, and +parahippocampal cortex. + +They're turned on if we show +you a movie where you're + +moving around in spaces. + +If you see spaces, you turn +those on, if you imagine + +spaces, you turn them on. + +So imagination in the brain is +perception run backwards, or + +physical action run backwards, +you're not actually doing it. + +But look at this patient who +got in the scanner, who was + +non responsive, you read her the +instructions, and see what + +she does, and look +at her brain. + +Asked to imagine tennis, +asked to imagine the + +rooms in her house. + +It looks just like that. + +What does that mean, just +in a common sense, + +what does that mean? + +Did she understand the +instruction, at some level + +yes, she wouldn't turn on those +parts of the brain if + +she didn't understand the +instruction, she imagines the + +thing you ask her to instruct. + +So this guy on the front page +of the New York Times said + +fMRI could tell you the internal +mental life of a + +person could no longer +speak, or communicate + +with any other way. + +Now it's turned out since then, +that when they put in + +other patients into the scanner, +most of them don't + +show this pattern. + +So it's not that every patient +in a vegetative state this is + +full of mental life +like this person. + +And a deeper way, we don't +really understand what this + +mental life is like. + +We don't know whether she +simply understands some + +things, but doesn't have +feelings, or plans, or + +desires, or whether +she has those too. + +We don't understand really the +full range of mental life, but + +we know that she can understand +an instruction, and + +her brain follows +through with it. + +Most patients, it turns out, +don't look like that in + +vegetative states. + +So again, brain imaging has +taken us inside the mind of + +somebody who cannot communicate +for themselves and + +let us say something about +what it is that's + +going on in that mind. + +In conclusion, we've talked +about different ways of + +learning about the brain, +different methods to record + +structure and function that +vary in their temporal and + +spatial acuity. + +And incredibly different ways in +which we can understand the + +organization in time and space +of how the brain supports the + +human mind. \ No newline at end of file diff --git a/09yIb3VHhMI.txt b/09yIb3VHhMI.txt new file mode 100644 index 0000000000000000000000000000000000000000..06d0497dbafb5acfbdba9cff39055318ebab1dd5 --- /dev/null +++ b/09yIb3VHhMI.txt @@ -0,0 +1,9369 @@ +align:start position:0% + +The Following content is provided under + + align:start position:0% +The Following content is provided under + + + align:start position:0% +The Following content is provided under +a Creative commons license your support + + align:start position:0% +a Creative commons license your support + + + align:start position:0% +a Creative commons license your support +will help mit open courseware continue + + align:start position:0% +will help mit open courseware continue + + + align:start position:0% +will help mit open courseware continue +to offer high quality educational + + align:start position:0% +to offer high quality educational + + + align:start position:0% +to offer high quality educational +Resources fore to make a donation VI + + align:start position:0% +Resources fore to make a donation VI + + + align:start position:0% +Resources fore to make a donation VI +addal materials of mit courses mit + + align:start position:0% + + + + align:start position:0% + +openedu + + align:start position:0% + + + + align:start position:0% + +inus + + align:start position:0% + + + + align:start position:0% + +Any inclusion exclusion principle is + + align:start position:0% +Any inclusion exclusion principle is + + + align:start position:0% +Any inclusion exclusion principle is +important the best exp is + + align:start position:0% +important the best exp is + + + align:start position:0% +important the best exp is +using + + align:start position:0% + + + + align:start position:0% + +diagrams we that + + align:start position:0% +diagrams we that + + + align:start position:0% +diagrams we that +if the Union + + align:start position:0% +if the Union + + + align:start position:0% +if the Union +of Whole collection ofs That are allj + + align:start position:0% +of Whole collection ofs That are allj + + + align:start position:0% +of Whole collection ofs That are allj +then we can Just Sum all the cardinali + + align:start position:0% +then we can Just Sum all the cardinali + + + align:start position:0% +then we can Just Sum all the cardinali +of each of the members so in the case + + align:start position:0% +of each of the members so in the case + + + align:start position:0% +of each of the members so in the case +Where we have intersections so sets are + + align:start position:0% +Where we have intersections so sets are + + + align:start position:0% +Where we have intersections so sets are +not disjointed well If You just Count + + align:start position:0% +not disjointed well If You just Count + + + align:start position:0% +not disjointed well If You just Count +all the cardinali all the sizes of the + + align:start position:0% +all the cardinali all the sizes of the + + + align:start position:0% +all the cardinali all the sizes of the +sets Together you will Start to do some + + align:start position:0% +sets Together you will Start to do some + + + align:start position:0% +sets Together you will Start to do some +Double + + align:start position:0% +Double + + + align:start position:0% +Double +counting so with the inclusion exclusion + + align:start position:0% +counting so with the inclusion exclusion + + + align:start position:0% +counting so with the inclusion exclusion +principle we can + + align:start position:0% +principle we can + + + align:start position:0% +principle we can +actually + + align:start position:0% +actually + + + align:start position:0% +actually +exactly compute The Cardinal of the + + align:start position:0% +exactly compute The Cardinal of the + + + align:start position:0% +exactly compute The Cardinal of the +Union of + + align:start position:0% + + + + align:start position:0% + +sets you will see that this principle + + align:start position:0% +sets you will see that this principle + + + align:start position:0% +sets you will see that this principle +can be used in plenty of examples + + align:start position:0% +can be used in plenty of examples + + + align:start position:0% +can be used in plenty of examples +including some of them That are + + align:start position:0% + + + + align:start position:0% + +on How Does It work let's take example + + align:start position:0% + + + + align:start position:0% + +we + + align:start position:0% + + + + align:start position:0% + +overlap + + align:start position:0% +overlap + + + align:start position:0% +overlap +over would like to + + align:start position:0% +over would like to + + + align:start position:0% +over would like to +out + + align:start position:0% + + + + align:start position:0% + +are is is + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + + align:start position:0% + +of over here + + align:start position:0% +of over here + + + align:start position:0% +of over here +we including what is in + + align:start position:0% +we including what is in + + + align:start position:0% +we including what is in +m just out the cardinali of the That We + + align:start position:0% +m just out the cardinali of the That We + + + align:start position:0% +m just out the cardinali of the That We +are interested in we would like to + + align:start position:0% +are interested in we would like to + + + align:start position:0% +are interested in we would like to +compute the Cardinal of the Union of m e + + align:start position:0% +compute the Cardinal of the Union of m e + + + align:start position:0% +compute the Cardinal of the Union of m e +Let's a + + align:start position:0% +Let's a + + + align:start position:0% +Let's a +look + + align:start position:0% +look + + + align:start position:0% +look +The Cardinal of M itself can be computerized + + align:start position:0% +The Cardinal of M itself can be computerized + + + align:start position:0% +The Cardinal of M itself can be computerized +If We Use the Sum rule Which says That + + align:start position:0% +If We Use the Sum rule Which says That + + + align:start position:0% +If We Use the Sum rule Which says That +We Can + + align:start position:0% +We Can + + + align:start position:0% +We Can +Simply + + align:start position:0% +Simply + + + align:start position:0% +Simply +add The Two diso sets that make up set m + + align:start position:0% +add The Two diso sets that make up set m + + + align:start position:0% +add The Two diso sets that make up set m +we can Count each Of Those Cardinal so + + align:start position:0% +we can Count each Of Those Cardinal so + + + align:start position:0% +we can Count each Of Those Cardinal so +we have M consisting of this part Which + + align:start position:0% +we have M consisting of this part Which + + + align:start position:0% +we have M consisting of this part Which +is m excl e plus the part is Right Here + + align:start position:0% +is m excl e plus the part is Right Here + + + align:start position:0% +is m excl e plus the part is Right Here +Which is the intersection so we Use the + + align:start position:0% +Which is the intersection so we Use the + + + align:start position:0% +Which is the intersection so we Use the +Sum + + align:start position:0% +Sum + + + align:start position:0% +Sum +rule and conclude + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +plus Cardinal of the + + align:start position:0% +plus Cardinal of the + + + align:start position:0% +plus Cardinal of the +intersection we can do completely + + align:start position:0% +intersection we can do completely + + + align:start position:0% +intersection we can do completely +similar we will have everything + + align:start position:0% +similar we will have everything + + + align:start position:0% +similar we will have everything +including is in + + align:start position:0% +including is in + + + align:start position:0% +including is in +M ​​And then We Still have the + + align:start position:0% + + + + align:start position:0% + +intersection of the sets m e and now we + + align:start position:0% +intersection of the sets m e and now we + + + align:start position:0% +intersection of the sets m e and now we +need to add This one This one and This + + align:start position:0% +need to add This one This one and This + + + align:start position:0% +need to add This one This one and This +one Together So What do we see we see + + align:start position:0% +one Together So What do we see we see + + + align:start position:0% +one Together So What do we see we see +that This Is actually equal to + + align:start position:0% +that This Is actually equal to + + + align:start position:0% +that This Is actually equal to +everything that is in M ​​but not in + + align:start position:0% +everything that is in M ​​but not in + + + align:start position:0% +everything that is in M ​​but not in +E Everything that is in + + align:start position:0% +E Everything that is in + + + align:start position:0% +E Everything that is in +intersection plus Everything in E but + + align:start position:0% +intersection plus Everything in E but + + + align:start position:0% +intersection plus Everything in E but +not in + + align:start position:0% +not in + + + align:start position:0% +not in +m SO we have + + align:start position:0% +m SO we have + + + align:start position:0% +m SO we have +These equation we canly derive from the + + align:start position:0% +These equation we canly derive from the + + + align:start position:0% +These equation we canly derive from the +Sum rule + + align:start position:0% +Sum rule + + + align:start position:0% +Sum rule +and we can Here If We Are toly + + align:start position:0% +and we can Here If We Are toly + + + align:start position:0% +and we can Here If We Are toly +add Simply cinal of n of M of + + align:start position:0% +add Simply cinal of n of M of + + + align:start position:0% +add Simply cinal of n of M of +e add two Together We will the + + align:start position:0% +e add two Together We will the + + + align:start position:0% +e add two Together We will the +intersection + + align:start position:0% +intersection + + + align:start position:0% +intersection +Dou to cancel that counted on in the + + align:start position:0% +Dou to cancel that counted on in the + + + align:start position:0% +Dou to cancel that counted on in the +Union If combine Th over here + + align:start position:0% + + + + align:start position:0% + +equations + + align:start position:0% + + + + align:start position:0% + +conclude + + align:start position:0% + + + + align:start position:0% + +CS M + + align:start position:0% + + + + align:start position:0% + +Inter + + align:start position:0% + + + + align:start position:0% + +we + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% + + + + align:start position:0% + +plus + + align:start position:0% +plus + + + align:start position:0% +plus +ex + + align:start position:0% +ex + + + align:start position:0% +ex +will the general + + align:start position:0% +will the general + + + align:start position:0% +will the general +equation suppose sets Now like One + + align:start position:0% +equation suppose sets Now like One + + + align:start position:0% +equation suppose sets Now like One +Another One + + align:start position:0% +Another One + + + align:start position:0% +Another One +Another One over H + + align:start position:0% + + + + align:start position:0% + +M + + align:start position:0% +M + + + align:start position:0% +M +S Let's look how many + + align:start position:0% +S Let's look how many + + + align:start position:0% +S Let's look how many +Times Different areas + + align:start position:0% +Times Different areas + + + align:start position:0% +Times Different areas +All How many times are we counted eh The + + align:start position:0% +All How many times are we counted eh The + + + align:start position:0% +All How many times are we counted eh The +Three eh cardinali Together so we have M + + align:start position:0% +Three eh cardinali Together so we have M + + + align:start position:0% +Three eh cardinali Together so we have M +plus The City Of e plus The Cardinal of + + align:start position:0% +plus The City Of e plus The Cardinal of + + + align:start position:0% +plus The City Of e plus The Cardinal of +s well if you do that then we Count this + + align:start position:0% +s well if you do that then we Count this + + + align:start position:0% +s well if you do that then we Count this +Area exactly Once because it's in M ​​this + + align:start position:0% +Area exactly Once because it's in M ​​this + + + align:start position:0% +Area exactly Once because it's in M ​​this +Area we Count Once because it's in M ​​and + + align:start position:0% +Area we Count Once because it's in M ​​and + + + align:start position:0% +Area we Count Once because it's in M ​​and +another time because it's in E so It's + + align:start position:0% +another time because it's in E so It's + + + align:start position:0% +another time because it's in E so It's +Twice this particular Area is Only + + align:start position:0% +Twice this particular Area is Only + + + align:start position:0% +Twice this particular Area is Only +counted Once In This Sum over here and + + align:start position:0% +counted Once In This Sum over here and + + + align:start position:0% +counted Once In This Sum over here and +similarly we have two times + + align:start position:0% + + + + align:start position:0% + +Times Inter Of All Of The counted When + + align:start position:0% +Times Inter Of All Of The counted When + + + align:start position:0% +Times Inter Of All Of The counted When +We Count Elements in M ​​but also When We + + align:start position:0% +We Count Elements in M ​​but also When We + + + align:start position:0% +We Count Elements in M ​​but also When We +Count Elements in E and also When We + + align:start position:0% +Count Elements in E and also When We + + + align:start position:0% +Count Elements in E and also When We +Count Elements in s So This is counted + + align:start position:0% +Count Elements in s So This is counted + + + align:start position:0% +Count Elements in s So This is counted +three + + align:start position:0% +three + + + align:start position:0% +three +times + + align:start position:0% +times + + + align:start position:0% +times +so Let's Have a look It seems like we + + align:start position:0% +so Let's Have a look It seems like we + + + align:start position:0% +so Let's Have a look It seems like we +want to do exactly the same as we + + align:start position:0% +want to do exactly the same as we + + + align:start position:0% +want to do exactly the same as we +did + + align:start position:0% +did + + + align:start position:0% +did +totra intersection of + + align:start position:0% + + + + align:start position:0% + +c + + align:start position:0% +c + + + align:start position:0% +c +simin + + align:start position:0% + + + + align:start position:0% + +counting + + align:start position:0% + + + + align:start position:0% + +to + + align:start position:0% + + + + align:start position:0% + +elimin All It is subtract Let's create + + align:start position:0% +elimin All It is subtract Let's create + + + align:start position:0% +elimin All It is subtract Let's create +the same + + align:start position:0% +the same + + + align:start position:0% +the same +diagram now we count + + align:start position:0% +diagram now we count + + + align:start position:0% +diagram now we count +the Sum of all those intersections we + + align:start position:0% +the Sum of all those intersections we + + + align:start position:0% +the Sum of all those intersections we +have the + + align:start position:0% +have the + + + align:start position:0% +have the +intersection of M intersect with + + align:start position:0% +intersection of M intersect with + + + align:start position:0% +intersection of M intersect with +e Inter of M + + align:start position:0% +e Inter of M + + + align:start position:0% +e Inter of M +S + + align:start position:0% + + + + align:start position:0% + +s Let's Look this Area h is zer Times + + align:start position:0% +s Let's Look this Area h is zer Times + + + align:start position:0% +s Let's Look this Area h is zer Times +not part of Any of these intersections + + align:start position:0% +not part of Any of these intersections + + + align:start position:0% +not part of Any of these intersections +because this part is Only in M ​​And Not + + align:start position:0% +because this part is Only in M ​​And Not + + + align:start position:0% +because this part is Only in M ​​And Not +In s OR e This is + + align:start position:0% + + + + align:start position:0% + +counted + + align:start position:0% + + + + align:start position:0% + +others Area is in this + + align:start position:0% +others Area is in this + + + align:start position:0% +others Area is in this +intersection + + align:start position:0% +intersection + + + align:start position:0% +intersection +also + + align:start position:0% +also + + + align:start position:0% +also +Times we + + align:start position:0% +Times we + + + align:start position:0% +Times we +Easily combine + + align:start position:0% +Easily combine + + + align:start position:0% +Easily combine +All + + align:start position:0% + + + + align:start position:0% + +We + + align:start position:0% + + + + align:start position:0% + +formed + + align:start position:0% + + + + align:start position:0% + +Un of cinal + + align:start position:0% + + + + align:start position:0% + +individual + + align:start position:0% + + + + align:start position:0% + +The intersections That We have up There + + align:start position:0% +The intersections That We have up There + + + align:start position:0% +The intersections That We have up There +so m intersect e min m intersect with s + + align:start position:0% +so m intersect e min m intersect with s + + + align:start position:0% +so m intersect e min m intersect with s +en min e Inter with + + align:start position:0% +en min e Inter with + + + align:start position:0% +en min e Inter with +s now we have eliminated If You Look at + + align:start position:0% +s now we have eliminated If You Look at + + + align:start position:0% +s now we have eliminated If You Look at +this fan diagram over here this diagram + + align:start position:0% +this fan diagram over here this diagram + + + align:start position:0% +this fan diagram over here this diagram +over here we eliminated Everything + + align:start position:0% +over here we eliminated Everything + + + align:start position:0% +over here we eliminated Everything +That's in the middle Area so We Still + + align:start position:0% +That's in the middle Area so We Still + + + align:start position:0% +That's in the middle Area so We Still +need to add intersection Everything that + + align:start position:0% +need to add intersection Everything that + + + align:start position:0% +need to add intersection Everything that +is counted in the intersection of m e + + align:start position:0% + + + + align:start position:0% + +equ Can We exclusion exclusion principle + + align:start position:0% +equ Can We exclusion exclusion principle + + + align:start position:0% +equ Can We exclusion exclusion principle +h We + + align:start position:0% +h We + + + align:start position:0% +h We +include all the Elements in m s we to + + align:start position:0% +include all the Elements in m s we to + + + align:start position:0% +include all the Elements in m s we to +exclude Too Much we exclusion over + + align:start position:0% +exclude Too Much we exclusion over + + + align:start position:0% +exclude Too Much we exclusion over +here now + + align:start position:0% + + + + align:start position:0% + +we And then we keep on going like this + + align:start position:0% +we And then we keep on going like this + + + align:start position:0% +we And then we keep on going like this +so in general We Get The Following + + align:start position:0% + + + + align:start position:0% + +eh + + align:start position:0% +eh + + + align:start position:0% +eh +theorem that says that If We Look at the + + align:start position:0% +theorem that says that If We Look at the + + + align:start position:0% +theorem that says that If We Look at the +cardinali uh of the Cardinal of the + + align:start position:0% +cardinali uh of the Cardinal of the + + + align:start position:0% +cardinali uh of the Cardinal of the +Union of eh a whole bunch of sets say we + + align:start position:0% +Union of eh a whole bunch of sets say we + + + align:start position:0% +Union of eh a whole bunch of sets say we +have n sets then This Is actually equal + + align:start position:0% +have n sets then This Is actually equal + + + align:start position:0% +have n sets then This Is actually equal +to we First include The sums of all the + + align:start position:0% +to we First include The sums of all the + + + align:start position:0% +to we First include The sums of all the +individual cardinali + + align:start position:0% +individual cardinali + + + align:start position:0% +individual cardinali +is I I to + + align:start position:0% +is I I to + + + align:start position:0% +is I I to +n Cardinal of + + align:start position:0% +n Cardinal of + + + align:start position:0% +n Cardinal of +Ai minus now + + align:start position:0% +Ai minus now + + + align:start position:0% +Ai minus now +we eliminate the double counting so + + align:start position:0% +we eliminate the double counting so + + + align:start position:0% +we eliminate the double counting so +we Look at Every pair of sets index by + + align:start position:0% +we Look at Every pair of sets index by + + + align:start position:0% +we Look at Every pair of sets index by +i1 and i2 and we Look at Their + + align:start position:0% +i1 and i2 and we Look at Their + + + align:start position:0% +i1 and i2 and we Look at Their +intersection and we take that Out using + + align:start position:0% +intersection and we take that Out using + + + align:start position:0% +intersection and we take that Out using +this minus we exclude + + align:start position:0% +this minus we exclude + + + align:start position:0% +this minus we exclude +this + + align:start position:0% +this + + + align:start position:0% +this +we continue like this + + align:start position:0% +we continue like this + + + align:start position:0% +we continue like this +we excluded to include + + align:start position:0% + + + + align:start position:0% + +More + + align:start position:0% +More + + + align:start position:0% +More +tri index i1 + + align:start position:0% +tri index i1 + + + align:start position:0% +tri index i1 +i2 and + + align:start position:0% + + + + align:start position:0% + +i3 + + align:start position:0% +i3 + + + align:start position:0% +i3 +we + + align:start position:0% + + + + align:start position:0% + +intersection + + align:start position:0% + + + + align:start position:0% + +Inter + + align:start position:0% + + + + align:start position:0% + +Inter is + + align:start position:0% +Inter is + + + align:start position:0% +Inter is +even + + align:start position:0% + + + + align:start position:0% + +incl + + align:start position:0% + + + + align:start position:0% + +n intersection Of + + align:start position:0% +n intersection Of + + + align:start position:0% +n intersection Of +All + + align:start position:0% +All + + + align:start position:0% +All +we can write this out in More elant + + align:start position:0% + + + + align:start position:0% + +Formula + + align:start position:0% + + + + align:start position:0% + +WS + + align:start position:0% + + + + align:start position:0% + +k min + + align:start position:0% +k min + + + align:start position:0% +k min +kend k is even + + align:start position:0% + + + + align:start position:0% + +inclusion Those + + align:start position:0% +inclusion Those + + + align:start position:0% +inclusion Those +are subsets of the index Set one up to + + align:start position:0% +are subsets of the index Set one up to + + + align:start position:0% +are subsets of the index Set one up to +n such + + align:start position:0% +n such + + + align:start position:0% +n such +that the Cardinal of the set s is equal + + align:start position:0% +that the Cardinal of the set s is equal + + + align:start position:0% +that the Cardinal of the set s is equal +to k and now we need to look at the + + align:start position:0% +to k and now we need to look at the + + + align:start position:0% +to k and now we need to look at the +Cardinal of all uh of the intersection + + align:start position:0% +Cardinal of all uh of the intersection + + + align:start position:0% +Cardinal of all uh of the intersection +of all the sets That are indexed by s so + + align:start position:0% +of all the sets That are indexed by s so + + + align:start position:0% +of all the sets That are indexed by s so +That's So I Run I put i + + align:start position:0% +That's So I Run I put i + + + align:start position:0% +That's So I Run I put i +so Do The intersection over All I in s + + align:start position:0% +so Do The intersection over All I in s + + + align:start position:0% +so Do The intersection over All I in s +of the sets + + align:start position:0% +of the sets + + + align:start position:0% +of the sets +Ai So This general Formula is the + + align:start position:0% +Ai So This general Formula is the + + + align:start position:0% +Ai So This general Formula is the +inclusion exclusion principle eh and + + align:start position:0% +inclusion exclusion principle eh and + + + align:start position:0% +inclusion exclusion principle eh and +this is the way how you can Think About + + align:start position:0% +this is the way how you can Think About + + + align:start position:0% +this is the way how you can Think About +It How to derive it eh of course this is + + align:start position:0% +It How to derive it eh of course this is + + + align:start position:0% +It How to derive it eh of course this is +not a Proof but you could do this + + align:start position:0% +not a Proof but you could do this + + + align:start position:0% +not a Proof but you could do this +yourself by using induction and you can + + align:start position:0% +yourself by using induction and you can + + + align:start position:0% +yourself by using induction and you can +use induction on n so That's eh a Pretty + + align:start position:0% +use induction on n so That's eh a Pretty + + + align:start position:0% +use induction on n so That's eh a Pretty +Straight forward + + align:start position:0% +Straight forward + + + align:start position:0% +Straight forward +exercise Ok so Let's Give an example + + align:start position:0% +exercise Ok so Let's Give an example + + + align:start position:0% +exercise Ok so Let's Give an example +ehm + + align:start position:0% +ehm + + + align:start position:0% +ehm +let do over + + align:start position:0% + + + + align:start position:0% + +h + + align:start position:0% + + + + align:start position:0% + +similar Go Like + + align:start position:0% + + + + align:start position:0% + +This like to know how many Perm + + align:start position:0% +This like to know how many Perm + + + align:start position:0% +This like to know how many Perm +Are Special property How + + align:start position:0% +Are Special property How + + + align:start position:0% +Are Special property How +Perm Do + + align:start position:0% + + + + align:start position:0% + +I + + align:start position:0% +I + + + align:start position:0% +I +of the + + align:start position:0% +of the + + + align:start position:0% +of the +set all the Up + + align:start position:0% +set all the Up + + + align:start position:0% +set all the Up +To All the + + align:start position:0% + + + + align:start position:0% + +digits + + align:start position:0% + + + + align:start position:0% + +consecutive cons + + align:start position:0% +consecutive cons + + + align:start position:0% +consecutive cons +either + + align:start position:0% + + + + align:start position:0% + +Next + + align:start position:0% +Next + + + align:start position:0% +Next +on I to Perm That a and two Next One + + align:start position:0% +on I to Perm That a and two Next One + + + align:start position:0% +on I to Perm That a and two Next One +Another in this way so we have 4 two or + + align:start position:0% +Another in this way so we have 4 two or + + + align:start position:0% +Another in this way so we have 4 two or +the permutation May + + align:start position:0% +the permutation May + + + align:start position:0% +the permutation May +have z04 + + align:start position:0% +have z04 + + + align:start position:0% +have z04 +or sier so very Curious How many + + align:start position:0% +or sier so very Curious How many + + + align:start position:0% +or sier so very Curious How many +permutation Do I have and I'm going to + + align:start position:0% +permutation Do I have and I'm going to + + + align:start position:0% +permutation Do I have and I'm going to +use this principle that I just + + align:start position:0% +use this principle that I just + + + align:start position:0% +use this principle that I just +described + + align:start position:0% +described + + + align:start position:0% +described +So how do we need to go ahead with this + + align:start position:0% +So how do we need to go ahead with this + + + align:start position:0% +So how do we need to go ahead with this +SO + + align:start position:0% +SO + + + align:start position:0% +SO +this I'm interested in the Perm that + + align:start position:0% +this I'm interested in the Perm that + + + align:start position:0% +this I'm interested in the Perm that +have f and two Next To One Another so + + align:start position:0% +have f and two Next To One Another so + + + align:start position:0% +have f and two Next To One Another so +that could be my first set M And then I + + align:start position:0% +that could be my first set M And then I + + + align:start position:0% +that could be my first set M And then I +have a set that I want to that Z and + + align:start position:0% +have a set that I want to that Z and + + + align:start position:0% +have a set that I want to that Z and +Next One That could be my e and the s + + align:start position:0% +Next One That could be my e and the s + + + align:start position:0% +Next One That could be my e and the s +Could Be Those Perm that have the and + + align:start position:0% +Could Be Those Perm that have the and + + + align:start position:0% +Could Be Those Perm that have the and +zer Next To One Another then I would + + align:start position:0% +zer Next To One Another then I would + + + align:start position:0% +zer Next To One Another then I would +like to use that rule over here so I + + align:start position:0% +like to use that rule over here so I + + + align:start position:0% +like to use that rule over here so I +Would also inters and + + align:start position:0% +Would also inters and + + + align:start position:0% +Would also inters and +do + + align:start position:0% + + + + align:start position:0% + +ex ex + + align:start position:0% +ex ex + + + align:start position:0% +ex ex +is sequence + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +6 example + + align:start position:0% + + + + align:start position:0% + +3 I all the digits That are in + + align:start position:0% + + + + align:start position:0% + +contain + + align:start position:0% + + + + align:start position:0% + +OK is type + + align:start position:0% + + + + align:start position:0% + +of OK + + align:start position:0% + + + + align:start position:0% + +let set + + align:start position:0% +let set + + + align:start position:0% +let set +p42 All + + align:start position:0% +p42 All + + + align:start position:0% +p42 All +Perm + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% + + + + align:start position:0% + +per + + align:start position:0% + + + + align:start position:0% + +P6 + + align:start position:0% +P6 + + + align:start position:0% +P6 +per Let's look what the size of + + align:start position:0% +per Let's look what the size of + + + align:start position:0% +per Let's look what the size of +individual set of Perm How can we do + + align:start position:0% +individual set of Perm How can we do + + + align:start position:0% +individual set of Perm How can we do +this let + + align:start position:0% + + + + align:start position:0% + +look size + + align:start position:0% + + + + align:start position:0% + +of + + align:start position:0% +of + + + align:start position:0% +of +P6 + + align:start position:0% + + + + align:start position:0% + +time and what I would like to do is + + align:start position:0% +time and what I would like to do is + + + align:start position:0% +time and what I would like to do is +slight comp + + align:start position:0% +slight comp + + + align:start position:0% +slight comp +structure would like to map this to a + + align:start position:0% +structure would like to map this to a + + + align:start position:0% +structure would like to map this to a +set means of B that + + align:start position:0% + + + + align:start position:0% + +Great Some Kind of + + align:start position:0% +Great Some Kind of + + + align:start position:0% +Great Some Kind of +other Isy + + align:start position:0% +other Isy + + + align:start position:0% +other Isy +To Rule able to figure cinal + + align:start position:0% + + + + align:start position:0% + +Treat One uni Syb Let it work What I Do + + align:start position:0% +Treat One uni Syb Let it work What I Do + + + align:start position:0% +Treat One uni Syb Let it work What I Do +Is can The + + align:start position:0% +Is can The + + + align:start position:0% +Is can The +of P6 + + align:start position:0% + + + + align:start position:0% + +Perm + + align:start position:0% +Perm + + + align:start position:0% +Perm +Perm of the + + align:start position:0% + + + + align:start position:0% + +set that + + align:start position:0% +set that + + + align:start position:0% +set that +have single + + align:start position:0% +have single + + + align:start position:0% +have single +symbol All symbols + + align:start position:0% +symbol All symbols + + + align:start position:0% +symbol All symbols +other 3 + + align:start position:0% +other 3 + + + align:start position:0% +other 3 +f + + align:start position:0% + + + + align:start position:0% + +7 let + + align:start position:0% + + + + align:start position:0% + +example + + align:start position:0% +example + + + align:start position:0% +example +so How would I map this this be M + + align:start position:0% +so How would I map this this be M + + + align:start position:0% +so How would I map this this be M +According to that + + align:start position:0% +According to that + + + align:start position:0% +According to that +definition + + align:start position:0% +definition + + + align:start position:0% +definition +to 7 5 Now I combine si into One symb In + + align:start position:0% +to 7 5 Now I combine si into One symb In + + + align:start position:0% +to 7 5 Now I combine si into One symb In +My sequence and then I the rest 4 3 + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +B and by the bac Rule The Cardinal of + + align:start position:0% +B and by the bac Rule The Cardinal of + + + align:start position:0% +B and by the bac Rule The Cardinal of +this set is equal to the Total Number of + + align:start position:0% +this set is equal to the Total Number of + + + align:start position:0% +this set is equal to the Total Number of +permutation on this set Now this set has + + align:start position:0% +permutation on this set Now this set has + + + align:start position:0% +permutation on this set Now this set has +exactly eight Elements so I Know How + + align:start position:0% +exactly eight Elements so I Know How + + + align:start position:0% +exactly eight Elements so I Know How +many There are so I know that Cardinal + + align:start position:0% +many There are so I know that Cardinal + + + align:start position:0% +many There are so I know that Cardinal +is equal to e factorial because There + + align:start position:0% +is equal to e factorial because There + + + align:start position:0% +is equal to e factorial because There +are e factorial permutation on sets of + + align:start position:0% +are e factorial permutation on sets of + + + align:start position:0% +are e factorial permutation on sets of +size e we Saw that Last Time so That's + + align:start position:0% +size e we Saw that Last Time so That's + + + align:start position:0% +size e we Saw that Last Time so That's +The trick or + + align:start position:0% + + + + align:start position:0% + +This + + align:start position:0% + + + + align:start position:0% + +is similarly in the same Way we can also + + align:start position:0% +is similarly in the same Way we can also + + + align:start position:0% +is similarly in the same Way we can also +we canat as One symbol or is one symbol + + align:start position:0% +we canat as One symbol or is one symbol + + + align:start position:0% +we canat as One symbol or is one symbol +I also Cardinal of are also equ + + align:start position:0% + + + + align:start position:0% + +to + + align:start position:0% + + + + align:start position:0% + +inters + + align:start position:0% +inters + + + align:start position:0% +inters +and if do + + align:start position:0% +and if do + + + align:start position:0% +and if do +that we going to use the exact Same + + align:start position:0% +that we going to use the exact Same + + + align:start position:0% +that we going to use the exact Same +trick we going to to find the B to Perm + + align:start position:0% +trick we going to to find the B to Perm + + + align:start position:0% +trick we going to to find the B to Perm +of a set of symbols + + align:start position:0% + + + + align:start position:0% + +wef do this Together and take for + + align:start position:0% +wef do this Together and take for + + + align:start position:0% +wef do this Together and take for +example The intersection of + + align:start position:0% +example The intersection of + + + align:start position:0% +example The intersection of +eh of + + align:start position:0% +eh of + + + align:start position:0% +eh of +p42 with + + align:start position:0% +p42 with + + + align:start position:0% +p42 with +P60 So What kind of a b could I + + align:start position:0% +P60 So What kind of a b could I + + + align:start position:0% +P60 So What kind of a b could I +have + + align:start position:0% +have + + + align:start position:0% +have +So It will be all to all the + + align:start position:0% +So It will be all to all the + + + align:start position:0% +So It will be all to all the +permit + + align:start position:0% +permit + + + align:start position:0% +permit +on what kind of a + + align:start position:0% +on what kind of a + + + align:start position:0% +on what kind of a +set I Use the exa trick Here + + align:start position:0% + + + + align:start position:0% + +other Digit 3 5 7 + + align:start position:0% +other Digit 3 5 7 + + + align:start position:0% +other Digit 3 5 7 +8 can this number + + align:start position:0% +8 can this number + + + align:start position:0% +8 can this number +isje rule + + align:start position:0% +isje rule + + + align:start position:0% +isje rule +we cinal of + + align:start position:0% + + + + align:start position:0% + +thisse + + align:start position:0% + + + + align:start position:0% + +Inter + + align:start position:0% + + + + align:start position:0% + +ex + + align:start position:0% + + + + align:start position:0% + +sus permutation + + align:start position:0% +sus permutation + + + align:start position:0% +sus permutation +If I + + align:start position:0% +If I + + + align:start position:0% +If I +Look over here i permutation in + + align:start position:0% +Look over here i permutation in + + + align:start position:0% +Look over here i permutation in +Which Next To One Another This is also + + align:start position:0% +Which Next To One Another This is also + + + align:start position:0% +Which Next To One Another This is also +permutation in and are Next + + align:start position:0% + + + + align:start position:0% + +One + + align:start position:0% + + + + align:start position:0% + +exactly Perm in + + align:start position:0% +exactly Perm in + + + align:start position:0% +exactly Perm in +Here + + align:start position:0% + + + + align:start position:0% + +Next Every permutation in Here has a Sub + + align:start position:0% +Next Every permutation in Here has a Sub + + + align:start position:0% +Next Every permutation in Here has a Sub +sequence of 6 like Next To One + + align:start position:0% +sequence of 6 like Next To One + + + align:start position:0% +sequence of 6 like Next To One +Another so we can Treat this as One + + align:start position:0% +Another so we can Treat this as One + + + align:start position:0% +Another so we can Treat this as One +symbol And then we have All The Other + + align:start position:0% + + + + align:start position:0% + +Ones and Again This Is are e Elements so + + align:start position:0% +Ones and Again This Is are e Elements so + + + align:start position:0% +Ones and Again This Is are e Elements so +we have that also for this intersection + + align:start position:0% +we have that also for this intersection + + + align:start position:0% +we have that also for this intersection +the Cardinal is equal by the Rule The + + align:start position:0% +the Cardinal is equal by the Rule The + + + align:start position:0% +the Cardinal is equal by the Rule The +Total Number of Perm on of + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +The Last One we also a + + align:start position:0% + + + + align:start position:0% + +similar Let Me One I need to do I + + align:start position:0% +similar Let Me One I need to do I + + + align:start position:0% +similar Let Me One I need to do I + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +Dock + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +Next Treat this as One + + align:start position:0% +Next Treat this as One + + + align:start position:0% +Next Treat this as One +symbol The Perm on the + + align:start position:0% +symbol The Perm on the + + + align:start position:0% +symbol The Perm on the +set 0 4 Two And then 1 3 f 7 Oh and si + + align:start position:0% +set 0 4 Two And then 1 3 f 7 Oh and si + + + align:start position:0% +set 0 4 Two And then 1 3 f 7 Oh and si +as well e and n the Cardinal or this set + + align:start position:0% +as well e and n the Cardinal or this set + + + align:start position:0% +as well e and n the Cardinal or this set +is also equal to + + align:start position:0% + + + + align:start position:0% + +inp + + align:start position:0% + + + + align:start position:0% + +trick + + align:start position:0% +trick + + + align:start position:0% +trick +P6 + + align:start position:0% + + + + align:start position:0% + +P4 + + align:start position:0% +P4 + + + align:start position:0% +P4 +me per + + align:start position:0% + + + + align:start position:0% + +H4 + + align:start position:0% + + + + align:start position:0% + +Next so The intersection of these three + + align:start position:0% +Next so The intersection of these three + + + align:start position:0% +Next so The intersection of these three +is equal to 7 + + align:start position:0% +is equal to 7 + + + align:start position:0% +is equal to 7 +factorial Now We Can Use the inclusion + + align:start position:0% +factorial Now We Can Use the inclusion + + + align:start position:0% +factorial Now We Can Use the inclusion +exclusion principle using this over + + align:start position:0% +exclusion principle using this over + + + align:start position:0% +exclusion principle using this over +here and + + align:start position:0% +here and + + + align:start position:0% +here and +eh When We Plug Everything in Here we + + align:start position:0% +eh When We Plug Everything in Here we + + + align:start position:0% +eh When We Plug Everything in Here we +can see that intersection that the Union + + align:start position:0% +can see that intersection that the Union + + + align:start position:0% +can see that intersection that the Union +When We count the Union of P60 with p04 + + align:start position:0% +When We count the Union of P60 with p04 + + + align:start position:0% +When We count the Union of P60 with p04 +and + + align:start position:0% +and + + + align:start position:0% +and +p42 actually + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +Plus + + align:start position:0% +Plus + + + align:start position:0% +Plus +7 inclusion exclusion + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +Princip + + align:start position:0% + + + + align:start position:0% + +It Once + + align:start position:0% +It Once + + + align:start position:0% +It Once +More All Rules will use in set of + + align:start position:0% + + + + align:start position:0% + +examples was the bookkeeper + + align:start position:0% + + + + align:start position:0% + +we + + align:start position:0% +we + + + align:start position:0% +we +de + + align:start position:0% +de + + + align:start position:0% +de +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +bookkeeper is if I have distinct copies + + align:start position:0% +bookkeeper is if I have distinct copies + + + align:start position:0% +bookkeeper is if I have distinct copies +of letters distinct copies + + align:start position:0% +of letters distinct copies + + + align:start position:0% +of letters distinct copies +of + + align:start position:0% + + + + align:start position:0% + +letters + + align:start position:0% +letters + + + align:start position:0% +letters +L1 L2 + + align:start position:0% +L1 L2 + + + align:start position:0% +L1 L2 +l3 + + align:start position:0% + + + + align:start position:0% + +l + + align:start position:0% + + + + align:start position:0% + +n1 letter Ty L1 N2 letters of the type + + align:start position:0% +n1 letter Ty L1 N2 letters of the type + + + align:start position:0% +n1 letter Ty L1 N2 letters of the type +L2 and + + align:start position:0% +L2 and + + + align:start position:0% +L2 and +we + + align:start position:0% +we + + + align:start position:0% +we +sequences n1 + + align:start position:0% +sequences n1 + + + align:start position:0% +sequences n1 +copies of + + align:start position:0% +copies of + + + align:start position:0% +copies of +L1 and + + align:start position:0% +L1 and + + + align:start position:0% +L1 and +N2 + + align:start position:0% +N2 + + + align:start position:0% +N2 +copies + + align:start position:0% + + + + align:start position:0% + +L2 + + align:start position:0% + + + + align:start position:0% + +n + + align:start position:0% + + + + align:start position:0% + +plus + + align:start position:0% +plus + + + align:start position:0% +plus +Products + + align:start position:0% +Products + + + align:start position:0% +Products +n1 + + align:start position:0% +n1 + + + align:start position:0% +n1 +N2 + + align:start position:0% +N2 + + + align:start position:0% +N2 +up to n k factorial and this we also can + + align:start position:0% +up to n k factorial and this we also can + + + align:start position:0% +up to n k factorial and this we also can +write is this is actually definition of + + align:start position:0% +write is this is actually definition of + + + align:start position:0% +write is this is actually definition of +What We Call the momal coefficient so + + align:start position:0% +What We Call the momal coefficient so + + + align:start position:0% +What We Call the momal coefficient so +you already seen the binomial + + align:start position:0% +you already seen the binomial + + + align:start position:0% +you already seen the binomial +coefficients and Which is special case + + align:start position:0% +coefficients and Which is special case + + + align:start position:0% +coefficients and Which is special case +of this One So we write this + + align:start position:0% +of this One So we write this + + + align:start position:0% +of this One So we write this +as n1 + + align:start position:0% +as n1 + + + align:start position:0% +as n1 +plus up to NK and we n1 N2 We Just + + align:start position:0% +plus up to NK and we n1 N2 We Just + + + align:start position:0% +plus up to NK and we n1 N2 We Just +Repeat all of + + align:start position:0% + + + + align:start position:0% + +coefficient + + align:start position:0% +coefficient + + + align:start position:0% +coefficient +k also Forget last + + align:start position:0% +k also Forget last + + + align:start position:0% +k also Forget last +term + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +expressions + + align:start position:0% + + + + align:start position:0% + +for example Last Time In lecture We were + + align:start position:0% +for example Last Time In lecture We were + + + align:start position:0% +for example Last Time In lecture We were +talking about the Number of Bit + + align:start position:0% +talking about the Number of Bit + + + align:start position:0% +talking about the Number of Bit +sequences of length 16 with Ones we + + align:start position:0% +sequences of length 16 with Ones we + + + align:start position:0% +sequences of length 16 with Ones we +Wanted to Count Because We Found Out + + align:start position:0% +Wanted to Count Because We Found Out + + + align:start position:0% +Wanted to Count Because We Found Out +that If we want to Select 12 donuts of + + align:start position:0% + + + + align:start position:0% + +varie + + align:start position:0% + + + + align:start position:0% + +Basic + + align:start position:0% +Basic + + + align:start position:0% +Basic +ex + + align:start position:0% +ex + + + align:start position:0% +ex +of of + + align:start position:0% + + + + align:start position:0% + +counting + + align:start position:0% + + + + align:start position:0% + +we of + + align:start position:0% +we of + + + align:start position:0% +we of +length 16 and uh + + align:start position:0% +length 16 and uh + + + align:start position:0% +length 16 and uh +with Four + + align:start position:0% +with Four + + + align:start position:0% +with Four +Ones well it's exactly equal to + + align:start position:0% +Ones well it's exactly equal to + + + align:start position:0% +Ones well it's exactly equal to +According to this rule as eh well length + + align:start position:0% +According to this rule as eh well length + + + align:start position:0% +According to this rule as eh well length +16 and we need to choose Four Ones Out + + align:start position:0% +16 and we need to choose Four Ones Out + + + align:start position:0% +16 and we need to choose Four Ones Out +Of The 16 and That's The binomial + + align:start position:0% +Of The 16 and That's The binomial + + + align:start position:0% +Of The 16 and That's The binomial +coefficients Where we + + align:start position:0% + + + + align:start position:0% + +uh choose f Out Of The 16 + + align:start position:0% +uh choose f Out Of The 16 + + + align:start position:0% +uh choose f Out Of The 16 +symbols eh and this is equal to + + align:start position:0% + + + + align:start position:0% + +also foll R Iden special + + align:start position:0% + + + + align:start position:0% + +case + + align:start position:0% +case + + + align:start position:0% +case +of k + + align:start position:0% +of k + + + align:start position:0% +of k +Els of k element + + align:start position:0% + + + + align:start position:0% + +subsets + + align:start position:0% +subsets + + + align:start position:0% +subsets +of n + + align:start position:0% +of n + + + align:start position:0% +of n +element + + align:start position:0% +element + + + align:start position:0% +element +z is actually equal to + + align:start position:0% + + + + align:start position:0% + +k many + + align:start position:0% + + + + align:start position:0% + +Times + + align:start position:0% + + + + align:start position:0% + +ok + + align:start position:0% + + + + align:start position:0% + +B The binomial theorem says that for all + + align:start position:0% +B The binomial theorem says that for all + + + align:start position:0% +B The binomial theorem says that for all +integers n Positive integers n we have + + align:start position:0% +integers n Positive integers n we have + + + align:start position:0% +integers n Positive integers n we have +a+ B to Power n equ to the Sum we Take + + align:start position:0% +a+ B to Power n equ to the Sum we Take + + + align:start position:0% +a+ B to Power n equ to the Sum we Take +k0 to n And + + align:start position:0% +k0 to n And + + + align:start position:0% +k0 to n And +then we The + + align:start position:0% +then we The + + + align:start position:0% +then we The +binomial this expression over here k out + + align:start position:0% +binomial this expression over here k out + + + align:start position:0% +binomial this expression over here k out +of + + align:start position:0% + + + + align:start position:0% + +n + + align:start position:0% +n + + + align:start position:0% +n +k b + + align:start position:0% + + + + align:start position:0% + +in this is theor ex to show we can + + align:start position:0% + + + + align:start position:0% + +about + + align:start position:0% + + + + align:start position:0% + +comin a and B of length 2 a a a b b a b + + align:start position:0% +comin a and B of length 2 a a a b b a b + + + align:start position:0% +comin a and B of length 2 a a a b b a b +b What do we see we a s+ Ab + b+ b + + align:start position:0% + + + + align:start position:0% + +s One Times a This one Times + + align:start position:0% + + + + align:start position:0% + +B this combines Together a s+ 2 Ab + b s + + align:start position:0% +B this combines Together a s+ 2 Ab + b s + + + align:start position:0% +B this combines Together a s+ 2 Ab + b s +If have n equ 3 we have a+ B to Power 3 + + align:start position:0% +If have n equ 3 we have a+ B to Power 3 + + + align:start position:0% +If have n equ 3 we have a+ B to Power 3 +We will get all The + + align:start position:0% + + + + align:start position:0% + +Different Products + + align:start position:0% + + + + align:start position:0% + +terms are all the Kinds Of combinations + + align:start position:0% +terms are all the Kinds Of combinations + + + align:start position:0% +terms are all the Kinds Of combinations +of a and b's so for example we have 3 + + align:start position:0% +of a and b's so for example we have 3 + + + align:start position:0% +of a and b's so for example we have 3 +a's so 3 Times a but I can also have ehm + + align:start position:0% +a's so 3 Times a but I can also have ehm + + + align:start position:0% +a's so 3 Times a but I can also have ehm +eh a Squ Tim B plus a a plus b a Squ and + + align:start position:0% +eh a Squ Tim B plus a a plus b a Squ and + + + align:start position:0% +eh a Squ Tim B plus a a plus b a Squ and +Those have exactly two times in a and + + align:start position:0% +Those have exactly two times in a and + + + align:start position:0% +Those have exactly two times in a and +one Times + + align:start position:0% +one Times + + + align:start position:0% +one Times +b i can Look at all the others eh so I + + align:start position:0% +b i can Look at all the others eh so I + + + align:start position:0% +b i can Look at all the others eh so I +May have two times the B and one Times + + align:start position:0% +May have two times the B and one Times + + + align:start position:0% +May have two times the B and one Times +The A So What are Those we have a Times + + align:start position:0% +The A So What are Those we have a Times + + + align:start position:0% +The A So What are Those we have a Times +b squar eh Plus eh B Ab Plus eh B Squ a + + align:start position:0% +b squar eh Plus eh B Ab Plus eh B Squ a + + + align:start position:0% +b squar eh Plus eh B Ab Plus eh B Squ a +so I Count These as uh is the same Right + + align:start position:0% +so I Count These as uh is the same Right + + + align:start position:0% +so I Count These as uh is the same Right +They each have the same Number of b's + + align:start position:0% +They each have the same Number of b's + + + align:start position:0% +They each have the same Number of b's +two times a b and one Times A and then + + align:start position:0% +two times a b and one Times A and then + + + align:start position:0% +two times a b and one Times A and then +finally ehm I have B to the power 3 + + align:start position:0% +finally ehm I have B to the power 3 + + + align:start position:0% +finally ehm I have B to the power 3 +Which CS Times B are all the Possible + + align:start position:0% +Which CS Times B are all the Possible + + + align:start position:0% +Which CS Times B are all the Possible +Terms that I have There are e in Total + + align:start position:0% +Terms that I have There are e in Total + + + align:start position:0% +Terms that I have There are e in Total +one up to e And that fits Right Because + + align:start position:0% +one up to e And that fits Right Because + + + align:start position:0% +one up to e And that fits Right Because +I Can have a Choice of a and B and I do + + align:start position:0% +I Can have a Choice of a and B and I do + + + align:start position:0% +I Can have a Choice of a and B and I do +Times 2 equ 8 e Terms I Group Them + + align:start position:0% +Times 2 equ 8 e Terms I Group Them + + + align:start position:0% +Times 2 equ 8 e Terms I Group Them +Together taking Power 3 plus + + align:start position:0% +Together taking Power 3 plus + + + align:start position:0% +Together taking Power 3 plus + + align:start position:0% + + + + align:start position:0% + +a now i b s + + align:start position:0% +a now i b s + + + align:start position:0% +a now i b s +a and finally B to Power + + align:start position:0% +a and finally B to Power + + + align:start position:0% +a and finally B to Power +3 So What do we see Here How many Terms + + align:start position:0% +3 So What do we see Here How many Terms + + + align:start position:0% +3 So What do we see Here How many Terms +are there that have exactly two times a + + align:start position:0% +are there that have exactly two times a + + + align:start position:0% +are there that have exactly two times a +one Times B it's like we have a set of + + align:start position:0% +one Times B it's like we have a set of + + + align:start position:0% +one Times B it's like we have a set of +three Elements + + align:start position:0% +three Elements + + + align:start position:0% +three Elements +Right Three positions And I two of them + + align:start position:0% +Right Three positions And I two of them + + + align:start position:0% +Right Three positions And I two of them +to Out Of A subset + + align:start position:0% + + + + align:start position:0% + +is of + + align:start position:0% + + + + align:start position:0% + +Terms + + align:start position:0% + + + + align:start position:0% + +k + + align:start position:0% + + + + align:start position:0% + +of of + + align:start position:0% +of of + + + align:start position:0% +of of + + align:start position:0% + + + + align:start position:0% + +Oops of L + + align:start position:0% + + + + align:start position:0% + +sequences that The Following + + align:start position:0% +sequences that The Following + + + align:start position:0% +sequences that The Following +property + + align:start position:0% + + + + align:start position:0% + +k n + + align:start position:0% +k n + + + align:start position:0% +k n +K's + + align:start position:0% +K's + + + align:start position:0% +K's +That's easy to Count is equ we h + + align:start position:0% +That's easy to Count is equ we h + + + align:start position:0% +That's easy to Count is equ we h +Before + + align:start position:0% + + + + align:start position:0% + +binomial is + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +balous + + align:start position:0% + + + + align:start position:0% + +stu + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +Technique de of + + align:start position:0% +Technique de of + + + align:start position:0% +Technique de of +Cards + + align:start position:0% +Cards + + + align:start position:0% +Cards +use + + align:start position:0% + + + + align:start position:0% + +Ty + + align:start position:0% + + + + align:start position:0% + +52s + + align:start position:0% +52s + + + align:start position:0% +52s +and a card itself actually has a + + align:start position:0% +and a card itself actually has a + + + align:start position:0% +and a card itself actually has a +Suit and the Suit can be Something That + + align:start position:0% +Suit and the Suit can be Something That + + + align:start position:0% +Suit and the Suit can be Something That +Looks Like This Which is called spad s + + align:start position:0% +Looks Like This Which is called spad s + + + align:start position:0% +Looks Like This Which is called spad s +of spad we have Another symbol Which is + + align:start position:0% +of spad we have Another symbol Which is + + + align:start position:0% +of spad we have Another symbol Which is +this Heart + + align:start position:0% + + + + align:start position:0% + +CLS we Diamonds and besides Suit card + + align:start position:0% +CLS we Diamonds and besides Suit card + + + align:start position:0% +CLS we Diamonds and besides Suit card +also has value and the values ​​are Range + + align:start position:0% +also has value and the values ​​are Range + + + align:start position:0% +also has value and the values ​​are Range +from 2 3 f all the way up to 10 then we + + align:start position:0% +from 2 3 f all the way up to 10 then we + + + align:start position:0% +from 2 3 f all the way up to 10 then we +have a special symbol Special value + + align:start position:0% +have a special symbol Special value + + + align:start position:0% +have a special symbol Special value +Which is called the Jack we got a Queen + + align:start position:0% +Which is called the Jack we got a Queen + + + align:start position:0% +Which is called the Jack we got a Queen +And The King and finally The Ace and in + + align:start position:0% +And The King and finally The Ace and in + + + align:start position:0% +And The King and finally The Ace and in +Total we have 13 Possible + + align:start position:0% +Total we have 13 Possible + + + align:start position:0% +Total we have 13 Possible +values ​​So you can see that we have Four + + align:start position:0% +values ​​So you can see that we have Four + + + align:start position:0% +values ​​So you can see that we have Four +Times Because We Four Different Suits 4 + + align:start position:0% +Times Because We Four Different Suits 4 + + + align:start position:0% +Times Because We Four Different Suits 4 +Times 13 is 52 Different Cards And that + + align:start position:0% +Times 13 is 52 Different Cards And that + + + align:start position:0% +Times 13 is 52 Different Cards And that +makes up a Deck so We're Going To Look + + align:start position:0% +makes up a Deck so We're Going To Look + + + align:start position:0% +makes up a Deck so We're Going To Look +at hands and a + + align:start position:0% +at hands and a + + + align:start position:0% +at hands and a +hand is actually a collection a set Of + + align:start position:0% +hand is actually a collection a set Of + + + align:start position:0% +hand is actually a collection a set Of +Five Cars + + align:start position:0% + + + + align:start position:0% + +do not worry the Order of the CS in + + align:start position:0% +do not worry the Order of the CS in + + + align:start position:0% +do not worry the Order of the CS in +hand + + align:start position:0% +hand + + + align:start position:0% +hand +pered order + + align:start position:0% +pered order + + + align:start position:0% +pered order +is subset of + + align:start position:0% +is subset of + + + align:start position:0% +is subset of +Cards How + + align:start position:0% + + + + align:start position:0% + +hand subs ofs out of of + + align:start position:0% +hand subs ofs out of of + + + align:start position:0% +hand subs ofs out of of +52s we canuse subset rule and we + + align:start position:0% +52s we canuse subset rule and we + + + align:start position:0% +52s we canuse subset rule and we +binomial 52 choose + + align:start position:0% + + + + align:start position:0% + +5 Which is By the way a lot so Let Me + + align:start position:0% +5 Which is By the way a lot so Let Me + + + align:start position:0% +5 Which is By the way a lot so Let Me +Write it out as well it's about 2 and + + align:start position:0% +Write it out as well it's about 2 and + + + align:start position:0% +Write it out as well it's about 2 and +half + + align:start position:0% + + + + align:start position:0% + +Million so We are interested in When We + + align:start position:0% +Million so We are interested in When We + + + align:start position:0% +Million so We are interested in When We +Play poker + + align:start position:0% +Play poker + + + align:start position:0% +Play poker +If do that eh in really good hands so + + align:start position:0% +If do that eh in really good hands so + + + align:start position:0% +If do that eh in really good hands so +We Like four of a kind Which means That + + align:start position:0% +We Like four of a kind Which means That + + + align:start position:0% +We Like four of a kind Which means That +We + + align:start position:0% +We + + + align:start position:0% +We +have Cards that actually have the same + + align:start position:0% +have Cards that actually have the same + + + align:start position:0% +have Cards that actually have the same +value or we have Cards + + align:start position:0% +value or we have Cards + + + align:start position:0% +value or we have Cards +that hands that have What We Call a Full + + align:start position:0% +that hands that have What We Call a Full + + + align:start position:0% +that hands that have What We Call a Full +House will Count Those In A Moment or + + align:start position:0% +House will Count Those In A Moment or + + + align:start position:0% +House will Count Those In A Moment or +other Kinds Of combinations and the rare + + align:start position:0% +other Kinds Of combinations and the rare + + + align:start position:0% +other Kinds Of combinations and the rare +The Combination Is In Your + + align:start position:0% +The Combination Is In Your + + + align:start position:0% +The Combination Is In Your +Hand The Higher Better hand is more like + + align:start position:0% +Hand The Higher Better hand is more like + + + align:start position:0% +Hand The Higher Better hand is more like +poker game + + align:start position:0% +poker game + + + align:start position:0% +poker game +do + + align:start position:0% + + + + align:start position:0% + +already Let's + + align:start position:0% +already Let's + + + align:start position:0% +already Let's +example + + align:start position:0% +example + + + align:start position:0% +example +of of kind we going to compute We will + + align:start position:0% +of of kind we going to compute We will + + + align:start position:0% +of of kind we going to compute We will +that we need to do use Combination of + + align:start position:0% +that we need to do use Combination of + + + align:start position:0% +that we need to do use Combination of +all these + + align:start position:0% + + + + align:start position:0% + +Rules + + align:start position:0% + + + + align:start position:0% + +Okay for of a + + align:start position:0% +Okay for of a + + + align:start position:0% +Okay for of a +kind is the Special hand Where we + + align:start position:0% +kind is the Special hand Where we + + + align:start position:0% +kind is the Special hand Where we +have f of one Kind of + + align:start position:0% + + + + align:start position:0% + +value + + align:start position:0% + + + + align:start position:0% + +There Only f Different Suits the Fifth + + align:start position:0% +There Only f Different Suits the Fifth + + + align:start position:0% +There Only f Different Suits the Fifth +card automatically a Different + + align:start position:0% +card automatically a Different + + + align:start position:0% +card automatically a Different +value + + align:start position:0% +value + + + align:start position:0% +value +ex we will + + align:start position:0% +ex we will + + + align:start position:0% +ex we will +have the e of spad And The N of Diamonds + + align:start position:0% +have the e of spad And The N of Diamonds + + + align:start position:0% +have the e of spad And The N of Diamonds +and all the other The e of Diamond The e + + align:start position:0% +and all the other The e of Diamond The e + + + align:start position:0% +and all the other The e of Diamond The e +Of Hearts And The e of clubs + + align:start position:0% + + + + align:start position:0% + +And how do we Count These types of hands + + align:start position:0% +And how do we Count These types of hands + + + align:start position:0% +And how do we Count These types of hands +We're Going To Look For A + + align:start position:0% +We're Going To Look For A + + + align:start position:0% +We're Going To Look For A +representation of How can we represent + + align:start position:0% +representation of How can we represent + + + align:start position:0% +representation of How can we represent +such hands such object so we have to + + align:start position:0% +such hands such object so we have to + + + align:start position:0% +such hands such object so we have to +Count a special Type of object a special + + align:start position:0% +Count a special Type of object a special + + + align:start position:0% +Count a special Type of object a special +Kind of Poker hand and in order to do + + align:start position:0% +Kind of Poker hand and in order to do + + + align:start position:0% +Kind of Poker hand and in order to do +that we going to look for a way to + + align:start position:0% +that we going to look for a way to + + + align:start position:0% +that we going to look for a way to +represent These objects And then in such a + + align:start position:0% +represent These objects And then in such a + + + align:start position:0% +represent These objects And then in such a +way That We Can Count Them very + + align:start position:0% +way That We Can Count Them very + + + align:start position:0% +way That We Can Count Them very +Easily and That's really The trick in + + align:start position:0% +Easily and That's really The trick in + + + align:start position:0% +Easily and That's really The trick in +order to solve Kinds Of counting + + align:start position:0% +order to solve Kinds Of counting + + + align:start position:0% +order to solve Kinds Of counting +problems so The representation That We + + align:start position:0% +problems so The representation That We + + + align:start position:0% +problems so The representation That We +have Here is We Can + + align:start position:0% +have Here is We Can + + + align:start position:0% +have Here is We Can +choose First Of All We Can choose the + + align:start position:0% +choose First Of All We Can choose the + + + align:start position:0% +choose First Of All We Can choose the +value of the f Kind of the + + align:start position:0% +value of the f Kind of the + + + align:start position:0% +value of the f Kind of the +cards So how many choices Do I + + align:start position:0% +cards So how many choices Do I + + + align:start position:0% +cards So how many choices Do I +have well + + align:start position:0% +have well + + + align:start position:0% +have well +I Any + + align:start position:0% +I Any + + + align:start position:0% +I Any +Choice 13 Different values ​​so I have 13 + + align:start position:0% +Choice 13 Different values ​​so I have 13 + + + align:start position:0% +Choice 13 Different values ​​so I have 13 +choices so That's Easy + + align:start position:0% +choices so That's Easy + + + align:start position:0% +choices so That's Easy +Eh secondly Eh I can choose the value of + + align:start position:0% +Eh secondly Eh I can choose the value of + + + align:start position:0% +Eh secondly Eh I can choose the value of +the extra + + align:start position:0% + + + + align:start position:0% + +card So how many choices Do I have Here + + align:start position:0% +card So how many choices Do I have Here + + + align:start position:0% +card So how many choices Do I have Here +well + + align:start position:0% +well + + + align:start position:0% +well +erm the four of a kind already + + align:start position:0% + + + + align:start position:0% + +even so I have 12 choices + + align:start position:0% +even so I have 12 choices + + + align:start position:0% +even so I have 12 choices +and lastly I can represent I need to + + align:start position:0% +and lastly I can represent I need to + + + align:start position:0% +and lastly I can represent I need to +Still represent the Suit of the extra + + align:start position:0% +Still represent the Suit of the extra + + + align:start position:0% +Still represent the Suit of the extra +card so I also want to know the Suit of + + align:start position:0% +card so I also want to know the Suit of + + + align:start position:0% +card so I also want to know the Suit of +the extra card And how many choices Do I + + align:start position:0% +the extra card And how many choices Do I + + + align:start position:0% +the extra card And how many choices Do I +have w i can choose Any Of Those Four so + + align:start position:0% +have w i can choose Any Of Those Four so + + + align:start position:0% +have w i can choose Any Of Those Four so +That's + + align:start position:0% +That's + + + align:start position:0% +That's +Four so essentially what we constructed + + align:start position:0% +Four so essentially what we constructed + + + align:start position:0% +Four so essentially what we constructed +Here is a mapping uh by using this + + align:start position:0% +Here is a mapping uh by using this + + + align:start position:0% +Here is a mapping uh by using this +representation + + align:start position:0% +representation + + + align:start position:0% +representation +eh and the mappings US + + align:start position:0% +eh and the mappings US + + + align:start position:0% +eh and the mappings US +eh is + + align:start position:0% + + + + align:start position:0% + +follows + + align:start position:0% + + + + align:start position:0% + +Keep the mapping Goes from poker Hands + + align:start position:0% +Keep the mapping Goes from poker Hands + + + align:start position:0% +Keep the mapping Goes from poker Hands +of hands + + align:start position:0% +of hands + + + align:start position:0% +of hands +to Hands of kind to this + + align:start position:0% +to Hands of kind to this + + + align:start position:0% +to Hands of kind to this +representation Let's write Out we have f + + align:start position:0% +representation Let's write Out we have f + + + align:start position:0% +representation Let's write Out we have f +of a + + align:start position:0% +of a + + + align:start position:0% +of a +kind And then we have a function a + + align:start position:0% +kind And then we have a function a + + + align:start position:0% +kind And then we have a function a +mapping f that goes to this + + align:start position:0% +mapping f that goes to this + + + align:start position:0% +mapping f that goes to this +representation we will have the first + + align:start position:0% +representation we will have the first + + + align:start position:0% +representation we will have the first +entry the value One and the value 2 and + + align:start position:0% +entry the value One and the value 2 and + + + align:start position:0% +entry the value One and the value 2 and +then the value + + align:start position:0% + + + + align:start position:0% + +3 for example + + align:start position:0% +3 for example + + + align:start position:0% +3 for example +Take Hands of + + align:start position:0% +Take Hands of + + + align:start position:0% +Take Hands of +Cards + + align:start position:0% + + + + align:start position:0% + +of second is of the n Diamonds + + align:start position:0% + + + + align:start position:0% + +card finally Suit Select + + align:start position:0% +card finally Suit Select + + + align:start position:0% +card finally Suit Select +ex Diamond is + + align:start position:0% + + + + align:start position:0% + +ex + + align:start position:0% + + + + align:start position:0% + +of + + align:start position:0% + + + + align:start position:0% + +chos According to + + align:start position:0% +chos According to + + + align:start position:0% +chos According to +representation we 13 choices the first + + align:start position:0% +representation we 13 choices the first + + + align:start position:0% +representation we 13 choices the first +value given this First value we have + + align:start position:0% +value given this First value we have + + + align:start position:0% +value given this First value we have +choices the second + + align:start position:0% +choices the second + + + align:start position:0% +choices the second +value i + + align:start position:0% + + + + align:start position:0% + +choices So This Is The generalized + + align:start position:0% +choices So This Is The generalized + + + align:start position:0% +choices So This Is The generalized +product rule that I'm using so we see + + align:start position:0% +product rule that I'm using so we see + + + align:start position:0% +product rule that I'm using so we see +that the Number of + + align:start position:0% +that the Number of + + + align:start position:0% +that the Number of +sequences is equal to 13 12 4 Turn is + + align:start position:0% +sequences is equal to 13 12 4 Turn is + + + align:start position:0% +sequences is equal to 13 12 4 Turn is +equ + + align:start position:0% +equ + + + align:start position:0% +equ +624 If divide It over the Total Number + + align:start position:0% +624 If divide It over the Total Number + + + align:start position:0% +624 If divide It over the Total Number +of Cards er + + align:start position:0% +of Cards er + + + align:start position:0% +of Cards er +so How did we do this this is the + + align:start position:0% +so How did we do this this is the + + + align:start position:0% +so How did we do this this is the +generalized product + + align:start position:0% + + + + align:start position:0% + +rule If this number of the Total Number + + align:start position:0% +rule If this number of the Total Number + + + align:start position:0% +rule If this number of the Total Number +ofs fraction of + + align:start position:0% + + + + align:start position:0% + +ok do More Or + + align:start position:0% + + + + align:start position:0% + +also like to know how many full + + align:start position:0% +also like to know how many full + + + align:start position:0% +also like to know how many full +houses are Full House is Special + + align:start position:0% +houses are Full House is Special + + + align:start position:0% +houses are Full House is Special +hand Cards of one value two CS of + + align:start position:0% +hand Cards of one value two CS of + + + align:start position:0% +hand Cards of one value two CS of +Another value er so + + align:start position:0% +Another value er so + + + align:start position:0% +Another value er so + + align:start position:0% + + + + align:start position:0% + +How many are there Again we to use + + align:start position:0% +How many are there Again we to use + + + align:start position:0% +How many are there Again we to use +exa principle we going to find + + align:start position:0% +exa principle we going to find + + + align:start position:0% +exa principle we going to find +representation of this Type of hand we + + align:start position:0% +representation of this Type of hand we + + + align:start position:0% +representation of this Type of hand we +Cards of one + + align:start position:0% +Cards of one + + + align:start position:0% +Cards of one +value + + align:start position:0% +value + + + align:start position:0% +value +and two + + align:start position:0% +and two + + + align:start position:0% +and two +Cards of + + align:start position:0% + + + + align:start position:0% + +Another + + align:start position:0% + + + + align:start position:0% + +ex hand + + align:start position:0% + + + + align:start position:0% + +that is also + + align:start position:0% + + + + align:start position:0% + +Diamond and uh Another example Could Be + + align:start position:0% +Diamond and uh Another example Could Be + + + align:start position:0% +Diamond and uh Another example Could Be +say a Five of Diamonds And The Five of + + align:start position:0% +say a Five of Diamonds And The Five of + + + align:start position:0% +say a Five of Diamonds And The Five of +hearts Five of clubs Seven of Hearts And + + align:start position:0% +hearts Five of clubs Seven of Hearts And + + + align:start position:0% +hearts Five of clubs Seven of Hearts And +also a seven of + + align:start position:0% +also a seven of + + + align:start position:0% +also a seven of +Club so now you can see that it's very + + align:start position:0% +Club so now you can see that it's very + + + align:start position:0% +Club so now you can see that it's very +easy to represent this Right we can + + align:start position:0% +easy to represent this Right we can + + + align:start position:0% +easy to represent this Right we can +uh you know we can start grouping things + + align:start position:0% +uh you know we can start grouping things + + + align:start position:0% +uh you know we can start grouping things +Together We Can Say represent this by + + align:start position:0% +Together We Can Say represent this by + + + align:start position:0% +Together We Can Say represent this by +First taking uh the value of the + + align:start position:0% +First taking uh the value of the + + + align:start position:0% +First taking uh the value of the +uh of the ofs that + + align:start position:0% +uh of the ofs that + + + align:start position:0% +uh of the ofs that +I then I want to indicate in second term + + align:start position:0% +I then I want to indicate in second term + + + align:start position:0% +I then I want to indicate in second term +in my sequence in my representation + + align:start position:0% +in my sequence in my representation + + + align:start position:0% +in my sequence in my representation +Which Suits did I Use over here i used + + align:start position:0% +Which Suits did I Use over here i used + + + align:start position:0% +Which Suits did I Use over here i used +Club spades and Diamond so It's set Club + + align:start position:0% +Club spades and Diamond so It's set Club + + + align:start position:0% +Club spades and Diamond so It's set Club +spad and + + align:start position:0% +spad and + + + align:start position:0% +spad and +Diamond and now I also have a pair + + align:start position:0% +Diamond and now I also have a pair + + + align:start position:0% +Diamond and now I also have a pair +like the the value + + align:start position:0% +like the the value + + + align:start position:0% +like the the value +Jack + + align:start position:0% + + + + align:start position:0% + +the formal definition of the + + align:start position:0% +the formal definition of the + + + align:start position:0% +the formal definition of the +representation see that you could do + + align:start position:0% +representation see that you could do + + + align:start position:0% +representation see that you could do +like this Often how we start out on + + align:start position:0% +like this Often how we start out on + + + align:start position:0% +like this Often how we start out on +piece of paper try to + + align:start position:0% +piece of paper try to + + + align:start position:0% +piece of paper try to +do hopefully it + + align:start position:0% +do hopefully it + + + align:start position:0% +do hopefully it +works we Here we Diamonds + + align:start position:0% + + + + align:start position:0% + +CLS + + align:start position:0% + + + + align:start position:0% + +Suits + + align:start position:0% +Suits + + + align:start position:0% +Suits +Ok + + align:start position:0% +Ok + + + align:start position:0% +Ok +representation + + align:start position:0% + + + + align:start position:0% + +is the follows Just + + align:start position:0% + + + + align:start position:0% + +started + + align:start position:0% + + + + align:start position:0% + +how choices do this Any of 1 Possible + + align:start position:0% +how choices do this Any of 1 Possible + + + align:start position:0% +how choices do this Any of 1 Possible +val + + align:start position:0% + + + + align:start position:0% + +choices the second part + + align:start position:0% + + + + align:start position:0% + +isit + + align:start position:0% + + + + align:start position:0% + +representation choices subset Els + + align:start position:0% + + + + align:start position:0% + +of + + align:start position:0% + + + + align:start position:0% + +subset + + align:start position:0% + + + + align:start position:0% + +choices the last part is the value of + + align:start position:0% +choices the last part is the value of + + + align:start position:0% +choices the last part is the value of +the Pair that I have of the two Cars + + align:start position:0% +the Pair that I have of the two Cars + + + align:start position:0% +the Pair that I have of the two Cars +That are having the same + + align:start position:0% + + + + align:start position:0% + +value now how many choices Do I have + + align:start position:0% +value now how many choices Do I have + + + align:start position:0% +value now how many choices Do I have +Here well I have to be a little bit + + align:start position:0% +Here well I have to be a little bit + + + align:start position:0% +Here well I have to be a little bit +careful though I Just Want To Make sure + + align:start position:0% +careful though I Just Want To Make sure + + + align:start position:0% +careful though I Just Want To Make sure +that I Do The Right reasoning Here eh I + + align:start position:0% +that I Do The Right reasoning Here eh I + + + align:start position:0% +that I Do The Right reasoning Here eh I +know that there still because this + + align:start position:0% +know that there still because this + + + align:start position:0% +know that there still because this +Because I chose A Triple of Cars of the + + align:start position:0% +Because I chose A Triple of Cars of the + + + align:start position:0% +Because I chose A Triple of Cars of the +same value for example over here I chose + + align:start position:0% +same value for example over here I chose + + + align:start position:0% +same value for example over here I chose +all these twos but I still have One card + + align:start position:0% +all these twos but I still have One card + + + align:start position:0% +all these twos but I still have One card +in my Deck Which has a two actually Here + + align:start position:0% +in my Deck Which has a two actually Here + + + align:start position:0% +in my Deck Which has a two actually Here +I've Chosen Club spad and Diamonds so + + align:start position:0% +I've Chosen Club spad and Diamonds so + + + align:start position:0% +I've Chosen Club spad and Diamonds so +The One That is missing Is The Two Of + + align:start position:0% +The One That is missing Is The Two Of + + + align:start position:0% +The One That is missing Is The Two Of +Hearts so could possibly choose The Two + + align:start position:0% +Hearts so could possibly choose The Two + + + align:start position:0% +Hearts so could possibly choose The Two +Of Hearts but wait a minute If I choose + + align:start position:0% +Of Hearts but wait a minute If I choose + + + align:start position:0% +Of Hearts but wait a minute If I choose +The Two Of Hearts How can I make a pair + + align:start position:0% +The Two Of Hearts How can I make a pair + + + align:start position:0% +The Two Of Hearts How can I make a pair +That's not Possible Right Because I + + align:start position:0% +That's not Possible Right Because I + + + align:start position:0% +That's not Possible Right Because I +already Chosen All The Other twos so + + align:start position:0% +already Chosen All The Other twos so + + + align:start position:0% +already Chosen All The Other twos so +There's No other Two to match to find a + + align:start position:0% +There's No other Two to match to find a + + + align:start position:0% +There's No other Two to match to find a +pair actually can choose this particular + + align:start position:0% +pair actually can choose this particular + + + align:start position:0% +pair actually can choose this particular +value of this + + align:start position:0% +value of this + + + align:start position:0% +value of this +Triple for the Pair so but all the other + + align:start position:0% +Triple for the Pair so but all the other + + + align:start position:0% +Triple for the Pair so but all the other +values ​​are Possible so I have 12 choices + + align:start position:0% +values ​​are Possible so I have 12 choices + + + align:start position:0% +values ​​are Possible so I have 12 choices +One Less than The One That already + + align:start position:0% +One Less than The One That already + + + align:start position:0% +One Less than The One That already +Chosen for the + + align:start position:0% +Chosen for the + + + align:start position:0% +Chosen for the +Triple n then similarly I can choose + + align:start position:0% +Triple n then similarly I can choose + + + align:start position:0% +Triple n then similarly I can choose +Suits of the Pair And how many choices + + align:start position:0% +Suits of the Pair And how many choices + + + align:start position:0% +Suits of the Pair And how many choices +Do I have Look at Every + + align:start position:0% +Do I have Look at Every + + + align:start position:0% +Do I have Look at Every +subset that I can size Out Of The + + align:start position:0% +subset that I can size Out Of The + + + align:start position:0% +subset that I can size Out Of The +Suits subset rule and find that This + + align:start position:0% +Suits subset rule and find that This + + + align:start position:0% +Suits subset rule and find that This +Is Is + + align:start position:0% + + + + align:start position:0% + +equ now we going to multiply all of + + align:start position:0% +equ now we going to multiply all of + + + align:start position:0% +equ now we going to multiply all of +these together we use generalized + + align:start position:0% +these together we use generalized + + + align:start position:0% +these together we use generalized +product rule + + align:start position:0% +product rule + + + align:start position:0% +product rule +Again we we mapping hands Full House to + + align:start position:0% +Again we we mapping hands Full House to + + + align:start position:0% +Again we we mapping hands Full House to +types of representations + + align:start position:0% +types of representations + + + align:start position:0% +types of representations +representation and this mapping is B The + + align:start position:0% +representation and this mapping is B The + + + align:start position:0% +representation and this mapping is B The +Number of full houses exactly equal to + + align:start position:0% +Number of full houses exactly equal to + + + align:start position:0% +Number of full houses exactly equal to +the Number of + + align:start position:0% +the Number of + + + align:start position:0% +the Number of +these + + align:start position:0% +these + + + align:start position:0% +these +representations and by the general + + align:start position:0% +representations and by the general + + + align:start position:0% +representations and by the general +product rule I can choose the first + + align:start position:0% +product rule I can choose the first + + + align:start position:0% +product rule I can choose the first +entry of such sequence in 13 ways the + + align:start position:0% +entry of such sequence in 13 ways the + + + align:start position:0% +entry of such sequence in 13 ways the +second One given The First One in f + + align:start position:0% +second One given The First One in f + + + align:start position:0% +second One given The First One in f +ways This one I can choose in ways + + align:start position:0% + + + + align:start position:0% + +given + + align:start position:0% +given + + + align:start position:0% +given +ru + + align:start position:0% + + + + align:start position:0% + +1 equ + + align:start position:0% + + + + align:start position:0% + +3744 of k lik One + + align:start position:0% + + + + align:start position:0% + +ofon + + align:start position:0% + + + + align:start position:0% + +much + + align:start position:0% +much + + + align:start position:0% +much +More + + align:start position:0% +More + + + align:start position:0% +More +House let's do Another example hand with + + align:start position:0% +House let's do Another example hand with + + + align:start position:0% +House let's do Another example hand with +two pairs we Ty of reasoning + + align:start position:0% +two pairs we Ty of reasoning + + + align:start position:0% +two pairs we Ty of reasoning +Pretty + + align:start position:0% +Pretty + + + align:start position:0% +Pretty +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +May do the + + align:start position:0% + + + + align:start position:0% + +Thing Lot of Care so Maybe you can + + align:start position:0% +Thing Lot of Care so Maybe you can + + + align:start position:0% +Thing Lot of Care so Maybe you can +already see What's happening When I + + align:start position:0% +already see What's happening When I + + + align:start position:0% +already see What's happening When I +start reasoning in the exact Same Way as + + align:start position:0% +start reasoning in the exact Same Way as + + + align:start position:0% +start reasoning in the exact Same Way as +Before so Let Me First define What I + + align:start position:0% +Before so Let Me First define What I + + + align:start position:0% +Before so Let Me First define What I +want to Count It's a hands that have + + align:start position:0% +want to Count It's a hands that have + + + align:start position:0% +want to Count It's a hands that have +exactly two + + align:start position:0% +exactly two + + + align:start position:0% +exactly two +pairs So What Does that Mean It means + + align:start position:0% +pairs So What Does that Mean It means + + + align:start position:0% +pairs So What Does that Mean It means +that + + align:start position:0% +that + + + align:start position:0% +that +uh that is that we have two + + align:start position:0% +uh that is that we have two + + + align:start position:0% +uh that is that we have two +Cards of one value and Another two cards + + align:start position:0% + + + + align:start position:0% + +Let's start Out Before We + + align:start position:0% +Let's start Out Before We + + + align:start position:0% +Let's start Out Before We +Do Out + + align:start position:0% +Do Out + + + align:start position:0% +Do Out +representation and + + align:start position:0% +representation and + + + align:start position:0% +representation and +see we can do this + + align:start position:0% + + + + align:start position:0% + +properly we use exa technique + + align:start position:0% +properly we use exa technique + + + align:start position:0% +properly we use exa technique +so First of we choose the value of the + + align:start position:0% +so First of we choose the value of the + + + align:start position:0% +so First of we choose the value of the +first + + align:start position:0% + + + + align:start position:0% + +Pair How many ways can I + + align:start position:0% +Pair How many ways can I + + + align:start position:0% +Pair How many ways can I +do + + align:start position:0% +do + + + align:start position:0% +do +Dos Any Possible value is + + align:start position:0% + + + + align:start position:0% + +possible I need to + + align:start position:0% +possible I need to + + + align:start position:0% +possible I need to +choose + + align:start position:0% + + + + align:start position:0% + +ofir + + align:start position:0% +ofir + + + align:start position:0% +ofir +How many ways can I do + + align:start position:0% +How many ways can I do + + + align:start position:0% +How many ways can I do +Tech Possible to Els out of + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + + align:start position:0% + +of + + align:start position:0% + + + + align:start position:0% + +and because the second definition a + + align:start position:0% +and because the second definition a + + + align:start position:0% +and because the second definition a +Different value The One In The First + + align:start position:0% +Different value The One In The First + + + align:start position:0% +Different value The One In The First +Pair al Chosen One value choices + + align:start position:0% + + + + align:start position:0% + +left Number of Suits That are Possible + + align:start position:0% +left Number of Suits That are Possible + + + align:start position:0% +left Number of Suits That are Possible +for the second + + align:start position:0% + + + + align:start position:0% + +Pair and That's The + + align:start position:0% +Pair and That's The + + + align:start position:0% +Pair and That's The +Same number as we have For The First + + align:start position:0% +Same number as we have For The First + + + align:start position:0% +Same number as we have For The First +Pair so we have Number of Suits of the + + align:start position:0% +Pair so we have Number of Suits of the + + + align:start position:0% +Pair so we have Number of Suits of the +second Pair Again we need to choose two + + align:start position:0% +second Pair Again we need to choose two + + + align:start position:0% +second Pair Again we need to choose two +Suits out of the complete set of Suits + + align:start position:0% +Suits out of the complete set of Suits + + + align:start position:0% +Suits out of the complete set of Suits +Which has Four possibilities so It's + + align:start position:0% +Which has Four possibilities so It's + + + align:start position:0% +Which has Four possibilities so It's +f now we + + align:start position:0% + + + + align:start position:0% + +canice + + align:start position:0% + + + + align:start position:0% + +Pair f f also + + align:start position:0% +Pair f f also + + + align:start position:0% +Pair f f also +value actually I did not Write it Down + + align:start position:0% +value actually I did not Write it Down + + + align:start position:0% +value actually I did not Write it Down +but if we talk about the hands with two + + align:start position:0% +but if we talk about the hands with two + + + align:start position:0% +but if we talk about the hands with two +pairs we Mean two Cards of one value two + + align:start position:0% +pairs we Mean two Cards of one value two + + + align:start position:0% +pairs we Mean two Cards of one value two +Cards of Another value and the Fifth + + align:start position:0% +Cards of Another value and the Fifth + + + align:start position:0% +Cards of Another value and the Fifth +card extra card has yet Another value + + align:start position:0% +card extra card has yet Another value + + + align:start position:0% +card extra card has yet Another value +because otherwise He would have a Full + + align:start position:0% +because otherwise He would have a Full + + + align:start position:0% +because otherwise He would have a Full +House we + + align:start position:0% +House we + + + align:start position:0% +House we +counted Okay value of the extra + + align:start position:0% + + + + align:start position:0% + +c well Chen already two values ​​The One + + align:start position:0% +c well Chen already two values ​​The One + + + align:start position:0% +c well Chen already two values ​​The One +For The First pa the one of the second + + align:start position:0% +For The First pa the one of the second + + + align:start position:0% +For The First pa the one of the second +Pair so There 11 choices left and + + align:start position:0% +Pair so There 11 choices left and + + + align:start position:0% +Pair so There 11 choices left and +finally I can choose a Suit of the extra + + align:start position:0% +finally I can choose a Suit of the extra + + + align:start position:0% +finally I can choose a Suit of the extra +card well I + + align:start position:0% +card well I + + + align:start position:0% +card well I +have one out of Four choices for my + + align:start position:0% +have one out of Four choices for my + + + align:start position:0% +have one out of Four choices for my +Suit so Again We Can Use the general + + align:start position:0% +Suit so Again We Can Use the general + + + align:start position:0% +Suit so Again We Can Use the general +product rule and we can say that we have + + align:start position:0% +product rule and we can say that we have + + + align:start position:0% +product rule and we can say that we have +13 choices for my first + + align:start position:0% + + + + align:start position:0% + +chice + + align:start position:0% +chice + + + align:start position:0% +chice +Choice choices + + align:start position:0% +Choice choices + + + align:start position:0% +Choice choices +second choices The + + align:start position:0% + + + + align:start position:0% + +Third + + align:start position:0% + + + + align:start position:0% + +product + + align:start position:0% + + + + align:start position:0% + +is Number of the + + align:start position:0% +is Number of the + + + align:start position:0% +is Number of the +pairs + + align:start position:0% + + + + align:start position:0% + +Reasonable + + align:start position:0% + + + + align:start position:0% + +I Number of hands + + align:start position:0% +I Number of hands + + + align:start position:0% +I Number of hands +pairs What Do I need to check in order + + align:start position:0% +pairs What Do I need to check in order + + + align:start position:0% +pairs What Do I need to check in order +to make that to make That Is + + align:start position:0% +to make that to make That Is + + + align:start position:0% +to make that to make That Is +True I need + + align:start position:0% +True I need + + + align:start position:0% +True I need +to I need to + + align:start position:0% + + + + align:start position:0% + +ess + + align:start position:0% + + + + align:start position:0% + +mapp + + align:start position:0% + + + + align:start position:0% + +property Let + + align:start position:0% + + + + align:start position:0% + +Me + + align:start position:0% + + + + align:start position:0% + +game + + align:start position:0% +game + + + align:start position:0% +game +ess had two RS That We Could choose and + + align:start position:0% +ess had two RS That We Could choose and + + + align:start position:0% +ess had two RS That We Could choose and +Them on positions With No no shared R + + align:start position:0% +Them on positions With No no shared R + + + align:start position:0% +Them on positions With No no shared R +shared columns and here we have sort of + + align:start position:0% +shared columns and here we have sort of + + + align:start position:0% +shared columns and here we have sort of +two pairs With No shared Suit With No + + align:start position:0% +two pairs With No shared Suit With No + + + align:start position:0% +two pairs With No shared Suit With No +shared values ​​What can we do we can + + align:start position:0% +shared values ​​What can we do we can + + + align:start position:0% +shared values ​​What can we do we can +actually interchange the first and the + + align:start position:0% +actually interchange the first and the + + + align:start position:0% +actually interchange the first and the +second Pair so as an + + align:start position:0% + + + + align:start position:0% + +example We Can representations M let ex + + align:start position:0% +example We Can representations M let ex + + + align:start position:0% +example We Can representations M let ex +ex chose the the Pair And then I'm + + align:start position:0% +ex chose the the Pair And then I'm + + + align:start position:0% +ex chose the the Pair And then I'm +choosing the set Diamonds and clubs for + + align:start position:0% +choosing the set Diamonds and clubs for + + + align:start position:0% +choosing the set Diamonds and clubs for +the Suits Of Those and say the second + + align:start position:0% +the Suits Of Those and say the second + + + align:start position:0% +the Suits Of Those and say the second +pair is a Queen of Diamonds and Hearts + + align:start position:0% +pair is a Queen of Diamonds and Hearts + + + align:start position:0% +pair is a Queen of Diamonds and Hearts +And finally I have an Ace of clubs this + + align:start position:0% +And finally I have an Ace of clubs this + + + align:start position:0% +And finally I have an Ace of clubs this +Beer sequence According to + + align:start position:0% +Beer sequence According to + + + align:start position:0% +Beer sequence According to +representation + + align:start position:0% + + + + align:start position:0% + +Queen For The First + + align:start position:0% +Queen For The First + + + align:start position:0% +Queen For The First +Pair we Diamond + + align:start position:0% +Pair we Diamond + + + align:start position:0% +Pair we Diamond +In + + align:start position:0% + + + + align:start position:0% + +we Diamonds + + align:start position:0% + + + + align:start position:0% + +CLS + + align:start position:0% + + + + align:start position:0% + +Fin of + + align:start position:0% + + + + align:start position:0% + +CLS to exactly the same hand We Just We + + align:start position:0% +CLS to exactly the same hand We Just We + + + align:start position:0% +CLS to exactly the same hand We Just We +Just interchange the first and the + + align:start position:0% +Just interchange the first and the + + + align:start position:0% +Just interchange the first and the +second Pair Now This is a Kind of uh + + align:start position:0% +second Pair Now This is a Kind of uh + + + align:start position:0% +second Pair Now This is a Kind of uh +Problem or like like a mental sort of uh + + align:start position:0% +Problem or like like a mental sort of uh + + + align:start position:0% +Problem or like like a mental sort of uh +eh confusion that very Easily happens + + align:start position:0% +eh confusion that very Easily happens + + + align:start position:0% +eh confusion that very Easily happens +This Is A Rather Easy example Where You + + align:start position:0% +This Is A Rather Easy example Where You + + + align:start position:0% +This Is A Rather Easy example Where You +can see it but if you do counting eh we + + align:start position:0% +can see it but if you do counting eh we + + + align:start position:0% +can see it but if you do counting eh we +really have to take care That We Make + + align:start position:0% +really have to take care That We Make + + + align:start position:0% +really have to take care That We Make +sure that each of the + + align:start position:0% + + + + align:start position:0% + +hand in Cas with two pairs but How can + + align:start position:0% +hand in Cas with two pairs but How can + + + align:start position:0% +hand in Cas with two pairs but How can +we remedy this it turns Out That We Can + + align:start position:0% +we remedy this it turns Out That We Can + + + align:start position:0% +we remedy this it turns Out That We Can +intering These two + + align:start position:0% +intering These two + + + align:start position:0% +intering These two +pairs These two sequences Are The Only + + align:start position:0% +pairs These two sequences Are The Only + + + align:start position:0% +pairs These two sequences Are The Only +two sequences that map to the same hand + + align:start position:0% +two sequences that map to the same hand + + + align:start position:0% +two sequences that map to the same hand +so We Know + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% +is + + + align:start position:0% +is +mapping + + align:start position:0% + + + + align:start position:0% + +use Division rule + + align:start position:0% +use Division rule + + + align:start position:0% +use Division rule +And The Division + + align:start position:0% +And The Division + + + align:start position:0% +And The Division +rule we Now know that the Number + + align:start position:0% +rule we Now know that the Number + + + align:start position:0% +rule we Now know that the Number +of hands with two + + align:start position:0% + + + + align:start position:0% + +pairs is actually equal to this Whole + + align:start position:0% +pairs is actually equal to this Whole + + + align:start position:0% +pairs is actually equal to this Whole +Thing over + + align:start position:0% +Thing over + + + align:start position:0% +Thing over +here + + align:start position:0% +here + + + align:start position:0% +here +dived Because We One + + align:start position:0% +dived Because We One + + + align:start position:0% +dived Because We One +function This is really something that + + align:start position:0% +function This is really something that + + + align:start position:0% +function This is really something that +is Pretty disturbing Because We have a + + align:start position:0% +is Pretty disturbing Because We have a + + + align:start position:0% +is Pretty disturbing Because We have a +near Miss in our reasoning in eh eh and + + align:start position:0% +near Miss in our reasoning in eh eh and + + + align:start position:0% +near Miss in our reasoning in eh eh and +therefore it is important to keep in + + align:start position:0% +therefore it is important to keep in + + + align:start position:0% +therefore it is important to keep in +Mind The Following guidelines When We Do + + align:start position:0% +Mind The Following guidelines When We Do + + + align:start position:0% +Mind The Following guidelines When We Do +counting + + align:start position:0% +counting + + + align:start position:0% +counting +ehm It's Always + + align:start position:0% +ehm It's Always + + + align:start position:0% +ehm It's Always +uh it's very important to first of all + + align:start position:0% +uh it's very important to first of all + + + align:start position:0% +uh it's very important to first of all +check whether It's truly a bje and you + + align:start position:0% +check whether It's truly a bje and you + + + align:start position:0% +check whether It's truly a bje and you +need to know how many uh sequences are + + align:start position:0% +need to know how many uh sequences are + + + align:start position:0% +need to know how many uh sequences are +mapped to the same + + align:start position:0% + + + + align:start position:0% + +msck + + align:start position:0% + + + + align:start position:0% + +care of + + align:start position:0% + + + + align:start position:0% + +El That are + + align:start position:0% + + + + align:start position:0% + +mapped + + align:start position:0% +mapped + + + align:start position:0% +mapped +to + + align:start position:0% +to + + + align:start position:0% +to +each + + align:start position:0% +each + + + align:start position:0% +each +eh + + align:start position:0% +eh + + + align:start position:0% +eh +element of + + align:start position:0% +element of + + + align:start position:0% +element of +B so we check How many to One of a + + align:start position:0% +B so we check How many to One of a + + + align:start position:0% +B so we check How many to One of a +mapping this really is and after this We + + align:start position:0% +mapping this really is and after this We + + + align:start position:0% +mapping this really is and after this We +will then apply uh The Division + + align:start position:0% + + + + align:start position:0% + +rule very important to check this + + align:start position:0% + + + + align:start position:0% + +mes ex resar + + align:start position:0% + + + + align:start position:0% + +c If + + align:start position:0% +c If + + + align:start position:0% +c If +I I use a different method to the same thing + + align:start position:0% +I I use a different method to the same thing + + + align:start position:0% + + + + align:start position:0% + + + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + + align:start position:0% + + + + align:start position:0% + + + + align:start position:0% + + + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + + align:start position:0% + + + + align:start position:0% + + + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + + align:start position:0% + + + + align:start position:0% + + + + align:start position:0% + + + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + + align:start position:0% + +that actually lead to + + align:start position:0% +that actually lead to + + + align:start position:0% +that actually lead to +a + + align:start position:0% + + + + align:start position:0% + +Okay Do + + align:start position:0% + + + + align:start position:0% + +Is First + + align:start position:0% +Is First + + + align:start position:0% +Is First +of choose + + align:start position:0% +of choose + + + align:start position:0% +of choose +values ​​of the pairs + + align:start position:0% +values ​​of the pairs + + + align:start position:0% +values ​​of the pairs +in this case I have the values ​​3 and the + + align:start position:0% +in this case I have the values ​​3 and the + + + align:start position:0% +in this case I have the values ​​3 and the +queen How many choices Do I Have I can + + align:start position:0% +queen How many choices Do I Have I can + + + align:start position:0% +queen How many choices Do I Have I can +choose out of 13 + + align:start position:0% + + + + align:start position:0% + +choices secondly I'm the Suit of the + + align:start position:0% +choices secondly I'm the Suit of the + + + align:start position:0% +choices secondly I'm the Suit of the +smaller + + align:start position:0% +smaller + + + align:start position:0% +smaller +pair is uniquely defined They two values + + align:start position:0% +pair is uniquely defined They two values + + + align:start position:0% +pair is uniquely defined They two values +one is smaller The Suit of + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% + + + + align:start position:0% + +The larger Pair I do + + align:start position:0% + + + + align:start position:0% + +the and I + + align:start position:0% + + + + align:start position:0% + +get Now again I the value of the extra + + align:start position:0% + + + + align:start position:0% + +card + + align:start position:0% +card + + + align:start position:0% +card +choices + + align:start position:0% + + + + align:start position:0% + +mly + + align:start position:0% +mly + + + align:start position:0% +mly + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + + align:start position:0% + +aent is + + align:start position:0% +aent is + + + align:start position:0% +aent is +mapping to find second way to Pro the + + align:start position:0% +mapping to find second way to Pro the + + + align:start position:0% +mapping to find second way to Pro the +same the same + + align:start position:0% +same the same + + + align:start position:0% +same the same +result + + align:start position:0% + + + + align:start position:0% + +eh so okay + + align:start position:0% + + + + align:start position:0% + +Let Me + + align:start position:0% + + + + align:start position:0% + +Do Let Me Do One + + align:start position:0% + + + + align:start position:0% + +More do about + + align:start position:0% + + + + align:start position:0% + +hu + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +I'm each Suit in + + align:start position:0% +I'm each Suit in + + + align:start position:0% +I'm each Suit in +it I count + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% +the + + + align:start position:0% +the +Su + + align:start position:0% + + + + align:start position:0% + +example I Can + + align:start position:0% +example I Can + + + align:start position:0% +example I Can +[Music] + + align:start position:0% + + + + align:start position:0% + +have I can Seven of Diamonds The King of + + align:start position:0% +have I can Seven of Diamonds The King of + + + align:start position:0% +have I can Seven of Diamonds The King of +clubs The of Diamonds The Of + + align:start position:0% +clubs The of Diamonds The Of + + + align:start position:0% +clubs The of Diamonds The Of +Hearts Of + + align:start position:0% +Hearts Of + + + align:start position:0% +Hearts Of +spad is proper hand because I can + + align:start position:0% +spad is proper hand because I can + + + align:start position:0% +spad is proper hand because I can +Diamonds + + align:start position:0% + + + + align:start position:0% + +CLS + + align:start position:0% +CLS + + + align:start position:0% +CLS +a hand in Which Every Suit Is + + align:start position:0% + + + + align:start position:0% + +represented What Do I Do My + + align:start position:0% +represented What Do I Do My + + + align:start position:0% +represented What Do I Do My +representation I Can have the + + align:start position:0% +representation I Can have the + + + align:start position:0% +representation I Can have the +values ​​of each + + align:start position:0% + + + + align:start position:0% + +Suit and I specific order + + align:start position:0% + + + + align:start position:0% + +to + + align:start position:0% +to + + + align:start position:0% +to +diamond + + align:start position:0% + + + + align:start position:0% + +in + + align:start position:0% + + + + align:start position:0% + +order + + align:start position:0% + + + + align:start position:0% + +DS + + align:start position:0% +DS + + + align:start position:0% +DS +SP hows + + align:start position:0% +SP hows + + + align:start position:0% +SP hows +I + + align:start position:0% + + + + align:start position:0% + +values ​​values ​​the + + align:start position:0% + + + + align:start position:0% + +king 13 values ​​This + + align:start position:0% +king 13 values ​​This + + + align:start position:0% +king 13 values ​​This +one so that uh is Pretty Straight + + align:start position:0% +one so that uh is Pretty Straight + + + align:start position:0% +one so that uh is Pretty Straight +forward Now I Still have the extra card + + align:start position:0% +forward Now I Still have the extra card + + + align:start position:0% +forward Now I Still have the extra card +and the extra + + align:start position:0% +and the extra + + + align:start position:0% +and the extra +card has a + + align:start position:0% + + + + align:start position:0% + +Suit Which I can do in Four ways because + + align:start position:0% +Suit Which I can do in Four ways because + + + align:start position:0% +Suit Which I can do in Four ways because +Four choices and finally eh It also has + + align:start position:0% +Four choices and finally eh It also has + + + align:start position:0% +Four choices and finally eh It also has +value and the value is eh + + align:start position:0% +value and the value is eh + + + align:start position:0% +value and the value is eh +is + + align:start position:0% +is + + + align:start position:0% +is +actually How much is this can this be 13 + + align:start position:0% +actually How much is this can this be 13 + + + align:start position:0% +actually How much is this can this be 13 + + align:start position:0% + + + align:start position:0% +values ​​no not really Right because for + + align:start position:0% +values ​​no not really Right because for + + + align:start position:0% +values ​​no not really Right because for +each Possible given Suit Chosen I + + align:start position:0% +each Possible given Suit Chosen I + + + align:start position:0% +each Possible given Suit Chosen I +already chose value + + align:start position:0% +already chose value + + + align:start position:0% +already chose value +Before + + align:start position:0% + + + + align:start position:0% + +in + + align:start position:0% +in + + + align:start position:0% +in +chue the + + align:start position:0% +chue the + + + align:start position:0% +chue the +Suit + + align:start position:0% + + + + align:start position:0% + +ex + + align:start position:0% +ex + + + align:start position:0% +ex +choices chos su ex would be + + align:start position:0% +choices chos su ex would be + + + align:start position:0% +choices chos su ex would be +able + + align:start position:0% + + + + align:start position:0% + +inck + + align:start position:0% + + + + align:start position:0% + +Let's + + align:start position:0% + + + + align:start position:0% + +I Suit extra + + align:start position:0% +I Suit extra + + + align:start position:0% +I Suit extra +Diamond value is + + align:start position:0% +Diamond value is + + + align:start position:0% +Diamond value is +A3 We Are tock guidelines + + align:start position:0% + + + + align:start position:0% + +h of + + align:start position:0% +h of + + + align:start position:0% +h of +Els The Number of sequences that map to + + align:start position:0% +Els The Number of sequences that map to + + + align:start position:0% +Els The Number of sequences that map to +the + + align:start position:0% +the + + + align:start position:0% +the +same hand over + + align:start position:0% +same hand over + + + align:start position:0% +same hand over +here a + + align:start position:0% +here a + + + align:start position:0% +here a +b not + + align:start position:0% + + + + align:start position:0% + +right so is this not B We Can also have + + align:start position:0% +right so is this not B We Can also have + + + align:start position:0% +right so is this not B We Can also have +the + + align:start position:0% +the + + + align:start position:0% +the +Following situation Where we Swap The + + align:start position:0% +Following situation Where we Swap The + + + align:start position:0% +Following situation Where we Swap The +Three Diamonds Seven Diamonds + + align:start position:0% +Three Diamonds Seven Diamonds + + + align:start position:0% +Three Diamonds Seven Diamonds +Around Cho the + + align:start position:0% +Around Cho the + + + align:start position:0% +Around Cho the +diamonds we King + + align:start position:0% + + + + align:start position:0% + +We the fth is also Diamonds + + align:start position:0% +We the fth is also Diamonds + + + align:start position:0% +We the fth is also Diamonds +The well This one also Maps to this + + align:start position:0% +The well This one also Maps to this + + + align:start position:0% +The well This one also Maps to this +uh particular hand so we have a two to + + align:start position:0% +uh particular hand so we have a two to + + + align:start position:0% +uh particular hand so we have a two to +One + + align:start position:0% +One + + + align:start position:0% +One +mapping And we conclude that the Total + + align:start position:0% +mapping And we conclude that the Total + + + align:start position:0% +mapping And we conclude that the Total +Number of hands Where Every Suit is + + align:start position:0% +Number of hands Where Every Suit is + + + align:start position:0% +Number of hands Where Every Suit is +represented is 13 Power 4 4 12 by + + align:start position:0% +represented is 13 Power 4 4 12 by + + + align:start position:0% +represented is 13 Power 4 4 12 by +generalized Okay + + align:start position:0% + + + + align:start position:0% + +now we come + + align:start position:0% +now we come + + + align:start position:0% +now we come +to combinatorial Pro + + align:start position:0% +to combinatorial Pro + + + align:start position:0% +to combinatorial Pro +is new Proof + + align:start position:0% + + + + align:start position:0% + +Technique and what we going to do is to + + align:start position:0% +Technique and what we going to do is to + + + align:start position:0% +Technique and what we going to do is to +set in two Different ways and that will + + align:start position:0% +set in two Different ways and that will + + + align:start position:0% +set in two Different ways and that will +lead to a combinatorial + + align:start position:0% +lead to a combinatorial + + + align:start position:0% +lead to a combinatorial +equation + + align:start position:0% +equation + + + align:start position:0% +equation +so the whole Idea + + align:start position:0% +so the whole Idea + + + align:start position:0% +so the whole Idea +Is as follows so Let Me Give an example + + align:start position:0% + + + + align:start position:0% + +First for combinatorial Proof eh for + + align:start position:0% +First for combinatorial Proof eh for + + + align:start position:0% +First for combinatorial Proof eh for +example suppose I + + align:start position:0% +example suppose I + + + align:start position:0% +example suppose I +have + + align:start position:0% + + + + align:start position:0% + +nirt and I want to choose + + align:start position:0% +nirt and I want to choose + + + align:start position:0% +nirt and I want to choose +k i + + align:start position:0% +k i + + + align:start position:0% +k i +Trash n min + + align:start position:0% +Trash n min + + + align:start position:0% +Trash n min +k So how do I + + align:start position:0% +k So how do I + + + align:start position:0% +k So how do I +count the Number of choices that I have + + align:start position:0% +count the Number of choices that I have + + + align:start position:0% +count the Number of choices that I have +I can choose out of n i can choose The k + + align:start position:0% +I can choose out of n i can choose The k + + + align:start position:0% +I can choose out of n i can choose The k +keepers but I also can Count it in a + + align:start position:0% +keepers but I also can Count it in a + + + align:start position:0% +keepers but I also can Count it in a +Different Way I can also Count this + + align:start position:0% +Different Way I can also Count this + + + align:start position:0% +Different Way I can also Count this +as How many ways I can Select The + + align:start position:0% +as How many ways I can Select The + + + align:start position:0% +as How many ways I can Select The +treasures n min k out of n SHS will + + align:start position:0% +treasures n min k out of n SHS will + + + align:start position:0% +treasures n min k out of n SHS will +Trash so There are two Different ways to + + align:start position:0% +Trash so There are two Different ways to + + + align:start position:0% +Trash so There are two Different ways to +count the + + align:start position:0% +count the + + + align:start position:0% +count the +same choices that I have + + align:start position:0% +same choices that I have + + + align:start position:0% +same choices that I have +so we have an equation over here eh and + + align:start position:0% +so we have an equation over here eh and + + + align:start position:0% +so we have an equation over here eh and +you already know this One Because by the + + align:start position:0% +you already know this One Because by the + + + align:start position:0% +you already know this One Because by the +definition of the binomial + + align:start position:0% +definition of the binomial + + + align:start position:0% +definition of the binomial +coefficient we This Is equ To + + align:start position:0% +coefficient we This Is equ To + + + align:start position:0% +coefficient we This Is equ To +This pretty Straight Forward + + align:start position:0% + + + + align:start position:0% + +ide + + align:start position:0% +ide + + + align:start position:0% +ide +is + + align:start position:0% +is + + + align:start position:0% +is +in example + + align:start position:0% +in example + + + align:start position:0% +in example +Is Where + + align:start position:0% +Is Where + + + align:start position:0% +Is Where +We The Following we choose + + align:start position:0% +We The Following we choose + + + align:start position:0% +We The Following we choose +te of + + align:start position:0% + + + + align:start position:0% + +k of k + + align:start position:0% + + + + align:start position:0% + +Elements + + align:start position:0% + + + + align:start position:0% + +of of k Elements out + + align:start position:0% +of of k Elements out + + + align:start position:0% +of of k Elements out +of Oh Talking team was Talking students + + align:start position:0% +of Oh Talking team was Talking students + + + align:start position:0% +of Oh Talking team was Talking students +of + + align:start position:0% + + + + align:start position:0% + +students out of n + + align:start position:0% +students out of n + + + align:start position:0% +students out of n +students How many ways can I do + + align:start position:0% +students How many ways can I do + + + align:start position:0% +students How many ways can I do +this and k + + align:start position:0% + + + + align:start position:0% + +right Let's First count the Total Number + + align:start position:0% +right Let's First count the Total Number + + + align:start position:0% +right Let's First count the Total Number +of ways in Which I choose ke students + + align:start position:0% +of ways in Which I choose ke students + + + align:start position:0% +of ways in Which I choose ke students +that includes Bob so let's do that so + + align:start position:0% +that includes Bob so let's do that so + + + align:start position:0% +that includes Bob so let's do that so +Bob is one of the students and + + align:start position:0% + + + + align:start position:0% + +eh If I count the Number of + + align:start position:0% +eh If I count the Number of + + + align:start position:0% +eh If I count the Number of +teams with + + align:start position:0% +teams with + + + align:start position:0% +teams with +Bob How many choices Do I have + + align:start position:0% +Bob How many choices Do I have + + + align:start position:0% +Bob How many choices Do I have +eh + + align:start position:0% + + + + align:start position:0% + +b k min + + align:start position:0% +b k min + + + align:start position:0% +b k min +stud n students taken Out Bob n students + + align:start position:0% +stud n students taken Out Bob n students + + + align:start position:0% +stud n students taken Out Bob n students +left choose k min + + align:start position:0% + + + + align:start position:0% + +students The Other possibility is we + + align:start position:0% + + + + align:start position:0% + +teams in Bob is not + + align:start position:0% + + + + align:start position:0% + +represented now we need to + + align:start position:0% +represented now we need to + + + align:start position:0% +represented now we need to +choose students + + align:start position:0% +choose students + + + align:start position:0% +choose students +out of all the students min Bob we n + + align:start position:0% +out of all the students min Bob we n + + + align:start position:0% +out of all the students min Bob we n +k The R we add Together equ To All + + align:start position:0% +k The R we add Together equ To All + + + align:start position:0% +k The R we add Together equ To All +possibilities Team of k + + align:start position:0% + + + + align:start position:0% + +students + + align:start position:0% + + + + align:start position:0% + +n + + align:start position:0% + + + + align:start position:0% + +Plus + + align:start position:0% + + + + align:start position:0% + +k is + + align:start position:0% +k is + + + align:start position:0% +k is +Pascal + + align:start position:0% + + + + align:start position:0% + +Identity and the general idea is that + + align:start position:0% +Identity and the general idea is that + + + align:start position:0% +Identity and the general idea is that +We Do The Following so We + + align:start position:0% + + + + align:start position:0% + +Are + + align:start position:0% +Are + + + align:start position:0% +Are +actually counting a set in two Different + + align:start position:0% +actually counting a set in two Different + + + align:start position:0% +actually counting a set in two Different +ways what we did So + + align:start position:0% +ways what we did So + + + align:start position:0% +ways what we did So +Far solve types + + align:start position:0% +Far solve types + + + align:start position:0% +Far solve types +ofs The difficulty is that you will need + + align:start position:0% +ofs The difficulty is that you will need + + + align:start position:0% +ofs The difficulty is that you will need +to + + align:start position:0% +to + + + align:start position:0% +to +define the set s so usually get a + + align:start position:0% +define the set s so usually get a + + + align:start position:0% +define the set s so usually get a +problem you need to prove some equation + + align:start position:0% +problem you need to prove some equation + + + align:start position:0% +problem you need to prove some equation +like this So you define a set s That's + + align:start position:0% +like this So you define a set s That's + + + align:start position:0% +like this So you define a set s That's +The hard Part Of It then we are going to + + align:start position:0% +The hard Part Of It then we are going to + + + align:start position:0% +The hard Part Of It then we are going to +show that the Cardinal of s is some + + align:start position:0% +show that the Cardinal of s is some + + + align:start position:0% +show that the Cardinal of s is some +number n say in one + + align:start position:0% +number n say in one + + + align:start position:0% +number n say in one +way so we have One Method to do this by + + align:start position:0% +way so we have One Method to do this by + + + align:start position:0% +way so we have One Method to do this by +Counting + + align:start position:0% + + + + align:start position:0% + +and We will show That s is also equal to + + align:start position:0% +and We will show That s is also equal to + + + align:start position:0% +and We will show That s is also equal to +some other number like in this case we + + align:start position:0% +some other number like in this case we + + + align:start position:0% +some other number like in this case we +Had One number and this Was My second + + align:start position:0% +Had One number and this Was My second + + + align:start position:0% +Had One number and this Was My second +One also by counting And then we can + + align:start position:0% +One also by counting And then we can + + + align:start position:0% +One also by counting And then we can +conclude that n we + + align:start position:0% +conclude that n we + + + align:start position:0% +conclude that n we +conclude n + + align:start position:0% + + + + align:start position:0% + +m + + align:start position:0% + + + + align:start position:0% + +we do + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% +is + + + align:start position:0% +is +R + + align:start position:0% + + + + align:start position:0% + +up + + align:start position:0% + + + + align:start position:0% + +El all the + + align:start position:0% + + + + align:start position:0% + +subsets of n + + align:start position:0% + + + + align:start position:0% + +BS + + align:start position:0% +BS + + + align:start position:0% +BS +Chosen a + + align:start position:0% + + + + align:start position:0% + +basket + + align:start position:0% +basket + + + align:start position:0% +basket +of en Red + + align:start position:0% +of en Red + + + align:start position:0% +of en Red +BS + + align:start position:0% + + + + align:start position:0% + +and Green + + align:start position:0% + + + + align:start position:0% + +BS + + align:start position:0% +BS + + + align:start position:0% +BS +how do we do this We are going to + + align:start position:0% + + + + align:start position:0% + +first choose The Red BS And then The + + align:start position:0% +first choose The Red BS And then The + + + align:start position:0% +first choose The Red BS And then The +Green + + align:start position:0% +Green + + + align:start position:0% +Green +BS Let's First Count as In The Very Easy + + align:start position:0% +BS Let's First Count as In The Very Easy + + + align:start position:0% +BS Let's First Count as In The Very Easy +Way well I just choose end BS Out Of A + + align:start position:0% +Way well I just choose end BS Out Of A + + + align:start position:0% +Way well I just choose end BS Out Of A +basket of three end BS I Don't Care How + + align:start position:0% +basket of three end BS I Don't Care How + + + align:start position:0% +basket of three end BS I Don't Care How +many Green or Red BS I I + + align:start position:0% +many Green or Red BS I I + + + align:start position:0% +many Green or Red BS I I +really choose n choices + + align:start position:0% +really choose n choices + + + align:start position:0% +really choose n choices +is Number + + align:start position:0% +is Number + + + align:start position:0% +is Number +of n element + + align:start position:0% + + + + align:start position:0% + +subsets element + + align:start position:0% + + + + align:start position:0% + +set with exactly R Red balls So how many + + align:start position:0% +set with exactly R Red balls So how many + + + align:start position:0% +set with exactly R Red balls So how many +are there well we choose R Red balls so + + align:start position:0% +are there well we choose R Red balls so + + + align:start position:0% +are there well we choose R Red balls so +we have n Red balls so we need to choose + + align:start position:0% +we have n Red balls so we need to choose + + + align:start position:0% +we have n Red balls so we need to choose +R Out Of + + align:start position:0% +R Out Of + + + align:start position:0% +R Out Of +Those now in Total I need to choose n + + align:start position:0% +Those now in Total I need to choose n + + + align:start position:0% +Those now in Total I need to choose n +balls so I Still need to choose n min R + + align:start position:0% +balls so I Still need to choose n min R + + + align:start position:0% +balls so I Still need to choose n min R +balls Out Of The set of green balls I + + align:start position:0% +balls Out Of The set of green balls I + + + align:start position:0% +balls Out Of The set of green balls I +have two n Green + + align:start position:0% +have two n Green + + + align:start position:0% +have two n Green +balls I'm going to choose n min R Green + + align:start position:0% +balls I'm going to choose n min R Green + + + align:start position:0% +balls I'm going to choose n min R Green +balls over here so These Are The Red + + align:start position:0% +balls over here so These Are The Red + + + align:start position:0% +balls over here so These Are The Red +balls that I + + align:start position:0% +balls that I + + + align:start position:0% +balls that I +Select and here Are The Green + + align:start position:0% +Select and here Are The Green + + + align:start position:0% +Select and here Are The Green +balls Now I Use the Sum rule and I add + + align:start position:0% +balls Now I Use the Sum rule and I add + + + align:start position:0% +balls Now I Use the Sum rule and I add +All The Different Possible subsets with + + align:start position:0% +All The Different Possible subsets with + + + align:start position:0% +All The Different Possible subsets with +Zero Red balls with one Red B two Red + + align:start position:0% +Zero Red balls with one Red B two Red + + + align:start position:0% +Zero Red balls with one Red B two Red +balls all the way up to n Red balls so + + align:start position:0% +balls all the way up to n Red balls so + + + align:start position:0% +balls all the way up to n Red balls so +essentially I get the + + align:start position:0% + + + + align:start position:0% + +Sum by the Sum + + align:start position:0% +Sum by the Sum + + + align:start position:0% +Sum by the Sum +rule + + align:start position:0% +rule + + + align:start position:0% +rule +of + + align:start position:0% +of + + + align:start position:0% +of +r0 all the way up to + + align:start position:0% +r0 all the way up to + + + align:start position:0% +r0 all the way up to +n Where I count the Number of subsets + + align:start position:0% +n Where I count the Number of subsets + + + align:start position:0% +n Where I count the Number of subsets +with exactly R Red balls so that means I + + align:start position:0% +with exactly R Red balls so that means I + + + align:start position:0% +with exactly R Red balls so that means I +can choose R Out Of The N Red balls and + + align:start position:0% +can choose R Out Of The N Red balls and + + + align:start position:0% +can choose R Out Of The N Red balls and +Another n min R Out Of The Two n balls + + align:start position:0% +Another n min R Out Of The Two n balls + + + align:start position:0% +Another n min R Out Of The Two n balls +two n Green + + align:start position:0% +two n Green + + + align:start position:0% +two n Green +balls so now we equate Those two + + align:start position:0% +balls so now we equate Those two + + + align:start position:0% +balls so now we equate Those two +Together And that proves the + + align:start position:0% +Together And that proves the + + + align:start position:0% +Together And that proves the +theorem so The really hard part in this + + align:start position:0% +theorem so The really hard part in this + + + align:start position:0% +theorem so The really hard part in this +Type Of proofs is That You Need some + + align:start position:0% +Type Of proofs is That You Need some + + + align:start position:0% +Type Of proofs is That You Need some +creativity to find And define that set s + + align:start position:0% +creativity to find And define that set s + + + align:start position:0% +creativity to find And define that set s +and see How that would work + + align:start position:0% + + + + align:start position:0% + +N Out of over here out of + + align:start position:0% +N Out of over here out of + + + align:start position:0% +N Out of over here out of +Elements May iide up the in Some Kind of + + align:start position:0% +Elements May iide up the in Some Kind of + + + align:start position:0% +Elements May iide up the in Some Kind of +specific Choice tomor duration also + + align:start position:0% +specific Choice tomor duration also + + + align:start position:0% +specific Choice tomor duration also +comori + + align:start position:0% +comori + + + align:start position:0% +comori +Pro thank + + align:start position:0% + + + + align:start position:0% + +you van \ No newline at end of file diff --git a/0a1EYZLXQRM.txt b/0a1EYZLXQRM.txt new file mode 100644 index 0000000000000000000000000000000000000000..ecb5d6a2a31f7d0d80c604cdc1302e5cc3755432 --- /dev/null +++ b/0a1EYZLXQRM.txt @@ -0,0 +1,939 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT open courseware + + align:start position:0% +of MIT courses visit MIT open courseware + + + align:start position:0% +of MIT courses visit MIT open courseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay so uh today we're going + + align:start position:0% +ocw.mit.edu okay so uh today we're going + + + align:start position:0% +ocw.mit.edu okay so uh today we're going +to have the final uh presentations from + + align:start position:0% +to have the final uh presentations from + + + align:start position:0% +to have the final uh presentations from +the student projects uh so they did a + + align:start position:0% +the student projects uh so they did a + + + align:start position:0% +the student projects uh so they did a +lot of hard work some of them are still + + align:start position:0% +lot of hard work some of them are still + + + align:start position:0% +lot of hard work some of them are still +working upstairs and will come down just + + align:start position:0% +working upstairs and will come down just + + + align:start position:0% +working upstairs and will come down just +in time presentations uh so just a few a + + align:start position:0% +in time presentations uh so just a few a + + + align:start position:0% +in time presentations uh so just a few a +few slides and uh on the format and how + + align:start position:0% +few slides and uh on the format and how + + + align:start position:0% +few slides and uh on the format and how +the judging will happen uh so each team + + align:start position:0% +the judging will happen uh so each team + + + align:start position:0% +the judging will happen uh so each team +will have 15 minutes uh during which to + + align:start position:0% +will have 15 minutes uh during which to + + + align:start position:0% +will have 15 minutes uh during which to +tell us about the little project and to + + align:start position:0% +tell us about the little project and to + + + align:start position:0% +tell us about the little project and to +give us a little demo we have oh at + + align:start position:0% +give us a little demo we have oh at + + + align:start position:0% +give us a little demo we have oh at +least two PlayStation 3s will be set up + + align:start position:0% +least two PlayStation 3s will be set up + + + align:start position:0% +least two PlayStation 3s will be set up +by the end of the uh the class uh one + + align:start position:0% +by the end of the uh the class uh one + + + align:start position:0% +by the end of the uh the class uh one +will have audio uh the other will have + + align:start position:0% +will have audio uh the other will have + + + align:start position:0% +will have audio uh the other will have +video and at least two teams will use + + align:start position:0% +video and at least two teams will use + + + align:start position:0% +video and at least two teams will use +them the others will sess H in and show + + align:start position:0% +them the others will sess H in and show + + + align:start position:0% +them the others will sess H in and show +you their programs running on the + + align:start position:0% +you their programs running on the + + + align:start position:0% +you their programs running on the +PlayStation 3s that we have upstairs on + + align:start position:0% +PlayStation 3s that we have upstairs on + + + align:start position:0% +PlayStation 3s that we have upstairs on +the network um one of the things that + + align:start position:0% +the network um one of the things that + + + align:start position:0% +the network um one of the things that +they'll be graded on or scored on is + + align:start position:0% +they'll be graded on or scored on is + + + align:start position:0% +they'll be graded on or scored on is +performance um some of the things we'll + + align:start position:0% +performance um some of the things we'll + + + align:start position:0% +performance um some of the things we'll +do after class is performance profiling + + align:start position:0% +do after class is performance profiling + + + align:start position:0% +do after class is performance profiling +to try to understand how much + + align:start position:0% +to try to understand how much + + + align:start position:0% +to try to understand how much +scalability you were able to achieve + + align:start position:0% +scalability you were able to achieve + + + align:start position:0% +scalability you were able to achieve +using one parallel processor versus two + + align:start position:0% +using one parallel processor versus two + + + align:start position:0% +using one parallel processor versus two +versus three all the way up to 6 um so + + align:start position:0% +versus three all the way up to 6 um so + + + align:start position:0% +versus three all the way up to 6 um so +what we'll do is we'll set up some time + + align:start position:0% +what we'll do is we'll set up some time + + + align:start position:0% +what we'll do is we'll set up some time +with the Tas to do the profiling after + + align:start position:0% +with the Tas to do the profiling after + + + align:start position:0% +with the Tas to do the profiling after +class and you can update your source + + align:start position:0% +class and you can update your source + + + align:start position:0% +class and you can update your source +code up until 9:00 a.m. uh so we'll do + + align:start position:0% +code up until 9:00 a.m. uh so we'll do + + + align:start position:0% +code up until 9:00 a.m. uh so we'll do +uh we can you'll show us how to do the + + align:start position:0% +uh we can you'll show us how to do the + + + align:start position:0% +uh we can you'll show us how to do the +profiling then we can you run that at + + align:start position:0% +profiling then we can you run that at + + + align:start position:0% +profiling then we can you run that at +9:00 a.m. Saturday morning uh sort of + + align:start position:0% +9:00 a.m. Saturday morning uh sort of + + + align:start position:0% +9:00 a.m. Saturday morning uh sort of +give you updated scores to uh to change + + align:start position:0% +give you updated scores to uh to change + + + align:start position:0% +give you updated scores to uh to change +your grades if uh assign the grades + + align:start position:0% +your grades if uh assign the grades + + + align:start position:0% +your grades if uh assign the grades +there are six scoring categories uh + + align:start position:0% +there are six scoring categories uh + + + align:start position:0% +there are six scoring categories uh +performance and this performance this + + align:start position:0% +performance and this performance this + + + align:start position:0% +performance and this performance this +first performance category is + + align:start position:0% +first performance category is + + + align:start position:0% +first performance category is +essentially uh what your performance + + align:start position:0% +essentially uh what your performance + + + align:start position:0% +essentially uh what your performance +metric is you're going to Define it + + align:start position:0% +metric is you're going to Define it + + + align:start position:0% +metric is you're going to Define it +hopefully and then you'll tell us how + + align:start position:0% +hopefully and then you'll tell us how + + + align:start position:0% +hopefully and then you'll tell us how +well you did uh project scope uh this is + + align:start position:0% +well you did uh project scope uh this is + + + align:start position:0% +well you did uh project scope uh this is +essentially a measure because each of + + align:start position:0% +essentially a measure because each of + + + align:start position:0% +essentially a measure because each of +different projects were different and + + align:start position:0% +different projects were different and + + + align:start position:0% +different projects were different and +you pick your own projects we'll try to + + align:start position:0% +you pick your own projects we'll try to + + + align:start position:0% +you pick your own projects we'll try to +get an understanding for how much you + + align:start position:0% +get an understanding for how much you + + + align:start position:0% +get an understanding for how much you +try to cover in your project what you + + align:start position:0% +try to cover in your project what you + + + align:start position:0% +try to cover in your project what you +actually did achieve uh so we'll uh + + align:start position:0% +actually did achieve uh so we'll uh + + + align:start position:0% +actually did achieve uh so we'll uh +hopefully you give us a good idea of + + align:start position:0% +hopefully you give us a good idea of + + + align:start position:0% +hopefully you give us a good idea of +that uh completeness you know how robust + + align:start position:0% +that uh completeness you know how robust + + + align:start position:0% +that uh completeness you know how robust +is your code how much did you actually + + align:start position:0% +is your code how much did you actually + + + align:start position:0% +is your code how much did you actually +achieve relative to what you wanted to + + align:start position:0% +achieve relative to what you wanted to + + + align:start position:0% +achieve relative to what you wanted to +do uh are there data races is your code + + align:start position:0% +do uh are there data races is your code + + + align:start position:0% +do uh are there data races is your code +uh reproducible with every run + + align:start position:0% +uh reproducible with every run + + + align:start position:0% +uh reproducible with every run +presentation and demo so we've decoupled + + align:start position:0% +presentation and demo so we've decoupled + + + align:start position:0% +presentation and demo so we've decoupled +the two just because there are different + + align:start position:0% +the two just because there are different + + + align:start position:0% +the two just because there are different +ways people will be doing a demo so you + + align:start position:0% +ways people will be doing a demo so you + + + align:start position:0% +ways people will be doing a demo so you +can sort of earn points in different + + align:start position:0% +can sort of earn points in different + + + align:start position:0% +can sort of earn points in different +categories if you have a really good + + align:start position:0% +categories if you have a really good + + + align:start position:0% +categories if you have a really good +presentation but your demo might not be + + align:start position:0% +presentation but your demo might not be + + + align:start position:0% +presentation but your demo might not be +uh so flashy uh we'll take that into + + align:start position:0% +uh so flashy uh we'll take that into + + + align:start position:0% +uh so flashy uh we'll take that into +account and then performance scalability + + align:start position:0% +account and then performance scalability + + + align:start position:0% +account and then performance scalability +which we'll do offline so each one of + + align:start position:0% +which we'll do offline so each one of + + + align:start position:0% +which we'll do offline so each one of +these categories scored on 10 point + + align:start position:0% +these categories scored on 10 point + + + align:start position:0% +these categories scored on 10 point +basis uh from 1 to 10 10 being really + + align:start position:0% +basis uh from 1 to 10 10 being really + + + align:start position:0% +basis uh from 1 to 10 10 being really +good and uh for a total of 60 points so + + align:start position:0% +good and uh for a total of 60 points so + + + align:start position:0% +good and uh for a total of 60 points so +for uh our judging panel uh fortunately + + align:start position:0% +for uh our judging panel uh fortunately + + + align:start position:0% +for uh our judging panel uh fortunately +we couldn't get virtual San to fully + + align:start position:0% +we couldn't get virtual San to fully + + + align:start position:0% +we couldn't get virtual San to fully +work so San's with us on the phone uh we + + align:start position:0% +work so San's with us on the phone uh we + + + align:start position:0% +work so San's with us on the phone uh we +have Michael Gordon Bill th to graduate + + align:start position:0% +have Michael Gordon Bill th to graduate + + + align:start position:0% +have Michael Gordon Bill th to graduate +students in San's group uh we have + + align:start position:0% +students in San's group uh we have + + + align:start position:0% +students in San's group uh we have +myself uh Professor Steve Ward from MIT + + align:start position:0% +myself uh Professor Steve Ward from MIT + + + align:start position:0% +myself uh Professor Steve Ward from MIT +and Professor wank fi Wong who's + + align:start position:0% +and Professor wank fi Wong who's + + + align:start position:0% +and Professor wank fi Wong who's +visiting from National University of + + align:start position:0% +visiting from National University of + + + align:start position:0% +visiting from National University of +Singapore doing a sabatical year + + align:start position:0% +Singapore doing a sabatical year + + + align:start position:0% +Singapore doing a sabatical year +here student presentations will + + align:start position:0% +here student presentations will + + + align:start position:0% +here student presentations will +dynamically reorder these based on who's + + align:start position:0% +dynamically reorder these based on who's + + + align:start position:0% +dynamically reorder these based on who's +available and who's ready to go uh this + + align:start position:0% +available and who's ready to go uh this + + + align:start position:0% +available and who's ready to go uh this +is a rough ordering that was picked + + align:start position:0% +is a rough ordering that was picked + + + align:start position:0% +is a rough ordering that was picked +randomly uh so peruk is here he'll go + + align:start position:0% +randomly uh so peruk is here he'll go + + + align:start position:0% +randomly uh so peruk is here he'll go +first and then I see a li Al pra so + + align:start position:0% +first and then I see a li Al pra so + + + align:start position:0% +first and then I see a li Al pra so +they'll go after that the rate tracing + + align:start position:0% +they'll go after that the rate tracing + + + align:start position:0% +they'll go after that the rate tracing +team is still in my office working so we + + align:start position:0% +team is still in my office working so we + + + align:start position:0% +team is still in my office working so we +might have to bump them down uh software + + align:start position:0% +might have to bump them down uh software + + + align:start position:0% +might have to bump them down uh software +your team is here yep speech is here + + align:start position:0% +your team is here yep speech is here + + + align:start position:0% +your team is here yep speech is here +back am in yeah those guys were already + + align:start position:0% +back am in yeah those guys were already + + + align:start position:0% +back am in yeah those guys were already +having breakfast at like 9:00 so uh the + + align:start position:0% +having breakfast at like 9:00 so uh the + + + align:start position:0% +having breakfast at like 9:00 so uh the +seventh team molecular Dynamic simulator + + align:start position:0% +seventh team molecular Dynamic simulator + + + align:start position:0% +seventh team molecular Dynamic simulator +uh unfortunately they're not here uh + + align:start position:0% +uh unfortunately they're not here uh + + + align:start position:0% +uh unfortunately they're not here uh +that team uh uh is not physically in + + align:start position:0% +that team uh uh is not physically in + + + align:start position:0% +that team uh uh is not physically in +Boston so they'll present tomorrow + + align:start position:0% +Boston so they'll present tomorrow + + + align:start position:0% +Boston so they'll present tomorrow +morning but will not be considered as uh + + align:start position:0% +morning but will not be considered as uh + + + align:start position:0% +morning but will not be considered as uh +competitors in the + + align:start position:0% +competitors in the + + + align:start position:0% +competitors in the +competition uh there is a countdown + + align:start position:0% +competition uh there is a countdown + + + align:start position:0% +competition uh there is a countdown +clock uh bill is running his laptop you + + align:start position:0% +clock uh bill is running his laptop you + + + align:start position:0% +clock uh bill is running his laptop you +can see it directly in front of you + + align:start position:0% +can see it directly in front of you + + + align:start position:0% +can see it directly in front of you +it'll start at 15 minutes and then every + + align:start position:0% +it'll start at 15 minutes and then every + + + align:start position:0% +it'll start at 15 minutes and then every +minute it'll take down 14 13 all the way + + align:start position:0% +minute it'll take down 14 13 all the way + + + align:start position:0% +minute it'll take down 14 13 all the way +down to zero and you can go into + + align:start position:0% +down to zero and you can go into + + + align:start position:0% +down to zero and you can go into +negative times but we'll start subract + + align:start position:0% +negative times but we'll start subract + + + align:start position:0% +negative times but we'll start subract +in points so the longer you run over the + + align:start position:0% +in points so the longer you run over the + + + align:start position:0% +in points so the longer you run over the +more points you uh you start uh losing + + align:start position:0% +more points you uh you start uh losing + + + align:start position:0% +more points you uh you start uh losing +okay so try to keep under the time what + + align:start position:0% +okay so try to keep under the time what + + + align:start position:0% +okay so try to keep under the time what +about questions uh there are questions + + align:start position:0% +about questions uh there are questions + + + align:start position:0% +about questions uh there are questions +we can take those after the presentation + + align:start position:0% +we can take those after the presentation + + + align:start position:0% +we can take those after the presentation +if it's a short question uh yeah let's + + align:start position:0% +if it's a short question uh yeah let's + + + align:start position:0% +if it's a short question uh yeah let's +leave all questions until after + + align:start position:0% +leave all questions until after + + + align:start position:0% +leave all questions until after +presentation done unless there's + + align:start position:0% +presentation done unless there's + + + align:start position:0% +presentation done unless there's +something pressing I'll try to moderate + + align:start position:0% +something pressing I'll try to moderate + + + align:start position:0% +something pressing I'll try to moderate +okay so if we're ready to start on \ No newline at end of file diff --git a/1-_pwzJ8nPw.txt b/1-_pwzJ8nPw.txt new file mode 100644 index 0000000000000000000000000000000000000000..b252170b255c7e8fd8f596593be87ba9949fdfa6 --- /dev/null +++ b/1-_pwzJ8nPw.txt @@ -0,0 +1,419 @@ +align:start position:0% + +the game of Jeopardy has three rounds + + align:start position:0% +the game of Jeopardy has three rounds + + + align:start position:0% +the game of Jeopardy has three rounds +jeopardy + + align:start position:0% +jeopardy + + + align:start position:0% +jeopardy +double jeopardy where the dollar values + + align:start position:0% +double jeopardy where the dollar values + + + align:start position:0% +double jeopardy where the dollar values +are doubled and Final Jeopardy + + align:start position:0% +are doubled and Final Jeopardy + + + align:start position:0% +are doubled and Final Jeopardy +when contentions can wager an amount of + + align:start position:0% +when contentions can wager an amount of + + + align:start position:0% +when contentions can wager an amount of +money on one single question each round + + align:start position:0% +money on one single question each round + + + align:start position:0% +money on one single question each round +has five questions in six categories it + + align:start position:0% +has five questions in six categories it + + + align:start position:0% +has five questions in six categories it +consists of a wide variety of topics + + align:start position:0% +consists of a wide variety of topics + + + align:start position:0% +consists of a wide variety of topics +over 2,500 different categories each + + align:start position:0% +over 2,500 different categories each + + + align:start position:0% +over 2,500 different categories each +question has a dollar value the first to + + align:start position:0% +question has a dollar value the first to + + + align:start position:0% +question has a dollar value the first to +buzz in and answer correctly wins the + + align:start position:0% +buzz in and answer correctly wins the + + + align:start position:0% +buzz in and answer correctly wins the +money if they answer incorrectly they + + align:start position:0% +money if they answer incorrectly they + + + align:start position:0% +money if they answer incorrectly they +lose the money an example of a round + + align:start position:0% +lose the money an example of a round + + + align:start position:0% +lose the money an example of a round +involves the following categories dinner + + align:start position:0% +involves the following categories dinner + + + align:start position:0% +involves the following categories dinner +service notable women Oxford English + + align:start position:0% +service notable women Oxford English + + + align:start position:0% +service notable women Oxford English +Dictionary name that instrument Belgium + + align:start position:0% +Dictionary name that instrument Belgium + + + align:start position:0% +Dictionary name that instrument Belgium +and composers by country the type of + + align:start position:0% +and composers by country the type of + + + align:start position:0% +and composers by country the type of +questions jeopardy includes includes + + align:start position:0% +questions jeopardy includes includes + + + align:start position:0% +questions jeopardy includes includes +cryptic definition of categories and + + align:start position:0% +cryptic definition of categories and + + + align:start position:0% +cryptic definition of categories and +clues and the answer is in the form of a + + align:start position:0% +clues and the answer is in the form of a + + + align:start position:0% +clues and the answer is in the form of a +question + + align:start position:0% +question + + + align:start position:0% +question +let me give you two examples question is + + align:start position:0% +let me give you two examples question is + + + align:start position:0% +let me give you two examples question is +motors last and perhaps most powerful + + align:start position:0% +motors last and perhaps most powerful + + + align:start position:0% +motors last and perhaps most powerful +symphony sells its name with this planet + + align:start position:0% +symphony sells its name with this planet + + + align:start position:0% +symphony sells its name with this planet +the answer should be + + align:start position:0% +the answer should be + + + align:start position:0% +the answer should be +what is Jupiter another example + + align:start position:0% +what is Jupiter another example + + + align:start position:0% +what is Jupiter another example +smaller than only Greenland it's the + + align:start position:0% +smaller than only Greenland it's the + + + align:start position:0% +smaller than only Greenland it's the +world's second largest island and the + + align:start position:0% +world's second largest island and the + + + align:start position:0% +world's second largest island and the +answer what is New Guinea for you to + + align:start position:0% +answer what is New Guinea for you to + + + align:start position:0% +answer what is New Guinea for you to +select from in double jeopardy first off + + align:start position:0% +select from in double jeopardy first off + + + align:start position:0% +select from in double jeopardy first off +a tude Brut a next Hedgehog Podge don't + + align:start position:0% +a tude Brut a next Hedgehog Podge don't + + + align:start position:0% +a tude Brut a next Hedgehog Podge don't +worry about it the art of the steel + + align:start position:0% +worry about it the art of the steel + + + align:start position:0% +worry about it the art of the steel +Cambridge and finally church and state + + align:start position:0% +Cambridge and finally church and state + + + align:start position:0% +Cambridge and finally church and state +with each of those words in quotation + + align:start position:0% +with each of those words in quotation + + + align:start position:0% +with each of those words in quotation +marks start us off let's try don't worry + + align:start position:0% +marks start us off let's try don't worry + + + align:start position:0% +marks start us off let's try don't worry +about it all the way down at 2005 it's + + align:start position:0% +about it all the way down at 2005 it's + + + align:start position:0% +about it all the way down at 2005 it's +just acne you don't have this skin + + align:start position:0% +just acne you don't have this skin + + + align:start position:0% +just acne you don't have this skin +infection also known as Hansen's disease + + align:start position:0% +infection also known as Hansen's disease + + + align:start position:0% +infection also known as Hansen's disease +Watson + + align:start position:0% +Watson + + + align:start position:0% +Watson +what is leprosy you are right dad Brut + + align:start position:0% +what is leprosy you are right dad Brut + + + align:start position:0% +what is leprosy you are right dad Brut +for 1600 music fans wax rhapsodic about + + align:start position:0% +for 1600 music fans wax rhapsodic about + + + align:start position:0% +for 1600 music fans wax rhapsodic about +this Hungarians transcendental a Tunes + + align:start position:0% +this Hungarians transcendental a Tunes + + + align:start position:0% +this Hungarians transcendental a Tunes +Watson who + + align:start position:0% +Watson who + + + align:start position:0% +Watson who +his France list you are right don't + + align:start position:0% +his France list you are right don't + + + align:start position:0% +his France list you are right don't +worry about it for 1600 you're just a + + align:start position:0% +worry about it for 1600 you're just a + + + align:start position:0% +worry about it for 1600 you're just a +little stiff you don't have this painful + + align:start position:0% +little stiff you don't have this painful + + + align:start position:0% +little stiff you don't have this painful +mosquito-borne joint illness with a + + align:start position:0% +mosquito-borne joint illness with a + + + align:start position:0% +mosquito-borne joint illness with a +Swahili named Watson what is dengue + + align:start position:0% +Swahili named Watson what is dengue + + + align:start position:0% +Swahili named Watson what is dengue +fever dengue fever correct attitude Brut + + align:start position:0% +fever dengue fever correct attitude Brut + + + align:start position:0% +fever dengue fever correct attitude Brut +for 1,200 Paganini's 24 Capri she set + + align:start position:0% +for 1,200 Paganini's 24 Capri she set + + + align:start position:0% +for 1,200 Paganini's 24 Capri she set +the standard for etudes for this + + align:start position:0% +the standard for etudes for this + + + align:start position:0% +the standard for etudes for this +instrument Watson what is violin good + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/16iPrwJMvSs.txt b/16iPrwJMvSs.txt new file mode 100644 index 0000000000000000000000000000000000000000..5d888b271e7b548ae86b1f526a5d2e32f592ed51 --- /dev/null +++ b/16iPrwJMvSs.txt @@ -0,0 +1,763 @@ +align:start position:0% + +hello welcome back to 8701 + + align:start position:0% +hello welcome back to 8701 + + + align:start position:0% +hello welcome back to 8701 +um in this lecture this little video + + align:start position:0% +um in this lecture this little video + + + align:start position:0% +um in this lecture this little video +we're going to look at reactions and how + + align:start position:0% +we're going to look at reactions and how + + + align:start position:0% +we're going to look at reactions and how +they relate + + align:start position:0% +they relate + + + align:start position:0% +they relate +to cross sections so we start + + align:start position:0% +to cross sections so we start + + + align:start position:0% +to cross sections so we start +um or continue the discussion um of + + align:start position:0% +um or continue the discussion um of + + + align:start position:0% +um or continue the discussion um of +how we can relate proper experimentally + + align:start position:0% +how we can relate proper experimentally + + + align:start position:0% +how we can relate proper experimentally +measured + + align:start position:0% +measured + + + align:start position:0% +measured +determined properties to the forces + + align:start position:0% +determined properties to the forces + + + align:start position:0% +determined properties to the forces +involved the last lecture we looked at + + align:start position:0% +involved the last lecture we looked at + + + align:start position:0% +involved the last lecture we looked at +decay rates and the width of unstable + + align:start position:0% +decay rates and the width of unstable + + + align:start position:0% +decay rates and the width of unstable +particles + + align:start position:0% +particles + + + align:start position:0% +particles +this time we want to look at the + + align:start position:0% +this time we want to look at the + + + align:start position:0% +this time we want to look at the +reaction rates expressed as + + align:start position:0% +reaction rates expressed as + + + align:start position:0% +reaction rates expressed as +cross-sections and we can start + + align:start position:0% +cross-sections and we can start + + + align:start position:0% +cross-sections and we can start +doing this um by looking at this + + align:start position:0% +doing this um by looking at this + + + align:start position:0% +doing this um by looking at this +simplified picture + + align:start position:0% +simplified picture + + + align:start position:0% +simplified picture +so the reaction rate is related or equal + + align:start position:0% +so the reaction rate is related or equal + + + align:start position:0% +so the reaction rate is related or equal +to + + align:start position:0% +to + + + align:start position:0% +to +the rate of the beam so how many + + align:start position:0% +the rate of the beam so how many + + + align:start position:0% +the rate of the beam so how many +particles per second + + align:start position:0% +particles per second + + + align:start position:0% +particles per second +are available for the interactions times + + align:start position:0% +are available for the interactions times + + + align:start position:0% +are available for the interactions times +the number density of the particle in a + + align:start position:0% + + + + align:start position:0% + +target + + align:start position:0% +target + + + align:start position:0% +target +so you have your target here and clearly + + align:start position:0% +so you have your target here and clearly + + + align:start position:0% +so you have your target here and clearly +the number of + + align:start position:0% +the number of + + + align:start position:0% +the number of +uh reactions depend on how dense your + + align:start position:0% +uh reactions depend on how dense your + + + align:start position:0% +uh reactions depend on how dense your +target is + + align:start position:0% +target is + + + align:start position:0% +target is +uh the thickness so you go along + + align:start position:0% +uh the thickness so you go along + + + align:start position:0% +uh the thickness so you go along +how you know the thicker the thicker the + + align:start position:0% +how you know the thicker the thicker the + + + align:start position:0% +how you know the thicker the thicker the +material the target is the more likely + + align:start position:0% +material the target is the more likely + + + align:start position:0% +material the target is the more likely +is for reactions to occur + + align:start position:0% +is for reactions to occur + + + align:start position:0% +is for reactions to occur +and then by the actual physics by the + + align:start position:0% +and then by the actual physics by the + + + align:start position:0% +and then by the actual physics by the +likelihood of a collision to occur + + align:start position:0% +likelihood of a collision to occur + + + align:start position:0% +likelihood of a collision to occur +and this likelihood is called a section + + align:start position:0% +and this likelihood is called a section + + + align:start position:0% +and this likelihood is called a section +and we can think about this cross + + align:start position:0% +and we can think about this cross + + + align:start position:0% +and we can think about this cross +section + + align:start position:0% +section + + + align:start position:0% +section +as a geometrical area + + align:start position:0% +as a geometrical area + + + align:start position:0% +as a geometrical area +all right so let's look at this a little + + align:start position:0% +all right so let's look at this a little + + + align:start position:0% +all right so let's look at this a little +bit more + + align:start position:0% +bit more + + + align:start position:0% +bit more +again we stay with a very classical + + align:start position:0% +again we stay with a very classical + + + align:start position:0% +again we stay with a very classical +model a model in which we have two + + align:start position:0% +model a model in which we have two + + + align:start position:0% +model a model in which we have two +billiard balls + + align:start position:0% +billiard balls + + + align:start position:0% +billiard balls +a light one a small one is radius r1 and + + align:start position:0% +a light one a small one is radius r1 and + + + align:start position:0% +a light one a small one is radius r1 and +a + + align:start position:0% +a + + + align:start position:0% +a +larger one with the radius r2 clearly + + align:start position:0% +larger one with the radius r2 clearly + + + align:start position:0% +larger one with the radius r2 clearly +a collision happens occurs when + + align:start position:0% +a collision happens occurs when + + + align:start position:0% +a collision happens occurs when +the impact parameter b + + align:start position:0% +the impact parameter b + + + align:start position:0% +the impact parameter b +here between those two billiard balls + + align:start position:0% +here between those two billiard balls + + + align:start position:0% +here between those two billiard balls +balls is smaller than + + align:start position:0% +balls is smaller than + + + align:start position:0% +balls is smaller than +the sum of the radius okay + + align:start position:0% +the sum of the radius okay + + + align:start position:0% +the sum of the radius okay +so now we can analyze this reaction a + + align:start position:0% +so now we can analyze this reaction a + + + align:start position:0% +so now we can analyze this reaction a +little bit more and look at angular + + align:start position:0% +little bit more and look at angular + + + align:start position:0% +little bit more and look at angular +distributions we find that this cross + + align:start position:0% +distributions we find that this cross + + + align:start position:0% +distributions we find that this cross +section + + align:start position:0% +section + + + align:start position:0% +section +differential distribution is given + + align:start position:0% +differential distribution is given + + + align:start position:0% +differential distribution is given +as a function of sine theta we can + + align:start position:0% +as a function of sine theta we can + + + align:start position:0% +as a function of sine theta we can +also express this using the azimuth or + + align:start position:0% +also express this using the azimuth or + + + align:start position:0% +also express this using the azimuth or +as a solid angle here the remainder is a + + align:start position:0% +as a solid angle here the remainder is a + + + align:start position:0% +as a solid angle here the remainder is a +solid angle + + align:start position:0% +solid angle + + + align:start position:0% +solid angle +theta is equal to sine theta + + align:start position:0% +theta is equal to sine theta + + + align:start position:0% +theta is equal to sine theta +e theta d phi + + align:start position:0% +e theta d phi + + + align:start position:0% +e theta d phi +all right so for this + + align:start position:0% +all right so for this + + + align:start position:0% +all right so for this +specific problem here we talk about an + + align:start position:0% +specific problem here we talk about an + + + align:start position:0% +specific problem here we talk about an +isotropic + + align:start position:0% +isotropic + + + align:start position:0% +isotropic +isotropic reaction because + + align:start position:0% +isotropic reaction because + + + align:start position:0% +isotropic reaction because +by definition the + + align:start position:0% +by definition the + + + align:start position:0% +by definition the +cross section per solid angle is + + align:start position:0% +cross section per solid angle is + + + align:start position:0% +cross section per solid angle is +independent + + align:start position:0% +independent + + + align:start position:0% +independent +of uh theta and phi + + align:start position:0% +of uh theta and phi + + + align:start position:0% +of uh theta and phi +uh the matting between theta sine theta + + align:start position:0% +uh the matting between theta sine theta + + + align:start position:0% +uh the matting between theta sine theta +and theta + + align:start position:0% +and theta + + + align:start position:0% +and theta +is not trivial that's why you see this + + align:start position:0% +is not trivial that's why you see this + + + align:start position:0% +is not trivial that's why you see this +shape of the distribution + + align:start position:0% +shape of the distribution + + + align:start position:0% +shape of the distribution +um yeah + + align:start position:0% +um yeah + + + align:start position:0% +um yeah +but the the sigma the cosine theta + + align:start position:0% +but the the sigma the cosine theta + + + align:start position:0% +but the the sigma the cosine theta +is fed if you look at this as a function + + align:start position:0% +is fed if you look at this as a function + + + align:start position:0% +is fed if you look at this as a function +of cosine + + align:start position:0% +of cosine + + + align:start position:0% +of cosine +all right so this is just a classical + + align:start position:0% +all right so this is just a classical + + + align:start position:0% +all right so this is just a classical +picture what we're going to do later in + + align:start position:0% +picture what we're going to do later in + + + align:start position:0% +picture what we're going to do later in +the class + + align:start position:0% +the class + + + align:start position:0% +the class +is using quantum field theory or + + align:start position:0% +is using quantum field theory or + + + align:start position:0% +is using quantum field theory or +feynman rules in order to calculate + + align:start position:0% +feynman rules in order to calculate + + + align:start position:0% +feynman rules in order to calculate +cross-sections also decay rates + + align:start position:0% +cross-sections also decay rates + + + align:start position:0% +cross-sections also decay rates +um but you know this classical picture + + align:start position:0% +um but you know this classical picture + + + align:start position:0% +um but you know this classical picture +is really something i would like you to + + align:start position:0% +is really something i would like you to + + + align:start position:0% +is really something i would like you to +keep in mind + + align:start position:0% +keep in mind + + + align:start position:0% +keep in mind +um the idea of the likelihood of the + + align:start position:0% +um the idea of the likelihood of the + + + align:start position:0% +um the idea of the likelihood of the +collision to occur + + align:start position:0% +collision to occur + + + align:start position:0% +collision to occur +is in units of an area and can be seen + + align:start position:0% +is in units of an area and can be seen + + + align:start position:0% +is in units of an area and can be seen +as a geometrical cross section this kind + + align:start position:0% +as a geometrical cross section this kind + + + align:start position:0% +as a geometrical cross section this kind +of conditions + + align:start position:0% +of conditions + + + align:start position:0% +of conditions +a very nice picture to keep in mind and + + align:start position:0% +a very nice picture to keep in mind and + + + align:start position:0% +a very nice picture to keep in mind and +it also helps + + align:start position:0% +it also helps + + + align:start position:0% +it also helps +estimating orders of magnitude of rates + + align:start position:0% +estimating orders of magnitude of rates + + + align:start position:0% +estimating orders of magnitude of rates +of collisions to occur \ No newline at end of file diff --git a/2Yl5IkDMoUU.txt b/2Yl5IkDMoUU.txt new file mode 100644 index 0000000000000000000000000000000000000000..a2bc9b49ffc706b5e1ad9a2bd7c08f5d9268e66f --- /dev/null +++ b/2Yl5IkDMoUU.txt @@ -0,0 +1,56 @@ +Let me comment on the +merits of heatmaps + +as a way of representing data +in the context of representing + +crime activity. + +Criminal activity-related +data often + +has both components +of time and location. + +Sometimes, all that is +required is a line chart, + +but heatmaps can +visualize data that + +will be too big for a table. + +Plotting data on maps +is much more effective + +than a table for location based +data, and is eye catching. + +What is the edge of +predictive policing? + +Many police forces are +exploiting their databases + +to focus finite resources +on problem areas. + +Not only do analytics +help improve policework, + +the outputs are also +good communication tools + +to decision makers in +government, and the wider + +public. + +The application of +analytics to data like this + +is new and growing, +with companies + +like PredPol and Palantir +leading the effort. \ No newline at end of file diff --git a/2eLeU6-0W7E.txt b/2eLeU6-0W7E.txt new file mode 100644 index 0000000000000000000000000000000000000000..90bb2d8caf0a6b4423c013361d864b46d6bf5785 --- /dev/null +++ b/2eLeU6-0W7E.txt @@ -0,0 +1,535 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses visit +MIT OpenCourseWare at + +ocw.mit.edu. + +Hi I'm Sal. + +Today we're going to be doing +problem number 5 of + +fall 2009, test 1. + +Make sure that you read the +problem in full detail before + +attempting the problem. + +And there's also some things +that you should know, pretty + +much background material. + +Before attempting the problem. + +And that's what I need, +which is W I N. + +You will win if you know how to +manipulate these equations. + +The first equation is the energy +of two charged species + +as a function of their +internuclear separation. + +And the other equation is +a function of just the + +separation between two ion pairs +at equilibrium, which is + +given by r naught. + +And r naught is just simply the +sum of the radii of the + +cation and the radii +of the anion. + +So if you look at this +equation there's two + +components to it. + +The first component is actually +the component that is + +responsible for the attraction +of your charged species. + +And the second component +is the repulsion of it. + +Because essentially ionic +bonding happens because of + +your electrostatic interaction +between an + +cation and an anion. + +So with this in mind we can +go ahead and read the + +problem and solve it. + +So the problem reads +as follows. + +On the same graph below-- + +and this is the actual graph +that we're going to be doing + +the problem on-- + +it says on the same graph +below, for one, BeF2, so + +beryllium fluoride, and two, +BeO, which is beryllium oxide, + +sketch the variation of +potential energy with + +internuclear separation arc +between a cation and an anion + +pair in each compound. + +The diagram need not to be drawn +to scale however you + +must convey the relative +magnitudes of key features. + +So the first thing that I would +do is write down my + +compounds that I'm using. + +So I'm focusing on beryllium +fluoride, is the first one. + +So if I look at beryllium +fluoride, I'm going to look at + +the relative magnitudes and +charges when they're in their + +cation and anion state. + +So I know that for beryllium, +beryllium forms a + +cation that is 2 plus. + +So it has a positive charge of +2, which means that it lost + +two electrons. + +So I can say that z plus for +beryllium is plus 2 and for + +fluorine, when it's in the +anion state, my charge is + +equal to minus 1. + +So 2 plus minus 1. + +So with this in mind, you can +take this and it will help you + +solve the problem. + +Because like I said, the first +part of the equation is pretty + +much the attraction part, which +involves the product of + +your charges. + +And I want to go ahead into +the same thing for-- + +so this is for BeF2. + +And for BeO we have the +oxygen 2 minus. + +So my anion has a z minus of +minus 2 and my cation just has + +z plus of plus 2. + +Now if you look at your +equation over here. + +There's two things that will +dominate at certain + +parameters. + +Now this value of n is known as +the Born Exponent, and that + +has a value between 6 and 12. + +So it's always greater than 1. + +And this is actually what's +nominating your repulsion, so + +I'll do some colored chalk. + +So for the attraction +part I'll circle it. + +And the fact that it's being +attractive means that one of + +these charges has to be negative +that will make the + +overall component negative. + +Right here because you'll +have q1 times q2. + +And in our case if we look up +beryllium fluoride, you have + +beryllium 2 plus you have +fluorine minus, so if you make + +the product of those two +you get minus 2. + +And you have this other +component, that is the + +repulsive part. + +So if I was to draw these +independently, not as a sum, I + +know that for my attractive +part, which is the negative, + +it should look something like +so, as a function of r. + +And my repulsive should look +something like so. + +And this makes sense because as +your radius becomes smaller + +and smaller then essentially +if you get below 1, your + +potential energy curve +for your-- + +the component for +your repulsion-- + +spikes up. + +So if I was to superimpose +these two, then I should + +expect that the curve to +look something like so. + +Now this is good because this +is exactly how the curve + +should look. + +And there's some characteristic +features here + +that we want to go ahead and +use BeF2 BeO2, draw on the + +same diagram to compare +together. + +And this point right here on +your r-axis is simply just + +your r naught. + +So it's just the sum of +your cation radius + +and your anion radius. + +And this valley here is your +energy at r naught. + +Which is the second +equation that you + +should know how to apply. + +So if I want to analyze my +system, how do I know which + +one has a bigger radii +than the other? + +Well I know that my +cation is common. + +So in both cases I'm dealing +with beryllium cations. + +But I'm dealing with +a different anion. + +Now I know that both fluorine +and oxygen anions have the + +same number of electrons, from +looking at the Periodic Table + +of Elements, or their charges +that they have. But fluorine + +has one more proton. + +So what that does is that it +allows the fluorine to pull + +the electron cloud tighter +together and that decreases + +your radius. + +So just by looking at the +Periodic Table of Elements, I + +can already assume that my +radius for my fluorine should + +be less than the radius +of my O2 minus anion. + +So if I look at my system than +I know that if I want to look + +at the internuclear separation, +the r naughts of + +the two compounds, then +I should assume-- + +or have an educated +guess based on my + +data that I have here-- + +that r naught for beryllium +fluoride should be less than + +the r naught for beryllium +oxide. + +So this allows you to put the +position of your radius on + +your curve. + +So I'm going to go ahead and +just redraw the a new axis + +over here just to compare +both of them so you + +won't confuse yourself. + +So we know this is the +energy of our system. + +And we concluded that our, +that the radius of your + +beryllium fluoride is +less than the radius + +of beryllium oxide. + +So I can go ahead and mark this +as r naught of BeF2 and + +I'll mark that as +r naught of BeO. + +So this tells me exactly where +the low point of my potential + +curve should lie. + +But how do I know how deep +it sits in the well? + +Well that's going to be dictated +by the equation that + +governs the energy +at r naught. + +And that's our simple equation +of when it's the + +function of r naught. + +And if you look at the equation, +the equation is just + +the product of your +two charges. + +So if we come back and we look +at our analysis here, we know + +that if I multiply these two +charges together, you know the + +combination of these two, +should be, q1 or q-- + +beryllium 2 plus, I'll +call that q1 and I'll + +call this one q2. + +The product of these two +gives you minus 2. + +But for this one, q1 q2 +gives us minus 4. + +So this tells me that the +electrostatic interaction for + +beryllium oxide is +a lot stronger + +than beryllium fluoride. + +And it makes sense because you +have plus 2 and minus 2 being + +attracted to each other instead +of plus 2, minus 1. + +So on my graph I can assume, I +can guess, that my value of my + +beryllium oxide should sit +lower, more negative, on the + +potential curve than +beryllium fluoride. + +So if I designate this as the +low point for my beryllium + +fluoride then my curve for +this system, for that + +particular compound should take +a certain type of shape. + +And so again, this is +your energy, the + +bottom point of r naught. + +And if this is the energy given +to the fact that we have + +a higher magnitude when you +multiply the two charges + +together, then it should sit +lower on the potential well. + +And this will be my low point. + +So my curve should also look +something like so. + +So if you were able to do this +on the exam you would have + +gotten full points, +which is good. + +And, again the key points about +this problem is just + +knowing what equations to use +by reading the problem. + +The problem talked about +internuclear separation, well + +we've learned in class how to +treat those problems and how + +to use equations to be able to +describe the way that the + +energy should look, which +is a good visual. + +And by looking at the Periodic +Table of Elements, just + +thinking about how many protons, +how many electrons + +certain cations have, you should +have an estimated guess + +of what your ionic +radius should be. + +And with that you can go ahead +and look at the math. + +Look where that parameter plays +a role in your equation. + +And then decide whether or not +it'll be greater or less or + +what have you. + +So with that in mind, I dare you +to try the problem now and + +give it a good shot. \ No newline at end of file diff --git a/2rnsbodsJVc.txt b/2rnsbodsJVc.txt new file mode 100644 index 0000000000000000000000000000000000000000..8462cd4b9b4027b178547cc75824af6f7851d683 --- /dev/null +++ b/2rnsbodsJVc.txt @@ -0,0 +1,1547 @@ +align:start position:0% + +so now we're going to try putting a + + align:start position:0% +so now we're going to try putting a + + + align:start position:0% +so now we're going to try putting a +world map of the new data set that has a + + align:start position:0% +world map of the new data set that has a + + + align:start position:0% +world map of the new data set that has a +number of international students from + + align:start position:0% +number of international students from + + + align:start position:0% +number of international students from +each country so first of all we're going + + align:start position:0% +each country so first of all we're going + + + align:start position:0% +each country so first of all we're going +to need to use the GG map package which + + align:start position:0% +to need to use the GG map package which + + + align:start position:0% +to need to use the GG map package which +you may need to install and we're going + + align:start position:0% +you may need to install and we're going + + + align:start position:0% +you may need to install and we're going +to load in the data set which is called + + align:start position:0% +to load in the data set which is called + + + align:start position:0% +to load in the data set which is called +int L all does CSV so read CSV int all + + align:start position:0% +int L all does CSV so read CSV int all + + + align:start position:0% +int L all does CSV so read CSV int all +CSV and I'm gonna do strings as vectors + + align:start position:0% +CSV and I'm gonna do strings as vectors + + + align:start position:0% +CSV and I'm gonna do strings as vectors +equals false okay let's look at this the + + align:start position:0% +equals false okay let's look at this the + + + align:start position:0% +equals false okay let's look at this the +the first few rows of international all + + align:start position:0% + + + + align:start position:0% + +so you see that each row corresponds to + + align:start position:0% +so you see that each row corresponds to + + + align:start position:0% +so you see that each row corresponds to +a country is a citizenship column that + + align:start position:0% +a country is a citizenship column that + + + align:start position:0% +a country is a citizenship column that +describes the country name number of + + align:start position:0% +describes the country name number of + + + align:start position:0% +describes the country name number of +undergraduates number of graduates + + align:start position:0% +undergraduates number of graduates + + + align:start position:0% +undergraduates number of graduates +special undergraduates and graduates + + align:start position:0% +special undergraduates and graduates + + + align:start position:0% +special undergraduates and graduates +exchange of visiting a total column now + + align:start position:0% +exchange of visiting a total column now + + + align:start position:0% +exchange of visiting a total column now +there's these n a's in here but they're + + align:start position:0% +there's these n a's in here but they're + + + align:start position:0% +there's these n a's in here but they're +not really in a is it just zeros so what + + align:start position:0% +not really in a is it just zeros so what + + + align:start position:0% +not really in a is it just zeros so what +we're gonna do is say all these in a's + + align:start position:0% +we're gonna do is say all these in a's + + + align:start position:0% +we're gonna do is say all these in a's +should be zeros so in international all + + align:start position:0% +should be zeros so in international all + + + align:start position:0% +should be zeros so in international all +all entries that in a whoops all + + align:start position:0% +all entries that in a whoops all + + + align:start position:0% +all entries that in a whoops all +interested in a should be 0 okay and + + align:start position:0% +interested in a should be 0 okay and + + + align:start position:0% +interested in a should be 0 okay and +let's look at the first few rows again + + align:start position:0% + + + + align:start position:0% + +okay much better right + + align:start position:0% +okay much better right + + + align:start position:0% +okay much better right +so next step is to load the world map so + + align:start position:0% +so next step is to load the world map so + + + align:start position:0% +so next step is to load the world map so +let's call it world map equals map data + + align:start position:0% +let's call it world map equals map data + + + align:start position:0% +let's call it world map equals map data +world which is something similar in the + + align:start position:0% +world which is something similar in the + + + align:start position:0% +world which is something similar in the +lecture with the state data so let's + + align:start position:0% +lecture with the state data so let's + + + align:start position:0% +lecture with the state data so let's +look at the structure of the world map + + align:start position:0% +look at the structure of the world map + + + align:start position:0% +look at the structure of the world map +so first two columns of a long student + + align:start position:0% +so first two columns of a long student + + + align:start position:0% +so first two columns of a long student +longitude and latitude third column is + + align:start position:0% +longitude and latitude third column is + + + align:start position:0% +longitude and latitude third column is +something called group that's actually a + + align:start position:0% +something called group that's actually a + + + align:start position:0% +something called group that's actually a +group for each country there's some + + align:start position:0% +group for each country there's some + + + align:start position:0% +group for each country there's some +different number for each country order + + align:start position:0% +different number for each country order + + + align:start position:0% +different number for each country order +get to that later region is just the + + align:start position:0% +get to that later region is just the + + + align:start position:0% +get to that later region is just the +country name and sub region is sometimes + + align:start position:0% +country name and sub region is sometimes + + + align:start position:0% +country name and sub region is sometimes +used + + align:start position:0% +used + + + align:start position:0% +used +some countries to describe like islands + + align:start position:0% +some countries to describe like islands + + + align:start position:0% +some countries to describe like islands +and other things like that so we want to + + align:start position:0% +and other things like that so we want to + + + align:start position:0% +and other things like that so we want to +shove the world map data frame and the + + align:start position:0% +shove the world map data frame and the + + + align:start position:0% +shove the world map data frame and the +International all data frame into one + + align:start position:0% +International all data frame into one + + + align:start position:0% +International all data frame into one +data frame so we can use it for ggplot + + align:start position:0% +data frame so we can use it for ggplot + + + align:start position:0% +data frame so we can use it for ggplot +so let's say world map is a merger + + align:start position:0% +so let's say world map is a merger + + + align:start position:0% +so let's say world map is a merger +emerge of world map and international + + align:start position:0% +emerge of world map and international + + + align:start position:0% +emerge of world map and international +all now in world map the country name is + + align:start position:0% +all now in world map the country name is + + + align:start position:0% +all now in world map the country name is +dis cold region as you can see right + + align:start position:0% +dis cold region as you can see right + + + align:start position:0% +dis cold region as you can see right +here and an international all the + + align:start position:0% +here and an international all the + + + align:start position:0% +here and an international all the +country name is actually cold + + align:start position:0% +country name is actually cold + + + align:start position:0% +country name is actually cold +citizenship okay so let's look at the + + align:start position:0% +citizenship okay so let's look at the + + + align:start position:0% +citizenship okay so let's look at the +structure of world map just to make sure + + align:start position:0% +structure of world map just to make sure + + + align:start position:0% +structure of world map just to make sure +it makes sense it looks good okay so to + + align:start position:0% +it makes sense it looks good okay so to + + + align:start position:0% +it makes sense it looks good okay so to +put a map we use the Giambi on geometry + + align:start position:0% +put a map we use the Giambi on geometry + + + align:start position:0% +put a map we use the Giambi on geometry +so start off ggplot world map the acidic + + align:start position:0% +so start off ggplot world map the acidic + + + align:start position:0% +so start off ggplot world map the acidic +X is a longitude Y this is a latitude + + align:start position:0% +X is a longitude Y this is a latitude + + + align:start position:0% +X is a longitude Y this is a latitude +group dozen grouped countries into their + + align:start position:0% +group dozen grouped countries into their + + + align:start position:0% +group dozen grouped countries into their +own individual polygons if we want to + + align:start position:0% +own individual polygons if we want to + + + align:start position:0% +own individual polygons if we want to +use GM polygons as a geometry let's make + + align:start position:0% +use GM polygons as a geometry let's make + + + align:start position:0% +use GM polygons as a geometry let's make +it a what countries will be filled in + + align:start position:0% +it a what countries will be filled in + + + align:start position:0% +it a what countries will be filled in +white and their borders will be in black + + align:start position:0% +white and their borders will be in black + + + align:start position:0% +white and their borders will be in black +and we'll use a Mercator projection with + + align:start position:0% +and we'll use a Mercator projection with + + + align:start position:0% +and we'll use a Mercator projection with +a few other options in here as well okay + + align:start position:0% +a few other options in here as well okay + + + align:start position:0% +a few other options in here as well okay +so that looks kind of like a word map + + align:start position:0% +so that looks kind of like a word map + + + align:start position:0% +so that looks kind of like a word map +there's a few things going on here so + + align:start position:0% +there's a few things going on here so + + + align:start position:0% +there's a few things going on here so +first of all all the countries look like + + align:start position:0% +first of all all the countries look like + + + align:start position:0% +first of all all the countries look like +big black blobs what on earth is going + + align:start position:0% +big black blobs what on earth is going + + + align:start position:0% +big black blobs what on earth is going +on you might say well sometimes the + + align:start position:0% +on you might say well sometimes the + + + align:start position:0% +on you might say well sometimes the +merge can reorder the data and it turns + + align:start position:0% +merge can reorder the data and it turns + + + align:start position:0% +merge can reorder the data and it turns +out that what the world map data frame + + align:start position:0% +out that what the world map data frame + + + align:start position:0% +out that what the world map data frame +really is is actually a list of letter + + align:start position:0% +really is is actually a list of letter + + + align:start position:0% +really is is actually a list of letter +longitude points that define the border + + align:start position:0% +longitude points that define the border + + + align:start position:0% +longitude points that define the border +of each country so if we accidentally + + align:start position:0% +of each country so if we accidentally + + + align:start position:0% +of each country so if we accidentally +reorder of a data frame they no longer + + align:start position:0% +reorder of a data frame they no longer + + + align:start position:0% +reorder of a data frame they no longer +make any sense and as it goes from point + + align:start position:0% +make any sense and as it goes from point + + + align:start position:0% +make any sense and as it goes from point +to point the points might be another + + align:start position:0% +to point the points might be another + + + align:start position:0% +to point the points might be another +side of a country as it defines the + + align:start position:0% +side of a country as it defines the + + + align:start position:0% +side of a country as it defines the +polygon so we have to reorder the data + + align:start position:0% +polygon so we have to reorder the data + + + align:start position:0% +polygon so we have to reorder the data +in the correct order so this command is + + align:start position:0% +in the correct order so this command is + + + align:start position:0% +in the correct order so this command is +a little bit complicated looking but + + align:start position:0% +a little bit complicated looking but + + + align:start position:0% +a little bit complicated looking but +when you break it down it's not so bad + + align:start position:0% +when you break it down it's not so bad + + + align:start position:0% +when you break it down it's not so bad +so we take a world map and we go just + + align:start position:0% +so we take a world map and we go just + + + align:start position:0% +so we take a world map and we go just +we're gonna reorder it so world map + + align:start position:0% +we're gonna reorder it so world map + + + align:start position:0% +we're gonna reorder it so world map +gonna real other rows we're gonna order + + align:start position:0% +gonna real other rows we're gonna order + + + align:start position:0% +gonna real other rows we're gonna order +the rows based on first of all the group + + align:start position:0% +the rows based on first of all the group + + + align:start position:0% +the rows based on first of all the group +which is pretty much equivalent to the + + align:start position:0% +which is pretty much equivalent to the + + + align:start position:0% +which is pretty much equivalent to the +country and then the order variable + + align:start position:0% +country and then the order variable + + + align:start position:0% +country and then the order variable +which is the correct order for the + + align:start position:0% +which is the correct order for the + + + align:start position:0% +which is the correct order for the +border points and we're gonna take all + + align:start position:0% +border points and we're gonna take all + + + align:start position:0% +border points and we're gonna take all +the columns of course done so if we go + + align:start position:0% +the columns of course done so if we go + + + align:start position:0% +the columns of course done so if we go +and try plotting it again + + align:start position:0% +and try plotting it again + + + align:start position:0% +and try plotting it again +so ggplot I guess I should go up there + + align:start position:0% +so ggplot I guess I should go up there + + + align:start position:0% +so ggplot I guess I should go up there +we go much easier right so now we have + + align:start position:0% +we go much easier right so now we have + + + align:start position:0% +we go much easier right so now we have +the map and it looks more reasonable ok + + align:start position:0% +the map and it looks more reasonable ok + + + align:start position:0% +the map and it looks more reasonable ok +next problem some of the countries are + + align:start position:0% +next problem some of the countries are + + + align:start position:0% +next problem some of the countries are +missing now of course the USA is missing + + align:start position:0% +missing now of course the USA is missing + + + align:start position:0% +missing now of course the USA is missing +because MIT is in the USA so that + + align:start position:0% +because MIT is in the USA so that + + + align:start position:0% +because MIT is in the USA so that +wouldn't be an international student can + + align:start position:0% +wouldn't be an international student can + + + align:start position:0% +wouldn't be an international student can +come from the USA and some parts of + + align:start position:0% +come from the USA and some parts of + + + align:start position:0% +come from the USA and some parts of +Africa are missing presumably because + + align:start position:0% +Africa are missing presumably because + + + align:start position:0% +Africa are missing presumably because +there are no students at MIT right now + + align:start position:0% +there are no students at MIT right now + + + align:start position:0% +there are no students at MIT right now +who from those countries but you'll also + + align:start position:0% +who from those countries but you'll also + + + align:start position:0% +who from those countries but you'll also +notice that Russia is missing a lot of + + align:start position:0% +notice that Russia is missing a lot of + + + align:start position:0% +notice that Russia is missing a lot of +countries near it as well as China which + + align:start position:0% +countries near it as well as China which + + + align:start position:0% +countries near it as well as China which +is definitely not true cuz I have many + + align:start position:0% +is definitely not true cuz I have many + + + align:start position:0% +is definitely not true cuz I have many +friends MIT who are from Russia and + + align:start position:0% +friends MIT who are from Russia and + + + align:start position:0% +friends MIT who are from Russia and +China so what do we do about that + + align:start position:0% +China so what do we do about that + + + align:start position:0% +China so what do we do about that +the reason China is missing is that it + + align:start position:0% +the reason China is missing is that it + + + align:start position:0% +the reason China is missing is that it +has a different name in the MIT data + + align:start position:0% +has a different name in the MIT data + + + align:start position:0% +has a different name in the MIT data +frame than in the world map data frame + + align:start position:0% +frame than in the world map data frame + + + align:start position:0% +frame than in the world map data frame +so when we merged them it was dropped + + align:start position:0% +so when we merged them it was dropped + + + align:start position:0% +so when we merged them it was dropped +from the dataset because I didn't match + + align:start position:0% +from the dataset because I didn't match + + + align:start position:0% +from the dataset because I didn't match +up so to see what is called in the MIT + + align:start position:0% +up so to see what is called in the MIT + + + align:start position:0% +up so to see what is called in the MIT +data frame + + align:start position:0% +data frame + + + align:start position:0% +data frame +let's just do a table there's a few ways + + align:start position:0% +let's just do a table there's a few ways + + + align:start position:0% +let's just do a table there's a few ways +to do this but this is pretty easy okay + + align:start position:0% +to do this but this is pretty easy okay + + + align:start position:0% +to do this but this is pretty easy okay +so we get a list of all the names if we + + align:start position:0% +so we get a list of all the names if we + + + align:start position:0% +so we get a list of all the names if we +scroll all the way up you'll see it says + + align:start position:0% +scroll all the way up you'll see it says + + + align:start position:0% +scroll all the way up you'll see it says +China People's Republic of now in the + + align:start position:0% +China People's Republic of now in the + + + align:start position:0% +China People's Republic of now in the +world map data frame is simply called + + align:start position:0% +world map data frame is simply called + + + align:start position:0% +world map data frame is simply called +China so what we can do is change the + + align:start position:0% +China so what we can do is change the + + + align:start position:0% +China so what we can do is change the +MIT data frame so say the citizenship + + align:start position:0% +MIT data frame so say the citizenship + + + align:start position:0% +MIT data frame so say the citizenship +column the one row where it equals + + align:start position:0% +column the one row where it equals + + + align:start position:0% +column the one row where it equals +China's people Republic off should just + + align:start position:0% +China's people Republic off should just + + + align:start position:0% +China's people Republic off should just +be China okay let's check do a table + + align:start position:0% +be China okay let's check do a table + + + align:start position:0% +be China okay let's check do a table +again scroll all the way up all the way + + align:start position:0% +again scroll all the way up all the way + + + align:start position:0% +again scroll all the way up all the way +up there it is China so we've fixed that + + align:start position:0% +up there it is China so we've fixed that + + + align:start position:0% +up there it is China so we've fixed that +so now the data frame for the MIT data + + align:start position:0% +so now the data frame for the MIT data + + + align:start position:0% +so now the data frame for the MIT data +frame sorry the MIT data frame is + + align:start position:0% +frame sorry the MIT data frame is + + + align:start position:0% +frame sorry the MIT data frame is +consistent with the world map data frame + + align:start position:0% +consistent with the world map data frame + + + align:start position:0% +consistent with the world map data frame +so now we have to go through the merge + + align:start position:0% +so now we have to go through the merge + + + align:start position:0% +so now we have to go through the merge +again so let's say world map is a merge + + align:start position:0% +again so let's say world map is a merge + + + align:start position:0% +again so let's say world map is a merge +of a fresh copy of the map data the + + align:start position:0% +of a fresh copy of the map data the + + + align:start position:0% +of a fresh copy of the map data the +International all data frame was China + + align:start position:0% +International all data frame was China + + + align:start position:0% +International all data frame was China +fixed + + align:start position:0% +fixed + + + align:start position:0% +fixed +it's called region and the world map + + align:start position:0% +it's called region and the world map + + + align:start position:0% +it's called region and the world map +data and it's called citizenship and MIT + + align:start position:0% +data and it's called citizenship and MIT + + + align:start position:0% +data and it's called citizenship and MIT +data all right now we do that we need to + + align:start position:0% +data all right now we do that we need to + + + align:start position:0% +data all right now we do that we need to +do the reordering game so let's just up + + align:start position:0% +do the reordering game so let's just up + + + align:start position:0% +do the reordering game so let's just up +tap press up a few times until we find + + align:start position:0% +tap press up a few times until we find + + + align:start position:0% +tap press up a few times until we find +it there it was so there's a reordering + + align:start position:0% +it there it was so there's a reordering + + + align:start position:0% +it there it was so there's a reordering +command okay and we should be good to go + + align:start position:0% +command okay and we should be good to go + + + align:start position:0% +command okay and we should be good to go +now so let's try plotting it so ggplot + + align:start position:0% +now so let's try plotting it so ggplot + + + align:start position:0% +now so let's try plotting it so ggplot +the world map data frame + + align:start position:0% +the world map data frame + + + align:start position:0% +the world map data frame +the acidic X is the longitude Y is the + + align:start position:0% +the acidic X is the longitude Y is the + + + align:start position:0% +the acidic X is the longitude Y is the +latitude need to group countries + + align:start position:0% +latitude need to group countries + + + align:start position:0% +latitude need to group countries +together so it doesn't all crisscross + + align:start position:0% +together so it doesn't all crisscross + + + align:start position:0% +together so it doesn't all crisscross +over the map + + align:start position:0% +over the map + + + align:start position:0% +over the map +we're gonna use G on polygon again this + + align:start position:0% +we're gonna use G on polygon again this + + + align:start position:0% +we're gonna use G on polygon again this +time though it let's actually fill them + + align:start position:0% +time though it let's actually fill them + + + align:start position:0% +time though it let's actually fill them +with a color that's repor tional to a + + align:start position:0% +with a color that's repor tional to a + + + align:start position:0% +with a color that's repor tional to a +total number of students will still + + align:start position:0% +total number of students will still + + + align:start position:0% +total number of students will still +outline them in black though and we'll + + align:start position:0% +outline them in black though and we'll + + + align:start position:0% +outline them in black though and we'll +use the makoto projection much better so + + align:start position:0% +use the makoto projection much better so + + + align:start position:0% +use the makoto projection much better so +Russia is missing for similar reasons + + align:start position:0% +Russia is missing for similar reasons + + + align:start position:0% +Russia is missing for similar reasons +but we won't do that now because it's a + + align:start position:0% +but we won't do that now because it's a + + + align:start position:0% +but we won't do that now because it's a +little bit annoying but you get the idea + + align:start position:0% +little bit annoying but you get the idea + + + align:start position:0% +little bit annoying but you get the idea +this is pretty interesting actually so + + align:start position:0% +this is pretty interesting actually so + + + align:start position:0% +this is pretty interesting actually so +we can see that Canada and China and + + align:start position:0% +we can see that Canada and China and + + + align:start position:0% +we can see that Canada and China and +India supply a large number of + + align:start position:0% +India supply a large number of + + + align:start position:0% +India supply a large number of +international students to MIT but it is + + align:start position:0% +international students to MIT but it is + + + align:start position:0% +international students to MIT but it is +a little bit confusing doing it on a per + + align:start position:0% +a little bit confusing doing it on a per + + + align:start position:0% +a little bit confusing doing it on a per +country basis because Europe presumably + + align:start position:0% +country basis because Europe presumably + + + align:start position:0% +country basis because Europe presumably +has quite a few students and an MIT but + + align:start position:0% +has quite a few students and an MIT but + + + align:start position:0% +has quite a few students and an MIT but +because you're preservative many small + + align:start position:0% +because you're preservative many small + + + align:start position:0% +because you're preservative many small +countries doesn't look very impressive + + align:start position:0% +countries doesn't look very impressive + + + align:start position:0% +countries doesn't look very impressive +maybe if all the European countries are + + align:start position:0% +maybe if all the European countries are + + + align:start position:0% +maybe if all the European countries are +grouped together it would look about the + + align:start position:0% +grouped together it would look about the + + + align:start position:0% +grouped together it would look about the +same color as Canada but it's hard to + + align:start position:0% +same color as Canada but it's hard to + + + align:start position:0% +same color as Canada but it's hard to +tell there are also other projections we + + align:start position:0% +tell there are also other projections we + + + align:start position:0% +tell there are also other projections we +can look at so this is America tall + + align:start position:0% +can look at so this is America tall + + + align:start position:0% +can look at so this is America tall +projection but what I want to show you + + align:start position:0% +projection but what I want to show you + + + align:start position:0% +projection but what I want to show you +is an orthographic projection that + + align:start position:0% +is an orthographic projection that + + + align:start position:0% +is an orthographic projection that +allows you to sort of view the map in 3d + + align:start position:0% +allows you to sort of view the map in 3d + + + align:start position:0% +allows you to sort of view the map in 3d +like a globe so let's try that out + + align:start position:0% +like a globe so let's try that out + + + align:start position:0% +like a globe so let's try that out +ggplot world map aesthetics are the same + + align:start position:0% +ggplot world map aesthetics are the same + + + align:start position:0% +ggplot world map aesthetics are the same +whoops + + align:start position:0% + + + + align:start position:0% + +actually let me do this the right way I + + align:start position:0% +actually let me do this the right way I + + + align:start position:0% +actually let me do this the right way I +just press up okay let's change it to + + align:start position:0% +just press up okay let's change it to + + + align:start position:0% +just press up okay let's change it to +orthographic projection and well define + + align:start position:0% +orthographic projection and well define + + + align:start position:0% +orthographic projection and well define +now an orientation and this is almost + + align:start position:0% +now an orientation and this is almost + + + align:start position:0% +now an orientation and this is almost +like thinking about where and the world + + align:start position:0% +like thinking about where and the world + + + align:start position:0% +like thinking about where and the world +you want to focus on so this is a + + align:start position:0% +you want to focus on so this is a + + + align:start position:0% +you want to focus on so this is a +latitude and longitude 20 degrees and 30 + + align:start position:0% +latitude and longitude 20 degrees and 30 + + + align:start position:0% +latitude and longitude 20 degrees and 30 +degrees if you run this we should get a + + align:start position:0% +degrees if you run this we should get a + + + align:start position:0% +degrees if you run this we should get a +map centered above North Africa this is + + align:start position:0% +map centered above North Africa this is + + + align:start position:0% +map centered above North Africa this is +quite a nice visualization because if + + align:start position:0% +quite a nice visualization because if + + + align:start position:0% +quite a nice visualization because if +you want to look just at Africa this is + + align:start position:0% +you want to look just at Africa this is + + + align:start position:0% +you want to look just at Africa this is +in Europe I guess this is a way to go we + + align:start position:0% +in Europe I guess this is a way to go we + + + align:start position:0% +in Europe I guess this is a way to go we +can still see China and Canada and South + + align:start position:0% +can still see China and Canada and South + + + align:start position:0% +can still see China and Canada and South +America in here as well let's do + + align:start position:0% +America in here as well let's do + + + align:start position:0% +America in here as well let's do +something a little bit more personal I + + align:start position:0% +something a little bit more personal I + + + align:start position:0% +something a little bit more personal I +want to change the coordinates now to + + align:start position:0% +want to change the coordinates now to + + + align:start position:0% +want to change the coordinates now to +negative 37 and 175 now it's centered on + + align:start position:0% +negative 37 and 175 now it's centered on + + + align:start position:0% +negative 37 and 175 now it's centered on +my hometown a call from New Zealand \ No newline at end of file diff --git a/3YjMdixww4c.txt b/3YjMdixww4c.txt new file mode 100644 index 0000000000000000000000000000000000000000..6ea3a2c790b165e2551260b0afad7d115dac73fd --- /dev/null +++ b/3YjMdixww4c.txt @@ -0,0 +1,1099 @@ +align:start position:0% + +on our to-do list from the previous + + align:start position:0% +on our to-do list from the previous + + + align:start position:0% +on our to-do list from the previous +section is figuring out how to build and + + align:start position:0% +section is figuring out how to build and + + + align:start position:0% +section is figuring out how to build and +and or gates with many inputs these will + + align:start position:0% +and or gates with many inputs these will + + + align:start position:0% +and or gates with many inputs these will +be needed when creating circuit + + align:start position:0% +be needed when creating circuit + + + align:start position:0% +be needed when creating circuit +implementations using a summer products + + align:start position:0% +implementations using a summer products + + + align:start position:0% +implementations using a summer products +equation as our template let's assume + + align:start position:0% +equation as our template let's assume + + + align:start position:0% +equation as our template let's assume +our gate library has only two input + + align:start position:0% +our gate library has only two input + + + align:start position:0% +our gate library has only two input +gates and figure out how to build wider + + align:start position:0% +gates and figure out how to build wider + + + align:start position:0% +gates and figure out how to build wider +gates using the two input gates as + + align:start position:0% +gates using the two input gates as + + + align:start position:0% +gates using the two input gates as +building blocks we'll work on creating + + align:start position:0% +building blocks we'll work on creating + + + align:start position:0% +building blocks we'll work on creating +three and four input gates but the + + align:start position:0% +three and four input gates but the + + + align:start position:0% +three and four input gates but the +approach we use can be generalized to + + align:start position:0% +approach we use can be generalized to + + + align:start position:0% +approach we use can be generalized to +create and and or gates of any desired + + align:start position:0% +create and and or gates of any desired + + + align:start position:0% +create and and or gates of any desired +width the approach shown here relies on + + align:start position:0% +width the approach shown here relies on + + + align:start position:0% +width the approach shown here relies on +the associative property of the and + + align:start position:0% +the associative property of the and + + + align:start position:0% +the associative property of the and +operator this means we can perform an N + + align:start position:0% +operator this means we can perform an N + + + align:start position:0% +operator this means we can perform an N +way and by doing pairwise ends in any + + align:start position:0% +way and by doing pairwise ends in any + + + align:start position:0% +way and by doing pairwise ends in any +convenient order the or and XOR + + align:start position:0% +convenient order the or and XOR + + + align:start position:0% +convenient order the or and XOR +operations are also associative so the + + align:start position:0% +operations are also associative so the + + + align:start position:0% +operations are also associative so the +same approach will work for designing + + align:start position:0% +same approach will work for designing + + + align:start position:0% +same approach will work for designing +wide or and XOR circuits from the + + align:start position:0% +wide or and XOR circuits from the + + + align:start position:0% +wide or and XOR circuits from the +corresponding two input gate simply + + align:start position:0% +corresponding two input gate simply + + + align:start position:0% +corresponding two input gate simply +substitute two input or gates or two + + align:start position:0% +substitute two input or gates or two + + + align:start position:0% +substitute two input or gates or two +input XOR gates for the two input and + + align:start position:0% +input XOR gates for the two input and + + + align:start position:0% +input XOR gates for the two input and +gate shown below and you're good to go + + align:start position:0% +gate shown below and you're good to go + + + align:start position:0% +gate shown below and you're good to go +let's start by designing a circuit that + + align:start position:0% +let's start by designing a circuit that + + + align:start position:0% +let's start by designing a circuit that +computes the and of three inputs a B and + + align:start position:0% +computes the and of three inputs a B and + + + align:start position:0% +computes the and of three inputs a B and +C in the circuit shown here we first + + align:start position:0% +C in the circuit shown here we first + + + align:start position:0% +C in the circuit shown here we first +compute a and B and then and that result + + align:start position:0% +compute a and B and then and that result + + + align:start position:0% +compute a and B and then and that result +with C using the same strategy we can + + align:start position:0% +with C using the same strategy we can + + + align:start position:0% +with C using the same strategy we can +build a four input and gate from three + + align:start position:0% +build a four input and gate from three + + + align:start position:0% +build a four input and gate from three +two input end gates + + align:start position:0% +two input end gates + + + align:start position:0% +two input end gates +essentially we're building a chain of an + + align:start position:0% +essentially we're building a chain of an + + + align:start position:0% +essentially we're building a chain of an +gates which implement an n way and using + + align:start position:0% +gates which implement an n way and using + + + align:start position:0% +gates which implement an n way and using +n minus 1 two input and gates we can + + align:start position:0% +n minus 1 two input and gates we can + + + align:start position:0% +n minus 1 two input and gates we can +also associate the four inputs a + + align:start position:0% +also associate the four inputs a + + + align:start position:0% +also associate the four inputs a +different way computing a and B in + + align:start position:0% +different way computing a and B in + + + align:start position:0% +different way computing a and B in +parallel with C and D then combining + + align:start position:0% +parallel with C and D then combining + + + align:start position:0% +parallel with C and D then combining +those two results using a third and gate + + align:start position:0% +those two results using a third and gate + + + align:start position:0% +those two results using a third and gate +using this approach we're building a + + align:start position:0% +using this approach we're building a + + + align:start position:0% +using this approach we're building a +tree of and gates which approach is best + + align:start position:0% +tree of and gates which approach is best + + + align:start position:0% +tree of and gates which approach is best +chains or trees first we have to decide + + align:start position:0% +chains or trees first we have to decide + + + align:start position:0% +chains or trees first we have to decide +what we mean by best when designing + + align:start position:0% +what we mean by best when designing + + + align:start position:0% +what we mean by best when designing +circuits were interested in cost which + + align:start position:0% +circuits were interested in cost which + + + align:start position:0% +circuits were interested in cost which +depends on the number of components and + + align:start position:0% +depends on the number of components and + + + align:start position:0% +depends on the number of components and +performance which we characterized by + + align:start position:0% +performance which we characterized by + + + align:start position:0% +performance which we characterized by +the propagation delay of the circuit + + align:start position:0% +the propagation delay of the circuit + + + align:start position:0% +the propagation delay of the circuit +both strategies require the same number + + align:start position:0% +both strategies require the same number + + + align:start position:0% +both strategies require the same number +of components since the total number of + + align:start position:0% +of components since the total number of + + + align:start position:0% +of components since the total number of +pairwise ands is the same in both cases + + align:start position:0% +pairwise ands is the same in both cases + + + align:start position:0% +pairwise ands is the same in both cases +so it's a tie when considering costs + + align:start position:0% +so it's a tie when considering costs + + + align:start position:0% +so it's a tie when considering costs +now consider propagation delay the chain + + align:start position:0% +now consider propagation delay the chain + + + align:start position:0% +now consider propagation delay the chain +circuit in the middle has a TPD of three + + align:start position:0% +circuit in the middle has a TPD of three + + + align:start position:0% +circuit in the middle has a TPD of three +gate delays and we can see that the TPD + + align:start position:0% +gate delays and we can see that the TPD + + + align:start position:0% +gate delays and we can see that the TPD +for an N input chain will be n minus one + + align:start position:0% +for an N input chain will be n minus one + + + align:start position:0% +for an N input chain will be n minus one +gate delays the propagation delay of + + align:start position:0% +gate delays the propagation delay of + + + align:start position:0% +gate delays the propagation delay of +change grows linearly with the number of + + align:start position:0% +change grows linearly with the number of + + + align:start position:0% +change grows linearly with the number of +inputs the tree circuit on the bottom + + align:start position:0% +inputs the tree circuit on the bottom + + + align:start position:0% +inputs the tree circuit on the bottom +has a TPD of two gates smaller than the + + align:start position:0% +has a TPD of two gates smaller than the + + + align:start position:0% +has a TPD of two gates smaller than the +chain the propagation delay of trees + + align:start position:0% +chain the propagation delay of trees + + + align:start position:0% +chain the propagation delay of trees +grows logarithmically with a number of + + align:start position:0% +grows logarithmically with a number of + + + align:start position:0% +grows logarithmically with a number of +inputs specifically the propagation + + align:start position:0% +inputs specifically the propagation + + + align:start position:0% +inputs specifically the propagation +delay of tree circuits built using two + + align:start position:0% +delay of tree circuits built using two + + + align:start position:0% +delay of tree circuits built using two +input gates grows as log base two of n + + align:start position:0% +input gates grows as log base two of n + + + align:start position:0% +input gates grows as log base two of n +when n is large tree circuits can have + + align:start position:0% +when n is large tree circuits can have + + + align:start position:0% +when n is large tree circuits can have +dramatically better propagation delay + + align:start position:0% +dramatically better propagation delay + + + align:start position:0% +dramatically better propagation delay +than chain circuits the propagation + + align:start position:0% +than chain circuits the propagation + + + align:start position:0% +than chain circuits the propagation +delay is an upper bound on the worst + + align:start position:0% +delay is an upper bound on the worst + + + align:start position:0% +delay is an upper bound on the worst +case delay from inputs to outputs and is + + align:start position:0% +case delay from inputs to outputs and is + + + align:start position:0% +case delay from inputs to outputs and is +a good measure of performance assuming + + align:start position:0% +a good measure of performance assuming + + + align:start position:0% +a good measure of performance assuming +that all inputs arrive at the same time + + align:start position:0% +that all inputs arrive at the same time + + + align:start position:0% +that all inputs arrive at the same time +but in large circuits a B C and D might + + align:start position:0% +but in large circuits a B C and D might + + + align:start position:0% +but in large circuits a B C and D might +arrive at different times depending on + + align:start position:0% +arrive at different times depending on + + + align:start position:0% +arrive at different times depending on +the TPD of the circuit generating each + + align:start position:0% +the TPD of the circuit generating each + + + align:start position:0% +the TPD of the circuit generating each +one suppose input D arrives considerably + + align:start position:0% +one suppose input D arrives considerably + + + align:start position:0% +one suppose input D arrives considerably +after the other inputs if we use the + + align:start position:0% +after the other inputs if we use the + + + align:start position:0% +after the other inputs if we use the +tree circuit to compute the and of all + + align:start position:0% +tree circuit to compute the and of all + + + align:start position:0% +tree circuit to compute the and of all +four inputs the additional delay in + + align:start position:0% +four inputs the additional delay in + + + align:start position:0% +four inputs the additional delay in +computing Z is two gate delays after the + + align:start position:0% +computing Z is two gate delays after the + + + align:start position:0% +computing Z is two gate delays after the +arrival of D however if we use the chain + + align:start position:0% +arrival of D however if we use the chain + + + align:start position:0% +arrival of D however if we use the chain +circuit the additional delay in + + align:start position:0% +circuit the additional delay in + + + align:start position:0% +circuit the additional delay in +computing Z might be as little as one + + align:start position:0% +computing Z might be as little as one + + + align:start position:0% +computing Z might be as little as one +gate delay the moral of this story it's + + align:start position:0% +gate delay the moral of this story it's + + + align:start position:0% +gate delay the moral of this story it's +hard to know which implementation of a + + align:start position:0% +hard to know which implementation of a + + + align:start position:0% +hard to know which implementation of a +sub circuit like the for input and + + align:start position:0% +sub circuit like the for input and + + + align:start position:0% +sub circuit like the for input and +showing here will yield the smallest + + align:start position:0% +showing here will yield the smallest + + + align:start position:0% +showing here will yield the smallest +overall tpd unless we know the tpd of + + align:start position:0% +overall tpd unless we know the tpd of + + + align:start position:0% +overall tpd unless we know the tpd of +the circuits that compute the values for + + align:start position:0% +the circuits that compute the values for + + + align:start position:0% +the circuits that compute the values for +the input signals in designing CMOS + + align:start position:0% +the input signals in designing CMOS + + + align:start position:0% +the input signals in designing CMOS +circuits the individual gates are + + align:start position:0% +circuits the individual gates are + + + align:start position:0% +circuits the individual gates are +naturally inverting so instead of using + + align:start position:0% +naturally inverting so instead of using + + + align:start position:0% +naturally inverting so instead of using +and in or gates for the best performance + + align:start position:0% +and in or gates for the best performance + + + align:start position:0% +and in or gates for the best performance +we want to use the NAND and nor gates + + align:start position:0% +we want to use the NAND and nor gates + + + align:start position:0% +we want to use the NAND and nor gates +show in here NAND and nor gates can be + + align:start position:0% +show in here NAND and nor gates can be + + + align:start position:0% +show in here NAND and nor gates can be +implemented as a single CMOS gate + + align:start position:0% +implemented as a single CMOS gate + + + align:start position:0% +implemented as a single CMOS gate +involving one pull-up circuit in one + + align:start position:0% +involving one pull-up circuit in one + + + align:start position:0% +involving one pull-up circuit in one +pulldown circuit and an or gate require + + align:start position:0% +pulldown circuit and an or gate require + + + align:start position:0% +pulldown circuit and an or gate require +two CMOS gates in the implementation for + + align:start position:0% +two CMOS gates in the implementation for + + + align:start position:0% +two CMOS gates in the implementation for +example a NAND gate followed by an + + align:start position:0% +example a NAND gate followed by an + + + align:start position:0% +example a NAND gate followed by an +inverter we'll talk about how to build + + align:start position:0% +inverter we'll talk about how to build + + + align:start position:0% +inverter we'll talk about how to build +some our product circuitry using nand's + + align:start position:0% +some our product circuitry using nand's + + + align:start position:0% +some our product circuitry using nand's +and NORs in the next section note that + + align:start position:0% +and NORs in the next section note that + + + align:start position:0% +and NORs in the next section note that +NAND and nor opera + + align:start position:0% +NAND and nor opera + + + align:start position:0% +NAND and nor opera +Asians are not associative NAND of a B + + align:start position:0% +Asians are not associative NAND of a B + + + align:start position:0% +Asians are not associative NAND of a B +and C is not equal to the nand of see + + align:start position:0% +and C is not equal to the nand of see + + + align:start position:0% +and C is not equal to the nand of see +with the nand of a and B so we can't + + align:start position:0% +with the nand of a and B so we can't + + + align:start position:0% +with the nand of a and B so we can't +build a NAND gate with many inputs by + + align:start position:0% +build a NAND gate with many inputs by + + + align:start position:0% +build a NAND gate with many inputs by +building a tree of two input Nance we'll + + align:start position:0% +building a tree of two input Nance we'll + + + align:start position:0% +building a tree of two input Nance we'll +talk about this in the next section too + + align:start position:0% +talk about this in the next section too + + + align:start position:0% +talk about this in the next section too +we've mentioned the exclusive or + + align:start position:0% +we've mentioned the exclusive or + + + align:start position:0% +we've mentioned the exclusive or +operation sometimes called XOR several + + align:start position:0% +operation sometimes called XOR several + + + align:start position:0% +operation sometimes called XOR several +times this logic function is very useful + + align:start position:0% +times this logic function is very useful + + + align:start position:0% +times this logic function is very useful +when building circuitry for arithmetic + + align:start position:0% +when building circuitry for arithmetic + + + align:start position:0% +when building circuitry for arithmetic +or parity calculations as you'll see in + + align:start position:0% +or parity calculations as you'll see in + + + align:start position:0% +or parity calculations as you'll see in +lab 2 implementing a two input XOR gate + + align:start position:0% +lab 2 implementing a two input XOR gate + + + align:start position:0% +lab 2 implementing a two input XOR gate +will take many more n FETs and p FS than + + align:start position:0% +will take many more n FETs and p FS than + + + align:start position:0% +will take many more n FETs and p FS than +required for a two input NAND or nor we + + align:start position:0% +required for a two input NAND or nor we + + + align:start position:0% +required for a two input NAND or nor we +know we can come up with a summer + + align:start position:0% +know we can come up with a summer + + + align:start position:0% +know we can come up with a summer +products expression for any truth table + + align:start position:0% +products expression for any truth table + + + align:start position:0% +products expression for any truth table +and hence build a circuit implementation + + align:start position:0% +and hence build a circuit implementation + + + align:start position:0% +and hence build a circuit implementation +using inverters and gates and or gates + + align:start position:0% +using inverters and gates and or gates + + + align:start position:0% +using inverters and gates and or gates +it turns out we can build circuits with + + align:start position:0% +it turns out we can build circuits with + + + align:start position:0% +it turns out we can build circuits with +the same functionality using only two + + align:start position:0% +the same functionality using only two + + + align:start position:0% +the same functionality using only two +input NAND gates we say the two input + + align:start position:0% +input NAND gates we say the two input + + + align:start position:0% +input NAND gates we say the two input +NAND is a universal gate here we show + + align:start position:0% +NAND is a universal gate here we show + + + align:start position:0% +NAND is a universal gate here we show +how to implement the summer products + + align:start position:0% +how to implement the summer products + + + align:start position:0% +how to implement the summer products +building blocks using just two input + + align:start position:0% +building blocks using just two input + + + align:start position:0% +building blocks using just two input +NAND gates in a minute + + align:start position:0% +NAND gates in a minute + + + align:start position:0% +NAND gates in a minute +we'll show a more direct implementation + + align:start position:0% +we'll show a more direct implementation + + + align:start position:0% +we'll show a more direct implementation +for summer products using only Nan's + + align:start position:0% +for summer products using only Nan's + + + align:start position:0% +for summer products using only Nan's +but these little schematics are a proof + + align:start position:0% +but these little schematics are a proof + + + align:start position:0% +but these little schematics are a proof +of concept showing that NAND only + + align:start position:0% +of concept showing that NAND only + + + align:start position:0% +of concept showing that NAND only +equivalent circuits exist to input nor + + align:start position:0% +equivalent circuits exist to input nor + + + align:start position:0% +equivalent circuits exist to input nor +gates are also universal as shown by + + align:start position:0% +gates are also universal as shown by + + + align:start position:0% +gates are also universal as shown by +these little schematics inverting logic + + align:start position:0% +these little schematics inverting logic + + + align:start position:0% +these little schematics inverting logic +takes a little getting used to but it's + + align:start position:0% +takes a little getting used to but it's + + + align:start position:0% +takes a little getting used to but it's +the key to designing low-cost high + + align:start position:0% +the key to designing low-cost high + + + align:start position:0% +the key to designing low-cost high +performance circuits in CMOS \ No newline at end of file diff --git a/4CBKF4LT8l8.txt b/4CBKF4LT8l8.txt new file mode 100644 index 0000000000000000000000000000000000000000..4149734538b7f9757549aee32e83edb83a638924 --- /dev/null +++ b/4CBKF4LT8l8.txt @@ -0,0 +1,1409 @@ +PROFESSOR: OK, ready for more? + +I defined a problem for you. + +Now let's address it. + +Said that if we have one +coordinate system, and if we + +have some vector, q, that's +defined as a second-rank + +tensor, aij times some other +vector p sub j-- + +and let me digress in passing. + +I am very careful to say "a +second-rank tensor" and not a + +"second-order tensor," because +higher-order order terms means + +negligible and non-important. + +And when I say "second-order +tensor," I don't mean to say + +it's not important +and negligible. + +It's very important, so I say +"rank," which has some sort of + +dignity to it. + +So I don't like the term +"order," because it has + +another meaning. + +OK, so here is a tensor that +relates a vector pj to give us + +the components of a vector qi. + +If we change coordinate system, +the components of p, + +representing exactly one in the +same vector, wink on and + +off and take different values. + +The values for q take on +different values, and + +therefore, of necessity, the +three by three array of + +coefficients, which relates +these different numbers, must + +also change its numerical +values. + +And I hopefully convinced you +at the end of last hour that + +there's times when you might +actually want to do this when + +you're cutting out a particular +sample from a + +single-crystal specimen. + +How do we get the new tensor +in terms of the direction + +cosine scheme that specifies +the change of axes and the + +original tensor? + +So I am going to refer to my +notes quite closely here, + +because I want it to come out +pretty and not have to + +redefine variables +when I'm done. + +So let's start with the original +tensor relation, q + +sub i equals aij +times p sub j. + +Now, what we want is something +of the form q sub i prime + +equals aij prime times +p sub j prime. + +And we know the relations +forward and reverse in terms + +of the direction cosine scheme +cij So let's begin by writing + +qi prime in terms of +qi And we know how + +that is going to transform. + +It's going to be elements of +the direction cosine scheme + +cim times q sub m. + +So that will give me the i-th +component of q in the new + +coordinate system. + +I know how q arises from +the applied vector p. + +So let me write qm in terms +of the applied pj. + +And this is going to +be aij times-- + +be careful of my variables +here-- + +this is going to be a +ml times p sub l. + +And that is going to, from my +definition of a second-rank + +tensor, give me the m-th +component of q. + +So far, so good. + +I've got two different repeated +subscripts here, so + +this is a double summation. + +Now, I'll have what I want to +have, namely a q sub i prime + +on the left-hand side and a p +sub j prime on the right-hand + +side if I can express the +original components of p in + +terms of the new components +of p. + +And I do that by the reverse +transformation. + +So let me now write a ml. + +And then in place of p sub +l, I will write cjl + +times p sub j prime. + +Notice the inverted order +of the subscripts. + +That is the reverse +transformation that's going to + +give me p sub l. + +So you really have now +what I'm after. + +This is a triple summation +in m, l, and j. + +I can write the terms that are +in what is going to be a + +triple summation over +a product of terms. + +I could write these terms +in any order. + +So to simplify it, let me write +q sub i prime is equal + +to cim cjl times a ml, +times p sub j prime. + +And now, hotcha, I've got an +expression that has q prime on + +the left and p prime on the +right, and paying close + +attention to my notes so that +the subscripts all came out + +the way I would like them to. + +So what this says is that the +transform tensor aij prime is + +going to be equal to, +by definition-- + +or what we've shown here, +it's going to be equal-- + +just picking off terms-- +it's going to be + +cim cjl times a ml. + +Just picking off these terms. + +m has no physical meaning, +because m simply is an index + +of summation. + +l has no specific meaning. + +That is just an index +of summation. + +But the i and the j +do have meaning. + +They go with the i and j on the +particular tensor element + +that we were attempting +to evaluate. + +So in other words, to be +specific, if we want the new + +value of the tensor element a1 +2 prime, it's going to be c1 + +something, c2 something, and +those somethings m and l would + +vary from 1 to 3. + +So if I write this out not in +the reduced subscript notation + +but put a summation sign in +there, so a12 prime is going + +to be the sum over m and the +sum over l of terms c1m-- + +the first index is always 1-- + +c2 something-- + +first index is always 2-- + +and then m and l take on +all possible values. + +OK, we've got two results. + +We learned how to transform +a vector. + +And a vector, if you will, is +simply a tensor of first rank. + +And transforming the vector, +we summed over all three + +components of the +original vector. + +And the coefficients in +that summation were + +one direction cosine. + +Now we're transforming +a second-rank tensor. + +Again, each new element is a +linear combination of all nine + +of the elements in the original +tensor, and the + +coefficients are a product +of two direction cosines. + +So we've got two points. + +Let's draw a line through them, +and we can say that, in + +general, any new tensor +element of any rank-- + +and you could prove it through +exactly this method by going + +up, now, to the third rank, +fourth rank, and so on, and + +writing substitutions +of this form-- + +it turns out that a new tensor +element aijkl however far you + +want to go, is going to be given +by a linear combination + +of direction cosine element ciI, +cj capital J, ck capital + +K, cl capital L, times however +far you have to go times + +aijkl, and so on. + +So these are the true indices. + +These have physical meaning. + +These have relevance +to how a particular + +property will behave. + +The capital I, capital J, +capital L, and so on, are what + +we referred to last time +as dummy indices. + +These are indices +of summation. + +But the first index on +the direction cosines + +has specific meaning. + +They are tied to the indices on +the subscript of the term + +that you would like +to evaluate. + +So we've got now a very profound +relation for a tensor + +of any rank. + +And really, it just involves +substitutions using the + +reverse or the forward +transformation until you get + +one element on the one side +related to another element on + +the right-hand side. + +And this is a specific element +in the new tensor, in our + +case, of the second-rank +tensor, aml. + +This is all very abstract. + +It is something that we'll have +to do a couple of times + +for a real problem before you +see how it works out. + +The number of elements that +figure into these + +transformations is really +astronomical. + +Suppose, for example, the tensor +involved were something + +like the elastic stiffness +tensor, which is + +represented by c. + +And we need four subscripts. + +This is a tensor +or fourth rank. + +If we wanted to transform a +particular stiffness to a new + +coordinate system, we would need +a summation ci capital I, + +cj capital J, ck capital K, cl +capital L, times all of the + +elements in the original +tensor, aijkl. + +A fourth-rank tensor consists +of an array of 9 by 9 terms. + +So there are 81 of these. + +We'd have four direction cosines +out in front, and + +there would be a total of 81 +times 5 characters that we + +would have to write. + +So to do the complete tensor +transformation, we would have + +to write on the order of 400 +quantities to get just one of + +the 81 elements in the +new transform tensor. + +So the total number of elements +we'd have to write to + +do this would be 81 +squared times 5. + +That's a lot of elements. + +We'll do a few of these +transformations directly, but + +let me assure you that if we +do a transformation that is + +going to involve symmetry, a lot +of the direction cosines, + +if we're lucky, will be 0. + +So it's not quite as onerous +as it seems. + +So we would make use of this +sort of formalism if we wanted + +to go from one set of reference +axes to a new set + +that might represent a special +specimen that we + +cut out of a crystal. + +But there's another formal way +in which we could make very + +profound and non-intuitive +use of these relations. + +Crystals, except for the +abominable triclinic crystals, + +have symmetry. + +If a crystal has symmetry, you +can transform the solid + +physically by that symmetry +operation. + +And you have to measure +the same + +property before and after. + +So suppose we have a crystal +that has a twofold axis. + +And this crystal is something +that looks like this. + +So this is side A, and this is +side B. We could move the + +crystal by a 180-degree +rotation. + +Put it down. + +I won't draw it, because it's +going to look exactly the + +same, except now this thing-- + +I won't draw, and +I do draw it-- + +this is face A, and this is face +B. If we had electrodes + +on the crystal before and after +that transformation, we + +have to measure, let's say, +the same electrical + +conductivity for both +orientations of the crystal. + +Now, moving a crystal relative +to some coordinate system, + +relative to a pair of electrodes +that we're + +fastening onto the crystal, is +exactly the same thing as + +doing the reverse transformation +of the + +coordinate system. + +That's a vague, strange-sounding +term. + +So suppose we have a crystal +with a fourfold axis with four + +faces, A, B, C, D. And here +are our electrodes. + +To move the crystal relative +to the electrodes by a + +90-degree rotation would involve +rotating face D up to + +this location. + +A would move to this location. + +C would move to this location. + +B would move to this location, +and we'd fasten electrodes on + +the crystal again. + +If the crystal originally had a +coordinate system such that + +this were X1 and this is X2, +moving the electrodes onto a + +different direction on the +crystal is the same as moving + +the crystal in the +opposite sense. + +So we could either envision +moving the crystal relative to + +the electrodes like this, or we +could move the electrodes + +relative to the crystal by the +reverse transformation. + +And the result is the same. + +So what I'm saying is that if +a crystal has symmetry-- + +and let me be specific and +suppose that our crystal has a + +twofold rotation +axis along X3. + +Let's ask how that twofold +access would change the + +coordinate system relative +to the crystal. + +That's the same as moving the +crystal relative to the + +coordinate system. + +It's going to take X1 and move +it to this location X1 prime. + +It's going to take +X2 and move it + +through 180-degree rotation. + +This is going to be X2 prime. + +And if the twofold axis +is along X3, X3 prime + +is the same as X3. + +So what is the direction +cosine scheme for + +this change of axes? + +You might immediately start +working and saying, well, C11 + +is the cosine of the angle +between X1 prime and X1. + +That's 180 degrees. + +Cosine of 180 degrees +is minus 1. + +But let me remind you that the +direction cosine scheme, c ij, + +simply gives us the relation +between the new axes x sub i + +prime and the old +axes, x sub j. + +So let me, just by inspection, +write down the relation + +between these two sets of +coordinate systems. + +So X1 prime is equal +to minus X1. + +X2 prime is equal to minus X2. + +X3 prime is equal to X3. + +So the direction cosine scheme +for this particular + +transformation is simply minus +1 0 0, 0 minus 1 0, 0 0 1. + +So I just evaluated a +nine-element direction cosine + +scheme by inspection, if I can +write the relation between the + +coordinate system before and +after the transformation. + +OK? + +And as we examine higher +symmetry, the same is going to + +be true for the threefold axis, +let's say, along the 1, + +1, 1 direction of a cubic +crystal, for a sixfold + +axis, and so on. + +So we'll be able to write the +direction cosine schemes for a + +symmetry transformation +simply by inspection. + +So for a twofold axis along X3, +this is the form of the + +direction cosine scheme. + +So now let me transform the +elements of a second-rank + +tensor term by term and +see what we get. + +Suppose I want-- + +let's stick with conductivity +as an example. + +Suppose I want the value for +the conductivity element + +sigma1 1 prime. + +That's going to be c1 something, +c1 something, + +because these are the elements +that go in here, times every + +element of a conductivity +tensor sigma lm. + +The only element of the form c1 +something that is non-zero + +in this row c11, c12, c13, +is the term c11. + +In the same way in the same row, +the only term of the form + +c1 something is c11. + +So this is going to be simply +c11 times c11 times sigma11. + +That's the only term +that survives. + +c11 has a numerical value of +minus 1, and that says that + +sigma11 prime is equal +to sigma11. + +So is there any constraint, any +restriction on sigma 11? + +No, sigma11 could be +anything it likes. + +So there's no constraint. + +Let's do another element. + +Let's see what sigma12 +prime would be. + +This will be c1 something times +c2 something times sigma + +something something. + +The only element of the +form c1 something that + +is non-zero is c11. + +So I'll put in a 1 for the l. + +The only direction cosine +element of the form c2 + +something which is +non-zero is c22. + +So I'll put in c22 and +let n be equal to 2. + +c11 is minus 1, c22 +is minus 1. + +So again, this gives us +something not terribly + +interesting. + +Sigma 12 prime is equal +to sigma 12. + +So there's no constraint, at +which point you're probably + +getting very restive, +say, this is + +not telling us anything. + +So let me shake you up +by doing one further + +transformation, and that is to +find the value for c13 prime. + +And that would be +c1 something, c3 + +something times sigma lm. + +The only form of this term of +the form c1 something, that's + +non-zero is c11, +as we've seen. + +So I'll put in just that +single term and + +replace l by 1. + +The term of the form +c3 something that + +is non-zero is c33. + +And I'll put in a 3 for m, and +this is then c11 times c33 + +times sigma13. + +1, And c11 is minus 1. + +c33 is plus 1. + +And that says that sigma13 +prime is minus sigma13. + +But if this is a symmetry +transformation, the tensor has + +to remain invariant. + +And if we're to have sigma13 +equals minus sigma13, there's + +only one number that can make +that claim, and that's 0. + +So sigma13 is identically 0. + +And that places a rather severe +constraint on the way + +in which the crystal is going to +relate an applied electric + +field to a current flow. + +Sigma11 is anything. + +Sigma12 is anything. + +Sigma13 has to be +identically 0. + +Now, let's cut to +the bottom line. + +The direction cosine scheme is +diagonal, so we can say that + +for any element that we pick to +transform sigma ij prime is + +going to be cii, the diagonal +term which has the second + +subscript equal to the first, +times cjj times sigma ij. + +And this says that if we have +i or j is equal to 3, then + +sigma ij has to be 0, because +we're going to have a minus 1 + +times a plus 1. + +If neither i or j is equal to 3, +then again, we will have a + +minus 1 times a minus 1. + +There will be no constraint. + +And the only final possibility +is that both i and j + +are equal to 3. + +That would be the single +element c33. + +Then we would have plus 1 times +plus 1 as the product of + +direction cosines, and there +will be no constraint. + +So for a crystal that has a +twofold axis, and in which + +that twofold axis is along the +direction of x3, the form of + +the tensor will be sigma11, +sigma12, 0, sigma21, sigma22, + +0, sigma31, that's going to be +equal to 0, and sigma33 has no + +constraints. + +So rather than having nine +elements, there are only five + +independent elements +rather than nine. + +And there is now another +relation that can occur in a + +second-rank tensor. + +The off-diagonal terms sigma12 +and sigma21 do + +not have to be related. + +But for most-- + +but not all-- + +most second-rank tensor +properties happily have sigma + +ij identical to sigma ji. + +In other words, the tensor +is symmetric across + +its principal diagonal. + +That is a condition that does +not arise from symmetry That + +depends on the specific +physical property. + +So let me emphasize +that this depends + +on the tensor property. + +And for a great many physical +properties-- + +conductivity, diffusivity, +permeability, susceptibility-- + +you can show that the tensor +has to be symmetric. + +But there are a lot of tensors, +particularly for the + +more obscure physical +properties, where to my + +knowledge, this proof has +never been given. + +And along the same lines, it +is well known that there is + +one physical property for +which this is not true. + +This is the thermal electricity +tensor. + +So for at least one property, +you can show for sure that the + +tensor does not have to be +symmetric and that for a + +crystal of symmetry 2, this +term and this term are + +definitely not equal. + +All right, let us do another +transformation for another + +symmetry, and we can see that +it goes fast when the + +direction cosine scheme +is relatively sparse. + +Let's ask the restrictions, +if any, that + +are imposed by inversion. + +So what is the direction +cosine scheme here? + +Here's x1, here's +x2, here's x3. + +Then operation of inversion at +the intersection of these axes + +will invert the direction +of x1 prime to here. + +It'll invert the direction +of x2 prime here. + +It will invert the direction +of x3 prime to here. + +So the relation between the +reference axes is that x1 + +prime is equal to minus x1. + +x2 prime is equal to minus x2. + +x3 prime is equal to minus x3, +so that the form of the + +direction cosine scheme crj +is minus 1, 00, 0 minus + +1 0, 00 minus 1. + +Slightly different from that for +a two-fold axis for which + +the first two diagonal elements +were minus 1, the + +third one was 0. + +Well, let's jump right +to it and see if we + +can generalize this. + +It's a diagonal direction cosine +scheme once again. + +And this says that if we +transform a particular element + +sigma ij, it's going to be given +by cil, cjm, sigma lm, + +where l and m are variables +of summation. + +The only ones that survive are +the ones for which i equals l + +and for which j equals m. + +So it's going to be cii, +cjj times sigma ij. + +Regardless of the values of i +and j, the diagonal terms are + +always minus 1. + +And therefore, sigma ij prime is +always going to turn out to + +be equal to sigma ij, so +there's going to be no + +constraint on any element. + +And this shortens the job that's +facing us immeasurably. + +So let me write that down, +because that's important. + +Inversion imposes no constraint +on any second-rank + +tensor property. + +So if we stay with monoclinic +crystals, we looked at + +symmetry 2. + +Symmetry 2 over m is equal +to 2 with an inversion + +center put on it. + +But inversion doesn't require +anything, so the symmetry + +constraints for 2 over m +have to be the same as + +for symmetry 2. + +We look at the constraints that +might be imposed by a + +mirror plane. + +A mirror plane plus inversion +is 2 over m. + +2 over m has to be +the same as 2. + +So this will be the same as 2. + +And now we've shown that for +any monoclinic crystal, + +regardless of whether the +symmetry, the point group, is + +2m or 2 over m, the form +of the tensor has to + +be exactly the same. + +So for any monoclinic crystal, +namely 2m or 2 over m, this is + +the form of the tensor where +the twofold axis, again, is + +along x3, the mirror plane would +have to be perpendicular + +to x3, and for 2 over m, both +of the preceding conditions. + +So how about that? + +Let me issue a caveat, because +we're almost out of time. + +There are five independent +elements. + +And that's true. + +But elements sigma12, sigma21, +sigma13, and sigma31 are 0 + +only for this arrangement +of axes relative to + +the symmetry elements. + +If you wanted to take a +different set of axes, you + +know how to get the tensor +for that set of axes. + +Each tensor element is going +to be given by a linear + +combination of these five +non-zero elements. + +And if the orientation of the +axes relative to the symmetry + +elements is quite general, all +nine elements of the tensor + +will be non-zero. + +There will be only five +independent numbers, which + +composes each of those nine +elements, and they will be + +given by a product of two +direction cosines, sometimes + +each of these five non-zero +elements. + +But there will be no zeros in +this array at all for an + +arbitrary set of coordinate +systems. + +Something that I think I'll ask +you to do as a problem, + +because it's really easy +to do, if the tensor is + +symmetric, which most of them +are, one thing that you can + +show quite directly is that +a symmetric tensor remains + +symmetric for any arbitrary +change of axes. + +And that, again, is something +that's fairly easy to prove, + +and I'll let you have the fun +and exhilaration of doing that + +for yourself. + +OK, so this means that for +everything except thermal + +electricity, you really have +to transform, at most, only + +six elements if you go from one + +coordinate system to another. + +That's still a lot, but it's +considerably better than + +transforming all nine. + +So if the tensor originally is +symmetric in one coordinate + +system, it stays symmetric in +any other coordinate system. + +Now, one thing that +I should mention-- + +I passed over it rather +quickly-- + +we said that a property of a +direction cosine scheme is + +that it is what's called a +unitary transformation. + +And it has the property that +the determinant of the + +coefficients is plus +1 if the axis + +retains the same chirality. + +The determinant is minus 1 if +you change the handedness. + +That is only true for what is +called a measure-preserving + +transformation. + +That's what it's called. + +And when it's a +measure-preserving + +transformation, then the +direction cosine scheme is a + +unitary matrix. + +What is measure-preserving +transformation? + +If it's a right-handed system + +beforehand, there's no squishing. + +It doesn't go to an oblique +coordinate system. + +Cartesian stays Cartesian. + +If the reference axes are of +equal lengths, they don't + +stretch upon the +transformation. + +You can define transformations +like that if you like, where + +the angles between them go from +orthogonal to oblique + +after the transformation, and +the units of length along the + +three axes change dimension. + +But then the determinant of the +coefficients is not unity, + +and a lot of the nice, +convenient properties that + +we've seen here do not hold. + +All right, that is a good +place to stop, I think. + +Next week, no quiz. + +If you came in late, we're +going to postpone + +the quiz for a week. + +And let's see, look at all I +can ask you just after one + +lecture on tensors. + +What we will do next is explore +the form of the + +tensors for other crystal +symmetries. + +It goes fairly quickly. + +And then having done all that, +I'll show you how you can + +determine the symmetry +constraints by inspection for + +a tensor of any rank. + +And you're going to despise me +for that, but this was useful, + +because we can get used to +manipulating the notation. + +But there is a method called-- + +appropriately enough-- the +method of direct inspection + +where you can very quickly and +very easily do the symmetry + +transformations. + +So all this and more will be +revealed next time, which is + +going to be a lot more +beneficial than taking a quiz. \ No newline at end of file diff --git a/4hTOGc93ZTc.txt b/4hTOGc93ZTc.txt new file mode 100644 index 0000000000000000000000000000000000000000..6d4161f0b13c2825884cc1a620e2fcfa5eb5017b --- /dev/null +++ b/4hTOGc93ZTc.txt @@ -0,0 +1,2262 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: So welcome back. + +And today, I'm going to +do some examples of what + +happens when you have more +than one charge radiating. + +This is a very +important example, + +because whenever you have many +charges radiating, if it's + +coherent, you get the +phenomenon of interference, + +and it plays a very important +role in many fields of physics, + +in particular, in optics. + +You may have heard terms +like interference patterns, + +diffraction, et cetera. + +All that is to do with when +you have more than one source + +radiating. + +So the example I'm going to +consider is the following. + +Suppose you have +two charges, both q. + +Each one is oscillating. + +It's oscillating with an angular +frequency 2 pi over lambda. + +This tells you the +position of the charge + +as a function of time. + +So it's centered to +distance d from here + +and oscillating +within amplitude a + +as a cosine 2 pi over lambda t. + +Well, lambda is, of +course, the wavelength + +of the radiated +electromagnetic wave. + +So this one is oscillating +up and down like that, + +and there is another one over +here oscillating just for fun + +in the other direction. + +This one is oscillating +in along the x-axis, + +and this one is oscillating +along the y-axis. + +And here is the +formula, which tells you + +what is the position of this one +at the given instant of time. + +They're both given in +terms of the same time, + +with the same time. + +t equals 0. + +Therefore, these are +two coherent sources. + +The question is, what will +be the resultant field + +anywhere in space? + +At some point we want to know +what is the resultant field. + +Now, each one of these-- +you know what it does. + +It radiates a spherical +wave with a certain angular + +distribution. + +Alright? + +And the waves overlap in space. + +Now because the +electromagnetic waves + +are solutions of the +electromagnetic wave + +equation, which is a +linear equation, if we have + +a coherent source of +radiation at any point, + +we simply add vectorially +the electromagnetic waves. + +The electric fields +you add vectorially + +all the magnetic field. + +Now in principle, we should +go-- to first principles. + +Consider Maxwell's equations. + +Consider what happens when +a charge is oscillating. + +And in fact, consider +both charges, + +what they're doing at +any instant of time, + +and solve in all of +space Maxwell's equation + +to see what the electric +field is everywhere. + +We build on our experience, +and what we will do + +is we will assume that we've +solved the problem of what + +happens when this single +charge is accelerating. + +We've done this several times +in the [? PAR sensor ?]. + +Professor Walter Lewin +has done it in the course. + +Whenever a charge is +accelerating, it radiates. + +And this is the +formula, which tells + +you what is the electric field +from the given charge, which + +is accelerating at +some position, r and t. + +I'm just reminding +you that what we find + +is that the electric field at +any position at some time t + +is given by, or related +to, the perpendicular + +component of the +acceleration of the charge. + +It's perpendicular to the +direction of propagation, + +but at a point t in space, +the electric field there + +is related to the acceleration +at an earlier time. + +At the time, t prime, which +is earlier than the time when + +we are considering +by the amount r/c. + +All that this does-- +it reflects the fact + +that if I have some with +an accelerated charge, + +at that instant, the +electromagnetic wave starts + +to propagate, and it takes a +time r/c to reach a distance r. + +That's all this is telling us. + +The other thing this is +telling us-- the wave front + +is a sphere. + +The amplitude of the electric +field drops off like 1/r. + +And it is not uniform +in all direction, + +as we've seen in the past. + +Right? + +For example, if I +take this charge + +as it's oscillating up and down, +the maximum amplitude radiated + +is in this plane +where we are looking, + +where the +perpendicular component + +of the acceleration of +this is the maximum. + +And its minimum upwards is +0, because this acceleration + +has no component +of x perpendicular + +component to this direction. + +And similarly, for this. + +The other thing which +I wish to point out + +is that the polarization of +the electromagnetic wave, + +the electric vector, is +parallel to the perpendicular + +component of a. + +So from this, the +electric vector, + +when it gets to +here or here, will + +be in the direction of +x, while from this one, + +it'll polarized in +the direction y. + +The other thing which +I want to stress, + +that we will in the +other examples-- + +always consider +a situation where + +the point where we're looking +at the electromagnetic field + +is far away from +where the charges are. + +The formula, which I +just showed you here, + +applies only in the far field. + +Nearby, the electric field +and the magnetic field + +are very complicated. + +They can be calculated, but they +cannot be summarized in that + +simple form. + +But if I'm far away from the +accelerating charge then, + +it is possible to write +it in this simple form. + +So our discussion is only valid +if the wave length radiated + +is much smaller +than the distance + +from where we're considering. + +This distance is also +much smaller than that. + +And this is to allow us +to approximate sine theta + +by theta, et cetera. + +And that's the case, alright? + +OK. + +With that, we can now +immediately solve the problem. + +Simply consider the +acceleration of each charge + +from our knowledge of +where the charge is. + +We can differentiate +it twice, and we + +can get the acceleration. + +So we know that the acceleration +of the first charge, + +which is oscillating +along the x-axis, + +is given by minus +a omega squared + +cosine omega in the x-direction. + +I want to emphasize, +because this + +is in the same direction as the +perpendicular component of a1. + +And, I'm sorry. + +I misspoke. + +The answer-- what +I said is correct + +but for the wrong reason. + +In this case, by definition, the +acceleration of the first one + +is this because the +displacement of the first one + +is in the x-direction. + +Similarly, the acceleration +on the second one + +is in the y-direction, +because the displacement + +is in the y-direction. + +Alright? + +So these are the +two accelerations. + +This is just some-- +occasionally I'll use omega, + +occasionally lambda just +to remind you of that. + +OK. + +So all I now have to do +for each of the charges + +is calculate this +quantity at the position + +where I want to calculate +the electric and the magnetic + +field. + +So, first of all +in this problem, + +we're asked to do +it in two places. + +We're asked to do +it at position p1 + +and at p2. p1 is +along the z-axis, + +and p2 is off the z-axis. + +First, let's do it for p1. + +So, the electric field, +due to the first charge + +at position p1 at time t, +is given by this formula + +if I insert in this for the +distance r, which is L. OK? + +And I put in the +acceleration of this one + +and the perpendicular +component of the acceleration + +perpendicular to the line +drawing my two charges. + +And the position +p1 is-- in fact, + +that line is along the z-axis. + +So the perpendicular +direction is, in fact, + +in the x-direction. + +OK. + +So I don't even have to take +the-- the actual acceleration + +is the perpendicular component. + +OK. + +And I have to calculate +it at a time which + +is t minus the distance p1 is +from in my charges, which is L. + +So it's minus omega L over c. + +I calculate t prime in here. + +Notice, I have not +tried to calculate + +the distance between the +charge and p1 exactly, + +because I told you that +the distance d is very much + +smaller than L. And so the +overall distance is negligently + +different from being +just L. So that's + +the electric field +due to the first one. + +Similarly, I can do the +same for the second one. + +Everything is the same. + +The only difference +in that case is + +that now the electric +vector-- the acceleration + +is along the y-axis and +therefore, the electric field + +is polarized along +the y-direction. + +So at the point p1, the two +electric fields are the same. + +They're both +oscillating in phase + +with the same +frequency, et cetera. + +But this one is pointing +in the x-direction. + +This in the y-direction. + +Now, as I mentioned at the +beginning, if at any point + +you have electric field +due to two sources, + +they simply add because the +system is a linear system. + +So we simply have to +add the electric fields. + +Electric fields are +vectors, therefore + +we don't add them +algebraic as scalars, + +but we have to add +them vectorially. + +And so, we take this vector +and that vector and add it. + +And that gives us the total +electric field at point p1. + +And simply from here, +I get d0 like that, + +which I can rewrite in +terms of a unit vector. + +Alright? + +This is a unit vector, +which is at 45 degrees. + +In other words, if that's +the z-direction x and y, + +it's at 45 degrees to +both the x and y-axes. + +That's the unit vector. + +This is the amplitude of it. + +And this is d-- tell us what +is the oscillating frequency + +and what is the phase. + +Notice, although each +one of these sources + +radiated there an electric +field of magnitude E0, + +when I add them, I did not get +to 2E0, because as I mentioned, + +electric fields +are vectors, and we + +have to add them vectorially. + +And that's why you +get here the root 2. + +So this is the first +example, which I've done. + +Now I want to take +the same geometry + +but calculate what is +the electric field. + +What we've just done, +we've calculated here. + +Now I want to do +the same situation-- + +two sources +oscillating coherently. + +But I want to look at what is +the electric field at the point + +p2. + +And I've taken p2 to be +in that the xz-plane, + +but in a direction that's +an angle lambda over a to d. + +d is this distance. + +Lambda is the wavelength of the +radiated electromagnetic wave. + +And I've taken this +crazy number simply + +to make the arithmetic +come out easier at the end. + +And so we now want to calculate +the electric field here. + +And we do exactly the same +except we go a little faster. + +What I will do is I will +calculate the electric field + +here. + +Due to this charge +oscillating, I'll + +then calculate the +electric field here. + +Due to this charge, this one +is oscillating like that. + +I'm reminding you this one +is oscillating like that. + +And we will vectorially +add the two. + +Now, from the point of +view of the amplitude, + +the difference in distance +between this and here or this + +and here or this and +here is insignificant. + +And so I have ignored that +in the previous calculations, + +and I'll do the same here. + +But when you add +to the two, we have + +to worry about +the relative phase + +of the alternating +the electric fields. + +And the difference of +this distance compared + +to that distance is no +longer insignificant + +when it comes to the relative +phase of the two radiations. + +So, in this formula when I'm +calculating the electric field, + +this r-- it doesn't +matter whether I + +call this L or L plus +a little bit or less. + +This doesn't change very much. + +But in calculating the +phase of the radiation, + +I cannot ignore that. + +In the previous case, +the phase was the same + +because this distance +and that distance + +are exactly the +same by symmetry. + +For this position, that +distance and that distance + +are not the same. + +And so I what I will do is I'll +use as reference that distance, + +and when I'm calculating +this distance, + +I will calculate by how much +I have to subtract from here + +to end up with this length +and for this one, by how much + +I've add to it to get to here. + +Pay attention to that when +I'm doing that in a second. + +And the rest is very +straightforward and similar + +to what I've just done. + +So now, as I say, I want to +calculate the electric field + +at the point p2, which is this. + +This is the x-coordinate, +y, and z-coordinate. + +And I pointed it out +to you a second ago. + +Alright. + +So I don't have to rewrite +all those q's and omegas, + +et cetera, by +analogy, what we've + +done-- the electric field due to +the first charge at position p2 + +will be that the +amplitude that we've got + +is the same for the +previous case of P1. + +So it's-- E0 is the amplitude. + +It's pointing in the +x-direction as before. + +And we know that the description +of the electric field + +will be given by cosine omega +t1 prime where t is-- so far + +I've always talked +about t prime, + +because I only had one when +I was considering just one + +charge. + +But here the t1 is +different to t2. + +So quickly, this term comes +from the perpendicular component + +of a right as before. + +And t1 prime is +equal to the time + +when I'm looking at the electric +field minus the time it takes + +for this signal from the +charge to get to the point + +where I'm looking at the +electric field to point p2. + +So, it will be-- as I +told you a second ago, + +I'll take L as the reference. + +And I'm subtracting from it that +distance d sine lambda over 8d. + +For a second, let me +go back to that picture + +because you can +easily get confused. + +So I'm coming back here. + +What we're trying to calculate-- +the distance from here to here. + +So I'm taking this +distance, which is L, + +and I'm subtracting from +it this distance, which + +is d sine this angle here, +which is the same as this angle. + +So that's what I'm +calculating there. + +So this is L minus d sine +lambda over 8d divided by c. + +Then the electric field is +then immediately followed + +from this d0 in the x-direction, +cosine omega t minus this. + +And if you assume that +this angle is small, + +and I told you that that's +given in the problem, + +the sine of an angle +is equal to an angle. + +Approximately, they're small. + +And if I multiply this out, +I simply get an angle here. + +That's pi/4. + +So I find that the +electric field at point p2 + +is pointing, due to the +first charge, is pointing + +in the x-direction, +as you'd expect, + +because of the direction +which the charge is moving + +times E0 times cosine omega +t minus omega L over c + +plus a phase like that. + +How about from the other charge? + +If I take the other +charge, everything + +will be the same except now +this charge is oscillating + +in the y-direction, so +the electric field will + +be in the y-direction. + +And this time, +it's omega t2 prime + +where t2 will be +very similar to t1 + +but now the distance is +greater by this amount. + +For a second, let's go +back to this picture + +so you see what +I'm talking about. + +If I calculate +this distance, it's + +the same as that distance +plus d sine this angle, which + +is this lambda over 8d, +and I'm subtracting. + +And I want to +emphasize that what + +I'm focusing on here, +what is important, + +is the difference +between this and that + +and not the absolute value. + +So when I'm +approximating-- if you + +do this calculation +for yourself, + +you'll see I'm doing +a slight approximation + +to calculate that. + +But this and this is +the same quantity. + +But the important thing is +the difference of this phase + +here is plus pi/4. + +Here is minus pi/4, +because here it's + +minus that little +bit of a distance, + +and here it's plus a +little bit of the distance. + +So we finished. + +The total electric +field at p2 and time t + +is the sum of the electric field +due to the first charge plus + +due to the second challenge. + +And as I mentioned a second ago, +electric fields are vectors. + +Thus, we have to add +these two vectorially. + +This is in the x-direction. + +This is in the y-direction. + +And so what we +have at that point + +is two electric oscillating +electric fields. + +They're oscillating +coherently but out of phase. + +This is a plus pi/4 phase. + +This is a minus pi/4 phase. + +So the difference of phase +between those two is pi/2. + +It's 90 degrees. + +So this is out of phase with, +one with respect to the other, + +by 90 degrees. + +They're coherent, but +90 degrees out of phase. + +The magnitudes are +the same, but this one + +is pointing in the x-direction +and this in the y-direction, + +and you know what +that corresponds to. + +If I have at the location +two electric fields, one + +doing that and the +other one doing this, + +if they're out of phase by 90 +degrees, and I add the two, + +what do I get? + +I get a constant +size of a radius, + +and the thing is rotating. + +That is the description +of a rotating + +vector of magnitude E0. + +In the other case, at P1, there +was not this phase difference, + +so the two were-- one was +oscillating like this. + +The other one was +oscillating like that. + +But they were oscillating +at the same phase. + +So this is what they were doing. + +And if you add those up, clearly +you get a line diagonally. + +And that's why before, the +result was a linearly polarized + +electric field there at 45 +degrees to the x and y-axis. + +In this case, these two are +out of phase by 90 degrees. + +So when one is doing +this, the other one + +is also but out of phase. + +And so when this +one's at the maximum, + +this one's at the minimum, and +so that's what's happening. + +So they're out of phase. + +And then if you +add the two up, you + +get something doing +this, which we + +called circularly +polarized light. + +And that's why I chose +that crazy angle, + +because it came out like this. + +So that's the end +of that problem. + +I will now do another +one, which to emphasize + +some technique-- a different +technique of doing it. + +OK. + +Let's move. + +So the next problem +is the following. + +We're again dealing with several +charges oscillating coherently. + +Their cohering sources. + +And we're asking, what +are the electric fields? + +Somewhere in space? + +And if we found the +electric field, of course, + +we could always calculate +the magnetic field + +at that location using Maxwell's +equations or our knowledge + +of the relation between +electromagnetic field + +in a progressive +electromagnetic way. + +Now I'll take three charges. + +But that's not the hope. + +It's more different, but +what this problem adds + +is I'll use it to show a +technique that is often used, + +which helps in the +solution of such problems. + +So the problem now +is the following. + +I have three charges. + +Each of the same magnitude. + +They're located along +the x-axis at position 0 + +minus d and minus 2d. + +So these distances are the +same-- each distance d. + +And what the problem +is-- up to t equals 0, + +these three charges are +displaced from equilibrium. + +I put y is 0. + +So, at the height, y0 here. + +Then, at t0-- don't ask me how. + +Magically, I get these three +charges to start oscillating. + +Such that at time +yt, the displacement + +is y0 cosine omega t. + +And they continue-- this +continues like that forever. + +The question is, as a result +of this oscillation of charges, + +what will be the electric +field a long way away from here + +at position L along the x-axis, +so we call that position p. + +So the problem is, calculate +E at position p for all times. + +Once we've calculated, we could +calculate the magnetic field, + +But to save you time--I mean, +you could do it for yourself. + +You know if you calculate +the electric field, + +there is a progressive +wave over here. + +if E is like this, +then b will be + +perpendicular to it +of the amplitude which + +is just a dE over c. + +So that will be straightforward, +so I'm not asking it. + +Now, let's just +think for a second + +what goes on in this problem. + +Initially, the charges +are stationary, + +so there will be a +Coulomb field around. + +But we are specifically asked +to ignore static fields. + +So in the last problem too, +I ignored static fields. + +We were only considering +the time-dependent fields. + +You can always have superimposed +on the time-dependent field + +some static field that +doesn't add anything. + +So what we have here is at +time up to time t equals 0, + +the charges are here. + +So let's take one +of the charges here. + +Then it starts moving. + +It will have an +acceleration, which + +is perpendicular to the +direction in which I'm + +interested the propagation +of the electromagnetic wave. + +So it will certainly +radiate in this direction. + +So this charge, which was +oscillating, will radiate. + +Over here at the point +p, the electric field + +will be initially 0. + +And it will continue being 0 +until the electric field, which + +is generated here, +propagates that distance. + +So, only after a time, L/c, will +the electric vector get here? + +So up to the time L/c, there +will be no electric field here. + +How about this charge? + +This charge is initially +is displaced at y0. + +Then it starts +oscillating the same. + +Initially, it's stationary. + +It'll produce a Coulomb field, +which is a static field. + +We're not interested in it. + +But once it starts accelerating, +it starts radiating. + +And that radiating progresses. + +So that will also produce +a field over here. + +But since these two +distances are different, + +the radiation from here, first +of all, will get there a little + +later. + +But also, once it gets here, +it will have a different phase + +because the radiation +traveled a different distance. + +And same for the last one. + +So now, how do we do this? + +I almost sound like +a broken record. + +As always, I can calculate +the electric field + +from each charge, and it'll be +given by this formula, which + +we've seen over and over +again where t prime is + +the distance from the +charge to the point p. + +Furthermore, I know the +perpendicular acceleration + +and also the perpendicular +component of it, + +because in this problem, +the perpendicular component + +is the same as the +actual acceleration. + +After time t equals +0, the acceleration + +of every one of these charges +a1, a2, a3, is the same. + +It's the same direction. + +And it's given by +that simply because we + +know what is the +displacement y of t. + +If I differentiate it twice, +I get the acceleration. + +If I plug this into +here for each charge, + +I will know what is the electric +fields from each charge. + +I can then add the electric +fields from each charge, + +and I'll get the +total electric field. + +You have to add +them vectorially. + +So, once again, for +t less than L/c, + +the electric field at +position p will be 0. + +There was no earlier +accelerated charge + +which radiated an +electric field which + +got here before this time. + +So that's nice and easy. + +How about for a later period, +a period between L/c or just + +after L/c. + +For t just after +L/c, the acceleration + +of the charge at x equals 0 +would produce an electric field + +which propagated and would +have got to my point p. + +So between that time +L/c and the time when + +the radiation from the second +charge got to the point p, + +I will have an +electric field but only + +from the first radiation +due to the first charge. + +I can forget the second +and third charge at minus d + +and a minus 2d but not +the charge at x equals 0. + +So that will be I +use this formula. + +I plug it in. + +I use the acceleration of a1. + +I put it in here, and I know +that t prime is t minus r/c. + +r in this case is +L. So this formula + +immediately tells me that's +what it is and lets me save-- + +I don't want to write +this over and over again. + +This-- I'll call that E0. + +So from the first +charge, this is + +what the electric field-- it's +an oscillating electric field-- + +what it looks like +at position p. + +But I'm reminding you, this is +only true for this time window + +when the radiation +from the charge at q + +equals 0 has got to point p, +but from the other one's not. + +How about from a little later? + +From the time L/c plus d +over c-- in other words, + +now radiation over +a distance L plus d + +has had time to +reach my point p. + +So now, the second charge, +the one that minused d, + +has had enough time +to reach my point p. + +But if I limit to the window, +this and that, in other words, + +there's still a difference +of d/c in time between those. + +I will get at point +p the radiation as + +from the first charge. + +That's exactly the same as this. + +That's obviously got there. + +But now from the second +charge, it has got there. + +And they're very similar. + +They are both-- the +charges are accelerating + +along y-direction in phase. + +So they have the same +frequency, and the amplitude + +is going to be the same, +because in this formula, + +this r is the total +distance between the charge + +and the point p. + +Now, there is a tiny +difference in that distance + +for the first and second charge. + +But if I take them +here a tiny difference, + +this will not change very much. + +I'm ignoring that difference. + +So I'm calling both of +them E0 and ignoring + +that tiny difference. + +But I cannot ignore the +difference on the phase. + +So the t prime into +two cases is different. + +In one case, it's t minus L/c. + +And the other case, +it's minus L/c + +minus this little extra +time where the radiation + +takes from the second +to the first charge. + +And the third one, +the radiation could + +not to reach the point p yet. + +So that is now the total +electric field from the two. + +And finally-- and +I have to do this. + +I haven't done the addition. + +And finally, if we take a time +which is greater than this, + +then we are in a situation +where the oscillation + +on the last charge +has had enough time + +to get to the point p. + +Let me go back to this +picture and just repeat this + +so that you don't get lost. + +So these charges have started +to move all at the same time. + +After a time L/c, the +radiation from this one + +will have got to here. + +If I add to the time +d/c, that's how long + +the electromagnetic radiation +takes to get to from here + +to here. + +So a little bit +later, the radiation + +from this plus the radiation +from this is getting here. + +And a little bit later, +the radiation from this + +also gets there. + +So at the end, there +is now radiation + +from all three charges +getting to this point. + +And from then on, +it'll continue forever + +as long as these +are oscillating. + +So from then on, you have +the radiation from the three. + +And the only +difference between them + +is they all have a +slightly different phase. + +So you might be satisfied +with just knowing + +that these are the +electric fields as sums + +of the algebraic +sum between those + +all pointing the same direction. + +So I don't have to worry +about the vector addition, + +but I have to worry about the +addition of the amplitudes. + +If we want to find +out what this sum is-- + +what happens when you add one +or two or three oscillatory + +functions like this? + +What is the resultant +oscillation? + +We have to algebraically, +or trigonometrically, add + +these three or these two. + +And I do this example +in order to introduce + +a mathematical technique, which +in situations of this kind, + +makes life much, much easier +than just going and adding + +cosines. + +And it is by using the +so-called complex amplitudes. + +So the issue is, how do we add +these three cosine functions + +and where they each have a +slightly different phase? + +One way is brute force. + +Do it by using trigonometrical +[? formulae ?]. + +For example, you could +add the first and second + +by using the formula cosine +a plus cosine b equals twice + +cosine half the +sum of the angles + +cosine half the +difference of the angle. + +And you could do that for +adding the first to the second, + +and then later, once +you've got an answer, + +you could add to that +the third, et cetera. + +But you can see that if +you have five, six, seven, + +eight sources, or many, many +more, this becomes cumbersome. + +There's a nice +mathematical trick. + +And that is by using +complex numbers. + +You know that this is +De Moivre's theorem + +that E to the j +theta can be written + +as the cosine of an angle +plus j sine of an angle. + +I can use this +mathematical trick + +to solve the problem +of adding these. + +Remember that at this stage, +this is pure mathematics. + +As always, we've converted +an experimental situation + +into a mathematical problem. + +And we've got to solve +this using mathematics. + +You don't have to +ask yourself what's + +the meaning of j +sine theta something. + +It is a mathematical expression. + +And we're going +to use mathematics + +to solve this problem. + +Using this, I could +always write-- + +that suppose I have the +cosine of some function, + +I can always write it +as the real part of E + +to the j that angle. + +So if cosine, for +example, of omega + +t minus kL, and you'll see it +somewhere up there for example. + +It can be written as the real +part of E to the j omega t + +minus j to the kL, but that is +the same as multiplying these + +as E to the j omega t times E +to the minus jkL, where here I'm + +just reminding you of k +omega c, et cetera, is. + +I can do this for +every-- if I want + +to d-- let's say we're +doing this one first. + +I want this to that. + +I can write this as the real +part of a complex number. + +And I can write this as a real +part of the complex number. + +What I will then do-- I +will first solve this. + +I will do the addition by +adding the two complex numbers, + +knowing full well that if I +added the complex numbers, + +I will have in the process +added the real parts and also + +the imaginary parts. + +And since you cannot have a real +number equal to an imaginary + +number in any way, if I take +during the process of addition, + +I would have continuously kept +separate the real and imaginary + +part. + +So for example, for this third +part, this addition here, + +I can write the first term as +the real part of each of the E + +to the j omega t, E to the minus +jkL in the y-direction times + +E0. + +This is, of course, +nothing other + +than E cosine omega t minus Lc. + +The second one I +can do the same. + +This is the same. + +And the only difference +between those two + +is that phase minus d/c, +which is kd [? using ?] here. + +And so, the real +part of this will + +be the answer to +the sum of those. + +So I'll do this in +a second, but then + +let me immediately go to the +third one so I do both of them + +at the same time. + +And in this third case, +the answer I'll want + +is the real part. + +This is the same as before. + +And here the three terms. + +The first term is just E0, +because all the phases are out + +here. + +The second one differs from +that by minus d/c, which + +is minus kd, so it's +E to the minus jkd. + +And the last one is E to +the minus j times 2 kd, + +because here we have a 2d. + +Now, why did I +bother to do this? + +Because this addition is +trivial while the other one + +was not trivial. + +It needed hard labor. + +Why do I say this is trivial? + +Because I've converted +this algebraic problem + +into a geometry one. + +I can represent each +one of these terms + +on an Argand diagram. + +So for example, here to here. + +Let's take the third case. + +We're adding these two vectors. + +This is only a real +part, so it's E0. + +That's a vector of length +E0 along the real axis. + +I'm reminding you on +an Argand diagram, + +this direction is the real axis, +and this is the imaginary axis. + +With that, so the +E0 is only real, + +and I'm adding to it E to +the minus jkd, which is what? + +Has a magnitude of E0. + +And this is the angle, +theta, with respect + +to the real axis, which +in this case is minus kd. + +So this is the +angle, so it's minus. + +So I'm going down. + +So it's a vector, +which is length E0, + +and it's pointing in +an angle of minus kd. + +It's this angle. + +I suppose, not to confuse +you, I'll call it minus kd. + +This is minus and minus, +just so not to confuse you. + +With the distance +between the charges of d, + +kd is 2 pi over 3, +which is a 120 degrees. + +So this term is a +vector like that. + +And we have to add +those two vectors. + +Well, this is easy to do. + +This angle is 60 degrees. + +This is 120. + +OK? + +And this length +is equal to that, + +so the result of +this plus of that + +will be this red vector +here, which has magnitude E0. + +And at what angle is it? + +This angle here 240 degrees. + +I'm sorry. + +I need that later in the +second for the next part. + +I don't need it at this stage. + +I'm sorry. + +I'm adding this to that. + +The result is this vector. + +And this vector +has a magnitude E0. + +And this angle +here is, of course, + +60 degrees, which +is 2 pi over 6. + +And so, so adding those two +will give me just the real part + +on each of E to the j +omega t to the minus + +jkL in the y-direction. + +And adding those two +is E0 in the direction + +of 60 degrees, which +is minus 2 pi over 6. + +Bracket right there. + +So this describes this addition. + +And this, of course, I +can now take the real part + +of this whole thing, +and there is the answer. + +E0 in the y-direction +cosine omega + +t minus omega over c and +with a phase of minus 2 pi + +over 6, which is of +course, 60 degrees. + +For the first one, so +this is the answer. + +And we didn't have +to add to any cosine. + +We just do a vector addition +on the Argand diagram. + +Let's do the last case. + +In the last case we have +three terms-- one, two, three. + +If I write these as the real +part of a complex amplitudes, + +by analogy with this, the +first term is the same. + +The second term is the same. + +And the third one is almost +the same as the second time, + +except the d has now become 2kd. + +This was d/c. + +Here it's 2d over c. + +So here we have minus j 2kd. + +So now I have to add these +three complex numbers. + +And again, this is much easier +to do it geometrically then + +trigonometrically. + +The first one I can represent +by this on the Argand diagram. + +The second one by this. + +And the third one, of course, +is at 240 degrees to here. + +This was 120. + +The next one is 240, which +means that the last one, all + +that it is, I'd +remove this vector, + +and it's in this direction. + +So now we're adding +this to that to this, + +and even I can solve +that in my head. + +If I add this vector to +that to that, I get 0. + +I'm back where I started. + +So this quantity is 0. + +And so the electric +field will be 0. + +And see how +relatively easy it is + +to do if you use this +complex amplitude method? + +One can do many problems to +do with waves and vibrations + +using complex amplitudes. + +In general, it makes +the algebra easier. + +But for most cases, I have +not done that in order + +to-- that you don't have the +double difficulty of trying + +to understand the physics and +struggling with the mathematics + +that you may not be so familiar. + +By the time we come to many +sources of the radiation, + +it is so much easier to +do using complex amplitude + +that I would urge you to learn +it on simple cases like this, + +and then use it in more +complicated situation. + +Finally, I just want +to save one word, + +and that is the following. + +Some of you may be surprised. + +How is it that I got-- +I have three charges. + +Three charges +oscillating, radiating. + +How is it that when +you get to here, + +you get after a certain +time, you get to [INAUDIBLE]. + +And the answer is-- +pictorially you + +can see what happens-- +at this point, + +the radiation from one of +the charges looks like that. + +From the second one, +it's out the phase + +by 1/3 of the wavelength, +and the next one by 2/3. + +And so you're adding three +waves, three oscillating + +motions on top of each other. + +And if you add these, +the result is 0. + +That is, pictorially, +the same as what + +I did here in this diagram. + +You simply-- you do have three +waves arriving from the three + +charges, but they +add to 0 because each + +has a different phase +from the previous one. + +And you can see it +here what happens. + +Here I'm plotting as +a function of time. + +The amplitude at the point p. \ No newline at end of file diff --git a/5C-Wp6sL8lg.txt b/5C-Wp6sL8lg.txt new file mode 100644 index 0000000000000000000000000000000000000000..7f9a106f3dc202d46367a30a46ead5d865e65128 --- /dev/null +++ b/5C-Wp6sL8lg.txt @@ -0,0 +1,16568 @@ +align:start position:0% + +welcome to lecture 18 of + + align:start position:0% +welcome to lecture 18 of + + + align:start position:0% +welcome to lecture 18 of +1413 this lecture is about gender + + align:start position:0% +1413 this lecture is about gender + + + align:start position:0% +1413 this lecture is about gender +discrimination and identity + + align:start position:0% +discrimination and identity + + + align:start position:0% +discrimination and identity +okay so what's the agenda today we're + + align:start position:0% +okay so what's the agenda today we're + + + align:start position:0% +okay so what's the agenda today we're +going to talk about gender and identity + + align:start position:0% +going to talk about gender and identity + + + align:start position:0% +going to talk about gender and identity +and particularly discrimination + + align:start position:0% +and particularly discrimination + + + align:start position:0% +and particularly discrimination +first i'm going to give you a broad a + + align:start position:0% +first i'm going to give you a broad a + + + align:start position:0% +first i'm going to give you a broad a +quick overview of why this is an + + align:start position:0% +quick overview of why this is an + + + align:start position:0% +quick overview of why this is an +important + + align:start position:0% +important + + + align:start position:0% +important +area to study then i'm going to give you + + align:start position:0% +area to study then i'm going to give you + + + align:start position:0% +area to study then i'm going to give you +an + + align:start position:0% +an + + + align:start position:0% +an +equally brief um overview of the gender + + align:start position:0% +equally brief um overview of the gender + + + align:start position:0% +equally brief um overview of the gender +gap + + align:start position:0% +gap + + + align:start position:0% +gap +what wages the fact that women earn less + + align:start position:0% +what wages the fact that women earn less + + + align:start position:0% +what wages the fact that women earn less +money than men + + align:start position:0% +money than men + + + align:start position:0% +money than men +for equal work how that has + + align:start position:0% +for equal work how that has + + + align:start position:0% +for equal work how that has +evolved over time and how much still is + + align:start position:0% +evolved over time and how much still is + + + align:start position:0% +evolved over time and how much still is +left of this gender gap + + align:start position:0% +left of this gender gap + + + align:start position:0% +left of this gender gap +then we're going to talk a little bit + + align:start position:0% +then we're going to talk a little bit + + + align:start position:0% +then we're going to talk a little bit +about potential technological solutions + + align:start position:0% +about potential technological solutions + + + align:start position:0% +about potential technological solutions +can we use technology to improve um or + + align:start position:0% +can we use technology to improve um or + + + align:start position:0% +can we use technology to improve um or +to reduce discrimination + + align:start position:0% +to reduce discrimination + + + align:start position:0% +to reduce discrimination +potentially and the answer will be yes + + align:start position:0% +potentially and the answer will be yes + + + align:start position:0% +potentially and the answer will be yes +to some extent but technology will not + + align:start position:0% +to some extent but technology will not + + + align:start position:0% +to some extent but technology will not +solve everything + + align:start position:0% +solve everything + + + align:start position:0% +solve everything +then we're going to talk about two + + align:start position:0% +then we're going to talk about two + + + align:start position:0% +then we're going to talk about two +particular important issues one is + + align:start position:0% +particular important issues one is + + + align:start position:0% +particular important issues one is +beliefs and people's um + + align:start position:0% +beliefs and people's um + + + align:start position:0% +beliefs and people's um +updating about beliefs when it comes to + + align:start position:0% +updating about beliefs when it comes to + + + align:start position:0% +updating about beliefs when it comes to +like man and woman and their skills + + align:start position:0% +like man and woman and their skills + + + align:start position:0% +like man and woman and their skills +um and then we're going to talk about + + align:start position:0% +um and then we're going to talk about + + + align:start position:0% +um and then we're going to talk about +gender identity norms in particular + + align:start position:0% +gender identity norms in particular + + + align:start position:0% +gender identity norms in particular +um which is the idea that people's + + align:start position:0% +um which is the idea that people's + + + align:start position:0% +um which is the idea that people's +deeply held beliefs about what should be + + align:start position:0% +deeply held beliefs about what should be + + + align:start position:0% +deeply held beliefs about what should be +done in society or not might affect + + align:start position:0% +done in society or not might affect + + + align:start position:0% +done in society or not might affect +their + + align:start position:0% +their + + + align:start position:0% +their +behavior and finally we're going to talk + + align:start position:0% +behavior and finally we're going to talk + + + align:start position:0% +behavior and finally we're going to talk +a little bit about + + align:start position:0% +a little bit about + + + align:start position:0% +a little bit about +demand and supply for different tasks + + align:start position:0% +demand and supply for different tasks + + + align:start position:0% +demand and supply for different tasks +so in particular i'm going to show you + + align:start position:0% +so in particular i'm going to show you + + + align:start position:0% +so in particular i'm going to show you +that women are + + align:start position:0% +that women are + + + align:start position:0% +that women are +more likely to say yes to what's called + + align:start position:0% +more likely to say yes to what's called + + + align:start position:0% +more likely to say yes to what's called +non-promotable tasks tasks that are good + + align:start position:0% +non-promotable tasks tasks that are good + + + align:start position:0% +non-promotable tasks tasks that are good +for society but perhaps not good for + + align:start position:0% +for society but perhaps not good for + + + align:start position:0% +for society but perhaps not good for +their career + + align:start position:0% +their career + + + align:start position:0% +their career +or tasks that are good for like a + + align:start position:0% +or tasks that are good for like a + + + align:start position:0% +or tasks that are good for like a +company or university as a whole + + align:start position:0% +company or university as a whole + + + align:start position:0% +company or university as a whole +but are not good not promotable in the + + align:start position:0% +but are not good not promotable in the + + + align:start position:0% +but are not good not promotable in the +sense that they they help women in fact + + align:start position:0% +sense that they they help women in fact + + + align:start position:0% +sense that they they help women in fact +i get promoted women are more likely to + + align:start position:0% +i get promoted women are more likely to + + + align:start position:0% +i get promoted women are more likely to +say yes to those things + + align:start position:0% +say yes to those things + + + align:start position:0% +say yes to those things +in addition on top of that precisely + + align:start position:0% +in addition on top of that precisely + + + align:start position:0% +in addition on top of that precisely +because they're more likely to say yes + + align:start position:0% +because they're more likely to say yes + + + align:start position:0% +because they're more likely to say yes +they're also more likely to be asked in + + align:start position:0% +they're also more likely to be asked in + + + align:start position:0% +they're also more likely to be asked in +the first place which sort of amplifies + + align:start position:0% +the first place which sort of amplifies + + + align:start position:0% +the first place which sort of amplifies +that difference i'm going to tell you + + align:start position:0% +that difference i'm going to tell you + + + align:start position:0% +that difference i'm going to tell you +about this in more detail the first + + align:start position:0% +about this in more detail the first + + + align:start position:0% +about this in more detail the first +question you might ask is why + + align:start position:0% +question you might ask is why + + + align:start position:0% +question you might ask is why +study gender differences i have four + + align:start position:0% +study gender differences i have four + + + align:start position:0% +study gender differences i have four +answers for you + + align:start position:0% +answers for you + + + align:start position:0% +answers for you +the first one is simple equity fairness + + align:start position:0% +the first one is simple equity fairness + + + align:start position:0% +the first one is simple equity fairness +and justice issues + + align:start position:0% +and justice issues + + + align:start position:0% +and justice issues +people simply should be rewarded equally + + align:start position:0% +people simply should be rewarded equally + + + align:start position:0% +people simply should be rewarded equally +for the same output + + align:start position:0% +for the same output + + + align:start position:0% +for the same output +so if a man and a woman works equally + + align:start position:0% +so if a man and a woman works equally + + + align:start position:0% +so if a man and a woman works equally +many hours and is equally productive + + align:start position:0% +many hours and is equally productive + + + align:start position:0% +many hours and is equally productive +they should be paid the same + + align:start position:0% +they should be paid the same + + + align:start position:0% +they should be paid the same +and if that's not the case that's not + + align:start position:0% +and if that's not the case that's not + + + align:start position:0% +and if that's not the case that's not +and that's unequal that's unfair or not + + align:start position:0% +and that's unequal that's unfair or not + + + align:start position:0% +and that's unequal that's unfair or not +unjust or not justified now + + align:start position:0% +unjust or not justified now + + + align:start position:0% +unjust or not justified now +there might be an additional uh equity + + align:start position:0% +there might be an additional uh equity + + + align:start position:0% +there might be an additional uh equity +and fairness issues that + + align:start position:0% +and fairness issues that + + + align:start position:0% +and fairness issues that +men and women might not even be allowed + + align:start position:0% +men and women might not even be allowed + + + align:start position:0% +men and women might not even be allowed +to work as much um + + align:start position:0% +to work as much um + + + align:start position:0% +to work as much um +women might not be allowed to work as + + align:start position:0% +women might not be allowed to work as + + + align:start position:0% +women might not be allowed to work as +much as men that's an additional sort of + + align:start position:0% +much as men that's an additional sort of + + + align:start position:0% +much as men that's an additional sort of +fairness + + align:start position:0% +fairness + + + align:start position:0% +fairness +concern second there's an efficiency + + align:start position:0% +concern second there's an efficiency + + + align:start position:0% +concern second there's an efficiency +argument which is + + align:start position:0% +argument which is + + + align:start position:0% +argument which is +overall productivity in welfare falls if + + align:start position:0% +overall productivity in welfare falls if + + + align:start position:0% +overall productivity in welfare falls if +women and other groups are held back by + + align:start position:0% +women and other groups are held back by + + + align:start position:0% +women and other groups are held back by +discrimination and other distortions + + align:start position:0% +discrimination and other distortions + + + align:start position:0% +discrimination and other distortions +and indeed a substantial share of recent + + align:start position:0% +and indeed a substantial share of recent + + + align:start position:0% +and indeed a substantial share of recent +u.s growth can be explained by the + + align:start position:0% +u.s growth can be explained by the + + + align:start position:0% +u.s growth can be explained by the +improved allocation of talent in the + + align:start position:0% +improved allocation of talent in the + + + align:start position:0% +improved allocation of talent in the +economy + + align:start position:0% +economy + + + align:start position:0% +economy +so this is just a simple idea that well + + align:start position:0% +so this is just a simple idea that well + + + align:start position:0% +so this is just a simple idea that well +if + + align:start position:0% +if + + + align:start position:0% +if +we exclude certain groups including + + align:start position:0% +we exclude certain groups including + + + align:start position:0% +we exclude certain groups including +women from + + align:start position:0% +women from + + + align:start position:0% +women from +certain jobs the most talented people in + + align:start position:0% +certain jobs the most talented people in + + + align:start position:0% +certain jobs the most talented people in +those groups + + align:start position:0% +those groups + + + align:start position:0% +those groups +will not be allowed to some of the most + + align:start position:0% +will not be allowed to some of the most + + + align:start position:0% +will not be allowed to some of the most +talented people in those groups might + + align:start position:0% +talented people in those groups might + + + align:start position:0% +talented people in those groups might +not be allowed to do those jobs + + align:start position:0% +not be allowed to do those jobs + + + align:start position:0% +not be allowed to do those jobs +and that's bad for society overall think + + align:start position:0% +and that's bad for society overall think + + + align:start position:0% +and that's bad for society overall think +about for example doctors if women + + align:start position:0% +about for example doctors if women + + + align:start position:0% +about for example doctors if women +cannot be doctors + + align:start position:0% +cannot be doctors + + + align:start position:0% +cannot be doctors +well then we will essentially just + + align:start position:0% +well then we will essentially just + + + align:start position:0% +well then we will essentially just +exclude a large fraction of the most + + align:start position:0% +exclude a large fraction of the most + + + align:start position:0% +exclude a large fraction of the most +talented people in terms of like being + + align:start position:0% +talented people in terms of like being + + + align:start position:0% +talented people in terms of like being +doctors + + align:start position:0% +doctors + + + align:start position:0% +doctors +the smartest brightest and hardest + + align:start position:0% +the smartest brightest and hardest + + + align:start position:0% +the smartest brightest and hardest +working + + align:start position:0% + + + + align:start position:0% + +women and that will be worse + + align:start position:0% +women and that will be worse + + + align:start position:0% +women and that will be worse +not just for those women but it will + + align:start position:0% +not just for those women but it will + + + align:start position:0% +not just for those women but it will +also be bad for medical + + align:start position:0% +also be bad for medical + + + align:start position:0% +also be bad for medical +medical care innovation and so on in the + + align:start position:0% +medical care innovation and so on in the + + + align:start position:0% +medical care innovation and so on in the +medical profession + + align:start position:0% +medical profession + + + align:start position:0% +medical profession +because it's we just essentially exclude + + align:start position:0% +because it's we just essentially exclude + + + align:start position:0% +because it's we just essentially exclude +some of the best people from + + align:start position:0% +some of the best people from + + + align:start position:0% +some of the best people from +that type of work and if you want to + + align:start position:0% +that type of work and if you want to + + + align:start position:0% +that type of work and if you want to +learn more about this the people that i + + align:start position:0% +learn more about this the people that i + + + align:start position:0% +learn more about this the people that i +see it all + + align:start position:0% +see it all + + + align:start position:0% +see it all +is an excellent sort of discussion of + + align:start position:0% +is an excellent sort of discussion of + + + align:start position:0% +is an excellent sort of discussion of +these issues + + align:start position:0% +these issues + + + align:start position:0% +these issues +third we might learn about the + + align:start position:0% +third we might learn about the + + + align:start position:0% +third we might learn about the +formation of preferences and personality + + align:start position:0% +formation of preferences and personality + + + align:start position:0% +formation of preferences and personality +by studying gender + + align:start position:0% +by studying gender + + + align:start position:0% +by studying gender +and here the idea is that there are in + + align:start position:0% +and here the idea is that there are in + + + align:start position:0% +and here the idea is that there are in +many cases differences + + align:start position:0% +many cases differences + + + align:start position:0% +many cases differences +in preferences such as risk preferences + + align:start position:0% +in preferences such as risk preferences + + + align:start position:0% +in preferences such as risk preferences +social preferences + + align:start position:0% +social preferences + + + align:start position:0% +social preferences +and taste for competition or + + align:start position:0% +and taste for competition or + + + align:start position:0% +and taste for competition or +competitiveness + + align:start position:0% +competitiveness + + + align:start position:0% +competitiveness +but also in attitudes towards + + align:start position:0% +but also in attitudes towards + + + align:start position:0% +but also in attitudes towards +negotiation or other things such as + + align:start position:0% +negotiation or other things such as + + + align:start position:0% +negotiation or other things such as +identity aspirations or over + + align:start position:0% +identity aspirations or over + + + align:start position:0% +identity aspirations or over +under confidence more generally well + + align:start position:0% +under confidence more generally well + + + align:start position:0% +under confidence more generally well +so if there are these differences at + + align:start position:0% +so if there are these differences at + + + align:start position:0% +so if there are these differences at +later ages we can sort of learn about + + align:start position:0% +later ages we can sort of learn about + + + align:start position:0% +later ages we can sort of learn about +the formation of those preferences and + + align:start position:0% +the formation of those preferences and + + + align:start position:0% +the formation of those preferences and +personality + + align:start position:0% +personality + + + align:start position:0% +personality +um by uh looking for instance at like + + align:start position:0% +um by uh looking for instance at like + + + align:start position:0% +um by uh looking for instance at like +people at different ages and uh trying + + align:start position:0% +people at different ages and uh trying + + + align:start position:0% +people at different ages and uh trying +to understand at which ages + + align:start position:0% +to understand at which ages + + + align:start position:0% +to understand at which ages +those differences emerge for instance + + align:start position:0% +those differences emerge for instance + + + align:start position:0% +those differences emerge for instance +you might um + + align:start position:0% +you might um + + + align:start position:0% +you might um +look at like five-year-olds or + + align:start position:0% +look at like five-year-olds or + + + align:start position:0% +look at like five-year-olds or +ten-year-olds fifteen-year-olds and look + + align:start position:0% +ten-year-olds fifteen-year-olds and look + + + align:start position:0% +ten-year-olds fifteen-year-olds and look +at their risks on social preferences + + align:start position:0% +at their risks on social preferences + + + align:start position:0% +at their risks on social preferences +and then try to understand when those + + align:start position:0% +and then try to understand when those + + + align:start position:0% +and then try to understand when those +gender gaps + + align:start position:0% +gender gaps + + + align:start position:0% +gender gaps +emerge over time and that will allow us + + align:start position:0% +emerge over time and that will allow us + + + align:start position:0% +emerge over time and that will allow us +then to understand + + align:start position:0% +then to understand + + + align:start position:0% +then to understand +questions of nature versus nurture + + align:start position:0% +questions of nature versus nurture + + + align:start position:0% +questions of nature versus nurture +whether there are + + align:start position:0% +whether there are + + + align:start position:0% +whether there are +inherent differences in preferences and + + align:start position:0% +inherent differences in preferences and + + + align:start position:0% +inherent differences in preferences and +personality overall just men and women + + align:start position:0% +personality overall just men and women + + + align:start position:0% +personality overall just men and women +are just + + align:start position:0% +are just + + + align:start position:0% +are just +different inherently for some reason or + + align:start position:0% +different inherently for some reason or + + + align:start position:0% +different inherently for some reason or +um it could be that + + align:start position:0% +um it could be that + + + align:start position:0% +um it could be that +it's really about socialization and + + align:start position:0% +it's really about socialization and + + + align:start position:0% +it's really about socialization and +education and the like + + align:start position:0% +education and the like + + + align:start position:0% +education and the like +girls and boys are just treated very + + align:start position:0% +girls and boys are just treated very + + + align:start position:0% +girls and boys are just treated very +differently by their parents + + align:start position:0% +differently by their parents + + + align:start position:0% +differently by their parents +by their social environments their + + align:start position:0% +by their social environments their + + + align:start position:0% +by their social environments their +teachers and so on and that might create + + align:start position:0% +teachers and so on and that might create + + + align:start position:0% +teachers and so on and that might create +such differences in preferences + + align:start position:0% +such differences in preferences + + + align:start position:0% +such differences in preferences +and other behaviors so that's another + + align:start position:0% +and other behaviors so that's another + + + align:start position:0% +and other behaviors so that's another +reason to study those + + align:start position:0% +reason to study those + + + align:start position:0% +reason to study those +you're gonna mostly focus on number one + + align:start position:0% +you're gonna mostly focus on number one + + + align:start position:0% +you're gonna mostly focus on number one +just simply the idea that are the + + align:start position:0% +just simply the idea that are the + + + align:start position:0% +just simply the idea that are the +objectives that people should be + + align:start position:0% +objectives that people should be + + + align:start position:0% +objectives that people should be +rewarded + + align:start position:0% +rewarded + + + align:start position:0% +rewarded +equally for the same um output + + align:start position:0% + + + + align:start position:0% + +now what is the gender gap or what do i + + align:start position:0% +now what is the gender gap or what do i + + + align:start position:0% +now what is the gender gap or what do i +mean when i talk about the gender gap + + align:start position:0% +mean when i talk about the gender gap + + + align:start position:0% +mean when i talk about the gender gap +so claudia golden who is a um abnormal + + align:start position:0% +so claudia golden who is a um abnormal + + + align:start position:0% +so claudia golden who is a um abnormal +researcher at harvard + + align:start position:0% +researcher at harvard + + + align:start position:0% +researcher at harvard +who has done a lot of seminal work on + + align:start position:0% +who has done a lot of seminal work on + + + align:start position:0% +who has done a lot of seminal work on +gender at the economics of gender + + align:start position:0% +gender at the economics of gender + + + align:start position:0% +gender at the economics of gender +he's written a very nice overview paper + + align:start position:0% +he's written a very nice overview paper + + + align:start position:0% +he's written a very nice overview paper +in 2014 and + + align:start position:0% +in 2014 and + + + align:start position:0% +in 2014 and +giving an overview of what what do we + + align:start position:0% +giving an overview of what what do we + + + align:start position:0% +giving an overview of what what do we +know and how far + + align:start position:0% +know and how far + + + align:start position:0% +know and how far +we come and trying to reduce and close + + align:start position:0% +we come and trying to reduce and close + + + align:start position:0% +we come and trying to reduce and close +the um + + align:start position:0% +the um + + + align:start position:0% +the um +gender gap um the graph that i'm showing + + align:start position:0% +gender gap um the graph that i'm showing + + + align:start position:0% +gender gap um the graph that i'm showing +you here + + align:start position:0% +you here + + + align:start position:0% +you here +summarizes this discussion fairly well + + align:start position:0% +summarizes this discussion fairly well + + + align:start position:0% +summarizes this discussion fairly well +um it's a bit of a messy graph so let me + + align:start position:0% +um it's a bit of a messy graph so let me + + + align:start position:0% +um it's a bit of a messy graph so let me +show you what it shows i'll tell you + + align:start position:0% +show you what it shows i'll tell you + + + align:start position:0% +show you what it shows i'll tell you +what it shows + + align:start position:0% +what it shows + + + align:start position:0% +what it shows +on the x-axis you see people's age from + + align:start position:0% +on the x-axis you see people's age from + + + align:start position:0% +on the x-axis you see people's age from +20 to 70. + + align:start position:0% +20 to 70. + + + align:start position:0% +20 to 70. +on the y-axis you see the log of + + align:start position:0% +on the y-axis you see the log of + + + align:start position:0% +on the y-axis you see the log of +female-to-male earnings for average + + align:start position:0% +female-to-male earnings for average + + + align:start position:0% +female-to-male earnings for average +female-to-male earnings which is + + align:start position:0% +female-to-male earnings which is + + + align:start position:0% +female-to-male earnings which is +essentially a measure of the gender gap + + align:start position:0% +essentially a measure of the gender gap + + + align:start position:0% +essentially a measure of the gender gap +and so the difference in blog is + + align:start position:0% +and so the difference in blog is + + + align:start position:0% +and so the difference in blog is +essentially the percentage difference + + align:start position:0% +essentially the percentage difference + + + align:start position:0% +essentially the percentage difference +in uh female versus male earnings so + + align:start position:0% +in uh female versus male earnings so + + + align:start position:0% +in uh female versus male earnings so +minus 0.3 you would think of that as + + align:start position:0% +minus 0.3 you would think of that as + + + align:start position:0% +minus 0.3 you would think of that as +that as like 30 difference in + + align:start position:0% +that as like 30 difference in + + + align:start position:0% +that as like 30 difference in +female versus male 1 earnings what do we + + align:start position:0% +female versus male 1 earnings what do we + + + align:start position:0% +female versus male 1 earnings what do we +see here real + + align:start position:0% +see here real + + + align:start position:0% +see here real +a we see like a pretty large gender gap + + align:start position:0% +a we see like a pretty large gender gap + + + align:start position:0% +a we see like a pretty large gender gap +anywhere in this graph + + align:start position:0% +anywhere in this graph + + + align:start position:0% +anywhere in this graph +i should have also said different lines + + align:start position:0% +i should have also said different lines + + + align:start position:0% +i should have also said different lines +are now different chords + + align:start position:0% +are now different chords + + + align:start position:0% +are now different chords +um so these are like starting in 1923 + + align:start position:0% +um so these are like starting in 1923 + + + align:start position:0% +um so these are like starting in 1923 +and he said people born in 1923 + + align:start position:0% +and he said people born in 1923 + + + align:start position:0% +and he said people born in 1923 +28 33 38 to 43 and so on and five-year + + align:start position:0% +28 33 38 to 43 and so on and five-year + + + align:start position:0% +28 33 38 to 43 and so on and five-year +intervals + + align:start position:0% +intervals + + + align:start position:0% +intervals +from the the oldest to like more recent + + align:start position:0% +from the the oldest to like more recent + + + align:start position:0% +from the the oldest to like more recent +um chords + + align:start position:0% +um chords + + + align:start position:0% +um chords +now what do we see we see a significant + + align:start position:0% +now what do we see we see a significant + + + align:start position:0% +now what do we see we see a significant +gender gap everywhere in this graph + + align:start position:0% +gender gap everywhere in this graph + + + align:start position:0% +gender gap everywhere in this graph +or in all lines of the graph we see that + + align:start position:0% +or in all lines of the graph we see that + + + align:start position:0% +or in all lines of the graph we see that +the gender gap even for the most recent + + align:start position:0% +the gender gap even for the most recent + + + align:start position:0% +the gender gap even for the most recent +quartz seems to be about 20 to 30 + + align:start position:0% +quartz seems to be about 20 to 30 + + + align:start position:0% +quartz seems to be about 20 to 30 +percent + + align:start position:0% +percent + + + align:start position:0% +percent +we see that the gender gap has um fallen + + align:start position:0% +we see that the gender gap has um fallen + + + align:start position:0% +we see that the gender gap has um fallen +so when you look at like the most + + align:start position:0% +so when you look at like the most + + + align:start position:0% +so when you look at like the most +um the oldest chords the tinder gap was + + align:start position:0% +um the oldest chords the tinder gap was + + + align:start position:0% +um the oldest chords the tinder gap was +even larger + + align:start position:0% +even larger + + + align:start position:0% +even larger +than the more recent cohorts we also see + + align:start position:0% +than the more recent cohorts we also see + + + align:start position:0% +than the more recent cohorts we also see +that there's sort of this + + align:start position:0% +that there's sort of this + + + align:start position:0% +that there's sort of this +u shape but we seem to find that the + + align:start position:0% +u shape but we seem to find that the + + + align:start position:0% +u shape but we seem to find that the +gender gap + + align:start position:0% +gender gap + + + align:start position:0% +gender gap +starts emerging already at like age + + align:start position:0% +starts emerging already at like age + + + align:start position:0% +starts emerging already at like age +27 28 30 there's already a gender gap of + + align:start position:0% +27 28 30 there's already a gender gap of + + + align:start position:0% +27 28 30 there's already a gender gap of +something like 10 to 15 percent + + align:start position:0% +something like 10 to 15 percent + + + align:start position:0% +something like 10 to 15 percent +even for the most recent cohorts but + + align:start position:0% +even for the most recent cohorts but + + + align:start position:0% +even for the most recent cohorts but +then that gender gap gets magnified + + align:start position:0% +then that gender gap gets magnified + + + align:start position:0% +then that gender gap gets magnified +towards like you know 20 30 40 + + align:start position:0% +towards like you know 20 30 40 + + + align:start position:0% +towards like you know 20 30 40 +um uh until like about age 40 to 45 when + + align:start position:0% +um uh until like about age 40 to 45 when + + + align:start position:0% +um uh until like about age 40 to 45 when +it's sort of like plateau so maybe like + + align:start position:0% +it's sort of like plateau so maybe like + + + align:start position:0% +it's sort of like plateau so maybe like +um + + align:start position:0% +um + + + align:start position:0% +um +falls a bit um or overall + + align:start position:0% +falls a bit um or overall + + + align:start position:0% +falls a bit um or overall +so what do we learn here well we say + + align:start position:0% +so what do we learn here well we say + + + align:start position:0% +so what do we learn here well we say +well there's substantial + + align:start position:0% +well there's substantial + + + align:start position:0% +well there's substantial +female labor market gains over the last + + align:start position:0% +female labor market gains over the last + + + align:start position:0% +female labor market gains over the last +half century but large gender gaps + + align:start position:0% +half century but large gender gaps + + + align:start position:0% +half century but large gender gaps +remain in 2010 for instance the ratio of + + align:start position:0% +remain in 2010 for instance the ratio of + + + align:start position:0% +remain in 2010 for instance the ratio of +mean annual earnings between male and + + align:start position:0% +mean annual earnings between male and + + + align:start position:0% +mean annual earnings between male and +female workers + + align:start position:0% +female workers + + + align:start position:0% +female workers +is that people who worked full-time full + + align:start position:0% +is that people who worked full-time full + + + align:start position:0% +is that people who worked full-time full +year 20 to 25 to 69 years + + align:start position:0% +year 20 to 25 to 69 years + + + align:start position:0% +year 20 to 25 to 69 years +was 0.72 and that of the median was 0.77 + + align:start position:0% +was 0.72 and that of the median was 0.77 + + + align:start position:0% +was 0.72 and that of the median was 0.77 +notice that these the figure here uh + + align:start position:0% +notice that these the figure here uh + + + align:start position:0% +notice that these the figure here uh +controls for work time and education + + align:start position:0% +controls for work time and education + + + align:start position:0% +controls for work time and education +so while of course it might also be the + + align:start position:0% +so while of course it might also be the + + + align:start position:0% +so while of course it might also be the +case and it's indeed the case that women + + align:start position:0% +case and it's indeed the case that women + + + align:start position:0% +case and it's indeed the case that women +work + + align:start position:0% +work + + + align:start position:0% +work +fewer hours and days than men do even + + align:start position:0% +fewer hours and days than men do even + + + align:start position:0% +fewer hours and days than men do even +conditional and work time education + + align:start position:0% +conditional and work time education + + + align:start position:0% +conditional and work time education +is a significant gender gap remaining of + + align:start position:0% +is a significant gender gap remaining of + + + align:start position:0% +is a significant gender gap remaining of +something like 20 to 30 percent + + align:start position:0% +something like 20 to 30 percent + + + align:start position:0% +something like 20 to 30 percent +that women are paid less for equal + + align:start position:0% +that women are paid less for equal + + + align:start position:0% +that women are paid less for equal +pork now first + + align:start position:0% +pork now first + + + align:start position:0% +pork now first +what are some of the reasons why there + + align:start position:0% +what are some of the reasons why there + + + align:start position:0% +what are some of the reasons why there +have been substantial female + + align:start position:0% +have been substantial female + + + align:start position:0% +have been substantial female +labor market gains over the last half + + align:start position:0% +labor market gains over the last half + + + align:start position:0% +labor market gains over the last half +century well + + align:start position:0% +century well + + + align:start position:0% +century well +um there's quite a few uh technological + + align:start position:0% +um there's quite a few uh technological + + + align:start position:0% +um there's quite a few uh technological +and other explanatory factors + + align:start position:0% +and other explanatory factors + + + align:start position:0% +and other explanatory factors +one uh big factor was reduction in the + + align:start position:0% +one uh big factor was reduction in the + + + align:start position:0% +one uh big factor was reduction in the +gender gap and education women are just + + align:start position:0% +gender gap and education women are just + + + align:start position:0% +gender gap and education women are just +more able and can afford + + align:start position:0% +more able and can afford + + + align:start position:0% +more able and can afford +to receive education that's true for + + align:start position:0% +to receive education that's true for + + + align:start position:0% +to receive education that's true for +both primary secondary + + align:start position:0% +both primary secondary + + + align:start position:0% +both primary secondary +education but also in particular for + + align:start position:0% +education but also in particular for + + + align:start position:0% +education but also in particular for +university or higher + + align:start position:0% +university or higher + + + align:start position:0% +university or higher +higher education more generally second + + align:start position:0% +higher education more generally second + + + align:start position:0% +higher education more generally second +there's been technological innovations + + align:start position:0% +there's been technological innovations + + + align:start position:0% +there's been technological innovations +such as the pill dishwasher and so on + + align:start position:0% +such as the pill dishwasher and so on + + + align:start position:0% +such as the pill dishwasher and so on +which + + align:start position:0% +which + + + align:start position:0% +which +allowed women to do more work outside of + + align:start position:0% +allowed women to do more work outside of + + + align:start position:0% +allowed women to do more work outside of +the household + + align:start position:0% +the household + + + align:start position:0% +the household +there have also been like labor demand + + align:start position:0% +there have also been like labor demand + + + align:start position:0% +there have also been like labor demand +shifts in particular as the us economy + + align:start position:0% +shifts in particular as the us economy + + + align:start position:0% +shifts in particular as the us economy +has been + + align:start position:0% +has been + + + align:start position:0% +has been +moving from manufacturing and + + align:start position:0% +moving from manufacturing and + + + align:start position:0% +moving from manufacturing and +agriculture towards + + align:start position:0% +agriculture towards + + + align:start position:0% +agriculture towards +services women tend to have comparative + + align:start position:0% +services women tend to have comparative + + + align:start position:0% +services women tend to have comparative +advantages + + align:start position:0% +advantages + + + align:start position:0% +advantages +in services compared to like a + + align:start position:0% +in services compared to like a + + + align:start position:0% +in services compared to like a +particular hard + + align:start position:0% +particular hard + + + align:start position:0% +particular hard +manual and so these labor demand shifts + + align:start position:0% +manual and so these labor demand shifts + + + align:start position:0% +manual and so these labor demand shifts +and have disproportionately + + align:start position:0% +and have disproportionately + + + align:start position:0% +and have disproportionately +benefited women finally there's been + + align:start position:0% +benefited women finally there's been + + + align:start position:0% +benefited women finally there's been +also lower discrimination in particular + + align:start position:0% +also lower discrimination in particular + + + align:start position:0% +also lower discrimination in particular +stronger regulatory controls and + + align:start position:0% +stronger regulatory controls and + + + align:start position:0% +stronger regulatory controls and +increased market competitiveness + + align:start position:0% +increased market competitiveness + + + align:start position:0% +increased market competitiveness +for the latter it's here that if there's + + align:start position:0% +for the latter it's here that if there's + + + align:start position:0% +for the latter it's here that if there's +more competition + + align:start position:0% +more competition + + + align:start position:0% +more competition +firms cannot afford to discriminate as + + align:start position:0% +firms cannot afford to discriminate as + + + align:start position:0% +firms cannot afford to discriminate as +much + + align:start position:0% +much + + + align:start position:0% +much +because it's actually a costly thing to + + align:start position:0% +because it's actually a costly thing to + + + align:start position:0% +because it's actually a costly thing to +do to to hire incompetent men + + align:start position:0% +do to to hire incompetent men + + + align:start position:0% +do to to hire incompetent men +compared to competent women + + align:start position:0% +compared to competent women + + + align:start position:0% +compared to competent women +now we're going to now discuss the + + align:start position:0% +now we're going to now discuss the + + + align:start position:0% +now we're going to now discuss the +people by golden brows + + align:start position:0% +people by golden brows + + + align:start position:0% +people by golden brows +which is an example of a simple + + align:start position:0% +which is an example of a simple + + + align:start position:0% +which is an example of a simple +technological solution + + align:start position:0% +technological solution + + + align:start position:0% +technological solution +in particular it's the question whether + + align:start position:0% +in particular it's the question whether + + + align:start position:0% +in particular it's the question whether +blind auditions and orchestras + + align:start position:0% +blind auditions and orchestras + + + align:start position:0% +blind auditions and orchestras +increase gender ratios in those + + align:start position:0% +increase gender ratios in those + + + align:start position:0% +increase gender ratios in those +orchestras so you know is the fact that + + align:start position:0% +orchestras so you know is the fact that + + + align:start position:0% +orchestras so you know is the fact that +people uh + + align:start position:0% +people uh + + + align:start position:0% +people uh +uh like the blind auditions were + + align:start position:0% +uh like the blind auditions were + + + align:start position:0% +uh like the blind auditions were +introduced did that contribute + + align:start position:0% +introduced did that contribute + + + align:start position:0% +introduced did that contribute +to the increase in the gender ratio in + + align:start position:0% +to the increase in the gender ratio in + + + align:start position:0% +to the increase in the gender ratio in +orchestras + + align:start position:0% +orchestras + + + align:start position:0% +orchestras +what do i mean by the increase in gender + + align:start position:0% +what do i mean by the increase in gender + + + align:start position:0% +what do i mean by the increase in gender +ratios in the orchestras + + align:start position:0% +ratios in the orchestras + + + align:start position:0% +ratios in the orchestras +so even until the 1960s 70s and 80s + + align:start position:0% +so even until the 1960s 70s and 80s + + + align:start position:0% +so even until the 1960s 70s and 80s +there have been shockingly low female + + align:start position:0% +there have been shockingly low female + + + align:start position:0% +there have been shockingly low female +ratios in + + align:start position:0% +ratios in + + + align:start position:0% +ratios in +top orchestras and orchestras more + + align:start position:0% +top orchestras and orchestras more + + + align:start position:0% +top orchestras and orchestras more +generally + + align:start position:0% +generally + + + align:start position:0% +generally +now um these ratios were below 10 + + align:start position:0% +now um these ratios were below 10 + + + align:start position:0% +now um these ratios were below 10 +and in many orchestras um + + align:start position:0% +and in many orchestras um + + + align:start position:0% +and in many orchestras um +and only recently in the 80s and 90s in + + align:start position:0% +and only recently in the 80s and 90s in + + + align:start position:0% +and only recently in the 80s and 90s in +particular there have been like stark + + align:start position:0% +particular there have been like stark + + + align:start position:0% +particular there have been like stark +increases + + align:start position:0% +increases + + + align:start position:0% +increases +in the number of women who play or in + + align:start position:0% +in the number of women who play or in + + + align:start position:0% +in the number of women who play or in +those orchestras + + align:start position:0% +those orchestras + + + align:start position:0% +those orchestras +um this increase + + align:start position:0% +um this increase + + + align:start position:0% +um this increase +um was the case in the top five + + align:start position:0% +um was the case in the top five + + + align:start position:0% +um was the case in the top five +orchestras + + align:start position:0% +orchestras + + + align:start position:0% +orchestras +but also has been uh have been similar + + align:start position:0% +but also has been uh have been similar + + + align:start position:0% +but also has been uh have been similar +improvements in generations in other + + align:start position:0% +improvements in generations in other + + + align:start position:0% +improvements in generations in other +orchestras which you can read + + align:start position:0% +orchestras which you can read + + + align:start position:0% +orchestras which you can read +the report that i linked in the uh + + align:start position:0% +the report that i linked in the uh + + + align:start position:0% +the report that i linked in the uh +in the slides now um one + + align:start position:0% +in the slides now um one + + + align:start position:0% +in the slides now um one +really important reason here uh seems to + + align:start position:0% +really important reason here uh seems to + + + align:start position:0% +really important reason here uh seems to +have been + + align:start position:0% +have been + + + align:start position:0% +have been +um blatant sexism even by very renowned + + align:start position:0% +um blatant sexism even by very renowned + + + align:start position:0% +um blatant sexism even by very renowned +or particularly by renowned + + align:start position:0% +or particularly by renowned + + + align:start position:0% +or particularly by renowned +conductors which you can have not gonna + + align:start position:0% +conductors which you can have not gonna + + + align:start position:0% +conductors which you can have not gonna +repeat here but you can read it in + + align:start position:0% +repeat here but you can read it in + + + align:start position:0% +repeat here but you can read it in +section one of the paper by golden + + align:start position:0% +section one of the paper by golden + + + align:start position:0% +section one of the paper by golden +browns + + align:start position:0% +browns + + + align:start position:0% +browns +and so one question is like well is is + + align:start position:0% +and so one question is like well is is + + + align:start position:0% +and so one question is like well is is +does this + + align:start position:0% +does this + + + align:start position:0% +does this +sexism and discrimination has that + + align:start position:0% +sexism and discrimination has that + + + align:start position:0% +sexism and discrimination has that +contributed + + align:start position:0% +contributed + + + align:start position:0% +contributed +to um the low gender + + align:start position:0% +to um the low gender + + + align:start position:0% +to um the low gender +ratio in uh in orchestras now + + align:start position:0% +ratio in uh in orchestras now + + + align:start position:0% +ratio in uh in orchestras now +um while there have been all these + + align:start position:0% +um while there have been all these + + + align:start position:0% +um while there have been all these +improvements in the + + align:start position:0% +improvements in the + + + align:start position:0% +improvements in the +gender ratio and like musicians in + + align:start position:0% +gender ratio and like musicians in + + + align:start position:0% +gender ratio and like musicians in +general + + align:start position:0% +general + + + align:start position:0% +general +there still are vast differences in + + align:start position:0% +there still are vast differences in + + + align:start position:0% +there still are vast differences in +conductors and the number of conductors + + align:start position:0% +conductors and the number of conductors + + + align:start position:0% +conductors and the number of conductors +and music directors they're essentially + + align:start position:0% +and music directors they're essentially + + + align:start position:0% +and music directors they're essentially +predominantly male still moreover + + align:start position:0% +predominantly male still moreover + + + align:start position:0% +predominantly male still moreover +while there have been a lot of + + align:start position:0% +while there have been a lot of + + + align:start position:0% +while there have been a lot of +improvements in terms of gender + + align:start position:0% +improvements in terms of gender + + + align:start position:0% +improvements in terms of gender +most musicians are still white + + align:start position:0% +most musicians are still white + + + align:start position:0% +most musicians are still white +so um african-americans and latinos are + + align:start position:0% +so um african-americans and latinos are + + + align:start position:0% +so um african-americans and latinos are +very much underrepresented in orchestras + + align:start position:0% +very much underrepresented in orchestras + + + align:start position:0% +very much underrepresented in orchestras +now let me tell you a short decide about + + align:start position:0% +now let me tell you a short decide about + + + align:start position:0% +now let me tell you a short decide about +women in economics + + align:start position:0% +women in economics + + + align:start position:0% +women in economics +this is not just the case that an + + align:start position:0% +this is not just the case that an + + + align:start position:0% +this is not just the case that an +orchestra on the fraction of women is + + align:start position:0% +orchestra on the fraction of women is + + + align:start position:0% +orchestra on the fraction of women is +low + + align:start position:0% +low + + + align:start position:0% +low +that's also true in economics + + align:start position:0% +that's also true in economics + + + align:start position:0% +that's also true in economics +um and here's sort of an overview of + + align:start position:0% +um and here's sort of an overview of + + + align:start position:0% +um and here's sort of an overview of +that there's a + + align:start position:0% +that there's a + + + align:start position:0% +that there's a +quite nice overview paper by moonberg + + align:start position:0% +quite nice overview paper by moonberg + + + align:start position:0% +quite nice overview paper by moonberg +and stearns in 2019 which sensei says + + align:start position:0% +and stearns in 2019 which sensei says + + + align:start position:0% +and stearns in 2019 which sensei says +that some progress has been made but + + align:start position:0% +that some progress has been made but + + + align:start position:0% +that some progress has been made but +lots more needs to be done and more + + align:start position:0% +lots more needs to be done and more + + + align:start position:0% +lots more needs to be done and more +recently in particular + + align:start position:0% +recently in particular + + + align:start position:0% +recently in particular +some of the progress seems to have + + align:start position:0% +some of the progress seems to have + + + align:start position:0% +some of the progress seems to have +stalled + + align:start position:0% +stalled + + + align:start position:0% +stalled +what would we mean by that well here + + align:start position:0% +what would we mean by that well here + + + align:start position:0% +what would we mean by that well here +this graph shows the fraction + + align:start position:0% +this graph shows the fraction + + + align:start position:0% +this graph shows the fraction +of women in different stages in the + + align:start position:0% +of women in different stages in the + + + align:start position:0% +of women in different stages in the +profession + + align:start position:0% +profession + + + align:start position:0% +profession +ranging from senior majors here at the + + align:start position:0% +ranging from senior majors here at the + + + align:start position:0% +ranging from senior majors here at the +top + + align:start position:0% +top + + + align:start position:0% +top +to first year phd students to assistant + + align:start position:0% +to first year phd students to assistant + + + align:start position:0% +to first year phd students to assistant +professors + + align:start position:0% +professors + + + align:start position:0% +professors +new phds assistant professors associate + + align:start position:0% +new phds assistant professors associate + + + align:start position:0% +new phds assistant professors associate +professors and + + align:start position:0% +professors and + + + align:start position:0% +professors and +for professors and what you see here + + align:start position:0% +for professors and what you see here + + + align:start position:0% +for professors and what you see here +there seems to be some trend that's + + align:start position:0% +there seems to be some trend that's + + + align:start position:0% +there seems to be some trend that's +upwards in particular for full + + align:start position:0% +upwards in particular for full + + + align:start position:0% +upwards in particular for full +professors and associate professors + + align:start position:0% +professors and associate professors + + + align:start position:0% +professors and associate professors +which is + + align:start position:0% +which is + + + align:start position:0% +which is +which is of course good um there uh + + align:start position:0% +which is of course good um there uh + + + align:start position:0% +which is of course good um there uh +there's less of a positive friend to be + + align:start position:0% +there's less of a positive friend to be + + + align:start position:0% +there's less of a positive friend to be +seen when in particular when it comes to + + align:start position:0% +seen when in particular when it comes to + + + align:start position:0% +seen when in particular when it comes to +assistant professors you know theories + + align:start position:0% +assistant professors you know theories + + + align:start position:0% +assistant professors you know theories +you essentially see + + align:start position:0% +you essentially see + + + align:start position:0% +you essentially see +since 2000 about 2007 uh + + align:start position:0% +since 2000 about 2007 uh + + + align:start position:0% +since 2000 about 2007 uh +or six has been no increase if anything + + align:start position:0% +or six has been no increase if anything + + + align:start position:0% +or six has been no increase if anything +like a decrease in the fraction of + + align:start position:0% +like a decrease in the fraction of + + + align:start position:0% +like a decrease in the fraction of +female assistant professors + + align:start position:0% +female assistant professors + + + align:start position:0% +female assistant professors +but even like the fraction of phd + + align:start position:0% +but even like the fraction of phd + + + align:start position:0% +but even like the fraction of phd +students is + + align:start position:0% +students is + + + align:start position:0% +students is +clearly below 50 and so + + align:start position:0% +clearly below 50 and so + + + align:start position:0% +clearly below 50 and so +the profession is starting to understand + + align:start position:0% +the profession is starting to understand + + + align:start position:0% +the profession is starting to understand +and address address the issues in + + align:start position:0% +and address address the issues in + + + align:start position:0% +and address address the issues in +particular to try to reduce + + align:start position:0% +particular to try to reduce + + + align:start position:0% +particular to try to reduce +a and other issues holding women back + + align:start position:0% +a and other issues holding women back + + + align:start position:0% +a and other issues holding women back +there's for example some particularly + + align:start position:0% +there's for example some particularly + + + align:start position:0% +there's for example some particularly +nice examples of the cement + + align:start position:0% +nice examples of the cement + + + align:start position:0% +nice examples of the cement +mentoring programs which are trying to + + align:start position:0% +mentoring programs which are trying to + + + align:start position:0% +mentoring programs which are trying to +support female and minority uh assistant + + align:start position:0% +support female and minority uh assistant + + + align:start position:0% +support female and minority uh assistant +professors and in terms of mentoring and + + align:start position:0% +professors and in terms of mentoring and + + + align:start position:0% +professors and in terms of mentoring and +trying to sort of foster their careers + + align:start position:0% +trying to sort of foster their careers + + + align:start position:0% +trying to sort of foster their careers +which has um uh been shown to + + align:start position:0% +which has um uh been shown to + + + align:start position:0% +which has um uh been shown to +impact and significantly uh improved the + + align:start position:0% +impact and significantly uh improved the + + + align:start position:0% +impact and significantly uh improved the +profession + + align:start position:0% +profession + + + align:start position:0% +profession +but what it's worth in 1413 and the + + align:start position:0% +but what it's worth in 1413 and the + + + align:start position:0% +but what it's worth in 1413 and the +majority of + + align:start position:0% +majority of + + + align:start position:0% +majority of +students tends to be female and moreover + + align:start position:0% +students tends to be female and moreover + + + align:start position:0% +students tends to be female and moreover +the best students tend to be female + + align:start position:0% +the best students tend to be female + + + align:start position:0% +the best students tend to be female +as well so very much hope you are still + + align:start position:0% +as well so very much hope you are still + + + align:start position:0% +as well so very much hope you are still +interested and + + align:start position:0% +interested and + + + align:start position:0% +interested and +all female students are very much still + + align:start position:0% +all female students are very much still + + + align:start position:0% +all female students are very much still +interested in economics and will pursue + + align:start position:0% +interested in economics and will pursue + + + align:start position:0% +interested in economics and will pursue +a career in economics perhaps + + align:start position:0% +a career in economics perhaps + + + align:start position:0% +a career in economics perhaps +academically + + align:start position:0% +academically + + + align:start position:0% +academically +now back to orchestras so many + + align:start position:0% +now back to orchestras so many + + + align:start position:0% +now back to orchestras so many +orchestras introduced blind editions in + + align:start position:0% +orchestras introduced blind editions in + + + align:start position:0% +orchestras introduced blind editions in +the 1970s and 1980s + + align:start position:0% +the 1970s and 1980s + + + align:start position:0% +the 1970s and 1980s +and if you look back at the graph that i + + align:start position:0% +and if you look back at the graph that i + + + align:start position:0% +and if you look back at the graph that i +showed you um this graph here you see in + + align:start position:0% +showed you um this graph here you see in + + + align:start position:0% +showed you um this graph here you see in +the + + align:start position:0% +the + + + align:start position:0% +the +1970s 80s and 90s that's also the time + + align:start position:0% +1970s 80s and 90s that's also the time + + + align:start position:0% +1970s 80s and 90s that's also the time +when there was a sharp increase + + align:start position:0% +when there was a sharp increase + + + align:start position:0% +when there was a sharp increase +in the uh share of women in industrial + + align:start position:0% +in the uh share of women in industrial + + + align:start position:0% +in the uh share of women in industrial +stress + + align:start position:0% +stress + + + align:start position:0% +stress +so um you can see here in the graph + + align:start position:0% +so um you can see here in the graph + + + align:start position:0% +so um you can see here in the graph +orchestras do you want to get a job in + + align:start position:0% +orchestras do you want to get a job in + + + align:start position:0% +orchestras do you want to get a job in +orchestras you have to do auditions + + align:start position:0% +orchestras you have to do auditions + + + align:start position:0% +orchestras you have to do auditions +these auditions are very very + + align:start position:0% +these auditions are very very + + + align:start position:0% +these auditions are very very +competitive and often have like several + + align:start position:0% +competitive and often have like several + + + align:start position:0% +competitive and often have like several +stages they're preliminary semi-finals + + align:start position:0% +stages they're preliminary semi-finals + + + align:start position:0% +stages they're preliminary semi-finals +and finals and many orchestras + + align:start position:0% +and finals and many orchestras + + + align:start position:0% +and finals and many orchestras +what you see here is uh 11 anonymized + + align:start position:0% +what you see here is uh 11 anonymized + + + align:start position:0% +what you see here is uh 11 anonymized +orchestras including the top orchestras + + align:start position:0% +orchestras including the top orchestras + + + align:start position:0% +orchestras including the top orchestras +in the us + + align:start position:0% +in the us + + + align:start position:0% +in the us +and the introduction of blind editions + + align:start position:0% +and the introduction of blind editions + + + align:start position:0% +and the introduction of blind editions +in those orchestras + + align:start position:0% +in those orchestras + + + align:start position:0% +in those orchestras +what you see is that most orchestras did + + align:start position:0% +what you see is that most orchestras did + + + align:start position:0% +what you see is that most orchestras did +introduce blind editions at least in + + align:start position:0% +introduce blind editions at least in + + + align:start position:0% +introduce blind editions at least in +some of their stages of the additions + + align:start position:0% +some of their stages of the additions + + + align:start position:0% +some of their stages of the additions +however many of them also only introduce + + align:start position:0% +however many of them also only introduce + + + align:start position:0% +however many of them also only introduce +it in some stages but not in others + + align:start position:0% +it in some stages but not in others + + + align:start position:0% +it in some stages but not in others +now you can think already that that's + + align:start position:0% +now you can think already that that's + + + align:start position:0% +now you can think already that that's +not + + align:start position:0% +not + + + align:start position:0% +not +sufficient in some cases if you have + + align:start position:0% +sufficient in some cases if you have + + + align:start position:0% +sufficient in some cases if you have +only like blind auditions in the + + align:start position:0% +only like blind auditions in the + + + align:start position:0% +only like blind auditions in the +preliminaries but not in the semi-finals + + align:start position:0% +preliminaries but not in the semi-finals + + + align:start position:0% +preliminaries but not in the semi-finals +or finals + + align:start position:0% +or finals + + + align:start position:0% +or finals +you might sort of reduce discrimination + + align:start position:0% +you might sort of reduce discrimination + + + align:start position:0% +you might sort of reduce discrimination +in the preliminaries but then if women + + align:start position:0% +in the preliminaries but then if women + + + align:start position:0% +in the preliminaries but then if women +are discriminated in the semi-finals or + + align:start position:0% +are discriminated in the semi-finals or + + + align:start position:0% +are discriminated in the semi-finals or +finals + + align:start position:0% +finals + + + align:start position:0% +finals +that's not going to help them get hired + + align:start position:0% +that's not going to help them get hired + + + align:start position:0% +that's not going to help them get hired +which at the end of the day we of course + + align:start position:0% +which at the end of the day we of course + + + align:start position:0% +which at the end of the day we of course +care about + + align:start position:0% + + + + align:start position:0% + +now golden and bruce look at + + align:start position:0% +now golden and bruce look at + + + align:start position:0% +now golden and bruce look at +technological solutions and and + + align:start position:0% +technological solutions and and + + + align:start position:0% +technological solutions and and +look at the question of whether such + + align:start position:0% +look at the question of whether such + + + align:start position:0% +look at the question of whether such +technological solutions in fact can help + + align:start position:0% +technological solutions in fact can help + + + align:start position:0% +technological solutions in fact can help +now the question they're asked now is + + align:start position:0% +now the question they're asked now is + + + align:start position:0% +now the question they're asked now is +looking at data from actual additions + + align:start position:0% +looking at data from actual additions + + + align:start position:0% +looking at data from actual additions +often using individual fixed effects + + align:start position:0% +often using individual fixed effects + + + align:start position:0% +often using individual fixed effects +do these blind emissions the + + align:start position:0% +do these blind emissions the + + + align:start position:0% +do these blind emissions the +introduction of blind auditions + + align:start position:0% +introduction of blind auditions + + + align:start position:0% +introduction of blind auditions +help candidates reach the next round or + + align:start position:0% +help candidates reach the next round or + + + align:start position:0% +help candidates reach the next round or +particularly + + align:start position:0% +particularly + + + align:start position:0% +particularly +get hired now the data is + + align:start position:0% +get hired now the data is + + + align:start position:0% +get hired now the data is +fairly rich and often includes or allows + + align:start position:0% +fairly rich and often includes or allows + + + align:start position:0% +fairly rich and often includes or allows +for the + + align:start position:0% +for the + + + align:start position:0% +for the +inclusion of individual fixed effects + + align:start position:0% +inclusion of individual fixed effects + + + align:start position:0% +inclusion of individual fixed effects +that is the case if you look at the + + align:start position:0% +that is the case if you look at the + + + align:start position:0% +that is the case if you look at the +musicians + + align:start position:0% +musicians + + + align:start position:0% +musicians +golden rules are going to ask the + + align:start position:0% +golden rules are going to ask the + + + align:start position:0% +golden rules are going to ask the +question is a particular + + align:start position:0% +question is a particular + + + align:start position:0% +question is a particular +musician more likely to + + align:start position:0% +musician more likely to + + + align:start position:0% +musician more likely to +make it to the next round when auditions + + align:start position:0% +make it to the next round when auditions + + + align:start position:0% +make it to the next round when auditions +are blinded + + align:start position:0% +are blinded + + + align:start position:0% +are blinded +and is that more likely the case for + + align:start position:0% +and is that more likely the case for + + + align:start position:0% +and is that more likely the case for +female than for a male + + align:start position:0% +female than for a male + + + align:start position:0% +female than for a male +uh musicians now what do they find + + align:start position:0% +uh musicians now what do they find + + + align:start position:0% +uh musicians now what do they find +overall they find evidence that + + align:start position:0% +overall they find evidence that + + + align:start position:0% +overall they find evidence that +blind conditions plan audition + + align:start position:0% +blind conditions plan audition + + + align:start position:0% +blind conditions plan audition +procedures fostered impartiality in + + align:start position:0% +procedures fostered impartiality in + + + align:start position:0% +procedures fostered impartiality in +hiring + + align:start position:0% +hiring + + + align:start position:0% +hiring +and increase the proportion of women in + + align:start position:0% +and increase the proportion of women in + + + align:start position:0% +and increase the proportion of women in +century orchestras + + align:start position:0% +century orchestras + + + align:start position:0% +century orchestras +now there's some caveats here that you + + align:start position:0% +now there's some caveats here that you + + + align:start position:0% +now there's some caveats here that you +know some of these estimates are fairly + + align:start position:0% +know some of these estimates are fairly + + + align:start position:0% +know some of these estimates are fairly +precise in particular at later stages + + align:start position:0% +precise in particular at later stages + + + align:start position:0% +precise in particular at later stages +because the number of + + align:start position:0% +because the number of + + + align:start position:0% +because the number of +observations was quite a bit down quite + + align:start position:0% +observations was quite a bit down quite + + + align:start position:0% +observations was quite a bit down quite +a bit there's um + + align:start position:0% +a bit there's um + + + align:start position:0% +a bit there's um +some of these results are a little bit + + align:start position:0% +some of these results are a little bit + + + align:start position:0% +some of these results are a little bit +mixed but overall the evidence suggests + + align:start position:0% +mixed but overall the evidence suggests + + + align:start position:0% +mixed but overall the evidence suggests +that these blind editions + + align:start position:0% +that these blind editions + + + align:start position:0% +that these blind editions +did indeed foster impartiality and + + align:start position:0% +did indeed foster impartiality and + + + align:start position:0% +did indeed foster impartiality and +helped women + + align:start position:0% +helped women + + + align:start position:0% +helped women +succeed in getting jobs in particular in + + align:start position:0% +succeed in getting jobs in particular in + + + align:start position:0% +succeed in getting jobs in particular in +these top orchestras + + align:start position:0% +these top orchestras + + + align:start position:0% +these top orchestras +in the us now + + align:start position:0% +in the us now + + + align:start position:0% +in the us now +why are these results perhaps somewhat + + align:start position:0% +why are these results perhaps somewhat + + + align:start position:0% +why are these results perhaps somewhat +less clear cut i already told you like + + align:start position:0% +less clear cut i already told you like + + + align:start position:0% +less clear cut i already told you like +one reason is that + + align:start position:0% +one reason is that + + + align:start position:0% +one reason is that +in later rounds the number of + + align:start position:0% +in later rounds the number of + + + align:start position:0% +in later rounds the number of +observation gets kind of small because + + align:start position:0% +observation gets kind of small because + + + align:start position:0% +observation gets kind of small because +you know only so many people make it to + + align:start position:0% +you know only so many people make it to + + + align:start position:0% +you know only so many people make it to +the later rounds + + align:start position:0% +the later rounds + + + align:start position:0% +the later rounds +but there's another reason which is the + + align:start position:0% +but there's another reason which is the + + + align:start position:0% +but there's another reason which is the +auditions on several rounds + + align:start position:0% +auditions on several rounds + + + align:start position:0% +auditions on several rounds +not all of which were blinded now if + + align:start position:0% +not all of which were blinded now if + + + align:start position:0% +not all of which were blinded now if +there's one + + align:start position:0% +there's one + + + align:start position:0% +there's one +uh if there's discrimination in one + + align:start position:0% +uh if there's discrimination in one + + + align:start position:0% +uh if there's discrimination in one +round but not in the next one + + align:start position:0% +round but not in the next one + + + align:start position:0% +round but not in the next one +this issue that in the next round there + + align:start position:0% +this issue that in the next round there + + + align:start position:0% +this issue that in the next round there +will be like selection + + align:start position:0% +will be like selection + + + align:start position:0% +will be like selection +in a uh the discriminated people who + + align:start position:0% +in a uh the discriminated people who + + + align:start position:0% +in a uh the discriminated people who +make it to the next round + + align:start position:0% +make it to the next round + + + align:start position:0% +make it to the next round +you expect them to do better right if + + align:start position:0% +you expect them to do better right if + + + align:start position:0% +you expect them to do better right if +there's discrimination + + align:start position:0% +there's discrimination + + + align:start position:0% +there's discrimination +against women in the first round um but + + align:start position:0% +against women in the first round um but + + + align:start position:0% +against women in the first round um but +not in a second + + align:start position:0% +not in a second + + + align:start position:0% +not in a second +you think that like women in the second + + align:start position:0% +you think that like women in the second + + + align:start position:0% +you think that like women in the second +round will do better because only the + + align:start position:0% +round will do better because only the + + + align:start position:0% +round will do better because only the +best woman will make it to the second + + align:start position:0% +best woman will make it to the second + + + align:start position:0% +best woman will make it to the second +second round + + align:start position:0% +second round + + + align:start position:0% +second round +uh because otherwise they will be um + + align:start position:0% +uh because otherwise they will be um + + + align:start position:0% +uh because otherwise they will be um +screened out in the first round due to + + align:start position:0% +screened out in the first round due to + + + align:start position:0% +screened out in the first round due to +discrimination right and if that's the + + align:start position:0% +discrimination right and if that's the + + + align:start position:0% +discrimination right and if that's the +case then like making comparisons in + + align:start position:0% +case then like making comparisons in + + + align:start position:0% +case then like making comparisons in +later + + align:start position:0% +later + + + align:start position:0% +later +rounds is potentially biased or + + align:start position:0% +rounds is potentially biased or + + + align:start position:0% +rounds is potentially biased or +problematic + + align:start position:0% +problematic + + + align:start position:0% +problematic +because you're comparing essentially + + align:start position:0% +because you're comparing essentially + + + align:start position:0% +because you're comparing essentially +different types of people in different + + align:start position:0% +different types of people in different + + + align:start position:0% +different types of people in different +routes + + align:start position:0% +routes + + + align:start position:0% +routes +and that and that might might lead to + + align:start position:0% +and that and that might might lead to + + + align:start position:0% +and that and that might might lead to +the results being less clear-cut + + align:start position:0% +the results being less clear-cut + + + align:start position:0% +the results being less clear-cut +overall let me give you another example + + align:start position:0% +overall let me give you another example + + + align:start position:0% +overall let me give you another example +suppose + + align:start position:0% +suppose + + + align:start position:0% +suppose +um a male and female workers get graded + + align:start position:0% +um a male and female workers get graded + + + align:start position:0% +um a male and female workers get graded +in that task to put a + + align:start position:0% +in that task to put a + + + align:start position:0% +in that task to put a +pose that's a quoting task online where + + align:start position:0% +pose that's a quoting task online where + + + align:start position:0% +pose that's a quoting task online where +you essentially see the output but you + + align:start position:0% +you essentially see the output but you + + + align:start position:0% +you essentially see the output but you +also see their gender + + align:start position:0% +also see their gender + + + align:start position:0% +also see their gender +now suppose women get rated + + align:start position:0% +now suppose women get rated + + + align:start position:0% +now suppose women get rated +systematically worse due to sexism and + + align:start position:0% +systematically worse due to sexism and + + + align:start position:0% +systematically worse due to sexism and +no other reasons because women and men + + align:start position:0% +no other reasons because women and men + + + align:start position:0% +no other reasons because women and men +are exactly the same in the work they do + + align:start position:0% +are exactly the same in the work they do + + + align:start position:0% +are exactly the same in the work they do +but some men are sexist and they're + + align:start position:0% +but some men are sexist and they're + + + align:start position:0% +but some men are sexist and they're +going to rate women worse + + align:start position:0% +going to rate women worse + + + align:start position:0% +going to rate women worse +now for any given score you should + + align:start position:0% +now for any given score you should + + + align:start position:0% +now for any given score you should +expect the women + + align:start position:0% +expect the women + + + align:start position:0% +expect the women +a woman that you hire compared to any + + align:start position:0% +a woman that you hire compared to any + + + align:start position:0% +a woman that you hire compared to any +other random man that you hire to do + + align:start position:0% +other random man that you hire to do + + + align:start position:0% +other random man that you hire to do +better + + align:start position:0% +better + + + align:start position:0% +better +than that man and the reason being that + + align:start position:0% +than that man and the reason being that + + + align:start position:0% +than that man and the reason being that +they have been like systematically + + align:start position:0% +they have been like systematically + + + align:start position:0% +they have been like systematically +disadvantaged + + align:start position:0% +disadvantaged + + + align:start position:0% +disadvantaged +due to the sexism in the rating to start + + align:start position:0% +due to the sexism in the rating to start + + + align:start position:0% +due to the sexism in the rating to start +with + + align:start position:0% +with + + + align:start position:0% +with +now you should think about this because + + align:start position:0% +now you should think about this because + + + align:start position:0% +now you should think about this because +you know there's also some + + align:start position:0% +you know there's also some + + + align:start position:0% +you know there's also some +evidence of teaching evaluations being + + align:start position:0% +evidence of teaching evaluations being + + + align:start position:0% +evidence of teaching evaluations being +biased against women + + align:start position:0% +biased against women + + + align:start position:0% +biased against women +now if you see a man and a woman with + + align:start position:0% +now if you see a man and a woman with + + + align:start position:0% +now if you see a man and a woman with +the exact same teaching rating + + align:start position:0% +the exact same teaching rating + + + align:start position:0% +the exact same teaching rating +well you probably want to take the + + align:start position:0% +well you probably want to take the + + + align:start position:0% +well you probably want to take the +woman's class because the woman has been + + align:start position:0% +woman's class because the woman has been + + + align:start position:0% +woman's class because the woman has been +the female professor has been + + align:start position:0% +the female professor has been + + + align:start position:0% +the female professor has been +discriminated to start with + + align:start position:0% +discriminated to start with + + + align:start position:0% +discriminated to start with +having that high score or this really + + align:start position:0% +having that high score or this really + + + align:start position:0% +having that high score or this really +high score as the male professor + + align:start position:0% +high score as the male professor + + + align:start position:0% +high score as the male professor +is is more impressive and likely to + + align:start position:0% +is is more impressive and likely to + + + align:start position:0% +is is more impressive and likely to +indicate that the class will be better + + align:start position:0% +indicate that the class will be better + + + align:start position:0% +indicate that the class will be better +there's an excellent people by born and + + align:start position:0% +there's an excellent people by born and + + + align:start position:0% +there's an excellent people by born and +all that considers the issue of + + align:start position:0% +all that considers the issue of + + + align:start position:0% +all that considers the issue of +the dynamics of discrimination in much + + align:start position:0% +the dynamics of discrimination in much + + + align:start position:0% +the dynamics of discrimination in much +more detail if you're interested in + + align:start position:0% +more detail if you're interested in + + + align:start position:0% +more detail if you're interested in +learning more about that + + align:start position:0% + + + + align:start position:0% + +now despite those technological + + align:start position:0% +now despite those technological + + + align:start position:0% +now despite those technological +solutions and advances that i mentioned + + align:start position:0% +solutions and advances that i mentioned + + + align:start position:0% +solutions and advances that i mentioned +you use substantial + + align:start position:0% +you use substantial + + + align:start position:0% +you use substantial +substantial gender gaps + + align:start position:0% +substantial gender gaps + + + align:start position:0% +substantial gender gaps +remain so while as i told you + + align:start position:0% +remain so while as i told you + + + align:start position:0% +remain so while as i told you +the gender gaps has been reduced both in + + align:start position:0% +the gender gaps has been reduced both in + + + align:start position:0% +the gender gaps has been reduced both in +terms of labor market or labor force + + align:start position:0% +terms of labor market or labor force + + + align:start position:0% +terms of labor market or labor force +participation + + align:start position:0% +participation + + + align:start position:0% +participation +how many days and hours how many women + + align:start position:0% +how many days and hours how many women + + + align:start position:0% +how many days and hours how many women +overall how many days and hours since + + align:start position:0% +overall how many days and hours since + + + align:start position:0% +overall how many days and hours since +we're in work + + align:start position:0% +we're in work + + + align:start position:0% +we're in work +and in their wages and earnings how much + + align:start position:0% +and in their wages and earnings how much + + + align:start position:0% +and in their wages and earnings how much +they're being paid + + align:start position:0% +they're being paid + + + align:start position:0% +they're being paid +conditional on working + + align:start position:0% + + + + align:start position:0% + +there there are still substantial gender + + align:start position:0% +there there are still substantial gender + + + align:start position:0% +there there are still substantial gender +gaps + + align:start position:0% +gaps + + + align:start position:0% +gaps +in particular women's labor market + + align:start position:0% +in particular women's labor market + + + align:start position:0% +in particular women's labor market +participation has plateaued since + + align:start position:0% +participation has plateaued since + + + align:start position:0% +participation has plateaued since +the early 1990s and even now among + + align:start position:0% +the early 1990s and even now among + + + align:start position:0% +the early 1990s and even now among +entering courts women still earn + + align:start position:0% +entering courts women still earn + + + align:start position:0% +entering courts women still earn +significantly less than men + + align:start position:0% +significantly less than men + + + align:start position:0% +significantly less than men +and that's true even for conditional + + align:start position:0% +and that's true even for conditional + + + align:start position:0% +and that's true even for conditional +unwork time education that's the graph + + align:start position:0% +unwork time education that's the graph + + + align:start position:0% +unwork time education that's the graph +that i was showing you earlier + + align:start position:0% +that i was showing you earlier + + + align:start position:0% +that i was showing you earlier +now given that there are these + + align:start position:0% +now given that there are these + + + align:start position:0% +now given that there are these +persistent remaining gender gaps + + align:start position:0% +persistent remaining gender gaps + + + align:start position:0% +persistent remaining gender gaps +even though a lot of the technological + + align:start position:0% +even though a lot of the technological + + + align:start position:0% +even though a lot of the technological +and other barriers have been reduced now + + align:start position:0% +and other barriers have been reduced now + + + align:start position:0% +and other barriers have been reduced now +women + + align:start position:0% +women + + + align:start position:0% +women +are educated or as educated as men are + + align:start position:0% +are educated or as educated as men are + + + align:start position:0% +are educated or as educated as men are +and there's less technological barriers + + align:start position:0% +and there's less technological barriers + + + align:start position:0% +and there's less technological barriers +that uh preclude women from working + + align:start position:0% +that uh preclude women from working + + + align:start position:0% +that uh preclude women from working +researchers have now started to consider + + align:start position:0% +researchers have now started to consider + + + align:start position:0% +researchers have now started to consider +it somewhat less traditional within + + align:start position:0% +it somewhat less traditional within + + + align:start position:0% +it somewhat less traditional within +economics + + align:start position:0% +economics + + + align:start position:0% +economics +factors including things such as risk + + align:start position:0% +factors including things such as risk + + + align:start position:0% +factors including things such as risk +attitudes + + align:start position:0% +attitudes + + + align:start position:0% +attitudes +negotiation skills teams for competition + + align:start position:0% +negotiation skills teams for competition + + + align:start position:0% +negotiation skills teams for competition +but also this is what we're going to + + align:start position:0% +but also this is what we're going to + + + align:start position:0% +but also this is what we're going to +focus on beliefs + + align:start position:0% +focus on beliefs + + + align:start position:0% +focus on beliefs +and social norms and identity + + align:start position:0% +and social norms and identity + + + align:start position:0% +and social norms and identity +i'm going to first talk about beliefs + + align:start position:0% +i'm going to first talk about beliefs + + + align:start position:0% +i'm going to first talk about beliefs +and then we're going to talk about + + align:start position:0% +and then we're going to talk about + + + align:start position:0% +and then we're going to talk about +social norms and identity + + align:start position:0% + + + + align:start position:0% + +um before we get to beliefs about gender + + align:start position:0% +um before we get to beliefs about gender + + + align:start position:0% +um before we get to beliefs about gender +people's women's and men's skills i'm + + align:start position:0% +people's women's and men's skills i'm + + + align:start position:0% +people's women's and men's skills i'm +going to tell you very briefly about a + + align:start position:0% +going to tell you very briefly about a + + + align:start position:0% +going to tell you very briefly about a +seminal paper by + + align:start position:0% +seminal paper by + + + align:start position:0% +seminal paper by +bertrand and mulanathan from 2004 that + + align:start position:0% +bertrand and mulanathan from 2004 that + + + align:start position:0% +bertrand and mulanathan from 2004 that +randomizes + + align:start position:0% +randomizes + + + align:start position:0% +randomizes +randomized names and job applications + + align:start position:0% +randomized names and job applications + + + align:start position:0% +randomized names and job applications +so what did bertrand and volunteon do + + align:start position:0% +so what did bertrand and volunteon do + + + align:start position:0% +so what did bertrand and volunteon do +they essentially + + align:start position:0% +they essentially + + + align:start position:0% +they essentially +um send out job obligations that were + + align:start position:0% +um send out job obligations that were + + + align:start position:0% +um send out job obligations that were +otherwise identical + + align:start position:0% +otherwise identical + + + align:start position:0% +otherwise identical +male and female workers these are + + align:start position:0% +male and female workers these are + + + align:start position:0% +male and female workers these are +fictitious job applications + + align:start position:0% +fictitious job applications + + + align:start position:0% +fictitious job applications +and they sent them to employers and then + + align:start position:0% +and they sent them to employers and then + + + align:start position:0% +and they sent them to employers and then +looked at + + align:start position:0% +looked at + + + align:start position:0% +looked at +callback rates by those employers and + + align:start position:0% +callback rates by those employers and + + + align:start position:0% +callback rates by those employers and +the only thing that was like varied in + + align:start position:0% +the only thing that was like varied in + + + align:start position:0% +the only thing that was like varied in +those applications was + + align:start position:0% +those applications was + + + align:start position:0% +those applications was +the name on the application and what did + + align:start position:0% +the name on the application and what did + + + align:start position:0% +the name on the application and what did +they do while they used + + align:start position:0% +they do while they used + + + align:start position:0% +they do while they used +white sounding names such as emily and + + align:start position:0% +white sounding names such as emily and + + + align:start position:0% +white sounding names such as emily and +greg as well as + + align:start position:0% +greg as well as + + + align:start position:0% +greg as well as +african-american sounding names such as + + align:start position:0% +african-american sounding names such as + + + align:start position:0% +african-american sounding names such as +lakisha and jamal + + align:start position:0% +lakisha and jamal + + + align:start position:0% +lakisha and jamal +and then they looked at well were these + + align:start position:0% +and then they looked at well were these + + + align:start position:0% +and then they looked at well were these +um uh + + align:start position:0% +um uh + + + align:start position:0% +um uh +applications when they had white + + align:start position:0% +applications when they had white + + + align:start position:0% +applications when they had white +sounding names and were + + align:start position:0% +sounding names and were + + + align:start position:0% +sounding names and were +otherwise identical more successful than + + align:start position:0% +otherwise identical more successful than + + + align:start position:0% +otherwise identical more successful than +applications + + align:start position:0% +applications + + + align:start position:0% +applications +by uh names with african-american + + align:start position:0% +by uh names with african-american + + + align:start position:0% +by uh names with african-american +sounding uh + + align:start position:0% +sounding uh + + + align:start position:0% +sounding uh +from african-american sounding names and + + align:start position:0% +from african-american sounding names and + + + align:start position:0% +from african-american sounding names and +again that were otherwise identical and + + align:start position:0% +again that were otherwise identical and + + + align:start position:0% +again that were otherwise identical and +uh + + align:start position:0% +uh + + + align:start position:0% +uh +bertrand and mulanathan find the + + align:start position:0% +bertrand and mulanathan find the + + + align:start position:0% +bertrand and mulanathan find the +striking key result that + + align:start position:0% +striking key result that + + + align:start position:0% +striking key result that +callback rates for white sounding names + + align:start position:0% +callback rates for white sounding names + + + align:start position:0% +callback rates for white sounding names +were fifty percent higher than for + + align:start position:0% +were fifty percent higher than for + + + align:start position:0% +were fifty percent higher than for +african-american sounding + + align:start position:0% +african-american sounding + + + align:start position:0% +african-american sounding +that's a huge difference um and that's + + align:start position:0% +that's a huge difference um and that's + + + align:start position:0% +that's a huge difference um and that's +important not just because it's like a + + align:start position:0% +important not just because it's like a + + + align:start position:0% +important not just because it's like a +hassle because you have to send out more + + align:start position:0% +hassle because you have to send out more + + + align:start position:0% +hassle because you have to send out more +applications + + align:start position:0% +applications + + + align:start position:0% +applications +well if you get called back more you're + + align:start position:0% +well if you get called back more you're + + + align:start position:0% +well if you get called back more you're +more likely to be + + align:start position:0% +more likely to be + + + align:start position:0% +more likely to be +interviewed or asked for an interview + + align:start position:0% +interviewed or asked for an interview + + + align:start position:0% +interviewed or asked for an interview +you're more likely to actually get the + + align:start position:0% +you're more likely to actually get the + + + align:start position:0% +you're more likely to actually get the +job you're more likely to + + align:start position:0% +job you're more likely to + + + align:start position:0% +job you're more likely to +less likely to be unemployed and + + align:start position:0% +less likely to be unemployed and + + + align:start position:0% +less likely to be unemployed and +you might also be less likely to just + + align:start position:0% +you might also be less likely to just + + + align:start position:0% +you might also be less likely to just +stop + + align:start position:0% +stop + + + align:start position:0% +stop +searching whatsoever because you might + + align:start position:0% +searching whatsoever because you might + + + align:start position:0% +searching whatsoever because you might +be disappointed or discouraged + + align:start position:0% +be disappointed or discouraged + + + align:start position:0% +be disappointed or discouraged +so that's a huge difference and + + align:start position:0% +so that's a huge difference and + + + align:start position:0% +so that's a huge difference and +essentially + + align:start position:0% +essentially + + + align:start position:0% +essentially +a discrimination against + + align:start position:0% +a discrimination against + + + align:start position:0% +a discrimination against +african-americans + + align:start position:0% + + + + align:start position:0% + +was plainly obvious from this research + + align:start position:0% +was plainly obvious from this research + + + align:start position:0% +was plainly obvious from this research +numerous other studies show gender and + + align:start position:0% +numerous other studies show gender and + + + align:start position:0% +numerous other studies show gender and +racial biases + + align:start position:0% +racial biases + + + align:start position:0% +racial biases +in various ways these are ranging + + align:start position:0% +in various ways these are ranging + + + align:start position:0% +in various ways these are ranging +from very similar studies including + + align:start position:0% +from very similar studies including + + + align:start position:0% +from very similar studies including +these audit studies where people are + + align:start position:0% +these audit studies where people are + + + align:start position:0% +these audit studies where people are +sent resumes for the like + + align:start position:0% +sent resumes for the like + + + align:start position:0% +sent resumes for the like +um but also arranging two studies where + + align:start position:0% +um but also arranging two studies where + + + align:start position:0% +um but also arranging two studies where +like people on ebay + + align:start position:0% +like people on ebay + + + align:start position:0% +like people on ebay +try to sell things where like they try + + align:start position:0% +try to sell things where like they try + + + align:start position:0% +try to sell things where like they try +to sell like an ipod drive + + align:start position:0% +to sell like an ipod drive + + + align:start position:0% +to sell like an ipod drive +iphone and they hold that iphone um with + + align:start position:0% +iphone and they hold that iphone um with + + + align:start position:0% +iphone and they hold that iphone um with +a hand that's either like white + + align:start position:0% +a hand that's either like white + + + align:start position:0% +a hand that's either like white +or or non-white and then they find + + align:start position:0% +or or non-white and then they find + + + align:start position:0% +or or non-white and then they find +essentially that + + align:start position:0% +essentially that + + + align:start position:0% +essentially that +white hands are more likely to sell + + align:start position:0% +white hands are more likely to sell + + + align:start position:0% +white hands are more likely to sell +their + + align:start position:0% +their + + + align:start position:0% +their +iphones than non-white hats now this is + + align:start position:0% +iphones than non-white hats now this is + + + align:start position:0% +iphones than non-white hats now this is +a very important + + align:start position:0% +a very important + + + align:start position:0% +a very important +and depressing result one thing to flag + + align:start position:0% +and depressing result one thing to flag + + + align:start position:0% +and depressing result one thing to flag +here that it's hard + + align:start position:0% +here that it's hard + + + align:start position:0% +here that it's hard +to distinguish statistical from t space + + align:start position:0% +to distinguish statistical from t space + + + align:start position:0% +to distinguish statistical from t space +discrimination + + align:start position:0% +discrimination + + + align:start position:0% +discrimination +you can talk more about this in in + + align:start position:0% +you can talk more about this in in + + + align:start position:0% +you can talk more about this in in +recitation what do i mean by that + + align:start position:0% +recitation what do i mean by that + + + align:start position:0% +recitation what do i mean by that +well it might be that there's uh people + + align:start position:0% +well it might be that there's uh people + + + align:start position:0% +well it might be that there's uh people +have a preference + + align:start position:0% +have a preference + + + align:start position:0% +have a preference +for white applicants that is to say + + align:start position:0% +for white applicants that is to say + + + align:start position:0% +for white applicants that is to say +controlling for performance + + align:start position:0% +controlling for performance + + + align:start position:0% +controlling for performance +it might just be that people are racist + + align:start position:0% +it might just be that people are racist + + + align:start position:0% +it might just be that people are racist +and they'd rather have like white + + align:start position:0% +and they'd rather have like white + + + align:start position:0% +and they'd rather have like white +applicants than + + align:start position:0% +applicants than + + + align:start position:0% +applicants than +african-american applicants this is what + + align:start position:0% +african-american applicants this is what + + + align:start position:0% +african-american applicants this is what +economists would call + + align:start position:0% +economists would call + + + align:start position:0% +economists would call +uh taste based discrimination uh which + + align:start position:0% +uh taste based discrimination uh which + + + align:start position:0% +uh taste based discrimination uh which +essentially is conditional on the + + align:start position:0% +essentially is conditional on the + + + align:start position:0% +essentially is conditional on the +performance + + align:start position:0% +performance + + + align:start position:0% +performance +people just like certain types of people + + align:start position:0% +people just like certain types of people + + + align:start position:0% +people just like certain types of people +better than others and therefore they + + align:start position:0% +better than others and therefore they + + + align:start position:0% +better than others and therefore they +call them are more likely to call them + + align:start position:0% +call them are more likely to call them + + + align:start position:0% +call them are more likely to call them +back + + align:start position:0% +back + + + align:start position:0% +back +a different explanation is a + + align:start position:0% +a different explanation is a + + + align:start position:0% +a different explanation is a +belief-based explanation + + align:start position:0% +belief-based explanation + + + align:start position:0% +belief-based explanation +it might be that employers think that + + align:start position:0% +it might be that employers think that + + + align:start position:0% +it might be that employers think that +african-american applicants will perform + + align:start position:0% +african-american applicants will perform + + + align:start position:0% +african-american applicants will perform +worse + + align:start position:0% +worse + + + align:start position:0% +worse +even controlling for all other aspects + + align:start position:0% +even controlling for all other aspects + + + align:start position:0% +even controlling for all other aspects +of the resume so it could be essentially + + align:start position:0% +of the resume so it could be essentially + + + align:start position:0% +of the resume so it could be essentially +you see + + align:start position:0% +you see + + + align:start position:0% +you see +people see this name and they think that + + align:start position:0% +people see this name and they think that + + + align:start position:0% +people see this name and they think that +well even if the resume is good that + + align:start position:0% +well even if the resume is good that + + + align:start position:0% +well even if the resume is good that +person will not perform + + align:start position:0% +person will not perform + + + align:start position:0% +person will not perform +as well as somebody with a white + + align:start position:0% +as well as somebody with a white + + + align:start position:0% +as well as somebody with a white +sounding name notice that these beliefs + + align:start position:0% +sounding name notice that these beliefs + + + align:start position:0% +sounding name notice that these beliefs +could be + + align:start position:0% +could be + + + align:start position:0% +could be +correct or not um uh but in any case we + + align:start position:0% +correct or not um uh but in any case we + + + align:start position:0% +correct or not um uh but in any case we +will uh and that's you will talk about + + align:start position:0% +will uh and that's you will talk about + + + align:start position:0% +will uh and that's you will talk about +this in recitation as well + + align:start position:0% +this in recitation as well + + + align:start position:0% +this in recitation as well +uh autonomous again would call this + + align:start position:0% +uh autonomous again would call this + + + align:start position:0% +uh autonomous again would call this +statistical discrimination this could be + + align:start position:0% +statistical discrimination this could be + + + align:start position:0% +statistical discrimination this could be +again correct statistical exclamation + + align:start position:0% +again correct statistical exclamation + + + align:start position:0% +again correct statistical exclamation +or statistical discrimination that's uh + + align:start position:0% +or statistical discrimination that's uh + + + align:start position:0% +or statistical discrimination that's uh +based on biased beliefs but either way + + align:start position:0% +based on biased beliefs but either way + + + align:start position:0% +based on biased beliefs but either way +these things um + + align:start position:0% +these things um + + + align:start position:0% +these things um +jointly um led to clear discrimination + + align:start position:0% +jointly um led to clear discrimination + + + align:start position:0% +jointly um led to clear discrimination +of african-american applications + + align:start position:0% +of african-american applications + + + align:start position:0% +of african-american applications +which in turn that leads to uh striking + + align:start position:0% +which in turn that leads to uh striking + + + align:start position:0% +which in turn that leads to uh striking +differences + + align:start position:0% +differences + + + align:start position:0% +differences +in unemployment or job-finding + + align:start position:0% +in unemployment or job-finding + + + align:start position:0% +in unemployment or job-finding +rates rates across races we're going to + + align:start position:0% +rates rates across races we're going to + + + align:start position:0% +rates rates across races we're going to +now focus on + + align:start position:0% +now focus on + + + align:start position:0% +now focus on +beliefs in particular about beliefs + + align:start position:0% +beliefs in particular about beliefs + + + align:start position:0% +beliefs in particular about beliefs +about skills and how people + + align:start position:0% +about skills and how people + + + align:start position:0% +about skills and how people +update on those beliefs depending on the + + align:start position:0% +update on those beliefs depending on the + + + align:start position:0% +update on those beliefs depending on the +gender of the person they're updating on + + align:start position:0% +gender of the person they're updating on + + + align:start position:0% +gender of the person they're updating on +the paper we're going to consider now is + + align:start position:0% +the paper we're going to consider now is + + + align:start position:0% +the paper we're going to consider now is +the people by star since 2019 + + align:start position:0% +the people by star since 2019 + + + align:start position:0% +the people by star since 2019 +which considers how people interpret + + align:start position:0% +which considers how people interpret + + + align:start position:0% +which considers how people interpret +signals in the labor market + + align:start position:0% +signals in the labor market + + + align:start position:0% +signals in the labor market +the question that sarson asks is whether + + align:start position:0% +the question that sarson asks is whether + + + align:start position:0% +the question that sarson asks is whether +somebody's gender + + align:start position:0% +somebody's gender + + + align:start position:0% +somebody's gender +influences the way how we interpret + + align:start position:0% +influences the way how we interpret + + + align:start position:0% +influences the way how we interpret +information about + + align:start position:0% +information about + + + align:start position:0% +information about +this person and about his or her peers + + align:start position:0% +this person and about his or her peers + + + align:start position:0% +this person and about his or her peers +what do i mean by that well uh in many + + align:start position:0% +what do i mean by that well uh in many + + + align:start position:0% +what do i mean by that well uh in many +situations when people + + align:start position:0% +situations when people + + + align:start position:0% +situations when people +do certain tasks and perform at work + + align:start position:0% +do certain tasks and perform at work + + + align:start position:0% +do certain tasks and perform at work +good things and bad things happen now + + align:start position:0% +good things and bad things happen now + + + align:start position:0% +good things and bad things happen now +you can infer + + align:start position:0% +you can infer + + + align:start position:0% +you can infer +from those things that occur from these + + align:start position:0% +from those things that occur from these + + + align:start position:0% +from those things that occur from these +events you can infer + + align:start position:0% +events you can infer + + + align:start position:0% +events you can infer +something about their competence and + + align:start position:0% +something about their competence and + + + align:start position:0% +something about their competence and +their performance + + align:start position:0% +their performance + + + align:start position:0% +their performance +now many of these situations are + + align:start position:0% +now many of these situations are + + + align:start position:0% +now many of these situations are +ambiguous in the sense it could be that + + align:start position:0% +ambiguous in the sense it could be that + + + align:start position:0% +ambiguous in the sense it could be that +the person was just really lucky + + align:start position:0% +the person was just really lucky + + + align:start position:0% +the person was just really lucky +or it could be that the person is really + + align:start position:0% +or it could be that the person is really + + + align:start position:0% +or it could be that the person is really +really good at what they're doing + + align:start position:0% +really good at what they're doing + + + align:start position:0% +really good at what they're doing +now what sarcasm is asking when we see + + align:start position:0% +now what sarcasm is asking when we see + + + align:start position:0% +now what sarcasm is asking when we see +those events so when people see those + + align:start position:0% +those events so when people see those + + + align:start position:0% +those events so when people see those +events + + align:start position:0% +events + + + align:start position:0% +events +are people interpreting those events + + align:start position:0% +are people interpreting those events + + + align:start position:0% +are people interpreting those events +differently for men versus women + + align:start position:0% +differently for men versus women + + + align:start position:0% +differently for men versus women +so for example if a man if something bad + + align:start position:0% +so for example if a man if something bad + + + align:start position:0% +so for example if a man if something bad +happens at work + + align:start position:0% +happens at work + + + align:start position:0% +happens at work +a boss might react to that + + align:start position:0% +a boss might react to that + + + align:start position:0% +a boss might react to that +person differently or a + + align:start position:0% +person differently or a + + + align:start position:0% +person differently or a +updates their beliefs about the person's + + align:start position:0% +updates their beliefs about the person's + + + align:start position:0% +updates their beliefs about the person's +skills differently depending whether + + align:start position:0% +skills differently depending whether + + + align:start position:0% +skills differently depending whether +it's man or woman + + align:start position:0% +it's man or woman + + + align:start position:0% +it's man or woman +in addition the boss might also + + align:start position:0% +in addition the boss might also + + + align:start position:0% +in addition the boss might also +update differently about the peers + + align:start position:0% +update differently about the peers + + + align:start position:0% +update differently about the peers +so if a woman makes a mistake the boss + + align:start position:0% +so if a woman makes a mistake the boss + + + align:start position:0% +so if a woman makes a mistake the boss +might not only + + align:start position:0% +might not only + + + align:start position:0% +might not only +update his beliefs about + + align:start position:0% +update his beliefs about + + + align:start position:0% +update his beliefs about +this woman but also about all other + + align:start position:0% +this woman but also about all other + + + align:start position:0% +this woman but also about all other +women that worked for him + + align:start position:0% +women that worked for him + + + align:start position:0% +women that worked for him +similarly for a man of course the boss + + align:start position:0% +similarly for a man of course the boss + + + align:start position:0% +similarly for a man of course the boss +might do the same + + align:start position:0% +might do the same + + + align:start position:0% +might do the same +and what heather sarsous now asks is the + + align:start position:0% +and what heather sarsous now asks is the + + + align:start position:0% +and what heather sarsous now asks is the +question but + + align:start position:0% +question but + + + align:start position:0% +question but +is this updating or the interpretation + + align:start position:0% +is this updating or the interpretation + + + align:start position:0% +is this updating or the interpretation +of information differently + + align:start position:0% +of information differently + + + align:start position:0% +of information differently +for male versus female workers + + align:start position:0% +for male versus female workers + + + align:start position:0% +for male versus female workers +now why do we care well we care a lot + + align:start position:0% +now why do we care well we care a lot + + + align:start position:0% +now why do we care well we care a lot +about this because hiring promotion + + align:start position:0% +about this because hiring promotion + + + align:start position:0% +about this because hiring promotion +and wage decisions hinge on information + + align:start position:0% +and wage decisions hinge on information + + + align:start position:0% +and wage decisions hinge on information +about worker's ability + + align:start position:0% +about worker's ability + + + align:start position:0% +about worker's ability +and in particular if this is thematic + + align:start position:0% +and in particular if this is thematic + + + align:start position:0% +and in particular if this is thematic +differences in how information about men + + align:start position:0% +differences in how information about men + + + align:start position:0% +differences in how information about men +and women is interpreted + + align:start position:0% +and women is interpreted + + + align:start position:0% +and women is interpreted +that could lead to differences in hiring + + align:start position:0% +that could lead to differences in hiring + + + align:start position:0% +that could lead to differences in hiring +promotion and wage decisions and in turn + + align:start position:0% +promotion and wage decisions and in turn + + + align:start position:0% +promotion and wage decisions and in turn +might contribute to the gender gap + + align:start position:0% + + + + align:start position:0% + +what does sarsons do to answer this + + align:start position:0% +what does sarsons do to answer this + + + align:start position:0% +what does sarsons do to answer this +question she looks at how do + + align:start position:0% +question she looks at how do + + + align:start position:0% +question she looks at how do +physicians change referrals to surgeons + + align:start position:0% +physicians change referrals to surgeons + + + align:start position:0% +physicians change referrals to surgeons +and appears + + align:start position:0% +and appears + + + align:start position:0% +and appears +after a patient after certain patient + + align:start position:0% +after a patient after certain patient + + + align:start position:0% +after a patient after certain patient +outcomes + + align:start position:0% +outcomes + + + align:start position:0% +outcomes +now um what i mean by that well + + align:start position:0% +now um what i mean by that well + + + align:start position:0% +now um what i mean by that well +physicians often refer + + align:start position:0% +physicians often refer + + + align:start position:0% +physicians often refer +patients needing surgery to a local + + align:start position:0% +patients needing surgery to a local + + + align:start position:0% +patients needing surgery to a local +surgeon so somebody breaks their + + align:start position:0% +surgeon so somebody breaks their + + + align:start position:0% +surgeon so somebody breaks their +arm or the leg while many physicians + + align:start position:0% +arm or the leg while many physicians + + + align:start position:0% +arm or the leg while many physicians +can't do this on their own so they will + + align:start position:0% +can't do this on their own so they will + + + align:start position:0% +can't do this on their own so they will +refer + + align:start position:0% +refer + + + align:start position:0% +refer +this patient to a local surgeon + + align:start position:0% +this patient to a local surgeon + + + align:start position:0% +this patient to a local surgeon +now the referral choice reflects the + + align:start position:0% +now the referral choice reflects the + + + align:start position:0% +now the referral choice reflects the +physician's beliefs about + + align:start position:0% +physician's beliefs about + + + align:start position:0% +physician's beliefs about +the surgeon's ability right you wanna + + align:start position:0% +the surgeon's ability right you wanna + + + align:start position:0% +the surgeon's ability right you wanna +you wanna + + align:start position:0% +you wanna + + + align:start position:0% +you wanna +do the best for your um uh patient + + align:start position:0% +do the best for your um uh patient + + + align:start position:0% +do the best for your um uh patient +and you wanna uh send that patient your + + align:start position:0% +and you wanna uh send that patient your + + + align:start position:0% +and you wanna uh send that patient your +patient to like the best possible + + align:start position:0% +patient to like the best possible + + + align:start position:0% +patient to like the best possible +surgeon + + align:start position:0% +surgeon + + + align:start position:0% +surgeon +so if you have the suspicion if you + + align:start position:0% +so if you have the suspicion if you + + + align:start position:0% +so if you have the suspicion if you +think a certain surgeon is not + + align:start position:0% +think a certain surgeon is not + + + align:start position:0% +think a certain surgeon is not +competent you better not send your + + align:start position:0% +competent you better not send your + + + align:start position:0% +competent you better not send your +patient to that surgeon + + align:start position:0% +patient to that surgeon + + + align:start position:0% +patient to that surgeon +in part because you might care a lot + + align:start position:0% +in part because you might care a lot + + + align:start position:0% +in part because you might care a lot +about the patient in part because you + + align:start position:0% +about the patient in part because you + + + align:start position:0% +about the patient in part because you +know + + align:start position:0% +know + + + align:start position:0% +know +um uh if you make bad referrals that + + align:start position:0% +um uh if you make bad referrals that + + + align:start position:0% +um uh if you make bad referrals that +might also reflect on you + + align:start position:0% +might also reflect on you + + + align:start position:0% +might also reflect on you +eventually now what does sarson's do + + align:start position:0% +eventually now what does sarson's do + + + align:start position:0% +eventually now what does sarson's do +specifically + + align:start position:0% +specifically + + + align:start position:0% +specifically +she um to document whether um the + + align:start position:0% +she um to document whether um the + + + align:start position:0% +she um to document whether um the +reaction + + align:start position:0% +reaction + + + align:start position:0% +reaction +uh depends on the surgeon's gender what + + align:start position:0% +uh depends on the surgeon's gender what + + + align:start position:0% +uh depends on the surgeon's gender what +does a + + align:start position:0% +does a + + + align:start position:0% +does a +surgeon's do she matches on uh surgeon + + align:start position:0% +surgeon's do she matches on uh surgeon + + + align:start position:0% +surgeon's do she matches on uh surgeon +and patient characteristics under + + align:start position:0% +and patient characteristics under + + + align:start position:0% +and patient characteristics under +procedures + + align:start position:0% +procedures + + + align:start position:0% +procedures +that is to say she takes male and female + + align:start position:0% +that is to say she takes male and female + + + align:start position:0% +that is to say she takes male and female +surgeons + + align:start position:0% +surgeons + + + align:start position:0% +surgeons +and patient characteristics and + + align:start position:0% +and patient characteristics and + + + align:start position:0% +and patient characteristics and +procedures which is like you know + + align:start position:0% +procedures which is like you know + + + align:start position:0% +procedures which is like you know +broken arms versus like more complicated + + align:start position:0% +broken arms versus like more complicated + + + align:start position:0% +broken arms versus like more complicated +procedures + + align:start position:0% +procedures + + + align:start position:0% +procedures +so she matches all of these + + align:start position:0% +so she matches all of these + + + align:start position:0% +so she matches all of these +characteristics and such that in your + + align:start position:0% +characteristics and such that in your + + + align:start position:0% +characteristics and such that in your +observations that she has + + align:start position:0% +observations that she has + + + align:start position:0% +observations that she has +surgeons only differ by gender and then + + align:start position:0% +surgeons only differ by gender and then + + + align:start position:0% +surgeons only differ by gender and then +she considers what we call like + + align:start position:0% +she considers what we call like + + + align:start position:0% +she considers what we call like +an event study which is comparing how + + align:start position:0% +an event study which is comparing how + + + align:start position:0% +an event study which is comparing how +physicians react + + align:start position:0% +physicians react + + + align:start position:0% +physicians react +to um male and female surgeons when good + + align:start position:0% +to um male and female surgeons when good + + + align:start position:0% +to um male and female surgeons when good +and bad things + + align:start position:0% +and bad things + + + align:start position:0% +and bad things +um happen let me now show you more + + align:start position:0% +um happen let me now show you more + + + align:start position:0% +um happen let me now show you more +precisely what we mean + + align:start position:0% +precisely what we mean + + + align:start position:0% +precisely what we mean +so we have here on the x-axis quarters + + align:start position:0% +so we have here on the x-axis quarters + + + align:start position:0% +so we have here on the x-axis quarters +on the y-axis we have the referrals from + + align:start position:0% +on the y-axis we have the referrals from + + + align:start position:0% +on the y-axis we have the referrals from +the physicians to the performing surgeon + + align:start position:0% +the physicians to the performing surgeon + + + align:start position:0% +the physicians to the performing surgeon +so these are essentially diets of pears + + align:start position:0% +so these are essentially diets of pears + + + align:start position:0% +so these are essentially diets of pears +or physicians and performing + + align:start position:0% +or physicians and performing + + + align:start position:0% +or physicians and performing +surgeons and you see here minus one is + + align:start position:0% +surgeons and you see here minus one is + + + align:start position:0% +surgeons and you see here minus one is +normalized to be zero + + align:start position:0% +normalized to be zero + + + align:start position:0% +normalized to be zero +zero and then essentially you see the + + align:start position:0% +zero and then essentially you see the + + + align:start position:0% +zero and then essentially you see the +evolution of + + align:start position:0% +evolution of + + + align:start position:0% +evolution of +the referrals from a specific position + + align:start position:0% +the referrals from a specific position + + + align:start position:0% +the referrals from a specific position +to a performing + + align:start position:0% +to a performing + + + align:start position:0% +to a performing +surgeon these are men and women and + + align:start position:0% +surgeon these are men and women and + + + align:start position:0% +surgeon these are men and women and +these are essentially cases in which + + align:start position:0% +these are essentially cases in which + + + align:start position:0% +these are essentially cases in which +there is no adverse event + + align:start position:0% +there is no adverse event + + + align:start position:0% +there is no adverse event +what are adverse events are like a + + align:start position:0% +what are adverse events are like a + + + align:start position:0% +what are adverse events are like a +patient's death for example + + align:start position:0% +patient's death for example + + + align:start position:0% +patient's death for example +what you see here essentially these are + + align:start position:0% +what you see here essentially these are + + + align:start position:0% +what you see here essentially these are +men and women that are matched they're + + align:start position:0% +men and women that are matched they're + + + align:start position:0% +men and women that are matched they're +supposed to look exactly the same + + align:start position:0% +supposed to look exactly the same + + + align:start position:0% +supposed to look exactly the same +and what we see here is that referrals + + align:start position:0% +and what we see here is that referrals + + + align:start position:0% +and what we see here is that referrals +increase over time + + align:start position:0% +increase over time + + + align:start position:0% +increase over time +uh uh they tend to sort of increase uh + + align:start position:0% +uh uh they tend to sort of increase uh + + + align:start position:0% +uh uh they tend to sort of increase uh +fairly steeply over time and then sort + + align:start position:0% +fairly steeply over time and then sort + + + align:start position:0% +fairly steeply over time and then sort +of plot to go off over or + + align:start position:0% +of plot to go off over or + + + align:start position:0% +of plot to go off over or +over time the exact shape and pattern of + + align:start position:0% +over time the exact shape and pattern of + + + align:start position:0% +over time the exact shape and pattern of +this relationship + + align:start position:0% +this relationship + + + align:start position:0% +this relationship +doesn't matter as much however what + + align:start position:0% +doesn't matter as much however what + + + align:start position:0% +doesn't matter as much however what +matters is that men and women look + + align:start position:0% +matters is that men and women look + + + align:start position:0% +matters is that men and women look +uh exactly on the same right so + + align:start position:0% +uh exactly on the same right so + + + align:start position:0% +uh exactly on the same right so +the performing surgeon is here the + + align:start position:0% +the performing surgeon is here the + + + align:start position:0% +the performing surgeon is here the +gender here that varies is the gender of + + align:start position:0% +gender here that varies is the gender of + + + align:start position:0% +gender here that varies is the gender of +the performing surgeon + + align:start position:0% +the performing surgeon + + + align:start position:0% +the performing surgeon +now then she looks at sarcasm looks at + + align:start position:0% +now then she looks at sarcasm looks at + + + align:start position:0% +now then she looks at sarcasm looks at +cases in which there is an adverse event + + align:start position:0% +cases in which there is an adverse event + + + align:start position:0% +cases in which there is an adverse event +again the adverse event happens around + + align:start position:0% +again the adverse event happens around + + + align:start position:0% +again the adverse event happens around +here + + align:start position:0% +here + + + align:start position:0% +here +so what you see here is that when there + + align:start position:0% +so what you see here is that when there + + + align:start position:0% +so what you see here is that when there +is an adverse event + + align:start position:0% +is an adverse event + + + align:start position:0% +is an adverse event +there's a clear punishment in the sense + + align:start position:0% +there's a clear punishment in the sense + + + align:start position:0% +there's a clear punishment in the sense +that like + + align:start position:0% +that like + + + align:start position:0% +that like +the male surgeon now gets fewer + + align:start position:0% +the male surgeon now gets fewer + + + align:start position:0% +the male surgeon now gets fewer +referrals + + align:start position:0% +referrals + + + align:start position:0% +referrals +from the from the physician + + align:start position:0% +from the from the physician + + + align:start position:0% +from the from the physician +right after the adverse event happens + + align:start position:0% +right after the adverse event happens + + + align:start position:0% +right after the adverse event happens +this is manifested by the blue bars + + align:start position:0% +this is manifested by the blue bars + + + align:start position:0% +this is manifested by the blue bars +being lower than + + align:start position:0% +being lower than + + + align:start position:0% +being lower than +the gray bars notice that the number + + align:start position:0% +the gray bars notice that the number + + + align:start position:0% +the gray bars notice that the number +doesn't go + + align:start position:0% +doesn't go + + + align:start position:0% +doesn't go +down it's still above everything here is + + align:start position:0% +down it's still above everything here is + + + align:start position:0% +down it's still above everything here is +above the red line + + align:start position:0% +above the red line + + + align:start position:0% +above the red line +so it's just the uh um the physician is + + align:start position:0% +so it's just the uh um the physician is + + + align:start position:0% +so it's just the uh um the physician is +not + + align:start position:0% +not + + + align:start position:0% +not +uh increasing the um referrals over time + + align:start position:0% +uh increasing the um referrals over time + + + align:start position:0% +uh increasing the um referrals over time +anymore or that increase gets dampened + + align:start position:0% +anymore or that increase gets dampened + + + align:start position:0% +anymore or that increase gets dampened +by the adverse event + + align:start position:0% +by the adverse event + + + align:start position:0% +by the adverse event +this is for the male surgeon let's look + + align:start position:0% +this is for the male surgeon let's look + + + align:start position:0% +this is for the male surgeon let's look +at now what happens to the female + + align:start position:0% +at now what happens to the female + + + align:start position:0% +at now what happens to the female +surgeon + + align:start position:0% +surgeon + + + align:start position:0% +surgeon +what we see here is like a clear + + align:start position:0% +what we see here is like a clear + + + align:start position:0% +what we see here is like a clear +difference that opens up + + align:start position:0% +difference that opens up + + + align:start position:0% +difference that opens up +after the adverse event notice that + + align:start position:0% +after the adverse event notice that + + + align:start position:0% +after the adverse event notice that +there's no pre-trends here before it + + align:start position:0% +there's no pre-trends here before it + + + align:start position:0% +there's no pre-trends here before it +looks men + + align:start position:0% +looks men + + + align:start position:0% +looks men +and women or female and male surgeons + + align:start position:0% +and women or female and male surgeons + + + align:start position:0% +and women or female and male surgeons +including the red and the blue bars look + + align:start position:0% +including the red and the blue bars look + + + align:start position:0% +including the red and the blue bars look +exactly the same + + align:start position:0% +exactly the same + + + align:start position:0% +exactly the same +but the bar the difference only opens up + + align:start position:0% +but the bar the difference only opens up + + + align:start position:0% +but the bar the difference only opens up +after the adverse event and there's a + + align:start position:0% +after the adverse event and there's a + + + align:start position:0% +after the adverse event and there's a +pretty large gap you can see that that + + align:start position:0% +pretty large gap you can see that that + + + align:start position:0% +pretty large gap you can see that that +shows up in the referrals + + align:start position:0% +shows up in the referrals + + + align:start position:0% +shows up in the referrals +and this gap is way larger if you + + align:start position:0% +and this gap is way larger if you + + + align:start position:0% +and this gap is way larger if you +compare the red versus the + + align:start position:0% +compare the red versus the + + + align:start position:0% +compare the red versus the +gray lines that's way larger compared to + + align:start position:0% +gray lines that's way larger compared to + + + align:start position:0% +gray lines that's way larger compared to +the gap that emerges between the blue + + align:start position:0% +the gap that emerges between the blue + + + align:start position:0% +the gap that emerges between the blue +and the grey lines so we see here is + + align:start position:0% +and the grey lines so we see here is + + + align:start position:0% +and the grey lines so we see here is +that + + align:start position:0% +that + + + align:start position:0% +that +when both men and women are punished in + + align:start position:0% +when both men and women are punished in + + + align:start position:0% +when both men and women are punished in +the sense of receiving fewer referrals + + align:start position:0% +the sense of receiving fewer referrals + + + align:start position:0% +the sense of receiving fewer referrals +after an adverse event that punishment + + align:start position:0% +after an adverse event that punishment + + + align:start position:0% +after an adverse event that punishment +is way more severe for female + + align:start position:0% +is way more severe for female + + + align:start position:0% +is way more severe for female +than for male surgeons now let's do the + + align:start position:0% +than for male surgeons now let's do the + + + align:start position:0% +than for male surgeons now let's do the +same for + + align:start position:0% +same for + + + align:start position:0% +same for +uh the absence of a good event or + + align:start position:0% +uh the absence of a good event or + + + align:start position:0% +uh the absence of a good event or +actually good events that happen where + + align:start position:0% +actually good events that happen where + + + align:start position:0% +actually good events that happen where +it's a good event while like + + align:start position:0% +it's a good event while like + + + align:start position:0% +it's a good event while like +it's essentially a surprisingly good + + align:start position:0% +it's essentially a surprisingly good + + + align:start position:0% +it's essentially a surprisingly good +thing that happened where there's a + + align:start position:0% +thing that happened where there's a + + + align:start position:0% +thing that happened where there's a +complicated surgery and the person does + + align:start position:0% +complicated surgery and the person does + + + align:start position:0% +complicated surgery and the person does +really well + + align:start position:0% +really well + + + align:start position:0% +really well +um what you see here is again sort of + + align:start position:0% +um what you see here is again sort of + + + align:start position:0% +um what you see here is again sort of +the the the + + align:start position:0% +the the the + + + align:start position:0% +the the the +men and women that look pretty much + + align:start position:0% +men and women that look pretty much + + + align:start position:0% +men and women that look pretty much +exactly the same you can see like here + + align:start position:0% +exactly the same you can see like here + + + align:start position:0% +exactly the same you can see like here +maybe men are doing slightly better + + align:start position:0% +maybe men are doing slightly better + + + align:start position:0% +maybe men are doing slightly better +uh overall but overall these gray lines + + align:start position:0% +uh overall but overall these gray lines + + + align:start position:0% +uh overall but overall these gray lines +look very similar over time + + align:start position:0% +look very similar over time + + + align:start position:0% +look very similar over time +now if there's a good event that happens + + align:start position:0% +now if there's a good event that happens + + + align:start position:0% +now if there's a good event that happens +you see essentially men get like very + + align:start position:0% +you see essentially men get like very + + + align:start position:0% +you see essentially men get like very +much like rewarded + + align:start position:0% +much like rewarded + + + align:start position:0% +much like rewarded +if the male surgeon does well um + + align:start position:0% + + + + align:start position:0% + +uh he gets rewarded in the sense of like + + align:start position:0% +uh he gets rewarded in the sense of like + + + align:start position:0% +uh he gets rewarded in the sense of like +receiving + + align:start position:0% +receiving + + + align:start position:0% +receiving +a lot more um uh referrals from the pcp + + align:start position:0% +a lot more um uh referrals from the pcp + + + align:start position:0% +a lot more um uh referrals from the pcp +from the + + align:start position:0% +from the + + + align:start position:0% +from the +from the doctor now if you do the same + + align:start position:0% +from the doctor now if you do the same + + + align:start position:0% +from the doctor now if you do the same +for um + + align:start position:0% +for um + + + align:start position:0% +for um +female surgeon again uh female surgeons + + align:start position:0% +female surgeon again uh female surgeons + + + align:start position:0% +female surgeon again uh female surgeons +benefit from that + + align:start position:0% +benefit from that + + + align:start position:0% +benefit from that +but the increase in referrals is + + align:start position:0% +but the increase in referrals is + + + align:start position:0% +but the increase in referrals is +a lot lower than uh for men so again + + align:start position:0% +a lot lower than uh for men so again + + + align:start position:0% +a lot lower than uh for men so again +both men + + align:start position:0% +both men + + + align:start position:0% +both men +and women there is a reaction to that + + align:start position:0% +and women there is a reaction to that + + + align:start position:0% +and women there is a reaction to that +information to a good or bad event + + align:start position:0% +information to a good or bad event + + + align:start position:0% +information to a good or bad event +but the reaction tends to be much + + align:start position:0% +but the reaction tends to be much + + + align:start position:0% +but the reaction tends to be much +stronger much more favorable for men + + align:start position:0% +stronger much more favorable for men + + + align:start position:0% +stronger much more favorable for men +in terms of the good events men get + + align:start position:0% +in terms of the good events men get + + + align:start position:0% +in terms of the good events men get +rewarded more for the good events + + align:start position:0% +rewarded more for the good events + + + align:start position:0% +rewarded more for the good events +and women get punished more for + + align:start position:0% +and women get punished more for + + + align:start position:0% +and women get punished more for +vitamins or surprising vitamins that + + align:start position:0% +vitamins or surprising vitamins that + + + align:start position:0% +vitamins or surprising vitamins that +happen + + align:start position:0% +happen + + + align:start position:0% +happen +let me summarize the main results after + + align:start position:0% +let me summarize the main results after + + + align:start position:0% +let me summarize the main results after +a bad outcome after + + align:start position:0% +a bad outcome after + + + align:start position:0% +a bad outcome after +for example like a patient death there's + + align:start position:0% +for example like a patient death there's + + + align:start position:0% +for example like a patient death there's +a 34 decrease in referrals to female + + align:start position:0% +a 34 decrease in referrals to female + + + align:start position:0% +a 34 decrease in referrals to female +surgeon + + align:start position:0% +surgeon + + + align:start position:0% +surgeon +surgeons and there's a stagnation in + + align:start position:0% +surgeons and there's a stagnation in + + + align:start position:0% +surgeons and there's a stagnation in +referrals to male surgeons so + + align:start position:0% +referrals to male surgeons so + + + align:start position:0% +referrals to male surgeons so +essentially women tend to be get + + align:start position:0% +essentially women tend to be get + + + align:start position:0% +essentially women tend to be get +punished quite a lot + + align:start position:0% +punished quite a lot + + + align:start position:0% +punished quite a lot +men a little bit in the sense that like + + align:start position:0% +men a little bit in the sense that like + + + align:start position:0% +men a little bit in the sense that like +referrals don't go up anymore but the + + align:start position:0% +referrals don't go up anymore but the + + + align:start position:0% +referrals don't go up anymore but the +punishment is much less + + align:start position:0% +punishment is much less + + + align:start position:0% +punishment is much less +now strikingly physicians are also less + + align:start position:0% +now strikingly physicians are also less + + + align:start position:0% +now strikingly physicians are also less +likely to refer + + align:start position:0% +likely to refer + + + align:start position:0% +likely to refer +to other female surgeons that is to say + + align:start position:0% +to other female surgeons that is to say + + + align:start position:0% +to other female surgeons that is to say +if a female + + align:start position:0% +if a female + + + align:start position:0% +if a female +surgeon if a patient dies for a female + + align:start position:0% +surgeon if a patient dies for a female + + + align:start position:0% +surgeon if a patient dies for a female +surgeon + + align:start position:0% +surgeon + + + align:start position:0% +surgeon +the physician is also less likely to + + align:start position:0% +the physician is also less likely to + + + align:start position:0% +the physician is also less likely to +refer + + align:start position:0% +refer + + + align:start position:0% +refer +patients or future patients to other + + align:start position:0% +patients or future patients to other + + + align:start position:0% +patients or future patients to other +female surgeons these other female + + align:start position:0% +female surgeons these other female + + + align:start position:0% +female surgeons these other female +surgeons + + align:start position:0% +surgeons + + + align:start position:0% +surgeons +nobody has died there so essentially + + align:start position:0% +nobody has died there so essentially + + + align:start position:0% +nobody has died there so essentially +what seems to be the case is that + + align:start position:0% +what seems to be the case is that + + + align:start position:0% +what seems to be the case is that +um the physicians also are + + align:start position:0% +um the physicians also are + + + align:start position:0% +um the physicians also are +updating about women or female surgeons + + align:start position:0% +updating about women or female surgeons + + + align:start position:0% +updating about women or female surgeons +in general + + align:start position:0% +in general + + + align:start position:0% +in general +if there is um a negative event that + + align:start position:0% +if there is um a negative event that + + + align:start position:0% +if there is um a negative event that +happens which is sort of very straight + + align:start position:0% +happens which is sort of very straight + + + align:start position:0% +happens which is sort of very straight +after a good outcome uh such as like + + align:start position:0% +after a good outcome uh such as like + + + align:start position:0% +after a good outcome uh such as like +unanticipated survival + + align:start position:0% +unanticipated survival + + + align:start position:0% +unanticipated survival +uh there's a doubling of referrals to + + align:start position:0% +uh there's a doubling of referrals to + + + align:start position:0% +uh there's a doubling of referrals to +male surgeons but only a 70 + + align:start position:0% +male surgeons but only a 70 + + + align:start position:0% +male surgeons but only a 70 +increase in referrals to females and + + align:start position:0% +increase in referrals to females and + + + align:start position:0% +increase in referrals to females and +they are here there's no spillovers to + + align:start position:0% +they are here there's no spillovers to + + + align:start position:0% +they are here there's no spillovers to +to to other female surgeons so + + align:start position:0% +to to other female surgeons so + + + align:start position:0% +to to other female surgeons so +so again what we find here well we find + + align:start position:0% +so again what we find here well we find + + + align:start position:0% +so again what we find here well we find +that + + align:start position:0% +that + + + align:start position:0% +that +women are punished way more for + + align:start position:0% +women are punished way more for + + + align:start position:0% +women are punished way more for +unexpected bad events + + align:start position:0% +unexpected bad events + + + align:start position:0% +unexpected bad events +and they're rewarded less for um + + align:start position:0% +and they're rewarded less for um + + + align:start position:0% +and they're rewarded less for um +unexpected um good events that is to say + + align:start position:0% +unexpected um good events that is to say + + + align:start position:0% +unexpected um good events that is to say +it's not just the case that like + + align:start position:0% +it's not just the case that like + + + align:start position:0% +it's not just the case that like +uh there's more updating going on in the + + align:start position:0% +uh there's more updating going on in the + + + align:start position:0% +uh there's more updating going on in the +sense maybe you learn more from good and + + align:start position:0% +sense maybe you learn more from good and + + + align:start position:0% +sense maybe you learn more from good and +bad events because maybe you have like + + align:start position:0% +bad events because maybe you have like + + + align:start position:0% +bad events because maybe you have like +less information about men and women to + + align:start position:0% +less information about men and women to + + + align:start position:0% +less information about men and women to +start with that's not the case here + + align:start position:0% +start with that's not the case here + + + align:start position:0% +start with that's not the case here +what is here the case is that there's + + align:start position:0% +what is here the case is that there's + + + align:start position:0% +what is here the case is that there's +more updating or more punishment for + + align:start position:0% +more updating or more punishment for + + + align:start position:0% +more updating or more punishment for +mistakes for women + + align:start position:0% +mistakes for women + + + align:start position:0% +mistakes for women +and less reward for good things that + + align:start position:0% +and less reward for good things that + + + align:start position:0% +and less reward for good things that +happen + + align:start position:0% +happen + + + align:start position:0% +happen +or good events for for women as well + + align:start position:0% +or good events for for women as well + + + align:start position:0% +or good events for for women as well +now why these asymmetries matter + + align:start position:0% +now why these asymmetries matter + + + align:start position:0% +now why these asymmetries matter +well one important issue here is that + + align:start position:0% +well one important issue here is that + + + align:start position:0% +well one important issue here is that +women have fewer chances to make + + align:start position:0% +women have fewer chances to make + + + align:start position:0% +women have fewer chances to make +mistakes + + align:start position:0% +mistakes + + + align:start position:0% +mistakes +and in particular if there's like + + align:start position:0% +and in particular if there's like + + + align:start position:0% +and in particular if there's like +dropping out if like + + align:start position:0% +dropping out if like + + + align:start position:0% +dropping out if like +if women don't get promoted or if they + + align:start position:0% +if women don't get promoted or if they + + + align:start position:0% +if women don't get promoted or if they +even drop out + + align:start position:0% +even drop out + + + align:start position:0% +even drop out +um that leads to like lower skill + + align:start position:0% +um that leads to like lower skill + + + align:start position:0% +um that leads to like lower skill +accumulation and you know women will be + + align:start position:0% +accumulation and you know women will be + + + align:start position:0% +accumulation and you know women will be +just less qualified overall in the end + + align:start position:0% +just less qualified overall in the end + + + align:start position:0% +just less qualified overall in the end +because they have like less chances to + + align:start position:0% +because they have like less chances to + + + align:start position:0% +because they have like less chances to +get promoted um + + align:start position:0% +get promoted um + + + align:start position:0% +get promoted um +uh uh i get more responsibility and so + + align:start position:0% +uh uh i get more responsibility and so + + + align:start position:0% +uh uh i get more responsibility and so +on and so forth when i may even drop + + align:start position:0% +on and so forth when i may even drop + + + align:start position:0% +on and so forth when i may even drop +out overall and we just have fewer women + + align:start position:0% +out overall and we just have fewer women + + + align:start position:0% +out overall and we just have fewer women +in the profession + + align:start position:0% +in the profession + + + align:start position:0% +in the profession +now moreover usually wage gaps are + + align:start position:0% +now moreover usually wage gaps are + + + align:start position:0% +now moreover usually wage gaps are +measured conditional and skills industry + + align:start position:0% +measured conditional and skills industry + + + align:start position:0% +measured conditional and skills industry +and position + + align:start position:0% +and position + + + align:start position:0% +and position +but if there's biased evaluations that + + align:start position:0% +but if there's biased evaluations that + + + align:start position:0% +but if there's biased evaluations that +lead to differences in skills and + + align:start position:0% +lead to differences in skills and + + + align:start position:0% +lead to differences in skills and +positions in the workplace + + align:start position:0% +positions in the workplace + + + align:start position:0% +positions in the workplace +not only is it the case that women are + + align:start position:0% +not only is it the case that women are + + + align:start position:0% +not only is it the case that women are +receiving like wage gaps conditional on + + align:start position:0% +receiving like wage gaps conditional on + + + align:start position:0% +receiving like wage gaps conditional on +those skills but they also have + + align:start position:0% +those skills but they also have + + + align:start position:0% +those skills but they also have +different skills and positions in the + + align:start position:0% +different skills and positions in the + + + align:start position:0% +different skills and positions in the +workplace because of biased evaluations + + align:start position:0% +workplace because of biased evaluations + + + align:start position:0% +workplace because of biased evaluations +so that's an additional scope for + + align:start position:0% +so that's an additional scope for + + + align:start position:0% +so that's an additional scope for +discrimination and differences in + + align:start position:0% +discrimination and differences in + + + align:start position:0% +discrimination and differences in +earnings and so on + + align:start position:0% +earnings and so on + + + align:start position:0% +earnings and so on +and then importantly this is also not a + + align:start position:0% +and then importantly this is also not a + + + align:start position:0% +and then importantly this is also not a +mistake that can get corrected over time + + align:start position:0% +mistake that can get corrected over time + + + align:start position:0% +mistake that can get corrected over time +because if women drop out in particular + + align:start position:0% +because if women drop out in particular + + + align:start position:0% +because if women drop out in particular +then + + align:start position:0% +then + + + align:start position:0% +then +or if there's no referrals that happen + + align:start position:0% +or if there's no referrals that happen + + + align:start position:0% +or if there's no referrals that happen +anymore then the doctor or any other + + align:start position:0% +anymore then the doctor or any other + + + align:start position:0% +anymore then the doctor or any other +person might not + + align:start position:0% +person might not + + + align:start position:0% +person might not +receive any signals anymore from women + + align:start position:0% +receive any signals anymore from women + + + align:start position:0% +receive any signals anymore from women +right if you sort of + + align:start position:0% +right if you sort of + + + align:start position:0% +right if you sort of +update on on a particular person that + + align:start position:0% +update on on a particular person that + + + align:start position:0% +update on on a particular person that +this + + align:start position:0% +this + + + align:start position:0% +this +patient of mine died because i sent them + + align:start position:0% +patient of mine died because i sent them + + + align:start position:0% +patient of mine died because i sent them +to that person + + align:start position:0% +to that person + + + align:start position:0% +to that person +if you then think you know this person + + align:start position:0% +if you then think you know this person + + + align:start position:0% +if you then think you know this person +is terrible and don't + + align:start position:0% +is terrible and don't + + + align:start position:0% +is terrible and don't +send any further patients anymore you'll + + align:start position:0% +send any further patients anymore you'll + + + align:start position:0% +send any further patients anymore you'll +never learn that this woman was in fact + + align:start position:0% +never learn that this woman was in fact + + + align:start position:0% +never learn that this woman was in fact +very much highly qualified + + align:start position:0% +very much highly qualified + + + align:start position:0% +very much highly qualified +and that was just an accident that could + + align:start position:0% +and that was just an accident that could + + + align:start position:0% +and that was just an accident that could +have happened to anyone + + align:start position:0% +have happened to anyone + + + align:start position:0% +have happened to anyone +so that's a really important issue that + + align:start position:0% +so that's a really important issue that + + + align:start position:0% +so that's a really important issue that +um so when women are underrepresented + + align:start position:0% +um so when women are underrepresented + + + align:start position:0% +um so when women are underrepresented +employers see fewer outcomes overall and + + align:start position:0% +employers see fewer outcomes overall and + + + align:start position:0% +employers see fewer outcomes overall and +if there's updates more after that + + align:start position:0% +if there's updates more after that + + + align:start position:0% +if there's updates more after that +outcomes + + align:start position:0% + + + + align:start position:0% + +in particular if there's also updates + + align:start position:0% +in particular if there's also updates + + + align:start position:0% +in particular if there's also updates +about all women then + + align:start position:0% +about all women then + + + align:start position:0% +about all women then +um there will be fewer chances um uh to + + align:start position:0% +um there will be fewer chances um uh to + + + align:start position:0% +um there will be fewer chances um uh to +learn + + align:start position:0% +learn + + + align:start position:0% +learn +and uh if then when they let go and so + + align:start position:0% +and uh if then when they let go and so + + + align:start position:0% +and uh if then when they let go and so +on + + align:start position:0% +on + + + align:start position:0% +on +uh or less likely to be hired then there + + align:start position:0% +uh or less likely to be hired then there + + + align:start position:0% +uh or less likely to be hired then there +will be no chance of actually correcting + + align:start position:0% +will be no chance of actually correcting + + + align:start position:0% +will be no chance of actually correcting +those police + + align:start position:0% +those police + + + align:start position:0% +those police +uh strikingly as i told you um what's + + align:start position:0% +uh strikingly as i told you um what's + + + align:start position:0% +uh strikingly as i told you um what's +really important + + align:start position:0% +really important + + + align:start position:0% +really important +um as a result is that it seems to be + + align:start position:0% +um as a result is that it seems to be + + + align:start position:0% +um as a result is that it seems to be +like updating + + align:start position:0% +like updating + + + align:start position:0% +like updating +not just about like one specific woman + + align:start position:0% +not just about like one specific woman + + + align:start position:0% +not just about like one specific woman +overall + + align:start position:0% +overall + + + align:start position:0% +overall +after the negative events but also about + + align:start position:0% +after the negative events but also about + + + align:start position:0% +after the negative events but also about +all other + + align:start position:0% +all other + + + align:start position:0% +all other +um other women um + + align:start position:0% +um other women um + + + align:start position:0% +um other women um +that that get punished for um the bad + + align:start position:0% +that that get punished for um the bad + + + align:start position:0% +that that get punished for um the bad +event that happens + + align:start position:0% +event that happens + + + align:start position:0% +event that happens +and if that's the case well if there's + + align:start position:0% +and if that's the case well if there's + + + align:start position:0% +and if that's the case well if there's +several women in the profession + + align:start position:0% +several women in the profession + + + align:start position:0% +several women in the profession +and all women always have to pay for any + + align:start position:0% +and all women always have to pay for any + + + align:start position:0% +and all women always have to pay for any +bad events that happen for any woman and + + align:start position:0% +bad events that happen for any woman and + + + align:start position:0% +bad events that happen for any woman and +sometimes you know mistakes in fact + + align:start position:0% +sometimes you know mistakes in fact + + + align:start position:0% +sometimes you know mistakes in fact +happen + + align:start position:0% +happen + + + align:start position:0% +happen +that's of course terrible because that + + align:start position:0% +that's of course terrible because that + + + align:start position:0% +that's of course terrible because that +sort of amplifies um + + align:start position:0% +sort of amplifies um + + + align:start position:0% +sort of amplifies um +a lot of the updating because uh even if + + align:start position:0% +a lot of the updating because uh even if + + + align:start position:0% +a lot of the updating because uh even if +somebody makes no mistakes whatsoever + + align:start position:0% +somebody makes no mistakes whatsoever + + + align:start position:0% +somebody makes no mistakes whatsoever +negative updates happen on their + + align:start position:0% +negative updates happen on their + + + align:start position:0% +negative updates happen on their +performance other women + + align:start position:0% +performance other women + + + align:start position:0% +performance other women +perform negatively in some ways + + align:start position:0% +perform negatively in some ways + + + align:start position:0% +perform negatively in some ways +now one question you might ask as well + + align:start position:0% +now one question you might ask as well + + + align:start position:0% +now one question you might ask as well +couldn't we just use algorithms machine + + align:start position:0% +couldn't we just use algorithms machine + + + align:start position:0% +couldn't we just use algorithms machine +learning etc to overcome + + align:start position:0% +learning etc to overcome + + + align:start position:0% +learning etc to overcome +such biases right in particular instead + + align:start position:0% +such biases right in particular instead + + + align:start position:0% +such biases right in particular instead +of hiring and so on + + align:start position:0% +of hiring and so on + + + align:start position:0% +of hiring and so on +couldn't we use um algorithms machine + + align:start position:0% +couldn't we use um algorithms machine + + + align:start position:0% +couldn't we use um algorithms machine +learning to + + align:start position:0% +learning to + + + align:start position:0% +learning to +to train those algorithms and you know + + align:start position:0% +to train those algorithms and you know + + + align:start position:0% +to train those algorithms and you know +instead of use computers instead of + + align:start position:0% +instead of use computers instead of + + + align:start position:0% +instead of use computers instead of +humans and then you know + + align:start position:0% +humans and then you know + + + align:start position:0% +humans and then you know +we might get rid of those biases well + + align:start position:0% +we might get rid of those biases well + + + align:start position:0% +we might get rid of those biases well +one key problem with that is that + + align:start position:0% +one key problem with that is that + + + align:start position:0% +one key problem with that is that +algorithms themselves can be biased + + align:start position:0% +algorithms themselves can be biased + + + align:start position:0% +algorithms themselves can be biased +now why is that is what we train + + align:start position:0% +now why is that is what we train + + + align:start position:0% +now why is that is what we train +algorithms based on human decisions + + align:start position:0% +algorithms based on human decisions + + + align:start position:0% +algorithms based on human decisions +as an example if you train an algorithm + + align:start position:0% + + + + align:start position:0% + +some companies did based on actual + + align:start position:0% +some companies did based on actual + + + align:start position:0% +some companies did based on actual +decisions if you ask the question this + + align:start position:0% +decisions if you ask the question this + + + align:start position:0% +decisions if you ask the question this +application if you train the algorithm + + align:start position:0% +application if you train the algorithm + + + align:start position:0% +application if you train the algorithm +actual + + align:start position:0% +actual + + + align:start position:0% +actual +hiring decisions or interview decisions + + align:start position:0% +hiring decisions or interview decisions + + + align:start position:0% +hiring decisions or interview decisions +where you say well would this person be + + align:start position:0% +where you say well would this person be + + + align:start position:0% +where you say well would this person be +um invited or is this person is his + + align:start position:0% +um invited or is this person is his + + + align:start position:0% +um invited or is this person is his +resume likely to be + + align:start position:0% +resume likely to be + + + align:start position:0% +resume likely to be +invited for an interview well if those + + align:start position:0% +invited for an interview well if those + + + align:start position:0% +invited for an interview well if those +interviewing decisions to start with + + align:start position:0% +interviewing decisions to start with + + + align:start position:0% +interviewing decisions to start with +were biased + + align:start position:0% +were biased + + + align:start position:0% +were biased +based on sexism racism and so on if you + + align:start position:0% +based on sexism racism and so on if you + + + align:start position:0% +based on sexism racism and so on if you +train your algorithm + + align:start position:0% +train your algorithm + + + align:start position:0% +train your algorithm +on it then very much you make that + + align:start position:0% +on it then very much you make that + + + align:start position:0% +on it then very much you make that +algorithm bias + + align:start position:0% +algorithm bias + + + align:start position:0% +algorithm bias +as well now crucially + + align:start position:0% +as well now crucially + + + align:start position:0% +as well now crucially +um that's of course uh problematic + + align:start position:0% +um that's of course uh problematic + + + align:start position:0% +um that's of course uh problematic +and very much would like to avoid that + + align:start position:0% +and very much would like to avoid that + + + align:start position:0% +and very much would like to avoid that +and so you want to be very careful + + align:start position:0% +and so you want to be very careful + + + align:start position:0% +and so you want to be very careful +but crucially some of these biases can + + align:start position:0% +but crucially some of these biases can + + + align:start position:0% +but crucially some of these biases can +be + + align:start position:0% +be + + + align:start position:0% +be +perhaps easier or fixed and perhaps + + align:start position:0% +perhaps easier or fixed and perhaps + + + align:start position:0% +perhaps easier or fixed and perhaps +fixed more easily + + align:start position:0% +fixed more easily + + + align:start position:0% +fixed more easily +than buy a seasoned human decision maker + + align:start position:0% +than buy a seasoned human decision maker + + + align:start position:0% +than buy a seasoned human decision maker +right if somebody is sexist or race it's + + align:start position:0% +right if somebody is sexist or race it's + + + align:start position:0% +right if somebody is sexist or race it's +very hard to fix this + + align:start position:0% +very hard to fix this + + + align:start position:0% +very hard to fix this +at least in the short run however + + align:start position:0% +at least in the short run however + + + align:start position:0% +at least in the short run however +an algorithm essentially is just doing + + align:start position:0% +an algorithm essentially is just doing + + + align:start position:0% +an algorithm essentially is just doing +whatever we train them to do + + align:start position:0% +whatever we train them to do + + + align:start position:0% +whatever we train them to do +so if we build equity concerns into the + + align:start position:0% +so if we build equity concerns into the + + + align:start position:0% +so if we build equity concerns into the +objective + + align:start position:0% +objective + + + align:start position:0% +objective +function of an algorithm then we can + + align:start position:0% +function of an algorithm then we can + + + align:start position:0% +function of an algorithm then we can +essentially reduce or even eliminate + + align:start position:0% +essentially reduce or even eliminate + + + align:start position:0% +essentially reduce or even eliminate +these biases explicitly because the + + align:start position:0% +these biases explicitly because the + + + align:start position:0% +these biases explicitly because the +algorithm is explicitly + + align:start position:0% +algorithm is explicitly + + + align:start position:0% +algorithm is explicitly +i'm asked to do so and so this is + + align:start position:0% +i'm asked to do so and so this is + + + align:start position:0% +i'm asked to do so and so this is +fascinating if you want to learn more + + align:start position:0% +fascinating if you want to learn more + + + align:start position:0% +fascinating if you want to learn more +about this overall it's a fascinating + + align:start position:0% +about this overall it's a fascinating + + + align:start position:0% +about this overall it's a fascinating +talk on discrimination by algorithms and + + align:start position:0% +talk on discrimination by algorithms and + + + align:start position:0% +talk on discrimination by algorithms and +people by assembling + + align:start position:0% +people by assembling + + + align:start position:0% +people by assembling +that i've linked here um in the slides + + align:start position:0% +that i've linked here um in the slides + + + align:start position:0% +that i've linked here um in the slides +that you can + + align:start position:0% +that you can + + + align:start position:0% +that you can +that you can watch and write more about + + align:start position:0% +that you can watch and write more about + + + align:start position:0% +that you can watch and write more about +but overall so + + align:start position:0% +but overall so + + + align:start position:0% +but overall so +so just to say to summarize algorithms + + align:start position:0% +so just to say to summarize algorithms + + + align:start position:0% +so just to say to summarize algorithms +can be biased + + align:start position:0% +can be biased + + + align:start position:0% +can be biased +but they can also be fixed and that's an + + align:start position:0% +but they can also be fixed and that's an + + + align:start position:0% +but they can also be fixed and that's an +important research agenda that people + + align:start position:0% +important research agenda that people + + + align:start position:0% +important research agenda that people +have been working on + + align:start position:0% +have been working on + + + align:start position:0% +have been working on +uh more recently design of fair + + align:start position:0% +uh more recently design of fair + + + align:start position:0% +uh more recently design of fair +algorithms + + align:start position:0% +algorithms + + + align:start position:0% +algorithms +next we're going to talk about gender + + align:start position:0% +next we're going to talk about gender + + + align:start position:0% +next we're going to talk about gender +identity norms and a very nice paper by + + align:start position:0% +identity norms and a very nice paper by + + + align:start position:0% +identity norms and a very nice paper by +patrandedal from 2015. + + align:start position:0% +patrandedal from 2015. + + + align:start position:0% +patrandedal from 2015. +identity considerations were imported + + align:start position:0% +identity considerations were imported + + + align:start position:0% +identity considerations were imported +from social psychology into economics + + align:start position:0% +from social psychology into economics + + + align:start position:0% +from social psychology into economics +and multiple papers by akolov and + + align:start position:0% +and multiple papers by akolov and + + + align:start position:0% +and multiple papers by akolov and +cranton in 2000 + + align:start position:0% +cranton in 2000 + + + align:start position:0% +cranton in 2000 +particularly in 2000 there's a very nice + + align:start position:0% +particularly in 2000 there's a very nice + + + align:start position:0% +particularly in 2000 there's a very nice +book about identity economics if you're + + align:start position:0% +book about identity economics if you're + + + align:start position:0% +book about identity economics if you're +interested in learning more about that + + align:start position:0% +interested in learning more about that + + + align:start position:0% +interested in learning more about that +um gender identity norms are an + + align:start position:0% +um gender identity norms are an + + + align:start position:0% +um gender identity norms are an +important + + align:start position:0% +important + + + align:start position:0% +important +example or application of such norms or + + align:start position:0% +example or application of such norms or + + + align:start position:0% +example or application of such norms or +identity considerations + + align:start position:0% +identity considerations + + + align:start position:0% +identity considerations +more generally in particular um uh + + align:start position:0% +more generally in particular um uh + + + align:start position:0% +more generally in particular um uh +alcoholic and quantum or + + align:start position:0% +alcoholic and quantum or + + + align:start position:0% +alcoholic and quantum or +we here as well focus on two social + + align:start position:0% +we here as well focus on two social + + + align:start position:0% +we here as well focus on two social +categories + + align:start position:0% +categories + + + align:start position:0% +categories +men and women for simplicity we can also + + align:start position:0% +men and women for simplicity we can also + + + align:start position:0% +men and women for simplicity we can also +just talk about + + align:start position:0% +just talk about + + + align:start position:0% +just talk about +husbands and wives understand that + + align:start position:0% +husbands and wives understand that + + + align:start position:0% +husbands and wives understand that +things are more complicated in reality + + align:start position:0% +things are more complicated in reality + + + align:start position:0% +things are more complicated in reality +but for simplicity we're going to focus + + align:start position:0% +but for simplicity we're going to focus + + + align:start position:0% +but for simplicity we're going to focus +on that for now + + align:start position:0% +on that for now + + + align:start position:0% +on that for now +um what do we mean by gender identity + + align:start position:0% +um what do we mean by gender identity + + + align:start position:0% +um what do we mean by gender identity +well gender identity is something that + + align:start position:0% +well gender identity is something that + + + align:start position:0% +well gender identity is something that +changes + + align:start position:0% +changes + + + align:start position:0% +changes +payoffs from different actions as + + align:start position:0% +payoffs from different actions as + + + align:start position:0% +payoffs from different actions as +dictated by some prescriptive norms + + align:start position:0% +dictated by some prescriptive norms + + + align:start position:0% +dictated by some prescriptive norms +what might those norms be one one one + + align:start position:0% +what might those norms be one one one + + + align:start position:0% +what might those norms be one one one +would be men should not do women's work + + align:start position:0% +would be men should not do women's work + + + align:start position:0% +would be men should not do women's work +in the house + + align:start position:0% +in the house + + + align:start position:0% +in the house +in the home like cooking cleaning + + align:start position:0% +in the home like cooking cleaning + + + align:start position:0% +in the home like cooking cleaning +and so on some men might consider that + + align:start position:0% +and so on some men might consider that + + + align:start position:0% +and so on some men might consider that +as women's work and they + + align:start position:0% +as women's work and they + + + align:start position:0% +as women's work and they +might feel particularly high disutility + + align:start position:0% +might feel particularly high disutility + + + align:start position:0% +might feel particularly high disutility +from doing so + + align:start position:0% +from doing so + + + align:start position:0% +from doing so +um if they violate that norm another + + align:start position:0% +um if they violate that norm another + + + align:start position:0% +um if they violate that norm another +norm would be + + align:start position:0% +norm would be + + + align:start position:0% +norm would be +men should earn more than their wives + + align:start position:0% +men should earn more than their wives + + + align:start position:0% +men should earn more than their wives +now uh husbands now lose identity + + align:start position:0% +now uh husbands now lose identity + + + align:start position:0% +now uh husbands now lose identity +experience lower utility and + + align:start position:0% +experience lower utility and + + + align:start position:0% +experience lower utility and +circumstances when these prescriptions + + align:start position:0% +circumstances when these prescriptions + + + align:start position:0% +circumstances when these prescriptions +are violated when the + + align:start position:0% +are violated when the + + + align:start position:0% +are violated when the +when he does a housework or when his + + align:start position:0% +when he does a housework or when his + + + align:start position:0% +when he does a housework or when his +wife earns more than half of the + + align:start position:0% +wife earns more than half of the + + + align:start position:0% +wife earns more than half of the +household income notice that wives might + + align:start position:0% +household income notice that wives might + + + align:start position:0% +household income notice that wives might +also lose identity + + align:start position:0% +also lose identity + + + align:start position:0% +also lose identity +for simplicity we're going to talk more + + align:start position:0% +for simplicity we're going to talk more + + + align:start position:0% +for simplicity we're going to talk more +only about husbands i'm doing so for now + + align:start position:0% +only about husbands i'm doing so for now + + + align:start position:0% +only about husbands i'm doing so for now +now we're trying to dial particularly + + align:start position:0% +now we're trying to dial particularly + + + align:start position:0% +now we're trying to dial particularly +focus on the + + align:start position:0% +focus on the + + + align:start position:0% +focus on the +the prescription that men should earn + + align:start position:0% +the prescription that men should earn + + + align:start position:0% +the prescription that men should earn +more than their wives + + align:start position:0% +more than their wives + + + align:start position:0% +more than their wives +and uh it's important to notice that + + align:start position:0% +and uh it's important to notice that + + + align:start position:0% +and uh it's important to notice that +this particular gender identity norm + + align:start position:0% +this particular gender identity norm + + + align:start position:0% +this particular gender identity norm +would only matter in a world where a + + align:start position:0% +would only matter in a world where a + + + align:start position:0% +would only matter in a world where a +woman + + align:start position:0% +woman + + + align:start position:0% +woman +could um or would not matter in a world + + align:start position:0% +could um or would not matter in a world + + + align:start position:0% +could um or would not matter in a world +where women + + align:start position:0% +where women + + + align:start position:0% +where women +could never earn more than her actual or + + align:start position:0% +could never earn more than her actual or + + + align:start position:0% +could never earn more than her actual or +potential husband + + align:start position:0% +potential husband + + + align:start position:0% +potential husband +but if women are held back by + + align:start position:0% +but if women are held back by + + + align:start position:0% +but if women are held back by +technological factors by education + + align:start position:0% +technological factors by education + + + align:start position:0% +technological factors by education +etc and never even earn + + align:start position:0% +etc and never even earn + + + align:start position:0% +etc and never even earn +close to as much as their husbands or + + align:start position:0% +close to as much as their husbands or + + + align:start position:0% +close to as much as their husbands or +potential husbands well then the gender + + align:start position:0% +potential husbands well then the gender + + + align:start position:0% +potential husbands well then the gender +identity norm is kind of irrelevant + + align:start position:0% +identity norm is kind of irrelevant + + + align:start position:0% +identity norm is kind of irrelevant +however as women make gains in the labor + + align:start position:0% +however as women make gains in the labor + + + align:start position:0% +however as women make gains in the labor +market + + align:start position:0% +market + + + align:start position:0% +market +these such slow-moving gender identity + + align:start position:0% +these such slow-moving gender identity + + + align:start position:0% +these such slow-moving gender identity +norms can become increasingly + + align:start position:0% +norms can become increasingly + + + align:start position:0% +norms can become increasingly +relevant and particularly increasingly + + align:start position:0% +relevant and particularly increasingly + + + align:start position:0% +relevant and particularly increasingly +relevant constraints + + align:start position:0% +relevant constraints + + + align:start position:0% +relevant constraints +so now as women have more and more + + align:start position:0% +so now as women have more and more + + + align:start position:0% +so now as women have more and more +earnings potential + + align:start position:0% +earnings potential + + + align:start position:0% +earnings potential +and are might be quite likely to earn + + align:start position:0% +and are might be quite likely to earn + + + align:start position:0% +and are might be quite likely to earn +more than their husbands + + align:start position:0% +more than their husbands + + + align:start position:0% +more than their husbands +these norm really bite and might hold + + align:start position:0% +these norm really bite and might hold + + + align:start position:0% +these norm really bite and might hold +women + + align:start position:0% +women + + + align:start position:0% +women +back now how would you still study this + + align:start position:0% +back now how would you still study this + + + align:start position:0% +back now how would you still study this +question empirically + + align:start position:0% +question empirically + + + align:start position:0% +question empirically +what the idea here and about triangle is + + align:start position:0% +what the idea here and about triangle is + + + align:start position:0% +what the idea here and about triangle is +that + + align:start position:0% +that + + + align:start position:0% +that +well if husbands + + align:start position:0% +well if husbands + + + align:start position:0% +well if husbands +lose identity when their wives earn more + + align:start position:0% +lose identity when their wives earn more + + + align:start position:0% +lose identity when their wives earn more +than half the household income well then + + align:start position:0% +than half the household income well then + + + align:start position:0% +than half the household income well then +they will + + align:start position:0% +they will + + + align:start position:0% +they will +try to avoid such situations either in + + align:start position:0% +try to avoid such situations either in + + + align:start position:0% +try to avoid such situations either in +various ways + + align:start position:0% +various ways + + + align:start position:0% +various ways +and particularly by avoiding such + + align:start position:0% +and particularly by avoiding such + + + align:start position:0% +and particularly by avoiding such +marriages in the first place + + align:start position:0% +marriages in the first place + + + align:start position:0% +marriages in the first place +but also if those marriages happen they + + align:start position:0% +but also if those marriages happen they + + + align:start position:0% +but also if those marriages happen they +might that might lead to divorces and so + + align:start position:0% +might that might lead to divorces and so + + + align:start position:0% +might that might lead to divorces and so +on and those marriages might break up + + align:start position:0% +on and those marriages might break up + + + align:start position:0% +on and those marriages might break up +so the idea of the paper then is look is + + align:start position:0% +so the idea of the paper then is look is + + + align:start position:0% +so the idea of the paper then is look is +to look for a missing mass + + align:start position:0% +to look for a missing mass + + + align:start position:0% +to look for a missing mass +in couples where uh um particular in + + align:start position:0% +in couples where uh um particular in + + + align:start position:0% +in couples where uh um particular in +places where the husband earns just a + + align:start position:0% +places where the husband earns just a + + + align:start position:0% +places where the husband earns just a +little bit more + + align:start position:0% +little bit more + + + align:start position:0% +little bit more +um than their one now how do they do + + align:start position:0% +um than their one now how do they do + + + align:start position:0% +um than their one now how do they do +that well they have to look at the + + align:start position:0% +that well they have to look at the + + + align:start position:0% +that well they have to look at the +distribution of relative income + + align:start position:0% +distribution of relative income + + + align:start position:0% +distribution of relative income +using u.s admin data what i mean by + + align:start position:0% +using u.s admin data what i mean by + + + align:start position:0% +using u.s admin data what i mean by +relative income relative income is the + + align:start position:0% +relative income relative income is the + + + align:start position:0% +relative income relative income is the +income between the husband and the wife + + align:start position:0% +income between the husband and the wife + + + align:start position:0% +income between the husband and the wife +they'll have essentially they're very + + align:start position:0% +they'll have essentially they're very + + + align:start position:0% +they'll have essentially they're very +nice survey + + align:start position:0% +nice survey + + + align:start position:0% +nice survey +data of the survey income and program + + align:start position:0% +data of the survey income and program + + + align:start position:0% +data of the survey income and program +participation + + align:start position:0% +participation + + + align:start position:0% +participation +these are as a series of representative + + align:start position:0% +these are as a series of representative + + + align:start position:0% +these are as a series of representative +national panels + + align:start position:0% +national panels + + + align:start position:0% +national panels +about 70 000 couple level observations + + align:start position:0% +about 70 000 couple level observations + + + align:start position:0% +about 70 000 couple level observations +from 1990 to 2004. + + align:start position:0% +from 1990 to 2004. + + + align:start position:0% +from 1990 to 2004. +this includes couples only uh in which + + align:start position:0% +this includes couples only uh in which + + + align:start position:0% +this includes couples only uh in which +both husbands and wives are + + align:start position:0% +both husbands and wives are + + + align:start position:0% +both husbands and wives are +earning positive income so uh notice + + align:start position:0% +earning positive income so uh notice + + + align:start position:0% +earning positive income so uh notice +that this is not about like husband and + + align:start position:0% +that this is not about like husband and + + + align:start position:0% +that this is not about like husband and +wife working + + align:start position:0% +wife working + + + align:start position:0% +wife working +at all it's not about women being at + + align:start position:0% +at all it's not about women being at + + + align:start position:0% +at all it's not about women being at +home versus working but it's about + + align:start position:0% +home versus working but it's about + + + align:start position:0% +home versus working but it's about +cases where both couples both + + align:start position:0% +cases where both couples both + + + align:start position:0% +cases where both couples both +spouses have positive income um + + align:start position:0% +spouses have positive income um + + + align:start position:0% +spouses have positive income um +their income measures annual total labor + + align:start position:0% +their income measures annual total labor + + + align:start position:0% +their income measures annual total labor +income + + align:start position:0% +income + + + align:start position:0% +income +plus self-employed income as well + + align:start position:0% +plus self-employed income as well + + + align:start position:0% +plus self-employed income as well +they're using that data + + align:start position:0% +they're using that data + + + align:start position:0% +they're using that data +by trying the dial can now compute the + + align:start position:0% +by trying the dial can now compute the + + + align:start position:0% +by trying the dial can now compute the +shares of couple earning different + + align:start position:0% +shares of couple earning different + + + align:start position:0% +shares of couple earning different +fractions of + + align:start position:0% +fractions of + + + align:start position:0% +fractions of +of total income so we're going to show + + align:start position:0% +of total income so we're going to show + + + align:start position:0% +of total income so we're going to show +you is the fraction of + + align:start position:0% +you is the fraction of + + + align:start position:0% +you is the fraction of +the wife as a share of total income in + + align:start position:0% +the wife as a share of total income in + + + align:start position:0% +the wife as a share of total income in +the household and that's graphed using + + align:start position:0% +the household and that's graphed using + + + align:start position:0% +the household and that's graphed using +20 bits + + align:start position:0% +20 bits + + + align:start position:0% +20 bits +what does this graph look like you can + + align:start position:0% +what does this graph look like you can + + + align:start position:0% +what does this graph look like you can +see here the share um + + align:start position:0% +see here the share um + + + align:start position:0% +see here the share um +earned by the wife and this is the + + align:start position:0% +earned by the wife and this is the + + + align:start position:0% +earned by the wife and this is the +fraction of couples this is this + + align:start position:0% +fraction of couples this is this + + + align:start position:0% +fraction of couples this is this +overall so this is like all the couples + + align:start position:0% +overall so this is like all the couples + + + align:start position:0% +overall so this is like all the couples +these are 20 bins this all + + align:start position:0% +these are 20 bins this all + + + align:start position:0% +these are 20 bins this all +adds up to 100 overall and what you see + + align:start position:0% +adds up to 100 overall and what you see + + + align:start position:0% +adds up to 100 overall and what you see +is perhaps not surprisingly that the + + align:start position:0% +is perhaps not surprisingly that the + + + align:start position:0% +is perhaps not surprisingly that the +share + + align:start position:0% +share + + + align:start position:0% +share +the fraction of couple um for which the + + align:start position:0% +the fraction of couple um for which the + + + align:start position:0% +the fraction of couple um for which the +share of + + align:start position:0% +share of + + + align:start position:0% +share of +earned by the wife is like uh higher + + align:start position:0% +earned by the wife is like uh higher + + + align:start position:0% +earned by the wife is like uh higher +than 50 + + align:start position:0% +than 50 + + + align:start position:0% +than 50 +is not super high that's not surprising + + align:start position:0% +is not super high that's not surprising + + + align:start position:0% +is not super high that's not surprising +given that men on average are earning + + align:start position:0% +given that men on average are earning + + + align:start position:0% +given that men on average are earning +more + + align:start position:0% +more + + + align:start position:0% +more +than uh so that's not the question here + + align:start position:0% +than uh so that's not the question here + + + align:start position:0% +than uh so that's not the question here +the question here is + + align:start position:0% +the question here is + + + align:start position:0% +the question here is +is there a missing mass just about about + + align:start position:0% +is there a missing mass just about about + + + align:start position:0% +is there a missing mass just about about + + align:start position:0% + + + align:start position:0% +the idea is if suppose there's some + + align:start position:0% +the idea is if suppose there's some + + + align:start position:0% +the idea is if suppose there's some +couples where + + align:start position:0% + + + + align:start position:0% + +women earn 45 or 46 or even 49 + + align:start position:0% +women earn 45 or 46 or even 49 + + + align:start position:0% +women earn 45 or 46 or even 49 +there the norm does not cause an issue + + align:start position:0% +there the norm does not cause an issue + + + align:start position:0% +there the norm does not cause an issue +or there's no identity problems + + align:start position:0% +or there's no identity problems + + + align:start position:0% +or there's no identity problems +because the husband earns somewhat more + + align:start position:0% +because the husband earns somewhat more + + + align:start position:0% +because the husband earns somewhat more +and feels happy about it + + align:start position:0% +and feels happy about it + + + align:start position:0% +and feels happy about it +but as soon as you cross the threshold + + align:start position:0% +but as soon as you cross the threshold + + + align:start position:0% +but as soon as you cross the threshold +to like 51 + + align:start position:0% +to like 51 + + + align:start position:0% +to like 51 +now there's a problem now the woman + + align:start position:0% +now there's a problem now the woman + + + align:start position:0% +now there's a problem now the woman +earns more the husband feels + + align:start position:0% +earns more the husband feels + + + align:start position:0% +earns more the husband feels +uncomfortable unhappy + + align:start position:0% +uncomfortable unhappy + + + align:start position:0% +uncomfortable unhappy +um and so on and uh + + align:start position:0% +um and so on and uh + + + align:start position:0% +um and so on and uh +and that might lead to those marriages + + align:start position:0% +and that might lead to those marriages + + + align:start position:0% +and that might lead to those marriages +disappearing in various ways + + align:start position:0% +disappearing in various ways + + + align:start position:0% +disappearing in various ways +a they might not form in the first place + + align:start position:0% +a they might not form in the first place + + + align:start position:0% +a they might not form in the first place +husband and potential husband and wife + + align:start position:0% +husband and potential husband and wife + + + align:start position:0% +husband and potential husband and wife +might never even marry + + align:start position:0% +might never even marry + + + align:start position:0% +might never even marry +because husband gets like uncomfortable + + align:start position:0% +because husband gets like uncomfortable + + + align:start position:0% +because husband gets like uncomfortable +and does not want to marry somebody who + + align:start position:0% +and does not want to marry somebody who + + + align:start position:0% +and does not want to marry somebody who +earns more + + align:start position:0% +earns more + + + align:start position:0% +earns more +second there might be divorces these + + align:start position:0% +second there might be divorces these + + + align:start position:0% +second there might be divorces these +marriages might essentially dissolve + + align:start position:0% +marriages might essentially dissolve + + + align:start position:0% +marriages might essentially dissolve +because there's lots of conflict in the + + align:start position:0% +because there's lots of conflict in the + + + align:start position:0% +because there's lots of conflict in the +household now how does that manifest + + align:start position:0% +household now how does that manifest + + + align:start position:0% +household now how does that manifest +here + + align:start position:0% +here + + + align:start position:0% +here +you can look at like if you come if you + + align:start position:0% +you can look at like if you come if you + + + align:start position:0% +you can look at like if you come if you +look at the + + align:start position:0% +look at the + + + align:start position:0% +look at the +graph and look at this line here coming + + align:start position:0% +graph and look at this line here coming + + + align:start position:0% +graph and look at this line here coming +from the left towards 50 + + align:start position:0% +from the left towards 50 + + + align:start position:0% +from the left towards 50 +you can kind of look at like try to + + align:start position:0% +you can kind of look at like try to + + + align:start position:0% +you can kind of look at like try to +predict and this is kind of the idea of + + align:start position:0% +predict and this is kind of the idea of + + + align:start position:0% +predict and this is kind of the idea of +the um + + align:start position:0% +the um + + + align:start position:0% +the um +the empirical strategy you can try to + + align:start position:0% +the empirical strategy you can try to + + + align:start position:0% +the empirical strategy you can try to +predict what fraction would you expect + + align:start position:0% +predict what fraction would you expect + + + align:start position:0% +predict what fraction would you expect +there to be just about 50 and when you + + align:start position:0% +there to be just about 50 and when you + + + align:start position:0% +there to be just about 50 and when you +do that you think you know the fraction + + align:start position:0% +do that you think you know the fraction + + + align:start position:0% +do that you think you know the fraction +should be about + + align:start position:0% +should be about + + + align:start position:0% +should be about +um uh something like seven percent + + align:start position:0% +um uh something like seven percent + + + align:start position:0% +um uh something like seven percent +should be about here but instead this is + + align:start position:0% +should be about here but instead this is + + + align:start position:0% +should be about here but instead this is +jump + + align:start position:0% +jump + + + align:start position:0% +jump +down to about six percent so there's + + align:start position:0% +down to about six percent so there's + + + align:start position:0% +down to about six percent so there's +about one percent of couples are missing + + align:start position:0% +about one percent of couples are missing + + + align:start position:0% +about one percent of couples are missing +here + + align:start position:0% +here + + + align:start position:0% +here +there's a missing mass going on here um + + align:start position:0% +there's a missing mass going on here um + + + align:start position:0% +there's a missing mass going on here um +which suggests that + + align:start position:0% +which suggests that + + + align:start position:0% +which suggests that +there are some marriages that do not + + align:start position:0% +there are some marriages that do not + + + align:start position:0% +there are some marriages that do not +happen or that just get + + align:start position:0% +happen or that just get + + + align:start position:0% +happen or that just get +dissolved um because of those identity + + align:start position:0% +dissolved um because of those identity + + + align:start position:0% +dissolved um because of those identity +concerns + + align:start position:0% +concerns + + + align:start position:0% +concerns +this is what i already said here there's + + align:start position:0% +this is what i already said here there's + + + align:start position:0% +this is what i already said here there's +a cliff to the right of 0.5 in the + + align:start position:0% +a cliff to the right of 0.5 in the + + + align:start position:0% +a cliff to the right of 0.5 in the +distribution of relative earnings across + + align:start position:0% +distribution of relative earnings across + + + align:start position:0% +distribution of relative earnings across +couples + + align:start position:0% +couples + + + align:start position:0% +couples +and that's an implication of the + + align:start position:0% +and that's an implication of the + + + align:start position:0% +and that's an implication of the +prescription that men should earn more + + align:start position:0% +prescription that men should earn more + + + align:start position:0% +prescription that men should earn more +than their lives now what are the + + align:start position:0% +than their lives now what are the + + + align:start position:0% +than their lives now what are the +mechanisms behind this + + align:start position:0% +mechanisms behind this + + + align:start position:0% +mechanisms behind this +missing mass we're trying to have a + + align:start position:0% +missing mass we're trying to have a + + + align:start position:0% +missing mass we're trying to have a +wealth of evidence + + align:start position:0% +wealth of evidence + + + align:start position:0% +wealth of evidence +additional evidence showing those + + align:start position:0% +additional evidence showing those + + + align:start position:0% +additional evidence showing those +mechanisms in particular + + align:start position:0% +mechanisms in particular + + + align:start position:0% +mechanisms in particular +they show three mechanisms which is + + align:start position:0% +they show three mechanisms which is + + + align:start position:0% +they show three mechanisms which is +first missing couples did not form in + + align:start position:0% +first missing couples did not form in + + + align:start position:0% +first missing couples did not form in +the first place so when you look at like + + align:start position:0% +the first place so when you look at like + + + align:start position:0% +the first place so when you look at like +when you just randomly match men and + + align:start position:0% +when you just randomly match men and + + + align:start position:0% +when you just randomly match men and +women um + + align:start position:0% +women um + + + align:start position:0% +women um +some of which were men have higher + + align:start position:0% +some of which were men have higher + + + align:start position:0% +some of which were men have higher +earnings potential compared to women and + + align:start position:0% +earnings potential compared to women and + + + align:start position:0% +earnings potential compared to women and +the other way around + + align:start position:0% +the other way around + + + align:start position:0% +the other way around +the couples where women are earning just + + align:start position:0% +the couples where women are earning just + + + align:start position:0% +the couples where women are earning just +somewhat less than women are just + + align:start position:0% +somewhat less than women are just + + + align:start position:0% +somewhat less than women are just +much less likely or less likely to marry + + align:start position:0% +much less likely or less likely to marry + + + align:start position:0% +much less likely or less likely to marry +compared to couples where women are just + + align:start position:0% +compared to couples where women are just + + + align:start position:0% +compared to couples where women are just +earning somewhat less than men + + align:start position:0% +earning somewhat less than men + + + align:start position:0% +earning somewhat less than men +second such couples are less happy and + + align:start position:0% +second such couples are less happy and + + + align:start position:0% +second such couples are less happy and +stable and more likely to end in divorce + + align:start position:0% +stable and more likely to end in divorce + + + align:start position:0% +stable and more likely to end in divorce +so conditional and marrying they're more + + align:start position:0% +so conditional and marrying they're more + + + align:start position:0% +so conditional and marrying they're more +likely to get divorced these marriages + + align:start position:0% +likely to get divorced these marriages + + + align:start position:0% +likely to get divorced these marriages +just + + align:start position:0% +just + + + align:start position:0% +just +end unhappily and that's of course then + + align:start position:0% +end unhappily and that's of course then + + + align:start position:0% +end unhappily and that's of course then +also contributes to this missing mass + + align:start position:0% +also contributes to this missing mass + + + align:start position:0% +also contributes to this missing mass +and then third in cases where wives have + + align:start position:0% +and then third in cases where wives have + + + align:start position:0% +and then third in cases where wives have +higher + + align:start position:0% +higher + + + align:start position:0% +higher +earnings potential than their husbands + + align:start position:0% +earnings potential than their husbands + + + align:start position:0% +earnings potential than their husbands +they decide now to work + + align:start position:0% +they decide now to work + + + align:start position:0% +they decide now to work +less outside of the household or you + + align:start position:0% +less outside of the household or you + + + align:start position:0% +less outside of the household or you +know + + align:start position:0% +know + + + align:start position:0% +know +put in less effort at work so they get + + align:start position:0% +put in less effort at work so they get + + + align:start position:0% +put in less effort at work so they get +less promoted which then sort of + + align:start position:0% +less promoted which then sort of + + + align:start position:0% +less promoted which then sort of +um pushes down their earnings or you + + align:start position:0% +um pushes down their earnings or you + + + align:start position:0% +um pushes down their earnings or you +know increased + + align:start position:0% +know increased + + + align:start position:0% +know increased +husbands earnings in relative terms such + + align:start position:0% +husbands earnings in relative terms such + + + align:start position:0% +husbands earnings in relative terms such +as that in such cases the woman earns + + align:start position:0% +as that in such cases the woman earns + + + align:start position:0% +as that in such cases the woman earns +uh less than 50 and that also leads to + + align:start position:0% +uh less than 50 and that also leads to + + + align:start position:0% +uh less than 50 and that also leads to +that missing mass + + align:start position:0% +that missing mass + + + align:start position:0% +that missing mass +in fact what you see here is this + + align:start position:0% +in fact what you see here is this + + + align:start position:0% +in fact what you see here is this +increase in mass going from like 20 to + + align:start position:0% +increase in mass going from like 20 to + + + align:start position:0% +increase in mass going from like 20 to +40 which perhaps is also like the the + + align:start position:0% +40 which perhaps is also like the the + + + align:start position:0% +40 which perhaps is also like the the +reason because some of the mass that's + + align:start position:0% +reason because some of the mass that's + + + align:start position:0% +reason because some of the mass that's +missing here is pushed here + + align:start position:0% +missing here is pushed here + + + align:start position:0% +missing here is pushed here +um to the left now + + align:start position:0% +um to the left now + + + align:start position:0% +um to the left now +um in addition to um + + align:start position:0% +um in addition to um + + + align:start position:0% +um in addition to um +working less outside of the household + + align:start position:0% +working less outside of the household + + + align:start position:0% +working less outside of the household +and just working few hours + + align:start position:0% +and just working few hours + + + align:start position:0% +and just working few hours +like working less overtime and so on um + + align:start position:0% +like working less overtime and so on um + + + align:start position:0% +like working less overtime and so on um +women then + + align:start position:0% +women then + + + align:start position:0% +women then +are also held back by non-market and + + align:start position:0% +are also held back by non-market and + + + align:start position:0% +are also held back by non-market and +child care work so women in particular + + align:start position:0% +child care work so women in particular + + + align:start position:0% +child care work so women in particular +women who are + + align:start position:0% +women who are + + + align:start position:0% +women who are +um are earning just a little bit more + + align:start position:0% +um are earning just a little bit more + + + align:start position:0% +um are earning just a little bit more +than their husbands + + align:start position:0% +than their husbands + + + align:start position:0% +than their husbands +are doing more non-market and child care + + align:start position:0% +are doing more non-market and child care + + + align:start position:0% +are doing more non-market and child care +work which is um often called the second + + align:start position:0% +work which is um often called the second + + + align:start position:0% +work which is um often called the second +shift + + align:start position:0% +shift + + + align:start position:0% +shift +so the idea here is that husband's ego + + align:start position:0% +so the idea here is that husband's ego + + + align:start position:0% +so the idea here is that husband's ego +or his identity gets like uh + + align:start position:0% +or his identity gets like uh + + + align:start position:0% +or his identity gets like uh +threatened by the woman earning more + + align:start position:0% +threatened by the woman earning more + + + align:start position:0% +threatened by the woman earning more +than he does + + align:start position:0% +than he does + + + align:start position:0% +than he does +and then he can particularly not do the + + align:start position:0% +and then he can particularly not do the + + + align:start position:0% +and then he can particularly not do the +child care or non-market work + + align:start position:0% +child care or non-market work + + + align:start position:0% +child care or non-market work +so the end the woman ends up not only + + align:start position:0% +so the end the woman ends up not only + + + align:start position:0% +so the end the woman ends up not only +working more outside of the household + + align:start position:0% +working more outside of the household + + + align:start position:0% +working more outside of the household +and earning more and being more + + align:start position:0% +and earning more and being more + + + align:start position:0% +and earning more and being more +productive in that work + + align:start position:0% +productive in that work + + + align:start position:0% +productive in that work +but also doing more work uh at home um + + align:start position:0% +but also doing more work uh at home um + + + align:start position:0% +but also doing more work uh at home um +and + + align:start position:0% +and + + + align:start position:0% +and +in addition um to that that's + + align:start position:0% +in addition um to that that's + + + align:start position:0% +in addition um to that that's +essentially what's called the second or + + align:start position:0% +essentially what's called the second or + + + align:start position:0% +essentially what's called the second or +double + + align:start position:0% +double + + + align:start position:0% +double +uh shift + + align:start position:0% + + + + align:start position:0% + +now an additional issue + + align:start position:0% +now an additional issue + + + align:start position:0% +now an additional issue +that is a really important still + + align:start position:0% +that is a really important still + + + align:start position:0% +that is a really important still +contributor to + + align:start position:0% +contributor to + + + align:start position:0% +contributor to +the gender gap is the arrival of + + align:start position:0% +the gender gap is the arrival of + + + align:start position:0% +the gender gap is the arrival of +children + + align:start position:0% +children + + + align:start position:0% +children +and this is a very nice paper by clavin + + align:start position:0% +and this is a very nice paper by clavin + + + align:start position:0% +and this is a very nice paper by clavin +and all that looks at + + align:start position:0% +and all that looks at + + + align:start position:0% +and all that looks at +people's earning in particular earning + + align:start position:0% +people's earning in particular earning + + + align:start position:0% +people's earning in particular earning +how earnings evolve after the birth of a + + align:start position:0% +how earnings evolve after the birth of a + + + align:start position:0% +how earnings evolve after the birth of a +couple's um first + + align:start position:0% +couple's um first + + + align:start position:0% +couple's um first +child this is an event study that looks + + align:start position:0% +child this is an event study that looks + + + align:start position:0% +child this is an event study that looks +at uh + + align:start position:0% +at uh + + + align:start position:0% +at uh +years over time for men and women + + align:start position:0% +years over time for men and women + + + align:start position:0% +years over time for men and women +and what you see essentially for men + + align:start position:0% +and what you see essentially for men + + + align:start position:0% +and what you see essentially for men +these are earnings and on the right here + + align:start position:0% +these are earnings and on the right here + + + align:start position:0% +these are earnings and on the right here +you have hours worked + + align:start position:0% +you have hours worked + + + align:start position:0% +you have hours worked +for men essentially there's barely any + + align:start position:0% +for men essentially there's barely any + + + align:start position:0% +for men essentially there's barely any +difference if any difference + + align:start position:0% +difference if any difference + + + align:start position:0% +difference if any difference +of the um of earnings once the first + + align:start position:0% +of the um of earnings once the first + + + align:start position:0% +of the um of earnings once the first +child is born + + align:start position:0% +child is born + + + align:start position:0% +child is born +essentially men's earnings tend to be + + align:start position:0% +essentially men's earnings tend to be + + + align:start position:0% +essentially men's earnings tend to be +pretty flat in contrast of course there + + align:start position:0% +pretty flat in contrast of course there + + + align:start position:0% +pretty flat in contrast of course there +could be like for the growth that's + + align:start position:0% +could be like for the growth that's + + + align:start position:0% +could be like for the growth that's +avoided but you know at least there's no + + align:start position:0% +avoided but you know at least there's no + + + align:start position:0% +avoided but you know at least there's no +reduction in men's learning this is by + + align:start position:0% +reduction in men's learning this is by + + + align:start position:0% +reduction in men's learning this is by +the way + + align:start position:0% +the way + + + align:start position:0% +the way +danish data now um for women however + + align:start position:0% +danish data now um for women however + + + align:start position:0% +danish data now um for women however +um there's a clear reduction in + + align:start position:0% +um there's a clear reduction in + + + align:start position:0% +um there's a clear reduction in +earnings and um + + align:start position:0% +earnings and um + + + align:start position:0% +earnings and um +uh the long-run child penance penalty is + + align:start position:0% +uh the long-run child penance penalty is + + + align:start position:0% +uh the long-run child penance penalty is +about um + + align:start position:0% +about um + + + align:start position:0% +about um +almost 20 so essentially women after + + align:start position:0% +almost 20 so essentially women after + + + align:start position:0% +almost 20 so essentially women after +if you look at like men and women that + + align:start position:0% +if you look at like men and women that + + + align:start position:0% +if you look at like men and women that +earn the same to start with + + align:start position:0% +earn the same to start with + + + align:start position:0% +earn the same to start with +um women earn about 20 less + + align:start position:0% +um women earn about 20 less + + + align:start position:0% +um women earn about 20 less +in the long run uh uh that is due to + + align:start position:0% +in the long run uh uh that is due to + + + align:start position:0% +in the long run uh uh that is due to +like the first child or after that or + + align:start position:0% +like the first child or after that or + + + align:start position:0% +like the first child or after that or +that this gap arises after the first + + align:start position:0% +that this gap arises after the first + + + align:start position:0% +that this gap arises after the first +child is born + + align:start position:0% +child is born + + + align:start position:0% +child is born +this is true for earnings it's also true + + align:start position:0% +this is true for earnings it's also true + + + align:start position:0% +this is true for earnings it's also true +for hours worked and there the penalty + + align:start position:0% +for hours worked and there the penalty + + + align:start position:0% +for hours worked and there the penalty +is about 10 + + align:start position:0% +is about 10 + + + align:start position:0% +is about 10 +it's also true for wages as unlike how + + align:start position:0% +it's also true for wages as unlike how + + + align:start position:0% +it's also true for wages as unlike how +much are people paid + + align:start position:0% +much are people paid + + + align:start position:0% +much are people paid +conditional on uh working so part of + + align:start position:0% +conditional on uh working so part of + + + align:start position:0% +conditional on uh working so part of +that is women working less + + align:start position:0% +that is women working less + + + align:start position:0% +that is women working less +but part of it is also women earning + + align:start position:0% +but part of it is also women earning + + + align:start position:0% +but part of it is also women earning +less + + align:start position:0% +less + + + align:start position:0% +less +like being promoted less being paid less + + align:start position:0% +like being promoted less being paid less + + + align:start position:0% +like being promoted less being paid less +getting fewer raises and so on + + align:start position:0% +getting fewer raises and so on + + + align:start position:0% +getting fewer raises and so on +once that child is born one very + + align:start position:0% +once that child is born one very + + + align:start position:0% +once that child is born one very +interesting fact is that + + align:start position:0% +interesting fact is that + + + align:start position:0% +interesting fact is that +in this paper is that child penalties + + align:start position:0% +in this paper is that child penalties + + + align:start position:0% +in this paper is that child penalties +are transmitted through generations + + align:start position:0% +are transmitted through generations + + + align:start position:0% +are transmitted through generations +from parents to daughters suggesting an + + align:start position:0% +from parents to daughters suggesting an + + + align:start position:0% +from parents to daughters suggesting an +influence of child environment on uh + + align:start position:0% +influence of child environment on uh + + + align:start position:0% +influence of child environment on uh +gender identity + + align:start position:0% +gender identity + + + align:start position:0% +gender identity +there seems to be something about the + + align:start position:0% +there seems to be something about the + + + align:start position:0% +there seems to be something about the +gender identity about like + + align:start position:0% +gender identity about like + + + align:start position:0% +gender identity about like +the woman is supposed to take care of + + align:start position:0% +the woman is supposed to take care of + + + align:start position:0% +the woman is supposed to take care of +the child + + align:start position:0% +the child + + + align:start position:0% +the child +and that runs in the family and that + + align:start position:0% +and that runs in the family and that + + + align:start position:0% +and that runs in the family and that +leads to particularly large + + align:start position:0% +leads to particularly large + + + align:start position:0% +leads to particularly large +what they call child penalties for those + + align:start position:0% +what they call child penalties for those + + + align:start position:0% +what they call child penalties for those +kinds of + + align:start position:0% + + + + align:start position:0% + +women compared to men + + align:start position:0% +women compared to men + + + align:start position:0% +women compared to men +now one thing you might say as well + + align:start position:0% +now one thing you might say as well + + + align:start position:0% +now one thing you might say as well +couldn't we have some gender-neutral + + align:start position:0% +couldn't we have some gender-neutral + + + align:start position:0% +couldn't we have some gender-neutral +family policies that alleviate that + + align:start position:0% +family policies that alleviate that + + + align:start position:0% +family policies that alleviate that +in particular in academia for instance + + align:start position:0% +in particular in academia for instance + + + align:start position:0% +in particular in academia for instance +one idea is one could use + + align:start position:0% +one idea is one could use + + + align:start position:0% +one idea is one could use +gender-neutral 10-year clock stopping + + align:start position:0% +gender-neutral 10-year clock stopping + + + align:start position:0% +gender-neutral 10-year clock stopping +policies + + align:start position:0% +policies + + + align:start position:0% +policies +um to alleviate such issues + + align:start position:0% +um to alleviate such issues + + + align:start position:0% +um to alleviate such issues +and the idea is that in particular sort + + align:start position:0% +and the idea is that in particular sort + + + align:start position:0% +and the idea is that in particular sort +of our early years in the career are + + align:start position:0% +of our early years in the career are + + + align:start position:0% +of our early years in the career are +particularly valuable + + align:start position:0% +particularly valuable + + + align:start position:0% +particularly valuable +so the very least we can do is we can + + align:start position:0% +so the very least we can do is we can + + + align:start position:0% +so the very least we can do is we can +stop the the tenure clocks + + align:start position:0% +stop the the tenure clocks + + + align:start position:0% +stop the the tenure clocks +to help women or couples to deal with + + align:start position:0% +to help women or couples to deal with + + + align:start position:0% +to help women or couples to deal with +child care + + align:start position:0% +child care + + + align:start position:0% +child care +and many many universities and research + + align:start position:0% +and many many universities and research + + + align:start position:0% +and many many universities and research +intensive universities in the us + + align:start position:0% +intensive universities in the us + + + align:start position:0% +intensive universities in the us +have adopted such what's called + + align:start position:0% +have adopted such what's called + + + align:start position:0% +have adopted such what's called +gender-neutral 10-year clock + + align:start position:0% +gender-neutral 10-year clock + + + align:start position:0% +gender-neutral 10-year clock +policies in the us now + + align:start position:0% +policies in the us now + + + align:start position:0% +policies in the us now +uh what do i mean by gender neutral + + align:start position:0% +uh what do i mean by gender neutral + + + align:start position:0% +uh what do i mean by gender neutral +essentially if a couple um has a child + + align:start position:0% +essentially if a couple um has a child + + + align:start position:0% +essentially if a couple um has a child +not only um does the uh + + align:start position:0% +not only um does the uh + + + align:start position:0% +not only um does the uh +the the woman um if she has given birth + + align:start position:0% +the the woman um if she has given birth + + + align:start position:0% +the the woman um if she has given birth +to the child + + align:start position:0% +to the child + + + align:start position:0% +to the child +uh does she get a an extension in the + + align:start position:0% +uh does she get a an extension in the + + + align:start position:0% +uh does she get a an extension in the +10-year clock + + align:start position:0% +10-year clock + + + align:start position:0% +10-year clock +but also the spouse will get such an + + align:start position:0% +but also the spouse will get such an + + + align:start position:0% +but also the spouse will get such an +extension as well so it's gender-neutral + + align:start position:0% +extension as well so it's gender-neutral + + + align:start position:0% +extension as well so it's gender-neutral +in that sense now what would such + + align:start position:0% +in that sense now what would such + + + align:start position:0% +in that sense now what would such +policies then do well they intended to + + align:start position:0% +policies then do well they intended to + + + align:start position:0% +policies then do well they intended to +involve + + align:start position:0% +involve + + + align:start position:0% +involve +men more in child care and sort of like + + align:start position:0% +men more in child care and sort of like + + + align:start position:0% +men more in child care and sort of like +foster that + + align:start position:0% +foster that + + + align:start position:0% +foster that +the idea being like if you only give + + align:start position:0% +the idea being like if you only give + + + align:start position:0% +the idea being like if you only give +that extension to + + align:start position:0% +that extension to + + + align:start position:0% +that extension to +to women it sort of like pushes women to + + align:start position:0% +to women it sort of like pushes women to + + + align:start position:0% +to women it sort of like pushes women to +um + + align:start position:0% +um + + + align:start position:0% +um +uh take care of + + align:start position:0% +uh take care of + + + align:start position:0% +uh take care of +their children and sort of not to do + + align:start position:0% +their children and sort of not to do + + + align:start position:0% +their children and sort of not to do +work and perhaps if we involve + + align:start position:0% +work and perhaps if we involve + + + align:start position:0% +work and perhaps if we involve +uh both spouses or parents in + + align:start position:0% +uh both spouses or parents in + + + align:start position:0% +uh both spouses or parents in +in the child care uh uh providing those + + align:start position:0% +in the child care uh uh providing those + + + align:start position:0% +in the child care uh uh providing those +gender neutral ten-year clock stopping + + align:start position:0% +gender neutral ten-year clock stopping + + + align:start position:0% +gender neutral ten-year clock stopping +policies might contribute to that + + align:start position:0% +policies might contribute to that + + + align:start position:0% +policies might contribute to that +but of course there's no enforcement and + + align:start position:0% +but of course there's no enforcement and + + + align:start position:0% +but of course there's no enforcement and +that's potentially + + align:start position:0% +that's potentially + + + align:start position:0% +that's potentially +of such policies in that potentially + + align:start position:0% +of such policies in that potentially + + + align:start position:0% +of such policies in that potentially +these policies might be + + align:start position:0% +these policies might be + + + align:start position:0% +these policies might be +even enhancing gender inequality and + + align:start position:0% +even enhancing gender inequality and + + + align:start position:0% +even enhancing gender inequality and +particularly if it's the case that + + align:start position:0% +particularly if it's the case that + + + align:start position:0% +particularly if it's the case that +if men take advantage of this 10-year + + align:start position:0% +if men take advantage of this 10-year + + + align:start position:0% +if men take advantage of this 10-year +clock + + align:start position:0% +clock + + + align:start position:0% +clock +stopping policy by essentially just + + align:start position:0% +stopping policy by essentially just + + + align:start position:0% +stopping policy by essentially just +having another year to do research + + align:start position:0% +having another year to do research + + + align:start position:0% +having another year to do research +but still don't do very much in + + align:start position:0% +but still don't do very much in + + + align:start position:0% +but still don't do very much in +supporting the child + + align:start position:0% +supporting the child + + + align:start position:0% +supporting the child +then men might actually benefit from it + + align:start position:0% +then men might actually benefit from it + + + align:start position:0% +then men might actually benefit from it +while women might + + align:start position:0% +while women might + + + align:start position:0% +while women might +not benefit at all in part because + + align:start position:0% +not benefit at all in part because + + + align:start position:0% +not benefit at all in part because +relatively they're going to do worse + + align:start position:0% +relatively they're going to do worse + + + align:start position:0% +relatively they're going to do worse +compared to men + + align:start position:0% +compared to men + + + align:start position:0% +compared to men +and um so uh anticoagulant look in fact + + align:start position:0% +and um so uh anticoagulant look in fact + + + align:start position:0% +and um so uh anticoagulant look in fact +at the impact of these adoptions of + + align:start position:0% +at the impact of these adoptions of + + + align:start position:0% +at the impact of these adoptions of +these + + align:start position:0% +these + + + align:start position:0% +these +uh supposedly gender neutral + + align:start position:0% +uh supposedly gender neutral + + + align:start position:0% +uh supposedly gender neutral +uh tenure-clock-stopping policies + + align:start position:0% +uh tenure-clock-stopping policies + + + align:start position:0% +uh tenure-clock-stopping policies +and they find that um the introduction + + align:start position:0% +and they find that um the introduction + + + align:start position:0% +and they find that um the introduction +of this policy at top 50 economics + + align:start position:0% +of this policy at top 50 economics + + + align:start position:0% +of this policy at top 50 economics +department substantially reduced female + + align:start position:0% +department substantially reduced female + + + align:start position:0% +department substantially reduced female +10-year rates + + align:start position:0% +10-year rates + + + align:start position:0% +10-year rates +by increasing male tenure rates so + + align:start position:0% +by increasing male tenure rates so + + + align:start position:0% +by increasing male tenure rates so +essentially what looks like a um + + align:start position:0% +essentially what looks like a um + + + align:start position:0% +essentially what looks like a um +neutral policy in fact is not gender + + align:start position:0% +neutral policy in fact is not gender + + + align:start position:0% +neutral policy in fact is not gender +neutral at all it makes things worse for + + align:start position:0% +neutral at all it makes things worse for + + + align:start position:0% +neutral at all it makes things worse for +women + + align:start position:0% +women + + + align:start position:0% +women +and um better for men let me tell you + + align:start position:0% +and um better for men let me tell you + + + align:start position:0% +and um better for men let me tell you +about one final paper on + + align:start position:0% +about one final paper on + + + align:start position:0% +about one final paper on +uh gender gender identity and uh the + + align:start position:0% +uh gender gender identity and uh the + + + align:start position:0% +uh gender gender identity and uh the +labor market + + align:start position:0% +labor market + + + align:start position:0% +labor market +this paper is called acting wife + + align:start position:0% +this paper is called acting wife + + + align:start position:0% +this paper is called acting wife +marriage market incentives and labor + + align:start position:0% +marriage market incentives and labor + + + align:start position:0% +marriage market incentives and labor +market investments + + align:start position:0% +market investments + + + align:start position:0% +market investments +it's by bush cinel and it asks the + + align:start position:0% +it's by bush cinel and it asks the + + + align:start position:0% +it's by bush cinel and it asks the +question whether women avoid career + + align:start position:0% +question whether women avoid career + + + align:start position:0% +question whether women avoid career +enhancing + + align:start position:0% +enhancing + + + align:start position:0% +enhancing +actions because these actions signal + + align:start position:0% +actions because these actions signal + + + align:start position:0% +actions because these actions signal +undesirable or seemingly undesirable + + align:start position:0% +undesirable or seemingly undesirable + + + align:start position:0% +undesirable or seemingly undesirable +traits + + align:start position:0% +traits + + + align:start position:0% +traits +such as ambition to the marriage market + + align:start position:0% +such as ambition to the marriage market + + + align:start position:0% +such as ambition to the marriage market +um there's two parts in the paper um one + + align:start position:0% +um there's two parts in the paper um one + + + align:start position:0% +um there's two parts in the paper um one +part is just observational + + align:start position:0% +part is just observational + + + align:start position:0% +part is just observational +data that finds that while married and + + align:start position:0% +data that finds that while married and + + + align:start position:0% +data that finds that while married and +unmarried female mba students perform + + align:start position:0% +unmarried female mba students perform + + + align:start position:0% +unmarried female mba students perform +similarly when their performance is + + align:start position:0% +similarly when their performance is + + + align:start position:0% +similarly when their performance is +unobserved by classmates such as on + + align:start position:0% +unobserved by classmates such as on + + + align:start position:0% +unobserved by classmates such as on +exams or problem sets + + align:start position:0% +exams or problem sets + + + align:start position:0% +exams or problem sets +unmarried women have lower participation + + align:start position:0% +unmarried women have lower participation + + + align:start position:0% +unmarried women have lower participation +grades which are observed by their + + align:start position:0% +grades which are observed by their + + + align:start position:0% +grades which are observed by their +classmates + + align:start position:0% +classmates + + + align:start position:0% +classmates +and so the idea here is that only + + align:start position:0% +and so the idea here is that only + + + align:start position:0% +and so the idea here is that only +unmarried female mba + + align:start position:0% +unmarried female mba + + + align:start position:0% +unmarried female mba +students have uh incentives on the + + align:start position:0% +students have uh incentives on the + + + align:start position:0% +students have uh incentives on the +marriage market and therefore when their + + align:start position:0% +marriage market and therefore when their + + + align:start position:0% +marriage market and therefore when their +participation + + align:start position:0% +participation + + + align:start position:0% +participation +is observed when their performance is + + align:start position:0% +is observed when their performance is + + + align:start position:0% +is observed when their performance is +observed + + align:start position:0% +observed + + + align:start position:0% +observed +they might want to scale back their + + align:start position:0% +they might want to scale back their + + + align:start position:0% +they might want to scale back their +admission + + align:start position:0% +admission + + + align:start position:0% +admission +because they look too ambitious on the + + align:start position:0% +because they look too ambitious on the + + + align:start position:0% +because they look too ambitious on the +marriage mark and then they might be + + align:start position:0% +marriage mark and then they might be + + + align:start position:0% +marriage mark and then they might be +adversely interpreted by potential + + align:start position:0% +adversely interpreted by potential + + + align:start position:0% +adversely interpreted by potential +dates and of course married women as + + align:start position:0% +dates and of course married women as + + + align:start position:0% +dates and of course married women as +it's already married don't have that + + align:start position:0% +it's already married don't have that + + + align:start position:0% +it's already married don't have that +incentives + + align:start position:0% +incentives + + + align:start position:0% +incentives +um so they don't engage in such behavior + + align:start position:0% +um so they don't engage in such behavior + + + align:start position:0% +um so they don't engage in such behavior +as you might know there's lots of dating + + align:start position:0% +as you might know there's lots of dating + + + align:start position:0% +as you might know there's lots of dating +uh going on so lots of + + align:start position:0% +uh going on so lots of + + + align:start position:0% +uh going on so lots of +mba students are actively looking for a + + align:start position:0% +mba students are actively looking for a + + + align:start position:0% +mba students are actively looking for a +spouse during their experience both men + + align:start position:0% +spouse during their experience both men + + + align:start position:0% +spouse during their experience both men +and women + + align:start position:0% +and women + + + align:start position:0% +and women +now in addition they have a field + + align:start position:0% +now in addition they have a field + + + align:start position:0% +now in addition they have a field +experiments with mbas + + align:start position:0% +experiments with mbas + + + align:start position:0% +experiments with mbas +in which they vary the expectation + + align:start position:0% +in which they vary the expectation + + + align:start position:0% +in which they vary the expectation +whether + + align:start position:0% +whether + + + align:start position:0% +whether +responses in a real estate placement + + align:start position:0% +responses in a real estate placement + + + align:start position:0% +responses in a real estate placement +questionnaire + + align:start position:0% +questionnaire + + + align:start position:0% +questionnaire +is going to may be made public in + + align:start position:0% +is going to may be made public in + + + align:start position:0% +is going to may be made public in +particular whether it's going to be + + align:start position:0% +particular whether it's going to be + + + align:start position:0% +particular whether it's going to be +observed by + + align:start position:0% +observed by + + + align:start position:0% +observed by +their peers and now female + + align:start position:0% +their peers and now female + + + align:start position:0% +their peers and now female +single female students reported lower + + align:start position:0% +single female students reported lower + + + align:start position:0% +single female students reported lower +desired + + align:start position:0% +desired + + + align:start position:0% +desired +salaries and willingness to travel and + + align:start position:0% +salaries and willingness to travel and + + + align:start position:0% +salaries and willingness to travel and +work long hours + + align:start position:0% +work long hours + + + align:start position:0% +work long hours +on those questionnaires when they + + align:start position:0% +on those questionnaires when they + + + align:start position:0% +on those questionnaires when they +expected their classmates to see their + + align:start position:0% +expected their classmates to see their + + + align:start position:0% +expected their classmates to see their +preferences + + align:start position:0% +preferences + + + align:start position:0% +preferences +that is to say when these questions are + + align:start position:0% +that is to say when these questions are + + + align:start position:0% +that is to say when these questions are +public + + align:start position:0% +public + + + align:start position:0% +public +single female students reported lower + + align:start position:0% + + + + align:start position:0% + +lower ambition as manifested by desired + + align:start position:0% +lower ambition as manifested by desired + + + align:start position:0% +lower ambition as manifested by desired +salaries and willingness to travel in + + align:start position:0% +salaries and willingness to travel in + + + align:start position:0% +salaries and willingness to travel in +work hours + + align:start position:0% +work hours + + + align:start position:0% +work hours +presumably because they want to look + + align:start position:0% +presumably because they want to look + + + align:start position:0% +presumably because they want to look +more favorable on the marriage market + + align:start position:0% +more favorable on the marriage market + + + align:start position:0% +more favorable on the marriage market +notably other groups responses were + + align:start position:0% +notably other groups responses were + + + align:start position:0% +notably other groups responses were +uninfected by + + align:start position:0% +uninfected by + + + align:start position:0% +uninfected by +such pure observation observability so + + align:start position:0% +such pure observation observability so + + + align:start position:0% +such pure observation observability so +in other groups it didn't matter whether + + align:start position:0% +in other groups it didn't matter whether + + + align:start position:0% +in other groups it didn't matter whether +it's in public and in private + + align:start position:0% +it's in public and in private + + + align:start position:0% +it's in public and in private +in addition there's a second experiment + + align:start position:0% +in addition there's a second experiment + + + align:start position:0% +in addition there's a second experiment +that indicates the effects were driven + + align:start position:0% +that indicates the effects were driven + + + align:start position:0% +that indicates the effects were driven +by + + align:start position:0% +by + + + align:start position:0% +by +the observability by single male peers + + align:start position:0% +the observability by single male peers + + + align:start position:0% +the observability by single male peers +that is to say if another woman saw + + align:start position:0% +that is to say if another woman saw + + + align:start position:0% +that is to say if another woman saw +the information that didn't matter so + + align:start position:0% +the information that didn't matter so + + + align:start position:0% +the information that didn't matter so +much but if this other + + align:start position:0% +much but if this other + + + align:start position:0% +much but if this other +single male peer were was likely or + + align:start position:0% +single male peer were was likely or + + + align:start position:0% +single male peer were was likely or +possibly going to see that information + + align:start position:0% +possibly going to see that information + + + align:start position:0% +possibly going to see that information +then + + align:start position:0% +then + + + align:start position:0% +then +these effects would um show up so that's + + align:start position:0% +these effects would um show up so that's + + + align:start position:0% +these effects would um show up so that's +um + + align:start position:0% +um + + + align:start position:0% +um +overall showing that uh essentially + + align:start position:0% +overall showing that uh essentially + + + align:start position:0% +overall showing that uh essentially +what's uh + + align:start position:0% +what's uh + + + align:start position:0% +what's uh +perceived to be undesirable traits um + + align:start position:0% +perceived to be undesirable traits um + + + align:start position:0% +perceived to be undesirable traits um +uh such as ambition um if that that is + + align:start position:0% +uh such as ambition um if that that is + + + align:start position:0% +uh such as ambition um if that that is +perceived to to be damaging on the on + + align:start position:0% +perceived to to be damaging on the on + + + align:start position:0% +perceived to to be damaging on the on +the marriage market + + align:start position:0% +the marriage market + + + align:start position:0% +the marriage market +that can then in turn reduce ambition + + align:start position:0% +that can then in turn reduce ambition + + + align:start position:0% +that can then in turn reduce ambition +and then contribute + + align:start position:0% +and then contribute + + + align:start position:0% +and then contribute +to the gender gap + + align:start position:0% + + + + align:start position:0% + +overall okay + + align:start position:0% +overall okay + + + align:start position:0% +overall okay +let me tell you now about a final paper + + align:start position:0% +let me tell you now about a final paper + + + align:start position:0% +let me tell you now about a final paper +on uh uh + + align:start position:0% +on uh uh + + + align:start position:0% +on uh uh +saying no and on demand and supply for + + align:start position:0% +saying no and on demand and supply for + + + align:start position:0% +saying no and on demand and supply for +different tasks + + align:start position:0% +different tasks + + + align:start position:0% +different tasks +this is a very nice paper by raster + + align:start position:0% +this is a very nice paper by raster + + + align:start position:0% +this is a very nice paper by raster +linganelle and asks the question whether + + align:start position:0% +linganelle and asks the question whether + + + align:start position:0% +linganelle and asks the question whether +women say no often enough + + align:start position:0% +women say no often enough + + + align:start position:0% +women say no often enough +and so that's motivated by the + + align:start position:0% +and so that's motivated by the + + + align:start position:0% +and so that's motivated by the +observation that female + + align:start position:0% +observation that female + + + align:start position:0% +observation that female +faculty members spend fewer hours on + + align:start position:0% +faculty members spend fewer hours on + + + align:start position:0% +faculty members spend fewer hours on +research and more hours + + align:start position:0% +research and more hours + + + align:start position:0% +research and more hours +on university survey committees than + + align:start position:0% +on university survey committees than + + + align:start position:0% +on university survey committees than +male faculty + + align:start position:0% +male faculty + + + align:start position:0% +male faculty +they also are more likely to have + + align:start position:0% +they also are more likely to have + + + align:start position:0% +they also are more likely to have +positions on university-wide communities + + align:start position:0% +positions on university-wide communities + + + align:start position:0% +positions on university-wide communities +they advise more undergrad students and + + align:start position:0% +they advise more undergrad students and + + + align:start position:0% +they advise more undergrad students and +participate more in departments and + + align:start position:0% +participate more in departments and + + + align:start position:0% +participate more in departments and +college level committees than real + + align:start position:0% +college level committees than real + + + align:start position:0% +college level committees than real +faculty + + align:start position:0% +faculty + + + align:start position:0% +faculty +more generally in mid-level jobs men + + align:start position:0% +more generally in mid-level jobs men + + + align:start position:0% +more generally in mid-level jobs men +more than women evaluate the individual + + align:start position:0% +more than women evaluate the individual + + + align:start position:0% +more than women evaluate the individual +task assignments as challenging + + align:start position:0% +task assignments as challenging + + + align:start position:0% +task assignments as challenging +and this is partially attributed to + + align:start position:0% +and this is partially attributed to + + + align:start position:0% +and this is partially attributed to +differential task assignments by + + align:start position:0% +differential task assignments by + + + align:start position:0% +differential task assignments by +supervisors + + align:start position:0% +supervisors + + + align:start position:0% +supervisors +so + + align:start position:0% + + + + align:start position:0% + +if you sort of see that these + + align:start position:0% +if you sort of see that these + + + align:start position:0% +if you sort of see that these +differences you might ask the question + + align:start position:0% +differences you might ask the question + + + align:start position:0% +differences you might ask the question +why do women + + align:start position:0% + + + + align:start position:0% + +decide to spend or spend their work time + + align:start position:0% +decide to spend or spend their work time + + + align:start position:0% +decide to spend or spend their work time +differently + + align:start position:0% +differently + + + align:start position:0% +differently +and there's two types of dimensions here + + align:start position:0% +and there's two types of dimensions here + + + align:start position:0% +and there's two types of dimensions here +one is demand and one is supply + + align:start position:0% +one is demand and one is supply + + + align:start position:0% +one is demand and one is supply +um so demand is essentially the question + + align:start position:0% +um so demand is essentially the question + + + align:start position:0% +um so demand is essentially the question +whether uh + + align:start position:0% +whether uh + + + align:start position:0% +whether uh +sex differences in the types of tasks + + align:start position:0% +sex differences in the types of tasks + + + align:start position:0% +sex differences in the types of tasks +that women and men are asked to do + + align:start position:0% +that women and men are asked to do + + + align:start position:0% +that women and men are asked to do +and works is that due to like + + align:start position:0% +and works is that due to like + + + align:start position:0% +and works is that due to like +essentially what they're being asked + + align:start position:0% +essentially what they're being asked + + + align:start position:0% +essentially what they're being asked +um and i wouldn't more likely than men + + align:start position:0% +um and i wouldn't more likely than men + + + align:start position:0% +um and i wouldn't more likely than men +to be asked to do what's called + + align:start position:0% +to be asked to do what's called + + + align:start position:0% +to be asked to do what's called +non-promotable tasks tasks that are not + + align:start position:0% +non-promotable tasks tasks that are not + + + align:start position:0% +non-promotable tasks tasks that are not +really hopeful for their career for + + align:start position:0% +really hopeful for their career for + + + align:start position:0% +really hopeful for their career for +getting promotions and then you might + + align:start position:0% +getting promotions and then you might + + + align:start position:0% +getting promotions and then you might +ask why that's the case + + align:start position:0% +ask why that's the case + + + align:start position:0% +ask why that's the case +supply is what other sex differences the + + align:start position:0% +supply is what other sex differences the + + + align:start position:0% +supply is what other sex differences the +willingness to agree to perform + + align:start position:0% +willingness to agree to perform + + + align:start position:0% +willingness to agree to perform +non-promotable tasks when asked with + + align:start position:0% +non-promotable tasks when asked with + + + align:start position:0% +non-promotable tasks when asked with +conditional i'm being asked a woman more + + align:start position:0% +conditional i'm being asked a woman more + + + align:start position:0% +conditional i'm being asked a woman more +likely to say + + align:start position:0% +likely to say + + + align:start position:0% +likely to say +yes and again + + align:start position:0% +yes and again + + + align:start position:0% +yes and again +are women more likely to demand to say + + align:start position:0% +are women more likely to demand to say + + + align:start position:0% +are women more likely to demand to say +yes to non-promotable tasks + + align:start position:0% +yes to non-promotable tasks + + + align:start position:0% +yes to non-promotable tasks +now why do we care while there's an + + align:start position:0% +now why do we care while there's an + + + align:start position:0% +now why do we care while there's an +individual decision-making perspective + + align:start position:0% +individual decision-making perspective + + + align:start position:0% +individual decision-making perspective +which is that people might make + + align:start position:0% +which is that people might make + + + align:start position:0% +which is that people might make +suboptimal decisions how to allocate + + align:start position:0% +suboptimal decisions how to allocate + + + align:start position:0% +suboptimal decisions how to allocate +their work + + align:start position:0% +their work + + + align:start position:0% +their work +time at work and understand these + + align:start position:0% +time at work and understand these + + + align:start position:0% +time at work and understand these +underlying reasons potential + + align:start position:0% +underlying reasons potential + + + align:start position:0% +underlying reasons potential +intervention better sort of understand + + align:start position:0% +intervention better sort of understand + + + align:start position:0% +intervention better sort of understand +these underlying reasons which will lead + + align:start position:0% +these underlying reasons which will lead + + + align:start position:0% +these underlying reasons which will lead +them potentially to some interventions + + align:start position:0% +them potentially to some interventions + + + align:start position:0% +them potentially to some interventions +to improve decision making for + + align:start position:0% +to improve decision making for + + + align:start position:0% +to improve decision making for +certain individuals which are a lot + + align:start position:0% +certain individuals which are a lot + + + align:start position:0% +certain individuals which are a lot +about vehicle economics is + + align:start position:0% +about vehicle economics is + + + align:start position:0% +about vehicle economics is +but there's also managerial and social + + align:start position:0% +but there's also managerial and social + + + align:start position:0% +but there's also managerial and social +planner perspectives + + align:start position:0% +planner perspectives + + + align:start position:0% +planner perspectives +that organizations may now be using + + align:start position:0% +that organizations may now be using + + + align:start position:0% +that organizations may now be using +their resources more + + align:start position:0% +their resources more + + + align:start position:0% +their resources more +most effectively and if you sort of + + align:start position:0% +most effectively and if you sort of + + + align:start position:0% +most effectively and if you sort of +reallocated some of the tasks + + align:start position:0% +reallocated some of the tasks + + + align:start position:0% +reallocated some of the tasks +um uh that would produce that would + + align:start position:0% +um uh that would produce that would + + + align:start position:0% +um uh that would produce that would +increase um + + align:start position:0% +increase um + + + align:start position:0% +increase um +output overall and then finally there's + + align:start position:0% +output overall and then finally there's + + + align:start position:0% +output overall and then finally there's +a public policy perspective well + + align:start position:0% +a public policy perspective well + + + align:start position:0% +a public policy perspective well +if these sex differences in the + + align:start position:0% +if these sex differences in the + + + align:start position:0% +if these sex differences in the +allocation of time explain + + align:start position:0% +allocation of time explain + + + align:start position:0% +allocation of time explain +uh vertical sex segregation essentially + + align:start position:0% +uh vertical sex segregation essentially + + + align:start position:0% +uh vertical sex segregation essentially +like women not being promoted enough + + align:start position:0% +like women not being promoted enough + + + align:start position:0% +like women not being promoted enough +then it would help us sort of improve + + align:start position:0% +then it would help us sort of improve + + + align:start position:0% +then it would help us sort of improve +gender equity overall and perhaps also + + align:start position:0% +gender equity overall and perhaps also + + + align:start position:0% +gender equity overall and perhaps also +try to + + align:start position:0% +try to + + + align:start position:0% +try to +reduce the gender gap now what are these + + align:start position:0% +reduce the gender gap now what are these + + + align:start position:0% +reduce the gender gap now what are these +promotable and non-promotional tasks and + + align:start position:0% +promotable and non-promotional tasks and + + + align:start position:0% +promotable and non-promotional tasks and +the type of like academics + + align:start position:0% +the type of like academics + + + align:start position:0% +the type of like academics +a promotable task is a task that's doing + + align:start position:0% +a promotable task is a task that's doing + + + align:start position:0% +a promotable task is a task that's doing +research that's essentially what people + + align:start position:0% +research that's essentially what people + + + align:start position:0% +research that's essentially what people +are evaluated on eventually + + align:start position:0% +are evaluated on eventually + + + align:start position:0% +are evaluated on eventually +but also in the other tasks essentially + + align:start position:0% +but also in the other tasks essentially + + + align:start position:0% +but also in the other tasks essentially +that's seen where other people will + + align:start position:0% +that's seen where other people will + + + align:start position:0% +that's seen where other people will +reward you for when you do it and + + align:start position:0% +reward you for when you do it and + + + align:start position:0% +reward you for when you do it and +non-promotable tasks essentially tasks + + align:start position:0% +non-promotable tasks essentially tasks + + + align:start position:0% +non-promotable tasks essentially tasks +it often discretionary + + align:start position:0% +it often discretionary + + + align:start position:0% +it often discretionary +many people could do the task and + + align:start position:0% +many people could do the task and + + + align:start position:0% +many people could do the task and +everybody wants it has to be done yet + + align:start position:0% +everybody wants it has to be done yet + + + align:start position:0% +everybody wants it has to be done yet +everybody prefers somebody else to do it + + align:start position:0% +everybody prefers somebody else to do it + + + align:start position:0% +everybody prefers somebody else to do it +for example would be an ethics committee + + align:start position:0% +for example would be an ethics committee + + + align:start position:0% +for example would be an ethics committee +at the university surely we should have + + align:start position:0% +at the university surely we should have + + + align:start position:0% +at the university surely we should have +one but surely + + align:start position:0% +one but surely + + + align:start position:0% +one but surely +sitting on the committee will not help + + align:start position:0% +sitting on the committee will not help + + + align:start position:0% +sitting on the committee will not help +people get promoted or get tenure when + + align:start position:0% +people get promoted or get tenure when + + + align:start position:0% +people get promoted or get tenure when +it comes to research + + align:start position:0% +it comes to research + + + align:start position:0% +it comes to research +now um the the authorization that we + + align:start position:0% +now um the the authorization that we + + + align:start position:0% +now um the the authorization that we +were killed studying with faculty + + align:start position:0% +were killed studying with faculty + + + align:start position:0% +were killed studying with faculty +at a large public university and they + + align:start position:0% +at a large public university and they + + + align:start position:0% +at a large public university and they +sent essentially emails from the chair + + align:start position:0% +sent essentially emails from the chair + + + align:start position:0% +sent essentially emails from the chair +of the faculty + + align:start position:0% +of the faculty + + + align:start position:0% +of the faculty +senate asking them to to volunteer to + + align:start position:0% +senate asking them to to volunteer to + + + align:start position:0% +senate asking them to to volunteer to +join one of several university-wide + + align:start position:0% +join one of several university-wide + + + align:start position:0% +join one of several university-wide +faculty senate committees + + align:start position:0% +faculty senate committees + + + align:start position:0% +faculty senate committees +and the clear answer in this study is + + align:start position:0% +and the clear answer in this study is + + + align:start position:0% +and the clear answer in this study is +that women are much more likely to + + align:start position:0% +that women are much more likely to + + + align:start position:0% +that women are much more likely to +volunteer + + align:start position:0% +volunteer + + + align:start position:0% +volunteer +when asked now + + align:start position:0% +when asked now + + + align:start position:0% +when asked now +that is an interesting fact but that + + align:start position:0% +that is an interesting fact but that + + + align:start position:0% +that is an interesting fact but that +doesn't really necessarily let us + + align:start position:0% +doesn't really necessarily let us + + + align:start position:0% +doesn't really necessarily let us +disentangle the demand and supply + + align:start position:0% +disentangle the demand and supply + + + align:start position:0% +disentangle the demand and supply +explanation that which that i showed you + + align:start position:0% +explanation that which that i showed you + + + align:start position:0% +explanation that which that i showed you +previously + + align:start position:0% +previously + + + align:start position:0% +previously +so in addition to men uh the authors do + + align:start position:0% +so in addition to men uh the authors do + + + align:start position:0% +so in addition to men uh the authors do +a lab experiments + + align:start position:0% +a lab experiments + + + align:start position:0% +a lab experiments +in which they do what's called the + + align:start position:0% +in which they do what's called the + + + align:start position:0% +in which they do what's called the +threshold public goods game + + align:start position:0% +threshold public goods game + + + align:start position:0% +threshold public goods game +and this is sort of very much trying to + + align:start position:0% +and this is sort of very much trying to + + + align:start position:0% +and this is sort of very much trying to +mirror or like + + align:start position:0% +mirror or like + + + align:start position:0% +mirror or like +resemble the reality in this game a + + align:start position:0% +resemble the reality in this game a + + + align:start position:0% +resemble the reality in this game a +small group + + align:start position:0% +small group + + + align:start position:0% +small group +needs to find a volunteer for a task and + + align:start position:0% +needs to find a volunteer for a task and + + + align:start position:0% +needs to find a volunteer for a task and +participants are anonymously matched in + + align:start position:0% +participants are anonymously matched in + + + align:start position:0% +participants are anonymously matched in +groups of three + + align:start position:0% +groups of three + + + align:start position:0% +groups of three +they're randomly rematched for each of + + align:start position:0% +they're randomly rematched for each of + + + align:start position:0% +they're randomly rematched for each of +10 rounds + + align:start position:0% +10 rounds + + + align:start position:0% +10 rounds +the game is set up such that everyone + + align:start position:0% +the game is set up such that everyone + + + align:start position:0% +the game is set up such that everyone +prefers that the caspian are taken by + + align:start position:0% +prefers that the caspian are taken by + + + align:start position:0% +prefers that the caspian are taken by +someone other than themselves + + align:start position:0% +someone other than themselves + + + align:start position:0% +someone other than themselves +people get two minutes to decide whether + + align:start position:0% +people get two minutes to decide whether + + + align:start position:0% +people get two minutes to decide whether +to invest and so + + align:start position:0% +to invest and so + + + align:start position:0% +to invest and so +the task is essentially you have to + + align:start position:0% +the task is essentially you have to + + + align:start position:0% +the task is essentially you have to +click a button and then you invest the + + align:start position:0% +click a button and then you invest the + + + align:start position:0% +click a button and then you invest the +money + + align:start position:0% +money + + + align:start position:0% +money +only one person can invest the round + + align:start position:0% +only one person can invest the round + + + align:start position:0% +only one person can invest the round +ends when somebody invests + + align:start position:0% +ends when somebody invests + + + align:start position:0% +ends when somebody invests +if no one invests group members all + + align:start position:0% +if no one invests group members all + + + align:start position:0% +if no one invests group members all +earned one dollar + + align:start position:0% +earned one dollar + + + align:start position:0% +earned one dollar +if a person invests that person earns + + align:start position:0% +if a person invests that person earns + + + align:start position:0% +if a person invests that person earns +1.25 and the remaining group of members + + align:start position:0% +1.25 and the remaining group of members + + + align:start position:0% +1.25 and the remaining group of members +earn + + align:start position:0% +earn + + + align:start position:0% +earn +two dollars the clock ticks down until + + align:start position:0% +two dollars the clock ticks down until + + + align:start position:0% +two dollars the clock ticks down until +one person invests or no investment is + + align:start position:0% +one person invests or no investment is + + + align:start position:0% +one person invests or no investment is +made in two minutes + + align:start position:0% +made in two minutes + + + align:start position:0% +made in two minutes +so the game is essentially set up in a + + align:start position:0% +so the game is essentially set up in a + + + align:start position:0% +so the game is essentially set up in a +way such that that + + align:start position:0% +way such that that + + + align:start position:0% +way such that that +everybody wants that somebody and it's + + align:start position:0% +everybody wants that somebody and it's + + + align:start position:0% +everybody wants that somebody and it's +included somebody should invest but + + align:start position:0% +included somebody should invest but + + + align:start position:0% +included somebody should invest but +nobody wants to mess because + + align:start position:0% +nobody wants to mess because + + + align:start position:0% +nobody wants to mess because +if you invest you get only a dollar 25 + + align:start position:0% +if you invest you get only a dollar 25 + + + align:start position:0% +if you invest you get only a dollar 25 +well if you don't invest or somebody + + align:start position:0% +well if you don't invest or somebody + + + align:start position:0% +well if you don't invest or somebody +else investing you don't invest you get + + align:start position:0% +else investing you don't invest you get + + + align:start position:0% +else investing you don't invest you get +two dollars + + align:start position:0% +two dollars + + + align:start position:0% +two dollars +now in this game women are significantly + + align:start position:0% +now in this game women are significantly + + + align:start position:0% +now in this game women are significantly +more likely to invest you essentially + + align:start position:0% +more likely to invest you essentially + + + align:start position:0% +more likely to invest you essentially +see the probability of resting here on + + align:start position:0% +see the probability of resting here on + + + align:start position:0% +see the probability of resting here on +the left side by + + align:start position:0% +the left side by + + + align:start position:0% +the left side by +round and the red line which is the + + align:start position:0% +round and the red line which is the + + + align:start position:0% +round and the red line which is the +upper line the women line the + + align:start position:0% +upper line the women line the + + + align:start position:0% +upper line the women line the +female line is way way higher compared + + align:start position:0% +female line is way way higher compared + + + align:start position:0% +female line is way way higher compared +to the male height there's much higher + + align:start position:0% +to the male height there's much higher + + + align:start position:0% +to the male height there's much higher +probability of investing in this game + + align:start position:0% +probability of investing in this game + + + align:start position:0% +probability of investing in this game +now why are women more likely to invest + + align:start position:0% +now why are women more likely to invest + + + align:start position:0% +now why are women more likely to invest +is it the case that women believe that + + align:start position:0% +is it the case that women believe that + + + align:start position:0% +is it the case that women believe that +their cooperation is necessary for an + + align:start position:0% +their cooperation is necessary for an + + + align:start position:0% +their cooperation is necessary for an +optimal group decision but men believe + + align:start position:0% +optimal group decision but men believe + + + align:start position:0% +optimal group decision but men believe +that their + + align:start position:0% +that their + + + align:start position:0% +that their +cooperation isn't required so it could + + align:start position:0% +cooperation isn't required so it could + + + align:start position:0% +cooperation isn't required so it could +be that women sort of think that they're + + align:start position:0% +be that women sort of think that they're + + + align:start position:0% +be that women sort of think that they're +like well + + align:start position:0% +like well + + + align:start position:0% +like well +somebody uh if i don't do it nobody else + + align:start position:0% +somebody uh if i don't do it nobody else + + + align:start position:0% +somebody uh if i don't do it nobody else +does it + + align:start position:0% +does it + + + align:start position:0% +does it +and then essentially think well somebody + + align:start position:0% +and then essentially think well somebody + + + align:start position:0% +and then essentially think well somebody +else can do it in particular women could + + align:start position:0% +else can do it in particular women could + + + align:start position:0% +else can do it in particular women could +do it if they're in the group + + align:start position:0% +do it if they're in the group + + + align:start position:0% +do it if they're in the group +so then the authors do the same + + align:start position:0% +so then the authors do the same + + + align:start position:0% +so then the authors do the same +experiment again + + align:start position:0% +experiment again + + + align:start position:0% +experiment again +um using a single sex sessions + + align:start position:0% +um using a single sex sessions + + + align:start position:0% +um using a single sex sessions +where essentially all three um + + align:start position:0% +where essentially all three um + + + align:start position:0% +where essentially all three um +people in the session are female or all + + align:start position:0% +people in the session are female or all + + + align:start position:0% +people in the session are female or all +people in the session are + + align:start position:0% +people in the session are + + + align:start position:0% +people in the session are +are male and then what they find is + + align:start position:0% +are male and then what they find is + + + align:start position:0% +are male and then what they find is +essentially interestingly + + align:start position:0% +essentially interestingly + + + align:start position:0% +essentially interestingly +these differences in gender now go away + + align:start position:0% +these differences in gender now go away + + + align:start position:0% +these differences in gender now go away +entirely there's no gender differences + + align:start position:0% +entirely there's no gender differences + + + align:start position:0% +entirely there's no gender differences +in same-sex + + align:start position:0% +in same-sex + + + align:start position:0% +in same-sex +sessions anymore so just to summarize + + align:start position:0% +sessions anymore so just to summarize + + + align:start position:0% +sessions anymore so just to summarize +so um experiment one when there's a + + align:start position:0% +so um experiment one when there's a + + + align:start position:0% +so um experiment one when there's a +mixed gender + + align:start position:0% +mixed gender + + + align:start position:0% +mixed gender +women are more likely to invest in + + align:start position:0% +women are more likely to invest in + + + align:start position:0% +women are more likely to invest in +experiment two women and men + + align:start position:0% +experiment two women and men + + + align:start position:0% +experiment two women and men +are equally likely to invest now one + + align:start position:0% +are equally likely to invest now one + + + align:start position:0% +are equally likely to invest now one +question you might ask as well + + align:start position:0% +question you might ask as well + + + align:start position:0% +question you might ask as well +is it the case that really um is this + + align:start position:0% +is it the case that really um is this + + + align:start position:0% +is it the case that really um is this +really about beliefs so it could be that + + align:start position:0% +really about beliefs so it could be that + + + align:start position:0% +really about beliefs so it could be that +like + + align:start position:0% +like + + + align:start position:0% +like +um there's no in fact no differences in + + align:start position:0% +um there's no in fact no differences in + + + align:start position:0% +um there's no in fact no differences in +the preferences for investing it's not + + align:start position:0% +the preferences for investing it's not + + + align:start position:0% +the preferences for investing it's not +like women are necessarily nicer than + + align:start position:0% +like women are necessarily nicer than + + + align:start position:0% +like women are necessarily nicer than +men + + align:start position:0% +men + + + align:start position:0% +men +but rather their differences and beliefs + + align:start position:0% +but rather their differences and beliefs + + + align:start position:0% +but rather their differences and beliefs +that the women + + align:start position:0% +that the women + + + align:start position:0% +that the women +will invest in particularly if there's a + + align:start position:0% +will invest in particularly if there's a + + + align:start position:0% +will invest in particularly if there's a +woman in the group everybody else may + + align:start position:0% +woman in the group everybody else may + + + align:start position:0% +woman in the group everybody else may +think oh the woman is going to invest + + align:start position:0% +think oh the woman is going to invest + + + align:start position:0% +think oh the woman is going to invest +and the woman might think like well if + + align:start position:0% +and the woman might think like well if + + + align:start position:0% +and the woman might think like well if +others don't invest + + align:start position:0% +others don't invest + + + align:start position:0% +others don't invest +or others will not invest and since she + + align:start position:0% +or others will not invest and since she + + + align:start position:0% +or others will not invest and since she +might believe that she might have to or + + align:start position:0% +might believe that she might have to or + + + align:start position:0% +might believe that she might have to or +like think that she needs to do it + + align:start position:0% +like think that she needs to do it + + + align:start position:0% +like think that she needs to do it +herself + + align:start position:0% +herself + + + align:start position:0% +herself +otherwise um everybody will end up with + + align:start position:0% +otherwise um everybody will end up with + + + align:start position:0% +otherwise um everybody will end up with +one dollar and less money + + align:start position:0% +one dollar and less money + + + align:start position:0% +one dollar and less money +so now there's a third experiment here + + align:start position:0% +so now there's a third experiment here + + + align:start position:0% +so now there's a third experiment here +um + + align:start position:0% +um + + + align:start position:0% +um +where people ask um + + align:start position:0% +where people ask um + + + align:start position:0% +where people ask um +to essentially pick whom they would like + + align:start position:0% +to essentially pick whom they would like + + + align:start position:0% +to essentially pick whom they would like +to to ask + + align:start position:0% +to to ask + + + align:start position:0% +to to ask +and so there's four people per group and + + align:start position:0% +and so there's four people per group and + + + align:start position:0% +and so there's four people per group and +three people can invest and the + + align:start position:0% +three people can invest and the + + + align:start position:0% +three people can invest and the +incentives are four these are like + + align:start position:0% +incentives are four these are like + + + align:start position:0% +incentives are four these are like +they're called the green players and one + + align:start position:0% +they're called the green players and one + + + align:start position:0% +they're called the green players and one +person is unable to invest but ask one + + align:start position:0% +person is unable to invest but ask one + + + align:start position:0% +person is unable to invest but ask one +of the three to invest + + align:start position:0% +of the three to invest + + + align:start position:0% +of the three to invest +importantly the request actually not + + align:start position:0% +importantly the request actually not + + + align:start position:0% +importantly the request actually not +even binding that's the red player + + align:start position:0% +even binding that's the red player + + + align:start position:0% +even binding that's the red player +the red player has essentially one scene + + align:start position:0% +the red player has essentially one scene + + + align:start position:0% +the red player has essentially one scene +has been to happen is incentivized + + align:start position:0% +has been to happen is incentivized + + + align:start position:0% +has been to happen is incentivized +that that happens so this is kind of + + align:start position:0% +that that happens so this is kind of + + + align:start position:0% +that that happens so this is kind of +what this looks like you would get like + + align:start position:0% +what this looks like you would get like + + + align:start position:0% +what this looks like you would get like +three different players here and you can + + align:start position:0% +three different players here and you can + + + align:start position:0% +three different players here and you can +essentially decide + + align:start position:0% +essentially decide + + + align:start position:0% +essentially decide +whom you would like to to ask and it's + + align:start position:0% +whom you would like to to ask and it's + + + align:start position:0% +whom you would like to to ask and it's +set up of course that you can see the + + align:start position:0% +set up of course that you can see the + + + align:start position:0% +set up of course that you can see the +gender some are male and some are + + align:start position:0% +gender some are male and some are + + + align:start position:0% +gender some are male and some are +female now women are way more likely to + + align:start position:0% +female now women are way more likely to + + + align:start position:0% +female now women are way more likely to +be asked + + align:start position:0% +be asked + + + align:start position:0% +be asked +this is the total times asked to invest + + align:start position:0% +this is the total times asked to invest + + + align:start position:0% +this is the total times asked to invest +for + + align:start position:0% +for + + + align:start position:0% +for +male and female players is the relative + + align:start position:0% +male and female players is the relative + + + align:start position:0% +male and female players is the relative +frequency you essentially see the + + align:start position:0% +frequency you essentially see the + + + align:start position:0% +frequency you essentially see the +distribution + + align:start position:0% +distribution + + + align:start position:0% +distribution +here is why shifted to the right for + + align:start position:0% +here is why shifted to the right for + + + align:start position:0% +here is why shifted to the right for +women + + align:start position:0% +women + + + align:start position:0% +women +compared to men now + + align:start position:0% +compared to men now + + + align:start position:0% +compared to men now +is it better to ask a woman but absent + + align:start position:0% +is it better to ask a woman but absent + + + align:start position:0% +is it better to ask a woman but absent +the requests invest the investment rate + + align:start position:0% +the requests invest the investment rate + + + align:start position:0% +the requests invest the investment rate +actually does not + + align:start position:0% +actually does not + + + align:start position:0% +actually does not +differ by gender but when asked to + + align:start position:0% +differ by gender but when asked to + + + align:start position:0% +differ by gender but when asked to +invest women are more likely to comply + + align:start position:0% +invest women are more likely to comply + + + align:start position:0% +invest women are more likely to comply +so when the woman is asked to invest 76 + + align:start position:0% +so when the woman is asked to invest 76 + + + align:start position:0% +so when the woman is asked to invest 76 +percent of women in best compared to 14 + + align:start position:0% +percent of women in best compared to 14 + + + align:start position:0% +percent of women in best compared to 14 +but not as + + align:start position:0% +but not as + + + align:start position:0% +but not as +in contrast men are also more likely to + + align:start position:0% +in contrast men are also more likely to + + + align:start position:0% +in contrast men are also more likely to +invest when asked but it's only 51 + + align:start position:0% +invest when asked but it's only 51 + + + align:start position:0% +invest when asked but it's only 51 +percent compared to 14 + + align:start position:0% +percent compared to 14 + + + align:start position:0% +percent compared to 14 +when i'm asked so the marginal increase + + align:start position:0% +when i'm asked so the marginal increase + + + align:start position:0% +when i'm asked so the marginal increase +of being asked is higher for women + + align:start position:0% +of being asked is higher for women + + + align:start position:0% +of being asked is higher for women +than for men so if you're thinking about + + align:start position:0% +than for men so if you're thinking about + + + align:start position:0% +than for men so if you're thinking about +like who should you ask well + + align:start position:0% +like who should you ask well + + + align:start position:0% +like who should you ask well +you kind of want to ask a woman because + + align:start position:0% +you kind of want to ask a woman because + + + align:start position:0% +you kind of want to ask a woman because +a woman is more likely + + align:start position:0% +a woman is more likely + + + align:start position:0% +a woman is more likely +to comply with your request and so now + + align:start position:0% +to comply with your request and so now + + + align:start position:0% +to comply with your request and so now +if + + align:start position:0% +if + + + align:start position:0% +if +women and women are more likely to be + + align:start position:0% +women and women are more likely to be + + + align:start position:0% +women and women are more likely to be +expected + + align:start position:0% +expected + + + align:start position:0% +expected +to say yes they also ask more so that + + align:start position:0% +to say yes they also ask more so that + + + align:start position:0% +to say yes they also ask more so that +sort of says you know the gender + + align:start position:0% +sort of says you know the gender + + + align:start position:0% +sort of says you know the gender +differences get amplified by increased + + align:start position:0% +differences get amplified by increased + + + align:start position:0% +differences get amplified by increased +demand for women to contribute + + align:start position:0% +demand for women to contribute + + + align:start position:0% +demand for women to contribute +but particularly if there's a man and a + + align:start position:0% +but particularly if there's a man and a + + + align:start position:0% +but particularly if there's a man and a +woman where both you think about like + + align:start position:0% +woman where both you think about like + + + align:start position:0% +woman where both you think about like +one of them could do it + + align:start position:0% +one of them could do it + + + align:start position:0% +one of them could do it +the man will think well the woman will + + align:start position:0% +the man will think well the woman will + + + align:start position:0% +the man will think well the woman will +do it anyway the women will think well + + align:start position:0% +do it anyway the women will think well + + + align:start position:0% +do it anyway the women will think well +the man is not going to do it and he's + + align:start position:0% +the man is not going to do it and he's + + + align:start position:0% +the man is not going to do it and he's +going to think that + + align:start position:0% +going to think that + + + align:start position:0% +going to think that +i will do it anyway and so then the + + align:start position:0% +i will do it anyway and so then the + + + align:start position:0% +i will do it anyway and so then the +woman ends up doing it + + align:start position:0% +woman ends up doing it + + + align:start position:0% +woman ends up doing it +more in addition when there's an + + align:start position:0% +more in addition when there's an + + + align:start position:0% +more in addition when there's an +opportunity to ask somebody but asking + + align:start position:0% +opportunity to ask somebody but asking + + + align:start position:0% +opportunity to ask somebody but asking +is kind of costly and you just want to + + align:start position:0% +is kind of costly and you just want to + + + align:start position:0% +is kind of costly and you just want to +find somebody who will do it well whom + + align:start position:0% +find somebody who will do it well whom + + + align:start position:0% +find somebody who will do it well whom +will you ask you ask the woman because + + align:start position:0% +will you ask you ask the woman because + + + align:start position:0% +will you ask you ask the woman because +she's more likely to comply more likely + + align:start position:0% +she's more likely to comply more likely + + + align:start position:0% +she's more likely to comply more likely +um to say yes + + align:start position:0% +um to say yes + + + align:start position:0% +um to say yes +let me sort of summarize what we + + align:start position:0% +let me sort of summarize what we + + + align:start position:0% +let me sort of summarize what we +discussed + + align:start position:0% +discussed + + + align:start position:0% +discussed +so first is large gender wage and + + align:start position:0% +so first is large gender wage and + + + align:start position:0% +so first is large gender wage and +earnings gaps + + align:start position:0% +earnings gaps + + + align:start position:0% +earnings gaps +they have been reduced due to + + align:start position:0% +they have been reduced due to + + + align:start position:0% +they have been reduced due to +technological advances and other + + align:start position:0% +technological advances and other + + + align:start position:0% +technological advances and other +improvements over time but they're + + align:start position:0% +improvements over time but they're + + + align:start position:0% +improvements over time but they're +there there are so persistent gender + + align:start position:0% +there there are so persistent gender + + + align:start position:0% +there there are so persistent gender +differences + + align:start position:0% +differences + + + align:start position:0% +differences +in the us and many other countries + + align:start position:0% +in the us and many other countries + + + align:start position:0% +in the us and many other countries +biased beliefs and identity concerns + + align:start position:0% +biased beliefs and identity concerns + + + align:start position:0% +biased beliefs and identity concerns +play in a major role in explaining + + align:start position:0% +play in a major role in explaining + + + align:start position:0% +play in a major role in explaining +those differences um + + align:start position:0% +those differences um + + + align:start position:0% +those differences um +in addition there are some feedback + + align:start position:0% +in addition there are some feedback + + + align:start position:0% +in addition there are some feedback +mechanisms between the demand and supply + + align:start position:0% +mechanisms between the demand and supply + + + align:start position:0% +mechanisms between the demand and supply +of non-promotable tasks that could be + + align:start position:0% +of non-promotable tasks that could be + + + align:start position:0% +of non-promotable tasks that could be +that are potentially quite important + + align:start position:0% +that are potentially quite important + + + align:start position:0% +that are potentially quite important +because i showed you only a lab + + align:start position:0% +because i showed you only a lab + + + align:start position:0% +because i showed you only a lab +experiment but these could be really + + align:start position:0% +experiment but these could be really + + + align:start position:0% +experiment but these could be really +important + + align:start position:0% +important + + + align:start position:0% +important +in real world situations so not only is + + align:start position:0% +in real world situations so not only is + + + align:start position:0% +in real world situations so not only is +it that + + align:start position:0% +it that + + + align:start position:0% +it that +what matters is what women decide to do + + align:start position:0% +what matters is what women decide to do + + + align:start position:0% +what matters is what women decide to do +but also what they're asked to do by + + align:start position:0% +but also what they're asked to do by + + + align:start position:0% +but also what they're asked to do by +others in part as a response to their + + align:start position:0% +others in part as a response to their + + + align:start position:0% +others in part as a response to their +propensity to say + + align:start position:0% +propensity to say + + + align:start position:0% +propensity to say +yes or no to certain tasks um better + + align:start position:0% +yes or no to certain tasks um better + + + align:start position:0% +yes or no to certain tasks um better +understanding these issues can now help + + align:start position:0% +understanding these issues can now help + + + align:start position:0% +understanding these issues can now help +us + + align:start position:0% +us + + + align:start position:0% +us +mitigate the gender gap and we can sort + + align:start position:0% +mitigate the gender gap and we can sort + + + align:start position:0% +mitigate the gender gap and we can sort +of then by understanding these issues + + align:start position:0% +of then by understanding these issues + + + align:start position:0% +of then by understanding these issues +better and particular beliefs you might + + align:start position:0% +better and particular beliefs you might + + + align:start position:0% +better and particular beliefs you might +be able to + + align:start position:0% +be able to + + + align:start position:0% +be able to +improve uh or correct bias beliefs and + + align:start position:0% +improve uh or correct bias beliefs and + + + align:start position:0% +improve uh or correct bias beliefs and +therefore + + align:start position:0% +therefore + + + align:start position:0% +therefore +um close on the gender gap potential + + align:start position:0% +um close on the gender gap potential + + + align:start position:0% +um close on the gender gap potential +what's next in the next few lectures + + align:start position:0% +what's next in the next few lectures + + + align:start position:0% +what's next in the next few lectures +lecture 19 we'll talk about frames + + align:start position:0% +lecture 19 we'll talk about frames + + + align:start position:0% +lecture 19 we'll talk about frames +defaults not just in mental accounting + + align:start position:0% +defaults not just in mental accounting + + + align:start position:0% +defaults not just in mental accounting +please read major and share + + align:start position:0% +please read major and share + + + align:start position:0% +please read major and share +and lecture 20 we'll look about talk + + align:start position:0% +and lecture 20 we'll look about talk + + + align:start position:0% +and lecture 20 we'll look about talk +about malleability malleability and + + align:start position:0% +about malleability malleability and + + + align:start position:0% +about malleability malleability and +accessibility of preferences + + align:start position:0% +accessibility of preferences + + + align:start position:0% +accessibility of preferences +please read ariely 2003 for that + + align:start position:0% +please read ariely 2003 for that + + + align:start position:0% +please read ariely 2003 for that +that was all i have to say and um thank + + align:start position:0% +that was all i have to say and um thank + + + align:start position:0% +that was all i have to say and um thank +you so much \ No newline at end of file diff --git a/5F6roh4pmJU.txt b/5F6roh4pmJU.txt new file mode 100644 index 0000000000000000000000000000000000000000..994911b01a140ce5c07106175ee42d1cee5b3ff8 --- /dev/null +++ b/5F6roh4pmJU.txt @@ -0,0 +1,7411 @@ +align:start position:0% + +okay so this + + align:start position:0% +okay so this + + + align:start position:0% +okay so this +is this just to let you know what this + + align:start position:0% +is this just to let you know what this + + + align:start position:0% +is this just to let you know what this +notebook is and isn't this this this + + align:start position:0% +notebook is and isn't this this this + + + align:start position:0% +notebook is and isn't this this this +notebook is kind of meant to let you see + + align:start position:0% +notebook is kind of meant to let you see + + + align:start position:0% +notebook is kind of meant to let you see +how automatic differentiation is kind of + + align:start position:0% +how automatic differentiation is kind of + + + align:start position:0% +how automatic differentiation is kind of +magical in a way that that's kind of the + + align:start position:0% +magical in a way that that's kind of the + + + align:start position:0% +magical in a way that that's kind of the +real purpose um you'll start to get a + + align:start position:0% +real purpose um you'll start to get a + + + align:start position:0% +real purpose um you'll start to get a +bit of a feel for forward mode works and + + align:start position:0% +bit of a feel for forward mode works and + + + align:start position:0% +bit of a feel for forward mode works and +what I like to emphasize is um to what + + align:start position:0% +what I like to emphasize is um to what + + + align:start position:0% +what I like to emphasize is um to what +extent this is possibly more computer + + align:start position:0% +extent this is possibly more computer + + + align:start position:0% +extent this is possibly more computer +science Than Mathematics like we all + + align:start position:0% +science Than Mathematics like we all + + + align:start position:0% +science Than Mathematics like we all +have this notion that you know what you + + align:start position:0% +have this notion that you know what you + + + align:start position:0% +have this notion that you know what you +know whatever what whatever courses that + + align:start position:0% +know whatever what whatever courses that + + + align:start position:0% +know whatever what whatever courses that +are now being taught in computer science + + align:start position:0% +are now being taught in computer science + + + align:start position:0% +are now being taught in computer science +that maybe used to be taught in in math + + align:start position:0% +that maybe used to be taught in in math + + + align:start position:0% +that maybe used to be taught in in math +courses like probability statistics I + + align:start position:0% +courses like probability statistics I + + + align:start position:0% +courses like probability statistics I +think everybody agrees that calculus is + + align:start position:0% +think everybody agrees that calculus is + + + align:start position:0% +think everybody agrees that calculus is +is lives in math departments all over + + align:start position:0% +is lives in math departments all over + + + align:start position:0% +is lives in math departments all over +the world right lots lots of other math + + align:start position:0% +the world right lots lots of other math + + + align:start position:0% +the world right lots lots of other math +subjects are being h jacked by Engineers + + align:start position:0% +subjects are being h jacked by Engineers + + + align:start position:0% +subjects are being h jacked by Engineers +computer scientists and so forth but + + align:start position:0% +computer scientists and so forth but + + + align:start position:0% +computer scientists and so forth but +calculus that that's sacred right that + + align:start position:0% +calculus that that's sacred right that + + + align:start position:0% +calculus that that's sacred right that +belongs in mathematics right well here's + + align:start position:0% +belongs in mathematics right well here's + + + align:start position:0% +belongs in mathematics right well here's +a case where um calculus is is as much + + align:start position:0% +a case where um calculus is is as much + + + align:start position:0% +a case where um calculus is is as much +of a computer science topic as as as it + + align:start position:0% +of a computer science topic as as as it + + + align:start position:0% +of a computer science topic as as as it +is a math topic and I think that's kind + + align:start position:0% +is a math topic and I think that's kind + + + align:start position:0% +is a math topic and I think that's kind +of what fascinated me most about this oh + + align:start position:0% +of what fascinated me most about this oh + + + align:start position:0% +of what fascinated me most about this oh +gosh I first put this together in 2017 + + align:start position:0% +gosh I first put this together in 2017 + + + align:start position:0% +gosh I first put this together in 2017 +is it really 2023 now six years later + + align:start position:0% +is it really 2023 now six years later + + + align:start position:0% +is it really 2023 now six years later +well it's it's so it's an oldie but + + align:start position:0% +well it's it's so it's an oldie but + + + align:start position:0% +well it's it's so it's an oldie but +goodie but I promise you you you'll like + + align:start position:0% +goodie but I promise you you you'll like + + + align:start position:0% +goodie but I promise you you you'll like +it just the same okay and I do like to + + align:start position:0% +it just the same okay and I do like to + + + align:start position:0% +it just the same okay and I do like to +tell people that I used to go to + + align:start position:0% +tell people that I used to go to + + + align:start position:0% +tell people that I used to go to +conferences and I would hear people + + align:start position:0% +conferences and I would hear people + + + align:start position:0% +conferences and I would hear people +talking about automatic differentiation + + align:start position:0% +talking about automatic differentiation + + + align:start position:0% +talking about automatic differentiation +people talked about it before it was hot + + align:start position:0% +people talked about it before it was hot + + + align:start position:0% +people talked about it before it was hot +I mean it it became hot because of + + align:start position:0% +I mean it it became hot because of + + + align:start position:0% +I mean it it became hot because of +machine learning but a couple of decades + + align:start position:0% +machine learning but a couple of decades + + + align:start position:0% +machine learning but a couple of decades +before machine learning people would do + + align:start position:0% +before machine learning people would do + + + align:start position:0% +before machine learning people would do +it and they would do it on the sidelines + + align:start position:0% +it and they would do it on the sidelines + + + align:start position:0% +it and they would do it on the sidelines +nobody paid attention back then to it + + align:start position:0% +nobody paid attention back then to it + + + align:start position:0% +nobody paid attention back then to it +didn't it didn't have sort of the the + + align:start position:0% +didn't it didn't have sort of the the + + + align:start position:0% +didn't it didn't have sort of the the +big excitement that it has today uh but + + align:start position:0% +big excitement that it has today uh but + + + align:start position:0% +big excitement that it has today uh but +I would go to conferences and you know + + align:start position:0% +I would go to conferences and you know + + + align:start position:0% +I would go to conferences and you know +somebody would get up and talk about it + + align:start position:0% +somebody would get up and talk about it + + + align:start position:0% +somebody would get up and talk about it +and I don't know I would read my email + + align:start position:0% +and I don't know I would read my email + + + align:start position:0% +and I don't know I would read my email +or tune out or or work on my own math or + + align:start position:0% +or tune out or or work on my own math or + + + align:start position:0% +or tune out or or work on my own math or +something I didn't really pay attention + + align:start position:0% +something I didn't really pay attention + + + align:start position:0% +something I didn't really pay attention +and so I missed the boat I didn't + + align:start position:0% +and so I missed the boat I didn't + + + align:start position:0% +and so I missed the boat I didn't +appreciate that what I thought was most + + align:start position:0% +appreciate that what I thought was most + + + align:start position:0% +appreciate that what I thought was most +important about automatic + + align:start position:0% +important about automatic + + + align:start position:0% +important about automatic +differentiation and you know I I just + + align:start position:0% +differentiation and you know I I just + + + align:start position:0% +differentiation and you know I I just +made it I I made a jump in my mind of + + align:start position:0% +made it I I made a jump in my mind of + + + align:start position:0% +made it I I made a jump in my mind of +what it is right and I figured it was + + align:start position:0% +what it is right and I figured it was + + + align:start position:0% +what it is right and I figured it was +something symbolic like Mathematica you + + align:start position:0% +something symbolic like Mathematica you + + + align:start position:0% +something symbolic like Mathematica you +know wolf from alpha you know like you + + align:start position:0% +know wolf from alpha you know like you + + + align:start position:0% +know wolf from alpha you know like you +know we've all memorized tables of + + align:start position:0% +know we've all memorized tables of + + + align:start position:0% +know we've all memorized tables of +derivatives you know here's a small + + align:start position:0% +derivatives you know here's a small + + + align:start position:0% +derivatives you know here's a small +table of derivatives you know I figured + + align:start position:0% +table of derivatives you know I figured + + + align:start position:0% +table of derivatives you know I figured +that if I could memorize it when I + + align:start position:0% +that if I could memorize it when I + + + align:start position:0% +that if I could memorize it when I +learned calculus then a computer could + + align:start position:0% +learned calculus then a computer could + + + align:start position:0% +learned calculus then a computer could +be taught to do this thing also so maybe + + align:start position:0% +be taught to do this thing also so maybe + + + align:start position:0% +be taught to do this thing also so maybe +that's what it is that's great I could + + align:start position:0% +that's what it is that's great I could + + + align:start position:0% +that's what it is that's great I could +do it a computer could do it better than + + align:start position:0% +do it a computer could do it better than + + + align:start position:0% +do it a computer could do it better than +me fine I didn't care turns out that's + + align:start position:0% +me fine I didn't care turns out that's + + + align:start position:0% +me fine I didn't care turns out that's +not what automatic differentiation is so + + align:start position:0% +not what automatic differentiation is so + + + align:start position:0% +not what automatic differentiation is so +then I said to myself oh maybe I got it + + align:start position:0% +then I said to myself oh maybe I got it + + + align:start position:0% +then I said to myself oh maybe I got it +wrong I'm just guessing anyway and I + + align:start position:0% +wrong I'm just guessing anyway and I + + + align:start position:0% +wrong I'm just guessing anyway and I +don't really care but maybe it's it's + + align:start position:0% +don't really care but maybe it's it's + + + align:start position:0% +don't really care but maybe it's it's +it's you know some sort of numerical + + align:start position:0% +it's you know some sort of numerical + + + align:start position:0% +it's you know some sort of numerical +difference like we do to check our our + + align:start position:0% +difference like we do to check our our + + + align:start position:0% +difference like we do to check our our +answers right and so you know there's + + align:start position:0% +answers right and so you know there's + + + align:start position:0% +answers right and so you know there's +there you know I want I want the + + align:start position:0% +there you know I want I want the + + + align:start position:0% +there you know I want I want the +derivative at this at at this point x + + align:start position:0% +derivative at this at at this point x + + + align:start position:0% +derivative at this at at this point x +right so I can do a forward derivative + + align:start position:0% +right so I can do a forward derivative + + + align:start position:0% +right so I can do a forward derivative +and get the slope of the tangent or I + + align:start position:0% +and get the slope of the tangent or I + + + align:start position:0% +and get the slope of the tangent or I +could do a backward derivative get the + + align:start position:0% +could do a backward derivative get the + + + align:start position:0% +could do a backward derivative get the +you know go backwards and get the slope + + align:start position:0% +you know go backwards and get the slope + + + align:start position:0% +you know go backwards and get the slope +of this I guess it's a c c to be + + align:start position:0% +of this I guess it's a c c to be + + + align:start position:0% +of this I guess it's a c c to be +technical um right but the slope of this + + align:start position:0% +technical um right but the slope of this + + + align:start position:0% +technical um right but the slope of this +line right or I could even do a central + + align:start position:0% +line right or I could even do a central + + + align:start position:0% +line right or I could even do a central +difference which connects these two dots + + align:start position:0% +difference which connects these two dots + + + align:start position:0% +difference which connects these two dots +and U you know and the whole big deal of + + align:start position:0% +and U you know and the whole big deal of + + + align:start position:0% +and U you know and the whole big deal of +course is is when you do that as Stephen + + align:start position:0% +course is is when you do that as Stephen + + + align:start position:0% +course is is when you do that as Stephen +explained what's a good Delta right in + + align:start position:0% +explained what's a good Delta right in + + + align:start position:0% +explained what's a good Delta right in +in math you want the Delta to go to zero + + align:start position:0% +in math you want the Delta to go to zero + + + align:start position:0% +in math you want the Delta to go to zero +right that's the very limiting + + align:start position:0% +right that's the very limiting + + + align:start position:0% +right that's the very limiting +definition of a derivative uh um but on + + align:start position:0% +definition of a derivative uh um but on + + + align:start position:0% +definition of a derivative uh um but on +a computer if Delta gets too small as + + align:start position:0% +a computer if Delta gets too small as + + + align:start position:0% +a computer if Delta gets too small as +you've seen you get you you get that + + align:start position:0% +you've seen you get you you get that + + + align:start position:0% +you've seen you get you you get that +catastrophic cancellation happening + + align:start position:0% +catastrophic cancellation happening + + + align:start position:0% +catastrophic cancellation happening +right and so so numerical analysis is + + align:start position:0% +right and so so numerical analysis is + + + align:start position:0% +right and so so numerical analysis is +kind of about what's Delta and Stevens + + align:start position:0% +kind of about what's Delta and Stevens + + + align:start position:0% +kind of about what's Delta and Stevens +basically said that something on the + + align:start position:0% +basically said that something on the + + + align:start position:0% +basically said that something on the +order of 2us 26 which is the square root + + align:start position:0% +order of 2us 26 which is the square root + + + align:start position:0% +order of 2us 26 which is the square root +of double prec precision machine Epsilon + + align:start position:0% +of double prec precision machine Epsilon + + + align:start position:0% +of double prec precision machine Epsilon +is is is is you know A good rule of + + align:start position:0% +is is is is you know A good rule of + + + align:start position:0% +is is is is you know A good rule of +thumb um where you know you might + + align:start position:0% +thumb um where you know you might + + + align:start position:0% +thumb um where you know you might +remember that curve where the error went + + align:start position:0% +remember that curve where the error went + + + align:start position:0% +remember that curve where the error went +down like an absolute value sign um as + + align:start position:0% +down like an absolute value sign um as + + + align:start position:0% +down like an absolute value sign um as +it got smaller and then it went up again + + align:start position:0% +it got smaller and then it went up again + + + align:start position:0% +it got smaller and then it went up again +and you know one the best one was at the + + align:start position:0% +and you know one the best one was at the + + + align:start position:0% +and you know one the best one was at the +bottom right that's the best Delta X but + + align:start position:0% +bottom right that's the best Delta X but + + + align:start position:0% +bottom right that's the best Delta X but +the key thing that's interesting is that + + align:start position:0% +the key thing that's interesting is that + + + align:start position:0% +the key thing that's interesting is that +automatic differentiation is not this + + align:start position:0% +automatic differentiation is not this + + + align:start position:0% +automatic differentiation is not this +and it's not that right and like so what + + align:start position:0% +and it's not that right and like so what + + + align:start position:0% +and it's not that right and like so what +could it be right and the way I like to + + align:start position:0% +could it be right and the way I like to + + + align:start position:0% +could it be right and the way I like to +show people of what it is + + align:start position:0% +show people of what it is + + + align:start position:0% +show people of what it is +and um is I like to start with a simple + + align:start position:0% +and um is I like to start with a simple + + + align:start position:0% +and um is I like to start with a simple +example of it in action right and this + + align:start position:0% +example of it in action right and this + + + align:start position:0% +example of it in action right and this +is where at first it's going to look + + align:start position:0% +is where at first it's going to look + + + align:start position:0% +is where at first it's going to look +like magic right nothing up my sleeve + + align:start position:0% +like magic right nothing up my sleeve + + + align:start position:0% +like magic right nothing up my sleeve +and then I will explain to you how it + + align:start position:0% +and then I will explain to you how it + + + align:start position:0% +and then I will explain to you how it +worked so I'm going to take one of the + + align:start position:0% +worked so I'm going to take one of the + + + align:start position:0% +worked so I'm going to take one of the +oldest algorithms you know one of the + + align:start position:0% +oldest algorithms you know one of the + + + align:start position:0% +oldest algorithms you know one of the +oldest interesting algorithms known to + + align:start position:0% +oldest interesting algorithms known to + + + align:start position:0% +oldest interesting algorithms known to +mankind um the Babylonian square root + + align:start position:0% +mankind um the Babylonian square root + + + align:start position:0% +mankind um the Babylonian square root +algorithm which I think maybe you've all + + align:start position:0% +algorithm which I think maybe you've all + + + align:start position:0% +algorithm which I think maybe you've all +seen But if you haven't you start with a + + align:start position:0% +seen But if you haven't you start with a + + + align:start position:0% +seen But if you haven't you start with a +guess T to square < TK of X right so + + align:start position:0% +guess T to square < TK of X right so + + + align:start position:0% +guess T to square < TK of X right so +I've got a t which I'm hoping is is + + align:start position:0% +I've got a t which I'm hoping is is + + + align:start position:0% +I've got a t which I'm hoping is is +close to square root of x now may right + + align:start position:0% +close to square root of x now may right + + + align:start position:0% +close to square root of x now may right +and if I take T and X over T right if T + + align:start position:0% +and if I take T and X over T right if T + + + align:start position:0% +and if I take T and X over T right if T +was too small X over T of course will be + + align:start position:0% +was too small X over T of course will be + + + align:start position:0% +was too small X over T of course will be +too will be kind of on the large side + + align:start position:0% +too will be kind of on the large side + + + align:start position:0% +too will be kind of on the large side +right if if T was a guess it's LGE + + align:start position:0% +right if if T was a guess it's LGE + + + align:start position:0% +right if if T was a guess it's LGE +between T and X over T one's one's one's + + align:start position:0% +between T and X over T one's one's one's + + + align:start position:0% +between T and X over T one's one's one's +on the large side one's on the small + + align:start position:0% +on the large side one's on the small + + + align:start position:0% +on the large side one's on the small +side so why don't we just take the + + align:start position:0% +side so why don't we just take the + + + align:start position:0% +side so why don't we just take the +average right and then this is something + + align:start position:0% +average right and then this is something + + + align:start position:0% +average right and then this is something +we could keep doing okay and that's the + + align:start position:0% +we could keep doing okay and that's the + + + align:start position:0% +we could keep doing okay and that's the +Babylonian algorithm to that converges + + align:start position:0% +Babylonian algorithm to that converges + + + align:start position:0% +Babylonian algorithm to that converges +to the square of X okay very simple + + align:start position:0% +to the square of X okay very simple + + + align:start position:0% +to the square of X okay very simple +algorithm you know it was known for + + align:start position:0% +algorithm you know it was known for + + + align:start position:0% +algorithm you know it was known for +thousands of years how complicated you + + align:start position:0% +thousands of years how complicated you + + + align:start position:0% +thousands of years how complicated you +know could it be U but but you know I + + align:start position:0% +know could it be U but but you know I + + + align:start position:0% +know could it be U but but you know I +still think it was pretty clever the + + align:start position:0% +still think it was pretty clever the + + + align:start position:0% +still think it was pretty clever the +Babylonians I mean you know they didn't + + align:start position:0% +Babylonians I mean you know they didn't + + + align:start position:0% +Babylonians I mean you know they didn't +they didn't have Julia I mean you know I + + align:start position:0% +they didn't have Julia I mean you know I + + + align:start position:0% +they didn't have Julia I mean you know I +thought it was pretty clever so in any + + align:start position:0% +thought it was pretty clever so in any + + + align:start position:0% +thought it was pretty clever so in any +event um I'm going to just for + + align:start position:0% +event um I'm going to just for + + + align:start position:0% +event um I'm going to just for +Simplicity sake I'm going to start at + + align:start position:0% +Simplicity sake I'm going to start at + + + align:start position:0% +Simplicity sake I'm going to start at +one for no reason I'm just doing an + + align:start position:0% +one for no reason I'm just doing an + + + align:start position:0% +one for no reason I'm just doing an +example so I'm going to start at at one + + align:start position:0% +example so I'm going to start at at one + + + align:start position:0% +example so I'm going to start at at one +right so I have one and X over one and + + align:start position:0% +right so I have one and X over one and + + + align:start position:0% +right so I have one and X over one and +I'll take the average and then um by + + align:start position:0% +I'll take the average and then um by + + + align:start position:0% +I'll take the average and then um by +default do 10 iterations of of t plus X + + align:start position:0% +default do 10 iterations of of t plus X + + + align:start position:0% +default do 10 iterations of of t plus X +over T over 2 right so you know even if + + align:start position:0% +over T over 2 right so you know even if + + + align:start position:0% +over T over 2 right so you know even if +you don't speak Julia I think this + + align:start position:0% +you don't speak Julia I think this + + + align:start position:0% +you don't speak Julia I think this +algorithm is easy to understand just + + align:start position:0% +algorithm is easy to understand just + + + align:start position:0% +algorithm is easy to understand just +it's a input x and by default we run 10 + + align:start position:0% +it's a input x and by default we run 10 + + + align:start position:0% +it's a input x and by default we run 10 +times but you can give an argument and + + align:start position:0% +times but you can give an argument and + + + align:start position:0% +times but you can give an argument and +make it run more times okay and so uh + + align:start position:0% +make it run more times okay and so uh + + + align:start position:0% +make it run more times okay and so uh +let's go using forward diff and let's + + align:start position:0% +let's go using forward diff and let's + + + align:start position:0% +let's go using forward diff and let's +take the um let's let's let forward let + + align:start position:0% +take the um let's let's let forward let + + + align:start position:0% +take the um let's let's let forward let +let forward diff do it and of course we + + align:start position:0% +let forward diff do it and of course we + + + align:start position:0% +let forward diff do it and of course we +with our modern view of the world we + + align:start position:0% +with our modern view of the world we + + + align:start position:0% +with our modern view of the world we +know how to take square roots right + + align:start position:0% +know how to take square roots right + + + align:start position:0% +know how to take square roots right +everybody in this building everybody in + + align:start position:0% +everybody in this building everybody in + + + align:start position:0% +everybody in this building everybody in +this institute could take the derivative + + align:start position:0% +this institute could take the derivative + + + align:start position:0% +this institute could take the derivative +of square root it's it's 1/2 over over + + align:start position:0% +of square root it's it's 1/2 over over + + + align:start position:0% +of square root it's it's 1/2 over over +the square root and so uh you know we we + + align:start position:0% +the square root and so uh you know we we + + + align:start position:0% +the square root and so uh you know we we +um get the derivative but before we do + + align:start position:0% +um get the derivative but before we do + + + align:start position:0% +um get the derivative but before we do +that let's actually make sure that the + + align:start position:0% +that let's actually make sure that the + + + align:start position:0% +that let's actually make sure that the +code works you know let's actually check + + align:start position:0% +code works you know let's actually check + + + align:start position:0% +code works you know let's actually check +the Babylonian algorithm that I wrote so + + align:start position:0% +the Babylonian algorithm that I wrote so + + + align:start position:0% +the Babylonian algorithm that I wrote so +here's the the second one is Julia's + + align:start position:0% +here's the the second one is Julia's + + + align:start position:0% +here's the the second one is Julia's +built in square root of Pi and here's + + align:start position:0% +built in square root of Pi and here's + + + align:start position:0% +built in square root of Pi and here's +the Babylonian calculating the square Ro + + align:start position:0% +the Babylonian calculating the square Ro + + + align:start position:0% +the Babylonian calculating the square Ro +of Pi and I guess this is pretty + + align:start position:0% +of Pi and I guess this is pretty + + + align:start position:0% +of Pi and I guess this is pretty +convincing that the Babylonians knew + + align:start position:0% +convincing that the Babylonians knew + + + align:start position:0% +convincing that the Babylonians knew +what they were doing right I mean we + + align:start position:0% +what they were doing right I mean we + + + align:start position:0% +what they were doing right I mean we +could do the same thing with two could + + align:start position:0% +could do the same thing with two could + + + align:start position:0% +could do the same thing with two could +run the Babylonian algorithm except for + + align:start position:0% +run the Babylonian algorithm except for + + + align:start position:0% +run the Babylonian algorithm except for +some little bit over here you know uh + + align:start position:0% +some little bit over here you know uh + + + align:start position:0% +some little bit over here you know uh +maybe the last bit we basically get the + + align:start position:0% +maybe the last bit we basically get the + + + align:start position:0% +maybe the last bit we basically get the +same answer with Julia's built-in square + + align:start position:0% +same answer with Julia's built-in square + + + align:start position:0% +same answer with Julia's built-in square +root and the Babylonian algorithm okay + + align:start position:0% +root and the Babylonian algorithm okay + + + align:start position:0% +root and the Babylonian algorithm okay +and um let's let's let's skip this for a + + align:start position:0% +and um let's let's let's skip this for a + + + align:start position:0% +and um let's let's let's skip this for a +minute okay and + + align:start position:0% +minute okay and + + + align:start position:0% +minute okay and +um I think that's not important so um + + align:start position:0% +um I think that's not important so um + + + align:start position:0% +um I think that's not important so um +just checking the algorithm for the + + align:start position:0% +just checking the algorithm for the + + + align:start position:0% +just checking the algorithm for the +moment not even the + + align:start position:0% +moment not even the + + + align:start position:0% +moment not even the +derivative + + align:start position:0% +derivative + + + align:start position:0% +derivative +so I'm going to I'm actually going to + + align:start position:0% +so I'm going to I'm actually going to + + + align:start position:0% +so I'm going to I'm actually going to +plot the a few iterates of the bonian + + align:start position:0% +plot the a few iterates of the bonian + + + align:start position:0% +plot the a few iterates of the bonian +algorithm just so you can see so the + + align:start position:0% +algorithm just so you can see so the + + + align:start position:0% +algorithm just so you can see so the +first iteration maybe remember was 1 + + align:start position:0% +first iteration maybe remember was 1 + + + align:start position:0% +first iteration maybe remember was 1 +plus X over2 right it's a I still want + + align:start position:0% +plus X over2 right it's a I still want + + + align:start position:0% +plus X over2 right it's a I still want +to call this a linear function but in + + align:start position:0% +to call this a linear function but in + + + align:start position:0% +to call this a linear function but in +this class I have to call it an apine + + align:start position:0% +this class I have to call it an apine + + + align:start position:0% +this class I have to call it an apine +function um yeah I don't know what the + + align:start position:0% +function um yeah I don't know what the + + + align:start position:0% +function um yeah I don't know what the +real terminology is when when do I get + + align:start position:0% +real terminology is when when do I get + + + align:start position:0% +real terminology is when when do I get +to say that a first-degree polinomial is + + align:start position:0% +to say that a first-degree polinomial is + + + align:start position:0% +to say that a first-degree polinomial is +a linear + + align:start position:0% +a linear + + + align:start position:0% +a linear +function um I think there's a context as + + align:start position:0% +function um I think there's a context as + + + align:start position:0% +function um I think there's a context as +as to whether I'm calling it a map or a + + align:start position:0% +as to whether I'm calling it a map or a + + + align:start position:0% +as to whether I'm calling it a map or a +function right but any event this + + align:start position:0% +function right but any event this + + + align:start position:0% +function right but any event this +thing's a line however you want to call + + align:start position:0% +thing's a line however you want to call + + + align:start position:0% +thing's a line however you want to call +it right the the first step of the babon + + align:start position:0% +it right the the first step of the babon + + + align:start position:0% +it right the the first step of the babon +algorithm iteration one is given X + + align:start position:0% +algorithm iteration one is given X + + + align:start position:0% +algorithm iteration one is given X +compute 1 plus x / two and and that's a + + align:start position:0% +compute 1 plus x / two and and that's a + + + align:start position:0% +compute 1 plus x / two and and that's a +first deegree function right um the + + align:start position:0% +first deegree function right um the + + + align:start position:0% +first deegree function right um the +second iteration I'm plotting it um is + + align:start position:0% +second iteration I'm plotting it um is + + + align:start position:0% +second iteration I'm plotting it um is +here right and then it gets closer and + + align:start position:0% +here right and then it gets closer and + + + align:start position:0% +here right and then it gets closer and +closer to the sideways Parabola which of + + align:start position:0% +closer to the sideways Parabola which of + + + align:start position:0% +closer to the sideways Parabola which of +course is the square root in fact by + + align:start position:0% +course is the square root in fact by + + + align:start position:0% +course is the square root in fact by +iteration five you can't even see much + + align:start position:0% +iteration five you can't even see much + + + align:start position:0% +iteration five you can't even see much +of a difference with your eye right so + + align:start position:0% +of a difference with your eye right so + + + align:start position:0% +of a difference with your eye right so +iteration four is the purple and + + align:start position:0% +iteration four is the purple and + + + align:start position:0% +iteration four is the purple and +iteration five you can't even see it + + align:start position:0% +iteration five you can't even see it + + + align:start position:0% +iteration five you can't even see it +because the the the black parabolas on + + align:start position:0% +because the the the black parabolas on + + + align:start position:0% +because the the the black parabolas on +top of it right and so just to kind of + + align:start position:0% +top of it right and so just to kind of + + + align:start position:0% +top of it right and so just to kind of +convince you that the Babylonian + + align:start position:0% +convince you that the Babylonian + + + align:start position:0% +convince you that the Babylonian +algorithm works and anyway I like plotly + + align:start position:0% +algorithm works and anyway I like plotly + + + align:start position:0% +algorithm works and anyway I like plotly +I love doing this all day I can go left + + align:start position:0% +I love doing this all day I can go left + + + align:start position:0% +I love doing this all day I can go left +and right and look at these numbers I + + align:start position:0% +and right and look at these numbers I + + + align:start position:0% +and right and look at these numbers I +love this so I like interactive things + + align:start position:0% +love this so I like interactive things + + + align:start position:0% +love this so I like interactive things +okay now um now what I'm going to do is + + align:start position:0% +okay now um now what I'm going to do is + + + align:start position:0% +okay now um now what I'm going to do is +in let me see how many how many Ru how I + + align:start position:0% +in let me see how many how many Ru how I + + + align:start position:0% +in let me see how many how many Ru how I +changed this over the years so three + + align:start position:0% +changed this over the years so three + + + align:start position:0% +changed this over the years so three +four five six in about nine lines I'm + + align:start position:0% +four five six in about nine lines I'm + + + align:start position:0% +four five six in about nine lines I'm +going to create a function that will + + align:start position:0% +going to create a function that will + + + align:start position:0% +going to create a function that will +calculate the derivative of the + + align:start position:0% +calculate the derivative of the + + + align:start position:0% +calculate the derivative of the +Babylonian algorithm and nowhere will I + + align:start position:0% +Babylonian algorithm and nowhere will I + + + align:start position:0% +Babylonian algorithm and nowhere will I +teach it like that like 12 over the otk + + align:start position:0% +teach it like that like 12 over the otk + + + align:start position:0% +teach it like that like 12 over the otk +of X right I will not do that I won't + + align:start position:0% +of X right I will not do that I won't + + + align:start position:0% +of X right I will not do that I won't +you'll see there'll be no finite + + align:start position:0% +you'll see there'll be no finite + + + align:start position:0% +you'll see there'll be no finite +differences and I there will be no + + align:start position:0% +differences and I there will be no + + + align:start position:0% +differences and I there will be no +symbolic like I'm not and it's it's + + align:start position:0% +symbolic like I'm not and it's it's + + + align:start position:0% +symbolic like I'm not and it's it's +going to be by Magic but we're going to + + align:start position:0% +going to be by Magic but we're going to + + + align:start position:0% +going to be by Magic but we're going to +get the right answer so you ready so I'm + + align:start position:0% +get the right answer so you ready so I'm + + + align:start position:0% +get the right answer so you ready so I'm +going to do it in nine lines um so the + + align:start position:0% +going to do it in nine lines um so the + + + align:start position:0% +going to do it in nine lines um so the +here's three lines I'm going to create a + + align:start position:0% +here's three lines I'm going to create a + + + align:start position:0% +here's three lines I'm going to create a +um Julia type I'm going to call it + + align:start position:0% +um Julia type I'm going to call it + + + align:start position:0% +um Julia type I'm going to call it +capital D um later on maybe some of you + + align:start position:0% +capital D um later on maybe some of you + + + align:start position:0% +capital D um later on maybe some of you +have heard this word d is for dual + + align:start position:0% +have heard this word d is for dual + + + align:start position:0% +have heard this word d is for dual +number so that's why we're going to call + + align:start position:0% +number so that's why we're going to call + + + align:start position:0% +number so that's why we're going to call +it use the D and um we're basically + + align:start position:0% +it use the D and um we're basically + + + align:start position:0% +it use the D and um we're basically +going to keep a function derivative pair + + align:start position:0% +going to keep a function derivative pair + + + align:start position:0% +going to keep a function derivative pair +an ordered pair um and so this is + + align:start position:0% +an ordered pair um and so this is + + + align:start position:0% +an ordered pair um and so this is +nothing but a a container uh to to be + + align:start position:0% +nothing but a a container uh to to be + + + align:start position:0% +nothing but a a container uh to to be +able to to keep two floats right but + + align:start position:0% +able to to keep two floats right but + + + align:start position:0% +able to to keep two floats right but +which floats am I going to keep I'm + + align:start position:0% +which floats am I going to keep I'm + + + align:start position:0% +which floats am I going to keep I'm +going to I'm going to have the value of + + align:start position:0% +going to I'm going to have the value of + + + align:start position:0% +going to I'm going to have the value of +a function at a point and the derivative + + align:start position:0% +a function at a point and the derivative + + + align:start position:0% +a function at a point and the derivative +of that function at a point all right + + align:start position:0% +of that function at a point all right + + + align:start position:0% +of that function at a point all right +I've used up three of my nine lines and + + align:start position:0% +I've used up three of my nine lines and + + + align:start position:0% +I've used up three of my nine lines and +everybody agrees there's no finite + + align:start position:0% +everybody agrees there's no finite + + + align:start position:0% +everybody agrees there's no finite +difference no no symbolic answer right + + align:start position:0% +difference no no symbolic answer right + + + align:start position:0% +difference no no symbolic answer right +so I've got six more lines here oh here + + align:start position:0% +so I've got six more lines here oh here + + + align:start position:0% +so I've got six more lines here oh here +this + + align:start position:0% +this + + + align:start position:0% +this +is U yeah let let me just show you what + + align:start position:0% +is U yeah let let me just show you what + + + align:start position:0% +is U yeah let let me just show you what +I've done here before I do anything else + + align:start position:0% +I've done here before I do anything else + + + align:start position:0% +I've done here before I do anything else +so if I wanted to uh if I want to create + + align:start position:0% +so if I wanted to uh if I want to create + + + align:start position:0% +so if I wanted to uh if I want to create +one of these objects so um I would have + + align:start position:0% +one of these objects so um I would have + + + align:start position:0% +one of these objects so um I would have +to put in a tuple like d of12 this line + + align:start position:0% +to put in a tuple like d of12 this line + + + align:start position:0% +to put in a tuple like d of12 this line +um lets me remove the parentheses which + + align:start position:0% +um lets me remove the parentheses which + + + align:start position:0% +um lets me remove the parentheses which +are sort of I just find them annoying so + + align:start position:0% +are sort of I just find them annoying so + + + align:start position:0% +are sort of I just find them annoying so +this this line doesn't count but you see + + align:start position:0% +this this line doesn't count but you see + + + align:start position:0% +this this line doesn't count but you see +I've got this this dual number it + + align:start position:0% +I've got this this dual number it + + + align:start position:0% +I've got this this dual number it +doesn't do anything yet right I can't I + + align:start position:0% +doesn't do anything yet right I can't I + + + align:start position:0% +doesn't do anything yet right I can't I +can't add dual numbers yet if I try it + + align:start position:0% +can't add dual numbers yet if I try it + + + align:start position:0% +can't add dual numbers yet if I try it +gets mad at me look plus not defined all + + align:start position:0% +gets mad at me look plus not defined all + + + align:start position:0% +gets mad at me look plus not defined all +I can do is Define a dual number that's + + align:start position:0% +I can do is Define a dual number that's + + + align:start position:0% +I can do is Define a dual number that's +it it's just a pair of numbers okay + + align:start position:0% +it it's just a pair of numbers okay + + + align:start position:0% +it it's just a pair of numbers okay +can't do anything at all with it right + + align:start position:0% +can't do anything at all with it right + + + align:start position:0% +can't do anything at all with it right +um other than store it right um but here + + align:start position:0% +um other than store it right um but here + + + align:start position:0% +um other than store it right um but here +what I'm going to do is create a few oh + + align:start position:0% +what I'm going to do is create a few oh + + + align:start position:0% +what I'm going to do is create a few oh +I don't need this greater than that's + + align:start position:0% +I don't need this greater than that's + + + align:start position:0% +I don't need this greater than that's +why I could have one F line you know I'm + + align:start position:0% +why I could have one F line you know I'm + + + align:start position:0% +why I could have one F line you know I'm +going to comment this one out I think + + align:start position:0% +going to comment this one out I think + + + align:start position:0% +going to comment this one out I think +somebody once asked me you know to find + + align:start position:0% +somebody once asked me you know to find + + + align:start position:0% +somebody once asked me you know to find +it for greater but yeah I don't need + + align:start position:0% +it for greater but yeah I don't need + + + align:start position:0% +it for greater but yeah I don't need +this line so I'm actually going to have + + align:start position:0% +this line so I'm actually going to have + + + align:start position:0% +this line so I'm actually going to have +3 + 5 eight + + align:start position:0% +3 + 5 eight + + + align:start position:0% +3 + 5 eight +lines okay so let me tell you about + + align:start position:0% +lines okay so let me tell you about + + + align:start position:0% +lines okay so let me tell you about +these next five lines mainly I want to + + align:start position:0% +these next five lines mainly I want to + + + align:start position:0% +these next five lines mainly I want to +Define add and divide on a dual number I + + align:start position:0% +Define add and divide on a dual number I + + + align:start position:0% +Define add and divide on a dual number I +don't need minus and and times yet + + align:start position:0% +don't need minus and and times yet + + + align:start position:0% +don't need minus and and times yet +because if you look at my Babylonian + + align:start position:0% +because if you look at my Babylonian + + + align:start position:0% +because if you look at my Babylonian +algorithm if you remember the algorithm + + align:start position:0% +algorithm if you remember the algorithm + + + align:start position:0% +algorithm if you remember the algorithm +where's the Babylonian algorithm I do a + + align:start position:0% +where's the Babylonian algorithm I do a + + + align:start position:0% +where's the Babylonian algorithm I do a +plus and a divide and nothing more okay + + align:start position:0% +plus and a divide and nothing more okay + + + align:start position:0% +plus and a divide and nothing more okay +so for now later on I'll add times and + + align:start position:0% +so for now later on I'll add times and + + + align:start position:0% +so for now later on I'll add times and +minus but I don't need it yet so uh I + + align:start position:0% +minus but I don't need it yet so uh I + + + align:start position:0% +minus but I don't need it yet so uh I +want to Def find a Define a plus and a + + align:start position:0% +want to Def find a Define a plus and a + + + align:start position:0% +want to Def find a Define a plus and a +divide so in Julia I don't need this one + + align:start position:0% +divide so in Julia I don't need this one + + + align:start position:0% +divide so in Julia I don't need this one +either this this thing could go away in + + align:start position:0% +either this this thing could go away in + + + align:start position:0% +either this this thing could go away in +Julia if you want to overload plus and + + align:start position:0% +Julia if you want to overload plus and + + + align:start position:0% +Julia if you want to overload plus and +divide and a few other things you have + + align:start position:0% +divide and a few other things you have + + + align:start position:0% +divide and a few other things you have +to import it from bass right so this is + + align:start position:0% +to import it from bass right so this is + + + align:start position:0% +to import it from bass right so this is +a this is just like a Julia detail thing + + align:start position:0% +a this is just like a Julia detail thing + + + align:start position:0% +a this is just like a Julia detail thing +that says give me permission to redefine + + align:start position:0% +that says give me permission to redefine + + + align:start position:0% +that says give me permission to redefine +plus right and divide and a few other + + align:start position:0% +plus right and divide and a few other + + + align:start position:0% +plus right and divide and a few other +things and what do I want to do when I + + align:start position:0% +things and what do I want to do when I + + + align:start position:0% +things and what do I want to do when I +plus a couple of dual numbers here let's + + align:start position:0% +plus a couple of dual numbers here let's + + + align:start position:0% +plus a couple of dual numbers here let's +let's just let me just do this one only + + align:start position:0% +let's just let me just do this one only + + + align:start position:0% +let's just let me just do this one only +just so you see I'll I'll execute only + + align:start position:0% +just so you see I'll I'll execute only + + + align:start position:0% +just so you see I'll I'll execute only +the plus okay now I can add dual numbers + + align:start position:0% +the plus okay now I can add dual numbers + + + align:start position:0% +the plus okay now I can add dual numbers +and I it's just going to be like adding + + align:start position:0% +and I it's just going to be like adding + + + align:start position:0% +and I it's just going to be like adding +vectors right so I'm just going to add + + align:start position:0% +vectors right so I'm just going to add + + + align:start position:0% +vectors right so I'm just going to add +the first uh element of the Tuple two + + align:start position:0% +the first uh element of the Tuple two + + + align:start position:0% +the first uh element of the Tuple two +and three and the second element okay so + + align:start position:0% +and three and the second element okay so + + + align:start position:0% +and three and the second element okay so +now I can add tupal but I can't divide + + align:start position:0% +now I can add tupal but I can't divide + + + align:start position:0% +now I can add tupal but I can't divide +them yet right so this this dot notation + + align:start position:0% +them yet right so this this dot notation + + + align:start position:0% +them yet right so this this dot notation +this broadcast or pointwise notation + + align:start position:0% +this broadcast or pointwise notation + + + align:start position:0% +this broadcast or pointwise notation +says to that um that that basically um + + align:start position:0% +says to that um that that basically um + + + align:start position:0% +says to that um that that basically um +add the the the two the two parts of X + + align:start position:0% +add the the the two the two parts of X + + + align:start position:0% +add the the the two the two parts of X +and the two parts of Y like a vector + + align:start position:0% +and the two parts of Y like a vector + + + align:start position:0% +and the two parts of Y like a vector +okay so this adds two and three to get + + align:start position:0% +okay so this adds two and three to get + + + align:start position:0% +okay so this adds two and three to get +five and three and four to seven all + + align:start position:0% +five and three and four to seven all + + + align:start position:0% +five and three and four to seven all +right now let me bring in the Divide I + + align:start position:0% +right now let me bring in the Divide I + + + align:start position:0% +right now let me bring in the Divide I +can't divide yet by the way I could try + + align:start position:0% +can't divide yet by the way I could try + + + align:start position:0% +can't divide yet by the way I could try +but it'll get mad at me you see oh did I + + align:start position:0% +but it'll get mad at me you see oh did I + + + align:start position:0% +but it'll get mad at me you see oh did I +I must have executed it oh did I execute + + align:start position:0% +I must have executed it oh did I execute + + + align:start position:0% +I must have executed it oh did I execute +it I'm sorry then I took away my well + + align:start position:0% +it I'm sorry then I took away my well + + + align:start position:0% +it I'm sorry then I took away my well +whatever all right I guess I must have + + align:start position:0% +whatever all right I guess I must have + + + align:start position:0% +whatever all right I guess I must have +executed it so I'm not getting away with + + align:start position:0% +executed it so I'm not getting away with + + + align:start position:0% +executed it so I'm not getting away with +it but here it doesn't matter so uh here + + align:start position:0% +it but here it doesn't matter so uh here + + + align:start position:0% +it but here it doesn't matter so uh here +it's this is 2id 3 is 2 thir but notice + + align:start position:0% +it's this is 2id 3 is 2 thir but notice + + + align:start position:0% +it's this is 2id 3 is 2 thir but notice +this isn't 3 / 4 right so I have a + + align:start position:0% +this isn't 3 / 4 right so I have a + + + align:start position:0% +this isn't 3 / 4 right so I have a +different rule for so the the add rule + + align:start position:0% +different rule for so the the add rule + + + align:start position:0% +different rule for so the the add rule +is just adding up like like a vector but + + align:start position:0% +is just adding up like like a vector but + + + align:start position:0% +is just adding up like like a vector but +the Divide rule is a little more + + align:start position:0% +the Divide rule is a little more + + + align:start position:0% +the Divide rule is a little more +complicated by the way Alan did you want + + align:start position:0% +complicated by the way Alan did you want + + + align:start position:0% +complicated by the way Alan did you want +to share your screen on Zoom I forgot + + align:start position:0% +to share your screen on Zoom I forgot + + + align:start position:0% +to share your screen on Zoom I forgot +about oh my gosh I didn't share my + + align:start position:0% +about oh my gosh I didn't share my + + + align:start position:0% +about oh my gosh I didn't share my +screen so you don't see a thing I've + + align:start position:0% +screen so you don't see a thing I've + + + align:start position:0% +screen so you don't see a thing I've +done can I can see it behind you on the + + align:start position:0% +done can I can see it behind you on the + + + align:start position:0% +done can I can see it behind you on the +oh that's + + align:start position:0% +oh that's + + + align:start position:0% +oh that's +funny + + align:start position:0% +funny + + + align:start position:0% +funny +okay um there we go all right + + align:start position:0% +okay um there we go all right + + + align:start position:0% +okay um there we go all right +better all right so + + align:start position:0% +better all right so + + + align:start position:0% +better all right so +uh right so divide so so uh everybody of + + align:start position:0% +uh right so divide so so uh everybody of + + + align:start position:0% +uh right so divide so so uh everybody of +course remembers the quotient rule from + + align:start position:0% +course remembers the quotient rule from + + + align:start position:0% +course remembers the quotient rule from +calculous uh when I think of it I hear + + align:start position:0% +calculous uh when I think of it I hear + + + align:start position:0% +calculous uh when I think of it I hear +my my math teacher singing it it wasn't + + align:start position:0% +my my math teacher singing it it wasn't + + + align:start position:0% +my my math teacher singing it it wasn't +just like I mean I'm not like it was + + align:start position:0% +just like I mean I'm not like it was + + + align:start position:0% +just like I mean I'm not like it was +there was like denominator times the Der + + align:start position:0% +there was like denominator times the Der + + + align:start position:0% +there was like denominator times the Der +of the numerator minus the numerator + + align:start position:0% +of the numerator minus the numerator + + + align:start position:0% +of the numerator minus the numerator +time the denominator denominator squared + + align:start position:0% +time the denominator denominator squared + + + align:start position:0% +time the denominator denominator squared +or I don't know did did your teacher + + align:start position:0% +or I don't know did did your teacher + + + align:start position:0% +or I don't know did did your teacher +sing it to you or or how did you sort of + + align:start position:0% +sing it to you or or how did you sort of + + + align:start position:0% +sing it to you or or how did you sort of +memorize the quotient + + align:start position:0% +memorize the quotient + + + align:start position:0% +memorize the quotient +rule anybody have a good song for it + + align:start position:0% +rule anybody have a good song for it + + + align:start position:0% +rule anybody have a good song for it +anyway it's it it it you know you drill + + align:start position:0% +anyway it's it it it you know you drill + + + align:start position:0% +anyway it's it it it you know you drill +it into your head right you know um you + + align:start position:0% +it into your head right you know um you + + + align:start position:0% +it into your head right you know um you +know uh VD minus UV over v^ 2 or or or + + align:start position:0% +know uh VD minus UV over v^ 2 or or or + + + align:start position:0% +know uh VD minus UV over v^ 2 or or or +or you know uh denominator Den numerator + + align:start position:0% +or you know uh denominator Den numerator + + + align:start position:0% +or you know uh denominator Den numerator +I mean I don't know you may have heard + + align:start position:0% +I mean I don't know you may have heard + + + align:start position:0% +I mean I don't know you may have heard +it different ways but you all know it + + align:start position:0% +it different ways but you all know it + + + align:start position:0% +it different ways but you all know it +right YX you know this thing over here + + align:start position:0% +right YX you know this thing over here + + + align:start position:0% +right YX you know this thing over here +the quo rule everybody knows it and so + + align:start position:0% +the quo rule everybody knows it and so + + + align:start position:0% +the quo rule everybody knows it and so +uh this the I'm just extracting the + + align:start position:0% +uh this the I'm just extracting the + + + align:start position:0% +uh this the I'm just extracting the +parts from so so so um why is the + + align:start position:0% +parts from so so so um why is the + + + align:start position:0% +parts from so so so um why is the +denominator and so this is one is is the + + align:start position:0% +denominator and so this is one is is the + + + align:start position:0% +denominator and so this is one is is the +value right so so so this is the + + align:start position:0% +value right so so so this is the + + + align:start position:0% +value right so so so this is the +denominator right X is the numerator so + + align:start position:0% +denominator right X is the numerator so + + + align:start position:0% +denominator right X is the numerator so +this is the and and two is the + + align:start position:0% +this is the and and two is the + + + align:start position:0% +this is the and and two is the +derivative so it's the denominator time + + align:start position:0% +derivative so it's the denominator time + + + align:start position:0% +derivative so it's the denominator time +the of the numerator minus the numerator + + align:start position:0% +the of the numerator minus the numerator + + + align:start position:0% +the of the numerator minus the numerator +time the of denominator over the + + align:start position:0% +time the of denominator over the + + + align:start position:0% +time the of denominator over the +denominator squared okay so that is what + + align:start position:0% +denominator squared okay so that is what + + + align:start position:0% +denominator squared okay so that is what +I'm going to teach I'm I'm going to + + align:start position:0% +I'm going to teach I'm I'm going to + + + align:start position:0% +I'm going to teach I'm I'm going to +teach Julia how to essentially add + + align:start position:0% +teach Julia how to essentially add + + + align:start position:0% +teach Julia how to essentially add +derivatives which is just add and how to + + align:start position:0% +derivatives which is just add and how to + + + align:start position:0% +derivatives which is just add and how to +divide derivatives which is just you + + align:start position:0% +divide derivatives which is just you + + + align:start position:0% +divide derivatives which is just you +know the the formula you know just apply + + align:start position:0% +know the the formula you know just apply + + + align:start position:0% +know the the formula you know just apply +it at a point right and so this this + + align:start position:0% +it at a point right and so this this + + + align:start position:0% +it at a point right and so this this +division is using all four numbers so + + align:start position:0% +division is using all four numbers so + + + align:start position:0% +division is using all four numbers so +that I can get the denominator times the + + align:start position:0% +that I can get the denominator times the + + + align:start position:0% +that I can get the denominator times the +deriva of the numerator minus the + + align:start position:0% +deriva of the numerator minus the + + + align:start position:0% +deriva of the numerator minus the +numerator time the deriva of the + + align:start position:0% +numerator time the deriva of the + + + align:start position:0% +numerator time the deriva of the +denominator over the denominator squared + + align:start position:0% +denominator over the denominator squared + + + align:start position:0% +denominator over the denominator squared +you see okay and that's what this 1 nth + + align:start position:0% +you see okay and that's what this 1 nth + + + align:start position:0% +you see okay and that's what this 1 nth +is all right that's it just these just + + align:start position:0% +is all right that's it just these just + + + align:start position:0% +is all right that's it just these just +these three plus what did I say three + + align:start position:0% +these three plus what did I say three + + + align:start position:0% +these three plus what did I say three +plus oh I haven't told you about convert + + align:start position:0% +plus oh I haven't told you about convert + + + align:start position:0% +plus oh I haven't told you about convert +and promote these are a little bit more + + align:start position:0% +and promote these are a little bit more + + + align:start position:0% +and promote these are a little bit more +sort of technical details but do you + + align:start position:0% +sort of technical details but do you + + + align:start position:0% +sort of technical details but do you +know how uh if you add a complex number + + align:start position:0% +know how uh if you add a complex number + + + align:start position:0% +know how uh if you add a complex number +in a real right like if you go 3 + 4 I + + align:start position:0% +in a real right like if you go 3 + 4 I + + + align:start position:0% +in a real right like if you go 3 + 4 I +and you add seven right now um what's + + align:start position:0% +and you add seven right now um what's + + + align:start position:0% +and you add seven right now um what's +really going on is that that seven in + + align:start position:0% +really going on is that that seven in + + + align:start position:0% +really going on is that that seven in +some abstract sense is being converted + + align:start position:0% +some abstract sense is being converted + + + align:start position:0% +some abstract sense is being converted +into 7 plus 0 I right and then you add + + align:start position:0% +into 7 plus 0 I right and then you add + + + align:start position:0% +into 7 plus 0 I right and then you add +the real parts and the imaginary parts + + align:start position:0% +the real parts and the imaginary parts + + + align:start position:0% +the real parts and the imaginary parts +right everybody does that all the time + + align:start position:0% +right everybody does that all the time + + + align:start position:0% +right everybody does that all the time +right so we want to do that sort of + + align:start position:0% +right so we want to do that sort of + + + align:start position:0% +right so we want to do that sort of +thing where um if if if you have a real + + align:start position:0% +thing where um if if if you have a real + + + align:start position:0% +thing where um if if if you have a real +number we want to think of it you know + + align:start position:0% +number we want to think of it you know + + + align:start position:0% +number we want to think of it you know +if you have a scaler we want in in + + align:start position:0% +if you have a scaler we want in in + + + align:start position:0% +if you have a scaler we want in in +effect you know a constant is really + + align:start position:0% +effect you know a constant is really + + + align:start position:0% +effect you know a constant is really +what's going on here we want to think of + + align:start position:0% +what's going on here we want to think of + + + align:start position:0% +what's going on here we want to think of +this as as as the constant X where the + + align:start position:0% +this as as as the constant X where the + + + align:start position:0% +this as as as the constant X where the +value is X and the derivative is zero + + align:start position:0% +value is X and the derivative is zero + + + align:start position:0% +value is X and the derivative is zero +right and we want that to be kind of + + align:start position:0% +right and we want that to be kind of + + + align:start position:0% +right and we want that to be kind of +automatic because it would be nuisance + + align:start position:0% +automatic because it would be nuisance + + + align:start position:0% +automatic because it would be nuisance +to type it all the time so that's what + + align:start position:0% +to type it all the time so that's what + + + align:start position:0% +to type it all the time so that's what +that does and then the promote rule says + + align:start position:0% +that does and then the promote rule says + + + align:start position:0% +that does and then the promote rule says +that if you give it a number um you + + align:start position:0% +that if you give it a number um you + + + align:start position:0% +that if you give it a number um you +should you know when you're doing when + + align:start position:0% +should you know when you're doing when + + + align:start position:0% +should you know when you're doing when +you when you see it in the context of a + + align:start position:0% +you when you see it in the context of a + + + align:start position:0% +you when you see it in the context of a +dual number everything should be + + align:start position:0% +dual number everything should be + + + align:start position:0% +dual number everything should be +promoted to the Dual number just like it + + align:start position:0% +promoted to the Dual number just like it + + + align:start position:0% +promoted to the Dual number just like it +happens with complex numbers right where + + align:start position:0% +happens with complex numbers right where + + + align:start position:0% +happens with complex numbers right where +like I said 3 plus 4 I plus a real + + align:start position:0% +like I said 3 plus 4 I plus a real + + + align:start position:0% +like I said 3 plus 4 I plus a real +number you would add you know you'd put + + align:start position:0% +number you would add you know you'd put + + + align:start position:0% +number you would add you know you'd put +that zeroi you know in your mind or or + + align:start position:0% +that zeroi you know in your mind or or + + + align:start position:0% +that zeroi you know in your mind or or +or on a computer but you know you would + + align:start position:0% +or on a computer but you know you would + + + align:start position:0% +or on a computer but you know you would +you would promote everything into the + + align:start position:0% +you would promote everything into the + + + align:start position:0% +you would promote everything into the +complex land and then do the addition + + align:start position:0% +complex land and then do the addition + + + align:start position:0% +complex land and then do the addition +okay so that those are two necessary + + align:start position:0% +okay so that those are two necessary + + + align:start position:0% +okay so that those are two necessary +things and um and now let me go ahead + + align:start position:0% +things and um and now let me go ahead + + + align:start position:0% +things and um and now let me go ahead +and run the Babylonian algorithm and I + + align:start position:0% +and run the Babylonian algorithm and I + + + align:start position:0% +and run the Babylonian algorithm and I +am without changing the algorithm + + align:start position:0% +am without changing the algorithm + + + align:start position:0% +am without changing the algorithm +remember the algorithm takes a scaler in + + align:start position:0% +remember the algorithm takes a scaler in + + + align:start position:0% +remember the algorithm takes a scaler in +let's see it again let's find it the + + align:start position:0% +let's see it again let's find it the + + + align:start position:0% +let's see it again let's find it the +Babylonian algorithm which is up here it + + align:start position:0% +Babylonian algorithm which is up here it + + + align:start position:0% +Babylonian algorithm which is up here it +takes a scaler I'm not going to rewrite + + align:start position:0% +takes a scaler I'm not going to rewrite + + + align:start position:0% +takes a scaler I'm not going to rewrite +the algorithm I'm just going to feed it + + align:start position:0% +the algorithm I'm just going to feed it + + + align:start position:0% +the algorithm I'm just going to feed it +something new something different from a + + align:start position:0% +something new something different from a + + + align:start position:0% +something new something different from a +scalar I'm going to feed it a dual + + align:start position:0% + + + + align:start position:0% + +number and so let's do it uh where did + + align:start position:0% +number and so let's do it uh where did + + + align:start position:0% +number and so let's do it uh where did +it happen here so um so I'm I'm feeding + + align:start position:0% +it happen here so um so I'm I'm feeding + + + align:start position:0% +it happen here so um so I'm I'm feeding +the Babylonian algorithm 49 comma 1 + + align:start position:0% +the Babylonian algorithm 49 comma 1 + + + align:start position:0% +the Babylonian algorithm 49 comma 1 +right so this is like the uh this is how + + align:start position:0% +right so this is like the uh this is how + + + align:start position:0% +right so this is like the uh this is how +you seed the we'll talk more about + + align:start position:0% +you seed the we'll talk more about + + + align:start position:0% +you seed the we'll talk more about +seeding the start of the story with the + + align:start position:0% +seeding the start of the story with the + + + align:start position:0% +seeding the start of the story with the +number one or if it was matrices it + + align:start position:0% +number one or if it was matrices it + + + align:start position:0% +number one or if it was matrices it +would be the identity and we get the + + align:start position:0% +would be the identity and we get the + + + align:start position:0% +would be the identity and we get the +square root being seven yep that's good + + align:start position:0% +square root being seven yep that's good + + + align:start position:0% +square root being seven yep that's good +square of 49 is 7 right and um and the + + align:start position:0% +square of 49 is 7 right and um and the + + + align:start position:0% +square of 49 is 7 right and um and the +derivative which you know you you all + + align:start position:0% +derivative which you know you you all + + + align:start position:0% +derivative which you know you you all +know Julia teken for us is 12 over the + + align:start position:0% +know Julia teken for us is 12 over the + + + align:start position:0% +know Julia teken for us is 12 over the +squ of X is this number right here right + + align:start position:0% +squ of X is this number right here right + + + align:start position:0% +squ of X is this number right here right +so um so so uh you know what whatever + + align:start position:0% +so um so so uh you know what whatever + + + align:start position:0% +so um so so uh you know what whatever +1/2 over 7 is you know 114th or + + align:start position:0% +1/2 over 7 is you know 114th or + + + align:start position:0% +1/2 over 7 is you know 114th or +something right so this is the number + + align:start position:0% +something right so this is the number + + + align:start position:0% +something right so this is the number +114th right and I you know you should be + + align:start position:0% +114th right and I you know you should be + + + align:start position:0% +114th right and I you know you should be +astounded by this that that I took an + + align:start position:0% +astounded by this that that I took an + + + align:start position:0% +astounded by this that that I took an +original piece of code without a re + + align:start position:0% +original piece of code without a re + + + align:start position:0% +original piece of code without a re +right and I fit it fed it this funny + + align:start position:0% +right and I fit it fed it this funny + + + align:start position:0% +right and I fit it fed it this funny +kind of argument and all that argument + + align:start position:0% +kind of argument and all that argument + + + align:start position:0% +kind of argument and all that argument +did was no it knew the quotient Rule and + + align:start position:0% +did was no it knew the quotient Rule and + + + align:start position:0% +did was no it knew the quotient Rule and +it knew the sum Rule and I got the right + + align:start position:0% +it knew the sum Rule and I got the right + + + align:start position:0% +it knew the sum Rule and I got the right +answer for the derivative not + + align:start position:0% +answer for the derivative not + + + align:start position:0% +answer for the derivative not +symbolically and not with finite + + align:start position:0% +symbolically and not with finite + + + align:start position:0% +symbolically and not with finite +differences okay it isn't that amazing + + align:start position:0% +differences okay it isn't that amazing + + + align:start position:0% +differences okay it isn't that amazing +like that that's even possible like + + align:start position:0% +like that that's even possible like + + + align:start position:0% +like that that's even possible like +wouldn't that blow your Calculus + + align:start position:0% +wouldn't that blow your Calculus + + + align:start position:0% +wouldn't that blow your Calculus +teacher's mind that this could happen + + align:start position:0% +teacher's mind that this could happen + + + align:start position:0% +teacher's mind that this could happen +right um here's another example where I + + align:start position:0% +right um here's another example where I + + + align:start position:0% +right um here's another example where I +do it with pi just in case seven wasn't + + align:start position:0% +do it with pi just in case seven wasn't + + + align:start position:0% +do it with pi just in case seven wasn't +convincing enough so uh so so this would + + align:start position:0% +convincing enough so uh so so this would + + + align:start position:0% +convincing enough so uh so so this would +be the square root of Pi and um 1 over 2 + + align:start position:0% +be the square root of Pi and um 1 over 2 + + + align:start position:0% +be the square root of Pi and um 1 over 2 +square of Pi and this is the way done + + align:start position:0% +square of Pi and this is the way done + + + align:start position:0% +square of Pi and this is the way done +with Julia and you could check the + + align:start position:0% +with Julia and you could check the + + + align:start position:0% +with Julia and you could check the +numbers you see it it all works um and + + align:start position:0% +numbers you see it it all works um and + + + align:start position:0% +numbers you see it it all works um and +in fact what you can do is actually look + + align:start position:0% +in fact what you can do is actually look + + + align:start position:0% +in fact what you can do is actually look +at what's happening is the Babylon + + align:start position:0% +at what's happening is the Babylon + + + align:start position:0% +at what's happening is the Babylon +algorithm was an + + align:start position:0% +algorithm was an + + + align:start position:0% +algorithm was an +iteration right and so somehow this + + align:start position:0% +iteration right and so somehow this + + + align:start position:0% +iteration right and so somehow this +square root is the result of an + + align:start position:0% +square root is the result of an + + + align:start position:0% +square root is the result of an +iteration we do 10 steps of an iteration + + align:start position:0% +iteration we do 10 steps of an iteration + + + align:start position:0% +iteration we do 10 steps of an iteration +and so um at each time we must be + + align:start position:0% +and so um at each time we must be + + + align:start position:0% +and so um at each time we must be +getting closer and closer to the + + align:start position:0% +getting closer and closer to the + + + align:start position:0% +getting closer and closer to the +derivative to so just like we get closer + + align:start position:0% +derivative to so just like we get closer + + + align:start position:0% +derivative to so just like we get closer +to the square root somehow by feeding + + align:start position:0% +to the square root somehow by feeding + + + align:start position:0% +to the square root somehow by feeding +this in we must be getting closer and + + align:start position:0% +this in we must be getting closer and + + + align:start position:0% +this in we must be getting closer and +closer to the derivative of the square + + align:start position:0% +closer to the derivative of the square + + + align:start position:0% +closer to the derivative of the square +root and in fact um you know I could + + align:start position:0% +root and in fact um you know I could + + + align:start position:0% +root and in fact um you know I could +plot each step of the algorithm so + + align:start position:0% +plot each step of the algorithm so + + + align:start position:0% +plot each step of the algorithm so +remember the first algorithm was first + + align:start position:0% +remember the first algorithm was first + + + align:start position:0% +remember the first algorithm was first +degree I I I still want to say linear + + align:start position:0% +degree I I I still want to say linear + + + align:start position:0% +degree I I I still want to say linear +but I'll say first degree and so its + + align:start position:0% +but I'll say first degree and so its + + + align:start position:0% +but I'll say first degree and so its +derivative of course is a constant right + + align:start position:0% +derivative of course is a constant right + + + align:start position:0% +derivative of course is a constant right +it's just the constant one/ half in fact + + align:start position:0% +it's just the constant one/ half in fact + + + align:start position:0% +it's just the constant one/ half in fact +so uh there it is uh and um and you know + + align:start position:0% +so uh there it is uh and um and you know + + + align:start position:0% +so uh there it is uh and um and you know +here are a couple of iterations and you + + align:start position:0% +here are a couple of iterations and you + + + align:start position:0% +here are a couple of iterations and you +know I also plotted 1/2 of the square of + + align:start position:0% +know I also plotted 1/2 of the square of + + + align:start position:0% +know I also plotted 1/2 of the square of +X the true answer the the you know the + + align:start position:0% +X the true answer the the you know the + + + align:start position:0% +X the true answer the the you know the +the the reciprocal of of the parabola in + + align:start position:0% +the the reciprocal of of the parabola in + + + align:start position:0% +the the reciprocal of of the parabola in +effect and you could see that it's + + align:start position:0% +effect and you could see that it's + + + align:start position:0% +effect and you could see that it's +heading closer and closer and pretty + + align:start position:0% +heading closer and closer and pretty + + + align:start position:0% +heading closer and closer and pretty +quickly the eye can't even see it so uh + + align:start position:0% +quickly the eye can't even see it so uh + + + align:start position:0% +quickly the eye can't even see it so uh +this doesn't explain to you how it works + + align:start position:0% +this doesn't explain to you how it works + + + align:start position:0% +this doesn't explain to you how it works +but maybe it kind of adds to the you + + align:start position:0% +but maybe it kind of adds to the you + + + align:start position:0% +but maybe it kind of adds to the you +know convincing nature of the fact that + + align:start position:0% +know convincing nature of the fact that + + + align:start position:0% +know convincing nature of the fact that +it does work right and it's still + + align:start position:0% +it does work right and it's still + + + align:start position:0% +it does work right and it's still +mysterious um I could say a little bit + + align:start position:0% +mysterious um I could say a little bit + + + align:start position:0% +mysterious um I could say a little bit +more I'm going to tell you how it works + + align:start position:0% +more I'm going to tell you how it works + + + align:start position:0% +more I'm going to tell you how it works +uh but before I do I like to show off a + + align:start position:0% +uh but before I do I like to show off a + + + align:start position:0% +uh but before I do I like to show off a +few things um I don't know how well this + + align:start position:0% +few things um I don't know how well this + + + align:start position:0% +few things um I don't know how well this +works these days but I do like to tell + + align:start position:0% +works these days but I do like to tell + + + align:start position:0% +works these days but I do like to tell +people that in Julia you can see + + align:start position:0% +people that in Julia you can see + + + align:start position:0% +people that in Julia you can see +assembler nobody reads assembler anybody + + align:start position:0% +assembler nobody reads assembler anybody + + + align:start position:0% +assembler nobody reads assembler anybody +here read + + align:start position:0% +here read + + + align:start position:0% +here read +assembler anybody here actually you do + + align:start position:0% +assembler anybody here actually you do + + + align:start position:0% +assembler anybody here actually you do +or have or a little bit one person is + + align:start position:0% +or have or a little bit one person is + + + align:start position:0% +or have or a little bit one person is +willing to admit that they do it a + + align:start position:0% +willing to admit that they do it a + + + align:start position:0% +willing to admit that they do it a +little bit um some computer science + + align:start position:0% +little bit um some computer science + + + align:start position:0% +little bit um some computer science +classes at MIT teach you this stuff most + + align:start position:0% +classes at MIT teach you this stuff most + + + align:start position:0% +classes at MIT teach you this stuff most +people don't never look at this don't + + align:start position:0% +people don't never look at this don't + + + align:start position:0% +people don't never look at this don't +want to look at this the thing that I + + align:start position:0% +want to look at this the thing that I + + + align:start position:0% +want to look at this the thing that I +like to just mention is that in Julia + + align:start position:0% +like to just mention is that in Julia + + + align:start position:0% +like to just mention is that in Julia +the assembler is short and so this is + + align:start position:0% +the assembler is short and so this is + + + align:start position:0% +the assembler is short and so this is +this is the assembler for this + + align:start position:0% +this is the assembler for this + + + align:start position:0% +this is the assembler for this +derivative code this kind of derived + + align:start position:0% +derivative code this kind of derived + + + align:start position:0% +derivative code this kind of derived +code and and um short short assembler is + + align:start position:0% +code and and um short short assembler is + + + align:start position:0% +code and and um short short assembler is +more or less correlated with fast code + + align:start position:0% +more or less correlated with fast code + + + align:start position:0% +more or less correlated with fast code +and so uh not only does it get the right + + align:start position:0% +and so uh not only does it get the right + + + align:start position:0% +and so uh not only does it get the right +answer but this sort of game is also + + align:start position:0% +answer but this sort of game is also + + + align:start position:0% +answer but this sort of game is also +quite fast in Julia right and that + + align:start position:0% +quite fast in Julia right and that + + + align:start position:0% +quite fast in Julia right and that +that's kind of a nice thing to be able + + align:start position:0% +that's kind of a nice thing to be able + + + align:start position:0% +that's kind of a nice thing to be able +to have okay so I'm still not going to + + align:start position:0% +to have okay so I'm still not going to + + + align:start position:0% +to have okay so I'm still not going to +tell you how it works but I'm going to + + align:start position:0% +tell you how it works but I'm going to + + + align:start position:0% +tell you how it works but I'm going to +grab + + align:start position:0% +grab + + + align:start position:0% +grab +simpai this is so this is python + + align:start position:0% +simpai this is so this is python + + + align:start position:0% +simpai this is so this is python +symbolic program there's a Julia + + align:start position:0% +symbolic program there's a Julia + + + align:start position:0% +symbolic program there's a Julia +symbolic program but I don't completely + + align:start position:0% +symbolic program but I don't completely + + + align:start position:0% +symbolic program but I don't completely +TR trust it yet maybe it's ready for + + align:start position:0% +TR trust it yet maybe it's ready for + + + align:start position:0% +TR trust it yet maybe it's ready for +prime time but I I did this originally + + align:start position:0% +prime time but I I did this originally + + + align:start position:0% +prime time but I I did this originally +with I wrote this before uh there even + + align:start position:0% +with I wrote this before uh there even + + + align:start position:0% +with I wrote this before uh there even +was Julia symbolic and anyway it just + + align:start position:0% +was Julia symbolic and anyway it just + + + align:start position:0% +was Julia symbolic and anyway it just +works so well I would take it and so one + + align:start position:0% +works so well I would take it and so one + + + align:start position:0% +works so well I would take it and so one +of the things that's sort of interesting + + align:start position:0% +of the things that's sort of interesting + + + align:start position:0% +of the things that's sort of interesting +is U is is is to ask how should I say + + align:start position:0% +is U is is is to ask how should I say + + + align:start position:0% +is U is is is to ask how should I say +this I'm going to tell you something + + align:start position:0% +this I'm going to tell you something + + + align:start position:0% +this I'm going to tell you something +that's mathematically equivalent to what + + align:start position:0% +that's mathematically equivalent to what + + + align:start position:0% +that's mathematically equivalent to what +we're doing but I don't want you to get + + align:start position:0% +we're doing but I don't want you to get + + + align:start position:0% +we're doing but I don't want you to get +the impression that this is how it's + + align:start position:0% +the impression that this is how it's + + + align:start position:0% +the impression that this is how it's +computed so let's talk about not the + + align:start position:0% +computed so let's talk about not the + + + align:start position:0% +computed so let's talk about not the +derivative yet but just the bonian + + align:start position:0% +derivative yet but just the bonian + + + align:start position:0% +derivative yet but just the bonian +algorithm you remember that this is the + + align:start position:0% +algorithm you remember that this is the + + + align:start position:0% +algorithm you remember that this is the +function at the first step x + 1 over2 I + + align:start position:0% +function at the first step x + 1 over2 I + + + align:start position:0% +function at the first step x + 1 over2 I +can use Julia's you know ability to + + align:start position:0% +can use Julia's you know ability to + + + align:start position:0% +can use Julia's you know ability to +overload to run it on a symbol X and + + align:start position:0% +overload to run it on a symbol X and + + + align:start position:0% +overload to run it on a symbol X and +then I could see what there is at the + + align:start position:0% +then I could see what there is at the + + + align:start position:0% +then I could see what there is at the +second step or at the third step and so + + align:start position:0% +second step or at the third step and so + + + align:start position:0% +second step or at the third step and so +in a way at the whatever this is the + + align:start position:0% +in a way at the whatever this is the + + + align:start position:0% +in a way at the whatever this is the +this is if this is the first step second + + align:start position:0% +this is if this is the first step second + + + align:start position:0% +this is if this is the first step second +third fourth fifth at the fifth step the + + align:start position:0% +third fourth fifth at the fifth step the + + + align:start position:0% +third fourth fifth at the fifth step the +bonning algorithm exactly computes this + + align:start position:0% +bonning algorithm exactly computes this + + + align:start position:0% +bonning algorithm exactly computes this +this rational function it's a 16th + + align:start position:0% +this rational function it's a 16th + + + align:start position:0% +this rational function it's a 16th +degree polinomial over a 15th degree + + align:start position:0% +degree polinomial over a 15th degree + + + align:start position:0% +degree polinomial over a 15th degree +polinomial but don't get the wrong idea + + align:start position:0% +polinomial but don't get the wrong idea + + + align:start position:0% +polinomial but don't get the wrong idea +nobody's nobody in the real world was + + align:start position:0% +nobody's nobody in the real world was + + + align:start position:0% +nobody's nobody in the real world was +calculating the coefficients of this + + align:start position:0% +calculating the coefficients of this + + + align:start position:0% +calculating the coefficients of this +polinomial I mean these coefficients we + + align:start position:0% +polinomial I mean these coefficients we + + + align:start position:0% +polinomial I mean these coefficients we +wouldn't want to store them they'd be + + align:start position:0% +wouldn't want to store them they'd be + + + align:start position:0% +wouldn't want to store them they'd be +unwieldy to work with but uh but as a + + align:start position:0% +unwieldy to work with but uh but as a + + + align:start position:0% +unwieldy to work with but uh but as a +mathematical sense the fifth step of of + + align:start position:0% +mathematical sense the fifth step of of + + + align:start position:0% +mathematical sense the fifth step of of +of of the Babylonian algorithm is + + align:start position:0% +of of the Babylonian algorithm is + + + align:start position:0% +of of the Babylonian algorithm is +calculating exactly this function and + + align:start position:0% +calculating exactly this function and + + + align:start position:0% +calculating exactly this function and +you know the plots tell us that this + + align:start position:0% +you know the plots tell us that this + + + align:start position:0% +you know the plots tell us that this +crazy function the 16th over 15th degree + + align:start position:0% +crazy function the 16th over 15th degree + + + align:start position:0% +crazy function the 16th over 15th degree +polinomial is not a bad approximation to + + align:start position:0% +polinomial is not a bad approximation to + + + align:start position:0% +polinomial is not a bad approximation to +square root of x at least you know + + align:start position:0% +square root of x at least you know + + + align:start position:0% +square root of x at least you know +visually on the graph right so so this + + align:start position:0% +visually on the graph right so so this + + + align:start position:0% +visually on the graph right so so this +is pretty good for square root of x + + align:start position:0% +is pretty good for square root of x + + + align:start position:0% +is pretty good for square root of x +right that's you know what we've seen um + + align:start position:0% +right that's you know what we've seen um + + + align:start position:0% +right that's you know what we've seen um +you know we could talk about where it is + + align:start position:0% +you know we could talk about where it is + + + align:start position:0% +you know we could talk about where it is +good where it isn't good but the point + + align:start position:0% +good where it isn't good but the point + + + align:start position:0% +good where it isn't good but the point +is that what it's Computing is this + + align:start position:0% +is that what it's Computing is this + + + align:start position:0% +is that what it's Computing is this +function and if you we could do the same + + align:start position:0% +function and if you we could do the same + + + align:start position:0% +function and if you we could do the same +game for the derivatives right so the + + align:start position:0% +game for the derivatives right so the + + + align:start position:0% +game for the derivatives right so the +the first derivative here is the + + align:start position:0% +the first derivative here is the + + + align:start position:0% +the first derivative here is the +coefficient of x is a half that constant + + align:start position:0% +coefficient of x is a half that constant + + + align:start position:0% +coefficient of x is a half that constant +and we can see what's being computed + + align:start position:0% +and we can see what's being computed + + + align:start position:0% +and we can see what's being computed +exactly here and you know this is a + + align:start position:0% +exactly here and you know this is a + + + align:start position:0% +exactly here and you know this is a +ratio of 30th degree polinomial and + + align:start position:0% +ratio of 30th degree polinomial and + + + align:start position:0% +ratio of 30th degree polinomial and +again I want to stress we are not I'm + + align:start position:0% +again I want to stress we are not I'm + + + align:start position:0% +again I want to stress we are not I'm +I'm just building this up just for fun + + align:start position:0% +I'm just building this up just for fun + + + align:start position:0% +I'm just building this up just for fun +we are not in the algorithm getting + + align:start position:0% +we are not in the algorithm getting + + + align:start position:0% +we are not in the algorithm getting +literally these coefficients they're too + + align:start position:0% +literally these coefficients they're too + + + align:start position:0% +literally these coefficients they're too +big anyway for for for working with um + + align:start position:0% +big anyway for for for working with um + + + align:start position:0% +big anyway for for for working with um +but it but in a mathematical sense the + + align:start position:0% +but it but in a mathematical sense the + + + align:start position:0% +but it but in a mathematical sense the +fifth step of this derivative Babylonian + + align:start position:0% +fifth step of this derivative Babylonian + + + align:start position:0% +fifth step of this derivative Babylonian +algorithm is calculating exactly this + + align:start position:0% +algorithm is calculating exactly this + + + align:start position:0% +algorithm is calculating exactly this +thing and so this has to be some sort of + + align:start position:0% +thing and so this has to be some sort of + + + align:start position:0% +thing and so this has to be some sort of +approximation + + align:start position:0% +approximation + + + align:start position:0% +approximation +to2 over the square Ro of X the + + align:start position:0% +to2 over the square Ro of X the + + + align:start position:0% +to2 over the square Ro of X the +derivative of square root of x right + + align:start position:0% +derivative of square root of x right + + + align:start position:0% +derivative of square root of x right +this is what that is okay so um so let + + align:start position:0% +this is what that is okay so um so let + + + align:start position:0% +this is what that is okay so um so let +me get a little closer as to how now you + + align:start position:0% +me get a little closer as to how now you + + + align:start position:0% +me get a little closer as to how now you +must be wondering I hope you're all kind + + align:start position:0% +must be wondering I hope you're all kind + + + align:start position:0% +must be wondering I hope you're all kind +of sitting in your seat saying how's + + align:start position:0% +of sitting in your seat saying how's + + + align:start position:0% +of sitting in your seat saying how's +this working right what what what's + + align:start position:0% +this working right what what what's + + + align:start position:0% +this working right what what what's +happening here and uh to get you a + + align:start position:0% +happening here and uh to get you a + + + align:start position:0% +happening here and uh to get you a +little bit kind of closer let me do what + + align:start position:0% +little bit kind of closer let me do what + + + align:start position:0% +little bit kind of closer let me do what +people used to do in the old days um + + align:start position:0% +people used to do in the old days um + + + align:start position:0% +people used to do in the old days um +people used to take derivatives of + + align:start position:0% +people used to take derivatives of + + + align:start position:0% +people used to take derivatives of +functions by hand before this became + + align:start position:0% +functions by hand before this became + + + align:start position:0% +functions by hand before this became +automatic people would take derivatives + + align:start position:0% +automatic people would take derivatives + + + align:start position:0% +automatic people would take derivatives +of functions by hand and so I'm going to + + align:start position:0% +of functions by hand and so I'm going to + + + align:start position:0% +of functions by hand and so I'm going to +do that for you here I'm going to create + + align:start position:0% +do that for you here I'm going to create + + + align:start position:0% +do that for you here I'm going to create +a d Babylonian algorithm the derivative + + align:start position:0% +a d Babylonian algorithm the derivative + + + align:start position:0% +a d Babylonian algorithm the derivative +of the bonian algorithm and you'll + + align:start position:0% +of the bonian algorithm and you'll + + + align:start position:0% +of the bonian algorithm and you'll +recognize that you know this line and + + align:start position:0% +recognize that you know this line and + + + align:start position:0% +recognize that you know this line and +this line are the original algorithm and + + align:start position:0% +this line are the original algorithm and + + + align:start position:0% +this line are the original algorithm and +below it I'll create variables I'll + + align:start position:0% +below it I'll create variables I'll + + + align:start position:0% +below it I'll create variables I'll +create derivative variables T Prime + + align:start position:0% +create derivative variables T Prime + + + align:start position:0% +create derivative variables T Prime +right and so T Prime the derivative of + + align:start position:0% +right and so T Prime the derivative of + + + align:start position:0% +right and so T Prime the derivative of +this is of course a half the derivative + + align:start position:0% +this is of course a half the derivative + + + align:start position:0% +this is of course a half the derivative +of this of this line of code well what + + align:start position:0% +of this of this line of code well what + + + align:start position:0% +of this of this line of code well what +is it it's it's you know the T prime + + align:start position:0% +is it it's it's you know the T prime + + + align:start position:0% +is it it's it's you know the T prime +plus you know the denominator time of + + align:start position:0% +plus you know the denominator time of + + + align:start position:0% +plus you know the denominator time of +the numerator which is 1 - x you know + + align:start position:0% +the numerator which is 1 - x you know + + + align:start position:0% +the numerator which is 1 - x you know +times uh you know T Prime over t^2 right + + align:start position:0% +times uh you know T Prime over t^2 right + + + align:start position:0% +times uh you know T Prime over t^2 right +you know so if if you check this is the + + align:start position:0% +you know so if if you check this is the + + + align:start position:0% +you know so if if you check this is the +ordinary calculus derivative uh with + + align:start position:0% +ordinary calculus derivative uh with + + + align:start position:0% +ordinary calculus derivative uh with +respect respect to X right so T Prime is + + align:start position:0% +respect respect to X right so T Prime is + + + align:start position:0% +respect respect to X right so T Prime is +the Der respect to X right so this is + + align:start position:0% +the Der respect to X right so this is + + + align:start position:0% +the Der respect to X right so this is +the ordinary calculus derivative and + + align:start position:0% +the ordinary calculus derivative and + + + align:start position:0% +the ordinary calculus derivative and +we're doing that at each and every step + + align:start position:0% +we're doing that at each and every step + + + align:start position:0% +we're doing that at each and every step +right and people used to do that by hand + + align:start position:0% +right and people used to do that by hand + + + align:start position:0% +right and people used to do that by hand +that you would you don't take you in + + align:start position:0% +that you would you don't take you in + + + align:start position:0% +that you would you don't take you in +other words you don't take the + + align:start position:0% +other words you don't take the + + + align:start position:0% +other words you don't take the +derivative analytically of the big thing + + align:start position:0% +derivative analytically of the big thing + + + align:start position:0% +derivative analytically of the big thing +rather you take the derivative of each + + align:start position:0% +rather you take the derivative of each + + + align:start position:0% +rather you take the derivative of each +line of code right and then you have + + align:start position:0% +line of code right and then you have + + + align:start position:0% +line of code right and then you have +faith that if you do that you'll get the + + align:start position:0% +faith that if you do that you'll get the + + + align:start position:0% +faith that if you do that you'll get the +derivative of the big thing that you + + align:start position:0% +derivative of the big thing that you + + + align:start position:0% +derivative of the big thing that you +wanted on the outside and you'll see + + align:start position:0% +wanted on the outside and you'll see + + + align:start position:0% +wanted on the outside and you'll see +that of course it works um adding these + + align:start position:0% +that of course it works um adding these + + + align:start position:0% +that of course it works um adding these +couple of lines of code with just this + + align:start position:0% +couple of lines of code with just this + + + align:start position:0% +couple of lines of code with just this +is now scalers right there's no dual + + align:start position:0% +is now scalers right there's no dual + + + align:start position:0% +is now scalers right there's no dual +numbers here right this will give me 12 + + align:start position:0% +numbers here right this will give me 12 + + + align:start position:0% +numbers here right this will give me 12 +over theun Pi um just by taking the + + align:start position:0% +over theun Pi um just by taking the + + + align:start position:0% +over theun Pi um just by taking the +derivative of every code line of code + + align:start position:0% +derivative of every code line of code + + + align:start position:0% +derivative of every code line of code +right and so you might realize that that + + align:start position:0% +right and so you might realize that that + + + align:start position:0% +right and so you might realize that that +this is not this is actually an + + align:start position:0% +this is not this is actually an + + + align:start position:0% +this is not this is actually an +iteration for the derivative of square + + align:start position:0% +iteration for the derivative of square + + + align:start position:0% +iteration for the derivative of square +root of x right that an iteration that + + align:start position:0% +root of x right that an iteration that + + + align:start position:0% +root of x right that an iteration that +we stop at we stop it at at 10 by + + align:start position:0% +we stop at we stop it at at 10 by + + + align:start position:0% +we stop at we stop it at at 10 by +default we could we could take more + + align:start position:0% +default we could we could take more + + + align:start position:0% +default we could we could take more +steps but but this is an iteration for + + align:start position:0% +steps but but this is an iteration for + + + align:start position:0% +steps but but this is an iteration for +the derivative square root obtained + + align:start position:0% +the derivative square root obtained + + + align:start position:0% +the derivative square root obtained +completely by taking the derivative of + + align:start position:0% +completely by taking the derivative of + + + align:start position:0% +completely by taking the derivative of +every line right and so so that's kind + + align:start position:0% +every line right and so so that's kind + + + align:start position:0% +every line right and so so that's kind +of what happened and so when I take the + + align:start position:0% +of what happened and so when I take the + + + align:start position:0% +of what happened and so when I take the +Babylonian of + + align:start position:0% +Babylonian of + + + align:start position:0% +Babylonian of +dx1 in + + align:start position:0% +dx1 in + + + align:start position:0% +dx1 in +effect I am using the magic of you know + + align:start position:0% +effect I am using the magic of you know + + + align:start position:0% +effect I am using the magic of you know +Julia's ability to to do dispatch and + + align:start position:0% +Julia's ability to to do dispatch and + + + align:start position:0% +Julia's ability to to do dispatch and +overload and all those fancy words but + + align:start position:0% +overload and all those fancy words but + + + align:start position:0% +overload and all those fancy words but +to use Simple English I am using the + + align:start position:0% +to use Simple English I am using the + + + align:start position:0% +to use Simple English I am using the +fact that I don't have to rewrite the + + align:start position:0% +fact that I don't have to rewrite the + + + align:start position:0% +fact that I don't have to rewrite the +code to get the derivative I just need + + align:start position:0% +code to get the derivative I just need + + + align:start position:0% +code to get the derivative I just need +the code to know the rules of taking + + align:start position:0% +the code to know the rules of taking + + + align:start position:0% +the code to know the rules of taking +derivatives of every operation that I + + align:start position:0% +derivatives of every operation that I + + + align:start position:0% +derivatives of every operation that I +you know more Atomic operations at the + + align:start position:0% +you know more Atomic operations at the + + + align:start position:0% +you know more Atomic operations at the +lowest level and rely on the computer to + + align:start position:0% +lowest level and rely on the computer to + + + align:start position:0% +lowest level and rely on the computer to +piece it all together right because + + align:start position:0% +piece it all together right because + + + align:start position:0% +piece it all together right because +humans are really bad at this sort of + + align:start position:0% +humans are really bad at this sort of + + + align:start position:0% +humans are really bad at this sort of +stuff they make mistakes all the time + + align:start position:0% +stuff they make mistakes all the time + + + align:start position:0% +stuff they make mistakes all the time +you know it's worse than long division + + align:start position:0% +you know it's worse than long division + + + align:start position:0% +you know it's worse than long division +right I mean no matter how good you are + + align:start position:0% +right I mean no matter how good you are + + + align:start position:0% +right I mean no matter how good you are +at long division you know humans are + + align:start position:0% +at long division you know humans are + + + align:start position:0% +at long division you know humans are +just make mistakes we just do right and + + align:start position:0% +just make mistakes we just do right and + + + align:start position:0% +just make mistakes we just do right and +so the trick is if you wanted to teach a + + align:start position:0% +so the trick is if you wanted to teach a + + + align:start position:0% +so the trick is if you wanted to teach a +computer to you know if you want to get + + align:start position:0% +computer to you know if you want to get + + + align:start position:0% +computer to you know if you want to get +a get the answers to a division problem + + align:start position:0% +a get the answers to a division problem + + + align:start position:0% +a get the answers to a division problem +we humans have taught computers to do + + align:start position:0% +we humans have taught computers to do + + + align:start position:0% +we humans have taught computers to do +the division for us so we don't have to + + align:start position:0% +the division for us so we don't have to + + + align:start position:0% +the division for us so we don't have to +right and this is what's going on with + + align:start position:0% +right and this is what's going on with + + + align:start position:0% +right and this is what's going on with +automatic differentiation we we teach + + align:start position:0% +automatic differentiation we we teach + + + align:start position:0% +automatic differentiation we we teach +the computer computer to do the atomic + + align:start position:0% +the computer computer to do the atomic + + + align:start position:0% +the computer computer to do the atomic +steps and then let it just go through + + align:start position:0% +steps and then let it just go through + + + align:start position:0% +steps and then let it just go through +the motions okay and so um so so um the + + align:start position:0% +the motions okay and so um so so um the + + + align:start position:0% +the motions okay and so um so so um the +derivatives goes in before the jit + + align:start position:0% +derivatives goes in before the jit + + + align:start position:0% +derivatives goes in before the jit +compiler and we get efficient code so um + + align:start position:0% +compiler and we get efficient code so um + + + align:start position:0% +compiler and we get efficient code so um +what there there's a notational trick + + align:start position:0% +what there there's a notational trick + + + align:start position:0% +what there there's a notational trick +which is rather nice which is instead of + + align:start position:0% +which is rather nice which is instead of + + + align:start position:0% +which is rather nice which is instead of +taking the Dual number which is a b we + + align:start position:0% +taking the Dual number which is a b we + + + align:start position:0% +taking the Dual number which is a b we +can write a plus b Epsilon and in effect + + align:start position:0% +can write a plus b Epsilon and in effect + + + align:start position:0% +can write a plus b Epsilon and in effect +what we're doing is the same thing that + + align:start position:0% +what we're doing is the same thing that + + + align:start position:0% +what we're doing is the same thing that +you know on on the first week of class + + align:start position:0% +you know on on the first week of class + + + align:start position:0% +you know on on the first week of class +when Steven said oh let's just write + + align:start position:0% +when Steven said oh let's just write + + + align:start position:0% +when Steven said oh let's just write +everything is like you know a plus b DX + + align:start position:0% +everything is like you know a plus b DX + + + align:start position:0% +everything is like you know a plus b DX +right just write everything to first + + align:start position:0% +right just write everything to first + + + align:start position:0% +right just write everything to first +order physicists do this all the time + + align:start position:0% +order physicists do this all the time + + + align:start position:0% +order physicists do this all the time +they they write everything to first + + align:start position:0% +they they write everything to first + + + align:start position:0% +they they write everything to first +order and they throw away higher order + + align:start position:0% +order and they throw away higher order + + + align:start position:0% +order and they throw away higher order +terms just just all the time so in + + align:start position:0% +terms just just all the time so in + + + align:start position:0% +terms just just all the time so in +effect what what what what's happening + + align:start position:0% +effect what what what what's happening + + + align:start position:0% +effect what what what what's happening +on the computer is we're just TR we're + + align:start position:0% +on the computer is we're just TR we're + + + align:start position:0% +on the computer is we're just TR we're +treating every computation as a first + + align:start position:0% +treating every computation as a first + + + align:start position:0% +treating every computation as a first +order computation and then the basic + + align:start position:0% +order computation and then the basic + + + align:start position:0% +order computation and then the basic +rules are let me just see there was one + + align:start position:0% +rules are let me just see there was one + + + align:start position:0% +rules are let me just see there was one +version of this was broken but let me + + align:start position:0% +version of this was broken but let me + + + align:start position:0% +version of this was broken but let me +see if this is right I think this is the + + align:start position:0% +see if this is right I think this is the + + + align:start position:0% +see if this is right I think this is the +right version so the basic rules you + + align:start position:0% +right version so the basic rules you + + + align:start position:0% +right version so the basic rules you +know every computation on a computer + + align:start position:0% +know every computation on a computer + + + align:start position:0% +know every computation on a computer +that's ever been written always can come + + align:start position:0% +that's ever been written always can come + + + align:start position:0% +that's ever been written always can come +down to plusus times and divide right + + align:start position:0% +down to plusus times and divide right + + + align:start position:0% +down to plusus times and divide right +even square root is implemented + + align:start position:0% +even square root is implemented + + + align:start position:0% +even square root is implemented +somewhere as plusus times and divide so + + align:start position:0% +somewhere as plusus times and divide so + + + align:start position:0% +somewhere as plusus times and divide so +um in effect if you wanted to do you + + align:start position:0% +um in effect if you wanted to do you + + + align:start position:0% +um in effect if you wanted to do you +could basically do you can get automatic + + align:start position:0% +could basically do you can get automatic + + + align:start position:0% +could basically do you can get automatic +differentiation just by having these + + align:start position:0% +differentiation just by having these + + + align:start position:0% +differentiation just by having these +basic rules right this is all you need + + align:start position:0% +basic rules right this is all you need + + + align:start position:0% +basic rules right this is all you need +now as a matter of practice we try to + + align:start position:0% +now as a matter of practice we try to + + + align:start position:0% +now as a matter of practice we try to +like intercept it all like you know + + align:start position:0% +like intercept it all like you know + + + align:start position:0% +like intercept it all like you know +we're we're happy to teach s and square + + align:start position:0% +we're we're happy to teach s and square + + + align:start position:0% +we're we're happy to teach s and square +root and cosine because you know who + + align:start position:0% +root and cosine because you know who + + + align:start position:0% +root and cosine because you know who +wants the you know whatever whatever + + align:start position:0% +wants the you know whatever whatever + + + align:start position:0% +wants the you know whatever whatever +method is being used to compute the sign + + align:start position:0% +method is being used to compute the sign + + + align:start position:0% +method is being used to compute the sign +and it's not tailor series by the way + + align:start position:0% +and it's not tailor series by the way + + + align:start position:0% +and it's not tailor series by the way +but whatever method is being used um we + + align:start position:0% +but whatever method is being used um we + + + align:start position:0% +but whatever method is being used um we +don't want it to go through all this + + align:start position:0% +don't want it to go through all this + + + align:start position:0% +don't want it to go through all this +work so we teach it things but but in + + align:start position:0% +work so we teach it things but but in + + + align:start position:0% +work so we teach it things but but in +principle all you need are these rules + + align:start position:0% +principle all you need are these rules + + + align:start position:0% +principle all you need are these rules +and you can take the derivative of + + align:start position:0% +and you can take the derivative of + + + align:start position:0% +and you can take the derivative of +anything in the world on a computer + + align:start position:0% +anything in the world on a computer + + + align:start position:0% +anything in the world on a computer +right this is all you need are the + + align:start position:0% +right this is all you need are the + + + align:start position:0% +right this is all you need are the +Here's the the the sum and minus rule um + + align:start position:0% +Here's the the the sum and minus rule um + + + align:start position:0% +Here's the the the sum and minus rule um +the multiplication rule which if you + + align:start position:0% +the multiplication rule which if you + + + align:start position:0% +the multiplication rule which if you +know if if you look at this right maybe + + align:start position:0% +know if if you look at this right maybe + + + align:start position:0% +know if if you look at this right maybe +if you squint correctly this this is is + + align:start position:0% +if you squint correctly this this is is + + + align:start position:0% +if you squint correctly this this is is +the the udv plus plus plus plus duv rule + + align:start position:0% +the the udv plus plus plus plus duv rule + + + align:start position:0% +the the udv plus plus plus plus duv rule +right the the product rule that you know + + align:start position:0% +right the the product rule that you know + + + align:start position:0% +right the the product rule that you know +you all learned in calculus and we kind + + align:start position:0% +you all learned in calculus and we kind + + + align:start position:0% +you all learned in calculus and we kind +of repeated it in its Matrix context in + + align:start position:0% +of repeated it in its Matrix context in + + + align:start position:0% +of repeated it in its Matrix context in +this class right this is udv plus vdu + + align:start position:0% +this class right this is udv plus vdu + + + align:start position:0% +this class right this is udv plus vdu +and and this is the quotient rule this + + align:start position:0% +and and this is the quotient rule this + + + align:start position:0% +and and this is the quotient rule this +is denominator time of the numerator + + align:start position:0% +is denominator time of the numerator + + + align:start position:0% +is denominator time of the numerator +numerator time the the denominator over + + align:start position:0% +numerator time the the denominator over + + + align:start position:0% +numerator time the the denominator over +the denominator squared right it's just + + align:start position:0% +the denominator squared right it's just + + + align:start position:0% +the denominator squared right it's just +kind of Rewritten in this first order + + align:start position:0% +kind of Rewritten in this first order + + + align:start position:0% +kind of Rewritten in this first order +kind of notation but these are rules + + align:start position:0% +kind of notation but these are rules + + + align:start position:0% +kind of notation but these are rules +that you all learned in firste calculus + + align:start position:0% +that you all learned in firste calculus + + + align:start position:0% +that you all learned in firste calculus +right and um and and um and I'll I'll + + align:start position:0% +right and um and and um and I'll I'll + + + align:start position:0% +right and um and and um and I'll I'll +even point out that you know you could + + align:start position:0% +even point out that you know you could + + + align:start position:0% +even point out that you know you could +do this + + align:start position:0% +do this + + + align:start position:0% +do this +symbolically just in case you don't you + + align:start position:0% +symbolically just in case you don't you + + + align:start position:0% +symbolically just in case you don't you +know you don't you don't even have to + + align:start position:0% +know you don't you don't even have to + + + align:start position:0% +know you don't you don't even have to +remember the rules you could actually + + align:start position:0% +remember the rules you could actually + + + align:start position:0% +remember the rules you could actually +derive the quotient rule um on the + + align:start position:0% +derive the quotient rule um on the + + + align:start position:0% +derive the quotient rule um on the +computer by just uh this says uh + + align:start position:0% +computer by just uh this says uh + + + align:start position:0% +computer by just uh this says uh +basically take a series around Epsilon + + align:start position:0% +basically take a series around Epsilon + + + align:start position:0% +basically take a series around Epsilon +equals z and give me two terms please no + + align:start position:0% +equals z and give me two terms please no + + + align:start position:0% +equals z and give me two terms please no +more so just give me to the first order + + align:start position:0% +more so just give me to the first order + + + align:start position:0% +more so just give me to the first order +in epsilon and here you see you get the + + align:start position:0% +in epsilon and here you see you get the + + + align:start position:0% +in epsilon and here you see you get the +the quotient and and the quotient rule + + align:start position:0% +the quotient and and the quotient rule + + + align:start position:0% +the quotient and and the quotient rule +from calculus right so um this is one + + align:start position:0% +from calculus right so um this is one + + + align:start position:0% +from calculus right so um this is one +way to to get your hands on that um if + + align:start position:0% +way to to get your hands on that um if + + + align:start position:0% +way to to get your hands on that um if +you wanted the the product rule I guess + + align:start position:0% +you wanted the the product rule I guess + + + align:start position:0% +you wanted the the product rule I guess +I could have just done this right and + + align:start position:0% +I could have just done this right and + + + align:start position:0% +I could have just done this right and +you get the the you know the udv plus + + align:start position:0% +you get the the you know the udv plus + + + align:start position:0% +you get the the you know the udv plus +plus duv rule right so you know those + + align:start position:0% +plus duv rule right so you know those + + + align:start position:0% +plus duv rule right so you know those +that's how you can get the rules um so + + align:start position:0% +that's how you can get the rules um so + + + align:start position:0% +that's how you can get the rules um so +I'm going to do something fun I am going + + align:start position:0% +I'm going to do something fun I am going + + + align:start position:0% +I'm going to do something fun I am going +to tell Julia this this is this is Julia + + align:start position:0% +to tell Julia this this is this is Julia + + + align:start position:0% +to tell Julia this this is this is Julia +magic that says to print a dual number + + align:start position:0% +magic that says to print a dual number + + + align:start position:0% +magic that says to print a dual number +um with epsilons and so now when I type + + align:start position:0% +um with epsilons and so now when I type + + + align:start position:0% +um with epsilons and so now when I type +a dual number you remember it was just + + align:start position:0% +a dual number you remember it was just + + + align:start position:0% +a dual number you remember it was just +with the D's once I execute this command + + align:start position:0% +with the D's once I execute this command + + + align:start position:0% +with the D's once I execute this command +I could see it in a way that's nice and + + align:start position:0% +I could see it in a way that's nice and + + + align:start position:0% +I could see it in a way that's nice and +human so I told you this was a function + + align:start position:0% +human so I told you this was a function + + + align:start position:0% +human so I told you this was a function +derivative pair but you could also think + + align:start position:0% +derivative pair but you could also think + + + align:start position:0% +derivative pair but you could also think +of it if you like as a first order + + align:start position:0% +of it if you like as a first order + + + align:start position:0% +of it if you like as a first order +expansion of it could be a first order + + align:start position:0% +expansion of it could be a first order + + + align:start position:0% +expansion of it could be a first order +expansion of a function right it could + + align:start position:0% +expansion of a function right it could + + + align:start position:0% +expansion of a function right it could +be the first order expansion of of X2 + + align:start position:0% +be the first order expansion of of X2 + + + align:start position:0% +be the first order expansion of of X2 +you know around xals + + align:start position:0% +you know around xals + + + align:start position:0% +you know around xals +1 okay uh so um so let's go ahead and + + align:start position:0% +1 okay uh so um so let's go ahead and + + + align:start position:0% +1 okay uh so um so let's go ahead and +add these last two rules remember I only + + align:start position:0% +add these last two rules remember I only + + + align:start position:0% +add these last two rules remember I only +did plus and divide I might as well add + + align:start position:0% +did plus and divide I might as well add + + + align:start position:0% +did plus and divide I might as well add +the this seems like a good time to do + + align:start position:0% +the this seems like a good time to do + + + align:start position:0% +the this seems like a good time to do +minus and times right and you see that + + align:start position:0% +minus and times right and you see that + + + align:start position:0% +minus and times right and you see that +if I do the Dual number one and zero I + + align:start position:0% +if I do the Dual number one and zero I + + + align:start position:0% +if I do the Dual number one and zero I +get this if I if + + align:start position:0% +get this if I if + + + align:start position:0% +get this if I if +I well actually let me ask you I'm not + + align:start position:0% +I well actually let me ask you I'm not + + + align:start position:0% +I well actually let me ask you I'm not +going to hit enter yet tell me what I + + align:start position:0% +going to hit enter yet tell me what I + + + align:start position:0% +going to hit enter yet tell me what I +should see when I hit return before I do + + align:start position:0% +should see when I hit return before I do + + + align:start position:0% +should see when I hit return before I do +it who who's quick what's the what's the + + align:start position:0% +it who who's quick what's the what's the + + + align:start position:0% +it who who's quick what's the what's the +first thing I'll + + align:start position:0% +first thing I'll + + + align:start position:0% +first thing I'll +see before the Epsilon and then what's + + align:start position:0% +see before the Epsilon and then what's + + + align:start position:0% +see before the Epsilon and then what's +the let me start with the the the the + + align:start position:0% +the let me start with the the the the + + + align:start position:0% +the let me start with the the the the +zero author term what will I see just + + align:start position:0% +zero author term what will I see just + + + align:start position:0% +zero author term what will I see just +shout it out four okay and then what's + + align:start position:0% +shout it out four okay and then what's + + + align:start position:0% +shout it out four okay and then what's +the next + + align:start position:0% +the next + + + align:start position:0% +the next +term + + align:start position:0% +term + + + align:start position:0% +term +four uh 2 * two four yep so four all you + + align:start position:0% +four uh 2 * two four yep so four all you + + + align:start position:0% +four uh 2 * two four yep so four all you +guys got it okay and this is you know I + + align:start position:0% +guys got it okay and this is you know I + + + align:start position:0% +guys got it okay and this is you know I +changed the output I might as well go + + align:start position:0% +changed the output I might as well go + + + align:start position:0% +changed the output I might as well go +the whole Direction why don't I make the + + align:start position:0% +the whole Direction why don't I make the + + + align:start position:0% +the whole Direction why don't I make the +input also like d01 I'll call it Epsilon + + align:start position:0% +input also like d01 I'll call it Epsilon + + + align:start position:0% +input also like d01 I'll call it Epsilon +right and so now I can actually input + + align:start position:0% +right and so now I can actually input + + + align:start position:0% +right and so now I can actually input +epsilons too not just see it as an + + align:start position:0% +epsilons too not just see it as an + + + align:start position:0% +epsilons too not just see it as an +output but I could do as anut so Epsilon + + align:start position:0% +output but I could do as anut so Epsilon + + + align:start position:0% +output but I could do as anut so Epsilon +squar of course is second order so we + + align:start position:0% +squar of course is second order so we + + + align:start position:0% +squar of course is second order so we +just get rid of it um by the way just + + align:start position:0% +just get rid of it um by the way just + + + align:start position:0% +just get rid of it um by the way just +something fun I actually never defines + + align:start position:0% +something fun I actually never defines + + + align:start position:0% +something fun I actually never defines +how to square you'll notice I Define + + align:start position:0% +how to square you'll notice I Define + + + align:start position:0% +how to square you'll notice I Define +times but I never Define Square for a + + align:start position:0% +times but I never Define Square for a + + + align:start position:0% +times but I never Define Square for a +dual number right but you know this is + + align:start position:0% +dual number right but you know this is + + + align:start position:0% +dual number right but you know this is +the this is sort of a little bit of a + + align:start position:0% +the this is sort of a little bit of a + + + align:start position:0% +the this is sort of a little bit of a +lesson but a good Software System would + + align:start position:0% +lesson but a good Software System would + + + align:start position:0% +lesson but a good Software System would +you know a would be one where when you + + align:start position:0% +you know a would be one where when you + + + align:start position:0% +you know a would be one where when you +square something it actually uh replaces + + align:start position:0% +square something it actually uh replaces + + + align:start position:0% +square something it actually uh replaces +it with a thing times itself so that um + + align:start position:0% +it with a thing times itself so that um + + + align:start position:0% +it with a thing times itself so that um +a matrix square is a matrix times a + + align:start position:0% +a matrix square is a matrix times a + + + align:start position:0% +a matrix square is a matrix times a +matrix and a scalar square is a scaler + + align:start position:0% +matrix and a scalar square is a scaler + + + align:start position:0% +matrix and a scalar square is a scaler +times a scaler and um in Julia for + + align:start position:0% +times a scaler and um in Julia for + + + align:start position:0% +times a scaler and um in Julia for +whatever reasons a string times a string + + align:start position:0% +whatever reasons a string times a string + + + align:start position:0% +whatever reasons a string times a string +is a conc of the string so uh string + + align:start position:0% +is a conc of the string so uh string + + + align:start position:0% +is a conc of the string so uh string +squared I don't know if this works + + align:start position:0% +squared I don't know if this works + + + align:start position:0% +squared I don't know if this works +anymore I have a feeling it doesn't work + + align:start position:0% +anymore I have a feeling it doesn't work + + + align:start position:0% +anymore I have a feeling it doesn't work +any it's not a number right this is + + align:start position:0% +any it's not a number right this is + + + align:start position:0% +any it's not a number right this is +going to fail but it shouldn't fail + + align:start position:0% +going to fail but it shouldn't fail + + + align:start position:0% +going to fail but it shouldn't fail +actually I think this is going to + + align:start position:0% +actually I think this is going to + + + align:start position:0% +actually I think this is going to +fail oh it doesn't fa oh no forget it it + + align:start position:0% +fail oh it doesn't fa oh no forget it it + + + align:start position:0% +fail oh it doesn't fa oh no forget it it +does work right so um multiplying two + + align:start position:0% +does work right so um multiplying two + + + align:start position:0% +does work right so um multiplying two +strings will concatenate them and + + align:start position:0% +strings will concatenate them and + + + align:start position:0% +strings will concatenate them and +squaring it concatenates it right and so + + align:start position:0% +squaring it concatenates it right and so + + + align:start position:0% +squaring it concatenates it right and so +if you have a good if you have sort of + + align:start position:0% +if you have a good if you have sort of + + + align:start position:0% +if you have a good if you have sort of +like a novice computer system every time + + align:start position:0% +like a novice computer system every time + + + align:start position:0% +like a novice computer system every time +you have another type you define another + + align:start position:0% +you have another type you define another + + + align:start position:0% +you have another type you define another +square but if you have a good computer + + align:start position:0% +square but if you have a good computer + + + align:start position:0% +square but if you have a good computer +system system then um the square in + + align:start position:0% +system system then um the square in + + + align:start position:0% +system system then um the square in +inherit it from multiply and then you + + align:start position:0% +inherit it from multiply and then you + + + align:start position:0% +inherit it from multiply and then you +just have to Define + + align:start position:0% +just have to Define + + + align:start position:0% +just have to Define +multiplication okay um what should I get + + align:start position:0% +multiplication okay um what should I get + + + align:start position:0% +multiplication okay um what should I get +here when I go 1 over 1 plus Epsilon and + + align:start position:0% +here when I go 1 over 1 plus Epsilon and + + + align:start position:0% +here when I go 1 over 1 plus Epsilon and +again nothing symbolic this is actually + + align:start position:0% +again nothing symbolic this is actually + + + align:start position:0% +again nothing symbolic this is actually +happening completely numerical by the + + align:start position:0% +happening completely numerical by the + + + align:start position:0% +happening completely numerical by the +way but what should I get when I hit + + align:start position:0% + + + + align:start position:0% + +return what should I see anybody you're + + align:start position:0% +return what should I see anybody you're + + + align:start position:0% +return what should I see anybody you're +smiling you see you think you know the + + align:start position:0% + + + + align:start position:0% + +answer so so I'll give you a hint what's + + align:start position:0% +answer so so I'll give you a hint what's + + + align:start position:0% +answer so so I'll give you a hint what's +written there is not what you'll + + align:start position:0% + + + + align:start position:0% + +see yeah how would it + + align:start position:0% +see yeah how would it + + + align:start position:0% +see yeah how would it +appear just read it to me how how it + + align:start position:0% +appear just read it to me how how it + + + align:start position:0% +appear just read it to me how how it +would + + align:start position:0% + + + + align:start position:0% + +appear there you go 1+ minus one Epsilon + + align:start position:0% +appear there you go 1+ minus one Epsilon + + + align:start position:0% +appear there you go 1+ minus one Epsilon +you could have just said 1 minus Epsilon + + align:start position:0% +you could have just said 1 minus Epsilon + + + align:start position:0% +you could have just said 1 minus Epsilon +I would have accepted + + align:start position:0% +I would have accepted + + + align:start position:0% +I would have accepted +that all right and doesn't that look + + align:start position:0% +that all right and doesn't that look + + + align:start position:0% +that all right and doesn't that look +like symbolic mathematics but it's not + + align:start position:0% +like symbolic mathematics but it's not + + + align:start position:0% +like symbolic mathematics but it's not +this whole thing happened + + align:start position:0% +this whole thing happened + + + align:start position:0% +this whole thing happened +through these D it's all it's all + + align:start position:0% +through these D it's all it's all + + + align:start position:0% +through these D it's all it's all +numerical right it's not there's nothing + + align:start position:0% +numerical right it's not there's nothing + + + align:start position:0% +numerical right it's not there's nothing +symbolic at all it just and and this is + + align:start position:0% +symbolic at all it just and and this is + + + align:start position:0% +symbolic at all it just and and this is +what another thing that people are + + align:start position:0% +what another thing that people are + + + align:start position:0% +what another thing that people are +saying that there's becoming more and + + align:start position:0% +saying that there's becoming more and + + + align:start position:0% +saying that there's becoming more and +more of a blurring between the symbolic + + align:start position:0% +more of a blurring between the symbolic + + + align:start position:0% +more of a blurring between the symbolic +and the numerical and that numerical + + align:start position:0% +and the numerical and that numerical + + + align:start position:0% +and the numerical and that numerical +stuff is starting to look more and more + + align:start position:0% +stuff is starting to look more and more + + + align:start position:0% +stuff is starting to look more and more +symbolic um but it's not symbolic all + + align:start position:0% +symbolic um but it's not symbolic all + + + align:start position:0% +symbolic um but it's not symbolic all +right what's the answer + + align:start position:0% +right what's the answer + + + align:start position:0% +right what's the answer +here I'm not using any weird packages + + align:start position:0% +here I'm not using any weird packages + + + align:start position:0% +here I'm not using any weird packages +everything that I'm using was defined + + align:start position:0% +everything that I'm using was defined + + + align:start position:0% +everything that I'm using was defined +right in front of you right I'm not + + align:start position:0% +right in front of you right I'm not + + + align:start position:0% +right in front of you right I'm not +using forward diff or anything + + align:start position:0% +using forward diff or anything + + + align:start position:0% +using forward diff or anything +everything here is just pure simple + + align:start position:0% +everything here is just pure simple + + + align:start position:0% +everything here is just pure simple +Julia you saw it there's nothing up my + + align:start position:0% +Julia you saw it there's nothing up my + + + align:start position:0% +Julia you saw it there's nothing up my +sleeve what should this answer be + + align:start position:0% + + + + align:start position:0% + +sorry you're right 1 plus 5 Epsilon okay + + align:start position:0% +sorry you're right 1 plus 5 Epsilon okay + + + align:start position:0% +sorry you're right 1 plus 5 Epsilon okay +and uh this one unfortunately won't work + + align:start position:0% +and uh this one unfortunately won't work + + + align:start position:0% +and uh this one unfortunately won't work +oh it does work oh that's amazing I + + align:start position:0% +oh it does work oh that's amazing I + + + align:start position:0% +oh it does work oh that's amazing I +don't know why that works all right + + align:start position:0% +don't know why that works all right + + + align:start position:0% +don't know why that works all right +never mind um I didn't think we could + + align:start position:0% +never mind um I didn't think we could + + + align:start position:0% +never mind um I didn't think we could +take negative Powers but I guess we + + align:start position:0% +take negative Powers but I guess we + + + align:start position:0% +take negative Powers but I guess we +could all right I I'm going to stop you + + align:start position:0% +could all right I I'm going to stop you + + + align:start position:0% +could all right I I'm going to stop you +could do this with enth roots you could + + align:start position:0% +could do this with enth roots you could + + + align:start position:0% +could do this with enth roots you could +do lots of other things um but I think + + align:start position:0% +do lots of other things um but I think + + + align:start position:0% +do lots of other things um but I think +this is a good time for a break and and + + align:start position:0% +this is a good time for a break and and + + + align:start position:0% +this is a good time for a break and and +you guys get the right idea that um so + + align:start position:0% +you guys get the right idea that um so + + + align:start position:0% +you guys get the right idea that um so +so now you're starting to see that that + + align:start position:0% +so now you're starting to see that that + + + align:start position:0% +so now you're starting to see that that +what if I were to summarize and I know + + align:start position:0% +what if I were to summarize and I know + + + align:start position:0% +what if I were to summarize and I know +it's still a little bit magical but I + + align:start position:0% +it's still a little bit magical but I + + + align:start position:0% +it's still a little bit magical but I +think you at least see that that you + + align:start position:0% +think you at least see that that you + + + align:start position:0% +think you at least see that that you +know roughly how this works is that one + + align:start position:0% +know roughly how this works is that one + + + align:start position:0% +know roughly how this works is that one +way or another um we we're training + + align:start position:0% +way or another um we we're training + + + align:start position:0% +way or another um we we're training +giving the rules of plus minus times and + + align:start position:0% +giving the rules of plus minus times and + + + align:start position:0% +giving the rules of plus minus times and +divide and we're writing programs and + + align:start position:0% +divide and we're writing programs and + + + align:start position:0% +divide and we're writing programs and +then these programs are in effect + + align:start position:0% +then these programs are in effect + + + align:start position:0% +then these programs are in effect +they're not really rewriting themselves + + align:start position:0% +they're not really rewriting themselves + + + align:start position:0% +they're not really rewriting themselves +what's really happening is that every + + align:start position:0% +what's really happening is that every + + + align:start position:0% +what's really happening is that every +time you execute a plus and minus times + + align:start position:0% +time you execute a plus and minus times + + + align:start position:0% +time you execute a plus and minus times +and a divide it's doing not just the the + + align:start position:0% +and a divide it's doing not just the the + + + align:start position:0% +and a divide it's doing not just the the +the basic operation that you'd all + + align:start position:0% +the basic operation that you'd all + + + align:start position:0% +the basic operation that you'd all +expect but it's also carrying along the + + align:start position:0% +expect but it's also carrying along the + + + align:start position:0% +expect but it's also carrying along the +derivative as well and the way Julia + + align:start position:0% +derivative as well and the way Julia + + + align:start position:0% +derivative as well and the way Julia +Works um Julia will actually look at + + align:start position:0% +Works um Julia will actually look at + + + align:start position:0% +Works um Julia will actually look at +that divide and say huh I'm not dividing + + align:start position:0% +that divide and say huh I'm not dividing + + + align:start position:0% +that divide and say huh I'm not dividing +scalers I'm dividing I'm dividing dual + + align:start position:0% +scalers I'm dividing I'm dividing dual + + + align:start position:0% +scalers I'm dividing I'm dividing dual +numbers or if it sees a star I'm not + + align:start position:0% +numbers or if it sees a star I'm not + + + align:start position:0% +numbers or if it sees a star I'm not +multiplying you know what how does Julia + + align:start position:0% +multiplying you know what how does Julia + + + align:start position:0% +multiplying you know what how does Julia +know what to do when it these two + + align:start position:0% +know what to do when it these two + + + align:start position:0% +know what to do when it these two +matrices you know Matrix star Matrix it + + align:start position:0% +matrices you know Matrix star Matrix it + + + align:start position:0% +matrices you know Matrix star Matrix it +knows because it's a matrix to do Matrix + + align:start position:0% +knows because it's a matrix to do Matrix + + + align:start position:0% +knows because it's a matrix to do Matrix +multiply so here when I did dual numbers + + align:start position:0% +multiply so here when I did dual numbers + + + align:start position:0% +multiply so here when I did dual numbers +I taught it to do this dual number thing + + align:start position:0% +I taught it to do this dual number thing + + + align:start position:0% +I taught it to do this dual number thing +right and once Julia knows how to do it + + align:start position:0% +right and once Julia knows how to do it + + + align:start position:0% +right and once Julia knows how to do it +it'll just carry all the way through + + align:start position:0% +it'll just carry all the way through + + + align:start position:0% +it'll just carry all the way through +right and in effect this is really the + + align:start position:0% +right and in effect this is really the + + + align:start position:0% +right and in effect this is really the +magic of great software where you just + + align:start position:0% +magic of great software where you just + + + align:start position:0% +magic of great software where you just +can Define some Atomic operations and + + align:start position:0% +can Define some Atomic operations and + + + align:start position:0% +can Define some Atomic operations and +the whole thing kind of composes itself + + align:start position:0% +the whole thing kind of composes itself + + + align:start position:0% +the whole thing kind of composes itself +almost by Magic right and in a way um + + align:start position:0% +almost by Magic right and in a way um + + + align:start position:0% +almost by Magic right and in a way um +it's almost opposite from what we teach + + align:start position:0% +it's almost opposite from what we teach + + + align:start position:0% +it's almost opposite from what we teach +students in a lot of classes where we + + align:start position:0% +students in a lot of classes where we + + + align:start position:0% +students in a lot of classes where we +want to teach the oldfashioned thing was + + align:start position:0% +want to teach the oldfashioned thing was + + + align:start position:0% +want to teach the oldfashioned thing was +to teach a student to carry through + + align:start position:0% +to teach a student to carry through + + + align:start position:0% +to teach a student to carry through +every operation and be really competent + + align:start position:0% +every operation and be really competent + + + align:start position:0% +every operation and be really competent +at it um in a way the the modern world + + align:start position:0% +at it um in a way the the modern world + + + align:start position:0% +at it um in a way the the modern world +is to teach students how to not have to + + align:start position:0% +is to teach students how to not have to + + + align:start position:0% +is to teach students how to not have to +think rather how to build a system that + + align:start position:0% +think rather how to build a system that + + + align:start position:0% +think rather how to build a system that +is is is is so simply designed that it + + align:start position:0% +is is is is so simply designed that it + + + align:start position:0% +is is is is so simply designed that it +just works right and that's you know + + align:start position:0% +just works right and that's you know + + + align:start position:0% +just works right and that's you know +that and actually that to to build a + + align:start position:0% +that and actually that to to build a + + + align:start position:0% +that and actually that to to build a +simple system is what takes the real + + align:start position:0% +simple system is what takes the real + + + align:start position:0% +simple system is what takes the real +human cleverness if if that sounds not + + align:start position:0% +human cleverness if if that sounds not + + + align:start position:0% +human cleverness if if that sounds not +not not not like some sort of + + align:start position:0% +not not not like some sort of + + + align:start position:0% +not not not like some sort of +contradiction but that's what it takes + + align:start position:0% +contradiction but that's what it takes + + + align:start position:0% +contradiction but that's what it takes +all right let's take the I'm a little + + align:start position:0% +all right let's take the I'm a little + + + align:start position:0% +all right let's take the I'm a little +late for the break but uh after the + + align:start position:0% +late for the break but uh after the + + + align:start position:0% +late for the break but uh after the +break on the Blackboard I'm going to do + + align:start position:0% +break on the Blackboard I'm going to do + + + align:start position:0% +break on the Blackboard I'm going to do +um I'm going to go into more detail + + align:start position:0% +um I'm going to go into more detail + + + align:start position:0% +um I'm going to go into more detail +about forward and reverse mode automatic + + align:start position:0% +about forward and reverse mode automatic + + + align:start position:0% +about forward and reverse mode automatic +differentiation + + align:start position:0% + + + + align:start position:0% + +that's \ No newline at end of file diff --git a/5av3kiejazQ.txt b/5av3kiejazQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..b182366d715e611780a70523977ae839ebdacaf5 --- /dev/null +++ b/5av3kiejazQ.txt @@ -0,0 +1,1803 @@ +align:start position:0% + +hi everyone welcome back so today we're + + align:start position:0% +hi everyone welcome back so today we're + + + align:start position:0% +hi everyone welcome back so today we're +going to take a look at solving uh uh + + align:start position:0% +going to take a look at solving uh uh + + + align:start position:0% +going to take a look at solving uh uh +solving differential equations using + + align:start position:0% +solving differential equations using + + + align:start position:0% +solving differential equations using +llast + + align:start position:0% +llast + + + align:start position:0% +llast +transforms and the problem we're going + + align:start position:0% +transforms and the problem we're going + + + align:start position:0% +transforms and the problem we're going +to take a look at is uh simple o e x do+ + + align:start position:0% +to take a look at is uh simple o e x do+ + + + align:start position:0% +to take a look at is uh simple o e x do+ +2x equal uh 3 Delta of t + 5 as a + + align:start position:0% +2x equal uh 3 Delta of t + 5 as a + + + align:start position:0% +2x equal uh 3 Delta of t + 5 as a +forcing on the right hand side we're + + align:start position:0% +forcing on the right hand side we're + + + align:start position:0% +forcing on the right hand side we're +going to uh look at having rest initial + + align:start position:0% +going to uh look at having rest initial + + + align:start position:0% +going to uh look at having rest initial +conditions X of 0 minus is is equal to + + align:start position:0% +conditions X of 0 minus is is equal to + + + align:start position:0% +conditions X of 0 minus is is equal to +zero and we're asked to use lass + + align:start position:0% +zero and we're asked to use lass + + + align:start position:0% +zero and we're asked to use lass +transforms to solve this initial value + + align:start position:0% +transforms to solve this initial value + + + align:start position:0% +transforms to solve this initial value +problem for Part B we're asked to have + + align:start position:0% +problem for Part B we're asked to have + + + align:start position:0% +problem for Part B we're asked to have +uh the initial value problem without any + + align:start position:0% +uh the initial value problem without any + + + align:start position:0% +uh the initial value problem without any +Delta function forcing on the right hand + + align:start position:0% +Delta function forcing on the right hand + + + align:start position:0% +Delta function forcing on the right hand +side to give an initial uh an equivalent + + align:start position:0% +side to give an initial uh an equivalent + + + align:start position:0% +side to give an initial uh an equivalent +initial value problem without a Delta + + align:start position:0% +initial value problem without a Delta + + + align:start position:0% +initial value problem without a Delta +function forcing on the right hand side + + align:start position:0% +function forcing on the right hand side + + + align:start position:0% +function forcing on the right hand side +but yields the same solution as in part + + align:start position:0% +but yields the same solution as in part + + + align:start position:0% +but yields the same solution as in part +A and then in question two we're uh + + align:start position:0% +A and then in question two we're uh + + + align:start position:0% +A and then in question two we're uh +asked to solve the differential equation + + align:start position:0% +asked to solve the differential equation + + + align:start position:0% +asked to solve the differential equation +the second order differential equation x + + align:start position:0% +the second order differential equation x + + + align:start position:0% +the second order differential equation x +do do + 9x equals U of T with rest ini + + align:start position:0% +do do + 9x equals U of T with rest ini + + + align:start position:0% +do do + 9x equals U of T with rest ini +condition so X of 0us is 0 x do of 0us + + align:start position:0% +condition so X of 0us is 0 x do of 0us + + + align:start position:0% +condition so X of 0us is 0 x do of 0us +is also 0 so I'll let you work on this + + align:start position:0% +is also 0 so I'll let you work on this + + + align:start position:0% +is also 0 so I'll let you work on this +problem and I'll be back in a + + align:start position:0% + + + + align:start position:0% + +moment hi everyone welcome + + align:start position:0% +moment hi everyone welcome + + + align:start position:0% +moment hi everyone welcome +back okay so for part a uh the first + + align:start position:0% +back okay so for part a uh the first + + + align:start position:0% +back okay so for part a uh the first +step is to llas transform both sides of + + align:start position:0% +step is to llas transform both sides of + + + align:start position:0% +step is to llas transform both sides of +the equation so we take the llas + + align:start position:0% +the equation so we take the llas + + + align:start position:0% +the equation so we take the llas +transform of x dot + + + align:start position:0% +transform of x dot + + + + align:start position:0% +transform of x dot + +2x and that's going to be equal to the + + align:start position:0% +2x and that's going to be equal to the + + + align:start position:0% +2x and that's going to be equal to the +llas + + align:start position:0% +llas + + + align:start position:0% +llas +transform of 3 Delta of + + align:start position:0% +transform of 3 Delta of + + + align:start position:0% +transform of 3 Delta of +t+ + + align:start position:0% +t+ + + + align:start position:0% +t+ +5 and we can use the uh distribution + + align:start position:0% +5 and we can use the uh distribution + + + align:start position:0% +5 and we can use the uh distribution +properties of the llas + + align:start position:0% +properties of the llas + + + align:start position:0% +properties of the llas +transform so this is going to be llas + + align:start position:0% +transform so this is going to be llas + + + align:start position:0% +transform so this is going to be llas +transform of x dot plus 2 * L transform + + align:start position:0% +transform of x dot plus 2 * L transform + + + align:start position:0% +transform of x dot plus 2 * L transform +of + + align:start position:0% +of + + + align:start position:0% +of +X on the right hand side we have three + + align:start position:0% +X on the right hand side we have three + + + align:start position:0% +X on the right hand side we have three +times theas + + align:start position:0% +times theas + + + align:start position:0% +times theas +transform of the delta + + align:start position:0% +transform of the delta + + + align:start position:0% +transform of the delta +function plus 5 * llast transform of + + align:start position:0% + + + + align:start position:0% + +one now we can replace the llast + + align:start position:0% +one now we can replace the llast + + + align:start position:0% +one now we can replace the llast +transform of x + + align:start position:0% + + + + align:start position:0% + +dot if we use the identity with s * the + + align:start position:0% +dot if we use the identity with s * the + + + align:start position:0% +dot if we use the identity with s * the +llas transform of x minus X at + + align:start position:0% +llas transform of x minus X at + + + align:start position:0% +llas transform of x minus X at +0us and we're told that X of 0 minus in + + align:start position:0% +0us and we're told that X of 0 minus in + + + align:start position:0% +0us and we're told that X of 0 minus in +this case is just zero so this term is + + align:start position:0% +this case is just zero so this term is + + + align:start position:0% +this case is just zero so this term is +going to vanish and just for brevity I'm + + align:start position:0% +going to vanish and just for brevity I'm + + + align:start position:0% +going to vanish and just for brevity I'm +going to write X of + + align:start position:0% +going to write X of + + + align:start position:0% +going to write X of +s as the llast transform of + + align:start position:0% +s as the llast transform of + + + align:start position:0% +s as the llast transform of +X so we now have S * X of + + align:start position:0% +X so we now have S * X of + + + align:start position:0% +X so we now have S * X of +s + 2 x of + + align:start position:0% +s + 2 x of + + + align:start position:0% +s + 2 x of +s equals and on the right hand side we + + align:start position:0% +s equals and on the right hand side we + + + align:start position:0% +s equals and on the right hand side we +have three times the llast transform of + + align:start position:0% +have three times the llast transform of + + + align:start position:0% +have three times the llast transform of +the Delta function llast transform of + + align:start position:0% +the Delta function llast transform of + + + align:start position:0% +the Delta function llast transform of +the Delta function is just one so we + + align:start position:0% +the Delta function is just one so we + + + align:start position:0% +the Delta function is just one so we +have 3 + 5 and the lass transform of one + + align:start position:0% +have 3 + 5 and the lass transform of one + + + align:start position:0% +have 3 + 5 and the lass transform of one +is just 1 / + + align:start position:0% + + + + align:start position:0% + +s so I can now Factor the right hand + + align:start position:0% +s so I can now Factor the right hand + + + align:start position:0% +s so I can now Factor the right hand +side or the left hand side and I get X + + align:start position:0% +side or the left hand side and I get X + + + align:start position:0% +side or the left hand side and I get X +of s * s + + + align:start position:0% +of s * s + + + + align:start position:0% +of s * s + +2 = 3 + 5 + + align:start position:0% +2 = 3 + 5 + + + align:start position:0% +2 = 3 + 5 +S and note how when we have X of s + + align:start position:0% +S and note how when we have X of s + + + align:start position:0% +S and note how when we have X of s +multiplied by some polinomial in s this + + align:start position:0% +multiplied by some polinomial in s this + + + align:start position:0% +multiplied by some polinomial in s this +is always going to be the characteristic + + align:start position:0% +is always going to be the characteristic + + + align:start position:0% +is always going to be the characteristic +polinomial so if we look back S Plus 2 + + align:start position:0% +polinomial so if we look back S Plus 2 + + + align:start position:0% +polinomial so if we look back S Plus 2 +is the characteristic polinomial of X do + + align:start position:0% +is the characteristic polinomial of X do + + + align:start position:0% +is the characteristic polinomial of X do +plus 2X + + align:start position:0% + + + + align:start position:0% + +X so this yields + + align:start position:0% +X so this yields + + + align:start position:0% +X so this yields +three / s + + + align:start position:0% +three / s + + + + align:start position:0% +three / s + +2 on the right hand side plus + + align:start position:0% +2 on the right hand side plus + + + align:start position:0% +2 on the right hand side plus +5 / s * s + + align:start position:0% + + + + align:start position:0% + ++2 and for the second piece we can use + + align:start position:0% ++2 and for the second piece we can use + + + align:start position:0% ++2 and for the second piece we can use +uh partial fractions to decompose it uh + + align:start position:0% +uh partial fractions to decompose it uh + + + align:start position:0% +uh partial fractions to decompose it uh +into a term uh Time s and a term times + + align:start position:0% +into a term uh Time s and a term times + + + align:start position:0% +into a term uh Time s and a term times +s+ 2 + + align:start position:0% +s+ 2 + + + align:start position:0% +s+ 2 +and when we do + + align:start position:0% + + + + align:start position:0% + +that we end up getting five + + align:start position:0% +that we end up getting five + + + align:start position:0% +that we end up getting five +halves 1 / s minus 1 / s + + + align:start position:0% + + + + align:start position:0% + +2 so I can combine the 3 divid s+ 2 with + + align:start position:0% +2 so I can combine the 3 divid s+ 2 with + + + align:start position:0% +2 so I can combine the 3 divid s+ 2 with +the minus 5 haves ID s plus2 into one + + align:start position:0% + + + + align:start position:0% + +term + + align:start position:0% +term + + + align:start position:0% +term +so this gives me 12 1/ s + + + align:start position:0% +so this gives me 12 1/ s + + + + align:start position:0% +so this gives me 12 1/ s + +2 and we we also have five halves 1/ s + + align:start position:0% +2 and we we also have five halves 1/ s + + + align:start position:0% +2 and we we also have five halves 1/ s +and now we just take the inverse llas + + align:start position:0% +and now we just take the inverse llas + + + align:start position:0% +and now we just take the inverse llas +transform of both + + align:start position:0% +transform of both + + + align:start position:0% +transform of both +sides so on the left hand side we + + align:start position:0% +sides so on the left hand side we + + + align:start position:0% +sides so on the left hand side we +recover X of T so we get + + align:start position:0% +recover X of T so we get + + + align:start position:0% +recover X of T so we get +12 eus + + align:start position:0% +12 eus + + + align:start position:0% +12 eus +2T plus 5 Hales the inverse llas + + align:start position:0% +2T plus 5 Hales the inverse llas + + + align:start position:0% +2T plus 5 Hales the inverse llas +transform of 1/ s is just t or sorry + + align:start position:0% +transform of 1/ s is just t or sorry + + + align:start position:0% +transform of 1/ s is just t or sorry +just one + + align:start position:0% + + + + align:start position:0% + +so we end up with X of T is 1 12 eus 2 t + + align:start position:0% +so we end up with X of T is 1 12 eus 2 t + + + align:start position:0% +so we end up with X of T is 1 12 eus 2 t +plus + + align:start position:0% +plus + + + align:start position:0% +plus +5ves and this solution is valid for T + + align:start position:0% +5ves and this solution is valid for T + + + align:start position:0% +5ves and this solution is valid for T +bigger than zero sometimes people write + + align:start position:0% +bigger than zero sometimes people write + + + align:start position:0% +bigger than zero sometimes people write +it as this quantity multiplied by a step + + align:start position:0% +it as this quantity multiplied by a step + + + align:start position:0% +it as this quantity multiplied by a step +function and X of + + align:start position:0% +function and X of + + + align:start position:0% +function and X of +T is also zero for T less than zero for + + align:start position:0% + + + + align:start position:0% + +example and it's just useful to quickly + + align:start position:0% +example and it's just useful to quickly + + + align:start position:0% +example and it's just useful to quickly +sketch what x of T looks like so it's an + + align:start position:0% +sketch what x of T looks like so it's an + + + align:start position:0% +sketch what x of T looks like so it's an +exponential decay for T bigger than + + align:start position:0% +exponential decay for T bigger than + + + align:start position:0% +exponential decay for T bigger than +zero and it's flat for T less than + + align:start position:0% +zero and it's flat for T less than + + + align:start position:0% +zero and it's flat for T less than +zero so here's zero there's X of + + align:start position:0% +zero so here's zero there's X of + + + align:start position:0% +zero so here's zero there's X of +t Okay so for part for Part B now we're + + align:start position:0% +t Okay so for part for Part B now we're + + + align:start position:0% +t Okay so for part for Part B now we're +asked to find a differential equation + + align:start position:0% +asked to find a differential equation + + + align:start position:0% +asked to find a differential equation +and new initial conditions uh that + + align:start position:0% +and new initial conditions uh that + + + align:start position:0% +and new initial conditions uh that +reproduce the solution uh for T bigger + + align:start position:0% +reproduce the solution uh for T bigger + + + align:start position:0% +reproduce the solution uh for T bigger +than zero so note how + + align:start position:0% +than zero so note how + + + align:start position:0% +than zero so note how +uh we'd be looking for a solution x a + + align:start position:0% +uh we'd be looking for a solution x a + + + align:start position:0% +uh we'd be looking for a solution x a +new solution X of T which would be an + + align:start position:0% +new solution X of T which would be an + + + align:start position:0% +new solution X of T which would be an +exponential + + align:start position:0% +exponential + + + align:start position:0% +exponential +decay and uh essentially would just grow + + align:start position:0% +decay and uh essentially would just grow + + + align:start position:0% +decay and uh essentially would just grow +so we're looking at uh initial + + align:start position:0% +so we're looking at uh initial + + + align:start position:0% +so we're looking at uh initial +conditions + + align:start position:0% +conditions + + + align:start position:0% +conditions +which uh start at + + align:start position:0% +which uh start at + + + align:start position:0% +which uh start at +zero if I were to write the original + + align:start position:0% +zero if I were to write the original + + + align:start position:0% +zero if I were to write the original +differential + + align:start position:0% +differential + + + align:start position:0% +differential +equation so this is the original + + align:start position:0% +equation so this is the original + + + align:start position:0% +equation so this is the original +differential + + align:start position:0% +differential + + + align:start position:0% +differential +equation uh from part + + align:start position:0% + + + + align:start position:0% + +A + + align:start position:0% +A + + + align:start position:0% +A +looks like this and just quickly denote + + align:start position:0% +looks like this and just quickly denote + + + align:start position:0% +looks like this and just quickly denote +that x dot near the origin is going to + + align:start position:0% +that x dot near the origin is going to + + + align:start position:0% +that x dot near the origin is going to +be approximately three times the Delta + + align:start position:0% +be approximately three times the Delta + + + align:start position:0% +be approximately three times the Delta +function which means in in the original + + align:start position:0% +function which means in in the original + + + align:start position:0% +function which means in in the original +differential equation x is going to have + + align:start position:0% +differential equation x is going to have + + + align:start position:0% +differential equation x is going to have +a jump of three about the + + align:start position:0% +a jump of three about the + + + align:start position:0% +a jump of three about the +origin so the new + + align:start position:0% +origin so the new + + + align:start position:0% +origin so the new +IV initial value + + align:start position:0% +IV initial value + + + align:start position:0% +IV initial value +problem well we don't want the Delta + + align:start position:0% +problem well we don't want the Delta + + + align:start position:0% +problem well we don't want the Delta +function on the right hand side so we're + + align:start position:0% +function on the right hand side so we're + + + align:start position:0% +function on the right hand side so we're +going to + + align:start position:0% +going to + + + align:start position:0% +going to +solve x dot + 2x is equal to 5 + + align:start position:0% +solve x dot + 2x is equal to 5 + + + align:start position:0% +solve x dot + 2x is equal to 5 +but what initial conditions do we need + + align:start position:0% +but what initial conditions do we need + + + align:start position:0% +but what initial conditions do we need +well we would need X of + + align:start position:0% +well we would need X of + + + align:start position:0% +well we would need X of +0 minus to now be + + align:start position:0% +0 minus to now be + + + align:start position:0% +0 minus to now be +three so when we eliminate the three + + align:start position:0% +three so when we eliminate the three + + + align:start position:0% +three so when we eliminate the three +Delta on the right hand side uh we have + + align:start position:0% +Delta on the right hand side uh we have + + + align:start position:0% +Delta on the right hand side uh we have +to introduce new initial conditions so + + align:start position:0% +to introduce new initial conditions so + + + align:start position:0% +to introduce new initial conditions so +that the solution agrees uh for T bigger + + align:start position:0% +that the solution agrees uh for T bigger + + + align:start position:0% +that the solution agrees uh for T bigger +than + + align:start position:0% +than + + + align:start position:0% +than +zero okay so this concludes part one for + + align:start position:0% +zero okay so this concludes part one for + + + align:start position:0% +zero okay so this concludes part one for +part + + align:start position:0% +part + + + align:start position:0% +part +two + + align:start position:0% +two + + + align:start position:0% +two +uh we're asked to solve a new + + align:start position:0% +uh we're asked to solve a new + + + align:start position:0% +uh we're asked to solve a new +differential + + align:start position:0% +differential + + + align:start position:0% +differential +equation x dot dot + + + align:start position:0% + + + + align:start position:0% + +9x equals U of + + align:start position:0% +9x equals U of + + + align:start position:0% +9x equals U of +T and we're just going to follow the + + align:start position:0% +T and we're just going to follow the + + + align:start position:0% +T and we're just going to follow the +same procedure where we laast transform + + align:start position:0% +same procedure where we laast transform + + + align:start position:0% +same procedure where we laast transform +both + + align:start position:0% +both + + + align:start position:0% +both +sides so llast transforming the left + + align:start position:0% +sides so llast transforming the left + + + align:start position:0% +sides so llast transforming the left +hand side gives me x dot dot plus + + align:start position:0% +hand side gives me x dot dot plus + + + align:start position:0% +hand side gives me x dot dot plus +9x equals the lla transform of U of + + align:start position:0% +9x equals the lla transform of U of + + + align:start position:0% +9x equals the lla transform of U of +T + + align:start position:0% + + + + align:start position:0% + +and again I can use the uh formula which + + align:start position:0% +and again I can use the uh formula which + + + align:start position:0% +and again I can use the uh formula which +relates uh derivatives of x uh back to + + align:start position:0% +relates uh derivatives of x uh back to + + + align:start position:0% +relates uh derivatives of x uh back to +the lass transform of + + align:start position:0% + + + + align:start position:0% + +X and so in this case the lass transform + + align:start position:0% +X and so in this case the lass transform + + + align:start position:0% +X and so in this case the lass transform +of x dot dot is going to be s^2 time the + + align:start position:0% +of x dot dot is going to be s^2 time the + + + align:start position:0% +of x dot dot is going to be s^2 time the +llast transform of + + align:start position:0% +llast transform of + + + align:start position:0% +llast transform of +X and then I'm going to have plus uh a + + align:start position:0% +X and then I'm going to have plus uh a + + + align:start position:0% +X and then I'm going to have plus uh a +term which involves X of 0us and a term + + align:start position:0% +term which involves X of 0us and a term + + + align:start position:0% +term which involves X of 0us and a term +which involves X do of 0us and uh if + + align:start position:0% +which involves X do of 0us and uh if + + + align:start position:0% +which involves X do of 0us and uh if +your initial condition were not zero you + + align:start position:0% +your initial condition were not zero you + + + align:start position:0% +your initial condition were not zero you +would have to keep these terms in + + align:start position:0% +would have to keep these terms in + + + align:start position:0% +would have to keep these terms in +however in our case these terms are both + + align:start position:0% +however in our case these terms are both + + + align:start position:0% +however in our case these terms are both +zero because we deal with rest initial + + align:start position:0% +zero because we deal with rest initial + + + align:start position:0% +zero because we deal with rest initial +conditions so I'm just not going to + + align:start position:0% +conditions so I'm just not going to + + + align:start position:0% +conditions so I'm just not going to +write + + align:start position:0% +write + + + align:start position:0% +write +them plus 9 x of + + align:start position:0% +them plus 9 x of + + + align:start position:0% +them plus 9 x of +s equals the laass transform of U of T + + align:start position:0% +s equals the laass transform of U of T + + + align:start position:0% +s equals the laass transform of U of T +is One of/ + + align:start position:0% +is One of/ + + + align:start position:0% +is One of/ +S so again we have X of + + align:start position:0% +S so again we have X of + + + align:start position:0% +S so again we have X of +s uh s^2 + 9 so note again how this is + + align:start position:0% +s uh s^2 + 9 so note again how this is + + + align:start position:0% +s uh s^2 + 9 so note again how this is +the same characteristic polinomial as in + + align:start position:0% +the same characteristic polinomial as in + + + align:start position:0% +the same characteristic polinomial as in +our differential + + align:start position:0% +our differential + + + align:start position:0% +our differential +equation is equal to 1 / + + align:start position:0% +equation is equal to 1 / + + + align:start position:0% +equation is equal to 1 / +s so X of s is 1 / s s^2 + + + align:start position:0% +s so X of s is 1 / s s^2 + + + + align:start position:0% +s so X of s is 1 / s s^2 + +9 which we can use partial fractions now + + align:start position:0% +9 which we can use partial fractions now + + + align:start position:0% +9 which we can use partial fractions now +to decompose it into a/ s + b s + + + align:start position:0% +to decompose it into a/ s + b s + + + + align:start position:0% +to decompose it into a/ s + b s + +C / s^2 + + + align:start position:0% +C / s^2 + + + + align:start position:0% +C / s^2 + +9 and if I were to take a look at my + + align:start position:0% +9 and if I were to take a look at my + + + align:start position:0% +9 and if I were to take a look at my +notes I have + + align:start position:0% +notes I have + + + align:start position:0% +notes I have +have in this case a is 1 nth B is + + align:start position:0% +have in this case a is 1 nth B is + + + align:start position:0% +have in this case a is 1 nth B is +negative 1 + + align:start position:0% +negative 1 + + + align:start position:0% +negative 1 +nth and C is equal to + + align:start position:0% +nth and C is equal to + + + align:start position:0% +nth and C is equal to +zero if you were to work out these + + align:start position:0% +zero if you were to work out these + + + align:start position:0% +zero if you were to work out these +coefficients so what this means is X of + + align:start position:0% +coefficients so what this means is X of + + + align:start position:0% +coefficients so what this means is X of +s is 1 + + align:start position:0% +s is 1 + + + align:start position:0% +s is 1 +9th uh 1 / + + align:start position:0% +9th uh 1 / + + + align:start position:0% +9th uh 1 / +s uh + + align:start position:0% +s uh + + + align:start position:0% +s uh +minus uh 1 + + align:start position:0% +minus uh 1 + + + align:start position:0% +minus uh 1 +nth 1 / s 2 + + + align:start position:0% + + + + align:start position:0% + +9 and when we inverse invert the llas + + align:start position:0% +9 and when we inverse invert the llas + + + align:start position:0% +9 and when we inverse invert the llas +transform uh the inverse of 1 / + + align:start position:0% +transform uh the inverse of 1 / + + + align:start position:0% +transform uh the inverse of 1 / +s is just one so X of T becomes one over + + align:start position:0% +s is just one so X of T becomes one over + + + align:start position:0% +s is just one so X of T becomes one over +n uh sorry this should be S up + + align:start position:0% +n uh sorry this should be S up + + + align:start position:0% +n uh sorry this should be S up +here the inverse the transform of s / + + align:start position:0% +here the inverse the transform of s / + + + align:start position:0% +here the inverse the transform of s / +s^2 + 9 is cosine 3 so we end up with 1 + + align:start position:0% +s^2 + 9 is cosine 3 so we end up with 1 + + + align:start position:0% +s^2 + 9 is cosine 3 so we end up with 1 +1 9 cosine of + + align:start position:0% +1 9 cosine of + + + align:start position:0% +1 9 cosine of +3T and again this is the solution for T + + align:start position:0% +3T and again this is the solution for T + + + align:start position:0% +3T and again this is the solution for T +bigger than + + align:start position:0% +bigger than + + + align:start position:0% +bigger than +zero so as soon as we turn on the input + + align:start position:0% +zero so as soon as we turn on the input + + + align:start position:0% +zero so as soon as we turn on the input +the function X of T starts growing + + align:start position:0% +the function X of T starts growing + + + align:start position:0% +the function X of T starts growing +continuously from one and then achieves + + align:start position:0% +continuously from one and then achieves + + + align:start position:0% +continuously from one and then achieves +uh an oscillation with period + + align:start position:0% +uh an oscillation with period + + + align:start position:0% +uh an oscillation with period +three okay so just to quickly recap in + + align:start position:0% +three okay so just to quickly recap in + + + align:start position:0% +three okay so just to quickly recap in +this problem we solved several Odes uh + + align:start position:0% +this problem we solved several Odes uh + + + align:start position:0% +this problem we solved several Odes uh +several initial value problem Odes using + + align:start position:0% +several initial value problem Odes using + + + align:start position:0% +several initial value problem Odes using +llast + + align:start position:0% +llast + + + align:start position:0% +llast +transforms llast transforms are + + align:start position:0% +transforms llast transforms are + + + align:start position:0% +transforms llast transforms are +particularly nice because they convert + + align:start position:0% +particularly nice because they convert + + + align:start position:0% +particularly nice because they convert +uh an OD into an algebraic equation + + align:start position:0% +uh an OD into an algebraic equation + + + align:start position:0% +uh an OD into an algebraic equation +which we can solve uh fairly easily the + + align:start position:0% +which we can solve uh fairly easily the + + + align:start position:0% +which we can solve uh fairly easily the +drawback is we sometimes have to + + align:start position:0% +drawback is we sometimes have to + + + align:start position:0% +drawback is we sometimes have to +manipulate using partial fractions the + + align:start position:0% +manipulate using partial fractions the + + + align:start position:0% +manipulate using partial fractions the +right hand side into functions that we + + align:start position:0% +right hand side into functions that we + + + align:start position:0% +right hand side into functions that we +know how to invert uh using the llas + + align:start position:0% +know how to invert uh using the llas + + + align:start position:0% +know how to invert uh using the llas +transform inverse so I'll just conclude + + align:start position:0% +transform inverse so I'll just conclude + + + align:start position:0% +transform inverse so I'll just conclude +here and I'll see you next + + align:start position:0% +here and I'll see you next + + + align:start position:0% +here and I'll see you next +time \ No newline at end of file diff --git a/66Hc7vnDQ8o.txt b/66Hc7vnDQ8o.txt new file mode 100644 index 0000000000000000000000000000000000000000..4097b628fec4ef8495ac012f4b057eaa5c5eab85 --- /dev/null +++ b/66Hc7vnDQ8o.txt @@ -0,0 +1,5683 @@ +align:start position:0% + +okay so last time I I talked about how + + align:start position:0% +okay so last time I I talked about how + + + align:start position:0% +okay so last time I I talked about how +uh in order to define a gradient you + + align:start position:0% +uh in order to define a gradient you + + + align:start position:0% +uh in order to define a gradient you +need an inter product right so that way + + align:start position:0% +need an inter product right so that way + + + align:start position:0% +need an inter product right so that way +if you have a scalar function of a + + align:start position:0% +if you have a scalar function of a + + + align:start position:0% +if you have a scalar function of a +vector the the the the gradient is + + align:start position:0% +vector the the the the gradient is + + + align:start position:0% +vector the the the the gradient is +defined basically the derivative has to + + align:start position:0% +defined basically the derivative has to + + + align:start position:0% +defined basically the derivative has to +be a linear function that takes a vector + + align:start position:0% +be a linear function that takes a vector + + + align:start position:0% +be a linear function that takes a vector +in and gives you a scaler out so this + + align:start position:0% +in and gives you a scaler out so this + + + align:start position:0% +in and gives you a scaler out so this +turns out this has to be if you have a + + align:start position:0% +turns out this has to be if you have a + + + align:start position:0% +turns out this has to be if you have a +DOT product this has to be a DOT product + + align:start position:0% +DOT product this has to be a DOT product + + + align:start position:0% +DOT product this has to be a DOT product +of something with the X then we call the + + align:start position:0% +of something with the X then we call the + + + align:start position:0% +of something with the X then we call the +gradient so the gradient is the thing + + align:start position:0% +gradient so the gradient is the thing + + + align:start position:0% +gradient so the gradient is the thing +with the same shape as X that we take + + align:start position:0% +with the same shape as X that we take + + + align:start position:0% +with the same shape as X that we take +the dot product with the X to get DF so + + align:start position:0% +the dot product with the X to get DF so + + + align:start position:0% +the dot product with the X to get DF so +what I didn't mention is in fact not + + align:start position:0% +what I didn't mention is in fact not + + + align:start position:0% +what I didn't mention is in fact not +only do we need a DOT product to define + + align:start position:0% +only do we need a DOT product to define + + + align:start position:0% +only do we need a DOT product to define +a gradient um actually we swept + + align:start position:0% +a gradient um actually we swept + + + align:start position:0% +a gradient um actually we swept +something under the under the rug + + align:start position:0% +something under the under the rug + + + align:start position:0% +something under the under the rug +earlier we actually need a norm in order + + align:start position:0% +earlier we actually need a norm in order + + + align:start position:0% +earlier we actually need a norm in order +to even Define a derivative in the first + + align:start position:0% +to even Define a derivative in the first + + + align:start position:0% +to even Define a derivative in the first +place right so a norm right is if if you + + align:start position:0% +place right so a norm right is if if you + + + align:start position:0% +place right so a norm right is if if you +have a vector space a norm is some + + align:start position:0% +have a vector space a norm is some + + + align:start position:0% +have a vector space a norm is some +measure of the length right of the + + align:start position:0% +measure of the length right of the + + + align:start position:0% +measure of the length right of the +vector or measure of + + align:start position:0% +vector or measure of + + + align:start position:0% +vector or measure of +distance and so a norm takes in a vector + + align:start position:0% +distance and so a norm takes in a vector + + + align:start position:0% +distance and so a norm takes in a vector +v and gives you out a scalar and + + align:start position:0% +v and gives you out a scalar and + + + align:start position:0% +v and gives you out a scalar and +technically to qualify as a norm it has + + align:start position:0% +technically to qualify as a norm it has + + + align:start position:0% +technically to qualify as a norm it has +to be you know this map has to be non- + + align:start position:0% +to be you know this map has to be non- + + + align:start position:0% +to be you know this map has to be non- +negative it can't be negative it can + + align:start position:0% +negative it can't be negative it can + + + align:start position:0% +negative it can't be negative it can +only be zero if V is zero if you + + align:start position:0% +only be zero if V is zero if you + + + align:start position:0% +only be zero if V is zero if you +multiply the vector by two it has to + + align:start position:0% +multiply the vector by two it has to + + + align:start position:0% +multiply the vector by two it has to +multiply the length by two or or if you + + align:start position:0% +multiply the length by two or or if you + + + align:start position:0% +multiply the length by two or or if you +multiply the the length by netive it has + + align:start position:0% +multiply the the length by netive it has + + + align:start position:0% +multiply the the length by netive it has +to multiply the length by two or you + + align:start position:0% +to multiply the length by two or you + + + align:start position:0% +to multiply the length by two or you +know basically absolute value of any + + align:start position:0% +know basically absolute value of any + + + align:start position:0% +know basically absolute value of any +scalar it has to satisfy something + + align:start position:0% +scalar it has to satisfy something + + + align:start position:0% +scalar it has to satisfy something +called a triangle + + align:start position:0% +called a triangle + + + align:start position:0% +called a triangle +inequality so usually we most commonly + + align:start position:0% +inequality so usually we most commonly + + + align:start position:0% +inequality so usually we most commonly +we're going to get a Norm just from an + + align:start position:0% +we're going to get a Norm just from an + + + align:start position:0% +we're going to get a Norm just from an +inner product so once you define an + + align:start position:0% +inner product so once you define an + + + align:start position:0% +inner product so once you define an +inner product we talked about those last + + align:start position:0% +inner product we talked about those last + + + align:start position:0% +inner product we talked about those last +time you can even Define inner products + + align:start position:0% +time you can even Define inner products + + + align:start position:0% +time you can even Define inner products +of matrices you get a norm for free you + + align:start position:0% +of matrices you get a norm for free you + + + align:start position:0% +of matrices you get a norm for free you +can take the + + align:start position:0% +can take the + + + align:start position:0% +can take the +norm uh is just a screw of the inner + + align:start position:0% +norm uh is just a screw of the inner + + + align:start position:0% +norm uh is just a screw of the inner +product itself and this satisfies all + + align:start position:0% +product itself and this satisfies all + + + align:start position:0% +product itself and this satisfies all +these properties uh for any inner + + align:start position:0% +these properties uh for any inner + + + align:start position:0% +these properties uh for any inner +product so the reason I mentioned this + + align:start position:0% +product so the reason I mentioned this + + + align:start position:0% +product so the reason I mentioned this +oh and by the way the just cultural note + + align:start position:0% +oh and by the way the just cultural note + + + align:start position:0% +oh and by the way the just cultural note +so if you have a continuous Vector space + + align:start position:0% +so if you have a continuous Vector space + + + align:start position:0% +so if you have a continuous Vector space +with an inner product we call that's a + + align:start position:0% +with an inner product we call that's a + + + align:start position:0% +with an inner product we call that's a +Hilbert space if you have a continuous + + align:start position:0% +Hilbert space if you have a continuous + + + align:start position:0% +Hilbert space if you have a continuous +Vector space with with a Norm that's + + align:start position:0% +Vector space with with a Norm that's + + + align:start position:0% +Vector space with with a Norm that's +called aonic space so you know don't + + align:start position:0% +called aonic space so you know don't + + + align:start position:0% +called aonic space so you know don't +this fancy sounding name but it just + + align:start position:0% +this fancy sounding name but it just + + + align:start position:0% +this fancy sounding name but it just +just means you have a norm you you can + + align:start position:0% +just means you have a norm you you can + + + align:start position:0% +just means you have a norm you you can +impress your friends with your fancy + + align:start position:0% +impress your friends with your fancy + + + align:start position:0% +impress your friends with your fancy +mathematics but that's all it is yes so + + align:start position:0% +mathematics but that's all it is yes so + + + align:start position:0% +mathematics but that's all it is yes so +so the reason I wanted to mention this + + align:start position:0% +so the reason I wanted to mention this + + + align:start position:0% +so the reason I wanted to mention this +is that really the definition of the + + align:start position:0% +is that really the definition of the + + + align:start position:0% +is that really the definition of the +derivative that we used earlier + + align:start position:0% +derivative that we used earlier + + + align:start position:0% +derivative that we used earlier +implicitly requires us to have a norm so + + align:start position:0% +implicitly requires us to have a norm so + + + align:start position:0% +implicitly requires us to have a norm so +it actually is of both the input and the + + align:start position:0% +it actually is of both the input and the + + + align:start position:0% +it actually is of both the input and the +output so it really only applies to Bono + + align:start position:0% +output so it really only applies to Bono + + + align:start position:0% +output so it really only applies to Bono +bases um so the reason for that is + + align:start position:0% +bases um so the reason for that is + + + align:start position:0% +bases um so the reason for that is +remember I Define the the derivative to + + align:start position:0% +remember I Define the the derivative to + + + align:start position:0% +remember I Define the the derivative to +start with is if if you look at the + + align:start position:0% +start with is if if you look at the + + + align:start position:0% +start with is if if you look at the +change in the output f ofx plus Delta + + align:start position:0% +change in the output f ofx plus Delta + + + align:start position:0% +change in the output f ofx plus Delta +xus f ofx for not not an infinite tmal + + align:start position:0% +xus f ofx for not not an infinite tmal + + + align:start position:0% +xus f ofx for not not an infinite tmal +but a finite Delta X but maybe small + + align:start position:0% +but a finite Delta X but maybe small + + + align:start position:0% +but a finite Delta X but maybe small +remember the we defined the derivative + + align:start position:0% +remember the we defined the derivative + + + align:start position:0% +remember the we defined the derivative +as the linear part is the linear + + align:start position:0% +as the linear part is the linear + + + align:start position:0% +as the linear part is the linear +operator that gives the change to first + + align:start position:0% +operator that gives the change to first + + + align:start position:0% +operator that gives the change to first +order which means we dropped any term + + align:start position:0% +order which means we dropped any term + + + align:start position:0% +order which means we dropped any term +that's + + align:start position:0% +that's + + + align:start position:0% +that's +we call it little o of Delta X any term + + align:start position:0% +we call it little o of Delta X any term + + + align:start position:0% +we call it little o of Delta X any term +that goes to zero faster than Delta X + + align:start position:0% +that goes to zero faster than Delta X + + + align:start position:0% +that goes to zero faster than Delta X +right so any term that's small compared + + align:start position:0% +right so any term that's small compared + + + align:start position:0% +right so any term that's small compared +to this right but in order to Define + + align:start position:0% +to this right but in order to Define + + + align:start position:0% +to this right but in order to Define +what it means to be small you need a + + align:start position:0% +what it means to be small you need a + + + align:start position:0% +what it means to be small you need a +norm like how how you know if I two + + align:start position:0% +norm like how how you know if I two + + + align:start position:0% +norm like how how you know if I two +Vector is a column vector and I want to + + align:start position:0% +Vector is a column vector and I want to + + + align:start position:0% +Vector is a column vector and I want to +say is this column Vector smaller than + + align:start position:0% +say is this column Vector smaller than + + + align:start position:0% +say is this column Vector smaller than +that column Vector how do I check it I I + + align:start position:0% +that column Vector how do I check it I I + + + align:start position:0% +that column Vector how do I check it I I +check the length right that you need you + + align:start position:0% +check the length right that you need you + + + align:start position:0% +check the length right that you need you +need you need to map it to a real number + + align:start position:0% +need you need to map it to a real number + + + align:start position:0% +need you need to map it to a real number +to get to get a this a distance or a + + align:start position:0% +to get to get a this a distance or a + + + align:start position:0% +to get to get a this a distance or a +small + + align:start position:0% +small + + + align:start position:0% +small +right so formally the the definition of + + align:start position:0% +right so formally the the definition of + + + align:start position:0% +right so formally the the definition of +this little o + + align:start position:0% +this little o + + + align:start position:0% +this little o +DX uh is is basically any + + align:start position:0% +DX uh is is basically any + + + align:start position:0% +DX uh is is basically any +function such that the norm of this over + + align:start position:0% +function such that the norm of this over + + + align:start position:0% +function such that the norm of this over +the norm of Delta X goes to zero as + + align:start position:0% +the norm of Delta X goes to zero as + + + align:start position:0% +the norm of Delta X goes to zero as +Delta X gets even goes to zero in fact + + align:start position:0% +Delta X gets even goes to zero in fact + + + align:start position:0% +Delta X gets even goes to zero in fact +even to define a limit you need a norm + + align:start position:0% +even to define a limit you need a norm + + + align:start position:0% +even to define a limit you need a norm +of Delta X because you know if you've + + align:start position:0% +of Delta X because you know if you've + + + align:start position:0% +of Delta X because you know if you've +taken a to 100 there's this Epsilon + + align:start position:0% +taken a to 100 there's this Epsilon + + + align:start position:0% +taken a to 100 there's this Epsilon +Delta meaning of a norm of of a limit + + align:start position:0% +Delta meaning of a norm of of a limit + + + align:start position:0% +Delta meaning of a norm of of a limit +sorry see it's like the this you can + + align:start position:0% +sorry see it's like the this you can + + + align:start position:0% +sorry see it's like the this you can +make this arbitrarily small for you know + + align:start position:0% +make this arbitrarily small for you know + + + align:start position:0% +make this arbitrarily small for you know +you can make this less than equal to + + align:start position:0% +you can make this less than equal to + + + align:start position:0% +you can make this less than equal to +Epsilon for all Epsilon greater than + + align:start position:0% +Epsilon for all Epsilon greater than + + + align:start position:0% +Epsilon for all Epsilon greater than +zero you I I'm not going to go through + + align:start position:0% +zero you I I'm not going to go through + + + align:start position:0% +zero you I I'm not going to go through +the definition if you've seen the + + align:start position:0% +the definition if you've seen the + + + align:start position:0% +the definition if you've seen the +definition of a limit there's some + + align:start position:0% +definition of a limit there's some + + + align:start position:0% +definition of a limit there's some +absolute values in there that for Vector + + align:start position:0% +absolute values in there that for Vector + + + align:start position:0% +absolute values in there that for Vector +spaces have to turn into Norms but + + align:start position:0% +spaces have to turn into Norms but + + + align:start position:0% +spaces have to turn into Norms but +basically my experience is everyone's + + align:start position:0% +basically my experience is everyone's + + + align:start position:0% +basically my experience is everyone's +seen the definition of delta and Epsilon + + align:start position:0% +seen the definition of delta and Epsilon + + + align:start position:0% +seen the definition of delta and Epsilon +limits and no one really understands it + + align:start position:0% +limits and no one really understands it + + + align:start position:0% +limits and no one really understands it +is that is that fair maybe some of you + + align:start position:0% +is that is that fair maybe some of you + + + align:start position:0% +is that is that fair maybe some of you +guys really do but most most of us don't + + align:start position:0% +guys really do but most most of us don't + + + align:start position:0% +guys really do but most most of us don't +yeah I mean it took it to be fair it + + align:start position:0% +yeah I mean it took it to be fair it + + + align:start position:0% +yeah I mean it took it to be fair it +took people 2,000 years years to figure + + align:start position:0% +took people 2,000 years years to figure + + + align:start position:0% +took people 2,000 years years to figure +it out right they really the the concept + + align:start position:0% +it out right they really the the concept + + + align:start position:0% +it out right they really the the concept +of a limit in an infinitesimal was a big + + align:start position:0% +of a limit in an infinitesimal was a big + + + align:start position:0% +of a limit in an infinitesimal was a big +struggle in mathematics going back to + + align:start position:0% +struggle in mathematics going back to + + + align:start position:0% +struggle in mathematics going back to +these you the ancient Greeks you know + + align:start position:0% +these you the ancient Greeks you know + + + align:start position:0% +these you the ancient Greeks you know +xenos paradoxes and so forth right so it + + align:start position:0% +xenos paradoxes and so forth right so it + + + align:start position:0% +xenos paradoxes and so forth right so it +really took a long time for people to + + align:start position:0% +really took a long time for people to + + + align:start position:0% +really took a long time for people to +nail down what this meant but yeah so + + align:start position:0% +nail down what this meant but yeah so + + + align:start position:0% +nail down what this meant but yeah so +you you need to be able to have a length + + align:start position:0% +you you need to be able to have a length + + + align:start position:0% +you you need to be able to have a length +a norm of the + + align:start position:0% +a norm of the + + + align:start position:0% +a norm of the +output you know because this has the + + align:start position:0% +output you know because this has the + + + align:start position:0% +output you know because this has the +same you know shape as the output these + + align:start position:0% +same you know shape as the output these + + + align:start position:0% +same you know shape as the output these +are the same shape as F right to to say + + align:start position:0% +are the same shape as F right to to say + + + align:start position:0% +are the same shape as F right to to say +that these terms are small compared to + + align:start position:0% +that these terms are small compared to + + + align:start position:0% +that these terms are small compared to +Delta X which you also need a norm of + + align:start position:0% +Delta X which you also need a norm of + + + align:start position:0% +Delta X which you also need a norm of +Delta X right so just implicitly you you + + align:start position:0% +Delta X right so just implicitly you you + + + align:start position:0% +Delta X right so just implicitly you you +always need a norm uh of all of these + + align:start position:0% +always need a norm uh of all of these + + + align:start position:0% +always need a norm uh of all of these +things to Define and usually we're going + + align:start position:0% +things to Define and usually we're going + + + align:start position:0% +things to Define and usually we're going +to get it because we're going to Define + + align:start position:0% +to get it because we're going to Define + + + align:start position:0% +to get it because we're going to Define +in most cases we'll Define an inner + + align:start position:0% +in most cases we'll Define an inner + + + align:start position:0% +in most cases we'll Define an inner +product because we'll want that anyway + + align:start position:0% +product because we'll want that anyway + + + align:start position:0% +product because we'll want that anyway +because if we want to take derivatives + + align:start position:0% +because if we want to take derivatives + + + align:start position:0% +because if we want to take derivatives +of scalar functions we want to be able + + align:start position:0% +of scalar functions we want to be able + + + align:start position:0% +of scalar functions we want to be able +to write down gradients um but this is + + align:start position:0% +to write down gradients um but this is + + + align:start position:0% +to write down gradients um but this is +what you really need so anyway so I just + + align:start position:0% +what you really need so anyway so I just + + + align:start position:0% +what you really need so anyway so I just +wanted to to to this is something we + + align:start position:0% +wanted to to to this is something we + + + align:start position:0% +wanted to to to this is something we +swept under the rug in the beginning um + + align:start position:0% +swept under the rug in the beginning um + + + align:start position:0% +swept under the rug in the beginning um +but since since we defined Hilbert + + align:start position:0% +but since since we defined Hilbert + + + align:start position:0% +but since since we defined Hilbert +spaces and uh I mean as I thought I + + align:start position:0% +spaces and uh I mean as I thought I + + + align:start position:0% +spaces and uh I mean as I thought I +should Define a Bono space I mean I'm + + align:start position:0% +should Define a Bono space I mean I'm + + + align:start position:0% +should Define a Bono space I mean I'm +still sweeping some things under the rug + + align:start position:0% +still sweeping some things under the rug + + + align:start position:0% +still sweeping some things under the rug +like I'm sweeping what does it mean for + + align:start position:0% +like I'm sweeping what does it mean for + + + align:start position:0% +like I'm sweeping what does it mean for +it to be continuous under the rug but + + align:start position:0% +it to be continuous under the rug but + + + align:start position:0% +it to be continuous under the rug but +um but uh yeah I wanted to throw that + + align:start position:0% +um but uh yeah I wanted to throw that + + + align:start position:0% +um but uh yeah I wanted to throw that +out there that's all I wanted to say + + align:start position:0% +out there that's all I wanted to say + + + align:start position:0% +out there that's all I wanted to say +that's it any yep any questions about + + align:start position:0% +that's it any yep any questions about + + + align:start position:0% +that's it any yep any questions about +that questions by all + + align:start position:0% +that questions by all + + + align:start position:0% +that questions by all +means okay good all right so this is + + align:start position:0% +means okay good all right so this is + + + align:start position:0% +means okay good all right so this is +just a little notebook and if we really + + align:start position:0% +just a little notebook and if we really + + + align:start position:0% +just a little notebook and if we really +need this isn't the live version so I + + align:start position:0% +need this isn't the live version so I + + + align:start position:0% +need this isn't the live version so I +can't really do anything um but I have a + + align:start position:0% +can't really do anything um but I have a + + + align:start position:0% +can't really do anything um but I have a +feeling that that this will be good + + align:start position:0% +feeling that that this will be good + + + align:start position:0% +feeling that that this will be good +enough U but if we need the live version + + align:start position:0% +enough U but if we need the live version + + + align:start position:0% +enough U but if we need the live version +we can just press a few buttons so um if + + align:start position:0% +we can just press a few buttons so um if + + + align:start position:0% +we can just press a few buttons so um if +I understood correctly uh last time you + + align:start position:0% +I understood correctly uh last time you + + + align:start position:0% +I understood correctly uh last time you +got the the answer for what is the + + align:start position:0% +got the the answer for what is the + + + align:start position:0% +got the the answer for what is the +gradient of the determinant is that + + align:start position:0% +gradient of the determinant is that + + + align:start position:0% +gradient of the determinant is that +right did you derive this formula that + + align:start position:0% +right did you derive this formula that + + + align:start position:0% +right did you derive this formula that +it I did not derive it I just gave the + + align:start position:0% +it I did not derive it I just gave the + + + align:start position:0% +it I did not derive it I just gave the +answer you gave the answer and there's a + + align:start position:0% +answer you gave the answer and there's a + + + align:start position:0% +answer you gave the answer and there's a +few different formats did you did you it + + align:start position:0% +few different formats did you did you it + + + align:start position:0% +few different formats did you did you it +the first one determinant + + align:start position:0% +the first one determinant + + + align:start position:0% +the first one determinant +a inverse transpose yeah oh the the the + + align:start position:0% +a inverse transpose yeah oh the the the + + + align:start position:0% +a inverse transpose yeah oh the the the +gradient is the determinant of a * a + + align:start position:0% +gradient is the determinant of a * a + + + align:start position:0% +gradient is the determinant of a * a +that's the second one right so the first + + align:start position:0% +that's the second one right so the first + + + align:start position:0% +that's the second one right so the first +one is the co-actor of a uh which is one + + align:start position:0% +one is the co-actor of a uh which is one + + + align:start position:0% +one is the co-actor of a uh which is one +of those linear algebra terms that you + + align:start position:0% +of those linear algebra terms that you + + + align:start position:0% +of those linear algebra terms that you +may or may not remember this is the one + + align:start position:0% +may or may not remember this is the one + + + align:start position:0% +may or may not remember this is the one +and uh just another uh term is the + + align:start position:0% +and uh just another uh term is the + + + align:start position:0% +and uh just another uh term is the +adjugate of a transpose um which is the + + align:start position:0% +adjugate of a transpose um which is the + + + align:start position:0% +adjugate of a transpose um which is the +the adjugate of a matrix is the inverse + + align:start position:0% +the adjugate of a matrix is the inverse + + + align:start position:0% +the adjugate of a matrix is the inverse +of the Matrix divided by the the the + + align:start position:0% +of the Matrix divided by the the the + + + align:start position:0% +of the Matrix divided by the the the +determinants so uh multip by the + + align:start position:0% +determinants so uh multip by the + + + align:start position:0% +determinants so uh multip by the +determinant multiply by the determinants + + align:start position:0% +determinant multiply by the determinants + + + align:start position:0% +determinant multiply by the determinants +right so it it's it's so uh let's see + + align:start position:0% +right so it it's it's so uh let's see + + + align:start position:0% +right so it it's it's so uh let's see +and um of course if you have the + + align:start position:0% +and um of course if you have the + + + align:start position:0% +and um of course if you have the +gradient then did you write down this + + align:start position:0% +gradient then did you write down this + + + align:start position:0% +gradient then did you write down this +version as well last time the the D of + + align:start position:0% +version as well last time the the D of + + + align:start position:0% +version as well last time the the D of +the determinant no well I did did D of + + align:start position:0% +the determinant no well I did did D of + + + align:start position:0% +the determinant no well I did did D of +any Matrix function so yes it's that I I + + align:start position:0% +any Matrix function so yes it's that I I + + + align:start position:0% +any Matrix function so yes it's that I I +Define the dot product Matrix dot + + align:start position:0% +Define the dot product Matrix dot + + + align:start position:0% +Define the dot product Matrix dot +product so right right I see so D of + + align:start position:0% +product so right right I see so D of + + + align:start position:0% +product so right right I see so D of +determinant will be the the trace of + + align:start position:0% +determinant will be the the trace of + + + align:start position:0% +determinant will be the the trace of +whatever formula you have over here this + + align:start position:0% +whatever formula you have over here this + + + align:start position:0% +whatever formula you have over here this +formula right times da d + + align:start position:0% +formula right times da d + + + align:start position:0% +formula right times da d +transposed to times it yeah uh yes right + + align:start position:0% +transposed to times it yeah uh yes right + + + align:start position:0% +transposed to times it yeah uh yes right +sorry let me clear my head yes the trace + + align:start position:0% +sorry let me clear my head yes the trace + + + align:start position:0% +sorry let me clear my head yes the trace +of this thing transposed times da right + + align:start position:0% +of this thing transposed times da right + + + align:start position:0% +of this thing transposed times da right +that which is the element wise you know + + align:start position:0% +that which is the element wise you know + + + align:start position:0% +that which is the element wise you know +it's just like the dot product you've + + align:start position:0% +it's just like the dot product you've + + + align:start position:0% +it's just like the dot product you've +all you you all get that it's the just + + align:start position:0% +all you you all get that it's the just + + + align:start position:0% +all you you all get that it's the just +like the vector dot product you you + + align:start position:0% +like the vector dot product you you + + + align:start position:0% +like the vector dot product you you +multiply corresponding elements and you + + align:start position:0% +multiply corresponding elements and you + + + align:start position:0% +multiply corresponding elements and you +take you take the sum whenever you have + + align:start position:0% +take you take the sum whenever you have + + + align:start position:0% +take you take the sum whenever you have +the trace of a transposed b as Stephen + + align:start position:0% +the trace of a transposed b as Stephen + + + align:start position:0% +the trace of a transposed b as Stephen +is writing very nicely over here that's + + align:start position:0% +is writing very nicely over here that's + + + align:start position:0% +is writing very nicely over here that's +the a dob so U so if we know the + + align:start position:0% +the a dob so U so if we know the + + + align:start position:0% +the a dob so U so if we know the +gradient then the D has to be this + + align:start position:0% +gradient then the D has to be this + + + align:start position:0% +gradient then the D has to be this +formula okay and um I'm letting I'm just + + align:start position:0% +formula okay and um I'm letting I'm just + + + align:start position:0% +formula okay and um I'm letting I'm just +defining the adjugate right here so that + + align:start position:0% +defining the adjugate right here so that + + + align:start position:0% +defining the adjugate right here so that +I can have it handy um as Stephen was + + align:start position:0% +I can have it handy um as Stephen was + + + align:start position:0% +I can have it handy um as Stephen was +saying it's just the determinant times + + align:start position:0% +saying it's just the determinant times + + + align:start position:0% +saying it's just the determinant times +the inverse this is just a a definition + + align:start position:0% +the inverse this is just a a definition + + + align:start position:0% +the inverse this is just a a definition +and then there's the co-actor Matrix + + align:start position:0% +and then there's the co-actor Matrix + + + align:start position:0% +and then there's the co-actor Matrix +which is the adjugate of a transpose so + + align:start position:0% +which is the adjugate of a transpose so + + + align:start position:0% +which is the adjugate of a transpose so +I'm just using I'm using this once I've + + align:start position:0% +I'm just using I'm using this once I've + + + align:start position:0% +I'm just using I'm using this once I've +defined this one to Define this one I + + align:start position:0% +defined this one to Define this one I + + + align:start position:0% +defined this one to Define this one I +just get to do the equality right so + + align:start position:0% +just get to do the equality right so + + + align:start position:0% +just get to do the equality right so +this defines these these functions and + + align:start position:0% +this defines these these functions and + + + align:start position:0% +this defines these these functions and +um here I've sort of written it every + + align:start position:0% +um here I've sort of written it every + + + align:start position:0% +um here I've sort of written it every +Which Way um the inverse in terms of the + + align:start position:0% +Which Way um the inverse in terms of the + + + align:start position:0% +Which Way um the inverse in terms of the +aggate the co-actor the aggate in terms + + align:start position:0% +aggate the co-actor the aggate in terms + + + align:start position:0% +aggate the co-actor the aggate in terms +of the the determinant you know the + + align:start position:0% +of the the determinant you know the + + + align:start position:0% +of the the determinant you know the +inverse and the co-actor oh you get it + + align:start position:0% +inverse and the co-actor oh you get it + + + align:start position:0% +inverse and the co-actor oh you get it +all three possibilities are written here + + align:start position:0% +all three possibilities are written here + + + align:start position:0% +all three possibilities are written here +okay so for 2x two + + align:start position:0% +okay so for 2x two + + + align:start position:0% +okay so for 2x two +matrices U you know here's a 2X two + + align:start position:0% +matrices U you know here's a 2X two + + + align:start position:0% +matrices U you know here's a 2X two +Matrix and here's the co-actor matrix + + align:start position:0% +Matrix and here's the co-actor matrix + + + align:start position:0% +Matrix and here's the co-actor matrix +it's the it it's you know some of you + + align:start position:0% +it's the it it's you know some of you + + + align:start position:0% +it's the it it's you know some of you +will recognize that when you when you + + align:start position:0% +will recognize that when you when you + + + align:start position:0% +will recognize that when you when you +form the inverse of a 2X two Matrix the + + align:start position:0% +form the inverse of a 2X two Matrix the + + + align:start position:0% +form the inverse of a 2X two Matrix the +determinant goes in the denominator and + + align:start position:0% +determinant goes in the denominator and + + + align:start position:0% +determinant goes in the denominator and +the thing that goes in the numerator + + align:start position:0% +the thing that goes in the numerator + + + align:start position:0% +the thing that goes in the numerator +right you're all good at 2 x two + + align:start position:0% +right you're all good at 2 x two + + + align:start position:0% +right you're all good at 2 x two +inverses do you know that by Heart Like + + align:start position:0% +inverses do you know that by Heart Like + + + align:start position:0% +inverses do you know that by Heart Like +would you be able to do it in your sleep + + align:start position:0% +would you be able to do it in your sleep + + + align:start position:0% +would you be able to do it in your sleep +right you you switch the A and the D and + + align:start position:0% +right you you switch the A and the D and + + + align:start position:0% +right you you switch the A and the D and +you negate the B and the C uh uh well no + + align:start position:0% +you negate the B and the C uh uh well no + + + align:start position:0% +you negate the B and the C uh uh well no +let's see you negate the B and the C but + + align:start position:0% +let's see you negate the B and the C but + + + align:start position:0% +let's see you negate the B and the C but +I'm also doing the transpose right so + + align:start position:0% +I'm also doing the transpose right so + + + align:start position:0% +I'm also doing the transpose right so +here it's um right so so you negate the + + align:start position:0% +here it's um right so so you negate the + + + align:start position:0% +here it's um right so so you negate the +BNC and transpose because it's the + + align:start position:0% +BNC and transpose because it's the + + + align:start position:0% +BNC and transpose because it's the +co-actor okay um for the adjugate you + + align:start position:0% +co-actor okay um for the adjugate you + + + align:start position:0% +co-actor okay um for the adjugate you +just take the the minus and anyway these + + align:start position:0% +just take the the minus and anyway these + + + align:start position:0% +just take the the minus and anyway these +are all the formulas here's the inverse + + align:start position:0% +are all the formulas here's the inverse + + + align:start position:0% +are all the formulas here's the inverse +right so the inverse is the adjugate + + align:start position:0% +right so the inverse is the adjugate + + + align:start position:0% +right so the inverse is the adjugate +divided by the determinant okay uh doing + + align:start position:0% +divided by the determinant okay uh doing + + + align:start position:0% +divided by the determinant okay uh doing +all this numerically just for fun so uh + + align:start position:0% +all this numerically just for fun so uh + + + align:start position:0% +all this numerically just for fun so uh +numerically here's a random Matrix and + + align:start position:0% +numerically here's a random Matrix and + + + align:start position:0% +numerically here's a random Matrix and +here's a random perturbation what we're + + align:start position:0% +here's a random perturbation what we're + + + align:start position:0% +here's a random perturbation what we're +going to do is look at at the + + align:start position:0% +going to do is look at at the + + + align:start position:0% +going to do is look at at the +determinant of the perturbed a minus the + + align:start position:0% +determinant of the perturbed a minus the + + + align:start position:0% +determinant of the perturbed a minus the +determinant of a right so there's the + + align:start position:0% +determinant of a right so there's the + + + align:start position:0% +determinant of a right so there's the +numerical value and by the way I know + + align:start position:0% +numerical value and by the way I know + + + align:start position:0% +numerical value and by the way I know +Stephen has recommended always using + + align:start position:0% +Stephen has recommended always using + + + align:start position:0% +Stephen has recommended always using +things on the order of square root of + + align:start position:0% +things on the order of square root of + + + align:start position:0% +things on the order of square root of +Epsilon U to make the perturbations 10 + + align:start position:0% +Epsilon U to make the perturbations 10 + + + align:start position:0% +Epsilon U to make the perturbations 10 +Theus 8 and he's right I never do that + + align:start position:0% +Theus 8 and he's right I never do that + + + align:start position:0% +Theus 8 and he's right I never do that +but he's you know you should listen to + + align:start position:0% +but he's you know you should listen to + + + align:start position:0% +but he's you know you should listen to +him I just start typing three or four + + align:start position:0% +him I just start typing three or four + + + align:start position:0% +him I just start typing three or four +zeros in a one and actually I it's been + + align:start position:0% +zeros in a one and actually I it's been + + + align:start position:0% +zeros in a one and actually I it's been +good enough for my purposes just to + + align:start position:0% +good enough for my purposes just to + + + align:start position:0% +good enough for my purposes just to +check things I mean Stevens is more you + + align:start position:0% +check things I mean Stevens is more you + + + align:start position:0% +check things I mean Stevens is more you +know it's it's the best possible one a + + align:start position:0% +know it's it's the best possible one a + + + align:start position:0% +know it's it's the best possible one a +square root of Epsilon uh but with a + + align:start position:0% +square root of Epsilon uh but with a + + + align:start position:0% +square root of Epsilon uh but with a +quick and dirty test I I don't have the + + align:start position:0% +quick and dirty test I I don't have the + + + align:start position:0% +quick and dirty test I I don't have the +time to type all those zeros and I never + + align:start position:0% +time to type all those zeros and I never + + + align:start position:0% +time to type all those zeros and I never +remember to type 1 E minus 8 so I just + + align:start position:0% +remember to type 1 E minus 8 so I just + + + align:start position:0% +remember to type 1 E minus 8 so I just +typed these these these four five zos or + + align:start position:0% +typed these these these four five zos or + + + align:start position:0% +typed these these these four five zos or +3 four five zos but in any event here's + + align:start position:0% +3 four five zos but in any event here's + + + align:start position:0% +3 four five zos but in any event here's +what the finite difference here here's + + align:start position:0% +what the finite difference here here's + + + align:start position:0% +what the finite difference here here's +the um the the you know the trace of the + + align:start position:0% +the um the the you know the trace of the + + + align:start position:0% +the um the the you know the trace of the +Agate times we see that they're correct + + align:start position:0% +Agate times we see that they're correct + + + align:start position:0% +Agate times we see that they're correct +to enough digits to believe it how come + + align:start position:0% +to enough digits to believe it how come + + + align:start position:0% +to enough digits to believe it how come +the adjugate is not transposed + + align:start position:0% +the adjugate is not transposed + + + align:start position:0% +the adjugate is not transposed +there there's something there's + + align:start position:0% +there there's something there's + + + align:start position:0% +there there's something there's +something something missing here it + + align:start position:0% +something something missing here it + + + align:start position:0% +something something missing here it +should be oh no it's the adjugate yeah + + align:start position:0% +should be oh no it's the adjugate yeah + + + align:start position:0% +should be oh no it's the adjugate yeah +okay right the determinant is the + + align:start position:0% +okay right the determinant is the + + + align:start position:0% +okay right the determinant is the +transpose the ad adjugate never mind + + align:start position:0% +transpose the ad adjugate never mind + + + align:start position:0% +transpose the ad adjugate never mind +never mind so this is the great adjugate + + align:start position:0% +never mind so this is the great adjugate + + + align:start position:0% +never mind so this is the great adjugate +is the great I have to go back and look + + align:start position:0% +is the great I have to go back and look + + + align:start position:0% +is the great I have to go back and look +at these formulas to answer it's the + + align:start position:0% +at these formulas to answer it's the + + + align:start position:0% +at these formulas to answer it's the +transpose of the gradient right so yes + + align:start position:0% +transpose of the gradient right so yes + + + align:start position:0% +transpose of the gradient right so yes +oh because it's it's the right because + + align:start position:0% +oh because it's it's the right because + + + align:start position:0% +oh because it's it's the right because +it's right let me say yes what you just + + align:start position:0% +it's right let me say yes what you just + + + align:start position:0% +it's right let me say yes what you just +said that the the the aggate of the + + align:start position:0% +said that the the the aggate of the + + + align:start position:0% +said that the the the aggate of the +transpose is the thing that you want and + + align:start position:0% +transpose is the thing that you want and + + + align:start position:0% +transpose is the thing that you want and +so the trace needs to transposed it + + align:start position:0% +so the trace needs to transposed it + + + align:start position:0% +so the trace needs to transposed it +twice so it's left + + align:start position:0% +twice so it's left + + + align:start position:0% +twice so it's left +non-trans + + align:start position:0% +non-trans + + + align:start position:0% +non-trans +yeah the you got it the gradient is the + + align:start position:0% +yeah the you got it the gradient is the + + + align:start position:0% +yeah the you got it the gradient is the +one transposed and this has to be the + + align:start position:0% +one transposed and this has to be the + + + align:start position:0% +one transposed and this has to be the +transpose of the gradient yeah this is + + align:start position:0% +transpose of the gradient yeah this is + + + align:start position:0% +transpose of the gradient yeah this is +this is gradient of + + align:start position:0% +this is gradient of + + + align:start position:0% +this is gradient of +determinant right like a double negative + + align:start position:0% +determinant right like a double negative + + + align:start position:0% +determinant right like a double negative +makes a positive a double transpose + + align:start position:0% +makes a positive a double transpose + + + align:start position:0% +makes a positive a double transpose +makes for a noop this is our this is our + + align:start position:0% +makes for a noop this is our this is our + + + align:start position:0% +makes for a noop this is our this is our +do product yep that's + + align:start position:0% +do product yep that's + + + align:start position:0% +do product yep that's +right okay uh so to actually see the + + align:start position:0% +right okay uh so to actually see the + + + align:start position:0% +right okay uh so to actually see the +gradient we can rely on Julia's internal + + align:start position:0% +gradient we can rely on Julia's internal + + + align:start position:0% +gradient we can rely on Julia's internal +forward difference mode for example + + align:start position:0% +forward difference mode for example + + + align:start position:0% +forward difference mode for example +which is um forward differentiation it's + + align:start position:0% +which is um forward differentiation it's + + + align:start position:0% +which is um forward differentiation it's +not forward difference it's it's + + align:start position:0% +not forward difference it's it's + + + align:start position:0% +not forward difference it's it's +automatic differentiation it's different + + align:start position:0% +automatic differentiation it's different + + + align:start position:0% +automatic differentiation it's different +from forward differencing um it's it's + + align:start position:0% +from forward differencing um it's it's + + + align:start position:0% +from forward differencing um it's it's +it's the forward mode automatic I see + + align:start position:0% +it's the forward mode automatic I see + + + align:start position:0% +it's the forward mode automatic I see +this and I think forward differences but + + align:start position:0% +this and I think forward differences but + + + align:start position:0% +this and I think forward differences but +it's not it's it's uh it's it's and I + + align:start position:0% +it's not it's it's uh it's it's and I + + + align:start position:0% +it's not it's it's uh it's it's and I +think in this Le + + align:start position:0% +think in this Le + + + align:start position:0% +think in this Le +if I get a chance to just a little bit + + align:start position:0% +if I get a chance to just a little bit + + + align:start position:0% +if I get a chance to just a little bit +I'll tell you about how this forward + + align:start position:0% +I'll tell you about how this forward + + + align:start position:0% +I'll tell you about how this forward +mode works Ste step kind of gave you one + + align:start position:0% +mode works Ste step kind of gave you one + + + align:start position:0% +mode works Ste step kind of gave you one +view of it I'll give you another view + + align:start position:0% +view of it I'll give you another view + + + align:start position:0% +view of it I'll give you another view +today um but you just say give me the + + align:start position:0% +today um but you just say give me the + + + align:start position:0% +today um but you just say give me the +derivative or the gradient of the + + align:start position:0% +derivative or the gradient of the + + + align:start position:0% +derivative or the gradient of the +determinant function and Julia will + + align:start position:0% +determinant function and Julia will + + + align:start position:0% +determinant function and Julia will +happily do it and of course I can + + align:start position:0% +happily do it and of course I can + + + align:start position:0% +happily do it and of course I can +compare that with the adjugate of a + + align:start position:0% +compare that with the adjugate of a + + + align:start position:0% +compare that with the adjugate of a +transpose and you guys know me by now + + align:start position:0% +transpose and you guys know me by now + + + align:start position:0% +transpose and you guys know me by now +when I see this these things matching uh + + align:start position:0% +when I see this these things matching uh + + + align:start position:0% +when I see this these things matching uh +looks like to all the digits um it makes + + align:start position:0% +looks like to all the digits um it makes + + + align:start position:0% +looks like to all the digits um it makes +me happy it makes me think wow this this + + align:start position:0% +me happy it makes me think wow this this + + + align:start position:0% +me happy it makes me think wow this this +this this this formula for the + + align:start position:0% +this this this formula for the + + + align:start position:0% +this this this formula for the +derivative is is correct right so this + + align:start position:0% +derivative is is correct right so this + + + align:start position:0% +derivative is is correct right so this +for sure is the derivative of of of of + + align:start position:0% +for sure is the derivative of of of of + + + align:start position:0% +for sure is the derivative of of of of +the the of the gradient okay I I don't + + align:start position:0% +the the of the gradient okay I I don't + + + align:start position:0% +the the of the gradient okay I I don't +know maybe I tried to say this be before + + align:start position:0% +know maybe I tried to say this be before + + + align:start position:0% +know maybe I tried to say this be before +but I'm just going to repeat it if if + + align:start position:0% +but I'm just going to repeat it if if + + + align:start position:0% +but I'm just going to repeat it if if +you've heard me say it but just + + align:start position:0% +you've heard me say it but just + + + align:start position:0% +you've heard me say it but just +philosophically I find it remarkable + + align:start position:0% +philosophically I find it remarkable + + + align:start position:0% +philosophically I find it remarkable +that you could think of a limit of a + + align:start position:0% +that you could think of a limit of a + + + align:start position:0% +that you could think of a limit of a +finite difference and like the great + + align:start position:0% +finite difference and like the great + + + align:start position:0% +finite difference and like the great +mathematical Gods let us have a formula + + align:start position:0% +mathematical Gods let us have a formula + + + align:start position:0% +mathematical Gods let us have a formula +for I mean you know you've all done it + + align:start position:0% +for I mean you know you've all done it + + + align:start position:0% +for I mean you know you've all done it +in calculus like the different of a you + + align:start position:0% +in calculus like the different of a you + + + align:start position:0% +in calculus like the different of a you +take a sign and a little bit more sign + + align:start position:0% +take a sign and a little bit more sign + + + align:start position:0% +take a sign and a little bit more sign +you get a cosine right or you know the + + align:start position:0% +you get a cosine right or you know the + + + align:start position:0% +you get a cosine right or you know the +log you get 1 /x or x s you get 2x but + + align:start position:0% +log you get 1 /x or x s you get 2x but + + + align:start position:0% +log you get 1 /x or x s you get 2x but +like I don't know could you guys imagine + + align:start position:0% +like I don't know could you guys imagine + + + align:start position:0% +like I don't know could you guys imagine +a universe where like the mathematical + + align:start position:0% +a universe where like the mathematical + + + align:start position:0% +a universe where like the mathematical +Gods weren't kind enough that like not + + align:start position:0% +Gods weren't kind enough that like not + + + align:start position:0% +Gods weren't kind enough that like not +every integral could be written as as a + + align:start position:0% +every integral could be written as as a + + + align:start position:0% +every integral could be written as as a +formula right I mean that as you know + + align:start position:0% +formula right I mean that as you know + + + align:start position:0% +formula right I mean that as you know +lots of integrals can't be written in + + align:start position:0% +lots of integrals can't be written in + + + align:start position:0% +lots of integrals can't be written in +terms of Elementary functions but right + + align:start position:0% +terms of Elementary functions but right + + + align:start position:0% +terms of Elementary functions but right +but derivatives are you could always do + + align:start position:0% +but derivatives are you could always do + + + align:start position:0% +but derivatives are you could always do +it right and you could do it for scalar + + align:start position:0% +it right and you could do it for scalar + + + align:start position:0% +it right and you could do it for scalar +calculus that's why calculus is so easy + + align:start position:0% +calculus that's why calculus is so easy + + + align:start position:0% +calculus that's why calculus is so easy +to teach and is is a beginning subject + + align:start position:0% +to teach and is is a beginning subject + + + align:start position:0% +to teach and is is a beginning subject +you could do it for Vector calculus and + + align:start position:0% +you could do it for Vector calculus and + + + align:start position:0% +you could do it for Vector calculus and +you could do it for for these + + align:start position:0% +you could do it for for these + + + align:start position:0% +you could do it for for these +complicated Matrix functions I don't + + align:start position:0% +complicated Matrix functions I don't + + + align:start position:0% +complicated Matrix functions I don't +know did do you ever stop and think + + align:start position:0% +know did do you ever stop and think + + + align:start position:0% +know did do you ever stop and think +about that being remarkable you just + + align:start position:0% +about that being remarkable you just + + + align:start position:0% +about that being remarkable you just +take it as a given and and move on with + + align:start position:0% +take it as a given and and move on with + + + align:start position:0% +take it as a given and and move on with +your lives I think it's amazing that we + + align:start position:0% +your lives I think it's amazing that we + + + align:start position:0% +your lives I think it's amazing that we +could have a formula for this difference + + align:start position:0% +could have a formula for this difference + + + align:start position:0% +could have a formula for this difference +I I just do that and a and a simple + + align:start position:0% +I I just do that and a and a simple + + + align:start position:0% +I I just do that and a and a simple +formula in effect uh but you know may + + align:start position:0% +formula in effect uh but you know may + + + align:start position:0% +formula in effect uh but you know may +maybe you guys just take it as as a + + align:start position:0% +maybe you guys just take it as as a + + + align:start position:0% +maybe you guys just take it as as a +granted given but I don't know I think + + align:start position:0% +granted given but I don't know I think + + + align:start position:0% +granted given but I don't know I think +formulas are gifts from the gods and I + + align:start position:0% +formulas are gifts from the gods and I + + + align:start position:0% +formulas are gifts from the gods and I +don't I don't I don't take them for + + align:start position:0% +don't I don't I don't take them for + + + align:start position:0% +don't I don't I don't take them for +granted all right uh so uh just to this + + align:start position:0% +granted all right uh so uh just to this + + + align:start position:0% +granted all right uh so uh just to this +is really just to show you how to do + + align:start position:0% +is really just to show you how to do + + + align:start position:0% +is really just to show you how to do +reverse mode in Julia um so it's it's + + align:start position:0% +reverse mode in Julia um so it's it's + + + align:start position:0% +reverse mode in Julia um so it's it's +it's not much different um it's I've + + align:start position:0% +it's not much different um it's I've + + + align:start position:0% +it's not much different um it's I've +just calling zygo which is one of the + + align:start position:0% +just calling zygo which is one of the + + + align:start position:0% +just calling zygo which is one of the +big popular packages in Julia to do + + align:start position:0% +big popular packages in Julia to do + + + align:start position:0% +big popular packages in Julia to do +reverse mode Auto diff and you see it's + + align:start position:0% +reverse mode Auto diff and you see it's + + + align:start position:0% +reverse mode Auto diff and you see it's +not much different this was for this is + + align:start position:0% +not much different this was for this is + + + align:start position:0% +not much different this was for this is +the for diff package duck gradient and + + align:start position:0% +the for diff package duck gradient and + + + align:start position:0% +the for diff package duck gradient and +this is the um zygo duck gradient and uh + + align:start position:0% +this is the um zygo duck gradient and uh + + + align:start position:0% +this is the um zygo duck gradient and uh +under the hood it's doing it's getting + + align:start position:0% +under the hood it's doing it's getting + + + align:start position:0% +under the hood it's doing it's getting +the answer in a completely different way + + align:start position:0% +the answer in a completely different way + + + align:start position:0% +the answer in a completely different way +by going mode but it actually gives the + + align:start position:0% +by going mode but it actually gives the + + + align:start position:0% +by going mode but it actually gives the +same + + align:start position:0% +same + + + align:start position:0% +same +answer okay um though I wouldn't be + + align:start position:0% +answer okay um though I wouldn't be + + + align:start position:0% +answer okay um though I wouldn't be +surprised maybe Steph knows better I + + align:start position:0% +surprised maybe Steph knows better I + + + align:start position:0% +surprised maybe Steph knows better I +wouldn't be surprised if this is just + + align:start position:0% +wouldn't be surprised if this is just + + + align:start position:0% +wouldn't be surprised if this is just +built in formulas in both cases I don't + + align:start position:0% +built in formulas in both cases I don't + + + align:start position:0% +built in formulas in both cases I don't +know uh let's see we could do it + + align:start position:0% +know uh let's see we could do it + + + align:start position:0% +know uh let's see we could do it +symbolically but let's get to the proof + + align:start position:0% +symbolically but let's get to the proof + + + align:start position:0% +symbolically but let's get to the proof +so there are a couple of ways to prove + + align:start position:0% +so there are a couple of ways to prove + + + align:start position:0% +so there are a couple of ways to prove +this uh mathematically so um one + + align:start position:0% +this uh mathematically so um one + + + align:start position:0% +this uh mathematically so um one +relatively simple proof is to remember + + align:start position:0% +relatively simple proof is to remember + + + align:start position:0% +relatively simple proof is to remember +the llao expansion of a of a determinant + + align:start position:0% +the llao expansion of a of a determinant + + + align:start position:0% +the llao expansion of a of a determinant +so I I I I suspect you all remember that + + align:start position:0% +so I I I I suspect you all remember that + + + align:start position:0% +so I I I I suspect you all remember that +if you want to calculate the determinant + + align:start position:0% +if you want to calculate the determinant + + + align:start position:0% +if you want to calculate the determinant +of a big Matrix uh usually people take + + align:start position:0% +of a big Matrix uh usually people take + + + align:start position:0% +of a big Matrix uh usually people take +maybe the first row but in fact you + + align:start position:0% +maybe the first row but in fact you + + + align:start position:0% +maybe the first row but in fact you +could take any row but do you remember + + align:start position:0% +could take any row but do you remember + + + align:start position:0% +could take any row but do you remember +you take the the first the the top left + + align:start position:0% +you take the the first the the top left + + + align:start position:0% +you take the the first the the top left +entry times the determinant of of of the + + align:start position:0% +entry times the determinant of of of the + + + align:start position:0% +entry times the determinant of of of the +you know what happens if you cross out + + align:start position:0% +you know what happens if you cross out + + + align:start position:0% +you know what happens if you cross out +the first row and First Column then the + + align:start position:0% +the first row and First Column then the + + + align:start position:0% +the first row and First Column then the +second entry and you cross out that row + + align:start position:0% +second entry and you cross out that row + + + align:start position:0% +second entry and you cross out that row +and column with a minus sign plus minus + + align:start position:0% +and column with a minus sign plus minus + + + align:start position:0% +and column with a minus sign plus minus +plus minus you remember that rule so + + align:start position:0% +plus minus you remember that rule so + + + align:start position:0% +plus minus you remember that rule so +that that that's lass's that's the lass + + align:start position:0% +that that that's lass's that's the lass + + + align:start position:0% +that that that's lass's that's the lass +expansion + + align:start position:0% +expansion + + + align:start position:0% +expansion +and um the key fact is that U if for + + align:start position:0% +and um the key fact is that U if for + + + align:start position:0% +and um the key fact is that U if for +example if I'm working with ai1 let's + + align:start position:0% +example if I'm working with ai1 let's + + + align:start position:0% +example if I'm working with ai1 let's +say I'm starting with the I throw then + + align:start position:0% +say I'm starting with the I throw then + + + align:start position:0% +say I'm starting with the I throw then +ai1 is not inside any of these C's right + + align:start position:0% +ai1 is not inside any of these C's right + + + align:start position:0% +ai1 is not inside any of these C's right +it's ai1 only appears here right + + align:start position:0% +it's ai1 only appears here right + + + align:start position:0% +it's ai1 only appears here right +everything else you see depends on other + + align:start position:0% +everything else you see depends on other + + + align:start position:0% +everything else you see depends on other +elements of the Matrix but it doesn't + + align:start position:0% +elements of the Matrix but it doesn't + + + align:start position:0% +elements of the Matrix but it doesn't +depend on ai1 right similarly if you + + align:start position:0% +depend on ai1 right similarly if you + + + align:start position:0% +depend on ai1 right similarly if you +look at ai2 ci2 and every every other + + align:start position:0% +look at ai2 ci2 and every every other + + + align:start position:0% +look at ai2 ci2 and every every other +term only depends on ai2 and just to + + align:start position:0% +term only depends on ai2 and just to + + + align:start position:0% +term only depends on ai2 and just to +make that point very clear uh here what + + align:start position:0% +make that point very clear uh here what + + + align:start position:0% +make that point very clear uh here what +I did was I took this Matrix and I made + + align:start position:0% +I did was I took this Matrix and I made + + + align:start position:0% +I did was I took this Matrix and I made +this Matrix uh this 3x3 Matrix you'll + + align:start position:0% +this Matrix uh this 3x3 Matrix you'll + + + align:start position:0% +this Matrix uh this 3x3 Matrix you'll +see it's almost completely numerical but + + align:start position:0% +see it's almost completely numerical but + + + align:start position:0% +see it's almost completely numerical but +I put one symbol in the bottom right + + align:start position:0% +I put one symbol in the bottom right + + + align:start position:0% +I put one symbol in the bottom right +okay and if you take the determinant + + align:start position:0% +okay and if you take the determinant + + + align:start position:0% +okay and if you take the determinant +right you see that this is an uh I don't + + align:start position:0% +right you see that this is an uh I don't + + + align:start position:0% +right you see that this is an uh I don't +know whether to call this a linear or an + + align:start position:0% +know whether to call this a linear or an + + + align:start position:0% +know whether to call this a linear or an +apine + + align:start position:0% +apine + + + align:start position:0% +apine +function + + align:start position:0% +function + + + align:start position:0% +function +aine aine for this class some people + + align:start position:0% +aine aine for this class some people + + + align:start position:0% +aine aine for this class some people +would actually say it's um it it's + + align:start position:0% +would actually say it's um it it's + + + align:start position:0% +would actually say it's um it it's +linear in in the sense of linear + + align:start position:0% +linear in in the sense of linear + + + align:start position:0% +linear in in the sense of linear +quadratic cub right it's first-degree + + align:start position:0% +quadratic cub right it's first-degree + + + align:start position:0% +quadratic cub right it's first-degree +polinomial um but let's call it + + align:start position:0% +polinomial um but let's call it + + + align:start position:0% +polinomial um but let's call it +apine for the purposes of this class + + align:start position:0% +apine for the purposes of this class + + + align:start position:0% +apine for the purposes of this class +because it's it's not 13A plus 0 um but + + align:start position:0% +because it's it's not 13A plus 0 um but + + + align:start position:0% +because it's it's not 13A plus 0 um but +whatever it is it's a first-degree + + align:start position:0% +whatever it is it's a first-degree + + + align:start position:0% +whatever it is it's a first-degree +polinomial right is is what it is um and + + align:start position:0% +polinomial right is is what it is um and + + + align:start position:0% +polinomial right is is what it is um and +the fact of the matter is the + + align:start position:0% +the fact of the matter is the + + + align:start position:0% +the fact of the matter is the +coefficient of a is exactly this + + align:start position:0% +coefficient of a is exactly this + + + align:start position:0% +coefficient of a is exactly this +determinant it's the one that it's 4 * 4 + + align:start position:0% +determinant it's the one that it's 4 * 4 + + + align:start position:0% +determinant it's the one that it's 4 * 4 +- 3 right it's 16 - 3 it's 13 right and + + align:start position:0% +- 3 right it's 16 - 3 it's 13 right and + + + align:start position:0% +- 3 right it's 16 - 3 it's 13 right and +so so the the coefficient of every if if + + align:start position:0% +so so the the coefficient of every if if + + + align:start position:0% +so so the the coefficient of every if if +you if you make any symbol Sy any + + align:start position:0% +you if you make any symbol Sy any + + + align:start position:0% +you if you make any symbol Sy any +element of symbol the coefficient that's + + align:start position:0% +element of symbol the coefficient that's + + + align:start position:0% +element of symbol the coefficient that's +in front of it is just this this minor + + align:start position:0% +in front of it is just this this minor + + + align:start position:0% +in front of it is just this this minor +right and so um so taking derivatives of + + align:start position:0% +right and so um so taking derivatives of + + + align:start position:0% +right and so um so taking derivatives of +of first-degree functions is easy it's + + align:start position:0% +of first-degree functions is easy it's + + + align:start position:0% +of first-degree functions is easy it's +just the slope right the derivative of + + align:start position:0% +just the slope right the derivative of + + + align:start position:0% +just the slope right the derivative of +this determinant with respect to this + + align:start position:0% +this determinant with respect to this + + + align:start position:0% +this determinant with respect to this +element is clearly the number 13 right + + align:start position:0% +element is clearly the number 13 right + + + align:start position:0% +element is clearly the number 13 right +and so the the way to say this in + + align:start position:0% +and so the the way to say this in + + + align:start position:0% +and so the the way to say this in +general is if I want to take the Der of + + align:start position:0% +general is if I want to take the Der of + + + align:start position:0% +general is if I want to take the Der of +the determinant with respect to any AI J + + align:start position:0% +the determinant with respect to any AI J + + + align:start position:0% +the determinant with respect to any AI J +element the slope is is the thing that + + align:start position:0% +element the slope is is the thing that + + + align:start position:0% +element the slope is is the thing that +multiplies it so it's the i j + + align:start position:0% +multiplies it so it's the i j + + + align:start position:0% +multiplies it so it's the i j +okay and so that is one immediate way to + + align:start position:0% +okay and so that is one immediate way to + + + align:start position:0% +okay and so that is one immediate way to +conclude that the gradient of the + + align:start position:0% +conclude that the gradient of the + + + align:start position:0% +conclude that the gradient of the +determinant is the co-actor matrix it's + + align:start position:0% +determinant is the co-actor matrix it's + + + align:start position:0% +determinant is the co-actor matrix it's +that simple okay there's another proof + + align:start position:0% +that simple okay there's another proof + + + align:start position:0% +that simple okay there's another proof +that is sort of uh if this is more I + + align:start position:0% +that is sort of uh if this is more I + + + align:start position:0% +that is sort of uh if this is more I +mean this proof is pretty simple I think + + align:start position:0% +mean this proof is pretty simple I think + + + align:start position:0% +mean this proof is pretty simple I think +it's easy to agree that this is a nice + + align:start position:0% +it's easy to agree that this is a nice + + + align:start position:0% +it's easy to agree that this is a nice +simple proof U there's another proof + + align:start position:0% +simple proof U there's another proof + + + align:start position:0% +simple proof U there's another proof +that might seem a slightly harder in one + + align:start position:0% +that might seem a slightly harder in one + + + align:start position:0% +that might seem a slightly harder in one +way but mathemat but in a way it's sort + + align:start position:0% +way but mathemat but in a way it's sort + + + align:start position:0% +way but mathemat but in a way it's sort +of you know mathematicians like this + + align:start position:0% +of you know mathematicians like this + + + align:start position:0% +of you know mathematicians like this +kind of proof and so you know you get to + + align:start position:0% +kind of proof and so you know you get to + + + align:start position:0% +kind of proof and so you know you get to +take your pick which one you like best + + align:start position:0% +take your pick which one you like best + + + align:start position:0% +take your pick which one you like best +but let me just show you an alternative + + align:start position:0% +but let me just show you an alternative + + + align:start position:0% +but let me just show you an alternative +proof so in this alternative proof what + + align:start position:0% +proof so in this alternative proof what + + + align:start position:0% +proof so in this alternative proof what +we're going to do is we're going to + + align:start position:0% +we're going to do is we're going to + + + align:start position:0% +we're going to do is we're going to +figure out the right answer near the + + align:start position:0% +figure out the right answer near the + + + align:start position:0% +figure out the right answer near the +identity and then we're going to you + + align:start position:0% +identity and then we're going to you + + + align:start position:0% +identity and then we're going to you +know and then we're going to use that to + + align:start position:0% +know and then we're going to use that to + + + align:start position:0% +know and then we're going to use that to +bootstrap ourselves to any other Matrix + + align:start position:0% +bootstrap ourselves to any other Matrix + + + align:start position:0% +bootstrap ourselves to any other Matrix +okay so if you you you know you know how + + align:start position:0% +okay so if you you you know you know how + + + align:start position:0% +okay so if you you you know you know how +to expand like you're you're all + + align:start position:0% +to expand like you're you're all + + + align:start position:0% +to expand like you're you're all +familiar if I ask you to compute the + + align:start position:0% +familiar if I ask you to compute the + + + align:start position:0% +familiar if I ask you to compute the +characteristic polinomial of a matrix + + align:start position:0% +characteristic polinomial of a matrix + + + align:start position:0% +characteristic polinomial of a matrix +let's call it m right if I need to do + + align:start position:0% +let's call it m right if I need to do + + + align:start position:0% +let's call it m right if I need to do +the charact I'll I'll do what Steven + + align:start position:0% +the charact I'll I'll do what Steven + + + align:start position:0% +the charact I'll I'll do what Steven +does and I'll do it like this so if + + align:start position:0% +does and I'll do it like this so if + + + align:start position:0% +does and I'll do it like this so if +anybody asked you to calculate uh the + + align:start position:0% +anybody asked you to calculate uh the + + + align:start position:0% +anybody asked you to calculate uh the +characteristic + + align:start position:0% +characteristic + + + align:start position:0% +characteristic +polinomial and I'm using the mouse which + + align:start position:0% +polinomial and I'm using the mouse which + + + align:start position:0% +polinomial and I'm using the mouse which +means that it's really + + align:start position:0% +means that it's really + + + align:start position:0% +means that it's really +sloppy not that my handwriting is so + + align:start position:0% +sloppy not that my handwriting is so + + + align:start position:0% +sloppy not that my handwriting is so +great but it's not this bad all right so + + align:start position:0% +great but it's not this bad all right so + + + align:start position:0% +great but it's not this bad all right so +the characteristic polinomial of any + + align:start position:0% +the characteristic polinomial of any + + + align:start position:0% +the characteristic polinomial of any +Matrix m is usually written like this + + align:start position:0% +Matrix m is usually written like this + + + align:start position:0% +Matrix m is usually written like this +right and U and and you know there's + + align:start position:0% +right and U and and you know there's + + + align:start position:0% +right and U and and you know there's +lots of factors there's know Lambda to + + align:start position:0% +lots of factors there's know Lambda to + + + align:start position:0% +lots of factors there's know Lambda to +the n and you know all the way down to + + align:start position:0% +the n and you know all the way down to + + + align:start position:0% +the n and you know all the way down to +to the determinant you know plus or + + align:start position:0% +to the determinant you know plus or + + + align:start position:0% +to the determinant you know plus or +minus the determinant of M right so you + + align:start position:0% +minus the determinant of M right so you + + + align:start position:0% +minus the determinant of M right so you +you remember that right + + align:start position:0% +you remember that right + + + align:start position:0% +you remember that right +and and if you want you can you you can + + align:start position:0% +and and if you want you can you you can + + + align:start position:0% +and and if you want you can you you can +uh if if you want you can make this a + + align:start position:0% +uh if if you want you can make this a + + + align:start position:0% +uh if if you want you can make this a +plus sign and then you get all plus + + align:start position:0% +plus sign and then you get all plus + + + align:start position:0% +plus sign and then you get all plus +signs in that in this whole formula + + align:start position:0% +signs in that in this whole formula + + + align:start position:0% +signs in that in this whole formula +right and so uh this is not much + + align:start position:0% +right and so uh this is not much + + + align:start position:0% +right and so uh this is not much +different here if Lambda was one if you + + align:start position:0% +different here if Lambda was one if you + + + align:start position:0% +different here if Lambda was one if you +just took Lambda equals 1 right you'd + + align:start position:0% +just took Lambda equals 1 right you'd + + + align:start position:0% +just took Lambda equals 1 right you'd +have determinant of I well here let's + + align:start position:0% +have determinant of I well here let's + + + align:start position:0% +have determinant of I well here let's +just see it this way determinant of i+ a + + align:start position:0% +just see it this way determinant of i+ a + + + align:start position:0% +just see it this way determinant of i+ a +matrix right would be + + align:start position:0% +matrix right would be + + + align:start position:0% +matrix right would be +1+ right and then there' be the terms + + align:start position:0% +1+ right and then there' be the terms + + + align:start position:0% +1+ right and then there' be the terms +that you get there would be the next + + align:start position:0% +that you get there would be the next + + + align:start position:0% +that you get there would be the next +terms right this thing here as you all + + align:start position:0% +terms right this thing here as you all + + + align:start position:0% +terms right this thing here as you all +know is the trace of the Matrix right so + + align:start position:0% +know is the trace of the Matrix right so + + + align:start position:0% +know is the trace of the Matrix right so +maybe I should have put that in you get + + align:start position:0% +maybe I should have put that in you get + + + align:start position:0% +maybe I should have put that in you get +Lambda to the N plus Lambda to the N + + align:start position:0% +Lambda to the N plus Lambda to the N + + + align:start position:0% +Lambda to the N plus Lambda to the N +minus1 times the trace of the Matrix + + align:start position:0% +minus1 times the trace of the Matrix + + + align:start position:0% +minus1 times the trace of the Matrix +right so + + align:start position:0% +right so + + + align:start position:0% +right so +that's so if you make a tiny little + + align:start position:0% +that's so if you make a tiny little + + + align:start position:0% +that's so if you make a tiny little +perturbation uh you know the determinant + + align:start position:0% +perturbation uh you know the determinant + + + align:start position:0% +perturbation uh you know the determinant +of I plus da I guess I should have made + + align:start position:0% +of I plus da I guess I should have made + + + align:start position:0% +of I plus da I guess I should have made +this 1 plus the trace of Da to be honest + + align:start position:0% +this 1 plus the trace of Da to be honest + + + align:start position:0% +this 1 plus the trace of Da to be honest +let's fix that right now right so the + + align:start position:0% +let's fix that right now right so the + + + align:start position:0% +let's fix that right now right so the +determinant of I + da would be 1 that + + align:start position:0% +determinant of I + da would be 1 that + + + align:start position:0% +determinant of I + da would be 1 that +would be like 1 to the N plus 1 the N + + align:start position:0% +would be like 1 to the N plus 1 the N + + + align:start position:0% +would be like 1 to the N plus 1 the N +minus 1 time the trace of the Matrix + + align:start position:0% +minus 1 time the trace of the Matrix + + + align:start position:0% +minus 1 time the trace of the Matrix +right and then they're the lower order + + align:start position:0% +right and then they're the lower order + + + align:start position:0% +right and then they're the lower order +terms right so + + align:start position:0% +terms right so + + + align:start position:0% +terms right so +um uh so that's one way to think of it + + align:start position:0% +um uh so that's one way to think of it + + + align:start position:0% +um uh so that's one way to think of it +and so there there we immediately get + + align:start position:0% +and so there there we immediately get + + + align:start position:0% +and so there there we immediately get +you know the answer around the identity + + align:start position:0% +you know the answer around the identity + + + align:start position:0% +you know the answer around the identity +and now if we want to get this anywhere + + align:start position:0% +and now if we want to get this anywhere + + + align:start position:0% +and now if we want to get this anywhere +all we have to do is recognize that if + + align:start position:0% +all we have to do is recognize that if + + + align:start position:0% +all we have to do is recognize that if +we want to go the determinant of a plus + + align:start position:0% +we want to go the determinant of a plus + + + align:start position:0% +we want to go the determinant of a plus +da then we just go a * a inverse over + + align:start position:0% +da then we just go a * a inverse over + + + align:start position:0% +da then we just go a * a inverse over +here that's just the identity but then + + align:start position:0% +here that's just the identity but then + + + align:start position:0% +here that's just the identity but then +we can use the properties of of + + align:start position:0% +we can use the properties of of + + + align:start position:0% +we can use the properties of of +determinants to pull out the determinant + + align:start position:0% +determinants to pull out the determinant + + + align:start position:0% +determinants to pull out the determinant +of a and you just get I plus a inverse + + align:start position:0% +of a and you just get I plus a inverse + + + align:start position:0% +of a and you just get I plus a inverse +da right and um and and so uh uh and + + align:start position:0% +da right and um and and so uh uh and + + + align:start position:0% +da right and um and and so uh uh and +this basically here here we just think + + align:start position:0% +this basically here here we just think + + + align:start position:0% +this basically here here we just think +of this a inverse da as as the trace + + align:start position:0% +of this a inverse da as as the trace + + + align:start position:0% +of this a inverse da as as the trace +formula right and therefore we get our + + align:start position:0% +formula right and therefore we get our + + + align:start position:0% +formula right and therefore we get our +answer + + align:start position:0% +answer + + + align:start position:0% +answer +right the very answer we're looking for + + align:start position:0% +right the very answer we're looking for + + + align:start position:0% +right the very answer we're looking for +in a way this is more complicated but + + align:start position:0% +in a way this is more complicated but + + + align:start position:0% +in a way this is more complicated but +mathematicians like this one better than + + align:start position:0% +mathematicians like this one better than + + + align:start position:0% +mathematicians like this one better than +I don't know why they're they're both + + align:start position:0% +I don't know why they're they're both + + + align:start position:0% +I don't know why they're they're both +valid you get to take your pick um + + align:start position:0% +valid you get to take your pick um + + + align:start position:0% +valid you get to take your pick um +there's something I like about this + + align:start position:0% +there's something I like about this + + + align:start position:0% +there's something I like about this +though it is a little bit more + + align:start position:0% +though it is a little bit more + + + align:start position:0% +though it is a little bit more +complicated okay but in any event we get + + align:start position:0% +complicated okay but in any event we get + + + align:start position:0% +complicated okay but in any event we get +the same answer okay so what do we have + + align:start position:0% +the same answer okay so what do we have + + + align:start position:0% +the same answer okay so what do we have +here so application to the derivative of + + align:start position:0% +here so application to the derivative of + + + align:start position:0% +here so application to the derivative of +the uh characteristic polinomial so + + align:start position:0% +the uh characteristic polinomial so + + + align:start position:0% +the uh characteristic polinomial so +U so uh once again there's the simple + + align:start position:0% +U so uh once again there's the simple + + + align:start position:0% +U so uh once again there's the simple +proof the characteristic polinomial of a + + align:start position:0% +proof the characteristic polinomial of a + + + align:start position:0% +proof the characteristic polinomial of a +matrix is the product of xus the igen + + align:start position:0% +matrix is the product of xus the igen + + + align:start position:0% +matrix is the product of xus the igen +values probably a different sign from + + align:start position:0% +values probably a different sign from + + + align:start position:0% +values probably a different sign from +what I had here you take the derivative + + align:start position:0% +what I had here you take the derivative + + + align:start position:0% +what I had here you take the derivative +of this product you get the sum of these + + align:start position:0% +of this product you get the sum of these + + + align:start position:0% +of this product you get the sum of these +products n minus one at a time which you + + align:start position:0% +products n minus one at a time which you + + + align:start position:0% +products n minus one at a time which you +could rewrite like this but you can also + + align:start position:0% +could rewrite like this but you can also + + + align:start position:0% +could rewrite like this but you can also +directly do with our with our technology + + align:start position:0% +directly do with our with our technology + + + align:start position:0% +directly do with our with our technology +you can do this and uh get basically the + + align:start position:0% +you can do this and uh get basically the + + + align:start position:0% +you can do this and uh get basically the +same answer as the direct proof okay and + + align:start position:0% +same answer as the direct proof okay and + + + align:start position:0% +same answer as the direct proof okay and +then I have some numerical + + align:start position:0% +then I have some numerical + + + align:start position:0% +then I have some numerical +checks uh let's see and the derivative + + align:start position:0% +checks uh let's see and the derivative + + + align:start position:0% +checks uh let's see and the derivative +of the log determin log of determinant + + align:start position:0% +of the log determin log of determinant + + + align:start position:0% +of the log determin log of determinant +comes up a lot logs of lots of functions + + align:start position:0% +comes up a lot logs of lots of functions + + + align:start position:0% +comes up a lot logs of lots of functions +come up a lot for example stepen about I + + align:start position:0% +come up a lot for example stepen about I + + + align:start position:0% +come up a lot for example stepen about I +don't know a few lectures ago talked + + align:start position:0% +don't know a few lectures ago talked + + + align:start position:0% +don't know a few lectures ago talked +about uh this F over fpre it's what + + align:start position:0% +about uh this F over fpre it's what + + + align:start position:0% +about uh this F over fpre it's what +shows up whenever you do anybody's + + align:start position:0% +shows up whenever you do anybody's + + + align:start position:0% +shows up whenever you do anybody's +Newton's method right and of course this + + align:start position:0% +Newton's method right and of course this + + + align:start position:0% +Newton's method right and of course this +could be written as one over the the log + + align:start position:0% +could be written as one over the the log + + + align:start position:0% +could be written as one over the the log +F Prime right so the basically the + + align:start position:0% +F Prime right so the basically the + + + align:start position:0% +F Prime right so the basically the +logarithmic derivative and it's + + align:start position:0% +logarithmic derivative and it's + + + align:start position:0% +logarithmic derivative and it's +reciprocal come up all over mathematics + + align:start position:0% +reciprocal come up all over mathematics + + + align:start position:0% +reciprocal come up all over mathematics +so uh the derivative of the log of the + + align:start position:0% +so uh the derivative of the log of the + + + align:start position:0% +so uh the derivative of the log of the +determinant is uh is simply the trace of + + align:start position:0% +determinant is uh is simply the trace of + + + align:start position:0% +determinant is uh is simply the trace of +the inverse times the The Da okay this + + align:start position:0% +the inverse times the The Da okay this + + + align:start position:0% +the inverse times the The Da okay this +you've seen a inverse and that's it okay + + align:start position:0% +you've seen a inverse and that's it okay + + + align:start position:0% +you've seen a inverse and that's it okay +any questions that that that basically + + align:start position:0% +any questions that that that basically + + + align:start position:0% +any questions that that that basically +covers the uh gradient of the + + align:start position:0% +covers the uh gradient of the + + + align:start position:0% +covers the uh gradient of the +determinant any questions about + + align:start position:0% +determinant any questions about + + + align:start position:0% +determinant any questions about +that so maybe a few words about + + align:start position:0% +that so maybe a few words about + + + align:start position:0% +that so maybe a few words about +determinant interestingly + + align:start position:0% +determinant interestingly + + + align:start position:0% +determinant interestingly +enough people often tell you that you + + align:start position:0% +enough people often tell you that you + + + align:start position:0% +enough people often tell you that you +should never compute a determinant or + + align:start position:0% +should never compute a determinant or + + + align:start position:0% +should never compute a determinant or +hardly ever might be a fair term so + + align:start position:0% +hardly ever might be a fair term so + + + align:start position:0% +hardly ever might be a fair term so +determinants are are are real you know + + align:start position:0% +determinants are are are real you know + + + align:start position:0% +determinants are are are real you know +it's a real favorite of Elementary + + align:start position:0% +it's a real favorite of Elementary + + + align:start position:0% +it's a real favorite of Elementary +linear algebra classes + + align:start position:0% +linear algebra classes + + + align:start position:0% +linear algebra classes +right determinants are great for telling + + align:start position:0% +right determinants are great for telling + + + align:start position:0% +right determinants are great for telling +you in exact arithmetic whether a matrix + + align:start position:0% +you in exact arithmetic whether a matrix + + + align:start position:0% +you in exact arithmetic whether a matrix +is singular or not right so a matrix has + + align:start position:0% +is singular or not right so a matrix has + + + align:start position:0% +is singular or not right so a matrix has +determinant zero it's singular if the + + align:start position:0% +determinant zero it's singular if the + + + align:start position:0% +determinant zero it's singular if the +determinant is not zero it's not and um + + align:start position:0% +determinant is not zero it's not and um + + + align:start position:0% +determinant is not zero it's not and um +you know and and that sounds like a + + align:start position:0% +you know and and that sounds like a + + + align:start position:0% +you know and and that sounds like a +really good idea to have something like + + align:start position:0% +really good idea to have something like + + + align:start position:0% +really good idea to have something like +that but it turns out that uh when + + align:start position:0% +that but it turns out that uh when + + + align:start position:0% +that but it turns out that uh when +you're doing when you're when you're + + align:start position:0% +you're doing when you're when you're + + + align:start position:0% +you're doing when you're when you're +doing computations in finite Precision + + align:start position:0% +doing computations in finite Precision + + + align:start position:0% +doing computations in finite Precision +if you're doing it on a computer uh the + + align:start position:0% +if you're doing it on a computer uh the + + + align:start position:0% +if you're doing it on a computer uh the +determinant turns out to be not so + + align:start position:0% +determinant turns out to be not so + + + align:start position:0% +determinant turns out to be not so +meaningful it gets to be hard to compute + + align:start position:0% +meaningful it gets to be hard to compute + + + align:start position:0% +meaningful it gets to be hard to compute +accurately there are a lot of issues + + align:start position:0% +accurately there are a lot of issues + + + align:start position:0% +accurately there are a lot of issues +with calculating the determinant it + + align:start position:0% +with calculating the determinant it + + + align:start position:0% +with calculating the determinant it +turns out that while the pure + + align:start position:0% +turns out that while the pure + + + align:start position:0% +turns out that while the pure +mathematicians live in a binary world + + align:start position:0% +mathematicians live in a binary world + + + align:start position:0% +mathematicians live in a binary world +where a matrix is singular or non-s + + align:start position:0% +where a matrix is singular or non-s + + + align:start position:0% +where a matrix is singular or non-s +singular the truth of the matter is is + + align:start position:0% +singular the truth of the matter is is + + + align:start position:0% +singular the truth of the matter is is +that the world of of of matrices is is + + align:start position:0% +that the world of of of matrices is is + + + align:start position:0% +that the world of of of matrices is is +not so binary it's it's a bit more of a + + align:start position:0% +not so binary it's it's a bit more of a + + + align:start position:0% +not so binary it's it's a bit more of a +of a spectrum where matrices are are + + align:start position:0% +of a spectrum where matrices are are + + + align:start position:0% +of a spectrum where matrices are are +singular or nearly singular or a little + + align:start position:0% +singular or nearly singular or a little + + + align:start position:0% +singular or nearly singular or a little +bit bad or not you know or or or or not + + align:start position:0% +bit bad or not you know or or or or not + + + align:start position:0% +bit bad or not you know or or or or not +at all bad and probably you've all heard + + align:start position:0% +at all bad and probably you've all heard + + + align:start position:0% +at all bad and probably you've all heard +the word that I'm I'm referring to the + + align:start position:0% +the word that I'm I'm referring to the + + + align:start position:0% +the word that I'm I'm referring to the +word that we use in numerical analysis + + align:start position:0% +word that we use in numerical analysis + + + align:start position:0% +word that we use in numerical analysis +is is conditioning so ill conditioned + + align:start position:0% +is is conditioning so ill conditioned + + + align:start position:0% +is is conditioning so ill conditioned +means a matrix is nearly singular right + + align:start position:0% +means a matrix is nearly singular right + + + align:start position:0% +means a matrix is nearly singular right +and well conditioned means that it's you + + align:start position:0% +and well conditioned means that it's you + + + align:start position:0% +and well conditioned means that it's you +know it's it's it's very it it it's very + + align:start position:0% +know it's it's it's very it it it's very + + + align:start position:0% +know it's it's it's very it it it's very +non-s singular right it's it's too many + + align:start position:0% +non-s singular right it's it's too many + + + align:start position:0% +non-s singular right it's it's too many +double negatives there but it's sort of + + align:start position:0% +double negatives there but it's sort of + + + align:start position:0% +double negatives there but it's sort of +the good side of singular right when we + + align:start position:0% +the good side of singular right when we + + + align:start position:0% +the good side of singular right when we +say it's well conditioned right and so + + align:start position:0% +say it's well conditioned right and so + + + align:start position:0% +say it's well conditioned right and so +uh and and so uh the determinant doesn't + + align:start position:0% +uh and and so uh the determinant doesn't + + + align:start position:0% +uh and and so uh the determinant doesn't +really good give the determinant is not + + align:start position:0% +really good give the determinant is not + + + align:start position:0% +really good give the determinant is not +really good give a good job of talking + + align:start position:0% +really good give a good job of talking + + + align:start position:0% +really good give a good job of talking +about you know how nearly singular + + align:start position:0% +about you know how nearly singular + + + align:start position:0% +about you know how nearly singular +matrices are the the condition number + + align:start position:0% +matrices are the the condition number + + + align:start position:0% +matrices are the the condition number +which which is related to singular + + align:start position:0% +which which is related to singular + + + align:start position:0% +which which is related to singular +values I'm not going to talk about that + + align:start position:0% +values I'm not going to talk about that + + + align:start position:0% +values I'm not going to talk about that +today is a much better way of talking + + align:start position:0% +today is a much better way of talking + + + align:start position:0% +today is a much better way of talking +about uh matrices being singular or not + + align:start position:0% +about uh matrices being singular or not + + + align:start position:0% +about uh matrices being singular or not +so you know you learned it all in in in + + align:start position:0% +so you know you learned it all in in in + + + align:start position:0% +so you know you learned it all in in in +a course like 1806 or Elementary linear + + align:start position:0% +a course like 1806 or Elementary linear + + + align:start position:0% +a course like 1806 or Elementary linear +algebra you learned about determinants + + align:start position:0% +algebra you learned about determinants + + + align:start position:0% +algebra you learned about determinants +and then later on when you compute + + align:start position:0% +and then later on when you compute + + + align:start position:0% +and then later on when you compute +people tell you to forget about + + align:start position:0% +people tell you to forget about + + + align:start position:0% +people tell you to forget about +determinance right mostly there are + + align:start position:0% +determinance right mostly there are + + + align:start position:0% +determinance right mostly there are +times but mostly okay so that uh and the + + align:start position:0% +times but mostly okay so that uh and the + + + align:start position:0% +times but mostly okay so that uh and the +other thing we tell people to do is + + align:start position:0% +other thing we tell people to do is + + + align:start position:0% +other thing we tell people to do is +forget about the characteristic + + align:start position:0% +forget about the characteristic + + + align:start position:0% +forget about the characteristic +polinomial as well that's that's not how + + align:start position:0% +polinomial as well that's that's not how + + + align:start position:0% +polinomial as well that's that's not how +we calculate igen values either we don't + + align:start position:0% +we calculate igen values either we don't + + + align:start position:0% +we calculate igen values either we don't +take roots of + + align:start position:0% +take roots of + + + align:start position:0% +take roots of +polinomial anybody happen to know how we + + align:start position:0% +polinomial anybody happen to know how we + + + align:start position:0% +polinomial anybody happen to know how we +compute igen values in the real world we + + align:start position:0% +compute igen values in the real world we + + + align:start position:0% +compute igen values in the real world we +don't we don't do cartic polinomial + + align:start position:0% +don't we don't do cartic polinomial + + + align:start position:0% +don't we don't do cartic polinomial +anybody know the magic two letters that + + align:start position:0% +anybody know the magic two letters that + + + align:start position:0% +anybody know the magic two letters that +that that that happen when you type igen + + align:start position:0% +that that that happen when you type igen + + + align:start position:0% +that that that happen when you type igen +values do you how many of you just + + align:start position:0% +values do you how many of you just + + + align:start position:0% +values do you how many of you just +thought it was the car polinomial you + + align:start position:0% +thought it was the car polinomial you + + + align:start position:0% +thought it was the car polinomial you +take the + + align:start position:0% +take the + + + align:start position:0% +take the +roots how many how many of you had any + + align:start position:0% +roots how many how many of you had any + + + align:start position:0% +roots how many how many of you had any +idea how Roots got taken on a ag got + + align:start position:0% +idea how Roots got taken on a ag got + + + align:start position:0% +idea how Roots got taken on a ag got +taken on a computer so you have any idea + + align:start position:0% +taken on a computer so you have any idea + + + align:start position:0% +taken on a computer so you have any idea +what what the algorithm is being + + align:start position:0% + + + + align:start position:0% + +used the power method yeah okay so um + + align:start position:0% +used the power method yeah okay so um + + + align:start position:0% +used the power method yeah okay so um +you probably didn't hear this student + + align:start position:0% +you probably didn't hear this student + + + align:start position:0% +you probably didn't hear this student +saying that well in 1806 I learned about + + align:start position:0% +saying that well in 1806 I learned about + + + align:start position:0% +saying that well in 1806 I learned about +something like the power method which + + align:start position:0% +something like the power method which + + + align:start position:0% +something like the power method which +gives you the dominant I value yeah so + + align:start position:0% +gives you the dominant I value yeah so + + + align:start position:0% +gives you the dominant I value yeah so +and then nobody else in the room has has + + align:start position:0% +and then nobody else in the room has has + + + align:start position:0% +and then nobody else in the room has has +any idea how I can calcul + + align:start position:0% +any idea how I can calcul + + + align:start position:0% +any idea how I can calcul +just a little bit of of culture + + align:start position:0% +just a little bit of of culture + + + align:start position:0% +just a little bit of of culture +here so ah people don't know I see I + + align:start position:0% +here so ah people don't know I see I + + + align:start position:0% +here so ah people don't know I see I +kind of felt like I ruined the question + + align:start position:0% +kind of felt like I ruined the question + + + align:start position:0% +kind of felt like I ruined the question +then I should have just asked how are + + align:start position:0% +then I should have just asked how are + + + align:start position:0% +then I should have just asked how are +ion vales computed because I imagine + + align:start position:0% +ion vales computed because I imagine + + + align:start position:0% +ion vales computed because I imagine +many of you would have said isn't it the + + align:start position:0% +many of you would have said isn't it the + + + align:start position:0% +many of you would have said isn't it the +characteristic polinomial you got the + + align:start position:0% +characteristic polinomial you got the + + + align:start position:0% +characteristic polinomial you got the +roots because every one of you have + + align:start position:0% +roots because every one of you have + + + align:start position:0% +roots because every one of you have +formed the characteristic polinomial of + + align:start position:0% +formed the characteristic polinomial of + + + align:start position:0% +formed the characteristic polinomial of +2 by two matrices and and I know you + + align:start position:0% +2 by two matrices and and I know you + + + align:start position:0% +2 by two matrices and and I know you +have right you got that quadratic + + align:start position:0% +have right you got that quadratic + + + align:start position:0% +have right you got that quadratic +equation and you sol for the roots I + + align:start position:0% +equation and you sol for the roots I + + + align:start position:0% +equation and you sol for the roots I +know you remember who remembers doing + + align:start position:0% +know you remember who remembers doing + + + align:start position:0% +know you remember who remembers doing +that right quadratics you get the roots + + align:start position:0% +that right quadratics you get the roots + + + align:start position:0% +that right quadratics you get the roots +you know if if you had a mean teacher + + align:start position:0% +you know if if you had a mean teacher + + + align:start position:0% +you know if if you had a mean teacher +maybe they forced you to do a cubic but + + align:start position:0% +maybe they forced you to do a cubic but + + + align:start position:0% +maybe they forced you to do a cubic but +I bet they didn't anyone ever do it for + + align:start position:0% +I bet they didn't anyone ever do it for + + + align:start position:0% +I bet they didn't anyone ever do it for +a cubic maybe it was rigged to to be + + align:start position:0% +a cubic maybe it was rigged to to be + + + align:start position:0% +a cubic maybe it was rigged to to be +easy though you know that the so right + + align:start position:0% +easy though you know that the so right + + + align:start position:0% +easy though you know that the so right +so none of that happens on the computer + + align:start position:0% +so none of that happens on the computer + + + align:start position:0% +so none of that happens on the computer +I'm not going to tell you uh in detail + + align:start position:0% +I'm not going to tell you uh in detail + + + align:start position:0% +I'm not going to tell you uh in detail +how it's done but I will will mention + + align:start position:0% +how it's done but I will will mention + + + align:start position:0% +how it's done but I will will mention +just the fact that it's not the + + align:start position:0% +just the fact that it's not the + + + align:start position:0% +just the fact that it's not the +characteristic polinomial is is is half + + align:start position:0% +characteristic polinomial is is is half + + + align:start position:0% +characteristic polinomial is is is half +of what I want you to know and the other + + align:start position:0% +of what I want you to know and the other + + + align:start position:0% +of what I want you to know and the other +half is there's something called um the + + align:start position:0% +half is there's something called um the + + + align:start position:0% +half is there's something called um the +QR algorithm for igen Value so so in + + align:start position:0% +QR algorithm for igen Value so so in + + + align:start position:0% +QR algorithm for igen Value so so in +general a QR for a matrix factors a + + align:start position:0% +general a QR for a matrix factors a + + + align:start position:0% +general a QR for a matrix factors a +matrix to orthogonal time upper + + align:start position:0% +matrix to orthogonal time upper + + + align:start position:0% +matrix to orthogonal time upper +triangular and a fun funny thing happens + + align:start position:0% +triangular and a fun funny thing happens + + + align:start position:0% +triangular and a fun funny thing happens +if you factor a matrix into QR and then + + align:start position:0% +if you factor a matrix into QR and then + + + align:start position:0% +if you factor a matrix into QR and then +reverse it and get + + align:start position:0% +reverse it and get + + + align:start position:0% +reverse it and get +RQ um and if you do that again factor + + align:start position:0% +RQ um and if you do that again factor + + + align:start position:0% +RQ um and if you do that again factor +that new Matrix into QR and reverse it + + align:start position:0% +that new Matrix into QR and reverse it + + + align:start position:0% +that new Matrix into QR and reverse it +to RQ and you keep doing that + + align:start position:0% +to RQ and you keep doing that + + + align:start position:0% +to RQ and you keep doing that +essentially the igen values magically + + align:start position:0% +essentially the igen values magically + + + align:start position:0% +essentially the igen values magically +appear right and there are some details + + align:start position:0% +appear right and there are some details + + + align:start position:0% +appear right and there are some details +if the Matrix is symmetric The Matrix + + align:start position:0% +if the Matrix is symmetric The Matrix + + + align:start position:0% +if the Matrix is symmetric The Matrix +will actually become more and more + + align:start position:0% +will actually become more and more + + + align:start position:0% +will actually become more and more +diagonal as you go um if it's non + + align:start position:0% +diagonal as you go um if it's non + + + align:start position:0% +diagonal as you go um if it's non +symmetric um but has real igen values + + align:start position:0% +symmetric um but has real igen values + + + align:start position:0% +symmetric um but has real igen values +it'll become triangular and you'll see + + align:start position:0% +it'll become triangular and you'll see + + + align:start position:0% +it'll become triangular and you'll see +the diagonals the the igen values on the + + align:start position:0% +the diagonals the the igen values on the + + + align:start position:0% +the diagonals the the igen values on the +diagonal eventually and if it's complex + + align:start position:0% +diagonal eventually and if it's complex + + + align:start position:0% +diagonal eventually and if it's complex +you'll get these little 2x two pieces + + align:start position:0% +you'll get these little 2x two pieces + + + align:start position:0% +you'll get these little 2x two pieces +which are easy to get the igen values + + align:start position:0% +which are easy to get the igen values + + + align:start position:0% +which are easy to get the igen values +from so um there are a bunch of tricks + + align:start position:0% +from so um there are a bunch of tricks + + + align:start position:0% +from so um there are a bunch of tricks +to accelerate all this but the basic + + align:start position:0% +to accelerate all this but the basic + + + align:start position:0% +to accelerate all this but the basic +idea is QR RQ QR RQ you might actually + + align:start position:0% +idea is QR RQ QR RQ you might actually + + + align:start position:0% +idea is QR RQ QR RQ you might actually +try it in Julio or or python or whatever + + align:start position:0% +try it in Julio or or python or whatever + + + align:start position:0% +try it in Julio or or python or whatever +m whatever you like to do one day you'll + + align:start position:0% +m whatever you like to do one day you'll + + + align:start position:0% +m whatever you like to do one day you'll +see it just works but it is related to + + align:start position:0% +see it just works but it is related to + + + align:start position:0% +see it just works but it is related to +the power method under the hood if you + + align:start position:0% +the power method under the hood if you + + + align:start position:0% +the power method under the hood if you +if you dig deep oh dig really deep + + align:start position:0% +if you dig deep oh dig really deep + + + align:start position:0% +if you dig deep oh dig really deep +that's right it's sort of like a block + + align:start position:0% +that's right it's sort of like a block + + + align:start position:0% +that's right it's sort of like a block +power method in in multiple Dimensions + + align:start position:0% +power method in in multiple Dimensions + + + align:start position:0% +power method in in multiple Dimensions +all at once it's it's crazy yeah okay + + align:start position:0% +all at once it's it's crazy yeah okay + + + align:start position:0% +all at once it's it's crazy yeah okay +all right so that's that + + align:start position:0% + + + + align:start position:0% + +one \ No newline at end of file diff --git a/6AS48fTXBBs.txt b/6AS48fTXBBs.txt new file mode 100644 index 0000000000000000000000000000000000000000..e49f032127af9959c86e78597a748686b8fcd91a --- /dev/null +++ b/6AS48fTXBBs.txt @@ -0,0 +1,16339 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu I usually start by asking if + + align:start position:0% +ocw.mit.edu I usually start by asking if + + + align:start position:0% +ocw.mit.edu I usually start by asking if +there are any question questions but I + + align:start position:0% +there are any question questions but I + + + align:start position:0% +there are any question questions but I +thought I'd say a few things about + + align:start position:0% +thought I'd say a few things about + + + align:start position:0% +thought I'd say a few things about +chapter 1 and then see if there are any + + align:start position:0% +chapter 1 and then see if there are any + + + align:start position:0% +chapter 1 and then see if there are any +questions I can't see the + + align:start position:0% +questions I can't see the + + + align:start position:0% +questions I can't see the +pointer oh anybody remember how to get + + align:start position:0% +pointer oh anybody remember how to get + + + align:start position:0% +pointer oh anybody remember how to get +word + + align:start position:0% +word + + + align:start position:0% +word +to make its pointer not + + align:start position:0% + + + + align:start position:0% + +disappear uh maybe I mentioned this the + + align:start position:0% +disappear uh maybe I mentioned this the + + + align:start position:0% +disappear uh maybe I mentioned this the +first lecture but + + align:start position:0% + + + + align:start position:0% + +uh I was taken by this + + align:start position:0% + + + + align:start position:0% + +uh cute poem by darthy + + align:start position:0% +uh cute poem by darthy + + + align:start position:0% +uh cute poem by darthy +Parker uh because the first chapter was + + align:start position:0% +Parker uh because the first chapter was + + + align:start position:0% +Parker uh because the first chapter was +about love and stuff like + + align:start position:0% +about love and stuff like + + + align:start position:0% +about love and stuff like +that um so I tried to get the rights to + + align:start position:0% +that um so I tried to get the rights to + + + align:start position:0% +that um so I tried to get the rights to +reproduce it and it turned out that uh + + align:start position:0% +reproduce it and it turned out that uh + + + align:start position:0% +reproduce it and it turned out that uh +she was angry at all her friends she + + align:start position:0% +she was angry at all her friends she + + + align:start position:0% +she was angry at all her friends she +must have been a + + align:start position:0% +must have been a + + + align:start position:0% +must have been a +perpetually pissed off + + align:start position:0% +perpetually pissed off + + + align:start position:0% +perpetually pissed off +person and so she left all her literary + + align:start position:0% +person and so she left all her literary + + + align:start position:0% +person and so she left all her literary +rights to the + + align:start position:0% + + + + align:start position:0% + +NAACP and I called them up for hours and + + align:start position:0% +NAACP and I called them up for hours and + + + align:start position:0% +NAACP and I called them up for hours and +they couldn't find the rights so + + align:start position:0% +they couldn't find the rights so + + + align:start position:0% +they couldn't find the rights so +finally so it's in the uh version of the + + align:start position:0% +finally so it's in the uh version of the + + + align:start position:0% +finally so it's in the uh version of the +emotion machine on the web but + + align:start position:0% +emotion machine on the web but + + + align:start position:0% +emotion machine on the web but +uh I had to resort to Shakespeare to + + align:start position:0% +uh I had to resort to Shakespeare to + + + align:start position:0% +uh I had to resort to Shakespeare to +replace her + + align:start position:0% +replace her + + + align:start position:0% +replace her +uh Shakespeare's a slightly better poet + + align:start position:0% +uh Shakespeare's a slightly better poet + + + align:start position:0% +uh Shakespeare's a slightly better poet +but he's not as funny as daroy + + align:start position:0% + + + + align:start position:0% + +Parker so the first chapter starts out + + align:start position:0% +Parker so the first chapter starts out + + + align:start position:0% +Parker so the first chapter starts out +or it's mostly + + align:start position:0% +or it's mostly + + + align:start position:0% +or it's mostly +about all the things we don't understand + + align:start position:0% +about all the things we don't understand + + + align:start position:0% +about all the things we don't understand +about the mind which is almost + + align:start position:0% +about the mind which is almost + + + align:start position:0% +about the mind which is almost +everything + + align:start position:0% +everything + + + align:start position:0% +everything +and the first + + align:start position:0% +and the first + + + align:start position:0% +and the first +discussion is well the whole chapter is + + align:start position:0% +discussion is well the whole chapter is + + + align:start position:0% +discussion is well the whole chapter is +making fun of the most popular ideas and + + align:start position:0% +making fun of the most popular ideas and + + + align:start position:0% +making fun of the most popular ideas and +the most popular idea of the mind is + + align:start position:0% +the most popular idea of the mind is + + + align:start position:0% +the most popular idea of the mind is +that people think that + + align:start position:0% +that people think that + + + align:start position:0% +that people think that +um that they're not doing the thinking + + align:start position:0% +um that they're not doing the thinking + + + align:start position:0% +um that they're not doing the thinking +but there's something inside them that's + + align:start position:0% +but there's something inside them that's + + + align:start position:0% +but there's something inside them that's +doing the thinking and it's + + align:start position:0% +doing the thinking and it's + + + align:start position:0% +doing the thinking and it's +a uh this idea that there is a self is + + align:start position:0% +a uh this idea that there is a self is + + + align:start position:0% +a uh this idea that there is a self is +uh embedded in just about everything we + + align:start position:0% +uh embedded in just about everything we + + + align:start position:0% +uh embedded in just about everything we +say and + + align:start position:0% +say and + + + align:start position:0% +say and +think and really it's hard to see how + + align:start position:0% +think and really it's hard to see how + + + align:start position:0% +think and really it's hard to see how +you would do without it but if you ask + + align:start position:0% +you would do without it but if you ask + + + align:start position:0% +you would do without it but if you ask +what is the + + align:start position:0% + + + + align:start position:0% + +self then since this idea is so + + align:start position:0% +self then since this idea is so + + + align:start position:0% +self then since this idea is so +popular people begin to believe that + + align:start position:0% +popular people begin to believe that + + + align:start position:0% +popular people begin to believe that +there is such a thing and it takes all + + align:start position:0% +there is such a thing and it takes all + + + align:start position:0% +there is such a thing and it takes all +sorts of various forms and the the most + + align:start position:0% +sorts of various forms and the the most + + + align:start position:0% +sorts of various forms and the the most +dangerous form maybe is the one that + + align:start position:0% +dangerous form maybe is the one that + + + align:start position:0% +dangerous form maybe is the one that +religions + + align:start position:0% +religions + + + align:start position:0% +religions +uh exploit which is that inside a person + + align:start position:0% +uh exploit which is that inside a person + + + align:start position:0% +uh exploit which is that inside a person +with all their complications there's a + + align:start position:0% +with all their complications there's a + + + align:start position:0% +with all their complications there's a +little pure Essence called the soul or + + align:start position:0% +little pure Essence called the soul or + + + align:start position:0% +little pure Essence called the soul or +the self or whatever you want to call it + + align:start position:0% +the self or whatever you want to call it + + + align:start position:0% +the self or whatever you want to call it +and uh it's impossible to describe it or + + align:start position:0% +and uh it's impossible to describe it or + + + align:start position:0% +and uh it's impossible to describe it or +explain it in physical + + align:start position:0% +explain it in physical + + + align:start position:0% +explain it in physical +terms + + align:start position:0% +terms + + + align:start position:0% +terms +um and + + align:start position:0% +um and + + + align:start position:0% +um and +so + + align:start position:0% +so + + + align:start position:0% +so +that is one of the reasons why we think + + align:start position:0% +that is one of the reasons why we think + + + align:start position:0% +that is one of the reasons why we think +there are two worlds a physical world + + align:start position:0% +there are two worlds a physical world + + + align:start position:0% +there are two worlds a physical world +and lots of other kinds of Worlds each + + align:start position:0% +and lots of other kinds of Worlds each + + + align:start position:0% +and lots of other kinds of Worlds each +of us has some imaginary model of + + align:start position:0% +of us has some imaginary model of + + + align:start position:0% +of us has some imaginary model of +what what they are and what they're in + + align:start position:0% +what what they are and what they're in + + + align:start position:0% +what what they are and what they're in +and + + align:start position:0% + + + + align:start position:0% + +um and philosophers talk about it and + + align:start position:0% +um and philosophers talk about it and + + + align:start position:0% +um and philosophers talk about it and +existentialists and so on so there are + + align:start position:0% +existentialists and so on so there are + + + align:start position:0% +existentialists and so on so there are +lots of problems about our ideas about + + align:start position:0% +lots of problems about our ideas about + + + align:start position:0% +lots of problems about our ideas about +ourselves and + + align:start position:0% + + + + align:start position:0% + +in Reading around for half my + + align:start position:0% +in Reading around for half my + + + align:start position:0% +in Reading around for half my +life uh I was puzzled + + align:start position:0% +life uh I was puzzled + + + align:start position:0% +life uh I was puzzled +at the strange ideas that are around and + + align:start position:0% +at the strange ideas that are around and + + + align:start position:0% +at the strange ideas that are around and +in + + align:start position:0% +in + + + align:start position:0% +in +Aristotle uh I find the first + + align:start position:0% +Aristotle uh I find the first + + + align:start position:0% +Aristotle uh I find the first +intelligible theories of mind and + + align:start position:0% +intelligible theories of mind and + + + align:start position:0% +intelligible theories of mind and +emotions so if you look at particular + + align:start position:0% +emotions so if you look at particular + + + align:start position:0% +emotions so if you look at particular +Aristotle's there are number of books + + align:start position:0% +Aristotle's there are number of books + + + align:start position:0% +Aristotle's there are number of books +and one of them is called + + align:start position:0% +and one of them is called + + + align:start position:0% +and one of them is called +rhetoric and it's full of theories about + + align:start position:0% +rhetoric and it's full of theories about + + + align:start position:0% +rhetoric and it's full of theories about +how people reason and influence each + + align:start position:0% +how people reason and influence each + + + align:start position:0% +how people reason and influence each +other and + + align:start position:0% + + + + align:start position:0% + +uh um I'll show you some quotes from + + align:start position:0% +uh um I'll show you some quotes from + + + align:start position:0% +uh um I'll show you some quotes from +that because when I look at the history + + align:start position:0% +that because when I look at the history + + + align:start position:0% +that because when I look at the history +that I've encountered about + + align:start position:0% +that I've encountered about + + + align:start position:0% +that I've encountered about +psychology uh sort of Aristotle stands + + align:start position:0% +psychology uh sort of Aristotle stands + + + align:start position:0% +psychology uh sort of Aristotle stands +out as being the first and and among the + + align:start position:0% +out as being the first and and among the + + + align:start position:0% +out as being the first and and among the +best and as far as I can see there were + + align:start position:0% +best and as far as I can see there were + + + align:start position:0% +best and as far as I can see there were +no + + align:start position:0% +no + + + align:start position:0% +no +psychologists nearly as good as him of + + align:start position:0% +psychologists nearly as good as him of + + + align:start position:0% +psychologists nearly as good as him of +course we don't know whether there was a + + align:start position:0% +course we don't know whether there was a + + + align:start position:0% +course we don't know whether there was a +himym + + align:start position:0% +himym + + + align:start position:0% +himym +exactly uh because he uh what we have of + + align:start position:0% +exactly uh because he uh what we have of + + + align:start position:0% +exactly uh because he uh what we have of +Aristotle and there's a lot of writing + + align:start position:0% +Aristotle and there's a lot of writing + + + align:start position:0% +Aristotle and there's a lot of writing +but it's all cobbled together by + + align:start position:0% +but it's all cobbled together by + + + align:start position:0% +but it's all cobbled together by +students from all sorts of manuscripts + + align:start position:0% +students from all sorts of manuscripts + + + align:start position:0% +students from all sorts of manuscripts +by other people and people who took + + align:start position:0% +by other people and people who took + + + align:start position:0% +by other people and people who took +notes and U Aristotle claims to have + + align:start position:0% +notes and U Aristotle claims to have + + + align:start position:0% +notes and U Aristotle claims to have +learned a lot from + + align:start position:0% +learned a lot from + + + align:start position:0% +learned a lot from +Plato well we have very little + + align:start position:0% +Plato well we have very little + + + align:start position:0% +Plato well we have very little +writing from him + + align:start position:0% +writing from him + + + align:start position:0% +writing from him +and so there you go three centuries + + align:start position:0% +and so there you go three centuries + + + align:start position:0% +and so there you go three centuries +before the Christian era as it's + + align:start position:0% +before the Christian era as it's + + + align:start position:0% +before the Christian era as it's +called and then uh a couple of thousand + + align:start position:0% +called and then uh a couple of thousand + + + align:start position:0% +called and then uh a couple of thousand +years later you start to find people + + align:start position:0% +years later you start to find people + + + align:start position:0% +years later you start to find people +like Spinosa and Kant and + + align:start position:0% + + + + align:start position:0% + +uh John Lock and David Hume Who start to + + align:start position:0% +uh John Lock and David Hume Who start to + + + align:start position:0% +uh John Lock and David Hume Who start to +make psychology + + align:start position:0% +make psychology + + + align:start position:0% +make psychology +theories very + + align:start position:0% +theories very + + + align:start position:0% +theories very +little of which is as good as the ones + + align:start position:0% +little of which is as good as the ones + + + align:start position:0% +little of which is as good as the ones +that Aristotle has in all his + + align:start position:0% +that Aristotle has in all his + + + align:start position:0% +that Aristotle has in all his +fragments so one question that + + align:start position:0% +fragments so one question that + + + align:start position:0% +fragments so one question that +frequently bothers me and it should + + align:start position:0% +frequently bothers me and it should + + + align:start position:0% +frequently bothers me and it should +bother everyone is + + align:start position:0% +bother everyone is + + + align:start position:0% +bother everyone is +uh why did science disappear for a + + align:start position:0% +uh why did science disappear for a + + + align:start position:0% +uh why did science disappear for a +thousand + + align:start position:0% +thousand + + + align:start position:0% +thousand +years and the standard explanation is + + align:start position:0% +years and the standard explanation is + + + align:start position:0% +years and the standard explanation is +the rise of the great + + align:start position:0% +the rise of the great + + + align:start position:0% +the rise of the great +religions + + align:start position:0% +religions + + + align:start position:0% +religions +um and why did it come back and you see + + align:start position:0% +um and why did it come back and you see + + + align:start position:0% +um and why did it come back and you see +with uh the first signs of anything like + + align:start position:0% +with uh the first signs of anything like + + + align:start position:0% +with uh the first signs of anything like +modern science at least in my view with + + align:start position:0% +modern science at least in my view with + + + align:start position:0% +modern science at least in my view with +Galileo and Newton there a couple of + + align:start position:0% +Galileo and Newton there a couple of + + + align:start position:0% +Galileo and Newton there a couple of +people before that uh there are some + + align:start position:0% +people before that uh there are some + + + align:start position:0% +people before that uh there are some +people in the Muslim world uh who + + align:start position:0% +people in the Muslim world uh who + + + align:start position:0% +people in the Muslim world uh who +invented some high school algebra and + + align:start position:0% +invented some high school algebra and + + + align:start position:0% +invented some high school algebra and +they make a big fuss about that it looks + + align:start position:0% +they make a big fuss about that it looks + + + align:start position:0% +they make a big fuss about that it looks +like + + align:start position:0% +like + + + align:start position:0% +like +Archimedes uh in a very recently + + align:start position:0% +Archimedes uh in a very recently + + + align:start position:0% +Archimedes uh in a very recently +discovered + + align:start position:0% +discovered + + + align:start position:0% +discovered +manuscript + + align:start position:0% +manuscript + + + align:start position:0% +manuscript +uh computed an integral he found the + + align:start position:0% +uh computed an integral he found the + + + align:start position:0% +uh computed an integral he found the +volume of a cone which is what is + + align:start position:0% +volume of a cone which is what is + + + align:start position:0% +volume of a cone which is what is +it6 BH I + + align:start position:0% +it6 BH I + + + align:start position:0% +it6 BH I +forget uh + + align:start position:0% +forget uh + + + align:start position:0% +forget uh +anyway + + align:start position:0% +anyway + + + align:start position:0% +anyway +uh so why did science disappear and why + + align:start position:0% +uh so why did science disappear and why + + + align:start position:0% +uh so why did science disappear and why +did psychology appear so late because + + align:start position:0% +did psychology appear so late because + + + align:start position:0% +did psychology appear so late because +there isn't much psychology in the + + align:start position:0% +there isn't much psychology in the + + + align:start position:0% +there isn't much psychology in the +modern sense until + + align:start position:0% +modern sense until + + + align:start position:0% +modern sense until +1900 or the late 1800s with Francis gold + + align:start position:0% +1900 or the late 1800s with Francis gold + + + align:start position:0% +1900 or the late 1800s with Francis gold +dton and uh William James lived around + + align:start position:0% +dton and uh William James lived around + + + align:start position:0% +dton and uh William James lived around +here and + + align:start position:0% +here and + + + align:start position:0% +here and +um Rudolph fce who Sigman Freud starts + + align:start position:0% +um Rudolph fce who Sigman Freud starts + + + align:start position:0% +um Rudolph fce who Sigman Freud starts +writing in + + align:start position:0% +writing in + + + align:start position:0% +writing in +1895 uh people make fun of Freud as I + + align:start position:0% +1895 uh people make fun of Freud as I + + + align:start position:0% +1895 uh people make fun of Freud as I +mentioned last week uh but uh in fact + + align:start position:0% +mentioned last week uh but uh in fact + + + align:start position:0% +mentioned last week uh but uh in fact +among other + + align:start position:0% +among other + + + align:start position:0% +among other +things how many of you have read the + + align:start position:0% +things how many of you have read the + + + align:start position:0% +things how many of you have read the +recent criticisms of Freud which + + align:start position:0% +recent criticisms of Freud which + + + align:start position:0% +recent criticisms of Freud which +claimed that he was a complete Faker and + + align:start position:0% +claimed that he was a complete Faker and + + + align:start position:0% +claimed that he was a complete Faker and +never cured a single + + align:start position:0% +never cured a single + + + align:start position:0% +never cured a single +patient this is popular stuff I don't + + align:start position:0% +patient this is popular stuff I don't + + + align:start position:0% +patient this is popular stuff I don't +believe Freud ever really claimed to + + align:start position:0% +believe Freud ever really claimed to + + + align:start position:0% +believe Freud ever really claimed to +cure a single + + align:start position:0% +cure a single + + + align:start position:0% +cure a single +patient so the critics who are really + + align:start position:0% +patient so the critics who are really + + + align:start position:0% +patient so the critics who are really +very ferocious claim that he made up all + + align:start position:0% +very ferocious claim that he made up all + + + align:start position:0% +very ferocious claim that he made up all +his data and so forth but most of what + + align:start position:0% +his data and so forth but most of what + + + align:start position:0% +his data and so forth but most of what +Freud says is that + + align:start position:0% +Freud says is that + + + align:start position:0% +Freud says is that +psychoanalysis is might be a good way to + + align:start position:0% +psychoanalysis is might be a good way to + + + align:start position:0% +psychoanalysis is might be a good way to +find out what you're really thinking and + + align:start position:0% +find out what you're really thinking and + + + align:start position:0% +find out what you're really thinking and +discover more about yourself and your + + align:start position:0% +discover more about yourself and your + + + align:start position:0% +discover more about yourself and your +goals and so forth and + + align:start position:0% +goals and so forth and + + + align:start position:0% +goals and so forth and +uh I had the good or bad luck uh to be + + align:start position:0% +uh I had the good or bad luck uh to be + + + align:start position:0% +uh I had the good or bad luck uh to be +introduced to elron hubard by John uh + + align:start position:0% +introduced to elron hubard by John uh + + + align:start position:0% +introduced to elron hubard by John uh +when I was an undergraduate John + + align:start position:0% +when I was an undergraduate John + + + align:start position:0% +when I was an undergraduate John +Campbell was the great editor of + + align:start position:0% +Campbell was the great editor of + + + align:start position:0% +Campbell was the great editor of +the I think it was called astounding + + align:start position:0% +the I think it was called astounding + + + align:start position:0% +the I think it was called astounding +science fiction in those days what a + + align:start position:0% +science fiction in those days what a + + + align:start position:0% +science fiction in those days what a +marvelous + + align:start position:0% +marvelous + + + align:start position:0% +marvelous +title and uh this uh mediocre science + + align:start position:0% +title and uh this uh mediocre science + + + align:start position:0% +title and uh this uh mediocre science +fiction writer elron hubard invented a + + align:start position:0% +fiction writer elron hubard invented a + + + align:start position:0% +fiction writer elron hubard invented a +new form of Psychiatry + + align:start position:0% +new form of Psychiatry + + + align:start position:0% +new form of Psychiatry +called what was it called DS + + align:start position:0% +called what was it called DS + + + align:start position:0% +called what was it called DS +sonetics it's pretty good and + + align:start position:0% +sonetics it's pretty good and + + + align:start position:0% +sonetics it's pretty good and +uh I'll tell you that story another time + + align:start position:0% +uh I'll tell you that story another time + + + align:start position:0% +uh I'll tell you that story another time +but + + align:start position:0% +but + + + align:start position:0% +but +uh John Campell had Thanksgiving in the + + align:start position:0% +uh John Campell had Thanksgiving in the + + + align:start position:0% +uh John Campell had Thanksgiving in the +commander Hotel every year and invited a + + align:start position:0% +commander Hotel every year and invited a + + + align:start position:0% +commander Hotel every year and invited a +bunch of friends and I don't remember if + + align:start position:0% +bunch of friends and I don't remember if + + + align:start position:0% +bunch of friends and I don't remember if +that's how I got to meet Asimov and hin + + align:start position:0% +that's how I got to meet Asimov and hin + + + align:start position:0% +that's how I got to meet Asimov and hin +Line and other people but anyway I did + + align:start position:0% +Line and other people but anyway I did + + + align:start position:0% +Line and other people but anyway I did +and science fiction had a big influence + + align:start position:0% +and science fiction had a big influence + + + align:start position:0% +and science fiction had a big influence +on me from + + align:start position:0% +on me from + + + align:start position:0% +on me from +my actually early years but uh starting + + align:start position:0% +my actually early years but uh starting + + + align:start position:0% +my actually early years but uh starting +in college it got very + + align:start position:0% + + + + align:start position:0% + +serious + + align:start position:0% +serious + + + align:start position:0% +serious +anyway + + align:start position:0% +anyway + + + align:start position:0% +anyway +uh so chapter one starts to talk about + + align:start position:0% +uh so chapter one starts to talk about + + + align:start position:0% +uh so chapter one starts to talk about +the + + align:start position:0% +the + + + align:start position:0% +the +this phenomenon + + align:start position:0% +this phenomenon + + + align:start position:0% +this phenomenon +of psychology and one of the funny parts + + align:start position:0% +of psychology and one of the funny parts + + + align:start position:0% +of psychology and one of the funny parts +is + + align:start position:0% + + + + align:start position:0% + +this little section three + + align:start position:0% +this little section three + + + align:start position:0% +this little section three +1.3 of uh trying to say what are + + align:start position:0% +1.3 of uh trying to say what are + + + align:start position:0% +1.3 of uh trying to say what are +emotions and I looked up emotions in + + align:start position:0% +emotions and I looked up emotions in + + + align:start position:0% +emotions and I looked up emotions in +dictionaries and uh can you all read + + align:start position:0% +dictionaries and uh can you all read + + + align:start position:0% +dictionaries and uh can you all read +that I don't feel like reading + + align:start position:0% +that I don't feel like reading + + + align:start position:0% +that I don't feel like reading +aloud + + align:start position:0% +aloud + + + align:start position:0% +aloud +uh but + + align:start position:0% +uh but + + + align:start position:0% +uh but +uh there's lots of discussion of + + align:start position:0% +uh there's lots of discussion of + + + align:start position:0% +uh there's lots of discussion of +emotions and how mysterious and complex + + align:start position:0% +emotions and how mysterious and complex + + + align:start position:0% +emotions and how mysterious and complex +they are and + + align:start position:0% +they are and + + + align:start position:0% +they are and +then The Marvelous thing is how many + + align:start position:0% +then The Marvelous thing is how many + + + align:start position:0% +then The Marvelous thing is how many +words there are for emotional + + align:start position:0% +words there are for emotional + + + align:start position:0% +words there are for emotional +states uh I think I got 300 but I don't + + align:start position:0% +states uh I think I got 300 but I don't + + + align:start position:0% +states uh I think I got 300 but I don't +remember anyway here's from a to + + align:start position:0% +remember anyway here's from a to + + + align:start position:0% +remember anyway here's from a to +d and I don't recall how I found those + + align:start position:0% +d and I don't recall how I found those + + + align:start position:0% +d and I don't recall how I found those +but I + + align:start position:0% +but I + + + align:start position:0% +but I +think but that's a + + align:start position:0% +think but that's a + + + align:start position:0% +think but that's a +lot how many words for ways to think are + + align:start position:0% + + + + align:start position:0% + +there now that's a serious question + + align:start position:0% + + + + align:start position:0% + +because I complained maybe on the next + + align:start position:0% +because I complained maybe on the next + + + align:start position:0% +because I complained maybe on the next +page no I + + align:start position:0% +page no I + + + align:start position:0% +page no I +didn't uh I found myself complaining + + align:start position:0% +didn't uh I found myself complaining + + + align:start position:0% +didn't uh I found myself complaining +that there were very few words for ways + + align:start position:0% +that there were very few words for ways + + + align:start position:0% +that there were very few words for ways +to think and then this afternoon when I + + align:start position:0% +to think and then this afternoon when I + + + align:start position:0% +to think and then this afternoon when I +was pruning these slides it occurred to + + align:start position:0% +was pruning these slides it occurred to + + + align:start position:0% +was pruning these slides it occurred to +me that but I didn't really try so + + align:start position:0% +me that but I didn't really try so + + + align:start position:0% +me that but I didn't really try so +uh + + align:start position:0% +uh + + + align:start position:0% +uh +maybe I just didn't think enough so if + + align:start position:0% +maybe I just didn't think enough so if + + + align:start position:0% +maybe I just didn't think enough so if +there are a couple of hundred words for + + align:start position:0% +there are a couple of hundred words for + + + align:start position:0% +there are a couple of hundred words for +everyday + + align:start position:0% +everyday + + + align:start position:0% +everyday +emotions uh if any of you can find me a + + align:start position:0% +emotions uh if any of you can find me a + + + align:start position:0% +emotions uh if any of you can find me a +list of 10 or + + align:start position:0% +list of 10 or + + + align:start position:0% +list of 10 or +20 common words for styles of thinking + + align:start position:0% +20 common words for styles of thinking + + + align:start position:0% +20 common words for styles of thinking +I'd appreciate it because uh I wonder if + + align:start position:0% +I'd appreciate it because uh I wonder if + + + align:start position:0% +I'd appreciate it because uh I wonder if +there are a lot and if not why + + align:start position:0% +there are a lot and if not why + + + align:start position:0% +there are a lot and if not why +not so + + align:start position:0% +not so + + + align:start position:0% +not so +so here's a list of typical situations + + align:start position:0% +so here's a list of typical situations + + + align:start position:0% +so here's a list of typical situations +grieving for a lost + + align:start position:0% + + + + align:start position:0% + +child Panic at being in an enclosed + + align:start position:0% +child Panic at being in an enclosed + + + align:start position:0% +child Panic at being in an enclosed +space I'm not sure any of the words in + + align:start position:0% +space I'm not sure any of the words in + + + align:start position:0% +space I'm not sure any of the words in +the list of 300 standard emotions are + + align:start position:0% +the list of 300 standard emotions are + + + align:start position:0% +the list of 300 standard emotions are +good enough to describe how you feel for + + align:start position:0% +good enough to describe how you feel for + + + align:start position:0% +good enough to describe how you feel for +any of these + + align:start position:0% +any of these + + + align:start position:0% +any of these +uh Not Unusual states have you ever lost + + align:start position:0% +uh Not Unusual states have you ever lost + + + align:start position:0% +uh Not Unusual states have you ever lost +control of your your car high + + align:start position:0% +control of your your car high + + + align:start position:0% +control of your your car high +speed no but when I first learned to + + align:start position:0% +speed no but when I first learned to + + + align:start position:0% +speed no but when I first learned to +drive I couldn't believe that you could + + align:start position:0% +drive I couldn't believe that you could + + + align:start position:0% +drive I couldn't believe that you could +read + + align:start position:0% +read + + + align:start position:0% +read +signs at the same time + + align:start position:0% + + + + align:start position:0% + +as well + + align:start position:0% +as well + + + align:start position:0% +as well +anyway one of the very best + + align:start position:0% +anyway one of the very best + + + align:start position:0% +anyway one of the very best +psychologists in + + align:start position:0% +psychologists in + + + align:start position:0% +psychologists in +history or pair of + + align:start position:0% +history or pair of + + + align:start position:0% +history or pair of +psychologists uh aren't even called + + align:start position:0% +psychologists uh aren't even called + + + align:start position:0% +psychologists uh aren't even called +psychologists these are two guys named + + align:start position:0% +psychologists these are two guys named + + + align:start position:0% +psychologists these are two guys named +uh Conrad Lauren and Nico + + align:start position:0% +uh Conrad Lauren and Nico + + + align:start position:0% +uh Conrad Lauren and Nico +tinbergen and they somebody made up the + + align:start position:0% +tinbergen and they somebody made up the + + + align:start position:0% +tinbergen and they somebody made up the +word ethology what they study is the + + align:start position:0% +word ethology what they study is the + + + align:start position:0% +word ethology what they study is the +behavior of animals and in some sense uh + + align:start position:0% +behavior of animals and in some sense uh + + + align:start position:0% +behavior of animals and in some sense uh +presumably they're studying the + + align:start position:0% +presumably they're studying the + + + align:start position:0% +presumably they're studying the +psychology of animals because uh just as + + align:start position:0% +psychology of animals because uh just as + + + align:start position:0% +psychology of animals because uh just as +with a + + align:start position:0% +with a + + + align:start position:0% +with a +person uh when somebody flies into a + + align:start position:0% +person uh when somebody flies into a + + + align:start position:0% +person uh when somebody flies into a +rage you're not describing their mental + + align:start position:0% +rage you're not describing their mental + + + align:start position:0% +rage you're not describing their mental +state you're describing something about + + align:start position:0% +state you're describing something about + + + align:start position:0% +state you're describing something about +how they behave and so the ethology IST + + align:start position:0% +how they behave and so the ethology IST + + + align:start position:0% +how they behave and so the ethology IST +too are psychologists and tinbergen and + + align:start position:0% +too are psychologists and tinbergen and + + + align:start position:0% +too are psychologists and tinbergen and +lorence uh starting around + + align:start position:0% +lorence uh starting around + + + align:start position:0% +lorence uh starting around +1920s started to analyze the behavior of + + align:start position:0% +1920s started to analyze the behavior of + + + align:start position:0% +1920s started to analyze the behavior of +animals in great detail and + + align:start position:0% + + + + align:start position:0% + +uh so here's an example of how a certain + + align:start position:0% +uh so here's an example of how a certain + + + align:start position:0% +uh so here's an example of how a certain +fish + + align:start position:0% +fish + + + align:start position:0% +fish +behaves I actually forgot which fish it + + align:start position:0% +behaves I actually forgot which fish it + + + align:start position:0% +behaves I actually forgot which fish it +is but there's a picture of it some in + + align:start position:0% +is but there's a picture of it some in + + + align:start position:0% +is but there's a picture of it some in +the + + align:start position:0% +the + + + align:start position:0% +the +book and + + align:start position:0% +book and + + + align:start position:0% +book and +uh at different points in its in its + + align:start position:0% +uh at different points in its in its + + + align:start position:0% +uh at different points in its in its +life it's in different phases and this + + align:start position:0% +life it's in different phases and this + + + align:start position:0% +life it's in different phases and this +is just one diagram of a dozen for this + + align:start position:0% +is just one diagram of a dozen for this + + + align:start position:0% +is just one diagram of a dozen for this +for this particular + + align:start position:0% +for this particular + + + align:start position:0% +for this particular +fish and it's reproduction which + + align:start position:0% +fish and it's reproduction which + + + align:start position:0% +fish and it's reproduction which +involves an environment with plants and + + align:start position:0% +involves an environment with plants and + + + align:start position:0% +involves an environment with plants and +other things and he divides Its Behavior + + align:start position:0% +other things and he divides Its Behavior + + + align:start position:0% +other things and he divides Its Behavior +into parenting courtship nesting and + + align:start position:0% +into parenting courtship nesting and + + + align:start position:0% +into parenting courtship nesting and +fighting and uh then you see each of + + align:start position:0% +fighting and uh then you see each of + + + align:start position:0% +fighting and uh then you see each of +those has a lot of + + align:start position:0% +those has a lot of + + + align:start position:0% +those has a lot of +subdivisions and uh tinbergen and + + align:start position:0% +subdivisions and uh tinbergen and + + + align:start position:0% +subdivisions and uh tinbergen and +Laurence and some + + align:start position:0% +Laurence and some + + + align:start position:0% +Laurence and some +students discovered all these things by + + align:start position:0% +students discovered all these things by + + + align:start position:0% +students discovered all these things by +sitting in front of fish tanks and + + align:start position:0% +sitting in front of fish tanks and + + + align:start position:0% +sitting in front of fish tanks and +watching the fish for uh months and + + align:start position:0% +watching the fish for uh months and + + + align:start position:0% +watching the fish for uh months and +years uh tinbergen also + + align:start position:0% +years uh tinbergen also + + + align:start position:0% +years uh tinbergen also +uh spent years + + align:start position:0% +uh spent years + + + align:start position:0% +uh spent years +on some beach watching seagulls and so + + align:start position:0% +on some beach watching seagulls and so + + + align:start position:0% +on some beach watching seagulls and so +he has a diagram like this for um + + align:start position:0% +he has a diagram like this for um + + + align:start position:0% +he has a diagram like this for um +particular class of + + align:start position:0% +particular class of + + + align:start position:0% +particular class of +Seagulls uh when I came to + + align:start position:0% + + + + align:start position:0% + +Boston uh my friends and I used to go to + + align:start position:0% +Boston uh my friends and I used to go to + + + align:start position:0% +Boston uh my friends and I used to go to +Nahant and look at these tide pools + + align:start position:0% +Nahant and look at these tide pools + + + align:start position:0% +Nahant and look at these tide pools +there where there are a lot of + + align:start position:0% +there where there are a lot of + + + align:start position:0% +there where there are a lot of +activities and it was very interesting + + align:start position:0% +activities and it was very interesting + + + align:start position:0% +activities and it was very interesting +and I got a big fish tank and imported + + align:start position:0% +and I got a big fish tank and imported + + + align:start position:0% +and I got a big fish tank and imported +all sorts of little animals and plants + + align:start position:0% +all sorts of little animals and plants + + + align:start position:0% +all sorts of little animals and plants +from uh the tide pools in the haunt and + + align:start position:0% +from uh the tide pools in the haunt and + + + align:start position:0% +from uh the tide pools in the haunt and +I watched them for about a year and + + align:start position:0% +I watched them for about a year and + + + align:start position:0% +I watched them for about a year and +didn't learn + + align:start position:0% +didn't learn + + + align:start position:0% +didn't learn +anything and uh uh that was before I + + align:start position:0% +anything and uh uh that was before I + + + align:start position:0% +anything and uh uh that was before I +read tinbergen and then I realized + + align:start position:0% +read tinbergen and then I realized + + + align:start position:0% +read tinbergen and then I realized +there's something about those people + + align:start position:0% +there's something about those people + + + align:start position:0% +there's something about those people +which is they could watch a fish and + + align:start position:0% +which is they could watch a fish and + + + align:start position:0% +which is they could watch a fish and +recognize all sorts of behaviors and I + + align:start position:0% +recognize all sorts of behaviors and I + + + align:start position:0% +recognize all sorts of behaviors and I +would just watch a fish and wonder + + align:start position:0% +would just watch a fish and wonder + + + align:start position:0% +would just watch a fish and wonder +whether it was hungry + + align:start position:0% +whether it was hungry + + + align:start position:0% +whether it was hungry +or wouldn't you get bored swimming back + + align:start position:0% +or wouldn't you get bored swimming back + + + align:start position:0% +or wouldn't you get bored swimming back +and forth for three years in + + align:start position:0% +and forth for three years in + + + align:start position:0% +and forth for three years in +us + + align:start position:0% +us + + + align:start position:0% +us +anyway so here the great psychologists + + align:start position:0% +anyway so here the great psychologists + + + align:start position:0% +anyway so here the great psychologists +of the of our day + + align:start position:0% +of the of our day + + + align:start position:0% +of the of our day +Aristotle 2,000 years ago and Laurence + + align:start position:0% +Aristotle 2,000 years ago and Laurence + + + align:start position:0% +Aristotle 2,000 years ago and Laurence +and tinbergen in the + + align:start position:0% +and tinbergen in the + + + align:start position:0% +and tinbergen in the +1930s and Sigman Freud and uh gton and + + align:start position:0% +1930s and Sigman Freud and uh gton and + + + align:start position:0% +1930s and Sigman Freud and uh gton and +uh William James around + + align:start position:0% +uh William James around + + + align:start position:0% +uh William James around +1900 and then what went + + align:start position:0% +1900 and then what went + + + align:start position:0% +1900 and then what went +wrong there's almost no good psychology + + align:start position:0% +wrong there's almost no good psychology + + + align:start position:0% +wrong there's almost no good psychology +between then and + + align:start position:0% +between then and + + + align:start position:0% +between then and +1950s when something called cognitive + + align:start position:0% +1950s when something called cognitive + + + align:start position:0% +1950s when something called cognitive +psychology + + align:start position:0% +psychology + + + align:start position:0% +psychology +started and it was partly due to people + + align:start position:0% +started and it was partly due to people + + + align:start position:0% +started and it was partly due to people +who said let's make science let's make + + align:start position:0% +who said let's make science let's make + + + align:start position:0% +who said let's make science let's make +psychology more scientific and you've + + align:start position:0% +psychology more scientific and you've + + + align:start position:0% +psychology more scientific and you've +probably all heard of Pavlov or Watson + + align:start position:0% +probably all heard of Pavlov or Watson + + + align:start position:0% +probably all heard of Pavlov or Watson +and what happened is around 1900 some + + align:start position:0% +and what happened is around 1900 some + + + align:start position:0% +and what happened is around 1900 some +psychologist said well these goons and + + align:start position:0% +psychologist said well these goons and + + + align:start position:0% +psychologist said well these goons and +freuds and William James are very poetic + + align:start position:0% +freuds and William James are very poetic + + + align:start position:0% +freuds and William James are very poetic +and expressive and literary and they + + align:start position:0% +and expressive and literary and they + + + align:start position:0% +and expressive and literary and they +write much better than we do and tells + + align:start position:0% +write much better than we do and tells + + + align:start position:0% +write much better than we do and tells +good stories but they're not scientists + + align:start position:0% +good stories but they're not scientists + + + align:start position:0% +good stories but they're not scientists +and they don't do reproducible + + align:start position:0% +and they don't do reproducible + + + align:start position:0% +and they don't do reproducible +experiments so what we have to do is + + align:start position:0% +experiments so what we have to do is + + + align:start position:0% +experiments so what we have to do is +simplify the situation to find the basic + + align:start position:0% +simplify the situation to find the basic + + + align:start position:0% +simplify the situation to find the basic +laws of + + align:start position:0% +laws of + + + align:start position:0% +laws of +behavior so let's let's take a pigeon + + align:start position:0% +behavior so let's let's take a pigeon + + + align:start position:0% +behavior so let's let's take a pigeon +and put it in a vacuum in the dark well + + align:start position:0% +and put it in a vacuum in the dark well + + + align:start position:0% +and put it in a vacuum in the dark well +well well they didn't go that + + align:start position:0% +well well they didn't go that + + + align:start position:0% +well well they didn't go that +far but but they did put it in the + + align:start position:0% +far but but they did put it in the + + + align:start position:0% +far but but they did put it in the +dark and uh there were two illuminated + + align:start position:0% +dark and uh there were two illuminated + + + align:start position:0% +dark and uh there were two illuminated +levers to work and you could make a + + align:start position:0% +levers to work and you could make a + + + align:start position:0% +levers to work and you could make a +sound and um the sound could be very + + align:start position:0% +sound and um the sound could be very + + + align:start position:0% +sound and um the sound could be very +annoying or you could have a uh bright + + align:start position:0% +annoying or you could have a uh bright + + + align:start position:0% +annoying or you could have a uh bright +annoying flashing light or something and + + align:start position:0% +annoying flashing light or something and + + + align:start position:0% +annoying flashing light or something and +the animal would push one of two levers + + align:start position:0% +the animal would push one of two levers + + + align:start position:0% +the animal would push one of two levers +and one of them would make the stimulus + + align:start position:0% +and one of them would make the stimulus + + + align:start position:0% +and one of them would make the stimulus +even more + + align:start position:0% +even more + + + align:start position:0% +even more +annoying and one of them would make it + + align:start position:0% +annoying and one of them would make it + + + align:start position:0% +annoying and one of them would make it +go away and you'd PL curves of how often + + align:start position:0% +go away and you'd PL curves of how often + + + align:start position:0% +go away and you'd PL curves of how often +the animal pressed these levers so you + + align:start position:0% +the animal pressed these levers so you + + + align:start position:0% +the animal pressed these levers so you +would get a quantitative theory of how + + align:start position:0% +would get a quantitative theory of how + + + align:start position:0% +would get a quantitative theory of how +much it learned and how much it could + + align:start position:0% +much it learned and how much it could + + + align:start position:0% +much it learned and how much it could +remember and how many trials it would + + align:start position:0% +remember and how many trials it would + + + align:start position:0% +remember and how many trials it would +have to do and + + align:start position:0% +have to do and + + + align:start position:0% +have to do and +um then uh instead of just looking at + + align:start position:0% +um then uh instead of just looking at + + + align:start position:0% +um then uh instead of just looking at +reactions to stimuli they uh quickly + + align:start position:0% +reactions to stimuli they uh quickly + + + align:start position:0% +reactions to stimuli they uh quickly +switch to trying to teach the animal + + align:start position:0% +switch to trying to teach the animal + + + align:start position:0% +switch to trying to teach the animal +things by giving it two two + + align:start position:0% +things by giving it two two + + + align:start position:0% +things by giving it two two +Alternatives turn left or turn right or + + align:start position:0% +Alternatives turn left or turn right or + + + align:start position:0% +Alternatives turn left or turn right or +push this Buton button or that or + + align:start position:0% +push this Buton button or that or + + + align:start position:0% +push this Buton button or that or +whatever and if they pushed the one you + + align:start position:0% +whatever and if they pushed the one you + + + align:start position:0% +whatever and if they pushed the one you +approve of then you'd give them a little + + align:start position:0% +approve of then you'd give them a little + + + align:start position:0% +approve of then you'd give them a little +pellet of food and there was a lot of + + align:start position:0% +pellet of food and there was a lot of + + + align:start position:0% +pellet of food and there was a lot of +engineering so that you would make sure + + align:start position:0% +engineering so that you would make sure + + + align:start position:0% +engineering so that you would make sure +that the food got to them right away + + align:start position:0% +that the food got to them right away + + + align:start position:0% +that the food got to them right away +because if there were a 10-second delay + + align:start position:0% +because if there were a 10-second delay + + + align:start position:0% +because if there were a 10-second delay +between an action and a reward the + + align:start position:0% +between an action and a reward the + + + align:start position:0% +between an action and a reward the +pigeon or squirrel or rat or cat or dog + + align:start position:0% +pigeon or squirrel or rat or cat or dog + + + align:start position:0% +pigeon or squirrel or rat or cat or dog +would learn much less quickly than if + + align:start position:0% +would learn much less quickly than if + + + align:start position:0% +would learn much less quickly than if +there was a one second + + align:start position:0% +there was a one second + + + align:start position:0% +there was a one second +delay and um + + align:start position:0% +delay and um + + + align:start position:0% +delay and um +anyway that went on for 50 years + + align:start position:0% +anyway that went on for 50 years + + + align:start position:0% +anyway that went on for 50 years +starting around 1900 Pavlov and his dogs + + align:start position:0% +starting around 1900 Pavlov and his dogs + + + align:start position:0% +starting around 1900 Pavlov and his dogs +and there's a great movie that some guy + + align:start position:0% +and there's a great movie that some guy + + + align:start position:0% +and there's a great movie that some guy +came around with that had been taken of + + align:start position:0% +came around with that had been taken of + + + align:start position:0% +came around with that had been taken of +Pavlov's lab and it shows the sort of + + align:start position:0% +Pavlov's lab and it shows the sort of + + + align:start position:0% +Pavlov's lab and it shows the sort of +like a Great Dictator or something + + align:start position:0% +like a Great Dictator or something + + + align:start position:0% +like a Great Dictator or something +there's this room with lot of cages and + + align:start position:0% +there's this room with lot of cages and + + + align:start position:0% +there's this room with lot of cages and +dogs and mostly dogs in this case and + + align:start position:0% +dogs and mostly dogs in this case and + + + align:start position:0% +dogs and mostly dogs in this case and +Pavlov comes in and there are a bunch of + + align:start position:0% +Pavlov comes in and there are a bunch of + + + align:start position:0% +Pavlov comes in and there are a bunch of +Lackey who sort of bow and scrape + + align:start position:0% +Lackey who sort of bow and scrape + + + align:start position:0% +Lackey who sort of bow and scrape +because he's a Lord and he comes in and + + align:start position:0% +because he's a Lord and he comes in and + + + align:start position:0% +because he's a Lord and he comes in and +all the dogs run into the corner of + + align:start position:0% +all the dogs run into the corner of + + + align:start position:0% +all the dogs run into the corner of +their cage and and Yelp so + + align:start position:0% +their cage and and Yelp so + + + align:start position:0% +their cage and and Yelp so +uh the uh pavlovian tried pretty hard to + + align:start position:0% +uh the uh pavlovian tried pretty hard to + + + align:start position:0% +uh the uh pavlovian tried pretty hard to +get that movie suppressed and I haven't + + align:start position:0% +get that movie suppressed and I haven't + + + align:start position:0% +get that movie suppressed and I haven't +seen it in recent years + + align:start position:0% +seen it in recent years + + + align:start position:0% +seen it in recent years +but uh but anyway + + align:start position:0% + + + + align:start position:0% + +uh Fred SK + + align:start position:0% +uh Fred SK + + + align:start position:0% +uh Fred SK +who was a professor when I was + + align:start position:0% +who was a professor when I was + + + align:start position:0% +who was a professor when I was +undergraduate + + align:start position:0% +undergraduate + + + align:start position:0% +undergraduate +Harvard uh was the first one to really + + align:start position:0% +Harvard uh was the first one to really + + + align:start position:0% +Harvard uh was the first one to really +automate this uh experiment of + + align:start position:0% +automate this uh experiment of + + + align:start position:0% +automate this uh experiment of +psychology and he invented what's called + + align:start position:0% +psychology and he invented what's called + + + align:start position:0% +psychology and he invented what's called +a Skinner box but it's just a soundproof + + align:start position:0% +a Skinner box but it's just a soundproof + + + align:start position:0% +a Skinner box but it's just a soundproof +lightproof well ventilated and uh + + align:start position:0% +lightproof well ventilated and uh + + + align:start position:0% +lightproof well ventilated and uh +thermally regulated cage and you can put + + align:start position:0% +thermally regulated cage and you can put + + + align:start position:0% +thermally regulated cage and you can put +a rat or a pigeon those are the most + + align:start position:0% +a rat or a pigeon those are the most + + + align:start position:0% +a rat or a pigeon those are the most +common + + align:start position:0% +common + + + align:start position:0% +common +animals they're very inexpensive because + + align:start position:0% +animals they're very inexpensive because + + + align:start position:0% +animals they're very inexpensive because +they're + + align:start position:0% + + + + align:start position:0% + +free uh no one knows much about + + align:start position:0% +free uh no one knows much about + + + align:start position:0% +free uh no one knows much about +[Laughter] + + align:start position:0% + + + + align:start position:0% + +dolphins they've been studied for 50 + + align:start position:0% +dolphins they've been studied for 50 + + + align:start position:0% +dolphins they've been studied for 50 +years whenever John what's his name + + align:start position:0% +years whenever John what's his name + + + align:start position:0% +years whenever John what's his name +remember the name of the great + + align:start position:0% + + + + align:start position:0% + +dolphin Lily thanks um he discovered a + + align:start position:0% +dolphin Lily thanks um he discovered a + + + align:start position:0% +dolphin Lily thanks um he discovered a +lot about + + align:start position:0% +lot about + + + align:start position:0% +lot about +dolphins and a certain amount about + + align:start position:0% +dolphins and a certain amount about + + + align:start position:0% +dolphins and a certain amount about +their + + align:start position:0% +their + + + align:start position:0% +their +communication uh and a little bit about + + align:start position:0% +communication uh and a little bit about + + + align:start position:0% +communication uh and a little bit about +whales but there's an interesting + + align:start position:0% +whales but there's an interesting + + + align:start position:0% +whales but there's an interesting +mystery uh I forget which whales but uh + + align:start position:0% +mystery uh I forget which whales but uh + + + align:start position:0% +mystery uh I forget which whales but uh +some whales have a 20 minute song and + + align:start position:0% +some whales have a 20 minute song and + + + align:start position:0% +some whales have a 20 minute song and +they repeat it for a whole season and + + align:start position:0% +they repeat it for a whole season and + + + align:start position:0% +they repeat it for a whole season and +next year uh that song is a little bit + + align:start position:0% +next year uh that song is a little bit + + + align:start position:0% +next year uh that song is a little bit +different but it goes essentially + + align:start position:0% +different but it goes essentially + + + align:start position:0% +different but it goes essentially +without repeating it's very complicated + + align:start position:0% +without repeating it's very complicated + + + align:start position:0% +without repeating it's very complicated +for 20 minutes and people have studied + + align:start position:0% +for 20 minutes and people have studied + + + align:start position:0% +for 20 minutes and people have studied +that a lot and no one has the slightest + + align:start position:0% +that a lot and no one has the slightest + + + align:start position:0% +that a lot and no one has the slightest +idea of what it + + align:start position:0% + + + + align:start position:0% + +means and nobody even has any good + + align:start position:0% +means and nobody even has any good + + + align:start position:0% +means and nobody even has any good +conjectures which bothers me what I + + align:start position:0% +conjectures which bothers me what I + + + align:start position:0% +conjectures which bothers me what I +think it probably means is this when + + align:start position:0% +think it probably means is this when + + + align:start position:0% +think it probably means is this when +there's a whole bunch of fish somewhere + + align:start position:0% +there's a whole bunch of fish somewhere + + + align:start position:0% +there's a whole bunch of fish somewhere +for uh one of these whales it might be + + align:start position:0% +for uh one of these whales it might be + + + align:start position:0% +for uh one of these whales it might be +200 miles away and it's very whales eat + + align:start position:0% +200 miles away and it's very whales eat + + + align:start position:0% +200 miles away and it's very whales eat +a + + align:start position:0% +a + + + align:start position:0% +a +lot and it's very important to find + + align:start position:0% +lot and it's very important to find + + + align:start position:0% +lot and it's very important to find +where the fish are and uh I believe this + + align:start position:0% +where the fish are and uh I believe this + + + align:start position:0% +where the fish are and uh I believe this +this uh message which changes a bit + + align:start position:0% +this uh message which changes a bit + + + align:start position:0% +this uh message which changes a bit +during the season might be telling you + + align:start position:0% +during the season might be telling you + + + align:start position:0% +during the season might be telling you +where the food is on the Atlantic or + + align:start position:0% +where the food is on the Atlantic or + + + align:start position:0% +where the food is on the Atlantic or +Pacific + + align:start position:0% +Pacific + + + align:start position:0% +Pacific +Coastline in great detail because uh if + + align:start position:0% +Coastline in great detail because uh if + + + align:start position:0% +Coastline in great detail because uh if +somebody finds a lot of fish somewhere + + align:start position:0% +somebody finds a lot of fish somewhere + + + align:start position:0% +somebody finds a lot of fish somewhere +you have to swim 300 miles and if + + align:start position:0% +you have to swim 300 miles and if + + + align:start position:0% +you have to swim 300 miles and if +they're not + + align:start position:0% +they're not + + + align:start position:0% +they're not +there so anyway it's interesting that uh + + align:start position:0% +there so anyway it's interesting that uh + + + align:start position:0% +there so anyway it's interesting that uh +John Lily got a lot of + + align:start position:0% +John Lily got a lot of + + + align:start position:0% +John Lily got a lot of +publicity but he didn't discover squat + + align:start position:0% +publicity but he didn't discover squat + + + align:start position:0% +publicity but he didn't discover squat +and finally + + align:start position:0% +and finally + + + align:start position:0% +and finally +uh the dolphin dolphin studiers gave up + + align:start position:0% +uh the dolphin dolphin studiers gave up + + + align:start position:0% +uh the dolphin dolphin studiers gave up +because nothing happened anybody have + + align:start position:0% +because nothing happened anybody have + + + align:start position:0% +because nothing happened anybody have +heard anything in I haven't paid any + + align:start position:0% +heard anything in I haven't paid any + + + align:start position:0% +heard anything in I haven't paid any +attention for 20 + + align:start position:0% +attention for 20 + + + align:start position:0% +attention for 20 +years have you heard of anybody + + align:start position:0% +years have you heard of anybody + + + align:start position:0% +years have you heard of anybody +discovering anything about + + align:start position:0% +discovering anything about + + + align:start position:0% +discovering anything about +dolphins except they're very good at + + align:start position:0% +dolphins except they're very good at + + + align:start position:0% +dolphins except they're very good at +solving a lot of physical + + align:start position:0% + + + + align:start position:0% + +problems anyway that's + + align:start position:0% + + + + align:start position:0% + +I'm bothered by the mystery + + align:start position:0% +I'm bothered by the mystery + + + align:start position:0% +I'm bothered by the mystery +of why was there some psychology in + + align:start position:0% +of why was there some psychology in + + + align:start position:0% +of why was there some psychology in +Aristotle's time and Why + + align:start position:0% +Aristotle's time and Why + + + align:start position:0% +Aristotle's time and Why +did Why didn't it get anywhere till + + align:start position:0% +did Why didn't it get anywhere till + + + align:start position:0% +did Why didn't it get anywhere till +1950 when the there was regular + + align:start position:0% +1950 when the there was regular + + + align:start position:0% +1950 when the there was regular +psychology but it was afflicted by what + + align:start position:0% +psychology but it was afflicted by what + + + align:start position:0% +psychology but it was afflicted by what +I call physics Envy namely you run into + + align:start position:0% +I call physics Envy namely you run into + + + align:start position:0% +I call physics Envy namely you run into +people like eses and well he was pretty + + align:start position:0% +people like eses and well he was pretty + + + align:start position:0% +people like eses and well he was pretty +good actually but there are a lot of + + align:start position:0% +good actually but there are a lot of + + + align:start position:0% +good actually but there are a lot of +psychologists who made up uh things like + + align:start position:0% +psychologists who made up uh things like + + + align:start position:0% +psychologists who made up uh things like +Maxwell's equations for how animals + + align:start position:0% +Maxwell's equations for how animals + + + align:start position:0% +Maxwell's equations for how animals +learn and there were generally three or + + align:start position:0% +learn and there were generally three or + + + align:start position:0% +learn and there were generally three or +four + + align:start position:0% +four + + + align:start position:0% +four +laws and + + align:start position:0% +laws and + + + align:start position:0% +laws and +uh if there's a sequence of + + align:start position:0% +uh if there's a sequence of + + + align:start position:0% +uh if there's a sequence of +events then animals + + align:start position:0% +events then animals + + + align:start position:0% +events then animals +remember a lot about the first few and + + align:start position:0% +remember a lot about the first few and + + + align:start position:0% +remember a lot about the first few and +the last few in the sequence they don't + + align:start position:0% +the last few in the sequence they don't + + + align:start position:0% +the last few in the sequence they don't +remember much about the middle and of + + align:start position:0% +remember much about the middle and of + + + align:start position:0% +remember much about the middle and of +course the uh reliability of their + + align:start position:0% +course the uh reliability of their + + + align:start position:0% +course the uh reliability of their +memory depends a lot on how recent it + + align:start position:0% +memory depends a lot on how recent it + + + align:start position:0% +memory depends a lot on how recent it +was and on how powerful the reward was + + align:start position:0% +was and on how powerful the reward was + + + align:start position:0% +was and on how powerful the reward was +and blah blah and so they get these + + align:start position:0% +and blah blah and so they get these + + + align:start position:0% +and blah blah and so they get these +little sets of rules that look like + + align:start position:0% +little sets of rules that look like + + + align:start position:0% +little sets of rules that look like +Newton's laws and that was the kind of + + align:start position:0% +Newton's laws and that was the kind of + + + align:start position:0% +Newton's laws and that was the kind of +sort of psychological physics that the + + align:start position:0% +sort of psychological physics that the + + + align:start position:0% +sort of psychological physics that the +so-called behaviorists were mostly + + align:start position:0% +so-called behaviorists were mostly + + + align:start position:0% +so-called behaviorists were mostly +looking for uh this was not what + + align:start position:0% +looking for uh this was not what + + + align:start position:0% +looking for uh this was not what +tinbergen and lorence did because they + + align:start position:0% +tinbergen and lorence did because they + + + align:start position:0% +tinbergen and lorence did because they +wrote books with extensive descriptions + + align:start position:0% +wrote books with extensive descriptions + + + align:start position:0% +wrote books with extensive descriptions +of + + align:start position:0% +of + + + align:start position:0% +of +of what the animals did and made little + + align:start position:0% +of what the animals did and made little + + + align:start position:0% +of what the animals did and made little +diagrammatic guesses about the structure + + align:start position:0% +diagrammatic guesses about the structure + + + align:start position:0% +diagrammatic guesses about the structure +of the sub routines and + + align:start position:0% +of the sub routines and + + + align:start position:0% +of the sub routines and +substructures um anyway end of + + align:start position:0% +substructures um anyway end of + + + align:start position:0% +substructures um anyway end of +History uh but it's a nice question why + + align:start position:0% +History uh but it's a nice question why + + + align:start position:0% +History uh but it's a nice question why +do some Sciences grow and why was + + align:start position:0% +do some Sciences grow and why was + + + align:start position:0% +do some Sciences grow and why was +psychology the just about the last + + align:start position:0% +psychology the just about the last + + + align:start position:0% +psychology the just about the last +one I suspect it was it could have been + + align:start position:0% +one I suspect it was it could have been + + + align:start position:0% +one I suspect it was it could have been +earlier but uh people tried to imitate + + align:start position:0% +earlier but uh people tried to imitate + + + align:start position:0% +earlier but uh people tried to imitate +the physicists and tried to say maybe + + align:start position:0% +the physicists and tried to say maybe + + + align:start position:0% +the physicists and tried to say maybe +there's something like Newton's or + + align:start position:0% +there's something like Newton's or + + + align:start position:0% +there's something like Newton's or +Maxwell's laws for the + + align:start position:0% +Maxwell's laws for the + + + align:start position:0% +Maxwell's laws for the +mind and they found a few but they + + align:start position:0% +mind and they found a few but they + + + align:start position:0% +mind and they found a few but they +weren't enough to explain + + align:start position:0% + + + + align:start position:0% + +much so there are a lot of questions + + align:start position:0% + + + + align:start position:0% + +uh uh when Seymour paper and I started + + align:start position:0% +uh uh when Seymour paper and I started + + + align:start position:0% +uh uh when Seymour paper and I started +thinking about these things which was + + align:start position:0% +thinking about these things which was + + + align:start position:0% +thinking about these things which was +really around + + align:start position:0% +really around + + + align:start position:0% +really around +1960 um + + align:start position:0% +1960 um + + + align:start position:0% +1960 um +I had been working + + align:start position:0% +I had been working + + + align:start position:0% +I had been working +on some ideas about + + align:start position:0% +on some ideas about + + + align:start position:0% +on some ideas about +AI in the late 50s and my PhD thesis was + + align:start position:0% +AI in the late 50s and my PhD thesis was + + + align:start position:0% +AI in the late 50s and my PhD thesis was +a a theory of neural networks which was + + align:start position:0% +a a theory of neural networks which was + + + align:start position:0% +a a theory of neural networks which was +sort of interesting but um never really + + align:start position:0% +sort of interesting but um never really + + + align:start position:0% +sort of interesting but um never really +went + + align:start position:0% +went + + + align:start position:0% +went +anywhere um I went to a meeting in + + align:start position:0% +anywhere um I went to a meeting in + + + align:start position:0% +anywhere um I went to a meeting in +London + + align:start position:0% +London + + + align:start position:0% +London +somewhere and gave a talk about a theory + + align:start position:0% +somewhere and gave a talk about a theory + + + align:start position:0% +somewhere and gave a talk about a theory +of learning that was based on some + + align:start position:0% +of learning that was based on some + + + align:start position:0% +of learning that was based on some +neural network + + align:start position:0% +neural network + + + align:start position:0% +neural network +ideas and there was this uh person from + + align:start position:0% +ideas and there was this uh person from + + + align:start position:0% +ideas and there was this uh person from +South Africa named Seymour + + align:start position:0% +South Africa named Seymour + + + align:start position:0% +South Africa named Seymour +papert who gave the same + + align:start position:0% +papert who gave the same + + + align:start position:0% +papert who gave the same +paper and + + align:start position:0% +paper and + + + align:start position:0% +paper and +uh I hope this happens to you + + align:start position:0% +uh I hope this happens to you + + + align:start position:0% +uh I hope this happens to you +someday find somebody who thinks so much + + align:start position:0% +someday find somebody who thinks so much + + + align:start position:0% +someday find somebody who thinks so much +like you only different enough that it's + + align:start position:0% +like you only different enough that it's + + + align:start position:0% +like you only different enough that it's +worth it and that uh you only have to + + align:start position:0% +worth it and that uh you only have to + + + align:start position:0% +worth it and that uh you only have to +say about three words a day in some + + align:start position:0% +say about three words a day in some + + + align:start position:0% +say about three words a day in some +whole new new thing starts because uh we + + align:start position:0% +whole new new thing starts because uh we + + + align:start position:0% +whole new new thing starts because uh we +really did write the same paper and it + + align:start position:0% +really did write the same paper and it + + + align:start position:0% +really did write the same paper and it +had the same equation in it + + align:start position:0% + + + + align:start position:0% + +uh and he had been working for + + align:start position:0% +uh and he had been working for + + + align:start position:0% +uh and he had been working for +p in the who was the first great child + + align:start position:0% +p in the who was the first great child + + + align:start position:0% +p in the who was the first great child +psychologist I should have mentioned P + + align:start position:0% +psychologist I should have mentioned P + + + align:start position:0% +psychologist I should have mentioned P +who probably discovered more things + + align:start position:0% +who probably discovered more things + + + align:start position:0% +who probably discovered more things +about psychology than any other s single + + align:start position:0% +about psychology than any other s single + + + align:start position:0% +about psychology than any other s single +person in history and uh + + align:start position:0% +person in history and uh + + + align:start position:0% +person in history and uh +there are lots of people now who saying + + align:start position:0% +there are lots of people now who saying + + + align:start position:0% +there are lots of people now who saying +he was wrong + + align:start position:0% +he was wrong + + + align:start position:0% +he was wrong +about + + align:start position:0% +about + + + align:start position:0% +about +73 uh because children learn that at the + + align:start position:0% +73 uh because children learn that at the + + + align:start position:0% +73 uh because children learn that at the +age of Two and a Half instead of two and + + align:start position:0% +age of Two and a Half instead of two and + + + align:start position:0% +age of Two and a Half instead of two and +3/4 I'm parodying the P critic Community + + align:start position:0% +3/4 I'm parodying the P critic Community + + + align:start position:0% +3/4 I'm parodying the P critic Community +but it's pretty bad and I think those + + align:start position:0% +but it's pretty bad and I think those + + + align:start position:0% +but it's pretty bad and I think those +poor guys are + + align:start position:0% +poor guys are + + + align:start position:0% +poor guys are +uncomfortable because uh Jean P + + align:start position:0% +uncomfortable because uh Jean P + + + align:start position:0% +uncomfortable because uh Jean P +published 20 books full of observations + + align:start position:0% +published 20 books full of observations + + + align:start position:0% +published 20 books full of observations +about children that uh as far as I know + + align:start position:0% +about children that uh as far as I know + + + align:start position:0% +about children that uh as far as I know +no one had made systematically before + + align:start position:0% +no one had made systematically before + + + align:start position:0% +no one had made systematically before +and + + align:start position:0% +and + + + align:start position:0% +and +uh in his later years he started + + align:start position:0% +uh in his later years he started + + + align:start position:0% +uh in his later years he started +courting algebra algebraic + + align:start position:0% +courting algebra algebraic + + + align:start position:0% +courting algebra algebraic +mathematicians because he wanted more + + align:start position:0% +mathematicians because he wanted more + + + align:start position:0% +mathematicians because he wanted more +formal theories and + + align:start position:0% +formal theories and + + + align:start position:0% +formal theories and +uh in my view he wanted to make his + + align:start position:0% +uh in my view he wanted to make his + + + align:start position:0% +uh in my view he wanted to make his +theories worse and uh nothing much + + align:start position:0% +theories worse and uh nothing much + + + align:start position:0% +theories worse and uh nothing much +happened but he did visit here a couple + + align:start position:0% +happened but he did visit here a couple + + + align:start position:0% +happened but he did visit here a couple +of times + + align:start position:0% +of times + + + align:start position:0% +of times +and it was really exciting to + + align:start position:0% +and it was really exciting to + + + align:start position:0% +and it was really exciting to +meet the starter of a whole new + + align:start position:0% + + + + align:start position:0% + +field anyway + + align:start position:0% +field anyway + + + align:start position:0% +field anyway +uh paper and I discussed lots of things + + align:start position:0% +uh paper and I discussed lots of things + + + align:start position:0% +uh paper and I discussed lots of things +and somehow or other we kept finding + + align:start position:0% +and somehow or other we kept finding + + + align:start position:0% +and somehow or other we kept finding +other more ideas about psychology and it + + align:start position:0% +other more ideas about psychology and it + + + align:start position:0% +other more ideas about psychology and it +finally jelled into the idea that well + + align:start position:0% +finally jelled into the idea that well + + + align:start position:0% +finally jelled into the idea that well +if you you look at the brain you know + + align:start position:0% +if you you look at the brain you know + + + align:start position:0% +if you you look at the brain you know +that there are several hundred different + + align:start position:0% +that there are several hundred different + + + align:start position:0% +that there are several hundred different +brain + + align:start position:0% +brain + + + align:start position:0% +brain +centers what's all that stuff for and + + align:start position:0% +centers what's all that stuff for and + + + align:start position:0% +centers what's all that stuff for and +uh how could it possibly make any sense + + align:start position:0% +uh how could it possibly make any sense + + + align:start position:0% +uh how could it possibly make any sense +to try to uh explain what it does in + + align:start position:0% +to try to uh explain what it does in + + + align:start position:0% +to try to uh explain what it does in +terms of four laws like + + align:start position:0% +terms of four laws like + + + align:start position:0% +terms of four laws like +Newton like how does a car + + align:start position:0% +Newton like how does a car + + + align:start position:0% +Newton like how does a car +work is there a magical Force inside the + + align:start position:0% +work is there a magical Force inside the + + + align:start position:0% +work is there a magical Force inside the +engine that causes the wheels to turn no + + align:start position:0% +engine that causes the wheels to turn no + + + align:start position:0% +engine that causes the wheels to turn no +uh there's this funny thing in the back + + align:start position:0% +uh there's this funny thing in the back + + + align:start position:0% +uh there's this funny thing in the back +to cause a differential so that if the + + align:start position:0% +to cause a differential so that if the + + + align:start position:0% +to cause a differential so that if the +car isn't going in a straight line + + align:start position:0% +car isn't going in a straight line + + + align:start position:0% +car isn't going in a straight line +uh the two wheels going at different + + align:start position:0% +uh the two wheels going at different + + + align:start position:0% +uh the two wheels going at different +speeds won't rip the + + align:start position:0% +speeds won't rip the + + + align:start position:0% +speeds won't rip the +uh if the two wheels were going at the + + align:start position:0% +uh if the two wheels were going at the + + + align:start position:0% +uh if the two wheels were going at the +same speed the tread would come off in + + align:start position:0% +same speed the tread would come off in + + + align:start position:0% +same speed the tread would come off in +five minutes do you ever wonder what a + + align:start position:0% +five minutes do you ever wonder what a + + + align:start position:0% +five minutes do you ever wonder what a +differential is for + + align:start position:0% +differential is for + + + align:start position:0% +differential is for +well so most of the car is fixing bugs + + align:start position:0% +well so most of the car is fixing bugs + + + align:start position:0% +well so most of the car is fixing bugs +in the other + + align:start position:0% +in the other + + + align:start position:0% +in the other +parts that's most of the brain is + + align:start position:0% +parts that's most of the brain is + + + align:start position:0% +parts that's most of the brain is +because we started out as fish or + + align:start position:0% +because we started out as fish or + + + align:start position:0% +because we started out as fish or +Lizards or whatever you + + align:start position:0% +Lizards or whatever you + + + align:start position:0% +Lizards or whatever you +like + + align:start position:0% +like + + + align:start position:0% +like +and making the brain bigger wouldn't + + align:start position:0% +and making the brain bigger wouldn't + + + align:start position:0% +and making the brain bigger wouldn't +help much because you just get a heavier + + align:start position:0% +help much because you just get a heavier + + + align:start position:0% +help much because you just get a heavier +lizard that had to eat more and would + + align:start position:0% +lizard that had to eat more and would + + + align:start position:0% +lizard that had to eat more and would +think more + + align:start position:0% +think more + + + align:start position:0% +think more +slowly so size is bad um but on the + + align:start position:0% +slowly so size is bad um but on the + + + align:start position:0% +slowly so size is bad um but on the +other hand if you need another cubic + + align:start position:0% +other hand if you need another cubic + + + align:start position:0% +other hand if you need another cubic +inch of brain to fix the bugs in the + + align:start position:0% +inch of brain to fix the bugs in the + + + align:start position:0% +inch of brain to fix the bugs in the +other part then + + align:start position:0% +other part then + + + align:start position:0% +other part then +you um then the evolutionary advantage + + align:start position:0% +you um then the evolutionary advantage + + + align:start position:0% +you um then the evolutionary advantage +of being + + align:start position:0% +of being + + + align:start position:0% +of being +smarter + + align:start position:0% +smarter + + + align:start position:0% +smarter +uh had better make you able to catch a + + align:start position:0% +uh had better make you able to catch a + + + align:start position:0% +uh had better make you able to catch a +little more food per hour and uh so each + + align:start position:0% +little more food per hour and uh so each + + + align:start position:0% +little more food per hour and uh so each +person is an Ecology of these different + + align:start position:0% +person is an Ecology of these different + + + align:start position:0% +person is an Ecology of these different +processes and + + align:start position:0% + + + + align:start position:0% + +um the brain reached its present size + + align:start position:0% +um the brain reached its present size + + + align:start position:0% +um the brain reached its present size +about a million years ago I guess what's + + align:start position:0% +about a million years ago I guess what's + + + align:start position:0% +about a million years ago I guess what's +what's the current guess anybody been + + align:start position:0% +what's the current guess anybody been + + + align:start position:0% +what's the current guess anybody been +tracked they keep discovering new + + align:start position:0% +tracked they keep discovering new + + + align:start position:0% +tracked they keep discovering new +ancestors of humans and I don't have the + + align:start position:0% +ancestors of humans and I don't have the + + + align:start position:0% +ancestors of humans and I don't have the +patience to read about them because you + + align:start position:0% +patience to read about them because you + + + align:start position:0% +patience to read about them because you +know that next week somebody will say oh + + align:start position:0% +know that next week somebody will say oh + + + align:start position:0% +know that next week somebody will say oh +that isn't in the main line and you were + + align:start position:0% +that isn't in the main line and you were + + + align:start position:0% +that isn't in the main line and you were +just unlucky to discover that + + align:start position:0% + + + + align:start position:0% + +skeleton + + align:start position:0% + + + + align:start position:0% + +so anyway + + align:start position:0% +so anyway + + + align:start position:0% +so anyway +uh Pap and I and a lot of + + align:start position:0% +uh Pap and I and a lot of + + + align:start position:0% +uh Pap and I and a lot of +students uh gradually develop this + + align:start position:0% +students uh gradually develop this + + + align:start position:0% +students uh gradually develop this +picture that the mind is made of lots of + + align:start position:0% +picture that the mind is made of lots of + + + align:start position:0% +picture that the mind is made of lots of +processes or agents or resources or + + align:start position:0% +processes or agents or resources or + + + align:start position:0% +processes or agents or resources or +whatever you want to call them and it's + + align:start position:0% +whatever you want to call them and it's + + + align:start position:0% +whatever you want to call them and it's +anybody's guess what they are uh if you + + align:start position:0% +anybody's guess what they are uh if you + + + align:start position:0% +anybody's guess what they are uh if you +look at the anatomy of the + + align:start position:0% +look at the anatomy of the + + + align:start position:0% +look at the anatomy of the +brain uh you know that people label + + align:start position:0% +brain uh you know that people label + + + align:start position:0% +brain uh you know that people label +region so it's very clear that this + + align:start position:0% +region so it's very clear that this + + + align:start position:0% +region so it's very clear that this +occipital lobe back here is largely + + align:start position:0% +occipital lobe back here is largely + + + align:start position:0% +occipital lobe back here is largely +concerned with vision but + + align:start position:0% +concerned with vision but + + + align:start position:0% +concerned with vision but +uh and I forget where the one for + + align:start position:0% +uh and I forget where the one for + + + align:start position:0% +uh and I forget where the one for +hearing is uh if you destroy + + align:start position:0% +hearing is uh if you destroy + + + align:start position:0% +hearing is uh if you destroy +the uh part of the brain for hearing in + + align:start position:0% +the uh part of the brain for hearing in + + + align:start position:0% +the uh part of the brain for hearing in +some + + align:start position:0% +some + + + align:start position:0% +some +animals you get a little bit of uh + + align:start position:0% +animals you get a little bit of uh + + + align:start position:0% +animals you get a little bit of uh +increased function in some part of the + + align:start position:0% +increased function in some part of the + + + align:start position:0% +increased function in some part of the +visual system that seems to enable the + + align:start position:0% +visual system that seems to enable the + + + align:start position:0% +visual system that seems to enable the +animal to hear a little bit and make + + align:start position:0% +animal to hear a little bit and make + + + align:start position:0% +animal to hear a little bit and make +some + + align:start position:0% +some + + + align:start position:0% +some +reactions and there's a whole lot of uh + + align:start position:0% +reactions and there's a whole lot of uh + + + align:start position:0% +reactions and there's a whole lot of uh +hype I think you have to call it about + + align:start position:0% +hype I think you have to call it about + + + align:start position:0% +hype I think you have to call it about +the flexibility of the nervous system + + align:start position:0% +the flexibility of the nervous system + + + align:start position:0% +the flexibility of the nervous system +that is if uh certain brain areas get + + align:start position:0% +that is if uh certain brain areas get + + + align:start position:0% +that is if uh certain brain areas get +destroyed other parts take over they + + align:start position:0% +destroyed other parts take over they + + + align:start position:0% +destroyed other parts take over they +almost never are as good and mostly they + + align:start position:0% +almost never are as good and mostly they + + + align:start position:0% +almost never are as good and mostly they +many functions never get taken over at + + align:start position:0% +many functions never get taken over at + + + align:start position:0% +many functions never get taken over at +all but are replaced by ones that + + align:start position:0% +all but are replaced by ones that + + + align:start position:0% +all but are replaced by ones that +superficially seem similar and so uh + + align:start position:0% +superficially seem similar and so uh + + + align:start position:0% +superficially seem similar and so uh +there's a whole lot of I guess wishful + + align:start position:0% +there's a whole lot of I guess wishful + + + align:start position:0% +there's a whole lot of I guess wishful +thinking that the brain is immensely + + align:start position:0% +thinking that the brain is immensely + + + align:start position:0% +thinking that the brain is immensely +resourceful and error correcting and + + align:start position:0% +resourceful and error correcting and + + + align:start position:0% +resourceful and error correcting and +repairing I + + align:start position:0% +repairing I + + + align:start position:0% +repairing I +think uh there was some idea that that + + align:start position:0% +think uh there was some idea that that + + + align:start position:0% +think uh there was some idea that that +was a general + + align:start position:0% +was a general + + + align:start position:0% +was a general +phenomenon but if you do some arithmetic + + align:start position:0% +phenomenon but if you do some arithmetic + + + align:start position:0% +phenomenon but if you do some arithmetic +you get an interesting result suppose + + align:start position:0% +you get an interesting result suppose + + + align:start position:0% +you get an interesting result suppose +that each function in the + + align:start position:0% +that each function in the + + + align:start position:0% +that each function in the +brain uh occurred in 10 different places + + align:start position:0% +brain uh occurred in 10 different places + + + align:start position:0% +brain uh occurred in 10 different places +at + + align:start position:0% +at + + + align:start position:0% +at +random + + align:start position:0% +random + + + align:start position:0% +random +then if you removed half the + + align:start position:0% +then if you removed half the + + + align:start position:0% +then if you removed half the +brain how many functions would you + + align:start position:0% + + + + align:start position:0% + +lose well almost no arithmetic tells you + + align:start position:0% +lose well almost no arithmetic tells you + + + align:start position:0% +lose well almost no arithmetic tells you +you would lose about one part in the + + align:start position:0% +you would lose about one part in the + + + align:start position:0% +you would lose about one part in the +thousand and so uh in fact you would + + align:start position:0% +thousand and so uh in fact you would + + + align:start position:0% +thousand and so uh in fact you would +never be able to detect it U so this + + align:start position:0% +never be able to detect it U so this + + + align:start position:0% +never be able to detect it U so this +idea that the brain has enormous + + align:start position:0% +idea that the brain has enormous + + + align:start position:0% +idea that the brain has enormous +redundancy will now change that number + + align:start position:0% +redundancy will now change that number + + + align:start position:0% +redundancy will now change that number +to five + + align:start position:0% +to five + + + align:start position:0% +to five +suppose each function is somewhat uh + + align:start position:0% +suppose each function is somewhat uh + + + align:start position:0% +suppose each function is somewhat uh +supported in five different parts of the + + align:start position:0% +supported in five different parts of the + + + align:start position:0% +supported in five different parts of the +brain then if you take off half + + align:start position:0% +brain then if you take off half + + + align:start position:0% +brain then if you take off half +the brain then what am I saying one part + + align:start position:0% +the brain then what am I saying one part + + + align:start position:0% +the brain then what am I saying one part +in + + align:start position:0% +in + + + align:start position:0% +in +32 chance of uh of losing some + + align:start position:0% +32 chance of uh of losing some + + + align:start position:0% +32 chance of uh of losing some +significant function so probably uh lots + + align:start position:0% +significant function so probably uh lots + + + align:start position:0% +significant function so probably uh lots +of things that we do are supported in + + align:start position:0% +of things that we do are supported in + + + align:start position:0% +of things that we do are supported in +several parts of the brain apparently + + align:start position:0% +several parts of the brain apparently + + + align:start position:0% +several parts of the brain apparently +The Language Center is pretty unique + + align:start position:0% +The Language Center is pretty unique + + + align:start position:0% +The Language Center is pretty unique +uh and some others but + + align:start position:0% +uh and some others but + + + align:start position:0% +uh and some others but +uh be careful about the conclusions you + + align:start position:0% +uh be careful about the conclusions you + + + align:start position:0% +uh be careful about the conclusions you +read + + align:start position:0% +read + + + align:start position:0% +read +from optimistic + + align:start position:0% + + + + align:start position:0% + +neuroscientists anyway paper and I + + align:start position:0% +neuroscientists anyway paper and I + + + align:start position:0% +neuroscientists anyway paper and I +worked on this idea + + align:start position:0% +worked on this idea + + + align:start position:0% +worked on this idea +of uh how could these large numbers of + + align:start position:0% +of uh how could these large numbers of + + + align:start position:0% +of uh how could these large numbers of +different processes be being organized + + align:start position:0% +different processes be being organized + + + align:start position:0% +different processes be being organized +be organized and we made various + + align:start position:0% +be organized and we made various + + + align:start position:0% +be organized and we made various +theories about it and uh then + + align:start position:0% +theories about it and uh then + + + align:start position:0% +theories about it and uh then +around I guess the late + + align:start position:0% +around I guess the late + + + align:start position:0% +around I guess the late +1970s we stopped working together and + + align:start position:0% +1970s we stopped working together and + + + align:start position:0% +1970s we stopped working together and +paper developed his revolutionary ideas + + align:start position:0% +paper developed his revolutionary ideas + + + align:start position:0% +paper developed his revolutionary ideas +about education which + + align:start position:0% +about education which + + + align:start position:0% +about education which +um certainly have had a lot of influence + + align:start position:0% +um certainly have had a lot of influence + + + align:start position:0% +um certainly have had a lot of influence +although they didn't sweep the world in + + align:start position:0% +although they didn't sweep the world in + + + align:start position:0% +although they didn't sweep the world in +the way we had hoped + + align:start position:0% +the way we had hoped + + + align:start position:0% +the way we had hoped +and I kept working on the Society of + + align:start position:0% +and I kept working on the Society of + + + align:start position:0% +and I kept working on the Society of +Mind Theory + + align:start position:0% +Mind Theory + + + align:start position:0% +Mind Theory +and uh we didn't work together so much + + align:start position:0% +and uh we didn't work together so much + + + align:start position:0% +and uh we didn't work together so much +but we + + align:start position:0% +but we + + + align:start position:0% +but we +still did plenty of criticizing and + + align:start position:0% +still did plenty of criticizing and + + + align:start position:0% +still did plenty of criticizing and +supporting of each + + align:start position:0% +supporting of each + + + align:start position:0% +supporting of each +other anyway my theory ended up with + + align:start position:0% +other anyway my theory ended up with + + + align:start position:0% +other anyway my theory ended up with +this idea that uh it's sort of based on + + align:start position:0% +this idea that uh it's sort of based on + + + align:start position:0% +this idea that uh it's sort of based on +Freud I don't know if I kept a picture + + align:start position:0% +Freud I don't know if I kept a picture + + + align:start position:0% +Freud I don't know if I kept a picture +of + + align:start position:0% +of + + + align:start position:0% +of +his here + + align:start position:0% +his here + + + align:start position:0% +his here +Freud concluded that the mind was an + + align:start position:0% +Freud concluded that the mind was an + + + align:start position:0% +Freud concluded that the mind was an +interesting Arena sort of and he had the + + align:start position:0% +interesting Arena sort of and he had the + + + align:start position:0% +interesting Arena sort of and he had the +Mind divided into three + + align:start position:0% +Mind divided into three + + + align:start position:0% +Mind divided into three +parts there's at one end of the Mind the + + align:start position:0% +parts there's at one end of the Mind the + + + align:start position:0% +parts there's at one end of the Mind the +which were inherited from most other + + align:start position:0% +which were inherited from most other + + + align:start position:0% +which were inherited from most other +animals are is called the ID which is a + + align:start position:0% +animals are is called the ID which is a + + + align:start position:0% +animals are is called the ID which is a +bunch of + + align:start position:0% +bunch of + + + align:start position:0% +bunch of +instinctive mainly built-in behavioral + + align:start position:0% +instinctive mainly built-in behavioral + + + align:start position:0% +instinctive mainly built-in behavioral +mechanisms and + + align:start position:0% + + + + align:start position:0% + +um a second part of the mind is what he + + align:start position:0% +um a second part of the mind is what he + + + align:start position:0% +um a second part of the mind is what he +called the super + + align:start position:0% +called the super + + + align:start position:0% +called the super +ego which is a collection of critics so + + align:start position:0% +ego which is a collection of critics so + + + align:start position:0% +ego which is a collection of critics so +in Freud's first image the brain is in + + align:start position:0% +in Freud's first image the brain is in + + + align:start position:0% +in Freud's first image the brain is in +two parts one is a set of instinctive + + align:start position:0% +two parts one is a set of instinctive + + + align:start position:0% +two parts one is a set of instinctive +built-in behaviors and the other is a + + align:start position:0% +built-in behaviors and the other is a + + + align:start position:0% +built-in behaviors and the other is a +set of critics which + + align:start position:0% +set of critics which + + + align:start position:0% +set of critics which +uh actually are associated with a + + align:start position:0% +uh actually are associated with a + + + align:start position:0% +uh actually are associated with a +culture or well culture and a tradition + + align:start position:0% +culture or well culture and a tradition + + + align:start position:0% +culture or well culture and a tradition +and you learn from other people things + + align:start position:0% +and you learn from other people things + + + align:start position:0% +and you learn from other people things +that are good to do and things that are + + align:start position:0% +that are good to do and things that are + + + align:start position:0% +that are good to do and things that are +bad to do and + + align:start position:0% +bad to do and + + + align:start position:0% +bad to do and +uh that's called the super ego this is + + align:start position:0% +uh that's called the super ego this is + + + align:start position:0% +uh that's called the super ego this is +your set of values and standards and + + align:start position:0% +your set of values and standards and + + + align:start position:0% +your set of values and standards and +tests for suitable Behavior and the + + align:start position:0% +tests for suitable Behavior and the + + + align:start position:0% +tests for suitable Behavior and the +middle is this strange object called the + + align:start position:0% +middle is this strange object called the + + + align:start position:0% +middle is this strange object called the +ego which is not what uh people think it + + align:start position:0% +ego which is not what uh people think it + + + align:start position:0% +ego which is not what uh people think it +is at least Freud's word the ego is a + + align:start position:0% +is at least Freud's word the ego is a + + + align:start position:0% +is at least Freud's word the ego is a +kind of big neutral Battle Ground where + + align:start position:0% +kind of big neutral Battle Ground where + + + align:start position:0% +kind of big neutral Battle Ground where +the uh instinctive + + align:start position:0% +the uh instinctive + + + align:start position:0% +the uh instinctive +behaviors I keep wanting + + align:start position:0% +behaviors I keep wanting + + + align:start position:0% +behaviors I keep wanting +to oh you can see that Arrow if I take + + align:start position:0% +to oh you can see that Arrow if I take + + + align:start position:0% +to oh you can see that Arrow if I take +my finger off + + align:start position:0% +my finger off + + + align:start position:0% +my finger off +it + + align:start position:0% + + + + align:start position:0% + +um and then gradually as + + align:start position:0% +um and then gradually as + + + align:start position:0% +um and then gradually as +I kept trying to figure out where how + + align:start position:0% +I kept trying to figure out where how + + + align:start position:0% +I kept trying to figure out where how +problems are solved and what kind of + + align:start position:0% +problems are solved and what kind of + + + align:start position:0% +problems are solved and what kind of +processes might be involved I got this + + align:start position:0% +processes might be involved I got this + + + align:start position:0% +processes might be involved I got this +picture which has six + + align:start position:0% +picture which has six + + + align:start position:0% +picture which has six +layers and various people come around + + align:start position:0% +layers and various people come around + + + align:start position:0% +layers and various people come around +and + + align:start position:0% +and + + + align:start position:0% +and +say I don't think you need to + + align:start position:0% +say I don't think you need to + + + align:start position:0% +say I don't think you need to +distinguish between layers four and five + + align:start position:0% +distinguish between layers four and five + + + align:start position:0% +distinguish between layers four and five +or uh why don't you just lump all the + + align:start position:0% +or uh why don't you just lump all the + + + align:start position:0% +or uh why don't you just lump all the +three top layers into + + align:start position:0% +three top layers into + + + align:start position:0% +three top layers into +one + + align:start position:0% +one + + + align:start position:0% +one +and I sort of laugh + + align:start position:0% +and I sort of laugh + + + align:start position:0% +and I sort of laugh +quietly and + + align:start position:0% + + + + align:start position:0% + +say these people are trying to find + + align:start position:0% +say these people are trying to find + + + align:start position:0% +say these people are trying to find +physics like unified minimal theory of + + align:start position:0% +physics like unified minimal theory of + + + align:start position:0% +physics like unified minimal theory of +psychology and they're probably right in + + align:start position:0% +psychology and they're probably right in + + + align:start position:0% +psychology and they're probably right in +one sense but if they do that they'll + + align:start position:0% +one sense but if they do that they'll + + + align:start position:0% +one sense but if they do that they'll +get stuck because if you get a new idea + + align:start position:0% +get stuck because if you get a new idea + + + align:start position:0% +get stuck because if you get a new idea +there'll be no place to put + + align:start position:0% + + + + align:start position:0% + +it so if you have something that's very + + align:start position:0% +it so if you have something that's very + + + align:start position:0% +it so if you have something that's very +mysterious don't imitate the + + align:start position:0% +mysterious don't imitate the + + + align:start position:0% +mysterious don't imitate the +physicists because if you make a theory + + align:start position:0% +physicists because if you make a theory + + + align:start position:0% +physicists because if you make a theory +that's exactly right and just accounts + + align:start position:0% +that's exactly right and just accounts + + + align:start position:0% +that's exactly right and just accounts +for the dat data and there's nothing + + align:start position:0% +for the dat data and there's nothing + + + align:start position:0% +for the dat data and there's nothing +extra and nothing + + align:start position:0% +extra and nothing + + + align:start position:0% +extra and nothing +loose then when you notice a new + + align:start position:0% +loose then when you notice a new + + + align:start position:0% +loose then when you notice a new +phenomenon like dark + + align:start position:0% +phenomenon like dark + + + align:start position:0% +phenomenon like dark +matter uh then the physicists don't know + + align:start position:0% +matter uh then the physicists don't know + + + align:start position:0% +matter uh then the physicists don't know +what to do should they regard dark + + align:start position:0% +what to do should they regard dark + + + align:start position:0% +what to do should they regard dark +matter as some + + align:start position:0% +matter as some + + + align:start position:0% +matter as some +obscure feature of SpaceTime or does it + + align:start position:0% +obscure feature of SpaceTime or does it + + + align:start position:0% +obscure feature of SpaceTime or does it +have something to do with this universe + + align:start position:0% +have something to do with this universe + + + align:start position:0% +have something to do with this universe +being near another one that you can't + + align:start position:0% +being near another one that you can't + + + align:start position:0% +being near another one that you can't +otherwise communicate with and uh it's + + align:start position:0% +otherwise communicate with and uh it's + + + align:start position:0% +otherwise communicate with and uh it's +all very + + align:start position:0% +all very + + + align:start position:0% +all very +puzzling but there are lots of things + + align:start position:0% +puzzling but there are lots of things + + + align:start position:0% +puzzling but there are lots of things +that don't fit into Newton's Laws these + + align:start position:0% +that don't fit into Newton's Laws these + + + align:start position:0% +that don't fit into Newton's Laws these +days and + + align:start position:0% +days and + + + align:start position:0% +days and +uh I'm not suggesting a six layer Theory + + align:start position:0% +uh I'm not suggesting a six layer Theory + + + align:start position:0% +uh I'm not suggesting a six layer Theory +of physics but it might be worth a + + align:start position:0% + + + + align:start position:0% + +try okay so what am I I made up some + + align:start position:0% +try okay so what am I I made up some + + + align:start position:0% +try okay so what am I I made up some +nice slides + + align:start position:0% +nice slides + + + align:start position:0% +nice slides +but + + align:start position:0% + + + + align:start position:0% + +I think I'll + + align:start position:0% +I think I'll + + + align:start position:0% +I think I'll +stop so who has some questions + + align:start position:0% +stop so who has some questions + + + align:start position:0% +stop so who has some questions +and what would you like to see in a + + align:start position:0% +and what would you like to see in a + + + align:start position:0% +and what would you like to see in a +theory of psychology what's what do you + + align:start position:0% +theory of psychology what's what do you + + + align:start position:0% +theory of psychology what's what do you +want to be + + align:start position:0% +want to be + + + align:start position:0% +want to be +explained a lot of people uh are + + align:start position:0% +explained a lot of people uh are + + + align:start position:0% +explained a lot of people uh are +convinced that there are some really + + align:start position:0% +convinced that there are some really + + + align:start position:0% +convinced that there are some really +serious problems and Mysteries like what + + align:start position:0% +serious problems and Mysteries like what + + + align:start position:0% +serious problems and Mysteries like what +is consciousness + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% +is + + + align:start position:0% +is +and if you look at chapter + + align:start position:0% +and if you look at chapter + + + align:start position:0% +and if you look at chapter +4 um my feeling + + align:start position:0% +4 um my feeling + + + align:start position:0% +4 um my feeling +is consciousness is an eological + + align:start position:0% +is consciousness is an eological + + + align:start position:0% +is consciousness is an eological +accident that people got a + + align:start position:0% +accident that people got a + + + align:start position:0% +accident that people got a +word which is a suitcase for all of the + + align:start position:0% +word which is a suitcase for all of the + + + align:start position:0% +word which is a suitcase for all of the +things they don't understand about the + + align:start position:0% +things they don't understand about the + + + align:start position:0% +things they don't understand about the +mind and + + align:start position:0% + + + + align:start position:0% + +more but once you've got a word in the + + align:start position:0% +more but once you've got a word in the + + + align:start position:0% +more but once you've got a word in the +goes in the + + align:start position:0% + + + + align:start position:0% + +culture consider the word Consciousness + + align:start position:0% +culture consider the word Consciousness + + + align:start position:0% +culture consider the word Consciousness +for a minute from a legal point of + + align:start position:0% +for a minute from a legal point of + + + align:start position:0% +for a minute from a legal point of +view suppose that you happen to be + + align:start position:0% +view suppose that you happen to be + + + align:start position:0% +view suppose that you happen to be +walking along + + align:start position:0% + + + + align:start position:0% + +and you're carrying + + align:start position:0% +and you're carrying + + + align:start position:0% +and you're carrying +something where is that + + align:start position:0% + + + + align:start position:0% + +pointer and it happens to stick + + align:start position:0% +pointer and it happens to stick + + + align:start position:0% +pointer and it happens to stick +somebody's eye + + align:start position:0% + + + + align:start position:0% + +out then + + align:start position:0% + + + + align:start position:0% + +it's very important when they sue + + align:start position:0% +it's very important when they sue + + + align:start position:0% +it's very important when they sue +you to establish whether you meant to do + + align:start position:0% +you to establish whether you meant to do + + + align:start position:0% +you to establish whether you meant to do +it or rather it was an + + align:start position:0% +it or rather it was an + + + align:start position:0% +it or rather it was an +accident did you consciously plan to + + align:start position:0% + + + + align:start position:0% + +uh I can't think of the English word for + + align:start position:0% +uh I can't think of the English word for + + + align:start position:0% +uh I can't think of the English word for +putting somebody's eye out there's + + align:start position:0% +putting somebody's eye out there's + + + align:start position:0% +putting somebody's eye out there's +beheading and all + + align:start position:0% + + + + align:start position:0% + +sorts gouge is a good word + + align:start position:0% + + + + align:start position:0% + +uh yeah so anyway uh it's very important + + align:start position:0% +uh yeah so anyway uh it's very important + + + align:start position:0% +uh yeah so anyway uh it's very important +for social + + align:start position:0% +for social + + + align:start position:0% +for social +reasons to have a word for + + align:start position:0% +reasons to have a word for + + + align:start position:0% +reasons to have a word for +whether uh an action was deliberately + + align:start position:0% +whether uh an action was deliberately + + + align:start position:0% +whether uh an action was deliberately +violating the rules as opposed to + + align:start position:0% +violating the rules as opposed to + + + align:start position:0% +violating the rules as opposed to +accidentally violating the rules like + + align:start position:0% +accidentally violating the rules like + + + align:start position:0% +accidentally violating the rules like +uh if you tripped on the stairs and + + align:start position:0% +uh if you tripped on the stairs and + + + align:start position:0% +uh if you tripped on the stairs and +landed on somebody and broke their neck + + align:start position:0% +landed on somebody and broke their neck + + + align:start position:0% +landed on somebody and broke their neck +that's not a + + align:start position:0% +that's not a + + + align:start position:0% +that's not a +crime unless you were so clever as to + + align:start position:0% +crime unless you were so clever as to + + + align:start position:0% +crime unless you were so clever as to +make it appear that it was an + + align:start position:0% +make it appear that it was an + + + align:start position:0% +make it appear that it was an +accident probably anyway you see what I + + align:start position:0% +accident probably anyway you see what I + + + align:start position:0% +accident probably anyway you see what I +mean so we need a our whole system of + + align:start position:0% +mean so we need a our whole system of + + + align:start position:0% +mean so we need a our whole system of +fairness and ethics and social + + align:start position:0% +fairness and ethics and social + + + align:start position:0% +fairness and ethics and social +responsibility is based on the + + align:start position:0% +responsibility is based on the + + + align:start position:0% +responsibility is based on the +distinction between whether an action + + align:start position:0% +distinction between whether an action + + + align:start position:0% +distinction between whether an action +was deliberate or + + align:start position:0% +was deliberate or + + + align:start position:0% +was deliberate or +not and so um did he do that + + align:start position:0% +not and so um did he do that + + + align:start position:0% +not and so um did he do that +consciously is a word for that and + + align:start position:0% +consciously is a word for that and + + + align:start position:0% +consciously is a word for that and +somehow the idea of conscious became + + align:start position:0% +somehow the idea of conscious became + + + align:start position:0% +somehow the idea of conscious became +elevated well that's a very superficial + + align:start position:0% +elevated well that's a very superficial + + + align:start position:0% +elevated well that's a very superficial +you can probably think of 10 other + + align:start position:0% +you can probably think of 10 other + + + align:start position:0% +you can probably think of 10 other +reasons why a word like + + align:start position:0% +reasons why a word like + + + align:start position:0% +reasons why a word like +that yes Mar sometimes in your writing I + + align:start position:0% +that yes Mar sometimes in your writing I + + + align:start position:0% +that yes Mar sometimes in your writing I +uh you know seem I it seems to me that + + align:start position:0% +uh you know seem I it seems to me that + + + align:start position:0% +uh you know seem I it seems to me that +that there's both sides it some you + + align:start position:0% +that there's both sides it some you + + + align:start position:0% +that there's both sides it some you +argue both sides of it like that it + + align:start position:0% +argue both sides of it like that it + + + align:start position:0% +argue both sides of it like that it +seems like in that kind of I can well + + align:start position:0% +seems like in that kind of I can well + + + align:start position:0% +seems like in that kind of I can well +imag there that kind of representation + + align:start position:0% +imag there that kind of representation + + + align:start position:0% +imag there that kind of representation +you have a representation of self and + + align:start position:0% +you have a representation of self and + + + align:start position:0% +you have a representation of self and +representation of your mind but then you + + align:start position:0% +representation of your mind but then you + + + align:start position:0% +representation of your mind but then you +say there's no self or no consciousness + + align:start position:0% +say there's no self or no consciousness + + + align:start position:0% +say there's no self or no consciousness +why can't you think about Consciousness + + align:start position:0% +why can't you think about Consciousness + + + align:start position:0% +why can't you think about Consciousness +is just a process that is reasoning + + align:start position:0% +is just a process that is reasoning + + + align:start position:0% +is just a process that is reasoning +about your own mind is problem with that + + align:start position:0% +about your own mind is problem with that + + + align:start position:0% +about your own mind is problem with that +I mean I understand you don't want to + + align:start position:0% +I mean I understand you don't want to + + + align:start position:0% +I mean I understand you don't want to +talk about Soul because that's a + + align:start position:0% +talk about Soul because that's a + + + align:start position:0% +talk about Soul because that's a +religious notion but no but sometimes + + align:start position:0% +religious notion but no but sometimes + + + align:start position:0% +religious notion but no but sometimes +when you say conscious that is do you + + align:start position:0% +when you say conscious that is do you + + + align:start position:0% +when you say conscious that is do you +remember doing + + align:start position:0% +remember doing + + + align:start position:0% +remember doing +it which is yeah but don't I load up my + + align:start position:0% +it which is yeah but don't I load up my + + + align:start position:0% +it which is yeah but don't I load up my +process that uh asks me what I think + + align:start position:0% +process that uh asks me what I think + + + align:start position:0% +process that uh asks me what I think +about my own mind and then I retrieve + + align:start position:0% +about my own mind and then I retrieve + + + align:start position:0% +about my own mind and then I retrieve +that and I say yeah I do remember it + + align:start position:0% +that and I say yeah I do remember it + + + align:start position:0% +that and I say yeah I do remember it +well you're right + + align:start position:0% +well you're right + + + align:start position:0% +well you're right +actually I went to a lot of trouble to + + align:start position:0% +actually I went to a lot of trouble to + + + align:start position:0% +actually I went to a lot of trouble to +find uh 25 or 30 different uses for the + + align:start position:0% +find uh 25 or 30 different uses for the + + + align:start position:0% +find uh 25 or 30 different uses for the +word Consciousness and probably if I or + + align:start position:0% +word Consciousness and probably if I or + + + align:start position:0% +word Consciousness and probably if I or +if one of us worked harder we could take + + align:start position:0% +if one of us worked harder we could take + + + align:start position:0% +if one of us worked harder we could take +those and condense them into five or six + + align:start position:0% +those and condense them into five or six + + + align:start position:0% +those and condense them into five or six +much better ones that account for more + + align:start position:0% +much better ones that account for more + + + align:start position:0% +much better ones that account for more +stuff than the 30 I think got five ideas + + align:start position:0% +stuff than the 30 I think got five ideas + + + align:start position:0% +stuff than the 30 I think got five ideas +goals memory thoughts and feelings right + + align:start position:0% +goals memory thoughts and feelings right + + + align:start position:0% +goals memory thoughts and feelings right +that might be just right for something + + align:start position:0% +that might be just right for something + + + align:start position:0% +that might be just right for something +who + + align:start position:0% +who + + + align:start position:0% +who +knows yes + + align:start position:0% +knows yes + + + align:start position:0% +knows yes +well + + align:start position:0% +well + + + align:start position:0% +well +uh I think that's a great criticism of + + align:start position:0% +uh I think that's a great criticism of + + + align:start position:0% +uh I think that's a great criticism of +uh one reason why people don't like + + align:start position:0% +uh one reason why people don't like + + + align:start position:0% +uh one reason why people don't like +these theories quite so much because I + + align:start position:0% +these theories quite so much because I + + + align:start position:0% +these theories quite so much because I +propose too many + + align:start position:0% +propose too many + + + align:start position:0% +propose too many +things uh I really should reprint that + + align:start position:0% +things uh I really should reprint that + + + align:start position:0% +things uh I really should reprint that +uh that criticism from restac + + align:start position:0% +uh that criticism from restac + + + align:start position:0% +uh that criticism from restac +or handed out because it's this + + align:start position:0% +or handed out because it's this + + + align:start position:0% +or handed out because it's this +neurologist who says why is he telling + + align:start position:0% +neurologist who says why is he telling + + + align:start position:0% +neurologist who says why is he telling +us all these things about K lines and um + + align:start position:0% +us all these things about K lines and um + + + align:start position:0% +us all these things about K lines and um +representations and so + + align:start position:0% +representations and so + + + align:start position:0% +representations and so +forth the answer is he's from a + + align:start position:0% +forth the answer is he's from a + + + align:start position:0% +forth the answer is he's from a +community + + align:start position:0% +community + + + align:start position:0% +community +that that doesn't have enough variety + + align:start position:0% +that that doesn't have enough variety + + + align:start position:0% +that that doesn't have enough variety +yet and uh I'd be the first to admit + + align:start position:0% +yet and uh I'd be the first to admit + + + align:start position:0% +yet and uh I'd be the first to admit +that I try to go overboard and think of + + align:start position:0% +that I try to go overboard and think of + + + align:start position:0% +that I try to go overboard and think of +five more things than are in the + + align:start position:0% + + + + align:start position:0% + +literature but that emotion thing is + + align:start position:0% +literature but that emotion thing is + + + align:start position:0% +literature but that emotion thing is +nice I remember that that was a serious + + align:start position:0% +nice I remember that that was a serious + + + align:start position:0% +nice I remember that that was a serious +challenge + + align:start position:0% +challenge + + + align:start position:0% +challenge +because when I made that + + align:start position:0% +because when I made that + + + align:start position:0% +because when I made that +list I do have a laser pointer somewhere + + align:start position:0% +list I do have a laser pointer somewhere + + + align:start position:0% +list I do have a laser pointer somewhere +in my jacket + + align:start position:0% +in my jacket + + + align:start position:0% +in my jacket +probably + + align:start position:0% +probably + + + align:start position:0% +probably +um how many how many words + + align:start position:0% +um how many how many words + + + align:start position:0% +um how many how many words +for at least noticeably distinct ways of + + align:start position:0% +for at least noticeably distinct ways of + + + align:start position:0% +for at least noticeably distinct ways of +thinking or reasoning or figuring out or + + align:start position:0% +thinking or reasoning or figuring out or + + + align:start position:0% +thinking or reasoning or figuring out or +solving problems can you think of know + + align:start position:0% +solving problems can you think of know + + + align:start position:0% +solving problems can you think of know +maybe there are 20 or + + align:start position:0% +maybe there are 20 or + + + align:start position:0% +maybe there are 20 or +30 I just I just realized this afternoon + + align:start position:0% +30 I just I just realized this afternoon + + + align:start position:0% +30 I just I just realized this afternoon +that I never + + align:start position:0% +that I never + + + align:start position:0% +that I never +looked I don't remember where I got this + + align:start position:0% + + + + align:start position:0% + +list yeah can I ask about your + + align:start position:0% +list yeah can I ask about your + + + align:start position:0% +list yeah can I ask about your +conception of Free Will and I I I got + + align:start position:0% +conception of Free Will and I I I got + + + align:start position:0% +conception of Free Will and I I I got +the readings that you don't have a + + align:start position:0% +the readings that you don't have a + + + align:start position:0% +the readings that you don't have a +strong sense of Free Will and so what is + + align:start position:0% +strong sense of Free Will and so what is + + + align:start position:0% +strong sense of Free Will and so what is +that I think it's the same as the one + + align:start position:0% +that I think it's the same as the one + + + align:start position:0% +that I think it's the same as the one +for Consciousness namely it's a legal + + align:start position:0% +for Consciousness namely it's a legal + + + align:start position:0% +for Consciousness namely it's a legal +concept the idea of Free Will is + + align:start position:0% +concept the idea of Free Will is + + + align:start position:0% +concept the idea of Free Will is +completely obscene isn't it what could + + align:start position:0% +completely obscene isn't it what could + + + align:start position:0% +completely obscene isn't it what could +it possibly mean if you did something + + align:start position:0% +it possibly mean if you did something + + + align:start position:0% +it possibly mean if you did something +for no + + align:start position:0% + + + + align:start position:0% + +reason so it's a thoroughly empty idea + + align:start position:0% +reason so it's a thoroughly empty idea + + + align:start position:0% +reason so it's a thoroughly empty idea +isn't it + + align:start position:0% +isn't it + + + align:start position:0% +isn't it +or what do you mean by it do you mean + + align:start position:0% +or what do you mean by it do you mean + + + align:start position:0% +or what do you mean by it do you mean +there's nobody ordering you around so + + align:start position:0% +there's nobody ordering you around so + + + align:start position:0% +there's nobody ordering you around so +you you're free to do whatever you + + align:start position:0% + + + + align:start position:0% + +want but of course you're not you can + + align:start position:0% +want but of course you're not you can + + + align:start position:0% +want but of course you're not you can +only do what your computer computes you + + align:start position:0% +only do what your computer computes you + + + align:start position:0% +only do what your computer computes you +to + + align:start position:0% +to + + + align:start position:0% +to +do so in a sense like in the same way + + align:start position:0% +do so in a sense like in the same way + + + align:start position:0% +do so in a sense like in the same way +that you draw like the in the you show + + align:start position:0% +that you draw like the in the you show + + + align:start position:0% +that you draw like the in the you show +the fish diagram right fish is is a the + + align:start position:0% +the fish diagram right fish is is a the + + + align:start position:0% +the fish diagram right fish is is a the +fish's actions are products of the + + align:start position:0% +fish's actions are products of the + + + align:start position:0% +fish's actions are products of the +environment and of its current state and + + align:start position:0% +environment and of its current state and + + + align:start position:0% +environment and of its current state and +it's essentially a turing machine well + + align:start position:0% +it's essentially a turing machine well + + + align:start position:0% +it's essentially a turing machine well +it's some kind of machine yes sure and + + align:start position:0% +it's some kind of machine yes sure and + + + align:start position:0% +it's some kind of machine yes sure and +so would you argue that we are also + + align:start position:0% +so would you argue that we are also + + + align:start position:0% +so would you argue that we are also +maches that are just running out in the + + align:start position:0% +maches that are just running out in the + + + align:start position:0% +maches that are just running out in the +world + + align:start position:0% +world + + + align:start position:0% +world +sure uh I've never heard of any even + + align:start position:0% +sure uh I've never heard of any even + + + align:start position:0% +sure uh I've never heard of any even +interesting + + align:start position:0% +interesting + + + align:start position:0% +interesting +alternative in other words people who + + align:start position:0% +alternative in other words people who + + + align:start position:0% +alternative in other words people who +insist on free will appear to me to be + + align:start position:0% +insist on free will appear to me to be + + + align:start position:0% +insist on free will appear to me to be +like people who believe that there must + + align:start position:0% +like people who believe that there must + + + align:start position:0% +like people who believe that there must +be a God who created the world what's + + align:start position:0% +be a God who created the world what's + + + align:start position:0% +be a God who created the world what's +the next step who created the god they + + align:start position:0% +the next step who created the god they + + + align:start position:0% +the next step who created the god they +don't take that step so if your will is + + align:start position:0% +don't take that step so if your will is + + + align:start position:0% +don't take that step so if your will is +free okay then who's controlling + + align:start position:0% +free okay then who's controlling + + + align:start position:0% +free okay then who's controlling +it there's nothing there but but legally + + align:start position:0% +it there's nothing there but but legally + + + align:start position:0% +it there's nothing there but but legally +it's great because if + + align:start position:0% +it's great because if + + + align:start position:0% +it's great because if +somebody uh stole so many of their own + + align:start position:0% +somebody uh stole so many of their own + + + align:start position:0% +somebody uh stole so many of their own +free will but suppose you were a + + align:start position:0% +free will but suppose you were a + + + align:start position:0% +free will but suppose you were a +peculiar kind of epileptic and every now + + align:start position:0% +peculiar kind of epileptic and every now + + + align:start position:0% +peculiar kind of epileptic and every now +and then when you go + + align:start position:0% + + + + align:start position:0% + +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +by your hand goes out and steals things + + align:start position:0% +by your hand goes out and steals things + + + align:start position:0% +by your hand goes out and steals things +then they what do they do they they put + + align:start position:0% +then they what do they do they they put + + + align:start position:0% +then they what do they do they they put +you on + + align:start position:0% + + + + align:start position:0% + +parole no this is very strange but if + + align:start position:0% +parole no this is very strange but if + + + align:start position:0% +parole no this is very strange but if +you look at religions you see that + + align:start position:0% +you look at religions you see that + + + align:start position:0% +you look at religions you see that +people make money on + + align:start position:0% +people make money on + + + align:start position:0% +people make money on +them 133% of the world's + + align:start position:0% +them 133% of the world's + + + align:start position:0% +them 133% of the world's +product goes to people who make their + + align:start position:0% +product goes to people who make their + + + align:start position:0% +product goes to people who make their +living on Concepts like Free Will and + + align:start position:0% +living on Concepts like Free Will and + + + align:start position:0% +living on Concepts like Free Will and +Consciousness so it's a big money thing + + align:start position:0% +Consciousness so it's a big money thing + + + align:start position:0% +Consciousness so it's a big money thing +it's not it's not just an accident it's + + align:start position:0% +it's not it's not just an accident it's + + + align:start position:0% +it's not it's not just an accident it's +it's an + + align:start position:0% +it's an + + + align:start position:0% +it's an +industry so both of those are constructs + + align:start position:0% +industry so both of those are constructs + + + align:start position:0% +industry so both of those are constructs +of + + align:start position:0% + + + + align:start position:0% + +society could imagine a society without + + align:start position:0% +society could imagine a society without + + + align:start position:0% +society could imagine a society without +the concept of Consciousness those AR + + align:start position:0% +the concept of Consciousness those AR + + + align:start position:0% +the concept of Consciousness those AR +requirements for being I don't think you + + align:start position:0% +requirements for being I don't think you + + + align:start position:0% +requirements for being I don't think you +could you'd have to make up something to + + align:start position:0% +could you'd have to make up something to + + + align:start position:0% +could you'd have to make up something to +keep people in check and under control + + align:start position:0% +keep people in check and under control + + + align:start position:0% +keep people in check and under control +and uh to train them it's like the rat + + align:start position:0% +and uh to train them it's like the rat + + + align:start position:0% +and uh to train them it's like the rat +being the rat needs somebody to press + + align:start position:0% +being the rat needs somebody to press + + + align:start position:0% +being the rat needs somebody to press +the reward or punish + + align:start position:0% +the reward or punish + + + align:start position:0% +the reward or punish +button and we have it built into our a + + align:start position:0% +button and we have it built into our a + + + align:start position:0% +button and we have it built into our a +culture works because you build into + + align:start position:0% +culture works because you build into + + + align:start position:0% +culture works because you build into +people's head the machinery for + + align:start position:0% +people's head the machinery for + + + align:start position:0% +people's head the machinery for +suppressing doubt + + align:start position:0% +suppressing doubt + + + align:start position:0% +suppressing doubt +and it's very clever but but it you + + align:start position:0% +and it's very clever but but it you + + + align:start position:0% +and it's very clever but but it you +should think of it as an industry rather + + align:start position:0% +should think of it as an industry rather + + + align:start position:0% +should think of it as an industry rather +than a inexplicable + + align:start position:0% +than a inexplicable + + + align:start position:0% +than a inexplicable +phenomenon how much money goes into yes + + align:start position:0% +phenomenon how much money goes into yes + + + align:start position:0% +phenomenon how much money goes into yes +how many ways of thinking say it again + + align:start position:0% +how many ways of thinking say it again + + + align:start position:0% +how many ways of thinking say it again +how many ways of thinking can you think + + align:start position:0% +how many ways of thinking can you think + + + align:start position:0% +how many ways of thinking can you think +of right now that's my challenge in fact + + align:start position:0% + + + + align:start position:0% + +uh there's probably a big list in some + + align:start position:0% +uh there's probably a big list in some + + + align:start position:0% +uh there's probably a big list in some +chapter or other but but there's nothing + + align:start position:0% +chapter or other but but there's nothing + + + align:start position:0% +chapter or other but but there's nothing +like + + align:start position:0% +like + + + align:start position:0% +like +this what's the trick three if I go like + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +actually dragon has a thing so you can + + align:start position:0% +actually dragon has a thing so you can + + + align:start position:0% +actually dragon has a thing so you can +tell it make things + + align:start position:0% +tell it make things + + + align:start position:0% +tell it make things +bigger how many of you use the new + + align:start position:0% +bigger how many of you use the new + + + align:start position:0% +bigger how many of you use the new +Dragon + + align:start position:0% +Dragon + + + align:start position:0% +Dragon +program speech + + align:start position:0% +program speech + + + align:start position:0% +program speech +thing I can't believe how good it + + align:start position:0% +thing I can't believe how good it + + + align:start position:0% +thing I can't believe how good it +is oh I was talking to Henry Lieberman + + align:start position:0% +is oh I was talking to Henry Lieberman + + + align:start position:0% +is oh I was talking to Henry Lieberman +about it + + align:start position:0% + + + + align:start position:0% + +earlier + + align:start position:0% +earlier + + + align:start position:0% +earlier +yes so I'm the impression that you would + + align:start position:0% +yes so I'm the impression that you would + + + align:start position:0% +yes so I'm the impression that you would +say that the side of mind the appes both + + align:start position:0% +say that the side of mind the appes both + + + align:start position:0% +say that the side of mind the appes both +animal uh is it just that we have higher + + align:start position:0% +animal uh is it just that we have higher + + + align:start position:0% +animal uh is it just that we have higher +levels of organization than them + + align:start position:0% +levels of organization than them + + + align:start position:0% +levels of organization than them +and so like where would you draw that + + align:start position:0% +and so like where would you draw that + + + align:start position:0% +and so like where would you draw that +line animals not have ation of the the + + align:start position:0% +line animals not have ation of the the + + + align:start position:0% +line animals not have ation of the the +way you describe + + align:start position:0% +way you describe + + + align:start position:0% +way you describe +long that's a great question + + align:start position:0% +long that's a great question + + + align:start position:0% +long that's a great question +and + + align:start position:0% + + + + align:start position:0% + +uh it'd be interesting to think about + + align:start position:0% +uh it'd be interesting to think about + + + align:start position:0% +uh it'd be interesting to think about +ways to investigate + + align:start position:0% +ways to investigate + + + align:start position:0% +ways to investigate +it people are researchers are often + + align:start position:0% +it people are researchers are often + + + align:start position:0% +it people are researchers are often +in fact raising that question + + align:start position:0% +in fact raising that question + + + align:start position:0% +in fact raising that question +of do animals have a representation of + + align:start position:0% +of do animals have a representation of + + + align:start position:0% +of do animals have a representation of +thems and there's a famous experiment + + align:start position:0% +thems and there's a famous experiment + + + align:start position:0% +thems and there's a famous experiment +but I can't remember what its current + + align:start position:0% +but I can't remember what its current + + + align:start position:0% +but I can't remember what its current +status is where you put a red dot on a + + align:start position:0% +status is where you put a red dot on a + + + align:start position:0% +status is where you put a red dot on a +chimpan chimpanze head and when the + + align:start position:0% +chimpan chimpanze head and when the + + + align:start position:0% +chimpan chimpanze head and when the +chimp passes a + + align:start position:0% +chimp passes a + + + align:start position:0% +chimp passes a +mirror and sees that the chimp might go + + align:start position:0% +mirror and sees that the chimp might go + + + align:start position:0% +mirror and sees that the chimp might go +like + + align:start position:0% +like + + + align:start position:0% +like +that + + align:start position:0% +that + + + align:start position:0% +that +whereas uh I don't think a + + align:start position:0% +whereas uh I don't think a + + + align:start position:0% +whereas uh I don't think a +dog when it passes a mirror + + align:start position:0% + + + + align:start position:0% + +would uh rub its forehead to see if it + + align:start position:0% +would uh rub its forehead to see if it + + + align:start position:0% +would uh rub its forehead to see if it +has a red spot I had a cat who walked + + align:start position:0% +has a red spot I had a cat who walked + + + align:start position:0% +has a red spot I had a cat who walked +past mirrors because we have some wall + + align:start position:0% +past mirrors because we have some wall + + + align:start position:0% +past mirrors because we have some wall +full-size mirrors around the + + align:start position:0% +full-size mirrors around the + + + align:start position:0% +full-size mirrors around the +house and the cat walks by and there's + + align:start position:0% +house and the cat walks by and there's + + + align:start position:0% +house and the cat walks by and there's +this other cat go in the mirror and she + + align:start position:0% +this other cat go in the mirror and she + + + align:start position:0% +this other cat go in the mirror and she +pays no attention to it + + align:start position:0% +pays no attention to it + + + align:start position:0% +pays no attention to it +whatever so of course I don't know what + + align:start position:0% +whatever so of course I don't know what + + + align:start position:0% +whatever so of course I don't know what +happened the first three times she + + align:start position:0% +happened the first three times she + + + align:start position:0% +happened the first three times she +walked by that mirror because if you see + + align:start position:0% +walked by that mirror because if you see + + + align:start position:0% +walked by that mirror because if you see +another cat going by you'd think it + + align:start position:0% +another cat going by you'd think it + + + align:start position:0% +another cat going by you'd think it +would anyway it's it's a good question + + align:start position:0% +would anyway it's it's a good question + + + align:start position:0% +would anyway it's it's a good question +and people ask that and uh there's some + + align:start position:0% +and people ask that and uh there's some + + + align:start position:0% +and people ask that and uh there's some +evidence that elephants have a model + + align:start position:0% + + + + align:start position:0% + +ofs + + align:start position:0% + + + + align:start position:0% + +and maybe dolphin + + align:start position:0% +and maybe dolphin + + + align:start position:0% +and maybe dolphin +and I don't know + + align:start position:0% +and I don't know + + + align:start position:0% +and I don't know +where have any of you heard any stories + + align:start position:0% +where have any of you heard any stories + + + align:start position:0% +where have any of you heard any stories +of other animals that can recognize for + + align:start position:0% +of other animals that can recognize for + + + align:start position:0% +of other animals that can recognize for +example when they've been + + align:start position:0% +example when they've been + + + align:start position:0% +example when they've been +painted which elephants yes I think + + align:start position:0% + + + + align:start position:0% + +elephants child psychology where where + + align:start position:0% +elephants child psychology where where + + + align:start position:0% +elephants child psychology where where +if you're less than a couple months old + + align:start position:0% +if you're less than a couple months old + + + align:start position:0% +if you're less than a couple months old +you actually fail this test oh + + align:start position:0% +you actually fail this test oh + + + align:start position:0% +you actually fail this test oh +so it's actually something that that + + align:start position:0% +so it's actually something that that + + + align:start position:0% +so it's actually something that that +comes and is a sign of their child + + align:start position:0% +comes and is a sign of their child + + + align:start position:0% +comes and is a sign of their child +progressing so it might not be intrinsic + + align:start position:0% +progressing so it might not be intrinsic + + + align:start position:0% +progressing so it might not be intrinsic +to humanity it might be so I'm sure CH + + align:start position:0% +to humanity it might be so I'm sure CH + + + align:start position:0% +to humanity it might be so I'm sure CH +probably do + + align:start position:0% + + + + align:start position:0% + +either this is a off the topic but I + + align:start position:0% +either this is a off the topic but I + + + align:start position:0% +either this is a off the topic but I +once had a great email correspondence + + align:start position:0% +once had a great email correspondence + + + align:start position:0% +once had a great email correspondence +with some woman who was getting a PhD in + + align:start position:0% +with some woman who was getting a PhD in + + + align:start position:0% +with some woman who was getting a PhD in +France about + + align:start position:0% +France about + + + align:start position:0% +France about +when B how babies recognize their + + align:start position:0% +when B how babies recognize their + + + align:start position:0% +when B how babies recognize their +mothers and she concluded with she did + + align:start position:0% +mothers and she concluded with she did + + + align:start position:0% +mothers and she concluded with she did +experiments of having other people walk + + align:start position:0% +experiments of having other people walk + + + align:start position:0% +experiments of having other people walk +into the room with a mask of the mother + + align:start position:0% +into the room with a mask of the mother + + + align:start position:0% +into the room with a mask of the mother +or a different haird and so forth and + + align:start position:0% +or a different haird and so forth and + + + align:start position:0% +or a different haird and so forth and +for the first two months or three months + + align:start position:0% +for the first two months or three months + + + align:start position:0% +for the first two months or three months +I think um it turned out that the baby + + align:start position:0% +I think um it turned out that the baby + + + align:start position:0% +I think um it turned out that the baby +recognizes the mother by the + + align:start position:0% +recognizes the mother by the + + + align:start position:0% +recognizes the mother by the +hairo which had not been known and um + + align:start position:0% +hairo which had not been known and um + + + align:start position:0% +hairo which had not been known and um +then uh I think after 3 months it's + + align:start position:0% +then uh I think after 3 months it's + + + align:start position:0% +then uh I think after 3 months it's +recognizing the mother by a face and + + align:start position:0% +recognizing the mother by a face and + + + align:start position:0% +recognizing the mother by a face and +that point uh she's doing + + align:start position:0% +that point uh she's doing + + + align:start position:0% +that point uh she's doing +experiments where you get another woman + + align:start position:0% +experiments where you get another woman + + + align:start position:0% +experiments where you get another woman +wearing the face a copy of the mother's + + align:start position:0% +wearing the face a copy of the mother's + + + align:start position:0% +wearing the face a copy of the mother's +face and so now there's two mothers and + + align:start position:0% +face and so now there's two mothers and + + + align:start position:0% +face and so now there's two mothers and +the baby is absolutely + + align:start position:0% + + + + align:start position:0% + +delighted and + + align:start position:0% +delighted and + + + align:start position:0% +delighted and +then as I I I can't remember but then I + + align:start position:0% +then as I I I can't remember but then I + + + align:start position:0% +then as I I I can't remember but then I +think at four or five months when two + + align:start position:0% +think at four or five months when two + + + align:start position:0% +think at four or five months when two +copies of the mother comes in the baby + + align:start position:0% +copies of the mother comes in the baby + + + align:start position:0% +copies of the mother comes in the baby +gets really + + align:start position:0% +gets really + + + align:start position:0% +gets really +panicked so + + align:start position:0% +panicked so + + + align:start position:0% +panicked so +uh I lost track of her if if you have a + + align:start position:0% +uh I lost track of her if if you have a + + + align:start position:0% +uh I lost track of her if if you have a +baby let me + + align:start position:0% + + + + align:start position:0% + +know uh she got her PhD for this and um + + align:start position:0% +know uh she got her PhD for this and um + + + align:start position:0% +know uh she got her PhD for this and um +I haven't heard anything since yes + + align:start position:0% +I haven't heard anything since yes + + + align:start position:0% +I haven't heard anything since yes +here's a sort of half formulated thought + + align:start position:0% +here's a sort of half formulated thought + + + align:start position:0% +here's a sort of half formulated thought +that I just thought of um regarding ways + + align:start position:0% +that I just thought of um regarding ways + + + align:start position:0% +that I just thought of um regarding ways +of thinking and ways of feeling um so it + + align:start position:0% +of thinking and ways of feeling um so it + + + align:start position:0% +of thinking and ways of feeling um so it +just occurred to me that it seems like + + align:start position:0% +just occurred to me that it seems like + + + align:start position:0% +just occurred to me that it seems like +um if you go back to the list of + + align:start position:0% +um if you go back to the list of + + + align:start position:0% +um if you go back to the list of +feelings it seems like uh when we talk + + align:start position:0% +feelings it seems like uh when we talk + + + align:start position:0% +feelings it seems like uh when we talk +about feeling we're talking about a + + align:start position:0% +about feeling we're talking about a + + + align:start position:0% +about feeling we're talking about a +state that the brain is in so it might + + align:start position:0% +state that the brain is in so it might + + + align:start position:0% +state that the brain is in so it might +be a complicated State that's like some + + align:start position:0% +be a complicated State that's like some + + + align:start position:0% +be a complicated State that's like some +combination of a lot of different + + align:start position:0% +combination of a lot of different + + + align:start position:0% +combination of a lot of different +parameters but it's a state that you can + + align:start position:0% +parameters but it's a state that you can + + + align:start position:0% +parameters but it's a state that you can +stay in for like an arbitrary amount of + + align:start position:0% +stay in for like an arbitrary amount of + + + align:start position:0% +stay in for like an arbitrary amount of +time but I think thinking is um + + align:start position:0% +time but I think thinking is um + + + align:start position:0% +time but I think thinking is um +something that's more sequential as in + + align:start position:0% +something that's more sequential as in + + + align:start position:0% +something that's more sequential as in +like when you're thinking you're + + align:start position:0% +like when you're thinking you're + + + align:start position:0% +like when you're thinking you're +necessarily changing the state of your + + align:start position:0% +necessarily changing the state of your + + + align:start position:0% +necessarily changing the state of your +brain all the time because you're moving + + align:start position:0% +brain all the time because you're moving + + + align:start position:0% +brain all the time because you're moving +bits around so I don't know I just + + align:start position:0% +bits around so I don't know I just + + + align:start position:0% +bits around so I don't know I just +thought of no I think that's that's uh + + align:start position:0% +thought of no I think that's that's uh + + + align:start position:0% +thought of no I think that's that's uh +right that think when we talk about + + align:start position:0% +right that think when we talk about + + + align:start position:0% +right that think when we talk about +intelligent Behavior you're absolutely + + align:start position:0% +intelligent Behavior you're absolutely + + + align:start position:0% +intelligent Behavior you're absolutely +right what you've got is a process + + align:start position:0% +right what you've got is a process + + + align:start position:0% +right what you've got is a process +that's criticizing itself and seeing + + align:start position:0% +that's criticizing itself and seeing + + + align:start position:0% +that's criticizing itself and seeing +when you got stuck and finding things to + + align:start position:0% +when you got stuck and finding things to + + + align:start position:0% +when you got stuck and finding things to +do and I suppose + + align:start position:0% + + + + align:start position:0% + +uh in each emotion + + align:start position:0% +uh in each emotion + + + align:start position:0% +uh in each emotion +State you're certainly also + + align:start position:0% +State you're certainly also + + + align:start position:0% +State you're certainly also +thinking so that's going on but but + + align:start position:0% +thinking so that's going on but but + + + align:start position:0% +thinking so that's going on but but +maybe it's more restricted like + + align:start position:0% +maybe it's more restricted like + + + align:start position:0% +maybe it's more restricted like +uh if you're confronting somebody and + + align:start position:0% +uh if you're confronting somebody and + + + align:start position:0% +uh if you're confronting somebody and +there's a sort of conflict uh then + + align:start position:0% +there's a sort of conflict uh then + + + align:start position:0% +there's a sort of conflict uh then +almost all your thoughts are constrained + + align:start position:0% +almost all your thoughts are constrained + + + align:start position:0% +almost all your thoughts are constrained +to to that subject and it's it's not as + + align:start position:0% +to to that subject and it's it's not as + + + align:start position:0% +to to that subject and it's it's not as +resourceful but I'm just I'm just + + align:start position:0% +resourceful but I'm just I'm just + + + align:start position:0% +resourceful but I'm just I'm just +improvising or you have like for each + + align:start position:0% +improvising or you have like for each + + + align:start position:0% +improvising or you have like for each +emotional state when we say that we're + + align:start position:0% +emotional state when we say that we're + + + align:start position:0% +emotional state when we say that we're +in an emotional state the things that + + align:start position:0% +in an emotional state the things that + + + align:start position:0% +in an emotional state the things that +we're talking about are like the certain + + align:start position:0% +we're talking about are like the certain + + + align:start position:0% +we're talking about are like the certain +switches that get flipped in a certain + + align:start position:0% +switches that get flipped in a certain + + + align:start position:0% +switches that get flipped in a certain +state or something is above a certain + + align:start position:0% +state or something is above a certain + + + align:start position:0% +state or something is above a certain +threshold and you can have thoughts that + + align:start position:0% +threshold and you can have thoughts that + + + align:start position:0% +threshold and you can have thoughts that +are about anything in that state but + + align:start position:0% +are about anything in that state but + + + align:start position:0% +are about anything in that state but +perhaps the state itself influences the + + align:start position:0% +perhaps the state itself influences the + + + align:start position:0% +perhaps the state itself influences the +type of thoughts that you're likely to + + align:start position:0% +type of thoughts that you're likely to + + + align:start position:0% +type of thoughts that you're likely to +have okay I think what I'm talking about + + align:start position:0% +have okay I think what I'm talking about + + + align:start position:0% +have okay I think what I'm talking about +in this context + + align:start position:0% +in this context + + + align:start position:0% +in this context +is sort of extreme forms where uh the + + align:start position:0% +is sort of extreme forms where uh the + + + align:start position:0% +is sort of extreme forms where uh the +person changed into another machine and + + align:start position:0% +person changed into another machine and + + + align:start position:0% +person changed into another machine and +it's like an angry person won't listen + + align:start position:0% +it's like an angry person won't listen + + + align:start position:0% +it's like an angry person won't listen +to reason so uh or it's very hard to + + align:start position:0% +to reason so uh or it's very hard to + + + align:start position:0% +to reason so uh or it's very hard to +deflect them and so it's a kind of rigid + + align:start position:0% +deflect them and so it's a kind of rigid + + + align:start position:0% +deflect them and so it's a kind of rigid +thing so U but humans are + + align:start position:0% +thing so U but humans are + + + align:start position:0% +thing so U but humans are +generally are rarely in such extreme + + align:start position:0% +generally are rarely in such extreme + + + align:start position:0% +generally are rarely in such extreme +states where nothing gets + + align:start position:0% + + + + align:start position:0% + +through the whole point of that was that + + align:start position:0% +through the whole point of that was that + + + align:start position:0% +through the whole point of that was that +uh and I just realized that I maybe was + + align:start position:0% +uh and I just realized that I maybe was + + + align:start position:0% +uh and I just realized that I maybe was +just too lazy that we have this huge + + align:start position:0% +just too lazy that we have this huge + + + align:start position:0% +just too lazy that we have this huge +vocabulary of of nuances of emotional + + align:start position:0% +vocabulary of of nuances of emotional + + + align:start position:0% +vocabulary of of nuances of emotional +activity and people think these are also + + align:start position:0% +activity and people think these are also + + + align:start position:0% +activity and people think these are also +people think these are hard to explain + + align:start position:0% +people think these are hard to explain + + + align:start position:0% +people think these are hard to explain +and + + align:start position:0% +and + + + align:start position:0% +and +mysterious and non-physical and blah + + align:start position:0% +mysterious and non-physical and blah + + + align:start position:0% +mysterious and non-physical and blah +blah blah but + + align:start position:0% +blah blah but + + + align:start position:0% +blah blah but +uh why do we wait till next week and see + + align:start position:0% +uh why do we wait till next week and see + + + align:start position:0% +uh why do we wait till next week and see +if somebody comes up with or see if we + + align:start position:0% +if somebody comes up with or see if we + + + align:start position:0% +if somebody comes up with or see if we +can come up with + + align:start position:0% +can come up with + + + align:start position:0% +can come up with +a set of 30 or 40 words about uh + + align:start position:0% +a set of 30 or 40 words about uh + + + align:start position:0% +a set of 30 or 40 words about uh +intellectual States curiosity of of of I + + align:start position:0% +intellectual States curiosity of of of I + + + align:start position:0% +intellectual States curiosity of of of I +just don't know how many there are and I + + align:start position:0% +just don't know how many there are and I + + + align:start position:0% +just don't know how many there are and I +I haven't thought of any in the last few + + align:start position:0% +I haven't thought of any in the last few + + + align:start position:0% +I haven't thought of any in the last few +minutes yes has anybody thought of a + + align:start position:0% +minutes yes has anybody thought of a + + + align:start position:0% +minutes yes has anybody thought of a +couple + + align:start position:0% +couple + + + align:start position:0% +couple +of like the + + align:start position:0% +of like the + + + align:start position:0% +of like the +concept what's the word flow like CHS in + + align:start position:0% +concept what's the word flow like CHS in + + + align:start position:0% +concept what's the word flow like CHS in +the high like when you're really engaged + + align:start position:0% +the high like when you're really engaged + + + align:start position:0% +the high like when you're really engaged +in some activity that you're doing and + + align:start position:0% +in some activity that you're doing and + + + align:start position:0% +in some activity that you're doing and +like you're really in the in the zone + + align:start position:0% +like you're really in the in the zone + + + align:start position:0% +like you're really in the in the zone +uhhuh yes there's this there's a state + + align:start position:0% +uhhuh yes there's this there's a state + + + align:start position:0% +uhhuh yes there's this there's a state +of keeping other things out so you can + + align:start position:0% +of keeping other things out so you can + + + align:start position:0% +of keeping other things out so you can +focus not not being interruptable yes so + + align:start position:0% +focus not not being interruptable yes so + + + align:start position:0% +focus not not being interruptable yes so +in the book side of mind you talk about + + align:start position:0% +in the book side of mind you talk about + + + align:start position:0% +in the book side of mind you talk about +agents and how like they divide between + + align:start position:0% +agents and how like they divide between + + + align:start position:0% +agents and how like they divide between +themselves but I don't I don't see + + align:start position:0% +themselves but I don't I don't see + + + align:start position:0% +themselves but I don't I don't see +anywhere about like how Evolution like + + align:start position:0% +anywhere about like how Evolution like + + + align:start position:0% +anywhere about like how Evolution like +modified a lot agents like I believe + + align:start position:0% +modified a lot agents like I believe + + + align:start position:0% +modified a lot agents like I believe +that Evolution modify the way we think + + align:start position:0% +that Evolution modify the way we think + + + align:start position:0% +that Evolution modify the way we think +right now I don't know if you saw + + align:start position:0% +right now I don't know if you saw + + + align:start position:0% +right now I don't know if you saw +there's a paper like uh wrote like two + + align:start position:0% +there's a paper like uh wrote like two + + + align:start position:0% +there's a paper like uh wrote like two +years ago it's called the region of + + align:start position:0% +years ago it's called the region of + + + align:start position:0% +years ago it's called the region of +behavior and this guy tried to explain + + align:start position:0% +behavior and this guy tried to explain + + + align:start position:0% +behavior and this guy tried to explain +like how we make some decisions + + align:start position:0% +like how we make some decisions + + + align:start position:0% +like how we make some decisions +evolutionary like in a point of view of + + align:start position:0% +evolutionary like in a point of view of + + + align:start position:0% +evolutionary like in a point of view of +like our speech we are uh maximizing the + + align:start position:0% +like our speech we are uh maximizing the + + + align:start position:0% +like our speech we are uh maximizing the +probability of we reproducing our our a + + align:start position:0% +probability of we reproducing our our a + + + align:start position:0% +probability of we reproducing our our a +s + + align:start position:0% +s + + + align:start position:0% +s +us but individually we are not kind + + align:start position:0% +us but individually we are not kind + + + align:start position:0% +us but individually we are not kind +of increasing the efficien and like I + + align:start position:0% +of increasing the efficien and like I + + + align:start position:0% +of increasing the efficien and like I +think somehow like these agents would be + + align:start position:0% +think somehow like these agents would be + + + align:start position:0% +think somehow like these agents would be +like the decisions of Agents or + + align:start position:0% +like the decisions of Agents or + + + align:start position:0% +like the decisions of Agents or +resources would be like very determined + + align:start position:0% +resources would be like very determined + + + align:start position:0% +resources would be like very determined +by Evolution since we have like a very + + align:start position:0% +by Evolution since we have like a very + + + align:start position:0% +by Evolution since we have like a very +long time to like of evolution of the + + align:start position:0% +long time to like of evolution of the + + + align:start position:0% +long time to like of evolution of the +human being and somehow we have like + + align:start position:0% +human being and somehow we have like + + + align:start position:0% +human being and somehow we have like +hard wire to make some decisions so uh + + align:start position:0% +hard wire to make some decisions so uh + + + align:start position:0% +hard wire to make some decisions so uh +for example like he gives the example of + + align:start position:0% +for example like he gives the example of + + + align:start position:0% +for example like he gives the example of +like a guy well for for lizards that's + + align:start position:0% +like a guy well for for lizards that's + + + align:start position:0% +like a guy well for for lizards that's +certainly true but how why do you humans + + align:start position:0% +certainly true but how why do you humans + + + align:start position:0% +certainly true but how why do you humans +keep changing their environment and so + + align:start position:0% +keep changing their environment and so + + + align:start position:0% +keep changing their environment and so +like for example yeah so he gives this + + align:start position:0% +like for example yeah so he gives this + + + align:start position:0% +like for example yeah so he gives this +example of like tossing uh a coin the + + align:start position:0% +example of like tossing uh a coin the + + + align:start position:0% +example of like tossing uh a coin the +guy says that like this coin is unfair + + align:start position:0% +guy says that like this coin is unfair + + + align:start position:0% +guy says that like this coin is unfair +and like There's 7 he doesn't say the + + align:start position:0% +and like There's 7 he doesn't say the + + + align:start position:0% +and like There's 7 he doesn't say the +probabilities but there is 75% of + + align:start position:0% +probabilities but there is 75% of + + + align:start position:0% +probabilities but there is 75% of +getting heads and 25 5% of getting uh + + align:start position:0% +getting heads and 25 5% of getting uh + + + align:start position:0% +getting heads and 25 5% of getting uh +tails and like we like the subjects they + + align:start position:0% +tails and like we like the subjects they + + + align:start position:0% +tails and like we like the subjects they +choose randomly 25% of the + + align:start position:0% +choose randomly 25% of the + + + align:start position:0% +choose randomly 25% of the +time uh the tails even though they like + + align:start position:0% +time uh the tails even though they like + + + align:start position:0% +time uh the tails even though they like +they can take a uh account of the number + + align:start position:0% +they can take a uh account of the number + + + align:start position:0% +they can take a uh account of the number +of the times that you put heads and even + + align:start position:0% +of the times that you put heads and even + + + align:start position:0% +of the times that you put heads and even +though uh if you choose always heads you + + align:start position:0% +though uh if you choose always heads you + + + align:start position:0% +though uh if you choose always heads you +would get more money or whatever you + + align:start position:0% +would get more money or whatever you + + + align:start position:0% +would get more money or whatever you +would uh make it the right decision like + + align:start position:0% +would uh make it the right decision like + + + align:start position:0% +would uh make it the right decision like +that's called probability + + align:start position:0% +that's called probability + + + align:start position:0% +that's called probability +matching and it's not a good + + align:start position:0% +matching and it's not a good + + + align:start position:0% +matching and it's not a good +strategy yeah but humans do that like no + + align:start position:0% +strategy yeah but humans do that like no + + + align:start position:0% +strategy yeah but humans do that like no +well they they do it if the psychologist + + align:start position:0% +well they they do it if the psychologist + + + align:start position:0% +well they they do it if the psychologist +rigs the experiment very + + align:start position:0% +rigs the experiment very + + + align:start position:0% +rigs the experiment very +carefully it turns out that the best + + align:start position:0% +carefully it turns out that the best + + + align:start position:0% +carefully it turns out that the best +thing to what do you think is the + + align:start position:0% +thing to what do you think is the + + + align:start position:0% +thing to what do you think is the +optimal + + align:start position:0% +optimal + + + align:start position:0% +optimal +strategy no the optimal strategy turns + + align:start position:0% +strategy no the optimal strategy turns + + + align:start position:0% +strategy no the optimal strategy turns +out it's the square roots of the + + align:start position:0% +out it's the square roots of the + + + align:start position:0% +out it's the square roots of the +probabilities normalized to add up to + + align:start position:0% +probabilities normalized to add up to + + + align:start position:0% +probabilities normalized to add up to +one + + align:start position:0% +one + + + align:start position:0% +one +and I I'll I'll give you a proof next + + align:start position:0% +and I I'll I'll give you a proof next + + + align:start position:0% +and I I'll I'll give you a proof next +time this theorem is due to Ray Solomon + + align:start position:0% +time this theorem is due to Ray Solomon + + + align:start position:0% +time this theorem is due to Ray Solomon +off who invented inductive probability + + align:start position:0% +off who invented inductive probability + + + align:start position:0% +off who invented inductive probability +Theory but but like Evolution so + + align:start position:0% +Theory but but like Evolution so + + + align:start position:0% +Theory but but like Evolution so +Evolution if it if evolution did + + align:start position:0% +Evolution if it if evolution did + + + align:start position:0% +Evolution if it if evolution did +probability + + align:start position:0% +probability + + + align:start position:0% +probability +matching then it would be wrong and I + + align:start position:0% +matching then it would be wrong and I + + + align:start position:0% +matching then it would be wrong and I +bet you'll find out that those + + align:start position:0% +bet you'll find out that those + + + align:start position:0% +bet you'll find out that those +experiments are + + align:start position:0% + + + + align:start position:0% + +wrong you have to see like how did rig + + align:start position:0% +wrong you have to see like how did rig + + + align:start position:0% +wrong you have to see like how did rig +the experiment so that people if it's + + align:start position:0% +the experiment so that people if it's + + + align:start position:0% +the experiment so that people if it's +probability 25% they guess that + + align:start position:0% +probability 25% they guess that + + + align:start position:0% +probability 25% they guess that +25% they meant thiss with goldfish I + + align:start position:0% +25% they meant thiss with goldfish I + + + align:start position:0% +25% they meant thiss with goldfish I +don't + + align:start position:0% +don't + + + align:start position:0% +don't +know there was a theory about why you + + align:start position:0% +know there was a theory about why you + + + align:start position:0% +know there was a theory about why you +would expected but it's it's a good + + align:start position:0% +would expected but it's it's a good + + + align:start position:0% +would expected but it's it's a good +question I don't think people use + + align:start position:0% +question I don't think people use + + + align:start position:0% +question I don't think people use +probabilities though so even if an + + align:start position:0% +probabilities though so even if an + + + align:start position:0% +probabilities though so even if an +experiment shows some I would look for a + + align:start position:0% +experiment shows some I would look for a + + + align:start position:0% +experiment shows some I would look for a +flaw in the design of the experiment + + align:start position:0% + + + + align:start position:0% + +yes so you talked about a lot about + + align:start position:0% +yes so you talked about a lot about + + + align:start position:0% +yes so you talked about a lot about +emotion leure and say is that + + align:start position:0% +emotion leure and say is that + + + align:start position:0% +emotion leure and say is that +like for someone who has a specific + + align:start position:0% +like for someone who has a specific + + + align:start position:0% +like for someone who has a specific +personality they might have a pre + + align:start position:0% +personality they might have a pre + + + align:start position:0% +personality they might have a pre +predisposition to feel a certain emotion + + align:start position:0% +predisposition to feel a certain emotion + + + align:start position:0% +predisposition to feel a certain emotion +like anger depression or whatnot um my + + align:start position:0% +like anger depression or whatnot um my + + + align:start position:0% +like anger depression or whatnot um my +my question is that you had Insight or + + align:start position:0% +my question is that you had Insight or + + + align:start position:0% +my question is that you had Insight or +theories on to what extent U our + + align:start position:0% +theories on to what extent U our + + + align:start position:0% +theories on to what extent U our +personality is uh affected by like sense + + align:start position:0% +personality is uh affected by like sense + + + align:start position:0% +personality is uh affected by like sense +or influences that happen to us over the + + align:start position:0% +or influences that happen to us over the + + + align:start position:0% +or influences that happen to us over the +course of a lifetime and to what extent + + align:start position:0% +course of a lifetime and to what extent + + + align:start position:0% +course of a lifetime and to what extent +is it impacted by sort of you know + + align:start position:0% +is it impacted by sort of you know + + + align:start position:0% +is it impacted by sort of you know +chemical or biological + + align:start position:0% +chemical or biological + + + align:start position:0% +chemical or biological +makeup well you're asking uh what things + + align:start position:0% +makeup well you're asking uh what things + + + align:start position:0% +makeup well you're asking uh what things +do what do people + + align:start position:0% +do what do people + + + align:start position:0% +do what do people +learn we don't care if it's chemical + + align:start position:0% +learn we don't care if it's chemical + + + align:start position:0% +learn we don't care if it's chemical +or see if it's chemical it's still + + align:start position:0% + + + + align:start position:0% + +physical + + align:start position:0% +physical + + + align:start position:0% +physical +I read that sort of treatment for + + align:start position:0% +I read that sort of treatment for + + + align:start position:0% +I read that sort of treatment for +depression and the argument is that a + + align:start position:0% +depression and the argument is that a + + + align:start position:0% +depression and the argument is that a +lot + + align:start position:0% +lot + + + align:start position:0% +lot +of a lot reasons for depressions because + + align:start position:0% +of a lot reasons for depressions because + + + align:start position:0% +of a lot reasons for depressions because +of some sort of chemal + + align:start position:0% +of some sort of chemal + + + align:start position:0% +of some sort of chemal +biological way our brain is constructed + + align:start position:0% +biological way our brain is constructed + + + align:start position:0% +biological way our brain is constructed +well there's lots of complicated things + + align:start position:0% +well there's lots of complicated things + + + align:start position:0% +well there's lots of complicated things +about the brain one feature of the brain + + align:start position:0% +about the brain one feature of the brain + + + align:start position:0% +about the brain one feature of the brain +that I don't know if + + align:start position:0% +that I don't know if + + + align:start position:0% +that I don't know if +everybody + + align:start position:0% +everybody + + + align:start position:0% +everybody +you know that there are inhibitory and + + align:start position:0% +you know that there are inhibitory and + + + align:start position:0% +you know that there are inhibitory and +excitatory synapses when one neuron + + align:start position:0% +excitatory synapses when one neuron + + + align:start position:0% +excitatory synapses when one neuron +connects to + + align:start position:0% +connects to + + + align:start position:0% +connects to +another + + align:start position:0% +another + + + align:start position:0% +another +um the impulse that goes along the axon + + align:start position:0% +um the impulse that goes along the axon + + + align:start position:0% +um the impulse that goes along the axon +to the Target neuron May reduce the + + align:start position:0% +to the Target neuron May reduce the + + + align:start position:0% +to the Target neuron May reduce the +probability or the strength of its + + align:start position:0% +probability or the strength of its + + + align:start position:0% +probability or the strength of its +firing or increase it so that's called + + align:start position:0% +firing or increase it so that's called + + + align:start position:0% +firing or increase it so that's called +inhibiting + + align:start position:0% + + + + align:start position:0% + +or there's + + align:start position:0% +or there's + + + align:start position:0% +or there's +no or exciting it's not quite the right + + align:start position:0% +no or exciting it's not quite the right + + + align:start position:0% +no or exciting it's not quite the right +word is it um now generally in the + + align:start position:0% +word is it um now generally in the + + + align:start position:0% +word is it um now generally in the +nervous system as a rule but not always + + align:start position:0% +nervous system as a rule but not always + + + align:start position:0% +nervous system as a rule but not always +if you follow a chain of activity it + + align:start position:0% +if you follow a chain of activity it + + + align:start position:0% +if you follow a chain of activity it +goes + + align:start position:0% +goes + + + align:start position:0% +goes +inhibiting exciting inhibiting + + align:start position:0% +inhibiting exciting inhibiting + + + align:start position:0% +inhibiting exciting inhibiting +exciting if you had too many excitatory + + align:start position:0% +exciting if you had too many excitatory + + + align:start position:0% +exciting if you had too many excitatory +things and there was a loop then it + + align:start position:0% +things and there was a loop then it + + + align:start position:0% +things and there was a loop then it +would explode and they it would wear + + align:start position:0% +would explode and they it would wear + + + align:start position:0% +would explode and they it would wear +itself out in jig time so there is this + + align:start position:0% +itself out in jig time so there is this + + + align:start position:0% +itself out in jig time so there is this +General feature of the anatomy that you + + align:start position:0% +General feature of the anatomy that you + + + align:start position:0% +General feature of the anatomy that you +alternate so when somebody talks about a + + align:start position:0% +alternate so when somebody talks about a + + + align:start position:0% +alternate so when somebody talks about a +drug having an inhibitory effect that's + + align:start position:0% +drug having an inhibitory effect that's + + + align:start position:0% +drug having an inhibitory effect that's +sort of weird because it's inhibiting + + align:start position:0% +sort of weird because it's inhibiting + + + align:start position:0% +sort of weird because it's inhibiting +half the neurons and uh therefore ex + + align:start position:0% +half the neurons and uh therefore ex + + + align:start position:0% +half the neurons and uh therefore ex +raise lowering the thresholds of the + + align:start position:0% +raise lowering the thresholds of the + + + align:start position:0% +raise lowering the thresholds of the +ones they're connected to and so on so I + + align:start position:0% +ones they're connected to and so on so I + + + align:start position:0% +ones they're connected to and so on so I +think the best thing is until you have a + + align:start position:0% +think the best thing is until you have a + + + align:start position:0% +think the best thing is until you have a +diagram of the functional relations + + align:start position:0% +diagram of the functional relations + + + align:start position:0% +diagram of the functional relations +between different brain centers + + align:start position:0% +between different brain centers + + + align:start position:0% +between different brain centers +uh it might be best not to try to make + + align:start position:0% +uh it might be best not to try to make + + + align:start position:0% +uh it might be best not to try to make +generalizations about how the chemistry + + align:start position:0% +generalizations about how the chemistry + + + align:start position:0% +generalizations about how the chemistry +works + + align:start position:0% +works + + + align:start position:0% +works +it's it's easy but you know people think + + align:start position:0% +it's it's easy but you know people think + + + align:start position:0% +it's it's easy but you know people think +of adrenaline as a + + align:start position:0% +of adrenaline as a + + + align:start position:0% +of adrenaline as a +stimulant but in the nervous epinephrine + + align:start position:0% +stimulant but in the nervous epinephrine + + + align:start position:0% +stimulant but in the nervous epinephrine +but in the nervous system it's uh + + align:start position:0% +but in the nervous system it's uh + + + align:start position:0% +but in the nervous system it's uh +locally it may be inhibiting things that + + align:start position:0% +locally it may be inhibiting things that + + + align:start position:0% +locally it may be inhibiting things that +are inhibiting something else and so it + + align:start position:0% +are inhibiting something else and so it + + + align:start position:0% +are inhibiting something else and so it +appears to be exciting yes so I have a + + align:start position:0% +appears to be exciting yes so I have a + + + align:start position:0% +appears to be exciting yes so I have a +problem understanding the difference + + align:start position:0% +problem understanding the difference + + + align:start position:0% +problem understanding the difference +between thoughts and emotions I know + + align:start position:0% +between thoughts and emotions I know + + + align:start position:0% +between thoughts and emotions I know +it's might be a simple but uh since the + + align:start position:0% +it's might be a simple but uh since the + + + align:start position:0% +it's might be a simple but uh since the +only thing that I can separate in my + + align:start position:0% +only thing that I can separate in my + + + align:start position:0% +only thing that I can separate in my +mind is that thoughts the so let's call + + align:start position:0% +mind is that thoughts the so let's call + + + align:start position:0% +mind is that thoughts the so let's call +it a time constant I can change it kind + + align:start position:0% +it a time constant I can change it kind + + + align:start position:0% +it a time constant I can change it kind +of rapidly emotions time constent is + + align:start position:0% +of rapidly emotions time constent is + + + align:start position:0% +of rapidly emotions time constent is +small and I can control it again much + + align:start position:0% +small and I can control it again much + + + align:start position:0% +small and I can control it again much +less uh but since there is no um at + + align:start position:0% +less uh but since there is no um at + + + align:start position:0% +less uh but since there is no um at +least in this class there is no preu uh + + align:start position:0% +least in this class there is no preu uh + + + align:start position:0% +least in this class there is no preu uh +how can I how can I make a decision on + + align:start position:0% +how can I how can I make a decision on + + + align:start position:0% +how can I how can I make a decision on +where where the dividing line between + + align:start position:0% +where where the dividing line between + + + align:start position:0% +where where the dividing line between +these two entities is oh I think uh it's + + align:start position:0% +these two entities is oh I think uh it's + + + align:start position:0% +these two entities is oh I think uh it's +a waste of + + align:start position:0% +a waste of + + + align:start position:0% +a waste of +time as far as I can see emotional + + align:start position:0% +time as far as I can see emotional + + + align:start position:0% +time as far as I can see emotional +mechanisms are generally lower level + + align:start position:0% +mechanisms are generally lower level + + + align:start position:0% +mechanisms are generally lower level +simpler ones than the ones that involve + + align:start position:0% +simpler ones than the ones that involve + + + align:start position:0% +simpler ones than the ones that involve +several layers of the more layers of the + + align:start position:0% +several layers of the more layers of the + + + align:start position:0% +several layers of the more layers of the +brain so it's just a relative thing it's + + align:start position:0% +brain so it's just a relative thing it's + + + align:start position:0% +brain so it's just a relative thing it's +it's not that some states are emotional + + align:start position:0% +it's not that some states are emotional + + + align:start position:0% +it's not that some states are emotional +you're always having some high level + + align:start position:0% +you're always having some high level + + + align:start position:0% +you're always having some high level +thoughts and low-level thoughts and the + + align:start position:0% +thoughts and low-level thoughts and the + + + align:start position:0% +thoughts and low-level thoughts and the +distinction I just don't know don't know + + align:start position:0% +distinction I just don't know don't know + + + align:start position:0% +distinction I just don't know don't know +why the + + align:start position:0% +why the + + + align:start position:0% +why the +distinction has occupied so much + + align:start position:0% +distinction has occupied so much + + + align:start position:0% +distinction has occupied so much +attention I think it's because and that + + align:start position:0% +attention I think it's because and that + + + align:start position:0% +attention I think it's because and that +goes back to the having more words + + align:start position:0% +goes back to the having more words + + + align:start position:0% +goes back to the having more words +for or asking how many words do we have + + align:start position:0% +for or asking how many words do we have + + + align:start position:0% +for or asking how many words do we have +for ways to + + align:start position:0% +for ways to + + + align:start position:0% +for ways to +think it seems to me that in popular + + align:start position:0% +think it seems to me that in popular + + + align:start position:0% +think it seems to me that in popular +culture there are very few words for + + align:start position:0% +culture there are very few words for + + + align:start position:0% +culture there are very few words for +ways to think and lots of words for + + align:start position:0% +ways to think and lots of words for + + + align:start position:0% +ways to think and lots of words for +emotions and so they're very + + align:start position:0% +emotions and so they're very + + + align:start position:0% +emotions and so they're very +prominent maybe you have to be smarter + + align:start position:0% +prominent maybe you have to be smarter + + + align:start position:0% +prominent maybe you have to be smarter +to distinguish between ways to think and + + align:start position:0% +to distinguish between ways to think and + + + align:start position:0% +to distinguish between ways to think and +people generally are + + align:start position:0% +people generally are + + + align:start position:0% +people generally are +dumb not because they're inherently dumb + + align:start position:0% +dumb not because they're inherently dumb + + + align:start position:0% +dumb not because they're inherently dumb +but they come from cultures which bully + + align:start position:0% +but they come from cultures which bully + + + align:start position:0% +but they come from cultures which bully +you if + + align:start position:0% +you if + + + align:start position:0% +you if +you're you know what happens if you're + + align:start position:0% +you're you know what happens if you're + + + align:start position:0% +you're you know what happens if you're +in third grade and you're smart you get + + align:start position:0% +in third grade and you're smart you get + + + align:start position:0% +in third grade and you're smart you get +it beaten out of you and you learn not + + align:start position:0% +it beaten out of you and you learn not + + + align:start position:0% +it beaten out of you and you learn not +to show + + align:start position:0% +to show + + + align:start position:0% +to show +it + + align:start position:0% + + + + align:start position:0% + +like that question why science happen + + align:start position:0% +like that question why science happen + + + align:start position:0% +like that question why science happen +earlier why don't have more ways to + + align:start position:0% +earlier why don't have more ways to + + + align:start position:0% +earlier why don't have more ways to +describe different ways to + + align:start position:0% +describe different ways to + + + align:start position:0% +describe different ways to +think and that of we just not reflected + + align:start position:0% +think and that of we just not reflected + + + align:start position:0% +think and that of we just not reflected +as much on different thinking States or + + align:start position:0% +as much on different thinking States or + + + align:start position:0% +as much on different thinking States or +different approaches I wonder if the + + align:start position:0% +different approaches I wonder if the + + + align:start position:0% +different approaches I wonder if the +Greeks had more but we I think I think + + align:start position:0% +Greeks had more but we I think I think + + + align:start position:0% +Greeks had more but we I think I think +they did I think they had also More + + align:start position:0% +they did I think they had also More + + + align:start position:0% +they did I think they had also More +Concept + + align:start position:0% +Concept + + + align:start position:0% +Concept +of + + align:start position:0% +of + + + align:start position:0% +of +in different different states different + + align:start position:0% + + + + align:start position:0% + +poci who has a theory of that what's + + align:start position:0% +poci who has a theory of that what's + + + align:start position:0% +poci who has a theory of that what's +your theory of the Middle + + align:start position:0% + + + + align:start position:0% + +Ages how could things get dark for so so + + align:start position:0% +Ages how could things get dark for so so + + + align:start position:0% +Ages how could things get dark for so so +dark for so long well I do have + + align:start position:0% + + + + align:start position:0% + +um and are we about to have + + align:start position:0% +um and are we about to have + + + align:start position:0% +um and are we about to have +one I think it has as much to do with + + align:start position:0% +one I think it has as much to do with + + + align:start position:0% +one I think it has as much to do with +the channels in which one can + + align:start position:0% +the channels in which one can + + + align:start position:0% +the channels in which one can +communicate ideas to other + + align:start position:0% +communicate ideas to other + + + align:start position:0% +communicate ideas to other +people whether they exist or not whether + + align:start position:0% +people whether they exist or not whether + + + align:start position:0% +people whether they exist or not whether +the at are open or close um um the + + align:start position:0% +the at are open or close um um the + + + align:start position:0% +the at are open or close um um the +Middle Ages were characterized by + + align:start position:0% +Middle Ages were characterized by + + + align:start position:0% +Middle Ages were characterized by +scientific discoveries being kept as + + align:start position:0% +scientific discoveries being kept as + + + align:start position:0% +scientific discoveries being kept as +family + + align:start position:0% +family + + + align:start position:0% +family +secrets + + align:start position:0% +secrets + + + align:start position:0% +secrets +ah cardan knew how to take cube roots + + align:start position:0% +ah cardan knew how to take cube roots + + + align:start position:0% +ah cardan knew how to take cube roots +and he wouldn't tell anyone well the + + align:start position:0% +and he wouldn't tell anyone well the + + + align:start position:0% +and he wouldn't tell anyone well the +classic stupid example is baby Tom which + + align:start position:0% +classic stupid example is baby Tom which + + + align:start position:0% +classic stupid example is baby Tom which +for 300 years made a single Italian + + align:start position:0% +for 300 years made a single Italian + + + align:start position:0% +for 300 years made a single Italian +family very rich you know using tongues + + align:start position:0% +family very rich you know using tongues + + + align:start position:0% +family very rich you know using tongues +to extract a baby and child birth + + align:start position:0% +to extract a baby and child birth + + + align:start position:0% +to extract a baby and child birth +increase success rate in difficult + + align:start position:0% +increase success rate in difficult + + + align:start position:0% +increase success rate in difficult +births by about 10% they say wow and + + align:start position:0% +births by about 10% they say wow and + + + align:start position:0% +births by about 10% they say wow and +that was enough to build a family fore + + align:start position:0% +that was enough to build a family fore + + + align:start position:0% +that was enough to build a family fore +until some servant party spilled the be + + align:start position:0% +until some servant party spilled the be + + + align:start position:0% +until some servant party spilled the be +and that was the end of + + align:start position:0% +and that was the end of + + + align:start position:0% +and that was the end of +that yeah + + align:start position:0% + + + + align:start position:0% + +wow so who has a theory of the Middle + + align:start position:0% +wow so who has a theory of the Middle + + + align:start position:0% +wow so who has a theory of the Middle +Ages is there a standard theory yes well + + align:start position:0% +Ages is there a standard theory yes well + + + align:start position:0% +Ages is there a standard theory yes well +the concept of the Middle Ages as the + + align:start position:0% +the concept of the Middle Ages as the + + + align:start position:0% +the concept of the Middle Ages as the +Dark Ages something that emerged mostly + + align:start position:0% +Dark Ages something that emerged mostly + + + align:start position:0% +Dark Ages something that emerged mostly +in the Renaissance when people in the 14 + + align:start position:0% +in the Renaissance when people in the 14 + + + align:start position:0% +in the Renaissance when people in the 14 +The Well 15th 16th century tried to + + align:start position:0% +The Well 15th 16th century tried to + + + align:start position:0% +The Well 15th 16th century tried to +present themselves as going back to the + + align:start position:0% +present themselves as going back to the + + + align:start position:0% +present themselves as going back to the +classical age of scholarship of ancient + + align:start position:0% +classical age of scholarship of ancient + + + align:start position:0% +classical age of scholarship of ancient +grece and Rome and as being better than + + align:start position:0% +grece and Rome and as being better than + + + align:start position:0% +grece and Rome and as being better than +their predecessor for the last few years + + align:start position:0% +their predecessor for the last few years + + + align:start position:0% +their predecessor for the last few years +this mostly happened because of + + align:start position:0% +this mostly happened because of + + + align:start position:0% +this mostly happened because of +discovery of manuscripts that were + + align:start position:0% +discovery of manuscripts that were + + + align:start position:0% +discovery of manuscripts that were +translated from the ancient Greek and in + + align:start position:0% +translated from the ancient Greek and in + + + align:start position:0% +translated from the ancient Greek and in +certain cases Latin by by Muslims uh who + + align:start position:0% +certain cases Latin by by Muslims uh who + + + align:start position:0% +certain cases Latin by by Muslims uh who +at the time were sort of receding from + + align:start position:0% +at the time were sort of receding from + + + align:start position:0% +at the time were sort of receding from +Europe but uh so the entire concept of + + align:start position:0% +Europe but uh so the entire concept of + + + align:start position:0% +Europe but uh so the entire concept of +the Middle Ages might be a fabrication + + align:start position:0% +the Middle Ages might be a fabrication + + + align:start position:0% +the Middle Ages might be a fabrication +of the Renaissance I mean there were + + align:start position:0% +of the Renaissance I mean there were + + + align:start position:0% +of the Renaissance I mean there were +some significant discoveries at the time + + align:start position:0% +some significant discoveries at the time + + + align:start position:0% +some significant discoveries at the time +that's a nice idea in other words when + + align:start position:0% +that's a nice idea in other words when + + + align:start position:0% +that's a nice idea in other words when +was St + + align:start position:0% +was St + + + align:start position:0% +was St +Patrick St Patrick I'm told that + + align:start position:0% +Patrick St Patrick I'm told that + + + align:start position:0% +Patrick St Patrick I'm told that +he + + align:start position:0% +he + + + align:start position:0% +he +he uh popularized a lot of technical + + align:start position:0% +he uh popularized a lot of technical + + + align:start position:0% +he uh popularized a lot of technical +manuscripts brought them to back into + + align:start position:0% + + + + align:start position:0% + +Europe which is he has two achievements + + align:start position:0% +Europe which is he has two achievements + + + align:start position:0% +Europe which is he has two achievements +one was bringing scientific culture back + + align:start position:0% +one was bringing scientific culture back + + + align:start position:0% +one was bringing scientific culture back +and the other was getting snakes out of + + align:start position:0% +and the other was getting snakes out of + + + align:start position:0% +and the other was getting snakes out of +England or + + align:start position:0% +England or + + + align:start position:0% +England or +something + + align:start position:0% +something + + + align:start position:0% +something +Ireland I don't know which he was + + align:start position:0% +Ireland I don't know which he was + + + align:start position:0% +Ireland I don't know which he was +sainted + + align:start position:0% +sainted + + + align:start position:0% +sainted +for don't you have to do three Miracles + + align:start position:0% +for don't you have to do three Miracles + + + align:start position:0% +for don't you have to do three Miracles +or is + + align:start position:0% +or is + + + align:start position:0% +or is +it what's what's yeah yeah my theory is + + align:start position:0% +it what's what's yeah yeah my theory is + + + align:start position:0% +it what's what's yeah yeah my theory is +that the Middle Ages ended around + + align:start position:0% + + + + align:start position:0% + +2100 because they'll say after the + + align:start position:0% +2100 because they'll say after the + + + align:start position:0% +2100 because they'll say after the +Middle Ages end they'll say say you know + + align:start position:0% +Middle Ages end they'll say say you know + + + align:start position:0% +Middle Ages end they'll say say you know +those guys back in the 21st century you + + align:start position:0% +those guys back in the 21st century you + + + align:start position:0% +those guys back in the 21st century you +know they had no idea how thinking work + + align:start position:0% +know they had no idea how thinking work + + + align:start position:0% +know they had no idea how thinking work +they couldn't even think of a few ways + + align:start position:0% +they couldn't even think of a few ways + + + align:start position:0% +they couldn't even think of a few ways +to + + align:start position:0% +to + + + align:start position:0% +to +think they had poverty they had Wars you + + align:start position:0% +think they had poverty they had Wars you + + + align:start position:0% +think they had poverty they had Wars you +know those guys were barely out of their + + align:start position:0% +know those guys were barely out of their + + + align:start position:0% +know those guys were barely out of their +Lo CLA + + align:start position:0% +Lo CLA + + + align:start position:0% +Lo CLA +right I just read a history of AI I + + align:start position:0% +right I just read a history of AI I + + + align:start position:0% +right I just read a history of AI I +forget who wrote it + + align:start position:0% +forget who wrote it + + + align:start position:0% +forget who wrote it +but it had this section + + align:start position:0% +but it had this section + + + align:start position:0% +but it had this section +saying mentioned the new Simon there was + + align:start position:0% +saying mentioned the new Simon there was + + + align:start position:0% +saying mentioned the new Simon there was +a thing called General Problem Solver + + align:start position:0% +a thing called General Problem Solver + + + align:start position:0% +a thing called General Problem Solver +which I mentioned a couple of times in + + align:start position:0% +which I mentioned a couple of times in + + + align:start position:0% +which I mentioned a couple of times in +the book and it's the idea that the way + + align:start position:0% +the book and it's the idea that the way + + + align:start position:0% +the book and it's the idea that the way +to solve a problem is to + + align:start position:0% +to solve a problem is to + + + align:start position:0% +to solve a problem is to +find it's a symbolic Servo find the + + align:start position:0% +find it's a symbolic Servo find the + + + align:start position:0% +find it's a symbolic Servo find the +difference between what you have and + + align:start position:0% +difference between what you have and + + + align:start position:0% +difference between what you have and +what you want and look in your memory + + align:start position:0% +what you want and look in your memory + + + align:start position:0% +what you want and look in your memory +for something that can reduce that + + align:start position:0% +for something that can reduce that + + + align:start position:0% +for something that can reduce that +difference keep doing that and of course + + align:start position:0% +difference keep doing that and of course + + + align:start position:0% +difference keep doing that and of course +it's it's important to pay attention to + + align:start position:0% +it's it's important to pay attention to + + + align:start position:0% +it's it's important to pay attention to +the more important differences first and + + align:start position:0% +the more important differences first and + + + align:start position:0% +the more important differences first and +so forth and I'll send you this article + + align:start position:0% +so forth and I'll send you this article + + + align:start position:0% +so forth and I'll send you this article +this article is + + align:start position:0% +this article is + + + align:start position:0% +this article is +saying that they made a terrible mistake + + align:start position:0% +saying that they made a terrible mistake + + + align:start position:0% +saying that they made a terrible mistake +and this was a trivial Theory and that's + + align:start position:0% +and this was a trivial Theory and that's + + + align:start position:0% +and this was a trivial Theory and that's +why nobody uses it anymore and it was + + align:start position:0% +why nobody uses it anymore and it was + + + align:start position:0% +why nobody uses it anymore and it was +interesting how many AI people fell for + + align:start position:0% +interesting how many AI people fell for + + + align:start position:0% +interesting how many AI people fell for +that idea in the + + align:start position:0% +that idea in the + + + align:start position:0% +that idea in the +1960s my complaint has been that uh if + + align:start position:0% +1960s my complaint has been that uh if + + + align:start position:0% +1960s my complaint has been that uh if +you look in a modern textbook + + align:start position:0% +you look in a modern textbook + + + align:start position:0% +you look in a modern textbook +on you must have some in your first + + align:start position:0% +on you must have some in your first + + + align:start position:0% +on you must have some in your first +volume Pat + + align:start position:0% +volume Pat + + + align:start position:0% +volume Pat +didn't you have some GPS things oh + + align:start position:0% + + + + align:start position:0% + +yeah if you want to keep up with AI you + + align:start position:0% +yeah if you want to keep up with AI you + + + align:start position:0% +yeah if you want to keep up with AI you +should read Patrick's textbook even + + align:start position:0% +should read Patrick's textbook even + + + align:start position:0% +should read Patrick's textbook even +though he's people are starting to use + + align:start position:0% +though he's people are starting to use + + + align:start position:0% +though he's people are starting to use +this new one which doesn't have any AI + + align:start position:0% +this new one which doesn't have any AI + + + align:start position:0% +this new one which doesn't have any AI +in + + align:start position:0% + + + + align:start position:0% + +it by who's it + + align:start position:0% +it by who's it + + + align:start position:0% +it by who's it +by Russell and norvig it's probably + + align:start position:0% +by Russell and norvig it's probably + + + align:start position:0% +by Russell and norvig it's probably +pretty good technically but I Leaf + + align:start position:0% +pretty good technically but I Leaf + + + align:start position:0% +pretty good technically but I Leaf +through it and it didn't have any never + + align:start position:0% +through it and it didn't have any never + + + align:start position:0% +through it and it didn't have any never +mind it's probably better than I think + + align:start position:0% +mind it's probably better than I think + + + align:start position:0% +mind it's probably better than I think +because I'm + + align:start position:0% + + + + align:start position:0% + +jealous + + align:start position:0% +jealous + + + align:start position:0% +jealous +yes kind of a different topic in Society + + align:start position:0% +yes kind of a different topic in Society + + + align:start position:0% +yes kind of a different topic in Society +of Mind you're talking about the Amia of + + align:start position:0% +of Mind you're talking about the Amia of + + + align:start position:0% +of Mind you're talking about the Amia of +infancy when you forget what You' + + align:start position:0% +infancy when you forget what You' + + + align:start position:0% +infancy when you forget what You' +learned and um things that were + + align:start position:0% +learned and um things that were + + + align:start position:0% +learned and um things that were +you can't even remember how it was you + + align:start position:0% +you can't even remember how it was you + + + align:start position:0% +you can't even remember how it was you +learn them so it's just kind of + + align:start position:0% +learn them so it's just kind of + + + align:start position:0% +learn them so it's just kind of +wondering about the reverse of that + + align:start position:0% +wondering about the reverse of that + + + align:start position:0% +wondering about the reverse of that +process when you try and say teach + + align:start position:0% +process when you try and say teach + + + align:start position:0% +process when you try and say teach +something to somebody that you turn deep + + align:start position:0% +something to somebody that you turn deep + + + align:start position:0% +something to somebody that you turn deep +that you're putting Awareness on and + + align:start position:0% +that you're putting Awareness on and + + + align:start position:0% +that you're putting Awareness on and +bring bringing back up different levels + + align:start position:0% +bring bringing back up different levels + + + align:start position:0% +bring bringing back up different levels +I not exactly sure there's a question + + align:start position:0% +I not exactly sure there's a question + + + align:start position:0% +I not exactly sure there's a question +just on and wondering about is that + + align:start position:0% +just on and wondering about is that + + + align:start position:0% +just on and wondering about is that +itself + + align:start position:0% + + + + align:start position:0% + +another + + align:start position:0% +another + + + align:start position:0% +another +there that's sure an interesting + + align:start position:0% +there that's sure an interesting + + + align:start position:0% +there that's sure an interesting +question when I first learned about + + align:start position:0% + + + + align:start position:0% + +programming I was inter I had the idea + + align:start position:0% +programming I was inter I had the idea + + + align:start position:0% +programming I was inter I had the idea +that maybe babies think in machine + + align:start position:0% +that maybe babies think in machine + + + align:start position:0% +that maybe babies think in machine +language and + + align:start position:0% +language and + + + align:start position:0% +language and +then after a while + + align:start position:0% +then after a while + + + align:start position:0% +then after a while +they start to think in + + align:start position:0% +they start to think in + + + align:start position:0% +they start to think in +Fortran and then finally when they're a + + align:start position:0% +Fortran and then finally when they're a + + + align:start position:0% +Fortran and then finally when they're a +little older they think in Alo or + + align:start position:0% +little older they think in Alo or + + + align:start position:0% +little older they think in Alo or +something and so uh but when they switch + + align:start position:0% +something and so uh but when they switch + + + align:start position:0% +something and so uh but when they switch +from machine language to Fortran then + + align:start position:0% +from machine language to Fortran then + + + align:start position:0% +from machine language to Fortran then +they can't remember their earlier + + align:start position:0% +they can't remember their earlier + + + align:start position:0% +they can't remember their earlier +thoughts and there's almost no + + align:start position:0% +thoughts and there's almost no + + + align:start position:0% +thoughts and there's almost no +evidence + + align:start position:0% +evidence + + + align:start position:0% +evidence +of genu people finding genuine + + align:start position:0% +of genu people finding genuine + + + align:start position:0% +of genu people finding genuine +Recollections from uh twoy + + align:start position:0% +Recollections from uh twoy + + + align:start position:0% +Recollections from uh twoy +olds at later + + align:start position:0% +olds at later + + + align:start position:0% +olds at later +ages now almost everybody thinks they + + align:start position:0% +ages now almost everybody thinks they + + + align:start position:0% +ages now almost everybody thinks they +remember something but there's the + + align:start position:0% +remember something but there's the + + + align:start position:0% +remember something but there's the +problem that you might have rehearsed it + + align:start position:0% +problem that you might have rehearsed it + + + align:start position:0% +problem that you might have rehearsed it +and trans translated it into the Fortran + + align:start position:0% +and trans translated it into the Fortran + + + align:start position:0% +and trans translated it into the Fortran +and the alol and the lisp and the logo + + align:start position:0% +and the alol and the lisp and the logo + + + align:start position:0% +and the alol and the lisp and the logo +you know + + align:start position:0% +you know + + + align:start position:0% +you know +whatever whatever it + + align:start position:0% +whatever whatever it + + + align:start position:0% +whatever whatever it +is I had one of my greatest influences + + align:start position:0% +is I had one of my greatest influences + + + align:start position:0% +is I had one of my greatest influences +was + + align:start position:0% +was + + + align:start position:0% +was +uh uh a great mathematician named Andrew + + align:start position:0% +uh uh a great mathematician named Andrew + + + align:start position:0% +uh uh a great mathematician named Andrew +Gleason at Harvard who I met practically + + align:start position:0% +Gleason at Harvard who I met practically + + + align:start position:0% +Gleason at Harvard who I met practically +the first day I got to + + align:start position:0% +the first day I got to + + + align:start position:0% +the first day I got to +Harvard + + align:start position:0% +Harvard + + + align:start position:0% +Harvard +and he would always talk about things I + + align:start position:0% +and he would always talk about things I + + + align:start position:0% +and he would always talk about things I +didn't understand and I would go home + + align:start position:0% +didn't understand and I would go home + + + align:start position:0% +didn't understand and I would go home +and look them up and try to anyway uh + + align:start position:0% +and look them up and try to anyway uh + + + align:start position:0% +and look them up and try to anyway uh +one day we were talking about number + + align:start position:0% +one day we were talking about number + + + align:start position:0% +one day we were talking about number +forms and number forms are a + + align:start position:0% +forms and number forms are a + + + align:start position:0% +forms and number forms are a +psychological phenomenon which about 30% + + align:start position:0% +psychological phenomenon which about 30% + + + align:start position:0% +psychological phenomenon which about 30% +of people + + align:start position:0% + + + + align:start position:0% + +have and it was first described by + + align:start position:0% +have and it was first described by + + + align:start position:0% +have and it was first described by +Francis + + align:start position:0% +Francis + + + align:start position:0% +Francis +gton and the pro the phenomenon is if I + + align:start position:0% +gton and the pro the phenomenon is if I + + + align:start position:0% +gton and the pro the phenomenon is if I +ask you + + align:start position:0% + + + + align:start position:0% + +close your eyes and tell me where is the + + align:start position:0% +close your eyes and tell me where is the + + + align:start position:0% +close your eyes and tell me where is the +number + + align:start position:0% +number + + + align:start position:0% +number +three how many of you in have a place + + align:start position:0% +three how many of you in have a place + + + align:start position:0% +three how many of you in have a place +for the number + + align:start position:0% +for the number + + + align:start position:0% +for the number +three well that's a few and so + + align:start position:0% +three well that's a few and so + + + align:start position:0% +three well that's a few and so +typically if you imagine the visual + + align:start position:0% + + + + align:start position:0% + +field that's a windshield I + + align:start position:0% +field that's a windshield I + + + align:start position:0% +field that's a windshield I +guess so there are these numbers and + + align:start position:0% +guess so there are these numbers and + + + align:start position:0% +guess so there are these numbers and +they're they're nowhere in + + align:start position:0% + + + + align:start position:0% + +particular except + + align:start position:0% + + + + align:start position:0% + +that it's usually like + + align:start position:0% +that it's usually like + + + align:start position:0% +that it's usually like +that for a older child so here are these + + align:start position:0% +that for a older child so here are these + + + align:start position:0% +that for a older child so here are these +numbers and what's more in some people + + align:start position:0% +numbers and what's more in some people + + + align:start position:0% +numbers and what's more in some people +they're + + align:start position:0% +they're + + + align:start position:0% +they're +colored so I was talking to Andrew I had + + align:start position:0% +colored so I was talking to Andrew I had + + + align:start position:0% +colored so I was talking to Andrew I had +read this goon paper which is 1890 or + + align:start position:0% +read this goon paper which is 1890 or + + + align:start position:0% +read this goon paper which is 1890 or +1885 or + + align:start position:0% +1885 or + + + align:start position:0% +1885 or +something and so I was asking people if + + align:start position:0% +something and so I was asking people if + + + align:start position:0% +something and so I was asking people if +they had number + + align:start position:0% +they had number + + + align:start position:0% +they had number +forms and he said oh yes he has + + align:start position:0% +forms and he said oh yes he has + + + align:start position:0% +forms and he said oh yes he has +one and uh he sketched it for + + align:start position:0% +one and uh he sketched it for + + + align:start position:0% +one and uh he sketched it for +me and he said and they're colored + + align:start position:0% +me and he said and they're colored + + + align:start position:0% +me and he said and they're colored +too oh and his went way up and the prime + + align:start position:0% +too oh and his went way up and the prime + + + align:start position:0% +too oh and his went way up and the prime +numbers were + + align:start position:0% + + + + align:start position:0% + +bright I what am I doing + + align:start position:0% +bright I what am I doing + + + align:start position:0% +bright I what am I doing +maybe the composite numbers were + + align:start position:0% +maybe the composite numbers were + + + align:start position:0% +maybe the composite numbers were +something was bright and they were + + align:start position:0% + + + + align:start position:0% + +colored so I wrote this down and + + align:start position:0% +colored so I wrote this down and + + + align:start position:0% +colored so I wrote this down and +I over the next couple of years I look + + align:start position:0% +I over the next couple of years I look + + + align:start position:0% +I over the next couple of years I look +in antique stores for old children's + + align:start position:0% +in antique stores for old children's + + + align:start position:0% +in antique stores for old children's +blocks and I found a set of blocks that + + align:start position:0% +blocks and I found a set of blocks that + + + align:start position:0% +blocks and I found a set of blocks that +matched + + align:start position:0% + + + + align:start position:0% + +that and Andrew gleon said that he knows + + align:start position:0% +that and Andrew gleon said that he knows + + + align:start position:0% +that and Andrew gleon said that he knows +when he acquired this thing and it was + + align:start position:0% +when he acquired this thing and it was + + + align:start position:0% +when he acquired this thing and it was +about four years old + + align:start position:0% +about four years old + + + align:start position:0% +about four years old +and he had a + + align:start position:0% +and he had a + + + align:start position:0% +and he had a +window which in his house and there was + + align:start position:0% +window which in his house and there was + + + align:start position:0% +window which in his house and there was +a hill and he could just re he could + + align:start position:0% +a hill and he could just re he could + + + align:start position:0% +a hill and he could just re he could +just see over the sill and he imagined + + align:start position:0% +just see over the sill and he imagined + + + align:start position:0% +just see over the sill and he imagined +these numbers on the side of that Hill + + align:start position:0% +these numbers on the side of that Hill + + + align:start position:0% +these numbers on the side of that Hill +blah blah blah anyway + + align:start position:0% +blah blah blah anyway + + + align:start position:0% +blah blah blah anyway +uh people who don't have a number form + + align:start position:0% +uh people who don't have a number form + + + align:start position:0% +uh people who don't have a number form +don't know what I'm talking about but + + align:start position:0% +don't know what I'm talking about but + + + align:start position:0% +don't know what I'm talking about but +um and I don't know if the 30% is still + + align:start position:0% +um and I don't know if the 30% is still + + + align:start position:0% +um and I don't know if the 30% is still +true but it's an interesting + + align:start position:0% +true but it's an interesting + + + align:start position:0% +true but it's an interesting +phenomenon and in most cases + + align:start position:0% +phenomenon and in most cases + + + align:start position:0% +phenomenon and in most cases +you of Early Childhood well that's you + + align:start position:0% +you of Early Childhood well that's you + + + align:start position:0% +you of Early Childhood well that's you +can't find out because CH children do + + align:start position:0% +can't find out because CH children do + + + align:start position:0% +can't find out because CH children do +remember details of a house they lived + + align:start position:0% +remember details of a house they lived + + + align:start position:0% +remember details of a house they lived +in but you don't know if they've copied + + align:start position:0% +in but you don't know if they've copied + + + align:start position:0% +in but you don't know if they've copied +it so what was the original + + align:start position:0% + + + + align:start position:0% + +question um how much can you remember + + align:start position:0% +question um how much can you remember + + + align:start position:0% +question um how much can you remember +from + + align:start position:0% +from + + + align:start position:0% +from +infancy elran haard thought you could go + + align:start position:0% +infancy elran haard thought you could go + + + align:start position:0% +infancy elran haard thought you could go +back to before you were + + align:start position:0% +back to before you were + + + align:start position:0% +back to before you were +born and uh you could + + align:start position:0% +born and uh you could + + + align:start position:0% +born and uh you could +remember people talking about you when + + align:start position:0% +remember people talking about you when + + + align:start position:0% +remember people talking about you when +you're still in the + + align:start position:0% + + + + align:start position:0% + +womb so anyway John Campbell said you + + align:start position:0% +womb so anyway John Campbell said you + + + align:start position:0% +womb so anyway John Campbell said you +should look into this and uh a few of us + + align:start position:0% +should look into this and uh a few of us + + + align:start position:0% +should look into this and uh a few of us +made an expedition we went down to + + align:start position:0% +made an expedition we went down to + + + align:start position:0% +made an expedition we went down to +Elizabeth New Jersey to visit the the + + align:start position:0% +Elizabeth New Jersey to visit the the + + + align:start position:0% +Elizabeth New Jersey to visit the the +just starting up Dione Center and I met + + align:start position:0% +just starting up Dione Center and I met + + + align:start position:0% +just starting up Dione Center and I met +this elron hubard who had green eyes and + + align:start position:0% +this elron hubard who had green eyes and + + + align:start position:0% +this elron hubard who had green eyes and +was quite hypnotic + + align:start position:0% +was quite hypnotic + + + align:start position:0% +was quite hypnotic +looking and the end of the story is he + + align:start position:0% +looking and the end of the story is he + + + align:start position:0% +looking and the end of the story is he +had been writing about how if you took + + align:start position:0% +had been writing about how if you took + + + align:start position:0% +had been writing about how if you took +this treatment of Dione XS then you + + align:start position:0% +this treatment of Dione XS then you + + + align:start position:0% +this treatment of Dione XS then you +could memorize an entire newspaper in + + align:start position:0% +could memorize an entire newspaper in + + + align:start position:0% +could memorize an entire newspaper in +five minutes and do all sorts of + + align:start position:0% +five minutes and do all sorts of + + + align:start position:0% +five minutes and do all sorts of +miraculous things like that once your + + align:start position:0% +miraculous things like that once your + + + align:start position:0% +miraculous things like that once your +mind has been cleared of aberration and + + align:start position:0% +mind has been cleared of aberration and + + + align:start position:0% +mind has been cleared of aberration and +obstacles and I became a big industry + + align:start position:0% +obstacles and I became a big industry + + + align:start position:0% +obstacles and I became a big industry +and turned into later Scientology I'm + + align:start position:0% +and turned into later Scientology I'm + + + align:start position:0% +and turned into later Scientology I'm +sure you've all heard about that so we + + align:start position:0% +sure you've all heard about that so we + + + align:start position:0% +sure you've all heard about that so we +asked hubard to look at a newspaper and + + align:start position:0% +asked hubard to look at a newspaper and + + + align:start position:0% +asked hubard to look at a newspaper and +tell us what was in it and he explained + + align:start position:0% +tell us what was in it and he explained + + + align:start position:0% +tell us what was in it and he explained +he was so busy training the other people + + align:start position:0% +he was so busy training the other people + + + align:start position:0% +he was so busy training the other people +to be cleared that he hadn't had time + + align:start position:0% +to be cleared that he hadn't had time + + + align:start position:0% +to be cleared that he hadn't had time +to + + align:start position:0% +to + + + align:start position:0% +to +go through the procedure + + align:start position:0% +go through the procedure + + + align:start position:0% +go through the procedure +himself and I never saw him + + align:start position:0% + + + + align:start position:0% + +again yes what are your thoughts on and + + align:start position:0% +again yes what are your thoughts on and + + + align:start position:0% +again yes what are your thoughts on and +the fact + + align:start position:0% + + + + align:start position:0% + +that of + + align:start position:0% + + + + align:start position:0% + +memes you mean + + align:start position:0% +memes you mean + + + align:start position:0% +memes you mean +Dawkins kind of + + align:start position:0% +Dawkins kind of + + + align:start position:0% +Dawkins kind of +I didn't quite get the whole question + + align:start position:0% +I didn't quite get the whole question + + + align:start position:0% +I didn't quite get the whole question +the idea + + align:start position:0% +the idea + + + align:start position:0% +the idea +that uh oh so so for example the way we + + align:start position:0% +that uh oh so so for example the way we + + + align:start position:0% +that uh oh so so for example the way we +talk and the way we all talk how we very + + align:start position:0% +talk and the way we all talk how we very + + + align:start position:0% +talk and the way we all talk how we very +much remic the way our parents talk for + + align:start position:0% +much remic the way our parents talk for + + + align:start position:0% +much remic the way our parents talk for +people around us um and possibly the way + + align:start position:0% +people around us um and possibly the way + + + align:start position:0% +people around us um and possibly the way +we think as well so how does that relate + + align:start position:0% +we think as well so how does that relate + + + align:start position:0% +we think as well so how does that relate +to how our mind develops are we actually + + align:start position:0% +to how our mind develops are we actually + + + align:start position:0% +to how our mind develops are we actually +creative original characters + + align:start position:0% +creative original characters + + + align:start position:0% +creative original characters +well of course it's both because you + + align:start position:0% +well of course it's both because you + + + align:start position:0% +well of course it's both because you +learn things from your culture and + + align:start position:0% +learn things from your culture and + + + align:start position:0% +learn things from your culture and +then uh you might just Mo mainly repeat + + align:start position:0% +then uh you might just Mo mainly repeat + + + align:start position:0% +then uh you might just Mo mainly repeat +things or you might get the Knack of + + align:start position:0% +things or you might get the Knack of + + + align:start position:0% +things or you might get the Knack of +making new + + align:start position:0% +making new + + + align:start position:0% +making new +ideas I'm trying to remember what + + align:start position:0% +ideas I'm trying to remember what + + + align:start position:0% +ideas I'm trying to remember what +Dawkins main ideas + + align:start position:0% +Dawkins main ideas + + + align:start position:0% +Dawkins main ideas +are + + align:start position:0% +are + + + align:start position:0% +are +uh he invented the word meme to say + + align:start position:0% +uh he invented the word meme to say + + + align:start position:0% +uh he invented the word meme to say +that the ideas that people + + align:start position:0% +that the ideas that people + + + align:start position:0% +that the ideas that people +have might be considered to be somewhat + + align:start position:0% +have might be considered to be somewhat + + + align:start position:0% +have might be considered to be somewhat +similar to the genes in our heredity and + + align:start position:0% +similar to the genes in our heredity and + + + align:start position:0% +similar to the genes in our heredity and +that societies are systems in which + + align:start position:0% +that societies are systems in which + + + align:start position:0% +that societies are systems in which +these memes which are uh conceptual + + align:start position:0% +these memes which are uh conceptual + + + align:start position:0% +these memes which are uh conceptual +units of meaning or knowledge uh + + align:start position:0% +units of meaning or knowledge uh + + + align:start position:0% +units of meaning or knowledge uh +propagate around and self- reproduce and + + align:start position:0% +propagate around and self- reproduce and + + + align:start position:0% +propagate around and self- reproduce and +mutate and + + align:start position:0% +mutate and + + + align:start position:0% +mutate and +spread + + align:start position:0% +spread + + + align:start position:0% +spread +and + + align:start position:0% +and + + + align:start position:0% +and +I don't know what to say about it except + + align:start position:0% +I don't know what to say about it except + + + align:start position:0% +I don't know what to say about it except +that it's obviously true that uh every + + align:start position:0% +that it's obviously true that uh every + + + align:start position:0% +that it's obviously true that uh every +now and then someone gets a new idea and + + align:start position:0% +now and then someone gets a new idea and + + + align:start position:0% +now and then someone gets a new idea and +tells people and for one reason or + + align:start position:0% +tells people and for one reason or + + + align:start position:0% +tells people and for one reason or +another they either forget it or or tell + + align:start position:0% +another they either forget it or or tell + + + align:start position:0% +another they either forget it or or tell +someone else and after a while it + + align:start position:0% +someone else and after a while it + + + align:start position:0% +someone else and after a while it +spreads and some of them fill up the + + align:start position:0% +spreads and some of them fill up the + + + align:start position:0% +spreads and some of them fill up the +whole culture and some just die + + align:start position:0% + + + + align:start position:0% + +out and whatever else Jawan says he's + + align:start position:0% +out and whatever else Jawan says he's + + + align:start position:0% +out and whatever else Jawan says he's +very smart guy but almost everything + + align:start position:0% +very smart guy but almost everything + + + align:start position:0% +very smart guy but almost everything +then uh in my mind is that he's + + align:start position:0% +then uh in my mind is that he's + + + align:start position:0% +then uh in my mind is that he's +explaining that religions are mostly + + align:start position:0% +explaining that religions are mostly + + + align:start position:0% +explaining that religions are mostly +made of these memes and they're very bad + + align:start position:0% +made of these memes and they're very bad + + + align:start position:0% +made of these memes and they're very bad +and cost the world a great deal in uh + + align:start position:0% +and cost the world a great deal in uh + + + align:start position:0% +and cost the world a great deal in uh +progress and productivity in other words + + align:start position:0% +progress and productivity in other words + + + align:start position:0% +progress and productivity in other words +he's a militant atheist and + + align:start position:0% +he's a militant atheist and + + + align:start position:0% +he's a militant atheist and +it's and there about five best sellers + + align:start position:0% +it's and there about five best sellers + + + align:start position:0% +it's and there about five best sellers +in that business + + align:start position:0% +in that business + + + align:start position:0% +in that business +today but I don't know what else to say + + align:start position:0% +today but I don't know what else to say + + + align:start position:0% +today but I don't know what else to say +about memes it's an + + align:start position:0% +about memes it's an + + + align:start position:0% +about memes it's an +obviously uh generally correct idea + + align:start position:0% +obviously uh generally correct idea + + + align:start position:0% +obviously uh generally correct idea +and + + align:start position:0% +and + + + align:start position:0% +and +but the great thing about genes is we + + align:start position:0% +but the great thing about genes is we + + + align:start position:0% +but the great thing about genes is we +know the four Amino a or four nucleic + + align:start position:0% +know the four Amino a or four nucleic + + + align:start position:0% +know the four Amino a or four nucleic +acids they're made of and how they're + + align:start position:0% +acids they're made of and how they're + + + align:start position:0% +acids they're made of and how they're +roped together and all that and I don't + + align:start position:0% +roped together and all that and I don't + + + align:start position:0% +roped together and all that and I don't +think Dawkins + + align:start position:0% +think Dawkins + + + align:start position:0% +think Dawkins +Theory uh develops anywhere nearly as + + align:start position:0% +Theory uh develops anywhere nearly as + + + align:start position:0% +Theory uh develops anywhere nearly as +elegantly as modern in genetics so it + + align:start position:0% +elegantly as modern in genetics so it + + + align:start position:0% +elegantly as modern in genetics so it +would be nice if it could + + align:start position:0% + + + + align:start position:0% + +but a really good theory of good ideas + + align:start position:0% +but a really good theory of good ideas + + + align:start position:0% +but a really good theory of good ideas +would be nice to + + align:start position:0% +would be nice to + + + align:start position:0% +would be nice to +have what would + + align:start position:0% +have what would + + + align:start position:0% +have what would +it what would it look + + align:start position:0% +it what would it look + + + align:start position:0% +it what would it look +like someday we'll have an AI that just + + align:start position:0% +like someday we'll have an AI that just + + + align:start position:0% +like someday we'll have an AI that just +punches them out I think I think it + + align:start position:0% +punches them out I think I think it + + + align:start position:0% +punches them out I think I think it +would look like a really good language + + align:start position:0% +would look like a really good language + + + align:start position:0% +would look like a really good language +ah oh + + align:start position:0% +ah oh + + + align:start position:0% +ah oh +right Robert heinlin had + + align:start position:0% +right Robert heinlin had + + + align:start position:0% +right Robert heinlin had +some stories in which the super + + align:start position:0% +some stories in which the super + + + align:start position:0% +some stories in which the super +intelligent people have a language + + align:start position:0% +intelligent people have a language + + + align:start position:0% +intelligent people have a language +that's so dense that in five syllables + + align:start position:0% +that's so dense that in five syllables + + + align:start position:0% +that's so dense that in five syllables +they can explain something that would + + align:start position:0% +they can explain something that would + + + align:start position:0% +they can explain something that would +take you a half hour I think I forget + + align:start position:0% +take you a half hour I think I forget + + + align:start position:0% +take you a half hour I think I forget +what it's + + align:start position:0% +what it's + + + align:start position:0% +what it's +loglan + + align:start position:0% +loglan + + + align:start position:0% +loglan +May anyway if you need a good idea read + + align:start position:0% +May anyway if you need a good idea read + + + align:start position:0% +May anyway if you need a good idea read +Robert + + align:start position:0% + + + + align:start position:0% + +hline sure + + align:start position:0% +hline sure + + + align:start position:0% +hline sure +um mentioned this but you talked about + + align:start position:0% +um mentioned this but you talked about + + + align:start position:0% +um mentioned this but you talked about +how Geniuses um they might have just + + align:start position:0% +how Geniuses um they might have just + + + align:start position:0% +how Geniuses um they might have just +come up come up with um better ways to + + align:start position:0% +come up come up with um better ways to + + + align:start position:0% +come up come up with um better ways to +um think better like better ways to + + align:start position:0% +um think better like better ways to + + + align:start position:0% +um think better like better ways to +think better ways to learn yes how + + align:start position:0% + + + + align:start position:0% + +to learning but why do you think um they + + align:start position:0% +to learning but why do you think um they + + + align:start position:0% +to learning but why do you think um they +never it and why hav't they like + + align:start position:0% +never it and why hav't they like + + + align:start position:0% +never it and why hav't they like +propagated + + align:start position:0% +propagated + + + align:start position:0% +propagated +like + + align:start position:0% + + + + align:start position:0% + +me that's a great + + align:start position:0% +me that's a great + + + align:start position:0% +me that's a great +question + + align:start position:0% + + + + align:start position:0% + +and think we have like you know a + + align:start position:0% +and think we have like you know a + + + align:start position:0% +and think we have like you know a +concept + + align:start position:0% +concept + + + align:start position:0% +concept +of an idea that like improves better + + align:start position:0% +of an idea that like improves better + + + align:start position:0% +of an idea that like improves better +learning that there's a couple of + + align:start position:0% +learning that there's a couple of + + + align:start position:0% +learning that there's a couple of +phenomena that like how come there were + + align:start position:0% +phenomena that like how come there were + + + align:start position:0% +phenomena that like how come there were +so many Geniuses in + + align:start position:0% +so many Geniuses in + + + align:start position:0% +so many Geniuses in +Athens and that's and then + + align:start position:0% +Athens and that's and then + + + align:start position:0% +Athens and that's and then +uh some of the best mathematicians came + + align:start position:0% +uh some of the best mathematicians came + + + align:start position:0% +uh some of the best mathematicians came +from + + align:start position:0% +from + + + align:start position:0% +from +some high + + align:start position:0% +some high + + + align:start position:0% +some high +school + + align:start position:0% +school + + + align:start position:0% +school +in some little country next to the + + align:start position:0% +in some little country next to the + + + align:start position:0% +in some little country next to the +Baltic Bulgaria I + + align:start position:0% +Baltic Bulgaria I + + + align:start position:0% +Baltic Bulgaria I +Romania yes there was some high school + + align:start position:0% +Romania yes there was some high school + + + align:start position:0% +Romania yes there was some high school +in + + align:start position:0% +in + + + align:start position:0% +in +Romania that not only produced van noyon + + align:start position:0% +Romania that not only produced van noyon + + + align:start position:0% +Romania that not only produced van noyon +but about five or six other worldclass + + align:start position:0% +but about five or six other worldclass + + + align:start position:0% +but about five or six other worldclass +mathematicians I don't remember the + + align:start position:0% +mathematicians I don't remember the + + + align:start position:0% +mathematicians I don't remember the +details so that's a nice question how + + align:start position:0% +details so that's a nice question how + + + align:start position:0% +details so that's a nice question how +come + + align:start position:0% + + + + align:start position:0% + +uh if there are these great memes how + + align:start position:0% +uh if there are these great memes how + + + align:start position:0% +uh if there are these great memes how +come there aren't more big pockets of + + align:start position:0% +come there aren't more big pockets of + + + align:start position:0% +come there aren't more big pockets of +them but there are a lot of cultures + + align:start position:0% +them but there are a lot of cultures + + + align:start position:0% +them but there are a lot of cultures +which were very inventive in in other + + align:start position:0% +which were very inventive in in other + + + align:start position:0% +which were very inventive in in other +than intellectual + + align:start position:0% + + + + align:start position:0% + +Fields how come Paris got all those + + align:start position:0% +Fields how come Paris got all those + + + align:start position:0% +Fields how come Paris got all those +artists in the how many of you saw the + + align:start position:0% +artists in the how many of you saw the + + + align:start position:0% +artists in the how many of you saw the +Woody Allen + + align:start position:0% +Woody Allen + + + align:start position:0% +Woody Allen +movie what's it called Paris at + + align:start position:0% + + + + align:start position:0% + +midnight so + + align:start position:0% + + + + align:start position:0% + +funny + + align:start position:0% + + + + align:start position:0% + +improve + + align:start position:0% +improve + + + align:start position:0% +improve +right + + align:start position:0% +right + + + align:start position:0% +right +that's a good question for each of us + + align:start position:0% +that's a good question for each of us + + + align:start position:0% +that's a good question for each of us +what's your very best idea and stop + + align:start position:0% +what's your very best idea and stop + + + align:start position:0% +what's your very best idea and stop +fussing with the other ones and get that + + align:start position:0% +fussing with the other ones and get that + + + align:start position:0% +fussing with the other ones and get that +one + + align:start position:0% + + + + align:start position:0% + +out there must be some people who are + + align:start position:0% +out there must be some people who are + + + align:start position:0% +out there must be some people who are +very quiet and only speak once in a long + + align:start position:0% +very quiet and only speak once in a long + + + align:start position:0% +very quiet and only speak once in a long +time we should watch them + + align:start position:0% +time we should watch them + + + align:start position:0% +time we should watch them +carefully yes I guess along do you ever + + align:start position:0% +carefully yes I guess along do you ever + + + align:start position:0% +carefully yes I guess along do you ever +feel restricted by language because + + align:start position:0% +feel restricted by language because + + + align:start position:0% +feel restricted by language because +every have wait + + align:start position:0% + + + + align:start position:0% + +it's the sound I can't hear + + align:start position:0% + + + + align:start position:0% + +from is that strong enough to lift + + align:start position:0% + + + + align:start position:0% + +you let's + + align:start position:0% +you let's + + + align:start position:0% +you let's +a I'm sure someone's done + + align:start position:0% +a I'm sure someone's done + + + align:start position:0% +a I'm sure someone's done +it sorry about that oh do you ever feel + + align:start position:0% +it sorry about that oh do you ever feel + + + align:start position:0% +it sorry about that oh do you ever feel +restricted by language and that you must + + align:start position:0% +restricted by language and that you must + + + align:start position:0% +restricted by language and that you must +represent + + align:start position:0% +represent + + + align:start position:0% +represent +mind or Anor idea + + align:start position:0% +mind or Anor idea + + + align:start position:0% +mind or Anor idea +language uh no I don't but I I once was + + align:start position:0% +language uh no I don't but I I once was + + + align:start position:0% +language uh no I don't but I I once was +jealous when Pap explained that he got + + align:start position:0% +jealous when Pap explained that he got + + + align:start position:0% +jealous when Pap explained that he got +he got some idea and then he explained + + align:start position:0% +he got some idea and then he explained + + + align:start position:0% +he got some idea and then he explained +he gets ideas like that when he thinks + + align:start position:0% +he gets ideas like that when he thinks + + + align:start position:0% +he gets ideas like that when he thinks +in French and and uh draw + + align:start position:0% +in French and and uh draw + + + align:start position:0% +in French and and uh draw +pictures what you draw pictures too oh + + align:start position:0% +pictures what you draw pictures too oh + + + align:start position:0% +pictures what you draw pictures too oh +yeah so it's not just language that's a + + align:start position:0% +yeah so it's not just language that's a + + + align:start position:0% +yeah so it's not just language that's a +language graphics + + align:start position:0% + + + + align:start position:0% + +so we ought to have + + align:start position:0% +so we ought to have + + + align:start position:0% +so we ought to have +devices within the next few years that + + align:start position:0% +devices within the next few years that + + + align:start position:0% +devices within the next few years that +um draw pictures when you think + + align:start position:0% + + + + align:start position:0% + +or it's so funny you know uh we + + align:start position:0% +or it's so funny you know uh we + + + align:start position:0% +or it's so funny you know uh we +had cyborgs what were they called I + + align:start position:0% +had cyborgs what were they called I + + + align:start position:0% +had cyborgs what were they called I +mentioned them last time we had Steve + + align:start position:0% +mentioned them last time we had Steve + + + align:start position:0% +mentioned them last time we had Steve +man and who's the other + + align:start position:0% + + + + align:start position:0% + +one + + align:start position:0% +one + + + align:start position:0% +one +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so there's these two guys around the + + align:start position:0% +so there's these two guys around the + + + align:start position:0% +so there's these two guys around the +media lab wearing various things on + + align:start position:0% +media lab wearing various things on + + + align:start position:0% +media lab wearing various things on +their head and they're always typing and + + align:start position:0% +their head and they're always typing and + + + align:start position:0% +their head and they're always typing and +you ask them a question and they've + + align:start position:0% +you ask them a question and they've + + + align:start position:0% +you ask them a question and they've +searched + + align:start position:0% +searched + + + align:start position:0% +searched +Google and + + align:start position:0% +Google and + + + align:start position:0% +Google and +uh when was that + + align:start position:0% + + + + align:start position:0% + +1990 but it's all gone nobody walks + + align:start position:0% +1990 but it's all gone nobody walks + + + align:start position:0% +1990 but it's all gone nobody walks +around with direct connection to the web + + align:start position:0% +around with direct connection to the web + + + align:start position:0% +around with direct connection to the web +stes + + align:start position:0% +stes + + + align:start position:0% +stes +yes anyway I certainly expected it to + + align:start position:0% +yes anyway I certainly expected it to + + + align:start position:0% +yes anyway I certainly expected it to +turn up + + align:start position:0% +turn up + + + align:start position:0% +turn up +and something wrong so anyway you should + + align:start position:0% +and something wrong so anyway you should + + + align:start position:0% +and something wrong so anyway you should +be able to buy one one of these days and + + align:start position:0% +be able to buy one one of these days and + + + align:start position:0% +be able to buy one one of these days and +uh what's her + + align:start position:0% +uh what's her + + + align:start position:0% +uh what's her +name who was that nice woman who had the + + align:start position:0% +name who was that nice woman who had the + + + align:start position:0% +name who was that nice woman who had the +EEG + + align:start position:0% + + + + align:start position:0% + +thing you remember at + + align:start position:0% + + + + align:start position:0% + +Ted forgot her name anyway she had a + + align:start position:0% +Ted forgot her name anyway she had a + + + align:start position:0% +Ted forgot her name anyway she had a +sort of helmet which had about 20 + + align:start position:0% +sort of helmet which had about 20 + + + align:start position:0% +sort of helmet which had about 20 +electrodes and she induced me to put it + + align:start position:0% +electrodes and she induced me to put it + + + align:start position:0% +electrodes and she induced me to put it +on I was on a stage with about a + + align:start position:0% +on I was on a stage with about a + + + align:start position:0% +on I was on a stage with about a +thousand people there which was rather + + align:start position:0% +thousand people there which was rather + + + align:start position:0% +thousand people there which was rather +funny and there's a little spot on a + + align:start position:0% +funny and there's a little spot on a + + + align:start position:0% +funny and there's a little spot on a +CRT and I get to think about it moving + + align:start position:0% +CRT and I get to think about it moving + + + align:start position:0% +CRT and I get to think about it moving +one way or the other and rewarding it + + align:start position:0% +one way or the other and rewarding it + + + align:start position:0% +one way or the other and rewarding it +when it did the right thing for only + + align:start position:0% +when it did the right thing for only + + + align:start position:0% +when it did the right thing for only +about half a minute and then I could + + align:start position:0% +about half a minute and then I could + + + align:start position:0% +about half a minute and then I could +steer it around so here was a nice uh + + align:start position:0% +steer it around so here was a nice uh + + + align:start position:0% +steer it around so here was a nice uh +primitive Gadget where you could sort of + + align:start position:0% +primitive Gadget where you could sort of + + + align:start position:0% +primitive Gadget where you could sort of +almost draw just by thinking this spot + + align:start position:0% +almost draw just by thinking this spot + + + align:start position:0% +almost draw just by thinking this spot +and then she started a company + + align:start position:0% +and then she started a company + + + align:start position:0% +and then she started a company +and hasn't sent me + + align:start position:0% +and hasn't sent me + + + align:start position:0% +and hasn't sent me +one because maybe it was just beginner's + + align:start position:0% +one because maybe it was just beginner's + + + align:start position:0% +one because maybe it was just beginner's +luck beginner's luck or + + align:start position:0% + + + + align:start position:0% + +something what her name t yes Lee yeah + + align:start position:0% + + + + align:start position:0% + +uh did you find the + + align:start position:0% + + + + align:start position:0% + +company but you think that there be lots + + align:start position:0% +company but you think that there be lots + + + align:start position:0% +company but you think that there be lots +of people wearing stuff and see she's + + align:start position:0% +of people wearing stuff and see she's + + + align:start position:0% +of people wearing stuff and see she's +doing it right + + align:start position:0% +doing it right + + + align:start position:0% +doing it right +now with your keyboard + + align:start position:0% + + + + align:start position:0% + +right why don't we take a five minute + + align:start position:0% + + + + align:start position:0% + +break + + align:start position:0% + + + + align:start position:0% + +I don't + + align:start position:0% + + + + align:start position:0% + +know + + align:start position:0% +know + + + align:start position:0% +know +well I hay to interrupt + + align:start position:0% + + + + align:start position:0% + +because I see 10 different productive + + align:start position:0% + + + + align:start position:0% + +discussions yes I I see a I saw quite a + + align:start position:0% +discussions yes I I see a I saw quite a + + + align:start position:0% +discussions yes I I see a I saw quite a +few apparently productive discussions + + align:start position:0% +few apparently productive discussions + + + align:start position:0% +few apparently productive discussions +maybe that's what the class needs but + + align:start position:0% +maybe that's what the class needs but + + + align:start position:0% +maybe that's what the class needs but +uh anybody come to a + + align:start position:0% +uh anybody come to a + + + align:start position:0% +uh anybody come to a +conclusion + + align:start position:0% + + + + align:start position:0% + +yeah see if you can knock the wall down + + align:start position:0% +yeah see if you can knock the wall down + + + align:start position:0% +yeah see if you can knock the wall down +and yeah uh it's not a conclusion but + + align:start position:0% +and yeah uh it's not a conclusion but + + + align:start position:0% +and yeah uh it's not a conclusion but +it's a question it's a thought + + align:start position:0% +it's a question it's a thought + + + align:start position:0% +it's a question it's a thought +experiment so if you had a black box + + align:start position:0% +experiment so if you had a black box + + + align:start position:0% +experiment so if you had a black box +that could uh sort of replace part of + + align:start position:0% +that could uh sort of replace part of + + + align:start position:0% +that could uh sort of replace part of +your brain and let's say you replace + + align:start position:0% +your brain and let's say you replace + + + align:start position:0% +your brain and let's say you replace +like 5% out of the time at what point if + + align:start position:0% +like 5% out of the time at what point if + + + align:start position:0% +like 5% out of the time at what point if +you assume that there's this self entity + + align:start position:0% +you assume that there's this self entity + + + align:start position:0% +you assume that there's this self entity +at what point would you lose + + align:start position:0% + + + + align:start position:0% + +yourself you if you + + align:start position:0% +yourself you if you + + + align:start position:0% +yourself you if you +change the question is are you how how + + align:start position:0% +change the question is are you how how + + + align:start position:0% +change the question is are you how how +much do you have in common with uh with + + align:start position:0% +much do you have in common with uh with + + + align:start position:0% +much do you have in common with uh with +the you of yesterday as compared to uh + + align:start position:0% +the you of yesterday as compared to uh + + + align:start position:0% +the you of yesterday as compared to uh +when you graduated grade + + align:start position:0% + + + + align:start position:0% + +school so this question of + + align:start position:0% +school so this question of + + + align:start position:0% +school so this question of +the idea of identity is very very + + align:start position:0% + + + + align:start position:0% + +fuzzy yeah so question sort of reminds + + align:start position:0% +fuzzy yeah so question sort of reminds + + + align:start position:0% +fuzzy yeah so question sort of reminds +me of these peculiar cases of + + align:start position:0% +me of these peculiar cases of + + + align:start position:0% +me of these peculiar cases of +transplantations suddenly having + + align:start position:0% +transplantations suddenly having + + + align:start position:0% +transplantations suddenly having +preferences like the person they got the + + align:start position:0% +preferences like the person they got the + + + align:start position:0% +preferences like the person they got the +transplant from like heart transplants + + align:start position:0% +transplant from like heart transplants + + + align:start position:0% +transplant from like heart transplants +and stuff Som how they they start to + + align:start position:0% +and stuff Som how they they start to + + + align:start position:0% +and stuff Som how they they start to +like same Foods or use the same words + + align:start position:0% +like same Foods or use the same words + + + align:start position:0% +like same Foods or use the same words +things like that the same spouses + + align:start position:0% + + + + align:start position:0% + +I read + + align:start position:0% +I read + + + align:start position:0% +I read +a a science fiction novel by Robert + + align:start position:0% +a a science fiction novel by Robert + + + align:start position:0% +a a science fiction novel by Robert +Sawyer any of you know of him Canadian + + align:start position:0% +Sawyer any of you know of him Canadian + + + align:start position:0% +Sawyer any of you know of him Canadian +writer and + + align:start position:0% + + + + align:start position:0% + +uh it has to do + + align:start position:0% +uh it has to do + + + align:start position:0% +uh it has to do +with somebody who has a fatal + + align:start position:0% +with somebody who has a fatal + + + align:start position:0% +with somebody who has a fatal +disease so he's going to die + + align:start position:0% +disease so he's going to die + + + align:start position:0% +disease so he's going to die +soon but the Technologies around where + + align:start position:0% +soon but the Technologies around where + + + align:start position:0% +soon but the Technologies around where +you can make a duplicate of + + align:start position:0% +you can make a duplicate of + + + align:start position:0% +you can make a duplicate of +him and + + align:start position:0% +him and + + + align:start position:0% +him and +uh so he has a duplicate + + align:start position:0% +uh so he has a duplicate + + + align:start position:0% +uh so he has a duplicate +made + + align:start position:0% +made + + + align:start position:0% +made +and he is sent to the moon for some + + align:start position:0% +and he is sent to the moon for some + + + align:start position:0% +and he is sent to the moon for some +reasons I can't remember which is a kind + + align:start position:0% +reasons I can't remember which is a kind + + + align:start position:0% +reasons I can't remember which is a kind +of a nursing home + + align:start position:0% +of a nursing home + + + align:start position:0% +of a nursing home +for I think people who are enfeebled and + + align:start position:0% +for I think people who are enfeebled and + + + align:start position:0% +for I think people who are enfeebled and +do much better with 17th gravity and so + + align:start position:0% +do much better with 17th gravity and so + + + align:start position:0% +do much better with 17th gravity and so +for some reason reason why anyway the + + align:start position:0% +for some reason reason why anyway the + + + align:start position:0% +for some reason reason why anyway the +the living the original copy is sent to + + align:start position:0% +the living the original copy is sent to + + + align:start position:0% +the living the original copy is sent to +the moon and the substitute takes over + + align:start position:0% +the moon and the substitute takes over + + + align:start position:0% +the moon and the substitute takes over +but + + align:start position:0% +but + + + align:start position:0% +but +then uh our hero is miraculously cured + + align:start position:0% +then uh our hero is miraculously cured + + + align:start position:0% +then uh our hero is miraculously cured +by uh eating the right stem cells or + + align:start position:0% +by uh eating the right stem cells or + + + align:start position:0% +by uh eating the right stem cells or +what I don't + + align:start position:0% +what I don't + + + align:start position:0% +what I don't +remember so now the so he wants to come + + align:start position:0% +remember so now the so he wants to come + + + align:start position:0% +remember so now the so he wants to come +back and the question is who gets the + + align:start position:0% + + + + align:start position:0% + +car + + align:start position:0% + + + + align:start position:0% + +so I can't remember the title of the + + align:start position:0% +so I can't remember the title of the + + + align:start position:0% +so I can't remember the title of the +novel except that it has alien in + + align:start position:0% +novel except that it has alien in + + + align:start position:0% +novel except that it has alien in +it alienable rights is not something + + align:start position:0% +it alienable rights is not something + + + align:start position:0% +it alienable rights is not something +like that but I wrote an article called + + align:start position:0% +like that but I wrote an article called + + + align:start position:0% +like that but I wrote an article called +alienable rights but anyway that's so + + align:start position:0% +alienable rights but anyway that's so + + + align:start position:0% +alienable rights but anyway that's so +are you the same as you were 5 minutes + + align:start position:0% +are you the same as you were 5 minutes + + + align:start position:0% +are you the same as you were 5 minutes +ago or five years ago or whatever and as + + align:start position:0% +ago or five years ago or whatever and as + + + align:start position:0% +ago or five years ago or whatever and as +far as I'm concerned the answer is who + + align:start position:0% + + + + align:start position:0% + +cares it's a sort of silly question + + align:start position:0% +cares it's a sort of silly question + + + align:start position:0% +cares it's a sort of silly question +because no two things are exactly the + + align:start position:0% +because no two things are exactly the + + + align:start position:0% +because no two things are exactly the +same ever + + align:start position:0% +same ever + + + align:start position:0% +same ever +anyway + + align:start position:0% +anyway + + + align:start position:0% +anyway +and but again a lot of these questions + + align:start position:0% +and but again a lot of these questions + + + align:start position:0% +and but again a lot of these questions +which look philosophical are + + align:start position:0% +which look philosophical are + + + align:start position:0% +which look philosophical are +legal so the joke of + + align:start position:0% +legal so the joke of + + + align:start position:0% +legal so the joke of +uh that novel is that who owns the + + align:start position:0% +uh that novel is that who owns the + + + align:start position:0% +uh that novel is that who owns the +car is what + + align:start position:0% +car is what + + + align:start position:0% +car is what +matters to decide who is the real + + align:start position:0% +matters to decide who is the real + + + align:start position:0% +matters to decide who is the real +uh original and who's the + + align:start position:0% +uh original and who's the + + + align:start position:0% +uh original and who's the +copy Frederick pole wrote a similar + + align:start position:0% +copy Frederick pole wrote a similar + + + align:start position:0% +copy Frederick pole wrote a similar +story much longer ago + + align:start position:0% + + + + align:start position:0% + +where people are copied and the copy is + + align:start position:0% +where people are copied and the copy is + + + align:start position:0% +where people are copied and the copy is +sent on a one-way trip to some planet to + + align:start position:0% +sent on a one-way trip to some planet to + + + align:start position:0% +sent on a one-way trip to some planet to +fix a broken reactor and they always die + + align:start position:0% +fix a broken reactor and they always die + + + align:start position:0% +fix a broken reactor and they always die +and you get a million dollars for + + align:start position:0% +and you get a million dollars for + + + align:start position:0% +and you get a million dollars for +providing this copy but one of the + + align:start position:0% +providing this copy but one of the + + + align:start position:0% +providing this copy but one of the +copies survived so it's the same + + align:start position:0% +copies survived so it's the same + + + align:start position:0% +copies survived so it's the same +plot I can't remember + + align:start position:0% +plot I can't remember + + + align:start position:0% +plot I can't remember +that if you're looking for a good + + align:start position:0% +that if you're looking for a good + + + align:start position:0% +that if you're looking for a good +idea if you go to 1950s science fiction + + align:start position:0% +idea if you go to 1950s science fiction + + + align:start position:0% +idea if you go to 1950s science fiction +look for AE van VOD or Frederick Pole + + align:start position:0% +look for AE van VOD or Frederick Pole + + + align:start position:0% +look for AE van VOD or Frederick Pole +or all those wonderful + + align:start position:0% +or all those wonderful + + + align:start position:0% +or all those wonderful +writers that was before it was necessary + + align:start position:0% +writers that was before it was necessary + + + align:start position:0% +writers that was before it was necessary +to descri describe really good + + align:start position:0% +to descri describe really good + + + align:start position:0% +to descri describe really good +characters and science fiction got + + align:start position:0% +characters and science fiction got + + + align:start position:0% +characters and science fiction got +better and better for the literary + + align:start position:0% +better and better for the literary + + + align:start position:0% +better and better for the literary +critics and generally worse and worse + + align:start position:0% +critics and generally worse and worse + + + align:start position:0% +critics and generally worse and worse +for + + align:start position:0% +for + + + align:start position:0% +for +the science fiction + + align:start position:0% + + + + align:start position:0% + +fans do we really have any more + + align:start position:0% +fans do we really have any more + + + align:start position:0% +fans do we really have any more +questions yes so we think age were uh + + align:start position:0% +questions yes so we think age were uh + + + align:start position:0% +questions yes so we think age were uh +sharing information between many people + + align:start position:0% +sharing information between many people + + + align:start position:0% +sharing information between many people +on short amount of time is quite easy + + align:start position:0% +on short amount of time is quite easy + + + align:start position:0% +on short amount of time is quite easy +internet and anything like this do you + + align:start position:0% +internet and anything like this do you + + + align:start position:0% +internet and anything like this do you +think that this will change uh this will + + align:start position:0% +think that this will change uh this will + + + align:start position:0% +think that this will change uh this will +bring up many more ideas do you think + + align:start position:0% +bring up many more ideas do you think + + + align:start position:0% +bring up many more ideas do you think +that this will hinder because before + + align:start position:0% +that this will hinder because before + + + align:start position:0% +that this will hinder because before +before this time + + align:start position:0% +before this time + + + align:start position:0% +before this time +people had like problems with sharing + + align:start position:0% +people had like problems with sharing + + + align:start position:0% +people had like problems with sharing +the information and also now it's much + + align:start position:0% +the information and also now it's much + + + align:start position:0% +the information and also now it's much +easier to have like a large group of + + align:start position:0% +easier to have like a large group of + + + align:start position:0% +easier to have like a large group of +people working on one thing do you think + + align:start position:0% +people working on one thing do you think + + + align:start position:0% +people working on one thing do you think +that this will change the way that we + + align:start position:0% +that this will change the way that we + + + align:start position:0% +that this will change the way that we +think and do you think that this will + + align:start position:0% +think and do you think that this will + + + align:start position:0% +think and do you think that this will +make us better make us it's a tough one + + align:start position:0% +make us better make us it's a tough one + + + align:start position:0% +make us better make us it's a tough one +uh bad things can happen and good things + + align:start position:0% +uh bad things can happen and good things + + + align:start position:0% +uh bad things can happen and good things +can happen + + align:start position:0% + + + + align:start position:0% + +and but that's funny because that + + align:start position:0% +and but that's funny because that + + + align:start position:0% +and but that's funny because that +reminds me again of Science Fiction + + align:start position:0% +reminds me again of Science Fiction + + + align:start position:0% +reminds me again of Science Fiction +because in science fiction many many + + align:start position:0% +because in science fiction many many + + + align:start position:0% +because in science fiction many many +years + + align:start position:0% +years + + + align:start position:0% +years +ago some writers got the idea that there + + align:start position:0% +ago some writers got the idea that there + + + align:start position:0% +ago some writers got the idea that there +would be something like an + + align:start position:0% +would be something like an + + + align:start position:0% +would be something like an +internet and some people realized there + + align:start position:0% +internet and some people realized there + + + align:start position:0% +internet and some people realized there +would be flash + + align:start position:0% +would be flash + + + align:start position:0% +would be flash +crowds and now there our flash + + align:start position:0% +crowds and now there our flash + + + align:start position:0% +crowds and now there our flash +crowds + + align:start position:0% +crowds + + + align:start position:0% +crowds +and I remember even as a kid talking to + + align:start position:0% +and I remember even as a kid talking to + + + align:start position:0% +and I remember even as a kid talking to +people who said why not wire up the + + align:start position:0% +people who said why not wire up the + + + align:start position:0% +people who said why not wire up the +voting machines so that they're always + + align:start position:0% +voting machines so that they're always + + + align:start position:0% +voting machines so that they're always +there and so if the government somebody + + align:start position:0% +there and so if the government somebody + + + align:start position:0% +there and so if the government somebody +in the government wants to know uh + + align:start position:0% +in the government wants to know uh + + + align:start position:0% +in the government wants to know uh +should we do this or that uh should we + + align:start position:0% +should we do this or that uh should we + + + align:start position:0% +should we do this or that uh should we +bomb China or + + align:start position:0% +bomb China or + + + align:start position:0% +bomb China or +not uh you could get a 100 million + + align:start position:0% +not uh you could get a 100 million + + + align:start position:0% +not uh you could get a 100 million +people to run up up to the keyboard and + + align:start position:0% +people to run up up to the keyboard and + + + align:start position:0% +people to run up up to the keyboard and +say yes or no + + align:start position:0% + + + + align:start position:0% + +and presumably when the what do they + + align:start position:0% +and presumably when the what do they + + + align:start position:0% +and presumably when the what do they +call those that great crowd of + + align:start position:0% +call those that great crowd of + + + align:start position:0% +call those that great crowd of +Jeffersons and Franklin and founding + + align:start position:0% +Jeffersons and Franklin and founding + + + align:start position:0% +Jeffersons and Franklin and founding +fathers the founding + + align:start position:0% +fathers the founding + + + align:start position:0% +fathers the founding +fathers did a lot of things to prevent + + align:start position:0% +fathers did a lot of things to prevent + + + align:start position:0% +fathers did a lot of things to prevent +that and the one that they focused + + align:start position:0% +that and the one that they focused + + + align:start position:0% +that and the one that they focused +on which was one of the most effective + + align:start position:0% +on which was one of the most effective + + + align:start position:0% +on which was one of the most effective +was called the electoral + + align:start position:0% +was called the electoral + + + align:start position:0% +was called the electoral +college in the United States is + + align:start position:0% +college in the United States is + + + align:start position:0% +college in the United States is +different from other places because we + + align:start position:0% +different from other places because we + + + align:start position:0% +different from other places because we +don't elect congressmen or + + align:start position:0% +don't elect congressmen or + + + align:start position:0% +don't elect congressmen or +presidents we elect smart people from + + align:start position:0% +presidents we elect smart people from + + + align:start position:0% +presidents we elect smart people from +the community who then get together and + + align:start position:0% +the community who then get together and + + + align:start position:0% +the community who then get together and +decide who should be + + align:start position:0% +decide who should be + + + align:start position:0% +decide who should be +president and of course now if anybody + + align:start position:0% +president and of course now if anybody + + + align:start position:0% +president and of course now if anybody +now they belong to parties and if any of + + align:start position:0% +now they belong to parties and if any of + + + align:start position:0% +now they belong to parties and if any of +them voted for the other Party's + + align:start position:0% +them voted for the other Party's + + + align:start position:0% +them voted for the other Party's +candidate they would be held to pay but + + align:start position:0% +candidate they would be held to pay but + + + align:start position:0% +candidate they would be held to pay but +it was a great idea because the founding + + align:start position:0% +it was a great idea because the founding + + + align:start position:0% +it was a great idea because the founding +fathers realized that if you had instant + + align:start position:0% +fathers realized that if you had instant + + + align:start position:0% +fathers realized that if you had instant +feedback which is what Hitler + + align:start position:0% +feedback which is what Hitler + + + align:start position:0% +feedback which is what Hitler +got uh then you could say something + + align:start position:0% +got uh then you could say something + + + align:start position:0% +got uh then you could say something +really exciting and everybody would + + align:start position:0% +really exciting and everybody would + + + align:start position:0% +really exciting and everybody would +press the yes button and then you kill + + align:start position:0% +press the yes button and then you kill + + + align:start position:0% +press the yes button and then you kill +all the Jews and then uh the next speech + + align:start position:0% +all the Jews and then uh the next speech + + + align:start position:0% +all the Jews and then uh the next speech +you kill all the black people and all + + align:start position:0% +you kill all the black people and all + + + align:start position:0% +you kill all the black people and all +the yellow people and all the people + + align:start position:0% +the yellow people and all the people + + + align:start position:0% +the yellow people and all the people +whose last name doesn't begin with + + align:start position:0% +whose last name doesn't begin with + + + align:start position:0% +whose last name doesn't begin with +m and so uh what you don't want is + + align:start position:0% +m and so uh what you don't want is + + + align:start position:0% +m and so uh what you don't want is +instant feedback now the new Social + + align:start position:0% +instant feedback now the new Social + + + align:start position:0% +instant feedback now the new Social +Network + + align:start position:0% +Network + + + align:start position:0% +Network +are getting us close to that and the + + align:start position:0% +are getting us close to that and the + + + align:start position:0% +are getting us close to that and the +question is is it time to + + align:start position:0% + + + + align:start position:0% + +have is it time to stop that is it + + align:start position:0% +have is it time to stop that is it + + + align:start position:0% +have is it time to stop that is it +getting dangerous I don't know but there + + align:start position:0% +getting dangerous I don't know but there + + + align:start position:0% +getting dangerous I don't know but there +must be a lot of people who are + + align:start position:0% +must be a lot of people who are + + + align:start position:0% +must be a lot of people who are +recognizing that this thing is creeping + + align:start position:0% +recognizing that this thing is creeping + + + align:start position:0% +recognizing that this thing is creeping +up on us and you might be able to get 50 + + align:start position:0% +up on us and you might be able to get 50 + + + align:start position:0% +up on us and you might be able to get 50 +million + + align:start position:0% +million + + + align:start position:0% +million +people to do something reckless in a few + + align:start position:0% +people to do something reckless in a few + + + align:start position:0% +people to do something reckless in a few +minutes if you if you don't uh put put + + align:start position:0% +minutes if you if you don't uh put put + + + align:start position:0% +minutes if you if you don't uh put put +some + + align:start position:0% +some + + + align:start position:0% +some +limits I don't think we could get the + + align:start position:0% +limits I don't think we could get the + + + align:start position:0% +limits I don't think we could get the +Electoral College back + + align:start position:0% +Electoral College back + + + align:start position:0% +Electoral College back +because you'd have to get a majority + + align:start position:0% +because you'd have to get a majority + + + align:start position:0% +because you'd have to get a majority +to what does it take to fix the + + align:start position:0% +to what does it take to fix the + + + align:start position:0% +to what does it take to fix the +Constitution + + align:start position:0% + + + + align:start position:0% + +2third we'll never see 2/3 + + align:start position:0% +2third we'll never see 2/3 + + + align:start position:0% +2third we'll never see 2/3 +again it's the end of + + align:start position:0% + + + + align:start position:0% + +America well we have three minutes + + align:start position:0% + + + + align:start position:0% + +yes if you design a direction for the + + align:start position:0% +yes if you design a direction for the + + + align:start position:0% +yes if you design a direction for the +field of psychology obviously you want + + align:start position:0% +field of psychology obviously you want + + + align:start position:0% +field of psychology obviously you want +more than just set of debugging tools + + align:start position:0% +more than just set of debugging tools + + + align:start position:0% +more than just set of debugging tools +what would you say they should be + + align:start position:0% + + + + align:start position:0% + +doing they should read Patrick Winston's + + align:start position:0% +doing they should read Patrick Winston's + + + align:start position:0% +doing they should read Patrick Winston's +thesis the psychologists now have + + align:start position:0% +thesis the psychologists now have + + + align:start position:0% +thesis the psychologists now have +disappeared into the tarpit of + + align:start position:0% +disappeared into the tarpit of + + + align:start position:0% +disappeared into the tarpit of +statistics + + align:start position:0% +statistics + + + align:start position:0% +statistics +and they don't have the idea that + + align:start position:0% +and they don't have the idea that + + + align:start position:0% +and they don't have the idea that +knowledge needs complicated + + align:start position:0% +knowledge needs complicated + + + align:start position:0% +knowledge needs complicated +representations + + align:start position:0% +representations + + + align:start position:0% +representations +and I don't care whether you assign + + align:start position:0% +and I don't care whether you assign + + + align:start position:0% +and I don't care whether you assign +probabilities to them or put them in the + + align:start position:0% +probabilities to them or put them in the + + + align:start position:0% +probabilities to them or put them in the +order in which you thought of them or + + align:start position:0% +order in which you thought of them or + + + align:start position:0% +order in which you thought of them or +you know or do what doug lennett did in + + align:start position:0% +you know or do what doug lennett did in + + + align:start position:0% +you know or do what doug lennett did in +his thesis of swapping things when one + + align:start position:0% +his thesis of swapping things when one + + + align:start position:0% +his thesis of swapping things when one +worked better than another but but + + align:start position:0% +worked better than another but but + + + align:start position:0% +worked better than another but but +uh I forget the question but I think we + + align:start position:0% +uh I forget the question but I think we + + + align:start position:0% +uh I forget the question but I think we +we've got to get better ideas about + + align:start position:0% +we've got to get better ideas about + + + align:start position:0% +we've got to get better ideas about +representation of knowledge and I don't + + align:start position:0% +representation of knowledge and I don't + + + align:start position:0% +representation of knowledge and I don't +know where they're going to come from + + align:start position:0% +know where they're going to come from + + + align:start position:0% +know where they're going to come from +now that uh the whole uh AI Community is + + align:start position:0% +now that uh the whole uh AI Community is + + + align:start position:0% +now that uh the whole uh AI Community is +drifting into + + align:start position:0% + + + + align:start position:0% + +these ways of avoiding + + align:start position:0% +these ways of avoiding + + + align:start position:0% +these ways of avoiding +representations I haven't read the norig + + align:start position:0% +representations I haven't read the norig + + + align:start position:0% +representations I haven't read the norig +Russell book so does + + align:start position:0% +Russell book so does + + + align:start position:0% +Russell book so does +he can anybody summarize what it says + + align:start position:0% +he can anybody summarize what it says + + + align:start position:0% +he can anybody summarize what it says +about knowledge + + align:start position:0% + + + + align:start position:0% + +representation who's read + + align:start position:0% + + + + align:start position:0% + +it was it there's a chapter on logic + + align:start position:0% +it was it there's a chapter on logic + + + align:start position:0% +it was it there's a chapter on logic +first + + align:start position:0% +first + + + align:start position:0% +first +logic that's so + + align:start position:0% +logic that's so + + + align:start position:0% +logic that's so +funny first order of logic is what new + + align:start position:0% +funny first order of logic is what new + + + align:start position:0% +funny first order of logic is what new +and Simon thought of in + + align:start position:0% +and Simon thought of in + + + align:start position:0% +and Simon thought of in +1956 before they thought + + align:start position:0% +1956 before they thought + + + align:start position:0% +1956 before they thought +of the so-called GPS + + align:start position:0% +of the so-called GPS + + + align:start position:0% +of the so-called GPS +thing + + align:start position:0% +thing + + + align:start position:0% +thing +logic can't make analogies it's a very + + align:start position:0% +logic can't make analogies it's a very + + + align:start position:0% +logic can't make analogies it's a very +bad thing + + align:start position:0% +bad thing + + + align:start position:0% +bad thing +to get stuck + + align:start position:0% +to get stuck + + + align:start position:0% +to get stuck +with zero or + + align:start position:0% + + + + align:start position:0% + +one maybe one of our papers should be on + + align:start position:0% +one maybe one of our papers should be on + + + align:start position:0% +one maybe one of our papers should be on +what should AI do next + + align:start position:0% + + + + align:start position:0% + +year 9 o' thanks for + + align:start position:0% +year 9 o' thanks for + + + align:start position:0% +year 9 o' thanks for +coming \ No newline at end of file diff --git a/6DOpp8zuYDE.txt b/6DOpp8zuYDE.txt new file mode 100644 index 0000000000000000000000000000000000000000..a447731202225a14d9ddc2147ef8db96c904fdbf --- /dev/null +++ b/6DOpp8zuYDE.txt @@ -0,0 +1,20651 @@ +align:start position:0% + +we are very grateful to V and the V + + align:start position:0% +we are very grateful to V and the V + + + align:start position:0% +we are very grateful to V and the V +studio for their inspiring and generous + + align:start position:0% +studio for their inspiring and generous + + + align:start position:0% +studio for their inspiring and generous +Presence at Cs and + + align:start position:0% +Presence at Cs and + + + align:start position:0% +Presence at Cs and +MIT and we are looking forward to the + + align:start position:0% +MIT and we are looking forward to the + + + align:start position:0% +MIT and we are looking forward to the +presentation this + + align:start position:0% +presentation this + + + align:start position:0% +presentation this +season V aoni is one of the most + + align:start position:0% +season V aoni is one of the most + + + align:start position:0% +season V aoni is one of the most +important figures in our architecture + + align:start position:0% +important figures in our architecture + + + align:start position:0% +important figures in our architecture +today from his days as the poet in the + + align:start position:0% +today from his days as the poet in the + + + align:start position:0% +today from his days as the poet in the +early 60s to his sem performance work in + + align:start position:0% +early 60s to his sem performance work in + + + align:start position:0% +early 60s to his sem performance work in +the 70s to the large scale architectural + + align:start position:0% +the 70s to the large scale architectural + + + align:start position:0% +the 70s to the large scale architectural +projects in recent years our country has + + align:start position:0% +projects in recent years our country has + + + align:start position:0% +projects in recent years our country has +pushed from one discipline to the next + + align:start position:0% +pushed from one discipline to the next + + + align:start position:0% +pushed from one discipline to the next +approaching each as a kind of + + align:start position:0% +approaching each as a kind of + + + align:start position:0% +approaching each as a kind of +challenging new + + align:start position:0% +challenging new + + + align:start position:0% +challenging new +vocation this is perhaps uh a unique + + align:start position:0% +vocation this is perhaps uh a unique + + + align:start position:0% +vocation this is perhaps uh a unique +occasion in which V will speak present + + align:start position:0% +occasion in which V will speak present + + + align:start position:0% +occasion in which V will speak present +uh uh the work together with the members + + align:start position:0% +uh uh the work together with the members + + + align:start position:0% +uh uh the work together with the members +of from the + + align:start position:0% +of from the + + + align:start position:0% +of from the +studio in his presentation uh I assume + + align:start position:0% +studio in his presentation uh I assume + + + align:start position:0% +studio in his presentation uh I assume +VTO they tell us among other things this + + align:start position:0% +VTO they tell us among other things this + + + align:start position:0% +VTO they tell us among other things this +story of his poetic philosophical + + align:start position:0% +story of his poetic philosophical + + + align:start position:0% +story of his poetic philosophical +Journey from art in art gallery through + + align:start position:0% +Journey from art in art gallery through + + + align:start position:0% +Journey from art in art gallery through +art in public space to art as + + align:start position:0% +art in public space to art as + + + align:start position:0% +art in public space to art as +architecture fashion and to other fields + + align:start position:0% +architecture fashion and to other fields + + + align:start position:0% +architecture fashion and to other fields +of art of + + align:start position:0% +of art of + + + align:start position:0% +of art of +design the three members of his + + align:start position:0% +design the three members of his + + + align:start position:0% +design the three members of his +seren Bast G ricardi and Lunes will + + align:start position:0% +seren Bast G ricardi and Lunes will + + + align:start position:0% +seren Bast G ricardi and Lunes will +hopefully speak talk about the project + + align:start position:0% +hopefully speak talk about the project + + + align:start position:0% +hopefully speak talk about the project +they have been involved + + align:start position:0% + + + + align:start position:0% + +with uh the Creative Energy of country + + align:start position:0% +with uh the Creative Energy of country + + + align:start position:0% +with uh the Creative Energy of country +studio is driven by an open process that + + align:start position:0% +studio is driven by an open process that + + + align:start position:0% +studio is driven by an open process that +inspires the evolution from one person's + + align:start position:0% +inspires the evolution from one person's + + + align:start position:0% +inspires the evolution from one person's +project and one person's interest to + + align:start position:0% +project and one person's interest to + + + align:start position:0% +project and one person's interest to +many from many into many more this is + + align:start position:0% +many from many into many more this is + + + align:start position:0% +many from many into many more this is +one among many methodological artistic + + align:start position:0% +one among many methodological artistic + + + align:start position:0% +one among many methodological artistic +reasons for our interest and joy in + + align:start position:0% +reasons for our interest and joy in + + + align:start position:0% +reasons for our interest and joy in +hosting V + + align:start position:0% +hosting V + + + align:start position:0% +hosting V +studio in correspondence with Mark + + align:start position:0% +studio in correspondence with Mark + + + align:start position:0% +studio in correspondence with Mark +Taylor uh VTO AI + + align:start position:0% +Taylor uh VTO AI + + + align:start position:0% +Taylor uh VTO AI +wrote Because art is + + align:start position:0% +wrote Because art is + + + align:start position:0% +wrote Because art is +desperate it needs to separate itself + + align:start position:0% +desperate it needs to separate itself + + + align:start position:0% +desperate it needs to separate itself +from all other things that are nonactive + + align:start position:0% +from all other things that are nonactive + + + align:start position:0% +from all other things that are nonactive +it can't survive without a frame or a + + align:start position:0% +it can't survive without a frame or a + + + align:start position:0% +it can't survive without a frame or a +pedestal or a v or a wall or a floor or + + align:start position:0% +pedestal or a v or a wall or a floor or + + + align:start position:0% +pedestal or a v or a wall or a floor or +a room or a label or a + + align:start position:0% +a room or a label or a + + + align:start position:0% +a room or a label or a +plaque architecture is + + align:start position:0% +plaque architecture is + + + align:start position:0% +plaque architecture is +different architecture survives by + + align:start position:0% +different architecture survives by + + + align:start position:0% +different architecture survives by +breaking the frame or more precisely by + + align:start position:0% +breaking the frame or more precisely by + + + align:start position:0% +breaking the frame or more precisely by +melting theame architecture persists + + align:start position:0% +melting theame architecture persists + + + align:start position:0% +melting theame architecture persists +when clothing elapses into furniture and + + align:start position:0% +when clothing elapses into furniture and + + + align:start position:0% +when clothing elapses into furniture and +furniture furniture elapses into house + + align:start position:0% +furniture furniture elapses into house + + + align:start position:0% +furniture furniture elapses into house +and house elapses into City and City + + align:start position:0% +and house elapses into City and City + + + align:start position:0% +and house elapses into City and City +elapses + + align:start position:0% +elapses + + + align:start position:0% +elapses +into this + + align:start position:0% +into this + + + align:start position:0% +into this +thinking is yet another reason why we're + + align:start position:0% +thinking is yet another reason why we're + + + align:start position:0% +thinking is yet another reason why we're +very happy to see all of you + + align:start position:0% + + + + align:start position:0% + +here the studio intelligent sensitive + + align:start position:0% +here the studio intelligent sensitive + + + align:start position:0% +here the studio intelligent sensitive +and imaginative life perceptive and + + align:start position:0% +and imaginative life perceptive and + + + align:start position:0% +and imaginative life perceptive and +generous to each place the work they + + align:start position:0% +generous to each place the work they + + + align:start position:0% +generous to each place the work they +work with is pointing to + + align:start position:0% +work with is pointing to + + + align:start position:0% +work with is pointing to +us whether we are artists Architects or + + align:start position:0% +us whether we are artists Architects or + + + align:start position:0% +us whether we are artists Architects or +planers what it is to see whom it is to + + align:start position:0% +planers what it is to see whom it is to + + + align:start position:0% +planers what it is to see whom it is to +meet and from whom it is to learn in our + + align:start position:0% +meet and from whom it is to learn in our + + + align:start position:0% +meet and from whom it is to learn in our +Institute as in their own public arts + + align:start position:0% +Institute as in their own public arts + + + align:start position:0% +Institute as in their own public arts +and architecture their entry to + + align:start position:0% +and architecture their entry to + + + align:start position:0% +and architecture their entry to +seemingly familiar place makes this + + align:start position:0% +seemingly familiar place makes this + + + align:start position:0% +seemingly familiar place makes this +place feel unfamiliar and pregnant with + + align:start position:0% +place feel unfamiliar and pregnant with + + + align:start position:0% +place feel unfamiliar and pregnant with +new created + + align:start position:0% +new created + + + align:start position:0% +new created +cultural and existential + + align:start position:0% +cultural and existential + + + align:start position:0% +cultural and existential +potential during their presence the + + align:start position:0% +potential during their presence the + + + align:start position:0% +potential during their presence the +country studio will be meeting and + + align:start position:0% +country studio will be meeting and + + + align:start position:0% +country studio will be meeting and +establishing preliminary work in TI with + + align:start position:0% +establishing preliminary work in TI with + + + align:start position:0% +establishing preliminary work in TI with +fellows graduate graduate students and + + align:start position:0% +fellows graduate graduate students and + + + align:start position:0% +fellows graduate graduate students and +Europe students faculty students of our + + align:start position:0% +Europe students faculty students of our + + + align:start position:0% +Europe students faculty students of our +uh Center for Advance visual studies and + + align:start position:0% +uh Center for Advance visual studies and + + + align:start position:0% +uh Center for Advance visual studies and +visual arts program the program Islamic + + align:start position:0% +visual arts program the program Islamic + + + align:start position:0% +visual arts program the program Islamic +architecture students and faculty from + + align:start position:0% +architecture students and faculty from + + + align:start position:0% +architecture students and faculty from +other department + + align:start position:0% +other department + + + align:start position:0% +other department +and programs in school of art and + + align:start position:0% +and programs in school of art and + + + align:start position:0% +and programs in school of art and +architecture the two day meeting agenda + + align:start position:0% +architecture the two day meeting agenda + + + align:start position:0% +architecture the two day meeting agenda +is incredible it's actually is similar + + align:start position:0% +is incredible it's actually is similar + + + align:start position:0% +is incredible it's actually is similar +some ways to the agenda of students and + + align:start position:0% +some ways to the agenda of students and + + + align:start position:0% +some ways to the agenda of students and +faculty and my but when I read this uh + + align:start position:0% +faculty and my but when I read this uh + + + align:start position:0% +faculty and my but when I read this uh +it still impresses me they will be uh + + align:start position:0% +it still impresses me they will be uh + + + align:start position:0% +it still impresses me they will be uh +speaking and uh + + align:start position:0% +speaking and uh + + + align:start position:0% +speaking and uh +discussing uh their interest and their + + align:start position:0% +discussing uh their interest and their + + + align:start position:0% +discussing uh their interest and their +ideas with Department of electrical + + align:start position:0% +ideas with Department of electrical + + + align:start position:0% +ideas with Department of electrical +engineering and computer science + + align:start position:0% +engineering and computer science + + + align:start position:0% +engineering and computer science +computer science and artificial + + align:start position:0% +computer science and artificial + + + align:start position:0% +computer science and artificial +intelligence lab including robotic lab + + align:start position:0% +intelligence lab including robotic lab + + + align:start position:0% +intelligence lab including robotic lab +department of Material Science and + + align:start position:0% +department of Material Science and + + + align:start position:0% +department of Material Science and +Engineering a microtonic center + + align:start position:0% +Engineering a microtonic center + + + align:start position:0% +Engineering a microtonic center +Department of mechanical engineering + + align:start position:0% +Department of mechanical engineering + + + align:start position:0% +Department of mechanical engineering +short R weaving room + + align:start position:0% +short R weaving room + + + align:start position:0% +short R weaving room +section and the ambient intelligence + + align:start position:0% +section and the ambient intelligence + + + align:start position:0% +section and the ambient intelligence +group we have beautiful names here for + + align:start position:0% +group we have beautiful names here for + + + align:start position:0% +group we have beautiful names here for +various programs + + align:start position:0% +various programs + + + align:start position:0% +various programs +research groups the human dynamics group + + align:start position:0% +research groups the human dynamics group + + + align:start position:0% +research groups the human dynamics group +The Computing culture group of the + + align:start position:0% + + + + align:start position:0% + +media what at CS called our + + align:start position:0% +media what at CS called our + + + align:start position:0% +media what at CS called our +H is that uh with the continued support + + align:start position:0% +H is that uh with the continued support + + + align:start position:0% +H is that uh with the continued support +of the School of Architecture planning + + align:start position:0% +of the School of Architecture planning + + + align:start position:0% +of the School of Architecture planning +MIT counil Council for the Arts who help + + align:start position:0% +MIT counil Council for the Arts who help + + + align:start position:0% +MIT counil Council for the Arts who help +with + + align:start position:0% +with + + + align:start position:0% +with +bringing Studio here the media + + align:start position:0% +bringing Studio here the media + + + align:start position:0% +bringing Studio here the media +uh and others the studio will come back + + align:start position:0% +uh and others the studio will come back + + + align:start position:0% +uh and others the studio will come back +and continue uh their work with our + + align:start position:0% +and continue uh their work with our + + + align:start position:0% +and continue uh their work with our +students faulty + + align:start position:0% +students faulty + + + align:start position:0% +students faulty +researchers in our programs laboratory + + align:start position:0% +researchers in our programs laboratory + + + align:start position:0% +researchers in our programs laboratory +research groups at MIT here at MIT there + + align:start position:0% +research groups at MIT here at MIT there + + + align:start position:0% +research groups at MIT here at MIT there +are materials processes techniques and + + align:start position:0% +are materials processes techniques and + + + align:start position:0% +are materials processes techniques and +what is most precious people with their + + align:start position:0% +what is most precious people with their + + + align:start position:0% +what is most precious people with their +new ideas skills and knowledge here + + align:start position:0% +new ideas skills and knowledge here + + + align:start position:0% +new ideas skills and knowledge here +there are those with whom young + + align:start position:0% +there are those with whom young + + + align:start position:0% +there are those with whom young +Architects designers and artists my to + + align:start position:0% +Architects designers and artists my to + + + align:start position:0% +Architects designers and artists my to +work together with whose Knowledge and + + align:start position:0% +work together with whose Knowledge and + + + align:start position:0% +work together with whose Knowledge and +Skills they might wish to become + + align:start position:0% +Skills they might wish to become + + + align:start position:0% +Skills they might wish to become +familiar this + + align:start position:0% +familiar this + + + align:start position:0% +familiar this +is the way to which an informed artistic + + align:start position:0% +is the way to which an informed 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your excellent work work in Art + + align:start position:0% +work uh your excellent work work in Art + + + align:start position:0% +work uh your excellent work work in Art +and Design VTO Serena gett + + align:start position:0% +and Design VTO Serena gett + + + align:start position:0% +and Design VTO Serena gett +andar as well as your open generous and + + align:start position:0% +andar as well as your open generous and + + + align:start position:0% +andar as well as your open generous and +generative approach to creative process + + align:start position:0% +generative approach to creative process + + + align:start position:0% +generative approach to creative process +is helping us enormously in this + + align:start position:0% +is helping us enormously in this + + + align:start position:0% +is helping us enormously in this +agenda we would like to thank you for + + align:start position:0% +agenda we would like to thank you for + + + align:start position:0% +agenda we would like to thank you for +being here for sharing your work and for + + align:start position:0% +being here for sharing your work and for + + + align:start position:0% +being here for sharing your work and for +your interest in working + + align:start position:0% +your interest in working + + + align:start position:0% +your interest in working +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +welcome + + align:start position:0% + + + + align:start position:0% + +all the occasions of everyday of + + align:start position:0% +all the occasions of everyday of + + + align:start position:0% +all the occasions of everyday of +everyday of everyday of everyday life uh + + align:start position:0% +everyday of everyday of everyday life uh + + + align:start position:0% +everyday of everyday of everyday life uh +the studio works you know the way the + + align:start position:0% +the studio works you know the way the + + + align:start position:0% +the studio works you know the way the +studio doesn't work is uh I start a + + align:start position:0% +studio doesn't work is uh I start a + + + align:start position:0% +studio doesn't work is uh I start a +project I I uh I have an idea for a + + align:start position:0% +project I I uh I have an idea for a + + + align:start position:0% +project I I uh I have an idea for a +project + + align:start position:0% +project + + + align:start position:0% +project +and + + align:start position:0% + + + + align:start position:0% + +oh + + align:start position:0% +oh + + + align:start position:0% +oh +I + + align:start position:0% + + + + align:start position:0% + +maybe just try a little louder for you + + align:start position:0% +maybe just try a little louder for you + + + align:start position:0% +maybe just try a little louder for you +have a mic yeah I have a + + align:start position:0% + + + + align:start position:0% + +mic is it + + align:start position:0% +mic is it + + + align:start position:0% +mic is it +on doesn't seem to I don't + + align:start position:0% + + + + align:start position:0% + +know just speak louder for really if I + + align:start position:0% +know just speak louder for really if I + + + align:start position:0% +know just speak louder for really if I +talk if I speak louder does that help no + + align:start position:0% + + + + align:start position:0% + +I think we should sh uh is there a + + align:start position:0% +I think we should sh uh is there a + + + align:start position:0% +I think we should sh uh is there a +particular light that's supposed to be + + align:start position:0% +particular light that's supposed to be + + + align:start position:0% +particular light that's supposed to be +on here because it's + + align:start position:0% + + + + align:start position:0% + +not oh okay that's + + align:start position:0% +not oh okay that's + + + align:start position:0% +not oh okay that's +it + + align:start position:0% +it + + + align:start position:0% +it +okay that again I I I didn't hear only + + align:start position:0% +okay that again I I I didn't hear only + + + align:start position:0% +okay that again I I I didn't hear only +going to the camera can we just get + + align:start position:0% +going to the camera can we just get + + + align:start position:0% +going to the camera can we just get +closer okay so so in other words we + + align:start position:0% +closer okay so so in other words we + + + align:start position:0% +closer okay so so in other words we +don't have a mic for this room no okay I + + align:start position:0% +don't have a mic for this room no okay I + + + align:start position:0% +don't have a mic for this room no okay I +I somehow assumed this was the mic uh + + align:start position:0% +I somehow assumed this was the mic uh + + + align:start position:0% +I somehow assumed this was the mic uh +sorry + + align:start position:0% +sorry + + + align:start position:0% +sorry +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh the way the studio doesn't work is I + + align:start position:0% +uh the way the studio doesn't work is I + + + align:start position:0% +uh the way the studio doesn't work is I +have an idea for a project everybody + + align:start position:0% +have an idea for a project everybody + + + align:start position:0% +have an idea for a project everybody +else carries it out the way the studio + + align:start position:0% +else carries it out the way the studio + + + align:start position:0% +else carries it out the way the studio +maybe it'll work better if I stand uh + + align:start position:0% +maybe it'll work better if I stand uh + + + align:start position:0% +maybe it'll work better if I stand uh +the way the studio does work is maybe I + + align:start position:0% +the way the studio does work is maybe I + + + align:start position:0% +the way the studio does work is maybe I +start a project off not always but maybe + + align:start position:0% +start a project off not always but maybe + + + align:start position:0% +start a project off not always but maybe +I start a project off uh with a general + + align:start position:0% +I start a project off uh with a general + + + align:start position:0% +I start a project off uh with a general +method a kind of general idea then we + + align:start position:0% +method a kind of general idea then we + + + align:start position:0% +method a kind of general idea then we +talk a lot we argue a lot we disc + + align:start position:0% +talk a lot we argue a lot we disc + + + align:start position:0% +talk a lot we argue a lot we disc +discuss we argue we uh uh we whatever + + align:start position:0% +discuss we argue we uh uh we whatever + + + align:start position:0% +discuss we argue we uh uh we whatever +that project started from becomes a very + + align:start position:0% +that project started from becomes a very + + + align:start position:0% +that project started from becomes a very +different thing once we work once we + + align:start position:0% +different thing once we work once we + + + align:start position:0% +different thing once we work once we +work on it together uh obviously the the + + align:start position:0% +work on it together uh obviously the the + + + align:start position:0% +work on it together uh obviously the the +work oops the work didn't start as as as + + align:start position:0% +work oops the work didn't start as as as + + + align:start position:0% +work oops the work didn't start as as as +design and I want to give a quick survey + + align:start position:0% +design and I want to give a quick survey + + + align:start position:0% +design and I want to give a quick survey +of how how work how worked got of design + + align:start position:0% +of how how work how worked got of design + + + align:start position:0% +of how how work how worked got of design +uh my uh yeah I should talk about + + align:start position:0% +uh my uh yeah I should talk about + + + align:start position:0% +uh my uh yeah I should talk about +backgrounds of people uh uh Dario Dario + + align:start position:0% +backgrounds of people uh uh Dario Dario + + + align:start position:0% +backgrounds of people uh uh Dario Dario +Dario is an architect Serena is Serena + + align:start position:0% +Dario is an architect Serena is Serena + + + align:start position:0% +Dario is an architect Serena is Serena +is from an art an art + + align:start position:0% +is from an art an art + + + align:start position:0% +is from an art an art +background uh a background a background + + align:start position:0% +background uh a background a background + + + align:start position:0% +background uh a background a background +a background of uh of uh being an art an + + align:start position:0% +a background of uh of uh being an art an + + + align:start position:0% +a background of uh of uh being an art an +art an art curator kind of interestingly + + align:start position:0% +art an art curator kind of interestingly + + + align:start position:0% +art an art curator kind of interestingly +and I I I find significantly that uh + + align:start position:0% +and I I I find significantly that uh + + + align:start position:0% +and I I I find significantly that uh +design starts to I think infect + + align:start position:0% +design starts to I think infect + + + align:start position:0% +design starts to I think infect +everybody who's in the studio and I + + align:start position:0% +everybody who's in the studio and I + + + align:start position:0% +everybody who's in the studio and I +think Serena has probably always been a + + align:start position:0% +think Serena has probably always been a + + + align:start position:0% +think Serena has probably always been a +des designer but maybe didn't realize it + + align:start position:0% +des designer but maybe didn't realize it + + + align:start position:0% +des designer but maybe didn't realize it +enough until we started working we + + align:start position:0% +enough until we started working we + + + align:start position:0% +enough until we started working we +started working to working together at + + align:start position:0% +started working to working together at + + + align:start position:0% +started working to working together at +the studio uh my work came my work + + align:start position:0% +the studio uh my work came my work + + + align:start position:0% +the studio uh my work came my work +started not as not as architecture not + + align:start position:0% +started not as not as architecture not + + + align:start position:0% +started not as not as architecture not +as art but as but as writing until 1968 + + align:start position:0% +as art but as but as writing until 1968 + + + align:start position:0% +as art but as but as writing until 1968 +stuff appeared in a context of writing + + align:start position:0% +stuff appeared in a context of writing + + + align:start position:0% +stuff appeared in a context of writing +context of poetry so stuff of mine did + + align:start position:0% +context of poetry so stuff of mine did + + + align:start position:0% +context of poetry so stuff of mine did +begin with space but it began with a + + align:start position:0% +begin with space but it began with a + + + align:start position:0% +begin with space but it began with a +space of a space of a space of a page uh + + align:start position:0% +space of a space of a space of a page uh + + + align:start position:0% +space of a space of a space of a page uh +I was concerned with question questions + + align:start position:0% +I was concerned with question questions + + + align:start position:0% +I was concerned with question questions +like uh what makes you move from left + + align:start position:0% +like uh what makes you move from left + + + align:start position:0% +like uh what makes you move from left +margin to the page to right margin what + + align:start position:0% +margin to the page to right margin what + + + align:start position:0% +margin to the page to right margin what +makes you turn from one page to the next + + align:start position:0% +makes you turn from one page to the next + + + align:start position:0% +makes you turn from one page to the next +page next page + + align:start position:0% +page next page + + + align:start position:0% +page next page +Etc I felt towards the end of the time I + + align:start position:0% +Etc I felt towards the end of the time I + + + align:start position:0% +Etc I felt towards the end of the time I +was writing that I couldn't use on the + + align:start position:0% +was writing that I couldn't use on the + + + align:start position:0% +was writing that I couldn't use on the +page a word like tree a word like chair + + align:start position:0% +page a word like tree a word like chair + + + align:start position:0% +page a word like tree a word like chair +because this referred to another space a + + align:start position:0% +because this referred to another space a + + + align:start position:0% +because this referred to another space a +space off the page whereas I could use + + align:start position:0% +space off the page whereas I could use + + + align:start position:0% +space off the page whereas I could use +on the page words like there then at + + align:start position:0% +on the page words like there then at + + + align:start position:0% +on the page words like there then at +that time in that place in other words + + align:start position:0% +that time in that place in other words + + + align:start position:0% +that time in that place in other words +words that directly referred to my + + align:start position:0% +words that directly referred to my + + + align:start position:0% +words that directly referred to my +activity of writing on the page your + + align:start position:0% +activity of writing on the page your + + + align:start position:0% +activity of writing on the page your +your activity of reading the page uh + + align:start position:0% +your activity of reading the page uh + + + align:start position:0% +your activity of reading the page uh +gradually something very obvious became + + align:start position:0% +gradually something very obvious became + + + align:start position:0% +gradually something very obvious became +clear to me that if I was so interested + + align:start position:0% +clear to me that if I was so interested + + + align:start position:0% +clear to me that if I was so interested +in movement if I was so interested in + + align:start position:0% +in movement if I was so interested in + + + align:start position:0% +in movement if I was so interested in +travel why limit that movement to an 8 + + align:start position:0% +travel why limit that movement to an 8 + + + align:start position:0% +travel why limit that movement to an 8 +and a half by 11 by 11 piece of paper + + align:start position:0% +and a half by 11 by 11 piece of paper + + + align:start position:0% +and a half by 11 by 11 piece of paper +there's a floor out there there's a + + align:start position:0% +there's a floor out there there's a + + + align:start position:0% +there's a floor out there there's a +ground out there there's a street + + align:start position:0% +ground out there there's a street + + + align:start position:0% +ground out there there's a street +there's a city so stuff stuff changed in + + align:start position:0% +there's a city so stuff stuff changed in + + + align:start position:0% +there's a city so stuff stuff changed in +1969 changed context from writing + + align:start position:0% +1969 changed context from writing + + + align:start position:0% +1969 changed context from writing +context to from writing context to an + + align:start position:0% +context to from writing context to an + + + align:start position:0% +context to from writing context to an +art context why an art context because + + align:start position:0% +art context why an art context because + + + align:start position:0% +art context why an art context because +at that time uh I think what interested + + align:start position:0% +at that time uh I think what interested + + + align:start position:0% +at that time uh I think what interested +what interested a lot of us in art was + + align:start position:0% +what interested a lot of us in art was + + + align:start position:0% +what interested a lot of us in art was +that art seemed to be a non-field field + + align:start position:0% +that art seemed to be a non-field field + + + align:start position:0% +that art seemed to be a non-field field +art was a field that didn't have any + + align:start position:0% +art was a field that didn't have any + + + align:start position:0% +art was a field that didn't have any +specific characteristics of its own + + align:start position:0% +specific characteristics of its own + + + align:start position:0% +specific characteristics of its own +except for the fact that it was called + + align:start position:0% +except for the fact that it was called + + + align:start position:0% +except for the fact that it was called +Art so art was a field into which you + + align:start position:0% +Art so art was a field into which you + + + align:start position:0% +Art so art was a field into which you +could import from other fields you could + + align:start position:0% +could import from other fields you could + + + align:start position:0% +could import from other fields you could +import from Psychology from sociology + + align:start position:0% +import from Psychology from sociology + + + align:start position:0% +import from Psychology from sociology +from from history from news when I + + align:start position:0% +from from history from news when I + + + align:start position:0% +from from history from news when I +started doing stuff in an art context + + align:start position:0% +started doing stuff in an art context + + + align:start position:0% +started doing stuff in an art context +the my starting point was that all my + + align:start position:0% +the my starting point was that all my + + + align:start position:0% +the my starting point was that all my +life up until that time I had been used + + align:start position:0% +life up until that time I had been used + + + align:start position:0% +life up until that time I had been used +to thinking that I knew what my ground + + align:start position:0% +to thinking that I knew what my ground + + + align:start position:0% +to thinking that I knew what my ground +was my ground was this piece of paper in + + align:start position:0% +was my ground was this piece of paper in + + + align:start position:0% +was my ground was this piece of paper in +front of me now I didn't have that + + align:start position:0% +front of me now I didn't have that + + + align:start position:0% +front of me now I didn't have that +ground anymore uh so now that I didn't + + align:start position:0% +ground anymore uh so now that I didn't + + + align:start position:0% +ground anymore uh so now that I didn't +have that ground what gives me a reason + + align:start position:0% +have that ground what gives me a reason + + + align:start position:0% +have that ground what gives me a reason +what gives me now that I'm in real space + + align:start position:0% +what gives me now that I'm in real space + + + align:start position:0% +what gives me now that I'm in real space +instead of on a piece of paper what + + align:start position:0% +instead of on a piece of paper what + + + align:start position:0% +instead of on a piece of paper what +gives me a reason to be there what gives + + align:start position:0% +gives me a reason to be there what gives + + + align:start position:0% +gives me a reason to be there what gives +me a reason what gives me a reason to + + align:start position:0% +me a reason what gives me a reason to + + + align:start position:0% +me a reason what gives me a reason to +move one exam one example of early stuff + + align:start position:0% +move one exam one example of early stuff + + + align:start position:0% +move one exam one example of early stuff +a piece called following piece done in + + align:start position:0% +a piece called following piece done in + + + align:start position:0% +a piece called following piece done in +1969 done for a program called Street + + align:start position:0% +1969 done for a program called Street + + + align:start position:0% +1969 done for a program called Street +Works in which a number of people were + + align:start position:0% +Works in which a number of people were + + + align:start position:0% +Works in which a number of people were +asked to do a piece over the period of a + + align:start position:0% +asked to do a piece over the period of a + + + align:start position:0% +asked to do a piece over the period of a +month a piece involving the street + + align:start position:0% +month a piece involving the street + + + align:start position:0% +month a piece involving the street +specifically New York streets the piece + + align:start position:0% +specifically New York streets the piece + + + align:start position:0% +specifically New York streets the piece +I did involved a very simple scheme each + + align:start position:0% +I did involved a very simple scheme each + + + align:start position:0% +I did involved a very simple scheme each +day for the month I would pick out at + + align:start position:0% +day for the month I would pick out at + + + align:start position:0% +day for the month I would pick out at +random a person a person walking a + + align:start position:0% +random a person a person walking a + + + align:start position:0% +random a person a person walking a +person in the street each day then I + + align:start position:0% +person in the street each day then I + + + align:start position:0% +person in the street each day then I +would each day then I would follow a + + align:start position:0% +would each day then I would follow a + + + align:start position:0% +would each day then I would follow a +person follow a person each day until + + align:start position:0% +person follow a person each day until + + + align:start position:0% +person follow a person each day until +that person entered a private place home + + align:start position:0% +that person entered a private place home + + + align:start position:0% +that person entered a private place home +office whatever so from page of the + + align:start position:0% +office whatever so from page of the + + + align:start position:0% +office whatever so from page of the +space I went to Street space uh the way + + align:start position:0% +space I went to Street space uh the way + + + align:start position:0% +space I went to Street space uh the way +I was thinking of pieces at that time I + + align:start position:0% +I was thinking of pieces at that time I + + + align:start position:0% +I was thinking of pieces at that time I +was I I think the terms I had was + + align:start position:0% +was I I think the terms I had was + + + align:start position:0% +was I I think the terms I had was +something like I a person an agent + + align:start position:0% +something like I a person an agent + + + align:start position:0% +something like I a person an agent +attend to it a world considered as if + + align:start position:0% +attend to it a world considered as if + + + align:start position:0% +attend to it a world considered as if +it's out there how do I key myself into + + align:start position:0% +it's out there how do I key myself into + + + align:start position:0% +it's out there how do I key myself into +that world how do I tie myself into that + + align:start position:0% +that world how do I tie myself into that + + + align:start position:0% +that world how do I tie myself into that +world gradually it became clear to me + + align:start position:0% +world gradually it became clear to me + + + align:start position:0% +world gradually it became clear to me +that maybe I was cheating I'm using my + + align:start position:0% +that maybe I was cheating I'm using my + + + align:start position:0% +that maybe I was cheating I'm using my +own person in pieces but I'm not making + + align:start position:0% +own person in pieces but I'm not making + + + align:start position:0% +own person in pieces but I'm not making +use of the person of my person I'm using + + align:start position:0% +use of the person of my person I'm using + + + align:start position:0% +use of the person of my person I'm using +my person as a kind of uh moving integer + + align:start position:0% +my person as a kind of uh moving integer + + + align:start position:0% +my person as a kind of uh moving integer +that's at the service of this external + + align:start position:0% +that's at the service of this external + + + align:start position:0% +that's at the service of this external +scheme so stuff started started to + + align:start position:0% +scheme so stuff started started to + + + align:start position:0% +scheme so stuff started started to +change in + + align:start position:0% +change in + + + align:start position:0% +change in +1970 um uh uh rather than focus on it a + + align:start position:0% +1970 um uh uh rather than focus on it a + + + align:start position:0% +1970 um uh uh rather than focus on it a +world considered as if it's out there I + + align:start position:0% +world considered as if it's out there I + + + align:start position:0% +world considered as if it's out there I +start to focus on me uh uh so the space + + align:start position:0% +start to focus on me uh uh so the space + + + align:start position:0% +start to focus on me uh uh so the space +again changed from page space to Street + + align:start position:0% +again changed from page space to Street + + + align:start position:0% +again changed from page space to Street +space to space of space of space of the + + align:start position:0% +space to space of space of space of the + + + align:start position:0% +space to space of space of space of the +body uh a piece called trademarks biting + + align:start position:0% +body uh a piece called trademarks biting + + + align:start position:0% +body uh a piece called trademarks biting +myself biting as much of my body as I + + align:start position:0% +myself biting as much of my body as I + + + align:start position:0% +myself biting as much of my body as I +could + + align:start position:0% +could + + + align:start position:0% +could +reach uh once I had bite mark once I had + + align:start position:0% +reach uh once I had bite mark once I had + + + align:start position:0% +reach uh once I had bite mark once I had +a bite mark I could apply print ink to + + align:start position:0% +a bite mark I could apply print ink to + + + align:start position:0% +a bite mark I could apply print ink to +the bite mark and make bite prints the + + align:start position:0% +the bite mark and make bite prints the + + + align:start position:0% +the bite mark and make bite prints the +way you normally make finger + + align:start position:0% +way you normally make finger + + + align:start position:0% +way you normally make finger +fingerprints + + align:start position:0% +fingerprints + + + align:start position:0% +fingerprints +uh uh after doing pieces like this for a + + align:start position:0% +uh uh after doing pieces like this for a + + + align:start position:0% +uh uh after doing pieces like this for a +while and what interested me at first in + + align:start position:0% +while and what interested me at first in + + + align:start position:0% +while and what interested me at first in +these pieces was that I thought of + + align:start position:0% +these pieces was that I thought of + + + align:start position:0% +these pieces was that I thought of +themselves I thought of them as a kind + + align:start position:0% +themselves I thought of them as a kind + + + align:start position:0% +themselves I thought of them as a kind +of + + align:start position:0% +of + + + align:start position:0% +of +self-reliance I had only myself to work + + align:start position:0% +self-reliance I had only myself to work + + + align:start position:0% +self-reliance I had only myself to work +on to work with I didn't need I didn't + + align:start position:0% +on to work with I didn't need I didn't + + + align:start position:0% +on to work with I didn't need I didn't +need I didn't need anything else after a + + align:start position:0% +need I didn't need anything else after a + + + align:start position:0% +need I didn't need anything else after a +while what I started thinking what I + + align:start position:0% +while what I started thinking what I + + + align:start position:0% +while what I started thinking what I +thought what I started by thinking as + + align:start position:0% +thought what I started by thinking as + + + align:start position:0% +thought what I started by thinking as +self-reliance I started to think is + + align:start position:0% +self-reliance I started to think is + + + align:start position:0% +self-reliance I started to think is +probably a kind of isolation + + align:start position:0% +probably a kind of isolation + + + align:start position:0% +probably a kind of isolation +self-isolation so I had to bring other + + align:start position:0% +self-isolation so I had to bring other + + + align:start position:0% +self-isolation so I had to bring other +people into the piece into pieces more + + align:start position:0% +people into the piece into pieces more + + + align:start position:0% +people into the piece into pieces more +specifically I had to bring you the + + align:start position:0% +specifically I had to bring you the + + + align:start position:0% +specifically I had to bring you the +viewer in so the piece so that again the + + align:start position:0% +viewer in so the piece so that again the + + + align:start position:0% +viewer in so the piece so that again the +kind of space changed not the space of + + align:start position:0% +kind of space changed not the space of + + + align:start position:0% +kind of space changed not the space of +the self not the space of the body but a + + align:start position:0% +the self not the space of the body but a + + + align:start position:0% +the self not the space of the body but a +kind of relation space inter relation + + align:start position:0% +kind of relation space inter relation + + + align:start position:0% +kind of relation space inter relation +relationship space one example a 1972 + + align:start position:0% +relationship space one example a 1972 + + + align:start position:0% +relationship space one example a 1972 +piece called seeded conventional Gallery + + align:start position:0% +piece called seeded conventional Gallery + + + align:start position:0% +piece called seeded conventional Gallery +room about 25 ft wide uh about 45 ft + + align:start position:0% +room about 25 ft wide uh about 45 ft + + + align:start position:0% +room about 25 ft wide uh about 45 ft +long halfway halfway across the room the + + align:start position:0% +long halfway halfway across the room the + + + align:start position:0% +long halfway halfway across the room the +floor becomes a ramp the floor Rises to + + align:start position:0% +floor becomes a ramp the floor Rises to + + + align:start position:0% +floor becomes a ramp the floor Rises to +a height to a height of about 3 feet at + + align:start position:0% +a height to a height of about 3 feet at + + + align:start position:0% +a height to a height of about 3 feet at +the at the far wall + + align:start position:0% +the at the far wall + + + align:start position:0% +the at the far wall +uh uh the piece is done for a number of + + align:start position:0% +uh uh the piece is done for a number of + + + align:start position:0% +uh uh the piece is done for a number of +days over over a a a two week two week + + align:start position:0% +days over over a a a two week two week + + + align:start position:0% +days over over a a a two week two week +two week period the ramp is a a + + align:start position:0% +two week period the ramp is a a + + + align:start position:0% +two week period the ramp is a a +continuation of the floor person enters + + align:start position:0% +continuation of the floor person enters + + + align:start position:0% +continuation of the floor person enters +the gallery probably without thinking + + align:start position:0% +the gallery probably without thinking + + + align:start position:0% +the gallery probably without thinking +about it too much walks up the ramp as a + + align:start position:0% +about it too much walks up the ramp as a + + + align:start position:0% +about it too much walks up the ramp as a +continuation of the floor uh for the8 + + align:start position:0% +continuation of the floor uh for the8 + + + align:start position:0% +continuation of the floor uh for the8 +hour day from opening time of the + + align:start position:0% +hour day from opening time of the + + + align:start position:0% +hour day from opening time of the +gallery to closing time of the gallery + + align:start position:0% +gallery to closing time of the gallery + + + align:start position:0% +gallery to closing time of the gallery +I'm underneath the ramp I'm moving + + align:start position:0% +I'm underneath the ramp I'm moving + + + align:start position:0% +I'm underneath the ramp I'm moving +around under the space where viewers are + + align:start position:0% +around under the space where viewers are + + + align:start position:0% +around under the space where viewers are +walking I'm trying to I'm trying to + + align:start position:0% +walking I'm trying to I'm trying to + + + align:start position:0% +walking I'm trying to I'm trying to +constantly masturbate in order to do so + + align:start position:0% +constantly masturbate in order to do so + + + align:start position:0% +constantly masturbate in order to do so +I use viewers as help help in the sense + + align:start position:0% +I use viewers as help help in the sense + + + align:start position:0% +I use viewers as help help in the sense +that I hear viewers footsteps on top of + + align:start position:0% +that I hear viewers footsteps on top of + + + align:start position:0% +that I hear viewers footsteps on top of +me I can build sexual fantasies on those + + align:start position:0% +me I can build sexual fantasies on those + + + align:start position:0% +me I can build sexual fantasies on those +footsteps those sexual fantasies can + + align:start position:0% +footsteps those sexual fantasies can + + + align:start position:0% +footsteps those sexual fantasies can +keep my masturbation going every now and + + align:start position:0% +keep my masturbation going every now and + + + align:start position:0% +keep my masturbation going every now and +then the masturbation reaches climax + + align:start position:0% +then the masturbation reaches climax + + + align:start position:0% +then the masturbation reaches climax +viewer on top of the ramp might be + + align:start position:0% +viewer on top of the ramp might be + + + align:start position:0% +viewer on top of the ramp might be +thinking something like oh he's done + + align:start position:0% +thinking something like oh he's done + + + align:start position:0% +thinking something like oh he's done +this with me he's done this for me in + + align:start position:0% +this with me he's done this for me in + + + align:start position:0% +this with me he's done this for me in +retrospect this was probably the + + align:start position:0% +retrospect this was probably the + + + align:start position:0% +retrospect this was probably the +beginning probably the beginning of + + align:start position:0% +beginning probably the beginning of + + + align:start position:0% +beginning probably the beginning of +architecture uh in my in my in my work I + + align:start position:0% +architecture uh in my in my in my work I + + + align:start position:0% +architecture uh in my in my in my work I +was part of I was part of the floor I + + align:start position:0% +was part of I was part of the floor I + + + align:start position:0% +was part of I was part of the floor I +was part I was part of the room uh the + + align:start position:0% +was part I was part of the room uh the + + + align:start position:0% +was part I was part of the room uh the +reason for example for the 8 hour day + + align:start position:0% +reason for example for the 8 hour day + + + align:start position:0% +reason for example for the 8 hour day +the reason I mentioned the 8 hour day + + align:start position:0% +the reason I mentioned the 8 hour day + + + align:start position:0% +the reason I mentioned the 8 hour day +wasn't so much to stress the endurance + + align:start position:0% +wasn't so much to stress the endurance + + + align:start position:0% +wasn't so much to stress the endurance +test quality of the piece they'll + + align:start position:0% +test quality of the piece they'll + + + align:start position:0% +test quality of the piece they'll +probably like it or not like it or not + + align:start position:0% +probably like it or not like it or not + + + align:start position:0% +probably like it or not like it or not +it was that it was kind of like a uh an8 + + align:start position:0% +it was that it was kind of like a uh an8 + + + align:start position:0% +it was that it was kind of like a uh an8 +an 8 hour job uh each day each day for + + align:start position:0% +an 8 hour job uh each day each day for + + + align:start position:0% +an 8 hour job uh each day each day for +that two we period did I knew what my + + align:start position:0% +that two we period did I knew what my + + + align:start position:0% +that two we period did I knew what my +task was the reason for the 8 hour day + + align:start position:0% +task was the reason for the 8 hour day + + + align:start position:0% +task was the reason for the 8 hour day +was that it seemed important to me that + + align:start position:0% +was that it seemed important to me that + + + align:start position:0% +was that it seemed important to me that +uh when the first viewer entered the + + align:start position:0% +uh when the first viewer entered the + + + align:start position:0% +uh when the first viewer entered the +gallery I was already part of the floor + + align:start position:0% +gallery I was already part of the floor + + + align:start position:0% +gallery I was already part of the floor +when the last viewer left I was still I + + align:start position:0% +when the last viewer left I was still I + + + align:start position:0% +when the last viewer left I was still I +was still I was still part of the part + + align:start position:0% +was still I was still part of the part + + + align:start position:0% +was still I was still part of the part +of the floor uh it was 1972 now I + + align:start position:0% +of the floor uh it was 1972 now I + + + align:start position:0% +of the floor uh it was 1972 now I +started to worry that where my pieces + + align:start position:0% +started to worry that where my pieces + + + align:start position:0% +started to worry that where my pieces +maybe too connected to another time my + + align:start position:0% +maybe too connected to another time my + + + align:start position:0% +maybe too connected to another time my +pieces were so much about self uh one my + + align:start position:0% +pieces were so much about self uh one my + + + align:start position:0% +pieces were so much about self uh one my +piece is part of the language of the 60s + + align:start position:0% +piece is part of the language of the 60s + + + align:start position:0% +piece is part of the language of the 60s +the language of finding oneself as if + + align:start position:0% +the language of finding oneself as if + + + align:start position:0% +the language of finding oneself as if +the self was a kind of precious Jewel + + align:start position:0% +the self was a kind of precious Jewel + + + align:start position:0% +the self was a kind of precious Jewel +that happened to be lost somewhere but + + align:start position:0% +that happened to be lost somewhere but + + + align:start position:0% +that happened to be lost somewhere but +it wasn't the 60s anymore it was 72 73 + + align:start position:0% +it wasn't the 60s anymore it was 72 73 + + + align:start position:0% +it wasn't the 60s anymore it was 72 73 +74 75 I and a lot of other people had + + align:start position:0% +74 75 I and a lot of other people had + + + align:start position:0% +74 75 I and a lot of other people had +very different Notions of self self + + align:start position:0% +very different Notions of self self + + + align:start position:0% +very different Notions of self self +wasn't something you could isolate and + + align:start position:0% +wasn't something you could isolate and + + + align:start position:0% +wasn't something you could isolate and +contemplate rather self was a kind of + + align:start position:0% +contemplate rather self was a kind of + + + align:start position:0% +contemplate rather self was a kind of +system of feelers maybe self existed + + align:start position:0% +system of feelers maybe self existed + + + align:start position:0% +system of feelers maybe self existed +only as part of a social system a + + align:start position:0% +only as part of a social system a + + + align:start position:0% +only as part of a social system a +cultural system a political system so by + + align:start position:0% +cultural system a political system so by + + + align:start position:0% +cultural system a political system so by +the mid-70s work work had changed it + + align:start position:0% +the mid-70s work work had changed it + + + align:start position:0% +the mid-70s work work had changed it +wasn't uh it wasn't live activity + + align:start position:0% +wasn't uh it wasn't live activity + + + align:start position:0% +wasn't uh it wasn't live activity +anymore it was a it was it was in the + + align:start position:0% +anymore it was a it was it was in the + + + align:start position:0% +anymore it was a it was it was in the +form of what people at that time was + + align:start position:0% +form of what people at that time was + + + align:start position:0% +form of what people at that time was +starting to call a very very vague a + + align:start position:0% +starting to call a very very vague a + + + align:start position:0% +starting to call a very very vague a +very very vague term inst inst + + align:start position:0% +very very vague term inst inst + + + align:start position:0% +very very vague term inst inst +installations the way I thought of + + align:start position:0% +installations the way I thought of + + + align:start position:0% +installations the way I thought of +installations were was that a gallery or + + align:start position:0% +installations were was that a gallery or + + + align:start position:0% +installations were was that a gallery or +museum is a place where where people are + + align:start position:0% +museum is a place where where people are + + + align:start position:0% +museum is a place where where people are +going to be anyway now that people are + + align:start position:0% +going to be anyway now that people are + + + align:start position:0% +going to be anyway now that people are +there could a piece be used could a + + align:start position:0% +there could a piece be used could a + + + align:start position:0% +there could a piece be used could a +piece be used maybe to gather people + + align:start position:0% +piece be used maybe to gather people + + + align:start position:0% +piece be used maybe to gather people +together form a community one example a + + align:start position:0% +together form a community one example a + + + align:start position:0% +together form a community one example a +1976 piece called where we are now who + + align:start position:0% +1976 piece called where we are now who + + + align:start position:0% +1976 piece called where we are now who +are we who are we who are we anyway you + + align:start position:0% +are we who are we who are we anyway you + + + align:start position:0% +are we who are we who are we anyway you +enter the gallery you enter the gallery + + align:start position:0% +enter the gallery you enter the gallery + + + align:start position:0% +enter the gallery you enter the gallery +by the elevator around the corner of + + align:start position:0% +by the elevator around the corner of + + + align:start position:0% +by the elevator around the corner of +that black of that black room the black + + align:start position:0% +that black of that black room the black + + + align:start position:0% +that black of that black room the black +room was usually used as the main room + + align:start position:0% +room was usually used as the main room + + + align:start position:0% +room was usually used as the main room +room of the gallery the doorway is + + align:start position:0% +room of the gallery the doorway is + + + align:start position:0% +room of the gallery the doorway is +blocked is block is blocked off uh next + + align:start position:0% +blocked is block is blocked off uh next + + + align:start position:0% +blocked is block is blocked off uh next +to the black room is a long table long + + align:start position:0% +to the black room is a long table long + + + align:start position:0% +to the black room is a long table long +wooden plank stool stools stools on + + align:start position:0% +wooden plank stool stools stools on + + + align:start position:0% +wooden plank stool stools stools on +either side on either side on either + + align:start position:0% +either side on either side on either + + + align:start position:0% +either side on either side on either +side of the table uh there's a hanging + + align:start position:0% +side of the table uh there's a hanging + + + align:start position:0% +side of the table uh there's a hanging +there's an audio speaker hanging above + + align:start position:0% +there's an audio speaker hanging above + + + align:start position:0% +there's an audio speaker hanging above +the table + + align:start position:0% +the table + + + align:start position:0% +the table +uh oh thank + + align:start position:0% +uh oh thank + + + align:start position:0% +uh oh thank +you okay thanks uh okay there's an audio + + align:start position:0% +you okay thanks uh okay there's an audio + + + align:start position:0% +you okay thanks uh okay there's an audio +speaker hanging above hanging hanging + + align:start position:0% +speaker hanging above hanging hanging + + + align:start position:0% +speaker hanging above hanging hanging +hanging above the table uh constant + + align:start position:0% +hanging above the table uh constant + + + align:start position:0% +hanging above the table uh constant +clock ticking as the clock is ticking + + align:start position:0% +clock ticking as the clock is ticking + + + align:start position:0% +clock ticking as the clock is ticking +voice comes in now that we're all here + + align:start position:0% +voice comes in now that we're all here + + + align:start position:0% +voice comes in now that we're all here +together and what do you think Bob now + + align:start position:0% +together and what do you think Bob now + + + align:start position:0% +together and what do you think Bob now +that we've gone as far as we can go and + + align:start position:0% +that we've gone as far as we can go and + + + align:start position:0% +that we've gone as far as we can go and +what do you think Barbara now that we're + + align:start position:0% +what do you think Barbara now that we're + + + align:start position:0% +what do you think Barbara now that we're +satisfied now that we know we failed Etc + + align:start position:0% +satisfied now that we know we failed Etc + + + align:start position:0% +satisfied now that we know we failed Etc +it was around this time I think that I + + align:start position:0% +it was around this time I think that I + + + align:start position:0% +it was around this time I think that I +started to have a really nagging nagging + + align:start position:0% +started to have a really nagging nagging + + + align:start position:0% +started to have a really nagging nagging +doubt about about art this piece for + + align:start position:0% +doubt about about art this piece for + + + align:start position:0% +doubt about about art this piece for +example was trying to treat a gallery or + + align:start position:0% +example was trying to treat a gallery or + + + align:start position:0% +example was trying to treat a gallery or +Museum as if it was a plaza as if it was + + align:start position:0% +Museum as if it was a plaza as if it was + + + align:start position:0% +Museum as if it was a plaza as if it was +a town square and I think I knew then + + align:start position:0% +a town square and I think I knew then + + + align:start position:0% +a town square and I think I knew then +that I was kidding myself a gallery or + + align:start position:0% +that I was kidding myself a gallery or + + + align:start position:0% +that I was kidding myself a gallery or +museum is never going to be a public + + align:start position:0% +museum is never going to be a public + + + align:start position:0% +museum is never going to be a public +space it's always going to be a private + + align:start position:0% +space it's always going to be a private + + + align:start position:0% +space it's always going to be a private +space if I really thought my work needed + + align:start position:0% +space if I really thought my work needed + + + align:start position:0% +space if I really thought my work needed +a public place a public space I'd better + + align:start position:0% +a public place a public space I'd better + + + align:start position:0% +a public place a public space I'd better +find i' i' I'd better find some way to + + align:start position:0% +find i' i' I'd better find some way to + + + align:start position:0% +find i' i' I'd better find some way to +get there and the way I tried to do it + + align:start position:0% +get there and the way I tried to do it + + + align:start position:0% +get there and the way I tried to do it +was + + align:start position:0% +was + + + align:start position:0% +was +uh it was obvious to me that there are + + align:start position:0% +uh it was obvious to me that there are + + + align:start position:0% +uh it was obvious to me that there are +disciplines that already deal with + + align:start position:0% +disciplines that already deal with + + + align:start position:0% +disciplines that already deal with +public space there's architecture maybe + + align:start position:0% +public space there's architecture maybe + + + align:start position:0% +public space there's architecture maybe +landscape architecture product product + + align:start position:0% +landscape architecture product product + + + align:start position:0% +landscape architecture product product +design so I thought maybe I have to sort + + align:start position:0% +design so I thought maybe I have to sort + + + align:start position:0% +design so I thought maybe I have to sort +of redo architecture for myself my work + + align:start position:0% +of redo architecture for myself my work + + + align:start position:0% +of redo architecture for myself my work +has always been about about the person + + align:start position:0% +has always been about about the person + + + align:start position:0% +has always been about about the person +about the body can I try to think of + + align:start position:0% +about the body can I try to think of + + + align:start position:0% +about the body can I try to think of +architecture in terms of the body AR + + align:start position:0% +architecture in terms of the body AR + + + align:start position:0% +architecture in terms of the body AR +obviously architecture is always in + + align:start position:0% +obviously architecture is always in + + + align:start position:0% +obviously architecture is always in +terms of the body architecture contain + + align:start position:0% +terms of the body architecture contain + + + align:start position:0% +terms of the body architecture contain +the body architecture acts as a kind of + + align:start position:0% +the body architecture acts as a kind of + + + align:start position:0% +the body architecture acts as a kind of +platform for the body but I wanted to do + + align:start position:0% +platform for the body but I wanted to do + + + align:start position:0% +platform for the body but I wanted to do +it maybe in a slightly different way I + + align:start position:0% +it maybe in a slightly different way I + + + align:start position:0% +it maybe in a slightly different way I +wanted the I wanted the body to be the + + align:start position:0% +wanted the I wanted the body to be the + + + align:start position:0% +wanted the I wanted the body to be the +cause of architecture so these first + + align:start position:0% +cause of architecture so these first + + + align:start position:0% +cause of architecture so these first +kind of grouping pieces at architecture + + align:start position:0% +kind of grouping pieces at architecture + + + align:start position:0% +kind of grouping pieces at architecture +uh in the beginning of the 80s were + + align:start position:0% +uh in the beginning of the 80s were + + + align:start position:0% +uh in the beginning of the 80s were +probably in retrospect a kind of uh uh + + align:start position:0% +probably in retrospect a kind of uh uh + + + align:start position:0% +probably in retrospect a kind of uh uh +rehearsal for architecture uh play + + align:start position:0% +rehearsal for architecture uh play + + + align:start position:0% +rehearsal for architecture uh play +architecture a kind of game of + + align:start position:0% +architecture a kind of game of + + + align:start position:0% +architecture a kind of game of +architecture this is a 1980 piece called + + align:start position:0% +architecture this is a 1980 piece called + + + align:start position:0% +architecture this is a 1980 piece called +called uh called instant house four + + align:start position:0% +called uh called instant house four + + + align:start position:0% +called uh called instant house four +Flags uh uh four panels American flag + + align:start position:0% +Flags uh uh four panels American flag + + + align:start position:0% +Flags uh uh four panels American flag +covered on the wall a swing in the + + align:start position:0% +covered on the wall a swing in the + + + align:start position:0% +covered on the wall a swing in the +middle if a person sits on the swing the + + align:start position:0% +middle if a person sits on the swing the + + + align:start position:0% +middle if a person sits on the swing the +swing goes down and the panels start to + + align:start position:0% +swing goes down and the panels start to + + + align:start position:0% +swing goes down and the panels start to +rise rise around the person sitting on + + align:start position:0% +rise rise around the person sitting on + + + align:start position:0% +rise rise around the person sitting on +the swing making this instant house and + + align:start position:0% +the swing making this instant house and + + + align:start position:0% +the swing making this instant house and +the instant house is American flag house + + align:start position:0% +the instant house is American flag house + + + align:start position:0% +the instant house is American flag house +inside Soviet flag house outside so you + + align:start position:0% +inside Soviet flag house outside so you + + + align:start position:0% +inside Soviet flag house outside so you +make one kind of space for yourself and + + align:start position:0% +make one kind of space for yourself and + + + align:start position:0% +make one kind of space for yourself and +as you're sitting on the swing you make + + align:start position:0% +as you're sitting on the swing you make + + + align:start position:0% +as you're sitting on the swing you make +another kind of space as an Ann as an as + + align:start position:0% +another kind of space as an Ann as an as + + + align:start position:0% +another kind of space as an Ann as an as +as an as an announcement for others uh + + align:start position:0% +as an as an announcement for others uh + + + align:start position:0% +as an as an announcement for others uh +so for me this was a like I said a kind + + align:start position:0% +so for me this was a like I said a kind + + + align:start position:0% +so for me this was a like I said a kind +of uh practicing practicing architecture + + align:start position:0% +of uh practicing practicing architecture + + + align:start position:0% +of uh practicing practicing architecture +playing + + align:start position:0% +playing + + + align:start position:0% +playing +architecture uh but I thought that I'm + + align:start position:0% +architecture uh but I thought that I'm + + + align:start position:0% +architecture uh but I thought that I'm +spending so much effort I'm spending so + + align:start position:0% +spending so much effort I'm spending so + + + align:start position:0% +spending so much effort I'm spending so +much effort making a demonstration of + + align:start position:0% +much effort making a demonstration of + + + align:start position:0% +much effort making a demonstration of +house building but there's no house left + + align:start position:0% +house building but there's no house left + + + align:start position:0% +house building but there's no house left +when you got up from the swing + + align:start position:0% +when you got up from the swing + + + align:start position:0% +when you got up from the swing +the panels went down to their original + + align:start position:0% +the panels went down to their original + + + align:start position:0% +the panels went down to their original +position I started to think that I + + align:start position:0% +position I started to think that I + + + align:start position:0% +position I started to think that I +needed a place that people could come + + align:start position:0% +needed a place that people could come + + + align:start position:0% +needed a place that people could come +back to by the end of the 80s the the + + align:start position:0% +back to by the end of the 80s the the + + + align:start position:0% +back to by the end of the 80s the the +pieces started to deal with probably uh + + align:start position:0% +pieces started to deal with probably uh + + + align:start position:0% +pieces started to deal with probably uh +architectural produ prototypes this is a + + align:start position:0% +architectural produ prototypes this is a + + + align:start position:0% +architectural produ prototypes this is a +1984 piece called uh called bad dream + + align:start position:0% +1984 piece called uh called bad dream + + + align:start position:0% +1984 piece called uh called bad dream +house uh actually done here at MIT in 80 + + align:start position:0% +house uh actually done here at MIT in 80 + + + align:start position:0% +house uh actually done here at MIT in 80 +in 8 in ' 84 uh three upside down houses + + align:start position:0% +in 8 in ' 84 uh three upside down houses + + + align:start position:0% +in 8 in ' 84 uh three upside down houses +two upside down houses leaning tilted + + align:start position:0% +two upside down houses leaning tilted + + + align:start position:0% +two upside down houses leaning tilted +against each other so that they support + + align:start position:0% +against each other so that they support + + + align:start position:0% +against each other so that they support +a third upside down house on top uh the + + align:start position:0% +a third upside down house on top uh the + + + align:start position:0% +a third upside down house on top uh the +houses on the ground like the houses you + + align:start position:0% +houses on the ground like the houses you + + + align:start position:0% +houses on the ground like the houses you +conventionally find on the ground brick + + align:start position:0% +conventionally find on the ground brick + + + align:start position:0% +conventionally find on the ground brick +facing shingled roof they support a + + align:start position:0% +facing shingled roof they support a + + + align:start position:0% +facing shingled roof they support a +glass house house in house in the house + + align:start position:0% +glass house house in house in the house + + + align:start position:0% +glass house house in house in the house +in the air you enter at either end at + + align:start position:0% +in the air you enter at either end at + + + align:start position:0% +in the air you enter at either end at +the open Gable you sit at or walk past + + align:start position:0% +the open Gable you sit at or walk past + + + align:start position:0% +the open Gable you sit at or walk past +an upside down table or you go upstairs + + align:start position:0% +an upside down table or you go upstairs + + + align:start position:0% +an upside down table or you go upstairs +to what used to be the underside of the + + align:start position:0% +to what used to be the underside of the + + + align:start position:0% +to what used to be the underside of the +house now that it's upside down it's a + + align:start position:0% +house now that it's upside down it's a + + + align:start position:0% +house now that it's upside down it's a +facing set of seats bleachers or you go + + align:start position:0% +facing set of seats bleachers or you go + + + align:start position:0% +facing set of seats bleachers or you go +further upstairs to The Glass House + + align:start position:0% +further upstairs to The Glass House + + + align:start position:0% +further upstairs to The Glass House +garden house at this time I think it was + + align:start position:0% +garden house at this time I think it was + + + align:start position:0% +garden house at this time I think it was +kind of clear that my stuff wasn't art + + align:start position:0% +kind of clear that my stuff wasn't art + + + align:start position:0% +kind of clear that my stuff wasn't art +anymore if it ever if it ever if it ever + + align:start position:0% +anymore if it ever if it ever if it ever + + + align:start position:0% +anymore if it ever if it ever if it ever +was if I was uh if I was making things + + align:start position:0% +was if I was uh if I was making things + + + align:start position:0% +was if I was uh if I was making things +like houses but again these were + + align:start position:0% +like houses but again these were + + + align:start position:0% +like houses but again these were +playhouses uh you couldn't live there + + align:start position:0% +playhouses uh you couldn't live there + + + align:start position:0% +playhouses uh you couldn't live there +you could possibly use it as a + + align:start position:0% +you could possibly use it as a + + + align:start position:0% +you could possibly use it as a +playground but you couldn't really + + align:start position:0% +playground but you couldn't really + + + align:start position:0% +playground but you couldn't really +inhabit it so if it was architecture it + + align:start position:0% +inhabit it so if it was architecture it + + + align:start position:0% +inhabit it so if it was architecture it +was the bare be bare beginnings of + + align:start position:0% +was the bare be bare beginnings of + + + align:start position:0% +was the bare be bare beginnings of +architecture + + align:start position:0% +architecture + + + align:start position:0% +architecture +uh okay so I was thinking if my stuff + + align:start position:0% +uh okay so I was thinking if my stuff + + + align:start position:0% +uh okay so I was thinking if my stuff +made made a place of their own made + + align:start position:0% +made made a place of their own made + + + align:start position:0% +made made a place of their own made +houses maybe they didn't need a gallery + + align:start position:0% +houses maybe they didn't need a gallery + + + align:start position:0% +houses maybe they didn't need a gallery +space they didn't need a museum space + + align:start position:0% +space they didn't need a museum space + + + align:start position:0% +space they didn't need a museum space +but I think maybe a a more important uh + + align:start position:0% +but I think maybe a a more important uh + + + align:start position:0% +but I think maybe a a more important uh +a more important perception uh was was + + align:start position:0% +a more important perception uh was was + + + align:start position:0% +a more important perception uh was was +was was operative at that time uh I I + + align:start position:0% +was was operative at that time uh I I + + + align:start position:0% +was was operative at that time uh I I +think I was getting to realize that I + + align:start position:0% +think I was getting to realize that I + + + align:start position:0% +think I was getting to realize that I +just wasn't interested anymore in an art + + align:start position:0% +just wasn't interested anymore in an art + + + align:start position:0% +just wasn't interested anymore in an art +viewer and Kristoff I think was talking + + align:start position:0% +viewer and Kristoff I think was talking + + + align:start position:0% +viewer and Kristoff I think was talking +Kristoff was talking the same way in his + + align:start position:0% +Kristoff was talking the same way in his + + + align:start position:0% +Kristoff was talking the same way in his +in his introduction uh and by Art viewer + + align:start position:0% +in his introduction uh and by Art viewer + + + align:start position:0% +in his introduction uh and by Art viewer +I mean when a person enters an art space + + align:start position:0% +I mean when a person enters an art space + + + align:start position:0% +I mean when a person enters an art space +that person in effect is saying I am an + + align:start position:0% +that person in effect is saying I am an + + + align:start position:0% +that person in effect is saying I am an +art viewer by extension I'm separating + + align:start position:0% +art viewer by extension I'm separating + + + align:start position:0% +art viewer by extension I'm separating +myself from all those others who aren't + + align:start position:0% +myself from all those others who aren't + + + align:start position:0% +myself from all those others who aren't +who aren't art viewers I realized I was + + align:start position:0% +who aren't art viewers I realized I was + + + align:start position:0% +who aren't art viewers I realized I was +more interested in the Casual passer by + + align:start position:0% +more interested in the Casual passer by + + + align:start position:0% +more interested in the Casual passer by +the street I was more interested in the + + align:start position:0% +the street I was more interested in the + + + align:start position:0% +the street I was more interested in the +person who stops at something not + + align:start position:0% +person who stops at something not + + + align:start position:0% +person who stops at something not +because it's announced as art but + + align:start position:0% +because it's announced as art but + + + align:start position:0% +because it's announced as art but +because for some reason or other it uh + + align:start position:0% +because for some reason or other it uh + + + align:start position:0% +because for some reason or other it uh +it it uh it means something in that + + align:start position:0% +it it uh it means something in that + + + align:start position:0% +it it uh it means something in that +person or it potentially means something + + align:start position:0% +person or it potentially means something + + + align:start position:0% +person or it potentially means something +at least curiosity interest for that + + align:start position:0% +at least curiosity interest for that + + + align:start position:0% +at least curiosity interest for that +person for that per for that person in + + align:start position:0% +person for that per for that person in + + + align:start position:0% +person for that per for that person in +the street + + align:start position:0% +the street + + + align:start position:0% +the street +so uh starting in the mid 80s and I + + align:start position:0% +so uh starting in the mid 80s and I + + + align:start position:0% +so uh starting in the mid 80s and I +think one thing that that was important + + align:start position:0% +think one thing that that was important + + + align:start position:0% +think one thing that that was important +to me through the 80s is that I was + + align:start position:0% +to me through the 80s is that I was + + + align:start position:0% +to me through the 80s is that I was +working with a person who I think is in + + align:start position:0% +working with a person who I think is in + + + align:start position:0% +working with a person who I think is in +the audience though I haven't seen him + + align:start position:0% +the audience though I haven't seen him + + + align:start position:0% +the audience though I haven't seen him +yet I was uh uh a person uh an artist + + align:start position:0% +yet I was uh uh a person uh an artist + + + align:start position:0% +yet I was uh uh a person uh an artist +named named to jury D John to jury who + + align:start position:0% +named named to jury D John to jury who + + + align:start position:0% +named named to jury D John to jury who +lives here uh was working on pieces for + + align:start position:0% +lives here uh was working on pieces for + + + align:start position:0% +lives here uh was working on pieces for +me at that time + + align:start position:0% +me at that time + + + align:start position:0% +me at that time +uh and I started to realize + + align:start position:0% +uh and I started to realize + + + align:start position:0% +uh and I started to realize +that uh the claim is being made by + + align:start position:0% +that uh the claim is being made by + + + align:start position:0% +that uh the claim is being made by +others and probably by me that these + + align:start position:0% +others and probably by me that these + + + align:start position:0% +others and probably by me that these +people are building pieces for me but + + align:start position:0% +people are building pieces for me but + + + align:start position:0% +people are building pieces for me but +but I started to realize that I'm + + align:start position:0% +but I started to realize that I'm + + + align:start position:0% +but I started to realize that I'm +getting ideas from these people uh for + + align:start position:0% +getting ideas from these people uh for + + + align:start position:0% +getting ideas from these people uh for +example John built pieces like instant + + align:start position:0% +example John built pieces like instant + + + align:start position:0% +example John built pieces like instant +house those movable those movable pieces + + align:start position:0% +house those movable those movable pieces + + + align:start position:0% +house those movable those movable pieces +I think I had ideas for those movable + + align:start position:0% +I think I had ideas for those movable + + + align:start position:0% +I think I had ideas for those movable +pieces for a few years before that but I + + align:start position:0% +pieces for a few years before that but I + + + align:start position:0% +pieces for a few years before that but I +didn't have the slightest idea how to do + + align:start position:0% +didn't have the slightest idea how to do + + + align:start position:0% +didn't have the slightest idea how to do +them once I met John the possibility of + + align:start position:0% +them once I met John the possibility of + + + align:start position:0% +them once I met John the possibility of +building them became became possible so + + align:start position:0% +building them became became possible so + + + align:start position:0% +building them became became possible so +gradually I realized that this is a + + align:start position:0% +gradually I realized that this is a + + + align:start position:0% +gradually I realized that this is a +collaboration though I'm not though I'm + + align:start position:0% +collaboration though I'm not though I'm + + + align:start position:0% +collaboration though I'm not though I'm +not though I'm not admitting it so so by + + align:start position:0% +not though I'm not admitting it so so by + + + align:start position:0% +not though I'm not admitting it so so by +the end of the 880s uh a country Studio + + align:start position:0% +the end of the 880s uh a country Studio + + + align:start position:0% +the end of the 880s uh a country Studio +started uh I you know wanted to admit + + align:start position:0% +started uh I you know wanted to admit + + + align:start position:0% +started uh I you know wanted to admit +admit a collaboration but not just admit + + align:start position:0% +admit a collaboration but not just admit + + + align:start position:0% +admit a collaboration but not just admit +it I wanted to I wanted to announce it I + + align:start position:0% +it I wanted to I wanted to announce it I + + + align:start position:0% +it I wanted to I wanted to announce it I +did a show at the end of the 80s I was + + align:start position:0% +did a show at the end of the 80s I was + + + align:start position:0% +did a show at the end of the 80s I was +still I then uh I did a show in 1988 at + + align:start position:0% +still I then uh I did a show in 1988 at + + + align:start position:0% +still I then uh I did a show in 1988 at +the Museum of Modern Art in New York and + + align:start position:0% +the Museum of Modern Art in New York and + + + align:start position:0% +the Museum of Modern Art in New York and +I called the show Public Public public + + align:start position:0% +I called the show Public Public public + + + align:start position:0% +I called the show Public Public public +places there was a green Banner hanging + + align:start position:0% +places there was a green Banner hanging + + + align:start position:0% +places there was a green Banner hanging +outside outside the museum + + align:start position:0% +outside outside the museum + + + align:start position:0% +outside outside the museum +with the words vdo public places and I + + align:start position:0% +with the words vdo public places and I + + + align:start position:0% +with the words vdo public places and I +think I felt the way at least the way + + align:start position:0% +think I felt the way at least the way + + + align:start position:0% +think I felt the way at least the way +Jean Paul SRA claims uh Jean Chan the + + align:start position:0% +Jean Paul SRA claims uh Jean Chan the + + + align:start position:0% +Jean Paul SRA claims uh Jean Chan the +French writer felt when as a child he + + align:start position:0% +French writer felt when as a child he + + + align:start position:0% +French writer felt when as a child he +stole uh I don't remember some money a + + align:start position:0% +stole uh I don't remember some money a + + + align:start position:0% +stole uh I don't remember some money a +loaf of bread and somebody called him a + + align:start position:0% +loaf of bread and somebody called him a + + + align:start position:0% +loaf of bread and somebody called him a +thief and according to SRA Jan from that + + align:start position:0% +thief and according to SRA Jan from that + + + align:start position:0% +thief and according to SRA Jan from that +day on said that if I'm called a thief I + + align:start position:0% +day on said that if I'm called a thief I + + + align:start position:0% +day on said that if I'm called a thief I +have to become a thief so when I saw + + align:start position:0% +have to become a thief so when I saw + + + align:start position:0% +have to become a thief so when I saw +those words public places associated + + align:start position:0% +those words public places associated + + + align:start position:0% +those words public places associated +with them with my name I realize there's + + align:start position:0% +with them with my name I realize there's + + + align:start position:0% +with them with my name I realize there's +no turning back you know I have to start + + align:start position:0% +no turning back you know I have to start + + + align:start position:0% +no turning back you know I have to start +dedicating myself to public places and + + align:start position:0% +dedicating myself to public places and + + + align:start position:0% +dedicating myself to public places and +the only way to do that is to start + + align:start position:0% +the only way to do that is to start + + + align:start position:0% +the only way to do that is to start +working the way an architect works I had + + align:start position:0% +working the way an architect works I had + + + align:start position:0% +working the way an architect works I had +to work with a group of people I had to + + align:start position:0% +to work with a group of people I had to + + + align:start position:0% +to work with a group of people I had to +work with a group group of people for + + align:start position:0% +work with a group group of people for + + + align:start position:0% +work with a group group of people for +two very for two for two reasons one I + + align:start position:0% +two very for two for two reasons one I + + + align:start position:0% +two very for two for two reasons one I +wanted to do I wanted to do I wanted to + + align:start position:0% +wanted to do I wanted to do I wanted to + + + align:start position:0% +wanted to do I wanted to do I wanted to +do architecture but I really didn't know + + align:start position:0% +do architecture but I really didn't know + + + align:start position:0% +do architecture but I really didn't know +how I didn't know I didn't know how to + + align:start position:0% +how I didn't know I didn't know how to + + + align:start position:0% +how I didn't know I didn't know how to +build things I probably didn't know how + + align:start position:0% +build things I probably didn't know how + + + align:start position:0% +build things I probably didn't know how +to design things so I needed people + + align:start position:0% +to design things so I needed people + + + align:start position:0% +to design things so I needed people +around me who could design let me let me + + align:start position:0% +around me who could design let me let me + + + align:start position:0% +around me who could design let me let me +uh backtrack for a minute I think my + + align:start position:0% +uh backtrack for a minute I think my + + + align:start position:0% +uh backtrack for a minute I think my +whole career has been built on the fact + + align:start position:0% +whole career has been built on the fact + + + align:start position:0% +whole career has been built on the fact +has been based on the fact of uh of not + + align:start position:0% +has been based on the fact of uh of not + + + align:start position:0% +has been based on the fact of uh of not +being able to do too much uh uh for + + align:start position:0% +being able to do too much uh uh for + + + align:start position:0% +being able to do too much uh uh for +example I I I think I've always assumed + + align:start position:0% +example I I I think I've always assumed + + + align:start position:0% +example I I I think I've always assumed +that I really don't have any basic + + align:start position:0% +that I really don't have any basic + + + align:start position:0% +that I really don't have any basic +skills uh I I possibly I used to say I + + align:start position:0% +skills uh I I possibly I used to say I + + + align:start position:0% +skills uh I I possibly I used to say I +know how to use the Yellow Pages I hope + + align:start position:0% +know how to use the Yellow Pages I hope + + + align:start position:0% +know how to use the Yellow Pages I hope +I can now say I know how to use know how + + align:start position:0% +I can now say I know how to use know how + + + align:start position:0% +I can now say I know how to use know how +to use the internet I might not have + + align:start position:0% +to use the internet I might not have + + + align:start position:0% +to use the internet I might not have +these skills but maybe I can find people + + align:start position:0% +these skills but maybe I can find people + + + align:start position:0% +these skills but maybe I can find people +who do have those skills uh in other + + align:start position:0% +who do have those skills uh in other + + + align:start position:0% +who do have those skills uh in other +words if uh when work of mine began in + + align:start position:0% +words if uh when work of mine began in + + + align:start position:0% +words if uh when work of mine began in +19 in 1968 in + + align:start position:0% +19 in 1968 in + + + align:start position:0% +19 in 1968 in +1969 if it wasn't for the fact that + + align:start position:0% +1969 if it wasn't for the fact that + + + align:start position:0% +1969 if it wasn't for the fact that +words like conceptual art was starting + + align:start position:0% +words like conceptual art was starting + + + align:start position:0% +words like conceptual art was starting +to be used there would have been + + align:start position:0% +to be used there would have been + + + align:start position:0% +to be used there would have been +absolutely nothing for me to do I + + align:start position:0% +absolutely nothing for me to do I + + + align:start position:0% +absolutely nothing for me to do I +couldn't paint I couldn't draw I could + + align:start position:0% +couldn't paint I couldn't draw I could + + + align:start position:0% +couldn't paint I couldn't draw I could +couldn't sculpt once the words + + align:start position:0% +couldn't sculpt once the words + + + align:start position:0% +couldn't sculpt once the words +conceptual art were used I could say to + + align:start position:0% +conceptual art were used I could say to + + + align:start position:0% +conceptual art were used I could say to +myself well I think I know how to have + + align:start position:0% +myself well I think I know how to have + + + align:start position:0% +myself well I think I know how to have +vague ideas so so there's a so there's a + + align:start position:0% +vague ideas so so there's a so there's a + + + align:start position:0% +vague ideas so so there's a so there's a +place for me uh okay skip forward again + + align:start position:0% +place for me uh okay skip forward again + + + align:start position:0% +place for me uh okay skip forward again +to the end of the 80s there was a just + + align:start position:0% +to the end of the 80s there was a just + + + align:start position:0% +to the end of the 80s there was a just +as important maybe more important reason + + align:start position:0% +as important maybe more important reason + + + align:start position:0% +as important maybe more important reason +why I felt I had to work with people uh + + align:start position:0% +why I felt I had to work with people uh + + + align:start position:0% +why I felt I had to work with people uh +I started to feel that if if something + + align:start position:0% +I started to feel that if if something + + + align:start position:0% +I started to feel that if if something +begins private it probably can only end + + align:start position:0% +begins private it probably can only end + + + align:start position:0% +begins private it probably can only end +private if I really really wanted + + align:start position:0% +private if I really really wanted + + + align:start position:0% +private if I really really wanted +something to be to result in a public + + align:start position:0% +something to be to result in a public + + + align:start position:0% +something to be to result in a public +space it had to start with at least a + + align:start position:0% +space it had to start with at least a + + + align:start position:0% +space it had to start with at least a +semi-public and public uh Public public + + align:start position:0% +semi-public and public uh Public public + + + align:start position:0% +semi-public and public uh Public public +probably starts with the number three + + align:start position:0% +probably starts with the number three + + + align:start position:0% +probably starts with the number three +one is a solo two is a couple or a + + align:start position:0% +one is a solo two is a couple or a + + + align:start position:0% +one is a solo two is a couple or a +mirror image the third person the third + + align:start position:0% +mirror image the third person the third + + + align:start position:0% +mirror image the third person the third +person starts an argument and public + + align:start position:0% +person starts an argument and public + + + align:start position:0% +person starts an argument and public +probably begins when an argument when an + + align:start position:0% +probably begins when an argument when an + + + align:start position:0% +probably begins when an argument when an +argument starts okay so from from from + + align:start position:0% +argument starts okay so from from from + + + align:start position:0% +argument starts okay so from from from +the end of the 80s on uh I can't talk as + + align:start position:0% +the end of the 80s on uh I can't talk as + + + align:start position:0% +the end of the 80s on uh I can't talk as +I anymore I have to talk I have to talk + + align:start position:0% +I anymore I have to talk I have to talk + + + align:start position:0% +I anymore I have to talk I have to talk +I have to I have to talk as we the work + + align:start position:0% +I have to I have to talk as we the work + + + align:start position:0% +I have to I have to talk as we the work +kind of inched its way towards our + + align:start position:0% +kind of inched its way towards our + + + align:start position:0% +kind of inched its way towards our +towards architecture from the beginning + + align:start position:0% +towards architecture from the beginning + + + align:start position:0% +towards architecture from the beginning +the people who worked for me were + + align:start position:0% +the people who worked for me were + + + align:start position:0% +the people who worked for me were +Architects were from an architecture + + align:start position:0% +Architects were from an architecture + + + align:start position:0% +Architects were from an architecture +background but even though that was true + + align:start position:0% +background but even though that was true + + + align:start position:0% +background but even though that was true +you know I wasn't known as an architect + + align:start position:0% +you know I wasn't known as an architect + + + align:start position:0% +you know I wasn't known as an architect +so the projects we were asked to do + + align:start position:0% +so the projects we were asked to do + + + align:start position:0% +so the projects we were asked to do +weren't real architecture projects but + + align:start position:0% +weren't real architecture projects but + + + align:start position:0% +weren't real architecture projects but +so-called public art projects uh uh and + + align:start position:0% +so-called public art projects uh uh and + + + align:start position:0% +so-called public art projects uh uh and +and the way public art public art + + align:start position:0% +and the way public art public art + + + align:start position:0% +and the way public art public art +projects exist at least in the United + + align:start position:0% +projects exist at least in the United + + + align:start position:0% +projects exist at least in the United +States is that when a public building is + + align:start position:0% +States is that when a public building is + + + align:start position:0% +States is that when a public building is +built 1% of the budget is allow is is + + align:start position:0% +built 1% of the budget is allow is is + + + align:start position:0% +built 1% of the budget is allow is is +allotted is allotted is allotted is + + align:start position:0% +allotted is allotted is allotted is + + + align:start position:0% +allotted is allotted is allotted is +allotted to Art one example of uh a + + align:start position:0% +allotted to Art one example of uh a + + + align:start position:0% +allotted to Art one example of uh a +public art kind of project this was the + + align:start position:0% +public art kind of project this was the + + + align:start position:0% +public art kind of project this was the +site of a project we built in 1995 at + + align:start position:0% +site of a project we built in 1995 at + + + align:start position:0% +site of a project we built in 1995 at +Queens College in New York the site is a + + align:start position:0% +Queens College in New York the site is a + + + align:start position:0% +Queens College in New York the site is a +kind of pass through space in front of + + align:start position:0% +kind of pass through space in front of + + + align:start position:0% +kind of pass through space in front of +the English Department building on + + align:start position:0% +the English Department building on + + + align:start position:0% +the English Department building on +either side of the English Department + + align:start position:0% +either side of the English Department + + + align:start position:0% +either side of the English Department +building is a pedestal on top of which + + align:start position:0% +building is a pedestal on top of which + + + align:start position:0% +building is a pedestal on top of which +is a sphere a 3ft diameter sphere those + + align:start position:0% +is a sphere a 3ft diameter sphere those + + + align:start position:0% +is a sphere a 3ft diameter sphere those +spheres were were were our starting + + align:start position:0% +spheres were were were our starting + + + align:start position:0% +spheres were were were our starting +point starting point in the sense that + + align:start position:0% +point starting point in the sense that + + + align:start position:0% +point starting point in the sense that +uh a starting point in the sense that + + align:start position:0% +uh a starting point in the sense that + + + align:start position:0% +uh a starting point in the sense that +the the Spheres + + align:start position:0% +the the Spheres + + + align:start position:0% +the the Spheres +are the Spheres seem to be trying to + + align:start position:0% +are the Spheres seem to be trying to + + + align:start position:0% +are the Spheres seem to be trying to +make a a kind of grandiose entrance to + + align:start position:0% +make a a kind of grandiose entrance to + + + align:start position:0% +make a a kind of grandiose entrance to +what was only the entrance to an English + + align:start position:0% +what was only the entrance to an English + + + align:start position:0% +what was only the entrance to an English +Department building on the other hand + + align:start position:0% +Department building on the other hand + + + align:start position:0% +Department building on the other hand +the uh the Spheres seemed uh kind of + + align:start position:0% +the uh the Spheres seemed uh kind of + + + align:start position:0% +the uh the Spheres seemed uh kind of +isolated and lonely in the space so what + + align:start position:0% +isolated and lonely in the space so what + + + align:start position:0% +isolated and lonely in the space so what +our project consisted of was to add + + align:start position:0% +our project consisted of was to add + + + align:start position:0% +our project consisted of was to add +other spheres to the space uh spheres + + align:start position:0% +other spheres to the space uh spheres + + + align:start position:0% +other spheres to the space uh spheres +ranging from very small 1 foot in + + align:start position:0% +ranging from very small 1 foot in + + + align:start position:0% +ranging from very small 1 foot in +diameter to uh to a sphere 12et 12et + + align:start position:0% +diameter to uh to a sphere 12et 12et + + + align:start position:0% +diameter to uh to a sphere 12et 12et +12et in diameter ranging through the + + align:start position:0% +12et in diameter ranging through the + + + align:start position:0% +12et in diameter ranging through the +existing sphere uh the Spheres the + + align:start position:0% +existing sphere uh the Spheres the + + + align:start position:0% +existing sphere uh the Spheres the +Spheres are cut are cut are cut into so + + align:start position:0% +Spheres are cut are cut are cut into so + + + align:start position:0% +Spheres are cut are cut are cut into so +you can walk through a sphere you can + + align:start position:0% +you can walk through a sphere you can + + + align:start position:0% +you can walk through a sphere you can +sit inside a sphere uh the Spheres are + + align:start position:0% +sit inside a sphere uh the Spheres are + + + align:start position:0% +sit inside a sphere uh the Spheres are +lit at night uh so they become a kind of + + align:start position:0% +lit at night uh so they become a kind of + + + align:start position:0% +lit at night uh so they become a kind of +they become a kind of Gathering Place I + + align:start position:0% +they become a kind of Gathering Place I + + + align:start position:0% +they become a kind of Gathering Place I +tried to believe at that time that there + + align:start position:0% +tried to believe at that time that there + + + align:start position:0% +tried to believe at that time that there +was a reason for public art that uh uh + + align:start position:0% +was a reason for public art that uh uh + + + align:start position:0% +was a reason for public art that uh uh +the uh since most of the money is spent + + align:start position:0% +the uh since most of the money is spent + + + align:start position:0% +the uh since most of the money is spent +on is spent on the architecture public + + align:start position:0% +on is spent on the architecture public + + + align:start position:0% +on is spent on the architecture public +art go only gets 1% of the budget I Tred + + align:start position:0% +art go only gets 1% of the budget I Tred + + + align:start position:0% +art go only gets 1% of the budget I Tred +to think well public art is marginal + + align:start position:0% +to think well public art is marginal + + + align:start position:0% +to think well public art is marginal +maybe it could make use of its of its + + align:start position:0% +maybe it could make use of its of its + + + align:start position:0% +maybe it could make use of its of its +marginal position maybe it can be the + + align:start position:0% +marginal position maybe it can be the + + + align:start position:0% +marginal position maybe it can be the +voice of the minority party maybe if you + + align:start position:0% +voice of the minority party maybe if you + + + align:start position:0% +voice of the minority party maybe if you +can think that the built architecture + + align:start position:0% +can think that the built architecture + + + align:start position:0% +can think that the built architecture +acts as the institution Maybe by + + align:start position:0% +acts as the institution Maybe by + + + align:start position:0% +acts as the institution Maybe by +proliferating the Spheres as in this + + align:start position:0% +proliferating the Spheres as in this + + + align:start position:0% +proliferating the Spheres as in this +piece maybe maybe we could provide a + + align:start position:0% +piece maybe maybe we could provide a + + + align:start position:0% +piece maybe maybe we could provide a +kind of disease on a kind of + + align:start position:0% +kind of disease on a kind of + + + align:start position:0% +kind of disease on a kind of +institutionalized architecture in + + align:start position:0% +institutionalized architecture in + + + align:start position:0% +institutionalized architecture in +retrospect that think that public art + + align:start position:0% +retrospect that think that public art + + + align:start position:0% +retrospect that think that public art +can only be can only be only be a Folly + + align:start position:0% +can only be can only be only be a Folly + + + align:start position:0% +can only be can only be only be a Folly +uh 1% of the budget is spent on public + + align:start position:0% +uh 1% of the budget is spent on public + + + align:start position:0% +uh 1% of the budget is spent on public +art another way of putting it is that + + align:start position:0% +art another way of putting it is that + + + align:start position:0% +art another way of putting it is that +the art is worth 1% 1% of the AR of the + + align:start position:0% +the art is worth 1% 1% of the AR of the + + + align:start position:0% +the art is worth 1% 1% of the AR of the +architecture uh I think more recently + + align:start position:0% +architecture uh I think more recently + + + align:start position:0% +architecture uh I think more recently +maybe our stuff has uh I hope our stuff + + align:start position:0% +maybe our stuff has uh I hope our stuff + + + align:start position:0% +maybe our stuff has uh I hope our stuff +at least since the year 2000 has + + align:start position:0% +at least since the year 2000 has + + + align:start position:0% +at least since the year 2000 has +probably has maybe I should say possibly + + align:start position:0% +probably has maybe I should say possibly + + + align:start position:0% +probably has maybe I should say possibly +or I hope has become has + + align:start position:0% +or I hope has become has + + + align:start position:0% +or I hope has become has +has become architecture everybody in the + + align:start position:0% +has become architecture everybody in the + + + align:start position:0% +has become architecture everybody in the +studio thinks we're doing we're doing + + align:start position:0% +studio thinks we're doing we're doing + + + align:start position:0% +studio thinks we're doing we're doing +we're doing design and design design + + align:start position:0% +we're doing design and design design + + + align:start position:0% +we're doing design and design design +design and + + align:start position:0% +design and + + + align:start position:0% +design and +architecture uh so I want to go through + + align:start position:0% +architecture uh so I want to go through + + + align:start position:0% +architecture uh so I want to go through +uh some examples of the pro of the + + align:start position:0% +uh some examples of the pro of the + + + align:start position:0% +uh some examples of the pro of the +projects of the of the last four years + + align:start position:0% +projects of the of the last four years + + + align:start position:0% +projects of the of the last four years +five years uh we tend to think of + + align:start position:0% +five years uh we tend to think of + + + align:start position:0% +five years uh we tend to think of +architecture as uh I mean what's + + align:start position:0% +architecture as uh I mean what's + + + align:start position:0% +architecture as uh I mean what's +important to us is that uh architecture + + align:start position:0% +important to us is that uh architecture + + + align:start position:0% +important to us is that uh architecture +architecture is an occasion for people + + align:start position:0% +architecture is an occasion for people + + + align:start position:0% +architecture is an occasion for people +architecture maybe as an hopefully as a + + align:start position:0% +architecture maybe as an hopefully as a + + + align:start position:0% +architecture maybe as an hopefully as a +kind of activity place for people I + + align:start position:0% +kind of activity place for people I + + + align:start position:0% +kind of activity place for people I +think one fear that joins the studio is + + align:start position:0% +think one fear that joins the studio is + + + align:start position:0% +think one fear that joins the studio is +that uh we're afraid that when we design + + align:start position:0% +that uh we're afraid that when we design + + + align:start position:0% +that uh we're afraid that when we design +a space are we necessarily designing + + align:start position:0% +a space are we necessarily designing + + + align:start position:0% +a space are we necessarily designing +people's behavior in that space and we + + align:start position:0% +people's behavior in that space and we + + + align:start position:0% +people's behavior in that space and we +want to obviously we want to we want to + + align:start position:0% +want to obviously we want to we want to + + + align:start position:0% +want to obviously we want to we want to +try we want to try to avoid that uh uh + + align:start position:0% +try we want to try to avoid that uh uh + + + align:start position:0% +try we want to try to avoid that uh uh +can a space be can a space you know I + + align:start position:0% +can a space be can a space you know I + + + align:start position:0% +can a space be can a space you know I +mean the great thing about that I I + + align:start position:0% +mean the great thing about that I I + + + align:start position:0% +mean the great thing about that I I +think again you know what drew me more + + align:start position:0% +think again you know what drew me more + + + align:start position:0% +think again you know what drew me more +and more towards design and architecture + + align:start position:0% +and more towards design and architecture + + + align:start position:0% +and more towards design and architecture +was the fact that everybody knows + + align:start position:0% +was the fact that everybody knows + + + align:start position:0% +was the fact that everybody knows +architecture whether they realize it or + + align:start position:0% +architecture whether they realize it or + + + align:start position:0% +architecture whether they realize it or +not everybody knows architecture because + + align:start position:0% +not everybody knows architecture because + + + align:start position:0% +not everybody knows architecture because +everybody's walked up a Stairway + + align:start position:0% +everybody's walked up a Stairway + + + align:start position:0% +everybody's walked up a Stairway +everybody's walked through a doorway + + align:start position:0% +everybody's walked through a doorway + + + align:start position:0% +everybody's walked through a doorway +maybe people know architecture because + + align:start position:0% +maybe people know architecture because + + + align:start position:0% +maybe people know architecture because +they've been possibly oppressed by + + align:start position:0% +they've been possibly oppressed by + + + align:start position:0% +they've been possibly oppressed by +architecture they walk through a doorway + + align:start position:0% +architecture they walk through a doorway + + + align:start position:0% +architecture they walk through a doorway +that's too narrow they're under a + + align:start position:0% +that's too narrow they're under a + + + align:start position:0% +that's too narrow they're under a +ceiling that's too low but in any case + + align:start position:0% +ceiling that's too low but in any case + + + align:start position:0% +ceiling that's too low but in any case +people know architecture with their + + align:start position:0% +people know architecture with their + + + align:start position:0% +people know architecture with their +bodies they know Arch ecture by + + align:start position:0% +bodies they know Arch ecture by + + + align:start position:0% +bodies they know Arch ecture by +traversing it + + align:start position:0% +traversing it + + + align:start position:0% +traversing it +uh we we tend to think of stuff in terms + + align:start position:0% +uh we we tend to think of stuff in terms + + + align:start position:0% +uh we we tend to think of stuff in terms +of uh just as we want a place to be an + + align:start position:0% +of uh just as we want a place to be an + + + align:start position:0% +of uh just as we want a place to be an +activity place for people I think the + + align:start position:0% +activity place for people I think the + + + align:start position:0% +activity place for people I think the +way we design is thinking of how can we + + align:start position:0% +way we design is thinking of how can we + + + align:start position:0% +way we design is thinking of how can we +perform an activity how can we perform a + + align:start position:0% +perform an activity how can we perform a + + + align:start position:0% +perform an activity how can we perform a +kind of operation on a site so I want to + + align:start position:0% +kind of operation on a site so I want to + + + align:start position:0% +kind of operation on a site so I want to +go through even though I don't know if I + + align:start position:0% +go through even though I don't know if I + + + align:start position:0% +go through even though I don't know if I +can read these with the existing light + + align:start position:0% +can read these with the existing light + + + align:start position:0% +can read these with the existing light +but uh uh but maybe I can remember most + + align:start position:0% +but uh uh but maybe I can remember most + + + align:start position:0% +but uh uh but maybe I can remember most +we uh I want to go through these + + align:start position:0% +we uh I want to go through these + + + align:start position:0% +we uh I want to go through these +projects uh uh by going through a series + + align:start position:0% +projects uh uh by going through a series + + + align:start position:0% +projects uh uh by going through a series +of + + align:start position:0% +of + + + align:start position:0% +of +operations we seem to do when designing + + align:start position:0% +operations we seem to do when designing + + + align:start position:0% +operations we seem to do when designing +when designing a project some projects + + align:start position:0% +when designing a project some projects + + + align:start position:0% +when designing a project some projects +will be used as examples of of of uh + + align:start position:0% +will be used as examples of of of uh + + + align:start position:0% +will be used as examples of of of uh +each oper each each operation sometimes + + align:start position:0% +each oper each each operation sometimes + + + align:start position:0% +each oper each each operation sometimes +a project will be used to partially + + align:start position:0% +a project will be used to partially + + + align:start position:0% +a project will be used to partially +demonstrate one project then it'll come + + align:start position:0% +demonstrate one project then it'll come + + + align:start position:0% +demonstrate one project then it'll come +one one one operation then it'll then + + align:start position:0% +one one one operation then it'll then + + + align:start position:0% +one one one operation then it'll then +it'll come back later operation number + + align:start position:0% +it'll come back later operation number + + + align:start position:0% +it'll come back later operation number +one + + align:start position:0% +one + + + align:start position:0% +one +make a world then poke the world dig + + align:start position:0% +make a world then poke the world dig + + + align:start position:0% +make a world then poke the world dig +into the world an architecture of holes + + align:start position:0% +into the world an architecture of holes + + + align:start position:0% +into the world an architecture of holes +this is a project or the start of a + + align:start position:0% +this is a project or the start of a + + + align:start position:0% +this is a project or the start of a +project we're working on now um it's a + + align:start position:0% +project we're working on now um it's a + + + align:start position:0% +project we're working on now um it's a +it's a project for a median in a street + + align:start position:0% +it's a project for a median in a street + + + align:start position:0% +it's a project for a median in a street +in a street in Vienna they asked us to + + align:start position:0% +in a street in Vienna they asked us to + + + align:start position:0% +in a street in Vienna they asked us to +do a kind of Park in this in this in + + align:start position:0% +do a kind of Park in this in this in + + + align:start position:0% +do a kind of Park in this in this in +this street thank thank you thank you + + align:start position:0% +this street thank thank you thank you + + + align:start position:0% +this street thank thank you thank you +Joe great it's perfect uh they asked us + + align:start position:0% +Joe great it's perfect uh they asked us + + + align:start position:0% +Joe great it's perfect uh they asked us +to do a park on this on on the on this + + align:start position:0% +to do a park on this on on the on this + + + align:start position:0% +to do a park on this on on the on this +median they made it clear to us that uh + + align:start position:0% +median they made it clear to us that uh + + + align:start position:0% +median they made it clear to us that uh +you had to be able to see through this + + align:start position:0% +you had to be able to see through this + + + align:start position:0% +you had to be able to see through this +park from one street to another very + + align:start position:0% +park from one street to another very + + + align:start position:0% +park from one street to another very +often when we're given a directive we + + align:start position:0% +often when we're given a directive we + + + align:start position:0% +often when we're given a directive we +think well maybe we can start in the + + align:start position:0% +think well maybe we can start in the + + + align:start position:0% +think well maybe we can start in the +opposite way if they're telling us to + + align:start position:0% +opposite way if they're telling us to + + + align:start position:0% +opposite way if they're telling us to +make an open space maybe we can start by + + align:start position:0% +make an open space maybe we can start by + + + align:start position:0% +make an open space maybe we can start by +making a closed space what if we act as + + align:start position:0% +making a closed space what if we act as + + + align:start position:0% +making a closed space what if we act as +if a kind of spaceship has landed has + + align:start position:0% +if a kind of spaceship has landed has + + + align:start position:0% +if a kind of spaceship has landed has +landed on this on on this on this median + + align:start position:0% +landed on this on on this on this median + + + align:start position:0% +landed on this on on this on this median +so it's a closed spaceship so now we + + align:start position:0% +so it's a closed spaceship so now we + + + align:start position:0% +so it's a closed spaceship so now we +have to perforate it so you can see + + align:start position:0% +have to perforate it so you can see + + + align:start position:0% +have to perforate it so you can see +through from one side to another this + + align:start position:0% +through from one side to another this + + + align:start position:0% +through from one side to another this +project will come back later this is a + + align:start position:0% +project will come back later this is a + + + align:start position:0% +project will come back later this is a +project we proposed recently um uh for + + align:start position:0% +project we proposed recently um uh for + + + align:start position:0% +project we proposed recently um uh for +soul in Korea it was a competition uh + + align:start position:0% +soul in Korea it was a competition uh + + + align:start position:0% +soul in Korea it was a competition uh +which we didn't win it was a it was a + + align:start position:0% +which we didn't win it was a it was a + + + align:start position:0% +which we didn't win it was a it was a +competition for a Performing Arts Center + + align:start position:0% +competition for a Performing Arts Center + + + align:start position:0% +competition for a Performing Arts Center +in Soul uh the Performing Arts Center + + align:start position:0% +in Soul uh the Performing Arts Center + + + align:start position:0% +in Soul uh the Performing Arts Center +was going to was going to be on an + + align:start position:0% +was going to was going to be on an + + + align:start position:0% +was going to was going to be on an +island + + align:start position:0% +island + + + align:start position:0% +island +uh the island is a flood is a flood is a + + align:start position:0% +uh the island is a flood is a flood is a + + + align:start position:0% +uh the island is a flood is a flood is a +floodable island + + align:start position:0% +floodable island + + + align:start position:0% +floodable island +uh uh their their directive was the base + + align:start position:0% +uh uh their their directive was the base + + + align:start position:0% +uh uh their their directive was the base +of the island maybe could be used for + + align:start position:0% +of the island maybe could be used for + + + align:start position:0% +of the island maybe could be used for +for landscaping whereas the uh the + + align:start position:0% +for landscaping whereas the uh the + + + align:start position:0% +for landscaping whereas the uh the +Performing Art Center should be raised + + align:start position:0% +Performing Art Center should be raised + + + align:start position:0% +Performing Art Center should be raised +at the top part of the base but we + + align:start position:0% +at the top part of the base but we + + + align:start position:0% +at the top part of the base but we +thought if this base if this base is + + align:start position:0% +thought if this base if this base is + + + align:start position:0% +thought if this base if this base is +floodable maybe you know it's it's only + + align:start position:0% +floodable maybe you know it's it's only + + + align:start position:0% +floodable maybe you know it's it's only +going to kill the landscap ape so could + + align:start position:0% +going to kill the landscap ape so could + + + align:start position:0% +going to kill the landscap ape so could +we think of this base of the island + + align:start position:0% +we think of this base of the island + + + align:start position:0% +we think of this base of the island +almost as a kind of alien alien planet + + align:start position:0% +almost as a kind of alien alien planet + + + align:start position:0% +almost as a kind of alien alien planet +it's a place of craters a place of holes + + align:start position:0% +it's a place of craters a place of holes + + + align:start position:0% +it's a place of craters a place of holes +so people can find places to be within + + align:start position:0% +so people can find places to be within + + + align:start position:0% +so people can find places to be within +these holes uh this project too will + + align:start position:0% +these holes uh this project too will + + + align:start position:0% +these holes uh this project too will +come back later uh the beginning of 2002 + + align:start position:0% +come back later uh the beginning of 2002 + + + align:start position:0% +come back later uh the beginning of 2002 +uh like probably many other people we + + align:start position:0% +uh like probably many other people we + + + align:start position:0% +uh like probably many other people we +made a theoretical proposal for a new + + align:start position:0% +made a theoretical proposal for a new + + + align:start position:0% +made a theoretical proposal for a new +World Trade Center we proposed a world + + align:start position:0% +World Trade Center we proposed a world + + + align:start position:0% +World Trade Center we proposed a world +trade Center uh full of holes our + + align:start position:0% +trade Center uh full of holes our + + + align:start position:0% +trade Center uh full of holes our +starting point was that if a building + + align:start position:0% +starting point was that if a building + + + align:start position:0% +starting point was that if a building +nowadays is going to be exploded anyway + + align:start position:0% +nowadays is going to be exploded anyway + + + align:start position:0% +nowadays is going to be exploded anyway +maybe maybe a building nowadays should + + align:start position:0% +maybe maybe a building nowadays should + + + align:start position:0% +maybe maybe a building nowadays should +come pre- exploded already exploded so + + align:start position:0% +come pre- exploded already exploded so + + + align:start position:0% +come pre- exploded already exploded so +uh we took the original site of the + + align:start position:0% +uh we took the original site of the + + + align:start position:0% +uh we took the original site of the +World Trade Center raised it to a height + + align:start position:0% +World Trade Center raised it to a height + + + align:start position:0% +World Trade Center raised it to a height +of 110 stories high so now you have more + + align:start position:0% +of 110 stories high so now you have more + + + align:start position:0% +of 110 stories high so now you have more +of a volume more of a mass than the + + align:start position:0% +of a volume more of a mass than the + + + align:start position:0% +of a volume more of a mass than the +original World Trade Center ever was you + + align:start position:0% +original World Trade Center ever was you + + + align:start position:0% +original World Trade Center ever was you +have more private office space than any + + align:start position:0% +have more private office space than any + + + align:start position:0% +have more private office space than any +could possibly need so we shoot cones + + align:start position:0% +could possibly need so we shoot cones + + + align:start position:0% +could possibly need so we shoot cones +through it making this building full of + + align:start position:0% +through it making this building full of + + + align:start position:0% +through it making this building full of +holes this project will come back we'll + + align:start position:0% +holes this project will come back we'll + + + align:start position:0% +holes this project will come back we'll +come back later uh operation Operation + + align:start position:0% +come back later uh operation Operation + + + align:start position:0% +come back later uh operation Operation +number two overlay screen camouflage a + + align:start position:0% +number two overlay screen camouflage a + + + align:start position:0% +number two overlay screen camouflage a +second skin this was a building where we + + align:start position:0% +second skin this was a building where we + + + align:start position:0% +second skin this was a building where we +uh did a clothing store in Tokyo in 2003 + + align:start position:0% +uh did a clothing store in Tokyo in 2003 + + + align:start position:0% +uh did a clothing store in Tokyo in 2003 +for a group of designers called United + + align:start position:0% +for a group of designers called United + + + align:start position:0% +for a group of designers called United +bamboo this modular system is a system + + align:start position:0% +bamboo this modular system is a system + + + align:start position:0% +bamboo this modular system is a system +that's conventionally used in Japan uh + + align:start position:0% +that's conventionally used in Japan uh + + + align:start position:0% +that's conventionally used in Japan uh +for houses for residences the United + + align:start position:0% +for houses for residences the United + + + align:start position:0% +for houses for residences the United +bamboo people worried that this was + + align:start position:0% +bamboo people worried that this was + + + align:start position:0% +bamboo people worried that this was +never going to look like a store it was + + align:start position:0% +never going to look like a store it was + + + align:start position:0% +never going to look like a store it was +always going to look like a house so we + + align:start position:0% +always going to look like a house so we + + + align:start position:0% +always going to look like a house so we +thought our first step had to be to + + align:start position:0% +thought our first step had to be to + + + align:start position:0% +thought our first step had to be to +screen it uh put a mesh screening over + + align:start position:0% +screen it uh put a mesh screening over + + + align:start position:0% +screen it uh put a mesh screening over +it the glass facades push in or bulge + + align:start position:0% +it the glass facades push in or bulge + + + align:start position:0% +it the glass facades push in or bulge +out through the through the mesh uh the + + align:start position:0% +out through the through the mesh uh the + + + align:start position:0% +out through the through the mesh uh the +clothing stores on the ground floor + + align:start position:0% +clothing stores on the ground floor + + + align:start position:0% +clothing stores on the ground floor +upper floors are our offices on the + + align:start position:0% +upper floors are our offices on the + + + align:start position:0% +upper floors are our offices on the +bouldering facade on the upper flooor + + align:start position:0% +bouldering facade on the upper flooor + + + align:start position:0% +bouldering facade on the upper flooor +floor there's a projection screen when + + align:start position:0% +floor there's a projection screen when + + + align:start position:0% +floor there's a projection screen when +you're inside the store if you're trying + + align:start position:0% +you're inside the store if you're trying + + + align:start position:0% +you're inside the store if you're trying +on United bamboo clothes if you like the + + align:start position:0% +on United bamboo clothes if you like the + + + align:start position:0% +on United bamboo clothes if you like the +way you look you can have yourself + + align:start position:0% +way you look you can have yourself + + + align:start position:0% +way you look you can have yourself +photographed you become the model for + + align:start position:0% +photographed you become the model for + + + align:start position:0% +photographed you become the model for +United bamboo clothes this project too + + align:start position:0% +United bamboo clothes this project too + + + align:start position:0% +United bamboo clothes this project too +will come back later um another example + + align:start position:0% +will come back later um another example + + + align:start position:0% +will come back later um another example +of a kind of screening system a gallery + + align:start position:0% +of a kind of screening system a gallery + + + align:start position:0% +of a kind of screening system a gallery +we did in New York in 2002 the gallery + + align:start position:0% +we did in New York in 2002 the gallery + + + align:start position:0% +we did in New York in 2002 the gallery +was part of a uh part of uh uh uh the + + align:start position:0% +was part of a uh part of uh uh uh the + + + align:start position:0% +was part of a uh part of uh uh uh the +gallery dealer's home a steel wall + + align:start position:0% +gallery dealer's home a steel wall + + + align:start position:0% +gallery dealer's home a steel wall +starts outside the doorway comes + + align:start position:0% +starts outside the doorway comes + + + align:start position:0% +starts outside the doorway comes +inside uh the the gallery dealer said + + align:start position:0% +inside uh the the gallery dealer said + + + align:start position:0% +inside uh the the gallery dealer said +that this was only going to be a + + align:start position:0% +that this was only going to be a + + + align:start position:0% +that this was only going to be a +temporary Gallery so we thought we can't + + align:start position:0% +temporary Gallery so we thought we can't + + + align:start position:0% +temporary Gallery so we thought we can't +change the walls we could only screen + + align:start position:0% +change the walls we could only screen + + + align:start position:0% +change the walls we could only screen +the walls cover the walls so we cover + + align:start position:0% +the walls cover the walls so we cover + + + align:start position:0% +the walls cover the walls so we cover +the walls with with expanded metal + + align:start position:0% +the walls with with expanded metal + + + align:start position:0% +the walls with with expanded metal +panels as a byproduct we we got a kind + + align:start position:0% +panels as a byproduct we we got a kind + + + align:start position:0% +panels as a byproduct we we got a kind +of universal hanging system you don't + + align:start position:0% +of universal hanging system you don't + + + align:start position:0% +of universal hanging system you don't +have to make holes in the walls the + + align:start position:0% +have to make holes in the walls the + + + align:start position:0% +have to make holes in the walls the +expanded metal is all all all holes + + align:start position:0% + + + + align:start position:0% + +uh uh another project we're working on + + align:start position:0% +uh uh another project we're working on + + + align:start position:0% +uh uh another project we're working on +we're working on now a facad in Milan a + + align:start position:0% +we're working on now a facad in Milan a + + + align:start position:0% +we're working on now a facad in Milan a +facade for a building in Milan uh we + + align:start position:0% +facade for a building in Milan uh we + + + align:start position:0% +facade for a building in Milan uh we +were asked to do a facade for a building + + align:start position:0% +were asked to do a facade for a building + + + align:start position:0% +were asked to do a facade for a building +that already had a facade uh which made + + align:start position:0% +that already had a facade uh which made + + + align:start position:0% +that already had a facade uh which made +us think that how can we think of this + + align:start position:0% +us think that how can we think of this + + + align:start position:0% +us think that how can we think of this +and uh uh you know the way we thought of + + align:start position:0% +and uh uh you know the way we thought of + + + align:start position:0% +and uh uh you know the way we thought of +it uh was maybe we can reclo the + + align:start position:0% +it uh was maybe we can reclo the + + + align:start position:0% +it uh was maybe we can reclo the +building maybe we can put a kind of + + align:start position:0% +building maybe we can put a kind of + + + align:start position:0% +building maybe we can put a kind of +drape over the over over the building uh + + align:start position:0% +drape over the over over the building uh + + + align:start position:0% +drape over the over over the building uh +uh unfold a kind of drapery over the + + align:start position:0% +uh unfold a kind of drapery over the + + + align:start position:0% +uh unfold a kind of drapery over the +building there's a private apartment on + + align:start position:0% +building there's a private apartment on + + + align:start position:0% +building there's a private apartment on +the roof so pull the drape down there + + align:start position:0% +the roof so pull the drape down there + + + align:start position:0% +the roof so pull the drape down there +are obviously entrances on the ground + + align:start position:0% +are obviously entrances on the ground + + + align:start position:0% +are obviously entrances on the ground +pull the drape up this project two comes + + align:start position:0% +pull the drape up this project two comes + + + align:start position:0% +pull the drape up this project two comes +back comes back later operation number + + align:start position:0% +back comes back later operation number + + + align:start position:0% +back comes back later operation number +three uh bubble wave soft architecture + + align:start position:0% +three uh bubble wave soft architecture + + + align:start position:0% +three uh bubble wave soft architecture +and architecture of flow back to the + + align:start position:0% +and architecture of flow back to the + + + align:start position:0% +and architecture of flow back to the +United bamboo Bamboo store uh uh you + + align:start position:0% +United bamboo Bamboo store uh uh you + + + align:start position:0% +United bamboo Bamboo store uh uh you +enter between between two between two + + align:start position:0% +enter between between two between two + + + align:start position:0% +enter between between two between two +mirrors the uh the doorway pushes in + + align:start position:0% +mirrors the uh the doorway pushes in + + + align:start position:0% +mirrors the uh the doorway pushes in +hopefully as if to sort of welcome you + + align:start position:0% +hopefully as if to sort of welcome you + + + align:start position:0% +hopefully as if to sort of welcome you +into the store we tried to make a store + + align:start position:0% +into the store we tried to make a store + + + align:start position:0% +into the store we tried to make a store +that was as soft as clothing as soft as + + align:start position:0% +that was as soft as clothing as soft as + + + align:start position:0% +that was as soft as clothing as soft as +Skin So the the material in the store is + + align:start position:0% +Skin So the the material in the store is + + + align:start position:0% +Skin So the the material in the store is +PVC the material that's usually used for + + align:start position:0% +PVC the material that's usually used for + + + align:start position:0% +PVC the material that's usually used for +projection screen rear screen rear + + align:start position:0% +projection screen rear screen rear + + + align:start position:0% +projection screen rear screen rear +screen rear screen projection PVC on the + + align:start position:0% +screen rear screen projection PVC on the + + + align:start position:0% +screen rear screen projection PVC on the +ceiling pull it down to make a wall pull + + align:start position:0% +ceiling pull it down to make a wall pull + + + align:start position:0% +ceiling pull it down to make a wall pull +it out to make a counter make shelves by + + align:start position:0% +it out to make a counter make shelves by + + + align:start position:0% +it out to make a counter make shelves by +by pulling out pushing back in since + + align:start position:0% +by pulling out pushing back in since + + + align:start position:0% +by pulling out pushing back in since +it's projection screen material we don't + + align:start position:0% +it's projection screen material we don't + + + align:start position:0% +it's projection screen material we don't +have to light the shelves from outside + + align:start position:0% +have to light the shelves from outside + + + align:start position:0% +have to light the shelves from outside +we can have lights we can have lights + + align:start position:0% +we can have lights we can have lights + + + align:start position:0% +we can have lights we can have lights +within the shelves it's a very the store + + align:start position:0% +within the shelves it's a very the store + + + align:start position:0% +within the shelves it's a very the store +is in a very small space about 40 ft + + align:start position:0% +is in a very small space about 40 ft + + + align:start position:0% +is in a very small space about 40 ft +long about 15 feet wide so we thought we + + align:start position:0% +long about 15 feet wide so we thought we + + + align:start position:0% +long about 15 feet wide so we thought we +could use all the space all the spa all + + align:start position:0% +could use all the space all the spa all + + + align:start position:0% +could use all the space all the spa all +the space we could get anytime there was + + align:start position:0% +the space we could get anytime there was + + + align:start position:0% +the space we could get anytime there was +a non-structural wall we got rid of the + + align:start position:0% +a non-structural wall we got rid of the + + + align:start position:0% +a non-structural wall we got rid of the +wall and made a curving glass Al Cove + + align:start position:0% +wall and made a curving glass Al Cove + + + align:start position:0% +wall and made a curving glass Al Cove +outside the store the hanging clothes + + align:start position:0% +outside the store the hanging clothes + + + align:start position:0% +outside the store the hanging clothes +are in the are in that Al Cove they come + + align:start position:0% +are in the are in that Al Cove they come + + + align:start position:0% +are in the are in that Al Cove they come +in they come in they come into the store + + align:start position:0% +in they come in they come into the store + + + align:start position:0% +in they come in they come into the store +operation Operation number four uh uh + + align:start position:0% +operation Operation number four uh uh + + + align:start position:0% +operation Operation number four uh uh +continuous surface endless space uh a + + align:start position:0% +continuous surface endless space uh a + + + align:start position:0% +continuous surface endless space uh a +piece done in the a piece done in two in + + align:start position:0% +piece done in the a piece done in two in + + + align:start position:0% +piece done in the a piece done in two in +two in 2000 an attempt to make a to make + + align:start position:0% +two in 2000 an attempt to make a to make + + + align:start position:0% +two in 2000 an attempt to make a to make +a a a SE to make a bench based on the + + align:start position:0% +a a a SE to make a bench based on the + + + align:start position:0% +a a a SE to make a bench based on the +notion of a m of a m of a Mia strip so + + align:start position:0% +notion of a m of a m of a Mia strip so + + + align:start position:0% +notion of a m of a m of a Mia strip so +the back of the seat twists to become + + align:start position:0% +the back of the seat twists to become + + + align:start position:0% +the back of the seat twists to become +the seat twists twist continuously to + + align:start position:0% +the seat twists twist continuously to + + + align:start position:0% +the seat twists twist continuously to +become the back of the seat outside + + align:start position:0% +become the back of the seat outside + + + align:start position:0% +become the back of the seat outside +twist to become to become + + align:start position:0% +twist to become to become + + + align:start position:0% +twist to become to become +inside uh you sit outside this circle + + align:start position:0% +inside uh you sit outside this circle + + + align:start position:0% +inside uh you sit outside this circle +you move over you're inside the circle + + align:start position:0% +you move over you're inside the circle + + + align:start position:0% +you move over you're inside the circle +at around the same time we were asked to + + align:start position:0% +at around the same time we were asked to + + + align:start position:0% +at around the same time we were asked to +uh we were asked by by UNICEF World + + align:start position:0% +uh we were asked by by UNICEF World + + + align:start position:0% +uh we were asked by by UNICEF World +Health Organization to uh + + align:start position:0% +Health Organization to uh + + + align:start position:0% +Health Organization to uh +uh to design a playground uh that could + + align:start position:0% +uh to design a playground uh that could + + + align:start position:0% +uh to design a playground uh that could +be produced in multiples we uh just like + + align:start position:0% +be produced in multiples we uh just like + + + align:start position:0% +be produced in multiples we uh just like +the Mia strip is a is a is a is a is a + + align:start position:0% +the Mia strip is a is a is a is a is a + + + align:start position:0% +the Mia strip is a is a is a is a is a +figure from from topological math we use + + align:start position:0% +figure from from topological math we use + + + align:start position:0% +figure from from topological math we use +the the notion of a Klein bottle uh kind + + align:start position:0% +the the notion of a Klein bottle uh kind + + + align:start position:0% +the the notion of a Klein bottle uh kind +of assuming everybody knows what a Klein + + align:start position:0% +of assuming everybody knows what a Klein + + + align:start position:0% +of assuming everybody knows what a Klein +bottle is but the way a CL if somebody + + align:start position:0% +bottle is but the way a CL if somebody + + + align:start position:0% +bottle is but the way a CL if somebody +doesn't the way a cim bottle works + + align:start position:0% +doesn't the way a cim bottle works + + + align:start position:0% +doesn't the way a cim bottle works +conventional bottle neck of the bottle + + align:start position:0% +conventional bottle neck of the bottle + + + align:start position:0% +conventional bottle neck of the bottle +in the case of the Klein bottle neck + + align:start position:0% +in the case of the Klein bottle neck + + + align:start position:0% +in the case of the Klein bottle neck +extend out from the bottle turns around + + align:start position:0% +extend out from the bottle turns around + + + align:start position:0% +extend out from the bottle turns around +goes back in so it's a kind of + + align:start position:0% +goes back in so it's a kind of + + + align:start position:0% +goes back in so it's a kind of +three-dimensional version of a Mia strip + + align:start position:0% +three-dimensional version of a Mia strip + + + align:start position:0% +three-dimensional version of a Mia strip +we try to make a playground uh uh a clim + + align:start position:0% +we try to make a playground uh uh a clim + + + align:start position:0% +we try to make a playground uh uh a clim +bottle with four necks children children + + align:start position:0% +bottle with four necks children children + + + align:start position:0% +bottle with four necks children children +enter enter in four possible ways uh + + align:start position:0% +enter enter in four possible ways uh + + + align:start position:0% +enter enter in four possible ways uh +it's transparent it's perforated uh + + align:start position:0% +it's transparent it's perforated uh + + + align:start position:0% +it's transparent it's perforated uh +children climbing outside can come face + + align:start position:0% +children climbing outside can come face + + + align:start position:0% +children climbing outside can come face +to face with children climbing inside + + align:start position:0% +to face with children climbing inside + + + align:start position:0% +to face with children climbing inside +you could slide from outside to inside + + align:start position:0% +you could slide from outside to inside + + + align:start position:0% +you could slide from outside to inside +and VI and vice and vice versa + + align:start position:0% +and VI and vice and vice versa + + + align:start position:0% +and VI and vice and vice versa +operation Operation number five push and + + align:start position:0% +operation Operation number five push and + + + align:start position:0% +operation Operation number five push and +pull + + align:start position:0% +pull + + + align:start position:0% +pull +uh uh this is a project that was built + + align:start position:0% +uh uh this is a project that was built + + + align:start position:0% +uh uh this is a project that was built +in Memphis in the beginning the + + align:start position:0% +in Memphis in the beginning the + + + align:start position:0% +in Memphis in the beginning the +beginning of 2004 it's outside or at the + + align:start position:0% +beginning of 2004 it's outside or at the + + + align:start position:0% +beginning of 2004 it's outside or at the +edge of a Performing Art Center in + + align:start position:0% +edge of a Performing Art Center in + + + align:start position:0% +edge of a Performing Art Center in +Memphis there's a leftover space outside + + align:start position:0% +Memphis there's a leftover space outside + + + align:start position:0% +Memphis there's a leftover space outside +of the Performing Art Center it was + + align:start position:0% +of the Performing Art Center it was + + + align:start position:0% +of the Performing Art Center it was +suggested to us that could we possibly + + align:start position:0% +suggested to us that could we possibly + + + align:start position:0% +suggested to us that could we possibly +turn this leftover space into a plaza a + + align:start position:0% +turn this leftover space into a plaza a + + + align:start position:0% +turn this leftover space into a plaza a +place where people might go out out of + + align:start position:0% +place where people might go out out of + + + align:start position:0% +place where people might go out out of +the Performing Art Center at + + align:start position:0% +the Performing Art Center at + + + align:start position:0% +the Performing Art Center at +intermissions the way we began was uh + + align:start position:0% +intermissions the way we began was uh + + + align:start position:0% +intermissions the way we began was uh +the Performing Art Center partially + + align:start position:0% +the Performing Art Center partially + + + align:start position:0% +the Performing Art Center partially +extends over this leftover space so we + + align:start position:0% +extends over this leftover space so we + + + align:start position:0% +extends over this leftover space so we +tried to begin as if we were standing + + align:start position:0% +tried to begin as if we were standing + + + align:start position:0% +tried to begin as if we were standing +under this overhang could we throw + + align:start position:0% +under this overhang could we throw + + + align:start position:0% +under this overhang could we throw +something out could we fling something + + align:start position:0% +something out could we fling something + + + align:start position:0% +something out could we fling something +out into the air fling something like a + + align:start position:0% +out into the air fling something like a + + + align:start position:0% +out into the air fling something like a +fluid out into the air but whatever we + + align:start position:0% +fluid out into the air but whatever we + + + align:start position:0% +fluid out into the air but whatever we +fling has to stand up so we pull it down + + align:start position:0% +fling has to stand up so we pull it down + + + align:start position:0% +fling has to stand up so we pull it down +to make columns at the same time that we + + align:start position:0% +to make columns at the same time that we + + + align:start position:0% +to make columns at the same time that we +pull it down to make columns we push it + + align:start position:0% +pull it down to make columns we push it + + + align:start position:0% +pull it down to make columns we push it +up push it up to make a funnel sunlight + + align:start position:0% +up push it up to make a funnel sunlight + + + align:start position:0% +up push it up to make a funnel sunlight +comes in like uh the spotlights on the + + align:start position:0% +comes in like uh the spotlights on the + + + align:start position:0% +comes in like uh the spotlights on the +stage inside at night the sunlight is + + align:start position:0% +stage inside at night the sunlight is + + + align:start position:0% +stage inside at night the sunlight is +replaced by artificial light another + + align:start position:0% +replaced by artificial light another + + + align:start position:0% +replaced by artificial light another +funnel is pulled down towards the + + align:start position:0% +funnel is pulled down towards the + + + align:start position:0% +funnel is pulled down towards the +entrance it lights it lights the + + align:start position:0% +entrance it lights it lights the + + + align:start position:0% +entrance it lights it lights the +entrance uh you're you you're going to + + align:start position:0% +entrance uh you're you you're going to + + + align:start position:0% +entrance uh you're you you're going to +talk about Fon Street no so let me let + + align:start position:0% +talk about Fon Street no so let me let + + + align:start position:0% +talk about Fon Street no so let me let +me skip over let me skip over + + align:start position:0% +me skip over let me skip over + + + align:start position:0% +me skip over let me skip over +right okay uh + + align:start position:0% +right okay uh + + + align:start position:0% +right okay uh +uh uh another example of push and pull + + align:start position:0% +uh uh another example of push and pull + + + align:start position:0% +uh uh another example of push and pull +uh we made a proposal for a uh uh + + align:start position:0% +uh we made a proposal for a uh uh + + + align:start position:0% +uh we made a proposal for a uh uh +basically kind of subway station in New + + align:start position:0% +basically kind of subway station in New + + + align:start position:0% +basically kind of subway station in New +York it was being built by it was being + + align:start position:0% +York it was being built by it was being + + + align:start position:0% +York it was being built by it was being +built by uh by uh Nicholas Nicholas + + align:start position:0% +built by uh by uh Nicholas Nicholas + + + align:start position:0% +built by uh by uh Nicholas Nicholas +Nicholas Grimshaw the Grimshaw space had + + align:start position:0% +Nicholas Grimshaw the Grimshaw space had + + + align:start position:0% +Nicholas Grimshaw the Grimshaw space had +uh had this Dome apparently the Dome is + + align:start position:0% +uh had this Dome apparently the Dome is + + + align:start position:0% +uh had this Dome apparently the Dome is +gone from his face so we're not the only + + align:start position:0% +gone from his face so we're not the only + + + align:start position:0% +gone from his face so we're not the only +people who are told what to do everybody + + align:start position:0% +people who are told what to do everybody + + + align:start position:0% +people who are told what to do everybody +is uh told what not what not to do + + align:start position:0% +is uh told what not what not to do + + + align:start position:0% +is uh told what not what not to do +um uh inside the Dome is an is an is an + + align:start position:0% +um uh inside the Dome is an is an is an + + + align:start position:0% +um uh inside the Dome is an is an is an +is an Atrium uh so what we tried to do + + align:start position:0% +is an Atrium uh so what we tried to do + + + align:start position:0% +is an Atrium uh so what we tried to do +was could we take this Atrium space and + + align:start position:0% +was could we take this Atrium space and + + + align:start position:0% +was could we take this Atrium space and +kind of turn it turn it in on itself uh + + align:start position:0% +kind of turn it turn it in on itself uh + + + align:start position:0% +kind of turn it turn it in on itself uh +turn it it turn it in on itself to make + + align:start position:0% +turn it it turn it in on itself to make + + + align:start position:0% +turn it it turn it in on itself to make +a kind of space space space within the + + align:start position:0% +a kind of space space space within the + + + align:start position:0% +a kind of space space space within the +space this project this project will + + align:start position:0% +space this project this project will + + + align:start position:0% +space this project this project will +come back will come back later back to + + align:start position:0% +come back will come back later back to + + + align:start position:0% +come back will come back later back to +the sole performing performing art + + align:start position:0% +the sole performing performing art + + + align:start position:0% +the sole performing performing art +Center on this marsik landscape is this + + align:start position:0% +Center on this marsik landscape is this + + + align:start position:0% +Center on this marsik landscape is this +spaceship like performing Performing Art + + align:start position:0% +spaceship like performing Performing Art + + + align:start position:0% +spaceship like performing Performing Art +Center uh we thought we thought we would + + align:start position:0% +Center uh we thought we thought we would + + + align:start position:0% +Center uh we thought we thought we would +make spaces theater spaces concert Halls + + align:start position:0% +make spaces theater spaces concert Halls + + + align:start position:0% +make spaces theater spaces concert Halls +by sucking the space into it into it + + align:start position:0% +by sucking the space into it into it + + + align:start position:0% +by sucking the space into it into it +into itself uh so that as this as this + + align:start position:0% +into itself uh so that as this as this + + + align:start position:0% +into itself uh so that as this as this +surface uh rather a surface sucked into + + align:start position:0% +surface uh rather a surface sucked into + + + align:start position:0% +surface uh rather a surface sucked into +itself to make a space to make a number + + align:start position:0% +itself to make a space to make a number + + + align:start position:0% +itself to make a space to make a number +of spaces um I had mentioned earlier + + align:start position:0% +of spaces um I had mentioned earlier + + + align:start position:0% +of spaces um I had mentioned earlier +that uh they had they had suggested they + + align:start position:0% +that uh they had they had suggested they + + + align:start position:0% +that uh they had they had suggested they +had suggested Landscaping the island + + align:start position:0% +had suggested Landscaping the island + + + align:start position:0% +had suggested Landscaping the island +since we had no Landscaping on the + + align:start position:0% +since we had no Landscaping on the + + + align:start position:0% +since we had no Landscaping on the +island because it was floodable once we + + align:start position:0% +island because it was floodable once we + + + align:start position:0% +island because it was floodable once we +sucked in these spaces the concert hall + + align:start position:0% +sucked in these spaces the concert hall + + + align:start position:0% +sucked in these spaces the concert hall +Etc was in the sucked in space and the + + align:start position:0% +Etc was in the sucked in space and the + + + align:start position:0% +Etc was in the sucked in space and the +concert hall Etc was surrounded by an + + align:start position:0% +concert hall Etc was surrounded by an + + + align:start position:0% +concert hall Etc was surrounded by an +indoor an indoor landscape so you walked + + align:start position:0% +indoor an indoor landscape so you walked + + + align:start position:0% +indoor an indoor landscape so you walked +into a theater into a concert hall + + align:start position:0% +into a theater into a concert hall + + + align:start position:0% +into a theater into a concert hall +through the through the landscape + + align:start position:0% +through the through the landscape + + + align:start position:0% +through the through the landscape +operation Operation number + + align:start position:0% +operation Operation number + + + align:start position:0% +operation Operation number +six not and not uh not an end but a + + align:start position:0% +six not and not uh not an end but a + + + align:start position:0% +six not and not uh not an end but a +medium not an object but an instrument + + align:start position:0% +medium not an object but an instrument + + + align:start position:0% +medium not an object but an instrument +an architecture of its surroundings a + + align:start position:0% +an architecture of its surroundings a + + + align:start position:0% +an architecture of its surroundings a +proposal we made last year for the + + align:start position:0% +proposal we made last year for the + + + align:start position:0% +proposal we made last year for the +Atlanta airport uh the proposal was for + + align:start position:0% +Atlanta airport uh the proposal was for + + + align:start position:0% +Atlanta airport uh the proposal was for +the transfer Corridor Corridor of the + + align:start position:0% +the transfer Corridor Corridor of the + + + align:start position:0% +the transfer Corridor Corridor of the +air of the airport uh it was important + + align:start position:0% +air of the airport uh it was important + + + align:start position:0% +air of the airport uh it was important +that uh it separated people who were + + align:start position:0% +that uh it separated people who were + + + align:start position:0% +that uh it separated people who were +getting off of plane getting off a plane + + align:start position:0% +getting off of plane getting off a plane + + + align:start position:0% +getting off of plane getting off a plane +leaving the airport from people who were + + align:start position:0% +leaving the airport from people who were + + + align:start position:0% +leaving the airport from people who were +getting off a domestic flight switching + + align:start position:0% +getting off a domestic flight switching + + + align:start position:0% +getting off a domestic flight switching +to an international flight or vice vice + + align:start position:0% +to an international flight or vice vice + + + align:start position:0% +to an international flight or vice vice +versa uh so it had to be a closed wall + + align:start position:0% +versa uh so it had to be a closed wall + + + align:start position:0% +versa uh so it had to be a closed wall +but we thought it didn't necessarily + + align:start position:0% +but we thought it didn't necessarily + + + align:start position:0% +but we thought it didn't necessarily +have to be as closed as all that maybe + + align:start position:0% +have to be as closed as all that maybe + + + align:start position:0% +have to be as closed as all that maybe +it could join people even though it was + + align:start position:0% +it could join people even though it was + + + align:start position:0% +it could join people even though it was +closed so we took the idea of the + + align:start position:0% +closed so we took the idea of the + + + align:start position:0% +closed so we took the idea of the +existing wall and waved it waved it + + align:start position:0% +existing wall and waved it waved it + + + align:start position:0% +existing wall and waved it waved it +waved it waved it in and in and out so + + align:start position:0% +waved it waved it in and in and out so + + + align:start position:0% +waved it waved it in and in and out so +that person sitting for example is + + align:start position:0% +that person sitting for example is + + + align:start position:0% +that person sitting for example is +sitting next to a person who's sitting + + align:start position:0% +sitting next to a person who's sitting + + + align:start position:0% +sitting next to a person who's sitting +on the other side of the wall so they're + + align:start position:0% +on the other side of the wall so they're + + + align:start position:0% +on the other side of the wall so they're +sitting next to each other even though + + align:start position:0% +sitting next to each other even though + + + align:start position:0% +sitting next to each other even though +they're on they're on separate sides of + + align:start position:0% +they're on they're on separate sides of + + + align:start position:0% +they're on they're on separate sides of +the wall uh we use the combination of + + align:start position:0% +the wall uh we use the combination of + + + align:start position:0% +the wall uh we use the combination of +transparent material and mirrored + + align:start position:0% +transparent material and mirrored + + + align:start position:0% +transparent material and mirrored +material so that as you looked from one + + align:start position:0% +material so that as you looked from one + + + align:start position:0% +material so that as you looked from one +one passage to another uh you could see + + align:start position:0% +one passage to another uh you could see + + + align:start position:0% +one passage to another uh you could see +yourself but through the mirror uh you + + align:start position:0% +yourself but through the mirror uh you + + + align:start position:0% +yourself but through the mirror uh you +can see yourself through the mirror uh + + align:start position:0% +can see yourself through the mirror uh + + + align:start position:0% +can see yourself through the mirror uh +at the same time that you saw that you + + align:start position:0% +at the same time that you saw that you + + + align:start position:0% +at the same time that you saw that you +saw another another person on the other + + align:start position:0% +saw another another person on the other + + + align:start position:0% +saw another another person on the other +side of the wall so you might see this + + align:start position:0% +side of the wall so you might see this + + + align:start position:0% +side of the wall so you might see this +other person with your head or your feet + + align:start position:0% +other person with your head or your feet + + + align:start position:0% +other person with your head or your feet +or your your your your + + align:start position:0% +or your your your your + + + align:start position:0% +or your your your your +arms + + align:start position:0% +arms + + + align:start position:0% +arms +uh another example of a mirror space + + align:start position:0% +uh another example of a mirror space + + + align:start position:0% +uh another example of a mirror space +back to the Memphis project uh the + + align:start position:0% +back to the Memphis project uh the + + + align:start position:0% +back to the Memphis project uh the +surface both inside and outside is + + align:start position:0% +surface both inside and outside is + + + align:start position:0% +surface both inside and outside is +mirrored uh the structure folds down at + + align:start position:0% +mirrored uh the structure folds down at + + + align:start position:0% +mirrored uh the structure folds down at +the base of the columns to make seating + + align:start position:0% +the base of the columns to make seating + + + align:start position:0% +the base of the columns to make seating +but you can also enter enter the columns + + align:start position:0% +but you can also enter enter the columns + + + align:start position:0% +but you can also enter enter the columns +uh again mirrored mirrored both outside + + align:start position:0% +uh again mirrored mirrored both outside + + + align:start position:0% +uh again mirrored mirrored both outside +both outside both outside and inside + + align:start position:0% +both outside both outside and inside + + + align:start position:0% +both outside both outside and inside +inside as you're sitting inside inside + + align:start position:0% +inside as you're sitting inside inside + + + align:start position:0% +inside as you're sitting inside inside +the column uh the sky is reflected down + + align:start position:0% +the column uh the sky is reflected down + + + align:start position:0% +the column uh the sky is reflected down +on this circular wall around you so it's + + align:start position:0% +on this circular wall around you so it's + + + align:start position:0% +on this circular wall around you so it's +as if you're sitting inside a room a + + align:start position:0% +as if you're sitting inside a room a + + + align:start position:0% +as if you're sitting inside a room a +room a room of Sky uh + + align:start position:0% +room a room of Sky uh + + + align:start position:0% +room a room of Sky uh +operation Opera operation thanks + + align:start position:0% +operation Opera operation thanks + + + align:start position:0% +operation Opera operation thanks +operation Operation number seven split + + align:start position:0% +operation Operation number seven split + + + align:start position:0% +operation Operation number seven split +separate planes strips strands back to + + align:start position:0% +separate planes strips strands back to + + + align:start position:0% +separate planes strips strands back to +the Milan project now that we have this + + align:start position:0% +the Milan project now that we have this + + + align:start position:0% +the Milan project now that we have this +extra facade it's got to do something + + align:start position:0% +extra facade it's got to do something + + + align:start position:0% +extra facade it's got to do something +that the first facade that the first + + align:start position:0% +that the first facade that the first + + + align:start position:0% +that the first facade that the first +facade didn't do so the facade can split + + align:start position:0% +facade didn't do so the facade can split + + + align:start position:0% +facade didn't do so the facade can split +by uh operating uh by operating a lever + + align:start position:0% +by uh operating uh by operating a lever + + + align:start position:0% +by uh operating uh by operating a lever +inside the office space you can uh you + + align:start position:0% +inside the office space you can uh you + + + align:start position:0% +inside the office space you can uh you +can open you can open this screen + + align:start position:0% +can open you can open this screen + + + align:start position:0% +can open you can open this screen +covering you can you can give it larger + + align:start position:0% +covering you can you can give it larger + + + align:start position:0% +covering you can you can give it larger +opening + + align:start position:0% +opening + + + align:start position:0% +opening +to bring in more sunlight smaller + + align:start position:0% +to bring in more sunlight smaller + + + align:start position:0% +to bring in more sunlight smaller +openings to bring it to bring it to + + align:start position:0% +openings to bring it to bring it to + + + align:start position:0% +openings to bring it to bring it to +bring in less back to the uh back to the + + align:start position:0% +bring in less back to the uh back to the + + + align:start position:0% +bring in less back to the uh back to the +Vienna gerle project our second step was + + align:start position:0% +Vienna gerle project our second step was + + + align:start position:0% +Vienna gerle project our second step was +once we started with this closed space + + align:start position:0% +once we started with this closed space + + + align:start position:0% +once we started with this closed space +our second step was to make this series + + align:start position:0% +our second step was to make this series + + + align:start position:0% +our second step was to make this series +of planes the planes were basically + + align:start position:0% +of planes the planes were basically + + + align:start position:0% +of planes the planes were basically +sandwiches of mesh planting planting + + align:start position:0% +sandwiches of mesh planting planting + + + align:start position:0% +sandwiches of mesh planting planting +grows inside these + + align:start position:0% +grows inside these + + + align:start position:0% +grows inside these +sandwiches uh holes Hol H are shot + + align:start position:0% +sandwiches uh holes Hol H are shot + + + align:start position:0% +sandwiches uh holes Hol H are shot +through these + + align:start position:0% +through these + + + align:start position:0% +through these +planes the holes the holes carry + + align:start position:0% +planes the holes the holes carry + + + align:start position:0% +planes the holes the holes carry +walkways elevated walkways they make an + + align:start position:0% +walkways elevated walkways they make an + + + align:start position:0% +walkways elevated walkways they make an +Amphitheater space uh they make a play + + align:start position:0% +Amphitheater space uh they make a play + + + align:start position:0% +Amphitheater space uh they make a play +they make a playground space another + + align:start position:0% +they make a playground space another + + + align:start position:0% +they make a playground space another +example of strips uh a project a project + + align:start position:0% +example of strips uh a project a project + + + align:start position:0% +example of strips uh a project a project +we we proposed for uh the novaris + + align:start position:0% +we we proposed for uh the novaris + + + align:start position:0% +we we proposed for uh the novaris +pharmaceutical company + + align:start position:0% +pharmaceutical company + + + align:start position:0% +pharmaceutical company +uh uh uh three three years ago uh + + align:start position:0% +uh uh uh three three years ago uh + + + align:start position:0% +uh uh uh three three years ago uh +the competition was for uh uh a parking + + align:start position:0% +the competition was for uh uh a parking + + + align:start position:0% +the competition was for uh uh a parking +garage for a thousand cars and an entry + + align:start position:0% +garage for a thousand cars and an entry + + + align:start position:0% +garage for a thousand cars and an entry +Gateway for the campus one note about + + align:start position:0% +Gateway for the campus one note about + + + align:start position:0% +Gateway for the campus one note about +this + + align:start position:0% +this + + + align:start position:0% +this +project + + align:start position:0% +project + + + align:start position:0% +project +sorry one one note or or maybe you can + + align:start position:0% +sorry one one note or or maybe you can + + + align:start position:0% +sorry one one note or or maybe you can +make you want to make note because you + + align:start position:0% +make you want to make note because you + + + align:start position:0% +make you want to make note because you +brought it up even more clearly than I + + align:start position:0% +brought it up even more clearly than I + + + align:start position:0% +brought it up even more clearly than I +did okay uh one note about the about + + align:start position:0% +did okay uh one note about the about + + + align:start position:0% +did okay uh one note about the about +this about this project uh one reason + + align:start position:0% +this about this project uh one reason + + + align:start position:0% +this about this project uh one reason +we're were interested in this + + align:start position:0% +we're were interested in this + + + align:start position:0% +we're were interested in this +competition is that we were competing + + align:start position:0% +competition is that we were competing + + + align:start position:0% +competition is that we were competing +against uh some Architects we paid a lot + + align:start position:0% +against uh some Architects we paid a lot + + + align:start position:0% +against uh some Architects we paid a lot +of attention to uh foreign office + + align:start position:0% +of attention to uh foreign office + + + align:start position:0% +of attention to uh foreign office +Architects zaha + + align:start position:0% +Architects zaha + + + align:start position:0% +Architects zaha +Hadid uh it turned out nobody won the + + align:start position:0% +Hadid uh it turned out nobody won the + + + align:start position:0% +Hadid uh it turned out nobody won the +competition but I think I think nobody + + align:start position:0% +competition but I think I think nobody + + + align:start position:0% +competition but I think I think nobody +should have competed for the competition + + align:start position:0% +should have competed for the competition + + + align:start position:0% +should have competed for the competition +uh it was a competition for the novaris + + align:start position:0% +uh it was a competition for the novaris + + + align:start position:0% +uh it was a competition for the novaris +pharmaceutical company you know a + + align:start position:0% +pharmaceutical company you know a + + + align:start position:0% +pharmaceutical company you know a +company that spends most of its time uh + + align:start position:0% +company that spends most of its time uh + + + align:start position:0% +company that spends most of its time uh +running campaigns against against + + align:start position:0% +running campaigns against against + + + align:start position:0% +running campaigns against against +against against generic drugs + + align:start position:0% +against against generic drugs + + + align:start position:0% +against against generic drugs +sometimes when you're designing a + + align:start position:0% +sometimes when you're designing a + + + align:start position:0% +sometimes when you're designing a +project you're so desperate to build + + align:start position:0% +project you're so desperate to build + + + align:start position:0% +project you're so desperate to build +that maybe you start to forget who + + align:start position:0% +that maybe you start to forget who + + + align:start position:0% +that maybe you start to forget who +you're building for and I hope we never + + align:start position:0% +you're building for and I hope we never + + + align:start position:0% +you're building for and I hope we never +forget that again uh anyway the the uh + + align:start position:0% +forget that again uh anyway the the uh + + + align:start position:0% +forget that again uh anyway the the uh +parking garage the parking garage was + + align:start position:0% +parking garage the parking garage was + + + align:start position:0% +parking garage the parking garage was +going to be under a park a private + + align:start position:0% +going to be under a park a private + + + align:start position:0% +going to be under a park a private +novaris park um so our starting point + + align:start position:0% +novaris park um so our starting point + + + align:start position:0% +novaris park um so our starting point +was that if a parking garage is under + + align:start position:0% +was that if a parking garage is under + + + align:start position:0% +was that if a parking garage is under +the park uh it's obvious that they were + + align:start position:0% +the park uh it's obvious that they were + + + align:start position:0% +the park uh it's obvious that they were +trying to they were trying to consider + + align:start position:0% +trying to they were trying to consider + + + align:start position:0% +trying to they were trying to consider +the uh the the park is being used as is + + align:start position:0% +the uh the the park is being used as is + + + align:start position:0% +the uh the the park is being used as is +a suppression of the parking garage the + + align:start position:0% +a suppression of the parking garage the + + + align:start position:0% +a suppression of the parking garage the +park is trying to pretend that the + + align:start position:0% +park is trying to pretend that the + + + align:start position:0% +park is trying to pretend that the +parking garage doesn't exist so our + + align:start position:0% +parking garage doesn't exist so our + + + align:start position:0% +parking garage doesn't exist so our +first step is to uh split the parking + + align:start position:0% +first step is to uh split the parking + + + align:start position:0% +first step is to uh split the parking +the the the park into strips like the + + align:start position:0% +the the the park into strips like the + + + align:start position:0% +the the the park into strips like the +strips of parking below below ground the + + align:start position:0% +strips of parking below below ground the + + + align:start position:0% +strips of parking below below ground the +strips of Park rise and fall like the + + align:start position:0% +strips of Park rise and fall like the + + + align:start position:0% +strips of Park rise and fall like the +like the parking ramps underground so + + align:start position:0% +like the parking ramps underground so + + + align:start position:0% +like the parking ramps underground so +now there's a mix of Park and parking at + + align:start position:0% +now there's a mix of Park and parking at + + + align:start position:0% +now there's a mix of Park and parking at +certain points you can walk out from + + align:start position:0% +certain points you can walk out from + + + align:start position:0% +certain points you can walk out from +parking from parking garage to park and + + align:start position:0% +parking from parking garage to park and + + + align:start position:0% +parking from parking garage to park and +vice and vice and vice and vice and vice + + align:start position:0% +vice and vice and vice and vice and vice + + + align:start position:0% +vice and vice and vice and vice and vice +versa uh + + align:start position:0% + + + + align:start position:0% + +operation Opera operation number eight + + align:start position:0% +operation Opera operation number eight + + + align:start position:0% +operation Opera operation number eight +uh an architecture of landscape Contin + + align:start position:0% +uh an architecture of landscape Contin + + + align:start position:0% +uh an architecture of landscape Contin +continuing with the novaris project the + + align:start position:0% +continuing with the novaris project the + + + align:start position:0% +continuing with the novaris project the +no the novaris buildings noard what they + + align:start position:0% +no the novaris buildings noard what they + + + align:start position:0% +no the novaris buildings noard what they +call the novaris campus though it's you + + align:start position:0% +call the novaris campus though it's you + + + align:start position:0% +call the novaris campus though it's you +know it's not a university it's a + + align:start position:0% +know it's not a university it's a + + + align:start position:0% +know it's not a university it's a +corporation uh as are some universities + + align:start position:0% +corporation uh as are some universities + + + align:start position:0% +corporation uh as are some universities +but um uh the parking garage the uh the + + align:start position:0% +but um uh the parking garage the uh the + + + align:start position:0% +but um uh the parking garage the uh the +novaris campus is recess from the street + + align:start position:0% +novaris campus is recess from the street + + + align:start position:0% +novaris campus is recess from the street +we thought maybe the novaris campus + + align:start position:0% +we thought maybe the novaris campus + + + align:start position:0% +we thought maybe the novaris campus +should should get more of a street + + align:start position:0% +should should get more of a street + + + align:start position:0% +should should get more of a street +presence now that we had the private + + align:start position:0% +presence now that we had the private + + + align:start position:0% +presence now that we had the private +park separated into strips we could + + align:start position:0% +park separated into strips we could + + + align:start position:0% +park separated into strips we could +stretch those strips stretch them uh + + align:start position:0% +stretch those strips stretch them uh + + + align:start position:0% +stretch those strips stretch them uh +stretch them out towards the street + + align:start position:0% +stretch them out towards the street + + + align:start position:0% +stretch them out towards the street +they're supported by arches made from + + align:start position:0% +they're supported by arches made from + + + align:start position:0% +they're supported by arches made from +concrete from the from the public + + align:start position:0% +concrete from the from the public + + + align:start position:0% +concrete from the from the public +sidewalk so now the Nar buildings come + + align:start position:0% +sidewalk so now the Nar buildings come + + + align:start position:0% +sidewalk so now the Nar buildings come +out come out come out to the + + align:start position:0% +out come out come out to the + + + align:start position:0% +out come out come out to the +campus uh another example of + + align:start position:0% +campus uh another example of + + + align:start position:0% +campus uh another example of +stretch is uh a project we're working + + align:start position:0% +stretch is uh a project we're working + + + align:start position:0% +stretch is uh a project we're working +we're working on now I want to give just + + align:start position:0% +we're working on now I want to give just + + + align:start position:0% +we're working on now I want to give just +a quick rundown of the project then I + + align:start position:0% +a quick rundown of the project then I + + + align:start position:0% +a quick rundown of the project then I +think you know Dario's worked really + + align:start position:0% +think you know Dario's worked really + + + align:start position:0% +think you know Dario's worked really +intensively on this project he's working + + align:start position:0% +intensively on this project he's working + + + align:start position:0% +intensively on this project he's working +on other projects too I mean most of the + + align:start position:0% +on other projects too I mean most of the + + + align:start position:0% +on other projects too I mean most of the +most of the + + align:start position:0% +most of the + + + align:start position:0% +most of the +projects that's what I thought he told + + align:start position:0% +projects that's what I thought he told + + + align:start position:0% +projects that's what I thought he told +me he said no but okay do you want to + + align:start position:0% +me he said no but okay do you want to + + + align:start position:0% +me he said no but okay do you want to +why don't why not why don't do you want + + align:start position:0% +why don't why not why don't do you want + + + align:start position:0% +why don't why not why don't do you want +to talk about project I think the reason + + align:start position:0% +to talk about project I think the reason + + + align:start position:0% +to talk about project I think the reason +to showing this project is made as a + + align:start position:0% +to showing this project is made as a + + + align:start position:0% +to showing this project is made as a +good example of of something weo has + + align:start position:0% +good example of of something weo has + + + align:start position:0% +good example of of something weo has +brought brought about brought up before + + align:start position:0% +brought brought about brought up before + + + align:start position:0% +brought brought about brought up before +uh when he said that he didn't really + + align:start position:0% +uh when he said that he didn't really + + + align:start position:0% +uh when he said that he didn't really +know how to how how to do anything and + + align:start position:0% +know how to how how to do anything and + + + align:start position:0% +know how to how how to do anything and +um and and and more and more working + + align:start position:0% +um and and and more and more working + + + align:start position:0% +um and and and more and more working +with zoo we find ourselves uh working on + + align:start position:0% +with zoo we find ourselves uh working on + + + align:start position:0% +with zoo we find ourselves uh working on +working on projects which we really + + align:start position:0% +working on projects which we really + + + align:start position:0% +working on projects which we really +don't know how to do uh because uh we've + + align:start position:0% +don't know how to do uh because uh we've + + + align:start position:0% +don't know how to do uh because uh we've +never + + align:start position:0% + + + + align:start position:0% + +hold + + align:start position:0% +hold + + + align:start position:0% +hold +uh uh we we because we we've never we've + + align:start position:0% +uh uh we we because we we've never we've + + + align:start position:0% +uh uh we we because we we've never we've +never done projects like that before and + + align:start position:0% +never done projects like that before and + + + align:start position:0% +never done projects like that before and +and even even though I studied + + align:start position:0% +and even even though I studied + + + align:start position:0% +and even even though I studied +architecture uh I nothing can really + + align:start position:0% +architecture uh I nothing can really + + + align:start position:0% +architecture uh I nothing can really +prepare you for for for for working with + + align:start position:0% +prepare you for for for for working with + + + align:start position:0% +prepare you for for for for working with +v uh + + align:start position:0% +v uh + + + align:start position:0% +v uh +it's it's it's so but and yeah but also + + align:start position:0% +it's it's it's so but and yeah but also + + + align:start position:0% +it's it's it's so but and yeah but also +nothing can push me as much as other + + align:start position:0% +nothing can push me as much as other + + + align:start position:0% +nothing can push me as much as other +people in stos so so it's a so we we + + align:start position:0% +people in stos so so it's a so we we + + + align:start position:0% +people in stos so so it's a so we we +push we push each other around a lot and + + align:start position:0% +push we push each other around a lot and + + + align:start position:0% +push we push each other around a lot and +um so so this project is is is a good + + align:start position:0% +um so so this project is is is a good + + + align:start position:0% +um so so this project is is is a good +example of that because uh uh Architects + + align:start position:0% +example of that because uh uh Architects + + + align:start position:0% +example of that because uh uh Architects +tend not to not to design skate parks uh + + align:start position:0% +tend not to not to design skate parks uh + + + align:start position:0% +tend not to not to design skate parks uh +in fact a lot a lot of Architects see to + + align:start position:0% +in fact a lot a lot of Architects see to + + + align:start position:0% +in fact a lot a lot of Architects see to +have a kind of an aversion to to to + + align:start position:0% +have a kind of an aversion to to to + + + align:start position:0% +have a kind of an aversion to to to +skating uh as it as it seems to to + + align:start position:0% +skating uh as it as it seems to to + + + align:start position:0% +skating uh as it as it seems to to +appropriate appropriate appropriate + + align:start position:0% +appropriate appropriate appropriate + + + align:start position:0% +appropriate appropriate appropriate +appropriate architecture to um to to + + align:start position:0% +appropriate architecture to um to to + + + align:start position:0% +appropriate architecture to um to to +skate uh just as as as as a as as as a + + align:start position:0% +skate uh just as as as as a as as as a + + + align:start position:0% +skate uh just as as as as a as as as a +note uh this happened because uh while + + align:start position:0% +note uh this happened because uh while + + + align:start position:0% +note uh this happened because uh while +skate parks uh uh were were were kind of + + align:start position:0% +skate parks uh uh were were were kind of + + + align:start position:0% +skate parks uh uh were were were kind of +a big thing in the 70s they they all B + + align:start position:0% +a big thing in the 70s they they all B + + + align:start position:0% +a big thing in the 70s they they all B +but died out in the in the 80s dur + + align:start position:0% +but died out in the in the 80s dur + + + align:start position:0% +but died out in the in the 80s dur +during this period um uh skaters didn't + + align:start position:0% +during this period um uh skaters didn't + + + align:start position:0% +during this period um uh skaters didn't +didn't have a lot of places to skate + + align:start position:0% +didn't have a lot of places to skate + + + align:start position:0% +didn't have a lot of places to skate +besides uh besides some some friends + + align:start position:0% +besides uh besides some some friends + + + align:start position:0% +besides uh besides some some friends +skate uh some some some friends swimming + + align:start position:0% +skate uh some some some friends swimming + + + align:start position:0% +skate uh some some some friends swimming +pool uh or a place where they could uh + + align:start position:0% +pool uh or a place where they could uh + + + align:start position:0% +pool uh or a place where they could uh +they could maybe invade and and and and + + align:start position:0% +they could maybe invade and and and and + + + align:start position:0% +they could maybe invade and and and and +and skate so they started uh skating + + align:start position:0% +and skate so they started uh skating + + + align:start position:0% +and skate so they started uh skating +whatever was available and and that was + + align:start position:0% +whatever was available and and that was + + + align:start position:0% +whatever was available and and that was +uh primarily streets um public spaces + + align:start position:0% +uh primarily streets um public spaces + + + align:start position:0% +uh primarily streets um public spaces +Parks uh in doing so they they probably + + align:start position:0% +Parks uh in doing so they they probably + + + align:start position:0% +Parks uh in doing so they they probably +uh they they they they caused some + + align:start position:0% +uh they they they they caused some + + + align:start position:0% +uh they they they they caused some +damage and and made some noise but uh + + align:start position:0% +damage and and made some noise but uh + + + align:start position:0% +damage and and made some noise but uh +but in in the process they they develop + + align:start position:0% +but in in the process they they develop + + + align:start position:0% +but in in the process they they develop +a new kind of new kind of skating uh in + + align:start position:0% +a new kind of new kind of skating uh in + + + align:start position:0% +a new kind of new kind of skating uh in +in in the '90s now um uh skate skate + + align:start position:0% +in in the '90s now um uh skate skate + + + align:start position:0% +in in the '90s now um uh skate skate +parks had had res Resurgence probably + + align:start position:0% +parks had had res Resurgence probably + + + align:start position:0% +parks had had res Resurgence probably +because uh the the the damage had had + + align:start position:0% +because uh the the the damage had had + + + align:start position:0% +because uh the the the damage had had +had gone to a point in which uh a lot of + + align:start position:0% +had gone to a point in which uh a lot of + + + align:start position:0% +had gone to a point in which uh a lot of +a lot of municipalities started thinking + + align:start position:0% +a lot of municipalities started thinking + + + align:start position:0% +a lot of municipalities started thinking +well maybe maybe we ought to have a + + align:start position:0% +well maybe maybe we ought to have a + + + align:start position:0% +well maybe maybe we ought to have a +space for these people to to do this um + + align:start position:0% +space for these people to to do this um + + + align:start position:0% +space for these people to to do this um +so uh we we even though we uh we we uh + + align:start position:0% +so uh we we even though we uh we we uh + + + align:start position:0% +so uh we we even though we uh we we uh +work uh as I said working on working on + + align:start position:0% +work uh as I said working on working on + + + align:start position:0% +work uh as I said working on working on +something that uh uh we don't know + + align:start position:0% +something that uh uh we don't know + + + align:start position:0% +something that uh uh we don't know +really how to do uh one one of the ways + + align:start position:0% +really how to do uh one one of the ways + + + align:start position:0% +really how to do uh one one of the ways +of approaching uh such such a project is + + align:start position:0% +of approaching uh such such a project is + + + align:start position:0% +of approaching uh such such a project is +to to to to find somebody who knows how + + align:start position:0% +to to to to find somebody who knows how + + + align:start position:0% +to to to to find somebody who knows how +to do that and um and and work with them + + align:start position:0% +to do that and um and and work with them + + + align:start position:0% +to do that and um and and work with them +and talk to them uh we we work with a + + align:start position:0% +and talk to them uh we we work with a + + + align:start position:0% +and talk to them uh we we work with a +consultant a Skate Park Builder somebody + + align:start position:0% +consultant a Skate Park Builder somebody + + + align:start position:0% +consultant a Skate Park Builder somebody +who's in in California uh a guy named + + align:start position:0% +who's in in California uh a guy named + + + align:start position:0% +who's in in California uh a guy named +Zach wormhout and he's designed a lot of + + align:start position:0% +Zach wormhout and he's designed a lot of + + + align:start position:0% +Zach wormhout and he's designed a lot of +a lot of skate parks um and uh so so the + + align:start position:0% +a lot of skate parks um and uh so so the + + + align:start position:0% +a lot of skate parks um and uh so so the +skate park let just just briefly the + + align:start position:0% +skate park let just just briefly the + + + align:start position:0% +skate park let just just briefly the +skate park is in is in sanan in Puerto + + align:start position:0% +skate park is in is in sanan in Puerto + + + align:start position:0% +skate park is in is in sanan in Puerto +Rico and the site for the skate park is + + align:start position:0% +Rico and the site for the skate park is + + + align:start position:0% +Rico and the site for the skate park is +a park a a a large park in front of in + + align:start position:0% +a park a a a large park in front of in + + + align:start position:0% +a park a a a large park in front of in +front of in front of the ocean uh we + + align:start position:0% +front of in front of the ocean uh we + + + align:start position:0% +front of in front of the ocean uh we +we're going down um in the park uh uh + + align:start position:0% +we're going down um in the park uh uh + + + align:start position:0% +we're going down um in the park uh uh +what what when when Le saw saw the site + + align:start position:0% +what what when when Le saw saw the site + + + align:start position:0% +what what when when Le saw saw the site +the first time he he he noticed that + + align:start position:0% +the first time he he he noticed that + + + align:start position:0% +the first time he he he noticed that +three three three main features in in + + align:start position:0% +three three three main features in in + + + align:start position:0% +three three three main features in in +this in this in this part of the park + + align:start position:0% +this in this in this part of the park + + + align:start position:0% +this in this in this part of the park +where the site was three high points uh + + align:start position:0% +where the site was three high points uh + + + align:start position:0% +where the site was three high points uh +one is this uh restaurant that um is a + + align:start position:0% +one is this uh restaurant that um is a + + + align:start position:0% +one is this uh restaurant that um is a +is like a very long long ramp underneath + + align:start position:0% +is like a very long long ramp underneath + + + align:start position:0% +is like a very long long ramp underneath +underneath which there is a a restaurant + + align:start position:0% +underneath which there is a a restaurant + + + align:start position:0% +underneath which there is a a restaurant +uh the other feature was this mound uh a + + align:start position:0% +uh the other feature was this mound uh a + + + align:start position:0% +uh the other feature was this mound uh a +mound in front in front of the in front + + align:start position:0% +mound in front in front of the in front + + + align:start position:0% +mound in front in front of the in front +of the ocean uh the other one I'm sorry + + align:start position:0% +of the ocean uh the other one I'm sorry + + + align:start position:0% +of the ocean uh the other one I'm sorry +sorry an oval Mound um not in front of + + align:start position:0% +sorry an oval Mound um not in front of + + + align:start position:0% +sorry an oval Mound um not in front of +the ocean um it has an oal oval-shaped + + align:start position:0% +the ocean um it has an oal oval-shaped + + + align:start position:0% +the ocean um it has an oal oval-shaped +plan and then another Mound uh a high uh + + align:start position:0% +plan and then another Mound uh a high uh + + + align:start position:0% +plan and then another Mound uh a high uh +a flat top mound in front in front of + + align:start position:0% +a flat top mound in front in front of + + + align:start position:0% +a flat top mound in front in front of +the ocean so the basic strategy uh uh + + align:start position:0% +the ocean so the basic strategy uh uh + + + align:start position:0% +the ocean so the basic strategy uh uh +here here here you can see the + + align:start position:0% +here here here you can see the + + + align:start position:0% +here here here you can see the +relationship of that that that that + + align:start position:0% +relationship of that that that that + + + align:start position:0% +relationship of that that that that +mount to to to the ocean it's right it's + + align:start position:0% +mount to to to the ocean it's right it's + + + align:start position:0% +mount to to to the ocean it's right it's +very very very very very close + + align:start position:0% +very very very very very close + + + align:start position:0% +very very very very very close +um so the the strategy uh the general + + align:start position:0% +um so the the strategy uh the general + + + align:start position:0% +um so the the strategy uh the general +strategy was then to connect these three + + align:start position:0% +strategy was then to connect these three + + + align:start position:0% +strategy was then to connect these three +high points uh since uh uh skating Works + + align:start position:0% +high points uh since uh uh skating Works + + + align:start position:0% +high points uh since uh uh skating Works +largely on gravity we we had a set up + + align:start position:0% +largely on gravity we we had a set up + + + align:start position:0% +largely on gravity we we had a set up +for for playing with gravity there high + + align:start position:0% +for for playing with gravity there high + + + align:start position:0% +for for playing with gravity there high +points and low points um so how how how + + align:start position:0% +points and low points um so how how how + + + align:start position:0% +points and low points um so how how how +it's organized is uh there's there's a + + align:start position:0% +it's organized is uh there's there's a + + + align:start position:0% +it's organized is uh there's there's a +part of the skate park on each of those + + align:start position:0% +part of the skate park on each of those + + + align:start position:0% +part of the skate park on each of those +high points uh uh on top of the of the + + align:start position:0% +high points uh uh on top of the of the + + + align:start position:0% +high points uh uh on top of the of the +of the of the restaurant there is uh uh + + align:start position:0% +of the of the restaurant there is uh uh + + + align:start position:0% +of the of the restaurant there is uh uh +two ramps two ramps that uh the kind of + + align:start position:0% +two ramps two ramps that uh the kind of + + + align:start position:0% +two ramps two ramps that uh the kind of +ramps are called snake runs uh skaters + + align:start position:0% +ramps are called snake runs uh skaters + + + align:start position:0% +ramps are called snake runs uh skaters +uh come down from in in in with those + + align:start position:0% +uh come down from in in in with those + + + align:start position:0% +uh come down from in in in with those +two Rams and then decide to turn left + + align:start position:0% +two Rams and then decide to turn left + + + align:start position:0% +two Rams and then decide to turn left +left or right if they decide to turn + + align:start position:0% +left or right if they decide to turn + + + align:start position:0% +left or right if they decide to turn +right they'll + + align:start position:0% +right they'll + + + align:start position:0% +right they'll +go + + align:start position:0% +go + + + align:start position:0% +go +okay well before that uh between between + + align:start position:0% +okay well before that uh between between + + + align:start position:0% +okay well before that uh between between +these these these ramps um the park uh + + align:start position:0% +these these these ramps um the park uh + + + align:start position:0% +these these these ramps um the park uh +the existing Park uh Still Still Still + + align:start position:0% +the existing Park uh Still Still Still + + + align:start position:0% +the existing Park uh Still Still Still +functions in a way we we overlaid a + + align:start position:0% +functions in a way we we overlaid a + + + align:start position:0% +functions in a way we we overlaid a +skate park over a park uh uh this is + + align:start position:0% +skate park over a park uh uh this is + + + align:start position:0% +skate park over a park uh uh this is +different H it's usually done skate + + align:start position:0% +different H it's usually done skate + + + align:start position:0% +different H it's usually done skate +parks tend to be shoved in a corner uh + + align:start position:0% +parks tend to be shoved in a corner uh + + + align:start position:0% +parks tend to be shoved in a corner uh +because of of of liabilities and issues + + align:start position:0% +because of of of liabilities and issues + + + align:start position:0% +because of of of liabilities and issues +like that we decided to uh uh try to + + align:start position:0% +like that we decided to uh uh try to + + + align:start position:0% +like that we decided to uh uh try to +make a safe Park that could as safe as + + align:start position:0% +make a safe Park that could as safe as + + + align:start position:0% +make a safe Park that could as safe as +as is needed to be so that it didn't + + align:start position:0% +as is needed to be so that it didn't + + + align:start position:0% +as is needed to be so that it didn't +have to be segre to to to a corner + + align:start position:0% +have to be segre to to to a corner + + + align:start position:0% +have to be segre to to to a corner +um so so you turn right and you go into + + align:start position:0% +um so so you turn right and you go into + + + align:start position:0% +um so so you turn right and you go into +the oval Mound the oval Mound now is + + align:start position:0% +the oval Mound the oval Mound now is + + + align:start position:0% +the oval Mound the oval Mound now is +used uh as an internal space uh you you + + align:start position:0% +used uh as an internal space uh you you + + + align:start position:0% +used uh as an internal space uh you you +dive into the the oval Mound inside the + + align:start position:0% +dive into the the oval Mound inside the + + + align:start position:0% +dive into the the oval Mound inside the +opal Mound uh it's a space of bowls a + + align:start position:0% +opal Mound uh it's a space of bowls a + + + align:start position:0% +opal Mound uh it's a space of bowls a +space of caverns uh it's uh a place + + align:start position:0% +space of caverns uh it's uh a place + + + align:start position:0% +space of caverns uh it's uh a place +where which in a way it's it's taking + + align:start position:0% +where which in a way it's it's taking + + + align:start position:0% +where which in a way it's it's taking +the notion of of of a swimming pool and + + align:start position:0% +the notion of of of a swimming pool and + + + align:start position:0% +the notion of of of a swimming pool and +turning it upside down and and and and + + align:start position:0% +turning it upside down and and and and + + + align:start position:0% +turning it upside down and and and and +inside out + + align:start position:0% +inside out + + + align:start position:0% +inside out +um on on the opposite side uh is uh the + + align:start position:0% +um on on the opposite side uh is uh the + + + align:start position:0% +um on on the opposite side uh is uh the +mountain is in front of the ocean uh in + + align:start position:0% +mountain is in front of the ocean uh in + + + align:start position:0% +mountain is in front of the ocean uh in +order to get up that mound uh we have a + + align:start position:0% +order to get up that mound uh we have a + + + align:start position:0% +order to get up that mound uh we have a +series of of steps of platforms + + align:start position:0% +series of of steps of platforms + + + align:start position:0% +series of of steps of platforms +something like what uh skaters tend to + + align:start position:0% +something like what uh skaters tend to + + + align:start position:0% +something like what uh skaters tend to +tend to use uh on streets they tend to + + align:start position:0% +tend to use uh on streets they tend to + + + align:start position:0% +tend to use uh on streets they tend to +use uh uh steps edges uh uh rails uh + + align:start position:0% +use uh uh steps edges uh uh rails uh + + + align:start position:0% +use uh uh steps edges uh uh rails uh +anything which uh uh in which they could + + align:start position:0% +anything which uh uh in which they could + + + align:start position:0% +anything which uh uh in which they could +use the board uh uh without the Wheels + + align:start position:0% +use the board uh uh without the Wheels + + + align:start position:0% +use the board uh uh without the Wheels +actually uh uh uh the the other space is + + align:start position:0% +actually uh uh uh the the other space is + + + align:start position:0% +actually uh uh uh the the other space is +is is more about rolling through this + + align:start position:0% +is is more about rolling through this + + + align:start position:0% +is is more about rolling through this +one is about jumping uh and and and and + + align:start position:0% +one is about jumping uh and and and and + + + align:start position:0% +one is about jumping uh and and and and +and stepping up up onto the mound um at + + align:start position:0% +and stepping up up onto the mound um at + + + align:start position:0% +and stepping up up onto the mound um at +at the end of these these stepped these + + align:start position:0% +at the end of these these stepped these + + + align:start position:0% +at the end of these these stepped these +stepped platforms are are half pipes the + + align:start position:0% +stepped platforms are are half pipes the + + + align:start position:0% +stepped platforms are are half pipes the +half pipes uh can't lever over over the + + align:start position:0% +half pipes uh can't lever over over the + + + align:start position:0% +half pipes uh can't lever over over the +ocean almost almost trying to deliver + + align:start position:0% +ocean almost almost trying to deliver + + + align:start position:0% +ocean almost almost trying to deliver +the skaters back to back back to the + + align:start position:0% +the skaters back to back back to the + + + align:start position:0% +the skaters back to back back to the +ocean because SK skating started at + + align:start position:0% +ocean because SK skating started at + + + align:start position:0% +ocean because SK skating started at +surfing uh basically uh uh when it was + + align:start position:0% +surfing uh basically uh uh when it was + + + align:start position:0% +surfing uh basically uh uh when it was +too cold for surfing uh you know and and + + align:start position:0% +too cold for surfing uh you know and and + + + align:start position:0% +too cold for surfing uh you know and and +pools were + + align:start position:0% +pools were + + + align:start position:0% +pools were +uh uh young people would would fashion + + align:start position:0% +uh uh young people would would fashion + + + align:start position:0% +uh uh young people would would fashion +these these boards with with with with + + align:start position:0% +these these boards with with with with + + + align:start position:0% +these these boards with with with with +with with roller skates and and and sort + + align:start position:0% +with with roller skates and and and sort + + + align:start position:0% +with with roller skates and and and sort +of keep keep keep having fun dur during + + align:start position:0% +of keep keep keep having fun dur during + + + align:start position:0% +of keep keep keep having fun dur during +during the during during the winter + + align:start position:0% +during the during during the winter + + + align:start position:0% +during the during during the winter +um okay um and so just to give a sense + + align:start position:0% +um okay um and so just to give a sense + + + align:start position:0% +um okay um and so just to give a sense +of of + + align:start position:0% +of of + + + align:start position:0% +of of +of know a little bit illustrate just a + + align:start position:0% +of know a little bit illustrate just a + + + align:start position:0% +of know a little bit illustrate just a +little bit what it means of to do + + align:start position:0% +little bit what it means of to do + + + align:start position:0% +little bit what it means of to do +something without really knowing how to + + align:start position:0% +something without really knowing how to + + + align:start position:0% +something without really knowing how to +how to do it + + align:start position:0% +how to do it + + + align:start position:0% +how to do it +uh it the our basic stry is one is is a + + align:start position:0% +uh it the our basic stry is one is is a + + + align:start position:0% +uh it the our basic stry is one is is a +lot of trial and a lot of error uh + + align:start position:0% +lot of trial and a lot of error uh + + + align:start position:0% +lot of trial and a lot of error uh +probably more error but also a lot of a + + align:start position:0% +probably more error but also a lot of a + + + align:start position:0% +probably more error but also a lot of a +lot of a lot more more error than + + align:start position:0% +lot of a lot more more error than + + + align:start position:0% +lot of a lot more more error than +anything but but a lot of trial um and + + align:start position:0% +anything but but a lot of trial um and + + + align:start position:0% +anything but but a lot of trial um and +and uh I just want to give a sense of of + + align:start position:0% +and uh I just want to give a sense of of + + + align:start position:0% +and uh I just want to give a sense of of +of what what uh what that might look + + align:start position:0% +of what what uh what that might look + + + align:start position:0% +of what what uh what that might look +like um and also it's the product of of + + align:start position:0% +like um and also it's the product of of + + + align:start position:0% +like um and also it's the product of of +the way we work uh of those discussions + + align:start position:0% +the way we work uh of those discussions + + + align:start position:0% +the way we work uh of those discussions +uh uh when when V was talking about U uh + + align:start position:0% +uh uh when when V was talking about U uh + + + align:start position:0% +uh uh when when V was talking about U uh +where are you where are we now yeah and + + align:start position:0% +where are you where are we now yeah and + + + align:start position:0% +where are you where are we now yeah and +uh it it doesn't sound like that and + + align:start position:0% +uh it it doesn't sound like that and + + + align:start position:0% +uh it it doesn't sound like that and +what do you think Tom and it it it + + align:start position:0% +what do you think Tom and it it it + + + align:start position:0% +what do you think Tom and it it it +certainly it doesn't sound like like + + align:start position:0% +certainly it doesn't sound like like + + + align:start position:0% +certainly it doesn't sound like like +that we I I I probably shouldn't try to + + align:start position:0% +that we I I I probably shouldn't try to + + + align:start position:0% +that we I I I probably shouldn't try to +repeat the kind of things we say but um + + align:start position:0% +repeat the kind of things we say but um + + + align:start position:0% +repeat the kind of things we say but um +but again there there it's it's never + + align:start position:0% +but again there there it's it's never + + + align:start position:0% +but again there there it's it's never +it's it's it's it is confrontational + + align:start position:0% +it's it's it's it is confrontational + + + align:start position:0% +it's it's it's it is confrontational +yeah it quite is but it's never about + + align:start position:0% +yeah it quite is but it's never about + + + align:start position:0% +yeah it quite is but it's never about +about who's who's right it's it's it's + + align:start position:0% +about who's who's right it's it's it's + + + align:start position:0% +about who's who's right it's it's it's +about uh what what what makes the more + + align:start position:0% +about uh what what what makes the more + + + align:start position:0% +about uh what what what makes the more +most sense uh there's ideas sorry this + + align:start position:0% +most sense uh there's ideas sorry this + + + align:start position:0% +most sense uh there's ideas sorry this +is not coming up uh there's ideas from + + align:start position:0% +is not coming up uh there's ideas from + + + align:start position:0% +is not coming up uh there's ideas from +just about any everybody everybody in + + align:start position:0% +just about any everybody everybody in + + + align:start position:0% +just about any everybody everybody in +the studio uh okay here here here here + + align:start position:0% +the studio uh okay here here here here + + + align:start position:0% +the studio uh okay here here here here +here here here's a little bit of a + + align:start position:0% +here here here's a little bit of a + + + align:start position:0% +here here here's a little bit of a +catalog of possibility can you + + align:start position:0% +catalog of possibility can you + + + align:start position:0% +catalog of possibility can you +hold so for example uh different parts + + align:start position:0% +hold so for example uh different parts + + + align:start position:0% +hold so for example uh different parts +let's let's look at at the M for a + + align:start position:0% + + + + align:start position:0% + +second uh these are all studies for what + + align:start position:0% +second uh these are all studies for what + + + align:start position:0% +second uh these are all studies for what +can happen inside this + + align:start position:0% +can happen inside this + + + align:start position:0% +can happen inside this +this Mount from B spaces now let's try + + align:start position:0% +this Mount from B spaces now let's try + + + align:start position:0% +this Mount from B spaces now let's try +to connect the bll spaces in a way that + + align:start position:0% +to connect the bll spaces in a way that + + + align:start position:0% +to connect the bll spaces in a way that +you can go from one to the other and + + align:start position:0% +you can go from one to the other and + + + align:start position:0% +you can go from one to the other and +here again we're not yet worried about + + align:start position:0% +here again we're not yet worried about + + + align:start position:0% +here again we're not yet worried about +uh pitches and slopes and and heads + + align:start position:0% +uh pitches and slopes and and heads + + + align:start position:0% +uh pitches and slopes and and heads +where're we're trying to determine what + + align:start position:0% +where're we're trying to determine what + + + align:start position:0% +where're we're trying to determine what +what what should happen not how it + + align:start position:0% +what what should happen not how it + + + align:start position:0% +what what should happen not how it +should happen uh not yet at least uh + + align:start position:0% +should happen uh not yet at least uh + + + align:start position:0% +should happen uh not yet at least uh +it's it's as if we we sort of keep this + + align:start position:0% +it's it's as if we we sort of keep this + + + align:start position:0% +it's it's as if we we sort of keep this +uh keep this sense of of everything is + + align:start position:0% +uh keep this sense of of everything is + + + align:start position:0% +uh keep this sense of of everything is +possible uh for for as long as possible + + align:start position:0% +possible uh for for as long as possible + + + align:start position:0% +possible uh for for as long as possible +um and until we find something that that + + align:start position:0% +um and until we find something that that + + + align:start position:0% +um and until we find something that that +uh can can exist in both in the space + + align:start position:0% +uh can can exist in both in the space + + + align:start position:0% +uh can can exist in both in the space +that excites us and the space that can + + align:start position:0% +that excites us and the space that can + + + align:start position:0% +that excites us and the space that can +can actually can can actually can + + align:start position:0% +can actually can can actually can + + + align:start position:0% +can actually can can actually can +actually happen um another uh uh just a + + align:start position:0% +actually happen um another uh uh just a + + + align:start position:0% +actually happen um another uh uh just a +just + + align:start position:0% +just + + + align:start position:0% +just +a a little bit the evolution of that + + align:start position:0% +a a little bit the evolution of that + + + align:start position:0% +a a little bit the evolution of that +that that that space that uh is within + + align:start position:0% +that that that space that uh is within + + + align:start position:0% +that that that space that uh is within +the internal space within within within + + align:start position:0% +the internal space within within within + + + align:start position:0% +the internal space within within within +within the mound um as we work on it uh + + align:start position:0% +within the mound um as we work on it uh + + + align:start position:0% +within the mound um as we work on it uh +we send our models to to our our + + align:start position:0% +we send our models to to our our + + + align:start position:0% +we send our models to to our our +consultant who uh tells us uh this + + align:start position:0% +consultant who uh tells us uh this + + + align:start position:0% +consultant who uh tells us uh this +radius is wrong this radius is okay uh + + align:start position:0% +radius is wrong this radius is okay uh + + + align:start position:0% +radius is wrong this radius is okay uh +here you're going to kill yourself here + + align:start position:0% +here you're going to kill yourself here + + + align:start position:0% +here you're going to kill yourself here +not much is going on um and um and then + + align:start position:0% +not much is going on um and um and then + + + align:start position:0% +not much is going on um and um and then +uh still we we have a a kind a hard time + + align:start position:0% +uh still we we have a a kind a hard time + + + align:start position:0% +uh still we we have a a kind a hard time +visualizing uh such a space uh sometimes + + align:start position:0% +visualizing uh such a space uh sometimes + + + align:start position:0% +visualizing uh such a space uh sometimes +we we I feel are we complicating things + + align:start position:0% +we we I feel are we complicating things + + + align:start position:0% +we we I feel are we complicating things +too too too too much are we are we + + align:start position:0% +too too too too much are we are we + + + align:start position:0% +too too too too much are we are we +setting up something that we don't know + + align:start position:0% +setting up something that we don't know + + + align:start position:0% +setting up something that we don't know +how to we we can't predict what the + + align:start position:0% +how to we we can't predict what the + + + align:start position:0% +how to we we can't predict what the +experience will be like so uh so we we + + align:start position:0% +experience will be like so uh so we we + + + align:start position:0% +experience will be like so uh so we we +resort to to to as whatever basically we + + align:start position:0% +resort to to to as whatever basically we + + + align:start position:0% +resort to to to as whatever basically we +can get our hands on that would would + + align:start position:0% +can get our hands on that would would + + + align:start position:0% +can get our hands on that would would +tell us what's what's going on so uh for + + align:start position:0% +tell us what's what's going on so uh for + + + align:start position:0% +tell us what's what's going on so uh for +example uh we in order to try to + + align:start position:0% +example uh we in order to try to + + + align:start position:0% +example uh we in order to try to +experience what it's like to to actually + + align:start position:0% +experience what it's like to to actually + + + align:start position:0% +experience what it's like to to actually +go through this space uh usually + + align:start position:0% +go through this space uh usually + + + align:start position:0% +go through this space uh usually +Architects tend to do these walkthroughs + + align:start position:0% +Architects tend to do these walkthroughs + + + align:start position:0% +Architects tend to do these walkthroughs +and and so we we we came up with a skate + + align:start position:0% +and and so we we we came up with a skate + + + align:start position:0% +and and so we we we came up with a skate +through in a way uh it's and it's not a + + align:start position:0% +through in a way uh it's and it's not a + + + align:start position:0% +through in a way uh it's and it's not a +real skateboard it's it's more like a + + align:start position:0% +real skateboard it's it's more like a + + + align:start position:0% +real skateboard it's it's more like a +hoverboard uh but I guess it'll it'll + + align:start position:0% +hoverboard uh but I guess it'll it'll + + + align:start position:0% +hoverboard uh but I guess it'll it'll +work for hover boards too eventually uh + + align:start position:0% +work for hover boards too eventually uh + + + align:start position:0% +work for hover boards too eventually uh +and uh and and you can uh we can now get + + align:start position:0% +and uh and and you can uh we can now get + + + align:start position:0% +and uh and and you can uh we can now get +a bit of a sense of what you could + + align:start position:0% +a bit of a sense of what you could + + + align:start position:0% +a bit of a sense of what you could +possibly do in in in a place like like + + align:start position:0% +possibly do in in in a place like like + + + align:start position:0% +possibly do in in in a place like like +like this uh the the the game was + + align:start position:0% +like this uh the the the game was + + + align:start position:0% +like this uh the the the game was +something we basically cannibalized + + align:start position:0% +something we basically cannibalized + + + align:start position:0% +something we basically cannibalized +another game and and replace the skate + + align:start position:0% +another game and and replace the skate + + + align:start position:0% +another game and and replace the skate +park um and the skate park part and uh + + align:start position:0% +park um and the skate park part and uh + + + align:start position:0% +park um and the skate park part and uh +and and and then added + + align:start position:0% + + + + align:start position:0% + +a yeah wouldn't that be cool + + align:start position:0% +a yeah wouldn't that be cool + + + align:start position:0% +a yeah wouldn't that be cool +Wai we're waiting for people at MIT to + + align:start position:0% +Wai we're waiting for people at MIT to + + + align:start position:0% +Wai we're waiting for people at MIT to +design this yeah but that's just that's + + align:start position:0% +design this yeah but that's just that's + + + align:start position:0% +design this yeah but that's just that's +that's that's all we need now um but you + + align:start position:0% +that's that's all we need now um but you + + + align:start position:0% +that's that's all we need now um but you +know uh beyond the the the the the fun + + align:start position:0% +know uh beyond the the the the the fun + + + align:start position:0% +know uh beyond the the the the the fun +aspect of things like that there's + + align:start position:0% +aspect of things like that there's + + + align:start position:0% +aspect of things like that there's +there's there's the real the real issues + + align:start position:0% +there's there's the real the real issues + + + align:start position:0% +there's there's the real the real issues +of you know will this be statable how + + align:start position:0% +of you know will this be statable how + + + align:start position:0% +of you know will this be statable how +how do how do we know that how do how do + + align:start position:0% +how do how do we know that how do how do + + + align:start position:0% +how do how do we know that how do how do +we well um we can't uh we can't at least + + align:start position:0% +we well um we can't uh we can't at least + + + align:start position:0% +we well um we can't uh we can't at least +not uh uh without uh probably the help + + align:start position:0% +not uh uh without uh probably the help + + + align:start position:0% +not uh uh without uh probably the help +of MIT we might be able to predict very + + align:start position:0% +of MIT we might be able to predict very + + + align:start position:0% +of MIT we might be able to predict very +precisely um but uh what so but still we + + align:start position:0% +precisely um but uh what so but still we + + + align:start position:0% +precisely um but uh what so but still we +try we try as much as as as as much as + + align:start position:0% +try we try as much as as as as much as + + + align:start position:0% +try we try as much as as as as much as +we can so we uh we study uh uh we we + + align:start position:0% +we can so we uh we study uh uh we we + + + align:start position:0% +we can so we uh we study uh uh we we +studied the for example one of + + align:start position:0% + + + + align:start position:0% + +the one of the snake runs + + align:start position:0% +the one of the snake runs + + + align:start position:0% +the one of the snake runs +uh we tried to study what happens if are + + align:start position:0% +uh we tried to study what happens if are + + + align:start position:0% +uh we tried to study what happens if are +we seeing yeah what happens is if if you + + align:start position:0% +we seeing yeah what happens is if if you + + + align:start position:0% +we seeing yeah what happens is if if you +just count account for gravity and you + + align:start position:0% +just count account for gravity and you + + + align:start position:0% +just count account for gravity and you +know skating is is a lot more than + + align:start position:0% +know skating is is a lot more than + + + align:start position:0% +know skating is is a lot more than +gravity it's maybe sculpting with + + align:start position:0% +gravity it's maybe sculpting with + + + align:start position:0% +gravity it's maybe sculpting with +gravity if you will but uh so we we + + align:start position:0% +gravity if you will but uh so we we + + + align:start position:0% +gravity if you will but uh so we we +basically drop balls in in in in in in + + align:start position:0% +basically drop balls in in in in in in + + + align:start position:0% +basically drop balls in in in in in in +in the surfaces and watch how they + + align:start position:0% +in the surfaces and watch how they + + + align:start position:0% +in the surfaces and watch how they +behave and uh you see on the upper right + + align:start position:0% +behave and uh you see on the upper right + + + align:start position:0% +behave and uh you see on the upper right +right corner we have a little problem + + align:start position:0% +right corner we have a little problem + + + align:start position:0% +right corner we have a little problem +there uh we would have a big a big a big + + align:start position:0% +there uh we would have a big a big a big + + + align:start position:0% +there uh we would have a big a big a big +mashup of skaters um and uh or you know + + align:start position:0% +mashup of skaters um and uh or you know + + + align:start position:0% +mashup of skaters um and uh or you know +we study it for example like that or we + + align:start position:0% +we study it for example like that or we + + + align:start position:0% +we study it for example like that or we +then try let me see if I can find the + + align:start position:0% +then try let me see if I can find the + + + align:start position:0% +then try let me see if I can find the +one + + align:start position:0% +one + + + align:start position:0% +one +with this one might be exactly the same + + align:start position:0% +with this one might be exactly the same + + + align:start position:0% +with this one might be exactly the same +oh no here + + align:start position:0% +oh no here + + + align:start position:0% +oh no here +here's oh yeah there we go uh with more + + align:start position:0% +here's oh yeah there we go uh with more + + + align:start position:0% +here's oh yeah there we go uh with more +more more like a crowd of of of of + + align:start position:0% +more more like a crowd of of of of + + + align:start position:0% +more more like a crowd of of of of +marbles this this actually a little bit + + align:start position:0% +marbles this this actually a little bit + + + align:start position:0% +marbles this this actually a little bit +V visually is is a bit a bit more clear + + align:start position:0% +V visually is is a bit a bit more clear + + + align:start position:0% +V visually is is a bit a bit more clear +and and here on the upper right corner + + align:start position:0% +and and here on the upper right corner + + + align:start position:0% +and and here on the upper right corner +again we have we have the the suicide + + align:start position:0% +again we have we have the the suicide + + + align:start position:0% +again we have we have the the suicide +Moon that which we we we we we we dealt + + align:start position:0% +Moon that which we we we we we we dealt + + + align:start position:0% +Moon that which we we we we we we dealt +with and and and now we have a better a + + align:start position:0% +with and and and now we have a better a + + + align:start position:0% +with and and and now we have a better a +better a better simulation than that we + + align:start position:0% +better a better simulation than that we + + + align:start position:0% +better a better simulation than that we +changed that area but basically like + + align:start position:0% +changed that area but basically like + + + align:start position:0% +changed that area but basically like +that um and and and very much all all + + align:start position:0% +that um and and and very much all all + + + align:start position:0% +that um and and and very much all all +all projects uh uh are developed this + + align:start position:0% +all projects uh uh are developed this + + + align:start position:0% +all projects uh uh are developed this +way uh we're not sort of + + align:start position:0% +way uh we're not sort of + + + align:start position:0% +way uh we're not sort of +following in a way we're not following a + + align:start position:0% +following in a way we're not following a + + + align:start position:0% +following in a way we're not following a +sort of a a vision or or or a direction + + align:start position:0% +sort of a a vision or or or a direction + + + align:start position:0% +sort of a a vision or or or a direction +which sometimes I used to complain to V + + align:start position:0% +which sometimes I used to complain to V + + + align:start position:0% +which sometimes I used to complain to V +what what are we doing and and and and + + align:start position:0% +what what are we doing and and and and + + + align:start position:0% +what what are we doing and and and and +and and a lot of times he says I don't + + align:start position:0% +and and a lot of times he says I don't + + + align:start position:0% +and and a lot of times he says I don't +know and uh and and and so we keep what + + align:start position:0% +know and uh and and and so we keep what + + + align:start position:0% +know and uh and and and so we keep what +we can do is is keep going keep going + + align:start position:0% +we can do is is keep going keep going + + + align:start position:0% +we can do is is keep going keep going +until I do say we want we want to find + + align:start position:0% +until I do say we want we want to find + + + align:start position:0% +until I do say we want we want to find +out yeah well + + align:start position:0% + + + + align:start position:0% + +yeah okay there's more on this project + + align:start position:0% +yeah okay there's more on this project + + + align:start position:0% +yeah okay there's more on this project +and the panel behind right here yeah + + align:start position:0% +and the panel behind right here yeah + + + align:start position:0% +and the panel behind right here yeah +this is a a bit of again try try to give + + align:start position:0% +this is a a bit of again try try to give + + + align:start position:0% +this is a a bit of again try try to give +a sense of what goes into coming up with + + align:start position:0% +a sense of what goes into coming up with + + + align:start position:0% +a sense of what goes into coming up with +with something or and developing + + align:start position:0% +with something or and developing + + + align:start position:0% +with something or and developing +something something some something + + align:start position:0% +something something some something + + + align:start position:0% +something something some something +something like that um do do you want to + + align:start position:0% +something like that um do do you want to + + + align:start position:0% +something like that um do do you want to +do you want to explain talk a little bit + + align:start position:0% +do you want to explain talk a little bit + + + align:start position:0% +do you want to explain talk a little bit +about um about fashion + + align:start position:0% +about um about fashion + + + align:start position:0% +about um about fashion +um okay I'll I'll take word that you + + align:start position:0% +um okay I'll I'll take word that you + + + align:start position:0% +um okay I'll I'll take word that you +us you want I'll plug in your laptop + + align:start position:0% +us you want I'll plug in your laptop + + + align:start position:0% +us you want I'll plug in your laptop +yeah needs needs a + + align:start position:0% + + + + align:start position:0% + +switch um there was a a no there was a + + align:start position:0% +switch um there was a a no there was a + + + align:start position:0% +switch um there was a a no there was a +word that g was using which was + + align:start position:0% +word that g was using which was + + + align:start position:0% +word that g was using which was +cannibalizing and + + align:start position:0% +cannibalizing and + + + align:start position:0% +cannibalizing and +talks um depending on some of the + + align:start position:0% +talks um depending on some of the + + + align:start position:0% +talks um depending on some of the +subjects um that he chooses to develop + + align:start position:0% +subjects um that he chooses to develop + + + align:start position:0% +subjects um that he chooses to develop +um one of one of them he might present + + align:start position:0% +um one of one of them he might present + + + align:start position:0% +um one of one of them he might present +um the idea of parasite or the idea of + + align:start position:0% +um the idea of parasite or the idea of + + + align:start position:0% +um the idea of parasite or the idea of +the idea of virus or the idea of + + align:start position:0% +the idea of virus or the idea of + + + align:start position:0% +the idea of virus or the idea of +parasites um which is a recurring theme + + align:start position:0% +parasites um which is a recurring theme + + + align:start position:0% +parasites um which is a recurring theme +in uh the Studio's work and that + + align:start position:0% + + + + align:start position:0% + +started yeah you have to I + + align:start position:0% +started yeah you have to I + + + align:start position:0% +started yeah you have to I +we lost lost I can't oh it's here it is + + align:start position:0% +we lost lost I can't oh it's here it is + + + align:start position:0% +we lost lost I can't oh it's here it is +there's another I got it I got it + + align:start position:0% +there's another I got it I got it + + + align:start position:0% +there's another I got it I got it +okay + + align:start position:0% +okay + + + align:start position:0% +okay +anyway um and the sometimes um when we + + align:start position:0% +anyway um and the sometimes um when we + + + align:start position:0% +anyway um and the sometimes um when we +have discussions among ourselves we we + + align:start position:0% +have discussions among ourselves we we + + + align:start position:0% +have discussions among ourselves we we +think I mean we we do pose a question + + align:start position:0% +think I mean we we do pose a question + + + align:start position:0% +think I mean we we do pose a question +are we really um are we trying to + + align:start position:0% +are we really um are we trying to + + + align:start position:0% +are we really um are we trying to +reflect or illustrate what a + + align:start position:0% +reflect or illustrate what a + + + align:start position:0% +reflect or illustrate what a +parasite is um um is like are we trying + + align:start position:0% +parasite is um um is like are we trying + + + align:start position:0% +parasite is um um is like are we trying +to um create a sort of um homology with + + align:start position:0% +to um create a sort of um homology with + + + align:start position:0% +to um create a sort of um homology with +the way the virus or parasite acts are + + align:start position:0% +the way the virus or parasite acts are + + + align:start position:0% +the way the virus or parasite acts are +we aware of the differences between the + + align:start position:0% +we aware of the differences between the + + + align:start position:0% +we aware of the differences between the +mode of behavior of a virus or a + + align:start position:0% +mode of behavior of a virus or a + + + align:start position:0% +mode of behavior of a virus or a +parasites I mean very often we use these + + align:start position:0% +parasites I mean very often we use these + + + align:start position:0% +parasites I mean very often we use these +words and um and these words are almost + + align:start position:0% +words and um and these words are almost + + + align:start position:0% +words and um and these words are almost +metaphors like when we use the word + + align:start position:0% +metaphors like when we use the word + + + align:start position:0% +metaphors like when we use the word +stretch we're not literally stretching + + align:start position:0% +stretch we're not literally stretching + + + align:start position:0% +stretch we're not literally stretching +material I wish we could more often and + + align:start position:0% +material I wish we could more often and + + + align:start position:0% +material I wish we could more often and +probably the Milan project we are quite + + align:start position:0% +probably the Milan project we are quite + + + align:start position:0% +probably the Milan project we are quite +a bit um just to pick up on some of + + align:start position:0% +a bit um just to pick up on some of + + + align:start position:0% +a bit um just to pick up on some of +veto's categories when like the Su + + align:start position:0% +veto's categories when like the Su + + + align:start position:0% +veto's categories when like the Su +project which is a project that we like + + align:start position:0% +project which is a project that we like + + + align:start position:0% +project which is a project that we like +very much it's a new project when we + + align:start position:0% +very much it's a new project when we + + + align:start position:0% +very much it's a new project when we +talk about sucking in and sucking out a + + align:start position:0% +talk about sucking in and sucking out a + + + align:start position:0% +talk about sucking in and sucking out a +space we're not unfortunately we're not + + align:start position:0% +space we're not unfortunately we're not + + + align:start position:0% +space we're not unfortunately we're not +literally sucking in and sucking out of + + align:start position:0% +literally sucking in and sucking out of + + + align:start position:0% +literally sucking in and sucking out of +space but so um so we're trying to think + + align:start position:0% +space but so um so we're trying to think + + + align:start position:0% +space but so um so we're trying to think +about the way we're using these words + + align:start position:0% +about the way we're using these words + + + align:start position:0% +about the way we're using these words +because words is just I mean at the + + align:start position:0% +because words is just I mean at the + + + align:start position:0% +because words is just I mean at the +studio I think that one of the things we + + align:start position:0% +studio I think that one of the things we + + + align:start position:0% +studio I think that one of the things we +can say is that in the beginning + + align:start position:0% +can say is that in the beginning + + + align:start position:0% +can say is that in the beginning +beginning there's there's the word um + + align:start position:0% +beginning there's there's the word um + + + align:start position:0% +beginning there's there's the word um +which + + align:start position:0% +which + + + align:start position:0% +which +is which is a great which is a a great + + align:start position:0% +is which is a great which is a a great + + + align:start position:0% +is which is a great which is a a great +way to start um and often we start with + + align:start position:0% +way to start um and often we start with + + + align:start position:0% +way to start um and often we start with +a story as well it's a great way to + + align:start position:0% +a story as well it's a great way to + + + align:start position:0% +a story as well it's a great way to +start maybe but I'm starting to think + + align:start position:0% +start maybe but I'm starting to think + + + align:start position:0% +start maybe but I'm starting to think +it's a real outdated way I can't help + + align:start position:0% +it's a real outdated way I can't help + + + align:start position:0% +it's a real outdated way I can't help +but start by thinking words but I don't + + align:start position:0% +but start by thinking words but I don't + + + align:start position:0% +but start by thinking words but I don't +think words are part of the 21st century + + align:start position:0% +think words are part of the 21st century + + + align:start position:0% +think words are part of the 21st century +and I think Serena can tell you what's + + align:start position:0% +and I think Serena can tell you what's + + + align:start position:0% +and I think Serena can tell you what's +part of the 21st century but yeah I mean + + align:start position:0% +part of the 21st century but yeah I mean + + + align:start position:0% +part of the 21st century but yeah I mean +I you know the 21st century is about Cod + + align:start position:0% +I you know the 21st century is about Cod + + + align:start position:0% +I you know the 21st century is about Cod +diagrams equations it's not it's not + + align:start position:0% +diagrams equations it's not it's not + + + align:start position:0% +diagrams equations it's not it's not +words but anyway so um I'll start with a + + align:start position:0% +words but anyway so um I'll start with a + + + align:start position:0% +words but anyway so um I'll start with a +project that I don't like so much that + + align:start position:0% +project that I don't like so much that + + + align:start position:0% +project that I don't like so much that +we presented very briefly and I know + + align:start position:0% +we presented very briefly and I know + + + align:start position:0% +we presented very briefly and I know +it's quite naughty to U bite the hand + + align:start position:0% +it's quite naughty to U bite the hand + + + align:start position:0% +it's quite naughty to U bite the hand +that feeds you but I hope you'll be + + align:start position:0% +that feeds you but I hope you'll be + + + align:start position:0% +that feeds you but I hope you'll be +indulgent with me it's this Fon Street + + align:start position:0% +indulgent with me it's this Fon Street + + + align:start position:0% +indulgent with me it's this Fon Street +um project that we've been develop that + + align:start position:0% +um project that we've been develop that + + + align:start position:0% +um project that we've been develop that +we've developed um and which looks to me + + align:start position:0% +we've developed um and which looks to me + + + align:start position:0% +we've developed um and which looks to me +like I mean it's very very phic sort of + + align:start position:0% +like I mean it's very very phic sort of + + + align:start position:0% +like I mean it's very very phic sort of +um result and when we had a discussion + + align:start position:0% +um result and when we had a discussion + + + align:start position:0% +um result and when we had a discussion +about this with veto I'm just flashing + + align:start position:0% +about this with veto I'm just flashing + + + align:start position:0% +about this with veto I'm just flashing +through the images veto would say I mean + + align:start position:0% +through the images veto would say I mean + + + align:start position:0% +through the images veto would say I mean +veto would say but no no no it acts like + + align:start position:0% +veto would say but no no no it acts like + + + align:start position:0% +veto would say but no no no it acts like +a parasite it's coming and and and + + align:start position:0% +a parasite it's coming and and and + + + align:start position:0% +a parasite it's coming and and and +sitting on the Dome and and then I was + + align:start position:0% +sitting on the Dome and and then I was + + + align:start position:0% +sitting on the Dome and and then I was +thinking well maybe we should try to + + align:start position:0% +thinking well maybe we should try to + + + align:start position:0% +thinking well maybe we should try to +think you know to try to define a little + + align:start position:0% +think you know to try to define a little + + + align:start position:0% +think you know to try to define a little +bit better some of the terms we're using + + align:start position:0% +bit better some of the terms we're using + + + align:start position:0% +bit better some of the terms we're using +because we're not acting like a parasite + + align:start position:0% +because we're not acting like a parasite + + + align:start position:0% +because we're not acting like a parasite +because this is a public art project and + + align:start position:0% +because this is a public art project and + + + align:start position:0% +because this is a public art project and +we're having the um we're having the the + + align:start position:0% +we're having the um we're having the the + + + align:start position:0% +we're having the um we're having the the +sort of supportive authorities what + + align:start position:0% +sort of supportive authorities what + + + align:start position:0% +sort of supportive authorities what +we're doing really is yeah but we didn't + + align:start position:0% +we're doing really is yeah but we didn't + + + align:start position:0% +we're doing really is yeah but we didn't +get the project built they didn't + + align:start position:0% +get the project built they didn't + + + align:start position:0% +get the project built they didn't +support it yeah they didn't support it I + + align:start position:0% +support it yeah they didn't support it I + + + align:start position:0% +support it yeah they didn't support it I +okay it is at least be fair and say why + + align:start position:0% +okay it is at least be fair and say why + + + align:start position:0% +okay it is at least be fair and say why +some of us thought it was a Paras can + + align:start position:0% +some of us thought it was a Paras can + + + align:start position:0% +some of us thought it was a Paras can +you tell us no no no because I don't + + align:start position:0% +you tell us no no no because I don't + + + align:start position:0% +you tell us no no no because I don't +believe it I mean one of the thing how + + align:start position:0% +believe it I mean one of the thing how + + + align:start position:0% +believe it I mean one of the thing how +how do you do this I mean one of the + + align:start position:0% +how do you do this I mean one of the + + + align:start position:0% +how do you do this I mean one of the +things that interested us was what once + + align:start position:0% +things that interested us was what once + + + align:start position:0% +things that interested us was what once +we turned this at yeah this Atrium is + + align:start position:0% +we turned this at yeah this Atrium is + + + align:start position:0% +we turned this at yeah this Atrium is +great it's a beautiful space but people + + align:start position:0% +great it's a beautiful space but people + + + align:start position:0% +great it's a beautiful space but people +can't people can use it there's all that + + align:start position:0% +can't people can use it there's all that + + + align:start position:0% +can't people can use it there's all that +space up there and no play and no place + + align:start position:0% +space up there and no play and no place + + + align:start position:0% +space up there and no play and no place +for people therefore therefore by + + align:start position:0% +for people therefore therefore by + + + align:start position:0% +for people therefore therefore by +turning the space inside Itself by + + align:start position:0% +turning the space inside Itself by + + + align:start position:0% +turning the space inside Itself by +turning the space inside itself we now + + align:start position:0% +turning the space inside itself we now + + + align:start position:0% +turning the space inside itself we now +still allow an Atrium space in the + + align:start position:0% +still allow an Atrium space in the + + + align:start position:0% +still allow an Atrium space in the +middle but we have this vertical park at + + align:start position:0% +middle but we have this vertical park at + + + align:start position:0% +middle but we have this vertical park at +the sides so people now can at least use + + align:start position:0% +the sides so people now can at least use + + + align:start position:0% +the sides so people now can at least use +the atrium and not just you know stand + + align:start position:0% +the atrium and not just you know stand + + + align:start position:0% +the atrium and not just you know stand +stand below and look up at look up at it + + align:start position:0% +stand below and look up at look up at it + + + align:start position:0% +stand below and look up at look up at it +in awe okay yeah so we and we infiltrate + + align:start position:0% +in awe okay yeah so we and we infiltrate + + + align:start position:0% +in awe okay yeah so we and we infiltrate +um in a very radical and subversive way + + align:start position:0% +um in a very radical and subversive way + + + align:start position:0% +um in a very radical and subversive way +parks and that grow and develop in these + + align:start position:0% +parks and that grow and develop in these + + + align:start position:0% +parks and that grow and develop in these +huge trees that grow within the ages + + align:start position:0% +huge trees that grow within the ages + + + align:start position:0% +huge trees that grow within the ages +subersive um yeah it was just a Point of + + align:start position:0% +subersive um yeah it was just a Point of + + + align:start position:0% +subersive um yeah it was just a Point of +Departure to say that something that + + align:start position:0% +Departure to say that something that + + + align:start position:0% +Departure to say that something that +does interest Us and something that um + + align:start position:0% +does interest Us and something that um + + + align:start position:0% +does interest Us and something that um +really um that really um left a mark + + align:start position:0% +really um that really um left a mark + + + align:start position:0% +really um that really um left a mark +pointy was when Dario said and I think + + align:start position:0% +pointy was when Dario said and I think + + + align:start position:0% +pointy was when Dario said and I think +other AR echoing also what some other + + align:start position:0% +other AR echoing also what some other + + + align:start position:0% +other AR echoing also what some other +Architects said you'd like to ideally + + align:start position:0% +Architects said you'd like to ideally + + + align:start position:0% +Architects said you'd like to ideally +we'd like to do an architecture that + + align:start position:0% +we'd like to do an architecture that + + + align:start position:0% +we'd like to do an architecture that +grows an architecture that mutates an + + align:start position:0% +grows an architecture that mutates an + + + align:start position:0% +grows an architecture that mutates an +architecture that changes um and so very + + align:start position:0% +architecture that changes um and so very + + + align:start position:0% +architecture that changes um and so very +briefly and suly I'm going to just talk + + align:start position:0% +briefly and suly I'm going to just talk + + + align:start position:0% +briefly and suly I'm going to just talk +a little bit about this idea of growth + + align:start position:0% +a little bit about this idea of growth + + + align:start position:0% +a little bit about this idea of growth +and try to tie in a couple of projects + + align:start position:0% +and try to tie in a couple of projects + + + align:start position:0% +and try to tie in a couple of projects +with some of the more recent design um + + align:start position:0% +with some of the more recent design um + + + align:start position:0% +with some of the more recent design um +design products that we're trying to + + align:start position:0% +design products that we're trying to + + + align:start position:0% +design products that we're trying to +develop right now + + align:start position:0% +develop right now + + + align:start position:0% +develop right now +um and so I'll start with um I'll start + + align:start position:0% +um and so I'll start with um I'll start + + + align:start position:0% +um and so I'll start with um I'll start +with this project which um came um as a + + align:start position:0% +with this project which um came um as a + + + align:start position:0% +with this project which um came um as a +k came during one of veto's um came + + align:start position:0% +k came during one of veto's um came + + + align:start position:0% +k came during one of veto's um came +about doing one of veto's exhibitions + + align:start position:0% +about doing one of veto's exhibitions + + + align:start position:0% +about doing one of veto's exhibitions +and there was a night there was + + align:start position:0% +and there was a night there was + + + align:start position:0% +and there was a night there was +this um Dilemma on how to show his sound + + align:start position:0% +this um Dilemma on how to show his sound + + + align:start position:0% +this um Dilemma on how to show his sound +archives that have that have just been + + align:start position:0% +archives that have that have just been + + + align:start position:0% +archives that have that have just been +transferred onto um that just been + + align:start position:0% +transferred onto um that just been + + + align:start position:0% +transferred onto um that just been +transferred from these old four Channel + + align:start position:0% +transferred from these old four Channel + + + align:start position:0% +transferred from these old four Channel +technology to this new technology and + + align:start position:0% +technology to this new technology and + + + align:start position:0% +technology to this new technology and +heo didn't feel comfortable with having + + align:start position:0% +heo didn't feel comfortable with having + + + align:start position:0% +heo didn't feel comfortable with having +headphones or that sort of way of of um + + align:start position:0% +headphones or that sort of way of of um + + + align:start position:0% +headphones or that sort of way of of um +of showing of presenting the archives so + + align:start position:0% +of showing of presenting the archives so + + + align:start position:0% +of showing of presenting the archives so +we were thinking together and between + + align:start position:0% +we were thinking together and between + + + align:start position:0% +we were thinking together and between +all this words like pods came about and + + align:start position:0% +all this words like pods came about and + + + align:start position:0% +all this words like pods came about and +and Dario and a couple of other um + + align:start position:0% +and Dario and a couple of other um + + + align:start position:0% +and Dario and a couple of other um +designers in the + + align:start position:0% +designers in the + + + align:start position:0% +designers in the +studio um were great I mean we were + + align:start position:0% +studio um were great I mean we were + + + align:start position:0% +studio um were great I mean we were +working a little bit together just to to + + align:start position:0% +working a little bit together just to to + + + align:start position:0% +working a little bit together just to to +find maybe needs that were in the museum + + align:start position:0% +find maybe needs that were in the museum + + + align:start position:0% +find maybe needs that were in the museum +and we developed idea of sound station + + align:start position:0% +and we developed idea of sound station + + + align:start position:0% +and we developed idea of sound station +so I think that what this project would + + align:start position:0% +so I think that what this project would + + + align:start position:0% +so I think that what this project would +have coming with the Fon is that um it's + + align:start position:0% +have coming with the Fon is that um it's + + + align:start position:0% +have coming with the Fon is that um it's +growth as in expansion um which means + + align:start position:0% +growth as in expansion um which means + + + align:start position:0% +growth as in expansion um which means +that it's a it's the volume or the + + align:start position:0% +that it's a it's the volume or the + + + align:start position:0% +that it's a it's the volume or the +surface or the mass of the object or the + + align:start position:0% +surface or the mass of the object or the + + + align:start position:0% +surface or the mass of the object or the +space it occupies that that + + align:start position:0% +space it occupies that that + + + align:start position:0% +space it occupies that that +grows also I think it's that it's like + + align:start position:0% +grows also I think it's that it's like + + + align:start position:0% +grows also I think it's that it's like +assuming that a person is going to be in + + align:start position:0% +assuming that a person is going to be in + + + align:start position:0% +assuming that a person is going to be in +here so let's have this space kind of + + align:start position:0% +here so let's have this space kind of + + + align:start position:0% +here so let's have this space kind of +emerge around the spiral around yeah + + align:start position:0% +emerge around the spiral around yeah + + + align:start position:0% +emerge around the spiral around yeah +yeah so I took as a centered word for + + align:start position:0% +yeah so I took as a centered word for + + + align:start position:0% +yeah so I took as a centered word for +this notion of expansion maybe the word + + align:start position:0% +this notion of expansion maybe the word + + + align:start position:0% +this notion of expansion maybe the word +of + + align:start position:0% +of + + + align:start position:0% +of +extension um and then there's a project + + align:start position:0% +extension um and then there's a project + + + align:start position:0% +extension um and then there's a project +that we like very much um which is a + + align:start position:0% +that we like very much um which is a + + + align:start position:0% +that we like very much um which is a +bilard table that's going to be built by + + align:start position:0% +bilard table that's going to be built by + + + align:start position:0% +bilard table that's going to be built by +zah for Ma andna and there was this very + + align:start position:0% +zah for Ma andna and there was this very + + + align:start position:0% +zah for Ma andna and there was this very +interesting um element of what would + + align:start position:0% +interesting um element of what would + + + align:start position:0% +interesting um element of what would +have been a fourth leg that's just it + + align:start position:0% +have been a fourth leg that's just it + + + align:start position:0% +have been a fourth leg that's just it +looks like it was stunted in its growth + + align:start position:0% +looks like it was stunted in its growth + + + align:start position:0% +looks like it was stunted in its growth +and um in a way I mean of course we + + align:start position:0% +and um in a way I mean of course we + + + align:start position:0% +and um in a way I mean of course we +could have shown like we could would + + align:start position:0% +could have shown like we could would + + + align:start position:0% +could have shown like we could would +talk about um the idea of something that + + align:start position:0% +talk about um the idea of something that + + + align:start position:0% +talk about um the idea of something that +sprouts and the idea of you know um I + + align:start position:0% +sprouts and the idea of you know um I + + + align:start position:0% +sprouts and the idea of you know um I +mean all these ideas of of um of growth + + align:start position:0% +mean all these ideas of of um of growth + + + align:start position:0% +mean all these ideas of of um of growth +and emergence that have been much wring + + align:start position:0% +and emergence that have been much wring + + + align:start position:0% +and emergence that have been much wring +about but we thought that there was + + align:start position:0% +about but we thought that there was + + + align:start position:0% +about but we thought that there was +something almost like an anomaly about + + align:start position:0% +something almost like an anomaly about + + + align:start position:0% +something almost like an anomaly about +this particular um this particular um + + align:start position:0% +this particular um this particular um + + + align:start position:0% +this particular um this particular um +design which we found kind of inspiring + + align:start position:0% +design which we found kind of inspiring + + + align:start position:0% +design which we found kind of inspiring +um and so for example in one of the + + align:start position:0% +um and so for example in one of the + + + align:start position:0% +um and so for example in one of the +projects that we're trying to develop um + + align:start position:0% +projects that we're trying to develop um + + + align:start position:0% +projects that we're trying to develop um +today which is a fashion project we're + + align:start position:0% +today which is a fashion project we're + + + align:start position:0% +today which is a fashion project we're +designing these ettes that could be put + + align:start position:0% +designing these ettes that could be put + + + align:start position:0% +designing these ettes that could be put +onto any sort of garment really at the + + align:start position:0% +onto any sort of garment really at the + + + align:start position:0% +onto any sort of garment really at the +last minute maybe one maybe two and + + align:start position:0% +last minute maybe one maybe two and + + + align:start position:0% +last minute maybe one maybe two and +ideally what we would like is that the + + align:start position:0% +ideally what we would like is that the + + + align:start position:0% +ideally what we would like is that the +the extensions from these eets would + + align:start position:0% +the extensions from these eets would + + + align:start position:0% +the extensions from these eets would +grow that we could pull on them and that + + align:start position:0% +grow that we could pull on them and that + + + align:start position:0% +grow that we could pull on them and that +the the length would be variable for + + align:start position:0% +the the length would be variable for + + + align:start position:0% +the the length would be variable for +example it could pull one way of course + + align:start position:0% +example it could pull one way of course + + + align:start position:0% +example it could pull one way of course +it would have to retract after that so + + align:start position:0% +it would have to retract after that so + + + align:start position:0% +it would have to retract after that so +this is um just + + align:start position:0% +this is um just + + + align:start position:0% +this is um just +um and the idea of extension is a + + align:start position:0% +um and the idea of extension is a + + + align:start position:0% +um and the idea of extension is a +project of um that of a country Studio + + align:start position:0% +project of um that of a country Studio + + + align:start position:0% +project of um that of a country Studio +what's the date of where go 99 of 99 um + + align:start position:0% +what's the date of where go 99 of 99 um + + + align:start position:0% +what's the date of where go 99 of 99 um +where + + align:start position:0% +where + + + align:start position:0% +where +um basically it's a + + align:start position:0% +um basically it's a + + + align:start position:0% +um basically it's a +house what kind + + align:start position:0% +house what kind + + + align:start position:0% +house what kind +of + + align:start position:0% +of + + + align:start position:0% +of +General I basically we did a kind of uh + + align:start position:0% +General I basically we did a kind of uh + + + align:start position:0% +General I basically we did a kind of uh +W to be wnab be wannabe ARR uh uh + + align:start position:0% +W to be wnab be wannabe ARR uh uh + + + align:start position:0% +W to be wnab be wannabe ARR uh uh +project uh uh would be we were asked to + + align:start position:0% +project uh uh would be we were asked to + + + align:start position:0% +project uh uh would be we were asked to +do + + align:start position:0% +do + + + align:start position:0% +do +something uh on the notion of a uh micro + + align:start position:0% +something uh on the notion of a uh micro + + + align:start position:0% +something uh on the notion of a uh micro +micro environment so we we suggested a + + align:start position:0% +micro environment so we we suggested a + + + align:start position:0% +micro environment so we we suggested a +project where uh an external skeleton + + align:start position:0% +project where uh an external skeleton + + + align:start position:0% +project where uh an external skeleton +would be screw would be screwed into + + align:start position:0% +would be screw would be screwed into + + + align:start position:0% +would be screw would be screwed into +your + + align:start position:0% +your + + + align:start position:0% +your +bones uh now that you have this external + + align:start position:0% +bones uh now that you have this external + + + align:start position:0% +bones uh now that you have this external +skeleton you know it's it's made of + + align:start position:0% +skeleton you know it's it's made of + + + align:start position:0% +skeleton you know it's it's made of +telescoping parts sming parts so you can + + align:start position:0% +telescoping parts sming parts so you can + + + align:start position:0% +telescoping parts sming parts so you can +move around it Prett free you can move + + align:start position:0% +move around it Prett free you can move + + + align:start position:0% +move around it Prett free you can move +around with freely except that you have + + align:start position:0% +around with freely except that you have + + + align:start position:0% +around with freely except that you have +the skel the Skeleton on your back uh + + align:start position:0% +the skel the Skeleton on your back uh + + + align:start position:0% +the skel the Skeleton on your back uh +you don't need Furniture because anytime + + align:start position:0% +you don't need Furniture because anytime + + + align:start position:0% +you don't need Furniture because anytime +because you can just pull down the + + align:start position:0% +because you can just pull down the + + + align:start position:0% +because you can just pull down the +telescoping legs and you can become your + + align:start position:0% +telescoping legs and you can become your + + + align:start position:0% +telescoping legs and you can become your +own + + align:start position:0% +own + + + align:start position:0% +own +Furniture uh uh you carry this backpack + + align:start position:0% +Furniture uh uh you carry this backpack + + + align:start position:0% +Furniture uh uh you carry this backpack +uh you can release the backpack uh uh so + + align:start position:0% +uh you can release the backpack uh uh so + + + align:start position:0% +uh you can release the backpack uh uh so +that you're wear your you don't just you + + align:start position:0% +that you're wear your you don't just you + + + align:start position:0% +that you're wear your you don't just you +don't just have a house you kind of are + + align:start position:0% +don't just have a house you kind of are + + + align:start position:0% +don't just have a house you kind of are +your house now that you are your house + + align:start position:0% +your house now that you are your house + + + align:start position:0% +your house now that you are your house +other people can come in it's a private + + align:start position:0% +other people can come in it's a private + + + align:start position:0% +other people can come in it's a private +house not everybody's allowed in like + + align:start position:0% +house not everybody's allowed in like + + + align:start position:0% +house not everybody's allowed in like +that person is is climbing on the roof + + align:start position:0% +that person is is climbing on the roof + + + align:start position:0% +that person is is climbing on the roof +because it's a private house could like + + align:start position:0% +because it's a private house could like + + + align:start position:0% +because it's a private house could like +could like could have not um so + + align:start position:0% +could like could have not um so + + + align:start position:0% +could like could have not um so +basically you have your private house + + align:start position:0% +basically you have your private house + + + align:start position:0% +basically you have your private house +and you're also like screwed to your own + + align:start position:0% +and you're also like screwed to your own + + + align:start position:0% +and you're also like screwed to your own +house which is the idea of Prosthetics + + align:start position:0% +house which is the idea of Prosthetics + + + align:start position:0% +house which is the idea of Prosthetics +which um which still we're so we're + + align:start position:0% +which um which still we're so we're + + + align:start position:0% +which um which still we're so we're +still in this idea of um extensions + + align:start position:0% +still in this idea of um extensions + + + align:start position:0% +still in this idea of um extensions +Prosthetics so um it was interesting to + + align:start position:0% +Prosthetics so um it was interesting to + + + align:start position:0% +Prosthetics so um it was interesting to +speak with veto but I'll come back to + + align:start position:0% +speak with veto but I'll come back to + + + align:start position:0% +speak with veto but I'll come back to +this later about what he thought were + + align:start position:0% +this later about what he thought were + + + align:start position:0% +this later about what he thought were +the limits of this even though it was + + align:start position:0% +the limits of this even though it was + + + align:start position:0% +the limits of this even though it was +just a sort of theoretical idea and why + + align:start position:0% +just a sort of theoretical idea and why + + + align:start position:0% +just a sort of theoretical idea and why +it was always nagging him but there was + + align:start position:0% +it was always nagging him but there was + + + align:start position:0% +it was always nagging him but there was +something very 19th century about the + + align:start position:0% +something very 19th century about the + + + align:start position:0% +something very 19th century about the +the whole idea one that and something + + align:start position:0% +the whole idea one that and something + + + align:start position:0% +the whole idea one that and something +that I found very seductive but that + + align:start position:0% +that I found very seductive but that + + + align:start position:0% +that I found very seductive but that +seemed to to B to bother you a little + + align:start position:0% +seemed to to B to bother you a little + + + align:start position:0% +seemed to to B to bother you a little +bit um so the second part of growth um + + align:start position:0% +bit um so the second part of growth um + + + align:start position:0% +bit um so the second part of growth um +the second dimension um is the one of + + align:start position:0% +the second dimension um is the one of + + + align:start position:0% +the second dimension um is the one of +multiplication um and as a sort of + + align:start position:0% +multiplication um and as a sort of + + + align:start position:0% +multiplication um and as a sort of +central word we could use the idea of + + align:start position:0% +central word we could use the idea of + + + align:start position:0% +central word we could use the idea of +code or seriality + + align:start position:0% +code or seriality + + + align:start position:0% +code or seriality +and I was very um interested to see that + + align:start position:0% +and I was very um interested to see that + + + align:start position:0% +and I was very um interested to see that +in some of V's earlier work pre ACR + + align:start position:0% +in some of V's earlier work pre ACR + + + align:start position:0% +in some of V's earlier work pre ACR +Studio there was already this desire to + + align:start position:0% +Studio there was already this desire to + + + align:start position:0% +Studio there was already this desire to +um to explore um the idea of modular + + align:start position:0% +um to explore um the idea of modular + + + align:start position:0% +um to explore um the idea of modular +furniture for example or something A + + align:start position:0% +furniture for example or something A + + + align:start position:0% +furniture for example or something A +system that would define a form the + + align:start position:0% +system that would define a form the + + + align:start position:0% +system that would define a form the +ultimate form so I mean I think in here + + align:start position:0% +ultimate form so I mean I think in here + + + align:start position:0% +ultimate form so I mean I think in here +you can see it better where every part + + align:start position:0% +you can see it better where every part + + + align:start position:0% +you can see it better where every part +is in relation negative or positive to + + align:start position:0% +is in relation negative or positive to + + + align:start position:0% +is in relation negative or positive to +the part that's right next to it the + + align:start position:0% +the part that's right next to it the + + + align:start position:0% +the part that's right next to it the +idea of pattern meres and here um four + + align:start position:0% +idea of pattern meres and here um four + + + align:start position:0% +idea of pattern meres and here um four +story table which is um basically four + + align:start position:0% +story table which is um basically four + + + align:start position:0% +story table which is um basically four +tables is that and you take four more + + align:start position:0% +tables is that and you take four more + + + align:start position:0% +tables is that and you take four more +tables and then you it's like a a very + + align:start position:0% +tables and then you it's like a a very + + + align:start position:0% +tables and then you it's like a a very +little table inside a normal table which + + align:start position:0% +little table inside a normal table which + + + align:start position:0% +little table inside a normal table which +it turns inside a larger table + + align:start position:0% + + + + align:start position:0% + +largest largest at the top the kind of + + align:start position:0% +largest largest at the top the kind of + + + align:start position:0% +largest largest at the top the kind of +band + + align:start position:0% +band + + + align:start position:0% +band +place so um so recently we tried to + + align:start position:0% +place so um so recently we tried to + + + align:start position:0% +place so um so recently we tried to +develop um well actually again Museum + + align:start position:0% +develop um well actually again Museum + + + align:start position:0% +develop um well actually again Museum +context um maybe I'm showing that + + align:start position:0% +context um maybe I'm showing that + + + align:start position:0% +context um maybe I'm showing that +because that was that's an environment + + align:start position:0% +because that was that's an environment + + + align:start position:0% +because that was that's an environment +that I'm more accustomed to but um what + + align:start position:0% +that I'm more accustomed to but um what + + + align:start position:0% +that I'm more accustomed to but um what +thing Museum gives us the opportunity to + + align:start position:0% +thing Museum gives us the opportunity to + + + align:start position:0% +thing Museum gives us the opportunity to +try things out uh and before we put put + + align:start position:0% +try things out uh and before we put put + + + align:start position:0% +try things out uh and before we put put +put them on the screen in in a way uh + + align:start position:0% +put them on the screen in in a way uh + + + align:start position:0% +put them on the screen in in a way uh +they're they're they're asking for art + + align:start position:0% +they're they're they're asking for art + + + align:start position:0% +they're they're they're asking for art +and uh and we don't give it to them we + + align:start position:0% +and uh and we don't give it to them we + + + align:start position:0% +and uh and we don't give it to them we +we we give them a space for people + + align:start position:0% +we we give them a space for people + + + align:start position:0% +we we give them a space for people +instead of a trial of SP so we try + + align:start position:0% +instead of a trial of SP so we try + + + align:start position:0% +instead of a trial of SP so we try +seating we try a place for film it's we + + align:start position:0% +seating we try a place for film it's we + + + align:start position:0% +seating we try a place for film it's we +we we we're pretty good at tricking + + align:start position:0% +we we we're pretty good at tricking + + + align:start position:0% +we we we're pretty good at tricking +them into doing that doing these + + align:start position:0% +them into doing that doing these + + + align:start position:0% +them into doing that doing these +things but anyway so for this we had a + + align:start position:0% +things but anyway so for this we had a + + + align:start position:0% +things but anyway so for this we had a +problem um trying to figure out what + + align:start position:0% +problem um trying to figure out what + + + align:start position:0% +problem um trying to figure out what +could be a quick easy and um cheap way + + align:start position:0% +could be a quick easy and um cheap way + + + align:start position:0% +could be a quick easy and um cheap way +of design of developing C so here we + + align:start position:0% +of design of developing C so here we + + + align:start position:0% +of design of developing C so here we +took we actually the walls of are made + + align:start position:0% +took we actually the walls of are made + + + align:start position:0% +took we actually the walls of are made +out of um acoustic foam and the + + align:start position:0% +out of um acoustic foam and the + + + align:start position:0% +out of um acoustic foam and the +we thought for why don't we just take um + + align:start position:0% +we thought for why don't we just take um + + + align:start position:0% +we thought for why don't we just take um +a little section of That acoustic bone + + align:start position:0% +a little section of That acoustic bone + + + align:start position:0% +a little section of That acoustic bone +blow it up um change the scale so really + + align:start position:0% +blow it up um change the scale so really + + + align:start position:0% +blow it up um change the scale so really +is something close to four story table + + align:start position:0% +is something close to four story table + + + align:start position:0% +is something close to four story table +but I I just thought about it maybe a + + align:start position:0% +but I I just thought about it maybe a + + + align:start position:0% +but I I just thought about it maybe a +couple days like the relation that there + + align:start position:0% +couple days like the relation that there + + + align:start position:0% +couple days like the relation that there +might be a relationship between them but + + align:start position:0% +might be a relationship between them but + + + align:start position:0% +might be a relationship between them but +and then what's fantast what was a great + + align:start position:0% +and then what's fantast what was a great + + + align:start position:0% +and then what's fantast what was a great +um what was great about it is that these + + align:start position:0% +um what was great about it is that these + + + align:start position:0% +um what was great about it is that these +would fit as mod modular this would + + align:start position:0% +would fit as mod modular this would + + + align:start position:0% +would fit as mod modular this would +become a modular um Furniture where + + align:start position:0% +become a modular um Furniture where + + + align:start position:0% +become a modular um Furniture where +people could actually lie down + + align:start position:0% +people could actually lie down + + + align:start position:0% +people could actually lie down +or sit down or sit sit low sit High Etc + + align:start position:0% +or sit down or sit sit low sit High Etc + + + align:start position:0% +or sit down or sit sit low sit High Etc +so it's basically um the the seating is + + align:start position:0% +so it's basically um the the seating is + + + align:start position:0% +so it's basically um the the seating is +a reflection of the surface of the uh of + + align:start position:0% +a reflection of the surface of the uh of + + + align:start position:0% +a reflection of the surface of the uh of +the what we call them the layers of the + + align:start position:0% +the what we call them the layers of the + + + align:start position:0% +the what we call them the layers of the +laay this is something that we' like to + + align:start position:0% +laay this is something that we' like to + + + align:start position:0% +laay this is something that we' like to +develop um maybe um with people and MIT + + align:start position:0% +develop um maybe um with people and MIT + + + align:start position:0% +develop um maybe um with people and MIT +hopefully um and it's a system it's a + + align:start position:0% +hopefully um and it's a system it's a + + + align:start position:0% +hopefully um and it's a system it's a +system also of modular Furniture except + + align:start position:0% +system also of modular Furniture except + + + align:start position:0% +system also of modular Furniture except +that here please + + align:start position:0% +that here please + + + align:start position:0% +that here please +um quality of the of the renderings + + align:start position:0% +um quality of the of the renderings + + + align:start position:0% +um quality of the of the renderings +they're not we put this up very quickly + + align:start position:0% +they're not we put this up very quickly + + + align:start position:0% +they're not we put this up very quickly +just as a way of explaining the project + + align:start position:0% +just as a way of explaining the project + + + align:start position:0% +just as a way of explaining the project +but you haven't actually designed it yet + + align:start position:0% +but you haven't actually designed it yet + + + align:start position:0% +but you haven't actually designed it yet +but one side would be um a rigid hard + + align:start position:0% +but one side would be um a rigid hard + + + align:start position:0% +but one side would be um a rigid hard +surface and the other side would be a + + align:start position:0% +surface and the other side would be a + + + align:start position:0% +surface and the other side would be a +soft surface and if we're able to + + align:start position:0% +soft surface and if we're able to + + + align:start position:0% +soft surface and if we're able to +develop to to know more and to apply a + + align:start position:0% +develop to to know more and to apply a + + + align:start position:0% +develop to to know more and to apply a +system of modular curvature we're can + + align:start position:0% +system of modular curvature we're can + + + align:start position:0% +system of modular curvature we're can +imagine that all of these different + + align:start position:0% +imagine that all of these different + + + align:start position:0% +imagine that all of these different +components would fit sply within + + align:start position:0% +components would fit sply within + + + align:start position:0% +components would fit sply within +themselves next to other at least from + + align:start position:0% +themselves next to other at least from + + + align:start position:0% +themselves next to other at least from +one side and then you could decide which + + align:start position:0% +one side and then you could decide which + + + align:start position:0% +one side and then you could decide which +side you wanted to be a table just by + + align:start position:0% +side you wanted to be a table just by + + + align:start position:0% +side you wanted to be a table just by +flipping them over and you could decide + + align:start position:0% +flipping them over and you could decide + + + align:start position:0% +flipping them over and you could decide +on the size of the table and you could + + align:start position:0% +on the size of the table and you could + + + align:start position:0% +on the size of the table and you could +decide on the size of the the seating + + align:start position:0% +decide on the size of the the seating + + + align:start position:0% +decide on the size of the the seating +area which would be soft etc etc so this + + align:start position:0% +area which would be soft etc etc so this + + + align:start position:0% +area which would be soft etc etc so this +is something that we're working on right + + align:start position:0% +is something that we're working on right + + + align:start position:0% +is something that we're working on right +now and within + + align:start position:0% +now and within + + + align:start position:0% +now and within +um + + align:start position:0% +um + + + align:start position:0% +um +um I think I think that's oh and so I + + align:start position:0% +um I think I think that's oh and so I + + + align:start position:0% +um I think I think that's oh and so I +just wanted to show a fashion project + + align:start position:0% +just wanted to show a fashion project + + + align:start position:0% +just wanted to show a fashion project +that I think has um really been + + align:start position:0% +that I think has um really been + + + align:start position:0% +that I think has um really been +inspirational to us even I mean it it's + + align:start position:0% +inspirational to us even I mean it it's + + + align:start position:0% +inspirational to us even I mean it it's +actually fed back a little bit into the + + align:start position:0% +actually fed back a little bit into the + + + align:start position:0% +actually fed back a little bit into the +way we're thinking about design and + + align:start position:0% +way we're thinking about design and + + + align:start position:0% +way we're thinking about design and +architecture is this project of isaki + + align:start position:0% +architecture is this project of isaki + + + align:start position:0% +architecture is this project of isaki +and I think it's actually not there's a + + align:start position:0% +and I think it's actually not there's a + + + align:start position:0% +and I think it's actually not there's a +second name + + align:start position:0% +second name + + + align:start position:0% +second name +d he present this APO book in which this + + align:start position:0% +d he present this APO book in which this + + + align:start position:0% +d he present this APO book in which this +project is contained and it's quite a + + align:start position:0% +project is contained and it's quite a + + + align:start position:0% +project is contained and it's quite a +revolution within the fashioning + + align:start position:0% +revolution within the fashioning + + + align:start position:0% +revolution within the fashioning +industry because everything is um the + + align:start position:0% +industry because everything is um the + + + align:start position:0% +industry because everything is um the +whole a whole multitude of clothing are + + align:start position:0% +whole a whole multitude of clothing are + + + align:start position:0% +whole a whole multitude of clothing are +made from one from a knitting machine + + align:start position:0% +made from one from a knitting machine + + + align:start position:0% +made from one from a knitting machine +where each individual is based on a Cod + + align:start position:0% +where each individual is based on a Cod + + + align:start position:0% +where each individual is based on a Cod +on a code on a variation of that code so + + align:start position:0% +on a code on a variation of that code so + + + align:start position:0% +on a code on a variation of that code so +there's a second dimension to this + + align:start position:0% +there's a second dimension to this + + + align:start position:0% +there's a second dimension to this +project at least the second dimension is + + align:start position:0% +project at least the second dimension is + + + align:start position:0% +project at least the second dimension is +that the user Cuts up and can um can + + align:start position:0% +that the user Cuts up and can um can + + + align:start position:0% +that the user Cuts up and can um can +customize the piece of coding but what + + align:start position:0% +customize the piece of coding but what + + + align:start position:0% +customize the piece of coding but what +interests me particularly is the fact + + align:start position:0% +interests me particularly is the fact + + + align:start position:0% +interests me particularly is the fact +that it's based like one computer feeds + + align:start position:0% +that it's based like one computer feeds + + + align:start position:0% +that it's based like one computer feeds +off information to a knitting machine + + align:start position:0% +off information to a knitting machine + + + align:start position:0% +off information to a knitting machine +which will create this huge huge Loom of + + align:start position:0% +which will create this huge huge Loom of + + + align:start position:0% +which will create this huge huge Loom of +clothing and there's + + align:start position:0% +clothing and there's + + + align:start position:0% +clothing and there's +something interesting in a in a shift in + + align:start position:0% +something interesting in a in a shift in + + + align:start position:0% +something interesting in a in a shift in +the mode of production and way we can + + align:start position:0% +the mode of production and way we can + + + align:start position:0% +the mode of production and way we can +think about it as + + align:start position:0% +think about it as + + + align:start position:0% +think about it as +clothing um then there's um there's um + + align:start position:0% +clothing um then there's um there's um + + + align:start position:0% +clothing um then there's um there's um +there's another side of two growth that + + align:start position:0% +there's another side of two growth that + + + align:start position:0% +there's another side of two growth that +we thinking about and it's a side of + + align:start position:0% +we thinking about and it's a side of + + + align:start position:0% +we thinking about and it's a side of +mutation and then the the the word that + + align:start position:0% +mutation and then the the the word that + + + align:start position:0% +mutation and then the the the word that +we're using as a center is + + align:start position:0% +we're using as a center is + + + align:start position:0% +we're using as a center is +metamorphosis um this is a project that + + align:start position:0% +metamorphosis um this is a project that + + + align:start position:0% +metamorphosis um this is a project that +Garrett ricardi um introduced to us G at + + align:start position:0% +Garrett ricardi um introduced to us G at + + + align:start position:0% +Garrett ricardi um introduced to us G at +theud it's a a clothing project by ad + + align:start position:0% +theud it's a a clothing project by ad + + + align:start position:0% +theud it's a a clothing project by ad +which is very beautiful as you'll see + + align:start position:0% +which is very beautiful as you'll see + + + align:start position:0% +which is very beautiful as you'll see +spreads out like this and um this is um + + align:start position:0% +spreads out like this and um this is um + + + align:start position:0% +spreads out like this and um this is um +something that's been interesting us + + align:start position:0% +something that's been interesting us + + + align:start position:0% +something that's been interesting us +more and more and that we're trying to + + align:start position:0% +more and more and that we're trying to + + + align:start position:0% +more and more and that we're trying to +incorporate at least within our fashion + + align:start position:0% +incorporate at least within our fashion + + + align:start position:0% +incorporate at least within our fashion +um design and it's the idea of mutation + + align:start position:0% +um design and it's the idea of mutation + + + align:start position:0% +um design and it's the idea of mutation +which interests us is that it's a change + + align:start position:0% +which interests us is that it's a change + + + align:start position:0% +which interests us is that it's a change +inherent to the identity of the object + + align:start position:0% +inherent to the identity of the object + + + align:start position:0% +inherent to the identity of the object +towards something else so it's growth + + align:start position:0% +towards something else so it's growth + + + align:start position:0% +towards something else so it's growth +that because it's a sort of between two + + align:start position:0% +that because it's a sort of between two + + + align:start position:0% +that because it's a sort of between two +states of course um 's metamorphosis is + + align:start position:0% +states of course um 's metamorphosis is + + + align:start position:0% +states of course um 's metamorphosis is +the sort of book that people often think + + align:start position:0% +the sort of book that people often think + + + align:start position:0% +the sort of book that people often think +about in terms of um that sort of + + align:start position:0% +about in terms of um that sort of + + + align:start position:0% +about in terms of um that sort of +metamorphosis in you know like um DNE + + align:start position:0% +metamorphosis in you know like um DNE + + + align:start position:0% +metamorphosis in you know like um DNE +and the L and the lural treade etc etc + + align:start position:0% +and the L and the lural treade etc etc + + + align:start position:0% +and the L and the lural treade etc etc +but this is I wanted to just present + + align:start position:0% +but this is I wanted to just present + + + align:start position:0% +but this is I wanted to just present +this because this is the way we're + + align:start position:0% +this because this is the way we're + + + align:start position:0% +this because this is the way we're +thinking about um design right now + + align:start position:0% +thinking about um design right now + + + align:start position:0% +thinking about um design right now +sometimes will say I want us to develop + + align:start position:0% +sometimes will say I want us to develop + + + align:start position:0% +sometimes will say I want us to develop +a system of Cutlery where everything + + align:start position:0% +a system of Cutlery where everything + + + align:start position:0% +a system of Cutlery where everything +will stay on one hand and we we say what + + align:start position:0% +will stay on one hand and we we say what + + + align:start position:0% +will stay on one hand and we we say what +would you like it to look like and he + + align:start position:0% +would you like it to look like and he + + + align:start position:0% +would you like it to look like and he +goes something that goes like + + align:start position:0% +goes something that goes like + + + align:start position:0% +goes something that goes like +this so it took me ages and a lot of + + align:start position:0% +this so it took me ages and a lot of + + + align:start position:0% +this so it took me ages and a lot of +patience to try to understand what veto + + align:start position:0% +patience to try to understand what veto + + + align:start position:0% +patience to try to understand what veto +meant by veto was so articulate by going + + align:start position:0% +meant by veto was so articulate by going + + + align:start position:0% +meant by veto was so articulate by going +and then the other day he presented um a + + align:start position:0% +and then the other day he presented um a + + + align:start position:0% +and then the other day he presented um a +exerpt of this film like David kenberg + + align:start position:0% +exerpt of this film like David kenberg + + + align:start position:0% +exerpt of this film like David kenberg +and suddenly I understood what he meant + + align:start position:0% +and suddenly I understood what he meant + + + align:start position:0% +and suddenly I understood what he meant +and this was an interesting this was + + align:start position:0% +and this was an interesting this was + + + align:start position:0% +and this was an interesting this was +interesting to me in relation to uh the + + align:start position:0% +interesting to me in relation to uh the + + + align:start position:0% +interesting to me in relation to uh the +world in your bones project this is the + + align:start position:0% +world in your bones project this is the + + + align:start position:0% +world in your bones project this is the +last thing that I'm show right now but + + align:start position:0% +last thing that I'm show right now but + + + align:start position:0% +last thing that I'm show right now but +it's basically this man takes the gun + + align:start position:0% +it's basically this man takes the gun + + + align:start position:0% +it's basically this man takes the gun +out of his um + + align:start position:0% +out of his um + + + align:start position:0% +out of his um +bosom and um out of his stomach and the + + align:start position:0% +bosom and um out of his stomach and the + + + align:start position:0% +bosom and um out of his stomach and the +Gun starts growing and mingling with the + + align:start position:0% +Gun starts growing and mingling with the + + + align:start position:0% +Gun starts growing and mingling with the +tendons in his hands like that so + + align:start position:0% +tendons in his hands like that so + + + align:start position:0% +tendons in his hands like that so +instead of like just until his his own + + align:start position:0% +instead of like just until his his own + + + align:start position:0% +instead of like just until his his own +hand metamorphosis into this instrument + + align:start position:0% +hand metamorphosis into this instrument + + + align:start position:0% +hand metamorphosis into this instrument +object um organ + + align:start position:0% +object um organ + + + align:start position:0% +object um organ +and this weird sort of thing so I mean I + + align:start position:0% +and this weird sort of thing so I mean I + + + align:start position:0% +and this weird sort of thing so I mean I +don't think our design is going to look + + align:start position:0% +don't think our design is going to look + + + align:start position:0% +don't think our design is going to look +like this + + align:start position:0% +like this + + + align:start position:0% +like this +but but the the concept of metamorphosis + + align:start position:0% +but but the the concept of metamorphosis + + + align:start position:0% +but but the the concept of metamorphosis +is something that interests us very much + + align:start position:0% +is something that interests us very much + + + align:start position:0% +is something that interests us very much +right + + align:start position:0% + + + + align:start position:0% + +now I don't know it's kind of late I + + align:start position:0% +now I don't know it's kind of late I + + + align:start position:0% +now I don't know it's kind of late I +would love to go through uh maybe can we + + align:start position:0% +would love to go through uh maybe can we + + + align:start position:0% +would love to go through uh maybe can we +maybe could just I just + + align:start position:0% +maybe could just I just + + + align:start position:0% +maybe could just I just +quickly try + + align:start position:0% + + + + align:start position:0% + +to start + + align:start position:0% + + + + align:start position:0% + +talking + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +actually I mean inad I think maybe + + align:start position:0% +actually I mean inad I think maybe + + + align:start position:0% +actually I mean inad I think maybe +instead of continuing even though + + align:start position:0% +instead of continuing even though + + + align:start position:0% +instead of continuing even though +there's other stuff to do I would have + + align:start position:0% +there's other stuff to do I would have + + + align:start position:0% +there's other stuff to do I would have +loved to have continued with the World + + align:start position:0% +loved to have continued with the World + + + align:start position:0% +loved to have continued with the World +Trade project but talked a long time and + + align:start position:0% +Trade project but talked a long time and + + + align:start position:0% +Trade project but talked a long time and +it might be good if we turn on the + + align:start position:0% +it might be good if we turn on the + + + align:start position:0% +it might be good if we turn on the +lights + + align:start position:0% +lights + + + align:start position:0% +lights +and see if anybody wants to talk with us + + align:start position:0% +and see if anybody wants to talk with us + + + align:start position:0% +and see if anybody wants to talk with us +say to talk each + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +other + + align:start position:0% +other + + + align:start position:0% +other +[Music] + + align:start position:0% + + + + align:start position:0% + +yeah please um why fashion I mean you + + align:start position:0% +yeah please um why fashion I mean you + + + align:start position:0% +yeah please um why fashion I mean you +you trace this very of seamless + + align:start position:0% +you trace this very of seamless + + + align:start position:0% +you trace this very of seamless +progression from the page through the + + align:start position:0% + + + + align:start position:0% + +body do you + + align:start position:0% + + + + align:start position:0% + +get one one very basic aspect of it is + + align:start position:0% +get one one very basic aspect of it is + + + align:start position:0% +get one one very basic aspect of it is +that think you can think question please + + align:start position:0% +that think you can think question please + + + align:start position:0% +that think you can think question please +sorry question uh he he he he asked us + + align:start position:0% +sorry question uh he he he he asked us + + + align:start position:0% +sorry question uh he he he he asked us +why fashion uh why go he seem to there + + align:start position:0% +why fashion uh why go he seem to there + + + align:start position:0% +why fashion uh why go he seem to there +seems to be a seamless sort of + + align:start position:0% +seems to be a seamless sort of + + + align:start position:0% +seems to be a seamless sort of +progression from from writing to to our + + align:start position:0% +progression from from writing to to our + + + align:start position:0% +progression from from writing to to our +white fashion but you think of it U + + align:start position:0% +white fashion but you think of it U + + + align:start position:0% +white fashion but you think of it U +architecture is is is in many ways a + + align:start position:0% +architecture is is is in many ways a + + + align:start position:0% +architecture is is is in many ways a +boundary between public and private uh + + align:start position:0% +boundary between public and private uh + + + align:start position:0% +boundary between public and private uh +as as your + + align:start position:0% +as as your + + + align:start position:0% +as as your +coding uh and in fact we play games with + + align:start position:0% +coding uh and in fact we play games with + + + align:start position:0% +coding uh and in fact we play games with +how we reveal and how much we include uh + + align:start position:0% +how we reveal and how much we include uh + + + align:start position:0% +how we reveal and how much we include uh +it's the public your Public Image your + + align:start position:0% +it's the public your Public Image your + + + align:start position:0% +it's the public your Public Image your +clothing as is architecture or as this + + align:start position:0% +clothing as is architecture or as this + + + align:start position:0% +clothing as is architecture or as this +the kind of architecture which we'll + + align:start position:0% +the kind of architecture which we'll + + + align:start position:0% +the kind of architecture which we'll +probably never do the kind which you + + align:start position:0% +probably never do the kind which you + + + align:start position:0% +probably never do the kind which you +know if you spend $20 million the client + + align:start position:0% +know if you spend $20 million the client + + + align:start position:0% +know if you spend $20 million the client +wants to make sure that it looks like + + align:start position:0% +wants to make sure that it looks like + + + align:start position:0% +wants to make sure that it looks like +they spent $20 mil so but you know + + align:start position:0% +they spent $20 mil so but you know + + + align:start position:0% +they spent $20 mil so but you know +there's other other other other aspects + + align:start position:0% +there's other other other other aspects + + + align:start position:0% +there's other other other other aspects +to that too but at a very basic level it + + align:start position:0% +to that too but at a very basic level it + + + align:start position:0% +to that too but at a very basic level it +it it has a very similar Sim similar + + align:start position:0% +it it has a very similar Sim similar + + + align:start position:0% +it it has a very similar Sim similar +function uh you know from from the body + + align:start position:0% +function uh you know from from the body + + + align:start position:0% +function uh you know from from the body +to the to clothes to your Corridor to + + align:start position:0% +to the to clothes to your Corridor to + + + align:start position:0% +to the to clothes to your Corridor to +your building to your city to to so it's + + align:start position:0% +your building to your city to to so it's + + + align:start position:0% +your building to your city to to so it's +it's it's it's a step in between it's + + align:start position:0% +it's it's it's a step in between it's + + + align:start position:0% +it's it's it's a step in between it's +just really the you know first first + + align:start position:0% +just really the you know first first + + + align:start position:0% +just really the you know first first +first architecture you have a body now + + align:start position:0% +first architecture you have a body now + + + align:start position:0% +first architecture you have a body now +you put some cover around it this cover + + align:start position:0% +you put some cover around it this cover + + + align:start position:0% +you put some cover around it this cover +is called clothing you know then the + + align:start position:0% +is called clothing you know then the + + + align:start position:0% +is called clothing you know then the +body covered by clothing sits in sits in + + align:start position:0% +body covered by clothing sits in sits in + + + align:start position:0% +body covered by clothing sits in sits in +Furniture sits in a chair that in turn + + align:start position:0% +Furniture sits in a chair that in turn + + + align:start position:0% +Furniture sits in a chair that in turn +is in a room but I think there's + + align:start position:0% +is in a room but I think there's + + + align:start position:0% +is in a room but I think there's +something else too though uh I think + + align:start position:0% +something else too though uh I think + + + align:start position:0% +something else too though uh I think +that the the architecture of the future + + align:start position:0% +that the the architecture of the future + + + align:start position:0% +that the the architecture of the future +has to be not the architecture that you + + align:start position:0% +has to be not the architecture that you + + + align:start position:0% +has to be not the architecture that you +go to but the architecture you carry + + align:start position:0% +go to but the architecture you carry + + + align:start position:0% +go to but the architecture you carry +with you uh the architecture the future + + align:start position:0% +with you uh the architecture the future + + + align:start position:0% +with you uh the architecture the future +is probably for a future in which there + + align:start position:0% +is probably for a future in which there + + + align:start position:0% +is probably for a future in which there +are you know no countries No Boundaries + + align:start position:0% +are you know no countries No Boundaries + + + align:start position:0% +are you know no countries No Boundaries +so we're all Nomads we carry our house + + align:start position:0% +so we're all Nomads we carry our house + + + align:start position:0% +so we're all Nomads we carry our house +like the like like the turtle you know + + align:start position:0% +like the like like the turtle you know + + + align:start position:0% +like the like like the turtle you know +instead of having to go home uh you just + + align:start position:0% +instead of having to go home uh you just + + + align:start position:0% +instead of having to go home uh you just +sort of fold up inside inside your shell + + align:start position:0% +sort of fold up inside inside your shell + + + align:start position:0% +sort of fold up inside inside your shell +inside your + + align:start position:0% + + + + align:start position:0% + +uh yeah you're you're you're already + + align:start position:0% +uh yeah you're you're you're already + + + align:start position:0% +uh yeah you're you're you're already +there uh I mean and I think one of the + + align:start position:0% +there uh I mean and I think one of the + + + align:start position:0% +there uh I mean and I think one of the +sure signs that that is the future is is + + align:start position:0% +sure signs that that is the future is is + + + align:start position:0% +sure signs that that is the future is is +the + + align:start position:0% +the + + + align:start position:0% +the +amazing uh conservativism and + + align:start position:0% +amazing uh conservativism and + + + align:start position:0% +amazing uh conservativism and +nationalism of almost every country now + + align:start position:0% +nationalism of almost every country now + + + align:start position:0% +nationalism of almost every country now +it's a kind of last ditch attempt to you + + align:start position:0% +it's a kind of last ditch attempt to you + + + align:start position:0% +it's a kind of last ditch attempt to you +know when we know there aren't going to + + align:start position:0% +know when we know there aren't going to + + + align:start position:0% +know when we know there aren't going to +be countries anymore well let's have a + + align:start position:0% +be countries anymore well let's have a + + + align:start position:0% +be countries anymore well let's have a +last ditch attempt to keep the + + align:start position:0% +last ditch attempt to keep the + + + align:start position:0% +last ditch attempt to keep the +immigrants out you just as Maybe you + + align:start position:0% +immigrants out you just as Maybe you + + + align:start position:0% +immigrants out you just as Maybe you +know maybe in a time when we know that + + align:start position:0% +know maybe in a time when we know that + + + align:start position:0% +know maybe in a time when we know that +we're probably not going to have bodies + + align:start position:0% +we're probably not going to have bodies + + + align:start position:0% +we're probably not going to have bodies +much longer everybody you know goes to + + align:start position:0% +much longer everybody you know goes to + + + align:start position:0% +much longer everybody you know goes to +the goes to the gym you always try to + + align:start position:0% +the goes to the gym you always try to + + + align:start position:0% +the goes to the gym you always try to +keep you always try to keep the old + + align:start position:0% +keep you always try to keep the old + + + align:start position:0% +keep you always try to keep the old +world because you know it's changing you + + align:start position:0% + + + + align:start position:0% + +know um so the first the first half of + + align:start position:0% +know um so the first the first half of + + + align:start position:0% +know um so the first the first half of +your talk + + align:start position:0% +your talk + + + align:start position:0% +your talk +uh + + align:start position:0% + + + + align:start position:0% + +say I say that that was an + + align:start position:0% +say I say that that was an + + + align:start position:0% +say I say that that was an +incredible + + align:start position:0% +incredible + + + align:start position:0% +incredible +journey that concept of discovery that + + align:start position:0% +journey that concept of discovery that + + + align:start position:0% +journey that concept of discovery that +you're going + + align:start position:0% + + + + align:start position:0% + +through but I just felt something + + align:start position:0% + + + + align:start position:0% + +stren the way through half through and + + align:start position:0% +stren the way through half through and + + + align:start position:0% +stren the way through half through and +try to GRA with what that is why I feel + + align:start position:0% +try to GRA with what that is why I feel + + + align:start position:0% +try to GRA with what that is why I feel +and looking at these + + align:start position:0% +and looking at these + + + align:start position:0% +and looking at these +images and sort of esoteric + + align:start position:0% +images and sort of esoteric + + + align:start position:0% +images and sort of esoteric +architectural + + align:start position:0% +architectural + + + align:start position:0% +architectural +language we're coming from this place + + align:start position:0% +language we're coming from this place + + + align:start position:0% +language we're coming from this place +discovering design in this but are we + + align:start position:0% +discovering design in this but are we + + + align:start position:0% +discovering design in this but are we +are we + + align:start position:0% +are we + + + align:start position:0% +are we +using I mean this is so familiar to the + + align:start position:0% +using I mean this is so familiar to the + + + align:start position:0% +using I mean this is so familiar to the +architect + + align:start position:0% +architect + + + align:start position:0% +architect +of and just you a skateboarder I think I + + align:start position:0% +of and just you a skateboarder I think I + + + align:start position:0% +of and just you a skateboarder I think I +mean skate the skateboard ramps of the ' + + align:start position:0% +mean skate the skateboard ramps of the ' + + + align:start position:0% +mean skate the skateboard ramps of the ' +80s and 9s looked for Story table they + + align:start position:0% +80s and 9s looked for Story table they + + + align:start position:0% +80s and 9s looked for Story table they +did like this I don't think that's + + align:start position:0% +did like this I don't think that's + + + align:start position:0% +did like this I don't think that's +insignificant it's actually incredibly + + align:start position:0% +insignificant it's actually incredibly + + + align:start position:0% +insignificant it's actually incredibly +significant that the kind of reading of + + align:start position:0% +significant that the kind of reading of + + + align:start position:0% +significant that the kind of reading of +the landscape skateboard is just as one + + align:start position:0% +the landscape skateboard is just as one + + + align:start position:0% +the landscape skateboard is just as one +example is is is actually the discovery + + align:start position:0% +example is is is actually the discovery + + + align:start position:0% +example is is is actually the discovery +of a Terrain that's not choreograph it's + + align:start position:0% +of a Terrain that's not choreograph it's + + + align:start position:0% +of a Terrain that's not choreograph it's +not + + align:start position:0% +not + + + align:start position:0% +not +um it's not discovered through + + align:start position:0% +um it's not discovered through + + + align:start position:0% +um it's not discovered through +simulations it's actually a forign + + align:start position:0% +simulations it's actually a forign + + + align:start position:0% +simulations it's actually a forign +condition that + + align:start position:0% +condition that + + + align:start position:0% +condition that +is + + align:start position:0% +is + + + align:start position:0% +is +confronted and when you did you said + + align:start position:0% +confronted and when you did you said + + + align:start position:0% +confronted and when you did you said +something about the everyone knows + + align:start position:0% +something about the everyone knows + + + align:start position:0% +something about the everyone knows +architecture that was like a climactic + + align:start position:0% +architecture that was like a climactic + + + align:start position:0% +architecture that was like a climactic +moment for me in your discussion because + + align:start position:0% +moment for me in your discussion because + + + align:start position:0% +moment for me in your discussion because +now we're entering the language of the + + align:start position:0% +now we're entering the language of the + + + align:start position:0% +now we're entering the language of the +everyday and we talk about public space + + align:start position:0% +everyday and we talk about public space + + + align:start position:0% +everyday and we talk about public space +and then suddenly we're talking about + + align:start position:0% +and then suddenly we're talking about + + + align:start position:0% +and then suddenly we're talking about +mut this whole other kind of that's my + + align:start position:0% +mut this whole other kind of that's my + + + align:start position:0% +mut this whole other kind of that's my +fault also + + align:start position:0% +fault also + + + align:start position:0% +fault also +um I mean I'd like to I'd like to let + + align:start position:0% +um I mean I'd like to I'd like to let + + + align:start position:0% +um I mean I'd like to I'd like to let +you finish your question + + align:start position:0% + + + + align:start position:0% + +I'm really I'm really impressed with + + align:start position:0% +I'm really I'm really impressed with + + + align:start position:0% +I'm really I'm really impressed with +with the + + align:start position:0% +with the + + + align:start position:0% +with the +discussion it's interesting that we're + + align:start position:0% +discussion it's interesting that we're + + + align:start position:0% +discussion it's interesting that we're +sitting at this boundary between art and + + align:start position:0% +sitting at this boundary between art and + + + align:start position:0% +sitting at this boundary between art and +architecture and at spr which was an + + align:start position:0% +architecture and at spr which was an + + + align:start position:0% +architecture and at spr which was an +incredible introduction to the top as + + align:start position:0% +incredible introduction to the top as + + + align:start position:0% +incredible introduction to the top as +well and there's I think a lot of + + align:start position:0% +well and there's I think a lot of + + + align:start position:0% +well and there's I think a lot of +confusion or or maybe a productive + + align:start position:0% +confusion or or maybe a productive + + + align:start position:0% +confusion or or maybe a productive +confusion about that negotiation between + + align:start position:0% +confusion about that negotiation between + + + align:start position:0% +confusion about that negotiation between +those + + align:start position:0% +those + + + align:start position:0% +those +two and + + align:start position:0% +two and + + + align:start position:0% +two and +uh I shouldn't any I'm just bobing this + + align:start position:0% +uh I shouldn't any I'm just bobing this + + + align:start position:0% +uh I shouldn't any I'm just bobing this +thing + + align:start position:0% +thing + + + align:start position:0% +thing +there it's possible that uh you the work + + align:start position:0% +there it's possible that uh you the work + + + align:start position:0% +there it's possible that uh you the work +that the work the V did until he started + + align:start position:0% +that the work the V did until he started + + + align:start position:0% +that the work the V did until he started +working in a studio context um you know + + align:start position:0% +working in a studio context um you know + + + align:start position:0% +working in a studio context um you know +he he asked certain questions and those + + align:start position:0% +he he asked certain questions and those + + + align:start position:0% +he he asked certain questions and those +questions were were were answered uh uh + + align:start position:0% +questions were were were answered uh uh + + + align:start position:0% +questions were were were answered uh uh +uh you know at at their time I think + + align:start position:0% +uh you know at at their time I think + + + align:start position:0% +uh you know at at their time I think +that we're still in the process of of a + + align:start position:0% +that we're still in the process of of a + + + align:start position:0% +that we're still in the process of of a +answering questions the questions that + + align:start position:0% +answering questions the questions that + + + align:start position:0% +answering questions the questions that +are maybe raised by by by the Notions + + align:start position:0% +are maybe raised by by by the Notions + + + align:start position:0% +are maybe raised by by by the Notions +that that Serena mentioned but um back + + align:start position:0% +that that Serena mentioned but um back + + + align:start position:0% +that that Serena mentioned but um back +to back to you were saying about skating + + align:start position:0% +to back to you were saying about skating + + + align:start position:0% +to back to you were saying about skating +you know I I in in working on this + + align:start position:0% +you know I I in in working on this + + + align:start position:0% +you know I I in in working on this +project I I was I was incredibly + + align:start position:0% +project I I was I was incredibly + + + align:start position:0% +project I I was I was incredibly +surprised because I've always uh you + + align:start position:0% +surprised because I've always uh you + + + align:start position:0% +surprised because I've always uh you +know I'm not a skater um then again I'm + + align:start position:0% +know I'm not a skater um then again I'm + + + align:start position:0% +know I'm not a skater um then again I'm +not a scientist and I'm not a musician + + align:start position:0% +not a scientist and I'm not a musician + + + align:start position:0% +not a scientist and I'm not a musician +and and I love I love music I think our + + align:start position:0% +and and I love I love music I think our + + + align:start position:0% +and and I love I love music I think our +our interest in skating and our interest + + align:start position:0% +our interest in skating and our interest + + + align:start position:0% +our interest in skating and our interest +in science is like our interest in music + + align:start position:0% +in science is like our interest in music + + + align:start position:0% +in science is like our interest in music +and none of us can really carry a tune + + align:start position:0% +and none of us can really carry a tune + + + align:start position:0% +and none of us can really carry a tune +but uh but but uh we we would we we very + + align:start position:0% +but uh but but uh we we would we we very + + + align:start position:0% +but uh but but uh we we would we we very +very very interested in in in in them + + align:start position:0% +very very interested in in in in them + + + align:start position:0% +very very interested in in in in them +not so much uh to get a sense of what it + + align:start position:0% +not so much uh to get a sense of what it + + + align:start position:0% +not so much uh to get a sense of what it +should + + align:start position:0% +should + + + align:start position:0% +should +be but maybe to allow ourselves to think + + align:start position:0% +be but maybe to allow ourselves to think + + + align:start position:0% +be but maybe to allow ourselves to think +of what it could be or what it can be + + align:start position:0% +of what it could be or what it can be + + + align:start position:0% +of what it could be or what it can be +and and and and and specifically in + + align:start position:0% +and and and and and specifically in + + + align:start position:0% +and and and and and specifically in +skating uh right now because I mean i' I + + align:start position:0% +skating uh right now because I mean i' I + + + align:start position:0% +skating uh right now because I mean i' I +found some of the most conservative + + align:start position:0% +found some of the most conservative + + + align:start position:0% +found some of the most conservative +skaters you've ever met you could ever + + align:start position:0% +skaters you've ever met you could ever + + + align:start position:0% +skaters you've ever met you could ever +think of and I don't know to to us it + + align:start position:0% +think of and I don't know to to us it + + + align:start position:0% +think of and I don't know to to us it +skating was about Freedom + + align:start position:0% +skating was about Freedom + + + align:start position:0% +skating was about Freedom +uh and and and then to find so much + + align:start position:0% +uh and and and then to find so much + + + align:start position:0% +uh and and and then to find so much +about uh no man that's not how it should + + align:start position:0% +about uh no man that's not how it should + + + align:start position:0% +about uh no man that's not how it should +be uh was was kind of a a let down and a + + align:start position:0% +be uh was was kind of a a let down and a + + + align:start position:0% +be uh was was kind of a a let down and a +disappointment again we we probably + + align:start position:0% +disappointment again we we probably + + + align:start position:0% +disappointment again we we probably +didn't talk to the right skaters and and + + align:start position:0% +didn't talk to the right skaters and and + + + align:start position:0% +didn't talk to the right skaters and and +that's probably probably the reason that + + align:start position:0% +that's probably probably the reason that + + + align:start position:0% +that's probably probably the reason that +actually it could be it could very well + + align:start position:0% +actually it could be it could very well + + + align:start position:0% +actually it could be it could very well +be uh you know we're Outsiders in in in + + align:start position:0% +be uh you know we're Outsiders in in in + + + align:start position:0% +be uh you know we're Outsiders in in in +pretty much everything we do uh and um + + align:start position:0% +pretty much everything we do uh and um + + + align:start position:0% +pretty much everything we do uh and um +and you know we we have we there's it's + + align:start position:0% +and you know we we have we there's it's + + + align:start position:0% +and you know we we have we there's it's +inevitable uh uh in the the kinds of + + align:start position:0% +inevitable uh uh in the the kinds of + + + align:start position:0% +inevitable uh uh in the the kinds of +things we we we try to do at least so + + align:start position:0% +things we we we try to do at least so + + + align:start position:0% +things we we we try to do at least so +there's always that risk uh you know we + + align:start position:0% +there's always that risk uh you know we + + + align:start position:0% +there's always that risk uh you know we +even if we tried to do a a more you know + + align:start position:0% +even if we tried to do a a more you know + + + align:start position:0% +even if we tried to do a a more you know +I suppose the word would be conventional + + align:start position:0% +I suppose the word would be conventional + + + align:start position:0% +I suppose the word would be conventional +skate park uh we wouldn't know how to do + + align:start position:0% +skate park uh we wouldn't know how to do + + + align:start position:0% +skate park uh we wouldn't know how to do +it uh uh any anymore that we know how to + + align:start position:0% +it uh uh any anymore that we know how to + + + align:start position:0% +it uh uh any anymore that we know how to +do this one um we it's just that this + + align:start position:0% +do this one um we it's just that this + + + align:start position:0% +do this one um we it's just that this +seems to excite us more than than + + align:start position:0% +seems to excite us more than than + + + align:start position:0% +seems to excite us more than than +anything let me be clear I'm not talking + + align:start position:0% +anything let me be clear I'm not talking + + + align:start position:0% +anything let me be clear I'm not talking +about a conservative notion what + + align:start position:0% +about a conservative notion what + + + align:start position:0% +about a conservative notion what +aate no I I me I meant more a state of + + align:start position:0% +aate no I I me I meant more a state of + + + align:start position:0% +aate no I I me I meant more a state of +mind uh about things are this way and + + align:start position:0% +mind uh about things are this way and + + + align:start position:0% +mind uh about things are this way and +you know I don't want to talk about how + + align:start position:0% +you know I don't want to talk about how + + + align:start position:0% +you know I don't want to talk about how +they could be that's that's all say I + + align:start position:0% +they could be that's that's all say I + + + align:start position:0% +they could be that's that's all say I +say + + align:start position:0% + + + + align:start position:0% + +it at all it's just that the discovery + + align:start position:0% +it at all it's just that the discovery + + + align:start position:0% +it at all it's just that the discovery +of familiar through skate like you see a + + align:start position:0% +of familiar through skate like you see a + + + align:start position:0% +of familiar through skate like you see a +railing and you think imagine if I could + + align:start position:0% +railing and you think imagine if I could + + + align:start position:0% +railing and you think imagine if I could +actually late myself on this rail and + + align:start position:0% +actually late myself on this rail and + + + align:start position:0% +actually late myself on this rail and +slide + + align:start position:0% + + + + align:start position:0% + +down that's true but but it does it have + + align:start position:0% +down that's true but but it does it have + + + align:start position:0% +down that's true but but it does it have +to be a + + align:start position:0% +to be a + + + align:start position:0% +to be a +rail I mean one of the one one one + + align:start position:0% +rail I mean one of the one one one + + + align:start position:0% +rail I mean one of the one one one +beautiful thing I found out uh you know + + align:start position:0% +beautiful thing I found out uh you know + + + align:start position:0% +beautiful thing I found out uh you know +you know when when I was I was I was + + align:start position:0% +you know when when I was I was I was + + + align:start position:0% +you know when when I was I was I was +talking to to to to people that you know + + align:start position:0% +talking to to to to people that you know + + + align:start position:0% +talking to to to to people that you know +why do you SK why do you need stairs + + align:start position:0% +why do you SK why do you need stairs + + + align:start position:0% +why do you SK why do you need stairs +because you know you're jumping + + align:start position:0% +because you know you're jumping + + + align:start position:0% +because you know you're jumping +basically from the top of the stair to + + align:start position:0% +basically from the top of the stair to + + + align:start position:0% +basically from the top of the stair to +the bottom of the stair uh I mean do + + align:start position:0% +the bottom of the stair uh I mean do + + + align:start position:0% +the bottom of the stair uh I mean do +there have to be steps in between don't + + align:start position:0% +there have to be steps in between don't + + + align:start position:0% +there have to be steps in between don't +you just need basically a place to jump + + align:start position:0% +you just need basically a place to jump + + + align:start position:0% +you just need basically a place to jump +from and and this guy said something + + align:start position:0% +from and and this guy said something + + + align:start position:0% +from and and this guy said something +really beautiful he said well you know + + align:start position:0% +really beautiful he said well you know + + + align:start position:0% +really beautiful he said well you know +if there's steps you can count the steps + + align:start position:0% +if there's steps you can count the steps + + + align:start position:0% +if there's steps you can count the steps +and if I can count the steps you know I + + align:start position:0% +and if I can count the steps you know I + + + align:start position:0% +and if I can count the steps you know I +can say well I can jump 10 steps uh and + + align:start position:0% +can say well I can jump 10 steps uh and + + + align:start position:0% +can say well I can jump 10 steps uh and +you know and there's + + align:start position:0% +you know and there's + + + align:start position:0% +you know and there's +something perfectly valid about that + + align:start position:0% +something perfectly valid about that + + + align:start position:0% +something perfectly valid about that +explanation and and and and humbling and + + align:start position:0% +explanation and and and and humbling and + + + align:start position:0% +explanation and and and and humbling and +like oh my God we need to you know we we + + align:start position:0% +like oh my God we need to you know we we + + + align:start position:0% +like oh my God we need to you know we we +need to account for this in some way and + + align:start position:0% +need to account for this in some way and + + + align:start position:0% +need to account for this in some way and +you know I I gave a very very brief you + + align:start position:0% +you know I I gave a very very brief you + + + align:start position:0% +you know I I gave a very very brief you +know I didn't want to turn the the the + + align:start position:0% +know I didn't want to turn the the the + + + align:start position:0% +know I didn't want to turn the the the +presentation into into into the + + align:start position:0% +presentation into into into the + + + align:start position:0% +presentation into into into the +presentation I just wanted to give a bit + + align:start position:0% +presentation I just wanted to give a bit + + + align:start position:0% +presentation I just wanted to give a bit +of a sense of how we work and the kind + + align:start position:0% +of a sense of how we work and the kind + + + align:start position:0% +of a sense of how we work and the kind +of things we we sort of touch on when + + align:start position:0% +of things we we sort of touch on when + + + align:start position:0% +of things we we sort of touch on when +when we work that's all um you know + + align:start position:0% +when we work that's all um you know + + + align:start position:0% +when we work that's all um you know +we're we're we're we're showing the park + + align:start position:0% +we're we're we're we're showing the park + + + align:start position:0% +we're we're we're we're showing the park +constantly to skateboarders and you know + + align:start position:0% +constantly to skateboarders and you know + + + align:start position:0% +constantly to skateboarders and you know +and and you know initially it's like oh + + align:start position:0% +and and you know initially it's like oh + + + align:start position:0% +and and you know initially it's like oh +that careful with that and then I go + + align:start position:0% +that careful with that and then I go + + + align:start position:0% +that careful with that and then I go +wait wait okay say you walking down this + + align:start position:0% +wait wait okay say you walking down this + + + align:start position:0% +wait wait okay say you walking down this +bar and you have your skateboard in your + + align:start position:0% +bar and you have your skateboard in your + + + align:start position:0% +bar and you have your skateboard in your +hand and you see this will you + + align:start position:0% +hand and you see this will you + + + align:start position:0% +hand and you see this will you +skate and they'll say well + + align:start position:0% +skate and they'll say well + + + align:start position:0% +skate and they'll say well +yeah uh but still you have to you know + + align:start position:0% +yeah uh but still you have to you know + + + align:start position:0% +yeah uh but still you have to you know +okay so so I mean that discussion we we + + align:start position:0% +okay so so I mean that discussion we we + + + align:start position:0% +okay so so I mean that discussion we we +we can have and we still do have and and + + align:start position:0% +we can have and we still do have and and + + + align:start position:0% +we can have and we still do have and and +again it's in development and and we + + align:start position:0% +again it's in development and and we + + + align:start position:0% +again it's in development and and we +listen we listen very very very very + + align:start position:0% +listen we listen very very very very + + + align:start position:0% +listen we listen very very very very +carefully um so yeah + + align:start position:0% +carefully um so yeah + + + align:start position:0% +carefully um so yeah +Sor there's this one that um I found + + align:start position:0% +Sor there's this one that um I found + + + align:start position:0% +Sor there's this one that um I found +kind of interesting in what you pointed + + align:start position:0% +kind of interesting in what you pointed + + + align:start position:0% +kind of interesting in what you pointed +out and maybe there was something there + + align:start position:0% +out and maybe there was something there + + + align:start position:0% +out and maybe there was something there +was a jump also that was done within the + + align:start position:0% +was a jump also that was done within the + + + align:start position:0% +was a jump also that was done within the +presentation there's one thing that has + + align:start position:0% +presentation there's one thing that has + + + align:start position:0% +presentation there's one thing that has +remained from 's very early work to now + + align:start position:0% +remained from 's very early work to now + + + align:start position:0% +remained from 's very early work to now +and maybe we didn't present that clearly + + align:start position:0% +and maybe we didn't present that clearly + + + align:start position:0% +and maybe we didn't present that clearly +enough is the idea of having a scheme so + + align:start position:0% +enough is the idea of having a scheme so + + + align:start position:0% +enough is the idea of having a scheme so +some from something like farming P or + + align:start position:0% +some from something like farming P or + + + align:start position:0% +some from something like farming P or +even torture there's something that's + + align:start position:0% +even torture there's something that's + + + align:start position:0% +even torture there's something that's +kind of beautiful when you're looking at + + align:start position:0% +kind of beautiful when you're looking at + + + align:start position:0% +kind of beautiful when you're looking at +that period of's work because you can + + align:start position:0% +that period of's work because you can + + + align:start position:0% +that period of's work because you can +evolution in the scheme um and a certain + + align:start position:0% +evolution in the scheme um and a certain + + + align:start position:0% +evolution in the scheme um and a certain +coherence in this in this Evolution now + + align:start position:0% +coherence in this in this Evolution now + + + align:start position:0% +coherence in this in this Evolution now +the scheme still exists it just reached + + align:start position:0% +the scheme still exists it just reached + + + align:start position:0% +the scheme still exists it just reached +um it just has a and and it's still + + align:start position:0% +um it just has a and and it's still + + + align:start position:0% +um it just has a and and it's still +there and it's still there within the + + align:start position:0% +there and it's still there within the + + + align:start position:0% +there and it's still there within the +descriptions as well and what's kind of + + align:start position:0% +descriptions as well and what's kind of + + + align:start position:0% +descriptions as well and what's kind of +interesting is the way and I think maybe + + align:start position:0% +interesting is the way and I think maybe + + + align:start position:0% +interesting is the way and I think maybe +it is a limit sometimes but it's + + align:start position:0% +it is a limit sometimes but it's + + + align:start position:0% +it is a limit sometimes but it's +something that characterizes the work + + align:start position:0% +something that characterizes the work + + + align:start position:0% +something that characterizes the work +the early work info now it's the + + align:start position:0% +the early work info now it's the + + + align:start position:0% +the early work info now it's the +importance of the plot and + + align:start position:0% +importance of the plot and + + + align:start position:0% +importance of the plot and +um that's why we decided with with Lissa + + align:start position:0% +um that's why we decided with with Lissa + + + align:start position:0% +um that's why we decided with with Lissa +that maybe it was good to show the + + align:start position:0% +that maybe it was good to show the + + + align:start position:0% +that maybe it was good to show the +descriptions of the projects in this + + align:start position:0% +descriptions of the projects in this + + + align:start position:0% +descriptions of the projects in this +room because you have time although + + align:start position:0% +room because you have time although + + + align:start position:0% +room because you have time although +they're pretty lengthy and we shouldn't + + align:start position:0% +they're pretty lengthy and we shouldn't + + + align:start position:0% +they're pretty lengthy and we shouldn't +really expect people to have time to + + align:start position:0% +really expect people to have time to + + + align:start position:0% +really expect people to have time to +read this sort of stuff but you'll see + + align:start position:0% +read this sort of stuff but you'll see + + + align:start position:0% +read this sort of stuff but you'll see +that there's there's still the idea of + + align:start position:0% +that there's there's still the idea of + + + align:start position:0% +that there's there's still the idea of +plot and + + align:start position:0% +plot and + + + align:start position:0% +plot and +within I want to maybe mention something + + align:start position:0% +within I want to maybe mention something + + + align:start position:0% +within I want to maybe mention something +about what you said about about the + + align:start position:0% +about what you said about about the + + + align:start position:0% +about what you said about about the +change in language the what you call an + + align:start position:0% +change in language the what you call an + + + align:start position:0% +change in language the what you call an +esoteric language I I didn't know you + + align:start position:0% +esoteric language I I didn't know you + + + align:start position:0% +esoteric language I I didn't know you +were referring to verbal language as + + align:start position:0% +were referring to verbal language as + + + align:start position:0% +were referring to verbal language as +much as visual language + + align:start position:0% +much as visual language + + + align:start position:0% +much as visual language +uh I mean I you know one thing I feel so + + align:start position:0% +uh I mean I you know one thing I feel so + + + align:start position:0% +uh I mean I you know one thing I feel so +deeply committed in is that committed to + + align:start position:0% +deeply committed in is that committed to + + + align:start position:0% +deeply committed in is that committed to +is that you know I want the stuff with + + align:start position:0% +is that you know I want the stuff with + + + align:start position:0% +is that you know I want the stuff with +design even though I don't think we we' + + align:start position:0% +design even though I don't think we we' + + + align:start position:0% +design even though I don't think we we' +have lived up to this a or can live up + + align:start position:0% +have lived up to this a or can live up + + + align:start position:0% +have lived up to this a or can live up +to this a I want the stuff with designed + + align:start position:0% +to this a I want the stuff with designed + + + align:start position:0% +to this a I want the stuff with designed +to be stuff that couldn't possibly have + + align:start position:0% +to be stuff that couldn't possibly have + + + align:start position:0% +to be stuff that couldn't possibly have +been built couldn't possibly have been + + align:start position:0% +been built couldn't possibly have been + + + align:start position:0% +been built couldn't possibly have been +designed and probably couldn't even + + align:start position:0% +designed and probably couldn't even + + + align:start position:0% +designed and probably couldn't even +possibly have been thought of before the + + align:start position:0% +possibly have been thought of before the + + + align:start position:0% +possibly have been thought of before the +the uh 21st century I feel sure that the + + align:start position:0% +the uh 21st century I feel sure that the + + + align:start position:0% +the uh 21st century I feel sure that the +only way to design now is you know with + + align:start position:0% +only way to design now is you know with + + + align:start position:0% +only way to design now is you know with +the with the with the with the computer + + align:start position:0% +the with the with the with the computer + + + align:start position:0% +the with the with the with the computer +but I got to find another word than with + + align:start position:0% +but I got to find another word than with + + + align:start position:0% +but I got to find another word than with +because I think we haven't quite reached + + align:start position:0% +because I think we haven't quite reached + + + align:start position:0% +because I think we haven't quite reached +it yet I mean maybe we're using the + + align:start position:0% +it yet I mean maybe we're using the + + + align:start position:0% +it yet I mean maybe we're using the +computer too much we have to we have to + + align:start position:0% +computer too much we have to we have to + + + align:start position:0% +computer too much we have to we have to +I don't we have to nudge the computer I + + align:start position:0% +I don't we have to nudge the computer I + + + align:start position:0% +I don't we have to nudge the computer I +know Dario who knows the computer much + + align:start position:0% +know Dario who knows the computer much + + + align:start position:0% +know Dario who knows the computer much +more than I do says that doesn't really + + align:start position:0% +more than I do says that doesn't really + + + align:start position:0% +more than I do says that doesn't really +work that way but I'm not so sure I + + align:start position:0% +work that way but I'm not so sure I + + + align:start position:0% +work that way but I'm not so sure I +think we have to we have to learn to not + + align:start position:0% +think we have to we have to learn to not + + + align:start position:0% +think we have to we have to learn to not +tell the computer what to do but + + align:start position:0% +tell the computer what to do but + + + align:start position:0% +tell the computer what to do but +to to nudge and pet until it until it + + align:start position:0% +to to nudge and pet until it until it + + + align:start position:0% +to to nudge and pet until it until it +trusts us and uh and is able to you know + + align:start position:0% +trusts us and uh and is able to you know + + + align:start position:0% +trusts us and uh and is able to you know +is able to do something that couldn't + + align:start position:0% +is able to do something that couldn't + + + align:start position:0% +is able to do something that couldn't +have been uh couldn't have been B before + + align:start position:0% +have been uh couldn't have been B before + + + align:start position:0% +have been uh couldn't have been B before +could never designed before I mean I I I + + align:start position:0% +could never designed before I mean I I I + + + align:start position:0% +could never designed before I mean I I I +I think this this is potentially the + + align:start position:0% +I think this this is potentially the + + + align:start position:0% +I think this this is potentially the +most incredible time in + + align:start position:0% +most incredible time in + + + align:start position:0% +most incredible time in +architecture uh in many many many many + + align:start position:0% +architecture uh in many many many many + + + align:start position:0% +architecture uh in many many many many +years but at the same time it's the time + + align:start position:0% +years but at the same time it's the time + + + align:start position:0% +years but at the same time it's the time +of a you know new invention and it's + + align:start position:0% +of a you know new invention and it's + + + align:start position:0% +of a you know new invention and it's +probably very similar to the way it was + + align:start position:0% +probably very similar to the way it was + + + align:start position:0% +probably very similar to the way it was +in the Renaissance when perspective was + + align:start position:0% +in the Renaissance when perspective was + + + align:start position:0% +in the Renaissance when perspective was +discovered you know and everybody's + + align:start position:0% +discovered you know and everybody's + + + align:start position:0% +discovered you know and everybody's +drawing probably exactly the same until + + align:start position:0% +drawing probably exactly the same until + + + align:start position:0% +drawing probably exactly the same until +somebody made a mistake you know until + + align:start position:0% +somebody made a mistake you know until + + + align:start position:0% +somebody made a mistake you know until +somebody + + align:start position:0% +somebody + + + align:start position:0% +somebody +made you know some incredible flaw and + + align:start position:0% +made you know some incredible flaw and + + + align:start position:0% +made you know some incredible flaw and +now I think you know yeah when you know + + align:start position:0% +now I think you know yeah when you know + + + align:start position:0% +now I think you know yeah when you know +when when we have some stuff in the uh + + align:start position:0% +when when we have some stuff in the uh + + + align:start position:0% +when when we have some stuff in the uh +in the uh architectural architectural + + align:start position:0% +in the uh architectural architectural + + + align:start position:0% +in the uh architectural architectural +vial in Venice two years ago and all the + + align:start position:0% +vial in Venice two years ago and all the + + + align:start position:0% +vial in Venice two years ago and all the +people we liked you know it was hard to + + align:start position:0% +people we liked you know it was hard to + + + align:start position:0% +people we liked you know it was hard to +it was hard to it was hard to separate + + align:start position:0% +it was hard to it was hard to separate + + + align:start position:0% +it was hard to it was hard to separate +but I wonder if that's if that's + + align:start position:0% +but I wonder if that's if that's + + + align:start position:0% +but I wonder if that's if that's +necessary now that until somebody + + align:start position:0% +necessary now that until somebody + + + align:start position:0% +necessary now that until somebody +figures out how to make a mistake how to + + align:start position:0% +figures out how to make a mistake how to + + + align:start position:0% +figures out how to make a mistake how to +make a real still good in stake with the + + align:start position:0% +make a real still good in stake with the + + + align:start position:0% +make a real still good in stake with the +language that uh maybe it's a testing + + align:start position:0% +language that uh maybe it's a testing + + + align:start position:0% +language that uh maybe it's a testing +time I don't + + align:start position:0% + + + + align:start position:0% + +know yes + + align:start position:0% +know yes + + + align:start position:0% +know yes +yes what are your new thoughts about + + align:start position:0% +yes what are your new thoughts about + + + align:start position:0% +yes what are your new thoughts about +encroachment + + align:start position:0% +encroachment + + + align:start position:0% +encroachment +now through take ability underground SP + + align:start position:0% +now through take ability underground SP + + + align:start position:0% +now through take ability underground SP +borders going across parking lots what + + align:start position:0% +borders going across parking lots what + + + align:start position:0% +borders going across parking lots what +are the new kinds of directions than + + align:start position:0% + + + + align:start position:0% + +you I when when Serena was talking about + + align:start position:0% +you I when when Serena was talking about + + + align:start position:0% +you I when when Serena was talking about +paraside and virus uh uh I mean I think + + align:start position:0% +paraside and virus uh uh I mean I think + + + align:start position:0% +paraside and virus uh uh I mean I think +that's the kind of field the field of + + align:start position:0% +that's the kind of field the field of + + + align:start position:0% +that's the kind of field the field of +approach with never got to never got to + + align:start position:0% +approach with never got to never got to + + + align:start position:0% +approach with never got to never got to +some of those projects except the full + + align:start position:0% +some of those projects except the full + + + align:start position:0% +some of those projects except the full +Street project but I I uh we did a + + align:start position:0% +Street project but I I uh we did a + + + align:start position:0% +Street project but I I uh we did a +project in s Paulo well we didn't do it + + align:start position:0% +project in s Paulo well we didn't do it + + + align:start position:0% +project in s Paulo well we didn't do it +we uh proposed the project in s Paulo a + + align:start position:0% +we uh proposed the project in s Paulo a + + + align:start position:0% +we uh proposed the project in s Paulo a +few years ago + + align:start position:0% +few years ago + + + align:start position:0% +few years ago +uh based on the elevated highways in + + align:start position:0% +uh based on the elevated highways in + + + align:start position:0% +uh based on the elevated highways in +South Pao since elevated highways have + + align:start position:0% +South Pao since elevated highways have + + + align:start position:0% +South Pao since elevated highways have +cut through neighborhoods killed + + align:start position:0% +cut through neighborhoods killed + + + align:start position:0% +cut through neighborhoods killed +neighborhoods so we tried to make this + + align:start position:0% +neighborhoods so we tried to make this + + + align:start position:0% +neighborhoods so we tried to make this +housing not exactly houses to live in + + align:start position:0% +housing not exactly houses to live in + + + align:start position:0% +housing not exactly houses to live in +but a kind of community housing that uh + + align:start position:0% +but a kind of community housing that uh + + + align:start position:0% +but a kind of community housing that uh +clung onto the underside of the highways + + align:start position:0% +clung onto the underside of the highways + + + align:start position:0% +clung onto the underside of the highways +elevated off the street for people who + + align:start position:0% +elevated off the street for people who + + + align:start position:0% +elevated off the street for people who +are forced to live on the street in a + + align:start position:0% +are forced to live on the street in a + + + align:start position:0% +are forced to live on the street in a +lot of ways I think we + + align:start position:0% +lot of ways I think we + + + align:start position:0% +lot of ways I think we +should you one thing that I love about + + align:start position:0% +should you one thing that I love about + + + align:start position:0% +should you one thing that I love about +doing architecture is that we get a + + align:start position:0% +doing architecture is that we get a + + + align:start position:0% +doing architecture is that we get a +program to + + align:start position:0% +program to + + + align:start position:0% +program to +follow but one thing I I start to hate + + align:start position:0% +follow but one thing I I start to hate + + + align:start position:0% +follow but one thing I I start to hate +is that are we always following somebody + + align:start position:0% +is that are we always following somebody + + + align:start position:0% +is that are we always following somebody +else's moves shouldn't start to make the + + align:start position:0% +else's moves shouldn't start to make the + + + align:start position:0% +else's moves shouldn't start to make the +first move that we're when we're asked + + align:start position:0% +first move that we're when we're asked + + + align:start position:0% +first move that we're when we're asked +to do a project we're reacting to a + + align:start position:0% +to do a project we're reacting to a + + + align:start position:0% +to do a project we're reacting to a +program somebody else has you know + + align:start position:0% +program somebody else has you know + + + align:start position:0% +program somebody else has you know +already given us and I I I think the + + align:start position:0% +already given us and I I I think the + + + align:start position:0% +already given us and I I I think the +ideal what I would really like our + + align:start position:0% +ideal what I would really like our + + + align:start position:0% +ideal what I would really like our +architecture to act as is a parasite and + + align:start position:0% +architecture to act as is a parasite and + + + align:start position:0% +architecture to act as is a parasite and +a virus you know you cling on to + + align:start position:0% +a virus you know you cling on to + + + align:start position:0% +a virus you know you cling on to +buildings where people aren't supposed + + align:start position:0% +buildings where people aren't supposed + + + align:start position:0% +buildings where people aren't supposed +to go you make places for people where + + align:start position:0% +to go you make places for people where + + + align:start position:0% +to go you make places for people where +they're not where they're not supposed + + align:start position:0% +they're not where they're not supposed + + + align:start position:0% +they're not where they're not supposed +to be there are a lot of buildings with + + align:start position:0% +to be there are a lot of buildings with + + + align:start position:0% +to be there are a lot of buildings with +you know blank + + align:start position:0% +you know blank + + + align:start position:0% +you know blank +walls why not use them for people you + + align:start position:0% +walls why not use them for people you + + + align:start position:0% +walls why not use them for people you +know why not if there's a lamp post at a + + align:start position:0% +know why not if there's a lamp post at a + + + align:start position:0% +know why not if there's a lamp post at a +corner why can't there be a spiral + + align:start position:0% +corner why can't there be a spiral + + + align:start position:0% +corner why can't there be a spiral +staircase somebody can like some to + + align:start position:0% +staircase somebody can like some to + + + align:start position:0% +staircase somebody can like some to +consider the top of a consider the top + + align:start position:0% +consider the top of a consider the top + + + align:start position:0% +consider the top of a consider the top +of a left post you know I I mean I + + align:start position:0% +of a left post you know I I mean I + + + align:start position:0% +of a left post you know I I mean I +ideally what I want I stuff to do and I + + align:start position:0% +ideally what I want I stuff to do and I + + + align:start position:0% +ideally what I want I stuff to do and I +know people have come close to this is + + align:start position:0% +know people have come close to this is + + + align:start position:0% +know people have come close to this is +make places for people where they aren't + + align:start position:0% +make places for people where they aren't + + + align:start position:0% +make places for people where they aren't +allow they aren't allowed to be I mean + + align:start position:0% +allow they aren't allowed to be I mean + + + align:start position:0% +allow they aren't allowed to be I mean +that's why that fton street project + + align:start position:0% +that's why that fton street project + + + align:start position:0% +that's why that fton street project +interests me I think more than interests + + align:start position:0% +interests me I think more than interests + + + align:start position:0% +interests me I think more than interests +Serena because that notion of this extra + + align:start position:0% +Serena because that notion of this extra + + + align:start position:0% +Serena because that notion of this extra +space for people you know there's all + + align:start position:0% +space for people you know there's all + + + align:start position:0% +space for people you know there's all +that space up there you know and it's uh + + align:start position:0% +that space up there you know and it's uh + + + align:start position:0% +that space up there you know and it's uh +I all I hate spaces that lead to + + align:start position:0% +I all I hate spaces that lead to + + + align:start position:0% +I all I hate spaces that lead to +all uh I love a lot of Richard Sarah's + + align:start position:0% +all uh I love a lot of Richard Sarah's + + + align:start position:0% +all uh I love a lot of Richard Sarah's +new stuff I wish there was a hot dog + + align:start position:0% +new stuff I wish there was a hot dog + + + align:start position:0% +new stuff I wish there was a hot dog +standing time I wish there was something + + align:start position:0% +standing time I wish there was something + + + align:start position:0% +standing time I wish there was something +to do there except just feel that you + + align:start position:0% +to do there except just feel that you + + + align:start position:0% +to do there except just feel that you +know I am going to look up and feel + + align:start position:0% +know I am going to look up and feel + + + align:start position:0% +know I am going to look up and feel +wow feel wow you felt wow as a child you + + align:start position:0% +wow feel wow you felt wow as a child you + + + align:start position:0% +wow feel wow you felt wow as a child you +don't you don't have to feel wow man I + + align:start position:0% +don't you don't have to feel wow man I + + + align:start position:0% +don't you don't have to feel wow man I +mean I want our stuff to libery can it + + align:start position:0% +mean I want our stuff to libery can it + + + align:start position:0% +mean I want our stuff to libery can it +ever do that I don't know but it's the + + align:start position:0% +ever do that I don't know but it's the + + + align:start position:0% +ever do that I don't know but it's the +only thing wor worth trying + + align:start position:0% +only thing wor worth trying + + + align:start position:0% +only thing wor worth trying +also encroachment was uh when when the + + align:start position:0% +also encroachment was uh when when the + + + align:start position:0% +also encroachment was uh when when the +work was in the context of public art + + align:start position:0% +work was in the context of public art + + + align:start position:0% +work was in the context of public art +it's pretty much everything it could be + + align:start position:0% +it's pretty much everything it could be + + + align:start position:0% +it's pretty much everything it could be +uh because you know it's part of an + + align:start position:0% +uh because you know it's part of an + + + align:start position:0% +uh because you know it's part of an +existing space it's always an add onto + + align:start position:0% +existing space it's always an add onto + + + align:start position:0% +existing space it's always an add onto +an existing space you know it's 1% of + + align:start position:0% +an existing space you know it's 1% of + + + align:start position:0% +an existing space you know it's 1% of +the budget so it it almost it's + + align:start position:0% +the budget so it it almost it's + + + align:start position:0% +the budget so it it almost it's +inevitable decision is that to be + + align:start position:0% +inevitable decision is that to be + + + align:start position:0% +inevitable decision is that to be +something that is a parasite something + + align:start position:0% +something that is a parasite something + + + align:start position:0% +something that is a parasite something +that's attached to and sure you might + + align:start position:0% +that's attached to and sure you might + + + align:start position:0% +that's attached to and sure you might +make an effort to make it appear as it + + align:start position:0% +make an effort to make it appear as it + + + align:start position:0% +make an effort to make it appear as it +was always there or or it belongs there + + align:start position:0% +was always there or or it belongs there + + + align:start position:0% +was always there or or it belongs there +um but it unless you're building from + + align:start position:0% +um but it unless you're building from + + + align:start position:0% +um but it unless you're building from +the ground up unless you're you're + + align:start position:0% +the ground up unless you're you're + + + align:start position:0% +the ground up unless you're you're +you're making a place you're always uh + + align:start position:0% +you're making a place you're always uh + + + align:start position:0% +you're making a place you're always uh +uh uh put in the position of being part + + align:start position:0% +uh uh put in the position of being part + + + align:start position:0% +uh uh put in the position of being part +of a place and uh and making choices as + + align:start position:0% +of a place and uh and making choices as + + + align:start position:0% +of a place and uh and making choices as +to how how to be part part of that + + align:start position:0% + + + + align:start position:0% + +place maybe you should from arit head + + align:start position:0% +place maybe you should from arit head + + + align:start position:0% +place maybe you should from arit head +towards City Planning predesign one of + + align:start position:0% +towards City Planning predesign one of + + + align:start position:0% +towards City Planning predesign one of +these cities that disappeared last + + align:start position:0% +these cities that disappeared last + + + align:start position:0% +these cities that disappeared last +month do a proposal + + align:start position:0% +month do a proposal + + + align:start position:0% +month do a proposal +for one the cities in + + align:start position:0% +for one the cities in + + + align:start position:0% +for one the cities in +Mississippi yeah we'd love to do a city + + align:start position:0% +Mississippi yeah we'd love to do a city + + + align:start position:0% +Mississippi yeah we'd love to do a city +but at the same time we' love to do + + align:start position:0% +but at the same time we' love to do + + + align:start position:0% +but at the same time we' love to do +class we'd love to do a school you know + + align:start position:0% +class we'd love to do a school you know + + + align:start position:0% +class we'd love to do a school you know +I I don't know uh would I love to do a + + align:start position:0% +I I don't know uh would I love to do a + + + align:start position:0% +I I don't know uh would I love to do a +city I don't know I mean s has bought + + align:start position:0% +city I don't know I mean s has bought + + + align:start position:0% +city I don't know I mean s has bought +Notions + + align:start position:0% +Notions + + + align:start position:0% +Notions +ofia talk about but we don't agree about + + align:start position:0% +ofia talk about but we don't agree about + + + align:start position:0% +ofia talk about but we don't agree about +this within the studio + + align:start position:0% +this within the studio + + + align:start position:0% +this within the studio +I mean we'll sort it out I love the idea + + align:start position:0% +I mean we'll sort it out I love the idea + + + align:start position:0% +I mean we'll sort it out I love the idea +of Utopia as an intention I hate if it's + + align:start position:0% +of Utopia as an intention I hate if it's + + + align:start position:0% +of Utopia as an intention I hate if it's +ever reached so if we're going to build + + align:start position:0% +ever reached so if we're going to build + + + align:start position:0% +ever reached so if we're going to build +a city somebody else going to come in + + align:start position:0% +a city somebody else going to come in + + + align:start position:0% +a city somebody else going to come in +and and uh uh mess it up a little + + align:start position:0% + + + + align:start position:0% + +bit yeah oh + + align:start position:0% + + + + align:start position:0% + +sorry + + align:start position:0% +sorry + + + align:start position:0% +sorry +book book + + align:start position:0% +book book + + + align:start position:0% +book book +design you know in a way it's funny + + align:start position:0% +design you know in a way it's funny + + + align:start position:0% +design you know in a way it's funny +because uh when we have we're we're in + + align:start position:0% +because uh when we have we're we're in + + + align:start position:0% +because uh when we have we're we're in +the process of having a new web page now + + align:start position:0% +the process of having a new web page now + + + align:start position:0% +the process of having a new web page now +and um one one of the the the critiques + + align:start position:0% +and um one one of the the the critiques + + + align:start position:0% +and um one one of the the the critiques +of of that we had of of of of web pages + + align:start position:0% +of of that we had of of of of web pages + + + align:start position:0% +of of that we had of of of of web pages +is that it's very basically like at + + align:start position:0% +is that it's very basically like at + + + align:start position:0% +is that it's very basically like at +least in in in most way versions of what + + align:start position:0% +least in in in most way versions of what + + + align:start position:0% +least in in in most way versions of what +we + + align:start position:0% +we + + + align:start position:0% +we +see almost like these glorified books + + align:start position:0% +see almost like these glorified books + + + align:start position:0% +see almost like these glorified books +it's a it's a very Advanced way of + + align:start position:0% +it's a it's a very Advanced way of + + + align:start position:0% +it's a it's a very Advanced way of +turning Pages um and and we try to to + + align:start position:0% +turning Pages um and and we try to to + + + align:start position:0% +turning Pages um and and we try to to +think of okay how how how how can this + + align:start position:0% +think of okay how how how how can this + + + align:start position:0% +think of okay how how how how can this +be different I mean here we have uh this + + align:start position:0% +be different I mean here we have uh this + + + align:start position:0% +be different I mean here we have uh this +amazing landscape with with its own laws + + align:start position:0% +amazing landscape with with its own laws + + + align:start position:0% +amazing landscape with with its own laws +and and we're almost forcing it to + + align:start position:0% +and and we're almost forcing it to + + + align:start position:0% +and and we're almost forcing it to +behave you know we're in Mars and we're + + align:start position:0% +behave you know we're in Mars and we're + + + align:start position:0% +behave you know we're in Mars and we're +trying to make Mars feel like Earth and + + align:start position:0% +trying to make Mars feel like Earth and + + + align:start position:0% +trying to make Mars feel like Earth and +uh let's just hop around in Mars for a + + align:start position:0% +uh let's just hop around in Mars for a + + + align:start position:0% +uh let's just hop around in Mars for a +while and so in a way we we that that's + + align:start position:0% +while and so in a way we we that that's + + + align:start position:0% +while and so in a way we we that that's +the way we approach approach that I'm + + align:start position:0% +the way we approach approach that I'm + + + align:start position:0% +the way we approach approach that I'm +not sure I mean we we we struggle with + + align:start position:0% +not sure I mean we we we struggle with + + + align:start position:0% +not sure I mean we we we struggle with +graphic design yeah we're we're really + + align:start position:0% +graphic design yeah we're we're really + + + align:start position:0% +graphic design yeah we're we're really +we're really bad we're not very good + + align:start position:0% +we're really bad we're not very good + + + align:start position:0% +we're really bad we're not very good +graphic designers I don't think we + + align:start position:0% +graphic designers I don't think we + + + align:start position:0% +graphic designers I don't think we +understand two two dimensional space + + align:start position:0% +understand two two dimensional space + + + align:start position:0% +understand two two dimensional space +uh that sounds great when you say oh we + + align:start position:0% +uh that sounds great when you say oh we + + + align:start position:0% +uh that sounds great when you say oh we +don't understand we're just we're just + + align:start position:0% +don't understand we're just we're just + + + align:start position:0% +don't understand we're just we're just +bad we're just + + align:start position:0% +bad we're just + + + align:start position:0% +bad we're just +bad I understand the space where I can + + align:start position:0% +bad I understand the space where I can + + + align:start position:0% +bad I understand the space where I can +put my feet in I mean the reason I've + + align:start position:0% +put my feet in I mean the reason I've + + + align:start position:0% +put my feet in I mean the reason I've +always hated art was because of + + align:start position:0% +always hated art was because of + + + align:start position:0% +always hated art was because of +two-dimensional space the reason I hated + + align:start position:0% +two-dimensional space the reason I hated + + + align:start position:0% +two-dimensional space the reason I hated +art the reason I hated art was that you + + align:start position:0% +art the reason I hated art was that you + + + align:start position:0% +art the reason I hated art was that you +the viewer are supposed to stand here + + align:start position:0% +the viewer are supposed to stand here + + + align:start position:0% +the viewer are supposed to stand here +and the art is there + + align:start position:0% +and the art is there + + + align:start position:0% +and the art is there +so you're always in the position of + + align:start position:0% +so you're always in the position of + + + align:start position:0% +so you're always in the position of +desire and that desire will always be + + align:start position:0% +desire and that desire will always be + + + align:start position:0% +desire and that desire will always be +frustrated you know uh the reason you + + align:start position:0% +frustrated you know uh the reason you + + + align:start position:0% +frustrated you know uh the reason you +know I like spaces you can touch and + + align:start position:0% +know I like spaces you can touch and + + + align:start position:0% +know I like spaces you can touch and +you're not supposed to touch art and + + align:start position:0% +you're not supposed to touch art and + + + align:start position:0% +you're not supposed to touch art and +you're not supposed to touch art because + + align:start position:0% +you're not supposed to touch art because + + + align:start position:0% +you're not supposed to touch art because +art is more expensive than people uh I + + align:start position:0% +art is more expensive than people uh I + + + align:start position:0% +art is more expensive than people uh I +like the space where you can't touch it + + align:start position:0% +like the space where you can't touch it + + + align:start position:0% +like the space where you can't touch it +you know but the one of the um only + + align:start position:0% +you know but the one of the um only + + + align:start position:0% +you know but the one of the um only +things the only sort of objects or + + align:start position:0% +things the only sort of objects or + + + align:start position:0% +things the only sort of objects or +material objects that video has ever + + align:start position:0% +material objects that video has ever + + + align:start position:0% +material objects that video has ever +shown any interest for are books and in + + align:start position:0% +shown any interest for are books and in + + + align:start position:0% +shown any interest for are books and in +the studio we live on B we eat over + + align:start position:0% +the studio we live on B we eat over + + + align:start position:0% +the studio we live on B we eat over +books and and CD grow up books CD CDs + + align:start position:0% +books and and CD grow up books CD CDs + + + align:start position:0% +books and and CD grow up books CD CDs +too and C but CDs are more compax and + + align:start position:0% +too and C but CDs are more compax and + + + align:start position:0% +too and C but CDs are more compax and +they're new phenomenon because the + + align:start position:0% +they're new phenomenon because the + + + align:start position:0% +they're new phenomenon because the +collection of books is about your age + + align:start position:0% +collection of books is about your age + + + align:start position:0% +collection of books is about your age +and + + align:start position:0% +and + + + align:start position:0% +and +um we we're very very interested and + + align:start position:0% +um we we're very very interested and + + + align:start position:0% +um we we're very very interested and +very curious in um in this in book of + + align:start position:0% +very curious in um in this in book of + + + align:start position:0% +very curious in um in this in book of +them actually um and we um it's more and + + align:start position:0% +them actually um and we um it's more and + + + align:start position:0% +them actually um and we um it's more and +more within architecture now um more and + + align:start position:0% +more within architecture now um more and + + + align:start position:0% +more within architecture now um more and +more groups of architecture have their + + align:start position:0% +more groups of architecture have their + + + align:start position:0% +more groups of architecture have their +own inhouse designers and books + + align:start position:0% +own inhouse designers and books + + + align:start position:0% +own inhouse designers and books +architecture of books or some of these + + align:start position:0% +architecture of books or some of these + + + align:start position:0% +architecture of books or some of these +Publications are actually mini + + align:start position:0% +Publications are actually mini + + + align:start position:0% +Publications are actually mini +manifestos and we're actually limited by + + align:start position:0% +manifestos and we're actually limited by + + + align:start position:0% +manifestos and we're actually limited by +our inability not to be able to hire + + align:start position:0% +our inability not to be able to hire + + + align:start position:0% +our inability not to be able to hire +someone that we would enjoy working with + + align:start position:0% +someone that we would enjoy working with + + + align:start position:0% +someone that we would enjoy working with +could design book with us or um or our + + align:start position:0% +could design book with us or um or our + + + align:start position:0% +could design book with us or um or our +own + + align:start position:0% +own + + + align:start position:0% +own +limits yeah we would love to have a + + align:start position:0% +limits yeah we would love to have a + + + align:start position:0% +limits yeah we would love to have a +graphic designer in the studio would' + + align:start position:0% +graphic designer in the studio would' + + + align:start position:0% +graphic designer in the studio would' +love to have a landscape architect we'd + + align:start position:0% +love to have a landscape architect we'd + + + align:start position:0% +love to have a landscape architect we'd +love to have a uh a product designer you + + align:start position:0% +love to have a uh a product designer you + + + align:start position:0% +love to have a uh a product designer you +know I mean we want to kind of mix of + + align:start position:0% +know I mean we want to kind of mix of + + + align:start position:0% +know I mean we want to kind of mix of +designs I mean I mean what Serena is + + align:start position:0% +designs I mean I mean what Serena is + + + align:start position:0% +designs I mean I mean what Serena is +saying about books is true at the same + + align:start position:0% +saying about books is true at the same + + + align:start position:0% +saying about books is true at the same +time I think books Serena and I have + + align:start position:0% +time I think books Serena and I have + + + align:start position:0% +time I think books Serena and I have +admitted to each other that we don't + + align:start position:0% +admitted to each other that we don't + + + align:start position:0% +admitted to each other that we don't +read as much as we used to and I don't + + align:start position:0% +read as much as we used to and I don't + + + align:start position:0% +read as much as we used to and I don't +think you should read that much in the + + align:start position:0% +think you should read that much in the + + + align:start position:0% +think you should read that much in the +21st century it's too fast you know I + + align:start position:0% +21st century it's too fast you know I + + + align:start position:0% +21st century it's too fast you know I +even don't see movies as much as I used + + align:start position:0% +even don't see movies as much as I used + + + align:start position:0% +even don't see movies as much as I used +to I would see movies more if they could + + align:start position:0% +to I would see movies more if they could + + + align:start position:0% +to I would see movies more if they could +be projected on buildings down a city + + align:start position:0% +be projected on buildings down a city + + + align:start position:0% +be projected on buildings down a city +street so uh you know why I think we're + + align:start position:0% +street so uh you know why I think we're + + + align:start position:0% +street so uh you know why I think we're +interested in music more why because you + + align:start position:0% +interested in music more why because you + + + align:start position:0% +interested in music more why because you +can do other things while you're listen + + align:start position:0% +can do other things while you're listen + + + align:start position:0% +can do other things while you're listen +listening to music just as an + + align:start position:0% +listening to music just as an + + + align:start position:0% +listening to music just as an +architecture you're meant to do other + + align:start position:0% +architecture you're meant to do other + + + align:start position:0% +architecture you're meant to do other +things 21st century is about multiple + + align:start position:0% +things 21st century is about multiple + + + align:start position:0% +things 21st century is about multiple +attention things that theand single + + align:start position:0% +attention things that theand single + + + align:start position:0% +attention things that theand single +Focus are maybe a little bit uh from + + align:start position:0% +Focus are maybe a little bit uh from + + + align:start position:0% +Focus are maybe a little bit uh from +another time you know how many books do + + align:start position:0% +another time you know how many books do + + + align:start position:0% +another time you know how many books do +you buy a we bu books I buy a lot I I li + + align:start position:0% +you buy a we bu books I buy a lot I I li + + + align:start position:0% +you buy a we bu books I buy a lot I I li +bu of but but just the fact that they're + + align:start position:0% +bu of but but just the fact that they're + + + align:start position:0% +bu of but but just the fact that they're +there is enough I don't have to read + + align:start position:0% +there is enough I don't have to read + + + align:start position:0% +there is enough I don't have to read +them I mean you if I you know I can Sly + + align:start position:0% +them I mean you if I you know I can Sly + + + align:start position:0% +them I mean you if I you know I can Sly +pass by skim I mean skimming is great + + align:start position:0% +pass by skim I mean skimming is great + + + align:start position:0% +pass by skim I mean skimming is great +you know reading is too much focus and + + align:start position:0% +you know reading is too much focus and + + + align:start position:0% +you know reading is too much focus and +attention uh it seems like more and more + + align:start position:0% +attention uh it seems like more and more + + + align:start position:0% +attention uh it seems like more and more +the best the books we prefer the most + + align:start position:0% +the best the books we prefer the most + + + align:start position:0% +the best the books we prefer the most +are the ones you can start reading from + + align:start position:0% +are the ones you can start reading from + + + align:start position:0% +are the ones you can start reading from +any page and and they still are + + align:start position:0% +any page and and they still are + + + align:start position:0% +any page and and they still are +significant there's still something some + + align:start position:0% +significant there's still something some + + + align:start position:0% +significant there's still something some +something in them + + align:start position:0% +something in them + + + align:start position:0% +something in them +um but um I should actually we we we are + + align:start position:0% +um but um I should actually we we we are + + + align:start position:0% +um but um I should actually we we we are +getting better on graphic design thanks + + align:start position:0% +getting better on graphic design thanks + + + align:start position:0% +getting better on graphic design thanks +to Dolly who's an architect she's not a + + align:start position:0% +to Dolly who's an architect she's not a + + + align:start position:0% +to Dolly who's an architect she's not a +graphic designer but uh uh she's she's + + align:start position:0% +graphic designer but uh uh she's she's + + + align:start position:0% +graphic designer but uh uh she's she's +helping us a lot she she had she had + + align:start position:0% +helping us a lot she she had she had + + + align:start position:0% +helping us a lot she she had she had +some more experience than than than than + + align:start position:0% +some more experience than than than than + + + align:start position:0% +some more experience than than than than +we did um for graph we we would think of + + align:start position:0% +we did um for graph we we would think of + + + align:start position:0% +we did um for graph we we would think of +Graphics a lot as as part of + + align:start position:0% +Graphics a lot as as part of + + + align:start position:0% +Graphics a lot as as part of +presentations and I think I think that's + + align:start position:0% +presentations and I think I think that's + + + align:start position:0% +presentations and I think I think that's +wrong I think there's something in it in + + align:start position:0% +wrong I think there's something in it in + + + align:start position:0% +wrong I think there's something in it in +in in there that uh we could distill you + + align:start position:0% +in in there that uh we could distill you + + + align:start position:0% +in in there that uh we could distill you +know back into space and uh we just + + align:start position:0% +know back into space and uh we just + + + align:start position:0% +know back into space and uh we just +don't don't don't don't know enough + + align:start position:0% +don't don't don't don't know enough + + + align:start position:0% +don't don't don't don't know enough +about it which doesn't doesn't really + + align:start position:0% + + + + align:start position:0% + +discourage + + align:start position:0% + + + + align:start position:0% + +yes any sacrifices you said were there + + align:start position:0% +yes any sacrifices you said were there + + + align:start position:0% +yes any sacrifices you said were there +any + + align:start position:0% +any + + + align:start position:0% +any +sacrifices + + align:start position:0% +sacrifices + + + align:start position:0% +sacrifices +uh well yeah I mean yeah in the sense + + align:start position:0% +uh well yeah I mean yeah in the sense + + + align:start position:0% +uh well yeah I mean yeah in the sense +that in art you can do anything you want + + align:start position:0% +that in art you can do anything you want + + + align:start position:0% +that in art you can do anything you want +of course you can because nobody in the + + align:start position:0% +of course you can because nobody in the + + + align:start position:0% +of course you can because nobody in the +world + + align:start position:0% +world + + + align:start position:0% +world +cares and in architecture in + + align:start position:0% +cares and in architecture in + + + align:start position:0% +cares and in architecture in +architecture you're dealing with an + + align:start position:0% +architecture you're dealing with an + + + align:start position:0% +architecture you're dealing with an +everyday world with everyday rules and + + align:start position:0% +everyday world with everyday rules and + + + align:start position:0% +everyday world with everyday rules and +conventional rules so yeah you can you + + align:start position:0% +conventional rules so yeah you can you + + + align:start position:0% +conventional rules so yeah you can you +know but you can find ways to be + + align:start position:0% +know but you can find ways to be + + + align:start position:0% +know but you can find ways to be +invented you know if you're forced to do + + align:start position:0% +invented you know if you're forced to do + + + align:start position:0% +invented you know if you're forced to do +something if you're forced to do a + + align:start position:0% +something if you're forced to do a + + + align:start position:0% +something if you're forced to do a +railing if you have a space that's over + + align:start position:0% +railing if you have a space that's over + + + align:start position:0% +railing if you have a space that's over +3 ft high but you don't want something + + align:start position:0% +3 ft high but you don't want something + + + align:start position:0% +3 ft high but you don't want something +to announce as a railing then maybe you + + align:start position:0% +to announce as a railing then maybe you + + + align:start position:0% +to announce as a railing then maybe you +can find you could be more invented than + + align:start position:0% +can find you could be more invented than + + + align:start position:0% +can find you could be more invented than +than you ever thought you could be CU + + align:start position:0% +than you ever thought you could be CU + + + align:start position:0% +than you ever thought you could be CU +you can camouflage this this railing + + align:start position:0% +you can camouflage this this railing + + + align:start position:0% +you can camouflage this this railing +sure you give you give up a lot you give + + align:start position:0% +sure you give you give up a lot you give + + + align:start position:0% +sure you give you give up a lot you give +up something to be in this world that + + align:start position:0% +up something to be in this world that + + + align:start position:0% +up something to be in this world that +other people share but I think it's kind + + align:start position:0% +other people share but I think it's kind + + + align:start position:0% +other people share but I think it's kind +of + + align:start position:0% + + + + align:start position:0% + +work maybe there's a form of opport also + + align:start position:0% +work maybe there's a form of opport also + + + align:start position:0% +work maybe there's a form of opport also +of being able to navigate between + + align:start position:0% +of being able to navigate between + + + align:start position:0% +of being able to navigate between +different worlds at very much at ease + + align:start position:0% +different worlds at very much at ease + + + align:start position:0% +different worlds at very much at ease +and I think that the fact that either + + align:start position:0% +and I think that the fact that either + + + align:start position:0% +and I think that the fact that either +was an + + align:start position:0% +was an + + + align:start position:0% +was an +artist slash is is still considered as + + align:start position:0% +artist slash is is still considered as + + + align:start position:0% +artist slash is is still considered as +an artist but many people has been + + align:start position:0% +an artist but many people has been + + + align:start position:0% +an artist but many people has been +beneficial to um his early stages in + + align:start position:0% +beneficial to um his early stages in + + + align:start position:0% +beneficial to um his early stages in +architecture now you can really say that + + align:start position:0% +architecture now you can really say that + + + align:start position:0% +architecture now you can really say that +it's enough to get help us win + + align:start position:0% +it's enough to get help us win + + + align:start position:0% +it's enough to get help us win +competitions anymore um and there still + + align:start position:0% +competitions anymore um and there still + + + align:start position:0% +competitions anymore um and there still +are a couple of commissions but I think + + align:start position:0% +are a couple of commissions but I think + + + align:start position:0% +are a couple of commissions but I think +it was probably helpful ino's early + + align:start position:0% +it was probably helpful ino's early + + + align:start position:0% +it was probably helpful ino's early +stage of public + + align:start position:0% + + + + align:start position:0% + +art yeah I mean one thing about art that + + align:start position:0% +art yeah I mean one thing about art that + + + align:start position:0% +art yeah I mean one thing about art that +now I find it almost impossible uh you + + align:start position:0% +now I find it almost impossible uh you + + + align:start position:0% +now I find it almost impossible uh you +know I I I I you know I said a statement + + align:start position:0% +know I I I I you know I said a statement + + + align:start position:0% +know I I I I you know I said a statement +that maybe was a little bit exaggerated + + align:start position:0% +that maybe was a little bit exaggerated + + + align:start position:0% +that maybe was a little bit exaggerated +that in art you can do anything anything + + align:start position:0% +that in art you can do anything anything + + + align:start position:0% +that in art you can do anything anything +you want not necessarily you can do + + align:start position:0% +you want not necessarily you can do + + + align:start position:0% +you want not necessarily you can do +anything you want as long as this is + + align:start position:0% +anything you want as long as this is + + + align:start position:0% +anything you want as long as this is +current in C art magazines at a at a + + align:start position:0% +current in C art magazines at a at a + + + align:start position:0% +current in C art magazines at a at a +certain time uh uh but so I'm not sure + + align:start position:0% +certain time uh uh but so I'm not sure + + + align:start position:0% +certain time uh uh but so I'm not sure +if you really do anything uh one thing + + align:start position:0% +if you really do anything uh one thing + + + align:start position:0% +if you really do anything uh one thing +about AR though is that you have the + + align:start position:0% +about AR though is that you have the + + + align:start position:0% +about AR though is that you have the +illusion that you can do something that + + align:start position:0% +illusion that you can do something that + + + align:start position:0% +illusion that you can do something that +you can do anything and I find that in + + align:start position:0% +you can do anything and I find that in + + + align:start position:0% +you can do anything and I find that in +position that if somebody says do + + align:start position:0% +position that if somebody says do + + + align:start position:0% +position that if somebody says do +anything you I me that's one reason why + + align:start position:0% +anything you I me that's one reason why + + + align:start position:0% +anything you I me that's one reason why +lately we've decided we can't do public + + align:start position:0% +lately we've decided we can't do public + + + align:start position:0% +lately we've decided we can't do public +our presence anymore because there isn't + + align:start position:0% +our presence anymore because there isn't + + + align:start position:0% +our presence anymore because there isn't +a program you know and you know all we + + align:start position:0% +a program you know and you know all we + + + align:start position:0% +a program you know and you know all we +can do is make places to places to sit + + align:start position:0% +can do is make places to places to sit + + + align:start position:0% +can do is make places to places to sit +down and you know I think we made some + + align:start position:0% +down and you know I think we made some + + + align:start position:0% +down and you know I think we made some +nice places but then we think couldn't + + align:start position:0% +nice places but then we think couldn't + + + align:start position:0% +nice places but then we think couldn't +if few both parents have done have done + + align:start position:0% +if few both parents have done have done + + + align:start position:0% +if few both parents have done have done +have done the same uh I a program gives + + align:start position:0% +have done the same uh I a program gives + + + align:start position:0% +have done the same uh I a program gives +you something to have a dialogue with + + align:start position:0% +you something to have a dialogue with + + + align:start position:0% +you something to have a dialogue with +have a discussion with have an argument + + align:start position:0% +have a discussion with have an argument + + + align:start position:0% +have a discussion with have an argument +with do anything you want uh is a + + align:start position:0% +with do anything you want uh is a + + + align:start position:0% +with do anything you want uh is a +difficult situation for you I mean I + + align:start position:0% +difficult situation for you I mean I + + + align:start position:0% +difficult situation for you I mean I +think there are some people in the + + align:start position:0% +think there are some people in the + + + align:start position:0% +think there are some people in the +studio and I think V also that better + + align:start position:0% +studio and I think V also that better + + + align:start position:0% +studio and I think V also that better +good art than bad Folly than in know + + align:start position:0% +good art than bad Folly than in know + + + align:start position:0% +good art than bad Folly than in know +public Arts situation and that's the big + + align:start position:0% +public Arts situation and that's the big + + + align:start position:0% +public Arts situation and that's the big +danger of public art is that sometimes + + align:start position:0% +danger of public art is that sometimes + + + align:start position:0% +danger of public art is that sometimes +we end up producing folies um because of + + align:start position:0% +we end up producing folies um because of + + + align:start position:0% +we end up producing folies um because of +the + + align:start position:0% +the + + + align:start position:0% +the +restrictions of a of a situation the + + align:start position:0% +restrictions of a of a situation the + + + align:start position:0% +restrictions of a of a situation the +SCOPE LA yeah or or the lack of + + align:start position:0% +SCOPE LA yeah or or the lack of + + + align:start position:0% +SCOPE LA yeah or or the lack of +restrictions I mean I'm talking about + + align:start position:0% +restrictions I mean I'm talking about + + + align:start position:0% +restrictions I mean I'm talking about +restrictions because once or twice you + + align:start position:0% +restrictions because once or twice you + + + align:start position:0% +restrictions because once or twice you +had a pause on you weren't really able + + align:start position:0% +had a pause on you weren't really able + + + align:start position:0% +had a pause on you weren't really able +to build architectural so we were + + align:start position:0% +to build architectural so we were + + + align:start position:0% +to build architectural so we were +basically being constrained to build + + align:start position:0% +basically being constrained to build + + + align:start position:0% +basically being constrained to build +something that was sculptural that sort + + align:start position:0% +something that was sculptural that sort + + + align:start position:0% +something that was sculptural that sort +of + + align:start position:0% + + + + align:start position:0% + +CH almost a demonstration of what if we + + align:start position:0% +CH almost a demonstration of what if we + + + align:start position:0% +CH almost a demonstration of what if we +were really + + align:start position:0% + + + + align:start position:0% + +free it be this what it looks like and + + align:start position:0% +free it be this what it looks like and + + + align:start position:0% +free it be this what it looks like and +um again I think we're more interested + + align:start position:0% +um again I think we're more interested + + + align:start position:0% +um again I think we're more interested +in in in doing doing something that is + + align:start position:0% +in in in doing doing something that is + + + align:start position:0% +in in in doing doing something that is +is is inherently in by by by by itself + + align:start position:0% +is is inherently in by by by by itself + + + align:start position:0% +is is inherently in by by by by itself +uh uh really really existing within + + align:start position:0% +uh uh really really existing within + + + align:start position:0% +uh uh really really existing within +public space not just sort of uh making + + align:start position:0% +public space not just sort of uh making + + + align:start position:0% +public space not just sort of uh making +the Contex of public space but being + + align:start position:0% +the Contex of public space but being + + + align:start position:0% +the Contex of public space but being +being part of it being being being + + align:start position:0% +being part of it being being being + + + align:start position:0% +being part of it being being being +within it at the same time I think I I I + + align:start position:0% +within it at the same time I think I I I + + + align:start position:0% +within it at the same time I think I I I +I sometimes think that if we were give + + align:start position:0% +I sometimes think that if we were give + + + align:start position:0% +I sometimes think that if we were give +programs and follow maybe we would spend + + align:start position:0% +programs and follow maybe we would spend + + + align:start position:0% +programs and follow maybe we would spend +more time uh designing a car or you know + + align:start position:0% +more time uh designing a car or you know + + + align:start position:0% +more time uh designing a car or you know +designing clothes uh designing something + + align:start position:0% +designing clothes uh designing something + + + align:start position:0% +designing clothes uh designing something +and and I means that these are the more + + align:start position:0% +and and I means that these are the more + + + align:start position:0% +and and I means that these are the more +the more important spaces for this + + align:start position:0% +the more important spaces for this + + + align:start position:0% +the more important spaces for this +century and the coming Century this is a + + align:start position:0% +century and the coming Century this is a + + + align:start position:0% +century and the coming Century this is a +time of capsules public space is not a + + align:start position:0% +time of capsules public space is not a + + + align:start position:0% +time of capsules public space is not a +plaza the only reason a plaza exists is + + align:start position:0% +plaza the only reason a plaza exists is + + + align:start position:0% +plaza the only reason a plaza exists is +that a large number of people in the + + align:start position:0% +that a large number of people in the + + + align:start position:0% +that a large number of people in the +city are put together in one place so + + align:start position:0% +city are put together in one place so + + + align:start position:0% +city are put together in one place so +the city can the city can exercise some + + align:start position:0% +the city can the city can exercise some + + + align:start position:0% +the city can the city can exercise some +surveillance system on them you know + + align:start position:0% +surveillance system on them you know + + + align:start position:0% +surveillance system on them you know +public space exists in alleys and back + + align:start position:0% +public space exists in alleys and back + + + align:start position:0% +public space exists in alleys and back +rooms it exists uh it exists in in + + align:start position:0% +rooms it exists uh it exists in in + + + align:start position:0% +rooms it exists uh it exists in in +movement and uh you know I every body's + + align:start position:0% +movement and uh you know I every body's + + + align:start position:0% +movement and uh you know I every body's +notion of public space has changed uh + + align:start position:0% +notion of public space has changed uh + + + align:start position:0% +notion of public space has changed uh +first of all you know by the by the by + + align:start position:0% +first of all you know by the by the by + + + align:start position:0% +first of all you know by the by the by +the computer I know when I first started + + align:start position:0% +the computer I know when I first started + + + align:start position:0% +the computer I know when I first started +using computer I thought this is an + + align:start position:0% +using computer I thought this is an + + + align:start position:0% +using computer I thought this is an +incredibly Progressive space it's like + + align:start position:0% +incredibly Progressive space it's like + + + align:start position:0% +incredibly Progressive space it's like +reading but obviously it's not you know + + align:start position:0% +reading but obviously it's not you know + + + align:start position:0% +reading but obviously it's not you know +but it's a very different notion of + + align:start position:0% +but it's a very different notion of + + + align:start position:0% +but it's a very different notion of +public than than we had before so a mix + + align:start position:0% +public than than we had before so a mix + + + align:start position:0% +public than than we had before so a mix +of that a mix of that at 911 where + + align:start position:0% +of that a mix of that at 911 where + + + align:start position:0% +of that a mix of that at 911 where +everybody feels you know you have to + + align:start position:0% +everybody feels you know you have to + + + align:start position:0% +everybody feels you know you have to +have a protection is it leads I think to + + align:start position:0% +have a protection is it leads I think to + + + align:start position:0% +have a protection is it leads I think to +the notion of capsule maybe public space + + align:start position:0% +the notion of capsule maybe public space + + + align:start position:0% +the notion of capsule maybe public space +in the future consists of everybody + + align:start position:0% +in the future consists of everybody + + + align:start position:0% +in the future consists of everybody +wears everybody is inside some capsule + + align:start position:0% +wears everybody is inside some capsule + + + align:start position:0% +wears everybody is inside some capsule +every once in a while these capsules + + align:start position:0% +every once in a while these capsules + + + align:start position:0% +every once in a while these capsules +bump and join for a while but then they + + align:start position:0% +bump and join for a while but then they + + + align:start position:0% +bump and join for a while but then they +separate become capsules again and then + + align:start position:0% +separate become capsules again and then + + + align:start position:0% +separate become capsules again and then +they reach join with other capsules it's + + align:start position:0% +they reach join with other capsules it's + + + align:start position:0% +they reach join with other capsules it's +a very different notion of public I + + align:start position:0% +a very different notion of public I + + + align:start position:0% +a very different notion of public I +think we ever + + align:start position:0% + + + + align:start position:0% + +have thank you thank you thank + + align:start position:0% +have thank you thank you thank + + + align:start position:0% +have thank you thank you thank +you \ No newline at end of file diff --git a/6QpLTfU9WPM.txt b/6QpLTfU9WPM.txt new file mode 100644 index 0000000000000000000000000000000000000000..e44e51c9994e6603b22d3ccf6a44f29a0c157ae7 --- /dev/null +++ b/6QpLTfU9WPM.txt @@ -0,0 +1,1371 @@ +align:start position:0% + +edgerton's Boomer illustrates the + + align:start position:0% +edgerton's Boomer illustrates the + + + align:start position:0% +edgerton's Boomer illustrates the +induction of a current in a conductor + + align:start position:0% +induction of a current in a conductor + + + align:start position:0% +induction of a current in a conductor +subjected to a Time varying magnetic + + align:start position:0% +subjected to a Time varying magnetic + + + align:start position:0% +subjected to a Time varying magnetic +field and the associated magnetic + + align:start position:0% +field and the associated magnetic + + + align:start position:0% +field and the associated magnetic +forces it illustrates the interplay + + align:start position:0% +forces it illustrates the interplay + + + align:start position:0% +forces it illustrates the interplay +between the laws of feraday ampere and + + align:start position:0% +between the laws of feraday ampere and + + + align:start position:0% +between the laws of feraday ampere and +ohm that determines the distribution + + align:start position:0% +ohm that determines the distribution + + + align:start position:0% +ohm that determines the distribution +duration and magnitude of currents in + + align:start position:0% +duration and magnitude of currents in + + + align:start position:0% +duration and magnitude of currents in +conductors under Magneto quasy static + + align:start position:0% + + + + align:start position:0% + +conditions this is the coil + + align:start position:0% +conditions this is the coil + + + align:start position:0% +conditions this is the coil +the winding wire circulates like + + align:start position:0% +the winding wire circulates like + + + align:start position:0% +the winding wire circulates like +so and is connected to the capacitors in + + align:start position:0% +so and is connected to the capacitors in + + + align:start position:0% +so and is connected to the capacitors in +this cabinet by these + + align:start position:0% + + + + align:start position:0% + +leads when the high voltage power supply + + align:start position:0% +leads when the high voltage power supply + + + align:start position:0% +leads when the high voltage power supply +in the cabinet is turned + + align:start position:0% + + + + align:start position:0% + +on the capacitor is charged to 4 + + align:start position:0% +on the capacitor is charged to 4 + + + align:start position:0% +on the capacitor is charged to 4 +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +K the switch then connects the capacitor + + align:start position:0% +K the switch then connects the capacitor + + + align:start position:0% +K the switch then connects the capacitor +to the coil it's closed when this button + + align:start position:0% +to the coil it's closed when this button + + + align:start position:0% +to the coil it's closed when this button +is + + align:start position:0% +is + + + align:start position:0% +is +[Music] + + align:start position:0% + + + + align:start position:0% + +pushed the switch consists of a spark + + align:start position:0% +pushed the switch consists of a spark + + + align:start position:0% +pushed the switch consists of a spark +gap which we just heard we can see it if + + align:start position:0% +gap which we just heard we can see it if + + + align:start position:0% +gap which we just heard we can see it if +we open this + + align:start position:0% + + + + align:start position:0% + +panel + + align:start position:0% +panel + + + align:start position:0% +panel +the switch is closed by a spark across + + align:start position:0% +the switch is closed by a spark across + + + align:start position:0% +the switch is closed by a spark across +this + + align:start position:0% +this + + + align:start position:0% +this +Gap that spark is activated by applying + + align:start position:0% +Gap that spark is activated by applying + + + align:start position:0% +Gap that spark is activated by applying +a voltage to this electrode to make a + + align:start position:0% +a voltage to this electrode to make a + + + align:start position:0% +a voltage to this electrode to make a +smaller electrical breakdown in the + + align:start position:0% + + + + align:start position:0% + +Gap just once we'll bypass the safety + + align:start position:0% +Gap just once we'll bypass the safety + + + align:start position:0% +Gap just once we'll bypass the safety +interlock that ordinarily disconnects + + align:start position:0% +interlock that ordinarily disconnects + + + align:start position:0% +interlock that ordinarily disconnects +the circuit when the panel is + + align:start position:0% + + + + align:start position:0% + +opened then when we push the button we + + align:start position:0% +opened then when we push the button we + + + align:start position:0% +opened then when we push the button we +can not only hear the spark discharge + + align:start position:0% +can not only hear the spark discharge + + + align:start position:0% +can not only hear the spark discharge +that closes the switch but see the + + align:start position:0% +that closes the switch but see the + + + align:start position:0% +that closes the switch but see the +associated flash as + + align:start position:0% + + + + align:start position:0% + +well maybe we can do it once + + align:start position:0% + + + + align:start position:0% + +more given the initial capacitor voltage + + align:start position:0% +more given the initial capacitor voltage + + + align:start position:0% +more given the initial capacitor voltage +of 4 Kilts and that the coil has 50 + + align:start position:0% +of 4 Kilts and that the coil has 50 + + + align:start position:0% +of 4 Kilts and that the coil has 50 +turns we can use basic principles to + + align:start position:0% +turns we can use basic principles to + + + align:start position:0% +turns we can use basic principles to +estimate the winding current and hence + + align:start position:0% +estimate the winding current and hence + + + align:start position:0% +estimate the winding current and hence +the magnetic field intensity produced by + + align:start position:0% +the magnetic field intensity produced by + + + align:start position:0% +the magnetic field intensity produced by +the + + align:start position:0% +the + + + align:start position:0% +the +coil first we use ampere's integral law + + align:start position:0% +coil first we use ampere's integral law + + + align:start position:0% +coil first we use ampere's integral law +to relate the current to the + + align:start position:0% +to relate the current to the + + + align:start position:0% +to relate the current to the +field the line Contour encloses the + + align:start position:0% +field the line Contour encloses the + + + align:start position:0% +field the line Contour encloses the +current in the + + align:start position:0% + + + + align:start position:0% + +coil before we go on let's see how well + + align:start position:0% +coil before we go on let's see how well + + + align:start position:0% +coil before we go on let's see how well +we've approximated the the current and + + align:start position:0% +we've approximated the the current and + + + align:start position:0% +we've approximated the the current and +field this current probe will link one + + align:start position:0% +field this current probe will link one + + + align:start position:0% +field this current probe will link one +of the wires connected to the + + align:start position:0% + + + + align:start position:0% + +coil we display the coil current on the + + align:start position:0% +coil we display the coil current on the + + + align:start position:0% +coil we display the coil current on the +lower scope + + align:start position:0% +lower scope + + + align:start position:0% +lower scope +trace the voltage induced at the + + align:start position:0% +trace the voltage induced at the + + + align:start position:0% +trace the voltage induced at the +terminals of this + + align:start position:0% +terminals of this + + + align:start position:0% +terminals of this +coil by the time varing magnetic flux + + align:start position:0% +coil by the time varing magnetic flux + + + align:start position:0% +coil by the time varing magnetic flux +density will be used to deduce + + align:start position:0% +density will be used to deduce + + + align:start position:0% +density will be used to deduce +B this voltage will be displayed as the + + align:start position:0% +B this voltage will be displayed as the + + + align:start position:0% +B this voltage will be displayed as the +upper scope + + align:start position:0% +upper scope + + + align:start position:0% +upper scope +Trace + + align:start position:0% + + + + align:start position:0% + +here are the responses to the discharge + + align:start position:0% +here are the responses to the discharge + + + align:start position:0% +here are the responses to the discharge +of the + + align:start position:0% + + + + align:start position:0% + +capacitor the time axis is 2/10 of a + + align:start position:0% +capacitor the time axis is 2/10 of a + + + align:start position:0% +capacitor the time axis is 2/10 of a +millisecond per + + align:start position:0% +millisecond per + + + align:start position:0% +millisecond per +division so the period of the + + align:start position:0% +division so the period of the + + + align:start position:0% +division so the period of the +oscillation is about 1/3 of a + + align:start position:0% +oscillation is about 1/3 of a + + + align:start position:0% +oscillation is about 1/3 of a +millisecond the illation frequency is + + align:start position:0% +millisecond the illation frequency is + + + align:start position:0% +millisecond the illation frequency is +roughly the predicted 4 + + align:start position:0% +roughly the predicted 4 + + + align:start position:0% +roughly the predicted 4 +khz the duration of the lower Trace + + align:start position:0% +khz the duration of the lower Trace + + + align:start position:0% +khz the duration of the lower Trace +current and hence of the field is on the + + align:start position:0% +current and hence of the field is on the + + + align:start position:0% +current and hence of the field is on the +order of 1 + + align:start position:0% + + + + align:start position:0% + +millisecond the peak in the current on + + align:start position:0% +millisecond the peak in the current on + + + align:start position:0% +millisecond the peak in the current on +the lower Trace is about one + + align:start position:0% +the lower Trace is about one + + + align:start position:0% +the lower Trace is about one +division there are 1,000 amps per + + align:start position:0% +division there are 1,000 amps per + + + align:start position:0% +division there are 1,000 amps per +division so the peak current is about + + align:start position:0% +division so the peak current is about + + + align:start position:0% +division so the peak current is about +1,000 + + align:start position:0% +1,000 + + + align:start position:0% +1,000 +amps this is in the range of the + + align:start position:0% +amps this is in the range of the + + + align:start position:0% +amps this is in the range of the +estimated value of, 1600 amps remember + + align:start position:0% +estimated value of, 1600 amps remember + + + align:start position:0% +estimated value of, 1600 amps remember +we've not accounted for losses in the + + align:start position:0% +we've not accounted for losses in the + + + align:start position:0% +we've not accounted for losses in the +spark gap in the + + align:start position:0% +spark gap in the + + + align:start position:0% +spark gap in the +coil + + align:start position:0% + + + + align:start position:0% + +the disc could represent a + + align:start position:0% +the disc could represent a + + + align:start position:0% +the disc could represent a +hand in that case the experiment can + + align:start position:0% +hand in that case the experiment can + + + align:start position:0% +hand in that case the experiment can +literally give a feel for the + + align:start position:0% +literally give a feel for the + + + align:start position:0% +literally give a feel for the +consequence of subjecting a conductor to + + align:start position:0% +consequence of subjecting a conductor to + + + align:start position:0% +consequence of subjecting a conductor to +a Time varying magnetic + + align:start position:0% +a Time varying magnetic + + + align:start position:0% +a Time varying magnetic +field if the dis represents a hand what + + align:start position:0% +field if the dis represents a hand what + + + align:start position:0% +field if the dis represents a hand what +current density would be + + align:start position:0% + + + + align:start position:0% + +felt magnetic field created by the coil + + align:start position:0% +felt magnetic field created by the coil + + + align:start position:0% +felt magnetic field created by the coil +is non-uniform + + align:start position:0% +is non-uniform + + + align:start position:0% +is non-uniform +far away that of a + + align:start position:0% +far away that of a + + + align:start position:0% +far away that of a +dipole so we can discern what we're + + align:start position:0% +dipole so we can discern what we're + + + align:start position:0% +dipole so we can discern what we're +getting into by feeling the induced + + align:start position:0% +getting into by feeling the induced + + + align:start position:0% +getting into by feeling the induced +current in + + align:start position:0% +current in + + + align:start position:0% +current in +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +stages the sensation is of a short + + align:start position:0% +stages the sensation is of a short + + + align:start position:0% +stages the sensation is of a short +duration + + align:start position:0% +duration + + + align:start position:0% +duration +twinge much as would be expected for a + + align:start position:0% +twinge much as would be expected for a + + + align:start position:0% +twinge much as would be expected for a +pulse that lasts 1 + + align:start position:0% +pulse that lasts 1 + + + align:start position:0% +pulse that lasts 1 +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +millisecond + + align:start position:0% +millisecond + + + align:start position:0% +millisecond +uh I've been given to understand that + + align:start position:0% +uh I've been given to understand that + + + align:start position:0% +uh I've been given to understand that +Professor Zan is not going to try it + + align:start position:0% +Professor Zan is not going to try it + + + align:start position:0% +Professor Zan is not going to try it +with his hand lower than + + align:start position:0% + + + + align:start position:0% + +this so that you can see evidence of the + + align:start position:0% +this so that you can see evidence of the + + + align:start position:0% +this so that you can see evidence of the +field that you can't feel + + align:start position:0% +field that you can't feel + + + align:start position:0% +field that you can't feel +firsthand let's replace his hand by this + + align:start position:0% +firsthand let's replace his hand by this + + + align:start position:0% +firsthand let's replace his hand by this +wire + + align:start position:0% + + + + align:start position:0% + +Loop the wire is open at this + + align:start position:0% +Loop the wire is open at this + + + align:start position:0% +Loop the wire is open at this +point with the ends barely + + align:start position:0% + + + + align:start position:0% + +touching so the field + + align:start position:0% +touching so the field + + + align:start position:0% +touching so the field +induced around the + + align:start position:0% + + + + align:start position:0% + +Contour is concentrated at the + + align:start position:0% +Contour is concentrated at the + + + align:start position:0% +Contour is concentrated at the +Gap we go to a higher f- stop to protect + + align:start position:0% +Gap we go to a higher f- stop to protect + + + align:start position:0% +Gap we go to a higher f- stop to protect +the + + align:start position:0% + + + + align:start position:0% + +camera the integral of the electric + + align:start position:0% +camera the integral of the electric + + + align:start position:0% +camera the integral of the electric +field intensity is concentrated in a gap + + align:start position:0% +field intensity is concentrated in a gap + + + align:start position:0% +field intensity is concentrated in a gap +region that is initially relatively + + align:start position:0% +region that is initially relatively + + + align:start position:0% +region that is initially relatively +insulating so the electric field + + align:start position:0% +insulating so the electric field + + + align:start position:0% +insulating so the electric field +intensity between the almost touching + + align:start position:0% +intensity between the almost touching + + + align:start position:0% +intensity between the almost touching +wires is enough to produce a + + align:start position:0% + + + + align:start position:0% + +spark the conductivity of this aluminum + + align:start position:0% +spark the conductivity of this aluminum + + + align:start position:0% +spark the conductivity of this aluminum +disc is more than 10 million times + + align:start position:0% +disc is more than 10 million times + + + align:start position:0% +disc is more than 10 million times +larger than for human flesh and there's + + align:start position:0% +larger than for human flesh and there's + + + align:start position:0% +larger than for human flesh and there's +no Gap to limit the induced + + align:start position:0% + + + + align:start position:0% + +current + + align:start position:0% +current + + + align:start position:0% +current +the force can be used to shape + + align:start position:0% + + + + align:start position:0% + +Metals here the upward force is evident + + align:start position:0% +Metals here the upward force is evident + + + align:start position:0% +Metals here the upward force is evident +in the shaping of the outer edge of a + + align:start position:0% +in the shaping of the outer edge of a + + + align:start position:0% +in the shaping of the outer edge of a +foil + + align:start position:0% + + + + align:start position:0% + +disc + + align:start position:0% + + + + align:start position:0% + +for this experiment we use three times + + align:start position:0% +for this experiment we use three times + + + align:start position:0% +for this experiment we use three times +as much + + align:start position:0% + + + + align:start position:0% + +capacitance if the force can be used to + + align:start position:0% +capacitance if the force can be used to + + + align:start position:0% +capacitance if the force can be used to +shape the metal it can also be used to + + align:start position:0% +shape the metal it can also be used to + + + align:start position:0% +shape the metal it can also be used to +launch the + + align:start position:0% + + + + align:start position:0% + +disc I'm melter and as you know that's + + align:start position:0% +disc I'm melter and as you know that's + + + align:start position:0% +disc I'm melter and as you know that's +Zan we've brought along an illuminary + + align:start position:0% +Zan we've brought along an illuminary + + + align:start position:0% +Zan we've brought along an illuminary +here to push that button finally this is + + align:start position:0% +here to push that button finally this is + + + align:start position:0% +here to push that button finally this is +Professor Doc ederton and uh it's his + + align:start position:0% +Professor Doc ederton and uh it's his + + + align:start position:0% +Professor Doc ederton and uh it's his +machine what we've done of course is to + + align:start position:0% +machine what we've done of course is to + + + align:start position:0% +machine what we've done of course is to +show you this disc and now if uh doc you + + align:start position:0% +show you this disc and now if uh doc you + + + align:start position:0% +show you this disc and now if uh doc you +turn on your machine ready here we go + + align:start position:0% +turn on your machine ready here we go + + + align:start position:0% +turn on your machine ready here we go +I'm going to step out of this I'll turn + + align:start position:0% +I'm going to step out of this I'll turn + + + align:start position:0% +I'm going to step out of this I'll turn +on the main power let it come up to + + align:start position:0% + + + + align:start position:0% + +charge want to do it again do you have a + + align:start position:0% +charge want to do it again do you have a + + + align:start position:0% +charge want to do it again do you have a +favorite one there well the everyone's a + + align:start position:0% +favorite one there well the everyone's a + + + align:start position:0% +favorite one there well the everyone's a +little different let's try this one what + + align:start position:0% +little different let's try this one what + + + align:start position:0% +little different let's try this one what +do you + + align:start position:0% +do you + + + align:start position:0% +do you +say + + align:start position:0% + + + + align:start position:0% + +power little different ring to it little + + align:start position:0% +power little different ring to it little + + + align:start position:0% +power little different ring to it little +different ring now as I understand it + + align:start position:0% +different ring now as I understand it + + + align:start position:0% +different ring now as I understand it +this thing's got uh more capacitors in + + align:start position:0% +this thing's got uh more capacitors in + + + align:start position:0% +this thing's got uh more capacitors in +it maybe we get Z to uh put a little + + align:start position:0% +it maybe we get Z to uh put a little + + + align:start position:0% +it maybe we get Z to uh put a little +more in there you like to have it go + + align:start position:0% +more in there you like to have it go + + + align:start position:0% +more in there you like to have it go +little one of the reasons I brought this + + align:start position:0% +little one of the reasons I brought this + + + align:start position:0% +little one of the reasons I brought this +man along is that uh in fact he mainly + + align:start position:0% +man along is that uh in fact he mainly + + + align:start position:0% +man along is that uh in fact he mainly +paid for this building so you see we + + align:start position:0% +paid for this building so you see we + + + align:start position:0% +paid for this building so you see we +don't care too much if we hurt that + + align:start position:0% + + + + align:start position:0% + +ceiling it' be nice to have an imprint + + align:start position:0% +ceiling it' be nice to have an imprint + + + align:start position:0% +ceiling it' be nice to have an imprint +up there wouldn't it right with you here + + align:start position:0% +up there wouldn't it right with you here + + + align:start position:0% +up there wouldn't it right with you here +I can say that okay let's see what + + align:start position:0% +I can say that okay let's see what + + + align:start position:0% +I can say that okay let's see what +happen this time well you got three + + align:start position:0% +happen this time well you got three + + + align:start position:0% +happen this time well you got three +capacitors on instead of one you should + + align:start position:0% +capacitors on instead of one you should + + + align:start position:0% +capacitors on instead of one you should +go a little + + align:start position:0% +go a little + + + align:start position:0% +go a little +higher one two 3 + + align:start position:0% +higher one two 3 + + + align:start position:0% +higher one two 3 +go missed me want to try our favorite + + align:start position:0% +go missed me want to try our favorite + + + align:start position:0% +go missed me want to try our favorite +yeah let's try that one + + align:start position:0% + + + + align:start position:0% + +hey knocked a hole in the ceiling I can + + align:start position:0% +hey knocked a hole in the ceiling I can + + + align:start position:0% +hey knocked a hole in the ceiling I can +see you enjoy that huh all right thank + + align:start position:0% +see you enjoy that huh all right thank + + + align:start position:0% +see you enjoy that huh all right thank +you very much sir \ No newline at end of file diff --git a/6dJnvu3-LeU.txt b/6dJnvu3-LeU.txt new file mode 100644 index 0000000000000000000000000000000000000000..7178430072c1940a4cdf819207dedb76abf7583a --- /dev/null +++ b/6dJnvu3-LeU.txt @@ -0,0 +1,9251 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +all right well good morning everyone I + + align:start position:0% +all right well good morning everyone I + + + align:start position:0% +all right well good morning everyone I +hope you had a some rest over the long + + align:start position:0% +hope you had a some rest over the long + + + align:start position:0% +hope you had a some rest over the long +weekend and looking forward to getting + + align:start position:0% +weekend and looking forward to getting + + + align:start position:0% +weekend and looking forward to getting +back talking about quantum so last time + + align:start position:0% +back talking about quantum so last time + + + align:start position:0% +back talking about quantum so last time +which was a whole week ago a long time + + align:start position:0% +which was a whole week ago a long time + + + align:start position:0% +which was a whole week ago a long time +ago we started talking about electronic + + align:start position:0% +ago we started talking about electronic + + + align:start position:0% +ago we started talking about electronic +structure we talked about the + + align:start position:0% +structure we talked about the + + + align:start position:0% +structure we talked about the +born-oppenheimer approximation and how + + align:start position:0% +born-oppenheimer approximation and how + + + align:start position:0% +born-oppenheimer approximation and how +that gives us an electronic Schrodinger + + align:start position:0% +that gives us an electronic Schrodinger + + + align:start position:0% +that gives us an electronic Schrodinger +equation how we look for what we're + + align:start position:0% +equation how we look for what we're + + + align:start position:0% +equation how we look for what we're +looking for are the eigenvalues and + + align:start position:0% +looking for are the eigenvalues and + + + align:start position:0% +looking for are the eigenvalues and +eigenvectors are that Schrodinger + + align:start position:0% +eigenvectors are that Schrodinger + + + align:start position:0% +eigenvectors are that Schrodinger +equation how we can get lots of + + align:start position:0% +equation how we can get lots of + + + align:start position:0% +equation how we can get lots of +information interesting information out + + align:start position:0% +information interesting information out + + + align:start position:0% +information interesting information out +of that + + align:start position:0% +of that + + + align:start position:0% +of that +and then we broke it down so that we saw + + align:start position:0% +and then we broke it down so that we saw + + + align:start position:0% +and then we broke it down so that we saw +that there were going to be two main + + align:start position:0% +that there were going to be two main + + + align:start position:0% +that there were going to be two main +knobs do we were gonna have to turn we + + align:start position:0% +knobs do we were gonna have to turn we + + + align:start position:0% +knobs do we were gonna have to turn we +were making approximations here we were + + align:start position:0% +were making approximations here we were + + + align:start position:0% +were making approximations here we were +gonna have to look at our atomic orbital + + align:start position:0% +gonna have to look at our atomic orbital + + + align:start position:0% +gonna have to look at our atomic orbital +basis sets and how we compute the energy + + align:start position:0% +basis sets and how we compute the energy + + + align:start position:0% +basis sets and how we compute the energy +and we spent the last half of class last + + align:start position:0% +and we spent the last half of class last + + + align:start position:0% +and we spent the last half of class last +time talking about choosing basis sets + + align:start position:0% +time talking about choosing basis sets + + + align:start position:0% +time talking about choosing basis sets +came up with Nate with these some + + align:start position:0% +came up with Nate with these some + + + align:start position:0% +came up with Nate with these some +understanding of these strange names + + align:start position:0% +understanding of these strange names + + + align:start position:0% +understanding of these strange names +that are written at the bottom here and + + align:start position:0% +that are written at the bottom here and + + + align:start position:0% +that are written at the bottom here and +then today we're gonna talk about some + + align:start position:0% +then today we're gonna talk about some + + + align:start position:0% +then today we're gonna talk about some +of these ways of computing the energy + + align:start position:0% +of these ways of computing the energy + + + align:start position:0% +of these ways of computing the energy +and then we're I'm gonna flip over and + + align:start position:0% +and then we're I'm gonna flip over and + + + align:start position:0% +and then we're I'm gonna flip over and +we're gonna talk about computational + + align:start position:0% +we're gonna talk about computational + + + align:start position:0% +we're gonna talk about computational +chemistry tools and how we sort of + + align:start position:0% +chemistry tools and how we sort of + + + align:start position:0% +chemistry tools and how we sort of +assemble that into doing a calculation + + align:start position:0% +assemble that into doing a calculation + + + align:start position:0% +assemble that into doing a calculation +but again the idea with basis sets was + + align:start position:0% +but again the idea with basis sets was + + + align:start position:0% +but again the idea with basis sets was +that we were sort of questing after this + + align:start position:0% +that we were sort of questing after this + + + align:start position:0% +that we were sort of questing after this +mythical complete basis set limit where + + align:start position:0% +mythical complete basis set limit where + + + align:start position:0% +mythical complete basis set limit where +the basis set was so big that it was + + align:start position:0% +the basis set was so big that it was + + + align:start position:0% +the basis set was so big that it was +infinitely big that you know that you + + align:start position:0% +infinitely big that you know that you + + + align:start position:0% +infinitely big that you know that you +were making a bigger didn't change your + + align:start position:0% +were making a bigger didn't change your + + + align:start position:0% +were making a bigger didn't change your +answer at all and we never actually get + + align:start position:0% +answer at all and we never actually get + + + align:start position:0% +answer at all and we never actually get +there but if we get close enough we + + align:start position:0% +there but if we get close enough we + + + align:start position:0% +there but if we get close enough we +decide that's good all right so now + + align:start position:0% +decide that's good all right so now + + + align:start position:0% +decide that's good all right so now +we're going to talk today about + + align:start position:0% +we're going to talk today about + + + align:start position:0% +we're going to talk today about +computing the energy and thankfully most + + align:start position:0% +computing the energy and thankfully most + + + align:start position:0% +computing the energy and thankfully most +of the methods for computing the energy + + align:start position:0% +of the methods for computing the energy + + + align:start position:0% +of the methods for computing the energy +start from something that I believe you + + align:start position:0% +start from something that I believe you + + + align:start position:0% +start from something that I believe you +are familiar with already from freshest + + align:start position:0% +are familiar with already from freshest + + + align:start position:0% +are familiar with already from freshest +one you guys talked about the + + align:start position:0% +one you guys talked about the + + + align:start position:0% +one you guys talked about the +hartree-fock approximation yeah yeah + + align:start position:0% +hartree-fock approximation yeah yeah + + + align:start position:0% +hartree-fock approximation yeah yeah +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so or maybe we talked about did we talk + + align:start position:0% +so or maybe we talked about did we talk + + + align:start position:0% +so or maybe we talked about did we talk +about singled do we talk about + + align:start position:0% +about singled do we talk about + + + align:start position:0% +about singled do we talk about +determinants yes alright so there we go + + align:start position:0% +determinants yes alright so there we go + + + align:start position:0% +determinants yes alright so there we go +alright so then we talked about a + + align:start position:0% +alright so then we talked about a + + + align:start position:0% +alright so then we talked about a +determinant the idea of a determinant is + + align:start position:0% +determinant the idea of a determinant is + + + align:start position:0% +determinant the idea of a determinant is +you have a set of orbitals they're + + align:start position:0% +you have a set of orbitals they're + + + align:start position:0% +you have a set of orbitals they're +independent and then you compute the + + align:start position:0% +independent and then you compute the + + + align:start position:0% +independent and then you compute the +average energy and so in one form or + + align:start position:0% +average energy and so in one form or + + + align:start position:0% +average energy and so in one form or +another I would write the energy of a + + align:start position:0% +another I would write the energy of a + + + align:start position:0% +another I would write the energy of a +determinant something like this I would + + align:start position:0% +determinant something like this I would + + + align:start position:0% +determinant something like this I would +say that there's a piece here which is + + align:start position:0% +say that there's a piece here which is + + + align:start position:0% +say that there's a piece here which is +the energy of each electron by itself so + + align:start position:0% +the energy of each electron by itself so + + + align:start position:0% +the energy of each electron by itself so +these are one electron energies so for + + align:start position:0% +these are one electron energies so for + + + align:start position:0% +these are one electron energies so for +every electron in my system if I have n + + align:start position:0% +every electron in my system if I have n + + + align:start position:0% +every electron in my system if I have n +electrons I add up the energies of each + + align:start position:0% +electrons I add up the energies of each + + + align:start position:0% +electrons I add up the energies of each +of those electrons but then because my + + align:start position:0% +of those electrons but then because my + + + align:start position:0% +of those electrons but then because my +Hamiltonian has electron-electron + + align:start position:0% +Hamiltonian has electron-electron + + + align:start position:0% +Hamiltonian has electron-electron +repulsion terms I end up with some + + align:start position:0% +repulsion terms I end up with some + + + align:start position:0% +repulsion terms I end up with some +additional contributions that don't + + align:start position:0% +additional contributions that don't + + + align:start position:0% +additional contributions that don't +can't be assigned to just one electron + + align:start position:0% +can't be assigned to just one electron + + + align:start position:0% +can't be assigned to just one electron +or another electron and those terms are + + align:start position:0% +or another electron and those terms are + + + align:start position:0% +or another electron and those terms are +here in this sum they're pairwise so for + + align:start position:0% +here in this sum they're pairwise so for + + + align:start position:0% +here in this sum they're pairwise so for +every mu and nu summing up something + + align:start position:0% +every mu and nu summing up something + + + align:start position:0% +every mu and nu summing up something +over independent pairs I have a Coulomb + + align:start position:0% +over independent pairs I have a Coulomb + + + align:start position:0% +over independent pairs I have a Coulomb +term J and an exchange term K and what + + align:start position:0% +term J and an exchange term K and what + + + align:start position:0% +term J and an exchange term K and what +these things show me is that there is an + + align:start position:0% +these things show me is that there is an + + + align:start position:0% +these things show me is that there is an +average repulsion here between the + + align:start position:0% +average repulsion here between the + + + align:start position:0% +average repulsion here between the +electrons so the electrons are + + align:start position:0% +electrons so the electrons are + + + align:start position:0% +electrons so the electrons are +independent they can't avoid each other + + align:start position:0% +independent they can't avoid each other + + + align:start position:0% +independent they can't avoid each other +but they still interact there's still + + align:start position:0% +but they still interact there's still + + + align:start position:0% +but they still interact there's still +the electron-electron repulsion between + + align:start position:0% +the electron-electron repulsion between + + + align:start position:0% +the electron-electron repulsion between +electrons here so that's an energy + + align:start position:0% +electrons here so that's an energy + + + align:start position:0% +electrons here so that's an energy +expression that in one form or another + + align:start position:0% +expression that in one form or another + + + align:start position:0% +expression that in one form or another +should be somewhat familiar I think from + + align:start position:0% +should be somewhat familiar I think from + + + align:start position:0% +should be somewhat familiar I think from +things you guys have done before the + + align:start position:0% +things you guys have done before the + + + align:start position:0% +things you guys have done before the +idea of hartree-fock is relatively + + align:start position:0% +idea of hartree-fock is relatively + + + align:start position:0% +idea of hartree-fock is relatively +simple which is we have an energy then + + align:start position:0% +simple which is we have an energy then + + + align:start position:0% +simple which is we have an energy then +this is true for any Slater determinant + + align:start position:0% +this is true for any Slater determinant + + + align:start position:0% +this is true for any Slater determinant +any set of orbitals so I have some + + align:start position:0% +any set of orbitals so I have some + + + align:start position:0% +any set of orbitals so I have some +orbitals here and the idea of + + align:start position:0% +orbitals here and the idea of + + + align:start position:0% +orbitals here and the idea of +hartree-fock is to choose the orbitals + + align:start position:0% + + + + align:start position:0% + +to minimize the energy + + align:start position:0% + + + + align:start position:0% + +now this independent particle model + + align:start position:0% +now this independent particle model + + + align:start position:0% +now this independent particle model +energy I want to minimize that I'm gonna + + align:start position:0% +energy I want to minimize that I'm gonna + + + align:start position:0% +energy I want to minimize that I'm gonna +choose the orbitals that minimize that + + align:start position:0% +choose the orbitals that minimize that + + + align:start position:0% +choose the orbitals that minimize that +and the way I'm gonna do that is I'm + + align:start position:0% +and the way I'm gonna do that is I'm + + + align:start position:0% +and the way I'm gonna do that is I'm +gonna write my orbitals Sime you as a + + align:start position:0% +gonna write my orbitals Sime you as a + + + align:start position:0% +gonna write my orbitals Sime you as a +some number some index I some + + align:start position:0% +some number some index I some + + + align:start position:0% +some number some index I some +coefficients C I mu times my basis + + align:start position:0% +coefficients C I mu times my basis + + + align:start position:0% +coefficients C I mu times my basis +functions Phii and I'll just emphasize + + align:start position:0% +functions Phii and I'll just emphasize + + + align:start position:0% +functions Phii and I'll just emphasize +that what I have here are functions from + + align:start position:0% +that what I have here are functions from + + + align:start position:0% +that what I have here are functions from +my AO basis the things that I talked + + align:start position:0% +my AO basis the things that I talked + + + align:start position:0% +my AO basis the things that I talked +about last time like the actual 1 s 2 s + + align:start position:0% +about last time like the actual 1 s 2 s + + + align:start position:0% +about last time like the actual 1 s 2 s +1 s like 2 s like 2 pi/3 p like orbitals + + align:start position:0% +1 s like 2 s like 2 pi/3 p like orbitals + + + align:start position:0% +1 s like 2 s like 2 pi/3 p like orbitals +and then on the other side what I have + + align:start position:0% +and then on the other side what I have + + + align:start position:0% +and then on the other side what I have +here are my molecular like orbitals so + + align:start position:0% +here are my molecular like orbitals so + + + align:start position:0% +here are my molecular like orbitals so +the molecular orbitals are linear + + align:start position:0% +the molecular orbitals are linear + + + align:start position:0% +the molecular orbitals are linear +combinations of my atomic orbital basis + + align:start position:0% +combinations of my atomic orbital basis + + + align:start position:0% +combinations of my atomic orbital basis +functions ok so that's the the general + + align:start position:0% +functions ok so that's the the general + + + align:start position:0% +functions ok so that's the the general +idea of hartree-fock there's that were + + align:start position:0% +idea of hartree-fock there's that were + + + align:start position:0% +idea of hartree-fock there's that were +just going to choose these orbitals to + + align:start position:0% +just going to choose these orbitals to + + + align:start position:0% +just going to choose these orbitals to +minimize the energy and because the + + align:start position:0% +minimize the energy and because the + + + align:start position:0% +minimize the energy and because the +orbitals are defined by these + + align:start position:0% +orbitals are defined by these + + + align:start position:0% +orbitals are defined by these +coefficients I can think of this energy + + align:start position:0% +coefficients I can think of this energy + + + align:start position:0% +coefficients I can think of this energy +as a as a function of the coefficients C + + align:start position:0% +as a as a function of the coefficients C + + + align:start position:0% +as a as a function of the coefficients C +so I can say alright that means that I + + align:start position:0% +so I can say alright that means that I + + + align:start position:0% +so I can say alright that means that I +have an independent particle model + + align:start position:0% +have an independent particle model + + + align:start position:0% +have an independent particle model +energy which depends on these + + align:start position:0% +energy which depends on these + + + align:start position:0% +energy which depends on these +coefficients C and if I want to minimize + + align:start position:0% +coefficients C and if I want to minimize + + + align:start position:0% +coefficients C and if I want to minimize +that energy I then need to look for the + + align:start position:0% +that energy I then need to look for the + + + align:start position:0% +that energy I then need to look for the +places where the derivatives are equal + + align:start position:0% +places where the derivatives are equal + + + align:start position:0% +places where the derivatives are equal +to 0 so I take the root of that energy + + align:start position:0% +to 0 so I take the root of that energy + + + align:start position:0% +to 0 so I take the root of that energy +set it equal to 0 + + align:start position:0% +set it equal to 0 + + + align:start position:0% +set it equal to 0 +now as you can might might suspect if I + + align:start position:0% +now as you can might might suspect if I + + + align:start position:0% +now as you can might might suspect if I +look at this function look at this + + align:start position:0% +look at this function look at this + + + align:start position:0% +look at this function look at this +expression I have or an orbital here + + align:start position:0% +expression I have or an orbital here + + + align:start position:0% +expression I have or an orbital here +here here here here here here here here + + align:start position:0% +here here here here here here here here + + + align:start position:0% +here here here here here here here here +here I have a lot of orbitals appearing + + align:start position:0% +here I have a lot of orbitals appearing + + + align:start position:0% +here I have a lot of orbitals appearing +in there and then I'm going to use the + + align:start position:0% +in there and then I'm going to use the + + + align:start position:0% +in there and then I'm going to use the +chain rule because every one of those + + align:start position:0% +chain rule because every one of those + + + align:start position:0% +chain rule because every one of those +orbitals depends on every one of the + + align:start position:0% +orbitals depends on every one of the + + + align:start position:0% +orbitals depends on every one of the +coefficients so I'm gonna have a chain + + align:start position:0% +coefficients so I'm gonna have a chain + + + align:start position:0% +coefficients so I'm gonna have a chain +rule expression you might expect that + + align:start position:0% +rule expression you might expect that + + + align:start position:0% +rule expression you might expect that +there's gonna be a lot of algebra + + align:start position:0% +there's gonna be a lot of algebra + + + align:start position:0% +there's gonna be a lot of algebra +involved in taking this derivative and + + align:start position:0% +involved in taking this derivative and + + + align:start position:0% +involved in taking this derivative and +there is that's where this is where I + + align:start position:0% +there is that's where this is where I + + + align:start position:0% +there is that's where this is where I +get to use my favorite abbreviation + + align:start position:0% +get to use my favorite abbreviation + + + align:start position:0% +get to use my favorite abbreviation +which is a SaaS a stands for after some + + align:start position:0% +which is a SaaS a stands for after some + + + align:start position:0% +which is a SaaS a stands for after some +algebra means I'm not gonna work through + + align:start position:0% +algebra means I'm not gonna work through + + + align:start position:0% +algebra means I'm not gonna work through +the algebra there's some algebra there's + + align:start position:0% +the algebra there's some algebra there's + + + align:start position:0% +the algebra there's some algebra there's +several pages of lecture notes where + + align:start position:0% +several pages of lecture notes where + + + align:start position:0% +several pages of lecture notes where +algebra has gone through after you do + + align:start position:0% +algebra has gone through after you do + + + align:start position:0% +algebra has gone through after you do +the algebra you + + align:start position:0% +the algebra you + + + align:start position:0% +the algebra you +end up with the left hand equation + + align:start position:0% +end up with the left hand equation + + + align:start position:0% +end up with the left hand equation +reducing to an equation that looks like + + align:start position:0% +reducing to an equation that looks like + + + align:start position:0% +reducing to an equation that looks like +this so there's a matrix which I will + + align:start position:0% +this so there's a matrix which I will + + + align:start position:0% +this so there's a matrix which I will +call H and then when I dot that matrix + + align:start position:0% +call H and then when I dot that matrix + + + align:start position:0% +call H and then when I dot that matrix +into a vector C mu the coefficient + + align:start position:0% +into a vector C mu the coefficient + + + align:start position:0% +into a vector C mu the coefficient +vector I get some energy e mu times the + + align:start position:0% +vector I get some energy e mu times the + + + align:start position:0% +vector I get some energy e mu times the +coefficient vector e Canada so that + + align:start position:0% +coefficient vector e Canada so that + + + align:start position:0% +coefficient vector e Canada so that +takes it takes a lot of algebra to get + + align:start position:0% +takes it takes a lot of algebra to get + + + align:start position:0% +takes it takes a lot of algebra to get +to that but you can get an equation + + align:start position:0% +to that but you can get an equation + + + align:start position:0% +to that but you can get an equation +looks like this and that's encouraging + + align:start position:0% +looks like this and that's encouraging + + + align:start position:0% +looks like this and that's encouraging +because this is familiar to me this is + + align:start position:0% +because this is familiar to me this is + + + align:start position:0% +because this is familiar to me this is +an eigenvalue equation and that's nice + + align:start position:0% +an eigenvalue equation and that's nice + + + align:start position:0% +an eigenvalue equation and that's nice +because I remember eigenvalue equations + + align:start position:0% +because I remember eigenvalue equations + + + align:start position:0% +because I remember eigenvalue equations +from I mean the Schrodinger equation is + + align:start position:0% +from I mean the Schrodinger equation is + + + align:start position:0% +from I mean the Schrodinger equation is +an eigenvalue equation so it's nice that + + align:start position:0% +an eigenvalue equation so it's nice that + + + align:start position:0% +an eigenvalue equation so it's nice that +when I do this minimization I get back + + align:start position:0% +when I do this minimization I get back + + + align:start position:0% +when I do this minimization I get back +and eigenvalue equation that's nice the + + align:start position:0% +and eigenvalue equation that's nice the + + + align:start position:0% +and eigenvalue equation that's nice the +one complication is that the Hamiltonian + + align:start position:0% +one complication is that the Hamiltonian + + + align:start position:0% +one complication is that the Hamiltonian +here depends on the coefficient C so + + align:start position:0% +here depends on the coefficient C so + + + align:start position:0% +here depends on the coefficient C so +it's some effective Hamiltonian I'm + + align:start position:0% +it's some effective Hamiltonian I'm + + + align:start position:0% +it's some effective Hamiltonian I'm +collect I'm intentionally collecting + + align:start position:0% +collect I'm intentionally collecting + + + align:start position:0% +collect I'm intentionally collecting +terms so that it looks like a + + align:start position:0% +terms so that it looks like a + + + align:start position:0% +terms so that it looks like a +Schrodinger equation but it's a little + + align:start position:0% +Schrodinger equation but it's a little + + + align:start position:0% +Schrodinger equation but it's a little +bit funny because the Hamiltonian here + + align:start position:0% +bit funny because the Hamiltonian here + + + align:start position:0% +bit funny because the Hamiltonian here +depends on the coefficients that solve + + align:start position:0% +depends on the coefficients that solve + + + align:start position:0% +depends on the coefficients that solve +the equation so this is sort of an + + align:start position:0% +the equation so this is sort of an + + + align:start position:0% +the equation so this is sort of an +eigenvalue equation and so what we're + + align:start position:0% +eigenvalue equation and so what we're + + + align:start position:0% +eigenvalue equation and so what we're +seeing here is that h depends on the + + align:start position:0% +seeing here is that h depends on the + + + align:start position:0% +seeing here is that h depends on the +wavefunction somehow seems like would + + align:start position:0% +wavefunction somehow seems like would + + + align:start position:0% +wavefunction somehow seems like would +depending on what the wavefunction is I + + align:start position:0% +depending on what the wavefunction is I + + + align:start position:0% +depending on what the wavefunction is I +have different and hamiltonians and to + + align:start position:0% +have different and hamiltonians and to + + + align:start position:0% +have different and hamiltonians and to +understand why this is the case I want + + align:start position:0% +understand why this is the case I want + + + align:start position:0% +understand why this is the case I want +you to I want us to think about the + + align:start position:0% +you to I want us to think about the + + + align:start position:0% +you to I want us to think about the +potential V that an electron feels in an + + align:start position:0% +potential V that an electron feels in an + + + align:start position:0% +potential V that an electron feels in an +atom or in a molecule and there's + + align:start position:0% +atom or in a molecule and there's + + + align:start position:0% +atom or in a molecule and there's +generally going to be two pieces here so + + align:start position:0% +generally going to be two pieces here so + + + align:start position:0% +generally going to be two pieces here so +and there actually I can color-code them + + align:start position:0% +and there actually I can color-code them + + + align:start position:0% +and there actually I can color-code them +with the terms that it exists in the + + align:start position:0% +with the terms that it exists in the + + + align:start position:0% +with the terms that it exists in the +independent particle expression so + + align:start position:0% +independent particle expression so + + + align:start position:0% +independent particle expression so +there's the one electron terms the terms + + align:start position:0% +there's the one electron terms the terms + + + align:start position:0% +there's the one electron terms the terms +in the energy that just come from one + + align:start position:0% +in the energy that just come from one + + + align:start position:0% +in the energy that just come from one +electron and those are gonna be things + + align:start position:0% +electron and those are gonna be things + + + align:start position:0% +electron and those are gonna be things +like well I might have a nucleus of + + align:start position:0% +like well I might have a nucleus of + + + align:start position:0% +like well I might have a nucleus of +charge plus Z and I might have my + + align:start position:0% +charge plus Z and I might have my + + + align:start position:0% +charge plus Z and I might have my +electron out here the one that I'm + + align:start position:0% +electron out here the one that I'm + + + align:start position:0% +electron out here the one that I'm +interested in and it's gonna have some + + align:start position:0% +interested in and it's gonna have some + + + align:start position:0% +interested in and it's gonna have some +attraction to that + + align:start position:0% +attraction to that + + + align:start position:0% +attraction to that +so that just involves one-electron + + align:start position:0% +so that just involves one-electron + + + align:start position:0% +so that just involves one-electron +involves a nucleus but just one electron + + align:start position:0% +involves a nucleus but just one electron + + + align:start position:0% +involves a nucleus but just one electron +so there's some nuclear potential that + + align:start position:0% +so there's some nuclear potential that + + + align:start position:0% +so there's some nuclear potential that +each electron is gonna feel but then + + align:start position:0% +each electron is gonna feel but then + + + align:start position:0% +each electron is gonna feel but then +there's the term that corresponds to + + align:start position:0% +there's the term that corresponds to + + + align:start position:0% +there's the term that corresponds to +these average repulsion terms so there + + align:start position:0% +these average repulsion terms so there + + + align:start position:0% +these average repulsion terms so there +are other electrons in my system in each + + align:start position:0% +are other electrons in my system in each + + + align:start position:0% +are other electrons in my system in each +of those electrons interacts with the + + align:start position:0% +of those electrons interacts with the + + + align:start position:0% +of those electrons interacts with the +electron that I'm looking at so there's + + align:start position:0% +electron that I'm looking at so there's + + + align:start position:0% +electron that I'm looking at so there's +going to be some electron-electron + + align:start position:0% +going to be some electron-electron + + + align:start position:0% +going to be some electron-electron +repulsion term here and that electron + + align:start position:0% +repulsion term here and that electron + + + align:start position:0% +repulsion term here and that electron +electron repulsion depends on where the + + align:start position:0% +electron repulsion depends on where the + + + align:start position:0% +electron repulsion depends on where the +other electrons are and those other + + align:start position:0% +other electrons are and those other + + + align:start position:0% +other electrons are and those other +electrons have some wavefunction they're + + align:start position:0% +electrons have some wavefunction they're + + + align:start position:0% +electrons have some wavefunction they're +kind of spread out here all over the + + align:start position:0% +kind of spread out here all over the + + + align:start position:0% +kind of spread out here all over the +place and depending on how spread out + + align:start position:0% +place and depending on how spread out + + + align:start position:0% +place and depending on how spread out +those other electrons are I might have + + align:start position:0% +those other electrons are I might have + + + align:start position:0% +those other electrons are I might have +more or less electron repulsion so if + + align:start position:0% +more or less electron repulsion so if + + + align:start position:0% +more or less electron repulsion so if +they're very very concentrated in the + + align:start position:0% +they're very very concentrated in the + + + align:start position:0% +they're very very concentrated in the +region that I'm looking at the electron + + align:start position:0% +region that I'm looking at the electron + + + align:start position:0% +region that I'm looking at the electron +repulsion is gonna be very large if + + align:start position:0% +repulsion is gonna be very large if + + + align:start position:0% +repulsion is gonna be very large if +they're very spread out the very diffuse + + align:start position:0% +they're very spread out the very diffuse + + + align:start position:0% +they're very spread out the very diffuse +not gonna have very much electron + + align:start position:0% +not gonna have very much electron + + + align:start position:0% +not gonna have very much electron +repulsion but overall the + + align:start position:0% +repulsion but overall the + + + align:start position:0% +repulsion but overall the +electron-electron repulsion depends on + + align:start position:0% +electron-electron repulsion depends on + + + align:start position:0% +electron-electron repulsion depends on +the wave functions that I've chosen + + align:start position:0% +the wave functions that I've chosen + + + align:start position:0% +the wave functions that I've chosen +so the potential here is called a mean + + align:start position:0% +so the potential here is called a mean + + + align:start position:0% +so the potential here is called a mean +field or average field and it's because + + align:start position:0% +field or average field and it's because + + + align:start position:0% +field or average field and it's because +it's the potential that comes from the + + align:start position:0% +it's the potential that comes from the + + + align:start position:0% +it's the potential that comes from the +average repulsion + + align:start position:0% +average repulsion + + + align:start position:0% +average repulsion +it's the effective potential due to the + + align:start position:0% +it's the effective potential due to the + + + align:start position:0% +it's the effective potential due to the +averaging the smearing out over all the + + align:start position:0% +averaging the smearing out over all the + + + align:start position:0% +averaging the smearing out over all the +other electrons so what we do have then + + align:start position:0% +other electrons so what we do have then + + + align:start position:0% +other electrons so what we do have then +is that the Hamiltonian doesn't indeed + + align:start position:0% +is that the Hamiltonian doesn't indeed + + + align:start position:0% +is that the Hamiltonian doesn't indeed +depend on the wave functions because the + + align:start position:0% +depend on the wave functions because the + + + align:start position:0% +depend on the wave functions because the +wave function to determine that average + + align:start position:0% +wave function to determine that average + + + align:start position:0% +wave function to determine that average +potential but then if I know the + + align:start position:0% +potential but then if I know the + + + align:start position:0% +potential but then if I know the +Hamiltonian I can solve for the wave + + align:start position:0% +Hamiltonian I can solve for the wave + + + align:start position:0% +Hamiltonian I can solve for the wave +functions because the wave functions are + + align:start position:0% +functions because the wave functions are + + + align:start position:0% +functions because the wave functions are +the eigenfunctions of the hamiltonian + + align:start position:0% +the eigenfunctions of the hamiltonian + + + align:start position:0% +the eigenfunctions of the hamiltonian +and so I have this sort of chicken and + + align:start position:0% +and so I have this sort of chicken and + + + align:start position:0% +and so I have this sort of chicken and +egg situation that the Hamiltonian + + align:start position:0% +egg situation that the Hamiltonian + + + align:start position:0% +egg situation that the Hamiltonian +defines the wave functions and the wave + + align:start position:0% +defines the wave functions and the wave + + + align:start position:0% +defines the wave functions and the wave +functions define the Hamiltonian and the + + align:start position:0% +functions define the Hamiltonian and the + + + align:start position:0% +functions define the Hamiltonian and the +solution to this is to do what are + + align:start position:0% +solution to this is to do what are + + + align:start position:0% +solution to this is to do what are +called self-consistent field iterations + + align:start position:0% + + + + align:start position:0% + +and you can more or less think about + + align:start position:0% +and you can more or less think about + + + align:start position:0% +and you can more or less think about +these as the simple process of guests + + align:start position:0% +these as the simple process of guests + + + align:start position:0% +these as the simple process of guests +and wave functions build the Hamiltonian + + align:start position:0% +and wave functions build the Hamiltonian + + + align:start position:0% +and wave functions build the Hamiltonian +get some new wave functions build a new + + align:start position:0% +get some new wave functions build a new + + + align:start position:0% +get some new wave functions build a new +Hamiltonian get some new wave functions + + align:start position:0% +Hamiltonian get some new wave functions + + + align:start position:0% +Hamiltonian get some new wave functions +build a new Hamiltonian and keep going + + align:start position:0% +build a new Hamiltonian and keep going + + + align:start position:0% +build a new Hamiltonian and keep going +until this everything + + align:start position:0% +until this everything + + + align:start position:0% +until this everything +comes consistent and the idea then is + + align:start position:0% +comes consistent and the idea then is + + + align:start position:0% +comes consistent and the idea then is +that the wavefunction we're looking for + + align:start position:0% +that the wavefunction we're looking for + + + align:start position:0% +that the wavefunction we're looking for +in hartree-fock are the eigenfunctions + + align:start position:0% + + + + align:start position:0% + +of H of psy HF which we just defined to + + align:start position:0% +of H of psy HF which we just defined to + + + align:start position:0% +of H of psy HF which we just defined to +be equal to H hartree-fock so there's + + align:start position:0% +be equal to H hartree-fock so there's + + + align:start position:0% +be equal to H hartree-fock so there's +some hartree-fock Hamiltonian and the + + align:start position:0% +some hartree-fock Hamiltonian and the + + + align:start position:0% +some hartree-fock Hamiltonian and the +hartree-fock wave functions are the + + align:start position:0% +hartree-fock wave functions are the + + + align:start position:0% +hartree-fock wave functions are the +eigenfunctions of those that Hamiltonian + + align:start position:0% +eigenfunctions of those that Hamiltonian + + + align:start position:0% +eigenfunctions of those that Hamiltonian +that make sense any questions about that + + align:start position:0% + + + + align:start position:0% + +alright so hard rock is the starting + + align:start position:0% +alright so hard rock is the starting + + + align:start position:0% +alright so hard rock is the starting +point so we we have that as an + + align:start position:0% +point so we we have that as an + + + align:start position:0% +point so we we have that as an +approximation it's a useful starting + + align:start position:0% +approximation it's a useful starting + + + align:start position:0% +approximation it's a useful starting +point in many cases hartree-fock is not + + align:start position:0% +point in many cases hartree-fock is not + + + align:start position:0% +point in many cases hartree-fock is not +good enough and so the real thing that + + align:start position:0% +good enough and so the real thing that + + + align:start position:0% +good enough and so the real thing that +we're trying to figure out is how do we + + align:start position:0% +we're trying to figure out is how do we + + + align:start position:0% +we're trying to figure out is how do we +make something that uses what we've + + align:start position:0% +make something that uses what we've + + + align:start position:0% +make something that uses what we've +learned from hartree-fock about orbitals + + align:start position:0% +learned from hartree-fock about orbitals + + + align:start position:0% +learned from hartree-fock about orbitals +and energies and average repulsion how + + align:start position:0% +and energies and average repulsion how + + + align:start position:0% +and energies and average repulsion how +do we make something that's heart rate + + align:start position:0% +do we make something that's heart rate + + + align:start position:0% +do we make something that's heart rate +like hartree-fock but better so one way + + align:start position:0% +like hartree-fock but better so one way + + + align:start position:0% +like hartree-fock but better so one way +to do this is something that we've + + align:start position:0% +to do this is something that we've + + + align:start position:0% +to do this is something that we've +you've spent a lot of time on this + + align:start position:0% +you've spent a lot of time on this + + + align:start position:0% +you've spent a lot of time on this +semester which is perturbation theory if + + align:start position:0% +semester which is perturbation theory if + + + align:start position:0% +semester which is perturbation theory if +you have something that's pretty good as + + align:start position:0% +you have something that's pretty good as + + + align:start position:0% +you have something that's pretty good as +a starting point and you want to make it + + align:start position:0% +a starting point and you want to make it + + + align:start position:0% +a starting point and you want to make it +better + + align:start position:0% +better + + + align:start position:0% +better +perturbation theory is the natural thing + + align:start position:0% +perturbation theory is the natural thing + + + align:start position:0% +perturbation theory is the natural thing +to turn to to do that and so the way we + + align:start position:0% +to turn to to do that and so the way we + + + align:start position:0% +to turn to to do that and so the way we +apply perturbation theory in + + align:start position:0% +apply perturbation theory in + + + align:start position:0% +apply perturbation theory in +hartree-fock is we say well we've got + + align:start position:0% +hartree-fock is we say well we've got + + + align:start position:0% +hartree-fock is we say well we've got +this hartree-fock hamiltonian which we + + align:start position:0% +this hartree-fock hamiltonian which we + + + align:start position:0% +this hartree-fock hamiltonian which we +can solve and then we've got the actual + + align:start position:0% +can solve and then we've got the actual + + + align:start position:0% +can solve and then we've got the actual +hamiltonian h which we can't solve and + + align:start position:0% +hamiltonian h which we can't solve and + + + align:start position:0% +hamiltonian h which we can't solve and +so what we can do is then we say aha + + align:start position:0% +so what we can do is then we say aha + + + align:start position:0% +so what we can do is then we say aha +well that means that if I just take the + + align:start position:0% +well that means that if I just take the + + + align:start position:0% +well that means that if I just take the +difference between the hamiltonian I can + + align:start position:0% +difference between the hamiltonian I can + + + align:start position:0% +difference between the hamiltonian I can +solve in the Hamiltonian I can't solve + + align:start position:0% +solve in the Hamiltonian I can't solve + + + align:start position:0% +solve in the Hamiltonian I can't solve +and I treat that as a perturbation then + + align:start position:0% +and I treat that as a perturbation then + + + align:start position:0% +and I treat that as a perturbation then +I can do a well-defined perturbation + + align:start position:0% +I can do a well-defined perturbation + + + align:start position:0% +I can do a well-defined perturbation +theory where I know the solutions to h0 + + align:start position:0% +theory where I know the solutions to h0 + + + align:start position:0% +theory where I know the solutions to h0 +and then I treat that additional term as + + align:start position:0% +and then I treat that additional term as + + + align:start position:0% +and then I treat that additional term as +a perturbation and so then if I do that + + align:start position:0% +a perturbation and so then if I do that + + + align:start position:0% +a perturbation and so then if I do that +I end up with the perturbation expansion + + align:start position:0% +I end up with the perturbation expansion + + + align:start position:0% +I end up with the perturbation expansion +where I can go to first second third + + align:start position:0% +where I can go to first second third + + + align:start position:0% +where I can go to first second third +fourth fifth order in that additional + + align:start position:0% +fourth fifth order in that additional + + + align:start position:0% +fourth fifth order in that additional +term that I can't that's the difference + + align:start position:0% +term that I can't that's the difference + + + align:start position:0% +term that I can't that's the difference +between the two and if I look at the + + align:start position:0% +between the two and if I look at the + + + align:start position:0% +between the two and if I look at the +first two terms added together + + align:start position:0% +first two terms added together + + + align:start position:0% +first two terms added together +they give me the hartree-fock energy so + + align:start position:0% +they give me the hartree-fock energy so + + + align:start position:0% +they give me the hartree-fock energy so +any if I'm the one making up a + + align:start position:0% +any if I'm the one making up a + + + align:start position:0% +any if I'm the one making up a +perturbation expansion I will always + + align:start position:0% +perturbation expansion I will always + + + align:start position:0% +perturbation expansion I will always +choose it so that the first order + + align:start position:0% +choose it so that the first order + + + align:start position:0% +choose it so that the first order +correction is zero so that if I + + align:start position:0% +correction is zero so that if I + + + align:start position:0% +correction is zero so that if I +otherwise I've chosen I will just + + align:start position:0% +otherwise I've chosen I will just + + + align:start position:0% +otherwise I've chosen I will just +re-engineer my perturbation so that's + + align:start position:0% +re-engineer my perturbation so that's + + + align:start position:0% +re-engineer my perturbation so that's +true so up through first order I just + + align:start position:0% +true so up through first order I just + + + align:start position:0% +true so up through first order I just +get what I started with I get + + align:start position:0% +get what I started with I get + + + align:start position:0% +get what I started with I get +hartree-fock but then I have these + + align:start position:0% +hartree-fock but then I have these + + + align:start position:0% +hartree-fock but then I have these +additional terms and so I can go to + + align:start position:0% +additional terms and so I can go to + + + align:start position:0% +additional terms and so I can go to +second order and I will get a method + + align:start position:0% +second order and I will get a method + + + align:start position:0% +second order and I will get a method +that I call + + align:start position:0% +that I call + + + align:start position:0% +that I call +it's called mp2 it's named after so + + align:start position:0% +it's called mp2 it's named after so + + + align:start position:0% +it's called mp2 it's named after so +hartree-fock is named after Hartree and + + align:start position:0% +hartree-fock is named after Hartree and + + + align:start position:0% +hartree-fock is named after Hartree and +Fock MP stands for molar and plus it + + align:start position:0% +Fock MP stands for molar and plus it + + + align:start position:0% +Fock MP stands for molar and plus it +names the two people who wrote the paper + + align:start position:0% +names the two people who wrote the paper + + + align:start position:0% +names the two people who wrote the paper +in 1938 about this particular thing and + + align:start position:0% +in 1938 about this particular thing and + + + align:start position:0% +in 1938 about this particular thing and +the two was second order and then I + + align:start position:0% +the two was second order and then I + + + align:start position:0% +the two was second order and then I +could go on and I could do mp3 mp4 dot + + align:start position:0% +could go on and I could do mp3 mp4 dot + + + align:start position:0% +could go on and I could do mp3 mp4 dot +dot dot dot so in general this is MP and + + align:start position:0% +dot dot dot so in general this is MP and + + + align:start position:0% +dot dot dot so in general this is MP and +some number n telling me the order I go + + align:start position:0% +some number n telling me the order I go + + + align:start position:0% +some number n telling me the order I go +to in perturbation theory so you can you + + align:start position:0% +to in perturbation theory so you can you + + + align:start position:0% +to in perturbation theory so you can you +could do this in principle this gets + + align:start position:0% +could do this in principle this gets + + + align:start position:0% +could do this in principle this gets +better and better answers however in + + align:start position:0% +better and better answers however in + + + align:start position:0% +better and better answers however in +practice about twenty years ago people + + align:start position:0% +practice about twenty years ago people + + + align:start position:0% +practice about twenty years ago people +discovered something was rather + + align:start position:0% +discovered something was rather + + + align:start position:0% +discovered something was rather +disturbing so if I take a look at the + + align:start position:0% +disturbing so if I take a look at the + + + align:start position:0% +disturbing so if I take a look at the +energy - the ago so let's say I have a + + align:start position:0% +energy - the ago so let's say I have a + + + align:start position:0% +energy - the ago so let's say I have a +case where I know the exact energy and I + + align:start position:0% +case where I know the exact energy and I + + + align:start position:0% +case where I know the exact energy and I +look at the energy of these different + + align:start position:0% +look at the energy of these different + + + align:start position:0% +look at the energy of these different +approximate methods for say one + + align:start position:0% +approximate methods for say one + + + align:start position:0% +approximate methods for say one +particular simple thing like a neon atom + + align:start position:0% +particular simple thing like a neon atom + + + align:start position:0% +particular simple thing like a neon atom +so I take a neon atom and I look at the + + align:start position:0% +so I take a neon atom and I look at the + + + align:start position:0% +so I take a neon atom and I look at the +energies of these MPN approximations and + + align:start position:0% +energies of these MPN approximations and + + + align:start position:0% +energies of these MPN approximations and +I look at them as a function of n so one + + align:start position:0% +I look at them as a function of n so one + + + align:start position:0% +I look at them as a function of n so one +two three four five six seven eight and + + align:start position:0% + + + + align:start position:0% + +I'll say that for neon neon or something + + align:start position:0% +I'll say that for neon neon or something + + + align:start position:0% +I'll say that for neon neon or something +for which hartree-fock is already pretty + + align:start position:0% +for which hartree-fock is already pretty + + + align:start position:0% +for which hartree-fock is already pretty +good so they differ between hartree-fock + + align:start position:0% +good so they differ between hartree-fock + + + align:start position:0% +good so they differ between hartree-fock +and the exact answer is not too bad so + + align:start position:0% +and the exact answer is not too bad so + + + align:start position:0% +and the exact answer is not too bad so +hartree-fock might be say there on this + + align:start position:0% +hartree-fock might be say there on this + + + align:start position:0% +hartree-fock might be say there on this +particular scale and then you do MP 2 MP + + align:start position:0% +particular scale and then you do MP 2 MP + + + align:start position:0% +particular scale and then you do MP 2 MP +2 is better Oh MP juice maybe their MP 3 + + align:start position:0% +2 is better Oh MP juice maybe their MP 3 + + + align:start position:0% +2 is better Oh MP juice maybe their MP 3 +is also a little bit better than that + + align:start position:0% +is also a little bit better than that + + + align:start position:0% +is also a little bit better than that +but it overshoots a little bit and p4 + + align:start position:0% +but it overshoots a little bit and p4 + + + align:start position:0% +but it overshoots a little bit and p4 +corrects back in the opposite direction + + align:start position:0% +corrects back in the opposite direction + + + align:start position:0% +corrects back in the opposite direction +and then we've got 5 + + align:start position:0% +and then we've got 5 + + + align:start position:0% +and then we've got 5 +6:7 and you can connect the dots you can + + align:start position:0% +6:7 and you can connect the dots you can + + + align:start position:0% +6:7 and you can connect the dots you can +sort of see what's starting to happen + + align:start position:0% +sort of see what's starting to happen + + + align:start position:0% +sort of see what's starting to happen +here so that's a series thanks so + + align:start position:0% +here so that's a series thanks so + + + align:start position:0% +here so that's a series thanks so +mathematically I've got something that + + align:start position:0% +mathematically I've got something that + + + align:start position:0% +mathematically I've got something that +there's there's a value for everything + + align:start position:0% +there's there's a value for everything + + + align:start position:0% +there's there's a value for everything +and n that's a series and the name for a + + align:start position:0% +and n that's a series and the name for a + + + align:start position:0% +and n that's a series and the name for a +series like this is one that is not + + align:start position:0% +series like this is one that is not + + + align:start position:0% +series like this is one that is not +converging chosen there's an answer + + align:start position:0% +converging chosen there's an answer + + + align:start position:0% +converging chosen there's an answer +which is the infinite order answer but + + align:start position:0% +which is the infinite order answer but + + + align:start position:0% +which is the infinite order answer but +these partial sums are not converging to + + align:start position:0% +these partial sums are not converging to + + + align:start position:0% +these partial sums are not converging to +the infinite answer and very often this + + align:start position:0% +the infinite answer and very often this + + + align:start position:0% +the infinite answer and very often this +turns out to be the case with + + align:start position:0% +turns out to be the case with + + + align:start position:0% +turns out to be the case with +perturbation theory there can be + + align:start position:0% +perturbation theory there can be + + + align:start position:0% +perturbation theory there can be +perturbation theories that are very + + align:start position:0% +perturbation theories that are very + + + align:start position:0% +perturbation theories that are very +useful at low orders for describing + + align:start position:0% +useful at low orders for describing + + + align:start position:0% +useful at low orders for describing +qualitatively how things shift but if + + align:start position:0% +qualitatively how things shift but if + + + align:start position:0% +qualitatively how things shift but if +you go out to infinite order they are + + align:start position:0% +you go out to infinite order they are + + + align:start position:0% +you go out to infinite order they are +series that in principle you can prove + + align:start position:0% +series that in principle you can prove + + + align:start position:0% +series that in principle you can prove +give the correct exact answer because + + align:start position:0% +give the correct exact answer because + + + align:start position:0% +give the correct exact answer because +we've derived it such as such but just + + align:start position:0% +we've derived it such as such but just + + + align:start position:0% +we've derived it such as such but just +because a series in principle sums + + align:start position:0% +because a series in principle sums + + + align:start position:0% +because a series in principle sums +something doesn't mean that any finite + + align:start position:0% +something doesn't mean that any finite + + + align:start position:0% +something doesn't mean that any finite +number of terms will give a a convergent + + align:start position:0% +number of terms will give a a convergent + + + align:start position:0% +number of terms will give a a convergent +answer or give smaller errors and people + + align:start position:0% +answer or give smaller errors and people + + + align:start position:0% +answer or give smaller errors and people +find that for perturbation theory for + + align:start position:0% +find that for perturbation theory for + + + align:start position:0% +find that for perturbation theory for +electronic structure theory this is not + + align:start position:0% +electronic structure theory this is not + + + align:start position:0% +electronic structure theory this is not +all the time but very often the case + + align:start position:0% +all the time but very often the case + + + align:start position:0% +all the time but very often the case +that the perturbation expansion doesn't + + align:start position:0% +that the perturbation expansion doesn't + + + align:start position:0% +that the perturbation expansion doesn't +converge and so this is one of those + + align:start position:0% +converge and so this is one of those + + + align:start position:0% +converge and so this is one of those +places where you make a nice empirical + + align:start position:0% +places where you make a nice empirical + + + align:start position:0% +places where you make a nice empirical +compromise and you say well gee every + + align:start position:0% +compromise and you say well gee every + + + align:start position:0% +compromise and you say well gee every +term it doesn't necessarily get better + + align:start position:0% +term it doesn't necessarily get better + + + align:start position:0% +term it doesn't necessarily get better +after MP 2 MP 2 usually improves on + + align:start position:0% +after MP 2 MP 2 usually improves on + + + align:start position:0% +after MP 2 MP 2 usually improves on +hartree-fock but higher order might be + + align:start position:0% +hartree-fock but higher order might be + + + align:start position:0% +hartree-fock but higher order might be +better or worse and certainly higher + + align:start position:0% +better or worse and certainly higher + + + align:start position:0% +better or worse and certainly higher +order is more expensive so MP 2 is a + + align:start position:0% +order is more expensive so MP 2 is a + + + align:start position:0% +order is more expensive so MP 2 is a +good place to get off the elevator + + align:start position:0% +good place to get off the elevator + + + align:start position:0% +good place to get off the elevator +because this is gonna get more expensive + + align:start position:0% +because this is gonna get more expensive + + + align:start position:0% +because this is gonna get more expensive +but not necessarily more accurate so + + align:start position:0% +but not necessarily more accurate so + + + align:start position:0% +but not necessarily more accurate so +this is a good place to stop and so + + align:start position:0% +this is a good place to stop and so + + + align:start position:0% +this is a good place to stop and so +you'll see a lot of calculations out + + align:start position:0% +you'll see a lot of calculations out + + + align:start position:0% +you'll see a lot of calculations out +there that are variations on MP 2 + + align:start position:0% +there that are variations on MP 2 + + + align:start position:0% +there that are variations on MP 2 +because it's the least expensive and + + align:start position:0% +because it's the least expensive and + + + align:start position:0% +because it's the least expensive and +it's somewhat more accurate okay so now + + align:start position:0% +it's somewhat more accurate okay so now + + + align:start position:0% +it's somewhat more accurate okay so now +we're gonna take a pause and we're gonna + + align:start position:0% +we're gonna take a pause and we're gonna + + + align:start position:0% +we're gonna take a pause and we're gonna +talk and this is where I mean we need + + align:start position:0% +talk and this is where I mean we need + + + align:start position:0% +talk and this is where I mean we need +audience I need audience participation + + align:start position:0% +audience I need audience participation + + + align:start position:0% +audience I need audience participation +so we're gonna discuss two different + + align:start position:0% +so we're gonna discuss two different + + + align:start position:0% +so we're gonna discuss two different +things that you might want to know we've + + align:start position:0% +things that you might want to know we've + + + align:start position:0% +things that you might want to know we've +got now got two methods hartree-fock and + + align:start position:0% +got now got two methods hartree-fock and + + + align:start position:0% +got now got two methods hartree-fock and +MP 2 and there are two things that you + + align:start position:0% +MP 2 and there are two things that you + + + align:start position:0% +MP 2 and there are two things that you +might want to know one is how accurate + + align:start position:0% +might want to know one is how accurate + + + align:start position:0% +might want to know one is how accurate +will one of these calculations be if I + + align:start position:0% +will one of these calculations be if I + + + align:start position:0% +will one of these calculations be if I +do it will it give me the right answer + + align:start position:0% +do it will it give me the right answer + + + align:start position:0% +do it will it give me the right answer +the other one is how long will it take + + align:start position:0% +the other one is how long will it take + + + align:start position:0% +the other one is how long will it take +in other words will it finish by Friday + + align:start position:0% +in other words will it finish by Friday + + + align:start position:0% +in other words will it finish by Friday +when the pset is due will it finish by + + align:start position:0% +when the pset is due will it finish by + + + align:start position:0% +when the pset is due will it finish by +the end of the semester will it finish + + align:start position:0% +the end of the semester will it finish + + + align:start position:0% +the end of the semester will it finish +by the the end of my time at MIT you + + align:start position:0% +by the the end of my time at MIT you + + + align:start position:0% +by the the end of my time at MIT you +know what what timescale are we looking + + align:start position:0% +know what what timescale are we looking + + + align:start position:0% +know what what timescale are we looking +at so we'll start off talking about + + align:start position:0% +at so we'll start off talking about + + + align:start position:0% +at so we'll start off talking about +properties so people have done many many + + align:start position:0% +properties so people have done many many + + + align:start position:0% +properties so people have done many many +many calculations using many different + + align:start position:0% +many calculations using many different + + + align:start position:0% +many calculations using many different +electronic structure methods so that now + + align:start position:0% +electronic structure methods so that now + + + align:start position:0% +electronic structure methods so that now +there's a risk there sort of an + + align:start position:0% +there's a risk there sort of an + + + align:start position:0% +there's a risk there sort of an +empirical rule of thumb for just about + + align:start position:0% +empirical rule of thumb for just about + + + align:start position:0% +empirical rule of thumb for just about +any property you want to know about + + align:start position:0% +any property you want to know about + + + align:start position:0% +any property you want to know about +there's a rule of thumb for how accurate + + align:start position:0% +there's a rule of thumb for how accurate + + + align:start position:0% +there's a rule of thumb for how accurate +one of these methods should be so what's + + align:start position:0% +one of these methods should be so what's + + + align:start position:0% +one of these methods should be so what's +a property that you might want to know + + align:start position:0% +a property that you might want to know + + + align:start position:0% +a property that you might want to know +and that this is where the the the + + align:start position:0% +and that this is where the the the + + + align:start position:0% +and that this is where the the the +audience-participation comes in I will + + align:start position:0% +audience-participation comes in I will + + + align:start position:0% +audience-participation comes in I will +only give you information about + + align:start position:0% +only give you information about + + + align:start position:0% +only give you information about +properties that you say are interesting + + align:start position:0% + + + + align:start position:0% + +time and space complexity all right can + + align:start position:0% +time and space complexity all right can + + + align:start position:0% +time and space complexity all right can +you be more specific what type of time + + align:start position:0% +you be more specific what type of time + + + align:start position:0% +you be more specific what type of time +in space complexity yes so that will be + + align:start position:0% +in space complexity yes so that will be + + + align:start position:0% +in space complexity yes so that will be +the second thing that we will talk about + + align:start position:0% +the second thing that we will talk about + + + align:start position:0% +the second thing that we will talk about +which those are the two variables we'll + + align:start position:0% +which those are the two variables we'll + + + align:start position:0% +which those are the two variables we'll +talk about in terms of in terms of how + + align:start position:0% +talk about in terms of in terms of how + + + align:start position:0% +talk about in terms of in terms of how +long and how fast I'm interested Hiro + + align:start position:0% +long and how fast I'm interested Hiro + + + align:start position:0% +long and how fast I'm interested Hiro +saying like molecular properties you + + align:start position:0% +saying like molecular properties you + + + align:start position:0% +saying like molecular properties you +might want to know about a molecule or a + + align:start position:0% +might want to know about a molecule or a + + + align:start position:0% +might want to know about a molecule or a +reaction or something like that okay + + align:start position:0% +reaction or something like that okay + + + align:start position:0% +reaction or something like that okay +so that would be sort of a activation + + align:start position:0% +so that would be sort of a activation + + + align:start position:0% +so that would be sort of a activation +energy right okay what's something else + + align:start position:0% + + + + align:start position:0% + +we only want to know about activation + + align:start position:0% +we only want to know about activation + + + align:start position:0% +we only want to know about activation +yeah great okay so I'll give any I'll + + align:start position:0% +yeah great okay so I'll give any I'll + + + align:start position:0% +yeah great okay so I'll give any I'll +give one variable that probe that which + + align:start position:0% +give one variable that probe that which + + + align:start position:0% +give one variable that probe that which +is a dipole moment for example you might + + align:start position:0% +is a dipole moment for example you might + + + align:start position:0% +is a dipole moment for example you might +want to know a dipole moment okay yeah + + align:start position:0% +want to know a dipole moment okay yeah + + + align:start position:0% +want to know a dipole moment okay yeah +so that's so that is something we want + + align:start position:0% +so that's so that is something we want + + + align:start position:0% +so that's so that is something we want +to know about but I read it but it's a + + align:start position:0% +to know about but I read it but it's a + + + align:start position:0% +to know about but I read it but it's a +qualitative one so it's like so what I'm + + align:start position:0% +qualitative one so it's like so what I'm + + + align:start position:0% +qualitative one so it's like so what I'm +gonna give you let me give you things + + align:start position:0% +gonna give you let me give you things + + + align:start position:0% +gonna give you let me give you things +where I can say oh it's for a dipole + + align:start position:0% +where I can say oh it's for a dipole + + + align:start position:0% +where I can say oh it's for a dipole +moment it's within this mini Debye or + + align:start position:0% +moment it's within this mini Debye or + + + align:start position:0% +moment it's within this mini Debye or +this men's percent so emmos are + + align:start position:0% +this men's percent so emmos are + + + align:start position:0% +this men's percent so emmos are +qualitative and we can get that but I + + align:start position:0% +qualitative and we can get that but I + + + align:start position:0% +qualitative and we can get that but I +can't say well this mo is 75% right + + align:start position:0% +can't say well this mo is 75% right + + + align:start position:0% +can't say well this mo is 75% right +right so yeah + + align:start position:0% + + + + align:start position:0% + +okay so so that would be like a like + + align:start position:0% +okay so so that would be like a like + + + align:start position:0% +okay so so that would be like a like +sighs yeah yeah what was that + + align:start position:0% +sighs yeah yeah what was that + + + align:start position:0% +sighs yeah yeah what was that +yes yeah do something that see it's + + align:start position:0% +yes yeah do something that see it's + + + align:start position:0% +yes yeah do something that see it's +somebody that's about an absorption + + align:start position:0% +somebody that's about an absorption + + + align:start position:0% +somebody that's about an absorption +spectra neck absorption spectrum so + + align:start position:0% + + + + align:start position:0% + +other things people might want to know + + align:start position:0% +other things people might want to know + + + align:start position:0% +other things people might want to know +bond links there you go anything else + + align:start position:0% +bond links there you go anything else + + + align:start position:0% +bond links there you go anything else +we've got a good list okay we use that + + align:start position:0% +we've got a good list okay we use that + + + align:start position:0% +we've got a good list okay we use that +as our list okay so I will start off + + align:start position:0% +as our list okay so I will start off + + + align:start position:0% +as our list okay so I will start off +with bond links cuz that's the one where + + align:start position:0% +with bond links cuz that's the one where + + + align:start position:0% +with bond links cuz that's the one where +hartree-fock does the best of these + + align:start position:0% +hartree-fock does the best of these + + + align:start position:0% +hartree-fock does the best of these +things so it makes you feel like it's + + align:start position:0% +things so it makes you feel like it's + + + align:start position:0% +things so it makes you feel like it's +encouraging so bond links hartree-fock + + align:start position:0% +encouraging so bond links hartree-fock + + + align:start position:0% +encouraging so bond links hartree-fock +usually predicts bond links to be a + + align:start position:0% +usually predicts bond links to be a + + + align:start position:0% +usually predicts bond links to be a +little bit too short um so the molecules + + align:start position:0% +little bit too short um so the molecules + + + align:start position:0% +little bit too short um so the molecules +are a little bit too compact but it's + + align:start position:0% +are a little bit too compact but it's + + + align:start position:0% +are a little bit too compact but it's +not too bad they're usually too short by + + align:start position:0% +not too bad they're usually too short by + + + align:start position:0% +not too bad they're usually too short by +about 1% just not too bad you know it + + align:start position:0% +about 1% just not too bad you know it + + + align:start position:0% +about 1% just not too bad you know it +gets 99 percent of the bond length right + + align:start position:0% +gets 99 percent of the bond length right + + + align:start position:0% +gets 99 percent of the bond length right +mp2 does better so that it's it doesn't + + align:start position:0% +mp2 does better so that it's it doesn't + + + align:start position:0% +mp2 does better so that it's it doesn't +actually have a systematic error it + + align:start position:0% +actually have a systematic error it + + + align:start position:0% +actually have a systematic error it +typically it gets bond bond links + + align:start position:0% +typically it gets bond bond links + + + align:start position:0% +typically it gets bond bond links +correct to plus or minus 1 picometer so + + align:start position:0% +correct to plus or minus 1 picometer so + + + align:start position:0% +correct to plus or minus 1 picometer so +picometer is ten to the minus twelfth + + align:start position:0% +picometer is ten to the minus twelfth + + + align:start position:0% +picometer is ten to the minus twelfth +meters so point zero one angstroms since + + align:start position:0% +meters so point zero one angstroms since + + + align:start position:0% +meters so point zero one angstroms since +a bond length is usually about an + + align:start position:0% +a bond length is usually about an + + + align:start position:0% +a bond length is usually about an +angstrom so we'll go from that to let's + + align:start position:0% +angstrom so we'll go from that to let's + + + align:start position:0% +angstrom so we'll go from that to let's +see + + align:start position:0% +see + + + align:start position:0% +see +sighs so so for the size of the of an + + align:start position:0% +sighs so so for the size of the of an + + + align:start position:0% +sighs so so for the size of the of an +atom or a molecule this has to do with + + align:start position:0% +atom or a molecule this has to do with + + + align:start position:0% +atom or a molecule this has to do with +the van der Waals radius basically and + + align:start position:0% +the van der Waals radius basically and + + + align:start position:0% +the van der Waals radius basically and +actually hartree-fock does fairly well + + align:start position:0% +actually hartree-fock does fairly well + + + align:start position:0% +actually hartree-fock does fairly well +does a fairly good job of describing van + + align:start position:0% +does a fairly good job of describing van + + + align:start position:0% +does a fairly good job of describing van +der Waals radii I would say that it more + + align:start position:0% +der Waals radii I would say that it more + + + align:start position:0% +der Waals radii I would say that it more +or less goes with the with the bond + + align:start position:0% +or less goes with the with the bond + + + align:start position:0% +or less goes with the with the bond +length prescription so that the size is + + align:start position:0% +length prescription so that the size is + + + align:start position:0% +length prescription so that the size is +a little bit too small so it might be + + align:start position:0% +a little bit too small so it might be + + + align:start position:0% +a little bit too small so it might be +minus two to three percent too small and + + align:start position:0% +minus two to three percent too small and + + + align:start position:0% +minus two to three percent too small and +then there's very few people that + + align:start position:0% +then there's very few people that + + + align:start position:0% +then there's very few people that +actually do sizes with MP two for + + align:start position:0% +actually do sizes with MP two for + + + align:start position:0% +actually do sizes with MP two for +various reasons so but I would say that + + align:start position:0% +various reasons so but I would say that + + + align:start position:0% +various reasons so but I would say that +it's + + align:start position:0% + + + + align:start position:0% + +I'll put accurate there because + + align:start position:0% +I'll put accurate there because + + + align:start position:0% +I'll put accurate there because +basically the size of an atom or + + align:start position:0% +basically the size of an atom or + + + align:start position:0% +basically the size of an atom or +molecule is fuzzy right so I can talk + + align:start position:0% +molecule is fuzzy right so I can talk + + + align:start position:0% +molecule is fuzzy right so I can talk +about the radius and it's a little bit + + align:start position:0% +about the radius and it's a little bit + + + align:start position:0% +about the radius and it's a little bit +fuzzy the errors and mp2 would be + + align:start position:0% +fuzzy the errors and mp2 would be + + + align:start position:0% +fuzzy the errors and mp2 would be +smaller than whatever fuzziness I could + + align:start position:0% +smaller than whatever fuzziness I could + + + align:start position:0% +smaller than whatever fuzziness I could +have in my definition of slots for + + align:start position:0% +have in my definition of slots for + + + align:start position:0% +have in my definition of slots for +activation energies hartree-fock is + + align:start position:0% +activation energies hartree-fock is + + + align:start position:0% +activation energies hartree-fock is +pretty poor so the activation barriers + + align:start position:0% +pretty poor so the activation barriers + + + align:start position:0% +pretty poor so the activation barriers +here are too high by 30 to 50 percent so + + align:start position:0% +here are too high by 30 to 50 percent so + + + align:start position:0% +here are too high by 30 to 50 percent so +the barrier Heights are very high in + + align:start position:0% +the barrier Heights are very high in + + + align:start position:0% +the barrier Heights are very high in +hartree-fock mp2 has barrier Heights + + align:start position:0% +hartree-fock mp2 has barrier Heights + + + align:start position:0% +hartree-fock mp2 has barrier Heights +that are still too high but only by + + align:start position:0% +that are still too high but only by + + + align:start position:0% +that are still too high but only by +about ten percent on average dipole + + align:start position:0% +about ten percent on average dipole + + + align:start position:0% +about ten percent on average dipole +moments in hartree-fock there are no + + align:start position:0% +moments in hartree-fock there are no + + + align:start position:0% +moments in hartree-fock there are no +systematic studies on that I will just + + align:start position:0% +systematic studies on that I will just + + + align:start position:0% +systematic studies on that I will just +say that they are bad they are bad + + align:start position:0% +say that they are bad they are bad + + + align:start position:0% +say that they are bad they are bad +enough that nobody does a systematic + + align:start position:0% +enough that nobody does a systematic + + + align:start position:0% +enough that nobody does a systematic +study but for mp2 they are quite a bit + + align:start position:0% +study but for mp2 they are quite a bit + + + align:start position:0% +study but for mp2 they are quite a bit +better + + align:start position:0% +better + + + align:start position:0% +better +and typically accurate within say 0.1 + + align:start position:0% +and typically accurate within say 0.1 + + + align:start position:0% +and typically accurate within say 0.1 +Dubai and then for excitation for + + align:start position:0% +Dubai and then for excitation for + + + align:start position:0% +Dubai and then for excitation for +absorption energy so there's gonna be + + align:start position:0% +absorption energy so there's gonna be + + + align:start position:0% +absorption energy so there's gonna be +the difference in the lowest electronic + + align:start position:0% +the difference in the lowest electronic + + + align:start position:0% +the difference in the lowest electronic +state in the next highest electronic + + align:start position:0% +state in the next highest electronic + + + align:start position:0% +state in the next highest electronic +state so you can get these things + + align:start position:0% +state so you can get these things + + + align:start position:0% +state so you can get these things +through various means the typical + + align:start position:0% +through various means the typical + + + align:start position:0% +through various means the typical +absorption you know there's and also + + align:start position:0% +absorption you know there's and also + + + align:start position:0% +absorption you know there's and also +I'll say that doing that involves an + + align:start position:0% +I'll say that doing that involves an + + + align:start position:0% +I'll say that doing that involves an +extension beyond what I've talked about + + align:start position:0% +extension beyond what I've talked about + + + align:start position:0% +extension beyond what I've talked about +so far cuz I've been focused on the + + align:start position:0% +so far cuz I've been focused on the + + + align:start position:0% +so far cuz I've been focused on the +ground state but if you use the logical + + align:start position:0% +ground state but if you use the logical + + + align:start position:0% +ground state but if you use the logical +extensions of these things absorption + + align:start position:0% +extensions of these things absorption + + + align:start position:0% +extensions of these things absorption +energies in the hartree-fock + + align:start position:0% +energies in the hartree-fock + + + align:start position:0% +energies in the hartree-fock +tend to be accurate - there tend to be + + align:start position:0% +tend to be accurate - there tend to be + + + align:start position:0% +tend to be accurate - there tend to be +too big and too big by say half an EP or + + align:start position:0% +too big and too big by say half an EP or + + + align:start position:0% +too big and too big by say half an EP or +so and then for MP - they're more + + align:start position:0% +so and then for MP - they're more + + + align:start position:0% +so and then for MP - they're more +accurate but not that much + + align:start position:0% +accurate but not that much + + + align:start position:0% +accurate but not that much +so plus or minus say 0.3 evie electronic + + align:start position:0% +so plus or minus say 0.3 evie electronic + + + align:start position:0% +so plus or minus say 0.3 evie electronic +excited states tend to be fairly + + align:start position:0% +excited states tend to be fairly + + + align:start position:0% +excited states tend to be fairly +difficult to get but we see that MP 2 is + + align:start position:0% +difficult to get but we see that MP 2 is + + + align:start position:0% +difficult to get but we see that MP 2 is +doing better on all counts and + + align:start position:0% +doing better on all counts and + + + align:start position:0% +doing better on all counts and +hartree-fock so it's improving that's + + align:start position:0% +hartree-fock so it's improving that's + + + align:start position:0% +hartree-fock so it's improving that's +good but then alright now what is what's + + align:start position:0% +good but then alright now what is what's + + + align:start position:0% +good but then alright now what is what's +it gonna cost me + + align:start position:0% +it gonna cost me + + + align:start position:0% +it gonna cost me +how long is it gonna take well there's + + align:start position:0% +how long is it gonna take well there's + + + align:start position:0% +how long is it gonna take well there's +two different ways that we can measure + + align:start position:0% +two different ways that we can measure + + + align:start position:0% +two different ways that we can measure +computation of complexity one is by the + + align:start position:0% +computation of complexity one is by the + + + align:start position:0% +computation of complexity one is by the +amount of storage that's required it's + + align:start position:0% +amount of storage that's required it's + + + align:start position:0% +amount of storage that's required it's +the amount of yeah information you have + + align:start position:0% +the amount of yeah information you have + + + align:start position:0% +the amount of yeah information you have +to store in order + + align:start position:0% +to store in order + + + align:start position:0% +to store in order +do the calculation the other way is by + + align:start position:0% +do the calculation the other way is by + + + align:start position:0% +do the calculation the other way is by +how long it's going to take how many + + align:start position:0% +how long it's going to take how many + + + align:start position:0% +how long it's going to take how many +operations the computer has to do to + + align:start position:0% +operations the computer has to do to + + + align:start position:0% +operations the computer has to do to +solve the problem and so for + + align:start position:0% +solve the problem and so for + + + align:start position:0% +solve the problem and so for +hartree-fock the main memory piece that + + align:start position:0% +hartree-fock the main memory piece that + + + align:start position:0% +hartree-fock the main memory piece that +we need is actually the Hamiltonian so + + align:start position:0% +we need is actually the Hamiltonian so + + + align:start position:0% +we need is actually the Hamiltonian so +we need that Hamiltonian matrix we've + + align:start position:0% +we need that Hamiltonian matrix we've + + + align:start position:0% +we need that Hamiltonian matrix we've +got to store that in order to compute + + align:start position:0% +got to store that in order to compute + + + align:start position:0% +got to store that in order to compute +its eigenvalues and it is an and it's a + + align:start position:0% +its eigenvalues and it is an and it's a + + + align:start position:0% +its eigenvalues and it is an and it's a +number of basis functions by a number of + + align:start position:0% +number of basis functions by a number of + + + align:start position:0% +number of basis functions by a number of +basis functions and and so then now we + + align:start position:0% +basis functions and and so then now we + + + align:start position:0% +basis functions and and so then now we +have to say all right well first of all + + align:start position:0% +have to say all right well first of all + + + align:start position:0% +have to say all right well first of all +we have to figure out how much ran so + + align:start position:0% +we have to figure out how much ran so + + + align:start position:0% +we have to figure out how much ran so +when I'm figuring out how much RAM is + + align:start position:0% +when I'm figuring out how much RAM is + + + align:start position:0% +when I'm figuring out how much RAM is +required + + align:start position:0% +required + + + align:start position:0% +required +does anybody have a know how much RAM + + align:start position:0% +does anybody have a know how much RAM + + + align:start position:0% +does anybody have a know how much RAM +they have on their laptop or desktop + + align:start position:0% +they have on their laptop or desktop + + + align:start position:0% +they have on their laptop or desktop +computer + + align:start position:0% +computer + + + align:start position:0% +computer +nobody knows 16 gigs + + align:start position:0% +nobody knows 16 gigs + + + align:start position:0% +nobody knows 16 gigs +all right that's against what I what + + align:start position:0% +all right that's against what I what + + + align:start position:0% +all right that's against what I what +that's that's one mic that's one on + + align:start position:0% +that's that's one mic that's one on + + + align:start position:0% +that's that's one mic that's one on +that's what's on mine too so 16 + + align:start position:0% +that's what's on mine too so 16 + + + align:start position:0% +that's what's on mine too so 16 +gigabytes which is 16 times 10 to the + + align:start position:0% +gigabytes which is 16 times 10 to the + + + align:start position:0% +gigabytes which is 16 times 10 to the +9th bytes roughly and and then so now we + + align:start position:0% +9th bytes roughly and and then so now we + + + align:start position:0% +9th bytes roughly and and then so now we +have to say all right for storing and + + align:start position:0% +have to say all right for storing and + + + align:start position:0% +have to say all right for storing and +basis by x and basis numbers how much + + align:start position:0% +basis by x and basis numbers how much + + + align:start position:0% +basis by x and basis numbers how much +does that take + + align:start position:0% +does that take + + + align:start position:0% +does that take +well let's say that we have a Adams okay + + align:start position:0% +well let's say that we have a Adams okay + + + align:start position:0% +well let's say that we have a Adams okay +so we've got a is that just some the + + align:start position:0% +so we've got a is that just some the + + + align:start position:0% +so we've got a is that just some the +number of atoms we have is a then the + + align:start position:0% +number of atoms we have is a then the + + + align:start position:0% +number of atoms we have is a then the +number of basis functions we have last + + align:start position:0% +number of basis functions we have last + + + align:start position:0% +number of basis functions we have last +time we figured out that a dzp basis + + align:start position:0% +time we figured out that a dzp basis + + + align:start position:0% +time we figured out that a dzp basis +which is a decent-size basis for carbon + + align:start position:0% +which is a decent-size basis for carbon + + + align:start position:0% +which is a decent-size basis for carbon +had around 50 was 14 basis functions per + + align:start position:0% +had around 50 was 14 basis functions per + + + align:start position:0% +had around 50 was 14 basis functions per +carbon i'm just going to round to 15 + + align:start position:0% +carbon i'm just going to round to 15 + + + align:start position:0% +carbon i'm just going to round to 15 +because it's easier math so that means + + align:start position:0% +because it's easier math so that means + + + align:start position:0% +because it's easier math so that means +that the number of basis functions is 15 + + align:start position:0% +that the number of basis functions is 15 + + + align:start position:0% +that the number of basis functions is 15 +roughly times the number of atoms so + + align:start position:0% +roughly times the number of atoms so + + + align:start position:0% +roughly times the number of atoms so +there's 15 a times 15 a + + align:start position:0% + + + + align:start position:0% + +things that I need to store to get this + + align:start position:0% +things that I need to store to get this + + + align:start position:0% +things that I need to store to get this +matrix and that means I need about 225 a + + align:start position:0% +matrix and that means I need about 225 a + + + align:start position:0% +matrix and that means I need about 225 a +squared numbers so these are how many + + align:start position:0% +squared numbers so these are how many + + + align:start position:0% +squared numbers so these are how many +numbers at the store and then I have to + + align:start position:0% +numbers at the store and then I have to + + + align:start position:0% +numbers at the store and then I have to +know that each number + + align:start position:0% +know that each number + + + align:start position:0% +know that each number +I'm usually storing these in double + + align:start position:0% +I'm usually storing these in double + + + align:start position:0% +I'm usually storing these in double +precision so each number requires 8 + + align:start position:0% +precision so each number requires 8 + + + align:start position:0% +precision so each number requires 8 +bytes in double precision so that means + + align:start position:0% +bytes in double precision so that means + + + align:start position:0% +bytes in double precision so that means +that I have something like 1700 a + + align:start position:0% + + + + align:start position:0% + +squared bytes to store that that object + + align:start position:0% + + + + align:start position:0% + +so then that's so now that says all + + align:start position:0% +so then that's so now that says all + + + align:start position:0% +so then that's so now that says all +right if I've only got 16 times 10 to + + align:start position:0% +right if I've only got 16 times 10 to + + + align:start position:0% +right if I've only got 16 times 10 to +the 9 bytes of storage space on my + + align:start position:0% +the 9 bytes of storage space on my + + + align:start position:0% +the 9 bytes of storage space on my +computer and I need 1700 a squared bytes + + align:start position:0% +computer and I need 1700 a squared bytes + + + align:start position:0% +computer and I need 1700 a squared bytes +for an molecule with a with a atoms that + + align:start position:0% +for an molecule with a with a atoms that + + + align:start position:0% +for an molecule with a with a atoms that +just gives me a natural limit on the + + align:start position:0% +just gives me a natural limit on the + + + align:start position:0% +just gives me a natural limit on the +number of atoms and if you back it out + + align:start position:0% +number of atoms and if you back it out + + + align:start position:0% +number of atoms and if you back it out +that implies that a is less than or + + align:start position:0% +that implies that a is less than or + + + align:start position:0% +that implies that a is less than or +about equal to 3000 which is a big + + align:start position:0% +about equal to 3000 which is a big + + + align:start position:0% +about equal to 3000 which is a big +number + + align:start position:0% +number + + + align:start position:0% +number +so as you're at your molecule could have + + align:start position:0% +so as you're at your molecule could have + + + align:start position:0% +so as you're at your molecule could have +up to about 3000 atoms in it in this + + align:start position:0% +up to about 3000 atoms in it in this + + + align:start position:0% +up to about 3000 atoms in it in this +calculation would run and that turn that + + align:start position:0% +calculation would run and that turn that + + + align:start position:0% +calculation would run and that turn that +rough calculation turns out to be about + + align:start position:0% +rough calculation turns out to be about + + + align:start position:0% +rough calculation turns out to be about +right now let's take a look at the CPU + + align:start position:0% +right now let's take a look at the CPU + + + align:start position:0% +right now let's take a look at the CPU +time required so the CPU time we're + + align:start position:0% +time required so the CPU time we're + + + align:start position:0% +time required so the CPU time we're +gonna measure this in hours because + + align:start position:0% +gonna measure this in hours because + + + align:start position:0% +gonna measure this in hours because +that's my human unit of time so 1 hour + + align:start position:0% +that's my human unit of time so 1 hour + + + align:start position:0% +that's my human unit of time so 1 hour +is 3600 seconds and then what I need to + + align:start position:0% +is 3600 seconds and then what I need to + + + align:start position:0% +is 3600 seconds and then what I need to +know is well what actually takes the + + align:start position:0% +know is well what actually takes the + + + align:start position:0% +know is well what actually takes the +computer time what takes the computer + + align:start position:0% +computer time what takes the computer + + + align:start position:0% +computer time what takes the computer +time is doing mathematical operations so + + align:start position:0% +time is doing mathematical operations so + + + align:start position:0% +time is doing mathematical operations so +add subtract multiply divide if things + + align:start position:0% +add subtract multiply divide if things + + + align:start position:0% +add subtract multiply divide if things +like that and usually we measure the + + align:start position:0% +like that and usually we measure the + + + align:start position:0% +like that and usually we measure the +speed of a process of a CPU in terms of + + align:start position:0% +speed of a process of a CPU in terms of + + + align:start position:0% +speed of a process of a CPU in terms of +the number operations you can do per + + align:start position:0% +the number operations you can do per + + + align:start position:0% +the number operations you can do per +second and does anybody know the order + + align:start position:0% +second and does anybody know the order + + + align:start position:0% +second and does anybody know the order +of magnitude of operations per second + + align:start position:0% +of magnitude of operations per second + + + align:start position:0% +of magnitude of operations per second +the CPU on your computer can do yeah + + align:start position:0% +the CPU on your computer can do yeah + + + align:start position:0% +the CPU on your computer can do yeah +it's about a billion some some number of + + align:start position:0% +it's about a billion some some number of + + + align:start position:0% +it's about a billion some some number of +billion operations per second depending + + align:start position:0% +billion operations per second depending + + + align:start position:0% +billion operations per second depending +on how recent if model you have and all + + align:start position:0% +on how recent if model you have and all + + + align:start position:0% +on how recent if model you have and all +of you know how many whether you play + + align:start position:0% +of you know how many whether you play + + + align:start position:0% +of you know how many whether you play +video games or not you will do more or + + align:start position:0% +video games or not you will do more or + + + align:start position:0% +video games or not you will do more or +less than that but so that means that we + + align:start position:0% +less than that but so that means that we + + + align:start position:0% +less than that but so that means that we +are our computer in one hour can do + + align:start position:0% +are our computer in one hour can do + + + align:start position:0% +are our computer in one hour can do +about one + + align:start position:0% +about one + + + align:start position:0% +about one +and now I'm gonna round up and say say + + align:start position:0% +and now I'm gonna round up and say say + + + align:start position:0% +and now I'm gonna round up and say say +you've got a really good ones we're + + align:start position:0% +you've got a really good ones we're + + + align:start position:0% +you've got a really good ones we're +gonna say it's got the earthing can do + + align:start position:0% +gonna say it's got the earthing can do + + + align:start position:0% +gonna say it's got the earthing can do +ten billion operations of a second if + + align:start position:0% +ten billion operations of a second if + + + align:start position:0% +ten billion operations of a second if +you've got multiple cores they can do + + align:start position:0% +you've got multiple cores they can do + + + align:start position:0% +you've got multiple cores they can do +they can each go independently so so one + + align:start position:0% +they can each go independently so so one + + + align:start position:0% +they can each go independently so so one +times ten to the ten operations per + + align:start position:0% +times ten to the ten operations per + + + align:start position:0% +times ten to the ten operations per +second and that means that you can do + + align:start position:0% +second and that means that you can do + + + align:start position:0% +second and that means that you can do +about three times ten to the thirteen + + align:start position:0% +about three times ten to the thirteen + + + align:start position:0% +about three times ten to the thirteen +operations in an hour + + align:start position:0% +operations in an hour + + + align:start position:0% +operations in an hour +I'm just gonna set the hour is my + + align:start position:0% +I'm just gonna set the hour is my + + + align:start position:0% +I'm just gonna set the hour is my +patience limit I don't want to wait + + align:start position:0% +patience limit I don't want to wait + + + align:start position:0% +patience limit I don't want to wait +longer than an hour and so then for + + align:start position:0% +longer than an hour and so then for + + + align:start position:0% +longer than an hour and so then for +hartree-fock the rate determining step + + align:start position:0% +hartree-fock the rate determining step + + + align:start position:0% +hartree-fock the rate determining step +is computing the eigenvalues of the hem + + align:start position:0% +is computing the eigenvalues of the hem + + + align:start position:0% +is computing the eigenvalues of the hem +of the hamiltonian and that requires and + + align:start position:0% +of the hamiltonian and that requires and + + + align:start position:0% +of the hamiltonian and that requires and +cubed operations so where n is the + + align:start position:0% +cubed operations so where n is the + + + align:start position:0% +cubed operations so where n is the +dimension of the matrix so if our matrix + + align:start position:0% +dimension of the matrix so if our matrix + + + align:start position:0% +dimension of the matrix so if our matrix +is n basis on a side it requires n cubed + + align:start position:0% +is n basis on a side it requires n cubed + + + align:start position:0% +is n basis on a side it requires n cubed +and basis functions cubed operations and + + align:start position:0% +and basis functions cubed operations and + + + align:start position:0% +and basis functions cubed operations and +so then again using our translation of + + align:start position:0% +so then again using our translation of + + + align:start position:0% +so then again using our translation of +that into atoms that's 15 times the + + align:start position:0% +that into atoms that's 15 times the + + + align:start position:0% +that into atoms that's 15 times the +number of atoms cubed which if I did my + + align:start position:0% +number of atoms cubed which if I did my + + + align:start position:0% +number of atoms cubed which if I did my +math right back in my office that's + + align:start position:0% +math right back in my office that's + + + align:start position:0% +math right back in my office that's +about three thousand a cubed and then if + + align:start position:0% +about three thousand a cubed and then if + + + align:start position:0% +about three thousand a cubed and then if +I back that out again if I compare that + + align:start position:0% +I back that out again if I compare that + + + align:start position:0% +I back that out again if I compare that +to the number of operations that gives + + align:start position:0% +to the number of operations that gives + + + align:start position:0% +to the number of operations that gives +me a limit on the number of atoms that I + + align:start position:0% +me a limit on the number of atoms that I + + + align:start position:0% +me a limit on the number of atoms that I +can handle in an hour and that turns out + + align:start position:0% +can handle in an hour and that turns out + + + align:start position:0% +can handle in an hour and that turns out +to be about one thousand so similar + + align:start position:0% +to be about one thousand so similar + + + align:start position:0% +to be about one thousand so similar +sizes so inter I run out of storage + + align:start position:0% +sizes so inter I run out of storage + + + align:start position:0% +sizes so inter I run out of storage +about the same time as I run out of + + align:start position:0% +about the same time as I run out of + + + align:start position:0% +about the same time as I run out of +patience if I was willing to be a little + + align:start position:0% +patience if I was willing to be a little + + + align:start position:0% +patience if I was willing to be a little +bit more patient I might be able to do a + + align:start position:0% +bit more patient I might be able to do a + + + align:start position:0% +bit more patient I might be able to do a +few more but order of magnitude we're at + + align:start position:0% +few more but order of magnitude we're at + + + align:start position:0% +few more but order of magnitude we're at +a thousand so the so I'll summarize what + + align:start position:0% +a thousand so the so I'll summarize what + + + align:start position:0% +a thousand so the so I'll summarize what +we found here is that the storage + + align:start position:0% +we found here is that the storage + + + align:start position:0% +we found here is that the storage +requirements dependent were something + + align:start position:0% +requirements dependent were something + + + align:start position:0% +requirements dependent were something +like a squared of order a squared the + + align:start position:0% +like a squared of order a squared the + + + align:start position:0% +like a squared of order a squared the +CPU time was of order a cubed the + + align:start position:0% +CPU time was of order a cubed the + + + align:start position:0% +CPU time was of order a cubed the +maximum feasible number of basis + + align:start position:0% +maximum feasible number of basis + + + align:start position:0% +maximum feasible number of basis +functions that I could do here so where + + align:start position:0% +functions that I could do here so where + + + align:start position:0% +functions that I could do here so where +it was something like so if I have a + + align:start position:0% +it was something like so if I have a + + + align:start position:0% +it was something like so if I have a +thousand atoms that was my limit + + align:start position:0% +thousand atoms that was my limit + + + align:start position:0% +thousand atoms that was my limit +something like fifteen thousand would be + + align:start position:0% +something like fifteen thousand would be + + + align:start position:0% +something like fifteen thousand would be +the maximum piece + + align:start position:0% +the maximum piece + + + align:start position:0% +the maximum piece +a number of basis functions and maximum + + align:start position:0% +a number of basis functions and maximum + + + align:start position:0% +a number of basis functions and maximum +feasible number of atoms was about a + + align:start position:0% +feasible number of atoms was about a + + + align:start position:0% +feasible number of atoms was about a +thousand okay so we won't go through the + + align:start position:0% +thousand okay so we won't go through the + + + align:start position:0% +thousand okay so we won't go through the +same exercise for mp2 in such detail I + + align:start position:0% +same exercise for mp2 in such detail I + + + align:start position:0% +same exercise for mp2 in such detail I +will just tell you that everything is + + align:start position:0% +will just tell you that everything is + + + align:start position:0% +will just tell you that everything is +worse for mp2 everything takes longer it + + align:start position:0% +worse for mp2 everything takes longer it + + + align:start position:0% +worse for mp2 everything takes longer it +takes more storage everything's worse + + align:start position:0% +takes more storage everything's worse + + + align:start position:0% +takes more storage everything's worse +so it requires order a cubed storage + + align:start position:0% +so it requires order a cubed storage + + + align:start position:0% +so it requires order a cubed storage +requires order a to the fifth CPU time + + align:start position:0% +requires order a to the fifth CPU time + + + align:start position:0% +requires order a to the fifth CPU time +the maximum feasible number of basis + + align:start position:0% +the maximum feasible number of basis + + + align:start position:0% +the maximum feasible number of basis +functions is therefore smaller about + + align:start position:0% +functions is therefore smaller about + + + align:start position:0% +functions is therefore smaller about +2000 and in mp2 you actually require + + align:start position:0% +2000 and in mp2 you actually require + + + align:start position:0% +2000 and in mp2 you actually require +more basis functions per atom to get an + + align:start position:0% +more basis functions per atom to get an + + + align:start position:0% +more basis functions per atom to get an +accurate answer so that the number of + + align:start position:0% +accurate answer so that the number of + + + align:start position:0% +accurate answer so that the number of +feasible atoms is more like 50 so that's + + align:start position:0% +feasible atoms is more like 50 so that's + + + align:start position:0% +feasible atoms is more like 50 so that's +the cumulative effect of larger basis + + align:start position:0% +the cumulative effect of larger basis + + + align:start position:0% +the cumulative effect of larger basis +sets and we're scaling with number of + + align:start position:0% +sets and we're scaling with number of + + + align:start position:0% +sets and we're scaling with number of +atoms that makes MP to deal with such + + align:start position:0% +atoms that makes MP to deal with such + + + align:start position:0% +atoms that makes MP to deal with such +small + + align:start position:0% +small + + + align:start position:0% +small +much smaller systems so questions about + + align:start position:0% +much smaller systems so questions about + + + align:start position:0% +much smaller systems so questions about +that no yes yes so C 60 is 60 atoms + + align:start position:0% +that no yes yes so C 60 is 60 atoms + + + align:start position:0% +that no yes yes so C 60 is 60 atoms +that's that's an easy one there are a + + align:start position:0% +that's that's an easy one there are a + + + align:start position:0% +that's that's an easy one there are a +number of small dies for example that we + + align:start position:0% +number of small dies for example that we + + + align:start position:0% +number of small dies for example that we +work with in our group that you know + + align:start position:0% +work with in our group that you know + + + align:start position:0% +work with in our group that you know +where you might read an absorption + + align:start position:0% +where you might read an absorption + + + align:start position:0% +where you might read an absorption +spectrum emission spectra or homos + + align:start position:0% +spectrum emission spectra or homos + + + align:start position:0% +spectrum emission spectra or homos +illumos or hole transport properties or + + align:start position:0% +illumos or hole transport properties or + + + align:start position:0% +illumos or hole transport properties or +or electron transport properties that + + align:start position:0% +or electron transport properties that + + + align:start position:0% +or electron transport properties that +are around 50 atoms in size and then the + + align:start position:0% +are around 50 atoms in size and then the + + + align:start position:0% +are around 50 atoms in size and then the +main thing that people get interested in + + align:start position:0% +main thing that people get interested in + + + align:start position:0% +main thing that people get interested in +that are and the thousand atom regimes + + align:start position:0% +that are and the thousand atom regimes + + + align:start position:0% +that are and the thousand atom regimes +are enzymes and peptides those are the + + align:start position:0% +are enzymes and peptides those are the + + + align:start position:0% +are enzymes and peptides those are the +sort of when you start saying oh I want + + align:start position:0% +sort of when you start saying oh I want + + + align:start position:0% +sort of when you start saying oh I want +to do a thousand atoms it's usually + + align:start position:0% +to do a thousand atoms it's usually + + + align:start position:0% +to do a thousand atoms it's usually +because it's really some polymer or + + align:start position:0% +because it's really some polymer or + + + align:start position:0% +because it's really some polymer or +hetero polymer another case where you + + align:start position:0% +hetero polymer another case where you + + + align:start position:0% +hetero polymer another case where you +also are sometimes interested in things + + align:start position:0% +also are sometimes interested in things + + + align:start position:0% +also are sometimes interested in things +where you do simulations for a thousand + + align:start position:0% +where you do simulations for a thousand + + + align:start position:0% +where you do simulations for a thousand +items if you're interested in a surface + + align:start position:0% +items if you're interested in a surface + + + align:start position:0% +items if you're interested in a surface +because if you have a chunk of gold for + + align:start position:0% +because if you have a chunk of gold for + + + align:start position:0% +because if you have a chunk of gold for +example a thousand I understand just ten + + align:start position:0% +example a thousand I understand just ten + + + align:start position:0% +example a thousand I understand just ten +gold atoms by ten gold atoms by ten gold + + align:start position:0% +gold atoms by ten gold atoms by ten gold + + + align:start position:0% +gold atoms by ten gold atoms by ten gold +atoms which is just a little chunk of + + align:start position:0% +atoms which is just a little chunk of + + + align:start position:0% +atoms which is just a little chunk of +very very small chunk of gold but still + + align:start position:0% +very very small chunk of gold but still + + + align:start position:0% +very very small chunk of gold but still +a chunk + + align:start position:0% + + + + align:start position:0% + +other questions + + align:start position:0% + + + + align:start position:0% + +okay so there's I'm going to spend seven + + align:start position:0% +okay so there's I'm going to spend seven + + + align:start position:0% +okay so there's I'm going to spend seven +minutes talking about density functional + + align:start position:0% +minutes talking about density functional + + + align:start position:0% +minutes talking about density functional +theory and then we're gonna go over and + + align:start position:0% +theory and then we're gonna go over and + + + align:start position:0% +theory and then we're gonna go over and +do do some examples so the idea of + + align:start position:0% +do do some examples so the idea of + + + align:start position:0% +do do some examples so the idea of +density functional theory is that it'd + + align:start position:0% +density functional theory is that it'd + + + align:start position:0% +density functional theory is that it'd +be really nice if you had some magical + + align:start position:0% +be really nice if you had some magical + + + align:start position:0% +be really nice if you had some magical +way to do a heart rate calculation but + + align:start position:0% +way to do a heart rate calculation but + + + align:start position:0% +way to do a heart rate calculation but +have a give you exactly the right answer + + align:start position:0% +have a give you exactly the right answer + + + align:start position:0% +have a give you exactly the right answer +that's basically that would be did the + + align:start position:0% +that's basically that would be did the + + + align:start position:0% +that's basically that would be did the +dream because we saw well you know four + + align:start position:0% +dream because we saw well you know four + + + align:start position:0% +dream because we saw well you know four +hundred five we can do big systems it's + + align:start position:0% +hundred five we can do big systems it's + + + align:start position:0% +hundred five we can do big systems it's +cheap as you know good scaling all these + + align:start position:0% +cheap as you know good scaling all these + + + align:start position:0% +cheap as you know good scaling all these +kinds of things just doesn't give us + + align:start position:0% +kinds of things just doesn't give us + + + align:start position:0% +kinds of things just doesn't give us +very good answer so that the results are + + align:start position:0% +very good answer so that the results are + + + align:start position:0% +very good answer so that the results are +pretty poor so what have you had + + align:start position:0% +pretty poor so what have you had + + + align:start position:0% +pretty poor so what have you had +something that's that scale like it had + + align:start position:0% +something that's that scale like it had + + + align:start position:0% +something that's that scale like it had +the computational cost of hartree-fock + + align:start position:0% +the computational cost of hartree-fock + + + align:start position:0% +the computational cost of hartree-fock +but was say the accuracy of MP two or + + align:start position:0% +but was say the accuracy of MP two or + + + align:start position:0% +but was say the accuracy of MP two or +even better than that + + align:start position:0% +even better than that + + + align:start position:0% +even better than that +and so in density functional theory what + + align:start position:0% +and so in density functional theory what + + + align:start position:0% +and so in density functional theory what +we use is the idea of looking at the + + align:start position:0% +we use is the idea of looking at the + + + align:start position:0% +we use is the idea of looking at the +electron density Rho of R as the + + align:start position:0% +electron density Rho of R as the + + + align:start position:0% +electron density Rho of R as the +fundamental variable so you can actually + + align:start position:0% +fundamental variable so you can actually + + + align:start position:0% +fundamental variable so you can actually +work out for a determinant what the + + align:start position:0% +work out for a determinant what the + + + align:start position:0% +work out for a determinant what the +electron density is and it's just the + + align:start position:0% +electron density is and it's just the + + + align:start position:0% +electron density is and it's just the +sum of the squares of the orbital + + align:start position:0% +sum of the squares of the orbital + + + align:start position:0% +sum of the squares of the orbital +densities so you square each or the sum + + align:start position:0% +densities so you square each or the sum + + + align:start position:0% +densities so you square each or the sum +of the orbit lens so you square each + + align:start position:0% +of the orbit lens so you square each + + + align:start position:0% +of the orbit lens so you square each +orbital then you add that up but that + + align:start position:0% +orbital then you add that up but that + + + align:start position:0% +orbital then you add that up but that +gives you the total electron density + + align:start position:0% +gives you the total electron density + + + align:start position:0% +gives you the total electron density +it's basically they're just the + + align:start position:0% +it's basically they're just the + + + align:start position:0% +it's basically they're just the +probability of finding an electron at a + + align:start position:0% +probability of finding an electron at a + + + align:start position:0% +probability of finding an electron at a +point R so + + align:start position:0% + + + + align:start position:0% + +okay so that's a nice observable the + + align:start position:0% +okay so that's a nice observable the + + + align:start position:0% +okay so that's a nice observable the +thing that's kind of amazing is that + + align:start position:0% +thing that's kind of amazing is that + + + align:start position:0% +thing that's kind of amazing is that +there is a theorem a mathematical + + align:start position:0% +there is a theorem a mathematical + + + align:start position:0% +there is a theorem a mathematical +theorem that you can prove in about two + + align:start position:0% +theorem that you can prove in about two + + + align:start position:0% +theorem that you can prove in about two +pages using just sort of proof by + + align:start position:0% +pages using just sort of proof by + + + align:start position:0% +pages using just sort of proof by +contradiction you can prove that there + + align:start position:0% +contradiction you can prove that there + + + align:start position:0% +contradiction you can prove that there +exists a functional which is always + + align:start position:0% +exists a functional which is always + + + align:start position:0% +exists a functional which is always +given the name ISA V of Rho such that + + align:start position:0% +given the name ISA V of Rho such that + + + align:start position:0% +given the name ISA V of Rho such that +when you're given the ground state + + align:start position:0% +when you're given the ground state + + + align:start position:0% +when you're given the ground state +density Rho zero if you plug that into + + align:start position:0% +density Rho zero if you plug that into + + + align:start position:0% +density Rho zero if you plug that into +this magical functional it will give you + + align:start position:0% +this magical functional it will give you + + + align:start position:0% +this magical functional it will give you +the ground state energy so if you found + + align:start position:0% +the ground state energy so if you found + + + align:start position:0% +the ground state energy so if you found +the ground state density lying around in + + align:start position:0% +the ground state density lying around in + + + align:start position:0% +the ground state density lying around in +the gutter and you picked it up and you + + align:start position:0% +the gutter and you picked it up and you + + + align:start position:0% +the gutter and you picked it up and you +put it into this functional it would + + align:start position:0% +put it into this functional it would + + + align:start position:0% +put it into this functional it would +give you the ground state energy and + + align:start position:0% +give you the ground state energy and + + + align:start position:0% +give you the ground state energy and +easy Rho is not just the approximate + + align:start position:0% +easy Rho is not just the approximate + + + align:start position:0% +easy Rho is not just the approximate +cross that energy it is the exact ground + + align:start position:0% +cross that energy it is the exact ground + + + align:start position:0% +cross that energy it is the exact ground +state energy exact thing further any + + align:start position:0% +state energy exact thing further any + + + align:start position:0% +state energy exact thing further any +dents for any density Rho prime that is + + align:start position:0% +dents for any density Rho prime that is + + + align:start position:0% +dents for any density Rho prime that is +not the ground state density if you plug + + align:start position:0% +not the ground state density if you plug + + + align:start position:0% +not the ground state density if you plug +that intensity into e V you get a higher + + align:start position:0% +that intensity into e V you get a higher + + + align:start position:0% +that intensity into e V you get a higher +energy so what you could do is you could + + align:start position:0% +energy so what you could do is you could + + + align:start position:0% +energy so what you could do is you could +say well let me just search let me try + + align:start position:0% +say well let me just search let me try + + + align:start position:0% +say well let me just search let me try +density see what energy it gives and + + align:start position:0% +density see what energy it gives and + + + align:start position:0% +density see what energy it gives and +I'll try another time see if it gives + + align:start position:0% +I'll try another time see if it gives + + + align:start position:0% +I'll try another time see if it gives +them a lower energy that's a better + + align:start position:0% +them a lower energy that's a better + + + align:start position:0% +them a lower energy that's a better +density and I'll keep going and going + + align:start position:0% +density and I'll keep going and going + + + align:start position:0% +density and I'll keep going and going +and going and going until I find that + + align:start position:0% +and going and going until I find that + + + align:start position:0% +and going and going until I find that +ground state density so the idea is that + + align:start position:0% +ground state density so the idea is that + + + align:start position:0% +ground state density so the idea is that +then you would say aha + + align:start position:0% +then you would say aha + + + align:start position:0% +then you would say aha +if I do solve that equation so I + + align:start position:0% +if I do solve that equation so I + + + align:start position:0% +if I do solve that equation so I +searched over densities and that's not + + align:start position:0% +searched over densities and that's not + + + align:start position:0% +searched over densities and that's not +going to be a very hard search because + + align:start position:0% +going to be a very hard search because + + + align:start position:0% +going to be a very hard search because +the density is just a three dimensional + + align:start position:0% +the density is just a three dimensional + + + align:start position:0% +the density is just a three dimensional +object it's not like the wave function + + align:start position:0% +object it's not like the wave function + + + align:start position:0% +object it's not like the wave function +that depends on a bunch of coordinates + + align:start position:0% +that depends on a bunch of coordinates + + + align:start position:0% +that depends on a bunch of coordinates +just three dimensional so I solved that + + align:start position:0% +just three dimensional so I solved that + + + align:start position:0% +just three dimensional so I solved that +equation that will give me Rho zero and + + align:start position:0% +equation that will give me Rho zero and + + + align:start position:0% +equation that will give me Rho zero and +then I can take that Rho zero I'll get + + align:start position:0% +then I can take that Rho zero I'll get + + + align:start position:0% +then I can take that Rho zero I'll get +back in there and I will get the ground + + align:start position:0% +back in there and I will get the ground + + + align:start position:0% +back in there and I will get the ground +state energy that gives me a closed set + + align:start position:0% +state energy that gives me a closed set + + + align:start position:0% +state energy that gives me a closed set +of conditions that lets me find the + + align:start position:0% +of conditions that lets me find the + + + align:start position:0% +of conditions that lets me find the +ground state energy and then report back + + align:start position:0% +ground state energy and then report back + + + align:start position:0% +ground state energy and then report back +the energy of that density that's a + + align:start position:0% +the energy of that density that's a + + + align:start position:0% +the energy of that density that's a +great question the the proof is a proof + + align:start position:0% +great question the the proof is a proof + + + align:start position:0% +great question the the proof is a proof +by contradiction it's not constructive + + align:start position:0% +by contradiction it's not constructive + + + align:start position:0% +by contradiction it's not constructive +it proves that it exists but gives you + + align:start position:0% +it proves that it exists but gives you + + + align:start position:0% +it proves that it exists but gives you +no way of constructing it so so it's a + + align:start position:0% +no way of constructing it so so it's a + + + align:start position:0% +no way of constructing it so so it's a +it's kind of the frustrating thing it's + + align:start position:0% +it's kind of the frustrating thing it's + + + align:start position:0% +it's kind of the frustrating thing it's +like Oh cookies exist but we don't know + + align:start position:0% +like Oh cookies exist but we don't know + + + align:start position:0% +like Oh cookies exist but we don't know +how to make them so + + align:start position:0% +how to make them so + + + align:start position:0% +how to make them so +so but but the idea that such a thing + + align:start position:0% +so but but the idea that such a thing + + + align:start position:0% +so but but the idea that such a thing +exists gives you it gives you hope to + + align:start position:0% +exists gives you it gives you hope to + + + align:start position:0% +exists gives you it gives you hope to +say well maybe we can construct if we + + align:start position:0% +say well maybe we can construct if we + + + align:start position:0% +say well maybe we can construct if we +can't find the exact one maybe we can + + align:start position:0% +can't find the exact one maybe we can + + + align:start position:0% +can't find the exact one maybe we can +find one that's very very good and that + + align:start position:0% +find one that's very very good and that + + + align:start position:0% +find one that's very very good and that +one that's very good we would just use + + align:start position:0% +one that's very good we would just use + + + align:start position:0% +one that's very good we would just use +we would pretend it was exact minimize + + align:start position:0% +we would pretend it was exact minimize + + + align:start position:0% +we would pretend it was exact minimize +the energy find the density and then + + align:start position:0% +the energy find the density and then + + + align:start position:0% +the energy find the density and then +report back to the ground state for that + + align:start position:0% +report back to the ground state for that + + + align:start position:0% +report back to the ground state for that +approximate thing and that's actually + + align:start position:0% +approximate thing and that's actually + + + align:start position:0% +approximate thing and that's actually +what you do in density functional theory + + align:start position:0% +what you do in density functional theory + + + align:start position:0% +what you do in density functional theory +you have approximate functionals and + + align:start position:0% +you have approximate functionals and + + + align:start position:0% +you have approximate functionals and +they're all just like with basis sets + + align:start position:0% +they're all just like with basis sets + + + align:start position:0% +they're all just like with basis sets +named after the authors of the people + + align:start position:0% +named after the authors of the people + + + align:start position:0% +named after the authors of the people +who wrote the papers almost all of them + + align:start position:0% +who wrote the papers almost all of them + + + align:start position:0% +who wrote the papers almost all of them +are so there's the local spin density + + align:start position:0% +are so there's the local spin density + + + align:start position:0% +are so there's the local spin density +approximation lsda there's the Purdue + + align:start position:0% +approximation lsda there's the Purdue + + + align:start position:0% +approximation lsda there's the Purdue +Burk Aaron's Ehrhoff functional + + align:start position:0% +Burk Aaron's Ehrhoff functional + + + align:start position:0% +Burk Aaron's Ehrhoff functional +there's the Becky Li yang par functional + + align:start position:0% +there's the Becky Li yang par functional + + + align:start position:0% +there's the Becky Li yang par functional +the Purdue Burk Aaron's Ehrhoff zero + + align:start position:0% +the Purdue Burk Aaron's Ehrhoff zero + + + align:start position:0% +the Purdue Burk Aaron's Ehrhoff zero +functional the Becky three Li yang are + + align:start position:0% +functional the Becky three Li yang are + + + align:start position:0% +functional the Becky three Li yang are +functional and then on and on and on now + + align:start position:0% +functional and then on and on and on now + + + align:start position:0% +functional and then on and on and on now +these things have been sort of there's a + + align:start position:0% +these things have been sort of there's a + + + align:start position:0% +these things have been sort of there's a +mishmash of different exact conditions + + align:start position:0% +mishmash of different exact conditions + + + align:start position:0% +mishmash of different exact conditions +that are you that it were used to derive + + align:start position:0% +that are you that it were used to derive + + + align:start position:0% +that are you that it were used to derive +these functionals and then empirically + + align:start position:0% +these functionals and then empirically + + + align:start position:0% +these functionals and then empirically +people have gone and shown that PBE is + + align:start position:0% +people have gone and shown that PBE is + + + align:start position:0% +people have gone and shown that PBE is +better than LSD a it's about as good as + + align:start position:0% +better than LSD a it's about as good as + + + align:start position:0% +better than LSD a it's about as good as +blip-blip is not as good as PB e zero + + align:start position:0% +blip-blip is not as good as PB e zero + + + align:start position:0% +blip-blip is not as good as PB e zero +but it is just about as good as b3 live + + align:start position:0% +but it is just about as good as b3 live + + + align:start position:0% +but it is just about as good as b3 live +so so we have then sort of an idea that + + align:start position:0% +so so we have then sort of an idea that + + + align:start position:0% +so so we have then sort of an idea that +okay if we go over towards the right + + align:start position:0% +okay if we go over towards the right + + + align:start position:0% +okay if we go over towards the right +hand side of this we're gonna get better + + align:start position:0% +hand side of this we're gonna get better + + + align:start position:0% +hand side of this we're gonna get better +results out of DFT + + align:start position:0% +results out of DFT + + + align:start position:0% +results out of DFT +but DFT because it's based off of a + + align:start position:0% +but DFT because it's based off of a + + + align:start position:0% +but DFT because it's based off of a +Slater determinant has exactly the same + + align:start position:0% +Slater determinant has exactly the same + + + align:start position:0% +Slater determinant has exactly the same +computational scaling and storage and + + align:start position:0% +computational scaling and storage and + + + align:start position:0% +computational scaling and storage and +everything as hartree-fock it's same + + align:start position:0% +everything as hartree-fock it's same + + + align:start position:0% +everything as hartree-fock it's same +kind of expense but if I go back to this + + align:start position:0% +kind of expense but if I go back to this + + + align:start position:0% +kind of expense but if I go back to this +accuracy thing and I say well what would + + align:start position:0% +accuracy thing and I say well what would + + + align:start position:0% +accuracy thing and I say well what would +I get from that best density functional + + align:start position:0% +I get from that best density functional + + + align:start position:0% +I get from that best density functional +whoopsy lip best density functional b3 + + align:start position:0% +whoopsy lip best density functional b3 + + + align:start position:0% +whoopsy lip best density functional b3 +lip well what I find is that activation + + align:start position:0% +lip well what I find is that activation + + + align:start position:0% +lip well what I find is that activation +energies are still a little bit + + align:start position:0% +energies are still a little bit + + + align:start position:0% +energies are still a little bit +difficult now I under product activation + + align:start position:0% +difficult now I under product activation + + + align:start position:0% +difficult now I under product activation +energies but my dipole moments are good + + align:start position:0% +energies but my dipole moments are good + + + align:start position:0% +energies but my dipole moments are good +my sizes are again accurate + + align:start position:0% +my sizes are again accurate + + + align:start position:0% +my sizes are again accurate +my absorption energy absorption energies + + align:start position:0% +my absorption energy absorption energies + + + align:start position:0% +my absorption energy absorption energies +are just as accurate as mp2 and my bond + + align:start position:0% +are just as accurate as mp2 and my bond + + + align:start position:0% +are just as accurate as mp2 and my bond +lengths are just as accurate as MP - + + align:start position:0% + + + + align:start position:0% + +there are other things but basically B 3 + + align:start position:0% +there are other things but basically B 3 + + + align:start position:0% +there are other things but basically B 3 +lip is as accurate or more accurate than + + align:start position:0% +lip is as accurate or more accurate than + + + align:start position:0% +lip is as accurate or more accurate than +MP 2 for virtually every property you + + align:start position:0% +MP 2 for virtually every property you + + + align:start position:0% +MP 2 for virtually every property you +would want but has hartree-fock light + + align:start position:0% +would want but has hartree-fock light + + + align:start position:0% +would want but has hartree-fock light +cost and so that makes density + + align:start position:0% +cost and so that makes density + + + align:start position:0% +cost and so that makes density +functional theory the workhorse of + + align:start position:0% +functional theory the workhorse of + + + align:start position:0% +functional theory the workhorse of +computational chemistry these days + + align:start position:0% +computational chemistry these days + + + align:start position:0% +computational chemistry these days +because it's inexpensive you can do lots + + align:start position:0% +because it's inexpensive you can do lots + + + align:start position:0% +because it's inexpensive you can do lots +of calculations with it but it's it's + + align:start position:0% +of calculations with it but it's it's + + + align:start position:0% +of calculations with it but it's it's +it's accurate enough for for grunt work + + align:start position:0% +it's accurate enough for for grunt work + + + align:start position:0% +it's accurate enough for for grunt work +and then there's a blank column there + + align:start position:0% +and then there's a blank column there + + + align:start position:0% +and then there's a blank column there +that if I had time I would talk about + + align:start position:0% +that if I had time I would talk about + + + align:start position:0% +that if I had time I would talk about +there's a whole other category of things + + align:start position:0% +there's a whole other category of things + + + align:start position:0% +there's a whole other category of things +where you say what well perturbation + + align:start position:0% +where you say what well perturbation + + + align:start position:0% +where you say what well perturbation +Theory doesn't work but are there more + + align:start position:0% +Theory doesn't work but are there more + + + align:start position:0% +Theory doesn't work but are there more +constructive ways that I could use wave + + align:start position:0% +constructive ways that I could use wave + + + align:start position:0% +constructive ways that I could use wave +functions to approximate the correlation + + align:start position:0% +functions to approximate the correlation + + + align:start position:0% +functions to approximate the correlation +energy and the answer is yes you can get + + align:start position:0% +energy and the answer is yes you can get + + + align:start position:0% +energy and the answer is yes you can get +good or good energies and good answers + + align:start position:0% +good or good energies and good answers + + + align:start position:0% +good or good energies and good answers +out but then it comes to the cost of the + + align:start position:0% +out but then it comes to the cost of the + + + align:start position:0% +out but then it comes to the cost of the +calculation getting much more expensive + + align:start position:0% +calculation getting much more expensive + + + align:start position:0% +calculation getting much more expensive +so there are methods that that improve + + align:start position:0% +so there are methods that that improve + + + align:start position:0% +so there are methods that that improve +the prove all these properties on the + + align:start position:0% +the prove all these properties on the + + + align:start position:0% +the prove all these properties on the +wave function side that just require + + align:start position:0% +wave function side that just require + + + align:start position:0% +wave function side that just require +more so you want to learn more about + + align:start position:0% +more so you want to learn more about + + + align:start position:0% +more so you want to learn more about +those there in the notes and so now I + + align:start position:0% +those there in the notes and so now I + + + align:start position:0% +those there in the notes and so now I +think I will switch over and show you + + align:start position:0% +think I will switch over and show you + + + align:start position:0% +think I will switch over and show you +how we do some calculations with this + + align:start position:0% +how we do some calculations with this + + + align:start position:0% +how we do some calculations with this +now I will switch there's two different + + align:start position:0% +now I will switch there's two different + + + align:start position:0% +now I will switch there's two different +tools that you have available to you for + + align:start position:0% +tools that you have available to you for + + + align:start position:0% +tools that you have available to you for +free on Athena that you can use to do + + align:start position:0% +free on Athena that you can use to do + + + align:start position:0% +free on Athena that you can use to do +electronic structure calculations one is + + align:start position:0% +electronic structure calculations one is + + + align:start position:0% +electronic structure calculations one is +gaussian and the other one is q chem + + align:start position:0% +gaussian and the other one is q chem + + + align:start position:0% +gaussian and the other one is q chem +there may be even some other ones but + + align:start position:0% +there may be even some other ones but + + + align:start position:0% +there may be even some other ones but +those are the two that I've collected + + align:start position:0% +those are the two that I've collected + + + align:start position:0% +those are the two that I've collected +notes about how to use so I'm gonna show + + align:start position:0% +notes about how to use so I'm gonna show + + + align:start position:0% +notes about how to use so I'm gonna show +you how we use Q chem I'm not gonna do + + align:start position:0% +you how we use Q chem I'm not gonna do + + + align:start position:0% +you how we use Q chem I'm not gonna do +it on Athena I'm gonna do it on my + + align:start position:0% +it on Athena I'm gonna do it on my + + + align:start position:0% +it on Athena I'm gonna do it on my +laptop + + align:start position:0% +laptop + + + align:start position:0% +laptop +but it's basically the same so there's + + align:start position:0% +but it's basically the same so there's + + + align:start position:0% +but it's basically the same so there's +this GUI called IQ Moll and when you + + align:start position:0% +this GUI called IQ Moll and when you + + + align:start position:0% +this GUI called IQ Moll and when you +open it up it gives you a window that + + align:start position:0% +open it up it gives you a window that + + + align:start position:0% +open it up it gives you a window that +looks like this and there's a few things + + align:start position:0% +looks like this and there's a few things + + + align:start position:0% +looks like this and there's a few things +here so there's like an open file a new + + align:start position:0% +here so there's like an open file a new + + + align:start position:0% +here so there's like an open file a new +you can create a new file something you + + align:start position:0% +you can create a new file something you + + + align:start position:0% +you can create a new file something you +can open a file you can save something + + align:start position:0% +can open a file you can save something + + + align:start position:0% +can open a file you can save something +you can move something around after you + + align:start position:0% +you can move something around after you + + + align:start position:0% +you can move something around after you +built it and then these are the build + + align:start position:0% +built it and then these are the build + + + align:start position:0% +built it and then these are the build +tools over here so this that just says + + align:start position:0% +tools over here so this that just says + + + align:start position:0% +tools over here so this that just says +build turns it into bill + + align:start position:0% +build turns it into bill + + + align:start position:0% +build turns it into bill +mode if I click on this I can choose any + + align:start position:0% +mode if I click on this I can choose any + + + align:start position:0% +mode if I click on this I can choose any +atom in the periodic table right now + + align:start position:0% +atom in the periodic table right now + + + align:start position:0% +atom in the periodic table right now +it's on carbon this lets me select + + align:start position:0% +it's on carbon this lets me select + + + align:start position:0% +it's on carbon this lets me select +various fragments and also what the + + align:start position:0% +various fragments and also what the + + + align:start position:0% +various fragments and also what the +attach point of the fragments going to + + align:start position:0% +attach point of the fragments going to + + + align:start position:0% +attach point of the fragments going to +be in some cases and I don't want to do + + align:start position:0% +be in some cases and I don't want to do + + + align:start position:0% +be in some cases and I don't want to do +so I'll select it for now but then I'm + + align:start position:0% +so I'll select it for now but then I'm + + + align:start position:0% +so I'll select it for now but then I'm +gonna go back to this one this is the + + align:start position:0% +gonna go back to this one this is the + + + align:start position:0% +gonna go back to this one this is the +add hydrogen's button so if you have + + align:start position:0% +add hydrogen's button so if you have + + + align:start position:0% +add hydrogen's button so if you have +something that you know you just wrote + + align:start position:0% +something that you know you just wrote + + + align:start position:0% +something that you know you just wrote +your lewis structure it had no hydrogens + + align:start position:0% +your lewis structure it had no hydrogens + + + align:start position:0% +your lewis structure it had no hydrogens +in it you click that button it'll put + + align:start position:0% +in it you click that button it'll put + + + align:start position:0% +in it you click that button it'll put +all the hydrogens where they should be + + align:start position:0% +all the hydrogens where they should be + + + align:start position:0% +all the hydrogens where they should be +or weird things they should be this is a + + align:start position:0% +or weird things they should be this is a + + + align:start position:0% +or weird things they should be this is a +minimize energy thing which basically if + + align:start position:0% +minimize energy thing which basically if + + + align:start position:0% +minimize energy thing which basically if +your structure looks really crazy it'll + + align:start position:0% +your structure looks really crazy it'll + + + align:start position:0% +your structure looks really crazy it'll +kind of make it look less crazy and and + + align:start position:0% +kind of make it look less crazy and and + + + align:start position:0% +kind of make it look less crazy and and +then this is the select button which + + align:start position:0% +then this is the select button which + + + align:start position:0% +then this is the select button which +lets you pick search atoms this lets you + + align:start position:0% +lets you pick search atoms this lets you + + + align:start position:0% +lets you pick search atoms this lets you +delete certain atoms take a picture do a + + align:start position:0% +delete certain atoms take a picture do a + + + align:start position:0% +delete certain atoms take a picture do a +movie then that sends it over to full + + align:start position:0% +movie then that sends it over to full + + + align:start position:0% +movie then that sends it over to full +screen mode and that's the life + + align:start position:0% +screen mode and that's the life + + + align:start position:0% +screen mode and that's the life +preserver for help but will do building + + align:start position:0% +preserver for help but will do building + + + align:start position:0% +preserver for help but will do building +a molecule so does somebody want to tell + + align:start position:0% +a molecule so does somebody want to tell + + + align:start position:0% +a molecule so does somebody want to tell +me a molecule that has less than 15 + + align:start position:0% +me a molecule that has less than 15 + + + align:start position:0% +me a molecule that has less than 15 +atoms in it that they would like me to + + align:start position:0% +atoms in it that they would like me to + + + align:start position:0% +atoms in it that they would like me to +draw here that I can actually draw + + align:start position:0% +draw here that I can actually draw + + + align:start position:0% +draw here that I can actually draw +diethyl ether yes I can do that okay all + + align:start position:0% +diethyl ether yes I can do that okay all + + + align:start position:0% +diethyl ether yes I can do that okay all +right so put a carbon carbon and I got a + + align:start position:0% +right so put a carbon carbon and I got a + + + align:start position:0% +right so put a carbon carbon and I got a +switch to it oxygen oxygen + + align:start position:0% + + + + align:start position:0% + +carbon/carbon and then I will click them + + align:start position:0% +carbon/carbon and then I will click them + + + align:start position:0% +carbon/carbon and then I will click them +out the add hydrogen button there we go + + align:start position:0% +out the add hydrogen button there we go + + + align:start position:0% +out the add hydrogen button there we go +I've got my diethyl ether now and while + + align:start position:0% +I've got my diethyl ether now and while + + + align:start position:0% +I've got my diethyl ether now and while +my geometry here is not perfect it + + align:start position:0% +my geometry here is not perfect it + + + align:start position:0% +my geometry here is not perfect it +doesn't look totally crazy so I'll just + + align:start position:0% +doesn't look totally crazy so I'll just + + + align:start position:0% +doesn't look totally crazy so I'll just +go with that and then the thing we're + + align:start position:0% +go with that and then the thing we're + + + align:start position:0% +go with that and then the thing we're +gonna be motion Asit in is this little + + align:start position:0% +gonna be motion Asit in is this little + + + align:start position:0% +gonna be motion Asit in is this little +tab here called calculation so if + + align:start position:0% +tab here called calculation so if + + + align:start position:0% +tab here called calculation so if +calculation here has a little button it + + align:start position:0% +calculation here has a little button it + + + align:start position:0% +calculation here has a little button it +says cue chem setup so cute chem setup + + align:start position:0% +says cue chem setup so cute chem setup + + + align:start position:0% +says cue chem setup so cute chem setup +and now it's got a bunch of things that + + align:start position:0% +and now it's got a bunch of things that + + + align:start position:0% +and now it's got a bunch of things that +I can specify the two things that are + + align:start position:0% +I can specify the two things that are + + + align:start position:0% +I can specify the two things that are +probably the there are a few things are + + align:start position:0% +probably the there are a few things are + + + align:start position:0% +probably the there are a few things are +most important so the first thing is + + align:start position:0% +most important so the first thing is + + + align:start position:0% +most important so the first thing is +what kind of calculation I want it to do + + align:start position:0% +what kind of calculation I want it to do + + + align:start position:0% +what kind of calculation I want it to do +so I could have it just compute the + + align:start position:0% +so I could have it just compute the + + + align:start position:0% +so I could have it just compute the +energy of the molecule for the + + align:start position:0% +energy of the molecule for the + + + align:start position:0% +energy of the molecule for the +configuration I specified that would be + + align:start position:0% +configuration I specified that would be + + + align:start position:0% +configuration I specified that would be +one useful thing I can compute forces in + + align:start position:0% +one useful thing I can compute forces in + + + align:start position:0% +one useful thing I can compute forces in +other words the forces on the atoms + + align:start position:0% +other words the forces on the atoms + + + align:start position:0% +other words the forces on the atoms +where the atoms want to move I could + + align:start position:0% +where the atoms want to move I could + + + align:start position:0% +where the atoms want to move I could +optimize the geometry which would then + + align:start position:0% +optimize the geometry which would then + + + align:start position:0% +optimize the geometry which would then +relax the thing down and figure out what + + align:start position:0% +relax the thing down and figure out what + + + align:start position:0% +relax the thing down and figure out what +the desk geometry is I can do various + + align:start position:0% +the desk geometry is I can do various + + + align:start position:0% +the desk geometry is I can do various +things that scan across the potential + + align:start position:0% +things that scan across the potential + + + align:start position:0% +things that scan across the potential +energy surface I can compute vibrational + + align:start position:0% +energy surface I can compute vibrational + + + align:start position:0% +energy surface I can compute vibrational +frequencies I can compute NMR chemical + + align:start position:0% +frequencies I can compute NMR chemical + + + align:start position:0% +frequencies I can compute NMR chemical +shifts I can do molecular dynamics I can + + align:start position:0% +shifts I can do molecular dynamics I can + + + align:start position:0% +shifts I can do molecular dynamics I can +compute properties so lots of things I'm + + align:start position:0% +compute properties so lots of things I'm + + + align:start position:0% +compute properties so lots of things I'm +just gonna optimize the geometry that's + + align:start position:0% +just gonna optimize the geometry that's + + + align:start position:0% +just gonna optimize the geometry that's +gonna be what I'm gonna choose for now + + align:start position:0% +gonna be what I'm gonna choose for now + + + align:start position:0% +gonna be what I'm gonna choose for now +and then I get to choose a method so I + + align:start position:0% +and then I get to choose a method so I + + + align:start position:0% +and then I get to choose a method so I +can do hartree-fock I can do b3 lip I + + align:start position:0% +can do hartree-fock I can do b3 lip I + + + align:start position:0% +can do hartree-fock I can do b3 lip I +can go down heat so here's of all the + + align:start position:0% +can go down heat so here's of all the + + + align:start position:0% +can go down heat so here's of all the +things above this dotted line here are + + align:start position:0% +things above this dotted line here are + + + align:start position:0% +things above this dotted line here are +different density functionals and then + + align:start position:0% +different density functionals and then + + + align:start position:0% +different density functionals and then +down here we've got MP 2 MP 2 bracket V + + align:start position:0% +down here we've got MP 2 MP 2 bracket V + + + align:start position:0% +down here we've got MP 2 MP 2 bracket V +I'm not actually sure what that is + + align:start position:0% +I'm not actually sure what that is + + + align:start position:0% +I'm not actually sure what that is +I've got various versions of MP 2 that + + align:start position:0% +I've got various versions of MP 2 that + + + align:start position:0% +I've got various versions of MP 2 that +try to make it faster and then I've got + + align:start position:0% +try to make it faster and then I've got + + + align:start position:0% +try to make it faster and then I've got +the couple cluster methods that we + + align:start position:0% +the couple cluster methods that we + + + align:start position:0% +the couple cluster methods that we +didn't talk about yet but that are in + + align:start position:0% +didn't talk about yet but that are in + + + align:start position:0% +didn't talk about yet but that are in +the notes and then various methods for + + align:start position:0% +the notes and then various methods for + + + align:start position:0% +the notes and then various methods for +getting electronic excited states down + + align:start position:0% +getting electronic excited states down + + + align:start position:0% +getting electronic excited states down +here at the bottom so for now let's just + + align:start position:0% +here at the bottom so for now let's just + + + align:start position:0% +here at the bottom so for now let's just +do b3 lip and then I get to choose a + + align:start position:0% +do b3 lip and then I get to choose a + + + align:start position:0% +do b3 lip and then I get to choose a +basis because this is on my laptop and + + align:start position:0% +basis because this is on my laptop and + + + align:start position:0% +basis because this is on my laptop and +we're in class I'm gonna choose a small + + align:start position:0% +we're in class I'm gonna choose a small + + + align:start position:0% +we're in class I'm gonna choose a small +basis so I'm gonna leave it at 3 to 1 G + + align:start position:0% +basis so I'm gonna leave it at 3 to 1 G + + + align:start position:0% +basis so I'm gonna leave it at 3 to 1 G +which is a small basis and + + align:start position:0% +which is a small basis and + + + align:start position:0% +which is a small basis and +and I can also specify the charge which + + align:start position:0% +and I can also specify the charge which + + + align:start position:0% +and I can also specify the charge which +is like the total charge of the molecule + + align:start position:0% +is like the total charge of the molecule + + + align:start position:0% +is like the total charge of the molecule +and the spin multiplicity so I want it + + align:start position:0% +and the spin multiplicity so I want it + + + align:start position:0% +and the spin multiplicity so I want it +to be a I wanted to be a neutral + + align:start position:0% +to be a I wanted to be a neutral + + + align:start position:0% +to be a I wanted to be a neutral +molecule spin one spins or spin + + align:start position:0% +molecule spin one spins or spin + + + align:start position:0% +molecule spin one spins or spin +multiplicity 1 which is spin 0 it's 2 s + + align:start position:0% +multiplicity 1 which is spin 0 it's 2 s + + + align:start position:0% +multiplicity 1 which is spin 0 it's 2 s +plus 1 is the spin multiplicity and then + + align:start position:0% +plus 1 is the spin multiplicity and then + + + align:start position:0% +plus 1 is the spin multiplicity and then +there's various things about convergence + + align:start position:0% +there's various things about convergence + + + align:start position:0% +there's various things about convergence +control that you probably won't need to + + align:start position:0% +control that you probably won't need to + + + align:start position:0% +control that you probably won't need to +worry about + + align:start position:0% +worry about + + + align:start position:0% +worry about +and then there's advanced things that + + align:start position:0% +and then there's advanced things that + + + align:start position:0% +and then there's advanced things that +you also probably won't need to worry + + align:start position:0% +you also probably won't need to worry + + + align:start position:0% +you also probably won't need to worry +about so now I can if I'm happy with + + align:start position:0% +about so now I can if I'm happy with + + + align:start position:0% +about so now I can if I'm happy with +that I can submit my job and I will call + + align:start position:0% +that I can submit my job and I will call + + + align:start position:0% +that I can submit my job and I will call +this all right Ethel ether hit OK and + + align:start position:0% +this all right Ethel ether hit OK and + + + align:start position:0% +this all right Ethel ether hit OK and +then in the back now it doesn't appear + + align:start position:0% +then in the back now it doesn't appear + + + align:start position:0% +then in the back now it doesn't appear +to be doing anything in the background + + align:start position:0% +to be doing anything in the background + + + align:start position:0% +to be doing anything in the background +it is doing something if you get I think + + align:start position:0% +it is doing something if you get I think + + + align:start position:0% +it is doing something if you get I think +this will finish in just a few seconds + + align:start position:0% +this will finish in just a few seconds + + + align:start position:0% +this will finish in just a few seconds +but if you get concerned that the job + + align:start position:0% +but if you get concerned that the job + + + align:start position:0% +but if you get concerned that the job +might not be running or something might + + align:start position:0% +might not be running or something might + + + align:start position:0% +might not be running or something might +have happened you can go over to the job + + align:start position:0% +have happened you can go over to the job + + + align:start position:0% +have happened you can go over to the job +monitor methane that was the job that I + + align:start position:0% +monitor methane that was the job that I + + + align:start position:0% +monitor methane that was the job that I +ran this morning to make sure that it + + align:start position:0% +ran this morning to make sure that it + + + align:start position:0% +ran this morning to make sure that it +works diethyl ether + + align:start position:0% +works diethyl ether + + + align:start position:0% +works diethyl ether +I'm telling we just submitted it 10:50 + + align:start position:0% +I'm telling we just submitted it 10:50 + + + align:start position:0% +I'm telling we just submitted it 10:50 +and 21 seconds ah there we go it's now + + align:start position:0% +and 21 seconds ah there we go it's now + + + align:start position:0% +and 21 seconds ah there we go it's now +it's been running for 4 seconds let's + + align:start position:0% +it's been running for 4 seconds let's + + + align:start position:0% +it's been running for 4 seconds let's +see how long it takes mm okay it's + + align:start position:0% +see how long it takes mm okay it's + + + align:start position:0% +see how long it takes mm okay it's +taking a lot longer than I think all + + align:start position:0% +taking a lot longer than I think all + + + align:start position:0% +taking a lot longer than I think all +right that's all right we've got a few + + align:start position:0% +right that's all right we've got a few + + + align:start position:0% +right that's all right we've got a few +minutes so so what will happen here in a + + align:start position:0% +minutes so so what will happen here in a + + + align:start position:0% +minutes so so what will happen here in a +minute when we that's all right it's + + align:start position:0% +minute when we that's all right it's + + + align:start position:0% +minute when we that's all right it's +going along so so when it's done what + + align:start position:0% +going along so so when it's done what + + + align:start position:0% +going along so so when it's done what +will happen is over here there let us + + align:start position:0% +will happen is over here there let us + + + align:start position:0% +will happen is over here there let us +know and they're over here it will + + align:start position:0% +know and they're over here it will + + + align:start position:0% +know and they're over here it will +appear a thing where we can start + + align:start position:0% +appear a thing where we can start + + + align:start position:0% +appear a thing where we can start +looking at the results might have gone + + align:start position:0% +looking at the results might have gone + + + align:start position:0% +looking at the results might have gone +faster if I had minimize the energy to + + align:start position:0% +faster if I had minimize the energy to + + + align:start position:0% +faster if I had minimize the energy to +begin with because then it would do less + + align:start position:0% +begin with because then it would do less + + + align:start position:0% +begin with because then it would do less +geometry steps it's going along I don't + + align:start position:0% +geometry steps it's going along I don't + + + align:start position:0% +geometry steps it's going along I don't +know we might run out of class time + + align:start position:0% +know we might run out of class time + + + align:start position:0% +know we might run out of class time +before it finishes 1051 we've got 4 + + align:start position:0% +before it finishes 1051 we've got 4 + + + align:start position:0% +before it finishes 1051 we've got 4 +minutes let's see + + align:start position:0% +minutes let's see + + + align:start position:0% +minutes let's see +come on laptop I've got the MacBook Pro + + align:start position:0% +come on laptop I've got the MacBook Pro + + + align:start position:0% +come on laptop I've got the MacBook Pro +I maybe I should do operation of + + align:start position:0% +I maybe I should do operation of + + + align:start position:0% +I maybe I should do operation of +upgrading the processor it's + + align:start position:0% + + + + align:start position:0% + +well in my research group we have 1000 + + align:start position:0% +well in my research group we have 1000 + + + align:start position:0% +well in my research group we have 1000 +cores that we maybe around 1200 cores + + align:start position:0% +cores that we maybe around 1200 cores + + + align:start position:0% +cores that we maybe around 1200 cores +even I think actually oh there we go it + + align:start position:0% +even I think actually oh there we go it + + + align:start position:0% +even I think actually oh there we go it +finished but we have around 1200 cores + + align:start position:0% +finished but we have around 1200 cores + + + align:start position:0% +finished but we have around 1200 cores +for around 10 people so that means that + + align:start position:0% +for around 10 people so that means that + + + align:start position:0% +for around 10 people so that means that +you can let a job run for a very very + + align:start position:0% +you can let a job run for a very very + + + align:start position:0% +you can let a job run for a very very +very long time + + align:start position:0% +very long time + + + align:start position:0% +very long time +on multiple cores and it doesn't get in + + align:start position:0% +on multiple cores and it doesn't get in + + + align:start position:0% +on multiple cores and it doesn't get in +anyone's way so that's what we so it's + + align:start position:0% +anyone's way so that's what we so it's + + + align:start position:0% +anyone's way so that's what we so it's +not unusual for us to put something in + + align:start position:0% +not unusual for us to put something in + + + align:start position:0% +not unusual for us to put something in +there that lasts a week so now it's + + align:start position:0% +there that lasts a week so now it's + + + align:start position:0% +there that lasts a week so now it's +finished we want to copy the results + + align:start position:0% +finished we want to copy the results + + + align:start position:0% +finished we want to copy the results +from the server + + align:start position:0% +from the server + + + align:start position:0% +from the server +this is arcane in an arcane way of + + align:start position:0% +this is arcane in an arcane way of + + + align:start position:0% +this is arcane in an arcane way of +saying things because it designed for + + align:start position:0% +saying things because it designed for + + + align:start position:0% +saying things because it designed for +super computers where you are sitting in + + align:start position:0% +super computers where you are sitting in + + + align:start position:0% +super computers where you are sitting in +a terminal in your office and then it + + align:start position:0% +a terminal in your office and then it + + + align:start position:0% +a terminal in your office and then it +sends all the results over to the + + align:start position:0% +sends all the results over to the + + + align:start position:0% +sends all the results over to the +supercomputer it runs the calculation + + align:start position:0% +supercomputer it runs the calculation + + + align:start position:0% +supercomputer it runs the calculation +and you have to copy the results back to + + align:start position:0% +and you have to copy the results back to + + + align:start position:0% +and you have to copy the results back to +your local computer I am actually + + align:start position:0% +your local computer I am actually + + + align:start position:0% +your local computer I am actually +running it on my computer it's just the + + align:start position:0% +running it on my computer it's just the + + + align:start position:0% +running it on my computer it's just the +computer is both let's put it + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +there we go now it has a little star + + align:start position:0% +there we go now it has a little star + + + align:start position:0% +there we go now it has a little star +next to it which lets me know that it's + + align:start position:0% +next to it which lets me know that it's + + + align:start position:0% +next to it which lets me know that it's +finished so let's see info so I can show + + align:start position:0% +finished so let's see info so I can show + + + align:start position:0% +finished so let's see info so I can show +the dipole moment so there we go that + + align:start position:0% +the dipole moment so there we go that + + + align:start position:0% +the dipole moment so there we go that +little blue arrow it's magnitude and + + align:start position:0% +little blue arrow it's magnitude and + + + align:start position:0% +little blue arrow it's magnitude and +direction is the dipole moment of + + align:start position:0% +direction is the dipole moment of + + + align:start position:0% +direction is the dipole moment of +diethyl ether so it does have a dipole + + align:start position:0% +diethyl ether so it does have a dipole + + + align:start position:0% +diethyl ether so it does have a dipole +moment with its positive end here + + align:start position:0% +moment with its positive end here + + + align:start position:0% +moment with its positive end here +pointing in that direction that seems + + align:start position:0% +pointing in that direction that seems + + + align:start position:0% +pointing in that direction that seems +about right let's see I can look at the + + align:start position:0% +about right let's see I can look at the + + + align:start position:0% +about right let's see I can look at the +files these are only if you're really + + align:start position:0% +files these are only if you're really + + + align:start position:0% +files these are only if you're really +really interested in details you see + + align:start position:0% +really interested in details you see + + + align:start position:0% +really interested in details you see +these are very verbose to have every bit + + align:start position:0% +these are very verbose to have every bit + + + align:start position:0% +these are very verbose to have every bit +of information you could possibly want + + align:start position:0% +of information you could possibly want + + + align:start position:0% +of information you could possibly want +in them so if you if there's ever + + align:start position:0% +in them so if you if there's ever + + + align:start position:0% +in them so if you if there's ever +something that you can't get out of the + + align:start position:0% +something that you can't get out of the + + + align:start position:0% +something that you can't get out of the +GUI you just kind of go you can eat you + + align:start position:0% +GUI you just kind of go you can eat you + + + align:start position:0% +GUI you just kind of go you can eat you +know you can search you know I can look + + align:start position:0% +know you can search you know I can look + + + align:start position:0% +know you can search you know I can look +for converge look optimization converged + + align:start position:0% +for converge look optimization converged + + + align:start position:0% +for converge look optimization converged +and then it tells me everything after + + align:start position:0% +and then it tells me everything after + + + align:start position:0% +and then it tells me everything after +that um I can look at the different + + align:start position:0% +that um I can look at the different + + + align:start position:0% +that um I can look at the different +atoms in the molecule and it will + + align:start position:0% +atoms in the molecule and it will + + + align:start position:0% +atoms in the molecule and it will +highlight them for me and then I can + + align:start position:0% +highlight them for me and then I can + + + align:start position:0% +highlight them for me and then I can +look at bonds and it will tell me I + + align:start position:0% +look at bonds and it will tell me I + + + align:start position:0% +look at bonds and it will tell me I +don't forgot you can read but down here + + align:start position:0% +don't forgot you can read but down here + + + align:start position:0% +don't forgot you can read but down here +it has the bond length in the corner so + + align:start position:0% +it has the bond length in the corner so + + + align:start position:0% +it has the bond length in the corner so +that CH bond is 1.09 3 all these CH + + align:start position:0% +that CH bond is 1.09 3 all these CH + + + align:start position:0% +that CH bond is 1.09 3 all these CH +bonds every 1.09 plus or minus a bit the + + align:start position:0% +bonds every 1.09 plus or minus a bit the + + + align:start position:0% +bonds every 1.09 plus or minus a bit the +carbon oxygen bond there is one point + + align:start position:0% +carbon oxygen bond there is one point + + + align:start position:0% +carbon oxygen bond there is one point +four six rounding now it's also one + + align:start position:0% +four six rounding now it's also one + + + align:start position:0% +four six rounding now it's also one +point four six and then this here so as + + align:start position:0% +point four six and then this here so as + + + align:start position:0% +point four six and then this here so as +it did the geometry optimization it was + + align:start position:0% +it did the geometry optimization it was + + + align:start position:0% +it did the geometry optimization it was +adjusting that the geometry trying to + + align:start position:0% +adjusting that the geometry trying to + + + align:start position:0% +adjusting that the geometry trying to +find the minimum and these are the + + align:start position:0% +find the minimum and these are the + + + align:start position:0% +find the minimum and these are the +different total energies that it had as + + align:start position:0% +different total energies that it had as + + + align:start position:0% +different total energies that it had as +it went through the optimization you'll + + align:start position:0% +it went through the optimization you'll + + + align:start position:0% +it went through the optimization you'll +see that eventually it sort of slows + + align:start position:0% +see that eventually it sort of slows + + + align:start position:0% +see that eventually it sort of slows +down energies going down every time and + + align:start position:0% +down energies going down every time and + + + align:start position:0% +down energies going down every time and +eventually it sort of slows down to + + align:start position:0% +eventually it sort of slows down to + + + align:start position:0% +eventually it sort of slows down to +where it's not changing anymore it says + + align:start position:0% +where it's not changing anymore it says + + + align:start position:0% +where it's not changing anymore it says +alright that's that's the minimum + + align:start position:0% +alright that's that's the minimum + + + align:start position:0% +alright that's that's the minimum +you also notice that these are these + + align:start position:0% +you also notice that these are these + + + align:start position:0% +you also notice that these are these +these are in atomic units so that's + + align:start position:0% +these are in atomic units so that's + + + align:start position:0% +these are in atomic units so that's +minus 232 hartrees which is not a so + + align:start position:0% +minus 232 hartrees which is not a so + + + align:start position:0% +minus 232 hartrees which is not a so +that's like 4,000 K cows no that's more + + align:start position:0% +that's like 4,000 K cows no that's more + + + align:start position:0% +that's like 4,000 K cows no that's more +that's more than 4,000 K girls anyway + + align:start position:0% +that's more than 4,000 K girls anyway + + + align:start position:0% +that's more than 4,000 K girls anyway +it's thousands tens of thousands of K + + align:start position:0% +it's thousands tens of thousands of K + + + align:start position:0% +it's thousands tens of thousands of K +Cal's the reason it's such a low number + + align:start position:0% +Cal's the reason it's such a low number + + + align:start position:0% +Cal's the reason it's such a low number +is this is the energy would take to rip + + align:start position:0% +is this is the energy would take to rip + + + align:start position:0% +is this is the energy would take to rip +every electron off of the molecule + + align:start position:0% +every electron off of the molecule + + + align:start position:0% +every electron off of the molecule +including all of the 1s electrons so the + + align:start position:0% +including all of the 1s electrons so the + + + align:start position:0% +including all of the 1s electrons so the +energies are typically going to be very + + align:start position:0% +energies are typically going to be very + + + align:start position:0% +energies are typically going to be very +very large negative numbers don't worry + + align:start position:0% +very large negative numbers don't worry + + + align:start position:0% +very large negative numbers don't worry +about that it's energy differences that + + align:start position:0% +about that it's energy differences that + + + align:start position:0% +about that it's energy differences that +matter so you notice you know even my + + align:start position:0% +matter so you notice you know even my + + + align:start position:0% +matter so you notice you know even my +bad geometry was already 232 point one + + align:start position:0% +bad geometry was already 232 point one + + + align:start position:0% +bad geometry was already 232 point one +and the correct answer is two hundred + + align:start position:0% +and the correct answer is two hundred + + + align:start position:0% +and the correct answer is two hundred +thirty-two point three so the total + + align:start position:0% +thirty-two point three so the total + + + align:start position:0% +thirty-two point three so the total +energy change wasn't that much + + align:start position:0% +energy change wasn't that much + + + align:start position:0% +energy change wasn't that much +and then the last cool thing that I want + + align:start position:0% +and then the last cool thing that I want + + + align:start position:0% +and then the last cool thing that I want +to show you is that we can do we can + + align:start position:0% +to show you is that we can do we can + + + align:start position:0% +to show you is that we can do we can +plot orbitals so I'm gonna okay + + align:start position:0% +plot orbitals so I'm gonna okay + + + align:start position:0% +plot orbitals so I'm gonna okay +calculate some little rules there we go + + align:start position:0% +calculate some little rules there we go + + + align:start position:0% +calculate some little rules there we go +so I just had it calculate the homo and + + align:start position:0% +so I just had it calculate the homo and + + + align:start position:0% +so I just had it calculate the homo and +the LUMO I didn't go through all of it + + align:start position:0% +the LUMO I didn't go through all of it + + + align:start position:0% +the LUMO I didn't go through all of it +with you but if you can go there it + + align:start position:0% +with you but if you can go there it + + + align:start position:0% +with you but if you can go there it +gives you some things I should go back + + align:start position:0% +gives you some things I should go back + + + align:start position:0% +gives you some things I should go back +and look show you so you get to choose a + + align:start position:0% +and look show you so you get to choose a + + + align:start position:0% +and look show you so you get to choose a +range of orbitals the ISO value is + + align:start position:0% +range of orbitals the ISO value is + + + align:start position:0% +range of orbitals the ISO value is +basically where it draws the surface so + + align:start position:0% +basically where it draws the surface so + + + align:start position:0% +basically where it draws the surface so +it's inverse of what you expect a larger + + align:start position:0% +it's inverse of what you expect a larger + + + align:start position:0% +it's inverse of what you expect a larger +ISO value is it's an isosurface so if + + align:start position:0% +ISO value is it's an isosurface so if + + + align:start position:0% +ISO value is it's an isosurface so if +you make it very the ISO value is larger + + align:start position:0% +you make it very the ISO value is larger + + + align:start position:0% +you make it very the ISO value is larger +is closer in so it makes a smaller + + align:start position:0% +is closer in so it makes a smaller + + + align:start position:0% +is closer in so it makes a smaller +bubble and a smaller ISO value makes a + + align:start position:0% +bubble and a smaller ISO value makes a + + + align:start position:0% +bubble and a smaller ISO value makes a +bigger bubble and you can change the + + align:start position:0% +bigger bubble and you can change the + + + align:start position:0% +bigger bubble and you can change the +number of points that it samples to make + + align:start position:0% +number of points that it samples to make + + + align:start position:0% +number of points that it samples to make +the surface and change the colours and + + align:start position:0% +the surface and change the colours and + + + align:start position:0% +the surface and change the colours and +change the opacity of it in terms of how + + align:start position:0% +change the opacity of it in terms of how + + + align:start position:0% +change the opacity of it in terms of how +you want to want to look I already did + + align:start position:0% +you want to want to look I already did + + + align:start position:0% +you want to want to look I already did +this so so there is the homo + + align:start position:0% +this so so there is the homo + + + align:start position:0% +this so so there is the homo +so the homo is a something in the PI + + align:start position:0% +so the homo is a something in the PI + + + align:start position:0% +so the homo is a something in the PI +manifold it spy spy star here and then I + + align:start position:0% +manifold it spy spy star here and then I + + + align:start position:0% +manifold it spy spy star here and then I +can take out the homo and show the LUMO + + align:start position:0% +can take out the homo and show the LUMO + + + align:start position:0% +can take out the homo and show the LUMO +and the LUMO is in this particular basis + + align:start position:0% +and the LUMO is in this particular basis + + + align:start position:0% +and the LUMO is in this particular basis +set not very useful because I don't have + + align:start position:0% +set not very useful because I don't have + + + align:start position:0% +set not very useful because I don't have +a lot of basis functions so by my basis + + align:start position:0% +a lot of basis functions so by my basis + + + align:start position:0% +a lot of basis functions so by my basis +functions just there's not enough of + + align:start position:0% +functions just there's not enough of + + + align:start position:0% +functions just there's not enough of +them to really describe the the LUMO the + + align:start position:0% +them to really describe the the LUMO the + + + align:start position:0% +them to really describe the the LUMO the +will plus one if I want to get a good + + align:start position:0% +will plus one if I want to get a good + + + align:start position:0% +will plus one if I want to get a good +LUMO I need a bigger basis set Innis so + + align:start position:0% +LUMO I need a bigger basis set Innis so + + + align:start position:0% +LUMO I need a bigger basis set Innis so +that's the kind of thing that you can do + + align:start position:0% +that's the kind of thing that you can do + + + align:start position:0% +that's the kind of thing that you can do +with Q chem or with Gaussian Gaussian + + align:start position:0% +with Q chem or with Gaussian Gaussian + + + align:start position:0% +with Q chem or with Gaussian Gaussian +has a GUI called Gauss view you can use + + align:start position:0% +has a GUI called Gauss view you can use + + + align:start position:0% +has a GUI called Gauss view you can use +either one but they both work pretty + + align:start position:0% +either one but they both work pretty + + + align:start position:0% +either one but they both work pretty +well and are pretty intuitive and so I + + align:start position:0% +well and are pretty intuitive and so I + + + align:start position:0% +well and are pretty intuitive and so I +think on the next problem set you will + + align:start position:0% +think on the next problem set you will + + + align:start position:0% +think on the next problem set you will +have some homework problems that involve + + align:start position:0% +have some homework problems that involve + + + align:start position:0% +have some homework problems that involve +running some calculations with these + + align:start position:0% +running some calculations with these + + + align:start position:0% +running some calculations with these +things and I hope you enjoy well I don't + + align:start position:0% +things and I hope you enjoy well I don't + + + align:start position:0% +things and I hope you enjoy well I don't +know if homework is ever really + + align:start position:0% +know if homework is ever really + + + align:start position:0% +know if homework is ever really +enjoyable but I hope it's marginally + + align:start position:0% +enjoyable but I hope it's marginally + + + align:start position:0% +enjoyable but I hope it's marginally +enjoyable anyway thanks \ No newline at end of file diff --git a/6xrabmU-gq8.txt b/6xrabmU-gq8.txt new file mode 100644 index 0000000000000000000000000000000000000000..dea514d0904ec86bc9e662615339769facde638d --- /dev/null +++ b/6xrabmU-gq8.txt @@ -0,0 +1,451 @@ +align:start position:0% + +so we also tried to learn how to use + + align:start position:0% +so we also tried to learn how to use + + + align:start position:0% +so we also tried to learn how to use +processing it's pretty verbose but so + + align:start position:0% +processing it's pretty verbose but so + + + align:start position:0% +processing it's pretty verbose but so +essentially we have a little widget and + + align:start position:0% +essentially we have a little widget and + + + align:start position:0% +essentially we have a little widget and +crunch so the SATs either gonna step to + + align:start position:0% +crunch so the SATs either gonna step to + + + align:start position:0% +crunch so the SATs either gonna step to +eight originally we wanted to be able to + + align:start position:0% +eight originally we wanted to be able to + + + align:start position:0% +eight originally we wanted to be able to +like remotely control it but so that's + + align:start position:0% +like remotely control it but so that's + + + align:start position:0% +like remotely control it but so that's +like one Kavitha cause these two three + + align:start position:0% +like one Kavitha cause these two three + + + align:start position:0% +like one Kavitha cause these two three +four so you can see that is seven and + + align:start position:0% +four so you can see that is seven and + + + align:start position:0% +four so you can see that is seven and +we've set it step size to eat so I'll + + align:start position:0% +we've set it step size to eat so I'll + + + align:start position:0% +we've set it step size to eat so I'll +stop one is eight and they don't recount + + align:start position:0% +stop one is eight and they don't recount + + + align:start position:0% +stop one is eight and they don't recount +we also have this thing that we labeled + + align:start position:0% +we also have this thing that we labeled + + + align:start position:0% +we also have this thing that we labeled +tempo because it's related to our game + + align:start position:0% +tempo because it's related to our game + + + align:start position:0% +tempo because it's related to our game +but it actually correlates with like how + + align:start position:0% +but it actually correlates with like how + + + align:start position:0% +but it actually correlates with like how +fast you're punching + + align:start position:0% +fast you're punching + + + align:start position:0% +fast you're punching +so if we smooth this out this is + + align:start position:0% +so if we smooth this out this is + + + align:start position:0% +so if we smooth this out this is +actually telling you how fast you're + + align:start position:0% +actually telling you how fast you're + + + align:start position:0% +actually telling you how fast you're +punching for each one yeah + + align:start position:0% +punching for each one yeah + + + align:start position:0% +punching for each one yeah +another guest average average that speed + + align:start position:0% +another guest average average that speed + + + align:start position:0% +another guest average average that speed +is pretty much that eight different + + align:start position:0% +is pretty much that eight different + + + align:start position:0% +is pretty much that eight different +punches that you have divided by the + + align:start position:0% +punches that you have divided by the + + + align:start position:0% +punches that you have divided by the +total + + align:start position:0% +total + + + align:start position:0% +total +Edge's so like I can do like my next set + + align:start position:0% +Edge's so like I can do like my next set + + + align:start position:0% +Edge's so like I can do like my next set +and you'll be like one two three four + + align:start position:0% +and you'll be like one two three four + + + align:start position:0% +and you'll be like one two three four +five six seven eight and then we'll be + + align:start position:0% +five six seven eight and then we'll be + + + align:start position:0% +five six seven eight and then we'll be +on like set to over step three + + align:start position:0% +on like set to over step three + + + align:start position:0% +on like set to over step three +so that's pretty basic right now but + + align:start position:0% +so that's pretty basic right now but + + + align:start position:0% +so that's pretty basic right now but +there's like a lot of different features + + align:start position:0% +there's like a lot of different features + + + align:start position:0% +there's like a lot of different features +that we can add with like the gyro if we + + align:start position:0% +that we can add with like the gyro if we + + + align:start position:0% +that we can add with like the gyro if we +have more time and if you have two hands + + align:start position:0% +have more time and if you have two hands + + + align:start position:0% +have more time and if you have two hands +and they could communicate maybe we can + + align:start position:0% +and they could communicate maybe we can + + + align:start position:0% +and they could communicate maybe we can +show the game yeah okay so some of the + + align:start position:0% +show the game yeah okay so some of the + + + align:start position:0% +show the game yeah okay so some of the +pieces it's not gonna water the summit + + align:start position:0% +pieces it's not gonna water the summit + + + align:start position:0% +pieces it's not gonna water the summit +you're first to play what places all for + + align:start position:0% +you're first to play what places all for + + + align:start position:0% +you're first to play what places all for +you first your turn and that suggests + + align:start position:0% +you first your turn and that suggests + + + align:start position:0% +you first your turn and that suggests +the first property like BAM fun I'll be + + align:start position:0% +the first property like BAM fun I'll be + + + align:start position:0% +the first property like BAM fun I'll be +like yeah it's that good to hop and then + + align:start position:0% +like yeah it's that good to hop and then + + + align:start position:0% +like yeah it's that good to hop and then +that is the second part so you punch + + align:start position:0% +that is the second part so you punch + + + align:start position:0% +that is the second part so you punch +that beat yeah okay have you got it and + + align:start position:0% +that beat yeah okay have you got it and + + + align:start position:0% +that beat yeah okay have you got it and +then it goes on to the next part + + align:start position:0% +then it goes on to the next part + + + align:start position:0% +then it goes on to the next part +and then basically you cycle through + + align:start position:0% +and then basically you cycle through + + + align:start position:0% +and then basically you cycle through +yeah protector with it breaks so ideally + + align:start position:0% +yeah protector with it breaks so ideally + + + align:start position:0% +yeah protector with it breaks so ideally +we could like actually play the music + + align:start position:0% + + + + align:start position:0% + +yeah but it was simply a really nice + + align:start position:0% +yeah but it was simply a really nice + + + align:start position:0% +yeah but it was simply a really nice +project to learn how to use a bunch of + + align:start position:0% +project to learn how to use a bunch of + + + align:start position:0% +project to learn how to use a bunch of +different sensors we also had a heart + + align:start position:0% +different sensors we also had a heart + + + align:start position:0% +different sensors we also had a heart +rate monitor which was able to get these + + align:start position:0% +rate monitor which was able to get these + + + align:start position:0% +rate monitor which was able to get these +per minute was pretty inaccurate but it + + align:start position:0% +per minute was pretty inaccurate but it + + + align:start position:0% +per minute was pretty inaccurate but it +was nice to learn how to set it up we + + align:start position:0% +was nice to learn how to set it up we + + + align:start position:0% +was nice to learn how to set it up we +have a baby sensor yeah the LEDs and we + + align:start position:0% +have a baby sensor yeah the LEDs and we + + + align:start position:0% +have a baby sensor yeah the LEDs and we +have LED is that much like depending on + + align:start position:0% +have LED is that much like depending on + + + align:start position:0% +have LED is that much like depending on +how hard you punch a certain amount of + + align:start position:0% +how hard you punch a certain amount of + + + align:start position:0% +how hard you punch a certain amount of +bump up just like turn around it was + + align:start position:0% +bump up just like turn around it was + + + align:start position:0% +bump up just like turn around it was +like a really easy project and sure just + + align:start position:0% +like a really easy project and sure just + + + align:start position:0% +like a really easy project and sure just +a good beginner learning projects but + + align:start position:0% +a good beginner learning projects but + + + align:start position:0% +a good beginner learning projects but +yeah I think this is like a good example + + align:start position:0% +yeah I think this is like a good example + + + align:start position:0% +yeah I think this is like a good example +like a wearable and I can invite a bunch + + align:start position:0% +like a wearable and I can invite a bunch + + + align:start position:0% +like a wearable and I can invite a bunch +of military to get friends teachers \ No newline at end of file diff --git a/9ICCzJGPaPA.txt b/9ICCzJGPaPA.txt new file mode 100644 index 0000000000000000000000000000000000000000..6a001cf591e1320bb7dd7c98e6f623c473efd2ef --- /dev/null +++ b/9ICCzJGPaPA.txt @@ -0,0 +1,2131 @@ +align:start position:0% + +hello I am Jose Pinera and MIT UTM + + align:start position:0% +hello I am Jose Pinera and MIT UTM + + + align:start position:0% +hello I am Jose Pinera and MIT UTM +visiting scholar this video shares some + + align:start position:0% +visiting scholar this video shares some + + + align:start position:0% +visiting scholar this video shares some +lessons of my research on Urban + + align:start position:0% +lessons of my research on Urban + + + align:start position:0% +lessons of my research on Urban +Innovation using case of Waste + + align:start position:0% +Innovation using case of Waste + + + align:start position:0% +Innovation using case of Waste +Management in panag Malaysia Urban + + align:start position:0% +Management in panag Malaysia Urban + + + align:start position:0% +Management in panag Malaysia Urban +Innovation means doing things + + align:start position:0% +Innovation means doing things + + + align:start position:0% +Innovation means doing things +differently in the urban context + + align:start position:0% +differently in the urban context + + + align:start position:0% +differently in the urban context +Innovation is important for improving + + align:start position:0% +Innovation is important for improving + + + align:start position:0% +Innovation is important for improving +Urban services in a context where many + + align:start position:0% +Urban services in a context where many + + + align:start position:0% +Urban services in a context where many +cities around the world face increasing + + align:start position:0% +cities around the world face increasing + + + align:start position:0% +cities around the world face increasing +budgetary constraints interaction among + + align:start position:0% +budgetary constraints interaction among + + + align:start position:0% +budgetary constraints interaction among +different governmental and + + align:start position:0% +different governmental and + + + align:start position:0% +different governmental and +non-governmental actors are key to + + align:start position:0% +non-governmental actors are key to + + + align:start position:0% +non-governmental actors are key to +Innovation interactions can bring new + + align:start position:0% +Innovation interactions can bring new + + + align:start position:0% +Innovation interactions can bring new +resources and knowledge to solve Urban + + align:start position:0% +resources and knowledge to solve Urban + + + align:start position:0% +resources and knowledge to solve Urban +problems more + + align:start position:0% +problems more + + + align:start position:0% +problems more +effectively the waste sector in Malaysia + + align:start position:0% +effectively the waste sector in Malaysia + + + align:start position:0% +effectively the waste sector in Malaysia +particularly offers an interesting + + align:start position:0% +particularly offers an interesting + + + align:start position:0% +particularly offers an interesting +laboratory for urban Innovations the + + align:start position:0% +laboratory for urban Innovations the + + + align:start position:0% +laboratory for urban Innovations the +country has Str tried to improve Waste + + align:start position:0% +country has Str tried to improve Waste + + + align:start position:0% +country has Str tried to improve Waste +Management Effectiveness in recent years + + align:start position:0% +Management Effectiveness in recent years + + + align:start position:0% +Management Effectiveness in recent years +making a series of institutional change + + align:start position:0% +making a series of institutional change + + + align:start position:0% +making a series of institutional change +such as decentralization of waste + + align:start position:0% +such as decentralization of waste + + + align:start position:0% +such as decentralization of waste +management at the federal level + + align:start position:0% +management at the federal level + + + align:start position:0% +management at the federal level +previously the waste management and + + align:start position:0% +previously the waste management and + + + align:start position:0% +previously the waste management and +public cleansing is under the prview of + + align:start position:0% +public cleansing is under the prview of + + + align:start position:0% +public cleansing is under the prview of +the each state government and uh being + + align:start position:0% +the each state government and uh being + + + align:start position:0% +the each state government and uh being +implemented uh or being responsible is + + align:start position:0% +implemented uh or being responsible is + + + align:start position:0% +implemented uh or being responsible is +under the local government somehow they + + align:start position:0% +under the local government somehow they + + + align:start position:0% +under the local government somehow they +have a difficulty to provide sufficient + + align:start position:0% +have a difficulty to provide sufficient + + + align:start position:0% +have a difficulty to provide sufficient +fund to manage at the same time do not + + align:start position:0% +fund to manage at the same time do not + + + align:start position:0% +fund to manage at the same time do not +have uh expertise or manpower to manage + + align:start position:0% +have uh expertise or manpower to manage + + + align:start position:0% +have uh expertise or manpower to manage +the solid waste previously almost all + + align:start position:0% +the solid waste previously almost all + + + align:start position:0% +the solid waste previously almost all +the waste is sent to The Dumping Ground + + align:start position:0% +the waste is sent to The Dumping Ground + + + align:start position:0% +the waste is sent to The Dumping Ground +local government are asking federal + + align:start position:0% +local government are asking federal + + + align:start position:0% +local government are asking federal +government to provide the fund for them + + align:start position:0% +government to provide the fund for them + + + align:start position:0% +government to provide the fund for them +we also want the local government to + + align:start position:0% +we also want the local government to + + + align:start position:0% +we also want the local government to +focus on other areas of services so + + align:start position:0% +focus on other areas of services so + + + align:start position:0% +focus on other areas of services so +that's the reason why the federal thinks + + align:start position:0% +that's the reason why the federal thinks + + + align:start position:0% +that's the reason why the federal thinks +is better so that the the responsibility + + align:start position:0% +is better so that the the responsibility + + + align:start position:0% +is better so that the the responsibility +of managing R is put under Federal + + align:start position:0% +of managing R is put under Federal + + + align:start position:0% +of managing R is put under Federal +responsibility panga Island in Malaysia + + align:start position:0% +responsibility panga Island in Malaysia + + + align:start position:0% +responsibility panga Island in Malaysia +decided to keep Waste Management under + + align:start position:0% +decided to keep Waste Management under + + + align:start position:0% +decided to keep Waste Management under +local + + align:start position:0% +local + + + align:start position:0% +local +control actually the urban Civic + + align:start position:0% +control actually the urban Civic + + + align:start position:0% +control actually the urban Civic +department is in charge of solid waste + + align:start position:0% +department is in charge of solid waste + + + align:start position:0% +department is in charge of solid waste +management and also public cleansing is + + align:start position:0% +management and also public cleansing is + + + align:start position:0% +management and also public cleansing is +the core business of the council the + + align:start position:0% +the core business of the council the + + + align:start position:0% +the core business of the council the +most uh challenging part in pinang + + align:start position:0% +most uh challenging part in pinang + + + align:start position:0% +most uh challenging part in pinang +island is uh domestic waste pinang + + align:start position:0% +island is uh domestic waste pinang + + + align:start position:0% +island is uh domestic waste pinang +Island concerns around 550 ton of wte is + + align:start position:0% +Island concerns around 550 ton of wte is + + + align:start position:0% +Island concerns around 550 ton of wte is +being disposed the city council spends + + align:start position:0% +being disposed the city council spends + + + align:start position:0% +being disposed the city council spends +about 40% of its budget just to dispose + + align:start position:0% +about 40% of its budget just to dispose + + + align:start position:0% +about 40% of its budget just to dispose +of waste our recycling rate at the + + align:start position:0% +of waste our recycling rate at the + + + align:start position:0% +of waste our recycling rate at the +moment is 27% with the active role of + + align:start position:0% +moment is 27% with the active role of + + + align:start position:0% +moment is 27% with the active role of +the recycling agent the Nos and the + + align:start position:0% +the recycling agent the Nos and the + + + align:start position:0% +the recycling agent the Nos and the +Environmental Group in + + align:start position:0% +Environmental Group in + + + align:start position:0% +Environmental Group in +1998 the domestic weighs around 700 ton + + align:start position:0% +1998 the domestic weighs around 700 ton + + + align:start position:0% +1998 the domestic weighs around 700 ton +now it's only it's around 440 ton per + + align:start position:0% +now it's only it's around 440 ton per + + + align:start position:0% +now it's only it's around 440 ton per +day so how we manage to reduce it Pang + + align:start position:0% +day so how we manage to reduce it Pang + + + align:start position:0% +day so how we manage to reduce it Pang +we had very quite active role of the + + align:start position:0% +we had very quite active role of the + + + align:start position:0% +we had very quite active role of the +stakeholders doing + + align:start position:0% +stakeholders doing + + + align:start position:0% +stakeholders doing +recycling Urban Innovations reduce waste + + align:start position:0% +recycling Urban Innovations reduce waste + + + align:start position:0% +recycling Urban Innovations reduce waste +we are going to see two of those + + align:start position:0% +we are going to see two of those + + + align:start position:0% +we are going to see two of those +initiatives to understand how Urban + + align:start position:0% +initiatives to understand how Urban + + + align:start position:0% +initiatives to understand how Urban +Innovations emerge through different + + align:start position:0% +Innovations emerge through different + + + align:start position:0% +Innovations emerge through different +kinds of institutional + + align:start position:0% +kinds of institutional + + + align:start position:0% +kinds of institutional +[Music] + + align:start position:0% + + + + align:start position:0% + +Arrangements this is a recycling + + align:start position:0% +Arrangements this is a recycling + + + align:start position:0% +Arrangements this is a recycling +education center more important is + + align:start position:0% +education center more important is + + + align:start position:0% +education center more important is +education to spread and to actually + + align:start position:0% +education to spread and to actually + + + align:start position:0% +education to spread and to actually +encouraging more people to do recycling + + align:start position:0% +encouraging more people to do recycling + + + align:start position:0% +encouraging more people to do recycling +together and in Malaysia is a lot of + + align:start position:0% +together and in Malaysia is a lot of + + + align:start position:0% +together and in Malaysia is a lot of +time uh the recycling sorting is not + + align:start position:0% +time uh the recycling sorting is not + + + align:start position:0% +time uh the recycling sorting is not +part of the life whole uh practices yet + + align:start position:0% +part of the life whole uh practices yet + + + align:start position:0% +part of the life whole uh practices yet +so we have to set up the proper + + align:start position:0% +so we have to set up the proper + + + align:start position:0% +so we have to set up the proper +infrastructure to teach the resident how + + align:start position:0% +infrastructure to teach the resident how + + + align:start position:0% +infrastructure to teach the resident how +recycling uh to be done so that when + + align:start position:0% +recycling uh to be done so that when + + + align:start position:0% +recycling uh to be done so that when +they go back home they know how to + + align:start position:0% +they go back home they know how to + + + align:start position:0% +they go back home they know how to +actually save the item into the + + align:start position:0% +actually save the item into the + + + align:start position:0% +actually save the item into the +different category so we had about 20 we + + align:start position:0% +different category so we had about 20 we + + + align:start position:0% +different category so we had about 20 we +are all volunteers uh in average per + + align:start position:0% +are all volunteers uh in average per + + + align:start position:0% +are all volunteers uh in average per +month uh we are running about 10 about + + align:start position:0% +month uh we are running about 10 about + + + align:start position:0% +month uh we are running about 10 about +10 tons of material that cover plastic + + align:start position:0% +10 tons of material that cover plastic + + + align:start position:0% +10 tons of material that cover plastic +papers Metals all proceed from the + + align:start position:0% +papers Metals all proceed from the + + + align:start position:0% +papers Metals all proceed from the +recycling are all Channel toward the + + align:start position:0% +recycling are all Channel toward the + + + align:start position:0% +recycling are all Channel toward the +dialysis + + align:start position:0% + + + + align:start position:0% + +center Bud Shi dialis Center actually we + + align:start position:0% +center Bud Shi dialis Center actually we + + + align:start position:0% +center Bud Shi dialis Center actually we +started in + + align:start position:0% +started in + + + align:start position:0% +started in +1997 from the first day it's actually + + align:start position:0% +1997 from the first day it's actually + + + align:start position:0% +1997 from the first day it's actually +free of charge everyone interested to + + align:start position:0% +free of charge everyone interested to + + + align:start position:0% +free of charge everyone interested to +know how we survive for the past 18 + + align:start position:0% +know how we survive for the past 18 + + + align:start position:0% +know how we survive for the past 18 +years about 70% come from donation from + + align:start position:0% +years about 70% come from donation from + + + align:start position:0% +years about 70% come from donation from +the public another nearly 30% are come + + align:start position:0% +the public another nearly 30% are come + + + align:start position:0% +the public another nearly 30% are come +from our recycling recycling Education + + align:start position:0% +from our recycling recycling Education + + + align:start position:0% +from our recycling recycling Education +Center C is something very new when they + + align:start position:0% +Center C is something very new when they + + + align:start position:0% +Center C is something very new when they +equate recycling center equal to rubish + + align:start position:0% +equate recycling center equal to rubish + + + align:start position:0% +equate recycling center equal to rubish +Center so when we want to set up this + + align:start position:0% +Center so when we want to set up this + + + align:start position:0% +Center so when we want to set up this +Center the resident Community say no we + + align:start position:0% +Center the resident Community say no we + + + align:start position:0% +Center the resident Community say no we +cannot allow a rubbish Center set up at + + align:start position:0% +cannot allow a rubbish Center set up at + + + align:start position:0% +cannot allow a rubbish Center set up at +the then we have to explain to them we + + align:start position:0% +the then we have to explain to them we + + + align:start position:0% +the then we have to explain to them we +are not setting up a rubbish Center we + + align:start position:0% +are not setting up a rubbish Center we + + + align:start position:0% +are not setting up a rubbish Center we +are set up education center no smell + + align:start position:0% +are set up education center no smell + + + align:start position:0% +are set up education center no smell +right and it's clean and then is a + + align:start position:0% +right and it's clean and then is a + + + align:start position:0% +right and it's clean and then is a +mosquito infested area Su was willing to + + align:start position:0% +mosquito infested area Su was willing to + + + align:start position:0% +mosquito infested area Su was willing to +come here to set it up so we work along + + align:start position:0% +come here to set it up so we work along + + + align:start position:0% +come here to set it up so we work along +with them we actually uh work out with + + align:start position:0% +with them we actually uh work out with + + + align:start position:0% +with them we actually uh work out with +the uh the mbpp the the the councel they + + align:start position:0% +the uh the mbpp the the the councel they + + + align:start position:0% +the uh the mbpp the the the councel they +they do actually facilitate they + + align:start position:0% +they do actually facilitate they + + + align:start position:0% +they do actually facilitate they +actually rent to us at a very minimum uh + + align:start position:0% +actually rent to us at a very minimum uh + + + align:start position:0% +actually rent to us at a very minimum uh +rental cost it's also they are very + + align:start position:0% +rental cost it's also they are very + + + align:start position:0% +rental cost it's also they are very +supportive of our recycling effort and + + align:start position:0% +supportive of our recycling effort and + + + align:start position:0% +supportive of our recycling effort and +at the same time by doing recycling we + + align:start position:0% +at the same time by doing recycling we + + + align:start position:0% +at the same time by doing recycling we +also reduce the amount of rubbish that + + align:start position:0% +also reduce the amount of rubbish that + + + align:start position:0% +also reduce the amount of rubbish that +they had to handle the whole country go + + align:start position:0% +they had to handle the whole country go + + + align:start position:0% +they had to handle the whole country go +for solid waste recycling so we are + + align:start position:0% +for solid waste recycling so we are + + + align:start position:0% +for solid waste recycling so we are +actually three years ahead gold green + + align:start position:0% +actually three years ahead gold green + + + align:start position:0% +actually three years ahead gold green +Safe Life from the recycling besides we + + align:start position:0% +Safe Life from the recycling besides we + + + align:start position:0% +Safe Life from the recycling besides we +are doing Environmental Protection we + + align:start position:0% +are doing Environmental Protection we + + + align:start position:0% +are doing Environmental Protection we +actually can save life so in terms of + + align:start position:0% +actually can save life so in terms of + + + align:start position:0% +actually can save life so in terms of +vas management uh it is not the right + + align:start position:0% +vas management uh it is not the right + + + align:start position:0% +vas management uh it is not the right +way to just like think of disposal we + + align:start position:0% +way to just like think of disposal we + + + align:start position:0% +way to just like think of disposal we +should try to reduce the consumption so + + align:start position:0% +should try to reduce the consumption so + + + align:start position:0% +should try to reduce the consumption so +that we will also reduce um production + + align:start position:0% +that we will also reduce um production + + + align:start position:0% +that we will also reduce um production +of waste we are trying to promote uh + + align:start position:0% +of waste we are trying to promote uh + + + align:start position:0% +of waste we are trying to promote uh +communities to be involved from the + + align:start position:0% +communities to be involved from the + + + align:start position:0% +communities to be involved from the +community it goes to the local + + align:start position:0% +community it goes to the local + + + align:start position:0% +community it goes to the local +government at least 45% to 55 50% is + + align:start position:0% +government at least 45% to 55 50% is + + + align:start position:0% +government at least 45% to 55 50% is +organic waste or food waste yeah how in + + align:start position:0% +organic waste or food waste yeah how in + + + align:start position:0% +organic waste or food waste yeah how in +the first place can you reduce food + + align:start position:0% +the first place can you reduce food + + + align:start position:0% +the first place can you reduce food +waste kitchen peelings or the green + + align:start position:0% +waste kitchen peelings or the green + + + align:start position:0% +waste kitchen peelings or the green +waste which can go into + + align:start position:0% + + + + align:start position:0% + +composting composting is the second case + + align:start position:0% +composting composting is the second case + + + align:start position:0% +composting composting is the second case +of urban innovation in which the private + + align:start position:0% +of urban innovation in which the private + + + align:start position:0% +of urban innovation in which the private +sector partners with this public sector + + align:start position:0% +sector partners with this public sector + + + align:start position:0% +sector partners with this public sector +seor in Civil Society most of the + + align:start position:0% +seor in Civil Society most of the + + + align:start position:0% +seor in Civil Society most of the +problem is that people expect the + + align:start position:0% +problem is that people expect the + + + align:start position:0% +problem is that people expect the +government to handle their waste waste + + align:start position:0% +government to handle their waste waste + + + align:start position:0% +government to handle their waste waste +is not their problem it's government's + + align:start position:0% +is not their problem it's government's + + + align:start position:0% +is not their problem it's government's +problem how people look at Food waste + + align:start position:0% +problem how people look at Food waste + + + align:start position:0% +problem how people look at Food waste +because to them it is a waste uh but to + + align:start position:0% +because to them it is a waste uh but to + + + align:start position:0% +because to them it is a waste uh but to +the world it is actually a resource most + + align:start position:0% +the world it is actually a resource most + + + align:start position:0% +the world it is actually a resource most +uh recycling companies don't survive for + + align:start position:0% +uh recycling companies don't survive for + + + align:start position:0% +uh recycling companies don't survive for +long because the cost is too high to do + + align:start position:0% +long because the cost is too high to do + + + align:start position:0% +long because the cost is too high to do +recycling uh and the economic returns or + + align:start position:0% +recycling uh and the economic returns or + + + align:start position:0% +recycling uh and the economic returns or +the value is too low uh the only way for + + align:start position:0% +the value is too low uh the only way for + + + align:start position:0% +the value is too low uh the only way for +them to make money is of course then to + + align:start position:0% +them to make money is of course then to + + + align:start position:0% +them to make money is of course then to +looking at government subsidies uh + + align:start position:0% +looking at government subsidies uh + + + align:start position:0% +looking at government subsidies uh +looking at Carbon credit mechanisms we + + align:start position:0% +looking at Carbon credit mechanisms we + + + align:start position:0% +looking at Carbon credit mechanisms we +have come up with something that we know + + align:start position:0% +have come up with something that we know + + + align:start position:0% +have come up with something that we know +that is um economically + + align:start position:0% +that is um economically + + + align:start position:0% +that is um economically +[Music] + + align:start position:0% + + + + align:start position:0% + +feasible + + align:start position:0% +feasible + + + align:start position:0% +feasible +[Music] + + align:start position:0% + + + + align:start position:0% + +process + + align:start position:0% + + + + align:start position:0% + +met boy School uh a few years back we + + align:start position:0% +met boy School uh a few years back we + + + align:start position:0% +met boy School uh a few years back we +were approached by one of our old boys + + align:start position:0% +were approached by one of our old boys + + + align:start position:0% +were approached by one of our old boys +who also happened to be a counselor in + + align:start position:0% +who also happened to be a counselor in + + + align:start position:0% +who also happened to be a counselor in +the uh City Council in Pang so he came + + align:start position:0% +the uh City Council in Pang so he came + + + align:start position:0% +the uh City Council in Pang so he came +out with the idea of uh turning the + + align:start position:0% +out with the idea of uh turning the + + + align:start position:0% +out with the idea of uh turning the +school green all canteen waste + + align:start position:0% +school green all canteen waste + + + align:start position:0% +school green all canteen waste +especially food waste churn up in the + + align:start position:0% +especially food waste churn up in the + + + align:start position:0% +especially food waste churn up in the +machine and converted into enzymes which + + align:start position:0% +machine and converted into enzymes which + + + align:start position:0% +machine and converted into enzymes which +later will be converted into fertilizer + + align:start position:0% +later will be converted into fertilizer + + + align:start position:0% +later will be converted into fertilizer +and that fertilizer will be brought to + + align:start position:0% +and that fertilizer will be brought to + + + align:start position:0% +and that fertilizer will be brought to +our Eco Green Farm we have a daily + + align:start position:0% +our Eco Green Farm we have a daily + + + align:start position:0% +our Eco Green Farm we have a daily +schedule for Monday to Friday for all + + align:start position:0% +schedule for Monday to Friday for all + + + align:start position:0% +schedule for Monday to Friday for all +these food we have to collect the food + + align:start position:0% +these food we have to collect the food + + + align:start position:0% +these food we have to collect the food +waste from the canteen just to be + + align:start position:0% +waste from the canteen just to be + + + align:start position:0% +waste from the canteen just to be +processed here we have uh the fruit + + align:start position:0% +processed here we have uh the fruit + + + align:start position:0% +processed here we have uh the fruit +section we also have the herbal section + + align:start position:0% +section we also have the herbal section + + + align:start position:0% +section we also have the herbal section +kitchen remedies over the other side you + + align:start position:0% +kitchen remedies over the other side you + + + align:start position:0% +kitchen remedies over the other side you +will find that we have this rain water + + align:start position:0% +will find that we have this rain water + + + align:start position:0% +will find that we have this rain water +harvesting system so this is um some + + align:start position:0% +harvesting system so this is um some + + + align:start position:0% +harvesting system so this is um some +collaboration with USM University s + + align:start position:0% + + + + align:start position:0% + +Malaysia pank hill we deal with the end + + align:start position:0% +Malaysia pank hill we deal with the end + + + align:start position:0% +Malaysia pank hill we deal with the end +product uh differently we ferment the + + align:start position:0% +product uh differently we ferment the + + + align:start position:0% +product uh differently we ferment the +food waste uh here itself without taking + + align:start position:0% +food waste uh here itself without taking + + + align:start position:0% +food waste uh here itself without taking +back to the factories and then we use + + align:start position:0% +back to the factories and then we use + + + align:start position:0% +back to the factories and then we use +the fermented food waste to treat Sea + + align:start position:0% +the fermented food waste to treat Sea + + + align:start position:0% +the fermented food waste to treat Sea +and the greas step has got no smell and + + align:start position:0% +and the greas step has got no smell and + + + align:start position:0% +and the greas step has got no smell and +no oil accumulation no grease + + align:start position:0% +no oil accumulation no grease + + + align:start position:0% +no oil accumulation no grease +accumulation if you ask me I think a lot + + align:start position:0% +accumulation if you ask me I think a lot + + + align:start position:0% +accumulation if you ask me I think a lot +of things work better on a small skill + + align:start position:0% +of things work better on a small skill + + + align:start position:0% +of things work better on a small skill +than on a large skill everybody has to + + align:start position:0% +than on a large skill everybody has to + + + align:start position:0% +than on a large skill everybody has to +cooporate you can develop the best + + align:start position:0% +cooporate you can develop the best + + + align:start position:0% +cooporate you can develop the best +machines in the world but if the people + + align:start position:0% +machines in the world but if the people + + + align:start position:0% +machines in the world but if the people +don't cooperate it's not the machine is + + align:start position:0% +don't cooperate it's not the machine is + + + align:start position:0% +don't cooperate it's not the machine is +not going to run by itself food waste + + align:start position:0% +not going to run by itself food waste + + + align:start position:0% +not going to run by itself food waste +doesn't get separated by itself you need + + align:start position:0% +doesn't get separated by itself you need + + + align:start position:0% +doesn't get separated by itself you need +people everybody has to chip in + + align:start position:0% +people everybody has to chip in + + + align:start position:0% +people everybody has to chip in +somewhere and this is where we are going + + align:start position:0% +somewhere and this is where we are going + + + align:start position:0% +somewhere and this is where we are going +with the schools to start teaching the + + align:start position:0% +with the schools to start teaching the + + + align:start position:0% +with the schools to start teaching the +students the importance of actually + + align:start position:0% +students the importance of actually + + + align:start position:0% +students the importance of actually +separating your foot waste and making + + align:start position:0% +separating your foot waste and making + + + align:start position:0% +separating your foot waste and making +sure that they're going to the correct + + align:start position:0% + + + + align:start position:0% + +places three main lessons from the case + + align:start position:0% +places three main lessons from the case + + + align:start position:0% +places three main lessons from the case +first Innovation capabilities were + + align:start position:0% +first Innovation capabilities were + + + align:start position:0% +first Innovation capabilities were +created by involving various + + align:start position:0% +created by involving various + + + align:start position:0% +created by involving various +stakeholders second broad stakeholder + + align:start position:0% +stakeholders second broad stakeholder + + + align:start position:0% +stakeholders second broad stakeholder +involvement brought resources like + + align:start position:0% +involvement brought resources like + + + align:start position:0% +involvement brought resources like +knowledge and finance from various + + align:start position:0% +knowledge and finance from various + + + align:start position:0% +knowledge and finance from various +sources these will not be possible + + align:start position:0% +sources these will not be possible + + + align:start position:0% +sources these will not be possible +possible if a stakeholder was working + + align:start position:0% +possible if a stakeholder was working + + + align:start position:0% +possible if a stakeholder was working +alone third Innovations were able to + + align:start position:0% +alone third Innovations were able to + + + align:start position:0% +alone third Innovations were able to +connect waste with other issues such as + + align:start position:0% +connect waste with other issues such as + + + align:start position:0% +connect waste with other issues such as +health sewage treatment and education + + align:start position:0% +health sewage treatment and education + + + align:start position:0% +health sewage treatment and education +Innovation can overcome problems of + + align:start position:0% +Innovation can overcome problems of + + + align:start position:0% +Innovation can overcome problems of +collective action where many + + align:start position:0% +collective action where many + + + align:start position:0% +collective action where many +stakeholders must work together there + + align:start position:0% +stakeholders must work together there + + + align:start position:0% +stakeholders must work together there +should be awareness amongst the + + align:start position:0% +should be awareness amongst the + + + align:start position:0% +should be awareness amongst the +communities yeah on how to reduce the + + align:start position:0% +communities yeah on how to reduce the + + + align:start position:0% +communities yeah on how to reduce the +waste and also in terms of the industry + + align:start position:0% +waste and also in terms of the industry + + + align:start position:0% +waste and also in terms of the industry +so there are lot of uh players in the + + align:start position:0% +so there are lot of uh players in the + + + align:start position:0% +so there are lot of uh players in the +field of uh Waste Management which + + align:start position:0% +field of uh Waste Management which + + + align:start position:0% +field of uh Waste Management which +everyone has to take part + + align:start position:0% +everyone has to take part + + + align:start position:0% +everyone has to take part +in the state and local authorities have + + align:start position:0% +in the state and local authorities have + + + align:start position:0% +in the state and local authorities have +helped to scale up such initiatives by + + align:start position:0% +helped to scale up such initiatives by + + + align:start position:0% +helped to scale up such initiatives by +providing support to coordinate the + + align:start position:0% +providing support to coordinate the + + + align:start position:0% +providing support to coordinate the +different efforts from federal + + align:start position:0% +different efforts from federal + + + align:start position:0% +different efforts from federal +government civil society and linking + + align:start position:0% +government civil society and linking + + + align:start position:0% +government civil society and linking +them with citizens we still feel that + + align:start position:0% +them with citizens we still feel that + + + align:start position:0% +them with citizens we still feel that +there is some to be done more we already + + align:start position:0% +there is some to be done more we already + + + align:start position:0% +there is some to be done more we already +come up to the policy in line with the + + align:start position:0% +come up to the policy in line with the + + + align:start position:0% +come up to the policy in line with the +federal uh policy to come up with the + + align:start position:0% +federal uh policy to come up with the + + + align:start position:0% +federal uh policy to come up with the +mechanism of collections we are not + + align:start position:0% +mechanism of collections we are not + + + align:start position:0% +mechanism of collections we are not +going to use the same mechanism as + + align:start position:0% +going to use the same mechanism as + + + align:start position:0% +going to use the same mechanism as +Federal what they are doing we are going + + align:start position:0% +Federal what they are doing we are going + + + align:start position:0% +Federal what they are doing we are going +to improvise this according to our own + + align:start position:0% +to improvise this according to our own + + + align:start position:0% +to improvise this according to our own +local environment a combination of top- + + align:start position:0% +local environment a combination of top- + + + align:start position:0% +local environment a combination of top- +down efforts from governments to support + + align:start position:0% +down efforts from governments to support + + + align:start position:0% +down efforts from governments to support +niches of botton up Urban Innovation + + align:start position:0% +niches of botton up Urban Innovation + + + align:start position:0% +niches of botton up Urban Innovation +brings the right combination to nurture + + align:start position:0% +brings the right combination to nurture + + + align:start position:0% +brings the right combination to nurture +broad transformation in urban service + + align:start position:0% + + + + align:start position:0% + +delivery the way you're disposing it + + align:start position:0% +delivery the way you're disposing it + + + align:start position:0% +delivery the way you're disposing it +whether you're land filling or you're + + align:start position:0% +whether you're land filling or you're + + + align:start position:0% +whether you're land filling or you're +incinerating or you're just dumping is + + align:start position:0% +incinerating or you're just dumping is + + + align:start position:0% +incinerating or you're just dumping is +all causing problems for for the climate + + align:start position:0% +all causing problems for for the climate + + + align:start position:0% +all causing problems for for the climate +too because of the greenhouse gas + + align:start position:0% +too because of the greenhouse gas + + + align:start position:0% +too because of the greenhouse gas +emissions how can we make a + + align:start position:0% +emissions how can we make a + + + align:start position:0% +emissions how can we make a +city + + align:start position:0% +city + + + align:start position:0% +city +suitable for our bodies and our health + + align:start position:0% +suitable for our bodies and our health + + + align:start position:0% +suitable for our bodies and our health +we've designed and managed cities often + + align:start position:0% +we've designed and managed cities often + + + align:start position:0% +we've designed and managed cities often +in the interest of Motorcars rather than + + align:start position:0% +in the interest of Motorcars rather than + + + align:start position:0% +in the interest of Motorcars rather than +in the interests of people we need to uh + + align:start position:0% +in the interests of people we need to uh + + + align:start position:0% +in the interests of people we need to uh +rethink the city in the interest of + + align:start position:0% +rethink the city in the interest of + + + align:start position:0% +rethink the city in the interest of +people even though there is some + + align:start position:0% +people even though there is some + + + align:start position:0% +people even though there is some +initiative being done but still the + + align:start position:0% +initiative being done but still the + + + align:start position:0% +initiative being done but still the +mindset still need to be changed the the + + align:start position:0% +mindset still need to be changed the the + + + align:start position:0% +mindset still need to be changed the the +current concept of development is the + + align:start position:0% +current concept of development is the + + + align:start position:0% +current concept of development is the +more buildings they have the more + + align:start position:0% +more buildings they have the more + + + align:start position:0% +more buildings they have the more +industri they have the more developed + + align:start position:0% +industri they have the more developed + + + align:start position:0% +industri they have the more developed +you are the better you become but uh + + align:start position:0% +you are the better you become but uh + + + align:start position:0% +you are the better you become but uh +they have not factored in actually the + + align:start position:0% +they have not factored in actually the + + + align:start position:0% +they have not factored in actually the +cost in terms of pollution in terms of + + align:start position:0% +cost in terms of pollution in terms of + + + align:start position:0% +cost in terms of pollution in terms of +traffic congestion creating the + + align:start position:0% +traffic congestion creating the + + + align:start position:0% +traffic congestion creating the +capabilities to innovate in governments + + align:start position:0% +capabilities to innovate in governments + + + align:start position:0% +capabilities to innovate in governments +and Civil Society is crucial to + + align:start position:0% +and Civil Society is crucial to + + + align:start position:0% +and Civil Society is crucial to +combating Global problems such as + + align:start position:0% +combating Global problems such as + + + align:start position:0% +combating Global problems such as +climate change which requires our higher + + align:start position:0% +climate change which requires our higher + + + align:start position:0% +climate change which requires our higher +degree of collective action to design + + align:start position:0% +degree of collective action to design + + + align:start position:0% +degree of collective action to design +and manag the cities of the future this + + align:start position:0% +and manag the cities of the future this + + + align:start position:0% +and manag the cities of the future this +will require innovation in our thinking + + align:start position:0% +will require innovation in our thinking + + + align:start position:0% +will require innovation in our thinking +about how we care out Urban + + align:start position:0% +about how we care out Urban + + + align:start position:0% +about how we care out Urban +[Music] + + align:start position:0% + + + + align:start position:0% + +Development + + align:start position:0% +Development + + + align:start position:0% +Development +[Music] \ No newline at end of file diff --git a/9QJt03983Gg.txt b/9QJt03983Gg.txt new file mode 100644 index 0000000000000000000000000000000000000000..cfe9f0b012c57bd84390bd2c26a450286fbdd611 --- /dev/null +++ b/9QJt03983Gg.txt @@ -0,0 +1,1443 @@ +align:start position:0% + +we now continue our discussion of + + align:start position:0% +we now continue our discussion of + + + align:start position:0% +we now continue our discussion of +infinite series sometimes we have to + + align:start position:0% +infinite series sometimes we have to + + + align:start position:0% +infinite series sometimes we have to +deal with series where the terms being + + align:start position:0% +deal with series where the terms being + + + align:start position:0% +deal with series where the terms being +added are indexed by multiple indices as + + align:start position:0% +added are indexed by multiple indices as + + + align:start position:0% +added are indexed by multiple indices as +in this example here we are given + + align:start position:0% +in this example here we are given + + + align:start position:0% +in this example here we are given +numbers a I J and I ranges over all the + + align:start position:0% +numbers a I J and I ranges over all the + + + align:start position:0% +numbers a I J and I ranges over all the +positive integers J also ranges over all + + align:start position:0% +positive integers J also ranges over all + + + align:start position:0% +positive integers J also ranges over all +the positive integers so what does this + + align:start position:0% +the positive integers so what does this + + + align:start position:0% +the positive integers so what does this +sum represent we can think of it as + + align:start position:0% +sum represent we can think of it as + + + align:start position:0% +sum represent we can think of it as +follows we have here the 2-dimensional + + align:start position:0% +follows we have here the 2-dimensional + + + align:start position:0% +follows we have here the 2-dimensional +grid that corresponds to all the pair's + + align:start position:0% +grid that corresponds to all the pair's + + + align:start position:0% +grid that corresponds to all the pair's +I J and in essence each one of those + + align:start position:0% +I J and in essence each one of those + + + align:start position:0% +I J and in essence each one of those +points corresponds to one of the terms + + align:start position:0% +points corresponds to one of the terms + + + align:start position:0% +points corresponds to one of the terms +that we want to add so we can sum the + + align:start position:0% +that we want to add so we can sum the + + + align:start position:0% +that we want to add so we can sum the +different terms in some arbitrary order + + align:start position:0% +different terms in some arbitrary order + + + align:start position:0% +different terms in some arbitrary order +let's say we start from here take that + + align:start position:0% +let's say we start from here take that + + + align:start position:0% +let's say we start from here take that +term add this term then add this term + + align:start position:0% +term add this term then add this term + + + align:start position:0% +term add this term then add this term +here then add this term then the next + + align:start position:0% +here then add this term then the next + + + align:start position:0% +here then add this term then the next +term next term and so on and we can keep + + align:start position:0% +term next term and so on and we can keep + + + align:start position:0% +term next term and so on and we can keep +going that way adding the different + + align:start position:0% +going that way adding the different + + + align:start position:0% +going that way adding the different +terms in according to some sequence so + + align:start position:0% +terms in according to some sequence so + + + align:start position:0% +terms in according to some sequence so +essentially what we are doing here is + + align:start position:0% +essentially what we are doing here is + + + align:start position:0% +essentially what we are doing here is +we're taking this two-dimensional grid + + align:start position:0% +we're taking this two-dimensional grid + + + align:start position:0% +we're taking this two-dimensional grid +and arranging the terms associated with + + align:start position:0% +and arranging the terms associated with + + + align:start position:0% +and arranging the terms associated with +that grid in some particular linear + + align:start position:0% +that grid in some particular linear + + + align:start position:0% +that grid in some particular linear +order and were summing those terms in + + align:start position:0% +order and were summing those terms in + + + align:start position:0% +order and were summing those terms in +sequence as long as this sum converges + + align:start position:0% +sequence as long as this sum converges + + + align:start position:0% +sequence as long as this sum converges +to something as we keep adding more and + + align:start position:0% +to something as we keep adding more and + + + align:start position:0% +to something as we keep adding more and +more terms then this double series will + + align:start position:0% +more terms then this double series will + + + align:start position:0% +more terms then this double series will +be well-defined notice however we can + + align:start position:0% +be well-defined notice however we can + + + align:start position:0% +be well-defined notice however we can +add those terms in many different orders + + align:start position:0% +add those terms in many different orders + + + align:start position:0% +add those terms in many different orders +and in principle those different orders + + align:start position:0% +and in principle those different orders + + + align:start position:0% +and in principle those different orders +might give us different kinds of results + + align:start position:0% +might give us different kinds of results + + + align:start position:0% +might give us different kinds of results +on the other hand as long as the sum of + + align:start position:0% +on the other hand as long as the sum of + + + align:start position:0% +on the other hand as long as the sum of +the absolute values of all the terms + + align:start position:0% +the absolute values of all the terms + + + align:start position:0% +the absolute values of all the terms +turns out to be finite then the + + align:start position:0% +turns out to be finite then the + + + align:start position:0% +turns out to be finite then the +particular order in which we are adding + + align:start position:0% +particular order in which we are adding + + + align:start position:0% +particular order in which we are adding +the different terms will turn out that + + align:start position:0% +the different terms will turn out that + + + align:start position:0% +the different terms will turn out that +it doesn't matter there's another way + + align:start position:0% +it doesn't matter there's another way + + + align:start position:0% +it doesn't matter there's another way +that we can add the terms together and + + align:start position:0% +that we can add the terms together and + + + align:start position:0% +that we can add the terms together and +this is the following let us consider + + align:start position:0% +this is the following let us consider + + + align:start position:0% +this is the following let us consider +fixing a particular choice of AI + + align:start position:0% +fixing a particular choice of AI + + + align:start position:0% +fixing a particular choice of AI +and adding all the terms that are + + align:start position:0% +and adding all the terms that are + + + align:start position:0% +and adding all the terms that are +associated with this particular choice + + align:start position:0% +associated with this particular choice + + + align:start position:0% +associated with this particular choice +of I as J ranges from one to infinity so + + align:start position:0% +of I as J ranges from one to infinity so + + + align:start position:0% +of I as J ranges from one to infinity so +what we're doing is we're taking the + + align:start position:0% +what we're doing is we're taking the + + + align:start position:0% +what we're doing is we're taking the +summation from J equal to 1 to infinity + + align:start position:0% +summation from J equal to 1 to infinity + + + align:start position:0% +summation from J equal to 1 to infinity +while keeping the value of I fixed we do + + align:start position:0% +while keeping the value of I fixed we do + + + align:start position:0% +while keeping the value of I fixed we do +this for every possible I so for every + + align:start position:0% +this for every possible I so for every + + + align:start position:0% +this for every possible I so for every +possible I we're going to get a + + align:start position:0% +possible I we're going to get a + + + align:start position:0% +possible I we're going to get a +particular number and then we take the + + align:start position:0% +particular number and then we take the + + + align:start position:0% +particular number and then we take the +numbers that we obtain for the different + + align:start position:0% +numbers that we obtain for the different + + + align:start position:0% +numbers that we obtain for the different +choices of I so I ranges from 1 to + + align:start position:0% +choices of I so I ranges from 1 to + + + align:start position:0% +choices of I so I ranges from 1 to +infinity and we add all those terms + + align:start position:0% +infinity and we add all those terms + + + align:start position:0% +infinity and we add all those terms +together so this is one particular order + + align:start position:0% +together so this is one particular order + + + align:start position:0% +together so this is one particular order +one particular way of doing the infinite + + align:start position:0% +one particular way of doing the infinite + + + align:start position:0% +one particular way of doing the infinite +summation now why start with a summation + + align:start position:0% +summation now why start with a summation + + + align:start position:0% +summation now why start with a summation +over J's while keeping eye fixed there's + + align:start position:0% +over J's while keeping eye fixed there's + + + align:start position:0% +over J's while keeping eye fixed there's +no reason for that we could also carry + + align:start position:0% +no reason for that we could also carry + + + align:start position:0% +no reason for that we could also carry +out the summation by fixing a particular + + align:start position:0% +out the summation by fixing a particular + + + align:start position:0% +out the summation by fixing a particular +choice of J and summing over all eyes so + + align:start position:0% +choice of J and summing over all eyes so + + + align:start position:0% +choice of J and summing over all eyes so +now it is I that ranges from 1 to + + align:start position:0% +now it is I that ranges from 1 to + + + align:start position:0% +now it is I that ranges from 1 to +infinity and we look at this infinite + + align:start position:0% +infinity and we look at this infinite + + + align:start position:0% +infinity and we look at this infinite +sum this is the infinite sum of those + + align:start position:0% +sum this is the infinite sum of those + + + align:start position:0% +sum this is the infinite sum of those +terms we obtain one such infinite sum + + align:start position:0% +terms we obtain one such infinite sum + + + align:start position:0% +terms we obtain one such infinite sum +for every choice of J and then we take + + align:start position:0% +for every choice of J and then we take + + + align:start position:0% +for every choice of J and then we take +that son that we obtain for any + + align:start position:0% +that son that we obtain for any + + + align:start position:0% +that son that we obtain for any +particular choice of J and add over the + + align:start position:0% +particular choice of J and add over the + + + align:start position:0% +particular choice of J and add over the +different possible values of J so J goes + + align:start position:0% +different possible values of J so J goes + + + align:start position:0% +different possible values of J so J goes +from 1 to infinity this is a different + + align:start position:0% +from 1 to infinity this is a different + + + align:start position:0% +from 1 to infinity this is a different +way of carrying out the summation and + + align:start position:0% +way of carrying out the summation and + + + align:start position:0% +way of carrying out the summation and +these are going to give us the same + + align:start position:0% +these are going to give us the same + + + align:start position:0% +these are going to give us the same +result and the same result that we would + + align:start position:0% +result and the same result that we would + + + align:start position:0% +result and the same result that we would +also obtain if we were to add the terms + + align:start position:0% +also obtain if we were to add the terms + + + align:start position:0% +also obtain if we were to add the terms +in this particular order as long as the + + align:start position:0% +in this particular order as long as the + + + align:start position:0% +in this particular order as long as the +double series is well defined in the + + align:start position:0% +double series is well defined in the + + + align:start position:0% +double series is well defined in the +following sense if we have a guarantee + + align:start position:0% +following sense if we have a guarantee + + + align:start position:0% +following sense if we have a guarantee +that the sum of the absolute values of + + align:start position:0% +that the sum of the absolute values of + + + align:start position:0% +that the sum of the absolute values of +those numbers is finite no matter which + + align:start position:0% +those numbers is finite no matter which + + + align:start position:0% +those numbers is finite no matter which +way we add them then it turns out that + + align:start position:0% +way we add them then it turns out that + + + align:start position:0% +way we add them then it turns out that +we can use any particular order to add + + align:start position:0% +we can use any particular order to add + + + align:start position:0% +we can use any particular order to add +the terms in the series we're going to + + align:start position:0% +the terms in the series we're going to + + + align:start position:0% +the terms in the series we're going to +get the same result and + + align:start position:0% +get the same result and + + + align:start position:0% +get the same result and +we can also carry out the double the + + align:start position:0% +we can also carry out the double the + + + align:start position:0% +we can also carry out the double the +double summation by doing by adding over + + align:start position:0% +double summation by doing by adding over + + + align:start position:0% +double summation by doing by adding over +one index at a time + + align:start position:0% +one index at a time + + + align:start position:0% +one index at a time +a word of caution this condition is not + + align:start position:0% +a word of caution this condition is not + + + align:start position:0% +a word of caution this condition is not +always satisfied and in those cases + + align:start position:0% +always satisfied and in those cases + + + align:start position:0% +always satisfied and in those cases +strange things can happen suppose that + + align:start position:0% +strange things can happen suppose that + + + align:start position:0% +strange things can happen suppose that +are the sequence that we're dealing with + + align:start position:0% +are the sequence that we're dealing with + + + align:start position:0% +are the sequence that we're dealing with +the AI J's take those particular values + + align:start position:0% +the AI J's take those particular values + + + align:start position:0% +the AI J's take those particular values +indicated in this picture and all the + + align:start position:0% +indicated in this picture and all the + + + align:start position:0% +indicated in this picture and all the +remaining terms the a IJ is associated + + align:start position:0% +remaining terms the a IJ is associated + + + align:start position:0% +remaining terms the a IJ is associated +with the other dots are all zeros so all + + align:start position:0% +with the other dots are all zeros so all + + + align:start position:0% +with the other dots are all zeros so all +these terms out there will be zeros if + + align:start position:0% +these terms out there will be zeros if + + + align:start position:0% +these terms out there will be zeros if +we carry out the summation by fixing a J + + align:start position:0% +we carry out the summation by fixing a J + + + align:start position:0% +we carry out the summation by fixing a J +and adding over all eyes what we get + + align:start position:0% +and adding over all eyes what we get + + + align:start position:0% +and adding over all eyes what we get +here is 0 + 0 + 0 + 0 that's because in + + align:start position:0% +here is 0 + 0 + 0 + 0 that's because in + + + align:start position:0% +here is 0 + 0 + 0 + 0 that's because in +each row we have a 1 and the minus 1 + + align:start position:0% +each row we have a 1 and the minus 1 + + + align:start position:0% +each row we have a 1 and the minus 1 +which cancel out and give us zeros so if + + align:start position:0% +which cancel out and give us zeros so if + + + align:start position:0% +which cancel out and give us zeros so if +we carry out the summation in this + + align:start position:0% +we carry out the summation in this + + + align:start position:0% +we carry out the summation in this +manner we get a sum of zeros which is 0 + + align:start position:0% +manner we get a sum of zeros which is 0 + + + align:start position:0% +manner we get a sum of zeros which is 0 +but if we carry out the summation in + + align:start position:0% +but if we carry out the summation in + + + align:start position:0% +but if we carry out the summation in +this order fix an AI and then add over + + align:start position:0% +this order fix an AI and then add over + + + align:start position:0% +this order fix an AI and then add over +all J's the first term that we get here + + align:start position:0% +all J's the first term that we get here + + + align:start position:0% +all J's the first term that we get here +is going to be 1 because in this column + + align:start position:0% +is going to be 1 because in this column + + + align:start position:0% +is going to be 1 because in this column +there's all this is the only nonzero + + align:start position:0% +there's all this is the only nonzero + + + align:start position:0% +there's all this is the only nonzero +number and then in the remaining columns + + align:start position:0% +number and then in the remaining columns + + + align:start position:0% +number and then in the remaining columns +as we add the terms we're going to get + + align:start position:0% +as we add the terms we're going to get + + + align:start position:0% +as we add the terms we're going to get +zeros and zeros and so on and so if we + + align:start position:0% +zeros and zeros and so on and so if we + + + align:start position:0% +zeros and zeros and so on and so if we +carry out the summation in this way we + + align:start position:0% +carry out the summation in this way we + + + align:start position:0% +carry out the summation in this way we +obtain a 1 so this is an example that + + align:start position:0% +obtain a 1 so this is an example that + + + align:start position:0% +obtain a 1 so this is an example that +shows you that the order of summation + + align:start position:0% +shows you that the order of summation + + + align:start position:0% +shows you that the order of summation +actually may matter in this example the + + align:start position:0% +actually may matter in this example the + + + align:start position:0% +actually may matter in this example the +sum of the absolute values of all the + + align:start position:0% +sum of the absolute values of all the + + + align:start position:0% +sum of the absolute values of all the +terms that are involved is infinity + + align:start position:0% +terms that are involved is infinity + + + align:start position:0% +terms that are involved is infinity +because we have infinitely many plus or + + align:start position:0% +because we have infinitely many plus or + + + align:start position:0% +because we have infinitely many plus or +minus ones so this condition here is not + + align:start position:0% +minus ones so this condition here is not + + + align:start position:0% +minus ones so this condition here is not +satisfied in this example let us now + + align:start position:0% +satisfied in this example let us now + + + align:start position:0% +satisfied in this example let us now +consider the case where we want to add + + align:start position:0% +consider the case where we want to add + + + align:start position:0% +consider the case where we want to add +the terms of a double sequence but + + align:start position:0% +the terms of a double sequence but + + + align:start position:0% +the terms of a double sequence but +over a limited range of indices as in + + align:start position:0% +over a limited range of indices as in + + + align:start position:0% +over a limited range of indices as in +this example where we have coefficients + + align:start position:0% +this example where we have coefficients + + + align:start position:0% +this example where we have coefficients +a IJ which we want to add but only for + + align:start position:0% +a IJ which we want to add but only for + + + align:start position:0% +a IJ which we want to add but only for +those eyes and J is for which J is less + + align:start position:0% +those eyes and J is for which J is less + + + align:start position:0% +those eyes and J is for which J is less +than or equal to I graphically this + + align:start position:0% +than or equal to I graphically this + + + align:start position:0% +than or equal to I graphically this +means that we only want to consider the + + align:start position:0% +means that we only want to consider the + + + align:start position:0% +means that we only want to consider the +pairs shown in this picture so these + + align:start position:0% +pairs shown in this picture so these + + + align:start position:0% +pairs shown in this picture so these +points here correspond to IJ pairs for + + align:start position:0% +points here correspond to IJ pairs for + + + align:start position:0% +points here correspond to IJ pairs for +which I is equal to J terms on the right + + align:start position:0% +which I is equal to J terms on the right + + + align:start position:0% +which I is equal to J terms on the right +or points to the right correspond to IJ + + align:start position:0% +or points to the right correspond to IJ + + + align:start position:0% +or points to the right correspond to IJ +pairs for which I is at least as large + + align:start position:0% +pairs for which I is at least as large + + + align:start position:0% +pairs for which I is at least as large +as J we can carry out this summation in + + align:start position:0% +as J we can carry out this summation in + + + align:start position:0% +as J we can carry out this summation in +two ways one way is the following we fix + + align:start position:0% +two ways one way is the following we fix + + + align:start position:0% +two ways one way is the following we fix +the value of I and we consider all the + + align:start position:0% +the value of I and we consider all the + + + align:start position:0% +the value of I and we consider all the +corresponding terms that correspond to + + align:start position:0% +corresponding terms that correspond to + + + align:start position:0% +corresponding terms that correspond to +different choices of J but we only go up + + align:start position:0% +different choices of J but we only go up + + + align:start position:0% +different choices of J but we only go up +to the point where I is equal to J this + + align:start position:0% +to the point where I is equal to J this + + + align:start position:0% +to the point where I is equal to J this +is the largest term so what are we doing + + align:start position:0% +is the largest term so what are we doing + + + align:start position:0% +is the largest term so what are we doing +here we're taking the coefficients a IJ + + align:start position:0% +here we're taking the coefficients a IJ + + + align:start position:0% +here we're taking the coefficients a IJ +and we are adding over all J's starting + + align:start position:0% +and we are adding over all J's starting + + + align:start position:0% +and we are adding over all J's starting +from 1 which corresponds to this term + + align:start position:0% +from 1 which corresponds to this term + + + align:start position:0% +from 1 which corresponds to this term +and J goes up to the point where it + + align:start position:0% +and J goes up to the point where it + + + align:start position:0% +and J goes up to the point where it +becomes equal to AI we do this for every + + align:start position:0% +becomes equal to AI we do this for every + + + align:start position:0% +becomes equal to AI we do this for every +value of AI and so we get a number for + + align:start position:0% +value of AI and so we get a number for + + + align:start position:0% +value of AI and so we get a number for +the sum of each one of the columns and + + align:start position:0% +the sum of each one of the columns and + + + align:start position:0% +the sum of each one of the columns and +then we add those numbers together so + + align:start position:0% +then we add those numbers together so + + + align:start position:0% +then we add those numbers together so +we're adding over all eyes and eye + + align:start position:0% +we're adding over all eyes and eye + + + align:start position:0% +we're adding over all eyes and eye +ranges from 1 up to infinity this is one + + align:start position:0% +ranges from 1 up to infinity this is one + + + align:start position:0% +ranges from 1 up to infinity this is one +way of carrying out the summation + + align:start position:0% +way of carrying out the summation + + + align:start position:0% +way of carrying out the summation +alternatively we could fix the value of + + align:start position:0% +alternatively we could fix the value of + + + align:start position:0% +alternatively we could fix the value of +J and consider doing the summation over + + align:start position:0% +J and consider doing the summation over + + + align:start position:0% +J and consider doing the summation over +all choices of I so this corresponds to + + align:start position:0% +all choices of I so this corresponds to + + + align:start position:0% +all choices of I so this corresponds to +the sum over all choices of AI from + + align:start position:0% +the sum over all choices of AI from + + + align:start position:0% +the sum over all choices of AI from +where the smallest term the first term + + align:start position:0% +where the smallest term the first term + + + align:start position:0% +where the smallest term the first term +happens when I is equal to the value of + + align:start position:0% +happens when I is equal to the value of + + + align:start position:0% +happens when I is equal to the value of +J and then we have larger choices of I + + align:start position:0% +J and then we have larger choices of I + + + align:start position:0% +J and then we have larger choices of I +numbers for which I is bigger than the + + align:start position:0% +numbers for which I is bigger than the + + + align:start position:0% +numbers for which I is bigger than the +corresponding value of J and so I ranges + + align:start position:0% +corresponding value of J and so I ranges + + + align:start position:0% +corresponding value of J and so I ranges +from J or + + align:start position:0% +from J or + + + align:start position:0% +from J or +the way to infinity and this is the sum + + align:start position:0% +the way to infinity and this is the sum + + + align:start position:0% +the way to infinity and this is the sum +over one of the rows in this diagram we + + align:start position:0% +over one of the rows in this diagram we + + + align:start position:0% +over one of the rows in this diagram we +do this for every J we get a result and + + align:start position:0% +do this for every J we get a result and + + + align:start position:0% +do this for every J we get a result and +then we need to add all those results + + align:start position:0% +then we need to add all those results + + + align:start position:0% +then we need to add all those results +together so we are summing for all J's + + align:start position:0% +together so we are summing for all J's + + + align:start position:0% +together so we are summing for all J's +from 1 up to infinity so these are two + + align:start position:0% +from 1 up to infinity so these are two + + + align:start position:0% +from 1 up to infinity so these are two +different ways that we can evaluate this + + align:start position:0% +different ways that we can evaluate this + + + align:start position:0% +different ways that we can evaluate this +series associated with a double sequence + + align:start position:0% +series associated with a double sequence + + + align:start position:0% +series associated with a double sequence +we can either add overall J's first and + + align:start position:0% +we can either add overall J's first and + + + align:start position:0% +we can either add overall J's first and +then over eyes or we can sum over all + + align:start position:0% +then over eyes or we can sum over all + + + align:start position:0% +then over eyes or we can sum over all +eyes first and then over all J's the two + + align:start position:0% +eyes first and then over all J's the two + + + align:start position:0% +eyes first and then over all J's the two +ways of approaching this problem this + + align:start position:0% +ways of approaching this problem this + + + align:start position:0% +ways of approaching this problem this +summation should give us the same answer + + align:start position:0% +summation should give us the same answer + + + align:start position:0% +summation should give us the same answer +and this is going to be again subject to + + align:start position:0% +and this is going to be again subject to + + + align:start position:0% +and this is going to be again subject to +the usual qualification as long as the + + align:start position:0% +the usual qualification as long as the + + + align:start position:0% +the usual qualification as long as the +sum of the absolute values of the terms + + align:start position:0% +sum of the absolute values of the terms + + + align:start position:0% +sum of the absolute values of the terms +that we are trying to add is less than + + align:start position:0% +that we are trying to add is less than + + + align:start position:0% +that we are trying to add is less than +infinity if this condition is true then + + align:start position:0% +infinity if this condition is true then + + + align:start position:0% +infinity if this condition is true then +the two ways of carrying out the + + align:start position:0% +the two ways of carrying out the + + + align:start position:0% +the two ways of carrying out the +summation are equal and they're just two + + align:start position:0% +summation are equal and they're just two + + + align:start position:0% +summation are equal and they're just two +different alternatives \ No newline at end of file diff --git a/9Rb85cOXTKU.txt b/9Rb85cOXTKU.txt new file mode 100644 index 0000000000000000000000000000000000000000..1efd5410c13c2e132342590f2e568a64900be54c --- /dev/null +++ b/9Rb85cOXTKU.txt @@ -0,0 +1,4251 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: So a couple of things +I want to say about the + +final project. + +You guys should start +thinking about it. + +So of course, you guys should +think about the teams first, + +and submit team information. + +Say who you're going +to team up with. + +By when? + +Team information, +Josh, by when? + +Team information +has to be in-- + +AUDIENCE: By tomorrow. + +PROFESSOR: By tomorrow. + +OK, good. + +You should know your teams. + +Get them together, use the same +mechanism that we used + +before to get the team +information before. + +So we are going to add one small +thing this year I think + +that would be useful. + +Once you have submitted your +design documents, we are going + +to get a design review +done by Masters. + +So what that means is next week +we are going to schedule + +a design review with +your Masters. + +And you should send mail to your +Masters, hopefully in the + +middle of next week, to schedule +a design review. + +The design review will happen +the week after Thanksgiving. + +So you'll submit your design +doc next week, and then the + +week after Thanksgiving, you'll + +schedule your design review. + +The earlier the better, because +you can hopefully get + +some really good feedback +before you go into + +implementation. + +So have an idea what +you're doing. + +Of course you're write it up +for your design document. + +And then go to your Masters +and say, here's what I'm + +planning to do. + +Get some good feedback, and +hopefully it will help your + +life to do that. + +And then beforehand, performance +only mattered for + +your grade. + +We did this absolute grading. + +This year, we are going to +have actually an in-class + +competition on the final day +of class, to figure out who + +has the fastest ray tracer +in the class. + +And for that we will actually +give [? you ?] + +a little but of a different +[UNINTELLIGIBLE] + +than what I have given you. + +And so you don't go too much +into really hand coding to + +that teammate because +that might not work. + +And so here's something +hot off the press. + +So for the winning team, there's +going to be an Akamai + +prize for the winning team. + +And this prize includes a +celebration/demonstration at + +Akamai headquarters. + +You're going to go visit +there [UNINTELLIGIBLE] + +and perhaps show off to their +engineers the cool + +ray tracer you did. + +And also every team member of +the winning team is going to + +get the iPod Nano. + +Sorry, guys, last year +it didn't happen. + +First time. + +So there's a lot at stake. + +So make sure your program +is going to run + +as fast as you can. + +OK, with that, let's +get your slides on. + +So I'd like to introduce +Bradley Kuszmaul. + +Bradley has been at MIT, in +and out of MIT, for a long + +time doing lots of cool stuff +with high-performance-- + +yeah, make the screen bigger-- + +high-performance computing. + +He has done some really +interesting data structure + +work, performance optimization +work, and stuff like that. + +And today he's going to talk +about an interesting data + +structure that goes all the way +from theory into getting + +really, really high-performance. + +Thank you, Bradley. + +OK, you have the mic. + +BRADLEY KUSZMAUL: So I'm going +to talk about a data structure + +called fractal trees, which in +the academic world are called + +streaming B-trees. + +But the marketing people didn't +think very much of + +that, and so a lot of these +slides are borrowed from a + +company that I've started. + +So rather than redo that, I'm +just going to stick to the + +terminology "fractal tree." I'm +research faculty at MIT, + +and I'm a founder at Tokutek. + +And so that's sort +of who I am. + +I'll do a little bit +more introduction. + +So I have been around +at MIT a long time. + +I have four MIT degrees. + +And I was one of the architects +of the Connection + +Machine CM-5. + +And Charles was also one of the + +architects of that machine. + +So at the time, that was the +fastest machine in the world, + +at least for some +applications. + +And after getting my degrees and +being an architect, I went + +and was a professor +at Yale, and then + +later I was at Akamai. + +So I don't know what an Akamai +prize is beyond an iPod, but + +maybe it's like all your content +delivered free for a + +month or something. + +And I'm now research faculty +in the SuperTech Group, + +working with Charles. + +And I'm a founder of Tokutek, +which is commercializing some + +work we did. + +A couple years ago, I started +collaborating with Michael + +Bender and Martin Farach-Colton +on data + +structures for that are suited +for storing data on disk. + +And we ended up a bit later +starting a company to + +commercialize the research. + +And basically, I'll tell you +sort of what the background + +is, and actually go into some + +technical on the data structure. + +So I don't know exactly what +you've spent most of your time + +on, but a lot of +high-performance work, + +especially in academia, focuses +on the CPUs and using + +the CPUs efficiently, +maybe getting + +lots of FLOPS or something. + +The Cilk work that Charles and +I did, for example, is + +squarely in the category of how +do you get more FLOPS, or + +more computrons out of +a particular machine. + +But it turns out often I/O is +a big bottleneck, and so you + +see systems that look a +little bit like this. + +You have a whole bunch of +sensors somewhere, and the + +sensors might be something like +a bunch of telescopes in + +an astronomy system. + +They're sending millions of +data items per second, and + +they have to be stored. + +And disk is where you have to +store large amounts of data, + +because disk is orders of +magnitude per byte than other + +storage systems. + +And then you want to do queries +on that data, and you + +want to look at the data +that's recent. + +So it's not good enough just to +look at yesterday's data. + +You want to know what's +going on right now. + +If your sensor array is a bunch +of telescopes, and a + +supernova starts happening, you +want to be able to find + +out quickly what's going on, so +that you can broadcast the + +message to everybody in the +world so they can all point + +their telescopes at the +supernova while it's fresh. + +So that's the picture. + +Another example of a sensor +system is the internet, where + +you have thousands or millions +of people clicking away on + +Facebook, for example. + +You could view that collection +of mice as, abstractly, a + +bunch of sensors. + +And so you see it in science. + +You see it in internet. + +There's lots of applications. + +For example, another one would +be that you're looking for + +attacks on your internet +infrastructure in a large + +corporation, or something. + +So trying to reduce this big +sensor system to what is the + +fundamental problem, basically +we need to index the data. + +So the data indexing +problem is this. + +Data is arriving in one order, +and you want to ask about it + +in another order. + +So typically data is arriving +in the order by time. + +When an observation is made, +the event is logged. + +When the next observation is +made, the event is logged. + +And then you want +to do a query. + +Tell me everything that's +happening in that particular + +area of the sky over +the past month. + +So there's a big transposition +that has to be done for these + +queries, abstractly, is the +data's coming in in one order, + +and you want to sort +it and get the data + +out in another order. + +So one solution to this problem +that a lot of people + +use is simply to +sort the data. + +The data comes in. + +Sort it. + +Then you can query it in the +order that it makes sense. + +This is basically a +simple-minded explanation of + +what a data warehouse is. + +A data warehouse is all +this data comes in-- + +Walmart runs one of +these in Arkansas. + +All these events which are +people scanning cans of soup + +on bar codes all over the +country out in Walmart stores, + +all that data arrives in +Arkansas, in one location. + +They sort the data overnight, +and then the next morning they + +can answer questions like what's +the most popular food + +in the week before a +hurricane strikes? + +Because this is the kind of +request that Walmart might + +care about, because they get a +forecast that a hurricane's + +coming, and it turns out they +need to ship beer and + +blueberry Pop-Tarts to the local +stores, which are the + +things that basically you can +eat even if power has failed. + +The problem with sorting +is that you + +have to wait overnight. + +And for Walmart, that might +actually be good enough. + +But if you're the +astronomer, that + +application is not so great. + +So this problem is called +the indexing problem. + +We have to maintain indexes. + +And traditionally, the classical +solution is to use a + +data structure called +a B-tree. + +So do you all know +what a B-tree is? + +[INAUDIBLE] data structures +to algorithms? + +A B-tree is like a search tree, +except it's got some + +fan-out, and I'll talk +about it in a second. + +They show up in virtually all +storage systems today, and + +they were invented about 40 +years ago, and they show up in + +databases such as MyISAM +or Oracle. + +They show up in file +systems like XFS. + +You can think of what Unix file +systems like EXT do as + +being a variation of a B-tree. + +Basically they're everywhere. + +Mike might drew this picture +of a B-tree. + +And I said, I don't get it. + +He said, well, there's a +tree, and there's bees. + +And I said, but those +are wasps. + +So anyway-- + +So a B-tree looks like this. + +It's a search tree, so that +means everything is organized. + +It's got left children and right +children, and there's + +actually many children. + +And like any other search tree, +all the things to the + +left are before all the +things to the right. + +That's sort of the property of +trees that lets you do more + +than just a hash table. + +A hash table lets you +do get and put. + +But a tree lets you do next. + +And that's the key observation, +why you need + +something like a tree instead +of a hash table. + +A lot of database queries-- if +you go and click on Facebook + +on somebody's page, there's +all these things that have + +been posted on somebody's +wall. + +And what they've done when they +organized that data is + +that they've organized it so +that each of those items is a + +row in the database, and they're +next to each other so + +that you fetch the first one, +which is like the home page of + +the person, and then the next +and next and next gives each + +of the messages that they +want to display. + +And by making those things +adjacent to each other, it + +means that they don't incur +a disk I/O every time. + +if it were just a hash table, +you'd be having to look all + +over the place to find +those things. + +So B-trees are really fast, if +you have to do insertions + +sequentially. + +And the reason is you have a +data structure that's too big + +to fit in main memory. + +If the data structure fits in +main memory, this is just the + +wrong data structure, right? + +If it fits in main memory, what +should you use to solve + +this problem? + +Any ideas? + +What data structure is like a +B-tree except it doesn't have + +lots of fan-out? + +Does anybody know this +stuff in this class? + +Do you people know data +structures at all? + +Maybe I'm in the wrong place. + +Because it's OK. + +Just a binary tree would be the +data structure if you were + +doing this in memory, right? + +A binary tree would be fine. + +Or maybe you would try to +minimize the number of cache + +misses or something. + +So for sequential inserts, if +you're inserting at the end, + +basically all the stuff down the +right spine of the tree is + +in main memory, and +an insertion + +just inserts and inserts. + +You have no disk I/Os, +and basically it + +runs extremely fast. + +The disk I/O is sequential. + +You get basically performance +that's limited by the disk + +bandwidth, which is the rate +at which the disk can write + +consecutive blocks. + +But B-trees are really slow if +you're doing insertions that + +look random. + +The database world calls +those high-entropy. + +And so basically the idea is I +pick some leaf at random, and + +then I have to bring it into +main memory, put the new + +record in there, and then +eventually write it back out. + +And because the data structure +is spread all over disk, then + +each of those random blocks that +I choose, when I bring it + +in, that's a random disk I/O, +which is very expensive. + +So here, for this workload, +unlike the previous workload, + +the performance of the system is +limited by how fast can you + +move the disk head around, +rather than how fast can you + +write having placed +the disk head. + +And you perhaps you can only, on +a disk drive, do something + +like 100 disk head movements +per second. + +And if you're writing small +records that are like 100 + +bytes or something, you might +find yourself using a + +thousandth of a percent of the +disk I/O, of the disk's + +bandwidth performance. + +And so people hate that. + +They hate buying something and +only being able to use a + +thousandth of a percent +of its capacity. + +Right? + +New B-trees. + +Something's wrong +with that title. + +So B-trees are really fast in +doing range queries, because + +basically once you've are +brought a block in and you + +want to do the next item, +chances are the next item's + +also on the same page. + +So once in while you go over a +page boundary, but mostly you + +just reading stuff very fast. + +Oh, I know what this is about. + +When a B-tree's new and it's +been constructed sequentially, + +it's also very fast. + +When it gets old, what happens +is the blocks themselves get + +moved around on disk. + +They're not next +to each other. + +And this is a problem that +people have spent a lot of + +time trying to solve, is that +as B-trees get older, their + +performance degrades. + +This aging problem-- + +I saw one report that suggested +that something like + +2% of all the money spent by +corporations on IT is spent + +dumping and reloading their +B-trees to try to make this + +problem go away. + +So that's a lot of money +or pain or something. + +Well, B-trees are optimal +for doing lookups. + +If you just want to look +something up, there's an old + +argument that says, gee, +if going to have a tree + +structure, which is what you +need in order to do next + +operations, then you're going to +have some path through the + +B-tree which is a certain depth, +and you do it optimally + +by having the fan-out +be the block size. + +And everything works. + +But that argument of optimality +is not actually + +true for insertion workloads. + +And this is where the data +structures work that I've done + +with Mike and Martin sort of +gets to be an advantage. + +To see that B-trees aren't +optimal for insertions-- + +here's a data structure that's +really good at insertions. + +What is the data structure? + +I'm just going to append +to the end of a file. + +Right? + +So it's great. + +Basically, it doesn't matter +what the keys are. + +I can insert data +into this data + +structure at disk bandwidth. + +What's the disadvantage of +this data structure? + +AUDIENCE: Lookups? + +BRADLEY KUSZMAUL: Lookups. + +So what is the disadvantage? + +Lookups aren't so good. + +What is the cost of +doing a lookup? + +AUDIENCE: Order N? + +BRADLEY KUSZMAUL: Order n. + +Yeah. + +You have to look +at everything. + +It requires a scan of +the entire table. + +And we'll get into what the +cost model is in a second. + +But basically, you have +to look at everything. + +So it's order n. + +It turns out the number of +blocks you have to read in, + +which is the thing +you care about-- + +it's order n over b. + +So we'll get into a performance + +model in just a second. + +So here we are. + +We have two data structures-- +a B-tree, which is not so + +great at insertions. + +It's quite good at point queries +and quite good at + +ranged queries, especially +when it's young. + +And we have this other data +structure, which is the append + +data structure, which is +wonderful for insertions and + +really bad for queries. + +So can you do something that's +like the best of + +all possible worlds? + +You can imagine a data structure +that's the worst of + +all possible, but it turns out +that there are data structures + +that do well for this. + +And I'll show you how one +works in a minute + +So to explain how it works and +to do the analysis, we need to + +have a cost model. + +And we got into this just a +minute ago, with what is the + +cost model for a table scan? + +Is it order N? + +Well, if you're only counting +the number of CPU cycles that + +you're using up, it's order N, +because you have to look at + +every item. + +But if what you really care +about is the number of disk + +I/Os, then you just count +up the number of blocks. + +And so in that model, the cost +is order N over B. And that's + +the model that we're going to +use to do this analysis. + +So in this model, we aren't +going to care about CPU cost. + +We are going to care about disk +I/O. And that's a pretty + +good place to design in if +you're an engineer, because + +right now the number of CPU +cycles that you get for a + +dollar is going up. + +It's been going up. + +It's continuing to go up. + +You have to write parallel +programs today to get that, + +but you get a lot of cycles +in a $100 package. + +But the number of disk I/Os +that you're getting is + +essentially unchanged. + +It's maybe improved by a factor +of two in 40 years. + +So that's the one to optimize +for, is the + +one that's not changing. + +And use all those CPU cycles, +if you can, to do something. + +So the model here is that we're +going to have a memory + +and a disk. + +And you could use this, and +there's some block size, B, + +which we may or may not +know what it is. + +And it's actually quite tricky +on real disk systems to figure + +out what the right +block size is. + +It's not 500 bytes, because +that's not going to be a good + +block size. + +It might be more like +a megabyte. + +And when we move stuff back and +forth, we're going to move + +a block at a time. + +We're going to bring in a whole +block from disk, and + +when we have to write a +block out, we write + +the whole block out. + +So we're just going +to count that up. + +There's two parameters. + +There's the block size, B, and +the memory size, M. So if the + +memory is as big as the entire +disk, then the problem goes + +away, and if the memory's way +too small-- like you can only + +have one block-- + +then it's very difficult +to get anything done. + +So you need to be able +to hold several + +blocks worth of storage. + +The memory is treated +as a cache for disk. + +So once we've brought a block +in, we can keep using it for a + +while until we get rid of it. + +So have you guys done any +cache-oblivious data + +structures? + +OK. + +So you've seen this model. + +So the game here is to minimize +the number of clock + +cycles and not worrying +about the CPU cycles. + +So here's the theoretical +results. + +We'll start with a B-tree. + +So a B-tree which has +a block size b-- + +and here I'm going to assume +that the things you're storing + +are unit sized. + +Because you can do the analysis, +but it gets more + +complicated. + +So the cost of a lookup, which +is the upper right side, is + +log N over log B. That's +the same as-- + +you may not be used to +manipulating these, but + +usually people write this as +log base B of N. But that's + +the same as log N over log B. +And I'm going to write it this + +way, because then it's easier +to compare things. + +So if B is 1,000 or +something, then + +basically instead of paying-- + +just as an example, if N is, +say, 2 to the 40th-- + +let's these all to +lg's because it + +basically doesn't matter. + +So it's 40 over log base B, +and if B is, say, 2 to the + +10th, then that means that if +you have a trillion items and + +you have a fan-out of 1,000, it +takes you at most four disk + +I/Os to find any particular +item. + +An insertion cost is the same, +because to do an insertion, we + +have to find the leaf that the +item should have been in, and + +then put it there. + +So the append log-- well, what's +the cost of insertion? + +Well, we're appending +away, right? + +And once every B items, we +actually have to do a disk + +I/O. So the cost of an +insertion in the + +append log isn't 0. + +It's one Bth of a block +I/O per object. + +And the point query cost +looks really bad. + +It's N over B, which we +already discussed. + +So the fractal tree has this +kind of performance. + +It's log N over-- + +it's not B, which would +be really great. + +It's something smaller. + +It's maybe square root of B +for the insertion cost. + +And the lookup cost is log N +over something, which I'm + +going to just hide. + +Let's set epsilon to 1/2 and +work out what that is. + +Because epsilon 1/2 is a +good engineering point. + +So the insertion cost is log N +over B to the 1/2, which is + +log N over root B. And the other +one, the lookup cost-- + +there's all big 0's around here, +but I'm not going to + +draw those again-- over 1/2-- + +so I'm going to maybe +ignore that-- + +of the log of the square root +of B. Did I do that right? + +B to the 1 minus 1/2. + +Put the 1/2 back in +to make you happy. + +So big-O of that-- + +well, what's log of root B? + +AUDIENCE: [INAUDIBLE] + +BRADLEY KUSZMAUL: I can't +quite hear you, + +but I know the answer. + +I can just say that's the same +as log B, when I'm doing big + +0's Get rid of the halves. + +So it's log N over log B. So +if you sort of choose block + +sizes, if you set this parameter +to be something + +where you're doing something +with the square root, you end + +up having lookups that cost, +asymptotically the + +same as for a B-tree. + +But there are these constants +in there. + +There's a factor of 4 +or something that + +I've glossed over. + +But asymptotically, +it's the same. + +And insertions have this much +better performance. + +What if B was 1,000? + +Then we're dividing +by 30 here. + +But B isn't really 1,000. + +B's more like a million +in a modern system. + +So you actually get to divide by +something like 1,000 here. + +And that's a huge advantage, to +basically make insertions + +asymptotically be 1,000 times +faster, whatever that means. + +When you actually work out the +constants, perhaps it's a + +factor of 100, is what +we see in practice. + +So this is basically working +out those details. + +So here's an example. + +Here is a data structure that +can achieve this kind of + +performance. + +It's a simple version of +a streaming B-tree + +or a fractal tree. + +And what this data +structure is-- + +so first of all, we're kind of +going to switch modes from + +marketoid, or at least +explaining what it's good for, + +to talking about what a data +structure is that actually + +solves the problem. + +So any questions before we +dive down that path? + +OK. + +So if there are any questions, +stop me. + +Because I like to race through +this stuff if possible. + +So the deal here is that you're +going to have log N + +arrays, and each one is a +power of two in size. + +And you're going to have one +for each power of 2. + +So there's going to be one array +of size 1, one of size + +2, one of size 4 and 8 and 16, +all the way up to a trillion, + +2 to the 40th. + +The second invariant of this +data structure is each array + +is either completely full +or completely empty. + +And the third one is that +each array is sorted. + +So I'll do an example here. + +If I have four elements in the +array, and these are the + +numbers, there's only one way +for me to put those in that + +satisfy all those +requirements. + +Because there's four items, +it has to go into the + +array of size four. + +It has to fill it up. + +I can't have any other +way of doing that. + +And within that array of size +four, they have to be sorted. + +So those four elements uniquely +go there, and that's + +the end of the story for +where four elements go. + +If there's 10 elements, you get +a little freedom, because, + +well, we have to fill up the 2 +array and we have to fill up + +the 8 array, because there's +only one way to write in + +binary 10, which is 0101. + +But we get a little choice. + +It turns out that the bottom +array has to be sorted and the + +top array, the array +containing 5 and + +10 has to be sorted. + +But we could have put the five +down here and, say, swapped + +the 5 and the 6, and that +would've been a perfectly + +valid data structure for this +set of data as well. + +So we get a little +bit of freedom. + +OK? + +So that's the basic +data structure. + +So now what do we do? + +How do you search this +data structure? + +Well, the idea is just to +perform a binary search in + +each of the arrays. + +The advantage of this is it +works, and it's a lot faster + +than a table scan. + +The disadvantage is it's +actually quite a bit slower + +than a B-tree, because if you do +the analysis here, which in + +this class, you probably-- +you've done things like master + +theorem and stuff, right? + +So you know what the cost of +doing the search in the + +biggest array is, right? + +How many disk I/Os is that +in the worst case? + +AUDIENCE: Log N. + +BRADLEY KUSZMAUL: It's log N. +It's going to be log base 2 of + +N, plus or minus a little bit. + +Just ignore all that stuff. + +I'll just do L-O-G. So what's +the size of doing the + +second-biggest array? + +What's the cost of searching +the second-biggest array? + +It's half as big, so it's +log of N over 2, right? + +I can't write. + +So this is log N. This is equal +to log of N minus 1. + +What's the next array? + +What's the cost of searching +the next biggest array? + +Log of N minus 2-- + +you add that up, and +what's the sum? + +We don't even need recurrences +for this. + +We could have done it that +way, but what's the sum? + +When we finally get down to 1, +and you search the bottom + +array, you have to do one disk +I/O in the worst case. + +So this is an arithmetic +sequence, right? + +So what's the answer? + +Big-O. I'm not even going +to ask for the-- + +pardon? + +AUDIENCE: Log squared? + +BRADLEY KUSZMAUL: Yes, it's log +squared, which is right + +there in green. + +So basically, this thing +is really expensive. + +Log squared N, when we were +trying to match a B-tree, + +which is log N over log B. So +not only is it not log base B, + +it's log base 2 or something. + +But it's squaring it. + +So if you think of having a +million items in your data + +structure, even a relatively +small one, log base + +1 million is 20. + +If you square that, +that's 400. + +Maybe you get to divide by 2. + +It's hundreds of disk I/Os +just to do a look + +up, instead of four. + +So this is just sucking +at this point. + +So let's put that aside and see +if we can do insertion, + +since we are doing so badly +at [? logging. ?] + +So to make this easier to think +about, I'm going to add + +another set of temporary +arrays. + +So I'm actually going to have +two arrays of each size. + +And the idea is at the beginning +of each step, after + +doing an insertion, all the +temporary arrays are empty. + +I'm only going to have arrays +on the left side that are + +going to have data in them. + +So to insert 15 into this data +structure, there's only one + +place to put it. + +I put it in the one array, if +I'm trying to be lazy about + +how much work I want to do. + +And it turns out, this is +exactly what you want to do. + +You have an an empty one array, +a new element comes in, + +just put it in there. + +Now I want to insert a 7. + +There's no place in the one +array, so I'm going to put it + +in the one array over +on the temp side. + +And then I'm going to merge +the two one arrays + +to make a two array. + +So the 15 and the 7 become +7 and 15 here. + +I couldn't put it there +because that + +array already was full. + +And then I merge those two +to make a new four array. + +So this is the final +result after + +inserting those two items. + +Does that make sense? + +It's not a hard data +structure. + +So one insertion can cause +a whole bunch of merges. + +Here we have sort +of an animation. + +So here I've laid out the one +array across the top, and then + +the temporary array just under +it, and then going down, we + +have a sequence of steps for the +data structure over time. + +So we have the whole arrays. + +We have one and the two and the +four and the eight array + +are all full, and we insert +one more item, which + +causes a big carry. + +So the one creates a two, the +two twos create two fours, the + +two fours and the eight create +two eights, and so forth. + +So here you are. + +You're running. + +You've built up a terabyte +of data. + +Your insert one more item, +and now you have to + +rewrite all of disk. + +So that also sounds a +little unappealing. + +But we'll build on this to make +a data structure that + +actually works. + +So first let's analyze what the +average cost for this data + +structure is. + +I've just sort of explained +why-- there are some really + +bad cases where you're doing an + +insertion and it's expensive. + +But on average, it turns +out it's really good. + +And the reason is that merging +of sorted arrays is really I/O + +efficient, because the merge +is essentially operating on + +that append data structure. + +We're reading two append data +structures and then writing + +the answer into another +append data structure. + +And that does hardly any I/O. + +So if you have two arrays of +size X, the cost to merge them + +is you have to read the two +arrays and you have to write + +the new array. + +And you add it all up, and +that's order X over B I/Os. + +Maybe it's 4x over +b or something. + +But big-O of X over B. So +the merge is efficient. + +The cost per element for the +merge is 1 over B, because + +order X elements were merged +when we did that. + +And we get to spread the cost. + +Sure, we had to rewrite a +trillion items when we filled + +up our disk, but actually, when +you divide that out over + +the trillion items, it's not +that much cost per item. + +And so the cost for each item of +that big operation is only + +1 over B disk I/Os. + +And each item only has to be +rewritten log N times. + +So the total average cost for an +insertion of one element is + +log N over B, which is actually +better than what I + +promised here. + +But this data structure's +going to be + +worse somewhere else. + +So this is a simplified +version. + +I'll get to within-- + +ignoring epsilons and things, +it'll be good enough. + +So does that analysis +makes sense? + +It's not hard analysis, so if +it doesn't make sense, it's + +not because of you. + +It's got to be because I didn't +explain it, because + +it's too easy to +not understand. + +So if you're going to build +something like this, you can't + +just say, oh, well, your +database is great except once + +every couple days it hangs for +an hour while we resort + +everything. + +So the fix of this is that we're +going to get rid of the + +worst case. + +And the idea is, well, let's +just have a separate thread + +that does the merging +of the arrays. + +So we insert something into +a temporary array and just + +return immediately. + +And as long as the merge thread +gets to do at least log + +N moves every time we insert +something, it can keep up. + +You could actually do a very +careful dance, where I insert + +something, and part of the +insertion is I have to move + +something from this array and +something from this array and + +something from this array, and +I can keep everything up to + +date that way. + +So it's not very hard to +de-amortize this algorithm-- + +that is, to turn the algorithm +from a good average-case + +behavior to good worst-case +behavior. + +The worst-case behavior just +becomes that it has to do log + +N work for an insertion, +which isn't so bad. + +Does that make sense? + +Yeah. + +AUDIENCE: Does that work if +these are [INAUDIBLE] items + +[INAUDIBLE]? + +What if somebody wants +[INAUDIBLE]? + +BRADLEY KUSZMAUL: Ah. + +Well, OK, so the question-- + +let me repeat it and see if-- + +so you're in the middle of doing +these merges and you + +have a background thread doing +that, say, and somebody comes + +along and wants to do a query. + +AUDIENCE: Yeah. + +[INAUDIBLE] + +BRADLEY KUSZMAUL: So the trick +to there is that you put a bit + +on the array that says, +the new arrays is + +not ready to query. + +Keep using the old arrays, +which are still there. + +Just don't destroy the +old ones until + +the new one's ready. + +So basically you have these +two megabyte-sized things. + +You're trying to make a two +megabyte-sized one. + +You leave the one-megabyte ones +lying around for a while + +while you're incrementally +moving things down. + +And then suddenly, when the big +ones done, you flip the + +bits, so in order one +operations, you can say, no, + +those two are no longer valid, +and this one's valid. + +So queries should use this +one instead of those. + +So that's basically the kind +of trick you might do. + +Or you would just search the +partially constructed arrays, + +if you have locks. + +There's lots of ways to do it. + +So that's a pretty +good question. + +Yes. + +That's one that we had to +think about a little. + +So it sounds glib, but it's +like, how do we do this? + +Any other questions? + +OK. + +So now we've got to do something +about the search, + +because the search +is really bad. + +Well, it's not as bad as the +insertion worst-case thing. + +I'm going to show you how to +shave off a factor of log N, + +and I don't think I'm going to +show you how to shave off the + +factor of 1 over log B. so we'll +just get it down to log + +N instead of log squared N. +Because if I actually want to + +get it down, then I +have to give up-- + +remember, the performance that +I had was log of N over B. If + +I actually want to get rid +of things, I have to + +do something else. + +There's a lower-bound +argument. + +So the idea here is +we're searching-- + +I'm going to flip those. + +We've got these arrays +of various sizes. + +And I've just done a binary +search on here and then here + +and then here, and I found out +the thing I'm looking for + +wasn't here and it wasn't +here and it wasn't here. + +That's where it would have been, +if it had been there. + +It should have been there +but it wasn't. + +It should have been here +but it wasn't. + +And then I'm going to start +searching in this array. + +And the intuition you might have +is that, gee, it's kind + +of wasteful to start a whole new +search on this array when + +we already knew where it +wasn't in this array. + +Right? + +So for example, if the data +were uniformly randomly + +distributed, and the thing was, +say, 1/3 of the array + +here, I might gain some +advantage by searching at the + +1/3 point over here to +see if it's there. + +Now, that's kind of +an intuition. + +I don't know how to +make that work. + +But I do know how to make +something work. + +But the intuition is, having +done some search here, I + +should in principal have +information about where to + +limit the search so that I don't +have to search the whole + +thing on the next array. + +OK? + +And here's basically what you +do, is every element, you get + +a forward pointer to where that +element would go in the + +next array. + +So for example, you have +something here and something + +here, which are the two things +that are less than and greater + +than the thing you're +looking for. + +And it says, oh, those +should have gone + +here in the next array. + +So if you maintain that + +information, it's almost enough. + +But let's gloss over +the almost part. + +If those two destinations of +those two pointers are close + +together, then you've +saved a lot of + +search in the next array. + +Does anybody see +a bug in this? + +There is one. + +The almost part. + +You don't have to see it, +because I've been thinking + +about this a lot. + +The problem is, what if all of +these items are less than all + +of these items, for example? + +In which case, these pointers +all point down to the + +beginning, and we've +got nothing. + +That's a case where +this fails. + +And that's allowed, right? + +In particular, if we were +inserting things-- + +yeah. + +AUDIENCE: Then we know the +element is in the biggest + +array, because the element +was supposed to + +go between the two. + +BRADLEY KUSZMAUL: Ah, but in +this array, we found out that + +it's above the last element, +when we did our search, right? + +That's one of the +possible ways-- + +the worst-case behavior is we've +got something where this + +array is less than this array. + +We're looking for that item. + +So we do a binary search and +find out, it's over here. + +And it doesn't help to special +case this or something, + +because they could be all to the +right or they could be all + +bunched up in funny ways. + +There's lots of screwy ways +that this could go wrong. + +But the simple version, it's +easy to come up with an + +example, which is everything's +to the left. + +Yeah. + +AUDIENCE: Can you still save +time by, when you do the + +binary search on the smallest +array-- but I guess you'd want + +[INAUDIBLE] + +search. + +It will help reduced cost +which gives you the + +next one and so on? + +BRADLEY KUSZMAUL: Yeah. + +So there is a way to fix it so +that the pointers in the + +smaller array do help +you reduce the + +cost in the next array. + +And that is to seed the smaller +array with some values + +from the next array. + +Like, suppose I put in every +20th item, and I stuck it in + +that array with a bit on it +that says, oh, this is a + +repeat, it's going to +be repeated again. + +So then I could guarantee that +there's these dummies that I + +throw in here, which are evenly +spaced, plus whatever + +else is in there. + +So put the other things in +there, and they have forward + +pointers too. + +And now I'm guaranteed that +the distance between two + +adjacent items is guaranteed +to be a constant. + +Does that make sense? + +The trick is to make it so that +having found two adjacent + +items that the thing +you want-- + +then on the next array, the +image of those two items is + +separated by at most 20 items. + +And so that gets you down to +only log of N instead of log + +squared of n, because you're +searching constant items in + +this array, and there's +only log N arrays. + +Yeah. + +AUDIENCE: Doesn't that slow down +the merging of the rays? + +BRADLEY KUSZMAUL: Not +asymptotically. + +Because asymptotically, +what this means-- + +if I'm going to build that +array, so I'm going to merge + +two arrays to make this array, +I have to do an additional + +scan of this other array as +I'm constructing this one. + +So the picture is I have two +arrays, and I'm trying to + +merge them into this array. + +And I'm trying to also insert +these dummy forward pointers + +from the next array, which +is only twice as big. + +So the big 0's are, if it's X, +instead of it being 1, 2, 3, + +4X, it's 8X. + +So it's only a constant. + +So basically, I can read +all three of these. + +I can read an array and the next +one and the next array, + +which is twice as big, and +the next array which is + +four times as big. + +It all adds up to 8 times the +size of the original array. + +So at least the asymptotics +aren't messed up. + +Maybe the engineer in you goes, +bleh, I have to read the + +data eight times. + +But remember, the game here is +not to get 100% of the disk's + +insertion capacity. + +That's not the game, going +back to the marketing + +perspective. + +The competition is only +getting 0.001% + +of the disk's capacity. + +That's what a B-tree gets +in the worst case. + +And so we don't have to get +100% to be three orders of + +magnitude better, which +is where we are. + +So it turns out that for this +kind of thing, we end up + +getting 1% of the disk's +capacity, and everybody's + +jumping around saying that's +great, because it's 1,000 + +times faster. + +And why do we only get 1%? + +Well, there's a factor of two +here and there's a log N over + +there, and you divide all that, +and it's a constant + +challenge, because the engineers +at Tokutek always + +are having ideas for how +to make it faster. + +And right now, making this data +structure faster is not + +the thing that's going to +make people buy it. + +Because it's already 1,000 +times faster than the + +competition. + +What's going to make it faster +is some other thing that adds + +features that make it +so it's easy to use. + +So I keep having to-- + +no, you really need to work on +making it so that we can do + +backups, or something. + +It turns out, if you're selling +a database, you need + +to do more than just queries +and insertions. + +You need to be able +to do backups. + +You need to be able to +recover from a crash. + +You need to be able to cope +with the problem of some + +particularly heavy query that's +going and starving all + +the other queries from getting +their work done. + +All those problems turn out to +be the problems that, if you + +do any of them badly, people +won't buy you. + +And so I suspect that there's +another factor of 10 to be + +gotten over this data structure, +if you were to sit + +down and try to say, how could +I make it be the fastest + +possible thing. + +And someday, that work will have +to be done, because the + +competition will have +it and we won't. + +So let's see. + +I mentioned some of +these just now. + +So some of the things you have +to do in order to have an + +industrial strength dictionary +are you need to cope with + +variable-size rows. + +Now we assumed for the analysis +that the rows were + +all unit size. + +In fact, database rows +vary in size. + +And some of them are huge. + +Some of them are megabytes. + +Or sometimes people do things +like they put satellite images + +into databases. + +So they end up having +very large rows. + +You have to do deletions +as well as insertions. + +And it turns out we can do +deletions just as fast as + +insertions. + +And the idea there is basically, +if you want to do a + +delete, you just you insert +the thing with a bit on it + +that says, hey, this is +really a deletion. + +And then, whatever you get a +chance, when you're doing a + +merge, if you find something +that has the same value, you + +just annihilate it. + +And the delete has to keep +going down, because there + +might be more copies +of it further + +down that were shadowed. + +And eventually, when you finally +do the last merge, + +that tombstone goes away. + +You have to do transactions +and logging. + +You have to do crash recovery. + +And it's a big pain to get +that right, and a lot of + +companies have foundered when +they tried to move from one + +mode to the other. + +How many of you have experienced +the phenomena that + +your file system didn't come +back properly after a crash? + +You see the difference +in age here. + +They're all using file systems +that have transactional + +logging underneath them. + +When's the last time +it happened? + +AUDIENCE: Tuesday. + +BRADLEY KUSZMAUL: Tuesday. + +So the difference is you're +paying attention and they're + +not, right? + +AUDIENCE: [INAUDIBLE] +disk failure. + +BRADLEY KUSZMAUL: +Disk failure. + +That's a different problem. + +AUDIENCE: Cacheing is +not [? finalized. ?] + +BRADLEY KUSZMAUL: Yeah. + +You say everybody's running +with their disk + +cache turned on. + +And on some file systems, +that's a bad idea. + +So we're still suffering that +it's been difficult to switch + +from the original Unix file +system, which is 30 years old + +and wasn't designed to +recover from crash. + +You have to run fsck, and +it doesn't always work. + +We still have file systems +that don't + +recover from crashes. + +So you can see why that +could be difficult. + +It turns out that one common use +case is that the data is + +coming in sequentially, and this +data structure just sucks + +compared to a B-tree in the case +where you're inserting + +things and the data actually +is already + +sorted as it's inserted. + +Because this is moving things +all around and moving things + +all around. + +And it's like, why didn't you +just notice that it's sorted + +and put it in? + +You have to get rid of the log +base B to get it down to log + +base B of N instead of log base +2 of N for search costs. + +Because people in fact do a +lot more searches than-- + +if you have to choose which +to do better, you want to + +generally do searches better. + +And compression turns +out to be important. + +I had one customer who +had a database + +which was 300 gigabytes. + +He has a whole bunch of servers, +and on each server, + +he had a 300 gigabyte +database. + +And with us, it was 70 + +gigabytes, because we compress. + +And we just do simple +compression of, basically, + +large blocks. + +When we do I/Os, we do I/Os +of like a megabyte. + +So when we take one of those +megabytes, we compress it. + +And it's a big advantage to +compress a megabyte at a time, + +instead of what-- + +a lot of B-trees, they have +maybe 16 kilobytes. + +And gzip hardly gets a chance to +get anywhere when you only + +have 16 kilobytes. + +And it gets down to +12 kilobytes. + +But if you have a megabyte to +work with and you compress it, + +particularly if it's sorted-- + +so this is a megabyte of data +that's sorted, so compression + +works pretty well +on sorted data. + +So you get factors of 5 +or 10 or something. + +And so we asked him to dump the +data without the indexes, + +so just the primary table with +no indexes, and then run that + +through gzip. + +And it was 50 gigabytes. + +So the smallest he could store +the raw data was 50 gigabytes, + +and we were giving him a useful +database that was 70 + +gigabytes that had a +bunch of indexes. + +So he was like, yeah. + +And you have to deal with +multithreading and lots of + +clients and stuff. + +So here's an example. + +We worked with Mark Callahan, +who was at Google at the + +time-- he's now at Facebook-- + +on trying to come up with some +benchmarks, because none of + +the benchmarks out in the +world do a good job of + +measuring this insertion +performance problem. + +So iiBench is an insertion +benchmark. + +And basically what it does is +it sets up a database with + +three indexes, and the +indexes are random. + +So it's actually harder +than real workloads. + +This workload, you basically +have a row and then you create + +a random key to point +into that from + +three different places. + +Real databases, it turns out, +probably have more of a + +Zipfian distribution. + +Have you talked at all about +Zipfian distributions of data? + +So this is sort of an +interesting thing. + +If you're dealing with +real-world caches, you should + +know that data ain't uniformly +randomly distributed. + +That's a poor model. + +So in particular, suppose I have +memory and disk, and this + +is 10% of the disk. + +Very simple situation. + +Very common ratio. + +You'll see, this +is how Facebook + +sets up their databases. + +They'll have a 300-gigabyte +database and 30 gigs of RAM. + +If the queries that you wanted +to do were random, it wouldn't + +matter what data structure +you were using. + +Let's suppose that God tells +you where it is on disk, so + +you don't have to find it. + +You just have to move the +disk head and move it. + +If they're random, then +basically, no matter what + +you've done, 90% of the queries +you have to do are + +going to do a random disk I/O. +10% are going to already be + +there, because you got lucky. + +So that is not reflecting +what's going on on any + +workload that I know. + +What they'll see is more like +99% of the queries hit here, + +and 1% go out here, or maybe 95% +here and 5% go out there. + +And it turns out that, that for +a lot of things, there is + +a model of what's going on +called a Zipfian distribution. + +This would a random uniform +distribution. + +It's like every item has equal +probability of being chosen + +for a query. + +It turns out that for things +like what's the popularity of + +web pages, or if you have a +library, what's the frequency + +at which words appear +in the library-- + +so words like "the" appear +frequently, and words like + +"polymorphic" are +less frequent. + +So Zipf came up with this model, +and there's a simple + +version of the model, which +says that the most popular + +word has probability +proportional to 1. + +It's not going to be 1. + +It's going to be proportional +to 1. + +The second most popular word +is going to have 1/2. + +The third most popular +word is 1/3. + +And the fourth most popular word +is 1/4 the probability of + +the first word, and so forth. + +So if you plot this +distribution, it kind of looks + +like this, right? + +It's like 1 over x. + +And what would you tell me if +I told you that I had an + +infinite universe of objects +that had a probability + +distribution like this. + +Does that seem plausible? + +Why? + +You're saying no. + +AUDIENCE: [INAUDIBLE PHRASE] + +try adding them all together. + +BRADLEY KUSZMAUL: If +you add them all + +together, it doesn't converge. + +So it's a heavy-tailed +distribution. + +So it turns out that if you sum +up these up to 1, the sum + +from 1 to n of 1 over i, it's +the nth harmonic number. + +And that grows over time. + +It's basically like the integral +under this curve, + +from 1 to n. + +It's close to that. + +And what is the integral +of that? + +It's like something you learned +seven years ago, and + +now you've forgotten, right? + +You learned it when you +were sophomores in + +high school, or something. + +So it's approximately +log of n. + +It's actually like log of n +plus 0.57, is a very good + +approximation for the +nth harmonic number. + +When you're doing this kind of +analysis, boy, it depresses + +people, because you say, oh, +that's H of n, and if you have + +a million items in your +database, then the sum of all + +those things is H of +1 million, and + +what's H of 1 million? + +Well, the log base 2 of 1 +million, I know that, because + +I'm a computer scientist. + +So it's going to be like 20, +and because we're doing log + +base e in that formula, maybe +it's 15 or something. + +So if you have 1 million items, +then the most popular + +item is going to-- you have +to divide by H of n here. + +So the most popular +item is going to + +appear 1/15 of the time. + +And the next most popular item +is going to appear-- + +emergency backup chalk. + +Somebody's been burning both +ends of this chalk. + +1/30 of the time, and 1/45 of +the time, and those add up. + +When you go up to 1 +over 1 million-- + +another zero in there-- + +times 15, that finite series +will add up to 1, + +approximately. + +Except to the extent that +I've approximated. + +So this is what's going on. + +So the most popular +Facebook page-- + +they might have 1 billion +pages, so how + +does that change things? + +Well, that means the most +popular one has a probability + +1 in 20, and the second +most is 1 in 40. + +And this explains why +cache works for + +this kind of workload. + +Nobody really knows why Facebook +pages and words in + +libraries and everything else +have this distribution, which + +is named after a +guy named Zipf. + +But they do. + +Everything has this property. + +And so you can sort of predict +what's happening. + +So iiBench should +have a Zipfian + +distribution and it doesn't. + +So this is painting +a worse picture. + +Or a better picture. + +It's making us look better than +we really are, because + +the real world is going to have +more hits on the stuff + +that's in memory for a B-tree +than this model, where + +basically you're completely +hosed all the time because + +it's random. + +So this is an example in the +category of how to lie with + +statistics. + +And it's a pretty sophisticated +lie. + +If you're going to lie, +be sophisticated. + +So these measurements were +taken in the top graph. + +Up is good. + +It's how many rows per second +we could insert. + +And this axis is how many rows +have been inserted so far. + +And the green one is a B-tree. + +According to Mark Callahan, +who's essentially a + +disinterested observer, it's the +best implementation of a + +B-tree ever. + +And you can sort of see what +happens, is that as you insert + +stuff, the system falls out +of main memory, and the + +performance was really good +at the beginning-- + +40,000 per second-- and then +boom, you're down to 200 down + +here at the end, by +the time you've + +inserted a billion rows. + +Whereas, for the fractal +tree, you can + +sort of see this noise. + +That's because some insertions +are a little cheaper than + +other insertions. + +Every other insertion's +completely free, right? + +You had a free spot. + +You just put it in. + +One out of four insertions, the +ones that weren't free, + +half of them only had to do a +little operation in memory. + +So you see this high frequency +noise, because some things are + +cheaper than others. + +And that's like a factor +of 30 or something. + +It turns out it even works +on SSD, solid state disk. + +You might think-- + +all this time I've been talking +about disk drives. + +Solid state disk has a +complicated cache hierarchy + +inside it, and we were +surprised to see that + +basically we're faster on this +workload on a rotating disk + +than a B-tree is on an SSD, +which is orders of magnitude + +faster in principle, but turns +out that for various + +reasons it's not. + +One question I get often is, the +world is moving away from + +rotating disk to solid +state disk. + +A lot of applications-- + +how many of you have solid state +disks in your laptops? + +That's a really good application +for a solid state + +disk, because it's +not sensitive to + +being knocked around. + +So it's worth it to have a solid +state disk even if it + +were more expensive, +which it is. + +It turns out it's not +that much more + +expensive for a laptop. + +It's a couple of hundred dollars +more or something. + +But the advantage of it is +that if you go up in an + +airplane and you're sitting +and trying to type in the + +middle of a thunderstorm, +flying across-- + +it doesn't care. + +Disk drives, if you do that-- + +disk drives do not like flying +at high altitude, because they + +work by having a cushion of air +that the head is flying + +on, and in airplanes, which +pressurize the cabin to the + +same altitude as 8,000 feet, +that's half an atmosphere. + +So there's only half as much +air keeping it off. + +So if you travel a lot, that's +when your disk drive will + +fail, is when you're flying. + +OK. + +So it looks like, however that +rotating disk is getting + +cheaper faster then solid +state disk is. + +So rotating disk is an order of +magnitude cheaper per byte + +than solid state disk today. + +Maybe two orders of +magnitude cheaper. + +It's hard to measure fairly. + +But rotating disk, according +to Seagate-- + +they're saying, by the end of +the decade, we'll have 70 + +terabyte drives that are +the same form factor. + +And so you figure out what the +Moore's Law is for that, and + +it's better than for +lithography. + +Lithography is not going +to be that much more + +dense in that timeframe. + +So at least for the next 5 or +10 years, it looks like disk + +drives are going to maintain +their cost advantage over + +solid state storage, +and maybe even + +spread that cost advantage. + +So for any particular +application, for storing your + +music, SSD will be cheap enough, +but for those people + +that have really big data +sets, like these new + +telescopes they're +putting up-- + +these new telescopes +are crazy. + +These people are putting +up these telescopes. + +They're putting up 1,500 +telescopes across the + +Australian Outback. + +And each of those telescopes in +the first 15 minutes live + +is going to produce more data +than has come down from the + +Hubble, total. + +And there's just no +way for them to-- + +I don't know what they're +going to do. + +But it's a huge amount of data, +and they're going to + +have to use disks to store +whatever it is that + +they want to keep. + +And they don't like throwing +away data, because it's so + +expensive to make. + +So if I were a disk maker, I'd +make sure that my salesmen had + +an office somewhere out there. + +So the conclusion is you're not +going to be able to, at + +least for those applications, +just have an + +index in main memory. + +You're going to have to have +a data structure that + +works well on disk. + +The speed trends-- + +well, seek time is not +going to change. + +It hasn't changed. + +It's not going to change. + +The bandwidth of a disk drive +grows with the square root of + +its capacity. + +So if you quadruple the storage +on the disk because + +you've made the bits twice as +dense in each dimension, then + +one spin of the disk sees twice +as many disks, not four + +times as many disks. + +So that projects out to +something like disks that are + +500 megabytes per second. + +So how long is it going to take +to back up a 67 terabyte + +disk drive? + +So there remain systems +problems. + +And I was explaining to my son +that there's all these + +problems in systems. + +Data structures aren't suited, +and all these systems suck. + +He said, well, isn't +that horrible if + +you're computer scientist? + +I said, no, because +we make our living + +off of these problems. + +So here are some problems. + +There's plenty of living +to be made yet. + +Power consumption is also a big +issue for these things. + +If you fill up a room a Google +data center, a room which is + +probably bigger than this +room, full of machines. + +The Facebook data center is +probably a room about this + +size, full of machines. + +And power and cooling is +something like half the cost + +of the machines. + +The machines for something like +Facebook, the hardware + +might cost them $10 million or +$20 million a year, and the + +heating and cooling is another +$10 million or $20 million a + +year, which is why they go off +and they build these data + +centers in places like North +Carolina, where I guess + +they're willing to give them +power for free or something. + +So making good use of disk +bandwidth offers huge power + +savings, because basically you +can use disks which are + +cheaper than solid +state for power. + +And you want to use that well. + +CPU trends. + +Well, you've probably talked +about this, right? + +CPUs are going to get +a lot more cores. + +I actually have a 48-core +machine that cost $10,000 that + +I bought about a month ago. + +And our customers mostly +use machines that + +are like $5,000 machines. + +So when I provisioned this +machine, I said, well, I + +should spend and buy a machine +that's twice as good as what + +they're buying, because I'm +developing software that + +they're going to +use next year. + +So I bought a $10,000 machine, +which is 48 cores. + +And we're having all +sorts of making a + +living with that machine. + +The memory bandwidth and the I/O +bus bandwidth will grow. + +And so I think it's going to get +more and more exciting to + +try to use all these cores. + +Fractal trees have a lot of +opportunity to use those cores + +to improve and reduce the +number of disk I/Os. + +So the conclusion is, basically, +these data + +structures dominate B-trees +asymptotically. + +And then B-trees have 40 years +of engineering advantage, but + +that will evaporate +eventually. + +These data structures ride +better technology curves than + +B-trees do, and so I find it +hard to believe that in 10 + +years that anybody would +design a system using a + +B-tree, because how do you +overcome those advantages. + +So basically all storage systems +are going to use data + +structures that are like this, +or something else. + +There's a whole bunch of other +kinds of indexes that we + +haven't attacked, things like +indexing multi-dimensional + +data or indexing data where you +have very large keys, very + +large rows. + +Imagine that you're trying to +index DNA sequences, which are + +much bigger than a disk block. + +So there's a whole bunch of +interesting opportunities. + +And that's what I'm +working on. + +So any questions or comments? + +Arguments? + +Fistfights? + +OK. + +AUDIENCE: Where's the mic? + +BRADLEY KUSZMAUL: Where +is the mic? + +AUDIENCE: That's OK. + +I can [INAUDIBLE]. + +BRADLEY KUSZMAUL: +It's on my coat. + +PROFESSOR: So actually, this is +a very interesting point, + +because if you think where the +world is leading, I think that + +big data is something that's +very, very interesting, + +because all these people are +gathering huge amounts of + +data, and they're storing +huge amounts of data. + +And what do with data, accessing +them, is going to be + +one big problem. + +I mean, if you look at what +people like Google are doing, + +they're just collecting +all those. + +Nobody's throwing +anything out. + +And I believe if you to kind of +look at them, analyze them, + +do cool things with the +data, it's going to + +be very, very important. + +So I think that would +be very interesting, + +high-performance end. + +It's not just doing +number crunching. + +Until now, when people look at + +high-performance, it's about CPU. + +It's about how many FLOPS +per second can you do? + +TeraFLOPS, petaFLOP machines +and stuff like that. + +But I think one thing +that's really + +interesting is it's not petaFLOPS. + +How many terabytes of +data can you process + +through to find something. + +BRADLEY KUSZMAUL: So I was at +a talk by Facebook, and they + +serve 37 gigabytes per data +per second out of their + +database tier. + +And that's a lot of serving. + +Out of one little piece of +whatever they're doing. + +Those guys have three +or five petabytes. + +And in the petabyte club, +they're small potatoes. + +There's people who have hundreds +of petabytes, people + +with three-letter acronyms. + +PROFESSOR: I mean, some of those +three-letter acronym + +places, the amount of data they +are getting and they are + +processing is just gigantic. + +And I think to a point that even +some of the interesting + +things about-- + +if they keep growing their data +centers at the rate they + +keep growing in the next couple +of decades, they will + +need the entire power of the +United States to power their + +data centers, because they +are at that kind of + +thing at this point. + +Even in these big national labs, +the reason they can't + +expand is not that they don't +have money to buy the + +machines, but they don't have +money to pay for the + +electricity, and also they don't +have electricity-- that + +much electricity-- + +[UNINTELLIGIBLE] + +them to basically feed it. + +BRADLEY KUSZMAUL: I've run into +people for whom the power + +issue was a big deal. + +I look at it and say, eh, you +bought a $5,000 machine. + +You spend $5,000 in power over +the lifetime of the machine. + +It doesn't seem like it's +that big a deal. + +But they've filled up their data +center, and the cost of + +adding one more machine has a +huge incremental cost, because + +they can't fit one more in. + +So that means they have to +build another building. + +And so almost everybody's facing +that problem who's in + +this business. + +And then they try to build a +building somewhere where + +there's natural cooled-- + +Google's written these papers +about, oh, it turns out if you + +don't air condition your +computers, most + +of them work anyway. + +So, well, air conditioning is a +quarter of the cost over the + +lifetime of the computer. + +So if you can make more than 3/4 +of them give you service, + +you come out ahead. + +GUEST SPEAKER: On that note, +MIT is part of a consortium + +that includes Harvard, +Northeastern, Boston + +University, and University of +Massachusetts Amherst, to + +relocate all of our +high-performance computing + +into a new green data center +in Holyoke, Massachusetts. + +So the idea is that rather than +us locating things here + +on campus, where the energy +costs are high and we get a + +lot of our energy from fuels +that have a big carbon + +footprint, locating +it in Holyoke-- + +they have a lot of hydro power +and nuclear power there. + +And they're able to build a +building that is extremely + +energy-efficient. + +And it turns out that a bunch +of years ago when they were + +digging up the Route 90, the +Mass Pike, they laid a lot of + +dark fiber down the length. + +And so what they're going to +do is light up that fiber, + +which comes right back here +to the Boston area. + +And so for most people who +are using these very + +high-performance things, it +doesn't really matter where + +it's located anymore, at +the level of that. + +So instead of just locating some +piece of equipment here, + +we just will locate it out +there, and the price will drop + +dramatically. + +And it'll be a much greener +way for us to be doing our + +high-end computing. + +Yeah, question? + +AUDIENCE: Isn't someone talking +about water-cooled + +offshore floating +data centers? + +GUEST SPEAKER: Sure. + +Sure. + +So the question is, are people +talking about water-coooled + +offshore floating data centers. + +Yeah. + +I mean, locating things in some +area where you can cool + +things easily makes +a lot of sense. + +Usually, they tend to want those +near rivers rather than + +in the middle of the ocean, +just because you get the + +hydropower. + +But even in the ocean, you can +use currents to do very much + +the same kind of thing. + +So for some of these things, +people are looking very + +seriously at a whole bunch of +different strategies for + +containing large-scale +equipment. + +PROFESSOR: So one that's very +counterintuitive is people are + +trying to build data centers in +the middle of deserts, when + +it's very hot. + +I mean, why do you think people +want to build a data + +center in the middle +of the desert? + +AUDIENCE: Solar power? + +PROFESSOR: Solar power +is one thing. + +No, it's not solar power. + +AUDIENCE: It gets really +cold at night. + +PROFESSOR: No, it's not +really cold at night. + +That's not it. + +GUEST SPEAKER: Cheap property. + +PROFESSOR: No, the biggest thing +about cooling is either + +you can do air conditioning, +where you're using power to + +pull heat out, or you can +use just water to cool. + +And what happens is most of +other places is the humidity + +is too high. + +And when you go to the desert, +humidity is low enough that + +you can just pump water through +the thing and get the + +water evaporation going +by, and then use + +that to cool the system. + +So sometimes they're looking +at data centers in places + +where it could be 120 degrees, +but very low humidity. + +And they think that is +a lot more efficient + +to cool than that. + +So there are a lot of these +interesting nonintuitive + +things people are looking at. + +So what [UNINTELLIGIBLE] they +say is that humidity's the + +killer, not the temperature. + +AUDIENCE: What if you're +located on the South-- + +if you're located on the South +Pole, then that's both cold + +and really low humidity. + +GUEST SPEAKER: Yeah. + +I mean it'll be interesting to +see how these things develop. + +It's a very so-called hot topic +these days, is energy + +for computing. + +And the energy for computing +of course matters also not + +only at the large scale but +also at the small scale, + +because you want your +favorite handheld to + +use very little battery. + +So your batteries last longer. + +So the issue of energy, using +that as a measure-- + +we've mostly been looking at +how fast we can make things + +run in this class, but many of +the lessons you can use to + +say, well, how can I +make this run as + +energy-efficient as possible? + +And what you'll learn is that +many of the lessons we've had + +in the class during the term +we focused, as I say, on + +performance. + +But there are many resources +in any given situation that + +you might want to optimize. + +And so understanding something +about how do I minimize + +energy, how do I minimize disk +I/Os, how do I minimize clock + +cycles, how do I minimize +off-chip accesses-- + +which tend to be much +more energy + +intensive than on-chip-- + +all those different kinds of +measures end up being part of + +the mix of what you have to do +when you're really engineering + +these systems. + +PROFESSOR: So I think another +interesting thing is, because + +we are in this time where some +stuff grows at exponential + +rates and stuff like that, some +of those ratios that made + +sense at some point just +suddenly start making really + +bad things. + +Like, for example, in this, at +some point the seek times were + +normal enough that +you didn't care. + +And at some point, because the +rest of the things took off so + +fast, suddenly it becomes +this really, really big + +bottlenecks. + +BRADLEY KUSZMAUL: B-trees +were a really good data + +structure in 1972. + +Because, well, the seek +time and the transfer + +time and the CPU-- + +the CPUs actually couldn't +read in the data in one + +rotation, so people didn't even +read consecutive blocks, + +because the CPU just couldn't +handle data + +coming in that fast. + +You would stagger blocks around +the disk, so that when + +you did sequential reads, you'd +get this one and then + +this one and this one. + +There was this whole thing about +tuning your file system. + +It's like-- + +AUDIENCE: By the way, back +when disks were-- + +BRADLEY KUSZMAUL: Yeah. + +Washing machine. + +AUDIENCE: Washing +machine size. + +BRADLEY KUSZMAUL: For +20 megabytes. + +PROFESSOR: Oh, yeah, that's +the big disk. + +So hopefully you guys +got a feel for-- + +we have been looking at this +performance on a small + +multi-core and stuff like that, +how it can scale in + +different directions and +the kind of impact + +performance can have. + +And in fact, if anybody has read +books on why Google is + +successful, one of the biggest +things for their success is + +they managed to do a huge amount +of work very cheaply, + +because the amount of work they +do, if anybody did in the + +traditional way, they can't +afford that model, to give it + +for free or give it supplied +for advertising. + +Because they can get it done +because it's about + +optimization. + +Performance, Performance +basically relates to cost. + +And if the cost is low enough, +then they don't have to keep + +charging a huge amount of +money for each search. + +GUEST SPEAKER: So let's +thank Dr. Kuszmaul for + +an excellent talk. + +And can you hang out for just +a little bit, if people want + +to come down? + +OK. + +Thanks. \ No newline at end of file diff --git a/9WwJr2yrv2I.txt b/9WwJr2yrv2I.txt new file mode 100644 index 0000000000000000000000000000000000000000..d8314f5fa36864910cd1eacf79067eefe7e66a72 --- /dev/null +++ b/9WwJr2yrv2I.txt @@ -0,0 +1,1301 @@ +Good morning. Good morning. Yes. So I want to pick up where we + +were last time. We talked last time about Mendel's + +elegant experimental design. And not just elegant but very + +careful, too, in having organisms that bred true. + +And a lot of work went into that. We talked about his observations + +and his really great choice to count. We talked about his ability to look + +at numbers that were approximate and somehow intuit what was interesting + +about them. Namely, he had to take rough numbers and say, + +hmm, I think this is a 3:1 ratio, although that was an abstraction, + +but a very good on his part. And it's hard to know when to make + +those leaps and when you're kidding yourself, but Mendel got a lot of + +data. I didn't mention that he worked on not just round and + +wrinkled, but he worked on seven different traits across pea plants. + +All seven showed these very consistent properties. + +There was a recessive and a dominant phenotype and then a + +first-generation. The dominant phenotype by + +definition was evident in full force. + +And in the second-generation we saw 3:1 segregation. + +He felt pretty good about that. He made other predictions based on + +this. And he was able to put together a very coherent story. + +And, as I also explained last time, it sunk like a stone because it was + +an utterly abstract story, the idea that there were these + +particles of inheritance, factors of inheritance. You + +couldn't put your finger on them, and people hate stuff you cannot put + +your finger on. They say it's just a model. + +Well, as I mentioned last time, the discovery of chromosomes in + +cells really laid the foundation for the beginning of a rebirth of + +interest in Mendelism, in Mendel's ideas. And the + +interesting part of that characterization of chromosomes was + +the choreography that we talked about last time. + +That normally in cells undergoing mitosis, normal mitotic division to + +make more and more cells, when you stained the cells and + +looked at them before they went into mitosis you saw these X-like + +structures. However many there were, they lined up along the midline of + +the cell. They appeared then to sometimes you could even see them + +kind of attached to something pulling them back. + +And they would pull back to make two cells each of which + +had half of the X. Somebody asked last time, + +I drew four chromosomes, was that because cells have four chromosomes? + +And the answer was no. It's because I had room to draw four + +chromosomes in that cell. And so this time I drew six + +chromosomes to indicate that you can have different numbers of + +chromosomes. They are usually, but I should note not always, an + +even number of chromosomes in higher organisms. But anyway. + +So I drew six this time. And what's interesting was this + +meiosis. The generation of sperm and eggs, for example, + +in animals, they are the chromosomes lined up with a different + +choreography. They lined up in pairs. And where you could see + +differences in the shapes of chromosomes, like maybe the little + +crossing point was lowered down or the chromosomes were shorter in + +length, there would appear to find their own partner, + +the one that had the same basic shape. And they would line up in + +pairs. And then they would undergo a series of two divisions, + +a meiotic one division, meiosis one and a second division, meiosis two. + +And in meiosis one you would get one copy of each pair. + +Then it would undergo a second round of division that looked very + +much like mitosis where these X structures would be split into two + +pieces. The notion then that pairs would go to singletons and then upon + +fertilization singletons would come together to reconstitute a pair + +really did fit Mendel. And thus was born the Chromosomal + +Theory of Inheritance. So, whoops, the Chromosomal Theory + +of Inheritance. Are you overwhelmed by the + +Chromosomal Theory of Inheritance? Have I given you overwhelming + +evidence to believe it? No. How come? + + It seems natural to you now. + +But, I mean, you know, the only evidence is that there's something + +else that has got pairs in cells, right? What's to say that some + +other thing that pairs up in cells actually is the carrier of genes? + +The Chromosomal Theory of Inheritance is that Mendel's + +abstract factors, genes live on these chromosomes, + +are these chromosomes, or something like that. They're carried + +by these chromosomes. And simply the fact that the + +choreography of the chromosomes is not the same, oh, + +sorry, is the same as the choreography of Mendel's genes, + +that's correlation. In fact, it's ex post facto correlation. + +I didn't have any prediction that these chromosomes would do it. + +I just saw that the chromosomes did it and I said, + +OK, you know, that could explain Mendel's observations about genes. + +And there's a world of difference between that could explain, + +that is consistent with the data, and that presents a compelling case + +that this is true. So there were some people who + +immediately bought into the idea of the Chromosomal Theory of + +Inheritance, and there were other people who remained great skeptics + +about this, that these chromosomes were themselves quite irrelevant to + +inheritance. And indeed many people who, at this point, + +the early 20th century, felt that the whole business of + +genes was still not such an overwhelming idea anyway. + +And trying to unit these two was going a bit far out. + +So now I have to bring you back to some of the things that we left + +unresolved last time, which is Mendel's Second Law of + +Inheritance. Because if we're really going to start building a + +case that chromosomes really do carry genes then we better get some + +serious consistency with much more complex aspects of the theory or we + +better look for some contradictions. So you recall, and I mentioned, + +that Mendel studies seven different traits. + +Two of them, roundness and greenness, both dominant phenotypes underlain + +by these hypothetical genes, big R, big R, big G, big G, and the + +recessive traits associated with these same genes, + +wrinkled and yellow, little R, little R, little G, + +little G. When you make a first-generation cross what + +do you get? Sorry? You get round and green + +phenotypically. And genotypically what are they? + +Big R, little R, big G, little G, right? That would be the genotype. + +These organisms would be heterozygotes. + +In fact, they would be double heterozygotes. + +They'd be a heterozygote for the gene that controls shape and they'd + +be heterozygous for the gene that controls seed color. + +OK? Now, suppose we do a cross back to RRGG, the parent that has + +the recessive phenotype for both of these traits. + +We're practicing our words here, right? What will this parent, the + +second parent contribute in its gametes? What will the gametes from + +that parent be? Little R, little G. + +They have to be little R, little G because that's all it's got + +to offer. So little R, little G. + +OK? What will this parent contribute? It could give a big R, + +big G. Could give a little R, little G. Could give, + +in principle, a little R, big G or a big R, little G. + +In theory any of those are possible. And what's the ratio + +that Mendel reports? 1:1:1:1:1, so equal. + +That's right. 1:1:1:1. That's the independent assortment + +of traits. That's what he calls this. Independent assortment + +of traits. + +That is to say the inheritance of round and the inheritance of green + +are uncorrelated to each other, right? + +Knowing which one you got for roundness, which one you got for + +greenness, they don't convey any information about each other. + +So how could we explain this in terms of Chromosomal Theory of + +Inheritance? Well, we could explain this in terms of + +the Chromosomal Theory of Inheritance by saying, + +for example, that in this heterozygous parent here big R and + +little R were carried on chromosomes that paired up with each other, + +homologous chromosomes. And big G, little G were carried on + +a different pair of homologous chromosomes in my meiosis picture + +there. OK? So if that was the case then when these chromosomes + +segregated in the first meiosis step, meiosis one, it might be that big R + +and big G were on the left side. It might be big R and little G were + +on the left side. It might be that little R and big G + +were on one side, etc. Because these are different + +chromosomes. They could have chosen to line up in different ways. + +That's all cool. So Mendel's Law of Independent Assortment is + +consistent with the Chromosomal Theory, except we pointed out last + +time, except if big R and big G were on the same chromosome. + +Then we'd have some explaining to do. So maybe Mendel was just lucky and + +big R and big G happened to be on different chromosomes. + +But what if he takes a third trait? Well, maybe the reason he got + +1:1:1:1 for those traits was it was also on a different chromosome, + +a fourth trait. And I said he studied how many traits? + +Seven traits. If they all gave 1:1:1:1 assortment they'd all have + +to be on different chromosomes. How many chromosomes do peas have? + +How many pairs of chromosomes do peas have? Seven. + +Very interesting. He might have just gotten lucky. + +In fact, he did. We know that. They are on different chromosomes. + +Though, it makes you wonder whether maybe he had an eighth trait that + +did something funny and decided not to put it in this paper. + +I don't know. It's interesting. Like I say, there's choice involved + +in what you want to report at what point here. So suppose we instead + +had big R and big G, little R and little G happen to have + +been on the same chromosome. Then they would have been inherited + +from the common parent here, say from here into the F1. The F1 + +would look like this. If they were on different + +chromosomes it would look like this. If it were from the same chromosome + +it would look like this. And now let's make a little + +scorecard of what's going to get passed onto the next generation. + +We've got the possibility that it will pass on. This one could pass + +on. Oh, let's keep score. Big R, big G could get passed on. + +Little R, little G could get passed on. Big R, little G could be passed + +on. And little R, big G could be passed on. + +And if they are on different chromosomes we expect a quarter, + +a quarter, a quarter and a quarter. But if they're on the same + +chromosome what do we expect? What will come out of this? Either + +you're going to get this, in which case you get both big R and + +big G, or you're going to get this one, in which case you get little R + +and little G, a half, a half, zero, zero. Ooh, + +that's very different. What is Mendel's Law of Independent + +Assortment say? It favors this. + +But Mendel's Law of Independent Assortment cannot possibly be right + +if we see this. So Mendel didn't observe this. + +But if we really believe this Chromosomal Theory we would expect + +to see it eventually. So who's going to be right, + +Mendel or Chromosomal Theory? You vote for both. + +How many vote for Mendel? How many vote for Chromosomal + +Theory? How many vote for both? How can you have both? The data + +would be contradictory. How many vote for neither? + +Hmm. OK. Fine. So we have a very different prediction. + +Notice that these are the parental types of chromosomes. + +They're the ones that went into the cross in the first place, + +big R and big G. These are the non-parental types of chromosomes. + +They're the ones, they're the combinations, a big R and a big G + +that didn't match either of the two parents. That's a new combination. + +Well, it took a while before folks sorted this out. + +And it was eventually sorted out in fruit flies. + +And it is, of course, the case that neither Mendel nor + +this strict prediction from the Chromosomal Theory turns out to be + +correct. Mendel's Law of Independent Assortment does not hold + +for all traits, but this very rigid model of two + +alternatives does not hold either. So let's take a look at some real + +data. The data comes from Thomas Hunt Morgan, a developmental + +biologist who eventually became one of the great geneticists of the + +century at Columbia. He was at Columbia University + +studying fruit flies. And he studies fruit flies rather + +than peas. Can you think of any good reasons why it would make sense + +to study fruit flies rather than peas? Sorry? It has four + +chromosomes instead of seven. No, four, seven. + +Anybody been to Columbia University? I mean where are you going to plant + +peas, right? [LAUGHTER] I mean it's in Manhattan. + +Also, what else is wrong with studying peas? + +They take too long. How many generations of peas are + +you going to get a year in Manhattan? Not so many. Fruit flies, + +how long do they take? A couple weeks. You get a generation every + +couple weeks. If you actually want to write some papers. + +I mean if you have a day job as a monk, you can do these pea things + +that take a long time. But, for example, if you were + +trying to get tenure at Columbia, you might want to actually do + +something that you could get a couple generations every month or + +something like that. So the fruit fly was much better. + +They also, you know, they don't take fields and things. + +You grow them in little vials with some food at the bottom, + +some yeast medium at the bottom and a little cotton stopper at the top. + +And, you know, it's very convenient. You can grow zillions and zillions + +of fruit flies. So that's why the fruit fly was + +chosen, easy, short generation time, etc. And there are a lot of natural + +variations out there. Geneticists love to choose + +organisms that are just easy to work with so you can do a lot of work. + +And fruit flies do have four chromosomes. So N equals four. + +That is four pairs of chromosomes. So he set up a cross. The F0 cross + +was between a normal fly. And the way we say normal in + +genetics in wild type. OK? Wild type. That is the type + +in the wild. It actually doesn't mean that it is the type in the wild. + +It means it's whatever type the geneticist has chosen as his or her + +reference strain, but it's called wild type. + +And he set up a cross between a wild type fly, + +by a fly that had two interesting properties. Its body was black and + +its wings were in bad shape, and they were called vestigial. + +You know, these funny little wingy things that didn't' work, + +hadn't grown out right, etc. So instead of the normal fly body + +color, which is kind of a tan around its middle, it was black all around + +its middle and its wings were very short. The hypothesis is that there + +were genes controlling. And, in fact, by demonstrating + +Mendelian Inheritance black was a single Mendelian trait which was + +recessive to the normal body color, vestigial was a single Mendelian + +trait which was recessive to the normal body shape. + +And the genotype of wild type was homozygous normal, + +which I'll write as plus over plus now. Geneticists actually prefer + +these plus terms rather than big Rs and little Rs. + +Plus over plus. And we'll take a female and we'll + +cross her to a male who is homozygous for the gene that + +controls the body color there and this gene that controls wing shape, + +and we'll look at the offspring. So makes F1. + +The F1 have what genotype? They're plus over black, plus over + +vestigial F1. OK? So then what he does is he takes, + +say these males, and he crosses them back to these flies here that have + +the doubly recessive phenotype doing what we call a test cross. + +That's now the name. We're beginning to introduce + +more of these names. A test cross, when you cross back to + +the homozygote for the recessive phenotype. And what he gets out, + +the same exact picture I drew before, but we're just getting used to + +nomenclature and getting used to slightly different nomenclatures + +here. He could either get, he always got black, vestigial, + +black, vestigial, black, vestigial from the parent on the right. + +And here he could get plus, plus, he could get black, vestigial, he + +could get black, plus or he could get plus, + +vestigial. And, as we said over there, + +the predictions would be that if these were on different chromosomes + +he would get 25%, 25%, 25%, 25%. If they were on the + +same chromosome under a very simple interpretation of the Chromosomal + +Theory of Inheritance, he would get 50%, 50%, zero, zero. + +And, in fact, what did he get? 965, 944, 206 and 185. What do you + +make of it? Which theory is confirmed? Neither? + +Well, maybe this is just a statistical fluctuation + +around the first line. + +You don't think so? How come? Way too wild. + +But, I mean, these are wild type so maybe. [LAUGHTER] So do you think + +those numbers are too far off, a quarter, quarter, quarter to be + +believable? Ooh. Not only are they way off 25%, + +25%, 25%, 25%, but something is fishy. The two parental types are + +much higher than the two non-parental types. + +That's saying something to you. Oh, interesting. + +What about this other one, 50%, 50%, zero, zero? Could this be + +a fluctuation around zero? No. This one is really pretty easy + +to reject because zero, this is not like close to zero. + +This should be zero. You shouldn't see any of those, + +right? Because they didn't go in if they were on the same chromosome. + +So what are we going to do? We're acting like Mendel, + +good. We're seeing something funny in the data here. + +You even saw something that is beyond just, it's a little weird, + +but it's actually a little weird in some interesting direction. + +How many of them are of the parental type? + +Well, it's 965 plus 944. How many are the non-parental type? + +It's 206 plus 185. So let's figure out what's the proportion, + +the frequency of non-parental types. + +Well, it's 206 plus 185 over 206 plus 185 plus 965 plus + +944, which is 17%. OK, so it's 17%. + +We now know what the answer is. When you take two traits and you + +cross them in this fashion, two recessive traits and do a test + +cross, the ratio will neither be 25%, 25%, 25%, 25% or it's not going to + +be 50%, 50%, zero, zero. In fact, it will always be 17%. + +Why not? But Mendel looks at his data, and he said 3:1. + +It's trying to say 3:1. Isn't this trying to say 17%? + +Yeah. Well, see, that's the thing, is what to make of this number. + +What does this 17% mean? Now, of course, you all know that + +this is genetic recombination, right? You know that these + +chromosomes are exchanging material. I cannot kid you about that. But + +put yourself in the days of Thomas Hunt Morgan looking at these data + +and trying to figure out what is this 17% trying to tell him. + +There were people around Columbia and elsewhere who were saying, + +oh, this 17% number says a lot about physiology. It's a statement about + +the developmental relationship of genes. And they were trying to read + +all sorts of things into these numbers. + +The first thing is let's test some more pairs of traits. + +How about another pair? If you do that, do you get 17%? + +No. It turns out maybe you get 8%. You do it with another pair, maybe + +you get 9%. So it's not a constant. We can reject the idea that 17% is + +some constant like e or one over pi or something like that. + +But we look at these numbers, and a lot of folks wanted to + +interpret these as physiological numbers. Something about the + +biology of these traits. So -- + +-- we can give this thing a name, the frequency of non-parental types. + +We can call this the Recombination Rate. Because we've got new + +combinations, right? This recombination rate might mean, + +and you know already that you're thinking what it really means is -- + + -- somehow we have black, + +black, plus, plus. And in the F1 we have vestigial, + +vestigial, plus, plus. And that somehow these two + +chromosomes have exchanged genetic material so that the new chromosome + +you get is like this. And you get a recombinant type. + +You get recombination between these chromosomes. And there's a + +recombination rate. And the recombination rate is how + +often this kind of an exchange occurs. And what does the + +recombination rate depend on? The distance between those two genes. + +You know this because you've been told this since kindergarten, + +right? It's in all the high school textbooks and things like or + +whatever. They teach genetics earlier and earlier these days and + +it's on TV and stuff. But that's a nice idea that the + +recombination rate depends on the distance. And this rate, + +which might be 17% or it might be 1% or it might be 8% or it might be who + +knows, depends on the distances, reflection of the distance. + +But, golly, what's the evidence for that? Aren't we just making up a + +theory to explain the data here? We don't have a theory to, we're + +just trying to fix the Chromosomal Theory. The Chromosomal Theory + +wouldn't predict these recombinant types. It would have predicted we + +only get parental types out. So because we do get non-parental + +types out we say, well, chromosomes are promiscuous + +and they'll exchange parts. Because we don't always get the same + +ratio, we have to make up the fact that somehow the ratio is different + +because of something, distance. We cannot observe + +distance. No way that Morgan was able to look at the chromosome and + +see where the genes were. So basically any number you want to + +give him, he'll just say it's the distance. This is not overwhelming. + +Now, what's even the evidence that chromosomes exchange material? + +Why do we think stuff like that even happens? + +Ah, it turns out you can take fruit fly gametes, and other gametes, + +and look at them in the microscope. What you do is to look at them + +closely, the chromosomes during meiosis. You put a cover slip on + +them, you squish them down, add a little dye and you look. + +And it turns out that really truly, when you look in the microscope, you + +can see stuff like that, of chromosomes lying on top of each + +other like that. These are called chiasmata, + +crosses. Chiasma or the plural chiasmata. You can see it in the + +microscope. So does that convincingly demonstrate that + +recombination occurs? Are you overwhelmed? Why not? + +Yeah. You put a bunch of chromosomes down, + +you put a glass cover slip and squish them. The fact that two + +things lie on top of each other, I mean this is what it takes to do + +science. Is you actually have to be pretty + +hardnosed about not being willing to take evidence that supports your + +theory just because it supports your theory. Skepticism is pretty + +important here. So you squish down the cover slip + +and sometimes, not always, sometimes some + +chromosome lands on top of some other chromosome. + +Big deal. So how are we going to actually get any convincing + +predictions? That's what it took with Mendel. What convincing + +predictions can we make that this recombination phenomenon has + +something to do with the disposition of genes along chromosomes? + +And, if so, might provide some support for the Chromosomal Theory + +of Inheritance? Well, when you're in a quandary, + +you've got some new area, you've got messy data, you need new thinking. + +Where do you get new thinking from? You get new thinking from students + +because old folks are thinking, you know, in whatever way they were + +thinking. So what you really need are young students to come along + +into the field and look at the data in some fresh way. + +So, in this case, the hero was a UROP student at + +Columbia. They didn't call it UROP, but it was the same thing. He was a + +sophomore working in the lab of Thomas Hunt Morgan who came along + +and solved this problem very nicely. You know, I think in part because + +sophomores had not been polluted by all sorts of prior thinking. + +So the idea of genetic maps arises through the work of one + +Alfred Sturtevant. Sturtevant was a sophomore at + +Columbia in 1911. And while an undergraduate working + +in the lab of Thomas Hunt Morgan, he went home, you know, he was + +working in the lab, and he took home a pile of data. + +And he said I've got to make sense out of all this data. + +I don't understand exactly what's going on. + +Here's some of the data he took home. Morgan's lab had set up crosses, + +not just involving two traits but three traits simultaneously. + +They actually set up crosses involving three traits, + +black, what's called cinnabar which is an eye color, + +and vestigial. And they looked at the F1 when crossing back to the + +triply homozygous fly here, and they counted the number of + +recombinant types of different sorts. + +You could look at recombinant types between black and vestigial. + +We've already got that data. You could look at recombinant types + +between black and cinnabar. You could look at recombinant types + +between cinnabar and vestigial. Now, I've drawn this as if these + +live on a chromosome and I know their order. You've got to remember, + +we don't know that they live on a chromosome. And Sturtevant + +certainly didn't know their order. OK? But I have to draw it for you, + +so I'm drawing it for you because the notation he would have used was + +much too messy and there's no point in learning it. + +So he begins to look at the data from these different crosses. + +What he finds is when he looks only at black and vestigial, + +so he ignores what happened with cinnabar, what's the recombination + +rate, the frequency with which he observes new types, + +non-parental types? Well, they had already done the + +experiment in the lab. And what's the answer? + +17%. Now, he then looks at black to cinnabar. So he just, + +you know, covers up the genotype of vestigial. There are four + +possibilities, black, cinnabar, + +black, plus, plus, cinnabar, black, cinnabar. + +He looks at the parental types, black, cinnabar or plus, plus. He + +looks at the non-parental types, the recombinant types, plus, + +cinnabar or black, plus. He counts up the number of + +non-parental types to the total number of flies and he gets a + +recombination rate of 9%. OK? So I'm just going to draw you + +this. He took out a piece of paper and he drew himself black, + +cinnabar, vestigial. He said I believe this has something to do + +with distance. This was 17%. The probability of a + +crossover occurring, of a recombination occurring between + +black and vestigial 17%. And the probability of a crossover + +occurring, the frequency of a crossover occurring between black + +and cinnabar was 9%. Got any prediction? Cinnabar, + +vestigial should be about 8%, give or take. + +But what if his picture is wrong. What's another picture that might + +be were cinnabar is? Oh, yeah. There's an alternative + +picture, isn't there? The alternative picture is black, + +vestigial, cinnabar over here at 9%, 17%. In which case, what's the + +prediction for cinnabar, vestigial? 26%, give or take, + +right? We've got to be a little rough about these things. + +Well, that's not a single prediction, but it's down to two alternatives. + +He's either expecting about 8% or he's expecting about 26%. + +So two alternative predictions. + +Cinnabar, vestigial combination rate 8%. Mm, that's good. + +That's very good. The first time anybody's made a prediction, + +and a quantitative prediction that's just gotten verified by data. + +Sturtevant also does one other interesting thing. + +He looks at a fourth thing, which is a little bit interesting. + +When I look at the types of gametes that can come out of her, + +right? If this idea of genetic recombination is correct, + +that sometimes in this F1 parent a crossover has occurred here, + +sometimes a crossover has occurred here, and the crossover here would + +give rise to black, plus, plus or plus, cinnabar, + +vestigial. Here it would give rise to black, cinnabar, + +plus or plus, plus, vestigial if it went the other way. + +Is it possible that occasionally, under this model, you might get two + +crossovers? Might it be the case, if we believe in this stuff, that a + +crossover might occur between black and cinnabar and a crossover might + +occur between vestigial and cinnabar? Could be. How often do you think + +that would happen? Sorry? Rarely. + +How rarely? What's the chance of a crossover here? + +About 9%, right? A crossover here? + +About 8%. Let's say 9%, 8% or about 10% just for roundness. + +There's about a 10% chance of a crossover in the first interval. + +It's about a 10% chance of a crossover in the second interval. + +It's about 1% of the time. Much lower than the others. + +But about 1% of the time you might see what kind of chromosomes + +emerging? Black plus, vestigial. + +So black plus, vestigial or plus, cinnabar, vestigial. These + +chromosomes, oops, plus. Thank you. These would be + +doubly recombinant chromosomes. They would need two recombination + +events to explain them. And you even have a prediction that + +you might see them at about 1%. And, sure enough, + +Sturtevant sees them. It's actually somewhat less than 1%. + +It turns out that double is a little less likely than the + +independent. There's a little bit of what's called interference, + +but don't worry about it. That's a second order effect. + +At a frequency of about 1% he sees double recombinants. + +That tells him who is in the middle. If cinnabar is the one that has + +this property, because if he asked how often does + +cinnabar get inherited together with plus, plus that's very rare. + +But vestigial gets inherited with plus, plus 9% of the time, + +black gets inherited with plus, plus, sorry, 8% or 9% of the time, + +but cinnabar is pretty rare. So all this together says that this model + +here of a linear chromosome is now making some pretty good quantitative + +predictions about what's going on. But of course this is just three + +different genes, black, cinnabar and vestigial. + +What would you like? More of them at least. Me, + +personally, I go for all. I'm with you. But he's an + +undergraduate and he's got what he can. So more. + +Well, it turns out that of course Morgan's lab was busily making + +crosses and all this kind of stuff and there was more data available. + +So when he saw this happening he said, all right, let's look + +at some more things. And he began, because there was so + +much data from the lab, going around and taking all this + +stuff, lobe and curved wing and other kinds of funny traits, + +and he began looking at frequencies. And he found this was about 9%. + +And this was about 8%. And he found this was about 5%. + +And he found that this was about 5%. And if these two were 5% + +his prediction was 10%. And his prediction here would be 13%, + +etc. And it all pretty closely checked out. This was highly + +constrained, the idea that the recombination rates would fit a + +simple linear model. It's not perfect, of course, + +because imagine what happens. Suppose I have 10%, + +10%, 10%, 10%, 10% and I have ten loci, you know, I have + +ten such intervals. What will the recombination rate be? + +100%. And then if have five more? 150%. What does that mean? + +So clearly something is wrong about just using percents. + +You have to kind of, I mean for the aficionados, + +really the percent reflects the number of crossovers. + +But obviously you have to do a little bit of correction because you + +cannot have, you know, if I keep piling on the intervals + +double crossovers will happen which won't produce recombinant types. + +But don't worry about it. We can just add percentages for today. + +And when you do all this it works. Sturtevant did this all in one + +evening. In his autobiography that he wrote about 50 years later he + +says I went home one evening, blew off all of my homework, and + +stayed up all night and was able to make sense out of all this data. + +So I think this is an example of a productive all-nighter. + +[LAUGHTER] And also this is an example of when it's the right + +choice to blow off your homework. If anyone wishes to do things like + +this and be as productive, you're certainly entitled to blow + +off the homework here, too. But do bring in good data like + +this when you're done. Anyway, this notion is a genetic + +map. A genetic map was a totally abstract concept, + +much like Mendel's abstract concept that there were even genes. + +Now we're going further and we're saying whatever genes are, + +we still don't know that they're DNA, etc. Whatever they are they live on + +a line, and they behave as if they live on a line, + +and they undergo recombinations, etc. + +And when I see a recombination rate, a recombination frequency, a + +recombination rate that's zero, it must mean the genes are very + +close together. If I see a recombination rate very, + +very close, never recombine, recombination rates, + +oh, I don't know, maybe 10% or something, well, + +there's some distance between them. And if they're further and further + +and further away, or on totally different chromosomes, + +what would be the recombination rate here for two different chromosomes? + +A half. Half of these are non-parental types. + +So when I get up to a recombination rate of 50% then it means that they + +live on, that they are so-called unlinked to each other. + +Either they are on different chromosomes entirely or I suppose + +it's possible, and in fact it is possible that + +they're so far away on the same chromosome that the probability of + +crossovers occurring is so high that they are de-correlated from each + +other and I cannot observe any recombination rate less than 50%, + +It turns out many chromosomes are sufficiently big that lots of + +crossovers can occur and you cannot actually detect linkage at the two + +ends of the chromosome. But if you string together some + +genes in between you can see that this is linked to this is linked to + +this is linked to this is linked to this is linked to this. + +OK? All right. Good. So Sturtevant is another one of my + +heroes because he comes up with this utterly abstract model here of + +chromosomes, of genetic maps. All right. I meant to get that + +board. Does someone have a call? OK. So last of all let me take + +Section 4 here. This begins to provide fairly + +convincing evidence for the Chromosomal Theory because it made a + +whole lot of pretty whacky predictions. + +And they pretty much hold up. Here's another thing that provided + +a lot of good evidence for it, and that was sex linkage. + + Also in Morgan's lab, + +which was a very productive place, I must say, folks were wondering + +about the fact that chromosomes, although they almost always occurred + +in pairs that lined up with each other perfectly, + +in many species there was one odd couple. + +A pair of chromosomes that always paired up with each other but they + +didn't look the same. This one looks like an X. + +This one kind of had the shape of a Y. And hence they got the names the + +X and the Y chromosomes. Now here was something very + +interesting. In fruit flies it was always the males that had an XY pair. + +In females it was always an XX pair. What does that tell us about these + +chromosomes and what they do? Sorry? Determines gender. Wait a + +minute. Why do you believe it determines gender? + +It just correlated with gender. Females have these two funny + +chromosomes. Males have, I'm sorry. Females have these two + +Xs. Males have an X and Y. + +Does it have to mean that they determine gender? + +Maybe gender determines them. Maybe what happens is that in + +female cells you get both chromosomes, but in male cells some + +enzyme comes along and chews off the end of the chromosome. + +No, no, really. Maybe this is some physiological state of the + +chromosomes. Why are you so ready to leap to the conclusion that the + +chromosomes determine sex, rather the gender, than the gender + +determines the chromosomes? It's because you know the answer, + +you've been told all this, etc. But I, again, invite you to take apart + +what support you have for that and ask how would you know, + +right? All of these things you get told, but how would you know? + +And there was great argument about was this really the case? + +So how could you convince people that this was true? + +It's not obvious to know which way it would go. + +The most convincing evidence, not the only evidence, but the most + +convincing evidence came from a single fly that had been isolated in + +Morgan's lab. And F0 fly that had the very interesting property that + +instead of the normal red drosophila eyes this fly had white eyes. + +Whereas, this was the normal fly with red eyes. And we'll + +use a female here. When you cross together the white + +eyed fly and the red eyed fly, what you find is that in the F1 + +generation all the flies, males and females, are normal red + +eyes. + +When I take, however, a normal female and I cross her back, + +sorry. A normal female emerging from this F1 generation, + +and now I cross her to a normal male, here's what happens. + +All of her daughters are normal, but her sons, half are normal and + +half are white-eyed again. + +That's weird. For the first time we have a genetic trait, + +eye color, that is showing correlation in its inheritance with + +sex. So that says for the first time we're beginning to see + +something that looks like linkage, like genetic correlation, genetic + +nearness, like genetic mapping that would relate eye color to sex. + +What's the model? Well, of course the model here is + +that this fly, we know the answer, + +is X over Y, it's a male. And the X chromosome here has a + +mutation that makes it white-eyed. What's this normal fly over here? + +X over X. And its X chromosomes are normal. + +When we go to the next generation, what kind of offspring are there? + +The daughters of this cross, what's their genotype? What did + +they get from dad? They always get a normal X + +chromosome from dad. I'm sorry, from mom I mean. + +What did they get from dad, these daughters? They always got the X + +with the white eye. Why didn't they get the Y? + +Because they're daughters, right? If they got the Y they'd be + +sons. But they're daughters. So the daughters always are getting + +this chromosome. Now, when you mate these back to a + +normal male, X over Y, the daughters are of what type? + +What did they get from their dad? Always an X plus. + +And what did they get from their mom? Either an X with a mutation or + +an X plus. Either way they're normal, because we're assuming that + +this white-eyed mutation is recessive. What did the sons get? + +What did they get from their dad? Y. Why don't they get the X? + +Because they're sons. What did they get from their mom? + +Half of them get the X plus, half of them get the X mutant, + +and that explains cleanly what's going on. Now, + +the Y chromosome, being a short stubby little + +chromosome, doesn't have a copy of this gene for eye color at all. + +So you might as well regard it as being, you know, + +recessive, as carrying the allele for the recessive trait. + +It doesn't have any functional copy. So for a male he only + +gets a copy from mom. And what he got from mom completely + +determines his phenotype. Thus, the transmission of eye color, + +a trait controlled by a gene on the X chromosome correlated so + +beautifully with the transmission of the trait sex. + +That provided a convincing argument that it was the chromosomes + +controlling sex rather than the sex controlling chromosomes. + +All right. So you know all this stuff. You've all heard of Mendel. + +You've all heard of recombination. You've heard of, I suppose, genetic + +maps. You know about X and Y chromosomes and things like that. + +What I want you to take away from all of this is that in order to + +really know things you have to struggle against models. + +You have to understand whether the model is just being made up to + +explain the data or whether the model has been proved by testing it + +in any serious kinds of ways. All this stuff took 30 or 40 years + +of serious battle before the last people caved in and said this is all + +proven. Of course, going forward we'll assume it's all + +proven and you know what to do with it. And onward to next time. \ No newline at end of file diff --git a/AYper3fzw-s.txt b/AYper3fzw-s.txt new file mode 100644 index 0000000000000000000000000000000000000000..0eb5c3416199ef3763581f6f5636c4402952ce95 --- /dev/null +++ b/AYper3fzw-s.txt @@ -0,0 +1,4347 @@ +align:start position:0% + +And um our next speaker is Eric Bosworth + + align:start position:0% +And um our next speaker is Eric Bosworth + + + align:start position:0% +And um our next speaker is Eric Bosworth +from Eversource Energy and he has + + align:start position:0% +from Eversource Energy and he has + + + align:start position:0% +from Eversource Energy and he has +collaborated with Eversource in the + + align:start position:0% +collaborated with Eversource in the + + + align:start position:0% +collaborated with Eversource in the +Framingham site acquiring temperature + + align:start position:0% +Framingham site acquiring temperature + + + align:start position:0% +Framingham site acquiring temperature +data down the bore holes. + + align:start position:0% +data down the bore holes. + + + align:start position:0% +data down the bore holes. +>> Awesome. + + align:start position:0% +>> Awesome. + + + align:start position:0% +>> Awesome. +>> What's your time? + + align:start position:0% +>> What's your time? + + + align:start position:0% +>> What's your time? +>> Hi, I'm good. I I am the uh privileged + + align:start position:0% +>> Hi, I'm good. I I am the uh privileged + + + align:start position:0% +>> Hi, I'm good. I I am the uh privileged +individual that gets to run anchor here + + align:start position:0% +individual that gets to run anchor here + + + align:start position:0% +individual that gets to run anchor here +before lunch. So, thanks for bearing + + align:start position:0% +before lunch. So, thanks for bearing + + + align:start position:0% +before lunch. So, thanks for bearing +with me. Um, for those of you that I + + align:start position:0% +with me. Um, for those of you that I + + + align:start position:0% +with me. Um, for those of you that I +don't know, my name is Eric Bosworth. I + + align:start position:0% +don't know, my name is Eric Bosworth. I + + + align:start position:0% +don't know, my name is Eric Bosworth. I +work in the clean technologies + + align:start position:0% +work in the clean technologies + + + align:start position:0% +work in the clean technologies +department at Eversource. And for better + + align:start position:0% +department at Eversource. And for better + + + align:start position:0% +department at Eversource. And for better +or worse, I have had the privilege of + + align:start position:0% +or worse, I have had the privilege of + + + align:start position:0% +or worse, I have had the privilege of +overseeing the Framingham project from + + align:start position:0% +overseeing the Framingham project from + + + align:start position:0% +overseeing the Framingham project from +before site selection. So, I joined on + + align:start position:0% +before site selection. So, I joined on + + + align:start position:0% +before site selection. So, I joined on +to the team to kind of oversee it as we + + align:start position:0% +to the team to kind of oversee it as we + + + align:start position:0% +to the team to kind of oversee it as we +were figuring out where and how we were + + align:start position:0% +were figuring out where and how we were + + + align:start position:0% +were figuring out where and how we were +going to do this. and all the way + + align:start position:0% +going to do this. and all the way + + + align:start position:0% +going to do this. and all the way +through today uh when we are up in + + align:start position:0% +through today uh when we are up in + + + align:start position:0% +through today uh when we are up in +operation with customers using the + + align:start position:0% +operation with customers using the + + + align:start position:0% +operation with customers using the +system. So folks have talked about the + + align:start position:0% +system. So folks have talked about the + + + align:start position:0% +system. So folks have talked about the +project a lot over the last day and a + + align:start position:0% +project a lot over the last day and a + + + align:start position:0% +project a lot over the last day and a +half here. I I don't need to go over + + align:start position:0% +half here. I I don't need to go over + + + align:start position:0% +half here. I I don't need to go over +Framingham necessarily. What I'm hoping + + align:start position:0% +Framingham necessarily. What I'm hoping + + + align:start position:0% +Framingham necessarily. What I'm hoping +to do is bring the perspective of we've + + align:start position:0% +to do is bring the perspective of we've + + + align:start position:0% +to do is bring the perspective of we've +had a lot of insight into what's the big + + align:start position:0% +had a lot of insight into what's the big + + + align:start position:0% +had a lot of insight into what's the big +picture? What's the policy direction we + + align:start position:0% +picture? What's the policy direction we + + + align:start position:0% +picture? What's the policy direction we +need to go into? How do we design a + + align:start position:0% +need to go into? How do we design a + + + align:start position:0% +need to go into? How do we design a +system like this? How do we operate a + + align:start position:0% +system like this? How do we operate a + + + align:start position:0% +system like this? How do we operate a +system like this? I'm going to bring you + + align:start position:0% +system like this? I'm going to bring you + + + align:start position:0% +system like this? I'm going to bring you +the perspective of what happens when you + + align:start position:0% +the perspective of what happens when you + + + align:start position:0% +the perspective of what happens when you +get out there and start tearing up + + align:start position:0% +get out there and start tearing up + + + align:start position:0% +get out there and start tearing up +pavement and actually putting it in + + align:start position:0% +pavement and actually putting it in + + + align:start position:0% +pavement and actually putting it in +because uh nothing really prepares you + + align:start position:0% +because uh nothing really prepares you + + + align:start position:0% +because uh nothing really prepares you +for that until you're into it. And + + align:start position:0% +for that until you're into it. And + + + align:start position:0% +for that until you're into it. And +there's certainly some some lessons + + align:start position:0% +there's certainly some some lessons + + + align:start position:0% +there's certainly some some lessons +learned and scars along the way that you + + align:start position:0% +learned and scars along the way that you + + + align:start position:0% +learned and scars along the way that you +pick up. + + align:start position:0% +pick up. + + + align:start position:0% +pick up. +Here's a basic breakdown of kind of the + + align:start position:0% +Here's a basic breakdown of kind of the + + + align:start position:0% +Here's a basic breakdown of kind of the +three main work streams that go into + + align:start position:0% +three main work streams that go into + + + align:start position:0% +three main work streams that go into +actually building a shared thermal + + align:start position:0% +actually building a shared thermal + + + align:start position:0% +actually building a shared thermal +network in a community. You've got the + + align:start position:0% +network in a community. You've got the + + + align:start position:0% +network in a community. You've got the +ground exchanger. Brock was just talking + + align:start position:0% +ground exchanger. Brock was just talking + + + align:start position:0% +ground exchanger. Brock was just talking +about drilling. Uh we've talked about + + align:start position:0% +about drilling. Uh we've talked about + + + align:start position:0% +about drilling. Uh we've talked about +thermal conductivity testing and kind of + + align:start position:0% +thermal conductivity testing and kind of + + + align:start position:0% +thermal conductivity testing and kind of +how the ground exchanger works. It's + + align:start position:0% +how the ground exchanger works. It's + + + align:start position:0% +how the ground exchanger works. It's +pretty straightforward, but that's your + + align:start position:0% +pretty straightforward, but that's your + + + align:start position:0% +pretty straightforward, but that's your +energy source. You're putting holes into + + align:start position:0% +energy source. You're putting holes into + + + align:start position:0% +energy source. You're putting holes into +the ground. You're pulling heat out in + + align:start position:0% +the ground. You're pulling heat out in + + + align:start position:0% +the ground. You're pulling heat out in +the winter. You're putting heat in in + + align:start position:0% +the winter. You're putting heat in in + + + align:start position:0% +the winter. You're putting heat in in +the summer. That's what's fueling your + + align:start position:0% +the summer. That's what's fueling your + + + align:start position:0% +the summer. That's what's fueling your +network. But the other pieces are just + + align:start position:0% +network. But the other pieces are just + + + align:start position:0% +network. But the other pieces are just +important. You have the distribution + + align:start position:0% +important. You have the distribution + + + align:start position:0% +important. You have the distribution +loop, the pipes in the street, the + + align:start position:0% +loop, the pipes in the street, the + + + align:start position:0% +loop, the pipes in the street, the +service lines that you're pulling into + + align:start position:0% +service lines that you're pulling into + + + align:start position:0% +service lines that you're pulling into +the homes. How do you move the energy + + align:start position:0% +the homes. How do you move the energy + + + align:start position:0% +the homes. How do you move the energy +through the neighborhood? And then + + align:start position:0% +through the neighborhood? And then + + + align:start position:0% +through the neighborhood? And then +finally, the building conversions. Um + + align:start position:0% +finally, the building conversions. Um + + + align:start position:0% +finally, the building conversions. Um +certainly not third in importance here. + + align:start position:0% +certainly not third in importance here. + + + align:start position:0% +certainly not third in importance here. +What are you doing to the building + + align:start position:0% +What are you doing to the building + + + align:start position:0% +What are you doing to the building +envelope and how are you interfacing + + align:start position:0% +envelope and how are you interfacing + + + align:start position:0% +envelope and how are you interfacing +with that thermal network? How are you + + align:start position:0% +with that thermal network? How are you + + + align:start position:0% +with that thermal network? How are you +keeping your customers warm in the + + align:start position:0% +keeping your customers warm in the + + + align:start position:0% +keeping your customers warm in the +winter, cool in the summer? And what + + align:start position:0% +winter, cool in the summer? And what + + + align:start position:0% +winter, cool in the summer? And what +equipment is involved there? So, sort of + + align:start position:0% +equipment is involved there? So, sort of + + + align:start position:0% +equipment is involved there? So, sort of +stepping through each of those, I I like + + align:start position:0% +stepping through each of those, I I like + + + align:start position:0% +stepping through each of those, I I like +to start with main installation pipes in + + align:start position:0% +to start with main installation pipes in + + + align:start position:0% +to start with main installation pipes in +the street because as a utility, this is + + align:start position:0% +the street because as a utility, this is + + + align:start position:0% +the street because as a utility, this is +our bread and butter. Um, we put in + + align:start position:0% +our bread and butter. Um, we put in + + + align:start position:0% +our bread and butter. Um, we put in +hundreds and hundreds of miles of this + + align:start position:0% +hundreds and hundreds of miles of this + + + align:start position:0% +hundreds and hundreds of miles of this +HDPE pipe every year. We know this. We + + align:start position:0% +HDPE pipe every year. We know this. We + + + align:start position:0% +HDPE pipe every year. We know this. We +know how to open the street. We know how + + align:start position:0% +know how to open the street. We know how + + + align:start position:0% +know how to open the street. We know how +to fuse pipe. We know how to get it into + + align:start position:0% +to fuse pipe. We know how to get it into + + + align:start position:0% +to fuse pipe. We know how to get it into +the ground. We know how to test it. Um + + align:start position:0% +the ground. We know how to test it. Um + + + align:start position:0% +the ground. We know how to test it. Um +to the points that Mark brought up, you + + align:start position:0% +to the points that Mark brought up, you + + + align:start position:0% +to the points that Mark brought up, you +know, making sure that the fusions are + + align:start position:0% +know, making sure that the fusions are + + + align:start position:0% +know, making sure that the fusions are +good and the pressure testing is + + align:start position:0% +good and the pressure testing is + + + align:start position:0% +good and the pressure testing is +appropriate and documented. Uh this part + + align:start position:0% +appropriate and documented. Uh this part + + + align:start position:0% +appropriate and documented. Uh this part +of the project was, I will say, the + + align:start position:0% +of the project was, I will say, the + + + align:start position:0% +of the project was, I will say, the +smoothest part from a timeline, a cost, + + align:start position:0% +smoothest part from a timeline, a cost, + + + align:start position:0% +smoothest part from a timeline, a cost, +an execution standpoint. Our crews know + + align:start position:0% +an execution standpoint. Our crews know + + + align:start position:0% +an execution standpoint. Our crews know +how to do this. We actually took crews + + align:start position:0% +how to do this. We actually took crews + + + align:start position:0% +how to do this. We actually took crews +that had been putting gas pipe in the + + align:start position:0% +that had been putting gas pipe in the + + + align:start position:0% +that had been putting gas pipe in the +year before, did a little bit of + + align:start position:0% +year before, did a little bit of + + + align:start position:0% +year before, did a little bit of +retraining on them, showed them how to + + align:start position:0% +retraining on them, showed them how to + + + align:start position:0% +retraining on them, showed them how to +stencil geothermal on the side of the + + align:start position:0% +stencil geothermal on the side of the + + + align:start position:0% +stencil geothermal on the side of the +pipe, and they were off to the races. + + align:start position:0% +pipe, and they were off to the races. + + + align:start position:0% +pipe, and they were off to the races. +They got out there and they installed + + align:start position:0% +They got out there and they installed + + + align:start position:0% +They got out there and they installed +all of this mile of pipe plus all 38 + + align:start position:0% +all of this mile of pipe plus all 38 + + + align:start position:0% +all of this mile of pipe plus all 38 +services in about 2 to 3 months. It was + + align:start position:0% +services in about 2 to 3 months. It was + + + align:start position:0% +services in about 2 to 3 months. It was +great. It was exactly as we planned it. + + align:start position:0% +great. It was exactly as we planned it. + + + align:start position:0% +great. It was exactly as we planned it. +Um, similarly, the service lines, just + + align:start position:0% +Um, similarly, the service lines, just + + + align:start position:0% +Um, similarly, the service lines, just +like a water service or a gas service or + + align:start position:0% +like a water service or a gas service or + + + align:start position:0% +like a water service or a gas service or +anything else that you would pull to a + + align:start position:0% +anything else that you would pull to a + + + align:start position:0% +anything else that you would pull to a +home, we dug a trench. There's two lines + + align:start position:0% +home, we dug a trench. There's two lines + + + align:start position:0% +home, we dug a trench. There's two lines +in this case instead of one. So, we have + + align:start position:0% +in this case instead of one. So, we have + + + align:start position:0% +in this case instead of one. So, we have +a send and a receive line, but for the + + align:start position:0% +a send and a receive line, but for the + + + align:start position:0% +a send and a receive line, but for the +most part, it's all the same materials. + + align:start position:0% +most part, it's all the same materials. + + + align:start position:0% +most part, it's all the same materials. +It's HDPE pipe that we're fusing. We're + + align:start position:0% +It's HDPE pipe that we're fusing. We're + + + align:start position:0% +It's HDPE pipe that we're fusing. We're +pulling it into the home. We're putting + + align:start position:0% +pulling it into the home. We're putting + + + align:start position:0% +pulling it into the home. We're putting +it into a pair of shut off valves on the + + align:start position:0% +it into a pair of shut off valves on the + + + align:start position:0% +it into a pair of shut off valves on the +inside of the basement. And it feels + + align:start position:0% +inside of the basement. And it feels + + + align:start position:0% +inside of the basement. And it feels +just like utility work. Even from the + + align:start position:0% +just like utility work. Even from the + + + align:start position:0% +just like utility work. Even from the +outside, if you watched a crew doing + + align:start position:0% +outside, if you watched a crew doing + + + align:start position:0% +outside, if you watched a crew doing +this trenching, um, repaving in the + + align:start position:0% +this trenching, um, repaving in the + + + align:start position:0% +this trenching, um, repaving in the +street, you'd have no idea that they + + align:start position:0% +street, you'd have no idea that they + + + align:start position:0% +street, you'd have no idea that they +were putting geothermal in. It just + + align:start position:0% +were putting geothermal in. It just + + + align:start position:0% +were putting geothermal in. It just +looks like everyday utility work. So, + + align:start position:0% +looks like everyday utility work. So, + + + align:start position:0% +looks like everyday utility work. So, +these two work streams. Great. + + align:start position:0% +these two work streams. Great. + + + align:start position:0% +these two work streams. Great. +Fantastic. We understand them. We do + + align:start position:0% +Fantastic. We understand them. We do + + + align:start position:0% +Fantastic. We understand them. We do +them all the time. They were easy. + + align:start position:0% +them all the time. They were easy. + + + align:start position:0% +them all the time. They were easy. +Borefield drilling, not necessarily a + + align:start position:0% +Borefield drilling, not necessarily a + + + align:start position:0% +Borefield drilling, not necessarily a +utility's forte. I think this is one of + + align:start position:0% +utility's forte. I think this is one of + + + align:start position:0% +utility's forte. I think this is one of +the first times that a at least a gas + + align:start position:0% +the first times that a at least a gas + + + align:start position:0% +the first times that a at least a gas +utility in the nation has drilled bore + + align:start position:0% +utility in the nation has drilled bore + + + align:start position:0% +utility in the nation has drilled bore +holes. Um, and there were some lessons + + align:start position:0% +holes. Um, and there were some lessons + + + align:start position:0% +holes. Um, and there were some lessons +learned. You know, Brock talked a lot + + align:start position:0% +learned. You know, Brock talked a lot + + + align:start position:0% +learned. You know, Brock talked a lot +about this, so I'm not going to harp too + + align:start position:0% +about this, so I'm not going to harp too + + + align:start position:0% +about this, so I'm not going to harp too +much on drilling specifically, but + + align:start position:0% +much on drilling specifically, but + + + align:start position:0% +much on drilling specifically, but +there's questions about site layout and + + align:start position:0% +there's questions about site layout and + + + align:start position:0% +there's questions about site layout and +what formation are you drilling in? How + + align:start position:0% +what formation are you drilling in? How + + + align:start position:0% +what formation are you drilling in? How +quickly can you drill? How do you manage + + align:start position:0% +quickly can you drill? How do you manage + + + align:start position:0% +quickly can you drill? How do you manage +your water and your cutings? We were + + align:start position:0% +your water and your cutings? We were + + + align:start position:0% +your water and your cutings? We were +learning. We brought in experts. They + + align:start position:0% +learning. We brought in experts. They + + + align:start position:0% +learning. We brought in experts. They +did a great job. They designed great + + align:start position:0% +did a great job. They designed great + + + align:start position:0% +did a great job. They designed great +ground exchangers. They executed well. + + align:start position:0% +ground exchangers. They executed well. + + + align:start position:0% +ground exchangers. They executed well. +Uh, but for us as the utility, you know, + + align:start position:0% +Uh, but for us as the utility, you know, + + + align:start position:0% +Uh, but for us as the utility, you know, +it was more a learning opportunity than + + align:start position:0% +it was more a learning opportunity than + + + align:start position:0% +it was more a learning opportunity than +anything. We certainly weren't out there + + align:start position:0% +anything. We certainly weren't out there + + + align:start position:0% +anything. We certainly weren't out there +directing the drillers on how to run + + align:start position:0% +directing the drillers on how to run + + + align:start position:0% +directing the drillers on how to run +their operation. We were letting the + + align:start position:0% +their operation. We were letting the + + + align:start position:0% +their operation. We were letting the +experts do what they do best. And then + + align:start position:0% +experts do what they do best. And then + + + align:start position:0% +experts do what they do best. And then +in the future, you know, we look at + + align:start position:0% +in the future, you know, we look at + + + align:start position:0% +in the future, you know, we look at +Framingham, we potentially have an + + align:start position:0% +Framingham, we potentially have an + + + align:start position:0% +Framingham, we potentially have an +expansion coming up here in the next + + align:start position:0% +expansion coming up here in the next + + + align:start position:0% +expansion coming up here in the next +year or two, and we've learned some + + align:start position:0% +year or two, and we've learned some + + + align:start position:0% +year or two, and we've learned some +lessons from the first time around that + + align:start position:0% +lessons from the first time around that + + + align:start position:0% +lessons from the first time around that +we will apply the next time we go out to + + align:start position:0% +we will apply the next time we go out to + + + align:start position:0% +we will apply the next time we go out to +drill a bore field. And hopefully we can + + align:start position:0% +drill a bore field. And hopefully we can + + + align:start position:0% +drill a bore field. And hopefully we can +do it quicker, we can do it more + + align:start position:0% +do it quicker, we can do it more + + + align:start position:0% +do it quicker, we can do it more +cost-effectively the second time around. + + align:start position:0% +cost-effectively the second time around. + + + align:start position:0% +cost-effectively the second time around. +Um just to talk a little bit to the + + align:start position:0% +Um just to talk a little bit to the + + + align:start position:0% +Um just to talk a little bit to the +pictures here there. There's a lot going + + align:start position:0% +pictures here there. There's a lot going + + + align:start position:0% +pictures here there. There's a lot going +on, but um we did take advantage of some + + align:start position:0% +on, but um we did take advantage of some + + + align:start position:0% +on, but um we did take advantage of some +of those nice deviated drilling + + align:start position:0% +of those nice deviated drilling + + + align:start position:0% +of those nice deviated drilling +techniques on our project that you can + + align:start position:0% +techniques on our project that you can + + + align:start position:0% +techniques on our project that you can +see here on the left and then on the + + align:start position:0% +see here on the left and then on the + + + align:start position:0% +see here on the left and then on the +right that's what the manifold looks + + align:start position:0% +right that's what the manifold looks + + + align:start position:0% +right that's what the manifold looks +like when you come out of a bore hole. + + align:start position:0% +like when you come out of a bore hole. + + + align:start position:0% +like when you come out of a bore hole. +So once you've got all those holes in + + align:start position:0% +So once you've got all those holes in + + + align:start position:0% +So once you've got all those holes in +the ground, you got to tie them together + + align:start position:0% +the ground, you got to tie them together + + + align:start position:0% +the ground, you got to tie them together +with pipes. So you pull all of the + + align:start position:0% +with pipes. So you pull all of the + + + align:start position:0% +with pipes. So you pull all of the +inlets and outlets together into a + + align:start position:0% +inlets and outlets together into a + + + align:start position:0% +inlets and outlets together into a +single vault. You have a nice long + + align:start position:0% +single vault. You have a nice long + + + align:start position:0% +single vault. You have a nice long +header for each of them. And that way + + align:start position:0% +header for each of them. And that way + + + align:start position:0% +header for each of them. And that way +you can control the individual borehole + + align:start position:0% +you can control the individual borehole + + + align:start position:0% +you can control the individual borehole +runs. You can turn them on and off with + + align:start position:0% +runs. You can turn them on and off with + + + align:start position:0% +runs. You can turn them on and off with +valves if you want to. You can pressure + + align:start position:0% +valves if you want to. You can pressure + + + align:start position:0% +valves if you want to. You can pressure +test them. You can make sure that the + + align:start position:0% +test them. You can make sure that the + + + align:start position:0% +test them. You can make sure that the +system is on and running appropriately + + align:start position:0% +system is on and running appropriately + + + align:start position:0% +system is on and running appropriately +uh before you cover it back up because + + align:start position:0% +uh before you cover it back up because + + + align:start position:0% +uh before you cover it back up because +again, Mark mentioned this multiple + + align:start position:0% +again, Mark mentioned this multiple + + + align:start position:0% +again, Mark mentioned this multiple +times, but you really, really want to + + align:start position:0% +times, but you really, really want to + + + align:start position:0% +times, but you really, really want to +make sure that there are no issues or + + align:start position:0% +make sure that there are no issues or + + + align:start position:0% +make sure that there are no issues or +leaks before you back fill these + + align:start position:0% +leaks before you back fill these + + + align:start position:0% +leaks before you back fill these +systems. + + align:start position:0% +systems. + + + align:start position:0% +systems. +The pump house, kind of similar to the + + align:start position:0% +The pump house, kind of similar to the + + + align:start position:0% +The pump house, kind of similar to the +distribution loop, but this is the only + + align:start position:0% +distribution loop, but this is the only + + + align:start position:0% +distribution loop, but this is the only +above ground structure on our system. We + + align:start position:0% +above ground structure on our system. We + + + align:start position:0% +above ground structure on our system. We +chose to do it as a pre-fabricated + + align:start position:0% +chose to do it as a pre-fabricated + + + align:start position:0% +chose to do it as a pre-fabricated +building. So, we came in and we laid a + + align:start position:0% +building. So, we came in and we laid a + + + align:start position:0% +building. So, we came in and we laid a +foundation. We had as much of the + + align:start position:0% +foundation. We had as much of the + + + align:start position:0% +foundation. We had as much of the +mechanical work and piping and + + align:start position:0% +mechanical work and piping and + + + align:start position:0% +mechanical work and piping and +electrical done as we possibly could + + align:start position:0% +electrical done as we possibly could + + + align:start position:0% +electrical done as we possibly could +beforehand and then dropped the building + + align:start position:0% +beforehand and then dropped the building + + + align:start position:0% +beforehand and then dropped the building +down on top of the foundation + + align:start position:0% +down on top of the foundation + + + align:start position:0% +down on top of the foundation +afterwards. + + align:start position:0% +afterwards. + + + align:start position:0% +afterwards. +And really, all it does is it's got the + + align:start position:0% +And really, all it does is it's got the + + + align:start position:0% +And really, all it does is it's got the +central pumps, it's got our control + + align:start position:0% +central pumps, it's got our control + + + align:start position:0% +central pumps, it's got our control +system, and it's got a little bit of + + align:start position:0% +system, and it's got a little bit of + + + align:start position:0% +system, and it's got a little bit of +backup in the sense that we have a + + align:start position:0% +backup in the sense that we have a + + + align:start position:0% +backup in the sense that we have a +central boiler in there just in case we + + align:start position:0% +central boiler in there just in case we + + + align:start position:0% +central boiler in there just in case we +need to add some heat to the system. It + + align:start position:0% +need to add some heat to the system. It + + + align:start position:0% +need to add some heat to the system. It +was designed to not need it, but you + + align:start position:0% +was designed to not need it, but you + + + align:start position:0% +was designed to not need it, but you +know, as a utility, the very first time + + align:start position:0% +know, as a utility, the very first time + + + align:start position:0% +know, as a utility, the very first time +out, we want to make absolutely sure + + align:start position:0% +out, we want to make absolutely sure + + + align:start position:0% +out, we want to make absolutely sure +that there are no problems with the + + align:start position:0% +that there are no problems with the + + + align:start position:0% +that there are no problems with the +operation of the system. That comes back + + align:start position:0% +operation of the system. That comes back + + + align:start position:0% +operation of the system. That comes back +to customer perception and could affect + + align:start position:0% +to customer perception and could affect + + + align:start position:0% +to customer perception and could affect +adoption long term. So, you know, for + + align:start position:0% +adoption long term. So, you know, for + + + align:start position:0% +adoption long term. So, you know, for +our project, it also now serves as a + + align:start position:0% +our project, it also now serves as a + + + align:start position:0% +our project, it also now serves as a +very nice area where when we come out + + align:start position:0% +very nice area where when we come out + + + align:start position:0% +very nice area where when we come out +and have tours, we can kind of talk + + align:start position:0% +and have tours, we can kind of talk + + + align:start position:0% +and have tours, we can kind of talk +through some of the equipment involved + + align:start position:0% +through some of the equipment involved + + + align:start position:0% +through some of the equipment involved +and how the system works. Uh, it's + + align:start position:0% +and how the system works. Uh, it's + + + align:start position:0% +and how the system works. Uh, it's +really paid dividends to end up going + + align:start position:0% +really paid dividends to end up going + + + align:start position:0% +really paid dividends to end up going +above ground in this case. We won't + + align:start position:0% +above ground in this case. We won't + + + align:start position:0% +above ground in this case. We won't +necessarily always do that. You know, + + align:start position:0% +necessarily always do that. You know, + + + align:start position:0% +necessarily always do that. You know, +looking to future iterations, we may + + align:start position:0% +looking to future iterations, we may + + + align:start position:0% +looking to future iterations, we may +vault pumps. We may bury things if we + + align:start position:0% +vault pumps. We may bury things if we + + + align:start position:0% +vault pumps. We may bury things if we +don't have the space to do it. Uh but at + + align:start position:0% +don't have the space to do it. Uh but at + + + align:start position:0% +don't have the space to do it. Uh but at +least in Framingham, the pump house was + + align:start position:0% +least in Framingham, the pump house was + + + align:start position:0% +least in Framingham, the pump house was +a critical part of the loop. Finally, + + align:start position:0% +a critical part of the loop. Finally, + + + align:start position:0% +a critical part of the loop. Finally, +getting into building conversions. This + + align:start position:0% +getting into building conversions. This + + + align:start position:0% +getting into building conversions. This +this has by far been and was the most + + align:start position:0% +this has by far been and was the most + + + align:start position:0% +this has by far been and was the most +challenging part of getting a system + + align:start position:0% +challenging part of getting a system + + + align:start position:0% +challenging part of getting a system +online and running. Having the loop in + + align:start position:0% +online and running. Having the loop in + + + align:start position:0% +online and running. Having the loop in +the street, having it on and running, we + + align:start position:0% +the street, having it on and running, we + + + align:start position:0% +the street, having it on and running, we +kind of knew what we were getting into. + + align:start position:0% +kind of knew what we were getting into. + + + align:start position:0% +kind of knew what we were getting into. +It wasn't necessarily all skill sets + + align:start position:0% +It wasn't necessarily all skill sets + + + align:start position:0% +It wasn't necessarily all skill sets +that we were familiar with, but we sort + + align:start position:0% +that we were familiar with, but we sort + + + align:start position:0% +that we were familiar with, but we sort +of knew what to expect. Um, building + + align:start position:0% +of knew what to expect. Um, building + + + align:start position:0% +of knew what to expect. Um, building +conversions are every single one. You + + align:start position:0% +conversions are every single one. You + + + align:start position:0% +conversions are every single one. You +have no idea what you're getting into + + align:start position:0% +have no idea what you're getting into + + + align:start position:0% +have no idea what you're getting into +when you get into that building. We + + align:start position:0% +when you get into that building. We + + + align:start position:0% +when you get into that building. We +found mold, we found asbestous, we found + + align:start position:0% +found mold, we found asbestous, we found + + + align:start position:0% +found mold, we found asbestous, we found +knob and tube wiring. You name it, we + + align:start position:0% +knob and tube wiring. You name it, we + + + align:start position:0% +knob and tube wiring. You name it, we +found it in one of these homes or + + align:start position:0% +found it in one of these homes or + + + align:start position:0% +found it in one of these homes or +buildings. And that may be somewhat + + align:start position:0% +buildings. And that may be somewhat + + + align:start position:0% +buildings. And that may be somewhat +unique to the building stock here in the + + align:start position:0% +unique to the building stock here in the + + + align:start position:0% +unique to the building stock here in the +Northeast. Uh, but it's a reality of + + align:start position:0% +Northeast. Uh, but it's a reality of + + + align:start position:0% +Northeast. Uh, but it's a reality of +large retrofit projects. you're going to + + align:start position:0% +large retrofit projects. you're going to + + + align:start position:0% +large retrofit projects. you're going to +have to tackle these types of problems. + + align:start position:0% +have to tackle these types of problems. + + + align:start position:0% +have to tackle these types of problems. +So, from an execution standpoint, we + + align:start position:0% +So, from an execution standpoint, we + + + align:start position:0% +So, from an execution standpoint, we +really tried to individualize it for all + + align:start position:0% +really tried to individualize it for all + + + align:start position:0% +really tried to individualize it for all +of our customers, get into their home, + + align:start position:0% +of our customers, get into their home, + + + align:start position:0% +of our customers, get into their home, +explain exactly what we needed to do, + + align:start position:0% +explain exactly what we needed to do, + + + align:start position:0% +explain exactly what we needed to do, +how we were going to do it. We ran + + align:start position:0% +how we were going to do it. We ran + + + align:start position:0% +how we were going to do it. We ran +ducting. We did about 15 to 20 main + + align:start position:0% +ducting. We did about 15 to 20 main + + + align:start position:0% +ducting. We did about 15 to 20 main +panel upgrades in this neighborhood. So, + + align:start position:0% +panel upgrades in this neighborhood. So, + + + align:start position:0% +panel upgrades in this neighborhood. So, +it wasn't just how do I put a heat pump + + align:start position:0% +it wasn't just how do I put a heat pump + + + align:start position:0% +it wasn't just how do I put a heat pump +in. That's generally pretty + + align:start position:0% +in. That's generally pretty + + + align:start position:0% +in. That's generally pretty +straightforward. You get the unit in, + + align:start position:0% +straightforward. You get the unit in, + + + align:start position:0% +straightforward. You get the unit in, +you may need some ducting. You may need + + align:start position:0% +you may need some ducting. You may need + + + align:start position:0% +you may need some ducting. You may need +to adjust the existing ducting in the + + align:start position:0% +to adjust the existing ducting in the + + + align:start position:0% +to adjust the existing ducting in the +room, but the rest of the building is + + align:start position:0% +room, but the rest of the building is + + + align:start position:0% +room, but the rest of the building is +important, too. Are we air sealing? Are + + align:start position:0% +important, too. Are we air sealing? Are + + + align:start position:0% +important, too. Are we air sealing? Are +we weatherizing? Are we upgrading + + align:start position:0% +we weatherizing? Are we upgrading + + + align:start position:0% +we weatherizing? Are we upgrading +electrical systems? So, the whole + + align:start position:0% +electrical systems? So, the whole + + + align:start position:0% +electrical systems? So, the whole +picture ends up playing into what the + + align:start position:0% +picture ends up playing into what the + + + align:start position:0% +picture ends up playing into what the +building conversions look like. And we + + align:start position:0% +building conversions look like. And we + + + align:start position:0% +building conversions look like. And we +demonstrated virtually every type of + + align:start position:0% +demonstrated virtually every type of + + + align:start position:0% +demonstrated virtually every type of +conversion as well on this project that + + align:start position:0% +conversion as well on this project that + + + align:start position:0% +conversion as well on this project that +you can have. The good news is there's + + align:start position:0% +you can have. The good news is there's + + + align:start position:0% +you can have. The good news is there's +equipment out there to tackle almost all + + align:start position:0% +equipment out there to tackle almost all + + + align:start position:0% +equipment out there to tackle almost all +of it. Most of the residential homes + + align:start position:0% +of it. Most of the residential homes + + + align:start position:0% +of it. Most of the residential homes +were using forced air systems. So we + + align:start position:0% +were using forced air systems. So we + + + align:start position:0% +were using forced air systems. So we +came in, we put a heat pump in, we + + align:start position:0% +came in, we put a heat pump in, we + + + align:start position:0% +came in, we put a heat pump in, we +distributed it with ducting and air + + align:start position:0% +distributed it with ducting and air + + + align:start position:0% +distributed it with ducting and air +systems. The commercial buildings, we + + align:start position:0% +systems. The commercial buildings, we + + + align:start position:0% +systems. The commercial buildings, we +had rooftop units that we could actually + + align:start position:0% +had rooftop units that we could actually + + + align:start position:0% +had rooftop units that we could actually +just lift their old unit off and drop + + align:start position:0% +just lift their old unit off and drop + + + align:start position:0% +just lift their old unit off and drop +their new unit on top of the roof and + + align:start position:0% +their new unit on top of the roof and + + + align:start position:0% +their new unit on top of the roof and +reuse all of the existing distribution + + align:start position:0% +reuse all of the existing distribution + + + align:start position:0% +reuse all of the existing distribution +system in the building. And then we had + + align:start position:0% +system in the building. And then we had + + + align:start position:0% +system in the building. And then we had +some more niche applications, um, things + + align:start position:0% +some more niche applications, um, things + + + align:start position:0% +some more niche applications, um, things +like console units that look almost like + + align:start position:0% +like console units that look almost like + + + align:start position:0% +like console units that look almost like +one of those hotel air conditioners that + + align:start position:0% +one of those hotel air conditioners that + + + align:start position:0% +one of those hotel air conditioners that +sit under the window. We put those into + + align:start position:0% +sit under the window. We put those into + + + align:start position:0% +sit under the window. We put those into +a number of the uh the subsidized + + align:start position:0% +a number of the uh the subsidized + + + align:start position:0% +a number of the uh the subsidized +housing apartments on this loop as well. + + align:start position:0% +housing apartments on this loop as well. + + + align:start position:0% +housing apartments on this loop as well. +And just to emphasize that it's not + + align:start position:0% +And just to emphasize that it's not + + + align:start position:0% +And just to emphasize that it's not +necessarily will it work, it's how do I + + align:start position:0% +necessarily will it work, it's how do I + + + align:start position:0% +necessarily will it work, it's how do I +make it work with every single one of + + align:start position:0% +make it work with every single one of + + + align:start position:0% +make it work with every single one of +these. + + align:start position:0% +these. + + + align:start position:0% +these. +Finally, overall project management. I + + align:start position:0% +Finally, overall project management. I + + + align:start position:0% +Finally, overall project management. I +talked a little bit about this on + + align:start position:0% +talked a little bit about this on + + + align:start position:0% +talked a little bit about this on +building conversions, but um you know, + + align:start position:0% +building conversions, but um you know, + + + align:start position:0% +building conversions, but um you know, +making sure that we were having a very + + align:start position:0% +making sure that we were having a very + + + align:start position:0% +making sure that we were having a very +detailed and customer focused approach + + align:start position:0% +detailed and customer focused approach + + + align:start position:0% +detailed and customer focused approach +through the entire project was important + + align:start position:0% +through the entire project was important + + + align:start position:0% +through the entire project was important +too. As a utility, generally we stay in + + align:start position:0% +too. As a utility, generally we stay in + + + align:start position:0% +too. As a utility, generally we stay in +the streets. We're putting pipes. We're + + align:start position:0% +the streets. We're putting pipes. We're + + + align:start position:0% +the streets. We're putting pipes. We're +pulling them. There's a demarcation + + align:start position:0% +pulling them. There's a demarcation + + + align:start position:0% +pulling them. There's a demarcation +point and everything downstream is is + + align:start position:0% +point and everything downstream is is + + + align:start position:0% +point and everything downstream is is +usually the customer's responsibility. + + align:start position:0% +usually the customer's responsibility. + + + align:start position:0% +usually the customer's responsibility. +Not in the case of this project. The + + align:start position:0% +Not in the case of this project. The + + + align:start position:0% +Not in the case of this project. The +scope of our pilot approved by the + + align:start position:0% +scope of our pilot approved by the + + + align:start position:0% +scope of our pilot approved by the +department was including all of the + + align:start position:0% +department was including all of the + + + align:start position:0% +department was including all of the +building side equipment and work. So, we + + align:start position:0% +building side equipment and work. So, we + + + align:start position:0% +building side equipment and work. So, we +had to manage that part of the project + + align:start position:0% +had to manage that part of the project + + + align:start position:0% +had to manage that part of the project +as well. We were meeting with the + + align:start position:0% +as well. We were meeting with the + + + align:start position:0% +as well. We were meeting with the +customers in the field. We were + + align:start position:0% +customers in the field. We were + + + align:start position:0% +customers in the field. We were +explaining things. We were having them + + align:start position:0% +explaining things. We were having them + + + align:start position:0% +explaining things. We were having them +look at exactly what was going in, where + + align:start position:0% +look at exactly what was going in, where + + + align:start position:0% +look at exactly what was going in, where +it was going in. We were getting + + align:start position:0% +it was going in. We were getting + + + align:start position:0% +it was going in. We were getting +feedback on things like, "I'd like the + + align:start position:0% +feedback on things like, "I'd like the + + + align:start position:0% +feedback on things like, "I'd like the +ducting over here versus over there. Can + + align:start position:0% +ducting over here versus over there. Can + + + align:start position:0% +ducting over here versus over there. Can +you box it in with drywall? Can you + + align:start position:0% +you box it in with drywall? Can you + + + align:start position:0% +you box it in with drywall? Can you +paint it after the fact?" All of these + + align:start position:0% +paint it after the fact?" All of these + + + align:start position:0% +paint it after the fact?" All of these +little details that make project + + align:start position:0% +little details that make project + + + align:start position:0% +little details that make project +management very challenging, but it's + + align:start position:0% +management very challenging, but it's + + + align:start position:0% +management very challenging, but it's +extremely important because at the end + + align:start position:0% +extremely important because at the end + + + align:start position:0% +extremely important because at the end +of the day, I want these customers to + + align:start position:0% +of the day, I want these customers to + + + align:start position:0% +of the day, I want these customers to +have a good experience. I want them to + + align:start position:0% +have a good experience. I want them to + + + align:start position:0% +have a good experience. I want them to +like their new systems and I want them + + align:start position:0% +like their new systems and I want them + + + align:start position:0% +like their new systems and I want them +to tell all of their neighbors about how + + align:start position:0% +to tell all of their neighbors about how + + + align:start position:0% +to tell all of their neighbors about how +great it was as well because that's how + + align:start position:0% +great it was as well because that's how + + + align:start position:0% +great it was as well because that's how +we grow the system and get adoption to + + align:start position:0% +we grow the system and get adoption to + + + align:start position:0% +we grow the system and get adoption to +continue. + + align:start position:0% +continue. + + + align:start position:0% +continue. +Sort of summing up the construction side + + align:start position:0% +Sort of summing up the construction side + + + align:start position:0% +Sort of summing up the construction side +of things, you know, timeline and + + align:start position:0% +of things, you know, timeline and + + + align:start position:0% +of things, you know, timeline and +parallel work streams. If I were to go + + align:start position:0% +parallel work streams. If I were to go + + + align:start position:0% +parallel work streams. If I were to go +do this project again, there are a lot + + align:start position:0% +do this project again, there are a lot + + + align:start position:0% +do this project again, there are a lot +of levers I could pull here for having + + align:start position:0% +of levers I could pull here for having + + + align:start position:0% +of levers I could pull here for having +simultaneous jobs go on so that my + + align:start position:0% +simultaneous jobs go on so that my + + + align:start position:0% +simultaneous jobs go on so that my +overall timeline could be shrunk. I + + align:start position:0% +overall timeline could be shrunk. I + + + align:start position:0% +overall timeline could be shrunk. I +think in the second iteration, I could + + align:start position:0% +think in the second iteration, I could + + + align:start position:0% +think in the second iteration, I could +probably trim about 25 to 30% of our + + align:start position:0% +probably trim about 25 to 30% of our + + + align:start position:0% +probably trim about 25 to 30% of our +schedule off if I was going into it + + align:start position:0% +schedule off if I was going into it + + + align:start position:0% +schedule off if I was going into it +knowing what I know now. Um, there are + + align:start position:0% +knowing what I know now. Um, there are + + + align:start position:0% +knowing what I know now. Um, there are +always the traditional utility + + align:start position:0% +always the traditional utility + + + align:start position:0% +always the traditional utility +challenges. You know, we ran into buried + + align:start position:0% +challenges. You know, we ran into buried + + + align:start position:0% +challenges. You know, we ran into buried +infrastructure that wasn't on any map, + + align:start position:0% +infrastructure that wasn't on any map, + + + align:start position:0% +infrastructure that wasn't on any map, +wasn't on any diagram, and you're + + align:start position:0% +wasn't on any diagram, and you're + + + align:start position:0% +wasn't on any diagram, and you're +digging along and all of a sudden you + + align:start position:0% +digging along and all of a sudden you + + + align:start position:0% +digging along and all of a sudden you +see a wooden conduit in the street. So, + + align:start position:0% +see a wooden conduit in the street. So, + + + align:start position:0% +see a wooden conduit in the street. So, +you got to navigate around it. You have + + align:start position:0% +you got to navigate around it. You have + + + align:start position:0% +you got to navigate around it. You have +to make some on the-job decisions, some + + align:start position:0% +to make some on the-job decisions, some + + + align:start position:0% +to make some on the-job decisions, some +on the-ly, you know, changes to your + + align:start position:0% +on the-ly, you know, changes to your + + + align:start position:0% +on the-ly, you know, changes to your +system. Those were manageable. There + + align:start position:0% +system. Those were manageable. There + + + align:start position:0% +system. Those were manageable. There +were some geothermal specific + + align:start position:0% +were some geothermal specific + + + align:start position:0% +were some geothermal specific +challenges. You know, the drilling went + + align:start position:0% +challenges. You know, the drilling went + + + align:start position:0% +challenges. You know, the drilling went +well, but there was a learning curve + + align:start position:0% +well, but there was a learning curve + + + align:start position:0% +well, but there was a learning curve +there. The geology, what type of + + align:start position:0% +there. The geology, what type of + + + align:start position:0% +there. The geology, what type of +drilling we were using. We tried air + + align:start position:0% +drilling we were using. We tried air + + + align:start position:0% +drilling we were using. We tried air +hammer, we did mud rotary. We kind of + + align:start position:0% +hammer, we did mud rotary. We kind of + + + align:start position:0% +hammer, we did mud rotary. We kind of +traded off to decide what was exactly + + align:start position:0% +traded off to decide what was exactly + + + align:start position:0% +traded off to decide what was exactly +the best way to drill in this specific + + align:start position:0% +the best way to drill in this specific + + + align:start position:0% +the best way to drill in this specific +neighborhood. And then on the HVAC side + + align:start position:0% +neighborhood. And then on the HVAC side + + + align:start position:0% +neighborhood. And then on the HVAC side +of things, you know, to this day, I'm + + align:start position:0% +of things, you know, to this day, I'm + + + align:start position:0% +of things, you know, to this day, I'm +still helping customers dial their + + align:start position:0% +still helping customers dial their + + + align:start position:0% +still helping customers dial their +systems in. So it's not necessarily as + + align:start position:0% +systems in. So it's not necessarily as + + + align:start position:0% +systems in. So it's not necessarily as +soon as everything is installed, you + + align:start position:0% +soon as everything is installed, you + + + align:start position:0% +soon as everything is installed, you +walk away and it runs perfectly. There + + align:start position:0% +walk away and it runs perfectly. There + + + align:start position:0% +walk away and it runs perfectly. There +is definitely a period of adjustment and + + align:start position:0% +is definitely a period of adjustment and + + + align:start position:0% +is definitely a period of adjustment and +improvement and optimization that you + + align:start position:0% +improvement and optimization that you + + + align:start position:0% +improvement and optimization that you +can make. Um site access and scheduling. + + align:start position:0% +can make. Um site access and scheduling. + + + align:start position:0% +can make. Um site access and scheduling. +This was actually something that ended + + align:start position:0% +This was actually something that ended + + + align:start position:0% +This was actually something that ended +up affecting us quite a lot in terms of + + align:start position:0% +up affecting us quite a lot in terms of + + + align:start position:0% +up affecting us quite a lot in terms of +overall project schedule, but the + + align:start position:0% +overall project schedule, but the + + + align:start position:0% +overall project schedule, but the +reality is you're installing these in a + + align:start position:0% +reality is you're installing these in a + + + align:start position:0% +reality is you're installing these in a +community. It's people's yards. It's + + align:start position:0% +community. It's people's yards. It's + + + align:start position:0% +community. It's people's yards. It's +people's homes. It's school property. + + align:start position:0% +people's homes. It's school property. + + + align:start position:0% +people's homes. It's school property. +And so when you're first planning the + + align:start position:0% +And so when you're first planning the + + + align:start position:0% +And so when you're first planning the +project, you're not necessarily thinking + + align:start position:0% +project, you're not necessarily thinking + + + align:start position:0% +project, you're not necessarily thinking +about, ooh, maybe they're not going to + + align:start position:0% +about, ooh, maybe they're not going to + + + align:start position:0% +about, ooh, maybe they're not going to +let me drill or have access to the + + align:start position:0% +let me drill or have access to the + + + align:start position:0% +let me drill or have access to the +school property in the fall as + + align:start position:0% +school property in the fall as + + + align:start position:0% +school property in the fall as +everything is ramping up and students + + align:start position:0% +everything is ramping up and students + + + align:start position:0% +everything is ramping up and students +are all coming back. Individual + + align:start position:0% +are all coming back. Individual + + + align:start position:0% +are all coming back. Individual +customers, they go on vacation. They + + align:start position:0% +customers, they go on vacation. They + + + align:start position:0% +customers, they go on vacation. They +have their own lives. They have their + + align:start position:0% +have their own lives. They have their + + + align:start position:0% +have their own lives. They have their +work schedules. So, you have to really + + align:start position:0% +work schedules. So, you have to really + + + align:start position:0% +work schedules. So, you have to really +work around all of the individual pieces + + align:start position:0% +work around all of the individual pieces + + + align:start position:0% +work around all of the individual pieces +to get everything to come together. + + align:start position:0% +to get everything to come together. + + + align:start position:0% +to get everything to come together. +Otherwise, you find yourself sitting and + + align:start position:0% +Otherwise, you find yourself sitting and + + + align:start position:0% +Otherwise, you find yourself sitting and +waiting and saying, "Well, I, you know, + + align:start position:0% +waiting and saying, "Well, I, you know, + + + align:start position:0% +waiting and saying, "Well, I, you know, +I guess I can't get access to the site + + align:start position:0% +I guess I can't get access to the site + + + align:start position:0% +I guess I can't get access to the site +today. let's wait a week until I can and + + align:start position:0% +today. let's wait a week until I can and + + + align:start position:0% +today. let's wait a week until I can and +that has impacts on the overall job. Um, + + align:start position:0% +that has impacts on the overall job. Um, + + + align:start position:0% +that has impacts on the overall job. Um, +finally, I mentioned these, but unknown + + align:start position:0% +finally, I mentioned these, but unknown + + + align:start position:0% +finally, I mentioned these, but unknown +building conditions. I'm going to + + align:start position:0% +building conditions. I'm going to + + + align:start position:0% +building conditions. I'm going to +mention it again because it was uh it + + align:start position:0% +mention it again because it was uh it + + + align:start position:0% +mention it again because it was uh it +was such a challenge on the project. + + align:start position:0% +was such a challenge on the project. + + + align:start position:0% +was such a challenge on the project. +Really taking good stock of what + + align:start position:0% +Really taking good stock of what + + + align:start position:0% +Really taking good stock of what +buildings are in your planned community + + align:start position:0% +buildings are in your planned community + + + align:start position:0% +buildings are in your planned community +or planned area, understanding what some + + align:start position:0% +or planned area, understanding what some + + + align:start position:0% +or planned area, understanding what some +of the common things that you may + + align:start position:0% +of the common things that you may + + + align:start position:0% +of the common things that you may +encounter are, and having a plan for it + + align:start position:0% +encounter are, and having a plan for it + + + align:start position:0% +encounter are, and having a plan for it +ahead of time. Um, asbestous remediation + + align:start position:0% +ahead of time. Um, asbestous remediation + + + align:start position:0% +ahead of time. Um, asbestous remediation +delayed some of our building conversions + + align:start position:0% +delayed some of our building conversions + + + align:start position:0% +delayed some of our building conversions +a good 3 to four months in this case. + + align:start position:0% +a good 3 to four months in this case. + + + align:start position:0% +a good 3 to four months in this case. +Um, we got into specifically the the + + align:start position:0% +Um, we got into specifically the the + + + align:start position:0% +Um, we got into specifically the the +lowincome housing apartment buildings. + + align:start position:0% +lowincome housing apartment buildings. + + + align:start position:0% +lowincome housing apartment buildings. +We realized there may be some asbestous + + align:start position:0% +We realized there may be some asbestous + + + align:start position:0% +We realized there may be some asbestous +in the joining compound and the walls + + align:start position:0% +in the joining compound and the walls + + + align:start position:0% +in the joining compound and the walls +that they had used to construct those. + + align:start position:0% +that they had used to construct those. + + + align:start position:0% +that they had used to construct those. +And it was about a four-month process to + + align:start position:0% +And it was about a four-month process to + + + align:start position:0% +And it was about a four-month process to +test every single unit, document it with + + align:start position:0% +test every single unit, document it with + + + align:start position:0% +test every single unit, document it with +the state, come up with a remediation + + align:start position:0% +the state, come up with a remediation + + + align:start position:0% +the state, come up with a remediation +plan, have that plan approved, and then + + align:start position:0% +plan, have that plan approved, and then + + + align:start position:0% +plan, have that plan approved, and then +have qualified contractors come in, set + + align:start position:0% +have qualified contractors come in, set + + + align:start position:0% +have qualified contractors come in, set +up all of their air containment, and do + + align:start position:0% +up all of their air containment, and do + + + align:start position:0% +up all of their air containment, and do +that remediation so that we could + + align:start position:0% +that remediation so that we could + + + align:start position:0% +that remediation so that we could +actually install the heat pumps. So, + + align:start position:0% +actually install the heat pumps. So, + + + align:start position:0% +actually install the heat pumps. So, +it's those types of things that when + + align:start position:0% +it's those types of things that when + + + align:start position:0% +it's those types of things that when +you're in the initial planning stage, if + + align:start position:0% +you're in the initial planning stage, if + + + align:start position:0% +you're in the initial planning stage, if +you know there's a chance that these + + align:start position:0% +you know there's a chance that these + + + align:start position:0% +you know there's a chance that these +buildings may have asbestous in them, go + + align:start position:0% +buildings may have asbestous in them, go + + + align:start position:0% +buildings may have asbestous in them, go +ahead and test it during design. come up + + align:start position:0% +ahead and test it during design. come up + + + align:start position:0% +ahead and test it during design. come up +with your remediation plan. That way + + align:start position:0% +with your remediation plan. That way + + + align:start position:0% +with your remediation plan. That way +when you're into project execution, + + align:start position:0% +when you're into project execution, + + + align:start position:0% +when you're into project execution, +you've got it all baked into the + + align:start position:0% +you've got it all baked into the + + + align:start position:0% +you've got it all baked into the +schedule and it's not going to delay + + align:start position:0% +schedule and it's not going to delay + + + align:start position:0% +schedule and it's not going to delay +that particular part of the project. + + align:start position:0% +that particular part of the project. + + + align:start position:0% +that particular part of the project. +Moving on a little bit to commissions + + align:start position:0% +Moving on a little bit to commissions + + + align:start position:0% +Moving on a little bit to commissions +and operations because as I said once + + align:start position:0% +and operations because as I said once + + + align:start position:0% +and operations because as I said once +the system is in the ground physically + + align:start position:0% +the system is in the ground physically + + + align:start position:0% +the system is in the ground physically +that does not necessarily mean it's up + + align:start position:0% +that does not necessarily mean it's up + + + align:start position:0% +that does not necessarily mean it's up +and running. Um a lot of lessons learned + + align:start position:0% +and running. Um a lot of lessons learned + + + align:start position:0% +and running. Um a lot of lessons learned +and challenges here as well. These + + align:start position:0% +and challenges here as well. These + + + align:start position:0% +and challenges here as well. These +screenshots here below are from our + + align:start position:0% +screenshots here below are from our + + + align:start position:0% +screenshots here below are from our +real-time SCA system. uh you know there + + align:start position:0% +real-time SCA system. uh you know there + + + align:start position:0% +real-time SCA system. uh you know there +was a great discussion earlier around + + align:start position:0% +was a great discussion earlier around + + + align:start position:0% +was a great discussion earlier around +optimization and control and feedback on + + align:start position:0% +optimization and control and feedback on + + + align:start position:0% +optimization and control and feedback on +how you run and operate one of these + + align:start position:0% +how you run and operate one of these + + + align:start position:0% +how you run and operate one of these +thermal energy networks. That's what we + + align:start position:0% +thermal energy networks. That's what we + + + align:start position:0% +thermal energy networks. That's what we +did. We had a SCADA system set up so + + align:start position:0% +did. We had a SCADA system set up so + + + align:start position:0% +did. We had a SCADA system set up so +that real time any time of the day I can + + align:start position:0% +that real time any time of the day I can + + + align:start position:0% +that real time any time of the day I can +see what my pump speeds are. I can see + + align:start position:0% +see what my pump speeds are. I can see + + + align:start position:0% +see what my pump speeds are. I can see +my temperatures. I can see my pressures. + + align:start position:0% +my temperatures. I can see my pressures. + + + align:start position:0% +my temperatures. I can see my pressures. +I can see customer behavior based on the + + align:start position:0% +I can see customer behavior based on the + + + align:start position:0% +I can see customer behavior based on the +historic temperature trends. So getting + + align:start position:0% +historic temperature trends. So getting + + + align:start position:0% +historic temperature trends. So getting +that system up and running was almost + + align:start position:0% +that system up and running was almost + + + align:start position:0% +that system up and running was almost +step one before I could even add a + + align:start position:0% +step one before I could even add a + + + align:start position:0% +step one before I could even add a +single customer. I wanted to be able to + + align:start position:0% +single customer. I wanted to be able to + + + align:start position:0% +single customer. I wanted to be able to +see the system remotely in a in a + + align:start position:0% +see the system remotely in a in a + + + align:start position:0% +see the system remotely in a in a +web-based SCADA. In addition to that, + + align:start position:0% +web-based SCADA. In addition to that, + + + align:start position:0% +web-based SCADA. In addition to that, +borefield flushing, pressure testing, + + align:start position:0% +borefield flushing, pressure testing, + + + align:start position:0% +borefield flushing, pressure testing, +getting air out of the system. These are + + align:start position:0% +getting air out of the system. These are + + + align:start position:0% +getting air out of the system. These are +all steps that we had to take as we + + align:start position:0% +all steps that we had to take as we + + + align:start position:0% +all steps that we had to take as we +turned it on, as we started the pumps + + align:start position:0% +turned it on, as we started the pumps + + + align:start position:0% +turned it on, as we started the pumps +up, and as we added customer loads to + + align:start position:0% +up, and as we added customer loads to + + + align:start position:0% +up, and as we added customer loads to +make sure that there wasn't any + + align:start position:0% +make sure that there wasn't any + + + align:start position:0% +make sure that there wasn't any +disruption in service because the last + + align:start position:0% +disruption in service because the last + + + align:start position:0% +disruption in service because the last +thing that I wanted was to add a + + align:start position:0% +thing that I wanted was to add a + + + align:start position:0% +thing that I wanted was to add a +customer and then shut them down + + align:start position:0% +customer and then shut them down + + + align:start position:0% +customer and then shut them down +immediately right there after and say, + + align:start position:0% +immediately right there after and say, + + + align:start position:0% +immediately right there after and say, +"Oo, something's wrong with the system. + + align:start position:0% +"Oo, something's wrong with the system. + + + align:start position:0% +"Oo, something's wrong with the system. +Hang on. let me address that and we'll + + align:start position:0% +Hang on. let me address that and we'll + + + align:start position:0% +Hang on. let me address that and we'll +come back in a few days and turn you + + align:start position:0% +come back in a few days and turn you + + + align:start position:0% +come back in a few days and turn you +back on. So, a lot of work went into + + align:start position:0% +back on. So, a lot of work went into + + + align:start position:0% +back on. So, a lot of work went into +making sure that the system was on, + + align:start position:0% +making sure that the system was on, + + + align:start position:0% +making sure that the system was on, +stable, free of air, running properly + + align:start position:0% +stable, free of air, running properly + + + align:start position:0% +stable, free of air, running properly +before we could add customer loads. + + align:start position:0% +before we could add customer loads. + + + align:start position:0% +before we could add customer loads. +And then on the building commissioning + + align:start position:0% +And then on the building commissioning + + + align:start position:0% +And then on the building commissioning +side, once the loop is on and running, + + align:start position:0% +side, once the loop is on and running, + + + align:start position:0% +side, once the loop is on and running, +now you got to turn the buildings on as + + align:start position:0% +now you got to turn the buildings on as + + + align:start position:0% +now you got to turn the buildings on as +well. So, that followed a very similar + + align:start position:0% +well. So, that followed a very similar + + + align:start position:0% +well. So, that followed a very similar +process, but it was about getting the + + align:start position:0% +process, but it was about getting the + + + align:start position:0% +process, but it was about getting the +equipment in, making sure the electrical + + align:start position:0% +equipment in, making sure the electrical + + + align:start position:0% +equipment in, making sure the electrical +work was done, the plumbing work was + + align:start position:0% +work was done, the plumbing work was + + + align:start position:0% +work was done, the plumbing work was +done. You then have to pressure test + + align:start position:0% +done. You then have to pressure test + + + align:start position:0% +done. You then have to pressure test +everything on the building side as well + + align:start position:0% +everything on the building side as well + + + align:start position:0% +everything on the building side as well +because the last thing you want is a + + align:start position:0% +because the last thing you want is a + + + align:start position:0% +because the last thing you want is a +leak in one of these pipes carrying + + align:start position:0% +leak in one of these pipes carrying + + + align:start position:0% +leak in one of these pipes carrying +water and some glycol in this case + + align:start position:0% +water and some glycol in this case + + + align:start position:0% +water and some glycol in this case +that's going to flood a basement, flood + + align:start position:0% +that's going to flood a basement, flood + + + align:start position:0% +that's going to flood a basement, flood +a room. Again, the perspective there + + align:start position:0% +a room. Again, the perspective there + + + align:start position:0% +a room. Again, the perspective there +from the customer, it's not going to be + + align:start position:0% +from the customer, it's not going to be + + + align:start position:0% +from the customer, it's not going to be +a very good one if you have to come in + + align:start position:0% +a very good one if you have to come in + + + align:start position:0% +a very good one if you have to come in +and say, "Sorry, I just flooded your + + align:start position:0% +and say, "Sorry, I just flooded your + + + align:start position:0% +and say, "Sorry, I just flooded your +basement. I'm going to pump it out, but + + align:start position:0% +basement. I'm going to pump it out, but + + + align:start position:0% +basement. I'm going to pump it out, but +let me try again." So, a lot of testing, + + align:start position:0% +let me try again." So, a lot of testing, + + + align:start position:0% +let me try again." So, a lot of testing, +getting the equipment on and running, + + align:start position:0% +getting the equipment on and running, + + + align:start position:0% +getting the equipment on and running, +and then opening those valves and + + align:start position:0% +and then opening those valves and + + + align:start position:0% +and then opening those valves and +actually tying it into the main loop and + + align:start position:0% +actually tying it into the main loop and + + + align:start position:0% +actually tying it into the main loop and +making sure that it's getting energy um + + align:start position:0% +making sure that it's getting energy um + + + align:start position:0% +making sure that it's getting energy um +from the system. + + align:start position:0% +from the system. + + + align:start position:0% +from the system. +One of the the challenges that I faced + + align:start position:0% +One of the the challenges that I faced + + + align:start position:0% +One of the the challenges that I faced +is because we were reusing traditional + + align:start position:0% +is because we were reusing traditional + + + align:start position:0% +is because we were reusing traditional +gas contractors, they had a perception + + align:start position:0% +gas contractors, they had a perception + + + align:start position:0% +gas contractors, they had a perception +around how you should handle valves on + + align:start position:0% +around how you should handle valves on + + + align:start position:0% +around how you should handle valves on +this system. In their mind, open valves + + align:start position:0% +this system. In their mind, open valves + + + align:start position:0% +this system. In their mind, open valves +are good. You want every valve on the + + align:start position:0% +are good. You want every valve on the + + + align:start position:0% +are good. You want every valve on the +system open because in a gas system + + align:start position:0% +system open because in a gas system + + + align:start position:0% +system open because in a gas system +that's what you do. You open everything + + align:start position:0% +that's what you do. You open everything + + + align:start position:0% +that's what you do. You open everything +up. You've got flow. You're great. I had + + align:start position:0% +up. You've got flow. You're great. I had + + + align:start position:0% +up. You've got flow. You're great. I had +to go through that entire system and + + align:start position:0% +to go through that entire system and + + + align:start position:0% +to go through that entire system and +check every single bypass valve that I + + align:start position:0% +check every single bypass valve that I + + + align:start position:0% +check every single bypass valve that I +had because 75% of them were left open. + + align:start position:0% +had because 75% of them were left open. + + + align:start position:0% +had because 75% of them were left open. +What that means is when I turn a + + align:start position:0% +What that means is when I turn a + + + align:start position:0% +What that means is when I turn a +customer's system on, they're not + + align:start position:0% +customer's system on, they're not + + + align:start position:0% +customer's system on, they're not +exchanging fluid with the loop. They're + + align:start position:0% +exchanging fluid with the loop. They're + + + align:start position:0% +exchanging fluid with the loop. They're +exchanging fluid with themselves and + + align:start position:0% +exchanging fluid with themselves and + + + align:start position:0% +exchanging fluid with themselves and +their systems very quickly cool down. + + align:start position:0% +their systems very quickly cool down. + + + align:start position:0% +their systems very quickly cool down. +They shut off. They throw an error. So, + + align:start position:0% +They shut off. They throw an error. So, + + + align:start position:0% +They shut off. They throw an error. So, +it's those types of things and + + align:start position:0% +it's those types of things and + + + align:start position:0% +it's those types of things and +troubleshooting through the + + align:start position:0% +troubleshooting through the + + + align:start position:0% +troubleshooting through the +commissioning that, you know, the next + + align:start position:0% +commissioning that, you know, the next + + + align:start position:0% +commissioning that, you know, the next +time around, I'm going to be totally + + align:start position:0% +time around, I'm going to be totally + + + align:start position:0% +time around, I'm going to be totally +sure every bypass on a system is closed + + align:start position:0% +sure every bypass on a system is closed + + + align:start position:0% +sure every bypass on a system is closed +before I turn a customer on. + + align:start position:0% +before I turn a customer on. + + + align:start position:0% +before I turn a customer on. +So, lessons learned, you know, + + align:start position:0% +So, lessons learned, you know, + + + align:start position:0% +So, lessons learned, you know, +procedures and compliance. I I cannot + + align:start position:0% +procedures and compliance. I I cannot + + + align:start position:0% +procedures and compliance. I I cannot +stress enough how important it is to + + align:start position:0% +stress enough how important it is to + + + align:start position:0% +stress enough how important it is to +know what you're doing before you do it. + + align:start position:0% +know what you're doing before you do it. + + + align:start position:0% +know what you're doing before you do it. +Have a documented procedure. Make sure + + align:start position:0% +Have a documented procedure. Make sure + + + align:start position:0% +Have a documented procedure. Make sure +you check it with your engineering team, + + align:start position:0% +you check it with your engineering team, + + + align:start position:0% +you check it with your engineering team, +your external engineers, experts in the + + align:start position:0% +your external engineers, experts in the + + + align:start position:0% +your external engineers, experts in the +industry that have done this before. + + align:start position:0% +industry that have done this before. + + + align:start position:0% +industry that have done this before. +have them look at it. They're going to + + align:start position:0% +have them look at it. They're going to + + + align:start position:0% +have them look at it. They're going to +have some great feedback. Valve + + align:start position:0% +have some great feedback. Valve + + + align:start position:0% +have some great feedback. Valve +positioning, don't need to harp on it + + align:start position:0% +positioning, don't need to harp on it + + + align:start position:0% +positioning, don't need to harp on it +again, but it's very important. Uh loop + + align:start position:0% +again, but it's very important. Uh loop + + + align:start position:0% +again, but it's very important. Uh loop +flushing and purging, you know, the + + align:start position:0% +flushing and purging, you know, the + + + align:start position:0% +flushing and purging, you know, the +biggest issue that I have seen on our + + align:start position:0% +biggest issue that I have seen on our + + + align:start position:0% +biggest issue that I have seen on our +system at least is air. There's a + + align:start position:0% +system at least is air. There's a + + + align:start position:0% +system at least is air. There's a +there's a procedure, there's a flushing + + align:start position:0% +there's a procedure, there's a flushing + + + align:start position:0% +there's a procedure, there's a flushing +procedure, but there's always a little + + align:start position:0% +procedure, but there's always a little + + + align:start position:0% +procedure, but there's always a little +bit of entrained air in these systems. + + align:start position:0% +bit of entrained air in these systems. + + + align:start position:0% +bit of entrained air in these systems. +And so getting it out is extremely + + align:start position:0% +And so getting it out is extremely + + + align:start position:0% +And so getting it out is extremely +important because it can shut down + + align:start position:0% +important because it can shut down + + + align:start position:0% +important because it can shut down +customer systems. You got to come out, + + align:start position:0% +customer systems. You got to come out, + + + align:start position:0% +customer systems. You got to come out, +it's a trouble call, you purge the air, + + align:start position:0% +it's a trouble call, you purge the air, + + + align:start position:0% +it's a trouble call, you purge the air, +you start them back up. Um, so + + align:start position:0% +you start them back up. Um, so + + + align:start position:0% +you start them back up. Um, so +definitely a step you don't want to + + align:start position:0% +definitely a step you don't want to + + + align:start position:0% +definitely a step you don't want to +shortcut or miss. Troubleshooting + + align:start position:0% +shortcut or miss. Troubleshooting + + + align:start position:0% +shortcut or miss. Troubleshooting +systems, you know, fortunately as we've + + align:start position:0% +systems, you know, fortunately as we've + + + align:start position:0% +systems, you know, fortunately as we've +gone into operation here, the problems + + align:start position:0% +gone into operation here, the problems + + + align:start position:0% +gone into operation here, the problems +have decreased dramatically. We're + + align:start position:0% +have decreased dramatically. We're + + + align:start position:0% +have decreased dramatically. We're +having less, you know, issues, errors, + + align:start position:0% +having less, you know, issues, errors, + + + align:start position:0% +having less, you know, issues, errors, +reasons that we need to go out and + + align:start position:0% +reasons that we need to go out and + + + align:start position:0% +reasons that we need to go out and +address things, but you always need to + + align:start position:0% +address things, but you always need to + + + align:start position:0% +address things, but you always need to +be ready to do that, especially at + + align:start position:0% +be ready to do that, especially at + + + align:start position:0% +be ready to do that, especially at +first. And then finally, I I threw + + align:start position:0% +first. And then finally, I I threw + + + align:start position:0% +first. And then finally, I I threw +temporary space conditioning in here + + align:start position:0% +temporary space conditioning in here + + + align:start position:0% +temporary space conditioning in here +because on the theme of scheduling and + + align:start position:0% +because on the theme of scheduling and + + + align:start position:0% +because on the theme of scheduling and +having work done simultaneously, + + align:start position:0% +having work done simultaneously, + + + align:start position:0% +having work done simultaneously, +you know, the way our project played + + align:start position:0% +you know, the way our project played + + + align:start position:0% +you know, the way our project played +out, you didn't necessarily have every + + align:start position:0% +out, you didn't necessarily have every + + + align:start position:0% +out, you didn't necessarily have every +single building ready to just be turned + + align:start position:0% +single building ready to just be turned + + + align:start position:0% +single building ready to just be turned +on straight away. There was a process + + align:start position:0% +on straight away. There was a process + + + align:start position:0% +on straight away. There was a process +for building conversions. So, we + + align:start position:0% +for building conversions. So, we + + + align:start position:0% +for building conversions. So, we +actually had to have a plan in the + + align:start position:0% +actually had to have a plan in the + + + align:start position:0% +actually had to have a plan in the +schools, for example, when we were + + align:start position:0% +schools, for example, when we were + + + align:start position:0% +schools, for example, when we were +pulling those rooftop units on and + + align:start position:0% +pulling those rooftop units on and + + + align:start position:0% +pulling those rooftop units on and +putting the new ones back, how are we + + align:start position:0% +putting the new ones back, how are we + + + align:start position:0% +putting the new ones back, how are we +keeping that space conditioned? Do we + + align:start position:0% +keeping that space conditioned? Do we + + + align:start position:0% +keeping that space conditioned? Do we +have temporary air conditioners? Do we + + align:start position:0% +have temporary air conditioners? Do we + + + align:start position:0% +have temporary air conditioners? Do we +have temporary heaters? So, all playing + + align:start position:0% +have temporary heaters? So, all playing + + + align:start position:0% +have temporary heaters? So, all playing +into the whole project management and + + align:start position:0% +into the whole project management and + + + align:start position:0% +into the whole project management and +logistics of a system like this and how + + align:start position:0% +logistics of a system like this and how + + + align:start position:0% +logistics of a system like this and how +you actually build it and turn it on. + + align:start position:0% +you actually build it and turn it on. + + + align:start position:0% +you actually build it and turn it on. +Um, you know, going forward, I I I have + + align:start position:0% +Um, you know, going forward, I I I have + + + align:start position:0% +Um, you know, going forward, I I I have +a laundry list of things that I'm going + + align:start position:0% +a laundry list of things that I'm going + + + align:start position:0% +a laundry list of things that I'm going +to be able to address the next time + + align:start position:0% +to be able to address the next time + + + align:start position:0% +to be able to address the next time +around and head off. So, with that, + + align:start position:0% +around and head off. So, with that, + + + align:start position:0% +around and head off. So, with that, +hopefully I stayed on time and we've got + + align:start position:0% +hopefully I stayed on time and we've got + + + align:start position:0% +hopefully I stayed on time and we've got +a little bit of time here for Q&A. + + align:start position:0% +a little bit of time here for Q&A. + + + align:start position:0% +a little bit of time here for Q&A. +>> Thank you. \ No newline at end of file diff --git a/B5y6fy5iUtg.txt b/B5y6fy5iUtg.txt new file mode 100644 index 0000000000000000000000000000000000000000..1d02018c432027d3e550c2562c0850b0f4dc183c --- /dev/null +++ b/B5y6fy5iUtg.txt @@ -0,0 +1,379 @@ +align:start position:0% + +suppose I look at the registry of + + align:start position:0% +suppose I look at the registry of + + + align:start position:0% +suppose I look at the registry of +residents of my town and pick a person + + align:start position:0% +residents of my town and pick a person + + + align:start position:0% +residents of my town and pick a person +at random what is the probability that + + align:start position:0% +at random what is the probability that + + + align:start position:0% +at random what is the probability that +this person is under 18 years of age the + + align:start position:0% +this person is under 18 years of age the + + + align:start position:0% +this person is under 18 years of age the +answer is about 25% suppose now that I + + align:start position:0% +answer is about 25% suppose now that I + + + align:start position:0% +answer is about 25% suppose now that I +told you that this person is married + + align:start position:0% +told you that this person is married + + + align:start position:0% +told you that this person is married +will you give the same answer of course + + align:start position:0% +will you give the same answer of course + + + align:start position:0% +will you give the same answer of course +not the probability of being less than + + align:start position:0% +not the probability of being less than + + + align:start position:0% +not the probability of being less than +18 years old is now much smaller what + + align:start position:0% +18 years old is now much smaller what + + + align:start position:0% +18 years old is now much smaller what +happened here + + align:start position:0% +happened here + + + align:start position:0% +happened here +we started with some initial + + align:start position:0% +we started with some initial + + + align:start position:0% +we started with some initial +probabilities that reflect what we know + + align:start position:0% +probabilities that reflect what we know + + + align:start position:0% +probabilities that reflect what we know +or believe about the world but we then + + align:start position:0% +or believe about the world but we then + + + align:start position:0% +or believe about the world but we then +acquired some additional knowledge some + + align:start position:0% +acquired some additional knowledge some + + + align:start position:0% +acquired some additional knowledge some +new evidence for example about this + + align:start position:0% +new evidence for example about this + + + align:start position:0% +new evidence for example about this +person's family situation this new + + align:start position:0% +person's family situation this new + + + align:start position:0% +person's family situation this new +knowledge should cause our beliefs to + + align:start position:0% +knowledge should cause our beliefs to + + + align:start position:0% +knowledge should cause our beliefs to +change and the original probabilities + + align:start position:0% +change and the original probabilities + + + align:start position:0% +change and the original probabilities +must be replaced by new probabilities + + align:start position:0% +must be replaced by new probabilities + + + align:start position:0% +must be replaced by new probabilities +that take into account the new + + align:start position:0% +that take into account the new + + + align:start position:0% +that take into account the new +information these revised probabilities + + align:start position:0% +information these revised probabilities + + + align:start position:0% +information these revised probabilities +are what we call conditional + + align:start position:0% +are what we call conditional + + + align:start position:0% +are what we call conditional +probabilities and this is the subject of + + align:start position:0% +probabilities and this is the subject of + + + align:start position:0% +probabilities and this is the subject of +this lecture we will start with a formal + + align:start position:0% +this lecture we will start with a formal + + + align:start position:0% +this lecture we will start with a formal +definition of conditional probabilities + + align:start position:0% +definition of conditional probabilities + + + align:start position:0% +definition of conditional probabilities +together with the motivation behind this + + align:start position:0% +together with the motivation behind this + + + align:start position:0% +together with the motivation behind this +particular definition we will then + + align:start position:0% +particular definition we will then + + + align:start position:0% +particular definition we will then +proceed to develop three tools that rely + + align:start position:0% +proceed to develop three tools that rely + + + align:start position:0% +proceed to develop three tools that rely +on conditional probabilities including + + align:start position:0% +on conditional probabilities including + + + align:start position:0% +on conditional probabilities including +the Bayes rule which provides a + + align:start position:0% +the Bayes rule which provides a + + + align:start position:0% +the Bayes rule which provides a +systematic way for incorporating new + + align:start position:0% +systematic way for incorporating new + + + align:start position:0% +systematic way for incorporating new +evidence into a probability model the + + align:start position:0% +evidence into a probability model the + + + align:start position:0% +evidence into a probability model the +three tools that we introduced in this + + align:start position:0% +three tools that we introduced in this + + + align:start position:0% +three tools that we introduced in this +lecture involve very simple and + + align:start position:0% +lecture involve very simple and + + + align:start position:0% +lecture involve very simple and +elementary mathematical formulas yet + + align:start position:0% +elementary mathematical formulas yet + + + align:start position:0% +elementary mathematical formulas yet +they encapsulate some very powerful + + align:start position:0% +they encapsulate some very powerful + + + align:start position:0% +they encapsulate some very powerful +ideas it is not an exaggeration to say + + align:start position:0% +ideas it is not an exaggeration to say + + + align:start position:0% +ideas it is not an exaggeration to say +that much of this class will revolve + + align:start position:0% +that much of this class will revolve + + + align:start position:0% +that much of this class will revolve +around the repeated application of + + align:start position:0% +around the repeated application of + + + align:start position:0% +around the repeated application of +variations of these three tools to + + align:start position:0% +variations of these three tools to + + + align:start position:0% +variations of these three tools to +increasingly complicated situations in + + align:start position:0% +increasingly complicated situations in + + + align:start position:0% +increasingly complicated situations in +particular the Bayes rule is the + + align:start position:0% +particular the Bayes rule is the + + + align:start position:0% +particular the Bayes rule is the +foundation for the field of inference it + + align:start position:0% +foundation for the field of inference it + + + align:start position:0% +foundation for the field of inference it +is a guide on how to process data and + + align:start position:0% +is a guide on how to process data and + + + align:start position:0% +is a guide on how to process data and +make inferences about unobserved + + align:start position:0% +make inferences about unobserved + + + align:start position:0% +make inferences about unobserved +quantities or phenomena as such it is a + + align:start position:0% +quantities or phenomena as such it is a + + + align:start position:0% +quantities or phenomena as such it is a +tool that is used all the time all over + + align:start position:0% +tool that is used all the time all over + + + align:start position:0% +tool that is used all the time all over +science and engineering \ No newline at end of file diff --git a/BPnbq6BobdA.txt b/BPnbq6BobdA.txt new file mode 100644 index 0000000000000000000000000000000000000000..332e1cc0f0c6f89e82f573b9245717d96775a1d3 --- /dev/null +++ b/BPnbq6BobdA.txt @@ -0,0 +1,811 @@ +align:start position:0% + +I would now like to calculate the moment + + align:start position:0% +I would now like to calculate the moment + + + align:start position:0% +I would now like to calculate the moment +of inertia for a very thin disc so we + + align:start position:0% +of inertia for a very thin disc so we + + + align:start position:0% +of inertia for a very thin disc so we +have a thin disc and the radius of that + + align:start position:0% +have a thin disc and the radius of that + + + align:start position:0% +have a thin disc and the radius of that +disc is r and it has a mass m and I + + align:start position:0% +disc is r and it has a mass m and I + + + align:start position:0% +disc is r and it has a mass m and I +would like to calculate the moment of + + align:start position:0% +would like to calculate the moment of + + + align:start position:0% +would like to calculate the moment of +inertia for this disc now let's just + + align:start position:0% +inertia for this disc now let's just + + + align:start position:0% +inertia for this disc now let's just +remind what point we're calculating it + + align:start position:0% +remind what point we're calculating it + + + align:start position:0% +remind what point we're calculating it +about about the center of mass so our + + align:start position:0% +about about the center of mass so our + + + align:start position:0% +about about the center of mass so our +definition of moment of inertia was take + + align:start position:0% +definition of moment of inertia was take + + + align:start position:0% +definition of moment of inertia was take +a small element Mass element of the disc + + align:start position:0% +a small element Mass element of the disc + + + align:start position:0% +a small element Mass element of the disc +in fact we're going to see it doesn't + + align:start position:0% +in fact we're going to see it doesn't + + + align:start position:0% +in fact we're going to see it doesn't +have to be small take a mass element of + + align:start position:0% +have to be small take a mass element of + + + align:start position:0% +have to be small take a mass element of +the disc that's useful and multiply by + + align:start position:0% +the disc that's useful and multiply by + + + align:start position:0% +the disc that's useful and multiply by +the perpendicular distance squared from + + align:start position:0% +the perpendicular distance squared from + + + align:start position:0% +the perpendicular distance squared from +the point we're calculating it so the + + align:start position:0% +the point we're calculating it so the + + + align:start position:0% +the point we're calculating it so the +way I'll do it is I will choose a ring + + align:start position:0% +way I'll do it is I will choose a ring + + + align:start position:0% +way I'll do it is I will choose a ring +I'm going to choose a + + align:start position:0% +I'm going to choose a + + + align:start position:0% +I'm going to choose a +ring of radius R and now I'll make the + + align:start position:0% +ring of radius R and now I'll make the + + + align:start position:0% +ring of radius R and now I'll make the +ring a certain + + align:start position:0% +ring a certain + + + align:start position:0% +ring a certain +thickness and this thickness + + align:start position:0% +thickness and this thickness + + + align:start position:0% +thickness and this thickness +is + + align:start position:0% +is + + + align:start position:0% +is +Dr now in this calculation we're going + + align:start position:0% +Dr now in this calculation we're going + + + align:start position:0% +Dr now in this calculation we're going +to take a limit as Dr goes to zero so + + align:start position:0% +to take a limit as Dr goes to zero so + + + align:start position:0% +to take a limit as Dr goes to zero so +even though the ring has some finite + + align:start position:0% +even though the ring has some finite + + + align:start position:0% +even though the ring has some finite +thickness its radius will eventually + + align:start position:0% +thickness its radius will eventually + + + align:start position:0% +thickness its radius will eventually +treat it as all of the mass element a + + align:start position:0% +treat it as all of the mass element a + + + align:start position:0% +treat it as all of the mass element a +distance R from the center so R will be + + align:start position:0% +distance R from the center so R will be + + + align:start position:0% +distance R from the center so R will be +our integration + + align:start position:0% +our integration + + + align:start position:0% +our integration +variable and that will be equal to R CM + + align:start position:0% +variable and that will be equal to R CM + + + align:start position:0% +variable and that will be equal to R CM +what we're calling R cm in our abstract + + align:start position:0% +what we're calling R cm in our abstract + + + align:start position:0% +what we're calling R cm in our abstract +result + + align:start position:0% +result + + + align:start position:0% +result +now the DM is the tricky part so what is + + align:start position:0% +now the DM is the tricky part so what is + + + align:start position:0% +now the DM is the tricky part so what is +the mass that's + + align:start position:0% +the mass that's + + + align:start position:0% +the mass that's +contained in this + + align:start position:0% +contained in this + + + align:start position:0% +contained in this +area uh dis of radius R and thickness Dr + + align:start position:0% +area uh dis of radius R and thickness Dr + + + align:start position:0% +area uh dis of radius R and thickness Dr +well one way to think about that is it's + + align:start position:0% +well one way to think about that is it's + + + align:start position:0% +well one way to think about that is it's +here we didn't say this but our thin dis + + align:start position:0% +here we didn't say this but our thin dis + + + align:start position:0% +here we didn't say this but our thin dis +is going to be + + align:start position:0% +is going to be + + + align:start position:0% +is going to be +uniform and so we can describe the UN + + align:start position:0% +uniform and so we can describe the UN + + + align:start position:0% +uniform and so we can describe the UN +mass per unit area as the total mass + + align:start position:0% +mass per unit area as the total mass + + + align:start position:0% +mass per unit area as the total mass +divided by the area of the whole + + align:start position:0% +divided by the area of the whole + + + align:start position:0% +divided by the area of the whole +disc and then we can say that the mass + + align:start position:0% +disc and then we can say that the mass + + + align:start position:0% +disc and then we can say that the mass +in that air in that ring is equal to + + align:start position:0% +in that air in that ring is equal to + + + align:start position:0% +in that air in that ring is equal to +Sigma mass per area + + align:start position:0% +Sigma mass per area + + + align:start position:0% +Sigma mass per area +times the area of the outer + + align:start position:0% +times the area of the outer + + + align:start position:0% +times the area of the outer +ring minus the area of the inner + + align:start position:0% +ring minus the area of the inner + + + align:start position:0% +ring minus the area of the inner +ring now when we expand this + + align:start position:0% +ring now when we expand this + + + align:start position:0% +ring now when we expand this +out DM Munk R 2 we get PK R 2 + 2 RDR + + + align:start position:0% +out DM Munk R 2 we get PK R 2 + 2 RDR + + + + align:start position:0% +out DM Munk R 2 we get PK R 2 + 2 RDR + +Dr r^ 2 - < R + + align:start position:0% +Dr r^ 2 - < R + + + align:start position:0% +Dr r^ 2 - < R +2 and you can see those terms cancel and + + align:start position:0% +2 and you can see those terms cancel and + + + align:start position:0% +2 and you can see those terms cancel and +so what I get is M * piun R 2 and in + + align:start position:0% +so what I get is M * piun R 2 and in + + + align:start position:0% +so what I get is M * piun R 2 and in +here I have 2 pi r Dr now this is only + + align:start position:0% +here I have 2 pi r Dr now this is only + + + align:start position:0% +here I have 2 pi r Dr now this is only +order Dr plus a second term that goes + + align:start position:0% +order Dr plus a second term that goes + + + align:start position:0% +order Dr plus a second term that goes +like Pi Dr squared and so when I take + + align:start position:0% +like Pi Dr squared and so when I take + + + align:start position:0% +like Pi Dr squared and so when I take +this + + align:start position:0% +this + + + align:start position:0% +this +limit as Dr goes to zero + + align:start position:0% +limit as Dr goes to zero + + + align:start position:0% +limit as Dr goes to zero +this term is much much smaller than that + + align:start position:0% +this term is much much smaller than that + + + align:start position:0% +this term is much much smaller than that +term and so I can say my mass element is + + align:start position:0% +term and so I can say my mass element is + + + align:start position:0% +term and so I can say my mass element is +m r 2 * 2i R Dr R now let's think about + + align:start position:0% +m r 2 * 2i R Dr R now let's think about + + + align:start position:0% +m r 2 * 2i R Dr R now let's think about +this term why it makes sense when we're + + align:start position:0% +this term why it makes sense when we're + + + align:start position:0% +this term why it makes sense when we're +shrinking our + + align:start position:0% +shrinking our + + + align:start position:0% +shrinking our +ring so taking the limit as Dr goes to + + align:start position:0% +ring so taking the limit as Dr goes to + + + align:start position:0% +ring so taking the limit as Dr goes to +zero and the ring just becomes extremely + + align:start position:0% +zero and the ring just becomes extremely + + + align:start position:0% +zero and the ring just becomes extremely +thin ring at radius R then this piece is + + align:start position:0% +thin ring at radius R then this piece is + + + align:start position:0% +thin ring at radius R then this piece is +a + + align:start position:0% + + + + align:start position:0% + +circumference and this piece is just the + + align:start position:0% +circumference and this piece is just the + + + align:start position:0% +circumference and this piece is just the +width and so it's no surprise that area + + align:start position:0% +width and so it's no surprise that area + + + align:start position:0% +width and so it's no surprise that area +is 2i R * d r Dr in the + + align:start position:0% +is 2i R * d r Dr in the + + + align:start position:0% +is 2i R * d r Dr in the +limit and now that enables us to write + + align:start position:0% +limit and now that enables us to write + + + align:start position:0% +limit and now that enables us to write +the moment of inertia about the center + + align:start position:0% +the moment of inertia about the center + + + align:start position:0% +the moment of inertia about the center +of mass I CM let's pull out these + + align:start position:0% +of mass I CM let's pull out these + + + align:start position:0% +of mass I CM let's pull out these +constants MK R 2 now we're integrating + + align:start position:0% +constants MK R 2 now we're integrating + + + align:start position:0% +constants MK R 2 now we're integrating +over the body let's hold off on the + + align:start position:0% +over the body let's hold off on the + + + align:start position:0% +over the body let's hold off on the +limits for the moment and put our values + + align:start position:0% +limits for the moment and put our values + + + align:start position:0% +limits for the moment and put our values +for DM that's a 2 pi r + + align:start position:0% +for DM that's a 2 pi r + + + align:start position:0% +for DM that's a 2 pi r +Dr and we have our distance squared + + align:start position:0% +Dr and we have our distance squared + + + align:start position:0% +Dr and we have our distance squared +which was again the radius R + + align:start position:0% +which was again the radius R + + + align:start position:0% +which was again the radius R +2 and so the two the pies will cancel I + + align:start position:0% +2 and so the two the pies will cancel I + + + align:start position:0% +2 and so the two the pies will cancel I +have 2 m/ r^ 2 time the integral of RB d + + align:start position:0% +have 2 m/ r^ 2 time the integral of RB d + + + align:start position:0% +have 2 m/ r^ 2 time the integral of RB d +r now we're supposedly integrating over + + align:start position:0% +r now we're supposedly integrating over + + + align:start position:0% +r now we're supposedly integrating over +the body but what does that body + + align:start position:0% +the body but what does that body + + + align:start position:0% +the body but what does that body +integral actually mean well what we're + + align:start position:0% +integral actually mean well what we're + + + align:start position:0% +integral actually mean well what we're +doing is we're taking a series of rings + + align:start position:0% +doing is we're taking a series of rings + + + align:start position:0% +doing is we're taking a series of rings +and adding them up as we go from a very + + align:start position:0% +and adding them up as we go from a very + + + align:start position:0% +and adding them up as we go from a very +from the origin out to the radius of the + + align:start position:0% +from the origin out to the radius of the + + + align:start position:0% +from the origin out to the radius of the +whole dis so the limits of our body + + align:start position:0% +whole dis so the limits of our body + + + align:start position:0% +whole dis so the limits of our body +integral with respect to our integration + + align:start position:0% +integral with respect to our integration + + + align:start position:0% +integral with respect to our integration +variable we start with rings that are + + align:start position:0% +variable we start with rings that are + + + align:start position:0% +variable we start with rings that are +essentially have no width and we're + + align:start position:0% +essentially have no width and we're + + + align:start position:0% +essentially have no width and we're +integrating these adding up the + + align:start position:0% +integrating these adding up the + + + align:start position:0% +integrating these adding up the +contribution of every ring until we get + + align:start position:0% +contribution of every ring until we get + + + align:start position:0% +contribution of every ring until we get +to rings of radius R and our integration + + align:start position:0% +to rings of radius R and our integration + + + align:start position:0% +to rings of radius R and our integration +variable R cubed Dr R now this is an + + align:start position:0% +variable R cubed Dr R now this is an + + + align:start position:0% +variable R cubed Dr R now this is an +integral that's easy to do that's R 4 + + align:start position:0% +integral that's easy to do that's R 4 + + + align:start position:0% +integral that's easy to do that's R 4 +over 4 between 0 and Ral R and when we + + align:start position:0% +over 4 between 0 and Ral R and when we + + + align:start position:0% +over 4 between 0 and Ral R and when we +put that in the two cancels the four and + + align:start position:0% +put that in the two cancels the four and + + + align:start position:0% +put that in the two cancels the four and +oh the pi we lost so let's make sure + + align:start position:0% +oh the pi we lost so let's make sure + + + align:start position:0% +oh the pi we lost so let's make sure +this Pi should be an m so we have the 2 + + align:start position:0% +this Pi should be an m so we have the 2 + + + align:start position:0% +this Pi should be an m so we have the 2 +over the 4 is 12 m r 2 and that is the + + align:start position:0% +over the 4 is 12 m r 2 and that is the + + + align:start position:0% +over the 4 is 12 m r 2 and that is the +moment of inertia of a disc about an + + align:start position:0% +moment of inertia of a disc about an + + + align:start position:0% +moment of inertia of a disc about an +axis passing through the center + + align:start position:0% +axis passing through the center + + + align:start position:0% +axis passing through the center +perpendicular to the plane of the disc \ No newline at end of file diff --git a/BbNMKMicWy8.txt b/BbNMKMicWy8.txt new file mode 100644 index 0000000000000000000000000000000000000000..11390d602fb7a15e6a2197d900de5f06a1422957 --- /dev/null +++ b/BbNMKMicWy8.txt @@ -0,0 +1,2074 @@ +align:start position:0% + +hi welcome back to recitation you've + + align:start position:0% +hi welcome back to recitation you've + + + align:start position:0% +hi welcome back to recitation you've +been learning in lecture about matrices + + align:start position:0% +been learning in lecture about matrices + + + align:start position:0% +been learning in lecture about matrices +and their various applications and one + + align:start position:0% +and their various applications and one + + + align:start position:0% +and their various applications and one +of them is to solving systems of linear + + align:start position:0% +of them is to solving systems of linear + + + align:start position:0% +of them is to solving systems of linear +equations so I have here a system of + + align:start position:0% +equations so I have here a system of + + + align:start position:0% +equations so I have here a system of +three linear equations for you 2x + CZ = + + align:start position:0% +three linear equations for you 2x + CZ = + + + align:start position:0% +three linear equations for you 2x + CZ = +4 x - y + 2z = < x - 2 y + 2 Z = -12 so + + align:start position:0% +4 x - y + 2z = < x - 2 y + 2 Z = -12 so + + + align:start position:0% +4 x - y + 2z = < x - 2 y + 2 Z = -12 so +what I'd like you to do is the following + + align:start position:0% +what I'd like you to do is the following + + + align:start position:0% +what I'd like you to do is the following +find a value of C or all values of c for + + align:start position:0% +find a value of C or all values of c for + + + align:start position:0% +find a value of C or all values of c for +which first of all there's a unique + + align:start position:0% +which first of all there's a unique + + + align:start position:0% +which first of all there's a unique +solution to this system second of all + + align:start position:0% +solution to this system second of all + + + align:start position:0% +solution to this system second of all +for which the corresponding homogeneous + + align:start position:0% +for which the corresponding homogeneous + + + align:start position:0% +for which the corresponding homogeneous +system has a unique solution so remember + + align:start position:0% +system has a unique solution so remember + + + align:start position:0% +system has a unique solution so remember +that the the corresponding homogeneous + + align:start position:0% +that the the corresponding homogeneous + + + align:start position:0% +that the the corresponding homogeneous +system is the system where you just + + align:start position:0% +system is the system where you just + + + align:start position:0% +system is the system where you just +replace these constants on the right by + + align:start position:0% +replace these constants on the right by + + + align:start position:0% +replace these constants on the right by +zero so it's a very similar looking + + align:start position:0% +zero so it's a very similar looking + + + align:start position:0% +zero so it's a very similar looking +system the left hand sides are all the + + align:start position:0% +system the left hand sides are all the + + + align:start position:0% +system the left hand sides are all the +same but the right hand sides are + + align:start position:0% +same but the right hand sides are + + + align:start position:0% +same but the right hand sides are +replaced with zero so you want to find + + align:start position:0% +replaced with zero so you want to find + + + align:start position:0% +replaced with zero so you want to find +the value of C for which this system has + + align:start position:0% +the value of C for which this system has + + + align:start position:0% +the value of C for which this system has +unique solution the value of C for which + + align:start position:0% +unique solution the value of C for which + + + align:start position:0% +unique solution the value of C for which +the corresponding homogeneous system has + + align:start position:0% +the corresponding homogeneous system has + + + align:start position:0% +the corresponding homogeneous system has +unique solution and also uh the values + + align:start position:0% +unique solution and also uh the values + + + align:start position:0% +unique solution and also uh the values +of c um for which the corresponding + + align:start position:0% +of c um for which the corresponding + + + align:start position:0% +of c um for which the corresponding +homogeneous system has infinitely many + + align:start position:0% +homogeneous system has infinitely many + + + align:start position:0% +homogeneous system has infinitely many +solutions note that I'm not asking you + + align:start position:0% +solutions note that I'm not asking you + + + align:start position:0% +solutions note that I'm not asking you +to solve this system of equations + + align:start position:0% +to solve this system of equations + + + align:start position:0% +to solve this system of equations +although you're welcome to to do so if + + align:start position:0% +although you're welcome to to do so if + + + align:start position:0% +although you're welcome to to do so if +you like um although of course whether + + align:start position:0% +you like um although of course whether + + + align:start position:0% +you like um although of course whether +you can or not might depend on the value + + align:start position:0% +you can or not might depend on the value + + + align:start position:0% +you can or not might depend on the value +of C so why don't you pause the video + + align:start position:0% +of C so why don't you pause the video + + + align:start position:0% +of C so why don't you pause the video +take a little while to uh to work out + + align:start position:0% +take a little while to uh to work out + + + align:start position:0% +take a little while to uh to work out +the solutions to these three questions + + align:start position:0% +the solutions to these three questions + + + align:start position:0% +the solutions to these three questions +come back and we can work it out + + align:start position:0% + + + + align:start position:0% + +together so hopefully you had some luck + + align:start position:0% +together so hopefully you had some luck + + + align:start position:0% +together so hopefully you had some luck +working out these problems Let's uh + + align:start position:0% +working out these problems Let's uh + + + align:start position:0% +working out these problems Let's uh +let's start working through them + + align:start position:0% +let's start working through them + + + align:start position:0% +let's start working through them +together so I'm actually going to going + + align:start position:0% +together so I'm actually going to going + + + align:start position:0% +together so I'm actually going to going +to take Parts A and B to together at the + + align:start position:0% +to take Parts A and B to together at the + + + align:start position:0% +to take Parts A and B to together at the +same time and the reason that I'm going + + align:start position:0% +same time and the reason that I'm going + + + align:start position:0% +same time and the reason that I'm going +to do that is that that one thing you've + + align:start position:0% +to do that is that that one thing you've + + + align:start position:0% +to do that is that that one thing you've +learned is that the system system has a + + align:start position:0% +learned is that the system system has a + + + align:start position:0% +learned is that the system system has a +unique solution for uh on on the right + + align:start position:0% +unique solution for uh on on the right + + + align:start position:0% +unique solution for uh on on the right +hand side um sorry the system has a + + align:start position:0% +hand side um sorry the system has a + + + align:start position:0% +hand side um sorry the system has a +unique + + align:start position:0% +unique + + + align:start position:0% +unique +solution like this a system a square + + align:start position:0% +solution like this a system a square + + + align:start position:0% +solution like this a system a square +system of linear equations has a unique + + align:start position:0% +system of linear equations has a unique + + + align:start position:0% +system of linear equations has a unique +solution um if and only if it has a + + align:start position:0% +solution um if and only if it has a + + + align:start position:0% +solution um if and only if it has a +unique solution regardless of what the + + align:start position:0% +unique solution regardless of what the + + + align:start position:0% +unique solution regardless of what the +right hand side is so in particular the + + align:start position:0% +right hand side is so in particular the + + + align:start position:0% +right hand side is so in particular the +answer to a and the answer to B are + + align:start position:0% +answer to a and the answer to B are + + + align:start position:0% +answer to a and the answer to B are +exactly the same so values of c for + + align:start position:0% +exactly the same so values of c for + + + align:start position:0% +exactly the same so values of c for +which this system has a unique solution + + align:start position:0% +which this system has a unique solution + + + align:start position:0% +which this system has a unique solution +are exactly the same as values of c for + + align:start position:0% +are exactly the same as values of c for + + + align:start position:0% +are exactly the same as values of c for +which the homogeneous system has a + + align:start position:0% +which the homogeneous system has a + + + align:start position:0% +which the homogeneous system has a +unique solution now the the solutions + + align:start position:0% +unique solution now the the solutions + + + align:start position:0% +unique solution now the the solutions +will be different of course but but the + + align:start position:0% +will be different of course but but the + + + align:start position:0% +will be different of course but but the +the value of C that or the values of c + + align:start position:0% +the value of C that or the values of c + + + align:start position:0% +the value of C that or the values of c +that make it that make it solvable + + align:start position:0% +that make it that make it solvable + + + align:start position:0% +that make it that make it solvable +uniquely make it solvable uniquely for + + align:start position:0% +uniquely make it solvable uniquely for + + + align:start position:0% +uniquely make it solvable uniquely for +all right hand sides and so which values + + align:start position:0% +all right hand sides and so which values + + + align:start position:0% +all right hand sides and so which values +of c are those well those are the values + + align:start position:0% +of c are those well those are the values + + + align:start position:0% +of c are those well those are the values +of c for which the coefficient Matrix on + + align:start position:0% +of c for which the coefficient Matrix on + + + align:start position:0% +of c for which the coefficient Matrix on +the left hand side is invertible so if + + align:start position:0% +the left hand side is invertible so if + + + align:start position:0% +the left hand side is invertible so if +the coefficient Matrix on the left hand + + align:start position:0% +the coefficient Matrix on the left hand + + + align:start position:0% +the coefficient Matrix on the left hand +side is invertible then we can solve + + align:start position:0% +side is invertible then we can solve + + + align:start position:0% +side is invertible then we can solve +this system and we get a unique solution + + align:start position:0% +this system and we get a unique solution + + + align:start position:0% +this system and we get a unique solution +if it's not invertible then and either + + align:start position:0% +if it's not invertible then and either + + + align:start position:0% +if it's not invertible then and either +we can't solve the system like there are + + align:start position:0% +we can't solve the system like there are + + + align:start position:0% +we can't solve the system like there are +no Solutions or we can solve the system + + align:start position:0% +no Solutions or we can solve the system + + + align:start position:0% +no Solutions or we can solve the system +but there are infinitely many solutions + + align:start position:0% +but there are infinitely many solutions + + + align:start position:0% +but there are infinitely many solutions +so in both questions A and B we're + + align:start position:0% +so in both questions A and B we're + + + align:start position:0% +so in both questions A and B we're +asking for the value of C for which the + + align:start position:0% +asking for the value of C for which the + + + align:start position:0% +asking for the value of C for which the +the the coefficient Matrix of the left + + align:start position:0% +the the coefficient Matrix of the left + + + align:start position:0% +the the coefficient Matrix of the left +hand side is invertible and that's and + + align:start position:0% +hand side is invertible and that's and + + + align:start position:0% +hand side is invertible and that's and +that'll be when we have a unique + + align:start position:0% +that'll be when we have a unique + + + align:start position:0% +that'll be when we have a unique +solution so how do we know when a matrix + + align:start position:0% +solution so how do we know when a matrix + + + align:start position:0% +solution so how do we know when a matrix +is invertible well let's let's write + + align:start position:0% +is invertible well let's let's write + + + align:start position:0% +is invertible well let's let's write +down what the Matrix is first of all so + + align:start position:0% +down what the Matrix is first of all so + + + align:start position:0% +down what the Matrix is first of all so +this Matrix M that we're after is equal + + align:start position:0% +this Matrix M that we're after is equal + + + align:start position:0% +this Matrix M that we're after is equal +to the Matrix 2 2 0 + + align:start position:0% +to the Matrix 2 2 0 + + + align:start position:0% +to the Matrix 2 2 0 +c + + align:start position:0% +c + + + align:start position:0% +c + + align:start position:0% + + + align:start position:0% +-1 2 1 - 2 + + align:start position:0% +-1 2 1 - 2 + + + align:start position:0% +-1 2 1 - 2 +2 so this is the m the coefficient + + align:start position:0% +2 so this is the m the coefficient + + + align:start position:0% +2 so this is the m the coefficient +Matrix M of that system and we want to + + align:start position:0% +Matrix M of that system and we want to + + + align:start position:0% +Matrix M of that system and we want to +know for which values of c is it + + align:start position:0% +know for which values of c is it + + + align:start position:0% +know for which values of c is it +invertible well when is a matrix + + align:start position:0% +invertible well when is a matrix + + + align:start position:0% +invertible well when is a matrix +invertible a matrix is invertible a + + align:start position:0% +invertible a matrix is invertible a + + + align:start position:0% +invertible a matrix is invertible a +square Matrix is invertible precisely + + align:start position:0% +square Matrix is invertible precisely + + + align:start position:0% +square Matrix is invertible precisely +when it has nonzero determinant so we + + align:start position:0% +when it has nonzero determinant so we + + + align:start position:0% +when it has nonzero determinant so we +just need to look at the determinant of + + align:start position:0% +just need to look at the determinant of + + + align:start position:0% +just need to look at the determinant of +this Matrix so you've you've uh learned + + align:start position:0% +this Matrix so you've you've uh learned + + + align:start position:0% +this Matrix so you've you've uh learned +how to compute determinants of matrices + + align:start position:0% +how to compute determinants of matrices + + + align:start position:0% +how to compute determinants of matrices +I think so + + align:start position:0% +I think so + + + align:start position:0% +I think so +let's in this case we have the Deb M so + + align:start position:0% +let's in this case we have the Deb M so + + + align:start position:0% +let's in this case we have the Deb M so +it's a su or difference of six different + + align:start position:0% +it's a su or difference of six different + + + align:start position:0% +it's a su or difference of six different +terms and you could get it for example + + align:start position:0% +terms and you could get it for example + + + align:start position:0% +terms and you could get it for example +by the llas expansion if you wanted to + + align:start position:0% +by the llas expansion if you wanted to + + + align:start position:0% +by the llas expansion if you wanted to +um so I'm just going to write out what + + align:start position:0% +um so I'm just going to write out what + + + align:start position:0% +um so I'm just going to write out what +the six terms are so it's 2 * -1 * 2 + 0 + + align:start position:0% +the six terms are so it's 2 * -1 * 2 + 0 + + + align:start position:0% +the six terms are so it's 2 * -1 * 2 + 0 +* 2 * 1 + C * 1 * - + + align:start position:0% + + + + align:start position:0% + +2us c * -1 * + + align:start position:0% +2us c * -1 * + + + align:start position:0% +2us c * -1 * +1 - 2 * -2 * 2 - 0 * 1 * 2 so this is + + align:start position:0% +1 - 2 * -2 * 2 - 0 * 1 * 2 so this is + + + align:start position:0% +1 - 2 * -2 * 2 - 0 * 1 * 2 so this is +the determinant of this Matrix you can + + align:start position:0% +the determinant of this Matrix you can + + + align:start position:0% +the determinant of this Matrix you can +get it either just by remembering which + + align:start position:0% +get it either just by remembering which + + + align:start position:0% +get it either just by remembering which +terms are which and which get a plus + + align:start position:0% +terms are which and which get a plus + + + align:start position:0% +terms are which and which get a plus +sign and which get a minus sign or by + + align:start position:0% +sign and which get a minus sign or by + + + align:start position:0% +sign and which get a minus sign or by +doing little Plass expansion or by some + + align:start position:0% +doing little Plass expansion or by some + + + align:start position:0% +doing little Plass expansion or by some +whatever other tricks you you might + + align:start position:0% +whatever other tricks you you might + + + align:start position:0% +whatever other tricks you you might +happen to know so now we need to know + + align:start position:0% +happen to know so now we need to know + + + align:start position:0% +happen to know so now we need to know +whether or not this determinant is zero + + align:start position:0% +whether or not this determinant is zero + + + align:start position:0% +whether or not this determinant is zero +so let's uh so let's work out what this + + align:start position:0% +so let's uh so let's work out what this + + + align:start position:0% +so let's uh so let's work out what this +is so this is let me let me start + + align:start position:0% +is so this is let me let me start + + + align:start position:0% +is so this is let me let me start +simplifying it so this is + + align:start position:0% +simplifying it so this is + + + align:start position:0% +simplifying it so this is +-4 + 0 - 2 C this is min -- C so plus C + + align:start position:0% +-4 + 0 - 2 C this is min -- C so plus C + + + align:start position:0% +-4 + 0 - 2 C this is min -- C so plus C +this is min - - 8 so + 8 which is equal + + align:start position:0% +this is min - - 8 so + 8 which is equal + + + align:start position:0% +this is min - - 8 so + 8 which is equal +to 4 - c + + align:start position:0% +to 4 - c + + + align:start position:0% +to 4 - c +so the determinant right I the two of + + align:start position:0% +so the determinant right I the two of + + + align:start position:0% +so the determinant right I the two of +those terms are zero and so I just get + + align:start position:0% +those terms are zero and so I just get + + + align:start position:0% +those terms are zero and so I just get +to leave them out um so the the + + align:start position:0% +to leave them out um so the the + + + align:start position:0% +to leave them out um so the the +determinant of this Matrix is 4 minus C + + align:start position:0% +determinant of this Matrix is 4 minus C + + + align:start position:0% +determinant of this Matrix is 4 minus C +and what we're interested in is when + + align:start position:0% +and what we're interested in is when + + + align:start position:0% +and what we're interested in is when +this determinant is non zero so in + + align:start position:0% +this determinant is non zero so in + + + align:start position:0% +this determinant is non zero so in +particular for c not equal to zero uh + + align:start position:0% +particular for c not equal to zero uh + + + align:start position:0% +particular for c not equal to zero uh +sorry for c not equal to 4 when C is not + + align:start position:0% +sorry for c not equal to 4 when C is not + + + align:start position:0% +sorry for c not equal to 4 when C is not +four + + align:start position:0% +four + + + align:start position:0% +four +the determinant of + + align:start position:0% +the determinant of + + + align:start position:0% +the determinant of +M is not zero so when C is not four + + align:start position:0% +M is not zero so when C is not four + + + align:start position:0% +M is not zero so when C is not four +determinant of n is not zero determinant + + align:start position:0% +determinant of n is not zero determinant + + + align:start position:0% +determinant of n is not zero determinant +of M is not + + align:start position:0% + + + + align:start position:0% + +zero so + + align:start position:0% + + + + align:start position:0% + +both systems both the original system + + align:start position:0% +both systems both the original system + + + align:start position:0% +both systems both the original system +and the the corresponding homogeneous + + align:start position:0% +and the the corresponding homogeneous + + + align:start position:0% +and the the corresponding homogeneous +system + + align:start position:0% + + + + align:start position:0% + +have + + align:start position:0% +have + + + align:start position:0% +have +a unique + + align:start position:0% + + + + align:start position:0% + +solution so when C is not uh when C is + + align:start position:0% +solution so when C is not uh when C is + + + align:start position:0% +solution so when C is not uh when C is +not four so for most values of c the + + align:start position:0% +not four so for most values of c the + + + align:start position:0% +not four so for most values of c the +determinant is not zero and and the the + + align:start position:0% +determinant is not zero and and the the + + + align:start position:0% +determinant is not zero and and the the +system has a unique solution so when C + + align:start position:0% +system has a unique solution so when C + + + align:start position:0% +system has a unique solution so when C +is equal to four what happens well when + + align:start position:0% +is equal to four what happens well when + + + align:start position:0% +is equal to four what happens well when +C is equal to four we're in we're in the + + align:start position:0% +C is equal to four we're in we're in the + + + align:start position:0% +C is equal to four we're in we're in the +bottom case we're in in the case where + + align:start position:0% +bottom case we're in in the case where + + + align:start position:0% +bottom case we're in in the case where +the homogeneous system has infinitely + + align:start position:0% +the homogeneous system has infinitely + + + align:start position:0% +the homogeneous system has infinitely +many solutions okay so let me write that + + align:start position:0% +many solutions okay so let me write that + + + align:start position:0% +many solutions okay so let me write that +over + + align:start position:0% +over + + + align:start position:0% +over +here when C + + align:start position:0% +here when C + + + align:start position:0% +here when C +equals + + align:start position:0% +equals + + + align:start position:0% +equals +for I'm going to abbreviate + + align:start position:0% +for I'm going to abbreviate + + + align:start position:0% +for I'm going to abbreviate +again the + + align:start position:0% + + + + align:start position:0% + +homogeneous + + align:start position:0% +homogeneous + + + align:start position:0% +homogeneous +system has I'm going to use this + + align:start position:0% +system has I'm going to use this + + + align:start position:0% +system has I'm going to use this +symbol this sort of sideways eight + + align:start position:0% +symbol this sort of sideways eight + + + align:start position:0% +symbol this sort of sideways eight +symbol means Infinity so I'm going to + + align:start position:0% +symbol means Infinity so I'm going to + + + align:start position:0% +symbol means Infinity so I'm going to +write it use it for + + align:start position:0% +write it use it for + + + align:start position:0% +write it use it for +infinitely + + align:start position:0% + + + + align:start position:0% + +many solutions so when when C is four + + align:start position:0% +many solutions so when when C is four + + + align:start position:0% +many solutions so when when C is four +the homogeneous system has infinite Ely + + align:start position:0% +the homogeneous system has infinite Ely + + + align:start position:0% +the homogeneous system has infinite Ely +many solutions and you might be curious + + align:start position:0% +many solutions and you might be curious + + + align:start position:0% +many solutions and you might be curious +well so let me say one more thing about + + align:start position:0% +well so let me say one more thing about + + + align:start position:0% +well so let me say one more thing about +that we know when when the coefficient + + align:start position:0% +that we know when when the coefficient + + + align:start position:0% +that we know when when the coefficient +Matrix isn't invertible that it either + + align:start position:0% +Matrix isn't invertible that it either + + + align:start position:0% +Matrix isn't invertible that it either +has that the system either has zero or + + align:start position:0% +has that the system either has zero or + + + align:start position:0% +has that the system either has zero or +infinitely many solutions so but the + + align:start position:0% +infinitely many solutions so but the + + + align:start position:0% +infinitely many solutions so but the +homogeneous system always has a solution + + align:start position:0% +homogeneous system always has a solution + + + align:start position:0% +homogeneous system always has a solution +it always has the solution where + + align:start position:0% +it always has the solution where + + + align:start position:0% +it always has the solution where +everything's all zero right so that's + + align:start position:0% +everything's all zero right so that's + + + align:start position:0% +everything's all zero right so that's +why we know that it's infinitely many + + align:start position:0% +why we know that it's infinitely many + + + align:start position:0% +why we know that it's infinitely many +here and one thing you might ask is can + + align:start position:0% +here and one thing you might ask is can + + + align:start position:0% +here and one thing you might ask is can +you find any others can you find any + + align:start position:0% +you find any others can you find any + + + align:start position:0% +you find any others can you find any +solutions that that uh aren't just 0 Z + + align:start position:0% +solutions that that uh aren't just 0 Z + + + align:start position:0% +solutions that that uh aren't just 0 Z +and the answer is yes so this is now + + align:start position:0% +and the answer is yes so this is now + + + align:start position:0% +and the answer is yes so this is now +going beyond what I asked you to do but + + align:start position:0% +going beyond what I asked you to do but + + + align:start position:0% +going beyond what I asked you to do but +but I think it's you know an interesting + + align:start position:0% +but I think it's you know an interesting + + + align:start position:0% +but I think it's you know an interesting +thing to see um + + align:start position:0% + + + + align:start position:0% + +so so if you wanted to find another + + align:start position:0% +so so if you wanted to find another + + + align:start position:0% +so so if you wanted to find another +another solution what do you know well + + align:start position:0% +another solution what do you know well + + + align:start position:0% +another solution what do you know well +let's let's go back to the to the + + align:start position:0% +let's let's go back to the to the + + + align:start position:0% +let's let's go back to the to the +equations that we had so when we're + + align:start position:0% +equations that we had so when we're + + + align:start position:0% +equations that we had so when we're +dealing with the homogenous system the + + align:start position:0% +dealing with the homogenous system the + + + align:start position:0% +dealing with the homogenous system the +right hand sides are zero so I'm just + + align:start position:0% +right hand sides are zero so I'm just + + + align:start position:0% +right hand sides are zero so I'm just +going to cross out these right hand + + align:start position:0% +going to cross out these right hand + + + align:start position:0% +going to cross out these right hand +sides and replace them with zero so we + + align:start position:0% +sides and replace them with zero so we + + + align:start position:0% +sides and replace them with zero so we +don't get confused used so this is + + align:start position:0% +don't get confused used so this is + + + align:start position:0% +don't get confused used so this is + + align:start position:0% + + + align:start position:0% +0 0 so we're we're dealing with this + + align:start position:0% +0 0 so we're we're dealing with this + + + align:start position:0% +0 0 so we're we're dealing with this +system 2x + CZ = 0 x - y + 2 Z = 0 and x + + align:start position:0% +system 2x + CZ = 0 x - y + 2 Z = 0 and x + + + align:start position:0% +system 2x + CZ = 0 x - y + 2 Z = 0 and x +- 2 y + 2 Z = 0 okay so if you want a + + align:start position:0% +- 2 y + 2 Z = 0 okay so if you want a + + + align:start position:0% +- 2 y + 2 Z = 0 okay so if you want a +solution + + align:start position:0% +solution + + + align:start position:0% +solution +XYZ to this system what do you know well + + align:start position:0% +XYZ to this system what do you know well + + + align:start position:0% +XYZ to this system what do you know well +from the second equation you know that + + align:start position:0% +from the second equation you know that + + + align:start position:0% +from the second equation you know that +the vector XYZ is orthogonal to the + + align:start position:0% +the vector XYZ is orthogonal to the + + + align:start position:0% +the vector XYZ is orthogonal to the +vector 1 -1 2 + + align:start position:0% +vector 1 -1 2 + + + align:start position:0% +vector 1 -1 2 +how do you know that because this left + + align:start position:0% +how do you know that because this left + + + align:start position:0% +how do you know that because this left +hand side x - y + 2 Z is equal to + + align:start position:0% +hand side x - y + 2 Z is equal to + + + align:start position:0% +hand side x - y + 2 Z is equal to +XYZ dot 1 -1 + + align:start position:0% +XYZ dot 1 -1 + + + align:start position:0% +XYZ dot 1 -1 +2 and similarly from the third equation + + align:start position:0% +2 and similarly from the third equation + + + align:start position:0% +2 and similarly from the third equation +you know that the vector XYZ is + + align:start position:0% +you know that the vector XYZ is + + + align:start position:0% +you know that the vector XYZ is +orthogonal to the vector 1 - 22 because + + align:start position:0% +orthogonal to the vector 1 - 22 because + + + align:start position:0% +orthogonal to the vector 1 - 22 because +this left hand side is equal to XYZ dot + + align:start position:0% +this left hand side is equal to XYZ dot + + + align:start position:0% +this left hand side is equal to XYZ dot + + align:start position:0% + + + align:start position:0% +-22 yeah and and that's equal to zero so + + align:start position:0% +-22 yeah and and that's equal to zero so + + + align:start position:0% +-22 yeah and and that's equal to zero so +from the second and third equations you + + align:start position:0% +from the second and third equations you + + + align:start position:0% +from the second and third equations you +know that you're looking for a vector + + align:start position:0% +know that you're looking for a vector + + + align:start position:0% +know that you're looking for a vector +that's orthogonal to both X well sorry + + align:start position:0% +that's orthogonal to both X well sorry + + + align:start position:0% +that's orthogonal to both X well sorry +both 1 -1 2 and 1 minus 2 two how do you + + align:start position:0% +both 1 -1 2 and 1 minus 2 two how do you + + + align:start position:0% +both 1 -1 2 and 1 minus 2 two how do you +get a vector perpendicular to two known + + align:start position:0% +get a vector perpendicular to two known + + + align:start position:0% +get a vector perpendicular to two known +vectors well you just take their cross + + align:start position:0% +vectors well you just take their cross + + + align:start position:0% +vectors well you just take their cross +product so let's go back over here so to + + align:start position:0% +product so let's go back over here so to + + + align:start position:0% +product so let's go back over here so to +find one + + align:start position:0% + + + + align:start position:0% + +so to find when you take a cross product + + align:start position:0% +so to find when you take a cross product + + + align:start position:0% +so to find when you take a cross product +of two rows of the coefficient Matrix so + + align:start position:0% +of two rows of the coefficient Matrix so + + + align:start position:0% +of two rows of the coefficient Matrix so +in this case for example we can take + + align:start position:0% +in this case for example we can take + + + align:start position:0% +in this case for example we can take +these rows 1 - one 2 and 1 - 22 + + align:start position:0% +these rows 1 - one 2 and 1 - 22 + + + align:start position:0% +these rows 1 - one 2 and 1 - 22 +so the for example the vector 1 - one 2 + + align:start position:0% +so the for example the vector 1 - one 2 + + + align:start position:0% +so the for example the vector 1 - one 2 +okay cross the vector 1 - 2 two now I've + + align:start position:0% +okay cross the vector 1 - 2 two now I've + + + align:start position:0% +okay cross the vector 1 - 2 two now I've +kind of run out of board space so I'm + + align:start position:0% +kind of run out of board space so I'm + + + align:start position:0% +kind of run out of board space so I'm +not going to work out precisely what + + align:start position:0% +not going to work out precisely what + + + align:start position:0% +not going to work out precisely what +this Vector is for you but if you like + + align:start position:0% +this Vector is for you but if you like + + + align:start position:0% +this Vector is for you but if you like +you can certainly check you can compute + + align:start position:0% +you can certainly check you can compute + + + align:start position:0% +you can certainly check you can compute +this cross product out with our nice + + align:start position:0% +this cross product out with our nice + + + align:start position:0% +this cross product out with our nice +formula for the cross product it'll give + + align:start position:0% +formula for the cross product it'll give + + + align:start position:0% +formula for the cross product it'll give +you some vector and then you can check + + align:start position:0% +you some vector and then you can check + + + align:start position:0% +you some vector and then you can check +that that Vector is indeed a solution of + + align:start position:0% +that that Vector is indeed a solution of + + + align:start position:0% +that that Vector is indeed a solution of +the homogeneous system so that'll give + + align:start position:0% +the homogeneous system so that'll give + + + align:start position:0% +the homogeneous system so that'll give +us another a second solution of the + + align:start position:0% +us another a second solution of the + + + align:start position:0% +us another a second solution of the +homogeneous system non-trivial we say + + align:start position:0% +homogeneous system non-trivial we say + + + align:start position:0% +homogeneous system non-trivial we say +because it's it's not just a zero + + align:start position:0% +because it's it's not just a zero + + + align:start position:0% +because it's it's not just a zero +solution so to quickly + + align:start position:0% +solution so to quickly + + + align:start position:0% +solution so to quickly +recap we had a system of linear + + align:start position:0% +recap we had a system of linear + + + align:start position:0% +recap we had a system of linear +equations I've now crossed out what the + + align:start position:0% +equations I've now crossed out what the + + + align:start position:0% +equations I've now crossed out what the +original right hand side was we had a + + align:start position:0% +original right hand side was we had a + + + align:start position:0% +original right hand side was we had a +system of linear equations and we were + + align:start position:0% +system of linear equations and we were + + + align:start position:0% +system of linear equations and we were +looking for a choice of c um for which + + align:start position:0% +looking for a choice of c um for which + + + align:start position:0% +looking for a choice of c um for which +that system had a unique solution and + + align:start position:0% +that system had a unique solution and + + + align:start position:0% +that system had a unique solution and +for which the corresponding homogeneous + + align:start position:0% +for which the corresponding homogeneous + + + align:start position:0% +for which the corresponding homogeneous +system had a unique solution and the + + align:start position:0% +system had a unique solution and the + + + align:start position:0% +system had a unique solution and the +values of c that make that work are + + align:start position:0% +values of c that make that work are + + + align:start position:0% +values of c that make that work are +precisely the values of c such that the + + align:start position:0% +precisely the values of c such that the + + + align:start position:0% +precisely the values of c such that the +such that the coefficient Matrix has + + align:start position:0% +such that the coefficient Matrix has + + + align:start position:0% +such that the coefficient Matrix has +nonzero determinant so that's true for + + align:start position:0% +nonzero determinant so that's true for + + + align:start position:0% +nonzero determinant so that's true for +both parts A and B and for part C when + + align:start position:0% +both parts A and B and for part C when + + + align:start position:0% +both parts A and B and for part C when +we were looking for what values of c + + align:start position:0% +we were looking for what values of c + + + align:start position:0% +we were looking for what values of c +give the homogeneous system infinitely + + align:start position:0% +give the homogeneous system infinitely + + + align:start position:0% +give the homogeneous system infinitely +many solutions um the the the answer is + + align:start position:0% +many solutions um the the the answer is + + + align:start position:0% +many solutions um the the the answer is +any other value of C any value of C for + + align:start position:0% +any other value of C any value of C for + + + align:start position:0% +any other value of C any value of C for +which the the coefficient Matrix does + + align:start position:0% +which the the coefficient Matrix does + + + align:start position:0% +which the the coefficient Matrix does +have zero determinant will give you + + align:start position:0% +have zero determinant will give you + + + align:start position:0% +have zero determinant will give you +infinitely many solutions in the + + align:start position:0% +infinitely many solutions in the + + + align:start position:0% +infinitely many solutions in the +homogeneous case and in non-homogeneous + + align:start position:0% +homogeneous case and in non-homogeneous + + + align:start position:0% +homogeneous case and in non-homogeneous +cases we'll either give you Zero + + align:start position:0% +cases we'll either give you Zero + + + align:start position:0% +cases we'll either give you Zero +Solutions or infinitely many + + align:start position:0% +Solutions or infinitely many + + + align:start position:0% +Solutions or infinitely many +solutions and then we also at the end we + + align:start position:0% +solutions and then we also at the end we + + + align:start position:0% +solutions and then we also at the end we +briefly discussed one way to find + + align:start position:0% +briefly discussed one way to find + + + align:start position:0% +briefly discussed one way to find +non-trivial Solutions in the case that + + align:start position:0% +non-trivial Solutions in the case that + + + align:start position:0% +non-trivial Solutions in the case that +you have uh in the in the in the + + align:start position:0% +you have uh in the in the in the + + + align:start position:0% +you have uh in the in the in the +homogeneous case um when there are + + align:start position:0% +homogeneous case um when there are + + + align:start position:0% +homogeneous case um when there are +infinitely many solutions so I'll end + + align:start position:0% +infinitely many solutions so I'll end + + + align:start position:0% +infinitely many solutions so I'll end +there \ No newline at end of file diff --git a/CFh3gu-z_rc.txt b/CFh3gu-z_rc.txt new file mode 100644 index 0000000000000000000000000000000000000000..92ece1e6e4716f4be97d65b5aa3af920345269ec --- /dev/null +++ b/CFh3gu-z_rc.txt @@ -0,0 +1,851 @@ +align:start position:0% + +so now we want to find the center of + + align:start position:0% +so now we want to find the center of + + + align:start position:0% +so now we want to find the center of +mass of a uniform rod and we have the + + align:start position:0% +mass of a uniform rod and we have the + + + align:start position:0% +mass of a uniform rod and we have the +result for a continuous body which is an + + align:start position:0% +result for a continuous body which is an + + + align:start position:0% +result for a continuous body which is an +integral over the body of DM r2 that + + align:start position:0% +integral over the body of DM r2 that + + + align:start position:0% +integral over the body of DM r2 that +mass element DM divided by an integral + + align:start position:0% +mass element DM divided by an integral + + + align:start position:0% +mass element DM divided by an integral +of DM now our goal is to figure out how + + align:start position:0% +of DM now our goal is to figure out how + + + align:start position:0% +of DM now our goal is to figure out how +to apply this result specifically to + + align:start position:0% +to apply this result specifically to + + + align:start position:0% +to apply this result specifically to +real physical objects and the key as + + align:start position:0% +real physical objects and the key as + + + align:start position:0% +real physical objects and the key as +always is choosing a coordinate system + + align:start position:0% +always is choosing a coordinate system + + + align:start position:0% +always is choosing a coordinate system +so now I'll draw the object again and + + align:start position:0% +so now I'll draw the object again and + + + align:start position:0% +so now I'll draw the object again and +the first thing I'll do is choose an + + align:start position:0% +the first thing I'll do is choose an + + + align:start position:0% +the first thing I'll do is choose an +origin I can pick my origin anywhere I + + align:start position:0% +origin I can pick my origin anywhere I + + + align:start position:0% +origin I can pick my origin anywhere I +want I could pick it in the middle I + + align:start position:0% +want I could pick it in the middle I + + + align:start position:0% +want I could pick it in the middle I +could put it in the middle I could put + + align:start position:0% +could put it in the middle I could put + + + align:start position:0% +could put it in the middle I could put +it this end I could put it that and I + + align:start position:0% +it this end I could put it that and I + + + align:start position:0% +it this end I could put it that and I +could put it down here but I'll choose + + align:start position:0% +could put it down here but I'll choose + + + align:start position:0% +could put it down here but I'll choose +it over here because the object is + + align:start position:0% +it over here because the object is + + + align:start position:0% +it over here because the object is +linear this is a very Cartesian system + + align:start position:0% +linear this is a very Cartesian system + + + align:start position:0% +linear this is a very Cartesian system +I'm only doing a one dimensional object + + align:start position:0% +I'm only doing a one dimensional object + + + align:start position:0% +I'm only doing a one dimensional object +so I choose my coordinate system plus X + + align:start position:0% +so I choose my coordinate system plus X + + + align:start position:0% +so I choose my coordinate system plus X +that's step one now my origin now here + + align:start position:0% +that's step one now my origin now here + + + align:start position:0% +that's step one now my origin now here +comes the crucial thing in this argument + + align:start position:0% +comes the crucial thing in this argument + + + align:start position:0% +comes the crucial thing in this argument +DM is the infinitesimal mass element and + + align:start position:0% +DM is the infinitesimal mass element and + + + align:start position:0% +DM is the infinitesimal mass element and +I want to pick that at an arbitrary + + align:start position:0% +I want to pick that at an arbitrary + + + align:start position:0% +I want to pick that at an arbitrary +place in the object I don't want to pick + + align:start position:0% +place in the object I don't want to pick + + + align:start position:0% +place in the object I don't want to pick +it at the origin I don't want to pick it + + align:start position:0% +it at the origin I don't want to pick it + + + align:start position:0% +it at the origin I don't want to pick it +at the end note down here this is x + + align:start position:0% +at the end note down here this is x + + + align:start position:0% +at the end note down here this is x +equals L so I'll arbitrarily pick an + + align:start position:0% +equals L so I'll arbitrarily pick an + + + align:start position:0% +equals L so I'll arbitrarily pick an +infinitesimally element I'll shade it in + + align:start position:0% +infinitesimally element I'll shade it in + + + align:start position:0% +infinitesimally element I'll shade it in +DM that represents this is what I'm + + align:start position:0% +DM that represents this is what I'm + + + align:start position:0% +DM that represents this is what I'm +gonna make my summation over when I do + + align:start position:0% +gonna make my summation over when I do + + + align:start position:0% +gonna make my summation over when I do +my integral I'm gonna add up all these + + align:start position:0% +my integral I'm gonna add up all these + + + align:start position:0% +my integral I'm gonna add up all these +DMS and the point is is that the DMS are + + align:start position:0% +DMS and the point is is that the DMS are + + + align:start position:0% +DMS and the point is is that the DMS are +different distances from the origin so + + align:start position:0% +different distances from the origin so + + + align:start position:0% +different distances from the origin so +the vector and here's the next step is I + + align:start position:0% +the vector and here's the next step is I + + + align:start position:0% +the vector and here's the next step is I +draw a picture of my vector RDF so now I + + align:start position:0% +draw a picture of my vector RDF so now I + + + align:start position:0% +draw a picture of my vector RDF so now I +have these terms at least explained in + + align:start position:0% +have these terms at least explained in + + + align:start position:0% +have these terms at least explained in +my diagram the next step is to turn is + + align:start position:0% +my diagram the next step is to turn is + + + align:start position:0% +my diagram the next step is to turn is +to introduce an integration variable for + + align:start position:0% +to introduce an integration variable for + + + align:start position:0% +to introduce an integration variable for +both of these quantities so step one was + + align:start position:0% +both of these quantities so step one was + + + align:start position:0% +both of these quantities so step one was +the coordinate system + + align:start position:0% + + + + align:start position:0% + +step2 was the identification of DM and + + align:start position:0% +step2 was the identification of DM and + + + align:start position:0% +step2 was the identification of DM and +step three and I think this is + + align:start position:0% +step three and I think this is + + + align:start position:0% +step three and I think this is +absolutely the crucial one is to + + align:start position:0% +absolutely the crucial one is to + + + align:start position:0% +absolutely the crucial one is to +introduce the integration variable now + + align:start position:0% +introduce the integration variable now + + + align:start position:0% +introduce the integration variable now +you'll see that will come in two + + align:start position:0% +you'll see that will come in two + + + align:start position:0% +you'll see that will come in two +different places so this is the quantity + + align:start position:0% +different places so this is the quantity + + + align:start position:0% +different places so this is the quantity +the distance from DM to the origin + + align:start position:0% +the distance from DM to the origin + + + align:start position:0% +the distance from DM to the origin +that's changing you can see for each of + + align:start position:0% +that's changing you can see for each of + + + align:start position:0% +that's changing you can see for each of +these little elements that changes + + align:start position:0% +these little elements that changes + + + align:start position:0% +these little elements that changes +so what I'll write DM as a vector is X + + align:start position:0% +so what I'll write DM as a vector is X + + + align:start position:0% +so what I'll write DM as a vector is X +Prime + + align:start position:0% +Prime + + + align:start position:0% +Prime +which will be my integration variable in + + align:start position:0% +which will be my integration variable in + + + align:start position:0% +which will be my integration variable in +the I hat direction so the integration + + align:start position:0% +the I hat direction so the integration + + + align:start position:0% +the I hat direction so the integration +variables X Prime that's the first place + + align:start position:0% +variables X Prime that's the first place + + + align:start position:0% +variables X Prime that's the first place +that I introduced the integration + + align:start position:0% +that I introduced the integration + + + align:start position:0% +that I introduced the integration +variable and X Prime you can see will + + align:start position:0% +variable and X Prime you can see will + + + align:start position:0% +variable and X Prime you can see will +vary and it varies from X prime equals + + align:start position:0% +vary and it varies from X prime equals + + + align:start position:0% +vary and it varies from X prime equals +zero to X prime equals L and that will + + align:start position:0% +zero to X prime equals L and that will + + + align:start position:0% +zero to X prime equals L and that will +show up in terms of the limits of my + + align:start position:0% +show up in terms of the limits of my + + + align:start position:0% +show up in terms of the limits of my +integral now the second place that the + + align:start position:0% +integral now the second place that the + + + align:start position:0% +integral now the second place that the +integration variable comes in is DM I + + align:start position:0% +integration variable comes in is DM I + + + align:start position:0% +integration variable comes in is DM I +want to express DM in terms of X prime + + align:start position:0% +want to express DM in terms of X prime + + + align:start position:0% +want to express DM in terms of X prime +which is a measure of where this object + + align:start position:0% +which is a measure of where this object + + + align:start position:0% +which is a measure of where this object +is and that's how if we choose this + + align:start position:0% +is and that's how if we choose this + + + align:start position:0% +is and that's how if we choose this +length here to be DX prime notice in + + align:start position:0% +length here to be DX prime notice in + + + align:start position:0% +length here to be DX prime notice in +terms of the integration variable then I + + align:start position:0% +terms of the integration variable then I + + + align:start position:0% +terms of the integration variable then I +have a relationship between DM and DX + + align:start position:0% +have a relationship between DM and DX + + + align:start position:0% +have a relationship between DM and DX +prime DM is mass in this little element + + align:start position:0% +prime DM is mass in this little element + + + align:start position:0% +prime DM is mass in this little element +DX prime is the length of the element + + align:start position:0% +DX prime is the length of the element + + + align:start position:0% +DX prime is the length of the element +and if the whole object is a uniform rod + + align:start position:0% +and if the whole object is a uniform rod + + + align:start position:0% +and if the whole object is a uniform rod +with a mass Capital m and a length L + + align:start position:0% +with a mass Capital m and a length L + + + align:start position:0% +with a mass Capital m and a length L +then it's just given by M over L DX + + align:start position:0% +then it's just given by M over L DX + + + align:start position:0% +then it's just given by M over L DX +prime and this quantity M over L is an + + align:start position:0% +prime and this quantity M over L is an + + + align:start position:0% +prime and this quantity M over L is an +example of a mass linear mass density + + align:start position:0% +example of a mass linear mass density + + + align:start position:0% +example of a mass linear mass density +which we have a skill challenge about so + + align:start position:0% +which we have a skill challenge about so + + + align:start position:0% +which we have a skill challenge about so +I have two places where my integration + + align:start position:0% +I have two places where my integration + + + align:start position:0% +I have two places where my integration +variable has been introduced and now I + + align:start position:0% +variable has been introduced and now I + + + align:start position:0% +variable has been introduced and now I +can write up every piece in this + + align:start position:0% +can write up every piece in this + + + align:start position:0% +can write up every piece in this +integral so let's now indicate that + + align:start position:0% +integral so let's now indicate that + + + align:start position:0% +integral so let's now indicate that +we're integrating from X prime equals + + align:start position:0% +we're integrating from X prime equals + + + align:start position:0% +we're integrating from X prime equals +zero to X prime equals L + + align:start position:0% +zero to X prime equals L + + + align:start position:0% +zero to X prime equals L +diem is M over L DX Prime and our vector + + align:start position:0% +diem is M over L DX Prime and our vector + + + align:start position:0% +diem is M over L DX Prime and our vector +is X Prime I hat and downstairs it's + + align:start position:0% +is X Prime I hat and downstairs it's + + + align:start position:0% +is X Prime I hat and downstairs it's +just + + align:start position:0% +just + + + align:start position:0% +just +M / L DX prime from X prime equals zero + + align:start position:0% +M / L DX prime from X prime equals zero + + + align:start position:0% +M / L DX prime from X prime equals zero +to x prime y equals L and that's how I + + align:start position:0% +to x prime y equals L and that's how I + + + align:start position:0% +to x prime y equals L and that's how I +set up the integral for the center of + + align:start position:0% +set up the integral for the center of + + + align:start position:0% +set up the integral for the center of +mass + + align:start position:0% +mass + + + align:start position:0% +mass +both of these integrals are now not + + align:start position:0% +both of these integrals are now not + + + align:start position:0% +both of these integrals are now not +difficult to do notice it's X prime DX + + align:start position:0% +difficult to do notice it's X prime DX + + + align:start position:0% +difficult to do notice it's X prime DX +prime so this integral is x squared over + + align:start position:0% +prime so this integral is x squared over + + + align:start position:0% +prime so this integral is x squared over +2 and I get 1/2 M over L l squared and + + align:start position:0% +2 and I get 1/2 M over L l squared and + + + align:start position:0% +2 and I get 1/2 M over L l squared and +downstairs DX prime from 0 to L is just + + align:start position:0% +downstairs DX prime from 0 to L is just + + + align:start position:0% +downstairs DX prime from 0 to L is just +L so the downstairs integral is just M + + align:start position:0% +L so the downstairs integral is just M + + + align:start position:0% +L so the downstairs integral is just M +over L and when you have M over L s + + align:start position:0% +over L and when you have M over L s + + + align:start position:0% +over L and when you have M over L s +cancel + + align:start position:0% +cancel + + + align:start position:0% +cancel +we just are left with a this is I'm + + align:start position:0% +we just are left with a this is I'm + + + align:start position:0% +we just are left with a this is I'm +sorry this is just M not M over L + + align:start position:0% +sorry this is just M not M over L + + + align:start position:0% +sorry this is just M not M over L +dimensionally incorrect so we get for + + align:start position:0% +dimensionally incorrect so we get for + + + align:start position:0% +dimensionally incorrect so we get for +the position of the center of mass the + + align:start position:0% +the position of the center of mass the + + + align:start position:0% +the position of the center of mass the +MS cancel one of the LS cancel and we + + align:start position:0% +MS cancel one of the LS cancel and we + + + align:start position:0% +MS cancel one of the LS cancel and we +have an I hat in this expression so our + + align:start position:0% +have an I hat in this expression so our + + + align:start position:0% +have an I hat in this expression so our +answer is R equals L over 2 I hat which + + align:start position:0% +answer is R equals L over 2 I hat which + + + align:start position:0% +answer is R equals L over 2 I hat which +is exactly what we expected we expected + + align:start position:0% +is exactly what we expected we expected + + + align:start position:0% +is exactly what we expected we expected +the center of mass to be halfway down + + align:start position:0% +the center of mass to be halfway down + + + align:start position:0% +the center of mass to be halfway down +the rod \ No newline at end of file diff --git a/CJehtdXHR7Q.txt b/CJehtdXHR7Q.txt new file mode 100644 index 0000000000000000000000000000000000000000..f2a810dfa9b22eec16c3b34e8b325c493054ca01 --- /dev/null +++ b/CJehtdXHR7Q.txt @@ -0,0 +1,13691 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +so that's it starting today again the + + align:start position:0% +so that's it starting today again the + + + align:start position:0% +so that's it starting today again the +topic is fair policy structure and + + align:start position:0% +topic is fair policy structure and + + + align:start position:0% +topic is fair policy structure and +technology so we'll cover policy + + align:start position:0% +technology so we'll cover policy + + + align:start position:0% +technology so we'll cover policy +objectives the issues that agencies face + + align:start position:0% +objectives the issues that agencies face + + + align:start position:0% +objectives the issues that agencies face +fair structure the man responds to fair + + align:start position:0% +fair structure the man responds to fair + + + align:start position:0% +fair structure the man responds to fair +changes and fair technology so what are + + align:start position:0% +changes and fair technology so what are + + + align:start position:0% +changes and fair technology so what are +the objectives of fair policy they are + + align:start position:0% +the objectives of fair policy they are + + + align:start position:0% +the objectives of fair policy they are +there are multiple objectives and they + + align:start position:0% +there are multiple objectives and they + + + align:start position:0% +there are multiple objectives and they +don't necessarily support each other in + + align:start position:0% +don't necessarily support each other in + + + align:start position:0% +don't necessarily support each other in +fact they often go against each other so + + align:start position:0% +fact they often go against each other so + + + align:start position:0% +fact they often go against each other so +the number one objective is to fund + + align:start position:0% +the number one objective is to fund + + + align:start position:0% +the number one objective is to fund +operations that's the reason we we + + align:start position:0% +operations that's the reason we we + + + align:start position:0% +operations that's the reason we we +there's a fee and their user fee for + + align:start position:0% +there's a fee and their user fee for + + + align:start position:0% +there's a fee and their user fee for +service and I say here at least + + align:start position:0% +service and I say here at least + + + align:start position:0% +service and I say here at least +partially because for the most part the + + align:start position:0% +partially because for the most part the + + + align:start position:0% +partially because for the most part the +revenues obtained by fair collection do + + align:start position:0% +revenues obtained by fair collection do + + + align:start position:0% +revenues obtained by fair collection do +not cover the full operational costs let + + align:start position:0% +not cover the full operational costs let + + + align:start position:0% +not cover the full operational costs let +alone capital costs so here we have some + + align:start position:0% +alone capital costs so here we have some + + + align:start position:0% +alone capital costs so here we have some +examples of fare recovery ratios based + + align:start position:0% +examples of fare recovery ratios based + + + align:start position:0% +examples of fare recovery ratios based +on the 2014 national transit database + + align:start position:0% +on the 2014 national transit database + + + align:start position:0% +on the 2014 national transit database +you might remember that we talked about + + align:start position:0% +you might remember that we talked about + + + align:start position:0% +you might remember that we talked about +the national transit database earlier in + + align:start position:0% +the national transit database earlier in + + + align:start position:0% +the national transit database earlier in +this course and here is a breakdown I + + align:start position:0% +this course and here is a breakdown I + + + align:start position:0% +this course and here is a breakdown I +looked at all heavy rail and I saw a + + align:start position:0% +looked at all heavy rail and I saw a + + + align:start position:0% +looked at all heavy rail and I saw a +range of between point fourteen and + + align:start position:0% +range of between point fourteen and + + + align:start position:0% +range of between point fourteen and +point 78 so between 14% and 78% of + + align:start position:0% +point 78 so between 14% and 78% of + + + align:start position:0% +point 78 so between 14% and 78% of +operational expenses covered by fair + + align:start position:0% +operational expenses covered by fair + + + align:start position:0% +operational expenses covered by fair +revenue right the highest one here is in + + align:start position:0% +revenue right the highest one here is in + + + align:start position:0% +revenue right the highest one here is in +California for light rail a little lower + + align:start position:0% +California for light rail a little lower + + + align:start position:0% +California for light rail a little lower +and for bus all over the place + + align:start position:0% +and for bus all over the place + + + align:start position:0% +and for bus all over the place +here we have the averages there tend to + + align:start position:0% +here we have the averages there tend to + + + align:start position:0% +here we have the averages there tend to +be higher for rail and lower for bus so + + align:start position:0% +be higher for rail and lower for bus so + + + align:start position:0% +be higher for rail and lower for bus so +why is that why would that be the case + + align:start position:0% + + + + align:start position:0% + +yep although there are you know you can + + align:start position:0% +yep although there are you know you can + + + align:start position:0% +yep although there are you know you can +fool it you can fill up a bus first + + align:start position:0% +fool it you can fill up a bus first + + + align:start position:0% +fool it you can fill up a bus first +right yep yep yep so there there is to + + align:start position:0% +right yep yep yep so there there is to + + + align:start position:0% +right yep yep yep so there there is to +sort of go back to my rebuttal there are + + align:start position:0% +sort of go back to my rebuttal there are + + + align:start position:0% +sort of go back to my rebuttal there are +some bus services here with fare + + align:start position:0% +some bus services here with fare + + + align:start position:0% +some bus services here with fare +recovery ratios over one so it's + + align:start position:0% +recovery ratios over one so it's + + + align:start position:0% +recovery ratios over one so it's +possible to have our Buster's that + + align:start position:0% +possible to have our Buster's that + + + align:start position:0% +possible to have our Buster's that +returns profit even so so why is it that + + align:start position:0% +returns profit even so so why is it that + + + align:start position:0% +returns profit even so so why is it that +system-wide bus services tend to have + + align:start position:0% +system-wide bus services tend to have + + + align:start position:0% +system-wide bus services tend to have +lower very high ratios because that you + + align:start position:0% +lower very high ratios because that you + + + align:start position:0% +lower very high ratios because that you +have a good point the productivity of + + align:start position:0% +have a good point the productivity of + + + align:start position:0% +have a good point the productivity of +rails can be higher of course is if rail + + align:start position:0% +rails can be higher of course is if rail + + + align:start position:0% +rails can be higher of course is if rail +is underutilized then you still have + + align:start position:0% +is underutilized then you still have + + + align:start position:0% +is underutilized then you still have +that issue + + align:start position:0% +that issue + + + align:start position:0% +that issue +any other ideas Emily right so there's + + align:start position:0% +any other ideas Emily right so there's + + + align:start position:0% +any other ideas Emily right so there's +an agency new system-wide have to cover + + align:start position:0% +an agency new system-wide have to cover + + + align:start position:0% +an agency new system-wide have to cover +of your territory that will include + + align:start position:0% +of your territory that will include + + + align:start position:0% +of your territory that will include +buses that are not very heavily utilized + + align:start position:0% +buses that are not very heavily utilized + + + align:start position:0% +buses that are not very heavily utilized +also you're providing service late at + + align:start position:0% +also you're providing service late at + + + align:start position:0% +also you're providing service late at +night and all those things so so there + + align:start position:0% +night and all those things so so there + + + align:start position:0% +night and all those things so so there +are many cases of buses not being very + + align:start position:0% +are many cases of buses not being very + + + align:start position:0% +are many cases of buses not being very +well utilized and that brings down the + + align:start position:0% +well utilized and that brings down the + + + align:start position:0% +well utilized and that brings down the +fare recovery ratio it did not include + + align:start position:0% +fare recovery ratio it did not include + + + align:start position:0% +fare recovery ratio it did not include +here demand responsive your unresponsive + + align:start position:0% +here demand responsive your unresponsive + + + align:start position:0% +here demand responsive your unresponsive +is usually around one percentage + + align:start position:0% +is usually around one percentage + + + align:start position:0% +is usually around one percentage +difference two percent so so I'm talking + + align:start position:0% +difference two percent so so I'm talking + + + align:start position:0% +difference two percent so so I'm talking +about what what here in Boston is called + + align:start position:0% +about what what here in Boston is called + + + align:start position:0% +about what what here in Boston is called +the ride for disabled have passengers + + align:start position:0% +the ride for disabled have passengers + + + align:start position:0% +the ride for disabled have passengers +and it can cost around $20 per ride and + + align:start position:0% +and it can cost around $20 per ride and + + + align:start position:0% +and it can cost around $20 per ride and +people pay a lot less so I think 20 is + + align:start position:0% +people pay a lot less so I think 20 is + + + align:start position:0% +people pay a lot less so I think 20 is +low I think it's higher sorry I don't + + align:start position:0% +low I think it's higher sorry I don't + + + align:start position:0% +low I think it's higher sorry I don't +remember the number but it's it's closer + + align:start position:0% +remember the number but it's it's closer + + + align:start position:0% +remember the number but it's it's closer +to 30 or 40 I think so so though the + + align:start position:0% +to 30 or 40 I think so so though the + + + align:start position:0% +to 30 or 40 I think so so though the +fare recovery ratio for demand + + align:start position:0% +fare recovery ratio for demand + + + align:start position:0% +fare recovery ratio for demand +responsive Transit is much lower okay so + + align:start position:0% +responsive Transit is much lower okay so + + + align:start position:0% +responsive Transit is much lower okay so +other goals keep transit affordable and + + align:start position:0% +other goals keep transit affordable and + + + align:start position:0% +other goals keep transit affordable and +promote social equity so here we have + + align:start position:0% +promote social equity so here we have + + + align:start position:0% +promote social equity so here we have +the first conflicts right the first + + align:start position:0% +the first conflicts right the first + + + align:start position:0% +the first conflicts right the first +objective would mean that you want to + + align:start position:0% +objective would mean that you want to + + + align:start position:0% +objective would mean that you want to +raise fares and if you raise fares then + + align:start position:0% +raise fares and if you raise fares then + + + align:start position:0% +raise fares and if you raise fares then +you get more fare revenue but there's + + align:start position:0% +you get more fare revenue but there's + + + align:start position:0% +you get more fare revenue but there's +another objective which is to keep + + align:start position:0% +another objective which is to keep + + + align:start position:0% +another objective which is to keep +chance of affordable internal social + + align:start position:0% +chance of affordable internal social + + + align:start position:0% +chance of affordable internal social +equity and that would indicate that you + + align:start position:0% +equity and that would indicate that you + + + align:start position:0% +equity and that would indicate that you +want to keep fares low right so also + + align:start position:0% +want to keep fares low right so also + + + align:start position:0% +want to keep fares low right so also +supporting growth for demand + + align:start position:0% +supporting growth for demand + + + align:start position:0% +supporting growth for demand +transit also keep very slow right make + + align:start position:0% +transit also keep very slow right make + + + align:start position:0% +transit also keep very slow right make +the fare structure easy to communicate + + align:start position:0% +the fare structure easy to communicate + + + align:start position:0% +the fare structure easy to communicate +talk about different fare structures and + + align:start position:0% +talk about different fare structures and + + + align:start position:0% +talk about different fare structures and +market segmentation later in this + + align:start position:0% +market segmentation later in this + + + align:start position:0% +market segmentation later in this +lecture but the point is that when you + + align:start position:0% +lecture but the point is that when you + + + align:start position:0% +lecture but the point is that when you +do market segmentation you can get more + + align:start position:0% +do market segmentation you can get more + + + align:start position:0% +do market segmentation you can get more +revenues out of your fare system when + + align:start position:0% +revenues out of your fare system when + + + align:start position:0% +revenues out of your fare system when +you want to keep things simple then + + align:start position:0% +you want to keep things simple then + + + align:start position:0% +you want to keep things simple then +you're probably going to suggest going + + align:start position:0% +you're probably going to suggest going + + + align:start position:0% +you're probably going to suggest going +for a flat fare structure where people + + align:start position:0% +for a flat fare structure where people + + + align:start position:0% +for a flat fare structure where people +that are that have much higher + + align:start position:0% +that are that have much higher + + + align:start position:0% +that are that have much higher +willingness to pay are still paying low + + align:start position:0% +willingness to pay are still paying low + + + align:start position:0% +willingness to pay are still paying low +fares so that objective of keeping the + + align:start position:0% +fares so that objective of keeping the + + + align:start position:0% +fares so that objective of keeping the +fare structure easy and easy to + + align:start position:0% +fare structure easy and easy to + + + align:start position:0% +fare structure easy and easy to +communicate and simple will reduce fare + + align:start position:0% +communicate and simple will reduce fare + + + align:start position:0% +communicate and simple will reduce fare +avenues and finally to reduce fare + + align:start position:0% +avenues and finally to reduce fare + + + align:start position:0% +avenues and finally to reduce fare +system costs so there are costs to fare + + align:start position:0% +system costs so there are costs to fare + + + align:start position:0% +system costs so there are costs to fare +collection and to the fare system as a + + align:start position:0% +collection and to the fare system as a + + + align:start position:0% +collection and to the fare system as a +whole fare collection is one of them so + + align:start position:0% +whole fare collection is one of them so + + + align:start position:0% +whole fare collection is one of them so +obviously the capital cost of installing + + align:start position:0% +obviously the capital cost of installing + + + align:start position:0% +obviously the capital cost of installing +the fare boxes and maintaining the whole + + align:start position:0% +the fare boxes and maintaining the whole + + + align:start position:0% +the fare boxes and maintaining the whole +AFC system though there is a cost for + + align:start position:0% +AFC system though there is a cost for + + + align:start position:0% +AFC system though there is a cost for +people who are maintaining those fare + + align:start position:0% +people who are maintaining those fare + + + align:start position:0% +people who are maintaining those fare +boxes and vaulting cash out of fare + + align:start position:0% +boxes and vaulting cash out of fare + + + align:start position:0% +boxes and vaulting cash out of fare +boxes and counting the cash and keeping + + align:start position:0% +boxes and counting the cash and keeping + + + align:start position:0% +boxes and counting the cash and keeping +it in a safe place and there's customer + + align:start position:0% +it in a safe place and there's customer + + + align:start position:0% +it in a safe place and there's customer +service so customer service involves + + align:start position:0% +service so customer service involves + + + align:start position:0% +service so customer service involves +more than the fare system but some + + align:start position:0% +more than the fare system but some + + + align:start position:0% +more than the fare system but some +aspects of customer service involve my + + align:start position:0% +aspects of customer service involve my + + + align:start position:0% +aspects of customer service involve my +Charlie card doesn't work can I get a + + align:start position:0% +Charlie card doesn't work can I get a + + + align:start position:0% +Charlie card doesn't work can I get a +new one or I already paid for that ride + + align:start position:0% +new one or I already paid for that ride + + + align:start position:0% +new one or I already paid for that ride +and you need to give me a refund so + + align:start position:0% +and you need to give me a refund so + + + align:start position:0% +and you need to give me a refund so +these kinds of inquiries are our + + align:start position:0% +these kinds of inquiries are our + + + align:start position:0% +these kinds of inquiries are our +complaints are coming from the fare + + align:start position:0% +complaints are coming from the fare + + + align:start position:0% +complaints are coming from the fare +system ok questions about these + + align:start position:0% +system ok questions about these + + + align:start position:0% +system ok questions about these +objectives No + + align:start position:0% +objectives No + + + align:start position:0% +objectives No +ok so how's fare policy intersect with + + align:start position:0% +ok so how's fare policy intersect with + + + align:start position:0% +ok so how's fare policy intersect with +other it intersects with many areas and + + align:start position:0% +other it intersects with many areas and + + + align:start position:0% +other it intersects with many areas and +that makes fare policy and fare + + align:start position:0% +that makes fare policy and fare + + + align:start position:0% +that makes fare policy and fare +structure a very powerful sort of lever + + align:start position:0% +structure a very powerful sort of lever + + + align:start position:0% +structure a very powerful sort of lever +or knob for a fare for a transit agency + + align:start position:0% +or knob for a fare for a transit agency + + + align:start position:0% +or knob for a fare for a transit agency +so obviously Finance right now we're + + align:start position:0% +so obviously Finance right now we're + + + align:start position:0% +so obviously Finance right now we're +talking about funding operational + + align:start position:0% +talking about funding operational + + + align:start position:0% +talking about funding operational +expenses from the revenues derived from + + align:start position:0% +expenses from the revenues derived from + + + align:start position:0% +expenses from the revenues derived from +the fare system and then there's + + align:start position:0% +the fare system and then there's + + + align:start position:0% +the fare system and then there's +operations so if you have a fare policy + + align:start position:0% +operations so if you have a fare policy + + + align:start position:0% +operations so if you have a fare policy +that makes people board faster because + + align:start position:0% +that makes people board faster because + + + align:start position:0% +that makes people board faster because +for example it's proof of payment so + + align:start position:0% +for example it's proof of payment so + + + align:start position:0% +for example it's proof of payment so +there's no validation required or you + + align:start position:0% +there's no validation required or you + + + align:start position:0% +there's no validation required or you +have fair technology that a you know + + align:start position:0% +have fair technology that a you know + + + align:start position:0% +have fair technology that a you know +smart card is much faster than paying + + align:start position:0% +smart card is much faster than paying + + + align:start position:0% +smart card is much faster than paying +that then that means that you'll have + + align:start position:0% +that then that means that you'll have + + + align:start position:0% +that then that means that you'll have +faster boarding shorter 12 times shorter + + align:start position:0% +faster boarding shorter 12 times shorter + + + align:start position:0% +faster boarding shorter 12 times shorter +cycle times higher reliability so you + + align:start position:0% +cycle times higher reliability so you + + + align:start position:0% +cycle times higher reliability so you +might well you might affect operations + + align:start position:0% +might well you might affect operations + + + align:start position:0% +might well you might affect operations +through fair technology some fare + + align:start position:0% +through fair technology some fare + + + align:start position:0% +through fair technology some fare +structures require fair inspection so + + align:start position:0% +structures require fair inspection so + + + align:start position:0% +structures require fair inspection so +proof of payment is one that people + + align:start position:0% +proof of payment is one that people + + + align:start position:0% +proof of payment is one that people +board without interacting with any fair + + align:start position:0% +board without interacting with any fair + + + align:start position:0% +board without interacting with any fair +system so then an inspector has to come + + align:start position:0% +system so then an inspector has to come + + + align:start position:0% +system so then an inspector has to come +in and yeah either for all passengers or + + align:start position:0% +in and yeah either for all passengers or + + + align:start position:0% +in and yeah either for all passengers or +more likely for a subset of passengers a + + align:start position:0% +more likely for a subset of passengers a + + + align:start position:0% +more likely for a subset of passengers a +sample of passengers request proof of + + align:start position:0% +sample of passengers request proof of + + + align:start position:0% +sample of passengers request proof of +having paid the fare and of course that + + align:start position:0% +having paid the fare and of course that + + + align:start position:0% +having paid the fare and of course that +involves some cost there's maintenance + + align:start position:0% +involves some cost there's maintenance + + + align:start position:0% +involves some cost there's maintenance +of equipment if equipment breaks down + + align:start position:0% +of equipment if equipment breaks down + + + align:start position:0% +of equipment if equipment breaks down +the bus needs to be taken out of service + + align:start position:0% +the bus needs to be taken out of service + + + align:start position:0% +the bus needs to be taken out of service +etc public support so politicians may + + align:start position:0% +etc public support so politicians may + + + align:start position:0% +etc public support so politicians may +promise not raising fares that's a + + align:start position:0% +promise not raising fares that's a + + + align:start position:0% +promise not raising fares that's a +popular campaign promise and then of + + align:start position:0% +popular campaign promise and then of + + + align:start position:0% +popular campaign promise and then of +course puts a lot of pressure on the + + align:start position:0% +course puts a lot of pressure on the + + + align:start position:0% +course puts a lot of pressure on the +agency to sort of do more with less and + + align:start position:0% +agency to sort of do more with less and + + + align:start position:0% +agency to sort of do more with less and +we'll talk more about that when we when + + align:start position:0% +we'll talk more about that when we when + + + align:start position:0% +we'll talk more about that when we when +we discuss transit finance there's + + align:start position:0% +we discuss transit finance there's + + + align:start position:0% +we discuss transit finance there's +difficulty gathering support to raise + + align:start position:0% +difficulty gathering support to raise + + + align:start position:0% +difficulty gathering support to raise +fares there's usually a well improve + + align:start position:0% +fares there's usually a well improve + + + align:start position:0% +fares there's usually a well improve +service first and then then that + + align:start position:0% +service first and then then that + + + align:start position:0% +service first and then then that +justifies raising fares right I don't + + align:start position:0% +justifies raising fares right I don't + + + align:start position:0% +justifies raising fares right I don't +want money service to get more expensive + + align:start position:0% +want money service to get more expensive + + + align:start position:0% +want money service to get more expensive +if if it's not very good service right + + align:start position:0% +if if it's not very good service right + + + align:start position:0% +if if it's not very good service right +and essentially if you have lower + + align:start position:0% +and essentially if you have lower + + + align:start position:0% +and essentially if you have lower +service quality then fewer people end up + + align:start position:0% +service quality then fewer people end up + + + align:start position:0% +service quality then fewer people end up +taking it or liking it and those people + + align:start position:0% +taking it or liking it and those people + + + align:start position:0% +taking it or liking it and those people +are not going to be the one for allying + + align:start position:0% +are not going to be the one for allying + + + align:start position:0% +are not going to be the one for allying +for more transit sort of fare hike then + + align:start position:0% +for more transit sort of fare hike then + + + align:start position:0% +for more transit sort of fare hike then +there's also Labor's push for higher + + align:start position:0% +there's also Labor's push for higher + + + align:start position:0% +there's also Labor's push for higher +wages so that's another sort of + + align:start position:0% +wages so that's another sort of + + + align:start position:0% +wages so that's another sort of +political pressure on the agency that + + align:start position:0% +political pressure on the agency that + + + align:start position:0% +political pressure on the agency that +increases operational costs and + + align:start position:0% +increases operational costs and + + + align:start position:0% +increases operational costs and +therefore may require an increase in + + align:start position:0% +therefore may require an increase in + + + align:start position:0% +therefore may require an increase in +fares but both a labor dispute and a + + align:start position:0% +fares but both a labor dispute and a + + + align:start position:0% +fares but both a labor dispute and a +dispute with the passengers on a fare + + align:start position:0% +dispute with the passengers on a fare + + + align:start position:0% +dispute with the passengers on a fare +hike are the result of well unpleasant + + align:start position:0% +hike are the result of well unpleasant + + + align:start position:0% +hike are the result of well unpleasant +negotiations or interactions in public + + align:start position:0% +negotiations or interactions in public + + + align:start position:0% +negotiations or interactions in public +administration so fair technology for + + align:start position:0% +administration so fair technology for + + + align:start position:0% +administration so fair technology for +policy and equity analysis if you're if + + align:start position:0% +policy and equity analysis if you're if + + + align:start position:0% +policy and equity analysis if you're if +you're considering any change to + + align:start position:0% +you're considering any change to + + + align:start position:0% +you're considering any change to +technology or policy or structure you + + align:start position:0% +technology or policy or structure you + + + align:start position:0% +technology or policy or structure you +have to analyze the socio-economic + + align:start position:0% +have to analyze the socio-economic + + + align:start position:0% +have to analyze the socio-economic +aspects of it and you have to prove that + + align:start position:0% +aspects of it and you have to prove that + + + align:start position:0% +aspects of it and you have to prove that +you're not + + align:start position:0% + + + + align:start position:0% + +discriminating against any one group + + align:start position:0% +discriminating against any one group + + + align:start position:0% +discriminating against any one group +even unintentionally so + + align:start position:0% +even unintentionally so + + + align:start position:0% +even unintentionally so +disproportionately affecting a + + align:start position:0% +disproportionately affecting a + + + align:start position:0% +disproportionately affecting a +disadvantaged community either by race + + align:start position:0% +disadvantaged community either by race + + + align:start position:0% +disadvantaged community either by race +or income so that's called title six in + + align:start position:0% +or income so that's called title six in + + + align:start position:0% +or income so that's called title six in +the US then there's another sort of big + + align:start position:0% +the US then there's another sort of big + + + align:start position:0% +the US then there's another sort of big +policy issue is revenue sharing across + + align:start position:0% +policy issue is revenue sharing across + + + align:start position:0% +policy issue is revenue sharing across +jurisdictions not so much an issue on + + align:start position:0% +jurisdictions not so much an issue on + + + align:start position:0% +jurisdictions not so much an issue on +east coast of the US but certainly if + + align:start position:0% +east coast of the US but certainly if + + + align:start position:0% +east coast of the US but certainly if +you go to the west coast you have you + + align:start position:0% +you go to the west coast you have you + + + align:start position:0% +you go to the west coast you have you +know in the in the San Francisco Bay + + align:start position:0% +know in the in the San Francisco Bay + + + align:start position:0% +know in the in the San Francisco Bay +Area dozens of operators some of them + + align:start position:0% +Area dozens of operators some of them + + + align:start position:0% +Area dozens of operators some of them +share the same fare system so how does + + align:start position:0% +share the same fare system so how does + + + align:start position:0% +share the same fare system so how does +how much does each operator pay for + + align:start position:0% +how much does each operator pay for + + + align:start position:0% +how much does each operator pay for +routes that serve multiple jurisdictions + + align:start position:0% +routes that serve multiple jurisdictions + + + align:start position:0% +routes that serve multiple jurisdictions +that's one that's one question the other + + align:start position:0% +that's one that's one question the other + + + align:start position:0% +that's one that's one question the other +question might be if if we are separate + + align:start position:0% +question might be if if we are separate + + + align:start position:0% +question might be if if we are separate +operators and we each have a route so + + align:start position:0% +operators and we each have a route so + + + align:start position:0% +operators and we each have a route so +where we take care of that we still are + + align:start position:0% +where we take care of that we still are + + + align:start position:0% +where we take care of that we still are +collecting fares with a joint system do + + align:start position:0% +collecting fares with a joint system do + + + align:start position:0% +collecting fares with a joint system do +we trust each other and often actually + + align:start position:0% +we trust each other and often actually + + + align:start position:0% +we trust each other and often actually +the the barriers to integration are more + + align:start position:0% +the the barriers to integration are more + + + align:start position:0% +the the barriers to integration are more +about trust and less about technology + + align:start position:0% +about trust and less about technology + + + align:start position:0% +about trust and less about technology +marketing is another sort of issue the + + align:start position:0% +marketing is another sort of issue the + + + align:start position:0% +marketing is another sort of issue the +agency has to deal with how much do they + + align:start position:0% +agency has to deal with how much do they + + + align:start position:0% +agency has to deal with how much do they +market and and what is the message and + + align:start position:0% +market and and what is the message and + + + align:start position:0% +market and and what is the message and +customer service which we already + + align:start position:0% +customer service which we already + + + align:start position:0% +customer service which we already +mentioned it's interesting to note that + + align:start position:0% +mentioned it's interesting to note that + + + align:start position:0% +mentioned it's interesting to note that +fares are one of the first things that a + + align:start position:0% +fares are one of the first things that a + + + align:start position:0% +fares are one of the first things that a +person has to sort of understand about + + align:start position:0% +person has to sort of understand about + + + align:start position:0% +person has to sort of understand about +our transit system to be able to take + + align:start position:0% +our transit system to be able to take + + + align:start position:0% +our transit system to be able to take +them so if you're a tourist and you go + + align:start position:0% +them so if you're a tourist and you go + + + align:start position:0% +them so if you're a tourist and you go +to a new city you've never been to + + align:start position:0% +to a new city you've never been to + + + align:start position:0% +to a new city you've never been to +before and you arrive at the airport and + + align:start position:0% +before and you arrive at the airport and + + + align:start position:0% +before and you arrive at the airport and +you want to take the bus or the train + + align:start position:0% +you want to take the bus or the train + + + align:start position:0% +you want to take the bus or the train +from the airport first thing you have to + + align:start position:0% +from the airport first thing you have to + + + align:start position:0% +from the airport first thing you have to +do is buy a ticket right and figure out + + align:start position:0% +do is buy a ticket right and figure out + + + align:start position:0% +do is buy a ticket right and figure out +the fare structure and where are the + + align:start position:0% +the fare structure and where are the + + + align:start position:0% +the fare structure and where are the +maps and etc so so this is a sort of one + + align:start position:0% +maps and etc so so this is a sort of one + + + align:start position:0% +maps and etc so so this is a sort of one +of the first issues that the first + + align:start position:0% +of the first issues that the first + + + align:start position:0% +of the first issues that the first +impression that a passenger has about + + align:start position:0% +impression that a passenger has about + + + align:start position:0% +impression that a passenger has about +the fare system about the transit agency + + align:start position:0% +the fare system about the transit agency + + + align:start position:0% +the fare system about the transit agency +is something related to the fare system + + align:start position:0% +is something related to the fare system + + + align:start position:0% +is something related to the fare system +okay what issues do agencies face + + align:start position:0% +okay what issues do agencies face + + + align:start position:0% +okay what issues do agencies face +regarding these topics one is fare + + align:start position:0% +regarding these topics one is fare + + + align:start position:0% +regarding these topics one is fare +recovery ratios so we looked at ranges + + align:start position:0% +recovery ratios so we looked at ranges + + + align:start position:0% +recovery ratios so we looked at ranges +typically fare recovery ratio + + align:start position:0% +typically fare recovery ratio + + + align:start position:0% +typically fare recovery ratio +system-wide across the modes is about a + + align:start position:0% +system-wide across the modes is about a + + + align:start position:0% +system-wide across the modes is about a +third it varies a lot as we saw it's + + align:start position:0% +third it varies a lot as we saw it's + + + align:start position:0% +third it varies a lot as we saw it's +rare to make a profit system so one of + + align:start position:0% +rare to make a profit system so one of + + + align:start position:0% +rare to make a profit system so one of +the issues is how much what the first + + align:start position:0% +the issues is how much what the first + + + align:start position:0% +the issues is how much what the first +question is how much of a fare recovery + + align:start position:0% +question is how much of a fare recovery + + + align:start position:0% +question is how much of a fare recovery +ratio do we + + align:start position:0% +ratio do we + + + align:start position:0% +ratio do we +need or do we set a goal to write to + + align:start position:0% +need or do we set a goal to write to + + + align:start position:0% +need or do we set a goal to write to +cover operational expenses and it's like + + align:start position:0% +cover operational expenses and it's like + + + align:start position:0% +cover operational expenses and it's like +a sort of a strong requirement as it is + + align:start position:0% +a sort of a strong requirement as it is + + + align:start position:0% +a sort of a strong requirement as it is +in some agencies so I mean you just have + + align:start position:0% +in some agencies so I mean you just have + + + align:start position:0% +in some agencies so I mean you just have +a loss let's say you know the fairy + + align:start position:0% +a loss let's say you know the fairy + + + align:start position:0% +a loss let's say you know the fairy +Curie ratio must be at least this much + + align:start position:0% +Curie ratio must be at least this much + + + align:start position:0% +Curie ratio must be at least this much +so if expenses go up automatic fare hike + + align:start position:0% +so if expenses go up automatic fare hike + + + align:start position:0% +so if expenses go up automatic fare hike +others it's more of a guideline or maybe + + align:start position:0% +others it's more of a guideline or maybe + + + align:start position:0% +others it's more of a guideline or maybe +there is no policy so that that's one of + + align:start position:0% +there is no policy so that that's one of + + + align:start position:0% +there is no policy so that that's one of +the key issues the second one is how + + align:start position:0% +the key issues the second one is how + + + align:start position:0% +the key issues the second one is how +often to raise fares I think most + + align:start position:0% +often to raise fares I think most + + + align:start position:0% +often to raise fares I think most +agencies are reactive so a reactive + + align:start position:0% +agencies are reactive so a reactive + + + align:start position:0% +agencies are reactive so a reactive +approach is one where you avoid the + + align:start position:0% +approach is one where you avoid the + + + align:start position:0% +approach is one where you avoid the +headache of a fare hike and all the sort + + align:start position:0% +headache of a fare hike and all the sort + + + align:start position:0% +headache of a fare hike and all the sort +of public engagement that goes with it + + align:start position:0% +of public engagement that goes with it + + + align:start position:0% +of public engagement that goes with it +and you only do that when you have to so + + align:start position:0% +and you only do that when you have to so + + + align:start position:0% +and you only do that when you have to so +you are in a financial situation where + + align:start position:0% +you are in a financial situation where + + + align:start position:0% +you are in a financial situation where +you absolutely need to raise fare of and + + align:start position:0% +you absolutely need to raise fare of and + + + align:start position:0% +you absolutely need to raise fare of and +use to continue operating so that + + align:start position:0% +use to continue operating so that + + + align:start position:0% +use to continue operating so that +happens less than once every year and + + align:start position:0% +happens less than once every year and + + + align:start position:0% +happens less than once every year and +it's a big effort some agencies take the + + align:start position:0% +it's a big effort some agencies take the + + + align:start position:0% +it's a big effort some agencies take the +approach of an animal fare hike with + + align:start position:0% +approach of an animal fare hike with + + + align:start position:0% +approach of an animal fare hike with +inflation so it's kind of predictable it + + align:start position:0% +inflation so it's kind of predictable it + + + align:start position:0% +inflation so it's kind of predictable it +happens every year at the same date it + + align:start position:0% +happens every year at the same date it + + + align:start position:0% +happens every year at the same date it +tends to make each one easier than one + + align:start position:0% +tends to make each one easier than one + + + align:start position:0% +tends to make each one easier than one +done ad hoc because it's more expectable + + align:start position:0% +done ad hoc because it's more expectable + + + align:start position:0% +done ad hoc because it's more expectable +and it there's sort of less public + + align:start position:0% +and it there's sort of less public + + + align:start position:0% +and it there's sort of less public +outrage so gathering and maintaining + + align:start position:0% +outrage so gathering and maintaining + + + align:start position:0% +outrage so gathering and maintaining +political support we talked a little bit + + align:start position:0% +political support we talked a little bit + + + align:start position:0% +political support we talked a little bit +a little bit about that of course that + + align:start position:0% +a little bit about that of course that + + + align:start position:0% +a little bit about that of course that +is an issue that will play out with sort + + align:start position:0% +is an issue that will play out with sort + + + align:start position:0% +is an issue that will play out with sort +of it'll affect how other issues are + + align:start position:0% +of it'll affect how other issues are + + + align:start position:0% +of it'll affect how other issues are +faced and dealt with one other issue is + + align:start position:0% +faced and dealt with one other issue is + + + align:start position:0% +faced and dealt with one other issue is +do we raise base fares or do we change + + align:start position:0% +do we raise base fares or do we change + + + align:start position:0% +do we raise base fares or do we change +the relative cost of passes and + + align:start position:0% +the relative cost of passes and + + + align:start position:0% +the relative cost of passes and +discounted fare products so if a base + + align:start position:0% +discounted fare products so if a base + + + align:start position:0% +discounted fare products so if a base +fare is $2 you might have you know a 50% + + align:start position:0% +fare is $2 you might have you know a 50% + + + align:start position:0% +fare is $2 you might have you know a 50% +subsidy for seniors and you might have + + align:start position:0% +subsidy for seniors and you might have + + + align:start position:0% +subsidy for seniors and you might have +some other discounts for students or + + align:start position:0% +some other discounts for students or + + + align:start position:0% +some other discounts for students or +other groups you might also have passes + + align:start position:0% +other groups you might also have passes + + + align:start position:0% +other groups you might also have passes +like a weekly pass which if you take + + align:start position:0% +like a weekly pass which if you take + + + align:start position:0% +like a weekly pass which if you take +some number of trips you break even and + + align:start position:0% +some number of trips you break even and + + + align:start position:0% +some number of trips you break even and +after that you're right free so you + + align:start position:0% +after that you're right free so you + + + align:start position:0% +after that you're right free so you +might actually leave the base fare the + + align:start position:0% +might actually leave the base fare the + + + align:start position:0% +might actually leave the base fare the +same and change though the percentages + + align:start position:0% +same and change though the percentages + + + align:start position:0% +same and change though the percentages +of subsidy or + + align:start position:0% +of subsidy or + + + align:start position:0% +of subsidy or +discounts or the break-even point of a + + align:start position:0% +discounts or the break-even point of a + + + align:start position:0% +discounts or the break-even point of a +pass and that can affect fair revenues + + align:start position:0% +pass and that can affect fair revenues + + + align:start position:0% +pass and that can affect fair revenues +it can affect ridership and it can + + align:start position:0% +it can affect ridership and it can + + + align:start position:0% +it can affect ridership and it can +affect people's choice of fare product + + align:start position:0% +affect people's choice of fare product + + + align:start position:0% +affect people's choice of fare product +so you might bump people towards not + + align:start position:0% +so you might bump people towards not + + + align:start position:0% +so you might bump people towards not +setting letting letting go of fair + + align:start position:0% +setting letting letting go of fair + + + align:start position:0% +setting letting letting go of fair +passes and opting to do pay-as-you-go + + align:start position:0% +passes and opting to do pay-as-you-go + + + align:start position:0% +passes and opting to do pay-as-you-go +more often or the other way around + + align:start position:0% +more often or the other way around + + + align:start position:0% +more often or the other way around +and that has implications on how people + + align:start position:0% +and that has implications on how people + + + align:start position:0% +and that has implications on how people +think about the transit system how much + + align:start position:0% +think about the transit system how much + + + align:start position:0% +think about the transit system how much +it costs for them for a pass holder of + + align:start position:0% +it costs for them for a pass holder of + + + align:start position:0% +it costs for them for a pass holder of +course once they've paid for it it's + + align:start position:0% +course once they've paid for it it's + + + align:start position:0% +course once they've paid for it it's +kind of a non salient expense right so + + align:start position:0% +kind of a non salient expense right so + + + align:start position:0% +kind of a non salient expense right so +you you don't think about it every time + + align:start position:0% +you you don't think about it every time + + + align:start position:0% +you you don't think about it every time +you are tapping as much as having value + + align:start position:0% +you are tapping as much as having value + + + align:start position:0% +you are tapping as much as having value +deducted from the card every time so + + align:start position:0% +deducted from the card every time so + + + align:start position:0% +deducted from the card every time so +those people might ride + + align:start position:0% +those people might ride + + + align:start position:0% +those people might ride +opportunistically because they've + + align:start position:0% +opportunistically because they've + + + align:start position:0% +opportunistically because they've +already paid for it and they might do + + align:start position:0% +already paid for it and they might do + + + align:start position:0% +already paid for it and they might do +shorter trips discretionary trips more + + align:start position:0% +shorter trips discretionary trips more + + + align:start position:0% +shorter trips discretionary trips more +so than someone who is paying every fare + + align:start position:0% +so than someone who is paying every fare + + + align:start position:0% +so than someone who is paying every fare +independently and another big issue is + + align:start position:0% +independently and another big issue is + + + align:start position:0% +independently and another big issue is +investing in nuclear technology that's a + + align:start position:0% +investing in nuclear technology that's a + + + align:start position:0% +investing in nuclear technology that's a +headache so big a headache you can + + align:start position:0% +headache so big a headache you can + + + align:start position:0% +headache so big a headache you can +imagine changing the way that all the + + align:start position:0% +imagine changing the way that all the + + + align:start position:0% +imagine changing the way that all the +technology although analytics and + + align:start position:0% +technology although analytics and + + + align:start position:0% +technology although analytics and +administration depends on a certain + + align:start position:0% +administration depends on a certain + + + align:start position:0% +administration depends on a certain +system and bringing in a new system that + + align:start position:0% +system and bringing in a new system that + + + align:start position:0% +system and bringing in a new system that +nobody understands yet might work or not + + align:start position:0% +nobody understands yet might work or not + + + align:start position:0% +nobody understands yet might work or not +so all the maintenance needs to be + + align:start position:0% +so all the maintenance needs to be + + + align:start position:0% +so all the maintenance needs to be +figured out and you have to communicate + + align:start position:0% +figured out and you have to communicate + + + align:start position:0% +figured out and you have to communicate +with the public about what impact that + + align:start position:0% +with the public about what impact that + + + align:start position:0% +with the public about what impact that +has on them and that could involve + + align:start position:0% +has on them and that could involve + + + align:start position:0% +has on them and that could involve +changes in the fare structure not just + + align:start position:0% +changes in the fare structure not just + + + align:start position:0% +changes in the fare structure not just +the technology so sometimes technology + + align:start position:0% +the technology so sometimes technology + + + align:start position:0% +the technology so sometimes technology +enables new fare structures or new fare + + align:start position:0% +enables new fare structures or new fare + + + align:start position:0% +enables new fare structures or new fare +policies and let them be one of the + + align:start position:0% +policies and let them be one of the + + + align:start position:0% +policies and let them be one of the +reasons for bringing new technology + + align:start position:0% +reasons for bringing new technology + + + align:start position:0% +reasons for bringing new technology +questions on the issues + + align:start position:0% + + + + align:start position:0% + +can you give me an example I'm not sure + + align:start position:0% +can you give me an example I'm not sure + + + align:start position:0% +can you give me an example I'm not sure +I follow the question so right sometimes + + align:start position:0% +I follow the question so right sometimes + + + align:start position:0% +I follow the question so right sometimes +the public sector is the one so if you + + align:start position:0% +the public sector is the one so if you + + + align:start position:0% +the public sector is the one so if you +look at the case of London for example + + align:start position:0% +look at the case of London for example + + + align:start position:0% +look at the case of London for example +even though buses are operated by + + align:start position:0% +even though buses are operated by + + + align:start position:0% +even though buses are operated by +private companies and they are in some + + align:start position:0% +private companies and they are in some + + + align:start position:0% +private companies and they are in some +way it's a contract right so the fare + + align:start position:0% +way it's a contract right so the fare + + + align:start position:0% +way it's a contract right so the fare +policy is still set by TfL which is the + + align:start position:0% +policy is still set by TfL which is the + + + align:start position:0% +policy is still set by TfL which is the +government that's I think usually the + + align:start position:0% +government that's I think usually the + + + align:start position:0% +government that's I think usually the +case if you have a push for a unified + + align:start position:0% +case if you have a push for a unified + + + align:start position:0% +case if you have a push for a unified +single brand of the system if maybe in + + align:start position:0% +single brand of the system if maybe in + + + align:start position:0% +single brand of the system if maybe in +other countries thinking more of Latin + + align:start position:0% +other countries thinking more of Latin + + + align:start position:0% +other countries thinking more of Latin +America Africa there are sort of + + align:start position:0% +America Africa there are sort of + + + align:start position:0% +America Africa there are sort of +independent people running their own + + align:start position:0% +independent people running their own + + + align:start position:0% +independent people running their own +systems and those are usually cash based + + align:start position:0% +systems and those are usually cash based + + + align:start position:0% +systems and those are usually cash based +so there's no integration whatsoever + + align:start position:0% +so there's no integration whatsoever + + + align:start position:0% +so there's no integration whatsoever +maybe you have a different example + + align:start position:0% + + + + align:start position:0% + +I wonder if the type of contracts + + align:start position:0% +I wonder if the type of contracts + + + align:start position:0% +I wonder if the type of contracts +communication when you concession I mean + + align:start position:0% +communication when you concession I mean + + + align:start position:0% +communication when you concession I mean +there's a difference there's a Meredith + + align:start position:0% +there's a difference there's a Meredith + + + align:start position:0% +there's a difference there's a Meredith +right + + align:start position:0% + + + + align:start position:0% + +yeah I'm not sure frankly I'm not sure + + align:start position:0% +yeah I'm not sure frankly I'm not sure + + + align:start position:0% +yeah I'm not sure frankly I'm not sure +that the sort of the issues related to + + align:start position:0% +that the sort of the issues related to + + + align:start position:0% +that the sort of the issues related to +concessions in that case depend a lot on + + align:start position:0% +concessions in that case depend a lot on + + + align:start position:0% +concessions in that case depend a lot on +the contract structure so some + + align:start position:0% +the contract structure so some + + + align:start position:0% +the contract structure so some +concessions derive revenue from the fair + + align:start position:0% +concessions derive revenue from the fair + + + align:start position:0% +concessions derive revenue from the fair +I think that's not the best way of doing + + align:start position:0% +I think that's not the best way of doing + + + align:start position:0% +I think that's not the best way of doing +it but if that's how the contract is + + align:start position:0% +it but if that's how the contract is + + + align:start position:0% +it but if that's how the contract is +structure essentially you say I want you + + align:start position:0% +structure essentially you say I want you + + + align:start position:0% +structure essentially you say I want you +to operate you keep the fares then of + + align:start position:0% +to operate you keep the fares then of + + + align:start position:0% +to operate you keep the fares then of +course any fair question will affect + + align:start position:0% +course any fair question will affect + + + align:start position:0% +course any fair question will affect +revenues and if they're only getting + + align:start position:0% +revenues and if they're only getting + + + align:start position:0% +revenues and if they're only getting +well it'll affect ridership too so so + + align:start position:0% +well it'll affect ridership too so so + + + align:start position:0% +well it'll affect ridership too so so +the private operator will be interested + + align:start position:0% +the private operator will be interested + + + align:start position:0% +the private operator will be interested +in any kind of fare policy change that + + align:start position:0% +in any kind of fare policy change that + + + align:start position:0% +in any kind of fare policy change that +if that increases their revenues and + + align:start position:0% +if that increases their revenues and + + + align:start position:0% +if that increases their revenues and +will be disinterested in any fair ballsy + + align:start position:0% +will be disinterested in any fair ballsy + + + align:start position:0% +will be disinterested in any fair ballsy +change that that decreases the revenues + + align:start position:0% +change that that decreases the revenues + + + align:start position:0% +change that that decreases the revenues +or increases the risk of revenue anyway + + align:start position:0% +or increases the risk of revenue anyway + + + align:start position:0% +or increases the risk of revenue anyway +so that is probably a poisonous topic + + align:start position:0% +so that is probably a poisonous topic + + + align:start position:0% +so that is probably a poisonous topic +during the length of a contract and you + + align:start position:0% +during the length of a contract and you + + + align:start position:0% +during the length of a contract and you +won't have to then do it between + + align:start position:0% +won't have to then do it between + + + align:start position:0% +won't have to then do it between +contracts here I'm speculating right but + + align:start position:0% +contracts here I'm speculating right but + + + align:start position:0% +contracts here I'm speculating right but +I imagine this is the case where you pay + + align:start position:0% +I imagine this is the case where you pay + + + align:start position:0% +I imagine this is the case where you pay +to run by distance which is or you might + + align:start position:0% +to run by distance which is or you might + + + align:start position:0% +to run by distance which is or you might +have some performance standards as well + + align:start position:0% +have some performance standards as well + + + align:start position:0% +have some performance standards as well +but it's not fair so much so the + + align:start position:0% +but it's not fair so much so the + + + align:start position:0% +but it's not fair so much so the +government keeps the fares and then pay + + align:start position:0% +government keeps the fares and then pay + + + align:start position:0% +government keeps the fares and then pay +the operators the contracted amount then + + align:start position:0% +the operators the contracted amount then + + + align:start position:0% +the operators the contracted amount then +that towards freeze up the disconnects + + align:start position:0% +that towards freeze up the disconnects + + + align:start position:0% +that towards freeze up the disconnects +the operators performance from fair + + align:start position:0% +the operators performance from fair + + + align:start position:0% +the operators performance from fair +revenue and it allows the government or + + align:start position:0% +revenue and it allows the government or + + + align:start position:0% +revenue and it allows the government or +the planning agency to change the fare + + align:start position:0% +the planning agency to change the fare + + + align:start position:0% +the planning agency to change the fare +structure change fair technology in the + + align:start position:0% +structure change fair technology in the + + + align:start position:0% +structure change fair technology in the +middle of a contract and so we in the + + align:start position:0% +middle of a contract and so we in the + + + align:start position:0% +middle of a contract and so we in the +former case I imagine it's quite + + align:start position:0% +former case I imagine it's quite + + + align:start position:0% +former case I imagine it's quite +complicated because usually the + + align:start position:0% +complicated because usually the + + + align:start position:0% +complicated because usually the +contracts are not awarded on on cycle ie + + align:start position:0% +contracts are not awarded on on cycle ie + + + align:start position:0% +contracts are not awarded on on cycle ie +at a certain moment in time you might + + align:start position:0% +at a certain moment in time you might + + + align:start position:0% +at a certain moment in time you might +have a contract that expires next month + + align:start position:0% +have a contract that expires next month + + + align:start position:0% +have a contract that expires next month +another one that expires in a year + + align:start position:0% +another one that expires in a year + + + align:start position:0% +another one that expires in a year +another one that expires in five years + + align:start position:0% +another one that expires in five years + + + align:start position:0% +another one that expires in five years +so to implement the system why change it + + align:start position:0% +so to implement the system why change it + + + align:start position:0% +so to implement the system why change it +would be very difficult if if the + + align:start position:0% +would be very difficult if if the + + + align:start position:0% +would be very difficult if if the +contracts depend on on on the fair + + align:start position:0% +contracts depend on on on the fair + + + align:start position:0% +contracts depend on on on the fair +revenues yeah + + align:start position:0% + + + + align:start position:0% + +yeah we're gonna talk about market + + align:start position:0% +yeah we're gonna talk about market + + + align:start position:0% +yeah we're gonna talk about market +segmentation yeah yeah so that goes back + + align:start position:0% +segmentation yeah yeah so that goes back + + + align:start position:0% +segmentation yeah yeah so that goes back +to this sort of annually with inflation + + align:start position:0% +to this sort of annually with inflation + + + align:start position:0% +to this sort of annually with inflation +strategy where you just do it every year + + align:start position:0% +strategy where you just do it every year + + + align:start position:0% +strategy where you just do it every year +and it just happens on January 1st Yeah + + align:start position:0% +and it just happens on January 1st Yeah + + + align:start position:0% +and it just happens on January 1st Yeah +right right so and there are many other + + align:start position:0% +right right so and there are many other + + + align:start position:0% +right right so and there are many other +examples of that kind of approach I + + align:start position:0% +examples of that kind of approach I + + + align:start position:0% +examples of that kind of approach I +think it's more effective or frankly + + align:start position:0% +think it's more effective or frankly + + + align:start position:0% +think it's more effective or frankly +expenses go up every year so why not you + + align:start position:0% +expenses go up every year so why not you + + + align:start position:0% +expenses go up every year so why not you +know make communicate what the strategy + + align:start position:0% +know make communicate what the strategy + + + align:start position:0% +know make communicate what the strategy +is make it fair no pun intended and + + align:start position:0% +is make it fair no pun intended and + + + align:start position:0% +is make it fair no pun intended and +write and do it so + + align:start position:0% + + + + align:start position:0% + +yes so what we'll talk in market + + align:start position:0% +yes so what we'll talk in market + + + align:start position:0% +yes so what we'll talk in market +segmentation one of the things you might + + align:start position:0% +segmentation one of the things you might + + + align:start position:0% +segmentation one of the things you might +segment by is social dynamic status yeah + + align:start position:0% +segment by is social dynamic status yeah + + + align:start position:0% +segment by is social dynamic status yeah +and there's different ways of doing that + + align:start position:0% +and there's different ways of doing that + + + align:start position:0% +and there's different ways of doing that +so we can talk more about that when we + + align:start position:0% +so we can talk more about that when we + + + align:start position:0% +so we can talk more about that when we +get mr. salience II absolutely yeah + + align:start position:0% +get mr. salience II absolutely yeah + + + align:start position:0% +get mr. salience II absolutely yeah +especially if you go to passes or a + + align:start position:0% +especially if you go to passes or a + + + align:start position:0% +especially if you go to passes or a +capping scheme which we'll discuss so + + align:start position:0% +capping scheme which we'll discuss so + + + align:start position:0% +capping scheme which we'll discuss so +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +the more obscure you make the fare + + align:start position:0% +the more obscure you make the fare + + + align:start position:0% +the more obscure you make the fare +system the less of an impact that will + + align:start position:0% +system the less of an impact that will + + + align:start position:0% +system the less of an impact that will +have on demand response and that that is + + align:start position:0% +have on demand response and that that is + + + align:start position:0% +have on demand response and that that is +true in other you know in other areas + + align:start position:0% +true in other you know in other areas + + + align:start position:0% +true in other you know in other areas +right if you look at from a + + align:start position:0% +right if you look at from a + + + align:start position:0% +right if you look at from a +macroeconomic perspective that's true in + + align:start position:0% +macroeconomic perspective that's true in + + + align:start position:0% +macroeconomic perspective that's true in +business + + align:start position:0% +business + + + align:start position:0% +business +oh if people don't understand pricing + + align:start position:0% +oh if people don't understand pricing + + + align:start position:0% +oh if people don't understand pricing +then they're gonna it might be you might + + align:start position:0% +then they're gonna it might be you might + + + align:start position:0% +then they're gonna it might be you might +get a sort of lower reaction to changes + + align:start position:0% +get a sort of lower reaction to changes + + + align:start position:0% +get a sort of lower reaction to changes +in pricing right you make less of a fuss + + align:start position:0% +in pricing right you make less of a fuss + + + align:start position:0% +in pricing right you make less of a fuss +about it + + align:start position:0% + + + + align:start position:0% + +okay okay fare structure so market + + align:start position:0% +okay okay fare structure so market + + + align:start position:0% +okay okay fare structure so market +segmentation sort of we was a good segue + + align:start position:0% +segmentation sort of we was a good segue + + + align:start position:0% +segmentation sort of we was a good segue +with these questions so one issue one + + align:start position:0% +with these questions so one issue one + + + align:start position:0% +with these questions so one issue one +possible way of having a fair structures + + align:start position:0% +possible way of having a fair structures + + + align:start position:0% +possible way of having a fair structures +have a flat fare structure that's the + + align:start position:0% +have a flat fare structure that's the + + + align:start position:0% +have a flat fare structure that's the +simplest one it costs some amount to + + align:start position:0% +simplest one it costs some amount to + + + align:start position:0% +simplest one it costs some amount to +ride no matter what and no matter where + + align:start position:0% +ride no matter what and no matter where + + + align:start position:0% +ride no matter what and no matter where +from what time of day what mode that's + + align:start position:0% +from what time of day what mode that's + + + align:start position:0% +from what time of day what mode that's +the price so again that's the simplest I + + align:start position:0% +the price so again that's the simplest I + + + align:start position:0% +the price so again that's the simplest I +think most most agencies if you look at + + align:start position:0% +think most most agencies if you look at + + + align:start position:0% +think most most agencies if you look at +the profile of all agencies including + + align:start position:0% +the profile of all agencies including + + + align:start position:0% +the profile of all agencies including +small ones have that fare structure + + align:start position:0% +small ones have that fare structure + + + align:start position:0% +small ones have that fare structure +bigger agencies tend to have some market + + align:start position:0% +bigger agencies tend to have some market + + + align:start position:0% +bigger agencies tend to have some market +segmentation because they are bigger and + + align:start position:0% +segmentation because they are bigger and + + + align:start position:0% +segmentation because they are bigger and +they can they sort of servo a wider + + align:start position:0% +they can they sort of servo a wider + + + align:start position:0% +they can they sort of servo a wider +range of people they serve a wider + + align:start position:0% +range of people they serve a wider + + + align:start position:0% +range of people they serve a wider +geographic area and they have some + + align:start position:0% +geographic area and they have some + + + align:start position:0% +geographic area and they have some +congestion problems so how can we + + align:start position:0% +congestion problems so how can we + + + align:start position:0% +congestion problems so how can we +differentiate fair how can we segment to + + align:start position:0% +differentiate fair how can we segment to + + + align:start position:0% +differentiate fair how can we segment to +the market one especially so you could + + align:start position:0% +the market one especially so you could + + + align:start position:0% +the market one especially so you could +a flat Geographic structure where no + + align:start position:0% +a flat Geographic structure where no + + + align:start position:0% +a flat Geographic structure where no +matter where you write from it costs the + + align:start position:0% +matter where you write from it costs the + + + align:start position:0% +matter where you write from it costs the +same you could have zones so I'm here in + + align:start position:0% +same you could have zones so I'm here in + + + align:start position:0% +same you could have zones so I'm here in +Boston we have no zones for outside of + + align:start position:0% +Boston we have no zones for outside of + + + align:start position:0% +Boston we have no zones for outside of +commuter rail we have no zones if you go + + align:start position:0% +commuter rail we have no zones if you go + + + align:start position:0% +commuter rail we have no zones if you go +to London + + align:start position:0% +to London + + + align:start position:0% +to London +there's zones one through well the end + + align:start position:0% +there's zones one through well the end + + + align:start position:0% +there's zones one through well the end +one through nine but most of Greater + + align:start position:0% +one through nine but most of Greater + + + align:start position:0% +one through nine but most of Greater +London is in the first three about so so + + align:start position:0% +London is in the first three about so so + + + align:start position:0% +London is in the first three about so so +yeah so it costs more to cross zones + + align:start position:0% +yeah so it costs more to cross zones + + + align:start position:0% +yeah so it costs more to cross zones +than to write within its own and you can + + align:start position:0% +than to write within its own and you can + + + align:start position:0% +than to write within its own and you can +buy passes that are zone 1 zone 1 2 etc + + align:start position:0% +buy passes that are zone 1 zone 1 2 etc + + + align:start position:0% +buy passes that are zone 1 zone 1 2 etc +so that's one way of doing it if you + + align:start position:0% +so that's one way of doing it if you + + + align:start position:0% +so that's one way of doing it if you +take that to the extreme and imagine + + align:start position:0% +take that to the extreme and imagine + + + align:start position:0% +take that to the extreme and imagine +many many zones you could end up with + + align:start position:0% +many many zones you could end up with + + + align:start position:0% +many many zones you could end up with +something called distance based pricing + + align:start position:0% +something called distance based pricing + + + align:start position:0% +something called distance based pricing +where each OD pair has a different fare + + align:start position:0% +where each OD pair has a different fare + + + align:start position:0% +where each OD pair has a different fare +depending on how what how long that + + align:start position:0% +depending on how what how long that + + + align:start position:0% +depending on how what how long that +right was so you can do that if you have + + align:start position:0% +right was so you can do that if you have + + + align:start position:0% +right was so you can do that if you have +a tap in tap out system you can do that + + align:start position:0% +a tap in tap out system you can do that + + + align:start position:0% +a tap in tap out system you can do that +with proof of payment in some cases it's + + align:start position:0% +with proof of payment in some cases it's + + + align:start position:0% +with proof of payment in some cases it's +more common in Europe and regarding + + align:start position:0% +more common in Europe and regarding + + + align:start position:0% +more common in Europe and regarding +zones a lot of agencies have used to + + align:start position:0% +zones a lot of agencies have used to + + + align:start position:0% +zones a lot of agencies have used to +have more zones that are going for + + align:start position:0% +have more zones that are going for + + + align:start position:0% +have more zones that are going for +reducing zones and simplifying the + + align:start position:0% +reducing zones and simplifying the + + + align:start position:0% +reducing zones and simplifying the +system it's an interesting curious trend + + align:start position:0% +system it's an interesting curious trend + + + align:start position:0% +system it's an interesting curious trend +because they've been doing this at the + + align:start position:0% +because they've been doing this at the + + + align:start position:0% +because they've been doing this at the +same time that they've been investing in + + align:start position:0% +same time that they've been investing in + + + align:start position:0% +same time that they've been investing in +new fare technology that enables more + + align:start position:0% +new fare technology that enables more + + + align:start position:0% +new fare technology that enables more +complex various structures but it's a + + align:start position:0% +complex various structures but it's a + + + align:start position:0% +complex various structures but it's a +matter of a choice of communicating to + + align:start position:0% +matter of a choice of communicating to + + + align:start position:0% +matter of a choice of communicating to +the public and keeping it simple easier + + align:start position:0% +the public and keeping it simple easier + + + align:start position:0% +the public and keeping it simple easier +to understand + + align:start position:0% + + + + align:start position:0% + +you go around the entire city just in + + align:start position:0% +you go around the entire city just in + + + align:start position:0% +you go around the entire city just in +zone 2 but if you don't tap in the right + + align:start position:0% +zone 2 but if you don't tap in the right + + + align:start position:0% +zone 2 but if you don't tap in the right +way when you transfer trains or + + align:start position:0% +way when you transfer trains or + + + align:start position:0% +way when you transfer trains or +something I don't think you went into + + align:start position:0% +something I don't think you went into + + + align:start position:0% +something I don't think you went into +the city and how all right it's a lot + + align:start position:0% +the city and how all right it's a lot + + + align:start position:0% +the city and how all right it's a lot +cheaper to go Bailey than it is go right + + align:start position:0% +cheaper to go Bailey than it is go right + + + align:start position:0% +cheaper to go Bailey than it is go right +because you stay in one side and some + + align:start position:0% +because you stay in one side and some + + + align:start position:0% +because you stay in one side and some +ways yes yeah because they have a yeah + + align:start position:0% +ways yes yeah because they have a yeah + + + align:start position:0% +ways yes yeah because they have a yeah +they have many sort of things that have + + align:start position:0% +they have many sort of things that have + + + align:start position:0% +they have many sort of things that have +influence price so I don't know if + + align:start position:0% +influence price so I don't know if + + + align:start position:0% +influence price so I don't know if +you've had the experience of going to + + align:start position:0% +you've had the experience of going to + + + align:start position:0% +you've had the experience of going to +CRB and trying to figure out how much + + align:start position:0% +CRB and trying to figure out how much + + + align:start position:0% +CRB and trying to figure out how much +money to put on your smart trip card + + align:start position:0% +money to put on your smart trip card + + + align:start position:0% +money to put on your smart trip card +because it varies by time of day by how + + align:start position:0% +because it varies by time of day by how + + + align:start position:0% +because it varies by time of day by how +long you you are going to travel and you + + align:start position:0% +long you you are going to travel and you + + + align:start position:0% +long you you are going to travel and you +don't necessarily know that ahead of + + align:start position:0% +don't necessarily know that ahead of + + + align:start position:0% +don't necessarily know that ahead of +time so you end up loading every works + + align:start position:0% +time so you end up loading every works + + + align:start position:0% +time so you end up loading every works +on their favor I just blow it up you + + align:start position:0% +on their favor I just blow it up you + + + align:start position:0% +on their favor I just blow it up you +know 20 or 40 depending on I don't + + align:start position:0% +know 20 or 40 depending on I don't + + + align:start position:0% +know 20 or 40 depending on I don't +really figure out how much my rights + + align:start position:0% +really figure out how much my rights + + + align:start position:0% +really figure out how much my rights +will cost and put in just that amount so + + align:start position:0% +will cost and put in just that amount so + + + align:start position:0% +will cost and put in just that amount so +eventually maybe I'll lose my card and + + align:start position:0% +eventually maybe I'll lose my card and + + + align:start position:0% +eventually maybe I'll lose my card and +they keep the revenue so okay another oh + + align:start position:0% + + + + align:start position:0% + +it could be proof of payment as well not + + align:start position:0% +it could be proof of payment as well not + + + align:start position:0% +it could be proof of payment as well not +just check-in though so in you know in + + align:start position:0% +just check-in though so in you know in + + + align:start position:0% +just check-in though so in you know in +Europe you have some systems especially + + align:start position:0% +Europe you have some systems especially + + + align:start position:0% +Europe you have some systems especially +not necessarily it happens more + + align:start position:0% +not necessarily it happens more + + + align:start position:0% +not necessarily it happens more +intercity so you you buy a ticket for + + align:start position:0% +intercity so you you buy a ticket for + + + align:start position:0% +intercity so you you buy a ticket for +you know between this station in that + + align:start position:0% +you know between this station in that + + + align:start position:0% +you know between this station in that +station and you you have a paper ticket + + align:start position:0% +station and you you have a paper ticket + + + align:start position:0% +station and you you have a paper ticket +and you when you board you validate it + + align:start position:0% +and you when you board you validate it + + + align:start position:0% +and you when you board you validate it +so essentially you it gets cancelled + + align:start position:0% +so essentially you it gets cancelled + + + align:start position:0% +so essentially you it gets cancelled +with a time stamp and if a fare + + align:start position:0% +with a time stamp and if a fare + + + align:start position:0% +with a time stamp and if a fare +inspector comes you better have one + + align:start position:0% +inspector comes you better have one + + + align:start position:0% +inspector comes you better have one +otherwise you'll be heavily fined so + + align:start position:0% +otherwise you'll be heavily fined so + + + align:start position:0% +otherwise you'll be heavily fined so +that's one way of doing it + + align:start position:0% + + + + align:start position:0% + +any other questions okay + + align:start position:0% +any other questions okay + + + align:start position:0% +any other questions okay +temporal segmentation so that's pretty + + align:start position:0% +temporal segmentation so that's pretty + + + align:start position:0% +temporal segmentation so that's pretty +straightforward you get have a flat + + align:start position:0% +straightforward you get have a flat + + + align:start position:0% +straightforward you get have a flat +system where there is no change in fares + + align:start position:0% +system where there is no change in fares + + + align:start position:0% +system where there is no change in fares +across time of day and another one where + + align:start position:0% +across time of day and another one where + + + align:start position:0% +across time of day and another one where +you have a peak surcharge or an off-peak + + align:start position:0% +you have a peak surcharge or an off-peak + + + align:start position:0% +you have a peak surcharge or an off-peak +discount same thing two ways of + + align:start position:0% +discount same thing two ways of + + + align:start position:0% +discount same thing two ways of +marketing it most agencies prefer to + + align:start position:0% +marketing it most agencies prefer to + + + align:start position:0% +marketing it most agencies prefer to +offer a discount on + + align:start position:0% +offer a discount on + + + align:start position:0% +offer a discount on +of pic than to charge more during the + + align:start position:0% +of pic than to charge more during the + + + align:start position:0% +of pic than to charge more during the +peak but it's all psychological so what + + align:start position:0% +peak but it's all psychological so what + + + align:start position:0% +peak but it's all psychological so what +are the why would an agency be + + align:start position:0% +are the why would an agency be + + + align:start position:0% +are the why would an agency be +interested in doing this and what are + + align:start position:0% +interested in doing this and what are + + + align:start position:0% +interested in doing this and what are +the impacts + + align:start position:0% + + + + align:start position:0% + +they are hard okay so so nudging people + + align:start position:0% +they are hard okay so so nudging people + + + align:start position:0% +they are hard okay so so nudging people +who can who can do off-peak to do + + align:start position:0% +who can who can do off-peak to do + + + align:start position:0% +who can who can do off-peak to do +off-peak rather than during the peak + + align:start position:0% +off-peak rather than during the peak + + + align:start position:0% +off-peak rather than during the peak +what else + + align:start position:0% +what else + + + align:start position:0% +what else +any other ideas right so more + + align:start position:0% +any other ideas right so more + + + align:start position:0% +any other ideas right so more +discretionary trips right so encourage + + align:start position:0% +discretionary trips right so encourage + + + align:start position:0% +discretionary trips right so encourage +more off-peak ridership okay and why + + align:start position:0% +more off-peak ridership okay and why + + + align:start position:0% +more off-peak ridership okay and why +does it make sense to charge more during + + align:start position:0% +does it make sense to charge more during + + + align:start position:0% +does it make sense to charge more during +the peak them off-peak regardless of how + + align:start position:0% +the peak them off-peak regardless of how + + + align:start position:0% +the peak them off-peak regardless of how +you market it + + align:start position:0% + + + + align:start position:0% + +exactly + + align:start position:0% +exactly + + + align:start position:0% +exactly +so the willingness to pay is higher + + align:start position:0% +so the willingness to pay is higher + + + align:start position:0% +so the willingness to pay is higher +either because they are actually willing + + align:start position:0% +either because they are actually willing + + + align:start position:0% +either because they are actually willing +or because they are captured on time + + align:start position:0% +or because they are captured on time + + + align:start position:0% +or because they are captured on time +like they have to arrive at some time up + + align:start position:0% +like they have to arrive at some time up + + + align:start position:0% +like they have to arrive at some time up +to work so they don't have many options + + align:start position:0% +to work so they don't have many options + + + align:start position:0% +to work so they don't have many options +and that means that they're much less + + align:start position:0% +and that means that they're much less + + + align:start position:0% +and that means that they're much less +flexible and then their response will be + + align:start position:0% +flexible and then their response will be + + + align:start position:0% +flexible and then their response will be +much lower so any price change okay my + + align:start position:0% +much lower so any price change okay my + + + align:start position:0% +much lower so any price change okay my +service + + align:start position:0% +service + + + align:start position:0% +service +that's this pretty simple - you could + + align:start position:0% +that's this pretty simple - you could + + + align:start position:0% +that's this pretty simple - you could +charge the same for bus and rail or you + + align:start position:0% +charge the same for bus and rail or you + + + align:start position:0% +charge the same for bus and rail or you +could say rail is a better service so + + align:start position:0% +could say rail is a better service so + + + align:start position:0% +could say rail is a better service so +it's gonna be more expensive + + align:start position:0% +it's gonna be more expensive + + + align:start position:0% +it's gonna be more expensive +the MBTA has this option right regular + + align:start position:0% +the MBTA has this option right regular + + + align:start position:0% +the MBTA has this option right regular +bus versus Express bus another way in + + align:start position:0% +bus versus Express bus another way in + + + align:start position:0% +bus versus Express bus another way in +which the MBTA segments the market so + + align:start position:0% +which the MBTA segments the market so + + + align:start position:0% +which the MBTA segments the market so +the idea is if it's nicer service you + + align:start position:0% +the idea is if it's nicer service you + + + align:start position:0% +the idea is if it's nicer service you +pay more by socioeconomic status so + + align:start position:0% +pay more by socioeconomic status so + + + align:start position:0% +pay more by socioeconomic status so +students might get a discount seniors + + align:start position:0% +students might get a discount seniors + + + align:start position:0% +students might get a discount seniors +disabled may get a discount we have some + + align:start position:0% +disabled may get a discount we have some + + + align:start position:0% +disabled may get a discount we have some +rules here where seniors have to be + + align:start position:0% +rules here where seniors have to be + + + align:start position:0% +rules here where seniors have to be +offered half the base fare so that's one + + align:start position:0% +offered half the base fare so that's one + + + align:start position:0% +offered half the base fare so that's one +example of that so somebody can be + + align:start position:0% +example of that so somebody can be + + + align:start position:0% +example of that so somebody can be +mandated by the government and then + + align:start position:0% +mandated by the government and then + + + align:start position:0% +mandated by the government and then +there's social programs so there's + + align:start position:0% +there's social programs so there's + + + align:start position:0% +there's social programs so there's +different ways of doing that it could be + + align:start position:0% +different ways of doing that it could be + + + align:start position:0% +different ways of doing that it could be +a part of your participation in some + + align:start position:0% +a part of your participation in some + + + align:start position:0% +a part of your participation in some +social program it could also be a needs + + align:start position:0% +social program it could also be a needs + + + align:start position:0% +social program it could also be a needs +based subsidy where you essentially + + align:start position:0% +based subsidy where you essentially + + + align:start position:0% +based subsidy where you essentially +prove that you have a financial need and + + align:start position:0% +prove that you have a financial need and + + + align:start position:0% +prove that you have a financial need and +based on your need you give some amount + + align:start position:0% +based on your need you give some amount + + + align:start position:0% +based on your need you give some amount +of subsidy so that subsidy could be on + + align:start position:0% +of subsidy so that subsidy could be on + + + align:start position:0% +of subsidy so that subsidy could be on +or off you either have the subsidy or + + align:start position:0% +or off you either have the subsidy or + + + align:start position:0% +or off you either have the subsidy or +you don't or it could be depending on + + align:start position:0% +you don't or it could be depending on + + + align:start position:0% +you don't or it could be depending on +your need you have more or less subs + + align:start position:0% +your need you have more or less subs + + + align:start position:0% +your need you have more or less subs +that you're less subsidy and usually + + align:start position:0% +that you're less subsidy and usually + + + align:start position:0% +that you're less subsidy and usually +it's the simpler one I don't actually + + align:start position:0% +it's the simpler one I don't actually + + + align:start position:0% +it's the simpler one I don't actually +know if any one example and that is done + + align:start position:0% +know if any one example and that is done + + + align:start position:0% +know if any one example and that is done +based on your specific case but you + + align:start position:0% +based on your specific case but you + + + align:start position:0% +based on your specific case but you +could think of doing it that way because + + align:start position:0% +could think of doing it that way because + + + align:start position:0% +could think of doing it that way because +if somebody is you know sort of very + + align:start position:0% +if somebody is you know sort of very + + + align:start position:0% +if somebody is you know sort of very +very poor then they might want more they + + align:start position:0% +very poor then they might want more they + + + align:start position:0% +very poor then they might want more they +might need more subsidy than somebody + + align:start position:0% +might need more subsidy than somebody + + + align:start position:0% +might need more subsidy than somebody +who was just to be a little poverty line + + align:start position:0% + + + + align:start position:0% + +that is usually the logic so yeah it's + + align:start position:0% +that is usually the logic so yeah it's + + + align:start position:0% +that is usually the logic so yeah it's +so it's again it's sort of social equity + + align:start position:0% +so it's again it's sort of social equity + + + align:start position:0% +so it's again it's sort of social equity +goal so seniors and students often can't + + align:start position:0% +goal so seniors and students often can't + + + align:start position:0% +goal so seniors and students often can't +drive etc so sorry goals of a transit + + align:start position:0% +drive etc so sorry goals of a transit + + + align:start position:0% +drive etc so sorry goals of a transit +agency a transit provider to to increase + + align:start position:0% +agency a transit provider to to increase + + + align:start position:0% +agency a transit provider to to increase +mobility for all groups of people way in + + align:start position:0% +mobility for all groups of people way in + + + align:start position:0% +mobility for all groups of people way in +which that goal is satisfied Henry + + align:start position:0% + + + + align:start position:0% + +yeah so yeah no no I I do have that in + + align:start position:0% +yeah so yeah no no I I do have that in + + + align:start position:0% +yeah so yeah no no I I do have that in +you know in another lecture yeah + + align:start position:0% +you know in another lecture yeah + + + align:start position:0% +you know in another lecture yeah +because that is done for people often + + align:start position:0% +because that is done for people often + + + align:start position:0% +because that is done for people often +they are employee employees who have a + + align:start position:0% +they are employee employees who have a + + + align:start position:0% +they are employee employees who have a +decent salary so that's all that's an + + align:start position:0% +decent salary so that's all that's an + + + align:start position:0% +decent salary so that's all that's an +incentive and that incentive exists for + + align:start position:0% +incentive and that incentive exists for + + + align:start position:0% +incentive and that incentive exists for +car as well so it's that's a different + + align:start position:0% +car as well so it's that's a different + + + align:start position:0% +car as well so it's that's a different +strategy another way of segmenting is + + align:start position:0% +strategy another way of segmenting is + + + align:start position:0% +strategy another way of segmenting is +like willingness to prepay so in other + + align:start position:0% +like willingness to prepay so in other + + + align:start position:0% +like willingness to prepay so in other +words are you willing to buy a pass so + + align:start position:0% +words are you willing to buy a pass so + + + align:start position:0% +words are you willing to buy a pass so +if you can buy if you can commit to a + + align:start position:0% +if you can buy if you can commit to a + + + align:start position:0% +if you can buy if you can commit to a +whole month then you get some discount + + align:start position:0% +whole month then you get some discount + + + align:start position:0% +whole month then you get some discount +and this depends heavily on what the + + align:start position:0% +and this depends heavily on what the + + + align:start position:0% +and this depends heavily on what the +break-even point is usually passes it + + align:start position:0% +break-even point is usually passes it + + + align:start position:0% +break-even point is usually passes it +used to be the case that passes had + + align:start position:0% +used to be the case that passes had + + + align:start position:0% +used to be the case that passes had +heavy discount so if you even without + + align:start position:0% +heavy discount so if you even without + + + align:start position:0% +heavy discount so if you even without +having a commute two times a week for + + align:start position:0% +having a commute two times a week for + + + align:start position:0% +having a commute two times a week for +five days you would still get a discount + + align:start position:0% +five days you would still get a discount + + + align:start position:0% +five days you would still get a discount +now it tends to be much it does require + + align:start position:0% +now it tends to be much it does require + + + align:start position:0% +now it tends to be much it does require +sometimes between two and three trips + + align:start position:0% +sometimes between two and three trips + + + align:start position:0% +sometimes between two and three trips +daily to get that break-even point some + + align:start position:0% +daily to get that break-even point some + + + align:start position:0% +daily to get that break-even point some +people still decide to go with that + + align:start position:0% +people still decide to go with that + + + align:start position:0% +people still decide to go with that +because it's more convenient it's less + + align:start position:0% +because it's more convenient it's less + + + align:start position:0% +because it's more convenient it's less +salient so it's yeah it's another way of + + align:start position:0% +salient so it's yeah it's another way of + + + align:start position:0% +salient so it's yeah it's another way of +discriminating or segmenting the market + + align:start position:0% +discriminating or segmenting the market + + + align:start position:0% +discriminating or segmenting the market +any questions on market segmentation + + align:start position:0% +any questions on market segmentation + + + align:start position:0% +any questions on market segmentation +yeah + + align:start position:0% + + + + align:start position:0% + +yeah it depends so it could be that the + + align:start position:0% +yeah it depends so it could be that the + + + align:start position:0% +yeah it depends so it could be that the +agency has a mandate well they have to + + align:start position:0% +agency has a mandate well they have to + + + align:start position:0% +agency has a mandate well they have to +do this that is often the model from an + + align:start position:0% +do this that is often the model from an + + + align:start position:0% +do this that is often the model from an +agency's perspective it would be much + + align:start position:0% +agency's perspective it would be much + + + align:start position:0% +agency's perspective it would be much +preferable to have the subsidy come from + + align:start position:0% +preferable to have the subsidy come from + + + align:start position:0% +preferable to have the subsidy come from +someone else because then that would + + align:start position:0% +someone else because then that would + + + align:start position:0% +someone else because then that would +allow the agency to focus on operating + + align:start position:0% +allow the agency to focus on operating + + + align:start position:0% +allow the agency to focus on operating +it would set fares to what it needs for + + align:start position:0% +it would set fares to what it needs for + + + align:start position:0% +it would set fares to what it needs for +to cover operational expenses and then + + align:start position:0% +to cover operational expenses and then + + + align:start position:0% +to cover operational expenses and then +if it's a social program well why isn't + + align:start position:0% +if it's a social program well why isn't + + + align:start position:0% +if it's a social program well why isn't +that social program provide the subsidy + + align:start position:0% +that social program provide the subsidy + + + align:start position:0% +that social program provide the subsidy +if it's you know if it's disabled maybe + + align:start position:0% +if it's you know if it's disabled maybe + + + align:start position:0% +if it's you know if it's disabled maybe +there's some some other government + + align:start position:0% +there's some some other government + + + align:start position:0% +there's some some other government +entity that can provide that subsidy for + + align:start position:0% +entity that can provide that subsidy for + + + align:start position:0% +entity that can provide that subsidy for +students why not you know the schools or + + align:start position:0% +students why not you know the schools or + + + align:start position:0% +students why not you know the schools or +the Department of Education so that's + + align:start position:0% +the Department of Education so that's + + + align:start position:0% +the Department of Education so that's +that's an interesting sort of policy in + + align:start position:0% +that's an interesting sort of policy in + + + align:start position:0% +that's an interesting sort of policy in +debate and we could talk about it for a + + align:start position:0% +debate and we could talk about it for a + + + align:start position:0% +debate and we could talk about it for a +long time because some people are very + + align:start position:0% +long time because some people are very + + + align:start position:0% +long time because some people are very +much against it and some people think + + align:start position:0% +much against it and some people think + + + align:start position:0% +much against it and some people think +that's a good idea so + + align:start position:0% + + + + align:start position:0% + +to prevent fraud right yeah yeah so + + align:start position:0% +to prevent fraud right yeah yeah so + + + align:start position:0% +to prevent fraud right yeah yeah so +smart cards smart carts are helpful with + + align:start position:0% +smart cards smart carts are helpful with + + + align:start position:0% +smart cards smart carts are helpful with +that because you can embed the transit + + align:start position:0% +that because you can embed the transit + + + align:start position:0% +that because you can embed the transit +chip into a student card for example and + + align:start position:0% +chip into a student card for example and + + + align:start position:0% +chip into a student card for example and +that's what we have here at MIT okay + + align:start position:0% +that's what we have here at MIT okay + + + align:start position:0% +that's what we have here at MIT okay +fair elasticity's so range from negative + + align:start position:0% +fair elasticity's so range from negative + + + align:start position:0% +fair elasticity's so range from negative +one to zero we know that demands of + + align:start position:0% +one to zero we know that demands of + + + align:start position:0% +one to zero we know that demands of +transit is inelastic right so it means + + align:start position:0% +transit is inelastic right so it means + + + align:start position:0% +transit is inelastic right so it means +that often well almost always virtually + + align:start position:0% +that often well almost always virtually + + + align:start position:0% +that often well almost always virtually +in every case if you raise fares you + + align:start position:0% +in every case if you raise fares you + + + align:start position:0% +in every case if you raise fares you +increase your revenue and your writer + + align:start position:0% +increase your revenue and your writer + + + align:start position:0% +increase your revenue and your writer +should be created not by too much and by + + align:start position:0% +should be created not by too much and by + + + align:start position:0% +should be created not by too much and by +so much that your favorite needs go down + + align:start position:0% +so much that your favorite needs go down + + + align:start position:0% +so much that your favorite needs go down +so here are some examples of typical + + align:start position:0% +so here are some examples of typical + + + align:start position:0% +so here are some examples of typical +Estes cities they usually are closer to + + align:start position:0% +Estes cities they usually are closer to + + + align:start position:0% +Estes cities they usually are closer to +negative point three and I got two point + + align:start position:0% +negative point three and I got two point + + + align:start position:0% +negative point three and I got two point +four for rail it's a little less so when + + align:start position:0% +four for rail it's a little less so when + + + align:start position:0% +four for rail it's a little less so when +I go to point 2 negative point 15 for + + align:start position:0% +I go to point 2 negative point 15 for + + + align:start position:0% +I go to point 2 negative point 15 for +off-peak it tends to be twice as much + + align:start position:0% +off-peak it tends to be twice as much + + + align:start position:0% +off-peak it tends to be twice as much +because more trips are discretionary for + + align:start position:0% +because more trips are discretionary for + + + align:start position:0% +because more trips are discretionary for +work trips it tends to be much more + + align:start position:0% +work trips it tends to be much more + + + align:start position:0% +work trips it tends to be much more +inelastic as we discussed so even half + + align:start position:0% +inelastic as we discussed so even half + + + align:start position:0% +inelastic as we discussed so even half +of a base one and there's something + + align:start position:0% +of a base one and there's something + + + align:start position:0% +of a base one and there's something +interesting that is maybe not as + + align:start position:0% +interesting that is maybe not as + + + align:start position:0% +interesting that is maybe not as +important anymore but I wanted to add it + + align:start position:0% +important anymore but I wanted to add it + + + align:start position:0% +important anymore but I wanted to add it +here there is a higher demand for free + + align:start position:0% +here there is a higher demand for free + + + align:start position:0% +here there is a higher demand for free +transit than there is for very very + + align:start position:0% +transit than there is for very very + + + align:start position:0% +transit than there is for very very +cheap transit even if you have to pay + + align:start position:0% +cheap transit even if you have to pay + + + align:start position:0% +cheap transit even if you have to pay +say a cent to bring it to to really get + + align:start position:0% +say a cent to bring it to to really get + + + align:start position:0% +say a cent to bring it to to really get +to the extreme the simplicity of not + + align:start position:0% +to the extreme the simplicity of not + + + align:start position:0% +to the extreme the simplicity of not +having to deal with paying fares not + + align:start position:0% +having to deal with paying fares not + + + align:start position:0% +having to deal with paying fares not +having to interact with a fair system + + align:start position:0% +having to interact with a fair system + + + align:start position:0% +having to interact with a fair system +and the from the marketing point of view + + align:start position:0% +and the from the marketing point of view + + + align:start position:0% +and the from the marketing point of view +oh it's free you can just take it + + align:start position:0% +oh it's free you can just take it + + + align:start position:0% +oh it's free you can just take it +whenever you don't have to be ready to + + align:start position:0% +whenever you don't have to be ready to + + + align:start position:0% +whenever you don't have to be ready to +take it then that sort of drives demand + + align:start position:0% +take it then that sort of drives demand + + + align:start position:0% +take it then that sort of drives demand +up so that's that's an interesting + + align:start position:0% +up so that's that's an interesting + + + align:start position:0% +up so that's that's an interesting +finding a lot of agencies have moved + + align:start position:0% +finding a lot of agencies have moved + + + align:start position:0% +finding a lot of agencies have moved +away from that because these are usually + + align:start position:0% +away from that because these are usually + + + align:start position:0% +away from that because these are usually +smaller agencies but of course + + align:start position:0% +smaller agencies but of course + + + align:start position:0% +smaller agencies but of course +operational costs increase and at some + + align:start position:0% +operational costs increase and at some + + + align:start position:0% +operational costs increase and at some +point you need to cover them somehow so + + align:start position:0% +point you need to cover them somehow so + + + align:start position:0% +point you need to cover them somehow so +right so that means these in an elastic + + align:start position:0% +right so that means these in an elastic + + + align:start position:0% +right so that means these in an elastic +the values mean that raising fares are + + align:start position:0% +the values mean that raising fares are + + + align:start position:0% +the values mean that raising fares are +an effective way of increasing revenues + + align:start position:0% +an effective way of increasing revenues + + + align:start position:0% +an effective way of increasing revenues +right + + align:start position:0% +right + + + align:start position:0% +right +not so much to increase the amount + + align:start position:0% +not so much to increase the amount + + + align:start position:0% +not so much to increase the amount +though sometimes + + align:start position:0% +though sometimes + + + align:start position:0% +though sometimes +some aspects of fear policy are changed + + align:start position:0% +some aspects of fear policy are changed + + + align:start position:0% +some aspects of fear policy are changed +to increase demand you know you're gonna + + align:start position:0% +to increase demand you know you're gonna + + + align:start position:0% +to increase demand you know you're gonna +get a small response to that from a + + align:start position:0% +get a small response to that from a + + + align:start position:0% +get a small response to that from a +microeconomics perspectives all right + + align:start position:0% +microeconomics perspectives all right + + + align:start position:0% +microeconomics perspectives all right +you should if you think about market + + align:start position:0% +you should if you think about market + + + align:start position:0% +you should if you think about market +segmentation and running transit like a + + align:start position:0% +segmentation and running transit like a + + + align:start position:0% +segmentation and running transit like a +business then you would want to charge + + align:start position:0% +business then you would want to charge + + + align:start position:0% +business then you would want to charge +more for longer trips trips and more + + align:start position:0% +more for longer trips trips and more + + + align:start position:0% +more for longer trips trips and more +convenient reliable comfortable and + + align:start position:0% +convenient reliable comfortable and + + + align:start position:0% +convenient reliable comfortable and +frequent modes peak period trips trips + + align:start position:0% +frequent modes peak period trips trips + + + align:start position:0% +frequent modes peak period trips trips +where other modes are inconvenient or + + align:start position:0% +where other modes are inconvenient or + + + align:start position:0% +where other modes are inconvenient or +costly therefore this is the best option + + align:start position:0% +costly therefore this is the best option + + + align:start position:0% +costly therefore this is the best option +why not charge more for it and trips + + align:start position:0% +why not charge more for it and trips + + + align:start position:0% +why not charge more for it and trips +subsidized by third parties because then + + align:start position:0% +subsidized by third parties because then + + + align:start position:0% +subsidized by third parties because then +you could capture some of the increased + + align:start position:0% +you could capture some of the increased + + + align:start position:0% +you could capture some of the increased +fare from an outside source right so of + + align:start position:0% +fare from an outside source right so of + + + align:start position:0% +fare from an outside source right so of +course not everybody would agree that + + align:start position:0% +course not everybody would agree that + + + align:start position:0% +course not everybody would agree that +this is what agency should do but if you + + align:start position:0% +this is what agency should do but if you + + + align:start position:0% +this is what agency should do but if you +were thinking of running an eensy it's a + + align:start position:0% +were thinking of running an eensy it's a + + + align:start position:0% +were thinking of running an eensy it's a +business this is exactly what you want + + align:start position:0% +business this is exactly what you want + + + align:start position:0% +business this is exactly what you want +if you have more willingness to pay for + + align:start position:0% +if you have more willingness to pay for + + + align:start position:0% +if you have more willingness to pay for +whatever reason your fare is higher and + + align:start position:0% +whatever reason your fare is higher and + + + align:start position:0% +whatever reason your fare is higher and +that means that fair revenues go up and + + align:start position:0% +that means that fair revenues go up and + + + align:start position:0% +that means that fair revenues go up and +your fare recovery ratio goes up and + + align:start position:0% +your fare recovery ratio goes up and + + + align:start position:0% +your fare recovery ratio goes up and +that means you can operate more service + + align:start position:0% +that means you can operate more service + + + align:start position:0% +that means you can operate more service +or you can operate more reliably or you + + align:start position:0% +or you can operate more reliably or you + + + align:start position:0% +or you can operate more reliably or you +can get nicer vehicles etc right right + + align:start position:0% +can get nicer vehicles etc right right + + + align:start position:0% +can get nicer vehicles etc right right +so transfer pricing and policy + + align:start position:0% +so transfer pricing and policy + + + align:start position:0% +so transfer pricing and policy +another issue some agencies don't have + + align:start position:0% +another issue some agencies don't have + + + align:start position:0% +another issue some agencies don't have +any sort of integration between rights + + align:start position:0% +any sort of integration between rights + + + align:start position:0% +any sort of integration between rights +so every time you board a vehicle you + + align:start position:0% +so every time you board a vehicle you + + + align:start position:0% +so every time you board a vehicle you +pay a full fare and there's no free + + align:start position:0% +pay a full fare and there's no free + + + align:start position:0% +pay a full fare and there's no free +transfer some agencies have a reduced + + align:start position:0% +transfer some agencies have a reduced + + + align:start position:0% +transfer some agencies have a reduced +price transfer or a free transfer and + + align:start position:0% +price transfer or a free transfer and + + + align:start position:0% +price transfer or a free transfer and +free transfers can be done in different + + align:start position:0% +free transfers can be done in different + + + align:start position:0% +free transfers can be done in different +ways one of the most common ways is to + + align:start position:0% +ways one of the most common ways is to + + + align:start position:0% +ways one of the most common ways is to +have a time-based + + align:start position:0% +have a time-based + + + align:start position:0% +have a time-based +free transfer so you tap and you get say + + align:start position:0% +free transfer so you tap and you get say + + + align:start position:0% +free transfer so you tap and you get say +an hour in two hours + + align:start position:0% +an hour in two hours + + + align:start position:0% +an hour in two hours +- you get two hours a free transit + + align:start position:0% +- you get two hours a free transit + + + align:start position:0% +- you get two hours a free transit +starting from that point so if you board + + align:start position:0% +starting from that point so if you board + + + align:start position:0% +starting from that point so if you board +if you transfer you'll presumably be in + + align:start position:0% +if you transfer you'll presumably be in + + + align:start position:0% +if you transfer you'll presumably be in +this two-hour window and the next time + + align:start position:0% +this two-hour window and the next time + + + align:start position:0% +this two-hour window and the next time +you tap it'll be a free transfer here in + + align:start position:0% +you tap it'll be a free transfer here in + + + align:start position:0% +you tap it'll be a free transfer here in +the MBTA the price is higher for rail + + align:start position:0% +the MBTA the price is higher for rail + + + align:start position:0% +the MBTA the price is higher for rail +and bus so if you transfer from bus to + + align:start position:0% +and bus so if you transfer from bus to + + + align:start position:0% +and bus so if you transfer from bus to +rail you pay the difference you transfer + + align:start position:0% +rail you pay the difference you transfer + + + align:start position:0% +rail you pay the difference you transfer +from rail to bus both is free + + align:start position:0% +from rail to bus both is free + + + align:start position:0% +from rail to bus both is free +interestingly with this time-based rule + + align:start position:0% +interestingly with this time-based rule + + + align:start position:0% +interestingly with this time-based rule +you can often do something very quickly + + align:start position:0% +you can often do something very quickly + + + align:start position:0% +you can often do something very quickly +and return and these are actually two + + align:start position:0% +and return and these are actually two + + + align:start position:0% +and return and these are actually two +different trips and you would still get + + align:start position:0% +different trips and you would still get + + + align:start position:0% +different trips and you would still get +you know a free return trip and it's not + + align:start position:0% +you know a free return trip and it's not + + + align:start position:0% +you know a free return trip and it's not +a transfer so with more complex fare + + align:start position:0% +a transfer so with more complex fare + + + align:start position:0% +a transfer so with more complex fare +rules you could say you should get free + + align:start position:0% +rules you could say you should get free + + + align:start position:0% +rules you could say you should get free +transfers within this window but not if + + align:start position:0% +transfers within this window but not if + + + align:start position:0% +transfers within this window but not if +you are on the same bus route or if you + + align:start position:0% +you are on the same bus route or if you + + + align:start position:0% +you are on the same bus route or if you +are tapping into the same station or + + align:start position:0% +are tapping into the same station or + + + align:start position:0% +are tapping into the same station or +things like this you could think of the + + align:start position:0% +things like this you could think of the + + + align:start position:0% +things like this you could think of the +rules though used for transfer inference + + align:start position:0% +rules though used for transfer inference + + + align:start position:0% +rules though used for transfer inference +and we discussed all the exit entrance + + align:start position:0% +and we discussed all the exit entrance + + + align:start position:0% +and we discussed all the exit entrance +these are not fare transfers those were + + align:start position:0% +these are not fare transfers those were + + + align:start position:0% +these are not fare transfers those were +two logical trip transfers and you could + + align:start position:0% +two logical trip transfers and you could + + + align:start position:0% +two logical trip transfers and you could +apply those rules you could put them + + align:start position:0% +apply those rules you could put them + + + align:start position:0% +apply those rules you could put them +into a fare engine and not give free + + align:start position:0% +into a fare engine and not give free + + + align:start position:0% +into a fare engine and not give free +transfers when it's not a transfer + + align:start position:0% +transfers when it's not a transfer + + + align:start position:0% +transfers when it's not a transfer +okay pays ego passes and capping okay + + align:start position:0% +okay pays ego passes and capping okay + + + align:start position:0% +okay pays ego passes and capping okay +one question before we Daniel yeah + + align:start position:0% + + + + align:start position:0% + +right usually don't have to because they + + align:start position:0% +right usually don't have to because they + + + align:start position:0% +right usually don't have to because they +sub the window wide enough so that you + + align:start position:0% +sub the window wide enough so that you + + + align:start position:0% +sub the window wide enough so that you +can get your your whole three trip three + + align:start position:0% +can get your your whole three trip three + + + align:start position:0% +can get your your whole three trip three +leg trip done and that two-hour window + + align:start position:0% +leg trip done and that two-hour window + + + align:start position:0% +leg trip done and that two-hour window +oh I think you could in theory I think + + align:start position:0% +oh I think you could in theory I think + + + align:start position:0% +oh I think you could in theory I think +you could go through customer service + + align:start position:0% +you could go through customer service + + + align:start position:0% +you could go through customer service +and say this was a transfer your policy + + align:start position:0% +and say this was a transfer your policy + + + align:start position:0% +and say this was a transfer your policy +is free transfers you need to give me + + align:start position:0% +is free transfers you need to give me + + + align:start position:0% +is free transfers you need to give me +the you know you need to refund me yeah + + align:start position:0% +the you know you need to refund me yeah + + + align:start position:0% +the you know you need to refund me yeah +yeah yeah I don't know the details of it + + align:start position:0% +yeah yeah I don't know the details of it + + + align:start position:0% +yeah yeah I don't know the details of it +but I imagine that's the case now you + + align:start position:0% +but I imagine that's the case now you + + + align:start position:0% +but I imagine that's the case now you +could argue the server refund okay I + + align:start position:0% +could argue the server refund okay I + + + align:start position:0% +could argue the server refund okay I +haven't clearly probably be very + + align:start position:0% +haven't clearly probably be very + + + align:start position:0% +haven't clearly probably be very +interesting actually any other questions + + align:start position:0% +interesting actually any other questions + + + align:start position:0% +interesting actually any other questions +on transfers transfers are more of an + + align:start position:0% +on transfers transfers are more of an + + + align:start position:0% +on transfers transfers are more of an +issue when there are multiple operators + + align:start position:0% +issue when there are multiple operators + + + align:start position:0% +issue when there are multiple operators +in a region right and we'll talk a + + align:start position:0% +in a region right and we'll talk a + + + align:start position:0% +in a region right and we'll talk a +little bit more about that if it's one + + align:start position:0% +little bit more about that if it's one + + + align:start position:0% +little bit more about that if it's one +Operator + + align:start position:0% +Operator + + + align:start position:0% +Operator +it's sort of less controversial + + align:start position:0% +it's sort of less controversial + + + align:start position:0% +it's sort of less controversial +okay so pay-as-you-go passes and capping + + align:start position:0% +okay so pay-as-you-go passes and capping + + + align:start position:0% +okay so pay-as-you-go passes and capping +so pay-as-you-go is the simplest way of + + align:start position:0% +so pay-as-you-go is the simplest way of + + + align:start position:0% +so pay-as-you-go is the simplest way of +paying for four trips you can do that + + align:start position:0% +paying for four trips you can do that + + + align:start position:0% +paying for four trips you can do that +with cash or with tickets or smart cards + + align:start position:0% +with cash or with tickets or smart cards + + + align:start position:0% +with cash or with tickets or smart cards +that have a balance so you load up some + + align:start position:0% +that have a balance so you load up some + + + align:start position:0% +that have a balance so you load up some +value into the card and every time you + + align:start position:0% +value into the card and every time you + + + align:start position:0% +value into the card and every time you +you interact with the fare box or fare + + align:start position:0% +you interact with the fare box or fare + + + align:start position:0% +you interact with the fare box or fare +gate and that balances some amount of + + align:start position:0% +gate and that balances some amount of + + + align:start position:0% +gate and that balances some amount of +that balances deducted from the card + + align:start position:0% +that balances deducted from the card + + + align:start position:0% +that balances deducted from the card +that's pretty clear hopefully then + + align:start position:0% +that's pretty clear hopefully then + + + align:start position:0% +that's pretty clear hopefully then +there's passes so the idea of a pass is + + align:start position:0% +there's passes so the idea of a pass is + + + align:start position:0% +there's passes so the idea of a pass is +that you sort of prepay for three days + + align:start position:0% +that you sort of prepay for three days + + + align:start position:0% +that you sort of prepay for three days +for a week sometimes for a day sometimes + + align:start position:0% +for a week sometimes for a day sometimes + + + align:start position:0% +for a week sometimes for a day sometimes +for a month and you yet it's a fixed + + align:start position:0% +for a month and you yet it's a fixed + + + align:start position:0% +for a month and you yet it's a fixed +price so you can you write with zero + + align:start position:0% +price so you can you write with zero + + + align:start position:0% +price so you can you write with zero +marginal costs after paying that fixed + + align:start position:0% +marginal costs after paying that fixed + + + align:start position:0% +marginal costs after paying that fixed +price if you write frequently enough + + align:start position:0% +price if you write frequently enough + + + align:start position:0% +price if you write frequently enough +then you break you in and anything + + align:start position:0% +then you break you in and anything + + + align:start position:0% +then you break you in and anything +beyond that is a free ride so it's + + align:start position:0% +beyond that is a free ride so it's + + + align:start position:0% +beyond that is a free ride so it's +interesting to note that because passes + + align:start position:0% +interesting to note that because passes + + + align:start position:0% +interesting to note that because passes +are convenient some fare revenues + + align:start position:0% +are convenient some fare revenues + + + align:start position:0% +are convenient some fare revenues +derived from past sales for people that + + align:start position:0% +derived from past sales for people that + + + align:start position:0% +derived from past sales for people that +don't break even that could happen for + + align:start position:0% +don't break even that could happen for + + + align:start position:0% +don't break even that could happen for +several reasons one of them might be + + align:start position:0% +several reasons one of them might be + + + align:start position:0% +several reasons one of them might be +it's more convenient and + + align:start position:0% +it's more convenient and + + + align:start position:0% +it's more convenient and +I'm gonna figure out every month if I'm + + align:start position:0% +I'm gonna figure out every month if I'm + + + align:start position:0% +I'm gonna figure out every month if I'm +gonna be having the password not the + + align:start position:0% +gonna be having the password not the + + + align:start position:0% +gonna be having the password not the +pass it could also be that some people + + align:start position:0% +pass it could also be that some people + + + align:start position:0% +pass it could also be that some people +receive a subsidy from somewhere and + + align:start position:0% +receive a subsidy from somewhere and + + + align:start position:0% +receive a subsidy from somewhere and +what they spend on the pass is lower + + align:start position:0% +what they spend on the pass is lower + + + align:start position:0% +what they spend on the pass is lower +than the past value and so for them the + + align:start position:0% +than the past value and so for them the + + + align:start position:0% +than the past value and so for them the +real break-even point is lower and you + + align:start position:0% +real break-even point is lower and you + + + align:start position:0% +real break-even point is lower and you +may not necessarily be considering that + + align:start position:0% +may not necessarily be considering that + + + align:start position:0% +may not necessarily be considering that +when you do this break-even point + + align:start position:0% +when you do this break-even point + + + align:start position:0% +when you do this break-even point +calculation so in some cases going back + + align:start position:0% +calculation so in some cases going back + + + align:start position:0% +calculation so in some cases going back +to transfers agencies that don't have + + align:start position:0% +to transfers agencies that don't have + + + align:start position:0% +to transfers agencies that don't have +free transfers you can get them + + align:start position:0% +free transfers you can get them + + + align:start position:0% +free transfers you can get them +indirectly through a pass right because + + align:start position:0% +indirectly through a pass right because + + + align:start position:0% +indirectly through a pass right because +they might say well you know you break + + align:start position:0% +they might say well you know you break + + + align:start position:0% +they might say well you know you break +even at ten rides per week so that's + + align:start position:0% +even at ten rides per week so that's + + + align:start position:0% +even at ten rides per week so that's +your five week days times two oh you + + align:start position:0% +your five week days times two oh you + + + align:start position:0% +your five week days times two oh you +know going and returning and if you're + + align:start position:0% +know going and returning and if you're + + + align:start position:0% +know going and returning and if you're +if you have no free transfers policy but + + align:start position:0% +if you have no free transfers policy but + + + align:start position:0% +if you have no free transfers policy but +your trip requires one transfer then + + align:start position:0% +your trip requires one transfer then + + + align:start position:0% +your trip requires one transfer then +you're gonna very quickly reach that + + align:start position:0% +you're gonna very quickly reach that + + + align:start position:0% +you're gonna very quickly reach that +limit and you're gonna ride free after + + align:start position:0% +limit and you're gonna ride free after + + + align:start position:0% +limit and you're gonna ride free after +that so in this that would be a free + + align:start position:0% +that so in this that would be a free + + + align:start position:0% +that so in this that would be a free +transfer policy although not directly so + + align:start position:0% +transfer policy although not directly so + + + align:start position:0% +transfer policy although not directly so +passes increase convenience we know that + + align:start position:0% +passes increase convenience we know that + + + align:start position:0% +passes increase convenience we know that +they reduce a lien see so you're not + + align:start position:0% +they reduce a lien see so you're not + + + align:start position:0% +they reduce a lien see so you're not +thinking about how much money you're + + align:start position:0% +thinking about how much money you're + + + align:start position:0% +thinking about how much money you're +paying every time because it's more + + align:start position:0% +paying every time because it's more + + + align:start position:0% +paying every time because it's more +convenient they can be subsidized by + + align:start position:0% +convenient they can be subsidized by + + + align:start position:0% +convenient they can be subsidized by +employers by universities by governments + + align:start position:0% +employers by universities by governments + + + align:start position:0% +employers by universities by governments +so here we talk about the pre-tax + + align:start position:0% +so here we talk about the pre-tax + + + align:start position:0% +so here we talk about the pre-tax +benefit Henry brought up and then + + align:start position:0% +benefit Henry brought up and then + + + align:start position:0% +benefit Henry brought up and then +there's social programs right so like + + align:start position:0% +there's social programs right so like + + + align:start position:0% +there's social programs right so like +access to jobs programs that give passes + + align:start position:0% +access to jobs programs that give passes + + + align:start position:0% +access to jobs programs that give passes +subsidized or sometimes even free for + + align:start position:0% +subsidized or sometimes even free for + + + align:start position:0% +subsidized or sometimes even free for +people that are economically + + align:start position:0% +people that are economically + + + align:start position:0% +people that are economically +disadvantaged questions on passes I + + align:start position:0% +disadvantaged questions on passes I + + + align:start position:0% +disadvantaged questions on passes I +think we're all familiar with passes + + align:start position:0% +think we're all familiar with passes + + + align:start position:0% +think we're all familiar with passes +okay so capping capping is less common + + align:start position:0% +okay so capping capping is less common + + + align:start position:0% +okay so capping capping is less common +it's a manure thing its more common in + + align:start position:0% +it's a manure thing its more common in + + + align:start position:0% +it's a manure thing its more common in +Europe London has it Germany has it in + + align:start position:0% +Europe London has it Germany has it in + + + align:start position:0% +Europe London has it Germany has it in +many places the Netherlands so the idea + + align:start position:0% +many places the Netherlands so the idea + + + align:start position:0% +many places the Netherlands so the idea +is that when you have a complex fare + + align:start position:0% +is that when you have a complex fare + + + align:start position:0% +is that when you have a complex fare +system + + align:start position:0% +system + + + align:start position:0% +system +complex fare structure I should say + + align:start position:0% +complex fare structure I should say + + + align:start position:0% +complex fare structure I should say +where the prices are difficult to figure + + align:start position:0% +where the prices are difficult to figure + + + align:start position:0% +where the prices are difficult to figure +out then the agency says don't worry + + align:start position:0% +out then the agency says don't worry + + + align:start position:0% +out then the agency says don't worry +about calculating which fare products + + align:start position:0% +about calculating which fare products + + + align:start position:0% +about calculating which fare products +you need to buy we'll do the math and + + align:start position:0% +you need to buy we'll do the math and + + + align:start position:0% +you need to buy we'll do the math and +give you the best price so that's called + + align:start position:0% +give you the best price so that's called + + + align:start position:0% +give you the best price so that's called +best price guarantee and the idea is + + align:start position:0% +best price guarantee and the idea is + + + align:start position:0% +best price guarantee and the idea is +that instead of committing to getting a + + align:start position:0% +that instead of committing to getting a + + + align:start position:0% +that instead of committing to getting a +pass or another pass you pay as you go + + align:start position:0% +pass or another pass you pay as you go + + + align:start position:0% +pass or another pass you pay as you go +but when you reach a certain daily limit + + align:start position:0% +but when you reach a certain daily limit + + + align:start position:0% +but when you reach a certain daily limit +no more is charged during that day so + + align:start position:0% +no more is charged during that day so + + + align:start position:0% +no more is charged during that day so +you can keep writing and that doesn't + + align:start position:0% +you can keep writing and that doesn't + + + align:start position:0% +you can keep writing and that doesn't +stop there so the card keeps counting + + align:start position:0% +stop there so the card keeps counting + + + align:start position:0% +stop there so the card keeps counting +the trips in one week the trips in one + + align:start position:0% +the trips in one week the trips in one + + + align:start position:0% +the trips in one week the trips in one +month and so you might have multiple + + align:start position:0% +month and so you might have multiple + + + align:start position:0% +month and so you might have multiple +caps and you might reach different caps + + align:start position:0% +caps and you might reach different caps + + + align:start position:0% +caps and you might reach different caps +on one session and sort of with one card + + align:start position:0% +on one session and sort of with one card + + + align:start position:0% +on one session and sort of with one card +so essentially you you end up getting + + align:start position:0% +so essentially you you end up getting + + + align:start position:0% +so essentially you you end up getting +the equivalent of a pass if it was worth + + align:start position:0% +the equivalent of a pass if it was worth + + + align:start position:0% +the equivalent of a pass if it was worth +it and not otherwise obviously that + + align:start position:0% +it and not otherwise obviously that + + + align:start position:0% +it and not otherwise obviously that +means agencies lose some revenue from + + align:start position:0% +means agencies lose some revenue from + + + align:start position:0% +means agencies lose some revenue from +people who didn't make the right + + align:start position:0% +people who didn't make the right + + + align:start position:0% +people who didn't make the right +decision but it's a one way of having a + + align:start position:0% +decision but it's a one way of having a + + + align:start position:0% +decision but it's a one way of having a +complex fare structure that is that + + align:start position:0% +complex fare structure that is that + + + align:start position:0% +complex fare structure that is that +heavily segments the market and + + align:start position:0% +heavily segments the market and + + + align:start position:0% +heavily segments the market and +therefore does obtain more fare revenues + + align:start position:0% +therefore does obtain more fare revenues + + + align:start position:0% +therefore does obtain more fare revenues +and it allows for simple communication + + align:start position:0% +and it allows for simple communication + + + align:start position:0% +and it allows for simple communication +with people by saying don't worry about + + align:start position:0% +with people by saying don't worry about + + + align:start position:0% +with people by saying don't worry about +it we know it's complicated but we'll + + align:start position:0% +it we know it's complicated but we'll + + + align:start position:0% +it we know it's complicated but we'll +figure it out for you that's one + + align:start position:0% +figure it out for you that's one + + + align:start position:0% +figure it out for you that's one +argument in London I one of the reasons + + align:start position:0% +argument in London I one of the reasons + + + align:start position:0% +argument in London I one of the reasons +capping was introduced was to with the + + align:start position:0% +capping was introduced was to with the + + + align:start position:0% +capping was introduced was to with the +movement to contactless bank cards + + align:start position:0% +movement to contactless bank cards + + + align:start position:0% +movement to contactless bank cards +so essentially you can pay with your + + align:start position:0% +so essentially you can pay with your + + + align:start position:0% +so essentially you can pay with your +Visa or MasterCard you can have it on + + align:start position:0% +Visa or MasterCard you can have it on + + + align:start position:0% +Visa or MasterCard you can have it on +your phone Apple pay Android pay you tap + + align:start position:0% +your phone Apple pay Android pay you tap + + + align:start position:0% +your phone Apple pay Android pay you tap +it works so obviously a normal visa + + align:start position:0% +it works so obviously a normal visa + + + align:start position:0% +it works so obviously a normal visa +might not have the logic inside the + + align:start position:0% +might not have the logic inside the + + + align:start position:0% +might not have the logic inside the +cards computer to hold a pass or + + align:start position:0% +cards computer to hold a pass or + + + align:start position:0% +cards computer to hold a pass or +anything like that so the card becomes a + + align:start position:0% +anything like that so the card becomes a + + + align:start position:0% +anything like that so the card becomes a +token one way of dealing with that is to + + align:start position:0% +token one way of dealing with that is to + + + align:start position:0% +token one way of dealing with that is to +say it's capped now we'll keep track of + + align:start position:0% +say it's capped now we'll keep track of + + + align:start position:0% +say it's capped now we'll keep track of +your usage for the month and when you + + align:start position:0% +your usage for the month and when you + + + align:start position:0% +your usage for the month and when you +reach the monthly cap we'll stop + + align:start position:0% +reach the monthly cap we'll stop + + + align:start position:0% +reach the monthly cap we'll stop +charging you for it so it it simplifies + + align:start position:0% +charging you for it so it it simplifies + + + align:start position:0% +charging you for it so it it simplifies +the move tour towards contactless bank + + align:start position:0% +the move tour towards contactless bank + + + align:start position:0% +the move tour towards contactless bank +card usage and we'll talk more about + + align:start position:0% +card usage and we'll talk more about + + + align:start position:0% +card usage and we'll talk more about +that yeah + + align:start position:0% + + + + align:start position:0% + +yes well they've seen an increase in the + + align:start position:0% +yes well they've seen an increase in the + + + align:start position:0% +yes well they've seen an increase in the +penetration for contactless bank card + + align:start position:0% +penetration for contactless bank card + + + align:start position:0% +penetration for contactless bank card +use has been increasing steadily and if + + align:start position:0% +use has been increasing steadily and if + + + align:start position:0% +use has been increasing steadily and if +you go to London my last experience + + align:start position:0% +you go to London my last experience + + + align:start position:0% +you go to London my last experience +there was on the train ride between the + + align:start position:0% +there was on the train ride between the + + + align:start position:0% +there was on the train ride between the +airport and and the centre of London I + + align:start position:0% +airport and and the centre of London I + + + align:start position:0% +airport and and the centre of London I +heard several people talking about how + + align:start position:0% +heard several people talking about how + + + align:start position:0% +heard several people talking about how +convenient it was so people are you + + align:start position:0% +convenient it was so people are you + + + align:start position:0% +convenient it was so people are you +excited about this and it's great for a + + align:start position:0% +excited about this and it's great for a + + + align:start position:0% +excited about this and it's great for a +city like London that has a lot of + + align:start position:0% +city like London that has a lot of + + + align:start position:0% +city like London that has a lot of +people that are occasional users a lot + + align:start position:0% +people that are occasional users a lot + + + align:start position:0% +people that are occasional users a lot +of business travellers being able to not + + align:start position:0% +of business travellers being able to not + + + align:start position:0% +of business travellers being able to not +have to think about it and just pay with + + align:start position:0% +have to think about it and just pay with + + + align:start position:0% +have to think about it and just pay with +a credit card really helps so and and I + + align:start position:0% +a credit card really helps so and and I + + + align:start position:0% +a credit card really helps so and and I +have several other benefits all discuss + + align:start position:0% +have several other benefits all discuss + + + align:start position:0% +have several other benefits all discuss +them more in detail when we get to smart + + align:start position:0% +them more in detail when we get to smart + + + align:start position:0% +them more in detail when we get to smart +cards well it's cupping so it's not it's + + align:start position:0% +cards well it's cupping so it's not it's + + + align:start position:0% +cards well it's cupping so it's not it's +equivalent to a pass the math works out + + align:start position:0% +equivalent to a pass the math works out + + + align:start position:0% +equivalent to a pass the math works out +so that it is a pass but it's not you're + + align:start position:0% +so that it is a pass but it's not you're + + + align:start position:0% +so that it is a pass but it's not you're +not selling once we pass so yeah it's + + align:start position:0% +not selling once we pass so yeah it's + + + align:start position:0% +not selling once we pass so yeah it's +not it's all passed you're paying + + align:start position:0% + + + + align:start position:0% + +today they have it yeah yeah yeah okay + + align:start position:0% +today they have it yeah yeah yeah okay + + + align:start position:0% +today they have it yeah yeah yeah okay +we'll discuss more on the contactless + + align:start position:0% +we'll discuss more on the contactless + + + align:start position:0% +we'll discuss more on the contactless +bankers it's a very interesting trend + + align:start position:0% +bankers it's a very interesting trend + + + align:start position:0% +bankers it's a very interesting trend +that we're seeing so fare policy demand + + align:start position:0% +that we're seeing so fare policy demand + + + align:start position:0% +that we're seeing so fare policy demand +analysis we talked a little bit about + + align:start position:0% +analysis we talked a little bit about + + + align:start position:0% +analysis we talked a little bit about +this on ridership forecasting just so + + align:start position:0% +this on ridership forecasting just so + + + align:start position:0% +this on ridership forecasting just so +recap the traditional four-step modeling + + align:start position:0% +recap the traditional four-step modeling + + + align:start position:0% +recap the traditional four-step modeling +process is not usually appropriate and + + align:start position:0% +process is not usually appropriate and + + + align:start position:0% +process is not usually appropriate and +that's because a it has an insufficient + + align:start position:0% +that's because a it has an insufficient + + + align:start position:0% +that's because a it has an insufficient +special temporal resolution and be their + + align:start position:0% +special temporal resolution and be their + + + align:start position:0% +special temporal resolution and be their +planning horizon for a fare hike is kind + + align:start position:0% +planning horizon for a fare hike is kind + + + align:start position:0% +planning horizon for a fare hike is kind +of short to medium term so you're not + + align:start position:0% +of short to medium term so you're not + + + align:start position:0% +of short to medium term so you're not +thinking about land-use changes that + + align:start position:0% +thinking about land-use changes that + + + align:start position:0% +thinking about land-use changes that +will generate new trips so therefore + + align:start position:0% +will generate new trips so therefore + + + align:start position:0% +will generate new trips so therefore +total demand this you can assume fixed + + align:start position:0% +total demand this you can assume fixed + + + align:start position:0% +total demand this you can assume fixed +and what you want to play with is the + + align:start position:0% +and what you want to play with is the + + + align:start position:0% +and what you want to play with is the +modal split and the assignment to + + align:start position:0% +modal split and the assignment to + + + align:start position:0% +modal split and the assignment to +specific trips the other thing is that + + align:start position:0% +specific trips the other thing is that + + + align:start position:0% +specific trips the other thing is that +these four-step models usually don't + + align:start position:0% +these four-step models usually don't + + + align:start position:0% +these four-step models usually don't +have all the details of all the fare + + align:start position:0% +have all the details of all the fare + + + align:start position:0% +have all the details of all the fare +products in them and for an agency it's + + align:start position:0% +products in them and for an agency it's + + + align:start position:0% +products in them and for an agency it's +important to know about what people will + + align:start position:0% +important to know about what people will + + + align:start position:0% +important to know about what people will +do about getting a pass or paying as + + align:start position:0% +do about getting a pass or paying as + + + align:start position:0% +do about getting a pass or paying as +soon as they go so usually Fairless the + + align:start position:0% +soon as they go so usually Fairless the + + + align:start position:0% +soon as they go so usually Fairless the +city analysis is simple in reality a + + align:start position:0% +city analysis is simple in reality a + + + align:start position:0% +city analysis is simple in reality a +passenger is considering multiple things + + align:start position:0% +passenger is considering multiple things + + + align:start position:0% +passenger is considering multiple things +at the same time so which mode are they + + align:start position:0% +at the same time so which mode are they + + + align:start position:0% +at the same time so which mode are they +going to take are they going to drive + + align:start position:0% +going to take are they going to drive + + + align:start position:0% +going to take are they going to drive +their car or are they going to take + + align:start position:0% +their car or are they going to take + + + align:start position:0% +their car or are they going to take +transit are they gonna take bus or rail + + align:start position:0% +transit are they gonna take bus or rail + + + align:start position:0% +transit are they gonna take bus or rail +fare products are they gonna go for the + + align:start position:0% +fare products are they gonna go for the + + + align:start position:0% +fare products are they gonna go for the +pass or are they gonna pay you so they + + align:start position:0% +pass or are they gonna pay you so they + + + align:start position:0% +pass or are they gonna pay you so they +go and maybe there are multiple passes + + align:start position:0% +go and maybe there are multiple passes + + + align:start position:0% +go and maybe there are multiple passes +which one and then costs not just in + + align:start position:0% +which one and then costs not just in + + + align:start position:0% +which one and then costs not just in +absolute terms + + align:start position:0% +absolute terms + + + align:start position:0% +absolute terms +so usually elasticity only looks at the + + align:start position:0% +so usually elasticity only looks at the + + + align:start position:0% +so usually elasticity only looks at the +percentage increase in fares for this + + align:start position:0% +percentage increase in fares for this + + + align:start position:0% +percentage increase in fares for this +mode but what if car costs have gonna + + align:start position:0% +mode but what if car costs have gonna + + + align:start position:0% +mode but what if car costs have gonna +buy more than that + + align:start position:0% +buy more than that + + + align:start position:0% +buy more than that +so really it's relative to your + + align:start position:0% +so really it's relative to your + + + align:start position:0% +so really it's relative to your +alternatives and each person might have + + align:start position:0% +alternatives and each person might have + + + align:start position:0% +alternatives and each person might have +a different choice set for some people + + align:start position:0% +a different choice set for some people + + + align:start position:0% +a different choice set for some people +transit might be the only mode choice a + + align:start position:0% +transit might be the only mode choice a + + + align:start position:0% +transit might be the only mode choice a +little only mode and the choice set + + align:start position:0% +little only mode and the choice set + + + align:start position:0% +little only mode and the choice set +because they don't own a car for others + + align:start position:0% +because they don't own a car for others + + + align:start position:0% +because they don't own a car for others +there may be multiple options so the + + align:start position:0% +there may be multiple options so the + + + align:start position:0% +there may be multiple options so the +other aspect of it is a exogenous + + align:start position:0% +other aspect of it is a exogenous + + + align:start position:0% +other aspect of it is a exogenous +factors influence demand response and + + align:start position:0% +factors influence demand response and + + + align:start position:0% +factors influence demand response and +they're not usually controlled for so + + align:start position:0% +they're not usually controlled for so + + + align:start position:0% +they're not usually controlled for so +fuel prices employment residential + + align:start position:0% +fuel prices employment residential + + + align:start position:0% +fuel prices employment residential +development tax policy search + + align:start position:0% +development tax policy search + + + align:start position:0% +development tax policy search +demographics new modes the introduction + + align:start position:0% +demographics new modes the introduction + + + align:start position:0% +demographics new modes the introduction +of TNCs like uber and lyft and other + + align:start position:0% +of TNCs like uber and lyft and other + + + align:start position:0% +of TNCs like uber and lyft and other +companies have + + align:start position:0% +companies have + + + align:start position:0% +companies have +potentially affected ridership we think + + align:start position:0% +potentially affected ridership we think + + + align:start position:0% +potentially affected ridership we think +they have and most of these soliciting + + align:start position:0% +they have and most of these soliciting + + + align:start position:0% +they have and most of these soliciting +models don't really sort of control for + + align:start position:0% +models don't really sort of control for + + + align:start position:0% +models don't really sort of control for +that to get at the real fair elasticity + + align:start position:0% +that to get at the real fair elasticity + + + align:start position:0% +that to get at the real fair elasticity +and that would be what you would want to + + align:start position:0% +and that would be what you would want to + + + align:start position:0% +and that would be what you would want to +do accurate model okay + + align:start position:0% +do accurate model okay + + + align:start position:0% +do accurate model okay +communication a fare policy so obviously + + align:start position:0% +communication a fare policy so obviously + + + align:start position:0% +communication a fare policy so obviously +to the public it needs to be + + align:start position:0% +to the public it needs to be + + + align:start position:0% +to the public it needs to be +communicated you can do that on your + + align:start position:0% +communicated you can do that on your + + + align:start position:0% +communicated you can do that on your +website you can have near fair vending + + align:start position:0% +website you can have near fair vending + + + align:start position:0% +website you can have near fair vending +machines those usually you know an + + align:start position:0% +machines those usually you know an + + + align:start position:0% +machines those usually you know an +explanation of the prices you have + + align:start position:0% +explanation of the prices you have + + + align:start position:0% +explanation of the prices you have +customer service booths if there's gonna + + align:start position:0% +customer service booths if there's gonna + + + align:start position:0% +customer service booths if there's gonna +be a fare change again you post things + + align:start position:0% +be a fare change again you post things + + + align:start position:0% +be a fare change again you post things +on the website there's flyers and + + align:start position:0% +on the website there's flyers and + + + align:start position:0% +on the website there's flyers and +posters everywhere public hearings of + + align:start position:0% +posters everywhere public hearings of + + + align:start position:0% +posters everywhere public hearings of +course to sort of hear complaints and + + align:start position:0% +course to sort of hear complaints and + + + align:start position:0% +course to sort of hear complaints and +defend the hike and I wanted to add one + + align:start position:0% +defend the hike and I wanted to add one + + + align:start position:0% +defend the hike and I wanted to add one +third of 3rd emerging but very important + + align:start position:0% +third of 3rd emerging but very important + + + align:start position:0% +third of 3rd emerging but very important +aspect that is not we haven't figured it + + align:start position:0% +aspect that is not we haven't figured it + + + align:start position:0% +aspect that is not we haven't figured it +out and it's via API sourced and they're + + align:start position:0% +out and it's via API sourced and they're + + + align:start position:0% +out and it's via API sourced and they're +two feeds for trip planners so if you + + align:start position:0% +two feeds for trip planners so if you + + + align:start position:0% +two feeds for trip planners so if you +have an app if you use Google Maps to + + align:start position:0% +have an app if you use Google Maps to + + + align:start position:0% +have an app if you use Google Maps to +get tons of directions and you want it + + align:start position:0% +get tons of directions and you want it + + + align:start position:0% +get tons of directions and you want it +to calculate what your fare will be + + align:start position:0% +to calculate what your fare will be + + + align:start position:0% +to calculate what your fare will be +unless the agency has a simple fare + + align:start position:0% +unless the agency has a simple fare + + + align:start position:0% +unless the agency has a simple fare +structure that can't be done even for + + align:start position:0% +structure that can't be done even for + + + align:start position:0% +structure that can't be done even for +agencies that have simple fare structure + + align:start position:0% +agencies that have simple fare structure + + + align:start position:0% +agencies that have simple fare structure +most of them don't provide the two files + + align:start position:0% +most of them don't provide the two files + + + align:start position:0% +most of them don't provide the two files +and ETFs that allow that calculation to + + align:start position:0% +and ETFs that allow that calculation to + + + align:start position:0% +and ETFs that allow that calculation to +happen and for agencies like London that + + align:start position:0% +happen and for agencies like London that + + + align:start position:0% +happen and for agencies like London that +have a capping scheme the GTFS + + align:start position:0% +have a capping scheme the GTFS + + + align:start position:0% +have a capping scheme the GTFS +specification does not provide the means + + align:start position:0% +specification does not provide the means + + + align:start position:0% +specification does not provide the means +by which to input the fare rules that + + align:start position:0% +by which to input the fare rules that + + + align:start position:0% +by which to input the fare rules that +would accurately calculate the person's + + align:start position:0% +would accurately calculate the person's + + + align:start position:0% +would accurately calculate the person's +fair because you would need to keep + + align:start position:0% +fair because you would need to keep + + + align:start position:0% +fair because you would need to keep +track of how often how much they've + + align:start position:0% +track of how often how much they've + + + align:start position:0% +track of how often how much they've +taken service for over a week over a day + + align:start position:0% +taken service for over a week over a day + + + align:start position:0% +taken service for over a week over a day +etc so that we haven't figured out + + align:start position:0% +etc so that we haven't figured out + + + align:start position:0% +etc so that we haven't figured out +third-party apps like the transit app + + align:start position:0% +third-party apps like the transit app + + + align:start position:0% +third-party apps like the transit app +would love to be able to calculate fares + + align:start position:0% +would love to be able to calculate fares + + + align:start position:0% +would love to be able to calculate fares +accurately and display them because they + + align:start position:0% +accurately and display them because they + + + align:start position:0% +accurately and display them because they +can do that for uber and they can do + + align:start position:0% +can do that for uber and they can do + + + align:start position:0% +can do that for uber and they can do +that for other mode so why not for + + align:start position:0% +that for other mode so why not for + + + align:start position:0% +that for other mode so why not for +chance it as well + + align:start position:0% +chance it as well + + + align:start position:0% +chance it as well +and although they would prefer to the + + align:start position:0% +and although they would prefer to the + + + align:start position:0% +and although they would prefer to the +in-house one alternative to that is to + + align:start position:0% +in-house one alternative to that is to + + + align:start position:0% +in-house one alternative to that is to +have to define some sir standard API + + align:start position:0% +have to define some sir standard API + + + align:start position:0% +have to define some sir standard API +where it's up to the agency to calculate + + align:start position:0% +where it's up to the agency to calculate + + + align:start position:0% +where it's up to the agency to calculate +what that would be but you you make an + + align:start position:0% +what that would be but you you make an + + + align:start position:0% +what that would be but you you make an +API call and you say this is the trip + + align:start position:0% +API call and you say this is the trip + + + align:start position:0% +API call and you say this is the trip +the hypothetical trip that I'm planning + + align:start position:0% +the hypothetical trip that I'm planning + + + align:start position:0% +the hypothetical trip that I'm planning +give me the how much right and the + + align:start position:0% +give me the how much right and the + + + align:start position:0% +give me the how much right and the +agency would respond but + + align:start position:0% +agency would respond but + + + align:start position:0% +agency would respond but +performance reasons I think the trends + + align:start position:0% +performance reasons I think the trends + + + align:start position:0% +performance reasons I think the trends +that I would prefer to be able to do + + align:start position:0% +that I would prefer to be able to do + + + align:start position:0% +that I would prefer to be able to do +that with their servers so there's a + + align:start position:0% +that with their servers so there's a + + + align:start position:0% +that with their servers so there's a +quick response partnerships another sort + + align:start position:0% +quick response partnerships another sort + + + align:start position:0% +quick response partnerships another sort +of emerging trend so employer + + align:start position:0% +of emerging trend so employer + + + align:start position:0% +of emerging trend so employer +partnerships is one example give the + + align:start position:0% +partnerships is one example give the + + + align:start position:0% +partnerships is one example give the +example of MIT actually MIT is something + + align:start position:0% +example of MIT actually MIT is something + + + align:start position:0% +example of MIT actually MIT is something +called access my commute our lab was + + align:start position:0% +called access my commute our lab was + + + align:start position:0% +called access my commute our lab was +actually involves in that so every MIT + + align:start position:0% +actually involves in that so every MIT + + + align:start position:0% +actually involves in that so every MIT +badge student or employee badge has a + + align:start position:0% +badge student or employee badge has a + + + align:start position:0% +badge student or employee badge has a +charlie chip embedded inside you can + + align:start position:0% +charlie chip embedded inside you can + + + align:start position:0% +charlie chip embedded inside you can +look at the back end so it's Charlie + + align:start position:0% +look at the back end so it's Charlie + + + align:start position:0% +look at the back end so it's Charlie +inside and two employees it's marketed + + align:start position:0% +inside and two employees it's marketed + + + align:start position:0% +inside and two employees it's marketed +as an unlimited use past so I can use my + + align:start position:0% +as an unlimited use past so I can use my + + + align:start position:0% +as an unlimited use past so I can use my +MIT ID and ride the MBTA MIT gets billed + + align:start position:0% +MIT ID and ride the MBTA MIT gets billed + + + align:start position:0% +MIT ID and ride the MBTA MIT gets billed +on a pay-as-you-go basis so the reason + + align:start position:0% +on a pay-as-you-go basis so the reason + + + align:start position:0% +on a pay-as-you-go basis so the reason +we did that or the other reason that was + + align:start position:0% +we did that or the other reason that was + + + align:start position:0% +we did that or the other reason that was +the agreement is that a lot of people + + align:start position:0% +the agreement is that a lot of people + + + align:start position:0% +the agreement is that a lot of people +don't use transit enough to justify the + + align:start position:0% +don't use transit enough to justify the + + + align:start position:0% +don't use transit enough to justify the +value of a pass so there was no way that + + align:start position:0% +value of a pass so there was no way that + + + align:start position:0% +value of a pass so there was no way that +MIT would agree to pay a pass for every + + align:start position:0% +MIT would agree to pay a pass for every + + + align:start position:0% +MIT would agree to pay a pass for every +employee and it's in the interest of MIT + + align:start position:0% +employee and it's in the interest of MIT + + + align:start position:0% +employee and it's in the interest of MIT +to foment to encourage ridership right + + align:start position:0% +to foment to encourage ridership right + + + align:start position:0% +to foment to encourage ridership right +so to decrease a lien see in this case + + align:start position:0% +so to decrease a lien see in this case + + + align:start position:0% +so to decrease a lien see in this case +to the extreme by making it free so the + + align:start position:0% +to the extreme by making it free so the + + + align:start position:0% +to the extreme by making it free so the +one way of doing that is to say market + + align:start position:0% +one way of doing that is to say market + + + align:start position:0% +one way of doing that is to say market +it as a free pass there is a mix of + + align:start position:0% +it as a free pass there is a mix of + + + align:start position:0% +it as a free pass there is a mix of +people that had passes and people that + + align:start position:0% +people that had passes and people that + + + align:start position:0% +people that had passes and people that +write less often I don't think so + + align:start position:0% +write less often I don't think so + + + align:start position:0% +write less often I don't think so +because many many employees yeah it's + + align:start position:0% +because many many employees yeah it's + + + align:start position:0% +because many many employees yeah it's +not close and and it's in some ways so + + align:start position:0% +not close and and it's in some ways so + + + align:start position:0% +not close and and it's in some ways so +some people write a lot more than right + + align:start position:0% +some people write a lot more than right + + + align:start position:0% +some people write a lot more than right +so MIT in some ways is like paying for + + align:start position:0% +so MIT in some ways is like paying for + + + align:start position:0% +so MIT in some ways is like paying for +some employees is paying more because + + align:start position:0% +some employees is paying more because + + + align:start position:0% +some employees is paying more because +they're paying by ride but many people + + align:start position:0% +they're paying by ride but many people + + + align:start position:0% +they're paying by ride but many people +that have a subsidized pass because + + align:start position:0% +that have a subsidized pass because + + + align:start position:0% +that have a subsidized pass because +their break-even point is so much lower + + align:start position:0% +their break-even point is so much lower + + + align:start position:0% +their break-even point is so much lower +don't really breakeven and so it works + + align:start position:0% +don't really breakeven and so it works + + + align:start position:0% +don't really breakeven and so it works +out too + + align:start position:0% + + + + align:start position:0% + +to find a way yeah one of the reasons + + align:start position:0% +to find a way yeah one of the reasons + + + align:start position:0% +to find a way yeah one of the reasons +parking is very expensive real estate is + + align:start position:0% +parking is very expensive real estate is + + + align:start position:0% +parking is very expensive real estate is +very very and that's of course not true + + align:start position:0% +very very and that's of course not true + + + align:start position:0% +very very and that's of course not true +everywhere it's not true in most places + + align:start position:0% +everywhere it's not true in most places + + + align:start position:0% +everywhere it's not true in most places +most places have free parking plenty of + + align:start position:0% +most places have free parking plenty of + + + align:start position:0% +most places have free parking plenty of +land so but in a place that has + + align:start position:0% +land so but in a place that has + + + align:start position:0% +land so but in a place that has +high-density building new parking is + + align:start position:0% +high-density building new parking is + + + align:start position:0% +high-density building new parking is +very expensive and you can use that real + + align:start position:0% +very expensive and you can use that real + + + align:start position:0% +very expensive and you can use that real +estate for something else and in fact + + align:start position:0% +estate for something else and in fact + + + align:start position:0% +estate for something else and in fact +MIT has taken a parking down near Sloane + + align:start position:0% +MIT has taken a parking down near Sloane + + + align:start position:0% +MIT has taken a parking down near Sloane +and is making a new building there so it + + align:start position:0% +and is making a new building there so it + + + align:start position:0% +and is making a new building there so it +costs less to provide transit to people + + align:start position:0% +costs less to provide transit to people + + + align:start position:0% +costs less to provide transit to people +and to encourage people to take transit + + align:start position:0% +and to encourage people to take transit + + + align:start position:0% +and to encourage people to take transit +than to build new parking and maintain + + align:start position:0% +than to build new parking and maintain + + + align:start position:0% +than to build new parking and maintain +your parking here's another example so + + align:start position:0% +your parking here's another example so + + + align:start position:0% +your parking here's another example so +Chicago Transit Authority they have + + align:start position:0% +Chicago Transit Authority they have + + + align:start position:0% +Chicago Transit Authority they have +partnerships with other transportation + + align:start position:0% +partnerships with other transportation + + + align:start position:0% +partnerships with other transportation +providers and they do that by providing + + align:start position:0% +providers and they do that by providing + + + align:start position:0% +providers and they do that by providing +buy there are there are some passes and + + align:start position:0% +buy there are there are some passes and + + + align:start position:0% +buy there are there are some passes and +some fare products that allow writhing + + align:start position:0% +some fare products that allow writhing + + + align:start position:0% +some fare products that allow writhing +in pace which is the regional bus + + align:start position:0% +in pace which is the regional bus + + + align:start position:0% +in pace which is the regional bus +provider Metro which is the commuter + + align:start position:0% +provider Metro which is the commuter + + + align:start position:0% +provider Metro which is the commuter +rail provider and divvy which is the + + align:start position:0% +rail provider and divvy which is the + + + align:start position:0% +rail provider and divvy which is the +Bike Share so you can buy things that + + align:start position:0% +Bike Share so you can buy things that + + + align:start position:0% +Bike Share so you can buy things that +there are some partnerships that allow + + align:start position:0% +there are some partnerships that allow + + + align:start position:0% +there are some partnerships that allow +some integration here and there's a + + align:start position:0% +some integration here and there's a + + + align:start position:0% +some integration here and there's a +trend towards mobility as a service so + + align:start position:0% +trend towards mobility as a service so + + + align:start position:0% +trend towards mobility as a service so +the idea of mobility as a service is + + align:start position:0% +the idea of mobility as a service is + + + align:start position:0% +the idea of mobility as a service is +that you make a monthly payment for a + + align:start position:0% +that you make a monthly payment for a + + + align:start position:0% +that you make a monthly payment for a +bundle of transportation options here's + + align:start position:0% +bundle of transportation options here's + + + align:start position:0% +bundle of transportation options here's +an example you could have unlimited + + align:start position:0% +an example you could have unlimited + + + align:start position:0% +an example you could have unlimited +transit pass five bike rides and five + + align:start position:0% +transit pass five bike rides and five + + + align:start position:0% +transit pass five bike rides and five +TNC rides right so so you you provide + + align:start position:0% +TNC rides right so so you you provide + + + align:start position:0% +TNC rides right so so you you provide +this bundle persons purchasing my + + align:start position:0% +this bundle persons purchasing my + + + align:start position:0% +this bundle persons purchasing my +transportation from home to work and + + align:start position:0% +transportation from home to work and + + + align:start position:0% +transportation from home to work and +back and on a combination about so if + + align:start position:0% +back and on a combination about so if + + + align:start position:0% +back and on a combination about so if +it's if today it's inconvenient to take + + align:start position:0% +it's if today it's inconvenient to take + + + align:start position:0% +it's if today it's inconvenient to take +transit that day I will use the bike + + align:start position:0% +transit that day I will use the bike + + + align:start position:0% +transit that day I will use the bike +share or the TNC the word is out on + + align:start position:0% +share or the TNC the word is out on + + + align:start position:0% +share or the TNC the word is out on +whether this will work or not many + + align:start position:0% +whether this will work or not many + + + align:start position:0% +whether this will work or not many +agencies are interested most of them + + align:start position:0% +agencies are interested most of them + + + align:start position:0% +agencies are interested most of them +don't want to talk about it and we'll + + align:start position:0% +don't want to talk about it and we'll + + + align:start position:0% +don't want to talk about it and we'll +see what happens + + align:start position:0% +see what happens + + + align:start position:0% +see what happens +as time goes by + + align:start position:0% + + + + align:start position:0% + +transit benefit to grad students because + + align:start position:0% +transit benefit to grad students because + + + align:start position:0% +transit benefit to grad students because +residents tend not to be Parker's that's + + align:start position:0% +residents tend not to be Parker's that's + + + align:start position:0% +residents tend not to be Parker's that's +that is a sort of a reason for why they + + align:start position:0% +that is a sort of a reason for why they + + + align:start position:0% +that is a sort of a reason for why they +shouldn't or wouldn't but I'm not sure + + align:start position:0% +shouldn't or wouldn't but I'm not sure + + + align:start position:0% +shouldn't or wouldn't but I'm not sure +that it is their actual reason I don't I + + align:start position:0% +that it is their actual reason I don't I + + + align:start position:0% +that it is their actual reason I don't I +think this was always conceived as an + + align:start position:0% +think this was always conceived as an + + + align:start position:0% +think this was always conceived as an +employee in benefits program is not + + align:start position:0% +employee in benefits program is not + + + align:start position:0% +employee in benefits program is not +quite so so yeah so it's I don't really + + align:start position:0% +quite so so yeah so it's I don't really + + + align:start position:0% +quite so so yeah so it's I don't really +know the actual reason now sometimes + + align:start position:0% +know the actual reason now sometimes + + + align:start position:0% +know the actual reason now sometimes +decisions are made for you justify them + + align:start position:0% +decisions are made for you justify them + + + align:start position:0% +decisions are made for you justify them +in all sorts of ways and then someone + + align:start position:0% +in all sorts of ways and then someone + + + align:start position:0% +in all sorts of ways and then someone +decides right so many other factors + + align:start position:0% +decides right so many other factors + + + align:start position:0% +decides right so many other factors +playing ok fair control tap-in you know + + align:start position:0% +playing ok fair control tap-in you know + + + align:start position:0% +playing ok fair control tap-in you know +what that is you interact with the fare + + align:start position:0% +what that is you interact with the fare + + + align:start position:0% +what that is you interact with the fare +box or fare gate only when you're + + align:start position:0% +box or fare gate only when you're + + + align:start position:0% +box or fare gate only when you're +entering the system or vehicle tap in + + align:start position:0% +entering the system or vehicle tap in + + + align:start position:0% +entering the system or vehicle tap in +and tap out you do that when you enter + + align:start position:0% +and tap out you do that when you enter + + + align:start position:0% +and tap out you do that when you enter +and exit usually tap in and tap out is + + align:start position:0% +and exit usually tap in and tap out is + + + align:start position:0% +and exit usually tap in and tap out is +for systems that have zones and you tap + + align:start position:0% +for systems that have zones and you tap + + + align:start position:0% +for systems that have zones and you tap +out so that we know if you've traveled + + align:start position:0% +out so that we know if you've traveled + + + align:start position:0% +out so that we know if you've traveled +multiple zones or not and therefore know + + align:start position:0% +multiple zones or not and therefore know + + + align:start position:0% +multiple zones or not and therefore know +how much to charge you because there's a + + align:start position:0% +how much to charge you because there's a + + + align:start position:0% +how much to charge you because there's a +segmentation by geography it also + + align:start position:0% +segmentation by geography it also + + + align:start position:0% +segmentation by geography it also +happens when there are multiple agencies + + align:start position:0% +happens when there are multiple agencies + + + align:start position:0% +happens when there are multiple agencies +sharing the revenue so of intercity bus + + align:start position:0% +sharing the revenue so of intercity bus + + + align:start position:0% +sharing the revenue so of intercity bus +in some cities if though if this bus + + align:start position:0% +in some cities if though if this bus + + + align:start position:0% +in some cities if though if this bus +route if a person takes a bus route + + align:start position:0% +route if a person takes a bus route + + + align:start position:0% +route if a person takes a bus route +within a city then that revenue would go + + align:start position:0% +within a city then that revenue would go + + + align:start position:0% +within a city then that revenue would go +to that city if the person travels + + align:start position:0% +to that city if the person travels + + + align:start position:0% +to that city if the person travels +across cities then the revenue would be + + align:start position:0% +across cities then the revenue would be + + + align:start position:0% +across cities then the revenue would be +shared across cities so that's one way + + align:start position:0% +shared across cities so that's one way + + + align:start position:0% +shared across cities so that's one way +you might want to do this + + align:start position:0% +you might want to do this + + + align:start position:0% +you might want to do this +I know that for it does exist in some + + align:start position:0% +I know that for it does exist in some + + + align:start position:0% +I know that for it does exist in some +places for bus or you have to tap in and + + align:start position:0% +places for bus or you have to tap in and + + + align:start position:0% +places for bus or you have to tap in and +hop out although it's much less common + + align:start position:0% +hop out although it's much less common + + + align:start position:0% +hop out although it's much less common +for bus and for real Henry + + align:start position:0% + + + + align:start position:0% + +yeah yeah yeah I don't know how they do + + align:start position:0% +yeah yeah yeah I don't know how they do + + + align:start position:0% +yeah yeah yeah I don't know how they do +it + + align:start position:0% +it + + + align:start position:0% +it +funding formulas are a huge debates and + + align:start position:0% +funding formulas are a huge debates and + + + align:start position:0% +funding formulas are a huge debates and +you know I would know how as an engineer + + align:start position:0% +you know I would know how as an engineer + + + align:start position:0% +you know I would know how as an engineer +I would propose to look at the other OD + + align:start position:0% +I would propose to look at the other OD + + + align:start position:0% +I would propose to look at the other OD +and and to figure out the most fair way + + align:start position:0% +and and to figure out the most fair way + + + align:start position:0% +and and to figure out the most fair way +of allocating that revenue but how what + + align:start position:0% +of allocating that revenue but how what + + + align:start position:0% +of allocating that revenue but how what +they actually do is probably simpler + + align:start position:0% +they actually do is probably simpler + + + align:start position:0% +they actually do is probably simpler +another thing about tappings about is + + align:start position:0% +another thing about tappings about is + + + align:start position:0% +another thing about tappings about is +you may require internal vending + + align:start position:0% +you may require internal vending + + + align:start position:0% +you may require internal vending +machines I mean it may increase your + + align:start position:0% +machines I mean it may increase your + + + align:start position:0% +machines I mean it may increase your +capital costs why is that because you + + align:start position:0% +capital costs why is that because you + + + align:start position:0% +capital costs why is that because you +have multiple costs the price of your + + align:start position:0% +have multiple costs the price of your + + + align:start position:0% +have multiple costs the price of your +right depends on how far you ride and if + + align:start position:0% +right depends on how far you ride and if + + + align:start position:0% +right depends on how far you ride and if +you cross zones or not so you might have + + align:start position:0% +you cross zones or not so you might have + + + align:start position:0% +you cross zones or not so you might have +just enough balance to enter not enough + + align:start position:0% +just enough balance to enter not enough + + + align:start position:0% +just enough balance to enter not enough +to exit if you cross multiple zones so + + align:start position:0% +to exit if you cross multiple zones so + + + align:start position:0% +to exit if you cross multiple zones so +you might have to top up the card before + + align:start position:0% +you might have to top up the card before + + + align:start position:0% +you might have to top up the card before +up being allowed to exit that means you + + align:start position:0% +up being allowed to exit that means you + + + align:start position:0% +up being allowed to exit that means you +need a fair vending machine that a + + align:start position:0% +need a fair vending machine that a + + + align:start position:0% +need a fair vending machine that a +person can use to to buy to top-up if + + align:start position:0% +person can use to to buy to top-up if + + + align:start position:0% +person can use to to buy to top-up if +they don't have a pass it means that you + + align:start position:0% +they don't have a pass it means that you + + + align:start position:0% +they don't have a pass it means that you +might need a station attendant to deal + + align:start position:0% +might need a station attendant to deal + + + align:start position:0% +might need a station attendant to deal +with somebody who's you know the very + + align:start position:0% +with somebody who's you know the very + + + align:start position:0% +with somebody who's you know the very +vending machine is not working or my + + align:start position:0% +vending machine is not working or my + + + align:start position:0% +vending machine is not working or my +bank card is not working and being + + align:start position:0% +bank card is not working and being + + + align:start position:0% +bank card is not working and being +rejected I need to get out of the + + align:start position:0% +rejected I need to get out of the + + + align:start position:0% +rejected I need to get out of the +station + + align:start position:0% +station + + + align:start position:0% +station +I'm trapped so what do I do + + align:start position:0% +I'm trapped so what do I do + + + align:start position:0% +I'm trapped so what do I do +so it can increase costs in that way you + + align:start position:0% +so it can increase costs in that way you + + + align:start position:0% +so it can increase costs in that way you +have a comment okay no right so that's + + align:start position:0% +have a comment okay no right so that's + + + align:start position:0% +have a comment okay no right so that's +when one potential issue something that + + align:start position:0% +when one potential issue something that + + + align:start position:0% +when one potential issue something that +some agencies do is allowing a negative + + align:start position:0% +some agencies do is allowing a negative + + + align:start position:0% +some agencies do is allowing a negative +balance so one way of softening the blow + + align:start position:0% +balance so one way of softening the blow + + + align:start position:0% +balance so one way of softening the blow +is to allow when you tap out to go below + + align:start position:0% +is to allow when you tap out to go below + + + align:start position:0% +is to allow when you tap out to go below +zero next time you top next time you you + + align:start position:0% +zero next time you top next time you you + + + align:start position:0% +zero next time you top next time you you +fill up the card you top up if you put + + align:start position:0% +fill up the card you top up if you put + + + align:start position:0% +fill up the card you top up if you put +in $20 and you had a one dollar deficit + + align:start position:0% +in $20 and you had a one dollar deficit + + + align:start position:0% +in $20 and you had a one dollar deficit +your balance is now 19 so you can't do + + align:start position:0% +your balance is now 19 so you can't do + + + align:start position:0% +your balance is now 19 so you can't do +that of course because people will then + + align:start position:0% +that of course because people will then + + + align:start position:0% +that of course because people will then +toss the card and get a new one so you + + align:start position:0% +toss the card and get a new one so you + + + align:start position:0% +toss the card and get a new one so you +you make people buy cards the cards are + + align:start position:0% +you make people buy cards the cards are + + + align:start position:0% +you make people buy cards the cards are +maybe ten dollars and five dollar + + align:start position:0% +maybe ten dollars and five dollar + + + align:start position:0% +maybe ten dollars and five dollar +balance or something so there's a + + align:start position:0% +balance or something so there's a + + + align:start position:0% +balance or something so there's a +disincentive to to tossing the card + + align:start position:0% +disincentive to to tossing the card + + + align:start position:0% +disincentive to to tossing the card +getting anyone and by the way smart + + align:start position:0% +getting anyone and by the way smart + + + align:start position:0% +getting anyone and by the way smart +cards costs money they're not that cheap + + align:start position:0% +cards costs money they're not that cheap + + + align:start position:0% +cards costs money they're not that cheap +some agencies have paid ten dollars per + + align:start position:0% +some agencies have paid ten dollars per + + + align:start position:0% +some agencies have paid ten dollars per +card for for their card so proof of + + align:start position:0% +card for for their card so proof of + + + align:start position:0% +card for for their card so proof of +payments we sort of discussed that you + + align:start position:0% +payments we sort of discussed that you + + + align:start position:0% +payments we sort of discussed that you +you buy a ticket it might be Oh Dee it + + align:start position:0% +you buy a ticket it might be Oh Dee it + + + align:start position:0% +you buy a ticket it might be Oh Dee it +might be flat fair doesn't matter you + + align:start position:0% +might be flat fair doesn't matter you + + + align:start position:0% +might be flat fair doesn't matter you +buy the ticket that you need and then + + align:start position:0% +buy the ticket that you need and then + + + align:start position:0% +buy the ticket that you need and then +when you board there's usually some + + align:start position:0% +when you board there's usually some + + + align:start position:0% +when you board there's usually some +validator that prints at times it can be + + align:start position:0% +validator that prints at times it can be + + + align:start position:0% +validator that prints at times it can be +electronic as well and what it requires + + align:start position:0% +electronic as well and what it requires + + + align:start position:0% +electronic as well and what it requires +is fair inspection so at random fair + + align:start position:0% +is fair inspection so at random fair + + + align:start position:0% +is fair inspection so at random fair +inspector will board the vehicle and + + align:start position:0% +inspector will board the vehicle and + + + align:start position:0% +inspector will board the vehicle and +have a handheld device requiring people + + align:start position:0% +have a handheld device requiring people + + + align:start position:0% +have a handheld device requiring people +to confirm if it's a electronic system + + align:start position:0% +to confirm if it's a electronic system + + + align:start position:0% +to confirm if it's a electronic system +then tap on here and I want to make sure + + align:start position:0% +then tap on here and I want to make sure + + + align:start position:0% +then tap on here and I want to make sure +that you've actually validated if it's + + align:start position:0% +that you've actually validated if it's + + + align:start position:0% +that you've actually validated if it's +paper than they would look at the paper + + align:start position:0% +paper than they would look at the paper + + + align:start position:0% +paper than they would look at the paper +and make sure that you've canceled it or + + align:start position:0% +and make sure that you've canceled it or + + + align:start position:0% +and make sure that you've canceled it or +validated that the paper ticket and + + align:start position:0% +validated that the paper ticket and + + + align:start position:0% +validated that the paper ticket and +otherwise a big fine so the + + align:start position:0% +otherwise a big fine so the + + + align:start position:0% +otherwise a big fine so the +discouragement to fare evasion is + + align:start position:0% +discouragement to fare evasion is + + + align:start position:0% +discouragement to fare evasion is +through fining and through policing but + + align:start position:0% +through fining and through policing but + + + align:start position:0% +through fining and through policing but +the research shows that there are still + + align:start position:0% +the research shows that there are still + + + align:start position:0% +the research shows that there are still +higher fare evasion rates on systems + + align:start position:0% +higher fare evasion rates on systems + + + align:start position:0% +higher fare evasion rates on systems +that are proof of payment people + + align:start position:0% +that are proof of payment people + + + align:start position:0% +that are proof of payment people +opportunistically board and they don't + + align:start position:0% +opportunistically board and they don't + + + align:start position:0% +opportunistically board and they don't +they don't pay anything okay fare + + align:start position:0% +they don't pay anything okay fare + + + align:start position:0% +they don't pay anything okay fare +technology so we've talked about + + align:start position:0% +technology so we've talked about + + + align:start position:0% +technology so we've talked about +structure and policy let's talk about + + align:start position:0% +structure and policy let's talk about + + + align:start position:0% +structure and policy let's talk about +technology so this is how an AFC system + + align:start position:0% +technology so this is how an AFC system + + + align:start position:0% +technology so this is how an AFC system +is usually set up you have a fair engine + + align:start position:0% +is usually set up you have a fair engine + + + align:start position:0% +is usually set up you have a fair engine +it's a server that has all the fair + + align:start position:0% +it's a server that has all the fair + + + align:start position:0% +it's a server that has all the fair +rules in it so we can cut fares based on + + align:start position:0% +rules in it so we can cut fares based on + + + align:start position:0% +rules in it so we can cut fares based on +a little sequence of taps and it's + + align:start position:0% +a little sequence of taps and it's + + + align:start position:0% +a little sequence of taps and it's +connected to different things so a fair + + align:start position:0% +connected to different things so a fair + + + align:start position:0% +connected to different things so a fair +vending machine that's where you + + align:start position:0% +vending machine that's where you + + + align:start position:0% +vending machine that's where you +purchase your your card or your ticket + + align:start position:0% +purchase your your card or your ticket + + + align:start position:0% +purchase your your card or your ticket +so these are usually fiber optic + + align:start position:0% +so these are usually fiber optic + + + align:start position:0% +so these are usually fiber optic +connections or sort of hard line + + align:start position:0% +connections or sort of hard line + + + align:start position:0% +connections or sort of hard line +connections and so they're fast it's + + align:start position:0% +connections and so they're fast it's + + + align:start position:0% +connections and so they're fast it's +also real time validation as soon as you + + align:start position:0% +also real time validation as soon as you + + + align:start position:0% +also real time validation as soon as you +buy a card and add value to it from a + + align:start position:0% +buy a card and add value to it from a + + + align:start position:0% +buy a card and add value to it from a +fair vending machine that balance is + + align:start position:0% +fair vending machine that balance is + + + align:start position:0% +fair vending machine that balance is +usually updated if if if the fare engine + + align:start position:0% +usually updated if if if the fare engine + + + align:start position:0% +usually updated if if if the fare engine +has balance in it it will be updated in + + align:start position:0% +has balance in it it will be updated in + + + align:start position:0% +has balance in it it will be updated in +the fare engine that's always the case + + align:start position:0% +the fare engine that's always the case + + + align:start position:0% +the fare engine that's always the case +or there's many kinds of systems so + + align:start position:0% +or there's many kinds of systems so + + + align:start position:0% +or there's many kinds of systems so +customer service booths are also + + align:start position:0% +customer service booths are also + + + align:start position:0% +customer service booths are also +connected fare gates are usually + + align:start position:0% +connected fare gates are usually + + + align:start position:0% +connected fare gates are usually +connected as + + align:start position:0% +connected as + + + align:start position:0% +connected as +so there's a quick when you tap to a + + align:start position:0% +so there's a quick when you tap to a + + + align:start position:0% +so there's a quick when you tap to a +fare gate there's a quick communication + + align:start position:0% +fare gate there's a quick communication + + + align:start position:0% +fare gate there's a quick communication +with the ferrant and saying is this card + + align:start position:0% +with the ferrant and saying is this card + + + align:start position:0% +with the ferrant and saying is this card +valid yes or no is there balance of + + align:start position:0% +valid yes or no is there balance of + + + align:start position:0% +valid yes or no is there balance of +solely ducks balance this is how much + + align:start position:0% +solely ducks balance this is how much + + + align:start position:0% +solely ducks balance this is how much +balancing so we ducted and fare gate + + align:start position:0% +balancing so we ducted and fare gate + + + align:start position:0% +balancing so we ducted and fare gate +opens or maybe Darrington says note + + align:start position:0% +opens or maybe Darrington says note + + + align:start position:0% +opens or maybe Darrington says note +cards not good + + align:start position:0% +cards not good + + + align:start position:0% +cards not good +sound the alarm don't open there are + + align:start position:0% +sound the alarm don't open there are + + + align:start position:0% +sound the alarm don't open there are +other ways of doing it so the card + + align:start position:0% +other ways of doing it so the card + + + align:start position:0% +other ways of doing it so the card +itself might hold the balance and the + + align:start position:0% +itself might hold the balance and the + + + align:start position:0% +itself might hold the balance and the +fare gate might have the logic to decide + + align:start position:0% +fare gate might have the logic to decide + + + align:start position:0% +fare gate might have the logic to decide +whether to open or not but there's a + + align:start position:0% +whether to open or not but there's a + + + align:start position:0% +whether to open or not but there's a +whole range of ways in which this can be + + align:start position:0% +whole range of ways in which this can be + + + align:start position:0% +whole range of ways in which this can be +configured fare boxes and validators are + + align:start position:0% +configured fare boxes and validators are + + + align:start position:0% +configured fare boxes and validators are +usually on vehicles although there can + + align:start position:0% +usually on vehicles although there can + + + align:start position:0% +usually on vehicles although there can +be hand-held validators again a + + align:start position:0% +be hand-held validators again a + + + align:start position:0% +be hand-held validators again a +validator is more often used for proof + + align:start position:0% +validator is more often used for proof + + + align:start position:0% +validator is more often used for proof +of payment a fare box is used when it's + + align:start position:0% +of payment a fare box is used when it's + + + align:start position:0% +of payment a fare box is used when it's +a zero or a past so that's what we have + + align:start position:0% +a zero or a past so that's what we have + + + align:start position:0% +a zero or a past so that's what we have +here in Boston these are usually there's + + align:start position:0% +here in Boston these are usually there's + + + align:start position:0% +here in Boston these are usually there's +two ways of doing this the it used to be + + align:start position:0% +two ways of doing this the it used to be + + + align:start position:0% +two ways of doing this the it used to be +the case that they were not + + align:start position:0% +the case that they were not + + + align:start position:0% +the case that they were not +communicating in real time with a fare + + align:start position:0% +communicating in real time with a fare + + + align:start position:0% +communicating in real time with a fare +engine so the card and the fare box have + + align:start position:0% +engine so the card and the fare box have + + + align:start position:0% +engine so the card and the fare box have +a little chat and the site how much + + align:start position:0% +a little chat and the site how much + + + align:start position:0% +a little chat and the site how much +value to deduct later that bus reaches + + align:start position:0% +value to deduct later that bus reaches + + + align:start position:0% +value to deduct later that bus reaches +the garage or it's being cleaned and at + + align:start position:0% +the garage or it's being cleaned and at + + + align:start position:0% +the garage or it's being cleaned and at +the garage is a garage server that wired + + align:start position:0% +the garage is a garage server that wired + + + align:start position:0% +the garage is a garage server that wired +wirelessly probes the fare box and + + align:start position:0% +wirelessly probes the fare box and + + + align:start position:0% +wirelessly probes the fare box and +extracts all the data from it and only + + align:start position:0% +extracts all the data from it and only + + + align:start position:0% +extracts all the data from it and only +then will the fur engine receive the + + align:start position:0% +then will the fur engine receive the + + + align:start position:0% +then will the fur engine receive the +information about what transactions have + + align:start position:0% +information about what transactions have + + + align:start position:0% +information about what transactions have +been done on that fare box so you might + + align:start position:0% +been done on that fare box so you might + + + align:start position:0% +been done on that fare box so you might +have again a real-time validation it's + + align:start position:0% +have again a real-time validation it's + + + align:start position:0% +have again a real-time validation it's +it can be a little slow over-the-air so + + align:start position:0% +it can be a little slow over-the-air so + + + align:start position:0% +it can be a little slow over-the-air so +what happens and this is being done with + + align:start position:0% +what happens and this is being done with + + + align:start position:0% +what happens and this is being done with +with in London for example with + + align:start position:0% +with in London for example with + + + align:start position:0% +with in London for example with +contactless bank cards what happens is + + align:start position:0% +contactless bank cards what happens is + + + align:start position:0% +contactless bank cards what happens is +that maybe the first time that a card is + + align:start position:0% +that maybe the first time that a card is + + + align:start position:0% +that maybe the first time that a card is +seen there is a this dialogue and + + align:start position:0% +seen there is a this dialogue and + + + align:start position:0% +seen there is a this dialogue and +validation after the card isn't marked + + align:start position:0% +validation after the card isn't marked + + + align:start position:0% +validation after the card isn't marked +is trusted then it can just validate + + align:start position:0% +is trusted then it can just validate + + + align:start position:0% +is trusted then it can just validate +immediately and the actual deduction can + + align:start position:0% +immediately and the actual deduction can + + + align:start position:0% +immediately and the actual deduction can +wait a little bit and be sent in batches + + align:start position:0% +wait a little bit and be sent in batches + + + align:start position:0% +wait a little bit and be sent in batches +to a fare engine so yeah there's a cash + + align:start position:0% +to a fare engine so yeah there's a cash + + + align:start position:0% +to a fare engine so yeah there's a cash +bolt that's where if your system effect + + align:start position:0% +bolt that's where if your system effect + + + align:start position:0% +bolt that's where if your system effect +accepts cash when the bus or fare box + + align:start position:0% +accepts cash when the bus or fare box + + + align:start position:0% +accepts cash when the bus or fare box +reaches the garage that + + align:start position:0% +reaches the garage that + + + align:start position:0% +reaches the garage that +cash bolt is taken out and the cash + + align:start position:0% +cash bolt is taken out and the cash + + + align:start position:0% +cash bolt is taken out and the cash +needs to be sort of counted and and + + align:start position:0% +needs to be sort of counted and and + + + align:start position:0% +needs to be sort of counted and and +moved out of the fare box into a safe + + align:start position:0% +moved out of the fare box into a safe + + + align:start position:0% +moved out of the fare box into a safe +place smart cards themselves are + + align:start position:0% +place smart cards themselves are + + + align:start position:0% +place smart cards themselves are +computers there are small computers with + + align:start position:0% +computers there are small computers with + + + align:start position:0% +computers there are small computers with +a battery and a clock and some amount of + + align:start position:0% +a battery and a clock and some amount of + + + align:start position:0% +a battery and a clock and some amount of +processing power so they have some + + align:start position:0% +processing power so they have some + + + align:start position:0% +processing power so they have some +memory so they can hold some history + + align:start position:0% +memory so they can hold some history + + + align:start position:0% +memory so they can hold some history +about your last trips they can hold how + + align:start position:0% +about your last trips they can hold how + + + align:start position:0% +about your last trips they can hold how +much balance there is in some cases they + + align:start position:0% +much balance there is in some cases they + + + align:start position:0% +much balance there is in some cases they +have they are able to encrypt and + + align:start position:0% +have they are able to encrypt and + + + align:start position:0% +have they are able to encrypt and +decrypt communication so that it's + + align:start position:0% +decrypt communication so that it's + + + align:start position:0% +decrypt communication so that it's +harder to break the security and say a + + align:start position:0% +harder to break the security and say a + + + align:start position:0% +harder to break the security and say a +balance your card and I want to add + + align:start position:0% +balance your card and I want to add + + + align:start position:0% +balance your card and I want to add +although this is not necessarily part of + + align:start position:0% +although this is not necessarily part of + + + align:start position:0% +although this is not necessarily part of +the fair system data palaces + + align:start position:0% +the fair system data palaces + + + align:start position:0% +the fair system data palaces +increasingly we are doing a lot of + + align:start position:0% +increasingly we are doing a lot of + + + align:start position:0% +increasingly we are doing a lot of +analytics so usually there's some + + align:start position:0% +analytics so usually there's some + + + align:start position:0% +analytics so usually there's some +connection between the live production + + align:start position:0% +connection between the live production + + + align:start position:0% +connection between the live production +system and a data warehouse where on a + + align:start position:0% +system and a data warehouse where on a + + + align:start position:0% +system and a data warehouse where on a +daily or weekly basis there is an + + align:start position:0% +daily or weekly basis there is an + + + align:start position:0% +daily or weekly basis there is an +extract of data into a data warehouse + + align:start position:0% +extract of data into a data warehouse + + + align:start position:0% +extract of data into a data warehouse +and that allows analyst analysts to run + + align:start position:0% +and that allows analyst analysts to run + + + align:start position:0% +and that allows analyst analysts to run +heavy queries on a server that is + + align:start position:0% +heavy queries on a server that is + + + align:start position:0% +heavy queries on a server that is +dedicated to analysis and not on the + + align:start position:0% +dedicated to analysis and not on the + + + align:start position:0% +dedicated to analysis and not on the +life system that are hitting whether or + + align:start position:0% +life system that are hitting whether or + + + align:start position:0% +life system that are hitting whether or +not to open a fit if that makes sense + + align:start position:0% + + + + align:start position:0% + +ok fare media any questions about fare + + align:start position:0% +ok fare media any questions about fare + + + align:start position:0% +ok fare media any questions about fare +technology and how the other framework + + align:start position:0% +technology and how the other framework + + + align:start position:0% +technology and how the other framework +of how this is set up there are lots of + + align:start position:0% +of how this is set up there are lots of + + + align:start position:0% +of how this is set up there are lots of +variants and I didn't get into the + + align:start position:0% +variants and I didn't get into the + + + align:start position:0% +variants and I didn't get into the +details of how any one system works but + + align:start position:0% +details of how any one system works but + + + align:start position:0% +details of how any one system works but +ok so fare media cash we all know what + + align:start position:0% +ok so fare media cash we all know what + + + align:start position:0% +ok so fare media cash we all know what +that is tokens so yeah I don't need to + + align:start position:0% +that is tokens so yeah I don't need to + + + align:start position:0% +that is tokens so yeah I don't need to +go into how cash is minted or anything + + align:start position:0% +go into how cash is minted or anything + + + align:start position:0% +go into how cash is minted or anything +right so so tokens are like little coins + + align:start position:0% +right so so tokens are like little coins + + + align:start position:0% +right so so tokens are like little coins +that you buy with money and it's like a + + align:start position:0% +that you buy with money and it's like a + + + align:start position:0% +that you buy with money and it's like a +ticket in some ways it has some value + + align:start position:0% +ticket in some ways it has some value + + + align:start position:0% +ticket in some ways it has some value +and sometimes it's possible to be able + + align:start position:0% +and sometimes it's possible to be able + + + align:start position:0% +and sometimes it's possible to be able +to have to pay two tokens for a ride + + align:start position:0% +to have to pay two tokens for a ride + + + align:start position:0% +to have to pay two tokens for a ride +although usually it's just one they're + + align:start position:0% +although usually it's just one they're + + + align:start position:0% +although usually it's just one they're +being fixed out because you can print + + align:start position:0% +being fixed out because you can print + + + align:start position:0% +being fixed out because you can print +paper tickets with magnetic stripes and + + align:start position:0% +paper tickets with magnetic stripes and + + + align:start position:0% +paper tickets with magnetic stripes and +there's more data to it yeah so they'd + + align:start position:0% +there's more data to it yeah so they'd + + + align:start position:0% +there's more data to it yeah so they'd +still exist + + align:start position:0% +still exist + + + align:start position:0% +still exist +yeah they still exist yeah this is a + + align:start position:0% +yeah they still exist yeah this is a + + + align:start position:0% +yeah they still exist yeah this is a +this is a Boston token by the way this + + align:start position:0% +this is a Boston token by the way this + + + align:start position:0% +this is a Boston token by the way this +one right here no this is uh this is I'm + + align:start position:0% +one right here no this is uh this is I'm + + + align:start position:0% +one right here no this is uh this is I'm +pretty sure that's like old Boston token + + align:start position:0% +pretty sure that's like old Boston token + + + align:start position:0% +pretty sure that's like old Boston token +yeah yeah yeah maybe I'm wrong but I + + align:start position:0% +yeah yeah yeah maybe I'm wrong but I + + + align:start position:0% +yeah yeah yeah maybe I'm wrong but I +think that's the case okay + + align:start position:0% +think that's the case okay + + + align:start position:0% +think that's the case okay +tickets so tickets are out there printed + + align:start position:0% +tickets so tickets are out there printed + + + align:start position:0% +tickets so tickets are out there printed +in paper and they have a magnetic stripe + + align:start position:0% +in paper and they have a magnetic stripe + + + align:start position:0% +in paper and they have a magnetic stripe +they don't have a computer in them the + + align:start position:0% +they don't have a computer in them the + + + align:start position:0% +they don't have a computer in them the +magnetic stripe holds information that + + align:start position:0% +magnetic stripe holds information that + + + align:start position:0% +magnetic stripe holds information that +can be encrypted so it can be it's not + + align:start position:0% +can be encrypted so it can be it's not + + + align:start position:0% +can be encrypted so it can be it's not +always encrypted so it's a little easier + + align:start position:0% +always encrypted so it's a little easier + + + align:start position:0% +always encrypted so it's a little easier +to for there to be fraud with tickets so + + align:start position:0% +to for there to be fraud with tickets so + + + align:start position:0% +to for there to be fraud with tickets so +yeah I don't know if there are there + + align:start position:0% +yeah I don't know if there are there + + + align:start position:0% +yeah I don't know if there are there +questions on tickets I'll talk more + + align:start position:0% +questions on tickets I'll talk more + + + align:start position:0% +questions on tickets I'll talk more +about them smart cards I've talked about + + align:start position:0% +about them smart cards I've talked about + + + align:start position:0% +about them smart cards I've talked about +mobile ticketing is another option so + + align:start position:0% +mobile ticketing is another option so + + + align:start position:0% +mobile ticketing is another option so +that's a recent development you have an + + align:start position:0% +that's a recent development you have an + + + align:start position:0% +that's a recent development you have an +app you pay for a ticket or for your + + align:start position:0% +app you pay for a ticket or for your + + + align:start position:0% +app you pay for a ticket or for your +ride on the app and it's usually kind of + + align:start position:0% +ride on the app and it's usually kind of + + + align:start position:0% +ride on the app and it's usually kind of +a proof of payment system where a fare + + align:start position:0% +a proof of payment system where a fare + + + align:start position:0% +a proof of payment system where a fare +inspector comes along and scans a QR + + align:start position:0% +inspector comes along and scans a QR + + + align:start position:0% +inspector comes along and scans a QR +code on the app it's proving that you've + + align:start position:0% +code on the app it's proving that you've + + + align:start position:0% +code on the app it's proving that you've +purchased a valid fare for that OD pair + + align:start position:0% +purchased a valid fare for that OD pair + + + align:start position:0% +purchased a valid fare for that OD pair +for example this is being used here in + + align:start position:0% +for example this is being used here in + + + align:start position:0% +for example this is being used here in +commuter rail in Boston and then the + + align:start position:0% +commuter rail in Boston and then the + + + align:start position:0% +commuter rail in Boston and then the +sort of newest form is contactless bank + + align:start position:0% +sort of newest form is contactless bank + + + align:start position:0% +sort of newest form is contactless bank +cards so that's a wireless Visa + + align:start position:0% +cards so that's a wireless Visa + + + align:start position:0% +cards so that's a wireless Visa +MasterCard credit charge card debit card + + align:start position:0% +MasterCard credit charge card debit card + + + align:start position:0% +MasterCard credit charge card debit card +and you you tap it on the there you go + + align:start position:0% +and you you tap it on the there you go + + + align:start position:0% +and you you tap it on the there you go +you can pass it if you watch oh can I + + align:start position:0% +you can pass it if you watch oh can I + + + align:start position:0% +you can pass it if you watch oh can I +see it so so right so you tap it just + + align:start position:0% +see it so so right so you tap it just + + + align:start position:0% +see it so so right so you tap it just +like you would a a Charlie card or an + + align:start position:0% +like you would a a Charlie card or an + + + align:start position:0% +like you would a a Charlie card or an +oyster card in London and there's the + + align:start position:0% +oyster card in London and there's the + + + align:start position:0% +oyster card in London and there's the +dialogue between the fare engine so and + + align:start position:0% +dialogue between the fare engine so and + + + align:start position:0% +dialogue between the fare engine so and +the card strong encryption as I said + + align:start position:0% +the card strong encryption as I said + + + align:start position:0% +the card strong encryption as I said +validation the full validation process + + align:start position:0% +validation the full validation process + + + align:start position:0% +validation the full validation process +doesn't always happen especially in bus + + align:start position:0% +doesn't always happen especially in bus + + + align:start position:0% +doesn't always happen especially in bus +because you can trust the card there is + + align:start position:0% +because you can trust the card there is + + + align:start position:0% +because you can trust the card there is +a separate antenna of course the + + align:start position:0% +a separate antenna of course the + + + align:start position:0% +a separate antenna of course the +frequencies and the protocols are + + align:start position:0% +frequencies and the protocols are + + + align:start position:0% +frequencies and the protocols are +different + + align:start position:0% +different + + + align:start position:0% +different +but there are good standards for this + + align:start position:0% +but there are good standards for this + + + align:start position:0% +but there are good standards for this +and London's moved to this the CTA's + + align:start position:0% +and London's moved to this the CTA's + + + align:start position:0% +and London's moved to this the CTA's +system is based on this technology even + + align:start position:0% +system is based on this technology even + + + align:start position:0% +system is based on this technology even +though they they opted to only used like + + align:start position:0% +though they they opted to only used like + + + align:start position:0% +though they they opted to only used like +tokens token cards so it's the same + + align:start position:0% +tokens token cards so it's the same + + + align:start position:0% +tokens token cards so it's the same +technology but it's branded as their own + + align:start position:0% +technology but it's branded as their own + + + align:start position:0% +technology but it's branded as their own +thing and I don't know if that you can + + align:start position:0% +thing and I don't know if that you can + + + align:start position:0% +thing and I don't know if that you can +now now it does right but at the + + align:start position:0% +now now it does right but at the + + + align:start position:0% +now now it does right but at the +beginning it wasn't yeah yeah so yeah + + align:start position:0% +beginning it wasn't yeah yeah so yeah + + + align:start position:0% +beginning it wasn't yeah yeah so yeah +yeah with this as you have more and more + + align:start position:0% +yeah with this as you have more and more + + + align:start position:0% +yeah with this as you have more and more +cards on your wallet that are + + align:start position:0% +cards on your wallet that are + + + align:start position:0% +cards on your wallet that are +contactless you should get you get like + + align:start position:0% +contactless you should get you get like + + + align:start position:0% +contactless you should get you get like +a copper lined wallet or something - + + align:start position:0% +a copper lined wallet or something - + + + align:start position:0% +a copper lined wallet or something - +like copper sleeves they exist to sort + + align:start position:0% +like copper sleeves they exist to sort + + + align:start position:0% +like copper sleeves they exist to sort +of prevent - reads from the same card + + align:start position:0% + + + + align:start position:0% + +nothing you get on the bus yes yeah it + + align:start position:0% +nothing you get on the bus yes yeah it + + + align:start position:0% +nothing you get on the bus yes yeah it +used to be the case in Chicago that it + + align:start position:0% +used to be the case in Chicago that it + + + align:start position:0% +used to be the case in Chicago that it +was kind of their own thing and you you + + align:start position:0% +was kind of their own thing and you you + + + align:start position:0% +was kind of their own thing and you you +you were given a card it was the same + + align:start position:0% +you were given a card it was the same + + + align:start position:0% +you were given a card it was the same +thing as a credit card but just as a + + align:start position:0% +thing as a credit card but just as a + + + align:start position:0% +thing as a credit card but just as a +token with no balance or account on it + + align:start position:0% +token with no balance or account on it + + + align:start position:0% +token with no balance or account on it +and now they've enabled this so that's + + align:start position:0% +and now they've enabled this so that's + + + align:start position:0% +and now they've enabled this so that's +the again you do validation there are + + align:start position:0% +the again you do validation there are + + + align:start position:0% +the again you do validation there are +there are policies that's what these + + align:start position:0% +there are policies that's what these + + + align:start position:0% +there are policies that's what these +card companies do they're good at it + + align:start position:0% +card companies do they're good at it + + + align:start position:0% +card companies do they're good at it +there's a there's insurance referred so + + align:start position:0% +there's a there's insurance referred so + + + align:start position:0% +there's a there's insurance referred so +they yeah they + + align:start position:0% + + + + align:start position:0% + +right so there's no there's no way of + + align:start position:0% +right so there's no there's no way of + + + align:start position:0% +right so there's no there's no way of +que they don't have capping scheme so if + + align:start position:0% +que they don't have capping scheme so if + + + align:start position:0% +que they don't have capping scheme so if +you need if you want the pass that's not + + align:start position:0% +you need if you want the pass that's not + + + align:start position:0% +you need if you want the pass that's not +an option for you it's what you're + + align:start position:0% +an option for you it's what you're + + + align:start position:0% +an option for you it's what you're +saying then you okay yeah so so that's + + align:start position:0% +saying then you okay yeah so so that's + + + align:start position:0% +saying then you okay yeah so so that's +an interesting comment which no one + + align:start position:0% +an interesting comment which no one + + + align:start position:0% +an interesting comment which no one +heard so I'm sure the comments on the + + align:start position:0% +heard so I'm sure the comments on the + + + align:start position:0% +heard so I'm sure the comments on the +back are also interesting no I'm + + align:start position:0% +back are also interesting no I'm + + + align:start position:0% +back are also interesting no I'm +genuinely interested are you like can + + align:start position:0% +genuinely interested are you like can + + + align:start position:0% +genuinely interested are you like can +you share with the class all right okay + + align:start position:0% +you share with the class all right okay + + + align:start position:0% +you share with the class all right okay +are supposed to EMV and yeah I think + + align:start position:0% +are supposed to EMV and yeah I think + + + align:start position:0% +are supposed to EMV and yeah I think +they will increase and that I think well + + align:start position:0% +they will increase and that I think well + + + align:start position:0% +they will increase and that I think well +it could be driven by agencies in big + + align:start position:0% +it could be driven by agencies in big + + + align:start position:0% +it could be driven by agencies in big +cities actually there's one example is + + align:start position:0% +cities actually there's one example is + + + align:start position:0% +cities actually there's one example is +that the US has been a little late in + + align:start position:0% +that the US has been a little late in + + + align:start position:0% +that the US has been a little late in +adopting credit card technology in + + align:start position:0% +adopting credit card technology in + + + align:start position:0% +adopting credit card technology in +general so alright smart cards so I've + + align:start position:0% +general so alright smart cards so I've + + + align:start position:0% +general so alright smart cards so I've +already talked a little bit about them + + align:start position:0% +already talked a little bit about them + + + align:start position:0% +already talked a little bit about them +they enable more complex fish structures + + align:start position:0% +they enable more complex fish structures + + + align:start position:0% +they enable more complex fish structures +they allow faster boarding and higher + + align:start position:0% +they allow faster boarding and higher + + + align:start position:0% +they allow faster boarding and higher +gate Bank throughput because the + + align:start position:0% +gate Bank throughput because the + + + align:start position:0% +gate Bank throughput because the +validation is much faster than a ticket + + align:start position:0% +validation is much faster than a ticket + + + align:start position:0% +validation is much faster than a ticket +magnetic stripe tickets need to needs to + + align:start position:0% +magnetic stripe tickets need to needs to + + + align:start position:0% +magnetic stripe tickets need to needs to +be sort of fed in and read multiple + + align:start position:0% +be sort of fed in and read multiple + + + align:start position:0% +be sort of fed in and read multiple +times sometimes and it takes more more + + align:start position:0% +times sometimes and it takes more more + + + align:start position:0% +times sometimes and it takes more more +time to do that certainly cache is + + align:start position:0% +time to do that certainly cache is + + + align:start position:0% +time to do that certainly cache is +slower so account registration is one of + + align:start position:0% +slower so account registration is one of + + + align:start position:0% +slower so account registration is one of +the benefits of smart cards you open an + + align:start position:0% +the benefits of smart cards you open an + + + align:start position:0% +the benefits of smart cards you open an +account you don't have to do this but + + align:start position:0% +account you don't have to do this but + + + align:start position:0% +account you don't have to do this but +you often can so you open an account and + + align:start position:0% +you often can so you open an account and + + + align:start position:0% +you often can so you open an account and +that gives you balance protection if + + align:start position:0% +that gives you balance protection if + + + align:start position:0% +that gives you balance protection if +your card is lost you can log into your + + align:start position:0% +your card is lost you can log into your + + + align:start position:0% +your card is lost you can log into your +account and remove that card the balance + + align:start position:0% +account and remove that card the balance + + + align:start position:0% +account and remove that card the balance +could be retained on the accounts you + + align:start position:0% +could be retained on the accounts you + + + align:start position:0% +could be retained on the accounts you +could get a new card associated with + + align:start position:0% +could get a new card associated with + + + align:start position:0% +could get a new card associated with +that account you have your balance + + align:start position:0% +that account you have your balance + + + align:start position:0% +that account you have your balance +autoloaders and other convenience you + + align:start position:0% +autoloaders and other convenience you + + + align:start position:0% +autoloaders and other convenience you +might have you know a rule that says if + + align:start position:0% +might have you know a rule that says if + + + align:start position:0% +might have you know a rule that says if +my balance drops below five dollars + + align:start position:0% +my balance drops below five dollars + + + align:start position:0% +my balance drops below five dollars +charge twenty so if it's top of you top + + align:start position:0% +charge twenty so if it's top of you top + + + align:start position:0% +charge twenty so if it's top of you top +up or pay as you go + + align:start position:0% +up or pay as you go + + + align:start position:0% +up or pay as you go +then you + + align:start position:0% +then you + + + align:start position:0% +then you +this is one feature of course it's much + + align:start position:0% +this is one feature of course it's much + + + align:start position:0% +this is one feature of course it's much +better for for us for us sort of + + align:start position:0% +better for for us for us sort of + + + align:start position:0% +better for for us for us sort of +researchers and data nerds right better + + align:start position:0% +researchers and data nerds right better + + + align:start position:0% +researchers and data nerds right better +data for analysis and planning + + align:start position:0% +data for analysis and planning + + + align:start position:0% +data for analysis and planning +longitudinal studies you can track a + + align:start position:0% +longitudinal studies you can track a + + + align:start position:0% +longitudinal studies you can track a +token longitudinally and understand more + + align:start position:0% +token longitudinally and understand more + + + align:start position:0% +token longitudinally and understand more +about behavior its embeddable and + + align:start position:0% +about behavior its embeddable and + + + align:start position:0% +about behavior its embeddable and +employing student badges as we've seen + + align:start position:0% +employing student badges as we've seen + + + align:start position:0% +employing student badges as we've seen +they are more expensive than tickets now + + align:start position:0% +they are more expensive than tickets now + + + align:start position:0% +they are more expensive than tickets now +there are some tickets so like you can + + align:start position:0% +there are some tickets so like you can + + + align:start position:0% +there are some tickets so like you can +print a card with a chip circuit inside + + align:start position:0% +print a card with a chip circuit inside + + + align:start position:0% +print a card with a chip circuit inside +those are a little cheaper one issue + + align:start position:0% +those are a little cheaper one issue + + + align:start position:0% +those are a little cheaper one issue +with smart cards has is that a lot of + + align:start position:0% +with smart cards has is that a lot of + + + align:start position:0% +with smart cards has is that a lot of +these systems are proprietary and there + + align:start position:0% +these systems are proprietary and there + + + align:start position:0% +these systems are proprietary and there +are some standards but there are several + + align:start position:0% +are some standards but there are several + + + align:start position:0% +are some standards but there are several +standards too many of them and they + + align:start position:0% +standards too many of them and they + + + align:start position:0% +standards too many of them and they +don't all work everywhere and and so you + + align:start position:0% +don't all work everywhere and and so you + + + align:start position:0% +don't all work everywhere and and so you +can't really use a card from one system + + align:start position:0% +can't really use a card from one system + + + align:start position:0% +can't really use a card from one system +on another system that's usually not the + + align:start position:0% +on another system that's usually not the + + + align:start position:0% +on another system that's usually not the +case there are some exceptions to that + + align:start position:0% +case there are some exceptions to that + + + align:start position:0% +case there are some exceptions to that +there is a move towards open source + + align:start position:0% +there is a move towards open source + + + align:start position:0% +there is a move towards open source +hardware and specifications New York is + + align:start position:0% +hardware and specifications New York is + + + align:start position:0% +hardware and specifications New York is +a good example of that they recently did + + align:start position:0% +a good example of that they recently did + + + align:start position:0% +a good example of that they recently did +some procurements where they asked all + + align:start position:0% +some procurements where they asked all + + + align:start position:0% +some procurements where they asked all +the parts to be it was an AVL system in + + align:start position:0% +the parts to be it was an AVL system in + + + align:start position:0% +the parts to be it was an AVL system in +this case to be open source hardware and + + align:start position:0% +this case to be open source hardware and + + + align:start position:0% +this case to be open source hardware and +communications technology that means + + align:start position:0% +communications technology that means + + + align:start position:0% +communications technology that means +there is not they're not locked into + + align:start position:0% +there is not they're not locked into + + + align:start position:0% +there is not they're not locked into +that vendor so if they need to replace + + align:start position:0% +that vendor so if they need to replace + + + align:start position:0% +that vendor so if they need to replace +one aspect of that system they can hire + + align:start position:0% +one aspect of that system they can hire + + + align:start position:0% +one aspect of that system they can hire +someone else that also complies with a + + align:start position:0% +someone else that also complies with a + + + align:start position:0% +someone else that also complies with a +standard and that part can be replaced + + align:start position:0% +standard and that part can be replaced + + + align:start position:0% +standard and that part can be replaced +that lowers costs increases competition + + align:start position:0% +that lowers costs increases competition + + + align:start position:0% +that lowers costs increases competition +and it means again that they're not + + align:start position:0% +and it means again that they're not + + + align:start position:0% +and it means again that they're not +locked in to that vendor Lee + + align:start position:0% + + + + align:start position:0% + +they're usually the systems have strong + + align:start position:0% +they're usually the systems have strong + + + align:start position:0% +they're usually the systems have strong +standard encryption part of the standard + + align:start position:0% +standard encryption part of the standard + + + align:start position:0% +standard encryption part of the standard +is what encryption is used and what + + align:start position:0% +is what encryption is used and what + + + align:start position:0% +is what encryption is used and what +encryption algorithms are used hashing + + align:start position:0% +encryption algorithms are used hashing + + + align:start position:0% +encryption algorithms are used hashing +etc yeah so the Charlie card has pretty + + align:start position:0% +etc yeah so the Charlie card has pretty + + + align:start position:0% +etc yeah so the Charlie card has pretty +weak encryption 40 bits I think and the + + align:start position:0% +weak encryption 40 bits I think and the + + + align:start position:0% +weak encryption 40 bits I think and the +same key on every card so a long time + + align:start position:0% +same key on every card so a long time + + + align:start position:0% +same key on every card so a long time +ago someone cracked the key by brute + + align:start position:0% +ago someone cracked the key by brute + + + align:start position:0% +ago someone cracked the key by brute +force and it's the same key on every + + align:start position:0% +force and it's the same key on every + + + align:start position:0% +force and it's the same key on every +Charlie card so once that key is public + + align:start position:0% +Charlie card so once that key is public + + + align:start position:0% +Charlie card so once that key is public +anyone with the equipment could load up + + align:start position:0% +anyone with the equipment could load up + + + align:start position:0% +anyone with the equipment could load up +fake balance to the card because the + + align:start position:0% +fake balance to the card because the + + + align:start position:0% +fake balance to the card because the +cards are the ones having the balance in + + align:start position:0% +cards are the ones having the balance in + + + align:start position:0% +cards are the ones having the balance in +and AFC system here not the fair engine + + align:start position:0% +and AFC system here not the fair engine + + + align:start position:0% +and AFC system here not the fair engine +that means that effectively you can lie + + align:start position:0% +that means that effectively you can lie + + + align:start position:0% +that means that effectively you can lie +to the fair system and say that you have + + align:start position:0% +to the fair system and say that you have + + + align:start position:0% +to the fair system and say that you have +more money than you have much harder to + + align:start position:0% +more money than you have much harder to + + + align:start position:0% +more money than you have much harder to +do with any modern system certainly a + + align:start position:0% +do with any modern system certainly a + + + align:start position:0% +do with any modern system certainly a +contactless bank card which has a very + + align:start position:0% +contactless bank card which has a very + + + align:start position:0% +contactless bank card which has a very +strong encryption and unique keys per + + align:start position:0% +strong encryption and unique keys per + + + align:start position:0% +strong encryption and unique keys per +card so the MIT students were the first + + align:start position:0% +card so the MIT students were the first + + + align:start position:0% +card so the MIT students were the first +to do this so they were caught and there + + align:start position:0% +to do this so they were caught and there + + + align:start position:0% +to do this so they were caught and there +was some issue with I think it ended up + + align:start position:0% +was some issue with I think it ended up + + + align:start position:0% +was some issue with I think it ended up +being just a slap on the wrist but but + + align:start position:0% +being just a slap on the wrist but but + + + align:start position:0% +being just a slap on the wrist but but +there was a lot of a lot of issue with + + align:start position:0% +there was a lot of a lot of issue with + + + align:start position:0% +there was a lot of a lot of issue with +it because they wanted to publish a + + align:start position:0% +it because they wanted to publish a + + + align:start position:0% +it because they wanted to publish a +paper or publish something and then yeah + + align:start position:0% +paper or publish something and then yeah + + + align:start position:0% +paper or publish something and then yeah +that was an issue + + align:start position:0% +that was an issue + + + align:start position:0% +that was an issue +okay so integration across agencies of a + + align:start position:0% +okay so integration across agencies of a + + + align:start position:0% +okay so integration across agencies of a +region is possible that's one of the + + align:start position:0% +region is possible that's one of the + + + align:start position:0% +region is possible that's one of the +reasons for moving towards smart cards + + align:start position:0% +reasons for moving towards smart cards + + + align:start position:0% +reasons for moving towards smart cards +especially in regions that have many + + align:start position:0% +especially in regions that have many + + + align:start position:0% +especially in regions that have many +providers but it's challenging and + + align:start position:0% +providers but it's challenging and + + + align:start position:0% +providers but it's challenging and +usually the challenges are less + + align:start position:0% +usually the challenges are less + + + align:start position:0% +usually the challenges are less +technical and more about trust and + + align:start position:0% +technical and more about trust and + + + align:start position:0% +technical and more about trust and +business and who gets to decide what + + align:start position:0% +business and who gets to decide what + + + align:start position:0% +business and who gets to decide what +color the card is or exactly what the + + align:start position:0% +color the card is or exactly what the + + + align:start position:0% +color the card is or exactly what the +fare policy will be this is another + + align:start position:0% +fare policy will be this is another + + + align:start position:0% +fare policy will be this is another +interesting thing in some countries and + + align:start position:0% +interesting thing in some countries and + + + align:start position:0% +interesting thing in some countries and +I'm thinking specifically with Japan and + + align:start position:0% +I'm thinking specifically with Japan and + + + align:start position:0% +I'm thinking specifically with Japan and +China there are examples of retail + + align:start position:0% +China there are examples of retail + + + align:start position:0% +China there are examples of retail +stores that have partnered with the + + align:start position:0% +stores that have partnered with the + + + align:start position:0% +stores that have partnered with the +transit agency and you can use the card + + align:start position:0% +transit agency and you can use the card + + + align:start position:0% +transit agency and you can use the card +for at retail locations Hong Kong is an + + align:start position:0% +for at retail locations Hong Kong is an + + + align:start position:0% +for at retail locations Hong Kong is an +example of that there's one more than + + align:start position:0% +example of that there's one more than + + + align:start position:0% +example of that there's one more than +100 retail locations except octopus and + + align:start position:0% +100 retail locations except octopus and + + + align:start position:0% +100 retail locations except octopus and +in Japan I know that there are entire + + align:start position:0% +in Japan I know that there are entire + + + align:start position:0% +in Japan I know that there are entire +cities where there's like a whole mall + + align:start position:0% +cities where there's like a whole mall + + + align:start position:0% +cities where there's like a whole mall +and this is what most people use as the + + align:start position:0% +and this is what most people use as the + + + align:start position:0% +and this is what most people use as the +chart + + align:start position:0% +chart + + + align:start position:0% +chart +card so that's injured if you don't have + + align:start position:0% +card so that's injured if you don't have + + + align:start position:0% +card so that's injured if you don't have +very tough privacy laws a civil in + + align:start position:0% +very tough privacy laws a civil in + + + align:start position:0% +very tough privacy laws a civil in +Europe and the US I don't I'm not sure + + align:start position:0% +Europe and the US I don't I'm not sure + + + align:start position:0% +Europe and the US I don't I'm not sure +what they are in Japan but but uh there + + align:start position:0% +what they are in Japan but but uh there + + + align:start position:0% +what they are in Japan but but uh there +was some research where they were + + align:start position:0% +was some research where they were + + + align:start position:0% +was some research where they were +combining all the data from shopping and + + align:start position:0% +combining all the data from shopping and + + + align:start position:0% +combining all the data from shopping and +transit to get really interesting + + align:start position:0% +transit to get really interesting + + + align:start position:0% +transit to get really interesting +behavioral analytics on and you can do + + align:start position:0% +behavioral analytics on and you can do + + + align:start position:0% +behavioral analytics on and you can do +interesting things like offer discounts + + align:start position:0% +interesting things like offer discounts + + + align:start position:0% +interesting things like offer discounts +at stores if you do something in transit + + align:start position:0% +at stores if you do something in transit + + + align:start position:0% +at stores if you do something in transit +so there's a lot of very interesting + + align:start position:0% + + + + align:start position:0% + +yeah yeah thanks for sharing + + align:start position:0% +yeah yeah thanks for sharing + + + align:start position:0% +yeah yeah thanks for sharing +so contactless bank cards we started + + align:start position:0% +so contactless bank cards we started + + + align:start position:0% +so contactless bank cards we started +talking about this we've mentioned that + + align:start position:0% +talking about this we've mentioned that + + + align:start position:0% +talking about this we've mentioned that +multiple times here's the logic for it a + + align:start position:0% +multiple times here's the logic for it a + + + align:start position:0% +multiple times here's the logic for it a +transit agency would prefer not having + + align:start position:0% +transit agency would prefer not having + + + align:start position:0% +transit agency would prefer not having +to deal with the complexities and costs + + align:start position:0% +to deal with the complexities and costs + + + align:start position:0% +to deal with the complexities and costs +of fare collection having essentially if + + align:start position:0% +of fare collection having essentially if + + + align:start position:0% +of fare collection having essentially if +you have a fare system it's like having + + align:start position:0% +you have a fare system it's like having + + + align:start position:0% +you have a fare system it's like having +a small bank right it doesn't give out + + align:start position:0% +a small bank right it doesn't give out + + + align:start position:0% +a small bank right it doesn't give out +loans it doesn't do other things that + + align:start position:0% +loans it doesn't do other things that + + + align:start position:0% +loans it doesn't do other things that +banks do but you are dealing with money + + align:start position:0% +banks do but you are dealing with money + + + align:start position:0% +banks do but you are dealing with money +and cards and customer service related + + align:start position:0% +and cards and customer service related + + + align:start position:0% +and cards and customer service related +to cards and all those things + + align:start position:0% +to cards and all those things + + + align:start position:0% +to cards and all those things +banks do that and they do it very well + + align:start position:0% +banks do that and they do it very well + + + align:start position:0% +banks do that and they do it very well +so why not outsource that part of the + + align:start position:0% +so why not outsource that part of the + + + align:start position:0% +so why not outsource that part of the +business + + align:start position:0% +business + + + align:start position:0% +business +- banks there are multiple banks so you + + align:start position:0% +- banks there are multiple banks so you + + + align:start position:0% +- banks there are multiple banks so you +can get competition so credit card + + align:start position:0% +can get competition so credit card + + + align:start position:0% +can get competition so credit card +companies specialize in payment + + align:start position:0% +companies specialize in payment + + + align:start position:0% +companies specialize in payment +contactless bank cards are very secure + + align:start position:0% +contactless bank cards are very secure + + + align:start position:0% +contactless bank cards are very secure +much more so than like say the Charlie + + align:start position:0% +much more so than like say the Charlie + + + align:start position:0% +much more so than like say the Charlie +card you can use cards like this in + + align:start position:0% +card you can use cards like this in + + + align:start position:0% +card you can use cards like this in +several ways so you could directly use + + align:start position:0% +several ways so you could directly use + + + align:start position:0% +several ways so you could directly use +them for payment as you would at a + + align:start position:0% +them for payment as you would at a + + + align:start position:0% +them for payment as you would at a +retail location or you can use the token + + align:start position:0% +retail location or you can use the token + + + align:start position:0% +retail location or you can use the token +that identifies that card tying it to an + + align:start position:0% +that identifies that card tying it to an + + + align:start position:0% +that identifies that card tying it to an +account and then you could you live your + + align:start position:0% +account and then you could you live your + + + align:start position:0% +account and then you could you live your +fare engine can calculate what the fair + + align:start position:0% +fare engine can calculate what the fair + + + align:start position:0% +fare engine can calculate what the fair +will be and capping and all that and + + align:start position:0% +will be and capping and all that and + + + align:start position:0% +will be and capping and all that and +then every now Arabs at a regular basis + + align:start position:0% +then every now Arabs at a regular basis + + + align:start position:0% +then every now Arabs at a regular basis +on a regular basis there would be a + + align:start position:0% +on a regular basis there would be a + + + align:start position:0% +on a regular basis there would be a +charge to your credit card or account + + align:start position:0% +charge to your credit card or account + + + align:start position:0% +charge to your credit card or account +for whatever total was calculated + + align:start position:0% +for whatever total was calculated + + + align:start position:0% + +so that also enables Apple pay and + + align:start position:0% +so that also enables Apple pay and + + + align:start position:0% +so that also enables Apple pay and +Android pay if you can put your credit + + align:start position:0% +Android pay if you can put your credit + + + align:start position:0% +Android pay if you can put your credit +card on your phone then you can use your + + align:start position:0% +card on your phone then you can use your + + + align:start position:0% +card on your phone then you can use your +phone to get into the system in London + + align:start position:0% +phone to get into the system in London + + + align:start position:0% +phone to get into the system in London +people love that it reduces fare + + align:start position:0% +people love that it reduces fare + + + align:start position:0% +people love that it reduces fare +collection cost so why not necessarily + + align:start position:0% +collection cost so why not necessarily + + + align:start position:0% +collection cost so why not necessarily +obvious but so it simplifies customer + + align:start position:0% +obvious but so it simplifies customer + + + align:start position:0% +obvious but so it simplifies customer +communication right you don't have to + + align:start position:0% +communication right you don't have to + + + align:start position:0% +communication right you don't have to +issue new cards and to to people you + + align:start position:0% +issue new cards and to to people you + + + align:start position:0% +issue new cards and to to people you +have to explain how you pay because + + align:start position:0% +have to explain how you pay because + + + align:start position:0% +have to explain how you pay because +people know how to use cards + + align:start position:0% +people know how to use cards + + + align:start position:0% +people know how to use cards +it relies on open standards so there's + + align:start position:0% +it relies on open standards so there's + + + align:start position:0% +it relies on open standards so there's +more competition on the market there's + + align:start position:0% +more competition on the market there's + + + align:start position:0% +more competition on the market there's +several banks for example and you can + + align:start position:0% +several banks for example and you can + + + align:start position:0% +several banks for example and you can +use you could have banks compete for + + align:start position:0% +use you could have banks compete for + + + align:start position:0% +use you could have banks compete for +which who will give you a better deal in + + align:start position:0% +which who will give you a better deal in + + + align:start position:0% +which who will give you a better deal in +terms of fees on on these cards it + + align:start position:0% +terms of fees on on these cards it + + + align:start position:0% +terms of fees on on these cards it +outsources some aspects of customer + + align:start position:0% +outsources some aspects of customer + + + align:start position:0% +outsources some aspects of customer +service to banks so my card stopped + + align:start position:0% +service to banks so my card stopped + + + align:start position:0% +service to banks so my card stopped +working who's gonna get the phone call + + align:start position:0% +working who's gonna get the phone call + + + align:start position:0% +working who's gonna get the phone call +no chance I didn't see or the bank and + + align:start position:0% +no chance I didn't see or the bank and + + + align:start position:0% +no chance I didn't see or the bank and +it eliminates costs of sort of creating + + align:start position:0% +it eliminates costs of sort of creating + + + align:start position:0% +it eliminates costs of sort of creating +and distributing smart cards so there + + align:start position:0% +and distributing smart cards so there + + + align:start position:0% +and distributing smart cards so there +are several ways in which this is + + align:start position:0% +are several ways in which this is + + + align:start position:0% +are several ways in which this is +reducing cost London has successfully + + align:start position:0% +reducing cost London has successfully + + + align:start position:0% +reducing cost London has successfully +been able to reduce a number of station + + align:start position:0% +been able to reduce a number of station + + + align:start position:0% +been able to reduce a number of station +attendants and and especially of sort of + + align:start position:0% +attendants and and especially of sort of + + + align:start position:0% +attendants and and especially of sort of +booths where they sell waster cards and + + align:start position:0% +booths where they sell waster cards and + + + align:start position:0% +booths where they sell waster cards and +after customer service related to a + + align:start position:0% +after customer service related to a + + + align:start position:0% +after customer service related to a +store card they've been able to close + + align:start position:0% +store card they've been able to close + + + align:start position:0% +store card they've been able to close +those and save money and then there's an + + align:start position:0% +those and save money and then there's an + + + align:start position:0% +those and save money and then there's an +equity issue that's this is what is + + align:start position:0% +equity issue that's this is what is + + + align:start position:0% +equity issue that's this is what is +always sort of brought up when when you + + align:start position:0% +always sort of brought up when when you + + + align:start position:0% +always sort of brought up when when you +talk about complex as bank cards which + + align:start position:0% +talk about complex as bank cards which + + + align:start position:0% +talk about complex as bank cards which +is what about the unbanked the poorest + + align:start position:0% +is what about the unbanked the poorest + + + align:start position:0% +is what about the unbanked the poorest +people are the ones who don't have a + + align:start position:0% +people are the ones who don't have a + + + align:start position:0% +people are the ones who don't have a +bank account so what can you do about + + align:start position:0% +bank account so what can you do about + + + align:start position:0% +bank account so what can you do about +that this does that make this not work + + align:start position:0% +that this does that make this not work + + + align:start position:0% +that this does that make this not work +so there are multiple ways of addressing + + align:start position:0% +so there are multiple ways of addressing + + + align:start position:0% +so there are multiple ways of addressing +that an agency can issue cards that have + + align:start position:0% +that an agency can issue cards that have + + + align:start position:0% +that an agency can issue cards that have +pre-loaded balance so that person could + + align:start position:0% +pre-loaded balance so that person could + + + align:start position:0% +pre-loaded balance so that person could +interact with the agency not the bank + + align:start position:0% +interact with the agency not the bank + + + align:start position:0% +interact with the agency not the bank +they don't necessarily need a bank + + align:start position:0% +they don't necessarily need a bank + + + align:start position:0% +they don't necessarily need a bank +account you can have banks offer free + + align:start position:0% +account you can have banks offer free + + + align:start position:0% +account you can have banks offer free +accounts so you can try to encourage + + align:start position:0% +accounts so you can try to encourage + + + align:start position:0% +accounts so you can try to encourage +people to open accounts that have no fee + + align:start position:0% +people to open accounts that have no fee + + + align:start position:0% +people to open accounts that have no fee +no minimum balance so some sort of + + align:start position:0% +no minimum balance so some sort of + + + align:start position:0% +no minimum balance so some sort of +special accounts created for that and + + align:start position:0% +special accounts created for that and + + + align:start position:0% +special accounts created for that and +one other issue is that you must be able + + align:start position:0% +one other issue is that you must be able + + + align:start position:0% +one other issue is that you must be able +to obtain these cards at many locations + + align:start position:0% +to obtain these cards at many locations + + + align:start position:0% +to obtain these cards at many locations +if you move towards a system like this + + align:start position:0% +if you move towards a system like this + + + align:start position:0% +if you move towards a system like this +and you can only get a card what one of + + align:start position:0% +and you can only get a card what one of + + + align:start position:0% +and you can only get a card what one of +these sort of equity issue cards if you + + align:start position:0% +these sort of equity issue cards if you + + + align:start position:0% +these sort of equity issue cards if you +want from you know one station downtown + + align:start position:0% +want from you know one station downtown + + + align:start position:0% +want from you know one station downtown +that means that the person who depends + + align:start position:0% +that means that the person who depends + + + align:start position:0% +that means that the person who depends +on two or three buses to get into + + align:start position:0% +on two or three buses to get into + + + align:start position:0% +on two or three buses to get into +downtown can't easily get a card so you + + align:start position:0% +downtown can't easily get a card so you + + + align:start position:0% +downtown can't easily get a card so you +must be able to maybe get these at + + align:start position:0% +must be able to maybe get these at + + + align:start position:0% +must be able to maybe get these at +several retail locations or have fare + + align:start position:0% +several retail locations or have fare + + + align:start position:0% +several retail locations or have fare +boxes or fair fair vending machines + + align:start position:0% +boxes or fair fair vending machines + + + align:start position:0% +boxes or fair fair vending machines +rather in multiple places especially in + + align:start position:0% +rather in multiple places especially in + + + align:start position:0% +rather in multiple places especially in +zones of high concentrations of people + + align:start position:0% +zones of high concentrations of people + + + align:start position:0% +zones of high concentrations of people +that depend on on transit and don't have + + align:start position:0% +that depend on on transit and don't have + + + align:start position:0% +that depend on on transit and don't have +bank accounts okay so that there there + + align:start position:0% +bank accounts okay so that there there + + + align:start position:0% +bank accounts okay so that there there +are ways of dealing with that + + align:start position:0% +are ways of dealing with that + + + align:start position:0% +are ways of dealing with that +Boston is considering now what they call + + align:start position:0% +Boston is considering now what they call + + + align:start position:0% +Boston is considering now what they call +AFC 2.0 their branding it that way and + + align:start position:0% +AFC 2.0 their branding it that way and + + + align:start position:0% +AFC 2.0 their branding it that way and +they're probably gonna be moving with + + align:start position:0% +they're probably gonna be moving with + + + align:start position:0% +they're probably gonna be moving with +forward with London model of using + + align:start position:0% +forward with London model of using + + + align:start position:0% +forward with London model of using +contactless bank cards and so we'll see + + align:start position:0% +contactless bank cards and so we'll see + + + align:start position:0% +contactless bank cards and so we'll see +how it plays out and we'll see what that + + align:start position:0% +how it plays out and we'll see what that + + + align:start position:0% +how it plays out and we'll see what that +does to the payment industry in general + + align:start position:0% +does to the payment industry in general + + + align:start position:0% +does to the payment industry in general +and in the u.s. in terms of that means + + align:start position:0% +and in the u.s. in terms of that means + + + align:start position:0% +and in the u.s. in terms of that means +more people have these does that mean + + align:start position:0% +more people have these does that mean + + + align:start position:0% +more people have these does that mean +that a lot of readers at retail + + align:start position:0% +that a lot of readers at retail + + + align:start position:0% +that a lot of readers at retail +locations will start accepting that and + + align:start position:0% +locations will start accepting that and + + + align:start position:0% +locations will start accepting that and +what will that do that isn't is a + + align:start position:0% +what will that do that isn't is a + + + align:start position:0% +what will that do that isn't is a +question we'll see what happens + + align:start position:0% +question we'll see what happens + + + align:start position:0% +question we'll see what happens +okay last topic is fare analytics so + + align:start position:0% +okay last topic is fare analytics so + + + align:start position:0% +okay last topic is fare analytics so +obviously a lot of data is generated by + + align:start position:0% +obviously a lot of data is generated by + + + align:start position:0% +obviously a lot of data is generated by +the systems we've used it fro the X + + align:start position:0% +the systems we've used it fro the X + + + align:start position:0% +the systems we've used it fro the X +where you've looked at it in your + + align:start position:0% +where you've looked at it in your + + + align:start position:0% +where you've looked at it in your +homeworks so here's an example from one + + align:start position:0% +homeworks so here's an example from one + + + align:start position:0% +homeworks so here's an example from one +of the students in the transit lab who + + align:start position:0% +of the students in the transit lab who + + + align:start position:0% +of the students in the transit lab who +has one more year to graduate but he's + + align:start position:0% +has one more year to graduate but he's + + + align:start position:0% +has one more year to graduate but he's +done great work his name is Andrew + + align:start position:0% +done great work his name is Andrew + + + align:start position:0% +done great work his name is Andrew +stunts and one of the examples of his + + align:start position:0% +stunts and one of the examples of his + + + align:start position:0% +stunts and one of the examples of his +work is dashboard where you can look at + + align:start position:0% +work is dashboard where you can look at + + + align:start position:0% +work is dashboard where you can look at +all sorts of fair transactions by fair + + align:start position:0% +all sorts of fair transactions by fair + + + align:start position:0% +all sorts of fair transactions by fair +product by pass or no pass by user type + + align:start position:0% +product by pass or no pass by user type + + + align:start position:0% +product by pass or no pass by user type +and you can sort of filter and see + + align:start position:0% +and you can sort of filter and see + + + align:start position:0% +and you can sort of filter and see +exactly who's using your system how + + align:start position:0% +exactly who's using your system how + + + align:start position:0% +exactly who's using your system how +often let me see if I can show that to + + align:start position:0% +often let me see if I can show that to + + + align:start position:0% +often let me see if I can show that to +you live + + align:start position:0% + + + + align:start position:0% + +okay so here's uh here's our AFC + + align:start position:0% +okay so here's uh here's our AFC + + + align:start position:0% +okay so here's uh here's our AFC +validations for October 2015 so if I + + align:start position:0% +validations for October 2015 so if I + + + align:start position:0% +validations for October 2015 so if I +want to see for example here we're + + align:start position:0% +want to see for example here we're + + + align:start position:0% +want to see for example here we're +looking at everything right so we're + + align:start position:0% +looking at everything right so we're + + + align:start position:0% +looking at everything right so we're +looking at tickets and cards and passes + + align:start position:0% +looking at tickets and cards and passes + + + align:start position:0% +looking at tickets and cards and passes +and monthly passes and pay-as-you-go so + + align:start position:0% +and monthly passes and pay-as-you-go so + + + align:start position:0% +and monthly passes and pay-as-you-go so +if I want to look at stored value so no + + align:start position:0% +if I want to look at stored value so no + + + align:start position:0% +if I want to look at stored value so no +passes I'll sort of filter that out then + + align:start position:0% +passes I'll sort of filter that out then + + + align:start position:0% +passes I'll sort of filter that out then +of course tariff type becomes a hundred + + align:start position:0% +of course tariff type becomes a hundred + + + align:start position:0% +of course tariff type becomes a hundred +percent pay as you go + + align:start position:0% +percent pay as you go + + + align:start position:0% +percent pay as you go +and then you see the breakdown between + + align:start position:0% +and then you see the breakdown between + + + align:start position:0% +and then you see the breakdown between +cards and tickets for stored value use + + align:start position:0% +cards and tickets for stored value use + + + align:start position:0% +cards and tickets for stored value use +we see the trends by time of day here + + align:start position:0% +we see the trends by time of day here + + + align:start position:0% +we see the trends by time of day here +and by date so you can see that weekends + + align:start position:0% +and by date so you can see that weekends + + + align:start position:0% +and by date so you can see that weekends +are lower and the user type right here + + align:start position:0% +are lower and the user type right here + + + align:start position:0% +are lower and the user type right here +so adults very high and then senior + + align:start position:0% +so adults very high and then senior + + + align:start position:0% +so adults very high and then senior +students below that if you want to look + + align:start position:0% +students below that if you want to look + + + align:start position:0% +students below that if you want to look +at passes for example we could then say + + align:start position:0% +at passes for example we could then say + + + align:start position:0% +at passes for example we could then say +passes and monthly passes in particular + + align:start position:0% +passes and monthly passes in particular + + + align:start position:0% +passes and monthly passes in particular +you see that most of those are cards and + + align:start position:0% +you see that most of those are cards and + + + align:start position:0% +you see that most of those are cards and +all tickets make sense higher number of + + align:start position:0% +all tickets make sense higher number of + + + align:start position:0% +all tickets make sense higher number of +students then we saw before etc so you + + align:start position:0% +students then we saw before etc so you + + + align:start position:0% +students then we saw before etc so you +can you can really sort of play with + + align:start position:0% +can you can really sort of play with + + + align:start position:0% +can you can really sort of play with +this and understand how how the market + + align:start position:0% +this and understand how how the market + + + align:start position:0% +this and understand how how the market +is like segments itself with with these + + align:start position:0% +is like segments itself with with these + + + align:start position:0% +is like segments itself with with these +different fare products that people are + + align:start position:0% +different fare products that people are + + + align:start position:0% +different fare products that people are +purchasing based on the fare policy and + + align:start position:0% +purchasing based on the fare policy and + + + align:start position:0% +purchasing based on the fare policy and +yeah there's another dashboard for a + + align:start position:0% +yeah there's another dashboard for a + + + align:start position:0% +yeah there's another dashboard for a +fair revenue so these are federal + + align:start position:0% +fair revenue so these are federal + + + align:start position:0% +fair revenue so these are federal +revenues by month across many years and + + align:start position:0% +revenues by month across many years and + + + align:start position:0% +revenues by month across many years and +you can see the total up here but you + + align:start position:0% +you can see the total up here but you + + + align:start position:0% +you can see the total up here but you +can break it down again so you can look + + align:start position:0% +can break it down again so you can look + + + align:start position:0% +can break it down again so you can look +at how much of it is monthly passes and + + align:start position:0% +at how much of it is monthly passes and + + + align:start position:0% +at how much of it is monthly passes and +you can see how much of it is normal + + align:start position:0% +you can see how much of it is normal + + + align:start position:0% +you can see how much of it is normal +commuter pass versus commuter rail and + + align:start position:0% +commuter pass versus commuter rail and + + + align:start position:0% +commuter pass versus commuter rail and +you can see if you're interested in + + align:start position:0% + + + + align:start position:0% + +students here's your students so we can + + align:start position:0% +students here's your students so we can + + + align:start position:0% +students here's your students so we can +sort of really slice and dice it any way + + align:start position:0% +sort of really slice and dice it any way + + + align:start position:0% +sort of really slice and dice it any way +you want to and there's many more + + align:start position:0% +you want to and there's many more + + + align:start position:0% +you want to and there's many more +applications what I just wanted to + + align:start position:0% +applications what I just wanted to + + + align:start position:0% +applications what I just wanted to +demonstrate a few okay so that was it + + align:start position:0% +demonstrate a few okay so that was it + + + align:start position:0% +demonstrate a few okay so that was it +I'm not gonna lecture any more for this + + align:start position:0% +I'm not gonna lecture any more for this + + + align:start position:0% +I'm not gonna lecture any more for this +semester so yeah I'll still come and + + align:start position:0% +semester so yeah I'll still come and + + + align:start position:0% +semester so yeah I'll still come and +I'll let you know about the test + + align:start position:0% +I'll let you know about the test + + + align:start position:0% +I'll let you know about the test +unless I have more information on it any + + align:start position:0% +unless I have more information on it any + + + align:start position:0% +unless I have more information on it any +questions on fear policy very structured + + align:start position:0% +questions on fear policy very structured + + + align:start position:0% +questions on fear policy very structured +fair technology + + align:start position:0% +fair technology + + + align:start position:0% +fair technology +no all right + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/CaLv-IWX5vo.txt b/CaLv-IWX5vo.txt new file mode 100644 index 0000000000000000000000000000000000000000..c1483e4396702750652fb40c6026cd1db83b8f26 --- /dev/null +++ b/CaLv-IWX5vo.txt @@ -0,0 +1,1019 @@ +align:start position:0% + +now that we've prepared our data set + + align:start position:0% +now that we've prepared our data set + + + align:start position:0% +now that we've prepared our data set +let's use cart to build a predictive + + align:start position:0% +let's use cart to build a predictive + + + align:start position:0% +let's use cart to build a predictive +model first we need to load the + + align:start position:0% +model first we need to load the + + + align:start position:0% +model first we need to load the +necessary packages and our our console + + align:start position:0% +necessary packages and our our console + + + align:start position:0% +necessary packages and our our console +by typing library our part and then + + align:start position:0% +by typing library our part and then + + + align:start position:0% +by typing library our part and then +library our part dot plot now let's + + align:start position:0% +library our part dot plot now let's + + + align:start position:0% +library our part dot plot now let's +build our model we'll call it tweet cart + + align:start position:0% +build our model we'll call it tweet cart + + + align:start position:0% +build our model we'll call it tweet cart +and we'll use the our part function to + + align:start position:0% +and we'll use the our part function to + + + align:start position:0% +and we'll use the our part function to +predict negative using all of the other + + align:start position:0% +predict negative using all of the other + + + align:start position:0% +predict negative using all of the other +variables as our independent variables + + align:start position:0% +variables as our independent variables + + + align:start position:0% +variables as our independent variables +and the data set train sparse we'll add + + align:start position:0% +and the data set train sparse we'll add + + + align:start position:0% +and the data set train sparse we'll add +one more argument here which is method + + align:start position:0% +one more argument here which is method + + + align:start position:0% +one more argument here which is method +equals class so that the our part + + align:start position:0% +equals class so that the our part + + + align:start position:0% +equals class so that the our part +function knows to build a classification + + align:start position:0% +function knows to build a classification + + + align:start position:0% +function knows to build a classification +model we're just using the default + + align:start position:0% +model we're just using the default + + + align:start position:0% +model we're just using the default +parameter settings so we won't add + + align:start position:0% +parameter settings so we won't add + + + align:start position:0% +parameter settings so we won't add +anything for min bucket or CP now let's + + align:start position:0% +anything for min bucket or CP now let's + + + align:start position:0% +anything for min bucket or CP now let's +plot the tree using the PRP function our + + align:start position:0% +plot the tree using the PRP function our + + + align:start position:0% +plot the tree using the PRP function our +tree says that if the word freak is in + + align:start position:0% +tree says that if the word freak is in + + + align:start position:0% +tree says that if the word freak is in +the tweet then predict true or negative + + align:start position:0% +the tweet then predict true or negative + + + align:start position:0% +the tweet then predict true or negative +sentiment if the word freak is not in + + align:start position:0% +sentiment if the word freak is not in + + + align:start position:0% +sentiment if the word freak is not in +the tweet but the word hate is again + + align:start position:0% +the tweet but the word hate is again + + + align:start position:0% +the tweet but the word hate is again +predict true if neither of these two + + align:start position:0% +predict true if neither of these two + + + align:start position:0% +predict true if neither of these two +words are in the tweet but the word WTF + + align:start position:0% +words are in the tweet but the word WTF + + + align:start position:0% +words are in the tweet but the word WTF +is also predict true or negative + + align:start position:0% +is also predict true or negative + + + align:start position:0% +is also predict true or negative +sentiment if none of these three words + + align:start position:0% +sentiment if none of these three words + + + align:start position:0% +sentiment if none of these three words +are in the tweet then predict false or + + align:start position:0% +are in the tweet then predict false or + + + align:start position:0% +are in the tweet then predict false or +non negative sentiment this tree makes + + align:start position:0% +non negative sentiment this tree makes + + + align:start position:0% +non negative sentiment this tree makes +sense intuitively since these three + + align:start position:0% +sense intuitively since these three + + + align:start position:0% +sense intuitively since these three +words are generally seen as negative + + align:start position:0% +words are generally seen as negative + + + align:start position:0% +words are generally seen as negative +words now let's go back to our our + + align:start position:0% +words now let's go back to our our + + + align:start position:0% +words now let's go back to our our +console and evaluate the numerical + + align:start position:0% +console and evaluate the numerical + + + align:start position:0% +console and evaluate the numerical +performance of our model by making + + align:start position:0% +performance of our model by making + + + align:start position:0% +performance of our model by making +predictions on the test set we'll call + + align:start position:0% +predictions on the test set we'll call + + + align:start position:0% +predictions on the test set we'll call +our predictions predict cart and we'll + + align:start position:0% +our predictions predict cart and we'll + + + align:start position:0% +our predictions predict cart and we'll +use the predict function to predict + + align:start position:0% +use the predict function to predict + + + align:start position:0% +use the predict function to predict +using our model tweet cart on the new + + align:start position:0% +using our model tweet cart on the new + + + align:start position:0% +using our model tweet cart on the new +dataset tests parse will add one more + + align:start position:0% +dataset tests parse will add one more + + + align:start position:0% +dataset tests parse will add one more +argument which is type e + + align:start position:0% +argument which is type e + + + align:start position:0% +argument which is type e +hols class to make sure we get class + + align:start position:0% +hols class to make sure we get class + + + align:start position:0% +hols class to make sure we get class +predictions now let's make our confusion + + align:start position:0% +predictions now let's make our confusion + + + align:start position:0% +predictions now let's make our confusion +matrix using the table function will + + align:start position:0% +matrix using the table function will + + + align:start position:0% +matrix using the table function will +give us the first argument the actual + + align:start position:0% +give us the first argument the actual + + + align:start position:0% +give us the first argument the actual +outcomes test sparse negative and then + + align:start position:0% +outcomes test sparse negative and then + + + align:start position:0% +outcomes test sparse negative and then +as a second argument our predictions + + align:start position:0% +as a second argument our predictions + + + align:start position:0% +as a second argument our predictions +predict carp to compute the accuracy of + + align:start position:0% +predict carp to compute the accuracy of + + + align:start position:0% +predict carp to compute the accuracy of +our model we add up the numbers on the + + align:start position:0% +our model we add up the numbers on the + + + align:start position:0% +our model we add up the numbers on the +diagonal 294 plus 18 these are the + + align:start position:0% +diagonal 294 plus 18 these are the + + + align:start position:0% +diagonal 294 plus 18 these are the +observations we predicted correctly and + + align:start position:0% +observations we predicted correctly and + + + align:start position:0% +observations we predicted correctly and +divided by the total number of + + align:start position:0% +divided by the total number of + + + align:start position:0% +divided by the total number of +observations in the table or the total + + align:start position:0% +observations in the table or the total + + + align:start position:0% +observations in the table or the total +number of observations in our test set + + align:start position:0% +number of observations in our test set + + + align:start position:0% +number of observations in our test set +so the accuracy of our carp model is + + align:start position:0% +so the accuracy of our carp model is + + + align:start position:0% +so the accuracy of our carp model is +about point 88 let's compare this to a + + align:start position:0% +about point 88 let's compare this to a + + + align:start position:0% +about point 88 let's compare this to a +simple baseline model that always + + align:start position:0% +simple baseline model that always + + + align:start position:0% +simple baseline model that always +predicts non negative to compute the + + align:start position:0% +predicts non negative to compute the + + + align:start position:0% +predicts non negative to compute the +accuracy of the baseline model let's + + align:start position:0% +accuracy of the baseline model let's + + + align:start position:0% +accuracy of the baseline model let's +make a table of just the outcome + + align:start position:0% +make a table of just the outcome + + + align:start position:0% +make a table of just the outcome +variable negative so we'll type table + + align:start position:0% +variable negative so we'll type table + + + align:start position:0% +variable negative so we'll type table +and then in parentheses test sparse + + align:start position:0% +and then in parentheses test sparse + + + align:start position:0% +and then in parentheses test sparse +negative this tells us that in our test + + align:start position:0% +negative this tells us that in our test + + + align:start position:0% +negative this tells us that in our test +set we have 300 observations with + + align:start position:0% +set we have 300 observations with + + + align:start position:0% +set we have 300 observations with +non-negative sentiment and fifty-five + + align:start position:0% +non-negative sentiment and fifty-five + + + align:start position:0% +non-negative sentiment and fifty-five +observations with negative sentiment so + + align:start position:0% +observations with negative sentiment so + + + align:start position:0% +observations with negative sentiment so +the accuracy of a baseline model that + + align:start position:0% +the accuracy of a baseline model that + + + align:start position:0% +the accuracy of a baseline model that +always predicts non negative would be + + align:start position:0% +always predicts non negative would be + + + align:start position:0% +always predicts non negative would be +three hundred divided by three + + align:start position:0% +three hundred divided by three + + + align:start position:0% +three hundred divided by three +fifty-five or 0.8 four five so our cart + + align:start position:0% +fifty-five or 0.8 four five so our cart + + + align:start position:0% +fifty-five or 0.8 four five so our cart +model does better than the simple + + align:start position:0% +model does better than the simple + + + align:start position:0% +model does better than the simple +baseline model how about a random force + + align:start position:0% +baseline model how about a random force + + + align:start position:0% +baseline model how about a random force +model how well would that do let's first + + align:start position:0% +model how well would that do let's first + + + align:start position:0% +model how well would that do let's first +load the random forest package with + + align:start position:0% +load the random forest package with + + + align:start position:0% +load the random forest package with +library random forest and then we'll set + + align:start position:0% +library random forest and then we'll set + + + align:start position:0% +library random forest and then we'll set +the seed to one two three so that we can + + align:start position:0% +the seed to one two three so that we can + + + align:start position:0% +the seed to one two three so that we can +replicate our model if we want to keep + + align:start position:0% +replicate our model if we want to keep + + + align:start position:0% +replicate our model if we want to keep +in mind that even if you set the seed to + + align:start position:0% +in mind that even if you set the seed to + + + align:start position:0% +in mind that even if you set the seed to +one two three + + align:start position:0% +one two three + + + align:start position:0% +one two three +you might get a different random forest + + align:start position:0% +you might get a different random forest + + + align:start position:0% +you might get a different random forest +model than me depending on your + + align:start position:0% +model than me depending on your + + + align:start position:0% +model than me depending on your +operating system now let's create our + + align:start position:0% +operating system now let's create our + + + align:start position:0% +operating system now let's create our +model we'll call it tweet RF and use the + + align:start position:0% +model we'll call it tweet RF and use the + + + align:start position:0% +model we'll call it tweet RF and use the +random forest function + + align:start position:0% +random forest function + + + align:start position:0% +random forest function +to predict negative again using all of + + align:start position:0% +to predict negative again using all of + + + align:start position:0% +to predict negative again using all of +our hit other variables as independent + + align:start position:0% +our hit other variables as independent + + + align:start position:0% +our hit other variables as independent +variables and the data set train sparse + + align:start position:0% +variables and the data set train sparse + + + align:start position:0% +variables and the data set train sparse +well again use the default parameter + + align:start position:0% +well again use the default parameter + + + align:start position:0% +well again use the default parameter +settings the random forest model takes + + align:start position:0% +settings the random forest model takes + + + align:start position:0% +settings the random forest model takes +significantly longer to build than the + + align:start position:0% +significantly longer to build than the + + + align:start position:0% +significantly longer to build than the +cart model we've seen this before when + + align:start position:0% +cart model we've seen this before when + + + align:start position:0% +cart model we've seen this before when +building cart and random forest models + + align:start position:0% +building cart and random forest models + + + align:start position:0% +building cart and random forest models +but in this case the difference is + + align:start position:0% +but in this case the difference is + + + align:start position:0% +but in this case the difference is +particularly drastic this is because we + + align:start position:0% +particularly drastic this is because we + + + align:start position:0% +particularly drastic this is because we +have so many independent variables about + + align:start position:0% +have so many independent variables about + + + align:start position:0% +have so many independent variables about +300 different words so far in this + + align:start position:0% +300 different words so far in this + + + align:start position:0% +300 different words so far in this +course we haven't seen data sets with + + align:start position:0% +course we haven't seen data sets with + + + align:start position:0% +course we haven't seen data sets with +this many independent variables so keep + + align:start position:0% +this many independent variables so keep + + + align:start position:0% +this many independent variables so keep +in mind that for texting analytics + + align:start position:0% +in mind that for texting analytics + + + align:start position:0% +in mind that for texting analytics +problems building a random forest model + + align:start position:0% +problems building a random forest model + + + align:start position:0% +problems building a random forest model +will take significantly longer than + + align:start position:0% +will take significantly longer than + + + align:start position:0% +will take significantly longer than +building a cart model so now that our + + align:start position:0% +building a cart model so now that our + + + align:start position:0% +building a cart model so now that our +models finished + + align:start position:0% +models finished + + + align:start position:0% +models finished +let's make predictions on our test set + + align:start position:0% +let's make predictions on our test set + + + align:start position:0% +let's make predictions on our test set +we'll call them predict RF and again + + align:start position:0% +we'll call them predict RF and again + + + align:start position:0% +we'll call them predict RF and again +we'll use the predict function to make + + align:start position:0% +we'll use the predict function to make + + + align:start position:0% +we'll use the predict function to make +predictions using the model tweet RF + + align:start position:0% +predictions using the model tweet RF + + + align:start position:0% +predictions using the model tweet RF +this time and again the new data set + + align:start position:0% +this time and again the new data set + + + align:start position:0% +this time and again the new data set +tests parse now let's make our confusion + + align:start position:0% +tests parse now let's make our confusion + + + align:start position:0% +tests parse now let's make our confusion +matrix using the table function first + + align:start position:0% +matrix using the table function first + + + align:start position:0% +matrix using the table function first +giving the actual outcomes test sparse + + align:start position:0% +giving the actual outcomes test sparse + + + align:start position:0% +giving the actual outcomes test sparse +negative and then giving our predictions + + align:start position:0% +negative and then giving our predictions + + + align:start position:0% +negative and then giving our predictions +predict RF to compute the accuracy of + + align:start position:0% +predict RF to compute the accuracy of + + + align:start position:0% +predict RF to compute the accuracy of +the random forest model we again some of + + align:start position:0% +the random forest model we again some of + + + align:start position:0% +the random forest model we again some of +the cases we got write to 93 plus 21 and + + align:start position:0% +the cases we got write to 93 plus 21 and + + + align:start position:0% +the cases we got write to 93 plus 21 and +divide by the total number of + + align:start position:0% +divide by the total number of + + + align:start position:0% +divide by the total number of +observations in the table so our random + + align:start position:0% +observations in the table so our random + + + align:start position:0% +observations in the table so our random +forest model has an accuracy of 0.85 + + align:start position:0% +forest model has an accuracy of 0.85 + + + align:start position:0% +forest model has an accuracy of 0.85 +this is a little better than our cart + + align:start position:0% +this is a little better than our cart + + + align:start position:0% +this is a little better than our cart +model but due to the interpret ability + + align:start position:0% +model but due to the interpret ability + + + align:start position:0% +model but due to the interpret ability +of our cart model I'd probably prefer it + + align:start position:0% +of our cart model I'd probably prefer it + + + align:start position:0% +of our cart model I'd probably prefer it +over the random forest model if you were + + align:start position:0% +over the random forest model if you were + + + align:start position:0% +over the random forest model if you were +to use cross-validation to pick the CP + + align:start position:0% +to use cross-validation to pick the CP + + + align:start position:0% +to use cross-validation to pick the CP +parameter for the cart model the + + align:start position:0% +parameter for the cart model the + + + align:start position:0% +parameter for the cart model the +accuracy would increase to about the + + align:start position:0% +accuracy would increase to about the + + + align:start position:0% +accuracy would increase to about the +same as the random forest model so by + + align:start position:0% +same as the random forest model so by + + + align:start position:0% +same as the random forest model so by +using a bag of words approach in these + + align:start position:0% +using a bag of words approach in these + + + align:start position:0% +using a bag of words approach in these +models we can reasonably predict + + align:start position:0% +models we can reasonably predict + + + align:start position:0% +models we can reasonably predict +sentiment even with a relatively small + + align:start position:0% +sentiment even with a relatively small + + + align:start position:0% +sentiment even with a relatively small +data set of tweets \ No newline at end of file diff --git a/CpYFD01gSWM.txt b/CpYFD01gSWM.txt new file mode 100644 index 0000000000000000000000000000000000000000..1d98960eaf46299e55effebd557bf6dc4cbcd0a6 --- /dev/null +++ b/CpYFD01gSWM.txt @@ -0,0 +1,1125 @@ +The following content is provided by MIT OpenCourseWare under a creative + +commons license. Additional information about our + +license and MIT OpenCourseWare in general is available + +at ocw.mit.edu + +We're going to continue our discussion about cancer and cancer + +genetics today. One small point of clarification: + +apparently some people were confused about my out of balance scales here + +related to proliferation and cell death, pointing out that if there + +were more proliferation and less cell death, then the scale should + +shift this way instead of this way. That's an astute observation. + +It doesn't really matter which way the scales point really. + +The point was that they are out of balance, which is critical for + +tumorigenesis. But anyway, in review, + +last time I told you that cancer cells arise from normal cells over a + +series of events that relate to mutations in cellular genes. + +And I gave you lots of evidence that things that cause cancer affect our + +genes, and that our genes are disrupted in cancer cells. + +And I briefly mentioned that we have evidence for mutations in + +cellular genes in cancer cells. And I'll show you that again today. + +But all of that brings us to the point of needing to know, + +what are the genes? What are the genes that are affected in cancer? + +And this is important to help us understand how cancers arise, + +so from a basic biomedical research point of view, + +but also as we'll see next time, this information is actually very + +useful in teaching us how to diagnose cancer more effectively or + +treat it more effectively. And I'll just show this slide, + +which I showed at the end again as a summary. The cancer cells arise + +from normal cells through the acquisition of + +mutations in cellular genes through this process which we call clonal + +evolution, more and more abnormal cells growing out from this + +accumulating mass of cells. And as we'll discuss today, + +these genes affect proliferation and cell death, this out of balance + +scheme that I alluded to before, but not only these processes. + +And I emphasize this because these other important processes get a + +little bit of short shrift in our discussions. But angiogenesis, + +this process of recruiting a new blood supply in cancer is very + +important, and also an important therapeutic target. + +Cell motility, movement of cells, as I mentioned, it's important to + +get cells away from the initial mass in the process of metastasis, + +and invasion likewise. And several other processes are also affected in + +the course of tumorigenesis. So what are the genes? + +How do we know which genes are affected in cancer? + +Well, this set of experiments, really, has occurred over the course + +of arguably the last century. I'm trying to find the genes that + +are mutated in cancer cells. And many people point to landmark + +experiments done in 1910 by an investigator at the Rockefeller + +University by the name of Payton Rauss. + +Payton Rauss was a virologist, studied viruses at Rockefeller + +University. And one day, a farmer from Long Island brought a + +prize-winning hen to this famous doctor at Rockefeller University in + +New York because the hen was sick. Specifically, the hen had a big + +tumor in its breast muscle. And if you remember, that would + +mean the tumor was a sarcoma. And he wanted the doctor to cure his + +prize-winning hen. Payton Rauss said, + +thank you, I'll do what I can, and then prominently killed the bird + +in order to try to study what was giving rise to this tumor. + +And he did a famous experiment. + +He took the tumor, ground it up, filtered it so that + +there were no cells present in the filtrate, and also used a small + +enough pour filter so that bacteria, which were also known at that time, + +were removed. So, he had a filtrate that contained no + +cells, no cancer cells, and no bacteria. + +And he took this and injected it into a non-tumor bearing bird. + +And he observed over time that this bird developed a tumor. + +So he was able to demonstrate the transmissibility of something which + +could cause cancer in an otherwise unaffected animal. + +Because it wasn't cells and it wasn't bacteria, + +he suggested that it was a virus. + +And it turned out to be, over the course of the next 50 years + +or so, the virus which was responsible for this disease was + +identified and given the name Rauss sarcoma virus, + +named after Payton Rauss. And the structure of this virus was + +also determined. It was found to be a retrovirus. + + Retroviruses are in the class of HIV. + +Their genomes are made of RNA, and they convert it to a DNA form. + +We'll learn a little bit more about retroviruses in a few lectures. + +It was a retrovirus, and the structure of its genome was + +determined eventually. And it was found to contain in its + +genome the genes that the virus required for replication. + +And all viruses of this class has a very similar set of replication + +genes. They need to produce more virus. But at the end of the viral + +genome, at the extreme right side of the viral genome, + +there was another gene which was given the name sarc for sarcoma. + +And it was termed an oncogene, onco for mass, + +oncology, cancer associated gene, sarc-oncogene. + +So, the virus it was found can cause cancer in birds by virtue of + +transferring into those cells a potent cancer associated gene called + +sarc. And Payton Rauss went onto win the Nobel Prize, + +actually about 50 years later in the early 1960s for this work on the + +discovery of Rauss sarcoma virus. And it was extremely important. + +But it was still a mystery as to where this cancer associated gene + +came from. Where did the sarc gene originate? Was it a viral gene + +which the virus used in some fashion to cause cells to proliferate, + +perhaps for its own replication? Or did it come from some other + +source, some other origin? And here in the story entered two + +researchers, Mike Bishop and Harold Varmus. Mike Bishop is now + +chancellor at UCSF. Harold Varmus is president at + +Memorial Sloan-Kettering. They did this work at UCSF, + +and I got quite familiar with it because I ended up working for + +Harold Varmus as a Ph. . student. This work was done + +before I got there in about 1975. And they set out to ask this + +question, what is the origin of this sarc-oncogene? + +Where did it come from? And what they were able to show was + +that this Rauss sarcoma virus derived from a virus that was + +related to it called avian leucosis virus. + +And avian leucosis virus had only those replication genes, + +the genes that the virus uses to produce more virus what they were + +able to show was that this avian leucosis virus, + +when it infects cells, and here's a chicken cell, + +and here's the nucleus of that cell, inside that cell are normal copies + +of the sarc gene. They were able to show that the + +virus actually acquires this sarc-oncogene from the cells that it + +infects. Now, it doesn't do that every time. + +In fact, most of the time, the virus just goes in and replicates + +and produces more virus. + +But rarely, and really it's very rarely, the virus actually acquires + +a piece of the sarc gene and sticks it into its own genome, + +thereby creating -- + +-- Rauss sarcoma virus, which has the structure that I + +showed you above with the replication genes and + +the sarc oncogene. And this is done through a process + +called transduction, which is a form of recombination. + + The main point of this observation, + +and the really important point of this observation was this potent + +oncogene is present in chicken cells. + + The sarc is a cellular gene. + +It's not just a viral gene. It's derived from host cells of chickens, + +and it's not only in chickens. It's in all vertebrates including + +humans. So, you all have a sarc gene in your + +cells, too. And this was a really momentous observation. + +And it led Bishop and Varmus to win the Nobel Prize back in 1989. + +So, what I've just told you is that your cells carry a potent oncogene, + +sarc. So, why don't you all have sarcomas? + + Anybody? Remember, + +we are still being filmed. Anybody? Yes, somebody's got their + +hand up, but I don't see them. Yes? Almost right. The gene is + +not expressed properly, OK? The virus has co-opted this + +gene and placed it into its own genome. And now this gene is being + +regulated improperly. Maybe it's expressed too well or at + +the wrong time, or in the wrong cells. + +And some combination of those things allows the gene to cause + +cancer in this setting, whereas when the gene is properly + +regulated, and the cells of chickens or in you, it's not cancer + +associated. It doesn't cause cancer in its state in the cellular genome. + +So, this was extremely important, and as I said, + +led to the Nobel Prize for these guys. RSV -- + + -- is what's called an acutely + +transforming retrovirus, acutely transforming meaning that it + +can transform cells, turn them from normal to cancerous + +quickly. And as I said, it's a retrovirus. We now know of + +many acutely transforming viruses of animals: mice, + +rats, chickens, turkeys, other things. + +And from them, we have learned the identity of + +about 50 or so oncogenes, all of which were derived from the + +host cell. So, we know from this type of experiment + +of many potential cancer associated genes. Importantly, + +there are no known acutely transforming viruses of humans. + +Importantly, the vast majority of human cancers are not associated + +with viral agents. Occasionally, there are such cases, + +but they are quite rare. Most major tumor types are not caused by viral + +infection. But there is one big exception to this -- + + -- human papilloma virus. + +Human papilloma virus, or HPV, and specifically high-risk types of + +HPV called type 16 and type 18 are associated with cervical cancer in + +the US, but mostly in other parts of the world. And that's important, + +because if one can control exposure to HPV, or eradication of HPV, + +one could do something about cervical cancer, + +and that's actually happening now. And I'll mention that again next + +lecture. But I want you to remember that most cancers, + +human cancers, are not virus associated. But the viruses have + +taught us a great deal about cancer genetics. OK, + +so if most human cancers don't arise from a viral infection, + +the infection with an oncogene carrying virus, + +then where do these mutations come from? + +What are the mutations in human cancer? And here, + +just after these experiments were done, around 1980, + +comes another one of our local heroes, Bob Weinberg, + +who has a laboratory at the Whitehead Institute here at MIT. + +He hasn't yet won the Nobel Prize, but I think he's going to, based on + +this work and a lot of other work probably in the next several years. + +And what Weinberg's lab did back in this early 1980s. + +Was to look in human cancers, so not cancers of animals, but in + +human cancers. And specifically, + +they took bladder cancers and isolated the cells, + +and grew them in the laboratory. + +They assumed that inside of the cells were altered genes, + +and to become altered through the life of this individual, + +giving rise to this cancer. And they wanted to know what those + +genes were. And so, they isolated the DNA from these + +bladder cancer cells, and they transfected it into cells + +from mice. They sheared it up, and they introduced it. That's what + +transfected means, into the cells of mice. + +And these cells that they put them into were fairly normal -- + + -- mouse cells, + +by which I mean they grew a single layer on the bottom of the dish. + +There are structures look like normal cells as opposed to cancer + +cells. They were relatively normal cells. And what they observed was + +that a small percentage of these cells that had picked up some bits + +and pieces of the DNA derived from this human cancer began to + +behave abnormally -- + +-- and produced what were referred to as transformed cells, + +cells that looked more like cancer cells. So they had converted + +otherwise normal mouse cells to what looked like cancer cells through the + +introduction of one or more human genes. + +And they further demonstrated that these were cancer associated cells, + +cancer-causing cells, by introducing them into immunocompromised mice, + +and observing that over time these cells could produce tumors. + +So these were cancer cells indeed. So that's very interesting because + +it says that there are altered genes in these cancer cells that can + +convert normal mouse cells into cancer cells. And then to obvious + +question was, what are those genes? What is the gene that's responsible + +for this process? So, they -- + +-- isolated the human DNA from the transformed mouse cells. + +And I won't tell you how they did that, but suffice it to say, + +it's possible to isolate the human DNA away from the mouse DNA in these + +transformed mouse cells. They cloned the human DNA into + +bacteria using recombinant DNA methods that we've talked to you + +about previously. + +And they sequenced the cancer-causing gene. + +It turns out it was just a single gene that was providing + +this property. + +And it turned out that this gene was H-RAS [SP?], RAS being a gene that + +we've talked to you about before, and important signaling protein in + +cells. Moreover, they sequenced the copy of RAS that + +was present in the cancer cells, and compared it to the sequence in + +normal cells in the other cells of this individual. + +And they found a single alteration. OK, so what you are looking at here + +now is the sequence of the H-RAS gene in normal people or in the + +normal cells of this cancer patient has a particular sequence. + +It encodes a protein, H-RAS, which if you recall is an important + +signaling protein that shuttles between a GTP-bound form + +and a GDP bound form. In its GTP bound form, + +it's active and signals, and then it undergoes hydrolysis + +reaction. So, the GTP is converted to GDP, + +and becomes inactive. The mutant copy found in the cancer cells and + +in these transformed mouse cells has been alteration which blocks the + +ability of the proteins undergo GTP hydrolysis. Therefore, + +the protein gets locked into this active signaling state, + +and stimulates proliferation continuously. + +And that's why it's a cancer associated gene. + +OK, so here we have for the first time evidence that a normal, + +cellular gene gets mutated, presumably by an error or by + +exposure to some mutagen that is responsible at least far an aspect + +of the transformed state. OK, so that's very, + +very interesting. It also raises an important question. + +If you note that the change between the normal gene and the abnormal + +gene is signal-base change that converts this alanine residue, + +sorry, this glycemic residue to a valine residue: single base change. + +Such single base changes occur in your cells all the time. + +It's estimated that the mutation rate inside your cells is about ten + +to the minus ninth per cell division. And if you calculate how many cells + +you have in your body at any given time based on how many cell + +divisions have arisen, we can estimate that there are about + +ten to the third to ten to the fifth -- + + -- rasmutin + +cells in all of U as you sit there now. You are all carrying 1, + +00-100,000 cells that have this very mutation. So, + +why don't all of you have cancer? Why don't all of you have bladder + +cancer or some other form of cancer? Anybody? + + The reason is that cancer is not a + +single step process. Cancer cells arise from normal + +cells to the acquisition of many mutations that occur over the + +lifetime of the individual. So a single mutation in RAS is not + +enough to give you a cancer. It might be enough to cause the + +cells to behave somewhat abnormally. But that in and of itself does not + +produce even hyperplasia necessarily, let alone an adenoma, + +an adenocarcinoma and invasive cancer. + +It's necessary to acquire multiple mutations. So you may have cells + +that are on their way. But they are not fully there. + +And hopefully they'll never get there. Now, I want to remind you + +that this pathway, this signaling pathway that involves + +RAS is something we taught you about previously. This should look + +familiar based on the cell signaling lectures that we had before. + +RAS sits right here, this important signaling molecule that links events + +that take place at the cell membrane. + +Sound at all familiar? Yes? Transmembrane receptors? + +Growth factor receptors that bind to ligands and cause a series of + +events that for example convert RAS to its GTP bound form, + +and then initiate a kinase cascade of protein kinases, + +map kinase, kinase, kinase, kinase, kinase, kinase, remember the + +little movie? Moves into the nucleus, phosphorylates + +transcription factors that initiate the expression of target genes that, + +for example cause cells to proliferate. + +And when RAS gets stuck in its on state as it does here, + +these signals are sent constitutively so that the cell is + +being told to divide all the time instead of in a regulated fashion. + +Now, I point out all the different components which I've told you about + +in previous lectures because, in fact, it's not just RAS, this one + +signaling protein that gets mutated in cancers. + +Many different of these signaling proteins get mutated in cancers. + +It is a very common pathway that's affected in not necessarily all but + +a very high percentage of cancers of different types. + +The RAS gene is mutated at about 30% of cancers. + +30% of all cancers have mutations in one of the RAS genes including, + +for example, 90% of pancreatic cancer, 50% of colon cancers, + +30% of lung cancers carry mutations in this gene. + +But other components get mutated as well. For example, + +the growth factor or growth factor receptor genes get altered in + +cancers. They become amplified. And I'll mention what I mean by + +that in a second period. We observe translocations, + +these chromosomal alterations in different genes, + +including the transcription factor genes that lie at the bottom of this + +pathway. There can be deletions that affect the function of these + +proteins, make the function abnormally, and subtle mutations + +like the one in RAS itself. And there are other examples, + +subtle mutations that lock the proteins, for example, + +in an active signaling state. + +So, DNA amplification is one such mechanism to alter the function of a + +cellular gene in cancer. And an example of that is in a case + +of a gene called HER2. + +It encodes a growth factor receptor like item number two up here. + +It encodes a growth factor receptor. And when it's present in single + +copy or two copies per cell, it produces a certain concentration + +of this growth factor receptor protein. And it signals + +at normal levels. And that gives rise to a normal + +amount of proliferation. And this is particularly important + +in cells of the mammary gland. Mammary epithelial cells depend on + +this signaling pathway to be produced in the right amounts. + +Unfortunately at some frequency in cancer cells, and specifically + +cancer cells of the breast, and sometimes ovary, an + +amplification event takes place so that now instead of having just one + +copy of this HER2 gene on the chromosome, there are many copies. + +An error takes place in the replication process so that instead + +of just copying this gene one time, it gets copied multiple times. + +So, now we have too many copies of this gene, and therefore in these + +cells, the concentration of this receptor is significantly higher + +than in normal cells such that in these cells, there might be ten + +times or a hundred times the amount of signaling, or ten to a hundred + +times the amount of proliferation. So, the dysregulation of this gene's + +function by making too much of the protein, it's an otherwise normal + +protein. There's just too much of it, causes the cells to get + +overstimulated and divide too often. That's bad news for cancer. The + +good news is we now have a therapy, and I'll put you about that next + +time, directed against this protein. + + I'll mention another mechanism of + +activation, and that's translocation. I showed you slides of cancer cells + +that have broken chromosomes or rearranged chromosomes. + +Those rearrangements often produce abnormal genes, + +sometimes fusions between one gene and another. Other times, + +rearrangements of the promoter of the gene such that the normal + +promoter of the gene, which is responsible for its level + +of expression is replaced by a different promoter, + +which might give too much expression. And that's true for an important + +oncogene called MIC . The MIC oncogene is a + +transcription factor. It's like number eight down there. + +It's a transcription factor that binds to DNA and regulates the + +expression of other genes. And it's normally expressed from a, + +let's call it, weak promoter. You don't want to have too much of this + +protein produced. It needs to be produced at normal + +levels. So, we get a certain concentration of the + +protein, which gives -- + +-- regulated cell division. You get as much television as you + +need based on the appropriate signals in the environment of those + +cells. In certain types of leukemia, one sees a translocation. + +The DNA is broken and rejoined so that the MIC oncogene doesn't have + +its own promoter anymore. Instead, it's next to a very strong + +promoter. + +And now, again, the concentration of this protein is + +increased. And this gives rise to deregulated cell + +division, same idea. Change the proper regulation of + +this signaling network, and now the signaling network is + +broken. And as I said, + +there are many, many such genes that are known. + +We know about 50 or so oncogenes from these acutely transforming + +viruses. We probably know of 50 more oncogenes because of their + +changes in the DNA of cancer cells. And by the way, there's a lot of + +overlap between these two sets. Many of the genes that were found + +in the context of viruses were later found to be mutant in human cells + +having nothing to do with viruses. And RAS is one such example. MIC, + +actually, is another example, and a relative of this HER2 gene + +is another example. + +OK. + +OK, so the slide is meant to reinforce this notion that cell + +division, normal production of cells, is tightly regulated through these + +signaling networks, and that oncogenes function normally, + +their normal cellular function is to control this process. + +That's what they do in normal development. That's what they do in + +normal individuals. But they can be subverted in cancer + +cells by mutation. It makes them act in a deregulated + +or uncontrolled fashion. There is another set of genes that + +act, in a sense, in opposition to the oncogenes. + +These genes function to inhibit this process of cell division. + +And they go by another name: tumor suppressor genes. + +Tumor suppressor genes function to block the normal cell division + +process or to inhibit the production of cells. And they, + +too, are important in cancer. You can think of these genes as the + +on switch and the off switch of an electrical circuit. + +In cancer cells, oncogenes become hyperactive. + +When the lights switch gets stuck in the on state. OK, + +it gets taped open. So now, you're getting signaling + +through this circuit continuously. Tumor suppressor genes normally + +inhibit cell division. And so, in cancer, these genes get + +inactivated. It's like the light switch getting turned off. + +And the process is normally regulated that way, and + +these get stuck off. OK, so want to tell you a little bit + +about tumor suppressor genes now which is the other major category of + +cancer associated genes that we'll cover here. Briefly, + +just to reiterate that point, in addition to the light switch + +analogy, people often use the gas pedal and breaks analogy, + +or the go signal and stop signal analogy. So, I'll use that as well. + +In normal cells, when they receive the signals to divide, + +they are stimulated to go, that is, to divide to make more such + +cells. This happens in development when you + +need to make more cells. It happens in wound healing. + +It happens in normal homeostasis. And then, when the process is + +completed, there are stop signals sent. The go signals represent + +oncogenes, normally regulated, stop signals tumor suppressor genes + +normally regulated. In cancer, oncogenes become + +deregulated. And pushed too strong they send constitutive signals. + +And as a consequence, too many cells are produced. + +And likewise, the stop signs, the stop signals are lost so that + +one produces even more cells. OK, so hopefully these are useful + +analogies to think about these two opposing sets of oncogenes and tumor + +suppressor genes. OK, so to get into tumor suppressor + +genes, sorry, this just makes the point, oncogene mutations, + +tumor suppressor gene mutations. To get into tumor suppressor genes, + +the second class, an important class of human cancer genes, + +let me tell you a little bit about this disease which is called + +retinoblastoma. Retinoblastoma is a childhood tumor + +of the eye, of the retina. It's not very common. Only about + +one in 40,000 children develop this tumor. But it's very important what + +it's taught us about cancer genes. And you can see in the normal eye a + +normal looking retina, and in the cancer containing eye, + +these blobs of tumors. We now know the gene that's responsible for this + +disease, the gene that's mutated in the formation of this disease. + +And that gene is the gene called RB, named after retinoblastoma. + + And this gene functions as an + +important regulator of cell cycle progression. If you remember cell + +cycle progression, mitosis, S phase mitosis, + +the G1 phase, the G2 phase, again, dim memories from earlier in + +the class. The RB protein, + +which goes by the name of PRB, this is the protein encoded by this + +tumor suppressor gene, RB, acts to inhibit cell cycle + +progression. That's its function. It blocks cell cycle progression + +literally like the brakes on a car. Now, you might ask, + +if it's there and functioning, then how do you ever get cell cycle + +progression? And the answer is that this active inhibitor can be + +inactivated through phosphorylation. When this protein gets + +phosphorylated, it becomes inactive. + + And now, cell cycle progression + +can occur. + +It becomes inactive when the cell receives growth stimulatory signals + +like through that signaling network that I mentioned previously. + +These signals, then, act on cycline CDK complexes, + +cell cycle associated kinases that you were taught about in the cell + +cycle lecture, and these go about inactivating the + +RB protein, allowing the cells to cycle. + +In addition, when the cells shouldn't be cycling in the presence + +of growth inhibitory signals, inhibitory signals are sent to the + +cycline dependent kinase proteins, and they don't function, thereby + +blocking the inactivation of RB. RB stays in its active state and + +blocks cell cycle progression. OK, so that's how this really + +important cell cycle regulator functions more or less. + +And it's a very important human tumor suppressor gene, + +which is itself mutated and probably 30 or 40% of human cancers. + +And the pathway that regulates this gene, this pathway, + +is mutated in probably 95% of human cancers very, very commonly affected. + +OK, so given what I've told you so far, would you expect the mutations + +that we find in the RB gene in human cancer to be activating mutations or + +inactivating mutations? Inactivating. It's the brakes. + +Cancer cells want to get rid of the brakes. + + And so we find inactivating + +mutations in the RB gene in human cancers like deletions or nonsense + +mutations, that is, stop codon mutations. + +OK, that's the kind of mutations we find in this gene. + +For the oncogenes, which we focused on at the beginning, + +are the mutations in oncogenes dominant or recessive? + +Are the mutations in the oncogenes dominant or recessive? + +The oncogene mutations are dominant. When you acquire mutation in an + +oncogene, whether it's a subtle mutation or an amplification, + +it doesn't matter what's happening to the other allele. + +This thing has new function, gain of function. It will transform + +or start the process of transformation, + +regardless of what is happening to the other allele. + +And that's evident, by the way, in this transfection + +experiment. This would only work if it were a dominant mutation. + +So, oncogene mutations are dominant mutations. Are tumor suppressor + +gene mutations dominant or recessive? These are recessive mutations. + +Here, it matters, the state of the other allele of the + +RB gene. As long as you have one functional copy of the brakes, + +you can do this. You can control cell cycle regulation. + +In order to make this dysregulated, you need to get rid of both copies. + +You need to get rid of the brakes entirely. So, these mutations + +are recessive. And this class of mutations are + +recessive. Tumor suppressor gene mutations are recessive. + +So this raises an interesting question. Tumor suppressor gene + +mutations are recessive. I've told you that tumor suppressor + +gene mutations occur commonly in human cancer, not just this RB gene + +but others too, and yet you are all diploid. + +You all carry two copies of the tumor suppressor genes. + +So, how do we ever find mutations in these genes in human cancer? + +Is it enough to mutate just one copy? No, because they are + +recessive mutations. So, to find mutations in tumor + +suppressor genes in human cancer, it's not enough to mutate just one + +copy. Both copies need to be mutated. + + Recessive mutations require there be + +two mutations. And this is what typically happens + +in the development of a tumor with a mutation in the RB gene, + +or any other tumor suppressor gene. Again, there are probably 20 to 50 + +different tumor suppressor genes. Initially, a cell, which has a + +normal copy of RB on both copies of chromosome 13, + +that's where this gene sits, and here we are looking at a linked + +polymorphic marker, big A little a, if you remember + +polymorphic markers, big A little A. + +First, one copy of RB gets mutated. In this cell, there is still a + +normal copy of RB. And therefore, + +this cell that has acquired this mutation is normal. + +It's functionally normal. However, it now has just one copy + +of the RB gene. And so, it's predisposed to + +becoming a cancer cell if that normal copy gets lost. + +And what this shows you are various mechanisms by which the + +normal copy of the RB gene can be lost. + +The other copy can acquire its own mutation. Or, + +the chromosome that carries the normal copy of the RB gene can get + +lost in the developing cancer cell. Or, it can be a recombination of + +that, that replaces the normal copy of the gene with the abnormal copy + +of the gene. And all three of these things happen in the development of + +cancer cells. And depending on which mechanism is used -- + + -- one can observe something + +referred to as loss -- + +-- of heterozygosity, loss of heterozygosity within the + +cancer cell. You will notice that this cancer cell, + +sorry, this normal cell, is heterozygous for this A allele, + +big A little A. And you will notice that here and here, + +the cell has become, the cell carries only one version of that A + +allele, big A. So, there was heterozygosity. + +And in the cancer cell, there's now loss of heterozygosity. + +Loss of heterozygosity is a hallmark for tumor suppressor genes, + +the involvement of tumor suppressor genes in the development of cancer. + +OK, now I told you several times that proliferation is important and + +cell death is important, too. + +Cell death control in cancer: I don't have a lot of time to tell you + +more about this in this class, but I want to just emphasize that + +the pathways that lead from cell death signals, + +the signals that tell cells to commit suicide to ultimately undergo + +this process called apoptosis are also dysregulated in cancer. + + For example, there's a gene called + +BCL2, which becomes mutated in certain types of cancer. + +BCL2 normally blocks this process of cell death. + +And in this type of cancer, it becomes hyperactive. So there's + +not as much cell death. BCL2 is an oncogene. + +Another gene, very important gene in human cancer is P53. + +It stimulates cell death. P53 gets lost in a high percentage + +of cancers. It's a tumor suppressor gene, and therefore gets + +inactivated. BCL2 is an oncogene. + +It gets hyperactivated in cancers. I'll talk more about this pathway + +next time, but just to put in your minds, P53 is a very important + +signaling protein responsive to many signals upstream, + +giving rise to signals that lead to death as well as arrest. + +Hang on, please. Hang on. Two minutes left. + +And this slide is just a summary of what we've been talking about so far. + +Control of proliferation, control of cell death, the normal + +balance, perturbations in these pathways, oncogene mutations that + +stimulate proliferation, tumor suppressor gene mutations that + +stimulate proliferation. Alterations in apoptosis, + +oncogene mutations that block apoptosis, tumor suppressor gene + +mutations that block apoptosis. All of these are important in + +cancer. Next time I'm going to tell you that + +some cancers are caused by inherited mutations. And this is a pedigree + +of such an example, and lastly to remind you, + +mutations affect proliferation in cell death. But they also affect + +many other things: invasion, angiogenesis, as well as metastasis. + +And I'll stop there. \ No newline at end of file diff --git a/Cslq_ZYdYwE.txt b/Cslq_ZYdYwE.txt new file mode 100644 index 0000000000000000000000000000000000000000..44a64c784be8848e160b51fb961abe522e46694d --- /dev/null +++ b/Cslq_ZYdYwE.txt @@ -0,0 +1,1315 @@ +align:start position:0% + +we now would like to analyze in more + + align:start position:0% +we now would like to analyze in more + + + align:start position:0% +we now would like to analyze in more +depth our result that for a system of + + align:start position:0% +depth our result that for a system of + + + align:start position:0% +depth our result that for a system of +particles so let's indicate our system + + align:start position:0% +particles so let's indicate our system + + + align:start position:0% +particles so let's indicate our system +we had particle one we have our J + + align:start position:0% +we had particle one we have our J + + + align:start position:0% +we had particle one we have our J +particle and we'll have our particle n + + align:start position:0% +particle and we'll have our particle n + + + align:start position:0% +particle and we'll have our particle n +so here's our system of particles where + + align:start position:0% +so here's our system of particles where + + + align:start position:0% +so here's our system of particles where +the total + + align:start position:0% +the total + + + align:start position:0% +the total +Force caused the momentum of the system + + align:start position:0% +Force caused the momentum of the system + + + align:start position:0% +Force caused the momentum of the system +of particles to change now I'd like to + + align:start position:0% +of particles to change now I'd like to + + + align:start position:0% +of particles to change now I'd like to +examine that concept of the total Force + + align:start position:0% +examine that concept of the total Force + + + align:start position:0% +examine that concept of the total Force +before we said that our total force on + + align:start position:0% +before we said that our total force on + + + align:start position:0% +before we said that our total force on +the J particle we just wrote it like + + align:start position:0% +the J particle we just wrote it like + + + align:start position:0% +the J particle we just wrote it like +this and I'm going to put a little T up + + align:start position:0% +this and I'm going to put a little T up + + + align:start position:0% +this and I'm going to put a little T up +here for the moment because when we + + align:start position:0% +here for the moment because when we + + + align:start position:0% +here for the moment because when we +examine what force we mean here and I + + align:start position:0% +examine what force we mean here and I + + + align:start position:0% +examine what force we mean here and I +also want to put a little + + align:start position:0% +also want to put a little + + + align:start position:0% +also want to put a little +boundary around our system and let's now + + align:start position:0% +boundary around our system and let's now + + + align:start position:0% +boundary around our system and let's now +consider another particle internal to + + align:start position:0% +consider another particle internal to + + + align:start position:0% +consider another particle internal to +the system and let's try to identify the + + align:start position:0% +the system and let's try to identify the + + + align:start position:0% +the system and let's try to identify the +types of forces on the J particle we can + + align:start position:0% +types of forces on the J particle we can + + + align:start position:0% +types of forces on the J particle we can +really have two types of forces here our + + align:start position:0% +really have two types of forces here our + + + align:start position:0% +really have two types of forces here our +first force can be an interaction + + align:start position:0% +first force can be an interaction + + + align:start position:0% +first force can be an interaction +between these two particles so what I'll + + align:start position:0% +between these two particles so what I'll + + + align:start position:0% +between these two particles so what I'll +write is the force on the jth particle + + align:start position:0% +write is the force on the jth particle + + + align:start position:0% +write is the force on the jth particle +due to the interaction between the K and + + align:start position:0% +due to the interaction between the K and + + + align:start position:0% +due to the interaction between the K and +the jth particle and I'm going to put a + + align:start position:0% +the jth particle and I'm going to put a + + + align:start position:0% +the jth particle and I'm going to put a +little sign up here I'm going to write + + align:start position:0% +little sign up here I'm going to write + + + align:start position:0% +little sign up here I'm going to write +this internal what do I mean by internal + + align:start position:0% +this internal what do I mean by internal + + + align:start position:0% +this internal what do I mean by internal +this is a force strict between the + + align:start position:0% +this is a force strict between the + + + align:start position:0% +this is a force strict between the +internal particles in the system now of + + align:start position:0% +internal particles in the system now of + + + align:start position:0% +internal particles in the system now of +course we know that there must be a + + align:start position:0% +course we know that there must be a + + + align:start position:0% +course we know that there must be a +force on the Ki particle due to the + + align:start position:0% +force on the Ki particle due to the + + + align:start position:0% +force on the Ki particle due to the +interaction between the ja and the K + + align:start position:0% +interaction between the ja and the K + + + align:start position:0% +interaction between the ja and the K +particle and we can call that + + align:start position:0% +particle and we can call that + + + align:start position:0% +particle and we can call that +internal so what we have here is that we + + align:start position:0% +internal so what we have here is that we + + + align:start position:0% +internal so what we have here is that we +can divide our there can still be other + + align:start position:0% +can divide our there can still be other + + + align:start position:0% +can divide our there can still be other +forces acting on the jth particle and + + align:start position:0% +forces acting on the jth particle and + + + align:start position:0% +forces acting on the jth particle and +we'll do a decomposition like this will + + align:start position:0% +we'll do a decomposition like this will + + + align:start position:0% +we'll do a decomposition like this will +say that the total force on the J + + align:start position:0% +say that the total force on the J + + + align:start position:0% +say that the total force on the J +particle can come from some external + + align:start position:0% +particle can come from some external + + + align:start position:0% +particle can come from some external +forces there could be an object outside + + align:start position:0% +forces there could be an object outside + + + align:start position:0% +forces there could be an object outside +our system if these were point if these + + align:start position:0% +our system if these were point if these + + + align:start position:0% +our system if these were point if these +were interacting gravitationally there + + align:start position:0% +were interacting gravitationally there + + + align:start position:0% +were interacting gravitationally there +could be a planet outside here and this + + align:start position:0% +could be a planet outside here and this + + + align:start position:0% +could be a planet outside here and this +could be a moon and our system is just + + align:start position:0% +could be a moon and our system is just + + + align:start position:0% +could be a moon and our system is just +the moons that would be an external + + align:start position:0% +the moons that would be an external + + + align:start position:0% +the moons that would be an external +gravitational force plus the total + + align:start position:0% +gravitational force plus the total + + + align:start position:0% +gravitational force plus the total +internal forces so I'm going to keep + + align:start position:0% +internal forces so I'm going to keep + + + align:start position:0% +internal forces so I'm going to keep +this same color + + align:start position:0% +this same color + + + align:start position:0% +this same color +internal on the J particle now how do we + + align:start position:0% +internal on the J particle now how do we + + + align:start position:0% +internal on the J particle now how do we +write this total internal Force well + + align:start position:0% +write this total internal Force well + + + align:start position:0% +write this total internal Force well +we're interested in the force on the ja + + align:start position:0% +we're interested in the force on the ja + + + align:start position:0% +we're interested in the force on the ja +particle but the internal forces can + + align:start position:0% +particle but the internal forces can + + + align:start position:0% +particle but the internal forces can +come from all the other particles in the + + align:start position:0% +come from all the other particles in the + + + align:start position:0% +come from all the other particles in the +system so what we're looking here is for + + align:start position:0% +system so what we're looking here is for + + + align:start position:0% +system so what we're looking here is for +a + + align:start position:0% +a + + + align:start position:0% +a +sum over all of the possible + + align:start position:0% +sum over all of the possible + + + align:start position:0% +sum over all of the possible +interactions where the other particles k + + align:start position:0% +interactions where the other particles k + + + align:start position:0% +interactions where the other particles k +go from 1 to n and we have to be very + + align:start position:0% +go from 1 to n and we have to be very + + + align:start position:0% +go from 1 to n and we have to be very +careful here that in this sum K cannot + + align:start position:0% +careful here that in this sum K cannot + + + align:start position:0% +careful here that in this sum K cannot +be equal to + + align:start position:0% +be equal to + + + align:start position:0% +be equal to +J now this + + align:start position:0% +J now this + + + align:start position:0% +J now this +sum again because it's a little bit + + align:start position:0% +sum again because it's a little bit + + + align:start position:0% +sum again because it's a little bit +tricky to + + align:start position:0% +tricky to + + + align:start position:0% +tricky to +understand is the internal force on the + + align:start position:0% +understand is the internal force on the + + + align:start position:0% +understand is the internal force on the +jth particle here's the kth one but this + + align:start position:0% +jth particle here's the kth one but this + + + align:start position:0% +jth particle here's the kth one but this +could be a sum I'll just draw one here + + align:start position:0% +could be a sum I'll just draw one here + + + align:start position:0% +could be a sum I'll just draw one here +this is the internal force on the J + + align:start position:0% +this is the internal force on the J + + + align:start position:0% +this is the internal force on the J +particle due to particle number one + + align:start position:0% +particle due to particle number one + + + align:start position:0% +particle due to particle number one +and so we're adding as K goes from 1 to + + align:start position:0% +and so we're adding as K goes from 1 to + + + align:start position:0% +and so we're adding as K goes from 1 to +n all of these internal forces but we're + + align:start position:0% +n all of these internal forces but we're + + + align:start position:0% +n all of these internal forces but we're +excluding the case when k equals J + + align:start position:0% +excluding the case when k equals J + + + align:start position:0% +excluding the case when k equals J +because that would be a force of an + + align:start position:0% +because that would be a force of an + + + align:start position:0% +because that would be a force of an +object on itself and this quantity here + + align:start position:0% +object on itself and this quantity here + + + align:start position:0% +object on itself and this quantity here +we can write as the total internal force + + align:start position:0% +we can write as the total internal force + + + align:start position:0% +we can write as the total internal force +on the J particle so in summary we see + + align:start position:0% +on the J particle so in summary we see + + + align:start position:0% +on the J particle so in summary we see +that the total force on the jth particle + + align:start position:0% +that the total force on the jth particle + + + align:start position:0% +that the total force on the jth particle +is equal to the total external forces I + + align:start position:0% +is equal to the total external forces I + + + align:start position:0% +is equal to the total external forces I +didn't say total there I'm assuming + + align:start position:0% +didn't say total there I'm assuming + + + align:start position:0% +didn't say total there I'm assuming +there could be many different types of + + align:start position:0% +there could be many different types of + + + align:start position:0% +there could be many different types of +external forces plus the total internal + + align:start position:0% +external forces plus the total internal + + + align:start position:0% +external forces plus the total internal +force a little bit later on we can drop + + align:start position:0% +force a little bit later on we can drop + + + align:start position:0% +force a little bit later on we can drop +the t's for Simplicity of notation but + + align:start position:0% +the t's for Simplicity of notation but + + + align:start position:0% +the t's for Simplicity of notation but +this is our big idea that a force on the + + align:start position:0% +this is our big idea that a force on the + + + align:start position:0% +this is our big idea that a force on the +J particle external plus + + align:start position:0% +J particle external plus + + + align:start position:0% +J particle external plus +internal and now when we look at this + + align:start position:0% +internal and now when we look at this + + + align:start position:0% +internal and now when we look at this +sum and we want to now apply our main + + align:start position:0% +sum and we want to now apply our main + + + align:start position:0% +sum and we want to now apply our main +idea we have that the + + align:start position:0% +idea we have that the + + + align:start position:0% +idea we have that the +force which we're writing + + align:start position:0% +force which we're writing + + + align:start position:0% +force which we're writing +as let's explore this our total + + align:start position:0% +as let's explore this our total + + + align:start position:0% +as let's explore this our total +force is the sum of the forces on the J + + align:start position:0% +force is the sum of the forces on the J + + + align:start position:0% +force is the sum of the forces on the J +particle and we've now done this + + align:start position:0% +particle and we've now done this + + + align:start position:0% +particle and we've now done this +decomposition I'm going to drop total so + + align:start position:0% +decomposition I'm going to drop total so + + + align:start position:0% +decomposition I'm going to drop total so +it's the + + align:start position:0% +it's the + + + align:start position:0% +it's the +um the sum of the external forces on the + + align:start position:0% +um the sum of the external forces on the + + + align:start position:0% +um the sum of the external forces on the +J + + align:start position:0% +J + + + align:start position:0% +J +particle J goes from one to n and + + align:start position:0% +particle J goes from one to n and + + + align:start position:0% +particle J goes from one to n and +here we have a sum of the internal + + align:start position:0% +here we have a sum of the internal + + + align:start position:0% +here we have a sum of the internal +forces so we have our sum J goes from 1 + + align:start position:0% +forces so we have our sum J goes from 1 + + + align:start position:0% +forces so we have our sum J goes from 1 +to n of the internal forces on the J + + align:start position:0% +to n of the internal forces on the J + + + align:start position:0% +to n of the internal forces on the J +particle now now we want to apply + + align:start position:0% +particle now now we want to apply + + + align:start position:0% +particle now now we want to apply +Newton's Second Law and in the concept + + align:start position:0% +Newton's Second Law and in the concept + + + align:start position:0% +Newton's Second Law and in the concept +is very straightforward but the + + align:start position:0% +is very straightforward but the + + + align:start position:0% +is very straightforward but the +mathematical expression can be a little + + align:start position:0% +mathematical expression can be a little + + + align:start position:0% +mathematical expression can be a little +bit messy We Know by Newton's second law + + align:start position:0% +bit messy We Know by Newton's second law + + + align:start position:0% +bit messy We Know by Newton's second law +that the sum of a pair of internal + + align:start position:0% +that the sum of a pair of internal + + + align:start position:0% +that the sum of a pair of internal +forces is zero third law by Newton's + + align:start position:0% +forces is zero third law by Newton's + + + align:start position:0% +forces is zero third law by Newton's +third law so what we're saying here is + + align:start position:0% +third law so what we're saying here is + + + align:start position:0% +third law so what we're saying here is +as an example for Newton's + + align:start position:0% +as an example for Newton's + + + align:start position:0% +as an example for Newton's +third + + align:start position:0% +third + + + align:start position:0% +third +law let's just focus on this particular + + align:start position:0% +law let's just focus on this particular + + + align:start position:0% +law let's just focus on this particular +pair that F + + align:start position:0% +pair that F + + + align:start position:0% +pair that F +internal + + align:start position:0% +internal + + + align:start position:0% +internal +KJ plus F + + align:start position:0% +KJ plus F + + + align:start position:0% +KJ plus F +internal J K is + + align:start position:0% +internal J K is + + + align:start position:0% +internal J K is +zero so this is the statement that + + align:start position:0% +zero so this is the statement that + + + align:start position:0% +zero so this is the statement that +internal + + align:start position:0% + + + + align:start position:0% + +forces + + align:start position:0% +forces + + + align:start position:0% +forces +cancel in + + align:start position:0% +cancel in + + + align:start position:0% +cancel in +pairs and so when I look at this total + + align:start position:0% +pairs and so when I look at this total + + + align:start position:0% +pairs and so when I look at this total +internal Force + + align:start position:0% + + + + align:start position:0% + +which is the sum of all of these pairs + + align:start position:0% +which is the sum of all of these pairs + + + align:start position:0% +which is the sum of all of these pairs +of internal forces I can see that the + + align:start position:0% +of internal forces I can see that the + + + align:start position:0% +of internal forces I can see that the +total internal + + align:start position:0% +total internal + + + align:start position:0% +total internal +Force has to be zero so internal Force + + align:start position:0% +Force has to be zero so internal Force + + + align:start position:0% +Force has to be zero so internal Force +cancel in pairs now here we can see it + + align:start position:0% +cancel in pairs now here we can see it + + + align:start position:0% +cancel in pairs now here we can see it +another way if we want to look at this + + align:start position:0% +another way if we want to look at this + + + align:start position:0% +another way if we want to look at this +notation we took the sum J goes from 1 + + align:start position:0% +notation we took the sum J goes from 1 + + + align:start position:0% +notation we took the sum J goes from 1 +to n of f internal J now we use our + + align:start position:0% +to n of f internal J now we use our + + + align:start position:0% +to n of f internal J now we use our +definition for f internal this is where + + align:start position:0% +definition for f internal this is where + + + align:start position:0% +definition for f internal this is where +things get a little bit messy K goes + + align:start position:0% +things get a little bit messy K goes + + + align:start position:0% +things get a little bit messy K goes +from 1 to + + align:start position:0% +from 1 to + + + align:start position:0% +from 1 to +n k not equal to J J goes from 1 to n f + + align:start position:0% +n k not equal to J J goes from 1 to n f + + + align:start position:0% +n k not equal to J J goes from 1 to n f +internal k + + align:start position:0% +internal k + + + align:start position:0% +internal k +j this looks terribly messy but what + + align:start position:0% +j this looks terribly messy but what + + + align:start position:0% +j this looks terribly messy but what +we're saying is this sum is just a sum + + align:start position:0% +we're saying is this sum is just a sum + + + align:start position:0% +we're saying is this sum is just a sum +of pairs + + align:start position:0% +of pairs + + + align:start position:0% +of pairs +and every single pair in this sum adds + + align:start position:0% +and every single pair in this sum adds + + + align:start position:0% +and every single pair in this sum adds +to zero so what we have for our + + align:start position:0% +to zero so what we have for our + + + align:start position:0% +to zero so what we have for our +statement now is that the total force is + + align:start position:0% +statement now is that the total force is + + + align:start position:0% +statement now is that the total force is +the sum of the external forces plus the + + align:start position:0% +the sum of the external forces plus the + + + align:start position:0% +the sum of the external forces plus the +sum of the internal forces which we now + + align:start position:0% +sum of the internal forces which we now + + + align:start position:0% +sum of the internal forces which we now +said that cancels in pairs so let's + + align:start position:0% +said that cancels in pairs so let's + + + align:start position:0% +said that cancels in pairs so let's +rewrite that as the total + + align:start position:0% +rewrite that as the total + + + align:start position:0% +rewrite that as the total +Force now instead of writing this sum + + align:start position:0% +Force now instead of writing this sum + + + align:start position:0% +Force now instead of writing this sum +let's write this as the sum of the exter + + align:start position:0% +let's write this as the sum of the exter + + + align:start position:0% +let's write this as the sum of the exter +external forces and the internal forces + + align:start position:0% +external forces and the internal forces + + + align:start position:0% +external forces and the internal forces +cancel in pairs and so this is now + + align:start position:0% +cancel in pairs and so this is now + + + align:start position:0% +cancel in pairs and so this is now +our force on our system it's only the + + align:start position:0% +our force on our system it's only the + + + align:start position:0% +our force on our system it's only the +external force and now we can + + align:start position:0% +external force and now we can + + + align:start position:0% +external force and now we can +recast our Newton Second Law for a + + align:start position:0% +recast our Newton Second Law for a + + + align:start position:0% +recast our Newton Second Law for a +system of particles with the following + + align:start position:0% +system of particles with the following + + + align:start position:0% +system of particles with the following +statement that the external force causes + + align:start position:0% +statement that the external force causes + + + align:start position:0% +statement that the external force causes +the momentum of the system to change + + align:start position:0% +the momentum of the system to change + + + align:start position:0% +the momentum of the system to change +and this becomes our expression for + + align:start position:0% +and this becomes our expression for + + + align:start position:0% +and this becomes our expression for +Newton's second law when we apply it to + + align:start position:0% +Newton's second law when we apply it to + + + align:start position:0% +Newton's second law when we apply it to +a system of particles where the beauty + + align:start position:0% +a system of particles where the beauty + + + align:start position:0% +a system of particles where the beauty +of this idea is that no matter how + + align:start position:0% +of this idea is that no matter how + + + align:start position:0% +of this idea is that no matter how +complicated the interaction is inside + + align:start position:0% +complicated the interaction is inside + + + align:start position:0% +complicated the interaction is inside +the system all of those interactive + + align:start position:0% +the system all of those interactive + + + align:start position:0% +the system all of those interactive +pairs sum to zero and so only thing that + + align:start position:0% +pairs sum to zero and so only thing that + + + align:start position:0% +pairs sum to zero and so only thing that +matters is the external force in terms + + align:start position:0% +matters is the external force in terms + + + align:start position:0% +matters is the external force in terms +of changing the momentum of the system + + align:start position:0% +of changing the momentum of the system + + + align:start position:0% +of changing the momentum of the system +and now we'll look at some applications + + align:start position:0% +and now we'll look at some applications + + + align:start position:0% +and now we'll look at some applications +of that \ No newline at end of file diff --git a/D7APJXFJsbc.txt b/D7APJXFJsbc.txt new file mode 100644 index 0000000000000000000000000000000000000000..4b28ac6be3200975b2ad4a500707eefd8bc05063 --- /dev/null +++ b/D7APJXFJsbc.txt @@ -0,0 +1,1582 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high-quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: Before I +continue with the material, + +I want to show you at least +the title of a recent paper + +in Nature, because it's +related to material + +we have covered in this course. + +It's about the Kerr +effect, the effect + +that one photon can create a +phase shift for another photon. + +And one goal, of course, +for quantum computation + +where things are +about single photons + +is to have a +single-photon Kerr effect + +that one photon can change +the phase of the other photon + +in a strong, noticeable way. + +So maybe one photon should +create a phase shift + +on the order of pi. + +And this was reported +here in this paper. + +Of course, the non-linearity +created by nonlinear crystals + +is much too weak for that. + +But what those authors did is +they used microwave photos, + +had microwave photons +into cavities. + +And they were coupled +through a sapphire substrate + +with a Josephson junction. + +So the non-linearity +here is the non-linearity + +of a Josephson junction, +which is actually + +realized with a +superconducting qubit. + +I can't explain you +many more details, + +but I just thought +it sort of cool + +to see how the Kerr +effect, which we discussed + +and which we discussed +for single-photon, + +is realized, at least +in the microwave domain. + +And also, just sort +of to illustrate + +that I hope this course enables +you to read recent research + +papers, what those +people measured + +is a [? key ?] representation. + +This is a coherent state. + +And then they showed, and this +is the subject of the paper, + +that the coherent state which +has a well-defined phase, + +lost its phase through +the Kerr medium. + +And you clearly see there +is a big phase uncertainty. + +But then after certain +time-- this is experiment + +and this is simulation-- +there is a re-phasing, + +and the phase is back. + +There is a revival of +the coherent state. + +All right. + +Now I want to address +one question which + +Cody asked about the g2 +function and fluctuations + +of single-mode light. + +Let me just summarize. + +I told you that if you +do the thermodynamics + +of a single mode, we find +Bose-Einstein distribution + +of photons. + +And we have a +thermal distribution. + +And a thermal distribution means +sometimes we have more photons, + +sometimes we have less +photons, depending + +on the thermal distribution. + +And when we calculated what the +intensity fluctuations were, + +we found they're characterized +by a g2 function of 2. + +OK. + +Then a little bit later +in this course-- actually, + +just this week-- I told you +that single-mode light always + +has a g2 function of one. + +And what I meant here is the +following, rather trivial. + +If you have a single mode, +that means that you [? align ?] + +[? it ?] is simply +e to the i omega t, + +the intensity is constant. + +There are no intensity +fluctuations. + +And also, because everything +is sort of predictable, + +it's just one wave. + +The Gn function +factorizes into-- can + +be re-expressed by +the g1 function. + +So therefore, this is +the most trivial case. + +But the question +now is, how do we + +reconcile those two statements, +that a single mode, e to the i + +omega t, does not have +intensity fluctuations? + +Therefore, is a g2 +function of one. + +And our earlier treatment +about single-mode black-body + +radiation. + +And of course, the +answer is, what + +is the single mode +in one context + +is different from the single +mode in the other context. + +Maybe let me explain that. + +Let's just create an +ensemble of cavities. + +We put them in thermal +contact with a reservoir. + +And then we break the thermal +contact with a reservoir. + +Each cavity has now a +perfect single mode, e + +to the i omega t. + +But each cavity is filled +with a different photon number + +according to the +thermal statistics. + +So therefore, if you +just look at one cavity, + +we find no intensity +fluctuations. + +The g2 function is one. + +But if you extend +the ensemble average + +over all the +different cavities, we + +find that there are +fluctuations in intensity. + +Well, we can now +keep that in mind. + +But now we can say, +well, let's just + +take one cavity which is weakly +coupled to a thermal reservoir. + +And instead of looking +at the ensemble average + +of many cavities, we look +at the long-time average + +of this one cavity. + +And what will happen is thermal +photons will be created, + +will disappear, and such. + +So now this one +cavity fluctuates. + +But technically, +what that means now + +is it means that the +sharp mode of the cavity + +is interacting with +the environment, + +and it becomes broadened. + +It has a broadening delta omega. + +And this can be +regarded as that we + +mix in modes of the environment. + +So in that case, +strictly speaking, + +it's no longer a +single-mode cavity. + +So you have to +consider those things. + +And depending what point +of view you want to take, + +you get the different result. + +Other questions? + +Then let me ask you a question. + +Last class, I explained +to you-- well, at least, + +tried to explain to you +that g2 function for bosons + +and fermions with the +counting statistics, + +with permutations and such. + +I wasn't sure, at +least from one question + +I got, whether this +was completely clear. + +Do you have any +question about that? + +[? Teroy. ?] + +AUDIENCE: This +seems very obvious. + +But during class, I +was trying to something + +with thermal state. + +What is the definition +of our thermal state + +in terms of any basis, +just generally speaking? + +We write it as-- I thought +it'd be something like e + +to the minus beta +light Hamiltonian. + +PROFESSOR: Yeah. + +So our definition of +the thermal state-- + +when we had thermal +light, we say + +that the statistical +operator is given by that. + +And H is the Hamiltonian +for a single-mode light, + +which is n plus 1/2 nn. + +Well, with suitable +parentheses and summations. + +Other questions? + +OK. + +Then let's get to the main +subject we want to discuss now. + +And these are actually +Feynman diagrams. + +I wanted to give you +an exact definition + +and a deep +understanding, what does + +it mean when we talk about +processes of absorption + +and emission, but also about +absorption, emission processes + +which violate energy. + +And some people refer to +them as virtual photons. + +The reason is that virtual +photons cannot really exist + +for a long time. + +When you emit a virtual +photon, another photon + +has to be absorbed immediately +to reconcile energy + +conservation, as we +want to see in a moment. + +So the goal of this +presentation is + +I want you that you realize +that each of those doodles + +has an exact +mathematical meaning. + +Each of those diagrams +represents one term, + +or a class of terms, +in an exact solution + +for the time evolution +of the system. + +So in other words, +if you would ask me, + +we have a ground +and excited state. + +Is it possible that the +ground state emits a photon, + +goes to a virtual state, +emits another photon + +of another frequency, and then +somehow absorbs the photon, + +goes to here, and eventually +takes another photon, + +and is back to the ground state. + +Is that a possibility? + +Can that happen? + +And I think what +the message here + +is yes, everything happens. + +The system is trying out +all of its possibility. + +And the two time +evolution is the sum + +of all those possibilities, +of all the amplitudes related + +to those diagrams. + +But what I want to show you +is how sort of the weirder + +the diagrams get, the more you +go in energy below the ground + +state, the more you go away +from real atomic states, + +the bigger is your +energy denominator. + +And that means +those diagrams have + +a smaller and smaller weight. + +And in all practical +calculations, we neglect those. + +But I want you sort of to be +able to see that and realize, + +I exactly know what it means. + +It means this and this +term in a summation + +over all the amplitudes +which the quantum + +system is exploring. + +And I think with that, we really +learn something about physics. + +We learn about what is +actually inside the Schrodinger + +equation. + +A lot of people actually, +before they take this class, + +think that this +is just nonsense, + +that this has no +physical reality. + +But I hope after +this class, you see + +that pretty much everything +you draw has physical reality. + +It's just-- it may +not contribute a lot. + +So what we have done-- +and let me just start here + +and invite your questions. + +We have figured out how +an initial state evolves + +with a time evolution operator +to another basis state, + +toward the final state. + +And formally, this is the formal +solution and exact solution + +of the Schrodinger equation. + +We have to sum over all orders, +orders in the interaction. + +Well, I will +immediately tell you + +what is the first +and second order. + +We are not going much higher. + +But if you want, here, you can. + +And then what you have to +do is in the time evolution, + +you have to sum over +intermediate times. + +You have to allow the system to +propagate, to change its state, + +propagate again, +change its state again. + +And the times where the +change of state happens, + +that can happen at any +time between your initial + +and your final time. + +And we integrate over +all possible times. + +And I showed you-- +and I think this + +was the very last thing +we did on Wednesday. + +I showed you how +this diagram can + +be translated into +mathematical equation. + +And I think I picked the +second order diagram. + +But I think from the way how I +presented should be clear now + +how any such diagram can be +translated into an equation. + +And eventually, you have +to perform an integral + +over all intermediate times. + +And this is part of the time +evolution of the system. + +Questions about that? + +AUDIENCE: We allowed these +to be [INAUDIBLE] right? + +Because we haven't done +anything with that? + +PROFESSOR: Good question. + +I assume that it's +time-independent. + +Actually, right now, I assume, +just to assume something, + +that it's a dipole interaction. + +My understanding is if it has +an explicit time dependence, + +it would just appear there, +and it would not change the-- + +would it? + +Wait, would it? + +Actually, when be derived +the differential equation + +for the time evolution +operator, did + +we assume that v was +time-independent or not? + +I don't think we did. + +We integrate over time. + +I think the formal solution. + +Remember, I wrote down +the differential equation + +for the time evolution +operator and then say, + +this is a formal solution. + +My gut feeling is +nothing changes + +when v is time-independent, +but this one step + +should be confirmed. + +Other questions? + +OK. + +Then let me just spend a few +minutes on connecting what we + +have done with standard +first and second + +[? auto-perturbation ?] theory. + +I want to sort of throw +a few definitions at you. + +S-matrix, T-matrix. + +But I'm not really +going into any details. + +I just want to sort of wrap +up the perturbative treatment + +by connecting it with the +standard first and second + +[? auto-perturbation ?] theory. + +But after that in +a few minutes, I + +want to have a discussion +about the nature + +of intermediate and +so-called virtual state, + +and then talk about the +interaction v, whether it's + +d, dot, e; or the p +minus e interaction. + +OK. + +So far, I've presented +the formalism + +that we started in initial +time and ended at final time. + +But usually, these +are microscopic times. + +And in the +experiment, we observe + +a system for macroscopic time. + +So for that purpose, we +usually go to the limit + +that initial and final +times are infinitely apart. + +And that actually means we +have energy conservation. + +The initial and final +energy has to be the same. + +And that can be, for instance, +even if you restrict ourselves + +to second order, remember we +had all those propagators, + +e to the i energy +over H bar times t. + +And when we integrated +over long times, + +it will just average +out to zero unless + +the initial and final +energy are the same. + +And technically, +you have seen that + +in undergraduate derivation +second order perturbation + +theory. + +You integrate the +exponential function. + +And eventually, for +sufficiently long time, + +capital T is the +difference between + +initial and final times. + +It approaches the +delta function. + +So that's how energy +conservation comes in. + +So the fact that we +have energy conservation + +is then used to +define s and T-matrix. + +The transition amplitude from +the initial to the final state, + +what we have just +calculated and discussed, + +is called the S-matrix. + +It's just how it is called. + +In first order, of +course, the time evolution + +is the unitary matrix. + +So therefore, we get +[? conical ?] delta. + +And then we discussed that +in the limit of large times, + +we have a delta function. + +So therefore, if we +take the S-matrix, which + +is the transition amplitudes +we have calculated, + +and sort of take out of the +S-matrix, the unity matrix, + +and factor out the delta +function, then what is left + +is the so-called T-matrix. + +When we talk about transition +amplitude, transition + +probabilities, we +are asking, what + +is the probability +that the system + +has gone from an initial +state, maybe the ground-- + +the excited state +to the ground state + +through spontaneous emission? + +Well, probability is +an amplitude squared. + +So we take the matrix element +of the S-matrix and square it. + +And from the line +above, this is now + +involving the matrix element +of the T-matrix squared. + +There's a delta +function which becomes + +a delta function squared. + +But if you integrate over all +final states, that's-- I mean, + +a delta function is always +requiring that you do some + +integration later. + +Otherwise, the delta +function doesn't make sense. + +The delta function squared. + +You can actually explicitly see +from the sine function above. + +The delta function squared +just turns into the time t. + +So therefore, if you divide +the probability by the time, + +we have our transition +probability. + +We have our transition rate. + +And what we obtain is the +second order expression + +for the transition rate, which +is essentially Fermi's Golden + +Rule. + +So anyway, this +is just finishing + +the formal derivation. + +But now I want to +discuss the nature + +of those intermediate states. + +And maybe what you +should have in mind-- + +the intermediate state, which +comes about when we have + +the system in the ground +state, it emits a photon + +and goes down to this +intermediate state, + +or this weird state which +seems to be lower in energy + +than the ground state. + +Well, what happens is those +intermediate states, when they + +appear after the vertex, they +propagate with the energy. + +But if their energy is less +than the initial energy, + +here, the energy-- the +intermediate state k + +has a phase factor +in its propagation + +which is determined by the +difference of its energy + +with the initial energy. + +So when we violate +energy conservation + +in intermediate state, +delta Ek is non-zero, + +and it is the larger, the more +we violate energy conservation. + +And then in the solution +of the time evolution, + +we have to integrate over +all intermediate times. + +So what we have here is we have +an oscillating phase vector. + +And when we integrate it, +when we integrate something + +oscillating over longer +than an oscillation period, + +it averages out to zero. + +So therefore, those +intermediate states + +which are off the energy shell, +which seem to violate energy, + +can only noticeably +contribute over + +a duration which is 1 over +the energy defect, delta Ek. + +So it is correct to say +that the system in its time + +evolution for short +times can, so to speak, + +violate energy protected +by Heisenberg's uncertainty + +relation. + +Or you can say, the system +can do whatever it wants. + +It can spontaneously +create 10 photons. + +But this is pretty much like +taking money, taking a deposit + +out of Heisenberg's bank. + +And after very, +very short time, you + +have to pay it back by +having another process which + +brings you back to +the correct energy. + +I should put it under +quotation marks when + +I said we violate energy, +because energy is not + +sort of defined or measurable +in this intermediate times. + +We start a process +with a quantum system, + +we look what happens afterwards. + +And whenever we +assess energy, it + +is assessed when +the final time is + +much, much larger +than the initial time. + +And I just showed you that +eventually, the system + +has to be back to +a final energy, Ef, + +which is identical to +the initial time, Ei. + +So in other words, I just +want you to keep it in mind. + +I've proven to you +energy conservation + +in the limit that t final +minus t initial is large. + +And when I'm now talking about +non-conservation of energy, + +I do that in quotation +marks, because we + +know energy is +conserved in the end. + +It's just that for very, +very short times in the time + +evolution of the system, there +appear virtual states which + +seem to violate energy. + +But you can think +about it in that way. + +Questions about that? + +Finally, let me now +address the question, + +is everything I'm explaining +to you really happening? + +Is it really happening +in a physical system? + +Well, the first answer +is, I wouldn't tell you + +about it if it had no reality. + +So yes. + +You can imagine that this +is what your atom is doing. + +You can imagine that +the hydrogen atom that's + +[INAUDIBLE] [? shift ?] +is permanently + +emitting and absorbing +photons and all sorts + +of weird photons from +the ground state, + +lower, up, and back +again, and such. + +Yes. + +This is the way +how we derive some + +of the most precise predictions +in physics, namely QED. + +However, we can represent +systems in different gauges, + +in different representations. + +And we had discussed +earlier that we often + +take the dipole representation +for the light atom interaction. + +But there's also the p +minus a representation. + +And if you look at the two, both +the e, dot, d and the a, dot, p + +interaction are the +product of something + +which creates and annihilates +single photons-- a plus a + +[? dega. ?] And then the p +operator or the d operator + +connect the ground +with the excited state. + +So those matrix +element would tell you, + +you can only emit +and absorb a photon + +when you go from the ground +to the excited state. + +However, in the p +minus a representation, + +we also have the a squared term. + +And the a squared +term allows you-- + +because there is no atomic +operator in front of it-- + +allows you to +scatter two photons + +without changing the +quantum state of the atom. + +But this does not +contradict anything. + +You can take either approach. + +And in your homework, +you will actually + +do that when you calculate +Rayleigh scattering and Thomson + +scattering. + +And you will find out +that the two approaches + +give identical results. + +So if you know ask the +philosophical question, + +can an atom scatter a photon +without changing its quantum + +state, well, the +answer to this question + +is actually gauge-dependent. + +But maybe to lift away +some of the confusion, + +one can, of course, +also say, the a + +squared term is +really important. + +And it's a simple description +of Thomson scattering. + +Thomson scattering +is about photons + +which have much, much more +energy than the energy + +difference between the +ground and excited state. + +So therefore, if you want +to completely describe + +the system-- and you can, +it's just more complicated-- + +with a dipole approximation, +we have to scatter a photon. + +But because the photon +has so much more energy, + +it's so far away from resonance, +this intermediate state + +has a huge energy defect. + +And that means what I +just explained to you-- + +the system wants to +immediately pay back + +the money to Heisenberg's bank. + +So it will remain in this state +only for very, very short time. + +And now the other +gauge tells you, + +this very, very short +time can also be zero. + +So see, it's not as dramatically +different as you might assume. + +But this is just +something which is common + +that, if you have +different representations, + +the physics tastes +different, but you always + +have to remind you that when you +calculate an observable result, + +the two different gauges +must exactly agree. + +Questions? + +All right. + +So this is all I wanted to say +about the diagrammatic solution + +for the time evolution +of a quantum system. + +But I want to use it now. + +I think this is +interesting stuff. + +It's a powerful method. + +And I want to illustrate +to you how this method can + +be used in the +next two sections. + +Our next section is van +der Waal's interactions. + +So the chapter on van +der Waals interaction + +is quite interesting for +the following reason. + +It really tells us +something about the vacuum. + +I think modern physics +has come to the conclusion + +that the vacuum is one of +the most interesting subjects + +to study, because +the vacuum is alive. + +It's filled by virtual +photons, virtual particles. + +And as we know now, by a +condensate of Higgs boson. + +So there is a lot of +stuff, a lot of structure, + +a lot of phenomena +associated in the vacuum. + +And the subject of van +der Waals interactions + +is it's a nice way to +talk about the vacuum, + +but it's nice also for +the following reason. + +There is a completely, I +would say, semi-classical way. + +Just use the +Schrodinger equation + +and calculate what +is the Van der Waals + +interaction between two atoms. + +So you can just calculate +in perturbation theory. + +And in your whole +calculation, you never + +use the quantized +electromagnetic field. + +Photons never appear. + +You just use +perturbation theory. + +And you do that +in your homework. + +It's rather straightforward. + +And you could have Van +der Waals interaction. + +On the other hand, I started +to derive for you the theory + +of the quantized +electromagnetic field by saying, + +we really look at everything. + +We have charges, and we have +the electric and magnetic field. + +And we described everything. + +And the way how we +separate it is we + +had this Hamiltonian H naught, +which gives us the atom. + +And the longitudinal Coulomb +field became part of it. + +So this is the degree +of freedom of the atom. + +And we have H naught +for the other atom. + +And then we had radiation +field and the coupling + +to the atom described +by our operator V, which + +can be the dipole operator +or can be written down + +in other gauge. + +But what I'm telling you is the +way how we have fundamentally + +divided the world into atoms, +atom's neutral objects, + +and the rest is interactions +with the radiation field. + +That should tell you +that the Van der Waals + +interaction between two atoms +must have a description in QED + +where the Van der Waals +indirection between atoms + +comes from the +exchange or photons. + +So there are two very simple +pictures at the same physics. + +One is you don't even +know that they're photons, + +you just do perturbation theory. + +But in a more +comprehensive description + +where we include +the photons, you + +should be able to +understand the Van der Waals + +action between two atoms +due to the exchange + +of virtual photons. + +In other words, one atom +is in the ground state, + +emits a photon that's going +down from the ground state. + +But until now, if you +have only one atom, + +it has to reabsorb the +photon again and be back + +in the ground state. + +Otherwise, energy +would be violated. + +But if you have two atoms, +one atom can emit a photon, + +and the other atom +can absorb it. + +And then the other atom +can send a photon back. + +And if we consider +that process, we + +will actually find the +Van der Waals interaction. + +So I hope this is showing +interesting physics from two + +angles-- that something +which looked maybe + +trivial a long +time ago now looks + +much richer, because +those forces are really + +mediated by virtual +photon pairs. + +So that's sort of the +discussion I want to go through. + +There is another aspect to it. + +And this is when we go from +the Van der Waals force + +to the Casimir force. + +The Casimir force has +one exact derivation, + +which I want to share with +you, which relates the Casimir + +force to the vacuum fluctuations +of the electromagnetic field. + +So eventually, for those +forces between two metal + +plates-- a neutral +atom in the plate, + +two neutral atoms-- we will +have three different pictures. + +One is we use the +semi-classical dipole field + +as a perturbation operator. + +You don't think about it. + +It's trivial, and you check +it off in your homework. + +The second one is you +look at the exchange + +of virtual photons. + +And the third one +is you only look + +at the zero-point fluctuations +of the electromagnetic field. + +What is real here? + +What causes it? + +We'll see. \ No newline at end of file diff --git a/Docl3KOqnHI.txt b/Docl3KOqnHI.txt new file mode 100644 index 0000000000000000000000000000000000000000..8099e9573dd93807b93c639a59dcfea3c6d5567e --- /dev/null +++ b/Docl3KOqnHI.txt @@ -0,0 +1,6076 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help +MIT OpenCourseWare + +continue to offer high quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: All right, so +for the rest of class, + +I'm going to talk +about post-production. + +Do you guys want to +take a five minute break + +before I jump into that? + +OK. + +I will do that when +you guys come back. + +All right, so last +lecture-- should I + +stand up for this since I +stood for all the other ones? + +OK. + +Feel free to interrupt +me at anytime. + +So I'm going to start off with +my favorite quote of all time, + +at least for this class, +which is, "In writing, + +you must kill all +your darlings." + +And that is what today's +lecture is about. + +Post-production 101 or +Killing All of Your Darlings. + +So when we think of production, +we think of the journey + +that we have taken in the +last week of this class. + +We start with +ideation, we script, + +we storyboard, shoot, +edit, and then we + +get to this product magically. + +And we have these three concrete +steps of pre-production, + +production, which is +what you're about to do, + +and post-production. + +Let me know when I can +go to the next slide. + +The reality is that it's +not like that at all. + +And maybe you've seen that. + +Hopefully, you've seen that in +the course in the last week-- + +that you don't do production +in this nice linear, sequential + +format, but you +ideate and you script. + +And when you script, you +go back to your idea. + +When you're storyboarding, it +affects your original idea. + +And that's how I'd like you guys +to approach editing as well. + +At least, I used +to think of editing + +as something that happened +after I shot everything. + +And once I got to +editing, that was sort of + +equivalent to just throwing +what you have together, + +but that that's not +necessarily the case. + +In post-production you're going +to find a lot of things that + +maybe help you re-shoot things. + +And thinking about +post-production + +before you've even +started production + +can help you think of ways to +shape what you're going to do. + +So that is why I'm talking about +editing before you have even + +started to film. + +So when we think of +editing, we think + +of taking or creating something +that is representative + +of continuous time. + +We think about putting +together a video that + +has just the bad bits removed. + +So has anyone done any +video editing whatsoever? + +Kenneth, you have. + +Yeah, so especially +with the webcam videos, + +what you're basically doing is +recording a continuous event + +and taking out the parts +where you mess up your line. + +That's what we think of. + +And we think of the bad +bits as being things + +that maybe as a take that +was out of focus, maybe + +your light was +overexposed, maybe + +your delivery wasn't so good. + +But in this simplest +sense, most people + +think of editing as +presenting something + +that is of continuous time. + +But the problem is that +sometimes the bad bits are not + +as obvious as things +like overexposed light, + +and sometimes, you're +not necessarily + +creating a product that +represents continuous time. + +So I love this book. + +It's on the syllabus. + +It's written by the editor of +Godfather III, Apocalypse Now. + +I think he did The +English Patient. + +He did a bunch of movies that +won a lot of Academy Awards, + +but he says that +editing is not so much a + +putting together of a path, as +it is the discovery of one-- + +or something like that. + +So the question is, how do +you best discover this path? + +So the nice thing about +editing right now-- we're + +in the digital age, +so we have the files + +that we shot available to us in +these chunks and it's up to us + +to tape pieces together. + +But back when film +was actually on film, + +you would have to +watch the entire reel + +through to know exactly what +was on the physical tape itself, + +which was very time +consuming, but it also + +allowed you to see everything +in your fresh perspective + +after you've shot it. + +And I think that's +the first step + +that you need to do when you +edit-- to review the pieces + +that you've shot. + +And I've mentioned this before +in one of the earlier lectures + +I think, but after +you shoot, take a day + +or take an afternoon. + +Don't look at your +stuff unless you're just + +checking to make sure +that all of the file's OK. + +But when you sit down to +edit, I encourage everyone + +to re-watch the +footage all over again + +because when you're +shooting stuff, + +or when you're +really tired and it's + +been an entire day of +shooting, the way you + +look at your footage may +be a little bit different. + +So this is one of +the camera reports + +from when we shot Lindsey's +video in D-Lab actually. + +And I also encourage you +to do this while you're + +shooting to keep +track of your files, + +keep track of +what's a good take. + +But then afterwards, +I would suggest + +that you re-log everything. + +And you don't necessarily have +to do it completely like this. + +But this was a log that +I did after we shot Snot. + +I could not review +the footage the day + +of because I was so +exhausted so I looked + +at it a couple days later. + +And I was able to see +like, oh, you know, + +this take wasn't really good +and it's not worth keeping. + +And I'm not just saying +that because I'm tired. + +So editing is really about +looking at the pieces + +to see which ones +are worth keeping + +and which ones are +not worth keeping. + +But as I said, the +bad bits are not + +necessarily as obvious as this +scene was really poorly lit. + +Bless you. + +What you're really +looking for are things + +that don't advance the video. + +And that is also not a +super tangible quality, + +and I'm going to give you a +bunch of examples that will + +hopefully help you understand +what is worth keeping and what + +isn't. + +But to understand +that, you have to ask + +yourself the basic question-- +why should I keep this scene? + +And this is a very seemingly +stupid and inane question, + +but I didn't ask myself that +the first couple videos that we + +edited for Science +Out Loud and it + +made for a very painful +editing experience. + +So I'm going to +give you an example. + +We shot a video on +how engines work-- + +and I showed you guys +clips of that earlier. + +And we went out to a +horse farm in Acton. + +And it was kind of a drive, and +it was a little bit complicated + +to get all that +set up, so I really + +wanted to get great footage +of the farm, and we did. + +We got awesome footage of +Luke with one of the horses. + +LUKE: We would need 230 +horses, like AJ here, + +to power our Cessna. + +But we need 290,000 to +power our Boeing 777. + +PROFESSOR: So it was +this really cool shot, + +and it took us an +extra couple hours + +to shoot with this horse, AJ. + +And we were talking +about horsepower, + +so that's why we had the visual. + +But in the context +of the rough cut, + +which I will show you +later on in this lecture-- + +it really didn't +make a lot of sense. + +It was just like, we're +learning about engines, + +and now here's all +this gratuitous B-roll + +of a horse prancing around. + +And I think that +I was really set + +on keeping it because +I had remembered + +how much extra time it took +us and how much extra planning + +it took us. + +But when you go to the +edit-- when you shoot, + +you're going to +shoot like you're + +going to keep everything. + +And what Chris was saying +about take multiple angles, + +take shots, take things that +you think you may not need. + +But when you edit, you +have no ties to anything. + +They are no longer +your darlings. + +You can kill any +of them, and really + +have a discerning eye for that. + +So that's just quick +tip number one. + +When you edit, try to +see what's on the screen + +and not so much +the circumstances + +in which you got the material. + +So if you were really +tired that day, + +don't think about +how much effort it + +took for you to get that shot. + +And I will admit that +I partially showed you + +that because it broke my +heart to take that out + +and I just feel like it needs +to see the light of day. + +So like I said, most +people think about editing + +as having a continuous linear +representation of an event. + +This is what Slideshow does. + +This is what +OpenCourseWare does. + +Like these lecture videos-- +when you watch them online, + +it's pretty much start +to end, nothing too fancy + +edited in between. + +But remember that +there are lots of ways + +that you can play with +this, either in the editing, + +or in the scripting +and in the production. + +So you have continuous linear. + +Josh also talked about +this idea of In Medias + +Res, which is starting +in the middle of things. + +I think it's a hard concept +to really understand + +so I'm going to show +you an example of it. + +This is Lindsey's video +that we did in D-Lab. + +And the way we start +it is with an opening + +that we revisit halfway +through the video again. + +LINDSEY: Corn husks burn +quickly and turn to ash. + +These lumps burn hot like +firewood, longer than charcoal, + +but are cleaner, greener, +and less expensive than both. + +This is actually made from this, +and I'm going to show you how. + +[MUSIC PLAYING] + +About 3 billion +people in the world + +use charcoal today to heat +their homes and cook their food. + +But charcoal can be expensive. + +It produces a lot +of smoke when burned + +and it's made from wood, which +contributes to deforestation. + +In fact, 98% of Haiti's forests +have been cut down for fuel. + +What we need is an +alternative fuel source. + +Let's take a look at +how charcoal is made. + +We have to first cut down +trees for wood, which we then + +place in a closed vessel +and deprive of oxygen. + +It carbonizes into charcoal +instead of burning to ash. + +We then mix the charcoal +with a binding solution + +and compress that into +lumps called briquettes. + +This process creates +a fuel source that + +works, but has its problems. + +So let's hack the charcoal +production process to make + +everything about it better. + +[MUSIC PLAYING] + +Part of what makes the charcoal +production process so expensive + +is the equipment. + +Instead of a fancy +vessel, you can + +make a simple kiln +out of an oil drum + +by cutting a large hole in the +top and several smaller ones + +in the bottom. + +Gather a couple large rocks +for the kiln to rest on, + +a lid for the top, and you +have yourself a $15 kiln. + +We also need some kind of tool +to mold the charcoal material + +from the kiln into briquettes. + +This is one of D Lab's earlier +designs for the hand press. + +We pour a mixture of charcoal +and binder into the spout here, + +hammer down the piston, slide +open the panel at the bottom, + +and the briquette +pops right out. + +This design costs about +$20 to manufacture, + +but the engineers at +D-Lab wanted to do better. + +They changed the +shape of the mold + +into a square to make +it easier to manufacture + +and significantly cut down on +the amount of material used. + +This time, the mold itself is +used to scoop the charcoal. + +Again, we hammer the piston. + +And the briquette +pops right out. + +This design is easy +to manufacture. + +It creates briquettes faster +and it only costs about $2.00 + +to make. + +Now that we've made the +equipment less expensive, + +what can we do about +making the fuel cleaner? + +If we can get all the smoke to +burn off while the charcoal is + +being made instead +of being used, + +we can decrease +the amount of smoke + +released in people's homes. + +Leaving the kiln open +for about five minutes + +at the beginning of the +process will allow the smoke + +to burn off outside. + +So that's why we cut a hole +in the top of the oil drum. + +All right, final challenge. + +What can we do to make +this fuel more sustainable? + +What if we replaced the +wood with something else? + +Something like dried corn +husks, or dried corn puffs, + +dried bean stocks, or +even dried banana peels? + +These agricultural waste +products, or ag waste, + +would normally be +discarded as trash. + +But we can use them to +make charcoal-- and poof! + +Your trash becomes +a precious resource. + +And that's how you turn +trash into treasure. + +Less expensive, cleaner burning, +more sustainable, treasure. + +PROFESSOR: So in +watching this, it's + +actually a little more +Bookend than In Medias Res, + +but the concept is that you +open immediately with the thing + +that you're not going to +talk about until later + +on in the video. + +And we could have opened +without her doing the, + +this is actually made from this. + +We could have just +opened with her at D-Lab + +and it would've been fine. + +It would've been the +continuous linear thing, + +but we kind of +used it as a hook. + +And I think a lot +of you are actually + +going with this format of +starting in the action. + +Julia's is kind of like this. + +Let's see, who else +kind of has-- sort + +of in the middle of things? + +I think Paul's is a +little bit like this, too. + +Just like you're in +the action immediately + +without a bunch set up. + +So that is one +way you can do it. + +Again, this was a little +more of an example + +of bookending stuff, too, which +is what Joshua's script does. + +Kenneth, yours does +this right now, too. + +Which is also a nice way to +encapsulate a video experience + +in a tidy package. + +So sort of opening the +same way you close. + +For George's video on farts, +we did this quite literally. + +We had him in the +exact same location + +and set that we +opened the video with. + +And that's how we did +my snot video as well. + +You don't have to +do it that way, + +but it's a very explicit way +of bookending your video. + +GEORGE: You know +what's more like life + +than a box of chocolates? + +Farts. + +You really never know +what you're going to get. + +A skunk? + +Rotten eggs? + +PROFESSOR: And then-- oh, shoot. + +Uh-oh. + +I wanted to skip to +the end of the video, + +so let me just do +that really quickly. + +So he opens in that location. + +And then-- + +GEORGE: We're at +the very beginning + +of understanding the incredible, +smellable science in your gut. + +And until we do, happy farting. + +[MUSIC PLAYING] + +PROFESSOR: So that's +just something + +to think about if you're +getting ready to film + +and you're deciding on the +location of where you're going + +to open and close your video. + +The other thing editing does +is it allows you to figure out + +what's best to keep. + +So this is an example of +where cutting out the bad bits + +isn't as obvious for us. + +In this section, it was +cutting out the bits + +that don't work the best. + +So I showed you +guys this before, + +but basically taking stills +of all of your scenes. + +And then seeing the shots in +the context of everything else + +can help during editing as well. + +The next concept I +wanted to talk about, + +which is also in +Walter Murch's book-- + +is the idea of referred pain +when you're at the doctor. + +You go to the doctor and +you have shoulder pain-- + +or like elbow pain. + +And if your doctor +says, OK, we're + +going to go in and +operate on your elbow, + +then you should leave because +maybe this person is not + +very good doctor. + +What a good doctor +would do is ask you + +about what kinds of +activities you've been doing. + +He or she would check out +the rest of your body, + +and then maybe find out that +the problem isn't your elbow, + +but the problem is a pinched +nerve somewhere upstream. + +So this is the analogy he makes. + +Same thing with your videos. + +If you're finding that +there's a certain scene that's + +not working, most +of the time it will + +be because you need +to change that scene. + +But a lot of times, it may +be because you've set it up + +in not the greatest way. + +Or maybe the scenes preceding +it don't make a lot of sense. + +So I will show you +an example of this. + +And this is super, +super nuanced, + +and it might just be because +we were being super nit-picky + +and getting really OCD about it. + +But this is a scene from the +fifth draft of Jamie's video. + +JAMIE: This Digi-Comp +has 31 switches + +and can count up to 127. + +But modern computer chips +have over a billion switches. + +They're made from wafers, +such as this one, where + +each square represents a chip. + +They're made from semiconductor +switches called transistors, + +which have the advantage +of being solid state, + +meaning they have +no moving parts. + +This allows engineers, like me, +to make them smaller, faster, + +and more energy efficient. + +We can make them +over a billion times + +faster than the Digi-Comp. + +These semiconductor +switches make + +modern electronics possible. + +PROFESSOR: So the whole +video is about how + +big, complicated +machines, like computers, + +are built out of actually very +simple parts, like a switch. + +And so the majority of his +video is with the Digi-Comp. + +And he's talking about how +the switches are calculating + +in binary, and then at +the very end of the video, + +he goes, these switches are +what make modern electronics + +possible, which is +true and it ties it + +into the bigger context. + +But when we were watching +the rough cut, our editor + +[INAUDIBLE] and +George and I were + +all like-- we felt like +the ending came super + +abruptly and seemed +a little bit random-- + +that we're talking about +basic switches the whole video + +and then all of a sudden, +he's like, and that's + +what makes things possible. + +So we thought about +re-recording the end, + +but then we realized-- +and again, maybe this + +is a personal taste thing. + +Maybe this video isn't actually +super different from the one + +we ended up +publishing, but this is + +an example of us troubleshooting +by looking at previous scenes + +and how we set up +the final shot. + +And we felt that the +gap between him talking + +about semiconductors, and +then his final sentence + +was a little bit too short. + +So we thought maybe we could +make the pause a little bit + +longer to signify that his final +shot is the encompassing idea. + +So that's what we did. + +JAMIE: Big the numbers can be. + +This Digi-Comp has 31 switches +and can count up to 127. + +But modern computer chips +have over a billion switches. + +They're made from wafers, +such as this one where + +each square represents a chip. + +They're made from semiconductor +switches called transistors, + +which have the advantage +of being solid state, + +meaning they have +no moving parts. + +This allows engineers, like me, +to make them smaller, faster, + +and more energy efficient. + +We can make them +over a billion times + +faster than the Digi-Comp. + +These semiconductor +switches make + +modern electronics possible. + +PROFESSOR: I mean, it's a +super, super nuanced thing. + +I'm not sure if you +guys noticed it, + +or even if it was +worth us doing. + +But I wanted to show it as an +example of the thought process + +that we had in troubleshooting +the final scene. + +And I think it makes +a little more sense + +in the context of +watching the entire video, + +but in the interest +of time, I didn't + +want to show you 10 +minutes of the same video. + +Edits can change a +lot more than just + +taking out the bad, though. + +They can completely +restructure things. + +And I'll show you a little +bit from the rough cut + +of the engines video. + +Someone was asking exactly +what a rough cut should be-- + +if we need everything +in there, if we don't. + +So this is an example of what +the first draft of a video + +can look like. + +We're missing a couple scenes. + +A lot of things change. + +ABHI: Hundreds of +years ago, James Watt + +decided that my friend, Helga, +could lift 550 pounds a foot + +in the air in one second. + +And that's the definition +of a horsepower. + +LUKE: This lawn mower +has 6 horsepower. + +ABHI: This car has +110 horsepower. + +LUKE: This Cessna +has 230 horsepower. + +ABHI: And this jet +has 85,000 horsepower. + +LUKE: But they do it +in different ways. + +ABHI: A car uses +a piston engine. + +This is a piston engine +that's been cut into a half + +so you can look into it. + +A mixture of fuel and air +enters through these valves + +into this metal cylinder. + +It's compressed when the +piston pushes up onto it, + +and then this mixture is +burned through a spark plug, + +causing the mixture to expand. + +And the piston comes back down, +and this happens over and over + +again. + +There are multiple +pistons in a car, + +and they're connected +through a series of linkages + +to the wheel, +causing them to turn. + +PROFESSOR: So I wanted +to show this example + +to highlight that editing is +a super, super collaborative + +process. + +So after you guys put +together your rough cuts + +and we screen-- for the +second half of that class, + +we'll randomly assign +you editing partners. + +And they're going to +look through your video + +and annotate on a live +software that we have at MITx. + +The editor who put +together that rough cut + +did not hate that +font as much as I did. + +And she did not hate that +music as much as I did. + +All right, so if you're the only +person looking at your video-- + +to this person, maybe they +really liked the style, + +they like the pacing of it. + +But to me, and to George, and to +the second editor that we had, + +we often have multiple editors +look through our stuff, + +even if one person's the +main one doing the editing. + +You get feedback that you +otherwise wouldn't have, + +which is a very +obvious statement, + +but I want you to see how +much it changed by the end. + +I'll show you the opening again. + +ABHI: Hundreds of +years ago, James Watt + +decided that my friend, Helga, +could lift 550 pounds a foot + +in the air in one second. + +And that's the definition +of a horsepower. + +LUKE: This lawn mower +has 6 horsepower. + +ABHI: This car has +130 horsepower. + +LUKE: This Cessna +has 230 horsepower. + +ABHI: And this jet +has 85,000 horsepower. + +All of these engines +produce power + +by forcing a mixture of fuel +and air into a tight space, + +and then burning it. + +LUKE: But they do it +in different ways. + +ABHI: A car uses +a piston engine. + +This is a piston engine +that's been cut into a half + +so you can look into it. + +A mixture of fuel and air +enters through these valves + +into this metal cylinder. + +It's compressed when the +piston pushes up onto it, + +and then mixture is burned +through a spark plug, + +causing the mixture to expand. + +And the piston comes back down, +and this happens over and over + +again. + +There are multiple +pistons in a car, + +and they're connected +through a series of linkages + +to the wheel, +causing them to turn. + +PROFESSOR: So we +changed a couple things, + +changed out the music. + +I'm still not a huge +fan of it, but I + +thought it was a lot better +than what was there before. + +We added a couple labels, +put in some stock footage. + +I mean, to me, I +think the feel of it + +changed a lot after having +the collaboration between four + +or five of us. + +And that happens with +every video, too. + +I wanted to mention the five +words that you should never + +say, which I often say, too-- +but the notion of, we'll + +fix it in post. + +Like oh, the sound isn't +super great for this take, + +but that's OK. + +I'll fix it in post-production. + +Thinking about +post is really good + +to set you up for creating +as high quality materials + +to work with as +you can possible. + +So really try not to lean on +post-production and editing + +as a space where you will +have a bunch of band-aids + +to cover up material +that isn't as good. + +You will save so, +so, so much time + +doing just that extra take to +get the good audio than you + +will if you tried to clean +it up in editing afterwards. + +So don't say these words. + +So we have to kill our darlings. + +We have to figure out what +things are worth keeping + +and what aren't. + +What is the way that we +actually kill the pieces. + +And that way is with the cut. + +So the cut is going to be +the spaces in which we decide + +to break the +footage that we have + +and align it with something +new-- a transition. + +Now this notion of seams +is an interesting one + +when you're editing. + +A seam is basically +like when you + +notice that the location changes +or that the scene changes. + +Being aware of +where your cuts are + +and what your +scenes look like are + +going to be important for the +overall feel of the video. + +So in an earlier +lecture, I think + +I'd mentioned storyboarding +is great because it gives you + +a sense of what the visual +pacing of your video + +is going to be. + +When you're doing +cuts in editing, + +watch through +sections of a portion + +that you've edited-- +maybe 30 seconds of it, + +and basically see how +many seams there are + +and if they're +really noticeable. + +What I personally +like-- this is my taste, + +and I think it's the +taste of most people-- + +is that I think +your seam should be + +as deliberate and +clean as possible + +so that they're not +very noticeable. + +What you don't want +to end up happening + +is someone to watch your video, +and notice every single time + +you take a cut. + +You don't want their reaction +to be, oh, she cut there. + +Oh, she cut there too. + +And for that reason, I +favor just clean cuts. + +No funky transitions, +no ripple effects. + +Do you guys know what +I'm talking about? + +No spins. + +I think we did one +push transition + +that I fought against. + +But that's my personal taste. + +But in general, the cut should +be as hidden as possible, + +I think. + +Because that's not what +your video is about. + +Your video is about the content. + +It's not about the transitions +in between the scenes. + +When you do clean cuts, though, +especially for these videos, + +it has to be deliberate enough +to where it makes sense. + +And I'll explain this further. + +So in this example-- + +[VIDEO PLAYBACK] + +-You can count up to 127. + +[END PLAYBACK] + +PROFESSOR: That is +the wrong example. + +Never mind. + +I'm not going to talk +about clean cuts. + +Apparently I'm going to +talk about transitions. + +So this is one transition +where something + +that wasn't a clean cut +worked for us, I think. + +Because we were being a little +tongue-in-cheek about the wipe. + +The way we achieved +this is, George actually + +loosened up his tripod. + +And when Jamie was in Stata, +at the end of his shot, + +he just flung the tripod up +so that the camera actually + +swung up. + +And then we used that to move +into the transition effect that + +was in Final Cut. + +It just makes the video +look a little more + +clean and deliberate, I think. + +Otherwise, you have +still frame, wipe up, + +wipe down, to still frame. + +It looks a little bit different. + +What was I going to talk about? + +So yes, sometimes it's +OK not to use clean cuts. + +This is another example. + +[VIDEO PLAYBACK] + +[TICKING] + +[BEEPING] + +PROFESSOR: All those were +clean cuts, by the way. + +-Radiation is frightening. + +At least, certain +types of it are. + +My Geiger counter doesn't +go off near my mobile phone, + +or the Wi-Fi router, +or my microwave. + +That's because a +Geiger counter only + +measures ionizing +radiation, that + +is, radiation with enough energy +to rip electrons off atoms. + +And it's measured in +units called sieverts. + +If you're exposed to more +than two sieverts all at once, + +you'll probably die +shortly after that. + +But we're exposed to low +levels of ionizing radiation-- + +[END PLAYBACK] + +PROFESSOR: So that was a wipe. + +But I don't feel like that's +super cheesy, because he only + +uses it very sparingly. + +Did you notice how +many cuts there were + +in that 30 seconds of clip? + +He must have cut 20 times. + +But as a viewer, I'm not +noticing, oh, he cut there, + +oh, he cut there, oh, +he cut there, right? + +So that's what I mean by +keeping your seams hidden. + +Yes. + +AUDIENCE: In a way, +it seems intuitive. + +But when you're editing, +and you're looking, + +and you're cringing +at your own speech, + +it's a practice that +you might want to do. + +You never cut in the +middle of a phrase, + +or in the middle +of your talking. + +Because that's really +jarring, like seeing your head + +in one place, and +then seeing your head + +in a slightly different place. + +It's always really jarring. + +But whenever he cut, +he cut to something + +that was other than his face. + +When he was walking through +with the Geiger counter, + +he was cutting to different +angles of that same shot. + +Or when he was just +talking to the camera, + +he cut away from his face, +and then cut back to it. + +So you don't see a little twitch +where he was saying one phrase + +and he did another take, and +he was in a different spot. + +It's something you don't +notice until you actually + +get into the editing process. + +And you see, whoa, +that's really weird. + +But it's something +good to keep in mind. + +So if you aren't going to +finish a two sentence phrase, + +think of a way to +transition between that, + +rather than just doing +a hard cut between them, + +because it won't look clean. + +PROFESSOR: I have +some examples of that, + +that I was going to show you. + +But that's a super, +super important point. + +Yes, Joshua. + +AUDIENCE: I wanted +to say a sentence, + +but I remember the plans video. + +What did they have in +common, [INAUDIBLE]? + +PROFESSOR: Yeah. + +So for that, we +are jumping ahead. + +I have this one slide, and +then I'm going to get to it, + +I promise. + +So this is going +off of the whole + +hide your seams type of thing. + +I like to keep +labels really simple. + +Sometimes you'll have +a need to label things. + +Again, this may be a +matter of personal taste. + +But I think the cleaner the +labels are-- no funky Word Art, + +I think those other things +look a little amateurish. + +If it's good content, it doesn't +need the frills, necessarily, + +to be engaging. + +So you were asking, cutting, +how do you do the thing + +that Sari was saying? + +For plants, we had +her really close up + +for the beginning, right? + +And then she goes, what do +all these chemical compounds + +have in common? + +And then we cut out to her +really wide, with her saying, + +plants. + +Right? + +So that is an example of +making your cuts deliberate. + +You want to cut +between two scenes that + +look different enough, to where +the cut looks intentional. + +So this is an example +from Jamie's video, + +and I think this +is the right one. + +[VIDEO PLAYBACK] + +-Even though we +think of computers + +as super complicated high-tech +machines with very tiny parts, + +they can also be huge, +wooden, and mechanical, + +just like this computer here. + +And even though they-- + +[END PLAYBACK] + +PROFESSOR: So right there, +I think in that take, + +he messed up. + +Or he took too long of a +pause in between the two words + +that he was delivering. + +So we wanted to +cut that pause out. + +But it would have +been weird if we + +just cut that +pause out, and then + +didn't do anything +else to the footage. + +So basically, he would have +been like, computers, blah blah + +blah. + +And then he would have +moved slightly to the left. + +And then you would have +seen him keep talking. + +Do you guys know what I mean? + +I'll show you an example. + +So to get around that, we had +his first part of the sentence + +delivered the way we filmed it. + +And then when we cut, we cut +to a digital zoom of him. + +So he was a lot more close up. + +And that's what Hank Green +does a lot in SciShow. + +He cuts back and forth, +between a wide shot + +and a close up shot, to make +the cuts a little less jarring. + +I'll just show you the example. + +[VIDEO PLAYBACK] + +-What it is the most +awesome place in the world? + +Seems like that would be +pretty much the most subjective + +question ever. + +But this week, scientists use +a set of objective criteria + +to come up with a list of +the world's most biologically + +important places. + +There might be one near you. + +[END PLAYBACK] + +PROFESSOR: He also cuts at the +ends of phrases and sentences. + +So it would feel a +little bit more awkward + +if he was cutting in +between, this is my sentence. + +And then he cut to +a close up, and I'm + +going to keep +talking about this. + +And then he didn't +cut, and he just + +kept talking about +the next idea. + +And then he cut back +to this wide shot. + +So again, when you're filming +and you mess up, keep going. + +But try to do as many continuous +thought takes as possible. + +Because again, don't say, +I'm going to fix it in post. + +Because sometimes you're going +to look at it, and be like, + +there's no way around this. + +It's OK if you can't get +an entire scene perfect. + +But at least try to get +chunks of sentences, + +or chunks of thoughts +continuously, + +because that'll be a lot +easier to work with in post. + +So this is the pitch that +I recorded for you guys. + +And I made it this +way because I wanted + +to show you that it does +look weird when you don't cut + +to something different enough. + +[VIDEO PLAYBACK] + +-When we think of +snot, we usually + +think of the stuff +that oozes out + +of us when we're sick, right? + +[SNEEZE] + +It's just more +gross bodily fluid + +that we seem to excrete +for whatever reason. + +But snot is more +than just the stuff + +that hangs out of the noses +of most two-year-olds, + +and some 20-year-olds. + +It's filled with all of these +cells, that do everything + +from fighting +infection, to keeping + +your esophagus from +ripping up every time you + +try to eat something. + +[CHOKING] + +And that junk actually can +keep stuff out of your body. + +And then it knows what to +keep out, what to let in, + +and when to do it all. + +What? + +That is so crazy. + +Snot and mucus is so important +that your body makes a gallon. + +[END PLAYBACK] + +PROFESSOR: It's visually +very hiccupy, right? + +Because I'm only moving +slightly to the left and right. + +And I think it's appropriate +for webcam YouTube videos. + +That's just kind +of the style of it. + +You're centered, +which is also breaking + +a rule of framing in thirds. + +So stylistically, I think it's +more acceptable in YouTube + +webcam videos. + +But for these, it will +look out of place. + +Because you have like a +very formalized script, + +and it's going to jar with +a very amateurish style + +of editing. + +Does that make sense to people? + +AUDIENCE: When you did +that, did you actually + +have it in your +head that you were + +going to cut to those +spots, or was it + +just what you put together +after you had everything? + +PROFESSOR: So I did that in +one long continuous take. + +I just hit Photo Booth on Mac +and I said my whole thing. + +And there were lots of spots +where I'd messed up in between. + +So I did the style of +editing that I first + +talked about, which is just +cutting out the bad bits. + +So I wasn't +intentionally doing that. + +But that's why the movements +are just a little off-kilter. + +I'm not trying to +move or anything. + +It's just that I +move when I talk. + +But it reads a little +bit weird and jarring. + +AUDIENCE: And you'd +recommend just leaving record + +on for however long it takes? + +Like in between scenes, maybe? + +PROFESSOR: I personally have +a really hard time remembering + +what I'm going to say. + +So I would feel better, +when I was shooting, + +if I knew that I only have to +say two or three sentences. + +But when you record, always +record the preceding sentence, + +and the sentence that +comes after the one + +that you're trying to record. + +Because your intonation +will sound different. + +Otherwise, every single +sentence will sound like this. + +It will sound like +you are talking + +in the same style of sentence. + +It will sound like +you were just reading + +a bunch of bullet points. + +So that's why, if +you're shooting scene 2, + +shoot the last +sentence of scene 1, + +and the second +sentence of scene 2. + +Make sense? + +And so this is also from +Walter Murch's book. + +But this is sort of a +tongue-in-cheek thing. + +Thing But he talks about what +makes a good cut, and the order + +of priority. + +A cut that maintains +the emotion of the scene + +is something that's +really important. + +Which sounds very strange. + +But if you have, say, +a very dramatic scene, + +with two people, like Sari and +I are getting into an argument, + +right? + +And we have the camera +that's focused on me, + +and a camera that's +focused on her. + +And you want to show both of us. + +So actually, you would show +Sari getting all mad at me. + +And then you'd show me +getting all mad at her. + +Maybe you'd show her again. + +If you did super rapid cuts +of her and me, back and forth, + +back and forth, +back and forth, it's + +going to read kind +of funny, right? + +It'll read like Western parody. + +You guys know what I mean? + +But if you wanted to highlight +the gravitas of the situation, + +you would cut from her +face to maybe a wide shot + +of the two of us. + +And you wouldn't make +the cuts as rapid. + +Does that make sense to people? + +So I think that's what +he means by maintaining + +the emotion of a cut. + +I think for the +purposes of your video, + +the main thing will +be just making sure + +that the cuts aren't happening +too rapidly, or too slowly. + +I think you'll know. + +You'll watch the +thing, and you'll + +feel like something's +a little off kilter. + +And if that's the +case, I would encourage + +you to adjust how long +you're making the clips, + +and how much dead space you're +leaving it between the clips. + +This is a way to inject-- + +[VIDEO PLAYBACK] + +-OK, so this might +be we our weak point. + +Or is it? + +[END PLAYBACK] + +PROFESSOR: So that's not a cut. + +But that was a type of +zoom that is emotionally + +appropriate for this +scene, because it's + +trying to be funny. + +But if you did that for you +talking about cargo ships + +not sinking carrying +lots of people, + +it would be totally +inappropriate, right? + +The other thing he talks about +is, does it advance the story? + +And I will show you +an example of this. + +[VIDEO PLAYBACK] + +-And all those bacteria +care about is staying alive. + +Our intestine +actually helps them + +do that, because the temperature +is warm and constant. + +They're sheltered +from the environment. + +And best of all, we +provide the food. + +[END PLAYBACK] + +PROFESSOR: So does +anyone want to guess + +how that particular +cut advanced the story? + +Or did you notice +where the cut was? + +AUDIENCE: Can you show it again? + +PROFESSOR: Sure. + +So try to pay attention +to where the cut happens. + +[VIDEO PLAYBACK] + +-All those bacteria care +about is staying alive. + +Our intestine +actually helps them + +do that, because the temperature +is warm and constant. + +They're sheltered +from the environment. + +And best of all, we +provide the food. + +[END PLAYBACK] + +PROFESSOR: So there are +actually two cuts in this. + +But the first cut +is of him walking. + +He's like, and best of all. + +And then it cuts to him +arriving to the place where + +he was walking. + +So in those five +seconds or so, the story + +was about George walking +to the hood to do his demo. + +That sounds like a dumb +story, but that's essentially + +what the story of those +five seconds were. + +So a cut that often +works is, if you're + +doing like a walk and +talk, for instance, + +and you're saying +blah blah blah. + +Navy ships, people might sink. + +And then you cut to the person +arriving at their station, + +like where the boats +or whatever are. + +Does that make sense to people? + +AUDIENCE: So how do you +ensure that your voice doesn't + +sound funny? + +PROFESSOR: Yeah, +like if your delivery + +of the sentence +in one location is + +too different from the other. + +AUDIENCE: Do you remember how +you spoke it in the shoot? + +PROFESSOR: So to shoot +that scene, for instance, + +he would say, we shelter them. + +And best of all-- +we didn't cut there. + +We made him finish the line, +when he's saying, best of all, + +we provide the food. + +And we took a complete cut +of him walking and saying + +the whole line. + +And then, when we shot the part +of him walking toward the hood, + +it wasn't like we +said action, and he + +said, we provide the food. + +We said action, and he +says, and best of all + +we provide the food. + +So that's what I mean by, +say the lines that precede + +and follow the line that you're +actually trying to capture. + +AUDIENCE: And do multiple takes. + +PROFESSOR: Yes. + +AUDIENCE: And say +the line a little bit + +differently each time. + +Because maybe you'll +find that your third take + +for the initial shot, +and your second take + +for your second shot, +are the most cohesive. + +PROFESSOR: Yeah, that's +very good advice. + +And as the directing partner +of whoever you're shooting, + +this is the thing that you need +to do to help your partner. + +If you notice that their +delivery in the second location + +is a lot more subdued +and tired, which + +is going to be the tendency for +most people, you can be like, + +you said that the +beginning of that line + +really energetically when +we were in that other place, + +so you need to match that. + +AUDIENCE: Even if you do +the take right, do it again. + +It's really easy to say, oh +I did it right this time, + +I'm done. + +I memorized my lines. + +But even if it's that struggle +to remember the last word + +in the sentence, +it's worth it to get + +another complete usable take +rather than be stuck with one. + +PROFESSOR: And you're going +to have to work within reason. + +Obviously you're not going +to do 100 takes of each scene + +perfectly. + +So this is up to your +discretion, and the amount + +of time that you have. + +But I would say, at least +try to get three good takes. + +I lost my train of +thought completely, + +but that was a very +important point. + +Thank you. + +And then the other +stuff is rhythm. + +And this is what I mean by +if your cuts are too rapid. + +Oh, I remembered what +I was going to say. + +Sorry, I'm going all +over the place today. + +So in the engines video, +that was the latest night + +that we had worked. + +I think I got home at 3:00 +in the morning that day. + +And at the end of the night, +obviously the two talents, + +their energy levels +were super depleted. + +And so that's what we +ended up re-shooting. + +And that's what +re-shoots are for. + +Even if you end up getting +all the shots that you need, + +oftentimes you won't notice that +someone's delivery was really + +different until you're +in the editing room, + +and you cut everything together. + +So that's why I wanted to +leave some room for you guys + +have time to re-shoot +if you needed to. + +I don't anticipate that +you're going to not + +get shots that you need to get. + +But that buffer room, we +always use it for Science + +Out Loud, regardless of +how perfect the host is. + +Just because stuff +like that happens. + +[VIDEO PLAYBACK] + +-This rock can absorb heat +from the sun during the day, + +and then release that heat hours +later, after the sun has set. + +This is fine when you're +dealing with rocks in the sun, + +but unfortunately it also +happens with bodies of water + +and toxins. + +Rivers, lakes, streams, +and oceans are still + +releasing contaminants +that we dumped + +into them up to 100 years ago. + +From 1947 to 1977, humans +dumped hundreds of thousands + +of pounds of +polychlorinated biphenyls + +into the Hudson River. + +Those PCBs attach themselves to +sediment particles and settle + +to the bottom. + +[END PLAYBACK] + +PROFESSOR: So for that +video, we had a sense, + +when we saw the rough cut, that +it was kind of a frantic video. + +There's a lot of information +being thrown at you. + +I'm not really following, +even though I've + +helped her edit the script. + +If I'm tuning out, +then the audience + +is probably going to tune out. + +So rhythmically, +the cuts maybe were + +happening a little too fast. + +And she's also, in real life, +a naturally fast talker. + +We had to slow her down a lot. + +But she's just an +animated person. + +So we knew that the +tendency of this video + +is going to just feel +super, super fast. + +And if you are +naturally a fast talker, + +this is something +to keep in mind, + +that you can help the +pacing, and the franticness, + +of maybe how you might read, +with how you cut the scenes. + +So what we did instead was, +we allowed for a lot of time + +in between her scenes to +fill with B-roll or music. + +We tried to make the cuts not +happen as rapidly, basically. + +[VIDEO PLAYBACK] + +-This rock can absorb heat +from the sun during the day, + +and then release it hours +later, after the sun has set. + +This is fine when you're +dealing with rocks in the sun, + +but unfortunately it also +happens with bodies of water + +and toxins. + +Rivers, lakes, streams, +and oceans are still + +releasing contaminants +that we dumped + +into them up to 100 years ago. + +From 1947 to 1977, humans +dumped hundreds of thousands + +of pounds of +polychlorinated biphenyls + +into the Hudson River. + +[END PLAYBACK] + +PROFESSOR: So again, it's a +super, super nuanced thing. + +I think the music +helped with it a lot. + +We tried to use very calm music. + +We used a still of that +old photograph of people + +cleaning up the Hudson +River, just to break up + +how many times we were changing +back and forth between all + +the locations. + +Is this making sense to people? + +Sometimes I feel +like I'm saying it. + +And then I watch it, and I'm +like, that doesn't look super + +different from the rough cut. + +But it helped me +sleep that night. + +And this is the other +stuff he talks about, + +which is not as important. + +But the eye trace, +like does it make + +sense for the audience's focus +of interest within the frame? + +So are you cutting +from something + +where you're in the top +corner, to all of a sudden, + +you're cutting to +something in the middle, + +centered, to all of a sudden, +you're cutting to something + +where you're on the left side? + +Are you cutting so rapidly, +and changing your position, + +to where it's not making +sense to the viewer? + +The 2D plan on screen, +are you are you + +consistent with the +stage line, basically? + +So I don't think this is going +to be as relevant for you guys. + +But if someone's +walking, for example, + +and then you cut to a scene +where they're continuing + +to walk, but they're in +the corner of the screen, + +then it doesn't +make as much sense. + +And then the 3D space of action. + +If you have multiple +people in the same room, + +or multiple objects, and +you cut from one angle + +to another angle, make +sure the objects are still + +the same relationship +to each other. + +And the reason why +he lists this out + +is, Walter Murch's theory +is, you should never + +compromise emotion before +you would compromise + +the eye trace with a cut. + +So if a cut satisfies +the eye trace, + +but it doesn't make +sense emotionally, + +then you shouldn't do it. + +Practically speaking, I +think what this translates + +for you guys, is that +if something feels weird + +when you see the rough cut of +your video, most of the time, + +it will be because you +cut it in a weird place. + +You either cut your +speech too short, + +or you didn't cut to a wide +enough shot from a close up. + +You are cutting too much, too +quickly, or not cutting enough. + +Does that make sense? + +I'm going to talk a +little bit about music, + +and some of the Creative +Commons resources + +that will be available to you, +if you want to use footage + +that you don't have access to. + +Before I go into +that, does anyone + +have further questions +about editing? + +Sari is good with Adobe, right? + +You use Premier? + +AUDIENCE: Yeah, I used Premier. + +I used iMovie before that, +so just give them those. + +Final Cut Pro, I +haven't looked at it, + +but professional editing +softwares usually + +have some weird rules. + +So, if that's what +you choose to use, + +I can definitely go and +work in the computer lab + +and figure it out. + +PROFESSOR: So Building +26, I'll show you + +at the end of class the website. + +But I've reserved it for the +rest of this class period, + +and it has all the software +on it if you want to use it. + +I have used Final Cut Pro +and Final Cut Express. + +I'm not super, super +good at it, though. + +But in the remaining class +time, when you basically + +have time to work +on your projects, + +we will be around if you want to +schedule a certain time to work + +on a particular problem +that you're having + +in your editing software. + +Just come talk to us. + +All the tutorials for a +bunch of these software, + +they're all listed +on the syllabus. + +So when it comes to music, +it's a bit like lighting, + +as Chris said. + +First, do no harm. + +So I would much prefer a +video that does not have music + +to a video that has music +that is super distracting, + +or an entirely different tone +from the video that you're + +trying to convey. + +So be careful with music. + +But music is a really, +really great tool, + +because I think it +establishes emotion + +better than any other tool that +you have in your video kit. + +That's my opinion. + +I'll show you an example of it. + +Do you guys remember the +video of Neil deGrasse Tyson + +that I showed you +on the first day? + +The 10 questions? + +[VIDEO PLAYBACK] + +-What is the most astounding +fact you can share with us + +about the universe? + +-The most astounding fact, +the most astounding fact, + +is the knowledge +that the atoms that + +comprise life on earth, +the atoms that make up + +the human body, are traceable +to the crucibles that + +cooked light elements into +heavy elements in their core. + +Under extreme temperatures +and pressures, + +these stars, the high +mass ones among them, + +went unstable in +their later years. + +They collapsed, +and then exploded, + +scattering their enriched +guts across the galaxy. + +Guts made of carbon +nitrogen, oxygen, + +and all the fundamental +ingredients of life itself. + +These ingredients become +part of gas clouds + +that condense, collapse, +form the next generation + +of solar systems, stars +with orbiting planets. + +And those planets now have the +ingredients for life itself. + +So that when I look +up at the night sky, + +and I know that yes, we +are part of this universe, + +we are in this universe. + +But perhaps more important +than both of those facts, + +is that the universe is in us. + +When I reflect on +that fact, I look up. + +Many people feel small, +because they're small, + +and the universe is big. + +But I feel big, because my +atoms came from those stars. + +[END PLAYBACK] + +PROFESSOR: So this video +is effective for a couple + +of different reasons. + +You feel like you're +sitting there with him. + +You feel like you're +the person who's + +sitting in the third chair, +watching an interview happen. + +Say what you will about +Neil deGrasse Tyson, + +but he's a very +engaging speaker. + +And I think that this video +encapsulates the wonder + +that he has for astrophysics. + +I'm going to show you +another video that took + +the audio from this interview. + +And this user Max +Schlickenmeyer put together + +a fan video that +highlights certain elements + +of this experience in +a very different way. + +[VIDEO PLAYBACK] + +-What is the most astounding +fact you can share with us + +about the universe? + +-The most astounding fact. + +The most astounding +fact is the knowledge + +that the atoms that comprise +life on earth, the atoms that + +make up the human body, are +traceable to the crucibles that + +cooked light elements into +heavy elements in their core. + +Under extreme temperatures +and pressures, + +these stars, the high +mass ones among them, + +went unstable in +their later years. + +They collapsed, +and then exploded, + +scattering their enriched +guts across the galaxy. + +Guts made of carbon, +nitrogen, oxygen, + +and all the fundamental +ingredients of life itself. + +These ingredients become +part of gas clouds + +that condense, collapse, +form the next generation + +of solar systems, stars +with orbiting planets. + +And those planets now have the +ingredients for life itself. + +So that when I look +up at the night sky, + +and I know that yes, we +are part of this universe, + +we are in this universe. + +But perhaps more important +than both of those + +facts is that the +universe is in us. + +When I reflect on +that fact, I look up. + +Many people feel small, +because they're small + +and the universe is big. + +Because my atoms came +from those stars. + +There's a level of connectivity. + +That's really what +you want in life. + +You want to feel connected, +want to feel relevant. + +You want to feel like +you're a participant + +in the goings-on of activities +and events around you. + +That's precisely what we +are, just by being alive. + +[END PLAYBACK] + +PROFESSOR: So, a very +different experience, right? + +And did you recognize that song? + +AUDIENCE: I don't, +but I thought it + +was particularly +terrible when there + +was a different set of words. + +PROFESSOR: Yes. + +So we won't question +the scientific accuracy + +of the video that he made. + +And my mom watched it. + +And she was like, Elizabeth, +this is super cheesy. + +But it elicits emotion, right? + +It's a very +different experience. + +I also wanted to +point out, how would + +it have felt if all +the images Max used + +were bombarding you with +cut, cut, cut, cut, universe, + +microbes, a tree of life, right? + +Would that have been emotionally +appropriate for this video? + +No. + +So that's what I mean. + +Visual pacing can change +the emotion of a video. + +Music, when intentionally +done, can be very effective. + +And when I look at seven or +eight Science Out Loud videos, + +it usually takes me about a +week to get the music for it. + +It's actually super +time-consuming. + +I'll basically take you through +two or three episodes where + +I looked for music, and +did a soundtrack for it, + +and sort of the +workflow that I had, + +and the reasoning behind +why I chose what I did. + +Any comments so far, questions? + +Everyone's OK? + +So, the farts video. + +George was very adamant +that he didn't want + +this to read like dad humor. + +So I wanted to put a +bunch of fart jokes in it. + +He was like, Elizabeth, +I'm not doing that. + +That's not who I am. + +That's not me. + +And I was like, OK, +I recognize that. + +I recognize that I'm +a different person. + +So he gave his +delivery very straight. + +He gave it very dry. + +He didn't make it +very outrageous. + +This is farts, without music. + +[VIDEO PLAYBACK] + +-You know what's more like +life than a box of chocolates? + +Farts. + +You really never know +what you're going to get. + +Skunk, rotten eggs, garbage +dumpster-- the possibilities + +are, unfortunately, endless. + +But why do we fart, and how +does your body make so many + +different smells? + +The answer is fermentation. + +This is a giant bioreactor. + +It's also called a fermenter. + +And in here, a fungus +known as brewer's yeast + +is transforming water and +dead plants into beer. + +[END PLAYBACK] + +PROFESSOR: So it feels +really weird, right? + +And part of it is that +you don't necessarily + +use the audio that you +record with the B-roll. + +You usually put +music underneath. + +So we didn't want it +to read as dad humor. + +So we use a couple of +more serious tracks + +at the beginning. + +But it was a little bit weird, +because he is inherently + +talking about a subject +that most sixth grade + +boys, and myself, laugh at. + +So the fact that we weren't +acknowledging the humor at all + +whatsoever, and we're being +totally straight and deadpan + +about it, it was a little +funny, unintentionally. + +So we wanted to introduce +the humor through the music + +that we used. + +So I will play +you the rough cut. + +Let me mirror this. + +And this was a personal +decision of mine. + +I'm sure that there are +people out there who would + +have done it very differently. + +And that's OK. + +But let's play this. + +Let's see. + +I will show you a track +that went a little overboard + +with the humor. + +This is a track that +the editor found, called + +Grandpa Is Scheming Again. + +Oh, sorry, it's the wrong one. + +Let me show you the +one before it, Ukulele. + +This is ukulele comedy swing. + +[VIDEO PLAYBACK] + +-You know what's more like +life than a box of chocolates? + +Farts. + +You really never know +what you're going to get. + +Skunk, rotten eggs, +garbage dumpster. + +[END PLAYBACK] + +PROFESSOR: But when I told +[INAUDIBLE], the editor, + +I think we've got to inject +a little bit of humor + +into it with the music. + +I'm sorry. + +There's too much tuba. + +I think the comment +I wrote was, it + +was in all caps, "LOL TOO MUCH." + +But that's an example +of music. [LAUGHS] + +So this is Grandpa +Is Scheming Again. + +[VIDEO PLAYBACK] + +-You know what's more like +life than a box of chocolates? + +Farts. + +PROFESSOR: I felt that +this one had little bit + +of potential, right? + +-Skunk, rotten eggs. + +PROFESSOR: But I thought +it was a little too + +frantic for the beginning. + +-The possibilities are, +unfortunately, endless. + +[END PLAYBACK] + +PROFESSOR: I'll show you +one more, Sharp Mind. + +[VIDEO PLAYBACK] + +-You know what's more like +life than a box of chocolates? + +PROFESSOR: We wanted +to highlight the wonder + +of your digestive system. + +So I said, [INAUDIBLE], find +me something that evokes + +amazing wonder, curiosity. + +-The possibilities are, +unfortunately, endless. + +But why do we fart? + +[END PLAYBACK] + +PROFESSOR: But it reminded +me a little bit too much + +of Willy Wonka and Harry Potter, +which is why we ultimately + +settled on-- + +[VIDEO PLAYBACK] + +-You know what's more like a +life than a box of chocolates? + +Farts. + +You really never know +what you're going to get. + +Skunk, rotten eggs, garbage +dumpster-- the possibilities + +are, unfortunately, endless. + +But why do we fart? + +And how does your body make +so many different smells? + +The answer is fermentation. + +This is a giant bioreactor. + +It's also called a fermenter. + +And in here, a fungus +known as brewers yeast-- + +PROFESSOR: So it's +casual enough. + +A super, super important +part about music + +is that you don't want +it to be too distracting + +from your audio. + +-So you know that thing +where you eat food? + +[END PLAYBACK] + +PROFESSOR: You should +stay away from music + +that is super high +tempo, a lot of noise. + +You want something +that's more uniform. + +So there are a couple of +tracks where it was OK. + +But then, every now +and then, there'd + +be this random cymbal +hit, or a guitar riff + +that would come out of nowhere. + +And it would be +really, really evident + +while the person was talking. + +So that's very distracting. + +Music, like everything +in post, I think, + +should be as hidden as possible. + +And by hidden, I +don't mean that you + +shouldn't be able to hear it. + +But you shouldn't be able +to notice it too much. + +Yes? + +AUDIENCE: Do you cut +the scenes in accordance + +with the beat of the song, or +can it be right in between? + +PROFESSOR: No. + +It can be in between. + +And I was going to +talk about this later. + +But all the examples I'm +going to show you do this. + +Sometimes, if you want to end a +track before your actual video + +ends-- say you're +talking and you want + +some music in the background. + +But then you cut +to a scene where + +it's OK not to have music, or +you want to change the track, + +you can do what's +called ducking. + +Which is when you +take the audio, + +and instead of just cutting +the audio cleanly and just + +making the music +end all of a sudden, + +in the editing software, +you can pull this cursor + +down to where the +music slowly fades. + +And it slowly becomes quiet. + +You can duck in +and out of scenes. + +So, go ahead. + +AUDIENCE: If you have +music and B-roll, + +that's a good way to help +with the pacing of B-roll, + +because otherwise it's +kind of ambiguous. + +Or it can kind of +ambiguous, how long you've + +spent on a single object. + +But music can help you, +if you're having trouble + +finding the pacing of that. + +Because then if you +have a music track, + +you can time with the +beats. [INAUDIBLE]. + +PROFESSOR: I'll show you an +example where we intentionally + +lined up the beats of the music +to the visuals with B-roll, + +actually. + +[VIDEO PLAYBACK] + +PROFESSOR: Like when he +does this thing like this. + +The editor did that +one [INAUDIBLE]. + +[END PLAYBACK] + +PROFESSOR: So that was +more of a stylistic thing. + +We wanted it to read like +bad-ass, like these skydivers + +are going to go. + +Yeah, that was a day +where we were getting + +as much footage as possible, and +didn't end up using half of it. + +Yeah, go big or go home, if +you have a skydiving license. + +Go film, and go skydiving. + +And shoot that. + +This is an interesting example. + +Because the computers one, +when I first saw the script-- + +I thought this is going to be +the hardest one to produce. + +Because computer science +videos inherently + +are just really hard to +do, because of the visuals. + +And that's why there +aren't that many of them. + +But this explanation, for +lack of a better term, + +it just kept reading +incredibly boring. + +Because it's essentially about +how you add in binary, right? + +Which is not the most +riveting material. + +[VIDEO PLAYBACK] + +-Just like a light switch, +these switches have two states. + +Either left and right, off +and on, or zero and one. + +What's really cool here is +that instead of programming + +this computer by writing +code, we program it + +by physically +setting the position + +of several different switches. + +I'll set this computer to +count the number of balls + +on the top tray by setting +the count switch to on. + +The sum is given by this +bank of switches here. + +We'll set the sum to zero +before we start counting. + +PROFESSOR: I think Jamie's +doing a good job of hosting, + +but it just gets +tedious, a little bit. + +Because it's the same +thing over and over again. + +You count the balls, +you set the switches. + +[END PLAYBACK] + +PROFESSOR: So my initial +thought with this + +was, I had a list of +brainstormed tracks. + +And I was like, let's +go with something + +boopy, sort of robotic +and electronic-y. + +And this is what I mean +by be careful of how + +distracting your music could be, +because this is what happened. + +Universal Fluff Theory. + +[VIDEO PLAYBACK] + +-Just like a light switch, +these switches have two states. + +Either left and right, off +and on, or zero and one. + +What's really cool here is +that instead of programming + +this computer by writing code-- + +PROFESSOR: It's just +a little much, right? + +-by physically +setting the position-- + +[END PLAYBACK] + +PROFESSOR: And we fell into +a stereotype a little bit, + +that a video about computers +has to be with electronic music. + +And everything has +to be very robotic. + +And the track that +[INAUDIBLE] ultimately + +found, I really loved, because +it was very Zen, actually. + +Which wasn't the +initial response + +that I had to the video. + +[VIDEO PLAYBACK] + +-has switches with a mechanical +input and mechanical output. + +Just like a light switch, +these switches have two states. + +Either left and right, off +and on, or zero and one. + +What's really cool here is +that instead of programming + +this computer by writing +code, we program it + +by physically +setting the position + +of several different switches. + +I'll now set this +computer to count + +the number of balls +in the top trade + +by setting the +count switch to on. + +The sum is given by this +bank of switches here. + +We'll set the sum to zero +before we start counting. + +Now let's start counting +by pressing this lever. + +[END PLAYBACK] + +PROFESSOR: So I actually +personally like that track, + +because there's +something about it that + +makes the scene very inviting. + +He seems really friendly. + +You have something that's +as scary as programming + +a computer, but then the +person is super friendly. + +Jamie's just a really +friendly person in real life. + +We were trying to make +computer programming as not + +scary as possible. + +And I think that having a track +that was a little more Zen, + +it was a little quieter. + +Someone was saying that +it's like a very mesmerizing + +experience to watch it. + +Yeah? + +AUDIENCE: [INAUDIBLE] how do you +know if the volume of the song + +is too much? + +Or the beats themselves +are too much? + +PROFESSOR: Again, a lot +of this is personal taste, + +which is not the answer that +you guys probably want to hear. + +But I would choose +what you like. + +And hopefully I'm giving you +some pointers as to maybe + +what works, and what +doesn't, as well. + +But that's also where the +other three people that you'll + +have looking at +your rough cuts will + +come in handy, quite a bit. + +You'll have the opinions of +at least five or six people. + +Which, ideally you'd have more. + +But that would give +you some sense. + +And this sounds dumb, +but if you can't clearly + +make out what the +person is saying + +because the music is too +loud or too distracting, + +then don't use it. + +But sometimes you +don't know, and that's + +why you ask other people. + +The last example I +wanted to show you-- + +did anyone have +questions besides that? + +Everyone's good? + +So the last example I wanted +to show you was of Anastasia. + +Now, I was very conscious +of who she was as a person + +when we were making this +video, because she was just + +this very bubbly, blonde girl. + +But she does intense, +legit systems biology. + +And I didn't want to undermine +her intelligence or her persona + +as this very +inspiring STEM figure + +by playing into the ditzy trope. + +So at first, I was putting +really hard rock music + +into her video to fight this. + +She's doing intense +science, give that vibe. + +It did not work for +obvious reasons, now. + +[VIDEO PLAYBACK] + +[END PLAYBACK] + +PROFESSOR: And what I realized +was that Anastasia as a person + +is super bubbly. + +And she loves science. + +And that doesn't +undermine her abilities + +as a scientist, or +her authority at all. + +And that if we +fought that too much, + +it read really weird, because +that's just not who she is. + +So we did go with a track that +was more capturing the wonder + +that she had for plants. + +[VIDEO PLAYBACK] + +-Paclitaxel is a compound +that can treat cancer. + +Salicylic acid reduces +headaches and fevers. + +Carotenoids can turn +your skin orange. + +And miraculin changes +your sense of taste. + +What do all of these awesome +compounds have in common? + +They all come from plants. + +[END PLAYBACK] + +PROFESSOR: So music is really +good for evoking emotion, + +establishing things +like wonder, creepiness. + +This is an example of one. + +And it can also help if you just +have some really funky audio + +going on from the environment +that you're filming in. + +I hate to say this, +but sometimes it + +can be a little bit of +a Band-Aid to cover up + +weird background noise. + +When we were shooting in the +brewery for George's video + +with all the vats, it was +just super noisy in there. + +And there's nothing that +we could do about it. + +So he just talked really +loud, and we put in the track. + +And I think it helps distract +from that a little bit. + +But again, don't say +we'll fix it in post. + +Last example, I lied +about the other one. + +[VIDEO PLAYBACK] + +-These patterns can +seem pretty complicated. + +Some people even think octopuses +use patterns like these + +to mesmerize their prey. + +But these intricate displays +emerge on the squid skin + +even after it's been +disconnected from the brain. + +So what's going on? + +First I wanted to measure +how the chromatophores-- + +[END PLAYBACK] + +PROFESSOR: So when +the music changes, + +we ducked from the +previous track. + +This is what I +was talking about. + +Hopefully it's not super +jarring or obvious to you + +that we were changing music +tracks in the background, + +because we ducked one +out and ducked one in. + +But the second track, where +the question mark comes, + +I liked it because +it was sort of eerie. + +And it emphasizes, +this is super weird + +that the squid skin does that. + +How exactly does it do it? + +And it's a way that we implied +that without her explicitly + +saying it in the script. + +So, when a lot of you +guys end your scripts, + +or have a line in there +that's like, this is awesome. + +Or, and that's how you do that. + +You don't have to +say that explicitly. + +Because a lot of the time, +the music can do that for you. + +All right. + +So I talked a lot about what +kind of music you should use, + +and you are probably +wondering, well, + +where am I going +to get this music? + +So I wanted to talk a little bit +about Creative Commons, which + +is the license that +MIT usually uses. + +It's what OpenCourseWare uses. + +It's what Science Out Loud uses. + +And basically, it's a type +of license or copyright. + +And in particular, we use CC +BY-NC-SA, which I will explain, + +which allows you to freely +share and adapt materials. + +So because this class, +and this lecture, + +is being recorded +under Creative Commons, + +under this license if someone +watches this video later on, + +and they want to take a +portion of this lecture, + +and remix it into a video +about best practices of music, + +they can do it. + +And I won't sue them. + +Because it's totally allowed. + +And I want them to take +the material and remix it, + +as long as they attribute. + +And this is true of any music +that you use for your videos. + +So if you go and search +for Creative Commons music, + +you will find a +ton of resources. + +I've listed the websites +that we have personally + +used in the day 7 +lecture on the syllabus. + +Things like ccMixter, +Jamendo-- thanks to Billy, + +we know about that one +now-- Free Music Archive. + +Unfortunately music is +not organized online + +in the best way possible. + +So a lot of it is sitting +and wading through tracks, + +and just listening +to a bunch of them. + +And that's why it's +so time consuming. + +But a quick note about +Creative Commons. + +So your videos will be +released under this license, + +meaning that the +music that you use, + +and any stock footage or +video that you find online, + +has to also be Creative Commons. + +And if you have +trouble with this, + +let me know, +because I have dealt + +with issues like that a lot. + +But basically, when you +upload your final projects + +onto YouTube, it's totally fine +for you to use other music, + +as long as, in the description, +you say we used this track. + +Here's a link to +the original site. + +This is the person who made it. + +That's just best +practices in general. + +Ideally, you would cite images +that you use in your video + +itself. + +You'll notice that Science +Out Loud doesn't annotate + +with citations on the +actual videos themselves, + +because that was a +stylistic decision of ours. + +But we put all the citations +in our YouTube descriptions. + +And everywhere the +video is online for us, + +we put all of the citations. + +So for our license, +it means that + +is free to share and adapt, as +long as you attribute, and it's + +not used for +commercial purposes, + +and that you're releasing your +work under the same terms. + +So if someone took this lecture +and then used a portion of it + +to record a lecture +for The Great Courses, + +for instance, which +you have to pay to use, + +because it's a commercial +company, that's not allowed. + +On the syllabus, you'll also +find links to stock music. + +Good music costs usually +around $30 to $40 per track. + +So sometimes, we use +things like PremiumBeat, + +which was where all the +tracks for the examples + +I showed you were found. + +And so sometimes, +if you just can't + +find something that's +free, it's really worth, + +I think, the money to +do music the right way. + +And then one more +note about video. + +So maybe you have the +Hudson River, for example. + +We obviously couldn't +film at the Hudson River. + +So I found a picture of it +on the Internet Archive, + +which is where you can find +a lot of videos, music. + +They're all under +Creative Commons. + +I'll put links to all +this in the syllabus, + +and I'll post something +on Tumblr later today + +that consolidates +all these resources. + +For biology videos, the +NIH has a lot, actually, + +under Creative Commons. + +A lot of open +source publications, + +you can use their figures, +as long as you cite. + +And Wikipedia, all +of those images + +are released under +Creative Commons. + +The US government websites +are actually really, + +really great resources, +because they release everything + +under public domain. + +So it's not even +Creative Commons. + +You can just use +whatever you want. + +NASA has awesome footage. + +NIH, I'm trying to +think of others. + +But that's actually +a go-to place for me + +if I'm searching for footage +that we just can't shoot. + +So that's all I had +planned for today. + +Does anyone have +questions off the bat? + +Yes. + +AUDIENCE: I have a question +about working with the music + +that you had. + +I've been doing +stock music before. + +Some of them are like a +one [INAUDIBLE] thing, + +and some are +repetitive [INAUDIBLE]. + +PROFESSOR: Yeah, it loops +the same tune over and over. + +AUDIENCE: Do you use those? + +PROFESSOR: Yeah. + +The looped ones are nice for +us, because sometimes the longer + +ones are like big orchestral +arrangements that take awhile + +to get to the point of the song. + +Whereas, for a lot of +the music, you just + +want something +that's present, that + +establishes a general +sound and atmosphere. + +But you're not looking for +a Mozart composition, right? + +You just want something to fill +in the background a little bit. + +So having something +that's looped + +is actually preferred for us. + +AUDIENCE: Have you done a video +where there was [INAUDIBLE]. + +PROFESSOR: Yeah, some +of our earlier videos + +don't have as much music. + +And part of it was that I +wasn't savvy enough to do it. + +And I watch some of them now. + +I'm like, man, this video +just feels super long. + +And it seems like they're +talking for a long time. + +And I think part of it's +because of the music. + +You don't need music +everywhere, though. + +And like I said, during the +presentation, first do no harm. + +So sometimes, if you just +can't find music for it, + +leave it out. + +I'm trying to +think of an example + +where we said we specifically +do not want music here. + +And I can't come up with +any off the top of my head. + +But maybe after class, I +can look for something. + +AUDIENCE: Elizabeth, can +you talk a little bit + +about how the next couple +days are going to work? + +PROFESSOR: Absolutely. + +Thank you for the reminder. + +So this is it for formal +lectures between now + +and next Thursday, which is when +the final presentations will + +be. + +You will have +class time to work. + +So we are going to pair you +up, or put you into groups + +for filming partners. + +And you will have class +time tomorrow, the day + +after, and Friday to work. + +We will have a screening of +the rough cuts next Tuesday. + +So that gives you the weekend +to edit together the footage + +that you shoot this week. + +We'll screen +everyone's rough cuts. + +We'll also assign +you editing partners. + +And I'll tell you more about +this on Tuesday as well. + +But you'll watch the videos. + +And we have a video annotation +software that you can use. + +So you'll make comments +on at least two + +or three other people's +videos during class time. + +And then you'll have +until Thursday, where we + +don't have normal class time. + +Our final screening is going +to be in Simmons Hall at 6:30 + +instead of at 1:00 PM. + +It'll be like a +red carpet event. + +But you'll have all day that +day to finish whatever you need. + +I wouldn't wait until 6:00 PM +to have your video finished. + +But if it comes down to that, +it's not like we have to know. + +Yeah, so it's pretty +much work time from here. + +The teaching staff will +be available to help you. + +So it's basically like +office hours from here + +on out, except for the rough +cut screening next Tuesday. + +And if you have specific +questions on editing, + +we'll send out a +Google spreadsheet + +so you can sign up +for specific people, + +or if you have certain +requests to go over things. + +AUDIENCE: Or, if it's in the +evening and you're editing, + +and you find a problem that you +just don't know how to solve, + +feel free to email us. + +Shoot out an email before +you start tackling it + +for two to four hours. + +Because if it's +a simple solution + +that we can relate over email, +that'll save you so much + +time and frustration. + +PROFESSOR: And I'll send +out an email to where + +everyone's emails are CC'd. + +You can ask your peers +questions as well, + +because I'm sure you're going to +run into very similar problems + +once you start +editing and shooting. + +So use each other as +a resource as well. + +And honestly, I can't feign +expertise over any of this. + +So oftentimes, I just Google. + +Why won't my clip snap +to the previous one? + +But, I will send out +shooting assignments. + +Actually, I have them with me. + +AUDIENCE: Elizabeth, +we'll be in here + +during class time +as a home base. + +So if you have any +questions, and you need help, + +we'll be physically in this +room for you to swing by. + +You don't have to come +into this room physically. + +You can use the entire class +time to be out and about. + +But just so that you +know that you can, + +at any point, during that +1:00 to 4:00 time frame. + +If you need help with anything, +I will as much as I physically + +can be-- + +PROFESSOR: Yeah, I will +definitely be here. + +AUDIENCE: They will +definitely be in this room, + +to be here if you want +physical help with anything. + +And if you want to, +just to make sure, + +you can feel free to email a +specific point person to say, + +I am coming in at +this time for sure. + +If you know ahead of time that +you need help with something, + +just so that we know +we should reserve time + +to deal with this +issue with you. + +PROFESSOR: Yeah. + +And if you need Chris's help +or Natalie's help on anything, + +just email them directly. + +Because they are available, +although they're a little bit + +busy. + +So as long as they have +enough of a heads up, + +we can make that work. + +I did want to let you +guys know about 26 139. + +Do guys know where the +801 TEAL classrooms are? + +Oh, I guess you guys would know. + +It is basically in that +building on the first floor, + +actually, right next to us. + +It says Building 26. + +It's on the first floor. + +You need key card access. + +You just swipe your MIT ID. + +And I have that room reserved +every day during class time + +until the final day. + +So if you want to use +their software, you can. + +I also have nicer headphones if +anyone needs to borrow those. + +I think everyone has a kit. + +I feel like I'm +forgetting something. + +Oh, I'm forgetting to tell +you the shooting assignments. + +So David and Joshua, we'll +put you guys together. + +[? Yulia, ?] Kenneth, and +Paul, you guys will be a group. + +And then Andrea and Nathan, you +guys will be shooting partners. + +AUDIENCE: That wasn't random. + +We really tried +to think about who + +you are, and your +scripts, and all of that. + +Because sometimes, if +you have a great partner + +that can really +complement you, that + +can really help your project. + +We really did put a +fair amount of thought + +into those partnerships. + +It's not just like a +random division of labor. + +PROFESSOR: If you have +any issues during filming + +whatsoever, about anything, if +you can't get into a location, + +if you need help +clearing something, + +if you're not sure something +is allowed to be filmed, + +if things are just +not going well, + +if Murphy's Law is +happening, email me. + +Or come find me during class. + +Or email any of us. + +We are definitely here to help +you guys for the home stretch. + +AUDIENCE: And I think +I've showed this to you, + +but when you're walking +to the bathroom, + +there's a big sign that +says communication lab. + +That's my office. + +So if ever during +normal business hours, + +outside from class +time, you literally + +need help with anything, +that is where I am. + +So you can always knock and +interrupt anything, and just + +say, I need help with +something, and it'll be fine. + +PROFESSOR: And my office is a +little far away from campus. + +But if you want to +meet in the morning, + +or sometime outside of class, +if you just email me ahead + +of time, I can definitely +meet with you guys. + +AUDIENCE: And one last thing is +the "kill your darlings" thing. + +As someone who has been +writing for quite a long time, + +and who has edited +people professionally, + +it's really hard. + +The more you get +invested in this, + +the harder it is to +be able to do that. + +And that's when as +a partner, that's + +a great point, when you're +not emotionally connected + +to the work. + +This is just advice. + +Instead of pointing out +that it's not working, + +maybe think about framing some +questions for your partner, + +to help them realize +that this isn't working. + +And that's a really great job +you have as a partner, to help + +your colleague realize +that this piece is awesome, + +it's really cool, +but it doesn't work. + +And that can be really, +really hard feedback. + +So thinking about how +to help your partner + +see that sometimes is a +really important task. + +PROFESSOR: And +part of your grade + +will come from how great +of a partner you are. + +So ha ha, you have to do it. + +I don't remember the +exact percentages, + +but 60% of the grade comes +from your writing and hosting. + +40% of it comes +from the producing + +that you do for your partner. + +And for the group of three, +figure it out how you want. + +But I was thinking +one person does + +for person 2 which +does for person 3 which + +does for person 1. + +Does anyone have +questions, concerns? + +AUDIENCE: You say the +assignment's on the quality. + +So what is that [INAUDIBLE]. + +AUDIENCE: She means just +that these are your partners + +to do the project. + +The people that +she just mentioned + +are your partners for +producing your project. + +It's a phrase that I'm +sure you use [INAUDIBLE]. + +PROFESSOR: Yeah, sorry. + +And also, don't feel limited to +only working during class time, + +if you and your partner would +rather meet in the morning. + +Or if you want to +just shoot some stuff + +on your own, like B-roll, +that's totally fine. + +I will put this link +up on the Tumblr. + +And I'll email it out +to you guys today, too. + +I would love it if sometime, +before the end of the weekend, + +you filled out this super, +super short midpoint survey, + +just to give us a +good idea of what + +is working best for you all. + +What type of feedback +is working best? + +Because I want to make sure +that for the last week, + +it's going to be a +lot of project time. + +So I just want to make +sure that the time is + +as valuable to you as possible. + +So it's really quick. + +It's super painless. + +It's just telling me what your +favorite day was, basically. + +So I'll send out a +link to you guys. + +Just any time between now and +the weekend would be awesome. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: No, for +most of the videos, we + +have at least two or three. + +I think we have around +three in all of them. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: I don't have +an algorithm for you, + +unfortunately. + +A lot of it is just +what feels right to me. + +AUDIENCE: And you can +ask for second opinions. + +PROFESSOR: Of course. + +AUDIENCE: This is a great +time to ask your group, + +or other people in the class. + +Or come in and ask us, too. + +If it's like, I +found this music, + +I'm not sure how +I feel about it. + +How do you guys feel about it? + +PROFESSOR: Yeah. + +And if you're in the +editing room on Friday + +during class time, and +you want us to look at it, + +just send me an email +and be like, hey, + +can you meet me in 26 at 2 +o'clock to help me with this? + +And I will do it. + +So, at the beginning it's funny. + +[VIDEO PLAYBACK] + +-A skunk, rotten eggs, garbage +dumpster-- the possibilities + +are, unfortunately, endless. + +PROFESSOR: And he's talking +about how funny it is. + +-Break food down to get energy. + +But your main byproducts are +carbon dioxide and water, + +and yeast's main byproducts +are carbon dioxide and alcohol. + +That's how this stuff +gets to be beer. + +And here's where +things get weird. + +[END PLAYBACK] + +PROFESSOR: So that's a +new break in thought. + +It was a logical +transition point for us, + +because he opens with farts +are like a box of chocolates. + +But this is the part +where you're starting + +to really get into the science. + +And he wants to highlight +the misconception of, + +the thing that you thought +was funny is actually really + +weird and super interesting. + +So we introduced this track that +I felt conveyed that sense of, + +this is weird. + +There's something +interesting about this. + +But yeah, unfortunately, +I don't have a recipe. + +I think once you start +doing it on your own, + +you're going to +get a sense of it. + +And once you start seeing +other people's projects, + +you'll get a sense of it. + +AUDIENCE: There's +always the mom test. + +My mom, I feel like she's +so like that-- oh, I + +don't understand, what +are you doing with this? + +I can't hear. + +I feel like my mom is like, +if I can show it to her, + +and she'll be like, oh, +I can hear everything, + +and your music's +not distracting me. + +Or, can you make it louder, +honey, I can't hear that part. + +If you have someone in your +life who plays that role, + +that's a great person +to check in with. + +PROFESSOR: I'm happy to be +that person for you guys. + +AUDIENCE: Can you talk +louder on this part? + +PROFESSOR: But that's why audio +is so important to get right + +when you're producing. + +Because if you record too +soft, there's only so much + +you can do in the editing. + +And if you record +too loud, you're + +going to peak the microphone. + +And it's going to +sound really scratchy. + +So when you're filming someone, +watch a take or two, just + +to make sure that the audio's +sounding clean and OK. + +AUDIENCE: Do you +have the GoPros here, + +or is that somewhere else? + +PROFESSOR: Oh, I have +them in my office. + +I can actually go +there after class + +right now, if you're +planning on using them + +before tomorrow's class. + +AUDIENCE: Probably Thursday. + +PROFESSOR: Thursday? + +OK, then I'll just bring them +with me to class tomorrow, + +and I'll leave them +in Jamie's office. + +They've never been +opened before. + +AUDIENCE: What's that? + +PROFESSOR: They've never +been opened before. + +They're brand new, +just for you guys. + +AUDIENCE: And if you need +access to something that's + +In my office, and there's a +code, and if you email me, + +and I'm not there, don't +steal anything, obviously. + +But if you need access +and I'm not around, + +I can give you the code +to get into that room. + +PROFESSOR: You guys +can come to my office, + +but it's all the way +out in Tech Square. + +So I would imagine most +people wouldn't want to. + +AUDIENCE: And if you see lots of +strange students in my office, + +that's just probably my fellows. + +So, say hey. + +PROFESSOR: Does anyone +have certain props + +that they want to use? + +Does anyone need a hand cart? + +Yes. + +AUDIENCE: I'll +need simple things, + +like a wire that I can bend. + +So maybe a couple, if it +doesn't work out the first time. + +PROFESSOR: So for +those props, I'm + +going to have you guys get them. + +For bigger things, +like a hand cart, + +or if you need another tripod, +or if you need a light kit, + +or something. + +AUDIENCE: I think that +may be [INAUDIBLE]. + +PROFESSOR: Yeah. + +If it's simple, +like under $20, I'm + +going to have you guys go ahead +and coordinate that, though. + +AUDIENCE: Just a quick question. + +What font is that? + +PROFESSOR: What font is it? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Actually, that font +was very, very intentional. + +For a while, I tried +to make my own font. + +But then I was +like, that's silly, + +just use an existing one. + +I can't remember +what the name of it + +is off the top of my head. + +But we use it to brand +Science Out Loud. + +But I can send it to +you once I find out. + +I think it's a Google +Font, actually. + +AUDIENCE: The O's are different, +and the H's are different. + +PROFESSOR: Oh, no, +that's just stuff I drew. + +But I think he's talking +about for the text font. + +I think it's actually Amatic SC. + +It's a Google font. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: I will +put it on the Tumblr. + +I've got to remember +to do that, though. + +AUDIENCE: So how +exactly do you do + +that, like draw something on the +computer or would [INAUDIBLE]. + +PROFESSOR: I don't have any +of the examples with me, + +but I just draw on a piece +of paper with Sharpie. + +And that's how I do all +these presentations, too. + +So for day 9, I did +this at the airport. + +This is basically all it is. + +And then I take a +picture with my iPhone. + +And then I blow out the +exposure in Keynote. + +It's nothing fancy. + +And Sari knows how to animate +the things in After Effects. + +But basically you +take a still image, + +and you draw a path +for the computer + +to wiggle it around for you. + +AUDIENCE: Before I knew how +to animate in After Effects, + +you can just use Illustrator, +which is a really good vector + +art program. + +Do you have a tablet? + +PROFESSOR: I have +10 Wacom tablets, + +in case anyone +wants to use them. + +AUDIENCE: The best way to +translate your handwriting + +to digitally, so if you +want your handwriting + +to just be digital, +then you open up + +a file in Illustrator that's +the same size of your screen, + +or your video, so, 1928 by 800. + +Or something like that. + +And you just draw +in it, and you can + +change the width of your lines. + +You can redo the +shapes that you do, + +because it's just a +readable document. + +And then you can export +that as an image file. + +It'll be the exact same +size as your video clips, + +when you've edited it. + +And you can make backgrounds +transparent then too. + +So you can just have +your vector art. + +PROFESSOR: You don't have +to make it black and white. + +I just tend to do it +because it's easier for me. + +But if you're trying to +draw the PDL or something, + +she's much better at that. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: You what? + +AUDIENCE: I thought +that was your font. + +PROFESSOR: Oh really? + +No, I made it at the airport. + +AUDIENCE: So how can you +avoid giving [INAUDIBLE]? + +PROFESSOR: Well, I will +show you exactly what + +I did for this slide. + +So I said, I'm going +to insert this image. + +And this is Keynote. + +I think you can +do in PowerPoint. + +You can definitely +do it in Photoshop. + +This is me just being +newb extraordinaire. + +I went to Image, and +first I flipped it. + +And I basically +adjusted the levels, + +so I blew out the +background first. + +And then I inverted it. + +I'm basically taking all +the whites to the extreme. + +Of course it's not working now. + +I promise it does work. + +OK, let's try this again. + +Sometimes it's finicky. + +Does anyone have other +questions while I + +try to get this to work? + +I'm going to try a +different picture. + +AUDIENCE: It makes us all +feel better that it's not + +[INAUDIBLE]. + +For me, it makes me feel better. + +PROFESSOR: No, it is. + +I'll go with this one. + +And I'm sure there is a +very streamlined way that + +kills fewer trees. + +Oh my goodness, I don't +know why it's not working. + +So if you're doing a black +image on a white background, + +this is all you would do. + +This is not clearing +the background, + +so the background is +going to be black. + +So you would have to do +what Sari's talking about + +as far as basically +creating a vector art that + +has a transparent background. + +AUDIENCE: And it's really easy. + +The hardest part is +getting used to the tablet, + +because it's weird writing, and +seeing your writing up here, + +somewhere else than +what's on the page. + +PROFESSOR: Ha, I got it. + +That is all I did. + +And I cropped it. + +AUDIENCE: I've done stuff +like this in PowerPoint. + +You could do it just as +easily in PowerPoint, yeah. + +They give you cool stuff +to make it look like teeth, + +or there's all these cool-- +and then just black and white. + +They're really easy. + +But that looks really cool. + +PROFESSOR: But for animations, +labels, overlay in general, + +I think simple is +better because clarity + +is most important for +graphics, and anything + +that's not the video. + +The video itself also +needs to be clear too. + +Clarity is very important. + +AUDIENCE: Can we use the +Wacoms in your office + +on our own computers, or do we +have to use that in the lab? + +PROFESSOR: No, +they're are my office. + +It's a USB hookup. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: And +they're kind of old. + +Yeah, they're not +the newest kind. + +I think they're five +or six years old. + +But I have a bunch of them. + +I didn't bring them with +me because I wasn't sure + +if people would be +interested in them. + +But yes, please take them, +because they're just sitting + +in a cabinet in my office. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Yeah. + +If you guys want +them tonight, I'm + +happy to go over +and get them now. + +But I can also just bring +them to class tomorrow. + +AUDIENCE: Can you +overlay the video + +with animations in iMovie +so I can [INAUDIBLE]? + +PROFESSOR: Yeah, +iMovie is great, + +because there's a very +low learning curve. + +And so, if you're doing +simpler things like cutting out + +the bad bits, people might say +iMovie is a newb thing to use. + +But I use it for +really simple videos + +that I don't need to do +a whole lot of work with. + +Unfortunately, for +the animations, + +I don't think it's +possible, and that you + +would need to use something +like After Effects. + +Or you would need to use +Final Cut to incorporate it. + +AUDIENCE: So the +problem with iMovie + +is because it's +so simple, it only + +has one video track +and one audio track. + +And in order to +overlay an animation, + +you need at least two +video tracks, which + +comes in Final Cut or Premier. + +PROFESSOR: Something that +you can do with iMovie, + +I'm not sure if some of +you guys would do this-- + +but say you are standing in the +side of the frame like this. + +And you want another movie +to play on the inside. + +You can do that in iMovie. + +You can do an inset. + +And that's something that's +pretty straightforward to do. + +AUDIENCE: And you can have +words show up over you. + +It's very easy to do in iMovie. + +If it's not an +animation, but just + +a word that you +want next to you, + +that's really easy to do, +and have text show up. + +AUDIENCE: Or an image. + +That would be [INAUDIBLE]. + +AUDIENCE: Yeah. + +PROFESSOR: I'll show +you the video later + +because I can't +find it right now. + +You can do insets, really +basic things on iMovie. + +But animations, you can't. + +What you could do, is you could +work with Sari in After Effects + +to get the video clip where +you want the animation, + +and export it as its own file. + +And then import it into iMovie. + +So you're basically using +a polished animation. + +That way, if you +want to keep working + +in iMovie for the rest of +your project, you can do that. + +AUDIENCE: And we need to +go to the [INAUDIBLE] lab + +to use the After Effects? + +PROFESSOR: Yeah, +because they only + +are in installed +computers on campus. + +And it's literally +in that building. + +AUDIENCE: And if you end +up wanting to work at home, + +it takes usually an hour, but +you can install all the Adobe + +software for free for a month. + +And they don't +automatically charge you, + +because you don't put in credit +card information, or anything. + +You just sign up with +an email address. + +And then you can download +them for a month trial. + +Did teams want to spend the +last little bit on a little game + +plan time? + +PROFESSOR: Don't forget, +a daily blog for today. + +I think I put this in the email. + +The syllabus is updated +with all the assignments. + +Basically, from +now until the end, + +it's just the video +itself that's due. + +And daily blogs are just for +today and the rough screening + +day. + +But if you take behind +the scenes pictures, which + +I love to do, behind +the scenes stuff, + +feel free to upload +that to the Tumblr. + +AUDIENCE: So there's no shot +list, or anything like that? + +PROFESSOR: Yeah. + +The scripts, I think everyone +has sent me, for the most + +part, updated scripts. + +The shot list and all that, +it's really for your benefit. + +I want you to feel as +ready as possible to shoot. + +Actually, I would like you +to upload the shot list. + +But I won't set a +due date for it. + +I'll change the +syllabus with that. + +But do upload your shot list. + +I would like to see it up +there by Thursday, at least. + +Because if you're not thinking +about shooting by then-- + +does that sound OK to everyone? + +Break, go team. + +Yay, people. + +It'll be awesome. + +I can't wait to see your videos. \ No newline at end of file diff --git a/DtTchZtor3g.txt b/DtTchZtor3g.txt new file mode 100644 index 0000000000000000000000000000000000000000..926995dae169f8f8f7ca9e9e2eb16e0d9057b13b --- /dev/null +++ b/DtTchZtor3g.txt @@ -0,0 +1,491 @@ +align:start position:0% + +i want to show you a little video of why + + align:start position:0% +i want to show you a little video of why + + + align:start position:0% +i want to show you a little video of why +this matters + + align:start position:0% +this matters + + + align:start position:0% +this matters +so weak forces now weak forces are + + align:start position:0% +so weak forces now weak forces are + + + align:start position:0% +so weak forces now weak forces are +really strong we know this + + align:start position:0% +really strong we know this + + + align:start position:0% +really strong we know this +because of mission impossible we know + + align:start position:0% +because of mission impossible we know + + + align:start position:0% +because of mission impossible we know +this + + align:start position:0% +this + + + align:start position:0% +this +also because of our own students there's + + align:start position:0% +also because of our own students there's + + + align:start position:0% +also because of our own students there's +there was one of my former students rory + + align:start position:0% +there was one of my former students rory + + + align:start position:0% +there was one of my former students rory +and uh he won all sorts of prizes + + align:start position:0% +and uh he won all sorts of prizes + + + align:start position:0% +and uh he won all sorts of prizes +because he was trying to be like a gecko + + align:start position:0% +because he was trying to be like a gecko + + + align:start position:0% +because he was trying to be like a gecko +and so he made gloves that were like + + align:start position:0% +and so he made gloves that were like + + + align:start position:0% +and so he made gloves that were like +gecko gloves and much to the delight + + align:start position:0% +gecko gloves and much to the delight + + + align:start position:0% +gecko gloves and much to the delight +of the uh facilities people at mit he + + align:start position:0% +of the uh facilities people at mit he + + + align:start position:0% +of the uh facilities people at mit he +actually climbed + + align:start position:0% +actually climbed + + + align:start position:0% +actually climbed +one of the buildings using these his + + align:start position:0% +one of the buildings using these his + + + align:start position:0% +one of the buildings using these his +gloves + + align:start position:0% +gloves + + + align:start position:0% +gloves +but in case you are wondering it wasn't + + align:start position:0% +but in case you are wondering it wasn't + + + align:start position:0% +but in case you are wondering it wasn't +actually their delight + + align:start position:0% +actually their delight + + + align:start position:0% +actually their delight +um but uh but it really cool stuff so + + align:start position:0% +um but uh but it really cool stuff so + + + align:start position:0% +um but uh but it really cool stuff so +let me show you just this is like a 30 + + align:start position:0% +let me show you just this is like a 30 + + + align:start position:0% +let me show you just this is like a 30 +second video + + align:start position:0% +second video + + + align:start position:0% +second video +he found the answer in the sheer number + + align:start position:0% +he found the answer in the sheer number + + + align:start position:0% +he found the answer in the sheer number +and design + + align:start position:0% +and design + + + align:start position:0% +and design +of the hairs on the gecko's feet + + align:start position:0% +of the hairs on the gecko's feet + + + align:start position:0% +of the hairs on the gecko's feet +geckos have millions of microscopic + + align:start position:0% +geckos have millions of microscopic + + + align:start position:0% +geckos have millions of microscopic +hairs on their toes of course we can't + + align:start position:0% +hairs on their toes of course we can't + + + align:start position:0% +hairs on their toes of course we can't +see this with our naked eye because each + + align:start position:0% +see this with our naked eye because each + + + align:start position:0% +see this with our naked eye because each +hair is only one-tenth the size of a + + align:start position:0% +hair is only one-tenth the size of a + + + align:start position:0% +hair is only one-tenth the size of a +human hair + + align:start position:0% +human hair + + + align:start position:0% +human hair +and each of those hairs branch down to + + align:start position:0% +and each of those hairs branch down to + + + align:start position:0% +and each of those hairs branch down to +billions of little split ends + + align:start position:0% +billions of little split ends + + + align:start position:0% +billions of little split ends +and they can make such close contact + + align:start position:0% +and they can make such close contact + + + align:start position:0% +and they can make such close contact +with the surface that + + align:start position:0% +with the surface that + + + align:start position:0% +with the surface that +weak intermolecular forces can begin to + + align:start position:0% +weak intermolecular forces can begin to + + + align:start position:0% +weak intermolecular forces can begin to +add up to something really strong + + align:start position:0% + + + + align:start position:0% + +turns out geckos exploit something + + align:start position:0% +turns out geckos exploit something + + + align:start position:0% +turns out geckos exploit something +called the van der waals + + align:start position:0% +called the van der waals + + + align:start position:0% +called the van der waals +force no london london if you think of + + align:start position:0% +force no london london if you think of + + + align:start position:0% +force no london london if you think of +an + + align:start position:0% +an + + + align:start position:0% +an +atom as a dancing couple when you bring + + align:start position:0% +atom as a dancing couple when you bring + + + align:start position:0% +atom as a dancing couple when you bring +two atoms into very close contact + + align:start position:0% +two atoms into very close contact + + + align:start position:0% +two atoms into very close contact +part of one atom can get attracted to + + align:start position:0% +part of one atom can get attracted to + + + align:start position:0% +part of one atom can get attracted to +part of the other + + align:start position:0% +part of the other + + + align:start position:0% +part of the other +that very weak bond is the van der waals + + align:start position:0% +that very weak bond is the van der waals + + + align:start position:0% +that very weak bond is the van der waals +force + + align:start position:0% +force + + + align:start position:0% +force +and it sticks atoms together proximity + + align:start position:0% +and it sticks atoms together proximity + + + align:start position:0% +and it sticks atoms together proximity +is the key + + align:start position:0% +is the key + + + align:start position:0% +is the key +but bringing two materials that near + + align:start position:0% +but bringing two materials that near + + + align:start position:0% +but bringing two materials that near +each other is harder than you'd think + + align:start position:0% +each other is harder than you'd think + + + align:start position:0% +each other is harder than you'd think +all right now obviously + + align:start position:0% +all right now obviously + + + align:start position:0% +all right now obviously +that got me very excited when i saw that + + align:start position:0% +that got me very excited when i saw that + + + align:start position:0% +that got me very excited when i saw that +because that is how i see atoms and that + + align:start position:0% +because that is how i see atoms and that + + + align:start position:0% +because that is how i see atoms and that +is how i see electrons and i saw this + + align:start position:0% +is how i see electrons and i saw this + + + align:start position:0% +is how i see electrons and i saw this +that i almost fell over + + align:start position:0% +that i almost fell over + + + align:start position:0% +that i almost fell over +and uh and of course i played it and i + + align:start position:0% +and uh and of course i played it and i + + + align:start position:0% +and uh and of course i played it and i +know all those moves i would suggest you + + align:start position:0% +know all those moves i would suggest you + + + align:start position:0% +know all those moves i would suggest you +guys + + align:start position:0% +guys + + + align:start position:0% +guys +it's a friday there's some good moves in + + align:start position:0% +it's a friday there's some good moves in + + + align:start position:0% +it's a friday there's some good moves in +there + + align:start position:0% +there + + + align:start position:0% +there +there's some good moves in there and you + + align:start position:0% +there's some good moves in there and you + + + align:start position:0% +there's some good moves in there and you +can take this on your phone and just + + align:start position:0% +can take this on your phone and just + + + align:start position:0% +can take this on your phone and just +kind of work it out at the club \ No newline at end of file diff --git a/EX0uHJbIw68.txt b/EX0uHJbIw68.txt new file mode 100644 index 0000000000000000000000000000000000000000..f05d6ce79fb03b118b31c92abf86398153b057a8 --- /dev/null +++ b/EX0uHJbIw68.txt @@ -0,0 +1,187 @@ +align:start position:0% + +this week we will continue our + + align:start position:0% +this week we will continue our + + + align:start position:0% +this week we will continue our +discussion of energy we will introduce + + align:start position:0% +discussion of energy we will introduce + + + align:start position:0% +discussion of energy we will introduce +the concept of potential energy which is + + align:start position:0% +the concept of potential energy which is + + + align:start position:0% +the concept of potential energy which is +related to the work done by a + + align:start position:0% +related to the work done by a + + + align:start position:0% +related to the work done by a +conservative force and also the concept + + align:start position:0% +conservative force and also the concept + + + align:start position:0% +conservative force and also the concept +of total mechanical energy which is + + align:start position:0% +of total mechanical energy which is + + + align:start position:0% +of total mechanical energy which is +defined as the sum of the kinetic and + + align:start position:0% +defined as the sum of the kinetic and + + + align:start position:0% +defined as the sum of the kinetic and +potential energies we will demonstrate + + align:start position:0% +potential energies we will demonstrate + + + align:start position:0% +potential energies we will demonstrate +that the total mechanical energy of the + + align:start position:0% +that the total mechanical energy of the + + + align:start position:0% +that the total mechanical energy of the +system remains constant if only + + align:start position:0% +system remains constant if only + + + align:start position:0% +system remains constant if only +conservative forces are acting this is + + align:start position:0% +conservative forces are acting this is + + + align:start position:0% +conservative forces are acting this is +known as the principle of conservation + + align:start position:0% +known as the principle of conservation + + + align:start position:0% +known as the principle of conservation +of mechanical energy we will also see + + align:start position:0% +of mechanical energy we will also see + + + align:start position:0% +of mechanical energy we will also see +how the work done by any non + + align:start position:0% +how the work done by any non + + + align:start position:0% +how the work done by any non +conservative forces causes the total + + align:start position:0% +conservative forces causes the total + + + align:start position:0% +conservative forces causes the total +mechanical energy of the system to + + align:start position:0% +mechanical energy of the system to + + + align:start position:0% +mechanical energy of the system to +change usually causing mechanical energy + + align:start position:0% +change usually causing mechanical energy + + + align:start position:0% +change usually causing mechanical energy +to be lost from the system finally we + + align:start position:0% +to be lost from the system finally we + + + align:start position:0% +to be lost from the system finally we +will see how graphs of the system's + + align:start position:0% +will see how graphs of the system's + + + align:start position:0% +will see how graphs of the system's +potential energy as a function of + + align:start position:0% +potential energy as a function of + + + align:start position:0% +potential energy as a function of +position provide an elegant way of + + align:start position:0% +position provide an elegant way of + + + align:start position:0% +position provide an elegant way of +understanding the behavior of the system + + align:start position:0% +understanding the behavior of the system + + + align:start position:0% +understanding the behavior of the system +for a given value of the total + + align:start position:0% +for a given value of the total + + + align:start position:0% +for a given value of the total +mechanical energy \ No newline at end of file diff --git a/EXBO08-78IU.txt b/EXBO08-78IU.txt new file mode 100644 index 0000000000000000000000000000000000000000..590a00f700fa061d360f900e38338edfb0b4b96a --- /dev/null +++ b/EXBO08-78IU.txt @@ -0,0 +1,14800 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu so today what we want to do + + align:start position:0% +ocw.mit.edu so today what we want to do + + + align:start position:0% +ocw.mit.edu so today what we want to do +is uh discuss various approaches that + + align:start position:0% +is uh discuss various approaches that + + + align:start position:0% +is uh discuss various approaches that +you might want to take towards trying to + + align:start position:0% +you might want to take towards trying to + + + align:start position:0% +you might want to take towards trying to +understand uh stochastic systems in + + align:start position:0% +understand uh stochastic systems in + + + align:start position:0% +understand uh stochastic systems in +particular how is it that we might model + + align:start position:0% +particular how is it that we might model + + + align:start position:0% +particular how is it that we might model +or simulate a stochastic system now uh + + align:start position:0% +or simulate a stochastic system now uh + + + align:start position:0% +or simulate a stochastic system now uh +we will kind of continue our discussion + + align:start position:0% +we will kind of continue our discussion + + + align:start position:0% +we will kind of continue our discussion +of the master equation from last time + + align:start position:0% +of the master equation from last time + + + align:start position:0% +of the master equation from last time +hopefully now you've kind of thought + + align:start position:0% +hopefully now you've kind of thought + + + align:start position:0% +hopefully now you've kind of thought +about it a bit more in the context of + + align:start position:0% +about it a bit more in the context of + + + align:start position:0% +about it a bit more in the context of +the reading then we'll discuss kind of + + align:start position:0% +the reading then we'll discuss kind of + + + align:start position:0% +the reading then we'll discuss kind of +what what it means to be using the + + align:start position:0% +what what it means to be using the + + + align:start position:0% +what what it means to be using the +master equation and how to formulate the + + align:start position:0% +master equation and how to formulate the + + + align:start position:0% +master equation and how to formulate the +master equation for more complicated + + align:start position:0% +master equation for more complicated + + + align:start position:0% +master equation for more complicated +situations for example when you have + + align:start position:0% +situations for example when you have + + + align:start position:0% +situations for example when you have +more than one chemical + + align:start position:0% +more than one chemical + + + align:start position:0% +more than one chemical +species and then we'll uh we'll talk + + align:start position:0% +species and then we'll uh we'll talk + + + align:start position:0% +species and then we'll uh we'll talk +about the idea of the gespi method which + + align:start position:0% +about the idea of the gespi method which + + + align:start position:0% +about the idea of the gespi method which +is uh an exact uh way to simulate + + align:start position:0% +is uh an exact uh way to simulate + + + align:start position:0% +is uh an exact uh way to simulate +stochastic systems and uh it's uh it's + + align:start position:0% +stochastic systems and uh it's uh it's + + + align:start position:0% +stochastic systems and uh it's uh it's +both exact and + + align:start position:0% +both exact and + + + align:start position:0% +both exact and +computationally um tractable as compared + + align:start position:0% +computationally um tractable as compared + + + align:start position:0% +computationally um tractable as compared +to what you might call various naive + + align:start position:0% +to what you might call various naive + + + align:start position:0% +to what you might call various naive +methods uh and the gespi method is is + + align:start position:0% +methods uh and the gespi method is is + + + align:start position:0% +methods uh and the gespi method is is +really qu sort of qualitatively + + align:start position:0% +really qu sort of qualitatively + + + align:start position:0% +really qu sort of qualitatively +different from from the master equation + + align:start position:0% +different from from the master equation + + + align:start position:0% +different from from the master equation +because uh in the master equation you're + + align:start position:0% +because uh in the master equation you're + + + align:start position:0% +because uh in the master equation you're +looking at the kind of the evolution of + + align:start position:0% +looking at the kind of the evolution of + + + align:start position:0% +looking at the kind of the evolution of +probability distributions across the + + align:start position:0% +probability distributions across the + + + align:start position:0% +probability distributions across the +system uh whereas the gpie method is + + align:start position:0% +system uh whereas the gpie method is + + + align:start position:0% +system uh whereas the gpie method is +really a way to generate individual + + align:start position:0% +really a way to generate individual + + + align:start position:0% +really a way to generate individual +stochastic trajectories okay so if you + + align:start position:0% +stochastic trajectories okay so if you + + + align:start position:0% +stochastic trajectories okay so if you +start with somehow similar initial + + align:start position:0% +start with somehow similar initial + + + align:start position:0% +start with somehow similar initial +conditions then you can actually get uh + + align:start position:0% +conditions then you can actually get uh + + + align:start position:0% +conditions then you can actually get uh +you can get for example the probability + + align:start position:0% +you can get for example the probability + + + align:start position:0% +you can get for example the probability +distributions from the gaspie method by + + align:start position:0% +distributions from the gaspie method by + + + align:start position:0% +distributions from the gaspie method by +running many individual trajectories but + + align:start position:0% +running many individual trajectories but + + + align:start position:0% +running many individual trajectories but +but it's it's kind of conceptually + + align:start position:0% +but it's it's kind of conceptually + + + align:start position:0% +but it's it's kind of conceptually +rather different because of this notion + + align:start position:0% +rather different because of this notion + + + align:start position:0% +rather different because of this notion +of whether you're thinking about + + align:start position:0% +of whether you're thinking about + + + align:start position:0% +of whether you're thinking about +probabilities or you're thinking about + + align:start position:0% +probabilities or you're thinking about + + + align:start position:0% +probabilities or you're thinking about +uh individual instantiations of some + + align:start position:0% +uh individual instantiations of some + + + align:start position:0% +uh individual instantiations of some +stochastic trajectory so we'll try to + + align:start position:0% +stochastic trajectory so we'll try to + + + align:start position:0% +stochastic trajectory so we'll try to +make sense of uh when you might want to + + align:start position:0% +make sense of uh when you might want to + + + align:start position:0% +make sense of uh when you might want to +use one or the other and then uh and + + align:start position:0% +use one or the other and then uh and + + + align:start position:0% +use one or the other and then uh and +then finally we'll talk about this uh + + align:start position:0% +then finally we'll talk about this uh + + + align:start position:0% +then finally we'll talk about this uh +fuer plank approximation which uh as the + + align:start position:0% +fuer plank approximation which uh as the + + + align:start position:0% +fuer plank approximation which uh as the +reading indicated for intermediate uh + + align:start position:0% +reading indicated for intermediate uh + + + align:start position:0% +reading indicated for intermediate uh +ends it's useful to make this kind of + + align:start position:0% +ends it's useful to make this kind of + + + align:start position:0% +ends it's useful to make this kind of +continuous approximation and then uh + + align:start position:0% +continuous approximation and then uh + + + align:start position:0% +continuous approximation and then uh +then you can get a lot of the intuition + + align:start position:0% +then you can get a lot of the intuition + + + align:start position:0% +then you can get a lot of the intuition +from uh your knowledge about diffusion + + align:start position:0% +from uh your knowledge about diffusion + + + align:start position:0% +from uh your knowledge about diffusion +on on effective potential + + align:start position:0% +on on effective potential + + + align:start position:0% +on on effective potential +Landscapes are there any any questions + + align:start position:0% +Landscapes are there any any questions + + + align:start position:0% +Landscapes are there any any questions +about this or administrative things + + align:start position:0% +about this or administrative things + + + align:start position:0% +about this or administrative things +before we get + + align:start position:0% +before we get + + + align:start position:0% +before we get +going uh I'll I just want to remind you + + align:start position:0% +going uh I'll I just want to remind you + + + align:start position:0% +going uh I'll I just want to remind you +that the uh midterm is indeed next + + align:start position:0% +that the uh midterm is indeed next + + + align:start position:0% +that the uh midterm is indeed next +Thursday evening 7: to 9:00 p.m. if you + + align:start position:0% +Thursday evening 7: to 9:00 p.m. if you + + + align:start position:0% +Thursday evening 7: to 9:00 p.m. if you +are if you have a problem with that time + + align:start position:0% +are if you have a problem with that time + + + align:start position:0% +are if you have a problem with that time +then you should have emailed sarab and + + align:start position:0% +then you should have emailed sarab and + + + align:start position:0% +then you should have emailed sarab and +uh if you haven't emailed him yet you + + align:start position:0% +uh if you haven't emailed him yet you + + + align:start position:0% +uh if you haven't emailed him yet you +should have do it right now um and + + align:start position:0% +should have do it right now um and + + + align:start position:0% +should have do it right now um and +yes okay all right so let's let's uh + + align:start position:0% +yes okay all right so let's let's uh + + + align:start position:0% +yes okay all right so let's let's uh +let's think about the master equation a + + align:start position:0% +let's think about the master equation a + + + align:start position:0% +let's think about the master equation a +little bit more okay uh now before what + + align:start position:0% +little bit more okay uh now before what + + + align:start position:0% +little bit more okay uh now before what +we did is we thought about the simplest + + align:start position:0% +we did is we thought about the simplest + + + align:start position:0% +we did is we thought about the simplest +possible case of the master equation + + align:start position:0% +possible case of the master equation + + + align:start position:0% +possible case of the master equation +which is if you just have uh something + + align:start position:0% +which is if you just have uh something + + + align:start position:0% +which is if you just have uh something +being created at a constant rate and + + align:start position:0% +being created at a constant rate and + + + align:start position:0% +being created at a constant rate and +then being degraded uh at at a rate + + align:start position:0% +then being degraded uh at at a rate + + + align:start position:0% +then being degraded uh at at a rate +that's kind of proportional to the + + align:start position:0% +that's kind of proportional to the + + + align:start position:0% +that's kind of proportional to the +number of of that chemical species right + + align:start position:0% +number of of that chemical species right + + + align:start position:0% +number of of that chemical species right +and I'm I'm going to be using the uh + + align:start position:0% +and I'm I'm going to be using the uh + + + align:start position:0% +and I'm I'm going to be using the uh +nomenclature that's a little bit closer + + align:start position:0% +nomenclature that's a little bit closer + + + align:start position:0% +nomenclature that's a little bit closer +to what what was in your reading just uh + + align:start position:0% +to what what was in your reading just uh + + + align:start position:0% +to what what was in your reading just uh +for hopefully Clarity and I think that + + align:start position:0% +for hopefully Clarity and I think that + + + align:start position:0% +for hopefully Clarity and I think that +some of my choices for from uh last + + align:start position:0% +some of my choices for from uh last + + + align:start position:0% +some of my choices for from uh last +lecture were maybe + + align:start position:0% +lecture were maybe + + + align:start position:0% +lecture were maybe +unfortunate uh so here this is for + + align:start position:0% +unfortunate uh so here this is for + + + align:start position:0% +unfortunate uh so here this is for +example uh M would be the number of mRNA + + align:start position:0% +example uh M would be the number of mRNA + + + align:start position:0% +example uh M would be the number of mRNA +for example in the cell this is the rate + + align:start position:0% +for example in the cell this is the rate + + + align:start position:0% +for example in the cell this is the rate +of creation of the MRNA and then uh the + + align:start position:0% +of creation of the MRNA and then uh the + + + align:start position:0% +of creation of the MRNA and then uh the +rate of degradation of the MRNA okay so + + align:start position:0% +rate of degradation of the MRNA okay so + + + align:start position:0% +rate of degradation of the MRNA okay so +m is the number of mRNA + + align:start position:0% + + + + align:start position:0% + +and uh if we want to understand gene + + align:start position:0% +and uh if we want to understand gene + + + align:start position:0% +and uh if we want to understand gene +expression we might include an equation + + align:start position:0% +expression we might include an equation + + + align:start position:0% +expression we might include an equation +for the protein so we might have some P + + align:start position:0% +for the protein so we might have some P + + + align:start position:0% +for the protein so we might have some P +dot but it's some + + align:start position:0% + + + + align:start position:0% + +KP okay now oh sorry again I always do + + align:start position:0% +KP okay now oh sorry again I always do + + + align:start position:0% +KP okay now oh sorry again I always do +this all right so this we're going to + + align:start position:0% +this all right so this we're going to + + + align:start position:0% +this all right so this we're going to +have this be an N + + align:start position:0% +have this be an N + + + align:start position:0% +have this be an N +dot all right so now n is uh is going to + + align:start position:0% +dot all right so now n is uh is going to + + + align:start position:0% +dot all right so now n is uh is going to +be the number of the protein + + align:start position:0% + + + + align:start position:0% + +okay now this really is kind of the + + align:start position:0% +okay now this really is kind of the + + + align:start position:0% +okay now this really is kind of the +simplest possible uh model that you + + align:start position:0% +simplest possible uh model that you + + + align:start position:0% +simplest possible uh model that you +might write down for gene expression + + align:start position:0% +might write down for gene expression + + + align:start position:0% +might write down for gene expression +that includes both the MRNA and the + + align:start position:0% +that includes both the MRNA and the + + + align:start position:0% +that includes both the MRNA and the +protein right so there's no uh no Auto + + align:start position:0% +protein right so there's no uh no Auto + + + align:start position:0% +protein right so there's no uh no Auto +regulation of any sort uh it's it's just + + align:start position:0% +regulation of any sort uh it's it's just + + + align:start position:0% +regulation of any sort uh it's it's just +that the MRNA is uh involved in uh in + + align:start position:0% +that the MRNA is uh involved in uh in + + + align:start position:0% +that the MRNA is uh involved in uh in +creating the protein but then we have we + + align:start position:0% +creating the protein but then we have we + + + align:start position:0% +creating the protein but then we have we +have degradation of the protein as + + align:start position:0% +have degradation of the protein as + + + align:start position:0% +have degradation of the protein as +well so what we want to do is kind of + + align:start position:0% +well so what we want to do is kind of + + + align:start position:0% +well so what we want to do is kind of +try to understand how to formulate the + + align:start position:0% +try to understand how to formulate the + + + align:start position:0% +try to understand how to formulate the +master equation here but then also we + + align:start position:0% +master equation here but then also we + + + align:start position:0% +master equation here but then also we +want to make sure that we understand + + align:start position:0% +want to make sure that we understand + + + align:start position:0% +want to make sure that we understand +what the master equation is actually + + align:start position:0% +what the master equation is actually + + + align:start position:0% +what the master equation is actually +telling us and how how it might be used + + align:start position:0% +telling us and how how it might be used + + + align:start position:0% +telling us and how how it might be used +right so first of all in this model I + + align:start position:0% +right so first of all in this model I + + + align:start position:0% +right so first of all in this model I +want to know is there uh in principle + + align:start position:0% +want to know is there uh in principle + + + align:start position:0% +want to know is there uh in principle +protein + + align:start position:0% +protein + + + align:start position:0% +protein +bursts right so before we talked + + align:start position:0% +bursts right so before we talked + + + align:start position:0% +bursts right so before we talked +about uh the fact that in at least in in + + align:start position:0% +about uh the fact that in at least in in + + + align:start position:0% +about uh the fact that in at least in in +that in Sunny's paper that we read they + + align:start position:0% +that in Sunny's paper that we read they + + + align:start position:0% +that in Sunny's paper that we read they +could observe protein bursts at least in + + align:start position:0% +could observe protein bursts at least in + + + align:start position:0% +could observe protein bursts at least in +that in those experiments in eoli the + + align:start position:0% +that in those experiments in eoli the + + + align:start position:0% +that in those experiments in eoli the +question is + + align:start position:0% +question is + + + align:start position:0% +question is +is + + align:start position:0% +is + + + align:start position:0% +is +there should should this model somehow + + align:start position:0% +there should should this model somehow + + + align:start position:0% +there should should this model somehow +exhibit protein bursts and you know why + + align:start position:0% +exhibit protein bursts and you know why + + + align:start position:0% +exhibit protein bursts and you know why +or why not all right I just want to uh + + align:start position:0% +or why not all right I just want to uh + + + align:start position:0% +or why not all right I just want to uh +see where we are on + + align:start position:0% + + + + align:start position:0% + +this and I think uh this is something + + align:start position:0% +this and I think uh this is something + + + align:start position:0% +this and I think uh this is something +that reasonable you know that depending + + align:start position:0% +that reasonable you know that depending + + + align:start position:0% +that reasonable you know that depending +on how you interpret the question you + + align:start position:0% +on how you interpret the question you + + + align:start position:0% +on how you interpret the question you +might decide the answer is yes or no but + + align:start position:0% +might decide the answer is yes or no but + + + align:start position:0% +might decide the answer is yes or no but +I'm I'm curious uh I I think it's it's + + align:start position:0% +I'm I'm curious uh I I think it's it's + + + align:start position:0% +I'm I'm curious uh I I think it's it's +worth discussing what the implications + + align:start position:0% +worth discussing what the implications + + + align:start position:0% +worth discussing what the implications +are here + + align:start position:0% + + + + align:start position:0% + +and uh you know and the the relevant + + align:start position:0% +and uh you know and the the relevant + + + align:start position:0% +and uh you know and the the relevant +part of this is going to be the + + align:start position:0% +part of this is going to be the + + + align:start position:0% +part of this is going to be the +discussion afterwards so I'd say uh + + align:start position:0% +discussion afterwards so I'd say uh + + + align:start position:0% +discussion afterwards so I'd say uh +don't worry too much about what you uh + + align:start position:0% +don't worry too much about what you uh + + + align:start position:0% +don't worry too much about what you uh +what you think right now but I'm just + + align:start position:0% +what you think right now but I'm just + + + align:start position:0% +what you think right now but I'm just +curious um you know you know this model + + align:start position:0% +curious um you know you know this model + + + align:start position:0% +curious um you know you know this model +does it some Does it include somehow + + align:start position:0% +does it some Does it include somehow + + + align:start position:0% +does it some Does it include somehow +protein bursts all right ready uh three + + align:start position:0% +protein bursts all right ready uh three + + + align:start position:0% +protein bursts all right ready uh three +two + + align:start position:0% +two + + + align:start position:0% +two +one okay so we got um we got I'd say at + + align:start position:0% +one okay so we got um we got I'd say at + + + align:start position:0% +one okay so we got um we got I'd say at +least a majority of the people are + + align:start position:0% +least a majority of the people are + + + align:start position:0% +least a majority of the people are +saying no okay so the um can you know + + align:start position:0% +saying no okay so the um can you know + + + align:start position:0% +saying no okay so the um can you know +but then some people are saying yes so + + align:start position:0% +but then some people are saying yes so + + + align:start position:0% +but then some people are saying yes so +can we can somebody volun + + align:start position:0% +can we can somebody volun + + + align:start position:0% +can we can somebody volun +ER yeah what's go you know why or why + + align:start position:0% +ER yeah what's go you know why or why + + + align:start position:0% +ER yeah what's go you know why or why +not yes I think the difference is if are + + align:start position:0% +not yes I think the difference is if are + + + align:start position:0% +not yes I think the difference is if are +we using this in a continu fashion or + + align:start position:0% +we using this in a continu fashion or + + + align:start position:0% +we using this in a continu fashion or +disc continu yeah okay all right all + + align:start position:0% +disc continu yeah okay all right all + + + align:start position:0% +disc continu yeah okay all right all +right so he's answering both both + + align:start position:0% +right so he's answering both both + + + align:start position:0% +right so he's answering both both +possible sides of the argument right and + + align:start position:0% +possible sides of the argument right and + + + align:start position:0% +possible sides of the argument right and +uh and and the point here is that if you + + align:start position:0% +uh and and the point here is that if you + + + align:start position:0% +uh and and the point here is that if you +just simulate this from the standpoint + + align:start position:0% +just simulate this from the standpoint + + + align:start position:0% +just simulate this from the standpoint +certainly for example you know there's + + align:start position:0% +certainly for example you know there's + + + align:start position:0% +certainly for example you know there's +continuous there right so if if you if + + align:start position:0% +continuous there right so if if you if + + + align:start position:0% +continuous there right so if if you if +you just simulate this as a + + align:start position:0% +you just simulate this as a + + + align:start position:0% +you just simulate this as a +deterministic pair of differential + + align:start position:0% +deterministic pair of differential + + + align:start position:0% +deterministic pair of differential +equations then will there be + + align:start position:0% +equations then will there be + + + align:start position:0% +equations then will there be +bursts no okay all right because + + align:start position:0% +bursts no okay all right because + + + align:start position:0% +bursts no okay all right because +everything is well behaved here right on + + align:start position:0% +everything is well behaved here right on + + + align:start position:0% +everything is well behaved here right on +the other hand if we go and we do what + + align:start position:0% +the other hand if we go and we do what + + + align:start position:0% +the other hand if we go and we do what +like a full Gillespie simulation of this + + align:start position:0% +like a full Gillespie simulation of this + + + align:start position:0% +like a full Gillespie simulation of this +pair of uh pair of equations then in the + + align:start position:0% +pair of uh pair of equations then in the + + + align:start position:0% +pair of uh pair of equations then in the +proper parameter regime we actually will + + align:start position:0% +proper parameter regime we actually will + + + align:start position:0% +proper parameter regime we actually will +get protein + + align:start position:0% + + + + align:start position:0% + +bursts okay which is in some ways weird + + align:start position:0% +bursts okay which is in some ways weird + + + align:start position:0% +bursts okay which is in some ways weird +right that depending upon the framework + + align:start position:0% +right that depending upon the framework + + + align:start position:0% +right that depending upon the framework +that you're going to be analyzing this + + align:start position:0% +that you're going to be analyzing this + + + align:start position:0% +that you're going to be analyzing this +in you're going to you can get + + align:start position:0% +in you're going to you can get + + + align:start position:0% +in you're going to you can get +qualitatively different behaviors for + + align:start position:0% +qualitatively different behaviors for + + + align:start position:0% +qualitatively different behaviors for +things right um but there's a sense here + + align:start position:0% +things right um but there's a sense here + + + align:start position:0% +things right um but there's a sense here +that the uh the deterministic uh + + align:start position:0% +that the uh the deterministic uh + + + align:start position:0% +that the uh the deterministic uh +continuous evolution of these quantities + + align:start position:0% +continuous evolution of these quantities + + + align:start position:0% +continuous evolution of these quantities +would be the average over many of these + + align:start position:0% +would be the average over many of these + + + align:start position:0% +would be the average over many of these +stochastic trajectories and the + + align:start position:0% +stochastic trajectories and the + + + align:start position:0% +stochastic trajectories and the +stochastic ones do have burst but if you + + align:start position:0% +stochastic ones do have burst but if you + + + align:start position:0% +stochastic ones do have burst but if you +average over many many of them then you + + align:start position:0% +average over many many of them then you + + + align:start position:0% +average over many many of them then you +end up getting some well behaved uh pair + + align:start position:0% +end up getting some well behaved uh pair + + + align:start position:0% +end up getting some well behaved uh pair +of equations so we'll kind of try to + + align:start position:0% +of equations so we'll kind of try to + + + align:start position:0% +of equations so we'll kind of try to +make sense of this more later on but I + + align:start position:0% +make sense of this more later on but I + + + align:start position:0% +make sense of this more later on but I +think that this just highlights that the + + align:start position:0% +think that this just highlights that the + + + align:start position:0% +think that this just highlights that the +uh that you you can get really + + align:start position:0% +uh that you you can get really + + + align:start position:0% +uh that you you can get really +qualitatively different behaviors for + + align:start position:0% +qualitatively different behaviors for + + + align:start position:0% +qualitatively different behaviors for +the same set of equations depending upon + + align:start position:0% +the same set of equations depending upon + + + align:start position:0% +the same set of equations depending upon +what you're what you're looking at right + + align:start position:0% +what you're what you're looking at right + + + align:start position:0% +what you're what you're looking at right +and this is not just you know it's U and + + align:start position:0% +and this is not just you know it's U and + + + align:start position:0% +and this is not just you know it's U and +you know these protein births can be + + align:start position:0% +you know these protein births can be + + + align:start position:0% +you know these protein births can be +dramatic events right I mean that where + + align:start position:0% +dramatic events right I mean that where + + + align:start position:0% +dramatic events right I mean that where +the protein number pops up by a lot + + align:start position:0% +the protein number pops up by a lot + + + align:start position:0% +the protein number pops up by a lot +right you know so this this really then + + align:start position:0% +right you know so this this really then + + + align:start position:0% +right you know so this this really then +if you look at the individual + + align:start position:0% +if you look at the individual + + + align:start position:0% +if you look at the individual +trajectories here they would look very + + align:start position:0% +trajectories here they would look very + + + align:start position:0% +trajectories here they would look very +different right whether you were doing + + align:start position:0% +different right whether you were doing + + + align:start position:0% +different right whether you were doing +kind of a stochastic treatment or the + + align:start position:0% +kind of a stochastic treatment or the + + + align:start position:0% +kind of a stochastic treatment or the +deterministic + + align:start position:0% +deterministic + + + align:start position:0% +deterministic +one okay can somebody remind us the + + align:start position:0% +one okay can somebody remind us the + + + align:start position:0% +one okay can somebody remind us the +situation in which we kind of get + + align:start position:0% +situation in which we kind of get + + + align:start position:0% +situation in which we kind of get +protein + + align:start position:0% +protein + + + align:start position:0% +protein +bursts uh in in the stochastic + + align:start position:0% +bursts uh in in the stochastic + + + align:start position:0% +bursts uh in in the stochastic +model particular will we always get will + + align:start position:0% +model particular will we always get will + + + align:start position:0% +model particular will we always get will +we always get these these discrete + + align:start position:0% +we always get these these discrete + + + align:start position:0% +we always get these these discrete +protein bursts or what determines the + + align:start position:0% +protein bursts or what determines the + + + align:start position:0% +protein bursts or what determines the +size of a protein + + align:start position:0% + + + + align:start position:0% + +burst + + align:start position:0% + + + + align:start position:0% + +yes okay right so okay so possibly + + align:start position:0% +yes okay right so okay so possibly + + + align:start position:0% +yes okay right so okay so possibly +there's a lag time between the time that + + align:start position:0% +there's a lag time between the time that + + + align:start position:0% +there's a lag time between the time that +an mRNA is created and and then the next + + align:start position:0% +an mRNA is created and and then the next + + + align:start position:0% +an mRNA is created and and then the next +thing would + + align:start position:0% +thing would + + + align:start position:0% +thing would +be + + align:start position:0% + + + + align:start position:0% + +when right and then when the protein is + + align:start position:0% +when right and then when the protein is + + + align:start position:0% +when right and then when the protein is +totally right so that okay so there are + + align:start position:0% +totally right so that okay so there are + + + align:start position:0% +totally right so that okay so there are +multiple time scales right so one is U + + align:start position:0% +multiple time scales right so one is U + + + align:start position:0% +multiple time scales right so one is U +right so after an mRNA is created and + + align:start position:0% +right so after an mRNA is created and + + + align:start position:0% +right so after an mRNA is created and +that's through this process here okay so + + align:start position:0% +that's through this process here okay so + + + align:start position:0% +that's through this process here okay so +now out pops an mRNA right now there now + + align:start position:0% +now out pops an mRNA right now there now + + + align:start position:0% +now out pops an mRNA right now there now +there are multiple time scales right + + align:start position:0% +there are multiple time scales right + + + align:start position:0% +there are multiple time scales right +there's the time scale for mRNA + + align:start position:0% +there's the time scale for mRNA + + + align:start position:0% +there's the time scale for mRNA +degradation that goes as one over gamma + + align:start position:0% +degradation that goes as one over gamma + + + align:start position:0% +degradation that goes as one over gamma +M right there's a time scale for protein + + align:start position:0% +M right there's a time scale for protein + + + align:start position:0% +M right there's a time scale for protein +degradation you know after a protein is + + align:start position:0% +degradation you know after a protein is + + + align:start position:0% +degradation you know after a protein is +made that goes as one over gamma P but + + align:start position:0% +made that goes as one over gamma P but + + + align:start position:0% +made that goes as one over gamma P but +then there's also a time scale + + align:start position:0% +then there's also a time scale + + + align:start position:0% +then there's also a time scale +associated with um kind of the rate of + + align:start position:0% +associated with um kind of the rate of + + + align:start position:0% +associated with um kind of the rate of +protein production from each of those + + align:start position:0% +protein production from each of those + + + align:start position:0% +protein production from each of those +mrnas and right and that's determined by + + align:start position:0% +mrnas and right and that's determined by + + + align:start position:0% +mrnas and right and that's determined by +KP right so we get these we get big + + align:start position:0% +KP right so we get these we get big + + + align:start position:0% +KP right so we get these we get big +protein bursts if what what what is it + + align:start position:0% +protein bursts if what what what is it + + + align:start position:0% +protein bursts if what what what is it +that what determines you know this the + + align:start position:0% +that what determines you know this the + + + align:start position:0% +that what determines you know this the +size of these protein + + align:start position:0% + + + + align:start position:0% + +bursts yes + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +that right it's always confusing we + + align:start position:0% +that right it's always confusing we + + + align:start position:0% +that right it's always confusing we +talking about times or right but in + + align:start position:0% +talking about times or right but in + + + align:start position:0% +talking about times or right but in +particular we have protein bursts in the + + align:start position:0% +particular we have protein bursts in the + + + align:start position:0% +particular we have protein bursts in the +in the stochastic situation right if we + + align:start position:0% +in the stochastic situation right if we + + + align:start position:0% +in the stochastic situation right if we +do a stochastic simulation and and + + align:start position:0% +do a stochastic simulation and and + + + align:start position:0% +do a stochastic simulation and and +that's in the regime if + + align:start position:0% +that's in the regime if + + + align:start position:0% +that's in the regime if +KP right the rate of protein synthesis + + align:start position:0% +KP right the rate of protein synthesis + + + align:start position:0% +KP right the rate of protein synthesis +uh from the MRNA is somehow much larger + + align:start position:0% +uh from the MRNA is somehow much larger + + + align:start position:0% +uh from the MRNA is somehow much larger +than uh than this gamma + + align:start position:0% +than uh than this gamma + + + align:start position:0% +than uh than this gamma +M + + align:start position:0% + + + + align:start position:0% + +right have I have I screwed up okay yes + + align:start position:0% +right have I have I screwed up okay yes + + + align:start position:0% +right have I have I screwed up okay yes +so just this is also like in the sense + + align:start position:0% +so just this is also like in the sense + + + align:start position:0% +so just this is also like in the sense +of being different from the + + align:start position:0% +of being different from the + + + align:start position:0% +of being different from the +deterministic equations we probably also + + align:start position:0% +deterministic equations we probably also + + + align:start position:0% +deterministic equations we probably also +want the total + + align:start position:0% + + + + align:start position:0% + +number right um yeah I think that it and + + align:start position:0% +number right um yeah I think that it and + + + align:start position:0% +number right um yeah I think that it and +this comes the question of of what mRNA + + align:start position:0% +this comes the question of of what mRNA + + + align:start position:0% +this comes the question of of what mRNA +number you need I mean it depends on + + align:start position:0% +number you need I mean it depends on + + + align:start position:0% +number you need I mean it depends on +what you mean by protein bursts I would + + align:start position:0% +what you mean by protein bursts I would + + + align:start position:0% +what you mean by protein bursts I would +say that if um if so long as this is + + align:start position:0% +say that if um if so long as this is + + + align:start position:0% +say that if um if so long as this is +true okay that what that means is that + + align:start position:0% +true okay that what that means is that + + + align:start position:0% +true okay that what that means is that +each mRNA will indeed kind of lead to + + align:start position:0% +each mRNA will indeed kind of lead to + + + align:start position:0% +each mRNA will indeed kind of lead to +you know a burst of proteins being made + + align:start position:0% +you know a burst of proteins being made + + + align:start position:0% +you know a burst of proteins being made +where where the burst is getting + + align:start position:0% +where where the burst is getting + + + align:start position:0% +where where the burst is getting +geometrically distributed with some + + align:start position:0% +geometrically distributed with some + + + align:start position:0% +geometrically distributed with some +right now there's another question which + + align:start position:0% +right now there's another question which + + + align:start position:0% +right now there's another question which +is are those protein bursts kind of + + align:start position:0% +is are those protein bursts kind of + + + align:start position:0% +is are those protein bursts kind of +large compared to the steady state + + align:start position:0% +large compared to the steady state + + + align:start position:0% +large compared to the steady state +protein + + align:start position:0% +protein + + + align:start position:0% +protein +concentration right and that's going to + + align:start position:0% +concentration right and that's going to + + + align:start position:0% +concentration right and that's going to +depend upon U km and and Gamma p as well + + align:start position:0% +depend upon U km and and Gamma p as well + + + align:start position:0% +depend upon U km and and Gamma p as well +is is that yeah I guess so + + align:start position:0% +is is that yeah I guess so + + + align:start position:0% +is is that yeah I guess so +guess I guess + + align:start position:0% +guess I guess + + + align:start position:0% +guess I guess +dep all right well and you're saying + + align:start position:0% +dep all right well and you're saying + + + align:start position:0% +dep all right well and you're saying +time resolution in terms of just + + align:start position:0% +time resolution in terms of just + + + align:start position:0% +time resolution in terms of just +measuring yeah okay yeah well okay but + + align:start position:0% +measuring yeah okay yeah well okay but + + + align:start position:0% +measuring yeah okay yeah well okay but +right now we're kind of imagining that + + align:start position:0% +right now we're kind of imagining that + + + align:start position:0% +right now we're kind of imagining that +we live in this perfect world where we + + align:start position:0% +we live in this perfect world where we + + + align:start position:0% +we live in this perfect world where we +know at every moment of time exactly how + + align:start position:0% +know at every moment of time exactly how + + + align:start position:0% +know at every moment of time exactly how +many of everything there is right so in + + align:start position:0% +many of everything there is right so in + + + align:start position:0% +many of everything there is right so in +some ways we haven't we haven't said + + align:start position:0% +some ways we haven't we haven't said + + + align:start position:0% +some ways we haven't we haven't said +anything yet about time resolution we're + + align:start position:0% +anything yet about time resolution we're + + + align:start position:0% +anything yet about time resolution we're +assuming that that our time resolution + + align:start position:0% +assuming that that our time resolution + + + align:start position:0% +assuming that that our time resolution +and and our number resolution is + + align:start position:0% +and and our number resolution is + + + align:start position:0% +and and our number resolution is +actually is perfect right but still + + align:start position:0% +actually is perfect right but still + + + align:start position:0% +actually is perfect right but still +depending upon the regime that you're in + + align:start position:0% +depending upon the regime that you're in + + + align:start position:0% +depending upon the regime that you're in +the protein all right numbers could look + + align:start position:0% +the protein all right numbers could look + + + align:start position:0% +the protein all right numbers could look +something like uh right so if you look + + align:start position:0% +something like uh right so if you look + + + align:start position:0% +something like uh right so if you look +at the protein number which is is + + align:start position:0% +at the protein number which is is + + + align:start position:0% +at the protein number which is is +defined as this n right as a function of + + align:start position:0% +defined as this n right as a function of + + + align:start position:0% +defined as this n right as a function of +time then you know in one regime you're + + align:start position:0% +time then you know in one regime you're + + + align:start position:0% +time then you know in one regime you're +going to see it where okay so it's kind + + align:start position:0% +going to see it where okay so it's kind + + + align:start position:0% +going to see it where okay so it's kind +of low you get a big burst and then you + + align:start position:0% +of low you get a big burst and then you + + + align:start position:0% +of low you get a big burst and then you +kind of It kind of comes down and then + + align:start position:0% +kind of It kind of comes down and then + + + align:start position:0% +kind of It kind of comes down and then +and then a big burst and then it kind of + + align:start position:0% +and then a big burst and then it kind of + + + align:start position:0% +and then a big burst and then it kind of +comes down and burst and kind of comes + + align:start position:0% +comes down and burst and kind of comes + + + align:start position:0% +comes down and burst and kind of comes +down right so this this is in the regime + + align:start position:0% +down right so this this is in the regime + + + align:start position:0% +down right so this this is in the regime +where you don't you have infrequent + + align:start position:0% +where you don't you have infrequent + + + align:start position:0% +where you don't you have infrequent +mrnas being produced and then large uh + + align:start position:0% +mrnas being produced and then large uh + + + align:start position:0% +mrnas being produced and then large uh +large uh size bursts from each mRNA + + align:start position:0% +large uh size bursts from each mRNA + + + align:start position:0% +large uh size bursts from each mRNA +right and then and then you kind of get + + align:start position:0% +right and then and then you kind of get + + + align:start position:0% +right and then and then you kind of get +this effective degradation or dilution + + align:start position:0% +this effective degradation or dilution + + + align:start position:0% +this effective degradation or dilution +of of the protein numbers over time + + align:start position:0% +of of the protein numbers over time + + + align:start position:0% +of of the protein numbers over time +right and this distribution if you take + + align:start position:0% +right and this distribution if you take + + + align:start position:0% +right and this distribution if you take +a histogram of it is + + align:start position:0% + + + + align:start position:0% + +what right so I when I'm I'm imagining + + align:start position:0% +what right so I when I'm I'm imagining + + + align:start position:0% +what right so I when I'm I'm imagining +that we we look at this for a long + + align:start position:0% +that we we look at this for a long + + + align:start position:0% +that we we look at this for a long +period of time right and then we come + + align:start position:0% +period of time right and then we come + + + align:start position:0% +period of time right and then we come +over here and we histogram it right so + + align:start position:0% +over here and we histogram it right so + + + align:start position:0% +over here and we histogram it right so +now we we come over here we turn to the + + align:start position:0% +now we we come over here we turn to the + + + align:start position:0% +now we we come over here we turn to the +left we say number as a function of this + + align:start position:0% +left we say number as a function of this + + + align:start position:0% +left we say number as a function of this +is number okay this is the the frequency + + align:start position:0% +is number okay this is the the frequency + + + align:start position:0% +is number okay this is the the frequency +that we observe some number of proteins + + align:start position:0% +that we observe some number of proteins + + + align:start position:0% +that we observe some number of proteins +this a + + align:start position:0% +this a + + + align:start position:0% +this a +frequency okay um and you know this is + + align:start position:0% +frequency okay um and you know this is + + + align:start position:0% +frequency okay um and you know this is +going to do + + align:start position:0% +going to do + + + align:start position:0% +going to do +something + + align:start position:0% +something + + + align:start position:0% +something +right so what you know what what if I it + + align:start position:0% +right so what you know what what if I it + + + align:start position:0% +right so what you know what what if I it +may not be a beautiful drawing but but + + align:start position:0% +may not be a beautiful drawing but but + + + align:start position:0% +may not be a beautiful drawing but but +you're supposed to know the answer um + + align:start position:0% +you're supposed to know the answer um + + + align:start position:0% +you're supposed to know the answer um +I'm trying to I'm trying to review + + align:start position:0% +I'm trying to I'm trying to review + + + align:start position:0% +I'm trying to I'm trying to review +things for you because I hear that you + + align:start position:0% +things for you because I hear that you + + + align:start position:0% +things for you because I hear that you +have a big exam coming up and I want to + + align:start position:0% +have a big exam coming up and I want to + + + align:start position:0% +have a big exam coming up and I want to +make sure that uh + + align:start position:0% + + + + align:start position:0% + +gamma it's a gamma right so this is U + + align:start position:0% +gamma it's a gamma right so this is U + + + align:start position:0% +gamma it's a gamma right so this is U +this is what + + align:start position:0% +this is what + + + align:start position:0% +this is what +we learned earlier so this is a gamma + + align:start position:0% +we learned earlier so this is a gamma + + + align:start position:0% +we learned earlier so this is a gamma +distribution and you should know what + + align:start position:0% +distribution and you should know what + + + align:start position:0% +distribution and you should know what +this gamma distribution looks like in + + align:start position:0% +this gamma distribution looks like in + + + align:start position:0% +this gamma distribution looks like in +particular there there are these two + + align:start position:0% +particular there there are these two + + + align:start position:0% +particular there there are these two +parameters describe the gamma + + align:start position:0% +parameters describe the gamma + + + align:start position:0% +parameters describe the gamma +distribution as a function of underlying + + align:start position:0% +distribution as a function of underlying + + + align:start position:0% +distribution as a function of underlying +parameters in the + + align:start position:0% + + + + align:start position:0% + +model maybe all right I I don't want to + + align:start position:0% +model maybe all right I I don't want to + + + align:start position:0% +model maybe all right I I don't want to +get get too much to this because I I + + align:start position:0% +get get too much to this because I I + + + align:start position:0% +get get too much to this because I I +because well on Thursday we spent a long + + align:start position:0% +because well on Thursday we spent a long + + + align:start position:0% +because well on Thursday we spent a long +time talking about it so you know once + + align:start position:0% +time talking about it so you know once + + + align:start position:0% +time talking about it so you know once +we get going we'll spend another long + + align:start position:0% +we get going we'll spend another long + + + align:start position:0% +we get going we'll spend another long +time talking about it again but uh but + + align:start position:0% +time talking about it again but uh but + + + align:start position:0% +time talking about it again but uh but +you should you should review uh review + + align:start position:0% +you should you should review uh review + + + align:start position:0% +you should you should review uh review +your notes from from Thursday before uh + + align:start position:0% +your notes from from Thursday before uh + + + align:start position:0% +your notes from from Thursday before uh +next before the exam + + align:start position:0% +next before the exam + + + align:start position:0% +next before the exam +okay um okay so this thing is gamma + + align:start position:0% +okay um okay so this thing is gamma + + + align:start position:0% +okay um okay so this thing is gamma +distributed and if we looked at the MRNA + + align:start position:0% +distributed and if we looked at the MRNA + + + align:start position:0% +distributed and if we looked at the MRNA +number as a function time we did a + + align:start position:0% +number as a function time we did a + + + align:start position:0% +number as a function time we did a +histogram of that the MRNA distribution + + align:start position:0% +histogram of that the MRNA distribution + + + align:start position:0% +histogram of that the MRNA distribution +would be + + align:start position:0% +would be + + + align:start position:0% +would be +what it's Plus on right so it's + + align:start position:0% +what it's Plus on right so it's + + + align:start position:0% +what it's Plus on right so it's +important remember that you + + align:start position:0% +important remember that you + + + align:start position:0% +important remember that you +know just because I tell you that oh the + + align:start position:0% +know just because I tell you that oh the + + + align:start position:0% +know just because I tell you that oh the +protein number is gamma distributed that + + align:start position:0% +protein number is gamma distributed that + + + align:start position:0% +protein number is gamma distributed that +doesn't immediately tell you exactly + + align:start position:0% +doesn't immediately tell you exactly + + + align:start position:0% +doesn't immediately tell you exactly +what you should be expecting for the uh + + align:start position:0% +what you should be expecting for the uh + + + align:start position:0% +what you should be expecting for the uh +the distribution of say the number of + + align:start position:0% +the distribution of say the number of + + + align:start position:0% +the distribution of say the number of +proteins is a function of time right I + + align:start position:0% +proteins is a function of time right I + + + align:start position:0% +proteins is a function of time right I +mean there are many different things I + + align:start position:0% +mean there are many different things I + + + align:start position:0% +mean there are many different things I +could have ploted over here they would + + align:start position:0% +could have ploted over here they would + + + align:start position:0% +could have ploted over here they would +all kind of come down to a gamma + + align:start position:0% +all kind of come down to a gamma + + + align:start position:0% +all kind of come down to a gamma +distribution over here right so it's + + align:start position:0% +distribution over here right so it's + + + align:start position:0% +distribution over here right so it's +important to kind of keep in mind the + + align:start position:0% +important to kind of keep in mind the + + + align:start position:0% +important to kind of keep in mind the +different representations that you might + + align:start position:0% +different representations that you might + + + align:start position:0% +different representations that you might +want to think about the data in + + align:start position:0% +want to think about the data in + + + align:start position:0% +want to think about the data in +okay um + + align:start position:0% + + + + align:start position:0% + +okay right so what we want to do now is + + align:start position:0% +okay right so what we want to do now is + + + align:start position:0% +okay right so what we want to do now is +we want to uh think a little bit more + + align:start position:0% +we want to uh think a little bit more + + + align:start position:0% +we want to uh think a little bit more +about this master equation in the + + align:start position:0% +about this master equation in the + + + align:start position:0% +about this master equation in the +context of um if we if we're going to + + align:start position:0% +context of um if we if we're going to + + + align:start position:0% +context of um if we if we're going to +divide it up into into these states now + + align:start position:0% +divide it up into into these states now + + + align:start position:0% +divide it up into into these states now +I would say that any time that you are + + align:start position:0% +I would say that any time that you are + + + align:start position:0% +I would say that any time that you are +asked to write down the the master + + align:start position:0% +asked to write down the the master + + + align:start position:0% +asked to write down the the master +equation for something right so + + align:start position:0% +equation for something right so + + + align:start position:0% +equation for something right so +now if how many how many equations will + + align:start position:0% +now if how many how many equations will + + + align:start position:0% +now if how many how many equations will +the master + + align:start position:0% +the master + + + align:start position:0% +the master +equation the how many yeah if I I say + + align:start position:0% +equation the how many yeah if I I say + + + align:start position:0% +equation the how many yeah if I I say +master equation but there's really more + + align:start position:0% +master equation but there's really more + + + align:start position:0% +master equation but there's really more +than one maybe so how many how many + + align:start position:0% +than one maybe so how many how many + + + align:start position:0% +than one maybe so how many how many +Master how many equations will be + + align:start position:0% +Master how many equations will be + + + align:start position:0% +Master how many equations will be +involved in the master equation dist uh + + align:start position:0% +involved in the master equation dist uh + + + align:start position:0% +involved in the master equation dist uh +kind of description of of this + + align:start position:0% + + + + align:start position:0% + +model infinitely many but there were + + align:start position:0% +model infinitely many but there were + + + align:start position:0% +model infinitely many but there were +infinitely many already when we had just + + align:start position:0% +infinitely many already when we had just + + + align:start position:0% +infinitely many already when we had just +one when we just had the MRNA + + align:start position:0% +one when we just had the MRNA + + + align:start position:0% +one when we just had the MRNA +distribution + + align:start position:0% +distribution + + + align:start position:0% +distribution +right well you know infinite times + + align:start position:0% +right well you know infinite times + + + align:start position:0% +right well you know infinite times +infinite is still infinite right so long + + align:start position:0% +infinite is still infinite right so long + + + align:start position:0% +infinite is still infinite right so long +as it's you know still it's a countably + + align:start position:0% +as it's you know still it's a countably + + + align:start position:0% +as it's you know still it's a countably +infinite number right okay but um yeah + + align:start position:0% +infinite number right okay but um yeah + + + align:start position:0% +infinite number right okay but um yeah +but it's still okay whatever you know + + align:start position:0% +but it's still okay whatever you know + + + align:start position:0% +but it's still okay whatever you know +still infinite always all right so what + + align:start position:0% +still infinite always all right so what + + + align:start position:0% +still infinite always all right so what +we want to do is uh divide up the states + + align:start position:0% +we want to do is uh divide up the states + + + align:start position:0% +we want to do is uh divide up the states +all right so you know when somebody asks + + align:start position:0% +all right so you know when somebody asks + + + align:start position:0% +all right so you know when somebody asks +you for you know the the equations + + align:start position:0% +you for you know the the equations + + + align:start position:0% +you for you know the the equations +describing how those probabilities are + + align:start position:0% +describing how those probabilities are + + + align:start position:0% +describing how those probabilities are +going to vary you know really what we're + + align:start position:0% +going to vary you know really what we're + + + align:start position:0% +going to vary you know really what we're +interested in is some derivative respect + + align:start position:0% +interested in is some derivative respect + + + align:start position:0% +interested in is some derivative respect +to time of some probabilities described + + align:start position:0% +to time of some probabilities described + + + align:start position:0% +to time of some probabilities described +by MN right we want know der respect of + + align:start position:0% +by MN right we want know der respect of + + + align:start position:0% +by MN right we want know der respect of +time right for all MNS right so that's + + align:start position:0% +time right for all MNS right so that's + + + align:start position:0% +time right for all MNS right so that's +why there are infinite number because M + + align:start position:0% +why there are infinite number because M + + + align:start position:0% +why there are infinite number because M +goes in One Direction n goes in another + + align:start position:0% +goes in One Direction n goes in another + + + align:start position:0% +goes in One Direction n goes in another +lots of them okay + + align:start position:0% +lots of them okay + + + align:start position:0% +lots of them okay +now it's always tempting to just write + + align:start position:0% +now it's always tempting to just write + + + align:start position:0% +now it's always tempting to just write +down this derivative and then and + + align:start position:0% +down this derivative and then and + + + align:start position:0% +down this derivative and then and +then just write down the equation uh if + + align:start position:0% +then just write down the equation uh if + + + align:start position:0% +then just write down the equation uh if +you can do that that's fine but I would + + align:start position:0% +you can do that that's fine but I would + + + align:start position:0% +you can do that that's fine but I would +recommend that in general what you do is + + align:start position:0% +recommend that in general what you do is + + + align:start position:0% +recommend that in general what you do is +you try to write a little chart out to + + align:start position:0% +you try to write a little chart out to + + + align:start position:0% +you try to write a little chart out to +keep track of what direction these + + align:start position:0% +keep track of what direction these + + + align:start position:0% +keep track of what direction these +things can go okay so for example here + + align:start position:0% +things can go okay so for example here + + + align:start position:0% +things can go okay so for example here +we have the probability of being the MN + + align:start position:0% +we have the probability of being the MN + + + align:start position:0% +we have the probability of being the MN +state right now there's going to be ways + + align:start position:0% +state right now there's going to be ways + + + align:start position:0% +state right now there's going to be ways +of going here and this is going to be + + align:start position:0% +of going here and this is going to be + + + align:start position:0% +of going here and this is going to be +going probability of being an m+ One + + align:start position:0% + + + + align:start position:0% + +n what I'm going to do is I'm going to + + align:start position:0% +n what I'm going to do is I'm going to + + + align:start position:0% +n what I'm going to do is I'm going to +give you uh just a couple minutes and in + + align:start position:0% +give you uh just a couple minutes and in + + + align:start position:0% +give you uh just a couple minutes and in +two minutes I want you to try to write + + align:start position:0% +two minutes I want you to try to write + + + align:start position:0% +two minutes I want you to try to write +down as many of the rates the fs and n's + + align:start position:0% +down as many of the rates the fs and n's + + + align:start position:0% +down as many of the rates the fs and n's +that correspond to all these transitions + + align:start position:0% +that correspond to all these transitions + + + align:start position:0% +that correspond to all these transitions +you may not be able to get through all + + align:start position:0% +you may not be able to get through all + + + align:start position:0% +you may not be able to get through all +of them but if you don't try to figure + + align:start position:0% +of them but if you don't try to figure + + + align:start position:0% +of them but if you don't try to figure +out some of them then you're going to + + align:start position:0% +out some of them then you're going to + + + align:start position:0% +out some of them then you're going to +have trouble doing it at later + + align:start position:0% + + + + align:start position:0% + +date all right all right do you + + align:start position:0% +date all right all right do you + + + align:start position:0% +date all right all right do you +understand what I'm asking you to + + align:start position:0% +understand what I'm asking you to + + + align:start position:0% +understand what I'm asking you to +do okay so next to each one of these + + align:start position:0% +do okay so next to each one of these + + + align:start position:0% +do okay so next to each one of these +arrows you should write + + align:start position:0% + + + + align:start position:0% + +something all right so I'll give you two + + align:start position:0% +something all right so I'll give you two + + + align:start position:0% +something all right so I'll give you two +minutes to to kind of do your best of of + + align:start position:0% +minutes to to kind of do your best of of + + + align:start position:0% +minutes to to kind of do your best of of +writing these things down for + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +that for + + align:start position:0% + + + + align:start position:0% + +all right why don't we uh why don't we + + align:start position:0% +all right why don't we uh why don't we + + + align:start position:0% +all right why don't we uh why don't we +reconvene and we'll uh we'll see see how + + align:start position:0% +reconvene and we'll uh we'll see see how + + + align:start position:0% +reconvene and we'll uh we'll see see how +we are um all right so this is uh this + + align:start position:0% +we are um all right so this is uh this + + + align:start position:0% +we are um all right so this is uh this +is very similar to what we did on + + align:start position:0% +is very similar to what we did on + + + align:start position:0% +is very similar to what we did on +Thursday right we have to remember that + + align:start position:0% +Thursday right we have to remember that + + + align:start position:0% +Thursday right we have to remember that +M's are the mras and this is what we uh + + align:start position:0% +M's are the mras and this is what we uh + + + align:start position:0% +M's are the mras and this is what we uh +this is what we solved before right + + align:start position:0% +this is what we solved before right + + + align:start position:0% +this is what we solved before right +where it's just a long long a row okay + + align:start position:0% +where it's just a long long a row okay + + + align:start position:0% +where it's just a long long a row okay +now + + align:start position:0% +now + + + align:start position:0% +now +first of all the MRNA distributions and + + align:start position:0% +first of all the MRNA distributions and + + + align:start position:0% +first of all the MRNA distributions and +the rates do they depend on the um on + + align:start position:0% +the rates do they depend on the um on + + + align:start position:0% +the rates do they depend on the um on +the protein + + align:start position:0% +the protein + + + align:start position:0% +the protein +numbers no so what does that mean about + + align:start position:0% +numbers no so what does that mean about + + + align:start position:0% +numbers no so what does that mean about +say this Arrow as compared to some the + + align:start position:0% +say this Arrow as compared to some the + + + align:start position:0% +say this Arrow as compared to some the +arrow that would be down well down here + + align:start position:0% +arrow that would be down well down here + + + align:start position:0% +arrow that would be down well down here +it's going to be the same right because + + align:start position:0% +it's going to be the same right because + + + align:start position:0% +it's going to be the same right because +n does not appear up in that equation + + align:start position:0% +n does not appear up in that equation + + + align:start position:0% +n does not appear up in that equation +describing mRNA okay if we had Auto + + align:start position:0% +describing mRNA okay if we had Auto + + + align:start position:0% +describing mRNA okay if we had Auto +regulation of some sort then it would + + align:start position:0% +regulation of some sort then it would + + + align:start position:0% +regulation of some sort then it would +okay but um that's helps all right so + + align:start position:0% +okay but um that's helps all right so + + + align:start position:0% +okay but um that's helps all right so +let's uh let's go through all right what + + align:start position:0% +let's uh let's go through all right what + + + align:start position:0% +let's uh let's go through all right what +we're going to do is we're going to do + + align:start position:0% +we're going to do is we're going to do + + + align:start position:0% +we're going to do is we're going to do +verbal yelling out okay ready this + + align:start position:0% + + + + align:start position:0% + +Arrow okay this one here is 32 1 km all + + align:start position:0% +Arrow okay this one here is 32 1 km all + + + align:start position:0% +Arrow okay this one here is 32 1 km all +right all right ready three 2 + + align:start position:0% +right all right ready three 2 + + + align:start position:0% +right all right ready three 2 +1 gamma M time + + align:start position:0% +1 gamma M time + + + align:start position:0% +1 gamma M time +M right 3 two + + align:start position:0% +M right 3 two + + + align:start position:0% +M right 3 two +1 gamma M * m + 1 okay now remember that + + align:start position:0% +1 gamma M * m + 1 okay now remember that + + + align:start position:0% +1 gamma M * m + 1 okay now remember that +there are more mRNA over here than there + + align:start position:0% +there are more mRNA over here than there + + + align:start position:0% +there are more mRNA over here than there +are here which means that the rate of + + align:start position:0% +are here which means that the rate of + + + align:start position:0% +are here which means that the rate of +degradation will increase + + align:start position:0% +degradation will increase + + + align:start position:0% +degradation will increase +right okay now uh coming here now this + + align:start position:0% +right okay now uh coming here now this + + + align:start position:0% +right okay now uh coming here now this +is talking about the creation and + + align:start position:0% +is talking about the creation and + + + align:start position:0% +is talking about the creation and +destruction of of the proteins changes + + align:start position:0% +destruction of of the proteins changes + + + align:start position:0% +destruction of of the proteins changes +in N all right this Arrow here already 3 + + align:start position:0% +in N all right this Arrow here already 3 + + + align:start position:0% +in N all right this Arrow here already 3 + + align:start position:0% + + + align:start position:0% +1 it's KP right times M right so this is + + align:start position:0% +1 it's KP right times M right so this is + + + align:start position:0% +1 it's KP right times M right so this is +the rate of creation right going from um + + align:start position:0% +the rate of creation right going from um + + + align:start position:0% +the rate of creation right going from um +right going from n minus one to n that's + + align:start position:0% +right going from n minus one to n that's + + + align:start position:0% +right going from n minus one to n that's +fine uh you know I I was looking at my + + align:start position:0% +fine uh you know I I was looking at my + + + align:start position:0% +fine uh you know I I was looking at my +notes from last year and I I got one of + + align:start position:0% +notes from last year and I I got one of + + + align:start position:0% +notes from last year and I I got one of +these things in correct so um right and + + align:start position:0% +these things in correct so um right and + + + align:start position:0% +these things in correct so um right and +then okay ready this one here three two + + align:start position:0% +then okay ready this one here three two + + + align:start position:0% +then okay ready this one here three two +one KP * m right so here it's the same + + align:start position:0% +one KP * m right so here it's the same + + + align:start position:0% +one KP * m right so here it's the same +rate and should we be surprised by that + + align:start position:0% +rate and should we be surprised by that + + + align:start position:0% +rate and should we be surprised by that +right so the number of proteins are + + align:start position:0% +right so the number of proteins are + + + align:start position:0% +right so the number of proteins are +changing but here it's the number of + + align:start position:0% +changing but here it's the number of + + + align:start position:0% +changing but here it's the number of +mRNA that matters because we're talking + + align:start position:0% +mRNA that matters because we're talking + + + align:start position:0% +mRNA that matters because we're talking +about the rate of translation right okay + + align:start position:0% +about the rate of translation right okay + + + align:start position:0% +about the rate of translation right okay +now uh this one here three two one + + align:start position:0% +now uh this one here three two one + + + align:start position:0% +now uh this one here three two one +gamma P * n and here 3 2 + + align:start position:0% +gamma P * n and here 3 2 + + + align:start position:0% +gamma P * n and here 3 2 +1 gamma P * n + 1 all right perfect now + + align:start position:0% +1 gamma P * n + 1 all right perfect now + + + align:start position:0% +1 gamma P * n + 1 all right perfect now +this is um of course as you can imagine + + align:start position:0% +this is um of course as you can imagine + + + align:start position:0% +this is um of course as you can imagine +the simplest possible kind of set of + + align:start position:0% +the simplest possible kind of set of + + + align:start position:0% +the simplest possible kind of set of +equations that we could have written + + align:start position:0% +equations that we could have written + + + align:start position:0% +equations that we could have written +down uh if you + + align:start position:0% +down uh if you + + + align:start position:0% +down uh if you +have other crazy things you get + + align:start position:0% +have other crazy things you get + + + align:start position:0% +have other crazy things you get +different distributions right if you + + align:start position:0% +different distributions right if you + + + align:start position:0% +different distributions right if you +have Auto regulation or if you have uh + + align:start position:0% +have Auto regulation or if you have uh + + + align:start position:0% +have Auto regulation or if you have uh +interactions of something with something + + align:start position:0% +interactions of something with something + + + align:start position:0% +interactions of something with something +else um or the same thing so forth but + + align:start position:0% +else um or the same thing so forth but + + + align:start position:0% +else um or the same thing so forth but +um it's uh I I think it's it's really + + align:start position:0% +um it's uh I I think it's it's really + + + align:start position:0% +um it's uh I I think it's it's really +very useful to to kind of write this + + align:start position:0% +very useful to to kind of write this + + + align:start position:0% +very useful to to kind of write this +thing down to to clarify to clarify your + + align:start position:0% +thing down to to clarify to clarify your + + + align:start position:0% +thing down to to clarify to clarify your +thinking in these in these problems you + + align:start position:0% +thinking in these in these problems you + + + align:start position:0% +thinking in these in these problems you +know and then you can and then you can + + align:start position:0% +know and then you can and then you can + + + align:start position:0% +know and then you can and then you can +kind of fill out for change of + + align:start position:0% +kind of fill out for change of + + + align:start position:0% +kind of fill out for change of +probability of MN you come here and you + + align:start position:0% +probability of MN you come here and you + + + align:start position:0% +probability of MN you come here and you +just go around and you count take all + + align:start position:0% +just go around and you count take all + + + align:start position:0% +just go around and you count take all +the arrows coming in and those are + + align:start position:0% +the arrows coming in and those are + + + align:start position:0% +the arrows coming in and those are +positive those are ways of increasing + + align:start position:0% +positive those are ways of increasing + + + align:start position:0% +positive those are ways of increasing +your probability right the ways going + + align:start position:0% +your probability right the ways going + + + align:start position:0% +your probability right the ways going +out are ways of decreasing your + + align:start position:0% +out are ways of decreasing your + + + align:start position:0% +out are ways of decreasing your +probability okay now in all those cases + + align:start position:0% +probability okay now in all those cases + + + align:start position:0% +probability okay now in all those cases +you have to multiply these raw rates by + + align:start position:0% +you have to multiply these raw rates by + + + align:start position:0% +you have to multiply these raw rates by +the probabilities of being in all these + + align:start position:0% +the probabilities of being in all these + + + align:start position:0% +the probabilities of being in all these +other + + align:start position:0% +other + + + align:start position:0% +other +states okay + + align:start position:0% + + + + align:start position:0% + +so can you use the master equation to + + align:start position:0% +so can you use the master equation to + + + align:start position:0% +so can you use the master equation to +get these + + align:start position:0% +get these + + + align:start position:0% +get these +probabilities uh if you're out of + + align:start position:0% +probabilities uh if you're out of + + + align:start position:0% +probabilities uh if you're out of +equilibrium out of steady + + align:start position:0% +equilibrium out of steady + + + align:start position:0% +equilibrium out of steady +state all right all right so that's + + align:start position:0% +state all right all right so that's + + + align:start position:0% +state all right all right so that's +question right so you know so the master + + align:start position:0% +question right so you know so the master + + + align:start position:0% +question right so you know so the master +equation useful out of steady state + + align:start position:0% + + + + align:start position:0% + +yes all right ready three two + + align:start position:0% +yes all right ready three two + + + align:start position:0% +yes all right ready three two +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +one all right so we + + align:start position:0% +one all right so we + + + align:start position:0% +one all right so we +got um a a fair number of so it + + align:start position:0% +got um a a fair number of so it + + + align:start position:0% +got um a a fair number of so it +um there there is some disagreement yeah + + align:start position:0% +um there there is some disagreement yeah + + + align:start position:0% +um there there is some disagreement yeah +so it actually the answer is yes okay + + align:start position:0% +so it actually the answer is yes okay + + + align:start position:0% +so it actually the answer is yes okay +and that's because you can start with + + align:start position:0% +and that's because you can start with + + + align:start position:0% +and that's because you can start with +any distribution of probabilities across + + align:start position:0% +any distribution of probabilities across + + + align:start position:0% +any distribution of probabilities across +all the states you'd like it could be + + align:start position:0% +all the states you'd like it could be + + + align:start position:0% +all the states you'd like it could be +that all of the probabilities at one + + align:start position:0% +that all of the probabilities at one + + + align:start position:0% +that all of the probabilities at one +state it could be that it's just however + + align:start position:0% +state it could be that it's just however + + + align:start position:0% +state it could be that it's just however +you like right and the master equation + + align:start position:0% +you like right and the master equation + + + align:start position:0% +you like right and the master equation +tells you about how that probability + + align:start position:0% +tells you about how that probability + + + align:start position:0% +tells you about how that probability +distribution will change over + + align:start position:0% +distribution will change over + + + align:start position:0% +distribution will change over +time okay now if you let that run + + align:start position:0% +time okay now if you let that run + + + align:start position:0% +time okay now if you let that run +forever then you come to some + + align:start position:0% +forever then you come to some + + + align:start position:0% +forever then you come to some +equilibrium steady state uh and that + + align:start position:0% +equilibrium steady state uh and that + + + align:start position:0% +equilibrium steady state uh and that +that tells and that's a very interesting + + align:start position:0% +that tells and that's a very interesting + + + align:start position:0% +that tells and that's a very interesting +quantity is the steady state + + align:start position:0% +quantity is the steady state + + + align:start position:0% +quantity is the steady state +distribution of these probabilities but + + align:start position:0% +distribution of these probabilities but + + + align:start position:0% +distribution of these probabilities but +you can actually calculate from uh from + + align:start position:0% +you can actually calculate from uh from + + + align:start position:0% +you can actually calculate from uh from +any initial distribution of + + align:start position:0% +any initial distribution of + + + align:start position:0% +any initial distribution of +probabilities evolving to any later time + + align:start position:0% +probabilities evolving to any later time + + + align:start position:0% +probabilities evolving to any later time +T what the probability would be + + align:start position:0% +T what the probability would be + + + align:start position:0% +T what the probability would be +later okay this comes to another + + align:start position:0% +later okay this comes to another + + + align:start position:0% +later okay this comes to another +question here + + align:start position:0% +question here + + + align:start position:0% +question here +all right so let's imagine that at time + + align:start position:0% +all right so let's imagine that at time + + + align:start position:0% +all right so let's imagine that at time +t equal to zero I tell you that there + + align:start position:0% +t equal to zero I tell you that there + + + align:start position:0% +t equal to zero I tell you that there +are M mRNA and + + align:start position:0% +are M mRNA and + + + align:start position:0% +are M mRNA and +P and not I I always do this this is I + + align:start position:0% +P and not I I always do this this is I + + + align:start position:0% +P and not I I always do this this is I +don't know somehow my brain does not + + align:start position:0% +don't know somehow my brain does not + + + align:start position:0% +don't know somehow my brain does not +like this okay and not right because the + + align:start position:0% +like this okay and not right because the + + + align:start position:0% +like this okay and not right because the +P's I want to be probabilities okay um + + align:start position:0% +P's I want to be probabilities okay um + + + align:start position:0% +P's I want to be probabilities okay um +all right we start with M mRNA n protein + + align:start position:0% +all right we start with M mRNA n protein + + + align:start position:0% +all right we start with M mRNA n protein +okay now we um you know in and maybe + + align:start position:0% +okay now we um you know in and maybe + + + align:start position:0% +okay now we um you know in and maybe +it's a complicated situation you know we + + align:start position:0% +it's a complicated situation you know we + + + align:start position:0% +it's a complicated situation you know we +can't calculate this analytically so + + align:start position:0% +can't calculate this analytically so + + + align:start position:0% +can't calculate this analytically so +what we do is we go to our computer and + + align:start position:0% +what we do is we go to our computer and + + + align:start position:0% +what we do is we go to our computer and +we have it solve how this probability + + align:start position:0% +we have it solve how this probability + + + align:start position:0% +we have it solve how this probability +distribution will evolve so that time t + + align:start position:0% +distribution will evolve so that time t + + + align:start position:0% +distribution will evolve so that time t +equal at some time if we'd like we could + + align:start position:0% +equal at some time if we'd like we could + + + align:start position:0% +equal at some time if we'd like we could +say this is T1 um I I'll tell you oh the + + align:start position:0% +say this is T1 um I I'll tell you oh the + + + align:start position:0% +say this is T1 um I I'll tell you oh the +probability of having M and N mRNA and + + align:start position:0% +probability of having M and N mRNA and + + + align:start position:0% +probability of having M and N mRNA and +protein is going to be equal to + + align:start position:0% +protein is going to be equal to + + + align:start position:0% +protein is going to be equal to +something P1 + + align:start position:0% +something P1 + + + align:start position:0% +something P1 +okay now the question is let's say I + + align:start position:0% +okay now the question is let's say I + + + align:start position:0% +okay now the question is let's say I +then go and I do this simulation again + + align:start position:0% +then go and I do this simulation again + + + align:start position:0% +then go and I do this simulation again +okay now I calculate some other at time + + align:start position:0% +okay now I calculate some other at time + + + align:start position:0% +okay now I calculate some other at time +T1 again the probability that you're in + + align:start position:0% +T1 again the probability that you're in + + + align:start position:0% +T1 again the probability that you're in +the MN State the question is will you + + align:start position:0% +the MN State the question is will you + + + align:start position:0% +the MN State the question is will you +again get + + align:start position:0% + + + + align:start position:0% + +P1 all right so this is a question mark + + align:start position:0% +P1 all right so this is a question mark + + + align:start position:0% +P1 all right so this is a question mark +and a is + + align:start position:0% +and a is + + + align:start position:0% +and a is +yes B is + + align:start position:0% + + + + align:start position:0% + +no right I'm going to give you 15 + + align:start position:0% +no right I'm going to give you 15 + + + align:start position:0% +no right I'm going to give you 15 +seconds uh I think that this is uh very + + align:start position:0% +seconds uh I think that this is uh very + + + align:start position:0% +seconds uh I think that this is uh very +important that you understand kind of + + align:start position:0% +important that you understand kind of + + + align:start position:0% +important that you understand kind of +what the master equation is doing and + + align:start position:0% +what the master equation is doing and + + + align:start position:0% +what the master equation is doing and +what it is not + + align:start position:0% + + + + align:start position:0% + +doing I'm sorry what's + + align:start position:0% +doing I'm sorry what's + + + align:start position:0% +doing I'm sorry what's +that right okay so I mean you know this + + align:start position:0% +that right okay so I mean you know this + + + align:start position:0% +that right okay so I mean you know this +is just uh you know uh you know you you + + align:start position:0% +is just uh you know uh you know you you + + + align:start position:0% +is just uh you know uh you know you you +program in your computer + + align:start position:0% +program in your computer + + + align:start position:0% +program in your computer +to solve this master you know this you + + align:start position:0% +to solve this master you know this you + + + align:start position:0% +to solve this master you know this you +know to use the master equation to solve + + align:start position:0% +know to use the master equation to solve + + + align:start position:0% +know to use the master equation to solve +how the probabilities are going to + + align:start position:0% +how the probabilities are going to + + + align:start position:0% +how the probabilities are going to +evolve right I'm tell I'm just telling + + align:start position:0% +evolve right I'm tell I'm just telling + + + align:start position:0% +evolve right I'm tell I'm just telling +you you start with some initial + + align:start position:0% +you you start with some initial + + + align:start position:0% +you you start with some initial +distribution and you if you do it once + + align:start position:0% +distribution and you if you do it once + + + align:start position:0% +distribution and you if you do it once +it says oh the probability that you're + + align:start position:0% +it says oh the probability that you're + + + align:start position:0% +it says oh the probability that you're +going to have M and you know this time + + align:start position:0% +going to have M and you know this time + + + align:start position:0% +going to have M and you know this time +you're going to have m m mRNA and + + align:start position:0% +you're going to have m m mRNA and + + + align:start position:0% +you're going to have m m mRNA and +proteins is going to be P1 says + + align:start position:0% +proteins is going to be P1 says + + + align:start position:0% +proteins is going to be P1 says +10% okay great now I'm asking just you + + align:start position:0% +10% okay great now I'm asking just you + + + align:start position:0% +10% okay great now I'm asking just you +know if you go back and do it again will + + align:start position:0% +know if you go back and do it again will + + + align:start position:0% +know if you go back and do it again will +you again get 10% or will or is um or is + + align:start position:0% +you again get 10% or will or is um or is + + + align:start position:0% +you again get 10% or will or is um or is +this output stochastic + + align:start position:0% + + + + align:start position:0% + +it's okay that if you're confused by + + align:start position:0% +it's okay that if you're confused by + + + align:start position:0% +it's okay that if you're confused by +this distinction um I think that it's + + align:start position:0% +this distinction um I think that it's + + + align:start position:0% +this distinction um I think that it's +easy to get confused by which is why I'm + + align:start position:0% +easy to get confused by which is why I'm + + + align:start position:0% +easy to get confused by which is why I'm +doing this but all right let's let's + + align:start position:0% +doing this but all right let's let's + + + align:start position:0% +doing this but all right let's let's +just see where we are ready three two + + align:start position:0% +just see where we are ready three two + + + align:start position:0% +just see where we are ready three two +one okay um all right so I'd say a + + align:start position:0% +one okay um all right so I'd say a + + + align:start position:0% +one okay um all right so I'd say a +majority again you know but we're kind + + align:start position:0% +majority again you know but we're kind + + + align:start position:0% +majority again you know but we're kind +of at the 8020 75 25 a majority here are + + align:start position:0% +of at the 8020 75 25 a majority here are + + + align:start position:0% +of at the 8020 75 25 a majority here are +saying that uh yes you will get the same + + align:start position:0% +saying that uh yes you will get the same + + + align:start position:0% +saying that uh yes you will get the same +prob ility okay uh and this is uh very + + align:start position:0% +prob ility okay uh and this is uh very + + + align:start position:0% +prob ility okay uh and this is uh very +important that we understand um kind of + + align:start position:0% +important that we understand um kind of + + + align:start position:0% +important that we understand um kind of +where this you know where the + + align:start position:0% +where this you know where the + + + align:start position:0% +where this you know where the +stochasticity is somehow embedded in + + align:start position:0% +stochasticity is somehow embedded in + + + align:start position:0% +stochasticity is somehow embedded in +these different uh representations of + + align:start position:0% +these different uh representations of + + + align:start position:0% +these different uh representations of +this of these modelings right + + align:start position:0% +this of these modelings right + + + align:start position:0% +this of these modelings right +so this this the master equation right + + align:start position:0% +so this this the master equation right + + + align:start position:0% +so this this the master equation right +it's a set of differential equations + + align:start position:0% +it's a set of differential equations + + + align:start position:0% +it's a set of differential equations +telling you about how the probabilities + + align:start position:0% +telling you about how the probabilities + + + align:start position:0% +telling you about how the probabilities +change over time given some initial + + align:start position:0% +change over time given some initial + + + align:start position:0% +change over time given some initial +conditions right now we're using these + + align:start position:0% +conditions right now we're using these + + + align:start position:0% +conditions right now we're using these +things to calculate the evolution of + + align:start position:0% +things to calculate the evolution of + + + align:start position:0% +things to calculate the evolution of +some random process but the + + align:start position:0% +some random process but the + + + align:start position:0% +some random process but the +probabilities themselves evolve + + align:start position:0% + + + + align:start position:0% + +deterministically + + align:start position:0% +deterministically + + + align:start position:0% +deterministically +okay so what that means is that although + + align:start position:0% +okay so what that means is that although + + + align:start position:0% +okay so what that means is that although +these things are + + align:start position:0% +these things are + + + align:start position:0% +these things are +probabilities if you do if you start + + align:start position:0% +probabilities if you do if you start + + + align:start position:0% +probabilities if you do if you start +somewhere and you use the master + + align:start position:0% +somewhere and you use the master + + + align:start position:0% +somewhere and you use the master +equation to solve you get the same thing + + align:start position:0% +equation to solve you get the same thing + + + align:start position:0% +equation to solve you get the same thing +every time you do it okay now this is + + align:start position:0% +every time you do it okay now this is + + + align:start position:0% +every time you do it okay now this is +not true for the Gillespie simulation + + align:start position:0% +not true for the Gillespie simulation + + + align:start position:0% +not true for the Gillespie simulation +because that you're looking at an + + align:start position:0% +because that you're looking at an + + + align:start position:0% +because that you're looking at an +individual trajectory right an + + align:start position:0% +individual trajectory right an + + + align:start position:0% +individual trajectory right an +individual trajectory then the then the + + align:start position:0% +individual trajectory then the then the + + + align:start position:0% +individual trajectory then the then the +the stochasticity is embedded in that + + align:start position:0% +the stochasticity is embedded in that + + + align:start position:0% +the stochasticity is embedded in that +trajectory trory + + align:start position:0% +trajectory trory + + + align:start position:0% +trajectory trory +itself right whereas in the master + + align:start position:0% +itself right whereas in the master + + + align:start position:0% +itself right whereas in the master +equation the stochasticity arises + + align:start position:0% +equation the stochasticity arises + + + align:start position:0% +equation the stochasticity arises +because these are probabilities they + + align:start position:0% +because these are probabilities they + + + align:start position:0% +because these are probabilities they +calculating and so any individual + + align:start position:0% +calculating and so any individual + + + align:start position:0% +calculating and so any individual +instantiation will be probabilistic as + + align:start position:0% +instantiation will be probabilistic as + + + align:start position:0% +instantiation will be probabilistic as +you are sampling from uh those different + + align:start position:0% +you are sampling from uh those different + + + align:start position:0% +you are sampling from uh those different +probability + + align:start position:0% +probability + + + align:start position:0% +probability +distributions + + align:start position:0% +distributions + + + align:start position:0% +distributions +okay now this is I think a sufficiently + + align:start position:0% +okay now this is I think a sufficiently + + + align:start position:0% +okay now this is I think a sufficiently +important point that if there are + + align:start position:0% +important point that if there are + + + align:start position:0% +important point that if there are +questions about it we + + align:start position:0% +questions about it we + + + align:start position:0% +questions about it we +should talk about + + align:start position:0% + + + + align:start position:0% + +it yeah how do you make + + align:start position:0% +it yeah how do you make + + + align:start position:0% +it yeah how do you make +simulations would you essentially can + + align:start position:0% +simulations would you essentially can + + + align:start position:0% +simulations would you essentially can +you take a over + + align:start position:0% +you take a over + + + align:start position:0% +you take a over +different okay so it's true that you can + + align:start position:0% +different okay so it's true that you can + + + align:start position:0% +different okay so it's true that you can +you can do a sum over different gaspie + + align:start position:0% +you can do a sum over different gaspie + + + align:start position:0% +you can do a sum over different gaspie +no but I we haven't yet told you about + + align:start position:0% +no but I we haven't yet told you about + + + align:start position:0% +no but I we haven't yet told you about +what the gaspie algorithm is so I'm you + + align:start position:0% +what the gaspie algorithm is so I'm you + + + align:start position:0% +what the gaspie algorithm is so I'm you +know so I can't use that but um but + + align:start position:0% +know so I can't use that but um but + + + align:start position:0% +know so I can't use that but um but +indeed uh you can just use a standard + + align:start position:0% +indeed uh you can just use a standard + + + align:start position:0% +indeed uh you can just use a standard +solver of differential + + align:start position:0% +solver of differential + + + align:start position:0% +solver of differential +equations right so whatever program you + + align:start position:0% +equations right so whatever program you + + + align:start position:0% +equations right so whatever program you +use is going to have some way of doing + + align:start position:0% +use is going to have some way of doing + + + align:start position:0% +use is going to have some way of doing +this right um and and once you've + + align:start position:0% +this right um and and once you've + + + align:start position:0% +this right um and and once you've +written down these equations the fact + + align:start position:0% +written down these equations the fact + + + align:start position:0% +written down these equations the fact +that these are actually probabilities + + align:start position:0% +that these are actually probabilities + + + align:start position:0% +that these are actually probabilities +doesn't matter right so those could have + + align:start position:0% +doesn't matter right so those could have + + + align:start position:0% +doesn't matter right so those could have +been something else right so this this + + align:start position:0% +been something else right so this this + + + align:start position:0% +been something else right so this this +could be the number of eggs on what + + align:start position:0% +could be the number of eggs on what + + + align:start position:0% +could be the number of eggs on what +whatever right um so then uh so yeah + + align:start position:0% +whatever right um so then uh so yeah + + + align:start position:0% +whatever right um so then uh so yeah +once you once you've gotten the + + align:start position:0% +once you once you've gotten the + + + align:start position:0% +once you once you've gotten the +equations then the equations just tell + + align:start position:0% +equations then the equations just tell + + + align:start position:0% +equations then the equations just tell +you how the probabilities are going to + + align:start position:0% +you how the probabilities are going to + + + align:start position:0% +you how the probabilities are going to +change over + + align:start position:0% +change over + + + align:start position:0% +change over +time yeah this maybe this is a silly + + align:start position:0% +time yeah this maybe this is a silly + + + align:start position:0% +time yeah this maybe this is a silly +question but in practice do do you have + + align:start position:0% +question but in practice do do you have + + + align:start position:0% +question but in practice do do you have +to like + + align:start position:0% +to like + + + align:start position:0% +to like +assume there all the probabilties zero + + align:start position:0% +assume there all the probabilties zero + + + align:start position:0% +assume there all the probabilties zero +above some number oh no it's not at all + + align:start position:0% +above some number oh no it's not at all + + + align:start position:0% +above some number oh no it's not at all +a silly question um right so um yeah + + align:start position:0% +a silly question um right so um yeah + + + align:start position:0% +a silly question um right so um yeah +because because you know Compu Sol + + align:start position:0% +because because you know Compu Sol + + + align:start position:0% +because because you know Compu Sol +exactly right um and uh yes no that's a + + align:start position:0% +exactly right um and uh yes no that's a + + + align:start position:0% +exactly right um and uh yes no that's a +very that's a very good question uh and + + align:start position:0% +very that's a very good question uh and + + + align:start position:0% +very that's a very good question uh and +right so I told you this an infinite set + + align:start position:0% +right so I told you this an infinite set + + + align:start position:0% +right so I told you this an infinite set +of differential equations and U but you + + align:start position:0% +of differential equations and U but you + + + align:start position:0% +of differential equations and U but you +know but at the same time I told you + + align:start position:0% +know but at the same time I told you + + + align:start position:0% +know but at the same time I told you +this master equation is supposed to be + + align:start position:0% +this master equation is supposed to be + + + align:start position:0% +this master equation is supposed to be +useful for something right and um kind + + align:start position:0% +useful for something right and um kind + + + align:start position:0% +useful for something right and um kind +of at the face of it these are + + align:start position:0% +of at the face of it these are + + + align:start position:0% +of at the face of it these are +incompatible ideas right uh and and the + + align:start position:0% +incompatible ideas right uh and and the + + + align:start position:0% +incompatible ideas right uh and and the +basic answer is that um you you have to + + align:start position:0% +basic answer is that um you you have to + + + align:start position:0% +basic answer is that um you you have to +you have to include all the states where + + align:start position:0% +you have to include all the states where + + + align:start position:0% +you have to include all the states where +there is a you know sort of + + align:start position:0% +there is a you know sort of + + + align:start position:0% +there is a you know sort of +non-negligible probability okay now uh + + align:start position:0% +non-negligible probability okay now uh + + + align:start position:0% +non-negligible probability okay now uh +let's let's we can be concrete though so + + align:start position:0% +let's let's we can be concrete though so + + + align:start position:0% +let's let's we can be concrete though so +let's let's imagine that we have that I + + align:start position:0% +let's let's imagine that we have that I + + + align:start position:0% +let's let's imagine that we have that I +tell you we want to look at the MRNA + + align:start position:0% +tell you we want to look at the MRNA + + + align:start position:0% +tell you we want to look at the MRNA +number + + align:start position:0% +number + + + align:start position:0% +number +here okay and I tell you that okay km is + + align:start position:0% +here okay and I tell you that okay km is + + + align:start position:0% +here okay and I tell you that okay km is +equal + + align:start position:0% + + + + align:start position:0% + +to um well okay well let me make sure + + align:start position:0% +to um well okay well let me make sure + + + align:start position:0% +to um well okay well let me make sure +okay gam M all right what are typical + + align:start position:0% +okay gam M all right what are typical + + + align:start position:0% +okay gam M all right what are typical +lifetimes of mras in in bacteria again + + align:start position:0% +lifetimes of mras in in bacteria again + + + align:start position:0% +lifetimes of mras in in bacteria again +right order a minute so so that that + + align:start position:0% +right order a minute so so that that + + + align:start position:0% +right order a minute so so that that +means that we let's say this is + + align:start position:0% +means that we let's say this is + + + align:start position:0% +means that we let's say this is +0.5 + + align:start position:0% +0.5 + + + align:start position:0% +0.5 +minutes to the minus + + align:start position:0% +minutes to the minus + + + align:start position:0% +minutes to the minus +one right to give a lifetime + + align:start position:0% +one right to give a lifetime + + + align:start position:0% +one right to give a lifetime +of around two minutes okay um all right + + align:start position:0% +of around two minutes okay um all right + + + align:start position:0% +of around two minutes okay um all right +and then let's imagine that this is then + + align:start position:0% +and then let's imagine that this is then + + + align:start position:0% +and then let's imagine that this is then +all right 50 per + + align:start position:0% + + + + align:start position:0% + +minute all right so an mRNA is kind of + + align:start position:0% +minute all right so an mRNA is kind of + + + align:start position:0% +minute all right so an mRNA is kind of +made once a minute uh there's 50 of them + + align:start position:0% +made once a minute uh there's 50 of them + + + align:start position:0% +made once a minute uh there's 50 of them +that's a lot but all right whatever + + align:start position:0% +that's a lot but all right whatever + + + align:start position:0% +that's a lot but all right whatever +there are a few genes all right I I + + align:start position:0% +there are a few genes all right I I + + + align:start position:0% +there are a few genes all right I I +wanted to number to be something you all + + align:start position:0% +wanted to number to be something you all + + + align:start position:0% +wanted to number to be something you all +right so this a fair rate of mRNA + + align:start position:0% +right so this a fair rate of mRNA + + + align:start position:0% +right so this a fair rate of mRNA +production okay now um how many + + align:start position:0% +production okay now um how many + + + align:start position:0% +production okay now um how many +equations do you think you might uh need + + align:start position:0% +equations do you think you might uh need + + + align:start position:0% +equations do you think you might uh need +to + + align:start position:0% +to + + + align:start position:0% +to +simulate all right so we'll think about + + align:start position:0% +simulate all right so we'll think about + + + align:start position:0% +simulate all right so we'll think about +this first of all does it depend upon + + align:start position:0% +this first of all does it depend upon + + + align:start position:0% +this first of all does it depend upon +the initial conditions or + + align:start position:0% + + + + align:start position:0% + +not yeah it does so okay so so be + + align:start position:0% +not yeah it does so okay so so be + + + align:start position:0% +not yeah it does so okay so so be +careful right + + align:start position:0% +careful right + + + align:start position:0% +careful right +um in particular okay but let's say that + + align:start position:0% +um in particular okay but let's say that + + + align:start position:0% +um in particular okay but let's say that +I tell you that we + + align:start position:0% +I tell you that we + + + align:start position:0% +I tell you that we +start with 50 mRNA right the question is + + align:start position:0% +start with 50 mRNA right the question is + + + align:start position:0% +start with 50 mRNA right the question is +how many equations do you think you + + align:start position:0% +how many equations do you think you + + + align:start position:0% +how many equations do you think you +might have to write down and let's say + + align:start position:0% +might have to write down and let's say + + + align:start position:0% +might have to write down and let's say +we want to we want to understand this + + align:start position:0% +we want to we want to understand this + + + align:start position:0% +we want to we want to understand this +you know you know once it gets to say + + align:start position:0% +you know you know once it gets to say + + + align:start position:0% +you know you know once it gets to say +the + + align:start position:0% +the + + + align:start position:0% +the +equilibrium okay all right number of + + align:start position:0% + + + + align:start position:0% + +equations all right give me give me a + + align:start position:0% +equations all right give me give me a + + + align:start position:0% +equations all right give me give me a +moment to come up with some reasonable + + align:start position:0% +moment to come up with some reasonable + + + align:start position:0% +moment to come up with some reasonable +options uh + + align:start position:0% + + + + align:start position:0% + +all right well these are + + align:start position:0% + + + + align:start position:0% + +um so if you were to actually I mean + + align:start position:0% +um so if you were to actually I mean + + + align:start position:0% +um so if you were to actually I mean +let's say that you know this could show + + align:start position:0% +let's say that you know this could show + + + align:start position:0% +let's say that you know this could show +up on your homework right so the + + align:start position:0% +up on your homework right so the + + + align:start position:0% +up on your homework right so the +question is how many equations are you + + align:start position:0% +question is how many equations are you + + + align:start position:0% +question is how many equations are you +going to program into your um into your + + align:start position:0% +going to program into your um into your + + + align:start position:0% +going to program into your um into your +simulation um and it may be you know + + align:start position:0% +simulation um and it may be you know + + + align:start position:0% +simulation um and it may be you know +doesn't have to be exactly any of these + + align:start position:0% +doesn't have to be exactly any of these + + + align:start position:0% +doesn't have to be exactly any of these +numbers but you know + + align:start position:0% + + + + align:start position:0% + +order do you guys understand the + + align:start position:0% + + + + align:start position:0% + +question all right so we need a + + align:start position:0% +question all right so we need a + + + align:start position:0% +question all right so we need a +different equation for each of these um + + align:start position:0% +different equation for each of these um + + + align:start position:0% +different equation for each of these um +each of these probabilities right so in + + align:start position:0% +each of these probabilities right so in + + + align:start position:0% +each of these probabilities right so in +principle we have uh an the master + + align:start position:0% +principle we have uh an the master + + + align:start position:0% +principle we have uh an the master +equation gives us an infinite number of + + align:start position:0% +equation gives us an infinite number of + + + align:start position:0% +equation gives us an infinite number of +equations right so we have D the + + align:start position:0% +equations right so we have D the + + + align:start position:0% +equations right so we have D the +probability of having zero mRNA with + + align:start position:0% +probability of having zero mRNA with + + + align:start position:0% +probability of having zero mRNA with +respect to time right that's going to + + align:start position:0% +respect to time right that's going to + + + align:start position:0% +respect to time right that's going to +be does anybody any idea what this is + + align:start position:0% +be does anybody any idea what this is + + + align:start position:0% +be does anybody any idea what this is +going to + + align:start position:0% + + + + align:start position:0% + +be right so we have a minus + + align:start position:0% +be right so we have a minus + + + align:start position:0% +be right so we have a minus +km times + + align:start position:0% + + + + align:start position:0% + +what time p 0 right so this is cuz you + + align:start position:0% +what time p 0 right so this is cuz you + + + align:start position:0% +what time p 0 right so this is cuz you +know if we start out down here p 0 now + + align:start position:0% +know if we start out down here p 0 now + + + align:start position:0% +know if we start out down here p 0 now +we have + + align:start position:0% +we have + + + align:start position:0% +we have +km all right so I I was just about to + + align:start position:0% +km all right so I I was just about to + + + align:start position:0% +km all right so I I was just about to +violate my rule and just write down an + + align:start position:0% +violate my rule and just write down an + + + align:start position:0% +violate my rule and just write down an +equation without drawing this thing but + + align:start position:0% +equation without drawing this thing but + + + align:start position:0% +equation without drawing this thing but +um right so it's you know it's km time + + align:start position:0% +um right so it's you know it's km time + + + align:start position:0% +um right so it's you know it's km time +P0 that's a way you lose probability but + + align:start position:0% +P0 that's a way you lose probability but + + + align:start position:0% +P0 that's a way you lose probability but +you can also gain probability right at a + + align:start position:0% +you can also gain probability right at a + + + align:start position:0% +you can also gain probability right at a +rate that is goes as gamma M + + align:start position:0% +rate that is goes as gamma M + + + align:start position:0% +rate that is goes as gamma M +times P1 + + align:start position:0% + + + + align:start position:0% + +okay all right so that's that's that's + + align:start position:0% +okay all right so that's that's that's + + + align:start position:0% +okay all right so that's that's that's +how this probability is going to change + + align:start position:0% +how this probability is going to change + + + align:start position:0% +how this probability is going to change +over time but we have a different + + align:start position:0% +over time but we have a different + + + align:start position:0% +over time but we have a different +equation for for P1 for P2 for P3 for P4 + + align:start position:0% +equation for for P1 for P2 for P3 for P4 + + + align:start position:0% +equation for for P1 for P2 for P3 for P4 +all the way in principle to P you know + + align:start position:0% +all the way in principle to P you know + + + align:start position:0% +all the way in principle to P you know +1,683 th000 blah blah blah right so + + align:start position:0% +1,683 th000 blah blah blah right so + + + align:start position:0% +1,683 th000 blah blah blah right so +that's problematic right because if we + + align:start position:0% +that's problematic right because if we + + + align:start position:0% +that's problematic right because if we +have to actually in our program code up + + align:start position:0% +have to actually in our program code up + + + align:start position:0% +have to actually in our program code up +you know a 100 million equations or or + + align:start position:0% +you know a 100 million equations or or + + + align:start position:0% +you know a 100 million equations or or +could be worse right you know uh then + + align:start position:0% +could be worse right you know uh then + + + align:start position:0% +could be worse right you know uh then +then then you know we're going to have + + align:start position:0% +then then you know we're going to have + + + align:start position:0% +then then you know we're going to have +trouble with with our with our computers + + align:start position:0% +trouble with with our with our computers + + + align:start position:0% +trouble with with our with our computers +right so so you always have to have some + + align:start position:0% +right so so you always have to have some + + + align:start position:0% +right so so you always have to have some +notion + + align:start position:0% +notion + + + align:start position:0% +notion +of what you should be doing and this + + align:start position:0% +of what you should be doing and this + + + align:start position:0% +of what you should be doing and this +also highlights that uh it it's it's + + align:start position:0% +also highlights that uh it it's it's + + + align:start position:0% +also highlights that uh it it's it's +really important to have some intuitive + + align:start position:0% +really important to have some intuitive + + + align:start position:0% +really important to have some intuitive +notion of what's going on in your system + + align:start position:0% +notion of what's going on in your system + + + align:start position:0% +notion of what's going on in your system +uh before you go and you start + + align:start position:0% +uh before you go and you start + + + align:start position:0% +uh before you go and you start +programming right because uh other if + + align:start position:0% +programming right because uh other if + + + align:start position:0% +programming right because uh other if +you know in that case well you're likely + + align:start position:0% +you know in that case well you're likely + + + align:start position:0% +you know in that case well you're likely +to write down something that's wrong you + + align:start position:0% +to write down something that's wrong you + + + align:start position:0% +to write down something that's wrong you +won't know if you have the right answer + + align:start position:0% +won't know if you have the right answer + + + align:start position:0% +won't know if you have the right answer +and you might do you know do something + + align:start position:0% +and you might do you know do something + + + align:start position:0% +and you might do you know do something +that doesn't make any sense right so um + + align:start position:0% +that doesn't make any sense right so um + + + align:start position:0% +that doesn't make any sense right so um +yeah so you have to have some notion of + + align:start position:0% +yeah so you have to have some notion of + + + align:start position:0% +yeah so you have to have some notion of +what what the system should look like + + align:start position:0% +what what the system should look like + + + align:start position:0% +what what the system should look like +before you even start um start coding + + align:start position:0% +before you even start um start coding + + + align:start position:0% +before you even start um start coding +it + + align:start position:0% + + + + align:start position:0% + +okay my question is how many how many of + + align:start position:0% +okay my question is how many how many of + + + align:start position:0% +okay my question is how many how many of +these equations should we + + align:start position:0% + + + + align:start position:0% + +simulate all right okay okay let's uh + + align:start position:0% +simulate all right okay okay let's uh + + + align:start position:0% +simulate all right okay okay let's uh +let let's let's just see where we are + + align:start position:0% +let let's let's just see where we are + + + align:start position:0% +let let's let's just see where we are +ready three two one + + align:start position:0% + + + + align:start position:0% + +okay so I'd say that we have um you know + + align:start position:0% +okay so I'd say that we have um you know + + + align:start position:0% +okay so I'd say that we have um you know +you know it's basically between C and D + + align:start position:0% +you know it's basically between C and D + + + align:start position:0% +you know it's basically between C and D +yeah um you know I would say uh you know + + align:start position:0% +yeah um you know I would say uh you know + + + align:start position:0% +yeah um you know I would say uh you know +some people are maybe more careful than + + align:start position:0% +some people are maybe more careful than + + + align:start position:0% +some people are maybe more careful than +I am all right can can one of the D's uh + + align:start position:0% +I am all right can can one of the D's uh + + + align:start position:0% +I am all right can can one of the D's uh +maybe defend why why they're saying + + align:start position:0% + + + + align:start position:0% + +D + + align:start position:0% + + + + align:start position:0% + +number okay the mean is 100 and when you + + align:start position:0% +number okay the mean is 100 and when you + + + align:start position:0% +number okay the mean is 100 and when you +say I mean I think that whatever you're + + align:start position:0% +say I mean I think that whatever you're + + + align:start position:0% +say I mean I think that whatever you're +thinking is correct but I think that the + + align:start position:0% +thinking is correct but I think that the + + + align:start position:0% +thinking is correct but I think that the +the words are a little dangerous why and + + align:start position:0% +the words are a little dangerous why and + + + align:start position:0% +the words are a little dangerous why and +why am I concerned about you said + + align:start position:0% + + + + align:start position:0% + +the okay I mean is is the mean 100 for + + align:start position:0% +the okay I mean is is the mean 100 for + + + align:start position:0% +the okay I mean is is the mean 100 for +all + + align:start position:0% + + + + align:start position:0% + +time steady + + align:start position:0% +time steady + + + align:start position:0% +time steady +St at steady state right I think that + + align:start position:0% +St at steady state right I think that + + + align:start position:0% +St at steady state right I think that +that that was the key you know it's just + + align:start position:0% +that that was the key you know it's just + + + align:start position:0% +that that was the key you know it's just +that yeah so um for long times the the + + align:start position:0% +that yeah so um for long times the the + + + align:start position:0% +that yeah so um for long times the the +mean number of mRNA will indeed be 100 + + align:start position:0% +mean number of mRNA will indeed be 100 + + + align:start position:0% +mean number of mRNA will indeed be 100 +right so the mean number of m in this + + align:start position:0% +right so the mean number of m in this + + + align:start position:0% +right so the mean number of m in this +case will be km / gamma M which is going + + align:start position:0% +case will be km / gamma M which is going + + + align:start position:0% +case will be km / gamma M which is going +to be equal to 50 ID that that gives us + + align:start position:0% +to be equal to 50 ID that that gives us + + + align:start position:0% +to be equal to 50 ID that that gives us +100 okay now will it be exactly + + align:start position:0% +100 okay now will it be exactly + + + align:start position:0% +100 okay now will it be exactly +100 no it's going to be 100 plus or + + align:start position:0% +100 no it's going to be 100 plus or + + + align:start position:0% +100 no it's going to be 100 plus or +minus + + align:start position:0% +minus + + + align:start position:0% +minus +what plus or minus 10 right because this + + align:start position:0% +what plus or minus 10 right because this + + + align:start position:0% +what plus or minus 10 right because this +distribution at steady state is + + align:start position:0% +distribution at steady state is + + + align:start position:0% +distribution at steady state is +what it's Pon what's the variance of a + + align:start position:0% +what it's Pon what's the variance of a + + + align:start position:0% +what it's Pon what's the variance of a +Pon distribution + + align:start position:0% +Pon distribution + + + align:start position:0% +Pon distribution +it's equal to the mean okay so for Plus + + align:start position:0% +it's equal to the mean okay so for Plus + + + align:start position:0% +it's equal to the mean okay so for Plus +on the variance is equal to the + + align:start position:0% +on the variance is equal to the + + + align:start position:0% +on the variance is equal to the +mean right variance is the square of the + + align:start position:0% +mean right variance is the square of the + + + align:start position:0% +mean right variance is the square of the +standard deviation right which means + + align:start position:0% +standard deviation right which means + + + align:start position:0% +standard deviation right which means +that this is going to be plus or minus + + align:start position:0% + + + + align:start position:0% + +10 that's kind of the typical width of + + align:start position:0% +10 that's kind of the typical width of + + + align:start position:0% +10 that's kind of the typical width of +the distribution right so what means is + + align:start position:0% +the distribution right so what means is + + + align:start position:0% +the distribution right so what means is +that at + + align:start position:0% +that at + + + align:start position:0% +that at +equilibrium we're going to be at + + align:start position:0% +equilibrium we're going to be at + + + align:start position:0% +equilibrium we're going to be at +100 and it's going to kind of look like + + align:start position:0% +100 and it's going to kind of look like + + + align:start position:0% +100 and it's going to kind of look like +this all right so this is you + + align:start position:0% + + + + align:start position:0% + +know this might be two Sigma so this + + align:start position:0% +know this might be two Sigma so this + + + align:start position:0% +know this might be two Sigma so this +could be 20 but you know each of these + + align:start position:0% +could be 20 but you know each of these + + + align:start position:0% +could be 20 but you know each of these +is 10 all + + align:start position:0% +is 10 all + + + align:start position:0% +is 10 all +right so if if you want to capture this + + align:start position:0% +right so if if you want to capture this + + + align:start position:0% +right so if if you want to capture this +that you you might want to go out to a + + align:start position:0% +that you you might want to go out to a + + + align:start position:0% +that you you might want to go out to a +few Sigma + + align:start position:0% +few Sigma + + + align:start position:0% +few Sigma +right right so let's say you want to go + + align:start position:0% +right right so let's say you want to go + + + align:start position:0% +right right so let's say you want to go +out to three sigma then you might want + + align:start position:0% +out to three sigma then you might want + + + align:start position:0% +out to three sigma then you might want +to get out to 130 + + align:start position:0% +to get out to 130 + + + align:start position:0% +to get out to 130 +maybe right you know so then if you want + + align:start position:0% +maybe right you know so then if you want + + + align:start position:0% +maybe right you know so then if you want +to be more careful you got to 140 150 + + align:start position:0% +to be more careful you got to 140 150 + + + align:start position:0% +to be more careful you got to 140 150 +but this thing is going to Decay + + align:start position:0% +but this thing is going to Decay + + + align:start position:0% +but this thing is going to Decay +exponentially right so you don't need to + + align:start position:0% +exponentially right so you don't need to + + + align:start position:0% +exponentially right so you don't need to +go up to a + + align:start position:0% +go up to a + + + align:start position:0% +go up to a +th right cuz the probability is going to + + align:start position:0% +th right cuz the probability is going to + + + align:start position:0% +th right cuz the probability is going to +be 0 0 0 certainly once you're at 200 I + + align:start position:0% +be 0 0 0 certainly once you're at 200 I + + + align:start position:0% +be 0 0 0 certainly once you're at 200 I +say don't have to worry about it okay + + align:start position:0% +say don't have to worry about it okay + + + align:start position:0% +say don't have to worry about it okay +but of course you have to remember the + + align:start position:0% +but of course you have to remember the + + + align:start position:0% +but of course you have to remember the +initial condition we started at + + align:start position:0% + + + + align:start position:0% + +50 okay so we started at at this point + + align:start position:0% +50 okay so we started at at this point + + + align:start position:0% +50 okay so we started at at this point +which means we definitely have to + + align:start position:0% +which means we definitely have to + + + align:start position:0% +which means we definitely have to +include that equation otherwise we're in + + align:start position:0% +include that equation otherwise we're in + + + align:start position:0% +include that equation otherwise we're in +trouble right now how much do we have to + + align:start position:0% +trouble right now how much do we have to + + + align:start position:0% +trouble right now how much do we have to +go to the um kind of below + + align:start position:0% +go to the um kind of below + + + align:start position:0% +go to the um kind of below +50 any + + align:start position:0% + + + + align:start position:0% + +my guess would be would be not much more + + align:start position:0% +my guess would be would be not much more + + + align:start position:0% +my guess would be would be not much more +than a few + + align:start position:0% +than a few + + + align:start position:0% +than a few +times because because if it were already + + align:start position:0% +times because because if it were already + + + align:start position:0% +times because because if it were already +an equilibrium that would be the me but + + align:start position:0% +an equilibrium that would be the me but + + + align:start position:0% +an equilibrium that would be the me but +it's not and so the driving force is + + align:start position:0% +it's not and so the driving force is + + + align:start position:0% +it's not and so the driving force is +still going to push it actually to right + + align:start position:0% +still going to push it actually to right + + + align:start position:0% +still going to push it actually to right +that's right so there's going to be a + + align:start position:0% +that's right so there's going to be a + + + align:start position:0% +that's right so there's going to be a +it's going to be a biased random walk + + align:start position:0% +it's going to be a biased random walk + + + align:start position:0% +it's going to be a biased random walk +here where it's going to be sort of + + align:start position:0% +here where it's going to be sort of + + + align:start position:0% +here where it's going to be sort of +maybe twice as likely at each step to be + + align:start position:0% +maybe twice as likely at each step to be + + + align:start position:0% +maybe twice as likely at each step to be +moving right as to moving left that + + align:start position:0% +moving right as to moving left that + + + align:start position:0% +moving right as to moving left that +means it could very well go to 49 48 but + + align:start position:0% +means it could very well go to 49 48 but + + + align:start position:0% +means it could very well go to 49 48 but +you know it's not really going to go + + align:start position:0% +you know it's not really going to go + + + align:start position:0% +you know it's not really going to go +below 40 say you know of course you have + + align:start position:0% +below 40 say you know of course you have + + + align:start position:0% +below 40 say you know of course you have +to quantify these things if you want to + + align:start position:0% +to quantify these things if you want to + + + align:start position:0% +to quantify these things if you want to +be careful but certainly I would say + + align:start position:0% +be careful but certainly I would say + + + align:start position:0% +be careful but certainly I would say +going from I don't know 35 to 135 would + + align:start position:0% +going from I don't know 35 to 135 would + + + align:start position:0% +going from I don't know 35 to 135 would +be fine with me you would get full + + align:start position:0% +be fine with me you would get full + + + align:start position:0% +be fine with me you would get full +credit on your problem set okay and so + + align:start position:0% +credit on your problem set okay and so + + + align:start position:0% +credit on your problem set okay and so +we'll say uh I'm going to make this up + + align:start position:0% +we'll say uh I'm going to make this up + + + align:start position:0% +we'll say uh I'm going to make this up +kind of from 35 to 135 134 just so it + + align:start position:0% +kind of from 35 to 135 134 just so it + + + align:start position:0% +kind of from 35 to 135 134 just so it +could be 100 equations so I'd say I'd be + + align:start position:0% +could be 100 equations so I'd say I'd be + + + align:start position:0% +could be 100 equations so I'd say I'd be +fine with 100 + + align:start position:0% + + + + align:start position:0% + +equations okay so you simulate the + + align:start position:0% +equations okay so you simulate the + + + align:start position:0% +equations okay so you simulate the +change in the probabilities of P35 to + + align:start position:0% +change in the probabilities of P35 to + + + align:start position:0% +change in the probabilities of P35 to +p134 for + + align:start position:0% + + + + align:start position:0% + +example right so although in principle + + align:start position:0% +example right so although in principle + + + align:start position:0% +example right so although in principle +the master equation specifies how the + + align:start position:0% +the master equation specifies how the + + + align:start position:0% +the master equation specifies how the +probabilities for an infinite number of + + align:start position:0% +probabilities for an infinite number of + + + align:start position:0% +probabilities for an infinite number of +equations are going to change um you + + align:start position:0% +equations are going to change um you + + + align:start position:0% +equations are going to change um you +only need to simulate a finite number of + + align:start position:0% +only need to simulate a finite number of + + + align:start position:0% +only need to simulate a finite number of +them depending upon the Dynamics of your + + align:start position:0% +them depending upon the Dynamics of your + + + align:start position:0% +them depending upon the Dynamics of your +system okay yes that's a very thank you + + align:start position:0% +system okay yes that's a very thank you + + + align:start position:0% +system okay yes that's a very thank you +for the question because it's a very you + + align:start position:0% +for the question because it's a very you + + + align:start position:0% +for the question because it's a very you +know very important practical thing yeah + + align:start position:0% +know very important practical thing yeah + + + align:start position:0% +know very important practical thing yeah +so in practice do you like in practice + + align:start position:0% +so in practice do you like in practice + + + align:start position:0% +so in practice do you like in practice +you don't know + + align:start position:0% + + + + align:start position:0% + +right so the question is yeah in this in + + align:start position:0% +right so the question is yeah in this in + + + align:start position:0% +right so the question is yeah in this in +this case it's a little bit cheating + + align:start position:0% +this case it's a little bit cheating + + + align:start position:0% +this case it's a little bit cheating +because we already kind of knew the + + align:start position:0% +because we already kind of knew the + + + align:start position:0% +because we already kind of knew the +answer right um we didn't know exactly + + align:start position:0% +answer right um we didn't know exactly + + + align:start position:0% +answer right um we didn't know exactly +how the time dependence was going to go + + align:start position:0% +how the time dependence was going to go + + + align:start position:0% +how the time dependence was going to go +right how is it that the mean is going + + align:start position:0% +right how is it that the mean is going + + + align:start position:0% +right how is it that the mean is going +to change over time on + + align:start position:0% +to change over time on + + + align:start position:0% +to change over time on +average + + align:start position:0% + + + + align:start position:0% + +no exponentially right so on average you + + align:start position:0% +no exponentially right so on average you + + + align:start position:0% +no exponentially right so on average you +will start at 50 you exponentially relax + + align:start position:0% +will start at 50 you exponentially relax + + + align:start position:0% +will start at 50 you exponentially relax +to 100 right yeah but but in many cases + + align:start position:0% +to 100 right yeah but but in many cases + + + align:start position:0% +to 100 right yeah but but in many cases +we don't know so much about the system + + align:start position:0% +we don't know so much about the system + + + align:start position:0% +we don't know so much about the system +and I'd say that what you can uh what in + + align:start position:0% +and I'd say that what you can uh what in + + + align:start position:0% +and I'd say that what you can uh what in +general what you can do is you have to + + align:start position:0% +general what you can do is you have to + + + align:start position:0% +general what you can do is you have to +always specify a finite number of + + align:start position:0% +always specify a finite number of + + + align:start position:0% +always specify a finite number of +equations but then what you can do is + + align:start position:0% +equations but then what you can do is + + + align:start position:0% +equations but then what you can do is +you can put in kind of maybe like + + align:start position:0% +you can put in kind of maybe like + + + align:start position:0% +you can put in kind of maybe like +reflecting boundary conditions or so on + + align:start position:0% +reflecting boundary conditions or so on + + + align:start position:0% +reflecting boundary conditions or so on +the end so you don't allow them you + + align:start position:0% +the end so you don't allow them you + + + align:start position:0% +the end so you don't allow them you +don't allow probability to escape okay + + align:start position:0% +don't allow probability to escape okay + + + align:start position:0% +don't allow probability to escape okay +but then and then what you can do is you + + align:start position:0% +but then and then what you can do is you + + + align:start position:0% +but then and then what you can do is you +can run the simulation and if you have + + align:start position:0% +can run the simulation and if you have + + + align:start position:0% +can run the simulation and if you have +some reasonable probability at any of + + align:start position:0% +some reasonable probability at any of + + + align:start position:0% +some reasonable probability at any of +your boundaries then you know you're in + + align:start position:0% +your boundaries then you know you're in + + + align:start position:0% +your boundaries then you know you're in +trouble and you have to extend it from + + align:start position:0% +trouble and you have to extend it from + + + align:start position:0% +trouble and you have to extend it from +there right yeah so you can for you know + + align:start position:0% +there right yeah so you can for you know + + + align:start position:0% +there right yeah so you can for you know +you can look to say oh is it above 10 + + align:start position:0% +you can look to say oh is it above 10 + + + align:start position:0% +you can look to say oh is it above 10 +the minus three or four you know + + align:start position:0% +the minus three or four you know + + + align:start position:0% +the minus three or four you know +whatever and and then if it is then you + + align:start position:0% +whatever and and then if it is then you + + + align:start position:0% +whatever and and then if it is then you +have then you know you have to go + + align:start position:0% +have then you know you have to go + + + align:start position:0% +have then you know you have to go +further + + align:start position:0% + + + + align:start position:0% + +right okay any other questions about how + + align:start position:0% +right okay any other questions about how + + + align:start position:0% +right okay any other questions about how +you're actually going to be doing + + align:start position:0% +you're actually going to be doing + + + align:start position:0% +you're actually going to be doing +simulations of this so you know these + + align:start position:0% +simulations of this so you know these + + + align:start position:0% +simulations of this so you know these +are relevant questions for you + + align:start position:0% + + + + align:start position:0% + +um all right + + align:start position:0% +um all right + + + align:start position:0% +um all right +um okay so that that's okay that's + + align:start position:0% +um okay so that that's okay that's + + + align:start position:0% +um okay so that that's okay that's +that's the master equation uh but I'd + + align:start position:0% +that's the master equation uh but I'd + + + align:start position:0% +that's the master equation uh but I'd +say the key key thing to remember is + + align:start position:0% +say the key key thing to remember is + + + align:start position:0% +say the key key thing to remember is +that it is it tells you how to calculate + + align:start position:0% +that it is it tells you how to calculate + + + align:start position:0% +that it is it tells you how to calculate +the deterministic evolution of the + + align:start position:0% +the deterministic evolution of the + + + align:start position:0% +the deterministic evolution of the +probability of these states uh given + + align:start position:0% +probability of these states uh given + + + align:start position:0% +probability of these states uh given +some potentially complicated set of + + align:start position:0% +some potentially complicated set of + + + align:start position:0% +some potentially complicated set of +interactions okay now a rather + + align:start position:0% +interactions okay now a rather + + + align:start position:0% +interactions okay now a rather +orthogonal view to the master equation + + align:start position:0% +orthogonal view to the master equation + + + align:start position:0% +orthogonal view to the master equation +is to use the Gillespie algorithm or in + + align:start position:0% +is to use the Gillespie algorithm or in + + + align:start position:0% +is to use the Gillespie algorithm or in +general to do direct stochastic + + align:start position:0% +general to do direct stochastic + + + align:start position:0% +general to do direct stochastic +simulations of individual trajectories + + align:start position:0% +simulations of individual trajectories + + + align:start position:0% +simulations of individual trajectories +Yeah question before we + + align:start position:0% +Yeah question before we + + + align:start position:0% +Yeah question before we +go we just set to + + align:start position:0% + + + + align:start position:0% + +zero right um okay so it's qu right so + + align:start position:0% +zero right um okay so it's qu right so + + + align:start position:0% +zero right um okay so it's qu right so +the question is whether we're somehow + + align:start position:0% +the question is whether we're somehow + + + align:start position:0% +the question is whether we're somehow +losing probability so what what I was + + align:start position:0% +losing probability so what what I was + + + align:start position:0% +losing probability so what what I was +proposing before is that all right you + + align:start position:0% +proposing before is that all right you + + + align:start position:0% +proposing before is that all right you +you always want probabilities to Su to + + align:start position:0% +you always want probabilities to Su to + + + align:start position:0% +you always want probabilities to Su to +one + + align:start position:0% +one + + + align:start position:0% +one +otherwise you know it's not a + + align:start position:0% +otherwise you know it's not a + + + align:start position:0% +otherwise you know it's not a +probability and the mathematicians get + + align:start position:0% +probability and the mathematicians get + + + align:start position:0% +probability and the mathematicians get +upset um and and you know and the key + + align:start position:0% +upset um and and you know and the key + + + align:start position:0% +upset um and and you know and the key +the key thing there is that you know you + + align:start position:0% +the key thing there is that you know you + + + align:start position:0% +the key thing there is that you know you +you want to start with i you you you + + align:start position:0% +you want to start with i you you you + + + align:start position:0% +you want to start with i you you you +have to include all the states that have + + align:start position:0% +have to include all the states that have + + + align:start position:0% +have to include all the states that have +probability at the + + align:start position:0% +probability at the + + + align:start position:0% +probability at the +beginning right so okay so in that sense + + align:start position:0% +beginning right so okay so in that sense + + + align:start position:0% +beginning right so okay so in that sense +you you're given an initial distribution + + align:start position:0% +you you're given an initial distribution + + + align:start position:0% +you you're given an initial distribution +and you have to include all those States + + align:start position:0% +and you have to include all those States + + + align:start position:0% +and you have to include all those States +otherwise you're you're definitely like + + align:start position:0% +otherwise you're you're definitely like + + + align:start position:0% +otherwise you're you're definitely like +going to do something funny right so you + + align:start position:0% +going to do something funny right so you + + + align:start position:0% +going to do something funny right so you +start out with a normalized probability + + align:start position:0% +start out with a normalized probability + + + align:start position:0% +start out with a normalized probability +distribution and then I guess what I was + + align:start position:0% +distribution and then I guess what I was + + + align:start position:0% +distribution and then I guess what I was +proposing is that you have a finite + + align:start position:0% +proposing is that you have a finite + + + align:start position:0% +proposing is that you have a finite +number of equations but you don't let + + align:start position:0% +number of equations but you don't let + + + align:start position:0% +number of equations but you don't let +the probability uh leave or come in from + + align:start position:0% +the probability uh leave or come in from + + + align:start position:0% +the probability uh leave or come in from +those + + align:start position:0% +those + + + align:start position:0% +those +ends right and if you do that then you + + align:start position:0% +ends right and if you do that then you + + + align:start position:0% +ends right and if you do that then you +will always have a normalized + + align:start position:0% +will always have a normalized + + + align:start position:0% +will always have a normalized +probability + + align:start position:0% +probability + + + align:start position:0% +probability +distribution of course uh at the ends + + align:start position:0% +distribution of course uh at the ends + + + align:start position:0% +distribution of course uh at the ends +you've kind of violated the actual + + align:start position:0% +you've kind of violated the actual + + + align:start position:0% +you've kind of violated the actual +equations right and and that's why you + + align:start position:0% +equations right and and that's why you + + + align:start position:0% +equations right and and that's why you +have to make sure that you don't have + + align:start position:0% +have to make sure that you don't have + + + align:start position:0% +have to make sure that you don't have +significant probability at any of your + + align:start position:0% +significant probability at any of your + + + align:start position:0% +significant probability at any of your +boundaries does that + + align:start position:0% +boundaries does that + + + align:start position:0% +boundaries does that +answer not + + align:start position:0% + + + + align:start position:0% + +quite + + align:start position:0% +quite + + + align:start position:0% +quite +Z excuse so I was not suggesting that + + align:start position:0% +Z excuse so I was not suggesting that + + + align:start position:0% +Z excuse so I was not suggesting that +you set the probabilities equal to zero + + align:start position:0% +you set the probabilities equal to zero + + + align:start position:0% +you set the probabilities equal to zero +I was suggesting that you do what's kind + + align:start position:0% +I was suggesting that you do what's kind + + + align:start position:0% +I was suggesting that you do what's kind +of like what what what the equations + + align:start position:0% +of like what what what the equations + + + align:start position:0% +of like what what what the equations +actually do here which is that you don't + + align:start position:0% +actually do here which is that you don't + + + align:start position:0% +actually do here which is that you don't +allow any probability to leave you know + + align:start position:0% +allow any probability to leave you know + + + align:start position:0% +allow any probability to leave you know +there's no probability flux on this Edge + + align:start position:0% +there's no probability flux on this Edge + + + align:start position:0% +there's no probability flux on this Edge +right so for example out at + + align:start position:0% +right so for example out at + + + align:start position:0% +right so for example out at +p134 I I would just say okay well here's + + align:start position:0% +p134 I I would just say okay well here's + + + align:start position:0% +p134 I I would just say okay well here's +the probability that you're you have 134 + + align:start position:0% +the probability that you're you have 134 + + + align:start position:0% +the probability that you're you have 134 +Mr + + align:start position:0% +Mr + + + align:start position:0% +Mr +and I would get you know in principle + + align:start position:0% +and I would get you know in principle + + + align:start position:0% +and I would get you know in principle +there are these two arrows right but I I + + align:start position:0% +there are these two arrows right but I I + + + align:start position:0% +there are these two arrows right but I I +would just but you can just get rid of + + align:start position:0% +would just but you can just get rid of + + + align:start position:0% +would just but you can just get rid of +them okay so now um now any probability + + align:start position:0% +them okay so now um now any probability + + + align:start position:0% +them okay so now um now any probability +that enters here you know can only come + + align:start position:0% +that enters here you know can only come + + + align:start position:0% +that enters here you know can only come +back right now and i' I've somehow + + align:start position:0% +back right now and i' I've somehow + + + align:start position:0% +back right now and i' I've somehow +violated my equations but if p134 is + + align:start position:0% +violated my equations but if p134 is + + + align:start position:0% +violated my equations but if p134 is +essentially zero then it doesn't it + + align:start position:0% +essentially zero then it doesn't it + + + align:start position:0% +essentially zero then it doesn't it +doesn't matter + + align:start position:0% + + + + align:start position:0% + +right okay + + align:start position:0% +right okay + + + align:start position:0% +right okay +um right so instead of looking at an + + align:start position:0% +um right so instead of looking at an + + + align:start position:0% +um right so instead of looking at an +individual um sorry instead of instead + + align:start position:0% +individual um sorry instead of instead + + + align:start position:0% +individual um sorry instead of instead +of looking at these abilities evolve + + align:start position:0% +of looking at these abilities evolve + + + align:start position:0% +of looking at these abilities evolve +kind of as a as a whole you can instead + + align:start position:0% +kind of as a as a whole you can instead + + + align:start position:0% +kind of as a as a whole you can instead +look at individual trajectories right so + + align:start position:0% +look at individual trajectories right so + + + align:start position:0% +look at individual trajectories right so +the idea here is that if we start with + + align:start position:0% +the idea here is that if we start with + + + align:start position:0% +the idea here is that if we start with +the situation actually we can take this + + align:start position:0% +the situation actually we can take this + + + align:start position:0% +the situation actually we can take this +this thing here okay we have um so we + + align:start position:0% +this thing here okay we have um so we + + + align:start position:0% +this thing here okay we have um so we +know that at stud State it's going to be + + align:start position:0% +know that at stud State it's going to be + + + align:start position:0% +know that at stud State it's going to be +100 starts out at 50 and in this case + + align:start position:0% +100 starts out at 50 and in this case + + + align:start position:0% +100 starts out at 50 and in this case +right with the master equation you say + + align:start position:0% +right with the master equation you say + + + align:start position:0% +right with the master equation you say +okay well you start out with all the + + align:start position:0% +okay well you start out with all the + + + align:start position:0% +okay well you start out with all the +probability right here so you have kind + + align:start position:0% +probability right here so you have kind + + + align:start position:0% +probability right here so you have kind +of a Delta function at 50 right but then + + align:start position:0% +of a Delta function at 50 right but then + + + align:start position:0% +of a Delta function at 50 right but then +what happens is this thing kind of + + align:start position:0% +what happens is this thing kind of + + + align:start position:0% +what happens is this thing kind of +evolves and over time you end this thing + + align:start position:0% +evolves and over time you end this thing + + + align:start position:0% +evolves and over time you end this thing +kind of spreads + + align:start position:0% + + + + align:start position:0% + +until you have something that looks like + + align:start position:0% +until you have something that looks like + + + align:start position:0% +until you have something that looks like +right looks like this right where you + + align:start position:0% +right looks like this right where you + + + align:start position:0% +right looks like this right where you +have a pan distribution centered around + + align:start position:0% +have a pan distribution centered around + + + align:start position:0% +have a pan distribution centered around +100 and uh and this this pan + + align:start position:0% +100 and uh and this this pan + + + align:start position:0% +100 and uh and this this pan +distribution is going to be very close + + align:start position:0% +distribution is going to be very close + + + align:start position:0% +distribution is going to be very close +to a gaussian right because you have a + + align:start position:0% +to a gaussian right because you have a + + + align:start position:0% +to a gaussian right because you have a +significant number right so the the + + align:start position:0% +significant number right so the the + + + align:start position:0% +significant number right so the the +master equation tells you how this + + align:start position:0% +master equation tells you how this + + + align:start position:0% +master equation tells you how this +probability distribution evolves okay + + align:start position:0% +probability distribution evolves okay + + + align:start position:0% +probability distribution evolves okay +now if we this is this is the number + + align:start position:0% +now if we this is this is the number + + + align:start position:0% +now if we this is this is the number +M and this is the uh this is kind of the + + align:start position:0% +M and this is the uh this is kind of the + + + align:start position:0% +M and this is the uh this is kind of the +frequency That You observe it right so + + align:start position:0% +frequency That You observe it right so + + + align:start position:0% +frequency That You observe it right so +we can also kind of flip things so that + + align:start position:0% +we can also kind of flip things so that + + + align:start position:0% +we can also kind of flip things so that +we instead plot the number M + + align:start position:0% +we instead plot the number M + + + align:start position:0% +we instead plot the number M +on the y- + + align:start position:0% +on the y- + + + align:start position:0% +on the y- +axis okay and we already said okay the + + align:start position:0% +axis okay and we already said okay the + + + align:start position:0% +axis okay and we already said okay the +the deterministic + + align:start position:0% +the deterministic + + + align:start position:0% +the deterministic +equations will look like this and the + + align:start position:0% +equations will look like this and the + + + align:start position:0% +equations will look like this and the +characteristic time scale for this is + + align:start position:0% + + + + align:start position:0% + +what one over gamma M right so this + + align:start position:0% +what one over gamma M right so this + + + align:start position:0% +what one over gamma M right so this +thing relaxes to the equilibrium time + + align:start position:0% +thing relaxes to the equilibrium time + + + align:start position:0% +thing relaxes to the equilibrium time +scale determined by the degradation time + + align:start position:0% +scale determined by the degradation time + + + align:start position:0% +scale determined by the degradation time +of the Mr + + align:start position:0% +of the Mr + + + align:start position:0% +of the Mr +right so this is these are things that + + align:start position:0% +right so this is these are things that + + + align:start position:0% +right so this is these are things that +should be really you you want to be kind + + align:start position:0% +should be really you you want to be kind + + + align:start position:0% +should be really you you want to be kind +of drilled into your head I'm trying to + + align:start position:0% +of drilled into your head I'm trying to + + + align:start position:0% +of drilled into your head I'm trying to +drill uh so you you'll hear them again + + align:start position:0% +drill uh so you you'll hear them again + + + align:start position:0% +drill uh so you you'll hear them again +and again all right + + align:start position:0% +and again all right + + + align:start position:0% +and again all right +now the the master equation indeed since + + align:start position:0% +now the the master equation indeed since + + + align:start position:0% +now the the master equation indeed since +everything's linear here the expectation + + align:start position:0% +everything's linear here the expectation + + + align:start position:0% +everything's linear here the expectation +value over the probability distributions + + align:start position:0% +value over the probability distributions + + + align:start position:0% +value over the probability distributions +actually does behave like this right so + + align:start position:0% +actually does behave like this right so + + + align:start position:0% +actually does behave like this right so +the mean of the distributions as a + + align:start position:0% +the mean of the distributions as a + + + align:start position:0% +the mean of the distributions as a +function of time look like that um and + + align:start position:0% +function of time look like that um and + + + align:start position:0% +function of time look like that um and +in some ways if we were to plot this + + align:start position:0% +in some ways if we were to plot this + + + align:start position:0% +in some ways if we were to plot this +we'd say okay well first of all it's all + + align:start position:0% +we'd say okay well first of all it's all + + + align:start position:0% +we'd say okay well first of all it's all +here then it's kind of it kind of looks + + align:start position:0% +here then it's kind of it kind of looks + + + align:start position:0% +here then it's kind of it kind of looks +like this right so the this is somehow + + align:start position:0% +like this right so the this is somehow + + + align:start position:0% +like this right so the this is somehow +how those probability distributions are + + align:start position:0% +how those probability distributions are + + + align:start position:0% +how those probability distributions are +kind of expanding over time okay now for + + align:start position:0% +kind of expanding over time okay now for + + + align:start position:0% +kind of expanding over time okay now for +in individual trajectories if we run a + + align:start position:0% +in individual trajectories if we run a + + + align:start position:0% +in individual trajectories if we run a +bunch of stochastic simulations we'll + + align:start position:0% +bunch of stochastic simulations we'll + + + align:start position:0% +bunch of stochastic simulations we'll +get something that on average looks like + + align:start position:0% +get something that on average looks like + + + align:start position:0% +get something that on average looks like +this but it might look like this a + + align:start position:0% +this but it might look like this a + + + align:start position:0% +this but it might look like this a +different one might look like this okay + + align:start position:0% +different one might look like this okay + + + align:start position:0% +different one might look like this okay +um and and so on whoa although they + + align:start position:0% +um and and so on whoa although they + + + align:start position:0% +um and and so on whoa although they +shouldn't converge there you know + + align:start position:0% +shouldn't converge there you know + + + align:start position:0% +shouldn't converge there you know +because that's not consistent right so + + align:start position:0% +because that's not consistent right so + + + align:start position:0% +because that's not consistent right so +you what you and if if you did a + + align:start position:0% +you what you and if if you did a + + + align:start position:0% +you what you and if if you did a +histogram + + align:start position:0% +histogram + + + align:start position:0% +histogram +at all those different times of the + + align:start position:0% +at all those different times of the + + + align:start position:0% +at all those different times of the +individual stochastic trajectories you + + align:start position:0% +individual stochastic trajectories you + + + align:start position:0% +individual stochastic trajectories you +should recover the probability + + align:start position:0% +should recover the probability + + + align:start position:0% +should recover the probability +distribution that you got from the + + align:start position:0% +distribution that you got from the + + + align:start position:0% +distribution that you got from the +master + + align:start position:0% +master + + + align:start position:0% +master +equation okay all right so this is a + + align:start position:0% +equation okay all right so this is a + + + align:start position:0% +equation okay all right so this is a +powerful way just to make sure that for + + align:start position:0% +powerful way just to make sure that for + + + align:start position:0% +powerful way just to make sure that for +example your simulations are working + + align:start position:0% +example your simulations are working + + + align:start position:0% +example your simulations are working +right that you can check to make sure + + align:start position:0% +right that you can check to make sure + + + align:start position:0% +right that you can check to make sure +that everything behaves um in a + + align:start position:0% +that everything behaves um in a + + + align:start position:0% +that everything behaves um in a +consistent + + align:start position:0% +consistent + + + align:start position:0% +consistent +way okay now there's a major question + + align:start position:0% +way okay now there's a major question + + + align:start position:0% +way okay now there's a major question +though how is it that you should + + align:start position:0% +though how is it that you should + + + align:start position:0% +though how is it that you should +generate these stochastic + + align:start position:0% +generate these stochastic + + + align:start position:0% +generate these stochastic +trajectories okay and um the the the + + align:start position:0% +trajectories okay and um the the the + + + align:start position:0% +trajectories okay and um the the the +sort of most straightforward thing to do + + align:start position:0% +sort of most straightforward thing to do + + + align:start position:0% +sort of most straightforward thing to do +is to just um divide up time into a + + align:start position:0% +is to just um divide up time into a + + + align:start position:0% +is to just um divide up time into a +bunch of little Delta T's and just ask + + align:start position:0% +bunch of little Delta T's and just ask + + + align:start position:0% +bunch of little Delta T's and just ask +whether anything happened okay so uh let + + align:start position:0% +whether anything happened okay so uh let + + + align:start position:0% +whether anything happened okay so uh let +me + + align:start position:0% + + + + align:start position:0% + +uh so what we want to do is we want to + + align:start position:0% +uh so what we want to do is we want to + + + align:start position:0% +uh so what we want to do is we want to +imagine we have + + align:start position:0% + + + + align:start position:0% + +uh maybe M chemical species okay so now + + align:start position:0% +uh maybe M chemical species okay so now + + + align:start position:0% +uh maybe M chemical species okay so now +the these are different M's and NS let's + + align:start position:0% +the these are different M's and NS let's + + + align:start position:0% +the these are different M's and NS let's +be careful M chemical species they could + + align:start position:0% +be careful M chemical species they could + + + align:start position:0% +be careful M chemical species they could +be anything could be proteins they could + + align:start position:0% +be anything could be proteins they could + + + align:start position:0% +be anything could be proteins they could +be small Mo something right and there + + align:start position:0% +be small Mo something right and there + + + align:start position:0% +be small Mo something right and there +are n possible + + align:start position:0% +are n possible + + + align:start position:0% +are n possible +reactions and indeed in some cases + + align:start position:0% +reactions and indeed in some cases + + + align:start position:0% +reactions and indeed in some cases +people want to study the stochastic + + align:start position:0% +people want to study the stochastic + + + align:start position:0% +people want to study the stochastic +dynamics of large networks right so you + + align:start position:0% +dynamics of large networks right so you + + + align:start position:0% +dynamics of large networks right so you +could + + align:start position:0% +could + + + align:start position:0% +could +have 50 chemical species and 300 + + align:start position:0% +have 50 chemical species and 300 + + + align:start position:0% +have 50 chemical species and 300 +chemical different reactions right so + + align:start position:0% +chemical different reactions right so + + + align:start position:0% +chemical different reactions right so +this could be rather complicated okay + + align:start position:0% +this could be rather complicated okay + + + align:start position:0% +this could be rather complicated okay +um and these M chemical + + align:start position:0% +um and these M chemical + + + align:start position:0% +um and these M chemical +species have um we'll say numbers uh or + + align:start position:0% +species have um we'll say numbers uh or + + + align:start position:0% +species have um we'll say numbers uh or +if you'd like in some cases it could be + + align:start position:0% +if you'd like in some cases it could be + + + align:start position:0% +if you'd like in some cases it could be +concentrations uh X XI so then the whole + + align:start position:0% +concentrations uh X XI so then the whole + + + align:start position:0% +concentrations uh X XI so then the whole +thing can be described by some some + + align:start position:0% +thing can be described by some some + + + align:start position:0% +thing can be described by some some +Vector + + align:start position:0% +Vector + + + align:start position:0% +Vector +X and and the question is you know how + + align:start position:0% +X and and the question is you know how + + + align:start position:0% +X and and the question is you know how +should we simulate this + + align:start position:0% +should we simulate this + + + align:start position:0% +should we simulate this +okay uh the so-called what we often call + + align:start position:0% +okay uh the so-called what we often call + + + align:start position:0% +okay uh the so-called what we often call +the naive protocol and this is + + align:start position:0% +the naive protocol and this is + + + align:start position:0% +the naive protocol and this is +indeed what I did in graduate school + + align:start position:0% +indeed what I did in graduate school + + + align:start position:0% +indeed what I did in graduate school +because nobody told me + + align:start position:0% +because nobody told me + + + align:start position:0% +because nobody told me +that I wasn't supposed to do it um is + + align:start position:0% +that I wasn't supposed to do it um is + + + align:start position:0% +that I wasn't supposed to do it um is +that you uh you divide time into little + + align:start position:0% +that you uh you divide time into little + + + align:start position:0% +that you uh you divide time into little +time segments delta T + + align:start position:0% + + + + align:start position:0% + +okay and small delta T and you just do + + align:start position:0% +okay and small delta T and you just do + + + align:start position:0% +okay and small delta T and you just do +this over and over and for each Delta + + align:start position:0% +this over and over and for each Delta + + + align:start position:0% +this over and over and for each Delta +you ask okay did anything + + align:start position:0% +you ask okay did anything + + + align:start position:0% +you ask okay did anything +happen okay if it did then you update if + + align:start position:0% +happen okay if it did then you update if + + + align:start position:0% +happen okay if it did then you update if +not you keep on going right now the + + align:start position:0% +not you keep on going right now the + + + align:start position:0% +not you keep on going right now the +problem with this approach well yeah I + + align:start position:0% +problem with this approach well yeah I + + + align:start position:0% +problem with this approach well yeah I +know what what is the problem with this + + align:start position:0% +know what what is the problem with this + + + align:start position:0% +know what what is the problem with this +approach + + align:start position:0% + + + + align:start position:0% + +yeah time is continuous okay so this is + + align:start position:0% +yeah time is continuous okay so this is + + + align:start position:0% +yeah time is continuous okay so this is +um all right so one problem is that uh + + align:start position:0% +um all right so one problem is that uh + + + align:start position:0% +um all right so one problem is that uh +well you know you don't like discret + + align:start position:0% +well you know you don't like discret + + + align:start position:0% +well you know you don't like discret +time that's that's understandable uh but + + align:start position:0% +time that's that's understandable uh but + + + align:start position:0% +time that's that's understandable uh but +you know I'm going to say well you know + + align:start position:0% +you know I'm going to say well you know + + + align:start position:0% +you know I'm going to say well you know +the details you know delta T maybe is + + align:start position:0% +the details you know delta T maybe is + + + align:start position:0% +the details you know delta T maybe is +small so you know you won't + + align:start position:0% +small so you know you won't + + + align:start position:0% +small so you know you won't +notice I'm saying if I said delta T + + align:start position:0% +notice I'm saying if I said delta T + + + align:start position:0% +notice I'm saying if I said delta T +being small then I'm going to claim that + + align:start position:0% +being small then I'm going to claim that + + + align:start position:0% +being small then I'm going to claim that +you're not going to notice that that + + align:start position:0% +you're not going to notice that that + + + align:start position:0% +you're not going to notice that that +I've that i' slow right but then the + + align:start position:0% +I've that i' slow right but then the + + + align:start position:0% +I've that i' slow right but then the +simulation is slow right so there's a + + align:start position:0% +simulation is slow right so there's a + + + align:start position:0% +simulation is slow right so there's a +fundamental trade-off here and in + + align:start position:0% +fundamental trade-off here and in + + + align:start position:0% +fundamental trade-off here and in +particular the problem with this + + align:start position:0% +particular the problem with this + + + align:start position:0% +particular the problem with this +protocol is that for it to behave + + align:start position:0% +protocol is that for it to behave + + + align:start position:0% +protocol is that for it to behave +reasonably delta T has to be very small + + align:start position:0% +reasonably delta T has to be very small + + + align:start position:0% +reasonably delta T has to be very small +right and and if um and and what do I + + align:start position:0% +right and and if um and and what do I + + + align:start position:0% +right and and if um and and what do I +mean by very small + + align:start position:0% + + + + align:start position:0% + +though that's right and right in for + + align:start position:0% +though that's right and right in for + + + align:start position:0% +though that's right and right in for +this to work delta T and this Delta B + + align:start position:0% +this to work delta T and this Delta B + + + align:start position:0% +this to work delta T and this Delta B +has to be + + align:start position:0% +has to be + + + align:start position:0% +has to be +um such that um such that unlikely for + + align:start position:0% +um such that um such that unlikely for + + + align:start position:0% +um such that um such that unlikely for +anything to + + align:start position:0% + + + + align:start position:0% + +happen but this is already a problem + + align:start position:0% +happen but this is already a problem + + + align:start position:0% +happen but this is already a problem +because that means that we're doing a + + align:start position:0% +because that means that we're doing a + + + align:start position:0% +because that means that we're doing a +lot of simulations and then just and + + align:start position:0% +lot of simulations and then just and + + + align:start position:0% +lot of simulations and then just and +nothing's happening right you + + align:start position:0% +nothing's happening right you + + + align:start position:0% +nothing's happening right you +know uh okay how do we um how do we + + align:start position:0% +know uh okay how do we um how do we + + + align:start position:0% +know uh okay how do we um how do we +figure out what that probability is + + align:start position:0% + + + + align:start position:0% + +right so in particular we can ask about + + align:start position:0% +right so in particular we can ask about + + + align:start position:0% +right so in particular we can ask about +well given um and okay possible + + align:start position:0% +well given um and okay possible + + + align:start position:0% +well given um and okay possible +reactions we'll say with rates um R sub + + align:start position:0% +reactions we'll say with rates um R sub + + + align:start position:0% +reactions we'll say with rates um R sub +I right so the probability that the I + + align:start position:0% +I right so the probability that the I + + + align:start position:0% +I right so the probability that the I +reaction + + align:start position:0% +reaction + + + align:start position:0% +reaction +occurs uh is equal to uh r i * delta T + + align:start position:0% +occurs uh is equal to uh r i * delta T + + + align:start position:0% +occurs uh is equal to uh r i * delta T +for for small delta T + + align:start position:0% + + + + align:start position:0% + +okay uh because each of these reactions + + align:start position:0% +okay uh because each of these reactions + + + align:start position:0% +okay uh because each of these reactions +will occur kind of at a at a rate you + + align:start position:0% +will occur kind of at a at a rate you + + + align:start position:0% +will occur kind of at a at a rate you +know they're going to be uh they're + + align:start position:0% +know they're going to be uh they're + + + align:start position:0% +know they're going to be uh they're +going to be exponential distributions of + + align:start position:0% +going to be exponential distributions of + + + align:start position:0% +going to be exponential distributions of +the times for them to occur you know + + align:start position:0% +the times for them to occur you know + + + align:start position:0% +the times for them to occur you know +this is a Pon process right because it's + + align:start position:0% +this is a Pon process right because it's + + + align:start position:0% +this is a Pon process right because it's +random now uh what we want to know is + + align:start position:0% +random now uh what we want to know is + + + align:start position:0% +random now uh what we want to know is +the probability um that nothing is going + + align:start position:0% +the probability um that nothing is going + + + align:start position:0% +the probability um that nothing is going +to + + align:start position:0% +to + + + align:start position:0% +to +happen right because that's what that's + + align:start position:0% +happen right because that's what that's + + + align:start position:0% +happen right because that's what that's +how we're going to have to set delta T + + align:start position:0% + + + + align:start position:0% + +right well what we can imagine then is + + align:start position:0% +right well what we can imagine then is + + + align:start position:0% +right well what we can imagine then is +that you know then we can say all right + + align:start position:0% +that you know then we can say all right + + + align:start position:0% +that you know then we can say all right +well what's the prob + + align:start position:0% +well what's the prob + + + align:start position:0% +well what's the prob +ability that is say you know not not + + align:start position:0% +ability that is say you know not not + + + align:start position:0% +ability that is say you know not not +reaction one + + align:start position:0% +reaction one + + + align:start position:0% +reaction one +and uh not + + align:start position:0% +and uh not + + + align:start position:0% +and uh not +two and okay dot dot dot okay well and + + align:start position:0% +two and okay dot dot dot okay well and + + + align:start position:0% +two and okay dot dot dot okay well and +this is this is in sometime delta + + align:start position:0% + + + + align:start position:0% + +T + + align:start position:0% +T + + + align:start position:0% +T +right well + + align:start position:0% + + + + align:start position:0% + +actually we know that if if the + + align:start position:0% +actually we know that if if the + + + align:start position:0% +actually we know that if if the +fundamental process just looks like this + + align:start position:0% +fundamental process just looks like this + + + align:start position:0% +fundamental process just looks like this +then we're going to get exponential + + align:start position:0% +then we're going to get exponential + + + align:start position:0% +then we're going to get exponential +distributions for each of + + align:start position:0% +distributions for each of + + + align:start position:0% +distributions for each of +those + + align:start position:0% +those + + + align:start position:0% +those +right so we get end up with e to the + + align:start position:0% +right so we get end up with e to the + + + align:start position:0% +right so we get end up with e to the +R1 and indeed once we write an + + align:start position:0% +R1 and indeed once we write an + + + align:start position:0% +R1 and indeed once we write an +exponential we don't even have to write + + align:start position:0% +exponential we don't even have to write + + + align:start position:0% +exponential we don't even have to write +Delta Delta T this is just some time + + align:start position:0% +Delta Delta T this is just some time + + + align:start position:0% +Delta Delta T this is just some time +T right for this to be true it requires + + align:start position:0% +T right for this to be true it requires + + + align:start position:0% +T right for this to be true it requires +that delta T is very small right but if + + align:start position:0% +that delta T is very small right but if + + + align:start position:0% +that delta T is very small right but if +we want to just ask what's the + + align:start position:0% +we want to just ask what's the + + + align:start position:0% +we want to just ask what's the +probability that reaction one has not + + align:start position:0% +probability that reaction one has not + + + align:start position:0% +probability that reaction one has not +happened in sometime T this actually is + + align:start position:0% +happened in sometime T this actually is + + + align:start position:0% +happened in sometime T this actually is +indeed precisely equal to e to the r1t + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +details all right this is e the minus + + align:start position:0% +details all right this is e the minus + + + align:start position:0% +details all right this is e the minus +r2t dot dot + + align:start position:0% +r2t dot dot + + + align:start position:0% +r2t dot dot +dot minus and there this we go up to n r + + align:start position:0% +dot minus and there this we go up to n r + + + align:start position:0% +dot minus and there this we go up to n r +to the n t Okay because each of those + + align:start position:0% +to the n t Okay because each of those + + + align:start position:0% +to the n t Okay because each of those +chemical reactions are going to be + + align:start position:0% +chemical reactions are going to be + + + align:start position:0% +chemical reactions are going to be +exponentially distributed in terms of + + align:start position:0% +exponentially distributed in terms of + + + align:start position:0% +exponentially distributed in terms of +how long you have to wait for them to + + align:start position:0% + + + + align:start position:0% + +happen Okay um and what's what's neat + + align:start position:0% +happen Okay um and what's what's neat + + + align:start position:0% +happen Okay um and what's what's neat +about this is that this means that if + + align:start position:0% +about this is that this means that if + + + align:start position:0% +about this is that this means that if +you just ask about the probability + + align:start position:0% +you just ask about the probability + + + align:start position:0% +you just ask about the probability +distribution for + + align:start position:0% +distribution for + + + align:start position:0% +distribution for +um for you know for all of them combined + + align:start position:0% +um for you know for all of them combined + + + align:start position:0% +um for you know for all of them combined +I saying that none of them have happened + + align:start position:0% +I saying that none of them have happened + + + align:start position:0% +I saying that none of them have happened +this is actually just equal to you know + + align:start position:0% +this is actually just equal to you know + + + align:start position:0% +this is actually just equal to you know +the exponent exponent of minus now we + + align:start position:0% +the exponent exponent of minus now we + + + align:start position:0% +the exponent exponent of minus now we +might put we might pull the T out and we + + align:start position:0% +might put we might pull the T out and we + + + align:start position:0% +might put we might pull the T out and we +just sum over + + align:start position:0% + + + + align:start position:0% + +ri right so this is actually somehow a + + align:start position:0% +ri right so this is actually somehow a + + + align:start position:0% +ri right so this is actually somehow a +little bit surprising Rising which is + + align:start position:0% +little bit surprising Rising which is + + + align:start position:0% +little bit surprising Rising which is +that each of those chemical reactions + + align:start position:0% +that each of those chemical reactions + + + align:start position:0% +that each of those chemical reactions +occur they're occurring at different + + align:start position:0% +occur they're occurring at different + + + align:start position:0% +occur they're occurring at different +rate some of them might be fast some of + + align:start position:0% +rate some of them might be fast some of + + + align:start position:0% +rate some of them might be fast some of +them might be slow the RIS could be + + align:start position:0% +them might be slow the RIS could be + + + align:start position:0% +them might be slow the RIS could be +different by you know orders of + + align:start position:0% +different by you know orders of + + + align:start position:0% +different by you know orders of +magnitude okay but still over these + + align:start position:0% +magnitude okay but still over these + + + align:start position:0% +magnitude okay but still over these +hundreds of chemical reactions if if the + + align:start position:0% +hundreds of chemical reactions if if the + + + align:start position:0% +hundreds of chemical reactions if if the +only thing you want to know is oh what's + + align:start position:0% +only thing you want to know is oh what's + + + align:start position:0% +only thing you want to know is oh what's +the probability that none of them have + + align:start position:0% +the probability that none of them have + + + align:start position:0% +the probability that none of them have +happened that is also going to end up + + align:start position:0% +happened that is also going to end up + + + align:start position:0% +happened that is also going to end up +that's going to Decay + + align:start position:0% +that's going to Decay + + + align:start position:0% +that's going to Decay +exponentially right and this actually + + align:start position:0% +exponentially right and this actually + + + align:start position:0% +exponentially right and this actually +tells us something very interesting + + align:start position:0% +tells us something very interesting + + + align:start position:0% +tells us something very interesting +which is that if we want to know the + + align:start position:0% +which is that if we want to know the + + + align:start position:0% +which is that if we want to know the +distribution of times for the first + + align:start position:0% +distribution of times for the first + + + align:start position:0% +distribution of times for the first +thing to happen that's also going to be + + align:start position:0% +thing to happen that's also going to be + + + align:start position:0% +thing to happen that's also going to be +exponentially + + align:start position:0% +exponentially + + + align:start position:0% +exponentially +distributed okay and it's just + + align:start position:0% +distributed okay and it's just + + + align:start position:0% +distributed okay and it's just +exponentially distributed with a rate + + align:start position:0% +exponentially distributed with a rate + + + align:start position:0% +exponentially distributed with a rate +that is given by the sum sum of the + + align:start position:0% +that is given by the sum sum of the + + + align:start position:0% +that is given by the sum sum of the +these rates okay now that uh that's the + + align:start position:0% +these rates okay now that uh that's the + + + align:start position:0% +these rates okay now that uh that's the +basic Insight behind the galespia + + align:start position:0% +basic Insight behind the galespia + + + align:start position:0% +basic Insight behind the galespia +algorithm where instead of dividing + + align:start position:0% +algorithm where instead of dividing + + + align:start position:0% +algorithm where instead of dividing +things up into a bunch of time little + + align:start position:0% +things up into a bunch of time little + + + align:start position:0% +things up into a bunch of time little +times delta T but instead what you do is + + align:start position:0% +times delta T but instead what you do is + + + align:start position:0% +times delta T but instead what you do is +you ask um how long am I going to have + + align:start position:0% +you ask um how long am I going to have + + + align:start position:0% +you ask um how long am I going to have +to wait before the first thing happens + + align:start position:0% +to wait before the first thing happens + + + align:start position:0% +to wait before the first thing happens +okay and you just sample from an + + align:start position:0% +okay and you just sample from an + + + align:start position:0% +okay and you just sample from an +exponential with this rate r that is the + + align:start position:0% +exponential with this rate r that is the + + + align:start position:0% +exponential with this rate r that is the +sum of the rates + + align:start position:0% + + + + align:start position:0% + +okay um oh and maybe it's even worth + + align:start position:0% +okay um oh and maybe it's even worth + + + align:start position:0% +okay um oh and maybe it's even worth +saying that okay so there's the the + + align:start position:0% +saying that okay so there's the the + + + align:start position:0% +saying that okay so there's the the +naive algorithm where you just divide a + + align:start position:0% +naive algorithm where you just divide a + + + align:start position:0% +naive algorithm where you just divide a +bunch of Delta T's you just take the + + align:start position:0% +bunch of Delta T's you just take the + + + align:start position:0% +bunch of Delta T's you just take the +little steps you say okay nothing + + align:start position:0% +little steps you say okay nothing + + + align:start position:0% +little steps you say okay nothing +nothing nothing nothing and then + + align:start position:0% +nothing nothing nothing and then + + + align:start position:0% +nothing nothing nothing and then +eventually something happens and then + + align:start position:0% +eventually something happens and then + + + align:start position:0% +eventually something happens and then +you update you keep on going there's the + + align:start position:0% +you update you keep on going there's the + + + align:start position:0% +you update you keep on going there's the +somewhat less naive algorithm which + + align:start position:0% +somewhat less naive algorithm which + + + align:start position:0% +somewhat less naive algorithm which +would be which is exact you know so it's + + align:start position:0% +would be which is exact you know so it's + + + align:start position:0% +would be which is exact you know so it's +not the same concerns that J had which + + align:start position:0% +not the same concerns that J had which + + + align:start position:0% +not the same concerns that J had which +is that you could just sample from n + + align:start position:0% +is that you could just sample from n + + + align:start position:0% +is that you could just sample from n +different + + align:start position:0% +different + + + align:start position:0% +different +exponentials you know each with their + + align:start position:0% +exponentials you know each with their + + + align:start position:0% +exponentials you know each with their +own rates and then just take the minimum + + align:start position:0% +own rates and then just take the minimum + + + align:start position:0% +own rates and then just take the minimum +of them and say okay that's the guy that + + align:start position:0% +of them and say okay that's the guy that + + + align:start position:0% +of them and say okay that's the guy that +to that's the guy to happened first and + + align:start position:0% +to that's the guy to happened first and + + + align:start position:0% +to that's the guy to happened first and +then update from that that's an exact + + align:start position:0% +then update from that that's an exact + + + align:start position:0% +then update from that that's an exact +algorithm right the problem is that you + + align:start position:0% +algorithm right the problem is that you + + + align:start position:0% +algorithm right the problem is that you +have to sample from many possibly many + + align:start position:0% +have to sample from many possibly many + + + align:start position:0% +have to sample from many possibly many +different exponentials right and then + + align:start position:0% +different exponentials right and then + + + align:start position:0% +different exponentials right and then +and that's not a disaster but again it's + + align:start position:0% +and that's not a disaster but again it's + + + align:start position:0% +and that's not a disaster but again it's +computationally slow so the gaspie + + align:start position:0% +computationally slow so the gaspie + + + align:start position:0% +computationally slow so the gaspie +algorithm removes the required sample + + align:start position:0% +algorithm removes the required sample + + + align:start position:0% +algorithm removes the required sample +from those n exponentials because + + align:start position:0% +from those n exponentials because + + + align:start position:0% +from those n exponentials because +instead what what you do is you just say + + align:start position:0% +instead what what you do is you just say + + + align:start position:0% +instead what what you do is you just say +um this you know so the the numbers of + + align:start position:0% +um this you know so the the numbers of + + + align:start position:0% +um this you know so the the numbers of +the concentrations um + + align:start position:0% +the concentrations um + + + align:start position:0% +the concentrations um +give all of the uh you know give you + + align:start position:0% +give all of the uh you know give you + + + align:start position:0% +give all of the uh you know give you +know the + + align:start position:0% +know the + + + align:start position:0% +know the +ri give you all the rates + + align:start position:0% + + + + align:start position:0% + +okay right and then what you do is you + + align:start position:0% +okay right and then what you do is you + + + align:start position:0% +okay right and then what you do is you +uh + + align:start position:0% +uh + + + align:start position:0% +uh +sample from U from from an exp + + align:start position:0% +sample from U from from an exp + + + align:start position:0% +sample from U from from an exp +exponential um with rate + + align:start position:0% + + + + align:start position:0% + +um R which is the the sum over all the + + align:start position:0% +um R which is the the sum over all the + + + align:start position:0% +um R which is the the sum over all the +ri and that tells you okay when is the + + align:start position:0% +ri and that tells you okay when is the + + + align:start position:0% +ri and that tells you okay when is the +first reaction going to + + align:start position:0% + + + + align:start position:0% + +occur and then what you do is you ask + + align:start position:0% +occur and then what you do is you ask + + + align:start position:0% +occur and then what you do is you ask +well which reaction did occur because + + align:start position:0% +well which reaction did occur because + + + align:start position:0% +well which reaction did occur because +you actually don't know know that + + align:start position:0% +you actually don't know know that + + + align:start position:0% +you actually don't know know that +yet right and and there it's just the + + align:start position:0% +yet right and and there it's just the + + + align:start position:0% +yet right and and there it's just the +probabilities of each of them so the + + align:start position:0% +probabilities of each of them so the + + + align:start position:0% +probabilities of each of them so the +probabilities Pi is just going to be the + + align:start position:0% +probabilities Pi is just going to be the + + + align:start position:0% +probabilities Pi is just going to be the +rid the sum over the R so this Big + + align:start position:0% + + + + align:start position:0% + +R okay so it may be that you had 300 + + align:start position:0% +R okay so it may be that you had 300 + + + align:start position:0% +R okay so it may be that you had 300 +possible chemical reactions but you only + + align:start position:0% +possible chemical reactions but you only + + + align:start position:0% +possible chemical reactions but you only +have to do two things here and they're + + align:start position:0% +have to do two things here and they're + + + align:start position:0% +have to do two things here and they're +both kind of simple right you sample + + align:start position:0% +both kind of simple right you sample + + + align:start position:0% +both kind of simple right you sample +from one exponential gives you how long + + align:start position:0% +from one exponential gives you how long + + + align:start position:0% +from one exponential gives you how long +you had to wait for something to happen + + align:start position:0% +you had to wait for something to happen + + + align:start position:0% +you had to wait for something to happen +and then you just sample from another + + align:start position:0% +and then you just sample from another + + + align:start position:0% +and then you just sample from another +Pro simple probability thing here that + + align:start position:0% +Pro simple probability thing here that + + + align:start position:0% +Pro simple probability thing here that +just tells you which which of the you + + align:start position:0% +just tells you which which of the you + + + align:start position:0% +just tells you which which of the you +know the N possible chemical reactions + + align:start position:0% +know the N possible chemical reactions + + + align:start position:0% +know the N possible chemical reactions +was it that actually occurred right and + + align:start position:0% +was it that actually occurred right and + + + align:start position:0% +was it that actually occurred right and +of course the chemical reactions that + + align:start position:0% +of course the chemical reactions that + + + align:start position:0% +of course the chemical reactions that +were occurring at a faster rate have a + + align:start position:0% +were occurring at a faster rate have a + + + align:start position:0% +were occurring at a faster rate have a +higher probability of being chosen okay + + align:start position:0% +higher probability of being chosen okay + + + align:start position:0% +higher probability of being chosen okay +so this actually is an exact procedure + + align:start position:0% +so this actually is an exact procedure + + + align:start position:0% +so this actually is an exact procedure +in the sense that there's no uh no no uh + + align:start position:0% +in the sense that there's no uh no no uh + + + align:start position:0% +in the sense that there's no uh no no uh +kind of digitization of time or anything + + align:start position:0% +kind of digitization of time or anything + + + align:start position:0% +kind of digitization of time or anything +of the sort right so this actually is um + + align:start position:0% +of the sort right so this actually is um + + + align:start position:0% +of the sort right so this actually is um +it's comput computationally efficient + + align:start position:0% +it's comput computationally efficient + + + align:start position:0% +it's comput computationally efficient +and um and is exact you know assuming + + align:start position:0% +and um and is exact you know assuming + + + align:start position:0% +and um and is exact you know assuming +that you live assuming that your + + align:start position:0% +that you live assuming that your + + + align:start position:0% +that you live assuming that your +description of the chemical reactions + + align:start position:0% +description of the chemical reactions + + + align:start position:0% +description of the chemical reactions +was accurate to begin with right um + + align:start position:0% +was accurate to begin with right um + + + align:start position:0% +was accurate to begin with right um +right so then what we do is we update + + align:start position:0% + + + + align:start position:0% + +time and I this is in some ways you know + + align:start position:0% +time and I this is in some ways you know + + + align:start position:0% +time and I this is in some ways you know +when you do computations when you when + + align:start position:0% +when you do computations when you when + + + align:start position:0% +when you do computations when you when +you actually do simulations this is + + align:start position:0% +you actually do simulations this is + + + align:start position:0% +you actually do simulations this is +maybe the annoying part about the gespi + + align:start position:0% +maybe the annoying part about the gespi + + + align:start position:0% +maybe the annoying part about the gespi +algorithm which is that now your times + + align:start position:0% +algorithm which is that now your times + + + align:start position:0% +algorithm which is that now your times +are not equally spaced and so then you + + align:start position:0% +are not equally spaced and so then you + + + align:start position:0% +are not equally spaced and so then you +just have to make sure you keep track + + align:start position:0% +just have to make sure you keep track + + + align:start position:0% +just have to make sure you keep track +you remember that you don't plot + + align:start position:0% +you remember that you don't plot + + + align:start position:0% +you remember that you don't plot +something that's incorrect right but + + align:start position:0% +something that's incorrect right but + + + align:start position:0% +something that's incorrect right but +because because your times are going to + + align:start position:0% +because because your times are going to + + + align:start position:0% +because because your times are going to +hop right at different time intervals um + + align:start position:0% +hop right at different time intervals um + + + align:start position:0% +hop right at different time intervals um +but you know that's doable up to you + + align:start position:0% +but you know that's doable up to you + + + align:start position:0% +but you know that's doable up to you +have to update your time and you have to + + align:start position:0% +have to update your time and you have to + + + align:start position:0% +have to update your time and you have to +update your your abundances okay and + + align:start position:0% +update your your abundances okay and + + + align:start position:0% +update your your abundances okay and +then uh and then what you do is + + align:start position:0% +then uh and then what you do is + + + align:start position:0% +then uh and then what you do is +repeat + + align:start position:0% + + + + align:start position:0% + +okay I think the notes kind of allude to + + align:start position:0% +okay I think the notes kind of allude to + + + align:start position:0% +okay I think the notes kind of allude to +this glpi algorithm but don't qu are not + + align:start position:0% +this glpi algorithm but don't qu are not + + + align:start position:0% +this glpi algorithm but don't qu are not +quite explicit about you know what you + + align:start position:0% +quite explicit about you know what you + + + align:start position:0% +quite explicit about you know what you +actually do in all to go to go through + + align:start position:0% +actually do in all to go to go through + + + align:start position:0% +actually do in all to go to go through +this process right for the simulations + + align:start position:0% +this process right for the simulations + + + align:start position:0% +this process right for the simulations +that you're going to do in this class I + + align:start position:0% +that you're going to do in this class I + + + align:start position:0% +that you're going to do in this class I +would say + + align:start position:0% +would say + + + align:start position:0% +would say +that you you the you don't get the full + + align:start position:0% +that you you the you don't get the full + + + align:start position:0% +that you you the you don't get the full +benefits of the glaspie in the sense + + align:start position:0% +benefits of the glaspie in the sense + + + align:start position:0% +benefits of the glaspie in the sense +that you're not going to be simulating + + align:start position:0% +that you're not going to be simulating + + + align:start position:0% +that you're not going to be simulating +hundreds of differential equations with + + align:start position:0% +hundreds of differential equations with + + + align:start position:0% +hundreds of differential equations with +hundreds of different you know things um + + align:start position:0% +hundreds of different you know things um + + + align:start position:0% +hundreds of different you know things um +but it's in those complicated uh models + + align:start position:0% +but it's in those complicated uh models + + + align:start position:0% +but it's in those complicated uh models +that you really have to do this kind of + + align:start position:0% +that you really have to do this kind of + + + align:start position:0% +that you really have to do this kind of +gpie approach as compared to even this + + align:start position:0% +gpie approach as compared to even this + + + align:start position:0% +gpie approach as compared to even this +somewhat more um you know better model + + align:start position:0% +somewhat more um you know better model + + + align:start position:0% +somewhat more um you know better model +which is a sample from the different + + align:start position:0% +which is a sample from the different + + + align:start position:0% +which is a sample from the different +exponentials + + align:start position:0% +exponentials + + + align:start position:0% +exponentials +right are there any questions about why + + align:start position:0% +right are there any questions about why + + + align:start position:0% +right are there any questions about why +this might work why you might want to do + + align:start position:0% +this might work why you might want to do + + + align:start position:0% +this might work why you might want to do +it + + align:start position:0% + + + + align:start position:0% + +yes right um what I mean is that you um + + align:start position:0% +yes right um what I mean is that you um + + + align:start position:0% +yes right um what I mean is that you um +you go to mat lab and you say you know + + align:start position:0% +you go to mat lab and you say you know + + + align:start position:0% +you go to mat lab and you say you know +random um yeah so I'm sort of serious + + align:start position:0% +random um yeah so I'm sort of serious + + + align:start position:0% +random um yeah so I'm sort of serious +but + + align:start position:0% + + + + align:start position:0% + +uh sorry I'm trying to get a new um okay + + align:start position:0% +uh sorry I'm trying to get a new um okay + + + align:start position:0% +uh sorry I'm trying to get a new um okay +right so you have a the exponential + + align:start position:0% +right so you have a the exponential + + + align:start position:0% +right so you have a the exponential +right so it's a it's a probability + + align:start position:0% +right so it's a it's a probability + + + align:start position:0% +right so it's a it's a probability +distribution right so this is uh the + + align:start position:0% +distribution right so this is uh the + + + align:start position:0% +distribution right so this is uh the +probability as a function of time uh as + + align:start position:0% +probability as a function of time uh as + + + align:start position:0% +probability as a function of time uh as +a you know and then t + + align:start position:0% +a you know and then t + + + align:start position:0% +a you know and then t +right and it's going to look something + + align:start position:0% +right and it's going to look something + + + align:start position:0% +right and it's going to look something +like + + align:start position:0% +like + + + align:start position:0% +like +this right this thing is going to be + + align:start position:0% +this right this thing is going to be + + + align:start position:0% +this right this thing is going to be +some well given that given that right in + + align:start position:0% +some well given that given that right in + + + align:start position:0% +some well given that given that right in +general it's going to be the probability + + align:start position:0% +general it's going to be the probability + + + align:start position:0% +general it's going to be the probability +T is going to be e to the minus + + align:start position:0% +T is going to be e to the minus + + + align:start position:0% +T is going to be e to the minus +RT and then do I put R here or do I put + + align:start position:0% +RT and then do I put R here or do I put + + + align:start position:0% +RT and then do I put R here or do I put +one over + + align:start position:0% + + + + align:start position:0% + +R is it one over + + align:start position:0% + + + + align:start position:0% + +R okay well what what should be the + + align:start position:0% +R okay well what what should be the + + + align:start position:0% +R okay well what what should be the +units of a + + align:start position:0% + + + + align:start position:0% + +distribution one over time in this case + + align:start position:0% +distribution one over time in this case + + + align:start position:0% +distribution one over time in this case +right it's one over whatever is on this + + align:start position:0% +right it's one over whatever is on this + + + align:start position:0% +right it's one over whatever is on this +x axxis because if you want to get the + + align:start position:0% +x axxis because if you want to get the + + + align:start position:0% +x axxis because if you want to get the +actual honest to goodness probability + + align:start position:0% +actual honest to goodness probability + + + align:start position:0% +actual honest to goodness probability +right so this is the if you want the + + align:start position:0% +right so this is the if you want the + + + align:start position:0% +right so this is the if you want the +probability that um T is + + align:start position:0% +probability that um T is + + + align:start position:0% +probability that um T is +say between some + + align:start position:0% +say between some + + + align:start position:0% +say between some +T1 and T1 plus delta + + align:start position:0% +T1 and T1 plus delta + + + align:start position:0% +T1 and T1 plus delta +T right if you want an actual + + align:start position:0% +T right if you want an actual + + + align:start position:0% +T right if you want an actual +probability then this thing is equal + + align:start position:0% +probability then this thing is equal + + + align:start position:0% +probability then this thing is equal +to the probability density Z at T1 in + + align:start position:0% +to the probability density Z at T1 in + + + align:start position:0% +to the probability density Z at T1 in +this + + align:start position:0% +this + + + align:start position:0% +this +case time delta + + align:start position:0% + + + + align:start position:0% + +T okay so that means this thing has to + + align:start position:0% +T okay so that means this thing has to + + + align:start position:0% +T okay so that means this thing has to +have a one over time and that gives us R + + align:start position:0% + + + + align:start position:0% + +here okay all right so now okay this is + + align:start position:0% +here okay all right so now okay this is + + + align:start position:0% +here okay all right so now okay this is +prob density right and and what I'm what + + align:start position:0% +prob density right and and what I'm what + + + align:start position:0% +prob density right and and what I'm what +I'm saying is that you want when I say + + align:start position:0% +I'm saying is that you want when I say + + + align:start position:0% +I'm saying is that you want when I say +sample from this probability + + align:start position:0% +sample from this probability + + + align:start position:0% +sample from this probability +distribution what it means is that it's + + align:start position:0% +distribution what it means is that it's + + + align:start position:0% +distribution what it means is that it's +like rolling a die okay but that it's a + + align:start position:0% +like rolling a die okay but that it's a + + + align:start position:0% +like rolling a die okay but that it's a +biased die because it's a continuous + + align:start position:0% +biased die because it's a continuous + + + align:start position:0% +biased die because it's a continuous +thing over the time right but just like + + align:start position:0% +thing over the time right but just like + + + align:start position:0% +thing over the time right but just like +when I you know when you have when you + + align:start position:0% +when I you know when you have when you + + + align:start position:0% +when I you know when you have when you +have a six-sided die and I say okay you + + align:start position:0% +have a six-sided die and I say okay you + + + align:start position:0% +have a six-sided die and I say okay you +know sample from the die you're playing + + align:start position:0% +know sample from the die you're playing + + + align:start position:0% +know sample from the die you're playing +Monopoly you throw the die and you get + + align:start position:0% +Monopoly you throw the die and you get + + + align:start position:0% +Monopoly you throw the die and you get +you know one two three four five six and + + align:start position:0% +you know one two three four five six and + + + align:start position:0% +you know one two three four five six and +you do that over and over again right + + align:start position:0% +you do that over and over again right + + + align:start position:0% +you do that over and over again right +same thing here you kind of you know + + align:start position:0% +same thing here you kind of you know + + + align:start position:0% +same thing here you kind of you know +roll the die and and see what happens + + align:start position:0% +roll the die and and see what happens + + + align:start position:0% +roll the die and and see what happens +and indeed in uh you're going to get + + align:start position:0% +and indeed in uh you're going to get + + + align:start position:0% +and indeed in uh you're going to get +some practice with probability + + align:start position:0% +some practice with probability + + + align:start position:0% +some practice with probability +distributions on the homework that I + + align:start position:0% +distributions on the homework that I + + + align:start position:0% +distributions on the homework that I +think you're doing right now because you + + align:start position:0% +think you're doing right now because you + + + align:start position:0% +think you're doing right now because you +you're asked to demonstrate that you can + + align:start position:0% +you're asked to demonstrate that you can + + + align:start position:0% +you're asked to demonstrate that you can +take you can sample from a uniform + + align:start position:0% +take you can sample from a uniform + + + align:start position:0% +take you can sample from a uniform +distribution right which is something + + align:start position:0% +distribution right which is something + + + align:start position:0% +distribution right which is something +it's just equally probable across the + + align:start position:0% +it's just equally probable across the + + + align:start position:0% +it's just equally probable across the +unit um unit line and and do a + + align:start position:0% +unit um unit line and and do a + + + align:start position:0% +unit um unit line and and do a +transformation and get an exponential + + align:start position:0% +transformation and get an exponential + + + align:start position:0% +transformation and get an exponential +distribution um now and it used to be + + align:start position:0% +distribution um now and it used to be + + + align:start position:0% +distribution um now and it used to be +that everybody knew all these tricks + + align:start position:0% +that everybody knew all these tricks + + + align:start position:0% +that everybody knew all these tricks +because you had to kind of know them in + + align:start position:0% +because you had to kind of know them in + + + align:start position:0% +because you had to kind of know them in +order to do computation but now I me mat + + align:start position:0% +order to do computation but now I me mat + + + align:start position:0% +order to do computation but now I me mat +lab or whatever program you use they + + align:start position:0% +lab or whatever program you use they + + + align:start position:0% +lab or whatever program you use they +know all the tricks so you just ask it + + align:start position:0% +know all the tricks so you just ask it + + + align:start position:0% +know all the tricks so you just ask it +to sample from an exponential with this + + align:start position:0% +to sample from an exponential with this + + + align:start position:0% +to sample from an exponential with this +uh property and it does it for you right + + align:start position:0% +uh property and it does it for you right + + + align:start position:0% +uh property and it does it for you right +but you still need to know what it's + + align:start position:0% +but you still need to know what it's + + + align:start position:0% +but you still need to know what it's +doing + + align:start position:0% +doing + + + align:start position:0% +doing +right so just to be clear what is the + + align:start position:0% +right so just to be clear what is the + + + align:start position:0% +right so just to be clear what is the +most likely + + align:start position:0% +most likely + + + align:start position:0% +most likely +time that you're going to get out from + + align:start position:0% +time that you're going to get out from + + + align:start position:0% +time that you're going to get out from +the + + align:start position:0% + + + + align:start position:0% + +exponential zero right okay has a peak + + align:start position:0% +exponential zero right okay has a peak + + + align:start position:0% +exponential zero right okay has a peak +here but the mean is over here + + align:start position:0% +here but the mean is over here + + + align:start position:0% +here but the mean is over here +okay + + align:start position:0% +okay + + + align:start position:0% +okay +right all + + align:start position:0% +right all + + + align:start position:0% +right all +right any other questions about about + + align:start position:0% +right any other questions about about + + + align:start position:0% +right any other questions about about +what the you know how the gesp algorithm + + align:start position:0% +what the you know how the gesp algorithm + + + align:start position:0% +what the you know how the gesp algorithm +works + + align:start position:0% +works + + + align:start position:0% +works +and + + align:start position:0% +and + + + align:start position:0% +and +um all right can somebody tell me me how + + align:start position:0% +um all right can somebody tell me me how + + + align:start position:0% +um all right can somebody tell me me how +a protein burst arises right so we we + + align:start position:0% +a protein burst arises right so we we + + + align:start position:0% +a protein burst arises right so we we +had this original question about whether + + align:start position:0% +had this original question about whether + + + align:start position:0% +had this original question about whether +there were protein bursts in that model + + align:start position:0% +there were protein bursts in that model + + + align:start position:0% +there were protein bursts in that model +that I wrote down right where we just + + align:start position:0% +that I wrote down right where we just + + + align:start position:0% +that I wrote down right where we just +had m dot is equal + + align:start position:0% + + + + align:start position:0% + +to okay now I what we had what we what + + align:start position:0% +to okay now I what we had what we what + + + align:start position:0% +to okay now I what we had what we what +what we said was that the master + + align:start position:0% +what we said was that the master + + + align:start position:0% +what we said was that the master +equation would not I mean the protein + + align:start position:0% +equation would not I mean the protein + + + align:start position:0% +equation would not I mean the protein +burst would somehow + + align:start position:0% +burst would somehow + + + align:start position:0% +burst would somehow +be there but you would never see them or + + align:start position:0% +be there but you would never see them or + + + align:start position:0% +be there but you would never see them or +you know somehow the protein burst would + + align:start position:0% +you know somehow the protein burst would + + + align:start position:0% +you know somehow the protein burst would +influence how the how the mean and + + align:start position:0% +influence how the how the mean and + + + align:start position:0% +influence how the how the mean and +everything have evolved but you wouldn't + + align:start position:0% +everything have evolved but you wouldn't + + + align:start position:0% +everything have evolved but you wouldn't +actually see any big jumps right but + + align:start position:0% +actually see any big jumps right but + + + align:start position:0% +actually see any big jumps right but +then we said oh but if you did a + + align:start position:0% +then we said oh but if you did a + + + align:start position:0% +then we said oh but if you did a +stochastic simulation you would right so + + align:start position:0% +stochastic simulation you would right so + + + align:start position:0% +stochastic simulation you would right so +the claim here is that the that the + + align:start position:0% +the claim here is that the that the + + + align:start position:0% +the claim here is that the that the +gespi algorithm what I've just told you + + align:start position:0% +gespi algorithm what I've just told you + + + align:start position:0% +gespi algorithm what I've just told you +here will lead to protein + + align:start position:0% +here will lead to protein + + + align:start position:0% +here will lead to protein +bursts but what do I mean by when I when + + align:start position:0% +bursts but what do I mean by when I when + + + align:start position:0% +bursts but what do I mean by when I when +I when I make that statement what is it + + align:start position:0% +I when I make that statement what is it + + + align:start position:0% +I when I make that statement what is it +that I actually + + align:start position:0% + + + + align:start position:0% + +mean if we do a glas of this will the + + align:start position:0% +mean if we do a glas of this will the + + + align:start position:0% +mean if we do a glas of this will the +okay let's just hold on let me let me do + + align:start position:0% +okay let's just hold on let me let me do + + + align:start position:0% +okay let's just hold on let me let me do +a quick vote will we have cases where + + align:start position:0% +a quick vote will we have cases where + + + align:start position:0% +a quick vote will we have cases where +Delta n is greater than + + align:start position:0% +Delta n is greater than + + + align:start position:0% +Delta n is greater than +one you know if I go through this + + align:start position:0% +one you know if I go through this + + + align:start position:0% +one you know if I go through this +process if I'm using the glaspie and I'm + + align:start position:0% +process if I'm using the glaspie and I'm + + + align:start position:0% +process if I'm using the glaspie and I'm +tracking how mRNA and protein number + + align:start position:0% +tracking how mRNA and protein number + + + align:start position:0% +tracking how mRNA and protein number +changing over time will I get you know + + align:start position:0% +changing over time will I get you know + + + align:start position:0% +changing over time will I get you know +these things protein burst where where + + align:start position:0% +these things protein burst where where + + + align:start position:0% +these things protein burst where where +Delta n is larger than one in one of + + align:start position:0% +Delta n is larger than one in one of + + + align:start position:0% +Delta n is larger than one in one of +these time + + align:start position:0% +these time + + + align:start position:0% +these time +Cycles okay + + align:start position:0% + + + + align:start position:0% + +okay ready three two + + align:start position:0% +okay ready three two + + + align:start position:0% +okay ready three two +one + + align:start position:0% +one + + + align:start position:0% +one +okay all right so we got so most of the + + align:start position:0% +okay all right so we got so most of the + + + align:start position:0% +okay all right so we got so most of the +group is saying that's it's going to be + + align:start position:0% +group is saying that's it's going to be + + + align:start position:0% +group is saying that's it's going to be +no but uh but it's not you know again + + align:start position:0% +no but uh but it's not you know again + + + align:start position:0% +no but uh but it's not you know again +there it's it's mixed so so can somebody + + align:start position:0% +there it's it's mixed so so can somebody + + + align:start position:0% +there it's it's mixed so so can somebody +say why why we don't + + align:start position:0% +say why why we don't + + + align:start position:0% +say why why we don't +get + + align:start position:0% + + + + align:start position:0% + +yeah it seems like the structure of the + + align:start position:0% +yeah it seems like the structure of the + + + align:start position:0% +yeah it seems like the structure of the +simulation is to make + + align:start position:0% +simulation is to make + + + align:start position:0% +simulation is to make +that's right yeah so the simulation as + + align:start position:0% +that's right yeah so the simulation as + + + align:start position:0% +that's right yeah so the simulation as +written and you could imagine some sort + + align:start position:0% +written and you could imagine some sort + + + align:start position:0% +written and you could imagine some sort +of phenomenological version of this + + align:start position:0% +of phenomenological version of this + + + align:start position:0% +of phenomenological version of this +where you allowed actually for protein + + align:start position:0% +where you allowed actually for protein + + + align:start position:0% +where you allowed actually for protein +but and as kind of specified is that we + + align:start position:0% +but and as kind of specified is that we + + + align:start position:0% +but and as kind of specified is that we +ask you know what's the time for one + + align:start position:0% +ask you know what's the time for one + + + align:start position:0% +ask you know what's the time for one +thing to happen right now uh why you but + + align:start position:0% +thing to happen right now uh why you but + + + align:start position:0% +thing to happen right now uh why you but +then but the claim somehow is okay well + + align:start position:0% +then but the claim somehow is okay well + + + align:start position:0% +then but the claim somehow is okay well +we can still get protein bursts from + + align:start position:0% +we can still get protein bursts from + + + align:start position:0% +we can still get protein bursts from +this and and how how does that + + align:start position:0% + + + + align:start position:0% + +happen yeah have the rate for something + + align:start position:0% +happen yeah have the rate for something + + + align:start position:0% +happen yeah have the rate for something +happening inre suddenly and that + + align:start position:0% + + + + align:start position:0% + +would yeah for example right if we + + align:start position:0% +would yeah for example right if we + + + align:start position:0% +would yeah for example right if we +didn't have an MR before and then we got + + align:start position:0% +didn't have an MR before and then we got + + + align:start position:0% +didn't have an MR before and then we got +an mRNA what it means is that if you + + align:start position:0% +an mRNA what it means is that if you + + + align:start position:0% +an mRNA what it means is that if you +look at n as a function of + + align:start position:0% +look at n as a function of + + + align:start position:0% +look at n as a function of +time during one of these protein bursts + + align:start position:0% +time during one of these protein bursts + + + align:start position:0% +time during one of these protein bursts +but you know before I was drawing it + + align:start position:0% +but you know before I was drawing it + + + align:start position:0% +but you know before I was drawing it +just hopping up but really in the + + align:start position:0% +just hopping up but really in the + + + align:start position:0% +just hopping up but really in the +context of the gesp it would be that it + + align:start position:0% +context of the gesp it would be that it + + + align:start position:0% +context of the gesp it would be that it +would hop hop you know so there would be + + align:start position:0% +would hop hop you know so there would be + + + align:start position:0% +would hop hop you know so there would be +little time + + align:start position:0% +little time + + + align:start position:0% +little time +jumps right + + align:start position:0% +jumps right + + + align:start position:0% +jumps right +so this is a protein burst but it's that + + align:start position:0% +so this is a protein burst but it's that + + + align:start position:0% +so this is a protein burst but it's that +oh it's it's really before this mRNA is + + align:start position:0% +oh it's it's really before this mRNA is + + + align:start position:0% +oh it's it's really before this mRNA is +degraded you get one one one one right + + align:start position:0% +degraded you get one one one one right + + + align:start position:0% +degraded you get one one one one right +so each of these is is Delta n of one + + align:start position:0% +so each of these is is Delta n of one + + + align:start position:0% +so each of these is is Delta n of one +right okay so this is uh you know + + align:start position:0% +right okay so this is uh you know + + + align:start position:0% +right okay so this is uh you know +whatever 67 right and then and then what + + align:start position:0% +whatever 67 right and then and then what + + + align:start position:0% +whatever 67 right and then and then what +can happen is that we get the MRNA + + align:start position:0% +can happen is that we get the MRNA + + + align:start position:0% +can happen is that we get the MRNA +degraded right and so then we're going + + align:start position:0% +degraded right and so then we're going + + + align:start position:0% +degraded right and so then we're going +to get a slower thing where + + align:start position:0% + + + + align:start position:0% + +it look you know it looks like that + + align:start position:0% +it look you know it looks like that + + + align:start position:0% +it look you know it looks like that +right so the gaspie everything is uh in + + align:start position:0% +right so the gaspie everything is uh in + + + align:start position:0% +right so the gaspie everything is uh in +uh everything's being created and + + align:start position:0% +uh everything's being created and + + + align:start position:0% +uh everything's being created and +destroyed in units of one but it could + + align:start position:0% +destroyed in units of one but it could + + + align:start position:0% +destroyed in units of one but it could +be that the time interval over this + + align:start position:0% +be that the time interval over this + + + align:start position:0% +be that the time interval over this +burst is just very short so then it goes + + align:start position:0% +burst is just very short so then it goes + + + align:start position:0% +burst is just very short so then it goes +up very quickly but then it's slower to + + align:start position:0% +up very quickly but then it's slower to + + + align:start position:0% +up very quickly but then it's slower to +go away + + align:start position:0% + + + + align:start position:0% + +okay so what I want to do in just the + + align:start position:0% +okay so what I want to do in just the + + + align:start position:0% +okay so what I want to do in just the +last 15 minutes is talk a bit about the + + align:start position:0% +last 15 minutes is talk a bit about the + + + align:start position:0% +last 15 minutes is talk a bit about the +fuer plun approximation um I would say + + align:start position:0% +fuer plun approximation um I would say + + + align:start position:0% +fuer plun approximation um I would say +that you know all of these different + + align:start position:0% +that you know all of these different + + + align:start position:0% +that you know all of these different +approaches are useful to varying degrees + + align:start position:0% +approaches are useful to varying degrees + + + align:start position:0% +approaches are useful to varying degrees +in terms of actually doing simulations + + align:start position:0% +in terms of actually doing simulations + + + align:start position:0% +in terms of actually doing simulations +doing analytic calculations getting + + align:start position:0% +doing analytic calculations getting + + + align:start position:0% +doing analytic calculations getting +intuition and um and the plon + + align:start position:0% +intuition and um and the plon + + + align:start position:0% +intuition and um and the plon +approach it give you know I'd say it's + + align:start position:0% +approach it give you know I'd say it's + + + align:start position:0% +approach it give you know I'd say it's +more or less useful for different people + + align:start position:0% +more or less useful for different people + + + align:start position:0% +more or less useful for different people +depending on um what you're doing okay + + align:start position:0% +depending on um what you're doing okay + + + align:start position:0% +depending on um what you're doing okay +so uh the basic ideas as kind of you you + + align:start position:0% +so uh the basic ideas as kind of you you + + + align:start position:0% +so uh the basic ideas as kind of you you +answered in the pre-class reading is + + align:start position:0% +answered in the pre-class reading is + + + align:start position:0% +answered in the pre-class reading is +that um in cases where n is is large + + align:start position:0% +that um in cases where n is is large + + + align:start position:0% +that um in cases where n is is large +enough that you don't feel like you need + + align:start position:0% +enough that you don't feel like you need + + + align:start position:0% +enough that you don't feel like you need +to take into account the discrete nature + + align:start position:0% +to take into account the discrete nature + + + align:start position:0% +to take into account the discrete nature +of the molecules um yet at the same time + + align:start position:0% +of the molecules um yet at the same time + + + align:start position:0% +of the molecules um yet at the same time +it's not so large you can totally ignore + + align:start position:0% +it's not so large you can totally ignore + + + align:start position:0% +it's not so large you can totally ignore +the fluctuations then the funer plun + + align:start position:0% +the fluctuations then the funer plun + + + align:start position:0% +the fluctuations then the funer plun +approach is nice because it allows you + + align:start position:0% +approach is nice because it allows you + + + align:start position:0% +approach is nice because it allows you +to + + align:start position:0% +to + + + align:start position:0% +to +get some sense of what's going on + + align:start position:0% +get some sense of what's going on + + + align:start position:0% +get some sense of what's going on +without all of the crazy details of um + + align:start position:0% +without all of the crazy details of um + + + align:start position:0% +without all of the crazy details of um +for example the master equation um but + + align:start position:0% +for example the master equation um but + + + align:start position:0% +for example the master equation um but +uh and and then it also because of this + + align:start position:0% +uh and and then it also because of this + + + align:start position:0% +uh and and then it also because of this +idea of an effective potential it allows + + align:start position:0% +idea of an effective potential it allows + + + align:start position:0% +idea of an effective potential it allows +you to bring all the intuition from that + + align:start position:0% +you to bring all the intuition from that + + + align:start position:0% +you to bring all the intuition from that +uh into your study of these Gene + + align:start position:0% +uh into your study of these Gene + + + align:start position:0% +uh into your study of these Gene +circuits um now I'm not going to go + + align:start position:0% +circuits um now I'm not going to go + + + align:start position:0% +circuits um now I'm not going to go +through the whole derivation but uh but + + align:start position:0% +through the whole derivation but uh but + + + align:start position:0% +through the whole derivation but uh but +if you have questions about that please + + align:start position:0% +if you have questions about that please + + + align:start position:0% +if you have questions about that please +uh come up after class and I'm happy to + + align:start position:0% +uh come up after class and I'm happy to + + + align:start position:0% +uh come up after class and I'm happy to +go through it with you because it's um + + align:start position:0% +go through it with you because it's um + + + align:start position:0% +go through it with you because it's um +you know it's it's sort of fun um + + align:start position:0% +you know it's it's sort of fun um + + + align:start position:0% +you know it's it's sort of fun um +but um but the the notes you know do do + + align:start position:0% +but um but the the notes you know do do + + + align:start position:0% +but um but the the notes you know do do +go over it uh I think that what's + + align:start position:0% +go over it uh I think that what's + + + align:start position:0% +go over it uh I think that what's +perhaps useful to just remind ourselves + + align:start position:0% +perhaps useful to just remind ourselves + + + align:start position:0% +perhaps useful to just remind ourselves +of is how it maybe leads to uh you know + + align:start position:0% +of is how it maybe leads to uh you know + + + align:start position:0% +of is how it maybe leads to uh you know +this g a gan with some width depending + + align:start position:0% +this g a gan with some width depending + + + align:start position:0% +this g a gan with some width depending +upon the shapes of the production + + align:start position:0% +upon the shapes of the production + + + align:start position:0% +upon the shapes of the production +degradation + + align:start position:0% + + + + align:start position:0% + +curse all right so the basic notion here + + align:start position:0% +curse all right so the basic notion here + + + align:start position:0% +curse all right so the basic notion here +is that depending on these + + align:start position:0% +is that depending on these + + + align:start position:0% +is that depending on these +F the fs and G's the production + + align:start position:0% +F the fs and G's the production + + + align:start position:0% +F the fs and G's the production +production degradation terms we we get + + align:start position:0% +production degradation terms we we get + + + align:start position:0% +production degradation terms we we get +different shaped uh effective potentials + + align:start position:0% +different shaped uh effective potentials + + + align:start position:0% +different shaped uh effective potentials +okay all right + + align:start position:0% + + + + align:start position:0% + +now right so in general we have + + align:start position:0% +now right so in general we have + + + align:start position:0% +now right so in general we have +something that looks like okay we have + + align:start position:0% +something that looks like okay we have + + + align:start position:0% +something that looks like okay we have +some n dot there's some FN and then + + align:start position:0% +some n dot there's some FN and then + + + align:start position:0% +some n dot there's some FN and then +there's a minus + + align:start position:0% +there's a minus + + + align:start position:0% +there's a minus +GN okay so for example for something + + align:start position:0% +GN okay so for example for something + + + align:start position:0% +GN okay so for example for something +that has just simple expression uh in + + align:start position:0% +that has just simple expression uh in + + + align:start position:0% +that has just simple expression uh in +the case of let's just imagine now now + + align:start position:0% +the case of let's just imagine now now + + + align:start position:0% +the case of let's just imagine now now +that there was if you want we could say + + align:start position:0% +that there was if you want we could say + + + align:start position:0% +that there was if you want we could say +It's A protein that is just where it's + + align:start position:0% +It's A protein that is just where it's + + + align:start position:0% +It's A protein that is just where it's +just some K minus gamma n or if you'd + + align:start position:0% +just some K minus gamma n or if you'd + + + align:start position:0% +just some K minus gamma n or if you'd +like we could say this is mRNA number + + align:start position:0% +like we could say this is mRNA number + + + align:start position:0% +like we could say this is mRNA number +you know but something it's just simple + + align:start position:0% +you know but something it's just simple + + + align:start position:0% +you know but something it's just simple +production and then uh first order + + align:start position:0% + + + + align:start position:0% + +degradation all right the question is + + align:start position:0% +degradation all right the question is + + + align:start position:0% +degradation all right the question is +how how do we how do we go about uh + + align:start position:0% +how how do we how do we go about uh + + + align:start position:0% +how how do we how do we go about uh +understanding this in the context of the + + align:start position:0% +understanding this in the context of the + + + align:start position:0% +understanding this in the context of the +fuer plun approximation and and it turns + + align:start position:0% +fuer plun approximation and and it turns + + + align:start position:0% +fuer plun approximation and and it turns +out that you can uh write it in what is + + align:start position:0% +out that you can uh write it in what is + + + align:start position:0% +out that you can uh write it in what is +a essentially some diffusion equation + + align:start position:0% +a essentially some diffusion equation + + + align:start position:0% +a essentially some diffusion equation +where you have some probability flux + + align:start position:0% +where you have some probability flux + + + align:start position:0% +where you have some probability flux +that is um that's moving around and and + + align:start position:0% +that is um that's moving around and and + + + align:start position:0% +that is um that's moving around and and +within that realm you can you know write + + align:start position:0% +within that realm you can you know write + + + align:start position:0% +within that realm you can you know write +that the the probability distribution of + + align:start position:0% +that the the probability distribution of + + + align:start position:0% +that the the probability distribution of +the number is going to be something to + + align:start position:0% +the number is going to be something to + + + align:start position:0% +the number is going to be something to +describe so there's going to be some + + align:start position:0% +describe so there's going to be some + + + align:start position:0% +describe so there's going to be some +constant there's the f plus G and + + align:start position:0% +constant there's the f plus G and + + + align:start position:0% +constant there's the f plus G and +they're both these are both functions of + + align:start position:0% +they're both these are both functions of + + + align:start position:0% +they're both these are both functions of +N and then you have an e to the + + align:start position:0% +N and then you have an e to the + + + align:start position:0% +N and then you have an e to the +minus n right so the idea here is + + align:start position:0% +minus n right so the idea here is + + + align:start position:0% +minus n right so the idea here is +that this behaves as some effective + + align:start position:0% +that this behaves as some effective + + + align:start position:0% +that this behaves as some effective +potential + + align:start position:0% + + + + align:start position:0% + +of course it's not quite true because f + + align:start position:0% +of course it's not quite true because f + + + align:start position:0% +of course it's not quite true because f +and g also are functions of N and + + align:start position:0% +and g also are functions of N and + + + align:start position:0% +and g also are functions of N and +they're not in here but this is the + + align:start position:0% +they're not in here but this is the + + + align:start position:0% +they're not in here but this is the +dominant term because it's in the + + align:start position:0% + + + + align:start position:0% + +exponential and here f is defined as the + + align:start position:0% +exponential and here f is defined as the + + + align:start position:0% +exponential and here f is defined as the +following so it's minus this integral + + align:start position:0% +following so it's minus this integral + + + align:start position:0% +following so it's minus this integral +Over N of the F minus G and f+ G + + align:start position:0% +Over N of the F minus G and f+ G + + + align:start position:0% +Over N of the F minus G and f+ G +DN and we my integrate Over N Prime + + align:start position:0% +DN and we my integrate Over N Prime + + + align:start position:0% +DN and we my integrate Over N Prime +okay right and we we're going to uh kind + + align:start position:0% +okay right and we we're going to uh kind + + + align:start position:0% +okay right and we we're going to uh kind +of go through what some of these + + align:start position:0% +of go through what some of these + + + align:start position:0% +of go through what some of these +different fs and G's might look like to + + align:start position:0% +different fs and G's might look like to + + + align:start position:0% +different fs and G's might look like to +try to get a sense of why this happened + + align:start position:0% +try to get a sense of why this happened + + + align:start position:0% +try to get a sense of why this happened +okay uh it is worth mentioning that you + + align:start position:0% +okay uh it is worth mentioning that you + + + align:start position:0% +okay uh it is worth mentioning that you +can do this for any f and g that um + + align:start position:0% +can do this for any f and g that um + + + align:start position:0% +can do this for any f and g that um +where when it's just in one dimension + + align:start position:0% +where when it's just in one dimension + + + align:start position:0% +where when it's just in one dimension +right so you just have n okay once you + + align:start position:0% +right so you just have n okay once you + + + align:start position:0% +right so you just have n okay once you +have uh it in two Dimensions right so + + align:start position:0% +have uh it in two Dimensions right so + + + align:start position:0% +have uh it in two Dimensions right so +once you actually have mRNA and protein + + align:start position:0% +once you actually have mRNA and protein + + + align:start position:0% +once you actually have mRNA and protein +for example um you're not guaranteed to + + align:start position:0% +for example um you're not guaranteed to + + + align:start position:0% +for example um you're not guaranteed to +be able to write it as an effective + + align:start position:0% +be able to write it as an effective + + + align:start position:0% +be able to write it as an effective +potential uh right uh although I guess + + align:start position:0% +potential uh right uh although I guess + + + align:start position:0% +potential uh right uh although I guess +if you're if you're willing to invoke a + + align:start position:0% +if you're if you're willing to invoke a + + + align:start position:0% +if you're if you're willing to invoke a +vector potential then U then uh then + + align:start position:0% +vector potential then U then uh then + + + align:start position:0% +vector potential then U then uh then +maybe uh then maybe you can all right + + align:start position:0% +maybe uh then maybe you can all right + + + align:start position:0% +maybe uh then maybe you can all right +but uh in terms of just a simple + + align:start position:0% +but uh in terms of just a simple + + + align:start position:0% +but uh in terms of just a simple +potential then uh you can do it in one + + align:start position:0% +potential then uh you can do it in one + + + align:start position:0% +potential then uh you can do it in one +dimension but not necessarily in more + + align:start position:0% + + + + align:start position:0% + +okay um and I think that in general our + + align:start position:0% +okay um and I think that in general our + + + align:start position:0% +okay um and I think that in general our +intuition is not as useful when you have + + align:start position:0% +intuition is not as useful when you have + + + align:start position:0% +intuition is not as useful when you have +the equivalent of magnetic fields and so + + align:start position:0% +the equivalent of magnetic fields and so + + + align:start position:0% +the equivalent of magnetic fields and so +forth here anyways all + + align:start position:0% +forth here anyways all + + + align:start position:0% +forth here anyways all +right what I to do is just try to + + align:start position:0% +right what I to do is just try to + + + align:start position:0% +right what I to do is just try to +understand why uh why this thing looks + + align:start position:0% +understand why uh why this thing looks + + + align:start position:0% +understand why uh why this thing looks +the way it does for um for this simple + + align:start position:0% +the way it does for um for this simple + + + align:start position:0% +the way it does for um for this simple +regulation case and then we're going to + + align:start position:0% +regulation case and then we're going to + + + align:start position:0% +regulation case and then we're going to +ask okay if we change one thing or + + align:start position:0% +ask okay if we change one thing or + + + align:start position:0% +ask okay if we change one thing or +another how does it + + align:start position:0% +another how does it + + + align:start position:0% +another how does it +affect uh the resulting + + align:start position:0% +affect uh the resulting + + + align:start position:0% +affect uh the resulting +variance + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +okay okay all right so for unregulated + + align:start position:0% +okay okay all right so for unregulated + + + align:start position:0% +okay okay all right so for unregulated +expression such as + + align:start position:0% + + + + align:start position:0% + +here the if we look at the production + + align:start position:0% +here the if we look at the production + + + align:start position:0% +here the if we look at the production +and degradation is a function of + + align:start position:0% +and degradation is a function of + + + align:start position:0% +and degradation is a function of +n right + + align:start position:0% +n right + + + align:start position:0% +n right +so FN is G is just some constant K + + align:start position:0% +so FN is G is just some constant K + + + align:start position:0% +so FN is G is just some constant K +whereas + + align:start position:0% +whereas + + + align:start position:0% +whereas +GN is a line that goes up as gamma n + + align:start position:0% + + + + align:start position:0% + +okay okay now in this situation + + align:start position:0% +okay okay now in this situation + + + align:start position:0% +okay okay now in this situation +we if you do this integral and really + + align:start position:0% +we if you do this integral and really + + + align:start position:0% +we if you do this integral and really +what you can imagine is what this + + align:start position:0% +what you can imagine is what this + + + align:start position:0% +what you can imagine is what this +integral looks like right around that + + align:start position:0% +integral looks like right around that + + + align:start position:0% +integral looks like right around that +steady um that steady state because + + align:start position:0% +steady um that steady state because + + + align:start position:0% +steady um that steady state because +that's kind of maybe what we want to + + align:start position:0% +that's kind of maybe what we want to + + + align:start position:0% +that's kind of maybe what we want to +know if we want to know something about + + align:start position:0% +know if we want to know something about + + + align:start position:0% +know if we want to know something about +for example the width of the + + align:start position:0% +for example the width of the + + + align:start position:0% +for example the width of the +distribution okay well there's going to + + align:start position:0% +distribution okay well there's going to + + + align:start position:0% +distribution okay well there's going to +be two terms in the numerator there's an + + align:start position:0% +be two terms in the numerator there's an + + + align:start position:0% +be two terms in the numerator there's an +F minus G in the denominator there's an + + align:start position:0% +F minus G in the denominator there's an + + + align:start position:0% +F minus G in the denominator there's an +f plus G okay now F minus G is actually + + align:start position:0% +f plus G okay now F minus G is actually + + + align:start position:0% +f plus G okay now F minus G is actually +equal to zero right at that steady state + + align:start position:0% +equal to zero right at that steady state + + + align:start position:0% +equal to zero right at that steady state +and that's why it's a steady state + + align:start position:0% +and that's why it's a steady state + + + align:start position:0% +and that's why it's a steady state +because production and degradation are + + align:start position:0% +because production and degradation are + + + align:start position:0% +because production and degradation are +equal okay now as you go away from that + + align:start position:0% +equal okay now as you go away from that + + + align:start position:0% +equal okay now as you go away from that +location you're what you're doing is + + align:start position:0% +location you're what you're doing is + + + align:start position:0% +location you're what you're doing is +you're integrating the difference + + align:start position:0% +you're integrating the difference + + + align:start position:0% +you're integrating the difference +between the F and the g okay and you can + + align:start position:0% +between the F and the g okay and you can + + + align:start position:0% +between the F and the g okay and you can +see that around here these things are + + align:start position:0% +see that around here these things are + + + align:start position:0% +see that around here these things are +separating kind of + + align:start position:0% +separating kind of + + + align:start position:0% +separating kind of +um well everything's a line here and + + align:start position:0% +um well everything's a line here and + + + align:start position:0% +um well everything's a line here and +indeed even if f and g were not linear + + align:start position:0% +indeed even if f and g were not linear + + + align:start position:0% +indeed even if f and g were not linear +uh close to the um to that steady state + + align:start position:0% +uh close to the um to that steady state + + + align:start position:0% +uh close to the um to that steady state +they would be linear right what we can + + align:start position:0% +they would be linear right what we can + + + align:start position:0% +they would be linear right what we can +see is that as you're integrating you're + + align:start position:0% +see is that as you're integrating you're + + + align:start position:0% +see is that as you're integrating you're +integrating across something that is + + align:start position:0% +integrating across something that is + + + align:start position:0% +integrating across something that is +growing linear L sry that's what gives + + align:start position:0% +growing linear L sry that's what gives + + + align:start position:0% +growing linear L sry that's what gives +you a + + align:start position:0% +you a + + + align:start position:0% +you a +quadratic okay and that's why this + + align:start position:0% +quadratic okay and that's why this + + + align:start position:0% +quadratic okay and that's why this +effective potential ends up behaving as + + align:start position:0% +effective potential ends up behaving as + + + align:start position:0% +effective potential ends up behaving as +uh as if you're in a quadratic + + align:start position:0% +uh as if you're in a quadratic + + + align:start position:0% +uh as if you're in a quadratic +trap okay now I encourage you to go + + align:start position:0% +trap okay now I encourage you to go + + + align:start position:0% +trap okay now I encourage you to go +ahead and like do that integral at some + + align:start position:0% +ahead and like do that integral at some + + + align:start position:0% +ahead and like do that integral at some +point I was planning on doing it for you + + align:start position:0% +point I was planning on doing it for you + + + align:start position:0% +point I was planning on doing it for you +today but uh we are running out of time + + align:start position:0% +today but uh we are running out of time + + + align:start position:0% +today but uh we are running out of time +once again I'm happy to do it just you + + align:start position:0% +once again I'm happy to do it just you + + + align:start position:0% +once again I'm happy to do it just you +know just after class uh and indeed what + + align:start position:0% +know just after class uh and indeed what + + + align:start position:0% +know just after class uh and indeed what +you can see is that because you're + + align:start position:0% +you can see is that because you're + + + align:start position:0% +you can see is that because you're +integrating across here you end up + + align:start position:0% +integrating across here you end up + + + align:start position:0% +integrating across here you end up +getting a quadratic increase in the + + align:start position:0% +getting a quadratic increase in the + + + align:start position:0% +getting a quadratic increase in the +effective potential right and if you + + align:start position:0% +effective potential right and if you + + + align:start position:0% +effective potential right and if you +look at what the variance of that thing + + align:start position:0% +look at what the variance of that thing + + + align:start position:0% +look at what the variance of that thing +is you indeed find that the variance is + + align:start position:0% +is you indeed find that the variance is + + + align:start position:0% +is you indeed find that the variance is +equal to the mean + + align:start position:0% +equal to the mean + + + align:start position:0% +equal to the mean +here + + align:start position:0% +here + + + align:start position:0% +here +okay so what I want to ask in terms of + + align:start position:0% +okay so what I want to ask in terms of + + + align:start position:0% +okay so what I want to ask in terms of +trying to get intuition is what happens + + align:start position:0% +trying to get intuition is what happens + + + align:start position:0% +trying to get intuition is what happens +if we pull these curves + + align:start position:0% +if we pull these curves + + + align:start position:0% +if we pull these curves +down okay so in particular let's imagine + + align:start position:0% +down okay so in particular let's imagine + + + align:start position:0% +down okay so in particular let's imagine +that we have a situation + + align:start position:0% +that we have a situation + + + align:start position:0% +that we have a situation +where all right I'm going to + + align:start position:0% +where all right I'm going to + + + align:start position:0% +where all right I'm going to +reparameterize things so again we're + + align:start position:0% +reparameterize things so again we're + + + align:start position:0% +reparameterize things so again we're +kind of keeping + + align:start position:0% +kind of keeping + + + align:start position:0% +kind of keeping +the number the number at the equilibrium + + align:start position:0% +the number the number at the equilibrium + + + align:start position:0% +the number the number at the equilibrium +constant but now what I'm going to do is + + align:start position:0% +constant but now what I'm going to do is + + + align:start position:0% +constant but now what I'm going to do is +I'm going to have an FN that looks like + + align:start position:0% +I'm going to have an FN that looks like + + + align:start position:0% +I'm going to have an FN that looks like +this and GN looks like so now GN is + + align:start position:0% +this and GN looks like so now GN is + + + align:start position:0% +this and GN looks like so now GN is +going to be some 1 half of Lambda and + + align:start position:0% +going to be some 1 half of Lambda and + + + align:start position:0% +going to be some 1 half of Lambda and +this FN is equal to K minus 12 of gamma + + align:start position:0% + + + + align:start position:0% + +n all right now the question is in this + + align:start position:0% +n all right now the question is in this + + + align:start position:0% +n all right now the question is in this +situation what will be the variance over + + align:start position:0% +situation what will be the variance over + + + align:start position:0% +situation what will be the variance over +the mean + + align:start position:0% + + + + align:start position:0% + +well first of all the variance over the + + align:start position:0% +well first of all the variance over the + + + align:start position:0% +well first of all the variance over the +mean here was equal to + + align:start position:0% + + + + align:start position:0% + +what although should I should we do a + + align:start position:0% + + + + align:start position:0% + +vote okay here are going to be some + + align:start position:0% +vote okay here are going to be some + + + align:start position:0% +vote okay here are going to be some +options + + align:start position:0% + + + + align:start position:0% + +question is variance over the mean in + + align:start position:0% +question is variance over the mean in + + + align:start position:0% +question is variance over the mean in +this in this + + align:start position:0% + + + + align:start position:0% + +situation all right I'm worried that + + align:start position:0% +situation all right I'm worried that + + + align:start position:0% +situation all right I'm worried that +this is not going to work but all right + + align:start position:0% +this is not going to work but all right + + + align:start position:0% +this is not going to work but all right +let's just see where we are uh ready uh + + align:start position:0% +let's just see where we are uh ready uh + + + align:start position:0% +let's just see where we are uh ready uh +three two one + + align:start position:0% +three two one + + + align:start position:0% +three two one +okay all right so I'd say that at least + + align:start position:0% +okay all right so I'd say that at least + + + align:start position:0% +okay all right so I'd say that at least +uh broadly everyone okay people are + + align:start position:0% +uh broadly everyone okay people are + + + align:start position:0% +uh broadly everyone okay people are +agreeing that yeah the variance over the + + align:start position:0% +agreeing that yeah the variance over the + + + align:start position:0% +agreeing that yeah the variance over the +mean here is equal to one and again this + + align:start position:0% +mean here is equal to one and again this + + + align:start position:0% +mean here is equal to one and again this +is the situation that we've analyzed + + align:start position:0% +is the situation that we've analyzed + + + align:start position:0% +is the situation that we've analyzed +many times which is that in this + + align:start position:0% +many times which is that in this + + + align:start position:0% +many times which is that in this +situation we get a Pon where the pon + + align:start position:0% +situation we get a Pon where the pon + + + align:start position:0% +situation we get a Pon where the pon +only has one free parameter and that + + align:start position:0% +only has one free parameter and that + + + align:start position:0% +only has one free parameter and that +parameter specifies both the mean and + + align:start position:0% +parameter specifies both the mean and + + + align:start position:0% +parameter specifies both the mean and +the variance okay so for a Pon the + + align:start position:0% +the variance okay so for a Pon the + + + align:start position:0% +the variance okay so for a Pon the +variance over the mean is indeed equal + + align:start position:0% +variance over the mean is indeed equal + + + align:start position:0% +variance over the mean is indeed equal +to one right so the fuer flan + + align:start position:0% +to one right so the fuer flan + + + align:start position:0% +to one right so the fuer flan +approximation actually uh sort of + + align:start position:0% +approximation actually uh sort of + + + align:start position:0% +approximation actually uh sort of +accurately recapitulates that + + align:start position:0% +accurately recapitulates that + + + align:start position:0% +accurately recapitulates that +okay now the question is what will the + + align:start position:0% +okay now the question is what will the + + + align:start position:0% +okay now the question is what will the +variance over the mean be in the + + align:start position:0% +variance over the mean be in the + + + align:start position:0% +variance over the mean be in the +situation that I've just drawn + + align:start position:0% +situation that I've just drawn + + + align:start position:0% +situation that I've just drawn +here right so I'm going to give you a + + align:start position:0% +here right so I'm going to give you a + + + align:start position:0% +here right so I'm going to give you a +minute to try to think about what this + + align:start position:0% +minute to try to think about what this + + + align:start position:0% +minute to try to think about what this +means and there are multiple ways of of + + align:start position:0% +means and there are multiple ways of of + + + align:start position:0% +means and there are multiple ways of of +figuring it out you can uh look at maybe + + align:start position:0% +figuring it out you can uh look at maybe + + + align:start position:0% +figuring it out you can uh look at maybe +the integral you can think about uh the + + align:start position:0% +the integral you can think about uh the + + + align:start position:0% +the integral you can think about uh the +biological intuition to make at least a + + align:start position:0% +biological intuition to make at least a + + + align:start position:0% +biological intuition to make at least a +guess of of where of what it should do + + align:start position:0% +guess of of where of what it should do + + + align:start position:0% +guess of of where of what it should do +right the question is if um if the + + align:start position:0% +right the question is if um if the + + + align:start position:0% +right the question is if um if the +production rate and the degradation rate + + align:start position:0% +production rate and the degradation rate + + + align:start position:0% +production rate and the degradation rate +look like this what does that um what + + align:start position:0% +look like this what does that um what + + + align:start position:0% +look like this what does that um what +does that mean for the the variance over + + align:start position:0% +does that mean for the the variance over + + + align:start position:0% +does that mean for the the variance over +the mean so I'll give you a minute to + + align:start position:0% +the mean so I'll give you a minute to + + + align:start position:0% +the mean so I'll give you a minute to +kind of to play with + + align:start position:0% + + + + align:start position:0% + +it for + + align:start position:0% + + + + align:start position:0% + +all right why don't we go ahead and vote + + align:start position:0% +all right why don't we go ahead and vote + + + align:start position:0% +all right why don't we go ahead and vote +just so I can and get a sense of where + + align:start position:0% +just so I can and get a sense of where + + + align:start position:0% +just so I can and get a sense of where +we are and also uh it's okay if you + + align:start position:0% +we are and also uh it's okay if you + + + align:start position:0% +we are and also uh it's okay if you +can't actually figure this out or you're + + align:start position:0% +can't actually figure this out or you're + + + align:start position:0% +can't actually figure this out or you're +confused but I but go ahead and and make + + align:start position:0% +confused but I but go ahead and and make + + + align:start position:0% +confused but I but go ahead and and make +your best guess anyways because it's + + align:start position:0% +your best guess anyways because it's + + + align:start position:0% +your best guess anyways because it's +also useful to um if you can guess kind + + align:start position:0% +also useful to um if you can guess kind + + + align:start position:0% +also useful to um if you can guess kind +of the direction it'll go even if you + + align:start position:0% +of the direction it'll go even if you + + + align:start position:0% +of the direction it'll go even if you +can't figure out its magnitude all right + + align:start position:0% +can't figure out its magnitude all right + + + align:start position:0% +can't figure out its magnitude all right +so uh let's let's vote ready three two + + align:start position:0% +so uh let's let's vote ready three two + + + align:start position:0% +so uh let's let's vote ready three two +one okay so um all right so it's it's + + align:start position:0% +one okay so um all right so it's it's + + + align:start position:0% +one okay so um all right so it's it's +it's a mixture now I would say of you + + align:start position:0% +it's a mixture now I would say of you + + + align:start position:0% +it's a mixture now I would say of you +know a b c's D's + + align:start position:0% +know a b c's D's + + + align:start position:0% +know a b c's D's +um okay um yeah no I think this is this + + align:start position:0% +um okay um yeah no I think this is this + + + align:start position:0% +um okay um yeah no I think this is this +is I think hard and + + align:start position:0% +is I think hard and + + + align:start position:0% +is I think hard and +confusing I maybe won't have + + align:start position:0% +confusing I maybe won't have + + + align:start position:0% +confusing I maybe won't have +um + + align:start position:0% + + + + align:start position:0% + +yeah all right I'll maybe say something + + align:start position:0% +yeah all right I'll maybe say something + + + align:start position:0% +yeah all right I'll maybe say something +because it may be that talking won't to + + align:start position:0% +because it may be that talking won't to + + + align:start position:0% +because it may be that talking won't to +each other won't help that much either + + align:start position:0% +each other won't help that much either + + + align:start position:0% +each other won't help that much either +um okay so in this case what's relevant + + align:start position:0% +um okay so in this case what's relevant + + + align:start position:0% +um okay so in this case what's relevant +is both the F minus G and the f plus + + align:start position:0% +is both the F minus G and the f plus + + + align:start position:0% +is both the F minus G and the f plus +G okay and and turns out that F minus G + + align:start position:0% +G okay and and turns out that F minus G + + + align:start position:0% +G okay and and turns out that F minus G +actually behaves the same way because at + + align:start position:0% +actually behaves the same way because at + + + align:start position:0% +actually behaves the same way because at +the fixed point or at the equilibrium it + + align:start position:0% +the fixed point or at the equilibrium it + + + align:start position:0% +the fixed point or at the equilibrium it +starts at zero and then it actually + + align:start position:0% +starts at zero and then it actually + + + align:start position:0% +starts at zero and then it actually +grows in the same way as you go away + + align:start position:0% +grows in the same way as you go away + + + align:start position:0% +grows in the same way as you go away +from it the difference is that the f + + align:start position:0% +from it the difference is that the f + + + align:start position:0% +from it the difference is that the f +plus G where U that's very much not + + align:start position:0% +plus G where U that's very much not + + + align:start position:0% +plus G where U that's very much not +equal to zero and f plus g at the + + align:start position:0% +equal to zero and f plus g at the + + + align:start position:0% +equal to zero and f plus g at the +equilibrium this f plus G here is around + + align:start position:0% +equilibrium this f plus G here is around + + + align:start position:0% +equilibrium this f plus G here is around +2K whereas f plus G over + + align:start position:0% +2K whereas f plus G over + + + align:start position:0% +2K whereas f plus G over +here is around uh + + align:start position:0% +here is around uh + + + align:start position:0% +here is around uh +1K right what that means is that the in + + align:start position:0% +1K right what that means is that the in + + + align:start position:0% +1K right what that means is that the in +both cases you have a quadratic + + align:start position:0% +both cases you have a quadratic + + + align:start position:0% +both cases you have a quadratic +potential but here the quadratic + + align:start position:0% +potential but here the quadratic + + + align:start position:0% +potential but here the quadratic +potential actually ends up being steeper + + align:start position:0% +potential actually ends up being steeper + + + align:start position:0% +potential actually ends up being steeper +so if this were unregulated then over + + align:start position:0% +so if this were unregulated then over + + + align:start position:0% +so if this were unregulated then over +here we still + + align:start position:0% +here we still + + + align:start position:0% +here we still +get a quadratic but it's a it's a with + + align:start position:0% +get a quadratic but it's a it's a with + + + align:start position:0% +get a quadratic but it's a it's a with +steeper walls okay so actually here um + + align:start position:0% +steeper walls okay so actually here um + + + align:start position:0% +steeper walls okay so actually here um +this the variance over the mean uh ends + + align:start position:0% +this the variance over the mean uh ends + + + align:start position:0% +this the variance over the mean uh ends +up being a + + align:start position:0% +up being a + + + align:start position:0% +up being a +half and it's useful to go ahead and + + align:start position:0% +half and it's useful to go ahead and + + + align:start position:0% +half and it's useful to go ahead and +just play with this play with these + + align:start position:0% +just play with this play with these + + + align:start position:0% +just play with this play with these +equations to see why that happens right + + align:start position:0% +equations to see why that happens right + + + align:start position:0% +equations to see why that happens right +and I think that a nice way to think + + align:start position:0% +and I think that a nice way to think + + + align:start position:0% +and I think that a nice way to think +about this is is in this limit where we + + align:start position:0% +about this is is in this limit where we + + + align:start position:0% +about this is is in this limit where we +pull this Crossing Point all the way + + align:start position:0% +pull this Crossing Point all the way + + + align:start position:0% +pull this Crossing Point all the way +down to + + align:start position:0% + + + + align:start position:0% + +zero right now we have something that + + align:start position:0% +zero right now we have something that + + + align:start position:0% +zero right now we have something that +looks kind of like + + align:start position:0% + + + + align:start position:0% + +this right so very very uh low rate of + + align:start position:0% +this right so very very uh low rate of + + + align:start position:0% +this right so very very uh low rate of +degradation but then also the production + + align:start position:0% +degradation but then also the production + + + align:start position:0% +degradation but then also the production +rate essentially goes to + + align:start position:0% +rate essentially goes to + + + align:start position:0% +rate essentially goes to +zero when we're at this + + align:start position:0% +zero when we're at this + + + align:start position:0% +zero when we're at this +point that we could still parameterize + + align:start position:0% +point that we could still parameterize + + + align:start position:0% +point that we could still parameterize +as K Over gamma if we want you know with + + align:start position:0% +as K Over gamma if we want you know with + + + align:start position:0% +as K Over gamma if we want you know with +some + + align:start position:0% +some + + + align:start position:0% +some +you know but you know this could we + + align:start position:0% +you know but you know this could we + + + align:start position:0% +you know but you know this could we +could just think about this as as being + + align:start position:0% +could just think about this as as being + + + align:start position:0% +could just think about this as as being +at a 100 of these mRNA say but then + + align:start position:0% +at a 100 of these mRNA say but then + + + align:start position:0% +at a 100 of these mRNA say but then +we're changing the production + + align:start position:0% +we're changing the production + + + align:start position:0% +we're changing the production +degradation rate right and the variance + + align:start position:0% +degradation rate right and the variance + + + align:start position:0% +degradation rate right and the variance +over the mean here does anybody have a + + align:start position:0% +over the mean here does anybody have a + + + align:start position:0% +over the mean here does anybody have a +guess of where that + + align:start position:0% + + + + align:start position:0% + +goes okay in this case it actually goes + + align:start position:0% +goes okay in this case it actually goes + + + align:start position:0% +goes okay in this case it actually goes +to + + align:start position:0% + + + + align:start position:0% + +zero and this is an interesting + + align:start position:0% +zero and this is an interesting + + + align:start position:0% +zero and this is an interesting +situation + + align:start position:0% +situation + + + align:start position:0% +situation +because really in the limit where + + align:start position:0% +because really in the limit where + + + align:start position:0% +because really in the limit where +there's no degradation and it's all at + + align:start position:0% +there's no degradation and it's all at + + + align:start position:0% +there's no degradation and it's all at +the production side what it's saying is + + align:start position:0% +the production side what it's saying is + + + align:start position:0% +the production side what it's saying is +that you produce you produce you produce + + align:start position:0% +that you produce you produce you produce + + + align:start position:0% +that you produce you produce you produce +until you get to this number which might + + align:start position:0% +until you get to this number which might + + + align:start position:0% +until you get to this number which might +be 100 and then you simply stop doing + + align:start position:0% +be 100 and then you simply stop doing + + + align:start position:0% +be 100 and then you simply stop doing +anything right you're not degrading + + align:start position:0% +anything right you're not degrading + + + align:start position:0% +anything right you're not degrading +you're not producing right but in that + + align:start position:0% +you're not producing right but in that + + + align:start position:0% +you're not producing right but in that +case that all the cells will have + + align:start position:0% +case that all the cells will have + + + align:start position:0% +case that all the cells will have +exactly 100 maybe + + align:start position:0% + + + + align:start position:0% + +mRNA and what the the fuer plun kind of + + align:start position:0% +mRNA and what the the fuer plun kind of + + + align:start position:0% +mRNA and what the the fuer plun kind of +formalism tells you is that just because + + align:start position:0% +formalism tells you is that just because + + + align:start position:0% +formalism tells you is that just because +production and degradation rates are + + align:start position:0% +production and degradation rates are + + + align:start position:0% +production and degradation rates are +equal right Fus G is equal to zero + + align:start position:0% +equal right Fus G is equal to zero + + + align:start position:0% +equal right Fus G is equal to zero +doesn't mean that um that tells you that + + align:start position:0% +doesn't mean that um that tells you that + + + align:start position:0% +doesn't mean that um that tells you that +that's the equilibrium but it doesn't + + align:start position:0% +that's the equilibrium but it doesn't + + + align:start position:0% +that's the equilibrium but it doesn't +tell you how much spread there's going + + align:start position:0% +tell you how much spread there's going + + + align:start position:0% +tell you how much spread there's going +to be around the equilibrium okay if f + + align:start position:0% +to be around the equilibrium okay if f + + + align:start position:0% +to be around the equilibrium okay if f +and g are each larger that leads to a + + align:start position:0% +and g are each larger that leads to a + + + align:start position:0% +and g are each larger that leads to a +larger spread because there's more + + align:start position:0% +larger spread because there's more + + + align:start position:0% +larger spread because there's more +Randomness okay whereas here f and g are + + align:start position:0% +Randomness okay whereas here f and g are + + + align:start position:0% +Randomness okay whereas here f and g are +both essentially zero at that point what + + align:start position:0% +both essentially zero at that point what + + + align:start position:0% +both essentially zero at that point what +that means is that that you kind of just + + align:start position:0% +that means is that that you kind of just + + + align:start position:0% +that means is that that you kind of just +pile up right at that precise + + align:start position:0% + + + + align:start position:0% + +value right we are out of time so I + + align:start position:0% +value right we are out of time so I + + + align:start position:0% +value right we are out of time so I +think we should quit but I am available + + align:start position:0% +think we should quit but I am available + + + align:start position:0% +think we should quit but I am available +for the next half hour if anybody has + + align:start position:0% +for the next half hour if anybody has + + + align:start position:0% +for the next half hour if anybody has +any questions all right thanks \ No newline at end of file diff --git a/EdRkQmmq7vk.txt b/EdRkQmmq7vk.txt new file mode 100644 index 0000000000000000000000000000000000000000..d1a038ac2cd2a89394760a75dcaee0db74832577 --- /dev/null +++ b/EdRkQmmq7vk.txt @@ -0,0 +1,1971 @@ +align:start position:0% + +today's a lecture continues the thing we + + align:start position:0% +today's a lecture continues the thing we + + + align:start position:0% +today's a lecture continues the thing we +were doing with scattering States we + + align:start position:0% +were doing with scattering States we + + + align:start position:0% +were doing with scattering States we +send in a scattering state that is an + + align:start position:0% +send in a scattering state that is an + + + align:start position:0% +send in a scattering state that is an +energy eigenstate that cannot be + + align:start position:0% +energy eigenstate that cannot be + + + align:start position:0% +energy eigenstate that cannot be +normalized into a step barrier and we + + align:start position:0% +normalized into a step barrier and we + + + align:start position:0% +normalized into a step barrier and we +looked at what could happen and we saw + + align:start position:0% +looked at what could happen and we saw + + + align:start position:0% +looked at what could happen and we saw +kinds of interesting things happening + + align:start position:0% +kinds of interesting things happening + + + align:start position:0% +kinds of interesting things happening +it was reflection and transmission when + + align:start position:0% +it was reflection and transmission when + + + align:start position:0% +it was reflection and transmission when +the energy was higher than the barrier + + align:start position:0% +the energy was higher than the barrier + + + align:start position:0% +the energy was higher than the barrier +and there was just reflection and a + + align:start position:0% +and there was just reflection and a + + + align:start position:0% +and there was just reflection and a +little exponential decay in the + + align:start position:0% +little exponential decay in the + + + align:start position:0% +little exponential decay in the +forbidden region if the energy was lower + + align:start position:0% +forbidden region if the energy was lower + + + align:start position:0% +forbidden region if the energy was lower +than the energy of the barrier we also + + align:start position:0% +than the energy of the barrier we also + + + align:start position:0% +than the energy of the barrier we also +observed when we did a packet analysis + + align:start position:0% +observed when we did a packet analysis + + + align:start position:0% +observed when we did a packet analysis +that a wave packet sending would have a + + align:start position:0% +that a wave packet sending would have a + + + align:start position:0% +that a wave packet sending would have a +delay in coming back out it doesn't come + + align:start position:0% +delay in coming back out it doesn't come + + + align:start position:0% +delay in coming back out it doesn't come +out immediately and that's the property + + align:start position:0% +out immediately and that's the property + + + align:start position:0% +out immediately and that's the property +of those complex numbers that entered + + align:start position:0% +of those complex numbers that entered + + + align:start position:0% +of those complex numbers that entered +into the reflection coefficient those + + align:start position:0% +into the reflection coefficient those + + + align:start position:0% +into the reflection coefficient those +complex numbers were a face that had an + + align:start position:0% +complex numbers were a face that had an + + + align:start position:0% +complex numbers were a face that had an +energy dependence and by the time you're + + align:start position:0% +energy dependence and by the time you're + + + align:start position:0% +energy dependence and by the time you're +done with analyzing how the wave packet + + align:start position:0% +done with analyzing how the wave packet + + + align:start position:0% +done with analyzing how the wave packet +is moving there was a delay so today + + align:start position:0% +is moving there was a delay so today + + + align:start position:0% +is moving there was a delay so today +we're going to see another effect that + + align:start position:0% +we're going to see another effect that + + + align:start position:0% +we're going to see another effect that +this sometimes called resonant + + align:start position:0% +this sometimes called resonant + + + align:start position:0% +this sometimes called resonant +transmission and it's a rather famous of + + align:start position:0% +transmission and it's a rather famous of + + + align:start position:0% +transmission and it's a rather famous of +led to the so-called rum sour Townsend + + align:start position:0% +led to the so-called rum sour Townsend + + + align:start position:0% +led to the so-called rum sour Townsend +effect so we'll discuss that and then + + align:start position:0% +effect so we'll discuss that and then + + + align:start position:0% +effect so we'll discuss that and then +I'll turn for the last half an hour into + + align:start position:0% +I'll turn for the last half an hour into + + + align:start position:0% +I'll turn for the last half an hour into +the setup where we can analyze more + + align:start position:0% +the setup where we can analyze more + + + align:start position:0% +the setup where we can analyze more +general scattering problems so let's + + align:start position:0% +general scattering problems so let's + + + align:start position:0% +general scattering problems so let's +begin with this rum sour Townsend effect + + align:start position:0% +begin with this rum sour Townsend effect + + + align:start position:0% +begin with this rum sour Townsend effect +and rum sour pounds and + + align:start position:0% + + + + align:start position:0% + +effect before discussing + + align:start position:0% +effect before discussing + + + align:start position:0% +effect before discussing +phenomenologically what was involved in + + align:start position:0% +phenomenologically what was involved in + + + align:start position:0% +phenomenologically what was involved in +this effect let's do the mathematical + + align:start position:0% +this effect let's do the mathematical + + + align:start position:0% +this effect let's do the mathematical +and physics analysis of a toy problem + + align:start position:0% +and physics analysis of a toy problem + + + align:start position:0% +and physics analysis of a toy problem +relevant to this effect and for that toy + + align:start position:0% +relevant to this effect and for that toy + + + align:start position:0% +relevant to this effect and for that toy +problem we have the finite square well + + align:start position:0% + + + + align:start position:0% + +we've normalized this square well having + + align:start position:0% +we've normalized this square well having + + + align:start position:0% +we've normalized this square well having +width to a so it extends from - a - a + + align:start position:0% +width to a so it extends from - a - a + + + align:start position:0% +width to a so it extends from - a - a +that's x equals 0 and there's a number - + + align:start position:0% +that's x equals 0 and there's a number - + + + align:start position:0% +that's x equals 0 and there's a number - +V naught V naught we always defined it + + align:start position:0% +V naught V naught we always defined it + + + align:start position:0% +V naught V naught we always defined it +to be positive therefore V naught is the + + align:start position:0% +to be positive therefore V naught is the + + + align:start position:0% +to be positive therefore V naught is the +depth of this potential and the question + + align:start position:0% +depth of this potential and the question + + + align:start position:0% +depth of this potential and the question +is what happens in you if you send in a + + align:start position:0% +is what happens in you if you send in a + + + align:start position:0% +is what happens in you if you send in a +wave so you're sending in a particle and + + align:start position:0% +wave so you're sending in a particle and + + + align:start position:0% +wave so you're sending in a particle and +you want to know what will happen to it + + align:start position:0% +you want to know what will happen to it + + + align:start position:0% +you want to know what will happen to it +will it get reflected will it get + + align:start position:0% +will it get reflected will it get + + + align:start position:0% +will it get reflected will it get +transmitted what probabilities for + + align:start position:0% +transmitted what probabilities for + + + align:start position:0% +transmitted what probabilities for +reflection will probabilities for + + align:start position:0% +reflection will probabilities for + + + align:start position:0% +reflection will probabilities for +transmission so of course would have to + + align:start position:0% +transmission so of course would have to + + + align:start position:0% +transmission so of course would have to +send a wave packet if you do represent + + align:start position:0% +send a wave packet if you do represent + + + align:start position:0% +send a wave packet if you do represent +the physical particle but we've learned + + align:start position:0% +the physical particle but we've learned + + + align:start position:0% +the physical particle but we've learned +that dealing with energy eigenstates + + align:start position:0% +that dealing with energy eigenstates + + + align:start position:0% +that dealing with energy eigenstates +teaches us the most important part of + + align:start position:0% +teaches us the most important part of + + + align:start position:0% +teaches us the most important part of +the story if a particle has some energy + + align:start position:0% +the story if a particle has some energy + + + align:start position:0% +the story if a particle has some energy +well roughly it will tend to behave the + + align:start position:0% +well roughly it will tend to behave the + + + align:start position:0% +well roughly it will tend to behave the +way an energy eigenstate of that energy + + align:start position:0% +way an energy eigenstate of that energy + + + align:start position:0% +way an energy eigenstate of that energy +does as far as reflection and as far as + + align:start position:0% +does as far as reflection and as far as + + + align:start position:0% +does as far as reflection and as far as +transmission is concerned so we'll set + + align:start position:0% +transmission is concerned so we'll set + + + align:start position:0% +transmission is concerned so we'll set +up a wave and there's a coefficient a so + + align:start position:0% +up a wave and there's a coefficient a so + + + align:start position:0% +up a wave and there's a coefficient a so +there's an EI e to the I KX that is our + + align:start position:0% +there's an EI e to the I KX that is our + + + align:start position:0% +there's an EI e to the I KX that is our +wave and it's moving to the right + + align:start position:0% +wave and it's moving to the right + + + align:start position:0% +wave and it's moving to the right +because you remember the time factor e + + align:start position:0% +because you remember the time factor e + + + align:start position:0% +because you remember the time factor e +to the minus IET over H bar and when you + + align:start position:0% +to the minus IET over H bar and when you + + + align:start position:0% +to the minus IET over H bar and when you +put them together you see that it's + + align:start position:0% +put them together you see that it's + + + align:start position:0% +put them together you see that it's +moving to the right + + align:start position:0% +moving to the right + + + align:start position:0% +moving to the right +but presumably there will be a + + align:start position:0% +but presumably there will be a + + + align:start position:0% +but presumably there will be a +reflection here you the wave comes in + + align:start position:0% +reflection here you the wave comes in + + + align:start position:0% +reflection here you the wave comes in +and some gets reflected and some gets + + align:start position:0% +and some gets reflected and some gets + + + align:start position:0% +and some gets reflected and some gets +transmitted I'm the part that gets + + align:start position:0% +transmitted I'm the part that gets + + + align:start position:0% +transmitted I'm the part that gets +transmitted probably will get partially + + align:start position:0% +transmitted probably will get partially + + + align:start position:0% +transmitted probably will get partially +reflected back here and partially + + align:start position:0% +reflected back here and partially + + + align:start position:0% +reflected back here and partially +transmitted forward but the part is + + align:start position:0% +transmitted forward but the part is + + + align:start position:0% +transmitted forward but the part is +partially reflected will get again + + align:start position:0% +partially reflected will get again + + + align:start position:0% +partially reflected will get again +reflected here and partially transmitted + + align:start position:0% +reflected here and partially transmitted + + + align:start position:0% +reflected here and partially transmitted +back + + align:start position:0% +back + + + align:start position:0% +back +it seems they can never end in process + + align:start position:0% +it seems they can never end in process + + + align:start position:0% +it seems they can never end in process +of which if you think physically what's + + align:start position:0% +of which if you think physically what's + + + align:start position:0% +of which if you think physically what's +happening there's a reflection at the + + align:start position:0% +happening there's a reflection at the + + + align:start position:0% +happening there's a reflection at the +first barrier now you take one wait a + + align:start position:0% +first barrier now you take one wait a + + + align:start position:0% +first barrier now you take one wait a +moment + + align:start position:0% +moment + + + align:start position:0% +moment +why would there be a reflection + + align:start position:0% +why would there be a reflection + + + align:start position:0% +why would there be a reflection +classically there would never be a + + align:start position:0% +classically there would never be a + + + align:start position:0% +classically there would never be a +reflection if the potential goes down + + align:start position:0% +reflection if the potential goes down + + + align:start position:0% +reflection if the potential goes down +the particle would just be able to + + align:start position:0% +the particle would just be able to + + + align:start position:0% +the particle would just be able to +continue we had reflection when we had a + + align:start position:0% +continue we had reflection when we had a + + + align:start position:0% +continue we had reflection when we had a +barrier and quantum mechanics any change + + align:start position:0% +barrier and quantum mechanics any change + + + align:start position:0% +barrier and quantum mechanics any change +in the potential is bound to produce a + + align:start position:0% +in the potential is bound to produce a + + + align:start position:0% +in the potential is bound to produce a +reflection so yes if you have a + + align:start position:0% +reflection so yes if you have a + + + align:start position:0% +reflection so yes if you have a +potential like this like a jumping board + + align:start position:0% +potential like this like a jumping board + + + align:start position:0% +potential like this like a jumping board +and you come in here there's a tiny + + align:start position:0% +and you come in here there's a tiny + + + align:start position:0% +and you come in here there's a tiny +probability that you will be reflected + + align:start position:0% +probability that you will be reflected + + + align:start position:0% +probability that you will be reflected +as you come into this potential drop so + + align:start position:0% + + + + align:start position:0% + +okay so this will be reflection so at + + align:start position:0% +okay so this will be reflection so at + + + align:start position:0% +okay so this will be reflection so at +the end of the day there might be many + + align:start position:0% +the end of the day there might be many + + + align:start position:0% +the end of the day there might be many +bouncing if you imagine a particle doing + + align:start position:0% +bouncing if you imagine a particle doing + + + align:start position:0% +bouncing if you imagine a particle doing +this and some probability of reflection + + align:start position:0% +this and some probability of reflection + + + align:start position:0% +this and some probability of reflection +some of transmission but the end of the + + align:start position:0% +some of transmission but the end of the + + + align:start position:0% +some of transmission but the end of the +day there will be some wave moving to + + align:start position:0% +day there will be some wave moving to + + + align:start position:0% +day there will be some wave moving to +the left here so we represented by be e + + align:start position:0% +the left here so we represented by be e + + + align:start position:0% +the left here so we represented by be e +to the minus ikx so in this region we + + align:start position:0% +to the minus ikx so in this region we + + + align:start position:0% +to the minus ikx so in this region we +have a and a wave with amplitude be + + align:start position:0% +have a and a wave with amplitude be + + + align:start position:0% +have a and a wave with amplitude be +going this way in the middle region the + + align:start position:0% +going this way in the middle region the + + + align:start position:0% +going this way in the middle region the +same will be true some of there will be + + align:start position:0% +same will be true some of there will be + + + align:start position:0% +same will be true some of there will be +some wave going here in some way that + + align:start position:0% +some wave going here in some way that + + + align:start position:0% +some wave going here in some way that +bounces you to this reflection so there + + align:start position:0% +bounces you to this reflection so there + + + align:start position:0% +bounces you to this reflection so there +will be a I don't know what letters are + + align:start position:0% +will be a I don't know what letters are + + + align:start position:0% +will be a I don't know what letters are +use it better keep the same see in this + + align:start position:0% +use it better keep the same see in this + + + align:start position:0% +use it better keep the same see in this +direction + + align:start position:0% +direction + + + align:start position:0% +direction +and V in this direction and now I would + + align:start position:0% +and V in this direction and now I would + + + align:start position:0% +and V in this direction and now I would +have C e to the I KX well that e to the + + align:start position:0% +have C e to the I KX well that e to the + + + align:start position:0% +have C e to the I KX well that e to the +ikx is not quite right because K here K + + align:start position:0% +ikx is not quite right because K here K + + + align:start position:0% +ikx is not quite right because K here K +squared represents the energy K is the + + align:start position:0% +squared represents the energy K is the + + + align:start position:0% +squared represents the energy K is the +momentum and K squared is the energy so + + align:start position:0% +momentum and K squared is the energy so + + + align:start position:0% +momentum and K squared is the energy so +if you have an energy eigenstate my + + align:start position:0% +if you have an energy eigenstate my + + + align:start position:0% +if you have an energy eigenstate my +pictures very crowded so I'll do it + + align:start position:0% +pictures very crowded so I'll do it + + + align:start position:0% +pictures very crowded so I'll do it +anyway + + align:start position:0% +anyway + + + align:start position:0% +anyway +ace here maybe I'll put C and B here and + + align:start position:0% + + + + align:start position:0% + +now with a and B here I can write this + + align:start position:0% +now with a and B here I can write this + + + align:start position:0% +now with a and B here I can write this +as the energy you have a particle with + + align:start position:0% +as the energy you have a particle with + + + align:start position:0% +as the energy you have a particle with +some energy coming in and there is this + + align:start position:0% +some energy coming in and there is this + + + align:start position:0% +some energy coming in and there is this +wave here at K squared is 2m e over H + + align:start position:0% +wave here at K squared is 2m e over H + + + align:start position:0% +wave here at K squared is 2m e over H +squared e is positive scattering States + + align:start position:0% +squared e is positive scattering States + + + align:start position:0% +squared e is positive scattering States +and up indeed e from that equation is H + + align:start position:0% +and up indeed e from that equation is H + + + align:start position:0% +and up indeed e from that equation is H +squared K squared over 2m what do you + + align:start position:0% +squared K squared over 2m what do you + + + align:start position:0% +squared K squared over 2m what do you +know but at this point the total energy + + align:start position:0% +know but at this point the total energy + + + align:start position:0% +know but at this point the total energy +kinetic energy of the particle is bigger + + align:start position:0% +kinetic energy of the particle is bigger + + + align:start position:0% +kinetic energy of the particle is bigger +it's as if E is replaced by E Plus V + + align:start position:0% +it's as if E is replaced by E Plus V + + + align:start position:0% +it's as if E is replaced by E Plus V +naught which is the magnitude of this + + align:start position:0% +naught which is the magnitude of this + + + align:start position:0% +naught which is the magnitude of this +drop so here there will be a K 2 K 2 X + + align:start position:0% +drop so here there will be a K 2 K 2 X + + + align:start position:0% +drop so here there will be a K 2 K 2 X +plus D into the minus I K 2 X and K 2 + + align:start position:0% +plus D into the minus I K 2 X and K 2 + + + align:start position:0% +plus D into the minus I K 2 X and K 2 +refers me to this region to pursue + + align:start position:0% +refers me to this region to pursue + + + align:start position:0% +refers me to this region to pursue +Mobley people use that name K 2 squared + + align:start position:0% +Mobley people use that name K 2 squared + + + align:start position:0% +Mobley people use that name K 2 squared +would be 2 M equals V naught over H + + align:start position:0% +would be 2 M equals V naught over H + + + align:start position:0% +would be 2 M equals V naught over H +square and finally to the right of the + + align:start position:0% +square and finally to the right of the + + + align:start position:0% +square and finally to the right of the +potential + + align:start position:0% +potential + + + align:start position:0% +potential +where well there will be just one wave + + align:start position:0% +where well there will be just one wave + + + align:start position:0% +where well there will be just one wave +because intuitively we should be able to + + align:start position:0% +because intuitively we should be able to + + + align:start position:0% +because intuitively we should be able to +interpret this as some wave that goes + + align:start position:0% +interpret this as some wave that goes + + + align:start position:0% +interpret this as some wave that goes +through but has nothing to make it + + align:start position:0% +through but has nothing to make it + + + align:start position:0% +through but has nothing to make it +bounce or reflect so we try to get a + + align:start position:0% +bounce or reflect so we try to get a + + + align:start position:0% +bounce or reflect so we try to get a +solution which will have just some wave + + align:start position:0% +solution which will have just some wave + + + align:start position:0% +solution which will have just some wave +going in this direction and it's called + + align:start position:0% +going in this direction and it's called + + + align:start position:0% +going in this direction and it's called +F e to the I KX and I can go back to the + + align:start position:0% +F e to the I KX and I can go back to the + + + align:start position:0% +F e to the I KX and I can go back to the +label K because you have the same energy + + align:start position:0% +label K because you have the same energy + + + align:start position:0% +label K because you have the same energy +available as kinetic energy as you had + + align:start position:0% +available as kinetic energy as you had + + + align:start position:0% +available as kinetic energy as you had +to the left of the barrier + + align:start position:0% + + + + align:start position:0% + +okay so we've set up the problem the + + align:start position:0% +okay so we've set up the problem the + + + align:start position:0% +okay so we've set up the problem the +wave function I would have to write it + + align:start position:0% +wave function I would have to write it + + + align:start position:0% +wave function I would have to write it +as three expressions one for X less than + + align:start position:0% +as three expressions one for X less than + + + align:start position:0% +as three expressions one for X less than +a 1 for X in between a and minus a and 1 + + align:start position:0% +a 1 for X in between a and minus a and 1 + + + align:start position:0% +a 1 for X in between a and minus a and 1 +for X greater than a and those are this + + align:start position:0% +for X greater than a and those are this + + + align:start position:0% +for X greater than a and those are this +one two and three formulas any questions + + align:start position:0% +one two and three formulas any questions + + + align:start position:0% +one two and three formulas any questions +about the set up so far + + align:start position:0% + + + + align:start position:0% + +okay well at this moment and you will + + align:start position:0% +okay well at this moment and you will + + + align:start position:0% +okay well at this moment and you will +eventually have some practice on that + + align:start position:0% +eventually have some practice on that + + + align:start position:0% +eventually have some practice on that +the thing that you want to do is relate + + align:start position:0% +the thing that you want to do is relate + + + align:start position:0% +the thing that you want to do is relate +the various coefficients and define some + + align:start position:0% +the various coefficients and define some + + + align:start position:0% +the various coefficients and define some +reflection and transmission coefficients + + align:start position:0% +reflection and transmission coefficients + + + align:start position:0% +reflection and transmission coefficients +we saw we had to think in terms of + + align:start position:0% +we saw we had to think in terms of + + + align:start position:0% +we saw we had to think in terms of +probability current that's the better + + align:start position:0% +probability current that's the better + + + align:start position:0% +probability current that's the better +way to get an idea what you should call + + align:start position:0% +way to get an idea what you should call + + + align:start position:0% +way to get an idea what you should call +reflection or transmission coefficient + + align:start position:0% +reflection or transmission coefficient + + + align:start position:0% +reflection or transmission coefficient +so it's we had to be careful with the + + align:start position:0% +so it's we had to be careful with the + + + align:start position:0% +so it's we had to be careful with the +case of the step potential when we + + align:start position:0% +case of the step potential when we + + + align:start position:0% +case of the step potential when we +compared the meaning of the wave that + + align:start position:0% +compared the meaning of the wave that + + + align:start position:0% +compared the meaning of the wave that +was moving to the right the amplitude + + align:start position:0% +was moving to the right the amplitude + + + align:start position:0% +was moving to the right the amplitude +divided by the incoming wave was not + + align:start position:0% +divided by the incoming wave was not + + + align:start position:0% +divided by the incoming wave was not +quite the transmission coefficient but + + align:start position:0% +quite the transmission coefficient but + + + align:start position:0% +quite the transmission coefficient but +in this case the nice thing is that the + + align:start position:0% +in this case the nice thing is that the + + + align:start position:0% +in this case the nice thing is that the +wave to the left that the wave to the + + align:start position:0% +wave to the left that the wave to the + + + align:start position:0% +wave to the left that the wave to the +right are experiencing the same + + align:start position:0% +right are experiencing the same + + + align:start position:0% +right are experiencing the same +potential so they can be compared + + align:start position:0% +potential so they can be compared + + + align:start position:0% +potential so they can be compared +directly so I will be able to conjecture + + align:start position:0% +directly so I will be able to conjecture + + + align:start position:0% +directly so I will be able to conjecture +it's reasonable to conjecture we can + + align:start position:0% +it's reasonable to conjecture we can + + + align:start position:0% +it's reasonable to conjecture we can +define reflection and transmission + + align:start position:0% +define reflection and transmission + + + align:start position:0% +define reflection and transmission +coefficients as follows we'll have a + + align:start position:0% +coefficients as follows we'll have a + + + align:start position:0% +coefficients as follows we'll have a +reflection coefficient should be B over + + align:start position:0% +reflection coefficient should be B over + + + align:start position:0% +reflection coefficient should be B over +a squared B represents a reflected wave + + align:start position:0% +a squared B represents a reflected wave + + + align:start position:0% +a squared B represents a reflected wave +a the incoming wave the transmission + + align:start position:0% +a the incoming wave the transmission + + + align:start position:0% +a the incoming wave the transmission +coefficient you may guess that it's F + + align:start position:0% +coefficient you may guess that it's F + + + align:start position:0% +coefficient you may guess that it's F +over a squared and this all will make + + align:start position:0% +over a squared and this all will make + + + align:start position:0% +over a squared and this all will make +sense if we have that the reflection + + align:start position:0% +sense if we have that the reflection + + + align:start position:0% +sense if we have that the reflection +plus the transmission is equal to 1 so + + align:start position:0% +plus the transmission is equal to 1 so + + + align:start position:0% +plus the transmission is equal to 1 so +we have current conservation + + align:start position:0% + + + + align:start position:0% + +conservation and the current which is + + align:start position:0% +conservation and the current which is + + + align:start position:0% +conservation and the current which is +the net probability flow to the left of + + align:start position:0% +the net probability flow to the left of + + + align:start position:0% +the net probability flow to the left of +the barrier or the depression over here + + align:start position:0% +the barrier or the depression over here + + + align:start position:0% +the barrier or the depression over here +of is J on the left is proportional to a + + align:start position:0% +of is J on the left is proportional to a + + + align:start position:0% +of is J on the left is proportional to a +squared minus B squared you remember we + + align:start position:0% +squared minus B squared you remember we + + + align:start position:0% +squared minus B squared you remember we +completed it last time if you compute + + align:start position:0% +completed it last time if you compute + + + align:start position:0% +completed it last time if you compute +the probability current due to this a to + + align:start position:0% +the probability current due to this a to + + + align:start position:0% +the probability current due to this a to +the ikx plus be e to the minus ikx you + + align:start position:0% +the ikx plus be e to the minus ikx you + + + align:start position:0% +the ikx plus be e to the minus ikx you +get two contributions essentially a + + align:start position:0% +get two contributions essentially a + + + align:start position:0% +get two contributions essentially a +squared minus b squared there's a factor + + align:start position:0% +squared minus b squared there's a factor + + + align:start position:0% +squared minus b squared there's a factor +of H Bar K over m in front at any rate + + align:start position:0% +of H Bar K over m in front at any rate + + + align:start position:0% +of H Bar K over m in front at any rate +this should be equivalent to the should + + align:start position:0% +this should be equivalent to the should + + + align:start position:0% +this should be equivalent to the should +be equal to the current that is flowing + + align:start position:0% +be equal to the current that is flowing + + + align:start position:0% +be equal to the current that is flowing +out in this directions you see whatever + + align:start position:0% +out in this directions you see whatever + + + align:start position:0% +out in this directions you see whatever +current is coming in to the left must be + + align:start position:0% +current is coming in to the left must be + + + align:start position:0% +current is coming in to the left must be +the current going out to the right so + + align:start position:0% +the current going out to the right so + + + align:start position:0% +the current going out to the right so +this is F squared so current + + align:start position:0% +this is F squared so current + + + align:start position:0% +this is F squared so current +conservation really tells you that a + + align:start position:0% +conservation really tells you that a + + + align:start position:0% +conservation really tells you that a +squared minus B squared is equal to F + + align:start position:0% +squared minus B squared is equal to F + + + align:start position:0% +squared minus B squared is equal to F +squared and if you pass the B to the + + align:start position:0% +squared and if you pass the B to the + + + align:start position:0% +squared and if you pass the B to the +other side you get a squared equal B + + align:start position:0% +other side you get a squared equal B + + + align:start position:0% +other side you get a squared equal B +squared plus F squared and dividing by a + + align:start position:0% +squared plus F squared and dividing by a + + + align:start position:0% +squared plus F squared and dividing by a +squared you get 1 is equal to B over a + + align:start position:0% +squared you get 1 is equal to B over a + + + align:start position:0% +squared you get 1 is equal to B over a +squared plus F over a squared and that's + + align:start position:0% +squared plus F over a squared and that's + + + align:start position:0% +squared plus F over a squared and that's +the reflection plus the transmission so + + align:start position:0% +the reflection plus the transmission so + + + align:start position:0% +the reflection plus the transmission so +yes the way we've defined things make + + align:start position:0% +yes the way we've defined things make + + + align:start position:0% +yes the way we've defined things make +sense reflection and transmission are + + align:start position:0% +sense reflection and transmission are + + + align:start position:0% +sense reflection and transmission are +properly defined and this is because + + align:start position:0% +properly defined and this is because + + + align:start position:0% +properly defined and this is because +current conservation works well so + + align:start position:0% +current conservation works well so + + + align:start position:0% +current conservation works well so +reflection coefficient + + align:start position:0% +reflection coefficient + + + align:start position:0% +reflection coefficient +it's essentially the flux in the + + align:start position:0% +it's essentially the flux in the + + + align:start position:0% +it's essentially the flux in the +reflected the probability current or the + + align:start position:0% +reflected the probability current or the + + + align:start position:0% +reflected the probability current or the +flux in the reflected wave compared to + + align:start position:0% +flux in the reflected wave compared to + + + align:start position:0% +flux in the reflected wave compared to +the flux in the incoming wave the + + align:start position:0% +the flux in the incoming wave the + + + align:start position:0% +the flux in the incoming wave the +transmission is the probability current + + align:start position:0% +transmission is the probability current + + + align:start position:0% +transmission is the probability current +or flux of probability in the + + align:start position:0% +or flux of probability in the + + + align:start position:0% +or flux of probability in the +transmitted wave compared with the one + + align:start position:0% +transmitted wave compared with the one + + + align:start position:0% +transmitted wave compared with the one +in incoming wave so you've done all of + + align:start position:0% +in incoming wave so you've done all of + + + align:start position:0% +in incoming wave so you've done all of +this setup now you can't avoid however + + align:start position:0% +this setup now you can't avoid however + + + align:start position:0% +this setup now you can't avoid however +doing a little bit of calculation which + + align:start position:0% +doing a little bit of calculation which + + + align:start position:0% +doing a little bit of calculation which +is boundary conditions you have one two + + align:start position:0% +is boundary conditions you have one two + + + align:start position:0% +is boundary conditions you have one two +three four five variables and somehow + + align:start position:0% +three four five variables and somehow + + + align:start position:0% +three four five variables and somehow +you want to calculate this ratios so you + + align:start position:0% +you want to calculate this ratios so you + + + align:start position:0% +you want to calculate this ratios so you +have to say that the wave function and + + align:start position:0% +have to say that the wave function and + + + align:start position:0% +have to say that the wave function and +the derivative is continuous at this + + align:start position:0% +the derivative is continuous at this + + + align:start position:0% +the derivative is continuous at this +point and the wave function at the + + align:start position:0% +point and the wave function at the + + + align:start position:0% +point and the wave function at the +derivative is continuous at this point + + align:start position:0% +derivative is continuous at this point + + + align:start position:0% +derivative is continuous at this point +that would give you four conditions and + + align:start position:0% +that would give you four conditions and + + + align:start position:0% +that would give you four conditions and +that's reasonable we have five variables + + align:start position:0% +that's reasonable we have five variables + + + align:start position:0% +that's reasonable we have five variables +but you know the overall normalization + + align:start position:0% +but you know the overall normalization + + + align:start position:0% +but you know the overall normalization +could never be determined so things can + + align:start position:0% +could never be determined so things can + + + align:start position:0% +could never be determined so things can +be determined in terms of a so you can + + align:start position:0% +be determined in terms of a so you can + + + align:start position:0% +be determined in terms of a so you can +expect that with four equations you can + + align:start position:0% +expect that with four equations you can + + + align:start position:0% +expect that with four equations you can +solve for B C D and F in terms of a but + + align:start position:0% +solve for B C D and F in terms of a but + + + align:start position:0% +solve for B C D and F in terms of a but +the overall scale of these total wave + + align:start position:0% +the overall scale of these total wave + + + align:start position:0% +the overall scale of these total wave +functions and determined it boundary + + align:start position:0% +functions and determined it boundary + + + align:start position:0% +functions and determined it boundary +conditions will give you constraints but + + align:start position:0% +conditions will give you constraints but + + + align:start position:0% +conditions will give you constraints but +will never determine the magnitude the + + align:start position:0% +will never determine the magnitude the + + + align:start position:0% +will never determine the magnitude the +overall magnitude of an energy + + align:start position:0% +overall magnitude of an energy + + + align:start position:0% +overall magnitude of an energy +eigenstate \ No newline at end of file diff --git a/Ei8CFin00PY.txt b/Ei8CFin00PY.txt new file mode 100644 index 0000000000000000000000000000000000000000..780a2791182082bea785324c1c4059561e760d86 --- /dev/null +++ b/Ei8CFin00PY.txt @@ -0,0 +1,4062 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: So +today, before we get + +into the meat of +today's lecture, + +Matt has very kindly-- +Professor Evans + +has very kindly agreed +to do an experiment. + +Yeah, so for those +of you all who + +are in recitations +both he and Barton + +talked about polarization +in recitation last week. + +And Matt will pick +it up from there. + +MATTHEW EVANS: So back +to the ancient past-- + +this was a week ago. + +We had our +hyper-intelligent monkeys + +that were sorting things. + +It all seemed very theoretical. + +And in recitation, I said +things about polarizers. + +And I said, look, if +we use polarizers, + +we can do exactly the same +thing as these monkeys. + +We just need to set up a +little polarization experiment + +and the results are identical. + +You can use the one +figure out the other. + +But I didn't have this or +a nice polarizer ready then + +to give a demo, so here we go. + +What I'm going to show +you is that, if we start + +with something polarized here +with all white-- and right + +now I have all vertical +polarization here-- + +and if I just put +on this other box + +there, which is going to be +another polarizer, if I put it + +the same way, this is all +of our white electrons + +coming through all white. + +See? + +It doesn't really do much. + +And if I look at the +black output over here + +of the second Keller +sorting box, that's + +the same as turning my +polarizer 90 degrees, + +so nothing comes out black. + +So if we remove this +guy from the middle, + +you have just exactly +what you'd expect. + +You sort here, you have white, +and you get all white out. + +Great. + +Everyone thought that was easy. + +We all had that figured out. + +This box got thrown +in the center here + +and it became sort of confusing, +because you thought, well, + +they were white-- +I'm going to throw + +my box in the middle here-- +that's this guy at 45 degrees. + +And then if I throw this guy +on the end again, the idea was, + +well, they were all white +here, so maybe this guy + +identified the soft ones +from the white ones. + +And now we have white and soft. + +And it should still +all be white, right? + +So I put this guy on up here. + +They should all come out +but they sort of don't. + +And if you say, +well, are they black? + +Well, no, they're not +really black, either. + +They're some sort of strange +combination of the two. + +All right, so that's this +experiment done in polarizers. + +But let me just play the +polarizer trick a little bit, + +because it's fun. + +So this is if I say, +vertical polarization + +and how many of them +come out horizontal? + +So here I'm saying, white, +and how many of them + +will come out black? + +That's the analogy. + +The answer is none of them. + +And strangely, if I +take this thing, which + +seems to just attenuate-- +this is our middle box here-- + +and I just stuff +it in between them, + +I can get something to come +out even though I still + +have crossed +polarizers on the side. + +So you can see the middle +region is now brighter + +and you can still see +the dark corners there + +of the crossed polarizers. + +And as I turn this guy around, +I can make that better or worse. + +The maximum is +somewhere right there, + +and then it goes off again. + +So this is a way +of understanding + +our electron-sorting, +hyper-intelligent monkeys + +in terms of polarizations. + +And here it's just +a vector projected + +on another vector projected +on another vector-- something + +everybody knows how to do. + +So here's the +polarization analogy + +of the Stern-Gerlach experiment. + +PROFESSOR: Awesome. + +So the polarization analogy +for interference effects + +in quantum mechanics +is a canonical one + +in the texts of +quantum mechanics. + +So you'll find lots of +books talking about this. + +It's a very useful +analogy, and I + +encourage you to +read more about it. + +We won't talk about +it a whole lot more, + +but it's a useful one. + +All right, before +I get going, any + +questions from last lecture? + +Last lecture was pretty +much self-contained. + +It was experimental results. + +No, nothing? + +All right. + +The one thing that I +want to add to the last + +lecture-- one last +experimental observation. + +I glossed over +something that's kind + +of important, which +is the following. + +So we started off +by saying, look, + +we know that if I +have a ray of light, + +it's an electromagnetic +wave, and it + +has some wavelength lambda. + +And yet the photoelectric +effect tells us + +that, in addition to having the +wavelength lambda, the energy-- + +it has a frequency, as +well, a frequency in time. + +And the photoelectric +effect suggested + +that the energy is +proportional to the frequency. + +And we write this as h nu and +h bar is equal to h upon 2 pi + +and omega is equal to 2 pi nu. + +So this is just the angular +frequency, rather than + +the number-per-time frequency. + +And h bar is the +reduced Planck constant. + +So I'll typically write h +bar omega rather than h nu, + +because these two pi's will +just cause us endless pain if we + +don't use the bar. + +Anyway, so to an +electromagnetic wave, + +we have a wavelength +and a frequency + +and the photoelectric +effect led us + +to predict that the +energy is linearly + +proportional to the frequency, +with the linear proportionality + +coefficient h bar-- Planck +constant-- and the momentum + +is equal to h upon +lambda, also known + +as-- I'm going to write +this as h bar k, which + +is equal to h upon +lambda, where here, again, + +h bar is h upon 2 pi. + +And so k is equal +to 2 pi upon lambda. + +So k is called the +wave number and you + +should have seen this in 8.03. + +So these are our basic +relations for light. + +We know that light, as +an electromagnetic wave, + +has a frequency +and a wavelength-- + +or a wave number, an +inverse wavelength. + +And the claim of the +photoelectric effect + +is that the energy and +the momenta of that light + +are thus quantized, that +light comes in chunks. + +So it has a wave-like +aspect and it also + +has properties that are more +familiar from particles. + +Now, early on shortly after +Einstein proposed this, + +a young French physicist named +de Broglie said, well, look, + +OK, this is true of light. + +Light has both wave-like and +particle-like properties. + +Why is it just light? + +The world would be +much more parsimonious + +if this relation were true +not just of light, but also + +of all particles. + +I am thus conjecturing, +with no evidence whatsoever, + +that, in fact, +this relation holds + +not just for light, +but for any object. + +Any object with momentum p has +associated to it a wavelength + +or a wave number, +which is p upon h bar. + +Every object that has energy +E has associated with it + +a wave with frequency omega. + +To those electrons that we send +through the Davisson-Germer + +experiment apparatus, which are +sent in with definite energy, + +there must be a frequency +associated with it, omega + +and a wavelength lambda +associated with it. + +And what we saw from the +Davisson-Germer experiment + +was experimental confirmation +of that prediction-- + +that electrons have both +particulate and wave-like + +features simultaneously. + +So these relations are called +the de Broglie relations or "de + +BROG-lee"-- I leave it up to +you to decide how to pronounce + +that. + +And those relations are going +to play an important role for us + +in the next few lectures. + +I just wanted to give them +a name and a little context. + +This is a good example of +parsimony and elegance-- + +the theoretical +elegance leading you + +to an idea that turns out +to be true of the world. + +Now, that's a dangerous +strategy for finding truth. + +Boy, wouldn't it be nice if--? + +Wouldn't it be nice if we +didn't have to pay taxes + +but we also had Medicare? + +So it's not a terribly +useful guide all the time, + +but sometimes it +really does lead you + +in the right direction. + +And this is a great example +of physical intuition, + +wildly divorced from +experiment, pushing you + +in the right direction. + +I'm making it sound a little +more shocking than-- well, + +it was shocking. + +It was just shocking. + +OK, so with that said, +let me introduce the moves + +for the next few lectures. + +For the next several lectures, +here's what we're going to do. + +I am not going to give you +experimental motivation. + +I've given you +experimental motivation. + +I'm going to give you a set +of rules, a set of postulates. + +These are going to be the +rules of quantum mechanics. + +And what quantum +mechanics is for us + +is a set of rules to allow +us to make predictions + +about the world. + +And these rules will be awesome +if their predictions are good. + +And if their predictions are +bad, these rules will suck. + +We will avoid bad rules +to the degree possible. + +I'm going to give you what +we've learned over the past 100 + +years-- wow-- of developing +quantum mechanics. + +That is amazing. + +Wow. + +OK, yeah, over +the past 100 years + +of developing quantum mechanics. + +And I'm going to give them to +you as a series of postulates + +and then we're going to work +through the consequences, + +and then we're going to spend +the rest of the semester + +studying examples to develop +an understanding for what + +the rules of quantum +mechanics are giving you. + +So we're just going to +scrap classical mechanics + +and start over from scratch. + +So let me do that. + +And to begin, let me start with +the definition of a system. + +And to understand +that definition, + +I want to start with classical +mechanics as a guide. + +So in classical mechanics-- +let's think about the easiest + +classical system you can-- +just a single particle + +sitting somewhere. + +In classical mechanics +of a single particle, + +how do you specify the +configuration, or the state-- + +just different words +for the same thing-- + +how do you specify +the configuration + +or state of the system? + +AUDIENCE: By position +and momentum. + +PROFESSOR: Specify the +position and momentum, exactly. + +So in classical mechanics, if +you want to completely specify + +the configuration of a +system, all you have to do + +is give me x and +p for my particle. + +And if you tell me +this, I know everything. + +If you know these numbers, +you know everything. + +In particular, what +I mean by saying + +you know everything is that, +if there's anything else + +you want to measure-- +the energy, for example. + +The energy is just some function +of the position and momentum. + +And if you know the +position and momentum, + +you can unambiguously +calculate the energy. + +Similarly, the angular +momentum, which is a vector, + +you can calculate +it if you know x + +and p-- which is just r cross p. + +So this gives you complete +knowledge of the system. + +There's nothing more to +know if you know that data. + +Now, there are certainly +still questions + +that you can't answer +given knowledge of x and p. + +For example, are there +14 invisible monkeys + +standing behind me? + +I'm here. + +I'm not moving. + +Are there 14 invisible +monkeys standing behind me? + +You can't answer that. + +It's a stupid question, right? + +OK, let me give you +another example. + +The electron is x +and p, some position. + +Is it happy? + +Right, so there are still +questions you can't answer. + +The point is, complete +knowledge of the system + +to answer any physically +observable question-- + +any question that could +be meaningfully turned + +into an experiment, +the answer is + +contained in knowing +the state of the system. + +But this can't possibly be +true in quantum mechanics, + +because, as you saw +in the problem set + +and as we've +discussed previously, + +there's an uncertainty +relation which + +says that your knowledge-- +or your uncertainty, rather, + +in the position of +a particle, quantum + +mechanically-- +I'm not even going + +to say quantum mechanically. + +I'm just going to +say the real world. + +So in the real world, +our uncertainty + +in the position of +our point-like object + +and our uncertainty +in the momentum + +is always greater than or +roughly equal to something + +that's proportional +to Planck's constant. + +You can't be arbitrarily +confident of the position + +and of the momentum +simultaneously. + +You worked through a +good example of this + +on the problem set. + +We saw this in the +two-slit experiment + +and the interference +of electrons. + +This is something we're +going to have to deal with. + +So as a consequence, +you can't possibly + +specify the position +and the momentum + +with confidence of a system. + +You can't do it. + +This was a myth. + +It was a good approximation-- +turned out to be false. + +So the first thing +we need is to specify + +the state, the +configuration of a system. + +So what specifies the +configuration of a system? + +And so this brings us +to the first postulate. + +The configuration, or +state, of a system-- + +and here again, +just for simplicity, + +I'm going to talk about a single +object-- of a quantum object + +is completely specified by +a single function, a wave + +function, which I +will denote generally + +psi of x, which is +a complex function. + +The state of the quantum +object is completely + +specified once you know the wave +function of the system, which + +is a function of position. + +Let me emphasize that this is +a first pass at the postulates. + +What we're going to do is go +through the basic postulates + +of quantum mechanics, then we'll +go through them again and give + +them a little more generality. + +And then we'll go through +them again and give them + +full generality. + +That last pass is 8.05. + +So let me give +you some examples. + +Let me just draw some +characteristic wave functions. + +And these are going to turn +out to be useful for us. + +So for example, consider +the following function. + +So here is 0 and we're +plotting as a function of x. + +And then plotting the +real part of psi of x. + +So first consider a very +narrowly supported function. + +It's basically 0 +everywhere, except it + +has some particular spot +at what I'll call x1. + +Here's another +wave function-- 0. + +It's basically 0 except for +some special spot at x2. + +And again, I'm plotting +the real part of psi. + +And I'm plotting +the real part of psi + +because A, psi is a complex +function-- at every point it + +specifies a complex number. + +And B, I can't draw +complex numbers. + +So to keep my head +from exploding, + +I'm just plotting the real +part of the wave function. + +But you should never forget that +the wave function is complex. + +So for the moment, +I'm going to assume + +that the imaginary part is 0. + +I'm just going to +draw the real parts. + +So let me draw a +couple more examples. + +What else could be a +good wave function? + +Well, those are fine. + +What about-- again, we want +a function of x and I'm + +going to draw the real part. + +And another one. + +So this is going to be a +perfectly good wave function. + +And let me draw two more. + +So what else could be a +reasonable wave function? + +Well-- this is harder +than you'd think. + +Oh, God. + +OK, so that could be the +wave function, I don't know. + +That is actually my signature. + +My wife calls it a +little [INAUDIBLE]. + +OK, so here's the deal. + +Psi is a complex function. + +Psi also needs to not +be a stupid function. + +OK so you have to ask me-- +look, could it be any function? + +Any arbitrary function? + +So this is going +to be a job for us. + +We're going to +define what it means + +to be not-stupid function. + +Well, this is a completely +reasonable function-- + +it's fine. + +This is a reasonable function. + +Another reasonable function. + +Reasonable. + +That's a little weird, +but it's not horrible. + +That's stupid. + +So we're going to +have to come up + +with a good definition +of what not stupid means. + +So fine, these +are all functions. + +One of them is multivalued and +that looks a little worrying, + +but they're all functions. + +So here's the problem. + +What does it mean? + +So postulate 2-- The +meaning of the wave function + +is that the probability +that upon measurement + +the object is found +at the position x + +is equal to the norm +squared of psi of x. + +If you know the system is +ascribed to the wave function + +psi, and you want +to look at point x, + +you want to know with +what probability will I + +find the particle there, +the answer is psi squared. + +Notice that this is a complex +number, but absolute value + +squared, or norm squared, +of a complex number + +is always a real, +non-negative number. + +And that's important because +we want our probabilities + +to be real, +non-negative numbers. + +Could be 0, right? + +Could be 0 chance of something. + +Can't be negative 7 chance. + +Incidentally, there also +can't be probability 2. + +So that means that the +total probability had better + +be normalized. + +So let me just say this +in words, though, first. + +So P, which is the +norm squared of psi, + +determines the probability-- +and, in particular, + +the probability density-- +that the object in state psi, + +in the state given by the +wave function psi of x, + +will be found at x. + +So there's the second postulate. + +So in particular, when +I say it's a probability + +density, what I mean is the +probability that it is found + +between the position +x and x plus dx + +is equal to P of x dx, which is +equal to psi of x squared dx. + +Does that make sense? + +So the probability +that it's found + +in this infinitesimal +interval is + +equal to this density +times dx or psi squared dx. + +Now again, it's crucial +that the wave function + +is in fact properly normalized. + +Because if I say, look, +something could either be here + +or it could be +here, what's the sum + +of the probability +that it's here + +plus the probability +that it's here? + +It had better be 1, or there's +some other possibility. + +So probabilities +have to sum to 1. + +Total probability that you find +something somewhere must be 1. + +So what that tells you is +that total probability, which + +is equal to the integral over +all possible values of x-- so + +if I sum over all possible +values of P of x-- + +all values-- should +be equal to 1. + +And we can write +this as integral dx + +over all values of x. + +And I write "all" here rather +than putting minus infinity + +to infinity because some +systems will be defined + +from 1 to minus 1, some systems +will be defined from minus + +infinity to infinity-- all +just means integrate over + +all possible values-- hold +on one sec-- of psi squared. + +AUDIENCE: Are you going +to use different notation + +for probability density +than probability? + +PROFESSOR: I'm not going to. + +Probability density is going +to have just one argument, + +and total probability +is going to have + +an interval as an argument. + +So they're distinct and this +is just the notation I like. + +Other questions? + +Just as a side note, +what are the dimensions + +of the wave function? + +So everyone think about +this one for second. + +What are the dimensions? + +AUDIENCE: Is it 1 over +square root length + +PROFESSOR: Awesome. + +Yes. + +It's 1 over root length. + +The dimensions of psi +are 1 over root length. + +And the way to see that is +that this should be equal to 1. + +It's a total probability. + +This is an infinitesimal +length, so this + +has dimensions of length. + +This has no dimension, so +this must have dimensions of 1 + +over length. + +And so psi itself of x most have +dimensions of 1 over length. + +Now, something I +want to emphasize, + +I'm going to emphasize, +over and over in this class + +is dimensional analysis. + +You need to become comfortable +with dimensional analysis. + +It's absolutely essential. + +It's essential for two reasons. + +First off, it's +essential because I'm + +going to be merciless +in taking off points + +if you do write down a +dimensionally false thing. + +If you write down something on +a problem set or an exam that's + +like, a length is equal to +a velocity-- ooh, not good. + +But the second thing +is, forget the fact + +that I'm going to +take off points. + +Dimensional analysis is an +incredibly powerful tool + +for you. + +You can check something +that you've just calculated + +and, better yet, +sometimes you can just + +avoid a calculation entirely +by doing a dimensional analysis + +and seeing that there's only one +possible way to build something + +of dimensions length +in your system. + +So we'll do that +over and over again. + +But this is a question +I want you guys to start + +asking yourselves at +every step along the way + +of a calculation-- what +are the dimensions of all + +the objects in my system? + +Something smells like smoke. + +So with that said, if that's the +meaning of the wave function, + +what physically can we take +away from knowing these wave + +functions? + +Well, if this is +the wave function, + +let's draw the +probability distribution. + +What's the probability +distribution? + +P of x. + +And the probability distribution +here is really very simple. + +It's again 0 squared is +still 0 so it's still + +just a big spike at x1 and +this one is a big spike at x2. + +Everyone cool with that? + +So what do you know +when I tell you + +that this is the wave function +describing your system? + +You know that with +great confidence, + +you will find the particle to +be sitting at x1 if you look. + +So what this is telling you +is you expect x is roughly x1 + +and our uncertainty +in x is small. + +Everyone cool with that? + +Similarly, here you see that +the position is likely to be x2, + +and your uncertainty +in your measurement-- + +your confidence +in your prediction + +is another way to say +it-- is quite good, + +so your uncertainty is small. + +Now what about these guys? + +Well, now it's norm squared. + +I need to tell you what +the wave function is. + +Here, the wave +function that I want-- + +so here is 0-- is +e to the i k1 x. + +And here the wave function +is equal to e to the i k2 x. + +And remember, I'm +drawing the real part + +because of practical +limitations. + +So the real part is just +a sinusoid-- or, in fact, + +the cosine-- and similarly, +here, the real part + +is a cosine. + +And I really should put 0 +in the appropriate place, + +but-- that worked out well. + +So now the question is, what's +the probability distribution, + +P of x, associated to +these wave functions? + +So what's the norm squared +of minus e to the i k1 x? + +If I have a complex number +of phase e to the i alpha, + +and I take its norm +squared, what do I get? + +1. + +Right? + +But remember complex numbers. + +If we have a complex +number alpha-- or sorry, + +if we have a +complex number beta, + +then beta squared +is by definition + +beta complex +conjugate times beta. + +So e to the i alpha, if +the complex conjugate + +is e to the minus i alpha, +e to the i alpha times + +e to the minus i alpha, +they cancel out-- that's 1. + +So if this is the +wave function, what's + +the probability distribution? + +Well, it's 1. + +It's independent of x. + +So from this we've learned +two important things. + +The first is, this is +not properly normalized. + +That's not so key. + +But the most important thing is, +if this is our wave function, + +and we subsequently measure the +position of the particle-- we + +look at it, we say ah, +there's the particle-- + +where are we likely to find it? + +Yeah, it could be anywhere. + +So what's the value of x +you expect-- typical x? + +I have no idea, no +information whatsoever. + +None. + +But and correspondingly, +what is our uncertainty + +in the position of x +that we'll measure? + +It's very large, exactly. + +Now, in order to tell you +it's actually infinite, + +I need to stretch this off and +tell you that it's actually + +constant off to infinity, +and my arms aren't that long, + +so I'll just say large. + +Similarly here, if +our wave function + +is e to the i k2 x-- +here k2 is larger, + +the wavelength is +shorter-- what's + +the probability distribution? + +It's, again, constant. + +So-- this is 0, 0. + +So again, x-- we have no idea, +and our uncertainty in the x + +is large. + +And in fact it's very large. + +Questions? + +What about these guys? + +OK, this is the real challenge. + +OK, so if this is +our wave function, + +and let's just say that +it's real-- hard as it + +is to believe that-- then what's +our probably distribution? + +Well, something +like-- I don't know, + +something-- you get the point. + +OK, so if this is our +probability distribution, + +where are we likely +to find the particle? + +Well, now it's a little +more difficult, right? + +Because we're unlikely +to find it here, + +while it's reasonably likely +to find here, unlikely here, + +reasonably likely, unlikely, +like-- you know, it's a mess. + +So where is this? + +I'm not really sure. + +What's our uncertainty? + +Well, our uncertainty +is not infinite + +because-- OK, my name +ends at some point. + +So this is going to go to 0. + +So whatever else we know, +we know it's in this region. + +So it's not infinite, +it's not small, we'll say. + +But it's not arbitrarily +small-- it's not tiny. + +Or sorry, it's not +gigantic is what I meant. + +Our uncertainty is not gigantic. + +But it's still +pretty nontrivial, + +because I can say +with some confidence + +that it's more likely +to be here than here, + +but I really don't know +which of those peaks + +it's going to be found. + +OK, now what about this guy? + +What's the probability +distribution well now + +you see why this is a +stupid wave function, + +because it's multiply valued. + +It has multiple different +values at every value of x. + +So what's the probability? + +Well, it might be root 2, +maybe it's 1 over root 3. + +I'm really not sure. + +So this tells us an important +lesson-- this is stupid. + +And what I mean by stupid +is, it is multiply valued. + +So the wave function-- +we just learned + +a lesson-- should +be single valued. + +And we will explore some more +on your problem set, which + +will be posted +immediately after lecture. + +There are problems that +walk you through a variety + +of other potential pathologies +of the wave function + +and guide you to +some more intuition. + +For example, the +wave function really + +needs to be continuous as well. + +You'll see why. + +All right. + +Questions at this point? + +No? + +OK. + +So these look like pretty +useful wave functions, + +because they corresponded +to the particle + +being at some definite spot. + +And I, for example, am at +a reasonably definite spot. + +These two wave +functions, though, + +look pretty much useless, +because they give us + +no information whatsoever +about what the position is. + +Everyone agree with that? + +Except-- remember the +de Broglie relations. + +The de Broglie relations say +that associated to a particle + +is also some wave. + +And the momentum +of that particle + +is determined by the wavelength. + +It's inversely related +to the wavelength. + +It's proportional +to the wave number. + +Any energy is proportional +to the frequency. + +Now, look at those +wave functions. + +Those wave functions give +us no position information + +whatsoever, but they have +very definite wavelengths. + +Those are periodic functions +with definite wavelengths. + +In particular, this guy has +a wavelength of from here + +to here. + +It has a wave number k1. + +So that tells us +that if we measure + +the momentum of +this particle, we + +can be pretty +confident, because it + +has a reasonably +well-defined wavelength + +corresponding to some +wave number k-- 2 pi + +upon the wavelength. + +It has some momentum, +and if we measure it, + +we should be pretty confident +that the momentum will + +be h-bar k1. + +Everybody agree with that? + +Looks like a sine wave. + +And de Broglie +tells us that if you + +have a wave of +wavelength lambda, + +that corresponds to a +particle having momentum p. + +Now, how confident can +we be in that estimation + +of the momentum? + +Well, if I tell you it's e +to the i k x, that's exactly + +a periodic function with +wavelength lambda 2 pi upon k. + +So how confident are we? + +Pretty confident. + +So our uncertainty in +the momentum is tiny. + +Everyone agree? + +Similarly, for +this wave, again we + +have a wavelength-- it's +a periodic function, + +but the wavelength +is much shorter. + +If the wavelength +is much shorter, + +then k is much larger-- the +momentum is much larger. + +So the momentum we +expect to measure, + +which is roughly h-bar k2, +is going to be much larger. + +What about our uncertainty? + +Again, it's a perfect +periodic function + +so our uncertainty in +the momentum is small. + +Everyone cool with that? + +And that comes, again, from +the de Broglie relations. + +So questions at this point? + +You guys are real quiet today. + +Questions? + +AUDIENCE: So delta +P is 0, basically? + +PROFESSOR: It's pretty small. + +Now, again, I haven't +drawn this off to infinity, + +but if it's exactly +the i k x, then yeah, + +it turns out to be 0. + +Now, an important thing, so +let me rephrase your question + +slightly. + +So the question +was, is delta P 0? + +Is it really 0? + +So here's a problem +for us right now. + +We don't have a +definition for delta P. + +So what is the +definition of delta P? + +I haven't given you one. + +So here, when I said +delta P is small, + +what I mean is, intuitively, +just by eyeball, + +our confidence in that +momentum is pretty good, + +using the de Broglie relations. + +I have not given +you a definition, + +and that will be part of +my job over the next couple + +of lectures. + +Very good question. + +Yeah. + +AUDIENCE: How do you code +noise in that function? + +PROFESSOR: Awesome. + +AUDIENCE: Do you just +have different wavelengths + +PROFESSOR: Yeah + +AUDIENCE: As you go along? + +PROFESSOR: Awesome. + +So for example, this-- does +it have a definite wavelength? + +Not so much. + +So hold that question and wait +until you see the next examples + +that I put on this board, +and if that doesn't answer + +your question, ask +it again, becayse + +it's a very important question. + +OK. + +AUDIENCE: When you +talk about a photon, + +you always say a photon +has a certain frequency. + +Doesn't that mean that it +must be a wave because you + +have to fix the wave number k? + +PROFESSOR: Awesome question. + +Does every wave packet of +light that hits your eye, + +does it always have a +single, unique frequency? + +No, you can take multiple +frequency sources + +and superpose them. + +An interesting choice +of words I used there. + +All right, so the +question is, since light + +has some wavelength, +does every chunk of light + +have a definite-- this +is the question, roughly. + +Yeah, so and the +answer is, light + +doesn't always +have a single-- You + +can have light +coming at you that + +has many different wavelengths +and put it in a prism + +and break it up into +its various components. + +So you can have a superposition +of different frequencies + +of light. + +We'll see the same +effect happening for us. + +OK, so again, de Broglie +made this conjecture + +that E is h-bar omega +and P is h-bar k. + +This was verified in the +Davisson-Germer experiment + +that we ran. + +But here, one of +the things that's + +sort of latent in +this is, what he means + +is, look, associated to +every particle with energy N + +and momentum P is a plane +wave of the form e to the i kx + +minus omega t. + +And this, properly, in three +dimensions should be k dot x. + +But at this point, this is +an important simplification. + +For the rest of 8.04, +until otherwise specified, + +we are going to be doing +one-dimensional quantum + +mechanics. + +So I'm going to remove arrow +marks and dot products. + +There's going to be one +spatial dimension and one time + +dimension. + +We're always going to have +just one time dimension, + +but sometimes we'll have +more spatial dimensions. + +But it's going to be a +while until we get there. + +So for now, we're +just going to have kx. + +So this is a general plane wave. + +And what de Broglie +really was saying + +is that, somehow, associated +to the particle with energy E + +and momentum P should be +some wave, a plane wave, + +with wave number k +and frequency omega. + +And that's the wave +function associated to it. + +The thing is, not every wave +function is a plane wave. + +Some wave functions +are well localized. + +Some of them are just +complicated morasses. + +Some of them are just a mess. + +So now is the most important +postulate in quantum mechanics. + +I remember vividly, +vividly, when + +I took the analog of this class. + +It was called Physics +143A at Harvard. + +And the professor +at this point said-- + +I know him well now, +he's a friend-- he said, + +this is what quantum +mechanics is all about. + +And I was so psyched. + +And then he told me And it +was like, that's ridiculous. + +Seriously? + +That's what quantum +mechanics is all about? + +So I always felt like this +is some weird thing, where + +old physicists go crazy. + +But it turns out I'm going to +say exactly the same thing. + +This is the most important thing +in all of quantum mechanics. + +It is all contained in +the following proposition. + +Everything-- the two +slit experiments, the box + +experiments, all the cool +stuff in quantum mechanics, + +all the strange and +counter intuitive stuff + +comes directly from +the next postulate. + +So here it is. + +I love this. + +Three-- put a star on it. + +Given two possible wave +functions or states-- + +I'll say configurations-- +of a quantum system-- + +I wish there was "Ride +of the Valkyries" + +playing in the background-- +corresponding to two + +distinct wave functions-- +f with an upper ns + +is going to be my +notation for functions + +because I have to write +it a lot-- psi1 and psi2-- + +and I'll say, of x-- +the system-- is down-- + +can also be in a superposition. + +of psi1 and psi2, where alpha +and beta are complex numbers. + +Given any two possible +configurations of the system, + +there is also an allowed +configuration of the system + +corresponding to +being in an arbitrary + +superposition of them. + +If an electron can be +hard and it can be soft, + +it can also be in an +arbitrary superposition + +of being hard and soft. + +And what I mean by that +is that hard corresponds + +to some particular +wave function, + +soft will correspond to some +particular wave function, + +and the superposition +corresponds to a different wave + +function which is a linear +combination of them. + +AUDIENCE: [INAUDIBLE] +combination also + +have to be normalized? + +PROFESSOR: Yeah, OK, that's +a very good question. + +So and alpha and beta +are some complex numbers + +subject to the +normalization condition. + +So indeed, this wave function +should be properly normalized. + +Now, let me step +back for second. + +There's an alternate way +to phrase the probability + +distribution here, +which goes like this, + +and I'm going to put it here. + +The alternate statement of +the probability distribution + +is that the probability +density at x + +is equal to psi of x +norm squared divided + +by the integral over +all x dx of psi squared. + +So notice that, if we properly +normalize the wave function, + +this denominator is equal to 1-- +and so it's not there, right, + +and then it's equivalent. + +But if we haven't +properly normalized it, + +then this probability +distribution + +is automatically +properly normalized. + +Because this is a constant, when +we integrate the top, that's + +equal to the bottom, +it integrates to 1. + +So I prefer, +personally, in thinking + +about this for the first pass +to just require that we always + +be careful to choose +some normalization. + +That won't always be easy, +and so sometimes it's + +useful to forget +about normalizing + +and just define the probability +distribution that way. + +Is that cool? + +OK. + +This is the beating soul +of quantum mechanics. + +Everything in quantum +mechanics is in here. + +Everything in quantum +mechanics is forced on us + +from these few principles +and a couple of requirements + +of matching to reality. + +AUDIENCE: When +you do this-- some + +of linear, some of +two wave functions, + +can you get interference? + +PROFESSOR: Yes. + +Excellent. + +So the question is, when +you have a sum of two wave + +functions, can you get some +sort of interference effect? + +And the answer is, absolutely. + +And that's exactly +we're going to do next. + +So in particular, let me +look at a particular pair + +of superpositions. + +So let's swap +these boards around + +so the parallelism is +a little more obvious. + +So let's scrap these +rather silly wave functions + +and come up with +something that's + +a little more interesting. + +So instead of using those as +characteristic wave functions, + +I want to build superpositions. + +So in particular, +I want to start + +by taking an arbitrary-- +both of these wave functions + +have a simple interpretation. + +This corresponds to a +particle being here. + +This corresponds to a +particle being here. + +I want to take a +superposition of them. + +So here's my superposition. + +Oops, let's try that again. + +And my superposition-- so here +is 0 and here is x1 and here is + +x2-- is going to be some +amount times the first one + +plus some amount +times the second one. + +There's a superposition. + +Similarly, I could have taken +a superposition of the two + +functions on the +second chalkboard. + +And again I'm taking +a superposition + +of the complex e to the +i k1 x and e to the i + +k2 x and then taking +the real part. + +So that's a particular +superposition, + +a particular linear combination. + +So now let's go back to this. + +This was a particle +that was here. + +This is a particle +that was there. + +When we take the +superposition, what + +is the probability distribution? + +Where is this particle? + +Well, there's some +amplitude that it's here, + +and there's some +amplitude that it's here. + +And there's rather more +amplitude that it's over here, + +but there's still +some probability + +that it's over here. + +Where am I going to +find the particle? + +I'm not so sure anymore. + +It's either going to be here +or here, but I'm not positive. + +It's more likely +to be here than it + +is to be here, but +not a whole lot more. + +So where am I going +to find the particle? + +Well, now we have +to define this-- + +where am I going to +find the particle? + +Look, if I did this experiment +a whole bunch of times, + +it'd be over here more +than it would be over here. + +So the average will be +somewhere around here-- + +it'll be in between the two. + +So x is somewhere in between. + +That's where we expect +to find it, on average. + +What's our uncertainty +in the position? + +Well, it's not +that small anymore. + +It's now of order x1 minus x2. + +Everyone agree with that? + +Now, what about this guy? + +Well, does this thing +have a single wavelength? + +No. + +This is like light that +comes at you from the sun. + +It has many wavelengths. + +In this case, it has just two-- +I've added those two together. + +So this is a plane wave which +is psi is e to the i k1 x plus + +e to the i k2 x. + +So in fact, it has two +wavelengths associated with it. + +lambda1 lambda2. + +And so the probability +distribution now, + +if we take the norm squared +of this-- the probability + +distribution is the norm +squared of this guy-- + +is no longer constant, but +there's an interference term. + +And let's just see +how that works out. + +Let me be very +explicit about this. + +Note that the probability +in our superposition of psi1 + +plus psi2, which I'll call e to +the i k1 x plus e to the i k2 + +x, is equal to the norm squared +of the wave function, which + +is the superposition psi1 +plus beta psi2, which + +is equal to alpha squared +psi1 squared plus beta squared + +psi2 squared plus alpha +star psi1 star-- actually, + +let me write this over +here-- beta psi2 plus + +alpha psi1 beta star +psi2 star, where star + +means complex conjugation. + +But notice that this is +equal to-- that first term + +is alpha squared times +the first probability, + +or the probability of +this thing, of alpha psi1, + +is equal to probability 1. + +This term, beta +squared psi2 squared, + +is the probability that +the second thing happens. + +But these terms +can't be understood + +in terms of the +probabilities of psi1 + +or the probability +of psi2 alone. + +They're interference terms. + +So the superposition +principle, together + +with the interpretation of +the probability as the norm + +squared of the wave function, +gives us a correction + +to the classical addition +of probabilities, + +which is these +interference terms. + +Everyone happy with that? + +Now, here's something very +important to keep in mind. + +These things are norms +squared of complex numbers. + +That means they're real, +but in particular, they're + +non-negative. + +So these two are both +real and non-negative. + +But what about this? + +This is not the norm +squared of anything. + +However, this is its +complex conjugate. + +When you take something +and its complex conjugate + +and you add them +together, you get + +something that's +necessarily real. + +But it's not +necessarily positive. + +So this is a funny thing. + +The probability that something +happens if we add together + +our two configurations, we +superpose two configurations, + +has a positive probability term. + +But it's also got +terms that don't + +have a definite sign, +that could be negative. + +It's always real. + +And you can check but +this quantity is always + +greater than or equal to 0. + +It's never negative, +the total quantity. + +So remember Bell's inequality +that we talked about? + +Bell's inequality +said, look, if we + +have the probability of one +thing happening being P1, + +and the probability of +the other thing happening + +being P2, the probability +of both things happening + +is just P1 plus P2. + +And here we see that, +in quantum mechanics, + +probabilities +don't add that way. + +The wave functions add-- +and the probability + +is the norm squared +of the wave function. + +The wave functions add, +not the probabilities. + +And that is what underlies all +of the interference effects + +we've seen. + +And it's going to be the +heart of the rest of quantum + +mechanics. + +So you're probably all going, +in your head, more or less + +like I was when I took +Intro Quantum, like-- yeah, + +but I mean, it's just, you know, +you're adding complex numbers. + +But trust me on this one. + +This is where it's all starting. + +OK so let's go back to this. + +Similarly, let's +look at this example. + +We've taken the norm squared. + +And now we have an +interference effect. + +And now, our probability +distribution, + +instead of being totally trivial +and containing no information, + +our probability distribution +now contains some information + +about the position +of the object. + +It's likely to be here. + +It is unlikely to be +here, likely and unlikely. + +We now have some +position information. + +We don't have enough +to say where it is. + +But x is-- you have +some information. + +Now, our uncertainty +still gigantic. + +Delta x is still huge. + +But OK, we just added +together two plane waves. + +Yeah? + +AUDIENCE: Why is +the probability not + +big, small, small, +big, small, small? + +PROFESSOR: Excellent. + +This was the real part +of the wave function. + +And the wave function +is a complex quantity. + +When you take e to +the i k1, and let + +me do this on the chalkboard. + +When we take e to the i +k1 x plus e to the i k2 + +x-- Let me write this +slightly differently-- + +e to the i a plus e to the i +b and take its norm squared. + +So this is equal to-- +I'm going to write + +this in a slightly +more suggestive way-- + +the norm squared of e to the +i a times 1 plus e to the i b + +minus a parentheses +norm squared. + +So first off, the norm +squared of a product of things + +is the product of +the norm squareds. + +So I can do that. + +And this overall phase, the norm +squared of a phase is just 1, + +so that's just 1. + +So now we have the norm squared +of 1 plus a complex number. + +And so the norm squared of +1 is going to give me 1. + +The norm squared of the complex +number is going to give me 1. + +And the cross terms are going +to give me the real part-- + +twice the real part-- +of e to the i b minus + +a, which is going to be +equal to cosine of b minus a. + +And so what you see +here is that you + +have a single frequency +in the superposition. + +So good, our +uncertainty is large. + +So let's look at +this second example + +in a little more detail. + +By superimposing two states with +wavelength lambda1 and lambda2 + +or k1 and k2 we get +something that, OK, + +it's still not +well localized-- we + +don't know where the +particle is going + +to be-- but it's better +localized than it was before, + +right? + +What happens if we superpose +with three wavelengths, + +or four, or more? + +So for that, I want to pull +out a Mathematica package. + +You guys should all have +seen Fourier analysis + +in 18.03, but just in case, +I'm putting on the web page, + +on the Stellar page, a +notebook that walks you + +through the basics of Fourier +analysis in Mathematica. + +You should all be +fluent in Mathematica. + +If you're not, you +should probably + +come up to speed on it. + +That's not what we wanted. + +Let's try that again. + +There we go. + +Oh, that's awesome-- where +by awesome, I mean not. + +It's coming. + +OK, good. + +I'm not even going to mess with +the screens after last time. + +So I'm not going to go through +the details of this package, + +but what this does is walk +you through the superposition + +of wave packets. + +So here I'm looking at the +probability distribution coming + +from summing up a +bunch of plane waves + +with some definite frequency. + +So here it's just one. + +That's one wave, +so first we have-- + +let me make this bigger-- yes, +stupid Mathematica tricks. + +So here we have +the wave function + +and here we have the probability +distribution, the norm squared. + +And it's sort of +badly normalized here. + +So that's for a single wave. + +And as you see, the probability +distribution is constant. + +And that's not 0, +that's 0.15, it's + +just that I arbitrarily +normalized this. + +So let's add two plane waves. + +And now what you see is the +same effect as we had here. + +You see a slightly more +localized wave function. + +Now you have a little bit of +structure in the probability + +distribution. + +So there's the structure in +the probability distribution. + +We have a little +more information + +about where the particle +is more likely to be here + +than it is to be here. + +Let's add one more. + +And as we keep adding +more and more plane waves + +to our superposition, the wave +function and the probability + +distribution associated +with it become + +more and more +well-localized until, as we + +go to very high numbers of plane +waves that we're superposing, + +we get an extremely narrow +probability distribution-- + +and wave function, for that +matter-- extremely narrow + +corresponding to a particle +that's very likely to be here + +and unlikely to +be anywhere else. + +Everyone cool with that? + +What's the expense? + +Want have we lost +in the process? + +Well we know with +great confidence + +now that the particle will be +found here upon observation. + +But what will its momentum be? + +Yeah, now it's the +superposition of a whole bunch + +of different momenta. + +So if it's a superposition +of a whole bunch + +of different +momenta, here this is + +like superposition of a whole +bunch of different positions-- + +likely to be here, +likely to be here, + +likely to be here, +likely to be here. + +What's our knowledge +of its position? + +It's not very good. + +Similarly, now that +we have superposed + +many different momenta +with comparable strength. + +In fact, here they were +all with unit strength. + +We now have no information about +what the momentum is anymore. + +It could be anything +in that superposition. + +So now we're seeing +quite sharply + +the uncertainty relation. + +And here it is. + +So the uncertainty +relation is now + +pretty clear from these guys. + +So that didn't work? + +And I'm going to leave it alone. + +This is enough for +the Fourier analysis, + +but that Fourier +package is available + +with extensive commentary +on the Stellar web page. + +AUDIENCE: Now is +that sharp definition + +in the position caused by +the interference between all + +those waves and all that-- + +PROFESSOR: That's +exactly what it is. + +Precisely. + +It's precisely the interference +between the different momentum + +nodes that leads to +certainty in the position. + +That's exactly right. + +Yeah. + +AUDIENCE: So as we're +certain of the position, + +we will not be certain +of the momentum. + +PROFESSOR: Exactly. + +And here we are. + +So in this example, we have +no idea what the position is, + +but we're quite confident +of the momentum. + +Here we have no idea +what the position is, + +but we have great +confidence in the momentum. + +Similarly here, we have +less perfect confidence + +of the position, and here we +have less perfect confidence + +in the momentum. + +It would be nice to +be able to estimate + +what our uncertainty +is in the momentum here + +and what our uncertainty +is in the position here. + +So we're going to +have to do that. + +That's going to be +one of our next tasks. + +Other questions? + +Yeah. + +AUDIENCE: In this half +of the blackboard, + +you said, obviously, if +we do it a bunch of times + +it'll have more in +the x2 than in the x1. + +PROFESSOR: Yes. + +AUDIENCE: The average, it will +never physically be at that-- + +PROFESSOR: Yeah, that's right, +so, because it's a probability + +distribution, it won't +be exactly at that point. + +But it'll be nearby. + +OK, so in order to be more +precise-- And so for example + +for this what we do +here's a quick question. + +How well do you know the +position of this particle? + +Pretty well, right? + +But how well do you +know its momentum? + +Well, we'd all like to say +not very, but tell me why. + +Why is your uncertainty in the +momentum of the particle large? + +AUDIENCE: Heisenberg's +uncertainty principle. + +PROFESSOR: Yeah, +but that's a cheat + +because we haven't actually +proved Heisenberg's uncertainty + +principle. + +It's just something +we're inheriting. + +AUDIENCE: I believe it. + +PROFESSOR: I believe it, too. + +But I want a better +argument because I + +believe all sorts +of crazy stuff. + +So-- I really do. + +Black holes, fluids, I mean +look, don't get me started. + +Yeah. + +AUDIENCE: You can take the +Fourier transform of it. + +PROFESSOR: Yeah, excellent. + +OK, we'll get to +that in just one sec. + +So before taking the +Fourier transform, which + +is an excellent-- +so the answer was, + +just take a Fourier +transform, that's + +going to give you +some information. + +We're going to do +that in just a moment. + +But before we do +Fourier transform, + +just intuitively, why would +de Broglie look at this + +and say, no, that doesn't +have a definite momentum. + +AUDIENCE: There's +no clear wavelength. + +PROFESSOR: Yeah, there's +no wavelength, right? + +It's not periodic by any +stretch of the imagination. + +It doesn't look like a thing +with a definite wavelength. + +And de Broglie said, look, if +you have a definite wavelength + +then you have a +definite momentum. + +And if you have a +definite momentum, + +you have a definite wavelength. + +This is not a wave with +a definite wavelength, + +so it is not corresponding +to the wave function + +for a particle with +a definite momentum. + +So our momentum is +unknown-- so this is large. + +And similarly, here, our +uncertainty in the momentum + +is large. + +So to do better +than this, we need + +to introduce the +Fourier transform, + +and I want to do that now. + +So you should all have seen +Fourier series in 8.03. + +Now we're going to do +the Fourier transform. + +And I'm going to +introduce this to you + +in 8.04 conventions +in the following way. + +And the theorem +says the following-- + +we're not going to prove it by +any stretch of the imagination, + +but the theorem +says-- any function + +f of x that is sufficiently +well-behaved-- it shouldn't be + +discontinuous, it +shouldn't be singular-- + +any reasonably well-behaved, +non-stupid function f + +of x can be built by superposing +enough plane waves of the form + +e to the ikx. + +Enough may be infinite. + +So any function f of x can be +expressed as 1 over root 2 pi, + +and this root 2 pi is a choice +of normalization-- everyone + +has their own +conventions, and these + +are the ones we'll be +using in 8.04 throughout-- + +minus infinity to infinity +dk f tilde of k e to the ikx. + +So here, what we're +doing is, we're + +summing over plane waves +of the form e to the ikx. + +These are modes with a definite +wavelength 2 pi upon k. + +f tilde of k is telling us +the amplitude of the wave + +with wavelengths lambda +or wave number k. + +And we sum over all +possible values. + +And the claim is, +any function can + +be expressed as a superposition +of plane waves in this form. + +Cool? + +And this is for +functions which are + +non-periodic on the real line, +rather than periodic functions + +on the interval, which is what +you should've seen in 8.03. + +Now, conveniently, if +you know f tilde of k, + +you can compute f of +x by doing the sum. + +But suppose you +know f of x and you + +want to determine what +the coefficients are, + +the expansion coefficients. + +That's the inverse +Fourier transform. + +And the statement for +that is that f tilde of k + +is equal to 1 over root 2 pi +integral from minus infinity + +to infinity dx f of +x e to the minus ikx. + +OK, that's sometimes referred +to as the inverse Fourier + +transform. + +And here's something +absolutely essential. + +f tilde of k, the Fourier +transform coefficients + +of f of x, are +completely equivalent. + +If you know f of x, you +can determine f tilde of k. + +And if you know +f tilde of k, you + +can determine f of x +by just doing a sum, + +by just adding them up. + +So now here's the physical +version of this-- oh, + +I can't slide that out-- +I'm now going to put here. + +Oh. + +No, I'm not. + +I'm going to put that down here. + +So the physical +version of this is + +that any wave function +psi of x can be expressed + +as the superposition +in the form psi of x + +is equal to 1 over root 2 pi +integral from minus infinity + +to infinity dk psi tilde of k +e to the ikx of states, or wave + +functions, with a definite +momentum p is equal to h bar k. + +And so now, it's useful +to sketch the Fourier + +transforms of each +of these functions. + +In fact, we want this up here. + +So here we have the function and +its probability distribution. + +Now I want to draw the Fourier +transforms of these guys. + +So here's psi tilde +of k, a function + +of a different +variable than of x, + +but nonetheless, +it's illuminating + +to draw them next to each other. + +And again, I'm +drawing the real part. + +And here, x2-- had I had +my druthers about me, + +I would have put x2 +at a larger value. + +Good, so it's further +off to the right there. + +I'm so loathe to erase the +superposition principle. + +But fortunately, +I'm not there yet. + +Let's look at the Fourier +transform of these guys. + +The Fourier transform +of this guy-- this is k. + +Psi tilde of k well, +that's something + +with a definite value of k. + +And it's Fourier transform-- +this is 0-- there's k1. + +And for this guy-- +there's 0-- k2. + +And now if we look at +the Fourier transforms + +of these guys, see, +this way I don't + +have to erase the superposition +principle-- and the Fourier + +transform of this guy, +so note that there's + +a sort of pleasing +symmetry here. + +If your wave function +is well localized, + +corresponding to a reasonably +well-defined position, + +then your Fourier transform +is not well localized, + +corresponding to not +having a definite momentum. + +On the other hand, if you +have definite momentum, + +your position is +not well defined, + +but the Fourier transform +has a single peak + +at the value of k corresponding +to the momentum of your wave + +function. + +Everyone cool with that? + +So here's a question-- sorry, +there was a raised hand. + +Yeah? + +AUDIENCE: Are we going +to learn in this class + +how to determine the +Fourier transforms + +of these non-stupid functions? + +PROFESSOR: Yes, that +will be your homework. + +On your homework is +an extensive list + +of functions for you to +compute Fourier transforms of. + +And that will be the job of +problem sets and recitation. + +So Fourier series +and computing-- yeah, + +you know what's +coming-- Fourier series + +are assumed to have been covered +for everyone in 8.03 and 18.03 + +in some linear +combination thereof. + +And Fourier transforms-- + +[LAUGHTER AND GROANS] + +I couldn't help it. + +So Fourier transforms +are a slight embiggening + +of the space of Fourier +series, because we're not + +looking at periodic functions. + +AUDIENCE: So when we're +doing the Fourier transforms + +of a wave function, we're +basically writing it + +as a continuous set +of different waves. + +Can we write it +as a discrete set? + +So as a Fourier series? + +PROFESSOR: Absolutely, +so, however, + +what is true about +Fourier series? + +When you use a discrete +set of momenta, + +which are linear, which are-- +It must be a periodic function, + +exactly. + +So here what we've +done is, we've said, + +look, we're writing +our wave function, + +our arbitrary wave function, +as a continuous superposition + +of a continuous value +of possible momenta. + +This is absolutely correct. + +This is exactly +what we're doing. + +However, that's +kind of annoying, + +because maybe you +just want one momentum + +and two momenta +and three momenta. + +What if you want +a discrete series? + +So discrete is fine. + +But if you make +that discrete series + +integer-related to +each other, which + +is what you do with +Fourier series, + +you force the function +f of x to be periodic. + +And we don't want +that, in general, + +because life isn't periodic. + +Thank goodness, right? + +I mean, there's like one film +in which it-- but so-- it's + +a good movie. + +So that's the +essential difference + +between Fourier series +and Fourier transforms. + +Fourier transforms +are continuous in k + +and do not assume +periodicity of the function. + +Other questions? + +Yeah. + +AUDIENCE: So +basically, the Fourier + +transform associates +an amplitude + +and a phase for each of +the individual momenta. + +PROFESSOR: Precisely. + +Precisely correct. + +So let me say that again. + +So the question was-- +so a Fourier transform + +effectively +associates a magnitude + +and a phase for each +possible wave vector. + +And that's exactly right. + +So here there's some +amplitude and phase-- + +this is a complex +number, because this + +is a complex function-- there's +some complex number which + +is an amplitude and +a phase associated + +to every possible momentum +going into the superposition. + +That amplitude may be 0. + +There may be no contribution +for a large number of momenta, + +or maybe insignificantly small. + +But it is indeed +doing precisely that. + +It is associating an amplitude +and a phase for every plane + +wave, with every different +value of momentum. + +And you can compute, +before panicking, + +precisely what that +amplitude and phase + +is by using the inverse +Fourier transform. + +So there's no magic here. + +You just calculate. + +You can use your calculator, +literally-- I hate that word. + +OK so now, here's +a natural question. + +So if this is the Fourier +transform of our wave function, + +we already knew that this +wave function corresponded + +to having a definite-- +from de Broglie, + +we know that it has +a definite momentum. + +We also see that its Fourier +transform looks like this. + +So that leads to a +reasonable guess. + +What do you think the +probability distribution P of k + +is-- the probability +density to find the momentum + +to have wave vector h-bar k? + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: Yeah, that's a +pretty reasonable guess. + +So we're totally +pulling this out + +of the dark-- psi +of k norm squared. + +OK, well let's +see if that works. + +So psy of k norm +squared for this + +is going to give us a nice, +well localized function. + +And so that makes +a lot of sense. + +That's exactly what +we expected, right? + +Definite value of P with +very small uncertainty. + +Similarly here. + +Definite value of P, with +a very small uncertainty. + +Rock on. + +However, let's look at this guy. + +What is the expected value +of P if this is the Fourier + +transform? + +Well remember, we have to take +the norm squared, and psi of k + +was e to the i k x1-- +the Fourier transform. + +You will do much +practice on taking + +Fourier transforms +on the problem set. + +Where did my eraser go? + +There it is. + +Farewell, principle one. + +So what does norm squared +of psi tilde look like? + +Well, just like before, +the norm squared + +is constant, because the norm +squared of a phase is constant. + +And again, the +norm squared-- this + +is psi tilde of k norm +squared-- we believe, + +we're conjecturing +this is P of k. + +You will prove this relation +on your problem set. + +You'll prove that it follow +from what we said before. + +And similarly, this is +constant-- e to the i k x2. + +So now we have no +knowledge of the momenta. + +So that also fits. + +The momenta is, we have no idea. + +And uncertainty is large. + +And the momenta is, +we have no idea. + +And the uncertainty is large. + +So in all these +cases, we see that we + +satisfy quite nicely the +uncertainty relation-- + +small position momentum, +large momentum uncertainty. + +Large position +uncertainty, we're + +allowed to have small +momentum uncertainty. + +And here, it's a little +more complicated. + +We have a little bit of +knowledge of position, + +and we have a little bit of +knowledge of the momenta. + +We have a little bit of +knowledge of position, + +and we have a little bit +of knowledge of momenta. + +So we'll walk through +examples with superposition + +like this on the problem set. + +Last questions +before we get going? + +OK so I have two things +to do before we're done. + +The first is, after lecture +ends, I have clickers. + +And anyone who wants +to borrow clickers, + +you're welcome to come +down and pick them up + +on a first come +first served basis. + +I will start using the +clickers in the next lecture. + +So if you don't already +have one, get one now. + +But the second thing is-- +don't get started yet. + +I have a demo to do. + +And last time I told +you-- this is awesome. + +It's like I'm an +experimentalist for a day. + +Last time I told you that one of +the experimental facts of lice + +is-- of lice. + +One of the experimental +facts of lice. + +One of the experimental +facts of life + +is that there is +uncertainty in the world + +and that there is probability. + +There are unlikely +events that happen + +with some probability, +some finite probability. + +And a good example of the +randomness of the real world + +involves radiation. + +So hopefully you can hear this. + +Apparently, I'm not +very radioactive. + +You'd be surprised at the +things that are radioactive. + +Ah, got a little tick. + +Shh. + +This is a plate sold at +an Amish county fair. + +It's called vaseline ware +and it's made of local clays. + +[GEIGER COUNTER CLICKS] + +It's got uranium in it. + +But + +I want to emphasize-- exactly +when something goes click, + +it sounds pretty random. + +And it's actually a better +random number generator + +than anything you'll find in +Mathematica or C. In fact, + +for some purposes, the decay +of radioactive isotopes + +is used as the perfect +random number generator. + +Because it really is totally +random, as far as anyone + +can tell. + +But here's my favorite. + +People used to eat off these. + +[MUCH LOUDER, DENSER CLICKS] + +See you next time. \ No newline at end of file diff --git a/FVzaznYPCes.txt b/FVzaznYPCes.txt new file mode 100644 index 0000000000000000000000000000000000000000..efdc651907f2680545b5d0cb5899937661456159 --- /dev/null +++ b/FVzaznYPCes.txt @@ -0,0 +1,2502 @@ +The following content is +provided under a Creative + +Commons License. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: OK, Let's get +down to business. + +Last day we started study +crystallography. + +And we were looking +at ordered solids. + +And we recognized the crystal +structure is the sum of the + +combination of a Bravais +lattice, which is the way that + +points are identified in +space, plus the basis. + +And we saw that we could put a +variety of elements at the + +corners of the Bravais +lattice. + +And this is taken from the +archival notes where we see + +the simple, single atoms at the +various lattice points. + +And we recognized last day that +we could put clusters of + +atoms and so on, and +even proteins will + +crystallize in this form. + +And actually, to make a point, +about five years ago, a group + +of students came to my office +after the final exam, and + +recognizing that I drink Fresca +during the lectures, + +they came to me with this + +body-centered Fresca unit cell. + +So this just makes the point +that you can put anything at + +the lattice point. + +So there it is. + +Oh, here's the point. + +This is me at a conference +in Copenhagen. + +This is outside the +Admiral Hotel. + +And just to show you I'm always +thinking about 3.091, I + +came outside-- + +and this is a colleague of mine +from France, Marcelle + +Gaune-Escard. + +How do we know she's French? + +She's got a cigarette. + +She's a scientist. +She's a woman. + +And she smoking. + +And it's fantastic. + +And she's a great gal. + +Anyways, so there we are out in +front of the Admiral Hotel. + +And I notice these +cannon balls. + +And what do you notice about +the cannon balls? + +They are sitting in one of +the Bravais lattices. + +So I couldn't resist having +my wife take this picture. + +Because I knew that this would +come back to 3.091. + +So here we are with the +individual cubic lattices + +where we're going to focus. + +And we started looking at the +properties of cubic lattices. + +And I started working +through this table. + +And we got down to nearest +neighbors, and so on, and this + +relationship between +the lattice + +constant and the radius. + +And I just wanted to show +this last point here + +about packing density. + +Because it comes up +considerations of properties + +of elements. + +And so I wanted to go through +the packing density + +calculation. + +And so the way we handle the +packing density, remember + +we're looking at a +unit cell here. + +This is the cube that's +the repeat unit. + +And it has a lattice constant +of dimension a. + +And then depending on where we +put atoms, I want to show that + +we've got three different +options here, simple cubic, + +body-centered cubic, and +face-centered cubic. + +And the last line of that slide +shows that the densest + +packing of atoms-- this is hard + +spheres, the cannon balls-- + +the densest packing is +face-centered cubic. + +And I wanted to show the +derivation of that where if we + +face-centered cubic where the +atoms are big enough to touch. + +If we have 4 atoms at the corner +touching on the face + +diagonal and then continuing +through the cell, we want to + +get packing density as the ratio +of the volume occupied + +by the atoms-- and here +we're modeling the + +atoms as hard spheres-- + +divided by the volume +of the cell itself. + +And so that's pretty +straightforward calculation. + +We're modeling the atoms +as hard spheres. + +And we saw last day that if we +take the fraction of the atom, + +1/8 times 1/8, and 6 times +1/2, we have 4 atom + +equivalents per unit cell. + +And each of these has a volume +of 4/3 pi r cubed. + +And then we divide +that by a cubed. + +And then we know the +relationship between a and r. + +This is 4r and that's +root 2 a. + +So we can say root +2 a equals 4r. + +Either eliminate a +or eliminate r. + +We eventually end up with this +dimensionless group, which is + +pi divided by 3 roots of 2. + +And that is 74%. + +And that's the densest +package. + +If you go through the same +calculation for body-centered + +packing, you'll find +it's 68% packing. + +And for simple cubic +it's 52% packing. + +That's the highest density that +you can have. So I urge + +you to spend some time. + +If you work the homework, you'll +work your way through + +that chart. + +So now I wanted to take a few +minutes and talk about + +crystallographic notation. + +Because we need to know this in +order to describe various + +features of a cell. + +So I'm going to start with a +Cartesian coordinate system + +that obeys the right-hand +rule. + +So we'll put down x, y and z. + +And then we'll put up a unit +cell here with edge a. + +So we have a on the x, +y and z coordinate. + +And we know that a equals +b equals c. + +That's the unit vectors here. + +There's a little a here, +a little b here, + +and a little c here. + +These are all equal to the +lattice constant value a. + +And all of the angles +are 90 degrees. + +This is what defines +the cubic system. + +So I'm going to put several +positions here. + +So here is the origin. + +And the origin we designate +as 0, 0, 0. + +I'm going to put a position +up here, a. + +And you just use the same +notation as you'd use + +mathematics. + +Only crystallographers don't +put parentheses around it. + +So what I'm really teaching +is notation. + +You already know the math. + +So a up here is what? + +It's 0 units on the x-axis. + +It's 1 unit on the y-axis, +and 1 unit on a z-axis. + +So that would make it 0, 1, 1. + +And I'm going to put +a b out here. + +B is out 1 unit on the x-axis. + +It's 0 units on the y-axis. + +And it looks like it's up at +about 1/2 unit on the z-axis. + +So that makes 1, 0, and 1/2. + +And so now what I want to do is +show you how we designate + +directions and planes. + +You use a slightly different +notation from what + +you used to in math. + +So this chart will be posted +at the website. + +Move the coordinate axes so the +line passes through the + +origin, define a vector from the +origin to the point on the + +line, and choose the smaller +set of integers. + +So let's do a simple one here. + +Let's do from origin to b. + +So o to b. + +That's this vector here. + +So how would we do that one? + +Well we're already +at the origin. + +So that's trivial. + +o to b, so we're going from +here out to here. + +And then what does it say? + +It says choose the smallest set +of integers, no commas, + +clear fractions. + +So that's going to take +us out to 1 0 1/2. + +But the crystallographers +don't like fractions. + +So you're supposed to +clear the fractions. + +You clear the fractions by +multiplying through. + +So make that 2 0 1. + +It's the same direction. + +See if I came out two units +here, I'd end up + +being one unit here. + +So it's the same direction. + +It really is the +same direction. + +Don't put any commas. + +And put brackets around it. + +So that's the 2, 0, 1 direction, +which is o b. + +And I want to do a +different one. + +I'm going to go this +way, a to o. + +So let's look at +that one, a o. + +And what happens on a o? + +Well now I'm going to +put the origin at a. + +I'm going to go to +0 in the x-axis. + +I'm going to go minus +1 in the z-axis, and + +minus 1 in the y-axis. + +So that gives me 0 +minus 1 minus 1. + +But see they don't use commas. + +And so this looks +kind of goofy. + +Because you get these +minus signs in here. + +So what the crystallographers do +is they put the minus sign + +on top of the number. + +So this becomes 0 1 +with a macron it. + +If you'd studied Latin, you'd +know this thing is a macron, a + +line over a vowel. + +So 0 1 bar 1 bar. + +And that's the direction a o. + +So that's the macron acting +as the minus sign. + +So that's the a o direction + +And then furthermore, we +can designate families. + +This is just the +0 1 bar 1 bar. + +If you want to be a hipster +with crystallography, + +you call this 0. + +You say it's 0 1 bar 1 bar. + +But if you're a nice chemistry +student, you'll say zero, + +minus 1 minus 1. + +No we don't do that in +3.091, 0 1 bar 1 bar. + +Now suppose I wanted to describe +all of the faces, + +every face. + +So what I could do, is I +could say I want the + +set of all face diagonals. + +Well, that's a face diagonal. + +But what I can do is in a +compact notation, I could + +write 0 1 1 and use the carat. + +This is called the carat. + +So if I enclose in carats, this +means the set up all 0 1 + +1 type planes. + +And so what that means is I can +unpack that, and write 0 1 + +1, 0 1 1 bar, 0 1 bar +1, et cetera. + +And what I'll end up doing +is describing the + +set up all face diagonals. + +So if I want to talk to you +later when we're studying + +x-ray diffraction, I want to +talk about face diagonals, I + +don't use that word. + +We're quantitative +here at MIT. + +I say look at the +0 1 1 planes. + +So you go face diagonals. + +That's the compact notation. + +If we want to look at all cell +edges, what's the cell edge? + +Here's the cell edge. + +This is an edge here, +isn't it? + +It's right on the edge +of the cell. + +So it's 0 on the +y, 0 in the z. + +It's 1 in the x. + +So the set of all cell +edges would be 0 0 1. + +And you could write 1 +0 0, that's OK too. + +Or you could write 0 1 0. + +That's OK. + +But if you want to be a hipster +in crystallography, + +put the zeroes out in front. + +So the set of 0 0 1 directions +is all the cube edges. + +And then lastly, if we wanted to +get all the diagonals that + +starts from here and goes up, +we'll have all cell diagonals, + +all, if you want to call it, +body diagonals, not face + +diagonals, body diagonals. + +Body diagonals is 1 1 1. + +And the mathematics +imitates reality. + +How many combinations +are there here? + +I've got 0 1, and I've +got minus 1. + +So I have 0 0 1, 0 0 1 bar, +0 1 0, 0 1 bar 0, + +1 0 0, 1 bar 0. + +There's 6 And how many +edges are there? + +6. + +Mathematics imitating reality, +what a concept. + +That's great. + +OK. + +So that's good. + +Now we want to look at planes. + +Let's look at planes. + +Now planes are a little +bit different. + +This is basically what you know +from math with a little + +bit of notation It's basically +the same thing. + +Planes are quite different. + +So let's go to the planes. + +So you know the equation +of a plane. + +It's x over a plus y over b +plus z over c equals 1. + +And a b and c are the intercepts +at the x, y z axes. + +Well, in order to make this +notation compatible to what we + +have here for lines, a British +meteorologist by the name of + +William Hallowes Miller in 1839 +said let's define h, k, + +and l as the reciprocals +of these intercepts. + +And now we'll write the equation +of a plane as hx plus + +ky plus lz equals 1. + +And we'll use those values of h, +k, and l as the indicators + +of a plane. + +So here's an example. + +So again, I've got the +right-handed rule coordinates. + +And here's the plane. + +And you can see that it +cuts the x-axis and a. + +It cuts the y-axis at b. + +And it's parallel +to the z-axis. + +So if we were just to use the +old mathematics notation, and + +put the a, b and c, you'd +have 1/2 here. + +You'd have 1 here. + +And you'd have infinity here. + +And that looks goofy. + +So instead what we want to do +is use the Miller indices, + +which are the reciprocals. + +So now the reciprocal +of 1/2 is 2. + +The reciprocal of 1 +trivially is 1. + +And the reciprocal +of infinity is 0. + +And so now you have something +that makes sense. + +And you put no commas +in between. + +And you put the whole thing +in parentheses. + +So that's the 2 1 0 plane. + +And there's a really +cool property here. + +And that is, using this same +formulation I just showed you + +for directions, the 2 1 0 +directions-- you see 2 1 0 + +with square brackets, +that's a direction. + +2 1 0 with parentheses +is a plane. + +The 2 1 0 direction +is perpendicular + +to the 2 1 0 plane. + +And that's one of the advantages +of using Miller + +indices notation with +the classical + +notation for direction. + +Here's another one. + +This is 0 1 0. + +This is the x, y, and the z. + +So this cuts at 1, 0 1 0. + +This is 0 2 0. + +An 0 1 0 directions are +perpendicular to 0 1 0 plane. + +0 2 0 directions are +perpendicular to 0 2 0 plane. + +Oh here's 1 1 1. + +That's cool. + +See it cuts it at 1 1 and 1. + +And 1 1 1 direction cuts +through the 1 1 1 plane + +perpendicular. + +This is an interesting one. + +See the origin. + +The plane cuts through +the origin. + +Now what do you do? + +What do you do? + +You move the origin. + +Because we don't know where the +origin of the universe is. + +It's just a unit cell. + +It doesn't matter. + +So we move the origin up here. + +And now what do we have? + +We have 1 1 and minus 1. + +And just as before, we put +1 with a macron over it. + +That's 1 1 1 bar plane. + +And there is the 1 1 +1 bar direction. + +It doesn't matter. + +It'll always give you +perpendicular. + +It's really cool. + +All right. + +And we can also specify +a set of planes. + +So instead of using +parentheses, + +we use brace brackets. + +And if we use brae brackets, +we get families of planes. + +So for example, we could say if +we wanted a particular face + +so that the face in the xy +plane, facing the xy plane + +would be 0 0 1. + +Right, because it cuts the z. + +So this is 0 0 1. + +But what if I wanted to say in +a compact way, all faces of + +the unit cell, all +of the faces. + +So this is the particular +plane. + +If I wanted to say all faces +I would write 0 0 1. + +But I can't use any of +these containers. + +So I'll use brace brackets. + +So 0 0 1 in brace brackets means +the whole setup, 0 0 1, + +0 0 1 bar, 0 1 0, 0 1 bar +0, 1 0 0, and 1 bar 0 0. + +So there's only 6. + +And there's 6 faces. + +Again mathematics imitating +reality. + +What a concept. + +Make the math work for you. + +You don't work for the math. + +All right and just to make the +point about the h k l plane, + +is perpendicular to the +h k l direction. + +So that's good. + +And the last thing I want to +show you that comes out of the + +use of the Miller indices for +planes, is that another + +property that we'd +like to know is + +the interplanar spacing. + +What's the spacing between +like planes. + +So interplanar spacing, that is +to say the distance between + +like planes, adjacent planes +identical index. + +I'm going to write it to be +specific to say Miller index, + +h k l in parentheses. + +And the property that comes out +of this-- and you don't + +have to derive it. + +Somebody worked this out for +you about a 150 years ago-- + +is that the distance between +adjacent planes with the index + +h k l is given by the ratio +of a, which is the lattice + +constant, this is the cubed +edge, divided by the sum of + +the squares of h, k, and l taken +to the power of 1/2, So + +the square root of h squared +plus k squared plus l squared + +divided into the lattice +constant, gives you the value + +of the spacing in between. + +And this is the a just +to be clear about it. + +So for example, I think I've +got some cartoons up + +here that show this. + +So here's 0 1 0. + +It's trivial. + +What's the distance here? + +The d 0 1 0 is just day. + +How about here? + +This is 0 squared, 2 squared. + +0 squared, this is d over 2. + +So this is a 0 2 0 plane. + +But if the distance between 0 +2 0 planes is 1/2 a, well, + +then that's an 0 2 0 plane. + +Then this is an 0 2 0 plane. + +So point of fact, every 0 1 +0 plane is an 0 2 0 plane. + +But every 0 2 0 plane isn't +an 0 1 0 plane. + +You can see that some planes +have multiple names. + +Here's another one. + +Look, this is the distance +between adjacent 1 1 1 planes. + +It's a over root 3. + +So as the index goes up, as h +k l goes up, the distance + +between successive +planes goes down. + +And the angle between +the planes goes up. + +The easiest one is orthogonal. + +OK, that's good. + +That's good. + +All right. + +I think that's a good +place to stop. + +I dread these kinds +of lessons. + +And I'm sorry that the +parents ended up here + +on a day like today. + +But there's a little bit of +this notation and taxonomy + +that they have to know. + +And so we suffer through it. + +And then we get on +to the meat. + +Now we're ready for some meat. + +Now that we can describe crystal +structure, we're ready + +for physical measurement +of crystal structure. + +So what I want to start today +is the characterization of + +crystal structure by x-rays. + +How do we measure? + +How do we know that +gold is fcc. + +We use x-rays. + +So today what I want to do is +start as I always do on new + +unit with history lesson. + +We'll start with the discovery +of x-rays. + +And we'll get into the +underlying physics. + +And the next day we'll look at +applications including x-ray + +diffraction. + +So first of all, what +are x-rays? + +They're a form of +electromagnetic radiation. + +And they have the property +of that. + +They have very short +wavelength. + +How short? + +It's on the order of about +angstroms. So strictly + +speaking, it goes from about +1/100 to 100 angstroms. So + +centered at about 1 angstrom is +the center of the x region + +of the spectrum. + +And because they're a form of +electromagnetic radiation, + +their energy is given by these +equations, hu equals hc over + +lambda or hc u bar. + +Those equations that you've seen +over and over again apply + +for the energy of an x-ray, +because an x-ray is identical + +to a photon of wavelength +somewhere down at this level. + +Why do we care about this? + +Because this is atomic +dimensions. + +If I want to measure the +dimension of the human hair, I + +don't use a yard stick. + +I use something that is of +the human hair dimension. + +If we want to get into the +characterization of atomic + +structure, we need a measurement +tool that is on + +the order of that blank scale. + +And that's why we're going +to use x-rays. + +Now other property, I said very, +very short wavelength. + +But because of this inverse +relationship between + +wavelength and energy, I want +to draw attention to these + +superbly high value of energy. + +So let's plug in the energy for +lambda equals 1 angstrom. + +When lambda equals 1 angstrom, +we end up with 12,400 electron + +volts per photon. + +Now what's that mean, just +to put it in perspective? + +Look up here at the +table I've shown. + +We know the ionization energy, +the lone electron in hydrogen + +is 13.6 electron volts, +which is 14 to + +2 significant figures. + +And then we go to helium. + +You pull these off the +periodic table. + +This is the first ionization +energy. + +And they're down around +somewhere + +about 10 electron volts. + +Look at. + +This is 12,400. + +So let's go down to the +1 electron atom. + +So this is helium plus. + +This is lithium 2 plus. + +And we see a set of numbers here +that follow this sequence + +1 4 9 16, which is nothing more +than the sequence you + +would expect for a series of 1 +electron atoms. It's K, which + +is 13.6 times the square of z/ +So z here is 2, z here is 3, z + +here is 4, and so on. + +But even so, this is the last +electron of nitrogen. + +The most tightly bound electron +of nitrogen, 668 + +electron volts. + +That's a huge amount +of energy. + +But that pales in comparison +to 12,400 electron volts. + +So this is clearly ionizing +radiation writ large. + +What do I mean by ionizing +radiation? + +It has the capacity to +ionize everything. + +Every electron will +be blown away. + +This is called knocking +the stuffing out of + +the electron structure. + +So that's what we're +dealing with. + +So now let's go to the +origin of x-rays. + +So how did we discover x-rays? + +Well, it was a dark and stormy +night, not unlike the weather + +today, apropos of the lesson. + +It was November 8, 1895. + +And it was at the home and +laboratory of a professor. + +Of course it's a professor, +Professor Wilhelm Roentgen. + +And he was a professor of +physics at the University of + +Wurzburg in Bavaria, now +part of Germany. + +And he was doing research, as +many people were in the 1890s, + +on the properties of gas +discharge tubes. + +He was studying gas +discharge tubes. + +And he had a special interest +in gas discharge tubes. + +Remember Lorentz? + +He like to put the gas +discharge tubes + +in a magnetic field. + +Stark liked the put them +in an electric field. + +And what was Roentgen's +pet project? + +Roentgen loved high voltage. + +He loved high voltage +an low pressure. + +He was focused high voltage, +low pressure, near vacuum. + +And so let's have a drawing +of what he used. + +And here's an image of the +museum that is literally in + +the house that was +occupied by him. + +So the apparatus is sitting +right there on the table. + +And here's the heart +of the apparatus. + +I'm going to go to a fresh board +because I need a little + +extra room here. + +So we know what the gas +discharge tube looks like. + +It's a glass tube, sealed. + +And we've got feedthroughs for +electrodes at both ends. + +And this goes down to +a power supply. + +And the power supply +that he used was + +batteries of chromic acid. + +And they were open beakers. + +And they were down in the +basement two floors below. + +And he had wires going +from the basement up + +to the second floor. + +And he was able to generate +about 20 volts. + +So he had a number of +these in series. + +Because this is roughly +a 1-volt system. + +So round numbers, you got +about two dozen of these + +things in series. + +And I'm going to write +here, in the cellar. + +Now how did he get +the high voltage? + +He put in here something that we +wouldn't recognize today as + +an inductor. + +He called it a choke coil. + +And what the choke coil did, is +it would charge up until it + +got to 35,000 volts. + +When it got to 35,000 volts, it +would discharge and send a + +current at 35,000 volts +to the cathode here. + +And with 35,000 volts, the +cathode would send electrons + +boiling off the cathode, heading +towards the anode with + +the kinetic energy associated +with 35,000 volts. + +And this discharged at about +eight times a second. + +So I'm going to write +8 hertz here. + +So eight times a second this +thing, bam, bam, bam, bam. + +And the electrons go +firing off here. + +And this to make sure he had +really low pressure, he had + +the cell open actually. + +And this went to +a vacuum pump. + +He had almost no gas +molecules in here. + +Now, the way he did the +experiment is, he'd set this + +thing up, started it going, +and this was after dinner. + +So on a Friday night after +dinner, he was upstairs. + +And he wanted to measure +emissions here. + +And so what he had, you either +get graduate students to sit + +there and you exploit their +labor, or what you do is you + +put up a detector here +which was a screen. + +So this is either a sheet of +paper or a sheet of cloth. + +So we call this a screen. + +And so you're going +to look here. + +All right you're looking at +this, seeing what's coming out + +of this gas discharge tube. + +And it was a screen up +paper or fabric. + +And it had been painted with a +chemical that would glow if it + +were struck by a particle, or by +a photon of a given energy. + +And they used in this case, +coated with the chemical + +barium platinocyanide, so +cyanide four times. + +So you make an aqueous +paste of this stuff. + +And you gob it on +to the screen. + +And when the screen is hit +by something, it sparks. + +And the latin word for +spark is scintilla. + +Have you ever heard of someone +being described as a + +scintillating conversationalist? + +It means they are a sparkling +conversationalist. So this is + +called a scintillation screen, +a scintillation screen. + +And so presumably, every +time there's an + +event, the screen glows. + +And so Roentgen starts +the experiment. + +And it's raining outside. + +There's thunder. + +There's lightning. + +There's a street light as +you can see right there. + +There's windows. + +And the thing is glowing. + +And he really can't detect +what's going on here. + +So he decides to +cover the tube. + +So he puts a wooden box around +the gas discharge tube. + +So now the gas discharge tube +is enclosed in a box. + +And he continues +the experiment. + +And what he sees is glowing on +this scintillation screen. + +The scintillation screen is +glowing even though the gas + +discharge tube is in a box. + +There was another observation +he made. + +The student earlier in the +day, who had painted the + +screen with the barium +platinocyanide. + +I guess he was practicing +his calligraphy. + +And he left a paper towel on +the edge of the bench. + +And he painted the letter +A on the paper towel. + +And the paper towel was glowing +with the letter A. + +And this thing is enclosed +in a box. + +So he's saying what's +going on here. + +So he decides that there's some +kind of an interaction + +between the screen and something +going on in here. + +So the first thing he does is +he says, well maybe it's + +electromagnetic. + +Maybe it's charged particles. + +So he takes a magnet. + +And he moves a magnet around. + +And nothing changes. + +He kills the power to the +gas discharge tube. + +Everything stops. + +So it's definitely inspired by +35,000 volts of energy going + +into the tube. + +So then he says, OK I'll take +a piece of black paper. + +And he puts the black +paper in between. + +And the screen continues +to glow. + +So then he takes a book. + +And he puts the book in front. + +And he sees the shadow +of the book. + +And he's standing +here like this. + +He sees the shadow +of the book. + +And he can see the shadow of +the bones of his hand. + +So he says, you know I don't +think it's particles. + +I think it's radiation. + +I think it's radiation. + +And maybe it's something like +that radiation that Hertz has + +been talking about. + +It's some kind of radiation. + +But I don't know exactly +what it is. + +It's mysterious. + +And x is the letter +of mystery. + +I'm going to call +it x-radiation. + +So he's discovered this +mysterious form of radiation. + +Does he rush to publish? + +No. + +He's not going to risk his +scientific career by + +announcing that he's discovered +a form of radiation + +that can see inside +the human body. + +That would be professional +suicide. + +So he continues to repeat the +experiments through November + +and December of 1895. + +And in January of 1896, +he finally publishers. + +And it takes the +world by storm. + +By the way, how did he +record this stuff? + +He used photographic plates. + +And he stored the photographic +plates in his lab in a wooden + +file cabinet. + +And so many of the plates were +fogged even before he got them + +to the experiment. + +Because of the x-ray, +they were going + +everywhere in the lab. + +And he was working there +the whole time. + +So what happens? + +What's the world's reaction? + +January 16, 1896, New York Times +reports radiation that + +can see through matter and peer +inside the human body. + +Peer inside the human +body, you say. + +Well, why is that? + +What's the big deal? + +Well, in London, immediately +there was a market response. + +A manufacturer claimed to be a +purveyor of x-ray proof lady's + +undergarments. + +I mean if you can see inside +the human body, + +it's Victorian England. + +How modest can you be? + +This is a calamity. + +In France, of course, they don't +care about such things. + +So they had a different +response. + +Remember this is where Daguerre +invented halide + +photography. + +So there it's very deep. + +It's very existential. + +Somebody claimed that with +x-rays he could irradiate and + +get a picture of +the human soul. + +How French. + +But I'm sorry to say +it, the wackiest + +comes from guess where? + +The United States. + +No lesser an institution than +the New York City College of + +Physicians and Surgeons. + +They proposed to use x-rays to +project drawings from text + +books of anatomy onto the brains +of students thereby + +creating, and I quote, an +enduring impression. + +In Iowa, we plumb new depths. + +There was a group out there +claiming that they could turn + +copper pennies into gold. + +So this was the response. + +But the thing that makes it so +fantastic is we take it for + +granted that if I want to +exercise power and exert a + +force on that can, I don't +necessarily have to make + +physical contact with it. + +We accept this as given that +you an either have direct + +mechanical contact, or indirect +contact, magnetics, + +what have you. + +But in 1896, this +wasn't given. + +So the notion that I could exert +a force on something + +from a distance was +very fresh. + +It wasn't so easy. + +But there were benefits of +the x-radiation already + +in middle of 1896. + +There was a seamstress who +had a broken needle in an + +industrial accident in Scotland +buried into her hand. + +This is trivial. + +Look, all you need is low +pressure in a gas tube, and + +you can set this up +in high school. + +It's nothing. + +People had this set up +in dentist offices. + +It's nothing. + +So this surgeon was able to find +where the needle was, and + +then use precision to go in and +take the needle out of the + +injured person's hand. + +In eighteen 1899 they were +already using radiation in + +treatment of cancer. + +So what is the relevant +physics? + +what's the relevant +physics here? + +Let's look at the relevant +physics. + +Well, when we're talking about +35,000 volts, and we're + +talking about energies in the +vicinity of tens of thousands + +of electron volts, you know +that this can't come from + +emission from an excited +electron in a gas molecule. + +The gas binding energies are +way lower than that. + +This must come from the solid. + +The electron leaves the +cathode, and it + +crashes into the anode. + +Here's the smoking gun. + +There's something going on here +when the electron crashes + +into the anode and then gives +rise to the radiation. + +So let's look inside +the anode. + +So what's the energy +level diagram? + +Let's say the anode +is made of copper. + +So what's the energy level +diagram look like? + +So we know up here we're going +to have energy is 0. + +And the energy quantum +state is infinity. + +Down here is the ground state. + +And the energy is the +ground state energy. + +And we know this is +up in the tens of + +thousands of electron volts. + +And then up here there's +an E2 for state 2. + +And up here is an +E3, energy 3. + +Then maybe an E4 for energy +4, et cetera. + +And I'm going to write +not to scale. + +This is just to give +you a sense. + +And so the ballistic electron +with, in this case, 35,000 + +volts of energy, comes crashing +in to the anode. + +And this is one of these +mixed metaphors. + +So this is a Cartesian drawing +of an electron. + +All right? + +This is the incident electron. + +And its energy is given by the +charge on the electron, which + +is E, and the plate voltage, +which is 35,000. + +So it's got 35,000 electron +volts, which + +turns into 1/2 mv squared. + +It goes crashing into +this thing. + +And it's got enough energy +it can kick out top level + +electrons, mid-level electrons, +and in the extreme, + +it an eject ground state +electrons in 1s. + +By the way, the spectroscopists, +they don't + +like numbers. + +Remember, this is K. + +This is L. + +This is M. + +This is N. + +So we can eject K +shell electrons. + +What happens if we create +a vacancy down here? + +all? + +Of these electrons above +are unstable. + +If its copper, there's +29 of them. + +Now there's 28 with a vacancy. + +And they fall down. + +And when they fall down from +N equals 2 to N equals 1, + +there's a photon emitted. + +And that photon emission is in +the x region of the spectrum. + +But we don't just get +one wavelength. + +We get a plurality +of wavelengths. + +n equals 2 to n equals +1, we get a photon. + +There's a possibility to go for +n equals 3 to n equals 1. + +We'll get a photon of even +higher energy or a lower + +wavelength. + +Well, heck, if you've got enough +energy to kick out an + +electron from n equals 1, you've +certainly got enough + +energy to kick out an electron +from n equals 2. + +So you can get a cascade from +3 to 2, which gives us a + +photon, or from 4 to 2, which +gives us a photon. + +Can you see that you're going to +get an entire set of lines? + +We're going to label them +because we don't + +have a single line. + +So what do we label them? + +We label them on the basis of +the destination shell and how + +far they traveled. + +So this line here is known +as a K alpha line. + +Why is it a K? + +Because that's the nf. + +That's the n number of +the final state. + +And why is it alpha? + +Because the delta n equals 1. + +It came from 1 shell away. + +What's this one? + +It's gotta be a K +line, because we + +ended at n equals 1. + +But the delta is 2. + +It went from n equals +3 to n equals 1. + +So this is called K beta. + +So there's a K beta line +and a K alpha line. + +This ends at n equals 2, which +the spectroscopists call L. + +So we call this L. + +Delta is 1 L alpha. + +This is L, but delta is 2. + +So this is L beta. + +And what I can do, is I can plot +all of this on a curve + +showing the spectrum of this +particular element. + +And what do I expect to see? + +I expect to see a spectrum that +plots intensity versus + +some energy coordinate. + +It could be wavelength in this +direction, which means that + +energy increases in +that direction. + +And which has the +highest energy? + +The highest energy up here +is K beta, n equals + +3 to n equals 1. + +So there's K beta. + +And then close to +it is K alpha. + +And why do I put the +K alpha line higher + +than the K beta line? + +I don't know what the relative +amounts should be. + +But I suspect that if there's +a vacancy, it's + +like musical chairs. + +If there's a vacancy in n equals +1, and an electron only + +has to go from n equals 2 versus +n equals 3, the chances + +are the journey from n equals 2 +to N equals 1 is easier, and + +therefore more frequent than the +journey from n equals 3, + +even though n equals 3 to +1 is greater energy. + +But 2 to 1 is more likely. + +And intensity reflects +frequency. + +The wavelength reflects +the energy. + +And then over here is +L alpha L beta. + +Now there's one more +piece here. + +The precise value here is +determined by the identity of + +the element in the anode. + +If it's copper-- + +and I had to do this +as a junior at the + +University of Toronto. + +I spent a whole year doing +x-ray crystallography. + +And I will know on my death bed +the wavelength of copper K + +alpha radiation is to five +significant figures, 1.5418 + +angstroms. + +Now if someone had fallen asleep +in this lecture and + +open their eyes right now, and +looked at the wavelength of + +this line as 1.5418 angstroms. +And I erase the letters Cu. + +You take one look at that, +and you say copper. + +Because only copper has a K +alpha wavelength of 1.5418, + +which means I can use x-ray +analysis to determine the + +identity of a unknown +specimen. + +And furthermore it's additive. + +So if I had a brass, which is +copper and zinc, the zinc K + +alpha line is over here. + +And I will have both lines. + +And the relative intensities +of the lines are related to + +the relative concentrations of +the copper in zinc. So now I + +have a tool for chemical +analysis. + +All of this from going upstairs +after dinner and + +horsing around with the +gas discharge tube. + +OK, so we're going to end +the formal lesson here. + +But we have a few +more minutes. + +So everybody is instructed to +not make a lot of noise and + +just sit quietly. + +So let's take a look. + +This is an image. + +This is an image of Bertha. + +This is Roentgen's wife. + +This is her hand. + +He invited her into the lab. + +And she stood for a full 15 +minutes in front of this tube. + +And in that 15 minutes, got a +lifetime's worth of radiation. + +But what we're looking at here, +and what I'm going to + +point out to you in the last +several minutes here, Roentgen + +was a prissy physicist, +a really prissy guy. + +And he was German, which meant +that the German academics had + +no contact with industry +whatsoever. + +On the night of November 8, +1895, he invented three modern + +technologies. + +This is Bertha's hand. + +It represents the birth of +medical radiography. + +Is there anybody in this +auditorium who has never had + +an x-ray, a dental +or body x-ray? + +It's very rare. + +We see them all the time. + +We use them all the time. + +This morning I had one taken +about 9:10, right here. + +And I'm OK. + +So that's radiography, +medical radiography. + +Roentgen had a balance +in his laboratory. + +The justice, and she's got +the torsion balance. + +So you put the unknown on one +side, and then you put weights + +that are calibrated. + +These are made of brass. + +And they're in a wooden box. + +And so Roentgen has already +covered the tube + +with a wooden box. + +And so he took the emission from +this, and he radiating + +his box of weights. + +And what he see? + +He saw dark regions where +the weights were. + +Because metals have a different +electron density, + +because they've got a greater +atom density than wood. + +Wood is a more open structure. + +And so by contrast, he could +see inside the box. + +This is the basis for +airport security. + +Roentgen had a gun. + +He was not holding up +convenience stores. + +He was a hunter. + +He went into the woods. + +And he x-rayed the gun. + +Now why did he x-ray the gun? + +Now the gun is made of steel. + +But deep inside the steel, +there could be a flaw. + +There could be a crack. + +There could be a blowhole. + +The surface of the steel +looks beautiful. + +But inside is a crack. + +And that crack could lead to +failure under pressure. + +So Roentgen irradiates. + +And we already know from this +that different electron + +densities give different +shading, which means if there + +were a crack right here, +you might see it in the + +radiograph. + +And this we use for +certification of pressure + +vessels today. + +Certain pressure vessels that +have to be welded, have a + +specification that requires that +every inch of the weld be + +inspected by radiation, to be +certain that there are no + +cracks deep inside the weld that +under high pressure could + +open up, have an explosion, and +cause injury, or in the + +worst case, death. + +So what's the outcome +of it all? + +In 1901 when the Nobel Prizes +were offered for the first + +time, Roentgen by unanimous +vote of the selection + +committee was the first +recipient of the Nobel Prize + +in Physics. + +So on that occasion, he was +invited to come from Wurzburg + +and to deliver a lecture +in Stockholm. + +I've been to the place, it's +a spectacular hall, gilded, + +beautiful champagne reception, +elegant dinner. + +And he gives a lecture. + +And what's his lecture on? + +The discovery of x-rays. + +He received a huge amount +of money at the + +time in prize money. + +And he returned to Wurzburg +What did he do + +with the prize money? + +he? + +Donated it to the University +to be used for scholarships + +for students studying physics. + +And to this day, students +who study physics at the + +University of Wurzburg are +beneficiaries of the + +generosity of the first winner +of the Nobel Prize in Physics. + +Such was his humanity. + +I hope you have a +great weekend. + +We'll see the students +back here on Monday. \ No newline at end of file diff --git a/FXWZr3mscUo.txt b/FXWZr3mscUo.txt new file mode 100644 index 0000000000000000000000000000000000000000..5f6dc908192eabfc5f97861567d46c44f84e647c --- /dev/null +++ b/FXWZr3mscUo.txt @@ -0,0 +1,494 @@ +In beer and wine production, enzymes in yeast +aid the conversion of sugar into ethanol. + +Enzymes are used in cheese-making to degrade +proteins in milk, changing their solubility, + +and causing the proteins to precipitate. Many +industrial processes ranging from fruit juice + +production to paper production to biofuel +production utilize enzymes. In this video + +you'll see that studying how enzymes catalyze +reactions can help us design better therapeutics. + +This video is part of the Differential Equations +video series. Laws that govern a system's + +properties can be modeled using differential +equations. + +Hi. My name is Krystyn Van Vliet and I am +a professor in the Materials Science and Engineering + +and Biological Engineering departments at +MIT. + +of reactions and after some practice, you +will be able to derive a rate law for a general + +enzyme-catalyzed reaction. + +In order to understand the topic of this video, +you should be familiar with determining rate + +laws from experimental data, predicting rate +laws from proposed chemical reaction mechanisms, + +and have some basic understanding of the effects +of catalysts on the kinetics of a reaction. + +The +study of enzyme catalysis has become important +for drug development. Many drugs work by inhibiting + +an enzyme. + +For example, enzymes thought to be important +for the survival and replication of the parasite + +that causes malaria are being explored as +therapeutic targets. The parasites enter the + +red blood cells of the host and use proteases +to catalyze the degradation of the hemoglobin + +inside of the red blood cells. Degrading hemoglobin, +a protein, yields amino acids, which can then + +be used by the parasite for its own protein +synthesis. Protease inhibitors could help + +slow the degradation of hemoglobin, which +in turn would slow the growth and reproduction + +of the malaria parasite. + +When a potential inhibitor is identified, +kinetic data is used to evaluate its efficacy. + +In order to understand how this can be done, +let's start by describing the kinetics of + +a simpler case -- that of an enzyme catalyzed +reaction without an inhibitor present. Then + +we'll think about what might happen if we +throw an inhibitor into the mix. + +This video will help you describe enzyme catalysis +mathematically by first reviewing some common + +biochemical terms, then by describing the +general characteristics of enzyme-catalyzed + +you will encounter throughout your undergraduate +experience. + +a reactant is called a substrate. This is +really just a matter of different fields using + +different terms, but it's important for you +to be aware of this. Next, catalysts found + +in biological organisms are called enzymes. +Textbooks frequently abbreviate "substrate" + +using the letter "S" and enzyme using the +letter "E." + +How do enzymes work? If we look at a reaction +coordinate, recall that the transition state + +represents a chemical species intermediate +between the reactant, or substrate in this + +case, and the product. The potential energy +difference between the transition state and + +the reactants is the activation energy for +the forward reaction. The potential energy + +difference between the transition state and +the products is the activation energy for + +the reverse reaction. Only reactants with +the energy to overcome the activation energy + +will form products. + +Like synthetic catalysts, enzymes accelerate +the rates of reactions by stabilizing the + +transition state, lowering its potential energy, +and providing a new pathway by which the reaction + +can occur. This new reaction pathway has a +lower activation energy than the uncatalyzed + +path making it more likely that a greater +number of reactant molecules will have the + +energy needed to overcome the activation energy +and proceed to product. + +Enzymes facilitate reactions, but, like other +catalysts, are not consumed in the reaction. + +Enzymes are typically proteins, but RNA has +also been shown to catalyze reactions. + +While there are different theories about how +enzymes work to catalyze reactions, there + +are a couple of things that are agreed upon. +One is that enzymes have a region called an + +active site. Substrates bind to this region. +The shape and chemistry of the active site + +determine the selectivity of the enzyme for +particular substrates. + +The second point is that when a substrate +binds to an enzyme, an enzyme-substrate complex + +is formed. This enzyme-substrate complex is +a reaction intermediate, meaning that it is + +formed and consumed in the reactions, but +does not appear in the overall chemical equation. + +For many enzyme-catalyzed reactions, if we +were to measure the rate of reaction at various + +substrate concentrations, we would see that +the rate of reaction appears to follow first + +order kinetics at low substrate concentrations +and then transitions to behavior that resembles + +zero-order kinetics at high substrate concentrations. +Please pause the video here, turn to the person + +beside you and discuss what it means for a +reaction to be first-order or zero-order. + +Remember, in a first-order reaction, the reaction +rate is directly proportional to the concentration + +of substrate. In a zero-order reaction, the +reaction rate is constant as the reaction + +progresses and is unaffected by substrate +concentration. So, if we look at this data, + +we see that, for a given enzyme concentration, +the addition of substrate above a certain + +value has no effect on the rate of reaction. + +So let's think about what reaction mechanism +might explain this data. + +Some scientists hypothesized that after an +enzyme and substrate combine to form the enzyme-substrate + +complex, this complex yields the product and +degrades to regenerate free enzyme. Does the + +rate law derived from this reaction mechanism +fit the experimental data? + +Let's derive the rate law and see. We can +derive this rate law just as we would for + +other chemical systems. + +Remember, each step of a reaction mechanism +is assumed to be an elementary reaction. Please + +pause the video here, turn to the person beside +you and discuss how you determine the rate + +law for an elementary reaction. + +Remember, for an elementary reaction, you +CAN predict the rate law from the chemical + +equation. + +With this in mind, can you write a differential +equation for the rate of product formation + +with time? Please pause the video, try to +write the equation, and continue playing the + +video to see if you are correct. + +From the 2nd step of the reaction mechanism, +we can write that the rate of formation of + +product is equal to the rate constant k2 multiplied +by the concentration of our enzyme-substrate + +complex. + +The enzyme-substrate complex is a reaction +intermediate and not something that is easily + +measured in experiments. How can we verify +if this expression is correct? It would be + +nice to restate the rate in terms of quantities +that are more easily measured such as the + +substrate concentration and the initial enzyme +concentration. + +To get an expression for the concentration +of the enzyme-substrate complex, let's write + +a differential equation for the net rate of +change of the enzyme-substrate complex concentration + +with time. Please pause the video here, try +to write the differential equation, and then + +continue playing the video to see if you are +correct. + +If we want to write an expression for d[ES]/dt, +we see that in the first step of our mechanism, + +the enzyme-substrate complex is produced in +the forward direction and consumed in the + +reverse direction. In the second step, the +enzyme-substrate complex is converted into + +product. + +This equation introduces two additional unknowns: +the free enzyme concentration and substrate + +concentration. So, we need two additional +equations in order to solve it. + +Can you write an equation for the rate of +change of substrate concentration with time? + +Please pause the video here, try to write +the differential equation, and then continue + +playing the video to see if you are correct. + +If we want to write an expression for d[S]/dt, +we see that the substrate will be consumed + +in the forward direction and produced in the +reverse direction of the first step of the + +reaction mechanism. + +We still need one more equation. This equation +is a simple relationship that says we know + +how much enzyme we added to our reaction mixture +at time zero, so at any time, we know that + +the amount of free enzyme plus the amount +of enzyme bound in the enzyme-substrate complex + +should equal the initial amount added. This +could also be written in differential form + +as d[E]/dt plus d[ES]/dt is equal to zero. + +So, we have a system of four ordinary differential +equations with four variables that all depend + +on time. Equation 1 and Equation 4 have analytic +solutions, but Equations 2 and 3 contain a + +non-linear term. When you learn about differential +equations in your future courses, you'll see + +why these equations are difficult to solve +and that you will need numerical methods to + +solve them. + +Here, we have integrated these equations numerically +using the boundary conditions that at time + +equals zero, the substrate concentration is +S0, the product concentration is zero, the + +enzyme concentration is E0 and the concentration +of enzyme bound to substrate is zero. + +We see that after a short start-up period, +the concentration of enzyme bound to substrate + +remains approximately constant. In this region, +where the substrate concentration is much + +greater than E0, as enzyme is released from +the enzyme-substrate complex, it quickly recombines + +with available substrate. + +As more substrate is converted to product +and the substrate concentration approaches + +E0, the concentration of enzyme bound to substrate +is no longer constant. + +In the regime where the substrate concentration +IS greater than E0, we can make a steady-state + +approximation and set d[ES]/dt equal to zero. +This approximation will allow us to obtain + +an analytic expression for the concentration +of enzyme bound to substrate. + +Setting d[ES]/dt equal to zero allows us to +solve for the concentration of enzyme-substrate + +complex, which is equal to the rate constant +k1 times the concentration of free enzyme + +times the concentration of substrate divided +by the sum of k-1 and k2. + +Let's lump the rate constants into a new term +called Km and substitute this into our expression + +for the concentration of enzyme-substrate +complex. + +Now we can use this expression... ... to rewrite +d[P]/dt. + +Let's try to eliminate the concentration of +free enzyme from this expression. We can use + +the enzyme balance that we wrote earlier, +which said that the concentration of free + +enzyme plus the concentration of enzyme-substrate +complex should equal the initial enzyme concentration. + +Substituting our expression for the concentration +of ES into the enzyme balance and doing a + +little bit of algebra, we can solve for the +concentration of free enzyme. + +And finally, we can substitute this into our +equation for d[P]/dt and obtain this expression. + +Let's check this rate law against our experimental +data. At low substrate concentration, the + +expression reduces to a first-order rate law +and at high substrate concentration; the expression + +reduces to a zero order rate law. + +It turns out that the rate law that we just +derived is called the Michaelis-Menten equation. + +To make our equation look more like the version +of the Michaelis-Menten equation that you + +will see in textbooks, there are a couple +of terms that we will use because they are + +the convention in enzyme kinetics. Instead +of saying d[P]/dt is the rate of the reaction, + +we will call it the velocity of the reaction +and use the notation of 'v.' + +Finally, we'll lump k2[E]o into a term called +vmax. At high substrate concentration, the + +reaction velocity approaches vmax. + +Remember that lump parameter Km? We can determine +Km from experimental data. If we look at the + +substrate concentration needed to reach half +of vmax, we see that the concentration of + +substrate required equals Km. Km values for +many enzyme-substrate pairs can be found in + +the literature allowing for comparison. + +You may be wondering why we went through all +of this. Let's go back to our drug development + +example. + +Let's say that you have designed a drug that +you think will inhibit one of the proteases + +used by the malaria parasite to degrade hemoglobin. +How will you test its effectiveness? + +First, you might add a fixed amount of protease +to solutions of varying hemoglobin concentration + +in order to measure reaction rates. Let's +say that this reaction follows Michaelis-Menten + +kinetics well and that you are able to estimate +vmax and Km. + +Next, you repeat the experiment, but this +time, you also add a fixed amount of the drug + +candidate to all of your solutions. You get +your rate data and see that the apparent vmax + +has decreased. But what does this mean? Can +you speculate how this inhibitor works? + +Is the drug interacting with the enzyme and +preventing it from binding substrate? + +Is the drug interacting with the enzyme-substrate +complex? Is it something else entirely? + +The thought process that you used today to +derive the Michaelis-Menten equation can be + +used to derive rate laws for other reaction +mechanisms. Then you can see which mechanism + +is best supported by the data. + +Today we learned a little bit about the importance +of enzymes and derived a rate law from a general + +reaction mechanism using differential equations +and a steady-state approximation. This rate + +law was compared against experimental rate +data for an enzyme catalyzing the conversion + +of a substrate to a product. The equation +that we derived is called the Michaelis-Menten + +equation. While all enzyme-catalyzed reactions +may not exhibit Michaelis-Menten kinetics, + +the same logic that you used to derive the +equation can be used to derive rate laws for + +other proposed reaction mechanisms. \ No newline at end of file diff --git a/FwRj2DL5zIg.txt b/FwRj2DL5zIg.txt new file mode 100644 index 0000000000000000000000000000000000000000..811f0ad25b57d6c725060092b0fbdb58db067b63 --- /dev/null +++ b/FwRj2DL5zIg.txt @@ -0,0 +1,171 @@ +align:start position:0% + +why is it so hard for some people to + + align:start position:0% +why is it so hard for some people to + + + align:start position:0% +why is it so hard for some people to +recognize faces + + align:start position:0% +recognize faces + + + align:start position:0% +recognize faces +is the pterodactyl really a dinosaur and + + align:start position:0% +is the pterodactyl really a dinosaur and + + + align:start position:0% +is the pterodactyl really a dinosaur and +what does that have to do with ethics + + align:start position:0% +what does that have to do with ethics + + + align:start position:0% +what does that have to do with ethics +and computing are gmos helpful or + + align:start position:0% +and computing are gmos helpful or + + + align:start position:0% +and computing are gmos helpful or +harmful and how do we know is calculus a + + align:start position:0% +harmful and how do we know is calculus a + + + align:start position:0% +harmful and how do we know is calculus a +language + + align:start position:0% +language + + + align:start position:0% +language +welcome to chalk radio season three this + + align:start position:0% +welcome to chalk radio season three this + + + align:start position:0% +welcome to chalk radio season three this +season we'll talk with more mit + + align:start position:0% +season we'll talk with more mit + + + align:start position:0% +season we'll talk with more mit +professors about the passions that fuel + + align:start position:0% +professors about the passions that fuel + + + align:start position:0% +professors about the passions that fuel +their cutting-edge research and + + align:start position:0% +their cutting-edge research and + + + align:start position:0% +their cutting-edge research and +innovative teaching of topics like + + align:start position:0% +innovative teaching of topics like + + + align:start position:0% +innovative teaching of topics like +neurocognitive science climate + + align:start position:0% +neurocognitive science climate + + + align:start position:0% +neurocognitive science climate +laboratory chemistry computer science + + align:start position:0% +laboratory chemistry computer science + + + align:start position:0% +laboratory chemistry computer science +and many more so tune in to hear candid + + align:start position:0% +and many more so tune in to hear candid + + + align:start position:0% +and many more so tune in to hear candid +funny serious and personal conversations + + align:start position:0% +funny serious and personal conversations + + + align:start position:0% +funny serious and personal conversations +and as always we'll share links in our + + align:start position:0% +and as always we'll share links in our + + + align:start position:0% +and as always we'll share links in our +show notes so you can find our guests + + align:start position:0% +show notes so you can find our guests + + + align:start position:0% +show notes so you can find our guests +open educational resources on mit + + align:start position:0% +open educational resources on mit + + + align:start position:0% +open educational resources on mit +opencourseware + + align:start position:0% +opencourseware + + + align:start position:0% +opencourseware +chalk radio it's the closest thing to + + align:start position:0% +chalk radio it's the closest thing to + + + align:start position:0% +chalk radio it's the closest thing to +being here \ No newline at end of file diff --git a/G-5KHKrNPMs.txt b/G-5KHKrNPMs.txt new file mode 100644 index 0000000000000000000000000000000000000000..edc4b17f363d1855142cfb4ada927c11cc72edb5 --- /dev/null +++ b/G-5KHKrNPMs.txt @@ -0,0 +1,1203 @@ +align:start position:0% + +so so far even though these things look + + align:start position:0% +so so far even though these things look + + + align:start position:0% +so so far even though these things look +maybe interesting or a little familiar + + align:start position:0% +maybe interesting or a little familiar + + + align:start position:0% +maybe interesting or a little familiar +we have not yet stated clearly how they + + align:start position:0% +we have not yet stated clearly how they + + + align:start position:0% +we have not yet stated clearly how they +apply to physics we've been talking + + align:start position:0% +apply to physics we've been talking + + + align:start position:0% +apply to physics we've been talking +about vector spaces v for a particle + + align:start position:0% +about vector spaces v for a particle + + + align:start position:0% +about vector spaces v for a particle +then V tensor and and we've looked at + + align:start position:0% +then V tensor and and we've looked at + + + align:start position:0% +then V tensor and and we've looked at +states there we've looked at permutation + + align:start position:0% +states there we've looked at permutation + + + align:start position:0% +states there we've looked at permutation +operators they're symmetric States + + align:start position:0% +operators they're symmetric States + + + align:start position:0% +operators they're symmetric States +they're anti symmetric States there what + + align:start position:0% +they're anti symmetric States there what + + + align:start position:0% +they're anti symmetric States there what +is missing is something that connects it + + align:start position:0% +is missing is something that connects it + + + align:start position:0% +is missing is something that connects it +to quantum mechanics and that is given + + align:start position:0% +to quantum mechanics and that is given + + + align:start position:0% +to quantum mechanics and that is given +by the so called symmetrization + + align:start position:0% + + + + align:start position:0% + +precision postulate so it's a postulate + + align:start position:0% +precision postulate so it's a postulate + + + align:start position:0% +precision postulate so it's a postulate +it's something that you technically + + align:start position:0% +it's something that you technically + + + align:start position:0% +it's something that you technically +can't derive therefore you posture you + + align:start position:0% +can't derive therefore you posture you + + + align:start position:0% +can't derive therefore you posture you +can say it's an extra axiom even quantum + + align:start position:0% +can say it's an extra axiom even quantum + + + align:start position:0% +can say it's an extra axiom even quantum +mechanics you would say also that + + align:start position:0% +mechanics you would say also that + + + align:start position:0% +mechanics you would say also that +probably there's no other way to do + + align:start position:0% +probably there's no other way to do + + + align:start position:0% +probably there's no other way to do +things so in some sense it's force but I + + align:start position:0% +things so in some sense it's force but I + + + align:start position:0% +things so in some sense it's force but I +think it's more honest to admit it's an + + align:start position:0% +think it's more honest to admit it's an + + + align:start position:0% +think it's more honest to admit it's an +extra postulate so here it goes I'll + + align:start position:0% +extra postulate so here it goes I'll + + + align:start position:0% +extra postulate so here it goes I'll +read it first and I'll write it so it + + align:start position:0% +read it first and I'll write it so it + + + align:start position:0% +read it first and I'll write it so it +says the following if you have a system + + align:start position:0% +says the following if you have a system + + + align:start position:0% +says the following if you have a system +of n identical particles our baterry + + align:start position:0% +of n identical particles our baterry + + + align:start position:0% +of n identical particles our baterry +states in V tensor and are not physical + + align:start position:0% +states in V tensor and are not physical + + + align:start position:0% +states in V tensor and are not physical +States the physical states are the + + align:start position:0% +States the physical states are the + + + align:start position:0% +States the physical states are the +states that are totally symmetric in + + align:start position:0% +states that are totally symmetric in + + + align:start position:0% +states that are totally symmetric in +that case the particles are called + + align:start position:0% +that case the particles are called + + + align:start position:0% +that case the particles are called +bosons or totally anti-symmetric in + + align:start position:0% +bosons or totally anti-symmetric in + + + align:start position:0% +bosons or totally anti-symmetric in +which case the particles are called + + align:start position:0% +which case the particles are called + + + align:start position:0% +which case the particles are called +fermions that's basically the arbitrary + + align:start position:0% +fermions that's basically the arbitrary + + + align:start position:0% +fermions that's basically the arbitrary +state that this neither symmetric nor + + align:start position:0% +state that this neither symmetric nor + + + align:start position:0% +state that this neither symmetric nor +anti-symmetric and all that is not a + + align:start position:0% +anti-symmetric and all that is not a + + + align:start position:0% +anti-symmetric and all that is not a +physical state of a system of identical + + align:start position:0% +physical state of a system of identical + + + align:start position:0% +physical state of a system of identical +particles so let stated here in a system + + align:start position:0% +particles so let stated here in a system + + + align:start position:0% +particles so let stated here in a system +system with and identical particles + + align:start position:0% + + + + align:start position:0% + +physical states are not arbitrary states + + align:start position:0% +physical states are not arbitrary states + + + align:start position:0% +physical states are not arbitrary states +in V tensor n rather they are totally + + align:start position:0% +in V tensor n rather they are totally + + + align:start position:0% +in V tensor n rather they are totally +symmetric metric in parentheses they + + align:start position:0% +symmetric metric in parentheses they + + + align:start position:0% +symmetric metric in parentheses they +belong to sim n of V in which case the + + align:start position:0% +belong to sim n of V in which case the + + + align:start position:0% +belong to sim n of V in which case the +particles are said to be bosons be + + align:start position:0% +particles are said to be bosons be + + + align:start position:0% +particles are said to be bosons be +bosons or they are totally + + align:start position:0% +bosons or they are totally + + + align:start position:0% +bosons or they are totally +anti-symmetric are totally + + align:start position:0% +anti-symmetric are totally + + + align:start position:0% +anti-symmetric are totally +anti-symmetric they belong to anti and V + + align:start position:0% +anti-symmetric they belong to anti and V + + + align:start position:0% +anti-symmetric they belong to anti and V +in which case they are said to be + + align:start position:0% +in which case they are said to be + + + align:start position:0% +in which case they are said to be +fermions + + align:start position:0% + + + + align:start position:0% + +all right so this is really pretty + + align:start position:0% +all right so this is really pretty + + + align:start position:0% +all right so this is really pretty +fundamental it's it's a statement that + + align:start position:0% +fundamental it's it's a statement that + + + align:start position:0% +fundamental it's it's a statement that +we began our discussion by saying we + + align:start position:0% +we began our discussion by saying we + + + align:start position:0% +we began our discussion by saying we +have an electron that is opening another + + align:start position:0% +have an electron that is opening another + + + align:start position:0% +have an electron that is opening another +electron that this down is said the + + align:start position:0% +electron that this down is said the + + + align:start position:0% +electron that this down is said the +plus/minus state or is it the - plus + + align:start position:0% +plus/minus state or is it the - plus + + + align:start position:0% +plus/minus state or is it the - plus +state and we said it's neither one it's + + align:start position:0% + + + + align:start position:0% + +you cannot declare those two to be + + align:start position:0% +you cannot declare those two to be + + + align:start position:0% +you cannot declare those two to be +equivalent and that's what this says is + + align:start position:0% +equivalent and that's what this says is + + + align:start position:0% +equivalent and that's what this says is +not arbitrary States on this but they + + align:start position:0% +not arbitrary States on this but they + + + align:start position:0% +not arbitrary States on this but they +have to become totally symmetric if + + align:start position:0% +have to become totally symmetric if + + + align:start position:0% +have to become totally symmetric if +they're bosons or totally anti symmetric + + align:start position:0% +they're bosons or totally anti symmetric + + + align:start position:0% +they're bosons or totally anti symmetric +if there are fermions so we have to make + + align:start position:0% +if there are fermions so we have to make + + + align:start position:0% +if there are fermions so we have to make +a few comments and that's what will keep + + align:start position:0% +a few comments and that's what will keep + + + align:start position:0% +a few comments and that's what will keep +us busy for the next 20 25 minutes and + + align:start position:0% +us busy for the next 20 25 minutes and + + + align:start position:0% +us busy for the next 20 25 minutes and +to understand this and see what it + + align:start position:0% +to understand this and see what it + + + align:start position:0% +to understand this and see what it +implies and how we use it so so here it + + align:start position:0% +implies and how we use it so so here it + + + align:start position:0% +implies and how we use it so so here it +is the statement we have made it's a + + align:start position:0% +is the statement we have made it's a + + + align:start position:0% +is the statement we have made it's a +statement of fact + + align:start position:0% +statement of fact + + + align:start position:0% +statement of fact +in three dimensions there's no four + + align:start position:0% +in three dimensions there's no four + + + align:start position:0% +in three dimensions there's no four +particles that we like and we study + + align:start position:0% +particles that we like and we study + + + align:start position:0% +particles that we like and we study +their r+ further possibilities in worlds + + align:start position:0% +their r+ further possibilities in worlds + + + align:start position:0% +their r+ further possibilities in worlds +of lower dimension to three dimensions + + align:start position:0% +of lower dimension to three dimensions + + + align:start position:0% +of lower dimension to three dimensions +space time or so two dimensional space + + align:start position:0% +space time or so two dimensional space + + + align:start position:0% +space time or so two dimensional space +that allows for further kinds of + + align:start position:0% +that allows for further kinds of + + + align:start position:0% +that allows for further kinds of +statistics that are interesting but this + + align:start position:0% +statistics that are interesting but this + + + align:start position:0% +statistics that are interesting but this +is the general statement so the first + + align:start position:0% +is the general statement so the first + + + align:start position:0% +is the general statement so the first +comment is this is the general statement + + align:start position:0% + + + + align:start position:0% + +but further statistics other types of + + align:start position:0% +but further statistics other types of + + + align:start position:0% +but further statistics other types of +states exist + + align:start position:0% +states exist + + + align:start position:0% +states exist +in two dimensions not in three where we + + align:start position:0% +in two dimensions not in three where we + + + align:start position:0% +in two dimensions not in three where we +live you know we say three in the + + align:start position:0% +live you know we say three in the + + + align:start position:0% +live you know we say three in the +galilean way it's three plus one time + + align:start position:0% +galilean way it's three plus one time + + + align:start position:0% +galilean way it's three plus one time +but this is spatial dimensions this is + + align:start position:0% +but this is spatial dimensions this is + + + align:start position:0% +but this is spatial dimensions this is +the statistical definition of bosons and + + align:start position:0% +the statistical definition of bosons and + + + align:start position:0% +the statistical definition of bosons and +fermions but then comes the spin + + align:start position:0% +fermions but then comes the spin + + + align:start position:0% +fermions but then comes the spin +statistics theorem theorem that applies + + align:start position:0% +statistics theorem theorem that applies + + + align:start position:0% +statistics theorem theorem that applies +that you understand with quantum + + align:start position:0% +that you understand with quantum + + + align:start position:0% +that you understand with quantum +mechanics and that's a deep theorem that + + align:start position:0% +mechanics and that's a deep theorem that + + + align:start position:0% +mechanics and that's a deep theorem that +ends up telling you that particles with + + align:start position:0% +ends up telling you that particles with + + + align:start position:0% +ends up telling you that particles with +spin zero one two integer are bosons and + + align:start position:0% +spin zero one two integer are bosons and + + + align:start position:0% +spin zero one two integer are bosons and +particles with spin 1/2 three halves are + + align:start position:0% +particles with spin 1/2 three halves are + + + align:start position:0% +particles with spin 1/2 three halves are +fermions so this is a great achievement + + align:start position:0% +fermions so this is a great achievement + + + align:start position:0% +fermions so this is a great achievement +of quantum field theory associating this + + align:start position:0% +of quantum field theory associating this + + + align:start position:0% +of quantum field theory associating this +the statistical properties with the spin + + align:start position:0% +the statistical properties with the spin + + + align:start position:0% +the statistical properties with the spin +it's a deep connection it's valid for + + align:start position:0% +it's a deep connection it's valid for + + + align:start position:0% +it's a deep connection it's valid for +elementary particles or composite + + align:start position:0% +elementary particles or composite + + + align:start position:0% +elementary particles or composite +particle so you know the list of parties + + align:start position:0% +particle so you know the list of parties + + + align:start position:0% +particle so you know the list of parties +not that big particles of spin one we + + align:start position:0% +not that big particles of spin one we + + + align:start position:0% +not that big particles of spin one we +know a lot of them photon is spin one + + align:start position:0% +know a lot of them photon is spin one + + + align:start position:0% +know a lot of them photon is spin one +gluons her spin one w's the C's or spin + + align:start position:0% +gluons her spin one w's the C's or spin + + + align:start position:0% +gluons her spin one w's the C's or spin +one particles particles spin zero we + + align:start position:0% +one particles particles spin zero we + + + align:start position:0% +one particles particles spin zero we +didn't know an element + + align:start position:0% +didn't know an element + + + align:start position:0% +didn't know an element +one for awhile we finally know the Higgs + + align:start position:0% +one for awhile we finally know the Higgs + + + align:start position:0% +one for awhile we finally know the Higgs +is there spin zero particles of spin to + + align:start position:0% +is there spin zero particles of spin to + + + align:start position:0% +is there spin zero particles of spin to +just the gravity along higher spin none + + align:start position:0% +just the gravity along higher spin none + + + align:start position:0% +just the gravity along higher spin none +known may exist string theory has them + + align:start position:0% +known may exist string theory has them + + + align:start position:0% +known may exist string theory has them +all kinds of theories postulate them + + align:start position:0% +all kinds of theories postulate them + + + align:start position:0% +all kinds of theories postulate them +they may exist they may not spin have + + align:start position:0% +they may exist they may not spin have + + + align:start position:0% +they may exist they may not spin have +fractional spin well all the matter + + align:start position:0% +fractional spin well all the matter + + + align:start position:0% +fractional spin well all the matter +particles quarks muons leptons neutrinos + + align:start position:0% +particles quarks muons leptons neutrinos + + + align:start position:0% +particles quarks muons leptons neutrinos +are spin one-half spin free half is + + align:start position:0% +are spin one-half spin free half is + + + align:start position:0% +are spin one-half spin free half is +hypothetical as an elementary particle + + align:start position:0% +hypothetical as an elementary particle + + + align:start position:0% +hypothetical as an elementary particle +if it exists it would be called the + + align:start position:0% +if it exists it would be called the + + + align:start position:0% +if it exists it would be called the +gravity no their composite particles you + + align:start position:0% +gravity no their composite particles you + + + align:start position:0% +gravity no their composite particles you +could bake with quarks or with other + + align:start position:0% +could bake with quarks or with other + + + align:start position:0% +could bake with quarks or with other +particles mesons barians you can get + + align:start position:0% +particles mesons barians you can get + + + align:start position:0% +particles mesons barians you can get +several spins not with elementary + + align:start position:0% +several spins not with elementary + + + align:start position:0% +several spins not with elementary +particles many times unstable particles + + align:start position:0% +particles many times unstable particles + + + align:start position:0% +particles many times unstable particles +so anyway those is those are very + + align:start position:0% +so anyway those is those are very + + + align:start position:0% +so anyway those is those are very +interesting things now next fact is that + + align:start position:0% +interesting things now next fact is that + + + align:start position:0% +interesting things now next fact is that +you can go from elementary particles to + + align:start position:0% + + + + align:start position:0% + +composite particles so if you have for + + align:start position:0% +composite particles so if you have for + + + align:start position:0% +composite particles so if you have for +example the hydrogen atom that it has a + + align:start position:0% +example the hydrogen atom that it has a + + + align:start position:0% +example the hydrogen atom that it has a +proton and an electron and you want to + + align:start position:0% +proton and an electron and you want to + + + align:start position:0% +proton and an electron and you want to +figure out if it's a boson or a fermion + + align:start position:0% +figure out if it's a boson or a fermion + + + align:start position:0% +figure out if it's a boson or a fermion +well you think of another hydrogen atom + + align:start position:0% +well you think of another hydrogen atom + + + align:start position:0% +well you think of another hydrogen atom +here P and E and you write a wave + + align:start position:0% +here P and E and you write a wave + + + align:start position:0% +here P and E and you write a wave +function that involves the the protons + + align:start position:0% +function that involves the the protons + + + align:start position:0% +function that involves the the protons +the first proton the second proton the + + align:start position:0% +the first proton the second proton the + + + align:start position:0% +the first proton the second proton the +first electron and the second electron + + align:start position:0% +first electron and the second electron + + + align:start position:0% +first electron and the second electron +that's a little bit of a funny notation + + align:start position:0% +that's a little bit of a funny notation + + + align:start position:0% +that's a little bit of a funny notation +this would correspond to maybe the + + align:start position:0% +this would correspond to maybe the + + + align:start position:0% +this would correspond to maybe the +coordinates of the first proton the + + align:start position:0% +coordinates of the first proton the + + + align:start position:0% +coordinates of the first proton the +second proton the first electron second + + align:start position:0% +second proton the first electron second + + + align:start position:0% +second proton the first electron second +electron since protons are identical + + align:start position:0% +electron since protons are identical + + + align:start position:0% +electron since protons are identical +particles that are fermions the + + align:start position:0% +particles that are fermions the + + + align:start position:0% +particles that are fermions the +wavefunction must change sign if p1 and + + align:start position:0% +wavefunction must change sign if p1 and + + + align:start position:0% +wavefunction must change sign if p1 and +p2 are exchanged + + align:start position:0% +p2 are exchanged + + + align:start position:0% +p2 are exchanged +would be a minus signs anti-symmetric + + align:start position:0% +would be a minus signs anti-symmetric + + + align:start position:0% +would be a minus signs anti-symmetric +since the electrodes are fermions it + + align:start position:0% +since the electrodes are fermions it + + + align:start position:0% +since the electrodes are fermions it +should be anti-symmetric by exchanging + + align:start position:0% +should be anti-symmetric by exchanging + + + align:start position:0% +should be anti-symmetric by exchanging +this tool so it's also anti-symmetric + + align:start position:0% +this tool so it's also anti-symmetric + + + align:start position:0% +this tool so it's also anti-symmetric +under this exchange so finally if you + + align:start position:0% +under this exchange so finally if you + + + align:start position:0% +under this exchange so finally if you +exchange this atom with this atom you + + align:start position:0% +exchange this atom with this atom you + + + align:start position:0% +exchange this atom with this atom you +must have change the two protons and the + + align:start position:0% +must have change the two protons and the + + + align:start position:0% +must have change the two protons and the +two electrons at the same time two + + align:start position:0% +two electrons at the same time two + + + align:start position:0% +two electrons at the same time two +minuses and you get a plus there for the + + align:start position:0% +minuses and you get a plus there for the + + + align:start position:0% +minuses and you get a plus there for the +hydrogen atom is a boson + + align:start position:0% +hydrogen atom is a boson + + + align:start position:0% +hydrogen atom is a boson +so this statistical properties built up + + align:start position:0% +so this statistical properties built up + + + align:start position:0% +so this statistical properties built up +so an object built with a number of + + align:start position:0% +so an object built with a number of + + + align:start position:0% +so an object built with a number of +bosons are a number of fermions will be + + align:start position:0% +bosons are a number of fermions will be + + + align:start position:0% +bosons are a number of fermions will be +a boson or a firm in depending on those + + align:start position:0% +a boson or a firm in depending on those + + + align:start position:0% +a boson or a firm in depending on those +numbers so that's a nice thing so the + + align:start position:0% +numbers so that's a nice thing so the + + + align:start position:0% +numbers so that's a nice thing so the +hydrogen atom atom is a boson \ No newline at end of file diff --git a/GZzrMyY01tE.txt b/GZzrMyY01tE.txt new file mode 100644 index 0000000000000000000000000000000000000000..c61be25efc5de0b234748ee701f4025c3fe30b24 --- /dev/null +++ b/GZzrMyY01tE.txt @@ -0,0 +1,1891 @@ +align:start position:0% + +today we begin with our study of + + align:start position:0% +today we begin with our study of + + + align:start position:0% +today we begin with our study of +scattering and so scattering is a the + + align:start position:0% +scattering and so scattering is a the + + + align:start position:0% +scattering and so scattering is a the +next chapter in our study for + + align:start position:0% +next chapter in our study for + + + align:start position:0% +next chapter in our study for +proximation what is the purpose of + + align:start position:0% +proximation what is the purpose of + + + align:start position:0% +proximation what is the purpose of +scattering physicists want to study the + + align:start position:0% +scattering physicists want to study the + + + align:start position:0% +scattering physicists want to study the +interactions between particles the + + align:start position:0% +interactions between particles the + + + align:start position:0% +interactions between particles the +forces we know for example in a hydrogen + + align:start position:0% +forces we know for example in a hydrogen + + + align:start position:0% +forces we know for example in a hydrogen +atom there's an electromagnetic force + + align:start position:0% +atom there's an electromagnetic force + + + align:start position:0% +atom there's an electromagnetic force +between the proton and electron when + + align:start position:0% +between the proton and electron when + + + align:start position:0% +between the proton and electron when +derstand it rather well but there are + + align:start position:0% +derstand it rather well but there are + + + align:start position:0% +derstand it rather well but there are +other forces in nature that we don't + + align:start position:0% +other forces in nature that we don't + + + align:start position:0% +other forces in nature that we don't +understand very well are harder to + + align:start position:0% +understand very well are harder to + + + align:start position:0% +understand very well are harder to +understand those at higher energies + + align:start position:0% +understand those at higher energies + + + align:start position:0% +understand those at higher energies +interactions between particles can be + + align:start position:0% +interactions between particles can be + + + align:start position:0% +interactions between particles can be +rather complicated also it may happen + + align:start position:0% +rather complicated also it may happen + + + align:start position:0% +rather complicated also it may happen +that you have a situation where there's + + align:start position:0% +that you have a situation where there's + + + align:start position:0% +that you have a situation where there's +a potential affecting particles maybe a + + align:start position:0% +a potential affecting particles maybe a + + + align:start position:0% +a potential affecting particles maybe a +trap or something that holds particles + + align:start position:0% +trap or something that holds particles + + + align:start position:0% +trap or something that holds particles +when there's a potential and you really + + align:start position:0% +when there's a potential and you really + + + align:start position:0% +when there's a potential and you really +kind of measure directly this potential + + align:start position:0% +kind of measure directly this potential + + + align:start position:0% +kind of measure directly this potential +there's no simple way of doing so and + + align:start position:0% +there's no simple way of doing so and + + + align:start position:0% +there's no simple way of doing so and +then what you do is you send particles + + align:start position:0% +then what you do is you send particles + + + align:start position:0% +then what you do is you send particles +in and you see how they get affected and + + align:start position:0% +in and you see how they get affected and + + + align:start position:0% +in and you see how they get affected and +by studying the reflection or the + + align:start position:0% +by studying the reflection or the + + + align:start position:0% +by studying the reflection or the +scattering of the particles off of this + + align:start position:0% +scattering of the particles off of this + + + align:start position:0% +scattering of the particles off of this +potential you learn a lot about what + + align:start position:0% +potential you learn a lot about what + + + align:start position:0% +potential you learn a lot about what +this potential can be so the subject + + align:start position:0% +this potential can be so the subject + + + align:start position:0% +this potential can be so the subject +today is scouring + + align:start position:0% + + + + align:start position:0% + +and in general you have a beam of + + align:start position:0% +and in general you have a beam of + + + align:start position:0% +and in general you have a beam of +particles a target and a number of + + align:start position:0% +particles a target and a number of + + + align:start position:0% +particles a target and a number of +detectors that's what happens in a big + + align:start position:0% +detectors that's what happens in a big + + + align:start position:0% +detectors that's what happens in a big +accelerator and in general you have such + + align:start position:0% +accelerator and in general you have such + + + align:start position:0% +accelerator and in general you have such +situations all the case so a beam some + + align:start position:0% +situations all the case so a beam some + + + align:start position:0% +situations all the case so a beam some +sort of target and particles get + + align:start position:0% +sort of target and particles get + + + align:start position:0% +sort of target and particles get +scattered and you have detectors and in + + align:start position:0% +scattered and you have detectors and in + + + align:start position:0% +scattered and you have detectors and in +general the detectors are all over in + + align:start position:0% +general the detectors are all over in + + + align:start position:0% +general the detectors are all over in +all directions because particles may + + align:start position:0% +all directions because particles may + + + align:start position:0% +all directions because particles may +back scatter may go in in different ways + + align:start position:0% +back scatter may go in in different ways + + + align:start position:0% +back scatter may go in in different ways +so collisions in general are rather + + align:start position:0% +so collisions in general are rather + + + align:start position:0% +so collisions in general are rather +intricate particles can change identity + + align:start position:0% +intricate particles can change identity + + + align:start position:0% +intricate particles can change identity +can do all kinds of different things for + + align:start position:0% +can do all kinds of different things for + + + align:start position:0% +can do all kinds of different things for +example you can have a proton colliding + + align:start position:0% +example you can have a proton colliding + + + align:start position:0% +example you can have a proton colliding +with a proton this could be the case + + align:start position:0% +with a proton this could be the case + + + align:start position:0% +with a proton this could be the case +when the beam is a beam of protons and + + align:start position:0% +when the beam is a beam of protons and + + + align:start position:0% +when the beam is a beam of protons and +here maybe there's a target in which you + + align:start position:0% +here maybe there's a target in which you + + + align:start position:0% +here maybe there's a target in which you +study what happens when a proton + + align:start position:0% +study what happens when a proton + + + align:start position:0% +study what happens when a proton +encounters a proton or it may be that in + + align:start position:0% +encounters a proton or it may be that in + + + align:start position:0% +encounters a proton or it may be that in +some cases there's another beam that is + + align:start position:0% +some cases there's another beam that is + + + align:start position:0% +some cases there's another beam that is +coming also with protons and they + + align:start position:0% +coming also with protons and they + + + align:start position:0% +coming also with protons and they +collide but when protons collide with + + align:start position:0% +collide but when protons collide with + + + align:start position:0% +collide but when protons collide with +protons funny things can happen for + + align:start position:0% +protons funny things can happen for + + + align:start position:0% +protons funny things can happen for +example you can get the two protons plus + + align:start position:0% +example you can get the two protons plus + + + align:start position:0% +example you can get the two protons plus +a PI on a neutral pion zero denoting + + align:start position:0% +a PI on a neutral pion zero denoting + + + align:start position:0% +a PI on a neutral pion zero denoting +zero charge + + align:start position:0% +zero charge + + + align:start position:0% +zero charge +that's a had run an inter strongly + + align:start position:0% +that's a had run an inter strongly + + + align:start position:0% +that's a had run an inter strongly +interacting particle like the proton is + + align:start position:0% +interacting particle like the proton is + + + align:start position:0% +interacting particle like the proton is +is made of quarks and this can happen + + align:start position:0% +is made of quarks and this can happen + + + align:start position:0% +is made of quarks and this can happen +there's no such thing as a conservation + + align:start position:0% +there's no such thing as a conservation + + + align:start position:0% +there's no such thing as a conservation +of the number of particles that is one + + align:start position:0% +of the number of particles that is one + + + align:start position:0% +of the number of particles that is one +of the reasons you need quantum field + + align:start position:0% +of the reasons you need quantum field + + + align:start position:0% +of the reasons you need quantum field +theory to do this kind of computation + + align:start position:0% +theory to do this kind of computation + + + align:start position:0% +theory to do this kind of computation +and this reaction is allowed because it + + align:start position:0% +and this reaction is allowed because it + + + align:start position:0% +and this reaction is allowed because it +at least the first thing you can't + + align:start position:0% +at least the first thing you can't + + + align:start position:0% +at least the first thing you can't +conserves charges proton and proton go + + align:start position:0% +conserves charges proton and proton go + + + align:start position:0% +conserves charges proton and proton go +to Croton and produce or charge is + + align:start position:0% +to Croton and produce or charge is + + + align:start position:0% +to Croton and produce or charge is +conserved and PI zeros neutral so that + + align:start position:0% +conserved and PI zeros neutral so that + + + align:start position:0% +conserved and PI zeros neutral so that +for example can happen or proton plus + + align:start position:0% +for example can happen or proton plus + + + align:start position:0% +for example can happen or proton plus +proton can go to proton plus neutral now + + align:start position:0% +proton can go to proton plus neutral now + + + align:start position:0% +proton can go to proton plus neutral now +charge is not conserved but this time a + + align:start position:0% +charge is not conserved but this time a + + + align:start position:0% +charge is not conserved but this time a +positively charged ion called pi plus + + align:start position:0% + + + + align:start position:0% + +the particles can completely change + + align:start position:0% +the particles can completely change + + + align:start position:0% +the particles can completely change +identity you can have a electron and a + + align:start position:0% +identity you can have a electron and a + + + align:start position:0% +identity you can have a electron and a +positron colliding so that's electron + + align:start position:0% +positron colliding so that's electron + + + align:start position:0% +positron colliding so that's electron +this is the positron the antiparticle of + + align:start position:0% +this is the positron the antiparticle of + + + align:start position:0% +this is the positron the antiparticle of +the electron equal mass oppositely + + align:start position:0% +the electron equal mass oppositely + + + align:start position:0% +the electron equal mass oppositely +charged and then they can go into a mu + + align:start position:0% +charged and then they can go into a mu + + + align:start position:0% +charged and then they can go into a mu +plus plus mu minus these are charged + + align:start position:0% +plus plus mu minus these are charged + + + align:start position:0% +plus plus mu minus these are charged +leptons again just like the electron are + + align:start position:0% +leptons again just like the electron are + + + align:start position:0% +leptons again just like the electron are +called leptons as opposed to these + + align:start position:0% +called leptons as opposed to these + + + align:start position:0% +called leptons as opposed to these +particles here there go hadrons these + + align:start position:0% +particles here there go hadrons these + + + align:start position:0% +particles here there go hadrons these +particles are as far as we know our + + align:start position:0% +particles are as far as we know our + + + align:start position:0% +particles are as far as we know our +elementary this particles are made out + + align:start position:0% +elementary this particles are made out + + + align:start position:0% +elementary this particles are made out +of quarks and in this case you have a + + align:start position:0% +of quarks and in this case you have a + + + align:start position:0% +of quarks and in this case you have a +complete change of identity the original + + align:start position:0% +complete change of identity the original + + + align:start position:0% +complete change of identity the original +particles have disappeared and new + + align:start position:0% +particles have disappeared and new + + + align:start position:0% +particles have disappeared and new +particles have been created and you can + + align:start position:0% +particles have been created and you can + + + align:start position:0% +particles have been created and you can +look forward to study these processes as + + align:start position:0% +look forward to study these processes as + + + align:start position:0% +look forward to study these processes as +you continuous of your studies of + + align:start position:0% +you continuous of your studies of + + + align:start position:0% +you continuous of your studies of +quantum mechanics but these are like + + align:start position:0% +quantum mechanics but these are like + + + align:start position:0% +quantum mechanics but these are like +reactions now in our name in our + + align:start position:0% +reactions now in our name in our + + + align:start position:0% +reactions now in our name in our +nomenclature for scattering we will call + + align:start position:0% +nomenclature for scattering we will call + + + align:start position:0% +nomenclature for scattering we will call +a processes scattering process where the + + align:start position:0% +a processes scattering process where the + + + align:start position:0% +a processes scattering process where the +identity of the particles is unchanged + + align:start position:0% +identity of the particles is unchanged + + + align:start position:0% +identity of the particles is unchanged +so we'll have scattering scattering + + align:start position:0% +so we'll have scattering scattering + + + align:start position:0% +so we'll have scattering scattering +strictly speaking speaking + + align:start position:0% + + + + align:start position:0% + +when there is no change of identity in + + align:start position:0% +when there is no change of identity in + + + align:start position:0% +when there is no change of identity in +the initial and final States no change + + align:start position:0% +the initial and final States no change + + + align:start position:0% +the initial and final States no change +of identity of the particles the pondage + + align:start position:0% +of identity of the particles the pondage + + + align:start position:0% +of identity of the particles the pondage +no change of particles in the process of + + align:start position:0% +no change of particles in the process of + + + align:start position:0% +no change of particles in the process of +going from initial to final states so a + + align:start position:0% +going from initial to final states so a + + + align:start position:0% +going from initial to final states so a +scattering process looks like a plus B + + align:start position:0% +scattering process looks like a plus B + + + align:start position:0% +scattering process looks like a plus B +goes to a plus B we don't change + + align:start position:0% +goes to a plus B we don't change + + + align:start position:0% +goes to a plus B we don't change +identity those processes where you + + align:start position:0% +identity those processes where you + + + align:start position:0% +identity those processes where you +change identity are harder to discuss + + align:start position:0% +change identity are harder to discuss + + + align:start position:0% +change identity are harder to discuss +and we want to discuss them here even + + align:start position:0% +and we want to discuss them here even + + + align:start position:0% +and we want to discuss them here even +here there's still a lot of things that + + align:start position:0% +here there's still a lot of things that + + + align:start position:0% +here there's still a lot of things that +can happen it's very intricate so we + + align:start position:0% +can happen it's very intricate so we + + + align:start position:0% +can happen it's very intricate so we +will demand even more we will call or + + align:start position:0% +will demand even more we will call or + + + align:start position:0% +will demand even more we will call or +look for elastic scattering scattering + + align:start position:0% + + + + align:start position:0% + +and that means that if this particles or + + align:start position:0% +and that means that if this particles or + + + align:start position:0% +and that means that if this particles or +objects have internal states those + + align:start position:0% +objects have internal states those + + + align:start position:0% +objects have internal states those +internal states are not changed so the + + align:start position:0% +internal states are not changed so the + + + align:start position:0% +internal states are not changed so the +internal states of the particles do not + + align:start position:0% +internal states of the particles do not + + + align:start position:0% +internal states of the particles do not +change of course that can happen + + align:start position:0% +change of course that can happen + + + align:start position:0% +change of course that can happen +essentially when the particles are + + align:start position:0% +essentially when the particles are + + + align:start position:0% +essentially when the particles are +complex they're bound states of other + + align:start position:0% +complex they're bound states of other + + + align:start position:0% +complex they're bound states of other +particles so you may have a bound state + + align:start position:0% +particles so you may have a bound state + + + align:start position:0% +particles so you may have a bound state +of one form and then when you have bound + + align:start position:0% +of one form and then when you have bound + + + align:start position:0% +of one form and then when you have bound +States you don't you have all kind of + + align:start position:0% +States you don't you have all kind of + + + align:start position:0% +States you don't you have all kind of +energy levels internal states and then + + align:start position:0% +energy levels internal states and then + + + align:start position:0% +energy levels internal states and then +when we say we have an elastic process + + align:start position:0% +when we say we have an elastic process + + + align:start position:0% +when we say we have an elastic process +it means that those internal states are + + align:start position:0% +it means that those internal states are + + + align:start position:0% +it means that those internal states are +not changed a classic example of + + align:start position:0% +not changed a classic example of + + + align:start position:0% +not changed a classic example of +inelastic scattering experiment the most + + align:start position:0% +inelastic scattering experiment the most + + + align:start position:0% +inelastic scattering experiment the most +famous historically of those experiments + + align:start position:0% +famous historically of those experiments + + + align:start position:0% +famous historically of those experiments +is an experiment by Frank and Hertz in + + align:start position:0% +is an experiment by Frank and Hertz in + + + align:start position:0% +is an experiment by Frank and Hertz in +1914 they were having a chamber with + + align:start position:0% +1914 they were having a chamber with + + + align:start position:0% +1914 they were having a chamber with +Mercury gas and they shot electrons from + + align:start position:0% +Mercury gas and they shot electrons from + + + align:start position:0% +Mercury gas and they shot electrons from +one side to the other and the electrons + + align:start position:0% +one side to the other and the electrons + + + align:start position:0% +one side to the other and the electrons +and the mercury atoms collided and they + + align:start position:0% +and the mercury atoms collided and they + + + align:start position:0% +and the mercury atoms collided and they +found that the electrons were slowed + + align:start position:0% +found that the electrons were slowed + + + align:start position:0% +found that the electrons were slowed +down by some quantized amount of energy + + align:start position:0% +down by some quantized amount of energy + + + align:start position:0% +down by some quantized amount of energy +and that was the first evidence that + + align:start position:0% +and that was the first evidence that + + + align:start position:0% +and that was the first evidence that +atoms had energy levels Bohr's theory of + + align:start position:0% +atoms had energy levels Bohr's theory of + + + align:start position:0% +atoms had energy levels Bohr's theory of +atoms had been proposed one year before + + align:start position:0% +atoms had been proposed one year before + + + align:start position:0% +atoms had been proposed one year before +that 1913 and then the process in which + + align:start position:0% +that 1913 and then the process in which + + + align:start position:0% +that 1913 and then the process in which +this electrons hit the atoms and lost + + align:start position:0% +this electrons hit the atoms and lost + + + align:start position:0% +this electrons hit the atoms and lost +energy corresponding to producing + + align:start position:0% +energy corresponding to producing + + + align:start position:0% +energy corresponding to producing +transitions in the atoms and that would + + align:start position:0% +transitions in the atoms and that would + + + align:start position:0% +transitions in the atoms and that would +be an + + align:start position:0% +be an + + + align:start position:0% +be an +elastic scattering because the atom + + align:start position:0% +elastic scattering because the atom + + + align:start position:0% +elastic scattering because the atom +changes internal state this is a + + align:start position:0% +changes internal state this is a + + + align:start position:0% +changes internal state this is a +collision between an electron or another + + align:start position:0% +collision between an electron or another + + + align:start position:0% +collision between an electron or another +but the atom has changed internal states + + align:start position:0% +but the atom has changed internal states + + + align:start position:0% +but the atom has changed internal states +so we will want to consider cases when + + align:start position:0% +so we will want to consider cases when + + + align:start position:0% +so we will want to consider cases when +we don't change the internal state and + + align:start position:0% +we don't change the internal state and + + + align:start position:0% +we don't change the internal state and +that will be when you have elastic + + align:start position:0% +that will be when you have elastic + + + align:start position:0% +that will be when you have elastic +scattering so a few more things that + + align:start position:0% +scattering so a few more things that + + + align:start position:0% +scattering so a few more things that +we're going to assume us we do elastic + + align:start position:0% +we're going to assume us we do elastic + + + align:start position:0% +we're going to assume us we do elastic +scattering we will work without spin all + + align:start position:0% +scattering we will work without spin all + + + align:start position:0% +scattering we will work without spin all +we will do in the next lectures one or + + align:start position:0% +we will do in the next lectures one or + + + align:start position:0% +we will do in the next lectures one or +two more lectures and this will be + + align:start position:0% +two more lectures and this will be + + + align:start position:0% +two more lectures and this will be +particles without spin as we're doing in + + align:start position:0% +particles without spin as we're doing in + + + align:start position:0% +particles without spin as we're doing in +our course we also work in the + + align:start position:0% +our course we also work in the + + + align:start position:0% +our course we also work in the +nonrelativistic approximation so these + + align:start position:0% +nonrelativistic approximation so these + + + align:start position:0% +nonrelativistic approximation so these +are the first things that we will assume + + align:start position:0% + + + + align:start position:0% + +one no spin this doesn't complicate + + align:start position:0% +one no spin this doesn't complicate + + + align:start position:0% +one no spin this doesn't complicate +matters as far as the scattering is + + align:start position:0% +matters as far as the scattering is + + + align:start position:0% +matters as far as the scattering is +concerned it just complicates the + + align:start position:0% +concerned it just complicates the + + + align:start position:0% +concerned it just complicates the +algebra and the calculations you have to + + align:start position:0% +algebra and the calculations you have to + + + align:start position:0% +algebra and the calculations you have to +do because you have more degrees of + + align:start position:0% +do because you have more degrees of + + + align:start position:0% +do because you have more degrees of +freedom we will be working + + align:start position:0% +freedom we will be working + + + align:start position:0% +freedom we will be working +nonrelativistic relativistically + + align:start position:0% + + + + align:start position:0% + +moreover we will assume their + + align:start position:0% +moreover we will assume their + + + align:start position:0% +moreover we will assume their +interactions their interactions between + + align:start position:0% +interactions their interactions between + + + align:start position:0% +interactions their interactions between +the particles that produce the + + align:start position:0% +the particles that produce the + + + align:start position:0% +the particles that produce the +scattering and those interactions are + + align:start position:0% +scattering and those interactions are + + + align:start position:0% +scattering and those interactions are +simple enough that they just depend on + + align:start position:0% +simple enough that they just depend on + + + align:start position:0% +simple enough that they just depend on +the difference of positions of the + + align:start position:0% +the difference of positions of the + + + align:start position:0% +the difference of positions of the +interactions potentials are of the form + + align:start position:0% +interactions potentials are of the form + + + align:start position:0% +interactions potentials are of the form +V of R 1 minus R 2 so processes in which + + align:start position:0% +V of R 1 minus R 2 so processes in which + + + align:start position:0% +V of R 1 minus R 2 so processes in which +will have two incoming particles and + + align:start position:0% +will have two incoming particles and + + + align:start position:0% +will have two incoming particles and +they interact + + align:start position:0% +they interact + + + align:start position:0% +they interact +and they'll scatter elastically and the + + align:start position:0% +and they'll scatter elastically and the + + + align:start position:0% +and they'll scatter elastically and the +potential depends on just the difference + + align:start position:0% +potential depends on just the difference + + + align:start position:0% +potential depends on just the difference +of the two positions eventually we will + + align:start position:0% +of the two positions eventually we will + + + align:start position:0% +of the two positions eventually we will +even assume it's only on the magnitude + + align:start position:0% +even assume it's only on the magnitude + + + align:start position:0% +even assume it's only on the magnitude +of these differences for particular + + align:start position:0% +of these differences for particular + + + align:start position:0% +of these differences for particular +cases but if you have a potential like + + align:start position:0% +cases but if you have a potential like + + + align:start position:0% +cases but if you have a potential like +this like when we were studying the + + align:start position:0% +this like when we were studying the + + + align:start position:0% +this like when we were studying the +hydrogen atom for the first time a + + align:start position:0% +hydrogen atom for the first time a + + + align:start position:0% +hydrogen atom for the first time a +potential that just depends on the + + align:start position:0% +potential that just depends on the + + + align:start position:0% +potential that just depends on the +differences of positions can be treated + + align:start position:0% +differences of positions can be treated + + + align:start position:0% +differences of positions can be treated +in the center-of-mass frame it's a nice + + align:start position:0% +in the center-of-mass frame it's a nice + + + align:start position:0% +in the center-of-mass frame it's a nice +frame where you can work on it and then + + align:start position:0% +frame where you can work on it and then + + + align:start position:0% +frame where you can work on it and then +you can think of it as a single particle + + align:start position:0% +you can think of it as a single particle + + + align:start position:0% +you can think of it as a single particle +scattering off a potential so you + + align:start position:0% +scattering off a potential so you + + + align:start position:0% +scattering off a potential so you +translate the Schrodinger equation into + + align:start position:0% +translate the Schrodinger equation into + + + align:start position:0% +translate the Schrodinger equation into +a center of mass degrees of freedom that + + align:start position:0% +a center of mass degrees of freedom that + + + align:start position:0% +a center of mass degrees of freedom that +are generally simple and we don't worry + + align:start position:0% +are generally simple and we don't worry + + + align:start position:0% +are generally simple and we don't worry +about and a relative degree of freedom + + align:start position:0% +about and a relative degree of freedom + + + align:start position:0% +about and a relative degree of freedom +so this can be done here so this makes a + + align:start position:0% +so this can be done here so this makes a + + + align:start position:0% +so this can be done here so this makes a +process equivalent to scattering of a + + align:start position:0% +process equivalent to scattering of a + + + align:start position:0% +process equivalent to scattering of a +particle off a potential V of R and that + + align:start position:0% +particle off a potential V of R and that + + + align:start position:0% +particle off a potential V of R and that +particle has the reduced mass just like + + align:start position:0% +particle has the reduced mass just like + + + align:start position:0% +particle has the reduced mass just like +happened with hydrogen atom the real + + align:start position:0% +happened with hydrogen atom the real + + + align:start position:0% +happened with hydrogen atom the real +mass of the equation we solve for the + + align:start position:0% +mass of the equation we solve for the + + + align:start position:0% +mass of the equation we solve for the +share inner Hamiltonian for a hydrogen + + align:start position:0% +share inner Hamiltonian for a hydrogen + + + align:start position:0% +share inner Hamiltonian for a hydrogen +atom the mass that shows up there is the + + align:start position:0% +atom the mass that shows up there is the + + + align:start position:0% +atom the mass that shows up there is the +reduced mass which is approximately + + align:start position:0% +reduced mass which is approximately + + + align:start position:0% +reduced mass which is approximately +equal to the electron mass but in + + align:start position:0% +equal to the electron mass but in + + + align:start position:0% +equal to the electron mass but in +general in this scattering process it + + align:start position:0% +general in this scattering process it + + + align:start position:0% +general in this scattering process it +might be between two identical particles + + align:start position:0% +might be between two identical particles + + + align:start position:0% +might be between two identical particles +in which case a reduced mass would be + + align:start position:0% +in which case a reduced mass would be + + + align:start position:0% +in which case a reduced mass would be +half the mass of the particle so again + + align:start position:0% +half the mass of the particle so again + + + align:start position:0% +half the mass of the particle so again +we will work scattering with energy + + align:start position:0% +we will work scattering with energy + + + align:start position:0% +we will work scattering with energy +eigenstates you may have studied already + + align:start position:0% +eigenstates you may have studied already + + + align:start position:0% +eigenstates you may have studied already +in 804 a little bit of problems of + + align:start position:0% +in 804 a little bit of problems of + + + align:start position:0% +in 804 a little bit of problems of +scattering of + + align:start position:0% +scattering of + + + align:start position:0% +scattering of +angular barriers tunneling all these + + align:start position:0% +angular barriers tunneling all these + + + align:start position:0% +angular barriers tunneling all these +things and we work with energy + + align:start position:0% +things and we work with energy + + + align:start position:0% +things and we work with energy +eigenstates in those cases and we will + + align:start position:0% +eigenstates in those cases and we will + + + align:start position:0% +eigenstates in those cases and we will +work with energy eigenstates as well + + align:start position:0% +work with energy eigenstates as well + + + align:start position:0% +work with energy eigenstates as well +here now in some versions of 804 you + + align:start position:0% +here now in some versions of 804 you + + + align:start position:0% +here now in some versions of 804 you +discuss a lot wave padlet I used to + + align:start position:0% +discuss a lot wave padlet I used to + + + align:start position:0% +discuss a lot wave padlet I used to +discuss a lot wave packets we would + + align:start position:0% +discuss a lot wave packets we would + + + align:start position:0% +discuss a lot wave packets we would +build wave packets and send them in and + + align:start position:0% +build wave packets and send them in and + + + align:start position:0% +build wave packets and send them in and +use the transmission and reflection + + align:start position:0% +use the transmission and reflection + + + align:start position:0% +use the transmission and reflection +coefficients to figure out what the wave + + align:start position:0% +coefficients to figure out what the wave + + + align:start position:0% +coefficients to figure out what the wave +packets do and in general a wave packet + + align:start position:0% +packets do and in general a wave packet + + + align:start position:0% +packets do and in general a wave packet +this is somewhat more physical way of + + align:start position:0% +this is somewhat more physical way of + + + align:start position:0% +this is somewhat more physical way of +thinking of the processes because the + + align:start position:0% +thinking of the processes because the + + + align:start position:0% +thinking of the processes because the +energy states eigenstates are + + align:start position:0% +energy states eigenstates are + + + align:start position:0% +energy states eigenstates are +unnormalized well and don't have a + + align:start position:0% +unnormalized well and don't have a + + + align:start position:0% +unnormalized well and don't have a +direct interpretation in terms of + + align:start position:0% +direct interpretation in terms of + + + align:start position:0% +direct interpretation in terms of +particles rigorously speaking you should + + align:start position:0% +particles rigorously speaking you should + + + align:start position:0% +particles rigorously speaking you should +always do things with wave packets but + + align:start position:0% +always do things with wave packets but + + + align:start position:0% +always do things with wave packets but +the fact is that we all work with energy + + align:start position:0% +the fact is that we all work with energy + + + align:start position:0% +the fact is that we all work with energy +eigenstates and most of the times what + + align:start position:0% +eigenstates and most of the times what + + + align:start position:0% +eigenstates and most of the times what +happens with wave packets can be more or + + align:start position:0% +happens with wave packets can be more or + + + align:start position:0% +happens with wave packets can be more or +less gleamed from what is happening with + + align:start position:0% +less gleamed from what is happening with + + + align:start position:0% +less gleamed from what is happening with +the energy eigenstate so we will not new + + align:start position:0% +the energy eigenstate so we will not new + + + align:start position:0% +the energy eigenstate so we will not new +wave packets here we will not bother to + + align:start position:0% +wave packets here we will not bother to + + + align:start position:0% +wave packets here we will not bother to +construct wave packets they would not + + align:start position:0% +construct wave packets they would not + + + align:start position:0% +construct wave packets they would not +teach us too much at this moment so we + + align:start position:0% +teach us too much at this moment so we + + + align:start position:0% +teach us too much at this moment so we +will work with energy eigenstates work + + align:start position:0% +will work with energy eigenstates work + + + align:start position:0% +will work with energy eigenstates work +with energy eigenstates eigenstates \ No newline at end of file diff --git a/HCBaApqRqSg.txt b/HCBaApqRqSg.txt new file mode 100644 index 0000000000000000000000000000000000000000..5ef73ae39b30812705b3f325262caa447d5ac199 --- /dev/null +++ b/HCBaApqRqSg.txt @@ -0,0 +1,14179 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu + + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu +I'm gonna talk about hearing I get I + + align:start position:0% +I'm gonna talk about hearing I get I + + + align:start position:0% +I'm gonna talk about hearing I get I +gathered this is the first time in this + + align:start position:0% +gathered this is the first time in this + + + align:start position:0% +gathered this is the first time in this +class that really people have talked + + align:start position:0% +class that really people have talked + + + align:start position:0% +class that really people have talked +about audition and usually when I give + + align:start position:0% +about audition and usually when I give + + + align:start position:0% +about audition and usually when I give +talks and in lectures it's I find it's + + align:start position:0% +talks and in lectures it's I find it's + + + align:start position:0% +talks and in lectures it's I find it's +often helpful to just start out by doing + + align:start position:0% +often helpful to just start out by doing + + + align:start position:0% +often helpful to just start out by doing +some listening so we're gonna start out + + align:start position:0% +some listening so we're gonna start out + + + align:start position:0% +some listening so we're gonna start out +this morning by just listening to some + + align:start position:0% +this morning by just listening to some + + + align:start position:0% +this morning by just listening to some +examples of typical auditory input that + + align:start position:0% +examples of typical auditory input that + + + align:start position:0% +examples of typical auditory input that +you might encounter during the course of + + align:start position:0% +you might encounter during the course of + + + align:start position:0% +you might encounter during the course of +your day so all you got to do is just + + align:start position:0% +your day so all you got to do is just + + + align:start position:0% +your day so all you got to do is just +close your eyes and listen here we go + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +release soon all right + + align:start position:0% +release soon all right + + + align:start position:0% +release soon all right +Debbie would adjourn sterling James + + align:start position:0% +Debbie would adjourn sterling James + + + align:start position:0% +Debbie would adjourn sterling James +wrapping things up + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +okay so um you guys could probably tell + + align:start position:0% +okay so um you guys could probably tell + + + align:start position:0% +okay so um you guys could probably tell +what all of those things were in case + + align:start position:0% +what all of those things were in case + + + align:start position:0% +what all of those things were in case +not here there are some labels so the + + align:start position:0% +not here there are some labels so the + + + align:start position:0% +not here there are some labels so the +first one is just a scene I recorded on + + align:start position:0% +first one is just a scene I recorded on + + + align:start position:0% +first one is just a scene I recorded on +my iPhone in a cafe second one was was + + align:start position:0% +my iPhone in a cafe second one was was + + + align:start position:0% +my iPhone in a cafe second one was was +something from a sports bar then there + + align:start position:0% +something from a sports bar then there + + + align:start position:0% +something from a sports bar then there +was a radio excerpt and then some some + + align:start position:0% +was a radio excerpt and then some some + + + align:start position:0% +was a radio excerpt and then some some +Barry White and the point is that in all + + align:start position:0% +Barry White and the point is that in all + + + align:start position:0% +Barry White and the point is that in all +of those cases I mean they're all pretty + + align:start position:0% +of those cases I mean they're all pretty + + + align:start position:0% +of those cases I mean they're all pretty +different but in all those cases your + + align:start position:0% +different but in all those cases your + + + align:start position:0% +different but in all those cases your +brain was inferring an awful lot about + + align:start position:0% +brain was inferring an awful lot about + + + align:start position:0% +brain was inferring an awful lot about +what was happening in the world from the + + align:start position:0% +what was happening in the world from the + + + align:start position:0% +what was happening in the world from the +sound signal that was that was entering + + align:start position:0% +sound signal that was that was entering + + + align:start position:0% +sound signal that was that was entering +your ears right and so what what makes + + align:start position:0% +your ears right and so what what makes + + + align:start position:0% +your ears right and so what what makes +that kind of amazing and remarkable is + + align:start position:0% +that kind of amazing and remarkable is + + + align:start position:0% +that kind of amazing and remarkable is +that the sensory input that it was + + align:start position:0% +that the sensory input that it was + + + align:start position:0% +that the sensory input that it was +getting to first order just looks like + + align:start position:0% +getting to first order just looks like + + + align:start position:0% +getting to first order just looks like +this right so there was sound energy + + align:start position:0% +this right so there was sound energy + + + align:start position:0% +this right so there was sound energy +that traveled through the air it was + + align:start position:0% +that traveled through the air it was + + + align:start position:0% +that traveled through the air it was +making your eardrums will go back and + + align:start position:0% +making your eardrums will go back and + + + align:start position:0% +making your eardrums will go back and +forth in some particular pattern that + + align:start position:0% +forth in some particular pattern that + + + align:start position:0% +forth in some particular pattern that +would be indicated by that waveform + + align:start position:0% +would be indicated by that waveform + + + align:start position:0% +would be indicated by that waveform +there that plots the pressure at your + + align:start position:0% +there that plots the pressure at your + + + align:start position:0% +there that plots the pressure at your +eardrum as a function of time and so + + align:start position:0% +eardrum as a function of time and so + + + align:start position:0% +eardrum as a function of time and so +from that particular funny pattern of + + align:start position:0% +from that particular funny pattern of + + + align:start position:0% +from that particular funny pattern of +Wiggles you were able to infer all those + + align:start position:0% +Wiggles you were able to infer all those + + + align:start position:0% +Wiggles you were able to infer all those +things so in the case of the of the cafe + + align:start position:0% +things so in the case of the of the cafe + + + align:start position:0% +things so in the case of the of the cafe +scene you could tell that there were a + + align:start position:0% +scene you could tell that there were a + + + align:start position:0% +scene you could tell that there were a +few people talking you could probably + + align:start position:0% +few people talking you could probably + + + align:start position:0% +few people talking you could probably +hear a man and a woman you could tell + + align:start position:0% +hear a man and a woman you could tell + + + align:start position:0% +hear a man and a woman you could tell +there was music in the background you + + align:start position:0% +there was music in the background you + + + align:start position:0% +there was music in the background you +could hear there was dishes clattering + + align:start position:0% +could hear there was dishes clattering + + + align:start position:0% +could hear there was dishes clattering +metal tell somebody had an Irish accent + + align:start position:0% +metal tell somebody had an Irish accent + + + align:start position:0% +metal tell somebody had an Irish accent +you could probably tell in the sports + + align:start position:0% +you could probably tell in the sports + + + align:start position:0% +you could probably tell in the sports +bar that people were watching football + + align:start position:0% +bar that people were watching football + + + align:start position:0% +bar that people were watching football +and talking about it and there were a + + align:start position:0% +and talking about it and there were a + + + align:start position:0% +and talking about it and there were a +bunch of people there you instantly + + align:start position:0% +bunch of people there you instantly + + + align:start position:0% +bunch of people there you instantly +recognized the radio extra fizz + + align:start position:0% +recognized the radio extra fizz + + + align:start position:0% +recognized the radio extra fizz +Drivetime radio that sort of like + + align:start position:0% +Drivetime radio that sort of like + + + align:start position:0% +Drivetime radio that sort of like +standard sound and in the case of the + + align:start position:0% +standard sound and in the case of the + + + align:start position:0% +standard sound and in the case of the +music excerpt you could probably hear + + align:start position:0% +music excerpt you could probably hear + + + align:start position:0% +music excerpt you could probably hear +six or seven or maybe eight different + + align:start position:0% +six or seven or maybe eight different + + + align:start position:0% +six or seven or maybe eight different +instruments that were each like in their + + align:start position:0% +instruments that were each like in their + + + align:start position:0% +instruments that were each like in their +own way contributing to the groove so + + align:start position:0% +own way contributing to the groove so + + + align:start position:0% +own way contributing to the groove so +that's kind of audition at work and so + + align:start position:0% +that's kind of audition at work and so + + + align:start position:0% +that's kind of audition at work and so +the the task of the brain is to take the + + align:start position:0% +the the task of the brain is to take the + + + align:start position:0% +the the task of the brain is to take the +the sound signal that arrives at your + + align:start position:0% +the sound signal that arrives at your + + + align:start position:0% +the sound signal that arrives at your +ears that isn't transduced into + + align:start position:0% +ears that isn't transduced into + + + align:start position:0% +ears that isn't transduced into +electrical signals by by your ears and + + align:start position:0% +electrical signals by by your ears and + + + align:start position:0% +electrical signals by by your ears and +then to interpret it and to figure out + + align:start position:0% +then to interpret it and to figure out + + + align:start position:0% +then to interpret it and to figure out +what's out there in the world so what + + align:start position:0% +what's out there in the world so what + + + align:start position:0% +what's out there in the world so what +you're interested in really is not the + + align:start position:0% +you're interested in really is not the + + + align:start position:0% +you're interested in really is not the +sound itself you're interested in + + align:start position:0% +sound itself you're interested in + + + align:start position:0% +sound itself you're interested in +whether it was a dog or a train or rain + + align:start position:0% +whether it was a dog or a train or rain + + + align:start position:0% +whether it was a dog or a train or rain +or people singing or or whatever it was + + align:start position:0% +or people singing or or whatever it was + + + align:start position:0% +or people singing or or whatever it was +and so the the interesting and hard + + align:start position:0% +and so the the interesting and hard + + + align:start position:0% +and so the the interesting and hard +problem that comes along with this is + + align:start position:0% +problem that comes along with this is + + + align:start position:0% +problem that comes along with this is +that most of the properties that we are + + align:start position:0% +that most of the properties that we are + + + align:start position:0% +that most of the properties that we are +interested in as listeners are not + + align:start position:0% +interested in as listeners are not + + + align:start position:0% +interested in as listeners are not +explicit in the waveform in the sense + + align:start position:0% +explicit in the waveform in the sense + + + align:start position:0% +explicit in the waveform in the sense +that if I hand you the sound waveform + + align:start position:0% +that if I hand you the sound waveform + + + align:start position:0% +that if I hand you the sound waveform +itself and you either look at it or you + + align:start position:0% +itself and you either look at it or you + + + align:start position:0% +itself and you either look at it or you +run sort of standard machine classifiers + + align:start position:0% +run sort of standard machine classifiers + + + align:start position:0% +run sort of standard machine classifiers +on it it would be very difficult to + + align:start position:0% +on it it would be very difficult to + + + align:start position:0% +on it it would be very difficult to +discern the kinds of things that you + + align:start position:0% +discern the kinds of things that you + + + align:start position:0% +discern the kinds of things that you +with your brain can + + align:start position:0% +with your brain can + + + align:start position:0% +with your brain can +easily justjust report and so that's + + align:start position:0% +easily justjust report and so that's + + + align:start position:0% +easily justjust report and so that's +really the the question that I'm + + align:start position:0% +really the the question that I'm + + + align:start position:0% +really the the question that I'm +interested in that that our lab studies + + align:start position:0% +interested in that that our lab studies + + + align:start position:0% +interested in that that our lab studies +namely how is it that we derive + + align:start position:0% +namely how is it that we derive + + + align:start position:0% +namely how is it that we derive +information about the world from sound + + align:start position:0% +information about the world from sound + + + align:start position:0% +information about the world from sound +and and so there's lots of different + + align:start position:0% +and and so there's lots of different + + + align:start position:0% +and and so there's lots of different +aspects to the problem of audition I'm + + align:start position:0% +aspects to the problem of audition I'm + + + align:start position:0% +aspects to the problem of audition I'm +gonna give you a taste of a few of them + + align:start position:0% +gonna give you a taste of a few of them + + + align:start position:0% +gonna give you a taste of a few of them +over the course of today's lecture a big + + align:start position:0% +over the course of today's lecture a big + + + align:start position:0% +over the course of today's lecture a big +one that lots of people have heard about + + align:start position:0% +one that lots of people have heard about + + + align:start position:0% +one that lots of people have heard about +is an often known as the cocktail party + + align:start position:0% +is an often known as the cocktail party + + + align:start position:0% +is an often known as the cocktail party +problem which refers to the fact that + + align:start position:0% +problem which refers to the fact that + + + align:start position:0% +problem which refers to the fact that +real-world settings often involve + + align:start position:0% +real-world settings often involve + + + align:start position:0% +real-world settings often involve +concurrent sounds so if you're in a room + + align:start position:0% +concurrent sounds so if you're in a room + + + align:start position:0% +concurrent sounds so if you're in a room +full of busy people you might be trying + + align:start position:0% +full of busy people you might be trying + + + align:start position:0% +full of busy people you might be trying +to have a conversation with one of them + + align:start position:0% +to have a conversation with one of them + + + align:start position:0% +to have a conversation with one of them +but there'll be lots of other people + + align:start position:0% +but there'll be lots of other people + + + align:start position:0% +but there'll be lots of other people +talking music in the background and so + + align:start position:0% +talking music in the background and so + + + align:start position:0% +talking music in the background and so +on and so forth and so from that kind of + + align:start position:0% +on and so forth and so from that kind of + + + align:start position:0% +on and so forth and so from that kind of +complicated mixed signal that enters + + align:start position:0% +complicated mixed signal that enters + + + align:start position:0% +complicated mixed signal that enters +your ears your brain has to estimate the + + align:start position:0% +your ears your brain has to estimate the + + + align:start position:0% +your ears your brain has to estimate the +content of one particular source of + + align:start position:0% +content of one particular source of + + + align:start position:0% +content of one particular source of +interest of the person that you're + + align:start position:0% +interest of the person that you're + + + align:start position:0% +interest of the person that you're +trying to converse with so really what + + align:start position:0% +trying to converse with so really what + + + align:start position:0% +trying to converse with so really what +you'd like to be hearing might be this + + align:start position:0% +you'd like to be hearing might be this + + + align:start position:0% +you'd like to be hearing might be this +she's with your sister but what my enter + + align:start position:0% +she's with your sister but what my enter + + + align:start position:0% +she's with your sister but what my enter +your ear could be this system maybe even + + align:start position:0% +your ear could be this system maybe even + + + align:start position:0% +your ear could be this system maybe even +this maybe even this so what I've done + + align:start position:0% +this maybe even this so what I've done + + + align:start position:0% +this maybe even this so what I've done +here plotted next to the icons are our + + align:start position:0% +here plotted next to the icons are our + + + align:start position:0% +here plotted next to the icons are our +spectrograms that's a way of taking a + + align:start position:0% +spectrograms that's a way of taking a + + + align:start position:0% +spectrograms that's a way of taking a +sound signal and turning that into an + + align:start position:0% +sound signal and turning that into an + + + align:start position:0% +sound signal and turning that into an +image so the plot of the frequency + + align:start position:0% +image so the plot of the frequency + + + align:start position:0% +image so the plot of the frequency +content over time and you can see with + + align:start position:0% +content over time and you can see with + + + align:start position:0% +content over time and you can see with +the single utterance up here at the top + + align:start position:0% +the single utterance up here at the top + + + align:start position:0% +the single utterance up here at the top +there's all kinds of structure right and + + align:start position:0% +there's all kinds of structure right and + + + align:start position:0% +there's all kinds of structure right and +we think that your brain uses that + + align:start position:0% +we think that your brain uses that + + + align:start position:0% +we think that your brain uses that +structure to understand what was being + + align:start position:0% +structure to understand what was being + + + align:start position:0% +structure to understand what was being +said and you can see that as more and + + align:start position:0% +said and you can see that as more and + + + align:start position:0% +said and you can see that as more and +more people are added to the party that + + align:start position:0% +more people are added to the party that + + + align:start position:0% +more people are added to the party that +that structure becomes progressively + + align:start position:0% +that structure becomes progressively + + + align:start position:0% +that structure becomes progressively +more and more obscured until by the time + + align:start position:0% +more and more obscured until by the time + + + align:start position:0% +more and more obscured until by the time +you get to the bottom it's kind of + + align:start position:0% +you get to the bottom it's kind of + + + align:start position:0% +you get to the bottom it's kind of +amazing that you can kind of pull + + align:start position:0% +amazing that you can kind of pull + + + align:start position:0% +amazing that you can kind of pull +anything out at all and yet as you + + align:start position:0% +anything out at all and yet as you + + + align:start position:0% +anything out at all and yet as you +hopefully heard your brain has this + + align:start position:0% +hopefully heard your brain has this + + + align:start position:0% +hopefully heard your brain has this +remarkable ability to attend to and + + align:start position:0% +remarkable ability to attend to and + + + align:start position:0% +remarkable ability to attend to and +understand the speech signal of interest + + align:start position:0% +understand the speech signal of interest + + + align:start position:0% +understand the speech signal of interest +and this is an ability that still to + + align:start position:0% +and this is an ability that still to + + + align:start position:0% +and this is an ability that still to +this day is really unmatched by but by + + align:start position:0% +this day is really unmatched by but by + + + align:start position:0% +this day is really unmatched by but by +machines so present-day speech + + align:start position:0% +machines so present-day speech + + + align:start position:0% +machines so present-day speech +recognition algorithms are getting + + align:start position:0% +recognition algorithms are getting + + + align:start position:0% +recognition algorithms are getting +better by the minute but this particular + + align:start position:0% +better by the minute but this particular + + + align:start position:0% +better by the minute but this particular +problem is still quite a significant + + align:start position:0% +problem is still quite a significant + + + align:start position:0% +problem is still quite a significant +challenge and you've probably + + align:start position:0% +challenge and you've probably + + + align:start position:0% +challenge and you've probably +encountered this when you try to talk to + + align:start position:0% +encountered this when you try to talk to + + + align:start position:0% +encountered this when you try to talk to +your iPhone when you're you know in a + + align:start position:0% +your iPhone when you're you know in a + + + align:start position:0% +your iPhone when you're you know in a +car or wherever else another kind of + + align:start position:0% +car or wherever else another kind of + + + align:start position:0% +car or wherever else another kind of +interesting complexity in in hearing is + + align:start position:0% +interesting complexity in in hearing is + + + align:start position:0% +interesting complexity in in hearing is +that sound interacts with the + + align:start position:0% +that sound interacts with the + + + align:start position:0% +that sound interacts with the +environment on its way to your ears + + align:start position:0% +environment on its way to your ears + + + align:start position:0% +environment on its way to your ears +you know you typically think of yourself + + align:start position:0% +you know you typically think of yourself + + + align:start position:0% +you know you typically think of yourself +as listening to say a person talking or + + align:start position:0% +as listening to say a person talking or + + + align:start position:0% +as listening to say a person talking or +just some sound source but in reality + + align:start position:0% +just some sound source but in reality + + + align:start position:0% +just some sound source but in reality +what's happening is something like this + + align:start position:0% +what's happening is something like this + + + align:start position:0% +what's happening is something like this +picture here so there's a speaker in the + + align:start position:0% +picture here so there's a speaker in the + + + align:start position:0% +picture here so there's a speaker in the +upper right corner from which sound is + + align:start position:0% +upper right corner from which sound is + + + align:start position:0% +upper right corner from which sound is +emanating but the sound takes a whole + + align:start position:0% +emanating but the sound takes a whole + + + align:start position:0% +emanating but the sound takes a whole +lot of different paths on its way to + + align:start position:0% +lot of different paths on its way to + + + align:start position:0% +lot of different paths on its way to +your ears there's the direct path which + + align:start position:0% +your ears there's the direct path which + + + align:start position:0% +your ears there's the direct path which +is shown in green but then there are all + + align:start position:0% +is shown in green but then there are all + + + align:start position:0% +is shown in green but then there are all +these other paths where it can reflect + + align:start position:0% +these other paths where it can reflect + + + align:start position:0% +these other paths where it can reflect +off of the walls in the room so the blue + + align:start position:0% +off of the walls in the room so the blue + + + align:start position:0% +off of the walls in the room so the blue +lines here indicate paths where there's + + align:start position:0% +lines here indicate paths where there's + + + align:start position:0% +lines here indicate paths where there's +a single reflection and the red lines + + align:start position:0% +a single reflection and the red lines + + + align:start position:0% +a single reflection and the red lines +indicate paths where there are two + + align:start position:0% +indicate paths where there are two + + + align:start position:0% +indicate paths where there are two +reflections and so you can see there's a + + align:start position:0% +reflections and so you can see there's a + + + align:start position:0% +reflections and so you can see there's a +lot of them and so the consequence of + + align:start position:0% +lot of them and so the consequence of + + + align:start position:0% +lot of them and so the consequence of +this is that your brain gets all these + + align:start position:0% +this is that your brain gets all these + + + align:start position:0% +this is that your brain gets all these +delayed copies of the source signal and + + align:start position:0% +delayed copies of the source signal and + + + align:start position:0% +delayed copies of the source signal and +what that amounts to is really massive + + align:start position:0% +what that amounts to is really massive + + + align:start position:0% +what that amounts to is really massive +distortion of the signal I mean this is + + align:start position:0% +distortion of the signal I mean this is + + + align:start position:0% +distortion of the signal I mean this is +known as a reverberation so this is + + align:start position:0% +known as a reverberation so this is + + + align:start position:0% +known as a reverberation so this is +gonna this is dry speech of course + + align:start position:0% +gonna this is dry speech of course + + + align:start position:0% +gonna this is dry speech of course +you're hearing this in this auditorium + + align:start position:0% +you're hearing this in this auditorium + + + align:start position:0% +you're hearing this in this auditorium +that itself has lots of reverberation so + + align:start position:0% +that itself has lots of reverberation so + + + align:start position:0% +that itself has lots of reverberation so +you're not actually going to hear it dry + + align:start position:0% +you're not actually going to hear it dry + + + align:start position:0% +you're not actually going to hear it dry +but you'll still be able to hear a + + align:start position:0% +but you'll still be able to hear a + + + align:start position:0% +but you'll still be able to hear a +difference they ate the lemon pie father + + align:start position:0% +difference they ate the lemon pie father + + + align:start position:0% +difference they ate the lemon pie father +forgot the bread and this is that signal + + align:start position:0% +forgot the bread and this is that signal + + + align:start position:0% +forgot the bread and this is that signal +with lots of reverberation added as + + align:start position:0% +with lots of reverberation added as + + + align:start position:0% +with lots of reverberation added as +though you were listening to it in a + + align:start position:0% +though you were listening to it in a + + + align:start position:0% +though you were listening to it in a +Cathedral or something of course you're + + align:start position:0% +Cathedral or something of course you're + + + align:start position:0% +Cathedral or something of course you're +again hearing it in this room as well + + align:start position:0% + + + + align:start position:0% + +and you can still hear a difference and + + align:start position:0% +and you can still hear a difference and + + + align:start position:0% +and you can still hear a difference and +if you if the reverb in this auditorium + + align:start position:0% +if you if the reverb in this auditorium + + + align:start position:0% +if you if the reverb in this auditorium +is swamp net you can just look at the + + align:start position:0% +is swamp net you can just look at the + + + align:start position:0% +is swamp net you can just look at the +waveforms and you can see that the + + align:start position:0% +waveforms and you can see that the + + + align:start position:0% +waveforms and you can see that the +waveforms of those two signals look + + align:start position:0% +waveforms of those two signals look + + + align:start position:0% +waveforms of those two signals look +pretty dramatically different as do the + + align:start position:0% +pretty dramatically different as do the + + + align:start position:0% +pretty dramatically different as do the +the spectrograms all right so the point + + align:start position:0% +the spectrograms all right so the point + + + align:start position:0% +the spectrograms all right so the point +is that the consequence of all of those + + align:start position:0% +is that the consequence of all of those + + + align:start position:0% +is that the consequence of all of those +delayed reflections massively distorts + + align:start position:0% +delayed reflections massively distorts + + + align:start position:0% +delayed reflections massively distorts +the signal right physically there are + + align:start position:0% +the signal right physically there are + + + align:start position:0% +the signal right physically there are +two really different things in those two + + align:start position:0% +two really different things in those two + + + align:start position:0% +two really different things in those two +cases but again your ability to + + align:start position:0% +cases but again your ability to + + + align:start position:0% +cases but again your ability to +recognize what's being said is + + align:start position:0% +recognize what's being said is + + + align:start position:0% +recognize what's being said is +remarkably invariant to the presence of + + align:start position:0% +remarkably invariant to the presence of + + + align:start position:0% +remarkably invariant to the presence of +that reverberation and again this is an + + align:start position:0% +that reverberation and again this is an + + + align:start position:0% +that reverberation and again this is an +instance where humans really are + + align:start position:0% +instance where humans really are + + + align:start position:0% +instance where humans really are +outperforming machines to a considerable + + align:start position:0% +outperforming machines to a considerable + + + align:start position:0% +outperforming machines to a considerable +extent + + align:start position:0% +extent + + + align:start position:0% +extent +this graph is a little bit dated this is + + align:start position:0% +this graph is a little bit dated this is + + + align:start position:0% +this graph is a little bit dated this is +from I think three years ago but but + + align:start position:0% +from I think three years ago but but + + + align:start position:0% +from I think three years ago but but +it's a plot of five different speech + + align:start position:0% +it's a plot of five different speech + + + align:start position:0% +it's a plot of five different speech +recognition algorithms and they're the + + align:start position:0% +recognition algorithms and they're the + + + align:start position:0% +recognition algorithms and they're the +the percent of errors they're making + + align:start position:0% +the percent of errors they're making + + + align:start position:0% +the percent of errors they're making +when given a speech signal as a function + + align:start position:0% +when given a speech signal as a function + + + align:start position:0% +when given a speech signal as a function +of the amount of reverberation and so + + align:start position:0% +of the amount of reverberation and so + + + align:start position:0% +of the amount of reverberation and so +zero means that there's no reverberation + + align:start position:0% +zero means that there's no reverberation + + + align:start position:0% +zero means that there's no reverberation +that's the dry case right and so speech + + align:start position:0% +that's the dry case right and so speech + + + align:start position:0% +that's the dry case right and so speech +recognition works pretty well without + + align:start position:0% +recognition works pretty well without + + + align:start position:0% +recognition works pretty well without +any reverb but when you add a little bit + + align:start position:0% +any reverb but when you add a little bit + + + align:start position:0% +any reverb but when you add a little bit +of a vibration and this is measured in + + align:start position:0% +of a vibration and this is measured in + + + align:start position:0% +of a vibration and this is measured in +terms of the reverberation time it's the + + align:start position:0% +terms of the reverberation time it's the + + + align:start position:0% +terms of the reverberation time it's the +amount of time that it takes the reverb + + align:start position:0% +amount of time that it takes the reverb + + + align:start position:0% +amount of time that it takes the reverb +to fall off by a certain specified + + align:start position:0% +to fall off by a certain specified + + + align:start position:0% +to fall off by a certain specified +amount + + align:start position:0% +amount + + + align:start position:0% +amount +and 300 and 500 milliseconds are + + align:start position:0% +and 300 and 500 milliseconds are + + + align:start position:0% +and 300 and 500 milliseconds are +actually very very modest so in this + + align:start position:0% +actually very very modest so in this + + + align:start position:0% +actually very very modest so in this +auditorium my guess would be that the + + align:start position:0% +auditorium my guess would be that the + + + align:start position:0% +auditorium my guess would be that the +reverberation time is maybe even a + + align:start position:0% +reverberation time is maybe even a + + + align:start position:0% +reverberation time is maybe even a +couple seconds so this is like you know + + align:start position:0% +couple seconds so this is like you know + + + align:start position:0% +couple seconds so this is like you know +what you get in a small a small + + align:start position:0% +what you get in a small a small + + + align:start position:0% +what you get in a small a small +classroom maybe maybe even less than + + align:start position:0% +classroom maybe maybe even less than + + + align:start position:0% +classroom maybe maybe even less than +that but you can see that it causes + + align:start position:0% +that but you can see that it causes + + + align:start position:0% +that but you can see that it causes +major problems for for speech + + align:start position:0% +major problems for for speech + + + align:start position:0% +major problems for for speech +recognition + + align:start position:0% +recognition + + + align:start position:0% +recognition +I mean it's because the the information + + align:start position:0% +I mean it's because the the information + + + align:start position:0% +I mean it's because the the information +and the speech signal gets blurred out + + align:start position:0% +and the speech signal gets blurred out + + + align:start position:0% +and the speech signal gets blurred out +over time and again it's just it's just + + align:start position:0% +over time and again it's just it's just + + + align:start position:0% +over time and again it's just it's just +massive distortion so your brain is + + align:start position:0% +massive distortion so your brain is + + + align:start position:0% +massive distortion so your brain is +doing something pretty complicated in + + align:start position:0% +doing something pretty complicated in + + + align:start position:0% +doing something pretty complicated in +order for you to be so robust to the + + align:start position:0% +order for you to be so robust to the + + + align:start position:0% +order for you to be so robust to the +presence of the reverberation so I run a + + align:start position:0% +presence of the reverberation so I run a + + + align:start position:0% +presence of the reverberation so I run a +research group where we study these + + align:start position:0% +research group where we study these + + + align:start position:0% +research group where we study these +kinds of problems is called the lab for + + align:start position:0% +kinds of problems is called the lab for + + + align:start position:0% +kinds of problems is called the lab for +computational audition in the Department + + align:start position:0% +computational audition in the Department + + + align:start position:0% +computational audition in the Department +of brain and cognitive sciences at MIT + + align:start position:0% +of brain and cognitive sciences at MIT + + + align:start position:0% +of brain and cognitive sciences at MIT +we operate at the intersection of + + align:start position:0% +we operate at the intersection of + + + align:start position:0% +we operate at the intersection of +psychology and neuroscience and + + align:start position:0% +psychology and neuroscience and + + + align:start position:0% +psychology and neuroscience and +engineering where what we aspire to do + + align:start position:0% +engineering where what we aspire to do + + + align:start position:0% +engineering where what we aspire to do +is to understand how it is that people + + align:start position:0% +is to understand how it is that people + + + align:start position:0% +is to understand how it is that people +hear so well in computational terms that + + align:start position:0% +hear so well in computational terms that + + + align:start position:0% +hear so well in computational terms that +would allow us to instantiate them in + + align:start position:0% +would allow us to instantiate them in + + + align:start position:0% +would allow us to instantiate them in +algorithms that we might replicate in + + align:start position:0% +algorithms that we might replicate in + + + align:start position:0% +algorithms that we might replicate in +machines and so the research that we try + + align:start position:0% +machines and so the research that we try + + + align:start position:0% +machines and so the research that we try +to do involves hopefully symbiotic + + align:start position:0% +to do involves hopefully symbiotic + + + align:start position:0% +to do involves hopefully symbiotic +relationships between experiments in + + align:start position:0% +relationships between experiments in + + + align:start position:0% +relationships between experiments in +humans auditory neuroscience and and + + align:start position:0% +humans auditory neuroscience and and + + + align:start position:0% +humans auditory neuroscience and and +machine algorithms and the general + + align:start position:0% +machine algorithms and the general + + + align:start position:0% +machine algorithms and the general +approach that that we take is to start + + align:start position:0% +approach that that we take is to start + + + align:start position:0% +approach that that we take is to start +with what the brain has to work with and + + align:start position:0% +with what the brain has to work with and + + + align:start position:0% +with what the brain has to work with and +by that I mean we try to work with + + align:start position:0% +by that I mean we try to work with + + + align:start position:0% +by that I mean we try to work with +representations like the ones that are + + align:start position:0% +representations like the ones that are + + + align:start position:0% +representations like the ones that are +in the early auditory system and so + + align:start position:0% +in the early auditory system and so + + + align:start position:0% +in the early auditory system and so +here's the plan for this morning and + + align:start position:0% +here's the plan for this morning and + + + align:start position:0% +here's the plan for this morning and +this is subject to change depending on + + align:start position:0% +this is subject to change depending on + + + align:start position:0% +this is subject to change depending on +what kind of feedback I get from you + + align:start position:0% +what kind of feedback I get from you + + + align:start position:0% +what kind of feedback I get from you +guys but my general plan was to start + + align:start position:0% +guys but my general plan was to start + + + align:start position:0% +guys but my general plan was to start +out with an overview of the auditory + + align:start position:0% +out with an overview of the auditory + + + align:start position:0% +out with an overview of the auditory +system because I gather there's sort of + + align:start position:0% +system because I gather there's sort of + + + align:start position:0% +system because I gather there's sort of +a diversity of backgrounds here and + + align:start position:0% +a diversity of backgrounds here and + + + align:start position:0% +a diversity of backgrounds here and +nobody here nobody's talked about + + align:start position:0% +nobody here nobody's talked about + + + align:start position:0% +nobody here nobody's talked about +audition so far so I was gonna go + + align:start position:0% +audition so far so I was gonna go + + + align:start position:0% +audition so far so I was gonna go +through a little overview and then + + align:start position:0% +through a little overview and then + + + align:start position:0% +through a little overview and then +there's been a special request to talk + + align:start position:0% +there's been a special request to talk + + + align:start position:0% +there's been a special request to talk +about sound texture perception I gather + + align:start position:0% +about sound texture perception I gather + + + align:start position:0% +about sound texture perception I gather +that there's there was some earlier + + align:start position:0% +that there's there was some earlier + + + align:start position:0% +that there's there was some earlier +lectures on visual texture and that + + align:start position:0% +lectures on visual texture and that + + + align:start position:0% +lectures on visual texture and that +might be a useful thing to talk about + + align:start position:0% +might be a useful thing to talk about + + + align:start position:0% +might be a useful thing to talk about +it's also a nice way to to understand + + align:start position:0% +it's also a nice way to to understand + + + align:start position:0% +it's also a nice way to to understand +auditory models a little bit better + + align:start position:0% +auditory models a little bit better + + + align:start position:0% +auditory models a little bit better +I was then going to talk a little bit + + align:start position:0% +I was then going to talk a little bit + + + align:start position:0% +I was then going to talk a little bit +about the perception of individual sound + + align:start position:0% +about the perception of individual sound + + + align:start position:0% +about the perception of individual sound +sources it's sort of the flipside to + + align:start position:0% +sources it's sort of the flipside to + + + align:start position:0% +sources it's sort of the flipside to +sound texture and then conclude with + + align:start position:0% +sound texture and then conclude with + + + align:start position:0% +sound texture and then conclude with +with a suction on auditory scene + + align:start position:0% +with a suction on auditory scene + + + align:start position:0% +with a suction on auditory scene +analysis so the what your brain is able + + align:start position:0% +analysis so the what your brain is able + + + align:start position:0% +analysis so the what your brain is able +to do when it gets a complicated sound + + align:start position:0% +to do when it gets a complicated sound + + + align:start position:0% +to do when it gets a complicated sound +signal like you would get normally in + + align:start position:0% +signal like you would get normally in + + + align:start position:0% +signal like you would get normally in +the world that consists that has + + align:start position:0% +the world that consists that has + + + align:start position:0% +the world that consists that has +contributions from multiple + + align:start position:0% +contributions from multiple + + + align:start position:0% +contributions from multiple +and you have to you have to infer those + + align:start position:0% +and you have to you have to infer those + + + align:start position:0% +and you have to you have to infer those +okay and so we'll and we'll take a break + + align:start position:0% +okay and so we'll and we'll take a break + + + align:start position:0% +okay and so we'll and we'll take a break +about halfway through as I guess is kind + + align:start position:0% +about halfway through as I guess is kind + + + align:start position:0% +about halfway through as I guess is kind +of standard and I'm happy for people to + + align:start position:0% +of standard and I'm happy for people to + + + align:start position:0% +of standard and I'm happy for people to +interrupt and ask questions okay so the + + align:start position:0% +interrupt and ask questions okay so the + + + align:start position:0% +interrupt and ask questions okay so the +general outline for hearing right is + + align:start position:0% +general outline for hearing right is + + + align:start position:0% +general outline for hearing right is +that the that sound is created when + + align:start position:0% +that the that sound is created when + + + align:start position:0% +that the that sound is created when +objects in the world vibrate right + + align:start position:0% +objects in the world vibrate right + + + align:start position:0% +objects in the world vibrate right +usually this is because you know + + align:start position:0% +usually this is because you know + + + align:start position:0% +usually this is because you know +something hits something else or in the + + align:start position:0% +something hits something else or in the + + + align:start position:0% +something hits something else or in the +case of a biological organism there's + + align:start position:0% +case of a biological organism there's + + + align:start position:0% +case of a biological organism there's +some energy imparted to the vocal cords + + align:start position:0% +some energy imparted to the vocal cords + + + align:start position:0% +some energy imparted to the vocal cords +and the object vibrates that vibration + + align:start position:0% +and the object vibrates that vibration + + + align:start position:0% +and the object vibrates that vibration +gets transmitted to the air molecules + + align:start position:0% +gets transmitted to the air molecules + + + align:start position:0% +gets transmitted to the air molecules +around it and you you get a sound wave + + align:start position:0% +around it and you you get a sound wave + + + align:start position:0% +around it and you you get a sound wave +that travels through the air and that + + align:start position:0% +that travels through the air and that + + + align:start position:0% +that travels through the air and that +sound wave it then gets measured by the + + align:start position:0% +sound wave it then gets measured by the + + + align:start position:0% +sound wave it then gets measured by the +ears and so that the ear is a pretty + + align:start position:0% +ears and so that the ear is a pretty + + + align:start position:0% +ears and so that the ear is a pretty +complicated device that is designed to + + align:start position:0% +complicated device that is designed to + + + align:start position:0% +complicated device that is designed to +measure sound it's typically divided up + + align:start position:0% +measure sound it's typically divided up + + + align:start position:0% +measure sound it's typically divided up +into three pieces so there's the outer + + align:start position:0% +into three pieces so there's the outer + + + align:start position:0% +into three pieces so there's the outer +ear consisting of the pinna and the + + align:start position:0% +ear consisting of the pinna and the + + + align:start position:0% +ear consisting of the pinna and the +eardrum in functional terms people + + align:start position:0% +eardrum in functional terms people + + + align:start position:0% +eardrum in functional terms people +usually think about this as a + + align:start position:0% +usually think about this as a + + + align:start position:0% +usually think about this as a +directional microphone there's the + + align:start position:0% +directional microphone there's the + + + align:start position:0% +directional microphone there's the +middle ear there these three little + + align:start position:0% +middle ear there these three little + + + align:start position:0% +middle ear there these three little +bones in between the ear the ear drum + + align:start position:0% +bones in between the ear the ear drum + + + align:start position:0% +bones in between the ear the ear drum +and the cochlea that are typically + + align:start position:0% +and the cochlea that are typically + + + align:start position:0% +and the cochlea that are typically +described the functions of impedance + + align:start position:0% +described the functions of impedance + + + align:start position:0% +described the functions of impedance +matching and overload protection I'm not + + align:start position:0% +matching and overload protection I'm not + + + align:start position:0% +matching and overload protection I'm not +going to talk about that today and then + + align:start position:0% +going to talk about that today and then + + + align:start position:0% +going to talk about that today and then +there's the inner ear that the cochlea + + align:start position:0% +there's the inner ear that the cochlea + + + align:start position:0% +there's the inner ear that the cochlea +which in very coarse engineering terms + + align:start position:0% +which in very coarse engineering terms + + + align:start position:0% +which in very coarse engineering terms +we think of as doing some kind of + + align:start position:0% +we think of as doing some kind of + + + align:start position:0% +we think of as doing some kind of +frequency analysis and so again at kind + + align:start position:0% +frequency analysis and so again at kind + + + align:start position:0% +frequency analysis and so again at kind +of a high level so you've got your ears + + align:start position:0% +of a high level so you've got your ears + + + align:start position:0% +of a high level so you've got your ears +here this is the the inner ear and on + + align:start position:0% +here this is the the inner ear and on + + + align:start position:0% +here this is the the inner ear and on +each side and then those send + + align:start position:0% +each side and then those send + + + align:start position:0% +each side and then those send +feed-forward input up to the midbrain + + align:start position:0% +feed-forward input up to the midbrain + + + align:start position:0% +feed-forward input up to the midbrain +and there's a few different way stations + + align:start position:0% +and there's a few different way stations + + + align:start position:0% +and there's a few different way stations +here the cochlear nucleus is superior + + align:start position:0% +here the cochlear nucleus is superior + + + align:start position:0% +here the cochlear nucleus is superior +superior ala very complex the inferior + + align:start position:0% +superior ala very complex the inferior + + + align:start position:0% +superior ala very complex the inferior +colliculus and then the medial + + align:start position:0% +colliculus and then the medial + + + align:start position:0% +colliculus and then the medial +geniculate nucleus of the thalamus and + + align:start position:0% +geniculate nucleus of the thalamus and + + + align:start position:0% +geniculate nucleus of the thalamus and +and the thalamus then projects to the + + align:start position:0% +and the thalamus then projects to the + + + align:start position:0% +and the thalamus then projects to the +auditory cortex and there's a couple + + align:start position:0% +auditory cortex and there's a couple + + + align:start position:0% +auditory cortex and there's a couple +things at a high level that are worth + + align:start position:0% +things at a high level that are worth + + + align:start position:0% +things at a high level that are worth +noting here one is it that the pathways + + align:start position:0% +noting here one is it that the pathways + + + align:start position:0% +noting here one is it that the pathways +here are actually pretty complicated + + align:start position:0% +here are actually pretty complicated + + + align:start position:0% +here are actually pretty complicated +especially relative to the visual system + + align:start position:0% +especially relative to the visual system + + + align:start position:0% +especially relative to the visual system +as you guys been hearing lots about + + align:start position:0% +as you guys been hearing lots about + + + align:start position:0% +as you guys been hearing lots about +right so there's a bunch of different + + align:start position:0% +right so there's a bunch of different + + + align:start position:0% +right so there's a bunch of different +stops on the way to the cortex another + + align:start position:0% +stops on the way to the cortex another + + + align:start position:0% +stops on the way to the cortex another +interesting thing is that input from the + + align:start position:0% +interesting thing is that input from the + + + align:start position:0% +interesting thing is that input from the +two years get mixed gets mixed at a + + align:start position:0% +two years get mixed gets mixed at a + + + align:start position:0% +two years get mixed gets mixed at a +pretty early stage okay all right so + + align:start position:0% +pretty early stage okay all right so + + + align:start position:0% +pretty early stage okay all right so +let's step back and and talk about the + + align:start position:0% +let's step back and and talk about the + + + align:start position:0% +let's step back and and talk about the +cochlea for a moment and I realize that + + align:start position:0% +cochlea for a moment and I realize that + + + align:start position:0% +cochlea for a moment and I realize that +some of you guys will know about this + + align:start position:0% +some of you guys will know about this + + + align:start position:0% +some of you guys will know about this +stuff so we'll go we'll go through it + + align:start position:0% +stuff so we'll go we'll go through it + + + align:start position:0% +stuff so we'll go we'll go through it +kind of quick now one of the signature + + align:start position:0% +kind of quick now one of the signature + + + align:start position:0% +kind of quick now one of the signature +features of cochlear transduction + + align:start position:0% +features of cochlear transduction + + + align:start position:0% +features of cochlear transduction +is that it's it's frequency tuned so + + align:start position:0% +is that it's it's frequency tuned so + + + align:start position:0% +is that it's it's frequency tuned so +this is an unwrapped version of the + + align:start position:0% +this is an unwrapped version of the + + + align:start position:0% +this is an unwrapped version of the +cochlea so if we step back to here all + + align:start position:0% +cochlea so if we step back to here all + + + align:start position:0% +cochlea so if we step back to here all +right so we've got the the outer ear the + + align:start position:0% +right so we've got the the outer ear the + + + align:start position:0% +right so we've got the the outer ear the +ear canal the ear drum those three + + align:start position:0% +ear canal the ear drum those three + + + align:start position:0% +ear canal the ear drum those three +little bones that I told you about that + + align:start position:0% +little bones that I told you about that + + + align:start position:0% +little bones that I told you about that +connected to the cochlea and the cochlea + + align:start position:0% +connected to the cochlea and the cochlea + + + align:start position:0% +connected to the cochlea and the cochlea +just think it looks like a snail and + + align:start position:0% +just think it looks like a snail and + + + align:start position:0% +just think it looks like a snail and +then if we unroll that snail and look at + + align:start position:0% +then if we unroll that snail and look at + + + align:start position:0% +then if we unroll that snail and look at +it like this you can see that the + + align:start position:0% +it like this you can see that the + + + align:start position:0% +it like this you can see that the +cochlea consists of these tubes + + align:start position:0% +cochlea consists of these tubes + + + align:start position:0% +cochlea consists of these tubes +separated by a membrane on the membranes + + align:start position:0% +separated by a membrane on the membranes + + + align:start position:0% +separated by a membrane on the membranes +called the basilar membrane that's worth + + align:start position:0% +called the basilar membrane that's worth + + + align:start position:0% +called the basilar membrane that's worth +knowing about so sound enters here at + + align:start position:0% +knowing about so sound enters here at + + + align:start position:0% +knowing about so sound enters here at +the base and sets up a traveling wave + + align:start position:0% +the base and sets up a traveling wave + + + align:start position:0% +the base and sets up a traveling wave +along this membrane so this is really a + + align:start position:0% +along this membrane so this is really a + + + align:start position:0% +along this membrane so this is really a +mechanical thing that happens um so + + align:start position:0% +mechanical thing that happens um so + + + align:start position:0% +mechanical thing that happens um so +there's actually like a physical + + align:start position:0% +there's actually like a physical + + + align:start position:0% +there's actually like a physical +vibration that occurs in this membrane + + align:start position:0% +vibration that occurs in this membrane + + + align:start position:0% +vibration that occurs in this membrane +and it's a wave that travels along the + + align:start position:0% +and it's a wave that travels along the + + + align:start position:0% +and it's a wave that travels along the +cochlea and one of the the signature + + align:start position:0% +cochlea and one of the the signature + + + align:start position:0% +cochlea and one of the the signature +discovers about the cochlea is that that + + align:start position:0% +discovers about the cochlea is that that + + + align:start position:0% +discovers about the cochlea is that that +traveling wave Peaks in different places + + align:start position:0% +traveling wave Peaks in different places + + + align:start position:0% +traveling wave Peaks in different places +depending on the frequency content of + + align:start position:0% +depending on the frequency content of + + + align:start position:0% +depending on the frequency content of +the sound and that's schematized in + + align:start position:0% +the sound and that's schematized in + + + align:start position:0% +the sound and that's schematized in +these drawings here on the right so if + + align:start position:0% +these drawings here on the right so if + + + align:start position:0% +these drawings here on the right so if +if the ear were to receive a + + align:start position:0% +if the ear were to receive a + + + align:start position:0% +if the ear were to receive a +high-frequency sound that traveling wave + + align:start position:0% +high-frequency sound that traveling wave + + + align:start position:0% +high-frequency sound that traveling wave +would peak near the base if we were to + + align:start position:0% +would peak near the base if we were to + + + align:start position:0% +would peak near the base if we were to +receive a medium frequency sound the + + align:start position:0% +receive a medium frequency sound the + + + align:start position:0% +receive a medium frequency sound the +wave would peak somewhere in the middle + + align:start position:0% +wave would peak somewhere in the middle + + + align:start position:0% +wave would peak somewhere in the middle +and a low frequency sound would peak + + align:start position:0% +and a low frequency sound would peak + + + align:start position:0% +and a low frequency sound would peak +near the apex and the the frequency + + align:start position:0% +near the apex and the the frequency + + + align:start position:0% +near the apex and the the frequency +tuning it's partly mechanical in origin + + align:start position:0% +tuning it's partly mechanical in origin + + + align:start position:0% +tuning it's partly mechanical in origin +so that membrane it varies in thickness + + align:start position:0% +so that membrane it varies in thickness + + + align:start position:0% +so that membrane it varies in thickness +and stiffness all along its length and + + align:start position:0% +and stiffness all along its length and + + + align:start position:0% +and stiffness all along its length and +there's also a contribution that that's + + align:start position:0% +there's also a contribution that that's + + + align:start position:0% +there's also a contribution that that's +non-linear and active that we'll talk + + align:start position:0% +non-linear and active that we'll talk + + + align:start position:0% +non-linear and active that we'll talk +briefly about in a little bit so this is + + align:start position:0% +briefly about in a little bit so this is + + + align:start position:0% +briefly about in a little bit so this is +a close-up this is a cross-section so + + align:start position:0% +a close-up this is a cross-section so + + + align:start position:0% +a close-up this is a cross-section so +imagine you took this diagram and you + + align:start position:0% +imagine you took this diagram and you + + + align:start position:0% +imagine you took this diagram and you +kind of cut it in the middle this is a + + align:start position:0% +kind of cut it in the middle this is a + + + align:start position:0% +kind of cut it in the middle this is a +cross-section of the cochlea so this + + align:start position:0% +cross-section of the cochlea so this + + + align:start position:0% +cross-section of the cochlea so this +here is the basilar membrane and this is + + align:start position:0% +here is the basilar membrane and this is + + + align:start position:0% +here is the basilar membrane and this is +the organ of Corti that sits on top of + + align:start position:0% +the organ of Corti that sits on top of + + + align:start position:0% +the organ of Corti that sits on top of +the basilar membrane and so if you look + + align:start position:0% +the basilar membrane and so if you look + + + align:start position:0% +the basilar membrane and so if you look +closely you can see that there's this + + align:start position:0% +closely you can see that there's this + + + align:start position:0% +closely you can see that there's this +thing in here this is the inner hair + + align:start position:0% +thing in here this is the inner hair + + + align:start position:0% +thing in here this is the inner hair +cell and that's the that's the guy that + + align:start position:0% +cell and that's the that's the guy that + + + align:start position:0% +cell and that's the that's the guy that +does the the transduction that takes the + + align:start position:0% +does the the transduction that takes the + + + align:start position:0% +does the the transduction that takes the +mechanical energy that's coming from the + + align:start position:0% +mechanical energy that's coming from the + + + align:start position:0% +mechanical energy that's coming from the +fact that this thing is vibrating up and + + align:start position:0% +fact that this thing is vibrating up and + + + align:start position:0% +fact that this thing is vibrating up and +down and turns that into an electrical + + align:start position:0% +down and turns that into an electrical + + + align:start position:0% +down and turns that into an electrical +signal gets sent to your brain and it's + + align:start position:0% +signal gets sent to your brain and it's + + + align:start position:0% +signal gets sent to your brain and it's +the way that the way that works is that + + align:start position:0% +the way that the way that works is that + + + align:start position:0% +the way that the way that works is that +there's this other membrane here called + + align:start position:0% +there's this other membrane here called + + + align:start position:0% +there's this other membrane here called +the tectorial membrane and the hair + + align:start position:0% +the tectorial membrane and the hair + + + align:start position:0% +the tectorial membrane and the hair +cells got these cilia that stick out of + + align:start position:0% +cells got these cilia that stick out of + + + align:start position:0% +cells got these cilia that stick out of +it and as it moves up and down there's a + + align:start position:0% +it and as it moves up and down there's a + + + align:start position:0% +it and as it moves up and down there's a +shearing that's created between the two + + align:start position:0% +shearing that's created between the two + + + align:start position:0% +shearing that's created between the two +membranes the hair cell body deforms + + align:start position:0% +membranes the hair cell body deforms + + + align:start position:0% +membranes the hair cell body deforms +and that deformation causes a change in + + align:start position:0% +and that deformation causes a change in + + + align:start position:0% +and that deformation causes a change in +its membrane potential and that causes + + align:start position:0% +its membrane potential and that causes + + + align:start position:0% +its membrane potential and that causes +neurotransmitter to be released all + + align:start position:0% +neurotransmitter to be released all + + + align:start position:0% +neurotransmitter to be released all +right so that's that's the mechanism by + + align:start position:0% +right so that's that's the mechanism by + + + align:start position:0% +right so that's that's the mechanism by +which the brain takes that mechanical + + align:start position:0% +which the brain takes that mechanical + + + align:start position:0% +which the brain takes that mechanical +signal and turns it into an electrical + + align:start position:0% +signal and turns it into an electrical + + + align:start position:0% +signal and turns it into an electrical +signal that gets sent to your brain the + + align:start position:0% +signal that gets sent to your brain the + + + align:start position:0% +signal that gets sent to your brain the +other thing to note here and we'll + + align:start position:0% +other thing to note here and we'll + + + align:start position:0% +other thing to note here and we'll +return to this is that there are these + + align:start position:0% +return to this is that there are these + + + align:start position:0% +return to this is that there are these +other three cells here that are labeled + + align:start position:0% +other three cells here that are labeled + + + align:start position:0% +other three cells here that are labeled +as outer hair cells and so those kind of + + align:start position:0% +as outer hair cells and so those kind of + + + align:start position:0% +as outer hair cells and so those kind of +do what the the inner hair cell does in + + align:start position:0% +do what the the inner hair cell does in + + + align:start position:0% +do what the the inner hair cell does in +Reverse so they get an electrical signal + + align:start position:0% +Reverse so they get an electrical signal + + + align:start position:0% +Reverse so they get an electrical signal +from your brain and that causes the the + + align:start position:0% +from your brain and that causes the the + + + align:start position:0% +from your brain and that causes the the +hair cell bodies to chip to deform and + + align:start position:0% +hair cell bodies to chip to deform and + + + align:start position:0% +hair cell bodies to chip to deform and +that actually alters the motion of the + + align:start position:0% +that actually alters the motion of the + + + align:start position:0% +that actually alters the motion of the +basilar membrane so it's like a feedback + + align:start position:0% +basilar membrane so it's like a feedback + + + align:start position:0% +basilar membrane so it's like a feedback +system that we believe serves to amplify + + align:start position:0% +system that we believe serves to amplify + + + align:start position:0% +system that we believe serves to amplify +sounds and to sharpen their tuning so + + align:start position:0% +sounds and to sharpen their tuning so + + + align:start position:0% +sounds and to sharpen their tuning so +there's feedback all the way to the all + + align:start position:0% +there's feedback all the way to the all + + + align:start position:0% +there's feedback all the way to the all +the width of the cochlea okay so this is + + align:start position:0% +the width of the cochlea okay so this is + + + align:start position:0% +the width of the cochlea okay so this is +just another view so here's the inner + + align:start position:0% +just another view so here's the inner + + + align:start position:0% +just another view so here's the inner +hair cell here as this thing vibrates up + + align:start position:0% +hair cell here as this thing vibrates up + + + align:start position:0% +hair cell here as this thing vibrates up +and down there's a shearing between + + align:start position:0% +and down there's a shearing between + + + align:start position:0% +and down there's a shearing between +these membranes the inner hair cell of + + align:start position:0% +these membranes the inner hair cell of + + + align:start position:0% +these membranes the inner hair cell of +membrane potential changes and that + + align:start position:0% +membrane potential changes and that + + + align:start position:0% +membrane potential changes and that +causes neurotransmitter release okay so + + align:start position:0% +causes neurotransmitter release okay so + + + align:start position:0% +causes neurotransmitter release okay so +here's the really important point so we + + align:start position:0% +here's the really important point so we + + + align:start position:0% +here's the really important point so we +just talked about how there's this + + align:start position:0% +just talked about how there's this + + + align:start position:0% +just talked about how there's this +traveling wave that gets set up that + + align:start position:0% +traveling wave that gets set up that + + + align:start position:0% +traveling wave that gets set up that +Peaks in different places depending on + + align:start position:0% +Peaks in different places depending on + + + align:start position:0% +Peaks in different places depending on +the frequency content of the sound and + + align:start position:0% +the frequency content of the sound and + + + align:start position:0% +the frequency content of the sound and +so because the first order only part of + + align:start position:0% +so because the first order only part of + + + align:start position:0% +so because the first order only part of +the basilar membrane moves for a given + + align:start position:0% +the basilar membrane moves for a given + + + align:start position:0% +the basilar membrane moves for a given +frequency of sound each hair cell and + + align:start position:0% +frequency of sound each hair cell and + + + align:start position:0% +frequency of sound each hair cell and +the auditory nerve fiber that it + + align:start position:0% +the auditory nerve fiber that it + + + align:start position:0% +the auditory nerve fiber that it +synapses with signals only particular + + align:start position:0% +synapses with signals only particular + + + align:start position:0% +synapses with signals only particular +frequencies of sound and so this is sort + + align:start position:0% +frequencies of sound and so this is sort + + + align:start position:0% +frequencies of sound and so this is sort +of the classic textbook figure that you + + align:start position:0% +of the classic textbook figure that you + + + align:start position:0% +of the classic textbook figure that you +would see on this where what's being + + align:start position:0% +would see on this where what's being + + + align:start position:0% +would see on this where what's being +plotted on the y-axis is the minimum + + align:start position:0% +plotted on the y-axis is the minimum + + + align:start position:0% +plotted on the y-axis is the minimum +sound intensity needed to elicit a + + align:start position:0% +sound intensity needed to elicit a + + + align:start position:0% +sound intensity needed to elicit a +neural response and the x-axis is the + + align:start position:0% +neural response and the x-axis is the + + + align:start position:0% +neural response and the x-axis is the +frequency of a tone with which you would + + align:start position:0% +frequency of a tone with which you would + + + align:start position:0% +frequency of a tone with which you would +be stimulating the ear so you have a + + align:start position:0% +be stimulating the ear so you have a + + + align:start position:0% +be stimulating the ear so you have a +little pure tone generator with a knob + + align:start position:0% +little pure tone generator with a knob + + + align:start position:0% +little pure tone generator with a knob +you allows you to change the frequency + + align:start position:0% +you allows you to change the frequency + + + align:start position:0% +you allows you to change the frequency +and another knob that allows you to + + align:start position:0% +and another knob that allows you to + + + align:start position:0% +and another knob that allows you to +change the level and you sit there + + align:start position:0% +change the level and you sit there + + + align:start position:0% +change the level and you sit there +recording from an auditory nerve fiber + + align:start position:0% +recording from an auditory nerve fiber + + + align:start position:0% +recording from an auditory nerve fiber +varying the frequency and then turning + + align:start position:0% +varying the frequency and then turning + + + align:start position:0% +varying the frequency and then turning +the level up and down until you you get + + align:start position:0% +the level up and down until you you get + + + align:start position:0% +the level up and down until you you get +spikes out of the nerve fiber and so for + + align:start position:0% +spikes out of the nerve fiber and so for + + + align:start position:0% +spikes out of the nerve fiber and so for +every nerve fiber there will be some + + align:start position:0% +every nerve fiber there will be some + + + align:start position:0% +every nerve fiber there will be some +frequency called the characteristic + + align:start position:0% +frequency called the characteristic + + + align:start position:0% +frequency called the characteristic +frequency at which you can elicit spikes + + align:start position:0% +frequency at which you can elicit spikes + + + align:start position:0% +frequency at which you can elicit spikes +when you present the sound at a fairly + + align:start position:0% +when you present the sound at a fairly + + + align:start position:0% +when you present the sound at a fairly +low level and then as you change the + + align:start position:0% +low level and then as you change the + + + align:start position:0% +low level and then as you change the +frequency either higher or lower the + + align:start position:0% +frequency either higher or lower the + + + align:start position:0% +frequency either higher or lower the +level that is needed to elicit a + + align:start position:0% +level that is needed to elicit a + + + align:start position:0% +level that is needed to elicit a +response grows and so you can think of + + align:start position:0% +response grows and so you can think of + + + align:start position:0% +response grows and so you can think of +this as like a tuning her for that + + align:start position:0% +this as like a tuning her for that + + + align:start position:0% +this as like a tuning her for that +auditory nerve fiber + + align:start position:0% +auditory nerve fiber + + + align:start position:0% +auditory nerve fiber +on different nerve fibers have different + + align:start position:0% +on different nerve fibers have different + + + align:start position:0% +on different nerve fibers have different +characteristic frequencies here's just a + + align:start position:0% +characteristic frequencies here's just a + + + align:start position:0% +characteristic frequencies here's just a +picture that shows a handful of them and + + align:start position:0% +picture that shows a handful of them and + + + align:start position:0% +picture that shows a handful of them and +so together collectively they kind of + + align:start position:0% +so together collectively they kind of + + + align:start position:0% +so together collectively they kind of +tile the space and of course given what + + align:start position:0% +tile the space and of course given what + + + align:start position:0% +tile the space and of course given what +I just told you you can probably guess + + align:start position:0% +I just told you you can probably guess + + + align:start position:0% +I just told you you can probably guess +that each of these nerve fibers would + + align:start position:0% +that each of these nerve fibers would + + + align:start position:0% +that each of these nerve fibers would +synapse to a different location along + + align:start position:0% +synapse to a different location along + + + align:start position:0% +synapse to a different location along +the cochlea the the ones that have high + + align:start position:0% +the cochlea the the ones that have high + + + align:start position:0% +the cochlea the the ones that have high +characteristic frequencies would be near + + align:start position:0% +characteristic frequencies would be near + + + align:start position:0% +characteristic frequencies would be near +the base the ones that have low + + align:start position:0% +the base the ones that have low + + + align:start position:0% +the base the ones that have low +characteristic regencies would meet me + + align:start position:0% +characteristic regencies would meet me + + + align:start position:0% +characteristic regencies would meet me +near the apex okay so in computational + + align:start position:0% +near the apex okay so in computational + + + align:start position:0% +near the apex okay so in computational +terms the the common way to think about + + align:start position:0% +terms the the common way to think about + + + align:start position:0% +terms the the common way to think about +this is to approximate auditory nerve + + align:start position:0% +this is to approximate auditory nerve + + + align:start position:0% +this is to approximate auditory nerve +fibers with bandpass filters and so this + + align:start position:0% +fibers with bandpass filters and so this + + + align:start position:0% +fibers with bandpass filters and so this +would be a way that you would do this in + + align:start position:0% +would be a way that you would do this in + + + align:start position:0% +would be a way that you would do this in +a model each of these curves is a + + align:start position:0% +a model each of these curves is a + + + align:start position:0% +a model each of these curves is a +bandpass filter so what you see on the + + align:start position:0% +bandpass filter so what you see on the + + + align:start position:0% +bandpass filter so what you see on the +y-axis is the response of the filter the + + align:start position:0% +y-axis is the response of the filter the + + + align:start position:0% +y-axis is the response of the filter the +x-axis is frequency + + align:start position:0% +x-axis is frequency + + + align:start position:0% +x-axis is frequency +so each filter has some particular + + align:start position:0% +so each filter has some particular + + + align:start position:0% +so each filter has some particular +frequency at which they give a peak + + align:start position:0% +frequency at which they give a peak + + + align:start position:0% +frequency at which they give a peak +response and then the signal is + + align:start position:0% +response and then the signal is + + + align:start position:0% +response and then the signal is +attenuated on either side of that of + + align:start position:0% +attenuated on either side of that of + + + align:start position:0% +attenuated on either side of that of +that peak frequency and so one way to + + align:start position:0% +that peak frequency and so one way to + + + align:start position:0% +that peak frequency and so one way to +think about what the the cochlea is + + align:start position:0% +think about what the the cochlea is + + + align:start position:0% +think about what the the cochlea is +doing to the signal is that it's taking + + align:start position:0% +doing to the signal is that it's taking + + + align:start position:0% +doing to the signal is that it's taking +the signal that enters the ears on this + + align:start position:0% +the signal that enters the ears on this + + + align:start position:0% +the signal that enters the ears on this +thing here so this is just a sound + + align:start position:0% +thing here so this is just a sound + + + align:start position:0% +thing here so this is just a sound +signal so the amplitude just varies over + + align:start position:0% +signal so the amplitude just varies over + + + align:start position:0% +signal so the amplitude just varies over +time in some particular way you take + + align:start position:0% +time in some particular way you take + + + align:start position:0% +time in some particular way you take +that signal you pass it through this + + align:start position:0% +that signal you pass it through this + + + align:start position:0% +that signal you pass it through this +Bank of man pass filters and then the + + align:start position:0% +Bank of man pass filters and then the + + + align:start position:0% +Bank of man pass filters and then the +output of each of these filters is a + + align:start position:0% +output of each of these filters is a + + + align:start position:0% +output of each of these filters is a +filtered version of the original signal + + align:start position:0% +filtered version of the original signal + + + align:start position:0% +filtered version of the original signal +and so in engineering terms we call that + + align:start position:0% +and so in engineering terms we call that + + + align:start position:0% +and so in engineering terms we call that +a sub band so this would be the result + + align:start position:0% +a sub band so this would be the result + + + align:start position:0% +a sub band so this would be the result +of taking that sound signal and + + align:start position:0% +of taking that sound signal and + + + align:start position:0% +of taking that sound signal and +filtering it with a filter that's tuned + + align:start position:0% +filtering it with a filter that's tuned + + + align:start position:0% +filtering it with a filter that's tuned +to relatively low frequencies three + + align:start position:0% +to relatively low frequencies three + + + align:start position:0% +to relatively low frequencies three +hundred fifty to five hundred twenty + + align:start position:0% +hundred fifty to five hundred twenty + + + align:start position:0% +hundred fifty to five hundred twenty +Hertz in this particular case and so you + + align:start position:0% +Hertz in this particular case and so you + + + align:start position:0% +Hertz in this particular case and so you +can see that the output of that filter + + align:start position:0% +can see that the output of that filter + + + align:start position:0% +can see that the output of that filter +is a signal that varies relatively + + align:start position:0% +is a signal that varies relatively + + + align:start position:0% +is a signal that varies relatively +slowly so it wiggles up and down but you + + align:start position:0% +slowly so it wiggles up and down but you + + + align:start position:0% +slowly so it wiggles up and down but you +can see that the Wiggles are in some + + align:start position:0% +can see that the Wiggles are in some + + + align:start position:0% +can see that the Wiggles are in some +sort of confined space of frequencies if + + align:start position:0% +sort of confined space of frequencies if + + + align:start position:0% +sort of confined space of frequencies if +we go a little bit further up we get the + + align:start position:0% +we go a little bit further up we get the + + + align:start position:0% +we go a little bit further up we get the +output of something that's tuned to + + align:start position:0% +output of something that's tuned to + + + align:start position:0% +output of something that's tuned to +slightly higher frequencies you can see + + align:start position:0% +slightly higher frequencies you can see + + + align:start position:0% +slightly higher frequencies you can see +that the output of that filter is + + align:start position:0% +that the output of that filter is + + + align:start position:0% +that the output of that filter is +wiggling at a faster rate and then if we + + align:start position:0% +wiggling at a faster rate and then if we + + + align:start position:0% +wiggling at a faster rate and then if we +go up further still we get a different + + align:start position:0% +go up further still we get a different + + + align:start position:0% +go up further still we get a different +thing that is again wiggling even faster + + align:start position:0% +thing that is again wiggling even faster + + + align:start position:0% +thing that is again wiggling even faster +and so collectively + + align:start position:0% +and so collectively + + + align:start position:0% +and so collectively +we we can take this original broadband + + align:start position:0% +we we can take this original broadband + + + align:start position:0% +we we can take this original broadband +signal and then represent it with with a + + align:start position:0% +signal and then represent it with with a + + + align:start position:0% +signal and then represent it with with a +whole bunch of these sub bands and + + align:start position:0% +whole bunch of these sub bands and + + + align:start position:0% +whole bunch of these sub bands and +typically you might use thirty or forty + + align:start position:0% +typically you might use thirty or forty + + + align:start position:0% +typically you might use thirty or forty +or fifty so one thing to note here you + + align:start position:0% +or fifty so one thing to note here you + + + align:start position:0% +or fifty so one thing to note here you +might have noticed that there's + + align:start position:0% +might have noticed that there's + + + align:start position:0% +might have noticed that there's +something funny about this picture and + + align:start position:0% +something funny about this picture and + + + align:start position:0% +something funny about this picture and +that the the the filters here which are + + align:start position:0% +that the the the filters here which are + + + align:start position:0% +that the the the filters here which are +indicated by these colored curves are + + align:start position:0% +indicated by these colored curves are + + + align:start position:0% +indicated by these colored curves are +not uniform alright so the ones down + + align:start position:0% +not uniform alright so the ones down + + + align:start position:0% +not uniform alright so the ones down +here are very narrow and the ones down + + align:start position:0% +here are very narrow and the ones down + + + align:start position:0% +here are very narrow and the ones down +here are very broad and that's not an + + align:start position:0% +here are very broad and that's not an + + + align:start position:0% +here are very broad and that's not an +accident that's that's roughly the what + + align:start position:0% +accident that's that's roughly the what + + + align:start position:0% +accident that's that's roughly the what +you find when you actually look in the + + align:start position:0% +you find when you actually look in the + + + align:start position:0% +you find when you actually look in the +ear and why why things are that that + + align:start position:0% +ear and why why things are that that + + + align:start position:0% +ear and why why things are that that +that way is something that might you + + align:start position:0% +that way is something that might you + + + align:start position:0% +that way is something that might you +could potentially debate but but it's + + align:start position:0% +could potentially debate but but it's + + + align:start position:0% +could potentially debate but but it's +very clear empirically that that's + + align:start position:0% +very clear empirically that that's + + + align:start position:0% +very clear empirically that that's +roughly what you find I'm not going to + + align:start position:0% +roughly what you find I'm not going to + + + align:start position:0% +roughly what you find I'm not going to +say too much more about this now but but + + align:start position:0% +say too much more about this now but but + + + align:start position:0% +say too much more about this now but but +remember that because it'll become + + align:start position:0% +remember that because it'll become + + + align:start position:0% +remember that because it'll become +important a little bit later on so we + + align:start position:0% +important a little bit later on so we + + + align:start position:0% +important a little bit later on so we +can take these these filters and turn + + align:start position:0% +can take these these filters and turn + + + align:start position:0% +can take these these filters and turn +that into an initial stage of an + + align:start position:0% +that into an initial stage of an + + + align:start position:0% +that into an initial stage of an +auditory model the stuff that we think + + align:start position:0% +auditory model the stuff that we think + + + align:start position:0% +auditory model the stuff that we think +is happening in the early auditory + + align:start position:0% +is happening in the early auditory + + + align:start position:0% +is happening in the early auditory +system where we've got our sound signal + + align:start position:0% +system where we've got our sound signal + + + align:start position:0% +system where we've got our sound signal +that gets passed through this bag of + + align:start position:0% +that gets passed through this bag of + + + align:start position:0% +that gets passed through this bag of +bandpass filters and you've now wrapped + + align:start position:0% +bandpass filters and you've now wrapped + + + align:start position:0% +bandpass filters and you've now wrapped +you're now representing that signal has + + align:start position:0% +you're now representing that signal has + + + align:start position:0% +you're now representing that signal has +a bunch of different sub bands just two + + align:start position:0% +a bunch of different sub bands just two + + + align:start position:0% +a bunch of different sub bands just two +of which are shown here for clarity and + + align:start position:0% +of which are shown here for clarity and + + + align:start position:0% +of which are shown here for clarity and +the the frequency selectivity that you + + align:start position:0% +the the frequency selectivity that you + + + align:start position:0% +the the frequency selectivity that you +find in the ear has a whole host of + + align:start position:0% +find in the ear has a whole host of + + + align:start position:0% +find in the ear has a whole host of +perceptual consequences I won't go + + align:start position:0% +perceptual consequences I won't go + + + align:start position:0% +perceptual consequences I won't go +through all of them exhaustively it's + + align:start position:0% +through all of them exhaustively it's + + + align:start position:0% +through all of them exhaustively it's +it's one of the main determinants of + + align:start position:0% +it's one of the main determinants of + + + align:start position:0% +it's one of the main determinants of +what masks what so for instance when you + + align:start position:0% +what masks what so for instance when you + + + align:start position:0% +what masks what so for instance when you +know you're trying to compress a sound + + align:start position:0% +know you're trying to compress a sound + + + align:start position:0% +know you're trying to compress a sound +signal like by turning it into an mp3 + + align:start position:0% +signal like by turning it into an mp3 + + + align:start position:0% +signal like by turning it into an mp3 +you have to really pay attention to what + + align:start position:0% +you have to really pay attention to what + + + align:start position:0% +you have to really pay attention to what +to the nature of these filters and you + + align:start position:0% +to the nature of these filters and you + + + align:start position:0% +to the nature of these filters and you +don't you know you don't need to + + align:start position:0% +don't you know you don't need to + + + align:start position:0% +don't you know you don't need to +represent parts of the filters that + + align:start position:0% +represent parts of the filters that + + + align:start position:0% +represent parts of the filters that +would be sorry parts of the signal will + + align:start position:0% +would be sorry parts of the signal will + + + align:start position:0% +would be sorry parts of the signal will +be masked and these filters tell you a + + align:start position:0% +be masked and these filters tell you a + + + align:start position:0% +be masked and these filters tell you a +lot about that one one respect in which + + align:start position:0% +lot about that one one respect in which + + + align:start position:0% +lot about that one one respect in which +frequency selectivity is evident is by + + align:start position:0% +frequency selectivity is evident is by + + + align:start position:0% +frequency selectivity is evident is by +the ability to hear out individual + + align:start position:0% +the ability to hear out individual + + + align:start position:0% +the ability to hear out individual +frequency components of sounds that have + + align:start position:0% +frequency components of sounds that have + + + align:start position:0% +frequency components of sounds that have +lots of frequencies in them so this is + + align:start position:0% +lots of frequencies in them so this is + + + align:start position:0% +lots of frequencies in them so this is +kind of a cool demonstration and to kind + + align:start position:0% +kind of a cool demonstration and to kind + + + align:start position:0% +kind of a cool demonstration and to kind +of help us see what's going on we're + + align:start position:0% +of help us see what's going on we're + + + align:start position:0% +of help us see what's going on we're +going to look at a spectrogram of what's + + align:start position:0% +going to look at a spectrogram of what's + + + align:start position:0% +going to look at a spectrogram of what's +coming in so hopefully this will work so + + align:start position:0% +coming in so hopefully this will work so + + + align:start position:0% +coming in so hopefully this will work so +that what this is that what this little + + align:start position:0% +that what this is that what this little + + + align:start position:0% +that what this is that what this little +thing is doing is there's a microphone + + align:start position:0% +thing is doing is there's a microphone + + + align:start position:0% +thing is doing is there's a microphone +in the laptop and it takes that + + align:start position:0% +in the laptop and it takes that + + + align:start position:0% +in the laptop and it takes that +microphone signal and turns it into a + + align:start position:0% +microphone signal and turns it into a + + + align:start position:0% +microphone signal and turns it into a +spectrogram it's using a logarithmic + + align:start position:0% +spectrogram it's using a logarithmic + + + align:start position:0% +spectrogram it's using a logarithmic +frequency scale here + + align:start position:0% +frequency scale here + + + align:start position:0% +frequency scale here +from about a hundred Hertz to 6400 and + + align:start position:0% +from about a hundred Hertz to 6400 and + + + align:start position:0% +from about a hundred Hertz to 6400 and +so if I don't see say anything you'll be + + align:start position:0% +so if I don't see say anything you'll be + + + align:start position:0% +so if I don't see say anything you'll be +able to hear the room noise or see the + + align:start position:0% +able to hear the room noise or see the + + + align:start position:0% +able to hear the room noise or see the +room noise it's not the baseline and + + align:start position:0% +room noise it's not the baseline and + + + align:start position:0% +room noise it's not the baseline and +also the UM the other thing to note is + + align:start position:0% +also the UM the other thing to note is + + + align:start position:0% +also the UM the other thing to note is +that the the microphone doesn't have a + + align:start position:0% +that the the microphone doesn't have a + + + align:start position:0% +that the the microphone doesn't have a +very good bass response and so the very + + align:start position:0% +very good bass response and so the very + + + align:start position:0% +very good bass response and so the very +low frequencies won't show up but + + align:start position:0% +low frequencies won't show up but + + + align:start position:0% +low frequencies won't show up but +everything else well okay cancelled + + align:start position:0% +everything else well okay cancelled + + + align:start position:0% +everything else well okay cancelled +harmonics a complex tone is presented + + align:start position:0% +harmonics a complex tone is presented + + + align:start position:0% +harmonics a complex tone is presented +followed by several cancellations and + + align:start position:0% +followed by several cancellations and + + + align:start position:0% +followed by several cancellations and +restorations of a particular harmonic + + align:start position:0% +restorations of a particular harmonic + + + align:start position:0% +restorations of a particular harmonic +this is done for harmonics one through + + align:start position:0% +this is done for harmonics one through + + + align:start position:0% +this is done for harmonics one through +ten + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +okay just to be clear the point of this + + align:start position:0% +okay just to be clear the point of this + + + align:start position:0% +okay just to be clear the point of this +right is that what's happening here just + + align:start position:0% +right is that what's happening here just + + + align:start position:0% +right is that what's happening here just +stop that for a second is you're hearing + + align:start position:0% +stop that for a second is you're hearing + + + align:start position:0% +stop that for a second is you're hearing +this what's called a complex tone that + + align:start position:0% +this what's called a complex tone that + + + align:start position:0% +this what's called a complex tone that +mean that just means a tone that has + + align:start position:0% +mean that just means a tone that has + + + align:start position:0% +mean that just means a tone that has +more than one frequency that's that's + + align:start position:0% +more than one frequency that's that's + + + align:start position:0% +more than one frequency that's that's +what constitutes complexity for a + + align:start position:0% +what constitutes complexity for a + + + align:start position:0% +what constitutes complexity for a +psychic acoustician it's a complex tone + + align:start position:0% +psychic acoustician it's a complex tone + + + align:start position:0% +psychic acoustician it's a complex tone +and each of the stripes here is one of + + align:start position:0% +and each of the stripes here is one of + + + align:start position:0% +and each of the stripes here is one of +the frequencies so this is a harmonic + + align:start position:0% +the frequencies so this is a harmonic + + + align:start position:0% +the frequencies so this is a harmonic +complex tone so the fundamental + + align:start position:0% +complex tone so the fundamental + + + align:start position:0% +complex tone so the fundamental +frequency is 200 Hertz and so all the + + align:start position:0% +frequency is 200 Hertz and so all the + + + align:start position:0% +frequency is 200 Hertz and so all the +other frequencies are integer multiples + + align:start position:0% +other frequencies are integer multiples + + + align:start position:0% +other frequencies are integer multiples +of that so there's 400 600 800 a + + align:start position:0% +of that so there's 400 600 800 a + + + align:start position:0% +of that so there's 400 600 800 a +thousand 1200 and so on and so forth + + align:start position:0% +thousand 1200 and so on and so forth + + + align:start position:0% +thousand 1200 and so on and so forth +okay and then what what's happening is + + align:start position:0% +okay and then what what's happening is + + + align:start position:0% +okay and then what what's happening is +that in each little cycle of this + + align:start position:0% +that in each little cycle of this + + + align:start position:0% +that in each little cycle of this +demonstration one of the harmonics is + + align:start position:0% +demonstration one of the harmonics is + + + align:start position:0% +demonstration one of the harmonics is +getting pulsed on and off right and the + + align:start position:0% +getting pulsed on and off right and the + + + align:start position:0% +getting pulsed on and off right and the +consequence of it being pulsed on and + + align:start position:0% +consequence of it being pulsed on and + + + align:start position:0% +consequence of it being pulsed on and +off is that you're able to actually hear + + align:start position:0% +off is that you're able to actually hear + + + align:start position:0% +off is that you're able to actually hear +it as like a distinct thing and the fact + + align:start position:0% +it as like a distinct thing and the fact + + + align:start position:0% +it as like a distinct thing and the fact +that that happens that's that's not + + align:start position:0% +that that happens that's that's not + + + align:start position:0% +that that happens that's that's not +itself happening in the ear right that's + + align:start position:0% +itself happening in the ear right that's + + + align:start position:0% +itself happening in the ear right that's +something kind of complicated and + + align:start position:0% +something kind of complicated and + + + align:start position:0% +something kind of complicated and +interesting that your brain is doing + + align:start position:0% +interesting that your brain is doing + + + align:start position:0% +interesting that your brain is doing +with that signal it's getting from the + + align:start position:0% +with that signal it's getting from the + + + align:start position:0% +with that signal it's getting from the +ear but the fact you're able to do that + + align:start position:0% +ear but the fact you're able to do that + + + align:start position:0% +ear but the fact you're able to do that +is only possible by virtue of the fact + + align:start position:0% +is only possible by virtue of the fact + + + align:start position:0% +is only possible by virtue of the fact +that the the signal that your brain gets + + align:start position:0% +that the the signal that your brain gets + + + align:start position:0% +that the the signal that your brain gets +from the ear um divides the signal up in + + align:start position:0% +from the ear um divides the signal up in + + + align:start position:0% +from the ear um divides the signal up in +a way that kind of preserves of the + + align:start position:0% +a way that kind of preserves of the + + + align:start position:0% +a way that kind of preserves of the +individual frequencies all right and so + + align:start position:0% +individual frequencies all right and so + + + align:start position:0% +individual frequencies all right and so +this is just a demonstration that you're + + align:start position:0% +this is just a demonstration that you're + + + align:start position:0% +this is just a demonstration that you're +actually able to under appropriate + + align:start position:0% +actually able to under appropriate + + + align:start position:0% +actually able to under appropriate +circumstances to hear out particular + + align:start position:0% +circumstances to hear out particular + + + align:start position:0% +circumstances to hear out particular +frequency components of this complicated + + align:start position:0% +frequency components of this complicated + + + align:start position:0% +frequency components of this complicated +thing even though if you just heard it + + align:start position:0% +thing even though if you just heard it + + + align:start position:0% +thing even though if you just heard it +by itself it would just sound like one + + align:start position:0% +by itself it would just sound like one + + + align:start position:0% +by itself it would just sound like one +thing so another kind of interesting and + + align:start position:0% +thing so another kind of interesting and + + + align:start position:0% +thing so another kind of interesting and +cool phenomenon that is related to + + align:start position:0% +cool phenomenon that is related to + + + align:start position:0% +cool phenomenon that is related to +frequency selectivity is the perception + + align:start position:0% +frequency selectivity is the perception + + + align:start position:0% +frequency selectivity is the perception +of beating um so how many people here + + align:start position:0% +of beating um so how many people here + + + align:start position:0% +of beating um so how many people here +know what beating is yeah okay so + + align:start position:0% +know what beating is yeah okay so + + + align:start position:0% +know what beating is yeah okay so +beating is is this is a physical + + align:start position:0% +beating is is this is a physical + + + align:start position:0% +beating is is this is a physical +phenomenon that happens whenever you + + align:start position:0% +phenomenon that happens whenever you + + + align:start position:0% +phenomenon that happens whenever you +have multiple different frequencies that + + align:start position:0% +have multiple different frequencies that + + + align:start position:0% +have multiple different frequencies that +are present at the same time so in this + + align:start position:0% +are present at the same time so in this + + + align:start position:0% +are present at the same time so in this +case that those are the red and blue + + align:start position:0% +case that those are the red and blue + + + align:start position:0% +case that those are the red and blue +curves up at the top so there's a + + align:start position:0% +curves up at the top so there's a + + + align:start position:0% +curves up at the top so there's a +sinusoidal to different frequencies and + + align:start position:0% +sinusoidal to different frequencies and + + + align:start position:0% +sinusoidal to different frequencies and +the consequence of them being two + + align:start position:0% +the consequence of them being two + + + align:start position:0% +the consequence of them being two +different frequencies is that over time + + align:start position:0% +different frequencies is that over time + + + align:start position:0% +different frequencies is that over time +they shift in and out of phase and so + + align:start position:0% +they shift in and out of phase and so + + + align:start position:0% +they shift in and out of phase and so +there's this particular point here where + + align:start position:0% +there's this particular point here where + + + align:start position:0% +there's this particular point here where +the two the peaks of the waveforms are + + align:start position:0% +the two the peaks of the waveforms are + + + align:start position:0% +the two the peaks of the waveforms are +aligned and then there's there's this + + align:start position:0% +aligned and then there's there's this + + + align:start position:0% +aligned and then there's there's this +point over here where the peak of one + + align:start position:0% +point over here where the peak of one + + + align:start position:0% +point over here where the peak of one +aligns with the trough of the other just + + align:start position:0% +aligns with the trough of the other just + + + align:start position:0% +aligns with the trough of the other just +because they're two different + + align:start position:0% +because they're two different + + + align:start position:0% +because they're two different +frequencies and they slide in and out of + + align:start position:0% +frequencies and they slide in and out of + + + align:start position:0% +frequencies and they slide in and out of +phase and so when you play those two + + align:start position:0% +phase and so when you play those two + + + align:start position:0% +phase and so when you play those two +frequencies at the same time you get the + + align:start position:0% +frequencies at the same time you get the + + + align:start position:0% +frequencies at the same time you get the +blackk waveform so they're just some + + align:start position:0% +blackk waveform so they're just some + + + align:start position:0% +blackk waveform so they're just some +linearly that's what that's what sounds + + align:start position:0% +linearly that's what that's what sounds + + + align:start position:0% +linearly that's what that's what sounds +do + + align:start position:0% +do + + + align:start position:0% +do +there's their both president wants and + + align:start position:0% +there's their both president wants and + + + align:start position:0% +there's their both president wants and +so the point at with it which the peaks + + align:start position:0% +so the point at with it which the peaks + + + align:start position:0% +so the point at with it which the peaks +of line there's constructive + + align:start position:0% +of line there's constructive + + + align:start position:0% +of line there's constructive +interference in the point at which the + + align:start position:0% +interference in the point at which the + + + align:start position:0% +interference in the point at which the +peak and the trough align there's + + align:start position:0% +peak and the trough align there's + + + align:start position:0% +peak and the trough align there's +destructive interference and so over + + align:start position:0% +destructive interference and so over + + + align:start position:0% +destructive interference and so over +time the amplitude waxes and wanes and + + align:start position:0% +time the amplitude waxes and wanes and + + + align:start position:0% +time the amplitude waxes and wanes and +so physically that's what's known as + + align:start position:0% +so physically that's what's known as + + + align:start position:0% +so physically that's what's known as +beating and the interesting thing is + + align:start position:0% +beating and the interesting thing is + + + align:start position:0% +beating and the interesting thing is +that the audibility of the beating is is + + align:start position:0% +that the audibility of the beating is is + + + align:start position:0% +that the audibility of the beating is is +very tightly constrained by the cochlea + + align:start position:0% +very tightly constrained by the cochlea + + + align:start position:0% +very tightly constrained by the cochlea +so here's one frequency here's the other + + align:start position:0% +so here's one frequency here's the other + + + align:start position:0% +so here's one frequency here's the other +and then you play them at the same time + + align:start position:0% +and then you play them at the same time + + + align:start position:0% +and then you play them at the same time +you hear that fluttering kind of + + align:start position:0% +you hear that fluttering kind of + + + align:start position:0% +you hear that fluttering kind of +sensation all right so that's the amp + + align:start position:0% +sensation all right so that's the amp + + + align:start position:0% +sensation all right so that's the amp +that's the amplitude modulation um + + align:start position:0% +that's the amplitude modulation um + + + align:start position:0% +that's the amplitude modulation um +and okay and so um so we just I've just + + align:start position:0% +and okay and so um so we just I've just + + + align:start position:0% +and okay and so um so we just I've just +told you how the the you can think of + + align:start position:0% +told you how the the you can think of + + + align:start position:0% +told you how the the you can think of +the cochlea as this set of filters um + + align:start position:0% +the cochlea as this set of filters um + + + align:start position:0% +the cochlea as this set of filters um +and so it's an interesting empirical + + align:start position:0% +and so it's an interesting empirical + + + align:start position:0% +and so it's an interesting empirical +fact that you only hear beating if the + + align:start position:0% +fact that you only hear beating if the + + + align:start position:0% +fact that you only hear beating if the +two frequencies that are beating fall + + align:start position:0% +two frequencies that are beating fall + + + align:start position:0% +two frequencies that are beating fall +roughly within the the same cochlear + + align:start position:0% +roughly within the the same cochlear + + + align:start position:0% +roughly within the the same cochlear +bandwidth okay and so when they're + + align:start position:0% +bandwidth okay and so when they're + + + align:start position:0% +bandwidth okay and so when they're +pretty close together on like one semi + + align:start position:0% +pretty close together on like one semi + + + align:start position:0% +pretty close together on like one semi +tone the beatings very audible but as + + align:start position:0% +tone the beatings very audible but as + + + align:start position:0% +tone the beatings very audible but as +you move them further apart so three + + align:start position:0% +you move them further apart so three + + + align:start position:0% +you move them further apart so three +semi tones is getting close to roughly + + align:start position:0% +semi tones is getting close to roughly + + + align:start position:0% +semi tones is getting close to roughly +what a typical cochlear filter bandwidth + + align:start position:0% +what a typical cochlear filter bandwidth + + + align:start position:0% +what a typical cochlear filter bandwidth +would be and the beating is a lot less + + align:start position:0% +would be and the beating is a lot less + + + align:start position:0% +would be and the beating is a lot less +audible and then by the time you get to + + align:start position:0% +audible and then by the time you get to + + + align:start position:0% +audible and then by the time you get to +eight semi tones you just don't hear + + align:start position:0% +eight semi tones you just don't hear + + + align:start position:0% +eight semi tones you just don't hear +anything it just sounds like two tones + + align:start position:0% +anything it just sounds like two tones + + + align:start position:0% +anything it just sounds like two tones +not very clear so contrast that with + + align:start position:0% +not very clear so contrast that with + + + align:start position:0% +not very clear so contrast that with +alright so in all and the important + + align:start position:0% +alright so in all and the important + + + align:start position:0% +alright so in all and the important +thing to emphasize is that in all three + + align:start position:0% +thing to emphasize is that in all three + + + align:start position:0% +thing to emphasize is that in all three +of these cases there's physically + + align:start position:0% +of these cases there's physically + + + align:start position:0% +of these cases there's physically +there's beating happening alright so if + + align:start position:0% +there's beating happening alright so if + + + align:start position:0% +there's beating happening alright so if +you are actually were to look at what + + align:start position:0% +you are actually were to look at what + + + align:start position:0% +you are actually were to look at what +the eardrum was doing you would see the + + align:start position:0% +the eardrum was doing you would see the + + + align:start position:0% +the eardrum was doing you would see the +amplitude modulation here but you don't + + align:start position:0% +amplitude modulation here but you don't + + + align:start position:0% +amplitude modulation here but you don't +hear that + + align:start position:0% +hear that + + + align:start position:0% +hear that +this is just another consequence of the + + align:start position:0% +this is just another consequence of the + + + align:start position:0% +this is just another consequence of the +way that your your cochlea is filtering + + align:start position:0% +way that your your cochlea is filtering + + + align:start position:0% +way that your your cochlea is filtering +sound okay alright so we've got our + + align:start position:0% +sound okay alright so we've got our + + + align:start position:0% +sound okay alright so we've got our +auditory model here what happens next so + + align:start position:0% +auditory model here what happens next so + + + align:start position:0% +auditory model here what happens next so +there's a couple of important caveats + + align:start position:0% +there's a couple of important caveats + + + align:start position:0% +there's a couple of important caveats +about this and I mentioned this in part + + align:start position:0% +about this and I mentioned this in part + + + align:start position:0% +about this and I mentioned this in part +because I some of these things are we + + align:start position:0% +because I some of these things are we + + + align:start position:0% +because I some of these things are we +don't really know exactly what this the + + align:start position:0% +don't really know exactly what this the + + + align:start position:0% +don't really know exactly what this the +what the true significance is of some of + + align:start position:0% +what the true significance is of some of + + + align:start position:0% +what the true significance is of some of +these things especially in computational + + align:start position:0% +these things especially in computational + + + align:start position:0% +these things especially in computational +terms so I've just told you about how we + + align:start position:0% +terms so I've just told you about how we + + + align:start position:0% +terms so I've just told you about how we +typically will model what the coca is + + align:start position:0% +typically will model what the coca is + + + align:start position:0% +typically will model what the coca is +doing as a set of linear bandpass filter + + align:start position:0% +doing as a set of linear bandpass filter + + + align:start position:0% +doing as a set of linear bandpass filter +so you get a signal you apply a linear + + align:start position:0% +so you get a signal you apply a linear + + + align:start position:0% +so you get a signal you apply a linear +filter you get a sub band but um in in + + align:start position:0% +filter you get a sub band but um in in + + + align:start position:0% +filter you get a sub band but um in in +actuality if you actually look at what + + align:start position:0% +actuality if you actually look at what + + + align:start position:0% +actuality if you actually look at what +the ear is doing it's pretty clear that + + align:start position:0% +the ear is doing it's pretty clear that + + + align:start position:0% +the ear is doing it's pretty clear that +linear filtering provides only an + + align:start position:0% +linear filtering provides only an + + + align:start position:0% +linear filtering provides only an +approximate description of cochlear + + align:start position:0% +approximate description of cochlear + + + align:start position:0% +approximate description of cochlear +and in particular this is evident when + + align:start position:0% +and in particular this is evident when + + + align:start position:0% +and in particular this is evident when +you change sound levels so what this is + + align:start position:0% +you change sound levels so what this is + + + align:start position:0% +you change sound levels so what this is +a plot of is tuning curves that were you + + align:start position:0% +a plot of is tuning curves that were you + + + align:start position:0% +a plot of is tuning curves that were you +would measure from an auditory nerve + + align:start position:0% +would measure from an auditory nerve + + + align:start position:0% +would measure from an auditory nerve +fiber so we've got spikes per second on + + align:start position:0% +fiber so we've got spikes per second on + + + align:start position:0% +fiber so we've got spikes per second on +the y-axis we've got the frequency of a + + align:start position:0% +the y-axis we've got the frequency of a + + + align:start position:0% +the y-axis we've got the frequency of a +pure tone stimulus on the x-axis and + + align:start position:0% +pure tone stimulus on the x-axis and + + + align:start position:0% +pure tone stimulus on the x-axis and +each curve plus the response at a + + align:start position:0% +each curve plus the response at a + + + align:start position:0% +each curve plus the response at a +different stimulus intensity alright so + + align:start position:0% +different stimulus intensity alright so + + + align:start position:0% +different stimulus intensity alright so +down here at the bottom we've got 35 DB + + align:start position:0% +down here at the bottom we've got 35 DB + + + align:start position:0% +down here at the bottom we've got 35 DB +SPL so that's like a very very low level + + align:start position:0% +SPL so that's like a very very low level + + + align:start position:0% +SPL so that's like a very very low level +like you know maybe if you rubbed your + + align:start position:0% +like you know maybe if you rubbed your + + + align:start position:0% +like you know maybe if you rubbed your +hands together or something that would + + align:start position:0% +hands together or something that would + + + align:start position:0% +hands together or something that would +be close to 35 right and 45 and you can + + align:start position:0% +be close to 35 right and 45 and you can + + + align:start position:0% +be close to 35 right and 45 and you can +see here that the tuning is pretty + + align:start position:0% +see here that the tuning is pretty + + + align:start position:0% +see here that the tuning is pretty +narrow here I'm at these low levels so + + align:start position:0% +narrow here I'm at these low levels so + + + align:start position:0% +narrow here I'm at these low levels so +45 DB SPL so you got a pretty big + + align:start position:0% +45 DB SPL so you got a pretty big + + + align:start position:0% +45 DB SPL so you got a pretty big +response here that looks like you know + + align:start position:0% +response here that looks like you know + + + align:start position:0% +response here that looks like you know +1700 Hertz and then by the time you know + + align:start position:0% +1700 Hertz and then by the time you know + + + align:start position:0% +1700 Hertz and then by the time you know +you go down half an octave or something + + align:start position:0% +you go down half an octave or something + + + align:start position:0% +you go down half an octave or something +there's almost no response but as the + + align:start position:0% +there's almost no response but as the + + + align:start position:0% +there's almost no response but as the +stimulus level increases you can see + + align:start position:0% +stimulus level increases you can see + + + align:start position:0% +stimulus level increases you can see +that the Tooting the tuning broadens + + align:start position:0% +that the Tooting the tuning broadens + + + align:start position:0% +that the Tooting the tuning broadens +like really very considerably and so I + + align:start position:0% +like really very considerably and so I + + + align:start position:0% +like really very considerably and so I +hear at like 75 or 85 dB you know you're + + align:start position:0% +hear at like 75 or 85 dB you know you're + + + align:start position:0% +hear at like 75 or 85 dB you know you're +getting a response from anywhere from + + align:start position:0% +getting a response from anywhere from + + + align:start position:0% +getting a response from anywhere from +500 Hertz out to you know over 2,000 + + align:start position:0% +500 Hertz out to you know over 2,000 + + + align:start position:0% +500 Hertz out to you know over 2,000 +Hertz that's like a two octave range + + align:start position:0% +Hertz that's like a two octave range + + + align:start position:0% +Hertz that's like a two octave range +right so the bandwidth is like growing + + align:start position:0% +right so the bandwidth is like growing + + + align:start position:0% +right so the bandwidth is like growing +pretty pretty dramatically and this is + + align:start position:0% +pretty pretty dramatically and this is + + + align:start position:0% +pretty pretty dramatically and this is +this is like very typical here's like a + + align:start position:0% +this is like very typical here's like a + + + align:start position:0% +this is like very typical here's like a +bunch of examples of different nerve + + align:start position:0% +bunch of examples of different nerve + + + align:start position:0% +bunch of examples of different nerve +fibers that are like doing the same + + align:start position:0% +fibers that are like doing the same + + + align:start position:0% +fibers that are like doing the same +thing so at high levels the tuning is + + align:start position:0% +thing so at high levels the tuning is + + + align:start position:0% +thing so at high levels the tuning is +really broad at low levels it's kind of + + align:start position:0% +really broad at low levels it's kind of + + + align:start position:0% +really broad at low levels it's kind of +narrow and so um mechanistically like in + + align:start position:0% +narrow and so um mechanistically like in + + + align:start position:0% +narrow and so um mechanistically like in +terms of the biology we we have a pretty + + align:start position:0% +terms of the biology we we have a pretty + + + align:start position:0% +terms of the biology we we have a pretty +good understanding of why this is + + align:start position:0% +good understanding of why this is + + + align:start position:0% +good understanding of why this is +happening so what's going on is that the + + align:start position:0% +happening so what's going on is that the + + + align:start position:0% +happening so what's going on is that the +outer hair cells are providing + + align:start position:0% +outer hair cells are providing + + + align:start position:0% +outer hair cells are providing +amplification of the frequencies kind of + + align:start position:0% +amplification of the frequencies kind of + + + align:start position:0% +amplification of the frequencies kind of +near the characteristic frequency of the + + align:start position:0% +near the characteristic frequency of the + + + align:start position:0% +near the characteristic frequency of the +nerve fiber I'm at low levels but not at + + align:start position:0% +nerve fiber I'm at low levels but not at + + + align:start position:0% +nerve fiber I'm at low levels but not at +high levels and so at high levels what + + align:start position:0% +high levels and so at high levels what + + + align:start position:0% +high levels and so at high levels what +you're seeing is just very broad kind of + + align:start position:0% +you're seeing is just very broad kind of + + + align:start position:0% +you're seeing is just very broad kind of +mechanical tuning but what really sort + + align:start position:0% +mechanical tuning but what really sort + + + align:start position:0% +mechanical tuning but what really sort +of remains unclear is what the + + align:start position:0% +of remains unclear is what the + + + align:start position:0% +of remains unclear is what the +consequences are of this RR for hearing + + align:start position:0% +consequences are of this RR for hearing + + + align:start position:0% +consequences are of this RR for hearing +and really how to think about it in + + align:start position:0% +and really how to think about it in + + + align:start position:0% +and really how to think about it in +computational terms so it's clear that + + align:start position:0% +computational terms so it's clear that + + + align:start position:0% +computational terms so it's clear that +that the linear filtering view is not + + align:start position:0% +that the linear filtering view is not + + + align:start position:0% +that the linear filtering view is not +exactly right and one of the kind of + + align:start position:0% +exactly right and one of the kind of + + + align:start position:0% +exactly right and one of the kind of +interesting things is that it's not like + + align:start position:0% +interesting things is that it's not like + + + align:start position:0% +interesting things is that it's not like +you get a lot worse at hearing when you + + align:start position:0% +you get a lot worse at hearing when you + + + align:start position:0% +you get a lot worse at hearing when you +go up to 75 or 85 dB alright in fact if + + align:start position:0% +go up to 75 or 85 dB alright in fact if + + + align:start position:0% +go up to 75 or 85 dB alright in fact if +anything most second physical phenomena + + align:start position:0% +anything most second physical phenomena + + + align:start position:0% +anything most second physical phenomena +actually are better and in some sense + + align:start position:0% +actually are better and in some sense + + + align:start position:0% +actually are better and in some sense +this phenomena as I said is related to + + align:start position:0% +this phenomena as I said is related to + + + align:start position:0% +this phenomena as I said is related to +this distinction between inner hair + + align:start position:0% +this distinction between inner hair + + + align:start position:0% +this distinction between inner hair +cells and outer Harris + + align:start position:0% +cells and outer Harris + + + align:start position:0% +cells and outer Harris +so the inner hair cells are the ones + + align:start position:0% +so the inner hair cells are the ones + + + align:start position:0% +so the inner hair cells are the ones +that actually are responsible for the + + align:start position:0% +that actually are responsible for the + + + align:start position:0% +that actually are responsible for the +transduction of sound energy and the + + align:start position:0% +transduction of sound energy and the + + + align:start position:0% +transduction of sound energy and the +outer hair cells we think of as part of + + align:start position:0% +outer hair cells we think of as part of + + + align:start position:0% +outer hair cells we think of as part of +a feedback system that amplifies the + + align:start position:0% +a feedback system that amplifies the + + + align:start position:0% +a feedback system that amplifies the +motion of the membrane and sharpens at + + align:start position:0% +motion of the membrane and sharpens at + + + align:start position:0% +motion of the membrane and sharpens at +the tuning and that amplification is is + + align:start position:0% +the tuning and that amplification is is + + + align:start position:0% +the tuning and that amplification is is +selective for frequencies at the + + align:start position:0% +selective for frequencies at the + + + align:start position:0% +selective for frequencies at the +characteristic frequency and really + + align:start position:0% +characteristic frequency and really + + + align:start position:0% +characteristic frequency and really +occurs at at very low levels okay so + + align:start position:0% +occurs at at very low levels okay so + + + align:start position:0% +occurs at at very low levels okay so +this is this is related to what honey + + align:start position:0% +this is this is related to what honey + + + align:start position:0% +this is this is related to what honey +was mentioning and the question that was + + align:start position:0% +was mentioning and the question that was + + + align:start position:0% +was mentioning and the question that was +asked earlier so there's this other + + align:start position:0% +asked earlier so there's this other + + + align:start position:0% +asked earlier so there's this other +important response property of the + + align:start position:0% +important response property of the + + + align:start position:0% +important response property of the +cochlea which is that for frequencies + + align:start position:0% +cochlea which is that for frequencies + + + align:start position:0% +cochlea which is that for frequencies +that are sufficiently low auditory nerve + + align:start position:0% +that are sufficiently low auditory nerve + + + align:start position:0% +that are sufficiently low auditory nerve +spikes are phase-locked to the stimulus + + align:start position:0% +spikes are phase-locked to the stimulus + + + align:start position:0% +spikes are phase-locked to the stimulus +and so what you're seeing here is a + + align:start position:0% +and so what you're seeing here is a + + + align:start position:0% +and so what you're seeing here is a +single trace of a recording from a nerve + + align:start position:0% +single trace of a recording from a nerve + + + align:start position:0% +single trace of a recording from a nerve +fiber that's up top and then at the + + align:start position:0% +fiber that's up top and then at the + + + align:start position:0% +fiber that's up top and then at the +bottom is the the stimulus that would be + + align:start position:0% +bottom is the the stimulus that would be + + + align:start position:0% +bottom is the the stimulus that would be +supplied to the year which is just a + + align:start position:0% +supplied to the year which is just a + + + align:start position:0% +supplied to the year which is just a +pure tone of some particular frequency + + align:start position:0% +pure tone of some particular frequency + + + align:start position:0% +pure tone of some particular frequency +and so you can note like two interesting + + align:start position:0% +and so you can note like two interesting + + + align:start position:0% +and so you can note like two interesting +things about about this response the + + align:start position:0% +things about about this response the + + + align:start position:0% +things about about this response the +first is that the spikes are + + align:start position:0% +first is that the spikes are + + + align:start position:0% +first is that the spikes are +intermittent right you don't get a spike + + align:start position:0% +intermittent right you don't get a spike + + + align:start position:0% +intermittent right you don't get a spike +at every cycle of the frequency but when + + align:start position:0% +at every cycle of the frequency but when + + + align:start position:0% +at every cycle of the frequency but when +the spikes occur sorry + + align:start position:0% +the spikes occur sorry + + + align:start position:0% +the spikes occur sorry +they occur at a particular phase + + align:start position:0% +they occur at a particular phase + + + align:start position:0% +they occur at a particular phase +relative to the the stimulus right so + + align:start position:0% +relative to the the stimulus right so + + + align:start position:0% +relative to the the stimulus right so +they're kind of just a little bit behind + + align:start position:0% +they're kind of just a little bit behind + + + align:start position:0% +they're kind of just a little bit behind +the the peak of the waveform in this + + align:start position:0% +the the peak of the waveform in this + + + align:start position:0% +the the peak of the waveform in this +particular case right in every single + + align:start position:0% +particular case right in every single + + + align:start position:0% +particular case right in every single +case alright so this is known as phase + + align:start position:0% +case alright so this is known as phase + + + align:start position:0% +case alright so this is known as phase +locking and it's it's a pretty robust + + align:start position:0% +locking and it's it's a pretty robust + + + align:start position:0% +locking and it's it's a pretty robust +phenomena for frequencies under a few + + align:start position:0% +phenomena for frequencies under a few + + + align:start position:0% +phenomena for frequencies under a few +kilohertz and this is in non-human + + align:start position:0% +kilohertz and this is in non-human + + + align:start position:0% +kilohertz and this is in non-human +animals there's no measurements of the + + align:start position:0% +animals there's no measurements of the + + + align:start position:0% +animals there's no measurements of the +auditory nerve in humans because it's to + + align:start position:0% +auditory nerve in humans because it's to + + + align:start position:0% +auditory nerve in humans because it's to +do so it's highly invasive and just + + align:start position:0% +do so it's highly invasive and just + + + align:start position:0% +do so it's highly invasive and just +nobody's ever ever done it and probably + + align:start position:0% +nobody's ever ever done it and probably + + + align:start position:0% +nobody's ever ever done it and probably +won't ever and so this is another + + align:start position:0% +won't ever and so this is another + + + align:start position:0% +won't ever and so this is another +example the same thing where again this + + align:start position:0% +example the same thing where again this + + + align:start position:0% +example the same thing where again this +is sort of the input waveform and this + + align:start position:0% +is sort of the input waveform and this + + + align:start position:0% +is sort of the input waveform and this +is a bunch of different recordings of + + align:start position:0% +is a bunch of different recordings of + + + align:start position:0% +is a bunch of different recordings of +the same nerve fibre that are time + + align:start position:0% +the same nerve fibre that are time + + + align:start position:0% +the same nerve fibre that are time +aligned and so you can see the spikes + + align:start position:0% +aligned and so you can see the spikes + + + align:start position:0% +aligned and so you can see the spikes +always occur at some particular at a + + align:start position:0% +always occur at some particular at a + + + align:start position:0% +always occur at some particular at a +particular region of face space so + + align:start position:0% +particular region of face space so + + + align:start position:0% +particular region of face space so +they're not uniformly distributed and + + align:start position:0% +they're not uniformly distributed and + + + align:start position:0% +they're not uniformly distributed and +the figure here on the right shows that + + align:start position:0% +the figure here on the right shows that + + + align:start position:0% +the figure here on the right shows that +this phenomenon deteriorates at very + + align:start position:0% +this phenomenon deteriorates at very + + + align:start position:0% +this phenomenon deteriorates at very +high frequencies so this is the plot of + + align:start position:0% +high frequencies so this is the plot of + + + align:start position:0% +high frequencies so this is the plot of +the strength of the phase-locking as a + + align:start position:0% +the strength of the phase-locking as a + + + align:start position:0% +the strength of the phase-locking as a +function of frequency and so you know up + + align:start position:0% +function of frequency and so you know up + + + align:start position:0% +function of frequency and so you know up +to a kilohertz it's quite strong and + + align:start position:0% +to a kilohertz it's quite strong and + + + align:start position:0% +to a kilohertz it's quite strong and +then it starts to kind of drop off and + + align:start position:0% +then it starts to kind of drop off and + + + align:start position:0% +then it starts to kind of drop off and +above about four K there's there's not + + align:start position:0% +above about four K there's there's not + + + align:start position:0% +above about four K there's there's not +really a whole lot okay and so I'm what + + align:start position:0% +really a whole lot okay and so I'm what + + + align:start position:0% +really a whole lot okay and so I'm what +do as I said one of the other salient + + align:start position:0% +do as I said one of the other salient + + + align:start position:0% +do as I said one of the other salient +things is that the fibers don't fire + + align:start position:0% +things is that the fibers don't fire + + + align:start position:0% +things is that the fibers don't fire +with every site + + align:start position:0% +with every site + + + align:start position:0% +with every site +of the stimulus um and one of the one + + align:start position:0% +of the stimulus um and one of the one + + + align:start position:0% +of the stimulus um and one of the one +interesting fact about the the ear is + + align:start position:0% +interesting fact about the the ear is + + + align:start position:0% +interesting fact about the the ear is +that there are a whole bunch of auditory + + align:start position:0% +that there are a whole bunch of auditory + + + align:start position:0% +that there are a whole bunch of auditory +nerve fibers for every inner hair cell + + align:start position:0% +nerve fibers for every inner hair cell + + + align:start position:0% +nerve fibers for every inner hair cell +and people think that one of the reasons + + align:start position:0% +and people think that one of the reasons + + + align:start position:0% +and people think that one of the reasons +for that is for this because of this + + align:start position:0% +for that is for this because of this + + + align:start position:0% +for that is for this because of this +phenomena here and this is probably due + + align:start position:0% +phenomena here and this is probably due + + + align:start position:0% +phenomena here and this is probably due +to things like like refractory periods + + align:start position:0% +to things like like refractory periods + + + align:start position:0% +to things like like refractory periods +and stuff right so but if you have a + + align:start position:0% +and stuff right so but if you have a + + + align:start position:0% +and stuff right so but if you have a +whole bunch of nerve fibers synapsing + + align:start position:0% +whole bunch of nerve fibers synapsing + + + align:start position:0% +whole bunch of nerve fibers synapsing +under the same hair cell the idea is + + align:start position:0% +under the same hair cell the idea is + + + align:start position:0% +under the same hair cell the idea is +that we'll collectively you know you'll + + align:start position:0% +that we'll collectively you know you'll + + + align:start position:0% +that we'll collectively you know you'll +get you'll get spikes at every single + + align:start position:0% +get you'll get spikes at every single + + + align:start position:0% +get you'll get spikes at every single +cycle so here's just some interesting + + align:start position:0% +cycle so here's just some interesting + + + align:start position:0% +cycle so here's just some interesting +numbers so the number of inner hair + + align:start position:0% +numbers so the number of inner hair + + + align:start position:0% +numbers so the number of inner hair +cells per year in human is estimated to + + align:start position:0% +cells per year in human is estimated to + + + align:start position:0% +cells per year in human is estimated to +be about 3,500 there's about four times + + align:start position:0% +be about 3,500 there's about four times + + + align:start position:0% +be about 3,500 there's about four times +as many outer hair cells or roughly + + align:start position:0% +as many outer hair cells or roughly + + + align:start position:0% +as many outer hair cells or roughly +12,000 but that's that's the key number + + align:start position:0% +12,000 but that's that's the key number + + + align:start position:0% +12,000 but that's that's the key number +here so coming out of every year are + + align:start position:0% +here so coming out of every year are + + + align:start position:0% +here so coming out of every year are +thirty a roughly thirty thousand + + align:start position:0% +thirty a roughly thirty thousand + + + align:start position:0% +thirty a roughly thirty thousand +auditory nerve fiber so there's about + + align:start position:0% +auditory nerve fiber so there's about + + + align:start position:0% +auditory nerve fiber so there's about +ten times as auditory ten times as many + + align:start position:0% +ten times as auditory ten times as many + + + align:start position:0% +ten times as auditory ten times as many +auditory nerve fibers as there are inner + + align:start position:0% +auditory nerve fibers as there are inner + + + align:start position:0% +auditory nerve fibers as there are inner +hair cells and it's interesting to + + align:start position:0% +hair cells and it's interesting to + + + align:start position:0% +hair cells and it's interesting to +compare those numbers to what you see in + + align:start position:0% +compare those numbers to what you see in + + + align:start position:0% +compare those numbers to what you see in +the eye so these are estimates from a + + align:start position:0% +the eye so these are estimates from a + + + align:start position:0% +the eye so these are estimates from a +from a few years ago from the I of + + align:start position:0% +from a few years ago from the I of + + + align:start position:0% +from a few years ago from the I of +roughly five million cones per eye lots + + align:start position:0% +roughly five million cones per eye lots + + + align:start position:0% +roughly five million cones per eye lots +of rods obviously but then you go to the + + align:start position:0% +of rods obviously but then you go to the + + + align:start position:0% +of rods obviously but then you go to the +optic nerve and the number of nerve + + align:start position:0% +optic nerve and the number of nerve + + + align:start position:0% +optic nerve and the number of nerve +optic nerve fibers is actually + + align:start position:0% +optic nerve fibers is actually + + + align:start position:0% +optic nerve fibers is actually +substantially less than the number of + + align:start position:0% +substantially less than the number of + + + align:start position:0% +substantially less than the number of +cones so one and a half million so + + align:start position:0% +cones so one and a half million so + + + align:start position:0% +cones so one and a half million so +there's this big compression that + + align:start position:0% +there's this big compression that + + + align:start position:0% +there's this big compression that +happens when you go into the auditory + + align:start position:0% +happens when you go into the auditory + + + align:start position:0% +happens when you go into the auditory +nerve sorry in the optic nerve whereas + + align:start position:0% +nerve sorry in the optic nerve whereas + + + align:start position:0% +nerve sorry in the optic nerve whereas +there's an expansion that happens in the + + align:start position:0% +there's an expansion that happens in the + + + align:start position:0% +there's an expansion that happens in the +auditory nerves and just for fun these + + align:start position:0% +auditory nerves and just for fun these + + + align:start position:0% +auditory nerves and just for fun these +are these are rough estimates of what + + align:start position:0% +are these are rough estimates of what + + + align:start position:0% +are these are rough estimates of what +you find in the cortex so I mean primary + + align:start position:0% +you find in the cortex so I mean primary + + + align:start position:0% +you find in the cortex so I mean primary +auditory cortex this is a very crude + + align:start position:0% +auditory cortex this is a very crude + + + align:start position:0% +auditory cortex this is a very crude +estimate I got from someone a couple + + align:start position:0% +estimate I got from someone a couple + + + align:start position:0% +estimate I got from someone a couple +days ago of sixty million neurons per + + align:start position:0% +days ago of sixty million neurons per + + + align:start position:0% +days ago of sixty million neurons per +hemisphere and in v1 that the estimate + + align:start position:0% +hemisphere and in v1 that the estimate + + + align:start position:0% +hemisphere and in v1 that the estimate +that I was able to find was a hundred + + align:start position:0% +that I was able to find was a hundred + + + align:start position:0% +that I was able to find was a hundred +and forty million so these are sort of + + align:start position:0% +and forty million so these are sort of + + + align:start position:0% +and forty million so these are sort of +roughly the same order of magnitude + + align:start position:0% +roughly the same order of magnitude + + + align:start position:0% +roughly the same order of magnitude +although it's it's obviously smaller in + + align:start position:0% +although it's it's obviously smaller in + + + align:start position:0% +although it's it's obviously smaller in +the auditory system but there is this + + align:start position:0% +the auditory system but there is this + + + align:start position:0% +the auditory system but there is this +something very different happening here + + align:start position:0% +something very different happening here + + + align:start position:0% +something very different happening here +in terms of the way the informations + + align:start position:0% +in terms of the way the informations + + + align:start position:0% +in terms of the way the informations +getting piped from the periphery onto + + align:start position:0% +getting piped from the periphery onto + + + align:start position:0% +getting piped from the periphery onto +the brain and one one reason for this + + align:start position:0% +the brain and one one reason for this + + + align:start position:0% +the brain and one one reason for this +might just be the fact that this + + align:start position:0% +might just be the fact that this + + + align:start position:0% +might just be the fact that this +phenomena here where the spiking in an + + align:start position:0% +phenomena here where the spiking in an + + + align:start position:0% +phenomena here where the spiking in an +individual auditory nerve fiber is going + + align:start position:0% +individual auditory nerve fiber is going + + + align:start position:0% +individual auditory nerve fiber is going +to be intermittent because the signals + + align:start position:0% +to be intermittent because the signals + + + align:start position:0% +to be intermittent because the signals +that it has to convey are very very fast + + align:start position:0% +that it has to convey are very very fast + + + align:start position:0% +that it has to convey are very very fast +and so you kind of have them you have to + + align:start position:0% +and so you kind of have them you have to + + + align:start position:0% +and so you kind of have them you have to +molt + + align:start position:0% +molt + + + align:start position:0% +molt +box in this way alright so the big + + align:start position:0% +box in this way alright so the big + + + align:start position:0% +box in this way alright so the big +picture here is that if you look at the + + align:start position:0% +picture here is that if you look at the + + + align:start position:0% +picture here is that if you look at the +the output of the cochlea um they're in + + align:start position:0% +the output of the cochlea um they're in + + + align:start position:0% +the output of the cochlea um they're in +some sense two cues to the frequencies + + align:start position:0% +some sense two cues to the frequencies + + + align:start position:0% +some sense two cues to the frequencies +that are contained in a sound so there's + + align:start position:0% +that are contained in a sound so there's + + + align:start position:0% +that are contained in a sound so there's +what is often referred to as the place + + align:start position:0% +what is often referred to as the place + + + align:start position:0% +what is often referred to as the place +of excitation in the cochlea these are + + align:start position:0% +of excitation in the cochlea these are + + + align:start position:0% +of excitation in the cochlea these are +the nerve fibers that are firing the + + align:start position:0% +the nerve fibers that are firing the + + + align:start position:0% +the nerve fibers that are firing the +most + + align:start position:0% +most + + + align:start position:0% +most +according to like a rate code and + + align:start position:0% +according to like a rate code and + + + align:start position:0% +according to like a rate code and +there's also the timing of the spikes + + align:start position:0% +there's also the timing of the spikes + + + align:start position:0% +there's also the timing of the spikes +that are that are fired in the sense + + align:start position:0% +that are that are fired in the sense + + + align:start position:0% +that are that are fired in the sense +that for frequencies below about four K + + align:start position:0% +that for frequencies below about four K + + + align:start position:0% +that for frequencies below about four K +you get phase-locking + + align:start position:0% +you get phase-locking + + + align:start position:0% +you get phase-locking +and so the interspike intervals will be + + align:start position:0% +and so the interspike intervals will be + + + align:start position:0% +and so the interspike intervals will be +stereotyped depending on the frequencies + + align:start position:0% +stereotyped depending on the frequencies + + + align:start position:0% +stereotyped depending on the frequencies +that come in and so it's one of these + + align:start position:0% +that come in and so it's one of these + + + align:start position:0% +that come in and so it's one of these +sort of I still find this kind of + + align:start position:0% +sort of I still find this kind of + + + align:start position:0% +sort of I still find this kind of +remarkable when I sort of step back and + + align:start position:0% +remarkable when I sort of step back and + + + align:start position:0% +remarkable when I sort of step back and +sort of think about the state of things + + align:start position:0% +sort of think about the state of things + + + align:start position:0% +sort of think about the state of things +that you know this is a very basic + + align:start position:0% +that you know this is a very basic + + + align:start position:0% +that you know this is a very basic +question about neural coding at the very + + align:start position:0% +question about neural coding at the very + + + align:start position:0% +question about neural coding at the very +front end of the system and the + + align:start position:0% +front end of the system and the + + + align:start position:0% +front end of the system and the +importance of these things really + + align:start position:0% +importance of these things really + + + align:start position:0% +importance of these things really +remains unresolved so people have been + + align:start position:0% +remains unresolved so people have been + + + align:start position:0% +remains unresolved so people have been +debating this for a really long time and + + align:start position:0% +debating this for a really long time and + + + align:start position:0% +debating this for a really long time and +we still don't really have very clear + + align:start position:0% +we still don't really have very clear + + + align:start position:0% +we still don't really have very clear +answers to the extent to which the spike + + align:start position:0% +answers to the extent to which the spike + + + align:start position:0% +answers to the extent to which the spike +timing really is critical for inferring + + align:start position:0% +timing really is critical for inferring + + + align:start position:0% +timing really is critical for inferring +frequency so I'm gonna play you a demo + + align:start position:0% +frequency so I'm gonna play you a demo + + + align:start position:0% +frequency so I'm gonna play you a demo +that provides it's an example of some of + + align:start position:0% +that provides it's an example of some of + + + align:start position:0% +that provides it's an example of some of +the circumstantial evidence for the + + align:start position:0% +the circumstantial evidence for the + + + align:start position:0% +the circumstantial evidence for the +importance of phase locking and broadly + + align:start position:0% +importance of phase locking and broadly + + + align:start position:0% +importance of phase locking and broadly +speaking the evidence for the importance + + align:start position:0% +speaking the evidence for the importance + + + align:start position:0% +speaking the evidence for the importance +of phase locking in humans comes from + + align:start position:0% +of phase locking in humans comes from + + + align:start position:0% +of phase locking in humans comes from +the fact that the perception of + + align:start position:0% +the fact that the perception of + + + align:start position:0% +the fact that the perception of +frequency seems to change once you kind + + align:start position:0% +frequency seems to change once you kind + + + align:start position:0% +frequency seems to change once you kind +of get above about four K so for + + align:start position:0% +of get above about four K so for + + + align:start position:0% +of get above about four K so for +instance if you if you give people a + + align:start position:0% +instance if you if you give people a + + + align:start position:0% +instance if you if you give people a +musical interval Dada and then you ask + + align:start position:0% +musical interval Dada and then you ask + + + align:start position:0% +musical interval Dada and then you ask +them to replicate that and say different + + align:start position:0% +them to replicate that and say different + + + align:start position:0% +them to replicate that and say different +octaves people can do that pretty well + + align:start position:0% +octaves people can do that pretty well + + + align:start position:0% +octaves people can do that pretty well +um until you get to about four K and + + align:start position:0% +um until you get to about four K and + + + align:start position:0% +um until you get to about four K and +above four K they just break down they + + align:start position:0% +above four K they just break down they + + + align:start position:0% +above four K they just break down they +become very very highly variable and + + align:start position:0% +become very very highly variable and + + + align:start position:0% +become very very highly variable and +that's evident in this demonstration so + + align:start position:0% +that's evident in this demonstration so + + + align:start position:0% +that's evident in this demonstration so +what what you're gonna hear in this demo + + align:start position:0% +what what you're gonna hear in this demo + + + align:start position:0% +what what you're gonna hear in this demo +and this is this is a demonstration that + + align:start position:0% +and this is this is a demonstration that + + + align:start position:0% +and this is this is a demonstration that +I got from from Peter Carey on a thanks + + align:start position:0% +I got from from Peter Carey on a thanks + + + align:start position:0% +I got from from Peter Carey on a thanks +to him it's a melody that is probably + + align:start position:0% +to him it's a melody that is probably + + + align:start position:0% +to him it's a melody that is probably +familiar to all of you on this being + + align:start position:0% +familiar to all of you on this being + + + align:start position:0% +familiar to all of you on this being +played with pure tones and it will be + + align:start position:0% +played with pure tones and it will be + + + align:start position:0% +played with pure tones and it will be +played repeatedly transposed from very + + align:start position:0% +played repeatedly transposed from very + + + align:start position:0% +played repeatedly transposed from very +high frequencies down in I don't know + + align:start position:0% +high frequencies down in I don't know + + + align:start position:0% +high frequencies down in I don't know +like third octaves or something to lower + + align:start position:0% +like third octaves or something to lower + + + align:start position:0% +like third octaves or something to lower +and lower frequencies and what you will + + align:start position:0% +and lower frequencies and what you will + + + align:start position:0% +and lower frequencies and what you will +experience um is that when you hear the + + align:start position:0% +experience um is that when you hear the + + + align:start position:0% +experience um is that when you hear the +very high frequencies well a they'll be + + align:start position:0% +very high frequencies well a they'll be + + + align:start position:0% +very high frequencies well a they'll be +kind of annoying so just bear with me + + align:start position:0% +kind of annoying so just bear with me + + + align:start position:0% +kind of annoying so just bear with me +but well the melody will also be + + align:start position:0% +but well the melody will also be + + + align:start position:0% +but well the melody will also be +unrecognizable and so it'll only be when + + align:start position:0% +unrecognizable and so it'll only be when + + + align:start position:0% +unrecognizable and so it'll only be when +you get below a certain point that + + align:start position:0% +you get below a certain point that + + + align:start position:0% +you get below a certain point that +you'll say AHA I know what that is + + align:start position:0% +you'll say AHA I know what that is + + + align:start position:0% +you'll say AHA I know what that is +and again we can um we can look at this + + align:start position:0% +and again we can um we can look at this + + + align:start position:0% +and again we can um we can look at this +in our spectrogram which is still going + + align:start position:0% +in our spectrogram which is still going + + + align:start position:0% +in our spectrogram which is still going +and you can actually see what's going on + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +okay so by the end hopefully everybody + + align:start position:0% +okay so by the end hopefully everybody + + + align:start position:0% +okay so by the end hopefully everybody +recognize what that what that was so + + align:start position:0% +recognize what that what that was so + + + align:start position:0% +recognize what that what that was so +let's just talk briefly about how these + + align:start position:0% +let's just talk briefly about how these + + + align:start position:0% +let's just talk briefly about how these +sub bands that we were talking about + + align:start position:0% +sub bands that we were talking about + + + align:start position:0% +sub bands that we were talking about +earlier relate to what we see in the + + align:start position:0% +earlier relate to what we see in the + + + align:start position:0% +earlier relate to what we see in the +auditory nerve and again this this + + align:start position:0% +auditory nerve and again this this + + + align:start position:0% +auditory nerve and again this this +relates to someone of one of the earlier + + align:start position:0% +relates to someone of one of the earlier + + + align:start position:0% +relates to someone of one of the earlier +questions so the sub band is this blue + + align:start position:0% +questions so the sub band is this blue + + + align:start position:0% +questions so the sub band is this blue +signal here right this is the output of + + align:start position:0% +signal here right this is the output of + + + align:start position:0% +signal here right this is the output of +a linear filter and one of the ways to + + align:start position:0% +a linear filter and one of the ways to + + + align:start position:0% +a linear filter and one of the ways to +characterize a sub band like this that + + align:start position:0% +characterize a sub band like this that + + + align:start position:0% +characterize a sub band like this that +van limited is by the instantaneous + + align:start position:0% +van limited is by the instantaneous + + + align:start position:0% +van limited is by the instantaneous +amplitude in the instantaneous phase and + + align:start position:0% +amplitude in the instantaneous phase and + + + align:start position:0% +amplitude in the instantaneous phase and +these things Loosli can be mapped on to + + align:start position:0% +these things Loosli can be mapped on to + + + align:start position:0% +these things Loosli can be mapped on to +rate a spike rate and Spike timing in + + align:start position:0% +rate a spike rate and Spike timing in + + + align:start position:0% +rate a spike rate and Spike timing in +the auditory nerve so again this is an + + align:start position:0% +the auditory nerve so again this is an + + + align:start position:0% +the auditory nerve so again this is an +example of what of the phase locking + + align:start position:0% +example of what of the phase locking + + + align:start position:0% +example of what of the phase locking +that you see where the spikes get fired + + align:start position:0% +that you see where the spikes get fired + + + align:start position:0% +that you see where the spikes get fired +at some particular point in the waveform + + align:start position:0% +at some particular point in the waveform + + + align:start position:0% +at some particular point in the waveform +and so if you observe this well you know + + align:start position:0% +and so if you observe this well you know + + + align:start position:0% +and so if you observe this well you know +something about exactly what's happening + + align:start position:0% +something about exactly what's happening + + + align:start position:0% +something about exactly what's happening +in the waveform namely you you know that + + align:start position:0% +in the waveform namely you you know that + + + align:start position:0% +in the waveform namely you you know that +there's there's energy there and there + + align:start position:0% +there's there's energy there and there + + + align:start position:0% +there's there's energy there and there +in the stimulus because you're getting + + align:start position:0% +in the stimulus because you're getting + + + align:start position:0% +in the stimulus because you're getting +spikes but you also actually know the + + align:start position:0% +spikes but you also actually know the + + + align:start position:0% +spikes but you also actually know the +phase of the wave form because the the + + align:start position:0% +phase of the wave form because the the + + + align:start position:0% +phase of the wave form because the the +spikes are happening in particular + + align:start position:0% +spikes are happening in particular + + + align:start position:0% +spikes are happening in particular +places and so the this issue of phase is + + align:start position:0% +places and so the this issue of phase is + + + align:start position:0% +places and so the this issue of phase is +sort of a tricky one because it's often + + align:start position:0% +sort of a tricky one because it's often + + + align:start position:0% +sort of a tricky one because it's often +not something that we really know how to + + align:start position:0% +not something that we really know how to + + + align:start position:0% +not something that we really know how to +deal with and so and it's also the it's + + align:start position:0% +deal with and so and it's also the it's + + + align:start position:0% +deal with and so and it's also the it's +just empirically the case that a lot of + + align:start position:0% +just empirically the case that a lot of + + + align:start position:0% +just empirically the case that a lot of +the information in sound um is carried + + align:start position:0% +the information in sound um is carried + + + align:start position:0% +the information in sound um is carried +by the way that frequencies are + + align:start position:0% +by the way that frequencies are + + + align:start position:0% +by the way that frequencies are +modulated over time as measured by the + + align:start position:0% +modulated over time as measured by the + + + align:start position:0% +modulated over time as measured by the +instantaneous amplitude in a sub man and + + align:start position:0% +instantaneous amplitude in a sub man and + + + align:start position:0% +instantaneous amplitude in a sub man and +so the instantaneous amplitude is + + align:start position:0% +so the instantaneous amplitude is + + + align:start position:0% +so the instantaneous amplitude is +measured by a quantity called the + + align:start position:0% +measured by a quantity called the + + + align:start position:0% +measured by a quantity called the +envelopes that's the red curve here that + + align:start position:0% +envelopes that's the red curve here that + + + align:start position:0% +envelopes that's the red curve here that +shows how the amplitude waxes and wanes + + align:start position:0% +shows how the amplitude waxes and wanes + + + align:start position:0% +shows how the amplitude waxes and wanes +and the envelope is easy to extract from + + align:start position:0% +and the envelope is easy to extract from + + + align:start position:0% +and the envelope is easy to extract from +auditory nerve response just by + + align:start position:0% +auditory nerve response just by + + + align:start position:0% +auditory nerve response just by +computing the firing rate over local + + align:start position:0% +computing the firing rate over local + + + align:start position:0% +computing the firing rate over local +time windows and in signal processing + + align:start position:0% +time windows and in signal processing + + + align:start position:0% +time windows and in signal processing +terms we typically extract it with + + align:start position:0% +terms we typically extract it with + + + align:start position:0% +terms we typically extract it with +something called the Hilbert transform + + align:start position:0% +something called the Hilbert transform + + + align:start position:0% +something called the Hilbert transform +by taking the magnitude of the analytic + + align:start position:0% +by taking the magnitude of the analytic + + + align:start position:0% +by taking the magnitude of the analytic +signal so it's a pretty easy thing to + + align:start position:0% +signal so it's a pretty easy thing to + + + align:start position:0% +signal so it's a pretty easy thing to +pull out like in MATLAB for instance and + + align:start position:0% +pull out like in MATLAB for instance and + + + align:start position:0% +pull out like in MATLAB for instance and +so just to again to relate this to stuff + + align:start position:0% +so just to again to relate this to stuff + + + align:start position:0% +so just to again to relate this to stuff +that may be more familiar on the + + align:start position:0% +that may be more familiar on the + + + align:start position:0% +that may be more familiar on the +spectrogram is that people have probably + + align:start position:0% +spectrogram is that people have probably + + + align:start position:0% +spectrogram is that people have probably +seen in the past again these are + + align:start position:0% +seen in the past again these are + + + align:start position:0% +seen in the past again these are +pictures that take a sound waveform and + + align:start position:0% +pictures that take a sound waveform and + + + align:start position:0% +pictures that take a sound waveform and +plot the frequency content over time one + + align:start position:0% +plot the frequency content over time one + + + align:start position:0% +plot the frequency content over time one +way to get a spectrogram is to have a + + align:start position:0% +way to get a spectrogram is to have a + + + align:start position:0% +way to get a spectrogram is to have a +bank of band pass filters to get a bunch + + align:start position:0% +bank of band pass filters to get a bunch + + + align:start position:0% +bank of band pass filters to get a bunch +of sub bands and then to extract the + + align:start position:0% +of sub bands and then to extract the + + + align:start position:0% +of sub bands and then to extract the +envelope of each sub band and just plot + + align:start position:0% +envelope of each sub band and just plot + + + align:start position:0% +envelope of each sub band and just plot +the envelope and greyscale horizontally + + align:start position:0% +the envelope and greyscale horizontally + + + align:start position:0% +the envelope and greyscale horizontally +alright so a stripe through this picture + + align:start position:0% +alright so a stripe through this picture + + + align:start position:0% +alright so a stripe through this picture +is the envelope in grayscale so it's + + align:start position:0% +is the envelope in grayscale so it's + + + align:start position:0% +is the envelope in grayscale so it's +black in the point the places where the + + align:start position:0% +black in the point the places where the + + + align:start position:0% +black in the point the places where the +where the + + align:start position:0% +where the + + + align:start position:0% +where the +energy is high and white in the places + + align:start position:0% +energy is high and white in the places + + + align:start position:0% +energy is high and white in the places +where it's low and so this is a + + align:start position:0% +where it's low and so this is a + + + align:start position:0% +where it's low and so this is a +spectrogram of this all right that's + + align:start position:0% +spectrogram of this all right that's + + + align:start position:0% +spectrogram of this all right that's +what you just heard just a drum break + + align:start position:0% +what you just heard just a drum break + + + align:start position:0% +what you just heard just a drum break +and you can probably see that there's + + align:start position:0% +and you can probably see that there's + + + align:start position:0% +and you can probably see that there's +sort of events in the spectrum that + + align:start position:0% +sort of events in the spectrum that + + + align:start position:0% +sort of events in the spectrum that +correspond to things like the drumbeats + + align:start position:0% +correspond to things like the drumbeats + + + align:start position:0% +correspond to things like the drumbeats +now one of the things writing things + + align:start position:0% +now one of the things writing things + + + align:start position:0% +now one of the things writing things +about this picture is it looks like a + + align:start position:0% +about this picture is it looks like a + + + align:start position:0% +about this picture is it looks like a +mess right I mean you you know you + + align:start position:0% +mess right I mean you you know you + + + align:start position:0% +mess right I mean you you know you +listen to that drum break and you know + + align:start position:0% +listen to that drum break and you know + + + align:start position:0% +listen to that drum break and you know +it sounded kind of crisp and clean and + + align:start position:0% +it sounded kind of crisp and clean and + + + align:start position:0% +it sounded kind of crisp and clean and +when you actually look at the the + + align:start position:0% +when you actually look at the the + + + align:start position:0% +when you actually look at the the +instantaneous amplitude in each of the + + align:start position:0% +instantaneous amplitude in each of the + + + align:start position:0% +instantaneous amplitude in each of the +sub bands it just sort of looks messy + + align:start position:0% +sub bands it just sort of looks messy + + + align:start position:0% +sub bands it just sort of looks messy +and noisy but one interesting fact is + + align:start position:0% +and noisy but one interesting fact is + + + align:start position:0% +and noisy but one interesting fact is +that this picture for most signals + + align:start position:0% +that this picture for most signals + + + align:start position:0% +that this picture for most signals +captures all of the information that + + align:start position:0% +captures all of the information that + + + align:start position:0% +captures all of the information that +matters perceptually in the following + + align:start position:0% +matters perceptually in the following + + + align:start position:0% +matters perceptually in the following +sense that if you you have some sound + + align:start position:0% +sense that if you you have some sound + + + align:start position:0% +sense that if you you have some sound +signal and you let me generate this + + align:start position:0% +signal and you let me generate this + + + align:start position:0% +signal and you let me generate this +picture and all you let me keep is that + + align:start position:0% +picture and all you let me keep is that + + + align:start position:0% +picture and all you let me keep is that +picture alright we throw out the + + align:start position:0% +picture alright we throw out the + + + align:start position:0% +picture alright we throw out the +original sound waveform from that + + align:start position:0% +original sound waveform from that + + + align:start position:0% +original sound waveform from that +picture I can generate a sound signal + + align:start position:0% +picture I can generate a sound signal + + + align:start position:0% +picture I can generate a sound signal +that to you will sound just like the + + align:start position:0% +that to you will sound just like the + + + align:start position:0% +that to you will sound just like the +original alright and in fact I've done + + align:start position:0% +original alright and in fact I've done + + + align:start position:0% +original alright and in fact I've done +this and here's a reconstruction from + + align:start position:0% +this and here's a reconstruction from + + + align:start position:0% +this and here's a reconstruction from +that picture here's the original + + align:start position:0% +that picture here's the original + + + align:start position:0% +that picture here's the original +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +it sound exactly the same okay and so + + align:start position:0% +it sound exactly the same okay and so + + + align:start position:0% +it sound exactly the same okay and so +the the and I'll tell you in a second + + align:start position:0% +the the and I'll tell you in a second + + + align:start position:0% +the the and I'll tell you in a second +how we do this but the the the fact that + + align:start position:0% +how we do this but the the the fact that + + + align:start position:0% +how we do this but the the the fact that +this picture looks messy and noisy is I + + align:start position:0% +this picture looks messy and noisy is I + + + align:start position:0% +this picture looks messy and noisy is I +think mostly just due to the fact that + + align:start position:0% +think mostly just due to the fact that + + + align:start position:0% +think mostly just due to the fact that +your brain is not used to getting the + + align:start position:0% +your brain is not used to getting the + + + align:start position:0% +your brain is not used to getting the +sensory input in this format right + + align:start position:0% +sensory input in this format right + + + align:start position:0% +sensory input in this format right +you're used to hearing it as sound + + align:start position:0% +you're used to hearing it as sound + + + align:start position:0% +you're used to hearing it as sound +alright and so your visual system is + + align:start position:0% +alright and so your visual system is + + + align:start position:0% +alright and so your visual system is +actually not you know optimally designed + + align:start position:0% +actually not you know optimally designed + + + align:start position:0% +actually not you know optimally designed +to interpret to interpret a spectrogram + + align:start position:0% +to interpret to interpret a spectrogram + + + align:start position:0% +to interpret to interpret a spectrogram +I want to just briefly explain how you + + align:start position:0% +I want to just briefly explain how you + + + align:start position:0% +I want to just briefly explain how you +take this picture and generate a sound + + align:start position:0% +take this picture and generate a sound + + + align:start position:0% +take this picture and generate a sound +signal this is sort of a useful thing to + + align:start position:0% +signal this is sort of a useful thing to + + + align:start position:0% +signal this is sort of a useful thing to +understand and it'll become relevant a + + align:start position:0% +understand and it'll become relevant a + + + align:start position:0% +understand and it'll become relevant a +little bit later so the the general game + + align:start position:0% +little bit later so the the general game + + + align:start position:0% +little bit later so the the general game +that we play here is you hand me this + + align:start position:0% +that we play here is you hand me this + + + align:start position:0% +that we play here is you hand me this +picture right and I want to synthesize a + + align:start position:0% +picture right and I want to synthesize a + + + align:start position:0% +picture right and I want to synthesize a +signal and so usually what we do is we + + align:start position:0% +signal and so usually what we do is we + + + align:start position:0% +signal and so usually what we do is we +start out with a noise signal and we + + align:start position:0% +start out with a noise signal and we + + + align:start position:0% +start out with a noise signal and we +transform that noise signal until it's + + align:start position:0% +transform that noise signal until it's + + + align:start position:0% +transform that noise signal until it's +in kind of the right representation so + + align:start position:0% +in kind of the right representation so + + + align:start position:0% +in kind of the right representation so +we split it up into its sub bands and + + align:start position:0% +we split it up into its sub bands and + + + align:start position:0% +we split it up into its sub bands and +then we'll replace the envelopes of the + + align:start position:0% +then we'll replace the envelopes of the + + + align:start position:0% +then we'll replace the envelopes of the +noise sub bands by the envelopes from + + align:start position:0% +noise sub bands by the envelopes from + + + align:start position:0% +noise sub bands by the envelopes from +this picture okay and so the way that we + + align:start position:0% +this picture okay and so the way that we + + + align:start position:0% +this picture okay and so the way that we +do that is we measure the envelope of + + align:start position:0% +do that is we measure the envelope of + + + align:start position:0% +do that is we measure the envelope of +each noise sub man we divide it out and + + align:start position:0% +each noise sub man we divide it out and + + + align:start position:0% +each noise sub man we divide it out and +then we multiply by the envelope of the + + align:start position:0% +then we multiply by the envelope of the + + + align:start position:0% +then we multiply by the envelope of the +thing that we want and that gives us new + + align:start position:0% +thing that we want and that gives us new + + + align:start position:0% +thing that we want and that gives us new +sub bands and we then add those up and + + align:start position:0% +sub bands and we then add those up and + + + align:start position:0% +sub bands and we then add those up and +we get a new sound signal and for + + align:start position:0% +we get a new sound signal and for + + + align:start position:0% +we get a new sound signal and for +various reasons this is a process that + + align:start position:0% +various reasons this is a process that + + + align:start position:0% +various reasons this is a process that +needs to be iterated so you take that + + align:start position:0% +needs to be iterated so you take that + + + align:start position:0% +needs to be iterated so you take that +new sound so you know you generate it + + align:start position:0% +new sound so you know you generate it + + + align:start position:0% +new sound so you know you generate it +sub bands you you replace their + + align:start position:0% +sub bands you you replace their + + + align:start position:0% +sub bands you you replace their +envelopes by the ones you want and you + + align:start position:0% +envelopes by the ones you want and you + + + align:start position:0% +envelopes by the ones you want and you +added them back up to get a sound signal + + align:start position:0% +added them back up to get a sound signal + + + align:start position:0% +added them back up to get a sound signal +and if you do this about ten times what + + align:start position:0% +and if you do this about ten times what + + + align:start position:0% +and if you do this about ten times what +you end up with is something that has + + align:start position:0% +you end up with is something that has + + + align:start position:0% +you end up with is something that has +the envelopes that you want and so then + + align:start position:0% +the envelopes that you want and so then + + + align:start position:0% +the envelopes that you want and so then +you can listen to it and that's the + + align:start position:0% +you can listen to it and that's the + + + align:start position:0% +you can listen to it and that's the +thing that I played you okay so it's + + align:start position:0% +thing that I played you okay so it's + + + align:start position:0% +thing that I played you okay so it's +this iterative procedure where you + + align:start position:0% +this iterative procedure where you + + + align:start position:0% +this iterative procedure where you +typically start with noise you project + + align:start position:0% +typically start with noise you project + + + align:start position:0% +typically start with noise you project +all the the signal that you want onto + + align:start position:0% +all the the signal that you want onto + + + align:start position:0% +all the the signal that you want onto +the noise collapse and then iterate okay + + align:start position:0% +the noise collapse and then iterate okay + + + align:start position:0% +the noise collapse and then iterate okay +and we'll see some more examples of this + + align:start position:0% +and we'll see some more examples of this + + + align:start position:0% +and we'll see some more examples of this +in action so I just told you how this + + align:start position:0% +in action so I just told you how this + + + align:start position:0% +in action so I just told you how this +the instantaneous amplitude in each of + + align:start position:0% +the instantaneous amplitude in each of + + + align:start position:0% +the instantaneous amplitude in each of +the filter outputs which we characterize + + align:start position:0% +the filter outputs which we characterize + + + align:start position:0% +the filter outputs which we characterize +what the envelope is an important thing + + align:start position:0% +what the envelope is an important thing + + + align:start position:0% +what the envelope is an important thing +for sound representation and so in the + + align:start position:0% +for sound representation and so in the + + + align:start position:0% +for sound representation and so in the +auditory model that I'm building here + + align:start position:0% +auditory model that I'm building here + + + align:start position:0% +auditory model that I'm building here +we've got a second stage of processing + + align:start position:0% +we've got a second stage of processing + + + align:start position:0% +we've got a second stage of processing +now where we've taken the sub bands and + + align:start position:0% +now where we've taken the sub bands and + + + align:start position:0% +now where we've taken the sub bands and +we extract the instantaneous amplitude + + align:start position:0% +we extract the instantaneous amplitude + + + align:start position:0% +we extract the instantaneous amplitude +and there's one other thing here that + + align:start position:0% +and there's one other thing here that + + + align:start position:0% +and there's one other thing here that +I'll just mention which is that another + + align:start position:0% +I'll just mention which is that another + + + align:start position:0% +I'll just mention which is that another +important feature of the cochlea is + + align:start position:0% +important feature of the cochlea is + + + align:start position:0% +important feature of the cochlea is +what's known as amplitude compression so + + align:start position:0% +what's known as amplitude compression so + + + align:start position:0% +what's known as amplitude compression so +the response of the cochlea as a + + align:start position:0% +the response of the cochlea as a + + + align:start position:0% +the response of the cochlea as a +function of sound + + align:start position:0% +function of sound + + + align:start position:0% +function of sound +is not linear rather it's compressive + + align:start position:0% +is not linear rather it's compressive + + + align:start position:0% +is not linear rather it's compressive +and this is due to the fact that there + + align:start position:0% +and this is due to the fact that there + + + align:start position:0% +and this is due to the fact that there +is selective amplification when sounds + + align:start position:0% +is selective amplification when sounds + + + align:start position:0% +is selective amplification when sounds +are quiet and not when they're very high + + align:start position:0% +are quiet and not when they're very high + + + align:start position:0% +are quiet and not when they're very high +high in intensity and so and I'm not + + align:start position:0% +high in intensity and so and I'm not + + + align:start position:0% +high in intensity and so and I'm not +gonna say anything more about this for + + align:start position:0% +gonna say anything more about this for + + + align:start position:0% +gonna say anything more about this for +now but it will become important later + + align:start position:0% +now but it will become important later + + + align:start position:0% +now but it will become important later +and this is something that has a lot of + + align:start position:0% +and this is something that has a lot of + + + align:start position:0% +and this is something that has a lot of +practical consequences so when people + + align:start position:0% +practical consequences so when people + + + align:start position:0% +practical consequences so when people +lose their hearing one of the things one + + align:start position:0% +lose their hearing one of the things one + + + align:start position:0% +lose their hearing one of the things one +of the common things that happens is + + align:start position:0% +of the common things that happens is + + + align:start position:0% +of the common things that happens is +that the outer hair cells stop working + + align:start position:0% +that the outer hair cells stop working + + + align:start position:0% +that the outer hair cells stop working +correctly and the outer hair cells are + + align:start position:0% +correctly and the outer hair cells are + + + align:start position:0% +correctly and the outer hair cells are +one of the things that generates that + + align:start position:0% +one of the things that generates that + + + align:start position:0% +one of the things that generates that +compressive response there there the + + align:start position:0% +compressive response there there the + + + align:start position:0% +compressive response there there the +nonlinear component of processing in the + + align:start position:0% +nonlinear component of processing in the + + + align:start position:0% +nonlinear component of processing in the +cochlea and so when people who lose + + align:start position:0% +cochlea and so when people who lose + + + align:start position:0% +cochlea and so when people who lose +their hearing the tuning both broadens + + align:start position:0% +their hearing the tuning both broadens + + + align:start position:0% +their hearing the tuning both broadens +and you get a linear response to to + + align:start position:0% +and you get a linear response to to + + + align:start position:0% +and you get a linear response to to +sound amplitude because you lose that + + align:start position:0% +sound amplitude because you lose that + + + align:start position:0% +sound amplitude because you lose that +that selective amplification and that's + + align:start position:0% +that selective amplification and that's + + + align:start position:0% +that selective amplification and that's +something that hearing aids try to + + align:start position:0% +something that hearing aids try to + + + align:start position:0% +something that hearing aids try to +replicate and that's hard to do okay so + + align:start position:0% +replicate and that's hard to do okay so + + + align:start position:0% +replicate and that's hard to do okay so +on what happens next + + align:start position:0% +on what happens next + + + align:start position:0% +on what happens next +so everybody here does ever hear to know + + align:start position:0% +so everybody here does ever hear to know + + + align:start position:0% +so everybody here does ever hear to know +what aspect record averages yeah blossom + + align:start position:0% +what aspect record averages yeah blossom + + + align:start position:0% +what aspect record averages yeah blossom +people talked about this probably okay + + align:start position:0% +people talked about this probably okay + + + align:start position:0% +people talked about this probably okay +so one of the standard ways that we + + align:start position:0% +so one of the standard ways that we + + + align:start position:0% +so one of the standard ways that we +investigate sensory systems when we have + + align:start position:0% +investigate sensory systems when we have + + + align:start position:0% +investigate sensory systems when we have +some reason to think that that things + + align:start position:0% +some reason to think that that things + + + align:start position:0% +some reason to think that that things +might be reasonably linear linear is by + + align:start position:0% +might be reasonably linear linear is by + + + align:start position:0% +might be reasonably linear linear is by +measures measuring something called a + + align:start position:0% +measures measuring something called a + + + align:start position:0% +measures measuring something called a +spike-triggered average and so the way + + align:start position:0% +spike-triggered average and so the way + + + align:start position:0% +spike-triggered average and so the way +this experiment one might work is you + + align:start position:0% +this experiment one might work is you + + + align:start position:0% +this experiment one might work is you +would play stimulus like this so that's + + align:start position:0% +would play stimulus like this so that's + + + align:start position:0% +would play stimulus like this so that's +that's a type of a noise signal alright + + align:start position:0% +that's a type of a noise signal alright + + + align:start position:0% +that's a type of a noise signal alright +so you'd play your your animal that + + align:start position:0% +so you'd play your your animal that + + + align:start position:0% +so you'd play your your animal that +signal you'd be recording spikes from a + + align:start position:0% +signal you'd be recording spikes from a + + + align:start position:0% +signal you'd be recording spikes from a +neuron that you might be interested in + + align:start position:0% +neuron that you might be interested in + + + align:start position:0% +neuron that you might be interested in +and every time there's a spike you would + + align:start position:0% +and every time there's a spike you would + + + align:start position:0% +and every time there's a spike you would +look back at what happens in the signal + + align:start position:0% +look back at what happens in the signal + + + align:start position:0% +look back at what happens in the signal +and then you would take all the little + + align:start position:0% +and then you would take all the little + + + align:start position:0% +and then you would take all the little +histories that preceded that spike you'd + + align:start position:0% +histories that preceded that spike you'd + + + align:start position:0% +histories that preceded that spike you'd +average them together and you get the + + align:start position:0% +average them together and you get the + + + align:start position:0% +average them together and you get the +average stimulus that preceded a spike + + align:start position:0% +average stimulus that preceded a spike + + + align:start position:0% +average stimulus that preceded a spike +okay and so in this particular case + + align:start position:0% +okay and so in this particular case + + + align:start position:0% +okay and so in this particular case +we're gonna actually do this in the + + align:start position:0% +we're gonna actually do this in the + + + align:start position:0% +we're gonna actually do this in the +domain of the spectrogram and and that's + + align:start position:0% +domain of the spectrogram and and that's + + + align:start position:0% +domain of the spectrogram and and that's +because you might hypothesize that + + align:start position:0% +because you might hypothesize that + + + align:start position:0% +because you might hypothesize that +really what the neurons would care about + + align:start position:0% +really what the neurons would care about + + + align:start position:0% +really what the neurons would care about +would be the instantaneous amplitude in + + align:start position:0% +would be the instantaneous amplitude in + + + align:start position:0% +would be the instantaneous amplitude in +the sound signal and not necessarily the + + align:start position:0% +the sound signal and not necessarily the + + + align:start position:0% +the sound signal and not necessarily the +phase so if you do that for instance in + + align:start position:0% +phase so if you do that for instance in + + + align:start position:0% +phase so if you do that for instance in +the in the inferior colliculus the stage + + align:start position:0% +the in the inferior colliculus the stage + + + align:start position:0% +the in the inferior colliculus the stage +of the midbrain + + align:start position:0% +of the midbrain + + + align:start position:0% +of the midbrain +um you see things that are pretty + + align:start position:0% +um you see things that are pretty + + + align:start position:0% +um you see things that are pretty +stereotyped and we're gonna refer to + + align:start position:0% +stereotyped and we're gonna refer to + + + align:start position:0% +stereotyped and we're gonna refer to +what we get out of this procedure as a + + align:start position:0% +what we get out of this procedure as a + + + align:start position:0% +what we get out of this procedure as a +spectra temporal receptive field and + + align:start position:0% +spectra temporal receptive field and + + + align:start position:0% +spectra temporal receptive field and +that would often be referred to as aster + + align:start position:0% +that would often be referred to as aster + + + align:start position:0% +that would often be referred to as aster +for short so if you hear people talk + + align:start position:0% +for short so if you hear people talk + + + align:start position:0% +for short so if you hear people talk +about stir-fry mean okay oh and so these + + align:start position:0% +about stir-fry mean okay oh and so these + + + align:start position:0% +about stir-fry mean okay oh and so these +are derived from methods that would be + + align:start position:0% +are derived from methods that would be + + + align:start position:0% +are derived from methods that would be +like the spike-triggered average people + + align:start position:0% +like the spike-triggered average people + + + align:start position:0% +like the spike-triggered average people +don't usually actually do a + + align:start position:0% +don't usually actually do a + + + align:start position:0% +don't usually actually do a +spike-triggered average for various + + align:start position:0% +spike-triggered average for various + + + align:start position:0% +spike-triggered average for various +reasons but but you get what you get out + + align:start position:0% +reasons but but you get what you get out + + + align:start position:0% +reasons but but you get what you get out +is is similar and so what you see here + + align:start position:0% +is is similar and so what you see here + + + align:start position:0% +is is similar and so what you see here +is the the average spectrogram on that + + align:start position:0% +is the the average spectrogram on that + + + align:start position:0% +is the the average spectrogram on that +would be preceding a spike and for this + + align:start position:0% +would be preceding a spike and for this + + + align:start position:0% +would be preceding a spike and for this +particular neuron you can see there's a + + align:start position:0% +particular neuron you can see there's a + + + align:start position:0% +particular neuron you can see there's a +bit of red and then a bit of blue + + align:start position:0% +bit of red and then a bit of blue + + + align:start position:0% +bit of red and then a bit of blue +um and so at this particular frequency + + align:start position:0% +um and so at this particular frequency + + + align:start position:0% +um and so at this particular frequency +which in this case is I don't know + + align:start position:0% +which in this case is I don't know + + + align:start position:0% +which in this case is I don't know +something like you know 10 kilohertz or + + align:start position:0% +something like you know 10 kilohertz or + + + align:start position:0% +something like you know 10 kilohertz or +something like that the optimal stimulus + + align:start position:0% +something like that the optimal stimulus + + + align:start position:0% +something like that the optimal stimulus +that would generate a spike is something + + align:start position:0% +that would generate a spike is something + + + align:start position:0% +that would generate a spike is something +that gives you an increase in energy and + + align:start position:0% +that gives you an increase in energy and + + + align:start position:0% +that gives you an increase in energy and +then a decrease and so I'm what what + + align:start position:0% +then a decrease and so I'm what what + + + align:start position:0% +then a decrease and so I'm what what +this corresponds to is is a amplitude + + align:start position:0% +this corresponds to is is a amplitude + + + align:start position:0% +this corresponds to is is a amplitude +modulation at a particular rate um and + + align:start position:0% +modulation at a particular rate um and + + + align:start position:0% +modulation at a particular rate um and +so you can see there's a characteristic + + align:start position:0% +so you can see there's a characteristic + + + align:start position:0% +so you can see there's a characteristic +timing here so the red thing has a + + align:start position:0% +timing here so the red thing has a + + + align:start position:0% +timing here so the red thing has a +certain duration and then there's the + + align:start position:0% +certain duration and then there's the + + + align:start position:0% +certain duration and then there's the +blue thing and so there's this very + + align:start position:0% +blue thing and so there's this very + + + align:start position:0% +blue thing and so there's this very +rapid increase in decrease in energy at + + align:start position:0% +rapid increase in decrease in energy at + + + align:start position:0% +rapid increase in decrease in energy at +that particular frequency so that's + + align:start position:0% +that particular frequency so that's + + + align:start position:0% +that particular frequency so that's +known as amplitude modulation and so + + align:start position:0% +known as amplitude modulation and so + + + align:start position:0% +known as amplitude modulation and so +this is this is one way of looking at + + align:start position:0% +this is this is one way of looking at + + + align:start position:0% +this is this is one way of looking at +this in the domain of the spectrogram um + + align:start position:0% +this in the domain of the spectrogram um + + + align:start position:0% +this in the domain of the spectrogram um +another way of looking at this would be + + align:start position:0% +another way of looking at this would be + + + align:start position:0% +another way of looking at this would be +to generate a tuning function as a + + align:start position:0% +to generate a tuning function as a + + + align:start position:0% +to generate a tuning function as a +function of the modulation rate so you + + align:start position:0% +function of the modulation rate so you + + + align:start position:0% +function of the modulation rate so you +could actually change how fast the + + align:start position:0% +could actually change how fast the + + + align:start position:0% +could actually change how fast the +amplitude is being modulated and you + + align:start position:0% +amplitude is being modulated and you + + + align:start position:0% +amplitude is being modulated and you +would see in a neuron like this that the + + align:start position:0% +would see in a neuron like this that the + + + align:start position:0% +would see in a neuron like this that the +response would exhibit tuning and so um + + align:start position:0% +response would exhibit tuning and so um + + + align:start position:0% +response would exhibit tuning and so um +each one of the the graphs here or each + + align:start position:0% +each one of the the graphs here or each + + + align:start position:0% +each one of the the graphs here or each +one of the plots the dash curves in the + + align:start position:0% +one of the plots the dash curves in the + + + align:start position:0% +one of the plots the dash curves in the +lower the lower right plot so each + + align:start position:0% +lower the lower right plot so each + + + align:start position:0% +lower the lower right plot so each +dashed line is a tuning curve for one + + align:start position:0% +dashed line is a tuning curve for one + + + align:start position:0% +dashed line is a tuning curve for one +neuron so it's a plot of the response of + + align:start position:0% +neuron so it's a plot of the response of + + + align:start position:0% +neuron so it's a plot of the response of +that neuron as a function of the + + align:start position:0% +that neuron as a function of the + + + align:start position:0% +that neuron as a function of the +temporal modulation frequency so that's + + align:start position:0% +temporal modulation frequency so that's + + + align:start position:0% +temporal modulation frequency so that's +how fast the amplitude is changing with + + align:start position:0% +how fast the amplitude is changing with + + + align:start position:0% +how fast the amplitude is changing with +time and if you look at this particular + + align:start position:0% +time and if you look at this particular + + + align:start position:0% +time and if you look at this particular +case here you can see that there's a + + align:start position:0% +case here you can see that there's a + + + align:start position:0% +case here you can see that there's a +peak response when the modulation + + align:start position:0% +peak response when the modulation + + + align:start position:0% +peak response when the modulation +frequency is maybe 70 Hertz and then the + + align:start position:0% +frequency is maybe 70 Hertz and then the + + + align:start position:0% +frequency is maybe 70 Hertz and then the +response decreases if you go in either + + align:start position:0% +response decreases if you go in either + + + align:start position:0% +response decreases if you go in either +direction this guy here's got a slightly + + align:start position:0% +direction this guy here's got a slightly + + + align:start position:0% +direction this guy here's got a slightly +lower preferred to frequency and down + + align:start position:0% +lower preferred to frequency and down + + + align:start position:0% +lower preferred to frequency and down +here lower still and so again what you + + align:start position:0% +here lower still and so again what you + + + align:start position:0% +here lower still and so again what you +can see is something that looks + + align:start position:0% +can see is something that looks + + + align:start position:0% +can see is something that looks +strikingly similar to the kinds of + + align:start position:0% +strikingly similar to the kinds of + + + align:start position:0% +strikingly similar to the kinds of +filter banks that we just saw when we + + align:start position:0% +filter banks that we just saw when we + + + align:start position:0% +filter banks that we just saw when we +were looking at the cochlea but there's + + align:start position:0% +were looking at the cochlea but there's + + + align:start position:0% +were looking at the cochlea but there's +a key difference here right that here + + align:start position:0% +a key difference here right that here + + + align:start position:0% +a key difference here right that here +we're seeing tuning to modulation + + align:start position:0% +we're seeing tuning to modulation + + + align:start position:0% +we're seeing tuning to modulation +frequency not to audio frequency so this + + align:start position:0% +frequency not to audio frequency so this + + + align:start position:0% +frequency not to audio frequency so this +is the rate at + + align:start position:0% +is the rate at + + + align:start position:0% +is the rate at +the amplitude changes that's the + + align:start position:0% +the amplitude changes that's the + + + align:start position:0% +the amplitude changes that's the +amplitude of the sound not the audio + + align:start position:0% +amplitude of the sound not the audio + + + align:start position:0% +amplitude of the sound not the audio +frequency so that there's a carrier + + align:start position:0% +frequency so that there's a carrier + + + align:start position:0% +frequency so that there's a carrier +frequency here which is 10 K but the + + align:start position:0% +frequency here which is 10 K but the + + + align:start position:0% +frequency here which is 10 K but the +frequency we're talking about here is + + align:start position:0% +frequency we're talking about here is + + + align:start position:0% +frequency we're talking about here is +the rate at which this changes and so in + + align:start position:0% +the rate at which this changes and so in + + + align:start position:0% +the rate at which this changes and so in +this case here you can see that the + + align:start position:0% +this case here you can see that the + + + align:start position:0% +this case here you can see that the +period here is like maybe 5 milliseconds + + align:start position:0% +period here is like maybe 5 milliseconds + + + align:start position:0% +period here is like maybe 5 milliseconds +and so this would correspond to a + + align:start position:0% +and so this would correspond to a + + + align:start position:0% +and so this would correspond to a +modulation of I guess 200 Hertz is that + + align:start position:0% +modulation of I guess 200 Hertz is that + + + align:start position:0% +modulation of I guess 200 Hertz is that +right I think that's right yeah okay and + + align:start position:0% +right I think that's right yeah okay and + + + align:start position:0% +right I think that's right yeah okay and +so as early as the midbrain you see + + align:start position:0% +so as early as the midbrain you see + + + align:start position:0% +so as early as the midbrain you see +stuff like this so in the inferior + + align:start position:0% +stuff like this so in the inferior + + + align:start position:0% +stuff like this so in the inferior +colliculus there's lots of it and so the + + align:start position:0% +colliculus there's lots of it and so the + + + align:start position:0% +colliculus there's lots of it and so the +this suggests a second or in this case a + + align:start position:0% +this suggests a second or in this case a + + + align:start position:0% +this suggests a second or in this case a +third stage of processing which are + + align:start position:0% +third stage of processing which are + + + align:start position:0% +third stage of processing which are +known as modulation filters this is a + + align:start position:0% +known as modulation filters this is a + + + align:start position:0% +known as modulation filters this is a +very old idea in in auditory assist in + + align:start position:0% +very old idea in in auditory assist in + + + align:start position:0% +very old idea in in auditory assist in +auditory science that now has a fair bit + + align:start position:0% +auditory science that now has a fair bit + + + align:start position:0% +auditory science that now has a fair bit +of empirical as importance the idea is + + align:start position:0% +of empirical as importance the idea is + + + align:start position:0% +of empirical as importance the idea is +that in our model we've got our sound + + align:start position:0% +that in our model we've got our sound + + + align:start position:0% +that in our model we've got our sound +signal it gets passed through this Bank + + align:start position:0% +signal it gets passed through this Bank + + + align:start position:0% +signal it gets passed through this Bank +of bandpass filters you get these sub + + align:start position:0% +of bandpass filters you get these sub + + + align:start position:0% +of bandpass filters you get these sub +bands you extract the instantaneous + + align:start position:0% +bands you extract the instantaneous + + + align:start position:0% +bands you extract the instantaneous +amplitude known as the envelope and then + + align:start position:0% +amplitude known as the envelope and then + + + align:start position:0% +amplitude known as the envelope and then +you take that envelope and you pass it + + align:start position:0% +you take that envelope and you pass it + + + align:start position:0% +you take that envelope and you pass it +to another filter Bank this time these + + align:start position:0% +to another filter Bank this time these + + + align:start position:0% +to another filter Bank this time these +are filters that are tuned in modulation + + align:start position:0% +are filters that are tuned in modulation + + + align:start position:0% +are filters that are tuned in modulation +frequency and the output of those + + align:start position:0% +frequency and the output of those + + + align:start position:0% +frequency and the output of those +filters again it's exactly conceptually + + align:start position:0% +filters again it's exactly conceptually + + + align:start position:0% +filters again it's exactly conceptually +analogous to the output of this first + + align:start position:0% +analogous to the output of this first + + + align:start position:0% +analogous to the output of this first +set of bandpass filters so in this case + + align:start position:0% +set of bandpass filters so in this case + + + align:start position:0% +set of bandpass filters so in this case +we have a filter that's tuned to low + + align:start position:0% +we have a filter that's tuned to low + + + align:start position:0% +we have a filter that's tuned to low +modulation rates and so you can see what + + align:start position:0% +modulation rates and so you can see what + + + align:start position:0% +modulation rates and so you can see what +it outputs is something that's + + align:start position:0% +it outputs is something that's + + + align:start position:0% +it outputs is something that's +fluctuating very slowly so it's just + + align:start position:0% +fluctuating very slowly so it's just + + + align:start position:0% +fluctuating very slowly so it's just +taking the very slow fluctuations out of + + align:start position:0% +taking the very slow fluctuations out of + + + align:start position:0% +taking the very slow fluctuations out of +that envelope here you have a filter + + align:start position:0% +that envelope here you have a filter + + + align:start position:0% +that envelope here you have a filter +that's tuned up to higher rates and so + + align:start position:0% +that's tuned up to higher rates and so + + + align:start position:0% +that's tuned up to higher rates and so +it's wiggling around it at faster rates + + align:start position:0% +it's wiggling around it at faster rates + + + align:start position:0% +it's wiggling around it at faster rates +and you have a different set of these + + align:start position:0% +and you have a different set of these + + + align:start position:0% +and you have a different set of these +filters for each cochlear channel each + + align:start position:0% +filters for each cochlear channel each + + + align:start position:0% +filters for each cochlear channel each +thing coming out of the Coco so this + + align:start position:0% +thing coming out of the Coco so this + + + align:start position:0% +thing coming out of the Coco so this +picture here that we've gradually built + + align:start position:0% +picture here that we've gradually built + + + align:start position:0% +picture here that we've gradually built +up gives us a model of the the signal + + align:start position:0% +up gives us a model of the the signal + + + align:start position:0% +up gives us a model of the the signal +processing that we think occurs between + + align:start position:0% +processing that we think occurs between + + + align:start position:0% +processing that we think occurs between +the cochlea and and the midbrain or the + + align:start position:0% +the cochlea and and the midbrain or the + + + align:start position:0% +the cochlea and and the midbrain or the +thalamus so you have the bandpass + + align:start position:0% +thalamus so you have the bandpass + + + align:start position:0% +thalamus so you have the bandpass +filtering that happens in the cochlea + + align:start position:0% +filtering that happens in the cochlea + + + align:start position:0% +filtering that happens in the cochlea +you get sub bins you extract the + + align:start position:0% +you get sub bins you extract the + + + align:start position:0% +you get sub bins you extract the +instantaneous amplitude and the + + align:start position:0% +instantaneous amplitude and the + + + align:start position:0% +instantaneous amplitude and the +envelopes and then you filter that again + + align:start position:0% +envelopes and then you filter that again + + + align:start position:0% +envelopes and then you filter that again +with these modulation filters this is + + align:start position:0% +with these modulation filters this is + + + align:start position:0% +with these modulation filters this is +sort of a rough understanding of like + + align:start position:0% +sort of a rough understanding of like + + + align:start position:0% +sort of a rough understanding of like +the front end of the auditory system and + + align:start position:0% +the front end of the auditory system and + + + align:start position:0% +the front end of the auditory system and +the question is given these + + align:start position:0% +the question is given these + + + align:start position:0% +the question is given these +representations how do we do the + + align:start position:0% +representations how do we do the + + + align:start position:0% +representations how do we do the +interesting things that we do with sound + + align:start position:0% +interesting things that we do with sound + + + align:start position:0% +interesting things that we do with sound +so how do we recognize things and their + + align:start position:0% +so how do we recognize things and their + + + align:start position:0% +so how do we recognize things and their +properties and and do scene analysis and + + align:start position:0% +properties and and do scene analysis and + + + align:start position:0% +properties and and do scene analysis and +so on and so forth and this is still + + align:start position:0% +so on and so forth and this is still + + + align:start position:0% +so on and so forth and this is still +something that is still very very much + + align:start position:0% +something that is still very very much + + + align:start position:0% +something that is still very very much +in its infancy in terms of our + + align:start position:0% +in its infancy in terms of our + + + align:start position:0% +in its infancy in terms of our +understanding one of the things one of + + align:start position:0% +understanding one of the things one of + + + align:start position:0% +understanding one of the things one of +the areas that I've spent a bit of time + + align:start position:0% +the areas that I've spent a bit of time + + + align:start position:0% +the areas that I've spent a bit of time +on to try to get a handle on this is + + align:start position:0% +on to try to get a handle on this is + + + align:start position:0% +on to try to get a handle on this is +sound texture and I started working on + + align:start position:0% +sound texture and I started working on + + + align:start position:0% +sound texture and I started working on +this because I sort of thought it would + + align:start position:0% +this because I sort of thought it would + + + align:start position:0% +this because I sort of thought it would +be a nice a nice way into understanding + + align:start position:0% +be a nice a nice way into understanding + + + align:start position:0% +be a nice a nice way into understanding +some of these issues and because I + + align:start position:0% +some of these issues and because I + + + align:start position:0% +some of these issues and because I +underst + + align:start position:0% +underst + + + align:start position:0% +underst +Eero was here talking about visual + + align:start position:0% +Eero was here talking about visual + + + align:start position:0% +Eero was here talking about visual +texture I was asked to just to feature + + align:start position:0% +texture I was asked to just to feature + + + align:start position:0% +texture I was asked to just to feature +this and and hopefully this will be + + align:start position:0% +this and and hopefully this will be + + + align:start position:0% +this and and hopefully this will be +useful so what are sound textures + + align:start position:0% +useful so what are sound textures + + + align:start position:0% +useful so what are sound textures +textures are sounds that result from + + align:start position:0% +textures are sounds that result from + + + align:start position:0% +textures are sounds that result from +large numbers of acoustic events and + + align:start position:0% +large numbers of acoustic events and + + + align:start position:0% +large numbers of acoustic events and +they occur include things that you hear + + align:start position:0% +they occur include things that you hear + + + align:start position:0% +they occur include things that you hear +all the time like rain or birds or + + align:start position:0% +all the time like rain or birds or + + + align:start position:0% +all the time like rain or birds or +running water insects applause fire so + + align:start position:0% +running water insects applause fire so + + + align:start position:0% +running water insects applause fire so +forth + + align:start position:0% + + + + align:start position:0% + +okay so these are these are sounds that + + align:start position:0% +okay so these are these are sounds that + + + align:start position:0% +okay so these are these are sounds that +the the typically are generated from + + align:start position:0% +the the typically are generated from + + + align:start position:0% +the the typically are generated from +large numbers of acoustic events they're + + align:start position:0% +large numbers of acoustic events they're + + + align:start position:0% +large numbers of acoustic events they're +very common in the world you hear these + + align:start position:0% +very common in the world you hear these + + + align:start position:0% +very common in the world you hear these +things all the time but that they've + + align:start position:0% +things all the time but that they've + + + align:start position:0% +things all the time but that they've +been largely unstudied so there was this + + align:start position:0% +been largely unstudied so there was this + + + align:start position:0% +been largely unstudied so there was this +you know there's been a long and storied + + align:start position:0% +you know there's been a long and storied + + + align:start position:0% +you know there's been a long and storied +history of research on visual texture + + align:start position:0% +history of research on visual texture + + + align:start position:0% +history of research on visual texture +and this really had not been thought + + align:start position:0% +and this really had not been thought + + + align:start position:0% +and this really had not been thought +about very much until until a few years + + align:start position:0% +about very much until until a few years + + + align:start position:0% +about very much until until a few years +ago now a lot of the things that people + + align:start position:0% +ago now a lot of the things that people + + + align:start position:0% +ago now a lot of the things that people +typically think about in hearing are the + + align:start position:0% +typically think about in hearing are the + + + align:start position:0% +typically think about in hearing are the +sounds that are produced by individual + + align:start position:0% +sounds that are produced by individual + + + align:start position:0% +sounds that are produced by individual +events and if we have time we'll talk + + align:start position:0% +events and if we have time we'll talk + + + align:start position:0% +events and if we have time we'll talk +about this more later but stuff like + + align:start position:0% +about this more later but stuff like + + + align:start position:0% +about this more later but stuff like +this January or this and these are the + + align:start position:0% +this January or this and these are the + + + align:start position:0% +this January or this and these are the +waveforms associate with those events + + align:start position:0% +waveforms associate with those events + + + align:start position:0% +waveforms associate with those events +and the point is that those those sounds + + align:start position:0% +and the point is that those those sounds + + + align:start position:0% +and the point is that those those sounds +they have a beginning and an end and the + + align:start position:0% +they have a beginning and an end and the + + + align:start position:0% +they have a beginning and an end and the +temporal evolution and that temporal + + align:start position:0% +temporal evolution and that temporal + + + align:start position:0% +temporal evolution and that temporal +evolution is sort of part of what makes + + align:start position:0% +evolution is sort of part of what makes + + + align:start position:0% +evolution is sort of part of what makes +the sound like what it is right and + + align:start position:0% +the sound like what it is right and + + + align:start position:0% +the sound like what it is right and +textures are a bit different so here's + + align:start position:0% +textures are a bit different so here's + + + align:start position:0% +textures are a bit different so here's +just the sound of rain now of course at + + align:start position:0% +just the sound of rain now of course at + + + align:start position:0% +just the sound of rain now of course at +some point the rain started and + + align:start position:0% +some point the rain started and + + + align:start position:0% +some point the rain started and +hopefully some when it will end but the + + align:start position:0% +hopefully some when it will end but the + + + align:start position:0% +hopefully some when it will end but the +start in the end or not what makes it + + align:start position:0% +start in the end or not what makes it + + + align:start position:0% +start in the end or not what makes it +sound like rain right the quasi make it + + align:start position:0% +sound like rain right the quasi make it + + + align:start position:0% +sound like rain right the quasi make it +sound like rain are just there so the + + align:start position:0% +sound like rain are just there so the + + + align:start position:0% +sound like rain are just there so the +texture isn't is stationary so the + + align:start position:0% +texture isn't is stationary so the + + + align:start position:0% +texture isn't is stationary so the +essential properties don't change over + + align:start position:0% +essential properties don't change over + + + align:start position:0% +essential properties don't change over +time and so I got interested in textures + + align:start position:0% +time and so I got interested in textures + + + align:start position:0% +time and so I got interested in textures +because it seemed like stationarity + + align:start position:0% +because it seemed like stationarity + + + align:start position:0% +because it seemed like stationarity +would make them a good starting point + + align:start position:0% +would make them a good starting point + + + align:start position:0% +would make them a good starting point +for understanding auditory + + align:start position:0% +for understanding auditory + + + align:start position:0% +for understanding auditory +representation because in some sense it + + align:start position:0% +representation because in some sense it + + + align:start position:0% +representation because in some sense it +sort of simplifies the kinds of the + + align:start position:0% +sort of simplifies the kinds of the + + + align:start position:0% +sort of simplifies the kinds of the +things you have to worry about you sort + + align:start position:0% +things you have to worry about you sort + + + align:start position:0% +things you have to worry about you sort +of don't have to worry about time in + + align:start position:0% +of don't have to worry about time in + + + align:start position:0% +of don't have to worry about time in +quite the same way and so the question + + align:start position:0% +quite the same way and so the question + + + align:start position:0% +quite the same way and so the question +that we were interested in is is how + + align:start position:0% +that we were interested in is is how + + + align:start position:0% +that we were interested in is is how +people represent and recognize textures + + align:start position:0% +people represent and recognize textures + + + align:start position:0% +people represent and recognize textures +so just to make that concrete listen to + + align:start position:0% +so just to make that concrete listen to + + + align:start position:0% +so just to make that concrete listen to +this + + align:start position:0% + + + + align:start position:0% + +and this so it's immediately apparent to + + align:start position:0% +and this so it's immediately apparent to + + + align:start position:0% +and this so it's immediately apparent to +you that those are the same kind of + + align:start position:0% +you that those are the same kind of + + + align:start position:0% +you that those are the same kind of +thing right in fact there are two + + align:start position:0% +thing right in fact there are two + + + align:start position:0% +thing right in fact there are two +different excerpts of like the same + + align:start position:0% +different excerpts of like the same + + + align:start position:0% +different excerpts of like the same +recording but the waveform itself is + + align:start position:0% +recording but the waveform itself is + + + align:start position:0% +recording but the waveform itself is +totally different in the two cases so + + align:start position:0% +totally different in the two cases so + + + align:start position:0% +totally different in the two cases so +there's something that your brain is + + align:start position:0% +there's something that your brain is + + + align:start position:0% +there's something that your brain is +extracting from those two excerpts that + + align:start position:0% +extracting from those two excerpts that + + + align:start position:0% +extracting from those two excerpts that +tells you that they're the same kind of + + align:start position:0% +tells you that they're the same kind of + + + align:start position:0% +tells you that they're the same kind of +thing and that for instance they're + + align:start position:0% +thing and that for instance they're + + + align:start position:0% +thing and that for instance they're +different from this so the question is + + align:start position:0% +different from this so the question is + + + align:start position:0% +different from this so the question is +what is it that you extract in store + + align:start position:0% +what is it that you extract in store + + + align:start position:0% +what is it that you extract in store +about those waveforms that tells you + + align:start position:0% +about those waveforms that tells you + + + align:start position:0% +about those waveforms that tells you +that certain some things are the same + + align:start position:0% +that certain some things are the same + + + align:start position:0% +that certain some things are the same +and other things are different and it + + align:start position:0% +and other things are different and it + + + align:start position:0% +and other things are different and it +allows you to recognize what what things + + align:start position:0% +allows you to recognize what what things + + + align:start position:0% +allows you to recognize what what things +are and so the key theoretical proposal + + align:start position:0% +are and so the key theoretical proposal + + + align:start position:0% +are and so the key theoretical proposal +that we made in this work is that + + align:start position:0% +that we made in this work is that + + + align:start position:0% +that we made in this work is that +because they're stationary textures can + + align:start position:0% +because they're stationary textures can + + + align:start position:0% +because they're stationary textures can +be captured by statistics that our time + + align:start position:0% +be captured by statistics that our time + + + align:start position:0% +be captured by statistics that our time +averages of acoustic measurements so the + + align:start position:0% +averages of acoustic measurements so the + + + align:start position:0% +averages of acoustic measurements so the +proposal that when you recognize the + + align:start position:0% +proposal that when you recognize the + + + align:start position:0% +proposal that when you recognize the +sound of fire or rain or what-have-you + + align:start position:0% +sound of fire or rain or what-have-you + + + align:start position:0% +sound of fire or rain or what-have-you +you're recognizing these statistics so + + align:start position:0% +you're recognizing these statistics so + + + align:start position:0% +you're recognizing these statistics so +what kinds of statistics might we be + + align:start position:0% +what kinds of statistics might we be + + + align:start position:0% +what kinds of statistics might we be +measuring if you think this proposal has + + align:start position:0% +measuring if you think this proposal has + + + align:start position:0% +measuring if you think this proposal has +some plausibility and so I'm part of the + + align:start position:0% +some plausibility and so I'm part of the + + + align:start position:0% +some plausibility and so I'm part of the +reason for walking you through this + + align:start position:0% +reason for walking you through this + + + align:start position:0% +reason for walking you through this +auditory model is that whatever + + align:start position:0% +auditory model is that whatever + + + align:start position:0% +auditory model is that whatever +statistics the auditory system measures + + align:start position:0% +statistics the auditory system measures + + + align:start position:0% +statistics the auditory system measures +are presumably derived from + + align:start position:0% +are presumably derived from + + + align:start position:0% +are presumably derived from +representations like this right that + + align:start position:0% +representations like this right that + + + align:start position:0% +representations like this right that +constitute the input that your brain is + + align:start position:0% +constitute the input that your brain is + + + align:start position:0% +constitute the input that your brain is +getting from the auditory periphery and + + align:start position:0% +getting from the auditory periphery and + + + align:start position:0% +getting from the auditory periphery and +so we initially asked how far one might + + align:start position:0% +so we initially asked how far one might + + + align:start position:0% +so we initially asked how far one might +get with representations consisting of + + align:start position:0% +get with representations consisting of + + + align:start position:0% +get with representations consisting of +fairly generic statistics of these + + align:start position:0% +fairly generic statistics of these + + + align:start position:0% +fairly generic statistics of these +standard auditory representations things + + align:start position:0% +standard auditory representations things + + + align:start position:0% +standard auditory representations things +like marginal moments and correlations + + align:start position:0% +like marginal moments and correlations + + + align:start position:0% +like marginal moments and correlations +so that the statistics that we initially + + align:start position:0% +so that the statistics that we initially + + + align:start position:0% +so that the statistics that we initially +consider we're not in any way + + align:start position:0% +consider we're not in any way + + + align:start position:0% +consider we're not in any way +specifically tailored to natural sounds + + align:start position:0% +specifically tailored to natural sounds + + + align:start position:0% +specifically tailored to natural sounds +and really ultimately what one what we'd + + align:start position:0% +and really ultimately what one what we'd + + + align:start position:0% +and really ultimately what one what we'd +like to do would be to actually learn + + align:start position:0% +like to do would be to actually learn + + + align:start position:0% +like to do would be to actually learn +statistics from data that actually we + + align:start position:0% +statistics from data that actually we + + + align:start position:0% +statistics from data that actually we +think are good representations that's + + align:start position:0% +think are good representations that's + + + align:start position:0% +think are good representations that's +something we're working on but these + + align:start position:0% +something we're working on but these + + + align:start position:0% +something we're working on but these +statistics are simple and involve + + align:start position:0% +statistics are simple and involve + + + align:start position:0% +statistics are simple and involve +operations that you could instantiate in + + align:start position:0% +operations that you could instantiate in + + + align:start position:0% +operations that you could instantiate in +neurons so it seemed like maybe a + + align:start position:0% +neurons so it seemed like maybe a + + + align:start position:0% +neurons so it seemed like maybe a +reasonable place to start to at least + + align:start position:0% +reasonable place to start to at least + + + align:start position:0% +reasonable place to start to at least +get a feel for what what the landscape + + align:start position:0% +get a feel for what what the landscape + + + align:start position:0% +get a feel for what what the landscape +was like and so what I want to do now is + + align:start position:0% +was like and so what I want to do now is + + + align:start position:0% +was like and so what I want to do now is +just to give you some intuitions as to + + align:start position:0% +just to give you some intuitions as to + + + align:start position:0% +just to give you some intuitions as to +what sorts of things might be captured + + align:start position:0% +what sorts of things might be captured + + + align:start position:0% +what sorts of things might be captured +by statistics of these representations + + align:start position:0% +by statistics of these representations + + + align:start position:0% +by statistics of these representations +and so at a minimum to be useful for + + align:start position:0% +and so at a minimum to be useful for + + + align:start position:0% +and so at a minimum to be useful for +recognition + + align:start position:0% +recognition + + + align:start position:0% +recognition +well statistics need to give you + + align:start position:0% +well statistics need to give you + + + align:start position:0% +well statistics need to give you +different values for different sounds + + align:start position:0% +different values for different sounds + + + align:start position:0% +different values for different sounds +and so let's see what happens + + align:start position:0% +and so let's see what happens + + + align:start position:0% +and so let's see what happens +so let's first have a look at what kinds + + align:start position:0% +so let's first have a look at what kinds + + + align:start position:0% +so let's first have a look at what kinds +of things might be captured by marginal + + align:start position:0% +of things might be captured by marginal + + + align:start position:0% +of things might be captured by marginal +moments of amplitude envelopes from from + + align:start position:0% +moments of amplitude envelopes from from + + + align:start position:0% +moments of amplitude envelopes from from +bandpass filters okay all right so + + align:start position:0% +bandpass filters okay all right so + + + align:start position:0% +bandpass filters okay all right so +remember the envelope here you can think + + align:start position:0% +remember the envelope here you can think + + + align:start position:0% +remember the envelope here you can think +of as a stripe through a spectrogram + + align:start position:0% +of as a stripe through a spectrogram + + + align:start position:0% +of as a stripe through a spectrogram +right so + + align:start position:0% +right so + + + align:start position:0% +right so +the instantaneous amplitude I'm gonna + + align:start position:0% +the instantaneous amplitude I'm gonna + + + align:start position:0% +the instantaneous amplitude I'm gonna +given frequency channel so the blue + + align:start position:0% +given frequency channel so the blue + + + align:start position:0% +given frequency channel so the blue +thing is the sub band the red thing here + + align:start position:0% +thing is the sub band the red thing here + + + align:start position:0% +thing is the sub band the red thing here +is the envelope and the the marginal + + align:start position:0% +is the envelope and the the marginal + + + align:start position:0% +is the envelope and the the marginal +moments will describe the way the + + align:start position:0% +moments will describe the way the + + + align:start position:0% +moments will describe the way the +envelope is distributed so imagine you + + align:start position:0% +envelope is distributed so imagine you + + + align:start position:0% +envelope is distributed so imagine you +took that red curve and you collapse + + align:start position:0% +took that red curve and you collapse + + + align:start position:0% +took that red curve and you collapse +that over time to get a histogram that + + align:start position:0% +that over time to get a histogram that + + + align:start position:0% +that over time to get a histogram that +tells you the frequency of occurrence of + + align:start position:0% +tells you the frequency of occurrence of + + + align:start position:0% +tells you the frequency of occurrence of +different amplitudes in that particular + + align:start position:0% +different amplitudes in that particular + + + align:start position:0% +different amplitudes in that particular +frequency Channel right and that's what + + align:start position:0% +frequency Channel right and that's what + + + align:start position:0% +frequency Channel right and that's what +it looks like for this particular + + align:start position:0% +it looks like for this particular + + + align:start position:0% +it looks like for this particular +example and you know you might think + + align:start position:0% +example and you know you might think + + + align:start position:0% +example and you know you might think +that well this sort of can't possibly be + + align:start position:0% +that well this sort of can't possibly be + + + align:start position:0% +that well this sort of can't possibly be +all that informative right because you + + align:start position:0% +all that informative right because you + + + align:start position:0% +all that informative right because you +know it's obviously got some central + + align:start position:0% +know it's obviously got some central + + + align:start position:0% +know it's obviously got some central +tendency and some spread but when you do + + align:start position:0% +tendency and some spread but when you do + + + align:start position:0% +tendency and some spread but when you do +this business of collapsing across time + + align:start position:0% +this business of collapsing across time + + + align:start position:0% +this business of collapsing across time +you're throwing out all kinds of + + align:start position:0% +you're throwing out all kinds of + + + align:start position:0% +you're throwing out all kinds of +information but one of the interesting + + align:start position:0% +information but one of the interesting + + + align:start position:0% +information but one of the interesting +things is that when you look at these + + align:start position:0% +things is that when you look at these + + + align:start position:0% +things is that when you look at these +kinds of distributions for different + + align:start position:0% +kinds of distributions for different + + + align:start position:0% +kinds of distributions for different +types of sounds um you see that they + + align:start position:0% +types of sounds um you see that they + + + align:start position:0% +types of sounds um you see that they +vary a fair bit and in particular that + + align:start position:0% +vary a fair bit and in particular that + + + align:start position:0% +vary a fair bit and in particular that +they're systematically different for a + + align:start position:0% +they're systematically different for a + + + align:start position:0% +they're systematically different for a +lot of natural sounds than they are for + + align:start position:0% +lot of natural sounds than they are for + + + align:start position:0% +lot of natural sounds than they are for +noise signals so this is that same thing + + align:start position:0% +noise signals so this is that same thing + + + align:start position:0% +noise signals so this is that same thing +so it's this histogram here just rotated + + align:start position:0% +so it's this histogram here just rotated + + + align:start position:0% +so it's this histogram here just rotated +90 degrees so we've got the probability + + align:start position:0% +90 degrees so we've got the probability + + + align:start position:0% +90 degrees so we've got the probability +of occurence on the y axis and the + + align:start position:0% +of occurence on the y axis and the + + + align:start position:0% +of occurence on the y axis and the +magnitude in the envelope of one + + align:start position:0% +magnitude in the envelope of one + + + align:start position:0% +magnitude in the envelope of one +particular frequency channel on the x + + align:start position:0% +particular frequency channel on the x + + + align:start position:0% +particular frequency channel on the x +axis for three different recordings so + + align:start position:0% +axis for three different recordings so + + + align:start position:0% +axis for three different recordings so +the red plots what you get for a + + align:start position:0% +the red plots what you get for a + + + align:start position:0% +the red plots what you get for a +recording of of noise the blue is a + + align:start position:0% +recording of of noise the blue is a + + + align:start position:0% +recording of of noise the blue is a +stream and the green is a bunch of geese + + align:start position:0% +stream and the green is a bunch of geese + + + align:start position:0% +stream and the green is a bunch of geese +he's don't quack whatever the geese do + + align:start position:0% +he's don't quack whatever the geese do + + + align:start position:0% +he's don't quack whatever the geese do +yeah honking yeah alright and this is a + + align:start position:0% +yeah honking yeah alright and this is a + + + align:start position:0% +yeah honking yeah alright and this is a +filter that's centered at 2200 Hertz and + + align:start position:0% +filter that's centered at 2200 Hertz and + + + align:start position:0% +filter that's centered at 2200 Hertz and +so and particularly these examples were + + align:start position:0% +so and particularly these examples were + + + align:start position:0% +so and particularly these examples were +chosen because the average value of the + + align:start position:0% +chosen because the average value of the + + + align:start position:0% +chosen because the average value of the +envelope is very similar in the three + + align:start position:0% +envelope is very similar in the three + + + align:start position:0% +envelope is very similar in the three +cases but you can see that the + + align:start position:0% +cases but you can see that the + + + align:start position:0% +cases but you can see that the +distributions have very different shapes + + align:start position:0% +distributions have very different shapes + + + align:start position:0% +distributions have very different shapes +so that the noise one here has got + + align:start position:0% +so that the noise one here has got + + + align:start position:0% +so that the noise one here has got +pretty low variance on the the stream + + align:start position:0% +pretty low variance on the the stream + + + align:start position:0% +pretty low variance on the the stream +has got larger variance and the geese + + align:start position:0% +has got larger variance and the geese + + + align:start position:0% +has got larger variance and the geese +larger still and it's also positively + + align:start position:0% +larger still and it's also positively + + + align:start position:0% +larger still and it's also positively +skewed so it's got this kind of long + + align:start position:0% +skewed so it's got this kind of long + + + align:start position:0% +skewed so it's got this kind of long +tail here and if you look at the + + align:start position:0% +tail here and if you look at the + + + align:start position:0% +tail here and if you look at the +spectrograms associated with these + + align:start position:0% +spectrograms associated with these + + + align:start position:0% +spectrograms associated with these +sounds you can see where this comes from + + align:start position:0% +sounds you can see where this comes from + + + align:start position:0% +sounds you can see where this comes from +so the spectrum spectrum of noise is + + align:start position:0% +so the spectrum spectrum of noise is + + + align:start position:0% +so the spectrum spectrum of noise is +pretty gray so the noise signal kind of + + align:start position:0% +pretty gray so the noise signal kind of + + + align:start position:0% +pretty gray so the noise signal kind of +hangs out around its average value most + + align:start position:0% +hangs out around its average value most + + + align:start position:0% +hangs out around its average value most +of the time whereas the stream has got + + align:start position:0% +of the time whereas the stream has got + + + align:start position:0% +of the time whereas the stream has got +more gray and more black and the geese + + align:start position:0% +more gray and more black and the geese + + + align:start position:0% +more gray and more black and the geese +actually has some white and some dark + + align:start position:0% +actually has some white and some dark + + + align:start position:0% +actually has some white and some dark +black so here white would correspond it + + align:start position:0% +black so here white would correspond it + + + align:start position:0% +black so here white would correspond it +down here black would correspond to up + + align:start position:0% +down here black would correspond to up + + + align:start position:0% +down here black would correspond to up +here and the intuition here is that + + align:start position:0% +here and the intuition here is that + + + align:start position:0% +here and the intuition here is that +natural signals are sparse and + + align:start position:0% +natural signals are sparse and + + + align:start position:0% +natural signals are sparse and +particularly their sparse or the noise + + align:start position:0% +particularly their sparse or the noise + + + align:start position:0% +particularly their sparse or the noise +so we think of natural signals as often + + align:start position:0% +so we think of natural signals as often + + + align:start position:0% +so we think of natural signals as often +being made up of events like raindrops + + align:start position:0% +being made up of events like raindrops + + + align:start position:0% +being made up of events like raindrops +or geese calls and these events are + + align:start position:0% +or geese calls and these events are + + + align:start position:0% +or geese calls and these events are +infrequent but when they occur they + + align:start position:0% +infrequent but when they occur they + + + align:start position:0% +infrequent but when they occur they +produce large amplitudes in the + + align:start position:0% +produce large amplitudes in the + + + align:start position:0% +produce large amplitudes in the +when they don't occur the amplitude is + + align:start position:0% +when they don't occur the amplitude is + + + align:start position:0% +when they don't occur the amplitude is +lower and contrast the noise signal + + align:start position:0% +lower and contrast the noise signal + + + align:start position:0% +lower and contrast the noise signal +doesn't really have those but the + + align:start position:0% +doesn't really have those but the + + + align:start position:0% +doesn't really have those but the +important point about this from the + + align:start position:0% +important point about this from the + + + align:start position:0% +important point about this from the +standpoint of wanting to characterize + + align:start position:0% +standpoint of wanting to characterize + + + align:start position:0% +standpoint of wanting to characterize +the signal of statistics is that this + + align:start position:0% +the signal of statistics is that this + + + align:start position:0% +the signal of statistics is that this +phenomenon of sparsity um is reflected + + align:start position:0% +phenomenon of sparsity um is reflected + + + align:start position:0% +phenomenon of sparsity um is reflected +in some pretty simple things that you + + align:start position:0% +in some pretty simple things that you + + + align:start position:0% +in some pretty simple things that you +could compute from the signal like the + + align:start position:0% +could compute from the signal like the + + + align:start position:0% +could compute from the signal like the +variance in the skew so you can see that + + align:start position:0% +variance in the skew so you can see that + + + align:start position:0% +variance in the skew so you can see that +the variance varies across these signals + + align:start position:0% +the variance varies across these signals + + + align:start position:0% +the variance varies across these signals +as does as does a skew alright let's + + align:start position:0% +as does as does a skew alright let's + + + align:start position:0% +as does as does a skew alright let's +take a quick look at what you might get + + align:start position:0% +take a quick look at what you might get + + + align:start position:0% +take a quick look at what you might get +by measuring correlations between these + + align:start position:0% +by measuring correlations between these + + + align:start position:0% +by measuring correlations between these +different channels so these things also + + align:start position:0% +different channels so these things also + + + align:start position:0% +different channels so these things also +vary across sound you can see them in + + align:start position:0% +vary across sound you can see them in + + + align:start position:0% +vary across sound you can see them in +the cochlea gram here in this particular + + align:start position:0% +the cochlea gram here in this particular + + + align:start position:0% +the cochlea gram here in this particular +example as reflected in these vertical + + align:start position:0% +example as reflected in these vertical + + + align:start position:0% +example as reflected in these vertical +streaks so this is the cochlea gram of + + align:start position:0% +streaks so this is the cochlea gram of + + + align:start position:0% +streaks so this is the cochlea gram of +fire + + align:start position:0% +fire + + + align:start position:0% +fire +um and fires got lots of crackles and + + align:start position:0% +um and fires got lots of crackles and + + + align:start position:0% +um and fires got lots of crackles and +pops and those crackles and pops of show + + align:start position:0% +pops and those crackles and pops of show + + + align:start position:0% +pops and those crackles and pops of show +up as these vertical streaks in the + + align:start position:0% +up as these vertical streaks in the + + + align:start position:0% +up as these vertical streaks in the +cochlea gram right so a crackle and pop + + align:start position:0% +cochlea gram right so a crackle and pop + + + align:start position:0% +cochlea gram right so a crackle and pop +is like a click like event clicks have + + align:start position:0% +is like a click like event clicks have + + + align:start position:0% +is like a click like event clicks have +lots of different frequencies in them + + align:start position:0% +lots of different frequencies in them + + + align:start position:0% +lots of different frequencies in them +and so you see these vertical streaks in + + align:start position:0% +and so you see these vertical streaks in + + + align:start position:0% +and so you see these vertical streaks in +the spectrogram and that introduces + + align:start position:0% +the spectrogram and that introduces + + + align:start position:0% +the spectrogram and that introduces +statistical dependencies between + + align:start position:0% +statistical dependencies between + + + align:start position:0% +statistical dependencies between +different frequency channels and so that + + align:start position:0% +different frequency channels and so that + + + align:start position:0% +different frequency channels and so that +can be measured by just computing + + align:start position:0% +can be measured by just computing + + + align:start position:0% +can be measured by just computing +correlations between the the envelopes + + align:start position:0% +correlations between the the envelopes + + + align:start position:0% +correlations between the the envelopes +of these different channels and that's + + align:start position:0% +of these different channels and that's + + + align:start position:0% +of these different channels and that's +reflected in this matrix here so every + + align:start position:0% +reflected in this matrix here so every + + + align:start position:0% +reflected in this matrix here so every +cell of this matrix is the correlation + + align:start position:0% +cell of this matrix is the correlation + + + align:start position:0% +cell of this matrix is the correlation +between a pair of channels and so we're + + align:start position:0% +between a pair of channels and so we're + + + align:start position:0% +between a pair of channels and so we're +going from low frequencies here to high + + align:start position:0% +going from low frequencies here to high + + + align:start position:0% +going from low frequencies here to high +and low to high the diagonal there's got + + align:start position:0% +and low to high the diagonal there's got + + + align:start position:0% +and low to high the diagonal there's got +to be one but the off-diagonal stuff + + align:start position:0% +to be one but the off-diagonal stuff + + + align:start position:0% +to be one but the off-diagonal stuff +give you whatever you can see for this + + align:start position:0% +give you whatever you can see for this + + + align:start position:0% +give you whatever you can see for this +example of fire um there's a lot of + + align:start position:0% +example of fire um there's a lot of + + + align:start position:0% +example of fire um there's a lot of +yellow and a lot of red which means that + + align:start position:0% +yellow and a lot of red which means that + + + align:start position:0% +yellow and a lot of red which means that +the the amplitudes of different channels + + align:start position:0% +the the amplitudes of different channels + + + align:start position:0% +the the amplitudes of different channels +tends to be correlated but this is not + + align:start position:0% +tends to be correlated but this is not + + + align:start position:0% +tends to be correlated but this is not +the case for everything so if you look + + align:start position:0% +the case for everything so if you look + + + align:start position:0% +the case for everything so if you look +at a water sound like a stream + + align:start position:0% + + + + align:start position:0% + +they're not very many things that are + + align:start position:0% +they're not very many things that are + + + align:start position:0% +they're not very many things that are +click like and most of the correlations + + align:start position:0% +click like and most of the correlations + + + align:start position:0% +click like and most of the correlations +are pretty close to zero so again this + + align:start position:0% +are pretty close to zero so again this + + + align:start position:0% +are pretty close to zero so again this +is a pretty simple thing that you can + + align:start position:0% +is a pretty simple thing that you can + + + align:start position:0% +is a pretty simple thing that you can +measure but you get different values for + + align:start position:0% +measure but you get different values for + + + align:start position:0% +measure but you get different values for +different sounds similarly if we look at + + align:start position:0% +different sounds similarly if we look at + + + align:start position:0% +different sounds similarly if we look at +the the power coming out of these + + align:start position:0% +the the power coming out of these + + + align:start position:0% +the the power coming out of these +modulation filters you also see big + + align:start position:0% +modulation filters you also see big + + + align:start position:0% +modulation filters you also see big +differences across sounds so that's + + align:start position:0% +differences across sounds so that's + + + align:start position:0% +differences across sounds so that's +plotted here for three different sound + + align:start position:0% +plotted here for three different sound + + + align:start position:0% +plotted here for three different sound +recordings sex waves and the stream and + + align:start position:0% +recordings sex waves and the stream and + + + align:start position:0% +recordings sex waves and the stream and +so remember that these modulation + + align:start position:0% +so remember that these modulation + + + align:start position:0% +so remember that these modulation +filters we think of them as being + + align:start position:0% +filters we think of them as being + + + align:start position:0% +filters we think of them as being +applied to each cochlear channel so the + + align:start position:0% +applied to each cochlear channel so the + + + align:start position:0% +applied to each cochlear channel so the +modulation power that you would get from + + align:start position:0% +modulation power that you would get from + + + align:start position:0% +modulation power that you would get from +all your modulation filters is like you + + align:start position:0% +all your modulation filters is like you + + + align:start position:0% +all your modulation filters is like you +can remember you can see that in a 2d + + align:start position:0% +can remember you can see that in a 2d + + + align:start position:0% +can remember you can see that in a 2d +plot so this is the frequency of the + + align:start position:0% +plot so this is the frequency of the + + + align:start position:0% +plot so this is the frequency of the +cochlear channel and this is the rate of + + align:start position:0% +cochlear channel and this is the rate of + + + align:start position:0% +cochlear channel and this is the rate of +the modulation channel so this is these + + align:start position:0% +the modulation channel so this is these + + + align:start position:0% +the modulation channel so this is these +are low milage slow modulations and + + align:start position:0% +are low milage slow modulations and + + + align:start position:0% +are low milage slow modulations and +these are fast modulations and so for + + align:start position:0% +these are fast modulations and so for + + + align:start position:0% +these are fast modulations and so for +the insects you can see that there are + + align:start position:0% +the insects you can see that there are + + + align:start position:0% +the insects you can see that there are +these like little blobs up here and that + + align:start position:0% +these like little blobs up here and that + + + align:start position:0% +these like little blobs up here and that +actually corresponds to their rates at + + align:start position:0% +actually corresponds to their rates at + + + align:start position:0% +actually corresponds to their rates at +which the insects rub their wings + + align:start position:0% +which the insects rub their wings + + + align:start position:0% +which the insects rub their wings +together and make the sound that they + + align:start position:0% +together and make the sound that they + + + align:start position:0% +together and make the sound that they +make which kind of gives it this + + align:start position:0% +make which kind of gives it this + + + align:start position:0% +make which kind of gives it this +shimmery quality in contrast the waves + + align:start position:0% +shimmery quality in contrast the waves + + + align:start position:0% +shimmery quality in contrast the waves +have got most of the power here at very + + align:start position:0% +have got most of the power here at very + + + align:start position:0% +have got most of the power here at very +slow modulations + + align:start position:0% + + + + align:start position:0% + +and the stream is is is pretty broadband + + align:start position:0% +and the stream is is is pretty broadband + + + align:start position:0% +and the stream is is is pretty broadband +so there's modulations that a whole + + align:start position:0% +so there's modulations that a whole + + + align:start position:0% +so there's modulations that a whole +bunch of different rates alright so just + + align:start position:0% +bunch of different rates alright so just + + + align:start position:0% +bunch of different rates alright so just +by measuring the power coming out of + + align:start position:0% +by measuring the power coming out of + + + align:start position:0% +by measuring the power coming out of +these channels we're potentially + + align:start position:0% +these channels we're potentially + + + align:start position:0% +these channels we're potentially +learning something about about what's in + + align:start position:0% +learning something about about what's in + + + align:start position:0% +learning something about about what's in +the signal and I'm gonna skip this last + + align:start position:0% +the signal and I'm gonna skip this last + + + align:start position:0% +the signal and I'm gonna skip this last +example alright so the point is just + + align:start position:0% +example alright so the point is just + + + align:start position:0% +example alright so the point is just +that when you look at these statistics + + align:start position:0% +that when you look at these statistics + + + align:start position:0% +that when you look at these statistics +they vary substantially across sound and + + align:start position:0% +they vary substantially across sound and + + + align:start position:0% +they vary substantially across sound and +so the question we were interested in is + + align:start position:0% +so the question we were interested in is + + + align:start position:0% +so the question we were interested in is +whether they could plausibly account for + + align:start position:0% +whether they could plausibly account for + + + align:start position:0% +whether they could plausibly account for +the perception of of real-world textures + + align:start position:0% +the perception of of real-world textures + + + align:start position:0% +the perception of of real-world textures +the key methodological proposal of this + + align:start position:0% +the key methodological proposal of this + + + align:start position:0% +the key methodological proposal of this +work was that synthesis is a potentially + + align:start position:0% +work was that synthesis is a potentially + + + align:start position:0% +work was that synthesis is a potentially +very powerful way to test a perceptual + + align:start position:0% +very powerful way to test a perceptual + + + align:start position:0% +very powerful way to test a perceptual +theory now maybe the the kind of + + align:start position:0% +theory now maybe the the kind of + + + align:start position:0% +theory now maybe the the kind of +standard thing that you might think that + + align:start position:0% +standard thing that you might think that + + + align:start position:0% +standard thing that you might think that +you might might try to do with this type + + align:start position:0% +you might might try to do with this type + + + align:start position:0% +you might might try to do with this type +of representation is measure these + + align:start position:0% +of representation is measure these + + + align:start position:0% +of representation is measure these +statistics and then see whether for + + align:start position:0% +statistics and then see whether for + + + align:start position:0% +statistics and then see whether for +instance you could discriminate between + + align:start position:0% +instance you could discriminate between + + + align:start position:0% +instance you could discriminate between +different signals or maybe please and + + align:start position:0% +different signals or maybe please and + + + align:start position:0% +different signals or maybe please and +and for various reasons I actually think + + align:start position:0% +and for various reasons I actually think + + + align:start position:0% +and for various reasons I actually think +that synthesis is potentially a lot more + + align:start position:0% +that synthesis is potentially a lot more + + + align:start position:0% +that synthesis is potentially a lot more +powerful and the notion is this is that + + align:start position:0% +powerful and the notion is this is that + + + align:start position:0% +powerful and the notion is this is that +if your brain is representing sounds + + align:start position:0% +if your brain is representing sounds + + + align:start position:0% +if your brain is representing sounds +with some set of measurements then + + align:start position:0% +with some set of measurements then + + + align:start position:0% +with some set of measurements then +signals that have the same values of + + align:start position:0% +signals that have the same values of + + + align:start position:0% +signals that have the same values of +those measurements ought to sound the + + align:start position:0% +those measurements ought to sound the + + + align:start position:0% +those measurements ought to sound the +same to you and so in particular if + + align:start position:0% +same to you and so in particular if + + + align:start position:0% +same to you and so in particular if +we've got some real-world recording and + + align:start position:0% +we've got some real-world recording and + + + align:start position:0% +we've got some real-world recording and +we synthesize a signal to cause it to + + align:start position:0% +we synthesize a signal to cause it to + + + align:start position:0% +we synthesize a signal to cause it to +have measurements the statistics in this + + align:start position:0% +have measurements the statistics in this + + + align:start position:0% +have measurements the statistics in this +case as that real-world recording well + + align:start position:0% +case as that real-world recording well + + + align:start position:0% +case as that real-world recording well +then the synthetic signal ought to sound + + align:start position:0% +then the synthetic signal ought to sound + + + align:start position:0% +then the synthetic signal ought to sound +like the the real-world recording if the + + align:start position:0% +like the the real-world recording if the + + + align:start position:0% +like the the real-world recording if the +measurements that we use are like the + + align:start position:0% +measurements that we use are like the + + + align:start position:0% +measurements that we use are like the +ones that the brain is using to + + align:start position:0% +ones that the brain is using to + + + align:start position:0% +ones that the brain is using to +represent sound and so we can + + align:start position:0% +represent sound and so we can + + + align:start position:0% +represent sound and so we can +potentially use synthesis then to test + + align:start position:0% +potentially use synthesis then to test + + + align:start position:0% +potentially use synthesis then to test +whether the candidate representation in + + align:start position:0% +whether the candidate representation in + + + align:start position:0% +whether the candidate representation in +this case these statistics that we're + + align:start position:0% +this case these statistics that we're + + + align:start position:0% +this case these statistics that we're +measuring are full representation for + + align:start position:0% +measuring are full representation for + + + align:start position:0% +measuring are full representation for +the brain to be using so here's just a + + align:start position:0% +the brain to be using so here's just a + + + align:start position:0% +the brain to be using so here's just a +simple example to kind of walk you + + align:start position:0% +simple example to kind of walk you + + + align:start position:0% +simple example to kind of walk you +through the logic so let's suppose that + + align:start position:0% +through the logic so let's suppose that + + + align:start position:0% +through the logic so let's suppose that +you had a relatively simple theory of + + align:start position:0% +you had a relatively simple theory of + + + align:start position:0% +you had a relatively simple theory of +sound texture perception which is that + + align:start position:0% +sound texture perception which is that + + + align:start position:0% +sound texture perception which is that +texture perception might be rooted in + + align:start position:0% +texture perception might be rooted in + + + align:start position:0% +texture perception might be rooted in +the power spectrum it's not so + + align:start position:0% +the power spectrum it's not so + + + align:start position:0% +the power spectrum it's not so +implausible lots of people think the + + align:start position:0% +implausible lots of people think the + + + align:start position:0% +implausible lots of people think the +power spectrum is sort of a useful way + + align:start position:0% +power spectrum is sort of a useful way + + + align:start position:0% +power spectrum is sort of a useful way +to characterize and you might think that + + align:start position:0% +to characterize and you might think that + + + align:start position:0% +to characterize and you might think that +it would have something to do with with + + align:start position:0% +it would have something to do with with + + + align:start position:0% +it would have something to do with with +the way textures would sound and so in + + align:start position:0% +the way textures would sound and so in + + + align:start position:0% +the way textures would sound and so in +the context of our auditory model the + + align:start position:0% +the context of our auditory model the + + + align:start position:0% +the context of our auditory model the +power spectrum is captured by the + + align:start position:0% +power spectrum is captured by the + + + align:start position:0% +power spectrum is captured by the +average value of each envelope remember + + align:start position:0% +average value of each envelope remember + + + align:start position:0% +average value of each envelope remember +the envelopes telling you the + + align:start position:0% +the envelopes telling you the + + + align:start position:0% +the envelopes telling you the +instantaneous amplitude and so you've + + align:start position:0% +instantaneous amplitude and so you've + + + align:start position:0% +instantaneous amplitude and so you've +just averaged that you're gonna find out + + align:start position:0% +just averaged that you're gonna find out + + + align:start position:0% +just averaged that you're gonna find out +how much power is in each frequency + + align:start position:0% +how much power is in each frequency + + + align:start position:0% +how much power is in each frequency +Channel and so that's that's how you + + align:start position:0% +Channel and so that's that's how you + + + align:start position:0% +Channel and so that's that's how you +would do it in the this framework so the + + align:start position:0% +would do it in the this framework so the + + + align:start position:0% +would do it in the this framework so the +way this is + + align:start position:0% +way this is + + + align:start position:0% +way this is +get some sound signal say this you'd + + align:start position:0% +get some sound signal say this you'd + + + align:start position:0% +get some sound signal say this you'd +pass it through the model you'd measure + + align:start position:0% +pass it through the model you'd measure + + + align:start position:0% +pass it through the model you'd measure +the average value of the envelope so you + + align:start position:0% +the average value of the envelope so you + + + align:start position:0% +the average value of the envelope so you +get a set of 30 numbers say if you have + + align:start position:0% +get a set of 30 numbers say if you have + + + align:start position:0% +get a set of 30 numbers say if you have +if you have 30 bandpass filters they're + + align:start position:0% +if you have 30 bandpass filters they're + + + align:start position:0% +if you have 30 bandpass filters they're +at the output of each one of those you + + align:start position:0% +at the output of each one of those you + + + align:start position:0% +at the output of each one of those you +get the average value the envelope so + + align:start position:0% +get the average value the envelope so + + + align:start position:0% +get the average value the envelope so +you get 30 numbers and then you take + + align:start position:0% +you get 30 numbers and then you take + + + align:start position:0% +you get 30 numbers and then you take +those 30 numbers and you want to signal + + align:start position:0% +those 30 numbers and you want to signal + + + align:start position:0% +those 30 numbers and you want to signal +subject to the constraint of it having + + align:start position:0% +subject to the constraint of it having + + + align:start position:0% +subject to the constraint of it having +the same values for those 30 numbers and + + align:start position:0% +the same values for those 30 numbers and + + + align:start position:0% +the same values for those 30 numbers and +so in this case it's pretty simple to do + + align:start position:0% +so in this case it's pretty simple to do + + + align:start position:0% +so in this case it's pretty simple to do +so we take a noise signal we want to + + align:start position:0% +so we take a noise signal we want to + + + align:start position:0% +so we take a noise signal we want to +start out as random as possible so we + + align:start position:0% +start out as random as possible so we + + + align:start position:0% +start out as random as possible so we +take a noise signal we generate its sub + + align:start position:0% +take a noise signal we generate its sub + + + align:start position:0% +take a noise signal we generate its sub +bands and then we just scale the sub + + align:start position:0% +bands and then we just scale the sub + + + align:start position:0% +bands and then we just scale the sub +bins up or down so that they have the + + align:start position:0% +bins up or down so that they have the + + + align:start position:0% +bins up or down so that they have the +right amount of power and we add them + + align:start position:0% +right amount of power and we add them + + + align:start position:0% +right amount of power and we add them +back up and we get a new sound suit well + + align:start position:0% +back up and we get a new sound suit well + + + align:start position:0% +back up and we get a new sound suit well +then we listen to it and we see whether + + align:start position:0% +then we listen to it and we see whether + + + align:start position:0% +then we listen to it and we see whether +it's I don't thing ok here do they sound + + align:start position:0% +it's I don't thing ok here do they sound + + + align:start position:0% +it's I don't thing ok here do they sound +like and as you as you'll hear they just + + align:start position:0% +like and as you as you'll hear they just + + + align:start position:0% +like and as you as you'll hear they just +sound like noise basically right so this + + align:start position:0% +sound like noise basically right so this + + + align:start position:0% +sound like noise basically right so this +is supposed to sound like rain or a + + align:start position:0% +is supposed to sound like rain or a + + + align:start position:0% +is supposed to sound like rain or a +stream + + align:start position:0% + + + + align:start position:0% + +our bubbles + + align:start position:0% +our bubbles + + + align:start position:0% +our bubbles +or fire or applause so you might notice + + align:start position:0% +or fire or applause so you might notice + + + align:start position:0% +or fire or applause so you might notice +that they sound different right and you + + align:start position:0% +that they sound different right and you + + + align:start position:0% +that they sound different right and you +might have even been able to convince + + align:start position:0% +might have even been able to convince + + + align:start position:0% +might have even been able to convince +yourself what a little bit like applause + + align:start position:0% +yourself what a little bit like applause + + + align:start position:0% +yourself what a little bit like applause +all right so there's something there but + + align:start position:0% +all right so there's something there but + + + align:start position:0% +all right so there's something there but +the point is that they don't sound + + align:start position:0% +the point is that they don't sound + + + align:start position:0% +the point is that they don't sound +anything like or so on and so forth okay + + align:start position:0% +anything like or so on and so forth okay + + + align:start position:0% +anything like or so on and so forth okay +all right so the point is that + + align:start position:0% +all right so the point is that + + + align:start position:0% +all right so the point is that +everything just sounds like noise and so + + align:start position:0% +everything just sounds like noise and so + + + align:start position:0% +everything just sounds like noise and so +what this tells us is that our brains + + align:start position:0% +what this tells us is that our brains + + + align:start position:0% +what this tells us is that our brains +are not simply registering the spectrum + + align:start position:0% +are not simply registering the spectrum + + + align:start position:0% +are not simply registering the spectrum +when we recognize these textures + + align:start position:0% +when we recognize these textures + + + align:start position:0% +when we recognize these textures +question is whether additional simple + + align:start position:0% +question is whether additional simple + + + align:start position:0% +question is whether additional simple +statistics will do any better and so + + align:start position:0% +statistics will do any better and so + + + align:start position:0% +statistics will do any better and so +we're gonna play the same game right + + align:start position:0% +we're gonna play the same game right + + + align:start position:0% +we're gonna play the same game right +except we have a souped up + + align:start position:0% +except we have a souped up + + + align:start position:0% +except we have a souped up +representation that's got all these + + align:start position:0% +representation that's got all these + + + align:start position:0% +representation that's got all these +other things in it and so the + + align:start position:0% +other things in it and so the + + + align:start position:0% +other things in it and so the +consequence of this is that the the + + align:start position:0% +consequence of this is that the the + + + align:start position:0% +consequence of this is that the the +process of synthesizing something is is + + align:start position:0% +process of synthesizing something is is + + + align:start position:0% +process of synthesizing something is is +less straightforward and so I was an + + align:start position:0% +less straightforward and so I was an + + + align:start position:0% +less straightforward and so I was an +heiress always at the lab at the time + + align:start position:0% +heiress always at the lab at the time + + + align:start position:0% +heiress always at the lab at the time +and spent like a while trying to get + + align:start position:0% +and spent like a while trying to get + + + align:start position:0% +and spent like a while trying to get +this to work and eventually we got it to + + align:start position:0% +this to work and eventually we got it to + + + align:start position:0% +this to work and eventually we got it to +work but conceptually the process is the + + align:start position:0% +work but conceptually the process is the + + + align:start position:0% +work but conceptually the process is the +same so you you have some original sound + + align:start position:0% +same so you you have some original sound + + + align:start position:0% +same so you you have some original sound +recording rain or what have you you pass + + align:start position:0% +recording rain or what have you you pass + + + align:start position:0% +recording rain or what have you you pass +it through your auditory model and then + + align:start position:0% +it through your auditory model and then + + + align:start position:0% +it through your auditory model and then +you measure some set of statistics and + + align:start position:0% +you measure some set of statistics and + + + align:start position:0% +you measure some set of statistics and +then you you start out with a noise + + align:start position:0% +then you you start out with a noise + + + align:start position:0% +then you you start out with a noise +signal you pass it through the same + + align:start position:0% +signal you pass it through the same + + + align:start position:0% +signal you pass it through the same +model you measure its statistics and + + align:start position:0% +model you measure its statistics and + + + align:start position:0% +model you measure its statistics and +those will in general be different from + + align:start position:0% +those will in general be different from + + + align:start position:0% +those will in general be different from +the target values and so you get some + + align:start position:0% +the target values and so you get some + + + align:start position:0% +the target values and so you get some +error signal here and you use that error + + align:start position:0% +error signal here and you use that error + + + align:start position:0% +error signal here and you use that error +signal to perform gradient descent on + + align:start position:0% +signal to perform gradient descent on + + + align:start position:0% +signal to perform gradient descent on +the representation of the noise in the + + align:start position:0% +the representation of the noise in the + + + align:start position:0% +the representation of the noise in the +auditory model and so you cause the the + + align:start position:0% +auditory model and so you cause the the + + + align:start position:0% +auditory model and so you cause the the +envelopes of the noise signal to change + + align:start position:0% +envelopes of the noise signal to change + + + align:start position:0% +envelopes of the noise signal to change +in ways that cause their statistics to + + align:start position:0% +in ways that cause their statistics to + + + align:start position:0% +in ways that cause their statistics to +move towards the target value um and + + align:start position:0% +move towards the target value um and + + + align:start position:0% +move towards the target value um and +there's there's a procedure here by + + align:start position:0% +there's there's a procedure here by + + + align:start position:0% +there's there's a procedure here by +which this is iterated and I'm not going + + align:start position:0% +which this is iterated and I'm not going + + + align:start position:0% +which this is iterated and I'm not going +to get into the details if you want to + + align:start position:0% +to get into the details if you want to + + + align:start position:0% +to get into the details if you want to +play around with it there's a toolbox + + align:start position:0% +play around with it there's a toolbox + + + align:start position:0% +play around with it there's a toolbox +that's now available on the lab website + + align:start position:0% +that's now available on the lab website + + + align:start position:0% +that's now available on the lab website +if if you want to do that and it's + + align:start position:0% +if if you want to do that and it's + + + align:start position:0% +if if you want to do that and it's +described in more detail in that paper + + align:start position:0% +described in more detail in that paper + + + align:start position:0% +described in more detail in that paper +all right so the result the whole point + + align:start position:0% +all right so the result the whole point + + + align:start position:0% +all right so the result the whole point +of this is that we get a signal that + + align:start position:0% +of this is that we get a signal that + + + align:start position:0% +of this is that we get a signal that +shares the statistics of some real words + + align:start position:0% +shares the statistics of some real words + + + align:start position:0% +shares the statistics of some real words +how do they sound and remember we're + + align:start position:0% +how do they sound and remember we're + + + align:start position:0% +how do they sound and remember we're +interested in this because if these + + align:start position:0% +interested in this because if these + + + align:start position:0% +interested in this because if these +statistics if this candidate + + align:start position:0% +statistics if this candidate + + + align:start position:0% +statistics if this candidate +representation accounts for our + + align:start position:0% +representation accounts for our + + + align:start position:0% +representation accounts for our +perception of texture well then the + + align:start position:0% +perception of texture well then the + + + align:start position:0% +perception of texture well then the +synthetic signals are ought to sound + + align:start position:0% +synthetic signals are ought to sound + + + align:start position:0% +synthetic signals are ought to sound +like new examples of the real thing and + + align:start position:0% +like new examples of the real thing and + + + align:start position:0% +like new examples of the real thing and +the cool thing and rewarding part of + + align:start position:0% +the cool thing and rewarding part of + + + align:start position:0% +the cool thing and rewarding part of +this whole thing is that it make as they + + align:start position:0% +this whole thing is that it make as they + + + align:start position:0% +this whole thing is that it make as they +do so I'm just gonna play the the + + align:start position:0% +do so I'm just gonna play the the + + + align:start position:0% +do so I'm just gonna play the the +synthetic versions all these were + + align:start position:0% +synthetic versions all these were + + + align:start position:0% +synthetic versions all these were +generated is just by causing + + align:start position:0% +generated is just by causing + + + align:start position:0% +generated is just by causing +the noise to match the statistics of in + + align:start position:0% +the noise to match the statistics of in + + + align:start position:0% +the noise to match the statistics of in +this case rain stream and crab noise + + align:start position:0% + + + + align:start position:0% + +alright also works for a lot of troll + + align:start position:0% +alright also works for a lot of troll + + + align:start position:0% +alright also works for a lot of troll +sounds there's rustling paper and eject + + align:start position:0% + + + + align:start position:0% + +all right so the cool thing about this + + align:start position:0% +all right so the cool thing about this + + + align:start position:0% +all right so the cool thing about this +is is you can put it whatever you want + + align:start position:0% +is is you can put it whatever you want + + + align:start position:0% +is is you can put it whatever you want +in there right you can measure the + + align:start position:0% +in there right you can measure the + + + align:start position:0% +in there right you can measure the +statistics from anything and you can + + align:start position:0% +statistics from anything and you can + + + align:start position:0% +statistics from anything and you can +generate something that is statistically + + align:start position:0% +generate something that is statistically + + + align:start position:0% +generate something that is statistically +matched and when you do this with a lot + + align:start position:0% +matched and when you do this with a lot + + + align:start position:0% +matched and when you do this with a lot +of textures you tend to get something + + align:start position:0% +of textures you tend to get something + + + align:start position:0% +of textures you tend to get something +that sort of captures some of the the + + align:start position:0% +that sort of captures some of the the + + + align:start position:0% +that sort of captures some of the the +qualitative properties um and so the + + align:start position:0% +qualitative properties um and so the + + + align:start position:0% +qualitative properties um and so the +success of the synthesis in this case + + align:start position:0% +success of the synthesis in this case + + + align:start position:0% +success of the synthesis in this case +the reason why this is scientifically + + align:start position:0% +the reason why this is scientifically + + + align:start position:0% +the reason why this is scientifically +interesting in addition to fun is that + + align:start position:0% +interesting in addition to fun is that + + + align:start position:0% +interesting in addition to fun is that +it lends plausibility to the notion that + + align:start position:0% +it lends plausibility to the notion that + + + align:start position:0% +it lends plausibility to the notion that +these statistics could underlie on the + + align:start position:0% +these statistics could underlie on the + + + align:start position:0% +these statistics could underlie on the +representation and recognition of + + align:start position:0% +representation and recognition of + + + align:start position:0% +representation and recognition of +textures + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/HeyEK0TWiBw.txt b/HeyEK0TWiBw.txt new file mode 100644 index 0000000000000000000000000000000000000000..35db23fee26ec1cc9a8814a448ccfe244db09bf2 --- /dev/null +++ b/HeyEK0TWiBw.txt @@ -0,0 +1,1715 @@ +align:start position:0% + +an advantage of expressing the + + align:start position:0% +an advantage of expressing the + + + align:start position:0% +an advantage of expressing the +asymptotic notations in terms of limits + + align:start position:0% +asymptotic notations in terms of limits + + + align:start position:0% +asymptotic notations in terms of limits +is that a bunch of their properties then + + align:start position:0% +is that a bunch of their properties then + + + align:start position:0% +is that a bunch of their properties then +become immediately obvious here's one if + + align:start position:0% +become immediately obvious here's one if + + + align:start position:0% +become immediately obvious here's one if +F is little o of J or F is + + align:start position:0% +F is little o of J or F is + + + align:start position:0% +F is little o of J or F is +asymptotically equal to J then in fact F + + align:start position:0% +asymptotically equal to J then in fact F + + + align:start position:0% +asymptotically equal to J then in fact F +is Big O of J well we can reason about + + align:start position:0% +is Big O of J well we can reason about + + + align:start position:0% +is Big O of J well we can reason about +this informally by saying that the first + + align:start position:0% +this informally by saying that the first + + + align:start position:0% +this informally by saying that the first +one means that F is much less than J and + + align:start position:0% +one means that F is much less than J and + + + align:start position:0% +one means that F is much less than J and +the second one means that F is about the + + align:start position:0% +the second one means that F is about the + + + align:start position:0% +the second one means that F is about the +same as J and the final one means that F + + align:start position:0% +same as J and the final one means that F + + + align:start position:0% +same as J and the final one means that F +is roughly less so being about the same + + align:start position:0% +is roughly less so being about the same + + + align:start position:0% +is roughly less so being about the same +in definitely less is certainly this + + align:start position:0% +in definitely less is certainly this + + + align:start position:0% +in definitely less is certainly this +implies roughly less but we can in fact + + align:start position:0% +implies roughly less but we can in fact + + + align:start position:0% +implies roughly less but we can in fact +be entirely precise just using the + + align:start position:0% +be entirely precise just using the + + + align:start position:0% +be entirely precise just using the +definitions because F equals o of G + + align:start position:0% +definitions because F equals o of G + + + align:start position:0% +definitions because F equals o of G +means the limit of F over G is 0 and F + + align:start position:0% +means the limit of F over G is 0 and F + + + align:start position:0% +means the limit of F over G is 0 and F +is asymptotically equal to G means that + + align:start position:0% +is asymptotically equal to G means that + + + align:start position:0% +is asymptotically equal to G means that +the limit of F over G is 1 and the + + align:start position:0% +the limit of F over G is 1 and the + + + align:start position:0% +the limit of F over G is 1 and the +definition of F equals Big O of G is + + align:start position:0% +definition of F equals Big O of G is + + + align:start position:0% +definition of F equals Big O of G is +that the limit is finite and clearly if + + align:start position:0% +that the limit is finite and clearly if + + + align:start position:0% +that the limit is finite and clearly if +it's 0 or 1 then it's finite um another + + align:start position:0% +it's 0 or 1 then it's finite um another + + + align:start position:0% +it's 0 or 1 then it's finite um another +such property is that if F is much less + + align:start position:0% +such property is that if F is much less + + + align:start position:0% +such property is that if F is much less +than G then G is not roughly less than F + + align:start position:0% +than G then G is not roughly less than F + + + align:start position:0% +than G then G is not roughly less than F +more precisely if F is little o of G + + align:start position:0% +more precisely if F is little o of G + + + align:start position:0% +more precisely if F is little o of G +then G is not Big O of F the left hand + + align:start position:0% +then G is not Big O of F the left hand + + + align:start position:0% +then G is not Big O of F the left hand +side says that the limit of F over G is + + align:start position:0% +side says that the limit of F over G is + + + align:start position:0% +side says that the limit of F over G is +0 but that implies that the limit of G + + align:start position:0% +0 but that implies that the limit of G + + + align:start position:0% +0 but that implies that the limit of G +over F is 1 over 0 or infinity which + + align:start position:0% +over F is 1 over 0 or infinity which + + + align:start position:0% +over F is 1 over 0 or infinity which +means it's not finite so G is not Big O + + align:start position:0% +means it's not finite so G is not Big O + + + align:start position:0% +means it's not finite so G is not Big O +of F now the usual way that Big O is + + align:start position:0% +of F now the usual way that Big O is + + + align:start position:0% +of F now the usual way that Big O is +defined in the literature doesn't + + align:start position:0% +defined in the literature doesn't + + + align:start position:0% +defined in the literature doesn't +mention limits at all and in fact as I + + align:start position:0% +mention limits at all and in fact as I + + + align:start position:0% +mention limits at all and in fact as I +said the definition really isn't a limit + + align:start position:0% +said the definition really isn't a limit + + + align:start position:0% +said the definition really isn't a limit +it's a limb soup and let me show you the + + align:start position:0% +it's a limb soup and let me show you the + + + align:start position:0% +it's a limb soup and let me show you the +standard definition and then he + + align:start position:0% +standard definition and then he + + + align:start position:0% +standard definition and then he +explained why the limb soup captures it + + align:start position:0% +explained why the limb soup captures it + + + align:start position:0% +explained why the limb soup captures it +and is needed so the definitely the + + align:start position:0% +and is needed so the definitely the + + + align:start position:0% +and is needed so the definitely the +official definition of F is Big O of G + + align:start position:0% +official definition of F is Big O of G + + + align:start position:0% +official definition of F is Big O of G +is that there's some constant multiplied + + align:start position:0% +is that there's some constant multiplied + + + align:start position:0% +is that there's some constant multiplied +or see that you can amplify G by such + + align:start position:0% +or see that you can amplify G by such + + + align:start position:0% +or see that you can amplify G by such +that once G is amplified by the factor C + + align:start position:0% +that once G is amplified by the factor C + + + align:start position:0% +that once G is amplified by the factor C +then in fact F is less than or equal to + + align:start position:0% +then in fact F is less than or equal to + + + align:start position:0% +then in fact F is less than or equal to +C times J but this doesn't may not hold + + align:start position:0% +C times J but this doesn't may not hold + + + align:start position:0% +C times J but this doesn't may not hold +right at the beginning there's a certain + + align:start position:0% +right at the beginning there's a certain + + + align:start position:0% +right at the beginning there's a certain +point and 0 after which it holds forever + + align:start position:0% +point and 0 after which it holds forever + + + align:start position:0% +point and 0 after which it holds forever +let's try to illustrate this + + align:start position:0% +let's try to illustrate this + + + align:start position:0% +let's try to illustrate this +complicated alternation of quantifiers + + align:start position:0% +complicated alternation of quantifiers + + + align:start position:0% +complicated alternation of quantifiers +expression with a diagram that may make + + align:start position:0% +expression with a diagram that may make + + + align:start position:0% +expression with a diagram that may make +it clearer so suppose that I want to + + align:start position:0% +it clearer so suppose that I want to + + + align:start position:0% +it clearer so suppose that I want to +express the fact that F is Big O of G + + align:start position:0% +express the fact that F is Big O of G + + + align:start position:0% +express the fact that F is Big O of G +where F is a green line so that green + + align:start position:0% +where F is a green line so that green + + + align:start position:0% +where F is a green line so that green +line is the graph of f of X the function + + align:start position:0% +line is the graph of f of X the function + + + align:start position:0% +line is the graph of f of X the function +and G in blue is shown and as a matter + + align:start position:0% +and G in blue is shown and as a matter + + + align:start position:0% +and G in blue is shown and as a matter +of fact G of X is less than or equal to + + align:start position:0% +of fact G of X is less than or equal to + + + align:start position:0% +of fact G of X is less than or equal to +f of X but nevertheless F is gonna be + + align:start position:0% +f of X but nevertheless F is gonna be + + + align:start position:0% +f of X but nevertheless F is gonna be +little o Big O of G because if you + + align:start position:0% +little o Big O of G because if you + + + align:start position:0% +little o Big O of G because if you +multiply G by a constant it becomes + + align:start position:0% +multiply G by a constant it becomes + + + align:start position:0% +multiply G by a constant it becomes +where we're sort of shifting it up to it + + align:start position:0% +where we're sort of shifting it up to it + + + align:start position:0% +where we're sort of shifting it up to it +be this constant times G it becomes this + + align:start position:0% +be this constant times G it becomes this + + + align:start position:0% +be this constant times G it becomes this +purple curve and the purple curve it + + align:start position:0% +purple curve and the purple curve it + + + align:start position:0% +purple curve and the purple curve it +gets to be above the green curve from a + + align:start position:0% +gets to be above the green curve from a + + + align:start position:0% +gets to be above the green curve from a +certain point on that's n0 so by raising + + align:start position:0% +certain point on that's n0 so by raising + + + align:start position:0% +certain point on that's n0 so by raising +up the blue curve G by an amount C to + + align:start position:0% +up the blue curve G by an amount C to + + + align:start position:0% +up the blue curve G by an amount C to +get it to be this purple curve the + + align:start position:0% +get it to be this purple curve the + + + align:start position:0% +get it to be this purple curve the +purple curve gets above F from a certain + + align:start position:0% +purple curve gets above F from a certain + + + align:start position:0% +purple curve gets above F from a certain +point n0 on and that's why F is Big O of + + align:start position:0% +point n0 on and that's why F is Big O of + + + align:start position:0% +point n0 on and that's why F is Big O of +G now of course multiplying the blue + + align:start position:0% +G now of course multiplying the blue + + + align:start position:0% +G now of course multiplying the blue +curve G by a constant doesn't raise it + + align:start position:0% +curve G by a constant doesn't raise it + + + align:start position:0% +curve G by a constant doesn't raise it +up a fixed amount it alters it but if we + + align:start position:0% +up a fixed amount it alters it but if we + + + align:start position:0% +up a fixed amount it alters it but if we +imagine that our curve was a log scale + + align:start position:0% +imagine that our curve was a log scale + + + align:start position:0% +imagine that our curve was a log scale +than in fact multiplying G by C is the + + align:start position:0% +than in fact multiplying G by C is the + + + align:start position:0% +than in fact multiplying G by C is the +same as adding log C on a log scale so + + align:start position:0% +same as adding log C on a log scale so + + + align:start position:0% +same as adding log C on a log scale so +the picture is actually accurate if the + + align:start position:0% +the picture is actually accurate if the + + + align:start position:0% +the picture is actually accurate if the +vertical scale is logarithmic so using + + align:start position:0% +vertical scale is logarithmic so using + + + align:start position:0% +vertical scale is logarithmic so using +this standard definition I can explain + + align:start position:0% +this standard definition I can explain + + + align:start position:0% +this standard definition I can explain +why in the equivalent definition of + + align:start position:0% +why in the equivalent definition of + + + align:start position:0% +why in the equivalent definition of +terms of limit I couldn't say limit I + + align:start position:0% +terms of limit I couldn't say limit I + + + align:start position:0% +terms of limit I couldn't say limit I +needed to say limb soup here's what limb + + align:start position:0% +needed to say limb soup here's what limb + + + align:start position:0% +needed to say limb soup here's what limb +soup does for us suppose I have a + + align:start position:0% +soup does for us suppose I have a + + + align:start position:0% +soup does for us suppose I have a +function f that say less than or equal + + align:start position:0% +function f that say less than or equal + + + align:start position:0% +function f that say less than or equal +to 2 G which means that surely F is Big + + align:start position:0% +to 2 G which means that surely F is Big + + + align:start position:0% +to 2 G which means that surely F is Big +O of g according to the previous + + align:start position:0% +O of g according to the previous + + + align:start position:0% +O of g according to the previous +definition because you amplify G by 2 + + align:start position:0% +definition because you amplify G by 2 + + + align:start position:0% +definition because you amplify G by 2 +and you get above F the problem is that + + align:start position:0% +and you get above F the problem is that + + + align:start position:0% +and you get above F the problem is that +F of n over G event may have no limit so + + align:start position:0% +F of n over G event may have no limit so + + + align:start position:0% +F of n over G event may have no limit so +I can't simply say that F is o of G + + align:start position:0% +I can't simply say that F is o of G + + + align:start position:0% +I can't simply say that F is o of G +because the limit of F over G is finite + + align:start position:0% +because the limit of F over G is finite + + + align:start position:0% +because the limit of F over G is finite +let's see what how that could happen + + align:start position:0% +let's see what how that could happen + + + align:start position:0% +let's see what how that could happen +suppose that F is in fact equal to G + + align:start position:0% +suppose that F is in fact equal to G + + + align:start position:0% +suppose that F is in fact equal to G +times a number that varies between 1 & 2 + + align:start position:0% +times a number that varies between 1 & 2 + + + align:start position:0% +times a number that varies between 1 & 2 +that's an example where um sine of n PI + + align:start position:0% +that's an example where um sine of n PI + + + align:start position:0% +that's an example where um sine of n PI +over two varies between 0 1 and -1 and + + align:start position:0% +over two varies between 0 1 and -1 and + + + align:start position:0% +over two varies between 0 1 and -1 and +you square it it becomes 0 or 1 and you + + align:start position:0% +you square it it becomes 0 or 1 and you + + + align:start position:0% +you square it it becomes 0 or 1 and you +add 1 to it it becomes 1 or 2 so this is + + align:start position:0% +add 1 to it it becomes 1 or 2 so this is + + + align:start position:0% +add 1 to it it becomes 1 or 2 so this is +an expression which as n grows + + align:start position:0% +an expression which as n grows + + + align:start position:0% +an expression which as n grows +alternates between the values 1 and 2 + + align:start position:0% +alternates between the values 1 and 2 + + + align:start position:0% +alternates between the values 1 and 2 +and I'm multiplying G of n by this + + align:start position:0% +and I'm multiplying G of n by this + + + align:start position:0% +and I'm multiplying G of n by this +constant that's either by this factor + + align:start position:0% +constant that's either by this factor + + + align:start position:0% +constant that's either by this factor +this either 1 or 2 but the limit of f of + + align:start position:0% +this either 1 or 2 but the limit of f of + + + align:start position:0% +this either 1 or 2 but the limit of f of +n over G of n does not exist it's + + align:start position:0% +n over G of n does not exist it's + + + align:start position:0% +n over G of n does not exist it's +alternating between 1 & 2 on the other + + align:start position:0% +alternating between 1 & 2 on the other + + + align:start position:0% +alternating between 1 & 2 on the other +hand the limb soup of F and of n over G + + align:start position:0% +hand the limb soup of F and of n over G + + + align:start position:0% +hand the limb soup of F and of n over G +is 2 which is finite and therefore + + align:start position:0% +is 2 which is finite and therefore + + + align:start position:0% +is 2 which is finite and therefore +according to the limb soup definition + + align:start position:0% +according to the limb soup definition + + + align:start position:0% +according to the limb soup definition +indeed f is o of G now the technical + + align:start position:0% +indeed f is o of G now the technical + + + align:start position:0% +indeed f is o of G now the technical +definition of limb soup is one that you + + align:start position:0% +definition of limb soup is one that you + + + align:start position:0% +definition of limb soup is one that you +can read in the text or find in a + + align:start position:0% +can read in the text or find in a + + + align:start position:0% +can read in the text or find in a +calculus book it's basically the largest + + align:start position:0% +calculus book it's basically the largest + + + align:start position:0% +calculus book it's basically the largest +limit point of the fraction f of n over + + align:start position:0% +limit point of the fraction f of n over + + + align:start position:0% +limit point of the fraction f of n over +G of n and if you don't know what a + + align:start position:0% +G of n and if you don't know what a + + + align:start position:0% +G of n and if you don't know what a +limit point is it's stuff that we don't + + align:start position:0% +limit point is it's stuff that we don't + + + align:start position:0% +limit point is it's stuff that we don't +need to go into but I did want you to + + align:start position:0% +need to go into but I did want you to + + + align:start position:0% +need to go into but I did want you to +understand why formally we need Lim soap + + align:start position:0% +understand why formally we need Lim soap + + + align:start position:0% +understand why formally we need Lim soap +in most cases the limit exists and we + + align:start position:0% +in most cases the limit exists and we + + + align:start position:0% +in most cases the limit exists and we +can use the simpler limit definition + + align:start position:0% +can use the simpler limit definition + + + align:start position:0% +can use the simpler limit definition +rather than the exists a constant such + + align:start position:0% +rather than the exists a constant such + + + align:start position:0% +rather than the exists a constant such +that for every number and grade wrinkles + + align:start position:0% +that for every number and grade wrinkles + + + align:start position:0% +that for every number and grade wrinkles +and 0 etc which is a more complicated + + align:start position:0% +and 0 etc which is a more complicated + + + align:start position:0% +and 0 etc which is a more complicated +definition okay + + align:start position:0% +definition okay + + + align:start position:0% +definition okay +let's collect a couple of more basic + + align:start position:0% +let's collect a couple of more basic + + + align:start position:0% +let's collect a couple of more basic +facts about little o on that and Big O + + align:start position:0% +facts about little o on that and Big O + + + align:start position:0% +facts about little o on that and Big O +that we're going to need namely that if + + align:start position:0% +that we're going to need namely that if + + + align:start position:0% +that we're going to need namely that if +a is less than B it can be negative + + align:start position:0% +a is less than B it can be negative + + + align:start position:0% +a is less than B it can be negative +numbers I don't care but real numbers if + + align:start position:0% +numbers I don't care but real numbers if + + + align:start position:0% +numbers I don't care but real numbers if +a is less than B then X to the a is + + align:start position:0% +a is less than B then X to the a is + + + align:start position:0% +a is less than B then X to the a is +little o of X to the B the proof follows + + align:start position:0% +little o of X to the B the proof follows + + + align:start position:0% +little o of X to the B the proof follows +almost immediately from the definitions + + align:start position:0% +almost immediately from the definitions + + + align:start position:0% +almost immediately from the definitions +because to prove that X to the a is + + align:start position:0% +because to prove that X to the a is + + + align:start position:0% +because to prove that X to the a is +little o of X to the B we want to look + + align:start position:0% +little o of X to the B we want to look + + + align:start position:0% +little o of X to the B we want to look +at the quotient of X to the a over X to + + align:start position:0% +at the quotient of X to the a over X to + + + align:start position:0% +at the quotient of X to the a over X to +the B but of course the quotient of X to + + align:start position:0% +the B but of course the quotient of X to + + + align:start position:0% +the B but of course the quotient of X to +the a over X to the B is equal to 1 over + + align:start position:0% +the a over X to the B is equal to 1 over + + + align:start position:0% +the a over X to the B is equal to 1 over +X to the B minus a and since a is less + + align:start position:0% +X to the B minus a and since a is less + + + align:start position:0% +X to the B minus a and since a is less +than B B minus a is positive so that + + align:start position:0% +than B B minus a is positive so that + + + align:start position:0% +than B B minus a is positive so that +means that as X approaches infinity the + + align:start position:0% +means that as X approaches infinity the + + + align:start position:0% +means that as X approaches infinity the +denominator is + + align:start position:0% +denominator is + + + align:start position:0% +denominator is +to a positive power also goes to + + align:start position:0% +to a positive power also goes to + + + align:start position:0% +to a positive power also goes to +infinity in therefore one over X to that + + align:start position:0% +infinity in therefore one over X to that + + + align:start position:0% +infinity in therefore one over X to that +positive power goes to zero which is the + + align:start position:0% +positive power goes to zero which is the + + + align:start position:0% +positive power goes to zero which is the +definition of X to the a being a little + + align:start position:0% +definition of X to the a being a little + + + align:start position:0% +definition of X to the a being a little +all of X to the B another crucial fact + + align:start position:0% +all of X to the B another crucial fact + + + align:start position:0% +all of X to the B another crucial fact +is that logarithms grow slower than + + align:start position:0% +is that logarithms grow slower than + + + align:start position:0% +is that logarithms grow slower than +roots so if you think of Epsilon is like + + align:start position:0% +roots so if you think of Epsilon is like + + + align:start position:0% +roots so if you think of Epsilon is like +a half or a third saying that the log of + + align:start position:0% +a half or a third saying that the log of + + + align:start position:0% +a half or a third saying that the log of +X is less than or equal to the square + + align:start position:0% +X is less than or equal to the square + + + align:start position:0% +X is less than or equal to the square +root it's less than equal to the cube + + align:start position:0% +root it's less than equal to the cube + + + align:start position:0% +root it's less than equal to the cube +root it's less than or equal to 50 you + + align:start position:0% +root it's less than or equal to 50 you + + + align:start position:0% +root it's less than or equal to 50 you +through it doesn't matter okay this is a + + align:start position:0% +through it doesn't matter okay this is a + + + align:start position:0% +through it doesn't matter okay this is a +proof that just falls back on elementary + + align:start position:0% +proof that just falls back on elementary + + + align:start position:0% +proof that just falls back on elementary +calculus and I guess I've highlighted it + + align:start position:0% +calculus and I guess I've highlighted it + + + align:start position:0% +calculus and I guess I've highlighted it +because it's definitely worth + + align:start position:0% +because it's definitely worth + + + align:start position:0% +because it's definitely worth +remembering logarithms grow slower than + + align:start position:0% +remembering logarithms grow slower than + + + align:start position:0% +remembering logarithms grow slower than +roots + + align:start position:0% +roots + + + align:start position:0% +roots +the proof is begins with the immediately + + align:start position:0% +the proof is begins with the immediately + + + align:start position:0% +the proof is begins with the immediately +obvious remark that 1 over Y is less + + align:start position:0% +obvious remark that 1 over Y is less + + + align:start position:0% +obvious remark that 1 over Y is less +than or equal to Y because they're equal + + align:start position:0% +than or equal to Y because they're equal + + + align:start position:0% +than or equal to Y because they're equal +when y is greater equal to 1 1 over Y is + + align:start position:0% +when y is greater equal to 1 1 over Y is + + + align:start position:0% +when y is greater equal to 1 1 over Y is +equal to Y when y is greater equal to 1 + + align:start position:0% +equal to Y when y is greater equal to 1 + + + align:start position:0% +equal to Y when y is greater equal to 1 +and as Y increases Y gets bigger and 1 + + align:start position:0% +and as Y increases Y gets bigger and 1 + + + align:start position:0% +and as Y increases Y gets bigger and 1 +over Y gets smaller so the inequality is + + align:start position:0% +over Y gets smaller so the inequality is + + + align:start position:0% +over Y gets smaller so the inequality is +preserved that's easy + + align:start position:0% +preserved that's easy + + + align:start position:0% +preserved that's easy +ok well that means that I can integrate + + align:start position:0% +ok well that means that I can integrate + + + align:start position:0% +ok well that means that I can integrate +both sides starting at 1 so if I take + + align:start position:0% +both sides starting at 1 so if I take + + + align:start position:0% +both sides starting at 1 so if I take +the integral of 1 over Y from 1 to Z + + align:start position:0% +the integral of 1 over Y from 1 to Z + + + align:start position:0% +the integral of 1 over Y from 1 to Z +it's gonna be less than or equal to the + + align:start position:0% +it's gonna be less than or equal to the + + + align:start position:0% +it's gonna be less than or equal to the +integral of Y from 1 to Z well integral + + align:start position:0% +integral of Y from 1 to Z well integral + + + align:start position:0% +integral of Y from 1 to Z well integral +of 1 over Y is log Z and the integral of + + align:start position:0% +of 1 over Y is log Z and the integral of + + + align:start position:0% +of 1 over Y is log Z and the integral of +Y is a 2 Z is Z squared over 2 so what + + align:start position:0% +Y is a 2 Z is Z squared over 2 so what + + + align:start position:0% +Y is a 2 Z is Z squared over 2 so what +we get is this new inequality the log of + + align:start position:0% +we get is this new inequality the log of + + + align:start position:0% +we get is this new inequality the log of +Z is less than or equal to Z squared + + align:start position:0% +Z is less than or equal to Z squared + + + align:start position:0% +Z is less than or equal to Z squared +over 2 for Z greater equal to 1 so we're + + align:start position:0% +over 2 for Z greater equal to 1 so we're + + + align:start position:0% +over 2 for Z greater equal to 1 so we're +on the way there we've got log of Z is + + align:start position:0% +on the way there we've got log of Z is + + + align:start position:0% +on the way there we've got log of Z is +less than Z squared but not Z to any + + align:start position:0% +less than Z squared but not Z to any + + + align:start position:0% +less than Z squared but not Z to any +epsilon power but we'll get that just + + align:start position:0% +epsilon power but we'll get that just + + + align:start position:0% +epsilon power but we'll get that just +biting a smart substitution for Z so + + align:start position:0% +biting a smart substitution for Z so + + + align:start position:0% +biting a smart substitution for Z so +that's the next step we have that log of + + align:start position:0% +that's the next step we have that log of + + + align:start position:0% +that's the next step we have that log of +Z is less than or equal to Z squared + + align:start position:0% +Z is less than or equal to Z squared + + + align:start position:0% +Z is less than or equal to Z squared +over 2 for any Z greater equal to 1 + + align:start position:0% +over 2 for any Z greater equal to 1 + + + align:start position:0% +over 2 for any Z greater equal to 1 +let's let Z be the square root of x to + + align:start position:0% +let's let Z be the square root of x to + + + align:start position:0% +let's let Z be the square root of x to +the Delta where Delta is simply some + + align:start position:0% +the Delta where Delta is simply some + + + align:start position:0% +the Delta where Delta is simply some +positive number so in that case what's + + align:start position:0% +positive number so in that case what's + + + align:start position:0% +positive number so in that case what's +the log of Z well the log of the square + + align:start position:0% +the log of Z well the log of the square + + + align:start position:0% +the log of Z well the log of the square +root of x to the Delta the square root + + align:start position:0% +root of x to the Delta the square root + + + align:start position:0% +root of x to the Delta the square root +means it's 1/2 of log of X to the Delta + + align:start position:0% +means it's 1/2 of log of X to the Delta + + + align:start position:0% +means it's 1/2 of log of X to the Delta +which is Delta log X so log of Z is + + align:start position:0% +which is Delta log X so log of Z is + + + align:start position:0% +which is Delta log X so log of Z is +Delta log of X over 2 and of course Z's + + align:start position:0% +Delta log of X over 2 and of course Z's + + + align:start position:0% +Delta log of X over 2 and of course Z's +squared is just X to the Delta sub Z + + align:start position:0% +squared is just X to the Delta sub Z + + + align:start position:0% +squared is just X to the Delta sub Z +squared over two is X to the Delta over + + align:start position:0% +squared over two is X to the Delta over + + + align:start position:0% +squared over two is X to the Delta over +two now I can just cancel the + + align:start position:0% +two now I can just cancel the + + + align:start position:0% +two now I can just cancel the +denominators to and I get that log of X + + align:start position:0% +denominators to and I get that log of X + + + align:start position:0% +denominators to and I get that log of X +and then transpose the Delta log of X is + + align:start position:0% +and then transpose the Delta log of X is + + + align:start position:0% +and then transpose the Delta log of X is +less than or equal to X to the Delta + + align:start position:0% +less than or equal to X to the Delta + + + align:start position:0% +less than or equal to X to the Delta +over Delta but Delta as long as Delta is + + align:start position:0% +over Delta but Delta as long as Delta is + + + align:start position:0% +over Delta but Delta as long as Delta is +less than epsilon Delta X to the Delta + + align:start position:0% +less than epsilon Delta X to the Delta + + + align:start position:0% +less than epsilon Delta X to the Delta +is going to be little lo of X to the + + align:start position:0% +is going to be little lo of X to the + + + align:start position:0% +is going to be little lo of X to the +epsilon which means that X to the Delta + + align:start position:0% +epsilon which means that X to the Delta + + + align:start position:0% +epsilon which means that X to the Delta +times a constant namely 1 over Delta is + + align:start position:0% +times a constant namely 1 over Delta is + + + align:start position:0% +times a constant namely 1 over Delta is +also going to be a little low of X to + + align:start position:0% +also going to be a little low of X to + + + align:start position:0% +also going to be a little low of X to +the epsilon and I've just figured out + + align:start position:0% +the epsilon and I've just figured out + + + align:start position:0% +the epsilon and I've just figured out +that I've shown that log of X is little + + align:start position:0% +that I've shown that log of X is little + + + align:start position:0% +that I've shown that log of X is little +o of X to the epsilon as required one + + align:start position:0% +o of X to the epsilon as required one + + + align:start position:0% +o of X to the epsilon as required one +more crucial fact that I'm gonna not + + align:start position:0% +more crucial fact that I'm gonna not + + + align:start position:0% +more crucial fact that I'm gonna not +prove but I'll state is that polynomials + + align:start position:0% +prove but I'll state is that polynomials + + + align:start position:0% +prove but I'll state is that polynomials +grow slower than Exponential's this is + + align:start position:0% +grow slower than Exponential's this is + + + align:start position:0% +grow slower than Exponential's this is +closely related to the fact that logs + + align:start position:0% +closely related to the fact that logs + + + align:start position:0% +closely related to the fact that logs +grow slower than roots but in particular + + align:start position:0% +grow slower than roots but in particular + + + align:start position:0% +grow slower than roots but in particular +if X is any kind of as C is any constant + + align:start position:0% +if X is any kind of as C is any constant + + + align:start position:0% +if X is any kind of as C is any constant +and a is greater than 1 then X to the C + + align:start position:0% +and a is greater than 1 then X to the C + + + align:start position:0% +and a is greater than 1 then X to the C +is little o of a to the X and there's a + + align:start position:0% +is little o of a to the X and there's a + + + align:start position:0% +is little o of a to the X and there's a +bunch of ways to prove this using + + align:start position:0% +bunch of ways to prove this using + + + align:start position:0% +bunch of ways to prove this using +l'hopital's rule or Maclaurin series and + + align:start position:0% +l'hopital's rule or Maclaurin series and + + + align:start position:0% +l'hopital's rule or Maclaurin series and +I'll leave it to you to look up your + + align:start position:0% +I'll leave it to you to look up your + + + align:start position:0% +I'll leave it to you to look up your +1801 calculus text to find a proof of + + align:start position:0% +1801 calculus text to find a proof of + + + align:start position:0% +1801 calculus text to find a proof of +that fact \ No newline at end of file diff --git a/Hmm9IqosCv4.txt b/Hmm9IqosCv4.txt new file mode 100644 index 0000000000000000000000000000000000000000..e48214bbc2485d604efe2027b1409664024ed0c9 --- /dev/null +++ b/Hmm9IqosCv4.txt @@ -0,0 +1,323 @@ +align:start position:0% + +the weak law of large numbers tells us + + align:start position:0% +the weak law of large numbers tells us + + + align:start position:0% +the weak law of large numbers tells us +that the sample mean that is the average + + align:start position:0% +that the sample mean that is the average + + + align:start position:0% +that the sample mean that is the average +of independent identically distributed + + align:start position:0% +of independent identically distributed + + + align:start position:0% +of independent identically distributed +random variables X I converges in a + + align:start position:0% +random variables X I converges in a + + + align:start position:0% +random variables X I converges in a +certain sense to a number namely the + + align:start position:0% +certain sense to a number namely the + + + align:start position:0% +certain sense to a number namely the +expected value of the random variables X + + align:start position:0% +expected value of the random variables X + + + align:start position:0% +expected value of the random variables X +I but it does not tell us much about the + + align:start position:0% +I but it does not tell us much about the + + + align:start position:0% +I but it does not tell us much about the +details of the distribution of the + + align:start position:0% +details of the distribution of the + + + align:start position:0% +details of the distribution of the +sample mean the central limit theorem + + align:start position:0% +sample mean the central limit theorem + + + align:start position:0% +sample mean the central limit theorem +provides us exactly with this kind of + + align:start position:0% +provides us exactly with this kind of + + + align:start position:0% +provides us exactly with this kind of +detail it tells us that the sum of many + + align:start position:0% +detail it tells us that the sum of many + + + align:start position:0% +detail it tells us that the sum of many +independent identically distributed + + align:start position:0% +independent identically distributed + + + align:start position:0% +independent identically distributed +random variables has approximately a + + align:start position:0% +random variables has approximately a + + + align:start position:0% +random variables has approximately a +normal distribution the mean and + + align:start position:0% +normal distribution the mean and + + + align:start position:0% +normal distribution the mean and +variance of this normal is easy to find + + align:start position:0% +variance of this normal is easy to find + + + align:start position:0% +variance of this normal is easy to find +if we know the mean and variance of the + + align:start position:0% +if we know the mean and variance of the + + + align:start position:0% +if we know the mean and variance of the +original random variables this enables + + align:start position:0% +original random variables this enables + + + align:start position:0% +original random variables this enables +us to carry out approximate calculations + + align:start position:0% +us to carry out approximate calculations + + + align:start position:0% +us to carry out approximate calculations +rather quickly by using the normal + + align:start position:0% +rather quickly by using the normal + + + align:start position:0% +rather quickly by using the normal +tables we will start with a precise + + align:start position:0% +tables we will start with a precise + + + align:start position:0% +tables we will start with a precise +statement of the central limit theorem + + align:start position:0% +statement of the central limit theorem + + + align:start position:0% +statement of the central limit theorem +and we will emphasize that it is a + + align:start position:0% +and we will emphasize that it is a + + + align:start position:0% +and we will emphasize that it is a +universal result it holds no matter what + + align:start position:0% +universal result it holds no matter what + + + align:start position:0% +universal result it holds no matter what +the distribution of the original random + + align:start position:0% +the distribution of the original random + + + align:start position:0% +the distribution of the original random +variables and for this reason it is very + + align:start position:0% +variables and for this reason it is very + + + align:start position:0% +variables and for this reason it is very +useful we will work through several + + align:start position:0% +useful we will work through several + + + align:start position:0% +useful we will work through several +examples of the typical ways that the + + align:start position:0% +examples of the typical ways that the + + + align:start position:0% +examples of the typical ways that the +central limit theorem is used we will + + align:start position:0% +central limit theorem is used we will + + + align:start position:0% +central limit theorem is used we will +develop a refinement that can be used + + align:start position:0% +develop a refinement that can be used + + + align:start position:0% +develop a refinement that can be used +when we are dealing with discrete + + align:start position:0% +when we are dealing with discrete + + + align:start position:0% +when we are dealing with discrete +distributions which provides us with + + align:start position:0% +distributions which provides us with + + + align:start position:0% +distributions which provides us with +even more accurate approximations and + + align:start position:0% +even more accurate approximations and + + + align:start position:0% +even more accurate approximations and +finally we will revisit the polling + + align:start position:0% +finally we will revisit the polling + + + align:start position:0% +finally we will revisit the polling +problem and inquire again about the + + align:start position:0% +problem and inquire again about the + + + align:start position:0% +problem and inquire again about the +number of samples that are needed to + + align:start position:0% +number of samples that are needed to + + + align:start position:0% +number of samples that are needed to +obtain a certain accuracy with a certain + + align:start position:0% +obtain a certain accuracy with a certain + + + align:start position:0% +obtain a certain accuracy with a certain +confidence we will see that the central + + align:start position:0% +confidence we will see that the central + + + align:start position:0% +confidence we will see that the central +limit theorem is much more informative + + align:start position:0% +limit theorem is much more informative + + + align:start position:0% +limit theorem is much more informative +much less conservative compared to the + + align:start position:0% +much less conservative compared to the + + + align:start position:0% +much less conservative compared to the +conclusions that we had gotten before + + align:start position:0% +conclusions that we had gotten before + + + align:start position:0% +conclusions that we had gotten before +based on the chebyshev inequality \ No newline at end of file diff --git a/IYlzo-bxrqs.txt b/IYlzo-bxrqs.txt new file mode 100644 index 0000000000000000000000000000000000000000..89752fad24bcd922970c761c67f0f191cf2f39dc --- /dev/null +++ b/IYlzo-bxrqs.txt @@ -0,0 +1,2603 @@ +align:start position:0% + +welcome back to recitation in this video + + align:start position:0% +welcome back to recitation in this video + + + align:start position:0% +welcome back to recitation in this video +I'd like us to consider the following + + align:start position:0% +I'd like us to consider the following + + + align:start position:0% +I'd like us to consider the following +problem the first part is I'd like to + + align:start position:0% +problem the first part is I'd like to + + + align:start position:0% +problem the first part is I'd like to +know for what values of B is this Vector + + align:start position:0% +know for what values of B is this Vector + + + align:start position:0% +know for what values of B is this Vector +field F conservative and F is defined as + + align:start position:0% +field F conservative and F is defined as + + + align:start position:0% +field F conservative and F is defined as +Yi plus the quantity X plus b yzj plus + + align:start position:0% +Yi plus the quantity X plus b yzj plus + + + align:start position:0% +Yi plus the quantity X plus b yzj plus +the quantity y^2 + 1 K so as you can see + + align:start position:0% +the quantity y^2 + 1 K so as you can see + + + align:start position:0% +the quantity y^2 + 1 K so as you can see +the only thing we're allowed to + + align:start position:0% +the only thing we're allowed to + + + align:start position:0% +the only thing we're allowed to +manipulate in this problem is b b will + + align:start position:0% +manipulate in this problem is b b will + + + align:start position:0% +manipulate in this problem is b b will +be some real number and I want to know + + align:start position:0% +be some real number and I want to know + + + align:start position:0% +be some real number and I want to know +what real numbers are + + align:start position:0% +what real numbers are + + + align:start position:0% +what real numbers are +allowed or what real numbers can I put + + align:start position:0% +allowed or what real numbers can I put + + + align:start position:0% +allowed or what real numbers can I put +in for B so that this Vector field is + + align:start position:0% +in for B so that this Vector field is + + + align:start position:0% +in for B so that this Vector field is +conservative the second part of this + + align:start position:0% +conservative the second part of this + + + align:start position:0% +conservative the second part of this +problem is for each B value you + + align:start position:0% +problem is for each B value you + + + align:start position:0% +problem is for each B value you +determined from one find a potential + + align:start position:0% +determined from one find a potential + + + align:start position:0% +determined from one find a potential +function so fix the B value for one of + + align:start position:0% +function so fix the B value for one of + + + align:start position:0% +function so fix the B value for one of +the ones that's acceptable based on + + align:start position:0% +the ones that's acceptable based on + + + align:start position:0% +the ones that's acceptable based on +number one and then find a potential + + align:start position:0% +number one and then find a potential + + + align:start position:0% +number one and then find a potential +function and then the third part says + + align:start position:0% +function and then the third part says + + + align:start position:0% +function and then the third part says +that that you should explain y FDR is + + align:start position:0% +that that you should explain y FDR is + + + align:start position:0% +that that you should explain y FDR is +exact and this is obviously for the B + + align:start position:0% +exact and this is obviously for the B + + + align:start position:0% +exact and this is obviously for the B +values determined from one so the second + + align:start position:0% +values determined from one so the second + + + align:start position:0% +values determined from one so the second +and third part are once you know the B + + align:start position:0% +and third part are once you know the B + + + align:start position:0% +and third part are once you know the B +values and you're only going to use + + align:start position:0% +values and you're only going to use + + + align:start position:0% +values and you're only going to use +those B values that make F conservative + + align:start position:0% +those B values that make F conservative + + + align:start position:0% +those B values that make F conservative +because that's the place where we can + + align:start position:0% +because that's the place where we can + + + align:start position:0% +because that's the place where we can +talk about finding a potential function + + align:start position:0% +talk about finding a potential function + + + align:start position:0% +talk about finding a potential function +and that's where we can talk about f. + + align:start position:0% +and that's where we can talk about f. + + + align:start position:0% +and that's where we can talk about f. +drr being exact are exactly those values + + align:start position:0% +drr being exact are exactly those values + + + align:start position:0% +drr being exact are exactly those values +okay so why don't you pause the video + + align:start position:0% +okay so why don't you pause the video + + + align:start position:0% +okay so why don't you pause the video +work on these three problems and then + + align:start position:0% +work on these three problems and then + + + align:start position:0% +work on these three problems and then +when you're feeling good about them uh + + align:start position:0% +when you're feeling good about them uh + + + align:start position:0% +when you're feeling good about them uh +bring the video back up I'll show you + + align:start position:0% +bring the video back up I'll show you + + + align:start position:0% +bring the video back up I'll show you +what I did + + align:start position:0% + + + + align:start position:0% + +okay welcome back again we're interested + + align:start position:0% +okay welcome back again we're interested + + + align:start position:0% +okay welcome back again we're interested +in doing three things with this Vector + + align:start position:0% +in doing three things with this Vector + + + align:start position:0% +in doing three things with this Vector +field the first thing we want to do is + + align:start position:0% +field the first thing we want to do is + + + align:start position:0% +field the first thing we want to do is +to find the values of B that make this + + align:start position:0% +to find the values of B that make this + + + align:start position:0% +to find the values of B that make this +Vector field conservative so I will + + align:start position:0% +Vector field conservative so I will + + + align:start position:0% +Vector field conservative so I will +start with that part and as we know from + + align:start position:0% +start with that part and as we know from + + + align:start position:0% +start with that part and as we know from +the lecture the thing I ultimately need + + align:start position:0% +the lecture the thing I ultimately need + + + align:start position:0% +the lecture the thing I ultimately need +to do is I need to find the curl of f + + align:start position:0% +to do is I need to find the curl of f + + + align:start position:0% +to do is I need to find the curl of f +okay so the curl of f is going to + + align:start position:0% +okay so the curl of f is going to + + + align:start position:0% +okay so the curl of f is going to +measure how far f is from being + + align:start position:0% +measure how far f is from being + + + align:start position:0% +measure how far f is from being +conservative so if the curl of f is zero + + align:start position:0% +conservative so if the curl of f is zero + + + align:start position:0% +conservative so if the curl of f is zero +I'm going to have F being conservative + + align:start position:0% +I'm going to have F being conservative + + + align:start position:0% +I'm going to have F being conservative +so that's really what I'm what I'm + + align:start position:0% +so that's really what I'm what I'm + + + align:start position:0% +so that's really what I'm what I'm +interested in doing first so I'm + + align:start position:0% +interested in doing first so I'm + + + align:start position:0% +interested in doing first so I'm +actually just going to + + align:start position:0% +actually just going to + + + align:start position:0% +actually just going to +rewrite uh what it means what the curl + + align:start position:0% +rewrite uh what it means what the curl + + + align:start position:0% +rewrite uh what it means what the curl +of f actually is so I'm going to let F + + align:start position:0% +of f actually is so I'm going to let F + + + align:start position:0% +of f actually is so I'm going to let F +I'm going to denote it in our usual Way + + align:start position:0% +I'm going to denote it in our usual Way + + + align:start position:0% +I'm going to denote it in our usual Way +by + + align:start position:0% +by + + + align:start position:0% +by +pqr and in this case that's specifically + + align:start position:0% +pqr and in this case that's specifically + + + align:start position:0% +pqr and in this case that's specifically +y comma x + B + + align:start position:0% +y comma x + B + + + align:start position:0% +y comma x + B +YZ comma y^2 + + + align:start position:0% +YZ comma y^2 + + + + align:start position:0% +YZ comma y^2 + +1 okay that's my pqr so p is y q is X + + align:start position:0% +1 okay that's my pqr so p is y q is X + + + align:start position:0% +1 okay that's my pqr so p is y q is X +plus b YZ and R is y^2 + 1 and now the + + align:start position:0% +plus b YZ and R is y^2 + 1 and now the + + + align:start position:0% +plus b YZ and R is y^2 + 1 and now the +curl of + + align:start position:0% + + + + align:start position:0% + +f which was which was uh found in the + + align:start position:0% +f which was which was uh found in the + + + align:start position:0% +f which was which was uh found in the +lecture so I'm not going to show you + + align:start position:0% +lecture so I'm not going to show you + + + align:start position:0% +lecture so I'm not going to show you +again how to find it I'm just going to + + align:start position:0% +again how to find it I'm just going to + + + align:start position:0% +again how to find it I'm just going to +write the formula for it it's exactly + + align:start position:0% +write the formula for it it's exactly + + + align:start position:0% +write the formula for it it's exactly +the following + + align:start position:0% +the following + + + align:start position:0% +the following +Vector it's the derivative of the R's + + align:start position:0% +Vector it's the derivative of the R's + + + align:start position:0% +Vector it's the derivative of the R's +component with respect to Y minus the + + align:start position:0% +component with respect to Y minus the + + + align:start position:0% +component with respect to Y minus the +q's component with respect to Z that's + + align:start position:0% +q's component with respect to Z that's + + + align:start position:0% +q's component with respect to Z that's +the I value + + align:start position:0% +the I value + + + align:start position:0% +the I value +the J value is p subz minus r + + align:start position:0% +the J value is p subz minus r + + + align:start position:0% +the J value is p subz minus r +subx j the K value is Q subx minus p + + align:start position:0% +subx j the K value is Q subx minus p + + + align:start position:0% +subx j the K value is Q subx minus p +suby uh K okay so there are three + + align:start position:0% +suby uh K okay so there are three + + + align:start position:0% +suby uh K okay so there are three +components here and let's just start + + align:start position:0% +components here and let's just start + + + align:start position:0% +components here and let's just start +figuring out what these values are and + + align:start position:0% +figuring out what these values are and + + + align:start position:0% +figuring out what these values are and +then we'll see what we what kind of + + align:start position:0% +then we'll see what we what kind of + + + align:start position:0% +then we'll see what we what kind of +restrictions we have on B so let's start + + align:start position:0% +restrictions we have on B so let's start + + + align:start position:0% +restrictions we have on B so let's start +doing this so again this is p this is q + + align:start position:0% +doing this so again this is p this is q + + + align:start position:0% +doing this so again this is p this is q +and this is R so R suby is the + + align:start position:0% +and this is R so R suby is the + + + align:start position:0% +and this is R so R suby is the +derivative of this component with + + align:start position:0% +derivative of this component with + + + align:start position:0% +derivative of this component with +respect to y That's Just 2 + + align:start position:0% +respect to y That's Just 2 + + + align:start position:0% +respect to y That's Just 2 +y q subz is the derivative of this with + + align:start position:0% +y q subz is the derivative of this with + + + align:start position:0% +y q subz is the derivative of this with +respect to Z well this is zero and this + + align:start position:0% +respect to Z well this is zero and this + + + align:start position:0% +respect to Z well this is zero and this +is b + + align:start position:0% + + + + align:start position:0% + +y okay let's look at the rest first P + + align:start position:0% +y okay let's look at the rest first P + + + align:start position:0% +y okay let's look at the rest first P +subz derivative of this with respect to + + align:start position:0% +subz derivative of this with respect to + + + align:start position:0% +subz derivative of this with respect to +Z is + + align:start position:0% +Z is + + + align:start position:0% +Z is +zero derivative of r with respect to X + + align:start position:0% +zero derivative of r with respect to X + + + align:start position:0% +zero derivative of r with respect to X +this is the r component with respect to + + align:start position:0% +this is the r component with respect to + + + align:start position:0% +this is the r component with respect to +X that's zero so that doesn't have any + + align:start position:0% +X that's zero so that doesn't have any + + + align:start position:0% +X that's zero so that doesn't have any +B's in it at all and then Q subx minus P + + align:start position:0% +B's in it at all and then Q subx minus P + + + align:start position:0% +B's in it at all and then Q subx minus P +sub y q is the middle one Q subx is + + align:start position:0% +sub y q is the middle one Q subx is + + + align:start position:0% +sub y q is the middle one Q subx is +1 P sub y is the first one p is the + + align:start position:0% +1 P sub y is the first one p is the + + + align:start position:0% +1 P sub y is the first one p is the +first one piece of Y is + + align:start position:0% + + + + align:start position:0% + +one okay so what do we get here should + + align:start position:0% +one okay so what do we get here should + + + align:start position:0% +one okay so what do we get here should +have written equals there + + align:start position:0% +have written equals there + + + align:start position:0% +have written equals there +maybe okay so the J's component is zero + + align:start position:0% +maybe okay so the J's component is zero + + + align:start position:0% +maybe okay so the J's component is zero +and the K's component is zero so all I'm + + align:start position:0% +and the K's component is zero so all I'm + + + align:start position:0% +and the K's component is zero so all I'm +left with is 2 y minus b + + align:start position:0% +left with is 2 y minus b + + + align:start position:0% +left with is 2 y minus b +y i and if I want F to be conservative + + align:start position:0% +y i and if I want F to be conservative + + + align:start position:0% +y i and if I want F to be conservative +ative this quantity has to be zero so I + + align:start position:0% +ative this quantity has to be zero so I + + + align:start position:0% +ative this quantity has to be zero so I +see there's only one B value that's + + align:start position:0% +see there's only one B value that's + + + align:start position:0% +see there's only one B value that's +going to work and that is B is equal to + + align:start position:0% + + + + align:start position:0% + +2 okay so I know part one the answer to + + align:start position:0% +2 okay so I know part one the answer to + + + align:start position:0% +2 okay so I know part one the answer to +the question is just for b equals 2 is f + + align:start position:0% +the question is just for b equals 2 is f + + + align:start position:0% +the question is just for b equals 2 is f +conservative was maybe poorly phrased f + + align:start position:0% +conservative was maybe poorly phrased f + + + align:start position:0% +conservative was maybe poorly phrased f +is conservative only when B is two okay + + align:start position:0% +is conservative only when B is two okay + + + align:start position:0% +is conservative only when B is two okay +and that's because the curl of f is zero + + align:start position:0% +and that's because the curl of f is zero + + + align:start position:0% +and that's because the curl of f is zero +only when B is two all right so now we + + align:start position:0% +only when B is two all right so now we + + + align:start position:0% +only when B is two all right so now we +can move on to the second part and the + + align:start position:0% +can move on to the second part and the + + + align:start position:0% +can move on to the second part and the +second part is four this particular + + align:start position:0% +second part is four this particular + + + align:start position:0% +second part is four this particular +value of B find a potential function and + + align:start position:0% +value of B find a potential function and + + + align:start position:0% +value of B find a potential function and +our strategy for that is going to be one + + align:start position:0% +our strategy for that is going to be one + + + align:start position:0% +our strategy for that is going to be one +of the methods from lecture and it's + + align:start position:0% +of the methods from lecture and it's + + + align:start position:0% +of the methods from lecture and it's +going to be the method from lecture that + + align:start position:0% +going to be the method from lecture that + + + align:start position:0% +going to be the method from lecture that +in three dimensions is much easier than + + align:start position:0% +in three dimensions is much easier than + + + align:start position:0% +in three dimensions is much easier than +than the other so the one method in + + align:start position:0% +than the other so the one method in + + + align:start position:0% +than the other so the one method in +lecture that's easy in three dimensions + + align:start position:0% +lecture that's easy in three dimensions + + + align:start position:0% +lecture that's easy in three dimensions +is where you start at the origin and you + + align:start position:0% +is where you start at the origin and you + + + align:start position:0% +is where you start at the origin and you +integrate f.d along a curve that's made + + align:start position:0% +integrate f.d along a curve that's made + + + align:start position:0% +integrate f.d along a curve that's made +up of line segments so this strategy + + align:start position:0% +up of line segments so this strategy + + + align:start position:0% +up of line segments so this strategy +I've done before in in two dimensions in + + align:start position:0% +I've done before in in two dimensions in + + + align:start position:0% +I've done before in in two dimensions in +one of the problems in recitation now + + align:start position:0% +one of the problems in recitation now + + + align:start position:0% +one of the problems in recitation now +we'll see it in three dimensions so what + + align:start position:0% +we'll see it in three dimensions so what + + + align:start position:0% +we'll see it in three dimensions so what +we're to do is we're going to integrate + + align:start position:0% +we're to do is we're going to integrate + + + align:start position:0% +we're to do is we're going to integrate +along a certain curve F dodr and this + + align:start position:0% +along a certain curve F dodr and this + + + align:start position:0% +along a certain curve F dodr and this +curve is going to go from the origin to + + align:start position:0% +curve is going to go from the origin to + + + align:start position:0% +curve is going to go from the origin to +X1 y1 Z1 and that will give + + align:start position:0% +X1 y1 Z1 and that will give + + + align:start position:0% +X1 y1 Z1 and that will give +us f of x oops almost wrote Z1 F of X1 + + align:start position:0% +us f of x oops almost wrote Z1 F of X1 + + + align:start position:0% +us f of x oops almost wrote Z1 F of X1 +y1 Z1 okay so this is the sort of + + align:start position:0% +y1 Z1 okay so this is the sort of + + + align:start position:0% +y1 Z1 okay so this is the sort of +General strategy and now we'll talk + + align:start position:0% +General strategy and now we'll talk + + + align:start position:0% +General strategy and now we'll talk +about it specifically this will actually + + align:start position:0% +about it specifically this will actually + + + align:start position:0% +about it specifically this will actually +be F of X1 y1 Z1 plus a constant but + + align:start position:0% +be F of X1 y1 Z1 plus a constant but + + + align:start position:0% +be F of X1 y1 Z1 plus a constant but +we'll deal with that part right at the + + align:start position:0% +we'll deal with that part right at the + + + align:start position:0% +we'll deal with that part right at the +the end okay so C in this case is going + + align:start position:0% +the end okay so C in this case is going + + + align:start position:0% +the end okay so C in this case is going +to be made up of three curves and I'm + + align:start position:0% +to be made up of three curves and I'm + + + align:start position:0% +to be made up of three curves and I'm +going to draw them in a picture and then + + align:start position:0% +going to draw them in a picture and then + + + align:start position:0% +going to draw them in a picture and then +we're going to describe + + align:start position:0% +we're going to describe + + + align:start position:0% +we're going to describe +them so I'm going to start at 00 0 my + + align:start position:0% +them so I'm going to start at 00 0 my + + + align:start position:0% +them so I'm going to start at 00 0 my +first + + align:start position:0% +first + + + align:start position:0% +first +curve will go out + + align:start position:0% +curve will go out + + + align:start position:0% +curve will go out +to X1 comma 0 + + align:start position:0% +to X1 comma 0 + + + align:start position:0% +to X1 comma 0 +0 and that's going to be the curve C1 + + align:start position:0% +0 and that's going to be the curve C1 + + + align:start position:0% +0 and that's going to be the curve C1 +oops I want that to go the other way + + align:start position:0% +oops I want that to go the other way + + + align:start position:0% +oops I want that to go the other way +that way okay C1 is going to go from the + + align:start position:0% +that way okay C1 is going to go from the + + + align:start position:0% +that way okay C1 is going to go from the +origin to X1 comma 0 0 so the the Y and + + align:start position:0% +origin to X1 comma 0 0 so the the Y and + + + align:start position:0% +origin to X1 comma 0 0 so the the Y and +Z values are going to be zero and zero + + align:start position:0% +Z values are going to be zero and zero + + + align:start position:0% +Z values are going to be zero and zero +all the way along and the x value is + + align:start position:0% +all the way along and the x value is + + + align:start position:0% +all the way along and the x value is +going to change my next one I'm going to + + align:start position:0% +going to change my next one I'm going to + + + align:start position:0% +going to change my next one I'm going to +make it long so I can have enough room + + align:start position:0% +make it long so I can have enough room + + + align:start position:0% +make it long so I can have enough room +to + + align:start position:0% +to + + + align:start position:0% +to +write that's going to be my + + align:start position:0% +write that's going to be my + + + align:start position:0% +write that's going to be my +C2 and that's going to + + align:start position:0% +C2 and that's going to + + + align:start position:0% +C2 and that's going to +be X1 comma y1 comma 0 so in the end + + align:start position:0% +be X1 comma y1 comma 0 so in the end + + + align:start position:0% +be X1 comma y1 comma 0 so in the end +what I've done is I've taken my x value + + align:start position:0% +what I've done is I've taken my x value + + + align:start position:0% +what I've done is I've taken my x value +I've kept it fixed all the way along + + align:start position:0% +I've kept it fixed all the way along + + + align:start position:0% +I've kept it fixed all the way along +here but I'm varying the Y value out to + + align:start position:0% +here but I'm varying the Y value out to + + + align:start position:0% +here but I'm varying the Y value out to +y1 and then the last one is going to go + + align:start position:0% +y1 and then the last one is going to go + + + align:start position:0% +y1 and then the last one is going to go +straight up whoa right there it's going + + align:start position:0% +straight up whoa right there it's going + + + align:start position:0% +straight up whoa right there it's going +to go straight up and so it's going to + + align:start position:0% +to go straight up and so it's going to + + + align:start position:0% +to go straight up and so it's going to +be with the x value and yvalue fixed and + + align:start position:0% +be with the x value and yvalue fixed and + + + align:start position:0% +be with the x value and yvalue fixed and +at the end I will be at X1 y1 Z1 and + + align:start position:0% +at the end I will be at X1 y1 Z1 and + + + align:start position:0% +at the end I will be at X1 y1 Z1 and +this is + + align:start position:0% +this is + + + align:start position:0% +this is +C3 so those are my three curves and this + + align:start position:0% +C3 so those are my three curves and this + + + align:start position:0% +C3 so those are my three curves and this +one I'm going to move in this direction + + align:start position:0% +one I'm going to move in this direction + + + align:start position:0% +one I'm going to move in this direction +those are my three curves and I want to + + align:start position:0% +those are my three curves and I want to + + + align:start position:0% +those are my three curves and I want to +point out that in order to understand + + align:start position:0% +point out that in order to understand + + + align:start position:0% +point out that in order to understand +how to simplify this problem I'm going + + align:start position:0% +how to simplify this problem I'm going + + + align:start position:0% +how to simplify this problem I'm going +to have to remind myself what f. drr is + + align:start position:0% +to have to remind myself what f. drr is + + + align:start position:0% +to have to remind myself what f. drr is +okay so f. + + align:start position:0% +okay so f. + + + align:start position:0% +okay so f. +drr if you remember is + + align:start position:0% +drr if you remember is + + + align:start position:0% +drr if you remember is +PDX plus + + align:start position:0% +PDX plus + + + align:start position:0% +PDX plus +qdy plus r DZ right that's what f. drr + + align:start position:0% +qdy plus r DZ right that's what f. drr + + + align:start position:0% +qdy plus r DZ right that's what f. drr +is and so what I'm interested in I'm + + align:start position:0% +is and so what I'm interested in I'm + + + align:start position:0% +is and so what I'm interested in I'm +going to integrate each of these things + + align:start position:0% +going to integrate each of these things + + + align:start position:0% +going to integrate each of these things +along C1 C2 C3 but let's notice what + + align:start position:0% +along C1 C2 C3 but let's notice what + + + align:start position:0% +along C1 C2 C3 but let's notice what +happens along certain certain numbers of + + align:start position:0% +happens along certain certain numbers of + + + align:start position:0% +happens along certain certain numbers of +these curves on + + align:start position:0% +these curves on + + + align:start position:0% +these curves on +C1 if we come back over here on C1 Y is + + align:start position:0% +C1 if we come back over here on C1 Y is + + + align:start position:0% +C1 if we come back over here on C1 Y is +fixed and Z is fixed so Dy and DZ are + + align:start position:0% +fixed and Z is fixed so Dy and DZ are + + + align:start position:0% +fixed and Z is fixed so Dy and DZ are +both zero so on C1 I only have to + + align:start position:0% +both zero so on C1 I only have to + + + align:start position:0% +both zero so on C1 I only have to +integrate P okay so I'm going to keep + + align:start position:0% +integrate P okay so I'm going to keep + + + align:start position:0% +integrate P okay so I'm going to keep +track of that on C1 which C1 is + + align:start position:0% +track of that on C1 which C1 is + + + align:start position:0% +track of that on C1 which C1 is +parameterized by x 0 to X I only need to + + align:start position:0% +parameterized by x 0 to X I only need to + + + align:start position:0% +parameterized by x 0 to X I only need to +worry about the p p of x0 0 DX this is + + align:start position:0% +worry about the p p of x0 0 DX this is + + + align:start position:0% +worry about the p p of x0 0 DX this is +my C1 component and there's nothing else + + align:start position:0% +my C1 component and there's nothing else + + + align:start position:0% +my C1 component and there's nothing else +there because these two are both + + align:start position:0% +there because these two are both + + + align:start position:0% +there because these two are both +zero all right now let's consider what + + align:start position:0% +zero all right now let's consider what + + + align:start position:0% +zero all right now let's consider what +happens on C2 on C2 if I look here on C2 + + align:start position:0% +happens on C2 on C2 if I look here on C2 + + + align:start position:0% +happens on C2 on C2 if I look here on C2 +the x value is fixed and the zv value is + + align:start position:0% +the x value is fixed and the zv value is + + + align:start position:0% +the x value is fixed and the zv value is +fixed X is fixed at X1 and Z is fixed at + + align:start position:0% +fixed X is fixed at X1 and Z is fixed at + + + align:start position:0% +fixed X is fixed at X1 and Z is fixed at +zero and so DX and DZ are both zero + + align:start position:0% +zero and so DX and DZ are both zero + + + align:start position:0% +zero and so DX and DZ are both zero +because x and z are not changing so + + align:start position:0% +because x and z are not changing so + + + align:start position:0% +because x and z are not changing so +there's only a Dy component so the on C2 + + align:start position:0% +there's only a Dy component so the on C2 + + + align:start position:0% +there's only a Dy component so the on C2 +which is parameterized in y from 0 to y1 + + align:start position:0% +which is parameterized in y from 0 to y1 + + + align:start position:0% +which is parameterized in y from 0 to y1 +I'm only interested in Q at X1 comma y + + align:start position:0% +I'm only interested in Q at X1 comma y + + + align:start position:0% +I'm only interested in Q at X1 comma y +comma 0 + + align:start position:0% +comma 0 + + + align:start position:0% +comma 0 +Dy okay so again this component is zero + + align:start position:0% +Dy okay so again this component is zero + + + align:start position:0% +Dy okay so again this component is zero +on C2 because DX is zero and this + + align:start position:0% +on C2 because DX is zero and this + + + align:start position:0% +on C2 because DX is zero and this +component is zero on C2 cuz DZ is zero + + align:start position:0% +component is zero on C2 cuz DZ is zero + + + align:start position:0% +component is zero on C2 cuz DZ is zero +and this component I'm evaluating it X1 + + align:start position:0% +and this component I'm evaluating it X1 + + + align:start position:0% +and this component I'm evaluating it X1 +is X is fixed at X1 Z is fixed at zero + + align:start position:0% +is X is fixed at X1 Z is fixed at zero + + + align:start position:0% +is X is fixed at X1 Z is fixed at zero +and the Y is varying from0 to y1 and + + align:start position:0% +and the Y is varying from0 to y1 and + + + align:start position:0% +and the Y is varying from0 to y1 and +then there's one more component and I'm + + align:start position:0% +then there's one more component and I'm + + + align:start position:0% +then there's one more component and I'm +going to write it below and then we'll + + align:start position:0% +going to write it below and then we'll + + + align:start position:0% +going to write it below and then we'll +do the rest over here and the third + + align:start position:0% +do the rest over here and the third + + + align:start position:0% +do the rest over here and the third +component is the C3 component now not + + align:start position:0% +component is the C3 component now not + + + align:start position:0% +component is the C3 component now not +surprisingly if I come back over here + + align:start position:0% +surprisingly if I come back over here + + + align:start position:0% +surprisingly if I come back over here +because X and Y are fixed all along the + + align:start position:0% +because X and Y are fixed all along the + + + align:start position:0% +because X and Y are fixed all along the +C3 component the only thing that's + + align:start position:0% +C3 component the only thing that's + + + align:start position:0% +C3 component the only thing that's +changing is z so DX and Dy are zero so + + align:start position:0% +changing is z so DX and Dy are zero so + + + align:start position:0% +changing is z so DX and Dy are zero so +I'm only worried about the DZ part okay + + align:start position:0% +I'm only worried about the DZ part okay + + + align:start position:0% +I'm only worried about the DZ part okay +so again as happened before before I + + align:start position:0% +so again as happened before before I + + + align:start position:0% +so again as happened before before I +only had p in the first one and Q in the + + align:start position:0% +only had p in the first one and Q in the + + + align:start position:0% +only had p in the first one and Q in the +second one well now I have R only in the + + align:start position:0% +second one well now I have R only in the + + + align:start position:0% +second one well now I have R only in the +third one and it's parameterized in Z + + align:start position:0% +third one and it's parameterized in Z + + + align:start position:0% +third one and it's parameterized in Z +from 0 to Z1 that's what Z varies over + + align:start position:0% +from 0 to Z1 that's what Z varies over + + + align:start position:0% +from 0 to Z1 that's what Z varies over +and it's going to be r at X1 comma y1 + + align:start position:0% +and it's going to be r at X1 comma y1 + + + align:start position:0% +and it's going to be r at X1 comma y1 +comma Z + + align:start position:0% +comma Z + + + align:start position:0% +comma Z +DZ because the X's are fixed at X1 the Y + + align:start position:0% +DZ because the X's are fixed at X1 the Y + + + align:start position:0% +DZ because the X's are fixed at X1 the Y +is fixed at y1 but Z is varying from Z + + align:start position:0% +is fixed at y1 but Z is varying from Z + + + align:start position:0% +is fixed at y1 but Z is varying from Z +to Z1 all right so I have these three + + align:start position:0% +to Z1 all right so I have these three + + + align:start position:0% +to Z1 all right so I have these three +parts and now I just have to fill them + + align:start position:0% +parts and now I just have to fill them + + + align:start position:0% +parts and now I just have to fill them +in with the Vector field that I have I + + align:start position:0% +in with the Vector field that I have I + + + align:start position:0% +in with the Vector field that I have I +want to find what p is at x0 0 what Q is + + align:start position:0% +want to find what p is at x0 0 what Q is + + + align:start position:0% +want to find what p is at x0 0 what Q is +at X1 y10 and what R is at X1 y1 Z and + + align:start position:0% +at X1 y10 and what R is at X1 y1 Z and + + + align:start position:0% +at X1 y10 and what R is at X1 y1 Z and +then integrate so I have sort of two + + align:start position:0% +then integrate so I have sort of two + + + align:start position:0% +then integrate so I have sort of two +steps left one is plugging in and one is + + align:start position:0% +steps left one is plugging in and one is + + + align:start position:0% +steps left one is plugging in and one is +evaluating so let me remind us what p q + + align:start position:0% +evaluating so let me remind us what p q + + + align:start position:0% +evaluating so let me remind us what p q +and R actually are and then we'll see + + align:start position:0% +and R actually are and then we'll see + + + align:start position:0% +and R actually are and then we'll see +what we get so p is actually y let me + + align:start position:0% +what we get so p is actually y let me + + + align:start position:0% +what we get so p is actually y let me +write it again maybe here + + align:start position:0% + + + + align:start position:0% + +pqr was equal to Y comma x + 2 YZ I'll + + align:start position:0% +pqr was equal to Y comma x + 2 YZ I'll + + + align:start position:0% +pqr was equal to Y comma x + 2 YZ I'll +put it here so you don't have to look + + align:start position:0% +put it here so you don't have to look + + + align:start position:0% +put it here so you don't have to look +and I don't have to look and then y^2 + + + align:start position:0% +and I don't have to look and then y^2 + + + + align:start position:0% +and I don't have to look and then y^2 + +1 okay so P at X comma 0 comma + + align:start position:0% +1 okay so P at X comma 0 comma + + + align:start position:0% +1 okay so P at X comma 0 comma +0 well if I plug in zero for y p is zero + + align:start position:0% +0 well if I plug in zero for y p is zero + + + align:start position:0% +0 well if I plug in zero for y p is zero +so P at x0 0 is equal to zero so I get + + align:start position:0% +so P at x0 0 is equal to zero so I get + + + align:start position:0% +so P at x0 0 is equal to zero so I get +nothing to integrate in the first part + + align:start position:0% +nothing to integrate in the first part + + + align:start position:0% +nothing to integrate in the first part +that's nice okay now what is Q at X x1a + + align:start position:0% +that's nice okay now what is Q at X x1a + + + align:start position:0% +that's nice okay now what is Q at X x1a +y comma + + align:start position:0% +y comma + + + align:start position:0% +y comma +0 well that would be an X1 here Zer for + + align:start position:0% +0 well that would be an X1 here Zer for + + + align:start position:0% +0 well that would be an X1 here Zer for +y makes this term go away so it's just + + align:start position:0% +y makes this term go away so it's just + + + align:start position:0% +y makes this term go away so it's just +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +X1 right and then + + align:start position:0% +X1 right and then + + + align:start position:0% +X1 right and then +r at X1 comma y1 comma + + align:start position:0% +r at X1 comma y1 comma + + + align:start position:0% +r at X1 comma y1 comma +Z is y1 ^2 + + + align:start position:0% + + + + align:start position:0% + +1 so now I'm going to substitute these + + align:start position:0% +1 so now I'm going to substitute these + + + align:start position:0% +1 so now I'm going to substitute these +in to what I'm integrating so the first + + align:start position:0% +in to what I'm integrating so the first + + + align:start position:0% +in to what I'm integrating so the first +one there's nothing there the Q let me + + align:start position:0% +one there's nothing there the Q let me + + + align:start position:0% +one there's nothing there the Q let me +just write it right here the Q is going + + align:start position:0% +just write it right here the Q is going + + + align:start position:0% +just write it right here the Q is going +to be the integral from 0 to y1 of X1 Dy + + align:start position:0% +to be the integral from 0 to y1 of X1 Dy + + + align:start position:0% +to be the integral from 0 to y1 of X1 Dy +and the r part is going to be the + + align:start position:0% +and the r part is going to be the + + + align:start position:0% +and the r part is going to be the +integral from 0 to + + align:start position:0% +integral from 0 to + + + align:start position:0% +integral from 0 to +Z1 of y12 + 1 DZ okay so the P part was + + align:start position:0% +Z1 of y12 + 1 DZ okay so the P part was + + + align:start position:0% +Z1 of y12 + 1 DZ okay so the P part was +disappeared this is the Q part evaluated + + align:start position:0% +disappeared this is the Q part evaluated + + + align:start position:0% +disappeared this is the Q part evaluated +where I need it needed it to be + + align:start position:0% +where I need it needed it to be + + + align:start position:0% +where I need it needed it to be +evaluated it's just X1 Dy and the r part + + align:start position:0% +evaluated it's just X1 Dy and the r part + + + align:start position:0% +evaluated it's just X1 Dy and the r part +evaluated at X1 y1 Z is just y12 + 1 and + + align:start position:0% +evaluated at X1 y1 Z is just y12 + 1 and + + + align:start position:0% +evaluated at X1 y1 Z is just y12 + 1 and +so that's I integrate that in z so if I + + align:start position:0% +so that's I integrate that in z so if I + + + align:start position:0% +so that's I integrate that in z so if I +integrate this in y all I get is X1 y + + align:start position:0% +integrate this in y all I get is X1 y + + + align:start position:0% +integrate this in y all I get is X1 y +evaluated zero and y1 so here I just get + + align:start position:0% +evaluated zero and y1 so here I just get + + + align:start position:0% +evaluated zero and y1 so here I just get +an X1 + + align:start position:0% +an X1 + + + align:start position:0% +an X1 +y1 right and then here if I integrate + + align:start position:0% +y1 right and then here if I integrate + + + align:start position:0% +y1 right and then here if I integrate +this in z i just get a z and so I + + align:start position:0% +this in z i just get a z and so I + + + align:start position:0% +this in z i just get a z and so I +evaluate that at Z1 and zero I just get + + align:start position:0% +evaluate that at Z1 and zero I just get + + + align:start position:0% +evaluate that at Z1 and zero I just get +Z1 * y1 ^ 2 + 1 okay so this is actually + + align:start position:0% +Z1 * y1 ^ 2 + 1 okay so this is actually + + + align:start position:0% +Z1 * y1 ^ 2 + 1 okay so this is actually +my potential function and so let me + + align:start position:0% +my potential function and so let me + + + align:start position:0% +my potential function and so let me +write it formally I should actually say + + align:start position:0% +write it formally I should actually say + + + align:start position:0% +write it formally I should actually say +this is my final answer right this was + + align:start position:0% +this is my final answer right this was + + + align:start position:0% +this is my final answer right this was +the I was integrating this is actually + + align:start position:0% +the I was integrating this is actually + + + align:start position:0% +the I was integrating this is actually +what I get + + align:start position:0% +what I get + + + align:start position:0% +what I get +and so what I was trying to find if you + + align:start position:0% +and so what I was trying to find if you + + + align:start position:0% +and so what I was trying to find if you +remember I'm going to come back here and + + align:start position:0% +remember I'm going to come back here and + + + align:start position:0% +remember I'm going to come back here and +just mention again what I was doing was + + align:start position:0% +just mention again what I was doing was + + + align:start position:0% +just mention again what I was doing was +I was integrating along a curve f. drr + + align:start position:0% +I was integrating along a curve f. drr + + + align:start position:0% +I was integrating along a curve f. drr +to give me f of X1 y1 Z1 right so now I + + align:start position:0% +to give me f of X1 y1 Z1 right so now I + + + align:start position:0% +to give me f of X1 y1 Z1 right so now I +found it the only thing I said is we + + align:start position:0% +found it the only thing I said is we + + + align:start position:0% +found it the only thing I said is we +also have to allow for there to be a + + align:start position:0% +also have to allow for there to be a + + + align:start position:0% +also have to allow for there to be a +constant okay so the the potential + + align:start position:0% +constant okay so the the potential + + + align:start position:0% +constant okay so the the potential +function is actually exactly this + + align:start position:0% +function is actually exactly this + + + align:start position:0% +function is actually exactly this +function plus a + + align:start position:0% +function plus a + + + align:start position:0% +function plus a +constant okay so this is f of X1 y1 Z1 + + align:start position:0% +constant okay so this is f of X1 y1 Z1 + + + align:start position:0% +constant okay so this is f of X1 y1 Z1 +and since I don't have much room above + + align:start position:0% +and since I don't have much room above + + + align:start position:0% +and since I don't have much room above +I'll just write + + align:start position:0% + + + + align:start position:0% + +low this is f of X1 y1 Z1 so that's my + + align:start position:0% +low this is f of X1 y1 Z1 so that's my + + + align:start position:0% +low this is f of X1 y1 Z1 so that's my +potential function okay for this Vector + + align:start position:0% +potential function okay for this Vector + + + align:start position:0% +potential function okay for this Vector +field capital F when it is conservative + + align:start position:0% +field capital F when it is conservative + + + align:start position:0% +field capital F when it is conservative +so when B is equal to two Okay and there + + align:start position:0% +so when B is equal to two Okay and there + + + align:start position:0% +so when B is equal to two Okay and there +was one last part to this question right + + align:start position:0% +was one last part to this question right + + + align:start position:0% +was one last part to this question right +so we come all the way back over we're + + align:start position:0% +so we come all the way back over we're + + + align:start position:0% +so we come all the way back over we're +reminded of there was one last part it + + align:start position:0% +reminded of there was one last part it + + + align:start position:0% +reminded of there was one last part it +was explain why f.d is exact for the B + + align:start position:0% +was explain why f.d is exact for the B + + + align:start position:0% +was explain why f.d is exact for the B +values determined from number one and + + align:start position:0% +values determined from number one and + + + align:start position:0% +values determined from number one and +the reason is exact exctly because of + + align:start position:0% +the reason is exact exctly because of + + + align:start position:0% +the reason is exact exctly because of +the following + + align:start position:0% +the following + + + align:start position:0% +the following +thing f is conservative based on the + + align:start position:0% +thing f is conservative based on the + + + align:start position:0% +thing f is conservative based on the +fact that b is two and so we when we + + align:start position:0% +fact that b is two and so we when we + + + align:start position:0% +fact that b is two and so we when we +talk about when f. drr is exact all we + + align:start position:0% +talk about when f. drr is exact all we + + + align:start position:0% +talk about when f. drr is exact all we +need to know is that or the simplest + + align:start position:0% +need to know is that or the simplest + + + align:start position:0% +need to know is that or the simplest +case is f is conservative capital F is + + align:start position:0% +case is f is conservative capital F is + + + align:start position:0% +case is f is conservative capital F is +conservative and I'm on a Simply + + align:start position:0% +conservative and I'm on a Simply + + + align:start position:0% +conservative and I'm on a Simply +Connected domain okay and if you notice + + align:start position:0% +Connected domain okay and if you notice + + + align:start position:0% +Connected domain okay and if you notice +capital F is + + align:start position:0% +capital F is + + + align:start position:0% +capital F is +defined for all values XY Z and it's + + align:start position:0% +defined for all values XY Z and it's + + + align:start position:0% +defined for all values XY Z and it's +differentiable for all values of XYZ so + + align:start position:0% +differentiable for all values of XYZ so + + + align:start position:0% +differentiable for all values of XYZ so +f is defined and differentiable + + align:start position:0% +f is defined and differentiable + + + align:start position:0% +f is defined and differentiable +everywhere on R3 R3 is Simply Connected + + align:start position:0% +everywhere on R3 R3 is Simply Connected + + + align:start position:0% +everywhere on R3 R3 is Simply Connected +so we have a conservative Vector field + + align:start position:0% +so we have a conservative Vector field + + + align:start position:0% +so we have a conservative Vector field +on a Simply Connected region and that's + + align:start position:0% +on a Simply Connected region and that's + + + align:start position:0% +on a Simply Connected region and that's +what it means that's one way we have of + + align:start position:0% +what it means that's one way we have of + + + align:start position:0% +what it means that's one way we have of +knowing f. drr is exact and so that + + align:start position:0% +knowing f. drr is exact and so that + + + align:start position:0% +knowing f. drr is exact and so that +actually answers the third part of the + + align:start position:0% +actually answers the third part of the + + + align:start position:0% +actually answers the third part of the +question so again let me just remind you + + align:start position:0% +question so again let me just remind you + + + align:start position:0% +question so again let me just remind you +what we did we started with a vector + + align:start position:0% +what we did we started with a vector + + + align:start position:0% +what we did we started with a vector +field F we found values for B that made + + align:start position:0% +field F we found values for B that made + + + align:start position:0% +field F we found values for B that made +that Vector field conservative and then + + align:start position:0% +that Vector field conservative and then + + + align:start position:0% +that Vector field conservative and then +we used one of the techniques in class + + align:start position:0% +we used one of the techniques in class + + + align:start position:0% +we used one of the techniques in class +to find a potential function for that + + align:start position:0% +to find a potential function for that + + + align:start position:0% +to find a potential function for that +value of B so there were a number of + + align:start position:0% +value of B so there were a number of + + + align:start position:0% +value of B so there were a number of +steps involved but ultimately again it's + + align:start position:0% +steps involved but ultimately again it's + + + align:start position:0% +steps involved but ultimately again it's +the same type of problem you've seen + + align:start position:0% +the same type of problem you've seen + + + align:start position:0% +the same type of problem you've seen +before when F was a vector field in two + + align:start position:0% +before when F was a vector field in two + + + align:start position:0% +before when F was a vector field in two +Dimensions so it shouldn't be feeling + + align:start position:0% +Dimensions so it shouldn't be feeling + + + align:start position:0% +Dimensions so it shouldn't be feeling +too different uh from some of the stuff + + align:start position:0% +too different uh from some of the stuff + + + align:start position:0% +too different uh from some of the stuff +you saw earlier okay I think that's + + align:start position:0% +you saw earlier okay I think that's + + + align:start position:0% +you saw earlier okay I think that's +where I'll stop \ No newline at end of file diff --git a/IbYdMkYn-20.txt b/IbYdMkYn-20.txt new file mode 100644 index 0000000000000000000000000000000000000000..3d501ff03f67e20114b7908a5497681614634c7a --- /dev/null +++ b/IbYdMkYn-20.txt @@ -0,0 +1,14602 @@ +align:start position:0% + +okay good + + align:start position:0% +okay good + + + align:start position:0% +okay good +afternoon so we are + + align:start position:0% + + + + align:start position:0% + +back with chemical + + align:start position:0% +back with chemical + + + align:start position:0% +back with chemical +reactions systems subject to chemical + + align:start position:0% + + + + align:start position:0% + +reactions and + + align:start position:0% +reactions and + + + align:start position:0% +reactions and +today we will uh talk about the + + align:start position:0% +today we will uh talk about the + + + align:start position:0% +today we will uh talk about the +statement of the second + + align:start position:0% + + + + align:start position:0% + +law and a small detail that is in there + + align:start position:0% +law and a small detail that is in there + + + align:start position:0% +law and a small detail that is in there +that regards chemical reactions and then + + align:start position:0% +that regards chemical reactions and then + + + align:start position:0% +that regards chemical reactions and then +we'll + + align:start position:0% +we'll + + + align:start position:0% +we'll +start playing + + align:start position:0% + + + + align:start position:0% + +some uh more + + align:start position:0% +some uh more + + + align:start position:0% +some uh more +interesting physics of of how chemical + + align:start position:0% +interesting physics of of how chemical + + + align:start position:0% +interesting physics of of how chemical +reactions happen + + align:start position:0% + + + + align:start position:0% + +so remember that in order to describe + + align:start position:0% +so remember that in order to describe + + + align:start position:0% +so remember that in order to describe +the chemical reaction mechanism we + + align:start position:0% +the chemical reaction mechanism we + + + align:start position:0% +the chemical reaction mechanism we +Define uh an + + align:start position:0% +Define uh an + + + align:start position:0% +Define uh an +equation uh which we can write in + + align:start position:0% +equation uh which we can write in + + + align:start position:0% +equation uh which we can write in +various + + align:start position:0% +various + + + align:start position:0% +various +forms formally the generic chemical + + align:start position:0% +forms formally the generic chemical + + + align:start position:0% +forms formally the generic chemical +equation reaction mechanism can be + + align:start position:0% +equation reaction mechanism can be + + + align:start position:0% +equation reaction mechanism can be +written this way where these are the + + align:start position:0% +written this way where these are the + + + align:start position:0% +written this way where these are the +chemical symbols and these are the + + align:start position:0% +chemical symbols and these are the + + + align:start position:0% +chemical symbols and these are the +stochiometric + + align:start position:0% +stochiometric + + + align:start position:0% +stochiometric +coefficients okay and the + + align:start position:0% +coefficients okay and the + + + align:start position:0% +coefficients okay and the +proportionality + + align:start position:0% + + + + align:start position:0% + +relations uh + + align:start position:0% +relations uh + + + align:start position:0% +relations uh +relate changes the possible changes in + + align:start position:0% +relate changes the possible changes in + + + align:start position:0% +relate changes the possible changes in +composition now uh let's go back to the + + align:start position:0% +composition now uh let's go back to the + + + align:start position:0% +composition now uh let's go back to the +statement of the second law this is the + + align:start position:0% +statement of the second law this is the + + + align:start position:0% +statement of the second law this is the +the same slide that we have seen + + align:start position:0% +the same slide that we have seen + + + align:start position:0% +the same slide that we have seen +um long + + align:start position:0% +um long + + + align:start position:0% +um long +ago second lecture I believe and + + align:start position:0% +ago second lecture I believe and + + + align:start position:0% +ago second lecture I believe and +uh or maybe even the first uh where I + + align:start position:0% +uh or maybe even the first uh where I + + + align:start position:0% +uh or maybe even the first uh where I +added some more specifics + + align:start position:0% +added some more specifics + + + align:start position:0% +added some more specifics +because we didn't stress it then but in + + align:start position:0% +because we didn't stress it then but in + + + align:start position:0% +because we didn't stress it then but in +the statement we wrote that + + align:start position:0% +the statement we wrote that + + + align:start position:0% +the statement we wrote that +um in the subset of states of a system + + align:start position:0% +um in the subset of states of a system + + + align:start position:0% +um in the subset of states of a system +compatible with given values of the + + align:start position:0% +compatible with given values of the + + + align:start position:0% +compatible with given values of the +amounts of + + align:start position:0% +amounts of + + + align:start position:0% +amounts of +constituents I sort of skipped + + align:start position:0% +constituents I sort of skipped + + + align:start position:0% +constituents I sort of skipped +discussing what that compatible means + + align:start position:0% +discussing what that compatible means + + + align:start position:0% +discussing what that compatible means +because now we have the tools so + + align:start position:0% +because now we have the tools so + + + align:start position:0% +because now we have the tools so +compatible means + + align:start position:0% + + + + align:start position:0% + +that uh the amounts of constituents may + + align:start position:0% +that uh the amounts of constituents may + + + align:start position:0% +that uh the amounts of constituents may +be different may change according to an + + align:start position:0% +be different may change according to an + + + align:start position:0% +be different may change according to an +internal mechanism such as a chemical + + align:start position:0% + + + + align:start position:0% + +reaction so in fact when we fix when we + + align:start position:0% +reaction so in fact when we fix when we + + + align:start position:0% +reaction so in fact when we fix when we +say that there is a stable equilibrium + + align:start position:0% +say that there is a stable equilibrium + + + align:start position:0% +say that there is a stable equilibrium +state for each value of the energy the + + align:start position:0% +state for each value of the energy the + + + align:start position:0% +state for each value of the energy the +amounts of constituents and the + + align:start position:0% +amounts of constituents and the + + + align:start position:0% +amounts of constituents and the +parameters it's + + align:start position:0% +parameters it's + + + align:start position:0% +parameters it's +really uh it's it's not exactly the + + align:start position:0% +really uh it's it's not exactly the + + + align:start position:0% +really uh it's it's not exactly the +amount of constituent + + align:start position:0% +amount of constituent + + + align:start position:0% +amount of constituent +but it's a given set of compatible uh + + align:start position:0% +but it's a given set of compatible uh + + + align:start position:0% +but it's a given set of compatible uh +possible U + + align:start position:0% +possible U + + + align:start position:0% +possible U +compositions corresponding to for + + align:start position:0% +compositions corresponding to for + + + align:start position:0% +compositions corresponding to for +example an initial am set of amounts so + + align:start position:0% +example an initial am set of amounts so + + + align:start position:0% +example an initial am set of amounts so +for example suppose we say we + + align:start position:0% +for example suppose we say we + + + align:start position:0% +for example suppose we say we +characterize a a set of + + align:start position:0% +characterize a a set of + + + align:start position:0% +characterize a a set of +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +compatible uh amounts of constituents by + + align:start position:0% +compatible uh amounts of constituents by + + + align:start position:0% +compatible uh amounts of constituents by +a given set of values of amounts like an + + align:start position:0% +a given set of values of amounts like an + + + align:start position:0% +a given set of values of amounts like an +initial set we put molecules in a box + + align:start position:0% +initial set we put molecules in a box + + + align:start position:0% +initial set we put molecules in a box +then we close the + + align:start position:0% +then we close the + + + align:start position:0% +then we close the +box but then uh the chemical reactions + + align:start position:0% +box but then uh the chemical reactions + + + align:start position:0% +box but then uh the chemical reactions +can change these amounts due + + align:start position:0% +can change these amounts due + + + align:start position:0% +can change these amounts due +to the collisions and the and the + + align:start position:0% +to the collisions and the and the + + + align:start position:0% +to the collisions and the and the +reactions themselves so according to + + align:start position:0% +reactions themselves so according to + + + align:start position:0% +reactions themselves so according to +these + + align:start position:0% + + + + align:start position:0% + +relation so that defines what we mean by + + align:start position:0% +relation so that defines what we mean by + + + align:start position:0% +relation so that defines what we mean by +compatible and also here it says that + + align:start position:0% + + + + align:start position:0% + +from any initial uh + + align:start position:0% +from any initial uh + + + align:start position:0% +from any initial uh +composition and the values of the + + align:start position:0% +composition and the values of the + + + align:start position:0% +composition and the values of the +parameters we can reach a stable + + align:start position:0% +parameters we can reach a stable + + + align:start position:0% +parameters we can reach a stable +equilibrium state by means of a + + align:start position:0% +equilibrium state by means of a + + + align:start position:0% +equilibrium state by means of a +reversible weight + + align:start position:0% +reversible weight + + + align:start position:0% +reversible weight +process uh that's really true also if + + align:start position:0% +process uh that's really true also if + + + align:start position:0% +process uh that's really true also if +you can change the composition + + align:start position:0% +you can change the composition + + + align:start position:0% +you can change the composition +compatibly with the chemical reaction + + align:start position:0% +compatibly with the chemical reaction + + + align:start position:0% +compatibly with the chemical reaction +mechanisms that you have defined as part + + align:start position:0% +mechanisms that you have defined as part + + + align:start position:0% +mechanisms that you have defined as part +of your of your model as being possible + + align:start position:0% +of your of your model as being possible + + + align:start position:0% +of your of your model as being possible +for your system remember that we're + + align:start position:0% +for your system remember that we're + + + align:start position:0% +for your system remember that we're +always talking about a model okay so in + + align:start position:0% +always talking about a model okay so in + + + align:start position:0% +always talking about a model okay so in +a model you specify what the what the + + align:start position:0% +a model you specify what the what the + + + align:start position:0% +a model you specify what the what the +constituents are and also you have to + + align:start position:0% +constituents are and also you have to + + + align:start position:0% +constituents are and also you have to +specify what the uh allowed chemical + + align:start position:0% +specify what the uh allowed chemical + + + align:start position:0% +specify what the uh allowed chemical +reaction mechanisms + + align:start position:0% +reaction mechanisms + + + align:start position:0% +reaction mechanisms +are you + + align:start position:0% +are you + + + align:start position:0% +are you +change one of these for example you you + + align:start position:0% +change one of these for example you you + + + align:start position:0% +change one of these for example you you +add one chemical reaction that is a + + align:start position:0% +add one chemical reaction that is a + + + align:start position:0% +add one chemical reaction that is a +different + + align:start position:0% +different + + + align:start position:0% +different +system so it's part of the definition of + + align:start position:0% +system so it's part of the definition of + + + align:start position:0% +system so it's part of the definition of +system is also + + align:start position:0% + + + + align:start position:0% + +this all right so what the what does + + align:start position:0% +this all right so what the what does + + + align:start position:0% +this all right so what the what does +that + + align:start position:0% +that + + + align:start position:0% +that +imply well it + + align:start position:0% +imply well it + + + align:start position:0% +imply well it +implies that since the composition can + + align:start position:0% +implies that since the composition can + + + align:start position:0% +implies that since the composition can +change they + + align:start position:0% +change they + + + align:start position:0% +change they +become like properties from state to + + align:start position:0% +become like properties from state to + + + align:start position:0% +become like properties from state to +state you have different composition so + + align:start position:0% +state you have different composition so + + + align:start position:0% +state you have different composition so +you can measure uh what's the current + + align:start position:0% +you can measure uh what's the current + + + align:start position:0% +you can measure uh what's the current +composition something that you can + + align:start position:0% +composition something that you can + + + align:start position:0% +composition something that you can +measure uh corresponds to a + + align:start position:0% + + + + align:start position:0% + +property so the amounts become + + align:start position:0% +property so the amounts become + + + align:start position:0% +property so the amounts become +properties and at stable + + align:start position:0% + + + + align:start position:0% + +equilibrium there is only + + align:start position:0% +equilibrium there is only + + + align:start position:0% +equilibrium there is only +one + + align:start position:0% +one + + + align:start position:0% +one +uh uh stable equilibrium state that + + align:start position:0% +uh uh stable equilibrium state that + + + align:start position:0% +uh uh stable equilibrium state that +means there is only one composition that + + align:start position:0% +means there is only one composition that + + + align:start position:0% +means there is only one composition that +stable that is a stable equilibrium for + + align:start position:0% +stable that is a stable equilibrium for + + + align:start position:0% +stable that is a stable equilibrium for +the given set of parameters energy and + + align:start position:0% +the given set of parameters energy and + + + align:start position:0% +the given set of parameters energy and +compatible composition so that means + + align:start position:0% +compatible composition so that means + + + align:start position:0% +compatible composition so that means +that within that set of compatible + + align:start position:0% +that within that set of compatible + + + align:start position:0% +that within that set of compatible +composition only one for each value of + + align:start position:0% +composition only one for each value of + + + align:start position:0% +composition only one for each value of +the energy is a a stable equilibrium + + align:start position:0% +the energy is a a stable equilibrium + + + align:start position:0% +the energy is a a stable equilibrium +composition all right so we have to deal + + align:start position:0% +composition all right so we have to deal + + + align:start position:0% +composition all right so we have to deal +with this uh difficulties so we + + align:start position:0% +with this uh difficulties so we + + + align:start position:0% +with this uh difficulties so we +can somehow + + align:start position:0% + + + + align:start position:0% + +restate uh the the state principle and + + align:start position:0% +restate uh the the state principle and + + + align:start position:0% +restate uh the the state principle and +the maximum entropy principle + + align:start position:0% + + + + align:start position:0% + +what I just + + align:start position:0% +what I just + + + align:start position:0% +what I just +said is that any property and now that + + align:start position:0% +said is that any property and now that + + + align:start position:0% +said is that any property and now that +list of properties includes the + + align:start position:0% +list of properties includes the + + + align:start position:0% +list of properties includes the +amounts of + + align:start position:0% +amounts of + + + align:start position:0% +amounts of +constituents uh is + + align:start position:0% +constituents uh is + + + align:start position:0% +constituents uh is +uniquely uh fixed by the state so the + + align:start position:0% +uniquely uh fixed by the state so the + + + align:start position:0% +uniquely uh fixed by the state so the +once you once you have a stable + + align:start position:0% +once you once you have a stable + + + align:start position:0% +once you once you have a stable +equilibrium State and you have one for + + align:start position:0% +equilibrium State and you have one for + + + align:start position:0% +equilibrium State and you have one for +each value of the energy volume initial + + align:start position:0% +each value of the energy volume initial + + + align:start position:0% +each value of the energy volume initial +amounts and stochiometric coefficients + + align:start position:0% +amounts and stochiometric coefficients + + + align:start position:0% +amounts and stochiometric coefficients +that defin what the mechanisms are in + + align:start position:0% +that defin what the mechanisms are in + + + align:start position:0% +that defin what the mechanisms are in +play okay for that + + align:start position:0% +play okay for that + + + align:start position:0% +play okay for that +one that fixes the state and therefore + + align:start position:0% +one that fixes the state and therefore + + + align:start position:0% +one that fixes the state and therefore +fixes the values of all the properties + + align:start position:0% +fixes the values of all the properties + + + align:start position:0% +fixes the values of all the properties +therefore each property is only at + + align:start position:0% +therefore each property is only at + + + align:start position:0% +therefore each property is only at +stable equilibrium because this is true + + align:start position:0% +stable equilibrium because this is true + + + align:start position:0% +stable equilibrium because this is true +only at stable equilibrium is a function + + align:start position:0% +only at stable equilibrium is a function + + + align:start position:0% +only at stable equilibrium is a function +of these variables and only + + align:start position:0% +of these variables and only + + + align:start position:0% +of these variables and only +these and among these + + align:start position:0% +these and among these + + + align:start position:0% +these and among these +properties is the + + align:start position:0% +properties is the + + + align:start position:0% +properties is the +amounts so we call n Sub Zero the + + align:start position:0% +amounts so we call n Sub Zero the + + + align:start position:0% +amounts so we call n Sub Zero the +amounts that Prevail at uh stable + + align:start position:0% +amounts that Prevail at uh stable + + + align:start position:0% +amounts that Prevail at uh stable +equilibrium so in addition to the + + align:start position:0% +equilibrium so in addition to the + + + align:start position:0% +equilibrium so in addition to the +fundamental relation for the entropy + + align:start position:0% +fundamental relation for the entropy + + + align:start position:0% +fundamental relation for the entropy +which is this + + align:start position:0% +which is this + + + align:start position:0% +which is this +one with which we have played a lot in + + align:start position:0% +one with which we have played a lot in + + + align:start position:0% +one with which we have played a lot in +Computing derivatives properties + + align:start position:0% +Computing derivatives properties + + + align:start position:0% +Computing derivatives properties +temperature chemical potential pressure + + align:start position:0% +temperature chemical potential pressure + + + align:start position:0% +temperature chemical potential pressure +and so + + align:start position:0% +and so + + + align:start position:0% +and so +on we now have also another + + align:start position:0% +on we now have also another + + + align:start position:0% +on we now have also another +we could call it another fundamental + + align:start position:0% +we could call it another fundamental + + + align:start position:0% +we could call it another fundamental +relation for + + align:start position:0% +relation for + + + align:start position:0% +relation for +composition or + + align:start position:0% +composition or + + + align:start position:0% +composition or +equivalently since composition and + + align:start position:0% +equivalently since composition and + + + align:start position:0% +equivalently since composition and +reaction coordinates are related this + + align:start position:0% +reaction coordinates are related this + + + align:start position:0% +reaction coordinates are related this +way you can also write it equivalently + + align:start position:0% +way you can also write it equivalently + + + align:start position:0% +way you can also write it equivalently +this is not an extra equation in terms + + align:start position:0% +this is not an extra equation in terms + + + align:start position:0% +this is not an extra equation in terms +of uh the Epsilon and here I have to + + align:start position:0% +of uh the Epsilon and here I have to + + + align:start position:0% +of uh the Epsilon and here I have to +correct this must be + + align:start position:0% + + + + align:start position:0% + +epsilon0 okay + + align:start position:0% +epsilon0 okay + + + align:start position:0% +epsilon0 okay +the maximum entropy principle then + + align:start position:0% + + + + align:start position:0% + +says that among all the + + align:start position:0% +says that among all the + + + align:start position:0% +says that among all the +states and here in the slide I didn't + + align:start position:0% +states and here in the slide I didn't + + + align:start position:0% +states and here in the slide I didn't +write it explicitly so now we should we + + align:start position:0% +write it explicitly so now we should we + + + align:start position:0% +write it explicitly so now we should we +we should go back and + + align:start position:0% +we should go back and + + + align:start position:0% +we should go back and +correct uh States compatible with given + + align:start position:0% +correct uh States compatible with given + + + align:start position:0% +correct uh States compatible with given +initial amounts of constituents + + align:start position:0% +initial amounts of constituents + + + align:start position:0% +initial amounts of constituents +parameters and energy so among all these + + align:start position:0% +parameters and energy so among all these + + + align:start position:0% +parameters and energy so among all these +states and there are many uh the stable + + align:start position:0% +states and there are many uh the stable + + + align:start position:0% +states and there are many uh the stable +equilibrium state is the one with the + + align:start position:0% +equilibrium state is the one with the + + + align:start position:0% +equilibrium state is the one with the +maximum Maxum + + align:start position:0% +maximum Maxum + + + align:start position:0% +maximum Maxum +entropy and we shall use this condition + + align:start position:0% +entropy and we shall use this condition + + + align:start position:0% +entropy and we shall use this condition +of Maximum + + align:start position:0% +of Maximum + + + align:start position:0% +of Maximum +entropy in a moment to determine what + + align:start position:0% +entropy in a moment to determine what + + + align:start position:0% +entropy in a moment to determine what +the equilibrium composition + + align:start position:0% + + + + align:start position:0% + +is in order to do so we have to Define + + align:start position:0% +is in order to do so we have to Define + + + align:start position:0% +is in order to do so we have to Define +better or maybe let's say refine + + align:start position:0% +better or maybe let's say refine + + + align:start position:0% +better or maybe let's say refine +with an important little detail the + + align:start position:0% +with an important little detail the + + + align:start position:0% +with an important little detail the +simple system model namely the model + + align:start position:0% +simple system model namely the model + + + align:start position:0% +simple system model namely the model +that applies when we have many particles + + align:start position:0% +that applies when we have many particles + + + align:start position:0% +that applies when we have many particles +large + + align:start position:0% + + + + align:start position:0% + +and remember this slide which tells us + + align:start position:0% +and remember this slide which tells us + + + align:start position:0% +and remember this slide which tells us +how strong the chemical bonds may + + align:start position:0% +how strong the chemical bonds may + + + align:start position:0% +how strong the chemical bonds may +be and + + align:start position:0% + + + + align:start position:0% + +yet as a result of + + align:start position:0% +yet as a result of + + + align:start position:0% +yet as a result of +cions these chemical bonds can be broken + + align:start position:0% +cions these chemical bonds can be broken + + + align:start position:0% +cions these chemical bonds can be broken +to form more stable + + align:start position:0% +to form more stable + + + align:start position:0% +to form more stable +ones or in fact also the collisions of + + align:start position:0% +ones or in fact also the collisions of + + + align:start position:0% +ones or in fact also the collisions of +these more stable ones sometimes if the + + align:start position:0% +these more stable ones sometimes if the + + + align:start position:0% +these more stable ones sometimes if the +Collision is strong + + align:start position:0% +Collision is strong + + + align:start position:0% +Collision is strong +enough can produce the breakup into uh + + align:start position:0% +enough can produce the breakup into uh + + + align:start position:0% +enough can produce the breakup into uh +products that are lesser stable and + + align:start position:0% +products that are lesser stable and + + + align:start position:0% +products that are lesser stable and +actually at equilibrium the mechanism + + align:start position:0% +actually at equilibrium the mechanism + + + align:start position:0% +actually at equilibrium the mechanism +that goes in One Direction equilibrates + + align:start position:0% +that goes in One Direction equilibrates + + + align:start position:0% +that goes in One Direction equilibrates +uh the rate at which things go in One + + align:start position:0% +uh the rate at which things go in One + + + align:start position:0% +uh the rate at which things go in One +Direction uh he equilibrates the rate in + + align:start position:0% +Direction uh he equilibrates the rate in + + + align:start position:0% +Direction uh he equilibrates the rate in +the opposite + + align:start position:0% + + + + align:start position:0% + +direction so this slide you'll read it + + align:start position:0% +direction so this slide you'll read it + + + align:start position:0% +direction so this slide you'll read it +later on but simply wants to talk about + + align:start position:0% +later on but simply wants to talk about + + + align:start position:0% +later on but simply wants to talk about +collisions I actually added this + + align:start position:0% +collisions I actually added this + + + align:start position:0% +collisions I actually added this +Photograph this morning because I was + + align:start position:0% +Photograph this morning because I was + + + align:start position:0% +Photograph this morning because I was +passing in the + + align:start position:0% +passing in the + + + align:start position:0% +passing in the +fourth floor Corridor in um building 10 + + align:start position:0% +fourth floor Corridor in um building 10 + + + align:start position:0% +fourth floor Corridor in um building 10 +where you probably uh have gone and seen + + align:start position:0% +where you probably uh have gone and seen + + + align:start position:0% +where you probably uh have gone and seen +these photographs by doc + + align:start position:0% +these photographs by doc + + + align:start position:0% +these photographs by doc +Edgerton + + align:start position:0% +Edgerton + + + align:start position:0% +Edgerton +um and you see how uh a + + align:start position:0% +um and you see how uh a + + + align:start position:0% +um and you see how uh a +collision uh between a golf club and the + + align:start position:0% +collision uh between a golf club and the + + + align:start position:0% +collision uh between a golf club and the +golf ball can + + align:start position:0% +golf ball can + + + align:start position:0% +golf ball can +deform the ball which if you take it in + + align:start position:0% +deform the ball which if you take it in + + + align:start position:0% +deform the ball which if you take it in +your hands you know it's kind of hard it + + align:start position:0% +your hands you know it's kind of hard it + + + align:start position:0% +your hands you know it's kind of hard it +looks like a very hard almost a hard + + align:start position:0% +looks like a very hard almost a hard + + + align:start position:0% +looks like a very hard almost a hard +sphere yet + + align:start position:0% +sphere yet + + + align:start position:0% +sphere yet +uh the photograph shows that even + + align:start position:0% +uh the photograph shows that even + + + align:start position:0% +uh the photograph shows that even +in I think uh yeah it says six six + + align:start position:0% + + + + align:start position:0% + +milliseconds uh I think it takes six + + align:start position:0% +milliseconds uh I think it takes six + + + align:start position:0% +milliseconds uh I think it takes six +milliseconds or less to uh during that + + align:start position:0% +milliseconds or less to uh during that + + + align:start position:0% +milliseconds or less to uh during that +impact which is very + + align:start position:0% +impact which is very + + + align:start position:0% +impact which is very +short + + align:start position:0% +short + + + align:start position:0% +short +uh the + + align:start position:0% +uh the + + + align:start position:0% +uh the +particle gets deformed so much so it + + align:start position:0% +particle gets deformed so much so it + + + align:start position:0% +particle gets deformed so much so it +since it is elastic it absorbs the + + align:start position:0% +since it is elastic it absorbs the + + + align:start position:0% +since it is elastic it absorbs the +energy kinetic energy that comes from + + align:start position:0% +energy kinetic energy that comes from + + + align:start position:0% +energy kinetic energy that comes from +from the club and it becomes the + + align:start position:0% +from the club and it becomes the + + + align:start position:0% +from the club and it becomes the +formation energy like a spring and then + + align:start position:0% +formation energy like a spring and then + + + align:start position:0% +formation energy like a spring and then +that energy stored in the spring uh will + + align:start position:0% +that energy stored in the spring uh will + + + align:start position:0% +that energy stored in the spring uh will +be + + align:start position:0% +be + + + align:start position:0% +be +released very quickly so in the case of + + align:start position:0% +released very quickly so in the case of + + + align:start position:0% +released very quickly so in the case of +the golf Bowl it + + align:start position:0% +the golf Bowl it + + + align:start position:0% +the golf Bowl it +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +will hit it at a very long distance in + + align:start position:0% +will hit it at a very long distance in + + + align:start position:0% +will hit it at a very long distance in +the case of + + align:start position:0% +the case of + + + align:start position:0% +the case of +molecules it may + + align:start position:0% +molecules it may + + + align:start position:0% +molecules it may +generate uh the breaking of some of the + + align:start position:0% +generate uh the breaking of some of the + + + align:start position:0% +generate uh the breaking of some of the +weaker bonds and uh the formation of + + align:start position:0% +weaker bonds and uh the formation of + + + align:start position:0% +weaker bonds and uh the formation of +other more stable + + align:start position:0% +other more stable + + + align:start position:0% +other more stable +bonds there is also this other video in + + align:start position:0% +bonds there is also this other video in + + + align:start position:0% +bonds there is also this other video in +YouTube which shows you + + align:start position:0% +YouTube which shows you + + + align:start position:0% +YouTube which shows you +again + + align:start position:0% +again + + + align:start position:0% +again +um the impact of a golf club of a + + align:start position:0% +um the impact of a golf club of a + + + align:start position:0% +um the impact of a golf club of a +golf bow into a rigid really rigid wall + + align:start position:0% +golf bow into a rigid really rigid wall + + + align:start position:0% +golf bow into a rigid really rigid wall +it's see how it it's impressive how it + + align:start position:0% +it's see how it it's impressive how it + + + align:start position:0% +it's see how it it's impressive how it +deforms it becomes almost flat and then + + align:start position:0% +deforms it becomes almost flat and then + + + align:start position:0% +deforms it becomes almost flat and then +it begins to oscillate as it goes + + align:start position:0% +it begins to oscillate as it goes + + + align:start position:0% +it begins to oscillate as it goes +away very impressive so this is uh + + align:start position:0% +away very impressive so this is uh + + + align:start position:0% +away very impressive so this is uh +collisions are play an important role in + + align:start position:0% +collisions are play an important role in + + + align:start position:0% +collisions are play an important role in +chemical + + align:start position:0% + + + + align:start position:0% + +reactions now so let's introduce now + + align:start position:0% +reactions now so let's introduce now + + + align:start position:0% +reactions now so let's introduce now +this + + align:start position:0% +this + + + align:start position:0% +this +concept that we will call + + align:start position:0% +concept that we will call + + + align:start position:0% +concept that we will call +the activated + + align:start position:0% +the activated + + + align:start position:0% +the activated +complex as a result of a collision + + align:start position:0% +complex as a result of a collision + + + align:start position:0% +complex as a result of a collision +between + + align:start position:0% +between + + + align:start position:0% +between +molecules + + align:start position:0% +molecules + + + align:start position:0% +molecules +typically as you + + align:start position:0% +typically as you + + + align:start position:0% +typically as you +know uh by thermal agitation molecules + + align:start position:0% +know uh by thermal agitation molecules + + + align:start position:0% +know uh by thermal agitation molecules +are move around and have many + + align:start position:0% + + + + align:start position:0% + +collisions per second billions and and + + align:start position:0% +collisions per second billions and and + + + align:start position:0% +collisions per second billions and and +um as a result of these collisions they + + align:start position:0% +um as a result of these collisions they + + + align:start position:0% +um as a result of these collisions they +get deformed they do what we just said + + align:start position:0% + + + + align:start position:0% + +sometimes uh the combined kinetic energy + + align:start position:0% +sometimes uh the combined kinetic energy + + + align:start position:0% +sometimes uh the combined kinetic energy +of the colliding uh atoms or molecules + + align:start position:0% +of the colliding uh atoms or molecules + + + align:start position:0% +of the colliding uh atoms or molecules +are enough to + + align:start position:0% +are enough to + + + align:start position:0% +are enough to +form um + + align:start position:0% +form um + + + align:start position:0% +form um +a sort of an unstable + + align:start position:0% +a sort of an unstable + + + align:start position:0% +a sort of an unstable +compound which we will call activated + + align:start position:0% +compound which we will call activated + + + align:start position:0% +compound which we will call activated +complex and uh call it with the star on + + align:start position:0% +complex and uh call it with the star on + + + align:start position:0% +complex and uh call it with the star on +top and this compound + + align:start position:0% +top and this compound + + + align:start position:0% +top and this compound +is momentary is + + align:start position:0% +is momentary is + + + align:start position:0% +is momentary is +momentary lives it's very short lived + + align:start position:0% +momentary lives it's very short lived + + + align:start position:0% +momentary lives it's very short lived +and uh it's + + align:start position:0% + + + + align:start position:0% + +unstable and uh and this is where if it + + align:start position:0% +unstable and uh and this is where if it + + + align:start position:0% +unstable and uh and this is where if it +decays the proper way in other words if + + align:start position:0% +decays the proper way in other words if + + + align:start position:0% +decays the proper way in other words if +it if the uh elastic energy the + + align:start position:0% +it if the uh elastic energy the + + + align:start position:0% +it if the uh elastic energy the +vibrational energies get the get um move + + align:start position:0% +vibrational energies get the get um move + + + align:start position:0% +vibrational energies get the get um move +to the right uh to the right bonds so as + + align:start position:0% +to the right uh to the right bonds so as + + + align:start position:0% +to the right uh to the right bonds so as +to break them and to uh so so that the + + align:start position:0% +to break them and to uh so so that the + + + align:start position:0% +to break them and to uh so so that the +atoms are free to recombine in a + + align:start position:0% +atoms are free to recombine in a + + + align:start position:0% +atoms are free to recombine in a +different way then you'll have an + + align:start position:0% +different way then you'll have an + + + align:start position:0% +different way then you'll have an +effective Collision that will transform + + align:start position:0% +effective Collision that will transform + + + align:start position:0% +effective Collision that will transform +your reactants in + + align:start position:0% + + + + align:start position:0% + +products + + align:start position:0% +products + + + align:start position:0% +products +uh of + + align:start position:0% +uh of + + + align:start position:0% +uh of +course this is um Contour through + + align:start position:0% +course this is um Contour through + + + align:start position:0% +course this is um Contour through +Contour plot of a of + + align:start position:0% +Contour plot of a of + + + align:start position:0% +Contour plot of a of +a of a diagram that wants to represent + + align:start position:0% +a of a diagram that wants to represent + + + align:start position:0% +a of a diagram that wants to represent +uh + + align:start position:0% +uh + + + align:start position:0% +uh +here the most stable + + align:start position:0% +here the most stable + + + align:start position:0% +here the most stable +potential configuration that represents + + align:start position:0% +potential configuration that represents + + + align:start position:0% +potential configuration that represents +the potential energy of your say uh AB + + align:start position:0% +the potential energy of your say uh AB + + + align:start position:0% +the potential energy of your say uh AB +plus C is the products okay and + + align:start position:0% +plus C is the products okay and + + + align:start position:0% +plus C is the products okay and +here the in this bottom of this other + + align:start position:0% +here the in this bottom of this other + + + align:start position:0% +here the in this bottom of this other +Valley uh you have the potential + + align:start position:0% +Valley uh you have the potential + + + align:start position:0% +Valley uh you have the potential +energy combined of the uh reactants + + align:start position:0% +energy combined of the uh reactants + + + align:start position:0% +energy combined of the uh reactants +and + + align:start position:0% +and + + + align:start position:0% +and +um so typically if you are at zero + + align:start position:0% +um so typically if you are at zero + + + align:start position:0% +um so typically if you are at zero +temperature particles don't move no + + align:start position:0% +temperature particles don't move no + + + align:start position:0% +temperature particles don't move no +collisions no chance to reach uh uh + + align:start position:0% +collisions no chance to reach uh uh + + + align:start position:0% +collisions no chance to reach uh uh +enough energy to overcome because you + + align:start position:0% +enough energy to overcome because you + + + align:start position:0% +enough energy to overcome because you +see this is a it's like two + + align:start position:0% +see this is a it's like two + + + align:start position:0% +see this is a it's like two +valys and this is a subtle point that + + align:start position:0% +valys and this is a subtle point that + + + align:start position:0% +valys and this is a subtle point that +connects the two valys okay and this one + + align:start position:0% +connects the two valys okay and this one + + + align:start position:0% +connects the two valys okay and this one +which is uh this dashed line + + align:start position:0% +which is uh this dashed line + + + align:start position:0% +which is uh this dashed line +represents the like the + + align:start position:0% + + + + align:start position:0% + +bottom let's say the steepest ascent and + + align:start position:0% +bottom let's say the steepest ascent and + + + align:start position:0% +bottom let's say the steepest ascent and +steepest + + align:start position:0% +steepest + + + align:start position:0% +steepest +descent uh path uh from the reactant + + align:start position:0% +descent uh path uh from the reactant + + + align:start position:0% +descent uh path uh from the reactant +Valley to + + align:start position:0% +Valley to + + + align:start position:0% +Valley to +the product Valley of the potential + + align:start position:0% + + + + align:start position:0% + +energy so if energy is only potential + + align:start position:0% +energy so if energy is only potential + + + align:start position:0% +energy so if energy is only potential +you are at zero + + align:start position:0% +you are at zero + + + align:start position:0% +you are at zero +temperature and the particles will like + + align:start position:0% +temperature and the particles will like + + + align:start position:0% +temperature and the particles will like +to stay in the + + align:start position:0% +to stay in the + + + align:start position:0% +to stay in the +bottom but as soon as the temperature + + align:start position:0% +bottom but as soon as the temperature + + + align:start position:0% +bottom but as soon as the temperature +increases the collisions the kinetic + + align:start position:0% +increases the collisions the kinetic + + + align:start position:0% +increases the collisions the kinetic +energy uh allows for collisions and the + + align:start position:0% +energy uh allows for collisions and the + + + align:start position:0% +energy uh allows for collisions and the +collisions allows particles to put + + align:start position:0% +collisions allows particles to put + + + align:start position:0% +collisions allows particles to put +energy together and therefore they can + + align:start position:0% +energy together and therefore they can + + + align:start position:0% +energy together and therefore they can +uh move + + align:start position:0% +uh move + + + align:start position:0% +uh move +around in these valleys and uh and find + + align:start position:0% +around in these valleys and uh and find + + + align:start position:0% +around in these valleys and uh and find +themselves in configurations that are + + align:start position:0% +themselves in configurations that are + + + align:start position:0% +themselves in configurations that are +not not the most stable but momentarily + + align:start position:0% +not not the most stable but momentarily + + + align:start position:0% +not not the most stable but momentarily +they can live also in very unstable + + align:start position:0% +they can live also in very unstable + + + align:start position:0% +they can live also in very unstable +situations along the sides of the valley + + align:start position:0% +situations along the sides of the valley + + + align:start position:0% +situations along the sides of the valley +and sometimes they can even reach the + + align:start position:0% +and sometimes they can even reach the + + + align:start position:0% +and sometimes they can even reach the +subtle + + align:start position:0% +subtle + + + align:start position:0% +subtle +Point perhaps also with additional + + align:start position:0% +Point perhaps also with additional + + + align:start position:0% +Point perhaps also with additional +energy than just what is barely enough + + align:start position:0% +energy than just what is barely enough + + + align:start position:0% +energy than just what is barely enough +to be + + align:start position:0% + + + + align:start position:0% + +there so this + + align:start position:0% +there so this + + + align:start position:0% +there so this +plot uh represents along this dust line + + align:start position:0% +plot uh represents along this dust line + + + align:start position:0% +plot uh represents along this dust line +potential + + align:start position:0% +potential + + + align:start position:0% +potential +energy and here we are assuming that the + + align:start position:0% +energy and here we are assuming that the + + + align:start position:0% +energy and here we are assuming that the +uh reactant Val is uh deeper than the um + + align:start position:0% +uh reactant Val is uh deeper than the um + + + align:start position:0% +uh reactant Val is uh deeper than the um +product + + align:start position:0% + + + + align:start position:0% + +Valley okay what is important for the + + align:start position:0% +Valley okay what is important for the + + + align:start position:0% +Valley okay what is important for the +moment then we will when we do kinetics + + align:start position:0% +moment then we will when we do kinetics + + + align:start position:0% +moment then we will when we do kinetics +um next + + align:start position:0% +um next + + + align:start position:0% +um next +time uh we will also talk about how to + + align:start position:0% +time uh we will also talk about how to + + + align:start position:0% +time uh we will also talk about how to +to model the rates at which this uh + + align:start position:0% +to model the rates at which this uh + + + align:start position:0% +to model the rates at which this uh +climbing of the valley to the sdle point + + align:start position:0% +climbing of the valley to the sdle point + + + align:start position:0% +climbing of the valley to the sdle point +happens but uh for the moment all that + + align:start position:0% +happens but uh for the moment all that + + + align:start position:0% +happens but uh for the moment all that +we need to to know is + + align:start position:0% +we need to to know is + + + align:start position:0% +we need to to know is +that this activated complex uh can be + + align:start position:0% +that this activated complex uh can be + + + align:start position:0% +that this activated complex uh can be +treated can be it's literally a a new + + align:start position:0% +treated can be it's literally a a new + + + align:start position:0% +treated can be it's literally a a new +compound so a super molecule in which U + + align:start position:0% +compound so a super molecule in which U + + + align:start position:0% +compound so a super molecule in which U +all the atoms that are in in play are + + align:start position:0% +all the atoms that are in in play are + + + align:start position:0% +all the atoms that are in in play are +very close to one another and they share + + align:start position:0% +very close to one another and they share + + + align:start position:0% +very close to one another and they share +a lot of elastic energy exactly like the + + align:start position:0% +a lot of elastic energy exactly like the + + + align:start position:0% +a lot of elastic energy exactly like the +golf bowl is uh deformed and then it + + align:start position:0% +golf bowl is uh deformed and then it + + + align:start position:0% +golf bowl is uh deformed and then it +only depend in the and then NE once + + align:start position:0% +only depend in the and then NE once + + + align:start position:0% +only depend in the and then NE once +you're there that thing could decay in + + align:start position:0% +you're there that thing could decay in + + + align:start position:0% +you're there that thing could decay in +One Direction or could decay in the + + align:start position:0% +One Direction or could decay in the + + + align:start position:0% +One Direction or could decay in the +other + + align:start position:0% +other + + + align:start position:0% +other +direction so there is a chance that it + + align:start position:0% +direction so there is a chance that it + + + align:start position:0% +direction so there is a chance that it +you are up here and you Decay down this + + align:start position:0% +you are up here and you Decay down this + + + align:start position:0% +you are up here and you Decay down this +Valley or you can Decay the other Valley + + align:start position:0% +Valley or you can Decay the other Valley + + + align:start position:0% +Valley or you can Decay the other Valley +after all this is an unstable + + align:start position:0% +after all this is an unstable + + + align:start position:0% +after all this is an unstable +Point + + align:start position:0% +Point + + + align:start position:0% +Point +okay so in principle + + align:start position:0% + + + + align:start position:0% + +see in principle if you have a + + align:start position:0% +see in principle if you have a + + + align:start position:0% +see in principle if you have a +box + + align:start position:0% + + + + align:start position:0% + +uh in which you have + + align:start position:0% +uh in which you have + + + align:start position:0% +uh in which you have +only say suppose you have just two + + align:start position:0% +only say suppose you have just two + + + align:start position:0% +only say suppose you have just two +hydrogen + + align:start position:0% + + + + align:start position:0% + +atoms so this + + align:start position:0% +atoms so this + + + align:start position:0% +atoms so this +is and U now as a result so this is a + + align:start position:0% +is and U now as a result so this is a + + + align:start position:0% +is and U now as a result so this is a +time say T1 + + align:start position:0% + + + + align:start position:0% + +at a later time as a result of + + align:start position:0% +at a later time as a result of + + + align:start position:0% +at a later time as a result of +collisions they find + + align:start position:0% +collisions they find + + + align:start position:0% +collisions they find +themselves in a highly deformed + + align:start position:0% +themselves in a highly deformed + + + align:start position:0% +themselves in a highly deformed +situation uh like this very close to one + + align:start position:0% +situation uh like this very close to one + + + align:start position:0% +situation uh like this very close to one +another this is the + + align:start position:0% +another this is the + + + align:start position:0% +another this is the +activated + + align:start position:0% +activated + + + align:start position:0% +activated +complex + + align:start position:0% +complex + + + align:start position:0% +complex +and there as a result of the Collision + + align:start position:0% +and there as a result of the Collision + + + align:start position:0% +and there as a result of the Collision +you could have two possibilities maybe I + + align:start position:0% +you could have two possibilities maybe I + + + align:start position:0% +you could have two possibilities maybe I +should do this uh + + align:start position:0% + + + + align:start position:0% + +that the thing + + align:start position:0% +that the thing + + + align:start position:0% +that the thing +breaks back to having two hydrogen + + align:start position:0% +breaks back to having two hydrogen + + + align:start position:0% +breaks back to having two hydrogen +atoms so maybe these ones were moving + + align:start position:0% +atoms so maybe these ones were moving + + + align:start position:0% +atoms so maybe these ones were moving +this way they Collide here they form + + align:start position:0% +this way they Collide here they form + + + align:start position:0% +this way they Collide here they form +this activated complex let + + align:start position:0% +this activated complex let + + + align:start position:0% +this activated complex let +me put that just to say well it's it has + + align:start position:0% +me put that just to say well it's it has + + + align:start position:0% +me put that just to say well it's it has +a lot of uh stored elastic energy in it + + align:start position:0% +a lot of uh stored elastic energy in it + + + align:start position:0% +a lot of uh stored elastic energy in it +so one way is that that elastic energy + + align:start position:0% +so one way is that that elastic energy + + + align:start position:0% +so one way is that that elastic energy +makes it explode in two uh two other uh + + align:start position:0% +makes it explode in two uh two other uh + + + align:start position:0% +makes it explode in two uh two other uh +atoms that will move far away or it + + align:start position:0% +atoms that will move far away or it + + + align:start position:0% +atoms that will move far away or it +could + + align:start position:0% +could + + + align:start position:0% +could +also + + align:start position:0% +also + + + align:start position:0% +also +uh if the angles of the collisions are + + align:start position:0% +uh if the angles of the collisions are + + + align:start position:0% +uh if the angles of the collisions are +appropriate and so on you can also form + + align:start position:0% +appropriate and so on you can also form + + + align:start position:0% +appropriate and so on you can also form +just a single uh single molecule that + + align:start position:0% +just a single uh single molecule that + + + align:start position:0% +just a single uh single molecule that +would move away this way of course you + + align:start position:0% +would move away this way of course you + + + align:start position:0% +would move away this way of course you +have to conserve also momentum so uh + + align:start position:0% +have to conserve also momentum so uh + + + align:start position:0% +have to conserve also momentum so uh +this molecule will have the same + + align:start position:0% +this molecule will have the same + + + align:start position:0% +this molecule will have the same +momentum that the sum of the two + + align:start position:0% +momentum that the sum of the two + + + align:start position:0% +momentum that the sum of the two +momentum okay so this would be an + + align:start position:0% +momentum okay so this would be an + + + align:start position:0% +momentum okay so this would be an +effective chemically effective Collision + + align:start position:0% +effective chemically effective Collision + + + align:start position:0% +effective chemically effective Collision +that produces the chemical reaction and + + align:start position:0% +that produces the chemical reaction and + + + align:start position:0% +that produces the chemical reaction and +this is an ineffective chemical + + align:start position:0% +this is an ineffective chemical + + + align:start position:0% +this is an ineffective chemical +Collision + + align:start position:0% +Collision + + + align:start position:0% +Collision +just this kind of collisions the + + align:start position:0% +just this kind of collisions the + + + align:start position:0% +just this kind of collisions the +ineffective ones are the ones that are + + align:start position:0% +ineffective ones are the ones that are + + + align:start position:0% +ineffective ones are the ones that are +um also uh + + align:start position:0% +um also uh + + + align:start position:0% +um also uh +responsible if you don't have to have to + + align:start position:0% +responsible if you don't have to have to + + + align:start position:0% +responsible if you don't have to have to +go to this kind of extreme uh they are + + align:start position:0% +go to this kind of extreme uh they are + + + align:start position:0% +go to this kind of extreme uh they are +responsible for redistributing the + + align:start position:0% +responsible for redistributing the + + + align:start position:0% +responsible for redistributing the +energy between uh the various atoms in + + align:start position:0% +energy between uh the various atoms in + + + align:start position:0% +energy between uh the various atoms in +your system and if you have enough + + align:start position:0% +your system and if you have enough + + + align:start position:0% +your system and if you have enough +particles that will give you uh produce + + align:start position:0% +particles that will give you uh produce + + + align:start position:0% +particles that will give you uh produce +the maxwellian distribution Maxwell bman + + align:start position:0% +the maxwellian distribution Maxwell bman + + + align:start position:0% +the maxwellian distribution Maxwell bman +distribution of velocities okay + + align:start position:0% + + + + align:start position:0% + +now you see here that uh for a system in + + align:start position:0% +now you see here that uh for a system in + + + align:start position:0% +now you see here that uh for a system in +which there are only few particles like + + align:start position:0% +which there are only few particles like + + + align:start position:0% +which there are only few particles like +two literally two particles here we have + + align:start position:0% +two literally two particles here we have + + + align:start position:0% +two literally two particles here we have +those two particles have disappeared at + + align:start position:0% +those two particles have disappeared at + + + align:start position:0% +those two particles have disappeared at +this moment in + + align:start position:0% + + + + align:start position:0% + +time + + align:start position:0% +time + + + align:start position:0% +time +uh in order to describe the the Dynamics + + align:start position:0% +uh in order to describe the the Dynamics + + + align:start position:0% +uh in order to describe the the Dynamics +of this system or the properties as a + + align:start position:0% +of this system or the properties as a + + + align:start position:0% +of this system or the properties as a +function of time we need to know also + + align:start position:0% +function of time we need to know also + + + align:start position:0% +function of time we need to know also +the properties of this activated complex + + align:start position:0% +the properties of this activated complex + + + align:start position:0% +the properties of this activated complex +because for some time it's the only + + align:start position:0% +because for some time it's the only + + + align:start position:0% +because for some time it's the only +thing in our + + align:start position:0% +thing in our + + + align:start position:0% +thing in our +box so if we want to describe properties + + align:start position:0% +box so if we want to describe properties + + + align:start position:0% +box so if we want to describe properties +uh we have to know what the structure of + + align:start position:0% +uh we have to know what the structure of + + + align:start position:0% +uh we have to know what the structure of +this molecule is and what's the specific + + align:start position:0% +this molecule is and what's the specific + + + align:start position:0% +this molecule is and what's the specific +Heats and so + + align:start position:0% + + + + align:start position:0% + +on uh so we treat this activated + + align:start position:0% +on uh so we treat this activated + + + align:start position:0% +on uh so we treat this activated +complex as as a molecule in + + align:start position:0% +complex as as a molecule in + + + align:start position:0% +complex as as a molecule in +itself however + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +uh okay let's uh uh do the the formal uh + + align:start position:0% +uh okay let's uh uh do the the formal uh + + + align:start position:0% +uh okay let's uh uh do the the formal uh +discussion about + + align:start position:0% + + + + align:start position:0% + +this so + + align:start position:0% +this so + + + align:start position:0% +this so +essentially what this says is that + + align:start position:0% +essentially what this says is that + + + align:start position:0% +essentially what this says is that +we we can + + align:start position:0% +we we can + + + align:start position:0% +we we can +split + + align:start position:0% +split + + + align:start position:0% +split +the uh reaction mechanism into two + + align:start position:0% +the uh reaction mechanism into two + + + align:start position:0% +the uh reaction mechanism into two +parts a forward half + + align:start position:0% +parts a forward half + + + align:start position:0% +parts a forward half +reaction that that + + align:start position:0% +reaction that that + + + align:start position:0% +reaction that that +takes uh the + + align:start position:0% +takes uh the + + + align:start position:0% +takes uh the +reactants + + align:start position:0% +reactants + + + align:start position:0% +reactants +and forms as a result of collision + + align:start position:0% +and forms as a result of collision + + + align:start position:0% +and forms as a result of collision +between the reactants forms deactivated + + align:start position:0% + + + + align:start position:0% + +complex and the backward half + + align:start position:0% +complex and the backward half + + + align:start position:0% +complex and the backward half +reaction which is a result of collisions + + align:start position:0% +reaction which is a result of collisions + + + align:start position:0% +reaction which is a result of collisions +between product molecules also gives + + align:start position:0% +between product molecules also gives + + + align:start position:0% +between product molecules also gives +right uh gives rise to + + align:start position:0% + + + + align:start position:0% + +this so you notice that we can write our + + align:start position:0% +this so you notice that we can write our + + + align:start position:0% +this so you notice that we can write our +original overall reaction in this + + align:start position:0% +original overall reaction in this + + + align:start position:0% +original overall reaction in this +way and by our rule since we have put + + align:start position:0% +way and by our rule since we have put + + + align:start position:0% +way and by our rule since we have put +the positive stric coefficients for the + + align:start position:0% +the positive stric coefficients for the + + + align:start position:0% +the positive stric coefficients for the +products and negative for the + + align:start position:0% + + + + align:start position:0% + +reactants if you want to start from the + + align:start position:0% +reactants if you want to start from the + + + align:start position:0% +reactants if you want to start from the +products and form the activated + + align:start position:0% +products and form the activated + + + align:start position:0% +products and form the activated +complex you have to put this + + align:start position:0% +complex you have to put this + + + align:start position:0% +complex you have to put this +uh put them this way and and so the net + + align:start position:0% +uh put them this way and and so the net + + + align:start position:0% +uh put them this way and and so the net +uh stochiometric coefficient of the + + align:start position:0% +uh stochiometric coefficient of the + + + align:start position:0% +uh stochiometric coefficient of the +original reaction is given by new minus + + align:start position:0% +original reaction is given by new minus + + + align:start position:0% +original reaction is given by new minus +minus new plus the + + align:start position:0% +minus new plus the + + + align:start position:0% +minus new plus the +the stochiometric coefficient eent of + + align:start position:0% +the stochiometric coefficient eent of + + + align:start position:0% +the stochiometric coefficient eent of +the backward reaction minus the + + align:start position:0% +the backward reaction minus the + + + align:start position:0% +the backward reaction minus the +stochiometric coefficient of the forward + + align:start position:0% + + + + align:start position:0% + +reaction so now we have two reactions + + align:start position:0% +reaction so now we have two reactions + + + align:start position:0% +reaction so now we have two reactions +instead of + + align:start position:0% +instead of + + + align:start position:0% +instead of +one and + + align:start position:0% +one and + + + align:start position:0% +one and +that's going to be very + + align:start position:0% +that's going to be very + + + align:start position:0% +that's going to be very +important as we see here uh in order to + + align:start position:0% +important as we see here uh in order to + + + align:start position:0% +important as we see here uh in order to +describe the + + align:start position:0% +describe the + + + align:start position:0% +describe the +possibility for the reaction to + + align:start position:0% +possibility for the reaction to + + + align:start position:0% +possibility for the reaction to +occur so this activated + + align:start position:0% +occur so this activated + + + align:start position:0% +occur so this activated +complexes are fundamental you have to go + + align:start position:0% +complexes are fundamental you have to go + + + align:start position:0% +complexes are fundamental you have to go +through that subtle point in order to go + + align:start position:0% +through that subtle point in order to go + + + align:start position:0% +through that subtle point in order to go +from one Valley to the other other + + align:start position:0% +from one Valley to the other other + + + align:start position:0% +from one Valley to the other other +Valley you can also go through higher + + align:start position:0% +Valley you can also go through higher + + + align:start position:0% +Valley you can also go through higher +than the sdle point or any any path that + + align:start position:0% +than the sdle point or any any path that + + + align:start position:0% +than the sdle point or any any path that +takes you from one Valley to the other + + align:start position:0% +takes you from one Valley to the other + + + align:start position:0% +takes you from one Valley to the other +but the most probable is uh going + + align:start position:0% +but the most probable is uh going + + + align:start position:0% +but the most probable is uh going +through the SLE + + align:start position:0% + + + + align:start position:0% + +point + + align:start position:0% +point + + + align:start position:0% +point +and so each reaction for each reaction + + align:start position:0% +and so each reaction for each reaction + + + align:start position:0% +and so each reaction for each reaction +we have defined + + align:start position:0% +we have defined + + + align:start position:0% +we have defined +properties like the enthalpy of the + + align:start position:0% +properties like the enthalpy of the + + + align:start position:0% +properties like the enthalpy of the +reaction so the enthalpy of the re of + + align:start position:0% +reaction so the enthalpy of the re of + + + align:start position:0% +reaction so the enthalpy of the re of +the overall reaction if you remember the + + align:start position:0% +the overall reaction if you remember the + + + align:start position:0% +the overall reaction if you remember the +other time is the weighted sum on the + + align:start position:0% +other time is the weighted sum on the + + + align:start position:0% +other time is the weighted sum on the +stochiometric weighted on the + + align:start position:0% +stochiometric weighted on the + + + align:start position:0% +stochiometric weighted on the +stochiometric coefficients of the pure + + align:start position:0% +stochiometric coefficients of the pure + + + align:start position:0% +stochiometric coefficients of the pure +component uh uh property at standard + + align:start position:0% +component uh uh property at standard + + + align:start position:0% +component uh uh property at standard +U pressure in this kind in this in + + align:start position:0% +U pressure in this kind in this in + + + align:start position:0% +U pressure in this kind in this in +this instance and and The Temper the + + align:start position:0% +this instance and and The Temper the + + + align:start position:0% +this instance and and The Temper the +generic temperature T well we can + + align:start position:0% +generic temperature T well we can + + + align:start position:0% +generic temperature T well we can +also apply this definition to this + + align:start position:0% +also apply this definition to this + + + align:start position:0% +also apply this definition to this +reactions the half reactions in order to + + align:start position:0% +reactions the half reactions in order to + + + align:start position:0% +reactions the half reactions in order to +do that I have to make the uh a half + + align:start position:0% +do that I have to make the uh a half + + + align:start position:0% +do that I have to make the uh a half +reaction with all the components to the + + align:start position:0% +reaction with all the components to the + + + align:start position:0% +reaction with all the components to the +left according to our rule so so if you + + align:start position:0% +left according to our rule so so if you + + + align:start position:0% +left according to our rule so so if you +take this to the left now you see this + + align:start position:0% +take this to the left now you see this + + + align:start position:0% +take this to the left now you see this +the product is a + + align:start position:0% +the product is a + + + align:start position:0% +the product is a +star and the reactants are the AI with + + align:start position:0% +star and the reactants are the AI with + + + align:start position:0% +star and the reactants are the AI with +this stochiometric coefficients A+ I + + align:start position:0% +this stochiometric coefficients A+ I + + + align:start position:0% +this stochiometric coefficients A+ I +mean new + + align:start position:0% + + + + align:start position:0% + +plus so in this summation I have to + + align:start position:0% +plus so in this summation I have to + + + align:start position:0% +plus so in this summation I have to +take uh with the plus one coefficient + + align:start position:0% +take uh with the plus one coefficient + + + align:start position:0% +take uh with the plus one coefficient +the enthalpy of the activated complex at + + align:start position:0% +the enthalpy of the activated complex at + + + align:start position:0% +the enthalpy of the activated complex at +standard pressure and temperature T and + + align:start position:0% +standard pressure and temperature T and + + + align:start position:0% +standard pressure and temperature T and +then put the stochiometric efficient + + align:start position:0% +then put the stochiometric efficient + + + align:start position:0% +then put the stochiometric efficient +therefore minus these + + align:start position:0% +therefore minus these + + + align:start position:0% +therefore minus these +things okay so that defines + + align:start position:0% + + + + align:start position:0% + +the property of the forward half + + align:start position:0% +the property of the forward half + + + align:start position:0% +the property of the forward half +reaction and this is the enthalpy of + + align:start position:0% +reaction and this is the enthalpy of + + + align:start position:0% +reaction and this is the enthalpy of +the forward I mean backward half + + align:start position:0% +the forward I mean backward half + + + align:start position:0% +the forward I mean backward half +reaction in order to Define them you + + align:start position:0% +reaction in order to Define them you + + + align:start position:0% +reaction in order to Define them you +need to know your to have characterized + + align:start position:0% +need to know your to have characterized + + + align:start position:0% +need to know your to have characterized +your activated complex because you need + + align:start position:0% +your activated complex because you need + + + align:start position:0% +your activated complex because you need +to know its enthalpy at standard + + align:start position:0% +to know its enthalpy at standard + + + align:start position:0% +to know its enthalpy at standard +conditions treating it as a + + align:start position:0% +conditions treating it as a + + + align:start position:0% +conditions treating it as a +molecule so in a sense + + align:start position:0% +molecule so in a sense + + + align:start position:0% +molecule so in a sense +because people don't really do + + align:start position:0% +because people don't really do + + + align:start position:0% +because people don't really do +this um this is just a sort of a + + align:start position:0% +this um this is just a sort of a + + + align:start position:0% +this um this is just a sort of a +hypothetical it's a way of looking at it + + align:start position:0% +hypothetical it's a way of looking at it + + + align:start position:0% +hypothetical it's a way of looking at it +which will allow nevertheless to + + align:start position:0% +which will allow nevertheless to + + + align:start position:0% +which will allow nevertheless to +uh Define a lot of useful things that + + align:start position:0% +uh Define a lot of useful things that + + + align:start position:0% +uh Define a lot of useful things that +then people do + + align:start position:0% + + + + align:start position:0% + +use okay + + align:start position:0% + + + + align:start position:0% + +so in spite of the + + align:start position:0% +so in spite of the + + + align:start position:0% +so in spite of the +fact that we have just + + align:start position:0% +fact that we have just + + + align:start position:0% +fact that we have just +said that that the activated complex is + + align:start position:0% +said that that the activated complex is + + + align:start position:0% +said that that the activated complex is +fundamental in order for the reactions + + align:start position:0% +fundamental in order for the reactions + + + align:start position:0% +fundamental in order for the reactions +to + + align:start position:0% + + + + align:start position:0% + +occur next we're going to neglect + + align:start position:0% +occur next we're going to neglect + + + align:start position:0% +occur next we're going to neglect +them so but it is not contradiction + + align:start position:0% +them so but it is not contradiction + + + align:start position:0% +them so but it is not contradiction +we're going to NE neglect them neglect + + align:start position:0% +we're going to NE neglect them neglect + + + align:start position:0% +we're going to NE neglect them neglect +them uh for just one aspect namely for + + align:start position:0% +them uh for just one aspect namely for + + + align:start position:0% +them uh for just one aspect namely for +calculating the properties of our + + align:start position:0% +calculating the properties of our + + + align:start position:0% +calculating the properties of our +reacting + + align:start position:0% +reacting + + + align:start position:0% +reacting +mixtures and only in a limit in which we + + align:start position:0% +mixtures and only in a limit in which we + + + align:start position:0% +mixtures and only in a limit in which we +have many particles so this is an an + + align:start position:0% +have many particles so this is an an + + + align:start position:0% +have many particles so this is an an +addendum to the simple system + + align:start position:0% +addendum to the simple system + + + align:start position:0% +addendum to the simple system +model it amounts to saying uh the + + align:start position:0% +model it amounts to saying uh the + + + align:start position:0% +model it amounts to saying uh the +following yes if I have a situation in + + align:start position:0% +following yes if I have a situation in + + + align:start position:0% +following yes if I have a situation in +which I have only two particles this + + align:start position:0% +which I have only two particles this + + + align:start position:0% +which I have only two particles this +passing through this is fundamental and + + align:start position:0% +passing through this is fundamental and + + + align:start position:0% +passing through this is fundamental and +also when I take a photograph at this + + align:start position:0% +also when I take a photograph at this + + + align:start position:0% +also when I take a photograph at this +instant of time + + align:start position:0% +instant of time + + + align:start position:0% +instant of time +uh the 100% of the scenario is made up + + align:start position:0% +uh the 100% of the scenario is made up + + + align:start position:0% +uh the 100% of the scenario is made up +of the activated complex there's + + align:start position:0% +of the activated complex there's + + + align:start position:0% +of the activated complex there's +only but if I have many + + align:start position:0% + + + + align:start position:0% + +particles it's true that there are many + + align:start position:0% +particles it's true that there are many + + + align:start position:0% +particles it's true that there are many +collisions but they do not occur all at + + align:start position:0% +collisions but they do not occur all at + + + align:start position:0% +collisions but they do not occur all at +once so that means that if I have many + + align:start position:0% +once so that means that if I have many + + + align:start position:0% +once so that means that if I have many +particles uh in this box in addition to + + align:start position:0% +particles uh in this box in addition to + + + align:start position:0% +particles uh in this box in addition to +the two particles that are going to + + align:start position:0% +the two particles that are going to + + + align:start position:0% +the two particles that are going to +collide and form these there are also + + align:start position:0% +collide and form these there are also + + + align:start position:0% +collide and form these there are also +large amount of other particles that are + + align:start position:0% +large amount of other particles that are + + + align:start position:0% +large amount of other particles that are +not colliding in that + + align:start position:0% + + + + align:start position:0% + +moment and since they form the + + align:start position:0% +moment and since they form the + + + align:start position:0% +moment and since they form the +majority the mo fraction of the + + align:start position:0% +majority the mo fraction of the + + + align:start position:0% +majority the mo fraction of the +activated complex is so + + align:start position:0% +activated complex is so + + + align:start position:0% +activated complex is so +small that we can neglect its + + align:start position:0% +small that we can neglect its + + + align:start position:0% +small that we can neglect its +contribution to the properties of the + + align:start position:0% +contribution to the properties of the + + + align:start position:0% +contribution to the properties of the +mixture so in that + + align:start position:0% +mixture so in that + + + align:start position:0% +mixture so in that +sense we say for many + + align:start position:0% +sense we say for many + + + align:start position:0% +sense we say for many +particles and when we are dealing with + + align:start position:0% +particles and when we are dealing with + + + align:start position:0% +particles and when we are dealing with +just looking at the properties for + + align:start position:0% +just looking at the properties for + + + align:start position:0% +just looking at the properties for +making like energy and entropy balances + + align:start position:0% +making like energy and entropy balances + + + align:start position:0% +making like energy and entropy balances +uh so properties like the entropy the + + align:start position:0% +uh so properties like the entropy the + + + align:start position:0% +uh so properties like the entropy the +enpy and and the energy uh or the volume + + align:start position:0% +enpy and and the energy uh or the volume + + + align:start position:0% +enpy and and the energy uh or the volume +we can we we we compute them by + + align:start position:0% +we can we we we compute them by + + + align:start position:0% +we can we we we compute them by +neglecting the minute uh amounts of + + align:start position:0% +neglecting the minute uh amounts of + + + align:start position:0% +neglecting the minute uh amounts of +activated complex that are there + + align:start position:0% + + + + align:start position:0% + +so essentially what we're what we're + + align:start position:0% +so essentially what we're what we're + + + align:start position:0% +so essentially what we're what we're +saying is that neglecting the activating + + align:start position:0% +saying is that neglecting the activating + + + align:start position:0% +saying is that neglecting the activating +complex is like neglecting the existence + + align:start position:0% +complex is like neglecting the existence + + + align:start position:0% +complex is like neglecting the existence +of the chemical reaction for the purpose + + align:start position:0% +of the chemical reaction for the purpose + + + align:start position:0% +of the chemical reaction for the purpose +of computing the + + align:start position:0% + + + + align:start position:0% + +properties in other + + align:start position:0% +properties in other + + + align:start position:0% +properties in other +words + + align:start position:0% + + + + align:start position:0% + +uh we assume when Computing properties + + align:start position:0% +uh we assume when Computing properties + + + align:start position:0% +uh we assume when Computing properties +of mixtures that are reacting we assume + + align:start position:0% +of mixtures that are reacting we assume + + + align:start position:0% +of mixtures that are reacting we assume +that they have the properties of the + + align:start position:0% +that they have the properties of the + + + align:start position:0% +that they have the properties of the +mixture with the reactions so to speak + + align:start position:0% +mixture with the reactions so to speak + + + align:start position:0% +mixture with the reactions so to speak +turned + + align:start position:0% +turned + + + align:start position:0% +turned +off if I turn off the + + align:start position:0% +off if I turn off the + + + align:start position:0% +off if I turn off the +reactions I stop the formation of + + align:start position:0% +reactions I stop the formation of + + + align:start position:0% +reactions I stop the formation of +activated complex so there is no + + align:start position:0% +activated complex so there is no + + + align:start position:0% +activated complex so there is no +activated complex in play and I'm in the + + align:start position:0% +activated complex in play and I'm in the + + + align:start position:0% +activated complex in play and I'm in the +usual uh situation in which I have only + + align:start position:0% +usual uh situation in which I have only + + + align:start position:0% +usual uh situation in which I have only +my + + align:start position:0% +my + + + align:start position:0% +my +um original + + align:start position:0% +um original + + + align:start position:0% +um original +particles although + + align:start position:0% + + + + align:start position:0% + +uh we're not actually turning reactions + + align:start position:0% +uh we're not actually turning reactions + + + align:start position:0% +uh we're not actually turning reactions +off but it's as if you + + align:start position:0% +off but it's as if you + + + align:start position:0% +off but it's as if you +could uh although the reaction is + + align:start position:0% + + + + align:start position:0% + +occurring and also what we are assuming + + align:start position:0% +occurring and also what we are assuming + + + align:start position:0% +occurring and also what we are assuming +is that + + align:start position:0% + + + + align:start position:0% + +um the + + align:start position:0% +um the + + + align:start position:0% +um the +you see with the reactions uh uh if I + + align:start position:0% +you see with the reactions uh uh if I + + + align:start position:0% +you see with the reactions uh uh if I +have this situation here and I turn uh + + align:start position:0% +have this situation here and I turn uh + + + align:start position:0% +have this situation here and I turn uh +off the reactions and I still have an + + align:start position:0% +off the reactions and I still have an + + + align:start position:0% +off the reactions and I still have an +activated complex that was already it + + align:start position:0% +activated complex that was already it + + + align:start position:0% +activated complex that was already it +was already there because it was just + + align:start position:0% +was already there because it was just + + + align:start position:0% +was already there because it was just +being + + align:start position:0% +being + + + align:start position:0% +being +formed uh that + + align:start position:0% +formed uh that + + + align:start position:0% +formed uh that +complex sometimes will break up like + + align:start position:0% +complex sometimes will break up like + + + align:start position:0% +complex sometimes will break up like +explode so that + + align:start position:0% +explode so that + + + align:start position:0% +explode so that +explosion uh delivers kinetic energy + + align:start position:0% + + + + align:start position:0% + +locally so produces a non equilibrium + + align:start position:0% +locally so produces a non equilibrium + + + align:start position:0% +locally so produces a non equilibrium +situation that amount of kinetic energy + + align:start position:0% +situation that amount of kinetic energy + + + align:start position:0% +situation that amount of kinetic energy +which is concentrated here in this + + align:start position:0% +which is concentrated here in this + + + align:start position:0% +which is concentrated here in this +bullets that go away from the + + align:start position:0% +bullets that go away from the + + + align:start position:0% +bullets that go away from the +explosion and they are they have a + + align:start position:0% +explosion and they are they have a + + + align:start position:0% +explosion and they are they have a +velocity which is much higher than the + + align:start position:0% +velocity which is much higher than the + + + align:start position:0% +velocity which is much higher than the +typical + + align:start position:0% +typical + + + align:start position:0% +typical +velocities it will take a + + align:start position:0% +velocities it will take a + + + align:start position:0% +velocities it will take a +while for a the other collisions not of + + align:start position:0% +while for a the other collisions not of + + + align:start position:0% +while for a the other collisions not of +the chemical kind to redistribute that + + align:start position:0% +the chemical kind to redistribute that + + + align:start position:0% +the chemical kind to redistribute that +excess in ktic energy due to the + + align:start position:0% +excess in ktic energy due to the + + + align:start position:0% +excess in ktic energy due to the +chemical reaction in redistributed to + + align:start position:0% +chemical reaction in redistributed to + + + align:start position:0% +chemical reaction in redistributed to +the other molecules + + align:start position:0% +the other molecules + + + align:start position:0% +the other molecules +around + + align:start position:0% + + + + align:start position:0% + +okay well we will we also + + align:start position:0% +okay well we will we also + + + align:start position:0% +okay well we will we also +assume that the + + align:start position:0% +assume that the + + + align:start position:0% +assume that the +uh that this + + align:start position:0% +uh that this + + + align:start position:0% +uh that this +non-chemical uh coll Vision + + align:start position:0% +non-chemical uh coll Vision + + + align:start position:0% +non-chemical uh coll Vision +redistribution + + align:start position:0% +redistribution + + + align:start position:0% +redistribution +mechanism is very fast so + + align:start position:0% +mechanism is very fast so + + + align:start position:0% +mechanism is very fast so +fast that as soon as we turn off the + + align:start position:0% +fast that as soon as we turn off the + + + align:start position:0% +fast that as soon as we turn off the +reactions or as soon as the activated + + align:start position:0% +reactions or as soon as the activated + + + align:start position:0% +reactions or as soon as the activated +complex has decayed into its fragments + + align:start position:0% +complex has decayed into its fragments + + + align:start position:0% +complex has decayed into its fragments +of of the Decay uh that energy gets + + align:start position:0% +of of the Decay uh that energy gets + + + align:start position:0% +of of the Decay uh that energy gets +almost immediately redistributed among + + align:start position:0% +almost immediately redistributed among + + + align:start position:0% +almost immediately redistributed among +all the other uh molecules so that they + + align:start position:0% +all the other uh molecules so that they + + + align:start position:0% +all the other uh molecules so that they +reach immediately uh the stable + + align:start position:0% +reach immediately uh the stable + + + align:start position:0% +reach immediately uh the stable +equilibrium state with with their with + + align:start position:0% +equilibrium state with with their with + + + align:start position:0% +equilibrium state with with their with +the Frozen composition that they are in + + align:start position:0% +the Frozen composition that they are in + + + align:start position:0% +the Frozen composition that they are in +at that + + align:start position:0% + + + + align:start position:0% + +moment okay so these are all the + + align:start position:0% +moment okay so these are all the + + + align:start position:0% +moment okay so these are all the +concepts that go + + align:start position:0% +concepts that go + + + align:start position:0% +concepts that go +into the idea that then we are going to + + align:start position:0% +into the idea that then we are going to + + + align:start position:0% +into the idea that then we are going to +uh model the properties of our system + + align:start position:0% +uh model the properties of our system + + + align:start position:0% +uh model the properties of our system +with chemical + + align:start position:0% + + + + align:start position:0% + +reactions as if they were not reacting + + align:start position:0% + + + + align:start position:0% + +but in stable chemical I'm sorry in + + align:start position:0% +but in stable chemical I'm sorry in + + + align:start position:0% +but in stable chemical I'm sorry in +stable + + align:start position:0% +stable + + + align:start position:0% +stable +equilibrium uh for the instantaneous + + align:start position:0% + + + + align:start position:0% + +composition talking in terms of + + align:start position:0% +composition talking in terms of + + + align:start position:0% +composition talking in terms of +characteristic + + align:start position:0% +characteristic + + + align:start position:0% +characteristic +times the chemical + + align:start position:0% +times the chemical + + + align:start position:0% +times the chemical +reactions we think we consider them much + + align:start position:0% +reactions we think we consider them much + + + align:start position:0% +reactions we think we consider them much +slow slower + + align:start position:0% +slow slower + + + align:start position:0% +slow slower +than the redistribution mechanism by + + align:start position:0% +than the redistribution mechanism by + + + align:start position:0% +than the redistribution mechanism by +Collision uh but chemically ineffective + + align:start position:0% +Collision uh but chemically ineffective + + + align:start position:0% +Collision uh but chemically ineffective +collisions which instead are very + + align:start position:0% +collisions which instead are very + + + align:start position:0% +collisions which instead are very +fast + + align:start position:0% +fast + + + align:start position:0% +fast +and and therefore the chemical reactions + + align:start position:0% +and and therefore the chemical reactions + + + align:start position:0% +and and therefore the chemical reactions +change the composition and according to + + align:start position:0% +change the composition and according to + + + align:start position:0% +change the composition and according to +the + + align:start position:0% +the + + + align:start position:0% +the +um proportionality relation + + align:start position:0% +um proportionality relation + + + align:start position:0% +um proportionality relation +so the the the reaction coordinate does + + align:start position:0% +so the the the reaction coordinate does + + + align:start position:0% +so the the the reaction coordinate does +advance in time but we assume that each + + align:start position:0% +advance in time but we assume that each + + + align:start position:0% +advance in time but we assume that each +instant of time the system immediately + + align:start position:0% +instant of time the system immediately + + + align:start position:0% +instant of time the system immediately +redistributes the energy caused uh the + + align:start position:0% +redistributes the energy caused uh the + + + align:start position:0% +redistributes the energy caused uh the +the local excesses or defects of + + align:start position:0% +the local excesses or defects of + + + align:start position:0% +the local excesses or defects of +energies produced by the chemical + + align:start position:0% +energies produced by the chemical + + + align:start position:0% +energies produced by the chemical +reactions and the activated complex and + + align:start position:0% +reactions and the activated complex and + + + align:start position:0% +reactions and the activated complex and +so on + + align:start position:0% +so on + + + align:start position:0% +so on +and and therefore keeps uh the + + align:start position:0% +and and therefore keeps uh the + + + align:start position:0% +and and therefore keeps uh the +state almost close to what it would be + + align:start position:0% +state almost close to what it would be + + + align:start position:0% +state almost close to what it would be +uh stable equilibrium if you didn't have + + align:start position:0% +uh stable equilibrium if you didn't have + + + align:start position:0% +uh stable equilibrium if you didn't have +chemical + + align:start position:0% + + + + align:start position:0% + +reactions okay so that's the + + align:start position:0% +reactions okay so that's the + + + align:start position:0% +reactions okay so that's the +scenario and of + + align:start position:0% +scenario and of + + + align:start position:0% +scenario and of +course this formula is going now to be + + align:start position:0% +course this formula is going now to be + + + align:start position:0% +course this formula is going now to be +our uh head of the + + align:start position:0% +our uh head of the + + + align:start position:0% +our uh head of the +game + + align:start position:0% +game + + + align:start position:0% +game +because for + + align:start position:0% + + + + align:start position:0% + +example uh + + align:start position:0% +example uh + + + align:start position:0% +example uh +we can Define we can + + align:start position:0% +we can Define we can + + + align:start position:0% +we can Define we can +compute the equilibrium composition by + + align:start position:0% + + + + align:start position:0% + +maximizing because the maximum entropy + + align:start position:0% +maximizing because the maximum entropy + + + align:start position:0% +maximizing because the maximum entropy +principle does + + align:start position:0% + + + + align:start position:0% + +apply in + + align:start position:0% + + + + align:start position:0% + +fact that same expression here it's + + align:start position:0% +fact that same expression here it's + + + align:start position:0% +fact that same expression here it's +written more even more formally saying + + align:start position:0% +written more even more formally saying + + + align:start position:0% +written more even more formally saying +that + + align:start position:0% +that + + + align:start position:0% +that +uh yeah this is the S of the off + + align:start position:0% +uh yeah this is the S of the off + + + align:start position:0% +uh yeah this is the S of the off +system with an N that is now variable + + align:start position:0% +system with an N that is now variable + + + align:start position:0% +system with an N that is now variable +and it depends on the initial amount on + + align:start position:0% +and it depends on the initial amount on + + + align:start position:0% +and it depends on the initial amount on +the chemical reactions that are in play + + align:start position:0% +the chemical reactions that are in play + + + align:start position:0% +the chemical reactions that are in play +and on the uh reaction + + align:start position:0% +and on the uh reaction + + + align:start position:0% +and on the uh reaction +coordinate so if you look at it this way + + align:start position:0% +coordinate so if you look at it this way + + + align:start position:0% +coordinate so if you look at it this way +it's going to be easy to do uh the + + align:start position:0% +it's going to be easy to do uh the + + + align:start position:0% +it's going to be easy to do uh the +partial derivatives that we have to do + + align:start position:0% +partial derivatives that we have to do + + + align:start position:0% +partial derivatives that we have to do +for example here because for example + + align:start position:0% +for example here because for example + + + align:start position:0% +for example here because for example +with with we like to be we are + + align:start position:0% +with with we like to be we are + + + align:start position:0% +with with we like to be we are +interested in taking the derivative of + + align:start position:0% +interested in taking the derivative of + + + align:start position:0% +interested in taking the derivative of +of the entropy with respect to the + + align:start position:0% +of the entropy with respect to the + + + align:start position:0% +of the entropy with respect to the +advancement of to the reaction + + align:start position:0% +advancement of to the reaction + + + align:start position:0% +advancement of to the reaction +coordinate of one + + align:start position:0% +coordinate of one + + + align:start position:0% +coordinate of one +reaction because that derivative is + + align:start position:0% +reaction because that derivative is + + + align:start position:0% +reaction because that derivative is +going to be called the Affinity of the + + align:start position:0% +going to be called the Affinity of the + + + align:start position:0% +going to be called the Affinity of the +reaction they they don't there uh + + align:start position:0% +reaction they they don't there uh + + + align:start position:0% +reaction they they don't there uh +Affinity of the + + align:start position:0% + + + + align:start position:0% + +reaction so we have to do that + + align:start position:0% +reaction so we have to do that + + + align:start position:0% +reaction so we have to do that +derivative but before we do that here's + + align:start position:0% +derivative but before we do that here's + + + align:start position:0% +derivative but before we do that here's +the graphic graph graphical + + align:start position:0% +the graphic graph graphical + + + align:start position:0% +the graphic graph graphical +representation of what we're doing + + align:start position:0% +representation of what we're doing + + + align:start position:0% +representation of what we're doing +here for if you fix the value of the + + align:start position:0% +here for if you fix the value of the + + + align:start position:0% +here for if you fix the value of the +composition so fix an Epsilon say + + align:start position:0% +composition so fix an Epsilon say + + + align:start position:0% +composition so fix an Epsilon say +epsilon + + align:start position:0% +epsilon + + + align:start position:0% +epsilon +one you you have fixed the composition + + align:start position:0% +one you you have fixed the composition + + + align:start position:0% +one you you have fixed the composition +and this blue this blue curve represents + + align:start position:0% +and this blue this blue curve represents + + + align:start position:0% +and this blue this blue curve represents +the stable equilibrium state of a + + align:start position:0% +the stable equilibrium state of a + + + align:start position:0% +the stable equilibrium state of a +mixture with that + + align:start position:0% + + + + align:start position:0% + +composition now you change the + + align:start position:0% +composition now you change the + + + align:start position:0% +composition now you change the +composition and here you have another + + align:start position:0% +composition and here you have another + + + align:start position:0% +composition and here you have another +stable equilibrium State curve and + + align:start position:0% +stable equilibrium State curve and + + + align:start position:0% +stable equilibrium State curve and +another + + align:start position:0% +another + + + align:start position:0% +another +yet + + align:start position:0% + + + + align:start position:0% + +okay these + + align:start position:0% +okay these + + + align:start position:0% +okay these +curves they do not represent all the + + align:start position:0% +curves they do not represent all the + + + align:start position:0% +curves they do not represent all the +states of your system they represents + + align:start position:0% +states of your system they represents + + + align:start position:0% +states of your system they represents +this family of + + align:start position:0% +this family of + + + align:start position:0% +this family of +States uh Frozen equilibrium stable + + align:start position:0% +States uh Frozen equilibrium stable + + + align:start position:0% +States uh Frozen equilibrium stable +equilibrium states that we have chosen + + align:start position:0% +equilibrium states that we have chosen + + + align:start position:0% +equilibrium states that we have chosen +to describe the + + align:start position:0% + + + + align:start position:0% + +properties but this family is Rich + + align:start position:0% +properties but this family is Rich + + + align:start position:0% +properties but this family is Rich +enough that it can uh span + + align:start position:0% +enough that it can uh span + + + align:start position:0% +enough that it can uh span +essentially uh all the allowed region of + + align:start position:0% +essentially uh all the allowed region of + + + align:start position:0% +essentially uh all the allowed region of +the energy versus + + align:start position:0% +the energy versus + + + align:start position:0% +the energy versus +entropy + + align:start position:0% +entropy + + + align:start position:0% +entropy +diagram for the reacting + + align:start position:0% + + + + align:start position:0% + +system and certainly these are allowed + + align:start position:0% +system and certainly these are allowed + + + align:start position:0% +system and certainly these are allowed +States so when we want now to + + align:start position:0% +States so when we want now to + + + align:start position:0% +States so when we want now to +apply the maximum entropy + + align:start position:0% + + + + align:start position:0% + +principle the max maximum entropy + + align:start position:0% +principle the max maximum entropy + + + align:start position:0% +principle the max maximum entropy +principle says well I fix the value of + + align:start position:0% +principle says well I fix the value of + + + align:start position:0% +principle says well I fix the value of +the energy I fix the value of the volume + + align:start position:0% +the energy I fix the value of the volume + + + align:start position:0% +the energy I fix the value of the volume +the initial amounts and the reaction and + + align:start position:0% +the initial amounts and the reaction and + + + align:start position:0% +the initial amounts and the reaction and +the stochiometric + + align:start position:0% + + + + align:start position:0% + +coefficients and the stable equilibrium + + align:start position:0% +coefficients and the stable equilibrium + + + align:start position:0% +coefficients and the stable equilibrium +state of the chemical reacting system is + + align:start position:0% +state of the chemical reacting system is + + + align:start position:0% +state of the chemical reacting system is +the one that has the highest + + align:start position:0% +the one that has the highest + + + align:start position:0% +the one that has the highest +entropy so you see along this line it + + align:start position:0% +entropy so you see along this line it + + + align:start position:0% +entropy so you see along this line it +this black line crosses many uh of these + + align:start position:0% +this black line crosses many uh of these + + + align:start position:0% +this black line crosses many uh of these +EPS blue + + align:start position:0% +EPS blue + + + align:start position:0% +EPS blue +curves until it reaches + + align:start position:0% +curves until it reaches + + + align:start position:0% +curves until it reaches +one which Beyond which there is + + align:start position:0% +one which Beyond which there is + + + align:start position:0% +one which Beyond which there is +nothing and if you do the same at + + align:start position:0% +nothing and if you do the same at + + + align:start position:0% +nothing and if you do the same at +another level of energy you're going to + + align:start position:0% +another level of energy you're going to + + + align:start position:0% +another level of energy you're going to +highlight this other equilibrium State + + align:start position:0% +highlight this other equilibrium State + + + align:start position:0% +highlight this other equilibrium State +and again this + + align:start position:0% + + + + align:start position:0% + +one so the envelope the red curve the + + align:start position:0% +one so the envelope the red curve the + + + align:start position:0% +one so the envelope the red curve the +envelope of these blue curves + + align:start position:0% +envelope of these blue curves + + + align:start position:0% +envelope of these blue curves +represents the stable equilibrium States + + align:start position:0% +represents the stable equilibrium States + + + align:start position:0% +represents the stable equilibrium States +the maximum anthropy so those are the + + align:start position:0% +the maximum anthropy so those are the + + + align:start position:0% +the maximum anthropy so those are the +stable equilibrium states of the + + align:start position:0% +stable equilibrium states of the + + + align:start position:0% +stable equilibrium states of the +chemically reacting + + align:start position:0% +chemically reacting + + + align:start position:0% +chemically reacting +system so that dotted red curve is the + + align:start position:0% +system so that dotted red curve is the + + + align:start position:0% +system so that dotted red curve is the +fundamental relation for the stable + + align:start position:0% +fundamental relation for the stable + + + align:start position:0% +fundamental relation for the stable +equilibrium uh stable chemical + + align:start position:0% +equilibrium uh stable chemical + + + align:start position:0% +equilibrium uh stable chemical +equilibrium + + align:start position:0% + + + + align:start position:0% + +States whereas these blue + + align:start position:0% +States whereas these blue + + + align:start position:0% +States whereas these blue +ones represent stable equilibria only if + + align:start position:0% +ones represent stable equilibria only if + + + align:start position:0% +ones represent stable equilibria only if +the reactions are + + align:start position:0% + + + + align:start position:0% + +Frozen + + align:start position:0% +Frozen + + + align:start position:0% +Frozen +Okay + + align:start position:0% +Okay + + + align:start position:0% +Okay +so this derivative is the + + align:start position:0% +so this derivative is the + + + align:start position:0% +so this derivative is the +affinity and uh now let's uh + + align:start position:0% + + + + align:start position:0% + +uh go into a little more details of the + + align:start position:0% +uh go into a little more details of the + + + align:start position:0% +uh go into a little more details of the +same same + + align:start position:0% +same same + + + align:start position:0% +same same +graph same definition of + + align:start position:0% +graph same definition of + + + align:start position:0% +graph same definition of +affinity what's new here is only a more + + align:start position:0% +affinity what's new here is only a more + + + align:start position:0% +affinity what's new here is only a more +explicit expression for this uh red + + align:start position:0% +explicit expression for this uh red + + + align:start position:0% +explicit expression for this uh red +curve which is a stable equilibrium + + align:start position:0% +curve which is a stable equilibrium + + + align:start position:0% +curve which is a stable equilibrium +State fundamental + + align:start position:0% + + + + align:start position:0% + +relation with the CH with the c in front + + align:start position:0% +relation with the CH with the c in front + + + align:start position:0% +relation with the CH with the c in front +which stands for + + align:start position:0% +which stands for + + + align:start position:0% +which stands for +chemical chemical stable equilibrium + + align:start position:0% +chemical chemical stable equilibrium + + + align:start position:0% +chemical chemical stable equilibrium +States + + align:start position:0% + + + + align:start position:0% + +you see uh uh at each level of energy + + align:start position:0% +you see uh uh at each level of energy + + + align:start position:0% +you see uh uh at each level of energy +there there is one particular Epsilon + + align:start position:0% +there there is one particular Epsilon + + + align:start position:0% +there there is one particular Epsilon +which we call Epsilon + + align:start position:0% +which we call Epsilon + + + align:start position:0% +which we call Epsilon +zero that corresponds to the composition + + align:start position:0% +zero that corresponds to the composition + + + align:start position:0% +zero that corresponds to the composition +at chemical + + align:start position:0% +at chemical + + + align:start position:0% +at chemical +equilibrium and that's the one that + + align:start position:0% +equilibrium and that's the one that + + + align:start position:0% +equilibrium and that's the one that +appears + + align:start position:0% +appears + + + align:start position:0% +appears +here so the entropy of the red curve the + + align:start position:0% +here so the entropy of the red curve the + + + align:start position:0% +here so the entropy of the red curve the +entropy of of the stable equilibrium + + align:start position:0% +entropy of of the stable equilibrium + + + align:start position:0% +entropy of of the stable equilibrium +with chemical + + align:start position:0% +with chemical + + + align:start position:0% +with chemical +included uh + + align:start position:0% +included uh + + + align:start position:0% +included uh +has this um shows for example the + + align:start position:0% +has this um shows for example the + + + align:start position:0% +has this um shows for example the +dependence on + + align:start position:0% +dependence on + + + align:start position:0% +dependence on +energy is not only from the original + + align:start position:0% +energy is not only from the original + + + align:start position:0% +energy is not only from the original +dependence of the Frozen + + align:start position:0% + + + + align:start position:0% + +equilibrium mixture but it's also + + align:start position:0% +equilibrium mixture but it's also + + + align:start position:0% +equilibrium mixture but it's also +through the Epsilon + + align:start position:0% +through the Epsilon + + + align:start position:0% +through the Epsilon +zero because as you change the energy + + align:start position:0% +zero because as you change the energy + + + align:start position:0% +zero because as you change the energy +Epsilon zero changes and so energy + + align:start position:0% +Epsilon zero changes and so energy + + + align:start position:0% +Epsilon zero changes and so energy +influences the the maximum entropy not + + align:start position:0% +influences the the maximum entropy not + + + align:start position:0% +influences the the maximum entropy not +only through the properties of + + align:start position:0% +only through the properties of + + + align:start position:0% +only through the properties of +regardless the chemical reactions but + + align:start position:0% +regardless the chemical reactions but + + + align:start position:0% +regardless the chemical reactions but +also through the composition at chemical + + align:start position:0% + + + + align:start position:0% + +equ all right so that means that when we + + align:start position:0% +equ all right so that means that when we + + + align:start position:0% +equ all right so that means that when we +need to + + align:start position:0% +need to + + + align:start position:0% +need to +compute derivatives for example the + + align:start position:0% +compute derivatives for example the + + + align:start position:0% +compute derivatives for example the +temperature you remember the temperature + + align:start position:0% +temperature you remember the temperature + + + align:start position:0% +temperature you remember the temperature +is the derivative or actually the + + align:start position:0% +is the derivative or actually the + + + align:start position:0% +is the derivative or actually the +inverse of the temperature is derivative + + align:start position:0% +inverse of the temperature is derivative + + + align:start position:0% +inverse of the temperature is derivative +of fundamental relation respect to + + align:start position:0% +of fundamental relation respect to + + + align:start position:0% +of fundamental relation respect to +energy + + align:start position:0% +energy + + + align:start position:0% +energy +well if I have to take this derivative + + align:start position:0% +well if I have to take this derivative + + + align:start position:0% +well if I have to take this derivative +with respect to energy I have to + + align:start position:0% +with respect to energy I have to + + + align:start position:0% +with respect to energy I have to +contribution from here but I have + + align:start position:0% +contribution from here but I have + + + align:start position:0% +contribution from here but I have +contributions also from + + align:start position:0% + + + + align:start position:0% + +here the first + + align:start position:0% +here the first + + + align:start position:0% +here the first +one is what would be the temperature if + + align:start position:0% +one is what would be the temperature if + + + align:start position:0% +one is what would be the temperature if +the reactions were + + align:start position:0% + + + + align:start position:0% + +off and these other contribution is a + + align:start position:0% +off and these other contribution is a + + + align:start position:0% +off and these other contribution is a +summation because these are vectors and + + align:start position:0% +summation because these are vectors and + + + align:start position:0% +summation because these are vectors and +so this a summation of over all the + + align:start position:0% +so this a summation of over all the + + + align:start position:0% +so this a summation of over all the +chemical reactions from J that goes for + + align:start position:0% +chemical reactions from J that goes for + + + align:start position:0% +chemical reactions from J that goes for +J that goes from one to Z how the + + align:start position:0% +J that goes from one to Z how the + + + align:start position:0% +J that goes from one to Z how the +derivative of s off uh with respect to + + align:start position:0% +derivative of s off uh with respect to + + + align:start position:0% +derivative of s off uh with respect to +Epsilon in here you could also do it + + align:start position:0% +Epsilon in here you could also do it + + + align:start position:0% +Epsilon in here you could also do it +with respect to n and then with respect + + align:start position:0% +with respect to n and then with respect + + + align:start position:0% +with respect to n and then with respect +to + + align:start position:0% +to + + + align:start position:0% +to +Epsilon uh times the derivative of EP + + align:start position:0% +Epsilon uh times the derivative of EP + + + align:start position:0% +Epsilon uh times the derivative of EP +with respect to + + align:start position:0% + + + + align:start position:0% + +U however + + align:start position:0% + + + + align:start position:0% + +since at chemical + + align:start position:0% + + + + align:start position:0% + +equilibrium the entropy is maximum + + align:start position:0% +equilibrium the entropy is maximum + + + align:start position:0% +equilibrium the entropy is maximum +maximum so if the entropy is maximum it + + align:start position:0% +maximum so if the entropy is maximum it + + + align:start position:0% +maximum so if the entropy is maximum it +means that it's derivative with respect + + align:start position:0% +means that it's derivative with respect + + + align:start position:0% +means that it's derivative with respect +to these variables here must be zero + + align:start position:0% +to these variables here must be zero + + + align:start position:0% +to these variables here must be zero +including this derivative the affinities + + align:start position:0% +including this derivative the affinities + + + align:start position:0% +including this derivative the affinities +that is what we call the the condition + + align:start position:0% +that is what we call the the condition + + + align:start position:0% +that is what we call the the condition +for chemical uh equilibrium the + + align:start position:0% +for chemical uh equilibrium the + + + align:start position:0% +for chemical uh equilibrium the +affinities must be equal to + + align:start position:0% +affinities must be equal to + + + align:start position:0% +affinities must be equal to +zero and in these + + align:start position:0% +zero and in these + + + align:start position:0% +zero and in these +summations this derivative is precisely + + align:start position:0% +summations this derivative is precisely + + + align:start position:0% +summations this derivative is precisely +that one so it's the + + align:start position:0% + + + + align:start position:0% + +affinity + + align:start position:0% +affinity + + + align:start position:0% +affinity +and maximum it's equal to zero so this + + align:start position:0% +and maximum it's equal to zero so this + + + align:start position:0% +and maximum it's equal to zero so this +summation is a bunch of + + align:start position:0% +summation is a bunch of + + + align:start position:0% +summation is a bunch of +zeros and it turns out therefore + + align:start position:0% +zeros and it turns out therefore + + + align:start position:0% +zeros and it turns out therefore +that the temperature so the derivative + + align:start position:0% +that the temperature so the derivative + + + align:start position:0% +that the temperature so the derivative +of the red curve + + align:start position:0% +of the red curve + + + align:start position:0% +of the red curve +is equal to the derivative of a blue + + align:start position:0% +is equal to the derivative of a blue + + + align:start position:0% +is equal to the derivative of a blue +curve in other words they have a contact + + align:start position:0% +curve in other words they have a contact + + + align:start position:0% +curve in other words they have a contact +of first degree they not only they touch + + align:start position:0% +of first degree they not only they touch + + + align:start position:0% +of first degree they not only they touch +but also they touch with the same + + align:start position:0% + + + + align:start position:0% + +tangent and this is true not only for + + align:start position:0% +tangent and this is true not only for + + + align:start position:0% +tangent and this is true not only for +temperature but also for pressure and + + align:start position:0% +temperature but also for pressure and + + + align:start position:0% +temperature but also for pressure and +for the chemical + + align:start position:0% + + + + align:start position:0% + +potentials okay so we have essentially + + align:start position:0% +potentials okay so we have essentially + + + align:start position:0% +potentials okay so we have essentially +already said what the condition the + + align:start position:0% +already said what the condition the + + + align:start position:0% +already said what the condition the +necessary condition for chemical + + align:start position:0% +necessary condition for chemical + + + align:start position:0% +necessary condition for chemical +equilibrium is is that the affinities + + align:start position:0% +equilibrium is is that the affinities + + + align:start position:0% +equilibrium is is that the affinities +must be equal to + + align:start position:0% + + + + align:start position:0% + +zero + + align:start position:0% +zero + + + align:start position:0% +zero +okay so now let's compute those + + align:start position:0% +okay so now let's compute those + + + align:start position:0% +okay so now let's compute those +affinities again that's the derivative + + align:start position:0% +affinities again that's the derivative + + + align:start position:0% +affinities again that's the derivative +we were talking about and here is a + + align:start position:0% +we were talking about and here is a + + + align:start position:0% +we were talking about and here is a +summary of what we just said + + align:start position:0% + + + + align:start position:0% + +now the derivative of s we of the + + align:start position:0% +now the derivative of s we of the + + + align:start position:0% +now the derivative of s we of the +off system the off fundamental relation + + align:start position:0% +off system the off fundamental relation + + + align:start position:0% +off system the off fundamental relation +with respect to n is the chemical + + align:start position:0% +with respect to n is the chemical + + + align:start position:0% +with respect to n is the chemical +potential divided by the temperature + + align:start position:0% +potential divided by the temperature + + + align:start position:0% +potential divided by the temperature +with the negative sign in + + align:start position:0% + + + + align:start position:0% + +front so when I do uh this derivative + + align:start position:0% +front so when I do uh this derivative + + + align:start position:0% +front so when I do uh this derivative +the result is a weighted sum of the + + align:start position:0% +the result is a weighted sum of the + + + align:start position:0% +the result is a weighted sum of the +stochiometric coefficients because here + + align:start position:0% +stochiometric coefficients because here + + + align:start position:0% +stochiometric coefficients because here +uh you're taking the derivative with + + align:start position:0% +uh you're taking the derivative with + + + align:start position:0% +uh you're taking the derivative with +respect to the Epsilon of one reaction J + + align:start position:0% +respect to the Epsilon of one reaction J + + + align:start position:0% +respect to the Epsilon of one reaction J +is the label of the reactions and I is + + align:start position:0% +is the label of the reactions and I is + + + align:start position:0% +is the label of the reactions and I is +the label of the + + align:start position:0% + + + + align:start position:0% + +components so these are the + + align:start position:0% +components so these are the + + + align:start position:0% +components so these are the +stochiometric coefficients of the J + + align:start position:0% +stochiometric coefficients of the J + + + align:start position:0% +stochiometric coefficients of the J +reaction for the I + + align:start position:0% +reaction for the I + + + align:start position:0% +reaction for the I +component and so it's the weight + + align:start position:0% +component and so it's the weight + + + align:start position:0% +component and so it's the weight +sum of the chemical potential divided by + + align:start position:0% +sum of the chemical potential divided by + + + align:start position:0% +sum of the chemical potential divided by +the temperature + + align:start position:0% +the temperature + + + align:start position:0% +the temperature +that's the + + align:start position:0% +that's the + + + align:start position:0% +that's the +Affinity of reaction + + align:start position:0% +Affinity of reaction + + + align:start position:0% +Affinity of reaction +J now we + + align:start position:0% +J now we + + + align:start position:0% +J now we +can uh use the tools that we uh have + + align:start position:0% +can uh use the tools that we uh have + + + align:start position:0% +can uh use the tools that we uh have +already developed in order to uh + + align:start position:0% +already developed in order to uh + + + align:start position:0% +already developed in order to uh +describe um chemical potentials of + + align:start position:0% +describe um chemical potentials of + + + align:start position:0% +describe um chemical potentials of +mixtures because we spent half of the + + align:start position:0% +mixtures because we spent half of the + + + align:start position:0% +mixtures because we spent half of the +course on + + align:start position:0% +course on + + + align:start position:0% +course on +this for example assume an ideal G + + align:start position:0% +this for example assume an ideal G + + + align:start position:0% +this for example assume an ideal G +Dalton mixture of Ideal gases + + align:start position:0% + + + + align:start position:0% + +off so these are the off allows us to + + align:start position:0% +off so these are the off allows us to + + + align:start position:0% +off so these are the off allows us to +use anything that we know of the system + + align:start position:0% +use anything that we know of the system + + + align:start position:0% +use anything that we know of the system +without chemical + + align:start position:0% + + + + align:start position:0% + +reactions if we it's remember it's like + + align:start position:0% +reactions if we it's remember it's like + + + align:start position:0% +reactions if we it's remember it's like +the chemical potential of the of the + + align:start position:0% +the chemical potential of the of the + + + align:start position:0% +the chemical potential of the of the +pure component at T and P plus RT log of + + align:start position:0% +pure component at T and P plus RT log of + + + align:start position:0% +pure component at T and P plus RT log of +y y being the mole fraction of that + + align:start position:0% +y y being the mole fraction of that + + + align:start position:0% +y y being the mole fraction of that +component if we want the reference to + + align:start position:0% +component if we want the reference to + + + align:start position:0% +component if we want the reference to +the standard pressure p not + + align:start position:0% +the standard pressure p not + + + align:start position:0% +the standard pressure p not +then here we have to put that integral + + align:start position:0% +then here we have to put that integral + + + align:start position:0% +then here we have to put that integral +from P not to P of the partial of new + + align:start position:0% +from P not to P of the partial of new + + + align:start position:0% +from P not to P of the partial of new +respect to P which is the specific + + align:start position:0% +respect to P which is the specific + + + align:start position:0% +respect to P which is the specific +volume and for the case of gas this + + align:start position:0% +volume and for the case of gas this + + + align:start position:0% +volume and for the case of gas this +gives the logarith + + align:start position:0% +gives the logarith + + + align:start position:0% +gives the logarith +contribution okay so we have seen this + + align:start position:0% +contribution okay so we have seen this + + + align:start position:0% +contribution okay so we have seen this +several + + align:start position:0% + + + + align:start position:0% + +times let's substitute it up here up + + align:start position:0% +times let's substitute it up here up + + + align:start position:0% +times let's substitute it up here up +here okay so if you put it up there you + + align:start position:0% +here okay so if you put it up there you + + + align:start position:0% +here okay so if you put it up there you +will that end up with a a summation of + + align:start position:0% +will that end up with a a summation of + + + align:start position:0% +will that end up with a a summation of +tetric coefficients times this mui mu I + + align:start position:0% +tetric coefficients times this mui mu I + + + align:start position:0% +tetric coefficients times this mui mu I +double eyes and this summation you may + + align:start position:0% +double eyes and this summation you may + + + align:start position:0% +double eyes and this summation you may +recognize is the Gibs free energy of + + align:start position:0% +recognize is the Gibs free energy of + + + align:start position:0% +recognize is the Gibs free energy of +that reaction because you remember that + + align:start position:0% +that reaction because you remember that + + + align:start position:0% +that reaction because you remember that +the chemical potentials of the pure + + align:start position:0% +the chemical potentials of the pure + + + align:start position:0% +the chemical potentials of the pure +components are equal to the GBS free + + align:start position:0% +components are equal to the GBS free + + + align:start position:0% +components are equal to the GBS free +energies of the pure + + align:start position:0% +energies of the pure + + + align:start position:0% +energies of the pure +component and it's the Delta G zero the + + align:start position:0% +component and it's the Delta G zero the + + + align:start position:0% +component and it's the Delta G zero the +zero here it's because we are doing it + + align:start position:0% +zero here it's because we are doing it + + + align:start position:0% +zero here it's because we are doing it +at the standard pressure and a function + + align:start position:0% +at the standard pressure and a function + + + align:start position:0% +at the standard pressure and a function +of temperature all right so from this + + align:start position:0% +of temperature all right so from this + + + align:start position:0% +of temperature all right so from this +part from this thing we obtain a + + align:start position:0% +part from this thing we obtain a + + + align:start position:0% +part from this thing we obtain a +contribution like + + align:start position:0% + + + + align:start position:0% + +that uh + + align:start position:0% +that uh + + + align:start position:0% +that uh +from this other + + align:start position:0% +from this other + + + align:start position:0% +from this other +one see there is no subscript I here so + + align:start position:0% +one see there is no subscript I here so + + + align:start position:0% +one see there is no subscript I here so +it goes uh off the summation sign and in + + align:start position:0% +it goes uh off the summation sign and in + + + align:start position:0% +it goes uh off the summation sign and in +the summation sign can remains only the + + align:start position:0% +the summation sign can remains only the + + + align:start position:0% +the summation sign can remains only the +summation of the stochiometric + + align:start position:0% +summation of the stochiometric + + + align:start position:0% +summation of the stochiometric +coefficient + + align:start position:0% +coefficient + + + align:start position:0% +coefficient +of which we're going to denote as new of + + align:start position:0% +of which we're going to denote as new of + + + align:start position:0% +of which we're going to denote as new of +J so that's the total stochiometric + + align:start position:0% +J so that's the total stochiometric + + + align:start position:0% +J so that's the total stochiometric +coefficients of of reaction + + align:start position:0% +coefficients of of reaction + + + align:start position:0% +coefficients of of reaction +J and the last + + align:start position:0% + + + + align:start position:0% + +term it's okay + + align:start position:0% +term it's okay + + + align:start position:0% +term it's okay +RT but the T goes away with the T at the + + align:start position:0% +RT but the T goes away with the T at the + + + align:start position:0% +RT but the T goes away with the T at the +denominator here and then it's the + + align:start position:0% +denominator here and then it's the + + + align:start position:0% +denominator here and then it's the +summation of + + align:start position:0% +summation of + + + align:start position:0% +summation of +stochiometric Times log of + + align:start position:0% + + + + align:start position:0% + +Y okay you can see that you can put + + align:start position:0% +Y okay you can see that you can put + + + align:start position:0% +Y okay you can see that you can put +the the preactor of the logarithm inside + + align:start position:0% +the the preactor of the logarithm inside + + + align:start position:0% +the the preactor of the logarithm inside +it becomes an exponent an exponent so + + align:start position:0% +it becomes an exponent an exponent so + + + align:start position:0% +it becomes an exponent an exponent so +this it becomes the summation of log of + + align:start position:0% +this it becomes the summation of log of + + + align:start position:0% +this it becomes the summation of log of +Y to the new new + + align:start position:0% + + + + align:start position:0% + +subi and then you so you know that the + + align:start position:0% +subi and then you so you know that the + + + align:start position:0% +subi and then you so you know that the +summation of the logarithms is equal to + + align:start position:0% +summation of the logarithms is equal to + + + align:start position:0% +summation of the logarithms is equal to +the logarithm of the + + align:start position:0% +the logarithm of the + + + align:start position:0% +the logarithm of the +products of the arguments of the + + align:start position:0% +products of the arguments of the + + + align:start position:0% +products of the arguments of the +logarithm this is simply a property of + + align:start position:0% +logarithm this is simply a property of + + + align:start position:0% +logarithm this is simply a property of +the + + align:start position:0% +the + + + align:start position:0% +the +logarithms + + align:start position:0% + + + + align:start position:0% + +okay all + + align:start position:0% +okay all + + + align:start position:0% +okay all +right so that that equation is like that + + align:start position:0% +right so that that equation is like that + + + align:start position:0% +right so that that equation is like that +we now in order to sort of get + + align:start position:0% +we now in order to sort of get + + + align:start position:0% +we now in order to sort of get +rid of the logarithm we can take the + + align:start position:0% +rid of the logarithm we can take the + + + align:start position:0% +rid of the logarithm we can take the +exponential uh so so if you take the + + align:start position:0% +exponential uh so so if you take the + + + align:start position:0% +exponential uh so so if you take the +exponential of this expression of + + align:start position:0% +exponential of this expression of + + + align:start position:0% +exponential of this expression of +Y actually take the exponential of Y + + align:start position:0% +Y actually take the exponential of Y + + + align:start position:0% +Y actually take the exponential of Y +divide also by R and change the + + align:start position:0% +divide also by R and change the + + + align:start position:0% +divide also by R and change the +sign okay so that can comes from + + align:start position:0% +sign okay so that can comes from + + + align:start position:0% +sign okay so that can comes from +here uh the exponential of the + + align:start position:0% +here uh the exponential of the + + + align:start position:0% +here uh the exponential of the +logarithm they cancel each other so I'm + + align:start position:0% +logarithm they cancel each other so I'm + + + align:start position:0% +logarithm they cancel each other so I'm +left with this product of the mole + + align:start position:0% +left with this product of the mole + + + align:start position:0% +left with this product of the mole +fractions to the power of the + + align:start position:0% +fractions to the power of the + + + align:start position:0% +fractions to the power of the +corresponding stochiometric coefficients + + align:start position:0% +corresponding stochiometric coefficients + + + align:start position:0% +corresponding stochiometric coefficients +and then I have the exponential of this + + align:start position:0% +and then I have the exponential of this + + + align:start position:0% +and then I have the exponential of this +Delta G which is divided by T and also + + align:start position:0% +Delta G which is divided by T and also + + + align:start position:0% +Delta G which is divided by T and also +by R because we divided also by R and + + align:start position:0% +by R because we divided also by R and + + + align:start position:0% +by R because we divided also by R and +change + + align:start position:0% +change + + + align:start position:0% +change +sign all right we call that exponential + + align:start position:0% +sign all right we call that exponential + + + align:start position:0% +sign all right we call that exponential +it's actually written + + align:start position:0% +it's actually written + + + align:start position:0% +it's actually written +here the equilibrium + + align:start position:0% +here the equilibrium + + + align:start position:0% +here the equilibrium +constant of the + + align:start position:0% +constant of the + + + align:start position:0% +constant of the +reaction um yeah here I should also + + align:start position:0% +reaction um yeah here I should also + + + align:start position:0% +reaction um yeah here I should also +correct it should be for precision it + + align:start position:0% +correct it should be for precision it + + + align:start position:0% +correct it should be for precision it +should be K Sub sub J now it's the it's + + align:start position:0% +should be K Sub sub J now it's the it's + + + align:start position:0% +should be K Sub sub J now it's the it's +related to uh the J uh label of the + + align:start position:0% +related to uh the J uh label of the + + + align:start position:0% +related to uh the J uh label of the +chemical reaction so this is the + + align:start position:0% +chemical reaction so this is the + + + align:start position:0% +chemical reaction so this is the +chemical reaction constant e to the + + align:start position:0% +chemical reaction constant e to the + + + align:start position:0% +chemical reaction constant e to the +minus the GS three energy over + + align:start position:0% +minus the GS three energy over + + + align:start position:0% +minus the GS three energy over +RT + + align:start position:0% +RT + + + align:start position:0% +RT +from uh this term here the log of P the + + align:start position:0% +from uh this term here the log of P the + + + align:start position:0% +from uh this term here the log of P the +log is gone away and the coefficient + + align:start position:0% +log is gone away and the coefficient + + + align:start position:0% +log is gone away and the coefficient +multiplying the log was the total so + + align:start position:0% +multiplying the log was the total so + + + align:start position:0% +multiplying the log was the total so +coefficient which goes inside the + + align:start position:0% +coefficient which goes inside the + + + align:start position:0% +coefficient which goes inside the +logarithm becomes an exponent + + align:start position:0% +logarithm becomes an exponent + + + align:start position:0% +logarithm becomes an exponent +okay and the product of this pressure + + align:start position:0% +okay and the product of this pressure + + + align:start position:0% +okay and the product of this pressure +dependent and temperature dependent is + + align:start position:0% +dependent and temperature dependent is + + + align:start position:0% +dependent and temperature dependent is +also called equilibrium constant so + + align:start position:0% +also called equilibrium constant so + + + align:start position:0% +also called equilibrium constant so +these are really not constants because + + align:start position:0% +these are really not constants because + + + align:start position:0% +these are really not constants because +they depend on temperature they depend + + align:start position:0% +they depend on temperature they depend + + + align:start position:0% +they depend on temperature they depend +on pressure what they don't depend on is + + align:start position:0% +on pressure what they don't depend on is + + + align:start position:0% +on pressure what they don't depend on is +composition that's why it's they're + + align:start position:0% +composition that's why it's they're + + + align:start position:0% +composition that's why it's they're +called in traditionally equilibrium + + align:start position:0% +called in traditionally equilibrium + + + align:start position:0% +called in traditionally equilibrium +constants + + align:start position:0% + + + + align:start position:0% + +so so far we have made no other + + align:start position:0% +so so far we have made no other + + + align:start position:0% +so so far we have made no other +assumption that than the modeling + + align:start position:0% +assumption that than the modeling + + + align:start position:0% +assumption that than the modeling +assumption so this is not yet the + + align:start position:0% +assumption so this is not yet the + + + align:start position:0% +assumption so this is not yet the +equilibrium uh law of mass + + align:start position:0% + + + + align:start position:0% + +action so we call it the non-e + + align:start position:0% +action so we call it the non-e + + + align:start position:0% +action so we call it the non-e +equilibrium low mass + + align:start position:0% +equilibrium low mass + + + align:start position:0% +equilibrium low mass +action it relates this that and that but + + align:start position:0% +action it relates this that and that but + + + align:start position:0% +action it relates this that and that but +of course since we know that at + + align:start position:0% +of course since we know that at + + + align:start position:0% +of course since we know that at +equilibrium the the affini are equal to + + align:start position:0% +equilibrium the the affini are equal to + + + align:start position:0% +equilibrium the the affini are equal to +zero and so e to the 0 is one so this + + align:start position:0% +zero and so e to the 0 is one so this + + + align:start position:0% +zero and so e to the 0 is one so this +take if you cancel this you have the + + align:start position:0% +take if you cancel this you have the + + + align:start position:0% +take if you cancel this you have the +equilibrium law of mass + + align:start position:0% + + + + align:start position:0% + +action here since we've always work with + + align:start position:0% +action here since we've always work with + + + align:start position:0% +action here since we've always work with +mole fractions the Y sub eyes it's + + align:start position:0% +mole fractions the Y sub eyes it's + + + align:start position:0% +mole fractions the Y sub eyes it's +written in the most natural way for uh + + align:start position:0% +written in the most natural way for uh + + + align:start position:0% +written in the most natural way for uh +for our treatment so + + align:start position:0% +for our treatment so + + + align:start position:0% +for our treatment so +far often + + align:start position:0% +far often + + + align:start position:0% +far often +in the practice of U + + align:start position:0% +in the practice of U + + + align:start position:0% +in the practice of U +chemical + + align:start position:0% +chemical + + + align:start position:0% +chemical +engineering instead of mole fraction one + + align:start position:0% +engineering instead of mole fraction one + + + align:start position:0% +engineering instead of mole fraction one +uses the + + align:start position:0% +uses the + + + align:start position:0% +uses the +uh um + + align:start position:0% +uh um + + + align:start position:0% +uh um +concentrations the molar concentration + + align:start position:0% +concentrations the molar concentration + + + align:start position:0% +concentrations the molar concentration +so the number of molecules per unit + + align:start position:0% +so the number of molecules per unit + + + align:start position:0% +so the number of molecules per unit +volume and sometimes you denote that by + + align:start position:0% +volume and sometimes you denote that by + + + align:start position:0% +volume and sometimes you denote that by +c c + + align:start position:0% +c c + + + align:start position:0% +c c +Sai concentration + + align:start position:0% +Sai concentration + + + align:start position:0% +Sai concentration +sometimes you denote it by this n in + + align:start position:0% +sometimes you denote it by this n in + + + align:start position:0% +sometimes you denote it by this n in +square + + align:start position:0% + + + + align:start position:0% + +brackets of course there is they + + align:start position:0% +brackets of course there is they + + + align:start position:0% +brackets of course there is they +related and therefore if you if you take + + align:start position:0% +related and therefore if you if you take + + + align:start position:0% +related and therefore if you if you take +this one and do this substitution you + + align:start position:0% +this one and do this substitution you + + + align:start position:0% +this one and do this substitution you +get the law of mass action written in + + align:start position:0% +get the law of mass action written in + + + align:start position:0% +get the law of mass action written in +terms of + + align:start position:0% +terms of + + + align:start position:0% +terms of +concentrations what changes is uh the + + align:start position:0% +concentrations what changes is uh the + + + align:start position:0% +concentrations what changes is uh the +constants so for example the pressure + + align:start position:0% +constants so for example the pressure + + + align:start position:0% +constants so for example the pressure +depend then goes + + align:start position:0% +depend then goes + + + align:start position:0% +depend then goes +away the P you see the P the total P + + align:start position:0% +away the P you see the P the total P + + + align:start position:0% +away the P you see the P the total P +disappeared and uh so this equilibrium + + align:start position:0% +disappeared and uh so this equilibrium + + + align:start position:0% +disappeared and uh so this equilibrium +constant based on concentration the the + + align:start position:0% +constant based on concentration the the + + + align:start position:0% +constant based on concentration the the +C up there is there just to distinguish + + align:start position:0% +C up there is there just to distinguish + + + align:start position:0% +C up there is there just to distinguish +between these equilibrium constants so + + align:start position:0% +between these equilibrium constants so + + + align:start position:0% +between these equilibrium constants so +you have to be careful when you are in + + align:start position:0% +you have to be careful when you are in + + + align:start position:0% +you have to be careful when you are in +this business to understand which + + align:start position:0% +this business to understand which + + + align:start position:0% +this business to understand which +equilibrium constant you're talking + + align:start position:0% +equilibrium constant you're talking + + + align:start position:0% +equilibrium constant you're talking +about there is also this + + align:start position:0% +about there is also this + + + align:start position:0% +about there is also this +last way of writing it also has an + + align:start position:0% +last way of writing it also has an + + + align:start position:0% +last way of writing it also has an +additional difficulty that has to do + + align:start position:0% +additional difficulty that has to do + + + align:start position:0% +additional difficulty that has to do +with the dimensions because + + align:start position:0% +with the dimensions because + + + align:start position:0% +with the dimensions because +whereas the top one is + + align:start position:0% +whereas the top one is + + + align:start position:0% +whereas the top one is +dimensionless because the M fractions + + align:start position:0% +dimensionless because the M fractions + + + align:start position:0% +dimensionless because the M fractions +are + + align:start position:0% +are + + + align:start position:0% +are +dimensionless p over p is + + align:start position:0% +dimensionless p over p is + + + align:start position:0% +dimensionless p over p is +dimensionless and Delta G over RT is + + align:start position:0% +dimensionless and Delta G over RT is + + + align:start position:0% +dimensionless and Delta G over RT is +dimensionless so everything is + + align:start position:0% +dimensionless so everything is + + + align:start position:0% +dimensionless so everything is +dimensionless up here down here it's not + + align:start position:0% +dimensionless up here down here it's not + + + align:start position:0% +dimensionless up here down here it's not +because this is n over + + align:start position:0% +because this is n over + + + align:start position:0% +because this is n over +V and so these equilibrium + + align:start position:0% +V and so these equilibrium + + + align:start position:0% +V and so these equilibrium +constants depend for example this is a + + align:start position:0% +constants depend for example this is a + + + align:start position:0% +constants depend for example this is a +this is + + align:start position:0% + + + + align:start position:0% + +a these as dimensions + + align:start position:0% +a these as dimensions + + + align:start position:0% +a these as dimensions +of moles per cubic + + align:start position:0% +of moles per cubic + + + align:start position:0% +of moles per cubic +meter so if your chemical reaction has + + align:start position:0% +meter so if your chemical reaction has + + + align:start position:0% +meter so if your chemical reaction has +the stochiometric coefficients that are + + align:start position:0% +the stochiometric coefficients that are + + + align:start position:0% +the stochiometric coefficients that are +equal that sum up to zero then this is + + align:start position:0% +equal that sum up to zero then this is + + + align:start position:0% +equal that sum up to zero then this is +dimensionless but if they don't sum up + + align:start position:0% +dimensionless but if they don't sum up + + + align:start position:0% +dimensionless but if they don't sum up +to zero then these as Dimensions that + + align:start position:0% +to zero then these as Dimensions that + + + align:start position:0% +to zero then these as Dimensions that +depend on the sum of the tetric + + align:start position:0% +depend on the sum of the tetric + + + align:start position:0% +depend on the sum of the tetric +coefficients so that sometimes it's a + + align:start position:0% +coefficients so that sometimes it's a + + + align:start position:0% +coefficients so that sometimes it's a +cause of little errors in + + align:start position:0% + + + + align:start position:0% + +computations + + align:start position:0% + + + + align:start position:0% + +clearly you can redo + + align:start position:0% +clearly you can redo + + + align:start position:0% +clearly you can redo +what we've just done also for + + align:start position:0% +what we've just done also for + + + align:start position:0% +what we've just done also for +liquids if you instead of having a the + + align:start position:0% +liquids if you instead of having a the + + + align:start position:0% +liquids if you instead of having a the +reaction occurring in the gasos phase + + align:start position:0% +reaction occurring in the gasos phase + + + align:start position:0% +reaction occurring in the gasos phase +you have it in the liquid phase and you + + align:start position:0% +you have it in the liquid phase and you + + + align:start position:0% +you have it in the liquid phase and you +can assume ideal Solutions solution at + + align:start position:0% +can assume ideal Solutions solution at + + + align:start position:0% +can assume ideal Solutions solution at +all compositions for all + + align:start position:0% +all compositions for all + + + align:start position:0% +all compositions for all +components which is rare but it's a + + align:start position:0% +components which is rare but it's a + + + align:start position:0% +components which is rare but it's a +starting + + align:start position:0% +starting + + + align:start position:0% +starting +point then of course you remember that + + align:start position:0% +point then of course you remember that + + + align:start position:0% +point then of course you remember that +integral when you write the chemical + + align:start position:0% +integral when you write the chemical + + + align:start position:0% +integral when you write the chemical +potential instead of the RT log of the p + + align:start position:0% +potential instead of the RT log of the p + + + align:start position:0% +potential instead of the RT log of the p +over P it's simply P minus P times the + + align:start position:0% +over P it's simply P minus P times the + + + align:start position:0% +over P it's simply P minus P times the +specific volume of the pure component + + align:start position:0% + + + + align:start position:0% + +liquid the pure liquid component + + align:start position:0% + + + + align:start position:0% + +I then you substitute up there then it + + align:start position:0% +I then you substitute up there then it + + + align:start position:0% +I then you substitute up there then it +appears also the weighted sum of the + + align:start position:0% +appears also the weighted sum of the + + + align:start position:0% +appears also the weighted sum of the +volumes that's the volume of the + + align:start position:0% +volumes that's the volume of the + + + align:start position:0% +volumes that's the volume of the +reaction + + align:start position:0% + + + + align:start position:0% + +and U when you + + align:start position:0% +and U when you + + + align:start position:0% +and U when you +do so when you go back here the non + + align:start position:0% +do so when you go back here the non + + + align:start position:0% +do so when you go back here the non +equilibrium law of mass + + align:start position:0% +equilibrium law of mass + + + align:start position:0% +equilibrium law of mass +action this side has the same uh format + + align:start position:0% +action this side has the same uh format + + + align:start position:0% +action this side has the same uh format +except that the equilibrium constant uh + + align:start position:0% +except that the equilibrium constant uh + + + align:start position:0% +except that the equilibrium constant uh +is different it has also it has one + + align:start position:0% +is different it has also it has one + + + align:start position:0% +is different it has also it has one +contribution which Remains the Delta G + + align:start position:0% +contribution which Remains the Delta G + + + align:start position:0% +contribution which Remains the Delta G +over RT that's the equilibrium constant + + align:start position:0% +over RT that's the equilibrium constant + + + align:start position:0% +over RT that's the equilibrium constant +k k of JT + + align:start position:0% +k k of JT + + + align:start position:0% +k k of JT +what what differs is that the other + + align:start position:0% +what what differs is that the other + + + align:start position:0% +what what differs is that the other +thing that you could also separate and + + align:start position:0% +thing that you could also separate and + + + align:start position:0% +thing that you could also separate and +make it two separate exponentials like + + align:start position:0% +make it two separate exponentials like + + + align:start position:0% +make it two separate exponentials like +uh this could be the + + align:start position:0% +uh this could be the + + + align:start position:0% +uh this could be the +preactor of the uh of the standard + + align:start position:0% +preactor of the uh of the standard + + + align:start position:0% +preactor of the uh of the standard +equilibrium con constant and you can + + align:start position:0% +equilibrium con constant and you can + + + align:start position:0% +equilibrium con constant and you can +also write it in terms of uh + + align:start position:0% +also write it in terms of uh + + + align:start position:0% +also write it in terms of uh +concentrations for a liquid of + + align:start position:0% +concentrations for a liquid of + + + align:start position:0% +concentrations for a liquid of +course uh the + + align:start position:0% +course uh the + + + align:start position:0% +course uh the +concentrations + + align:start position:0% +concentrations + + + align:start position:0% +concentrations +uh the relation between Mo fractions and + + align:start position:0% +uh the relation between Mo fractions and + + + align:start position:0% +uh the relation between Mo fractions and +concentrations are this + + align:start position:0% +concentrations are this + + + align:start position:0% +concentrations are this +way and + + align:start position:0% +way and + + + align:start position:0% +way and +again by + + align:start position:0% +again by + + + align:start position:0% +again by +setting + + align:start position:0% +setting + + + align:start position:0% +setting +all the affinities equal to zero your + + align:start position:0% +all the affinities equal to zero your + + + align:start position:0% +all the affinities equal to zero your +system is at equilibrium chemical + + align:start position:0% +system is at equilibrium chemical + + + align:start position:0% +system is at equilibrium chemical +equilibrium all the reactions have zero + + align:start position:0% +equilibrium all the reactions have zero + + + align:start position:0% +equilibrium all the reactions have zero +Affinity at equilibrium so you can set + + align:start position:0% +Affinity at equilibrium so you can set + + + align:start position:0% +Affinity at equilibrium so you can set +zero all these ones and with this law of + + align:start position:0% +zero all these ones and with this law of + + + align:start position:0% +zero all these ones and with this law of +mass action you can compute the + + align:start position:0% +mass action you can compute the + + + align:start position:0% +mass action you can compute the +equilibrium compon + + align:start position:0% + + + + align:start position:0% + +position if instead of + + align:start position:0% +position if instead of + + + align:start position:0% +position if instead of +having + + align:start position:0% +having + + + align:start position:0% +having +ideal um M gas mixtures or Solutions you + + align:start position:0% +ideal um M gas mixtures or Solutions you + + + align:start position:0% +ideal um M gas mixtures or Solutions you +have a uh + + align:start position:0% +have a uh + + + align:start position:0% +have a uh +real uh mixtures that you + + align:start position:0% +real uh mixtures that you + + + align:start position:0% +real uh mixtures that you +model according + + align:start position:0% +model according + + + align:start position:0% +model according +to Mar goues van are all those models + + align:start position:0% +to Mar goues van are all those models + + + align:start position:0% +to Mar goues van are all those models +that we have introduced for the models + + align:start position:0% +that we have introduced for the models + + + align:start position:0% +that we have introduced for the models +of nonideal behavior of + + align:start position:0% +of nonideal behavior of + + + align:start position:0% +of nonideal behavior of +mixtures + + align:start position:0% + + + + align:start position:0% + +then you can always put that um the + + align:start position:0% +then you can always put that um the + + + align:start position:0% +then you can always put that um the +expression for the chemical potential in + + align:start position:0% +expression for the chemical potential in + + + align:start position:0% +expression for the chemical potential in +this way in + + align:start position:0% +this way in + + + align:start position:0% +this way in +terms of the + + align:start position:0% +terms of the + + + align:start position:0% +terms of the +affinities which which become Mo play + + align:start position:0% +affinities which which become Mo play + + + align:start position:0% +affinities which which become Mo play +the same role as M fra fractions for the + + align:start position:0% +the same role as M fra fractions for the + + + align:start position:0% +the same role as M fra fractions for the +uh ideal + + align:start position:0% +uh ideal + + + align:start position:0% +uh ideal +Behavior instead of calling it yabi you + + align:start position:0% +Behavior instead of calling it yabi you + + + align:start position:0% +Behavior instead of calling it yabi you +call it aabi and it becomes non ideal + + align:start position:0% +call it aabi and it becomes non ideal + + + align:start position:0% +call it aabi and it becomes non ideal +but the mathematical steps are exactly + + align:start position:0% +but the mathematical steps are exactly + + + align:start position:0% +but the mathematical steps are exactly +the same so here is what you + + align:start position:0% + + + + align:start position:0% + +obtain uh but then obviously you need to + + align:start position:0% +obtain uh but then obviously you need to + + + align:start position:0% +obtain uh but then obviously you need to +know to have those van or marulas or + + align:start position:0% +know to have those van or marulas or + + + align:start position:0% +know to have those van or marulas or +whatever relations that allow you to + + align:start position:0% +whatever relations that allow you to + + + align:start position:0% +whatever relations that allow you to +write the affinities in terms of mole + + align:start position:0% +write the affinities in terms of mole + + + align:start position:0% +write the affinities in terms of mole +fractions and then this will be a set of + + align:start position:0% +fractions and then this will be a set of + + + align:start position:0% +fractions and then this will be a set of +equations that will allow you to compute + + align:start position:0% +equations that will allow you to compute + + + align:start position:0% +equations that will allow you to compute +the mole + + align:start position:0% + + + + align:start position:0% + +fractions now the main part of the + + align:start position:0% +fractions now the main part of the + + + align:start position:0% +fractions now the main part of the +equilibrium constant that exponential of + + align:start position:0% +equilibrium constant that exponential of + + + align:start position:0% +equilibrium constant that exponential of +minus Delta G / + + align:start position:0% +minus Delta G / + + + align:start position:0% +minus Delta G / +RT is something that + + align:start position:0% + + + + align:start position:0% + +we have uh already encountered at the + + align:start position:0% +we have uh already encountered at the + + + align:start position:0% +we have uh already encountered at the +beginning of uh last + + align:start position:0% +beginning of uh last + + + align:start position:0% +beginning of uh last +lecture when we talked about + + align:start position:0% +lecture when we talked about + + + align:start position:0% +lecture when we talked about +the the the role of the Gibs free energy + + align:start position:0% +the the the role of the Gibs free energy + + + align:start position:0% +the the the role of the Gibs free energy +in determining when a reaction is react + + align:start position:0% +in determining when a reaction is react + + + align:start position:0% +in determining when a reaction is react +reactant favored or product + + align:start position:0% +reactant favored or product + + + align:start position:0% +reactant favored or product +favored because it turned out that + + align:start position:0% +favored because it turned out that + + + align:start position:0% +favored because it turned out that +the uh entropy produced by + + align:start position:0% +the uh entropy produced by + + + align:start position:0% +the uh entropy produced by +irreversibility is related to + + align:start position:0% + + + + align:start position:0% + +this okay so if I take this expression + + align:start position:0% +this okay so if I take this expression + + + align:start position:0% +this okay so if I take this expression +and take the logarithm and actually take + + align:start position:0% +and take the logarithm and actually take + + + align:start position:0% +and take the logarithm and actually take +the logarithm in base + + align:start position:0% + + + + align:start position:0% + +10 I can plot that + + align:start position:0% +10 I can plot that + + + align:start position:0% +10 I can plot that +logarithm versus the inverse of the + + align:start position:0% + + + + align:start position:0% + +temperature and we already proved last + + align:start position:0% +temperature and we already proved last + + + align:start position:0% +temperature and we already proved last +time that this derivative with respect + + align:start position:0% +time that this derivative with respect + + + align:start position:0% +time that this derivative with respect +of this logarithm with respect to 1 / T + + align:start position:0% +of this logarithm with respect to 1 / T + + + align:start position:0% +of this logarithm with respect to 1 / T +is related to the enthalpy the Nega is + + align:start position:0% +is related to the enthalpy the Nega is + + + align:start position:0% +is related to the enthalpy the Nega is +the the negative of the enthalpy of + + align:start position:0% +the the negative of the enthalpy of + + + align:start position:0% +the the negative of the enthalpy of +reaction so when a reaction is + + align:start position:0% +reaction so when a reaction is + + + align:start position:0% +reaction so when a reaction is +exothermic Delta H is negative so that + + align:start position:0% +exothermic Delta H is negative so that + + + align:start position:0% +exothermic Delta H is negative so that +means that this slope is positive for + + align:start position:0% +means that this slope is positive for + + + align:start position:0% +means that this slope is positive for +the exothermic reactions so for example + + align:start position:0% +the exothermic reactions so for example + + + align:start position:0% +the exothermic reactions so for example +this reaction is exothermic this one is + + align:start position:0% +this reaction is exothermic this one is + + + align:start position:0% +this reaction is exothermic this one is +endothermic because it goes down with 1 + + align:start position:0% +endothermic because it goes down with 1 + + + align:start position:0% +endothermic because it goes down with 1 +/ + + align:start position:0% + + + + align:start position:0% + +T so you see that the + + align:start position:0% +T so you see that the + + + align:start position:0% +T so you see that the +chemical equilibrium + + align:start position:0% + + + + align:start position:0% + +constants + + align:start position:0% +constants + + + align:start position:0% +constants +span over a wide range + + align:start position:0% +span over a wide range + + + align:start position:0% +span over a wide range +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +of of + + align:start position:0% + + + + align:start position:0% + +um how do you + + align:start position:0% +um how do you + + + align:start position:0% +um how do you +say the senior moment uh uh orders of + + align:start position:0% +say the senior moment uh uh orders of + + + align:start position:0% +say the senior moment uh uh orders of +magnitude okay + + align:start position:0% +magnitude okay + + + align:start position:0% +magnitude okay +thanks um so you + + align:start position:0% +thanks um so you + + + align:start position:0% +thanks um so you +see so it can go from from very high to + + align:start position:0% +see so it can go from from very high to + + + align:start position:0% +see so it can go from from very high to +very + + align:start position:0% +very + + + align:start position:0% +very +small and the reaction in equilibrium + + align:start position:0% +small and the reaction in equilibrium + + + align:start position:0% +small and the reaction in equilibrium +constant is what + + align:start position:0% +constant is what + + + align:start position:0% +constant is what +determines uh the + + align:start position:0% +determines uh the + + + align:start position:0% +determines uh the +compositions if it is very much so if + + align:start position:0% +compositions if it is very much so if + + + align:start position:0% +compositions if it is very much so if +the equilibrium is very much uh towards + + align:start position:0% +the equilibrium is very much uh towards + + + align:start position:0% +the equilibrium is very much uh towards +the products + + align:start position:0% +the products + + + align:start position:0% +the products +when the chemical equilibrium is uh if + + align:start position:0% +when the chemical equilibrium is uh if + + + align:start position:0% +when the chemical equilibrium is uh if +you go back here if the equilibrium + + align:start position:0% +you go back here if the equilibrium + + + align:start position:0% +you go back here if the equilibrium +constant is + + align:start position:0% + + + + align:start position:0% + +large uh it will make uh uh Prevail the + + align:start position:0% +large uh it will make uh uh Prevail the + + + align:start position:0% +large uh it will make uh uh Prevail the +um the mole fractions that have positive + + align:start position:0% +um the mole fractions that have positive + + + align:start position:0% +um the mole fractions that have positive +stochiometric coefficients so it will + + align:start position:0% +stochiometric coefficients so it will + + + align:start position:0% +stochiometric coefficients so it will +make Prevail the uh products whereas if + + align:start position:0% +make Prevail the uh products whereas if + + + align:start position:0% +make Prevail the uh products whereas if +it is small it will make Prevail the one + + align:start position:0% +it is small it will make Prevail the one + + + align:start position:0% +it is small it will make Prevail the one +that are at the denominator so they have + + align:start position:0% +that are at the denominator so they have + + + align:start position:0% +that are at the denominator so they have +negative stochiometric + + align:start position:0% + + + + align:start position:0% + +coefficient so what how do we how do we + + align:start position:0% +coefficient so what how do we how do we + + + align:start position:0% +coefficient so what how do we how do we +compute the equilibrium + + align:start position:0% + + + + align:start position:0% + +constants yeah they are + + align:start position:0% +constants yeah they are + + + align:start position:0% +constants yeah they are +defined for each reaction but since they + + align:start position:0% +defined for each reaction but since they + + + align:start position:0% +defined for each reaction but since they +related to the Gibs free energy of + + align:start position:0% +related to the Gibs free energy of + + + align:start position:0% +related to the Gibs free energy of +reaction + + align:start position:0% + + + + align:start position:0% + +we + + align:start position:0% +we + + + align:start position:0% +we +can uh use the S relation that you + + align:start position:0% +can uh use the S relation that you + + + align:start position:0% +can uh use the S relation that you +remember allows you to compute the + + align:start position:0% +remember allows you to compute the + + + align:start position:0% +remember allows you to compute the +properties of reaction from the + + align:start position:0% +properties of reaction from the + + + align:start position:0% +properties of reaction from the +properties of formations of your + + align:start position:0% + + + + align:start position:0% + +constituents so all you know all you + + align:start position:0% +constituents so all you know all you + + + align:start position:0% +constituents so all you know all you +need to know is uh the properties of + + align:start position:0% +need to know is uh the properties of + + + align:start position:0% +need to know is uh the properties of +formation but you need to know them as a + + align:start position:0% +formation but you need to know them as a + + + align:start position:0% +formation but you need to know them as a +function of temperature + + align:start position:0% +function of temperature + + + align:start position:0% +function of temperature +so for + + align:start position:0% +so for + + + align:start position:0% +so for +each component in principle you should + + align:start position:0% +each component in principle you should + + + align:start position:0% +each component in principle you should +know you should measure it as a function + + align:start position:0% +know you should measure it as a function + + + align:start position:0% +know you should measure it as a function +of temperature however there's a + + align:start position:0% +of temperature however there's a + + + align:start position:0% +of temperature however there's a +simplifica + + align:start position:0% +simplifica + + + align:start position:0% +simplifica +So based just on that turns out + + align:start position:0% +So based just on that turns out + + + align:start position:0% +So based just on that turns out +that the equilibrium constant for your + + align:start position:0% +that the equilibrium constant for your + + + align:start position:0% +that the equilibrium constant for your +reaction can be computed as the + + align:start position:0% +reaction can be computed as the + + + align:start position:0% +reaction can be computed as the +product of the equilibrium constants of + + align:start position:0% +product of the equilibrium constants of + + + align:start position:0% +product of the equilibrium constants of +the reactions of formations of your + + align:start position:0% +the reactions of formations of your + + + align:start position:0% +the reactions of formations of your +various constituents that that appear in + + align:start position:0% +various constituents that that appear in + + + align:start position:0% +various constituents that that appear in +the chemical reaction mechanism to the + + align:start position:0% +the chemical reaction mechanism to the + + + align:start position:0% +the chemical reaction mechanism to the +power uh of the stochiometric respective + + align:start position:0% +power uh of the stochiometric respective + + + align:start position:0% +power uh of the stochiometric respective +stric + + align:start position:0% + + + + align:start position:0% + +coefficients okay and this is + + align:start position:0% +coefficients okay and this is + + + align:start position:0% +coefficients okay and this is +General + + align:start position:0% +General + + + align:start position:0% +General +now if we use that derivative that we + + align:start position:0% +now if we use that derivative that we + + + align:start position:0% +now if we use that derivative that we +done in the previous slide and also + + align:start position:0% +done in the previous slide and also + + + align:start position:0% +done in the previous slide and also +earlier to show that this derivative is + + align:start position:0% +earlier to show that this derivative is + + + align:start position:0% +earlier to show that this derivative is +equal to the minus of the enpy of + + align:start position:0% +equal to the minus of the enpy of + + + align:start position:0% +equal to the minus of the enpy of +reaction and then if we know notice that + + align:start position:0% +reaction and then if we know notice that + + + align:start position:0% +reaction and then if we know notice that +the enthalpy of + + align:start position:0% +the enthalpy of + + + align:start position:0% +the enthalpy of +reaction seems to be pretty constant + + align:start position:0% +reaction seems to be pretty constant + + + align:start position:0% +reaction seems to be pretty constant +with temperature how how how do I why do + + align:start position:0% +with temperature how how how do I why do + + + align:start position:0% +with temperature how how how do I why do +I say that because if you look at these + + align:start position:0% +I say that because if you look at these + + + align:start position:0% +I say that because if you look at these +uh curves here they look like almost + + align:start position:0% +uh curves here they look like almost + + + align:start position:0% +uh curves here they look like almost +straight + + align:start position:0% + + + + align:start position:0% + +lines so straight lines means that the + + align:start position:0% +lines so straight lines means that the + + + align:start position:0% +lines so straight lines means that the +slope is almost + + align:start position:0% +slope is almost + + + align:start position:0% +slope is almost +constant so if you assume if you make + + align:start position:0% +constant so if you assume if you make + + + align:start position:0% +constant so if you assume if you make +that + + align:start position:0% +that + + + align:start position:0% +that +approximation if you look close it + + align:start position:0% +approximation if you look close it + + + align:start position:0% +approximation if you look close it +they're not literally uh straight + + align:start position:0% +they're not literally uh straight + + + align:start position:0% +they're not literally uh straight +lines so it is an + + align:start position:0% +lines so it is an + + + align:start position:0% +lines so it is an +approximation but if you make that + + align:start position:0% +approximation but if you make that + + + align:start position:0% +approximation but if you make that +approximation it means you can do can do + + align:start position:0% +approximation it means you can do can do + + + align:start position:0% +approximation it means you can do can do +this integral you assume this is + + align:start position:0% + + + + align:start position:0% + +constant and and that integral therefore + + align:start position:0% +constant and and that integral therefore + + + align:start position:0% +constant and and that integral therefore +it's like an integrate integrate of D of + + align:start position:0% +it's like an integrate integrate of D of + + + align:start position:0% +it's like an integrate integrate of D of +one / T it's uh it's like a linear + + align:start position:0% +one / T it's uh it's like a linear + + + align:start position:0% +one / T it's uh it's like a linear +relation between the logarithm of of KT + + align:start position:0% +relation between the logarithm of of KT + + + align:start position:0% +relation between the logarithm of of KT +and one / T these are exactly the + + align:start position:0% +and one / T these are exactly the + + + align:start position:0% +and one / T these are exactly the +equation of those line lines of the + + align:start position:0% +equation of those line lines of the + + + align:start position:0% +equation of those line lines of the +previous + + align:start position:0% +previous + + + align:start position:0% +previous +plot then if you notice that this one is + + align:start position:0% +plot then if you notice that this one is + + + align:start position:0% +plot then if you notice that this one is +still the the concept of integration is + + align:start position:0% +still the the concept of integration is + + + align:start position:0% +still the the concept of integration is +the equilibrium constant evaluated at + + align:start position:0% +the equilibrium constant evaluated at + + + align:start position:0% +the equilibrium constant evaluated at +standard temperature and so that's also + + align:start position:0% +standard temperature and so that's also + + + align:start position:0% +standard temperature and so that's also +related to Delta G over uh I think + + align:start position:0% +related to Delta G over uh I think + + + align:start position:0% +related to Delta G over uh I think +there's a t missing here this is should + + align:start position:0% +there's a t missing here this is should + + + align:start position:0% +there's a t missing here this is should +be rt0 + + align:start position:0% + + + + align:start position:0% + +and U yeah I have to correct that so if + + align:start position:0% +and U yeah I have to correct that so if + + + align:start position:0% +and U yeah I have to correct that so if +you substitute that up here and remember + + align:start position:0% +you substitute that up here and remember + + + align:start position:0% +you substitute that up here and remember +that Delta G is Delta H minus t Delta + + align:start position:0% +that Delta G is Delta H minus t Delta + + + align:start position:0% +that Delta G is Delta H minus t Delta +s you finally get this expression which + + align:start position:0% +s you finally get this expression which + + + align:start position:0% +s you finally get this expression which +gives the logarithm of KT as a linear + + align:start position:0% +gives the logarithm of KT as a linear + + + align:start position:0% +gives the logarithm of KT as a linear +relation in one / + + align:start position:0% + + + + align:start position:0% + +T and those Delta s and Delta H are the + + align:start position:0% +T and those Delta s and Delta H are the + + + align:start position:0% +T and those Delta s and Delta H are the +properties of reaction at standard + + align:start position:0% +properties of reaction at standard + + + align:start position:0% +properties of reaction at standard +conditions of temperature and + + align:start position:0% + + + + align:start position:0% + +pressure so essentially by just + + align:start position:0% +pressure so essentially by just + + + align:start position:0% +pressure so essentially by just +knowing the entropies the entropies of + + align:start position:0% +knowing the entropies the entropies of + + + align:start position:0% +knowing the entropies the entropies of +formation and the enalis of formation of + + align:start position:0% +formation and the enalis of formation of + + + align:start position:0% +formation and the enalis of formation of +your virus + + align:start position:0% +your virus + + + align:start position:0% +your virus +constituents this expression gives you + + align:start position:0% +constituents this expression gives you + + + align:start position:0% +constituents this expression gives you +the chemical equilibrium constant at any + + align:start position:0% +the chemical equilibrium constant at any + + + align:start position:0% +the chemical equilibrium constant at any +temperature + + align:start position:0% + + + + align:start position:0% + +and if you if you want to correct for + + align:start position:0% +and if you if you want to correct for + + + align:start position:0% +and if you if you want to correct for +that + + align:start position:0% +that + + + align:start position:0% +that +minor uh difference that is due to the + + align:start position:0% +minor uh difference that is due to the + + + align:start position:0% +minor uh difference that is due to the +fact that those lines are not exactly + + align:start position:0% +fact that those lines are not exactly + + + align:start position:0% +fact that those lines are not exactly +straight lines but you want to do the + + align:start position:0% +straight lines but you want to do the + + + align:start position:0% +straight lines but you want to do the +approximation instead of using those you + + align:start position:0% +approximation instead of using those you + + + align:start position:0% +approximation instead of using those you +can use those from a table which does a + + align:start position:0% +can use those from a table which does a + + + align:start position:0% +can use those from a table which does a +at least square feet which does a better + + align:start position:0% +at least square feet which does a better + + + align:start position:0% +at least square feet which does a better +job for example this table uh gives you + + align:start position:0% +job for example this table uh gives you + + + align:start position:0% +job for example this table uh gives you +good numbers in a wide range of + + align:start position:0% +good numbers in a wide range of + + + align:start position:0% +good numbers in a wide range of +temperatur from 300 to + + align:start position:0% +temperatur from 300 to + + + align:start position:0% +temperatur from 300 to +5,000k which is + + align:start position:0% +5,000k which is + + + align:start position:0% +5,000k which is +plenty uh what you need uh for for + + align:start position:0% +plenty uh what you need uh for for + + + align:start position:0% +plenty uh what you need uh for for +example combustion + + align:start position:0% +example combustion + + + align:start position:0% +example combustion +applications all right so we know the + + align:start position:0% +applications all right so we know the + + + align:start position:0% +applications all right so we know the +the chemical equilibrium + + align:start position:0% +the chemical equilibrium + + + align:start position:0% +the chemical equilibrium +constant so let me give you an + + align:start position:0% + + + + align:start position:0% + +example you've probably seen these kind + + align:start position:0% +example you've probably seen these kind + + + align:start position:0% +example you've probably seen these kind +of things in the previous course 2452 I + + align:start position:0% +of things in the previous course 2452 I + + + align:start position:0% +of things in the previous course 2452 I +mean two um + + align:start position:0% + + + + align:start position:0% + +242 in any case suppose we + + align:start position:0% +242 in any case suppose we + + + align:start position:0% +242 in any case suppose we +consider the reaction of dissociation of + + align:start position:0% +consider the reaction of dissociation of + + + align:start position:0% +consider the reaction of dissociation of +CO2 which is important in combustion + + align:start position:0% +CO2 which is important in combustion + + + align:start position:0% +CO2 which is important in combustion +because CO2 is a product of combustion + + align:start position:0% +because CO2 is a product of combustion + + + align:start position:0% +because CO2 is a product of combustion +and at high temperatures uh this + + align:start position:0% +and at high temperatures uh this + + + align:start position:0% +and at high temperatures uh this +dissociation may occur so let's assume + + align:start position:0% +dissociation may occur so let's assume + + + align:start position:0% +dissociation may occur so let's assume +the temperature is of the is three + + align:start position:0% +the temperature is of the is three + + + align:start position:0% +the temperature is of the is three +3200k and that we are at atmospheric + + align:start position:0% + + + + align:start position:0% + +somehow using the previous um U table + + align:start position:0% +somehow using the previous um U table + + + align:start position:0% +somehow using the previous um U table +you can compute the equilibrium + + align:start position:0% +you can compute the equilibrium + + + align:start position:0% +you can compute the equilibrium +constant + + align:start position:0% +constant + + + align:start position:0% +constant +um which is + + align:start position:0% + + + + align:start position:0% + +64 and so in order to do the calculation + + align:start position:0% +64 and so in order to do the calculation + + + align:start position:0% +64 and so in order to do the calculation +we need to apply the law of mass action + + align:start position:0% +we need to apply the law of mass action + + + align:start position:0% +we need to apply the law of mass action +and the law of mass action says that the + + align:start position:0% +and the law of mass action says that the + + + align:start position:0% +and the law of mass action says that the +product of a mole fractions to the + + align:start position:0% +product of a mole fractions to the + + + align:start position:0% +product of a mole fractions to the +stochiometric + + align:start position:0% +stochiometric + + + align:start position:0% +stochiometric +coefficients it must be equal to to + + align:start position:0% +coefficients it must be equal to to + + + align:start position:0% +coefficients it must be equal to to +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +constant the equilibrium constant that + + align:start position:0% +constant the equilibrium constant that + + + align:start position:0% +constant the equilibrium constant that +depends on temperature and + + align:start position:0% +depends on temperature and + + + align:start position:0% +depends on temperature and +pressure uh now in this case the + + align:start position:0% +pressure uh now in this case the + + + align:start position:0% +pressure uh now in this case the +pressure is is equal to P not so this + + align:start position:0% +pressure is is equal to P not so this + + + align:start position:0% +pressure is is equal to P not so this +preactor + + align:start position:0% +preactor + + + align:start position:0% +preactor +uh is equal to one so it cancels out so + + align:start position:0% +uh is equal to one so it cancels out so + + + align:start position:0% +uh is equal to one so it cancels out so +you're left with K of T which is e to + + align:start position:0% +you're left with K of T which is e to + + + align:start position:0% +you're left with K of T which is e to +the minus Delta g/ RT okay so we know + + align:start position:0% +the minus Delta g/ RT okay so we know + + + align:start position:0% +the minus Delta g/ RT okay so we know +the value of the right hand side now for + + align:start position:0% +the value of the right hand side now for + + + align:start position:0% +the value of the right hand side now for +the left hand side + + align:start position:0% +the left hand side + + + align:start position:0% +the left hand side +we need to express we need to find the + + align:start position:0% +we need to express we need to find the + + + align:start position:0% +we need to express we need to find the +mole fractions and the mole fractions + + align:start position:0% +mole fractions and the mole fractions + + + align:start position:0% +mole fractions and the mole fractions +they're not all independent of of one + + align:start position:0% +they're not all independent of of one + + + align:start position:0% +they're not all independent of of one +another because they are + + align:start position:0% +another because they are + + + align:start position:0% +another because they are +related through the proportionality + + align:start position:0% +related through the proportionality + + + align:start position:0% +related through the proportionality +relations so Mo fraction is n over total + + align:start position:0% +relations so Mo fraction is n over total + + + align:start position:0% +relations so Mo fraction is n over total +n so n of component I is equal to the + + align:start position:0% +n so n of component I is equal to the + + + align:start position:0% +n so n of component I is equal to the +initial amount plus the stochiometric + + align:start position:0% +initial amount plus the stochiometric + + + align:start position:0% +initial amount plus the stochiometric +coefficient times the reaction + + align:start position:0% +coefficient times the reaction + + + align:start position:0% +coefficient times the reaction +coordinate Epsilon + + align:start position:0% +coordinate Epsilon + + + align:start position:0% +coordinate Epsilon +and the denominator is the sum of the + + align:start position:0% +and the denominator is the sum of the + + + align:start position:0% +and the denominator is the sum of the +numerators so to speak uh so it's the + + align:start position:0% +numerators so to speak uh so it's the + + + align:start position:0% +numerators so to speak uh so it's the +total n initial the total stum + + align:start position:0% +total n initial the total stum + + + align:start position:0% +total n initial the total stum +coefficient and the uh reaction + + align:start position:0% +coefficient and the uh reaction + + + align:start position:0% +coefficient and the uh reaction +coordinate if we divide by N Sub + + align:start position:0% +coordinate if we divide by N Sub + + + align:start position:0% +coordinate if we divide by N Sub +a denominator and + + align:start position:0% +a denominator and + + + align:start position:0% +a denominator and +numerator above I get the mole fractions + + align:start position:0% +numerator above I get the mole fractions + + + align:start position:0% +numerator above I get the mole fractions +the initial mole fractions below I get + + align:start position:0% +the initial mole fractions below I get + + + align:start position:0% +the initial mole fractions below I get +one and Epsilon over n sub a I call it + + align:start position:0% +one and Epsilon over n sub a I call it + + + align:start position:0% +one and Epsilon over n sub a I call it +C okay so each Mo + + align:start position:0% + + + + align:start position:0% + +fraction depends on the initial mole + + align:start position:0% +fraction depends on the initial mole + + + align:start position:0% +fraction depends on the initial mole +fractions and on a + + align:start position:0% +fractions and on a + + + align:start position:0% +fractions and on a +single variable + + align:start position:0% +single variable + + + align:start position:0% +single variable +C so if I substitute that in the low of + + align:start position:0% +C so if I substitute that in the low of + + + align:start position:0% +C so if I substitute that in the low of +mass + + align:start position:0% +mass + + + align:start position:0% +mass +action this gives us one equation in the + + align:start position:0% +action this gives us one equation in the + + + align:start position:0% +action this gives us one equation in the +single variable + + align:start position:0% +single variable + + + align:start position:0% +single variable +C and therefore I can solve for + + align:start position:0% +C and therefore I can solve for + + + align:start position:0% +C and therefore I can solve for +C given the initial compositions and + + align:start position:0% +C given the initial compositions and + + + align:start position:0% +C given the initial compositions and +theal composition for this problem is + + align:start position:0% +theal composition for this problem is + + + align:start position:0% +theal composition for this problem is +given somewhere uh here can look up the + + align:start position:0% + + + + align:start position:0% + +details so once I know C I go back here + + align:start position:0% +details so once I know C I go back here + + + align:start position:0% +details so once I know C I go back here +and I have the entire composition so I + + align:start position:0% +and I have the entire composition so I + + + align:start position:0% +and I have the entire composition so I +have the M fractions of all the various + + align:start position:0% +have the M fractions of all the various + + + align:start position:0% +have the M fractions of all the various +constituents so that how that's how you + + align:start position:0% +constituents so that how that's how you + + + align:start position:0% +constituents so that how that's how you +compute chemical equilibrium uh + + align:start position:0% +compute chemical equilibrium uh + + + align:start position:0% +compute chemical equilibrium uh +compositions using Mo fraction + + align:start position:0% + + + + align:start position:0% + +clearly if you have more than one + + align:start position:0% +clearly if you have more than one + + + align:start position:0% +clearly if you have more than one +reaction in + + align:start position:0% +reaction in + + + align:start position:0% +reaction in +play you have one law of mass + + align:start position:0% +play you have one law of mass + + + align:start position:0% +play you have one law of mass +action per + + align:start position:0% +action per + + + align:start position:0% +action per +reaction so each reaction brings in a + + align:start position:0% +reaction so each reaction brings in a + + + align:start position:0% +reaction so each reaction brings in a +new unknown which is the reaction + + align:start position:0% +new unknown which is the reaction + + + align:start position:0% +new unknown which is the reaction +coordinate so if you have three + + align:start position:0% +coordinate so if you have three + + + align:start position:0% +coordinate so if you have three +reactions or five say for the example + + align:start position:0% +reactions or five say for the example + + + align:start position:0% +reactions or five say for the example +that will follow we have five reactions + + align:start position:0% +that will follow we have five reactions + + + align:start position:0% +that will follow we have five reactions +so you have five know which are + + align:start position:0% +so you have five know which are + + + align:start position:0% +so you have five know which are +the uh reaction coordinates epsilons or + + align:start position:0% +the uh reaction coordinates epsilons or + + + align:start position:0% +the uh reaction coordinates epsilons or +the CES which + + align:start position:0% +the CES which + + + align:start position:0% +the CES which +are the per + + align:start position:0% +are the per + + + align:start position:0% +are the per +mole + + align:start position:0% +mole + + + align:start position:0% +mole +coordinates uh five unknown but you have + + align:start position:0% +coordinates uh five unknown but you have + + + align:start position:0% +coordinates uh five unknown but you have +five equations which are the the + + align:start position:0% +five equations which are the the + + + align:start position:0% +five equations which are the the +corresponding to setting equal to zero + + align:start position:0% +corresponding to setting equal to zero + + + align:start position:0% +corresponding to setting equal to zero +the five um + + align:start position:0% +the five um + + + align:start position:0% +the five um +affinities of each of the reactions + + align:start position:0% +affinities of each of the reactions + + + align:start position:0% +affinities of each of the reactions +so of course you have to compute five + + align:start position:0% +so of course you have to compute five + + + align:start position:0% +so of course you have to compute five +chemical equilibrium constants but then + + align:start position:0% +chemical equilibrium constants but then + + + align:start position:0% +chemical equilibrium constants but then +you have a system of five equations in + + align:start position:0% +you have a system of five equations in + + + align:start position:0% +you have a system of five equations in +five unknowns which gives you uh all uh + + align:start position:0% +five unknowns which gives you uh all uh + + + align:start position:0% +five unknowns which gives you uh all uh +that you + + align:start position:0% + + + + align:start position:0% + +need this is for + + align:start position:0% +need this is for + + + align:start position:0% +need this is for +example I think we we' have seen already + + align:start position:0% +example I think we we' have seen already + + + align:start position:0% +example I think we we' have seen already +part of this table when we did a diotic + + align:start position:0% +part of this table when we did a diotic + + + align:start position:0% +part of this table when we did a diotic +flame temperature for an internal + + align:start position:0% +flame temperature for an internal + + + align:start position:0% +flame temperature for an internal +combustion + + align:start position:0% +combustion + + + align:start position:0% +combustion +engine so here is the is that + + align:start position:0% +engine so here is the is that + + + align:start position:0% +engine so here is the is that +computation that + + align:start position:0% +computation that + + + align:start position:0% +computation that +does at the same time it computes + + align:start position:0% +does at the same time it computes + + + align:start position:0% +does at the same time it computes +the uh the energy + + align:start position:0% +the uh the energy + + + align:start position:0% +the uh the energy +balance that gives you the adiabatic + + align:start position:0% +balance that gives you the adiabatic + + + align:start position:0% +balance that gives you the adiabatic +flame + + align:start position:0% +flame + + + align:start position:0% +flame +temperature in terms uh but + + align:start position:0% +temperature in terms uh but + + + align:start position:0% +temperature in terms uh but +also at the same time it you compute the + + align:start position:0% +also at the same time it you compute the + + + align:start position:0% +also at the same time it you compute the +five + + align:start position:0% +five + + + align:start position:0% +five +equilibrium low of mass + + align:start position:0% +equilibrium low of mass + + + align:start position:0% +equilibrium low of mass +actions and therefore as a result you + + align:start position:0% +actions and therefore as a result you + + + align:start position:0% +actions and therefore as a result you +can compute the compositions of all the + + align:start position:0% +can compute the compositions of all the + + + align:start position:0% +can compute the compositions of all the +various + + align:start position:0% + + + + align:start position:0% + +components notice that these numbers + + align:start position:0% +components notice that these numbers + + + align:start position:0% +components notice that these numbers +this is in mole this is in Mill moles + + align:start position:0% +this is in mole this is in Mill moles + + + align:start position:0% +this is in mole this is in Mill moles +and this is in + + align:start position:0% +and this is in + + + align:start position:0% +and this is in +micromoles uh turns out that U the first + + align:start position:0% +micromoles uh turns out that U the first + + + align:start position:0% +micromoles uh turns out that U the first +two reactions here the dissociation + + align:start position:0% +two reactions here the dissociation + + + align:start position:0% +two reactions here the dissociation +reactions are important in + + align:start position:0% +reactions are important in + + + align:start position:0% +reactions are important in +determining um the thermal aspects of + + align:start position:0% +determining um the thermal aspects of + + + align:start position:0% +determining um the thermal aspects of +the + + align:start position:0% +the + + + align:start position:0% +the +combustion they will affect the thetic + + align:start position:0% +combustion they will affect the thetic + + + align:start position:0% +combustion they will affect the thetic +flame temp flame temperature if you + + align:start position:0% +flame temp flame temperature if you + + + align:start position:0% +flame temp flame temperature if you +don't consider them you overestimate + + align:start position:0% +don't consider them you overestimate + + + align:start position:0% +don't consider them you overestimate +it + + align:start position:0% +it + + + align:start position:0% +it +whereas the last three um give you an + + align:start position:0% +whereas the last three um give you an + + + align:start position:0% +whereas the last three um give you an +estimate of the uh formation of + + align:start position:0% +estimate of the uh formation of + + + align:start position:0% +estimate of the uh formation of +the nitrogen oxides that are pollutants + + align:start position:0% +the nitrogen oxides that are pollutants + + + align:start position:0% +the nitrogen oxides that are pollutants +as you know uh of combustion of + + align:start position:0% +as you know uh of combustion of + + + align:start position:0% +as you know uh of combustion of +combustion products + + align:start position:0% + + + + align:start position:0% + +that correspond to various ways in + + align:start position:0% +that correspond to various ways in + + + align:start position:0% +that correspond to various ways in +which nitrogen and oxygen molecules can + + align:start position:0% +which nitrogen and oxygen molecules can + + + align:start position:0% +which nitrogen and oxygen molecules can +Collide and at high temperatures and uh + + align:start position:0% +Collide and at high temperatures and uh + + + align:start position:0% +Collide and at high temperatures and uh +combine to + + align:start position:0% +combine to + + + align:start position:0% +combine to +form these various + + align:start position:0% + + + + align:start position:0% + +oxides now I told you that um + + align:start position:0% + + + + align:start position:0% + +uh life is not that uh + + align:start position:0% +uh life is not that uh + + + align:start position:0% +uh life is not that uh +simple I + + align:start position:0% + + + + align:start position:0% + +remember collaborator of Professor kek + + align:start position:0% +remember collaborator of Professor kek + + + align:start position:0% +remember collaborator of Professor kek +downstairs who used to say that uh what + + align:start position:0% +downstairs who used to say that uh what + + + align:start position:0% +downstairs who used to say that uh what +I just told you so far is Disneyland + + align:start position:0% +I just told you so far is Disneyland + + + align:start position:0% +I just told you so far is Disneyland +with respect to the real world + + align:start position:0% +with respect to the real world + + + align:start position:0% +with respect to the real world +because even for the simplest uh uh Hy + + align:start position:0% +because even for the simplest uh uh Hy + + + align:start position:0% +because even for the simplest uh uh Hy +carbon which is + + align:start position:0% + + + + align:start position:0% + +hydrogen in order to describe the + + align:start position:0% +hydrogen in order to describe the + + + align:start position:0% +hydrogen in order to describe the +chemical reactions in play and these + + align:start position:0% +chemical reactions in play and these + + + align:start position:0% +chemical reactions in play and these +activated complexes and so on you + + align:start position:0% +activated complexes and so on you + + + align:start position:0% +activated complexes and so on you +need this is the official scheme 24 + + align:start position:0% +need this is the official scheme 24 + + + align:start position:0% +need this is the official scheme 24 +reactions and eight + + align:start position:0% +reactions and eight + + + align:start position:0% +reactions and eight +species and these are the parameters + + align:start position:0% +species and these are the parameters + + + align:start position:0% +species and these are the parameters +that allow you to compute the reaction + + align:start position:0% + + + + align:start position:0% + +rates this is a diagram + + align:start position:0% +rates this is a diagram + + + align:start position:0% +rates this is a diagram +which shows for + + align:start position:0% +which shows for + + + align:start position:0% +which shows for +various hydrocarbons for example ISO + + align:start position:0% +various hydrocarbons for example ISO + + + align:start position:0% +various hydrocarbons for example ISO +octane which is like gasoline say you're + + align:start position:0% +octane which is like gasoline say you're + + + align:start position:0% +octane which is like gasoline say you're +here methane is + + align:start position:0% + + + + align:start position:0% + +here uh and it it gives you in a log + + align:start position:0% +here uh and it it gives you in a log + + + align:start position:0% +here uh and it it gives you in a log +scale the number of species that are + + align:start position:0% +scale the number of species that are + + + align:start position:0% +scale the number of species that are +that you need to consider and the number + + align:start position:0% +that you need to consider and the number + + + align:start position:0% +that you need to consider and the number +of + + align:start position:0% + + + + align:start position:0% + +reactions turns out that the number of + + align:start position:0% +reactions turns out that the number of + + + align:start position:0% +reactions turns out that the number of +reactions is time is about five times + + align:start position:0% +reactions is time is about five times + + + align:start position:0% +reactions is time is about five times +this straight line is an equation uh it + + align:start position:0% +this straight line is an equation uh it + + + align:start position:0% +this straight line is an equation uh it +says that I need five times the number + + align:start position:0% +says that I need five times the number + + + align:start position:0% +says that I need five times the number +of + + align:start position:0% + + + + align:start position:0% + +species hydrogen is really a bit of an + + align:start position:0% +species hydrogen is really a bit of an + + + align:start position:0% +species hydrogen is really a bit of an +exception because uh 5 by 8 is not 24 + + align:start position:0% +exception because uh 5 by 8 is not 24 + + + align:start position:0% +exception because uh 5 by 8 is not 24 +but uh in any case hydrogen would be + + align:start position:0% +but uh in any case hydrogen would be + + + align:start position:0% +but uh in any case hydrogen would be +here in the skin uh and you see for + + align:start position:0% +here in the skin uh and you see for + + + align:start position:0% +here in the skin uh and you see for +example for a uh + + align:start position:0% +example for a uh + + + align:start position:0% +example for a uh +methane I think you need the + + align:start position:0% +methane I think you need the + + + align:start position:0% +methane I think you need the +um yeah 50 + + align:start position:0% +um yeah 50 + + + align:start position:0% +um yeah 50 +something um species we could read it + + align:start position:0% +something um species we could read it + + + align:start position:0% +something um species we could read it +here and + + align:start position:0% +here and + + + align:start position:0% +here and + + align:start position:0% + + + + align:start position:0% + +reactions at least this is for is true + + align:start position:0% +reactions at least this is for is true + + + align:start position:0% +reactions at least this is for is true +for kinetics whereas for + + align:start position:0% + + + + align:start position:0% + +equilibrium uh we can avoid this kind of + + align:start position:0% +equilibrium uh we can avoid this kind of + + + align:start position:0% +equilibrium uh we can avoid this kind of +complication but but for the + + align:start position:0% +complication but but for the + + + align:start position:0% +complication but but for the +kinetics it's not so simple actually if + + align:start position:0% +kinetics it's not so simple actually if + + + align:start position:0% +kinetics it's not so simple actually if +you look up uh even this is not a + + align:start position:0% +you look up uh even this is not a + + + align:start position:0% +you look up uh even this is not a +settled uh issue because people are + + align:start position:0% +settled uh issue because people are + + + align:start position:0% +settled uh issue because people are +still working on determining these + + align:start position:0% +still working on determining these + + + align:start position:0% +still working on determining these +detail mechanisms for new fuels but also + + align:start position:0% +detail mechanisms for new fuels but also + + + align:start position:0% +detail mechanisms for new fuels but also +for old fuels and now uh there is a lot + + align:start position:0% +for old fuels and now uh there is a lot + + + align:start position:0% +for old fuels and now uh there is a lot +of uh the artificial intelligence is is + + align:start position:0% +of uh the artificial intelligence is is + + + align:start position:0% +of uh the artificial intelligence is is +playing a game also here because + + align:start position:0% +playing a game also here because + + + align:start position:0% +playing a game also here because +developing these schemes with so many + + align:start position:0% +developing these schemes with so many + + + align:start position:0% +developing these schemes with so many +reactions is first of all + + align:start position:0% +reactions is first of all + + + align:start position:0% +reactions is first of all +complicated second it makes life uh + + align:start position:0% +complicated second it makes life uh + + + align:start position:0% +complicated second it makes life uh +uh + + align:start position:0% +uh + + + align:start position:0% +uh +very + + align:start position:0% + + + + align:start position:0% + +uh difficult because you how do you know + + align:start position:0% +uh difficult because you how do you know + + + align:start position:0% +uh difficult because you how do you know +first of all if I have 5,000 uh + + align:start position:0% +first of all if I have 5,000 uh + + + align:start position:0% +first of all if I have 5,000 uh +reactions to be considered how do I know + + align:start position:0% +reactions to be considered how do I know + + + align:start position:0% +reactions to be considered how do I know +that the 5,000 parameters that that + + align:start position:0% +that the 5,000 parameters that that + + + align:start position:0% +that the 5,000 parameters that that +Define the reaction right Ates are are + + align:start position:0% + + + + align:start position:0% + +correct uh + + align:start position:0% +correct uh + + + align:start position:0% +correct uh +and and what if are they all + + align:start position:0% + + + + align:start position:0% + +important so in fact many people are + + align:start position:0% +important so in fact many people are + + + align:start position:0% +important so in fact many people are +working on uh and artificial + + align:start position:0% +working on uh and artificial + + + align:start position:0% +working on uh and artificial +intelligence may help in model reduction + + align:start position:0% +intelligence may help in model reduction + + + align:start position:0% +intelligence may help in model reduction +schemes so you say you start with the + + align:start position:0% +schemes so you say you start with the + + + align:start position:0% +schemes so you say you start with the +complete uh scheme but then you you try + + align:start position:0% +complete uh scheme but then you you try + + + align:start position:0% +complete uh scheme but then you you try +to cut out at least for ranges of + + align:start position:0% +to cut out at least for ranges of + + + align:start position:0% +to cut out at least for ranges of +conditions and do a simplif simplified + + align:start position:0% +conditions and do a simplif simplified + + + align:start position:0% +conditions and do a simplif simplified +model that allows you to to do a good + + align:start position:0% +model that allows you to to do a good + + + align:start position:0% +model that allows you to to do a good +job anyway so uh a lot of and again + + align:start position:0% +job anyway so uh a lot of and again + + + align:start position:0% +job anyway so uh a lot of and again +mentioned Professor kek because he was + + align:start position:0% +mentioned Professor kek because he was + + + align:start position:0% +mentioned Professor kek because he was +one great contributor uh to this issue + + align:start position:0% +one great contributor uh to this issue + + + align:start position:0% +one great contributor uh to this issue +through the rate controlled constrained + + align:start position:0% +through the rate controlled constrained + + + align:start position:0% +through the rate controlled constrained +equilibrium method that uh you might if + + align:start position:0% +equilibrium method that uh you might if + + + align:start position:0% +equilibrium method that uh you might if +you're interested you should uh should + + align:start position:0% +you're interested you should uh should + + + align:start position:0% +you're interested you should uh should +read + + align:start position:0% + + + + align:start position:0% + +about okay now so the affinities at + + align:start position:0% +about okay now so the affinities at + + + align:start position:0% +about okay now so the affinities at +equilibrium are equal to + + align:start position:0% +equilibrium are equal to + + + align:start position:0% +equilibrium are equal to +zero uh here is a another way of of + + align:start position:0% +zero uh here is a another way of of + + + align:start position:0% +zero uh here is a another way of of +saying + + align:start position:0% + + + + align:start position:0% + +it which gives us a + + align:start position:0% + + + + align:start position:0% + +chance know I should say a again or + + align:start position:0% +chance know I should say a again or + + + align:start position:0% +chance know I should say a again or +first chance to use the method of lrange + + align:start position:0% +first chance to use the method of lrange + + + align:start position:0% +first chance to use the method of lrange +multipliers for maximizing + + align:start position:0% +multipliers for maximizing + + + align:start position:0% +multipliers for maximizing +functions subject to + + align:start position:0% +functions subject to + + + align:start position:0% +functions subject to +constraints because after all the + + align:start position:0% +constraints because after all the + + + align:start position:0% +constraints because after all the +chemical equilibrium condition comes as + + align:start position:0% +chemical equilibrium condition comes as + + + align:start position:0% +chemical equilibrium condition comes as +a condition uh from the maximization of + + align:start position:0% +a condition uh from the maximization of + + + align:start position:0% +a condition uh from the maximization of +the + + align:start position:0% + + + + align:start position:0% + +entropy of the entropy of our uh system + + align:start position:0% +entropy of the entropy of our uh system + + + align:start position:0% +entropy of the entropy of our uh system +with chemical reactions so therefore + + align:start position:0% +with chemical reactions so therefore + + + align:start position:0% +with chemical reactions so therefore +this is the we adopt this model model + + align:start position:0% +this is the we adopt this model model + + + align:start position:0% +this is the we adopt this model model +for describing its + + align:start position:0% + + + + align:start position:0% + +entropy where the N the + + align:start position:0% + + + + align:start position:0% + +amounts uh can be varied but only in a + + align:start position:0% +amounts uh can be varied but only in a + + + align:start position:0% +amounts uh can be varied but only in a +constrained way constrained by the + + align:start position:0% +constrained way constrained by the + + + align:start position:0% +constrained way constrained by the +proportionality relations so we + + align:start position:0% +proportionality relations so we + + + align:start position:0% +proportionality relations so we +consider maximize this + + align:start position:0% +consider maximize this + + + align:start position:0% +consider maximize this +function + + align:start position:0% +function + + + align:start position:0% +function +subject to keeping energy volume initial + + align:start position:0% +subject to keeping energy volume initial + + + align:start position:0% +subject to keeping energy volume initial +amounts stomri coefficients fixed and + + align:start position:0% +amounts stomri coefficients fixed and + + + align:start position:0% +amounts stomri coefficients fixed and +varing the constituents only according + + align:start position:0% +varing the constituents only according + + + align:start position:0% +varing the constituents only according +to these equations so this is a + + align:start position:0% +to these equations so this is a + + + align:start position:0% +to these equations so this is a +constrained maximization + + align:start position:0% +constrained maximization + + + align:start position:0% +constrained maximization +problem and as you may + + align:start position:0% +problem and as you may + + + align:start position:0% +problem and as you may +know I'm sure you've seen it somewhere + + align:start position:0% +know I'm sure you've seen it somewhere + + + align:start position:0% +know I'm sure you've seen it somewhere +else + + align:start position:0% +else + + + align:start position:0% +else +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um the method of lrange multipliers + + align:start position:0% +um the method of lrange multipliers + + + align:start position:0% +um the method of lrange multipliers +consists in taking the the function you + + align:start position:0% +consists in taking the the function you + + + align:start position:0% +consists in taking the the function you +want to maximize and + + align:start position:0% +want to maximize and + + + align:start position:0% +want to maximize and +subtracting uh uh the constraints each + + align:start position:0% +subtracting uh uh the constraints each + + + align:start position:0% +subtracting uh uh the constraints each +one multiplied by its own undetermined + + align:start position:0% +one multiplied by its own undetermined + + + align:start position:0% +one multiplied by its own undetermined +parameter + + align:start position:0% +parameter + + + align:start position:0% +parameter +Lambda and so I write the constraint + + align:start position:0% +Lambda and so I write the constraint + + + align:start position:0% +Lambda and so I write the constraint +constraint by putting everything on one + + align:start position:0% +constraint by putting everything on one + + + align:start position:0% +constraint by putting everything on one +side and setting it to zero and that + + align:start position:0% +side and setting it to zero and that + + + align:start position:0% +side and setting it to zero and that +that thing on the one side is the thing + + align:start position:0% +that thing on the one side is the thing + + + align:start position:0% +that thing on the one side is the thing +that is multiplied by the lrange + + align:start position:0% +that is multiplied by the lrange + + + align:start position:0% +that is multiplied by the lrange +multiplier so now I have a + + align:start position:0% +multiplier so now I have a + + + align:start position:0% +multiplier so now I have a +function in which I have the R + + align:start position:0% +function in which I have the R + + + align:start position:0% +function in which I have the R +multipliers I have the N I have the + + align:start position:0% +multipliers I have the N I have the + + + align:start position:0% +multipliers I have the N I have the +epsilons and I want to maximize this uh + + align:start position:0% +epsilons and I want to maximize this uh + + + align:start position:0% +epsilons and I want to maximize this uh +function so essentially need to take the + + align:start position:0% +function so essentially need to take the + + + align:start position:0% +function so essentially need to take the +derivative with respect and set it equal + + align:start position:0% +derivative with respect and set it equal + + + align:start position:0% +derivative with respect and set it equal +to zero with respect to those the + + align:start position:0% +to zero with respect to those the + + + align:start position:0% +to zero with respect to those the +derivative with respect to those + + align:start position:0% +derivative with respect to those + + + align:start position:0% +derivative with respect to those +variables that + + align:start position:0% +variables that + + + align:start position:0% +variables that +are um + + align:start position:0% + + + + align:start position:0% + +undetermined so the n and the Epsilon so + + align:start position:0% +undetermined so the n and the Epsilon so + + + align:start position:0% +undetermined so the n and the Epsilon so +I take the derivative of L with respect + + align:start position:0% +I take the derivative of L with respect + + + align:start position:0% +I take the derivative of L with respect +to n + + align:start position:0% + + + + align:start position:0% + +so uh I get one contribution + + align:start position:0% +so uh I get one contribution + + + align:start position:0% +so uh I get one contribution +from s from the entropy the derivative + + align:start position:0% +from s from the entropy the derivative + + + align:start position:0% +from s from the entropy the derivative +of s with respect to n this is equal to + + align:start position:0% +of s with respect to n this is equal to + + + align:start position:0% +of s with respect to n this is equal to +the minus of the St of the minus equal + + align:start position:0% +the minus of the St of the minus equal + + + align:start position:0% +the minus of the St of the minus equal +potential over the + + align:start position:0% +potential over the + + + align:start position:0% +potential over the +temperature and then when I take the + + align:start position:0% +temperature and then when I take the + + + align:start position:0% +temperature and then when I take the +derivative with respect to N I also have + + align:start position:0% +derivative with respect to N I also have + + + align:start position:0% +derivative with respect to N I also have +a contribution from here because this is + + align:start position:0% +a contribution from here because this is + + + align:start position:0% +a contribution from here because this is +an + + align:start position:0% +an + + + align:start position:0% +an +N which is minus Lambda and that's this + + align:start position:0% +N which is minus Lambda and that's this + + + align:start position:0% +N which is minus Lambda and that's this +minus Lambda + + align:start position:0% +minus Lambda + + + align:start position:0% +minus Lambda +here this has to be set to be equal to + + align:start position:0% +here this has to be set to be equal to + + + align:start position:0% +here this has to be set to be equal to +zero for this Max this lran function to + + align:start position:0% +zero for this Max this lran function to + + + align:start position:0% +zero for this Max this lran function to +be unconstrained maximum so apply the + + align:start position:0% +be unconstrained maximum so apply the + + + align:start position:0% +be unconstrained maximum so apply the +rules of maximizing function so you set + + align:start position:0% +rules of maximizing function so you set + + + align:start position:0% +rules of maximizing function so you set +the derivative is equal to + + align:start position:0% +the derivative is equal to + + + align:start position:0% +the derivative is equal to +zero so this + + align:start position:0% +zero so this + + + align:start position:0% +zero so this +says Ah okay the lrange multiplier must + + align:start position:0% +says Ah okay the lrange multiplier must + + + align:start position:0% +says Ah okay the lrange multiplier must +be equal to uh the chemical potential + + align:start position:0% +be equal to uh the chemical potential + + + align:start position:0% +be equal to uh the chemical potential +over T fine + + align:start position:0% +over T fine + + + align:start position:0% +over T fine +then I take the derivative of L with + + align:start position:0% +then I take the derivative of L with + + + align:start position:0% +then I take the derivative of L with +respect to + + align:start position:0% + + + + align:start position:0% + +Epsilon okay I pick up nothing from here + + align:start position:0% +Epsilon okay I pick up nothing from here + + + align:start position:0% +Epsilon okay I pick up nothing from here +because the Epsilon doesn't appear here + + align:start position:0% +because the Epsilon doesn't appear here + + + align:start position:0% +because the Epsilon doesn't appear here +Epsilon is only + + align:start position:0% +Epsilon is only + + + align:start position:0% +Epsilon is only +there so it it's with a plus because + + align:start position:0% +there so it it's with a plus because + + + align:start position:0% +there so it it's with a plus because +there's two minuses here and the Epsilon + + align:start position:0% +there's two minuses here and the Epsilon + + + align:start position:0% +there's two minuses here and the Epsilon +J picks + + align:start position:0% +J picks + + + align:start position:0% +J picks +up uh the stochiometric coefficients of + + align:start position:0% +up uh the stochiometric coefficients of + + + align:start position:0% +up uh the stochiometric coefficients of +uh of the J + + align:start position:0% +uh of the J + + + align:start position:0% +uh of the J +reaction multiplied by the lrange + + align:start position:0% +reaction multiplied by the lrange + + + align:start position:0% +reaction multiplied by the lrange +multipliers so this is what we get but + + align:start position:0% +multipliers so this is what we get but + + + align:start position:0% +multipliers so this is what we get but +since the LR multipliers is minus mu / T + + align:start position:0% +since the LR multipliers is minus mu / T + + + align:start position:0% +since the LR multipliers is minus mu / T +we can + + align:start position:0% +we can + + + align:start position:0% +we can +substitute and + + align:start position:0% +substitute and + + + align:start position:0% +substitute and +that is the expression of what we called + + align:start position:0% +that is the expression of what we called + + + align:start position:0% +that is the expression of what we called +the Affinity of the + + align:start position:0% +the Affinity of the + + + align:start position:0% +the Affinity of the +reaction and taking the derivative equal + + align:start position:0% +reaction and taking the derivative equal + + + align:start position:0% +reaction and taking the derivative equal +to zero and therefore imposes the + + align:start position:0% +to zero and therefore imposes the + + + align:start position:0% +to zero and therefore imposes the +Affinity to be equal to zero okay so + + align:start position:0% +Affinity to be equal to zero okay so + + + align:start position:0% +Affinity to be equal to zero okay so +just another way of deriving the + + align:start position:0% +just another way of deriving the + + + align:start position:0% +just another way of deriving the +chemical equilibrium + + align:start position:0% + + + + align:start position:0% + +conditions however this is useful also + + align:start position:0% +conditions however this is useful also + + + align:start position:0% +conditions however this is useful also +to introduce + + align:start position:0% + + + + align:start position:0% + +another + + align:start position:0% +another + + + align:start position:0% +another +possibility precisely + + align:start position:0% +possibility precisely + + + align:start position:0% +possibility precisely +because we have so + + align:start position:0% +because we have so + + + align:start position:0% +because we have so +many chemical reactions and and chemical + + align:start position:0% +many chemical reactions and and chemical + + + align:start position:0% +many chemical reactions and and chemical +species in + + align:start position:0% +species in + + + align:start position:0% +species in +play + + align:start position:0% +play + + + align:start position:0% +play +uh maybe we can + + align:start position:0% +uh maybe we can + + + align:start position:0% +uh maybe we can +also uh work and people do work in fact + + align:start position:0% +also uh work and people do work in fact + + + align:start position:0% +also uh work and people do work in fact +uh uh in all the simulation softwares + + align:start position:0% +uh uh in all the simulation softwares + + + align:start position:0% +uh uh in all the simulation softwares +commercial softwares that have + + align:start position:0% +commercial softwares that have + + + align:start position:0% +commercial softwares that have +properties for uh + + align:start position:0% +properties for uh + + + align:start position:0% +properties for uh +Computing + + align:start position:0% +Computing + + + align:start position:0% +Computing +equilibrium uh they are based on this + + align:start position:0% +equilibrium uh they are based on this + + + align:start position:0% +equilibrium uh they are based on this +concept of complete chemical equilibrium + + align:start position:0% +concept of complete chemical equilibrium + + + align:start position:0% +concept of complete chemical equilibrium +what what is it + + align:start position:0% +what what is it + + + align:start position:0% +what what is it +the idea is all right why should I + + align:start position:0% +the idea is all right why should I + + + align:start position:0% +the idea is all right why should I +list uh such a large number of reactions + + align:start position:0% +list uh such a large number of reactions + + + align:start position:0% +list uh such a large number of reactions +couldn't just just say that uh all + + align:start position:0% +couldn't just just say that uh all + + + align:start position:0% +couldn't just just say that uh all +reactions are + + align:start position:0% +reactions are + + + align:start position:0% +reactions are +possible all conceivable + + align:start position:0% +possible all conceivable + + + align:start position:0% +possible all conceivable +reactions so instead of listing the + + align:start position:0% +reactions so instead of listing the + + + align:start position:0% +reactions so instead of listing the +reactions let's assume that all + + align:start position:0% +reactions let's assume that all + + + align:start position:0% +reactions let's assume that all +conceivable reactions are possible in + + align:start position:0% +conceivable reactions are possible in + + + align:start position:0% +conceivable reactions are possible in +order to compute chemical + + align:start position:0% + + + + align:start position:0% + +equ so what would be the only constraint + + align:start position:0% +equ so what would be the only constraint + + + align:start position:0% +equ so what would be the only constraint +in chemical + + align:start position:0% +in chemical + + + align:start position:0% +in chemical +reactions chemical reactions the only + + align:start position:0% +reactions chemical reactions the only + + + align:start position:0% +reactions chemical reactions the only +thing that they cannot do is to change + + align:start position:0% +thing that they cannot do is to change + + + align:start position:0% +thing that they cannot do is to change +the nuclei so the inventory of nuclei in + + align:start position:0% +the nuclei so the inventory of nuclei in + + + align:start position:0% +the nuclei so the inventory of nuclei in +your mixture is + + align:start position:0% +your mixture is + + + align:start position:0% +your mixture is +fixed so the constraints here is count + + align:start position:0% +fixed so the constraints here is count + + + align:start position:0% +fixed so the constraints here is count +the number of nuclei in your mixture + + align:start position:0% +the number of nuclei in your mixture + + + align:start position:0% +the number of nuclei in your mixture +initial you you must be sure that they + + align:start position:0% +initial you you must be sure that they + + + align:start position:0% +initial you you must be sure that they +remain what they were otherwise you + + align:start position:0% +remain what they were otherwise you + + + align:start position:0% +remain what they were otherwise you +would be doing nuclear uh + + align:start position:0% +would be doing nuclear uh + + + align:start position:0% +would be doing nuclear uh +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +okay so the idea is uh you want to + + align:start position:0% +okay so the idea is uh you want to + + + align:start position:0% +okay so the idea is uh you want to +maximize is usually the entropy because + + align:start position:0% +maximize is usually the entropy because + + + align:start position:0% +maximize is usually the entropy because +we are applying the maximum entropy + + align:start position:0% +we are applying the maximum entropy + + + align:start position:0% +we are applying the maximum entropy +principle now the constraint is that I + + align:start position:0% +principle now the constraint is that I + + + align:start position:0% +principle now the constraint is that I +want to con constraint the this c subk c + + align:start position:0% +want to con constraint the this c subk c + + + align:start position:0% +want to con constraint the this c subk c +is the + + align:start position:0% +is the + + + align:start position:0% +is the +number of uh nuclei of a given + + align:start position:0% +number of uh nuclei of a given + + + align:start position:0% +number of uh nuclei of a given +type and they are given + + align:start position:0% +type and they are given + + + align:start position:0% +type and they are given +initially this way and at a generic + + align:start position:0% +initially this way and at a generic + + + align:start position:0% +initially this way and at a generic +composition this way so what are these + + align:start position:0% +composition this way so what are these + + + align:start position:0% +composition this way so what are these +coefficients a sub I + + align:start position:0% +coefficients a sub I + + + align:start position:0% +coefficients a sub I +K let me explain it with this table + + align:start position:0% +K let me explain it with this table + + + align:start position:0% +K let me explain it with this table +here a sub by K represents for each uh + + align:start position:0% +here a sub by K represents for each uh + + + align:start position:0% +here a sub by K represents for each uh +for the molecule for example uh I say + + align:start position:0% + + + + align:start position:0% + +methane it gives you the number of of + + align:start position:0% +methane it gives you the number of of + + + align:start position:0% +methane it gives you the number of of +nuclei of each type so the first type is + + align:start position:0% +nuclei of each type so the first type is + + + align:start position:0% +nuclei of each type so the first type is +carbon yes in methane there is one + + align:start position:0% +carbon yes in methane there is one + + + align:start position:0% +carbon yes in methane there is one +carbon so I put a one here there are + + align:start position:0% +carbon so I put a one here there are + + + align:start position:0% +carbon so I put a one here there are +four + + align:start position:0% +four + + + align:start position:0% +four +hydrogens so I put a four there are no + + align:start position:0% +hydrogens so I put a four there are no + + + align:start position:0% +hydrogens so I put a four there are no +oxyg no + + align:start position:0% +oxyg no + + + align:start position:0% +oxyg no +nitrogens okay so these are the uh + + align:start position:0% +nitrogens okay so these are the uh + + + align:start position:0% +nitrogens okay so these are the uh +Matrix of um com nuclear nuclear + + align:start position:0% +Matrix of um com nuclear nuclear + + + align:start position:0% +Matrix of um com nuclear nuclear +composition of the uh of your various + + align:start position:0% +composition of the uh of your various + + + align:start position:0% +composition of the uh of your various +constituents so you list the + + align:start position:0% +constituents so you list the + + + align:start position:0% +constituents so you list the +constituents and you for each one of + + align:start position:0% +constituents and you for each one of + + + align:start position:0% +constituents and you for each one of +them you put how many nuclei of each + + align:start position:0% +them you put how many nuclei of each + + + align:start position:0% +them you put how many nuclei of each +kind there is it turns out that for a + + align:start position:0% +kind there is it turns out that for a + + + align:start position:0% +kind there is it turns out that for a +very large number of organic + + align:start position:0% +very large number of organic + + + align:start position:0% +very large number of organic +molecules uh the number of nuclei is + + align:start position:0% +molecules uh the number of nuclei is + + + align:start position:0% +molecules uh the number of nuclei is +very + + align:start position:0% +very + + + align:start position:0% +very +small carbon hydrogen oxygen nitrogen + + align:start position:0% +small carbon hydrogen oxygen nitrogen + + + align:start position:0% +small carbon hydrogen oxygen nitrogen +what else yeah maybe argon because it's + + align:start position:0% +what else yeah maybe argon because it's + + + align:start position:0% +what else yeah maybe argon because it's +present in air + + align:start position:0% +present in air + + + align:start position:0% +present in air +but um + + align:start position:0% +but um + + + align:start position:0% +but um +okay so that means + + align:start position:0% +okay so that means + + + align:start position:0% +okay so that means +since the index that runs here so the + + align:start position:0% +since the index that runs here so the + + + align:start position:0% +since the index that runs here so the +number of constraints is that you have + + align:start position:0% +number of constraints is that you have + + + align:start position:0% +number of constraints is that you have +is the count of the nuclei in these + + align:start position:0% +is the count of the nuclei in these + + + align:start position:0% +is the count of the nuclei in these +columns so you have few + + align:start position:0% +columns so you have few + + + align:start position:0% +columns so you have few +constraints just as many at kinds of + + align:start position:0% +constraints just as many at kinds of + + + align:start position:0% +constraints just as many at kinds of +atoms are around + + align:start position:0% +atoms are around + + + align:start position:0% +atoms are around +okay so with the initial composition and + + align:start position:0% +okay so with the initial composition and + + + align:start position:0% +okay so with the initial composition and +sub a + + align:start position:0% +sub a + + + align:start position:0% +sub a +uh sub a and with this table you compute + + align:start position:0% +uh sub a and with this table you compute + + + align:start position:0% +uh sub a and with this table you compute +how many you have + + align:start position:0% +how many you have + + + align:start position:0% +how many you have +initially and you have to make sure by + + align:start position:0% +initially and you have to make sure by + + + align:start position:0% +initially and you have to make sure by +this maximization constraint + + align:start position:0% +this maximization constraint + + + align:start position:0% +this maximization constraint +maximization that also at equilibrium + + align:start position:0% +maximization that also at equilibrium + + + align:start position:0% +maximization that also at equilibrium +you have that same number + + align:start position:0% +you have that same number + + + align:start position:0% +you have that same number +of of of of + + align:start position:0% +of of of of + + + align:start position:0% +of of of of +nuclei everything else is allowed so + + align:start position:0% +nuclei everything else is allowed so + + + align:start position:0% +nuclei everything else is allowed so +that means you assume that there will be + + align:start position:0% +that means you assume that there will be + + + align:start position:0% +that means you assume that there will be +some chemical reactions that will do + + align:start position:0% +some chemical reactions that will do + + + align:start position:0% +some chemical reactions that will do +that change will take you to that + + align:start position:0% +that change will take you to that + + + align:start position:0% +that change will take you to that +equilibrium because everything is + + align:start position:0% +equilibrium because everything is + + + align:start position:0% +equilibrium because everything is +allowed provided the nuclear + + align:start position:0% +allowed provided the nuclear + + + align:start position:0% +allowed provided the nuclear +conservation is is done is + + align:start position:0% +conservation is is done is + + + align:start position:0% +conservation is is done is +satisfied so again to proceed we we we + + align:start position:0% +satisfied so again to proceed we we we + + + align:start position:0% +satisfied so again to proceed we we we +assign a lrange multiplier to each + + align:start position:0% +assign a lrange multiplier to each + + + align:start position:0% +assign a lrange multiplier to each +constraint and the constraint here uh is + + align:start position:0% +constraint and the constraint here uh is + + + align:start position:0% +constraint and the constraint here uh is +written uh by taking on the same side + + align:start position:0% +written uh by taking on the same side + + + align:start position:0% +written uh by taking on the same side +here these two so it's n i minus initial + + align:start position:0% +here these two so it's n i minus initial + + + align:start position:0% +here these two so it's n i minus initial +n i * a + + align:start position:0% +n i * a + + + align:start position:0% +n i * a +summation and then you multiply each one + + align:start position:0% +summation and then you multiply each one + + + align:start position:0% +summation and then you multiply each one +by the L + + align:start position:0% + + + + align:start position:0% + +multiply and now you take you + + align:start position:0% +multiply and now you take you + + + align:start position:0% +multiply and now you take you +impose that this function be + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +maximum so you impose the derivative + + align:start position:0% +maximum so you impose the derivative + + + align:start position:0% +maximum so you impose the derivative +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +zero with respect to the only variable + + align:start position:0% +zero with respect to the only variable + + + align:start position:0% +zero with respect to the only variable +which is the NS the an + + align:start position:0% + + + + align:start position:0% + +subbi so you do + + align:start position:0% +subbi so you do + + + align:start position:0% +subbi so you do +that and of course the this one still + + align:start position:0% +that and of course the this one still + + + align:start position:0% +that and of course the this one still +gives you the chemical potential over + + align:start position:0% +gives you the chemical potential over + + + align:start position:0% +gives you the chemical potential over +the temperature and this uh + + align:start position:0% +the temperature and this uh + + + align:start position:0% +the temperature and this uh +here and gives you the summation over K + + align:start position:0% +here and gives you the summation over K + + + align:start position:0% +here and gives you the summation over K +of Lambda K time a i + + align:start position:0% +of Lambda K time a i + + + align:start position:0% +of Lambda K time a i +k + + align:start position:0% +k + + + align:start position:0% +k +now for example let's + + align:start position:0% +now for example let's + + + align:start position:0% +now for example let's +assume uh ideal gas + + align:start position:0% +assume uh ideal gas + + + align:start position:0% +assume uh ideal gas +mixture or ideal + + align:start position:0% + + + + align:start position:0% + +Behavior like this chemical potential + + align:start position:0% +Behavior like this chemical potential + + + align:start position:0% +Behavior like this chemical potential +goes with the logarithm of + + align:start position:0% + + + + align:start position:0% + +Y so you substitute it up + + align:start position:0% +Y so you substitute it up + + + align:start position:0% +Y so you substitute it up +there and so you obain an equation since + + align:start position:0% +there and so you obain an equation since + + + align:start position:0% +there and so you obain an equation since +this must be equal to zero you get an + + align:start position:0% +this must be equal to zero you get an + + + align:start position:0% +this must be equal to zero you get an +equation that gives you the log of Y in + + align:start position:0% +equation that gives you the log of Y in + + + align:start position:0% +equation that gives you the log of Y in +terms + + align:start position:0% +terms + + + align:start position:0% +terms +of this chemical potential of the pure + + align:start position:0% +of this chemical potential of the pure + + + align:start position:0% +of this chemical potential of the pure +component and this summation of the + + align:start position:0% +component and this summation of the + + + align:start position:0% +component and this summation of the +lrange + + align:start position:0% +lrange + + + align:start position:0% +lrange +multipliers times these coefficients of + + align:start position:0% +multipliers times these coefficients of + + + align:start position:0% +multipliers times these coefficients of +the + + align:start position:0% + + + + align:start position:0% + +Matrix so this is the this gives you the + + align:start position:0% +Matrix so this is the this gives you the + + + align:start position:0% +Matrix so this is the this gives you the +composition but it is in terms of lrange + + align:start position:0% +composition but it is in terms of lrange + + + align:start position:0% +composition but it is in terms of lrange +multipliers so you need in this case + + align:start position:0% +multipliers so you need in this case + + + align:start position:0% +multipliers so you need in this case +four lrange multipliers how do I + + align:start position:0% +four lrange multipliers how do I + + + align:start position:0% +four lrange multipliers how do I +determine the lar multipliers as + + align:start position:0% +determine the lar multipliers as + + + align:start position:0% +determine the lar multipliers as +typically in the method uh you to + + align:start position:0% +typically in the method uh you to + + + align:start position:0% +typically in the method uh you to +substitute the solution back into the + + align:start position:0% +substitute the solution back into the + + + align:start position:0% +substitute the solution back into the +constraints and that will give you an + + align:start position:0% +constraints and that will give you an + + + align:start position:0% +constraints and that will give you an +equation that allows you to compute the + + align:start position:0% +equation that allows you to compute the + + + align:start position:0% +equation that allows you to compute the +uh multipliers so I take this + + align:start position:0% +uh multipliers so I take this + + + align:start position:0% +uh multipliers so I take this +expression and put it here in order to + + align:start position:0% +expression and put it here in order to + + + align:start position:0% +expression and put it here in order to +compute uh + + align:start position:0% +compute uh + + + align:start position:0% +compute uh +the uh the amount of nuclei that it + + align:start position:0% +the uh the amount of nuclei that it + + + align:start position:0% +the uh the amount of nuclei that it +implies okay so this is the ends then + + align:start position:0% +implies okay so this is the ends then + + + align:start position:0% +implies okay so this is the ends then +the ends can be m can be n n subis can + + align:start position:0% +the ends can be m can be n n subis can + + + align:start position:0% +the ends can be m can be n n subis can +be computed as n times the mole + + align:start position:0% +be computed as n times the mole + + + align:start position:0% +be computed as n times the mole +fractions all right so this is an + + align:start position:0% +fractions all right so this is an + + + align:start position:0% +fractions all right so this is an +equation or actually it's a system of + + align:start position:0% +equation or actually it's a system of + + + align:start position:0% +equation or actually it's a system of +four + + align:start position:0% + + + + align:start position:0% + +equations because I know the initial + + align:start position:0% +equations because I know the initial + + + align:start position:0% +equations because I know the initial +amounts of the of the nuclei so I know + + align:start position:0% +amounts of the of the nuclei so I know + + + align:start position:0% +amounts of the of the nuclei so I know +the left hand + + align:start position:0% +the left hand + + + align:start position:0% +the left hand +side and the only unknowns are the + + align:start position:0% +side and the only unknowns are the + + + align:start position:0% +side and the only unknowns are the +um lrange multipliers so I can solve + + align:start position:0% +um lrange multipliers so I can solve + + + align:start position:0% +um lrange multipliers so I can solve +this four system four by four system + + align:start position:0% +this four system four by four system + + + align:start position:0% +this four system four by four system +four equations in four unknowns and get + + align:start position:0% +four equations in four unknowns and get + + + align:start position:0% +four equations in four unknowns and get +the lrange multipliers as a function of + + align:start position:0% +the lrange multipliers as a function of + + + align:start position:0% +the lrange multipliers as a function of +the initial composition I plug it back + + align:start position:0% +the initial composition I plug it back + + + align:start position:0% +the initial composition I plug it back +here and then I have the mole fractions + + align:start position:0% +here and then I have the mole fractions + + + align:start position:0% +here and then I have the mole fractions +and + + align:start position:0% +and + + + align:start position:0% +and +notice + + align:start position:0% +notice + + + align:start position:0% +notice +that uh it's very interesting + + align:start position:0% +that uh it's very interesting + + + align:start position:0% +that uh it's very interesting +because uh we didn't put any limit to + + align:start position:0% +because uh we didn't put any limit to + + + align:start position:0% +because uh we didn't put any limit to +the number of chemical compounds that + + align:start position:0% +the number of chemical compounds that + + + align:start position:0% +the number of chemical compounds that +you can + + align:start position:0% +you can + + + align:start position:0% +you can +consider so this L list can be + + align:start position:0% +consider so this L list can be + + + align:start position:0% +consider so this L list can be +as long as you + + align:start position:0% +as long as you + + + align:start position:0% +as long as you +please you could take the entire J of + + align:start position:0% +please you could take the entire J of + + + align:start position:0% +please you could take the entire J of +tables uh or uh you can just consider + + align:start position:0% +tables uh or uh you can just consider + + + align:start position:0% +tables uh or uh you can just consider +the ones that you want and uh and this + + align:start position:0% +the ones that you want and uh and this + + + align:start position:0% +the ones that you want and uh and this +expression will give you the mole + + align:start position:0% +expression will give you the mole + + + align:start position:0% +expression will give you the mole +fractions of anything that you're + + align:start position:0% +fractions of anything that you're + + + align:start position:0% +fractions of anything that you're +interested + + align:start position:0% + + + + align:start position:0% + +in + + align:start position:0% +in + + + align:start position:0% +in +and this + + align:start position:0% + + + + align:start position:0% + +method was is was implemented by Gordon + + align:start position:0% +method was is was implemented by Gordon + + + align:start position:0% +method was is was implemented by Gordon +and McBride uh in the 50s I believe and + + align:start position:0% +and McBride uh in the 50s I believe and + + + align:start position:0% +and McBride uh in the 50s I believe and +it is still um the method used um in + + align:start position:0% +it is still um the method used um in + + + align:start position:0% +it is still um the method used um in +almost all + + align:start position:0% +almost all + + + align:start position:0% +almost all +softwares I know it very well because + + align:start position:0% +softwares I know it very well because + + + align:start position:0% +softwares I know it very well because +when I started when I did my masters uh + + align:start position:0% +when I started when I did my masters uh + + + align:start position:0% +when I started when I did my masters uh +with Professor + + align:start position:0% +with Professor + + + align:start position:0% +with Professor +kek uh I worked for one year uh and + + align:start position:0% +kek uh I worked for one year uh and + + + align:start position:0% +kek uh I worked for one year uh and +those times we didn't have a + + align:start position:0% +those times we didn't have a + + + align:start position:0% +those times we didn't have a +uh easy computerss the computer building + + align:start position:0% +uh easy computerss the computer building + + + align:start position:0% +uh easy computerss the computer building +was uh like a building uh near the + + align:start position:0% +was uh like a building uh near the + + + align:start position:0% +was uh like a building uh near the +nuclear engineering department and uh he + + align:start position:0% +nuclear engineering department and uh he + + + align:start position:0% +nuclear engineering department and uh he +gave + + align:start position:0% +gave + + + align:start position:0% +gave +me this computer program was a set of + + align:start position:0% +me this computer program was a set of + + + align:start position:0% +me this computer program was a set of +cards like a thousand or 2,000 cards in + + align:start position:0% +cards like a thousand or 2,000 cards in + + + align:start position:0% +cards like a thousand or 2,000 cards in +a box for the program something that + + align:start position:0% +a box for the program something that + + + align:start position:0% +a box for the program something that +today I think stays in like uh maybe + + align:start position:0% +today I think stays in like uh maybe + + + align:start position:0% +today I think stays in like uh maybe +28k + + align:start position:0% +28k + + + align:start position:0% +28k +kilobytes and another box + + align:start position:0% +kilobytes and another box + + + align:start position:0% +kilobytes and another box +with the properties of the + + align:start position:0% +with the properties of the + + + align:start position:0% +with the properties of the +various + + align:start position:0% +various + + + align:start position:0% +various +constituents and uh and he asked me to + + align:start position:0% +constituents and uh and he asked me to + + + align:start position:0% +constituents and uh and he asked me to +implement his model reduction uh method + + align:start position:0% +implement his model reduction uh method + + + align:start position:0% +implement his model reduction uh method +constraint equilibrium method into that + + align:start position:0% +constraint equilibrium method into that + + + align:start position:0% +constraint equilibrium method into that +software which was very nice + + align:start position:0% +software which was very nice + + + align:start position:0% +software which was very nice +start uh here and now I notice also that + + align:start position:0% +start uh here and now I notice also that + + + align:start position:0% +start uh here and now I notice also that +there is something I have to correct + + align:start position:0% +there is something I have to correct + + + align:start position:0% +there is something I have to correct +here because is it plus or is it + + align:start position:0% +here because is it plus or is it + + + align:start position:0% +here because is it plus or is it +minus I'll figure it out and let let you + + align:start position:0% +minus I'll figure it out and let let you + + + align:start position:0% +minus I'll figure it out and let let you +know okay so I think we are done for + + align:start position:0% +know okay so I think we are done for + + + align:start position:0% +know okay so I think we are done for +today \ No newline at end of file diff --git a/IpFIp68ODNI.txt b/IpFIp68ODNI.txt new file mode 100644 index 0000000000000000000000000000000000000000..0545804851491e9a609f8167fcd42bf426436a13 --- /dev/null +++ b/IpFIp68ODNI.txt @@ -0,0 +1,10784 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a creative commons license your support + + align:start position:0% +a creative commons license your support + + + align:start position:0% +a creative commons license your support +will help mit opencourseware continue to + + align:start position:0% +will help mit opencourseware continue to + + + align:start position:0% +will help mit opencourseware continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of mit courses + + align:start position:0% +materials from hundreds of mit courses + + + align:start position:0% +materials from hundreds of mit courses +visit mit opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +right okay so i think this was where we + + align:start position:0% +right okay so i think this was where we + + + align:start position:0% +right okay so i think this was where we +were up to i wasn't here last time so i + + align:start position:0% +were up to i wasn't here last time so i + + + align:start position:0% +were up to i wasn't here last time so i +don't really know but uh george + + align:start position:0% +don't really know but uh george + + + align:start position:0% +don't really know but uh george +told me that this this was where you're + + align:start position:0% +told me that this this was where you're + + + align:start position:0% +told me that this this was where you're +up to so that's where i'm gonna carry on + + align:start position:0% +up to so that's where i'm gonna carry on + + + align:start position:0% +up to so that's where i'm gonna carry on +from + + align:start position:0% +from + + + align:start position:0% +from +uh and uh so um this section is all + + align:start position:0% +uh and uh so um this section is all + + + align:start position:0% +uh and uh so um this section is all +about um imaging + + align:start position:0% +about um imaging + + + align:start position:0% +about um imaging +uh and resolution and it starts off here + + align:start position:0% +uh and resolution and it starts off here + + + align:start position:0% +uh and resolution and it starts off here +uh looking in uh some strange uh + + align:start position:0% +uh looking in uh some strange uh + + + align:start position:0% +uh looking in uh some strange uh +american dictionary + + align:start position:0% +american dictionary + + + align:start position:0% +american dictionary +uh there were at the definition of uh + + align:start position:0% +uh there were at the definition of uh + + + align:start position:0% +uh there were at the definition of uh +uh resolution of course you know myself + + align:start position:0% +uh resolution of course you know myself + + + align:start position:0% +uh resolution of course you know myself +coming from oxford i would always use + + align:start position:0% +coming from oxford i would always use + + + align:start position:0% +coming from oxford i would always use +the oxford dictionary i don't know what + + align:start position:0% +the oxford dictionary i don't know what + + + align:start position:0% +the oxford dictionary i don't know what +that says + + align:start position:0% +that says + + + align:start position:0% +that says +but anyway um + + align:start position:0% +but anyway um + + + align:start position:0% +but anyway um +it's quite interesting uh the the verb + + align:start position:0% +it's quite interesting uh the the verb + + + align:start position:0% +it's quite interesting uh the the verb +here uh resolve to break up into + + align:start position:0% +here uh resolve to break up into + + + align:start position:0% +here uh resolve to break up into +constituent parts to analyze + + align:start position:0% +constituent parts to analyze + + + align:start position:0% +constituent parts to analyze +to find an answer to + + align:start position:0% +to find an answer to + + + align:start position:0% +to find an answer to +to solve determine decide whatever but + + align:start position:0% +to solve determine decide whatever but + + + align:start position:0% +to solve determine decide whatever but +anyway i think this first part is the + + align:start position:0% +anyway i think this first part is the + + + align:start position:0% +anyway i think this first part is the +very first thing is the is is a good one + + align:start position:0% +very first thing is the is is a good one + + + align:start position:0% +very first thing is the is is a good one +isn't it so break up in it into its + + align:start position:0% +isn't it so break up in it into its + + + align:start position:0% +isn't it so break up in it into its +constituent parts + + align:start position:0% +constituent parts + + + align:start position:0% +constituent parts +so you look at an image + + align:start position:0% +so you look at an image + + + align:start position:0% +so you look at an image +and you've got to actually + + align:start position:0% +and you've got to actually + + + align:start position:0% +and you've got to actually +determine what the different parts of + + align:start position:0% +determine what the different parts of + + + align:start position:0% +determine what the different parts of +the image really mean and if they sort + + align:start position:0% +the image really mean and if they sort + + + align:start position:0% +the image really mean and if they sort +of merge together you won't be able to + + align:start position:0% +of merge together you won't be able to + + + align:start position:0% +of merge together you won't be able to +resolve what the image is trying to say + + align:start position:0% +resolve what the image is trying to say + + + align:start position:0% +resolve what the image is trying to say +okay so that's what it means + + align:start position:0% + + + + align:start position:0% + +and um + + align:start position:0% +and um + + + align:start position:0% +and um +yeah now there are lots of different + + align:start position:0% +yeah now there are lots of different + + + align:start position:0% +yeah now there are lots of different +ways of determining resolution different + + align:start position:0% +ways of determining resolution different + + + align:start position:0% +ways of determining resolution different +definitions that people apply uh the + + align:start position:0% +definitions that people apply uh the + + + align:start position:0% +definitions that people apply uh the +most uh used one perhaps is the + + align:start position:0% +most uh used one perhaps is the + + + align:start position:0% +most uh used one perhaps is the +rayleigh resolution limit uh which was + + align:start position:0% +rayleigh resolution limit uh which was + + + align:start position:0% +rayleigh resolution limit uh which was +proposed by lord raleigh lord rady was + + align:start position:0% +proposed by lord raleigh lord rady was + + + align:start position:0% +proposed by lord raleigh lord rady was +very interested in astronomy + + align:start position:0% +very interested in astronomy + + + align:start position:0% +very interested in astronomy +uh and uh so + + align:start position:0% +uh and uh so + + + align:start position:0% +uh and uh so +uh he was interested in trying to + + align:start position:0% +uh he was interested in trying to + + + align:start position:0% +uh he was interested in trying to +quantify + + align:start position:0% +quantify + + + align:start position:0% +quantify +uh the imaging of of of uh of stars so + + align:start position:0% +uh the imaging of of of uh of stars so + + + align:start position:0% +uh the imaging of of of uh of stars so +if you look out up in a telescope but + + align:start position:0% +if you look out up in a telescope but + + + align:start position:0% +if you look out up in a telescope but +the sky and you've got two stars very + + align:start position:0% +the sky and you've got two stars very + + + align:start position:0% +the sky and you've got two stars very +close together + + align:start position:0% +close together + + + align:start position:0% +close together +uh then you'll see + + align:start position:0% +uh then you'll see + + + align:start position:0% +uh then you'll see +uh + + align:start position:0% +uh + + + align:start position:0% +uh +like the two images of the stars uh this + + align:start position:0% +like the two images of the stars uh this + + + align:start position:0% +like the two images of the stars uh this +shows two two different separations of + + align:start position:0% +shows two two different separations of + + + align:start position:0% +shows two two different separations of +those two points + + align:start position:0% +those two points + + + align:start position:0% +those two points +uh and um + + align:start position:0% +uh and um + + + align:start position:0% +uh and um +now it's important to note that uh stars + + align:start position:0% +now it's important to note that uh stars + + + align:start position:0% +now it's important to note that uh stars +of course two independent stars would be + + align:start position:0% +of course two independent stars would be + + + align:start position:0% +of course two independent stars would be +completely incoherent with respect to + + align:start position:0% +completely incoherent with respect to + + + align:start position:0% +completely incoherent with respect to +each other uh because they obviously + + align:start position:0% +each other uh because they obviously + + + align:start position:0% +each other uh because they obviously +don't know the one doesn't know what the + + align:start position:0% +don't know the one doesn't know what the + + + align:start position:0% +don't know the one doesn't know what the +others doing right so they emit light + + align:start position:0% +others doing right so they emit light + + + align:start position:0% +others doing right so they emit light +incoherently with respect to each other + + align:start position:0% +incoherently with respect to each other + + + align:start position:0% +incoherently with respect to each other +uh so to calculate the image of these + + align:start position:0% +uh so to calculate the image of these + + + align:start position:0% +uh so to calculate the image of these +two points you have to add together the + + align:start position:0% +two points you have to add together the + + + align:start position:0% +two points you have to add together the +intensities of the two + + align:start position:0% +intensities of the two + + + align:start position:0% +intensities of the two +uh images and that's what this shows + + align:start position:0% +uh images and that's what this shows + + + align:start position:0% +uh images and that's what this shows +here + + align:start position:0% +here + + + align:start position:0% +here +uh and uh so this shows uh two different + + align:start position:0% +uh and uh so this shows uh two different + + + align:start position:0% +uh and uh so this shows uh two different +spacings in this one here this is what i + + align:start position:0% +spacings in this one here this is what i + + + align:start position:0% +spacings in this one here this is what i +think is really the normal + + align:start position:0% +think is really the normal + + + align:start position:0% +think is really the normal +uh normally taken as the rayleigh + + align:start position:0% +uh normally taken as the rayleigh + + + align:start position:0% +uh normally taken as the rayleigh +resolution limit + + align:start position:0% +resolution limit + + + align:start position:0% +resolution limit +uh + + align:start position:0% +uh + + + align:start position:0% +uh +i i don't know about this other one i + + align:start position:0% +i i don't know about this other one i + + + align:start position:0% +i i don't know about this other one i +don't know where george has got this + + align:start position:0% +don't know where george has got this + + + align:start position:0% +don't know where george has got this +from but + + align:start position:0% +from but + + + align:start position:0% +from but +uh he he talks about these two different + + align:start position:0% +uh he he talks about these two different + + + align:start position:0% +uh he he talks about these two different +uh limits in these notes uh so in this + + align:start position:0% +uh limits in these notes uh so in this + + + align:start position:0% +uh limits in these notes uh so in this +one here + + align:start position:0% +one here + + + align:start position:0% +one here +uh you'll see that uh this peak here is + + align:start position:0% +uh you'll see that uh this peak here is + + + align:start position:0% +uh you'll see that uh this peak here is +placed exactly over + + align:start position:0% +placed exactly over + + + align:start position:0% +placed exactly over +the zero of the other of the first zero + + align:start position:0% +the zero of the other of the first zero + + + align:start position:0% +the zero of the other of the first zero +of the other image + + align:start position:0% +of the other image + + + align:start position:0% +of the other image +right so that's + + align:start position:0% +right so that's + + + align:start position:0% +right so that's +uh what defines this separation shown in + + align:start position:0% +uh what defines this separation shown in + + + align:start position:0% +uh what defines this separation shown in +this picture + + align:start position:0% +this picture + + + align:start position:0% +this picture +uh and uh we find + + align:start position:0% +uh and uh we find + + + align:start position:0% +uh and uh we find +uh that + + align:start position:0% +uh that + + + align:start position:0% +uh that +if they're separated by that amount + + align:start position:0% +if they're separated by that amount + + + align:start position:0% +if they're separated by that amount +the total image is given by this blue + + align:start position:0% +the total image is given by this blue + + + align:start position:0% +the total image is given by this blue +line we get that just by adding together + + align:start position:0% +line we get that just by adding together + + + align:start position:0% +line we get that just by adding together +the two intensities of the two points + + align:start position:0% +the two intensities of the two points + + + align:start position:0% +the two intensities of the two points +together right + + align:start position:0% +together right + + + align:start position:0% +together right +and you can see that um + + align:start position:0% +and you can see that um + + + align:start position:0% +and you can see that um +this + + align:start position:0% +this + + + align:start position:0% +this +drops + + align:start position:0% +drops + + + align:start position:0% +drops +uh a bit at the center + + align:start position:0% +uh a bit at the center + + + align:start position:0% +uh a bit at the center +um what is it it's uh i think the + + align:start position:0% +um what is it it's uh i think the + + + align:start position:0% +um what is it it's uh i think the +intensity there is point eight eight + + align:start position:0% +intensity there is point eight eight + + + align:start position:0% +intensity there is point eight eight +eight + + align:start position:0% +eight + + + align:start position:0% +eight +seven uh + + align:start position:0% +seven uh + + + align:start position:0% +seven uh +i can't remember that no it doesn't + + align:start position:0% +i can't remember that no it doesn't + + + align:start position:0% +i can't remember that no it doesn't +matter + + align:start position:0% +matter + + + align:start position:0% +matter +but anyway it's about point eight isn't + + align:start position:0% +but anyway it's about point eight isn't + + + align:start position:0% +but anyway it's about point eight isn't +it + + align:start position:0% +it + + + align:start position:0% +it +uh i point eight three five that's + + align:start position:0% +uh i point eight three five that's + + + align:start position:0% +uh i point eight three five that's +that's that figure sounds + + align:start position:0% +that's that figure sounds + + + align:start position:0% +that's that figure sounds +uh but anyway the the other interesting + + align:start position:0% +uh but anyway the the other interesting + + + align:start position:0% +uh but anyway the the other interesting +thing of course is that because this one + + align:start position:0% +thing of course is that because this one + + + align:start position:0% +thing of course is that because this one +is zero at this point it means that this + + align:start position:0% +is zero at this point it means that this + + + align:start position:0% +is zero at this point it means that this +maximum is one it's exactly one it's + + align:start position:0% +maximum is one it's exactly one it's + + + align:start position:0% +maximum is one it's exactly one it's +it's uh it's just the one point with no + + align:start position:0% +it's uh it's just the one point with no + + + align:start position:0% +it's uh it's just the one point with no +no contribution from the other one + + align:start position:0% +no contribution from the other one + + + align:start position:0% +no contribution from the other one +right anyway so that + + align:start position:0% +right anyway so that + + + align:start position:0% +right anyway so that +that is arbitrarily taken as being the + + align:start position:0% +that is arbitrarily taken as being the + + + align:start position:0% +that is arbitrarily taken as being the +definition of the points being just + + align:start position:0% +definition of the points being just + + + align:start position:0% +definition of the points being just +resolved so we say that if they're any + + align:start position:0% +resolved so we say that if they're any + + + align:start position:0% +resolved so we say that if they're any +closer together than that you can't + + align:start position:0% +closer together than that you can't + + + align:start position:0% +closer together than that you can't +resolve them you would see a little bit + + align:start position:0% +resolve them you would see a little bit + + + align:start position:0% +resolve them you would see a little bit +of a a dip still + + align:start position:0% +of a a dip still + + + align:start position:0% +of a a dip still +but we we say that the dips not really + + align:start position:0% +but we we say that the dips not really + + + align:start position:0% +but we we say that the dips not really +big enough for you to really be + + align:start position:0% +big enough for you to really be + + + align:start position:0% +big enough for you to really be +confident that there are two objects + + align:start position:0% +confident that there are two objects + + + align:start position:0% +confident that there are two objects +there + + align:start position:0% +there + + + align:start position:0% +there +and um + + align:start position:0% +and um + + + align:start position:0% +and um +if you make them further apart then of + + align:start position:0% +if you make them further apart then of + + + align:start position:0% +if you make them further apart then of +course they'll become more distinguished + + align:start position:0% +course they'll become more distinguished + + + align:start position:0% +course they'll become more distinguished +and this it shows an example here + + align:start position:0% +and this it shows an example here + + + align:start position:0% +and this it shows an example here +where you can see now that this is twice + + align:start position:0% +where you can see now that this is twice + + + align:start position:0% +where you can see now that this is twice +the separation + + align:start position:0% +the separation + + + align:start position:0% +the separation +so + + align:start position:0% +so + + + align:start position:0% +so +so this is where the psf diameter equals + + align:start position:0% +so this is where the psf diameter equals + + + align:start position:0% +so this is where the psf diameter equals +the point source spacing right so + + align:start position:0% +the point source spacing right so + + + align:start position:0% +the point source spacing right so +uh so the + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +what does he mean by that sorry um + + align:start position:0% +what does he mean by that sorry um + + + align:start position:0% +what does he mean by that sorry um +the hit this one the psf radius equals + + align:start position:0% +the hit this one the psf radius equals + + + align:start position:0% +the hit this one the psf radius equals +the point source spacing yeah so okay so + + align:start position:0% +the point source spacing yeah so okay so + + + align:start position:0% +the point source spacing yeah so okay so +that is the distance between + + align:start position:0% +that is the distance between + + + align:start position:0% +that is the distance between +uh the center of the + + align:start position:0% +uh the center of the + + + align:start position:0% +uh the center of the +image and the first dark ring + + align:start position:0% +image and the first dark ring + + + align:start position:0% +image and the first dark ring +in this one + + align:start position:0% +in this one + + + align:start position:0% +in this one +the + + align:start position:0% +the + + + align:start position:0% +the +psf diameter equals the point source + + align:start position:0% +psf diameter equals the point source + + + align:start position:0% +psf diameter equals the point source +spacing + + align:start position:0% +spacing + + + align:start position:0% +spacing +you've got this right + + align:start position:0% + + + + align:start position:0% + +uh no it's not the second zero it's not + + align:start position:0% +uh no it's not the second zero it's not + + + align:start position:0% +uh no it's not the second zero it's not +at the second zero exactly anymore + + align:start position:0% +at the second zero exactly anymore + + + align:start position:0% +at the second zero exactly anymore +is it + + align:start position:0% +is it + + + align:start position:0% +is it +um + + align:start position:0% +um + + + align:start position:0% +um +okay so the spacing here is twice the + + align:start position:0% +okay so the spacing here is twice the + + + align:start position:0% +okay so the spacing here is twice the +spacing there anyway i think that's what + + align:start position:0% +spacing there anyway i think that's what + + + align:start position:0% +spacing there anyway i think that's what +i'm taking at this meeting but as as + + align:start position:0% +i'm taking at this meeting but as as + + + align:start position:0% +i'm taking at this meeting but as as +challenges pointed out + + align:start position:0% +challenges pointed out + + + align:start position:0% +challenges pointed out +uh that means that this is not actually + + align:start position:0% +uh that means that this is not actually + + + align:start position:0% +uh that means that this is not actually +at the at a zero this is not placed at a + + align:start position:0% +at the at a zero this is not placed at a + + + align:start position:0% +at the at a zero this is not placed at a +zero of this other one + + align:start position:0% +zero of this other one + + + align:start position:0% +zero of this other one +uh because + + align:start position:0% +uh because + + + align:start position:0% +uh because +uh the if you remember the zeros of the + + align:start position:0% +uh the if you remember the zeros of the + + + align:start position:0% +uh the if you remember the zeros of the +airy disc are irregularly spaced aren't + + align:start position:0% +airy disc are irregularly spaced aren't + + + align:start position:0% +airy disc are irregularly spaced aren't +they right so they're not equally spaced + + align:start position:0% +they right so they're not equally spaced + + + align:start position:0% +they right so they're not equally spaced +like the like for a sink + + align:start position:0% +like the like for a sink + + + align:start position:0% +like the like for a sink +uh and so + + align:start position:0% +uh and so + + + align:start position:0% +uh and so +uh + + align:start position:0% +uh + + + align:start position:0% +uh +because this isn't zero at this point + + align:start position:0% +because this isn't zero at this point + + + align:start position:0% +because this isn't zero at this point +here this maximum here will be not + + align:start position:0% +here this maximum here will be not + + + align:start position:0% +here this maximum here will be not +exactly one it will be slightly more + + align:start position:0% +exactly one it will be slightly more + + + align:start position:0% +exactly one it will be slightly more +than one + + align:start position:0% +than one + + + align:start position:0% +than one +okay and if um + + align:start position:0% + + + + align:start position:0% + +so so if this condition is satisfied uh + + align:start position:0% +so so if this condition is satisfied uh + + + align:start position:0% +so so if this condition is satisfied uh +then in this case the the delta r + + align:start position:0% +then in this case the the delta r + + + align:start position:0% +then in this case the the delta r +uh the the um + + align:start position:0% +uh the the um + + + align:start position:0% +uh the the um +where does he define that that that's + + align:start position:0% +where does he define that that that's + + + align:start position:0% +where does he define that that that's +the the i guess it's this distance here + + align:start position:0% +the the i guess it's this distance here + + + align:start position:0% +the the i guess it's this distance here +isn't it + + align:start position:0% + + + + align:start position:0% + +it's the separation of the peaks + + align:start position:0% +it's the separation of the peaks + + + align:start position:0% +it's the separation of the peaks +uh yeah okay it's the separation of the + + align:start position:0% +uh yeah okay it's the separation of the + + + align:start position:0% +uh yeah okay it's the separation of the +peaks is 0.61 lambda over n a + + align:start position:0% +peaks is 0.61 lambda over n a + + + align:start position:0% +peaks is 0.61 lambda over n a +uh oh yeah okay so here is the r and r + + align:start position:0% +uh oh yeah okay so here is the r and r + + + align:start position:0% +uh oh yeah okay so here is the r and r +dash are obviously coordinates in the + + align:start position:0% +dash are obviously coordinates in the + + + align:start position:0% +dash are obviously coordinates in the +object plane and the image plane + + align:start position:0% +object plane and the image plane + + + align:start position:0% +object plane and the image plane +effectively yeah so of course it depends + + align:start position:0% +effectively yeah so of course it depends + + + align:start position:0% +effectively yeah so of course it depends +on the the the numerical aperture + + align:start position:0% +on the the the numerical aperture + + + align:start position:0% +on the the the numerical aperture +in those two spaces won't be the same of + + align:start position:0% +in those two spaces won't be the same of + + + align:start position:0% +in those two spaces won't be the same of +course but there will be magnification + + align:start position:0% +course but there will be magnification + + + align:start position:0% +course but there will be magnification +as well which is gonna mean that you get + + align:start position:0% +as well which is gonna mean that you get + + + align:start position:0% +as well which is gonna mean that you get +the same answer for the resolution in + + align:start position:0% +the same answer for the resolution in + + + align:start position:0% +the same answer for the resolution in +both planes so this this point six one + + align:start position:0% +both planes so this this point six one + + + align:start position:0% +both planes so this this point six one +as this magic figure + + align:start position:0% +as this magic figure + + + align:start position:0% +as this magic figure +uh that comes about uh basically because + + align:start position:0% +uh that comes about uh basically because + + + align:start position:0% +uh that comes about uh basically because +of the it's related to the first zero of + + align:start position:0% +of the it's related to the first zero of + + + align:start position:0% +of the it's related to the first zero of +the bessel function j1 + + align:start position:0% +the bessel function j1 + + + align:start position:0% +the bessel function j1 +and the first zero of the vessel + + align:start position:0% +and the first zero of the vessel + + + align:start position:0% +and the first zero of the vessel +function j1 is 3.83 + + align:start position:0% +function j1 is 3.83 + + + align:start position:0% +function j1 is 3.83 +and this is 3.83 divided by two pi + + align:start position:0% +and this is 3.83 divided by two pi + + + align:start position:0% +and this is 3.83 divided by two pi +that does that sound right uh no + + align:start position:0% +that does that sound right uh no + + + align:start position:0% +that does that sound right uh no +yeah yeah i think that sounds right + + align:start position:0% +yeah yeah i think that sounds right + + + align:start position:0% +yeah yeah i think that sounds right +this one here is twice the spacing + + align:start position:0% +this one here is twice the spacing + + + align:start position:0% +this one here is twice the spacing +so 1.22 lambda over n a + + align:start position:0% +so 1.22 lambda over n a + + + align:start position:0% +so 1.22 lambda over n a +and uh so this is 3.83 divided by pi + + align:start position:0% +and uh so this is 3.83 divided by pi + + + align:start position:0% +and uh so this is 3.83 divided by pi +yeah so here actually these are + + align:start position:0% +yeah so here actually these are + + + align:start position:0% +yeah so here actually these are +obviously extremely well + + align:start position:0% +obviously extremely well + + + align:start position:0% +obviously extremely well +uh well resolved you wouldn't have any + + align:start position:0% +uh well resolved you wouldn't have any + + + align:start position:0% +uh well resolved you wouldn't have any +problem in seeing that there's two + + align:start position:0% +problem in seeing that there's two + + + align:start position:0% +problem in seeing that there's two +points there + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and uh so yeah so + + align:start position:0% +and uh so yeah so + + + align:start position:0% +and uh so yeah so +here he calls these two definitions the + + align:start position:0% +here he calls these two definitions the + + + align:start position:0% +here he calls these two definitions the +safe definition and the pushy definition + + align:start position:0% +safe definition and the pushy definition + + + align:start position:0% +safe definition and the pushy definition +uh + + align:start position:0% +uh + + + align:start position:0% +uh +my experience is that the pushy + + align:start position:0% +my experience is that the pushy + + + align:start position:0% +my experience is that the pushy +definition is the one that is normally + + align:start position:0% +definition is the one that is normally + + + align:start position:0% +definition is the one that is normally +uh quoted in places + + align:start position:0% +uh quoted in places + + + align:start position:0% +uh quoted in places +uh and uh so this is this one where you + + align:start position:0% +uh and uh so this is this one where you + + + align:start position:0% +uh and uh so this is this one where you +can only just see a bit of a dip in + + align:start position:0% +can only just see a bit of a dip in + + + align:start position:0% +can only just see a bit of a dip in +between them okay uh note that um if we + + align:start position:0% +between them okay uh note that um if we + + + align:start position:0% +between them okay uh note that um if we +did the same thing + + align:start position:0% +did the same thing + + + align:start position:0% +did the same thing +for the 1d system ie for a sli aperture + + align:start position:0% +for the 1d system ie for a sli aperture + + + align:start position:0% +for the 1d system ie for a sli aperture +rather than a circular aperture + + align:start position:0% +rather than a circular aperture + + + align:start position:0% +rather than a circular aperture +uh then uh you'd be looking at the first + + align:start position:0% +uh then uh you'd be looking at the first + + + align:start position:0% +uh then uh you'd be looking at the first +zero of a sink rather than a bessel + + align:start position:0% +zero of a sink rather than a bessel + + + align:start position:0% +zero of a sink rather than a bessel +function + + align:start position:0% +function + + + align:start position:0% +function +and so you get these expressions rather + + align:start position:0% +and so you get these expressions rather + + + align:start position:0% +and so you get these expressions rather +than these so 1.22 rather than 1 + + align:start position:0% +than these so 1.22 rather than 1 + + + align:start position:0% +than these so 1.22 rather than 1 +or 0.61 + + align:start position:0% +or 0.61 + + + align:start position:0% +or 0.61 +rather than 0.5 so in this case you + + align:start position:0% +rather than 0.5 so in this case you + + + align:start position:0% +rather than 0.5 so in this case you +actually you can see you can resolve + + align:start position:0% +actually you can see you can resolve + + + align:start position:0% +actually you can see you can resolve +slightly smaller spacing + + align:start position:0% +slightly smaller spacing + + + align:start position:0% +slightly smaller spacing +uh with with a slit aperture + + align:start position:0% +uh with with a slit aperture + + + align:start position:0% +uh with with a slit aperture +than with a circular aperture + + align:start position:0% +than with a circular aperture + + + align:start position:0% +than with a circular aperture +and and this is a true effect that + + align:start position:0% +and and this is a true effect that + + + align:start position:0% +and and this is a true effect that +sometimes people try to take advantage + + align:start position:0% +sometimes people try to take advantage + + + align:start position:0% +sometimes people try to take advantage +of + + align:start position:0% +of + + + align:start position:0% +of +okay you will see that different authors + + align:start position:0% +okay you will see that different authors + + + align:start position:0% +okay you will see that different authors +give different definitions right so yeah + + align:start position:0% +give different definitions right so yeah + + + align:start position:0% +give different definitions right so yeah +so i'm not going to go into all that + + align:start position:0% +so i'm not going to go into all that + + + align:start position:0% +so i'm not going to go into all that +because it's not + + align:start position:0% +because it's not + + + align:start position:0% +because it's not +really important at this stage uh + + align:start position:0% +really important at this stage uh + + + align:start position:0% +really important at this stage uh +rayleigh in his original paper noted + + align:start position:0% +rayleigh in his original paper noted + + + align:start position:0% +rayleigh in his original paper noted +that the issue of noise and warned that + + align:start position:0% +that the issue of noise and warned that + + + align:start position:0% +that the issue of noise and warned that +the definition of just resolvable + + align:start position:0% +the definition of just resolvable + + + align:start position:0% +the definition of just resolvable +uh points is system or + + align:start position:0% +uh points is system or + + + align:start position:0% +uh points is system or +application + + align:start position:0% +application + + + align:start position:0% +application +uh actually what you find well that a + + align:start position:0% +uh actually what you find well that a + + + align:start position:0% +uh actually what you find well that a +lot of that is true of course here we're + + align:start position:0% +lot of that is true of course here we're + + + align:start position:0% +lot of that is true of course here we're +uh you know it very much depends on the + + align:start position:0% +uh you know it very much depends on the + + + align:start position:0% +uh you know it very much depends on the +actual system and what you're trying to + + align:start position:0% +actual system and what you're trying to + + + align:start position:0% +actual system and what you're trying to +measure and all these sorts of things + + align:start position:0% +measure and all these sorts of things + + + align:start position:0% +measure and all these sorts of things +and you can come up with lots of + + align:start position:0% +and you can come up with lots of + + + align:start position:0% +and you can come up with lots of +different + + align:start position:0% +different + + + align:start position:0% +different +resolution criteria for different shaped + + align:start position:0% +resolution criteria for different shaped + + + align:start position:0% +resolution criteria for different shaped +objects + + align:start position:0% +objects + + + align:start position:0% +objects +and + + align:start position:0% +and + + + align:start position:0% +and +the comparison of different systems + + align:start position:0% +the comparison of different systems + + + align:start position:0% +the comparison of different systems +doesn't always give the same answers + + align:start position:0% +doesn't always give the same answers + + + align:start position:0% +doesn't always give the same answers +according to what you choose + + align:start position:0% +according to what you choose + + + align:start position:0% +according to what you choose +so beware there's not not one answer to + + align:start position:0% +so beware there's not not one answer to + + + align:start position:0% +so beware there's not not one answer to +this question of resolution uh the other + + align:start position:0% +this question of resolution uh the other + + + align:start position:0% +this question of resolution uh the other +thing is as he says here is noise is an + + align:start position:0% +thing is as he says here is noise is an + + + align:start position:0% +thing is as he says here is noise is an +important thing of course + + align:start position:0% +important thing of course + + + align:start position:0% +important thing of course +uh if you add noise to these images + + align:start position:0% +uh if you add noise to these images + + + align:start position:0% +uh if you add noise to these images +we've got some examples later where uh + + align:start position:0% +we've got some examples later where uh + + + align:start position:0% +we've got some examples later where uh +there's noise added to the the images so + + align:start position:0% +there's noise added to the the images so + + + align:start position:0% +there's noise added to the the images so +that you can see what it does to it + + align:start position:0% +that you can see what it does to it + + + align:start position:0% +that you can see what it does to it +but one thing that is perhaps + + align:start position:0% +but one thing that is perhaps + + + align:start position:0% +but one thing that is perhaps +not quite what george is saying there + + align:start position:0% +not quite what george is saying there + + + align:start position:0% +not quite what george is saying there +actually you do find + + align:start position:0% +actually you do find + + + align:start position:0% +actually you do find +if you look at the image of these two + + align:start position:0% +if you look at the image of these two + + + align:start position:0% +if you look at the image of these two +points as you bring them together + + align:start position:0% +points as you bring them together + + + align:start position:0% +points as you bring them together +you actually do find that the + + align:start position:0% +you actually do find that the + + + align:start position:0% +you actually do find that the +uh this this + + align:start position:0% +uh this this + + + align:start position:0% +uh this this +degradation in the image + + align:start position:0% +degradation in the image + + + align:start position:0% +degradation in the image +is is really rather sudden + + align:start position:0% +is is really rather sudden + + + align:start position:0% +is is really rather sudden +uh so although + + align:start position:0% +uh so although + + + align:start position:0% +uh so although +okay it's not a specific point + + align:start position:0% +okay it's not a specific point + + + align:start position:0% +okay it's not a specific point +uh it is it is quite sudden and uh so + + align:start position:0% +uh it is it is quite sudden and uh so + + + align:start position:0% +uh it is it is quite sudden and uh so +you'll find that uh if you + + align:start position:0% +you'll find that uh if you + + + align:start position:0% +you'll find that uh if you +change the separation + + align:start position:0% +change the separation + + + align:start position:0% +change the separation +um + + align:start position:0% + + + + align:start position:0% + +around + + align:start position:0% +around + + + align:start position:0% +around +slightly more or slightly less than that + + align:start position:0% +slightly more or slightly less than that + + + align:start position:0% +slightly more or slightly less than that +you'd find that this is this central bit + + align:start position:0% +you'd find that this is this central bit + + + align:start position:0% +you'd find that this is this central bit +would go up and down quite a lot + + align:start position:0% +would go up and down quite a lot + + + align:start position:0% +would go up and down quite a lot +actually + + align:start position:0% +actually + + + align:start position:0% +actually +so it is quite a sensitive + + align:start position:0% +so it is quite a sensitive + + + align:start position:0% +so it is quite a sensitive +uh change around that spacing + + align:start position:0% +uh change around that spacing + + + align:start position:0% +uh change around that spacing +so that gives us some idea that that + + align:start position:0% +so that gives us some idea that that + + + align:start position:0% +so that gives us some idea that that +maybe this this um + + align:start position:0% +maybe this this um + + + align:start position:0% +maybe this this um +resolution limit as it's defined does + + align:start position:0% +resolution limit as it's defined does + + + align:start position:0% +resolution limit as it's defined does +it does mean something anyway + + align:start position:0% +it does mean something anyway + + + align:start position:0% +it does mean something anyway +right now that's for a perfect + + align:start position:0% +right now that's for a perfect + + + align:start position:0% +right now that's for a perfect +aberration free system + + align:start position:0% +aberration free system + + + align:start position:0% +aberration free system +uh but very often you've got systems + + align:start position:0% +uh but very often you've got systems + + + align:start position:0% +uh but very often you've got systems +where you've got aberrations + + align:start position:0% +where you've got aberrations + + + align:start position:0% +where you've got aberrations +and that's obviously going to mean that + + align:start position:0% +and that's obviously going to mean that + + + align:start position:0% +and that's obviously going to mean that +your the resolution's not going to be as + + align:start position:0% +your the resolution's not going to be as + + + align:start position:0% +your the resolution's not going to be as +good + + align:start position:0% +good + + + align:start position:0% +good +so this picture shows an example with + + align:start position:0% +so this picture shows an example with + + + align:start position:0% +so this picture shows an example with +coma + + align:start position:0% +coma + + + align:start position:0% +coma +so this is with an off axis ray off axis + + align:start position:0% +so this is with an off axis ray off axis + + + align:start position:0% +so this is with an off axis ray off axis +beam going through a lens and you get + + align:start position:0% +beam going through a lens and you get + + + align:start position:0% +beam going through a lens and you get +this + + align:start position:0% +this + + + align:start position:0% +this +this + + align:start position:0% +this + + + align:start position:0% +this +coma spot here + + align:start position:0% +coma spot here + + + align:start position:0% +coma spot here +so now of course this spot is bigger + + align:start position:0% +so now of course this spot is bigger + + + align:start position:0% +so now of course this spot is bigger +than it would be if there were no + + align:start position:0% +than it would be if there were no + + + align:start position:0% +than it would be if there were no +aberrations + + align:start position:0% +aberrations + + + align:start position:0% +aberrations +and therefore you'd expect that the + + align:start position:0% +and therefore you'd expect that the + + + align:start position:0% +and therefore you'd expect that the +resolution would be worse + + align:start position:0% +resolution would be worse + + + align:start position:0% +resolution would be worse +so + + align:start position:0% + + + + align:start position:0% + +this is another thing you have to take + + align:start position:0% +this is another thing you have to take + + + align:start position:0% +this is another thing you have to take +into account + + align:start position:0% +into account + + + align:start position:0% +into account +i don't think there's going to be much + + align:start position:0% +i don't think there's going to be much + + + align:start position:0% +i don't think there's going to be much +more about that + + align:start position:0% +more about that + + + align:start position:0% +more about that +what why did that do something then or + + align:start position:0% +what why did that do something then or + + + align:start position:0% +what why did that do something then or +perhaps i just didn't push it fast + + align:start position:0% +perhaps i just didn't push it fast + + + align:start position:0% +perhaps i just didn't push it fast +enough right now the other the other way + + align:start position:0% +enough right now the other the other way + + + align:start position:0% +enough right now the other the other way +of looking at the effects resolution and + + align:start position:0% +of looking at the effects resolution and + + + align:start position:0% +of looking at the effects resolution and +the effects of aberrations + + align:start position:0% +the effects of aberrations + + + align:start position:0% +the effects of aberrations +uh is looking at the transfer function + + align:start position:0% +uh is looking at the transfer function + + + align:start position:0% +uh is looking at the transfer function +approach + + align:start position:0% +approach + + + align:start position:0% +approach +uh and so this is this is giving results + + align:start position:0% +uh and so this is this is giving results + + + align:start position:0% +uh and so this is this is giving results +uh for a one-dimensional system + + align:start position:0% +uh for a one-dimensional system + + + align:start position:0% +uh for a one-dimensional system +uh and it's it you see it's an mtf + + align:start position:0% +uh and it's it you see it's an mtf + + + align:start position:0% +uh and it's it you see it's an mtf +modulation transfer function so that + + align:start position:0% +modulation transfer function so that + + + align:start position:0% +modulation transfer function so that +means it's an incoherent system + + align:start position:0% +means it's an incoherent system + + + align:start position:0% +means it's an incoherent system +right the + + align:start position:0% +right the + + + align:start position:0% +right the +the mtf + + align:start position:0% +the mtf + + + align:start position:0% +the mtf +uh is the fourier transform of the point + + align:start position:0% +uh is the fourier transform of the point + + + align:start position:0% +uh is the fourier transform of the point +spread function + + align:start position:0% +spread function + + + align:start position:0% +spread function +right so this is for the aberration free + + align:start position:0% +right so this is for the aberration free + + + align:start position:0% +right so this is for the aberration free +case this is a sink squared the point + + align:start position:0% +case this is a sink squared the point + + + align:start position:0% +case this is a sink squared the point +spread function for the 1d case and if + + align:start position:0% +spread function for the 1d case and if + + + align:start position:0% +spread function for the 1d case and if +you take the fourier transform you get + + align:start position:0% +you take the fourier transform you get + + + align:start position:0% +you take the fourier transform you get +the + + align:start position:0% +the + + + align:start position:0% +the +the modulation transfer function as he + + align:start position:0% +the modulation transfer function as he + + + align:start position:0% +the modulation transfer function as he +calls it + + align:start position:0% +calls it + + + align:start position:0% +calls it +and vice versa of course these are + + align:start position:0% +and vice versa of course these are + + + align:start position:0% +and vice versa of course these are +fourier transform pairs this is just a + + align:start position:0% +fourier transform pairs this is just a + + + align:start position:0% +fourier transform pairs this is just a +triangle function + + align:start position:0% +triangle function + + + align:start position:0% +triangle function +uh and uh and this shows what would um + + align:start position:0% +uh and uh and this shows what would um + + + align:start position:0% +uh and uh and this shows what would um +happen if you've got some aberrations + + align:start position:0% +happen if you've got some aberrations + + + align:start position:0% +happen if you've got some aberrations +there in general what would happen is + + align:start position:0% +there in general what would happen is + + + align:start position:0% +there in general what would happen is +that this would be broader + + align:start position:0% +that this would be broader + + + align:start position:0% +that this would be broader +and this would be deformed uh so that + + align:start position:0% +and this would be deformed uh so that + + + align:start position:0% +and this would be deformed uh so that +you've got a lower spatial frequency + + align:start position:0% +you've got a lower spatial frequency + + + align:start position:0% +you've got a lower spatial frequency +response here actually he seems to be + + align:start position:0% +response here actually he seems to be + + + align:start position:0% +response here actually he seems to be +showing something which has got + + align:start position:0% +showing something which has got + + + align:start position:0% +showing something which has got +an improved + + align:start position:0% +an improved + + + align:start position:0% +an improved +response at the very high frequencies + + align:start position:0% +response at the very high frequencies + + + align:start position:0% +response at the very high frequencies +which is quite interesting because you + + align:start position:0% +which is quite interesting because you + + + align:start position:0% +which is quite interesting because you +know what that would mean actually is + + align:start position:0% +know what that would mean actually is + + + align:start position:0% +know what that would mean actually is +that + + align:start position:0% +that + + + align:start position:0% +that +uh if your object only had those high + + align:start position:0% +uh if your object only had those high + + + align:start position:0% +uh if your object only had those high +spatial frequencies this + + align:start position:0% +spatial frequencies this + + + align:start position:0% +spatial frequencies this +the aberration uh the system with + + align:start position:0% +the aberration uh the system with + + + align:start position:0% +the aberration uh the system with +aberrations would actually give a better + + align:start position:0% +aberrations would actually give a better + + + align:start position:0% +aberrations would actually give a better +image than the one without aberrations + + align:start position:0% +image than the one without aberrations + + + align:start position:0% +image than the one without aberrations +so maybe that's a bit anomalous + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now some common misinterpretations + + align:start position:0% +so now some common misinterpretations + + + align:start position:0% +so now some common misinterpretations +uh attempting to resolve object features + + align:start position:0% +uh attempting to resolve object features + + + align:start position:0% +uh attempting to resolve object features +smaller than the resolution limit i.e + + align:start position:0% +smaller than the resolution limit i.e + + + align:start position:0% +smaller than the resolution limit i.e +1.22 lambda over na is hopeless + + align:start position:0% +1.22 lambda over na is hopeless + + + align:start position:0% +1.22 lambda over na is hopeless +so he's saying that + + align:start position:0% +so he's saying that + + + align:start position:0% +so he's saying that +that's not strictly true because this is + + align:start position:0% +that's not strictly true because this is + + + align:start position:0% +that's not strictly true because this is +not for a start it's not a + + align:start position:0% +not for a start it's not a + + + align:start position:0% +not for a start it's not a +a a sudden cut off + + align:start position:0% +a a sudden cut off + + + align:start position:0% +a a sudden cut off +uh and + + align:start position:0% +uh and + + + align:start position:0% +uh and +and it depends on the presence of noise + + align:start position:0% +and it depends on the presence of noise + + + align:start position:0% +and it depends on the presence of noise +and other features so there's a very big + + align:start position:0% +and other features so there's a very big + + + align:start position:0% +and other features so there's a very big +no + + align:start position:0% +no + + + align:start position:0% +no +uh to say that + + align:start position:0% +uh to say that + + + align:start position:0% +uh to say that +yes you can sometimes see things which + + align:start position:0% +yes you can sometimes see things which + + + align:start position:0% +yes you can sometimes see things which +are smaller than the + + align:start position:0% +are smaller than the + + + align:start position:0% +are smaller than the +uh resolution limit + + align:start position:0% +uh resolution limit + + + align:start position:0% +uh resolution limit +and + + align:start position:0% +and + + + align:start position:0% +and +and then also another point is that + + align:start position:0% +and then also another point is that + + + align:start position:0% +and then also another point is that +there are ways you can actually improve + + align:start position:0% +there are ways you can actually improve + + + align:start position:0% +there are ways you can actually improve +the performance + + align:start position:0% +the performance + + + align:start position:0% +the performance +uh using for example the clean algorithm + + align:start position:0% +uh using for example the clean algorithm + + + align:start position:0% +uh using for example the clean algorithm +the clean algorithm is a thing they use + + align:start position:0% +the clean algorithm is a thing they use + + + align:start position:0% +the clean algorithm is a thing they use +in astronomy for + + align:start position:0% +in astronomy for + + + align:start position:0% +in astronomy for +doing deconvolution + + align:start position:0% +doing deconvolution + + + align:start position:0% +doing deconvolution +it works particularly well + + align:start position:0% +it works particularly well + + + align:start position:0% +it works particularly well +it would be very good actually for some + + align:start position:0% +it would be very good actually for some + + + align:start position:0% +it would be very good actually for some +of these microscope things that people + + align:start position:0% +of these microscope things that people + + + align:start position:0% +of these microscope things that people +do nowadays with these very sparse + + align:start position:0% +do nowadays with these very sparse + + + align:start position:0% +do nowadays with these very sparse +uh sparse molecules because it's + + align:start position:0% +uh sparse molecules because it's + + + align:start position:0% +uh sparse molecules because it's +designed to work with + + align:start position:0% +designed to work with + + + align:start position:0% +designed to work with +you know in astronomy with isolated + + align:start position:0% +you know in astronomy with isolated + + + align:start position:0% +you know in astronomy with isolated +point images right so if he looks at a + + align:start position:0% +point images right so if he looks at a + + + align:start position:0% +point images right so if he looks at a +comp a continuous object + + align:start position:0% +comp a continuous object + + + align:start position:0% +comp a continuous object +like a motor car or something like that + + align:start position:0% +like a motor car or something like that + + + align:start position:0% +like a motor car or something like that +it would wouldn't work it has to only + + align:start position:0% +it would wouldn't work it has to only + + + align:start position:0% +it would wouldn't work it has to only +work on + + align:start position:0% +work on + + + align:start position:0% +work on +uh on on + + align:start position:0% +uh on on + + + align:start position:0% +uh on on +point type + + align:start position:0% +point type + + + align:start position:0% +point type +images + + align:start position:0% +images + + + align:start position:0% +images +then vena filtering will say something + + align:start position:0% +then vena filtering will say something + + + align:start position:0% +then vena filtering will say something +more about that expectation expectation + + align:start position:0% +more about that expectation expectation + + + align:start position:0% +more about that expectation expectation +maximization etc so there are various uh + + align:start position:0% +maximization etc so there are various uh + + + align:start position:0% +maximization etc so there are various uh +digital ways you can improve the image + + align:start position:0% +digital ways you can improve the image + + + align:start position:0% +digital ways you can improve the image +and get information out of the image + + align:start position:0% +and get information out of the image + + + align:start position:0% +and get information out of the image +even if you can't see it by how i + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +then there's this other word super + + align:start position:0% +then there's this other word super + + + align:start position:0% +then there's this other word super +resolution + + align:start position:0% +resolution + + + align:start position:0% +resolution +uh super resolution is it means + + align:start position:0% +uh super resolution is it means + + + align:start position:0% +uh super resolution is it means +basically getting better resolution than + + align:start position:0% +basically getting better resolution than + + + align:start position:0% +basically getting better resolution than +you're supposed to + + align:start position:0% +you're supposed to + + + align:start position:0% +you're supposed to +i + + align:start position:0% +i + + + align:start position:0% +i +beating the rayleigh diffraction limit + + align:start position:0% +beating the rayleigh diffraction limit + + + align:start position:0% +beating the rayleigh diffraction limit +and various ways have been proposed for + + align:start position:0% +and various ways have been proposed for + + + align:start position:0% +and various ways have been proposed for +doing this + + align:start position:0% +doing this + + + align:start position:0% +doing this +uh and uh until recently i guess most of + + align:start position:0% +uh and uh until recently i guess most of + + + align:start position:0% +uh and uh until recently i guess most of +them were pretty uh unsuccessful + + align:start position:0% +them were pretty uh unsuccessful + + + align:start position:0% +them were pretty uh unsuccessful +but + + align:start position:0% +but + + + align:start position:0% +but +more recently nowadays some of these + + align:start position:0% +more recently nowadays some of these + + + align:start position:0% +more recently nowadays some of these +techniques are doing really well and i + + align:start position:0% +techniques are doing really well and i + + + align:start position:0% +techniques are doing really well and i +think the most noticeable one probably + + align:start position:0% +think the most noticeable one probably + + + align:start position:0% +think the most noticeable one probably +is stead + + align:start position:0% +is stead + + + align:start position:0% +is stead +stimulated emission depletion microscopy + + align:start position:0% +stimulated emission depletion microscopy + + + align:start position:0% +stimulated emission depletion microscopy +where + + align:start position:0% +where + + + align:start position:0% +where +where stefan hell is getting resolutions + + align:start position:0% +where stefan hell is getting resolutions + + + align:start position:0% +where stefan hell is getting resolutions +which are + + align:start position:0% +which are + + + align:start position:0% +which are +i don't know + + align:start position:0% +i don't know + + + align:start position:0% +i don't know +more than a factor of 10 better than + + align:start position:0% +more than a factor of 10 better than + + + align:start position:0% +more than a factor of 10 better than +than you should according to the + + align:start position:0% +than you should according to the + + + align:start position:0% +than you should according to the +rayleigh diffraction limit + + align:start position:0% +rayleigh diffraction limit + + + align:start position:0% +rayleigh diffraction limit +but anyway here we here he's talking + + align:start position:0% +but anyway here we here he's talking + + + align:start position:0% +but anyway here we here he's talking +about uh what are called super super + + align:start position:0% +about uh what are called super super + + + align:start position:0% +about uh what are called super super +resolving filters what you do + + align:start position:0% +resolving filters what you do + + + align:start position:0% +resolving filters what you do +is you you alter the pupil function of + + align:start position:0% +is you you alter the pupil function of + + + align:start position:0% +is you you alter the pupil function of +the lens + + align:start position:0% +the lens + + + align:start position:0% +the lens +uh by some + + align:start position:0% +uh by some + + + align:start position:0% +uh by some +clever trick in order to sharpen up the + + align:start position:0% +clever trick in order to sharpen up the + + + align:start position:0% +clever trick in order to sharpen up the +point spread function and i think that + + align:start position:0% +point spread function and i think that + + + align:start position:0% +point spread function and i think that +maybe george did mention that earlier on + + align:start position:0% +maybe george did mention that earlier on + + + align:start position:0% +maybe george did mention that earlier on +at some point + + align:start position:0% +at some point + + + align:start position:0% +at some point +but the problem is what always happens + + align:start position:0% +but the problem is what always happens + + + align:start position:0% +but the problem is what always happens +uh is that + + align:start position:0% +uh is that + + + align:start position:0% +uh is that +uh it doesn't actually you know you + + align:start position:0% +uh it doesn't actually you know you + + + align:start position:0% +uh it doesn't actually you know you +never get anything for nothing that's + + align:start position:0% +never get anything for nothing that's + + + align:start position:0% +never get anything for nothing that's +the problem you make the set that you + + align:start position:0% +the problem you make the set that you + + + align:start position:0% +the problem you make the set that you +make the central lobe + + align:start position:0% +make the central lobe + + + align:start position:0% +make the central lobe +uh + + align:start position:0% +uh + + + align:start position:0% +uh +a central lobe + + align:start position:0% +a central lobe + + + align:start position:0% +a central lobe +narrower + + align:start position:0% +narrower + + + align:start position:0% +narrower +but you find that the side lobes become + + align:start position:0% +but you find that the side lobes become + + + align:start position:0% +but you find that the side lobes become +stronger + + align:start position:0% +stronger + + + align:start position:0% +stronger +and the other thing is that very often + + align:start position:0% +and the other thing is that very often + + + align:start position:0% +and the other thing is that very often +the power transmitted through the system + + align:start position:0% +the power transmitted through the system + + + align:start position:0% +the power transmitted through the system +is much reduced + + align:start position:0% +is much reduced + + + align:start position:0% +is much reduced +so you can imagine if you've got some + + align:start position:0% +so you can imagine if you've got some + + + align:start position:0% +so you can imagine if you've got some +filter that absorbs part of the + + align:start position:0% +filter that absorbs part of the + + + align:start position:0% +filter that absorbs part of the +uh part of the power + + align:start position:0% +uh part of the power + + + align:start position:0% +uh part of the power +then you're wasting power right so both + + align:start position:0% +then you're wasting power right so both + + + align:start position:0% +then you're wasting power right so both +of these can be bad + + align:start position:0% +of these can be bad + + + align:start position:0% +of these can be bad +uh and + + align:start position:0% +uh and + + + align:start position:0% +uh and +so consequently this idea of + + align:start position:0% +so consequently this idea of + + + align:start position:0% +so consequently this idea of +super resolving filters + + align:start position:0% +super resolving filters + + + align:start position:0% +super resolving filters +in practice has never really + + align:start position:0% +in practice has never really + + + align:start position:0% +in practice has never really +up until now been very + + align:start position:0% +up until now been very + + + align:start position:0% +up until now been very +successful from a practical point of + + align:start position:0% +successful from a practical point of + + + align:start position:0% +successful from a practical point of +view + + align:start position:0% +view + + + align:start position:0% +view +but anyway this shows one example + + align:start position:0% +but anyway this shows one example + + + align:start position:0% +but anyway this shows one example +this shows a circular pupil + + align:start position:0% +this shows a circular pupil + + + align:start position:0% +this shows a circular pupil +uh and + + align:start position:0% +uh and + + + align:start position:0% +uh and +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and that yeah so and then this one is is + + align:start position:0% +and that yeah so and then this one is is + + + align:start position:0% +and that yeah so and then this one is is +is a an annular pupil which you can + + align:start position:0% +is a an annular pupil which you can + + + align:start position:0% +is a an annular pupil which you can +model as being one circ circular + + align:start position:0% +model as being one circ circular + + + align:start position:0% +model as being one circ circular +function minus another one + + align:start position:0% +function minus another one + + + align:start position:0% +function minus another one +and of course once you write it in that + + align:start position:0% +and of course once you write it in that + + + align:start position:0% +and of course once you write it in that +simple way + + align:start position:0% +simple way + + + align:start position:0% +simple way +as a circ function + + align:start position:0% +as a circ function + + + align:start position:0% +as a circ function +uh + + align:start position:0% +uh + + + align:start position:0% +uh +as the difference between two circ + + align:start position:0% +as the difference between two circ + + + align:start position:0% +as the difference between two circ +functions you can do the fourier + + align:start position:0% +functions you can do the fourier + + + align:start position:0% +functions you can do the fourier +transform of that very easily and get + + align:start position:0% +transform of that very easily and get + + + align:start position:0% +transform of that very easily and get +the point spread function of these two + + align:start position:0% +the point spread function of these two + + + align:start position:0% +the point spread function of these two +cases very easily + + align:start position:0% +cases very easily + + + align:start position:0% +cases very easily +and so he's working it out for + + align:start position:0% +and so he's working it out for + + + align:start position:0% +and so he's working it out for +a focal length of 20 centimeters and a + + align:start position:0% +a focal length of 20 centimeters and a + + + align:start position:0% +a focal length of 20 centimeters and a +wavelength of 0.5 + + align:start position:0% +wavelength of 0.5 + + + align:start position:0% +wavelength of 0.5 +microns + + align:start position:0% +microns + + + align:start position:0% +microns +and the width of that aperture is um + + align:start position:0% +and the width of that aperture is um + + + align:start position:0% +and the width of that aperture is um +what does it looks about it looks about + + align:start position:0% +what does it looks about it looks about + + + align:start position:0% +what does it looks about it looks about +four millimeters + + align:start position:0% +four millimeters + + + align:start position:0% +four millimeters +diameter + + align:start position:0% +diameter + + + align:start position:0% +diameter +something like that + + align:start position:0% +something like that + + + align:start position:0% +something like that +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +anyway + + align:start position:0% +anyway + + + align:start position:0% +anyway +so this is he worked out what it looks + + align:start position:0% +so this is he worked out what it looks + + + align:start position:0% +so this is he worked out what it looks +like + + align:start position:0% +like + + + align:start position:0% +like +uh so this is the psf this is supposed + + align:start position:0% +uh so this is the psf this is supposed + + + align:start position:0% +uh so this is the psf this is supposed +to be + + align:start position:0% +to be + + + align:start position:0% +to be +uh an airy disc um it's been um sampled + + align:start position:0% +uh an airy disc um it's been um sampled + + + align:start position:0% +uh an airy disc um it's been um sampled +a bit coarsely so it looks a bit + + align:start position:0% +a bit coarsely so it looks a bit + + + align:start position:0% +a bit coarsely so it looks a bit +ragged + + align:start position:0% +ragged + + + align:start position:0% +ragged +and so you what you see is when you + + align:start position:0% +and so you what you see is when you + + + align:start position:0% +and so you what you see is when you +when you look at the annular case + + align:start position:0% +when you look at the annular case + + + align:start position:0% +when you look at the annular case +you put this central + + align:start position:0% +you put this central + + + align:start position:0% +you put this central +central obscuration in the center there + + align:start position:0% +central obscuration in the center there + + + align:start position:0% +central obscuration in the center there +what it does is it narrows up that + + align:start position:0% +what it does is it narrows up that + + + align:start position:0% +what it does is it narrows up that +central lobe + + align:start position:0% +central lobe + + + align:start position:0% +central lobe +and + + align:start position:0% +and + + + align:start position:0% +and +and you can see though it also increases + + align:start position:0% +and you can see though it also increases + + + align:start position:0% +and you can see though it also increases +the strength of these side lobes these + + align:start position:0% +the strength of these side lobes these + + + align:start position:0% +the strength of these side lobes these +are much higher than these ones + + align:start position:0% +are much higher than these ones + + + align:start position:0% +are much higher than these ones +so although + + align:start position:0% +so although + + + align:start position:0% +so although +uh in some cases this can give a good an + + align:start position:0% +uh in some cases this can give a good an + + + align:start position:0% +uh in some cases this can give a good an +improved image compared with this + + align:start position:0% +improved image compared with this + + + align:start position:0% +improved image compared with this +uh for example for + + align:start position:0% +uh for example for + + + align:start position:0% +uh for example for +point objects it would do well but if + + align:start position:0% +point objects it would do well but if + + + align:start position:0% +point objects it would do well but if +you've got an extended object like an + + align:start position:0% +you've got an extended object like an + + + align:start position:0% +you've got an extended object like an +image of a car or something it might not + + align:start position:0% +image of a car or something it might not + + + align:start position:0% +image of a car or something it might not +work so well uh the other way of + + align:start position:0% +work so well uh the other way of + + + align:start position:0% +work so well uh the other way of +thinking on it into is in terms of the + + align:start position:0% +thinking on it into is in terms of the + + + align:start position:0% +thinking on it into is in terms of the +mtf + + align:start position:0% +mtf + + + align:start position:0% +mtf +uh and this is our normal + + align:start position:0% +uh and this is our normal + + + align:start position:0% +uh and this is our normal +uh mtf for a circular pupil it's this uh + + align:start position:0% +uh mtf for a circular pupil it's this uh + + + align:start position:0% +uh mtf for a circular pupil it's this uh +so-called chinese hat function + + align:start position:0% +so-called chinese hat function + + + align:start position:0% +so-called chinese hat function +uh and then for the annular pupil this + + align:start position:0% +uh and then for the annular pupil this + + + align:start position:0% +uh and then for the annular pupil this +is what you get you remember you you + + align:start position:0% +is what you get you remember you you + + + align:start position:0% +is what you get you remember you you +calculate these this is the convolution + + align:start position:0% +calculate these this is the convolution + + + align:start position:0% +calculate these this is the convolution +the autocorrelation + + align:start position:0% +the autocorrelation + + + align:start position:0% +the autocorrelation +of a circle + + align:start position:0% +of a circle + + + align:start position:0% +of a circle +right so you have to + + align:start position:0% +right so you have to + + + align:start position:0% +right so you have to +you get two circles and you displace it + + align:start position:0% +you get two circles and you displace it + + + align:start position:0% +you get two circles and you displace it +one relative to the other you calculate + + align:start position:0% +one relative to the other you calculate + + + align:start position:0% +one relative to the other you calculate +the area of overlap + + align:start position:0% +the area of overlap + + + align:start position:0% +the area of overlap +and you plot the area of overlap as a + + align:start position:0% +and you plot the area of overlap as a + + + align:start position:0% +and you plot the area of overlap as a +function of the distance between the two + + align:start position:0% +function of the distance between the two + + + align:start position:0% +function of the distance between the two +centers + + align:start position:0% +centers + + + align:start position:0% +centers +so that's how you actually calculate + + align:start position:0% +so that's how you actually calculate + + + align:start position:0% +so that's how you actually calculate +this + + align:start position:0% +this + + + align:start position:0% +this +and you do the same with this one + + align:start position:0% +and you do the same with this one + + + align:start position:0% +and you do the same with this one +and you can see what you get + + align:start position:0% +and you can see what you get + + + align:start position:0% +and you can see what you get +is um you see that it drops more quickly + + align:start position:0% +is um you see that it drops more quickly + + + align:start position:0% +is um you see that it drops more quickly +first of all + + align:start position:0% +first of all + + + align:start position:0% +first of all +this is normalized to one because you + + align:start position:0% +this is normalized to one because you + + + align:start position:0% +this is normalized to one because you +normally normalize + + align:start position:0% +normally normalize + + + align:start position:0% +normally normalize +transfer functions to one for + + align:start position:0% +transfer functions to one for + + + align:start position:0% +transfer functions to one for +zero spatial frequencies that's the way + + align:start position:0% +zero spatial frequencies that's the way + + + align:start position:0% +zero spatial frequencies that's the way +we normally do it but i guess + + align:start position:0% +we normally do it but i guess + + + align:start position:0% +we normally do it but i guess +uh maybe + + align:start position:0% +uh maybe + + + align:start position:0% +uh maybe +maybe it's not the only way of doing it + + align:start position:0% +maybe it's not the only way of doing it + + + align:start position:0% +maybe it's not the only way of doing it +this drops down quickly because you can + + align:start position:0% +this drops down quickly because you can + + + align:start position:0% +this drops down quickly because you can +see if you're working out the auto + + align:start position:0% +see if you're working out the auto + + + align:start position:0% +see if you're working out the auto +correlation of this annular aperture you + + align:start position:0% +correlation of this annular aperture you + + + align:start position:0% +correlation of this annular aperture you +can see that immediately you move it a + + align:start position:0% +can see that immediately you move it a + + + align:start position:0% +can see that immediately you move it a +small amount + + align:start position:0% +small amount + + + align:start position:0% +small amount +uh the the the one uh the one bright + + align:start position:0% +uh the the the one uh the one bright + + + align:start position:0% +uh the the the one uh the one bright +region is not going to overlap with the + + align:start position:0% +region is not going to overlap with the + + + align:start position:0% +region is not going to overlap with the +other one anymore + + align:start position:0% +other one anymore + + + align:start position:0% +other one anymore +right so that's why it drops off quickly + + align:start position:0% +right so that's why it drops off quickly + + + align:start position:0% +right so that's why it drops off quickly +there and then it has another blip out + + align:start position:0% +there and then it has another blip out + + + align:start position:0% +there and then it has another blip out +here + + align:start position:0% +here + + + align:start position:0% +here +which basically comes about from when + + align:start position:0% +which basically comes about from when + + + align:start position:0% +which basically comes about from when +the two the two annually + + align:start position:0% +the two the two annually + + + align:start position:0% +the two the two annually +where they're both got their bright bits + + align:start position:0% +where they're both got their bright bits + + + align:start position:0% +where they're both got their bright bits +on top of each other + + align:start position:0% +on top of each other + + + align:start position:0% +on top of each other +right and + + align:start position:0% +right and + + + align:start position:0% +right and +so if you compare this one with this one + + align:start position:0% +so if you compare this one with this one + + + align:start position:0% +so if you compare this one with this one +you can see that here + + align:start position:0% +you can see that here + + + align:start position:0% +you can see that here +the spatial frequency response is much + + align:start position:0% +the spatial frequency response is much + + + align:start position:0% +the spatial frequency response is much +lower + + align:start position:0% +lower + + + align:start position:0% +lower +uh here actually it can be higher + + align:start position:0% +uh here actually it can be higher + + + align:start position:0% +uh here actually it can be higher +the cutoff of course is still the same + + align:start position:0% +the cutoff of course is still the same + + + align:start position:0% +the cutoff of course is still the same +right + + align:start position:0% + + + + align:start position:0% + +so you could calculate the image of any + + align:start position:0% +so you could calculate the image of any + + + align:start position:0% +so you could calculate the image of any +object you fancied from + + align:start position:0% +object you fancied from + + + align:start position:0% +object you fancied from +from knowing that uh and this is another + + align:start position:0% +from knowing that uh and this is another + + + align:start position:0% +from knowing that uh and this is another +example + + align:start position:0% +example + + + align:start position:0% +example +uh this is the case of a + + align:start position:0% +uh this is the case of a + + + align:start position:0% +uh this is the case of a +uh a gaussian apodization so what we're + + align:start position:0% +uh a gaussian apodization so what we're + + + align:start position:0% +uh a gaussian apodization so what we're +now doing is instead of you know the the + + align:start position:0% +now doing is instead of you know the the + + + align:start position:0% +now doing is instead of you know the the +uh the annulus is effectively boosting + + align:start position:0% +uh the annulus is effectively boosting + + + align:start position:0% +uh the annulus is effectively boosting +out the edges of the pupil which is why + + align:start position:0% +out the edges of the pupil which is why + + + align:start position:0% +out the edges of the pupil which is why +you get this improved + + align:start position:0% +you get this improved + + + align:start position:0% +you get this improved +uh high spatial frequency response here + + align:start position:0% +uh high spatial frequency response here + + + align:start position:0% +uh high spatial frequency response here +we're doing the opposite of that + + align:start position:0% +we're doing the opposite of that + + + align:start position:0% +we're doing the opposite of that +apodization if george was here it would + + align:start position:0% +apodization if george was here it would + + + align:start position:0% +apodization if george was here it would +he he would tell us + + align:start position:0% +he he would tell us + + + align:start position:0% +he he would tell us +in fact he already did in one of the + + align:start position:0% +in fact he already did in one of the + + + align:start position:0% +in fact he already did in one of the +previous lectures + + align:start position:0% +previous lectures + + + align:start position:0% +previous lectures +apodization means to cut off the feet in + + align:start position:0% +apodization means to cut off the feet in + + + align:start position:0% +apodization means to cut off the feet in +greek + + align:start position:0% +greek + + + align:start position:0% +greek +i believe + + align:start position:0% +i believe + + + align:start position:0% +i believe +he'll probably be listening to my + + align:start position:0% +he'll probably be listening to my + + + align:start position:0% +he'll probably be listening to my +lecture and uh tell me i've got my greek + + align:start position:0% +lecture and uh tell me i've got my greek + + + align:start position:0% +lecture and uh tell me i've got my greek +all wrong but anyway it's to do it's it + + align:start position:0% +all wrong but anyway it's to do it's it + + + align:start position:0% +all wrong but anyway it's to do it's it +means to cut off the feet + + align:start position:0% +means to cut off the feet + + + align:start position:0% +means to cut off the feet +uh and what it means that why it's given + + align:start position:0% +uh and what it means that why it's given + + + align:start position:0% +uh and what it means that why it's given +that name is because it cuts off the + + align:start position:0% +that name is because it cuts off the + + + align:start position:0% +that name is because it cuts off the +side lobes so you see the side lobes of + + align:start position:0% +side lobes so you see the side lobes of + + + align:start position:0% +side lobes so you see the side lobes of +the airy disc + + align:start position:0% +the airy disc + + + align:start position:0% +the airy disc +have disappeared now + + align:start position:0% +have disappeared now + + + align:start position:0% +have disappeared now +so by making this shaded aperture in + + align:start position:0% +so by making this shaded aperture in + + + align:start position:0% +so by making this shaded aperture in +this case it's a gaussian function + + align:start position:0% +this case it's a gaussian function + + + align:start position:0% +this case it's a gaussian function +uh you make something which is a bit + + align:start position:0% +uh you make something which is a bit + + + align:start position:0% +uh you make something which is a bit +broader actually in this case doesn't + + align:start position:0% +broader actually in this case doesn't + + + align:start position:0% +broader actually in this case doesn't +look very much broader at all + + align:start position:0% +look very much broader at all + + + align:start position:0% +look very much broader at all +but the side lobes have gone + + align:start position:0% +but the side lobes have gone + + + align:start position:0% +but the side lobes have gone +uh and and this is what it's done to the + + align:start position:0% +uh and and this is what it's done to the + + + align:start position:0% +uh and and this is what it's done to the +uh to the um + + align:start position:0% +uh to the um + + + align:start position:0% +uh to the um +transfer function you see now it's + + align:start position:0% +transfer function you see now it's + + + align:start position:0% +transfer function you see now it's +it's slower to fall off here than + + align:start position:0% +it's slower to fall off here than + + + align:start position:0% +it's slower to fall off here than +than this one + + align:start position:0% +than this one + + + align:start position:0% +than this one +but the high spatial frequencies are now + + align:start position:0% +but the high spatial frequencies are now + + + align:start position:0% +but the high spatial frequencies are now +uh reduced relative to this other one + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +uh overview on this then this is what we + + align:start position:0% +uh overview on this then this is what we + + + align:start position:0% +uh overview on this then this is what we +call + + align:start position:0% +call + + + align:start position:0% +call +or what george is calling pupil + + align:start position:0% +or what george is calling pupil + + + align:start position:0% +or what george is calling pupil +engineering + + align:start position:0% +engineering + + + align:start position:0% +engineering +uh and uh + + align:start position:0% +uh and uh + + + align:start position:0% +uh and uh +so so if you try to make the main the + + align:start position:0% +so so if you try to make the main the + + + align:start position:0% +so so if you try to make the main the +central + + align:start position:0% +central + + + align:start position:0% +central +lobe of the psf smaller + + align:start position:0% +lobe of the psf smaller + + + align:start position:0% +lobe of the psf smaller +then you're going to get bigger side + + align:start position:0% +then you're going to get bigger side + + + align:start position:0% +then you're going to get bigger side +loads and that seems to be something + + align:start position:0% +loads and that seems to be something + + + align:start position:0% +loads and that seems to be something +that you can't avoid nobody's come up + + align:start position:0% +that you can't avoid nobody's come up + + + align:start position:0% +that you can't avoid nobody's come up +with a way + + align:start position:0% +with a way + + + align:start position:0% +with a way +of doing something clever that avoids + + align:start position:0% +of doing something clever that avoids + + + align:start position:0% +of doing something clever that avoids +that + + align:start position:0% +that + + + align:start position:0% +that +and the opposite of course if you make + + align:start position:0% +and the opposite of course if you make + + + align:start position:0% +and the opposite of course if you make +the main side lobes + + align:start position:0% +the main side lobes + + + align:start position:0% +the main side lobes +main side lobe bigger the side lobes get + + align:start position:0% +main side lobe bigger the side lobes get + + + align:start position:0% +main side lobe bigger the side lobes get +smaller + + align:start position:0% +smaller + + + align:start position:0% +smaller +no doubt that is maybe not so + + align:start position:0% +no doubt that is maybe not so + + + align:start position:0% +no doubt that is maybe not so +necessarily going to happen i suspect + + align:start position:0% +necessarily going to happen i suspect + + + align:start position:0% +necessarily going to happen i suspect +that if you really wanted you could + + align:start position:0% +that if you really wanted you could + + + align:start position:0% +that if you really wanted you could +probably make something that had a big + + align:start position:0% +probably make something that had a big + + + align:start position:0% +probably make something that had a big +central lobe and big side lobes but + + align:start position:0% +central lobe and big side lobes but + + + align:start position:0% +central lobe and big side lobes but +nobody would really want that anyway + + align:start position:0% +nobody would really want that anyway + + + align:start position:0% +nobody would really want that anyway +okay and and then also uh this power + + align:start position:0% +okay and and then also uh this power + + + align:start position:0% +okay and and then also uh this power +loss problem uh that there is going to + + align:start position:0% +loss problem uh that there is going to + + + align:start position:0% +loss problem uh that there is going to +be some worse signal to noise sort of + + align:start position:0% +be some worse signal to noise sort of + + + align:start position:0% +be some worse signal to noise sort of +performance + + align:start position:0% +performance + + + align:start position:0% +performance +right so annular annular type pupils + + align:start position:0% +right so annular annular type pupils + + + align:start position:0% +right so annular annular type pupils +typically narrow the main lobe of the + + align:start position:0% +typically narrow the main lobe of the + + + align:start position:0% +typically narrow the main lobe of the +point spread function at the expense of + + align:start position:0% +point spread function at the expense of + + + align:start position:0% +point spread function at the expense of +higher side lobes gaussian type pupil + + align:start position:0% +higher side lobes gaussian type pupil + + + align:start position:0% +higher side lobes gaussian type pupil +functions typically suppress the side + + align:start position:0% +functions typically suppress the side + + + align:start position:0% +functions typically suppress the side +lobes but broaden the main lobe + + align:start position:0% +lobes but broaden the main lobe + + + align:start position:0% +lobes but broaden the main lobe +and uh so + + align:start position:0% +and uh so + + + align:start position:0% +and uh so +as it says here different sorts of + + align:start position:0% +as it says here different sorts of + + + align:start position:0% +as it says here different sorts of +filters like this might possibly be + + align:start position:0% +filters like this might possibly be + + + align:start position:0% +filters like this might possibly be +uh + + align:start position:0% +uh + + + align:start position:0% +uh +worth considering it for certain + + align:start position:0% +worth considering it for certain + + + align:start position:0% +worth considering it for certain +particular applications + + align:start position:0% +particular applications + + + align:start position:0% +particular applications +uh yeah and then he gives another couple + + align:start position:0% +uh yeah and then he gives another couple + + + align:start position:0% +uh yeah and then he gives another couple +of um + + align:start position:0% +of um + + + align:start position:0% +of um +problems with these things uh + + align:start position:0% +problems with these things uh + + + align:start position:0% +problems with these things uh +making a filter which is a varying + + align:start position:0% +making a filter which is a varying + + + align:start position:0% +making a filter which is a varying +amplitude is not easy + + align:start position:0% +amplitude is not easy + + + align:start position:0% +amplitude is not easy +uh and uh i guess nowadays you might do + + align:start position:0% +uh and uh i guess nowadays you might do + + + align:start position:0% +uh and uh i guess nowadays you might do +it with some liquid crystal device + + align:start position:0% +it with some liquid crystal device + + + align:start position:0% +it with some liquid crystal device +uh hopefully we we might be doing that + + align:start position:0% +uh hopefully we we might be doing that + + + align:start position:0% +uh hopefully we we might be doing that +soon one we shall do + + align:start position:0% +soon one we shall do + + + align:start position:0% +soon one we shall do +and uh but uh but you know + + align:start position:0% +and uh but uh but you know + + + align:start position:0% +and uh but uh but you know +until recently this would have to have + + align:start position:0% +until recently this would have to have + + + align:start position:0% +until recently this would have to have +been done by some sort of photo + + align:start position:0% +been done by some sort of photo + + + align:start position:0% +been done by some sort of photo +lithographic process + + align:start position:0% +lithographic process + + + align:start position:0% +lithographic process +and + + align:start position:0% +and + + + align:start position:0% +and +actually getting controlling + + align:start position:0% +actually getting controlling + + + align:start position:0% +actually getting controlling +uh the absorption of the filter + + align:start position:0% +uh the absorption of the filter + + + align:start position:0% +uh the absorption of the filter +to accurately + + align:start position:0% +to accurately + + + align:start position:0% +to accurately +fit what you designed is not trivial + + align:start position:0% +fit what you designed is not trivial + + + align:start position:0% +fit what you designed is not trivial +and there's also this energy loss + + align:start position:0% +and there's also this energy loss + + + align:start position:0% +and there's also this energy loss +problems then + + align:start position:0% +problems then + + + align:start position:0% +problems then +yeah nowadays people are very interested + + align:start position:0% +yeah nowadays people are very interested + + + align:start position:0% +yeah nowadays people are very interested +in uh in phase filters + + align:start position:0% +in uh in phase filters + + + align:start position:0% +in uh in phase filters +you can do a lot of these clever things + + align:start position:0% +you can do a lot of these clever things + + + align:start position:0% +you can do a lot of these clever things +also + + align:start position:0% +also + + + align:start position:0% +also +by using + + align:start position:0% +by using + + + align:start position:0% +by using +phase masks rather than amplitude masks + + align:start position:0% +phase masks rather than amplitude masks + + + align:start position:0% +phase masks rather than amplitude masks +and + + align:start position:0% +and + + + align:start position:0% +and +of course a phase + + align:start position:0% +of course a phase + + + align:start position:0% +of course a phase +appetizer is going to be lossless + + align:start position:0% +appetizer is going to be lossless + + + align:start position:0% +appetizer is going to be lossless +so that might make it sound attractive + + align:start position:0% +so that might make it sound attractive + + + align:start position:0% +so that might make it sound attractive +uh and uh so george + + align:start position:0% +uh and uh so george + + + align:start position:0% +uh and uh so george +says that maybe maybe it is attractive + + align:start position:0% +says that maybe maybe it is attractive + + + align:start position:0% +says that maybe maybe it is attractive +actually it turns out i think it's not + + align:start position:0% +actually it turns out i think it's not + + + align:start position:0% +actually it turns out i think it's not +quite as attractive as it might sound + + align:start position:0% +quite as attractive as it might sound + + + align:start position:0% +quite as attractive as it might sound +because actually very often what happens + + align:start position:0% +because actually very often what happens + + + align:start position:0% +because actually very often what happens +uh is if you use an absorbing filter + + align:start position:0% +uh is if you use an absorbing filter + + + align:start position:0% +uh is if you use an absorbing filter +uh the absorption that you can introduce + + align:start position:0% +uh the absorption that you can introduce + + + align:start position:0% +uh the absorption that you can introduce +actually can reduce the size of the size + + align:start position:0% +actually can reduce the size of the size + + + align:start position:0% +actually can reduce the size of the size +of the side lobes + + align:start position:0% +of the side lobes + + + align:start position:0% +of the side lobes +so + + align:start position:0% +so + + + align:start position:0% +so +if you if you do it cleverly you might + + align:start position:0% +if you if you do it cleverly you might + + + align:start position:0% +if you if you do it cleverly you might +be able to + + align:start position:0% +be able to + + + align:start position:0% +be able to +uh make the side lobes + + align:start position:0% +uh make the side lobes + + + align:start position:0% +uh make the side lobes +uh lower and also still get as much + + align:start position:0% +uh lower and also still get as much + + + align:start position:0% +uh lower and also still get as much +energy into the central lobe with as + + align:start position:0% +energy into the central lobe with as + + + align:start position:0% +energy into the central lobe with as +with an absorbing mask as with a pure + + align:start position:0% +with an absorbing mask as with a pure + + + align:start position:0% +with an absorbing mask as with a pure +face mask + + align:start position:0% + + + + align:start position:0% + +right yeah and then we get on to all + + align:start position:0% +right yeah and then we get on to all + + + align:start position:0% +right yeah and then we get on to all +these uh terminologies that uh george is + + align:start position:0% +these uh terminologies that uh george is + + + align:start position:0% +these uh terminologies that uh george is +obviously annoyed by as much as me + + align:start position:0% +obviously annoyed by as much as me + + + align:start position:0% +obviously annoyed by as much as me +this is one + + align:start position:0% +this is one + + + align:start position:0% +this is one +this super cool digital camera has a + + align:start position:0% +this super cool digital camera has a + + + align:start position:0% +this super cool digital camera has a +resolution of eight megapixels + + align:start position:0% +resolution of eight megapixels + + + align:start position:0% +resolution of eight megapixels +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +so what's he going to say about this + + align:start position:0% +so what's he going to say about this + + + align:start position:0% +so what's he going to say about this +a big no again + + align:start position:0% +a big no again + + + align:start position:0% +a big no again +right so + + align:start position:0% +right so + + + align:start position:0% +right so +um + + align:start position:0% +um + + + align:start position:0% +um +this this is + + align:start position:0% +this this is + + + align:start position:0% +this this is +using the word wrongly it's this this is + + align:start position:0% +using the word wrongly it's this this is + + + align:start position:0% +using the word wrongly it's this this is +nothing to do with resolution + + align:start position:0% +nothing to do with resolution + + + align:start position:0% +nothing to do with resolution +uh and uh so what they are actually + + align:start position:0% +uh and uh so what they are actually + + + align:start position:0% +uh and uh so what they are actually +referring to is the space bandwidth + + align:start position:0% +referring to is the space bandwidth + + + align:start position:0% +referring to is the space bandwidth +product + + align:start position:0% +product + + + align:start position:0% +product +of of the of the camera how many pixels + + align:start position:0% +of of the of the camera how many pixels + + + align:start position:0% +of of the of the camera how many pixels +there are which is not really measured + + align:start position:0% +there are which is not really measured + + + align:start position:0% +there are which is not really measured +as as resolution + + align:start position:0% +as as resolution + + + align:start position:0% +as as resolution +uh the other the other one as uh all the + + align:start position:0% +uh the other the other one as uh all the + + + align:start position:0% +uh the other the other one as uh all the +people in my group would know that i + + align:start position:0% +people in my group would know that i + + + align:start position:0% +people in my group would know that i +always get very cross about is these + + align:start position:0% +always get very cross about is these + + + align:start position:0% +always get very cross about is these +interferometry people who are always + + align:start position:0% +interferometry people who are always + + + align:start position:0% +interferometry people who are always +talking about interferometers being able + + align:start position:0% +talking about interferometers being able + + + align:start position:0% +talking about interferometers being able +to resolve one angstrom + + align:start position:0% +to resolve one angstrom + + + align:start position:0% +to resolve one angstrom +uh which is also wrong because it's + + align:start position:0% +uh which is also wrong because it's + + + align:start position:0% +uh which is also wrong because it's +nothing about resolving + + align:start position:0% +nothing about resolving + + + align:start position:0% +nothing about resolving +right so resolving resolution we've said + + align:start position:0% +right so resolving resolution we've said + + + align:start position:0% +right so resolving resolution we've said +what resolution means + + align:start position:0% +what resolution means + + + align:start position:0% +what resolution means +okay uh so this uh + + align:start position:0% +okay uh so this uh + + + align:start position:0% +okay uh so this uh +question of the number of pixels is + + align:start position:0% +question of the number of pixels is + + + align:start position:0% +question of the number of pixels is +there a connection between the two + + align:start position:0% +there a connection between the two + + + align:start position:0% +there a connection between the two +um well + + align:start position:0% +um well + + + align:start position:0% +um well +i guess the answer is there isn't there + + align:start position:0% +i guess the answer is there isn't there + + + align:start position:0% +i guess the answer is there isn't there +isn't + + align:start position:0% +isn't + + + align:start position:0% +isn't +uh there are there is a relationship if + + align:start position:0% +uh there are there is a relationship if + + + align:start position:0% +uh there are there is a relationship if +you design the optical system properly + + align:start position:0% +you design the optical system properly + + + align:start position:0% +you design the optical system properly +um but what what um george is pointing + + align:start position:0% +um but what what um george is pointing + + + align:start position:0% +um but what what um george is pointing +out here is that actually you know this + + align:start position:0% +out here is that actually you know this + + + align:start position:0% +out here is that actually you know this +is an example where the pixels are very + + align:start position:0% +is an example where the pixels are very + + + align:start position:0% +is an example where the pixels are very +much smaller than the point spread + + align:start position:0% +much smaller than the point spread + + + align:start position:0% +much smaller than the point spread +function of the of the optical system so + + align:start position:0% +function of the of the optical system so + + + align:start position:0% +function of the of the optical system so +actually here you're very much over + + align:start position:0% +actually here you're very much over + + + align:start position:0% +actually here you're very much over +sampling + + align:start position:0% +sampling + + + align:start position:0% +sampling +this image so + + align:start position:0% +this image so + + + align:start position:0% +this image so +all you're measuring you're measuring + + align:start position:0% +all you're measuring you're measuring + + + align:start position:0% +all you're measuring you're measuring +very accurately a blurred picture + + align:start position:0% +very accurately a blurred picture + + + align:start position:0% +very accurately a blurred picture +so that's not really giving you very + + align:start position:0% +so that's not really giving you very + + + align:start position:0% +so that's not really giving you very +good uh resolution and not really very + + align:start position:0% +good uh resolution and not really very + + + align:start position:0% +good uh resolution and not really very +you know the the the number of + + align:start position:0% +you know the the the number of + + + align:start position:0% +you know the the the number of +resolution image + + align:start position:0% +resolution image + + + align:start position:0% +resolution image +resolution uh elements in your image is + + align:start position:0% +resolution uh elements in your image is + + + align:start position:0% +resolution uh elements in your image is +actually much smaller than the number of + + align:start position:0% +actually much smaller than the number of + + + align:start position:0% +actually much smaller than the number of +pixels + + align:start position:0% + + + + align:start position:0% + +sometimes they use this word uh results + + align:start position:0% +sometimes they use this word uh results + + + align:start position:0% +sometimes they use this word uh results +don't they resolution elements have you + + align:start position:0% +don't they resolution elements have you + + + align:start position:0% +don't they resolution elements have you +seen that + + align:start position:0% +seen that + + + align:start position:0% +seen that +they spell it r e s e l + + align:start position:0% +they spell it r e s e l + + + align:start position:0% +they spell it r e s e l +it's an abbreviation for resolution + + align:start position:0% +it's an abbreviation for resolution + + + align:start position:0% +it's an abbreviation for resolution +element + + align:start position:0% +element + + + align:start position:0% +element +so it's the number of resolved + + align:start position:0% +so it's the number of resolved + + + align:start position:0% +so it's the number of resolved +spots that you've got in your in your + + align:start position:0% +spots that you've got in your in your + + + align:start position:0% +spots that you've got in your in your +device rather than the number of pixels + + align:start position:0% +device rather than the number of pixels + + + align:start position:0% +device rather than the number of pixels +okay some more misstatements + + align:start position:0% +okay some more misstatements + + + align:start position:0% +okay some more misstatements +uh it is pointless to attempt to resolve + + align:start position:0% +uh it is pointless to attempt to resolve + + + align:start position:0% +uh it is pointless to attempt to resolve +beyond the rayleigh criterion however + + align:start position:0% +beyond the rayleigh criterion however + + + align:start position:0% +beyond the rayleigh criterion however +defined uh no the difficulty increases + + align:start position:0% +defined uh no the difficulty increases + + + align:start position:0% +defined uh no the difficulty increases +gradually as feature sizes shrink and + + align:start position:0% +gradually as feature sizes shrink and + + + align:start position:0% +gradually as feature sizes shrink and +difficulty is noise dependence so it's + + align:start position:0% +difficulty is noise dependence so it's + + + align:start position:0% +difficulty is noise dependence so it's +not a + + align:start position:0% +not a + + + align:start position:0% +not a +sharp hard and fast line + + align:start position:0% +sharp hard and fast line + + + align:start position:0% +sharp hard and fast line +but + + align:start position:0% +but + + + align:start position:0% +but +that said i think you i think it + + align:start position:0% +that said i think you i think it + + + align:start position:0% +that said i think you i think it +probably would be + + align:start position:0% +probably would be + + + align:start position:0% +probably would be +pointless to attempt to resolve + + align:start position:0% +pointless to attempt to resolve + + + align:start position:0% +pointless to attempt to resolve +10 times the radi limit with an ordinary + + align:start position:0% +10 times the radi limit with an ordinary + + + align:start position:0% +10 times the radi limit with an ordinary +optical system because you know you're + + align:start position:0% +optical system because you know you're + + + align:start position:0% +optical system because you know you're +not going to be able to do that + + align:start position:0% +not going to be able to do that + + + align:start position:0% +not going to be able to do that +uh but + + align:start position:0% +uh but + + + align:start position:0% +uh but +instead that we were talking about + + align:start position:0% +instead that we were talking about + + + align:start position:0% +instead that we were talking about +earlier does do that right so this is + + align:start position:0% +earlier does do that right so this is + + + align:start position:0% +earlier does do that right so this is +and they taped well okay so maybe it is + + align:start position:0% +and they taped well okay so maybe it is + + + align:start position:0% +and they taped well okay so maybe it is +uh worth attempting to do it because + + align:start position:0% +uh worth attempting to do it because + + + align:start position:0% +uh worth attempting to do it because +people have come up up with ways of + + align:start position:0% +people have come up up with ways of + + + align:start position:0% +people have come up up with ways of +doing it now + + align:start position:0% +doing it now + + + align:start position:0% +doing it now +uh advertisation can be used to beat the + + align:start position:0% +uh advertisation can be used to beat the + + + align:start position:0% +uh advertisation can be used to beat the +resolution limit imposed by the + + align:start position:0% +resolution limit imposed by the + + + align:start position:0% +resolution limit imposed by the +numerical aperture + + align:start position:0% +numerical aperture + + + align:start position:0% +numerical aperture +and + + align:start position:0% +and + + + align:start position:0% +and +there's a big no there again watch the + + align:start position:0% +there's a big no there again watch the + + + align:start position:0% +there's a big no there again watch the +side lobe lights the side lobe growth + + align:start position:0% +side lobe lights the side lobe growth + + + align:start position:0% +side lobe lights the side lobe growth +and poor efficiency loss + + align:start position:0% +and poor efficiency loss + + + align:start position:0% +and poor efficiency loss +uh i don't know if you noticed but um i + + align:start position:0% +uh i don't know if you noticed but um i + + + align:start position:0% +uh i don't know if you noticed but um i +spoke to what one of + + align:start position:0% +spoke to what one of + + + align:start position:0% +spoke to what one of +maybe sheldon i can't i can't remember + + align:start position:0% +maybe sheldon i can't i can't remember + + + align:start position:0% +maybe sheldon i can't i can't remember +now there was a paper + + align:start position:0% +now there was a paper + + + align:start position:0% +now there was a paper +uh + + align:start position:0% +uh + + + align:start position:0% +uh +in uh nature methods recently by uh + + align:start position:0% +in uh nature methods recently by uh + + + align:start position:0% +in uh nature methods recently by uh +nikolai zejulev where he gave an example + + align:start position:0% +nikolai zejulev where he gave an example + + + align:start position:0% +nikolai zejulev where he gave an example +of a super resolving mask and he gave + + align:start position:0% +of a super resolving mask and he gave + + + align:start position:0% +of a super resolving mask and he gave +the pic this picture of a very narrow + + align:start position:0% +the pic this picture of a very narrow + + + align:start position:0% +the pic this picture of a very narrow +point spread function + + align:start position:0% +point spread function + + + align:start position:0% +point spread function +um + + align:start position:0% +um + + + align:start position:0% +um +you know improving on the + + align:start position:0% +you know improving on the + + + align:start position:0% +you know improving on the +rayleigh rate resolution limit by a + + align:start position:0% +rayleigh rate resolution limit by a + + + align:start position:0% +rayleigh rate resolution limit by a +factor of i don't know + + align:start position:0% + + + + align:start position:0% + +a few i think + + align:start position:0% +a few i think + + + align:start position:0% +a few i think +uh but i did so i did some calculations + + align:start position:0% +uh but i did so i did some calculations + + + align:start position:0% +uh but i did so i did some calculations +on the design he gave it turned out that + + align:start position:0% +on the design he gave it turned out that + + + align:start position:0% +on the design he gave it turned out that +this this little central peak was + + align:start position:0% +this this little central peak was + + + align:start position:0% +this this little central peak was +surrounded + + align:start position:0% +surrounded + + + align:start position:0% +surrounded +uh by side lobes that went up to + + align:start position:0% +uh by side lobes that went up to + + + align:start position:0% +uh by side lobes that went up to +something like 10 to the power 10 to the + + align:start position:0% +something like 10 to the power 10 to the + + + align:start position:0% +something like 10 to the power 10 to the +power 40 something or + + align:start position:0% +power 40 something or + + + align:start position:0% +power 40 something or +something really ridiculous + + align:start position:0% +something really ridiculous + + + align:start position:0% +something really ridiculous +and and the amount of energy that went + + align:start position:0% +and and the amount of energy that went + + + align:start position:0% +and and the amount of energy that went +into this central spot was like nothing + + align:start position:0% +into this central spot was like nothing + + + align:start position:0% +into this central spot was like nothing +and what made it even worse was that if + + align:start position:0% +and what made it even worse was that if + + + align:start position:0% +and what made it even worse was that if +you actually calculated what happened as + + align:start position:0% +you actually calculated what happened as + + + align:start position:0% +you actually calculated what happened as +you went out of focus + + align:start position:0% +you went out of focus + + + align:start position:0% +you went out of focus +you found that you also got these big + + align:start position:0% +you found that you also got these big + + + align:start position:0% +you found that you also got these big +walls around it + + align:start position:0% +walls around it + + + align:start position:0% +walls around it +very high all around it actually so it + + align:start position:0% +very high all around it actually so it + + + align:start position:0% +very high all around it actually so it +was this like this very small + + align:start position:0% +was this like this very small + + + align:start position:0% +was this like this very small +uh bright spots + + align:start position:0% +uh bright spots + + + align:start position:0% +uh bright spots +completely surrounded by something which + + align:start position:0% +completely surrounded by something which + + + align:start position:0% +completely surrounded by something which +was + + align:start position:0% +was + + + align:start position:0% +was +like 10 to the 40 times higher so how + + align:start position:0% +like 10 to the 40 times higher so how + + + align:start position:0% +like 10 to the 40 times higher so how +you would ever use that in practice you + + align:start position:0% +you would ever use that in practice you + + + align:start position:0% +you would ever use that in practice you +you can think + + align:start position:0% +you can think + + + align:start position:0% +you can think +uh it + + align:start position:0% +uh it + + + align:start position:0% +uh it +it really obviously wouldn't be a very + + align:start position:0% +it really obviously wouldn't be a very + + + align:start position:0% +it really obviously wouldn't be a very +practical device + + align:start position:0% +practical device + + + align:start position:0% +practical device +right + + align:start position:0% +right + + + align:start position:0% +right +and then uh right then the the number of + + align:start position:0% +and then uh right then the the number of + + + align:start position:0% +and then uh right then the the number of +um + + align:start position:0% +um + + + align:start position:0% +um +res uh pixels in your camera is not the + + align:start position:0% +res uh pixels in your camera is not the + + + align:start position:0% +res uh pixels in your camera is not the +resolution + + align:start position:0% + + + + align:start position:0% + +so what is resolution + + align:start position:0% +so what is resolution + + + align:start position:0% +so what is resolution +okay + + align:start position:0% +okay + + + align:start position:0% +okay +our ability to resolve two point objects + + align:start position:0% +our ability to resolve two point objects + + + align:start position:0% +our ability to resolve two point objects +uh based on on the image however this + + align:start position:0% +uh based on on the image however this + + + align:start position:0% +uh based on on the image however this +may be difficult to quantify + + align:start position:0% +may be difficult to quantify + + + align:start position:0% +may be difficult to quantify +um resolution is related to the n a i is + + align:start position:0% +um resolution is related to the n a i is + + + align:start position:0% +um resolution is related to the n a i is +proportional um to the n a + + align:start position:0% +proportional um to the n a + + + align:start position:0% +proportional um to the n a +the distance is inversely proportional + + align:start position:0% +the distance is inversely proportional + + + align:start position:0% +the distance is inversely proportional +to the n a + + align:start position:0% +to the n a + + + align:start position:0% +to the n a +um + + align:start position:0% +um + + + align:start position:0% +um +that's another thing that people + + align:start position:0% +that's another thing that people + + + align:start position:0% +that's another thing that people +sometimes get into nuts about of course + + align:start position:0% +sometimes get into nuts about of course + + + align:start position:0% +sometimes get into nuts about of course +because + + align:start position:0% +because + + + align:start position:0% +because +resolution + + align:start position:0% +resolution + + + align:start position:0% +resolution +means that + + align:start position:0% +means that + + + align:start position:0% +means that +the bigger the number + + align:start position:0% +the bigger the number + + + align:start position:0% +the bigger the number +the more is the resolution but actually + + align:start position:0% +the more is the resolution but actually + + + align:start position:0% +the more is the resolution but actually +the smaller the size the more the + + align:start position:0% +the smaller the size the more the + + + align:start position:0% +the smaller the size the more the +resolution so beware so uh sometimes + + align:start position:0% +resolution so beware so uh sometimes + + + align:start position:0% +resolution so beware so uh sometimes +actually people use the word uh the term + + align:start position:0% +actually people use the word uh the term + + + align:start position:0% +actually people use the word uh the term +resolving power + + align:start position:0% +resolving power + + + align:start position:0% +resolving power +to get around that problem + + align:start position:0% +to get around that problem + + + align:start position:0% +to get around that problem +uh because otherwise people say things + + align:start position:0% +uh because otherwise people say things + + + align:start position:0% +uh because otherwise people say things +which they don't really mean sometimes + + align:start position:0% + + + + align:start position:0% + +yeah so + + align:start position:0% +yeah so + + + align:start position:0% +yeah so +okay so other factors that + + align:start position:0% +okay so other factors that + + + align:start position:0% +okay so other factors that +can affect resolution aberrations + + align:start position:0% +can affect resolution aberrations + + + align:start position:0% +can affect resolution aberrations +appetization + + align:start position:0% +appetization + + + align:start position:0% +appetization +and noise + + align:start position:0% +and noise + + + align:start position:0% +and noise +right so + + align:start position:0% +right so + + + align:start position:0% +right so +is there an easy answer + + align:start position:0% +is there an easy answer + + + align:start position:0% +is there an easy answer +when in doubt quote 0.61 lambda over rna + + align:start position:0% +when in doubt quote 0.61 lambda over rna + + + align:start position:0% +when in doubt quote 0.61 lambda over rna +and then you'll get the marks in the + + align:start position:0% +and then you'll get the marks in the + + + align:start position:0% +and then you'll get the marks in the +exam + + align:start position:0% + + + + align:start position:0% + +okay so that's that one done + + align:start position:0% + + + + align:start position:0% + +so how we going + + align:start position:0% +so how we going + + + align:start position:0% +so how we going +got a bit more time yeah + + align:start position:0% +got a bit more time yeah + + + align:start position:0% +got a bit more time yeah +but + + align:start position:0% +but + + + align:start position:0% +but +that was last week's lecture i just gave + + align:start position:0% +that was last week's lecture i just gave + + + align:start position:0% +that was last week's lecture i just gave +them anyway so + + align:start position:0% +them anyway so + + + align:start position:0% +them anyway so +um + + align:start position:0% +um + + + align:start position:0% +um +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +i think it must be + + align:start position:0% +i think it must be + + + align:start position:0% +i think it must be +this one + + align:start position:0% + + + + align:start position:0% + +so i don't know how far we're going to + + align:start position:0% +so i don't know how far we're going to + + + align:start position:0% +so i don't know how far we're going to +get with this one + + align:start position:0% +get with this one + + + align:start position:0% +get with this one +but we can at least start it + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +um so what we're supposed to be doing + + align:start position:0% +um so what we're supposed to be doing + + + align:start position:0% +um so what we're supposed to be doing +today + + align:start position:0% +today + + + align:start position:0% +today +more applications of the transfer + + align:start position:0% +more applications of the transfer + + + align:start position:0% +more applications of the transfer +function a bit about depth of focus and + + align:start position:0% +function a bit about depth of focus and + + + align:start position:0% +function a bit about depth of focus and +a bit about deconvolution and there's + + align:start position:0% +a bit about deconvolution and there's + + + align:start position:0% +a bit about deconvolution and there's +some nice + + align:start position:0% +some nice + + + align:start position:0% +some nice +uh + + align:start position:0% +uh + + + align:start position:0% +uh +some nice um + + align:start position:0% +some nice um + + + align:start position:0% +some nice um +simulations that george has done to show + + align:start position:0% +simulations that george has done to show + + + align:start position:0% +simulations that george has done to show +that and then + + align:start position:0% +that and then + + + align:start position:0% +that and then +he's got down for wednesday which i'm + + align:start position:0% +he's got down for wednesday which i'm + + + align:start position:0% +he's got down for wednesday which i'm +also going to be giving i i think george + + align:start position:0% +also going to be giving i i think george + + + align:start position:0% +also going to be giving i i think george +is not back do you know when george + + align:start position:0% +is not back do you know when george + + + align:start position:0% +is not back do you know when george +comes back + + align:start position:0% +comes back + + + align:start position:0% +comes back +no okay + + align:start position:0% +no okay + + + align:start position:0% +no okay +no anyway so i i shall be giving the + + align:start position:0% +no anyway so i i shall be giving the + + + align:start position:0% +no anyway so i i shall be giving the +lecture on wednesday and uh so + + align:start position:0% +lecture on wednesday and uh so + + + align:start position:0% +lecture on wednesday and uh so +um + + align:start position:0% + + + + align:start position:0% + +uh polarization what what we don't + + align:start position:0% +uh polarization what what we don't + + + align:start position:0% +uh polarization what what we don't +finish from today will obviously also be + + align:start position:0% +finish from today will obviously also be + + + align:start position:0% +finish from today will obviously also be +on wednesday + + align:start position:0% +on wednesday + + + align:start position:0% +on wednesday +uh and then there's polarization + + align:start position:0% +uh and then there's polarization + + + align:start position:0% +uh and then there's polarization +intensity distribution near the focus of + + align:start position:0% +intensity distribution near the focus of + + + align:start position:0% +intensity distribution near the focus of +high in a imaging systems + + align:start position:0% +high in a imaging systems + + + align:start position:0% +high in a imaging systems +and + + align:start position:0% +and + + + align:start position:0% +and +yeah i don't know what else we're going + + align:start position:0% +yeah i don't know what else we're going + + + align:start position:0% +yeah i don't know what else we're going +to do actually because george keeps + + align:start position:0% +to do actually because george keeps + + + align:start position:0% +to do actually because george keeps +changing his mind about what we ought to + + align:start position:0% +changing his mind about what we ought to + + + align:start position:0% +changing his mind about what we ought to +put in that last lecture + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so defocus so this is an example of + + align:start position:0% +so defocus so this is an example of + + + align:start position:0% +so defocus so this is an example of +defocus anyone know what this movie is i + + align:start position:0% +defocus anyone know what this movie is i + + + align:start position:0% +defocus anyone know what this movie is i +don't i'm + + align:start position:0% +don't i'm + + + align:start position:0% +don't i'm +i'm out + + align:start position:0% +i'm out + + + align:start position:0% +i'm out +out of touch with the + + align:start position:0% +out of touch with the + + + align:start position:0% +out of touch with the +cinema recognize who the who the + + align:start position:0% +cinema recognize who the who the + + + align:start position:0% +cinema recognize who the who the +stars are no + + align:start position:0% +stars are no + + + align:start position:0% +stars are no +no all right i'm only asking because i + + align:start position:0% +no all right i'm only asking because i + + + align:start position:0% +no all right i'm only asking because i +just it's fake club + + align:start position:0% +just it's fake club + + + align:start position:0% +just it's fake club +is that right okay + + align:start position:0% +is that right okay + + + align:start position:0% +is that right okay +right anyway what you'll notice is this + + align:start position:0% +right anyway what you'll notice is this + + + align:start position:0% +right anyway what you'll notice is this +guy here is it a guy i can't really + + align:start position:0% +guy here is it a guy i can't really + + + align:start position:0% +guy here is it a guy i can't really +recognize what it is actually + + align:start position:0% +recognize what it is actually + + + align:start position:0% +recognize what it is actually +uh but it's out of focus + + align:start position:0% +uh but it's out of focus + + + align:start position:0% +uh but it's out of focus +so + + align:start position:0% +so + + + align:start position:0% +so +yeah it could be yeah okay so anyway so + + align:start position:0% +yeah it could be yeah okay so anyway so + + + align:start position:0% +yeah it could be yeah okay so anyway so +that's an example of defocus + + align:start position:0% + + + + align:start position:0% + +right then um + + align:start position:0% +right then um + + + align:start position:0% +right then um +this is what happens when you get a lens + + align:start position:0% +this is what happens when you get a lens + + + align:start position:0% +this is what happens when you get a lens +uh in the paraxial approximation and + + align:start position:0% +uh in the paraxial approximation and + + + align:start position:0% +uh in the paraxial approximation and +look at the + + align:start position:0% +look at the + + + align:start position:0% +look at the +uh intensity in the focal region you get + + align:start position:0% +uh intensity in the focal region you get + + + align:start position:0% +uh intensity in the focal region you get +something that looks a bit like that + + align:start position:0% +something that looks a bit like that + + + align:start position:0% +something that looks a bit like that +it doesn't look quite the same as bourne + + align:start position:0% +it doesn't look quite the same as bourne + + + align:start position:0% +it doesn't look quite the same as bourne +and wolf give it i don't know how george + + align:start position:0% +and wolf give it i don't know how george + + + align:start position:0% +and wolf give it i don't know how george +did this calculation but + + align:start position:0% +did this calculation but + + + align:start position:0% +did this calculation but +but you'll notice uh the this is the + + align:start position:0% +but you'll notice uh the this is the + + + align:start position:0% +but you'll notice uh the this is the +focal plane so this is a cross section + + align:start position:0% +focal plane so this is a cross section + + + align:start position:0% +focal plane so this is a cross section +through the airy disc so you see the + + align:start position:0% +through the airy disc so you see the + + + align:start position:0% +through the airy disc so you see the +central ah well i can tell you what why + + align:start position:0% +central ah well i can tell you what why + + + align:start position:0% +central ah well i can tell you what why +it's different then you can see these + + align:start position:0% +it's different then you can see these + + + align:start position:0% +it's different then you can see these +have got + + align:start position:0% +have got + + + align:start position:0% +have got +regularly spaced zeros so he's done this + + align:start position:0% +regularly spaced zeros so he's done this + + + align:start position:0% +regularly spaced zeros so he's done this +for a slight aperture + + align:start position:0% +for a slight aperture + + + align:start position:0% +for a slight aperture +hasn't he + + align:start position:0% +hasn't he + + + align:start position:0% +hasn't he +uh and so that might explain why it + + align:start position:0% +uh and so that might explain why it + + + align:start position:0% +uh and so that might explain why it +looks a bit different + + align:start position:0% +looks a bit different + + + align:start position:0% +looks a bit different +uh but what you see + + align:start position:0% + + + + align:start position:0% + +excuse me + + align:start position:0% +excuse me + + + align:start position:0% +excuse me +is that as you go out of focus + + align:start position:0% +is that as you go out of focus + + + align:start position:0% +is that as you go out of focus +um well note one thing it's symmetrical + + align:start position:0% +um well note one thing it's symmetrical + + + align:start position:0% +um well note one thing it's symmetrical +about the focal plane + + align:start position:0% +about the focal plane + + + align:start position:0% +about the focal plane +and uh and this is um + + align:start position:0% +and uh and this is um + + + align:start position:0% +and uh and this is um +uh i think we've probably had that + + align:start position:0% +uh i think we've probably had that + + + align:start position:0% +uh i think we've probably had that +somewhere before actually that it's + + align:start position:0% +somewhere before actually that it's + + + align:start position:0% +somewhere before actually that it's +symmetrical uh + + align:start position:0% +symmetrical uh + + + align:start position:0% +symmetrical uh +if um + + align:start position:0% +if um + + + align:start position:0% +if um +uh if if it's if it's calculated using + + align:start position:0% +uh if if it's if it's calculated using + + + align:start position:0% +uh if if it's if it's calculated using +the usual dubai approximation you you + + align:start position:0% +the usual dubai approximation you you + + + align:start position:0% +the usual dubai approximation you you +get a result like that so if you've got + + align:start position:0% +get a result like that so if you've got + + + align:start position:0% +get a result like that so if you've got +uh for example + + align:start position:0% +uh for example + + + align:start position:0% +uh for example +uh the aperture stop is in the front + + align:start position:0% +uh the aperture stop is in the front + + + align:start position:0% +uh the aperture stop is in the front +focal plane of the lens and you look at + + align:start position:0% +focal plane of the lens and you look at + + + align:start position:0% +focal plane of the lens and you look at +what happens in the back focal plane + + align:start position:0% +what happens in the back focal plane + + + align:start position:0% +what happens in the back focal plane +then that would be the case you get this + + align:start position:0% +then that would be the case you get this + + + align:start position:0% +then that would be the case you get this +symmetrical behavior like this + + align:start position:0% +symmetrical behavior like this + + + align:start position:0% +symmetrical behavior like this +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +you can see also these sort of bright + + align:start position:0% +you can see also these sort of bright + + + align:start position:0% +you can see also these sort of bright +bands that seem to go off uh uh diagonal + + align:start position:0% +bands that seem to go off uh uh diagonal + + + align:start position:0% +bands that seem to go off uh uh diagonal +lines here + + align:start position:0% +lines here + + + align:start position:0% +lines here +i guess um + + align:start position:0% +i guess um + + + align:start position:0% +i guess um +yeah so that corresponds roughly to the + + align:start position:0% +yeah so that corresponds roughly to the + + + align:start position:0% +yeah so that corresponds roughly to the +edge of the aperture then of course + + align:start position:0% +edge of the aperture then of course + + + align:start position:0% +edge of the aperture then of course +right + + align:start position:0% + + + + align:start position:0% + +and oh yeah so so the the width of the + + align:start position:0% +and oh yeah so so the the width of the + + + align:start position:0% +and oh yeah so so the the width of the +the central spot in this direction then + + align:start position:0% +the central spot in this direction then + + + align:start position:0% +the central spot in this direction then +we've said is this 0.61 lambda over n a + + align:start position:0% +we've said is this 0.61 lambda over n a + + + align:start position:0% +we've said is this 0.61 lambda over n a +and this distance + + align:start position:0% +and this distance + + + align:start position:0% +and this distance +from from the focal plane where you get + + align:start position:0% +from from the focal plane where you get + + + align:start position:0% +from from the focal plane where you get +to this first zero is given by some + + align:start position:0% +to this first zero is given by some + + + align:start position:0% +to this first zero is given by some +expression like this it goes as if this + + align:start position:0% +expression like this it goes as if this + + + align:start position:0% +expression like this it goes as if this +is really only true for the praxial case + + align:start position:0% +is really only true for the praxial case + + + align:start position:0% +is really only true for the praxial case +but for the praxial case + + align:start position:0% +but for the praxial case + + + align:start position:0% +but for the praxial case +uh this n a here n a squared here + + align:start position:0% +uh this n a here n a squared here + + + align:start position:0% +uh this n a here n a squared here +if it's the high aperture case which we + + align:start position:0% +if it's the high aperture case which we + + + align:start position:0% +if it's the high aperture case which we +might we might consider on wednesday uh + + align:start position:0% +might we might consider on wednesday uh + + + align:start position:0% +might we might consider on wednesday uh +you find that this is not quite + + align:start position:0% +you find that this is not quite + + + align:start position:0% +you find that this is not quite +right anymore + + align:start position:0% + + + + align:start position:0% + +okay yeah so delta x is the radio + + align:start position:0% +okay yeah so delta x is the radio + + + align:start position:0% +okay yeah so delta x is the radio +resolution delta z is the depth of focus + + align:start position:0% +resolution delta z is the depth of focus + + + align:start position:0% +resolution delta z is the depth of focus +today's top topics uh depth of focus or + + align:start position:0% +today's top topics uh depth of focus or + + + align:start position:0% +today's top topics uh depth of focus or +depth of field + + align:start position:0% +depth of field + + + align:start position:0% +depth of field +and both of those he calls dof + + align:start position:0% +and both of those he calls dof + + + align:start position:0% +and both of those he calls dof +note the very high numerical apertures + + align:start position:0% +note the very high numerical apertures + + + align:start position:0% +note the very high numerical apertures +the scalar approximation is no longer + + align:start position:0% +the scalar approximation is no longer + + + align:start position:0% +the scalar approximation is no longer +good the vectorial nature of the + + align:start position:0% +good the vectorial nature of the + + + align:start position:0% +good the vectorial nature of the +electromagnetic field becomes important + + align:start position:0% +electromagnetic field becomes important + + + align:start position:0% +electromagnetic field becomes important +um that is true there's there's other + + align:start position:0% +um that is true there's there's other + + + align:start position:0% +um that is true there's there's other +things as well though uh when you do all + + align:start position:0% +things as well though uh when you do all + + + align:start position:0% +things as well though uh when you do all +this practical stuff + + align:start position:0% +this practical stuff + + + align:start position:0% +this practical stuff +if you remember you all the time you're + + align:start position:0% +if you remember you all the time you're + + + align:start position:0% +if you remember you all the time you're +replacing sine theta by theta and things + + align:start position:0% +replacing sine theta by theta and things + + + align:start position:0% +replacing sine theta by theta and things +like that making approximations like + + align:start position:0% +like that making approximations like + + + align:start position:0% +like that making approximations like +that so + + align:start position:0% +that so + + + align:start position:0% +that so +there are actually lots of + + align:start position:0% +there are actually lots of + + + align:start position:0% +there are actually lots of +approximations you make + + align:start position:0% +approximations you make + + + align:start position:0% +approximations you make +uh one one is uh the the fact that the + + align:start position:0% +uh one one is uh the the fact that the + + + align:start position:0% +uh one one is uh the the fact that the +angles are small the other is that you + + align:start position:0% +angles are small the other is that you + + + align:start position:0% +angles are small the other is that you +neglect the polarization effects when + + align:start position:0% +neglect the polarization effects when + + + align:start position:0% +neglect the polarization effects when +the apertures become big uh then the + + align:start position:0% +the apertures become big uh then the + + + align:start position:0% +the apertures become big uh then the +polarization effects become very + + align:start position:0% +polarization effects become very + + + align:start position:0% +polarization effects become very +important + + align:start position:0% + + + + align:start position:0% + +okay so we're going to look at this sort + + align:start position:0% +okay so we're going to look at this sort + + + align:start position:0% +okay so we're going to look at this sort +of system + + align:start position:0% +of system + + + align:start position:0% +of system +uh and so this is a 4f system + + align:start position:0% +uh and so this is a 4f system + + + align:start position:0% +uh and so this is a 4f system +with magnification + + align:start position:0% +with magnification + + + align:start position:0% +with magnification +uh and so the two the focal lengths of + + align:start position:0% +uh and so the two the focal lengths of + + + align:start position:0% +uh and so the two the focal lengths of +the two lenses are different in this + + align:start position:0% +the two lenses are different in this + + + align:start position:0% +the two lenses are different in this +case + + align:start position:0% +case + + + align:start position:0% +case +uh and + + align:start position:0% +uh and + + + align:start position:0% +uh and +so this shows what happens if you + + align:start position:0% +so this shows what happens if you + + + align:start position:0% +so this shows what happens if you +if you're looking at + + align:start position:0% +if you're looking at + + + align:start position:0% +if you're looking at +an object which is placed a distance f + + align:start position:0% +an object which is placed a distance f + + + align:start position:0% +an object which is placed a distance f +in front of this lens + + align:start position:0% +in front of this lens + + + align:start position:0% +in front of this lens +and your screen is placed the difference + + align:start position:0% +and your screen is placed the difference + + + align:start position:0% +and your screen is placed the difference +f2 behind this lens + + align:start position:0% +f2 behind this lens + + + align:start position:0% +f2 behind this lens +and your aperture is f1 from this one + + align:start position:0% +and your aperture is f1 from this one + + + align:start position:0% +and your aperture is f1 from this one +and f2 from this one so everything there + + align:start position:0% +and f2 from this one so everything there + + + align:start position:0% +and f2 from this one so everything there +is set up properly + + align:start position:0% +is set up properly + + + align:start position:0% +is set up properly +right for a as as defined for a four f + + align:start position:0% +right for a as as defined for a four f + + + align:start position:0% +right for a as as defined for a four f +system uh and this is the case where + + align:start position:0% +system uh and this is the case where + + + align:start position:0% +system uh and this is the case where +you'd expect as i was just describing + + align:start position:0% +you'd expect as i was just describing + + + align:start position:0% +you'd expect as i was just describing +uh the the defocus point spread function + + align:start position:0% +uh the the defocus point spread function + + + align:start position:0% +uh the the defocus point spread function +is going to be symmetric + + align:start position:0% +is going to be symmetric + + + align:start position:0% +is going to be symmetric +right so we place our mask there + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +we've got our + + align:start position:0% +we've got our + + + align:start position:0% +we've got our +pupil so this is our object function + + align:start position:0% +pupil so this is our object function + + + align:start position:0% +pupil so this is our object function +this is uh the um + + align:start position:0% +this is uh the um + + + align:start position:0% +this is uh the um +angular spectra the uh the spectrum of + + align:start position:0% +angular spectra the uh the spectrum of + + + align:start position:0% +angular spectra the uh the spectrum of +the object + + align:start position:0% +the object + + + align:start position:0% +the object +uh in this plane plane here which is + + align:start position:0% +uh in this plane plane here which is + + + align:start position:0% +uh in this plane plane here which is +then filtered by the aperture stop + + align:start position:0% +then filtered by the aperture stop + + + align:start position:0% +then filtered by the aperture stop +uh and then that gives + + align:start position:0% +uh and then that gives + + + align:start position:0% +uh and then that gives +uh some + + align:start position:0% +uh some + + + align:start position:0% +uh some +uh some sort of amplitude in this + + align:start position:0% +uh some sort of amplitude in this + + + align:start position:0% +uh some sort of amplitude in this +uh plane here which is going to be + + align:start position:0% +uh plane here which is going to be + + + align:start position:0% +uh plane here which is going to be +inverted and also + + align:start position:0% +inverted and also + + + align:start position:0% +inverted and also +magnified or otherwise according to the + + align:start position:0% +magnified or otherwise according to the + + + align:start position:0% +magnified or otherwise according to the +ratio of f1 over f2 + + align:start position:0% +ratio of f1 over f2 + + + align:start position:0% +ratio of f1 over f2 +and there's the rays going through it + + align:start position:0% + + + + align:start position:0% + +and this is showing how + + align:start position:0% +and this is showing how + + + align:start position:0% +and this is showing how +yeah this plane this is his terminology + + align:start position:0% +yeah this plane this is his terminology + + + align:start position:0% +yeah this plane this is his terminology +this is x + + align:start position:0% +this is x + + + align:start position:0% +this is x +this is x prime this is x double prime + + align:start position:0% +this is x prime this is x double prime + + + align:start position:0% +this is x prime this is x double prime +uh and you can see here + + align:start position:0% +uh and you can see here + + + align:start position:0% +uh and you can see here +x double prime maximum is equal to the + + align:start position:0% +x double prime maximum is equal to the + + + align:start position:0% +x double prime maximum is equal to the +at the + + align:start position:0% +at the + + + align:start position:0% +at the +radius of the aperture + + align:start position:0% +radius of the aperture + + + align:start position:0% +radius of the aperture +so this is this terminology we're going + + align:start position:0% +so this is this terminology we're going + + + align:start position:0% +so this is this terminology we're going +to get that + + align:start position:0% +to get that + + + align:start position:0% +to get that +in a minute coming out again this is + + align:start position:0% +in a minute coming out again this is + + + align:start position:0% +in a minute coming out again this is +this is a function of x this is a + + align:start position:0% +this is a function of x this is a + + + align:start position:0% +this is a function of x this is a +function of x double prime this is a + + align:start position:0% +function of x double prime this is a + + + align:start position:0% +function of x double prime this is a +function of x prime + + align:start position:0% + + + + align:start position:0% + +this is the numerical aperture of the + + align:start position:0% +this is the numerical aperture of the + + + align:start position:0% +this is the numerical aperture of the +lens that's looking at it + + align:start position:0% +lens that's looking at it + + + align:start position:0% +lens that's looking at it +uh and uh + + align:start position:0% +uh and uh + + + align:start position:0% +uh and uh +yeah so + + align:start position:0% +yeah so + + + align:start position:0% +yeah so +okay so the numerical aperture is equal + + align:start position:0% +okay so the numerical aperture is equal + + + align:start position:0% +okay so the numerical aperture is equal +to x double + + align:start position:0% +to x double + + + align:start position:0% +to x double +double prime + + align:start position:0% +double prime + + + align:start position:0% +double prime +maximum which is equal to a over f1 + + align:start position:0% + + + + align:start position:0% + +again + + align:start position:0% +again + + + align:start position:0% +again +assuming that + + align:start position:0% + + + + align:start position:0% + +sine theta or tan theta is at both theta + + align:start position:0% +sine theta or tan theta is at both theta + + + align:start position:0% +sine theta or tan theta is at both theta +right now what we're going to look at + + align:start position:0% +right now what we're going to look at + + + align:start position:0% +right now what we're going to look at +now is what happens if we defocus this + + align:start position:0% +now is what happens if we defocus this + + + align:start position:0% +now is what happens if we defocus this +system so now our object has been + + align:start position:0% +system so now our object has been + + + align:start position:0% +system so now our object has been +displaced the distance delta away + + align:start position:0% +displaced the distance delta away + + + align:start position:0% +displaced the distance delta away +and we want to calculate what the image + + align:start position:0% +and we want to calculate what the image + + + align:start position:0% +and we want to calculate what the image +of that looks like now + + align:start position:0% +of that looks like now + + + align:start position:0% +of that looks like now +and so what we can say is that + + align:start position:0% +and so what we can say is that + + + align:start position:0% +and so what we can say is that +after we've illuminated this object + + align:start position:0% +after we've illuminated this object + + + align:start position:0% +after we've illuminated this object +we've got this gt of x + + align:start position:0% +we've got this gt of x + + + align:start position:0% +we've got this gt of x +and then that light is going to + + align:start position:0% +and then that light is going to + + + align:start position:0% +and then that light is going to +propagate from here to here + + align:start position:0% +propagate from here to here + + + align:start position:0% +propagate from here to here +and in order to calculate that we have + + align:start position:0% +and in order to calculate that we have + + + align:start position:0% +and in order to calculate that we have +to convolve it + + align:start position:0% +to convolve it + + + align:start position:0% +to convolve it +uh with the propagation kernel + + align:start position:0% +uh with the propagation kernel + + + align:start position:0% +uh with the propagation kernel +right so you convolve it with this thing + + align:start position:0% + + + + align:start position:0% + +for some reason when george converted + + align:start position:0% +for some reason when george converted + + + align:start position:0% +for some reason when george converted +this from his um + + align:start position:0% +this from his um + + + align:start position:0% +this from his um +whatever his other thing's called + + align:start position:0% +whatever his other thing's called + + + align:start position:0% +whatever his other thing's called +keynotes + + align:start position:0% +keynotes + + + align:start position:0% +keynotes +uh to powerpoint all the equations are + + align:start position:0% +uh to powerpoint all the equations are + + + align:start position:0% +uh to powerpoint all the equations are +like um as though someone's had their + + align:start position:0% +like um as though someone's had their + + + align:start position:0% +like um as though someone's had their +martinis before the lecture + + align:start position:0% +martinis before the lecture + + + align:start position:0% +martinis before the lecture +uh and uh right so we then look at the + + align:start position:0% +uh and uh right so we then look at the + + + align:start position:0% +uh and uh right so we then look at the +fourier transform of that in this plane + + align:start position:0% +fourier transform of that in this plane + + + align:start position:0% +fourier transform of that in this plane +here + + align:start position:0% +here + + + align:start position:0% +here +so this thing convolves uh fourier + + align:start position:0% +so this thing convolves uh fourier + + + align:start position:0% +so this thing convolves uh fourier +transforms to this + + align:start position:0% +transforms to this + + + align:start position:0% +transforms to this +the convolution + + align:start position:0% +the convolution + + + align:start position:0% +the convolution +uh transforms to a product + + align:start position:0% +uh transforms to a product + + + align:start position:0% +uh transforms to a product +and this gaussian + + align:start position:0% +and this gaussian + + + align:start position:0% +and this gaussian +transforms to another gaussian and + + align:start position:0% +transforms to another gaussian and + + + align:start position:0% +transforms to another gaussian and +notice that as usual of course you + + align:start position:0% +notice that as usual of course you + + + align:start position:0% +notice that as usual of course you +remember that the scaling thing for + + align:start position:0% +remember that the scaling thing for + + + align:start position:0% +remember that the scaling thing for +fourier transforms the bigger a function + + align:start position:0% +fourier transforms the bigger a function + + + align:start position:0% +fourier transforms the bigger a function +is the smaller its fourier transform and + + align:start position:0% +is the smaller its fourier transform and + + + align:start position:0% +is the smaller its fourier transform and +vice versa so this lambda delta at the + + align:start position:0% +vice versa so this lambda delta at the + + + align:start position:0% +vice versa so this lambda delta at the +bottom + + align:start position:0% +bottom + + + align:start position:0% +bottom +appears now at the top right so the + + align:start position:0% +appears now at the top right so the + + + align:start position:0% +appears now at the top right so the +bigger + + align:start position:0% +bigger + + + align:start position:0% +bigger +the bigger delta is the bigger this + + align:start position:0% +the bigger delta is the bigger this + + + align:start position:0% +the bigger delta is the bigger this +thing's going to be here + + align:start position:0% +thing's going to be here + + + align:start position:0% +thing's going to be here +right yeah + + align:start position:0% + + + + align:start position:0% + +yeah is e to the imaginary x square a + + align:start position:0% +yeah is e to the imaginary x square a + + + align:start position:0% +yeah is e to the imaginary x square a +gaussian or only the e to the real x + + align:start position:0% +gaussian or only the e to the real x + + + align:start position:0% +gaussian or only the e to the real x +square okay yeah the real gaussian is e + + align:start position:0% +square okay yeah the real gaussian is e + + + align:start position:0% +square okay yeah the real gaussian is e +to the minus x squared isn't it + + align:start position:0% +to the minus x squared isn't it + + + align:start position:0% +to the minus x squared isn't it +e to the minus x squared does that yeah + + align:start position:0% +e to the minus x squared does that yeah + + + align:start position:0% +e to the minus x squared does that yeah +this is uh this is what you might call a + + align:start position:0% +this is uh this is what you might call a + + + align:start position:0% +this is uh this is what you might call a +uh + + align:start position:0% +uh + + + align:start position:0% +uh +an imaginary gaussian + + align:start position:0% +an imaginary gaussian + + + align:start position:0% +an imaginary gaussian +but it all comes out in the wash + + align:start position:0% +but it all comes out in the wash + + + align:start position:0% +but it all comes out in the wash +actually + + align:start position:0% +actually + + + align:start position:0% +actually +so just the same as the fourier + + align:start position:0% +so just the same as the fourier + + + align:start position:0% +so just the same as the fourier +transform + + align:start position:0% +transform + + + align:start position:0% +transform +of the normal gaussian is another + + align:start position:0% +of the normal gaussian is another + + + align:start position:0% +of the normal gaussian is another +gaussian so the fourier transform of + + align:start position:0% +gaussian so the fourier transform of + + + align:start position:0% +gaussian so the fourier transform of +this imaginary gaussian is another + + align:start position:0% +this imaginary gaussian is another + + + align:start position:0% +this imaginary gaussian is another +imaginary gaussian + + align:start position:0% +imaginary gaussian + + + align:start position:0% +imaginary gaussian +right so what it's really converting is + + align:start position:0% +right so what it's really converting is + + + align:start position:0% +right so what it's really converting is +a a parabolic phase front here to a + + align:start position:0% +a a parabolic phase front here to a + + + align:start position:0% +a a parabolic phase front here to a +parabolic face front here + + align:start position:0% +parabolic face front here + + + align:start position:0% +parabolic face front here +yeah so it um you can get it just by + + align:start position:0% +yeah so it um you can get it just by + + + align:start position:0% +yeah so it um you can get it just by +just by getting the normal expression i + + align:start position:0% +just by getting the normal expression i + + + align:start position:0% +just by getting the normal expression i +mean + + align:start position:0% +mean + + + align:start position:0% +mean +it's it sometimes amazes me how much + + align:start position:0% +it's it sometimes amazes me how much + + + align:start position:0% +it's it sometimes amazes me how much +liberties you can take with these things + + align:start position:0% +liberties you can take with these things + + + align:start position:0% +liberties you can take with these things +but you just take the expressions for + + align:start position:0% +but you just take the expressions for + + + align:start position:0% +but you just take the expressions for +the gaussian and you put in this complex + + align:start position:0% +the gaussian and you put in this complex + + + align:start position:0% +the gaussian and you put in this complex +number and it gives the right answer so + + align:start position:0% +number and it gives the right answer so + + + align:start position:0% +number and it gives the right answer so +it's very nice + + align:start position:0% +it's very nice + + + align:start position:0% +it's very nice +guess occasionally there might be + + align:start position:0% +guess occasionally there might be + + + align:start position:0% +guess occasionally there might be +occasions when it doesn't work + + align:start position:0% + + + + align:start position:0% + +yeah okay so what he's then saying is + + align:start position:0% +yeah okay so what he's then saying is + + + align:start position:0% +yeah okay so what he's then saying is +that + + align:start position:0% +that + + + align:start position:0% +that +you can think of this + + align:start position:0% +you can think of this + + + align:start position:0% +you can think of this +this is the object + + align:start position:0% +this is the object + + + align:start position:0% +this is the object +for our this is the spectrum for our + + align:start position:0% +for our this is the spectrum for our + + + align:start position:0% +for our this is the spectrum for our +defocused objects which is multiplied by + + align:start position:0% +defocused objects which is multiplied by + + + align:start position:0% +defocused objects which is multiplied by +the + + align:start position:0% +the + + + align:start position:0% +the +uh the um + + align:start position:0% +uh the um + + + align:start position:0% +uh the um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +pupil function of the system + + align:start position:0% +pupil function of the system + + + align:start position:0% +pupil function of the system +uh but that is exactly equivalent of + + align:start position:0% +uh but that is exactly equivalent of + + + align:start position:0% +uh but that is exactly equivalent of +course to thinking of of it as the the + + align:start position:0% +course to thinking of of it as the the + + + align:start position:0% +course to thinking of of it as the the +ordinary object spectrum + + align:start position:0% +ordinary object spectrum + + + align:start position:0% +ordinary object spectrum +multiplied by + + align:start position:0% +multiplied by + + + align:start position:0% +multiplied by +a + + align:start position:0% +a + + + align:start position:0% +a +a modified + + align:start position:0% +a modified + + + align:start position:0% +a modified +pupil function right so it doesn't + + align:start position:0% +pupil function right so it doesn't + + + align:start position:0% +pupil function right so it doesn't +matter whether you associate this with + + align:start position:0% +matter whether you associate this with + + + align:start position:0% +matter whether you associate this with +this or with the pupil function + + align:start position:0% +this or with the pupil function + + + align:start position:0% +this or with the pupil function +uh so so that's what we can think of we + + align:start position:0% +uh so so that's what we can think of we + + + align:start position:0% +uh so so that's what we can think of we +can think of the + + align:start position:0% +can think of the + + + align:start position:0% +can think of the +uh the objects as being the same as when + + align:start position:0% +uh the objects as being the same as when + + + align:start position:0% +uh the objects as being the same as when +if as if it wasn't defocused and we can + + align:start position:0% +if as if it wasn't defocused and we can + + + align:start position:0% +if as if it wasn't defocused and we can +think of the + + align:start position:0% +think of the + + + align:start position:0% +think of the +uh pupil function of the thing being + + align:start position:0% +uh pupil function of the thing being + + + align:start position:0% +uh pupil function of the thing being +modified to take into account of the + + align:start position:0% +modified to take into account of the + + + align:start position:0% +modified to take into account of the +defocus we sometimes call that the + + align:start position:0% +defocus we sometimes call that the + + + align:start position:0% +defocus we sometimes call that the +default defocus transfer function + + align:start position:0% +default defocus transfer function + + + align:start position:0% +default defocus transfer function +and so he's now going to calculate that + + align:start position:0% +and so he's now going to calculate that + + + align:start position:0% +and so he's now going to calculate that +yeah so the defocus he calls it here the + + align:start position:0% +yeah so the defocus he calls it here the + + + align:start position:0% +yeah so the defocus he calls it here the +defocus amplitude transfer function + + align:start position:0% +defocus amplitude transfer function + + + align:start position:0% +defocus amplitude transfer function +right so remember here we're dealing + + align:start position:0% +right so remember here we're dealing + + + align:start position:0% +right so remember here we're dealing +this is dealing now with coherent system + + align:start position:0% +this is dealing now with coherent system + + + align:start position:0% +this is dealing now with coherent system +uh we before when we were doing the + + align:start position:0% +uh we before when we were doing the + + + align:start position:0% +uh we before when we were doing the +resolution we were looking at incoherent + + align:start position:0% +resolution we were looking at incoherent + + + align:start position:0% +resolution we were looking at incoherent +systems so now we've gone back to + + align:start position:0% +systems so now we've gone back to + + + align:start position:0% +systems so now we've gone back to +coherent systems + + align:start position:0% +coherent systems + + + align:start position:0% +coherent systems +so + + align:start position:0% +so + + + align:start position:0% +so +you have to be wary of that because + + align:start position:0% +you have to be wary of that because + + + align:start position:0% +you have to be wary of that because +sometimes there's some differences + + align:start position:0% +sometimes there's some differences + + + align:start position:0% +sometimes there's some differences +okay so all this is saying then yeah or + + align:start position:0% +okay so all this is saying then yeah or + + + align:start position:0% +okay so all this is saying then yeah or +you remember + + align:start position:0% +you remember + + + align:start position:0% +you remember +to go from the + + align:start position:0% +to go from the + + + align:start position:0% +to go from the +uh from the pupil + + align:start position:0% +uh from the pupil + + + align:start position:0% +uh from the pupil +to the transfer function all you have to + + align:start position:0% +to the transfer function all you have to + + + align:start position:0% +to the transfer function all you have to +do is a coordinate scaling + + align:start position:0% +do is a coordinate scaling + + + align:start position:0% +do is a coordinate scaling +right so + + align:start position:0% +right so + + + align:start position:0% +right so +so the uh the + + align:start position:0% +so the uh the + + + align:start position:0% +so the uh the +amplitude transfer function is just the + + align:start position:0% +amplitude transfer function is just the + + + align:start position:0% +amplitude transfer function is just the +scaled version of this pupil function + + align:start position:0% +scaled version of this pupil function + + + align:start position:0% +scaled version of this pupil function +and again it comes out to be now of + + align:start position:0% +and again it comes out to be now of + + + align:start position:0% +and again it comes out to be now of +course it's going to be + + align:start position:0% +course it's going to be + + + align:start position:0% +course it's going to be +it's multiplied of course still by the + + align:start position:0% +it's multiplied of course still by the + + + align:start position:0% +it's multiplied of course still by the +circular aperture + + align:start position:0% +circular aperture + + + align:start position:0% +circular aperture +but inside that circular aperture where + + align:start position:0% +but inside that circular aperture where + + + align:start position:0% +but inside that circular aperture where +it's got some value + + align:start position:0% +it's got some value + + + align:start position:0% +it's got some value +its value is given by this complex + + align:start position:0% +its value is given by this complex + + + align:start position:0% +its value is given by this complex +exponential a complex uh a complex + + align:start position:0% +exponential a complex uh a complex + + + align:start position:0% +exponential a complex uh a complex +gaussian like we were just + + align:start position:0% +gaussian like we were just + + + align:start position:0% +gaussian like we were just +saying before + + align:start position:0% + + + + align:start position:0% + +and that's what this looks like + + align:start position:0% +and that's what this looks like + + + align:start position:0% +and that's what this looks like +now notice so this is cosine this is + + align:start position:0% +now notice so this is cosine this is + + + align:start position:0% +now notice so this is cosine this is +looking at just the real part so + + align:start position:0% +looking at just the real part so + + + align:start position:0% +looking at just the real part so +actually it was a complex it was an e to + + align:start position:0% +actually it was a complex it was an e to + + + align:start position:0% +actually it was a complex it was an e to +the minus i something + + align:start position:0% +the minus i something + + + align:start position:0% +the minus i something +so you can break that up into cos plus i + + align:start position:0% +so you can break that up into cos plus i + + + align:start position:0% +so you can break that up into cos plus i +sine + + align:start position:0% +sine + + + align:start position:0% +sine +and the cos part + + align:start position:0% +and the cos part + + + align:start position:0% +and the cos part +is the real part and the sign part is + + align:start position:0% +is the real part and the sign part is + + + align:start position:0% +is the real part and the sign part is +the imaginary part + + align:start position:0% +the imaginary part + + + align:start position:0% +the imaginary part +and + + align:start position:0% +and + + + align:start position:0% +and +as we when we looked at imaging earlier + + align:start position:0% +as we when we looked at imaging earlier + + + align:start position:0% +as we when we looked at imaging earlier +the the real part images real objects so + + align:start position:0% +the the real part images real objects so + + + align:start position:0% +the the real part images real objects so +an amplitude object will be imaged by + + align:start position:0% +an amplitude object will be imaged by + + + align:start position:0% +an amplitude object will be imaged by +the real path a phase object would be + + align:start position:0% +the real path a phase object would be + + + align:start position:0% +the real path a phase object would be +imaged by + + align:start position:0% +imaged by + + + align:start position:0% +imaged by +the imaginary part + + align:start position:0% +the imaginary part + + + align:start position:0% +the imaginary part +but we're not going to say anything + + align:start position:0% +but we're not going to say anything + + + align:start position:0% +but we're not going to say anything +about that we just keep with the real + + align:start position:0% +about that we just keep with the real + + + align:start position:0% +about that we just keep with the real +part so this is cos but it's not a + + align:start position:0% +part so this is cos but it's not a + + + align:start position:0% +part so this is cos but it's not a +normal cause it's cos of an x squared so + + align:start position:0% +normal cause it's cos of an x squared so + + + align:start position:0% +normal cause it's cos of an x squared so +that's why it looks a rather strange + + align:start position:0% +that's why it looks a rather strange + + + align:start position:0% +that's why it looks a rather strange +shape + + align:start position:0% +shape + + + align:start position:0% +shape +compared with a normal cosine you can + + align:start position:0% +compared with a normal cosine you can + + + align:start position:0% +compared with a normal cosine you can +see it's become very flat there + + align:start position:0% +see it's become very flat there + + + align:start position:0% +see it's become very flat there +and then it becomes + + align:start position:0% +and then it becomes + + + align:start position:0% +and then it becomes +more oscillating later on + + align:start position:0% +more oscillating later on + + + align:start position:0% +more oscillating later on +and so this is what it looks like of + + align:start position:0% +and so this is what it looks like of + + + align:start position:0% +and so this is what it looks like of +course the actual scaling of this + + align:start position:0% +course the actual scaling of this + + + align:start position:0% +course the actual scaling of this +is going to depend + + align:start position:0% +is going to depend + + + align:start position:0% +is going to depend +uh on + + align:start position:0% +uh on + + + align:start position:0% +uh on +uh + + align:start position:0% +uh + + + align:start position:0% +uh +on on the the value of this delta + + align:start position:0% +on on the the value of this delta + + + align:start position:0% +on on the the value of this delta +right so here he looks at where this + + align:start position:0% +right so here he looks at where this + + + align:start position:0% +right so here he looks at where this +crosses + + align:start position:0% +crosses + + + align:start position:0% +crosses +the axis + + align:start position:0% +the axis + + + align:start position:0% +the axis +so + + align:start position:0% +so + + + align:start position:0% +so +this this parameter x double prime over + + align:start position:0% +this this parameter x double prime over + + + align:start position:0% +this this parameter x double prime over +lambda f1 is equal to u the spatial + + align:start position:0% +lambda f1 is equal to u the spatial + + + align:start position:0% +lambda f1 is equal to u the spatial +frequency + + align:start position:0% +frequency + + + align:start position:0% +frequency +so this is just u squared here + + align:start position:0% +so this is just u squared here + + + align:start position:0% +so this is just u squared here +and he says that this crosses the axis + + align:start position:0% +and he says that this crosses the axis + + + align:start position:0% +and he says that this crosses the axis +where this argument is equal to pi over + + align:start position:0% +where this argument is equal to pi over + + + align:start position:0% +where this argument is equal to pi over + + align:start position:0% + + + align:start position:0% +and if you solve that + + align:start position:0% +and if you solve that + + + align:start position:0% +and if you solve that +you'll get + + align:start position:0% +you'll get + + + align:start position:0% +you'll get +this + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +so that's where it crosses the axis + + align:start position:0% +so that's where it crosses the axis + + + align:start position:0% +so that's where it crosses the axis +and then + + align:start position:0% +and then + + + align:start position:0% +and then +you have to multiply this of course by + + align:start position:0% +you have to multiply this of course by + + + align:start position:0% +you have to multiply this of course by +the the the circular aperture + + align:start position:0% +the the the circular aperture + + + align:start position:0% +the the the circular aperture +right so this is the circular aperture + + align:start position:0% +right so this is the circular aperture + + + align:start position:0% +right so this is the circular aperture +this is the region where the object + + align:start position:0% +this is the region where the object + + + align:start position:0% +this is the region where the object +spectrum is non-zero + + align:start position:0% +spectrum is non-zero + + + align:start position:0% +spectrum is non-zero +and um + + align:start position:0% +and um + + + align:start position:0% +and um +so you can see + + align:start position:0% +so you can see + + + align:start position:0% +so you can see +that + + align:start position:0% +that + + + align:start position:0% +that +only the parts of this blue curve up to + + align:start position:0% +only the parts of this blue curve up to + + + align:start position:0% +only the parts of this blue curve up to +here are going to have any meaning that + + align:start position:0% +here are going to have any meaning that + + + align:start position:0% +here are going to have any meaning that +bits out here are not going to do + + align:start position:0% +bits out here are not going to do + + + align:start position:0% +bits out here are not going to do +anything so this is obviously looking at + + align:start position:0% +anything so this is obviously looking at + + + align:start position:0% +anything so this is obviously looking at +a case where this is almost flat + + align:start position:0% +a case where this is almost flat + + + align:start position:0% +a case where this is almost flat +if if you made it a bit smaller even it + + align:start position:0% +if if you made it a bit smaller even it + + + align:start position:0% +if if you made it a bit smaller even it +would look even flatter + + align:start position:0% +would look even flatter + + + align:start position:0% +would look even flatter +so so this is a + + align:start position:0% +so so this is a + + + align:start position:0% +so so this is a +not a lot of defocus + + align:start position:0% +not a lot of defocus + + + align:start position:0% +not a lot of defocus +uh and uh so + + align:start position:0% +uh and uh so + + + align:start position:0% +uh and uh so +here he's got then yeah so hit now he's + + align:start position:0% +here he's got then yeah so hit now he's + + + align:start position:0% +here he's got then yeah so hit now he's +labeling where that cutoff is + + align:start position:0% +labeling where that cutoff is + + + align:start position:0% +labeling where that cutoff is +uh so this is equal to n a over lambda + + align:start position:0% +uh so this is equal to n a over lambda + + + align:start position:0% +uh so this is equal to n a over lambda +as we know and in terms of the x prime + + align:start position:0% +as we know and in terms of the x prime + + + align:start position:0% +as we know and in terms of the x prime +coordinate is given by by this thing + + align:start position:0% +coordinate is given by by this thing + + + align:start position:0% +coordinate is given by by this thing +here + + align:start position:0% + + + + align:start position:0% + +so this is talking about what he calls + + align:start position:0% +so this is talking about what he calls + + + align:start position:0% +so this is talking about what he calls +mild defocus + + align:start position:0% +mild defocus + + + align:start position:0% +mild defocus +and the condition for that to occur + + align:start position:0% +and the condition for that to occur + + + align:start position:0% +and the condition for that to occur +is that this has got to be it's much + + align:start position:0% +is that this has got to be it's much + + + align:start position:0% +is that this has got to be it's much +smaller than this + + align:start position:0% + + + + align:start position:0% + +and then + + align:start position:0% + + + + align:start position:0% + +yeah and that corresponds then in terms + + align:start position:0% +yeah and that corresponds then in terms + + + align:start position:0% +yeah and that corresponds then in terms +of delta + + align:start position:0% +of delta + + + align:start position:0% +of delta +so we've now got a condition for this to + + align:start position:0% +so we've now got a condition for this to + + + align:start position:0% +so we've now got a condition for this to +happen the value of delta has to be + + align:start position:0% +happen the value of delta has to be + + + align:start position:0% +happen the value of delta has to be +small compared with lambda over two and + + align:start position:0% +small compared with lambda over two and + + + align:start position:0% +small compared with lambda over two and +a squared right so you remember this is + + align:start position:0% +a squared right so you remember this is + + + align:start position:0% +a squared right so you remember this is +what we said was the depth of focus that + + align:start position:0% +what we said was the depth of focus that + + + align:start position:0% +what we said was the depth of focus that +depth of field or depth of focus of the + + align:start position:0% +depth of field or depth of focus of the + + + align:start position:0% +depth of field or depth of focus of the +system + + align:start position:0% + + + + align:start position:0% + +depth of field + + align:start position:0% +depth of field + + + align:start position:0% +depth of field +is measured in the object space + + align:start position:0% +is measured in the object space + + + align:start position:0% +is measured in the object space +oh he doesn't say anything about that + + align:start position:0% +oh he doesn't say anything about that + + + align:start position:0% +oh he doesn't say anything about that +for the focus on that one i thought i + + align:start position:0% +for the focus on that one i thought i + + + align:start position:0% +for the focus on that one i thought i +was going to get + + align:start position:0% +was going to get + + + align:start position:0% +was going to get +he says a bit about that later this is + + align:start position:0% +he says a bit about that later this is + + + align:start position:0% +he says a bit about that later this is +showing that in another case then this + + align:start position:0% +showing that in another case then this + + + align:start position:0% +showing that in another case then this +is with a much more defocus now so now + + align:start position:0% +is with a much more defocus now so now + + + align:start position:0% +is with a much more defocus now so now +it's oscillating a lot more wildly + + align:start position:0% +it's oscillating a lot more wildly + + + align:start position:0% +it's oscillating a lot more wildly +so now this cutoff is much smaller than + + align:start position:0% +so now this cutoff is much smaller than + + + align:start position:0% +so now this cutoff is much smaller than +this + + align:start position:0% +this + + + align:start position:0% +this +and uh so this is where you've got a lot + + align:start position:0% +and uh so this is where you've got a lot + + + align:start position:0% +and uh so this is where you've got a lot +of the focus + + align:start position:0% +of the focus + + + align:start position:0% +of the focus +and the fact the fact that + + align:start position:0% +and the fact the fact that + + + align:start position:0% +and the fact the fact that +this goes negative is probably the worst + + align:start position:0% +this goes negative is probably the worst + + + align:start position:0% +this goes negative is probably the worst +thing it means that some spatial + + align:start position:0% +thing it means that some spatial + + + align:start position:0% +thing it means that some spatial +frequencies are going to be imaged with + + align:start position:0% +frequencies are going to be imaged with + + + align:start position:0% +frequencies are going to be imaged with +the wrong contrast + + align:start position:0% +the wrong contrast + + + align:start position:0% +the wrong contrast +so when you try doing your fourier + + align:start position:0% +so when you try doing your fourier + + + align:start position:0% +so when you try doing your fourier +synthesis to add up to make the + + align:start position:0% +synthesis to add up to make the + + + align:start position:0% +synthesis to add up to make the +make the image it's not going to work + + align:start position:0% +make the image it's not going to work + + + align:start position:0% +make the image it's not going to work +right + + align:start position:0% +right + + + align:start position:0% +right +uh and the other point he makes is that + + align:start position:0% +uh and the other point he makes is that + + + align:start position:0% +uh and the other point he makes is that +the regions around here of course + + align:start position:0% +the regions around here of course + + + align:start position:0% +the regions around here of course +uh these spatial frequencies around + + align:start position:0% +uh these spatial frequencies around + + + align:start position:0% +uh these spatial frequencies around +these zeros are not imaged at all so + + align:start position:0% +these zeros are not imaged at all so + + + align:start position:0% +these zeros are not imaged at all so +that's another reason why it doesn't + + align:start position:0% +that's another reason why it doesn't + + + align:start position:0% +that's another reason why it doesn't +give a very good image + + align:start position:0% +give a very good image + + + align:start position:0% +give a very good image +right so + + align:start position:0% +right so + + + align:start position:0% +right so +uh so this is the case of strong defocus + + align:start position:0% +uh so this is the case of strong defocus + + + align:start position:0% +uh so this is the case of strong defocus +where delta's much is bigger than this + + align:start position:0% +where delta's much is bigger than this + + + align:start position:0% +where delta's much is bigger than this +thing + + align:start position:0% +thing + + + align:start position:0% +thing +not necessarily much bigger i suppose + + align:start position:0% + + + + align:start position:0% + +okay i think we ought to stop there + + align:start position:0% +okay i think we ought to stop there + + + align:start position:0% +okay i think we ought to stop there +we've run over time anyway so let's + + align:start position:0% +we've run over time anyway so let's + + + align:start position:0% +we've run over time anyway so let's +let's stop at this point and we'll pick + + align:start position:0% +let's stop at this point and we'll pick + + + align:start position:0% +let's stop at this point and we'll pick +that up next time \ No newline at end of file diff --git a/IuQjBqzmUKA.txt b/IuQjBqzmUKA.txt new file mode 100644 index 0000000000000000000000000000000000000000..34c0cd6d992af57f08094f97297f5628e09fb7b3 --- /dev/null +++ b/IuQjBqzmUKA.txt @@ -0,0 +1,2745 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +mitopencourseware@ocw.mit.edu. + +PROFESSOR: OK, so what we're +going to do today is the last + +in what I'd say are the +core set of lectures. + +Our core set of lectures, +we started with + +talking about the market. + +We then moved on and talked +about consumer theory and did + +a series of lectures on that. + +Now we're doing producer +theory. + +This is the last in our series +of lectures on producer theory + +and then basically we +move on to topics. + +So the remainder of the section +we'll talk about + +things like international trade, +uncertainty, equity and + +efficiency, asymmetric +information + +in insurance markets. + +We'll move on to in the last +part of the course showing you + +how you can apply what we've +learned in the basics to + +answer a bunch of interesting, +real world questions. + +So this is the last of our +core basics lectures. + +What we're going to do here is +fit in something that's fallen + +through the cracks, which is +we've talked about firms and + +their decisions about +how much to produce. + +And we've talked about +the output side. + +But we haven't talked about +the input side at all. + +How do firms decide what kind +of the inputs to use and in + +what ratio to use et cetera. + +We talked a bit about it. + +We talked about isoquants and +isocosts and doing that + +tradeoff between inputs. + +We haven't really talked about +the input markets themselves. + +So firms go and they say, look +I've done my isoquants and + +isocosts and I want +63 workers. + +Well they've then got to go to +a market for labor and hire + +those workers and how does +that actually work. + +So today what we want to +focus on is the demand + +side of input markets. + +That is, what's the actual +market analysis by which a + +firm having maximized its +profits and deciding how many + +workers it wants goes and +actually finds those workers. + +So we're going to do is talk +about demand for factors. + +In particular today we'll focus +on the demand for labor. + +Although the demand for capital, +the analysis will be + +very similar. + +But today we're going to focus +on the demand for labor. + +And what we're going to do is +begin by focusing on the + +demand for labor in a +competitive factor market. + +So we're going to begin by +talking about competitive + +factor markets. + +What I mean by that is that a +perfectly competitive factor + +market is one where, just as +perfect competition and output + +markets means there's lots of +sellers selling the same good, + +a perfectly competitive factor +market means there's lots of + +sellers, in this case workers, +selling an identical good. + +That is their labor. + +So the notion is we're in a +market where there's many, + +many workers firms could hire, +all of whom are equally + +qualified for a job. + +So this is not, obviously, +a high-tech market. + +This is some low-tech, +construction, other sort of + +blue collar market, where +there's lots of workers out + +there who could equally well +be qualified for a job. + +In fact what we're going to +assume is that there's a + +perfectly flat labor +supply curve. + +Let's assume a perfectly flat +labor supply curve. + +Perfectly elastic labor supply +just to make life easy. + +Obviously it's not +true in reality. + +Let's assume we're looking at +some market with perfectly + +elastic labor supply. + +Now how do we think about what +happens in factor markets in + +that world? + +Well once again let's start +with the short run. + +So in the short run +capital's fixed. + +So a firm has said, look, I've +done my short run profit + +maximization, my isoquants +and isocosts. + +I've decided how many workers +I want given a + +fixed level of capital. + +And that gives me some +demand for labor. + +I can derive a demand for labor +curve by essentially + +saying, at different wage rates, +given a fixed capital + +price, that will shift my +isocost curve, going back to + +the producer theory, at +different wage rates that will + +shift my isocost curve, that +will cause me to demand + +different amounts of labor. + +So that traces out a demand +curve for labor. + +And we can see that graphically +in figure 18-1. + +So you've got a perfectly +elastic labor supply curve and + +then you've got a downward +sloping labor demand curve. + +And that labor demand curve +comes from the profit + +maximization. + +The other way to think about +how we get there though is + +interesting. + +You say, how do we think about +the marginal benefit versus + +the marginal cost of hiring +another worker. + +We know the marginal cost is +the wage, that's easy. + +What's the marginal benefit +of hiring another worker? + +Well recall that another unit of +labor raises output by the + +marginal product of labor. + +Remember the marginal +product of labor. + +We talked about this +a while ago. + +This is delta q delta l. + +So the next worker raises your +output by an amount marginal + +product of labor. + +That's what you get from +the next worker. + +But that's a quantity. + +The firm cares about profit +not quantity. + +So what it cares about +is revenues. + +So the revenues from the next +worker would be the marginal + +revenues that are made on that +next unit times the marginal + +product of labor. + +That's the marginal benefit to +the firm of the next unit of + +labor is the marginal product +that that worker produces + +times the marginal revenue +the firm raises from + +selling that next unit. + +So they have to consider two +things, two margins. + +How much is it worth them to +sell that next unit and how + +much will be produced by that +next unit of worker? + +So if we have a perfectly +competitive labor market, the + +marginal cost is going +to be the wage. + +So we're going to set this +equal to the wage. + +So in a perfectly competitive +labor market the marginal cost + +of another worker is the wage +and this is the marginal + +benefit of another worker. + +So this is going to be the +condition the firm's going to + +use to decide how many +workers to hire. + +We're going to call +this the marginal + +revenue product of labor. + +So you're going to set the +marginal revenue product of + +labor equal to the wage. + +That's going to be your profit +maximizing condition-- + +the marginal revenue product. + +The marginal product is +about quantities. + +Marginal revenue product +is about dollars. + +What's the dollars that the next +unit of labor produces + +for you is your marginal +revenue product. + +Now if the output market is also +perfectly competitive. + +That is, imagine for a minute +now, take one further step. + +Not a perfectly competitive +labor supply but also a + +perfectly competitive +output market. + +So it's not a monopolist. It's +selling in a perfectly + +competitive output market. + +Then we know what the +marginal revenue is. + +We know the marginal revenue +is the price. + +So for a perfectly competitive +output market we could rewrite + +this as price times marginal +product of + +labor equals the wage. + +Because we know the marginal +revenue is the price in a + +perfectly competitive +output market. + +And basically this makes it even +easier to see which is to + +say, look, how many workers +do you hire? + +You hire until the wage you pay +that worker is equal to + +the price you sell your good for +times how many goods that + +worker produces. + +If one worker produces 100 goods +and each good sells for + +100, then you'll only pay +the worker $10,000. + +Basically that is going +to determine your + +labor demand curve. + +And so the labor demand curve +is also labeled the marginal + +revenue product of labor +curve, I'm sorry. + +Why is this diminishing? + +Why is it downward sloping? + +Because remember the marginal +product of labor's + +diminishing. + +The marginal product of +labor's diminishing. + +As a result this curve +is downward sloping. + +Now here price is fixed, +so it doesn't matter. + +Marginal revenue also is +diminishing so that's going to + +make it even more downward +sloping than the + +more general case. + +But in this specific case of +perfectly competitive output + +markets where this is just a +constant price you get this + +downward sloping marginal +revenue product of labor curve + +because the marginal product of +labor is diminishing, as we + +talked about. + +So that's the analysis of what +we see for a perfectly + +competitive factor market. + +So the equilibrium is where the +labor supply curve, which + +is perfectly elastic, intersects +this marginal + +revenue product curve, which +is determined by how + +productive the workers are and +how much money they're making + +for you with each unit +they produce. + +And that gets you the short +run equilibrium. + +Questions about that? + +Questions about what +we're doing here? + +So that just says the underlying +analysis of where + +demand for labor comes from or +where the equilibrium level of + +labor is going to come. + +It's going to come from +intersection of this demand + +with the supply, +which is flat. + +Now how is this going to +differ in the long run? + +Well let me ask the question +this way, forget the math, + +forget the graphs, I'm just +going to ask you intuitively. + +In the long run, do we think +the long run demand for + +workers will be more elastic or +less elastic than the short + +run demand, in general. + +Will the long run demand curve, +this is short run + +demand curve, will the long run +demand curve typically be + +more elastic or less elastic +than the short run demand + +curve for workers? + +Somebody take a guess. + +Yeah. + +AUDIENCE: More elastic. + +PROFESSOR: More elastic. + +Why? + +It's more elastic. + +But intuitively, don't worry +about the graph, I'm just + +looking for intuition. + +Yeah. + +AUDIENCE: Because in +the long run you + +can substitute capital. + +PROFESSOR: Exactly. + +More substitutability equals +more elasticity. + +General intuition you want to +remember for this course. + +In the long run if I can +substitute towards capital, + +then that long run demand curve +for labor will be even + +more elastic than the short +run demand curve. + +I'm not going to work through +the math or anything. + +I just want you to remember that +intuition that when you + +have more margins you can use, +that's more substitutability, + +that means more elasticity. + +So the idea is in the short run, +if the wage increases for + +workers all you can do is if +you hire fewer workers you + +just produce less, so you're +sort of stuck. + +But in the long run if the wage +decreases you just say, + +fine, I'll just use +machines instead. + +So in the long run you can +substitute away from workers + +towards machines. + +So in the long run your +demand curve is + +going to be more elastic. + +Questions about that? + +Now this is all relatively +straightforward, just follows + +from producer theory. + +The sort of stuff you had to +do in the exam last night. + +Let's now talk about a little +more interesting case which is + +one of my other favorite words +in economics which is the case + +of monopsony. + +Not monopoly, but monopsony. + +We've been talking in lectures +about monopoly which is the + +case where one firm +is the only seller + +in the output market. + +One firm is the only seller +in the output market. + +A parallel case in input +markets is the case of + +monopsony which is when one firm +is the only demander in + +the input market. + +So monopoly is when one firm +is the only seller in the + +output market. + +The parallel in input markets +is monopsony which is where + +one firm is the only buyer +in the input market. + +And the key thing that's going +to drive monopsony is that + +when there are barriers to exit +from a factor market it's + +going to create a monopsony. + +And any time there are barriers +to exit, any time + +workers are stuck and cannot +leave a market, workers are + +stuck working one place, that +will give the employer market + +power over those workers. + +The classic example is +the company town. + +In the 1800s when there were +mining operations and they'd + +come in and they'd +hire people. + +And basically there +was nowhere else + +to work in the area. + +These were areas which were +dying agricultural areas there + +was nowhere else to work. + +You'd go work for the +mining company. + +That mining company had +tremendous monopsony power + +over you because basically there +was nowhere else to work + +within a decent area. + +There weren't cars yet. + +You couldn't just commute +to somewhere else. + +A modern example is MIT's +monopsony power over me. + +MIT has monopsony +power over me. + +Why is that? + +Well that's because my life's +pretty comfortable now. + +I'm in a house I've lived +in a long time. + +My kids are in schools I like. + +I've got a lot of friends. + +It'd be a real pain in the +ass for me to move. + +And as a result MIT has some, +not unlimited, don't tell + +them, but they have some +monopsony power over me + +because they know that that's +a barrier to my exit. + +To my exiting MIT a barrier +is that I'm very + +comfortable and satisfied. + +And given the nature tenets of +psychology, it is harder to + +move someone with a pull +than with the push. + +So someone could come and try +to pull me away, but they're + +going to have to blow me +away with an offer-- + +once again, don't +tell MIT this-- + +they'll have to blow +me away an offer + +because I'm pretty satisfied. + +And that satisfaction inherently +gives MIT some + +monopsony power over me. + +Now the question is what +implications does this have. + +And the implications are +quite interesting. + +And what they are is a +complicated flip of the + +monopoly case. + +Let's look at figure 18-2. + +Here's an example of +a company town. + +Now let's imagine a labor market +where you've got some + +labor demand curve, the marginal +revenue product of + +labor, MRPL, and some +labor supply curve. + +And now labor supply +is upward sloping. + +This is a not a perfectly +competitive labor market now. + +This labor supply is +now upward sloping. + +So the demand curve for +labor we're going to + +say is 60 minus l. + +So in our example the marginal +revenue product of labor is + +going to be 60 minus l. + +The notion is you have some +downward sloping demand curve + +for labor because of diminishing +marginal product. + +The wage you're willing to pay +is diminishing in the number + +of workers. + +To get that first worker +you'll pay a high wage, + +because you got to produce +something. + +But as you hire more workers +the wage you're + +willing to pay falls. + +So the demand curve is +downward sloping. + +And let's say that our labor +supply curve is that the + +amount of labor workers are +willing to supply is + +the wage over 2. + +I'm just making this up. + +These are just made up numbers +just to make the math work. + +So this is it just an upward +sloping labor supply curve. + +A higher wage calls +forth more labor. + +So let's ask what happens +in the competitive case. + +Well in the competitive case +you set the supply equal to + +the demand. + +Well supply is that firms are +going to set the wage equals + +60 minus l. + +Labor supply is l +equals w over 2. + +So we could just have two +equations and two unknowns we + +can solve and get that the +amount of labor supplied in + +the competitive case +is 20 units. + +20 hours, 20 days, +weeks, whatever. + +20 units. + +That's the competitive +outcome. + +And the wage we can read off +the labor supply curve. + +If they're going to supply 20 +units, they're going to need a + +wage of 40. + +So once again we can read that +off the labor supply or the + +labor demand curve if there's +going to be 20 workers the + +wage is going to be 40. + +So the wage, labor competitive +and the wage + +competitive is 40. + +So in a competitive market with +this demand and supply + +curve you should know by now you +just set them equal, you + +solve, you get an outcome +of 20 workers + +working a wage of 40. + +Now let's imagine this isn't +the competitive case. + +Let's imagine it's the +monopsony case. + +Let's imagine this firm +has monopsony power. + +Workers can't exit. + +And let's further assume that +the firm cannot wage + +discriminate. + +Just as we talked about +monopolists that couldn't + +price discriminate, we're going +to talk about a firm + +they can't wage discriminate. + +It has to pay one wage to +all of its workers. + +And we'll come back once again +with this assumption. + +Just as we talked about price +discrimination we'll come back + +and talk about wage +discrimination. + +But for now assume a non-wage +discriminating monopsonist. + +They have to pay one wage +to all their workers. + +Well what that means is just as +when a monopolist wanted to + +sell more goods it had to +lower the price, if a + +monopsonist wants to hire +more workers it has + +to raise the wage. + +Parallel thing. + +Just as the monopolist had to +lower the price to sell more + +units because it had to respect +the demand curve, a + +monopsonist if it wants to hire +more workers has to raise + +the wage because it has to +respect the supply curve-- + +parallel. + +And what this will do is that +will lead them to under hire + +workers ct too low a wage. + +Just as monopoly led firms to +under produce at too high a + +price, monopsony will +lead to under hiring + +at too high a wage. + +So once again, to think about +this, let's think about the + +firm's decision to hire +an extra worker. + +What is the firm's total +expenditure on labor? + +Its expenditure on labor is the +wage, which is a function + +of the amount of labor, times +the amount of labor. + +That's the expenditure +on labor. + +So its marginal expenditure, if +you take the derivative, is + +going to be w plus +dw/dl times l. + +That's its marginal +expenditure. + +If you want to hire an +additional worker what's the + +marginal cost. + +Well I want to hire +an additional + +worker, what's the cost? + +I've got a pay him w and to hire +him I have to raise the + +wage, so I have to pay all my +previous workers more as well. + +So to hire one more worker I've +got to pay that worker a + +wage and in order to entice +him I've got to raise the + +wage, which means I've got to +pay a higher wage to all my + +previous workers too. + +Once again, remember, I +have to pay one wage. + +So if I'm going to hire that +worker there is the same + +poisoning effect that we +saw with monopolists. + +With monopolists the poisoning +effect was if I want to sell + +one more unit I'm going to have +to undercut my price on + +all previous units. + +For a monopsonist, if I want to +hire one more worker I have + +to pay all my previous +workers more. + +And that's going to mean that +there's a poisoning effective + +in reverse. + +That's going to cost me +a lot of money to + +hire that extra worker. + +So we can actually derive now +a marginal expenditure curve + +just as we derived a marginal +revenue curve for the + +monopolist. + +The marginal expenditure +curve. + +So we know expenditure +is w of l times l. + +And we know from the supply +curve, we can rewrite this as + +w equals 2l. + +So that says that the +expenditure on + +labor is 2l times l. + +So plugging in from the supply +curve the expenditure on labor + +is 2l times l. + +Its wage is a function +of labor times labor. + +So 2l times l. + +So that means that marginal +expenditure is 4l. + +The marginal expenditure +is 4l. + +So we can now draw a marginal +expenditure curve that's + +steeper than the labor +supply curve. + +Once again it's confusing +but it's all parallel. + +It's just we're flipping +everything around from + +monopolist. Instead of drawing +that marginal revenue curve + +that was steeper than the +product demand curve, now + +we're drawing a marginal +expenditure curve which is + +steeper than the labor +supply curve. + +And once again to find the +outcome we'll find the + +intersection of that marginal +expenditure curve with + +marginal cost. + +Well here we'll find the +intersection of marginal + +expenditure curve, I'm sorry, +with labor demand. + +I'm sorry, so the parallel was +we found the intersection of + +marginal revenue with marginal +cost. Now find the + +intersection of marginal +expenditure with labor demand. + +That intersection is going +to happen at 12 workers. + +So the firm is going +to hire 12 workers. + +But what ways you're going to +pay-- once again our first + +temptation is to look at that +high intersection and say, + +well at that intersection +what's the wage. + +We didn't put that on the +diagram for a reason. + +Maybe we should have +to throw you off. + +Remember, to figure out the wage +you've got to respect the + +labor supply curve. + +Just like you have to respect +the product demand curve to + +figure out the price. + +So what's the wage when I hire +12 workers they pay 24. + +So the monopsonist is going to +hire 12 workers and pay 24. + +It's going to hire the number +of workers where marginal + +expenditure equals +the labor demand. + +That's going to determine +the quantity. + +And the wage they're going +to read off the + +labor supply curve. + +And as a result this firm is +going to under hire at too low + +a wage relative to the +perfect competition. + +Relative to the competition +they're going to hire fewer + +workers at a lower wage. + +So if you think about this, +let's come back to + +the example of MIT. + +MIT, say, would like to expand +the economics department. + +But to do so it's got to poach +an economics professor away + +from another university. + +Well, it poaches another +professor away from another + +university. + +And let's say that at MIT pays +all its professors the same. + +If they're going to poach +a professor from another + +university they're going +to have to pay + +the rest of us more. + +And that's going to cost +them a ton of money. + +So they think think we'd rather +have a little bit more + +crowded undergrad class, we +don't really see it here + +today, but maybe in general, +more crowded undergrad class + +and not get that extra professor +to avoid having to + +pay a higher wage to all our +existing professors. + +So as a result MIT will under +hire professors and they'll + +under hire professors +at too low a wage. + +And once you can determine how +big monopsony power is, what + +determined how big monopoly +power was? + +What was the key thing I don't +want to say what it is because + +it will give it away, what's the +key thing that determined + +the size of monopoly power. + +Yeah. + +AUDIENCE: Elasticity demand. + +PROFESSOR: Elasticity +of demand. + +So just like that, the key +factors going to determine the + +market power of monopsonist is +going to be the elasticity of + +supply of labor. + +The elasticity of demand for a +good is what determined the + +market power of monopolist +because as goods were more + +elasticity demanded, they +had less ability + +to jack up the price. + +The elasticity of supply of +labor is what's going to + +determine the market power +of monopsonists. + +Because if I have +more options. + +they can't underpay me. + +So if I'm very willing to move +to another university. + +That is as my labor supply +curve gets flatter, then + +there's less market power that +they have. In particular, in a + +perfectly competitive labor +market there's no monopsony + +power at all. + +So monopsony power is a function +of the options facing + +their workers. + +Questions about that? + +Now the key question this all +raises, at least when I first + +learned about it and think +about it, is it maybe was + +plausible to think that +monopolists can only charge + +one price for their good. + +That the iPod is what +the iPod costs. + +And you couldn't start charging +different amounts for + +iPods to different people. + +That would get bad +press and stuff. + +But it's seems a little bit +stranger to think that + +employers have to pay one wage +to all their workers. + +As a matter of fact we know that +MIT doesn't pay the same + +to all its professors. + +There is some wage +discrimination. + +In particular, it's a well known +fact that the way to get + +a raise as a professor is to +get an offer from another + +university. + +Because MIT, the pay structure +professors at competitive + +departments like economics is +typically they will underpay + +you until the university comes +and says you're worth more, + +and then they'll ratchet up +to try to match them. + +So there is wage discrimination +in practice at + +universities as there is +in most workplaces. + +There's very few workplaces +where all + +workers make the same. + +There's wage discrimination. + +So does that mean this +model is irrelevant? + +And the answer is, +no, it doesn't. + +Because there are still major +barriers to perfect wage + +discrimination. + +There's some wage +discrimination, but there's a + +lot of barriers to perfect +wage discrimination. + +The most important one is +workplace norms or fairness. + +So what MIT should do, here's +the MIT optimal strategy. + +The older the professor, the +less they should pay them. + +Not because they're +less productive. + +Marginal productivity is +constant, it's not, we get + +less productive as we get older, +but put that aside. + +It's because the older you are, +the less likely you are + +to get up and move. + +And the less likely, quite +frankly, other universities + +are going to want to hire +you and take you away. + +Because no one gets +that excited about + +hiring a 60 year old. + +So what you should do is take +all the 60 over professors and + +say we're cutting your wage +in half or by a third. + +Because the truth, we've written +our lectures already, + +the wage is already well above +our marginal product. + +We're all doing pretty +well anyway. + +And the truth is people +wouldn't leave. + +So why doesn't MIT do that? + +MIT doesn't do that because I'm +going to someday be one of + +those old guys. + +I'm getting there rapidly. + +I say, wait a second, if they're +going to do to me when + +I'm 60, I'm going to get out of +here while I'm 45 because I + +don't want to be in +that situation. + +Because that's unfair. + +Workplace norms matter. + +Employers really do not like +to discriminate within the + +workplace because it breeds bad +blood and ultimately can + +lower productivity. + +And this is something that we +miss in our basic models. + +We don't have fairness and +workplace norms in our models. + +So wage is just about setting +the wage that maximizes the + +profit, which means screwing +the 60 year olds. + +But in fact, in reality, +that's not the + +way workplaces work. + +And that's what the point +of labor economics is. + +If you're interested in this we +have an excellent course in + +labor economics that follows +up on these issues. + +But a key issue is how much +wage discrimination can be + +done given workplace norms, +given the notions of fairness + +we have. And the answer is it +might be kind of tough. + +Because basically MIT doesn't +want to worry about upsetting + +all its younger faculty by +mistreating its older faculty. + +And part of that could +be solidarity. + +Some of those guys are +my friends and I + +feel bad for them. + +But partly it could be just more +selfish which is, I don't + +want to be at a place that's +going to discriminate in that + +way against me when +I get older. + +And that's just something that's +missed by the basic + +14.01 models. + +Questions about that? + +Yeah. + +AUDIENCE: Couldn't you +model the person's + +life wage or something? + +PROFESSOR: So yeah. + +So what you can do is you could +say to people, look, + +when we're hiring you we're +going to overpay you relative + +to other universities when +you're young and we'll + +underpay you when +you're older. + +And so on a lifetime basis +you'll be fine. + +What would the problem +with that be? + +So let's say the say-- yeah. + +AUDIENCE: You'd leave. + +PROFESSOR: I'd leave as soon as +I reached that point where + +I was being paid more elsewhere +that didn't pay this + +downward slope. + +And, in fact, there's a lot of +interesting labor economics + +theory which says the optimal +formal labor contract is + +actually the opposite. + +It's to overpay when +you're old and + +underpay when you're young. + +And the notion is +to get people to + +want to stick around. + +And so in some sense, common +labor theory says exactly the + +opposite of what +you suggested. + +You want to overpay older +people to get + +them to stick around. + +And for many years in America +that's often the way labor + +markets worked. + +We had very generous pensions +and health benefits and high + +wages for older workers. + +That equilibrium is now breaking +down because in this + +more competitive labor market +you can't afford to overpay + +those older workers because +then you can't attract the + +younger workers in +the first place. + +And we're moving towards a +flatter profile by age. + +But that's exactly the set of +interesting issues we have to + +deal with in labor economics in +setting pay that we don't + +really get into here. + +Other questions or +comments on that? + +Of course there's another every +reason why MIT couldn't + +do this, which is it's +against the law. + +We have age discrimination laws +in our country which say + +you cannot discriminate +against people based + +purely on their age. + +MIT could say, well look, +I could demonstrate a + +productivity difference. + +This guy is publishing fewer +articles than he did 20 years + +ago et cetera, but they do +have a legal hurdle to + +overcome as well as an +administrative hurdle. + +It would be a pain in the ass +for MIT to have to figure out + +exactly how to shift their wage +schedule to do all this. + +And that causes administrative +costs and extra Deans and + +extra things and they just don't +want to deal with it. + +So there are other barriers as +well which is administrative + +costs and legal costs. + +But I think probably the main +barrier is just the difficult + +issue of workplace norms +and how it affects the + +productivity of the workers who +are behind while you get + +rid of these older workers or +underpay these older workers + +who aren't as productive. + +Questions or thoughts on that? + +So now with this monopsony model +in mind I want to go + +back and revisit a major topic +that we talked about early in + +the course. + +And a couple times in this +course we talked about as an + +example of how governments can +screw up markets we talked + +about the minimum wage. + +We talked about if you take a +competitive labor market and + +impose a minimum wage above the +competitive level, that + +could lead to deadweight loss. + +Because what will happen is at +that higher wage firms will + +want fewer workers. + +Workers who would be happy to +work at the competitive wage + +will not be able to work. + +Trades which would make social +welfare higher won't be made. + +And there will be +deadweight loss. + +The monopsony model says that +may not be the case. + +Because in the monopsony model, +a minimum wage can play + +the same role that optimal price +regulation paid with + +monopolists. + +Remember with monopolists we +said if you regulated a + +monopolist and forced them to +charge a competitive price, + +that you could actually +force them into + +the competitive outcome. + +Well if a minimum wage is set +above the prevailing wage but + +that's because a monopsony +prevailing wage is too low, + +and the minimum wage is set at +the competitive level, then + +you could actually increase +employment and improve + +outcomes with a minimum wage. + +Sort of counter intuitive. + +So let's look at it, +pretty confusing. + +Let's look at figure 18-3. + +Figure 18-3 once again parallels +a figure you saw on + +the entire flip side for price +regulation of a monopolist, + +this is the parallel which +is wage regulation of a + +monopsonist. Let's walk +through this. + +It's pretty confusing so let's +walk through this slowly. + +Initially you have a monopsonist +who is hiring at + +the point where their marginal +expenditure curve, which is + +the dashed line and then +the solid line. + +So the line me1 is original +marginal expenditure curve. + +It's the me1 plus the me2, +it's that segment. + +That line which is, once again, +more elastic than the + +supply curve. + +That intersects the demand curve +at a labor supply l1. + +So they hire l1 workers and +they pay a wage w1. + +That's the initial monopsony +equilibrium. + +The competitive equilibrium is +where supply equals demand. + +That would be hiring l2 +workers and paying + +a higher wage w2. + +So the monopsonist is under +hiring relative to the + +competitive firm. + +Now let's say the government +rolls in and says we're going + +to set a minimum wage and we're +going to happen to get + +it right and set it at the +competitive wage level, w2. + +Well now let's think about +the monopsonist calculus. + +The monopsonist new marginal +expenditure curve is the old + +one for the solid segment. + +So where it says me2, that solid +segment is still the + +marginal expenditure curve. + +So as they think about hiring +additional workers, they're + +working down that curve. + +But once they get to l2 workers +they can't lower the + +wage anymore. + +So that marginal expenditure +curve, they can no longer + +lower the wage below w2. + +So their new marginal +expenditure curve hops down + +and becomes the minimum wage. + +So the new marginal expenditure +curve is the two + +segments labeled me2. + +It's the horizontal segment +from the y-axis to e2. + +And then it jumps up to that +upward sloping segment to the + +right of l2. + +So the new marginal expenditure +curve is basically + +at a wage that's above minimum +wage they continue to behave + +like a monopsonist. But once you +hit the minimum wage and + +they can't lower the wage +anymore, what happens? + +The poisoning effect goes away, +just like we talked + +about with the monopolist. +Essentially what this has done + +has killed the poisoning +effect. + +Because it said as you're +thinking about hiring that + +next worker to the right of l1, +typically say I want to + +hire them because I'm going to +have to raise my wage to + +everybody else. + +But you're already paying +everybody else a higher wage. + +You're already paying everybody + +else the minimum wage. + +So there's no poisoning +effect. + +You're not going to have to pay +them a higher wage to hire + +that next worker because you're +already paying them + +that higher wage. + +So just as optimal price +regulation undoes the + +poisoning effect on the demand +side, optimal wage regulation + +undoes that poisoning effect +on the supply side and can + +lead you to the optimal +outcome. + +So minimum wage can actually +increase employment. + +Pretty bizarre. + +Minimum wage is our whipping boy +for this course about how + +it causes dead weight loss and +leads to lower employment. + +Here we're saying, actually, +if we start a monopsony + +equilibrium, a minimum wage +could increase employment. + +Of course, as you should know, +the minimum wage could reduce + +employment even in a monopsony +setting if it + +gets set too high. + +So if the minimum wage +got set very high-- + +Jessica maybe this is something +we should actually + +add for next year-- so if you +can imagine a minimum wage + +that's set very high, that could +lead to a level of labor + +supply that's actually below +the monopsony level. + +So just as with optimal price +regulation, we talked about + +how setting a price too high can +make things worse, setting + +a minimum wage too high +can make things worse. + +So it's ultimately an empirical +question of does the + +minimum wage raise employment, +which would require two + +conditions, a monopsony market +and a well-set minimum wage. + +Or does it lower employment? + +Which can happen either with a +competitive labor market or it + +could happen with a poorly-set +minimum wage. + +This pretty confusing so you'll +probably have to go + +home and think more +about this. + +But are there questions now +about anything that's not + +apparent from the diagram? + +So now this is why we have +empirical economics. + +We have empirical +economics, well + +really we have two reasons. + +One, is sometimes we know the +direction of what we're + +looking for, we want measure +its magnitude. + +Sometimes we don't even know the +direction, not to mention + +the magnitude. + +Here's a case we don't even +know the direction. + +Will increasing the minimum wage +raise or lower employment + +and by how much? + +Well how do we test this? + +Well the traditional way to +look at it to say, OK, the + +minimum wage changes over +time, let's look at what + +happens to employment when +the minimum wage goes up. + +And what people found was an +increase in minimum wage + +tended to be associated +with lower employment. + +When the minimum wage went +up, employment fell. + +So people took that to mean +that there was a situation + +where we're either in a +competitive market or we're + +screwing up the monopsony market +by setting too high a + +minimum wage. + +Because we raised the minimum +wage, employment fell. + +And what is wrong with +drawing that + +conclusion from that evidence? + +Or could someone tell me a story +about why that might not + +be a convincing piece +of evidence? + +Why the fact that when we +raise the minimum wage + +employment falls, why that +may not be by itself be + +compelling. + +What problem you might have with +that piece of evidence. + +If you read that in the New York +Times tomorrow, look at + +this graph, we raised the wage +and employment falls. + +Clearly minimum wage is bad. + +What should your first thought +be upon reading that article? + +Well what do we care about? + +We care about causation +not correlation. + +So what could be causing this +to be correlation but not a + +causation effect? + +Someone want to try? + +AUDIENCE: It would depend +on when you + +raise the minimum wage. + +PROFESSOR: Right, in particular +what story might + +cause this effect? + +AUDIENCE: If they're in a +depression and they decide to + +raise the minimum wage. + +PROFESSOR: Right, what if +governments, worried about + +workers in bad economies, that's +exactly when they raise + +the minimum wage. + +What if the government raised +the minimum wage in bad + +economy, because that's exactly +when they're worried + +about workers suffering. + +Then you would see that a +higher minimum wage is + +associated with lower +employment. + +But it's got nothing to do with +the higher minimum wage. + +It's got to do with the fact +that you raised the minimum + +wage when unemployment +is falling anyway. + +It's causation versus +correlation. + +You have to be critical reader +of evidence like this. + +The minimum wage is not +handed down by God. + +It's determined by legislators +who are subject to political + +pressures which may depend +the state of the economy. + +If the minimum wage increases +when employment happens to be + +falling, then it will look +like the minimum wage has + +harmed employment when +it really hasn't. + +So what we do about this? + +What we do about this is to try +to think about a way we + +can find a causal relationship +between the minimum wage and + +employment. + +And one way to do that is to +try to find cases where a + +minimum wage increased and +yet we know there was no + +independent change in +economic activity. + +And the way economists have +done that is by looking at + +state minimum wages. + +Turns out a lot of states +actually set minimum wages + +higher than the national +minimum wage. + +Not really much anymore because +the national minimum + +wage has gone up a lot +the last decade. + +But about a decade ago the +national minimum wage, or + +about 15 years ago, the national +minimum wage was at a + +real historical minimum in +real terms. And a lot of + +states exceeded that in setting +their minimum wage. + +So take two states, for +example New Jersey and + +Pennsylvania. + +New Jersey raised its minimum +wage, Pennsylvania doesn't. + +But any economic shock is going +to hit New Jersey and + +Pennsylvania pretty similarly. + +They're both right next to each +other on the East coast. + +Any recession's going to hit +them pretty similarly. + +So what you could do is you +could ask what happens to + +employment in New Jersey when +they raise their minimum wage + +relative to Pennsylvania, +which suffers the same + +economic shocks but doesn't +raise its minimum wage. + +We try to achieve the +gold standard. + +What's the gold standard? + +The gold standard is +a randomized trial. + +What we'd like is literally a +trial where we change the + +minimum wage randomly +at different places + +and different times. + +That's ever going to happen. + +So we try to approximate in +what we call a natural + +experiment or quasi experiment +which say, are there + +experimental interventions that +nature gives us, even if + +they're not perfectly +randomized trials. + +And this is one. + +Here's a situation where we have +two states, very similar, + +one raises the minimum +wage and one doesn't. + +And they're set by +economic shocks. + +You can look at that. + +Another way people have taken +this approach is say, well + +when the minimum wage increases +it's going to have + +different effects in +different places. + +And why is that? + +That's because the minimum wage +is going to be higher + +relative to the market wage in +some areas than in others. + +So, for example, when they +raised the minimum wage a + +dollar nationally, most people +in Massachusetts already make + +more than they raised it to. + +So it's not going to affect +Massachusetts much. + +Whereas in Mississippi +that's a big hit. + +So given a national raise we can +compare states that were + +hit harder by that raise to +states that were hit less + +hard, another way to +try to do this. + +A number of studies have done +this and they've come up with + +the striking conclusion that the +minimum wage, if anything, + +raises employment, at least at +the levels that we've seen + +over the last 15,20 years. + +Changes in the minimum wage are +actually associated with + +modest, but increases +in employment. + +And certainly no decreases. + +They've been associated with +modest increases in employment + +and not decreases. + +And this is really, really +striking because this is + +something that economists +just never + +even really took seriously. + +We always taught that minimum +wage was the bad boy of + +economics, and this is saying, +no, in fact, if you take it + +seriously and look at the +evidence carefully you can + +actually see that a minimum +wage can actually increase + +employment as this +model shows. + +Now, this is still the subject +of some controversy, there's + +still a lot of work on it. + +But it then raises the +question of, well how + +can this really be? + +Don't we have a pretty +competitive labor market? + +How do we really have a +monopsony labor market? + +And the answer is that if you +look at who's getting the + +minimum wage it's largely +younger and low-skilled + +workers who don't have a lot +of employment options. + +So basically McDonald's in a +given area in a city could + +have some monopsony power. + +Because people don't +have cars. + +These low-income urban youths +don't have cars. + +They can't go somewhere +else to work. + +They don't have skills so they +can even work retail because + +they don't have good enough +skills to work retail. + +So McDonald's has them. + +McDonald's has some monopsony +power over them because + +McDonald's is a job +they can get. + +Or McDonald's and Burger King +together maybe are the jobs + +they can get. + +That gives them some +monopsony power. + +So given that's where the +minimum wage is going to bite + +the most it's maybe not +implausible that the minimum + +wage could actually increase +employment which is what we + +see in the studies. + +Questions about that? + +Yeah. + +AUDIENCE: [INAUDIBLE] anti-trust +would it be + +possible [INAUDIBLE] + +PROFESSOR: Yeah exactly. + +So let's take my inner +city example. + +McDonald's isn't the +only employer. + +There's Burger King and Wendy's +and lots of other + +low-skilled employers. + +The notion is if there's a few +of them that should be enough + +to break any monopsony power +unless they collude. + +So likewise just as there's not +supposed to be collusion + +on the output side, there are +laws against collusion on the + +input side in the same way. + +But once again, just as those +laws are hard to enforce on + +the output side they're +hard to enforce. + +Because what you can do is you +can get together in the back + +room, or they can just say, +Wendy's and Burger King can + +wait and see what McDonald's +does and just + +follow in lock step. + +So there's lots of ways to +get around those rules. + +But yes, just as there's +antitrust laws on the output + +side, there are the labor market +laws on the input side + +which get in the way +of collusion. + +The difference is those +are more on a + +sector by sector basis. + +So, for example, the +unionization of the workers + +affects the collusion ability +of the employers. + +So if the workers are unionized +it's more lax in + +terms of allowing employers to +collude as well because the + +workers are colluding. + +If workers aren't unionized +it's less lax. + +And there's a complicated body +of labor law about that. + +Other questions? + +Yeah. + +AUDIENCE: So it would be bad for +unions to try and get an + +industry-wide standard +wage or-- + +PROFESSOR: Well that's about +efficiency versus equity. + +If a union got an industry-wide +standardized + +wage then that's going to +penalize the talented workers + +who would want to go work +elsewhere and help the less + +talented workers. + +And basically a lot of the +complaints employers have + +about unions is that they lose +their talented workers because + +the union doesn't allow them +to pay those differentials. + +Teachers is a great example +that's very controversial + +right now which is, +should there be + +merit pay for teachers. + +A lot of teachers say, no, there +shouldn't be merit pay + +because that's going to violate +workplace norms and + +it's unfair. + +But we might not be getting the +most talented people into + +teaching as a result. + +So we'll come back next time +and we'll start our topics + +part of the course by talking +about international trade and + +whether it's good or bad. + +Answer, it's good. + +But we'll talk about why. \ No newline at end of file diff --git a/JAmiDL8pBhg.txt b/JAmiDL8pBhg.txt new file mode 100644 index 0000000000000000000000000000000000000000..6baf3bd206367335a270d7c447b112a701f9da76 --- /dev/null +++ b/JAmiDL8pBhg.txt @@ -0,0 +1,403 @@ +align:start position:0% + +the good the bad and the ugly this is a + + align:start position:0% +the good the bad and the ugly this is a + + + align:start position:0% +the good the bad and the ugly this is a +recitation for the visualization week + + align:start position:0% +recitation for the visualization week + + + align:start position:0% +recitation for the visualization week +with great power comes great + + align:start position:0% +with great power comes great + + + align:start position:0% +with great power comes great +responsibility there are many ways to + + align:start position:0% +responsibility there are many ways to + + + align:start position:0% +responsibility there are many ways to +visualize the same data you have just + + align:start position:0% +visualize the same data you have just + + + align:start position:0% +visualize the same data you have just +seen how to make a trek quite attractive + + align:start position:0% +seen how to make a trek quite attractive + + + align:start position:0% +seen how to make a trek quite attractive +for visualizations with ggplot2 which + + align:start position:0% +for visualizations with ggplot2 which + + + align:start position:0% +for visualizations with ggplot2 which +has good default settings but judgment + + align:start position:0% +has good default settings but judgment + + + align:start position:0% +has good default settings but judgment +is still required from the user for + + align:start position:0% +is still required from the user for + + + align:start position:0% +is still required from the user for +example do I decide to vary the size of + + align:start position:0% +example do I decide to vary the size of + + + align:start position:0% +example do I decide to vary the size of +a point or do I vary the color of a + + align:start position:0% +a point or do I vary the color of a + + + align:start position:0% +a point or do I vary the color of a +point it is worth noting at this point + + align:start position:0% +point it is worth noting at this point + + + align:start position:0% +point it is worth noting at this point +that Excel and other similar programs + + align:start position:0% +that Excel and other similar programs + + + align:start position:0% +that Excel and other similar programs +can also be used to make perfectly + + align:start position:0% +can also be used to make perfectly + + + align:start position:0% +can also be used to make perfectly +extendable visualizations all terrible + + align:start position:0% +extendable visualizations all terrible + + + align:start position:0% +extendable visualizations all terrible +ones the tool can help but is ultimately + + align:start position:0% +ones the tool can help but is ultimately + + + align:start position:0% +ones the tool can help but is ultimately +up to the user to make decisions so what + + align:start position:0% +up to the user to make decisions so what + + + align:start position:0% +up to the user to make decisions so what +is the difference between a good + + align:start position:0% +is the difference between a good + + + align:start position:0% +is the difference between a good +visualization and a bad visualization + + align:start position:0% +visualization and a bad visualization + + + align:start position:0% +visualization and a bad visualization +then I would argue that a good + + align:start position:0% +then I would argue that a good + + + align:start position:0% +then I would argue that a good +visualization clearly and accurately + + align:start position:0% +visualization clearly and accurately + + + align:start position:0% +visualization clearly and accurately +conveys the key messages in the data a + + align:start position:0% +conveys the key messages in the data a + + + align:start position:0% +conveys the key messages in the data a +bad visualization will obfuscate the + + align:start position:0% +bad visualization will obfuscate the + + + align:start position:0% +bad visualization will obfuscate the +data + + align:start position:0% +data + + + align:start position:0% +data +Ivan through ignorance or malice so what + + align:start position:0% +Ivan through ignorance or malice so what + + + align:start position:0% +Ivan through ignorance or malice so what +does this mean visualizations can be + + align:start position:0% +does this mean visualizations can be + + + align:start position:0% +does this mean visualizations can be +used by an analyst for their own + + align:start position:0% +used by an analyst for their own + + + align:start position:0% +used by an analyst for their own +consumption to gain insights into data + + align:start position:0% +consumption to gain insights into data + + + align:start position:0% +consumption to gain insights into data +visualizations can also be used to + + align:start position:0% +visualizations can also be used to + + + align:start position:0% +visualizations can also be used to +provide information to a decision maker + + align:start position:0% +provide information to a decision maker + + + align:start position:0% +provide information to a decision maker +and order convince someone of something + + align:start position:0% +and order convince someone of something + + + align:start position:0% +and order convince someone of something +now a bad visualization can hide + + align:start position:0% +now a bad visualization can hide + + + align:start position:0% +now a bad visualization can hide +patterns that could give insight or + + align:start position:0% +patterns that could give insight or + + + align:start position:0% +patterns that could give insight or +mislead decision makers this is where + + align:start position:0% +mislead decision makers this is where + + + align:start position:0% +mislead decision makers this is where +the malice part comes in so today we + + align:start position:0% +the malice part comes in so today we + + + align:start position:0% +the malice part comes in so today we +will look at a few examples of + + align:start position:0% +will look at a few examples of + + + align:start position:0% +will look at a few examples of +visualizations taken from a variety of + + align:start position:0% +visualizations taken from a variety of + + + align:start position:0% +visualizations taken from a variety of +sources we'll discuss what is good and + + align:start position:0% +sources we'll discuss what is good and + + + align:start position:0% +sources we'll discuss what is good and +what is bad about them then we will + + align:start position:0% +what is bad about them then we will + + + align:start position:0% +what is bad about them then we will +switch into our to build better versions + + align:start position:0% +switch into our to build better versions + + + align:start position:0% +switch into our to build better versions +of em for ourselves but I want you to + + align:start position:0% +of em for ourselves but I want you to + + + align:start position:0% +of em for ourselves but I want you to +think for yourself in this recitation + + align:start position:0% +think for yourself in this recitation + + + align:start position:0% +think for yourself in this recitation +you might not agree with all the points + + align:start position:0% +you might not agree with all the points + + + align:start position:0% +you might not agree with all the points +I make on my opinions about these + + align:start position:0% +I make on my opinions about these + + + align:start position:0% +I make on my opinions about these +visualizations visualization is + + align:start position:0% +visualizations visualization is + + + align:start position:0% +visualizations visualization is +inherently subjective and the right + + align:start position:0% +inherently subjective and the right + + + align:start position:0% +inherently subjective and the right +visualization will depend on the + + align:start position:0% +visualization will depend on the + + + align:start position:0% +visualization will depend on the +situation so use your own judgement and + + align:start position:0% +situation so use your own judgement and + + + align:start position:0% +situation so use your own judgement and +think about what I talked about before + + align:start position:0% +think about what I talked about before + + + align:start position:0% +think about what I talked about before +with a good visualization and a bad + + align:start position:0% +with a good visualization and a bad + + + align:start position:0% +with a good visualization and a bad +visualization \ No newline at end of file diff --git a/JGeTcRfKgBo.txt b/JGeTcRfKgBo.txt new file mode 100644 index 0000000000000000000000000000000000000000..27c52f544d5a35a043acc72a97db1df578c90f15 --- /dev/null +++ b/JGeTcRfKgBo.txt @@ -0,0 +1,382 @@ +You've tested positive for a rare and deadly +cancer that afflicts 1 out of 1000 people, + +based on a test that is 99% accurate. What +are the chances that you actually have the + +cancer? By the end of this video, you'll be +able to answer this question! + +This video is part of the Probability and +Statistics video series. Many natural and + +social phenomena are probabilistic in nature. +Engineers, scientists, and policymakers often + +use probability to model and predict system +behavior. + +Hi, my name is Sam Watson, and I'm a graduate +student in mathematics at MIT. + +Before watching this video, you should be +familiar with basic probability vocabulary + +and the definition of conditional probability. + +After watching this video, you'll be able +to: Calculate the conditional probability + +of a given event using tables and trees; and +Understand how conditional probability can + +be used to interpret medical diagnoses. + +Suppose that in front of you are two bowls, +labeled A and B. Each bowl contains five marbles. + +Bowl A has 1 blue and 4 yellow marbles. Bowl +B has 3 blue and 2 yellow marbles. + +Now choose a bowl at random and draw a marble +uniformly at random from it. Based on your + +existing knowledge of probability, how likely +is it that you pick a blue marble? How about + +a yellow marble? + +Out of +the 10 marbles you could choose from, 4 are +blue. So the probability of choosing a blue + +marble is 4 out of 10. + +There are 6 yellow marbles out of 10 total, +so the probability of choosing yellow is 6 + +out of 10. + +When the number of possible outcomes is finite, +and all events are equally likely, the probability + +of one event happening is the number of favorable +outcomes divided by the total number of possible + +outcomes. + +What if you must draw from Bowl A? What's +the probability of drawing a blue marble, + +given that you draw from Bowl A? + +Let's go back to the table and consider only +Bowl A. Bowl A contains 5 marbles of which + +1 is blue, so the probability of picking a +blue one is 1 in 5. + +Notice the probability has changed. In the +first scenario, the sample space consists + +of all 10 marbles, because we are free to +draw from both bowls. + +In the second scenario, we are restricted +to Bowl A. Our new sample space consists of + +only the five marbles in Bowl A. We ignore +these marbles in Bowl. + +Restricting our attention to a specific set +of outcomes changes the sample space, and + +can also change the probability of an event. +This new probability is what we call a conditional + +In the previous example, we calculated the +conditional probability of drawing a blue + +marble, given that we draw from Bowl A. + +This is standard notation for conditional +probability. The vertical bar ( | ) is read + +as "given." The probability we are looking +for precedes the bar, and the condition follows + +the bar. + +Now let's flip things around. Suppose someone +picks a marble at random from either bowl + +A or bowl B and reveals to you that the marble +drawn was blue. What is the probability that + +the blue marble came from Bowl A? + +In other words, what's the conditional probability +that the marble was drawn from Bowl A, given + +that it is blue? Pause the video and try to +work this out. + +Going back to the table, because we are dealing +with the condition that the marble is blue, + +the sample space is restricted to the four +blue marbles. + +Of these four blue marbles, one is in Bowl +A, and each is equally likely to be drawn. + +Thus, the conditional probability is 1 out +of 4. + +Notice that the probability of picking a blue +marble given that the marble came from Bowl + +A is NOT equal to the probability that the +marble came from Bowl A given that the marble + +was blue. Each has a different condition, +so be careful not to mix them up! + +We've seen how tables can help us organize +our data and visualize changes in the sample + +space. + +Let's look at another tool that is useful +for understanding conditional probabilities + +- a tree diagram. + +Suppose we have a jar containing 5 marbles; +2 are blue and 3 are yellow. If we draw any + +one marble at random, the probability of drawing +a blue marble is 2/5. + +Now, without replacing the first marble, draw +a second marble from the jar. Given that the + +first marble is blue, is the probability of +drawing a second blue marble still 2/5? + +NO, it isn't. Our sample space has changed. +If a blue marble is drawn first, you are left + +with 4 marbles; 1 blue and 3 yellow. + +In other words, if a blue marble is selected +first, the probability that you draw blue + +second is 1/4. And the probability you draw +yellow second is 3/4. + +Now pause the video and determine the probabilities +if the yellow marble is selected first instead. + +If a yellow marble is selected first, you +are left with 2 yellow and 2 blue marbles. + +There is now a 2/4 chance of drawing a blue +marble and a 2/4 chance of drawing a yellow + +marble. + +What we have drawn here is called a tree diagram. +The probability assigned to the second branch + +denotes the conditional probability given +that the first happened. + +Tree diagrams help us to visualize our sample +space and reason out probabilities. + +We can answer questions like "What is the +probability of drawing 2 blue marbles in a + +row?" In other words, what is the probability +of drawing a blue marble first AND a blue + +marble second? + +This event is represented by these two branches +in the tree diagram. + +We have a 2/5 chance followed by a 1/4 chance. +We multiply these to get 2/20, or 1/10. The + +probability of drawing two blue marbles in +a row is 1/10. + +Now you do it. Use the tree diagram to calculate +the probabilities of the other possibilities: + +blue, yellow; yellow, blue; and yellow, yellow. + +The probabilities each work out to 3/10. The +four probabilities add up to a total of 1, + +as they should. + +What if we don't care about the first marble? +We just want to determine the probability + +that the second marble is yellow. + +Because it does not matter whether the first +marble is blue or yellow, we consider both + +the blue, yellow, and the yellow, yellow paths. +Adding the probabilities gives us 3/10 + 3/10, + +which works out to 3/5. + +Here's another interesting question. What +is the probability that the first marble drawn + +is blue, given that the second marble drawn +is yellow? + +Intuitively, this seems tricky. Pause the +video and reason through the probability tree + +with a friend. + +Because we are conditioning on the event that +the second marble drawn is yellow, our sample + +space is restricted to these two paths: P(blue, +yellow) and P(yellow, yellow). + +Of these two paths, only the top one meets +our criteria - that the blue marble is drawn + +first. + +We represent the probability as a fraction +of favorable to possible outcomes. Hence, + +the probability that the first marble drawn +is blue, given that the second marble drawn + +is yellow is 3/10 divided by (3/10 +3/10), +which works out to 1/2. + +I hope you appreciate that tree diagrams and +tables make these types of probability problems + +doable without having to memorize any formulas! + +Let's return to our opening question. Recall +that you've tested positive for a cancer that + +afflicts 1 out of 1000 people, based on a +test that is 99% accurate. + +More precisely, out of 100 test results, we +expect about 99 correct results and only 1 + +incorrect result. + +Since the test is highly accurate, you might +conclude that the test is unlikely to be wrong, + +and that you most likely have cancer. + +But wait! Let's first use conditional probability +to make sense of our seemingly gloomy diagnosis. + +Now pause the video and determine the probability +that you have the cancer, given that you test + +positive. + +Let's use a tree diagram to help with our +calculations. + +The first branch of the tree represents the +likelihood of cancer in the general population. + +The probability of having the rare cancer +is 1 in 1000, or 0.001. The probability of + +having no cancer is 0.999. + +Let's extend the tree diagram to illustrate +the possible results of the medical test that + +is 99% accurate. + +In the cancer population, 99% will test positive +(correctly), but 1% will test negative (incorrectly). + +These incorrect results are called false negatives. + +In the cancer-free population, 99% will test +negative (correctly), but 1% will test positive + +(incorrectly). These incorrect results are +called false positives. + +Given that you test positive, our sample space +is now restricted to only the population that + +test positive. This is represented by these +two paths. + +The top path shows the probability you have +the cancer AND test positive. The lower path + +shows the probability that you don't have +cancer AND still test positive. + +The probability that you +actually do have the cancer, given that you +test positive, is (0.001*0.99)/((0.001*0.99)+(0.999*0.01)), + +which works out to about 0.09 - less than +10%! + +The error rate of the test is only 1 percent, +but the chance of a misdiagnosis is more than + +90%! Chances are pretty good that you do not +actually have cancer, despite the rather accurate + +test. Why is this so? + +The accuracy of the test actually reflects +the conditional probability that one tests + +positive, given that one has cancer. + +But in practice, what you want to know is +the conditional probability that you have + +cancer, given that you test positive! These +probabilities are NOT the same! + +Whenever we take medical tests, or perform +experiments, it is important to understand + +what events our results are conditioned on, +and how that might affect the accuracy of + +our conclusions. + +In this video, you've seen that conditional +probability must be used to understand and + +predict the outcomes of many events. You've +also learned to evaluate and manage conditional + +probabilities using tables and trees. + +We hope that you will now think more carefully +about the probabilities you encounter, and + +consider how conditioning affects their interpretation. \ No newline at end of file diff --git a/JZplGZVCdN8.txt b/JZplGZVCdN8.txt new file mode 100644 index 0000000000000000000000000000000000000000..813251f18787b433cdcfd157bff72b57fa6ebbd4 --- /dev/null +++ b/JZplGZVCdN8.txt @@ -0,0 +1,13807 @@ +align:start position:0% + +greetings everyone + + align:start position:0% +greetings everyone + + + align:start position:0% +greetings everyone +uh so before i start sharing my screen + + align:start position:0% +uh so before i start sharing my screen + + + align:start position:0% +uh so before i start sharing my screen +let me ask if there are any questions + + align:start position:0% +let me ask if there are any questions + + + align:start position:0% +let me ask if there are any questions +from the last lecture + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +where are we in terms of + + align:start position:0% +where are we in terms of + + + align:start position:0% +where are we in terms of +class + + align:start position:0% +class + + + align:start position:0% +class +we have a review session today + + align:start position:0% +we have a review session today + + + align:start position:0% +we have a review session today +exam is next thursday + + align:start position:0% +exam is next thursday + + + align:start position:0% +exam is next thursday +and it covers material from lectures 8 + + align:start position:0% +and it covers material from lectures 8 + + + align:start position:0% +and it covers material from lectures 8 +through 15 and i'm gonna take questions + + align:start position:0% +through 15 and i'm gonna take questions + + + align:start position:0% +through 15 and i'm gonna take questions +on those or scroll through them or + + align:start position:0% +on those or scroll through them or + + + align:start position:0% +on those or scroll through them or +review or something + + align:start position:0% +review or something + + + align:start position:0% +review or something +so that's the main thing that's + + align:start position:0% +so that's the main thing that's + + + align:start position:0% +so that's the main thing that's +happening so the overview of that + + align:start position:0% +happening so the overview of that + + + align:start position:0% +happening so the overview of that +is + + align:start position:0% +is + + + align:start position:0% +is +you know we did the theory and then we + + align:start position:0% +you know we did the theory and then we + + + align:start position:0% +you know we did the theory and then we +started in + + align:start position:0% +started in + + + align:start position:0% +started in +risk sharing we've got two applications + + align:start position:0% +risk sharing we've got two applications + + + align:start position:0% +risk sharing we've got two applications +including production we went to + + align:start position:0% +including production we went to + + + align:start position:0% +including production we went to +financial modeling then we went to + + align:start position:0% +financial modeling then we went to + + + align:start position:0% +financial modeling then we went to +contracts to get at obstacles like + + align:start position:0% +contracts to get at obstacles like + + + align:start position:0% +contracts to get at obstacles like +information + + align:start position:0% +information + + + align:start position:0% +information +and moral hazard problems we did sort of + + align:start position:0% +and moral hazard problems we did sort of + + + align:start position:0% +and moral hazard problems we did sort of +a theory + + align:start position:0% +a theory + + + align:start position:0% +a theory +lecture of sorts + + align:start position:0% +lecture of sorts + + + align:start position:0% +lecture of sorts +links to bitcoin + + align:start position:0% +links to bitcoin + + + align:start position:0% +links to bitcoin +and ledgers and then + + align:start position:0% +and ledgers and then + + + align:start position:0% +and ledgers and then +another application lecture we went to + + align:start position:0% +another application lecture we went to + + + align:start position:0% +another application lecture we went to +international trade + + align:start position:0% +international trade + + + align:start position:0% +international trade +in the context of all raising equilibria + + align:start position:0% +in the context of all raising equilibria + + + align:start position:0% +in the context of all raising equilibria +and we did two + + align:start position:0% +and we did two + + + align:start position:0% +and we did two +trade lectures including the one we did + + align:start position:0% +trade lectures including the one we did + + + align:start position:0% +trade lectures including the one we did +last time so that's the overview + + align:start position:0% +last time so that's the overview + + + align:start position:0% +last time so that's the overview +some words about the exam again + + align:start position:0% +some words about the exam again + + + align:start position:0% +some words about the exam again +even though in principle the thing is + + align:start position:0% +even though in principle the thing is + + + align:start position:0% +even though in principle the thing is +comprehensive that's because it's + + align:start position:0% +comprehensive that's because it's + + + align:start position:0% +comprehensive that's because it's +building on material that had previously + + align:start position:0% +building on material that had previously + + + align:start position:0% +building on material that had previously +been covered but the focus will be on + + align:start position:0% +been covered but the focus will be on + + + align:start position:0% +been covered but the focus will be on +the majority from lectures 8 through 15 + + align:start position:0% +the majority from lectures 8 through 15 + + + align:start position:0% +the majority from lectures 8 through 15 +and again because it's limited to + + align:start position:0% + + + + align:start position:0% + +80 minutes + + align:start position:0% +80 minutes + + + align:start position:0% +80 minutes +there's no way i can ask a question + + align:start position:0% +there's no way i can ask a question + + + align:start position:0% +there's no way i can ask a question +about everything you might be + + align:start position:0% +about everything you might be + + + align:start position:0% +about everything you might be +anticipating + + align:start position:0% +anticipating + + + align:start position:0% +anticipating +but + + align:start position:0% +but + + + align:start position:0% +but +hopefully it the questions themselves + + align:start position:0% +hopefully it the questions themselves + + + align:start position:0% +hopefully it the questions themselves +are reasonable and fair and not terribly + + align:start position:0% +are reasonable and fair and not terribly + + + align:start position:0% +are reasonable and fair and not terribly +surprising + + align:start position:0% +surprising + + + align:start position:0% +surprising +if you've been following the lectures + + align:start position:0% +if you've been following the lectures + + + align:start position:0% +if you've been following the lectures +doing the psets and keeping up to date + + align:start position:0% +doing the psets and keeping up to date + + + align:start position:0% +doing the psets and keeping up to date +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +and you have all the review + + align:start position:0% +and you have all the review + + + align:start position:0% +and you have all the review +session material as well those that's + + align:start position:0% +session material as well those that's + + + align:start position:0% +session material as well those that's +the best guide to the lectures are + + align:start position:0% +the best guide to the lectures are + + + align:start position:0% +the best guide to the lectures are +there's review questions we do + + align:start position:0% +there's review questions we do + + + align:start position:0% +there's review questions we do +at the beginning of each class which + + align:start position:0% +at the beginning of each class which + + + align:start position:0% +at the beginning of each class which +brings me to the next thing so here's + + align:start position:0% +brings me to the next thing so here's + + + align:start position:0% +brings me to the next thing so here's +the study guide + + align:start position:0% +the study guide + + + align:start position:0% +the study guide +and + + align:start position:0% +and + + + align:start position:0% +and +from let's start with what we did last + + align:start position:0% +from let's start with what we did last + + + align:start position:0% +from let's start with what we did last +time + + align:start position:0% +time + + + align:start position:0% +time +focusing on the us + + align:start position:0% +focusing on the us + + + align:start position:0% +focusing on the us +i talked about china shocks + + align:start position:0% +i talked about china shocks + + + align:start position:0% +i talked about china shocks +and accounting identities which led up + + align:start position:0% +and accounting identities which led up + + + align:start position:0% +and accounting identities which led up +to this question using the lens of the + + align:start position:0% +to this question using the lens of the + + + align:start position:0% +to this question using the lens of the +accounting identity is what is the + + align:start position:0% +accounting identity is what is the + + + align:start position:0% +accounting identity is what is the +preliminary evidence for the impact of + + align:start position:0% +preliminary evidence for the impact of + + + align:start position:0% +preliminary evidence for the impact of +china shocks on the variables of the + + align:start position:0% +china shocks on the variables of the + + + align:start position:0% +china shocks on the variables of the +current account + + align:start position:0% +current account + + + align:start position:0% +current account +so + + align:start position:0% + + + + align:start position:0% + +somehow i'm in the mood to take + + align:start position:0% +somehow i'm in the mood to take + + + align:start position:0% +somehow i'm in the mood to take +volunteers rather than call on you + + align:start position:0% +volunteers rather than call on you + + + align:start position:0% +volunteers rather than call on you +any volunteers for that + + align:start position:0% + + + + align:start position:0% + +quiet group today + + align:start position:0% +quiet group today + + + align:start position:0% +quiet group today +well i will how about charles + + align:start position:0% + + + + align:start position:0% + +oh let's see + + align:start position:0% + + + + align:start position:0% + +i think i'm haven't gotten around to + + align:start position:0% +i think i'm haven't gotten around to + + + align:start position:0% +i think i'm haven't gotten around to +watching last lectures recording yes so + + align:start position:0% +watching last lectures recording yes so + + + align:start position:0% +watching last lectures recording yes so +uh not exactly sure but + + align:start position:0% +uh not exactly sure but + + + align:start position:0% +uh not exactly sure but +yeah sorry + + align:start position:0% +yeah sorry + + + align:start position:0% +yeah sorry +this one + + align:start position:0% +this one + + + align:start position:0% +this one +yeah it's + + align:start position:0% +yeah it's + + + align:start position:0% +yeah it's +in and out synchronous and asynchronous + + align:start position:0% +in and out synchronous and asynchronous + + + align:start position:0% +in and out synchronous and asynchronous +how about any + + align:start position:0% +how about any + + + align:start position:0% +how about any +uh someone ready to volunteer china + + align:start position:0% +uh someone ready to volunteer china + + + align:start position:0% +uh someone ready to volunteer china +shock financial accounts and + + align:start position:0% +shock financial accounts and + + + align:start position:0% +shock financial accounts and +what did we find + + align:start position:0% +what did we find + + + align:start position:0% +what did we find +can try um i'm also very unsure but is + + align:start position:0% +can try um i'm also very unsure but is + + + align:start position:0% +can try um i'm also very unsure but is +this about like looking at the + + align:start position:0% +this about like looking at the + + + align:start position:0% +this about like looking at the +um like the current account and how like + + align:start position:0% +um like the current account and how like + + + align:start position:0% +um like the current account and how like +the trade balance would be negative + + align:start position:0% +the trade balance would be negative + + + align:start position:0% +the trade balance would be negative +um + + align:start position:0% +um + + + align:start position:0% +um +and then that's + + align:start position:0% +and then that's + + + align:start position:0% +and then that's +kind of giving us evidence about how um + + align:start position:0% +kind of giving us evidence about how um + + + align:start position:0% +kind of giving us evidence about how um +like close like the china shock was + + align:start position:0% +like close like the china shock was + + + align:start position:0% +like close like the china shock was +about how since um low-skilled workers + + align:start position:0% +about how since um low-skilled workers + + + align:start position:0% +about how since um low-skilled workers +are like um + + align:start position:0% +are like um + + + align:start position:0% +are like um +we have less of that commodity and more + + align:start position:0% +we have less of that commodity and more + + + align:start position:0% +we have less of that commodity and more +of high skilled workers so then we're + + align:start position:0% +of high skilled workers so then we're + + + align:start position:0% +of high skilled workers so then we're +like + + align:start position:0% +like + + + align:start position:0% +like +low skilled workers are going to be + + align:start position:0% +low skilled workers are going to be + + + align:start position:0% +low skilled workers are going to be +losing in trade + + align:start position:0% + + + + align:start position:0% + +that's also true so + + align:start position:0% +that's also true so + + + align:start position:0% +that's also true so +i was in part looking for this thing + + align:start position:0% +i was in part looking for this thing + + + align:start position:0% +i was in part looking for this thing +about the current account deficit and so + + align:start position:0% +about the current account deficit and so + + + align:start position:0% +about the current account deficit and so +yes + + align:start position:0% +yes + + + align:start position:0% +yes +it's interstate trade and states that + + align:start position:0% +it's interstate trade and states that + + + align:start position:0% +it's interstate trade and states that +are hit the worst by + + align:start position:0% +are hit the worst by + + + align:start position:0% +are hit the worst by +china shock meaning that their local + + align:start position:0% +china shock meaning that their local + + + align:start position:0% +china shock meaning that their local +manufacturers + + align:start position:0% +manufacturers + + + align:start position:0% +manufacturers +had to compete with these chinese + + align:start position:0% +had to compete with these chinese + + + align:start position:0% +had to compete with these chinese +imports those states export less to + + align:start position:0% +imports those states export less to + + + align:start position:0% +imports those states export less to +other states + + align:start position:0% +other states + + + align:start position:0% +other states +uh and + + align:start position:0% +uh and + + + align:start position:0% +uh and +also to some extent import more + + align:start position:0% +also to some extent import more + + + align:start position:0% +also to some extent import more +does anyone remember what else is on the + + align:start position:0% +does anyone remember what else is on the + + + align:start position:0% +does anyone remember what else is on the +left-hand side of the current account + + align:start position:0% +left-hand side of the current account + + + align:start position:0% +left-hand side of the current account +current account consists the trade + + align:start position:0% +current account consists the trade + + + align:start position:0% +current account consists the trade +balance plus something + + align:start position:0% + + + + align:start position:0% + +not income + + align:start position:0% +not income + + + align:start position:0% +not income +net income yeah + + align:start position:0% +net income yeah + + + align:start position:0% +net income yeah +so + + align:start position:0% +so + + + align:start position:0% +so +meaning + + align:start position:0% +meaning + + + align:start position:0% +meaning +gifts incoming or + + align:start position:0% +gifts incoming or + + + align:start position:0% +gifts incoming or +remittances from + + align:start position:0% +remittances from + + + align:start position:0% +remittances from +for factor payments earned in other + + align:start position:0% +for factor payments earned in other + + + align:start position:0% +for factor payments earned in other +states + + align:start position:0% +states + + + align:start position:0% +states +and does anyone remember + + align:start position:0% +and does anyone remember + + + align:start position:0% +and does anyone remember +did it go up or down + + align:start position:0% + + + + align:start position:0% + +yeah i'm sorry go ahead + + align:start position:0% + + + + align:start position:0% + +i was going to say that i think + + align:start position:0% +i was going to say that i think + + + align:start position:0% +i was going to say that i think +transfers were positive + + align:start position:0% +transfers were positive + + + align:start position:0% +transfers were positive +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +good + + align:start position:0% +good + + + align:start position:0% +good +okay so this linked up to risk sharing + + align:start position:0% +okay so this linked up to risk sharing + + + align:start position:0% +okay so this linked up to risk sharing +and i'm not sure if i emphasized it + + align:start position:0% +and i'm not sure if i emphasized it + + + align:start position:0% +and i'm not sure if i emphasized it +sized it + + align:start position:0% +sized it + + + align:start position:0% +sized it +last time but you know given that it's + + align:start position:0% +last time but you know given that it's + + + align:start position:0% +last time but you know given that it's +quote a shock a china shock or at least + + align:start position:0% +quote a shock a china shock or at least + + + align:start position:0% +quote a shock a china shock or at least +an adverse trend + + align:start position:0% +an adverse trend + + + align:start position:0% +an adverse trend +the question is you know what + + align:start position:0% +the question is you know what + + + align:start position:0% +the question is you know what +arrangements would cover these shocks + + align:start position:0% + + + + align:start position:0% + +public transfers in principle could have + + align:start position:0% +public transfers in principle could have + + + align:start position:0% +public transfers in principle could have +done that through fiscal + + align:start position:0% +done that through fiscal + + + align:start position:0% +done that through fiscal +taxes and transfers but what we found in + + align:start position:0% +taxes and transfers but what we found in + + + align:start position:0% +taxes and transfers but what we found in +the data was that it was the private + + align:start position:0% +the data was that it was the private + + + align:start position:0% +the data was that it was the private +transfers + + align:start position:0% +transfers + + + align:start position:0% +transfers +that seemed over 10-year period to go up + + align:start position:0% +that seemed over 10-year period to go up + + + align:start position:0% +that seemed over 10-year period to go up +so it definitely relates to all the risk + + align:start position:0% +so it definitely relates to all the risk + + + align:start position:0% +so it definitely relates to all the risk +sharing stuff + + align:start position:0% +sharing stuff + + + align:start position:0% +sharing stuff +we did in the last few lectures and that + + align:start position:0% +we did in the last few lectures and that + + + align:start position:0% +we did in the last few lectures and that +we are about to review today + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +and what about the other side of the + + align:start position:0% +and what about the other side of the + + + align:start position:0% +and what about the other side of the +current account financial stuff anyone + + align:start position:0% +current account financial stuff anyone + + + align:start position:0% +current account financial stuff anyone +remember + + align:start position:0% + + + + align:start position:0% + +now maybe these financial counts are + + align:start position:0% +now maybe these financial counts are + + + align:start position:0% +now maybe these financial counts are +tricky well we'll review it today + + align:start position:0% +tricky well we'll review it today + + + align:start position:0% +tricky well we'll review it today +but what we didn't find very much + + align:start position:0% +but what we didn't find very much + + + align:start position:0% +but what we didn't find very much +adjusting on the right hand side we + + align:start position:0% +adjusting on the right hand side we + + + align:start position:0% +adjusting on the right hand side we +should see a given state + + align:start position:0% +should see a given state + + + align:start position:0% +should see a given state +uh + + align:start position:0% + + + + align:start position:0% + +losing losing its claims on foreigners + + align:start position:0% +losing losing its claims on foreigners + + + align:start position:0% +losing losing its claims on foreigners +and this other states in the sense of + + align:start position:0% +and this other states in the sense of + + + align:start position:0% +and this other states in the sense of +running a deficit + + align:start position:0% +running a deficit + + + align:start position:0% +running a deficit +so they should be running down their + + align:start position:0% +so they should be running down their + + + align:start position:0% +so they should be running down their +savings accounts and so on but so far we + + align:start position:0% +savings accounts and so on but so far we + + + align:start position:0% +savings accounts and so on but so far we +haven't found that in the data + + align:start position:0% +haven't found that in the data + + + align:start position:0% +haven't found that in the data +but it's still good to know what was on + + align:start position:0% +but it's still good to know what was on + + + align:start position:0% +but it's still good to know what was on +what was the financial adjustment + + align:start position:0% +what was the financial adjustment + + + align:start position:0% +what was the financial adjustment +on the right hand side because the + + align:start position:0% +on the right hand side because the + + + align:start position:0% +on the right hand side because the +accounts have to balance + + align:start position:0% +accounts have to balance + + + align:start position:0% +accounts have to balance +let's do one more + + align:start position:0% +let's do one more + + + align:start position:0% +let's do one more +what in practice in the u.s is the + + align:start position:0% +what in practice in the u.s is the + + + align:start position:0% +what in practice in the u.s is the +difficulty in reconciling income flows + + align:start position:0% +difficulty in reconciling income flows + + + align:start position:0% +difficulty in reconciling income flows +with the change in the balance sheet + + align:start position:0% +with the change in the balance sheet + + + align:start position:0% +with the change in the balance sheet +that is to say explain what the + + align:start position:0% +that is to say explain what the + + + align:start position:0% +that is to say explain what the +accounting identity + + align:start position:0% +accounting identity + + + align:start position:0% +accounting identity +ought to hold what accounting identity + + align:start position:0% +ought to hold what accounting identity + + + align:start position:0% +ought to hold what accounting identity +ought to hold + + align:start position:0% +ought to hold + + + align:start position:0% +ought to hold +and what in contrast we actually have + + align:start position:0% +and what in contrast we actually have + + + align:start position:0% +and what in contrast we actually have +in integrated macro accounts and + + align:start position:0% +in integrated macro accounts and + + + align:start position:0% +in integrated macro accounts and +household surveys + + align:start position:0% +household surveys + + + align:start position:0% +household surveys +um i think i could take a shot at like + + align:start position:0% +um i think i could take a shot at like + + + align:start position:0% +um i think i could take a shot at like +what the identity might i think i know + + align:start position:0% +what the identity might i think i know + + + align:start position:0% +what the identity might i think i know +what the identity is i'm not sure + + align:start position:0% +what the identity is i'm not sure + + + align:start position:0% +what the identity is i'm not sure +exactly how it might fail though + + align:start position:0% +exactly how it might fail though + + + align:start position:0% +exactly how it might fail though +go ahead + + align:start position:0% +go ahead + + + align:start position:0% +go ahead +i it's like the identity should probably + + align:start position:0% +i it's like the identity should probably + + + align:start position:0% +i it's like the identity should probably +be something like um + + align:start position:0% +be something like um + + + align:start position:0% +be something like um +the + + align:start position:0% +the + + + align:start position:0% +the +expenditures buy households should match + + align:start position:0% +expenditures buy households should match + + + align:start position:0% +expenditures buy households should match +up with like the inc which should be + + align:start position:0% +up with like the inc which should be + + + align:start position:0% +up with like the inc which should be +matched up by like the um incomes to the + + align:start position:0% +matched up by like the um incomes to the + + + align:start position:0% +matched up by like the um incomes to the +company and whatever firm is selling the + + align:start position:0% +company and whatever firm is selling the + + + align:start position:0% +company and whatever firm is selling the +goods or something like that + + align:start position:0% +goods or something like that + + + align:start position:0% +goods or something like that +those two sides of the balance sheet + + align:start position:0% +those two sides of the balance sheet + + + align:start position:0% +those two sides of the balance sheet +should should like match up if it's like + + align:start position:0% +should should like match up if it's like + + + align:start position:0% +should should like match up if it's like +with if it's like within a country + + align:start position:0% +with if it's like within a country + + + align:start position:0% +with if it's like within a country +within the country + + align:start position:0% +within the country + + + align:start position:0% +within the country +um + + align:start position:0% +um + + + align:start position:0% +um +right + + align:start position:0% +right + + + align:start position:0% +right +so it's something that like that is it + + align:start position:0% +so it's something that like that is it + + + align:start position:0% +so it's something that like that is it +well it has to do more with the + + align:start position:0% +well it has to do more with the + + + align:start position:0% +well it has to do more with the +what is the relationship between flows + + align:start position:0% +what is the relationship between flows + + + align:start position:0% +what is the relationship between flows +and the income statement and + + align:start position:0% +and the income statement and + + + align:start position:0% +and the income statement and +assets in the balance sheet + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +yeah sorry + + align:start position:0% +yeah sorry + + + align:start position:0% +yeah sorry +anyone else + + align:start position:0% +anyone else + + + align:start position:0% +anyone else +uh sure but basically i think like it + + align:start position:0% +uh sure but basically i think like it + + + align:start position:0% +uh sure but basically i think like it +all should be able to like match in a + + align:start position:0% +all should be able to like match in a + + + align:start position:0% +all should be able to like match in a +sense that like we should be able to + + align:start position:0% +sense that like we should be able to + + + align:start position:0% +sense that like we should be able to +account for these dollars on both sides + + align:start position:0% +account for these dollars on both sides + + + align:start position:0% +account for these dollars on both sides +and both like the flows and in the + + align:start position:0% +and both like the flows and in the + + + align:start position:0% +and both like the flows and in the +assets + + align:start position:0% +assets + + + align:start position:0% +assets +um but because of the way that the data + + align:start position:0% +um but because of the way that the data + + + align:start position:0% +um but because of the way that the data +is structured there's no basically + + align:start position:0% +is structured there's no basically + + + align:start position:0% +is structured there's no basically +central accounting place where all of + + align:start position:0% +central accounting place where all of + + + align:start position:0% +central accounting place where all of +these are accounted for on a regional + + align:start position:0% +these are accounted for on a regional + + + align:start position:0% +these are accounted for on a regional +level in a way that just like has all + + align:start position:0% +level in a way that just like has all + + + align:start position:0% +level in a way that just like has all +the data and so basically nothing + + align:start position:0% +the data and so basically nothing + + + align:start position:0% +the data and so basically nothing +matches up but they're like + + align:start position:0% +matches up but they're like + + + align:start position:0% +matches up but they're like +like we had like that table with like + + align:start position:0% +like we had like that table with like + + + align:start position:0% +like we had like that table with like +errors in the i forget what it was like + + align:start position:0% +errors in the i forget what it was like + + + align:start position:0% +errors in the i forget what it was like +20 plus percent or something like that + + align:start position:0% +20 plus percent or something like that + + + align:start position:0% +20 plus percent or something like that +yes that's correct great answer so + + align:start position:0% +yes that's correct great answer so + + + align:start position:0% +yes that's correct great answer so +the logic of it is you have flows + + align:start position:0% +the logic of it is you have flows + + + align:start position:0% +the logic of it is you have flows +in the income statement you have + + align:start position:0% +in the income statement you have + + + align:start position:0% +in the income statement you have +revenues less expenses equal profits + + align:start position:0% +revenues less expenses equal profits + + + align:start position:0% +revenues less expenses equal profits +or for households you know net income + + align:start position:0% +or for households you know net income + + + align:start position:0% +or for households you know net income +and what they don't eat + + align:start position:0% +and what they don't eat + + + align:start position:0% +and what they don't eat +or + + align:start position:0% +or + + + align:start position:0% +or +pay out is dividends + + align:start position:0% +pay out is dividends + + + align:start position:0% +pay out is dividends +they should be saving so the the changes + + align:start position:0% +they should be saving so the the changes + + + align:start position:0% +they should be saving so the the changes +in the balance sheet + + align:start position:0% +in the balance sheet + + + align:start position:0% +in the balance sheet +well some balance sheet items ought to + + align:start position:0% +well some balance sheet items ought to + + + align:start position:0% +well some balance sheet items ought to +go out up + + align:start position:0% +go out up + + + align:start position:0% +go out up +if households or firms are saving and in + + align:start position:0% +if households or firms are saving and in + + + align:start position:0% +if households or firms are saving and in +practice + + align:start position:0% +practice + + + align:start position:0% +practice +uh + + align:start position:0% +uh + + + align:start position:0% +uh +since as was just said + + align:start position:0% +since as was just said + + + align:start position:0% +since as was just said +the balance sheet and income statements + + align:start position:0% +the balance sheet and income statements + + + align:start position:0% +the balance sheet and income statements +are not + + align:start position:0% +are not + + + align:start position:0% +are not +collected at the same time we see very + + align:start position:0% +collected at the same time we see very + + + align:start position:0% +collected at the same time we see very +big discrepancies between the two + + align:start position:0% + + + + align:start position:0% + +so the the rest of the class last time + + align:start position:0% +so the the rest of the class last time + + + align:start position:0% +so the the rest of the class last time +almost up to the very end was about + + align:start position:0% +almost up to the very end was about + + + align:start position:0% +almost up to the very end was about +what this discrepancy means for attempts + + align:start position:0% +what this discrepancy means for attempts + + + align:start position:0% +what this discrepancy means for attempts +to measure inequality + + align:start position:0% +to measure inequality + + + align:start position:0% +to measure inequality +or the impact of covet and so on + + align:start position:0% + + + + align:start position:0% + +so i'll just say what what i was trying + + align:start position:0% +so i'll just say what what i was trying + + + align:start position:0% +so i'll just say what what i was trying +to do in the class is not to get you to + + align:start position:0% +to do in the class is not to get you to + + + align:start position:0% +to do in the class is not to get you to +memorize + + align:start position:0% + + + + align:start position:0% + +financial account identities but rather + + align:start position:0% +financial account identities but rather + + + align:start position:0% +financial account identities but rather +to think creatively about how to use + + align:start position:0% +to think creatively about how to use + + + align:start position:0% +to think creatively about how to use +financial account data and so on + + align:start position:0% +financial account data and so on + + + align:start position:0% +financial account data and so on +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +which brought me to the very end where i + + align:start position:0% +which brought me to the very end where i + + + align:start position:0% +which brought me to the very end where i +talked about + + align:start position:0% +talked about + + + align:start position:0% +talked about +trying to fill in those gaps + + align:start position:0% +trying to fill in those gaps + + + align:start position:0% +trying to fill in those gaps +and gathering + + align:start position:0% +and gathering + + + align:start position:0% +and gathering +detailed level information from + + align:start position:0% +detailed level information from + + + align:start position:0% +detailed level information from +households + + align:start position:0% +households + + + align:start position:0% +households +in west virginia and so on + + align:start position:0% + + + + align:start position:0% + +but i won't ask about that + + align:start position:0% +but i won't ask about that + + + align:start position:0% +but i won't ask about that +that may come up again today actually + + align:start position:0% +that may come up again today actually + + + align:start position:0% +that may come up again today actually +so let's go to the review + + align:start position:0% +so let's go to the review + + + align:start position:0% +so let's go to the review +from lecture eight on + + align:start position:0% +from lecture eight on + + + align:start position:0% +from lecture eight on +so i will try to highlight we did risk + + align:start position:0% +so i will try to highlight we did risk + + + align:start position:0% +so i will try to highlight we did risk +sharing in india in the villages and + + align:start position:0% +sharing in india in the villages and + + + align:start position:0% +sharing in india in the villages and +also + + align:start position:0% +also + + + align:start position:0% +also +in medieval + + align:start position:0% +in medieval + + + align:start position:0% +in medieval +england in terms of dividing up the land + + align:start position:0% +england in terms of dividing up the land + + + align:start position:0% +england in terms of dividing up the land +i talked at the beginning of the lecture + + align:start position:0% +i talked at the beginning of the lecture + + + align:start position:0% +i talked at the beginning of the lecture +about the high-risk environment and the + + align:start position:0% +about the high-risk environment and the + + + align:start position:0% +about the high-risk environment and the +way households could respond to it + + align:start position:0% +way households could respond to it + + + align:start position:0% +way households could respond to it +either by diversifying or by helping + + align:start position:0% +either by diversifying or by helping + + + align:start position:0% +either by diversifying or by helping +each other out with financial gifts and + + align:start position:0% +each other out with financial gifts and + + + align:start position:0% +each other out with financial gifts and +transfers + + align:start position:0% +transfers + + + align:start position:0% +transfers +and then + + align:start position:0% +and then + + + align:start position:0% +and then +ways to test so + + align:start position:0% +ways to test so + + + align:start position:0% +ways to test so +in india + + align:start position:0% +in india + + + align:start position:0% +in india +we decided to test by looking at incomes + + align:start position:0% +we decided to test by looking at incomes + + + align:start position:0% +we decided to test by looking at incomes +and consumptions + + align:start position:0% +and consumptions + + + align:start position:0% +and consumptions +and not looking at the mechanism + + align:start position:0% +and not looking at the mechanism + + + align:start position:0% +and not looking at the mechanism +and in contrast with medieval england + + align:start position:0% +and in contrast with medieval england + + + align:start position:0% +and in contrast with medieval england +we focus more on whether or not + + align:start position:0% +we focus more on whether or not + + + align:start position:0% +we focus more on whether or not +the mechanism of dividing up land could + + align:start position:0% +the mechanism of dividing up land could + + + align:start position:0% +the mechanism of dividing up land could +achieve + + align:start position:0% +achieve + + + align:start position:0% +achieve +an optimal allocation + + align:start position:0% +an optimal allocation + + + align:start position:0% +an optimal allocation +so then we went through characteristics + + align:start position:0% +so then we went through characteristics + + + align:start position:0% +so then we went through characteristics +of village economies + + align:start position:0% +of village economies + + + align:start position:0% +of village economies +and + + align:start position:0% +and + + + align:start position:0% +and +main thing here was the risk + + align:start position:0% +main thing here was the risk + + + align:start position:0% +main thing here was the risk +in particular in village india + + align:start position:0% +in particular in village india + + + align:start position:0% +in particular in village india +we looked at the risk + + align:start position:0% +we looked at the risk + + + align:start position:0% +we looked at the risk +of harvest yields on various crops of + + align:start position:0% +of harvest yields on various crops of + + + align:start position:0% +of harvest yields on various crops of +crops by soil type + + align:start position:0% +crops by soil type + + + align:start position:0% +crops by soil type +of + + align:start position:0% +of + + + align:start position:0% +of +income by type + + align:start position:0% +income by type + + + align:start position:0% +income by type +and we uniformly saw a very high risk on + + align:start position:0% +and we uniformly saw a very high risk on + + + align:start position:0% +and we uniformly saw a very high risk on +all these categories + + align:start position:0% +all these categories + + + align:start position:0% +all these categories +as well as + + align:start position:0% +as well as + + + align:start position:0% +as well as +some diversification possibilities so i + + align:start position:0% +some diversification possibilities so i + + + align:start position:0% +some diversification possibilities so i +was + + align:start position:0% +was + + + align:start position:0% +was +if for income exam you know not everyone + + align:start position:0% +if for income exam you know not everyone + + + align:start position:0% +if for income exam you know not everyone +has the same income sources and there's + + align:start position:0% +has the same income sources and there's + + + align:start position:0% +has the same income sources and there's +high risk of each but the covariances + + align:start position:0% +high risk of each but the covariances + + + align:start position:0% +high risk of each but the covariances +are + + align:start position:0% +are + + + align:start position:0% +are +sometimes relatively low + + align:start position:0% +sometimes relatively low + + + align:start position:0% +sometimes relatively low +so the focus here was on + + align:start position:0% +so the focus here was on + + + align:start position:0% +so the focus here was on +the fact that households are not + + align:start position:0% +the fact that households are not + + + align:start position:0% +the fact that households are not +completely diversified if if all the + + align:start position:0% +completely diversified if if all the + + + align:start position:0% +completely diversified if if all the +households did the same thing if they + + align:start position:0% +households did the same thing if they + + + align:start position:0% +households did the same thing if they +planted the same crops in the same soil + + align:start position:0% +planted the same crops in the same soil + + + align:start position:0% +planted the same crops in the same soil +and had the same income sources + + align:start position:0% +and had the same income sources + + + align:start position:0% +and had the same income sources +then + + align:start position:0% +then + + + align:start position:0% +then +their + + align:start position:0% +their + + + align:start position:0% +their +initial outcomes would be essentially + + align:start position:0% +initial outcomes would be essentially + + + align:start position:0% +initial outcomes would be essentially +the same + + align:start position:0% +the same + + + align:start position:0% +the same +and if that's true then there's not much + + align:start position:0% +and if that's true then there's not much + + + align:start position:0% +and if that's true then there's not much +left to share + + align:start position:0% +left to share + + + align:start position:0% +left to share +but we see the opposite we see they're + + align:start position:0% +but we see the opposite we see they're + + + align:start position:0% +but we see the opposite we see they're +not diversified over all these various + + align:start position:0% +not diversified over all these various + + + align:start position:0% +not diversified over all these various +crops and soils and activities so + + align:start position:0% +crops and soils and activities so + + + align:start position:0% +crops and soils and activities so +there's a lot of idiosyncratic risk and + + align:start position:0% +there's a lot of idiosyncratic risk and + + + align:start position:0% +there's a lot of idiosyncratic risk and +that was what was clear from this + + align:start position:0% +that was what was clear from this + + + align:start position:0% +that was what was clear from this +picture of what we call the rocky + + align:start position:0% +picture of what we call the rocky + + + align:start position:0% +picture of what we call the rocky +mountains where the ups and downs are + + align:start position:0% +mountains where the ups and downs are + + + align:start position:0% +mountains where the ups and downs are +not together + + align:start position:0% +not together + + + align:start position:0% +not together +not going up together across households + + align:start position:0% +not going up together across households + + + align:start position:0% +not going up together across households +in a given year and so on + + align:start position:0% +in a given year and so on + + + align:start position:0% +in a given year and so on +whereas they do achieve a lot of + + align:start position:0% +whereas they do achieve a lot of + + + align:start position:0% +whereas they do achieve a lot of +smoothing so + + align:start position:0% +smoothing so + + + align:start position:0% +smoothing so +something is happening in the villages + + align:start position:0% +something is happening in the villages + + + align:start position:0% +something is happening in the villages +that + + align:start position:0% +that + + + align:start position:0% +that +whatever mechanism it is + + align:start position:0% +whatever mechanism it is + + + align:start position:0% +whatever mechanism it is +is allowing them to smooth + + align:start position:0% +is allowing them to smooth + + + align:start position:0% +is allowing them to smooth +now + + align:start position:0% +now + + + align:start position:0% +now +one question that's come up in + + align:start position:0% +one question that's come up in + + + align:start position:0% +one question that's come up in +piazza + + align:start position:0% +piazza + + + align:start position:0% +piazza +are these profiles i mean you + + align:start position:0% +are these profiles i mean you + + + align:start position:0% +are these profiles i mean you +so this is a bit of + + align:start position:0% +so this is a bit of + + + align:start position:0% +so this is a bit of +a review but kind of interesting we see + + align:start position:0% +a review but kind of interesting we see + + + align:start position:0% +a review but kind of interesting we see +this income profile from + + align:start position:0% +this income profile from + + + align:start position:0% +this income profile from +low to high + + align:start position:0% +low to high + + + align:start position:0% +low to high +households with a lot of land are + + align:start position:0% +households with a lot of land are + + + align:start position:0% +households with a lot of land are +consistently getting higher income + + align:start position:0% +consistently getting higher income + + + align:start position:0% +consistently getting higher income +despite the fluctuations and they + + align:start position:0% +despite the fluctuations and they + + + align:start position:0% +despite the fluctuations and they +there's a big compression here + + align:start position:0% +there's a big compression here + + + align:start position:0% +there's a big compression here +so something is transferring income from + + align:start position:0% +so something is transferring income from + + + align:start position:0% +so something is transferring income from +the landed households to the landless + + align:start position:0% +the landed households to the landless + + + align:start position:0% +the landed households to the landless +but a little bit of this profile does + + align:start position:0% +but a little bit of this profile does + + + align:start position:0% +but a little bit of this profile does +remain so it's not equal treatment it's + + align:start position:0% +remain so it's not equal treatment it's + + + align:start position:0% +remain so it's not equal treatment it's +not as though everyone's getting the + + align:start position:0% +not as though everyone's getting the + + + align:start position:0% +not as though everyone's getting the +same amount of everything + + align:start position:0% +same amount of everything + + + align:start position:0% +same amount of everything +there is heterogeneity in the treatment + + align:start position:0% +there is heterogeneity in the treatment + + + align:start position:0% +there is heterogeneity in the treatment +what that mechanism is is not so clear + + align:start position:0% +what that mechanism is is not so clear + + + align:start position:0% +what that mechanism is is not so clear +some kind of at least over these 10 + + align:start position:0% +some kind of at least over these 10 + + + align:start position:0% +some kind of at least over these 10 +years you know redistribution of income + + align:start position:0% +years you know redistribution of income + + + align:start position:0% +years you know redistribution of income +from the wealthy to the poor + + align:start position:0% +from the wealthy to the poor + + + align:start position:0% +from the wealthy to the poor +but it doesn't work perfectly + + align:start position:0% +but it doesn't work perfectly + + + align:start position:0% +but it doesn't work perfectly +it doesn't completely equalize things + + align:start position:0% +it doesn't completely equalize things + + + align:start position:0% +it doesn't completely equalize things +so this lecture was featuring something + + align:start position:0% +so this lecture was featuring something + + + align:start position:0% +so this lecture was featuring something +we had done in the previous one which is + + align:start position:0% +we had done in the previous one which is + + + align:start position:0% +we had done in the previous one which is +to determine the pareto optimal + + align:start position:0% +to determine the pareto optimal + + + align:start position:0% +to determine the pareto optimal +allocation of risk we maximize lambda + + align:start position:0% +allocation of risk we maximize lambda + + + align:start position:0% +allocation of risk we maximize lambda +weighted sums of expected utilities + + align:start position:0% +weighted sums of expected utilities + + + align:start position:0% +weighted sums of expected utilities +subject to the resource constraint + + align:start position:0% +subject to the resource constraint + + + align:start position:0% +subject to the resource constraint +and this + + align:start position:0% +and this + + + align:start position:0% +and this +way of dealing + + align:start position:0% +way of dealing + + + align:start position:0% +way of dealing +with problems generalizes considerably + + align:start position:0% +with problems generalizes considerably + + + align:start position:0% +with problems generalizes considerably +in + + align:start position:0% +in + + + align:start position:0% +in +in the subsequent lectures + + align:start position:0% +in the subsequent lectures + + + align:start position:0% +in the subsequent lectures +so when we solve this problem we looked + + align:start position:0% +so when we solve this problem we looked + + + align:start position:0% +so when we solve this problem we looked +at the first order conditions + + align:start position:0% +at the first order conditions + + + align:start position:0% +at the first order conditions +we could see that weighted marginal + + align:start position:0% +we could see that weighted marginal + + + align:start position:0% +we could see that weighted marginal +utilities should be equalized + + align:start position:0% +utilities should be equalized + + + align:start position:0% +utilities should be equalized +to a common lagrange multiplier + + align:start position:0% +to a common lagrange multiplier + + + align:start position:0% +to a common lagrange multiplier +and you can do the algebra and actually + + align:start position:0% +and you can do the algebra and actually + + + align:start position:0% +and you can do the algebra and actually +solve for the consumption that's + + align:start position:0% +solve for the consumption that's + + + align:start position:0% +solve for the consumption that's +supposed to result + + align:start position:0% +supposed to result + + + align:start position:0% +supposed to result +and get these kinds of closed form + + align:start position:0% +and get these kinds of closed form + + + align:start position:0% +and get these kinds of closed form +solutions + + align:start position:0% +solutions + + + align:start position:0% +solutions +having to do with consumption + + align:start position:0% +having to do with consumption + + + align:start position:0% +having to do with consumption +moving with the aggregate + + align:start position:0% +moving with the aggregate + + + align:start position:0% +moving with the aggregate +and + + align:start position:0% +and + + + align:start position:0% +and +not moving at all with idiosyncratic + + align:start position:0% +not moving at all with idiosyncratic + + + align:start position:0% +not moving at all with idiosyncratic +shocks + + align:start position:0% +shocks + + + align:start position:0% +shocks +if the risk sharing is optimal + + align:start position:0% +if the risk sharing is optimal + + + align:start position:0% +if the risk sharing is optimal +which is another version of it + + align:start position:0% +which is another version of it + + + align:start position:0% +which is another version of it +individual consumption + + align:start position:0% +individual consumption + + + align:start position:0% +individual consumption +moves with aggregate consumption for all + + align:start position:0% +moves with aggregate consumption for all + + + align:start position:0% +moves with aggregate consumption for all +the households + + align:start position:0% +the households + + + align:start position:0% +the households +but should not move with things like + + align:start position:0% +but should not move with things like + + + align:start position:0% +but should not move with things like +individual incomes once we control for + + align:start position:0% +individual incomes once we control for + + + align:start position:0% +individual incomes once we control for +the aggregate so we tested this model to + + align:start position:0% +the aggregate so we tested this model to + + + align:start position:0% +the aggregate so we tested this model to +see whether these exceed + + align:start position:0% +see whether these exceed + + + align:start position:0% +see whether these exceed +coefficients were zero or not and + + align:start position:0% +coefficients were zero or not and + + + align:start position:0% +coefficients were zero or not and +largely + + align:start position:0% +largely + + + align:start position:0% +largely +they are i mean there is some residual + + align:start position:0% +they are i mean there is some residual + + + align:start position:0% +they are i mean there is some residual +risk that is being borne by the + + align:start position:0% +risk that is being borne by the + + + align:start position:0% +risk that is being borne by the +households depending on the village and + + align:start position:0% +households depending on the village and + + + align:start position:0% +households depending on the village and +the source of income but the benchmark + + align:start position:0% +the source of income but the benchmark + + + align:start position:0% +the source of income but the benchmark +was doing quite well + + align:start position:0% +was doing quite well + + + align:start position:0% +was doing quite well +i would be delighted yeah i mean + + align:start position:0% +i would be delighted yeah i mean + + + align:start position:0% +i would be delighted yeah i mean +um + + align:start position:0% +um + + + align:start position:0% +um +here we assume uh i see the sample there + + align:start position:0% +here we assume uh i see the sample there + + + align:start position:0% +here we assume uh i see the sample there +was about + + align:start position:0% +was about + + + align:start position:0% +was about +40 households in each villagers + + align:start position:0% +40 households in each villagers + + + align:start position:0% +40 households in each villagers +but in this model we assume that the + + align:start position:0% +but in this model we assume that the + + + align:start position:0% +but in this model we assume that the +household should be large amount + + align:start position:0% +household should be large amount + + + align:start position:0% +household should be large amount +if not + + align:start position:0% +if not + + + align:start position:0% +if not +then the idiosyncratic risk might not be + + align:start position:0% +then the idiosyncratic risk might not be + + + align:start position:0% +then the idiosyncratic risk might not be +shared right and for example if there + + align:start position:0% +shared right and for example if there + + + align:start position:0% +shared right and for example if there +was just two households and + + align:start position:0% +was just two households and + + + align:start position:0% +was just two households and +two situations + + align:start position:0% +two situations + + + align:start position:0% +two situations +then + + align:start position:0% +then + + + align:start position:0% +then +although they faced the idiosyncratic + + align:start position:0% + + + + align:start position:0% + +risks but + + align:start position:0% +risks but + + + align:start position:0% +risks but +uh there was + + align:start position:0% +uh there was + + + align:start position:0% +uh there was +like uh 0.25 + + align:start position:0% +like uh 0.25 + + + align:start position:0% +like uh 0.25 +probability both of them were fake the + + align:start position:0% +probability both of them were fake the + + + align:start position:0% +probability both of them were fake the +negative shocks and or + + align:start position:0% +negative shocks and or + + + align:start position:0% +negative shocks and or +both of them failed the positive shock + + align:start position:0% +both of them failed the positive shock + + + align:start position:0% +both of them failed the positive shock +so they cannot share the risks so + + align:start position:0% +so they cannot share the risks so + + + align:start position:0% +so they cannot share the risks so +in this model we assume the + + align:start position:0% +in this model we assume the + + + align:start position:0% +in this model we assume the +sample is large enough + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +that is why + + align:start position:0% +that is why + + + align:start position:0% +that is why +we think that the idiosyncratic shocks + + align:start position:0% +we think that the idiosyncratic shocks + + + align:start position:0% +we think that the idiosyncratic shocks +will not affect people's + + align:start position:0% +will not affect people's + + + align:start position:0% +will not affect people's +consumption + + align:start position:0% +consumption + + + align:start position:0% +consumption +yeah each household's consumption + + align:start position:0% +yeah each household's consumption + + + align:start position:0% +yeah each household's consumption +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +it's a great question + + align:start position:0% +it's a great question + + + align:start position:0% +it's a great question +you know what can we + + align:start position:0% +you know what can we + + + align:start position:0% +you know what can we +test if we only have a subset of the + + align:start position:0% +test if we only have a subset of the + + + align:start position:0% +test if we only have a subset of the +households + + align:start position:0% +households + + + align:start position:0% +households +and are we being misled + + align:start position:0% +and are we being misled + + + align:start position:0% +and are we being misled +well + + align:start position:0% +well + + + align:start position:0% +well +actually you could think about it as + + align:start position:0% +actually you could think about it as + + + align:start position:0% +actually you could think about it as +testing for subsets + + align:start position:0% +testing for subsets + + + align:start position:0% +testing for subsets +and the theory holds of course what is + + align:start position:0% +and the theory holds of course what is + + + align:start position:0% +and the theory holds of course what is +aggregate consumption + + align:start position:0% +aggregate consumption + + + align:start position:0% +aggregate consumption +for two households would be different + + align:start position:0% +for two households would be different + + + align:start position:0% +for two households would be different +from what it would be if you had data on + + align:start position:0% +from what it would be if you had data on + + + align:start position:0% +from what it would be if you had data on +all of them + + align:start position:0% +all of them + + + align:start position:0% +all of them +but it but the theory still works for + + align:start position:0% +but it but the theory still works for + + + align:start position:0% +but it but the theory still works for +two or three or just a handful + + align:start position:0% +two or three or just a handful + + + align:start position:0% +two or three or just a handful +once you control they should if they are + + align:start position:0% +once you control they should if they are + + + align:start position:0% +once you control they should if they are +bearing risk optimally then they should + + align:start position:0% +bearing risk optimally then they should + + + align:start position:0% +bearing risk optimally then they should +be bearing risk optimally in any subset + + align:start position:0% + + + + align:start position:0% + +let me put that a different way + + align:start position:0% +let me put that a different way + + + align:start position:0% +let me put that a different way +the the aggregate consumption within the + + align:start position:0% +the the aggregate consumption within the + + + align:start position:0% +the the aggregate consumption within the +group may be moving around + + align:start position:0% +group may be moving around + + + align:start position:0% +group may be moving around +individual consumptions in the group + + align:start position:0% +individual consumptions in the group + + + align:start position:0% +individual consumptions in the group +should move with that + + align:start position:0% +should move with that + + + align:start position:0% +should move with that +that group consumption actually could + + align:start position:0% +that group consumption actually could + + + align:start position:0% +that group consumption actually could +look like an idiosyncratic shock if we + + align:start position:0% +look like an idiosyncratic shock if we + + + align:start position:0% +look like an idiosyncratic shock if we +considered the whole village + + align:start position:0% +considered the whole village + + + align:start position:0% +considered the whole village +so yet more restrictions are implied + + align:start position:0% +so yet more restrictions are implied + + + align:start position:0% +so yet more restrictions are implied +when we and if we had data from the + + align:start position:0% +when we and if we had data from the + + + align:start position:0% +when we and if we had data from the +larger sample + + align:start position:0% +larger sample + + + align:start position:0% +larger sample +but you can still test the theory + + align:start position:0% +but you can still test the theory + + + align:start position:0% +but you can still test the theory +at a with a small number of households + + align:start position:0% +at a with a small number of households + + + align:start position:0% +at a with a small number of households +it's just that it's not as powerful + + align:start position:0% +it's just that it's not as powerful + + + align:start position:0% +it's just that it's not as powerful +you could reject however + + align:start position:0% +you could reject however + + + align:start position:0% +you could reject however +does that help + + align:start position:0% +does that help + + + align:start position:0% +does that help +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +okay it was a great question + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +then the next thing we did was to take + + align:start position:0% +then the next thing we did was to take + + + align:start position:0% +then the next thing we did was to take +the same theory to a different + + align:start position:0% +the same theory to a different + + + align:start position:0% +the same theory to a different +applications back to medieval villages + + align:start position:0% +applications back to medieval villages + + + align:start position:0% +applications back to medieval villages +and the land holding patterns which are + + align:start position:0% +and the land holding patterns which are + + + align:start position:0% +and the land holding patterns which are +spread out all over the different fields + + align:start position:0% +spread out all over the different fields + + + align:start position:0% +spread out all over the different fields +and the idea is does that make sense or + + align:start position:0% +and the idea is does that make sense or + + + align:start position:0% +and the idea is does that make sense or +not and and would dividing up the land + + align:start position:0% +not and and would dividing up the land + + + align:start position:0% +not and and would dividing up the land +in that way + + align:start position:0% +in that way + + + align:start position:0% +in that way +exactly achieve an optimal allocation of + + align:start position:0% +exactly achieve an optimal allocation of + + + align:start position:0% +exactly achieve an optimal allocation of +risk bearing or not + + align:start position:0% +risk bearing or not + + + align:start position:0% +risk bearing or not +so + + align:start position:0% +so + + + align:start position:0% +so +we took the different types of land to + + align:start position:0% +we took the different types of land to + + + align:start position:0% +we took the different types of land to +have a different vector of yields we + + align:start position:0% +have a different vector of yields we + + + align:start position:0% +have a different vector of yields we +talked about the endowment + + align:start position:0% +talked about the endowment + + + align:start position:0% +talked about the endowment +so to speak the yields of land type k + + align:start position:0% +so to speak the yields of land type k + + + align:start position:0% +so to speak the yields of land type k +across states epsilon + + align:start position:0% +across states epsilon + + + align:start position:0% +across states epsilon +and then we have you know capital + + align:start position:0% +and then we have you know capital + + + align:start position:0% +and then we have you know capital +k + + align:start position:0% +k + + + align:start position:0% +k +types of land and + + align:start position:0% +types of land and + + + align:start position:0% +types of land and +capital s types of shocks we can look at + + align:start position:0% +capital s types of shocks we can look at + + + align:start position:0% +capital s types of shocks we can look at +the covariance and the risk just the way + + align:start position:0% +the covariance and the risk just the way + + + align:start position:0% +the covariance and the risk just the way +we did in + + align:start position:0% +we did in + + + align:start position:0% +we did in +in india so again we get this picture + + align:start position:0% +in india so again we get this picture + + + align:start position:0% +in india so again we get this picture +very very risky with some covariances + + align:start position:0% +very very risky with some covariances + + + align:start position:0% +very very risky with some covariances +pretty low + + align:start position:0% +pretty low + + + align:start position:0% +pretty low +then i took you through a series of + + align:start position:0% +then i took you through a series of + + + align:start position:0% +then i took you through a series of +examples to see how close we could get + + align:start position:0% +examples to see how close we could get + + + align:start position:0% +examples to see how close we could get +to an optimal allocation of risk bearing + + align:start position:0% +to an optimal allocation of risk bearing + + + align:start position:0% +to an optimal allocation of risk bearing +the first was + + align:start position:0% +the first was + + + align:start position:0% +the first was +household one as all of land type one + + align:start position:0% +household one as all of land type one + + + align:start position:0% +household one as all of land type one +household two has all of land type two + + align:start position:0% +household two has all of land type two + + + align:start position:0% +household two has all of land type two +but these returns do not co-move + + align:start position:0% +but these returns do not co-move + + + align:start position:0% +but these returns do not co-move +hence + + align:start position:0% +hence + + + align:start position:0% +hence +this would not constitute an optimal + + align:start position:0% +this would not constitute an optimal + + + align:start position:0% +this would not constitute an optimal +optimal allocation of risk bearing + + align:start position:0% +optimal allocation of risk bearing + + + align:start position:0% +optimal allocation of risk bearing +household one would go 10-6 household 2 + + align:start position:0% +household one would go 10-6 household 2 + + + align:start position:0% +household one would go 10-6 household 2 +would go 2-4 + + align:start position:0% +would go 2-4 + + + align:start position:0% +would go 2-4 +so although the aggregate going down i + + align:start position:0% +so although the aggregate going down i + + + align:start position:0% +so although the aggregate going down i +should say + + align:start position:0% +should say + + + align:start position:0% +should say +from 12 to 10 + + align:start position:0% +from 12 to 10 + + + align:start position:0% +from 12 to 10 +household 2's consumption if they ate + + align:start position:0% +household 2's consumption if they ate + + + align:start position:0% +household 2's consumption if they ate +all their own crops would be going up + + align:start position:0% +all their own crops would be going up + + + align:start position:0% +all their own crops would be going up +so that's a restriction now we + + align:start position:0% +so that's a restriction now we + + + align:start position:0% +so that's a restriction now we +considered a different way of doing it + + align:start position:0% +considered a different way of doing it + + + align:start position:0% +considered a different way of doing it +give those household shares household + + align:start position:0% +give those household shares household + + + align:start position:0% +give those household shares household +j say + + align:start position:0% +j say + + + align:start position:0% +j say +having a share + + align:start position:0% +having a share + + + align:start position:0% +having a share +alpha j + + align:start position:0% +alpha j + + + align:start position:0% +alpha j +of the two + + align:start position:0% +of the two + + + align:start position:0% +of the two +different crops so + + align:start position:0% +different crops so + + + align:start position:0% +different crops so +now this thing goes in the aggregate 12 + + align:start position:0% +now this thing goes in the aggregate 12 + + + align:start position:0% +now this thing goes in the aggregate 12 +10 7. + + align:start position:0% +10 7. + + + align:start position:0% +10 7. +obviously whatever household ones share + + align:start position:0% +obviously whatever household ones share + + + align:start position:0% +obviously whatever household ones share +is if it's like one-third it's one-third + + align:start position:0% +is if it's like one-third it's one-third + + + align:start position:0% +is if it's like one-third it's one-third +of that aggregate + + align:start position:0% +of that aggregate + + + align:start position:0% +of that aggregate +household two shares would be two-thirds + + align:start position:0% +household two shares would be two-thirds + + + align:start position:0% +household two shares would be two-thirds +of that aggregate + + align:start position:0% +of that aggregate + + + align:start position:0% +of that aggregate +so now they're each bearing a constant + + align:start position:0% +so now they're each bearing a constant + + + align:start position:0% +so now they're each bearing a constant +share of the aggregate and their com + + align:start position:0% +share of the aggregate and their com + + + align:start position:0% +share of the aggregate and their com +consumptions are + + align:start position:0% +consumptions are + + + align:start position:0% +consumptions are +moving with the aggregate so that might + + align:start position:0% +moving with the aggregate so that might + + + align:start position:0% +moving with the aggregate so that might +actually work + + align:start position:0% +actually work + + + align:start position:0% +actually work +that's this and then we looked at + + align:start position:0% +that's this and then we looked at + + + align:start position:0% +that's this and then we looked at +special utility functions and started + + align:start position:0% +special utility functions and started + + + align:start position:0% +special utility functions and started +fussing about intercepts and risk + + align:start position:0% +fussing about intercepts and risk + + + align:start position:0% +fussing about intercepts and risk +aversion and so on but then we come to + + align:start position:0% +aversion and so on but then we come to + + + align:start position:0% +aversion and so on but then we come to +the general idea that we have + + align:start position:0% +the general idea that we have + + + align:start position:0% +the general idea that we have +as many land types with independent + + align:start position:0% +as many land types with independent + + + align:start position:0% +as many land types with independent +return vectors as we have states of the + + align:start position:0% +return vectors as we have states of the + + + align:start position:0% +return vectors as we have states of the +world and then we have a target an + + align:start position:0% +world and then we have a target an + + + align:start position:0% +world and then we have a target an +optimal consumption allocation + + align:start position:0% +optimal consumption allocation + + + align:start position:0% +optimal consumption allocation +so we're trying to achieve this + + align:start position:0% +so we're trying to achieve this + + + align:start position:0% +so we're trying to achieve this +allocation that came from maximizing a + + align:start position:0% +allocation that came from maximizing a + + + align:start position:0% +allocation that came from maximizing a +lambda weighted sums of utilities + + align:start position:0% +lambda weighted sums of utilities + + + align:start position:0% +lambda weighted sums of utilities +by + + align:start position:0% +by + + + align:start position:0% +by +dividing the different + + align:start position:0% +dividing the different + + + align:start position:0% +dividing the different +land types into shares except now we + + align:start position:0% +land types into shares except now we + + + align:start position:0% +land types into shares except now we +have even more power + + align:start position:0% +have even more power + + + align:start position:0% +have even more power +because we do not require that household + + align:start position:0% +because we do not require that household + + + align:start position:0% +because we do not require that household +j have the same shares and all of the + + align:start position:0% +j have the same shares and all of the + + + align:start position:0% +j have the same shares and all of the +land types k we have this alpha jk for + + align:start position:0% +land types k we have this alpha jk for + + + align:start position:0% +land types k we have this alpha jk for +household j and the land type k and it's + + align:start position:0% +household j and the land type k and it's + + + align:start position:0% +household j and the land type k and it's +not perfect but in general since this + + align:start position:0% +not perfect but in general since this + + + align:start position:0% +not perfect but in general since this +vector of endowments is + + align:start position:0% +vector of endowments is + + + align:start position:0% +vector of endowments is +non-singular you can solve for the + + align:start position:0% +non-singular you can solve for the + + + align:start position:0% +non-singular you can solve for the +consumptions + + align:start position:0% +consumptions + + + align:start position:0% +consumptions +someone hopes that the shares will be + + align:start position:0% +someone hopes that the shares will be + + + align:start position:0% +someone hopes that the shares will be +positive in the end + + align:start position:0% +positive in the end + + + align:start position:0% +positive in the end +so + + align:start position:0% +so + + + align:start position:0% +so +so if there are as many types of land as + + align:start position:0% +so if there are as many types of land as + + + align:start position:0% +so if there are as many types of land as +there are + + align:start position:0% +there are + + + align:start position:0% +there are +states of the world they have a shot at + + align:start position:0% +states of the world they have a shot at + + + align:start position:0% +states of the world they have a shot at +achieving the optimum + + align:start position:0% +achieving the optimum + + + align:start position:0% +achieving the optimum +by entirely dividing up the land and not + + align:start position:0% +by entirely dividing up the land and not + + + align:start position:0% +by entirely dividing up the land and not +having to give gifts or transfers to one + + align:start position:0% +having to give gifts or transfers to one + + + align:start position:0% +having to give gifts or transfers to one +another after the fact + + align:start position:0% +another after the fact + + + align:start position:0% +another after the fact +so then we come to + + align:start position:0% +so then we come to + + + align:start position:0% +so then we come to +we put in particular utility functions + + align:start position:0% +we put in particular utility functions + + + align:start position:0% +we put in particular utility functions +and + + align:start position:0% +and + + + align:start position:0% +and +we assumed + + align:start position:0% +we assumed + + + align:start position:0% +we assumed +that we're going to + + align:start position:0% +that we're going to + + + align:start position:0% +that we're going to +solve this problem + + align:start position:0% +solve this problem + + + align:start position:0% +solve this problem +maximizing lambda weighted sums of + + align:start position:0% +maximizing lambda weighted sums of + + + align:start position:0% +maximizing lambda weighted sums of +utilities + + align:start position:0% +utilities + + + align:start position:0% +utilities +by the shares alpha jk + + align:start position:0% +by the shares alpha jk + + + align:start position:0% +by the shares alpha jk +but we're going to assume that there are + + align:start position:0% +but we're going to assume that there are + + + align:start position:0% +but we're going to assume that there are +fewer land types than there are states + + align:start position:0% +fewer land types than there are states + + + align:start position:0% +fewer land types than there are states +of the world namely uh only two types of + + align:start position:0% +of the world namely uh only two types of + + + align:start position:0% +of the world namely uh only two types of +land + + align:start position:0% +land + + + align:start position:0% +land +and + + align:start position:0% +and + + + align:start position:0% +and +a larger number s states of the world + + align:start position:0% +a larger number s states of the world + + + align:start position:0% +a larger number s states of the world +so now + + align:start position:0% +so now + + + align:start position:0% +so now +we know we in general cannot achieve an + + align:start position:0% +we know we in general cannot achieve an + + + align:start position:0% +we know we in general cannot achieve an +optimum but we were trying to describe + + align:start position:0% +optimum but we were trying to describe + + + align:start position:0% +optimum but we were trying to describe +this constrained optimum arrangement i + + align:start position:0% +this constrained optimum arrangement i + + + align:start position:0% +this constrained optimum arrangement i +guess what i want to emphasize is + + align:start position:0% +guess what i want to emphasize is + + + align:start position:0% +guess what i want to emphasize is +despite the restrictions we're still + + align:start position:0% +despite the restrictions we're still + + + align:start position:0% +despite the restrictions we're still +solving this programming problem we're + + align:start position:0% +solving this programming problem we're + + + align:start position:0% +solving this programming problem we're +maximizing + + align:start position:0% +maximizing + + + align:start position:0% +maximizing +lambda weighted sums of utilities + + align:start position:0% +lambda weighted sums of utilities + + + align:start position:0% +lambda weighted sums of utilities +subject to constraints namely the shares + + align:start position:0% +subject to constraints namely the shares + + + align:start position:0% +subject to constraints namely the shares +have to add up so the method of + + align:start position:0% +have to add up so the method of + + + align:start position:0% +have to add up so the method of +achieving + + align:start position:0% +achieving + + + align:start position:0% +achieving +characterizing pareto optimal + + align:start position:0% +characterizing pareto optimal + + + align:start position:0% +characterizing pareto optimal +allocations is the same + + align:start position:0% +allocations is the same + + + align:start position:0% +allocations is the same +and then we look to see + + align:start position:0% +and then we look to see + + + align:start position:0% +and then we look to see +with those particular utility functions + + align:start position:0% +with those particular utility functions + + + align:start position:0% +with those particular utility functions +how far off we would be + + align:start position:0% +how far off we would be + + + align:start position:0% +how far off we would be +from achieving the optimum and here you + + align:start position:0% +from achieving the optimum and here you + + + align:start position:0% +from achieving the optimum and here you +can actually see as the aggregate + + align:start position:0% +can actually see as the aggregate + + + align:start position:0% +can actually see as the aggregate +endowment moves the adjustment in other + + align:start position:0% +endowment moves the adjustment in other + + + align:start position:0% +endowment moves the adjustment in other +words even if they did as much as they + + align:start position:0% +words even if they did as much as they + + + align:start position:0% +words even if they did as much as they +could by dividing up the two land types + + align:start position:0% +could by dividing up the two land types + + + align:start position:0% +could by dividing up the two land types +it would not be perfect and there should + + align:start position:0% +it would not be perfect and there should + + + align:start position:0% +it would not be perfect and there should +be + + align:start position:0% +be + + + align:start position:0% +be +incoming or outgoing transfers to try to + + align:start position:0% +incoming or outgoing transfers to try to + + + align:start position:0% +incoming or outgoing transfers to try to +make up the difference to get to the + + align:start position:0% +make up the difference to get to the + + + align:start position:0% +make up the difference to get to the +full + + align:start position:0% +full + + + align:start position:0% +full +re-sharing optimum + + align:start position:0% +re-sharing optimum + + + align:start position:0% +re-sharing optimum +and that was the end of this lecture are + + align:start position:0% +and that was the end of this lecture are + + + align:start position:0% +and that was the end of this lecture are +there questions about + + align:start position:0% +there questions about + + + align:start position:0% +there questions about +what we did or what we were trying to + + align:start position:0% +what we did or what we were trying to + + + align:start position:0% +what we did or what we were trying to +accomplish in lecture eight + + align:start position:0% + + + + align:start position:0% + +so then the second of the two + + align:start position:0% +so then the second of the two + + + align:start position:0% +so then the second of the two +application lectures included production + + align:start position:0% +application lectures included production + + + align:start position:0% +application lectures included production +in lecture nine and the main difference + + align:start position:0% +in lecture nine and the main difference + + + align:start position:0% +in lecture nine and the main difference +between what we did just now and this + + align:start position:0% +between what we did just now and this + + + align:start position:0% +between what we did just now and this +lecture is we actually have physical + + align:start position:0% +lecture is we actually have physical + + + align:start position:0% +lecture is we actually have physical +production rather than treating output + + align:start position:0% +production rather than treating output + + + align:start position:0% +production rather than treating output +as an endowment + + align:start position:0% +as an endowment + + + align:start position:0% +as an endowment +but + + align:start position:0% +but + + + align:start position:0% +but +we still solve this programming problem + + align:start position:0% +we still solve this programming problem + + + align:start position:0% +we still solve this programming problem +so + + align:start position:0% +so + + + align:start position:0% +so +we're maximizing lambda weighted sums of + + align:start position:0% +we're maximizing lambda weighted sums of + + + align:start position:0% +we're maximizing lambda weighted sums of +expected utilities + + align:start position:0% +expected utilities + + + align:start position:0% +expected utilities +just as before + + align:start position:0% +just as before + + + align:start position:0% +just as before +subject to resource constraints just as + + align:start position:0% +subject to resource constraints just as + + + align:start position:0% +subject to resource constraints just as +before + + align:start position:0% +before + + + align:start position:0% +before +the choice variables now include + + align:start position:0% +the choice variables now include + + + align:start position:0% +the choice variables now include +the transfers just as before + + align:start position:0% +the transfers just as before + + + align:start position:0% +the transfers just as before +but we also are choosing which projects + + align:start position:0% +but we also are choosing which projects + + + align:start position:0% +but we also are choosing which projects +to fund and by how much capital + + align:start position:0% +to fund and by how much capital + + + align:start position:0% +to fund and by how much capital +investment + + align:start position:0% +investment + + + align:start position:0% +investment +so the reason that transfers + + align:start position:0% +so the reason that transfers + + + align:start position:0% +so the reason that transfers +are the same as before is because we + + align:start position:0% +are the same as before is because we + + + align:start position:0% +are the same as before is because we +have transfers or consumption you can + + align:start position:0% +have transfers or consumption you can + + + align:start position:0% +have transfers or consumption you can +move consumption around by moving + + align:start position:0% +move consumption around by moving + + + align:start position:0% +move consumption around by moving +transfers so it's an arbitrary choice + + align:start position:0% +transfers so it's an arbitrary choice + + + align:start position:0% +transfers so it's an arbitrary choice +whether to solve for c or tau + + align:start position:0% +whether to solve for c or tau + + + align:start position:0% +whether to solve for c or tau +the more interesting part because it's + + align:start position:0% +the more interesting part because it's + + + align:start position:0% +the more interesting part because it's +new to this lecture + + align:start position:0% +new to this lecture + + + align:start position:0% +new to this lecture +are these capital stocks which has to do + + align:start position:0% +are these capital stocks which has to do + + + align:start position:0% +are these capital stocks which has to do +with deciding + + align:start position:0% +with deciding + + + align:start position:0% +with deciding +what to do with the current wealth + + align:start position:0% +what to do with the current wealth + + + align:start position:0% +what to do with the current wealth +namely eat it or invest it in new pro in + + align:start position:0% +namely eat it or invest it in new pro in + + + align:start position:0% +namely eat it or invest it in new pro in +projects for tomorrow here's the + + align:start position:0% +projects for tomorrow here's the + + + align:start position:0% +projects for tomorrow here's the +starting point + + align:start position:0% +starting point + + + align:start position:0% +starting point +w which is the trees and the fruit from + + align:start position:0% +w which is the trees and the fruit from + + + align:start position:0% +w which is the trees and the fruit from +the trees and this was the ending point + + align:start position:0% +the trees and this was the ending point + + + align:start position:0% +the trees and this was the ending point +what you do + + align:start position:0% +what you do + + + align:start position:0% +what you do +either eat or save oh then back to the + + align:start position:0% +either eat or save oh then back to the + + + align:start position:0% +either eat or save oh then back to the +accounting identities you either eat + + align:start position:0% +accounting identities you either eat + + + align:start position:0% +accounting identities you either eat +something or save something that's in + + align:start position:0% +something or save something that's in + + + align:start position:0% +something or save something that's in +the flows + + align:start position:0% +the flows + + + align:start position:0% +the flows +so we got two first order conditions out + + align:start position:0% +so we got two first order conditions out + + + align:start position:0% +so we got two first order conditions out +of this problem + + align:start position:0% +of this problem + + + align:start position:0% +of this problem +one very familiar lambda weighted margin + + align:start position:0% +one very familiar lambda weighted margin + + + align:start position:0% +one very familiar lambda weighted margin +utilities are equated to each other we + + align:start position:0% +utilities are equated to each other we + + + align:start position:0% +utilities are equated to each other we +also got a new equation having to do + + align:start position:0% +also got a new equation having to do + + + align:start position:0% +also got a new equation having to do +with the margin utility of consumption + + align:start position:0% +with the margin utility of consumption + + + align:start position:0% +with the margin utility of consumption +today and the marginal utility of + + align:start position:0% +today and the marginal utility of + + + align:start position:0% +today and the marginal utility of +consumption next period + + align:start position:0% +consumption next period + + + align:start position:0% +consumption next period +and those typically will balance each + + align:start position:0% +and those typically will balance each + + + align:start position:0% +and those typically will balance each +other off for any project they're + + align:start position:0% +other off for any project they're + + + align:start position:0% +other off for any project they're +running there was an issue that this + + align:start position:0% +running there was an issue that this + + + align:start position:0% +running there was an issue that this +thing could have been negative in which + + align:start position:0% +thing could have been negative in which + + + align:start position:0% +thing could have been negative in which +case that project would not be + + align:start position:0% +case that project would not be + + + align:start position:0% +case that project would not be +implemented + + align:start position:0% +implemented + + + align:start position:0% +implemented +because they would actually not want to + + align:start position:0% +because they would actually not want to + + + align:start position:0% +because they would actually not want to +put stuff in there they'd want to take + + align:start position:0% +put stuff in there they'd want to take + + + align:start position:0% +put stuff in there they'd want to take +stuff out but they hit zero + + align:start position:0% +stuff out but they hit zero + + + align:start position:0% +stuff out but they hit zero +so + + align:start position:0% +so + + + align:start position:0% +so +the rest of it was to take + + align:start position:0% +the rest of it was to take + + + align:start position:0% +the rest of it was to take +expressions for these first order + + align:start position:0% +expressions for these first order + + + align:start position:0% +expressions for these first order +conditions and start manipulating them + + align:start position:0% +conditions and start manipulating them + + + align:start position:0% +conditions and start manipulating them +i'm not going to review that today + + align:start position:0% +i'm not going to review that today + + + align:start position:0% +i'm not going to review that today +it's algebra it's straightforward + + align:start position:0% +it's algebra it's straightforward + + + align:start position:0% +it's algebra it's straightforward +we can even make some assumptions about + + align:start position:0% +we can even make some assumptions about + + + align:start position:0% +we can even make some assumptions about +linear technologies subject to risk and + + align:start position:0% +linear technologies subject to risk and + + + align:start position:0% +linear technologies subject to risk and +quadratic utility functions + + align:start position:0% +quadratic utility functions + + + align:start position:0% +quadratic utility functions +and when we did that we got + + align:start position:0% +and when we did that we got + + + align:start position:0% +and when we did that we got +two expressions directly from the theory + + align:start position:0% +two expressions directly from the theory + + + align:start position:0% +two expressions directly from the theory +that we could take to the data one + + align:start position:0% +that we could take to the data one + + + align:start position:0% +that we could take to the data one +we can measure from the data + + align:start position:0% +we can measure from the data + + + align:start position:0% +we can measure from the data +how households j + + align:start position:0% +how households j + + + align:start position:0% +how households j +returns + + align:start position:0% +returns + + + align:start position:0% +returns +are moving with a village aggregate + + align:start position:0% +are moving with a village aggregate + + + align:start position:0% +are moving with a village aggregate +return this beta being a measure of the + + align:start position:0% +return this beta being a measure of the + + + align:start position:0% +return this beta being a measure of the +co-variation + + align:start position:0% +co-variation + + + align:start position:0% +co-variation +of household j's return with a village + + align:start position:0% +of household j's return with a village + + + align:start position:0% +of household j's return with a village +average + + align:start position:0% +average + + + align:start position:0% +average +then having + + align:start position:0% +then having + + + align:start position:0% +then having +used the panel data to get these beta + + align:start position:0% +used the panel data to get these beta + + + align:start position:0% +used the panel data to get these beta +j's + + align:start position:0% +j's + + + align:start position:0% +j's +we look in the cross section to see how + + align:start position:0% +we look in the cross section to see how + + + align:start position:0% +we look in the cross section to see how +their + + align:start position:0% +their + + + align:start position:0% +their +the betas are related to each other and + + align:start position:0% +the betas are related to each other and + + + align:start position:0% +the betas are related to each other and +in particular + + align:start position:0% +in particular + + + align:start position:0% +in particular +to the + + align:start position:0% +to the + + + align:start position:0% +to the +overall average or expected return + + align:start position:0% +overall average or expected return + + + align:start position:0% +overall average or expected return +so the main empirical finding here was + + align:start position:0% +so the main empirical finding here was + + + align:start position:0% +so the main empirical finding here was +that + + align:start position:0% +that + + + align:start position:0% +that +returns have to be higher + + align:start position:0% +returns have to be higher + + + align:start position:0% +returns have to be higher +when the betas are higher because those + + align:start position:0% +when the betas are higher because those + + + align:start position:0% +when the betas are higher because those +particular activities + + align:start position:0% +particular activities + + + align:start position:0% +particular activities +from household j + + align:start position:0% +from household j + + + align:start position:0% +from household j +co move a lot with the aggregate so in + + align:start position:0% +co move a lot with the aggregate so in + + + align:start position:0% +co move a lot with the aggregate so in +effect is very risky not so many + + align:start position:0% +effect is very risky not so many + + + align:start position:0% +effect is very risky not so many +diversification + + align:start position:0% +diversification + + + align:start position:0% +diversification +possibilities come from including + + align:start position:0% +possibilities come from including + + + align:start position:0% +possibilities come from including +household j in the village portfolio + + align:start position:0% +household j in the village portfolio + + + align:start position:0% +household j in the village portfolio +and so if they're going to be + + align:start position:0% +and so if they're going to be + + + align:start position:0% +and so if they're going to be +running those projects of household j + + align:start position:0% +running those projects of household j + + + align:start position:0% +running those projects of household j +they + + align:start position:0% +they + + + align:start position:0% +they +there has to be a compensating + + align:start position:0% +there has to be a compensating + + + align:start position:0% +there has to be a compensating +differential and that's the higher + + align:start position:0% +differential and that's the higher + + + align:start position:0% +differential and that's the higher +expected return + + align:start position:0% +expected return + + + align:start position:0% +expected return +so then we started + + align:start position:0% +so then we started + + + align:start position:0% +so then we started +adopting this language of risk premia + + align:start position:0% +adopting this language of risk premia + + + align:start position:0% +adopting this language of risk premia +which the difference between the + + align:start position:0% +which the difference between the + + + align:start position:0% +which the difference between the +expected return + + align:start position:0% +expected return + + + align:start position:0% +expected return +and the risk-free rate + + align:start position:0% +and the risk-free rate + + + align:start position:0% +and the risk-free rate +the brisk premia has to compensate for + + align:start position:0% +the brisk premia has to compensate for + + + align:start position:0% +the brisk premia has to compensate for +the risk so we then we went to the thai + + align:start position:0% +the risk so we then we went to the thai + + + align:start position:0% +the risk so we then we went to the thai +data where we have everything we need we + + align:start position:0% +data where we have everything we need we + + + align:start position:0% +data where we have everything we need we +have the income and the balance sheet oh + + align:start position:0% +have the income and the balance sheet oh + + + align:start position:0% +have the income and the balance sheet oh +yes so + + align:start position:0% +yes so + + + align:start position:0% +yes so +here are these accounts this i think was + + align:start position:0% +here are these accounts this i think was + + + align:start position:0% +here are these accounts this i think was +the first time + + align:start position:0% +the first time + + + align:start position:0% +the first time +the account started to come up + + align:start position:0% +the account started to come up + + + align:start position:0% +the account started to come up +explicitly + + align:start position:0% +explicitly + + + align:start position:0% +explicitly +we used the time monthly data over 13 + + align:start position:0% +we used the time monthly data over 13 + + + align:start position:0% +we used the time monthly data over 13 +years + + align:start position:0% +years + + + align:start position:0% +years +and i featured net income to be + + align:start position:0% +and i featured net income to be + + + align:start position:0% +and i featured net income to be +profits to be revenue minus costs + + align:start position:0% +profits to be revenue minus costs + + + align:start position:0% +profits to be revenue minus costs +and then we looked at the assets + + align:start position:0% +and then we looked at the assets + + + align:start position:0% +and then we looked at the assets +to be assets of various kinds typically + + align:start position:0% +to be assets of various kinds typically + + + align:start position:0% +to be assets of various kinds typically +physical + + align:start position:0% +physical + + + align:start position:0% +physical +tangible assets so here you have the + + align:start position:0% +tangible assets so here you have the + + + align:start position:0% +tangible assets so here you have the +income statement and the balance sheet i + + align:start position:0% +income statement and the balance sheet i + + + align:start position:0% +income statement and the balance sheet i +just didn't call it that at the time + + align:start position:0% +just didn't call it that at the time + + + align:start position:0% +just didn't call it that at the time +but that's what we're using so then we + + align:start position:0% +but that's what we're using so then we + + + align:start position:0% +but that's what we're using so then we +tested the model and found that the + + align:start position:0% +tested the model and found that the + + + align:start position:0% +tested the model and found that the +betas the expected returns are indeed + + align:start position:0% +betas the expected returns are indeed + + + align:start position:0% +betas the expected returns are indeed +higher when the betas are higher just + + align:start position:0% +higher when the betas are higher just + + + align:start position:0% +higher when the betas are higher just +like the model predicted + + align:start position:0% +like the model predicted + + + align:start position:0% +like the model predicted +and + + align:start position:0% +and + + + align:start position:0% +and +here we are back to idiosyncratic and + + align:start position:0% +here we are back to idiosyncratic and + + + align:start position:0% +here we are back to idiosyncratic and +aggregate risk which was the theme i + + align:start position:0% +aggregate risk which was the theme i + + + align:start position:0% +aggregate risk which was the theme i +mentioned in the previous lecture we can + + align:start position:0% +mentioned in the previous lecture we can + + + align:start position:0% +mentioned in the previous lecture we can +decompose the + + align:start position:0% +decompose the + + + align:start position:0% +decompose the +aggregate variation of household j + + align:start position:0% +aggregate variation of household j + + + align:start position:0% +aggregate variation of household j +into an explained and unexplained part + + align:start position:0% +into an explained and unexplained part + + + align:start position:0% +into an explained and unexplained part +the explained part has to do with the + + align:start position:0% +the explained part has to do with the + + + align:start position:0% +the explained part has to do with the +covariation with the village average + + align:start position:0% +covariation with the village average + + + align:start position:0% +covariation with the village average +and the unexplained part is if there + + align:start position:0% +and the unexplained part is if there + + + align:start position:0% +and the unexplained part is if there +were some idiosyncratic risk + + align:start position:0% +were some idiosyncratic risk + + + align:start position:0% +were some idiosyncratic risk +and we decompose the risk premium as + + align:start position:0% +and we decompose the risk premium as + + + align:start position:0% +and we decompose the risk premium as +well + + align:start position:0% +well + + + align:start position:0% +well +into the part that's coming from the + + align:start position:0% +into the part that's coming from the + + + align:start position:0% +into the part that's coming from the +village as a whole + + align:start position:0% +village as a whole + + + align:start position:0% +village as a whole +through the beta j as well as + + align:start position:0% +through the beta j as well as + + + align:start position:0% +through the beta j as well as +the + + align:start position:0% +the + + + align:start position:0% +the +sigma square + + align:start position:0% +sigma square + + + align:start position:0% +sigma square +sigma j on that epsilon + + align:start position:0% +sigma j on that epsilon + + + align:start position:0% +sigma j on that epsilon +and then got another decomposition so it + + align:start position:0% +and then got another decomposition so it + + + align:start position:0% +and then got another decomposition so it +turned out that + + align:start position:0% +turned out that + + + align:start position:0% +turned out that +as a quick review idiosyncratic risk was + + align:start position:0% +as a quick review idiosyncratic risk was + + + align:start position:0% +as a quick review idiosyncratic risk was +the largest contributor to total risk + + align:start position:0% +the largest contributor to total risk + + + align:start position:0% +the largest contributor to total risk +aggregate village level risk was a small + + align:start position:0% +aggregate village level risk was a small + + + align:start position:0% +aggregate village level risk was a small +part so there are a lot of idiosyncratic + + align:start position:0% +part so there are a lot of idiosyncratic + + + align:start position:0% +part so there are a lot of idiosyncratic +shocks in these villages just like we + + align:start position:0% +shocks in these villages just like we + + + align:start position:0% +shocks in these villages just like we +imagined that there were in medieval + + align:start position:0% +imagined that there were in medieval + + + align:start position:0% +imagined that there were in medieval +england and also in that we documented + + align:start position:0% +england and also in that we documented + + + align:start position:0% +england and also in that we documented +there were in village india + + align:start position:0% +there were in village india + + + align:start position:0% +there were in village india +but when you looked at the risk premia + + align:start position:0% +but when you looked at the risk premia + + + align:start position:0% +but when you looked at the risk premia +it went the other way + + align:start position:0% +it went the other way + + + align:start position:0% +it went the other way +namely + + align:start position:0% +namely + + + align:start position:0% +namely +most of the risk has to do with the + + align:start position:0% +most of the risk has to do with the + + + align:start position:0% +most of the risk has to do with the +aggregate risk so that's consistent with + + align:start position:0% +aggregate risk so that's consistent with + + + align:start position:0% +aggregate risk so that's consistent with +them + + align:start position:0% +them + + + align:start position:0% +them +finding a way to diversify their + + align:start position:0% +finding a way to diversify their + + + align:start position:0% +finding a way to diversify their +idiosyncratic shocks + + align:start position:0% +idiosyncratic shocks + + + align:start position:0% +idiosyncratic shocks +and there's evidence that i presented + + align:start position:0% +and there's evidence that i presented + + + align:start position:0% +and there's evidence that i presented +that they're doing that by gifts and + + align:start position:0% +that they're doing that by gifts and + + + align:start position:0% +that they're doing that by gifts and +borrowing and lending + + align:start position:0% +borrowing and lending + + + align:start position:0% +borrowing and lending +and that's the mechanism + + align:start position:0% +and that's the mechanism + + + align:start position:0% +and that's the mechanism +we started out talking about how we + + align:start position:0% +we started out talking about how we + + + align:start position:0% +we started out talking about how we +weren't going to test for mechanisms + + align:start position:0% +weren't going to test for mechanisms + + + align:start position:0% +weren't going to test for mechanisms +then we looked at xant division of land + + align:start position:0% +then we looked at xant division of land + + + align:start position:0% +then we looked at xant division of land +now we're looking at x post + + align:start position:0% +now we're looking at x post + + + align:start position:0% +now we're looking at x post +gifts and and borrowing as a way of + + align:start position:0% +gifts and and borrowing as a way of + + + align:start position:0% +gifts and and borrowing as a way of +getting from their quote production + + align:start position:0% +getting from their quote production + + + align:start position:0% +getting from their quote production +endowments to + + align:start position:0% +endowments to + + + align:start position:0% +endowments to +their ultimate consumptions + + align:start position:0% +their ultimate consumptions + + + align:start position:0% +their ultimate consumptions +and and + + align:start position:0% +and and + + + align:start position:0% +and and +most of the shocks are covered + + align:start position:0% +most of the shocks are covered + + + align:start position:0% +most of the shocks are covered +not all of them so they're not + + align:start position:0% +not all of them so they're not + + + align:start position:0% +not all of them so they're not +completely following the full risk + + align:start position:0% +completely following the full risk + + + align:start position:0% +completely following the full risk +sharing program but they definitely + + align:start position:0% +sharing program but they definitely + + + align:start position:0% +sharing program but they definitely +diversified mostly 90 of it + + align:start position:0% +diversified mostly 90 of it + + + align:start position:0% +diversified mostly 90 of it +so then we got to particular health + + align:start position:0% +so then we got to particular health + + + align:start position:0% +so then we got to particular health +shocks + + align:start position:0% +shocks + + + align:start position:0% +shocks +and illness specific illnesses + + align:start position:0% +and illness specific illnesses + + + align:start position:0% +and illness specific illnesses +and i showed you that again those + + align:start position:0% +and i showed you that again those + + + align:start position:0% +and i showed you that again those +illness shocks not production shocks per + + align:start position:0% +illness shocks not production shocks per + + + align:start position:0% +illness shocks not production shocks per +se were also covered by gifts largely + + align:start position:0% +se were also covered by gifts largely + + + align:start position:0% +se were also covered by gifts largely +although not entirely and when they were + + align:start position:0% +although not entirely and when they were + + + align:start position:0% +although not entirely and when they were +not covered they spill over into the + + align:start position:0% +not covered they spill over into the + + + align:start position:0% +not covered they spill over into the +labor network with less hiring of + + align:start position:0% +labor network with less hiring of + + + align:start position:0% +labor network with less hiring of +employed labor and also + + align:start position:0% +employed labor and also + + + align:start position:0% +employed labor and also +less purchasing of intermediate goods + + align:start position:0% +less purchasing of intermediate goods + + + align:start position:0% +less purchasing of intermediate goods +from other households + + align:start position:0% +from other households + + + align:start position:0% +from other households +so this was + + align:start position:0% +so this was + + + align:start position:0% +so this was +documenting that so you know + + align:start position:0% +documenting that so you know + + + align:start position:0% +documenting that so you know +this is about kinship groups and risk + + align:start position:0% +this is about kinship groups and risk + + + align:start position:0% +this is about kinship groups and risk +sharing in village + + align:start position:0% +sharing in village + + + align:start position:0% +sharing in village +villages in thailand + + align:start position:0% +villages in thailand + + + align:start position:0% +villages in thailand +it also was about an illness as a shock + + align:start position:0% +it also was about an illness as a shock + + + align:start position:0% +it also was about an illness as a shock +it was not about covet although it was + + align:start position:0% +it was not about covet although it was + + + align:start position:0% +it was not about covet although it was +about illness the illness was + + align:start position:0% +about illness the illness was + + + align:start position:0% +about illness the illness was +idiosyncratic and not aggregate the + + align:start position:0% +idiosyncratic and not aggregate the + + + align:start position:0% +idiosyncratic and not aggregate the +closest we could get in the thai data to + + align:start position:0% +closest we could get in the thai data to + + + align:start position:0% +closest we could get in the thai data to +an aggregate was watching those shrimp + + align:start position:0% +an aggregate was watching those shrimp + + + align:start position:0% +an aggregate was watching those shrimp +ponds suffer catastrophe in one of the + + align:start position:0% +ponds suffer catastrophe in one of the + + + align:start position:0% +ponds suffer catastrophe in one of the +four provinces and because it becomes an + + align:start position:0% +four provinces and because it becomes an + + + align:start position:0% +four provinces and because it becomes an +aggregate shock rather than + + align:start position:0% +aggregate shock rather than + + + align:start position:0% +aggregate shock rather than +idiosyncratic shock it's the gifts + + align:start position:0% +idiosyncratic shock it's the gifts + + + align:start position:0% +idiosyncratic shock it's the gifts +didn't come in as much and it's very + + align:start position:0% +didn't come in as much and it's very + + + align:start position:0% +didn't come in as much and it's very +harder to diversify so that's a theme i + + align:start position:0% +harder to diversify so that's a theme i + + + align:start position:0% +harder to diversify so that's a theme i +keep mentioning now for the last 10 or + + align:start position:0% +keep mentioning now for the last 10 or + + + align:start position:0% +keep mentioning now for the last 10 or +15 minutes video syncratic stuff in + + align:start position:0% +15 minutes video syncratic stuff in + + + align:start position:0% +15 minutes video syncratic stuff in +principle you can diversify aggregate + + align:start position:0% +principle you can diversify aggregate + + + align:start position:0% +principle you can diversify aggregate +shock stuff you cannot + + align:start position:0% +shock stuff you cannot + + + align:start position:0% +shock stuff you cannot +but the other thing i want to + + align:start position:0% +but the other thing i want to + + + align:start position:0% +but the other thing i want to +draw your attention to is this network + + align:start position:0% +draw your attention to is this network + + + align:start position:0% +draw your attention to is this network +stuff + + align:start position:0% +stuff + + + align:start position:0% +stuff +so the issue is uh not just in thailand + + align:start position:0% +so the issue is uh not just in thailand + + + align:start position:0% +so the issue is uh not just in thailand +or india for that matter but do these + + align:start position:0% +or india for that matter but do these + + + align:start position:0% +or india for that matter but do these +networks exist in the us and you know + + align:start position:0% +networks exist in the us and you know + + + align:start position:0% +networks exist in the us and you know +and what's going on with colgate + + align:start position:0% +and what's going on with colgate + + + align:start position:0% +and what's going on with colgate +so + + align:start position:0% +so + + + align:start position:0% +so +that interstate risk sharing stuff + + align:start position:0% +that interstate risk sharing stuff + + + align:start position:0% +that interstate risk sharing stuff +suggests that networks are not + + align:start position:0% +suggests that networks are not + + + align:start position:0% +suggests that networks are not +necessarily local + + align:start position:0% +necessarily local + + + align:start position:0% +necessarily local +they could be global but your relatives + + align:start position:0% +they could be global but your relatives + + + align:start position:0% +they could be global but your relatives +or other family members are are engaged + + align:start position:0% +or other family members are are engaged + + + align:start position:0% +or other family members are are engaged +in risk sharing + + align:start position:0% +in risk sharing + + + align:start position:0% +in risk sharing +when you experience a shock back home + + align:start position:0% +when you experience a shock back home + + + align:start position:0% +when you experience a shock back home +and then this project in west virginia + + align:start position:0% +and then this project in west virginia + + + align:start position:0% +and then this project in west virginia +you know well michael i hope you don't + + align:start position:0% +you know well michael i hope you don't + + + align:start position:0% +you know well michael i hope you don't +mind mentioning it but michael + + align:start position:0% +mind mentioning it but michael + + + align:start position:0% +mind mentioning it but michael +thinking about you know networks + + align:start position:0% +thinking about you know networks + + + align:start position:0% +thinking about you know networks +wondered about networks in the us and + + align:start position:0% +wondered about networks in the us and + + + align:start position:0% +wondered about networks in the us and +the advantage of collecting our own data + + align:start position:0% +the advantage of collecting our own data + + + align:start position:0% +the advantage of collecting our own data +indeed would be to better measure the + + align:start position:0% +indeed would be to better measure the + + + align:start position:0% +indeed would be to better measure the +networks among relatives or friends and + + align:start position:0% +networks among relatives or friends and + + + align:start position:0% +networks among relatives or friends and +so on in you know + + align:start position:0% +so on in you know + + + align:start position:0% +so on in you know +towns and rural areas in west virginia + + align:start position:0% +towns and rural areas in west virginia + + + align:start position:0% +towns and rural areas in west virginia +so everything that we've been doing + + align:start position:0% +so everything that we've been doing + + + align:start position:0% +so everything that we've been doing +featuring thailand because we have all + + align:start position:0% +featuring thailand because we have all + + + align:start position:0% +featuring thailand because we have all +that data + + align:start position:0% +that data + + + align:start position:0% +that data +could be done in other contexts like the + + align:start position:0% +could be done in other contexts like the + + + align:start position:0% +could be done in other contexts like the +us if we if we can add that data + + align:start position:0% +us if we if we can add that data + + + align:start position:0% +us if we if we can add that data +and we've definitely decided to try to + + align:start position:0% +and we've definitely decided to try to + + + align:start position:0% +and we've definitely decided to try to +measure these networks as a + + align:start position:0% +measure these networks as a + + + align:start position:0% +measure these networks as a +suggestion that michael had from last + + align:start position:0% +suggestion that michael had from last + + + align:start position:0% +suggestion that michael had from last +time + + align:start position:0% +time + + + align:start position:0% +time +all right so that any questions on + + align:start position:0% +all right so that any questions on + + + align:start position:0% +all right so that any questions on +on this lecture nine + + align:start position:0% + + + + align:start position:0% + +i have a question um + + align:start position:0% +i have a question um + + + align:start position:0% +i have a question um +in slice 19 that when we are discom + + align:start position:0% +in slice 19 that when we are discom + + + align:start position:0% +in slice 19 that when we are discom +when we decomposing the + + align:start position:0% +when we decomposing the + + + align:start position:0% +when we decomposing the +risk + + align:start position:0% +risk + + + align:start position:0% +risk +yeah here + + align:start position:0% +yeah here + + + align:start position:0% +yeah here +um i remember at the before we have + + align:start position:0% +um i remember at the before we have + + + align:start position:0% +um i remember at the before we have +offer that was represented the risk-free + + align:start position:0% +offer that was represented the risk-free + + + align:start position:0% +offer that was represented the risk-free +uh return but why here we did yeah right + + align:start position:0% +uh return but why here we did yeah right + + + align:start position:0% +uh return but why here we did yeah right +here we + + align:start position:0% +here we + + + align:start position:0% +here we +live with the uh we we just + + align:start position:0% +live with the uh we we just + + + align:start position:0% +live with the uh we we just +have beta and using credit that is + + align:start position:0% +have beta and using credit that is + + + align:start position:0% +have beta and using credit that is +because we both subjected the offer from + + align:start position:0% +because we both subjected the offer from + + + align:start position:0% +because we both subjected the offer from +left hand side and right hand side or + + align:start position:0% +left hand side and right hand side or + + + align:start position:0% +left hand side and right hand side or +because + + align:start position:0% +because + + + align:start position:0% +because +the results we get + + align:start position:0% +the results we get + + + align:start position:0% +the results we get +before that offer is not significant so + + align:start position:0% +before that offer is not significant so + + + align:start position:0% +before that offer is not significant so +we + + align:start position:0% +we + + + align:start position:0% +we +we + + align:start position:0% +we + + + align:start position:0% +we +don't care about it + + align:start position:0% +don't care about it + + + align:start position:0% +don't care about it +yeah another great question so there are + + align:start position:0% +yeah another great question so there are + + + align:start position:0% +yeah another great question so there are +two ways to do it + + align:start position:0% +two ways to do it + + + align:start position:0% +two ways to do it +we should have been thinking about the + + align:start position:0% +we should have been thinking about the + + + align:start position:0% +we should have been thinking about the +rate of return minus the risk-free rate + + align:start position:0% +rate of return minus the risk-free rate + + + align:start position:0% +rate of return minus the risk-free rate +but in fact in the thai data we took the + + align:start position:0% +but in fact in the thai data we took the + + + align:start position:0% +but in fact in the thai data we took the +position that the risk free rate was + + align:start position:0% +position that the risk free rate was + + + align:start position:0% +position that the risk free rate was +zero + + align:start position:0% + + + + align:start position:0% + +so that's why + + align:start position:0% +so that's why + + + align:start position:0% +so that's why +we kind of dropped it + + align:start position:0% +we kind of dropped it + + + align:start position:0% +we kind of dropped it +thank you + + align:start position:0% +thank you + + + align:start position:0% +thank you +it's like having rice you can put rice + + align:start position:0% +it's like having rice you can put rice + + + align:start position:0% +it's like having rice you can put rice +in storage + + align:start position:0% +in storage + + + align:start position:0% +in storage +and you're gonna get + + align:start position:0% +and you're gonna get + + + align:start position:0% +and you're gonna get +back more or less what you put in etc + + align:start position:0% +back more or less what you put in etc + + + align:start position:0% +back more or less what you put in etc +so that was the rationale for it + + align:start position:0% + + + + align:start position:0% + +other questions + + align:start position:0% +other questions + + + align:start position:0% +other questions +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +that was all this stuff on risk sharing + + align:start position:0% +that was all this stuff on risk sharing + + + align:start position:0% +that was all this stuff on risk sharing +then + + align:start position:0% +then + + + align:start position:0% +then +in lecture 10 + + align:start position:0% +in lecture 10 + + + align:start position:0% +in lecture 10 +we started to introduce these ledgers + + align:start position:0% +we started to introduce these ledgers + + + align:start position:0% +we started to introduce these ledgers +and financial accounts + + align:start position:0% +and financial accounts + + + align:start position:0% +and financial accounts +and other measurement issues actually + + align:start position:0% +and other measurement issues actually + + + align:start position:0% +and other measurement issues actually +there's a lot going on in this lecture + + align:start position:0% +there's a lot going on in this lecture + + + align:start position:0% +there's a lot going on in this lecture +as i'll show review with you + + align:start position:0% +as i'll show review with you + + + align:start position:0% +as i'll show review with you +we did the wealth planner stuff looking + + align:start position:0% +we did the wealth planner stuff looking + + + align:start position:0% +we did the wealth planner stuff looking +at the + + align:start position:0% +at the + + + align:start position:0% +at the +balance sheet and the income statement + + align:start position:0% +balance sheet and the income statement + + + align:start position:0% +balance sheet and the income statement +then i + + align:start position:0% +then i + + + align:start position:0% +then i +went to the other statement the + + align:start position:0% +went to the other statement the + + + align:start position:0% +went to the other statement the +statement of cash flow + + align:start position:0% +statement of cash flow + + + align:start position:0% +statement of cash flow +and we thought about bitcoin as an + + align:start position:0% +and we thought about bitcoin as an + + + align:start position:0% +and we thought about bitcoin as an +example having the balance sheet and the + + align:start position:0% +example having the balance sheet and the + + + align:start position:0% +example having the balance sheet and the +cash flow in one place and with bitcoin + + align:start position:0% +cash flow in one place and with bitcoin + + + align:start position:0% +cash flow in one place and with bitcoin +that motivated a review of distributed + + align:start position:0% +that motivated a review of distributed + + + align:start position:0% +that motivated a review of distributed +ledgers and + + align:start position:0% +ledgers and + + + align:start position:0% +ledgers and +you know how it works with currency + + align:start position:0% +you know how it works with currency + + + align:start position:0% +you know how it works with currency +physical currency as opposed to the + + align:start position:0% +physical currency as opposed to the + + + align:start position:0% +physical currency as opposed to the +ledgers + + align:start position:0% +ledgers + + + align:start position:0% +ledgers +and then we touched on sweden and kenya + + align:start position:0% +and then we touched on sweden and kenya + + + align:start position:0% +and then we touched on sweden and kenya +so this lecture introduced bitcoin it + + align:start position:0% +so this lecture introduced bitcoin it + + + align:start position:0% +so this lecture introduced bitcoin it +also introduced distributed ledgers + + align:start position:0% +also introduced distributed ledgers + + + align:start position:0% +also introduced distributed ledgers +as financial accounts + + align:start position:0% +as financial accounts + + + align:start position:0% +as financial accounts +and also value transfer so + + align:start position:0% +and also value transfer so + + + align:start position:0% +and also value transfer so +we talked about this statement of income + + align:start position:0% +we talked about this statement of income + + + align:start position:0% +we talked about this statement of income +by now you may or not remember it + + align:start position:0% +by now you may or not remember it + + + align:start position:0% +by now you may or not remember it +doesn't really matter this household a + + align:start position:0% +doesn't really matter this household a + + + align:start position:0% +doesn't really matter this household a +appears twice subsequently this was the + + align:start position:0% +appears twice subsequently this was the + + + align:start position:0% +appears twice subsequently this was the +first time we introduced it as an + + align:start position:0% +first time we introduced it as an + + + align:start position:0% +first time we introduced it as an +example of the income statement and also + + align:start position:0% +example of the income statement and also + + + align:start position:0% +example of the income statement and also +household a's balance sheet + + align:start position:0% +household a's balance sheet + + + align:start position:0% +household a's balance sheet +and then we started to talk about the + + align:start position:0% +and then we started to talk about the + + + align:start position:0% +and then we started to talk about the +wealth planner so + + align:start position:0% +wealth planner so + + + align:start position:0% +wealth planner so +we implemented this in thailand + + align:start position:0% +we implemented this in thailand + + + align:start position:0% +we implemented this in thailand +maximize discount expected utility over + + align:start position:0% +maximize discount expected utility over + + + align:start position:0% +maximize discount expected utility over +the lifetime even allowing for bequests + + align:start position:0% +the lifetime even allowing for bequests + + + align:start position:0% +the lifetime even allowing for bequests +to their kids you know subject to + + align:start position:0% +to their kids you know subject to + + + align:start position:0% +to their kids you know subject to +the stocks and flows constraint + + align:start position:0% +the stocks and flows constraint + + + align:start position:0% +the stocks and flows constraint +investing in risky and safe assets + + align:start position:0% +investing in risky and safe assets + + + align:start position:0% +investing in risky and safe assets +and allowing for the risk sharing which + + align:start position:0% +and allowing for the risk sharing which + + + align:start position:0% +and allowing for the risk sharing which +you don't usually see + + align:start position:0% +you don't usually see + + + align:start position:0% +you don't usually see +in wealth planners but we know we needed + + align:start position:0% +in wealth planners but we know we needed + + + align:start position:0% +in wealth planners but we know we needed +it for thailand because you've already + + align:start position:0% +it for thailand because you've already + + + align:start position:0% +it for thailand because you've already +seen how much risk sharing there is + + align:start position:0% +seen how much risk sharing there is + + + align:start position:0% +seen how much risk sharing there is +so we want to smooth out the income + + align:start position:0% +so we want to smooth out the income + + + align:start position:0% +so we want to smooth out the income +profile consistent with the ins and outs + + align:start position:0% +profile consistent with the ins and outs + + + align:start position:0% +profile consistent with the ins and outs +of those gifts and the residual is the + + align:start position:0% +of those gifts and the residual is the + + + align:start position:0% +of those gifts and the residual is the +household's exposure to their own income + + align:start position:0% +household's exposure to their own income + + + align:start position:0% +household's exposure to their own income +shocks so we explain to those thai + + align:start position:0% +shocks so we explain to those thai + + + align:start position:0% +shocks so we explain to those thai +households how the planner works and i + + align:start position:0% +households how the planner works and i + + + align:start position:0% +households how the planner works and i +again to motivate this think about going + + align:start position:0% +again to motivate this think about going + + + align:start position:0% +again to motivate this think about going +to the doorstep of a household living in + + align:start position:0% +to the doorstep of a household living in + + + align:start position:0% +to the doorstep of a household living in +west virginia having collected some of + + align:start position:0% +west virginia having collected some of + + + align:start position:0% +west virginia having collected some of +their data or better yet + + align:start position:0% +their data or better yet + + + align:start position:0% +their data or better yet +what data do we want to collect in west + + align:start position:0% +what data do we want to collect in west + + + align:start position:0% +what data do we want to collect in west +virginia consistent with running this + + align:start position:0% +virginia consistent with running this + + + align:start position:0% +virginia consistent with running this +wealth planner so we can give them + + align:start position:0% +wealth planner so we can give them + + + align:start position:0% +wealth planner so we can give them +advice + + align:start position:0% +advice + + + align:start position:0% +advice +the setting would be different but the + + align:start position:0% +the setting would be different but the + + + align:start position:0% +the setting would be different but the +idea is the same + + align:start position:0% +idea is the same + + + align:start position:0% +idea is the same +so with the wealth planner we find out + + align:start position:0% +so with the wealth planner we find out + + + align:start position:0% +so with the wealth planner we find out +how much they're planning to give to + + align:start position:0% +how much they're planning to give to + + + align:start position:0% +how much they're planning to give to +their kids if anything we calibrated + + align:start position:0% +their kids if anything we calibrated + + + align:start position:0% +their kids if anything we calibrated +their income processes with trends and + + align:start position:0% +their income processes with trends and + + + align:start position:0% +their income processes with trends and +fluctuations + + align:start position:0% +fluctuations + + + align:start position:0% +fluctuations +we looked at their committed consumption + + align:start position:0% +we looked at their committed consumption + + + align:start position:0% +we looked at their committed consumption +goals and were very careful about their + + align:start position:0% +goals and were very careful about their + + + align:start position:0% +goals and were very careful about their +initial wealth + + align:start position:0% +initial wealth + + + align:start position:0% +initial wealth +again you come into the period with a + + align:start position:0% +again you come into the period with a + + + align:start position:0% +again you come into the period with a +certain amount of wealth and you could + + align:start position:0% +certain amount of wealth and you could + + + align:start position:0% +certain amount of wealth and you could +consume it or you could save it + + align:start position:0% +consume it or you could save it + + + align:start position:0% +consume it or you could save it +you can save it in risky or safe assets + + align:start position:0% +you can save it in risky or safe assets + + + align:start position:0% +you can save it in risky or safe assets +in principle you could also borrow and + + align:start position:0% +in principle you could also borrow and + + + align:start position:0% +in principle you could also borrow and +then that is going to determine wealth + + align:start position:0% +then that is going to determine wealth + + + align:start position:0% +then that is going to determine wealth +for next time so i probably didn't + + align:start position:0% +for next time so i probably didn't + + + align:start position:0% +for next time so i probably didn't +emphasize it as much but this is where + + align:start position:0% +emphasize it as much but this is where + + + align:start position:0% +emphasize it as much but this is where +the stocks and flows are coming together + + align:start position:0% +the stocks and flows are coming together + + + align:start position:0% +the stocks and flows are coming together +again early on + + align:start position:0% +again early on + + + align:start position:0% +again early on +through this budget constraint + + align:start position:0% +through this budget constraint + + + align:start position:0% +through this budget constraint +initial wealth + + align:start position:0% +initial wealth + + + align:start position:0% +initial wealth +and consumption is subtracted off and + + align:start position:0% +and consumption is subtracted off and + + + align:start position:0% +and consumption is subtracted off and +the remainder goes into risky and safe + + align:start position:0% +the remainder goes into risky and safe + + + align:start position:0% +the remainder goes into risky and safe +assets + + align:start position:0% +assets + + + align:start position:0% +assets +which will determine wealth next time + + align:start position:0% +which will determine wealth next time + + + align:start position:0% +which will determine wealth next time +and then we looked at actual + + align:start position:0% +and then we looked at actual + + + align:start position:0% +and then we looked at actual +flows in the data + + align:start position:0% +flows in the data + + + align:start position:0% +flows in the data +the second household the recommendation + + align:start position:0% +the second household the recommendation + + + align:start position:0% +the second household the recommendation +of the planner + + align:start position:0% +of the planner + + + align:start position:0% +of the planner +in terms of life cycle which is + + align:start position:0% +in terms of life cycle which is + + + align:start position:0% +in terms of life cycle which is +saving up enough when you're relatively + + align:start position:0% +saving up enough when you're relatively + + + align:start position:0% +saving up enough when you're relatively +young to be able to + + align:start position:0% +young to be able to + + + align:start position:0% +young to be able to +survive through older ages + + align:start position:0% +survive through older ages + + + align:start position:0% +survive through older ages +some of these households get in trouble + + align:start position:0% +some of these households get in trouble + + + align:start position:0% +some of these households get in trouble +so we try to help this guy + + align:start position:0% +so we try to help this guy + + + align:start position:0% +so we try to help this guy +giving advice and actually + + align:start position:0% +giving advice and actually + + + align:start position:0% +giving advice and actually +talking about the realism of the goals + + align:start position:0% +talking about the realism of the goals + + + align:start position:0% +talking about the realism of the goals +and i made the point that this planner + + align:start position:0% +and i made the point that this planner + + + align:start position:0% +and i made the point that this planner +exists for the u.s + + align:start position:0% +exists for the u.s + + + align:start position:0% +exists for the u.s +although i don't know that it's + + align:start position:0% +although i don't know that it's + + + align:start position:0% +although i don't know that it's +particularly well designed for + + align:start position:0% +particularly well designed for + + + align:start position:0% +particularly well designed for +households in west virginia it does take + + align:start position:0% +households in west virginia it does take + + + align:start position:0% +households in west virginia it does take +into account details of the u.s tax code + + align:start position:0% +into account details of the u.s tax code + + + align:start position:0% +into account details of the u.s tax code +and social security and so on but + + align:start position:0% +and social security and so on but + + + align:start position:0% +and social security and so on but +acting as if there's no networks no risk + + align:start position:0% +acting as if there's no networks no risk + + + align:start position:0% +acting as if there's no networks no risk +sharing + + align:start position:0% +sharing + + + align:start position:0% +sharing +who knows + + align:start position:0% +who knows + + + align:start position:0% +who knows +we'll eventually find out then i made + + align:start position:0% +we'll eventually find out then i made + + + align:start position:0% +we'll eventually find out then i made +this transition to bitcoin + + align:start position:0% +this transition to bitcoin + + + align:start position:0% +this transition to bitcoin +as an account so bitcoin accounts have + + align:start position:0% +as an account so bitcoin accounts have + + + align:start position:0% +as an account so bitcoin accounts have +the ownership of the coin and also a way + + align:start position:0% +the ownership of the coin and also a way + + + align:start position:0% +the ownership of the coin and also a way +to to buy something else and transfer + + align:start position:0% +to to buy something else and transfer + + + align:start position:0% +to to buy something else and transfer +the coin to a third party by sending + + align:start position:0% +the coin to a third party by sending + + + align:start position:0% +the coin to a third party by sending +the proposed transaction to be validated + + align:start position:0% +the proposed transaction to be validated + + + align:start position:0% +the proposed transaction to be validated +so the bitcoin ledgers + + align:start position:0% +so the bitcoin ledgers + + + align:start position:0% +so the bitcoin ledgers +are a combination of the balance sheet + + align:start position:0% +are a combination of the balance sheet + + + align:start position:0% +are a combination of the balance sheet +and the statement of cash flow + + align:start position:0% +and the statement of cash flow + + + align:start position:0% +and the statement of cash flow +and with the introduction of the idea of + + align:start position:0% +and with the introduction of the idea of + + + align:start position:0% +and with the introduction of the idea of +cash flow i went back to the thai + + align:start position:0% +cash flow i went back to the thai + + + align:start position:0% +cash flow i went back to the thai +financial accounts to look at that for + + align:start position:0% +financial accounts to look at that for + + + align:start position:0% +financial accounts to look at that for +the first time we'd already looked at + + align:start position:0% +the first time we'd already looked at + + + align:start position:0% +the first time we'd already looked at +the income and balance sheet statement + + align:start position:0% +the income and balance sheet statement + + + align:start position:0% +the income and balance sheet statement +now we're looking at the cash flow + + align:start position:0% +now we're looking at the cash flow + + + align:start position:0% +now we're looking at the cash flow +statement + + align:start position:0% +statement + + + align:start position:0% +statement +cash flow from production consumption + + align:start position:0% +cash flow from production consumption + + + align:start position:0% +cash flow from production consumption +financing and so on + + align:start position:0% +financing and so on + + + align:start position:0% +financing and so on +so then the issue is what do the ledgers + + align:start position:0% +so then the issue is what do the ledgers + + + align:start position:0% +so then the issue is what do the ledgers +do well + + align:start position:0% +do well + + + align:start position:0% +do well +in thailand they're + + align:start position:0% +in thailand they're + + + align:start position:0% +in thailand they're +largely using paper currencies so they + + align:start position:0% +largely using paper currencies so they + + + align:start position:0% +largely using paper currencies so they +do not keep accounts and there are no + + align:start position:0% +do not keep accounts and there are no + + + align:start position:0% +do not keep accounts and there are no +common ledgers bitcoin is all on an + + align:start position:0% +common ledgers bitcoin is all on an + + + align:start position:0% +common ledgers bitcoin is all on an +account and there are common ledgers + + align:start position:0% +account and there are common ledgers + + + align:start position:0% +account and there are common ledgers +that's why it's called distributed + + align:start position:0% +that's why it's called distributed + + + align:start position:0% +that's why it's called distributed +common ledger so + + align:start position:0% +common ledger so + + + align:start position:0% +common ledger so +we actually went to create + + align:start position:0% +we actually went to create + + + align:start position:0% +we actually went to create +ledgers that would be common in the thai + + align:start position:0% +ledgers that would be common in the thai + + + align:start position:0% +ledgers that would be common in the thai +data and discovered a lot of data + + align:start position:0% +data and discovered a lot of data + + + align:start position:0% +data and discovered a lot of data +discrepancies because we hadn't + + align:start position:0% +discrepancies because we hadn't + + + align:start position:0% +discrepancies because we hadn't +collected the data that way in the first + + align:start position:0% +collected the data that way in the first + + + align:start position:0% +collected the data that way in the first +place this is also a reminder if we're + + align:start position:0% +place this is also a reminder if we're + + + align:start position:0% +place this is also a reminder if we're +collecting data in west virginia + + align:start position:0% +collecting data in west virginia + + + align:start position:0% +collecting data in west virginia +and we're getting the identity of the + + align:start position:0% +and we're getting the identity of the + + + align:start position:0% +and we're getting the identity of the +transacting partner when we interview + + align:start position:0% +transacting partner when we interview + + + align:start position:0% +transacting partner when we interview +that partner those transactions should + + align:start position:0% +that partner those transactions should + + + align:start position:0% +that partner those transactions should +also show up so ideally one would do + + align:start position:0% +also show up so ideally one would do + + + align:start position:0% +also show up so ideally one would do +that in real time almost + + align:start position:0% +that in real time almost + + + align:start position:0% +that in real time almost +when memory is fresh + + align:start position:0% +when memory is fresh + + + align:start position:0% +when memory is fresh +or for that matter their understanding + + align:start position:0% +or for that matter their understanding + + + align:start position:0% +or for that matter their understanding +of a transaction with a commercial bank + + align:start position:0% +of a transaction with a commercial bank + + + align:start position:0% +of a transaction with a commercial bank +which is opposed to what commercial + + align:start position:0% +which is opposed to what commercial + + + align:start position:0% +which is opposed to what commercial +banks doing at least you think that of + + align:start position:0% +banks doing at least you think that of + + + align:start position:0% +banks doing at least you think that of +course the commercial banks are honest + + align:start position:0% +course the commercial banks are honest + + + align:start position:0% +course the commercial banks are honest +just remember wells fargo + + align:start position:0% +just remember wells fargo + + + align:start position:0% +just remember wells fargo +that actually created accounts for + + align:start position:0% +that actually created accounts for + + + align:start position:0% +that actually created accounts for +households they didn't know about + + align:start position:0% +households they didn't know about + + + align:start position:0% +households they didn't know about +and then charged them money for it + + align:start position:0% +and then charged them money for it + + + align:start position:0% +and then charged them money for it +uh so we then talked about the advantage + + align:start position:0% +uh so we then talked about the advantage + + + align:start position:0% +uh so we then talked about the advantage +of bitcoin like distributed ledgers + + align:start position:0% +of bitcoin like distributed ledgers + + + align:start position:0% +of bitcoin like distributed ledgers +namely data reconciliation + + align:start position:0% +namely data reconciliation + + + align:start position:0% +namely data reconciliation +but in practice of course they're using + + align:start position:0% +but in practice of course they're using + + + align:start position:0% +but in practice of course they're using +paper currency so with that opportunity + + align:start position:0% +paper currency so with that opportunity + + + align:start position:0% +paper currency so with that opportunity +we looked at + + align:start position:0% +we looked at + + + align:start position:0% +we looked at +another problem + + align:start position:0% +another problem + + + align:start position:0% +another problem +of management which is managing the + + align:start position:0% +of management which is managing the + + + align:start position:0% +of management which is managing the +currency + + align:start position:0% +currency + + + align:start position:0% +currency +managing the cash flow + + align:start position:0% +managing the cash flow + + + align:start position:0% +managing the cash flow +which we modeled and fit to the data as + + align:start position:0% +which we modeled and fit to the data as + + + align:start position:0% +which we modeled and fit to the data as +having trends and stochastic + + align:start position:0% +having trends and stochastic + + + align:start position:0% +having trends and stochastic +fluctuations we have the evolution of + + align:start position:0% +fluctuations we have the evolution of + + + align:start position:0% +fluctuations we have the evolution of +cash flow + + align:start position:0% +cash flow + + + align:start position:0% +cash flow +adjusted taking into account the ups and + + align:start position:0% +adjusted taking into account the ups and + + + align:start position:0% +adjusted taking into account the ups and +downs with shocks of revenues and + + align:start position:0% +downs with shocks of revenues and + + + align:start position:0% +downs with shocks of revenues and +expenses and adjusted by withdrawals and + + align:start position:0% +expenses and adjusted by withdrawals and + + + align:start position:0% +expenses and adjusted by withdrawals and +deposits the two costs were going to the + + align:start position:0% +deposits the two costs were going to the + + + align:start position:0% +deposits the two costs were going to the +bank to make the physical adjustment and + + align:start position:0% +bank to make the physical adjustment and + + + align:start position:0% +bank to make the physical adjustment and +the opportunity cost foregone interest + + align:start position:0% +the opportunity cost foregone interest + + + align:start position:0% +the opportunity cost foregone interest +of holding the currency in the house + + align:start position:0% +of holding the currency in the house + + + align:start position:0% +of holding the currency in the house +which led to another optimization + + align:start position:0% +which led to another optimization + + + align:start position:0% +which led to another optimization +problem + + align:start position:0% +problem + + + align:start position:0% +problem +let me minimizing the expected cost let + + align:start position:0% +let me minimizing the expected cost let + + + align:start position:0% +let me minimizing the expected cost let +me just say that our vision for west + + align:start position:0% +me just say that our vision for west + + + align:start position:0% +me just say that our vision for west +virginia is to combine the cash high + + align:start position:0% +virginia is to combine the cash high + + + align:start position:0% +virginia is to combine the cash high +frequency cash flow with the longer term + + align:start position:0% +frequency cash flow with the longer term + + + align:start position:0% +frequency cash flow with the longer term +life cycle because in practice they are + + align:start position:0% +life cycle because in practice they are + + + align:start position:0% +life cycle because in practice they are +intimately related so we'll have a + + align:start position:0% +intimately related so we'll have a + + + align:start position:0% +intimately related so we'll have a +synthesis of those frameworks in mind + + align:start position:0% +synthesis of those frameworks in mind + + + align:start position:0% +synthesis of those frameworks in mind +and in thailand they don't manage the + + align:start position:0% +and in thailand they don't manage the + + + align:start position:0% +and in thailand they don't manage the +currency very well + + align:start position:0% +currency very well + + + align:start position:0% +currency very well +in the rural areas they're holding far + + align:start position:0% +in the rural areas they're holding far + + + align:start position:0% +in the rural areas they're holding far +too much of it and in the urban areas + + align:start position:0% +too much of it and in the urban areas + + + align:start position:0% +too much of it and in the urban areas +actually did better of course one + + align:start position:0% +actually did better of course one + + + align:start position:0% +actually did better of course one +advantage of getting them to switch from + + align:start position:0% +advantage of getting them to switch from + + + align:start position:0% +advantage of getting them to switch from +paper currency into electronic entries + + align:start position:0% +paper currency into electronic entries + + + align:start position:0% +paper currency into electronic entries +that is that in principle it's easier to + + align:start position:0% +that is that in principle it's easier to + + + align:start position:0% +that is that in principle it's easier to +manage portfolios or to send reminders + + align:start position:0% +manage portfolios or to send reminders + + + align:start position:0% +manage portfolios or to send reminders +about cash management on apps on phones + + align:start position:0% +about cash management on apps on phones + + + align:start position:0% +about cash management on apps on phones +if all the transactions are on our + + align:start position:0% +if all the transactions are on our + + + align:start position:0% +if all the transactions are on our +electronic and i gave you some examples + + align:start position:0% +electronic and i gave you some examples + + + align:start position:0% +electronic and i gave you some examples +of yodlee and other + + align:start position:0% +of yodlee and other + + + align:start position:0% +of yodlee and other +other apps that do this that collect + + align:start position:0% +other apps that do this that collect + + + align:start position:0% +other apps that do this that collect +electronic data okay so + + align:start position:0% +electronic data okay so + + + align:start position:0% +electronic data okay so +anyway + + align:start position:0% +anyway + + + align:start position:0% +anyway +that led finally to well do you have to + + align:start position:0% +that led finally to well do you have to + + + align:start position:0% +that led finally to well do you have to +use paper currency the answer being no + + align:start position:0% +use paper currency the answer being no + + + align:start position:0% +use paper currency the answer being no +sweden doesn't much anymore + + align:start position:0% +sweden doesn't much anymore + + + align:start position:0% +sweden doesn't much anymore +although they're worried about it in the + + align:start position:0% +although they're worried about it in the + + + align:start position:0% +although they're worried about it in the +sense of worry that the private sector + + align:start position:0% +sense of worry that the private sector + + + align:start position:0% +sense of worry that the private sector +takes over all of the payments and the + + align:start position:0% +takes over all of the payments and the + + + align:start position:0% +takes over all of the payments and the +rix bank isn't needed anymore the + + align:start position:0% +rix bank isn't needed anymore the + + + align:start position:0% +rix bank isn't needed anymore the +central bank and the stuff in between + + align:start position:0% +central bank and the stuff in between + + + align:start position:0% +central bank and the stuff in between +which was kenya + + align:start position:0% +which was kenya + + + align:start position:0% +which was kenya +so kenya e-money + + align:start position:0% +so kenya e-money + + + align:start position:0% +so kenya e-money +digital money is created by the cell + + align:start position:0% +digital money is created by the cell + + + align:start position:0% +digital money is created by the cell +phone company + + align:start position:0% +phone company + + + align:start position:0% +phone company +allowing people to cash in and cash out + + align:start position:0% +allowing people to cash in and cash out + + + align:start position:0% +allowing people to cash in and cash out +and electronically transfer the credits + + align:start position:0% +and electronically transfer the credits + + + align:start position:0% +and electronically transfer the credits +on the sell account which turned out to + + align:start position:0% +on the sell account which turned out to + + + align:start position:0% +on the sell account which turned out to +help with guess what risk sharing so you + + align:start position:0% +help with guess what risk sharing so you + + + align:start position:0% +help with guess what risk sharing so you +see a tie-in here back to those risk + + align:start position:0% +see a tie-in here back to those risk + + + align:start position:0% +see a tie-in here back to those risk +sharing lectures in this case it's in + + align:start position:0% +sharing lectures in this case it's in + + + align:start position:0% +sharing lectures in this case it's in +the context of kenya and the fact that + + align:start position:0% +the context of kenya and the fact that + + + align:start position:0% +the context of kenya and the fact that +you know + + align:start position:0% +you know + + + align:start position:0% +you know +your kin back in the village have had a + + align:start position:0% +your kin back in the village have had a + + + align:start position:0% +your kin back in the village have had a +terrible harvest can be + + align:start position:0% +terrible harvest can be + + + align:start position:0% +terrible harvest can be +mitigated by having the migrant worker + + align:start position:0% +mitigated by having the migrant worker + + + align:start position:0% +mitigated by having the migrant worker +in nairobi send more money and evidently + + align:start position:0% +in nairobi send more money and evidently + + + align:start position:0% +in nairobi send more money and evidently +that is exactly what happens as opposed + + align:start position:0% +that is exactly what happens as opposed + + + align:start position:0% +that is exactly what happens as opposed +to having to give the kenyan shillings + + align:start position:0% +to having to give the kenyan shillings + + + align:start position:0% +to having to give the kenyan shillings +paper currency to a friend put it in an + + align:start position:0% +paper currency to a friend put it in an + + + align:start position:0% +paper currency to a friend put it in an +envelope hope for the best or in a very + + align:start position:0% +envelope hope for the best or in a very + + + align:start position:0% +envelope hope for the best or in a very +costly way go back home and hand over + + align:start position:0% +costly way go back home and hand over + + + align:start position:0% +costly way go back home and hand over +the cash so risk sharing on the ledgers + + align:start position:0% +the cash so risk sharing on the ledgers + + + align:start position:0% +the cash so risk sharing on the ledgers +actually helped but these are private + + align:start position:0% +actually helped but these are private + + + align:start position:0% +actually helped but these are private +accounts so they don't have + + align:start position:0% +accounts so they don't have + + + align:start position:0% +accounts so they don't have +what we typically refer to as + + align:start position:0% +what we typically refer to as + + + align:start position:0% +what we typically refer to as +distributed ledgers where there's + + align:start position:0% +distributed ledgers where there's + + + align:start position:0% +distributed ledgers where there's +third-party validation all of these + + align:start position:0% +third-party validation all of these + + + align:start position:0% +third-party validation all of these +transactions cell phone companies + + align:start position:0% +transactions cell phone companies + + + align:start position:0% +transactions cell phone companies +accounts are trusted to be accurate + + align:start position:0% +accounts are trusted to be accurate + + + align:start position:0% +accounts are trusted to be accurate +households can check them when they + + align:start position:0% +households can check them when they + + + align:start position:0% +households can check them when they +happen to see that they got credited + + align:start position:0% +happen to see that they got credited + + + align:start position:0% +happen to see that they got credited +the way they're supposed to + + align:start position:0% +the way they're supposed to + + + align:start position:0% +the way they're supposed to +but other than that safaricom could + + align:start position:0% +but other than that safaricom could + + + align:start position:0% +but other than that safaricom could +steal the money + + align:start position:0% +steal the money + + + align:start position:0% +steal the money +if they wanted to they don't evidently + + align:start position:0% +if they wanted to they don't evidently + + + align:start position:0% +if they wanted to they don't evidently +they put it in the bank but still and + + align:start position:0% +they put it in the bank but still and + + + align:start position:0% +they put it in the bank but still and +the banks are subject to runs so there's + + align:start position:0% +the banks are subject to runs so there's + + + align:start position:0% +the banks are subject to runs so there's +a lot of risk remaining even though + + align:start position:0% +a lot of risk remaining even though + + + align:start position:0% +a lot of risk remaining even though +these this digital currency uh you know + + align:start position:0% +these this digital currency uh you know + + + align:start position:0% +these this digital currency uh you know +is is an innovation in the context of + + align:start position:0% +is is an innovation in the context of + + + align:start position:0% +is is an innovation in the context of +kenya it certainly would not be in the + + align:start position:0% +kenya it certainly would not be in the + + + align:start position:0% +kenya it certainly would not be in the +context of sweden they have their own + + align:start position:0% +context of sweden they have their own + + + align:start position:0% +context of sweden they have their own +interbank method so are there questions + + align:start position:0% +interbank method so are there questions + + + align:start position:0% +interbank method so are there questions +about this lecture 10. + + align:start position:0% + + + + align:start position:0% + +again it's kind of a mouthful this + + align:start position:0% +again it's kind of a mouthful this + + + align:start position:0% +again it's kind of a mouthful this +lecture does both the financial accounts + + align:start position:0% +lecture does both the financial accounts + + + align:start position:0% +lecture does both the financial accounts +income statement balance sheet and cash + + align:start position:0% +income statement balance sheet and cash + + + align:start position:0% +income statement balance sheet and cash +flow and is also looking at two problems + + align:start position:0% +flow and is also looking at two problems + + + align:start position:0% +flow and is also looking at two problems +namely cash management and life cycle + + align:start position:0% +namely cash management and life cycle + + + align:start position:0% +namely cash management and life cycle +management + + align:start position:0% +management + + + align:start position:0% +management +and finally merging into a discussion of + + align:start position:0% +and finally merging into a discussion of + + + align:start position:0% +and finally merging into a discussion of +what distributed ledgers bitcoin and + + align:start position:0% +what distributed ledgers bitcoin and + + + align:start position:0% +what distributed ledgers bitcoin and +distributed ledgers do or don't do and + + align:start position:0% +distributed ledgers do or don't do and + + + align:start position:0% +distributed ledgers do or don't do and +potential substitutes + + align:start position:0% +potential substitutes + + + align:start position:0% +potential substitutes +how good or how bad is currency and + + align:start position:0% +how good or how bad is currency and + + + align:start position:0% +how good or how bad is currency and +safaricom digital credits relative to + + align:start position:0% +safaricom digital credits relative to + + + align:start position:0% +safaricom digital credits relative to +validated systems although we haven't + + align:start position:0% +validated systems although we haven't + + + align:start position:0% +validated systems although we haven't +really talked about validation that + + align:start position:0% +really talked about validation that + + + align:start position:0% +really talked about validation that +happens i think in the next lecture + + align:start position:0% +happens i think in the next lecture + + + align:start position:0% +happens i think in the next lecture +okay so that was lecture 10. + + align:start position:0% +okay so that was lecture 10. + + + align:start position:0% +okay so that was lecture 10. +lecture 11 was about contracts and + + align:start position:0% +lecture 11 was about contracts and + + + align:start position:0% +lecture 11 was about contracts and +mechanism design + + align:start position:0% +mechanism design + + + align:start position:0% +mechanism design +and there were let me just give an + + align:start position:0% +and there were let me just give an + + + align:start position:0% +and there were let me just give an +overview + + align:start position:0% +overview + + + align:start position:0% +overview +there were two parts to this lecture + + align:start position:0% +there were two parts to this lecture + + + align:start position:0% +there were two parts to this lecture +the first part is figuring out what to + + align:start position:0% +the first part is figuring out what to + + + align:start position:0% +the first part is figuring out what to +do when there's private information + + align:start position:0% +do when there's private information + + + align:start position:0% +do when there's private information +and the main conclusion was + + align:start position:0% +and the main conclusion was + + + align:start position:0% +and the main conclusion was +there is a way to write down additional + + align:start position:0% +there is a way to write down additional + + + align:start position:0% +there is a way to write down additional +constraints + + align:start position:0% +constraints + + + align:start position:0% +constraints +called truth-telling or incentive + + align:start position:0% +called truth-telling or incentive + + + align:start position:0% +called truth-telling or incentive +constraints that capture the problem of + + align:start position:0% +constraints that capture the problem of + + + align:start position:0% +constraints that capture the problem of +private information and we + + align:start position:0% +private information and we + + + align:start position:0% +private information and we +will be able to append those on top + + align:start position:0% +will be able to append those on top + + + align:start position:0% +will be able to append those on top +of the usual programming problems that + + align:start position:0% +of the usual programming problems that + + + align:start position:0% +of the usual programming problems that +maximize it lambda weighted sums of + + align:start position:0% +maximize it lambda weighted sums of + + + align:start position:0% +maximize it lambda weighted sums of +utilities so we got a tool and the tools + + align:start position:0% +utilities so we got a tool and the tools + + + align:start position:0% +utilities so we got a tool and the tools +getting better and better because we can + + align:start position:0% +getting better and better because we can + + + align:start position:0% +getting better and better because we can +do more and more with it so that was one + + align:start position:0% +do more and more with it so that was one + + + align:start position:0% +do more and more with it so that was one +of the main points of this and the other + + align:start position:0% +of the main points of this and the other + + + align:start position:0% +of the main points of this and the other +was to think about mechanism design + + align:start position:0% +was to think about mechanism design + + + align:start position:0% +was to think about mechanism design +private contracts having to do with + + align:start position:0% +private contracts having to do with + + + align:start position:0% +private contracts having to do with +messages + + align:start position:0% +messages + + + align:start position:0% +messages +and then back to the ledgers which have + + align:start position:0% +and then back to the ledgers which have + + + align:start position:0% +and then back to the ledgers which have +to do with the cryptography part of + + align:start position:0% +to do with the cryptography part of + + + align:start position:0% +to do with the cryptography part of +ledgers and keeping messages secret and + + align:start position:0% +ledgers and keeping messages secret and + + + align:start position:0% +ledgers and keeping messages secret and +whether or not they have to be validated + + align:start position:0% +whether or not they have to be validated + + + align:start position:0% +whether or not they have to be validated +so + + align:start position:0% +so + + + align:start position:0% +so +the motivation for the first part was + + align:start position:0% +the motivation for the first part was + + + align:start position:0% +the motivation for the first part was +the fact that some of these villages lie + + align:start position:0% +the fact that some of these villages lie + + + align:start position:0% +the fact that some of these villages lie +far away + + align:start position:0% +far away + + + align:start position:0% +far away +from the central monastery some are very + + align:start position:0% +from the central monastery some are very + + + align:start position:0% +from the central monastery some are very +near + + align:start position:0% +near + + + align:start position:0% +near +some households work as serfs slaves + + align:start position:0% +some households work as serfs slaves + + + align:start position:0% +some households work as serfs slaves +others far away pay rent so we wanted to + + align:start position:0% +others far away pay rent so we wanted to + + + align:start position:0% +others far away pay rent so we wanted to +explain this kind of variation + + align:start position:0% +explain this kind of variation + + + align:start position:0% +explain this kind of variation +in the organizations that we see so we + + align:start position:0% +in the organizations that we see so we + + + align:start position:0% +in the organizations that we see so we +introduced a simple two agent model + + align:start position:0% +introduced a simple two agent model + + + align:start position:0% +introduced a simple two agent model +where only one of the two agent one had + + align:start position:0% +where only one of the two agent one had + + + align:start position:0% +where only one of the two agent one had +some privately observed endowment agent + + align:start position:0% +some privately observed endowment agent + + + align:start position:0% +some privately observed endowment agent +one agent two was the villa of the + + align:start position:0% +one agent two was the villa of the + + + align:start position:0% +one agent two was the villa of the +monastery and we wanted to know + + align:start position:0% +monastery and we wanted to know + + + align:start position:0% +monastery and we wanted to know +what would be an optimal resource + + align:start position:0% +what would be an optimal resource + + + align:start position:0% +what would be an optimal resource +allocation mechanism granted that agent + + align:start position:0% +allocation mechanism granted that agent + + + align:start position:0% +allocation mechanism granted that agent +one has private information so we did + + align:start position:0% +one has private information so we did + + + align:start position:0% +one has private information so we did +some derivation + + align:start position:0% +some derivation + + + align:start position:0% +some derivation +had + + align:start position:0% +had + + + align:start position:0% +had +agent one sending messages looked at + + align:start position:0% +agent one sending messages looked at + + + align:start position:0% +agent one sending messages looked at +what would be a maximizing message + + align:start position:0% +what would be a maximizing message + + + align:start position:0% +what would be a maximizing message +derived a series of inequalities + + align:start position:0% +derived a series of inequalities + + + align:start position:0% +derived a series of inequalities +and then changed the problems to sending + + align:start position:0% +and then changed the problems to sending + + + align:start position:0% +and then changed the problems to sending +messages about the underlying endowment + + align:start position:0% +messages about the underlying endowment + + + align:start position:0% +messages about the underlying endowment +and ended up with something we call the + + align:start position:0% +and ended up with something we call the + + + align:start position:0% +and ended up with something we call the +truth-telling constraint which captures + + align:start position:0% +truth-telling constraint which captures + + + align:start position:0% +truth-telling constraint which captures +all of the problems associated with + + align:start position:0% +all of the problems associated with + + + align:start position:0% +all of the problems associated with +private information + + align:start position:0% +private information + + + align:start position:0% +private information +in this context so then we're able to + + align:start position:0% +in this context so then we're able to + + + align:start position:0% +in this context so then we're able to +solve for optimal resource allocations + + align:start position:0% +solve for optimal resource allocations + + + align:start position:0% +solve for optimal resource allocations +just by adding on + + align:start position:0% +just by adding on + + + align:start position:0% +just by adding on +these kinds of incentive constraints in + + align:start position:0% +these kinds of incentive constraints in + + + align:start position:0% +these kinds of incentive constraints in +addition to maximizing the lambda + + align:start position:0% +addition to maximizing the lambda + + + align:start position:0% +addition to maximizing the lambda +weighted sums of utilities we did this + + align:start position:0% +weighted sums of utilities we did this + + + align:start position:0% +weighted sums of utilities we did this +in levels then we went to lotteries to + + align:start position:0% +in levels then we went to lotteries to + + + align:start position:0% +in levels then we went to lotteries to +make it more general we had a good + + align:start position:0% +make it more general we had a good + + + align:start position:0% +make it more general we had a good +discussion at the beginning of one of + + align:start position:0% +discussion at the beginning of one of + + + align:start position:0% +discussion at the beginning of one of +the classes of the advantages of these + + align:start position:0% +the classes of the advantages of these + + + align:start position:0% +the classes of the advantages of these +lotteries which we had talked about in + + align:start position:0% +lotteries which we had talked about in + + + align:start position:0% +lotteries which we had talked about in +the first one third of the class as well + + align:start position:0% +the first one third of the class as well + + + align:start position:0% +the first one third of the class as well +oh and + + align:start position:0% +oh and + + + align:start position:0% +oh and +you know at some point there was a + + align:start position:0% +you know at some point there was a + + + align:start position:0% +you know at some point there was a +starred article on the reading list + + align:start position:0% +starred article on the reading list + + + align:start position:0% +starred article on the reading list +which was how to actually + + align:start position:0% +which was how to actually + + + align:start position:0% +which was how to actually +code these things up + + align:start position:0% +code these things up + + + align:start position:0% +code these things up +more related to the next lecture but um + + align:start position:0% +more related to the next lecture but um + + + align:start position:0% +more related to the next lecture but um +anyway trying not to be abstract about + + align:start position:0% +anyway trying not to be abstract about + + + align:start position:0% +anyway trying not to be abstract about +it + + align:start position:0% +it + + + align:start position:0% +it +so then we went from one period to two + + align:start position:0% +so then we went from one period to two + + + align:start position:0% +so then we went from one period to two +periods we solved the two period problem + + align:start position:0% +periods we solved the two period problem + + + align:start position:0% +periods we solved the two period problem +and had incentive constraints true + + align:start position:0% +and had incentive constraints true + + + align:start position:0% +and had incentive constraints true +telling constraints for both periods in + + align:start position:0% +telling constraints for both periods in + + + align:start position:0% +telling constraints for both periods in +this case what i was emphasizing + + align:start position:0% +this case what i was emphasizing + + + align:start position:0% +this case what i was emphasizing +both the dynamic program how to work + + align:start position:0% +both the dynamic program how to work + + + align:start position:0% +both the dynamic program how to work +back from the second period to the first + + align:start position:0% +back from the second period to the first + + + align:start position:0% +back from the second period to the first +period sequentially but also the fact + + align:start position:0% +period sequentially but also the fact + + + align:start position:0% +period sequentially but also the fact +that moving forward from the first to + + align:start position:0% +that moving forward from the first to + + + align:start position:0% +that moving forward from the first to +the second + + align:start position:0% +the second + + + align:start position:0% +the second +the messages about underlying unobserved + + align:start position:0% +the messages about underlying unobserved + + + align:start position:0% +the messages about underlying unobserved +states would be + + align:start position:0% +states would be + + + align:start position:0% +states would be +key to implementing the optimal + + align:start position:0% +key to implementing the optimal + + + align:start position:0% +key to implementing the optimal +information constraint solution and by + + align:start position:0% +information constraint solution and by + + + align:start position:0% +information constraint solution and by +emphasizing messages i was already + + align:start position:0% +emphasizing messages i was already + + + align:start position:0% +emphasizing messages i was already +anticipating contracts smart contracts + + align:start position:0% +anticipating contracts smart contracts + + + align:start position:0% +anticipating contracts smart contracts +written on ledgers where messages + + align:start position:0% +written on ledgers where messages + + + align:start position:0% +written on ledgers where messages +replace transactions and and the optimal + + align:start position:0% +replace transactions and and the optimal + + + align:start position:0% +replace transactions and and the optimal +solution of that two-period problem was + + align:start position:0% +solution of that two-period problem was + + + align:start position:0% +solution of that two-period problem was +neither full insurance which wouldn't be + + align:start position:0% +neither full insurance which wouldn't be + + + align:start position:0% +neither full insurance which wouldn't be +feasible nor limited borrowing and + + align:start position:0% +feasible nor limited borrowing and + + + align:start position:0% +feasible nor limited borrowing and +lending which was not optimal + + align:start position:0% +lending which was not optimal + + + align:start position:0% +lending which was not optimal +and again in class we had a very good + + align:start position:0% +and again in class we had a very good + + + align:start position:0% +and again in class we had a very good +discussion about this hybrid borrowing + + align:start position:0% +discussion about this hybrid borrowing + + + align:start position:0% +discussion about this hybrid borrowing +and lending scheme did costly state + + align:start position:0% +and lending scheme did costly state + + + align:start position:0% +and lending scheme did costly state +verification i won't dwell on that + + align:start position:0% +verification i won't dwell on that + + + align:start position:0% +verification i won't dwell on that +except that some over a range of shocks + + align:start position:0% +except that some over a range of shocks + + + align:start position:0% +except that some over a range of shocks +you don't need to be verifying + + align:start position:0% +you don't need to be verifying + + + align:start position:0% +you don't need to be verifying +anything at all but it's still effective + + align:start position:0% +anything at all but it's still effective + + + align:start position:0% +anything at all but it's still effective +because there's the threat of of an + + align:start position:0% +because there's the threat of of an + + + align:start position:0% +because there's the threat of of an +audit + + align:start position:0% +audit + + + align:start position:0% +audit +for low + + align:start position:0% +for low + + + align:start position:0% +for low +claims + + align:start position:0% +claims + + + align:start position:0% +claims +and then we went back and sort of argued + + align:start position:0% +and then we went back and sort of argued + + + align:start position:0% +and then we went back and sort of argued +that costly state verification can help + + align:start position:0% +that costly state verification can help + + + align:start position:0% +that costly state verification can help +explain + + align:start position:0% +explain + + + align:start position:0% +explain +what we saw in the initial part of the + + align:start position:0% +what we saw in the initial part of the + + + align:start position:0% +what we saw in the initial part of the +lecture so here is where the transition + + align:start position:0% +lecture so here is where the transition + + + align:start position:0% +lecture so here is where the transition +happened to distributed ledgers again + + align:start position:0% +happened to distributed ledgers again + + + align:start position:0% +happened to distributed ledgers again +and + + align:start position:0% +and + + + align:start position:0% +and +there was a lot of material here i kind + + align:start position:0% +there was a lot of material here i kind + + + align:start position:0% +there was a lot of material here i kind +of argued that encryption was one + + align:start position:0% +of argued that encryption was one + + + align:start position:0% +of argued that encryption was one +third key element of distributed ledgers + + align:start position:0% +third key element of distributed ledgers + + + align:start position:0% +third key element of distributed ledgers +we've seen it historically we see it in + + align:start position:0% +we've seen it historically we see it in + + + align:start position:0% +we've seen it historically we see it in +contemporary applications it really + + align:start position:0% +contemporary applications it really + + + align:start position:0% +contemporary applications it really +breaks down into encryption of incoming + + align:start position:0% +breaks down into encryption of incoming + + + align:start position:0% +breaks down into encryption of incoming +and outgoing messages of hashing of data + + align:start position:0% +and outgoing messages of hashing of data + + + align:start position:0% +and outgoing messages of hashing of data +and others so that it's uninterpretable + + align:start position:0% +and others so that it's uninterpretable + + + align:start position:0% +and others so that it's uninterpretable +unless one wants to prove that it was + + align:start position:0% +unless one wants to prove that it was + + + align:start position:0% +unless one wants to prove that it was +the original which is possible to do in + + align:start position:0% +the original which is possible to do in + + + align:start position:0% +the original which is possible to do in +cryptographic puzzles which are hard but + + align:start position:0% +cryptographic puzzles which are hard but + + + align:start position:0% +cryptographic puzzles which are hard but +not impossible to solve + + align:start position:0% +not impossible to solve + + + align:start position:0% +not impossible to solve +bitcoin is using + + align:start position:0% +bitcoin is using + + + align:start position:0% +bitcoin is using +various of those things + + align:start position:0% +various of those things + + + align:start position:0% +various of those things +including + + align:start position:0% +including + + + align:start position:0% +including +a way of organizing the data + + align:start position:0% +a way of organizing the data + + + align:start position:0% +a way of organizing the data +through mining as the validation and i + + align:start position:0% +through mining as the validation and i + + + align:start position:0% +through mining as the validation and i +emphasized + + align:start position:0% +emphasized + + + align:start position:0% +emphasized +that mining was not the only way to + + align:start position:0% +that mining was not the only way to + + + align:start position:0% +that mining was not the only way to +validate transactions on ledgers if you + + align:start position:0% +validate transactions on ledgers if you + + + align:start position:0% +validate transactions on ledgers if you +don't trust safaricom or some third + + align:start position:0% +don't trust safaricom or some third + + + align:start position:0% +don't trust safaricom or some third +party + + align:start position:0% +party + + + align:start position:0% +party +and i also emphasize the encryption part + + align:start position:0% +and i also emphasize the encryption part + + + align:start position:0% +and i also emphasize the encryption part +which bitcoin doesn't use homomorphic + + align:start position:0% +which bitcoin doesn't use homomorphic + + + align:start position:0% +which bitcoin doesn't use homomorphic +and + + align:start position:0% +and + + + align:start position:0% +and +that's not quite fair the encryption + + align:start position:0% +that's not quite fair the encryption + + + align:start position:0% +that's not quite fair the encryption +part for the messages is related to + + align:start position:0% +part for the messages is related to + + + align:start position:0% +part for the messages is related to +homomorphic encryption + + align:start position:0% +homomorphic encryption + + + align:start position:0% +homomorphic encryption +but bitcoin doesn't use multi-party + + align:start position:0% +but bitcoin doesn't use multi-party + + + align:start position:0% +but bitcoin doesn't use multi-party +computation + + align:start position:0% +computation + + + align:start position:0% +computation +so then we came back to the essence of + + align:start position:0% +so then we came back to the essence of + + + align:start position:0% +so then we came back to the essence of +the lecture which was + + align:start position:0% +the lecture which was + + + align:start position:0% +the lecture which was +what is the difference between + + align:start position:0% +what is the difference between + + + align:start position:0% +what is the difference between +validation on distributed ledgers + + align:start position:0% +validation on distributed ledgers + + + align:start position:0% +validation on distributed ledgers +and incentives in mechanism design + + align:start position:0% +and incentives in mechanism design + + + align:start position:0% +and incentives in mechanism design +and the different philosophies of + + align:start position:0% +and the different philosophies of + + + align:start position:0% +and the different philosophies of +economics versus computer science + + align:start position:0% +economics versus computer science + + + align:start position:0% +economics versus computer science +computer science assumes that most nodes + + align:start position:0% +computer science assumes that most nodes + + + align:start position:0% +computer science assumes that most nodes +are honest and reliable + + align:start position:0% +are honest and reliable + + + align:start position:0% +are honest and reliable +and + + align:start position:0% +and + + + align:start position:0% +and +designs algorithms on the assumption + + align:start position:0% +designs algorithms on the assumption + + + align:start position:0% +designs algorithms on the assumption +that the honest nodes will follow the + + align:start position:0% +that the honest nodes will follow the + + + align:start position:0% +that the honest nodes will follow the +algorithms + + align:start position:0% +algorithms + + + align:start position:0% +algorithms +and just have to have enough + + align:start position:0% +and just have to have enough + + + align:start position:0% +and just have to have enough +total new nodes relative to the faulty + + align:start position:0% +total new nodes relative to the faulty + + + align:start position:0% +total new nodes relative to the faulty +nodes in the population for those + + align:start position:0% +nodes in the population for those + + + align:start position:0% +nodes in the population for those +protocols to work but if you take the + + align:start position:0% +protocols to work but if you take the + + + align:start position:0% +protocols to work but if you take the +mechanism design point of view + + align:start position:0% +mechanism design point of view + + + align:start position:0% +mechanism design point of view +the protocols may not be incentive + + align:start position:0% +the protocols may not be incentive + + + align:start position:0% +the protocols may not be incentive +compatible + + align:start position:0% +compatible + + + align:start position:0% +compatible +economists assume everyone's + + align:start position:0% +economists assume everyone's + + + align:start position:0% +economists assume everyone's +very selfish and maximizing so + + align:start position:0% +very selfish and maximizing so + + + align:start position:0% +very selfish and maximizing so +even the miners in bitcoin have to have + + align:start position:0% +even the miners in bitcoin have to have + + + align:start position:0% +even the miners in bitcoin have to have +incentives to follow the prescribed + + align:start position:0% +incentives to follow the prescribed + + + align:start position:0% +incentives to follow the prescribed +protocol + + align:start position:0% +protocol + + + align:start position:0% +protocol +and that point is true more generally so + + align:start position:0% +and that point is true more generally so + + + align:start position:0% +and that point is true more generally so +that kind of led to the idea that why + + align:start position:0% +that kind of led to the idea that why + + + align:start position:0% +that kind of led to the idea that why +not separate the two things + + align:start position:0% +not separate the two things + + + align:start position:0% +not separate the two things +write down the contract or mechanism + + align:start position:0% +write down the contract or mechanism + + + align:start position:0% +write down the contract or mechanism +design problem + + align:start position:0% +design problem + + + align:start position:0% +design problem +in code + + align:start position:0% +in code + + + align:start position:0% +in code +as in a smart contract + + align:start position:0% +as in a smart contract + + + align:start position:0% +as in a smart contract +let the parties agree to it make sure + + align:start position:0% +let the parties agree to it make sure + + + align:start position:0% +let the parties agree to it make sure +that it functions the way they think + + align:start position:0% +that it functions the way they think + + + align:start position:0% +that it functions the way they think +that it does + + align:start position:0% +that it does + + + align:start position:0% +that it does +and then send messages to implement it + + align:start position:0% +and then send messages to implement it + + + align:start position:0% +and then send messages to implement it +those messages would be encrypted + + align:start position:0% +those messages would be encrypted + + + align:start position:0% +those messages would be encrypted +through + + align:start position:0% +through + + + align:start position:0% +through +he and mpc + + align:start position:0% +he and mpc + + + align:start position:0% +he and mpc +and that's a contribution the mechanism + + align:start position:0% +and that's a contribution the mechanism + + + align:start position:0% +and that's a contribution the mechanism +design literature assumes we have a + + align:start position:0% +design literature assumes we have a + + + align:start position:0% +design literature assumes we have a +planner i hate that language + + align:start position:0% +planner i hate that language + + + align:start position:0% +planner i hate that language +and the planner is trusted to implement + + align:start position:0% +and the planner is trusted to implement + + + align:start position:0% +and the planner is trusted to implement +the mechanism + + align:start position:0% +the mechanism + + + align:start position:0% +the mechanism +what encryption does nowadays is to get + + align:start position:0% +what encryption does nowadays is to get + + + align:start position:0% +what encryption does nowadays is to get +rid of trusted third parties and + + align:start position:0% +rid of trusted third parties and + + + align:start position:0% +rid of trusted third parties and +planners agents can keep secrets from + + align:start position:0% +planners agents can keep secrets from + + + align:start position:0% +planners agents can keep secrets from +each other and implement the optimal + + align:start position:0% +each other and implement the optimal + + + align:start position:0% +each other and implement the optimal +contract + + align:start position:0% +contract + + + align:start position:0% +contract +the ledgers still play a role i mean as + + align:start position:0% +the ledgers still play a role i mean as + + + align:start position:0% +the ledgers still play a role i mean as +in borrowing and lending + + align:start position:0% +in borrowing and lending + + + align:start position:0% +in borrowing and lending +you can sequester the collateral + + align:start position:0% +you can sequester the collateral + + + align:start position:0% +you can sequester the collateral +and have it automatically transfer to + + align:start position:0% +and have it automatically transfer to + + + align:start position:0% +and have it automatically transfer to +the lender if the borrower + + align:start position:0% +the lender if the borrower + + + align:start position:0% +the lender if the borrower +were to default so + + align:start position:0% +were to default so + + + align:start position:0% +were to default so +so we're not claiming that we only need + + align:start position:0% +so we're not claiming that we only need + + + align:start position:0% +so we're not claiming that we only need +the cryptography we also need the + + align:start position:0% +the cryptography we also need the + + + align:start position:0% +the cryptography we also need the +ledgers + + align:start position:0% +ledgers + + + align:start position:0% +ledgers +on the other hand you don't need to have + + align:start position:0% +on the other hand you don't need to have + + + align:start position:0% +on the other hand you don't need to have +all the line items of the code in the + + align:start position:0% +all the line items of the code in the + + + align:start position:0% +all the line items of the code in the +ledger being done + + align:start position:0% +ledger being done + + + align:start position:0% +ledger being done +as with ethereum on a distributed ledger + + align:start position:0% +as with ethereum on a distributed ledger + + + align:start position:0% +as with ethereum on a distributed ledger +because that's really really costly + + align:start position:0% +because that's really really costly + + + align:start position:0% +because that's really really costly +so again there was a lot in this lecture + + align:start position:0% +so again there was a lot in this lecture + + + align:start position:0% +so again there was a lot in this lecture +questions about lecture 11. + + align:start position:0% +questions about lecture 11. + + + align:start position:0% +questions about lecture 11. +lecture 12 was the application of + + align:start position:0% +lecture 12 was the application of + + + align:start position:0% +lecture 12 was the application of +contract theory + + align:start position:0% +contract theory + + + align:start position:0% +contract theory +and uh we took it to the thai villages + + align:start position:0% +and uh we took it to the thai villages + + + align:start position:0% +and uh we took it to the thai villages +and looked at occupation choice + + align:start position:0% +and looked at occupation choice + + + align:start position:0% +and looked at occupation choice +there's a couple of things going on here + + align:start position:0% +there's a couple of things going on here + + + align:start position:0% +there's a couple of things going on here +one + + align:start position:0% +one + + + align:start position:0% +one +we now know how to incorporate private + + align:start position:0% +we now know how to incorporate private + + + align:start position:0% +we now know how to incorporate private +information and incentives + + align:start position:0% +information and incentives + + + align:start position:0% +information and incentives +and collateral + + align:start position:0% +and collateral + + + align:start position:0% +and collateral +by just appending + + align:start position:0% +by just appending + + + align:start position:0% +by just appending +extra constraints onto the problem so + + align:start position:0% +extra constraints onto the problem so + + + align:start position:0% +extra constraints onto the problem so +let me start + + align:start position:0% +let me start + + + align:start position:0% +let me start +skipping a little bit + + align:start position:0% +skipping a little bit + + + align:start position:0% +skipping a little bit +so we have + + align:start position:0% +so we have + + + align:start position:0% +so we have +will the entrepreneur take appropriate + + align:start position:0% +will the entrepreneur take appropriate + + + align:start position:0% +will the entrepreneur take appropriate +action not necessarily if it's not seen + + align:start position:0% +action not necessarily if it's not seen + + + align:start position:0% +action not necessarily if it's not seen +then you have to induce it + + align:start position:0% +then you have to induce it + + + align:start position:0% +then you have to induce it +will the entrepreneur pay back the loan + + align:start position:0% +will the entrepreneur pay back the loan + + + align:start position:0% +will the entrepreneur pay back the loan +if not you have to have collateral which + + align:start position:0% +if not you have to have collateral which + + + align:start position:0% +if not you have to have collateral which +is another kind of constraint + + align:start position:0% +is another kind of constraint + + + align:start position:0% +is another kind of constraint +so + + align:start position:0% +so + + + align:start position:0% +so +so here we have the household's utility + + align:start position:0% +so here we have the household's utility + + + align:start position:0% +so here we have the household's utility +in consumption and disutility of effort + + align:start position:0% +in consumption and disutility of effort + + + align:start position:0% +in consumption and disutility of effort +and potentially risk neutral potentially + + align:start position:0% +and potentially risk neutral potentially + + + align:start position:0% +and potentially risk neutral potentially +risk-averse + + align:start position:0% +risk-averse + + + align:start position:0% +risk-averse +and households vary by talent wealth and + + align:start position:0% +and households vary by talent wealth and + + + align:start position:0% +and households vary by talent wealth and +schooling + + align:start position:0% +schooling + + + align:start position:0% +schooling +and we have they're running a firm with + + align:start position:0% +and we have they're running a firm with + + + align:start position:0% +and we have they're running a firm with +stochastic output as a function of + + align:start position:0% +stochastic output as a function of + + + align:start position:0% +stochastic output as a function of +effort + + align:start position:0% +effort + + + align:start position:0% +effort +and capital and they can borrow + + align:start position:0% +and capital and they can borrow + + + align:start position:0% +and capital and they can borrow +this is the slide it's kind of racing to + + align:start position:0% +this is the slide it's kind of racing to + + + align:start position:0% +this is the slide it's kind of racing to +get to + + align:start position:0% +get to + + + align:start position:0% +get to +so here is the problem which we posed as + + align:start position:0% +so here is the problem which we posed as + + + align:start position:0% +so here is the problem which we posed as +maximizing the utility of the borrower + + align:start position:0% +maximizing the utility of the borrower + + + align:start position:0% +maximizing the utility of the borrower +or entrepreneur + + align:start position:0% +or entrepreneur + + + align:start position:0% +or entrepreneur +subject to the bank + + align:start position:0% +subject to the bank + + + align:start position:0% +subject to the bank +making zero profits so + + align:start position:0% +making zero profits so + + + align:start position:0% +making zero profits so +it's worth emphasizing that in the + + align:start position:0% +it's worth emphasizing that in the + + + align:start position:0% +it's worth emphasizing that in the +previous lectures we've been maximizing + + align:start position:0% +previous lectures we've been maximizing + + + align:start position:0% +previous lectures we've been maximizing +lambda weighted sums of utilities + + align:start position:0% +lambda weighted sums of utilities + + + align:start position:0% +lambda weighted sums of utilities +subject to resource constraints and + + align:start position:0% +subject to resource constraints and + + + align:start position:0% +subject to resource constraints and +incentive constraints and so on well + + align:start position:0% +incentive constraints and so on well + + + align:start position:0% +incentive constraints and so on well +here we made a shift from maximizing the + + align:start position:0% +here we made a shift from maximizing the + + + align:start position:0% +here we made a shift from maximizing the +utility of one party subject to a fixed + + align:start position:0% +utility of one party subject to a fixed + + + align:start position:0% +utility of one party subject to a fixed +utility of the other or here the utility + + align:start position:0% +utility of the other or here the utility + + + align:start position:0% +utility of the other or here the utility +of the entrepreneur subject to a fixed + + align:start position:0% +of the entrepreneur subject to a fixed + + + align:start position:0% +of the entrepreneur subject to a fixed +and zero profit level of the bank one + + align:start position:0% +and zero profit level of the bank one + + + align:start position:0% +and zero profit level of the bank one +could have solved this problem the other + + align:start position:0% +could have solved this problem the other + + + align:start position:0% +could have solved this problem the other +way around to maximize the profits of + + align:start position:0% +way around to maximize the profits of + + + align:start position:0% +way around to maximize the profits of +the bank subject to a fixed reservation + + align:start position:0% +the bank subject to a fixed reservation + + + align:start position:0% +the bank subject to a fixed reservation +utility on the part of the borrower + + align:start position:0% +utility on the part of the borrower + + + align:start position:0% +utility on the part of the borrower +should get the same answers of course + + align:start position:0% +should get the same answers of course + + + align:start position:0% +should get the same answers of course +there are many many solutions if you + + align:start position:0% +there are many many solutions if you + + + align:start position:0% +there are many many solutions if you +allow profits to be positive if you + + align:start position:0% +allow profits to be positive if you + + + align:start position:0% +allow profits to be positive if you +allow + + align:start position:0% +allow + + + align:start position:0% +allow +some of the surplus to go to the bank + + align:start position:0% +some of the surplus to go to the bank + + + align:start position:0% +some of the surplus to go to the bank +etc in fact the borrower could be pushed + + align:start position:0% +etc in fact the borrower could be pushed + + + align:start position:0% +etc in fact the borrower could be pushed +down to the point that they're + + align:start position:0% +down to the point that they're + + + align:start position:0% +down to the point that they're +almost indifferent to participating if + + align:start position:0% +almost indifferent to participating if + + + align:start position:0% +almost indifferent to participating if +the banks are getting the bulk of the + + align:start position:0% +the banks are getting the bulk of the + + + align:start position:0% +the banks are getting the bulk of the +surplus + + align:start position:0% +surplus + + + align:start position:0% +surplus +but what i want to emphasize is + + align:start position:0% +but what i want to emphasize is + + + align:start position:0% +but what i want to emphasize is +it's all the same in the end maximizing + + align:start position:0% +it's all the same in the end maximizing + + + align:start position:0% +it's all the same in the end maximizing +lambda weighted sum of utilities is the + + align:start position:0% +lambda weighted sum of utilities is the + + + align:start position:0% +lambda weighted sum of utilities is the +same as maximizing the utility of one + + align:start position:0% +same as maximizing the utility of one + + + align:start position:0% +same as maximizing the utility of one +type subject to fixed utility of the + + align:start position:0% +type subject to fixed utility of the + + + align:start position:0% +type subject to fixed utility of the +other and then varying those okay so + + align:start position:0% +other and then varying those okay so + + + align:start position:0% +other and then varying those okay so +the rest of it was just implementing the + + align:start position:0% +the rest of it was just implementing the + + + align:start position:0% +the rest of it was just implementing the +solution + + align:start position:0% +solution + + + align:start position:0% +solution +limited liability moral hazard + + align:start position:0% +limited liability moral hazard + + + align:start position:0% +limited liability moral hazard +with separate equations + + align:start position:0% +with separate equations + + + align:start position:0% +with separate equations +and then we got to this diagram + + align:start position:0% +and then we got to this diagram + + + align:start position:0% +and then we got to this diagram +where i said you know if there were no + + align:start position:0% +where i said you know if there were no + + + align:start position:0% +where i said you know if there were no +constraints at all + + align:start position:0% +constraints at all + + + align:start position:0% +constraints at all +that would be like the full information + + align:start position:0% +that would be like the full information + + + align:start position:0% +that would be like the full information +full commitment solution + + align:start position:0% +full commitment solution + + + align:start position:0% +full commitment solution +hit the bull's-eye + + align:start position:0% +hit the bull's-eye + + + align:start position:0% +hit the bull's-eye +it could be entirely moral hazard and + + align:start position:0% +it could be entirely moral hazard and + + + align:start position:0% +it could be entirely moral hazard and +not limited liability it could be + + align:start position:0% +not limited liability it could be + + + align:start position:0% +not limited liability it could be +entirely limited liability and not moral + + align:start position:0% +entirely limited liability and not moral + + + align:start position:0% +entirely limited liability and not moral +hazard although in this case if you had + + align:start position:0% +hazard although in this case if you had + + + align:start position:0% +hazard although in this case if you had +both constraints you have two equations + + align:start position:0% +both constraints you have two equations + + + align:start position:0% +both constraints you have two equations +and two unknowns the capital and the + + align:start position:0% +and two unknowns the capital and the + + + align:start position:0% +and two unknowns the capital and the +effort level + + align:start position:0% +effort level + + + align:start position:0% +effort level +so when those two constraints are + + align:start position:0% +so when those two constraints are + + + align:start position:0% +so when those two constraints are +satisfied if they're both in the program + + align:start position:0% +satisfied if they're both in the program + + + align:start position:0% +satisfied if they're both in the program +you get a solution that has nothing to + + align:start position:0% +you get a solution that has nothing to + + + align:start position:0% +you get a solution that has nothing to +do with utility maximization because + + align:start position:0% +do with utility maximization because + + + align:start position:0% +do with utility maximization because +there's only one + + align:start position:0% +there's only one + + + align:start position:0% +there's only one +point in the input space where both + + align:start position:0% +point in the input space where both + + + align:start position:0% +point in the input space where both +constraints are satisfied + + align:start position:0% +constraints are satisfied + + + align:start position:0% +constraints are satisfied +but in general if you have only one or + + align:start position:0% +but in general if you have only one or + + + align:start position:0% +but in general if you have only one or +the other + + align:start position:0% +the other + + + align:start position:0% +the other +you have to both max utility and then + + align:start position:0% +you have to both max utility and then + + + align:start position:0% +you have to both max utility and then +and subject to constraints the rest of + + align:start position:0% +and subject to constraints the rest of + + + align:start position:0% +and subject to constraints the rest of +this lecture was about implementation + + align:start position:0% +this lecture was about implementation + + + align:start position:0% +this lecture was about implementation +namely + + align:start position:0% +namely + + + align:start position:0% +namely +solving linear programming problems and + + align:start position:0% +solving linear programming problems and + + + align:start position:0% +solving linear programming problems and +trying to + + align:start position:0% +trying to + + + align:start position:0% +trying to +pick parameters in such a way that + + align:start position:0% +pick parameters in such a way that + + + align:start position:0% +pick parameters in such a way that +maximize the probability + + align:start position:0% +maximize the probability + + + align:start position:0% +maximize the probability +that the model is true given what we see + + align:start position:0% +that the model is true given what we see + + + align:start position:0% +that the model is true given what we see +in the data + + align:start position:0% +in the data + + + align:start position:0% +in the data +maximize the probability that the data + + align:start position:0% +maximize the probability that the data + + + align:start position:0% +maximize the probability that the data +we see in reality + + align:start position:0% +we see in reality + + + align:start position:0% +we see in reality +could have come from the model + + align:start position:0% +could have come from the model + + + align:start position:0% +could have come from the model +by choosing the parameters of the model + + align:start position:0% +by choosing the parameters of the model + + + align:start position:0% +by choosing the parameters of the model +so that + + align:start position:0% +so that + + + align:start position:0% +so that +there was uh that was the the + + align:start position:0% +there was uh that was the the + + + align:start position:0% +there was uh that was the the +application and then we had the findings + + align:start position:0% +application and then we had the findings + + + align:start position:0% +application and then we had the findings +that the constraints varied by region + + align:start position:0% +that the constraints varied by region + + + align:start position:0% +that the constraints varied by region +are there questions about this lecture + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +lecture 13 + + align:start position:0% +lecture 13 + + + align:start position:0% +lecture 13 +was also loaded although it's more + + align:start position:0% +was also loaded although it's more + + + align:start position:0% +was also loaded although it's more +recent + + align:start position:0% +recent + + + align:start position:0% +recent +i'm somewhat comforted just like the + + align:start position:0% +i'm somewhat comforted just like the + + + align:start position:0% +i'm somewhat comforted just like the +first review session by the time we get + + align:start position:0% +first review session by the time we get + + + align:start position:0% +first review session by the time we get +to 13 and then 14 15 you've already seen + + align:start position:0% +to 13 and then 14 15 you've already seen + + + align:start position:0% +to 13 and then 14 15 you've already seen +15 tonight today we just reviewed it so + + align:start position:0% +15 tonight today we just reviewed it so + + + align:start position:0% +15 tonight today we just reviewed it so +we're actually getting close to the end + + align:start position:0% +we're actually getting close to the end + + + align:start position:0% +we're actually getting close to the end +here this lecture did two important + + align:start position:0% +here this lecture did two important + + + align:start position:0% +here this lecture did two important +things + + align:start position:0% +things + + + align:start position:0% +things +one the theory + + align:start position:0% +one the theory + + + align:start position:0% +one the theory +which was to define the notion of a + + align:start position:0% +which was to define the notion of a + + + align:start position:0% +which was to define the notion of a +volrasian equilibrium within without + + align:start position:0% +volrasian equilibrium within without + + + align:start position:0% +volrasian equilibrium within without +transfers and the second was to apply it + + align:start position:0% +transfers and the second was to apply it + + + align:start position:0% +transfers and the second was to apply it +so we get general equilibrium solution + + align:start position:0% +so we get general equilibrium solution + + + align:start position:0% +so we get general equilibrium solution +in a + + align:start position:0% +in a + + + align:start position:0% +in a +small open economy with production + + align:start position:0% +small open economy with production + + + align:start position:0% +small open economy with production +all of this slide had to do with + + align:start position:0% +all of this slide had to do with + + + align:start position:0% +all of this slide had to do with +remember what an economy means this is + + align:start position:0% +remember what an economy means this is + + + align:start position:0% +remember what an economy means this is +partly review of the first one-third of + + align:start position:0% +partly review of the first one-third of + + + align:start position:0% +partly review of the first one-third of +the class + + align:start position:0% +the class + + + align:start position:0% +the class +numbers of households numbers of firms + + align:start position:0% +numbers of households numbers of firms + + + align:start position:0% +numbers of households numbers of firms +what consumers do what firms do + + align:start position:0% +what consumers do what firms do + + + align:start position:0% +what consumers do what firms do +aggregate resources we went over private + + align:start position:0% +aggregate resources we went over private + + + align:start position:0% +aggregate resources we went over private +ownership and again we had a very good + + align:start position:0% +ownership and again we had a very good + + + align:start position:0% +ownership and again we had a very good +discussion at the beginning of the + + align:start position:0% +discussion at the beginning of the + + + align:start position:0% +discussion at the beginning of the +following class to review this slide in + + align:start position:0% +following class to review this slide in + + + align:start position:0% +following class to review this slide in +terms of individual endowments and + + align:start position:0% +terms of individual endowments and + + + align:start position:0% +terms of individual endowments and +ownership shares + + align:start position:0% +ownership shares + + + align:start position:0% +ownership shares +and the key definition of a + + align:start position:0% +and the key definition of a + + + align:start position:0% +and the key definition of a +vulnerability in equilibrium + + align:start position:0% +vulnerability in equilibrium + + + align:start position:0% +vulnerability in equilibrium +with three items + + align:start position:0% +with three items + + + align:start position:0% +with three items +in it + + align:start position:0% +in it + + + align:start position:0% +in it +maximizing profits for firms maximizing + + align:start position:0% +maximizing profits for firms maximizing + + + align:start position:0% +maximizing profits for firms maximizing +utility for households + + align:start position:0% +utility for households + + + align:start position:0% +utility for households +and the feasibility of the allocations + + align:start position:0% +and the feasibility of the allocations + + + align:start position:0% +and the feasibility of the allocations +that result from those two optimization + + align:start position:0% +that result from those two optimization + + + align:start position:0% +that result from those two optimization +problems the key being that prices are + + align:start position:0% +problems the key being that prices are + + + align:start position:0% +problems the key being that prices are +the things that allow the reconciliation + + align:start position:0% +the things that allow the reconciliation + + + align:start position:0% +the things that allow the reconciliation +you can do partial equilibrium we did + + align:start position:0% +you can do partial equilibrium we did + + + align:start position:0% +you can do partial equilibrium we did +you can solve for profit maximization + + align:start position:0% +you can solve for profit maximization + + + align:start position:0% +you can solve for profit maximization +taking prices as given you can solve for + + align:start position:0% +taking prices as given you can solve for + + + align:start position:0% +taking prices as given you can solve for +utility maximization taking prices as + + align:start position:0% +utility maximization taking prices as + + + align:start position:0% +utility maximization taking prices as +given here in general equilibrium we are + + align:start position:0% +given here in general equilibrium we are + + + align:start position:0% +given here in general equilibrium we are +only allowing certain prices where those + + align:start position:0% +only allowing certain prices where those + + + align:start position:0% +only allowing certain prices where those +decentralized optimization problems are + + align:start position:0% +decentralized optimization problems are + + + align:start position:0% +decentralized optimization problems are +consistent with each other in the sense + + align:start position:0% +consistent with each other in the sense + + + align:start position:0% +consistent with each other in the sense +that supply + + align:start position:0% +that supply + + + align:start position:0% +that supply +is equal to demand + + align:start position:0% +is equal to demand + + + align:start position:0% +is equal to demand +although when we oh and then this + + align:start position:0% +although when we oh and then this + + + align:start position:0% +although when we oh and then this +edgeworth box which is like economist's + + align:start position:0% +edgeworth box which is like economist's + + + align:start position:0% +edgeworth box which is like economist's +favorite environment a sad statement + + align:start position:0% +favorite environment a sad statement + + + align:start position:0% +favorite environment a sad statement +putting the two types of households on + + align:start position:0% +putting the two types of households on + + + align:start position:0% +putting the two types of households on +the axis and talking about what a + + align:start position:0% +the axis and talking about what a + + + align:start position:0% +the axis and talking about what a +competitive equilibrium would look like + + align:start position:0% +competitive equilibrium would look like + + + align:start position:0% +competitive equilibrium would look like +and the price equilibrium with transfers + + align:start position:0% +and the price equilibrium with transfers + + + align:start position:0% +and the price equilibrium with transfers +and the welfare theorems which so far i + + align:start position:0% +and the welfare theorems which so far i + + + align:start position:0% +and the welfare theorems which so far i +have only stated although the last one + + align:start position:0% +have only stated although the last one + + + align:start position:0% +have only stated although the last one +third of the class next week will be + + align:start position:0% +third of the class next week will be + + + align:start position:0% +third of the class next week will be +focusing in part on these welfare + + align:start position:0% +focusing in part on these welfare + + + align:start position:0% +focusing in part on these welfare +theorems starting next week so then we + + align:start position:0% +theorems starting next week so then we + + + align:start position:0% +theorems starting next week so then we +did production in a small open economy + + align:start position:0% +did production in a small open economy + + + align:start position:0% +did production in a small open economy +and we again went through this algorithm + + align:start position:0% +and we again went through this algorithm + + + align:start position:0% +and we again went through this algorithm +pretty carefully so i don't think i want + + align:start position:0% +pretty carefully so i don't think i want + + + align:start position:0% +pretty carefully so i don't think i want +to say too much about it too too much + + align:start position:0% +to say too much about it too too much + + + align:start position:0% +to say too much about it too too much +but we simplify the problem down into + + align:start position:0% +but we simplify the problem down into + + + align:start position:0% +but we simplify the problem down into +firms hiring inputs and trying to find + + align:start position:0% +firms hiring inputs and trying to find + + + align:start position:0% +firms hiring inputs and trying to find +the factor prices that clear the input + + align:start position:0% +the factor prices that clear the input + + + align:start position:0% +the factor prices that clear the input +markets taking out external prices of + + align:start position:0% +markets taking out external prices of + + + align:start position:0% +markets taking out external prices of +goods as given + + align:start position:0% +goods as given + + + align:start position:0% +goods as given +so we had the firm's maximization + + align:start position:0% +so we had the firm's maximization + + + align:start position:0% +so we had the firm's maximization +problem we wrote down that the sum of + + align:start position:0% +problem we wrote down that the sum of + + + align:start position:0% +problem we wrote down that the sum of +the input demands equal the endowments + + align:start position:0% +the input demands equal the endowments + + + align:start position:0% +the input demands equal the endowments +and + + align:start position:0% +and + + + align:start position:0% +and +reminded ourselves of shepard's lemma so + + align:start position:0% +reminded ourselves of shepard's lemma so + + + align:start position:0% +reminded ourselves of shepard's lemma so +we had a different statement of the + + align:start position:0% +we had a different statement of the + + + align:start position:0% +we had a different statement of the +input demands which we could then solve + + align:start position:0% +input demands which we could then solve + + + align:start position:0% +input demands which we could then solve +especially in the 2x2 model input + + align:start position:0% +especially in the 2x2 model input + + + align:start position:0% +especially in the 2x2 model input +demands are entirely a function of input + + align:start position:0% +demands are entirely a function of input + + + align:start position:0% +demands are entirely a function of input +price ratios and + + align:start position:0% +price ratios and + + + align:start position:0% +price ratios and +with constant returns to scale it's even + + align:start position:0% +with constant returns to scale it's even + + + align:start position:0% +with constant returns to scale it's even +easier we can talk about cost + + align:start position:0% +easier we can talk about cost + + + align:start position:0% +easier we can talk about cost +minimization to achieve a unit of output + + align:start position:0% +minimization to achieve a unit of output + + + align:start position:0% +minimization to achieve a unit of output +and then to scale up and down + + align:start position:0% +and then to scale up and down + + + align:start position:0% +and then to scale up and down +when we get to determining output + + align:start position:0% +when we get to determining output + + + align:start position:0% +when we get to determining output +talked about the intensity of goods + + align:start position:0% +talked about the intensity of goods + + + align:start position:0% +talked about the intensity of goods +factor intensity of the different goods + + align:start position:0% +factor intensity of the different goods + + + align:start position:0% +factor intensity of the different goods +with the definition here was the cost + + align:start position:0% +with the definition here was the cost + + + align:start position:0% +with the definition here was the cost +curves no and their properties concave + + align:start position:0% +curves no and their properties concave + + + align:start position:0% +curves no and their properties concave +we solve for the equilibrium factor + + align:start position:0% +we solve for the equilibrium factor + + + align:start position:0% +we solve for the equilibrium factor +prices where both firms face common + + align:start position:0% +prices where both firms face common + + + align:start position:0% +prices where both firms face common +prices hence + + align:start position:0% +prices hence + + + align:start position:0% +prices hence +there's only one point where that's true + + align:start position:0% +there's only one point where that's true + + + align:start position:0% +there's only one point where that's true +on this diagram + + align:start position:0% +on this diagram + + + align:start position:0% +on this diagram +and then we went from that to production + + align:start position:0% +and then we went from that to production + + + align:start position:0% +and then we went from that to production +from production we were able to solve + + align:start position:0% +from production we were able to solve + + + align:start position:0% +from production we were able to solve +for the input quantities and the outputs + + align:start position:0% +for the input quantities and the outputs + + + align:start position:0% +for the input quantities and the outputs +and then we got the external goods + + align:start position:0% +and then we got the external goods + + + align:start position:0% +and then we got the external goods +prices + + align:start position:0% +prices + + + align:start position:0% +prices +by considering this sort of free trade + + align:start position:0% +by considering this sort of free trade + + + align:start position:0% +by considering this sort of free trade +equilibrium with two countries + + align:start position:0% +equilibrium with two countries + + + align:start position:0% +equilibrium with two countries +determining a price ratio moving from + + align:start position:0% +determining a price ratio moving from + + + align:start position:0% +determining a price ratio moving from +autarky + + align:start position:0% +autarky + + + align:start position:0% +autarky +to international trade + + align:start position:0% +to international trade + + + align:start position:0% +to international trade +so there were there were three theorems + + align:start position:0% +so there were there were three theorems + + + align:start position:0% +so there were there were three theorems +we had this textural lien theorem of + + align:start position:0% +we had this textural lien theorem of + + + align:start position:0% +we had this textural lien theorem of +someone mentioned at the beginning of + + align:start position:0% +someone mentioned at the beginning of + + + align:start position:0% +someone mentioned at the beginning of +class today that the + + align:start position:0% +class today that the + + + align:start position:0% +class today that the +returns to factors depend on whether the + + align:start position:0% +returns to factors depend on whether the + + + align:start position:0% +returns to factors depend on whether the +country is abundant in one factor versus + + align:start position:0% +country is abundant in one factor versus + + + align:start position:0% +country is abundant in one factor versus +another one that's alpha samus then + + align:start position:0% +another one that's alpha samus then + + + align:start position:0% +another one that's alpha samus then +having to do with how factor prices are + + align:start position:0% +having to do with how factor prices are + + + align:start position:0% +having to do with how factor prices are +moving when we vary the price of + + align:start position:0% +moving when we vary the price of + + + align:start position:0% +moving when we vary the price of +outputs and + + align:start position:0% +outputs and + + + align:start position:0% +outputs and +yeah and + + align:start position:0% +yeah and + + + align:start position:0% +yeah and +that's all + + align:start position:0% +that's all + + + align:start position:0% +that's all +okay + + align:start position:0% +okay + + + align:start position:0% +okay +are there questions about this lecture + + align:start position:0% + + + + align:start position:0% + +here the ho theorem that + + align:start position:0% +here the ho theorem that + + + align:start position:0% +here the ho theorem that +say that in the artaki the price of the + + align:start position:0% +say that in the artaki the price of the + + + align:start position:0% +say that in the artaki the price of the +capital intensive goods in the capital + + align:start position:0% +capital intensive goods in the capital + + + align:start position:0% +capital intensive goods in the capital +abundant country will be buy down so + + align:start position:0% +abundant country will be buy down so + + + align:start position:0% +abundant country will be buy down so +here by that i mean the relative price + + align:start position:0% +here by that i mean the relative price + + + align:start position:0% +here by that i mean the relative price +was + + align:start position:0% +was + + + align:start position:0% +was +in this capital about in the country was + + align:start position:0% +in this capital about in the country was + + + align:start position:0% +in this capital about in the country was +lower than the + + align:start position:0% +lower than the + + + align:start position:0% +lower than the +another country right not the obvious + + align:start position:0% +another country right not the obvious + + + align:start position:0% +another country right not the obvious +route crisis + + align:start position:0% +route crisis + + + align:start position:0% +route crisis +uh + + align:start position:0% + + + + align:start position:0% + +the the + + align:start position:0% +the the + + + align:start position:0% +the the +good that is being produced which is + + align:start position:0% +good that is being produced which is + + + align:start position:0% +good that is being produced which is +capital intensive + + align:start position:0% +capital intensive + + + align:start position:0% +capital intensive +if produced in the capital abundant + + align:start position:0% +if produced in the capital abundant + + + align:start position:0% +if produced in the capital abundant +country + + align:start position:0% +country + + + align:start position:0% +country +should be relatively cheap + + align:start position:0% +should be relatively cheap + + + align:start position:0% +should be relatively cheap +because the other country is abundant in + + align:start position:0% +because the other country is abundant in + + + align:start position:0% +because the other country is abundant in +labor + + align:start position:0% +labor + + + align:start position:0% +labor +and + + align:start position:0% +and + + + align:start position:0% +and +and uh scarcity in capital + + align:start position:0% +and uh scarcity in capital + + + align:start position:0% +and uh scarcity in capital +so + + align:start position:0% +so + + + align:start position:0% +so +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +my question is that this cheap means + + align:start position:0% +my question is that this cheap means + + + align:start position:0% +my question is that this cheap means +that the relative price was cheap i mean + + align:start position:0% +that the relative price was cheap i mean + + + align:start position:0% +that the relative price was cheap i mean +in this capital about in the country the + + align:start position:0% +in this capital about in the country the + + + align:start position:0% +in this capital about in the country the +ratio price of these capital intensive + + align:start position:0% +ratio price of these capital intensive + + + align:start position:0% +ratio price of these capital intensive +goods was + + align:start position:0% +goods was + + + align:start position:0% +goods was +lower than the + + align:start position:0% +lower than the + + + align:start position:0% +lower than the +uh these cat the the same same relative + + align:start position:0% +uh these cat the the same same relative + + + align:start position:0% +uh these cat the the same same relative +price of the capital intensive goods in + + align:start position:0% +price of the capital intensive goods in + + + align:start position:0% +price of the capital intensive goods in +another country like labor abound in the + + align:start position:0% +another country like labor abound in the + + + align:start position:0% +another country like labor abound in the +country right yeah so + + align:start position:0% +country right yeah so + + + align:start position:0% +country right yeah so +you know when you look at this diet + + align:start position:0% +you know when you look at this diet + + + align:start position:0% +you know when you look at this diet +another great question thank you + + align:start position:0% +another great question thank you + + + align:start position:0% +another great question thank you +when you look at this diagram it's + + align:start position:0% +when you look at this diagram it's + + + align:start position:0% +when you look at this diagram it's +really only the relative price of the + + align:start position:0% +really only the relative price of the + + + align:start position:0% +really only the relative price of the +goods that matters + + align:start position:0% +goods that matters + + + align:start position:0% +goods that matters +it's like p1 over p2 + + align:start position:0% +it's like p1 over p2 + + + align:start position:0% +it's like p1 over p2 +so there's a lot of things that are + + align:start position:0% +so there's a lot of things that are + + + align:start position:0% +so there's a lot of things that are +relative here + + align:start position:0% +relative here + + + align:start position:0% +relative here +that + + align:start position:0% +that + + + align:start position:0% +that +look like they're + + align:start position:0% +look like they're + + + align:start position:0% +look like they're +an actual lien stated as absolute + + align:start position:0% +an actual lien stated as absolute + + + align:start position:0% +an actual lien stated as absolute +prices but it's really only the relative + + align:start position:0% +prices but it's really only the relative + + + align:start position:0% +prices but it's really only the relative +price + + align:start position:0% +price + + + align:start position:0% +price +um + + align:start position:0% +um + + + align:start position:0% +um +i get it + + align:start position:0% +i get it + + + align:start position:0% +i get it +okay + + align:start position:0% + + + + align:start position:0% + +all right so that's + + align:start position:0% + + + + align:start position:0% + +that was lecture + + align:start position:0% +that was lecture + + + align:start position:0% +that was lecture + + align:start position:0% + + + align:start position:0% +and + + align:start position:0% +and + + + align:start position:0% +and +you know the other two lectures + + align:start position:0% +you know the other two lectures + + + align:start position:0% +you know the other two lectures +14 we took that trade model to thailand + + align:start position:0% +14 we took that trade model to thailand + + + align:start position:0% +14 we took that trade model to thailand +and did some more with the financial + + align:start position:0% +and did some more with the financial + + + align:start position:0% +and did some more with the financial +accounts to get not just individual + + align:start position:0% +accounts to get not just individual + + + align:start position:0% +accounts to get not just individual +income and balance sheet statements but + + align:start position:0% +income and balance sheet statements but + + + align:start position:0% +income and balance sheet statements but +to aggregate up those statements to get + + align:start position:0% +to aggregate up those statements to get + + + align:start position:0% +to aggregate up those statements to get +to village asset accounts village level + + align:start position:0% +to village asset accounts village level + + + align:start position:0% +to village asset accounts village level +savings accounts flows across the + + align:start position:0% +savings accounts flows across the + + + align:start position:0% +savings accounts flows across the +villages and so on but you know my time + + align:start position:0% +villages and so on but you know my time + + + align:start position:0% +villages and so on but you know my time +is up so i can't review it of course the + + align:start position:0% +is up so i can't review it of course the + + + align:start position:0% +is up so i can't review it of course the +other thing we're doing is taking that + + align:start position:0% +other thing we're doing is taking that + + + align:start position:0% +other thing we're doing is taking that +two by two model to actual data + + align:start position:0% +two by two model to actual data + + + align:start position:0% +two by two model to actual data +with the exception that the model here + + align:start position:0% +with the exception that the model here + + + align:start position:0% +with the exception that the model here +actually + + align:start position:0% +actually + + + align:start position:0% +actually +did not have constant returns to scale + + align:start position:0% +did not have constant returns to scale + + + align:start position:0% +did not have constant returns to scale +it had capital mobility + + align:start position:0% +it had capital mobility + + + align:start position:0% +it had capital mobility +whereas the two by two did not factor + + align:start position:0% +whereas the two by two did not factor + + + align:start position:0% +whereas the two by two did not factor +prices would be equalized even without + + align:start position:0% +prices would be equalized even without + + + align:start position:0% +prices would be equalized even without +factor flows the thing that's mucking up + + align:start position:0% +factor flows the thing that's mucking up + + + align:start position:0% +factor flows the thing that's mucking up +the tie data is that there's a borrowing + + align:start position:0% +the tie data is that there's a borrowing + + + align:start position:0% +the tie data is that there's a borrowing +constraint so we have both real and + + align:start position:0% +constraint so we have both real and + + + align:start position:0% +constraint so we have both real and +financial flows + + align:start position:0% +financial flows + + + align:start position:0% +financial flows +subject to borrowing constraints and + + align:start position:0% +subject to borrowing constraints and + + + align:start position:0% +subject to borrowing constraints and +and the lecture 15 was what i reviewed + + align:start position:0% +and the lecture 15 was what i reviewed + + + align:start position:0% +and the lecture 15 was what i reviewed +at the beginning of class + + align:start position:0% +at the beginning of class + + + align:start position:0% +at the beginning of class +any questions about + + align:start position:0% +any questions about + + + align:start position:0% +any questions about + + align:start position:0% + + + + align:start position:0% + +okay well i hope you find these reviews + + align:start position:0% +okay well i hope you find these reviews + + + align:start position:0% +okay well i hope you find these reviews +useful + + align:start position:0% +useful + + + align:start position:0% +useful +i must say you should all feel really + + align:start position:0% +i must say you should all feel really + + + align:start position:0% +i must say you should all feel really +good because + + align:start position:0% +good because + + + align:start position:0% +good because +you're doing well in the class and we + + align:start position:0% +you're doing well in the class and we + + + align:start position:0% +you're doing well in the class and we +are covering a lot of material you know + + align:start position:0% +are covering a lot of material you know + + + align:start position:0% +are covering a lot of material you know +the constant themes here are + + align:start position:0% +the constant themes here are + + + align:start position:0% +the constant themes here are +theory data both + + align:start position:0% +theory data both + + + align:start position:0% +theory data both +lots of tools lots of concepts + + align:start position:0% +lots of tools lots of concepts + + + align:start position:0% +lots of tools lots of concepts +by now you're functioning like + + align:start position:0% +by now you're functioning like + + + align:start position:0% +by now you're functioning like +actual real economists and the + + align:start position:0% +actual real economists and the + + + align:start position:0% +actual real economists and the +conversations on piazza reflect that so + + align:start position:0% +conversations on piazza reflect that so + + + align:start position:0% +conversations on piazza reflect that so +i'm really happy with how the class is + + align:start position:0% +i'm really happy with how the class is + + + align:start position:0% +i'm really happy with how the class is +going + + align:start position:0% +going + + + align:start position:0% +going +and i hope you found this review to be + + align:start position:0% +and i hope you found this review to be + + + align:start position:0% +and i hope you found this review to be +useful and to be a reminder of how much + + align:start position:0% +useful and to be a reminder of how much + + + align:start position:0% +useful and to be a reminder of how much +you have learned + + align:start position:0% +you have learned + + + align:start position:0% +you have learned +all right thank you very much \ No newline at end of file diff --git a/JzpkXLH9zLQ.txt b/JzpkXLH9zLQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..e37296a5a39ff905d2e883b178935edf22fbc731 --- /dev/null +++ b/JzpkXLH9zLQ.txt @@ -0,0 +1,4005 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation, or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: Welcome to 6.172, +Performance Engineering of + +Software Systems. + +This is a fun class. + +It's all about going fast. + +We all like to go fast-- + +well, not all of us. + +But everybody in this class +likes to go fast. + +Otherwise you won't like +the class very much. + +It's all about making +stuff go fast. + +So a couple of brief +announcements. + +We're going to be videotaping +for OpenCourseWare. + +So if you don't want to be +videotaped, you should sit it + +in a place where the camera +won't catch you. + +Because we're in such a large +classroom, I'd like everybody + +to sort of every day, without +me having to draw-- + +I'm not really an artist. + +My sister's an artist, +actually. + +She's a painter. + +But maybe that gene +escaped me. + +It went that way and +not this way. + +So I don't want to have +to draw it up again. + +So everybody, try to confine +yourself to this sort of + +quarter of the classroom. + +And that way, it'll feel more +like a size room that + +we ought to be in. + +Let me go to our course +information sheet. + +Did everybody get a copy of the + +course information handout? + +So we're going to the class-- +we're going to start at the + +beginning with the Administrivia +stuff, try to + +run through that as +quickly as we can. + +And then my co-lecturer, +professor Saman Amarasinghe-- + +if you can't pronounce or spell +his last name, you can + +just say "Saman"-- + +will give today's lecture. + +And we have four teaching +assistants. + +So teaching assistants, +please stand up. + +They are Josh, John, +Reed, and Eric. + +And let me tell you, what they +have done in the last few days + +to get us ready for this course +is nothing short of + +superhuman. + +So you really need to accord +them your respect, and they're + +going to really work hard +to help you folks do + +well in this class. + +We have, I think, a pretty +decent ratio. + +I think even with concerns about +cutbacks, et cetera, to + +have four TAs for this +is really good. + +And we need it, because +it's a software class. + +And software is, as you know, +bugs can take an arbitrarily + +long time to find. + +You guys can sit. + +Besides our teaching assistants, +we have two + +support staff people helping us, +Mary McDavitt, who works + +for Saman, and Marcia Davidson, +who works for me. + +And they're generally pretty +good about being able to track + +us down if we're in +some far corner of + +the world or something. + +Our lectures are going to be +held on Tuesdays and Thursdays + +in this room, 2:30 to 4:00 PM. + +You should plan to +attend regularly. + +We dispense all kinds of +wonderful gems that you will + +miss if you think you're going +to get it just from reading + +and even looking at videotapes +or whatever. + +I'm not sure what our +arrangement is going to be + +about having videos available. + +OK, they're not going to be +available, except unless + +there's something really +extenuating circumstance. + +You have to go into a hospital +to have your forebrain removed + +or something-- + +something serious, OK? + +All material in the lecture, +even if it's delivered oral, + +is fair game for projects +and quizzes. + +We will post the lecture +slides, but they don't + +generally convey all +of the information. + +And we're going to be + +video-recorded, as I mentioned. + +If you don't want to appear, sit +behind the camera, and you + +won't appear. + +We have no recitations +in this class. + +However, the teaching assistants +will periodically + +hold primers where we will +bring you up to speed on + +various technologies that you +may not be up to speed in, + +such as C. How many people have +programmed in C before? + +And how many have not programmed +in C before? + +A few. + +OK. + +Tools such as VTune. + +Who's used VTune before? + +Who has not used VTune? + +Good. + +Pin-- who's used Pin? + +OK. + +Who has used Cilk++? + +OK, a couple people. + +So you see, we're going to have +some primers to bring you + +up to speed in those +kinds of things. + +We don't expect that you came +in knowing any of those + +things, particularly. + +We're going to be using +Stellar for our course + +management. + +And here's the URL. + +And you should make sure that +you're registered as a member + +of 6.172, because otherwise, +you're not going to get any + +announcements. + +We're going to do all of our + +administration through Stellar. + +So make sure that you're +registered there. + +At the end of today, I think +it is, we'll send out an + +announcement to the student +mailing list. + +If you don't get something +by the end today-- + +so you wake up tomorrow morning, +you have no email + +from the course staff. + +What that means is you +should email us. + +AUDIENCE: Well, that mailing +list would be the + +preregistered ones. + +PROFESSOR: That'd be the +preregistered ones. + +And then that way, we'll +get all the people. + +So if you know you're not +preregistered, you can send us + +email before then. + +There are two one-hour quizzes +given during class time. + +AUDIENCE: One and a half. + +PROFESSOR: What's that? + +AUDIENCE: One and a half hour. + +PROFESSOR: Oh, you're right. + +It's one and a half +hour quizzes. + +Yes, two one and a half +hour quizzes. + +We'll correct that in +the online version. + +Given during class time. + +Can somebody, by the way, +correct this as we go along? + +Great. + +The dates are on the course +calendar, which is available + +on Stellar. + +We've had mixed results with the +ICS feed from Stellar, but + +you're supposed to be able to +download the calendar to your + +iPhone or other ICS-capable +devices. + +But we were successful in +downloading, but all the times + +were screwed up. + +But anyway, hopefully, maybe +they'll allow that. + +But anyway, the calendar +is there. + +The quizzes will generally be +closed book and closed notes, + +but you will be permitted crib +sheets, one sheet that you + +summarize anything that you feel +that you need to know. + +Generally, everything that we +cover in here is fair game for + +the quizzes, including +things that are in + +prerequisite courses. + +There is no final exam because +we have a final project. + +This is a fast-moving class, so +if you get caught behind, + +it's not a good sign, because +it's really hard to work + +double-hard to keep +up in this class. + +You really have to keep +on top of things. + +And so for that reason +and others-- + +because it's really +difficult for us-- + +it's fast moving for +us as well-- + +we generally cannot accept +late projects. + +If you haven't been able to +complete a project, you should + +just package up your partial +solution and hand that in, and + +you'll get partial +credit on it. + +Do not just say, oh, I'm not +going to hand something in, + +and expect it to get +it done later. + +If you do find yourself in an +unusual situation which you + +think there are some extenuating +circumstances, + +like the aforementioned brain +surgery or something, let us + +know in advance. + +So if you're going to get in +a car accident, it's really + +helpful if you tell us the day +before so that we can plan. + +Obviously can't always do that, +but if it is something + +for which there is any +reasonable expectation it + +should be done beforehand, +you should let us know. + +And we may require, for those +kinds of exceptions, some kind + +of confirmation from a dean +or medical professional. + +So if that's the route that +you're in, you can plan a + +little bit and make sure that +those confirmations + +are on their way. + +The grading, this is essentially +approximately how + +we're going to grade. + +As you can see, there's a +bunch of content in the + +projects and a bunch +in the quizzes. + +And then there's also +participation grade. + +And the participation +is both in-- + +we will have design reviews and +such, so that's part of + +the participation, +as well as asking + +questions and such in class. + +And because we're +video-recording everything, we + +know exactly who's asking +questions, unless you choose + +to sit outside the video zone. + +In addition, if there is a +significant missing element to + +your work, it doesn't matter how +well you did on the other + +things, you will receive +a failing grade. + +You must, essentially, +do all the work. + +So if you do not get substantial +credit on the + +final project or any other two +assignments, for example, you + +can expect to receive +a failing grade. + +It goes downhill very quickly. + +If you're missing one +assignment, generally don't + +expect to get higher than +a C, for example. + +It goes downhill very, very +quickly, because that's what + +this is all about is hands on. + +What's permissible +in this class? + +So it's your responsibility to +satisfy both the letter and + +spirit of the rules. + +So if you have any questions, +let us know. + +Here's what the rules are. + +Also, let me just say how +Saman and I treat this. + +We have been involved in +cheating incidents off and on + +over the years. + +I've been at MIT almost +30 years. + +Saman, you've been here-- + +PROFESSOR: 13. + +PROFESSOR: 13 years. + +So we've been here long time, +longer than you folks. + +We've been through this +a bunch of times. + +It's really a pain when +somebody cheats. + +It robs me of a huge amount of +my time that I could otherwise + +be spending on teaching and +students and my own + +professional development. + +However, we both take cheating +incidents extremely seriously. + +So we have this thing that is +sometimes really inconvenient + +called integrity. + +And I'd rather, if I find +somebody's cheating, just give + +you an F and not deal with it. + +Drat. + +Instead, when somebody's +cheating, I tend to want to + +take it to the Committee on +Discipline, where you face + +things like expulsion, +et cetera. + +So I don't like to do that. + +It's very time consuming +for me. + +But I find it hard to just look +the other way, because I + +view the issue of integrity as +protecting the vast majority + +of students who are +obeying the rules. + +So when a cheating incident +occurs, I sort of feel honor + +bound to push it to its +proper conclusion. + +So please don't cheat. + +We will use a variety of means +at our disposal, including + +technological ones, to +detect cheating. + +Also, if you think that sharing +your results with + +somebody else means +that they're + +cheating and you're not-- + +in some cultures that's +the way it's treated-- + +no. + +In this culture, in particular +the culture in this classroom, + +they're both equally guilty of +academic dishonesty, whether + +you are the giver +or the taker. + +Equally, we treat that +as equal offense. + +So here's the particular +things. + +You may not share, generally, +your solutions with people who + +are not in your group. + +So we will have a bunch +of group projects, + +generally in pairs. + +And that includes both people +in the class and people + +outside the class. + +So generally, you keep +things to yourself. + +When you're in a group, of +course, you can share ideas + +within the group. + +But we expect that everybody's +making a fair contribution. + +So you should be concerned if +you are not holding up your + +end of your group +participation. + +And we're going to ask you to +describe the contributions of + +the people in your group. + +Generally, the group, +as I say, is two. + +So it's basically saying, +what did you do? + +How did you divide +up your project? + +What did you do? + +What did the other person do? + +You generally can't share +it with anybody else. + +You can't copy or transcribe +solutions from other places. + +The work you submit +must be your own. + +Pretty straightforward. + +You may go out and use general +conceptual material, such that + +you might get from a good +textbook or from Wikipedia or + +someplace like that. + +That's perfectly fine, resources +you would ordinarily + +have available. + +But if you do use any material +from an external source, you + +should properly cite it in +normal academic that fashion. + +Cite where it is so that +somebody else can go and find + +and look to see what it +is that you're citing. + +If you feel that you have +transgressed in + +some way, let us know. + +It always goes way easier. + +I generally tend to be kind of a +nice guy when somebody comes + +to me saying, oops, verses I +hear from somewhere else or + +one of our tools detects +something else. + +Then I'm kind of cranky. + +So I'd rather, if you come to +me, we could work something + +out, generally. + +Most of your out-of-class +time will spent + +completing six projects. + +And there's an outline of +what the projects are. + +They're all fun projects. + +You can ask the TAs. + +The TAs will tell you how much +fun they are, because they've + +generally helped to design +and built their own + +solutions to them. + +Some will be done in pairs, +some individually. + +The final project can either be +done in pairs or in threes, + +I think we said. + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: Yes, we also have-- +we didn't put that in here. + +We also have a Project 0, which +will be available today + +after class. + +So you should go to Stellar +and get Project 0. + +Project 0 is not to +be handed in. + +It's getting warmed up with all +of the machines and tools + +that we'll be using +in the class. + +We have been very fortunate to +have very nice contributions + +from Dell and Intel of a new +Cluster facility that has 16 + +12-core machines. + +And they're Intel Core +i7 machines. + +Each chip has six cores, and +there's two cores per machine, + +each with 48 gigabytes +of memory. + +So these are kind of honking +modern facility. + +So as I say, it's fun. + +It's fun when you do something +on your laptop, and then you + +go and you do it on one +of these machines and + +it goes like this. + +It's really fun when these +things go fast. + +So Project 0, you should +start on today. + +And it's basically the handout +called Getting Started. + +It will be available +on Stellar. + +And it will take you through +getting access to these + +machines and so forth. + +In particular, in order to use +these machines, you must have + +a CSAIL account. + +Who does not have +a CSAIL account? + +So that is going to be the first +thing you need to do, + +because you've got +to get that. + +So what you want to do is get + +registered for a CSAIL account-- + +and we give instructions +in there. + +It's basically going +to a web page-- + +pretty much as soon as you +get out of the classroom. + +Because you won't be able to +start anything until you have + +this CSAIL account. + +And hopefully, we'll be able +to give you access within a + +few hours after you register. + +Yeah, question? + +AUDIENCE: What operating +systems are the tools-- + +PROFESSOR: Linux. + +We'll be using Linux. + +So there are a variety of ways +that we describe for how you + +use these machines remotely. + +We have the Andrew +File System-- + +AFS-- + +which you can use so that you +can edit things locally but + +have an SSH terminal window on +the machine, which makes it + +very convenient. + +On the other hand, for some +people, often some dorm rooms + +with poor connectivity, doing +things by AFS may be + +too slow for you. + +But there are a variety of other +ways that you can-- you + +can actually edit right +on the machine. + +And there are a variety of ways +of having a repository on + +your machine, because we'll +be using Git as + +our versioning mechanism. + +So you'd be able to have it +there and be able to make + +copies back on the +other machine. + +So there are a variety +of ways to work. + +And you're free to make the +software run on your own + +laptops or workstations. + +The one thing I'll say is we +will not support that. + +We don't have the resources to +support beyond using the + +machines that we actually +provide. + +I think I've got to +go faster here. + +So let's see. + +So software engineering. + +So research in programmer +productivity has demonstrated + +that pair programming, where two +programmers sit together, + +one at the keyboard and one +looking on, is actually faster + +than two programmers +coding separately. + +Why do you suppose that is? + +Yeah? + +AUDIENCE: You don't get stuck. + +The other person can tell you-- +it's like when you're + +[INAUDIBLE] writing on the +blackboard, you get nervous. + +You don't know what +you're doing. + +[INAUDIBLE] + +PROFESSOR: Yeah, you +could be stuck. + +What else? + +AUDIENCE: You don't +procrastinate. + +PROFESSOR: Yeah, you don't +procrastinate. + +That's a good one. + +Don't procrastinate. + +AUDIENCE: Finding bugs. + +PROFESSOR: Yeah, finding bugs. + +So the main one is finding bugs, +that the person who's + +looking on finds bugs. + +In fact, I was just pair +programming with Reed the + +other day, and we were trying +to figure out, why is this + +thing not working? + +And I say, gee, it looks fine. + +It says, next y equals x. + +And he says, no, next y is +supposed to equal y. + +And it's like, we had both read +over that code, but as + +soon as I spelled it out, +I didn't even notice. + +But of course, him in hearing it +says, oh, it's supposed to + +be x and y and y, not x and y. + +So anyway, that kind of thing, +you pick up very quickly. + +It makes it very +easy to debug. + +Likewise, regression testing +demonstrably promotes fast + +co-development. + +So this is where you build a +battery of tests that includes + +tests for every mistake +that you've ever made. + +And it can also be helpful to +write unit tests, where you + +test individual ones. + +And you should also use tools +like the assert package. + +And some of these things will be +taken through in Project 0. + +The MIT POSSE. + +We have recruited senior +software engineers in the + +region to share with you their +invaluable knowledge and + +experience. + +We call them Masters In The +Practice Of Software Systems + +Engineering, which has the +great acronym MIT POSSE. + +These are people who +are not being paid. + +And they're senior. + +They're doing this because +they're volunteering, because + +they want to help. + +You have a lot to learn from +these people, and we will have + +code and design reviews with +these people with your + +assigned master. + +You want to treat them nicely. + +They're not doing this so that +some snotty-nosed kid can say, + +I don't care about you. + +That's not what they're doing. + +They're there to help you +get a good grade. + +And these are some really +talented people, people who + +are very famous in their +own areas of expertise. + +So be gracious, is the main +thing I would say. + +Be gracious. + +Let's see. + +The assignments. + +You can read about +the assignments. + +Basically, generally, what we're +going to do is have a + +beta submission in which we're +going to test everything. + +And we're also going to +take all your tests. + +We're going to throw all the +tests into a big pool and run + +everybody's tests against +everybody software. + +You will lose points if you +fail some of the tests, + +assuming the tests are +correct tests. + +You will lose points if you +have an incorrect test. + +You will lose points if somebody +passes your test and + +they have a bug. + +You will get points if your test +picks up something that + +very few other groups +tested for. + +So you have to both submit code +and submit tests, which + +is OK, because you've got to +test your own stuff before you + +hand it in. + +But we're also going to be using +it to test each other. + +After beta, we will have a +design and code review with + +your master. + +And let me just say, the +master's there not affecting + +your grade in any way. + +They do give us reports about +what happened in their + +meeting, but they have no +bearing on the grade. + +They're just there to help. + +So you don't have to +view them as-- + +they're not part of +the course staff. + +If you want to get angry at +somebody about how things are + +done, get angry at +Saman and me. + +Don't get angry at them. + +The final submission is +generally due a couple weeks + +after the beta. + +And it's after you've gotten +feedback on your design, + +feedback on things. + +We'll give you the whole +battery of everybody's + +regression tests, so you can +test out your code against + +everybody's regression +test and use that. + +And then generally, the scoring +is such that people + +who get fast code +get high marks. + +People who get slow codes +get lower marks. + +If you need help, +[UNINTELLIGIBLE]. + +Speed is fun. + +Enjoy the class. + +Yeah, question? + +AUDIENCE: In terms of +the bug testing, I'm + +thinking of bugs like-- + +I don't know-- + +[INAUDIBLE] + +or something like that. + +If you happen to not have made +a bug in your own program + +[INAUDIBLE] + +would that count against you +in the final testing. + +PROFESSOR: You have to view +your beta test as testing + +other peoples' code also. + +PROFESSOR: But if you +[UNINTELLIGIBLE] a test that + +finds bugs in somebody's +program, and if very few + +people wrote that test, then +you will get points. + +So you don't have to test for +the world, everything. + +If you fail somebody's test, +but not yours, you will be + +deducted points. + +If your test finds other +people's bugs, you will gain + +points for that. + +But on the other hand, if you +don't have a test for-- + +what you said, I think you don't +have to go and test for + +every possible condition +in there. + +The negative side is, if +you miss something, + +we will deduct points. + +Positive side is, if your test +finds somebody else's bugs, + +you'll get points for it. + +We'll go into detail exactly +how [UNINTELLIGIBLE]. + +Another thing we did last +year, which was kind of + +interesting-- + +I think there were mixed-- + +some people really liked +it, some people + +were not that happy-- + +is a little bit of competitive +grading. + +So here, what we are doing +is not the full grade-- + +small part of the grade. + +What you do is when you first +submit your beta, rerun + +performance tests +of everybody. + +And of course, one of you +are going to get the + +fastest code for that. + +At that point, we are going +to say, OK, this + +is the fastest code. + +And how [UNINTELLIGIBLE] + +everybody else with that code? + +And the person who gets fastest +code for that part of + +the grade gets the +full points. + +And everybody else will get a +partial part of the points. + +However, you get a chance in +your final submission to + +basically improve your code. + +If you do better than the last +time's best code, you won't + +get any more additional points, +because then we don't + +want to create +[? an arms race. ?] + +So you at least had to +match the previous + +times to get full points. + +So you get a chance to see how +you stand against your peers + +and get a chance to actually +[UNINTELLIGIBLE] math with + +your peers. + +So first time we did it, we +said, OK, it's the fraction of + +your performance against the +performance of the best code. + +The problem was, there were a +couple of codes that 1000x + +performance improvement, +and everybody got 10x. + +So you've got, like, +0.25 grade. + +That didn't help. + +So now we actually are doing +a logarithmic log scale. + +So we'll get the fraction, and +we'll take the log off that. + +So there will be a little +bit more equality. + +So you will know how worse off +you are, and you get a chance + +to [UNINTELLIGIBLE]. + +Because it is very important, +because a lot of times, there + +might be a crucial thing +that you missed. + +And instead of trying to be, +"aha, got you" in this class, + +we are trying to give you a +chance to actually learn. + +So if you missed it, OK, you +missed it the first time. + +But you get the second chance +to come and fix it and see + +whether you can do well. + +And of course, if you do better +than the best grade, + +there are bragging rights, but +you don't get extra points. + +With that, let me-- + +where are we? + +So again, as Charles pointed +out, I'm pretty excited about + +this class. + +This is a really fun class. + +Unfortunately, I'm a little +bit under the weather. + +So I'm going to sit down. + +And if I don't sound that +enthusiastic, hopefully I'll + +get enthusiastic later. + +And that's one reason we ask you +to come forward, because + +we don't have to come +here and shout. + +So hopefully people in +the back can here. + +If you don't, still, there are +some seats in the front. + +You can move forward. + +So for the rest of the class, +what we want to do is go + +through an example and look at +why performance matters. + +For that, I selected +matrix multiply. + +And I think your Project 0, +you are going to also play + +with matrix multiply. + +And I think that you'll get a +feel for what kind of things + +will happened and how much +room you have in + +doing well in here. + +And at the same time, as I go +through this, you'll get a + +feel for what's the process that +you might be following + +through the class and what +kind of things-- + +because linear programming, +after taking a bunch of + +programming classes, probably, +you have a methodology set up + +in your mind, how to go +about doing that. + +And the same thing after this +class, we want you to have a + +methodology of going through +and improving performance. + +And this is basically a little +bit of a contrite example, but + +you'll get a feel. + +So what's matrix multiply? + +It's a very fundamental +operation for many + +computations. + +So you are going to produce +Matrix A by multiplying Matrix + +B and C. So you want to +calculate each value in here + +to take a row of B and a column +of C, and you get each + +element of A. And you do that +for every element of A. And + +this is the possible simplest +code you can write in a + +language like C, a +[? three-loop nest, ?] + +and this matrix multiply. + +So, so far, things should +be pretty simple. + +So what I did was I looked at +matrix multiply and said, + +look, you have taken software +engineering class. + +You have thought about +object-oriented programming, + +lot of nice techniques +to build very + +useful, portable software. + +And let's try to write +matrix multiply with + +some of those concepts. + +So the first thing I want to +do is matrix multiply write + +object oriented using immutable +classes, and that, + +in fact, I want matrix class +to represent both + +integers and doubles. + +So here's my class +structuring here. + +And actually, I'm going to show +you a bunch of code now, + +next couple of slides. + +I'm not expecting you +to follow everything + +instantaneously. + +I'm going to go through +somewhat faster. + +But you have the slides. + +So I always expect you to, +perhaps, in some free time, to + +go and look at some of the +slides, get a little bit of + +better feel for what happened. + +So here's what matrix +multiply does. + +I have a value class that +figures out the matrix type. + +And if it's integer, +it keep integers. + +If it's a double, +I keep a double. + +And here, basically, do +this value in here. + +And then I have a +matrix class. + +Basically, given a matrix type +and a matrix, it can create a + +matrix here. + +This basically creates your +matrix in here by first + +creating a bunch of rows here, +and then instantiating each + +row in here, whether it's +integer or double, depending + +on the type you want. + +And then, of course, there are +other things in matrix, + +basically, in here. + +And you can update a matrix. + +This is going to be a little +bit interesting. + +I will give a little bit here, +because what I'm going is I'm + +doing immutable types. + +That means I can't change +anything in the matrix. + +If you are updating, you have +to create a new matrix. + +So I'll show a little +bit about how to + +go about doing that. + +And then there's +this row class. + +I'm going through this +fast, because + +it's not that important. + +If you get a chance, go through +this and get a feel + +for what I'm doing. + +But the idea is doing this very +software engineering way + +of implementing a +matrix multiply. + +So then here's my matrix +multiply in here, that what + +I'm doing is I'm updating each +of these matrices by giving a + +value of B and C and +adding it to A and + +updating A again in here. + +So when I run matrix multiply, +1,024 by 1,024 matrix, this is + +the time I got. + +Actually, it took a long +time, in fact. + +And the key thing, is the +performance good? + +That's the first question +to ask. + +Because you run, you +get a result. + +When the result is correct, +OK, great. + +You get the correct result. + +But how do you do? + +And this is sometimes a very +hard thing, to know that you + +have a problem is itself +a huge win-- + +that you figure out you +have a problem. + +And what I'm going to do is go +through a little bit of a + +calculation to see +how we did it. + +It took about five hours to do +this matrix multiply, and that + +doesn't look right already. + +So if you think about matrix +multiply, it's an N-cube + +operation, basically, what +matrix multiply is doing. + +That's the algorithmic +[? class. ?] + +If you look at Charles' book, +that's what it would say. + +It's N-cube operation. + +So this is the number of +operations you want to do. + +And for each matrix operation, +you only do three index + +updaters, add, a multiply, +and a check-- + +probably six ops to +do, basically. + +And that means I need to do +this many operations. + +Basically, you can think about +machine operations to do, + +basically, because you have to +read three values, update one, + +do a multiply and add, +and do a branch. + +And if I look at that with my +hours, I am doing this many + +operations per second, +which looks high. + +Big number. + +But my machine, actually, on my +somewhat old PC, transfers + +even much faster. + +So if you think about it, I am +taking about 8,300 cycles to + +do any kind of a machine +operation. + +This doesn't look right. + +So at this point, this is what +I would call a "backup + +[UNINTELLIGIBLE] calculation." +I haven't proven anything. + +This one worked well in the +theory class, but if you can + +just jot down a couple of these +things, you can get a + +feel for where you +stand very fast. + +And then you realize, OK, I +am a couple of orders of + +magnitude off here on what +best I could do. + +And that should give you a +feel for what's going on. + +OK, so what's going on here? + +How can we improve +performance? + +Because we know we +have a problem. + +So what we can do is +we can look deeply + +into the program execution. + +And at some points, OK, this +program runs slow. + +[UNINTELLIGIBLE] + +time spent. + +So we can figure out time spent, +basically, things like + +by method-- + +which method you spend most +of the time running. + +Sometimes by line. + +And we will learn a bunch of +profiling tools that will give + +you this feel. + +So instead of reading a million +lines of code, looking + +at every line in there, you can +very fast converge onto + +the culprits where most of +the time being spent. + +And that's a very easy way +of triaging your problem. + +And you look at things like time +spent, cumulative time + +spent within that and everything +called underneath, + +number of invocations +of the functions. + +And a lot times, you have a feel +for what it should be. + +And when you look at this, if +it doesn't look right, you + +say, wait a minute, this goes +against my intuition. + +Perhaps there's a problem. + +So what you can do is, by +doing this, you can + +identify hot spots. + +Basically, if 90% of the time +it's it one routine, that's + +what you want to fix. + +And hopefully, that routine is +doing something too slow. + +Then you can actually get good +performance in here. + +So here's the profile I ran +for a matrix multiply. + +And interestingly, what I found +was, most of the time + +spent in basically creating +doubles-- + +number of calls, time spent +here, this much time was + +spending, basically creating +new values in here, this + +initializing a double in here. + +So I'm doing matrix multiply. + +Why should I be initializing +values? + +So this is an issue. + +And I have the most number +of calls to that too. + +So we can go look at it and say, +hey, that would seem to + +be a problem here. + +So the problem here was +kind of obvious. + +What happened was I didn't use +immutable [? class. ?] + +So this is my matrix +representation. + +I have a bunch of pointers +pointing to each row. + +And now assume I won't +update this element. + +And of course, I can't modify +the entire thing. + +It's immutable. + +So what I had to do is create +a copy that updates. + +And then, of course, I had +to create a new matrix. + +I don't have to copy everybody +else, because these guys were + +not changed. + +So I can place a pointer to +these things and create this + +new matrix that points +to these things. + +And then, if you think about +what's going on, in fact, and + +this is my new matrix after I +do that, I [? updated ?] two + +end copies for each update, +because what I had to do is I + +had to copy this entire +row up to get that. + +And I had to create this entire +index again for each + +point in each row. + +So just to update one element, +I am creating two end copies. + +So what that means is now our N +cube matrix multiply ends up + +being N to the power +of 4 algorithm. + +So suddenly, you realize, wait +a minute, I'm doing something + +bad in here. + +I'm actually [UNINTELLIGIBLE] + +N-cube algorithm, and the way +I saw, it becomes n to the + +power of 4 because I'm making +all these copies in there. + +So this is a bad thing +to do, of course. + +And copying is very costly, +because you're making + +duplicates in here. + +And of course, you're creating +a huge amount of garbage, + +because you are just copying and +leaving the previous value + +for garbage collection. + +So garbage collector's coming +up all the time, and huge + +memory footprint. + +So this is no good. + +And can we do better? + +Hopefully, we can. + +So the next thing we did was, +OK, just get rid of these + +immutable types. + +That seemed to be a +[UNINTELLIGIBLE] + +here. + +And then, I actually have-- + +I will go faster over the +code, so if you are + +interested, you can go look +at the code in here. + +So here, what we did was, still +we have the issues like + +object oriented and ability +to represent both + +integers and doubles. + +So what that means is each +matrix can be the integer + +matrix or a double matrix. + +So this is where you're +instantiating with integers or + +doubles in here. + +So we do that. + +And how much you think this +can improve performance by + +doing that? + +In fact, this was pretty nice. + +I actually got a 219x +performance improvement + +because I went from n to the +power 4 algorithm to n to the + +power 3 algorithm. + +So here is interesting, +algorithm has changed with it, + +and we have a pretty nice +performance improvement. + +So if I look at this now, what +I find is I'm spending a lot + +of method time, I'm doing +matrix multiply. + +That's good. + +But I'm spending all +this time doing get + +double and get methods. + +I'm trying to do matrix +multiply. + +Why am I spending all this +time trying to do + +get double and get? + +What I found was issue is the +method call overhead. + +Now, what happened is matrix row +has two different matrix + +types, the integer row +and double row. + +So every time I want to get a +row, I don't know if I have + +integer row or double row. + +I have to do a look-up to +figure out my type. + +Am I working with the integer +matrix or matrix in doubles? + +And this is what we call +"dynamic dispatch." So instead + +of knowing exactly the methods +we are to go, I had to + +actually look up, OK, which +method I'm supposed to go. + +I have to do that since, if the +matrix is integer, I might + +have to call a different method +than matrix is double. + +I have to check that. + +And then that call, instead +of direct call, + +becomes indirect branch. + +I have to check that and +basically branch on that. + +And these indirect branches are +costly, because what that + +means is I don't where I am +going until I do that test. + +So no machine-- + +we'll go into details +and pipelines and + +stuff as we go on. + +What that means is normally, +a machine can have a lot of + +instruction in flight. + +So that means that I have to +know a lot more information to + +get the instructions going. + +But here, until you resolve the +instructions, you can't do + +the next one. + +So it's called a, basically, +pipeline stall. + +So instead of having hundreds +of instructions going, + +basically, suddenly I can't do +anything until the previous + +instruction is done. + +So the machine slows down +a lot because of this. + +Normally, what you can do +is keep fetching next + +instructions here. + +We have to fetch, test, then the +test result is available, + +then that's when you can fetch +the next instruction. + +Let me go through that file. + +So direct batch means target +address is known. + +You can fetch ahead of the +targets/ If I know where I am + +going, even if I don't get +there, I can fetch ahead of + +the target. + +I can go start fetching what +happens next ahead, basically, + +into [? the branch. ?] + +Sometimes, you can even fetch +both directions, or the + +direction you might always +go might get + +fetched by the architect. + +We'll talk about a lot of +architecture details in the + +future lectures. + +Indirect branch means until I +calculate the address, I have + +no idea where I'm going. + +That address is only +calculated. + +And because of that, hardware +slows down like crazy. + +So this seems to be not a good +thing to have these integers + +and doubles instead of having +one nice class of just + +[UNINTELLIGIBLE] + +might be nice. + +I just basically create +a double class. + +It's all matrices are doubles. + +If I want integers, I will just +rewrite my matrix class + +or copy and replace. + +Now my matrix class becomes +much more simpler. + +This is what I got, and this +is my row in here. + +And voila, minute I do that, I +basically went up about a 2.4x + +performance improvement, because +now I don't have to + +keep doing that. + +And altogether now, I have +improved my performance by + +about 500x here. + +And for ops per cycle, we +have gone down from + +8,000 to 38 to 16. + +So we do still better. + +And now we look at, again, +my profile data. + +And what I see is, OK, I am +spending a lot of time in + +matrix multiply. + +That's OK. + +But also, I am spending time +in this matrix get method. + +I am trying to get each, +basically, row and data + +elements of the matrix. + +So here is the summary +of these things. + +I'm going to just keep that +one, because I gave you + +[INAUDIBLE]. + +So the problem in this +object-orientedness is I + +[? handle ?] each row is +represented separately-- + +nice objects. + +These objects overload +the memory. + +And in fact, if I want to get to +my row, I have to appoint a + +[? chase ?] + +to go get that. + +It's not contiguous in memory. + +And to get to every row, I have +to actually go through + +this [? point ?] indexing +in here. + +[UNINTELLIGIBLE] matrices are +one, nice, simple objects. + +So we can say, OK, +wait a minute. + +This method call overhead +actually keeps dominating. + +And because I have done this +nice object-oriented thing in + +here, so I can get to the +object-oriented file here and + +say, OK, get to the objects. + +And I write this nice loop +of [UNINTELLIGIBLE]. + +And I have two-dimensional +matrices in here. + +And voila, I got another +2.2x performance + +improvement in here. + +OK, now I am down to about +seven cycles for each + +operation in here. + +That's good. + +So what can we do here? + +So we did all of these things in +Java, because it's supposed + +to be a nice language. + +But Java has a lot +of overhead. + +It's like you do memory-bound +checks. + +You have to do this bytecode +interpreter + +and stuff like that. + +On the other hand, C can +run much faster. + +You don't have to do any kind +of memory-bound checks. + +The compilation happens before +you run, so it is not part of + +your cost of doing anything. + +So this can work very much like +C. You can just almost + +cut and paste. + +And if you know, C is +[? index chain, ?] + +[? and this ?] + +to C is just changing +a few lines. + +And I did that, and this is, +basically, the C code in here. + +This is the matrix multiply. + +This is the kind of allocation +in here. + +C can be a little bit +painful to allocate. + +This is my matrix multiply. + +It will look similar. + +And I got 2.1x just by going +from Java to C. This, I was + +surprised, because that piece of +Java code looked very much + +close to C. But by just doing +that, I actually got another + +2.1x performance gain. + +Now this is kind of the +high-level stuff. + +Now we have to go +to nitty-gritty + +details in the hardware. + +So in modern hardware, there +are these things called + +"performance counters" that +hardware [UNINTELLIGIBLE] + +that we can look at what's +happening inside hardware. + +We can get a feel for what +happens inside hardware. + +And there are things called CPI, +which clock cycles per + +instruction. + +So that means if the +instructions are running very + +slow, you will have multiple +clock cycles per instructions. + +That means instructions +are stalling. + +Something is wrong. + +Cache misses. + +So data [UNINTELLIGIBLE] + +[? pay attention to ?] + +caches and stuff like that. + +If data are supposed to be in +cache and have cache hits all + +the time, but if you are +getting cache misses, + +something is wrong. + +Accesses are not good. + +And then also the instructions +retired. + +That means, how many +instructions are being + +executed and retired? + +If you are doing too much +work, the number of + +instructions retired will +go high in here. + +This will give you a few how +many [? work been done. ?] + +So if you look at this one, +I have a CPI of 4. + +That means for every +instruction, need about almost + +close to five clock cycles, +which is not good. + +I have pretty high cache +miss rate, too-- + +L1 cache miss rate and some +L2 cache miss rate. + +This shows how many instruction +are in what they + +call [? vector in the ?] +instruction form called SSE + +instructions. + +And here's the number of +instructions got retired. + +So we just use that +baseline case. + +So one thing I can look at was +my cache miss rates seem to be + +pretty darn high. + +What might be happening here? + +So if you look at matrix +multiply-- + +so I have Matrix A in +here and Matrix B-- + +what happens is, to calculate +this value in [? Matrix A ?] + +here, basically, I'm going to +go through this row in here, + +and I'm going through +column in here. + +Problem with the column is +it's all [? low in ?] + +the cache. + +This is your linear memory. + +So because this is here two +dimensional, but inside your + +hardware, there's no +two-dimensional memory. + +You have a linear memory, so +this is your linear memory. + +This is how the memory +look like. + +And this is how the +memory look like. + +So each row and column +is in these areas. + +But here, to calculate this +value, this is nice. + +I go through memory that +is contiguous. + +But C, I am jumping all +over my memory. + +And jumping on memory is not +that great cache behavior. + +And contiguous can do much +better, because what you do + +is, when you get a cache, you +get a cache line that has more + +than one word. + +So in here, what you're doing is +you are getting large cache + +lines only using one word before +you go to the next one. + +So that's not great +in cache behavior. + +So what you can do is you can +make this memory contiguous. + +So what you can do is, in matrix +multiply, normally, n + +to the cubed computation +to the squared data. + +So to help on n to the cubed, +it's OK to do some n to the + +squared processing. + +That means you can do a data +transport before you start + +matrix multiply. + +Do some pre-processing. + +So this will also +come in handy. + +A lot of these problems you'll +do, you'll say, wait a minute, + +can I do a pre-process that's +cheaper that will really + +improve my main processing? + +This is a theme that comes +again and again. + +And then we can get this n to +the cubed running faster since + +this n to the cubed is much +larger than n to the squared. + +You can amortize the +cost of doing that. + +And basically, to get that, we +can transpose some matrix + +going into the squared +operations. + +And then now n to the cubed +might run much faster. + +And in fact, what I have done +here is do the transpose of + +this matrix. + +And now we run this one, and +then everything will be in + +contiguous memory. + +And voila, I got another 3.4x +performance improvement. + +Now I am running almost +at one cycle per op, + +which is really nice. + +But modern superscalars actually +can do better, so we + +can actually end up +being even better. + +So let's see. + +So we are doing that. + +So here is the interesting +thing. + +Now I look at my transpose +[? spot. ?] + +So if you look at that number of +retired instructions, it's + +more or less the same. + +Number of SSE instructions, +more or less the same. + +I have a 2x improvement in +my L1 cache miss rate. + +But more than that, I have a +5x improvement in the CPI. + +That means my instructions +are stalling a lot + +less now than before. + +So this is where I got all my +performance [UNINTELLIGIBLE], + +because my instructions are +running much faster. + +So by looking at data-- + +this is the kind of +things you're + +learning during the class-- + +then you can get a feel for what +actually is happening and + +why you are getting that. + +You can go do more in the +cache, in memory system. + +So remember, the memory +system, if you're + +[UNINTELLIGIBLE], if you look +at cache, what they're doing + +is we have a small amount of +memory called cache that are + +very fast access. + +And you have a large amount of +memory that is sitting out + +that has slow access. + +So what you want to give user +feel as if they have a lot of + +memory, everything is +very fast access. + +So hardware does a lot of crazy +things to give you the + +illusion that you have very +fast memory and you have a + +huge amount of that. + +Of course, that's not true, +because you have these caches. + +And what happens is, if +you do things wrong, + +these get to slow down. + +So in the cache system, you have +cache [UNINTELLIGIBLE] + +You have each multicore going to +its own L1 cache that goes + +L2 cache, which goes to L3 +cache, which goes to the main + +memory system. + +And you want all of the +data to be here. + +If that's the case, things +run very fast. + +If not, you have to go here. + +It will be a lot more +slow, here, even + +slower, here, very slow. + +So the key thing is to get the +data as much as possible here. + +So here's the kind of +cycles, basically. + +One cycle to get here-- +three cycles. + +If you go to L2 to L3, you +have to do 14 cycles + +[UNINTELLIGIBLE]. + +If you go to L3 to main memory, +you might sometimes + +get hundreds of cycles +delaying here, + +so it's very costly. + +So the caches are very +temperamental beasts. + +They work beautifully, but when +they don't work, these go + +really haywire. + +So a lot of times, if there's +a performance issue, look at + +the cache miss rate +and say, aha, the + +caches are not behaving. + +And can I help in here? + +So the interesting way +to look at that is + +how much data I touch. + +These graphics didn't show up. + +Let me explain. + +So if you do matrix multiply, +I am trying to calculate one + +value in here. + +So this is one value. + +I have to calculate row +and the column. + +This slide got screwed +up a little bit. + +So just look at this calculating +[? row bar. ?] + +So if I want to calculate a +row of values here, what I + +have to do is I have to get this +row in B, and I have to + +use entire C to calculate one +row of A. That means I have + +touched this much data items +just to get one row of A. So + +that means I am calculating +1,024 values of A. I am + +touching this much data +items to get that. + +On the other hand, if I do block +matrix multiply, that + +means I calculate, basically, +a block in here. + +This block is also 32 by 32. + +It has 1,024 elements in here. + +But I only need a block +here and block here. + +Voila, I only have looked +at 25,000 elements. + +I got the same number of +output calculated. + +But I have only touched much +less elements altogether to + +calculate that. + +Do you see that? + +And nice thing is, if this thing +fits in the cache, I am + +much better than this might +not fit in the cache. + +So I can calculate blocks in +matrix multiply by looking at + +a lot less number of data, +that has a good chance at + +fitting in cache-- and of +course, when you calculate. + +you make sure it +fits in cache-- + +than trying to just calculate +row by row. + +So one thing you can do is-- + +this is a lot of common +things we do. + +There's many ways to +get same results. + +You can change the +execution order. + +You can change the algorithm. + +You contain data structures. + +And some of them actually +might do + +better than the other. + +And here, we can actually say we +can do the execution of the + +change and make sure we are only +looking at small amount + +of data, you get the same number +of data calculated. + +And of course, sometimes you +have to be careful, because if + +you do things in different +order, you might not get the + +exact same results. + +So if you are a numerical +[UNINTELLIGIBLE], you say, OK, + +of course, if you're doing A +plus B plus C, what order you + +do will make a difference +[UNINTELLIGIBLE]. + +So if you're really careful, you +can't do too many things. + +But most times, you can do +some of these things. + +And in fact, in our final +thing, we might say-- + +the final project-- + +we will give you something +that you can change the + +algorithm as long as the outcome +of the [? image ?] + +is the same. + +If you look at the [? image, ?] +and the + +[? image ?] outcome +is the same, you + +can go change things. + +So a lot of times, you might +have a lot of freedom to + +change the amount of errors you +get, the precision, and, + +in fact, doing that, that you +can actually get a lot of good + +performance. + +So in here, we are not trying +to change the matrix + +multiply, of course. + +But we are going to change the +way order of operations is + +being done. + +So some people say you +can't do that. + +It would make matrix +multiply different. + +But in most cases, it's OK. + +So what we have done is +done what we call + +block matrix multiply. + +So instead of calculating +rows, you + +calculate blocks at a time. + +So calculating each block, +you only need a + +few amount of data. + +So this is block matrix +multiply. + +And voila, by doing block matrix +multiply, I got even + +1.7x performance +gain from that. + +Now, it's very interesting. + +Now with each block cycle, I +am doing two operations. + +So my [? superscale ?] + +is finally coming to being. + +So every clock cycle, +I am doing + +multiple operations here. + +So this is very interesting, +the number here. + +So now when you look at what +happens here, I am actually + +executing a little bit more +instructions here. + +Why? + +Because I did block +matrix multiply. + +That means I am doing a little +bit more overhead in here. + +I have more loops in here. + +My inner loops are small. + +So I'm doing more instructions +to do execute there. + +So I'm doing more instructions, +but I have a + +huge cache performance gain. + +My cache miss rate now going +down to very, very little-- + +0.02%. + +And I have an 8x improvement in +cache, and that means I got + +a 3x improvement in +my CPI in here. + +That's very nice. + +That means even though I'm doing +a little bit more work, + +my cache behavior really, really +helped me in here. + +So kind of says why I am getting +this performance gain. + +So what else can we do? + +We can go look at trying to do a +lot more crazy optimizations + +because if you look at the +modern Intel, they have this + +thing called [? retro ?] +instructions. + +We'll get a little bit more +detail into that later. + +And what we can do sometimes is +you can nudge the compiler + +to take advantage of +these instructions. + +Of course, if nothing helps, you +can actually go write to + +assembly [UNINTELLIGIBLE]. + +But hey, I don't want you guys +to write assembly code, at + +least in this class, even though +you can get really good + +performance sometimes. + +But you can kind of give enough +hints to compiler and + +pray and kind of +[UNINTELLIGIBLE] + +there's no nice way on these +things, and hope for the + +compiler to do the +right thing. + +So in here, we can play +with, a lot of + +times, compiler flags. + +And this is not exact size. + +We keep trying those things, and +sometimes we can even get + +information back and say, OK, +what did the compiler do? + +It might give you some good +hints and say, I couldn't do + +something because of this +part of the code. + +And worst comes to worst, you +can actually generate assembly + +and stare at it. + +And sometimes in this class, +you might actually want to + +stare at assembly and see +what goes on in here. + +So here is the assembly +for here. + +And this is my loop +body in here. + +And then what I can see, I'm not +going to go through that. + +Everything is converted +into SSE instructions. + +At least I know what SSE +instructions mean, so this + +seems to be doing well, +so I'm happy. + +And in fact, I'm really happy +because I got a 2.8x + +improvement by doing this. + +Now what I am actually doing +each clock cycle about + +[? five of my ?] + +operations. + +So I'm going really +fast in here. + +So now, incidentally, I'm +running my program about + +30,000x faster than +when I started. + +So if you haven't noticed, +these things + +slowly add up in here. + +And now, if we look at what's +going on here, it's very + +interesting. + +What I have done is actually, my +each instruction is now CPI + +has gone down. + +That means each instruction is +running slower because I'm + +doing these SSE instructions. + +And in fact, my cache miss +rate has also gone up. + +But I am doing a lot less +instructions, because SSE + +means in one instruction, +I am doing a vector. + +So I'm actually getting four +operations done in one + +instruction. + +So the number of instructions +I execute has + +drastically gone down. + +So even though my instructions +are running a little bit + +slower, I can basically amortize +that, and I get good + +performance in here. + +And of course, this one says, +OK, now 88% of the + +instructions are SSEs. + +So I have [UNINTELLIGIBLE] + +most of the things to run +on vector mode in here. + +And of course, you can keep +doing more and more and more. + +And there are these four things +[UNINTELLIGIBLE] matrix + +multiply, there are people who +spend their entire lifetime + +trying to run it faster. + +And they have libraries like +that, and this thing called a + +BLAS library and this thing +called Intel Math Kernel. + +So they have done a lot more +other things, like + +pre-fetching, getting +everything right. + +So here what I do is basically +call their library, don't do + +anything myself, and this +library will do it for me. + +And in fact, that library itself +gave me another 2.7x + +performance gain in there. + +Now I'm actually doing 11 +instructions every clock cycle + +by doing that. + +And if I look at it carefully, +what they have done is they + +are also very into SSE heavy, so +they are running almost the + +same amount of instructions. + +But they managed to actually +get, again, + +a better miss rate. + +They probably figured out some +stuff in here, things like + +pre-fetching instructions. + +And that means they actually +brought down the CPI back to + +where it was before. + +And that's why they gave that +performance [INAUDIBLE]. + +And finally, we are +doing a little + +bit of parallel execution. + +So as you know, multicores +are here. + +And you're actually going to +these 12-core machines, which + +is really nice. + +Fastest possible machines +you can get your + +hands on these days. + +And it's kind of fun +to work with them. + +And we can basically get +concurrency for parallel + +performance. + +And a large part of this class +at the end is trying to get + +good parallel performance. + +But there are a lot of issues +with parallelism. + +I will go a couple +of issues now. + +Of course, when we get to that +part, we will go in detail. + +One thing is called +Amdahl's Law. + +Because if you're trying to run +something parallel, you + +can't run everything parallel. + +When you start something, +there's part of the code that + +basically starts the +computation. + +And then there are the parts you +can run parallel, and then + +other parts you have +to also wind down, + +measure, things like that. + +So what Amdahl's Law says is, +even if you have an infinite + +number of processors, the +maximum speedup you can get is + +this-- this the part of the code +that are sequential and + +[? parts of ?] the code +are parallel. + +That means if you have only +90% of the code can be + +parallelized, the maximum +speedup you can get is 10, + +even if you have an infinite +number of processors. + +So 99% of the code is parallel, +the maximum speedup + +you can get is 100. + +So this is very interesting, +because even if you have huge + +[UNINTELLIGIBLE], if your code +has a certain amount of + +sequential part, there is a +limit of what you can do. + +[UNINTELLIGIBLE] + +also think of load balancing. + +That means when you get +parallel, what you are + +assuming is all processes +are busy all the time. + +That's very hard to achieve. + +Sometimes some processes +are busy. + +Sometimes others are not. + +Sometimes something's +finished early. + +So if that happens, even though +you have parallels, you + +might not get really good +performance in here. + +And then, of course, there's a +thing called granularity of + +parallelism. + +Normally, what happens in +programming, you run + +sequential part, you run +parallel part, you run + +sequential parallel part. + +To start parallelism +is a big task. + +You have to tell all the other +processors, OK, look, you guys + +have some work. + +Go do that, and finish +that, and come back. + +And that itself is +very expensive. + +And the work you give +is very small. + +You give the work. + +The start-up and tear-down cost +of parallelism itself + +might be too much than +the speedup you get. + +In fact, you can make programs +parallel and slow them down + +really drastically. + +So you have to be very careful +in that, because you can say, + +oh, I'm running in parallel, +but it's running slow. + +Why? + +Because you might have a +granularity issue, because we + +are giving so little work that +even though you're getting + +parallelism, you might not get +that much performance. + +So if you look at matrix +multiply, what happens here is + +you can divide the matrix into +two different parts in here + +and calculate as two different +matrix multiplies in a + +different core or a +different process. + +Or in here, I can make it two +or whatever in matrix + +multiplies to do that. + +So this is nicely +parallelized. + +No big issue in here. + +And when I parallelize, I got +rather 3.5x performance + +improvement. + +Of course, I could have gotten +more here, but because I had + +to start here, since I didn't +want to wait for a week for + +this to finish, I had to come up +with a smaller matrix size. + +But now, when I get here, +this is so fast, my + +granularity is too small. + +So that's why I didn't get-- + +because this was an eight-core +machine, I didn't get 8x + +because the minute I get +parallelism, it just is over + +because it's running +so fast in here. + +Now, at this point, using eight +cores, I am actually + +getting 36. + +So this is not that interesting, +because this is + +not running on one core, every +clock cycle, I am trying to + +get 36 operations done. + +So the interesting thing to +follow in here is that this + +example might be somewhat +contrived, because I started + +with this immutable-type +matrix multiply. + +Hopefully, you and your +colleagues who haven't taken + +this class probably +won't go that far. + +But even if you start somewhere +here, still, there's + +a huge gain to be made. + +So to put this in perspective, +OK, so if you look at here, + +even if I start here somewhere +out in C, I already got 131x + +performance improvement. + +That's huge. + +So that means in this +class, we are not + +talking about small things. + +And in fact, this is why I had +to go log scale in doing + +absolute grades, because we +had people who figured out + +exactly how, in some problems, +to change data structures, + +change execution ordering, do +some really cool thing, get + +1,000x performance +improvement. + +And there are other people who +did little bit things and got + +2x improvement. + +So the fact that what you can +do the best here can be + +really, really high. + +So that's why we actually +started giving you the second + +chance to also go basically see, +if you missed a critical + +point, to go back +and learn that. + +So to put this in +perspective-- + +so in summary, what +we have done is-- + +matrix multiply might +be an exception. + +Every time you go, you might +not get that much, but in + +here, going from this very +software-engineered, nice + +[UNINTELLIGIBLE] + +to a BLAS [UNINTELLIGIBLE], +I got a 296,000 times + +performance improvement. + +This is huge. + +If you put this in perspective, +if you look at + +miles per gallon between +these two-- a + +supertanker and this scooter-- + +it's only 14,000x, basically. + +So what that means is you have +to have 20 supertankers to + +basically match this +much improvement. + +So if somebody can tell you, +look, I can't get a + +supertanker to run at the same +miles per gallon as your + +scooter, that would +be revolutionary. + +But you can do something similar +in your computer. + +And in fact, if you look at +these large data centers, the + +computers are actually +burning a lot of + +energy, a lot of cost. + +And in fact, if you can reduce +that, that can have impact. + +So what you get out of this +class is to think through + +these programs this way. + +Learn about correctness before +[UNINTELLIGIBLE] + +6.170, you hopefully are good +at writing correct programs. + +But that's not good enough +in a lot of times. + +And how to think about programs, +how to make it run + +faster, there are multiple +[UNINTELLIGIBLE] necessary. + +So for example, in here, it's +basically direct energy. + +So can you get the data center +to burn 10% less energy, + +that's huge. + +For example, if you look at +today's supercomputing + +centers, they spend about $10 +million a year on energy, just + +for the power grid. + +So if you can say, I'm +[? playing with ?] + +10%, that's huge. + +Other thing, one thing Charles +says a lot of times is, what + +performance gives you is +currency, because performance + +itself might not be that +directly useful, but it gives + +you currency to buy +something else. + +What it is? + +So assume you have a +nice application. + +Your GUI is doing OK. + +It's up to the point that people +don't feel stalled. + +But if you want to do something +addition, if you add + +a feature, you don't want to +slow down the program too + +much, because your users +are going to complain. + +So what performance gives you +is, if you improve the + +performance, it gives you +currency, the ability to buy + +some additional features +into your system. + +Or you have a system that you +created a start up, and you + +created this nice server +somewhere. + +Suddenly, it became very +popular, and a million people + +want to use your software. + +And the software might not +be ready to do that. + +It might just crash and burn, or +you might have to pay a lot + +of money for Amazon for +the [? cycles, ?] + +so by actually making programs +faster, you can make it + +scalable, you can make +it efficient. + +So this gives you the ability, +this currency, to go do a lot + +more other interesting things +to your software because now + +you can run it faster. + +It gives you this margin +to play with. + +So in this class, we are +going to learn a + +lot about these things. + +We are going to learn about +architecture, how looking at + +the architectural issues, +how to identify when + +something is wrong. + +We are going to look at +algorithmic issues in here, + +how to look at things. + +We are looking at architectural +things like + +memory systems, parallelism. + +And also we will talk about +all the tools, so you will + +actually know something +has gone wrong. + +Because today, you run the +program, it runs, it runs + +correctly, is it good +enough or not? + +How do you identify that? + +That's, I think, the very +interesting place to start. + +So that's all I have today. + +Make sure you get a Project 0. + +And especially people who +haven't done C, we will-- + +Charles, are we going to +do a C remediation? + +We did last time, didn't we? + +OK, guys, one more thing. + +Last year, we did an evening +C remediation class. + +So if you know Java, if you want +to know C, we will send + +out a time with TAs that will +give you kind of a one-hour + +crash course into C in there. + +And we will send information. + +So this class moves very fast. + +Get on with Project 0, and +see you next week. \ No newline at end of file diff --git a/KFq33hsMxr4.txt b/KFq33hsMxr4.txt new file mode 100644 index 0000000000000000000000000000000000000000..f10d9c75a2b677cc2477c0a7192ad6b9123e2901 --- /dev/null +++ b/KFq33hsMxr4.txt @@ -0,0 +1,9395 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +all right I think we're gathered soon + + align:start position:0% +all right I think we're gathered soon + + + align:start position:0% +all right I think we're gathered soon +let's get going we were going to start + + align:start position:0% +let's get going we were going to start + + + align:start position:0% +let's get going we were going to start +da Yi's today but we decided to postpone + + align:start position:0% +da Yi's today but we decided to postpone + + + align:start position:0% +da Yi's today but we decided to postpone +for one day and do a little catch-up on + + align:start position:0% +for one day and do a little catch-up on + + + align:start position:0% +for one day and do a little catch-up on +different things that you should know + + align:start position:0% + + + + align:start position:0% + +and I thought I'd first back up a minute + + align:start position:0% +and I thought I'd first back up a minute + + + align:start position:0% +and I thought I'd first back up a minute +and talk about recall what you have + + align:start position:0% +and talk about recall what you have + + + align:start position:0% +and talk about recall what you have +learned so far so we started out talking + + align:start position:0% +learned so far so we started out talking + + + align:start position:0% +learned so far so we started out talking +a lot about linear algebra and + + align:start position:0% +a lot about linear algebra and + + + align:start position:0% +a lot about linear algebra and +particularly the problems of this type + + align:start position:0% +particularly the problems of this type + + + align:start position:0% +particularly the problems of this type +where you're given the matrix and you + + align:start position:0% +where you're given the matrix and you + + + align:start position:0% +where you're given the matrix and you +give it a vector and you want to figure + + align:start position:0% +give it a vector and you want to figure + + + align:start position:0% +give it a vector and you want to figure +out what the X is that makes this + + align:start position:0% +out what the X is that makes this + + + align:start position:0% +out what the X is that makes this +equation true and you've become + + align:start position:0% +equation true and you've become + + + align:start position:0% +equation true and you've become +extremely familiar with the convenient + + align:start position:0% +extremely familiar with the convenient + + + align:start position:0% +extremely familiar with the convenient +MATLAB that backslash function you + + align:start position:0% +MATLAB that backslash function you + + + align:start position:0% +MATLAB that backslash function you +probably it's just a lot of times and + + align:start position:0% +probably it's just a lot of times and + + + align:start position:0% +probably it's just a lot of times and +you remember this is one of the only + + align:start position:0% +you remember this is one of the only + + + align:start position:0% +you remember this is one of the only +problems where we often have a unique + + align:start position:0% +problems where we often have a unique + + + align:start position:0% +problems where we often have a unique +solution we know a solution exists and + + align:start position:0% +solution we know a solution exists and + + + align:start position:0% +solution we know a solution exists and +we can do a finite number of steps in + + align:start position:0% +we can do a finite number of steps in + + + align:start position:0% +we can do a finite number of steps in +order to get the solution and and + + align:start position:0% +order to get the solution and and + + + align:start position:0% +order to get the solution and and +actually the bet that we have is really + + align:start position:0% +actually the bet that we have is really + + + align:start position:0% +actually the bet that we have is really +good so it almost always give us a + + align:start position:0% +good so it almost always give us a + + + align:start position:0% +good so it almost always give us a +solution and to busine accuracy so this + + align:start position:0% +solution and to busine accuracy so this + + + align:start position:0% +solution and to busine accuracy so this +is a brilliant method and so everything + + align:start position:0% +is a brilliant method and so everything + + + align:start position:0% +is a brilliant method and so everything +is based on this in our whole field + + align:start position:0% +is based on this in our whole field + + + align:start position:0% +is based on this in our whole field +actually so we learned this first we + + align:start position:0% +actually so we learned this first we + + + align:start position:0% +actually so we learned this first we +learned it takes what n cubed operations + + align:start position:0% +learned it takes what n cubed operations + + + align:start position:0% +learned it takes what n cubed operations +in order to to get the solution where n + + align:start position:0% +in order to to get the solution where n + + + align:start position:0% +in order to to get the solution where n +is the size of the vectors and and when + + align:start position:0% +is the size of the vectors and and when + + + align:start position:0% +is the size of the vectors and and when +we do the solution the X we get for + + align:start position:0% +we do the solution the X we get for + + + align:start position:0% +we do the solution the X we get for +backslash invariably if there is a + + align:start position:0% +backslash invariably if there is a + + + align:start position:0% +backslash invariably if there is a +solution solves this equation to machine + + align:start position:0% +solution solves this equation to machine + + + align:start position:0% +solution solves this equation to machine +accuracy necessity multiply M times + + align:start position:0% +accuracy necessity multiply M times + + + align:start position:0% +accuracy necessity multiply M times +actually get thee to as many digits as + + align:start position:0% +actually get thee to as many digits as + + + align:start position:0% +actually get thee to as many digits as +you can read however we talked about how + + align:start position:0% +you can read however we talked about how + + + align:start position:0% +you can read however we talked about how +M can be poorly conditioned so that + + align:start position:0% +M can be poorly conditioned so that + + + align:start position:0% +M can be poorly conditioned so that +there might be multiple access that + + align:start position:0% +there might be multiple access that + + + align:start position:0% +there might be multiple access that +would solve this equation to machine + + align:start position:0% +would solve this equation to machine + + + align:start position:0% +would solve this equation to machine +accuracy and so that that's the problem + + align:start position:0% +accuracy and so that that's the problem + + + align:start position:0% +accuracy and so that that's the problem +with ill conditioning so it's not that + + align:start position:0% +with ill conditioning so it's not that + + + align:start position:0% +with ill conditioning so it's not that +it doesn't solve the equation it's that + + align:start position:0% +it doesn't solve the equation it's that + + + align:start position:0% +it doesn't solve the equation it's that +we're not really sure that's the right X + + align:start position:0% +we're not really sure that's the right X + + + align:start position:0% +we're not really sure that's the right X +you could get a bunch of different X's + + align:start position:0% +you could get a bunch of different X's + + + align:start position:0% +you could get a bunch of different X's +that basically solve it as well as we + + align:start position:0% +that basically solve it as well as we + + + align:start position:0% +that basically solve it as well as we +can tell all right so you guys remember + + align:start position:0% +can tell all right so you guys remember + + + align:start position:0% +can tell all right so you guys remember +this all right and so that also implies + + align:start position:0% +this all right and so that also implies + + + align:start position:0% +this all right and so that also implies +that you make a very small change in B + + align:start position:0% +that you make a very small change in B + + + align:start position:0% +that you make a very small change in B +you might get a gigantic change in X + + align:start position:0% +you might get a gigantic change in X + + + align:start position:0% +you might get a gigantic change in X +because even for one day you have a + + align:start position:0% +because even for one day you have a + + + align:start position:0% +because even for one day you have a +quite a range of X's anywhere alright + + align:start position:0% +quite a range of X's anywhere alright + + + align:start position:0% +quite a range of X's anywhere alright +then we tried to solve problems like + + align:start position:0% +then we tried to solve problems like + + + align:start position:0% +then we tried to solve problems like +this right + + align:start position:0% +this right + + + align:start position:0% +this right +sisters and equations not just linear + + align:start position:0% +sisters and equations not just linear + + + align:start position:0% +sisters and equations not just linear +ones but nonlinear ones as well and what + + align:start position:0% +ones but nonlinear ones as well and what + + + align:start position:0% +ones but nonlinear ones as well and what +we decide to do is one of my best + + align:start position:0% +we decide to do is one of my best + + + align:start position:0% +we decide to do is one of my best +methods is newton-raphson where we keep + + align:start position:0% +methods is newton-raphson where we keep + + + align:start position:0% +methods is newton-raphson where we keep +doing doing J backslash f- it right so + + align:start position:0% +doing doing J backslash f- it right so + + + align:start position:0% +doing doing J backslash f- it right so +all we did in this method a lot of times + + align:start position:0% +all we did in this method a lot of times + + + align:start position:0% +all we did in this method a lot of times +is we just kept one calling this method + + align:start position:0% +is we just kept one calling this method + + + align:start position:0% +is we just kept one calling this method +over and over again all right so this + + align:start position:0% +over and over again all right so this + + + align:start position:0% +over and over again all right so this +took order of n cubes this thing is + + align:start position:0% +took order of n cubes this thing is + + + align:start position:0% +took order of n cubes this thing is +going to take order of and I don't know + + align:start position:0% +going to take order of and I don't know + + + align:start position:0% +going to take order of and I don't know +what you call it snaps or something you + + align:start position:0% +what you call it snaps or something you + + + align:start position:0% +what you call it snaps or something you +guys have a word for what do you what do + + align:start position:0% +guys have a word for what do you what do + + + align:start position:0% +guys have a word for what do you what do +you call the iterations iterations + + align:start position:0% +you call the iterations iterations + + + align:start position:0% +you call the iterations iterations +santisuk all right number of iterations + + align:start position:0% +santisuk all right number of iterations + + + align:start position:0% +santisuk all right number of iterations +times n cubed now if you really can make + + align:start position:0% +times n cubed now if you really can make + + + align:start position:0% +times n cubed now if you really can make +it wraps at work and you have a really + + align:start position:0% +it wraps at work and you have a really + + + align:start position:0% +it wraps at work and you have a really +great initial gasps the number of + + align:start position:0% +great initial gasps the number of + + + align:start position:0% +great initial gasps the number of +iterations are really tiny + + align:start position:0% +iterations are really tiny + + + align:start position:0% +iterations are really tiny +because then wraps into such a + + align:start position:0% +because then wraps into such a + + + align:start position:0% +because then wraps into such a +fantastically great convergence however + + align:start position:0% +fantastically great convergence however + + + align:start position:0% +fantastically great convergence however +we're usually not such good guessers and + + align:start position:0% +we're usually not such good guessers and + + + align:start position:0% +we're usually not such good guessers and +so it might take a lot of iterations and + + align:start position:0% +so it might take a lot of iterations and + + + align:start position:0% +so it might take a lot of iterations and +the fact we use the dogleg method to + + align:start position:0% +the fact we use the dogleg method to + + + align:start position:0% +the fact we use the dogleg method to +solve this as we discussed about or you + + align:start position:0% +solve this as we discussed about or you + + + align:start position:0% +solve this as we discussed about or you +mix up different methods and you have a + + align:start position:0% +mix up different methods and you have a + + + align:start position:0% +mix up different methods and you have a +trust region and all this baloney and so + + align:start position:0% +trust region and all this baloney and so + + + align:start position:0% +trust region and all this baloney and so +you might actually be quite a lot of + + align:start position:0% +you might actually be quite a lot of + + + align:start position:0% +you might actually be quite a lot of +iterations together and then we went and + + align:start position:0% +iterations together and then we went and + + + align:start position:0% +iterations together and then we went and +tried to solve this problem + + align:start position:0% + + + + align:start position:0% + +and what we decided to do for both of + + align:start position:0% +and what we decided to do for both of + + + align:start position:0% +and what we decided to do for both of +these is almost do the same thing + + align:start position:0% +these is almost do the same thing + + + align:start position:0% +these is almost do the same thing +say say well we solve this one by + + align:start position:0% +say say well we solve this one by + + + align:start position:0% +say say well we solve this one by +instead solving right that's really what + + align:start position:0% +instead solving right that's really what + + + align:start position:0% +instead solving right that's really what +we ended up doing that's what happens + + align:start position:0% +we ended up doing that's what happens + + + align:start position:0% +we ended up doing that's what happens +inside F solve is it converts the + + align:start position:0% +inside F solve is it converts the + + + align:start position:0% +inside F solve is it converts the +problem of finding FX equals zero into a + + align:start position:0% +problem of finding FX equals zero into a + + + align:start position:0% +problem of finding FX equals zero into a +minimization problem to try to make the + + align:start position:0% +minimization problem to try to make the + + + align:start position:0% +minimization problem to try to make the +norm of F as small as possible because + + align:start position:0% +norm of F as small as possible because + + + align:start position:0% +norm of F as small as possible because +the answer will be when the norm is 0 + + align:start position:0% +the answer will be when the norm is 0 + + + align:start position:0% +the answer will be when the norm is 0 +and if FX equals zero has a solution + + align:start position:0% +and if FX equals zero has a solution + + + align:start position:0% +and if FX equals zero has a solution +then the global minimum here is a + + align:start position:0% +then the global minimum here is a + + + align:start position:0% +then the global minimum here is a +solution as long as your initial guess + + align:start position:0% +solution as long as your initial guess + + + align:start position:0% +solution as long as your initial guess +is good enough that you're in the valley + + align:start position:0% +is good enough that you're in the valley + + + align:start position:0% +is good enough that you're in the valley +that leads to the to the true minimum + + align:start position:0% +that leads to the to the true minimum + + + align:start position:0% +that leads to the to the true minimum +then this will work and that's actually + + align:start position:0% +then this will work and that's actually + + + align:start position:0% +then this will work and that's actually +what f solve does so these two guys gets + + align:start position:0% +what f solve does so these two guys gets + + + align:start position:0% +what f solve does so these two guys gets +kind of coupled together the + + align:start position:0% +kind of coupled together the + + + align:start position:0% +kind of coupled together the +minimization problem and and the root + + align:start position:0% +minimization problem and and the root + + + align:start position:0% +minimization problem and and the root +finding problem or the problem of + + align:start position:0% +finding problem or the problem of + + + align:start position:0% +finding problem or the problem of +solving systems of nonlinear equations + + align:start position:0% +solving systems of nonlinear equations + + + align:start position:0% +solving systems of nonlinear equations +and in both of them we're gonna call the + + align:start position:0% +and in both of them we're gonna call the + + + align:start position:0% +and in both of them we're gonna call the +first method a million times okay so + + align:start position:0% +first method a million times okay so + + + align:start position:0% +first method a million times okay so +that's the way we're working so far and + + align:start position:0% +that's the way we're working so far and + + + align:start position:0% +that's the way we're working so far and +actually when you do F min con which was + + align:start position:0% +actually when you do F min con which was + + + align:start position:0% +actually when you do F min con which was +the next level then you actually end up + + align:start position:0% +the next level then you actually end up + + + align:start position:0% +the next level then you actually end up +looking for saddle points which again we + + align:start position:0% +looking for saddle points which again we + + + align:start position:0% +looking for saddle points which again we +look for as minimizing the norm of a + + align:start position:0% +look for as minimizing the norm of a + + + align:start position:0% +look for as minimizing the norm of a +gradient squared which gets it back into + + align:start position:0% +gradient squared which gets it back into + + + align:start position:0% +gradient squared which gets it back into +this kind of form and so they're all the + + align:start position:0% +this kind of form and so they're all the + + + align:start position:0% +this kind of form and so they're all the +same thing + + align:start position:0% +same thing + + + align:start position:0% +same thing +all right and you can again work out + + align:start position:0% +all right and you can again work out + + + align:start position:0% +all right and you can again work out +estimates of how much effort it takes + + align:start position:0% +estimates of how much effort it takes + + + align:start position:0% +estimates of how much effort it takes +and it's something times n cubed + + align:start position:0% +and it's something times n cubed + + + align:start position:0% +and it's something times n cubed +typically if your work if most your work + + align:start position:0% +typically if your work if most your work + + + align:start position:0% +typically if your work if most your work +is this now I should make a comment that + + align:start position:0% +is this now I should make a comment that + + + align:start position:0% +is this now I should make a comment that +in practice that's not always true so in + + align:start position:0% +in practice that's not always true so in + + + align:start position:0% +in practice that's not always true so in +practice sometimes although the highest + + align:start position:0% +practice sometimes although the highest + + + align:start position:0% +practice sometimes although the highest +order term is n cubed the linear algebra + + align:start position:0% +order term is n cubed the linear algebra + + + align:start position:0% +order term is n cubed the linear algebra +programs that do this are so great that + + align:start position:0% +programs that do this are so great that + + + align:start position:0% +programs that do this are so great that +the prefactor is tiny so in order to get + + align:start position:0% +the prefactor is tiny so in order to get + + + align:start position:0% +the prefactor is tiny so in order to get +the limit where the n cubed term was + + align:start position:0% +the limit where the n cubed term was + + + align:start position:0% +the limit where the n cubed term was +actually dominate the CPU time you would + + align:start position:0% +actually dominate the CPU time you would + + + align:start position:0% +actually dominate the CPU time you would +have to have a gigantic + + align:start position:0% +have to have a gigantic + + + align:start position:0% +have to have a gigantic +again and in fact the limit it's often + + align:start position:0% +again and in fact the limit it's often + + + align:start position:0% +again and in fact the limit it's often +the effort to construct the matrix J and + + align:start position:0% +the effort to construct the matrix J and + + + align:start position:0% +the effort to construct the matrix J and +so it really goes as N squared so + + align:start position:0% +so it really goes as N squared so + + + align:start position:0% +so it really goes as N squared so +although this anomaly is like n cubed in + + align:start position:0% +although this anomaly is like n cubed in + + + align:start position:0% +although this anomaly is like n cubed in +practice a lot of times it's N squared + + align:start position:0% +practice a lot of times it's N squared + + + align:start position:0% +practice a lot of times it's N squared +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and that's same for these other methods + + align:start position:0% +and that's same for these other methods + + + align:start position:0% +and that's same for these other methods +and then a lot of them get into how good + + align:start position:0% +and then a lot of them get into how good + + + align:start position:0% +and then a lot of them get into how good +the initial guesses are because the + + align:start position:0% +the initial guesses are because the + + + align:start position:0% +the initial guesses are because the +number of iterations can get go get + + align:start position:0% +number of iterations can get go get + + + align:start position:0% +number of iterations can get go get +crazy and in fact maybe you never + + align:start position:0% +crazy and in fact maybe you never + + + align:start position:0% +crazy and in fact maybe you never +converges if your initial guess is bad + + align:start position:0% +converges if your initial guess is bad + + + align:start position:0% +converges if your initial guess is bad +so that can be a really critical thing + + align:start position:0% +so that can be a really critical thing + + + align:start position:0% +so that can be a really critical thing +make this better because you can't + + align:start position:0% +make this better because you can't + + + align:start position:0% +make this better because you can't +change in you know I mean how many + + align:start position:0% +change in you know I mean how many + + + align:start position:0% +change in you know I mean how many +unknowns you got is only one energy got + + align:start position:0% +unknowns you got is only one energy got + + + align:start position:0% +unknowns you got is only one energy got +but you can change the iterations by say + + align:start position:0% +but you can change the iterations by say + + + align:start position:0% +but you can change the iterations by say +more clever initial guessing and that + + align:start position:0% +more clever initial guessing and that + + + align:start position:0% +more clever initial guessing and that +was the whole concept about continuation + + align:start position:0% +was the whole concept about continuation + + + align:start position:0% +was the whole concept about continuation +and Homa taupey and all kind of stuff + + align:start position:0% +and Homa taupey and all kind of stuff + + + align:start position:0% +and Homa taupey and all kind of stuff +was trying to help reduce this this + + align:start position:0% +was trying to help reduce this this + + + align:start position:0% +was trying to help reduce this this +number last time we talked about + + align:start position:0% +number last time we talked about + + + align:start position:0% +number last time we talked about +implicitly solving oh two E's and so we + + align:start position:0% +implicitly solving oh two E's and so we + + + align:start position:0% +implicitly solving oh two E's and so we +had an update formula so we were solving + + align:start position:0% +had an update formula so we were solving + + + align:start position:0% +had an update formula so we were solving +a know de initial value problem right + + align:start position:0% +a know de initial value problem right + + + align:start position:0% +a know de initial value problem right +and you know we said that first we went + + align:start position:0% +and you know we said that first we went + + + align:start position:0% +and you know we said that first we went +through the explicit methods and they're + + align:start position:0% +through the explicit methods and they're + + + align:start position:0% +through the explicit methods and they're +like perfectly straightforward to do and + + align:start position:0% +like perfectly straightforward to do and + + + align:start position:0% +like perfectly straightforward to do and +you don't have to solve any systems and + + align:start position:0% +you don't have to solve any systems and + + + align:start position:0% +you don't have to solve any systems and +other equations to do them and so that + + align:start position:0% +other equations to do them and so that + + + align:start position:0% +other equations to do them and so that +was great but then we pointed out that a + + align:start position:0% +was great but then we pointed out that a + + + align:start position:0% +was great but then we pointed out that a +lot of times they're numerically + + align:start position:0% +lot of times they're numerically + + + align:start position:0% +lot of times they're numerically +unstable and so then you have to use + + align:start position:0% +unstable and so then you have to use + + + align:start position:0% +unstable and so then you have to use +instead use implicit methods but the + + align:start position:0% +instead use implicit methods but the + + + align:start position:0% +instead use implicit methods but the +implicit methods generally work this way + + align:start position:0% +implicit methods generally work this way + + + align:start position:0% +implicit methods generally work this way +that you have your new value of y you're + + align:start position:0% +that you have your new value of y you're + + + align:start position:0% +that you have your new value of y you're +trying to compute is your current value + + align:start position:0% +trying to compute is your current value + + + align:start position:0% +trying to compute is your current value +of y plus delta T sometimes times G + + align:start position:0% +of y plus delta T sometimes times G + + + align:start position:0% +of y plus delta T sometimes times G +depends on the size of delta T and why + + align:start position:0% +depends on the size of delta T and why + + + align:start position:0% +depends on the size of delta T and why +old no I knew maybe my old also and + + align:start position:0% +old no I knew maybe my old also and + + + align:start position:0% +old no I knew maybe my old also and +these G's are things like the crank + + align:start position:0% +these G's are things like the crank + + + align:start position:0% +these G's are things like the crank +Nicholson which you're going to work on + + align:start position:0% +Nicholson which you're going to work on + + + align:start position:0% +Nicholson which you're going to work on +in the homework and we always show it in + + align:start position:0% +in the homework and we always show it in + + + align:start position:0% +in the homework and we always show it in +class too and so there's different + + align:start position:0% +class too and so there's different + + + align:start position:0% +class too and so there's different +update formula so people suggested how + + align:start position:0% +update formula so people suggested how + + + align:start position:0% +update formula so people suggested how +to do this the trick of this is that the + + align:start position:0% +to do this the trick of this is that the + + + align:start position:0% +to do this the trick of this is that the +Y nu is inside the function so for + + align:start position:0% +Y nu is inside the function so for + + + align:start position:0% +Y nu is inside the function so for +therefore this is really + + align:start position:0% +therefore this is really + + + align:start position:0% +therefore this is really +another problem like we had before you + + align:start position:0% +another problem like we had before you + + + align:start position:0% +another problem like we had before you +can really rewrite this that way by just + + align:start position:0% +can really rewrite this that way by just + + + align:start position:0% +can really rewrite this that way by just +putting this on the one side put them on + + align:start position:0% +putting this on the one side put them on + + + align:start position:0% +putting this on the one side put them on +one side of zero and now I'm trying to + + align:start position:0% +one side of zero and now I'm trying to + + + align:start position:0% +one side of zero and now I'm trying to +figure out why nu is and I'm gonna solve + + align:start position:0% +figure out why nu is and I'm gonna solve + + + align:start position:0% +figure out why nu is and I'm gonna solve +that using this method and they've + + align:start position:0% +that using this method and they've + + + align:start position:0% +that using this method and they've +solved that by using this with it all + + align:start position:0% +solved that by using this with it all + + + align:start position:0% +solved that by using this with it all +right so now how does the scaling gonna + + align:start position:0% +right so now how does the scaling gonna + + + align:start position:0% +right so now how does the scaling gonna +go at each time step I have to solve one + + align:start position:0% +go at each time step I have to solve one + + + align:start position:0% +go at each time step I have to solve one +of these guys how much effort did that + + align:start position:0% +of these guys how much effort did that + + + align:start position:0% +of these guys how much effort did that +take we did that right here it is and + + align:start position:0% +take we did that right here it is and + + + align:start position:0% +take we did that right here it is and +inner times N squared and then how many + + align:start position:0% +inner times N squared and then how many + + + align:start position:0% +inner times N squared and then how many +times do I have to do it right so it + + align:start position:0% +times do I have to do it right so it + + + align:start position:0% +times do I have to do it right so it +depends how many time steps I have so + + align:start position:0% +depends how many time steps I have so + + + align:start position:0% +depends how many time steps I have so +house all adults up to you so it's like + + align:start position:0% +house all adults up to you so it's like + + + align:start position:0% +house all adults up to you so it's like +something like T final minus T naught + + align:start position:0% +something like T final minus T naught + + + align:start position:0% +something like T final minus T naught +over delta T that's the number of time + + align:start position:0% +over delta T that's the number of time + + + align:start position:0% +over delta T that's the number of time +steps if I have constant delta T times + + align:start position:0% +steps if I have constant delta T times + + + align:start position:0% +steps if I have constant delta T times +then we're venerations that it takes to + + align:start position:0% +then we're venerations that it takes to + + + align:start position:0% +then we're venerations that it takes to +do the linear solve times N squared + + align:start position:0% +do the linear solve times N squared + + + align:start position:0% +do the linear solve times N squared +which is a cost of forming the Jacobian + + align:start position:0% +which is a cost of forming the Jacobian + + + align:start position:0% +which is a cost of forming the Jacobian +matrix now this starts can be pretty + + align:start position:0% +matrix now this starts can be pretty + + + align:start position:0% +matrix now this starts can be pretty +large so as we talked about this might + + align:start position:0% +large so as we talked about this might + + + align:start position:0% +large so as we talked about this might +be as big as 10 to the 8th in a in a bad + + align:start position:0% +be as big as 10 to the 8th in a in a bad + + + align:start position:0% +be as big as 10 to the 8th in a in a bad +case certainly be less intent the Yates + + align:start position:0% +case certainly be less intent the Yates + + + align:start position:0% +case certainly be less intent the Yates +because otherwise you'll have numerical + + align:start position:0% +because otherwise you'll have numerical + + + align:start position:0% +because otherwise you'll have numerical +problems maybe it's really going to be + + align:start position:0% +problems maybe it's really going to be + + + align:start position:0% +problems maybe it's really going to be +10 to the sixth for a real problem so + + align:start position:0% +10 to the sixth for a real problem so + + + align:start position:0% +10 to the sixth for a real problem so +you have a million time steps at each + + align:start position:0% +you have a million time steps at each + + + align:start position:0% +you have a million time steps at each +time step you have to solve the number + + align:start position:0% +time step you have to solve the number + + + align:start position:0% +time step you have to solve the number +of it are the solve the solve cost as + + align:start position:0% +of it are the solve the solve cost as + + + align:start position:0% +of it are the solve the solve cost as +much number of iterations might be on + + align:start position:0% +much number of iterations might be on + + + align:start position:0% +much number of iterations might be on +how many iterations you guys takes to + + align:start position:0% +how many iterations you guys takes to + + + align:start position:0% +how many iterations you guys takes to +find solve nonlinear equations you solve + + align:start position:0% +find solve nonlinear equations you solve + + + align:start position:0% +find solve nonlinear equations you solve +a lot of them now how many iterations it + + align:start position:0% +a lot of them now how many iterations it + + + align:start position:0% +a lot of them now how many iterations it +to take 10 does that sense on right + + align:start position:0% + + + + align:start position:0% + +you're good neutral guess 10 it bet if + + align:start position:0% +you're good neutral guess 10 it bet if + + + align:start position:0% +you're good neutral guess 10 it bet if +you have a medium initial guess maybe + + align:start position:0% +you have a medium initial guess maybe + + + align:start position:0% +you have a medium initial guess maybe +100 maybe it's more than hundred you're + + align:start position:0% +100 maybe it's more than hundred you're + + + align:start position:0% +100 maybe it's more than hundred you're +not going to converge right yeah okay so + + align:start position:0% +not going to converge right yeah okay so + + + align:start position:0% +not going to converge right yeah okay so +so this is order 10 maybe so a million + + align:start position:0% +so this is order 10 maybe so a million + + + align:start position:0% +so this is order 10 maybe so a million +ten and then n square just depends on + + align:start position:0% +ten and then n square just depends on + + + align:start position:0% +ten and then n square just depends on +how big your problem is so in my group + + align:start position:0% +how big your problem is so in my group + + + align:start position:0% +how big your problem is so in my group +the problems we typically do and it's + + align:start position:0% +the problems we typically do and it's + + + align:start position:0% +the problems we typically do and it's +approximately 200 so this is like 200 + + align:start position:0% +approximately 200 so this is like 200 + + + align:start position:0% +approximately 200 so this is like 200 +squared + + align:start position:0% +squared + + + align:start position:0% +squared +okay and now you can see that the number + + align:start position:0% +okay and now you can see that the number + + + align:start position:0% +okay and now you can see that the number +of iterations and maybe my this is made + + align:start position:0% +of iterations and maybe my this is made + + + align:start position:0% +of iterations and maybe my this is made +a little bit over estimate maybe I get + + align:start position:0% +a little bit over estimate maybe I get + + + align:start position:0% +a little bit over estimate maybe I get +away to the fifth something like that + + align:start position:0% +away to the fifth something like that + + + align:start position:0% +away to the fifth something like that +but you can see it starts to get pretty + + align:start position:0% +but you can see it starts to get pretty + + + align:start position:0% +but you can see it starts to get pretty +big and but for writing it as as you + + align:start position:0% +big and but for writing it as as you + + + align:start position:0% +big and but for writing it as as you +guys writing software it's not that big + + align:start position:0% +guys writing software it's not that big + + + align:start position:0% +guys writing software it's not that big +a deal so I can't assign it as part one + + align:start position:0% +a deal so I can't assign it as part one + + + align:start position:0% +a deal so I can't assign it as part one +of a you know a three part homework + + align:start position:0% +of a you know a three part homework + + + align:start position:0% +of a you know a three part homework +problem it's to write an OD solver + + align:start position:0% +problem it's to write an OD solver + + + align:start position:0% +problem it's to write an OD solver +dissolves implicit equations and you can + + align:start position:0% +dissolves implicit equations and you can + + + align:start position:0% +dissolves implicit equations and you can +write it and the reason you can be is + + align:start position:0% +write it and the reason you can be is + + + align:start position:0% +write it and the reason you can be is +because you already written right + + align:start position:0% +because you already written right + + + align:start position:0% +because you already written right +methods that solve it it's actually + + align:start position:0% +methods that solve it it's actually + + + align:start position:0% +methods that solve it it's actually +MATLAB did it for you but you could + + align:start position:0% +MATLAB did it for you but you could + + + align:start position:0% +MATLAB did it for you but you could +write yourself I sign to the 1010 + + align:start position:0% +write yourself I sign to the 1010 + + + align:start position:0% +write yourself I sign to the 1010 +students so you write this the back sub + + align:start position:0% +students so you write this the back sub + + + align:start position:0% +students so you write this the back sub +solution you have to solve the equations + + align:start position:0% +solution you have to solve the equations + + + align:start position:0% +solution you have to solve the equations +and we've already west of this and you + + align:start position:0% +and we've already west of this and you + + + align:start position:0% +and we've already west of this and you +could end you I think you guys run one + + align:start position:0% +could end you I think you guys run one + + + align:start position:0% +could end you I think you guys run one +of these yourself and also we can the + + align:start position:0% +of these yourself and also we can the + + + align:start position:0% +of these yourself and also we can the +desktop which is just another little bit + + align:start position:0% +desktop which is just another little bit + + + align:start position:0% +desktop which is just another little bit +better implementation of the same thing + + align:start position:0% +better implementation of the same thing + + + align:start position:0% +better implementation of the same thing +and then now you write your next level + + align:start position:0% +and then now you write your next level + + + align:start position:0% +and then now you write your next level +and it's so you can see you doing a + + align:start position:0% +and it's so you can see you doing a + + + align:start position:0% +and it's so you can see you doing a +composite process where you're doing + + align:start position:0% +composite process where you're doing + + + align:start position:0% +composite process where you're doing +something at the top level it's calling + + align:start position:0% +something at the top level it's calling + + + align:start position:0% +something at the top level it's calling +something a lower level that's calling + + align:start position:0% +something a lower level that's calling + + + align:start position:0% +something a lower level that's calling +something at a lower level and then what + + align:start position:0% +something at a lower level and then what + + + align:start position:0% +something at a lower level and then what +you really have to be concerned about if + + align:start position:0% +you really have to be concerned about if + + + align:start position:0% +you really have to be concerned about if +you're worried about CPU time or whether + + align:start position:0% +you're worried about CPU time or whether + + + align:start position:0% +you're worried about CPU time or whether +you're the things gonna solve before the + + align:start position:0% +you're the things gonna solve before the + + + align:start position:0% +you're the things gonna solve before the +homework is due is it's having you know + + align:start position:0% +homework is due is it's having you know + + + align:start position:0% +homework is due is it's having you know +how big does this get yeah how many + + align:start position:0% +how big does this get yeah how many + + + align:start position:0% +how big does this get yeah how many +operations are you asking the computer + + align:start position:0% +operations are you asking the computer + + + align:start position:0% +operations are you asking the computer +to do now remember the computer is fast + + align:start position:0% +to do now remember the computer is fast + + + align:start position:0% +to do now remember the computer is fast +right good so it can do a jika Hertz or + + align:start position:0% +right good so it can do a jika Hertz or + + + align:start position:0% +right good so it can do a jika Hertz or +something so you do like you know 10 to + + align:start position:0% +something so you do like you know 10 to + + + align:start position:0% +something so you do like you know 10 to +the eighth + + align:start position:0% +the eighth + + + align:start position:0% +the eighth +something's per second and what should I + + align:start position:0% +something's per second and what should I + + + align:start position:0% +something's per second and what should I +say about this I have not included I + + align:start position:0% +say about this I have not included I + + + align:start position:0% +say about this I have not included I +should that it's well I'm assuming here + + align:start position:0% +should that it's well I'm assuming here + + + align:start position:0% +should that it's well I'm assuming here +that the function evaluation is sort of + + align:start position:0% +that the function evaluation is sort of + + + align:start position:0% +that the function evaluation is sort of +order end of how many variables they + + align:start position:0% +order end of how many variables they + + + align:start position:0% +order end of how many variables they +have okay sometimes function evaluations + + align:start position:0% +have okay sometimes function evaluations + + + align:start position:0% +have okay sometimes function evaluations +are much more difficult than that + + align:start position:0% +are much more difficult than that + + + align:start position:0% +are much more difficult than that +primarily because sometimes they're + + align:start position:0% +primarily because sometimes they're + + + align:start position:0% +primarily because sometimes they're +actually including further nested stuff + + align:start position:0% +actually including further nested stuff + + + align:start position:0% +actually including further nested stuff +inside so your F is actually coming from + + align:start position:0% +inside so your F is actually coming from + + + align:start position:0% +inside so your F is actually coming from +some really complicated calculation + + align:start position:0% +some really complicated calculation + + + align:start position:0% +some really complicated calculation +itself and then this thing then you have + + align:start position:0% +itself and then this thing then you have + + + align:start position:0% +itself and then this thing then you have +another big giant factor of how much it + + align:start position:0% +another big giant factor of how much it + + + align:start position:0% +another big giant factor of how much it +costs to do that but on this right here + + align:start position:0% +costs to do that but on this right here + + + align:start position:0% +costs to do that but on this right here +I'm just assuming it goes is it all + + align:start position:0% +I'm just assuming it goes is it all + + + align:start position:0% +I'm just assuming it goes is it all +right so it actually lists a small put + + align:start position:0% +right so it actually lists a small put + + + align:start position:0% +right so it actually lists a small put +this out so this is about 10 to the + + align:start position:0% +this out so this is about 10 to the + + + align:start position:0% +this out so this is about 10 to the +fourth to the tenth so this is a 10 to + + align:start position:0% +fourth to the tenth so this is a 10 to + + + align:start position:0% +fourth to the tenth so this is a 10 to +the 10 to the 10 kind of flops + + align:start position:0% +the 10 to the 10 kind of flops + + + align:start position:0% +the 10 to the 10 kind of flops +but your computer does tend to the four + + align:start position:0% +but your computer does tend to the four + + + align:start position:0% +but your computer does tend to the four +types and the nine per second is that + + align:start position:0% +types and the nine per second is that + + + align:start position:0% +types and the nine per second is that +right so I tell us before GG hurts yeah + + align:start position:0% +right so I tell us before GG hurts yeah + + + align:start position:0% +right so I tell us before GG hurts yeah +so is this really not bad right this is + + align:start position:0% +so is this really not bad right this is + + + align:start position:0% +so is this really not bad right this is +a few seconds on your computer so that's + + align:start position:0% +a few seconds on your computer so that's + + + align:start position:0% +a few seconds on your computer so that's +why you can do these homework problems + + align:start position:0% +why you can do these homework problems + + + align:start position:0% +why you can do these homework problems +and they still get them done and if you + + align:start position:0% +and they still get them done and if you + + + align:start position:0% +and they still get them done and if you +have even poorer implementations it + + align:start position:0% +have even poorer implementations it + + + align:start position:0% +have even poorer implementations it +takes a thousand times longer it's still + + align:start position:0% +takes a thousand times longer it's still + + + align:start position:0% +takes a thousand times longer it's still +a thousand second twenty minutes on your + + align:start position:0% +a thousand second twenty minutes on your + + + align:start position:0% +a thousand second twenty minutes on your +computer okay so so you're okay but you + + align:start position:0% +computer okay so so you're okay but you + + + align:start position:0% +computer okay so so you're okay but you +can see we're starting to get up there + + align:start position:0% +can see we're starting to get up there + + + align:start position:0% +can see we're starting to get up there +and it's not that hard to really make it + + align:start position:0% +and it's not that hard to really make it + + + align:start position:0% +and it's not that hard to really make it +a big problem if you do something a + + align:start position:0% +a big problem if you do something a + + + align:start position:0% +a big problem if you do something a +little bit or something wrong alright + + align:start position:0% + + + + align:start position:0% + +and just a notation thing a lot of these + + align:start position:0% +and just a notation thing a lot of these + + + align:start position:0% +and just a notation thing a lot of these +things we're doing our writing software + + align:start position:0% +things we're doing our writing software + + + align:start position:0% +things we're doing our writing software +that takes this input not just numbers + + align:start position:0% +that takes this input not just numbers + + + align:start position:0% +that takes this input not just numbers +or vectors so those are things that we + + align:start position:0% +or vectors so those are things that we + + + align:start position:0% +or vectors so those are things that we +call functions right things that take a + + align:start position:0% +call functions right things that take a + + + align:start position:0% +call functions right things that take a +number or vectors and input and give us + + align:start position:0% +number or vectors and input and give us + + + align:start position:0% +number or vectors and input and give us +a function a number or vector is an + + align:start position:0% +a function a number or vector is an + + + align:start position:0% +a function a number or vector is an +output but oftentimes we actually want + + align:start position:0% +output but oftentimes we actually want + + + align:start position:0% +output but oftentimes we actually want +to take the names of functions as inputs + + align:start position:0% +to take the names of functions as inputs + + + align:start position:0% +to take the names of functions as inputs +so for example the root funding problem + + align:start position:0% +so for example the root funding problem + + + align:start position:0% +so for example the root funding problem +it takes his input what is f right you + + align:start position:0% +it takes his input what is f right you + + + align:start position:0% +it takes his input what is f right you +have two Talent the name of a function + + align:start position:0% +have two Talent the name of a function + + + align:start position:0% +have two Talent the name of a function +for F solve to be able to call it so F + + align:start position:0% +for F solve to be able to call it so F + + + align:start position:0% +for F solve to be able to call it so F +solve is it's an object that takes this + + align:start position:0% +solve is it's an object that takes this + + + align:start position:0% +solve is it's an object that takes this +input that name of a function and things + + align:start position:0% +input that name of a function and things + + + align:start position:0% +input that name of a function and things +that do that are called function Al's so + + align:start position:0% +that do that are called function Al's so + + + align:start position:0% +that do that are called function Al's so +for example this one is X is equal to + + align:start position:0% +for example this one is X is equal to + + + align:start position:0% +for example this one is X is equal to +this root finding function now that's + + align:start position:0% +this root finding function now that's + + + align:start position:0% +this root finding function now that's +all and I'm going to write with square + + align:start position:0% +all and I'm going to write with square + + + align:start position:0% +all and I'm going to write with square +brackets it depends on F that's it right + + align:start position:0% + + + + align:start position:0% + +so you give it the function f and if f + + align:start position:0% +so you give it the function f and if f + + + align:start position:0% +so you give it the function f and if f +cell is good it should be able to find + + align:start position:0% +cell is good it should be able to find + + + align:start position:0% +cell is good it should be able to find +tell you what the x's now in reality we + + align:start position:0% +tell you what the x's now in reality we + + + align:start position:0% +tell you what the x's now in reality we +help it out so we give it X not Tim just + + align:start position:0% +help it out so we give it X not Tim just + + + align:start position:0% +help it out so we give it X not Tim just +to give it give a better chance all + + align:start position:0% +to give it give a better chance all + + + align:start position:0% +to give it give a better chance all +right + + align:start position:0% +right + + + align:start position:0% +right +I write the square brackets just to + + align:start position:0% +I write the square brackets just to + + + align:start position:0% +I write the square brackets just to +indicate one of the things inside as a + + align:start position:0% +indicate one of the things inside as a + + + align:start position:0% +indicate one of the things inside as a +function not just not just numbers all + + align:start position:0% +function not just not just numbers all + + + align:start position:0% +function not just not just numbers all +right + + align:start position:0% +right + + + align:start position:0% +right +we do this a lot so you guys have done + + align:start position:0% +we do this a lot so you guys have done + + + align:start position:0% +we do this a lot so you guys have done +this + + align:start position:0% +this + + + align:start position:0% +this +since your kids so derivatives + + align:start position:0% +since your kids so derivatives + + + align:start position:0% +since your kids so derivatives +yeah DDX of f right so no we have I + + align:start position:0% +yeah DDX of f right so no we have I + + + align:start position:0% +yeah DDX of f right so no we have I +don't know for example brat kind of F + + align:start position:0% +don't know for example brat kind of F + + + align:start position:0% +don't know for example brat kind of F +right that's a that's a function now the + + align:start position:0% +right that's a that's a function now the + + + align:start position:0% +right that's a that's a function now the +grant the symbol means means the + + align:start position:0% +grant the symbol means means the + + + align:start position:0% +grant the symbol means means the +operator the functionality efforts and + + align:start position:0% +operator the functionality efforts and + + + align:start position:0% +operator the functionality efforts and +functions you could write a general + + align:start position:0% +functions you could write a general + + + align:start position:0% +functions you could write a general +gradient function that takes any any + + align:start position:0% +gradient function that takes any any + + + align:start position:0% +gradient function that takes any any +vector valued in a scalar valued + + align:start position:0% +vector valued in a scalar valued + + + align:start position:0% +vector valued in a scalar valued +function and computes the gradients + + align:start position:0% +function and computes the gradients + + + align:start position:0% +function and computes the gradients +respect to the inputs right this week we + + align:start position:0% +respect to the inputs right this week we + + + align:start position:0% +respect to the inputs right this week we +give you one that the computed Jacobian + + align:start position:0% +give you one that the computed Jacobian + + + align:start position:0% +give you one that the computed Jacobian +give it any f of X it gives you the + + align:start position:0% +give it any f of X it gives you the + + + align:start position:0% +give it any f of X it gives you the +Jacobian of F with respect to X okay so + + align:start position:0% +Jacobian of F with respect to X okay so + + + align:start position:0% +Jacobian of F with respect to X okay so +that's a function L so anyway we'll do a + + align:start position:0% +that's a function L so anyway we'll do a + + + align:start position:0% +that's a function L so anyway we'll do a +lot with function nails you've been + + align:start position:0% +lot with function nails you've been + + + align:start position:0% +lot with function nails you've been +using them all the time I'm just trying + + align:start position:0% +using them all the time I'm just trying + + + align:start position:0% +using them all the time I'm just trying +to look at you to think about abstractly + + align:start position:0% +to look at you to think about abstractly + + + align:start position:0% +to look at you to think about abstractly +and then there's a whole math about + + align:start position:0% +and then there's a whole math about + + + align:start position:0% +and then there's a whole math about +function else and there's a whole thing + + align:start position:0% +function else and there's a whole thing + + + align:start position:0% +function else and there's a whole thing +go calculus of variations it's all about + + align:start position:0% +go calculus of variations it's all about + + + align:start position:0% +go calculus of variations it's all about +if the objects you're wearing about our + + align:start position:0% +if the objects you're wearing about our + + + align:start position:0% +if the objects you're wearing about our +function a lot functions then you have + + align:start position:0% +function a lot functions then you have + + + align:start position:0% +function a lot functions then you have +another whole bunch of theorems and + + align:start position:0% +another whole bunch of theorems and + + + align:start position:0% +another whole bunch of theorems and +stuff you can do with that what you'll + + align:start position:0% +stuff you can do with that what you'll + + + align:start position:0% +stuff you can do with that what you'll +probably end up doing before you get out + + align:start position:0% +probably end up doing before you get out + + + align:start position:0% +probably end up doing before you get out +of this place but I'm not gonna do it + + align:start position:0% +of this place but I'm not gonna do it + + + align:start position:0% +of this place but I'm not gonna do it +right now + + align:start position:0% +right now + + + align:start position:0% +right now +all right I would comment that a one + + align:start position:0% +all right I would comment that a one + + + align:start position:0% +all right I would comment that a one +kind of functionality that's + + align:start position:0% +kind of functionality that's + + + align:start position:0% +kind of functionality that's +particularly important to a lot of + + align:start position:0% +particularly important to a lot of + + + align:start position:0% +particularly important to a lot of +people in your research is the fact that + + align:start position:0% +people in your research is the fact that + + + align:start position:0% +people in your research is the fact that +the energy of any molecule is a function + + align:start position:0% +the energy of any molecule is a function + + + align:start position:0% +the energy of any molecule is a function +L of the electron density and this is + + align:start position:0% +L of the electron density and this is + + + align:start position:0% +L of the electron density and this is +the basis of what's called density + + align:start position:0% +the basis of what's called density + + + align:start position:0% +the basis of what's called density +functional theory + + align:start position:0% + + + + align:start position:0% + +and so this is why a lot of people you + + align:start position:0% +and so this is why a lot of people you + + + align:start position:0% +and so this is why a lot of people you +and many of you included are gonna end + + align:start position:0% +and many of you included are gonna end + + + align:start position:0% +and many of you included are gonna end +up using computer programs they're + + align:start position:0% +up using computer programs they're + + + align:start position:0% +up using computer programs they're +trying to find the electron with the + + align:start position:0% +trying to find the electron with the + + + align:start position:0% +trying to find the electron with the +electron density shape is thinks of + + align:start position:0% +electron density shape is thinks of + + + align:start position:0% +electron density shape is thinks of +molecular orbitals it's not before I + + align:start position:0% +molecular orbitals it's not before I + + + align:start position:0% +molecular orbitals it's not before I +heard these before and then there's a + + align:start position:0% +heard these before and then there's a + + + align:start position:0% +heard these before and then there's a +functionality gives the energy the + + align:start position:0% +functionality gives the energy the + + + align:start position:0% +functionality gives the energy the +molecule you care about mostly as energy + + align:start position:0% +molecule you care about mostly as energy + + + align:start position:0% +molecule you care about mostly as energy +because that connects to all your thermo + + align:start position:0% +because that connects to all your thermo + + + align:start position:0% +because that connects to all your thermo +you're doing 1040 is all about the + + align:start position:0% +you're doing 1040 is all about the + + + align:start position:0% +you're doing 1040 is all about the +energies right and once you know all the + + align:start position:0% +energies right and once you know all the + + + align:start position:0% +energies right and once you know all the +energies you can actually compute the + + align:start position:0% +energies you can actually compute the + + + align:start position:0% +energies you can actually compute the +entropy is not kind of stuff too and so + + align:start position:0% +entropy is not kind of stuff too and so + + + align:start position:0% +entropy is not kind of stuff too and so +this is one applications really + + align:start position:0% +this is one applications really + + + align:start position:0% +this is one applications really +important it was a little bit surprising + + align:start position:0% +important it was a little bit surprising + + + align:start position:0% +important it was a little bit surprising +that this was true and be able to be + + align:start position:0% +that this was true and be able to be + + + align:start position:0% +that this was true and be able to be +proven to be true and so the guy who did + + align:start position:0% +proven to be true and so the guy who did + + + align:start position:0% +proven to be true and so the guy who did +that got the Nobel Prize his name is + + align:start position:0% +that got the Nobel Prize his name is + + + align:start position:0% +that got the Nobel Prize his name is +Cohn a few years ago right actually in a + + align:start position:0% +Cohn a few years ago right actually in a + + + align:start position:0% +Cohn a few years ago right actually in a +liquid phase stuff that you work with + + align:start position:0% +liquid phase stuff that you work with + + + align:start position:0% +liquid phase stuff that you work with +professor blanks gene they also have a + + align:start position:0% +professor blanks gene they also have a + + + align:start position:0% +professor blanks gene they also have a +version of this for properties of + + align:start position:0% +version of this for properties of + + + align:start position:0% +version of this for properties of +solution and then where it's not the + + align:start position:0% +solution and then where it's not the + + + align:start position:0% +solution and then where it's not the +electron density but it's actually a + + align:start position:0% +electron density but it's actually a + + + align:start position:0% +electron density but it's actually a +density of the material in this in the + + align:start position:0% +density of the material in this in the + + + align:start position:0% +density of the material in this in the +solution phase may be press respond to + + align:start position:0% +solution phase may be press respond to + + + align:start position:0% +solution phase may be press respond to +you guys do that yep say we're + + align:start position:0% +you guys do that yep say we're + + + align:start position:0% +you guys do that yep say we're +compressors one you might learn about + + align:start position:0% +compressors one you might learn about + + + align:start position:0% +compressors one you might learn about +that too so that's one where that the + + align:start position:0% +that too so that's one where that the + + + align:start position:0% +that too so that's one where that the +actual functional is like a big focus of + + align:start position:0% +actual functional is like a big focus of + + + align:start position:0% +actual functional is like a big focus of +the entire the entire project and the + + align:start position:0% +the entire the entire project and the + + + align:start position:0% +the entire the entire project and the +key is that this is a function the + + align:start position:0% +key is that this is a function the + + + align:start position:0% +key is that this is a function the +density is a function of the position + + align:start position:0% +density is a function of the position + + + align:start position:0% +density is a function of the position +and then the function now if you're set + + align:start position:0% +and then the function now if you're set + + + align:start position:0% +and then the function now if you're set +into a number e all right it's all page + + align:start position:0% +into a number e all right it's all page + + + align:start position:0% +into a number e all right it's all page +one here now I want to sort of change + + align:start position:0% +one here now I want to sort of change + + + align:start position:0% +one here now I want to sort of change +topics but it's related is about the + + align:start position:0% +topics but it's related is about the + + + align:start position:0% +topics but it's related is about the +connections between numerical + + align:start position:0% +connections between numerical + + + align:start position:0% +connections between numerical +integration interpolation and basis + + align:start position:0% +integration interpolation and basis + + + align:start position:0% +integration interpolation and basis +functions these things are all like + + align:start position:0% +functions these things are all like + + + align:start position:0% +functions these things are all like +intimately tied up together so I'll try + + align:start position:0% +intimately tied up together so I'll try + + + align:start position:0% +intimately tied up together so I'll try +to show you so we're trying to set up + + align:start position:0% +to show you so we're trying to set up + + + align:start position:0% +to show you so we're trying to set up +solve a numerical integral + + align:start position:0% + + + + align:start position:0% + +and then let's look at what we're really + + align:start position:0% +and then let's look at what we're really + + + align:start position:0% +and then let's look at what we're really +doing when we're doing this we typically + + align:start position:0% +doing when we're doing this we typically + + + align:start position:0% +doing when we're doing this we typically +only do a few function evaluations so we + + align:start position:0% +only do a few function evaluations so we + + + align:start position:0% +only do a few function evaluations so we +have a few points where we know the + + align:start position:0% +have a few points where we know the + + + align:start position:0% +have a few points where we know the +numbers half of TN we picked a few at a + + align:start position:0% +numbers half of TN we picked a few at a + + + align:start position:0% +numbers half of TN we picked a few at a +few T's we evaluated F and from those + + align:start position:0% +few T's we evaluated F and from those + + + align:start position:0% +few T's we evaluated F and from those +few points that small number of function + + align:start position:0% +few points that small number of function + + + align:start position:0% +few points that small number of function +evaluations we want to get a good + + align:start position:0% +evaluations we want to get a good + + + align:start position:0% +evaluations we want to get a good +estimate of this whole integral now it's + + align:start position:0% +estimate of this whole integral now it's + + + align:start position:0% +estimate of this whole integral now it's +a little goofy actually you think about + + align:start position:0% +a little goofy actually you think about + + + align:start position:0% +a little goofy actually you think about +we're trying to do so suppose we're + + align:start position:0% +we're trying to do so suppose we're + + + align:start position:0% +we're trying to do so suppose we're +trying to do an integral from negative + + align:start position:0% +trying to do an integral from negative + + + align:start position:0% +trying to do an integral from negative +one to one we have some function has a + + align:start position:0% +one to one we have some function has a + + + align:start position:0% +one to one we have some function has a +point here a point here and just for + + align:start position:0% +point here a point here and just for + + + align:start position:0% +point here a point here and just for +concreteness that let's say this is 1 + + align:start position:0% +concreteness that let's say this is 1 + + + align:start position:0% +concreteness that let's say this is 1 +over 26 and this is 1 this is 1 over 26 + + align:start position:0% +over 26 and this is 1 this is 1 over 26 + + + align:start position:0% +over 26 and this is 1 this is 1 over 26 +and I haven't particularly my function + + align:start position:0% +and I haven't particularly my function + + + align:start position:0% +and I haven't particularly my function +in mind that has this those straight + + align:start position:0% +in mind that has this those straight + + + align:start position:0% +in mind that has this those straight +points now first thing to keep in mind + + align:start position:0% +points now first thing to keep in mind + + + align:start position:0% +points now first thing to keep in mind +is there's an infinite number of + + align:start position:0% +is there's an infinite number of + + + align:start position:0% +is there's an infinite number of +functions that go through those three + + align:start position:0% +functions that go through those three + + + align:start position:0% +functions that go through those three +points right now what we've been doing + + align:start position:0% +points right now what we've been doing + + + align:start position:0% +points right now what we've been doing +is we've been fitting some function to + + align:start position:0% +is we've been fitting some function to + + + align:start position:0% +is we've been fitting some function to +these points and then integrating that + + align:start position:0% +these points and then integrating that + + + align:start position:0% +these points and then integrating that +function that we fitted right so when + + align:start position:0% +function that we fitted right so when + + + align:start position:0% +function that we fitted right so when +you're in high school you did the + + align:start position:0% +you're in high school you did the + + + align:start position:0% +you're in high school you did the +rectangle rule and what the function was + + align:start position:0% +rectangle rule and what the function was + + + align:start position:0% +rectangle rule and what the function was +that you used was this and this and you + + align:start position:0% +that you used was this and this and you + + + align:start position:0% +that you used was this and this and you +knew the integral of this function and + + align:start position:0% +knew the integral of this function and + + + align:start position:0% +knew the integral of this function and +the integral this function and you added + + align:start position:0% +the integral this function and you added + + + align:start position:0% +the integral this function and you added +them up and you decided from the + + align:start position:0% +them up and you decided from the + + + align:start position:0% +them up and you decided from the +rectangle rule that the integral is + + align:start position:0% +rectangle rule that the integral is + + + align:start position:0% +rectangle rule that the integral is +equal to 1 and 1 26 ok but then some + + align:start position:0% +equal to 1 and 1 26 ok but then some + + + align:start position:0% +equal to 1 and 1 26 ok but then some +other people in high school were a + + align:start position:0% +other people in high school were a + + + align:start position:0% +other people in high school were a +little smarter and they said you know + + align:start position:0% +little smarter and they said you know + + + align:start position:0% +little smarter and they said you know +it's not so smart at start the engine + + align:start position:0% +it's not so smart at start the engine + + + align:start position:0% +it's not so smart at start the engine +this thing was symmetrical to begin with + + align:start position:0% +this thing was symmetrical to begin with + + + align:start position:0% +this thing was symmetrical to begin with +and now I'm fitting it with a function + + align:start position:0% +and now I'm fitting it with a function + + + align:start position:0% +and now I'm fitting it with a function +that's like wildly unsymmetrical so + + align:start position:0% +that's like wildly unsymmetrical so + + + align:start position:0% +that's like wildly unsymmetrical so +let's instead not evaluate those points + + align:start position:0% +let's instead not evaluate those points + + + align:start position:0% +let's instead not evaluate those points +let's instead evaluate the midpoints and + + align:start position:0% +let's instead evaluate the midpoints and + + + align:start position:0% +let's instead evaluate the midpoints and +maybe I find out that the midpoint + + align:start position:0% +maybe I find out that the midpoint + + + align:start position:0% +maybe I find out that the midpoint +values are here and here and so I would + + align:start position:0% + + + + align:start position:0% + +assume that the function is just a flat + + align:start position:0% +assume that the function is just a flat + + + align:start position:0% +assume that the function is just a flat +line that's kind of looks not so good + + align:start position:0% +line that's kind of looks not so good + + + align:start position:0% +line that's kind of looks not so good +either because it doesn't go through + + align:start position:0% +either because it doesn't go through + + + align:start position:0% +either because it doesn't go through +these points but anyway for the to point + + align:start position:0% +these points but anyway for the to point + + + align:start position:0% +these points but anyway for the to point +I knew if I only used those two points + + align:start position:0% +I knew if I only used those two points + + + align:start position:0% +I knew if I only used those two points +that would be the midpoint method and I + + align:start position:0% +that would be the midpoint method and I + + + align:start position:0% +that would be the midpoint method and I +would get the item in point + + align:start position:0% +would get the item in point + + + align:start position:0% +would get the item in point +and I get something and I did it for + + align:start position:0% +and I get something and I did it for + + + align:start position:0% +and I get something and I did it for +this particular function I have in mind + + align:start position:0% +this particular function I have in mind + + + align:start position:0% +this particular function I have in mind +and it was eight over twenty nine and + + align:start position:0% +and it was eight over twenty nine and + + + align:start position:0% +and it was eight over twenty nine and +then some other people say well let's + + align:start position:0% +then some other people say well let's + + + align:start position:0% +then some other people say well let's +use the trapezoid rule so let's + + align:start position:0% +use the trapezoid rule so let's + + + align:start position:0% +use the trapezoid rule so let's +approximate the function as as this over + + align:start position:0% +approximate the function as as this over + + + align:start position:0% +approximate the function as as this over +the interval which looks kind of + + align:start position:0% +the interval which looks kind of + + + align:start position:0% +the interval which looks kind of +sensible and if you do that it turns out + + align:start position:0% +sensible and if you do that it turns out + + + align:start position:0% +sensible and if you do that it turns out +you get the same numbers you do it + + align:start position:0% +you get the same numbers you do it + + + align:start position:0% +you get the same numbers you do it +rectangle move so I trapezoid now let me + + align:start position:0% +rectangle move so I trapezoid now let me + + + align:start position:0% +rectangle move so I trapezoid now let me +just as a warning if you just did the + + align:start position:0% +just as a warning if you just did the + + + align:start position:0% +just as a warning if you just did the +rectangle rule then the chapel's were + + align:start position:0% +rectangle rule then the chapel's were + + + align:start position:0% +rectangle rule then the chapel's were +going you got the same number both times + + align:start position:0% +going you got the same number both times + + + align:start position:0% +going you got the same number both times +you might be tempted to conclude you + + align:start position:0% +you might be tempted to conclude you + + + align:start position:0% +you might be tempted to conclude you +have converged and you have the true + + align:start position:0% +have converged and you have the true + + + align:start position:0% +have converged and you have the true +solution because you did two methods of + + align:start position:0% +solution because you did two methods of + + + align:start position:0% +solution because you did two methods of +couple of different orders and you got + + align:start position:0% +couple of different orders and you got + + + align:start position:0% +couple of different orders and you got +exactly the same number and you're super + + align:start position:0% +exactly the same number and you're super + + + align:start position:0% +exactly the same number and you're super +happy and you're ready to publish your + + align:start position:0% +happy and you're ready to publish your + + + align:start position:0% +happy and you're ready to publish your +paper okay but of course the function + + align:start position:0% +paper okay but of course the function + + + align:start position:0% +paper okay but of course the function +might not look like this so the + + align:start position:0% +might not look like this so the + + + align:start position:0% +might not look like this so the +particular function that I was head in + + align:start position:0% +particular function that I was head in + + + align:start position:0% +particular function that I was head in +mind was f of t is equal to 1 over 1 + + align:start position:0% +mind was f of t is equal to 1 over 1 + + + align:start position:0% +mind was f of t is equal to 1 over 1 +plus 25 T squared okay that was just a + + align:start position:0% +plus 25 T squared okay that was just a + + + align:start position:0% +plus 25 T squared okay that was just a +function I had in mind + + align:start position:0% +function I had in mind + + + align:start position:0% +function I had in mind +and the way that function looks like is + + align:start position:0% + + + + align:start position:0% + +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +like that and the real integral of that + + align:start position:0% +like that and the real integral of that + + + align:start position:0% +like that and the real integral of that +function which you guys have you're good + + align:start position:0% +function which you guys have you're good + + + align:start position:0% +function which you guys have you're good +you remember how to do it from high + + align:start position:0% +you remember how to do it from high + + + align:start position:0% +you remember how to do it from high +school you can actually evaluate that + + align:start position:0% +school you can actually evaluate that + + + align:start position:0% +school you can actually evaluate that +integral it's like nothing to do with + + align:start position:0% +integral it's like nothing to do with + + + align:start position:0% +integral it's like nothing to do with +one either a 29 or 1 and 126 it's not + + align:start position:0% +one either a 29 or 1 and 126 it's not + + + align:start position:0% +one either a 29 or 1 and 126 it's not +completely different now those of you + + align:start position:0% +completely different now those of you + + + align:start position:0% +completely different now those of you +who went to really advanced high schools + + align:start position:0% +who went to really advanced high schools + + + align:start position:0% +who went to really advanced high schools +you also learned Simpsons rule two and + + align:start position:0% +you also learned Simpsons rule two and + + + align:start position:0% +you also learned Simpsons rule two and +sisters rule said let's head it to a + + align:start position:0% +sisters rule said let's head it to a + + + align:start position:0% +sisters rule said let's head it to a +parabola and so they would do something + + align:start position:0% +parabola and so they would do something + + + align:start position:0% +parabola and so they would do something +like this and if you do Simpsons rule I + + align:start position:0% +like this and if you do Simpsons rule I + + + align:start position:0% +like this and if you do Simpsons rule I +ended up getting this if I did the + + align:start position:0% +ended up getting this if I did the + + + align:start position:0% +ended up getting this if I did the +arithmetic right 101 third plus two 78 + + align:start position:0% +arithmetic right 101 third plus two 78 + + + align:start position:0% +arithmetic right 101 third plus two 78 +who knew okay which also has little + + align:start position:0% +who knew okay which also has little + + + align:start position:0% +who knew okay which also has little +relation to the true value of the + + align:start position:0% +relation to the true value of the + + + align:start position:0% +relation to the true value of the +integral now if you're smart needed + + align:start position:0% +integral now if you're smart needed + + + align:start position:0% +integral now if you're smart needed +trapezoid and then compared it to + + align:start position:0% +trapezoid and then compared it to + + + align:start position:0% +trapezoid and then compared it to +Simpsons then you say oh my goodness + + align:start position:0% +Simpsons then you say oh my goodness + + + align:start position:0% +Simpsons then you say oh my goodness +these are not really that dissimilar and + + align:start position:0% +these are not really that dissimilar and + + + align:start position:0% +these are not really that dissimilar and +so I'm not going to urge an I better do + + align:start position:0% +so I'm not going to urge an I better do + + + align:start position:0% +so I'm not going to urge an I better do +something else okay so I just want you + + align:start position:0% +something else okay so I just want you + + + align:start position:0% +something else okay so I just want you +to be aware when we do these rules what + + align:start position:0% +to be aware when we do these rules what + + + align:start position:0% +to be aware when we do these rules what +we're actually doing is we're fitting + + align:start position:0% +we're actually doing is we're fitting + + + align:start position:0% +we're actually doing is we're fitting +our points to some continuous function + + align:start position:0% +our points to some continuous function + + + align:start position:0% +our points to some continuous function +that we know how to integrate + + align:start position:0% +that we know how to integrate + + + align:start position:0% +that we know how to integrate +and then we do the analytical integral + + align:start position:0% +and then we do the analytical integral + + + align:start position:0% +and then we do the analytical integral +of that function which is a fine thing + + align:start position:0% +of that function which is a fine thing + + + align:start position:0% +of that function which is a fine thing +to do but just be aware that it's like + + align:start position:0% +to do but just be aware that it's like + + + align:start position:0% +to do but just be aware that it's like +extrapolation it's like we're imagining + + align:start position:0% +extrapolation it's like we're imagining + + + align:start position:0% +extrapolation it's like we're imagining +what the function is doing between these + + align:start position:0% +what the function is doing between these + + + align:start position:0% +what the function is doing between these +points when we actually had we haven't + + align:start position:0% +points when we actually had we haven't + + + align:start position:0% +points when we actually had we haven't +tested it now we could we could ask all + + align:start position:0% +tested it now we could we could ask all + + + align:start position:0% +tested it now we could we could ask all +more points right we can calculate it we + + align:start position:0% +more points right we can calculate it we + + + align:start position:0% +more points right we can calculate it we +do but that will cost some more function + + align:start position:0% +do but that will cost some more function + + + align:start position:0% +do but that will cost some more function +of Alice and we're kind of trying to + + align:start position:0% +of Alice and we're kind of trying to + + + align:start position:0% +of Alice and we're kind of trying to +save our computer time so you want to + + align:start position:0% +save our computer time so you want to + + + align:start position:0% +save our computer time so you want to +finish off before the TV so you go buy + + align:start position:0% +finish off before the TV so you go buy + + + align:start position:0% +finish off before the TV so you go buy +some beer and so let's you know we've + + align:start position:0% +some beer and so let's you know we've + + + align:start position:0% +some beer and so let's you know we've +got a we got we have to take some + + align:start position:0% +got a we got we have to take some + + + align:start position:0% +got a we got we have to take some +choices about what to do when we can't + + align:start position:0% +choices about what to do when we can't + + + align:start position:0% +choices about what to do when we can't +do a different number of points for sure + + align:start position:0% +do a different number of points for sure + + + align:start position:0% +do a different number of points for sure +all right so all these methods what + + align:start position:0% +all right so all these methods what + + + align:start position:0% +all right so all these methods what +we're doing was we're approximating our + + align:start position:0% +we're doing was we're approximating our + + + align:start position:0% +we're doing was we're approximating our +true F with some approximate F which is + + align:start position:0% +true F with some approximate F which is + + + align:start position:0% +true F with some approximate F which is +equal to a sum of some basis functions + + align:start position:0% + + + + align:start position:0% + +like this so we pick some basis + + align:start position:0% +like this so we pick some basis + + + align:start position:0% +like this so we pick some basis +functions we know how to integral it + + align:start position:0% +functions we know how to integral it + + + align:start position:0% +functions we know how to integral it +integrate we fit somehow determine what + + align:start position:0% +integrate we fit somehow determine what + + + align:start position:0% +integrate we fit somehow determine what +these C's are and then we decide that + + align:start position:0% +these C's are and then we decide that + + + align:start position:0% +these C's are and then we decide that +the integral is equal to the integral of + + align:start position:0% +the integral is equal to the integral of + + + align:start position:0% +the integral is equal to the integral of +F tilde not F not the actual original F + + align:start position:0% +F tilde not F not the actual original F + + + align:start position:0% +F tilde not F not the actual original F +and then that's gonna actually going to + + align:start position:0% +and then that's gonna actually going to + + + align:start position:0% +and then that's gonna actually going to +be the sum of ck times the integral and + + align:start position:0% +be the sum of ck times the integral and + + + align:start position:0% +be the sum of ck times the integral and +we carefully chose basis functions that + + align:start position:0% +we carefully chose basis functions that + + + align:start position:0% +we carefully chose basis functions that +we know how to do this integral + + align:start position:0% +we know how to do this integral + + + align:start position:0% +we know how to do this integral +analytically + + align:start position:0% +analytically + + + align:start position:0% +analytically +so we have we just plug that to N we + + align:start position:0% +so we have we just plug that to N we + + + align:start position:0% +so we have we just plug that to N we +just have to figure out the C's are get + + align:start position:0% +just have to figure out the C's are get + + + align:start position:0% +just have to figure out the C's are get +then to get this to work okay so that's + + align:start position:0% +then to get this to work okay so that's + + + align:start position:0% +then to get this to work okay so that's +what you really did when you're doing + + align:start position:0% +what you really did when you're doing + + + align:start position:0% +what you really did when you're doing +all this trapezoid roll on since its + + align:start position:0% +all this trapezoid roll on since its + + + align:start position:0% +all this trapezoid roll on since its +norm all kind of stuff and it's just + + align:start position:0% +norm all kind of stuff and it's just + + + align:start position:0% +norm all kind of stuff and it's just +different choices of what the basis + + align:start position:0% +different choices of what the basis + + + align:start position:0% +different choices of what the basis +functions were they used now there's a + + align:start position:0% +functions were they used now there's a + + + align:start position:0% +functions were they used now there's a +lot of choices about how to do that kind + + align:start position:0% +lot of choices about how to do that kind + + + align:start position:0% +lot of choices about how to do that kind +of approximation to make f Tilda's that + + align:start position:0% +of approximation to make f Tilda's that + + + align:start position:0% +of approximation to make f Tilda's that +are sort of like F's with some limit + + align:start position:0% +are sort of like F's with some limit + + + align:start position:0% +are sort of like F's with some limit +limited amount of information and + + align:start position:0% +limited amount of information and + + + align:start position:0% +limited amount of information and +generally has to do with how many case + + align:start position:0% +generally has to do with how many case + + + align:start position:0% +generally has to do with how many case +we have so if K is less than n then it's + + align:start position:0% +we have so if K is less than n then it's + + + align:start position:0% +we have so if K is less than n then it's +really an approximation because there's + + align:start position:0% +really an approximation because there's + + + align:start position:0% +really an approximation because there's +no way we would expect that with just a + + align:start position:0% +no way we would expect that with just a + + + align:start position:0% +no way we would expect that with just a +few parameters we could get a lot of F + + align:start position:0% +few parameters we could get a lot of F + + + align:start position:0% +few parameters we could get a lot of F +of T and so we would expect that F tilde + + align:start position:0% +of T and so we would expect that F tilde + + + align:start position:0% +of T and so we would expect that F tilde +of T and is not equal to + + align:start position:0% +of T and is not equal to + + + align:start position:0% +of T and is not equal to +half of TN at least not at all the + + align:start position:0% +half of TN at least not at all the + + + align:start position:0% +half of TN at least not at all the +points because if n is if you have a lot + + align:start position:0% +points because if n is if you have a lot + + + align:start position:0% +points because if n is if you have a lot +of points and we only have a few + + align:start position:0% +of points and we only have a few + + + align:start position:0% +of points and we only have a few +parameters we don't expect to be able to + + align:start position:0% +parameters we don't expect to be able to + + + align:start position:0% +parameters we don't expect to be able to +fit it perfectly ok so I know this is + + align:start position:0% +fit it perfectly ok so I know this is + + + align:start position:0% +fit it perfectly ok so I know this is +what we expect might might happen if by + + align:start position:0% +what we expect might might happen if by + + + align:start position:0% +what we expect might might happen if by +some luck we chose the basis function + + align:start position:0% +some luck we chose the basis function + + + align:start position:0% +some luck we chose the basis function +with exactly the true function f then it + + align:start position:0% +with exactly the true function f then it + + + align:start position:0% +with exactly the true function f then it +would actually fit perfectly but most + + align:start position:0% +would actually fit perfectly but most + + + align:start position:0% +would actually fit perfectly but most +the time not right by Murphy's Law in + + align:start position:0% +the time not right by Murphy's Law in + + + align:start position:0% +the time not right by Murphy's Law in +fact simply completely wrong but this is + + align:start position:0% +fact simply completely wrong but this is + + + align:start position:0% +fact simply completely wrong but this is +not such a bad idea yeah we come back to + + align:start position:0% +not such a bad idea yeah we come back to + + + align:start position:0% +not such a bad idea yeah we come back to +this later another possibility is to + + align:start position:0% +this later another possibility is to + + + align:start position:0% +this later another possibility is to +choose K equals to N and then we can + + align:start position:0% +choose K equals to N and then we can + + + align:start position:0% +choose K equals to N and then we can +usually we can force F tilde of T n to + + align:start position:0% +usually we can force F tilde of T n to + + + align:start position:0% +usually we can force F tilde of T n to +equal F 2 TN so at the points that we + + align:start position:0% +equal F 2 TN so at the points that we + + + align:start position:0% +equal F 2 TN so at the points that we +have if we have enough parameters equal + + align:start position:0% +have if we have enough parameters equal + + + align:start position:0% +have if we have enough parameters equal +to the number of points then we often we + + align:start position:0% +to the number of points then we often we + + + align:start position:0% +to the number of points then we often we +can get an exact fit we can force the + + align:start position:0% +can get an exact fit we can force the + + + align:start position:0% +can get an exact fit we can force the +function to go through all the points + + align:start position:0% +function to go through all the points + + + align:start position:0% +function to go through all the points +all right and when we do this this is + + align:start position:0% +all right and when we do this this is + + + align:start position:0% +all right and when we do this this is +called interpolation ok now when should + + align:start position:0% +called interpolation ok now when should + + + align:start position:0% +called interpolation ok now when should +you do the one or the other + + align:start position:0% +you do the one or the other + + + align:start position:0% +you do the one or the other +when should I make K as big as an or + + align:start position:0% +when should I make K as big as an or + + + align:start position:0% +when should I make K as big as an or +wench I use K lesson it a really crucial + + align:start position:0% +wench I use K lesson it a really crucial + + + align:start position:0% +wench I use K lesson it a really crucial +thing is whether you really believe your + + align:start position:0% +thing is whether you really believe your + + + align:start position:0% +thing is whether you really believe your +points if you really believe you know f + + align:start position:0% +points if you really believe you know f + + + align:start position:0% +points if you really believe you know f +of T n like two very very high number of + + align:start position:0% +of T n like two very very high number of + + + align:start position:0% +of T n like two very very high number of +significant figures then it makes sense + + align:start position:0% +significant figures then it makes sense + + + align:start position:0% +significant figures then it makes sense +you know that's true so you should force + + align:start position:0% +you know that's true so you should force + + + align:start position:0% +you know that's true so you should force +your fitting function to actually match + + align:start position:0% +your fitting function to actually match + + + align:start position:0% +your fitting function to actually match +that however if you get the f of T n so + + align:start position:0% +that however if you get the f of T n so + + + align:start position:0% +that however if you get the f of T n so +for example from an experiment or from a + + align:start position:0% +for example from an experiment or from a + + + align:start position:0% +for example from an experiment or from a +stochastic simulation that has some + + align:start position:0% +stochastic simulation that has some + + + align:start position:0% +stochastic simulation that has some +noise in it then you might not really + + align:start position:0% +noise in it then you might not really + + + align:start position:0% +noise in it then you might not really +want to do this because you'll be + + align:start position:0% +want to do this because you'll be + + + align:start position:0% +want to do this because you'll be +fitting the noise in the experiment as + + align:start position:0% +fitting the noise in the experiment as + + + align:start position:0% +fitting the noise in the experiment as +well and then you might want to use a + + align:start position:0% +well and then you might want to use a + + + align:start position:0% +well and then you might want to use a +smaller number of case it's smaller + + align:start position:0% +smaller number of case it's smaller + + + align:start position:0% +smaller number of case it's smaller +number of fitting functions smaller + + align:start position:0% +number of fitting functions smaller + + + align:start position:0% +number of fitting functions smaller +number of parameters to make the fit + + align:start position:0% +number of parameters to make the fit + + + align:start position:0% +number of parameters to make the fit +okay so you can do either one you're in + + align:start position:0% +okay so you can do either one you're in + + + align:start position:0% +okay so you can do either one you're in +charge right you get the problem you + + align:start position:0% +charge right you get the problem you + + + align:start position:0% +charge right you get the problem you +know somebody tells you please give me + + align:start position:0% +know somebody tells you please give me + + + align:start position:0% +know somebody tells you please give me +this integral they don't care how you do + + align:start position:0% +this integral they don't care how you do + + + align:start position:0% +this integral they don't care how you do +it + + align:start position:0% +it + + + align:start position:0% +it +right they just want you to come back + + align:start position:0% +right they just want you to come back + + + align:start position:0% +right they just want you to come back +and give them a true value the integral + + align:start position:0% +and give them a true value the integral + + + align:start position:0% +and give them a true value the integral +that's right to some significant figures + + align:start position:0% +that's right to some significant figures + + + align:start position:0% +that's right to some significant figures +and and then so it's up to you to choose + + align:start position:0% +and and then so it's up to you to choose + + + align:start position:0% +and and then so it's up to you to choose +I what to do so you can decide what to + + align:start position:0% +I what to do so you can decide what to + + + align:start position:0% +I what to do so you can decide what to +do what a lot of people do in the + + align:start position:0% +do what a lot of people do in the + + + align:start position:0% +do what a lot of people do in the +world is this one interpolation where + + align:start position:0% +world is this one interpolation where + + + align:start position:0% +world is this one interpolation where +you're assuming that the F of T ends are + + align:start position:0% +you're assuming that the F of T ends are + + + align:start position:0% +you're assuming that the F of T ends are +known exactly and your till your + + align:start position:0% +known exactly and your till your + + + align:start position:0% +known exactly and your till your +function evaluating function is great + + align:start position:0% +function evaluating function is great + + + align:start position:0% +function evaluating function is great +and in that case you can write down this + + align:start position:0% +and in that case you can write down this + + + align:start position:0% +and in that case you can write down this +nice linear equation so we're trying to + + align:start position:0% +nice linear equation so we're trying to + + + align:start position:0% +nice linear equation so we're trying to +make f of T n for the true function to + + align:start position:0% +make f of T n for the true function to + + + align:start position:0% +make f of T n for the true function to +be equal to CK PN of T sorry which and + + align:start position:0% +be equal to CK PN of T sorry which and + + + align:start position:0% +be equal to CK PN of T sorry which and +then subtract eight K is equal to N and + + align:start position:0% +then subtract eight K is equal to N and + + + align:start position:0% +then subtract eight K is equal to N and +I can rewrite this this way this is like + + align:start position:0% +I can rewrite this this way this is like + + + align:start position:0% +I can rewrite this this way this is like +a set of numbers so I can write it as a + + align:start position:0% +a set of numbers so I can write it as a + + + align:start position:0% +a set of numbers so I can write it as a +vector Y and this thing has two indices + + align:start position:0% +vector Y and this thing has two indices + + + align:start position:0% +vector Y and this thing has two indices +on it so it looks like a matrix so I'll + + align:start position:0% +on it so it looks like a matrix so I'll + + + align:start position:0% +on it so it looks like a matrix so I'll +call that M and C is my vector of + + align:start position:0% +call that M and C is my vector of + + + align:start position:0% +call that M and C is my vector of +unknown parameters and wow I know how to + + align:start position:0% +unknown parameters and wow I know how to + + + align:start position:0% +unknown parameters and wow I know how to +solve this one right so C is equal to Y + + align:start position:0% +solve this one right so C is equal to Y + + + align:start position:0% +solve this one right so C is equal to Y +backslash N or n backslash y yeah all + + align:start position:0% +backslash N or n backslash y yeah all + + + align:start position:0% +backslash N or n backslash y yeah all +right now for this to work and have a + + align:start position:0% +right now for this to work and have a + + + align:start position:0% +right now for this to work and have a +unique solution I need em not to be + + align:start position:0% +unique solution I need em not to be + + + align:start position:0% +unique solution I need em not to be +singular and what that means is that the + + align:start position:0% +singular and what that means is that the + + + align:start position:0% +singular and what that means is that the +columns of M have to be linearly + + align:start position:0% +columns of M have to be linearly + + + align:start position:0% +columns of M have to be linearly +independent so what are the columns of M + + align:start position:0% +independent so what are the columns of M + + + align:start position:0% +independent so what are the columns of M +they are fee one no fee K of T 1 CK of T + + align:start position:0% +they are fee one no fee K of T 1 CK of T + + + align:start position:0% +they are fee one no fee K of T 1 CK of T +2 TK of T n right and I want that this + + align:start position:0% +2 TK of T n right and I want that this + + + align:start position:0% +2 TK of T n right and I want that this +column is not a sum of the other columns + + align:start position:0% + + + + align:start position:0% + +so this is kind of a requirement for J + + align:start position:0% +so this is kind of a requirement for J + + + align:start position:0% +so this is kind of a requirement for J +not equal this is kind of requirement if + + align:start position:0% +not equal this is kind of requirement if + + + align:start position:0% +not equal this is kind of requirement if +I'm going to do this kind of procedure + + align:start position:0% +I'm going to do this kind of procedure + + + align:start position:0% +I'm going to do this kind of procedure +is I can't choose a set of basis + + align:start position:0% +is I can't choose a set of basis + + + align:start position:0% +is I can't choose a set of basis +functions that's gonna have this that + + align:start position:0% +functions that's gonna have this that + + + align:start position:0% +functions that's gonna have this that +wouldn't be a linear combination of the + + align:start position:0% +wouldn't be a linear combination of the + + + align:start position:0% +wouldn't be a linear combination of the +other ones because then I'm going to a + + align:start position:0% +other ones because then I'm going to a + + + align:start position:0% +other ones because then I'm going to a +singular matrix my whole process we have + + align:start position:0% +singular matrix my whole process we have + + + align:start position:0% +singular matrix my whole process we have +a big problem right for the beginning so + + align:start position:0% +a big problem right for the beginning so + + + align:start position:0% +a big problem right for the beginning so +I have to insure this this is not true + + align:start position:0% +I have to insure this this is not true + + + align:start position:0% +I have to insure this this is not true +okay really yeah this is true these are + + align:start position:0% +okay really yeah this is true these are + + + align:start position:0% +okay really yeah this is true these are +not equal some of them another way to + + align:start position:0% +not equal some of them another way to + + + align:start position:0% +not equal some of them another way to +write that is to write that we want is + + align:start position:0% +write that is to write that we want is + + + align:start position:0% +write that is to write that we want is +to choose the fees the columns of feed + + align:start position:0% +to choose the fees the columns of feed + + + align:start position:0% +to choose the fees the columns of feed +to be orthogonal to each other and so I + + align:start position:0% +to be orthogonal to each other and so I + + + align:start position:0% +to be orthogonal to each other and so I +could write it this way okay so I want + + align:start position:0% +could write it this way okay so I want + + + align:start position:0% +could write it this way okay so I want +them to be orthogonal to each other and + + align:start position:0% +them to be orthogonal to each other and + + + align:start position:0% +them to be orthogonal to each other and +then you can see how this kind of + + align:start position:0% +then you can see how this kind of + + + align:start position:0% +then you can see how this kind of +generalizes if I had a lot of T's this + + align:start position:0% +generalizes if I had a lot of T's this + + + align:start position:0% +generalizes if I had a lot of T's this +what sort of like looked like the + + align:start position:0% +what sort of like looked like the + + + align:start position:0% +what sort of like looked like the +integral of feet km T V J of T and so + + align:start position:0% +integral of feet km T V J of T and so + + + align:start position:0% +integral of feet km T V J of T and so +this gives the idea of orthogonal + + align:start position:0% +this gives the idea of orthogonal + + + align:start position:0% +this gives the idea of orthogonal +functions so this is our thuggin all + + align:start position:0% +functions so this is our thuggin all + + + align:start position:0% +functions so this is our thuggin all +functions in my discrete at my discrete + + align:start position:0% +functions in my discrete at my discrete + + + align:start position:0% +functions in my discrete at my discrete +points TN and this is the general + + align:start position:0% +points TN and this is the general + + + align:start position:0% +points TN and this is the general +concept of orthogonal functions and then + + align:start position:0% +concept of orthogonal functions and then + + + align:start position:0% +concept of orthogonal functions and then +when I define it this way I need to + + align:start position:0% +when I define it this way I need to + + + align:start position:0% +when I define it this way I need to +actually decide my own A's and B's and I + + align:start position:0% +actually decide my own A's and B's and I + + + align:start position:0% +actually decide my own A's and B's and I +want to use and if you use different + + align:start position:0% +want to use and if you use different + + + align:start position:0% +want to use and if you use different +ones you actually you have different + + align:start position:0% +ones you actually you have different + + + align:start position:0% +ones you actually you have different +rules about what's orthogonal to each + + align:start position:0% +rules about what's orthogonal to each + + + align:start position:0% +rules about what's orthogonal to each +other and also sometimes people are + + align:start position:0% +other and also sometimes people are + + + align:start position:0% +other and also sometimes people are +fishy and they spit a little W of T in + + align:start position:0% +fishy and they spit a little W of T in + + + align:start position:0% +fishy and they spit a little W of T in +here just to do because they have some + + align:start position:0% +here just to do because they have some + + + align:start position:0% +here just to do because they have some +special problem where this W keeps + + align:start position:0% +special problem where this W keeps + + + align:start position:0% +special problem where this W keeps +showing up or something and they want to + + align:start position:0% +showing up or something and they want to + + + align:start position:0% +showing up or something and they want to +do that but that's that's up to them + + align:start position:0% +do that but that's that's up to them + + + align:start position:0% +do that but that's that's up to them +right well we won't specify that but + + align:start position:0% +right well we won't specify that but + + + align:start position:0% +right well we won't specify that but +this is the general idea of making basis + + align:start position:0% +this is the general idea of making basis + + + align:start position:0% +this is the general idea of making basis +functions orthogonal to each other and + + align:start position:0% +functions orthogonal to each other and + + + align:start position:0% +functions orthogonal to each other and +it's very analogous to making adventures + + align:start position:0% +it's very analogous to making adventures + + + align:start position:0% +it's very analogous to making adventures +of each other which is what we did here + + align:start position:0% +of each other which is what we did here + + + align:start position:0% +of each other which is what we did here +these are actually vectors right + + align:start position:0% +these are actually vectors right + + + align:start position:0% +these are actually vectors right +it's just as the vector gets longer and + + align:start position:0% +it's just as the vector gets longer and + + + align:start position:0% +it's just as the vector gets longer and +longer it gets more and more like a + + align:start position:0% +longer it gets more and more like a + + + align:start position:0% +longer it gets more and more like a +continuous function and we have more Chi + + align:start position:0% +continuous function and we have more Chi + + + align:start position:0% +continuous function and we have more Chi +points and eventually it looks like that + + align:start position:0% +points and eventually it looks like that + + + align:start position:0% +points and eventually it looks like that +interval as you go to infinity alright + + align:start position:0% +interval as you go to infinity alright + + + align:start position:0% +interval as you go to infinity alright +so anyway so a lot of you times people + + align:start position:0% +so anyway so a lot of you times people + + + align:start position:0% +so anyway so a lot of you times people +will choose functions which are designed + + align:start position:0% +will choose functions which are designed + + + align:start position:0% +will choose functions which are designed +to be orthogonal and one way to do it is + + align:start position:0% +to be orthogonal and one way to do it is + + + align:start position:0% +to be orthogonal and one way to do it is +just go with a continuous want to start + + align:start position:0% +just go with a continuous want to start + + + align:start position:0% +just go with a continuous want to start +now we can choose any basis functions we + + align:start position:0% +now we can choose any basis functions we + + + align:start position:0% +now we can choose any basis functions we +want over here we already chose a whole + + align:start position:0% +want over here we already chose a whole + + + align:start position:0% +want over here we already chose a whole +bunch you guys have done this already I + + align:start position:0% +bunch you guys have done this already I + + + align:start position:0% +bunch you guys have done this already I +know if you knew you're doing it but you + + align:start position:0% +know if you knew you're doing it but you + + + align:start position:0% +know if you knew you're doing it but you +chose a lot of different baselines look + + align:start position:0% +chose a lot of different baselines look + + + align:start position:0% +chose a lot of different baselines look +completely different from each other you + + align:start position:0% +completely different from each other you + + + align:start position:0% +completely different from each other you +can choose two different ones if you + + align:start position:0% +can choose two different ones if you + + + align:start position:0% +can choose two different ones if you +want and one popular choice is + + align:start position:0% +want and one popular choice is + + + align:start position:0% +want and one popular choice is +polynomials but it's not the only choice + + align:start position:0% +polynomials but it's not the only choice + + + align:start position:0% +polynomials but it's not the only choice +and in fact a little bit later we're + + align:start position:0% +and in fact a little bit later we're + + + align:start position:0% +and in fact a little bit later we're +gonna in the homework problem six I + + align:start position:0% +gonna in the homework problem six I + + + align:start position:0% +gonna in the homework problem six I +think we're gonna have a problem where + + align:start position:0% +think we're gonna have a problem where + + + align:start position:0% +think we're gonna have a problem where +you have to do the different kind of + + align:start position:0% +you have to do the different kind of + + + align:start position:0% +you have to do the different kind of +basic functions you can use any basic I + + align:start position:0% +basic functions you can use any basic I + + + align:start position:0% +basic functions you can use any basic I +should you want and there's kind of ones + + align:start position:0% +should you want and there's kind of ones + + + align:start position:0% +should you want and there's kind of ones +that match naturally to the problem + + align:start position:0% +that match naturally to the problem + + + align:start position:0% +that match naturally to the problem +however people know a lot about + + align:start position:0% +however people know a lot about + + + align:start position:0% +however people know a lot about +polynomials and so they decide these + + align:start position:0% +polynomials and so they decide these + + + align:start position:0% +polynomials and so they decide these +polynomials align and so that's the most + + align:start position:0% +polynomials align and so that's the most + + + align:start position:0% +polynomials align and so that's the most +common choice for numerical integrations + + align:start position:0% +common choice for numerical integrations + + + align:start position:0% +common choice for numerical integrations +polynomials one thing is polymers are + + align:start position:0% +polynomials one thing is polymers are + + + align:start position:0% +polynomials one thing is polymers are +super easy to integrate because that was + + align:start position:0% +super easy to integrate because that was + + + align:start position:0% +super easy to integrate because that was +the first thing you learned right how do + + align:start position:0% +the first thing you learned right how do + + + align:start position:0% +the first thing you learned right how do +you do the integrals of polynomials and + + align:start position:0% +you do the integrals of polynomials and + + + align:start position:0% +you do the integrals of polynomials and +also they're easy to evaluate it only + + align:start position:0% +also they're easy to evaluate it only + + + align:start position:0% +also they're easy to evaluate it only +takes ten operations to evaluate a + + align:start position:0% +takes ten operations to evaluate a + + + align:start position:0% +takes ten operations to evaluate a +polynomial of nth order and there's a + + align:start position:0% +polynomial of nth order and there's a + + + align:start position:0% +polynomial of nth order and there's a +ton of theorems and things are known + + align:start position:0% +ton of theorems and things are known + + + align:start position:0% +ton of theorems and things are known +about polynomials have all kinds of + + align:start position:0% +about polynomials have all kinds of + + + align:start position:0% +about polynomials have all kinds of +special properties and they have all + + align:start position:0% +special properties and they have all + + + align:start position:0% +special properties and they have all +kinds of convenient tools for handling + + align:start position:0% +kinds of convenient tools for handling + + + align:start position:0% +kinds of convenient tools for handling +them so let's go with polynomials for + + align:start position:0% +them so let's go with polynomials for + + + align:start position:0% +them so let's go with polynomials for +now now I want to warn you though that + + align:start position:0% +now now I want to warn you though that + + + align:start position:0% +now now I want to warn you though that +high order polynomials are really not + + align:start position:0% +high order polynomials are really not + + + align:start position:0% +high order polynomials are really not +very good very good fitting functions or + + align:start position:0% +very good very good fitting functions or + + + align:start position:0% +very good very good fitting functions or +interpolating functions for a lot of + + align:start position:0% +interpolating functions for a lot of + + + align:start position:0% +interpolating functions for a lot of +problems and in particular for this one + + align:start position:0% +problems and in particular for this one + + + align:start position:0% +problems and in particular for this one +I showed here with that this is the + + align:start position:0% +I showed here with that this is the + + + align:start position:0% +I showed here with that this is the +function up here that function you can + + align:start position:0% +function up here that function you can + + + align:start position:0% +function up here that function you can +try to fit that with higher and higher + + align:start position:0% +try to fit that with higher and higher + + + align:start position:0% +try to fit that with higher and higher +order polynomials so I can have my + + align:start position:0% +order polynomials so I can have my + + + align:start position:0% +order polynomials so I can have my +function the function value at 0 is 1 so + + align:start position:0% +function the function value at 0 is 1 so + + + align:start position:0% +function the function value at 0 is 1 so +it's a fun to function looks kind of + + align:start position:0% +it's a fun to function looks kind of + + + align:start position:0% +it's a fun to function looks kind of +reasonable that centrical better than I + + align:start position:0% +reasonable that centrical better than I + + + align:start position:0% +reasonable that centrical better than I +drew it okay and you can put some number + + align:start position:0% +drew it okay and you can put some number + + + align:start position:0% +drew it okay and you can put some number +of points in here + + align:start position:0% +of points in here + + + align:start position:0% +of points in here +and then you can do it interpolating + + align:start position:0% +and then you can do it interpolating + + + align:start position:0% +and then you can do it interpolating +polynomial that goes through all the + + align:start position:0% +polynomial that goes through all the + + + align:start position:0% +polynomial that goes through all the +points alright and if you do it for this + + align:start position:0% +points alright and if you do it for this + + + align:start position:0% +points alright and if you do it for this +one with five points you get something + + align:start position:0% +one with five points you get something + + + align:start position:0% +one with five points you get something +looks like this because negative comes + + align:start position:0% +looks like this because negative comes + + + align:start position:0% +looks like this because negative comes +up like this so that's that's the one + + align:start position:0% +up like this so that's that's the one + + + align:start position:0% +up like this so that's that's the one +you got to use five points across this + + align:start position:0% +you got to use five points across this + + + align:start position:0% +you got to use five points across this +interval if you use ten points then you + + align:start position:0% +interval if you use ten points then you + + + align:start position:0% +interval if you use ten points then you +get one that looks like this where the + + align:start position:0% +get one that looks like this where the + + + align:start position:0% +get one that looks like this where the +peak value here is two whereas the + + align:start position:0% +peak value here is two whereas the + + + align:start position:0% +peak value here is two whereas the +maxima drizzle function just one and the + + align:start position:0% +maxima drizzle function just one and the + + + align:start position:0% +maxima drizzle function just one and the +original functions always positive but + + align:start position:0% +original functions always positive but + + + align:start position:0% +original functions always positive but +this they both go negative so even + + align:start position:0% +this they both go negative so even + + + align:start position:0% +this they both go negative so even +within the range of the interpolation + + align:start position:0% +within the range of the interpolation + + + align:start position:0% +within the range of the interpolation +the pounding those kind of wild swings + + align:start position:0% +the pounding those kind of wild swings + + + align:start position:0% +the pounding those kind of wild swings +and this so this first one was for a + + align:start position:0% +and this so this first one was for a + + + align:start position:0% +and this so this first one was for a +fifth order to third a polynomial or + + align:start position:0% +fifth order to third a polynomial or + + + align:start position:0% +fifth order to third a polynomial or +maybe fourth order five points and then + + align:start position:0% +maybe fourth order five points and then + + + align:start position:0% +maybe fourth order five points and then +and this one is for the next ten Twitter + + align:start position:0% +and this one is for the next ten Twitter + + + align:start position:0% +and this one is for the next ten Twitter +or ninth order oh no Meah I'm not sure + + align:start position:0% +or ninth order oh no Meah I'm not sure + + + align:start position:0% +or ninth order oh no Meah I'm not sure +which way yeah so I didn't drive very + + align:start position:0% +which way yeah so I didn't drive very + + + align:start position:0% +which way yeah so I didn't drive very +well hey you guys go home do this right + + align:start position:0% +well hey you guys go home do this right + + + align:start position:0% +well hey you guys go home do this right +with MATLAB will take you a minute to do + + align:start position:0% +with MATLAB will take you a minute to do + + + align:start position:0% +with MATLAB will take you a minute to do +the fit just solve this equation where + + align:start position:0% +the fit just solve this equation where + + + align:start position:0% +the fit just solve this equation where +you put in the function values here and + + align:start position:0% +you put in the function values here and + + + align:start position:0% +you put in the function values here and +put in the polynomial values at the + + align:start position:0% +put in the polynomial values at the + + + align:start position:0% +put in the polynomial values at the +front here for monomials do you do the + + align:start position:0% +front here for monomials do you do the + + + align:start position:0% +front here for monomials do you do the +first power to the second power to user + + align:start position:0% +first power to the second power to user + + + align:start position:0% +first power to the second power to user +however like that and just do it and you + + align:start position:0% +however like that and just do it and you + + + align:start position:0% +however like that and just do it and you +can get the plot yourself and just this + + align:start position:0% +can get the plot yourself and just this + + + align:start position:0% +can get the plot yourself and just this +just to convince yourself about the + + align:start position:0% +just to convince yourself about the + + + align:start position:0% +just to convince yourself about the +problem and this is very important to + + align:start position:0% +problem and this is very important to + + + align:start position:0% +problem and this is very important to +keep in mind because we're so used to + + align:start position:0% +keep in mind because we're so used to + + + align:start position:0% +keep in mind because we're so used to +using polynomials to think that their + + align:start position:0% +using polynomials to think that their + + + align:start position:0% +using polynomials to think that their +solution of everything in Excel doesn't + + align:start position:0% +solution of everything in Excel doesn't + + + align:start position:0% +solution of everything in Excel doesn't +great but it's not the solution to + + align:start position:0% +great but it's not the solution to + + + align:start position:0% +great but it's not the solution to +everything + + align:start position:0% +everything + + + align:start position:0% +everything +nonetheless we're going to plow on and + + align:start position:0% +nonetheless we're going to plow on and + + + align:start position:0% +nonetheless we're going to plow on and +keep using for a few minutes so one + + align:start position:0% +keep using for a few minutes so one + + + align:start position:0% +keep using for a few minutes so one +possibility when I'm choosing this basis + + align:start position:0% +possibility when I'm choosing this basis + + + align:start position:0% +possibility when I'm choosing this basis +set + + align:start position:0% +set + + + align:start position:0% +set +is I could choose what are called + + align:start position:0% +is I could choose what are called + + + align:start position:0% +is I could choose what are called +monomials which is CK is equal to X to + + align:start position:0% +monomials which is CK is equal to X to + + + align:start position:0% +monomials which is CK is equal to X to +the K minus okay and this one is super + + align:start position:0% +the K minus okay and this one is super + + + align:start position:0% +the K minus okay and this one is super +simple and a lot of times it satisfies + + align:start position:0% +simple and a lot of times it satisfies + + + align:start position:0% +simple and a lot of times it satisfies +this orthogonality thing which I showed + + align:start position:0% +this orthogonality thing which I showed + + + align:start position:0% +this orthogonality thing which I showed +you before but it's a really bad choice + + align:start position:0% +you before but it's a really bad choice + + + align:start position:0% +you before but it's a really bad choice +usually and what it is is that the + + align:start position:0% +usually and what it is is that the + + + align:start position:0% +usually and what it is is that the +matrix you have to solve for this + + align:start position:0% +matrix you have to solve for this + + + align:start position:0% +matrix you have to solve for this +interpolation if you have evenly spaced + + align:start position:0% +interpolation if you have evenly spaced + + + align:start position:0% +interpolation if you have evenly spaced +points and you have X to the K it turns + + align:start position:0% +points and you have X to the K it turns + + + align:start position:0% +points and you have X to the K it turns +out that this matrix usually has a + + align:start position:0% +out that this matrix usually has a + + + align:start position:0% +out that this matrix usually has a +condition number that grows + + align:start position:0% +condition number that grows + + + align:start position:0% +condition number that grows +exponentially with the number of terms + + align:start position:0% +exponentially with the number of terms + + + align:start position:0% +exponentially with the number of terms +in your basis the number of how many 1l + + align:start position:0% +in your basis the number of how many 1l + + + align:start position:0% +in your basis the number of how many 1l +meals you include so condition number to + + align:start position:0% +meals you include so condition number to + + + align:start position:0% +meals you include so condition number to +grow exponentially it's a bad really bad + + align:start position:0% +grow exponentially it's a bad really bad + + + align:start position:0% +grow exponentially it's a bad really bad +idea okay + + align:start position:0% +idea okay + + + align:start position:0% +idea okay +so this is not what people use so you + + align:start position:0% +so this is not what people use so you + + + align:start position:0% +so this is not what people use so you +might be tempted to do this and maybe + + align:start position:0% +might be tempted to do this and maybe + + + align:start position:0% +might be tempted to do this and maybe +you did it once in your life I won't I + + align:start position:0% +you did it once in your life I won't I + + + align:start position:0% +you did it once in your life I won't I +won't blame you if you did but it's not + + align:start position:0% +won't blame you if you did but it's not + + + align:start position:0% +won't blame you if you did but it's not +really smart idea so instead a lot of + + align:start position:0% +really smart idea so instead a lot of + + + align:start position:0% +really smart idea so instead a lot of +the mathematicians of the 1700 and 1800 + + align:start position:0% +the mathematicians of the 1700 and 1800 + + + align:start position:0% +the mathematicians of the 1700 and 1800 +spent a lot of time worried about this + + align:start position:0% +spent a lot of time worried about this + + + align:start position:0% +spent a lot of time worried about this +and and they'd end up deciding to use + + align:start position:0% +and and they'd end up deciding to use + + + align:start position:0% +and and they'd end up deciding to use +other parlament we also have people's + + align:start position:0% +other parlament we also have people's + + + align:start position:0% +other parlament we also have people's +names on them + + align:start position:0% +names on them + + + align:start position:0% +names on them +so a guy named mr. Abe's right so guy + + align:start position:0% +so a guy named mr. Abe's right so guy + + + align:start position:0% +so a guy named mr. Abe's right so guy +named Lagrange's ain't I he did the + + align:start position:0% +named Lagrange's ain't I he did the + + + align:start position:0% +named Lagrange's ain't I he did the +multiplier he suggested two polynomials + + align:start position:0% +multiplier he suggested two polynomials + + + align:start position:0% +multiplier he suggested two polynomials +they're given their kind of complicated + + align:start position:0% +they're given their kind of complicated + + + align:start position:0% +they're given their kind of complicated +they're given in the book but what they + + align:start position:0% +they're given in the book but what they + + + align:start position:0% +they're given in the book but what they +really are is I'm taking the monomial + + align:start position:0% +really are is I'm taking the monomial + + + align:start position:0% +really are is I'm taking the monomial +basis set and I'm making a new basis set + + align:start position:0% +basis set and I'm making a new basis set + + + align:start position:0% +basis set and I'm making a new basis set +so I want Phi al to be equal to the sum + + align:start position:0% +so I want Phi al to be equal to the sum + + + align:start position:0% +so I want Phi al to be equal to the sum +dl k by k where this Phi K is the + + align:start position:0% +dl k by k where this Phi K is the + + + align:start position:0% +dl k by k where this Phi K is the +monomials okay so really you can choose + + align:start position:0% +monomials okay so really you can choose + + + align:start position:0% +monomials okay so really you can choose +any D you want you're just taking linear + + align:start position:0% +any D you want you're just taking linear + + + align:start position:0% +any D you want you're just taking linear +combinations of the original monomial + + align:start position:0% +combinations of the original monomial + + + align:start position:0% +combinations of the original monomial +basis set to make up polynomials and if + + align:start position:0% +basis set to make up polynomials and if + + + align:start position:0% +basis set to make up polynomials and if +you cleverly choose the D you can choose + + align:start position:0% +you cleverly choose the D you can choose + + + align:start position:0% +you cleverly choose the D you can choose +the test special properties so + + align:start position:0% +the test special properties so + + + align:start position:0% +the test special properties so +Lagrangian choices the D that is + + align:start position:0% +Lagrangian choices the D that is + + + align:start position:0% +Lagrangian choices the D that is +brilliant in the sense that when you do + + align:start position:0% +brilliant in the sense that when you do + + + align:start position:0% +brilliant in the sense that when you do +the solve + + align:start position:0% +the solve + + + align:start position:0% +the solve +problem M times C is equal to Y to try + + align:start position:0% +problem M times C is equal to Y to try + + + align:start position:0% +problem M times C is equal to Y to try +to do your interpolation it turns out + + align:start position:0% +to do your interpolation it turns out + + + align:start position:0% +to do your interpolation it turns out +that the C's you want CK is equal to f + + align:start position:0% +that the C's you want CK is equal to f + + + align:start position:0% +that the C's you want CK is equal to f +of T so you don't have to do any work to + + align:start position:0% +of T so you don't have to do any work to + + + align:start position:0% +of T so you don't have to do any work to +solve for the CSR it's just the F values + + align:start position:0% +solve for the CSR it's just the F values + + + align:start position:0% +solve for the CSR it's just the F values +directly no chance for condition numbers + + align:start position:0% +directly no chance for condition numbers + + + align:start position:0% +directly no chance for condition numbers +no problems it's it so that's the the + + align:start position:0% +no problems it's it so that's the the + + + align:start position:0% +no problems it's it so that's the the +Lagrange polynomials now Newton had a + + align:start position:0% +Lagrange polynomials now Newton had a + + + align:start position:0% +Lagrange polynomials now Newton had a +different idea + + align:start position:0% +different idea + + + align:start position:0% +different idea +so this is this is for you choose a loop + + align:start position:0% +so this is this is for you choose a loop + + + align:start position:0% +so this is this is for you choose a loop +notion of hilio basis then this is the + + align:start position:0% +notion of hilio basis then this is the + + + align:start position:0% +notion of hilio basis then this is the +and you do the square system that's it + + align:start position:0% +and you do the square system that's it + + + align:start position:0% +and you do the square system that's it +if you choose the Newton he was he got + + align:start position:0% +if you choose the Newton he was he got + + + align:start position:0% +if you choose the Newton he was he got +into this business too and he made some + + align:start position:0% +into this business too and he made some + + + align:start position:0% +into this business too and he made some +polynomials and he made ones that have a + + align:start position:0% +polynomials and he made ones that have a + + + align:start position:0% +polynomials and he made ones that have a +special property that if you solve you + + align:start position:0% +special property that if you solve you + + + align:start position:0% +special property that if you solve you +solve it so he chose a different D get + + align:start position:0% +solve it so he chose a different D get + + + align:start position:0% +solve it so he chose a different D get +something you have to stuff to do some + + align:start position:0% +something you have to stuff to do some + + + align:start position:0% +something you have to stuff to do some +saw you get the solution and then you + + align:start position:0% +saw you get the solution and then you + + + align:start position:0% +saw you get the solution and then you +decide you know that I don't like that + + align:start position:0% +decide you know that I don't like that + + + align:start position:0% +decide you know that I don't like that +interpolation I want to put some more + + align:start position:0% +interpolation I want to put some more + + + align:start position:0% +interpolation I want to put some more +points in I'm going to do a few more + + align:start position:0% +points in I'm going to do a few more + + + align:start position:0% +points in I'm going to do a few more +function evaluations then we gonna add + + align:start position:0% +function evaluations then we gonna add + + + align:start position:0% +function evaluations then we gonna add +some more so I have from the first solve + + align:start position:0% +some more so I have from the first solve + + + align:start position:0% +some more so I have from the first solve +I have the values of C 1 C 2 C 3 up to + + align:start position:0% +I have the values of C 1 C 2 C 3 up to + + + align:start position:0% +I have the values of C 1 C 2 C 3 up to +see the number of points I had initially + + align:start position:0% +see the number of points I had initially + + + align:start position:0% +see the number of points I had initially +and now I want to add another say I had + + align:start position:0% +and now I want to add another say I had + + + align:start position:0% +and now I want to add another say I had +one more data point or add one more F of + + align:start position:0% +one more data point or add one more F of + + + align:start position:0% +one more data point or add one more F of +T n a bit more function evaluation I + + align:start position:0% +T n a bit more function evaluation I + + + align:start position:0% +T n a bit more function evaluation I +want to figure out what C of n plus 1 is + + align:start position:0% +want to figure out what C of n plus 1 is + + + align:start position:0% +want to figure out what C of n plus 1 is +what the next one is it turns out that + + align:start position:0% +what the next one is it turns out that + + + align:start position:0% +what the next one is it turns out that +it's his phone Daniel's the values of + + align:start position:0% +it's his phone Daniel's the values of + + + align:start position:0% +it's his phone Daniel's the values of +DCs don't change when I when I make this + + align:start position:0% +DCs don't change when I when I make this + + + align:start position:0% +DCs don't change when I when I make this +matrix little bit bigger by adding one + + align:start position:0% +matrix little bit bigger by adding one + + + align:start position:0% +matrix little bit bigger by adding one +more y and I add one more parameter and + + align:start position:0% +more y and I add one more parameter and + + + align:start position:0% +more y and I add one more parameter and +I make the one more row in the matrix + + align:start position:0% +I make the one more row in the matrix + + + align:start position:0% +I make the one more row in the matrix +one more column in the matrix when I do + + align:start position:0% +one more column in the matrix when I do + + + align:start position:0% +one more column in the matrix when I do +that it's a unique property that none of + + align:start position:0% +that it's a unique property that none of + + + align:start position:0% +that it's a unique property that none of +these other C's change the solution is + + align:start position:0% +these other C's change the solution is + + + align:start position:0% +these other C's change the solution is +going to be the same except for the n + + align:start position:0% +going to be the same except for the n + + + align:start position:0% +going to be the same except for the n +plus one one so then I can write a neat + + align:start position:0% +plus one one so then I can write a neat + + + align:start position:0% +plus one one so then I can write a neat +cute little equation just for the n plus + + align:start position:0% +cute little equation just for the n plus + + + align:start position:0% +cute little equation just for the n plus +one one I don't have s with the previous + + align:start position:0% +one one I don't have s with the previous + + + align:start position:0% +one one I don't have s with the previous +ones and so I'm just adding a base punch + + align:start position:0% +ones and so I'm just adding a base punch + + + align:start position:0% +ones and so I'm just adding a base punch +and it sort of polishes up my original + + align:start position:0% +and it sort of polishes up my original + + + align:start position:0% +and it sort of polishes up my original +thing okay so that's a nice property too + + align:start position:0% +thing okay so that's a nice property too + + + align:start position:0% +thing okay so that's a nice property too +whereas with the Lagrangian feet + + align:start position:0% +whereas with the Lagrangian feet + + + align:start position:0% +whereas with the Lagrangian feet +everything and all the C's will change + + align:start position:0% + + + + align:start position:0% + +all right I see what the season won't + + align:start position:0% +all right I see what the season won't + + + align:start position:0% +all right I see what the season won't +change I take that back you had points + + align:start position:0% +change I take that back you had points + + + align:start position:0% +change I take that back you had points +the season won't change but the actual + + align:start position:0% +the season won't change but the actual + + + align:start position:0% +the season won't change but the actual +polynomials will change the D will + + align:start position:0% +polynomials will change the D will + + + align:start position:0% +polynomials will change the D will +change because the D depends on the + + align:start position:0% +change because the D depends on the + + + align:start position:0% +change because the D depends on the +choice of the date time points in a + + align:start position:0% +choice of the date time points in a + + + align:start position:0% +choice of the date time points in a +complicated way in the garage all right + + align:start position:0% +complicated way in the garage all right + + + align:start position:0% +complicated way in the garage all right +so now he's trying to think oh my + + align:start position:0% +so now he's trying to think oh my + + + align:start position:0% +so now he's trying to think oh my +goodness I have all these choices I can + + align:start position:0% +goodness I have all these choices I can + + + align:start position:0% +goodness I have all these choices I can +use legrasse I could use Newton I could + + align:start position:0% +use legrasse I could use Newton I could + + + align:start position:0% +use legrasse I could use Newton I could +use monomials maybe I should you know to + + align:start position:0% +use monomials maybe I should you know to + + + align:start position:0% +use monomials maybe I should you know to +go back to bed and you think well is + + align:start position:0% +go back to bed and you think well is + + + align:start position:0% +go back to bed and you think well is +could somebody just tell me what the + + align:start position:0% +could somebody just tell me what the + + + align:start position:0% +could somebody just tell me what the +best one is I'll just do that one I + + align:start position:0% +best one is I'll just do that one I + + + align:start position:0% +best one is I'll just do that one I +don't know I need to learn about all + + align:start position:0% +don't know I need to learn about all + + + align:start position:0% +don't know I need to learn about all +this historical stuff about development + + align:start position:0% +this historical stuff about development + + + align:start position:0% +this historical stuff about development +of polynomial mathematics I just like to + + align:start position:0% +of polynomial mathematics I just like to + + + align:start position:0% +of polynomial mathematics I just like to +just tell me what the answer is so Gauss + + align:start position:0% +just tell me what the answer is so Gauss + + + align:start position:0% +just tell me what the answer is so Gauss +typically figured out what the best one + + align:start position:0% +typically figured out what the best one + + + align:start position:0% +typically figured out what the best one +is and he said you know if we're gonna + + align:start position:0% +is and he said you know if we're gonna + + + align:start position:0% +is and he said you know if we're gonna +do integrals we'd really like to just + + align:start position:0% +do integrals we'd really like to just + + + align:start position:0% +do integrals we'd really like to just +write our integrals this way so our + + align:start position:0% +write our integrals this way so our + + + align:start position:0% +write our integrals this way so our +approximate integral value to be equal + + align:start position:0% +approximate integral value to be equal + + + align:start position:0% +approximate integral value to be equal +to some weight functions times the + + align:start position:0% +to some weight functions times the + + + align:start position:0% +to some weight functions times the +function evaluations at some times right + + align:start position:0% +function evaluations at some times right + + + align:start position:0% +function evaluations at some times right +that's easy to evaluate that'll be good + + align:start position:0% +that's easy to evaluate that'll be good + + + align:start position:0% +that's easy to evaluate that'll be good +if I pre-computer the weight functions + + align:start position:0% +if I pre-computer the weight functions + + + align:start position:0% +if I pre-computer the weight functions +at the x then I put any function f in + + align:start position:0% +at the x then I put any function f in + + + align:start position:0% +at the x then I put any function f in +here I could just do this like a zip all + + align:start position:0% +here I could just do this like a zip all + + + align:start position:0% +here I could just do this like a zip all +right it's one dot product of the F of T + + align:start position:0% +right it's one dot product of the F of T + + + align:start position:0% +right it's one dot product of the F of T +ends I'll have the solution so I want to + + align:start position:0% +ends I'll have the solution so I want to + + + align:start position:0% +ends I'll have the solution so I want to +do that so what's the best possible + + align:start position:0% +do that so what's the best possible + + + align:start position:0% +do that so what's the best possible +choices of the W's and the t's to make + + align:start position:0% +choices of the W's and the t's to make + + + align:start position:0% +choices of the W's and the t's to make +this really be close well the problem is + + align:start position:0% +this really be close well the problem is + + + align:start position:0% +this really be close well the problem is +there's infinite number of functions + + align:start position:0% +there's infinite number of functions + + + align:start position:0% +there's infinite number of functions +that somebody might want to integrate I + + align:start position:0% +that somebody might want to integrate I + + + align:start position:0% +that somebody might want to integrate I +can't do them all so he said let's just + + align:start position:0% +can't do them all so he said let's just + + + align:start position:0% +can't do them all so he said let's just +find the one that works for as many + + align:start position:0% +find the one that works for as many + + + align:start position:0% +find the one that works for as many +monomials as possible to the highest + + align:start position:0% +monomials as possible to the highest + + + align:start position:0% +monomials as possible to the highest +order there's many as far as I can go + + align:start position:0% +order there's many as far as I can go + + + align:start position:0% +order there's many as far as I can go +and it turns out I have I have n w's I + + align:start position:0% +and it turns out I have I have n w's I + + + align:start position:0% +and it turns out I have I have n w's I +have n T so I have two n parameters that + + align:start position:0% +have n T so I have two n parameters that + + + align:start position:0% +have n T so I have two n parameters that +I can fiddle around with and so I should + + align:start position:0% +I can fiddle around with and so I should + + + align:start position:0% +I can fiddle around with and so I should +get something like two ends and my + + align:start position:0% +get something like two ends and my + + + align:start position:0% +get something like two ends and my +polynomials may to n minus one all right + + align:start position:0% +polynomials may to n minus one all right + + + align:start position:0% +polynomials may to n minus one all right +so what I want is that I want to choose + + align:start position:0% +so what I want is that I want to choose + + + align:start position:0% +so what I want is that I want to choose +this so that for the monomial one and + + align:start position:0% +this so that for the monomial one and + + + align:start position:0% +this so that for the monomial one and +the moment you'll T in the motif squared + + align:start position:0% +the moment you'll T in the motif squared + + + align:start position:0% +the moment you'll T in the motif squared +that this is actually going to be exact + + align:start position:0% +that this is actually going to be exact + + + align:start position:0% +that this is actually going to be exact +so what I want + + align:start position:0% +so what I want + + + align:start position:0% +so what I want +is for the monomial one I want the + + align:start position:0% +is for the monomial one I want the + + + align:start position:0% +is for the monomial one I want the +summation of W and my F for the movia + + align:start position:0% +summation of W and my F for the movia + + + align:start position:0% +summation of W and my F for the movia +one is always one so it's x one I want + + align:start position:0% +one is always one so it's x one I want + + + align:start position:0% +one is always one so it's x one I want +this to equal the integral from A to B + + align:start position:0% +this to equal the integral from A to B + + + align:start position:0% +this to equal the integral from A to B +of 1 DT which is B minus a ok so that + + align:start position:0% +of 1 DT which is B minus a ok so that + + + align:start position:0% +of 1 DT which is B minus a ok so that +gives me one equation for the W's then + + align:start position:0% +gives me one equation for the W's then + + + align:start position:0% +gives me one equation for the W's then +for the next one I want the summation W + + align:start position:0% +for the next one I want the summation W + + + align:start position:0% +for the next one I want the summation W +n times T and to equal the integral of A + + align:start position:0% +n times T and to equal the integral of A + + + align:start position:0% +n times T and to equal the integral of A +to B of T DT which is equal to B squared + + align:start position:0% +to B of T DT which is equal to B squared + + + align:start position:0% +to B of T DT which is equal to B squared +or a No - whatever - my do my calculus + + align:start position:0% +or a No - whatever - my do my calculus + + + align:start position:0% +or a No - whatever - my do my calculus +correctly and so there's another + + align:start position:0% +correctly and so there's another + + + align:start position:0% +correctly and so there's another +equation I have another question for + + align:start position:0% +equation I have another question for + + + align:start position:0% +equation I have another question for +these guys and I keep going until I get + + align:start position:0% +these guys and I keep going until I get + + + align:start position:0% +these guys and I keep going until I get +enough equations to determine all the + + align:start position:0% +enough equations to determine all the + + + align:start position:0% +enough equations to determine all the +W's and T's all right so I do it for T + + align:start position:0% +W's and T's all right so I do it for T + + + align:start position:0% +W's and T's all right so I do it for T +Square it's like the W and T again + + align:start position:0% +Square it's like the W and T again + + + align:start position:0% +Square it's like the W and T again +squared is equal to G square DT and so + + align:start position:0% +squared is equal to G square DT and so + + + align:start position:0% +squared is equal to G square DT and so +on okay and so if you do this process + + align:start position:0% +on okay and so if you do this process + + + align:start position:0% +on okay and so if you do this process +you get the weights and the points to + + align:start position:0% +you get the weights and the points to + + + align:start position:0% +you get the weights and the points to +use that will give you what's called the + + align:start position:0% +use that will give you what's called the + + + align:start position:0% +use that will give you what's called the +Gaussian quadrature rule now the + + align:start position:0% +Gaussian quadrature rule now the + + + align:start position:0% +Gaussian quadrature rule now the +brilliant thing about this is it by this + + align:start position:0% +brilliant thing about this is it by this + + + align:start position:0% +brilliant thing about this is it by this +set up it's going to be exact for + + align:start position:0% +set up it's going to be exact for + + + align:start position:0% +set up it's going to be exact for +integrating any polynomial up to order + + align:start position:0% +integrating any polynomial up to order + + + align:start position:0% +integrating any polynomial up to order +two and minus one so if I have if I + + align:start position:0% +two and minus one so if I have if I + + + align:start position:0% +two and minus one so if I have if I +choose three here I'll be able to + + align:start position:0% +choose three here I'll be able to + + + align:start position:0% +choose three here I'll be able to +determine if I choose three points I'll + + align:start position:0% +determine if I choose three points I'll + + + align:start position:0% +determine if I choose three points I'll +have six parameters so I'll be able to + + align:start position:0% +have six parameters so I'll be able to + + + align:start position:0% +have six parameters so I'll be able to +determine up to the 11th 11th order + + align:start position:0% +determine up to the 11th 11th order + + + align:start position:0% +determine up to the 11th 11th order +polynomial would integrate exactly hey + + align:start position:0% +polynomial would integrate exactly hey + + + align:start position:0% +polynomial would integrate exactly hey +there right no that's wrong three I have + + align:start position:0% +there right no that's wrong three I have + + + align:start position:0% +there right no that's wrong three I have +three as only three and I have six + + align:start position:0% +three as only three and I have six + + + align:start position:0% +three as only three and I have six +parameters get to this two times three + + align:start position:0% +parameters get to this two times three + + + align:start position:0% +parameters get to this two times three +minus one one five five there yeah five + + align:start position:0% +minus one one five five there yeah five + + + align:start position:0% +minus one one five five there yeah five +after the fifth order polynomial you + + align:start position:0% +after the fifth order polynomial you + + + align:start position:0% +after the fifth order polynomial you +know got exactly I'll have an error for + + align:start position:0% +know got exactly I'll have an error for + + + align:start position:0% +know got exactly I'll have an error for +six waterfall in it so this is a rule so + + align:start position:0% +six waterfall in it so this is a rule so + + + align:start position:0% +six waterfall in it so this is a rule so +before if I gave you three points like + + align:start position:0% +before if I gave you three points like + + + align:start position:0% +before if I gave you three points like +here + + align:start position:0% +here + + + align:start position:0% +here +don't don't most of you probably would + + align:start position:0% +don't don't most of you probably would + + + align:start position:0% +don't don't most of you probably would +do some central fit this to a parabola + + align:start position:0% +do some central fit this to a parabola + + + align:start position:0% +do some central fit this to a parabola +has three parameters a ax squared plus + + align:start position:0% +has three parameters a ax squared plus + + + align:start position:0% +has three parameters a ax squared plus +BX plus C right for a second-order + + align:start position:0% +BX plus C right for a second-order + + + align:start position:0% +BX plus C right for a second-order +polynomial I would fit it that I need to + + align:start position:0% +polynomial I would fit it that I need to + + + align:start position:0% +polynomial I would fit it that I need to +grade that that would be the normal + + align:start position:0% +grade that that would be the normal + + + align:start position:0% +grade that that would be the normal +thing a lot of people would do I don't + + align:start position:0% +thing a lot of people would do I don't + + + align:start position:0% +thing a lot of people would do I don't +know if you would do that but a lot of + + align:start position:0% +know if you would do that but a lot of + + + align:start position:0% +know if you would do that but a lot of +people will do that so that would be + + align:start position:0% +people will do that so that would be + + + align:start position:0% +people will do that so that would be +that what you get and what are would you + + align:start position:0% +that what you get and what are would you + + + align:start position:0% +that what you get and what are would you +get you'd have earned that would be the + + align:start position:0% +get you'd have earned that would be the + + + align:start position:0% +get you'd have earned that would be the +scale of the width of the interval to + + align:start position:0% +scale of the width of the interval to + + + align:start position:0% +scale of the width of the interval to +the fourth power right because since + + align:start position:0% +the fourth power right because since + + + align:start position:0% +the fourth power right because since +it's all exact up to the cubic you guys + + align:start position:0% +it's all exact up to the cubic you guys + + + align:start position:0% +it's all exact up to the cubic you guys +remember this high school delta T that I + + align:start position:0% +remember this high school delta T that I + + + align:start position:0% +remember this high school delta T that I +don't remember Delta to the fourth yeah + + align:start position:0% +don't remember Delta to the fourth yeah + + + align:start position:0% +don't remember Delta to the fourth yeah +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that so Simpsons role as our order of + + align:start position:0% +so that so Simpsons role as our order of + + + align:start position:0% +so that so Simpsons role as our order of +delta T to the fourth by Gauss's method + + align:start position:0% +delta T to the fourth by Gauss's method + + + align:start position:0% +delta T to the fourth by Gauss's method +has order of delta T to the sixth this + + align:start position:0% +has order of delta T to the sixth this + + + align:start position:0% +has order of delta T to the sixth this +is for three points and Gauss's method + + align:start position:0% +is for three points and Gauss's method + + + align:start position:0% +is for three points and Gauss's method +you can extend it to as many points as + + align:start position:0% +you can extend it to as many points as + + + align:start position:0% +you can extend it to as many points as +you want alright so that's that's kind + + align:start position:0% +you want alright so that's that's kind + + + align:start position:0% +you want alright so that's that's kind +of nice you only do three points you get + + align:start position:0% +of nice you only do three points you get + + + align:start position:0% +of nice you only do three points you get +in the six order so that seems like + + align:start position:0% +in the six order so that seems like + + + align:start position:0% +in the six order so that seems like +pretty efficient so people kept going + + align:start position:0% +pretty efficient so people kept going + + + align:start position:0% +pretty efficient so people kept going +and so the very very popular one is to + + align:start position:0% +and so the very very popular one is to + + + align:start position:0% +and so the very very popular one is to +you seven is to use actually seven + + align:start position:0% +you seven is to use actually seven + + + align:start position:0% +you seven is to use actually seven +points for Gauss so you'd be able to get + + align:start position:0% +points for Gauss so you'd be able to get + + + align:start position:0% +points for Gauss so you'd be able to get +to the to the N minus one so you be + + align:start position:0% +to the to the N minus one so you be + + + align:start position:0% +to the to the N minus one so you be +exact for 13 well okay we have Delta T + + align:start position:0% +exact for 13 well okay we have Delta T + + + align:start position:0% +exact for 13 well okay we have Delta T +to the 14th power is your air pretty + + align:start position:0% +to the 14th power is your air pretty + + + align:start position:0% +to the 14th power is your air pretty +good and and then what people often do + + align:start position:0% +good and and then what people often do + + + align:start position:0% +good and and then what people often do +is they'll add eight more points and + + align:start position:0% +is they'll add eight more points and + + + align:start position:0% +is they'll add eight more points and +they make another method that uses all + + align:start position:0% +they make another method that uses all + + + align:start position:0% +they make another method that uses all +these points that's called con-rods + + align:start position:0% +these points that's called con-rods + + + align:start position:0% +these points that's called con-rods +on or odd matt said he made another + + align:start position:0% +on or odd matt said he made another + + + align:start position:0% +on or odd matt said he made another +method that gives you the best possible + + align:start position:0% +method that gives you the best possible + + + align:start position:0% +method that gives you the best possible +solution if you have the fifteen points + + align:start position:0% +solution if you have the fifteen points + + + align:start position:0% +solution if you have the fifteen points +given as seven then we're already fixed + + align:start position:0% +given as seven then we're already fixed + + + align:start position:0% +given as seven then we're already fixed +by the gauss procedure and so you can + + align:start position:0% +by the gauss procedure and so you can + + + align:start position:0% +by the gauss procedure and so you can +get the integral using Gauss's method + + align:start position:0% +get the integral using Gauss's method + + + align:start position:0% +get the integral using Gauss's method +and using connor odds method + + align:start position:0% + + + + align:start position:0% + +so you can compute the I using Gauss's + + align:start position:0% +so you can compute the I using Gauss's + + + align:start position:0% +so you can compute the I using Gauss's +method the seven points the I with the + + align:start position:0% +method the seven points the I with the + + + align:start position:0% +method the seven points the I with the +con rod method and how spells name + + align:start position:0% +con rod method and how spells name + + + align:start position:0% +con rod method and how spells name +actually I think it's like this fifteen + + align:start position:0% +actually I think it's like this fifteen + + + align:start position:0% +actually I think it's like this fifteen +points and then you can take the + + align:start position:0% +points and then you can take the + + + align:start position:0% +points and then you can take the +difference between these two and if + + align:start position:0% +difference between these two and if + + + align:start position:0% +difference between these two and if +these two are really similar then you + + align:start position:0% +these two are really similar then you + + + align:start position:0% +these two are really similar then you +might think your inner goes pretty good + + align:start position:0% +might think your inner goes pretty good + + + align:start position:0% +might think your inner goes pretty good +cuz they're pretty different methods and + + align:start position:0% +cuz they're pretty different methods and + + + align:start position:0% +cuz they're pretty different methods and +if they give the same number you're good + + align:start position:0% +if they give the same number you're good + + + align:start position:0% +if they give the same number you're good +and people come on numerical studies in + + align:start position:0% +and people come on numerical studies in + + + align:start position:0% +and people come on numerical studies in +this particular case because it's used a + + align:start position:0% +this particular case because it's used a + + + align:start position:0% +this particular case because it's used a +lot in actual practice and it turns out + + align:start position:0% +lot in actual practice and it turns out + + + align:start position:0% +lot in actual practice and it turns out +that the R is almost always less than + + align:start position:0% +that the R is almost always less than + + + align:start position:0% +that the R is almost always less than +this quantity to the three guess power + + align:start position:0% +this quantity to the three guess power + + + align:start position:0% +this quantity to the three guess power +so you have an error estimate so you did + + align:start position:0% +so you have an error estimate so you did + + + align:start position:0% +so you have an error estimate so you did +you take you 15 function evaluations you + + align:start position:0% +you take you 15 function evaluations you + + + align:start position:0% +you take you 15 function evaluations you +get a pretty accurate value for your + + align:start position:0% +get a pretty accurate value for your + + + align:start position:0% +get a pretty accurate value for your +integral maybe if you can be fit well + + align:start position:0% +integral maybe if you can be fit well + + + align:start position:0% +integral maybe if you can be fit well +with a whatever order polynomial 32 + + align:start position:0% +with a whatever order polynomial 32 + + + align:start position:0% +with a whatever order polynomial 32 +order polynomial 13th one I mean yeah + + align:start position:0% +order polynomial 13th one I mean yeah + + + align:start position:0% +order polynomial 13th one I mean yeah +and so any function e we fit pretty well + + align:start position:0% +and so any function e we fit pretty well + + + align:start position:0% +and so any function e we fit pretty well +with 32 order polynomial you should get + + align:start position:0% +with 32 order polynomial you should get + + + align:start position:0% +with 32 order polynomial you should get +pretty good value of the integral and + + align:start position:0% +pretty good value of the integral and + + + align:start position:0% +pretty good value of the integral and +you can check by comparing to the code + + align:start position:0% +you can check by comparing to the code + + + align:start position:0% +you can check by comparing to the code +estimate which use a lot more points and + + align:start position:0% +estimate which use a lot more points and + + + align:start position:0% +estimate which use a lot more points and +the two these guys give the same number + + align:start position:0% +the two these guys give the same number + + + align:start position:0% +the two these guys give the same number +or pretty close then you're pretty + + align:start position:0% +or pretty close then you're pretty + + + align:start position:0% +or pretty close then you're pretty +confident that you're you're good and + + align:start position:0% +confident that you're you're good and + + + align:start position:0% +confident that you're you're good and +there's even a math proof about this so + + align:start position:0% +there's even a math proof about this so + + + align:start position:0% +there's even a math proof about this so +this is like really popular and it's a + + align:start position:0% +this is like really popular and it's a + + + align:start position:0% +this is like really popular and it's a +lot better than Simpsons rule but it's a + + align:start position:0% +lot better than Simpsons rule but it's a + + + align:start position:0% +lot better than Simpsons rule but it's a +little complicated and part of this you + + align:start position:0% +little complicated and part of this you + + + align:start position:0% +little complicated and part of this you +have to recompute these TN s and W ends + + align:start position:0% +have to recompute these TN s and W ends + + + align:start position:0% +have to recompute these TN s and W ends +for the kind of problem you have yeah + + align:start position:0% + + + + align:start position:0% + +so the that's we should probably the + + align:start position:0% +so the that's we should probably the + + + align:start position:0% +so the that's we should probably the +maths right so it's say we did since the + + align:start position:0% +maths right so it's say we did since the + + + align:start position:0% +maths right so it's say we did since the +draw and we have delta T and we divide + + align:start position:0% +draw and we have delta T and we divide + + + align:start position:0% +draw and we have delta T and we divide +it by 15 or something then we can figure + + align:start position:0% +it by 15 or something then we can figure + + + align:start position:0% +it by 15 or something then we can figure +out what this is but it's still gonna + + align:start position:0% +out what this is but it's still gonna + + + align:start position:0% +out what this is but it's still gonna +have this scaling to the fourth power so + + align:start position:0% +have this scaling to the fourth power so + + + align:start position:0% +have this scaling to the fourth power so +the prefactor will be really tiny + + align:start position:0% +the prefactor will be really tiny + + + align:start position:0% +the prefactor will be really tiny +because of y1 over 15th to the fourth + + align:start position:0% +because of y1 over 15th to the fourth + + + align:start position:0% +because of y1 over 15th to the fourth +power + + align:start position:0% +power + + + align:start position:0% +power +but the scaling of just be bad so that + + align:start position:0% +but the scaling of just be bad so that + + + align:start position:0% +but the scaling of just be bad so that +if I decide that my integrals not good + + align:start position:0% +if I decide that my integrals not good + + + align:start position:0% +if I decide that my integrals not good +enough and I need to do more points I + + align:start position:0% +enough and I need to do more points I + + + align:start position:0% +enough and I need to do more points I +say double the number of points to get + + align:start position:0% +say double the number of points to get + + + align:start position:0% +say double the number of points to get +better accuracy I whip my thing won't + + align:start position:0% +better accuracy I whip my thing won't + + + align:start position:0% +better accuracy I whip my thing won't +improve that much because it's only just + + align:start position:0% +improve that much because it's only just + + + align:start position:0% +improve that much because it's only just +killing the fourth power whereas the + + align:start position:0% +killing the fourth power whereas the + + + align:start position:0% +killing the fourth power whereas the +Gauss won't say it's going in six power + + align:start position:0% +Gauss won't say it's going in six power + + + align:start position:0% +Gauss won't say it's going in six power +values to the three points where were + + align:start position:0% +values to the three points where were + + + align:start position:0% +values to the three points where were +used 15 points is gonna get scale some + + align:start position:0% +used 15 points is gonna get scale some + + + align:start position:0% +used 15 points is gonna get scale some +16th power or 15 powers on some really + + align:start position:0% +16th power or 15 powers on some really + + + align:start position:0% +16th power or 15 powers on some really +high power so for doing sequences the + + align:start position:0% +high power so for doing sequences the + + + align:start position:0% +high power so for doing sequences the +Gauss is ones a lot better however what + + align:start position:0% +Gauss is ones a lot better however what + + + align:start position:0% +Gauss is ones a lot better however what +people do is they usually pre solve the + + align:start position:0% +people do is they usually pre solve the + + + align:start position:0% +people do is they usually pre solve the +system of equations because this + + align:start position:0% +system of equations because this + + + align:start position:0% +system of equations because this +equations does not depend when you do + + align:start position:0% +equations does not depend when you do + + + align:start position:0% +equations does not depend when you do +with the monomial is it doesn't it + + align:start position:0% +with the monomial is it doesn't it + + + align:start position:0% +with the monomial is it doesn't it +doesn't have been an F but F is you can + + align:start position:0% +doesn't have been an F but F is you can + + + align:start position:0% +doesn't have been an F but F is you can +figure out the optimal T's and w's ahead + + align:start position:0% +figure out the optimal T's and w's ahead + + + align:start position:0% +figure out the optimal T's and w's ahead +of time and so you they peel of tables + + align:start position:0% +of time and so you they peel of tables + + + align:start position:0% +of time and so you they peel of tables +of them four depending on what what were + + align:start position:0% +of them four depending on what what were + + + align:start position:0% +of them four depending on what what were +you want to go people recomputed them + + align:start position:0% +you want to go people recomputed them + + + align:start position:0% +you want to go people recomputed them +and then you can get it that way + + align:start position:0% + + + + align:start position:0% + +time is running out it's just when I + + align:start position:0% +time is running out it's just when I + + + align:start position:0% +time is running out it's just when I +just jump up the now for single + + align:start position:0% +just jump up the now for single + + + align:start position:0% +just jump up the now for single +integrals I didn't have to tell you any + + align:start position:0% +integrals I didn't have to tell you any + + + align:start position:0% +integrals I didn't have to tell you any +of this because you could have just + + align:start position:0% +of this because you could have just + + + align:start position:0% +of this because you could have just +solved it with your ODU solver right so + + align:start position:0% +solved it with your ODU solver right so + + + align:start position:0% +solved it with your ODU solver right so +you can just go to OD one 5s or OD four + + align:start position:0% +you can just go to OD one 5s or OD four + + + align:start position:0% +you can just go to OD one 5s or OD four +five and you'll get good enough it won't + + align:start position:0% +five and you'll get good enough it won't + + + align:start position:0% +five and you'll get good enough it won't +be as efficient as Gaussian but who + + align:start position:0% +be as efficient as Gaussian but who + + + align:start position:0% +be as efficient as Gaussian but who +cares you still get a good answer you + + align:start position:0% +cares you still get a good answer you + + + align:start position:0% +cares you still get a good answer you +can read for to your boss it'd take you + + align:start position:0% +can read for to your boss it'd take you + + + align:start position:0% +can read for to your boss it'd take you +three minutes alright to do call it a + + align:start position:0% +three minutes alright to do call it a + + + align:start position:0% +three minutes alright to do call it a +4/5 to integrate a fundamental integral + + align:start position:0% +4/5 to integrate a fundamental integral + + + align:start position:0% +4/5 to integrate a fundamental integral +the real challenge comes with a molded + + align:start position:0% +the real challenge comes with a molded + + + align:start position:0% +the real challenge comes with a molded +eventual integrals so in a lot of + + align:start position:0% +eventual integrals so in a lot of + + + align:start position:0% +eventual integrals so in a lot of +problems we have more than one variable + + align:start position:0% +problems we have more than one variable + + + align:start position:0% +problems we have more than one variable +you want to integrate over and so if you + + align:start position:0% +you want to integrate over and so if you + + + align:start position:0% +you want to integrate over and so if you +have an integral save a to be from the + + align:start position:0% +have an integral save a to be from the + + + align:start position:0% +have an integral save a to be from the +lower bound of X to upper bound of X so + + align:start position:0% +lower bound of X to upper bound of X so + + + align:start position:0% +lower bound of X to upper bound of X so +this is DX dy f of X Y this is a + + align:start position:0% +this is DX dy f of X Y this is a + + + align:start position:0% +this is DX dy f of X Y this is a +commenter goal that you might need to do + + align:start position:0% +commenter goal that you might need to do + + + align:start position:0% +commenter goal that you might need to do +sometimes okay because you might have + + align:start position:0% +sometimes okay because you might have + + + align:start position:0% +sometimes okay because you might have +two variables you want to integrate over + + align:start position:0% +two variables you want to integrate over + + + align:start position:0% +two variables you want to integrate over +and so how do we do this the wait is the + + align:start position:0% +and so how do we do this the wait is the + + + align:start position:0% +and so how do we do this the wait is the +best way to think about I think is it + + align:start position:0% +best way to think about I think is it + + + align:start position:0% +best way to think about I think is it +right f of X is equal to the integral of + + align:start position:0% +right f of X is equal to the integral of + + + align:start position:0% +right f of X is equal to the integral of +L of X to U of X dy F X Y and then if I + + align:start position:0% +L of X to U of X dy F X Y and then if I + + + align:start position:0% +L of X to U of X dy F X Y and then if I +knew what that was I would evaluate that + + align:start position:0% +knew what that was I would evaluate that + + + align:start position:0% +knew what that was I would evaluate that +say with the Gaussian quadrature so I + + align:start position:0% +say with the Gaussian quadrature so I + + + align:start position:0% +say with the Gaussian quadrature so I +think so I'd say that this I to D is + + align:start position:0% +think so I'd say that this I to D is + + + align:start position:0% +think so I'd say that this I to D is +approximately equal to the sum of some + + align:start position:0% +approximately equal to the sum of some + + + align:start position:0% +approximately equal to the sum of some +weights of labeled max just to remind + + align:start position:0% +weights of labeled max just to remind + + + align:start position:0% +weights of labeled max just to remind +you where they came from times f of xn + + align:start position:0% +you where they came from times f of xn + + + align:start position:0% +you where they came from times f of xn +and I would use take Gaussian quadrature + + align:start position:0% +and I would use take Gaussian quadrature + + + align:start position:0% +and I would use take Gaussian quadrature +figure out what the best value of the X + + align:start position:0% +figure out what the best value of the X + + + align:start position:0% +figure out what the best value of the X +is and the wife started to use and then + + align:start position:0% +is and the wife started to use and then + + + align:start position:0% +is and the wife started to use and then +I would actually evaluate this guy with + + align:start position:0% +I would actually evaluate this guy with + + + align:start position:0% +I would actually evaluate this guy with +a quadrature - sorry I'd say f of X K + + align:start position:0% +a quadrature - sorry I'd say f of X K + + + align:start position:0% +a quadrature - sorry I'd say f of X K +her xn is equal to the integral from L + + align:start position:0% +her xn is equal to the integral from L + + + align:start position:0% +her xn is equal to the integral from L +of xn to U of X n dy F of xn Y and so + + align:start position:0% +of xn to U of X n dy F of xn Y and so + + + align:start position:0% +of xn to U of X n dy F of xn Y and so +this itself I would give it another + + align:start position:0% +this itself I would give it another + + + align:start position:0% +this itself I would give it another +quadrature but this going to be equal to + + align:start position:0% +quadrature but this going to be equal to + + + align:start position:0% +quadrature but this going to be equal to +sum over some other weights and J f of X + + align:start position:0% +sum over some other weights and J f of X + + + align:start position:0% +sum over some other weights and J f of X +and YJ said all right and so this is + + align:start position:0% +and YJ said all right and so this is + + + align:start position:0% +and YJ said all right and so this is +nested inside this so now I have a + + align:start position:0% +nested inside this so now I have a + + + align:start position:0% +nested inside this so now I have a +double loop so if I took me I don't know + + align:start position:0% +double loop so if I took me I don't know + + + align:start position:0% +double loop so if I took me I don't know +15 points 15 functional value a shion's + + align:start position:0% +15 points 15 functional value a shion's + + + align:start position:0% +15 points 15 functional value a shion's +to get good number for my integral in + + align:start position:0% +to get good number for my integral in + + + align:start position:0% +to get good number for my integral in +one dimension then it might take me 15 + + align:start position:0% +one dimension then it might take me 15 + + + align:start position:0% +one dimension then it might take me 15 +squared operations 15 squared function + + align:start position:0% +squared operations 15 squared function + + + align:start position:0% +squared operations 15 squared function +evaluations to get a pretty good email + + align:start position:0% +evaluations to get a pretty good email + + + align:start position:0% +evaluations to get a pretty good email +for 250 might be a little optimistic so + + align:start position:0% +for 250 might be a little optimistic so + + + align:start position:0% +for 250 might be a little optimistic so +I'm a is maybe 100 is more like you + + align:start position:0% +I'm a is maybe 100 is more like you + + + align:start position:0% +I'm a is maybe 100 is more like you +really want a good number so it one + + align:start position:0% +really want a good number so it one + + + align:start position:0% +really want a good number so it one +hundred and one dimension hundred in the + + align:start position:0% +hundred and one dimension hundred in the + + + align:start position:0% +hundred and one dimension hundred in the +second dimension square because I + + align:start position:0% +second dimension square because I + + + align:start position:0% +second dimension square because I +subdivide the integral into six equal + + align:start position:0% +subdivide the integral into six equal + + + align:start position:0% +subdivide the integral into six equal +pieces say and then now so this is okay + + align:start position:0% +pieces say and then now so this is okay + + + align:start position:0% +pieces say and then now so this is okay +so you can do this hundred it's only + + align:start position:0% +so you can do this hundred it's only + + + align:start position:0% +so you can do this hundred it's only +10,000 function evaluations no problem + + align:start position:0% +10,000 function evaluations no problem + + + align:start position:0% +10,000 function evaluations no problem +you got a gigahertz computer now in + + align:start position:0% +you got a gigahertz computer now in + + + align:start position:0% +you got a gigahertz computer now in +reality a lot that we do have a lot more + + align:start position:0% +reality a lot that we do have a lot more + + + align:start position:0% +reality a lot that we do have a lot more +in dimensions than that so in my life I + + align:start position:0% +in dimensions than that so in my life I + + + align:start position:0% +in dimensions than that so in my life I +do a lot of electronic structure + + align:start position:0% +do a lot of electronic structure + + + align:start position:0% +do a lot of electronic structure +integrals we have integrals that are DX + + align:start position:0% +integrals we have integrals that are DX + + + align:start position:0% +integrals we have integrals that are DX +1d + + align:start position:0% +1d + + + align:start position:0% +1d +z14 the first electron interacting with + + align:start position:0% +z14 the first electron interacting with + + + align:start position:0% +z14 the first electron interacting with +a second electron and and then something + + align:start position:0% +a second electron and and then something + + + align:start position:0% +a second electron and and then something +stopped trying to integrate that + + align:start position:0% +stopped trying to integrate that + + + align:start position:0% +stopped trying to integrate that +dependence say the distance between + + align:start position:0% +dependence say the distance between + + + align:start position:0% +dependence say the distance between +electron one electron to okay + + align:start position:0% +electron one electron to okay + + + align:start position:0% +electron one electron to okay +so this is actually six integrals okay + + align:start position:0% +so this is actually six integrals okay + + + align:start position:0% +so this is actually six integrals okay +and so instead of being a two in the + + align:start position:0% +and so instead of being a two in the + + + align:start position:0% +and so instead of being a two in the +exponent this is gonna be like a six in + + align:start position:0% +exponent this is gonna be like a six in + + + align:start position:0% +exponent this is gonna be like a six in +the exponent so now this is ten to the + + align:start position:0% +the exponent so now this is ten to the + + + align:start position:0% +the exponent so now this is ten to the +twelfth that means it's just evaluating + + align:start position:0% +twelfth that means it's just evaluating + + + align:start position:0% +twelfth that means it's just evaluating +one integral this way might take me a + + align:start position:0% +one integral this way might take me a + + + align:start position:0% +one integral this way might take me a +hundred seconds if I can evaluate the + + align:start position:0% +hundred seconds if I can evaluate the + + + align:start position:0% +hundred seconds if I can evaluate the +functions like that but in fact the + + align:start position:0% +functions like that but in fact the + + + align:start position:0% +functions like that but in fact the +functions I want to evaluate here this + + align:start position:0% +functions I want to evaluate here this + + + align:start position:0% +functions I want to evaluate here this +guys are take multiple operations to + + align:start position:0% +guys are take multiple operations to + + + align:start position:0% +guys are take multiple operations to +evaluate the function and so this turns + + align:start position:0% +evaluate the function and so this turns + + + align:start position:0% +evaluate the function and so this turns +out I can't do it I can't do one + + align:start position:0% +out I can't do it I can't do one + + + align:start position:0% +out I can't do it I can't do one +integral this way with it six integrals + + align:start position:0% +integral this way with it six integrals + + + align:start position:0% +integral this way with it six integrals +deep and so this is the general problem + + align:start position:0% +deep and so this is the general problem + + + align:start position:0% +deep and so this is the general problem +well mole demential integration is + + align:start position:0% +well mole demential integration is + + + align:start position:0% +well mole demential integration is +called the curse of dimensionality each + + align:start position:0% +called the curse of dimensionality each + + + align:start position:0% +called the curse of dimensionality each +each time you add one more integral your + + align:start position:0% +each time you add one more integral your + + + align:start position:0% +each time you add one more integral your +nested there ulsan the effort goes up + + align:start position:0% +nested there ulsan the effort goes up + + + align:start position:0% +nested there ulsan the effort goes up +tremendously more you know a couple + + align:start position:0% +tremendously more you know a couple + + + align:start position:0% +tremendously more you know a couple +orders many more and so we'll come back + + align:start position:0% +orders many more and so we'll come back + + + align:start position:0% +orders many more and so we'll come back +later in the class about how to how to + + align:start position:0% +later in the class about how to how to + + + align:start position:0% +later in the class about how to how to +deal with cases like this when you have + + align:start position:0% +deal with cases like this when you have + + + align:start position:0% +deal with cases like this when you have +high dimensionality cases to try to get + + align:start position:0% +high dimensionality cases to try to get + + + align:start position:0% +high dimensionality cases to try to get +better scaling instead of having it + + align:start position:0% +better scaling instead of having it + + + align:start position:0% +better scaling instead of having it +being an exponential it was really a + + align:start position:0% +being an exponential it was really a + + + align:start position:0% +being an exponential it was really a +hundred to the N right now under the N + + align:start position:0% +hundred to the N right now under the N + + + align:start position:0% +hundred to the N right now under the N +dimensions + + align:start position:0% +dimensions + + + align:start position:0% +dimensions +yeah come me to figure out some better + + align:start position:0% +yeah come me to figure out some better + + + align:start position:0% +yeah come me to figure out some better +way to do it + + align:start position:0% +way to do it + + + align:start position:0% +way to do it +all right thank you \ No newline at end of file diff --git a/KG0vOWQm1ZI.txt b/KG0vOWQm1ZI.txt new file mode 100644 index 0000000000000000000000000000000000000000..a36d534aab8501ec5932827f748015499090000f --- /dev/null +++ b/KG0vOWQm1ZI.txt @@ -0,0 +1,219 @@ +align:start position:0% + +in this section + + align:start position:0% +in this section + + + align:start position:0% +in this section +of today's class we talked about cell + + align:start position:0% +of today's class we talked about cell + + + align:start position:0% +of today's class we talked about cell +division + + align:start position:0% +division + + + align:start position:0% +division +you should be familiar with the notion + + align:start position:0% +you should be familiar with the notion + + + align:start position:0% +you should be familiar with the notion +of dna replication + + align:start position:0% +of dna replication + + + align:start position:0% +of dna replication +at least you've heard of it and you + + align:start position:0% +at least you've heard of it and you + + + align:start position:0% +at least you've heard of it and you +understand the + + align:start position:0% +understand the + + + align:start position:0% +understand the +outcome you should be familiar with the + + align:start position:0% +outcome you should be familiar with the + + + align:start position:0% +outcome you should be familiar with the +term mitosis + + align:start position:0% +term mitosis + + + align:start position:0% +term mitosis +and understand the two processes + + align:start position:0% +and understand the two processes + + + align:start position:0% +and understand the two processes +that are occurring during this type of + + align:start position:0% +that are occurring during this type of + + + align:start position:0% +that are occurring during this type of +cell division + + align:start position:0% +cell division + + + align:start position:0% +cell division +and you should be familiar with meiosis + + align:start position:0% +and you should be familiar with meiosis + + + align:start position:0% +and you should be familiar with meiosis +a kind of + + align:start position:0% +a kind of + + + align:start position:0% +a kind of +complicated cell division that leads to + + align:start position:0% +complicated cell division that leads to + + + align:start position:0% +complicated cell division that leads to +formation + + align:start position:0% +formation + + + align:start position:0% +formation +of the germ cells what we've done + + align:start position:0% +of the germ cells what we've done + + + align:start position:0% +of the germ cells what we've done +in class today is to talk about three + + align:start position:0% +in class today is to talk about three + + + align:start position:0% +in class today is to talk about three +big topics that have to do with the cell + + align:start position:0% +big topics that have to do with the cell + + + align:start position:0% +big topics that have to do with the cell +and its chemistry we talked about + + align:start position:0% +and its chemistry we talked about + + + align:start position:0% +and its chemistry we talked about +cellular chemistry + + align:start position:0% +cellular chemistry + + + align:start position:0% +cellular chemistry +and the notion of some thermodynamic + + align:start position:0% +and the notion of some thermodynamic + + + align:start position:0% +and the notion of some thermodynamic +parameters + + align:start position:0% +parameters + + + align:start position:0% +parameters +that govern cellular reactions we talked + + align:start position:0% +that govern cellular reactions we talked + + + align:start position:0% +that govern cellular reactions we talked +about the organization of the + + align:start position:0% +about the organization of the + + + align:start position:0% +about the organization of the +cell and what it contains and we talked + + align:start position:0% +cell and what it contains and we talked + + + align:start position:0% +cell and what it contains and we talked +about cell division + + align:start position:0% +about cell division + + + align:start position:0% +about cell division +one of the huge basic processes of life \ No newline at end of file diff --git a/KhY97qoDPMg.txt b/KhY97qoDPMg.txt new file mode 100644 index 0000000000000000000000000000000000000000..3678e09816043e7713367e67e94fff3fe357d066 --- /dev/null +++ b/KhY97qoDPMg.txt @@ -0,0 +1,2067 @@ +align:start position:0% + +all right so hi everyone uh my name is + + align:start position:0% +all right so hi everyone uh my name is + + + align:start position:0% +all right so hi everyone uh my name is +Nicole I'm here with Elaine and both of + + align:start position:0% +Nicole I'm here with Elaine and both of + + + align:start position:0% +Nicole I'm here with Elaine and both of +us are part of the Society of women + + align:start position:0% +us are part of the Society of women + + + align:start position:0% +us are part of the Society of women +Engineers um so we both just wanted to + + align:start position:0% +Engineers um so we both just wanted to + + + align:start position:0% +Engineers um so we both just wanted to +give you a little bit of background on + + align:start position:0% +give you a little bit of background on + + + align:start position:0% +give you a little bit of background on +ourselves and then talk about some of + + align:start position:0% +ourselves and then talk about some of + + + align:start position:0% +ourselves and then talk about some of +the opportunities thatu has so I + + align:start position:0% +the opportunities thatu has so I + + + align:start position:0% +the opportunities thatu has so I +actually didn't know anything about s + + align:start position:0% +actually didn't know anything about s + + + align:start position:0% +actually didn't know anything about s +when I was in high school either um I + + align:start position:0% +when I was in high school either um I + + + align:start position:0% +when I was in high school either um I +learned about it during my senior year + + align:start position:0% +learned about it during my senior year + + + align:start position:0% +learned about it during my senior year +so s has a scholarship um or multiple + + align:start position:0% +so s has a scholarship um or multiple + + + align:start position:0% +so s has a scholarship um or multiple +scholarships we give away thousands and + + align:start position:0% +scholarships we give away thousands and + + + align:start position:0% +scholarships we give away thousands and +thousands of dollars to support girls + + align:start position:0% +thousands of dollars to support girls + + + align:start position:0% +thousands of dollars to support girls +who are excited about stem and about + + align:start position:0% +who are excited about stem and about + + + align:start position:0% +who are excited about stem and about +engineering and getting involved in + + align:start position:0% +engineering and getting involved in + + + align:start position:0% +engineering and getting involved in +those fields so when I was had no idea + + align:start position:0% +those fields so when I was had no idea + + + align:start position:0% +those fields so when I was had no idea +what I wanted to do um I really liked + + align:start position:0% +what I wanted to do um I really liked + + + align:start position:0% +what I wanted to do um I really liked +doing the engineering side of things so + + align:start position:0% +doing the engineering side of things so + + + align:start position:0% +doing the engineering side of things so +I had worked in a lab for a couple + + align:start position:0% +I had worked in a lab for a couple + + + align:start position:0% +I had worked in a lab for a couple +summers at UCLA um in a bioengineering + + align:start position:0% +summers at UCLA um in a bioengineering + + + align:start position:0% +summers at UCLA um in a bioengineering +lab um but I also really like the + + align:start position:0% +lab um but I also really like the + + + align:start position:0% +lab um but I also really like the +business side um so I was part of a + + align:start position:0% +business side um so I was part of a + + + align:start position:0% +business side um so I was part of a +floral arrangement business actually + + align:start position:0% +floral arrangement business actually + + + align:start position:0% +floral arrangement business actually +that was run by my school and so we did + + align:start position:0% +that was run by my school and so we did + + + align:start position:0% +that was run by my school and so we did +everything from marketing to sales to + + align:start position:0% +everything from marketing to sales to + + + align:start position:0% +everything from marketing to sales to +actually like putting the flower + + align:start position:0% +actually like putting the flower + + + align:start position:0% +actually like putting the flower +arrangements together so that was really + + align:start position:0% +arrangements together so that was really + + + align:start position:0% +arrangements together so that was really +cool um I went to Penn for college and + + align:start position:0% +cool um I went to Penn for college and + + + align:start position:0% +cool um I went to Penn for college and +what's really neat is they have a + + align:start position:0% +what's really neat is they have a + + + align:start position:0% +what's really neat is they have a +program called the management and + + align:start position:0% +program called the management and + + + align:start position:0% +program called the management and +technology program and so you get a + + align:start position:0% +technology program and so you get a + + + align:start position:0% +technology program and so you get a +degree from their business school and a + + align:start position:0% +degree from their business school and a + + + align:start position:0% +degree from their business school and a +degree from their engineering school so + + align:start position:0% +degree from their engineering school so + + + align:start position:0% +degree from their engineering school so +I am end up going um to do + + align:start position:0% +I am end up going um to do + + + align:start position:0% +I am end up going um to do +entrepreneurial management and + + align:start position:0% +entrepreneurial management and + + + align:start position:0% +entrepreneurial management and +bioengineering as my bachelor's and + + align:start position:0% +bioengineering as my bachelor's and + + + align:start position:0% +bioengineering as my bachelor's and +mechanical engineering for my masters um + + align:start position:0% +mechanical engineering for my masters um + + + align:start position:0% +mechanical engineering for my masters um +so I just want to share a little bit of + + align:start position:0% +so I just want to share a little bit of + + + align:start position:0% +so I just want to share a little bit of +howu was able to affect my college + + align:start position:0% +howu was able to affect my college + + + align:start position:0% +howu was able to affect my college +experience it was amazing um I think the + + align:start position:0% +experience it was amazing um I think the + + + align:start position:0% +experience it was amazing um I think the +thing that really impresses me most + + align:start position:0% +thing that really impresses me most + + + align:start position:0% +thing that really impresses me most +about s is that it really touches on + + align:start position:0% +about s is that it really touches on + + + align:start position:0% +about s is that it really touches on +three different aspects so you have the + + align:start position:0% +three different aspects so you have the + + + align:start position:0% +three different aspects so you have the +Outreach part of it so getting to speak + + align:start position:0% +Outreach part of it so getting to speak + + + align:start position:0% +Outreach part of it so getting to speak +with you guys um getting to engage with + + align:start position:0% +with you guys um getting to engage with + + + align:start position:0% +with you guys um getting to engage with +K through 12 students and really get + + align:start position:0% +K through 12 students and really get + + + align:start position:0% +K through 12 students and really get +them excited about stem and show them + + align:start position:0% +them excited about stem and show them + + + align:start position:0% +them excited about stem and show them +what's possible um second part is with + + align:start position:0% +what's possible um second part is with + + + align:start position:0% +what's possible um second part is with +the professional devel velopment so + + align:start position:0% +the professional devel velopment so + + + align:start position:0% +the professional devel velopment so +being able to look at resumés do mock + + align:start position:0% +being able to look at resumés do mock + + + align:start position:0% +being able to look at resumés do mock +interviews um just grow yourself + + align:start position:0% +interviews um just grow yourself + + + align:start position:0% +interviews um just grow yourself +personally and professionally I think is + + align:start position:0% +personally and professionally I think is + + + align:start position:0% +personally and professionally I think is +so important No Matter What fields you + + align:start position:0% +so important No Matter What fields you + + + align:start position:0% +so important No Matter What fields you +end up going into and then third just + + align:start position:0% +end up going into and then third just + + + align:start position:0% +end up going into and then third just +the fun social aspects so the fact that + + align:start position:0% +the fun social aspects so the fact that + + + align:start position:0% +the fun social aspects so the fact that +you guys are getting to have lunch here + + align:start position:0% +you guys are getting to have lunch here + + + align:start position:0% +you guys are getting to have lunch here +right now um getting to engage with + + align:start position:0% +right now um getting to engage with + + + align:start position:0% +right now um getting to engage with +people at different socials and things + + align:start position:0% +people at different socials and things + + + align:start position:0% +people at different socials and things +like that is just really fun um so I + + align:start position:0% +like that is just really fun um so I + + + align:start position:0% +like that is just really fun um so I +have in the upper leftand corner it's a + + align:start position:0% +have in the upper leftand corner it's a + + + align:start position:0% +have in the upper leftand corner it's a +picture of the sweet Boston group here + + align:start position:0% +picture of the sweet Boston group here + + + align:start position:0% +picture of the sweet Boston group here +so everyone in the Boston area um can be + + align:start position:0% +so everyone in the Boston area um can be + + + align:start position:0% +so everyone in the Boston area um can be +part of that um I was on the board of + + align:start position:0% +part of that um I was on the board of + + + align:start position:0% +part of that um I was on the board of +directors actually for s during my + + align:start position:0% +directors actually for s during my + + + align:start position:0% +directors actually for s during my +senior year um super senior year when I + + align:start position:0% +senior year um super senior year when I + + + align:start position:0% +senior year um super senior year when I +was doing my um Masters which is really + + align:start position:0% +was doing my um Masters which is really + + + align:start position:0% +was doing my um Masters which is really +cool so getting to interact with people + + align:start position:0% +cool so getting to interact with people + + + align:start position:0% +cool so getting to interact with people +um from all around the world and really + + align:start position:0% +um from all around the world and really + + + align:start position:0% +um from all around the world and really +move the strategy ofu forward and then + + align:start position:0% +move the strategy ofu forward and then + + + align:start position:0% +move the strategy ofu forward and then +just a couple fun pictures one from my + + align:start position:0% +just a couple fun pictures one from my + + + align:start position:0% +just a couple fun pictures one from my +Collegiate section at pen um with our + + align:start position:0% +Collegiate section at pen um with our + + + align:start position:0% +Collegiate section at pen um with our +engineering CH t-shirts and then um a + + align:start position:0% +engineering CH t-shirts and then um a + + + align:start position:0% +engineering CH t-shirts and then um a +fun photo booth at one of our annual + + align:start position:0% +fun photo booth at one of our annual + + + align:start position:0% +fun photo booth at one of our annual +conferences um so Ela if you want to + + align:start position:0% +conferences um so Ela if you want to + + + align:start position:0% +conferences um so Ela if you want to +tell a little bit about yourself yeah so + + align:start position:0% +tell a little bit about yourself yeah so + + + align:start position:0% +tell a little bit about yourself yeah so +uh how many of you people + + align:start position:0% +uh how many of you people + + + align:start position:0% +uh how many of you people +like uh math classes + + align:start position:0% +like uh math classes + + + align:start position:0% +like uh math classes +quite a few of you what about science + + align:start position:0% +quite a few of you what about science + + + align:start position:0% +quite a few of you what about science +classes quite just about everybody right + + align:start position:0% +classes quite just about everybody right + + + align:start position:0% +classes quite just about everybody right +how many of you like + + align:start position:0% +how many of you like + + + align:start position:0% +how many of you like +English still a lot of people right + + align:start position:0% +English still a lot of people right + + + align:start position:0% +English still a lot of people right +about + + align:start position:0% +about + + + align:start position:0% +about +writing so I will tell you right now + + align:start position:0% +writing so I will tell you right now + + + align:start position:0% +writing so I will tell you right now +that um when I started in high school I + + align:start position:0% +that um when I started in high school I + + + align:start position:0% +that um when I started in high school I +actually hated my science classes and so + + align:start position:0% +actually hated my science classes and so + + + align:start position:0% +actually hated my science classes and so +I'm here to tell you about my journey + + align:start position:0% +I'm here to tell you about my journey + + + align:start position:0% +I'm here to tell you about my journey +from being an English major to becoming + + align:start position:0% +from being an English major to becoming + + + align:start position:0% +from being an English major to becoming +an + + align:start position:0% +an + + + align:start position:0% +an +engineer and so when I was in uh in high + + align:start position:0% +engineer and so when I was in uh in high + + + align:start position:0% +engineer and so when I was in uh in high +school I I actually hated science class + + align:start position:0% +school I I actually hated science class + + + align:start position:0% +school I I actually hated science class +because all we did was fill in the she + + align:start position:0% +because all we did was fill in the she + + + align:start position:0% +because all we did was fill in the she +fill in the blank worksheets we didn't + + align:start position:0% +fill in the blank worksheets we didn't + + + align:start position:0% +fill in the blank worksheets we didn't +do anything like you know take apart + + align:start position:0% +do anything like you know take apart + + + align:start position:0% +do anything like you know take apart +cameras like you guys are doing today um + + align:start position:0% +cameras like you guys are doing today um + + + align:start position:0% +cameras like you guys are doing today um +and so I was really bored with science + + align:start position:0% +and so I was really bored with science + + + align:start position:0% +and so I was really bored with science +even though I was really good at it so + + align:start position:0% +even though I was really good at it so + + + align:start position:0% +even though I was really good at it so +when I applied to college I went to Rice + + align:start position:0% +when I applied to college I went to Rice + + + align:start position:0% +when I applied to college I went to Rice +University I um decided to become an + + align:start position:0% +University I um decided to become an + + + align:start position:0% +University I um decided to become an +English major and at the end of the the + + align:start position:0% +English major and at the end of the the + + + align:start position:0% +English major and at the end of the the +my freshman year I applied for an + + align:start position:0% +my freshman year I applied for an + + + align:start position:0% +my freshman year I applied for an +internship in writing at the Texas Heart + + align:start position:0% +internship in writing at the Texas Heart + + + align:start position:0% +internship in writing at the Texas Heart +Institute and so basically what they did + + align:start position:0% +Institute and so basically what they did + + + align:start position:0% +Institute and so basically what they did +there was they took all the writing that + + align:start position:0% +there was they took all the writing that + + + align:start position:0% +there was they took all the writing that +any of the surgeons did on all the + + align:start position:0% +any of the surgeons did on all the + + + align:start position:0% +any of the surgeons did on all the +surgeries that they do or all the + + align:start position:0% +surgeries that they do or all the + + + align:start position:0% +surgeries that they do or all the +science research that they do and they + + align:start position:0% +science research that they do and they + + + align:start position:0% +science research that they do and they +try they send it to us so that way we + + align:start position:0% +try they send it to us so that way we + + + align:start position:0% +try they send it to us so that way we +can actually put it into a form that + + align:start position:0% +can actually put it into a form that + + + align:start position:0% +can actually put it into a form that +everybody else can read and so while I + + align:start position:0% +everybody else can read and so while I + + + align:start position:0% +everybody else can read and so while I +was sitting there and like you know they + + align:start position:0% +was sitting there and like you know they + + + align:start position:0% +was sitting there and like you know they +they wanted me because they wanted me to + + align:start position:0% +they wanted me because they wanted me to + + + align:start position:0% +they wanted me because they wanted me to +trck the English or like you know make + + align:start position:0% +trck the English or like you know make + + + align:start position:0% +trck the English or like you know make +sure that that the ideas flowed well but + + align:start position:0% +sure that that the ideas flowed well but + + + align:start position:0% +sure that that the ideas flowed well but +while I was reading all these things I + + align:start position:0% +while I was reading all these things I + + + align:start position:0% +while I was reading all these things I +had no idea what they were saying I + + align:start position:0% +had no idea what they were saying I + + + align:start position:0% +had no idea what they were saying I +didn't know what was going on um you + + align:start position:0% +didn't know what was going on um you + + + align:start position:0% +didn't know what was going on um you +know there's a lot of Disconnect that + + align:start position:0% +know there's a lot of Disconnect that + + + align:start position:0% +know there's a lot of Disconnect that +people say that scientists don't know + + align:start position:0% +people say that scientists don't know + + + align:start position:0% +people say that scientists don't know +how to explain things to everybody else + + align:start position:0% +how to explain things to everybody else + + + align:start position:0% +how to explain things to everybody else +and so that was the problem that I was + + align:start position:0% +and so that was the problem that I was + + + align:start position:0% +and so that was the problem that I was +seeing and I didn't know what was going + + align:start position:0% +seeing and I didn't know what was going + + + align:start position:0% +seeing and I didn't know what was going +on so I asked my boss can I go see a + + align:start position:0% +on so I asked my boss can I go see a + + + align:start position:0% +on so I asked my boss can I go see a +surgery I don't know what they're + + align:start position:0% +surgery I don't know what they're + + + align:start position:0% +surgery I don't know what they're +talking about and while I was in that + + align:start position:0% +talking about and while I was in that + + + align:start position:0% +talking about and while I was in that +surgery room uh the surgery I saw was on + + align:start position:0% +surgery room uh the surgery I saw was on + + + align:start position:0% +surgery room uh the surgery I saw was on +a cow that had had a mechanical valve + + align:start position:0% +a cow that had had a mechanical valve + + + align:start position:0% +a cow that had had a mechanical valve +implanted into the heart and this valve + + align:start position:0% +implanted into the heart and this valve + + + align:start position:0% +implanted into the heart and this valve +had + + align:start position:0% +had + + + align:start position:0% +had +failed now I mean you know that's really + + align:start position:0% +failed now I mean you know that's really + + + align:start position:0% +failed now I mean you know that's really +disappointing right but there are a lot + + align:start position:0% +disappointing right but there are a lot + + + align:start position:0% +disappointing right but there are a lot +of things that we can learn from failure + + align:start position:0% +of things that we can learn from failure + + + align:start position:0% +of things that we can learn from failure +and so everything that they were doing + + align:start position:0% +and so everything that they were doing + + + align:start position:0% +and so everything that they were doing +when as they were taking out the valve + + align:start position:0% +when as they were taking out the valve + + + align:start position:0% +when as they were taking out the valve +and running tests through the cow and + + align:start position:0% +and running tests through the cow and + + + align:start position:0% +and running tests through the cow and +figuring out what went wrong I started + + align:start position:0% +figuring out what went wrong I started + + + align:start position:0% +figuring out what went wrong I started +to see wow you know there are these real + + align:start position:0% +to see wow you know there are these real + + + align:start position:0% +to see wow you know there are these real +applications of science that can be + + align:start position:0% +applications of science that can be + + + align:start position:0% +applications of science that can be +really + + align:start position:0% +really + + + align:start position:0% +really +fascinating and so as I was working my + + align:start position:0% +fascinating and so as I was working my + + + align:start position:0% +fascinating and so as I was working my +way through the summer I thought more + + align:start position:0% +way through the summer I thought more + + + align:start position:0% +way through the summer I thought more +and more about these experiences and + + align:start position:0% +and more about these experiences and + + + align:start position:0% +and more about these experiences and +these things that I was seeing in the in + + align:start position:0% +these things that I was seeing in the in + + + align:start position:0% +these things that I was seeing in the in +the science realm in the research realm + + align:start position:0% +the science realm in the research realm + + + align:start position:0% +the science realm in the research realm +and I was like okay you know maybe I can + + align:start position:0% +and I was like okay you know maybe I can + + + align:start position:0% +and I was like okay you know maybe I can +go back to school and check out a bio + + align:start position:0% +go back to school and check out a bio + + + align:start position:0% +go back to school and check out a bio +engineering class and I have to tell you + + align:start position:0% +engineering class and I have to tell you + + + align:start position:0% +engineering class and I have to tell you +that I loved it + + align:start position:0% +that I loved it + + + align:start position:0% +that I loved it +so when I went to graduate school um + + align:start position:0% +so when I went to graduate school um + + + align:start position:0% +so when I went to graduate school um +because I had seen all these failures + + align:start position:0% +because I had seen all these failures + + + align:start position:0% +because I had seen all these failures +with these mechanical valves um and with + + align:start position:0% +with these mechanical valves um and with + + + align:start position:0% +with these mechanical valves um and with +all these heart devices I thought maybe + + align:start position:0% +all these heart devices I thought maybe + + + align:start position:0% +all these heart devices I thought maybe +tissue engineering would be a better way + + align:start position:0% +tissue engineering would be a better way + + + align:start position:0% +tissue engineering would be a better way +to go do does anybody here know what + + align:start position:0% +to go do does anybody here know what + + + align:start position:0% +to go do does anybody here know what +tissue engineering + + align:start position:0% +tissue engineering + + + align:start position:0% +tissue engineering +is would you like to tell + + align:start position:0% +is would you like to tell + + + align:start position:0% +is would you like to tell +us I + + align:start position:0% + + + + align:start position:0% + +just I'm not that oh no that's fine so + + align:start position:0% +just I'm not that oh no that's fine so + + + align:start position:0% +just I'm not that oh no that's fine so +um for for people who are not aware of + + align:start position:0% +um for for people who are not aware of + + + align:start position:0% +um for for people who are not aware of +tissue engineering tissue engineering is + + align:start position:0% +tissue engineering tissue engineering is + + + align:start position:0% +tissue engineering tissue engineering is +figuring out how we can use cells from + + align:start position:0% +figuring out how we can use cells from + + + align:start position:0% +figuring out how we can use cells from +the body and figuring out how we can + + align:start position:0% +the body and figuring out how we can + + + align:start position:0% +the body and figuring out how we can +implant them and put them into repair + + align:start position:0% +implant them and put them into repair + + + align:start position:0% +implant them and put them into repair +for our tissues that way we can um not + + align:start position:0% +for our tissues that way we can um not + + + align:start position:0% +for our tissues that way we can um not +use mechanical devices and the problem + + align:start position:0% +use mechanical devices and the problem + + + align:start position:0% +use mechanical devices and the problem +with that is that a lot of things that + + align:start position:0% +with that is that a lot of things that + + + align:start position:0% +with that is that a lot of things that +uh it's very hard to get our cells to do + + align:start position:0% +uh it's very hard to get our cells to do + + + align:start position:0% +uh it's very hard to get our cells to do +what we want them to do right we don't + + align:start position:0% +what we want them to do right we don't + + + align:start position:0% +what we want them to do right we don't +know enough about them um and so then + + align:start position:0% +know enough about them um and so then + + + align:start position:0% +know enough about them um and so then +when I became um a graduate student in + + align:start position:0% +when I became um a graduate student in + + + align:start position:0% +when I became um a graduate student in +biomedical engineering I decided I want + + align:start position:0% +biomedical engineering I decided I want + + + align:start position:0% +biomedical engineering I decided I want +to work with stem cells they can turn + + align:start position:0% +to work with stem cells they can turn + + + align:start position:0% +to work with stem cells they can turn +into any different potential cell type + + align:start position:0% +into any different potential cell type + + + align:start position:0% +into any different potential cell type +right so that the thing that was + + align:start position:0% +right so that the thing that was + + + align:start position:0% +right so that the thing that was +fascinating is I knew a lot about stem + + align:start position:0% +fascinating is I knew a lot about stem + + + align:start position:0% +fascinating is I knew a lot about stem +cells and I was trying to tell all these + + align:start position:0% +cells and I was trying to tell all these + + + align:start position:0% +cells and I was trying to tell all these +people but it was really difficult to + + align:start position:0% +people but it was really difficult to + + + align:start position:0% +people but it was really difficult to +for people to understand that and so as + + align:start position:0% +for people to understand that and so as + + + align:start position:0% +for people to understand that and so as +I was going through my journey and + + align:start position:0% +I was going through my journey and + + + align:start position:0% +I was going through my journey and +trying to tell people this is + + align:start position:0% +trying to tell people this is + + + align:start position:0% +trying to tell people this is +interesting this is fascinating this is + + align:start position:0% +interesting this is fascinating this is + + + align:start position:0% +interesting this is fascinating this is +why you should learn it I realized more + + align:start position:0% +why you should learn it I realized more + + + align:start position:0% +why you should learn it I realized more +and more people need to understand that + + align:start position:0% +and more people need to understand that + + + align:start position:0% +and more people need to understand that +they need to have an English background + + align:start position:0% +they need to have an English background + + + align:start position:0% +they need to have an English background +and need to have a writing background as + + align:start position:0% +and need to have a writing background as + + + align:start position:0% +and need to have a writing background as +well well and so my love in English and + + align:start position:0% +well well and so my love in English and + + + align:start position:0% +well well and so my love in English and +writing came back and now the two have + + align:start position:0% +writing came back and now the two have + + + align:start position:0% +writing came back and now the two have +merged and so right now I'm applying for + + align:start position:0% +merged and so right now I'm applying for + + + align:start position:0% +merged and so right now I'm applying for +a lot of uh positions in uh Journal + + align:start position:0% +a lot of uh positions in uh Journal + + + align:start position:0% +a lot of uh positions in uh Journal +editing as an editor for like nature or + + align:start position:0% +editing as an editor for like nature or + + + align:start position:0% +editing as an editor for like nature or +like science um I'm sure you've heard of + + align:start position:0% +like science um I'm sure you've heard of + + + align:start position:0% +like science um I'm sure you've heard of +some of these journals and basically + + align:start position:0% +some of these journals and basically + + + align:start position:0% +some of these journals and basically +what I'm going to do is going to be + + align:start position:0% +what I'm going to do is going to be + + + align:start position:0% +what I'm going to do is going to be +combining my love of science and + + align:start position:0% +combining my love of science and + + + align:start position:0% +combining my love of science and +engineering and turning it into writing + + align:start position:0% +engineering and turning it into writing + + + align:start position:0% +engineering and turning it into writing +that everybody else can understand and + + align:start position:0% +that everybody else can understand and + + + align:start position:0% +that everybody else can understand and +so that way we can get even more people + + align:start position:0% +so that way we can get even more people + + + align:start position:0% +so that way we can get even more people +excited + + align:start position:0% + + + + align:start position:0% + +so we just want to share a few different + + align:start position:0% +so we just want to share a few different + + + align:start position:0% +so we just want to share a few different +opportunities that you can look into um + + align:start position:0% +opportunities that you can look into um + + + align:start position:0% +opportunities that you can look into um +no matter what grade you're in and I + + align:start position:0% +no matter what grade you're in and I + + + align:start position:0% +no matter what grade you're in and I +think it's really cool to just kind of + + align:start position:0% +think it's really cool to just kind of + + + align:start position:0% +think it's really cool to just kind of +keep these on the back of your mind + + align:start position:0% +keep these on the back of your mind + + + align:start position:0% +keep these on the back of your mind +because you never know what might get + + align:start position:0% +because you never know what might get + + + align:start position:0% +because you never know what might get +you really excited about something um so + + align:start position:0% +you really excited about something um so + + + align:start position:0% +you really excited about something um so +one program that's really neat and is + + align:start position:0% +one program that's really neat and is + + + align:start position:0% +one program that's really neat and is +run by the society as a whole is s next + + align:start position:0% +run by the society as a whole is s next + + + align:start position:0% +run by the society as a whole is s next +and so this is for um girls who are up + + align:start position:0% +and so this is for um girls who are up + + + align:start position:0% +and so this is for um girls who are up +to the age of 18 I believe and so what + + align:start position:0% +to the age of 18 I believe and so what + + + align:start position:0% +to the age of 18 I believe and so what +you can do is there's tons of different + + align:start position:0% +you can do is there's tons of different + + + align:start position:0% +you can do is there's tons of different +activities that are through the program + + align:start position:0% +activities that are through the program + + + align:start position:0% +activities that are through the program +um you can learn about scholarships that + + align:start position:0% +um you can learn about scholarships that + + + align:start position:0% +um you can learn about scholarships that +are available to you um they do + + align:start position:0% +are available to you um they do + + + align:start position:0% +are available to you um they do +quarterly webinars so that you can kind + + align:start position:0% +quarterly webinars so that you can kind + + + align:start position:0% +quarterly webinars so that you can kind +of interact with the rest of the + + align:start position:0% +of interact with the rest of the + + + align:start position:0% +of interact with the rest of the +community around you and um just get to + + align:start position:0% +community around you and um just get to + + + align:start position:0% +community around you and um just get to +see other girls who are really excited + + align:start position:0% +see other girls who are really excited + + + align:start position:0% +see other girls who are really excited +about it um so definitely look into that + + align:start position:0% +about it um so definitely look into that + + + align:start position:0% +about it um so definitely look into that +um it's a really great thing that we + + align:start position:0% +um it's a really great thing that we + + + align:start position:0% +um it's a really great thing that we +launched um either last year or a couple + + align:start position:0% +launched um either last year or a couple + + + align:start position:0% +launched um either last year or a couple +years ago and it's really been exploding + + align:start position:0% +years ago and it's really been exploding + + + align:start position:0% +years ago and it's really been exploding +um the other thing that I would say + + align:start position:0% +um the other thing that I would say + + + align:start position:0% +um the other thing that I would say +since I assume most of you are based in + + align:start position:0% +since I assume most of you are based in + + + align:start position:0% +since I assume most of you are based in +the Boston area um look into some of the + + align:start position:0% +the Boston area um look into some of the + + + align:start position:0% +the Boston area um look into some of the +events that are hosted by su sections so + + align:start position:0% +events that are hosted by su sections so + + + align:start position:0% +events that are hosted by su sections so +um us from sweet Boston um we host + + align:start position:0% +um us from sweet Boston um we host + + + align:start position:0% +um us from sweet Boston um we host +things as a professional section um this + + align:start position:0% +things as a professional section um this + + + align:start position:0% +things as a professional section um this +is a taste of some of the activities + + align:start position:0% +is a taste of some of the activities + + + align:start position:0% +is a taste of some of the activities +that we did this year and so you can see + + align:start position:0% +that we did this year and so you can see + + + align:start position:0% +that we did this year and so you can see +we partner with the Girl Scouts we + + align:start position:0% +we partner with the Girl Scouts we + + + align:start position:0% +we partner with the Girl Scouts we +partner with a lot of organizations + + align:start position:0% +partner with a lot of organizations + + + align:start position:0% +partner with a lot of organizations +partner Kristen for the girls who build + + align:start position:0% +partner Kristen for the girls who build + + + align:start position:0% +partner Kristen for the girls who build +um and we also get to interact with a + + align:start position:0% +um and we also get to interact with a + + + align:start position:0% +um and we also get to interact with a +lot of the community events so the + + align:start position:0% +lot of the community events so the + + + align:start position:0% +lot of the community events so the +Cambridge Science Festival for instance + + align:start position:0% +Cambridge Science Festival for instance + + + align:start position:0% +Cambridge Science Festival for instance +which happened a couple um months ago um + + align:start position:0% +which happened a couple um months ago um + + + align:start position:0% +which happened a couple um months ago um +the other thing I would say is also look + + align:start position:0% +the other thing I would say is also look + + + align:start position:0% +the other thing I would say is also look +into some of the collegate Su events I + + align:start position:0% +into some of the collegate Su events I + + + align:start position:0% +into some of the collegate Su events I +know MIT has a huge presence with their + + align:start position:0% +know MIT has a huge presence with their + + + align:start position:0% +know MIT has a huge presence with their +s section and they do a lot of Outreach + + align:start position:0% +s section and they do a lot of Outreach + + + align:start position:0% +s section and they do a lot of Outreach +opportunities um for high school girls + + align:start position:0% +opportunities um for high school girls + + + align:start position:0% +opportunities um for high school girls +um and a lot of the other s sections in + + align:start position:0% +um and a lot of the other s sections in + + + align:start position:0% +um and a lot of the other s sections in +the area do that as well um and I think + + align:start position:0% +the area do that as well um and I think + + + align:start position:0% +the area do that as well um and I think +just like the biggest takeaway is that + + align:start position:0% +just like the biggest takeaway is that + + + align:start position:0% +just like the biggest takeaway is that +you never know what might excite you um + + align:start position:0% +you never know what might excite you um + + + align:start position:0% +you never know what might excite you um +I certainly did not imagine that I would + + align:start position:0% +I certainly did not imagine that I would + + + align:start position:0% +I certainly did not imagine that I would +be working at Microsoft now um with my + + align:start position:0% +be working at Microsoft now um with my + + + align:start position:0% +be working at Microsoft now um with my +background being bioengineering + + align:start position:0% +background being bioengineering + + + align:start position:0% +background being bioengineering +mechanical coal engineering but as long + + align:start position:0% +mechanical coal engineering but as long + + + align:start position:0% +mechanical coal engineering but as long +as you're passionate about something and + + align:start position:0% +as you're passionate about something and + + + align:start position:0% +as you're passionate about something and +as elain said you can go from English + + align:start position:0% +as elain said you can go from English + + + align:start position:0% +as elain said you can go from English +into science as well um there's just + + align:start position:0% +into science as well um there's just + + + align:start position:0% +into science as well um there's just +really so much potential for you um so + + align:start position:0% +really so much potential for you um so + + + align:start position:0% +really so much potential for you um so +if you want to get in touch with us um I + + align:start position:0% +if you want to get in touch with us um I + + + align:start position:0% +if you want to get in touch with us um I +put my contact here and then the sweet + + align:start position:0% +put my contact here and then the sweet + + + align:start position:0% +put my contact here and then the sweet +Boston section contacts as well um so if + + align:start position:0% +Boston section contacts as well um so if + + + align:start position:0% +Boston section contacts as well um so if +you have any questions about some of the + + align:start position:0% +you have any questions about some of the + + + align:start position:0% +you have any questions about some of the +Outreach event things um that we do feel + + align:start position:0% +Outreach event things um that we do feel + + + align:start position:0% +Outreach event things um that we do feel +free to get in touch with us + + align:start position:0% +free to get in touch with us + + + align:start position:0% +free to get in touch with us +cool thank you very much \ No newline at end of file diff --git a/Kwg7x9LFsDc.txt b/Kwg7x9LFsDc.txt new file mode 100644 index 0000000000000000000000000000000000000000..660223b20d0a81bd665f21c42a7d199db5553cdb --- /dev/null +++ b/Kwg7x9LFsDc.txt @@ -0,0 +1,1307 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +decision analysis provide a structured + + align:start position:0% +decision analysis provide a structured + + + align:start position:0% +decision analysis provide a structured +efficient way to help people recognize + + align:start position:0% +efficient way to help people recognize + + + align:start position:0% +efficient way to help people recognize +this complexity to recognize the + + align:start position:0% +this complexity to recognize the + + + align:start position:0% +this complexity to recognize the +probabilities and to deal with it + + align:start position:0% + + + + align:start position:0% + +so uh what are the general features of + + align:start position:0% +so uh what are the general features of + + + align:start position:0% +so uh what are the general features of +this method + + align:start position:0% +this method + + + align:start position:0% +this method +first of all it offers a simple way of + + align:start position:0% +first of all it offers a simple way of + + + align:start position:0% +first of all it offers a simple way of +defining the choices + + align:start position:0% +defining the choices + + + align:start position:0% +defining the choices +indeed it assumes that everything is a + + align:start position:0% +indeed it assumes that everything is a + + + align:start position:0% +indeed it assumes that everything is a +discrete choice that is either yes no or + + align:start position:0% +discrete choice that is either yes no or + + + align:start position:0% +discrete choice that is either yes no or +yes somewhat a lot maybe not at all but + + align:start position:0% +yes somewhat a lot maybe not at all but + + + align:start position:0% +yes somewhat a lot maybe not at all but +it has discreeted it forces you to think + + align:start position:0% +it has discreeted it forces you to think + + + align:start position:0% +it has discreeted it forces you to think +in terms of discrete choices not a + + align:start position:0% +in terms of discrete choices not a + + + align:start position:0% +in terms of discrete choices not a +continuum + + align:start position:0% +continuum + + + align:start position:0% +continuum +it also + + align:start position:0% +it also + + + align:start position:0% +it also +enables you but generally compels you to + + align:start position:0% +enables you but generally compels you to + + + align:start position:0% +enables you but generally compels you to +look over several periods it is it's not + + align:start position:0% +look over several periods it is it's not + + + align:start position:0% +look over several periods it is it's not +just what you do in the first period but + + align:start position:0% +just what you do in the first period but + + + align:start position:0% +just what you do in the first period but +then what you do just like going to uh a + + align:start position:0% +then what you do just like going to uh a + + + align:start position:0% +then what you do just like going to uh a +course at MIT you have your choice of + + align:start position:0% +course at MIT you have your choice of + + + align:start position:0% +course at MIT you have your choice of +first semester courses and the choices + + align:start position:0% +first semester courses and the choices + + + align:start position:0% +first semester courses and the choices +you make then enable you to do certain + + align:start position:0% +you make then enable you to do certain + + + align:start position:0% +you make then enable you to do certain +things or prevent you from doing other + + align:start position:0% +things or prevent you from doing other + + + align:start position:0% +things or prevent you from doing other +things because you didn't take the + + align:start position:0% +things because you didn't take the + + + align:start position:0% +things because you didn't take the +prerequisite course and so forth so that + + align:start position:0% +prerequisite course and so forth so that + + + align:start position:0% +prerequisite course and so forth so that +you want to think about over several + + align:start position:0% +you want to think about over several + + + align:start position:0% +you want to think about over several +periods + + align:start position:0% +periods + + + align:start position:0% +periods +the third element which is key to the + + align:start position:0% +the third element which is key to the + + + align:start position:0% +the third element which is key to the +whole reason we're even discussing it is + + align:start position:0% +whole reason we're even discussing it is + + + align:start position:0% +whole reason we're even discussing it is +because it deals with uncertainties + + align:start position:0% + + + + align:start position:0% + +um and it is also a standardized method + + align:start position:0% +um and it is also a standardized method + + + align:start position:0% +um and it is also a standardized method +so there are tools available to do this + + align:start position:0% +so there are tools available to do this + + + align:start position:0% +so there are tools available to do this +to do decision analysis and uh so it's + + align:start position:0% +to do decision analysis and uh so it's + + + align:start position:0% +to do decision analysis and uh so it's +it's + + align:start position:0% +it's + + + align:start position:0% +it's +if you are in the decision analysis + + align:start position:0% +if you are in the decision analysis + + + align:start position:0% +if you are in the decision analysis +there are a lot of other people who do + + align:start position:0% +there are a lot of other people who do + + + align:start position:0% +there are a lot of other people who do +it the same way they do it a standard + + align:start position:0% +it the same way they do it a standard + + + align:start position:0% +it the same way they do it a standard +way so it's a it's a structured process + + align:start position:0% +way so it's a it's a structured process + + + align:start position:0% +way so it's a it's a structured process +it's a it's like Excel it provides a + + align:start position:0% +it's a it's like Excel it provides a + + + align:start position:0% +it's a it's like Excel it provides a +widespread language to think about + + align:start position:0% +widespread language to think about + + + align:start position:0% +widespread language to think about +certain things + + align:start position:0% +certain things + + + align:start position:0% +certain things +and finally + + align:start position:0% +and finally + + + align:start position:0% +and finally +um which is uh which I think is relevant + + align:start position:0% +um which is uh which I think is relevant + + + align:start position:0% +um which is uh which I think is relevant +here is that it can include your not + + align:start position:0% +here is that it can include your not + + + align:start position:0% +here is that it can include your not +just a numerical result in terms of the + + align:start position:0% +just a numerical result in terms of the + + + align:start position:0% +just a numerical result in terms of the +income that maybe or the present value + + align:start position:0% +income that maybe or the present value + + + align:start position:0% +income that maybe or the present value +but also can deal with uh risk aversions + + align:start position:0% +but also can deal with uh risk aversions + + + align:start position:0% +but also can deal with uh risk aversions +your consumer satisfaction some kind of + + align:start position:0% +your consumer satisfaction some kind of + + + align:start position:0% +your consumer satisfaction some kind of +notion of utility we'll talk more about + + align:start position:0% +notion of utility we'll talk more about + + + align:start position:0% +notion of utility we'll talk more about +that in a in a later session uh in this + + align:start position:0% +that in a in a later session uh in this + + + align:start position:0% +that in a in a later session uh in this +in the half semester course but for the + + align:start position:0% +in the half semester course but for the + + + align:start position:0% +in the half semester course but for the +moment uh it allows you to say well yeah + + align:start position:0% +moment uh it allows you to say well yeah + + + align:start position:0% +moment uh it allows you to say well yeah +we could have + + align:start position:0% +we could have + + + align:start position:0% +we could have +um on average our outcome is good but + + align:start position:0% +um on average our outcome is good but + + + align:start position:0% +um on average our outcome is good but +the bad outcome is I really don't like + + align:start position:0% +the bad outcome is I really don't like + + + align:start position:0% +the bad outcome is I really don't like +it at all + + align:start position:0% +it at all + + + align:start position:0% +it at all +um if I'm for example if I'm saving for + + align:start position:0% +um if I'm for example if I'm saving for + + + align:start position:0% +um if I'm for example if I'm saving for +my pension uh uh I don't just will think + + align:start position:0% +my pension uh uh I don't just will think + + + align:start position:0% +my pension uh uh I don't just will think +on average I might have a million + + align:start position:0% +on average I might have a million + + + align:start position:0% +on average I might have a million +dollars to retire on but it makes a + + align:start position:0% +dollars to retire on but it makes a + + + align:start position:0% +dollars to retire on but it makes a +great deal of difference for me if that + + align:start position:0% +great deal of difference for me if that + + + align:start position:0% +great deal of difference for me if that +million is uh + + align:start position:0% +million is uh + + + align:start position:0% +million is uh +for an extreme it's either 2 million or + + align:start position:0% +for an extreme it's either 2 million or + + + align:start position:0% +for an extreme it's either 2 million or +nothing that would be an average of a + + align:start position:0% +nothing that would be an average of a + + + align:start position:0% +nothing that would be an average of a +million but if I had nothing I'd be + + align:start position:0% +million but if I had nothing I'd be + + + align:start position:0% +million but if I had nothing I'd be +feeling very unhappy about my retirement + + align:start position:0% +feeling very unhappy about my retirement + + + align:start position:0% +feeling very unhappy about my retirement +and so that I would wait against that + + align:start position:0% +and so that I would wait against that + + + align:start position:0% +and so that I would wait against that +possibility so it can it allows you to + + align:start position:0% +possibility so it can it allows you to + + + align:start position:0% +possibility so it can it allows you to +think about utility assessment + + align:start position:0% + + + + align:start position:0% + +now all right + + align:start position:0% +now all right + + + align:start position:0% +now all right +the central element of the decision + + align:start position:0% +the central element of the decision + + + align:start position:0% +the central element of the decision +analysis is the decision tree + + align:start position:0% +analysis is the decision tree + + + align:start position:0% +analysis is the decision tree +it shows the choices over several period + + align:start position:0% +it shows the choices over several period + + + align:start position:0% +it shows the choices over several period +and it has basically + + align:start position:0% +and it has basically + + + align:start position:0% +and it has basically +four outcomes + + align:start position:0% +four outcomes + + + align:start position:0% +four outcomes +uh Force elements it has the choices the + + align:start position:0% +uh Force elements it has the choices the + + + align:start position:0% +uh Force elements it has the choices the +structure the way you draw it + + align:start position:0% +structure the way you draw it + + + align:start position:0% +structure the way you draw it +um it has the choices and the possible + + align:start position:0% +um it has the choices and the possible + + + align:start position:0% +um it has the choices and the possible +outcomes + + align:start position:0% +outcomes + + + align:start position:0% +outcomes +I'll show you those in a moment + + align:start position:0% +I'll show you those in a moment + + + align:start position:0% +I'll show you those in a moment +and secondly it has data the data both + + align:start position:0% +and secondly it has data the data both + + + align:start position:0% +and secondly it has data the data both +about uncertainties that may occur and + + align:start position:0% +about uncertainties that may occur and + + + align:start position:0% +about uncertainties that may occur and +the value of the outcomes so four + + align:start position:0% +the value of the outcomes so four + + + align:start position:0% +the value of the outcomes so four +elements choices and outgo the structure + + align:start position:0% +elements choices and outgo the structure + + + align:start position:0% +elements choices and outgo the structure +and the data + + align:start position:0% + + + + align:start position:0% + +so here is a structure so it's a + + align:start position:0% +so here is a structure so it's a + + + align:start position:0% +so here is a structure so it's a +basically it's a disciplined way of + + align:start position:0% +basically it's a disciplined way of + + + align:start position:0% +basically it's a disciplined way of +present Alternatives and it has two + + align:start position:0% +present Alternatives and it has two + + + align:start position:0% +present Alternatives and it has two +elements it has the decision points so + + align:start position:0% +elements it has the decision points so + + + align:start position:0% +elements it has the decision points so +over on the left hand side + + align:start position:0% +over on the left hand side + + + align:start position:0% +over on the left hand side +here we have I'm starting and I have a + + align:start position:0% +here we have I'm starting and I have a + + + align:start position:0% +here we have I'm starting and I have a +choice to make and in this I'm going to + + align:start position:0% +choice to make and in this I'm going to + + + align:start position:0% +choice to make and in this I'm going to +have a very simple case just to + + align:start position:0% +have a very simple case just to + + + align:start position:0% +have a very simple case just to +illustrate it but I can either do Choice + + align:start position:0% +illustrate it but I can either do Choice + + + align:start position:0% +illustrate it but I can either do Choice +One or Choice two I have these two + + align:start position:0% +One or Choice two I have these two + + + align:start position:0% +One or Choice two I have these two +branches of course I could have five or + + align:start position:0% +branches of course I could have five or + + + align:start position:0% +branches of course I could have five or +six but for I haven't then having done + + align:start position:0% +six but for I haven't then having done + + + align:start position:0% +six but for I haven't then having done +something say uh I decided to take + + align:start position:0% +something say uh I decided to take + + + align:start position:0% +something say uh I decided to take +um + + align:start position:0% +um + + + align:start position:0% +um +whatever I decided to build a plant + + align:start position:0% +whatever I decided to build a plant + + + align:start position:0% +whatever I decided to build a plant +somewhere that then I have a result a + + align:start position:0% +somewhere that then I have a result a + + + align:start position:0% +somewhere that then I have a result a +chance outcome of that it performed well + + align:start position:0% +chance outcome of that it performed well + + + align:start position:0% +chance outcome of that it performed well +not so well it was a disaster whatever + + align:start position:0% +not so well it was a disaster whatever + + + align:start position:0% +not so well it was a disaster whatever +it might be I have possible outcomes + + align:start position:0% +it might be I have possible outcomes + + + align:start position:0% +it might be I have possible outcomes +and for each uh of the + + align:start position:0% +and for each uh of the + + + align:start position:0% +and for each uh of the +choices typically known as a branch + + align:start position:0% +choices typically known as a branch + + + align:start position:0% +choices typically known as a branch +um you'll have a possible outcomes and + + align:start position:0% +um you'll have a possible outcomes and + + + align:start position:0% +um you'll have a possible outcomes and +they will lead you to another place + + align:start position:0% +they will lead you to another place + + + align:start position:0% +they will lead you to another place +where you say all right I built this + + align:start position:0% +where you say all right I built this + + + align:start position:0% +where you say all right I built this +plant it was a success now do I build up + + align:start position:0% +plant it was a success now do I build up + + + align:start position:0% +plant it was a success now do I build up +some more or stay put or I build this + + align:start position:0% +some more or stay put or I build this + + + align:start position:0% +some more or stay put or I build this +plant it was a failure I can now decide + + align:start position:0% +plant it was a failure I can now decide + + + align:start position:0% +plant it was a failure I can now decide +to sell it or + + align:start position:0% +to sell it or + + + align:start position:0% +to sell it or +renovate it whatever + + align:start position:0% +renovate it whatever + + + align:start position:0% +renovate it whatever +so we got sequences decision chance this + + align:start position:0% +so we got sequences decision chance this + + + align:start position:0% +so we got sequences decision chance this +isn't a chance is the basic structure of + + align:start position:0% +isn't a chance is the basic structure of + + + align:start position:0% +isn't a chance is the basic structure of +this + + align:start position:0% +this + + + align:start position:0% +this +um + + align:start position:0% + + + + align:start position:0% + +now the data then is all right so I have + + align:start position:0% +now the data then is all right so I have + + + align:start position:0% +now the data then is all right so I have +elements about the outcome so given all + + align:start position:0% +elements about the outcome so given all + + + align:start position:0% +elements about the outcome so given all +this I've made a decision uh I observed + + align:start position:0% +this I've made a decision uh I observed + + + align:start position:0% +this I've made a decision uh I observed +what happened I made another decision I + + align:start position:0% +what happened I made another decision I + + + align:start position:0% +what happened I made another decision I +observed what happens and I have an + + align:start position:0% +observed what happens and I have an + + + align:start position:0% +observed what happens and I have an +outcome one outcome two and in this + + align:start position:0% +outcome one outcome two and in this + + + align:start position:0% +outcome one outcome two and in this +particular case we'll have + + align:start position:0% +particular case we'll have + + + align:start position:0% +particular case we'll have +two choices two outcomes at each stage I + + align:start position:0% +two choices two outcomes at each stage I + + + align:start position:0% +two choices two outcomes at each stage I +have and it's two very simple two-stage + + align:start position:0% +have and it's two very simple two-stage + + + align:start position:0% +have and it's two very simple two-stage +process I've uh 16 outcomes + + align:start position:0% +process I've uh 16 outcomes + + + align:start position:0% +process I've uh 16 outcomes +now you might ask well where is the + + align:start position:0% +now you might ask well where is the + + + align:start position:0% +now you might ask well where is the +decision tree well basically you gotta + + align:start position:0% +decision tree well basically you gotta + + + align:start position:0% +decision tree well basically you gotta +think that this tree is lying on his + + align:start position:0% +think that this tree is lying on his + + + align:start position:0% +think that this tree is lying on his +side and that this is the root here and + + align:start position:0% +side and that this is the root here and + + + align:start position:0% +side and that this is the root here and +the branches go up and + + align:start position:0% +the branches go up and + + + align:start position:0% +the branches go up and +leaves and so forth and what I invite + + align:start position:0% +leaves and so forth and what I invite + + + align:start position:0% +leaves and so forth and what I invite +you to consider first of all here is + + align:start position:0% +you to consider first of all here is + + + align:start position:0% +you to consider first of all here is +when does this decision tree become a + + align:start position:0% +when does this decision tree become a + + + align:start position:0% +when does this decision tree become a +messy Bush because + + align:start position:0% +messy Bush because + + + align:start position:0% +messy Bush because +realize that I've only had two choices + + align:start position:0% +realize that I've only had two choices + + + align:start position:0% +realize that I've only had two choices +two decisions here I could have had five + + align:start position:0% +two decisions here I could have had five + + + align:start position:0% +two decisions here I could have had five +and I could have five outcomes and now I + + align:start position:0% +and I could have five outcomes and now I + + + align:start position:0% +and I could have five outcomes and now I +would have uh 25 and I repeat this and + + align:start position:0% +would have uh 25 and I repeat this and + + + align:start position:0% +would have uh 25 and I repeat this and +I'm going to have 25 squared and I have + + align:start position:0% +I'm going to have 25 squared and I have + + + align:start position:0% +I'm going to have 25 squared and I have +600 some outcomes + + align:start position:0% +600 some outcomes + + + align:start position:0% +600 some outcomes +Etc it can really easily get very + + align:start position:0% +Etc it can really easily get very + + + align:start position:0% +Etc it can really easily get very +complicated + + align:start position:0% +complicated + + + align:start position:0% +complicated +um when I haven't uh looked at a + + align:start position:0% +um when I haven't uh looked at a + + + align:start position:0% +um when I haven't uh looked at a +particularly difficult problem so for + + align:start position:0% +particularly difficult problem so for + + + align:start position:0% +particularly difficult problem so for +example if I were trying to represent a + + align:start position:0% +example if I were trying to represent a + + + align:start position:0% +example if I were trying to represent a +game of chess here and I could move + + align:start position:0% +game of chess here and I could move + + + align:start position:0% +game of chess here and I could move +um basically something like uh uh eight + + align:start position:0% +um basically something like uh uh eight + + + align:start position:0% +um basically something like uh uh eight +a ten + + align:start position:0% +a ten + + + align:start position:0% +a ten +ten moves at the beginning with my pawns + + align:start position:0% +ten moves at the beginning with my pawns + + + align:start position:0% +ten moves at the beginning with my pawns +and my castle on my Rooks I would have + + align:start position:0% +and my castle on my Rooks I would have + + + align:start position:0% +and my castle on my Rooks I would have +uh 10 possible choices or 12 possible + + align:start position:0% +uh 10 possible choices or 12 possible + + + align:start position:0% +uh 10 possible choices or 12 possible +choices here and then I could have what + + align:start position:0% +choices here and then I could have what + + + align:start position:0% +choices here and then I could have what +my opponent does and uh I realistically + + align:start position:0% +my opponent does and uh I realistically + + + align:start position:0% +my opponent does and uh I realistically +problem can explode on you so one of the + + align:start position:0% +problem can explode on you so one of the + + + align:start position:0% +problem can explode on you so one of the +issues here again back to my + + align:start position:0% +issues here again back to my + + + align:start position:0% +issues here again back to my +emphasis at the beginning or my remark + + align:start position:0% +emphasis at the beginning or my remark + + + align:start position:0% +emphasis at the beginning or my remark +at the beginning is that decision + + align:start position:0% +at the beginning is that decision + + + align:start position:0% +at the beginning is that decision +analysis good for simple problems for + + align:start position:0% +analysis good for simple problems for + + + align:start position:0% +analysis good for simple problems for +complicated problems it just gets too + + align:start position:0% +complicated problems it just gets too + + + align:start position:0% +complicated problems it just gets too +messy \ No newline at end of file diff --git a/M7cl1Zi5YYE.txt b/M7cl1Zi5YYE.txt new file mode 100644 index 0000000000000000000000000000000000000000..dc65b774f2bf7305de454d27e639707bafa74b75 --- /dev/null +++ b/M7cl1Zi5YYE.txt @@ -0,0 +1,14323 @@ +align:start position:0% + +okay good + + align:start position:0% +okay good + + + align:start position:0% +okay good +afternoon okay + + align:start position:0% + + + + align:start position:0% + +so the last time we defined + + align:start position:0% +so the last time we defined + + + align:start position:0% +so the last time we defined +the diffusive and convective + + align:start position:0% +the diffusive and convective + + + align:start position:0% +the diffusive and convective +flaxes + + align:start position:0% +flaxes + + + align:start position:0% +flaxes +I I want to review this um + + align:start position:0% +I I want to review this um + + + align:start position:0% +I I want to review this um +definition with some uh + + align:start position:0% +definition with some uh + + + align:start position:0% +definition with some uh +Graphics uh the idea is that + + align:start position:0% +Graphics uh the idea is that + + + align:start position:0% +Graphics uh the idea is that +uh we have a a + + align:start position:0% +uh we have a a + + + align:start position:0% +uh we have a a +Continuum with all the assumptions that + + align:start position:0% +Continuum with all the assumptions that + + + align:start position:0% +Continuum with all the assumptions that +go under this this + + align:start position:0% +go under this this + + + align:start position:0% +go under this this +description and uh suppose that anywhere + + align:start position:0% +description and uh suppose that anywhere + + + align:start position:0% +description and uh suppose that anywhere +somewhere inside your Continuum you will + + align:start position:0% +somewhere inside your Continuum you will + + + align:start position:0% +somewhere inside your Continuum you will +set up a small um surface area + + align:start position:0% + + + + align:start position:0% + +with a an + + align:start position:0% +with a an + + + align:start position:0% +with a an +oriented normal + + align:start position:0% +oriented normal + + + align:start position:0% +oriented normal +n and then you look at uh what + + align:start position:0% +n and then you look at uh what + + + align:start position:0% +n and then you look at uh what +properties and here we are talking about + + align:start position:0% +properties and here we are talking about + + + align:start position:0% +properties and here we are talking about +uh the extensive properties those that + + align:start position:0% +uh the extensive properties those that + + + align:start position:0% +uh the extensive properties those that +we said that can be described as + + align:start position:0% +we said that can be described as + + + align:start position:0% +we said that can be described as +integrals over + + align:start position:0% +integrals over + + + align:start position:0% +integrals over +volume uh + + align:start position:0% +volume uh + + + align:start position:0% +volume uh +of densities of those of that properties + + align:start position:0% +of densities of those of that properties + + + align:start position:0% +of densities of those of that properties +like energy entropy Mass + + align:start position:0% +like energy entropy Mass + + + align:start position:0% +like energy entropy Mass +momentum so this is pro how much of that + + align:start position:0% +momentum so this is pro how much of that + + + align:start position:0% +momentum so this is pro how much of that +property crosses uh the um that uh + + align:start position:0% + + + + align:start position:0% + +area and which and with which um U speed + + align:start position:0% +area and which and with which um U speed + + + align:start position:0% +area and which and with which um U speed +so how much it transfers it goes across + + align:start position:0% +so how much it transfers it goes across + + + align:start position:0% +so how much it transfers it goes across +divided by the area of this surface that + + align:start position:0% +divided by the area of this surface that + + + align:start position:0% +divided by the area of this surface that +we call uh + + align:start position:0% +we call uh + + + align:start position:0% +we call uh +D + + align:start position:0% + + + + align:start position:0% + +Omega and divided by + + align:start position:0% +Omega and divided by + + + align:start position:0% +Omega and divided by +the time interval during which we + + align:start position:0% +the time interval during which we + + + align:start position:0% +the time interval during which we +measure the amount that + + align:start position:0% +measure the amount that + + + align:start position:0% +measure the amount that +crosses + + align:start position:0% +crosses + + + align:start position:0% +crosses +that uh defines the + + align:start position:0% + + + + align:start position:0% + +flux + + align:start position:0% +flux + + + align:start position:0% +flux +uh so let's consider first the flux the + + align:start position:0% +uh so let's consider first the flux the + + + align:start position:0% +uh so let's consider first the flux the +measurement in terms of the reference + + align:start position:0% +measurement in terms of the reference + + + align:start position:0% +measurement in terms of the reference +frame of the + + align:start position:0% +frame of the + + + align:start position:0% +frame of the +laboratory and that we call it J + + align:start position:0% +laboratory and that we call it J + + + align:start position:0% +laboratory and that we call it J +Zer I also call it lren but maybe the + + align:start position:0% +Zer I also call it lren but maybe the + + + align:start position:0% +Zer I also call it lren but maybe the +term lent is not really appropriate but + + align:start position:0% +term lent is not really appropriate but + + + align:start position:0% +term lent is not really appropriate but +in any case it's it's the flux with + + align:start position:0% +in any case it's it's the flux with + + + align:start position:0% +in any case it's it's the flux with +respect to the laboratory reference + + align:start position:0% +respect to the laboratory reference + + + align:start position:0% +respect to the laboratory reference +frame and once I have done that and I + + align:start position:0% +frame and once I have done that and I + + + align:start position:0% +frame and once I have done that and I +know the um density which means the + + align:start position:0% +know the um density which means the + + + align:start position:0% +know the um density which means the +property per unit uh uh volume that + + align:start position:0% +property per unit uh uh volume that + + + align:start position:0% +property per unit uh uh volume that +prevails in that + + align:start position:0% +prevails in that + + + align:start position:0% +prevails in that +position that defines also a + + align:start position:0% +position that defines also a + + + align:start position:0% +position that defines also a +velocity which is the velocity of + + align:start position:0% +velocity which is the velocity of + + + align:start position:0% +velocity which is the velocity of +transport of that + + align:start position:0% +transport of that + + + align:start position:0% +transport of that +property which is this Vector + + align:start position:0% +property which is this Vector + + + align:start position:0% +property which is this Vector +here okay so multiply so the long Vector + + align:start position:0% +here okay so multiply so the long Vector + + + align:start position:0% +here okay so multiply so the long Vector +is is the flux the short Vector is the + + align:start position:0% + + + + align:start position:0% + +velocity one of the properties is + + align:start position:0% +velocity one of the properties is + + + align:start position:0% +velocity one of the properties is +Mass so if I do that same measurement + + align:start position:0% +Mass so if I do that same measurement + + + align:start position:0% +Mass so if I do that same measurement +for mass I get the flux of + + align:start position:0% +for mass I get the flux of + + + align:start position:0% +for mass I get the flux of +mass which is what we call + + align:start position:0% + + + + align:start position:0% + +Momentum momentum density and + + align:start position:0% +Momentum momentum density and + + + align:start position:0% +Momentum momentum density and +uh and the velocity associated with with + + align:start position:0% +uh and the velocity associated with with + + + align:start position:0% +uh and the velocity associated with with +that flux we call it bicentric velocity + + align:start position:0% +that flux we call it bicentric velocity + + + align:start position:0% +that flux we call it bicentric velocity +of the flow it's the velocity of fluid + + align:start position:0% + + + + align:start position:0% + +mechanics + + align:start position:0% +mechanics + + + align:start position:0% +mechanics +okay then we Define also a a uh for + + align:start position:0% +okay then we Define also a a uh for + + + align:start position:0% +okay then we Define also a a uh for +property a we go back to property a and + + align:start position:0% +property a we go back to property a and + + + align:start position:0% +property a we go back to property a and +we Define a relative velocity so the + + align:start position:0% +we Define a relative velocity so the + + + align:start position:0% +we Define a relative velocity so the +difference between VA + + align:start position:0% +difference between VA + + + align:start position:0% +difference between VA +and the velocity with which uh fluid + + align:start position:0% +and the velocity with which uh fluid + + + align:start position:0% +and the velocity with which uh fluid +Parcels uh cross that + + align:start position:0% +Parcels uh cross that + + + align:start position:0% +Parcels uh cross that +surface which is the ventric + + align:start position:0% +surface which is the ventric + + + align:start position:0% +surface which is the ventric +velocity so the difference you compute + + align:start position:0% +velocity so the difference you compute + + + align:start position:0% +velocity so the difference you compute +since these are vectors the this way + + align:start position:0% +since these are vectors the this way + + + align:start position:0% +since these are vectors the this way +know like the typical Vector + + align:start position:0% +know like the typical Vector + + + align:start position:0% +know like the typical Vector +construction so this blue Vector is the + + align:start position:0% +construction so this blue Vector is the + + + align:start position:0% +construction so this blue Vector is the +difference between the two it's the + + align:start position:0% +difference between the two it's the + + + align:start position:0% +difference between the two it's the +relative velocity it's the velocity of + + align:start position:0% +relative velocity it's the velocity of + + + align:start position:0% +relative velocity it's the velocity of +transport of property a relative to the + + align:start position:0% +transport of property a relative to the + + + align:start position:0% +transport of property a relative to the +bicentric + + align:start position:0% +bicentric + + + align:start position:0% +bicentric +velocity and then you + + align:start position:0% +velocity and then you + + + align:start position:0% +velocity and then you +multiply by the same factor that goes + + align:start position:0% +multiply by the same factor that goes + + + align:start position:0% +multiply by the same factor that goes +between the short and the long Vector + + align:start position:0% +between the short and the long Vector + + + align:start position:0% +between the short and the long Vector +here so the density of property a and + + align:start position:0% +here so the density of property a and + + + align:start position:0% +here so the density of property a and +that gives you the diffusive flux of + + align:start position:0% +that gives you the diffusive flux of + + + align:start position:0% +that gives you the diffusive flux of +property a + + align:start position:0% + + + + align:start position:0% + +and the + + align:start position:0% +and the + + + align:start position:0% +and the +difference between j z and the diffusive + + align:start position:0% +difference between j z and the diffusive + + + align:start position:0% +difference between j z and the diffusive +flat is flux is the convective flux + + align:start position:0% +flat is flux is the convective flux + + + align:start position:0% +flat is flux is the convective flux +which is this Vector red Vector which of + + align:start position:0% +which is this Vector red Vector which of + + + align:start position:0% +which is this Vector red Vector which of +course by construction is directed in + + align:start position:0% +course by construction is directed in + + + align:start position:0% +course by construction is directed in +the same direction as + + align:start position:0% +the same direction as + + + align:start position:0% +the same direction as +the velocity bicentric + + align:start position:0% +the velocity bicentric + + + align:start position:0% +the velocity bicentric +velocity and so you can take it also as + + align:start position:0% +velocity and so you can take it also as + + + align:start position:0% +velocity and so you can take it also as +the bicentric velocity times the density + + align:start position:0% +the bicentric velocity times the density + + + align:start position:0% +the bicentric velocity times the density +of property a so it's this Vector + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% + + + + align:start position:0% + +okay then we have defined uh this + + align:start position:0% +okay then we have defined uh this + + + align:start position:0% +okay then we have defined uh this +extension or generalization of the idea + + align:start position:0% +extension or generalization of the idea + + + align:start position:0% +extension or generalization of the idea +of a heat + + align:start position:0% +of a heat + + + align:start position:0% +of a heat +interaction to when of the same in the + + align:start position:0% +interaction to when of the same in the + + + align:start position:0% +interaction to when of the same in the +same way as we did heat we + + align:start position:0% +same way as we did heat we + + + align:start position:0% +same way as we did heat we +approach the interactions between + + align:start position:0% +approach the interactions between + + + align:start position:0% +approach the interactions between +systems that uh uh are + + align:start position:0% +systems that uh uh are + + + align:start position:0% +systems that uh uh are +almost in mutual equilibrium so exactly + + align:start position:0% +almost in mutual equilibrium so exactly + + + align:start position:0% +almost in mutual equilibrium so exactly +or almost exactly the same temperature + + align:start position:0% +or almost exactly the same temperature + + + align:start position:0% +or almost exactly the same temperature +and the same chemical + + align:start position:0% +and the same chemical + + + align:start position:0% +and the same chemical +potentials and they + + align:start position:0% +potentials and they + + + align:start position:0% +potentials and they +exchange not only energy but also + + align:start position:0% +exchange not only energy but also + + + align:start position:0% +exchange not only energy but also +amounts of + + align:start position:0% +amounts of + + + align:start position:0% +amounts of +constituents and the relation Q overt + + align:start position:0% +constituents and the relation Q overt + + + align:start position:0% +constituents and the relation Q overt +for heat generalizes to this relation + + align:start position:0% +for heat generalizes to this relation + + + align:start position:0% +for heat generalizes to this relation +between the flux of entropy the flux of + + align:start position:0% +between the flux of entropy the flux of + + + align:start position:0% +between the flux of entropy the flux of +energy the flux of uh + + align:start position:0% +energy the flux of uh + + + align:start position:0% +energy the flux of uh +constituents + + align:start position:0% +constituents + + + align:start position:0% +constituents +here we + + align:start position:0% +here we + + + align:start position:0% +here we +are introducing also this variables that + + align:start position:0% +are introducing also this variables that + + + align:start position:0% +are introducing also this variables that +are sort of + + align:start position:0% +are sort of + + + align:start position:0% +are sort of +shorthand instead of carrying all the + + align:start position:0% +shorthand instead of carrying all the + + + align:start position:0% +shorthand instead of carrying all the +times one over the temperature we just + + align:start position:0% +times one over the temperature we just + + + align:start position:0% +times one over the temperature we just +call it + + align:start position:0% +call it + + + align:start position:0% +call it +tow which I know it's a bit + + align:start position:0% +tow which I know it's a bit + + + align:start position:0% +tow which I know it's a bit +unfortunate nomenclator because then we + + align:start position:0% +unfortunate nomenclator because then we + + + align:start position:0% +unfortunate nomenclator because then we +will use to double underline also for + + align:start position:0% +will use to double underline also for + + + align:start position:0% +will use to double underline also for +the stress tensor + + align:start position:0% +the stress tensor + + + align:start position:0% +the stress tensor +but that double underline will will keep + + align:start position:0% +but that double underline will will keep + + + align:start position:0% +but that double underline will will keep +the difference and also + + align:start position:0% +the difference and also + + + align:start position:0% +the difference and also +Lambda Lambda J denotes uh minus the the + + align:start position:0% +Lambda Lambda J denotes uh minus the the + + + align:start position:0% +Lambda Lambda J denotes uh minus the the +potential over T so we use Lambda or + + align:start position:0% +potential over T so we use Lambda or + + + align:start position:0% +potential over T so we use Lambda or +Lambda tot for the chemical potential or + + align:start position:0% +Lambda tot for the chemical potential or + + + align:start position:0% +Lambda tot for the chemical potential or +the total + + align:start position:0% + + + + align:start position:0% + +potential and so the relation + + align:start position:0% +potential and so the relation + + + align:start position:0% +potential and so the relation +between + + align:start position:0% +between + + + align:start position:0% +between +energy will + + align:start position:0% +energy will + + + align:start position:0% +energy will +energy entropy and uh + + align:start position:0% +energy entropy and uh + + + align:start position:0% +energy entropy and uh +n is is can be written this way so once + + align:start position:0% +n is is can be written this way so once + + + align:start position:0% +n is is can be written this way so once +we have this relation between vectors + + align:start position:0% +we have this relation between vectors + + + align:start position:0% +we have this relation between vectors +we're going to use it for example in the + + align:start position:0% +we're going to use it for example in the + + + align:start position:0% +we're going to use it for example in the +balance equations where there is a + + align:start position:0% +balance equations where there is a + + + align:start position:0% +balance equations where there is a +Divergence of of the + + align:start position:0% +Divergence of of the + + + align:start position:0% +Divergence of of the +flaxes um well we can take the the + + align:start position:0% +flaxes um well we can take the the + + + align:start position:0% +flaxes um well we can take the the +Divergence of these and that's how it + + align:start position:0% +Divergence of these and that's how it + + + align:start position:0% +Divergence of these and that's how it +goes it's typically a product so the + + align:start position:0% +goes it's typically a product so the + + + align:start position:0% +goes it's typically a product so the +Divergence of a product of a scalar + + align:start position:0% +Divergence of a product of a scalar + + + align:start position:0% +Divergence of a product of a scalar +times a vector is given by these two + + align:start position:0% +times a vector is given by these two + + + align:start position:0% +times a vector is given by these two +terms the gradient of the scalar dotted + + align:start position:0% +terms the gradient of the scalar dotted + + + align:start position:0% +terms the gradient of the scalar dotted +into the vector times the scalar times + + align:start position:0% +into the vector times the scalar times + + + align:start position:0% +into the vector times the scalar times +the Divergence of the + + align:start position:0% + + + + align:start position:0% + +vector now remember that + + align:start position:0% +vector now remember that + + + align:start position:0% +vector now remember that +energy in our model has a several + + align:start position:0% +energy in our model has a several + + + align:start position:0% +energy in our model has a several +components one is uh the internal energy + + align:start position:0% +components one is uh the internal energy + + + align:start position:0% +components one is uh the internal energy +proper of the stable equilibrium state + + align:start position:0% +proper of the stable equilibrium state + + + align:start position:0% +proper of the stable equilibrium state +that is underlying that is there that + + align:start position:0% +that is underlying that is there that + + + align:start position:0% +that is underlying that is there that +would be the only thing if we view our + + align:start position:0% +would be the only thing if we view our + + + align:start position:0% +would be the only thing if we view our +fluid element from a reference frame + + align:start position:0% +fluid element from a reference frame + + + align:start position:0% +fluid element from a reference frame +that moves with uh the bicentric + + align:start position:0% +that moves with uh the bicentric + + + align:start position:0% +that moves with uh the bicentric +velocity and therefore with respect to + + align:start position:0% +velocity and therefore with respect to + + + align:start position:0% +velocity and therefore with respect to +that reference frame there is no uh + + align:start position:0% +that reference frame there is no uh + + + align:start position:0% +that reference frame there is no uh +kinetic energy and also an accelerated + + align:start position:0% +kinetic energy and also an accelerated + + + align:start position:0% +kinetic energy and also an accelerated +frame where you don't also see the + + align:start position:0% +frame where you don't also see the + + + align:start position:0% +frame where you don't also see the +potential gravitational energy and then + + align:start position:0% +potential gravitational energy and then + + + align:start position:0% +potential gravitational energy and then +here you have the additional + + align:start position:0% +here you have the additional + + + align:start position:0% +here you have the additional +contribution for the + + align:start position:0% +contribution for the + + + align:start position:0% +contribution for the +electrostatic um + + align:start position:0% + + + + align:start position:0% + +energy if you + + align:start position:0% +energy if you + + + align:start position:0% +energy if you +multiply this by row and I I put all the + + align:start position:0% +multiply this by row and I I put all the + + + align:start position:0% +multiply this by row and I I put all the +stars just to be pedantic but at least + + align:start position:0% +stars just to be pedantic but at least + + + align:start position:0% +stars just to be pedantic but at least +we know that we're talking what we're + + align:start position:0% +we know that we're talking what we're + + + align:start position:0% +we know that we're talking what we're +talking about + + align:start position:0% +talking about + + + align:start position:0% +talking about +uh um we get this um expression + + align:start position:0% +uh um we get this um expression + + + align:start position:0% +uh um we get this um expression +here the total po potential therefore is + + align:start position:0% +here the total po potential therefore is + + + align:start position:0% +here the total po potential therefore is +Define this way it's the derivative of e + + align:start position:0% +Define this way it's the derivative of e + + + align:start position:0% +Define this way it's the derivative of e +with respect to n uh is given by these + + align:start position:0% +with respect to n uh is given by these + + + align:start position:0% +with respect to n uh is given by these +contributions the chemical potential + + align:start position:0% +contributions the chemical potential + + + align:start position:0% +contributions the chemical potential +plus uh this potential for + + align:start position:0% +plus uh this potential for + + + align:start position:0% +plus uh this potential for +kinetic + + align:start position:0% +kinetic + + + align:start position:0% +kinetic +um gravitational and + + align:start position:0% + + + + align:start position:0% + +electrostatic + + align:start position:0% +electrostatic + + + align:start position:0% +electrostatic +potentials + + align:start position:0% +potentials + + + align:start position:0% +potentials +okay so this is where we were I guess + + align:start position:0% +okay so this is where we were I guess + + + align:start position:0% +okay so this is where we were I guess +and of course we the next step is to uh + + align:start position:0% +and of course we the next step is to uh + + + align:start position:0% +and of course we the next step is to uh +substitute uh these assumptions about + + align:start position:0% +substitute uh these assumptions about + + + align:start position:0% +substitute uh these assumptions about +the interactions between fluid + + align:start position:0% +the interactions between fluid + + + align:start position:0% +the interactions between fluid +elements into the uh energy uh entropy + + align:start position:0% +elements into the uh energy uh entropy + + + align:start position:0% +elements into the uh energy uh entropy +constituent balance and here I've also + + align:start position:0% +constituent balance and here I've also + + + align:start position:0% +constituent balance and here I've also +done although I'm not going to talk too + + align:start position:0% +done although I'm not going to talk too + + + align:start position:0% +done although I'm not going to talk too +much about it but I also written the + + align:start position:0% +much about it but I also written the + + + align:start position:0% +much about it but I also written the +momentum balance that this is the fluid + + align:start position:0% +momentum balance that this is the fluid + + + align:start position:0% +momentum balance that this is the fluid +mechanics uh + + align:start position:0% +mechanics uh + + + align:start position:0% +mechanics uh +part for reference and uh as you + + align:start position:0% +part for reference and uh as you + + + align:start position:0% +part for reference and uh as you +remember I have written the balance + + align:start position:0% +remember I have written the balance + + + align:start position:0% +remember I have written the balance +balance equation in the two equivalent + + align:start position:0% +balance equation in the two equivalent + + + align:start position:0% +balance equation in the two equivalent +forms that we have + + align:start position:0% +forms that we have + + + align:start position:0% +forms that we have +derived one in terms of the lent + + align:start position:0% +derived one in terms of the lent + + + align:start position:0% +derived one in terms of the lent +flues with the partial derivative of Ro + + align:start position:0% +flues with the partial derivative of Ro + + + align:start position:0% +flues with the partial derivative of Ro +with respect to time the other with + + align:start position:0% +with respect to time the other with + + + align:start position:0% +with respect to time the other with +respect to the diffusive flaxes with the + + align:start position:0% +respect to the diffusive flaxes with the + + + align:start position:0% +respect to the diffusive flaxes with the +material + + align:start position:0% +material + + + align:start position:0% +material +derivative uh of of the mass specific + + align:start position:0% +derivative uh of of the mass specific + + + align:start position:0% +derivative uh of of the mass specific +properties we + + align:start position:0% +properties we + + + align:start position:0% +properties we +proved the last time that these are + + align:start position:0% +proved the last time that these are + + + align:start position:0% +proved the last time that these are +equivalent + + align:start position:0% + + + + align:start position:0% + +from these equations + + align:start position:0% +from these equations + + + align:start position:0% +from these equations +here and + + align:start position:0% +here and + + + align:start position:0% +here and +possibly um well no from these equations + + align:start position:0% +possibly um well no from these equations + + + align:start position:0% +possibly um well no from these equations +here you can obtain also these other + + align:start position:0% +here you can obtain also these other + + + align:start position:0% +here you can obtain also these other +equations below that I'm skipping uh the + + align:start position:0% +equations below that I'm skipping uh the + + + align:start position:0% +equations below that I'm skipping uh the +details but it's + + align:start position:0% +details but it's + + + align:start position:0% +details but it's +simply uh for example uh the equation + + align:start position:0% +simply uh for example uh the equation + + + align:start position:0% +simply uh for example uh the equation +for the conservation of mass which + + align:start position:0% +for the conservation of mass which + + + align:start position:0% +for the conservation of mass which +derives from this one of the amounts + + align:start position:0% +derives from this one of the amounts + + + align:start position:0% +derives from this one of the amounts +multiplied by the molecular masses this + + align:start position:0% +multiplied by the molecular masses this + + + align:start position:0% +multiplied by the molecular masses this +is the so-call continuity equation of + + align:start position:0% +is the so-call continuity equation of + + + align:start position:0% +is the so-call continuity equation of +mechanics which you can also write this + + align:start position:0% + + + + align:start position:0% + +way and so this is the the Divergence of + + align:start position:0% +way and so this is the the Divergence of + + + align:start position:0% +way and so this is the the Divergence of +V + + align:start position:0% +V + + + align:start position:0% +V +represents uh the rate of change of the + + align:start position:0% +represents uh the rate of change of the + + + align:start position:0% +represents uh the rate of change of the +volume of your fluid element as you + + align:start position:0% +volume of your fluid element as you + + + align:start position:0% +volume of your fluid element as you +follow it during the motion during the + + align:start position:0% +follow it during the motion during the + + + align:start position:0% +follow it during the motion during the +flow along its + + align:start position:0% +flow along its + + + align:start position:0% +flow along its +path and typically uh + + align:start position:0% +path and typically uh + + + align:start position:0% +path and typically uh +unless the flow is very Speedy so unless + + align:start position:0% +unless the flow is very Speedy so unless + + + align:start position:0% +unless the flow is very Speedy so unless +the the mark number is is is + + align:start position:0% +the the mark number is is is + + + align:start position:0% +the the mark number is is is +high uh you can assume incompressible + + align:start position:0% +high uh you can assume incompressible + + + align:start position:0% +high uh you can assume incompressible +flow and so this Divergence is equal to + + align:start position:0% +flow and so this Divergence is equal to + + + align:start position:0% +flow and so this Divergence is equal to +zero but for example from the momentum + + align:start position:0% +zero but for example from the momentum + + + align:start position:0% +zero but for example from the momentum +balance equation if you dot it + + align:start position:0% +balance equation if you dot it + + + align:start position:0% +balance equation if you dot it +into VM the velocity you can obtain a + + align:start position:0% +into VM the velocity you can obtain a + + + align:start position:0% +into VM the velocity you can obtain a +balance for the kinetic + + align:start position:0% +balance for the kinetic + + + align:start position:0% +balance for the kinetic +energy and then you can also get a + + align:start position:0% +energy and then you can also get a + + + align:start position:0% +energy and then you can also get a +balance for the gravitational potential + + align:start position:0% +balance for the gravitational potential + + + align:start position:0% +balance for the gravitational potential +energy and and a balance for the + + align:start position:0% +energy and and a balance for the + + + align:start position:0% +energy and and a balance for the +electrostatic potential energy so + + align:start position:0% +electrostatic potential energy so + + + align:start position:0% +electrostatic potential energy so +that you can uh + + align:start position:0% +that you can uh + + + align:start position:0% +that you can uh +subtract from the overall energy of your + + align:start position:0% +subtract from the overall energy of your + + + align:start position:0% +subtract from the overall energy of your +fluid + + align:start position:0% +fluid + + + align:start position:0% +fluid +uh uh uh + + align:start position:0% +uh uh uh + + + align:start position:0% +uh uh uh +the um the internal + + align:start position:0% +the um the internal + + + align:start position:0% +the um the internal +energy and so that difference is made up + + align:start position:0% +energy and so that difference is made up + + + align:start position:0% +energy and so that difference is made up +of just kinetic potential gravitational + + align:start position:0% +of just kinetic potential gravitational + + + align:start position:0% +of just kinetic potential gravitational +and electrostatic so the sum of these + + align:start position:0% +and electrostatic so the sum of these + + + align:start position:0% +and electrostatic so the sum of these +three gives you + + align:start position:0% + + + + align:start position:0% + +this and it's the rate of change of the + + align:start position:0% +this and it's the rate of change of the + + + align:start position:0% +this and it's the rate of change of the +mechanical + + align:start position:0% +mechanical + + + align:start position:0% +mechanical +energy uh content of uh of your uh + + align:start position:0% + + + + align:start position:0% + +fluid + + align:start position:0% + + + + align:start position:0% + +okay and now we can put them all + + align:start position:0% + + + + align:start position:0% + +together so we have + + align:start position:0% +together so we have + + + align:start position:0% +together so we have +assumed the local simple system + + align:start position:0% +assumed the local simple system + + + align:start position:0% +assumed the local simple system +equilibrium so that we can + + align:start position:0% +equilibrium so that we can + + + align:start position:0% +equilibrium so that we can +write uh the energy this way that we + + align:start position:0% +write uh the energy this way that we + + + align:start position:0% +write uh the energy this way that we +just just + + align:start position:0% +just just + + + align:start position:0% +just just +described uh the simple system Model + + align:start position:0% +described uh the simple system Model + + + align:start position:0% +described uh the simple system Model +includes the oiler relations so that + + align:start position:0% +includes the oiler relations so that + + + align:start position:0% +includes the oiler relations so that +together it allows you to write the Gibs + + align:start position:0% +together it allows you to write the Gibs + + + align:start position:0% +together it allows you to write the Gibs +relation in this + + align:start position:0% +relation in this + + + align:start position:0% +relation in this +way remember T is 1 / T and Lambda is + + align:start position:0% +way remember T is 1 / T and Lambda is + + + align:start position:0% +way remember T is 1 / T and Lambda is +minus mu over + + align:start position:0% + + + + align:start position:0% + +T which as you uh + + align:start position:0% +T which as you uh + + + align:start position:0% +T which as you uh +recall gets rid of the + + align:start position:0% +recall gets rid of the + + + align:start position:0% +recall gets rid of the +pressure so that the if you need the + + align:start position:0% +pressure so that the if you need the + + + align:start position:0% +pressure so that the if you need the +pressure need to go to the Gibs do + + align:start position:0% +pressure need to go to the Gibs do + + + align:start position:0% +pressure need to go to the Gibs do +relation to get you the pressure from + + align:start position:0% +relation to get you the pressure from + + + align:start position:0% +relation to get you the pressure from +the uh concentrations and temperature + + align:start position:0% + + + + align:start position:0% + +gradients uh so we are going to assume + + align:start position:0% +gradients uh so we are going to assume + + + align:start position:0% +gradients uh so we are going to assume +this relation between the properties of + + align:start position:0% +this relation between the properties of + + + align:start position:0% +this relation between the properties of +the particles and notice this is the + + align:start position:0% +the particles and notice this is the + + + align:start position:0% +the particles and notice this is the +internal energy just this part of the + + align:start position:0% +internal energy just this part of the + + + align:start position:0% +internal energy just this part of the +energy so we assume this relation holds + + align:start position:0% +energy so we assume this relation holds + + + align:start position:0% +energy so we assume this relation holds +as You Follow the the fluid particle + + align:start position:0% +as You Follow the the fluid particle + + + align:start position:0% +as You Follow the the fluid particle +along its + + align:start position:0% +along its + + + align:start position:0% +along its +path so that assume that it is + + align:start position:0% +path so that assume that it is + + + align:start position:0% +path so that assume that it is +valid uh for the material + + align:start position:0% + + + + align:start position:0% + +derivatives that + + align:start position:0% +derivatives that + + + align:start position:0% +derivatives that +means that uh the left hand side of the + + align:start position:0% +means that uh the left hand side of the + + + align:start position:0% +means that uh the left hand side of the +balance equations uh that we have in the + + align:start position:0% +balance equations uh that we have in the + + + align:start position:0% +balance equations uh that we have in the +previous slide where we have these uh + + align:start position:0% +previous slide where we have these uh + + + align:start position:0% +previous slide where we have these uh +material derivatives they are related we + + align:start position:0% +material derivatives they are related we + + + align:start position:0% +material derivatives they are related we +can essentially uh substitute the + + align:start position:0% +can essentially uh substitute the + + + align:start position:0% +can essentially uh substitute the +balance equations into this one and we + + align:start position:0% +balance equations into this one and we + + + align:start position:0% +balance equations into this one and we +get an + + align:start position:0% +get an + + + align:start position:0% +get an +extra + + align:start position:0% +extra + + + align:start position:0% +extra +relation + + align:start position:0% +relation + + + align:start position:0% +relation +plus we are going to + + align:start position:0% +plus we are going to + + + align:start position:0% +plus we are going to +assume the mode of interaction that we + + align:start position:0% +assume the mode of interaction that we + + + align:start position:0% +assume the mode of interaction that we +call heat and + + align:start position:0% + + + + align:start position:0% + +diffusion to + + align:start position:0% +diffusion to + + + align:start position:0% +diffusion to +be uh + + align:start position:0% +be uh + + + align:start position:0% +be uh +valid and holding between uh + + align:start position:0% +valid and holding between uh + + + align:start position:0% +valid and holding between uh +fluid + + align:start position:0% +fluid + + + align:start position:0% +fluid +elements as they move + + align:start position:0% +elements as they move + + + align:start position:0% +elements as they move +along so it's the + + align:start position:0% +along so it's the + + + align:start position:0% +along so it's the +diffusive fluxes that are related in + + align:start position:0% +diffusive fluxes that are related in + + + align:start position:0% +diffusive fluxes that are related in +that way that we have + + align:start position:0% +that way that we have + + + align:start position:0% +that way that we have +discussed with the exclusion + + align:start position:0% +discussed with the exclusion + + + align:start position:0% +discussed with the exclusion +though of the flux of energy which is uh + + align:start position:0% +though of the flux of energy which is uh + + + align:start position:0% +though of the flux of energy which is uh +related which is which is + + align:start position:0% +related which is which is + + + align:start position:0% +related which is which is +work because when you have the fluid + + align:start position:0% +work because when you have the fluid + + + align:start position:0% +work because when you have the fluid +element that deforms + + align:start position:0% +element that deforms + + + align:start position:0% +element that deforms +especially uh it changes in in + + align:start position:0% +especially uh it changes in in + + + align:start position:0% +especially uh it changes in in +volume uh that change in volume against + + align:start position:0% +volume uh that change in volume against + + + align:start position:0% +volume uh that change in volume against +uh the normal components of the + + align:start position:0% +uh the normal components of the + + + align:start position:0% +uh the normal components of the +stress uh imply work that is a kind of + + align:start position:0% +stress uh imply work that is a kind of + + + align:start position:0% +stress uh imply work that is a kind of +interaction between adjacent fluid + + align:start position:0% +interaction between adjacent fluid + + + align:start position:0% +interaction between adjacent fluid +elements that is not of the Heat and + + align:start position:0% +elements that is not of the Heat and + + + align:start position:0% +elements that is not of the Heat and +diffusion kind so we + + align:start position:0% +diffusion kind so we + + + align:start position:0% +diffusion kind so we +excluded that's why I call this uh NW + + align:start position:0% +excluded that's why I call this uh NW + + + align:start position:0% +excluded that's why I call this uh NW +non work so the nonwork component of the + + align:start position:0% +non work so the nonwork component of the + + + align:start position:0% +non work so the nonwork component of the +heat transfer between uh the fluid + + align:start position:0% +heat transfer between uh the fluid + + + align:start position:0% +heat transfer between uh the fluid +elements as they move along the path + + align:start position:0% +elements as they move along the path + + + align:start position:0% +elements as they move along the path +line uh is related to entropy flux and + + align:start position:0% +line uh is related to entropy flux and + + + align:start position:0% +line uh is related to entropy flux and +constituent flux as in the heat + + align:start position:0% +constituent flux as in the heat + + + align:start position:0% +constituent flux as in the heat +diffusion mode of + + align:start position:0% +diffusion mode of + + + align:start position:0% +diffusion mode of +interaction but energy has an additional + + align:start position:0% +interaction but energy has an additional + + + align:start position:0% +interaction but energy has an additional +contribution which is the work + + align:start position:0% +contribution which is the work + + + align:start position:0% +contribution which is the work +component given by the stress tensor + + align:start position:0% +component given by the stress tensor + + + align:start position:0% +component given by the stress tensor +into the + + align:start position:0% + + + + align:start position:0% + +velocity okay this one as we said we + + align:start position:0% +velocity okay this one as we said we + + + align:start position:0% +velocity okay this one as we said we +take uh since in the balance equations + + align:start position:0% +take uh since in the balance equations + + + align:start position:0% +take uh since in the balance equations +there appear divergencies all this stuff + + align:start position:0% +there appear divergencies all this stuff + + + align:start position:0% +there appear divergencies all this stuff +all these + + align:start position:0% +all these + + + align:start position:0% +all these +fluxes um we can combine those with the + + align:start position:0% +fluxes um we can combine those with the + + + align:start position:0% +fluxes um we can combine those with the +Divergence of this uh relation which is + + align:start position:0% +Divergence of this uh relation which is + + + align:start position:0% +Divergence of this uh relation which is +here and a few things will come cancel + + align:start position:0% +here and a few things will come cancel + + + align:start position:0% +here and a few things will come cancel +out and here are the terms that + + align:start position:0% +out and here are the terms that + + + align:start position:0% +out and here are the terms that +survive and we write what + + align:start position:0% +survive and we write what + + + align:start position:0% +survive and we write what +survives as an expression we took on the + + align:start position:0% +survives as an expression we took on the + + + align:start position:0% +survives as an expression we took on the +left hand side only the rate of entropy + + align:start position:0% +left hand side only the rate of entropy + + + align:start position:0% +left hand side only the rate of entropy +production the density of entropy + + align:start position:0% +production the density of entropy + + + align:start position:0% +production the density of entropy +production so the rate of entropy + + align:start position:0% +production so the rate of entropy + + + align:start position:0% +production so the rate of entropy +production per unit volume + + align:start position:0% +production per unit volume + + + align:start position:0% +production per unit volume +Sigma and we have on the right hand side + + align:start position:0% +Sigma and we have on the right hand side + + + align:start position:0% +Sigma and we have on the right hand side +all the terms that contribute to that + + align:start position:0% +all the terms that contribute to that + + + align:start position:0% +all the terms that contribute to that +entropy + + align:start position:0% + + + + align:start position:0% + +production this is the most General uh + + align:start position:0% +production this is the most General uh + + + align:start position:0% +production this is the most General uh +form it uh includes all sorts of terms + + align:start position:0% +form it uh includes all sorts of terms + + + align:start position:0% +form it uh includes all sorts of terms +one is an old friend of from chemical um + + align:start position:0% + + + + align:start position:0% + +kinetics this term here will give rise + + align:start position:0% +kinetics this term here will give rise + + + align:start position:0% +kinetics this term here will give rise +as you will see to the dissipation + + align:start position:0% +as you will see to the dissipation + + + align:start position:0% +as you will see to the dissipation +function of fluid mechanics we see it in + + align:start position:0% +function of fluid mechanics we see it in + + + align:start position:0% +function of fluid mechanics we see it in +a + + align:start position:0% +a + + + align:start position:0% +a +moment the first term + + align:start position:0% +moment the first term + + + align:start position:0% +moment the first term +is the one that U uh gives + + align:start position:0% +is the one that U uh gives + + + align:start position:0% +is the one that U uh gives +the the Fier uh expression when you have + + align:start position:0% +the the Fier uh expression when you have + + + align:start position:0% +the the Fier uh expression when you have +only uh heat and not also diffusion and + + align:start position:0% +only uh heat and not also diffusion and + + + align:start position:0% +only uh heat and not also diffusion and +these are terms that we have to see what + + align:start position:0% +these are terms that we have to see what + + + align:start position:0% +these are terms that we have to see what +they do because they do important uh + + align:start position:0% +they do because they do important uh + + + align:start position:0% +they do because they do important uh +effects for many Publications + + align:start position:0% + + + + align:start position:0% + +now the other time we + + align:start position:0% +now the other time we + + + align:start position:0% +now the other time we +also + + align:start position:0% +also + + + align:start position:0% +also +uh have seen how to uh + + align:start position:0% +uh have seen how to uh + + + align:start position:0% +uh have seen how to uh +recognize uh in the + + align:start position:0% +recognize uh in the + + + align:start position:0% +recognize uh in the +um heat I'm sorry energy uh in the + + align:start position:0% +um heat I'm sorry energy uh in the + + + align:start position:0% +um heat I'm sorry energy uh in the +energy flux a portion of the energy flux + + align:start position:0% +energy flux a portion of the energy flux + + + align:start position:0% +energy flux a portion of the energy flux +that we can still recognize as and call + + align:start position:0% +that we can still recognize as and call + + + align:start position:0% +that we can still recognize as and call +heat or we call it the measurable heat + + align:start position:0% +heat or we call it the measurable heat + + + align:start position:0% +heat or we call it the measurable heat +more properly but essentially it's the + + align:start position:0% +more properly but essentially it's the + + + align:start position:0% +more properly but essentially it's the +part that we + + align:start position:0% +part that we + + + align:start position:0% +part that we +can identify with the heat of heat + + align:start position:0% +can identify with the heat of heat + + + align:start position:0% +can identify with the heat of heat +transfer so again with this Q double + + align:start position:0% +transfer so again with this Q double + + + align:start position:0% +transfer so again with this Q double +prime + + align:start position:0% + + + + align:start position:0% + +notation so if we take the nonwork part + + align:start position:0% +notation so if we take the nonwork part + + + align:start position:0% +notation so if we take the nonwork part +of the energy flux it's given by the + + align:start position:0% +of the energy flux it's given by the + + + align:start position:0% +of the energy flux it's given by the +heat + + align:start position:0% +heat + + + align:start position:0% +heat +plus a portion which is related to the + + align:start position:0% +plus a portion which is related to the + + + align:start position:0% +plus a portion which is related to the +flux so it's this is the energy which is + + align:start position:0% +flux so it's this is the energy which is + + + align:start position:0% +flux so it's this is the energy which is +carried by uh the particles + + align:start position:0% +carried by uh the particles + + + align:start position:0% +carried by uh the particles +uh + + align:start position:0% + + + + align:start position:0% + +in just because they are + + align:start position:0% +in just because they are + + + align:start position:0% +in just because they are +diffusing this is not convective because + + align:start position:0% +diffusing this is not convective because + + + align:start position:0% +diffusing this is not convective because +this is a + + align:start position:0% +this is a + + + align:start position:0% +this is a +diffusive part so this is part particles + + align:start position:0% +diffusive part so this is part particles + + + align:start position:0% +diffusive part so this is part particles +that are moving different at a different + + align:start position:0% +that are moving different at a different + + + align:start position:0% +that are moving different at a different +velocity than the bicentric velocity so + + align:start position:0% +velocity than the bicentric velocity so + + + align:start position:0% +velocity than the bicentric velocity so +they diffuse away or into our fluid + + align:start position:0% +they diffuse away or into our fluid + + + align:start position:0% +they diffuse away or into our fluid +element and as they do so they carry + + align:start position:0% +element and as they do so they carry + + + align:start position:0% +element and as they do so they carry +with them their backpack of internal + + align:start position:0% +with them their backpack of internal + + + align:start position:0% +with them their backpack of internal +energy and plus they also have to + + align:start position:0% +energy and plus they also have to + + + align:start position:0% +energy and plus they also have to +um advance and face the the pressure + + align:start position:0% +um advance and face the the pressure + + + align:start position:0% +um advance and face the the pressure +that is present and therefore there is + + align:start position:0% +that is present and therefore there is + + + align:start position:0% +that is present and therefore there is +also this + + align:start position:0% + + + + align:start position:0% + +uh there is this pure work which is p + + align:start position:0% +uh there is this pure work which is p + + + align:start position:0% +uh there is this pure work which is p +times the the uh partial volume which is + + align:start position:0% +times the the uh partial volume which is + + + align:start position:0% +times the the uh partial volume which is +hidden here because you remember the + + align:start position:0% +hidden here because you remember the + + + align:start position:0% +hidden here because you remember the +enthalpy is U plus PV so this is a + + align:start position:0% +enthalpy is U plus PV so this is a + + + align:start position:0% +enthalpy is U plus PV so this is a +partial enthalpy so it's partial energy + + align:start position:0% +partial enthalpy so it's partial energy + + + align:start position:0% +partial enthalpy so it's partial energy +plus uh P times partial volume and uh + + align:start position:0% +plus uh P times partial volume and uh + + + align:start position:0% +plus uh P times partial volume and uh +and that P times partial volume is the + + align:start position:0% +and that P times partial volume is the + + + align:start position:0% +and that P times partial volume is the +pulsion work equivalent to what you + + align:start position:0% +pulsion work equivalent to what you + + + align:start position:0% +pulsion work equivalent to what you +would have in a bulk flow + + align:start position:0% +would have in a bulk flow + + + align:start position:0% +would have in a bulk flow +situation but here we are in diffusion + + align:start position:0% + + + + align:start position:0% + +okay so we can + + align:start position:0% +okay so we can + + + align:start position:0% +okay so we can +substitute this terms here into our + + align:start position:0% +substitute this terms here into our + + + align:start position:0% +substitute this terms here into our +expression and this is a very typical + + align:start position:0% +expression and this is a very typical + + + align:start position:0% +expression and this is a very typical +procedure that uh we + + align:start position:0% +procedure that uh we + + + align:start position:0% +procedure that uh we +like uh somehow to + + align:start position:0% + + + + align:start position:0% + +express uh to rewrite every time you + + align:start position:0% +express uh to rewrite every time you + + + align:start position:0% +express uh to rewrite every time you +formulate a a problem in non equilibrium + + align:start position:0% +formulate a a problem in non equilibrium + + + align:start position:0% +formulate a a problem in non equilibrium +thermodynamics you typically typically + + align:start position:0% +thermodynamics you typically typically + + + align:start position:0% +thermodynamics you typically typically +start and it's the safer way to do it uh + + align:start position:0% +start and it's the safer way to do it uh + + + align:start position:0% +start and it's the safer way to do it uh +start from the entropic point of view so + + align:start position:0% +start from the entropic point of view so + + + align:start position:0% +start from the entropic point of view so +you write it in this way you identify + + align:start position:0% +you write it in this way you identify + + + align:start position:0% +you write it in this way you identify +these gradients as + + align:start position:0% +these gradients as + + + align:start position:0% +these gradients as +the degrees of non-e equilibrium related + + align:start position:0% +the degrees of non-e equilibrium related + + + align:start position:0% +the degrees of non-e equilibrium related +to the various transport of the various + + align:start position:0% + + + + align:start position:0% + +properties but then you like to + + align:start position:0% +properties but then you like to + + + align:start position:0% +properties but then you like to +translate this into a more common and + + align:start position:0% +translate this into a more common and + + + align:start position:0% +translate this into a more common and +familiar language and we since we + + align:start position:0% +familiar language and we since we + + + align:start position:0% +familiar language and we since we +consider more familiar talking about + + align:start position:0% +consider more familiar talking about + + + align:start position:0% +consider more familiar talking about +heat because it's related to q and Q + + align:start position:0% +heat because it's related to q and Q + + + align:start position:0% +heat because it's related to q and Q +over t uh we often go back to these and + + align:start position:0% +over t uh we often go back to these and + + + align:start position:0% +over t uh we often go back to these and +then also the fluxes of particles um and + + align:start position:0% +then also the fluxes of particles um and + + + align:start position:0% +then also the fluxes of particles um and +and the chemical + + align:start position:0% +and the chemical + + + align:start position:0% +and the chemical +potentials uh so we substitute this to + + align:start position:0% +potentials uh so we substitute this to + + + align:start position:0% +potentials uh so we substitute this to +there we also use a relation that uh I + + align:start position:0% +there we also use a relation that uh I + + + align:start position:0% +there we also use a relation that uh I +think we we've we' we've + + align:start position:0% +think we we've we' we've + + + align:start position:0% +think we we've we' we've +discussed that you can write uh when you + + align:start position:0% +discussed that you can write uh when you + + + align:start position:0% +discussed that you can write uh when you +write the differential of the chemical + + align:start position:0% +write the differential of the chemical + + + align:start position:0% +write the differential of the chemical +potential you can separate the part that + + align:start position:0% +potential you can separate the part that + + + align:start position:0% +potential you can separate the part that +depends on temperature and the parts + + align:start position:0% +depends on temperature and the parts + + + align:start position:0% +depends on temperature and the parts +that uh changes that constant uh + + align:start position:0% +that uh changes that constant uh + + + align:start position:0% +that uh changes that constant uh +temperature so it depends on pressure + + align:start position:0% +temperature so it depends on pressure + + + align:start position:0% +temperature so it depends on pressure +and concentrations and so we we keep + + align:start position:0% +and concentrations and so we we keep + + + align:start position:0% +and concentrations and so we we keep +that uh + + align:start position:0% +that uh + + + align:start position:0% +that uh +part written this way and so the bottom + + align:start position:0% +part written this way and so the bottom + + + align:start position:0% +part written this way and so the bottom +line is that we can write + + align:start position:0% +line is that we can write + + + align:start position:0% +line is that we can write +uh the entropy production density Sigma + + align:start position:0% +uh the entropy production density Sigma + + + align:start position:0% +uh the entropy production density Sigma +in this way so here we have more + + align:start position:0% +in this way so here we have more + + + align:start position:0% +in this way so here we have more +explicitly the Fier kind + + align:start position:0% +explicitly the Fier kind + + + align:start position:0% +explicitly the Fier kind +of entropy + + align:start position:0% +of entropy + + + align:start position:0% +of entropy +production here you have a similar term + + align:start position:0% +production here you have a similar term + + + align:start position:0% +production here you have a similar term +related to diffusion here we still have + + align:start position:0% +related to diffusion here we still have + + + align:start position:0% +related to diffusion here we still have +the usual uh term related to chemical + + align:start position:0% +the usual uh term related to chemical + + + align:start position:0% +the usual uh term related to chemical +kinetics and uh what is left here is the + + align:start position:0% +kinetics and uh what is left here is the + + + align:start position:0% +kinetics and uh what is left here is the +dissipation function one over the + + align:start position:0% +dissipation function one over the + + + align:start position:0% +dissipation function one over the +temperature times the dissipation + + align:start position:0% +temperature times the dissipation + + + align:start position:0% +temperature times the dissipation +function and here are the details of the + + align:start position:0% +function and here are the details of the + + + align:start position:0% +function and here are the details of the +dissipation functions if you like if you + + align:start position:0% +dissipation functions if you like if you + + + align:start position:0% +dissipation functions if you like if you +are a fluid + + align:start position:0% +are a fluid + + + align:start position:0% +are a fluid +mechanist uh it has two contributions + + align:start position:0% +mechanist uh it has two contributions + + + align:start position:0% +mechanist uh it has two contributions +it's not just the devor deviator part of + + align:start position:0% +it's not just the devor deviator part of + + + align:start position:0% +it's not just the devor deviator part of +the stress tensor and the theoric + + align:start position:0% +the stress tensor and the theoric + + + align:start position:0% +the stress tensor and the theoric +component of the + + align:start position:0% +component of the + + + align:start position:0% +component of the +strain temperature I'm sorry + + align:start position:0% +strain temperature I'm sorry + + + align:start position:0% +strain temperature I'm sorry +tensor but it has also this term which + + align:start position:0% +tensor but it has also this term which + + + align:start position:0% +tensor but it has also this term which +is related to the Divergence of + + align:start position:0% +is related to the Divergence of + + + align:start position:0% +is related to the Divergence of +B and it's true that for most flu flows + + align:start position:0% +B and it's true that for most flu flows + + + align:start position:0% +B and it's true that for most flu flows +like low ma number flows this is zero so + + align:start position:0% +like low ma number flows this is zero so + + + align:start position:0% +like low ma number flows this is zero so +this is really not important + + align:start position:0% +this is really not important + + + align:start position:0% +this is really not important +but uh in principle this is one of the + + align:start position:0% +but uh in principle this is one of the + + + align:start position:0% +but uh in principle this is one of the +dissipative terms and in fact notice + + align:start position:0% +dissipative terms and in fact notice + + + align:start position:0% +dissipative terms and in fact notice +also that in our doing the the procedure + + align:start position:0% +also that in our doing the the procedure + + + align:start position:0% +also that in our doing the the procedure +here there was a + + align:start position:0% +here there was a + + + align:start position:0% +here there was a +pressure uh which is which came in uh + + align:start position:0% +pressure uh which is which came in uh + + + align:start position:0% +pressure uh which is which came in uh +here and there is a PM which is a + + align:start position:0% +here and there is a PM which is a + + + align:start position:0% +here and there is a PM which is a +mechanical pressure that is the the the + + align:start position:0% +mechanical pressure that is the the the + + + align:start position:0% +mechanical pressure that is the the the +trace over oneir of the trace of the + + align:start position:0% +trace over oneir of the trace of the + + + align:start position:0% +trace over oneir of the trace of the +stress + + align:start position:0% + + + + align:start position:0% + +tensor uh they're not + + align:start position:0% +tensor uh they're not + + + align:start position:0% +tensor uh they're not +necessarily uh the + + align:start position:0% + + + + align:start position:0% + +same and so they give rise their + + align:start position:0% +same and so they give rise their + + + align:start position:0% +same and so they give rise their +difference gives rise to this + + align:start position:0% +difference gives rise to this + + + align:start position:0% +difference gives rise to this +uh uh entropy production + + align:start position:0% + + + + align:start position:0% + +term you can still view each of these uh + + align:start position:0% +term you can still view each of these uh + + + align:start position:0% +term you can still view each of these uh +terms as a + + align:start position:0% +terms as a + + + align:start position:0% +terms as a +product of a rate and an affinity or a + + align:start position:0% +product of a rate and an affinity or a + + + align:start position:0% +product of a rate and an affinity or a +degree of this equilibrium so the + + align:start position:0% +degree of this equilibrium so the + + + align:start position:0% +degree of this equilibrium so the +gradient in + + align:start position:0% +gradient in + + + align:start position:0% +gradient in +temperature more properly minus one / T + + align:start position:0% +temperature more properly minus one / T + + + align:start position:0% +temperature more properly minus one / T +squ times the gradient in temperature + + align:start position:0% +squ times the gradient in temperature + + + align:start position:0% +squ times the gradient in temperature +can be interpreted as the degree of this + + align:start position:0% +can be interpreted as the degree of this + + + align:start position:0% +can be interpreted as the degree of this +equilibrium associated with heat + + align:start position:0% +equilibrium associated with heat + + + align:start position:0% +equilibrium associated with heat +uh + + align:start position:0% +uh + + + align:start position:0% +uh +transport uh similarly minus one /t + + align:start position:0% +transport uh similarly minus one /t + + + align:start position:0% +transport uh similarly minus one /t +times the gradient of the chemical + + align:start position:0% +times the gradient of the chemical + + + align:start position:0% +times the gradient of the chemical +potential done at constant + + align:start position:0% +potential done at constant + + + align:start position:0% +potential done at constant +t uh + + align:start position:0% +t uh + + + align:start position:0% +t uh +is the degree of dise equilibrium with + + align:start position:0% +is the degree of dise equilibrium with + + + align:start position:0% +is the degree of dise equilibrium with +respect to uh diffusion of + + align:start position:0% + + + + align:start position:0% + +particles the affinities in chemical in + + align:start position:0% +particles the affinities in chemical in + + + align:start position:0% +particles the affinities in chemical in +chemistry one / R they are already being + + align:start position:0% +chemistry one / R they are already being + + + align:start position:0% +chemistry one / R they are already being +recognized as the degrees of the execu + + align:start position:0% +recognized as the degrees of the execu + + + align:start position:0% +recognized as the degrees of the execu +equilibrium and here for for for the + + align:start position:0% +equilibrium and here for for for the + + + align:start position:0% +equilibrium and here for for for the +fluid part we have a degree of thise + + align:start position:0% +fluid part we have a degree of thise + + + align:start position:0% +fluid part we have a degree of thise +equilibrium which is related to the rate + + align:start position:0% +equilibrium which is related to the rate + + + align:start position:0% +equilibrium which is related to the rate +of + + align:start position:0% +of + + + align:start position:0% +of +strain just the symmetric part of the + + align:start position:0% +strain just the symmetric part of the + + + align:start position:0% +strain just the symmetric part of the +rate of strain of the local stress + + align:start position:0% +rate of strain of the local stress + + + align:start position:0% +rate of strain of the local stress +tensor I'm sorry velocity of the local + + align:start position:0% +tensor I'm sorry velocity of the local + + + align:start position:0% +tensor I'm sorry velocity of the local +velocity field it's the gradient of the + + align:start position:0% +velocity field it's the gradient of the + + + align:start position:0% +velocity field it's the gradient of the +Velocity field and uh whereas the + + align:start position:0% +Velocity field and uh whereas the + + + align:start position:0% +Velocity field and uh whereas the +conjugated flux is the flux of momentum + + align:start position:0% +conjugated flux is the flux of momentum + + + align:start position:0% +conjugated flux is the flux of momentum +which is related to + + align:start position:0% +which is related to + + + align:start position:0% +which is related to +uh the stress tensor but then there is + + align:start position:0% +uh the stress tensor but then there is + + + align:start position:0% +uh the stress tensor but then there is +also this one so + + align:start position:0% +also this one so + + + align:start position:0% +also this one so +the Divergence of velocity which as we + + align:start position:0% +the Divergence of velocity which as we + + + align:start position:0% +the Divergence of velocity which as we +said it's is the rate of change of + + align:start position:0% +said it's is the rate of change of + + + align:start position:0% +said it's is the rate of change of +volume as you FL as You Follow the flu + + align:start position:0% +volume as you FL as You Follow the flu + + + align:start position:0% +volume as you FL as You Follow the flu +the fluid + + align:start position:0% +the fluid + + + align:start position:0% +the fluid +element that is also an + + align:start position:0% +element that is also an + + + align:start position:0% +element that is also an +affinity for a for a + + align:start position:0% +affinity for a for a + + + align:start position:0% +affinity for a for a +dissipation for which the flux is given + + align:start position:0% +dissipation for which the flux is given + + + align:start position:0% +dissipation for which the flux is given +by these uh difference between the + + align:start position:0% +by these uh difference between the + + + align:start position:0% +by these uh difference between the +thermodynamic pressure and the uh + + align:start position:0% +thermodynamic pressure and the uh + + + align:start position:0% +thermodynamic pressure and the uh +mechanical + + align:start position:0% + + + + align:start position:0% + +pressure if we also have um + + align:start position:0% +pressure if we also have um + + + align:start position:0% +pressure if we also have um +charged particles so if some of the + + align:start position:0% +charged particles so if some of the + + + align:start position:0% +charged particles so if some of the +constituents of our fluid that are uh + + align:start position:0% +constituents of our fluid that are uh + + + align:start position:0% +constituents of our fluid that are uh +charged + + align:start position:0% +charged + + + align:start position:0% +charged +particles and we still we talk + + align:start position:0% +particles and we still we talk + + + align:start position:0% +particles and we still we talk +electrostatics not the electrodynamics + + align:start position:0% +electrostatics not the electrodynamics + + + align:start position:0% +electrostatics not the electrodynamics +is is even more complicated because of + + align:start position:0% +is is even more complicated because of + + + align:start position:0% +is is even more complicated because of +course then you get the Maxell equations + + align:start position:0% +course then you get the Maxell equations + + + align:start position:0% +course then you get the Maxell equations +the magnetic field the vector potential + + align:start position:0% +the magnetic field the vector potential + + + align:start position:0% +the magnetic field the vector potential +and so on too complicated to to to cover + + align:start position:0% +and so on too complicated to to to cover + + + align:start position:0% +and so on too complicated to to to cover +uh and but in any case so here we have + + align:start position:0% +uh and but in any case so here we have + + + align:start position:0% +uh and but in any case so here we have +just + + align:start position:0% +just + + + align:start position:0% +just +electrostatics and uh so Fe is the + + align:start position:0% +electrostatics and uh so Fe is the + + + align:start position:0% +electrostatics and uh so Fe is the +electrostatic + + align:start position:0% +electrostatic + + + align:start position:0% +electrostatic +field + + align:start position:0% + + + + align:start position:0% + +JQ okay JQ + + align:start position:0% +JQ okay JQ + + + align:start position:0% +JQ okay JQ +is the + + align:start position:0% +is the + + + align:start position:0% +is the +diffusive + + align:start position:0% +diffusive + + + align:start position:0% +diffusive +component of the electric current + + align:start position:0% + + + + align:start position:0% + +density because if this fluid element + + align:start position:0% +density because if this fluid element + + + align:start position:0% +density because if this fluid element +contains + + align:start position:0% +contains + + + align:start position:0% +contains +charges and these fluid element moves + + align:start position:0% +charges and these fluid element moves + + + align:start position:0% +charges and these fluid element moves +with the bicentric + + align:start position:0% +with the bicentric + + + align:start position:0% +with the bicentric +velocity okay there is a convective part + + align:start position:0% +velocity okay there is a convective part + + + align:start position:0% +velocity okay there is a convective part +of the charge which produces an electric + + align:start position:0% +of the charge which produces an electric + + + align:start position:0% +of the charge which produces an electric +current okay we're not talking about + + align:start position:0% +current okay we're not talking about + + + align:start position:0% +current okay we're not talking about +this part we talking about the part of + + align:start position:0% +this part we talking about the part of + + + align:start position:0% +this part we talking about the part of +uh charge exchange between adjacent + + align:start position:0% +uh charge exchange between adjacent + + + align:start position:0% +uh charge exchange between adjacent +fluid elements due to the fact that they + + align:start position:0% +fluid elements due to the fact that they + + + align:start position:0% +fluid elements due to the fact that they +have uh the diffusion the diffusion with + + align:start position:0% +have uh the diffusion the diffusion with + + + align:start position:0% +have uh the diffusion the diffusion with +respect to the bicentric velocity so + + align:start position:0% +respect to the bicentric velocity so + + + align:start position:0% +respect to the bicentric velocity so +this is diffusion flux of + + align:start position:0% +this is diffusion flux of + + + align:start position:0% +this is diffusion flux of +charge and in fact so the total current + + align:start position:0% +charge and in fact so the total current + + + align:start position:0% +charge and in fact so the total current +density would May denote it with I + + align:start position:0% +density would May denote it with I + + + align:start position:0% +density would May denote it with I +double + + align:start position:0% +double + + + align:start position:0% +double +Prime and it is the uh the flux of + + align:start position:0% +Prime and it is the uh the flux of + + + align:start position:0% +Prime and it is the uh the flux of +charge with respect to the laboratory + + align:start position:0% +charge with respect to the laboratory + + + align:start position:0% +charge with respect to the laboratory +frame so it's the flux with a zero on + + align:start position:0% +frame so it's the flux with a zero on + + + align:start position:0% +frame so it's the flux with a zero on +top and it's made up of the diffusive + + align:start position:0% +top and it's made up of the diffusive + + + align:start position:0% +top and it's made up of the diffusive +plus the convective + + align:start position:0% + + + + align:start position:0% + +term and r q is the density of + + align:start position:0% +term and r q is the density of + + + align:start position:0% +term and r q is the density of +charges the local density of + + align:start position:0% + + + + align:start position:0% + +charges + + align:start position:0% +charges + + + align:start position:0% +charges +so + + align:start position:0% +so + + + align:start position:0% +so +uh the work part of the diffusive energy + + align:start position:0% +uh the work part of the diffusive energy + + + align:start position:0% +uh the work part of the diffusive energy +flux is related to + + align:start position:0% +flux is related to + + + align:start position:0% +flux is related to +heat to the diffusion of particles and + + align:start position:0% +heat to the diffusion of particles and + + + align:start position:0% +heat to the diffusion of particles and +to the diffusion of of part of of of + + align:start position:0% +to the diffusion of of part of of of + + + align:start position:0% +to the diffusion of of part of of of +charge okay so we have this extra term + + align:start position:0% +charge okay so we have this extra term + + + align:start position:0% +charge okay so we have this extra term +which uh we can um sort of single out in + + align:start position:0% +which uh we can um sort of single out in + + + align:start position:0% +which uh we can um sort of single out in +here when you do the same procedure as + + align:start position:0% +here when you do the same procedure as + + + align:start position:0% +here when you do the same procedure as +before to write this expression in terms + + align:start position:0% +before to write this expression in terms + + + align:start position:0% +before to write this expression in terms +of the familiar + + align:start position:0% +of the familiar + + + align:start position:0% +of the familiar +variables so here + + align:start position:0% +variables so here + + + align:start position:0% +variables so here +the entropy + + align:start position:0% +the entropy + + + align:start position:0% +the entropy +production is related also to U minus + + align:start position:0% +production is related also to U minus + + + align:start position:0% +production is related also to U minus +one / T times the gradient in the + + align:start position:0% +one / T times the gradient in the + + + align:start position:0% +one / T times the gradient in the +electrostatic field is the degree of + + align:start position:0% +electrostatic field is the degree of + + + align:start position:0% +electrostatic field is the degree of +dise equilibrium with respect + + align:start position:0% +dise equilibrium with respect + + + align:start position:0% +dise equilibrium with respect +to to moving charges and the associated + + align:start position:0% +to to moving charges and the associated + + + align:start position:0% +to to moving charges and the associated +or the conjugated + + align:start position:0% +or the conjugated + + + align:start position:0% +or the conjugated +flux is this difference here which is + + align:start position:0% +flux is this difference here which is + + + align:start position:0% +flux is this difference here which is +just the diffusive flux of charge + + align:start position:0% + + + + align:start position:0% + +that's again the same + + align:start position:0% +that's again the same + + + align:start position:0% +that's again the same +equation now the next step to introduce + + align:start position:0% +equation now the next step to introduce + + + align:start position:0% +equation now the next step to introduce +the next notion is to group these + + align:start position:0% + + + + align:start position:0% + +terms uh in order of increasing + + align:start position:0% +terms uh in order of increasing + + + align:start position:0% +terms uh in order of increasing +tensorial character so some of these are + + align:start position:0% +tensorial character so some of these are + + + align:start position:0% +tensorial character so some of these are +Scholars like chemistry + + align:start position:0% +Scholars like chemistry + + + align:start position:0% +Scholars like chemistry +and + + align:start position:0% +and + + + align:start position:0% +and +also uh inside the dissipation function + + align:start position:0% +also uh inside the dissipation function + + + align:start position:0% +also uh inside the dissipation function +there is a scolar term which is the one + + align:start position:0% +there is a scolar term which is the one + + + align:start position:0% +there is a scolar term which is the one +that we described before and then there + + align:start position:0% +that we described before and then there + + + align:start position:0% +that we described before and then there +is a tensorial term which is the one + + align:start position:0% +is a tensorial term which is the one + + + align:start position:0% +is a tensorial term which is the one +related + + align:start position:0% +related + + + align:start position:0% +related +to uh the the contraction between the uh + + align:start position:0% +to uh the the contraction between the uh + + + align:start position:0% +to uh the the contraction between the uh +deviatoric parts of stress and strain + + align:start position:0% +deviatoric parts of stress and strain + + + align:start position:0% +deviatoric parts of stress and strain +tensors and the rest are + + align:start position:0% +tensors and the rest are + + + align:start position:0% +tensors and the rest are +vectorial um terms heat + + align:start position:0% +vectorial um terms heat + + + align:start position:0% +vectorial um terms heat +flux uh + + align:start position:0% + + + + align:start position:0% + +current flux of particles these are + + align:start position:0% + + + + align:start position:0% + +vectors why is that + + align:start position:0% + + + + align:start position:0% + +important all right now so I I started + + align:start position:0% +important all right now so I I started + + + align:start position:0% +important all right now so I I started +with um some coloring here just to + + align:start position:0% +with um some coloring here just to + + + align:start position:0% +with um some coloring here just to +single out + + align:start position:0% +single out + + + align:start position:0% +single out +the + + align:start position:0% +the + + + align:start position:0% +the +uh the degrees of the dise equilibrium + + align:start position:0% +uh the degrees of the dise equilibrium + + + align:start position:0% +uh the degrees of the dise equilibrium +are the red stuff and the flues are the + + align:start position:0% +are the red stuff and the flues are the + + + align:start position:0% +are the red stuff and the flues are the +blue and so you see H1 is written is a + + align:start position:0% +blue and so you see H1 is written is a + + + align:start position:0% +blue and so you see H1 is written is a +is a product of a degree of this + + align:start position:0% +is a product of a degree of this + + + align:start position:0% +is a product of a degree of this +equilibrium time times a + + align:start position:0% + + + + align:start position:0% + +flux and if we recall what we said about + + align:start position:0% +flux and if we recall what we said about + + + align:start position:0% +flux and if we recall what we said about +exergy you can also read this uh + + align:start position:0% +exergy you can also read this uh + + + align:start position:0% +exergy you can also read this uh +expression as a a representation of how + + align:start position:0% +expression as a a representation of how + + + align:start position:0% +expression as a a representation of how +locally your uh + + align:start position:0% +locally your uh + + + align:start position:0% +locally your uh +fluid or Continuum is dissipating exergy + + align:start position:0% +fluid or Continuum is dissipating exergy + + + align:start position:0% +fluid or Continuum is dissipating exergy +multiply that by the temperature of the + + align:start position:0% +multiply that by the temperature of the + + + align:start position:0% +multiply that by the temperature of the +environment with respect to which you + + align:start position:0% +environment with respect to which you + + + align:start position:0% +environment with respect to which you +want to or the reservoir which respect + + align:start position:0% +want to or the reservoir which respect + + + align:start position:0% +want to or the reservoir which respect +to which you want to measure + + align:start position:0% +to which you want to measure + + + align:start position:0% +to which you want to measure +exergy and so these terms tell you that + + align:start position:0% +exergy and so these terms tell you that + + + align:start position:0% +exergy and so these terms tell you that +um you have dissipation whenever you + + align:start position:0% +um you have dissipation whenever you + + + align:start position:0% +um you have dissipation whenever you +drive like I read here you drive a + + align:start position:0% +drive like I read here you drive a + + + align:start position:0% +drive like I read here you drive a +chemical + + align:start position:0% +chemical + + + align:start position:0% +chemical +reaction uh down the direction of a + + align:start position:0% +reaction uh down the direction of a + + + align:start position:0% +reaction uh down the direction of a +decreasing affinity and that gives you + + align:start position:0% +decreasing affinity and that gives you + + + align:start position:0% +decreasing affinity and that gives you +entropy production you drive a heat flux + + align:start position:0% +entropy production you drive a heat flux + + + align:start position:0% +entropy production you drive a heat flux +down great temperature + + align:start position:0% +down great temperature + + + align:start position:0% +down great temperature +gradient also you you D you drive a + + align:start position:0% +gradient also you you D you drive a + + + align:start position:0% +gradient also you you D you drive a +diffusion flux down a chemical potential + + align:start position:0% +diffusion flux down a chemical potential + + + align:start position:0% +diffusion flux down a chemical potential +gradient or an electric current down a + + align:start position:0% +gradient or an electric current down a + + + align:start position:0% +gradient or an electric current down a +voltage drop or a momentum flux down a + + align:start position:0% +voltage drop or a momentum flux down a + + + align:start position:0% +voltage drop or a momentum flux down a +velocity uh gradient which is the rate + + align:start position:0% +velocity uh gradient which is the rate + + + align:start position:0% +velocity uh gradient which is the rate +of + + align:start position:0% +of + + + align:start position:0% +of +strength + + align:start position:0% + + + + align:start position:0% + +okay uh you may find if you uh look into + + align:start position:0% +okay uh you may find if you uh look into + + + align:start position:0% +okay uh you may find if you uh look into +papers that deal with nilium + + align:start position:0% + + + + align:start position:0% + +thermodynamics that expression up there + + align:start position:0% +thermodynamics that expression up there + + + align:start position:0% +thermodynamics that expression up there +this one with all these terms written in + + align:start position:0% +this one with all these terms written in + + + align:start position:0% +this one with all these terms written in +a compact form in this way as a sum of + + align:start position:0% +a compact form in this way as a sum of + + + align:start position:0% +a compact form in this way as a sum of +products of fluxes and + + align:start position:0% +products of fluxes and + + + align:start position:0% +products of fluxes and +uh instead of degrees of dise + + align:start position:0% +uh instead of degrees of dise + + + align:start position:0% +uh instead of degrees of dise +equilibrium they're called + + align:start position:0% +equilibrium they're called + + + align:start position:0% +equilibrium they're called +forces fluxes and forces so this is a + + align:start position:0% +forces fluxes and forces so this is a + + + align:start position:0% +forces fluxes and forces so this is a +force flux representation of the same or + + align:start position:0% +force flux representation of the same or + + + align:start position:0% +force flux representation of the same or +or short hand notation and um this + + align:start position:0% +or short hand notation and um this + + + align:start position:0% +or short hand notation and um this +symbol here is that is is whatever is + + align:start position:0% +symbol here is that is is whatever is + + + align:start position:0% +symbol here is that is is whatever is +appropriate to use when you have to + + align:start position:0% +appropriate to use when you have to + + + align:start position:0% +appropriate to use when you have to +multiply a scalar flux times a scalar um + + align:start position:0% +multiply a scalar flux times a scalar um + + + align:start position:0% +multiply a scalar flux times a scalar um +degree of dise equilibrium it's just a + + align:start position:0% +degree of dise equilibrium it's just a + + + align:start position:0% +degree of dise equilibrium it's just a +simple + + align:start position:0% +simple + + + align:start position:0% +simple +multiplication like + + align:start position:0% +multiplication like + + + align:start position:0% +multiplication like +here uh when you have to + + align:start position:0% +here uh when you have to + + + align:start position:0% +here uh when you have to +multiply a vector another Vector it is + + align:start position:0% +multiply a vector another Vector it is + + + align:start position:0% +multiply a vector another Vector it is +the dot it's the vector product I'm + + align:start position:0% +the dot it's the vector product I'm + + + align:start position:0% +the dot it's the vector product I'm +soorry not sorry the dot the dot product + + align:start position:0% +soorry not sorry the dot the dot product + + + align:start position:0% +soorry not sorry the dot the dot product +because the vector product is something + + align:start position:0% +because the vector product is something + + + align:start position:0% +because the vector product is something +else and U if you have uh to multiply + + align:start position:0% +else and U if you have uh to multiply + + + align:start position:0% +else and U if you have uh to multiply +the tensor two tensors and get a scal + + align:start position:0% +the tensor two tensors and get a scal + + + align:start position:0% +the tensor two tensors and get a scal +it's the contraction so if you take the + + align:start position:0% +it's the contraction so if you take the + + + align:start position:0% +it's the contraction so if you take the +two matrices of the two tensors you + + align:start position:0% +two matrices of the two tensors you + + + align:start position:0% +two matrices of the two tensors you +multiply them and then you take the + + align:start position:0% +multiply them and then you take the + + + align:start position:0% +multiply them and then you take the +trace and that's the equivalent of of + + align:start position:0% +trace and that's the equivalent of of + + + align:start position:0% +trace and that's the equivalent of of +this double dot + + align:start position:0% +this double dot + + + align:start position:0% +this double dot +operation okay so we will we'll proceed + + align:start position:0% +operation okay so we will we'll proceed + + + align:start position:0% +operation okay so we will we'll proceed +uh now for a + + align:start position:0% +uh now for a + + + align:start position:0% +uh now for a +while uh I mean for today uh for the + + align:start position:0% +while uh I mean for today uh for the + + + align:start position:0% +while uh I mean for today uh for the +rest of today I guess uh with this um + + align:start position:0% +rest of today I guess uh with this um + + + align:start position:0% +rest of today I guess uh with this um +more abstract and short end + + align:start position:0% +more abstract and short end + + + align:start position:0% +more abstract and short end +notation because we want to + + align:start position:0% +notation because we want to + + + align:start position:0% +notation because we want to +discuss + + align:start position:0% +discuss + + + align:start position:0% +discuss +some geometry of these uh uh of the + + align:start position:0% +some geometry of these uh uh of the + + + align:start position:0% +some geometry of these uh uh of the +relations that um we we can write in + + align:start position:0% +relations that um we we can write in + + + align:start position:0% +relations that um we we can write in +order to model how a flux is related to + + align:start position:0% +order to model how a flux is related to + + + align:start position:0% +order to model how a flux is related to +a the force or vice + + align:start position:0% + + + + align:start position:0% + +versa uh yeah um actually maybe should + + align:start position:0% +versa uh yeah um actually maybe should + + + align:start position:0% +versa uh yeah um actually maybe should +go back a + + align:start position:0% +go back a + + + align:start position:0% +go back a +moment + + align:start position:0% +moment + + + align:start position:0% +moment +I I miss there was one slide that I + + align:start position:0% +I I miss there was one slide that I + + + align:start position:0% +I I miss there was one slide that I +don't know where it got where it went + + align:start position:0% +don't know where it got where it went + + + align:start position:0% +don't know where it got where it went +but in any case uh What uh maybe it will + + align:start position:0% +but in any case uh What uh maybe it will + + + align:start position:0% +but in any case uh What uh maybe it will +come up later but uh uh what I need to + + align:start position:0% +come up later but uh uh what I need to + + + align:start position:0% +come up later but uh uh what I need to +say at this moment is that uh + + align:start position:0% +say at this moment is that uh + + + align:start position:0% +say at this moment is that uh +this + + align:start position:0% +this + + + align:start position:0% +this +relation is what I called an extrinsic + + align:start position:0% +relation is what I called an extrinsic + + + align:start position:0% +relation is what I called an extrinsic +relation extrinsic + + align:start position:0% +relation extrinsic + + + align:start position:0% +relation extrinsic +means uh that it has been obtained using + + align:start position:0% +means uh that it has been obtained using + + + align:start position:0% +means uh that it has been obtained using +only uh + + align:start position:0% +only uh + + + align:start position:0% +only uh +assumptions about the Continuum the + + align:start position:0% +assumptions about the Continuum the + + + align:start position:0% +assumptions about the Continuum the +balance equations things that all in + + align:start position:0% +balance equations things that all in + + + align:start position:0% +balance equations things that all in +general it doesn't contain anything that + + align:start position:0% +general it doesn't contain anything that + + + align:start position:0% +general it doesn't contain anything that +has to do with how the material behaves + + align:start position:0% +has to do with how the material behaves + + + align:start position:0% +has to do with how the material behaves +it doesn't yet contain any property of + + align:start position:0% +it doesn't yet contain any property of + + + align:start position:0% +it doesn't yet contain any property of +the material for example here the + + align:start position:0% +the material for example here the + + + align:start position:0% +the material for example here the +property of the material when you do + + align:start position:0% +property of the material when you do + + + align:start position:0% +property of the material when you do +heat transfer comes in when you write + + align:start position:0% +heat transfer comes in when you write + + + align:start position:0% +heat transfer comes in when you write +the for LA and therefore you U insert + + align:start position:0% +the for LA and therefore you U insert + + + align:start position:0% +the for LA and therefore you U insert +the thermal conductivity tensor which is + + align:start position:0% +the thermal conductivity tensor which is + + + align:start position:0% +the thermal conductivity tensor which is +uh um the description of which contains + + align:start position:0% +uh um the description of which contains + + + align:start position:0% +uh um the description of which contains +how your system behaves and so that + + align:start position:0% +how your system behaves and so that + + + align:start position:0% +how your system behaves and so that +takes me + + align:start position:0% + + + + align:start position:0% + +here in other words + + align:start position:0% +here in other words + + + align:start position:0% +here in other words +uh once we have written the extreme IC + + align:start position:0% +uh once we have written the extreme IC + + + align:start position:0% +uh once we have written the extreme IC +General relation for Sigma then we have + + align:start position:0% +General relation for Sigma then we have + + + align:start position:0% +General relation for Sigma then we have +to go into the detail of the particular + + align:start position:0% +to go into the detail of the particular + + + align:start position:0% +to go into the detail of the particular +problem and the particular material or + + align:start position:0% +problem and the particular material or + + + align:start position:0% +problem and the particular material or +materials that we are dealing with and + + align:start position:0% +materials that we are dealing with and + + + align:start position:0% +materials that we are dealing with and +each material has its own + + align:start position:0% +each material has its own + + + align:start position:0% +each material has its own +way of um + + align:start position:0% +way of um + + + align:start position:0% +way of um +reacting uh to fluxes and + + align:start position:0% +reacting uh to fluxes and + + + align:start position:0% +reacting uh to fluxes and +forces the principle in general is that + + align:start position:0% +forces the principle in general is that + + + align:start position:0% +forces the principle in general is that +the material tends to um + + align:start position:0% +the material tends to um + + + align:start position:0% +the material tends to um +spontaneously uh go if it can uh towards + + align:start position:0% +spontaneously uh go if it can uh towards + + + align:start position:0% +spontaneously uh go if it can uh towards +a uh stable equilibrium but sometimes if + + align:start position:0% +a uh stable equilibrium but sometimes if + + + align:start position:0% +a uh stable equilibrium but sometimes if +it is subjected to uh permanent forces + + align:start position:0% +it is subjected to uh permanent forces + + + align:start position:0% +it is subjected to uh permanent forces +it will reach a steady + + align:start position:0% +it will reach a steady + + + align:start position:0% +it will reach a steady +state because that those uh um fluxes + + align:start position:0% +state because that those uh um fluxes + + + align:start position:0% +state because that those uh um fluxes +and forces that are imposed by the by + + align:start position:0% +and forces that are imposed by the by + + + align:start position:0% +and forces that are imposed by the by +the exterior or by the adjacent fluid + + align:start position:0% +the exterior or by the adjacent fluid + + + align:start position:0% +the exterior or by the adjacent fluid +Elements by the flow situation by the + + align:start position:0% +Elements by the flow situation by the + + + align:start position:0% +Elements by the flow situation by the +boundary conditions + + align:start position:0% +boundary conditions + + + align:start position:0% +boundary conditions +uh + + align:start position:0% +uh + + + align:start position:0% +uh +those uh prevent the system from + + align:start position:0% +those uh prevent the system from + + + align:start position:0% +those uh prevent the system from +relaxing spontaneously to equilibrium so + + align:start position:0% +relaxing spontaneously to equilibrium so + + + align:start position:0% +relaxing spontaneously to equilibrium so +it will keep the the state of of + + align:start position:0% + + + + align:start position:0% + +equilibri and typically uh boundary + + align:start position:0% +equilibri and typically uh boundary + + + align:start position:0% +equilibri and typically uh boundary +conditions most of the + + align:start position:0% +conditions most of the + + + align:start position:0% +conditions most of the +times uh impose either the forces or the + + align:start position:0% +times uh impose either the forces or the + + + align:start position:0% +times uh impose either the forces or the +fluxes uh but there sometimes you also U + + align:start position:0% +fluxes uh but there sometimes you also U + + + align:start position:0% +fluxes uh but there sometimes you also U +impose a related a relation between + + align:start position:0% +impose a related a relation between + + + align:start position:0% +impose a related a relation between +force and flux like when you do + + align:start position:0% +force and flux like when you do + + + align:start position:0% +force and flux like when you do +convective heat transfer the that is a + + align:start position:0% +convective heat transfer the that is a + + + align:start position:0% +convective heat transfer the that is a +boundary condition of U Robin + + align:start position:0% + + + + align:start position:0% + +type + + align:start position:0% + + + + align:start position:0% + +uh in any case you can + + align:start position:0% +uh in any case you can + + + align:start position:0% +uh in any case you can +view uh there is a dual point of + + align:start position:0% +view uh there is a dual point of + + + align:start position:0% +view uh there is a dual point of +view you can uh describe + + align:start position:0% +view you can uh describe + + + align:start position:0% +view you can uh describe +your material resistance to flux by + + align:start position:0% +your material resistance to flux by + + + align:start position:0% +your material resistance to flux by +saying uh how it is how it + + align:start position:0% +saying uh how it is how it + + + align:start position:0% +saying uh how it is how it +reacts uh when you impose some flaxes uh + + align:start position:0% +reacts uh when you impose some flaxes uh + + + align:start position:0% +reacts uh when you impose some flaxes uh +in + + align:start position:0% +in + + + align:start position:0% +in +it and the material typically reacts to + + align:start position:0% +it and the material typically reacts to + + + align:start position:0% +it and the material typically reacts to +a + + align:start position:0% +a + + + align:start position:0% +a +flux by building up a degree of this + + align:start position:0% +flux by building up a degree of this + + + align:start position:0% +flux by building up a degree of this +equilibrium remember the chatelier brown + + align:start position:0% +equilibrium remember the chatelier brown + + + align:start position:0% +equilibrium remember the chatelier brown +theorem degree of this equilibrium that + + align:start position:0% +theorem degree of this equilibrium that + + + align:start position:0% +theorem degree of this equilibrium that +will enhance its tendency to uh + + align:start position:0% +will enhance its tendency to uh + + + align:start position:0% +will enhance its tendency to uh +contrast that flux and return to + + align:start position:0% + + + + align:start position:0% + +equilibrium so your model for for the + + align:start position:0% +equilibrium so your model for for the + + + align:start position:0% +equilibrium so your model for for the +material will be a relation that gives + + align:start position:0% +material will be a relation that gives + + + align:start position:0% +material will be a relation that gives +you the force as a function of the flux + + align:start position:0% +you the force as a function of the flux + + + align:start position:0% +you the force as a function of the flux +and the gamma gamas are the other + + align:start position:0% +and the gamma gamas are the other + + + align:start position:0% +and the gamma gamas are the other +properties like equilibrium properties + + align:start position:0% +properties like equilibrium properties + + + align:start position:0% +properties like equilibrium properties +if you are near equilibrium like + + align:start position:0% +if you are near equilibrium like + + + align:start position:0% +if you are near equilibrium like +temperatures chemical potentials + + align:start position:0% + + + + align:start position:0% + +electrostatic + + align:start position:0% +electrostatic + + + align:start position:0% +electrostatic +field but of course you can also view it + + align:start position:0% +field but of course you can also view it + + + align:start position:0% +field but of course you can also view it +in the opposite way it's just the + + align:start position:0% +in the opposite way it's just the + + + align:start position:0% +in the opposite way it's just the +inverse function or the dual point of + + align:start position:0% +inverse function or the dual point of + + + align:start position:0% +inverse function or the dual point of +view you impose Force for example you + + align:start position:0% +view you impose Force for example you + + + align:start position:0% +view you impose Force for example you +impose a gradient in temperature on a + + align:start position:0% +impose a gradient in temperature on a + + + align:start position:0% +impose a gradient in temperature on a +specimen of a piece of + + align:start position:0% +specimen of a piece of + + + align:start position:0% +specimen of a piece of +metal and uh the + + align:start position:0% +metal and uh the + + + align:start position:0% +metal and uh the +this the material reacts by building up + + align:start position:0% +this the material reacts by building up + + + align:start position:0% +this the material reacts by building up +a + + align:start position:0% +a + + + align:start position:0% +a +flux which will try to go in the + + align:start position:0% +flux which will try to go in the + + + align:start position:0% +flux which will try to go in the +direction of reestablishing a a flat so + + align:start position:0% +direction of reestablishing a a flat so + + + align:start position:0% +direction of reestablishing a a flat so +of of killing that temperature gradient + + align:start position:0% +of of killing that temperature gradient + + + align:start position:0% +of of killing that temperature gradient +that you are + + align:start position:0% +that you are + + + align:start position:0% +that you are +imposing again + + align:start position:0% +imposing again + + + align:start position:0% +imposing again +uh in this case you write the relation + + align:start position:0% +uh in this case you write the relation + + + align:start position:0% +uh in this case you write the relation +flux as a function of + + align:start position:0% + + + + align:start position:0% + +force and clearly then you have uh you + + align:start position:0% +force and clearly then you have uh you + + + align:start position:0% +force and clearly then you have uh you +put it + + align:start position:0% +put it + + + align:start position:0% +put it +into the extrinsic formula for the + + align:start position:0% +into the extrinsic formula for the + + + align:start position:0% +into the extrinsic formula for the +entropy production that we just uh + + align:start position:0% +entropy production that we just uh + + + align:start position:0% +entropy production that we just uh +uh obtained and and uh here comes + + align:start position:0% +uh obtained and and uh here comes + + + align:start position:0% +uh obtained and and uh here comes +a relation in in this picture the + + align:start position:0% +a relation in in this picture the + + + align:start position:0% +a relation in in this picture the +entropy production is related to the + + align:start position:0% +entropy production is related to the + + + align:start position:0% +entropy production is related to the +fluxes that you have imposed or this one + + align:start position:0% +fluxes that you have imposed or this one + + + align:start position:0% +fluxes that you have imposed or this one +it's related to the forces that you have + + align:start position:0% +it's related to the forces that you have + + + align:start position:0% +it's related to the forces that you have +imposed + + align:start position:0% + + + + align:start position:0% + +and then you + + align:start position:0% + + + + align:start position:0% + +start particular + + align:start position:0% +start particular + + + align:start position:0% +start particular +models particular but pretty + + align:start position:0% + + + + align:start position:0% + +General uh for example here we uh if you + + align:start position:0% +General uh for example here we uh if you + + + align:start position:0% +General uh for example here we uh if you +want to model the relation between force + + align:start position:0% +want to model the relation between force + + + align:start position:0% +want to model the relation between force +and flux in heat transfer you adopt the + + align:start position:0% +and flux in heat transfer you adopt the + + + align:start position:0% +and flux in heat transfer you adopt the +fu + + align:start position:0% +fu + + + align:start position:0% +fu +law which for an isotropic material is + + align:start position:0% +law which for an isotropic material is + + + align:start position:0% +law which for an isotropic material is +doesn't have a tensor here is just a + + align:start position:0% +doesn't have a tensor here is just a + + + align:start position:0% +doesn't have a tensor here is just a +scalar but if it is anisotropic we have + + align:start position:0% +scalar but if it is anisotropic we have + + + align:start position:0% +scalar but if it is anisotropic we have +seen that this should become a tensor a + + align:start position:0% +seen that this should become a tensor a + + + align:start position:0% +seen that this should become a tensor a +symmetric tensor due to the onager + + align:start position:0% + + + + align:start position:0% + +reciprocity the relation + + align:start position:0% +reciprocity the relation + + + align:start position:0% +reciprocity the relation +between the difference between + + align:start position:0% +between the difference between + + + align:start position:0% +between the difference between +mechanical and thermodynamic pressure + + align:start position:0% +mechanical and thermodynamic pressure + + + align:start position:0% +mechanical and thermodynamic pressure +and + + align:start position:0% +and + + + align:start position:0% +and +the Divergence of the velocity + + align:start position:0% + + + + align:start position:0% + +is called the lamb law of for nutonian + + align:start position:0% +is called the lamb law of for nutonian + + + align:start position:0% +is called the lamb law of for nutonian +fluid and the constant between the two I + + align:start position:0% +fluid and the constant between the two I + + + align:start position:0% +fluid and the constant between the two I +mean the yeah the the constant of + + align:start position:0% +mean the yeah the the constant of + + + align:start position:0% +mean the yeah the the constant of +proportionality between the two is + + align:start position:0% +proportionality between the two is + + + align:start position:0% +proportionality between the two is +called The Bu + + align:start position:0% + + + + align:start position:0% + +viscosity in + + align:start position:0% +viscosity in + + + align:start position:0% +viscosity in +U fluid + + align:start position:0% +U fluid + + + align:start position:0% +U fluid +mechanics the relation between + + align:start position:0% +mechanics the relation between + + + align:start position:0% +mechanics the relation between +deviatoric part of the stress tensor and + + align:start position:0% +deviatoric part of the stress tensor and + + + align:start position:0% +deviatoric part of the stress tensor and +deviatoric part of the rate of strain + + align:start position:0% +deviatoric part of the rate of strain + + + align:start position:0% +deviatoric part of the rate of strain +tensor is what we call is this linear + + align:start position:0% +tensor is what we call is this linear + + + align:start position:0% +tensor is what we call is this linear +relation and uh the proportionality + + align:start position:0% +relation and uh the proportionality + + + align:start position:0% +relation and uh the proportionality +relation is called the sheer viscosity + + align:start position:0% +relation is called the sheer viscosity + + + align:start position:0% +relation is called the sheer viscosity +we typic just call it + + align:start position:0% + + + + align:start position:0% + +viscosity and with this plus + + align:start position:0% + + + + align:start position:0% + +lamb you may rewrite the stress tensor + + align:start position:0% +lamb you may rewrite the stress tensor + + + align:start position:0% +lamb you may rewrite the stress tensor +in this + + align:start position:0% + + + + align:start position:0% + +way where notice here that I'm using the + + align:start position:0% +way where notice here that I'm using the + + + align:start position:0% +way where notice here that I'm using the +thermodynamic pressure not the + + align:start position:0% +thermodynamic pressure not the + + + align:start position:0% +thermodynamic pressure not the +mechanical pressure because the + + align:start position:0% +mechanical pressure because the + + + align:start position:0% +mechanical pressure because the +difference between the two has been uh + + align:start position:0% +difference between the two has been uh + + + align:start position:0% +difference between the two has been uh +shifted on this + + align:start position:0% +shifted on this + + + align:start position:0% +shifted on this +side to use the + + align:start position:0% +side to use the + + + align:start position:0% +side to use the +lamb + + align:start position:0% +lamb + + + align:start position:0% +lamb +law and so here you have the standard + + align:start position:0% +law and so here you have the standard + + + align:start position:0% +law and so here you have the standard +stuff and here you have the stuff that + + align:start position:0% +stuff and here you have the stuff that + + + align:start position:0% +stuff and here you have the stuff that +you usually neglect + + align:start position:0% +you usually neglect + + + align:start position:0% +you usually neglect +because this + + align:start position:0% +because this + + + align:start position:0% +because this +is + + align:start position:0% +is + + + align:start position:0% +is +typically zero but this is the second + + align:start position:0% +typically zero but this is the second + + + align:start position:0% +typically zero but this is the second +coefficient of + + align:start position:0% + + + + align:start position:0% + +viscosity and then if you have + + align:start position:0% +viscosity and then if you have + + + align:start position:0% +viscosity and then if you have +electricity + + align:start position:0% +electricity + + + align:start position:0% +electricity +conduction diffusion you have a ohms + + align:start position:0% + + + + align:start position:0% + +law the coefficient proportionality + + align:start position:0% +law the coefficient proportionality + + + align:start position:0% +law the coefficient proportionality +between the charge diffusive flux and + + align:start position:0% +between the charge diffusive flux and + + + align:start position:0% +between the charge diffusive flux and +the gradient in the so minus the + + align:start position:0% +the gradient in the so minus the + + + align:start position:0% +the gradient in the so minus the +gradient in the electrostatic field is + + align:start position:0% +gradient in the electrostatic field is + + + align:start position:0% +gradient in the electrostatic field is +the is the electric + + align:start position:0% +the is the electric + + + align:start position:0% +the is the electric +field so this is you could also write it + + align:start position:0% +field so this is you could also write it + + + align:start position:0% +field so this is you could also write it +as + + align:start position:0% +as + + + align:start position:0% +as +e and in any case this is the inverse of + + align:start position:0% +e and in any case this is the inverse of + + + align:start position:0% +e and in any case this is the inverse of +the uh electrical resistivity of your + + align:start position:0% + + + + align:start position:0% + +material and this is one way of + + align:start position:0% +material and this is one way of + + + align:start position:0% +material and this is one way of +proceeding and it is + + align:start position:0% + + + + align:start position:0% + +it has been the way for most of + + align:start position:0% +it has been the way for most of + + + align:start position:0% +it has been the way for most of +uh uh the + + align:start position:0% +uh uh the + + + align:start position:0% +uh uh the +applications + + align:start position:0% + + + + align:start position:0% + +however there is some + + align:start position:0% +however there is some + + + align:start position:0% +however there is some +arbitrariness + + align:start position:0% +arbitrariness + + + align:start position:0% +arbitrariness +in saying as we've seen + + align:start position:0% +in saying as we've seen + + + align:start position:0% +in saying as we've seen +here that for example the heat transfer + + align:start position:0% +here that for example the heat transfer + + + align:start position:0% +here that for example the heat transfer +is not related to some other U degrees + + align:start position:0% +is not related to some other U degrees + + + align:start position:0% +is not related to some other U degrees +of dis equilibrium + + align:start position:0% + + + + align:start position:0% + +and in fact there is this possibility + + align:start position:0% +and in fact there is this possibility + + + align:start position:0% +and in fact there is this possibility +and the Matrix of possibilities is is + + align:start position:0% +and the Matrix of possibilities is is + + + align:start position:0% +and the Matrix of possibilities is is +this + + align:start position:0% +this + + + align:start position:0% +this +one so here is all your degrees of this + + align:start position:0% +one so here is all your degrees of this + + + align:start position:0% +one so here is all your degrees of this +equilibriums possible ones and here is + + align:start position:0% +equilibriums possible ones and here is + + + align:start position:0% +equilibriums possible ones and here is +all the + + align:start position:0% +all the + + + align:start position:0% +all the +flues and those laws that we have seen + + align:start position:0% +flues and those laws that we have seen + + + align:start position:0% +flues and those laws that we have seen +uh in the previous slide are just the + + align:start position:0% +uh in the previous slide are just the + + + align:start position:0% +uh in the previous slide are just the +diagonal terms in these Matrix of + + align:start position:0% +diagonal terms in these Matrix of + + + align:start position:0% +diagonal terms in these Matrix of +coupling they presume a direct + + align:start position:0% +coupling they presume a direct + + + align:start position:0% +coupling they presume a direct +coupling between I mean chemical + + align:start position:0% +coupling between I mean chemical + + + align:start position:0% +coupling between I mean chemical +reaction rate and the Affinity of the + + align:start position:0% +reaction rate and the Affinity of the + + + align:start position:0% +reaction rate and the Affinity of the +reaction uh coupling between these + + align:start position:0% +reaction uh coupling between these + + + align:start position:0% +reaction uh coupling between these +mechanical rate of change of velocity + + align:start position:0% +mechanical rate of change of velocity + + + align:start position:0% +mechanical rate of change of velocity +I'm sorry of volume of the fluid + + align:start position:0% +I'm sorry of volume of the fluid + + + align:start position:0% +I'm sorry of volume of the fluid +elements and this + + align:start position:0% +elements and this + + + align:start position:0% +elements and this +difference in + + align:start position:0% +difference in + + + align:start position:0% +difference in +pressures or these and the the heat + + align:start position:0% +pressures or these and the the heat + + + align:start position:0% +pressures or these and the the heat +transfer and so on so but as you + + align:start position:0% +transfer and so on so but as you + + + align:start position:0% +transfer and so on so but as you +see at least part of this Matrix is + + align:start position:0% +see at least part of this Matrix is + + + align:start position:0% +see at least part of this Matrix is +filled with other + + align:start position:0% +filled with other + + + align:start position:0% +filled with other +possibilities that have names so they + + align:start position:0% +possibilities that have names so they + + + align:start position:0% +possibilities that have names so they +correspond to effects that have been + + align:start position:0% +correspond to effects that have been + + + align:start position:0% +correspond to effects that have been +observed and long ago as you see they're + + align:start position:0% +observed and long ago as you see they're + + + align:start position:0% +observed and long ago as you see they're +talking about the 19th century + + align:start position:0% + + + + align:start position:0% + +still uh these are typically called + + align:start position:0% +still uh these are typically called + + + align:start position:0% +still uh these are typically called +cross effect effects because because + + align:start position:0% +cross effect effects because because + + + align:start position:0% +cross effect effects because because +they happen in the off + + align:start position:0% +they happen in the off + + + align:start position:0% +they happen in the off +diagonal terms of these coupling + + align:start position:0% +diagonal terms of these coupling + + + align:start position:0% +diagonal terms of these coupling +Matrix and also you may have noticed + + align:start position:0% +Matrix and also you may have noticed + + + align:start position:0% +Matrix and also you may have noticed +that I haven't put anything in these + + align:start position:0% +that I haven't put anything in these + + + align:start position:0% +that I haven't put anything in these +parts so why don't I fill completely + + align:start position:0% +parts so why don't I fill completely + + + align:start position:0% +parts so why don't I fill completely +this matx + + align:start position:0% +this matx + + + align:start position:0% +this matx +Matrix okay well in + + align:start position:0% +Matrix okay well in + + + align:start position:0% +Matrix okay well in +principle you you + + align:start position:0% +principle you you + + + align:start position:0% +principle you you +should except that there are + + align:start position:0% +should except that there are + + + align:start position:0% +should except that there are +uh many applications in which your uh + + align:start position:0% +uh many applications in which your uh + + + align:start position:0% +uh many applications in which your uh +fluid is is + + align:start position:0% +fluid is is + + + align:start position:0% +fluid is is +isotropic okay if the fluid is isotropic + + align:start position:0% +isotropic okay if the fluid is isotropic + + + align:start position:0% +isotropic okay if the fluid is isotropic +if the symmetry of your problem uh the + + align:start position:0% +if the symmetry of your problem uh the + + + align:start position:0% +if the symmetry of your problem uh the +like the + + align:start position:0% +like the + + + align:start position:0% +like the +material as well as the boundary + + align:start position:0% +material as well as the boundary + + + align:start position:0% +material as well as the boundary +conditions are + + align:start position:0% +conditions are + + + align:start position:0% +conditions are +isotropic uh + + align:start position:0% +isotropic uh + + + align:start position:0% +isotropic uh +then there is this princip symmetry + + align:start position:0% +then there is this princip symmetry + + + align:start position:0% +then there is this princip symmetry +U takes + + align:start position:0% +U takes + + + align:start position:0% +U takes +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +uh uh it's uh it's saying and it uh it + + align:start position:0% +uh uh it's uh it's saying and it uh it + + + align:start position:0% +uh uh it's uh it's saying and it uh it +it implements what what what what Pier + + align:start position:0% +it implements what what what what Pier + + + align:start position:0% +it implements what what what what Pier +KY described in with this word that the + + align:start position:0% +KY described in with this word that the + + + align:start position:0% +KY described in with this word that the +symmetry of the cause must be preserved + + align:start position:0% +symmetry of the cause must be preserved + + + align:start position:0% +symmetry of the cause must be preserved +into its + + align:start position:0% +into its + + + align:start position:0% +into its +effects + + align:start position:0% +effects + + + align:start position:0% +effects +so what this means is that if you are in + + align:start position:0% +so what this means is that if you are in + + + align:start position:0% +so what this means is that if you are in +isotropic conditions there is no way you + + align:start position:0% +isotropic conditions there is no way you + + + align:start position:0% +isotropic conditions there is no way you +can couple a phenomenon which is of say + + align:start position:0% +can couple a phenomenon which is of say + + + align:start position:0% +can couple a phenomenon which is of say +vectorial character with one which is of + + align:start position:0% +vectorial character with one which is of + + + align:start position:0% +vectorial character with one which is of +a different character like a scalar or a + + align:start position:0% +a different character like a scalar or a + + + align:start position:0% +a different character like a scalar or a +tensor so tensors and couple on only + + align:start position:0% +tensor so tensors and couple on only + + + align:start position:0% +tensor so tensors and couple on only +with + + align:start position:0% +with + + + align:start position:0% +with +tensors uh and scolars only with + + align:start position:0% +tensors uh and scolars only with + + + align:start position:0% +tensors uh and scolars only with +scolars and sorry here the scolars and + + align:start position:0% +scolars and sorry here the scolars and + + + align:start position:0% +scolars and sorry here the scolars and +vectors only with + + align:start position:0% +vectors only with + + + align:start position:0% +vectors only with +vectors + + align:start position:0% +vectors + + + align:start position:0% +vectors +so for but but remember also that this + + align:start position:0% +so for but but remember also that this + + + align:start position:0% +so for but but remember also that this +is true only for isotropic conditions + + align:start position:0% + + + + align:start position:0% + +uh because for example and uh + + align:start position:0% +uh because for example and uh + + + align:start position:0% +uh because for example and uh +um there is an important uh aspect when + + align:start position:0% +um there is an important uh aspect when + + + align:start position:0% +um there is an important uh aspect when +you have + + align:start position:0% +you have + + + align:start position:0% +you have +a for example a + + align:start position:0% +a for example a + + + align:start position:0% +a for example a +uh an interface so this supposed to + + align:start position:0% +uh an interface so this supposed to + + + align:start position:0% +uh an interface so this supposed to +represent an interface between two + + align:start position:0% +represent an interface between two + + + align:start position:0% +represent an interface between two +phases for example uh let's + + align:start position:0% +phases for example uh let's + + + align:start position:0% +phases for example uh let's +say F on one side and G on the other + + align:start position:0% +say F on one side and G on the other + + + align:start position:0% +say F on one side and G on the other +side + + align:start position:0% +side + + + align:start position:0% +side +okay two different phases separated by + + align:start position:0% +okay two different phases separated by + + + align:start position:0% +okay two different phases separated by +an + + align:start position:0% +an + + + align:start position:0% +an +interface and an + + align:start position:0% +interface and an + + + align:start position:0% +interface and an +interface okay let's view it also in + + align:start position:0% +interface okay let's view it also in + + + align:start position:0% +interface okay let's view it also in +this other point of + + align:start position:0% +this other point of + + + align:start position:0% +this other point of +view + + align:start position:0% +view + + + align:start position:0% +view +F and let's plot the + + align:start position:0% +F and let's plot the + + + align:start position:0% +F and let's plot the +density now as we know if we plot the + + align:start position:0% +density now as we know if we plot the + + + align:start position:0% +density now as we know if we plot the +density uh uh of + + align:start position:0% +density uh uh of + + + align:start position:0% +density uh uh of +um of a liquid + + align:start position:0% +um of a liquid + + + align:start position:0% +um of a liquid +and the + + align:start position:0% +and the + + + align:start position:0% +and the +density of a vapor there is a big + + align:start position:0% +density of a vapor there is a big + + + align:start position:0% +density of a vapor there is a big +difference the vapor is about for water + + align:start position:0% +difference the vapor is about for water + + + align:start position:0% +difference the vapor is about for water +it's about a thousand times less dense + + align:start position:0% +it's about a thousand times less dense + + + align:start position:0% +it's about a thousand times less dense +than the + + align:start position:0% +than the + + + align:start position:0% +than the +liquid so in the + + align:start position:0% +liquid so in the + + + align:start position:0% +liquid so in the +interface things are not sharp things + + align:start position:0% +interface things are not sharp things + + + align:start position:0% +interface things are not sharp things +are + + align:start position:0% +are + + + align:start position:0% +are +smooth there is a smooth inter interface + + align:start position:0% +smooth there is a smooth inter interface + + + align:start position:0% +smooth there is a smooth inter interface +there is a lay there is + + align:start position:0% +there is a lay there is + + + align:start position:0% +there is a lay there is +a a a small layer in which there is this + + align:start position:0% +a a a small layer in which there is this + + + align:start position:0% +a a a small layer in which there is this +a + + align:start position:0% +a + + + align:start position:0% +a +huge gradient in + + align:start position:0% +huge gradient in + + + align:start position:0% +huge gradient in +density and this is at + + align:start position:0% +density and this is at + + + align:start position:0% +density and this is at +equilibrium so this is not a kind of + + align:start position:0% +equilibrium so this is not a kind of + + + align:start position:0% +equilibrium so this is not a kind of +gradient that would cause + + align:start position:0% +gradient that would cause + + + align:start position:0% +gradient that would cause +uh uh fluxes it's not it's not a degree + + align:start position:0% +uh uh fluxes it's not it's not a degree + + + align:start position:0% +uh uh fluxes it's not it's not a degree +of this equilibrium this happens at + + align:start position:0% +of this equilibrium this happens at + + + align:start position:0% +of this equilibrium this happens at +equilibrium but still you have a + + align:start position:0% +equilibrium but still you have a + + + align:start position:0% +equilibrium but still you have a +gradient + + align:start position:0% +gradient + + + align:start position:0% +gradient +there + + align:start position:0% +there + + + align:start position:0% +there +and the description of this situation + + align:start position:0% + + + + align:start position:0% + +can be done in several ways Gibbs did it + + align:start position:0% +can be done in several ways Gibbs did it + + + align:start position:0% +can be done in several ways Gibbs did it +by assuming a sharp + + align:start position:0% +by assuming a sharp + + + align:start position:0% +by assuming a sharp +equivalent jump from this value to that + + align:start position:0% +equivalent jump from this value to that + + + align:start position:0% +equivalent jump from this value to that +value which is a good uh approach and uh + + align:start position:0% +value which is a good uh approach and uh + + + align:start position:0% +value which is a good uh approach and uh +uh I will direct you to a very nice + + align:start position:0% +uh I will direct you to a very nice + + + align:start position:0% +uh I will direct you to a very nice +paper + + align:start position:0% +paper + + + align:start position:0% +paper +by uh bed mazour and another author I + + align:start position:0% +by uh bed mazour and another author I + + + align:start position:0% +by uh bed mazour and another author I +forget the name now uh that um does + + align:start position:0% +forget the name now uh that um does + + + align:start position:0% +forget the name now uh that um does +writes exactly the equations that we + + align:start position:0% +writes exactly the equations that we + + + align:start position:0% +writes exactly the equations that we +have written here + + align:start position:0% +have written here + + + align:start position:0% +have written here +this this um + + align:start position:0% +this this um + + + align:start position:0% +this this um +extrinsic relation for + + align:start position:0% +extrinsic relation for + + + align:start position:0% +extrinsic relation for +Sigma uh in the case of a jump + + align:start position:0% +Sigma uh in the case of a jump + + + align:start position:0% +Sigma uh in the case of a jump +description between two + + align:start position:0% +description between two + + + align:start position:0% +description between two +uh between two + + align:start position:0% +uh between two + + + align:start position:0% +uh between two +phases + + align:start position:0% +phases + + + align:start position:0% +phases +okay uh in in this situation here + + align:start position:0% +okay uh in in this situation here + + + align:start position:0% +okay uh in in this situation here +definitely there is no uh isotop + + align:start position:0% + + + + align:start position:0% + +because one thing is to move uh + + align:start position:0% +because one thing is to move uh + + + align:start position:0% +because one thing is to move uh +across uh this interface and one thing + + align:start position:0% +across uh this interface and one thing + + + align:start position:0% +across uh this interface and one thing +is move to move along the interface so + + align:start position:0% +is move to move along the interface so + + + align:start position:0% +is move to move along the interface so +uh if you if you sit on the interface + + align:start position:0% +uh if you if you sit on the interface + + + align:start position:0% +uh if you if you sit on the interface +and move uh on the on the interfacial + + align:start position:0% +and move uh on the on the interfacial + + + align:start position:0% +and move uh on the on the interfacial +region okay + + align:start position:0% +region okay + + + align:start position:0% +region okay +maybe that is isotropic + + align:start position:0% +maybe that is isotropic + + + align:start position:0% +maybe that is isotropic +in the tangent + + align:start position:0% +in the tangent + + + align:start position:0% +in the tangent +Direction but it's not uh in the uh + + align:start position:0% +Direction but it's not uh in the uh + + + align:start position:0% +Direction but it's not uh in the uh +orthogonal Direction so for example in + + align:start position:0% +orthogonal Direction so for example in + + + align:start position:0% +orthogonal Direction so for example in +this + + align:start position:0% + + + + align:start position:0% + +case uh the the stress + + align:start position:0% + + + + align:start position:0% + +tensor which is a you know you can + + align:start position:0% +tensor which is a you know you can + + + align:start position:0% +tensor which is a you know you can +represent it uh in as a 3X3 Matrix + + align:start position:0% + + + + align:start position:0% + +splits uh and and so you you have uh a a + + align:start position:0% +splits uh and and so you you have uh a a + + + align:start position:0% +splits uh and and so you you have uh a a +a pressure an orthogonal pressure and a + + align:start position:0% +a pressure an orthogonal pressure and a + + + align:start position:0% +a pressure an orthogonal pressure and a +tangent pressure and a tangent tensor uh + + align:start position:0% +tangent pressure and a tangent tensor uh + + + align:start position:0% +tangent pressure and a tangent tensor uh +tensor field so you have a + + align:start position:0% +tensor field so you have a + + + align:start position:0% +tensor field so you have a +two-dimensional uh tensor field which is + + align:start position:0% +two-dimensional uh tensor field which is + + + align:start position:0% +two-dimensional uh tensor field which is +um + + align:start position:0% +um + + + align:start position:0% +um +isotropic represents the stress + + align:start position:0% +isotropic represents the stress + + + align:start position:0% +isotropic represents the stress +component in the tangential part plus a + + align:start position:0% + + + + align:start position:0% + +scalar a scalar for the the orthogonal + + align:start position:0% +scalar a scalar for the the orthogonal + + + align:start position:0% +scalar a scalar for the the orthogonal +pressure becomes a + + align:start position:0% +pressure becomes a + + + align:start position:0% +pressure becomes a +scalar and uh so in this + + align:start position:0% +scalar and uh so in this + + + align:start position:0% +scalar and uh so in this +situation this is very interesting + + align:start position:0% +situation this is very interesting + + + align:start position:0% +situation this is very interesting +because that scalar now since it is a + + align:start position:0% +because that scalar now since it is a + + + align:start position:0% +because that scalar now since it is a +scalar it can + + align:start position:0% +scalar it can + + + align:start position:0% +scalar it can +couple with all these scalars + + align:start position:0% +couple with all these scalars + + + align:start position:0% +couple with all these scalars +here so you may have the possibility at + + align:start position:0% +here so you may have the possibility at + + + align:start position:0% +here so you may have the possibility at +interfacing and interfaces to + + align:start position:0% +interfacing and interfaces to + + + align:start position:0% +interfacing and interfaces to +couple uh chemistry + + align:start position:0% +couple uh chemistry + + + align:start position:0% +couple uh chemistry +and uh the flow field and the the + + align:start position:0% +and uh the flow field and the the + + + align:start position:0% +and uh the flow field and the the +pressure field the the orthogonal + + align:start position:0% + + + + align:start position:0% + +pressure and that is uh used that is um + + align:start position:0% +pressure and that is uh used that is um + + + align:start position:0% +pressure and that is uh used that is um +I think uh used in models also for + + align:start position:0% + + + + align:start position:0% + +biological biological systems because + + align:start position:0% +biological biological systems because + + + align:start position:0% +biological biological systems because +that that coupling is + + align:start position:0% +that that coupling is + + + align:start position:0% +that that coupling is +important so it's mechanical mechanical + + align:start position:0% +important so it's mechanical mechanical + + + align:start position:0% +important so it's mechanical mechanical +and chemical uh + + align:start position:0% +and chemical uh + + + align:start position:0% +and chemical uh +coupling but you need to break the + + align:start position:0% +coupling but you need to break the + + + align:start position:0% +coupling but you need to break the +isotropic the isotropy uh in order to + + align:start position:0% +isotropic the isotropy uh in order to + + + align:start position:0% +isotropic the isotropy uh in order to +have this kind + + align:start position:0% + + + + align:start position:0% + +of say exotic + + align:start position:0% + + + + align:start position:0% + +couplings + + align:start position:0% +couplings + + + align:start position:0% +couplings +now we have already talk uh talked about + + align:start position:0% +now we have already talk uh talked about + + + align:start position:0% +now we have already talk uh talked about +Saga relations and you remember that we + + align:start position:0% +Saga relations and you remember that we + + + align:start position:0% +Saga relations and you remember that we +we did it in the context of chemical + + align:start position:0% +we did it in the context of chemical + + + align:start position:0% +we did it in the context of chemical +reactions and we did it we + + align:start position:0% +reactions and we did it we + + + align:start position:0% +reactions and we did it we +proved the the reciprocity on sag + + align:start position:0% +proved the the reciprocity on sag + + + align:start position:0% +proved the the reciprocity on sag +reciprocity theorem you we've shown that + + align:start position:0% +reciprocity theorem you we've shown that + + + align:start position:0% +reciprocity theorem you we've shown that +in the linear regime we could prove it + + align:start position:0% +in the linear regime we could prove it + + + align:start position:0% +in the linear regime we could prove it +as a consequence of the principle of + + align:start position:0% +as a consequence of the principle of + + + align:start position:0% +as a consequence of the principle of +Maximum entropy production by + + align:start position:0% + + + + align:start position:0% + +Ziggler + + align:start position:0% +Ziggler + + + align:start position:0% +Ziggler +here I'm not + + align:start position:0% +here I'm not + + + align:start position:0% +here I'm not +discussing this slide a lot a lot + + align:start position:0% +discussing this slide a lot a lot + + + align:start position:0% +discussing this slide a lot a lot +because essentially it is exactly the + + align:start position:0% +because essentially it is exactly the + + + align:start position:0% +because essentially it is exactly the +same slide that we had then where I + + align:start position:0% +same slide that we had then where I + + + align:start position:0% +same slide that we had then where I +changed some of the symbols here instead + + align:start position:0% +changed some of the symbols here instead + + + align:start position:0% +changed some of the symbols here instead +of Sigma we had entropy production s + + align:start position:0% +of Sigma we had entropy production s + + + align:start position:0% +of Sigma we had entropy production s +dot + + align:start position:0% +dot + + + align:start position:0% +dot +irreversible here we had the reaction + + align:start position:0% +irreversible here we had the reaction + + + align:start position:0% +irreversible here we had the reaction +rate so the Epsilon dots and here we had + + align:start position:0% +rate so the Epsilon dots and here we had + + + align:start position:0% +rate so the Epsilon dots and here we had +the affinities of the reactions and + + align:start position:0% +the affinities of the reactions and + + + align:start position:0% +the affinities of the reactions and +instead of of uh + + align:start position:0% +instead of of uh + + + align:start position:0% +instead of of uh +this + + align:start position:0% +this + + + align:start position:0% +this +super dot symbol we just said nothing + + align:start position:0% +super dot symbol we just said nothing + + + align:start position:0% +super dot symbol we just said nothing +because they were + + align:start position:0% + + + + align:start position:0% + +Scholars and the procedure was just the + + align:start position:0% +Scholars and the procedure was just the + + + align:start position:0% +Scholars and the procedure was just the +same we we we proved we we + + align:start position:0% +same we we we proved we we + + + align:start position:0% +same we we we proved we we +assumed that the + + align:start position:0% +assumed that the + + + align:start position:0% +assumed that the +material in the linear regime so we + + align:start position:0% +material in the linear regime so we + + + align:start position:0% +material in the linear regime so we +assume a linear + + align:start position:0% +assume a linear + + + align:start position:0% +assume a linear +relation and the linear relation is + + align:start position:0% +relation and the linear relation is + + + align:start position:0% +relation and the linear relation is +therefore uh in terms of this um tensor + + align:start position:0% +therefore uh in terms of this um tensor + + + align:start position:0% +therefore uh in terms of this um tensor +here + + align:start position:0% + + + + align:start position:0% + +L it's actually a super tensor because + + align:start position:0% +L it's actually a super tensor because + + + align:start position:0% +L it's actually a super tensor because +it's uh it's it has as many entries as + + align:start position:0% +it's uh it's it has as many entries as + + + align:start position:0% +it's uh it's it has as many entries as +that metrix that we just uh had in the + + align:start position:0% +that metrix that we just uh had in the + + + align:start position:0% +that metrix that we just uh had in the +previous + + align:start position:0% +previous + + + align:start position:0% +previous +slide uh with some zeros around but uh + + align:start position:0% +slide uh with some zeros around but uh + + + align:start position:0% +slide uh with some zeros around but uh +it's it's not a full because of the K + + align:start position:0% +it's it's not a full because of the K + + + align:start position:0% +it's it's not a full because of the K +principle but it's + + align:start position:0% +principle but it's + + + align:start position:0% +principle but it's +still okay so this + + align:start position:0% +still okay so this + + + align:start position:0% +still okay so this +is what we assume a linear + + align:start position:0% +is what we assume a linear + + + align:start position:0% +is what we assume a linear +relation and the bottom line will be + + align:start position:0% +relation and the bottom line will be + + + align:start position:0% +relation and the bottom line will be +that this super tensor has to be + + align:start position:0% + + + + align:start position:0% + +symmetric and uh the Assumption in order + + align:start position:0% +symmetric and uh the Assumption in order + + + align:start position:0% +symmetric and uh the Assumption in order +to obtain this + + align:start position:0% +to obtain this + + + align:start position:0% +to obtain this +result is that the uh entropy production + + align:start position:0% +result is that the uh entropy production + + + align:start position:0% +result is that the uh entropy production +should be maximal subject to the + + align:start position:0% +should be maximal subject to the + + + align:start position:0% +should be maximal subject to the +constraint given by the extrinsic + + align:start position:0% +constraint given by the extrinsic + + + align:start position:0% +constraint given by the extrinsic +relation and in in passing we uh obtain + + align:start position:0% +relation and in in passing we uh obtain + + + align:start position:0% +relation and in in passing we uh obtain +this + + align:start position:0% +this + + + align:start position:0% +this +orthogonality uh Ziggler orthogonality + + align:start position:0% +orthogonality uh Ziggler orthogonality + + + align:start position:0% +orthogonality uh Ziggler orthogonality +relation that we also described + + align:start position:0% +relation that we also described + + + align:start position:0% +relation that we also described +graphically in one of the previous + + align:start position:0% + + + + align:start position:0% + +lectures + + align:start position:0% +lectures + + + align:start position:0% +lectures +okay so okay fine you can proceed this + + align:start position:0% + + + + align:start position:0% + +way U Ziggler actually introduced this + + align:start position:0% +way U Ziggler actually introduced this + + + align:start position:0% +way U Ziggler actually introduced this +this um idea of Maximum entropy + + align:start position:0% +this um idea of Maximum entropy + + + align:start position:0% +this um idea of Maximum entropy +production because his uh objective was + + align:start position:0% +production because his uh objective was + + + align:start position:0% +production because his uh objective was +to he was a material science I guess uh + + align:start position:0% +to he was a material science I guess uh + + + align:start position:0% +to he was a material science I guess uh +person and uh he wanted to be able to + + align:start position:0% +person and uh he wanted to be able to + + + align:start position:0% +person and uh he wanted to be able to +describe things like + + align:start position:0% +describe things like + + + align:start position:0% +describe things like +plasticity uh and + + align:start position:0% +plasticity uh and + + + align:start position:0% +plasticity uh and +plasticity doesn't have a linear regime + + align:start position:0% +plasticity doesn't have a linear regime + + + align:start position:0% +plasticity doesn't have a linear regime +so he wanted to extend uh on Sager + + align:start position:0% +so he wanted to extend uh on Sager + + + align:start position:0% +so he wanted to extend uh on Sager +reciprocity to uh nonlinear regimes and + + align:start position:0% +reciprocity to uh nonlinear regimes and + + + align:start position:0% +reciprocity to uh nonlinear regimes and +in fact here is how you do it again I + + align:start position:0% +in fact here is how you do it again I + + + align:start position:0% +in fact here is how you do it again I +just skip the details but just to give + + align:start position:0% +just skip the details but just to give + + + align:start position:0% +just skip the details but just to give +you a + + align:start position:0% +you a + + + align:start position:0% +you a +flavor all it takes is to instead of + + align:start position:0% +flavor all it takes is to instead of + + + align:start position:0% +flavor all it takes is to instead of +assuming like we did in the previous + + align:start position:0% +assuming like we did in the previous + + + align:start position:0% +assuming like we did in the previous +Slide the linear relation + + align:start position:0% +Slide the linear relation + + + align:start position:0% +Slide the linear relation +between forces and flaxes we assume a + + align:start position:0% +between forces and flaxes we assume a + + + align:start position:0% +between forces and flaxes we assume a +generic relation + + align:start position:0% + + + + align:start position:0% + +J and still apply the principle of + + align:start position:0% +J and still apply the principle of + + + align:start position:0% +J and still apply the principle of +Maximum entry production so maximize + + align:start position:0% +Maximum entry production so maximize + + + align:start position:0% +Maximum entry production so maximize +Sigma subject to to the extrinsic uh + + align:start position:0% +Sigma subject to to the extrinsic uh + + + align:start position:0% +Sigma subject to to the extrinsic uh +relation for + + align:start position:0% +relation for + + + align:start position:0% +relation for +the between forces and + + align:start position:0% +the between forces and + + + align:start position:0% +the between forces and +flaxes and you come up with an + + align:start position:0% +flaxes and you come up with an + + + align:start position:0% +flaxes and you come up with an +orthogonality + + align:start position:0% +orthogonality + + + align:start position:0% +orthogonality +condition in terms of the lrange + + align:start position:0% +condition in terms of the lrange + + + align:start position:0% +condition in terms of the lrange +multiplier which is still only one + + align:start position:0% +multiplier which is still only one + + + align:start position:0% +multiplier which is still only one +because it's still only one + + align:start position:0% + + + + align:start position:0% + +constraint the only problem is that + + align:start position:0% +constraint the only problem is that + + + align:start position:0% +constraint the only problem is that +now remember when you have a in the + + align:start position:0% +now remember when you have a in the + + + align:start position:0% +now remember when you have a in the +method of lrange multipliers you in + + align:start position:0% +method of lrange multipliers you in + + + align:start position:0% +method of lrange multipliers you in +order to find the value of the lrange + + align:start position:0% +order to find the value of the lrange + + + align:start position:0% +order to find the value of the lrange +multiplier you have to uh substitute + + align:start position:0% +multiplier you have to uh substitute + + + align:start position:0% +multiplier you have to uh substitute +back into the constraint so you take + + align:start position:0% +back into the constraint so you take + + + align:start position:0% +back into the constraint so you take +this orthogonality relation this way put + + align:start position:0% +this orthogonality relation this way put + + + align:start position:0% +this orthogonality relation this way put +it back in the constraint and this is + + align:start position:0% +it back in the constraint and this is + + + align:start position:0% +it back in the constraint and this is +done + + align:start position:0% +done + + + align:start position:0% +done +here and then solve for uh + + align:start position:0% +here and then solve for uh + + + align:start position:0% +here and then solve for uh +Lambda in the case of linear case we + + align:start position:0% +Lambda in the case of linear case we + + + align:start position:0% +Lambda in the case of linear case we +found that Lambda is equal to two here + + align:start position:0% +found that Lambda is equal to two here + + + align:start position:0% +found that Lambda is equal to two here +it's more complicated because Lambda is + + align:start position:0% +it's more complicated because Lambda is + + + align:start position:0% +it's more complicated because Lambda is +a is this + + align:start position:0% +a is this + + + align:start position:0% +a is this +function of whatever functional form you + + align:start position:0% +function of whatever functional form you + + + align:start position:0% +function of whatever functional form you +have chosen for your uh um relations + + align:start position:0% +have chosen for your uh um relations + + + align:start position:0% +have chosen for your uh um relations +between forces and fluxes which is + + align:start position:0% +between forces and fluxes which is + + + align:start position:0% +between forces and fluxes which is +nonlinear in + + align:start position:0% +nonlinear in + + + align:start position:0% +nonlinear in +general so you can substitute this into + + align:start position:0% +general so you can substitute this into + + + align:start position:0% +general so you can substitute this into +here and you get this complicated stuff + + align:start position:0% +here and you get this complicated stuff + + + align:start position:0% +here and you get this complicated stuff +which nevertheless is a is an + + align:start position:0% +which nevertheless is a is an + + + align:start position:0% +which nevertheless is a is an +orthogonality it's a + + align:start position:0% +orthogonality it's a + + + align:start position:0% +orthogonality it's a +condition that must be satisfied by the + + align:start position:0% +condition that must be satisfied by the + + + align:start position:0% +condition that must be satisfied by the +functional relation of your uh of your + + align:start position:0% +functional relation of your uh of your + + + align:start position:0% +functional relation of your uh of your +um that you have chosen here so it tells + + align:start position:0% +um that you have chosen here so it tells + + + align:start position:0% +um that you have chosen here so it tells +you that you don't have complete freedom + + align:start position:0% +you that you don't have complete freedom + + + align:start position:0% +you that you don't have complete freedom +in choosing these functions they have to + + align:start position:0% +in choosing these functions they have to + + + align:start position:0% +in choosing these functions they have to +satisfy + + align:start position:0% +satisfy + + + align:start position:0% +satisfy +this for example if you if you choose + + align:start position:0% +this for example if you if you choose + + + align:start position:0% +this for example if you if you choose +the the linear relation which is this + + align:start position:0% +the the linear relation which is this + + + align:start position:0% +the the linear relation which is this +one this + + align:start position:0% +one this + + + align:start position:0% +one this +expression uh reduces to the + + align:start position:0% +expression uh reduces to the + + + align:start position:0% +expression uh reduces to the +one that required the symmetry of the + + align:start position:0% +one that required the symmetry of the + + + align:start position:0% +one that required the symmetry of the +Dion Sager conductivity uh + + align:start position:0% +Dion Sager conductivity uh + + + align:start position:0% +Dion Sager conductivity uh +tensor in a general case you get + + align:start position:0% +tensor in a general case you get + + + align:start position:0% +tensor in a general case you get +something else uh which is a sort of a + + align:start position:0% +something else uh which is a sort of a + + + align:start position:0% +something else uh which is a sort of a +generalization to nonlinear case + + align:start position:0% +generalization to nonlinear case + + + align:start position:0% +generalization to nonlinear case +of + + align:start position:0% +of + + + align:start position:0% +of +of of on Saga relation Al + + align:start position:0% + + + + align:start position:0% + +Ziggler there is another uh way of + + align:start position:0% +Ziggler there is another uh way of + + + align:start position:0% +Ziggler there is another uh way of +viewing uh things they're all sort of + + align:start position:0% + + + + align:start position:0% + +equivalent and uh let me try to explain + + align:start position:0% +equivalent and uh let me try to explain + + + align:start position:0% +equivalent and uh let me try to explain +it in this + + align:start position:0% +it in this + + + align:start position:0% +it in this +uh heat transfer + + align:start position:0% +uh heat transfer + + + align:start position:0% +uh heat transfer +example they are all equivalent and uh + + align:start position:0% +example they are all equivalent and uh + + + align:start position:0% +example they are all equivalent and uh +there's so much and as you see I'll I'll + + align:start position:0% +there's so much and as you see I'll I'll + + + align:start position:0% +there's so much and as you see I'll I'll +say a little bit later about this uh u i + + align:start position:0% +say a little bit later about this uh u i + + + align:start position:0% +say a little bit later about this uh u i +collected this point of view in in a + + align:start position:0% +collected this point of view in in a + + + align:start position:0% +collected this point of view in in a +paper couple of years + + align:start position:0% +paper couple of years + + + align:start position:0% +paper couple of years +ago + + align:start position:0% +ago + + + align:start position:0% +ago +uh and u + + align:start position:0% + + + + align:start position:0% + +let's let's do it for the heat transfer + + align:start position:0% +let's let's do it for the heat transfer + + + align:start position:0% +let's let's do it for the heat transfer +case so + + align:start position:0% +case so + + + align:start position:0% +case so +consider this anisotropic material made + + align:start position:0% +consider this anisotropic material made + + + align:start position:0% +consider this anisotropic material made +of so that micr structure is made of + + align:start position:0% +of so that micr structure is made of + + + align:start position:0% +of so that micr structure is made of +layers um + + align:start position:0% +layers um + + + align:start position:0% +layers um +sandwiched of high conductivity and low + + align:start position:0% +sandwiched of high conductivity and low + + + align:start position:0% +sandwiched of high conductivity and low +conductivity + + align:start position:0% + + + + align:start position:0% + +materials and so suppose you + + align:start position:0% +materials and so suppose you + + + align:start position:0% +materials and so suppose you +subject this + + align:start position:0% +subject this + + + align:start position:0% +subject this +material to a you impose a gradient in + + align:start position:0% +material to a you impose a gradient in + + + align:start position:0% +material to a you impose a gradient in +temperature so material then is + + align:start position:0% +temperature so material then is + + + align:start position:0% +temperature so material then is +under I shouldn't say stress but in any + + align:start position:0% +under I shouldn't say stress but in any + + + align:start position:0% +under I shouldn't say stress but in any +case it's it has to decide all right how + + align:start position:0% +case it's it has to decide all right how + + + align:start position:0% +case it's it has to decide all right how +do I react to that um gradient in + + align:start position:0% +do I react to that um gradient in + + + align:start position:0% +do I react to that um gradient in +temperature that you + + align:start position:0% + + + + align:start position:0% + +impose uh + + align:start position:0% +impose uh + + + align:start position:0% +impose uh +definitely want to react in a way that + + align:start position:0% +definitely want to react in a way that + + + align:start position:0% +definitely want to react in a way that +will allow me to uh like Brown says H to + + align:start position:0% +will allow me to uh like Brown says H to + + + align:start position:0% +will allow me to uh like Brown says H to +reduce that gradient in temperature and + + align:start position:0% +reduce that gradient in temperature and + + + align:start position:0% +reduce that gradient in temperature and +try to reestablish + + align:start position:0% +try to reestablish + + + align:start position:0% +try to reestablish +equilibrium + + align:start position:0% + + + + align:start position:0% + +but you see here what I'm am showing is + + align:start position:0% +but you see here what I'm am showing is + + + align:start position:0% +but you see here what I'm am showing is +that there are many possibilities it + + align:start position:0% +that there are many possibilities it + + + align:start position:0% +that there are many possibilities it +could uh decide to move heat in One + + align:start position:0% +could uh decide to move heat in One + + + align:start position:0% +could uh decide to move heat in One +Direction or in another and how come it + + align:start position:0% +Direction or in another and how come it + + + align:start position:0% +Direction or in another and how come it +chooses this particular + + align:start position:0% + + + + align:start position:0% + +direction in some + + align:start position:0% + + + + align:start position:0% + +sense uh it's like um suppose you are in + + align:start position:0% +sense uh it's like um suppose you are in + + + align:start position:0% +sense uh it's like um suppose you are in +a in a in a crowd you're in the middle + + align:start position:0% +a in a in a crowd you're in the middle + + + align:start position:0% +a in a in a crowd you're in the middle +of a lot of people uh maybe at a concert + + align:start position:0% +of a lot of people uh maybe at a concert + + + align:start position:0% +of a lot of people uh maybe at a concert +or + + align:start position:0% +or + + + align:start position:0% +or +going into or out of a soccer stadium + + align:start position:0% +going into or out of a soccer stadium + + + align:start position:0% +going into or out of a soccer stadium +lots of people and everybody wants to + + align:start position:0% +lots of people and everybody wants to + + + align:start position:0% +lots of people and everybody wants to +reach or get next to the the podium or + + align:start position:0% +reach or get next to the the podium or + + + align:start position:0% +reach or get next to the the podium or +to the entrance or go or go to your car + + align:start position:0% +to the entrance or go or go to your car + + + align:start position:0% +to the entrance or go or go to your car +but you have a crowd in front of you and + + align:start position:0% +but you have a crowd in front of you and + + + align:start position:0% +but you have a crowd in front of you and +so uh even + + align:start position:0% +so uh even + + + align:start position:0% +so uh even +though uh the + + align:start position:0% +though uh the + + + align:start position:0% +though uh the +direct path would be apparently shorter + + align:start position:0% +direct path would be apparently shorter + + + align:start position:0% +direct path would be apparently shorter +but it would require less effort for you + + align:start position:0% +but it would require less effort for you + + + align:start position:0% +but it would require less effort for you +to move in another Direction where you + + align:start position:0% +to move in another Direction where you + + + align:start position:0% +to move in another Direction where you +see less uh resistance to to to your + + align:start position:0% +see less uh resistance to to to your + + + align:start position:0% +see less uh resistance to to to your +motion okay + + align:start position:0% +motion okay + + + align:start position:0% +motion okay +so this is a this is what happens here + + align:start position:0% +so this is a this is what happens here + + + align:start position:0% +so this is a this is what happens here +so there is you you + + align:start position:0% +so there is you you + + + align:start position:0% +so there is you you +evaluate and the + + align:start position:0% +evaluate and the + + + align:start position:0% +evaluate and the +material uh does a a local + + align:start position:0% +material uh does a a local + + + align:start position:0% +material uh does a a local +evaluation uh + + align:start position:0% +evaluation uh + + + align:start position:0% +evaluation uh +sensing okay how much would would it + + align:start position:0% +sensing okay how much would would it + + + align:start position:0% +sensing okay how much would would it +cost me to move in in terms of effort no + + align:start position:0% +cost me to move in in terms of effort no + + + align:start position:0% +cost me to move in in terms of effort no +or in terms of uh yes effort in order to + + align:start position:0% +or in terms of uh yes effort in order to + + + align:start position:0% +or in terms of uh yes effort in order to +move in the crowd how how much would it + + align:start position:0% +move in the crowd how how much would it + + + align:start position:0% +move in the crowd how how much would it +cost me to go in this direction or in + + align:start position:0% +cost me to go in this direction or in + + + align:start position:0% +cost me to go in this direction or in +that + + align:start position:0% +that + + + align:start position:0% +that +direction and so there is a this tensor + + align:start position:0% +direction and so there is a this tensor + + + align:start position:0% +direction and so there is a this tensor +G which I would call a + + align:start position:0% +G which I would call a + + + align:start position:0% +G which I would call a +metric it's the driver of that logic it + + align:start position:0% +metric it's the driver of that logic it + + + align:start position:0% +metric it's the driver of that logic it +measures + + align:start position:0% +measures + + + align:start position:0% +measures +uh uh how dissipative is uh moving in + + align:start position:0% +uh uh how dissipative is uh moving in + + + align:start position:0% +uh uh how dissipative is uh moving in +the various + + align:start position:0% +the various + + + align:start position:0% +the various +directions and if you write an equation + + align:start position:0% +directions and if you write an equation + + + align:start position:0% +directions and if you write an equation +like this + + align:start position:0% +like this + + + align:start position:0% +like this +you + + align:start position:0% +you + + + align:start position:0% +you +you this is a quadratic form with with + + align:start position:0% +you this is a quadratic form with with + + + align:start position:0% +you this is a quadratic form with with +that + + align:start position:0% +that + + + align:start position:0% +that +g uh for given um heat + + align:start position:0% +g uh for given um heat + + + align:start position:0% +g uh for given um heat +fluxes and that it equal to some + + align:start position:0% +fluxes and that it equal to some + + + align:start position:0% +fluxes and that it equal to some +constant that gives you an equation of + + align:start position:0% +constant that gives you an equation of + + + align:start position:0% +constant that gives you an equation of +an + + align:start position:0% +an + + + align:start position:0% +an +ellipsoid and that ellipsoid represents + + align:start position:0% +ellipsoid and that ellipsoid represents + + + align:start position:0% +ellipsoid and that ellipsoid represents +the locus of all + + align:start position:0% +the locus of all + + + align:start position:0% +the locus of all +the uh tips of the vectors that uh would + + align:start position:0% +the uh tips of the vectors that uh would + + + align:start position:0% +the uh tips of the vectors that uh would +cost the material the same effort so the + + align:start position:0% +cost the material the same effort so the + + + align:start position:0% +cost the material the same effort so the +same + + align:start position:0% +same + + + align:start position:0% +same +um + + align:start position:0% + + + + align:start position:0% + +dissipation and so it turns + + align:start position:0% +dissipation and so it turns + + + align:start position:0% +dissipation and so it turns +out + + align:start position:0% +out + + + align:start position:0% +out +that you know the the entropy production + + align:start position:0% +that you know the the entropy production + + + align:start position:0% +that you know the the entropy production +is the scalar product between the blue + + align:start position:0% +is the scalar product between the blue + + + align:start position:0% +is the scalar product between the blue +vector and the red vector + + align:start position:0% +vector and the red vector + + + align:start position:0% +vector and the red vector +okay and the scalar product + + align:start position:0% +okay and the scalar product + + + align:start position:0% +okay and the scalar product +here between two vectors is given by the + + align:start position:0% +here between two vectors is given by the + + + align:start position:0% +here between two vectors is given by the +projection of one vector onto the onto + + align:start position:0% +projection of one vector onto the onto + + + align:start position:0% +projection of one vector onto the onto +the other one so for example this blue + + align:start position:0% +the other one so for example this blue + + + align:start position:0% +the other one so for example this blue +one you see that this blue one the + + align:start position:0% +one you see that this blue one the + + + align:start position:0% +one you see that this blue one the +actual uh full not the dotted ones is + + align:start position:0% +actual uh full not the dotted ones is + + + align:start position:0% +actual uh full not the dotted ones is +the one that has the maximum projection + + align:start position:0% +the one that has the maximum projection + + + align:start position:0% +the one that has the maximum projection +onto the red Vector so the maximize it + + align:start position:0% +onto the red Vector so the maximize it + + + align:start position:0% +onto the red Vector so the maximize it +maximizes among all these possibilities + + align:start position:0% +maximizes among all these possibilities + + + align:start position:0% +maximizes among all these possibilities +that have equal + + align:start position:0% +that have equal + + + align:start position:0% +that have equal +effort the one that uh maximizes the + + align:start position:0% +effort the one that uh maximizes the + + + align:start position:0% +effort the one that uh maximizes the +sigma is this blue one and that's the + + align:start position:0% +sigma is this blue one and that's the + + + align:start position:0% +sigma is this blue one and that's the +one that the material + + align:start position:0% + + + + align:start position:0% + +chooses uh it turns out that g is the + + align:start position:0% +chooses uh it turns out that g is the + + + align:start position:0% +chooses uh it turns out that g is the +inverse of the conductivity + + align:start position:0% +inverse of the conductivity + + + align:start position:0% +inverse of the conductivity +tensor so you can read for + + align:start position:0% +tensor so you can read for + + + align:start position:0% +tensor so you can read for +law with the for an anisotropic material + + align:start position:0% +law with the for an anisotropic material + + + align:start position:0% +law with the for an anisotropic material +in in this way that the material + + align:start position:0% +in in this way that the material + + + align:start position:0% +in in this way that the material +is is choosing the direction + + align:start position:0% +is is choosing the direction + + + align:start position:0% +is is choosing the direction +of maximal entropy production for a + + align:start position:0% +of maximal entropy production for a + + + align:start position:0% +of maximal entropy production for a +given + + align:start position:0% + + + + align:start position:0% + +effort like in your crowd you choose the + + align:start position:0% +effort like in your crowd you choose the + + + align:start position:0% +effort like in your crowd you choose the +Direction with with which you feel that + + align:start position:0% +Direction with with which you feel that + + + align:start position:0% +Direction with with which you feel that +you are moving uh farther away with this + + align:start position:0% +you are moving uh farther away with this + + + align:start position:0% +you are moving uh farther away with this +with with a given effort for a given + + align:start position:0% +with with a given effort for a given + + + align:start position:0% +with with a given effort for a given +amount of effort that you put into that + + align:start position:0% +amount of effort that you put into that + + + align:start position:0% +amount of effort that you put into that +movement + + align:start position:0% + + + + align:start position:0% + +okay so these are words just to explain + + align:start position:0% +okay so these are words just to explain + + + align:start position:0% +okay so these are words just to explain +what + + align:start position:0% +what + + + align:start position:0% +what +uh what I just + + align:start position:0% + + + + align:start position:0% + +said + + align:start position:0% + + + + align:start position:0% + +and so if + + align:start position:0% + + + + align:start position:0% + +you so you you could have a an isotropic + + align:start position:0% +you so you you could have a an isotropic + + + align:start position:0% +you so you you could have a an isotropic +material for an isotropic material + + align:start position:0% +material for an isotropic material + + + align:start position:0% +material for an isotropic material +that ellipsoid becomes a + + align:start position:0% +that ellipsoid becomes a + + + align:start position:0% +that ellipsoid becomes a +sphere a + + align:start position:0% +sphere a + + + align:start position:0% +sphere a +hypersphere all directions are + + align:start position:0% +hypersphere all directions are + + + align:start position:0% +hypersphere all directions are +equivalent and if all directions are + + align:start position:0% + + + + align:start position:0% + +equivalent which one is the direction of + + align:start position:0% +equivalent which one is the direction of + + + align:start position:0% +equivalent which one is the direction of +steepest entropy scent it's the same as + + align:start position:0% +steepest entropy scent it's the same as + + + align:start position:0% +steepest entropy scent it's the same as +the gradient of of T because Vector + + align:start position:0% +the gradient of of T because Vector + + + align:start position:0% +the gradient of of T because Vector +Q + + align:start position:0% + + + + align:start position:0% + +uh as the maximal projection of on on on + + align:start position:0% +uh as the maximal projection of on on on + + + align:start position:0% +uh as the maximal projection of on on on +on the red Vector when they are Co + + align:start position:0% + + + + align:start position:0% + +colinear and so here's + + align:start position:0% +colinear and so here's + + + align:start position:0% +colinear and so here's +the the construction in the same diagram + + align:start position:0% +the the construction in the same diagram + + + align:start position:0% +the the construction in the same diagram +for which we have seen + + align:start position:0% +for which we have seen + + + align:start position:0% +for which we have seen +the uh the + + align:start position:0% +the uh the + + + align:start position:0% +the uh the +orthogonality + + align:start position:0% +orthogonality + + + align:start position:0% +orthogonality +Ziggler + + align:start position:0% + + + + align:start position:0% + +relation so we have + + align:start position:0% +relation so we have + + + align:start position:0% +relation so we have +a an ex y or one and + + align:start position:0% +a an ex y or one and + + + align:start position:0% +a an ex y or one and +two + + align:start position:0% +two + + + align:start position:0% +two +versors so think of it X and Y I impose + + align:start position:0% +versors so think of it X and Y I impose + + + align:start position:0% +versors so think of it X and Y I impose +a gradient in temperature which has two + + align:start position:0% + + + + align:start position:0% + +components and + + align:start position:0% +components and + + + align:start position:0% +components and +uh uh that places me the two + + align:start position:0% +uh uh that places me the two + + + align:start position:0% +uh uh that places me the two +components places me somewhere not at + + align:start position:0% +components places me somewhere not at + + + align:start position:0% +components places me somewhere not at +equilibrium if there if there are zero + + align:start position:0% +equilibrium if there if there are zero + + + align:start position:0% +equilibrium if there if there are zero +I'm at the center so I'm already in an + + align:start position:0% +I'm at the center so I'm already in an + + + align:start position:0% +I'm at the center so I'm already in an +equilibrium State and nothing happens + + align:start position:0% +equilibrium State and nothing happens + + + align:start position:0% +equilibrium State and nothing happens +but if you I'm off equilibrium these are + + align:start position:0% +but if you I'm off equilibrium these are + + + align:start position:0% +but if you I'm off equilibrium these are +the lines of Contours of constant + + align:start position:0% +the lines of Contours of constant + + + align:start position:0% +the lines of Contours of constant +entropy no so the higher the gradient + + align:start position:0% +entropy no so the higher the gradient + + + align:start position:0% +entropy no so the higher the gradient +the farther I am and the highest is the + + align:start position:0% +the farther I am and the highest is the + + + align:start position:0% +the farther I am and the highest is the +uh + + align:start position:0% + + + + align:start position:0% + +entropy I'm sorry the the highest is the + + align:start position:0% +entropy I'm sorry the the highest is the + + + align:start position:0% +entropy I'm sorry the the highest is the +degree of this equilibrium + + align:start position:0% + + + + align:start position:0% + +this is the maximum entropy so this is + + align:start position:0% +this is the maximum entropy so this is + + + align:start position:0% +this is the maximum entropy so this is +the uh the entropy goes decreasing as I + + align:start position:0% +the uh the entropy goes decreasing as I + + + align:start position:0% +the uh the entropy goes decreasing as I +go + + align:start position:0% + + + + align:start position:0% + +further so if I um am here + + align:start position:0% +further so if I um am here + + + align:start position:0% +further so if I um am here +and and that degree of dis equilibrium + + align:start position:0% +and and that degree of dis equilibrium + + + align:start position:0% +and and that degree of dis equilibrium +has been generated at one instant of + + align:start position:0% +has been generated at one instant of + + + align:start position:0% +has been generated at one instant of +time and then the system is allowed to + + align:start position:0% +time and then the system is allowed to + + + align:start position:0% +time and then the system is allowed to +evolve by itself as if were isolated + + align:start position:0% +evolve by itself as if were isolated + + + align:start position:0% +evolve by itself as if were isolated +nothing else uh no constraints just + + align:start position:0% +nothing else uh no constraints just + + + align:start position:0% +nothing else uh no constraints just +you can go to + + align:start position:0% + + + + align:start position:0% + +equilibrium it doesn't go to + + align:start position:0% +equilibrium it doesn't go to + + + align:start position:0% +equilibrium it doesn't go to +equilibrium in the straight path it + + align:start position:0% +equilibrium in the straight path it + + + align:start position:0% +equilibrium in the straight path it +follows the path that is dictated by its + + align:start position:0% +follows the path that is dictated by its + + + align:start position:0% +follows the path that is dictated by its +local metric now true the uh isotropic + + align:start position:0% +local metric now true the uh isotropic + + + align:start position:0% +local metric now true the uh isotropic +material is + + align:start position:0% +material is + + + align:start position:0% +material is +um doesn't favor any direction so these + + align:start position:0% +um doesn't favor any direction so these + + + align:start position:0% +um doesn't favor any direction so these +although it doesn't show exactly as a as + + align:start position:0% +although it doesn't show exactly as a as + + + align:start position:0% +although it doesn't show exactly as a as +a sphere it should be a circle in any + + align:start position:0% +a sphere it should be a circle in any + + + align:start position:0% +a sphere it should be a circle in any +case uh it has to um evolve though in a + + align:start position:0% +case uh it has to um evolve though in a + + + align:start position:0% +case uh it has to um evolve though in a +scenario in + + align:start position:0% +scenario in + + + align:start position:0% +scenario in +which the entropy contour lines may not + + align:start position:0% +which the entropy contour lines may not + + + align:start position:0% +which the entropy contour lines may not +be also circles if they were also + + align:start position:0% +be also circles if they were also + + + align:start position:0% +be also circles if they were also +circles you would go down straight but + + align:start position:0% +circles you would go down straight but + + + align:start position:0% +circles you would go down straight but +if they are not like here they are + + align:start position:0% +if they are not like here they are + + + align:start position:0% +if they are not like here they are +ellipses then uh it it would choose no + + align:start position:0% +ellipses then uh it it would choose no + + + align:start position:0% +ellipses then uh it it would choose no +among uh the ones that are all + + align:start position:0% +among uh the ones that are all + + + align:start position:0% +among uh the ones that are all +equivalent effort you chooses the one + + align:start position:0% +equivalent effort you chooses the one + + + align:start position:0% +equivalent effort you chooses the one +that takes you to the highest entropy + + align:start position:0% +that takes you to the highest entropy + + + align:start position:0% +that takes you to the highest entropy +possible so it's the one that is tangent + + align:start position:0% +possible so it's the one that is tangent + + + align:start position:0% +possible so it's the one that is tangent +here and that is also for this other + + align:start position:0% +here and that is also for this other + + + align:start position:0% +here and that is also for this other +metric and then of course you can + + align:start position:0% +metric and then of course you can + + + align:start position:0% +metric and then of course you can +proceed and go on as you at each + + align:start position:0% +proceed and go on as you at each + + + align:start position:0% +proceed and go on as you at each +point you you sort stop and pause I it + + align:start position:0% +point you you sort stop and pause I it + + + align:start position:0% +point you you sort stop and pause I it +doesn't happen of course but stop and + + align:start position:0% +doesn't happen of course but stop and + + + align:start position:0% +doesn't happen of course but stop and +consider which one is the direction in + + align:start position:0% +consider which one is the direction in + + + align:start position:0% +consider which one is the direction in +which I should go next step and that's + + align:start position:0% +which I should go next step and that's + + + align:start position:0% +which I should go next step and that's +how it how it gets to equilibrium they + + align:start position:0% +how it how it gets to equilibrium they + + + align:start position:0% +how it how it gets to equilibrium they +all get to equilibrium of course but + + align:start position:0% +all get to equilibrium of course but + + + align:start position:0% +all get to equilibrium of course but +along different paths and if I start + + align:start position:0% +along different paths and if I start + + + align:start position:0% +along different paths and if I start +even from this exactly same state but + + align:start position:0% +even from this exactly same state but + + + align:start position:0% +even from this exactly same state but +with a material that is uh uh that has a + + align:start position:0% +with a material that is uh uh that has a + + + align:start position:0% +with a material that is uh uh that has a +that is oriented + + align:start position:0% +that is oriented + + + align:start position:0% +that is oriented +differently and therefore uh for for it + + align:start position:0% +differently and therefore uh for for it + + + align:start position:0% +differently and therefore uh for for it +the the + + align:start position:0% +the the + + + align:start position:0% +the the +the metric uh and these ellipsoids of + + align:start position:0% +the metric uh and these ellipsoids of + + + align:start position:0% +the metric uh and these ellipsoids of +equal dissipation or equal effort is + + align:start position:0% +equal dissipation or equal effort is + + + align:start position:0% +equal dissipation or equal effort is +oriented in a different way and + + align:start position:0% +oriented in a different way and + + + align:start position:0% +oriented in a different way and +therefore it would move there and then + + align:start position:0% +therefore it would move there and then + + + align:start position:0% +therefore it would move there and then +it will search again and it will move + + align:start position:0% +it will search again and it will move + + + align:start position:0% +it will search again and it will move +maybe even overshoots a little bit and + + align:start position:0% +maybe even overshoots a little bit and + + + align:start position:0% +maybe even overshoots a little bit and +then goes back to equili okay so this is + + align:start position:0% +then goes back to equili okay so this is + + + align:start position:0% +then goes back to equili okay so this is +U the role of uh + + align:start position:0% +U the role of uh + + + align:start position:0% +U the role of uh +the + + align:start position:0% +the + + + align:start position:0% +the +metric that uh + + align:start position:0% +metric that uh + + + align:start position:0% +metric that uh +describes this is for a heat transfer + + align:start position:0% +describes this is for a heat transfer + + + align:start position:0% +describes this is for a heat transfer +problem but you can also view it in a + + align:start position:0% +problem but you can also view it in a + + + align:start position:0% +problem but you can also view it in a +more General + + align:start position:0% +more General + + + align:start position:0% +more General +context and that is what I I I like to + + align:start position:0% +context and that is what I I I like to + + + align:start position:0% +context and that is what I I I like to +call it the fourth + + align:start position:0% +call it the fourth + + + align:start position:0% +call it the fourth +flow simply because it is a something + + align:start position:0% +flow simply because it is a something + + + align:start position:0% +flow simply because it is a something +that + + align:start position:0% +that + + + align:start position:0% +that +has emerged let me see do I have oh I + + align:start position:0% +has emerged let me see do I have oh I + + + align:start position:0% +has emerged let me see do I have oh I +think I had a + + align:start position:0% +think I had a + + + align:start position:0% +think I had a +uh keep missing slides today uh there + + align:start position:0% +uh keep missing slides today uh there + + + align:start position:0% +uh keep missing slides today uh there +there will be a slide somewhere + + align:start position:0% +there will be a slide somewhere + + + align:start position:0% +there will be a slide somewhere +sometime with a list + + align:start position:0% +sometime with a list + + + align:start position:0% +sometime with a list +of uh many different theories of non + + align:start position:0% +of uh many different theories of non + + + align:start position:0% +of uh many different theories of non +equilibrium over the last 40 years H in + + align:start position:0% +equilibrium over the last 40 years H in + + + align:start position:0% +equilibrium over the last 40 years H in +which people uh in different languages + + align:start position:0% +which people uh in different languages + + + align:start position:0% +which people uh in different languages +different mathematics different uh + + align:start position:0% +different mathematics different uh + + + align:start position:0% +different mathematics different uh +Frameworks often they don't talk to each + + align:start position:0% +Frameworks often they don't talk to each + + + align:start position:0% +Frameworks often they don't talk to each +other they completely ignore each other + + align:start position:0% +other they completely ignore each other + + + align:start position:0% +other they completely ignore each other +uh they admit that they're doing the + + align:start position:0% +uh they admit that they're doing the + + + align:start position:0% +uh they admit that they're doing the +same thing but they are doing the same + + align:start position:0% +same thing but they are doing the same + + + align:start position:0% +same thing but they are doing the same +thing and that is uh what I was trying + + align:start position:0% +thing and that is uh what I was trying + + + align:start position:0% +thing and that is uh what I was trying +to to point out to to the community here + + align:start position:0% +to to point out to to the community here + + + align:start position:0% +to to point out to to the community here +by calling it The for forth flow and why + + align:start position:0% +by calling it The for forth flow and why + + + align:start position:0% +by calling it The for forth flow and why +why do + + align:start position:0% +why do + + + align:start position:0% +why do +I uh why do I dare uh elevating it to + + align:start position:0% +I uh why do I dare uh elevating it to + + + align:start position:0% +I uh why do I dare uh elevating it to +such a high level in the hierarchy of of + + align:start position:0% +such a high level in the hierarchy of of + + + align:start position:0% +such a high level in the hierarchy of of +of physical laws okay that's + + align:start position:0% +of physical laws okay that's + + + align:start position:0% +of physical laws okay that's +because uh because of the generality you + + align:start position:0% +because uh because of the generality you + + + align:start position:0% +because uh because of the generality you +know remember the great great + + align:start position:0% +know remember the great great + + + align:start position:0% +know remember the great great +conservation principles + + align:start position:0% +conservation principles + + + align:start position:0% +conservation principles +are are great the greatness comes from + + align:start position:0% +are are great the greatness comes from + + + align:start position:0% +are are great the greatness comes from +the + + align:start position:0% +the + + + align:start position:0% +the +generality should should hold for every + + align:start position:0% +generality should should hold for every + + + align:start position:0% +generality should should hold for every +model of physical reality well it turns + + align:start position:0% +model of physical reality well it turns + + + align:start position:0% +model of physical reality well it turns +out that in every model of non-e + + align:start position:0% +out that in every model of non-e + + + align:start position:0% +out that in every model of non-e +equilibrium uh Dynamics U there is + + align:start position:0% +equilibrium uh Dynamics U there is + + + align:start position:0% +equilibrium uh Dynamics U there is +something that maybe you don't call it a + + align:start position:0% +something that maybe you don't call it a + + + align:start position:0% +something that maybe you don't call it a +metric uh but it is it has the + + align:start position:0% +metric uh but it is it has the + + + align:start position:0% +metric uh but it is it has the +properties of a + + align:start position:0% +properties of a + + + align:start position:0% +properties of a +metric and uh uh + + align:start position:0% +metric and uh uh + + + align:start position:0% +metric and uh uh +and therefore it is it appears to be an + + align:start position:0% +and therefore it is it appears to be an + + + align:start position:0% +and therefore it is it appears to be an +essential feature of any + + align:start position:0% +essential feature of any + + + align:start position:0% +essential feature of any +model and + + align:start position:0% +model and + + + align:start position:0% +model and +also uh I like also the fact that it is + + align:start position:0% +also uh I like also the fact that it is + + + align:start position:0% +also uh I like also the fact that it is +a is a statement of existence like like + + align:start position:0% +a is a statement of existence like like + + + align:start position:0% +a is a statement of existence like like +the first law is a statement of + + align:start position:0% +the first law is a statement of + + + align:start position:0% +the first law is a statement of +existence of energy the second law is a + + align:start position:0% +existence of energy the second law is a + + + align:start position:0% +existence of energy the second law is a +statement of existence of entropy this + + align:start position:0% +statement of existence of entropy this + + + align:start position:0% +statement of existence of entropy this +is a statement of existence of a metric + + align:start position:0% +is a statement of existence of a metric + + + align:start position:0% +is a statement of existence of a metric +in non-e equilibrium States another it's + + align:start position:0% +in non-e equilibrium States another it's + + + align:start position:0% +in non-e equilibrium States another it's +a + + align:start position:0% +a + + + align:start position:0% +a +property like this thermal + + align:start position:0% +property like this thermal + + + align:start position:0% +property like this thermal +conductivity uh that has to be + + align:start position:0% +conductivity uh that has to be + + + align:start position:0% +conductivity uh that has to be +defined at every uh state every + + align:start position:0% +defined at every uh state every + + + align:start position:0% +defined at every uh state every +non-equilibrium state of your system for + + align:start position:0% +non-equilibrium state of your system for + + + align:start position:0% +non-equilibrium state of your system for +it to decide in which direction to move + + align:start position:0% +it to decide in which direction to move + + + align:start position:0% +it to decide in which direction to move +when you let it alone and want to and + + align:start position:0% +when you let it alone and want to and + + + align:start position:0% +when you let it alone and want to and +let it go towards + + align:start position:0% + + + + align:start position:0% + +equilibrium yeah uh + + align:start position:0% + + + + align:start position:0% + +here this is to show that this same + + align:start position:0% +here this is to show that this same + + + align:start position:0% +here this is to show that this same +construction can be also uh + + align:start position:0% +construction can be also uh + + + align:start position:0% +construction can be also uh +done more formally and mathematically + + align:start position:0% +done more formally and mathematically + + + align:start position:0% +done more formally and mathematically +again with the method of lrange + + align:start position:0% + + + + align:start position:0% + +multipliers you you see you maximize the + + align:start position:0% +multipliers you you see you maximize the + + + align:start position:0% +multipliers you you see you maximize the +scalar product between the X and the + + align:start position:0% +scalar product between the X and the + + + align:start position:0% +scalar product between the X and the +J subject + + align:start position:0% +J subject + + + align:start position:0% +J subject +so that's the the lrange multiplier to + + align:start position:0% +so that's the the lrange multiplier to + + + align:start position:0% +so that's the the lrange multiplier to +the constraint given by an equal effort + + align:start position:0% +the constraint given by an equal effort + + + align:start position:0% +the constraint given by an equal effort +ellipsoid so if I have so it expresses + + align:start position:0% +ellipsoid so if I have so it expresses + + + align:start position:0% +ellipsoid so if I have so it expresses +exactly + + align:start position:0% +exactly + + + align:start position:0% +exactly +mathematically uh the worthy description + + align:start position:0% +mathematically uh the worthy description + + + align:start position:0% +mathematically uh the worthy description +that I + + align:start position:0% +that I + + + align:start position:0% +that I +gave there is a matric that descri + + align:start position:0% +gave there is a matric that descri + + + align:start position:0% +gave there is a matric that descri +describes this ellipsoid tells you for a + + align:start position:0% +describes this ellipsoid tells you for a + + + align:start position:0% +describes this ellipsoid tells you for a +given distance I want to move which one + + align:start position:0% +given distance I want to move which one + + + align:start position:0% +given distance I want to move which one +is the best Direction and best is in + + align:start position:0% +is the best Direction and best is in + + + align:start position:0% +is the best Direction and best is in +terms of maximizing the rate of entropy + + align:start position:0% +terms of maximizing the rate of entropy + + + align:start position:0% +terms of maximizing the rate of entropy +production from this + + align:start position:0% +production from this + + + align:start position:0% +production from this +one using the method the gr multiplier + + align:start position:0% +one using the method the gr multiplier + + + align:start position:0% +one using the method the gr multiplier +setting the derivative equal to + + align:start position:0% +setting the derivative equal to + + + align:start position:0% +setting the derivative equal to +zero U substituting back into constraint + + align:start position:0% +zero U substituting back into constraint + + + align:start position:0% +zero U substituting back into constraint +and so on you get a relation between + + align:start position:0% +and so on you get a relation between + + + align:start position:0% +and so on you get a relation between +forces and + + align:start position:0% + + + + align:start position:0% + +fluxes we can you can always write it in + + align:start position:0% +fluxes we can you can always write it in + + + align:start position:0% +fluxes we can you can always write it in +in this way which looks like a linear + + align:start position:0% +in this way which looks like a linear + + + align:start position:0% +in this way which looks like a linear +relation but it's not because this R + + align:start position:0% +relation but it's not because this R + + + align:start position:0% +relation but it's not because this R +which is a + + align:start position:0% +which is a + + + align:start position:0% +which is a +resistance + + align:start position:0% +resistance + + + align:start position:0% +resistance +um it's + + align:start position:0% +um it's + + + align:start position:0% +um it's +not constant in general but it's just a + + align:start position:0% +not constant in general but it's just a + + + align:start position:0% +not constant in general but it's just a +function of the fluis which is given by + + align:start position:0% +function of the fluis which is given by + + + align:start position:0% +function of the fluis which is given by +the solution of this problem + + align:start position:0% +the solution of this problem + + + align:start position:0% +the solution of this problem +here so this is a nonlinear + + align:start position:0% + + + + align:start position:0% + +relation and of course you can do the + + align:start position:0% +relation and of course you can do the + + + align:start position:0% +relation and of course you can do the +exact uh same in the uh Force picture + + align:start position:0% +exact uh same in the uh Force picture + + + align:start position:0% +exact uh same in the uh Force picture +pause the the + + align:start position:0% +pause the the + + + align:start position:0% +pause the the +X and there is a a metric also from that + + align:start position:0% +X and there is a a metric also from that + + + align:start position:0% +X and there is a a metric also from that +point of view and the two are related to + + align:start position:0% +point of view and the two are related to + + + align:start position:0% +point of view and the two are related to +one another they the inverse + + align:start position:0% +one another they the inverse + + + align:start position:0% +one another they the inverse +somehow so you also + + align:start position:0% +somehow so you also + + + align:start position:0% +somehow so you also +maximize these projection subject to + + align:start position:0% +maximize these projection subject to + + + align:start position:0% +maximize these projection subject to +this other blue ellipsoid which also + + align:start position:0% +this other blue ellipsoid which also + + + align:start position:0% +this other blue ellipsoid which also +represents the + + align:start position:0% +represents the + + + align:start position:0% +represents the +effort at this time it's the effort for + + align:start position:0% +effort at this time it's the effort for + + + align:start position:0% +effort at this time it's the effort for +the system to set up + + align:start position:0% +the system to set up + + + align:start position:0% +the system to set up +uh a a gradient in temperature so as to + + align:start position:0% +uh a a gradient in temperature so as to + + + align:start position:0% +uh a a gradient in temperature so as to +contrast the flux + + align:start position:0% +contrast the flux + + + align:start position:0% +contrast the flux +of heat that you have imposed in it and + + align:start position:0% +of heat that you have imposed in it and + + + align:start position:0% +of heat that you have imposed in it and +of course when you get close to + + align:start position:0% +of course when you get close to + + + align:start position:0% +of course when you get close to +equilibrium when you get close to + + align:start position:0% +equilibrium when you get close to + + + align:start position:0% +equilibrium when you get close to +equilibrium then you go to the linear uh + + align:start position:0% +equilibrium then you go to the linear uh + + + align:start position:0% +equilibrium then you go to the linear uh +regime you get on Saga relations and of + + align:start position:0% +regime you get on Saga relations and of + + + align:start position:0% +regime you get on Saga relations and of +course these two are um the metric + + align:start position:0% +course these two are um the metric + + + align:start position:0% +course these two are um the metric +becomes + + align:start position:0% +becomes + + + align:start position:0% +becomes +the uh onager + + align:start position:0% +the uh onager + + + align:start position:0% +the uh onager +generalized + + align:start position:0% +generalized + + + align:start position:0% +generalized +conductivity for the L's or resistivity + + align:start position:0% +conductivity for the L's or resistivity + + + align:start position:0% +conductivity for the L's or resistivity +for the r for the + + align:start position:0% +for the r for the + + + align:start position:0% +for the r for the +RS one is the inverse of the + + align:start position:0% +RS one is the inverse of the + + + align:start position:0% +RS one is the inverse of the +other ah there is okay here is the the + + align:start position:0% +other ah there is okay here is the the + + + align:start position:0% +other ah there is okay here is the the +list + + align:start position:0% +list + + + align:start position:0% +list +of uh + + align:start position:0% +of uh + + + align:start position:0% +of uh +theories uh that + + align:start position:0% +theories uh that + + + align:start position:0% +theories uh that +uh converge + + align:start position:0% +uh converge + + + align:start position:0% +uh converge +to the four + + align:start position:0% +to the four + + + align:start position:0% +to the four +FL + + align:start position:0% + + + + align:start position:0% + +uh of course we contributed to + + align:start position:0% +uh of course we contributed to + + + align:start position:0% +uh of course we contributed to +it but u in the same period already you + + align:start position:0% +it but u in the same period already you + + + align:start position:0% +it but u in the same period already you +have Gela morison cavman who did the + + align:start position:0% +have Gela morison cavman who did the + + + align:start position:0% +have Gela morison cavman who did the +uh completely from completely different + + align:start position:0% +uh completely from completely different + + + align:start position:0% +uh completely from completely different +point of view so in fact I I met + + align:start position:0% +point of view so in fact I I met + + + align:start position:0% +point of view so in fact I I met +Miroslav Gela + + align:start position:0% +Miroslav Gela + + + align:start position:0% +Miroslav Gela +only maybe 30 years + + align:start position:0% + + + + align:start position:0% + +later and so these all + + align:start position:0% +later and so these all + + + align:start position:0% +later and so these all +are uh independent uh + + align:start position:0% +are uh independent uh + + + align:start position:0% +are uh independent uh +contributions uh generic has become very + + align:start position:0% +contributions uh generic has become very + + + align:start position:0% +contributions uh generic has become very +popular because some Compu some + + align:start position:0% +popular because some Compu some + + + align:start position:0% +popular because some Compu some +communities are more effective than + + align:start position:0% +communities are more effective than + + + align:start position:0% +communities are more effective than +others to propagating and + + align:start position:0% +others to propagating and + + + align:start position:0% +others to propagating and +Publishing + + align:start position:0% +Publishing + + + align:start position:0% +Publishing +U I will say a few words also about the + + align:start position:0% +U I will say a few words also about the + + + align:start position:0% +U I will say a few words also about the +Constructor law Bean + + align:start position:0% +Constructor law Bean + + + align:start position:0% +Constructor law Bean +although he would be unhappy if I + + align:start position:0% +although he would be unhappy if I + + + align:start position:0% +although he would be unhappy if I +say that he belongs here because I think + + align:start position:0% +say that he belongs here because I think + + + align:start position:0% +say that he belongs here because I think +he believes that his uh point of view is + + align:start position:0% +he believes that his uh point of view is + + + align:start position:0% +he believes that his uh point of view is +more General and I think I agree with + + align:start position:0% +more General and I think I agree with + + + align:start position:0% +more General and I think I agree with +him uh I'll explain a moment I mean + + align:start position:0% +him uh I'll explain a moment I mean + + + align:start position:0% +him uh I'll explain a moment I mean +later when why + + align:start position:0% +later when why + + + align:start position:0% +later when why +uh these other also some + + align:start position:0% +uh these other also some + + + align:start position:0% +uh these other also some +mathematicians from the point of view of + + align:start position:0% +mathematicians from the point of view of + + + align:start position:0% +mathematicians from the point of view of +certain classes of partial differential + + align:start position:0% +certain classes of partial differential + + + align:start position:0% +certain classes of partial differential +equations have + + align:start position:0% +equations have + + + align:start position:0% +equations have +developed uh now it's already 25 years + + align:start position:0% +developed uh now it's already 25 years + + + align:start position:0% +developed uh now it's already 25 years +uh ago um this theory of gradient + + align:start position:0% + + + + align:start position:0% + +flows uh + + align:start position:0% +flows uh + + + align:start position:0% +flows uh +they in order to do that they have + + align:start position:0% +they in order to do that they have + + + align:start position:0% +they in order to do that they have +introduced a part particular metric + + align:start position:0% +introduced a part particular metric + + + align:start position:0% +introduced a part particular metric +pretty complicated mathematical but it + + align:start position:0% +pretty complicated mathematical but it + + + align:start position:0% +pretty complicated mathematical but it +is a metric that regularizes those + + align:start position:0% +is a metric that regularizes those + + + align:start position:0% +is a metric that regularizes those +differential equations and make make + + align:start position:0% +differential equations and make make + + + align:start position:0% +differential equations and make make +them fit into this same scheme so that's + + align:start position:0% +them fit into this same scheme so that's + + + align:start position:0% +them fit into this same scheme so that's +very + + align:start position:0% + + + + align:start position:0% + +interesting uh okay then there is also + + align:start position:0% +interesting uh okay then there is also + + + align:start position:0% +interesting uh okay then there is also +more modern stuff like large deviation + + align:start position:0% +more modern stuff like large deviation + + + align:start position:0% +more modern stuff like large deviation +Theory + + align:start position:0% +Theory + + + align:start position:0% +Theory +Theory and not only that but also there + + align:start position:0% +Theory and not only that but also there + + + align:start position:0% +Theory and not only that but also there +is some people + + align:start position:0% +is some people + + + align:start position:0% +is some people +um that are + + align:start position:0% +um that are + + + align:start position:0% +um that are +applying + + align:start position:0% +applying + + + align:start position:0% +applying +this notion to solve in original way + + align:start position:0% +this notion to solve in original way + + + align:start position:0% +this notion to solve in original way +uh complicated + + align:start position:0% +uh complicated + + + align:start position:0% +uh complicated +problems in a much simpler way than um + + align:start position:0% +problems in a much simpler way than um + + + align:start position:0% +problems in a much simpler way than um +the traditional + + align:start position:0% +the traditional + + + align:start position:0% +the traditional +descriptions + + align:start position:0% +descriptions + + + align:start position:0% +descriptions +because this view uh geometrical + + align:start position:0% +because this view uh geometrical + + + align:start position:0% +because this view uh geometrical +View ER you know the power of + + align:start position:0% +View ER you know the power of + + + align:start position:0% +View ER you know the power of +mathematics and of geometry is if you if + + align:start position:0% +mathematics and of geometry is if you if + + + align:start position:0% +mathematics and of geometry is if you if +you can uh view something from a + + align:start position:0% +you can uh view something from a + + + align:start position:0% +you can uh view something from a +geometrical point of view you have you + + align:start position:0% +geometrical point of view you have you + + + align:start position:0% +geometrical point of view you have you +you've captured the essence and youve + + align:start position:0% +you've captured the essence and youve + + + align:start position:0% +you've captured the essence and youve +also often simplified uh the uh even the + + align:start position:0% +also often simplified uh the uh even the + + + align:start position:0% +also often simplified uh the uh even the +numeric uh numerical uh Solutions of + + align:start position:0% +numeric uh numerical uh Solutions of + + + align:start position:0% +numeric uh numerical uh Solutions of +your + + align:start position:0% +your + + + align:start position:0% +your +problem I'll give you some references + + align:start position:0% +problem I'll give you some references + + + align:start position:0% +problem I'll give you some references +here just for for fun if you're + + align:start position:0% +here just for for fun if you're + + + align:start position:0% +here just for for fun if you're +interested + + align:start position:0% +interested + + + align:start position:0% +interested +in now regarding Bean Constructor + + align:start position:0% +in now regarding Bean Constructor + + + align:start position:0% +in now regarding Bean Constructor +law + + align:start position:0% +law + + + align:start position:0% +law +uh if you haven't uh come across uh + + align:start position:0% +uh if you haven't uh come across uh + + + align:start position:0% +uh if you haven't uh come across uh +Adrian Bean was a graduate of this + + align:start position:0% +Adrian Bean was a graduate of this + + + align:start position:0% +Adrian Bean was a graduate of this +department uh two or three years before + + align:start position:0% +department uh two or three years before + + + align:start position:0% +department uh two or three years before +me I guess he did PhD in mechanical + + align:start position:0% +me I guess he did PhD in mechanical + + + align:start position:0% +me I guess he did PhD in mechanical +engineering + + align:start position:0% +engineering + + + align:start position:0% +engineering +here and U is + + align:start position:0% + + + + align:start position:0% + +um you see his Focus + + align:start position:0% +um you see his Focus + + + align:start position:0% +um you see his Focus +is + + align:start position:0% +is + + + align:start position:0% +is +uh uh + + align:start position:0% +uh uh + + + align:start position:0% +uh uh +on design and evolution in nature the + + align:start position:0% +on design and evolution in nature the + + + align:start position:0% +on design and evolution in nature the +role of design now + + align:start position:0% +role of design now + + + align:start position:0% +role of design now +design uh for + + align:start position:0% +design uh for + + + align:start position:0% +design uh for +example uh the structure of the tree + + align:start position:0% +example uh the structure of the tree + + + align:start position:0% +example uh the structure of the tree +structure of uh + + align:start position:0% +structure of uh + + + align:start position:0% +structure of uh +lungs or even the structure of trees + + align:start position:0% +lungs or even the structure of trees + + + align:start position:0% +lungs or even the structure of trees +which are sorts of U optimiz the result + + align:start position:0% +which are sorts of U optimiz the result + + + align:start position:0% +which are sorts of U optimiz the result +of + + align:start position:0% +of + + + align:start position:0% +of +optimization + + align:start position:0% +optimization + + + align:start position:0% +optimization +of of uh of two con contrasting + + align:start position:0% +of of uh of two con contrasting + + + align:start position:0% +of of uh of two con contrasting +Tendencies and the system is trying to + + align:start position:0% +Tendencies and the system is trying to + + + align:start position:0% +Tendencies and the system is trying to +find the best direction in which to uh + + align:start position:0% +find the best direction in which to uh + + + align:start position:0% +find the best direction in which to uh +to to build and to uh but uh in which to + + align:start position:0% +to to build and to uh but uh in which to + + + align:start position:0% +to to build and to uh but uh in which to +make things + + align:start position:0% +make things + + + align:start position:0% +make things +flow and things flow to me is also uh + + align:start position:0% +flow and things flow to me is also uh + + + align:start position:0% +flow and things flow to me is also uh +translated + + align:start position:0% +translated + + + align:start position:0% +translated +into uh + + align:start position:0% +into uh + + + align:start position:0% +into uh +choose uh the way in which you can + + align:start position:0% +choose uh the way in which you can + + + align:start position:0% +choose uh the way in which you can +produce as much as possible your entropy + + align:start position:0% +produce as much as possible your entropy + + + align:start position:0% +produce as much as possible your entropy +uh at the at the fastest rate compatible + + align:start position:0% +uh at the at the fastest rate compatible + + + align:start position:0% +uh at the at the fastest rate compatible +with the constraints and so for this + + align:start position:0% +with the constraints and so for this + + + align:start position:0% +with the constraints and so for this +part I think that we're saying the same + + align:start position:0% +part I think that we're saying the same + + + align:start position:0% +part I think that we're saying the same +thing so he also fitting into the forlow + + align:start position:0% +thing so he also fitting into the forlow + + + align:start position:0% +thing so he also fitting into the forlow +but what the uh what's beyond that and I + + align:start position:0% +but what the uh what's beyond that and I + + + align:start position:0% +but what the uh what's beyond that and I +think is right is that uh he's saying + + align:start position:0% +think is right is that uh he's saying + + + align:start position:0% +think is right is that uh he's saying +that u in nature + + align:start position:0% +that u in nature + + + align:start position:0% +that u in nature +things + + align:start position:0% +things + + + align:start position:0% +things +evolve uh and uh also the design of uh + + align:start position:0% +evolve uh and uh also the design of uh + + + align:start position:0% +evolve uh and uh also the design of uh +natural things including the design for + + align:start position:0% +natural things including the design for + + + align:start position:0% +natural things including the design for +example of the wings of + + align:start position:0% +example of the wings of + + + align:start position:0% +example of the wings of +animals and how they uh how um they + + align:start position:0% +animals and how they uh how um they + + + align:start position:0% +animals and how they uh how um they +are related + + align:start position:0% +are related + + + align:start position:0% +are related +to to Evolution so how + + align:start position:0% +to to Evolution so how + + + align:start position:0% +to to Evolution so how +um the from the I forget the names of uh + + align:start position:0% +um the from the I forget the names of uh + + + align:start position:0% +um the from the I forget the names of uh +the the ancient uh + + align:start position:0% +the the ancient uh + + + align:start position:0% +the the ancient uh +Birds uh when you had the + + align:start position:0% +Birds uh when you had the + + + align:start position:0% +Birds uh when you had the +T-Rex and uh and and how that evolved + + align:start position:0% +T-Rex and uh and and how that evolved + + + align:start position:0% +T-Rex and uh and and how that evolved +and that evolution is an evolution in + + align:start position:0% +and that evolution is an evolution in + + + align:start position:0% +and that evolution is an evolution in +the design of how uh structures are + + align:start position:0% +the design of how uh structures are + + + align:start position:0% +the design of how uh structures are +built in nature they always have the + + align:start position:0% +built in nature they always have the + + + align:start position:0% +built in nature they always have the +purpose of uh favoring flows that means + + align:start position:0% +purpose of uh favoring flows that means + + + align:start position:0% +purpose of uh favoring flows that means +uh favoring entropy generation and + + align:start position:0% +uh favoring entropy generation and + + + align:start position:0% +uh favoring entropy generation and +making it as as as effective as possible + + align:start position:0% +making it as as as effective as possible + + + align:start position:0% +making it as as as effective as possible +because as you know uh life is + + align:start position:0% +because as you know uh life is + + + align:start position:0% +because as you know uh life is +impossible without entropy generation + + align:start position:0% +impossible without entropy generation + + + align:start position:0% +impossible without entropy generation +and we need that uh that is the the + + align:start position:0% +and we need that uh that is the the + + + align:start position:0% +and we need that uh that is the the +driving force while you produce entropy + + align:start position:0% +driving force while you produce entropy + + + align:start position:0% +driving force while you produce entropy +you also produce useful + + align:start position:0% +you also produce useful + + + align:start position:0% +you also produce useful +things so entropy production is not + + align:start position:0% +things so entropy production is not + + + align:start position:0% +things so entropy production is not +completely + + align:start position:0% +completely + + + align:start position:0% +completely +negative it's not just a waste of exergy + + align:start position:0% +negative it's not just a waste of exergy + + + align:start position:0% +negative it's not just a waste of exergy +it's you need it because if you didn't + + align:start position:0% +it's you need it because if you didn't + + + align:start position:0% +it's you need it because if you didn't +have it you nothing useful would + + align:start position:0% +have it you nothing useful would + + + align:start position:0% +have it you nothing useful would +happen uh but what Bean says is that + + align:start position:0% +happen uh but what Bean says is that + + + align:start position:0% +happen uh but what Bean says is that +also uh structures + + align:start position:0% +also uh structures + + + align:start position:0% +also uh structures +evolve and + + align:start position:0% +evolve and + + + align:start position:0% +evolve and +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh the choice there is some Randomness + + align:start position:0% +uh the choice there is some Randomness + + + align:start position:0% +uh the choice there is some Randomness +in how uh a particular + + align:start position:0% +in how uh a particular + + + align:start position:0% +in how uh a particular +structure uh is given + + align:start position:0% +structure uh is given + + + align:start position:0% +structure uh is given +birth it was nonexistent and then all of + + align:start position:0% +birth it was nonexistent and then all of + + + align:start position:0% +birth it was nonexistent and then all of +a sudden perhaps because of of of of a + + align:start position:0% +a sudden perhaps because of of of of a + + + align:start position:0% +a sudden perhaps because of of of of a +fluctuation or + + align:start position:0% +fluctuation or + + + align:start position:0% +fluctuation or +perturbation uh uh it becomes + + align:start position:0% +perturbation uh uh it becomes + + + align:start position:0% +perturbation uh uh it becomes +possible uh now regarding structure + + align:start position:0% + + + + align:start position:0% + +though for example there is this problem + + align:start position:0% +though for example there is this problem + + + align:start position:0% +though for example there is this problem +of the it's + + align:start position:0% +of the it's + + + align:start position:0% +of the it's +called Berard + + align:start position:0% +called Berard + + + align:start position:0% +called Berard +uh conduction it's it's a problem in + + align:start position:0% +uh conduction it's it's a problem in + + + align:start position:0% +uh conduction it's it's a problem in +which you um you + + align:start position:0% +which you um you + + + align:start position:0% +which you um you +hit you have a + + align:start position:0% +hit you have a + + + align:start position:0% +hit you have a +fluid and like you have a pan with some + + align:start position:0% +fluid and like you have a pan with some + + + align:start position:0% +fluid and like you have a pan with some +oil and you have Heen from below and + + align:start position:0% +oil and you have Heen from below and + + + align:start position:0% +oil and you have Heen from below and +cooled from + + align:start position:0% +cooled from + + + align:start position:0% +cooled from +above + + align:start position:0% + + + + align:start position:0% + +uh now + + align:start position:0% +uh now + + + align:start position:0% +uh now +typically if + + align:start position:0% +typically if + + + align:start position:0% +typically if +you if your heating is is is is not + + align:start position:0% +you if your heating is is is is not + + + align:start position:0% +you if your heating is is is is not +strong enough you would have just a + + align:start position:0% +strong enough you would have just a + + + align:start position:0% +strong enough you would have just a +conduction but + + align:start position:0% +conduction but + + + align:start position:0% +conduction but +then there is also the possibility + + align:start position:0% +then there is also the possibility + + + align:start position:0% +then there is also the possibility +because of the instability uh due to the + + align:start position:0% +because of the instability uh due to the + + + align:start position:0% +because of the instability uh due to the +fact that uh the stratification is you + + align:start position:0% +fact that uh the stratification is you + + + align:start position:0% +fact that uh the stratification is you +get hot stuff below and cold above and + + align:start position:0% +get hot stuff below and cold above and + + + align:start position:0% +get hot stuff below and cold above and +and they like to switch so this uh + + align:start position:0% +and they like to switch so this uh + + + align:start position:0% +and they like to switch so this uh +movement which requires uh moving a flow + + align:start position:0% +movement which requires uh moving a flow + + + align:start position:0% +movement which requires uh moving a flow +therefore it involves friction so if + + align:start position:0% +therefore it involves friction so if + + + align:start position:0% +therefore it involves friction so if +you + + align:start position:0% +you + + + align:start position:0% +you +if if if you have + + align:start position:0% +if if if you have + + + align:start position:0% +if if if you have +enough uh motivation for doing it + + align:start position:0% +enough uh motivation for doing it + + + align:start position:0% +enough uh motivation for doing it +eventually that flow will start and + + align:start position:0% +eventually that flow will start and + + + align:start position:0% +eventually that flow will start and +therefore you'll get U convective it you + + align:start position:0% +therefore you'll get U convective it you + + + align:start position:0% +therefore you'll get U convective it you +will switch from conductive heat + + align:start position:0% +will switch from conductive heat + + + align:start position:0% +will switch from conductive heat +transfer to convective roles of uh heat + + align:start position:0% +transfer to convective roles of uh heat + + + align:start position:0% +transfer to convective roles of uh heat +conduction which will + + align:start position:0% +conduction which will + + + align:start position:0% +conduction which will +enhance the heat conduction it's more + + align:start position:0% +enhance the heat conduction it's more + + + align:start position:0% +enhance the heat conduction it's more +effective so you here it is a a + + align:start position:0% +effective so you here it is a a + + + align:start position:0% +effective so you here it is a a +situation in which you you build + + align:start position:0% +situation in which you you build + + + align:start position:0% +situation in which you you build +structure gets built in order to uh make + + align:start position:0% +structure gets built in order to uh make + + + align:start position:0% +structure gets built in order to uh make +uh the entropy production more + + align:start position:0% + + + + align:start position:0% + +effective and in this + + align:start position:0% + + + + align:start position:0% + +paper uh you view it from the point of + + align:start position:0% +paper uh you view it from the point of + + + align:start position:0% +paper uh you view it from the point of +view of U um of of Maximum entropy + + align:start position:0% +view of U um of of Maximum entropy + + + align:start position:0% +view of U um of of Maximum entropy +production + + align:start position:0% +production + + + align:start position:0% +production +so you see for example here you have a + + align:start position:0% +so you see for example here you have a + + + align:start position:0% +so you see for example here you have a +situation in which uh like you + + align:start position:0% + + + + align:start position:0% + +are for example you have the the rolls + + align:start position:0% +are for example you have the the rolls + + + align:start position:0% +are for example you have the the rolls +so you have the high non-e equilibrium + + align:start position:0% +so you have the high non-e equilibrium + + + align:start position:0% +so you have the high non-e equilibrium +situation high flux in which you have + + align:start position:0% +situation high flux in which you have + + + align:start position:0% +situation high flux in which you have +the Riley Berard rols and those that + + align:start position:0% +the Riley Berard rols and those that + + + align:start position:0% +the Riley Berard rols and those that +structure is the one that maximizes the + + align:start position:0% +structure is the one that maximizes the + + + align:start position:0% +structure is the one that maximizes the +the entropy so among all the + + align:start position:0% +the entropy so among all the + + + align:start position:0% +the entropy so among all the +possibilities the system chooses that + + align:start position:0% +possibilities the system chooses that + + + align:start position:0% +possibilities the system chooses that +one maximizes the entropy product + + align:start position:0% +one maximizes the entropy product + + + align:start position:0% +one maximizes the entropy product +ction but as you turn uh the heat off + + align:start position:0% +ction but as you turn uh the heat off + + + align:start position:0% +ction but as you turn uh the heat off +and here you're + + align:start position:0% +and here you're + + + align:start position:0% +and here you're +going so as time goes on you reduce that + + align:start position:0% +going so as time goes on you reduce that + + + align:start position:0% +going so as time goes on you reduce that +the heat from Bel + + align:start position:0% +the heat from Bel + + + align:start position:0% +the heat from Bel +below + + align:start position:0% +below + + + align:start position:0% +below +uh + + align:start position:0% +uh + + + align:start position:0% +uh +that tendency goes down + + align:start position:0% +that tendency goes down + + + align:start position:0% +that tendency goes down +until uh it becomes + + align:start position:0% +until uh it becomes + + + align:start position:0% +until uh it becomes +comparable or or even less efficient + + align:start position:0% +comparable or or even less efficient + + + align:start position:0% +comparable or or even less efficient +than the the direct simple conduction + + align:start position:0% +than the the direct simple conduction + + + align:start position:0% +than the the direct simple conduction +and then what happens the system + + align:start position:0% +and then what happens the system + + + align:start position:0% +and then what happens the system +switches and the convection gets uh + + align:start position:0% +switches and the convection gets uh + + + align:start position:0% +switches and the convection gets uh +stopped and the the system switches into + + align:start position:0% +stopped and the the system switches into + + + align:start position:0% +stopped and the the system switches into +just to another to the to another + + align:start position:0% +just to another to the to another + + + align:start position:0% +just to another to the to another +maximum so this is also a + + align:start position:0% +maximum so this is also a + + + align:start position:0% +maximum so this is also a +jump in configuration so it's a + + align:start position:0% +jump in configuration so it's a + + + align:start position:0% +jump in configuration so it's a +construction + + align:start position:0% +construction + + + align:start position:0% +construction +of it's a design so so to speak a design + + align:start position:0% +of it's a design so so to speak a design + + + align:start position:0% +of it's a design so so to speak a design +choice that your system has made in + + align:start position:0% +choice that your system has made in + + + align:start position:0% +choice that your system has made in +order to move from one maximum to + + align:start position:0% +order to move from one maximum to + + + align:start position:0% +order to move from one maximum to +another + + align:start position:0% + + + + align:start position:0% + +maximum and this of course + + align:start position:0% +maximum and this of course + + + align:start position:0% +maximum and this of course +corresponds to a critical value of the + + align:start position:0% +corresponds to a critical value of the + + + align:start position:0% +corresponds to a critical value of the +rile number that is uh the onset number + + align:start position:0% +rile number that is uh the onset number + + + align:start position:0% +rile number that is uh the onset number +for uh this Riley + + align:start position:0% +for uh this Riley + + + align:start position:0% +for uh this Riley +benar + + align:start position:0% +benar + + + align:start position:0% +benar +instability which is very very famous + + align:start position:0% +instability which is very very famous + + + align:start position:0% +instability which is very very famous +problem in fluid mechanics and heat + + align:start position:0% +problem in fluid mechanics and heat + + + align:start position:0% +problem in fluid mechanics and heat +trans + + align:start position:0% + + + + align:start position:0% + +and by the way Adrian + + align:start position:0% +and by the way Adrian + + + align:start position:0% +and by the way Adrian +ban has + + align:start position:0% +ban has + + + align:start position:0% +ban has +written hundreds of papers but also many + + align:start position:0% +written hundreds of papers but also many + + + align:start position:0% +written hundreds of papers but also many +books including one at the beginning + + align:start position:0% +books including one at the beginning + + + align:start position:0% +books including one at the beginning +which is entropy production in heat + + align:start position:0% + + + + align:start position:0% + +transfer which is uh very good + + align:start position:0% + + + + align:start position:0% + +let me uh conclude today with this um um + + align:start position:0% +let me uh conclude today with this um um + + + align:start position:0% +let me uh conclude today with this um um +last + + align:start position:0% +last + + + align:start position:0% +last +idea just to add to the confusion if you + + align:start position:0% +idea just to add to the confusion if you + + + align:start position:0% +idea just to add to the confusion if you +[Music] + + align:start position:0% + + + + align:start position:0% + +want + + align:start position:0% +want + + + align:start position:0% +want +um the idea that there is a there is a + + align:start position:0% +um the idea that there is a there is a + + + align:start position:0% +um the idea that there is a there is a +theorem famous theorem proved by + + align:start position:0% +theorem famous theorem proved by + + + align:start position:0% +theorem famous theorem proved by +glandorf and + + align:start position:0% + + + + align:start position:0% + +PRI called minimum entropy production PR + + align:start position:0% + + + + align:start position:0% + +so many people uh we are facing simply + + align:start position:0% +so many people uh we are facing simply + + + align:start position:0% +so many people uh we are facing simply +the the words in a superficial way they + + align:start position:0% +the the words in a superficial way they + + + align:start position:0% +the the words in a superficial way they +say well is it minimum or is it + + align:start position:0% +say well is it minimum or is it + + + align:start position:0% +say well is it minimum or is it +maximum + + align:start position:0% +maximum + + + align:start position:0% +maximum +okay all right so the difference in the + + align:start position:0% +okay all right so the difference in the + + + align:start position:0% +okay all right so the difference in the +key is local and + + align:start position:0% + + + + align:start position:0% + +Global so the the system + + align:start position:0% +Global so the the system + + + align:start position:0% +Global so the the system +locally chooses + + align:start position:0% +locally chooses + + + align:start position:0% +locally chooses +uh so the material locally chooses to + + align:start position:0% +uh so the material locally chooses to + + + align:start position:0% +uh so the material locally chooses to +react in a in a direction that goes + + align:start position:0% +react in a in a direction that goes + + + align:start position:0% +react in a in a direction that goes +towards the steepest entropy asent so + + align:start position:0% +towards the steepest entropy asent so + + + align:start position:0% +towards the steepest entropy asent so +it's the local maximal entropy + + align:start position:0% + + + + align:start position:0% + +production this theorem instead looks at + + align:start position:0% +production this theorem instead looks at + + + align:start position:0% +production this theorem instead looks at +a global situation like an integral over + + align:start position:0% +a global situation like an integral over + + + align:start position:0% +a global situation like an integral over +a volume of many pieces of material and + + align:start position:0% +a volume of many pieces of material and + + + align:start position:0% +a volume of many pieces of material and +it takes it does the integral not of + + align:start position:0% +it takes it does the integral not of + + + align:start position:0% +it takes it does the integral not of +Sigma that which is the rate of but of + + align:start position:0% +Sigma that which is the rate of but of + + + align:start position:0% +Sigma that which is the rate of but of +the rate of change of + + align:start position:0% + + + + align:start position:0% + +Sigma and it + + align:start position:0% +Sigma and it + + + align:start position:0% +Sigma and it +proves + + align:start position:0% +proves + + + align:start position:0% +proves +that the rate of change of + + align:start position:0% +that the rate of change of + + + align:start position:0% +that the rate of change of +Sigma under a broad set of boundary + + align:start position:0% +Sigma under a broad set of boundary + + + align:start position:0% +Sigma under a broad set of boundary +conditions and assumptions that are + + align:start position:0% +conditions and assumptions that are + + + align:start position:0% +conditions and assumptions that are +listed + + align:start position:0% +listed + + + align:start position:0% +listed +there very larger set of + + align:start position:0% +there very larger set of + + + align:start position:0% +there very larger set of +conditions + + align:start position:0% +conditions + + + align:start position:0% +conditions +is negative + + align:start position:0% +is negative + + + align:start position:0% +is negative +so that means that Sigma if you if you + + align:start position:0% +so that means that Sigma if you if you + + + align:start position:0% +so that means that Sigma if you if you +start like in the previous slide if you + + align:start position:0% +start like in the previous slide if you + + + align:start position:0% +start like in the previous slide if you +start + + align:start position:0% +start + + + align:start position:0% +start +uh from a situation in which in + + align:start position:0% +uh from a situation in which in + + + align:start position:0% +uh from a situation in which in +your control volume there is a um a lot + + align:start position:0% +your control volume there is a um a lot + + + align:start position:0% +your control volume there is a um a lot +of entropy + + align:start position:0% +of entropy + + + align:start position:0% +of entropy +production and you let it go if it is + + align:start position:0% +production and you let it go if it is + + + align:start position:0% +production and you let it go if it is +not already in a steady + + align:start position:0% +not already in a steady + + + align:start position:0% +not already in a steady +state it will change + + align:start position:0% +state it will change + + + align:start position:0% +state it will change +evolve towards a less a lesser and + + align:start position:0% +evolve towards a less a lesser and + + + align:start position:0% +evolve towards a less a lesser and +lesser entropy production situation + + align:start position:0% +lesser entropy production situation + + + align:start position:0% +lesser entropy production situation +until it gets to + + align:start position:0% +until it gets to + + + align:start position:0% +until it gets to +zero and the zero will be either a + + align:start position:0% +zero and the zero will be either a + + + align:start position:0% +zero and the zero will be either a +steady state if it is sustained by the + + align:start position:0% +steady state if it is sustained by the + + + align:start position:0% +steady state if it is sustained by the +boundary conditions or the equilibrium + + align:start position:0% + + + + align:start position:0% + +State instead of doing the details here + + align:start position:0% +State instead of doing the details here + + + align:start position:0% +State instead of doing the details here +that are not really essential for us let + + align:start position:0% +that are not really essential for us let + + + align:start position:0% +that are not really essential for us let +me give you this + + align:start position:0% +me give you this + + + align:start position:0% +me give you this +example consider one dimensional heat + + align:start position:0% +example consider one dimensional heat + + + align:start position:0% +example consider one dimensional heat +transfer + + align:start position:0% +transfer + + + align:start position:0% +transfer +problem and that suppose that you have a + + align:start position:0% +problem and that suppose that you have a + + + align:start position:0% +problem and that suppose that you have a +a Time equal equal zero you have + + align:start position:0% +a Time equal equal zero you have + + + align:start position:0% +a Time equal equal zero you have +imposed this temperature + + align:start position:0% + + + + align:start position:0% + +profile and your boundary conditions are + + align:start position:0% +profile and your boundary conditions are + + + align:start position:0% +profile and your boundary conditions are +that the temperature here is is given + + align:start position:0% +that the temperature here is is given + + + align:start position:0% +that the temperature here is is given +fixed so you you fix the temperatures + + align:start position:0% +fixed so you you fix the temperatures + + + align:start position:0% +fixed so you you fix the temperatures +left and + + align:start position:0% +left and + + + align:start position:0% +left and +right of course that is not a steady + + align:start position:0% +right of course that is not a steady + + + align:start position:0% +right of course that is not a steady +state the system will evolve you can + + align:start position:0% +state the system will evolve you can + + + align:start position:0% +state the system will evolve you can +solve this with any uh with the for year + + align:start position:0% +solve this with any uh with the for year + + + align:start position:0% +solve this with any uh with the for year +equation or any software that does this + + align:start position:0% +equation or any software that does this + + + align:start position:0% +equation or any software that does this +solution and you you see it will evolve + + align:start position:0% +solution and you you see it will evolve + + + align:start position:0% +solution and you you see it will evolve +and will at the end it will reach the + + align:start position:0% +and will at the end it will reach the + + + align:start position:0% +and will at the end it will reach the +steady linear uh solution of the typical + + align:start position:0% +steady linear uh solution of the typical + + + align:start position:0% +steady linear uh solution of the typical +heat transfer problem now if you compute + + align:start position:0% +heat transfer problem now if you compute + + + align:start position:0% +heat transfer problem now if you compute +the entropy production rate + + align:start position:0% +the entropy production rate + + + align:start position:0% +the entropy production rate +here it's it's this much + + align:start position:0% + + + + align:start position:0% + +if you compute it here it's this much + + align:start position:0% +if you compute it here it's this much + + + align:start position:0% +if you compute it here it's this much +it's a + + align:start position:0% + + + + align:start position:0% + +half so the system as it moves from here + + align:start position:0% +half so the system as it moves from here + + + align:start position:0% +half so the system as it moves from here +to + + align:start position:0% +to + + + align:start position:0% +to +there has goes has an an overall Global + + align:start position:0% +there has goes has an an overall Global + + + align:start position:0% +there has goes has an an overall Global +entropy production that goes down in + + align:start position:0% +entropy production that goes down in + + + align:start position:0% +entropy production that goes down in +time until it reaches a minimum uh at + + align:start position:0% +time until it reaches a minimum uh at + + + align:start position:0% +time until it reaches a minimum uh at +steady state if you start this is + + align:start position:0% +steady state if you start this is + + + align:start position:0% +steady state if you start this is +another example in which you have a + + align:start position:0% +another example in which you have a + + + align:start position:0% +another example in which you have a +different boundary conditions that would + + align:start position:0% +different boundary conditions that would + + + align:start position:0% +different boundary conditions that would +allow an equilibrium state so you start + + align:start position:0% +allow an equilibrium state so you start + + + align:start position:0% +allow an equilibrium state so you start +from this one and you have an entropy + + align:start position:0% +from this one and you have an entropy + + + align:start position:0% +from this one and you have an entropy +production right which is given by this + + align:start position:0% +production right which is given by this + + + align:start position:0% +production right which is given by this +you let it go it will reach a flat + + align:start position:0% +you let it go it will reach a flat + + + align:start position:0% +you let it go it will reach a flat +temperature profile which is equilibrium + + align:start position:0% +temperature profile which is equilibrium + + + align:start position:0% +temperature profile which is equilibrium +zero entropy production again a + + align:start position:0% + + + + align:start position:0% + +minimum so + + align:start position:0% +minimum so + + + align:start position:0% +minimum so +globally it has gone + + align:start position:0% +globally it has gone + + + align:start position:0% +globally it has gone +down but + + align:start position:0% +down but + + + align:start position:0% +down but +locally at every instant at every local + + align:start position:0% +locally at every instant at every local + + + align:start position:0% +locally at every instant at every local +uh + + align:start position:0% +uh + + + align:start position:0% +uh +each material element here has followed + + align:start position:0% +each material element here has followed + + + align:start position:0% +each material element here has followed +for Law and + + align:start position:0% +for Law and + + + align:start position:0% +for Law and +therefore at any time chosen the + + align:start position:0% +therefore at any time chosen the + + + align:start position:0% +therefore at any time chosen the +direction of a flow that is compatible + + align:start position:0% +direction of a flow that is compatible + + + align:start position:0% +direction of a flow that is compatible +with that the + + align:start position:0% +with that the + + + align:start position:0% +with that the +gradient imposed all right so we're just + + align:start position:0% +gradient imposed all right so we're just + + + align:start position:0% +gradient imposed all right so we're just +on time and just + + align:start position:0% +on time and just + + + align:start position:0% +on time and just +uh finished \ No newline at end of file diff --git a/MEz1J9wY2iM.txt b/MEz1J9wY2iM.txt new file mode 100644 index 0000000000000000000000000000000000000000..0a47cd710a552173f9104f1df4d7493541b0ed14 --- /dev/null +++ b/MEz1J9wY2iM.txt @@ -0,0 +1,12843 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu let's get started uh thanks + + align:start position:0% +ocw.mit.edu let's get started uh thanks + + + align:start position:0% +ocw.mit.edu let's get started uh thanks +for coming to lecture now there's a quiz + + align:start position:0% +for coming to lecture now there's a quiz + + + align:start position:0% +for coming to lecture now there's a quiz +coming up there will be a tangible + + align:start position:0% +coming up there will be a tangible + + + align:start position:0% +coming up there will be a tangible +benefit of attending this lecture + + align:start position:0% +benefit of attending this lecture + + + align:start position:0% +benefit of attending this lecture +uh and it's not + + align:start position:0% +uh and it's not + + + align:start position:0% +uh and it's not +frisbees + + align:start position:0% +frisbees + + + align:start position:0% +frisbees +okay we'll figure it out soon um so um + + align:start position:0% +okay we'll figure it out soon um so um + + + align:start position:0% +okay we'll figure it out soon um so um +two lectures on um approximation + + align:start position:0% +two lectures on um approximation + + + align:start position:0% +two lectures on um approximation +algorithms uh one today and uh one uh I + + align:start position:0% +algorithms uh one today and uh one uh I + + + align:start position:0% +algorithms uh one today and uh one uh I +guess a week and two days from today on + + align:start position:0% +guess a week and two days from today on + + + align:start position:0% +guess a week and two days from today on +Thursday after the break uh Eric will + + align:start position:0% +Thursday after the break uh Eric will + + + align:start position:0% +Thursday after the break uh Eric will +give that one so this is more of a + + align:start position:0% +give that one so this is more of a + + + align:start position:0% +give that one so this is more of a +introductory lecture Eric talked about + + align:start position:0% +introductory lecture Eric talked about + + + align:start position:0% +introductory lecture Eric talked about +uh NP complete problems and NP hard + + align:start position:0% +uh NP complete problems and NP hard + + + align:start position:0% +uh NP complete problems and NP hard +problems uh he talked about how you + + align:start position:0% +problems uh he talked about how you + + + align:start position:0% +problems uh he talked about how you +could show that problems uh are NP + + align:start position:0% +could show that problems uh are NP + + + align:start position:0% +could show that problems uh are NP +complete or NP hard so what happens when + + align:start position:0% +complete or NP hard so what happens when + + + align:start position:0% +complete or NP hard so what happens when +you discover that a problem is NP + + align:start position:0% +you discover that a problem is NP + + + align:start position:0% +you discover that a problem is NP +complete or NP hard well there's a + + align:start position:0% +complete or NP hard well there's a + + + align:start position:0% +complete or NP hard well there's a +variety of uh strategies uh you could + + align:start position:0% +variety of uh strategies uh you could + + + align:start position:0% +variety of uh strategies uh you could +just kind of give up and say this is + + align:start position:0% +just kind of give up and say this is + + + align:start position:0% +just kind of give up and say this is +intractable I want a different job uh + + align:start position:0% +intractable I want a different job uh + + + align:start position:0% +intractable I want a different job uh +you could uh say that I'm just going to + + align:start position:0% +you could uh say that I'm just going to + + + align:start position:0% +you could uh say that I'm just going to +uh do the best I can without any + + align:start position:0% +uh do the best I can without any + + + align:start position:0% +uh do the best I can without any +theoretical guarantees uh I'm going to + + align:start position:0% +theoretical guarantees uh I'm going to + + + align:start position:0% +theoretical guarantees uh I'm going to +use a heuristic I'm going to think of + + align:start position:0% +use a heuristic I'm going to think of + + + align:start position:0% +use a heuristic I'm going to think of +this simplest greedy heuristic I'm going + + align:start position:0% +this simplest greedy heuristic I'm going + + + align:start position:0% +this simplest greedy heuristic I'm going +to code it up and I'm going to move on + + align:start position:0% +to code it up and I'm going to move on + + + align:start position:0% +to code it up and I'm going to move on +um or you could do approximation + + align:start position:0% +um or you could do approximation + + + align:start position:0% +um or you could do approximation +algorithms you could uh you could say + + align:start position:0% +algorithms you could uh you could say + + + align:start position:0% +algorithms you could uh you could say +I'm going to think up of a interesting + + align:start position:0% +I'm going to think up of a interesting + + + align:start position:0% +I'm going to think up of a interesting +greedy heuristic but I'm going to + + align:start position:0% +greedy heuristic but I'm going to + + + align:start position:0% +greedy heuristic but I'm going to +prove uh that this greedy heuristic in + + align:start position:0% +prove uh that this greedy heuristic in + + + align:start position:0% +prove uh that this greedy heuristic in +every conceivable situation with respect + + align:start position:0% +every conceivable situation with respect + + + align:start position:0% +every conceivable situation with respect +to the inputs is going to be within some + + align:start position:0% +to the inputs is going to be within some + + + align:start position:0% +to the inputs is going to be within some +factor of optimal right and that's what + + align:start position:0% +factor of optimal right and that's what + + + align:start position:0% +factor of optimal right and that's what +we're going to do today we're going to + + align:start position:0% +we're going to do today we're going to + + + align:start position:0% +we're going to do today we're going to +take a bunch of NP complete problems and + + align:start position:0% +take a bunch of NP complete problems and + + + align:start position:0% +take a bunch of NP complete problems and +we're going + + align:start position:0% +we're going + + + align:start position:0% +we're going +to essentially create create uh simple + + align:start position:0% +to essentially create create uh simple + + + align:start position:0% +to essentially create create uh simple +heuristics for these problems simple + + align:start position:0% +heuristics for these problems simple + + + align:start position:0% +heuristics for these problems simple +strategies that are polinomial time to + + align:start position:0% +strategies that are polinomial time to + + + align:start position:0% +strategies that are polinomial time to +quote solve these problems and uh what + + align:start position:0% +quote solve these problems and uh what + + + align:start position:0% +quote solve these problems and uh what +does it mean to solve these problems + + align:start position:0% +does it mean to solve these problems + + + align:start position:0% +does it mean to solve these problems +well you know that if it's polinomial + + align:start position:0% +well you know that if it's polinomial + + + align:start position:0% +well you know that if it's polinomial +time you're not guaranteed to get the + + align:start position:0% +time you're not guaranteed to get the + + + align:start position:0% +time you're not guaranteed to get the +optimum answer every time but you'll + + align:start position:0% +optimum answer every time but you'll + + + align:start position:0% +optimum answer every time but you'll +call it a solution an approximate + + align:start position:0% +call it a solution an approximate + + + align:start position:0% +call it a solution an approximate +solution because you're within a factor + + align:start position:0% +solution because you're within a factor + + + align:start position:0% +solution because you're within a factor +of two for every possible input that's + + align:start position:0% +of two for every possible input that's + + + align:start position:0% +of two for every possible input that's +one example or you have a + + align:start position:0% +one example or you have a + + + align:start position:0% +one example or you have a +more complicated approximation factor + + align:start position:0% +more complicated approximation factor + + + align:start position:0% +more complicated approximation factor +that we'll get to in a second where it's + + align:start position:0% +that we'll get to in a second where it's + + + align:start position:0% +that we'll get to in a second where it's +not quite a factor of two might be a + + align:start position:0% +not quite a factor of two might be a + + + align:start position:0% +not quite a factor of two might be a +factor of two for small size problems + + align:start position:0% +factor of two for small size problems + + + align:start position:0% +factor of two for small size problems +might be a factor of 10 for larger + + align:start position:0% +might be a factor of 10 for larger + + + align:start position:0% +might be a factor of 10 for larger +problems and so on and so forth and then + + align:start position:0% +problems and so on and so forth and then + + + align:start position:0% +problems and so on and so forth and then +the last thing is it'd be great if you + + align:start position:0% +the last thing is it'd be great if you + + + align:start position:0% +the last thing is it'd be great if you +could spend more time and get better + + align:start position:0% +could spend more time and get better + + + align:start position:0% +could spend more time and get better +Solutions and those are approximation + + align:start position:0% +Solutions and those are approximation + + + align:start position:0% +Solutions and those are approximation +schemes and we'll look at an + + align:start position:0% +schemes and we'll look at an + + + align:start position:0% +schemes and we'll look at an +approximation schemes as well right so + + align:start position:0% +approximation schemes as well right so + + + align:start position:0% +approximation schemes as well right so +just dive in each of these problems + + align:start position:0% +just dive in each of these problems + + + align:start position:0% +just dive in each of these problems +depending on whether it's + + align:start position:0% +depending on whether it's + + + align:start position:0% +depending on whether it's +decision or optimization is NP complete + + align:start position:0% +decision or optimization is NP complete + + + align:start position:0% +decision or optimization is NP complete +or NP hard I'll Define these problems as + + align:start position:0% +or NP hard I'll Define these problems as + + + align:start position:0% +or NP hard I'll Define these problems as +we go along but basically the name of + + align:start position:0% +we go along but basically the name of + + + align:start position:0% +we go along but basically the name of +the game here is uh grab a problem + + align:start position:0% +the game here is uh grab a problem + + + align:start position:0% +the game here is uh grab a problem +Define it uh think of a interesting + + align:start position:0% +Define it uh think of a interesting + + + align:start position:0% +Define it uh think of a interesting +heuristic uh do a proof okay and that's + + align:start position:0% +heuristic uh do a proof okay and that's + + + align:start position:0% +heuristic uh do a proof okay and that's +uh essentially what we're going to do + + align:start position:0% +uh essentially what we're going to do + + + align:start position:0% +uh essentially what we're going to do +three times uh the good news is the + + align:start position:0% +three times uh the good news is the + + + align:start position:0% +three times uh the good news is the +proofs aren't tortous they're not 30 + + align:start position:0% +proofs aren't tortous they're not 30 + + + align:start position:0% +proofs aren't tortous they're not 30 +minute proofs uh and they should be + + align:start position:0% +minute proofs uh and they should be + + + align:start position:0% +minute proofs uh and they should be +pretty intuitive and we'll see if we can + + align:start position:0% +pretty intuitive and we'll see if we can + + + align:start position:0% +pretty intuitive and we'll see if we can +extract them out of + + align:start position:0% +extract them out of + + + align:start position:0% +extract them out of +you a painful extraction + + align:start position:0% +you a painful extraction + + + align:start position:0% +you a painful extraction +process I went to the dentist + + align:start position:0% +process I went to the dentist + + + align:start position:0% +process I went to the dentist +yesterday not for + + align:start position:0% + + + + align:start position:0% + +extraction I should have said I went to + + align:start position:0% +extraction I should have said I went to + + + align:start position:0% +extraction I should have said I went to +the dentist yesterday and I'm now going + + align:start position:0% +the dentist yesterday and I'm now going + + + align:start position:0% +the dentist yesterday and I'm now going +to take it out on you + + align:start position:0% +to take it out on you + + + align:start position:0% +to take it out on you +right okay so what's an approximation + + align:start position:0% +right okay so what's an approximation + + + align:start position:0% +right okay so what's an approximation +algorithm an algorithm + + align:start position:0% + + + + align:start position:0% + +for a problem of size + + align:start position:0% + + + + align:start position:0% + +n and so it's going to be parameterized + + align:start position:0% +n and so it's going to be parameterized + + + align:start position:0% +n and so it's going to be parameterized +and the approximation Factor may also be + + align:start position:0% +and the approximation Factor may also be + + + align:start position:0% +and the approximation Factor may also be +parameterized it'd be nice if it weren't + + align:start position:0% +parameterized it'd be nice if it weren't + + + align:start position:0% +parameterized it'd be nice if it weren't +that it was a constant Factor + + align:start position:0% +that it was a constant Factor + + + align:start position:0% +that it was a constant Factor +approximation but sometimes you can't do + + align:start position:0% +approximation but sometimes you can't do + + + align:start position:0% +approximation but sometimes you can't do +that and in fact sometimes you can prove + + align:start position:0% +that and in fact sometimes you can prove + + + align:start position:0% +that and in fact sometimes you can prove +that constant Factor approximation + + align:start position:0% +that constant Factor approximation + + + align:start position:0% +that constant Factor approximation +algorithms don't exist and if they do + + align:start position:0% +algorithms don't exist and if they do + + + align:start position:0% +algorithms don't exist and if they do +then P equals NP right so it's uh gets + + align:start position:0% +then P equals NP right so it's uh gets + + + align:start position:0% +then P equals NP right so it's uh gets +very + + align:start position:0% +very + + + align:start position:0% +very +interesting so in this case + + align:start position:0% +interesting so in this case + + + align:start position:0% +interesting so in this case +approximation algorithms or schemes + + align:start position:0% +approximation algorithms or schemes + + + align:start position:0% +approximation algorithms or schemes +exist for these three problems which is + + align:start position:0% +exist for these three problems which is + + + align:start position:0% +exist for these three problems which is +why we looking at them today but you got + + align:start position:0% +why we looking at them today but you got + + + align:start position:0% +why we looking at them today but you got +a problem of size n and we're going to + + align:start position:0% +a problem of size n and we're going to + + + align:start position:0% +a problem of size n and we're going to +Define an approximation + + align:start position:0% + + + + align:start position:0% + +ratio row of + + align:start position:0% +ratio row of + + + align:start position:0% +ratio row of +n for any input + + align:start position:0% +n for any input + + + align:start position:0% +n for any input +uh if for any input excuse + + align:start position:0% + + + + align:start position:0% + +me the algorithm produces a + + align:start position:0% + + + + align:start position:0% + +solution with c + + align:start position:0% + + + + align:start position:0% + +c that satisfies this little property um + + align:start position:0% +c that satisfies this little property um + + + align:start position:0% +c that satisfies this little property um +which says that the max of C ided by C + + align:start position:0% +which says that the max of C ided by C + + + align:start position:0% +which says that the max of C ided by C +op divided by uh sorry and C op divided + + align:start position:0% +op divided by uh sorry and C op divided + + + align:start position:0% +op divided by uh sorry and C op divided +by C is less than or equal to row + + align:start position:0% +by C is less than or equal to row + + + align:start position:0% +by C is less than or equal to row +M right and the only reason you have two + + align:start position:0% +M right and the only reason you have two + + + align:start position:0% +M right and the only reason you have two +terms in here is because you haven't + + align:start position:0% +terms in here is because you haven't + + + align:start position:0% +terms in here is because you haven't +said whether it's a minimization problem + + align:start position:0% +said whether it's a minimization problem + + + align:start position:0% +said whether it's a minimization problem +or a maximization problem right so if + + align:start position:0% +or a maximization problem right so if + + + align:start position:0% +or a maximization problem right so if +it's a minimization problem you you + + align:start position:0% +it's a minimization problem you you + + + align:start position:0% +it's a minimization problem you you +don't want to be too much greater than + + align:start position:0% +don't want to be too much greater than + + + align:start position:0% +don't want to be too much greater than +the minimum if it's a maximization + + align:start position:0% +the minimum if it's a maximization + + + align:start position:0% +the minimum if it's a maximization +problem you don't want to be too much + + align:start position:0% +problem you don't want to be too much + + + align:start position:0% +problem you don't want to be too much +smaller than the maximum and so you just + + align:start position:0% +smaller than the maximum and so you just + + + align:start position:0% +smaller than the maximum and so you just +stick those two things in there and you + + align:start position:0% +stick those two things in there and you + + + align:start position:0% +stick those two things in there and you +don't worry about whether it's Min or + + align:start position:0% +don't worry about whether it's Min or + + + align:start position:0% +don't worry about whether it's Min or +Max in terms of the objective function + + align:start position:0% +Max in terms of the objective function + + + align:start position:0% +Max in terms of the objective function +and you want it to be at that particular + + align:start position:0% +and you want it to be at that particular + + + align:start position:0% +and you want it to be at that particular +ratio okay now I did say row of n there + + align:start position:0% +ratio okay now I did say row of n there + + + align:start position:0% +ratio okay now I did say row of n there +so this could be a constant or it could + + align:start position:0% +so this could be a constant or it could + + + align:start position:0% +so this could be a constant or it could +be a function of n if it's a function of + + align:start position:0% +be a function of n if it's a function of + + + align:start position:0% +be a function of n if it's a function of +n u is going to be an increasing + + align:start position:0% +n u is going to be an increasing + + + align:start position:0% +n u is going to be an increasing +function of n okay um otherwise you + + align:start position:0% +function of n okay um otherwise you + + + align:start position:0% +function of n okay um otherwise you +could just bound it and have a a + + align:start position:0% +could just bound it and have a a + + + align:start position:0% +could just bound it and have a a +constant obviously so um you might have + + align:start position:0% +constant obviously so um you might have + + + align:start position:0% +constant obviously so um you might have +something like and we'll see one of + + align:start position:0% +something like and we'll see one of + + + align:start position:0% +something like and we'll see one of +these log n approximation scheme uh + + align:start position:0% +these log n approximation scheme uh + + + align:start position:0% +these log n approximation scheme uh +which uh which says + + align:start position:0% +which uh which says + + + align:start position:0% +which uh which says +that uh uh you're going to be within + + align:start position:0% +that uh uh you're going to be within + + + align:start position:0% +that uh uh you're going to be within +logarithmic uh of the answer minimum or + + align:start position:0% +logarithmic uh of the answer minimum or + + + align:start position:0% +logarithmic uh of the answer minimum or +maximum but uh if it's a million then uh + + align:start position:0% +maximum but uh if it's a million then uh + + + align:start position:0% +maximum but uh if it's a million then uh +if you do log of base two then you know + + align:start position:0% +if you do log of base two then you know + + + align:start position:0% +if you do log of base two then you know +you're within a factor of 20 uh which + + align:start position:0% +you're within a factor of 20 uh which + + + align:start position:0% +you're within a factor of 20 uh which +isn't that great but let's just say we + + align:start position:0% +isn't that great but let's just say we + + + align:start position:0% +isn't that great but let's just say we +happy with it and then if it goes to a + + align:start position:0% +happy with it and then if it goes to a + + + align:start position:0% +happy with it and then if it goes to a +billion it's a factor of 30 and so on + + align:start position:0% +billion it's a factor of 30 and so on + + + align:start position:0% +billion it's a factor of 30 and so on +and so forth right so it could grow so + + align:start position:0% +and so forth right so it could grow so + + + align:start position:0% +and so forth right so it could grow so +that's an + + align:start position:0% +that's an + + + align:start position:0% +that's an +algorithm um that these terms are are + + align:start position:0% +algorithm um that these terms are are + + + align:start position:0% +algorithm um that these terms are are +used in changeably uh we'll try and + + align:start position:0% +used in changeably uh we'll try and + + + align:start position:0% +used in changeably uh we'll try and +differentiate but we do have something + + align:start position:0% +differentiate but we do have something + + + align:start position:0% +differentiate but we do have something +that we call an approximation + + align:start position:0% +that we call an approximation + + + align:start position:0% +that we call an approximation +scheme and the big difference between + + align:start position:0% +scheme and the big difference between + + + align:start position:0% +scheme and the big difference between +approximation algorithms and + + align:start position:0% +approximation algorithms and + + + align:start position:0% +approximation algorithms and +approximation schemes is that I'm going + + align:start position:0% +approximation schemes is that I'm going + + + align:start position:0% +approximation schemes is that I'm going +to have a little knob in an + + align:start position:0% +to have a little knob in an + + + align:start position:0% +to have a little knob in an +approximation scheme that's let going to + + align:start position:0% +approximation scheme that's let going to + + + align:start position:0% +approximation scheme that's let going to +let me do more work to get something + + align:start position:0% +let me do more work to get something + + + align:start position:0% +let me do more work to get something +better okay and that's essentially what + + align:start position:0% +better okay and that's essentially what + + + align:start position:0% +better okay and that's essentially what +a scheme is where we're going to take an + + align:start position:0% +a scheme is where we're going to take an + + + align:start position:0% +a scheme is where we're going to take an +input an additional + + align:start position:0% + + + + align:start position:0% + +input Epsilon strictly greater than + + align:start position:0% +input Epsilon strictly greater than + + + align:start position:0% +input Epsilon strictly greater than +zero + + align:start position:0% +zero + + + align:start position:0% +zero +and for + + align:start position:0% +and for + + + align:start position:0% +and for +any fixed + + align:start position:0% +any fixed + + + align:start position:0% +any fixed +Epsilon the + + align:start position:0% +Epsilon the + + + align:start position:0% +Epsilon the +scheme this is an approximation scheme + + align:start position:0% +scheme this is an approximation scheme + + + align:start position:0% +scheme this is an approximation scheme +as opposed to an + + align:start position:0% +as opposed to an + + + align:start position:0% +as opposed to an +algorithm is a 1 + + + align:start position:0% +algorithm is a 1 + + + + align:start position:0% +algorithm is a 1 + +Epsilon approximation + + align:start position:0% + + + + align:start position:0% + +algorithm and so here we just say that + + align:start position:0% +algorithm and so here we just say that + + + align:start position:0% +algorithm and so here we just say that +this is a row N approximation + + align:start position:0% +this is a row N approximation + + + align:start position:0% +this is a row N approximation +algorithm if it satisfies this property + + align:start position:0% +algorithm if it satisfies this property + + + align:start position:0% +algorithm if it satisfies this property +and here we have a family of algorithms + + align:start position:0% +and here we have a family of algorithms + + + align:start position:0% +and here we have a family of algorithms +that are + + align:start position:0% +that are + + + align:start position:0% +that are +parameterized by n in terms of + + align:start position:0% +parameterized by n in terms of + + + align:start position:0% +parameterized by n in terms of +runtime as well as + + align:start position:0% +runtime as well as + + + align:start position:0% +runtime as well as +Epsilon and so um you might have a + + align:start position:0% +Epsilon and so um you might have a + + + align:start position:0% +Epsilon and so um you might have a +situation where you have order n raed to + + align:start position:0% +situation where you have order n raed to + + + align:start position:0% +situation where you have order n raed to +2 / Epsilon + + align:start position:0% +2 / Epsilon + + + align:start position:0% +2 / Epsilon +running + + align:start position:0% + + + + align:start position:0% + +time for an approximation algorithm and + + align:start position:0% +time for an approximation algorithm and + + + align:start position:0% +time for an approximation algorithm and +what this means is that if you're within + + align:start position:0% +what this means is that if you're within + + + align:start position:0% +what this means is that if you're within +10% of optimal then you're going to put + + align:start position:0% +10% of optimal then you're going to put + + + align:start position:0% +10% of optimal then you're going to put +0.1 down here and this is going to be an + + align:start position:0% +0.1 down here and this is going to be an + + + align:start position:0% +0.1 down here and this is going to be an +N raised to + + align:start position:0% +N raised to + + + align:start position:0% +N raised to +20 algorithm polinomial time wonderful + + align:start position:0% +20 algorithm polinomial time wonderful + + + align:start position:0% +20 algorithm polinomial time wonderful +solve The World's problems not really I + + align:start position:0% +solve The World's problems not really I + + + align:start position:0% +solve The World's problems not really I +mean end R to 20 is pretty bad but uh + + align:start position:0% +mean end R to 20 is pretty bad but uh + + + align:start position:0% +mean end R to 20 is pretty bad but uh +it's not exponential right so you you + + align:start position:0% +it's not exponential right so you you + + + align:start position:0% +it's not exponential right so you you +see that there's a there's + + align:start position:0% +see that there's a there's + + + align:start position:0% +see that there's a there's +a a growth here of um polinomial degree + + align:start position:0% +a a growth here of um polinomial degree + + + align:start position:0% +a a growth here of um polinomial degree +with respect to Epsilon and it's a + + align:start position:0% +with respect to Epsilon and it's a + + + align:start position:0% +with respect to Epsilon and it's a +pretty fast growth if you want to go to + + align:start position:0% +pretty fast growth if you want to go to + + + align:start position:0% +pretty fast growth if you want to go to +Epsilon equals 01 I mean even n ra to 20 + + align:start position:0% +Epsilon equals 01 I mean even n ra to 20 + + + align:start position:0% +Epsilon equals 01 I mean even n ra to 20 +is probably untenable but certainly n ra + + align:start position:0% +is probably untenable but certainly n ra + + + align:start position:0% +is probably untenable but certainly n ra +to 200 is is completely untenable right + + align:start position:0% +to 200 is is completely untenable right + + + align:start position:0% +to 200 is is completely untenable right +so this is what's called + + align:start position:0% +so this is what's called + + + align:start position:0% +so this is what's called +AAS which + + align:start position:0% + + + + align:start position:0% + +is a probabilistic + + align:start position:0% + + + + align:start position:0% + +time approximation + + align:start position:0% +time approximation + + + align:start position:0% +time approximation +scheme and don't worry too much about + + align:start position:0% +scheme and don't worry too much about + + + align:start position:0% +scheme and don't worry too much about +the + + align:start position:0% +the + + + align:start position:0% +the +probabilistic it's a function + + align:start position:0% +probabilistic it's a function + + + align:start position:0% +probabilistic it's a function +of um of Epsilon that's the way you want + + align:start position:0% +of um of Epsilon that's the way you want + + + align:start position:0% +of um of Epsilon that's the way you want +to think about it the runtime and we'll + + align:start position:0% +to think about it the runtime and we'll + + + align:start position:0% +to think about it the runtime and we'll +look at a particular + + align:start position:0% +look at a particular + + + align:start position:0% +look at a particular +scheme later in the lecture but clearly + + align:start position:0% +scheme later in the lecture but clearly + + + align:start position:0% +scheme later in the lecture but clearly +this is a polinomial in N okay but it's + + align:start position:0% +this is a polinomial in N okay but it's + + + align:start position:0% +this is a polinomial in N okay but it's +um not polinomial in epsilon all right + + align:start position:0% +um not polinomial in epsilon all right + + + align:start position:0% +um not polinomial in epsilon all right +so a ptas is going to be + + align:start position:0% +so a ptas is going to be + + + align:start position:0% +so a ptas is going to be +poly in + + align:start position:0% +poly in + + + align:start position:0% +poly in +N but not + + align:start position:0% + + + + align:start position:0% + +necessarily in epsilon and I say not + + align:start position:0% +necessarily in epsilon and I say not + + + align:start position:0% +necessarily in epsilon and I say not +necessarily because uh I we still call + + align:start position:0% +necessarily because uh I we still call + + + align:start position:0% +necessarily because uh I we still call +it a p Tas we just say fully polinomial + + align:start position:0% +it a p Tas we just say fully polinomial + + + align:start position:0% +it a p Tas we just say fully polinomial +time approximation scheme FP task if + + align:start position:0% +time approximation scheme FP task if + + + align:start position:0% +time approximation scheme FP task if +it's polinomial in both n and 1 / + + align:start position:0% +it's polinomial in both n and 1 / + + + align:start position:0% +it's polinomial in both n and 1 / +Epsilon + + align:start position:0% +Epsilon + + + align:start position:0% +Epsilon +right so fully P + + align:start position:0% + + + + align:start position:0% + +test + + align:start position:0% +test + + + align:start position:0% +test +is poly in n and 1 / Epsilon so a fully + + align:start position:0% +is poly in n and 1 / Epsilon so a fully + + + align:start position:0% +is poly in n and 1 / Epsilon so a fully +P + + align:start position:0% +P + + + align:start position:0% +P +scheme would be something like n / + + align:start position:0% +scheme would be something like n / + + + align:start position:0% +scheme would be something like n / +Epsilon + + align:start position:0% +Epsilon + + + align:start position:0% +Epsilon +Square okay so as Epsilon shrinks um + + align:start position:0% +Square okay so as Epsilon shrinks um + + + align:start position:0% +Square okay so as Epsilon shrinks um +obviously the runtime is going to grow + + align:start position:0% +obviously the runtime is going to grow + + + align:start position:0% +obviously the runtime is going to grow +because you got 1 / Epsilon square but + + align:start position:0% +because you got 1 / Epsilon square but + + + align:start position:0% +because you got 1 / Epsilon square but +it's not anywhere as bad as the N raised + + align:start position:0% +it's not anywhere as bad as the N raised + + + align:start position:0% +it's not anywhere as bad as the N raised +to 2 ided Epsilon in terms of its growth + + align:start position:0% +to 2 ided Epsilon in terms of its growth + + + align:start position:0% +to 2 ided Epsilon in terms of its growth +rate okay so there's lots of NP complete + + align:start position:0% +rate okay so there's lots of NP complete + + + align:start position:0% +rate okay so there's lots of NP complete +problems that have ptases and that some + + align:start position:0% +problems that have ptases and that some + + + align:start position:0% +problems that have ptases and that some +of them have FP tases as well and so on + + align:start position:0% +of them have FP tases as well and so on + + + align:start position:0% +of them have FP tases as well and so on +and so forth question what does the what + + align:start position:0% +and so forth question what does the what + + + align:start position:0% +and so forth question what does the what +problem um so we won't get into that uh + + align:start position:0% +problem um so we won't get into that uh + + + align:start position:0% +problem um so we won't get into that uh +today but you can think of it as um um + + align:start position:0% +today but you can think of it as um um + + + align:start position:0% +today but you can think of it as um um +as uh the the the the probability uh + + align:start position:0% +as uh the the the the probability uh + + + align:start position:0% +as uh the the the the probability uh +over the the space of um possible + + align:start position:0% +over the the space of um possible + + + align:start position:0% +over the the space of um possible +solutions that you have uh you can you + + align:start position:0% +solutions that you have uh you can you + + + align:start position:0% +solutions that you have uh you can you +can distribution of uh distribution of + + align:start position:0% +can distribution of uh distribution of + + + align:start position:0% +can distribution of uh distribution of +inputs it that the bottom line is that + + align:start position:0% +inputs it that the bottom line is that + + + align:start position:0% +inputs it that the bottom line is that +we actually won't cover that uh today so + + align:start position:0% +we actually won't cover that uh today so + + + align:start position:0% +we actually won't cover that uh today so +let's shove that for uh uh for next + + align:start position:0% +let's shove that for uh uh for next + + + align:start position:0% +let's shove that for uh uh for next +lecture okay so just worry about the + + align:start position:0% +lecture okay so just worry about the + + + align:start position:0% +lecture okay so just worry about the +fact that um this this it's uh uh it's a + + align:start position:0% +fact that um this this it's uh uh it's a + + + align:start position:0% +fact that um this this it's uh uh it's a +polinomial in n and uh not in epsilon + + align:start position:0% +polinomial in n and uh not in epsilon + + + align:start position:0% +polinomial in n and uh not in epsilon +for the first part and it's polinomial + + align:start position:0% +for the first part and it's polinomial + + + align:start position:0% +for the first part and it's polinomial +in n and Epsilon for the second part + + align:start position:0% +in n and Epsilon for the second part + + + align:start position:0% +in n and Epsilon for the second part +okay + + align:start position:0% + + + + align:start position:0% + +oh I see so this a good point so for + + align:start position:0% +oh I see so this a good point so for + + + align:start position:0% +oh I see so this a good point so for +this the purposes of this lecture thank + + align:start position:0% +this the purposes of this lecture thank + + + align:start position:0% +this the purposes of this lecture thank +you so much uh I'm glad I didn't have to + + align:start position:0% +you so much uh I'm glad I didn't have to + + + align:start position:0% +you so much uh I'm glad I didn't have to +get into that polinomial time good + + align:start position:0% +get into that polinomial time good + + + align:start position:0% +get into that polinomial time good +better answer either way we're not going + + align:start position:0% +better answer either way we're not going + + + align:start position:0% +better answer either way we're not going +to cover that all right good so it's + + align:start position:0% +to cover that all right good so it's + + + align:start position:0% +to cover that all right good so it's +polinomial I mean you could have + + align:start position:0% +polinomial I mean you could have + + + align:start position:0% +polinomial I mean you could have +probabilistic algorithms that have this + + align:start position:0% +probabilistic algorithms that have this + + + align:start position:0% +probabilistic algorithms that have this +kind of um uh behavior of course uh but + + align:start position:0% +kind of um uh behavior of course uh but + + + align:start position:0% +kind of um uh behavior of course uh but +we're not going to cover that uh in + + align:start position:0% +we're not going to cover that uh in + + + align:start position:0% +we're not going to cover that uh in +today's lecture but thanks for pointing + + align:start position:0% +today's lecture but thanks for pointing + + + align:start position:0% +today's lecture but thanks for pointing +that out Eric uh so that's our setup uh + + align:start position:0% +that out Eric uh so that's our setup uh + + + align:start position:0% +that out Eric uh so that's our setup uh +we essentially have + + align:start position:0% +we essentially have + + + align:start position:0% +we essentially have +u a situation where it'd be great if we + + align:start position:0% +u a situation where it'd be great if we + + + align:start position:0% +u a situation where it'd be great if we +could tackle NP complete problems using + + align:start position:0% +could tackle NP complete problems using + + + align:start position:0% +could tackle NP complete problems using +this uh hammer right uh any questions so + + align:start position:0% + + + + align:start position:0% + +far all + + align:start position:0% +far all + + + align:start position:0% +far all +right vertex + + align:start position:0% +right vertex + + + align:start position:0% +right vertex +cover so let's Dive Right + + align:start position:0% + + + + align:start position:0% + +In I talk about uh a particular problem + + align:start position:0% +In I talk about uh a particular problem + + + align:start position:0% +In I talk about uh a particular problem +very simple problem uh what you have is + + align:start position:0% +very simple problem uh what you have is + + + align:start position:0% +very simple problem uh what you have is +an undirected graph + + align:start position:0% + + + + align:start position:0% + +gve and all we want is a set of vertices + + align:start position:0% +gve and all we want is a set of vertices + + + align:start position:0% +gve and all we want is a set of vertices +that cover all of the + + align:start position:0% + + + + align:start position:0% + +edges so a set of + + align:start position:0% + + + + align:start position:0% + +vertices that cover + + align:start position:0% +vertices that cover + + + align:start position:0% +vertices that cover +all edges what does it mean to cover + + align:start position:0% +all edges what does it mean to cover + + + align:start position:0% +all edges what does it mean to cover +it's the obvious thing if I have + + align:start position:0% +it's the obvious thing if I have + + + align:start position:0% +it's the obvious thing if I have +something like + + align:start position:0% +something like + + + align:start position:0% +something like +this as long + + align:start position:0% +this as long + + + align:start position:0% +this as long +as I have a vertex in my set of vertices + + align:start position:0% +as I have a vertex in my set of vertices + + + align:start position:0% +as I have a vertex in my set of vertices +that I'm calling a cover that touches + + align:start position:0% +that I'm calling a cover that touches + + + align:start position:0% +that I'm calling a cover that touches +one end point of an edge we're going to + + align:start position:0% +one end point of an edge we're going to + + + align:start position:0% +one end point of an edge we're going to +call that edge cover okay so in this + + align:start position:0% +call that edge cover okay so in this + + + align:start position:0% +call that edge cover okay so in this +case it's a pretty clear that the vertex + + align:start position:0% +case it's a pretty clear that the vertex + + + align:start position:0% +case it's a pretty clear that the vertex +cover is simply that because that vertex + + align:start position:0% +cover is simply that because that vertex + + + align:start position:0% +cover is simply that because that vertex +touches all of the edges at least uh one + + align:start position:0% +touches all of the edges at least uh one + + + align:start position:0% +touches all of the edges at least uh one +of the end points a Vertex is going to + + align:start position:0% +of the end points a Vertex is going to + + + align:start position:0% +of the end points a Vertex is going to +touch one end point of an edge but this + + align:start position:0% +touch one end point of an edge but this + + + align:start position:0% +touch one end point of an edge but this +uh vertex cover that I've shaded + + align:start position:0% +uh vertex cover that I've shaded + + + align:start position:0% +uh vertex cover that I've shaded +touches every Edge right so that's a + + align:start position:0% +touches every Edge right so that's a + + + align:start position:0% +touches every Edge right so that's a +Vertex cover um if in fact I had an + + align:start position:0% +Vertex cover um if in fact I had an + + + align:start position:0% +Vertex cover um if in fact I had an +extra edge here then um I now have to + + align:start position:0% +extra edge here then um I now have to + + + align:start position:0% +extra edge here then um I now have to +pick one or this one or that one in + + align:start position:0% +pick one or this one or that one in + + + align:start position:0% +pick one or this one or that one in +order to complete my cover okay that's + + align:start position:0% +order to complete my cover okay that's + + + align:start position:0% +order to complete my cover okay that's +it that's vertex cover um decision + + align:start position:0% +it that's vertex cover um decision + + + align:start position:0% +it that's vertex cover um decision +problem uh and NP complete uh to figure + + align:start position:0% +problem uh and NP complete uh to figure + + + align:start position:0% +problem uh and NP complete uh to figure +out if there's a certain number uh that + + align:start position:0% +out if there's a certain number uh that + + + align:start position:0% +out if there's a certain number uh that +uh is below a certain value that do do + + align:start position:0% +uh is below a certain value that do do + + + align:start position:0% +uh is below a certain value that do do +the covering uh uh you obviously have an + + align:start position:0% +the covering uh uh you obviously have an + + + align:start position:0% +the covering uh uh you obviously have an +optimization problem associated with + + align:start position:0% +optimization problem associated with + + + align:start position:0% +optimization problem associated with +that and so on and so forth so that's + + align:start position:0% +that and so on and so forth so that's + + + align:start position:0% +that and so on and so forth so that's +our simple setup for our first hard + + align:start position:0% +our simple setup for our first hard + + + align:start position:0% +our simple setup for our first hard +problem right um and so just write that + + align:start position:0% +problem right um and so just write that + + + align:start position:0% +problem right um and so just write that +out find the + + align:start position:0% + + + + align:start position:0% + +subset + + align:start position:0% +subset + + + align:start position:0% +subset +V Prime which is a subset of capital V + + align:start position:0% +V Prime which is a subset of capital V + + + align:start position:0% +V Prime which is a subset of capital V +such that if + + align:start position:0% + + + + align:start position:0% + +UV is an + + align:start position:0% +UV is an + + + align:start position:0% +UV is an +edge of G or belongs to + + align:start position:0% +edge of G or belongs to + + + align:start position:0% +edge of G or belongs to +e + + align:start position:0% + + + + align:start position:0% + +then we have either U belonging to V + + align:start position:0% +then we have either U belonging to V + + + align:start position:0% +then we have either U belonging to V +prime or V belonging to V prime or + + align:start position:0% +prime or V belonging to V prime or + + + align:start position:0% +prime or V belonging to V prime or +both it's quite possible that your + + align:start position:0% +both it's quite possible that your + + + align:start position:0% +both it's quite possible that your +vertex cover is such that for a given + + align:start position:0% +vertex cover is such that for a given + + + align:start position:0% +vertex cover is such that for a given +Edge you have two vertices that touch + + align:start position:0% +Edge you have two vertices that touch + + + align:start position:0% +Edge you have two vertices that touch +each of the end points of the edge and + + align:start position:0% +each of the end points of the edge and + + + align:start position:0% +each of the end points of the edge and +the optimization problem which is what + + align:start position:0% +the optimization problem which is what + + + align:start position:0% +the optimization problem which is what +we'd like to do + + align:start position:0% +we'd like to do + + + align:start position:0% +we'd like to do +here is find a v + + align:start position:0% +here is find a v + + + align:start position:0% +here is find a v +Prime so the + + align:start position:0% +Prime so the + + + align:start position:0% +Prime so the +cardinality is + + align:start position:0% + + + + align:start position:0% + +minimum okay + + align:start position:0% + + + + align:start position:0% + +so that's + + align:start position:0% + + + + align:start position:0% + +it + + align:start position:0% +it + + + align:start position:0% +it +so we don't know of a polinomial Time + + align:start position:0% +so we don't know of a polinomial Time + + + align:start position:0% +so we don't know of a polinomial Time +algorithm to solve this problem so we + + align:start position:0% +algorithm to solve this problem so we + + + align:start position:0% +algorithm to solve this problem so we +resort to + + align:start position:0% +resort to + + + align:start position:0% +resort to +heuristics what is an intuitive + + align:start position:0% +heuristics what is an intuitive + + + align:start position:0% +heuristics what is an intuitive +heuristic for this + + align:start position:0% +heuristic for this + + + align:start position:0% +heuristic for this +problem suppose I wanted to implement a + + align:start position:0% +problem suppose I wanted to implement a + + + align:start position:0% +problem suppose I wanted to implement a +poly + + align:start position:0% +poly + + + align:start position:0% +poly +time greedy algorithm for this problem + + align:start position:0% +time greedy algorithm for this problem + + + align:start position:0% +time greedy algorithm for this problem +what would + + align:start position:0% +what would + + + align:start position:0% +what would +be the first thing that you think + + align:start position:0% +be the first thing that you think + + + align:start position:0% +be the first thing that you think +of yeah go + + align:start position:0% +of yeah go + + + align:start position:0% +of yeah go +ahead find a Max degree I love that + + align:start position:0% +ahead find a Max degree I love that + + + align:start position:0% +ahead find a Max degree I love that +answer it's the wrong answer but for + + align:start position:0% +answer it's the wrong answer but for + + + align:start position:0% +answer it's the wrong answer but for +this problem but I love it because it + + align:start position:0% +this problem but I love it because it + + + align:start position:0% +this problem but I love it because it +sets me up + + align:start position:0% +sets me up + + + align:start position:0% +sets me up +for all this work I did before + + align:start position:0% +for all this work I did before + + + align:start position:0% +for all this work I did before +lecture + + align:start position:0% +lecture + + + align:start position:0% +lecture +okay all right so um it turns out that + + align:start position:0% +okay all right so um it turns out that + + + align:start position:0% +okay all right so um it turns out that +it's not an incorrect answer I it's uh + + align:start position:0% +it's not an incorrect answer I it's uh + + + align:start position:0% +it's not an incorrect answer I it's uh +it's it's really not the best answer in + + align:start position:0% +it's it's really not the best answer in + + + align:start position:0% +it's it's really not the best answer in +terms of theistic you apply to get an + + align:start position:0% +terms of theistic you apply to get an + + + align:start position:0% +terms of theistic you apply to get an +approximation algorithm so we're we're + + align:start position:0% +approximation algorithm so we're we're + + + align:start position:0% +approximation algorithm so we're we're +still in in the context of an + + align:start position:0% +still in in the context of an + + + align:start position:0% +still in in the context of an +approximation algorithm not an + + align:start position:0% +approximation algorithm not an + + + align:start position:0% +approximation algorithm not an +approximation scheme and uh what we have + + align:start position:0% +approximation scheme and uh what we have + + + align:start position:0% +approximation scheme and uh what we have +here is a perfectly fine heuristic that + + align:start position:0% +here is a perfectly fine heuristic that + + + align:start position:0% +here is a perfectly fine heuristic that +you know who knows it might actually + + align:start position:0% +you know who knows it might actually + + + align:start position:0% +you know who knows it might actually +work better in practice than this + + align:start position:0% +work better in practice than this + + + align:start position:0% +work better in practice than this +another approximation algorithm that I'm + + align:start position:0% +another approximation algorithm that I'm + + + align:start position:0% +another approximation algorithm that I'm +going to talk about and prove but the + + align:start position:0% +going to talk about and prove but the + + + align:start position:0% +going to talk about and prove but the +fact of the matter is that this + + align:start position:0% +fact of the matter is that this + + + align:start position:0% +fact of the matter is that this +approximation algorithm that has as a + + align:start position:0% +approximation algorithm that has as a + + + align:start position:0% +approximation algorithm that has as a +heuristic uh picking the maximum degree + + align:start position:0% +heuristic uh picking the maximum degree + + + align:start position:0% +heuristic uh picking the maximum degree +continually and uh completing your + + align:start position:0% +continually and uh completing your + + + align:start position:0% +continually and uh completing your +vertex cover by picking the maximum + + align:start position:0% +vertex cover by picking the maximum + + + align:start position:0% +vertex cover by picking the maximum +degree continually is uh a log n + + align:start position:0% +degree continually is uh a log n + + + align:start position:0% +degree continually is uh a log n +approximation algorithm and what that + + align:start position:0% +approximation algorithm and what that + + + align:start position:0% +approximation algorithm and what that +means is that I can construct and that + + align:start position:0% +means is that I can construct and that + + + align:start position:0% +means is that I can construct and that +example is right up there and a an + + align:start position:0% +example is right up there and a an + + + align:start position:0% +example is right up there and a an +example where um regardless of of what n + + align:start position:0% +example where um regardless of of what n + + + align:start position:0% +example where um regardless of of what n +is U this particularistic the maximum + + align:start position:0% +is U this particularistic the maximum + + + align:start position:0% +is U this particularistic the maximum +degree heuristic might be Logan off from + + align:start position:0% +degree heuristic might be Logan off from + + + align:start position:0% +degree heuristic might be Logan off from +optimal okay whereas this other scheme + + align:start position:0% +optimal okay whereas this other scheme + + + align:start position:0% +optimal okay whereas this other scheme +that we're going to talk about is going + + align:start position:0% +that we're going to talk about is going + + + align:start position:0% +that we're going to talk about is going +to be within a factor two of optimal + + align:start position:0% +to be within a factor two of optimal + + + align:start position:0% +to be within a factor two of optimal +regardless of the input that you apply + + align:start position:0% +regardless of the input that you apply + + + align:start position:0% +regardless of the input that you apply +right so so you have a domination here + + align:start position:0% +right so so you have a domination here + + + align:start position:0% +right so so you have a domination here +with respect to the two approximation + + align:start position:0% +with respect to the two approximation + + + align:start position:0% +with respect to the two approximation +algorithms you got one that is log n row + + align:start position:0% +algorithms you got one that is log n row + + + align:start position:0% +algorithms you got one that is log n row +N is log n as I've defined over there + + align:start position:0% +N is log n as I've defined over there + + + align:start position:0% +N is log n as I've defined over there +and on the other side you got two right + + align:start position:0% +and on the other side you got two right + + + align:start position:0% +and on the other side you got two right +so if you're a theoretician you know + + align:start position:0% +so if you're a theoretician you know + + + align:start position:0% +so if you're a theoretician you know +what you're going to pick right you're + + align:start position:0% +what you're going to pick right you're + + + align:start position:0% +what you're going to pick right you're +going to pick two now it turns out if + + align:start position:0% +going to pick two now it turns out if + + + align:start position:0% +going to pick two now it turns out if +you're a practitioner you might actually + + align:start position:0% +you're a practitioner you might actually + + + align:start position:0% +you're a practitioner you might actually +pick this one right but you know this is + + align:start position:0% +pick this one right but you know this is + + + align:start position:0% +pick this one right but you know this is +a theory course um so what is going on + + align:start position:0% +a theory course um so what is going on + + + align:start position:0% +a theory course um so what is going on +here well this is a concocted example + + align:start position:0% +here well this is a concocted example + + + align:start position:0% +here well this is a concocted example +that shows you that a maximum degree + + align:start position:0% +that shows you that a maximum degree + + + align:start position:0% +that shows you that a maximum degree +heuristic could be as far off as um as + + align:start position:0% +heuristic could be as far off as um as + + + align:start position:0% +heuristic could be as far off as um as +Logan right and so if you look at what's + + align:start position:0% +Logan right and so if you look at what's + + + align:start position:0% +Logan right and so if you look at what's +going on + + align:start position:0% + + + + align:start position:0% + +here um you end + + align:start position:0% +here um you end + + + align:start position:0% +here um you end +up uh with um with with something + + align:start position:0% +up uh with um with with something + + + align:start position:0% +up uh with um with with something +where you have a bunch of vertices up on + + align:start position:0% +where you have a bunch of vertices up on + + + align:start position:0% +where you have a bunch of vertices up on +top okay and uh you you end up + + align:start position:0% +top okay and uh you you end up + + + align:start position:0% +top okay and uh you you end up +with case K factorial vertices up on top + + align:start position:0% +with case K factorial vertices up on top + + + align:start position:0% +with case K factorial vertices up on top +so k equals 3 in this case so I have six + + align:start position:0% +so k equals 3 in this case so I have six + + + align:start position:0% +so k equals 3 in this case so I have six +vertices up there um I got two down here + + align:start position:0% +vertices up there um I got two down here + + + align:start position:0% +vertices up there um I got two down here +because this is 6 divided by three + + align:start position:0% +because this is 6 divided by three + + + align:start position:0% +because this is 6 divided by three +because K is three and then I got six + + align:start position:0% +because K is three and then I got six + + + align:start position:0% +because K is three and then I got six +divided by three here so that's two and + + align:start position:0% +divided by three here so that's two and + + + align:start position:0% +divided by three here so that's two and +six divided by one here and so that's + + align:start position:0% +six divided by one here and so that's + + + align:start position:0% +six divided by one here and so that's +six okay and so these edges are set up + + align:start position:0% +six okay and so these edges are set up + + + align:start position:0% +six okay and so these edges are set up +in such a way that U it's a pathological + + align:start position:0% +in such a way that U it's a pathological + + + align:start position:0% +in such a way that U it's a pathological +example um and I I misspoke in terms of + + align:start position:0% +example um and I I misspoke in terms of + + + align:start position:0% +example um and I I misspoke in terms of +the approximation algorithm I'm I I'll + + align:start position:0% +the approximation algorithm I'm I I'll + + + align:start position:0% +the approximation algorithm I'm I I'll +correct myself in just a second in terms + + align:start position:0% +correct myself in just a second in terms + + + align:start position:0% +correct myself in just a second in terms +of log it does does grow with u uh with + + align:start position:0% +of log it does does grow with u uh with + + + align:start position:0% +of log it does does grow with u uh with +with the size of the graph but I'll + + align:start position:0% +with the size of the graph but I'll + + + align:start position:0% +with the size of the graph but I'll +precisely tell you what this uh + + align:start position:0% +precisely tell you what this uh + + + align:start position:0% +precisely tell you what this uh +approximation algorithm is in terms of + + align:start position:0% +approximation algorithm is in terms of + + + align:start position:0% +approximation algorithm is in terms of +the row and factor in just a minute but + + align:start position:0% +the row and factor in just a minute but + + + align:start position:0% +the row and factor in just a minute but +let's just take a look at um this + + align:start position:0% +let's just take a look at um this + + + align:start position:0% +let's just take a look at um this +problem here and see what happens when + + align:start position:0% +problem here and see what happens when + + + align:start position:0% +problem here and see what happens when +you apply this maximum degree heuristic + + align:start position:0% +you apply this maximum degree heuristic + + + align:start position:0% +you apply this maximum degree heuristic +right and we have to take into account + + align:start position:0% +right and we have to take into account + + + align:start position:0% +right and we have to take into account +the fact that if you have ties in terms + + align:start position:0% +the fact that if you have ties in terms + + + align:start position:0% +the fact that if you have ties in terms +of Maximum degree you may end up doing + + align:start position:0% +of Maximum degree you may end up doing + + + align:start position:0% +of Maximum degree you may end up doing +the wrong thing because you haven't + + align:start position:0% +the wrong thing because you haven't + + + align:start position:0% +the wrong thing because you haven't +defined what the tiebreak is when you + + align:start position:0% +defined what the tiebreak is when you + + + align:start position:0% +defined what the tiebreak is when you +have two noes that have the same degree + + align:start position:0% +have two noes that have the same degree + + + align:start position:0% +have two noes that have the same degree +you could do the wrong thing and pick + + align:start position:0% +you could do the wrong thing and pick + + + align:start position:0% +you could do the wrong thing and pick +the bad node for this particular problem + + align:start position:0% +the bad node for this particular problem + + + align:start position:0% +the bad node for this particular problem +right you have to do a verse case + + align:start position:0% +right you have to do a verse case + + + align:start position:0% +right you have to do a verse case +analysis right so um in the worst case + + align:start position:0% +analysis right so um in the worst case + + + align:start position:0% +analysis right so um in the worst case +when you create a Vertex cover using + + align:start position:0% +when you create a Vertex cover using + + + align:start position:0% +when you create a Vertex cover using +maximum degree what is the worst case in + + align:start position:0% +maximum degree what is the worst case in + + + align:start position:0% +maximum degree what is the worst case in +terms of the number of vertices that we + + align:start position:0% +terms of the number of vertices that we + + + align:start position:0% +terms of the number of vertices that we +pick for this particular + + align:start position:0% +pick for this particular + + + align:start position:0% +pick for this particular +example so what is the worst case in + + align:start position:0% +example so what is the worst case in + + + align:start position:0% +example so what is the worst case in +terms of the number of vertices yeah + + align:start position:0% +terms of the number of vertices yeah + + + align:start position:0% +terms of the number of vertices yeah +back there 11 11 and where did you get + + align:start position:0% +back there 11 11 and where did you get + + + align:start position:0% +back there 11 11 and where did you get +that from + + align:start position:0% +that from + + + align:start position:0% +that from +all the bot you grab all of the ones on + + align:start position:0% +all the bot you grab all of the ones on + + + align:start position:0% +all the bot you grab all of the ones on +the bottom fantastic right there you go + + align:start position:0% +the bottom fantastic right there you go + + + align:start position:0% +the bottom fantastic right there you go +could you uh stand + + align:start position:0% +could you uh stand + + + align:start position:0% +could you uh stand +up yeah whoa all + + align:start position:0% +up yeah whoa all + + + align:start position:0% +up yeah whoa all +right it was the dentist + + align:start position:0% +right it was the dentist + + + align:start position:0% +right it was the dentist +yesterday um + + align:start position:0% +yesterday um + + + align:start position:0% +yesterday um +so uh that's exactly right that's + + align:start position:0% +so uh that's exactly right that's + + + align:start position:0% +so uh that's exactly right that's +exactly right so what could happen + + align:start position:0% +exactly right so what could happen + + + align:start position:0% +exactly right so what could happen +is you could pick this because that's + + align:start position:0% +is you could pick this because that's + + + align:start position:0% +is you could pick this because that's +degree three notice that the maximum + + align:start position:0% +degree three notice that the maximum + + + align:start position:0% +degree three notice that the maximum +degree here is three of of any note + + align:start position:0% +degree here is three of of any note + + + align:start position:0% +degree here is three of of any note +right so if I pick something of degree + + align:start position:0% +right so if I pick something of degree + + + align:start position:0% +right so if I pick something of degree +three I'm good I'm in keeping with my + + align:start position:0% +three I'm good I'm in keeping with my + + + align:start position:0% +three I'm good I'm in keeping with my +heris um I could pick all the ones at + + align:start position:0% +heris um I could pick all the ones at + + + align:start position:0% +heris um I could pick all the ones at +the top right and then I'm done right + + align:start position:0% +the top right and then I'm done right + + + align:start position:0% +the top right and then I'm done right +that's + + align:start position:0% +that's + + + align:start position:0% +that's +good uh that's a good uh Solution that's + + align:start position:0% +good uh that's a good uh Solution that's + + + align:start position:0% +good uh that's a good uh Solution that's +a a good trajectory but all I've said is + + align:start position:0% +a a good trajectory but all I've said is + + + align:start position:0% +a a good trajectory but all I've said is +theistic is maximum degree so there's + + align:start position:0% +theistic is maximum degree so there's + + + align:start position:0% +theistic is maximum degree so there's +nothing that's stopping me from picking + + align:start position:0% +nothing that's stopping me from picking + + + align:start position:0% +nothing that's stopping me from picking +this and then once I pick that I could + + align:start position:0% +this and then once I pick that I could + + + align:start position:0% +this and then once I pick that I could +pick this one and then I'm down to once + + align:start position:0% +pick this one and then I'm down to once + + + align:start position:0% +pick this one and then I'm down to once +I've taken away these two remember that + + align:start position:0% +I've taken away these two remember that + + + align:start position:0% +I've taken away these two remember that +now the maximum degree in the entire + + align:start position:0% +now the maximum degree in the entire + + + align:start position:0% +now the maximum degree in the entire +graph is two right because I've each of + + align:start position:0% +graph is two right because I've each of + + + align:start position:0% +graph is two right because I've each of +these things is losing a degree losing + + align:start position:0% +these things is losing a degree losing + + + align:start position:0% +these things is losing a degree losing +one from its degree as I go along so + + align:start position:0% +one from its degree as I go along so + + + align:start position:0% +one from its degree as I go along so +then I could pick this one this one this + + align:start position:0% +then I could pick this one this one this + + + align:start position:0% +then I could pick this one this one this +one Etc and so I could end up with 11 + + align:start position:0% +one Etc and so I could end up with 11 + + + align:start position:0% +one Etc and so I could end up with 11 +okay so if you go do the do the math + + align:start position:0% +okay so if you go do the do the math + + + align:start position:0% +okay so if you go do the do the math +really quickly and this is where I'll + + align:start position:0% +really quickly and this is where I'll + + + align:start position:0% +really quickly and this is where I'll +I'll I'll correct uh what I said before + + align:start position:0% +I'll I'll correct uh what I said before + + + align:start position:0% +I'll I'll correct uh what I said before +um the + + align:start position:0% +um the + + + align:start position:0% +um the +algo could + + align:start position:0% + + + + align:start position:0% + +pick all the bottom + + align:start position:0% + + + + align:start position:0% + +vertices and so the + + align:start position:0% +vertices and so the + + + align:start position:0% +vertices and so the +solution uh and the top vertices are + + align:start position:0% +solution uh and the top vertices are + + + align:start position:0% +solution uh and the top vertices are +optimal top + + align:start position:0% +optimal top + + + align:start position:0% +optimal top +optimal so that's K factorial right + + align:start position:0% +optimal so that's K factorial right + + + align:start position:0% +optimal so that's K factorial right +according to + + align:start position:0% +according to + + + align:start position:0% +according to +my parameterized graph that's K + + align:start position:0% +my parameterized graph that's K + + + align:start position:0% +my parameterized graph that's K +factorial in terms of the optimal + + align:start position:0% +factorial in terms of the optimal + + + align:start position:0% +factorial in terms of the optimal +solution for this graph but if I pick + + align:start position:0% +solution for this graph but if I pick + + + align:start position:0% +solution for this graph but if I pick +the ones that are uh that are at the + + align:start position:0% +the ones that are uh that are at the + + + align:start position:0% +the ones that are uh that are at the +bottom then it's K factorial divid 1 / k + + align:start position:0% +bottom then it's K factorial divid 1 / k + + + align:start position:0% +bottom then it's K factorial divid 1 / k ++ 1 / K - 1 plus da d d da + 1 which is + + align:start position:0% ++ 1 / K - 1 plus da d d da + 1 which is + + + align:start position:0% ++ 1 / K - 1 plus da d d da + 1 which is +our harmonic number and that's + + align:start position:0% +our harmonic number and that's + + + align:start position:0% +our harmonic number and that's +approximately K factorial log + + align:start position:0% +approximately K factorial log + + + align:start position:0% +approximately K factorial log +K okay and and this is where I misspoke + + align:start position:0% +K okay and and this is where I misspoke + + + align:start position:0% +K okay and and this is where I misspoke +I kept saying log n log n but that's not + + align:start position:0% +I kept saying log n log n but that's not + + + align:start position:0% +I kept saying log n log n but that's not +completely correct because um if I think + + align:start position:0% +completely correct because um if I think + + + align:start position:0% +completely correct because um if I think +of n as being the size of the input uh K + + align:start position:0% +of n as being the size of the input uh K + + + align:start position:0% +of n as being the size of the input uh K +factorial is n right um and so if you + + align:start position:0% +factorial is n right um and so if you + + + align:start position:0% +factorial is n right um and so if you +see that I have log K + + align:start position:0% +see that I have log K + + + align:start position:0% +see that I have log K +here uh then um remember that um this is + + align:start position:0% +here uh then um remember that um this is + + + align:start position:0% +here uh then um remember that um this is +log K where where K factorial equals n + + align:start position:0% +log K where where K factorial equals n + + + align:start position:0% +log K where where K factorial equals n +so there's another log Factor roughly + + align:start position:0% +so there's another log Factor roughly + + + align:start position:0% +so there's another log Factor roughly +speaking right so think of it + + align:start position:0% +speaking right so think of it + + + align:start position:0% +speaking right so think of it +approximately as log log n approximation + + align:start position:0% +approximately as log log n approximation + + + align:start position:0% +approximately as log log n approximation +okay so which is pretty good but it does + + align:start position:0% +okay so which is pretty good but it does + + + align:start position:0% +okay so which is pretty good but it does +grow with n right the point is this does + + align:start position:0% +grow with n right the point is this does + + + align:start position:0% +grow with n right the point is this does +grow with n so it's not the best + + align:start position:0% +grow with n so it's not the best + + + align:start position:0% +grow with n so it's not the best +approximation scheme that you can think + + align:start position:0% +approximation scheme that you can think + + + align:start position:0% +approximation scheme that you can think +of + + align:start position:0% +of + + + align:start position:0% +of +uh because uh the approximation Factor + + align:start position:0% +uh because uh the approximation Factor + + + align:start position:0% +uh because uh the approximation Factor +grows with the size of your problem so + + align:start position:0% +grows with the size of your problem so + + + align:start position:0% +grows with the size of your problem so +it'd be great if we could come up with a + + align:start position:0% +it'd be great if we could come up with a + + + align:start position:0% +it'd be great if we could come up with a +constant Factor approximation scheme + + align:start position:0% +constant Factor approximation scheme + + + align:start position:0% +constant Factor approximation scheme +that would beat this one certainly from + + align:start position:0% +that would beat this one certainly from + + + align:start position:0% +that would beat this one certainly from +a theoretical standpoint right but this + + align:start position:0% +a theoretical standpoint right but this + + + align:start position:0% +a theoretical standpoint right but this +one maximum degree chances are if you're + + align:start position:0% +one maximum degree chances are if you're + + + align:start position:0% +one maximum degree chances are if you're +a practitioner this is what you you'd + + align:start position:0% +a practitioner this is what you you'd + + + align:start position:0% +a practitioner this is what you you'd +code not the one I'm going to describe + + align:start position:0% +code not the one I'm going to describe + + + align:start position:0% +code not the one I'm going to describe +okay but we're going to analyze the one + + align:start position:0% +okay but we're going to analyze the one + + + align:start position:0% +okay but we're going to analyze the one +I've described I've just shown you that + + align:start position:0% +I've described I've just shown you that + + + align:start position:0% +I've described I've just shown you that +there is an example where uh you have + + align:start position:0% +there is an example where uh you have + + + align:start position:0% +there is an example where uh you have +this log K Factor but we haven't done a + + align:start position:0% +this log K Factor but we haven't done a + + + align:start position:0% +this log K Factor but we haven't done a +proof of the fact that there's no worse + + align:start position:0% +proof of the fact that there's no worse + + + align:start position:0% +proof of the fact that there's no worse +example than this one okay so I'm just + + align:start position:0% +example than this one okay so I'm just + + + align:start position:0% +example than this one okay so I'm just +claiming at this point that uh this is + + align:start position:0% +claiming at this point that uh this is + + + align:start position:0% +claiming at this point that uh this is +at + + align:start position:0% +at + + + align:start position:0% +at +best a a log K approximation algorithm + + align:start position:0% +best a a log K approximation algorithm + + + align:start position:0% +best a a log K approximation algorithm +we haven't actually shown that it is in + + align:start position:0% +we haven't actually shown that it is in + + + align:start position:0% +we haven't actually shown that it is in +fact a log K approximation algorithm at + + align:start position:0% +fact a log K approximation algorithm at + + + align:start position:0% +fact a log K approximation algorithm at +best it's that okay uh any + + align:start position:0% + + + + align:start position:0% + +questions all right so what's another + + align:start position:0% +questions all right so what's another + + + align:start position:0% +questions all right so what's another +heris what's uh what's another heuristic + + align:start position:0% +heris what's uh what's another heuristic + + + align:start position:0% +heris what's uh what's another heuristic +for uh doing vertex + + align:start position:0% +for uh doing vertex + + + align:start position:0% +for uh doing vertex +cover we did this uh picking the maximum + + align:start position:0% +cover we did this uh picking the maximum + + + align:start position:0% +cover we did this uh picking the maximum +degree nice and + + align:start position:0% +degree nice and + + + align:start position:0% +degree nice and +simple but didn't quite work out for + + align:start position:0% + + + + align:start position:0% + +us any other + + align:start position:0% + + + + align:start position:0% + +ideas so I picked vertices what else + + align:start position:0% +ideas so I picked vertices what else + + + align:start position:0% +ideas so I picked vertices what else +could I + + align:start position:0% +could I + + + align:start position:0% +could I +pick I could pick edges right so I could + + align:start position:0% +pick I could pick edges right so I could + + + align:start position:0% +pick I could pick edges right so I could +pick I could pick random + + align:start position:0% +pick I could pick random + + + align:start position:0% +pick I could pick random +edges it turns out that actually works + + align:start position:0% +edges it turns out that actually works + + + align:start position:0% +edges it turns out that actually works +better from a theoretical standpoint + + align:start position:0% + + + + align:start position:0% + +uh so what we're going to do here is + + align:start position:0% +uh so what we're going to do here is + + + align:start position:0% +uh so what we're going to do here is +simply uh set the + + align:start position:0% +simply uh set the + + + align:start position:0% +simply uh set the +cover to be null go ahead and set all of + + align:start position:0% +cover to be null go ahead and set all of + + + align:start position:0% +cover to be null go ahead and set all of +the edges to be e Prime and then we're + + align:start position:0% +the edges to be e Prime and then we're + + + align:start position:0% +the edges to be e Prime and then we're +going to + + align:start position:0% +going to + + + align:start position:0% +going to +iterate over these + + align:start position:0% + + + + align:start position:0% + +edges I'm not even specifying the way + + align:start position:0% +edges I'm not even specifying the way + + + align:start position:0% +edges I'm not even specifying the way +I'm going to select these edges and I + + align:start position:0% +I'm going to select these edges and I + + + align:start position:0% +I'm going to select these edges and I +still will be able to do a proof of two + + align:start position:0% +still will be able to do a proof of two + + + align:start position:0% +still will be able to do a proof of two +approximation okay + + align:start position:0% + + + + align:start position:0% + +oh I forgot the best + + align:start position:0% +oh I forgot the best + + + align:start position:0% +oh I forgot the best +part this is on your + + align:start position:0% +part this is on your + + + align:start position:0% +part this is on your +quiz right that was the tangible benefit + + align:start position:0% +quiz right that was the tangible benefit + + + align:start position:0% +quiz right that was the tangible benefit +of attending the + + align:start position:0% +of attending the + + + align:start position:0% +of attending the +lecture so copy that + + align:start position:0% + + + + align:start position:0% + +down so this is very simple it's it's + + align:start position:0% +down so this is very simple it's it's + + + align:start position:0% +down so this is very simple it's it's +it's it's not a a complicated uh problem + + align:start position:0% +it's it's not a a complicated uh problem + + + align:start position:0% +it's it's not a a complicated uh problem +there's there's uh not simple heris that + + align:start position:0% +there's there's uh not simple heris that + + + align:start position:0% +there's there's uh not simple heris that +are going to be particularly complicated + + align:start position:0% +are going to be particularly complicated + + + align:start position:0% +are going to be particularly complicated +uh you just do some selections and then + + align:start position:0% +uh you just do some selections and then + + + align:start position:0% +uh you just do some selections and then +you iterate over the graph and you take + + align:start position:0% +you iterate over the graph and you take + + + align:start position:0% +you iterate over the graph and you take +away stuff from the graph typically you + + align:start position:0% +away stuff from the graph typically you + + + align:start position:0% +away stuff from the graph typically you +take away vertices as well as edges and + + align:start position:0% +take away vertices as well as edges and + + + align:start position:0% +take away vertices as well as edges and +uh you keep going until you got nothing + + align:start position:0% +uh you keep going until you got nothing + + + align:start position:0% +uh you keep going until you got nothing +left right and then you look at your + + align:start position:0% +left right and then you look at your + + + align:start position:0% +left right and then you look at your +cover and you say what is the size of my + + align:start position:0% +cover and you say what is the size of my + + + align:start position:0% +cover and you say what is the size of my +cover + + align:start position:0% + + + + align:start position:0% + +and here we + + align:start position:0% + + + + align:start position:0% + +return C all right so I won't spend any + + align:start position:0% +return C all right so I won't spend any + + + align:start position:0% +return C all right so I won't spend any +time on that uh you can read it it's a + + align:start position:0% +time on that uh you can read it it's a + + + align:start position:0% +time on that uh you can read it it's a +simple iterative + + align:start position:0% +simple iterative + + + align:start position:0% +simple iterative +algorithm uh that picks edges uh + + align:start position:0% +algorithm uh that picks edges uh + + + align:start position:0% +algorithm uh that picks edges uh +randomly and keeps going okay + + align:start position:0% +randomly and keeps going okay + + + align:start position:0% +randomly and keeps going okay +so now comes the fun part which is we + + align:start position:0% +so now comes the fun part which is we + + + align:start position:0% +so now comes the fun part which is we +need to show that + + align:start position:0% +need to show that + + + align:start position:0% +need to show that +that little + + align:start position:0% +that little + + + align:start position:0% +that little +algorithm is always going to + + align:start position:0% +algorithm is always going to + + + align:start position:0% +algorithm is always going to +be within a factor of two of optimal + + align:start position:0% +be within a factor of two of optimal + + + align:start position:0% +be within a factor of two of optimal +okay and you can play around with this + + align:start position:0% +okay and you can play around with this + + + align:start position:0% +okay and you can play around with this +example and as in fact in this case you + + align:start position:0% +example and as in fact in this case you + + + align:start position:0% +example and as in fact in this case you +have six and 11 so that's a factor of + + align:start position:0% +have six and 11 so that's a factor of + + + align:start position:0% +have six and 11 so that's a factor of +two of course uh so even this algorithm + + align:start position:0% +two of course uh so even this algorithm + + + align:start position:0% +two of course uh so even this algorithm +is better than a factor of two but it + + align:start position:0% +is better than a factor of two but it + + + align:start position:0% +is better than a factor of two but it +won't be if I expanded the graph and + + align:start position:0% +won't be if I expanded the graph and + + + align:start position:0% +won't be if I expanded the graph and +increased K but that algorithm that I + + align:start position:0% +increased K but that algorithm that I + + + align:start position:0% +increased K but that algorithm that I +have up there is always going to be + + align:start position:0% +have up there is always going to be + + + align:start position:0% +have up there is always going to be +within a factor two and we want to prove + + align:start position:0% +within a factor two and we want to prove + + + align:start position:0% +within a factor two and we want to prove +that all + + align:start position:0% +that all + + + align:start position:0% +that all +right um so how do we go about uh + + align:start position:0% +right um so how do we go about uh + + + align:start position:0% +right um so how do we go about uh +proving + + align:start position:0% +proving + + + align:start position:0% +proving +that + + align:start position:0% +that + + + align:start position:0% +that +uh we want to prove in particular + + align:start position:0% +uh we want to prove in particular + + + align:start position:0% +uh we want to prove in particular +that approx vertex + + align:start position:0% + + + + align:start position:0% + +cover is a two + + align:start position:0% + + + + align:start position:0% + +approximation + + align:start position:0% + + + + align:start position:0% + +algorithm right + + align:start position:0% +algorithm right + + + align:start position:0% +algorithm right +um so any + + align:start position:0% +um so any + + + align:start position:0% +um so any +ideas how do I prove something like + + align:start position:0% + + + + align:start position:0% + +this where do you think this Factor two + + align:start position:0% +this where do you think this Factor two + + + align:start position:0% +this where do you think this Factor two +comes + + align:start position:0% +comes + + + align:start position:0% +comes +from right someone who hasn't answered + + align:start position:0% + + + + align:start position:0% + +yet you answered a lot of questions in + + align:start position:0% +yet you answered a lot of questions in + + + align:start position:0% +yet you answered a lot of questions in +the + + align:start position:0% +the + + + align:start position:0% +the +past + + align:start position:0% +past + + + align:start position:0% +past +right no + + align:start position:0% +right no + + + align:start position:0% +right no +someone all + + align:start position:0% + + + + align:start position:0% + +right I'm sorry the edges you pick not + + align:start position:0% +right I'm sorry the edges you pick not + + + align:start position:0% +right I'm sorry the edges you pick not +intersect that's an excellent + + align:start position:0% +intersect that's an excellent + + + align:start position:0% +intersect that's an excellent +observation the the observation is that + + align:start position:0% +observation the the observation is that + + + align:start position:0% +observation the the observation is that +the + + align:start position:0% +the + + + align:start position:0% +the +edges we pick do not intersect each + + align:start position:0% +edges we pick do not intersect each + + + align:start position:0% +edges we pick do not intersect each +other so I gave you a Frisbee for kind + + align:start position:0% +other so I gave you a Frisbee for kind + + + align:start position:0% +other so I gave you a Frisbee for kind +of the wrong answer so for this correct + + align:start position:0% +of the wrong answer so for this correct + + + align:start position:0% +of the wrong answer so for this correct +one I won't give you one that's fair + + align:start position:0% +one I won't give you one that's fair + + + align:start position:0% +one I won't give you one that's fair +right no that's that's unfair right + + align:start position:0% +right no that's that's unfair right + + + align:start position:0% +right no that's that's unfair right +there you go + + align:start position:0% +there you go + + + align:start position:0% +there you go +sorry um so the the key observation was + + align:start position:0% +sorry um so the the key observation was + + + align:start position:0% +sorry um so the the key observation was +in this algorithm + + align:start position:0% +in this algorithm + + + align:start position:0% +in this algorithm +I'm going to be picking edges and the + + align:start position:0% +I'm going to be picking edges and the + + + align:start position:0% +I'm going to be picking edges and the +edges will not share + + align:start position:0% +edges will not share + + + align:start position:0% +edges will not share +vertices right because I delete the + + align:start position:0% +vertices right because I delete the + + + align:start position:0% +vertices right because I delete the +vertices once I've picked an edge + + align:start position:0% +vertices once I've picked an edge + + + align:start position:0% +vertices once I've picked an edge +correct so there's no way that the edges + + align:start position:0% +correct so there's no way that the edges + + + align:start position:0% +correct so there's no way that the edges +would share vertices so what does that + + align:start position:0% +would share vertices so what does that + + + align:start position:0% +would share vertices so what does that +mean well that means + + align:start position:0% +mean well that means + + + align:start position:0% +mean well that means +that um I'm getting let's say I + + align:start position:0% +that um I'm getting let's say I + + + align:start position:0% +that um I'm getting let's say I +get a edges so let a denote + + align:start position:0% + + + + align:start position:0% + +the edges that are + + align:start position:0% + + + + align:start position:0% + +picked so I'm going to get edges that + + align:start position:0% +picked so I'm going to get edges that + + + align:start position:0% +picked so I'm going to get edges that +look like + + align:start position:0% +look like + + + align:start position:0% +look like +that okay and I got cality of a edges I + + align:start position:0% +that okay and I got cality of a edges I + + + align:start position:0% +that okay and I got cality of a edges I +know that in my vertex + + align:start position:0% +know that in my vertex + + + align:start position:0% +know that in my vertex +cover that obviously I have to I have to + + align:start position:0% +cover that obviously I have to I have to + + + align:start position:0% +cover that obviously I have to I have to +pick vertices that cover all the edges + + align:start position:0% +pick vertices that cover all the edges + + + align:start position:0% +pick vertices that cover all the edges +now I'm picking edges and what's + + align:start position:0% +now I'm picking edges and what's + + + align:start position:0% +now I'm picking edges and what's +happening of course is that I'm picking + + align:start position:0% +happening of course is that I'm picking + + + align:start position:0% +happening of course is that I'm picking +two a + + align:start position:0% + + + + align:start position:0% + +vertices so my + + align:start position:0% +vertices so my + + + align:start position:0% +vertices so my +C remember my cost was C and I had C opt + + align:start position:0% +C remember my cost was C and I had C opt + + + align:start position:0% +C remember my cost was C and I had C opt +that corresponds to the optimum cost and + + align:start position:0% +that corresponds to the optimum cost and + + + align:start position:0% +that corresponds to the optimum cost and +so the cost that this algorithm produces + + align:start position:0% +so the cost that this algorithm produces + + + align:start position:0% +so the cost that this algorithm produces +is 2 * a right Mak sense because I'm + + align:start position:0% +is 2 * a right Mak sense because I'm + + + align:start position:0% +is 2 * a right Mak sense because I'm +picking vertices V are picking edges + + align:start position:0% +picking vertices V are picking edges + + + align:start position:0% +picking vertices V are picking edges +there's no um overlap and therefore the + + align:start position:0% +there's no um overlap and therefore the + + + align:start position:0% +there's no um overlap and therefore the +cost is is 2 * a right so as long as I + + align:start position:0% +cost is is 2 * a right so as long as I + + + align:start position:0% +cost is is 2 * a right so as long as I +can now say that copt which is the + + align:start position:0% +can now say that copt which is the + + + align:start position:0% +can now say that copt which is the +optimum is less than or equal to a right + + align:start position:0% +optimum is less than or equal to a right + + + align:start position:0% +optimum is less than or equal to a right +I have my Factor two approximation + + align:start position:0% +I have my Factor two approximation + + + align:start position:0% +I have my Factor two approximation +algorithm right so that's it it's a it's + + align:start position:0% +algorithm right so that's it it's a it's + + + align:start position:0% +algorithm right so that's it it's a it's +a simple argument that says now + + align:start position:0% + + + + align:start position:0% + +show that + + align:start position:0% + + + + align:start position:0% + +copt + + align:start position:0% +copt + + + align:start position:0% +copt +is at least a um cop I'm minimizing cop + + align:start position:0% +is at least a um cop I'm minimizing cop + + + align:start position:0% +is at least a um cop I'm minimizing cop +should be at least a right uh I hope I + + align:start position:0% +should be at least a right uh I hope I + + + align:start position:0% +should be at least a right uh I hope I +said that right before but I wrote that + + align:start position:0% +said that right before but I wrote that + + + align:start position:0% +said that right before but I wrote that +down here correctly so if I say that + + align:start position:0% +down here correctly so if I say that + + + align:start position:0% +down here correctly so if I say that +copt is at least a then I got my I got + + align:start position:0% +copt is at least a then I got my I got + + + align:start position:0% +copt is at least a then I got my I got +my proof here of two approximation + + align:start position:0% +my proof here of two approximation + + + align:start position:0% +my proof here of two approximation +because I'm getting 2 a back right so if + + align:start position:0% +because I'm getting 2 a back right so if + + + align:start position:0% +because I'm getting 2 a back right so if +you go look at C divided by so this + + align:start position:0% +you go look at C divided by so this + + + align:start position:0% +you go look at C divided by so this +means of course that um uh C is um less + + align:start position:0% +means of course that um uh C is um less + + + align:start position:0% +means of course that um uh C is um less +than or equal to two copt if I can show + + align:start position:0% +than or equal to two copt if I can show + + + align:start position:0% +than or equal to two copt if I can show +uh make that statement and and it turns + + align:start position:0% +uh make that statement and and it turns + + + align:start position:0% +uh make that statement and and it turns +out that's uh a fairly easy statement to + + align:start position:0% +out that's uh a fairly easy statement to + + + align:start position:0% +out that's uh a fairly easy statement to +argue uh simply because of the + + align:start position:0% +argue uh simply because of the + + + align:start position:0% +argue uh simply because of the +definition of vertex cover um remember + + align:start position:0% +definition of vertex cover um remember + + + align:start position:0% +definition of vertex cover um remember +that um I'm going to have to cover every + + align:start position:0% +that um I'm going to have to cover every + + + align:start position:0% +that um I'm going to have to cover every +Edge correct so I'm going to cover need + + align:start position:0% +Edge correct so I'm going to cover need + + + align:start position:0% +Edge correct so I'm going to cover need +to + + align:start position:0% + + + + align:start position:0% + +cover every Edge + + align:start position:0% + + + + align:start position:0% + +including all edges in + + align:start position:0% + + + + align:start position:0% + +a a is a subset of edges I have to cover + + align:start position:0% +a a is a subset of edges I have to cover + + + align:start position:0% +a a is a subset of edges I have to cover +all the edges clearly I have to cover + + align:start position:0% +all the edges clearly I have to cover + + + align:start position:0% +all the edges clearly I have to cover +the a edges which are a subset of all of + + align:start position:0% +the a edges which are a subset of all of + + + align:start position:0% +the a edges which are a subset of all of +the edges right how am I going to cover + + align:start position:0% +the edges right how am I going to cover + + + align:start position:0% +the edges right how am I going to cover +all of the a edges that happen to all be + + align:start position:0% +all of the a edges that happen to all be + + + align:start position:0% +all of the a edges that happen to all be +disjoint in terms of their vertices I'm + + align:start position:0% +disjoint in terms of their vertices I'm + + + align:start position:0% +disjoint in terms of their vertices I'm +going to have to pick one vertex for + + align:start position:0% +going to have to pick one vertex for + + + align:start position:0% +going to have to pick one vertex for +each of these edges right I mean I could + + align:start position:0% +each of these edges right I mean I could + + + align:start position:0% +each of these edges right I mean I could +pick this one or that one but I have to + + align:start position:0% +pick this one or that one but I have to + + + align:start position:0% +pick this one or that one but I have to +pick one of them I could pick this one + + align:start position:0% +pick one of them I could pick this one + + + align:start position:0% +pick one of them I could pick this one +or that + + align:start position:0% +or that + + + align:start position:0% +or that +one and so on and so forth right so it + + align:start position:0% +one and so on and so forth right so it + + + align:start position:0% +one and so on and so forth right so it +is clear that given this + + align:start position:0% +is clear that given this + + + align:start position:0% +is clear that given this +disjoint collection of edges + + align:start position:0% +disjoint collection of edges + + + align:start position:0% +disjoint collection of edges +corresponding to a that c opt is greater + + align:start position:0% +corresponding to a that c opt is greater + + + align:start position:0% +corresponding to a that c opt is greater +than or equal to a okay and and that's + + align:start position:0% +than or equal to a okay and and that's + + + align:start position:0% +than or equal to a okay and and that's +it so I had to cover all this + + align:start position:0% +it so I had to cover all this + + + align:start position:0% +it so I had to cover all this +requires since uh + + align:start position:0% + + + + align:start position:0% + +no two edges share an end point this + + align:start position:0% +no two edges share an end point this + + + align:start position:0% +no two edges share an end point this +means that need to + + align:start position:0% +means that need to + + + align:start position:0% +means that need to +pick a different + + align:start position:0% + + + + align:start position:0% + +vertex from each Edge in + + align:start position:0% + + + + align:start position:0% + +a and that + + align:start position:0% + + + + align:start position:0% + +implies that c opt is greater than or + + align:start position:0% +implies that c opt is greater than or + + + align:start position:0% +implies that c opt is greater than or +equal to a all right any questions about + + align:start position:0% +equal to a all right any questions about + + + align:start position:0% +equal to a all right any questions about +that we all good here yep understood the + + align:start position:0% +that we all good here yep understood the + + + align:start position:0% +that we all good here yep understood the +proof so that's our first uh + + align:start position:0% +proof so that's our first uh + + + align:start position:0% +proof so that's our first uh +approximation algorithm where we + + align:start position:0% +approximation algorithm where we + + + align:start position:0% +approximation algorithm where we +actually had a + + align:start position:0% +actually had a + + + align:start position:0% +actually had a +proof and so this is kind of cool it was + + align:start position:0% +proof and so this is kind of cool it was + + + align:start position:0% +proof and so this is kind of cool it was +obviously a pretty simple algorithm + + align:start position:0% +obviously a pretty simple algorithm + + + align:start position:0% +obviously a pretty simple algorithm +you're guaranteed to be within a factor + + align:start position:0% +you're guaranteed to be within a factor + + + align:start position:0% +you're guaranteed to be within a factor +two um doesn't mean that that's the best + + align:start position:0% +two um doesn't mean that that's the best + + + align:start position:0% +two um doesn't mean that that's the best +juristic you can come up with um doesn't + + align:start position:0% +juristic you can come up with um doesn't + + + align:start position:0% +juristic you can come up with um doesn't +mean uh that um this is what you you'd + + align:start position:0% +mean uh that um this is what you you'd + + + align:start position:0% +mean uh that um this is what you you'd +code uh but uh this is the best + + align:start position:0% +code uh but uh this is the best + + + align:start position:0% +code uh but uh this is the best +approximation algorithm uh that uh we're + + align:start position:0% +approximation algorithm uh that uh we're + + + align:start position:0% +approximation algorithm uh that uh we're +going to cover for vertex cover okay um + + align:start position:0% +going to cover for vertex cover okay um + + + align:start position:0% +going to cover for vertex cover okay um +so what about other problems what's the + + align:start position:0% +so what about other problems what's the + + + align:start position:0% +so what about other problems what's the +state of the world with respect to + + align:start position:0% +state of the world with respect to + + + align:start position:0% +state of the world with respect to +approximation there's lots of uh NP + + align:start position:0% +approximation there's lots of uh NP + + + align:start position:0% +approximation there's lots of uh NP +complete and NP hard problems for which + + align:start position:0% +complete and NP hard problems for which + + + align:start position:0% +complete and NP hard problems for which +we know approximation schemes and we + + align:start position:0% +we know approximation schemes and we + + + align:start position:0% +we know approximation schemes and we +like to move towards approximation + + align:start position:0% +like to move towards approximation + + + align:start position:0% +like to move towards approximation +schemes slowly but I'd like to look at a + + align:start position:0% +schemes slowly but I'd like to look at a + + + align:start position:0% +schemes slowly but I'd like to look at a +problem that perhaps is a little more + + align:start position:0% +problem that perhaps is a little more + + + align:start position:0% +problem that perhaps is a little more +compelling than vertex cover before we + + align:start position:0% +compelling than vertex cover before we + + + align:start position:0% +compelling than vertex cover before we +get to approximation schemes and that's + + align:start position:0% +get to approximation schemes and that's + + + align:start position:0% +get to approximation schemes and that's +what's called set + + align:start position:0% + + + + align:start position:0% + +cover so set + + align:start position:0% +cover so set + + + align:start position:0% +cover so set +cover tries to cover a set with + + align:start position:0% +cover tries to cover a set with + + + align:start position:0% +cover tries to cover a set with +subsets and it's very useful in + + align:start position:0% +subsets and it's very useful in + + + align:start position:0% +subsets and it's very useful in +optimization + + align:start position:0% + + + + align:start position:0% + +where you have overlapping + + align:start position:0% +where you have overlapping + + + align:start position:0% +where you have overlapping +sets maybe it's schedules it's tasks + + align:start position:0% +sets maybe it's schedules it's tasks + + + align:start position:0% +sets maybe it's schedules it's tasks +it's uh uh people getting invited to + + align:start position:0% +it's uh uh people getting invited to + + + align:start position:0% +it's uh uh people getting invited to +dinner Etc and you want to make sure + + align:start position:0% +dinner Etc and you want to make sure + + + align:start position:0% +dinner Etc and you want to make sure +everybody gets invited you want to + + align:start position:0% +everybody gets invited you want to + + + align:start position:0% +everybody gets invited you want to +invite + + align:start position:0% +invite + + + align:start position:0% +invite +families and there's overlapping + + align:start position:0% +families and there's overlapping + + + align:start position:0% +families and there's overlapping +families because people have + + align:start position:0% +families because people have + + + align:start position:0% +families because people have +relationships and uh you want to uh + + align:start position:0% +relationships and uh you want to uh + + + align:start position:0% +relationships and uh you want to uh +eventually minimize the number of + + align:start position:0% +eventually minimize the number of + + + align:start position:0% +eventually minimize the number of +dinners you actually have to have and + + align:start position:0% +dinners you actually have to have and + + + align:start position:0% +dinners you actually have to have and +that's I don't know hopefully a + + align:start position:0% +that's I don't know hopefully a + + + align:start position:0% +that's I don't know hopefully a +motivating example + + align:start position:0% +motivating example + + + align:start position:0% +motivating example +if it wasn't too + + align:start position:0% + + + + align:start position:0% + +bad so you do have a family of possibly + + align:start position:0% +bad so you do have a family of possibly + + + align:start position:0% +bad so you do have a family of possibly +overlapping + + align:start position:0% + + + + align:start position:0% + +subsets um S1 + + align:start position:0% +subsets um S1 + + + align:start position:0% +subsets um S1 +S2 + + align:start position:0% +S2 + + + align:start position:0% +S2 +SM subset of equal to X so that's that + + align:start position:0% +SM subset of equal to X so that's that + + + align:start position:0% +SM subset of equal to X so that's that +big set that we have such that I want to + + align:start position:0% +big set that we have such that I want to + + + align:start position:0% +big set that we have such that I want to +cover all of the elements so that's what + + align:start position:0% +cover all of the elements so that's what + + + align:start position:0% +cover all of the elements so that's what +this uh little uh equation corresponds + + align:start position:0% +this uh little uh equation corresponds + + + align:start position:0% +this uh little uh equation corresponds +to the union of all the selected SI + + align:start position:0% +to the union of all the selected SI + + + align:start position:0% +to the union of all the selected SI +should equal uh X right I need to cover + + align:start position:0% +should equal uh X right I need to cover + + + align:start position:0% +should equal uh X right I need to cover +it all um and I do want to + + align:start position:0% + + + + align:start position:0% + +minimize called the + + align:start position:0% +minimize called the + + + align:start position:0% +minimize called the +C find C + + align:start position:0% +C find C + + + align:start position:0% +C find C +subset one 2 m so I'm selecting a bunch + + align:start position:0% +subset one 2 m so I'm selecting a bunch + + + align:start position:0% +subset one 2 m so I'm selecting a bunch +of these things so so C is simply + + align:start position:0% +of these things so so C is simply + + + align:start position:0% +of these things so so C is simply +Capital C here is um is some subset of + + align:start position:0% +Capital C here is um is some subset of + + + align:start position:0% +Capital C here is um is some subset of +the the + + align:start position:0% +the the + + + align:start position:0% +the the +indices and the only reason I I + + align:start position:0% +indices and the only reason I I + + + align:start position:0% +indices and the only reason I I +do + + align:start position:0% +do + + + align:start position:0% +do +that is to say that I want to do this + + align:start position:0% +that is to say that I want to do this + + + align:start position:0% +that is to say that I want to do this +while minimizing I want to do IAL 1 + + align:start position:0% +while minimizing I want to do IAL 1 + + + align:start position:0% +while minimizing I want to do IAL 1 +through + + align:start position:0% +through + + + align:start position:0% +through +M um while minimizing + + align:start position:0% + + + + align:start position:0% + +C + + align:start position:0% +C + + + align:start position:0% +C +okay oh let me get this right so that + + align:start position:0% +okay oh let me get this right so that + + + align:start position:0% +okay oh let me get this right so that +that's that this is what I have find + + align:start position:0% +that's that this is what I have find + + + align:start position:0% +that's that this is what I have find +C uh uh subset of these + + align:start position:0% +C uh uh subset of these + + + align:start position:0% +C uh uh subset of these +uh such that I'm sorry there's one + + align:start position:0% + + + + align:start position:0% + +more Union of I belonging to + + align:start position:0% +more Union of I belonging to + + + align:start position:0% +more Union of I belonging to +C SI equal x + + align:start position:0% + + + + align:start position:0% + +okay sorry for the mess here uh but so + + align:start position:0% +okay sorry for the mess here uh but so + + + align:start position:0% +okay sorry for the mess here uh but so +that's the line there so this is simply + + align:start position:0% +that's the line there so this is simply + + + align:start position:0% +that's the line there so this is simply +a a specification of the problem I'm + + align:start position:0% +a a specification of the problem I'm + + + align:start position:0% +a a specification of the problem I'm +going to be given X and I'm going to be + + align:start position:0% +going to be given X and I'm going to be + + + align:start position:0% +going to be given X and I'm going to be +given a large collection of subsets such + + align:start position:0% +given a large collection of subsets such + + + align:start position:0% +given a large collection of subsets such +that um the union of all of those + + align:start position:0% +that um the union of all of those + + + align:start position:0% +that um the union of all of those +subsets are going to cover X and now I'm + + align:start position:0% +subsets are going to cover X and now I'm + + + align:start position:0% +subsets are going to cover X and now I'm +saying I want to look inside and I want + + align:start position:0% +saying I want to look inside and I want + + + align:start position:0% +saying I want to look inside and I want +to select all of + + align:start position:0% +to select all of + + + align:start position:0% +to select all of +them um I have uh I want to select a + + align:start position:0% +them um I have uh I want to select a + + + align:start position:0% +them um I have uh I want to select a +bunch of these things you know C which + + align:start position:0% +bunch of these things you know C which + + + align:start position:0% +bunch of these things you know C which +is some subset of these indices so one + + align:start position:0% +is some subset of these indices so one + + + align:start position:0% +is some subset of these indices so one +may not be in it two may be in it four + + align:start position:0% +may not be in it two may be in it four + + + align:start position:0% +may not be in it two may be in it four +may be in it Etc and such that those uh + + align:start position:0% +may be in it Etc and such that those uh + + + align:start position:0% +may be in it Etc and such that those uh +uh subsets that are in this Capital C + + align:start position:0% +uh subsets that are in this Capital C + + + align:start position:0% +uh subsets that are in this Capital C +set add up to X + + align:start position:0% +set add up to X + + + align:start position:0% +set add up to X +okay all so + + align:start position:0% +okay all so + + + align:start position:0% +okay all so +pictorially may make things + + align:start position:0% +pictorially may make things + + + align:start position:0% +pictorially may make things +um + + align:start position:0% +um + + + align:start position:0% +um +clearer you + + align:start position:0% +clearer you + + + align:start position:0% +clearer you +have let's say a grid here corresponding + + align:start position:0% +have let's say a grid here corresponding + + + align:start position:0% +have let's say a grid here corresponding +to + + align:start position:0% +to + + + align:start position:0% +to +X so each of these dots that I'm drawing + + align:start position:0% +X so each of these dots that I'm drawing + + + align:start position:0% +X so each of these dots that I'm drawing +here are elements that need to be + + align:start position:0% + + + + align:start position:0% + +covered right so that's my + + align:start position:0% +covered right so that's my + + + align:start position:0% +covered right so that's my +X and I might + + align:start position:0% + + + + align:start position:0% + +have S1 corresponding to that um + + align:start position:0% +have S1 corresponding to that um + + + align:start position:0% +have S1 corresponding to that um +this is + + align:start position:0% +this is + + + align:start position:0% +this is +S3 right and S2 is this thing in the + + align:start position:0% + + + + align:start position:0% + +middle that's + + align:start position:0% +middle that's + + + align:start position:0% +middle that's +S2 um + + align:start position:0% + + + + align:start position:0% + +S5 is this one + + align:start position:0% +S5 is this one + + + align:start position:0% +S5 is this one +here and uh I got a little S4 over + + align:start position:0% + + + + align:start position:0% + +here and finally + + align:start position:0% + + + + align:start position:0% + +uh I got uh let's + + align:start position:0% +uh I got uh let's + + + align:start position:0% +uh I got uh let's +see S6 + + align:start position:0% + + + + align:start position:0% + +yep which is kind of this funky + + align:start position:0% +yep which is kind of this funky + + + align:start position:0% +yep which is kind of this funky +thing that goes like that + + align:start position:0% + + + + align:start position:0% + +okay so this thing here is + + align:start position:0% +okay so this thing here is + + + align:start position:0% +okay so this thing here is +S6 all + + align:start position:0% +S6 all + + + align:start position:0% +S6 all +right okay what's the optimum you got + + align:start position:0% +right okay what's the optimum you got + + + align:start position:0% +right okay what's the optimum you got +you got 30 + + align:start position:0% + + + + align:start position:0% + +seconds what's uh what's the optimum + + align:start position:0% +seconds what's uh what's the optimum + + + align:start position:0% +seconds what's uh what's the optimum +cover yeah go + + align:start position:0% +cover yeah go + + + align:start position:0% +cover yeah go +ahead you had your hand + + align:start position:0% +ahead you had your hand + + + align:start position:0% +ahead you had your hand +up s + + align:start position:0% +up s + + + align:start position:0% +up s +s yep that's exactly right so the + + align:start position:0% +s yep that's exactly right so the + + + align:start position:0% +s yep that's exactly right so the +optimum + + align:start position:0% +optimum + + + align:start position:0% +optimum +S3 S4 S5 + + align:start position:0% + + + + align:start position:0% + +right s S6 + + align:start position:0% +right s S6 + + + align:start position:0% +right s S6 +s oh S3 yeah S4 is this one here right + + align:start position:0% +s oh S3 yeah S4 is this one here right + + + align:start position:0% +s oh S3 yeah S4 is this one here right +S6 X5 okay + + align:start position:0% +S6 X5 okay + + + align:start position:0% +S6 X5 okay +good + + align:start position:0% +good + + + align:start position:0% +good +S3 and then oh you know what you're + + align:start position:0% +S3 and then oh you know what you're + + + align:start position:0% +S3 and then oh you know what you're +right let's let's make you + + align:start position:0% + + + + align:start position:0% + +right all right I don't want to erase + + align:start position:0% +right all right I don't want to erase + + + align:start position:0% +right all right I don't want to erase +that all right here you + + align:start position:0% + + + + align:start position:0% + +go um so that's three right so uh C uh + + align:start position:0% +go um so that's three right so uh C uh + + + align:start position:0% +go um so that's three right so uh C uh +would be uh cardinality of C would be + + align:start position:0% +would be uh cardinality of C would be + + + align:start position:0% +would be uh cardinality of C would be +three um so the it's non-trivial problem + + align:start position:0% +three um so the it's non-trivial problem + + + align:start position:0% +three um so the it's non-trivial problem +um not clear how you're going to do this + + align:start position:0% +um not clear how you're going to do this + + + align:start position:0% +um not clear how you're going to do this +I got to use a + + align:start position:0% +I got to use a + + + align:start position:0% +I got to use a +heuristic um hard in terms of + + align:start position:0% +heuristic um hard in terms of + + + align:start position:0% +heuristic um hard in terms of +optimization optimal requires + + align:start position:0% +optimization optimal requires + + + align:start position:0% +optimization optimal requires +exponential time as far as we know and + + align:start position:0% +exponential time as far as we know and + + + align:start position:0% +exponential time as far as we know and +uh we're just going to go off and say + + align:start position:0% +uh we're just going to go off and say + + + align:start position:0% +uh we're just going to go off and say +hey let's um design an approximation + + align:start position:0% +hey let's um design an approximation + + + align:start position:0% +hey let's um design an approximation +algorithm right so let's think of a + + align:start position:0% +algorithm right so let's think of a + + + align:start position:0% +algorithm right so let's think of a +heuristic what's a what's a good + + align:start position:0% +heuristic what's a what's a good + + + align:start position:0% +heuristic what's a what's a good +heuristic what's uh what's a good + + align:start position:0% +heuristic what's uh what's a good + + + align:start position:0% +heuristic what's uh what's a good +heuristic for this problem I hope I + + align:start position:0% +heuristic for this problem I hope I + + + align:start position:0% +heuristic for this problem I hope I +haven't scared you what's a good + + align:start position:0% +haven't scared you what's a good + + + align:start position:0% +haven't scared you what's a good +heuristic for this problem what's the + + align:start position:0% +heuristic for this problem what's the + + + align:start position:0% +heuristic for this problem what's the +obvious heuristic + + align:start position:0% +obvious heuristic + + + align:start position:0% +obvious heuristic +yeah the largest subset and in this + + align:start position:0% +yeah the largest subset and in this + + + align:start position:0% +yeah the largest subset and in this +particular case it's actually the best + + align:start position:0% +particular case it's actually the best + + + align:start position:0% +particular case it's actually the best +also in terms of uh in terms of + + align:start position:0% +also in terms of uh in terms of + + + align:start position:0% +also in terms of uh in terms of +theory uh + + align:start position:0% +theory uh + + + align:start position:0% +theory uh +so + + align:start position:0% + + + + align:start position:0% + +um approximate set + + align:start position:0% + + + + align:start position:0% + +cover at least the best that we're + + align:start position:0% +cover at least the best that we're + + + align:start position:0% +cover at least the best that we're +concerned about in this + + align:start position:0% + + + + align:start position:0% + +lecture and what is uh approximate set + + align:start position:0% +lecture and what is uh approximate set + + + align:start position:0% +lecture and what is uh approximate set +cover + + align:start position:0% +cover + + + align:start position:0% +cover +it's uh + + align:start position:0% +it's uh + + + align:start position:0% +it's uh +pick + + align:start position:0% +pick + + + align:start position:0% +pick +largest + + align:start position:0% +largest + + + align:start position:0% +largest +si uh + + align:start position:0% +si uh + + + align:start position:0% +si uh +remove all + + align:start position:0% + + + + align:start position:0% + +elements in si from + + align:start position:0% +elements in si from + + + align:start position:0% +elements in si from +X + + align:start position:0% +X + + + align:start position:0% +X +um and other + + align:start position:0% + + + + align:start position:0% + +SJ so you're constantly shrinking and + + align:start position:0% +SJ so you're constantly shrinking and + + + align:start position:0% +SJ so you're constantly shrinking and +then keep doing + + align:start position:0% +then keep doing + + + align:start position:0% +then keep doing +that so you I have a new problem and + + align:start position:0% +that so you I have a new problem and + + + align:start position:0% +that so you I have a new problem and +you're going to specify that new problem + + align:start position:0% +you're going to specify that new problem + + + align:start position:0% +you're going to specify that new problem +on every iteration just like we did for + + align:start position:0% +on every iteration just like we did for + + + align:start position:0% +on every iteration just like we did for +vertex cover and we've done many a time + + align:start position:0% +vertex cover and we've done many a time + + + align:start position:0% +vertex cover and we've done many a time +if you do that over here notice that U + + align:start position:0% +if you do that over here notice that U + + + align:start position:0% +if you do that over here notice that U +what you end up uh with is is picking S1 + + align:start position:0% +what you end up uh with is is picking S1 + + + align:start position:0% +what you end up uh with is is picking S1 +because S1 is the is is the big boy here + + align:start position:0% +because S1 is the is is the big boy here + + + align:start position:0% +because S1 is the is is the big boy here +uh in the sense that it's got six + + align:start position:0% +uh in the sense that it's got six + + + align:start position:0% +uh in the sense that it's got six +elements in it right it up on top uh and + + align:start position:0% +elements in it right it up on top uh and + + + align:start position:0% +elements in it right it up on top uh and +so so You' pick uh approx or heuristic + + align:start position:0% +so so You' pick uh approx or heuristic + + + align:start position:0% +so so You' pick uh approx or heuristic +algo I would pick S1 S4 S5 and S3 in + + align:start position:0% +algo I would pick S1 S4 S5 and S3 in + + + align:start position:0% +algo I would pick S1 S4 S5 and S3 in +that order right I won't go over it it's + + align:start position:0% +that order right I won't go over it it's + + + align:start position:0% +that order right I won't go over it it's +not that + + align:start position:0% +not that + + + align:start position:0% +not that +important the point is it doesn't get + + align:start position:0% +important the point is it doesn't get + + + align:start position:0% +important the point is it doesn't get +you the optimum for this problem and in + + align:start position:0% +you the optimum for this problem and in + + + align:start position:0% +you the optimum for this problem and in +general you could always concoct + + align:start position:0% +general you could always concoct + + + align:start position:0% +general you could always concoct +examples where any heuristic fails of + + align:start position:0% +examples where any heuristic fails of + + + align:start position:0% +examples where any heuristic fails of +course right because this problem is + + align:start position:0% +course right because this problem is + + + align:start position:0% +course right because this problem is +hard uh but it's four as opposed to + + align:start position:0% +hard uh but it's four as opposed to + + + align:start position:0% +hard uh but it's four as opposed to +three and and the big question again as + + align:start position:0% +three and and the big question again as + + + align:start position:0% +three and and the big question again as +always is what's the bound what's the + + align:start position:0% +always is what's the bound what's the + + + align:start position:0% +always is what's the bound what's the +bound if you applied this + + align:start position:0% +bound if you applied this + + + align:start position:0% +bound if you applied this +heuristic uh in and what can you show + + align:start position:0% +heuristic uh in and what can you show + + + align:start position:0% +heuristic uh in and what can you show +with respect to the approximation + + align:start position:0% +with respect to the approximation + + + align:start position:0% +with respect to the approximation +algorithm what is row N here right so + + align:start position:0% +algorithm what is row N here right so + + + align:start position:0% +algorithm what is row N here right so +that's what we have to do here in terms + + align:start position:0% +that's what we have to do here in terms + + + align:start position:0% +that's what we have to do here in terms +of what the bound is and we actually + + align:start position:0% +of what the bound is and we actually + + + align:start position:0% +of what the bound is and we actually +going to do an analysis here that uh is + + align:start position:0% +going to do an analysis here that uh is + + + align:start position:0% +going to do an analysis here that uh is +pretty straightforward it's got a little + + align:start position:0% +pretty straightforward it's got a little + + + align:start position:0% +pretty straightforward it's got a little +bit of algebra in it uh but if you go + + align:start position:0% +bit of algebra in it uh but if you go + + + align:start position:0% +bit of algebra in it uh but if you go +look at that this is covered in clrs the + + align:start position:0% +look at that this is covered in clrs the + + + align:start position:0% +look at that this is covered in clrs the +textbook but the analysis in there uses + + align:start position:0% +textbook but the analysis in there uses + + + align:start position:0% +textbook but the analysis in there uses +harmonic numbers and uh is substantially + + align:start position:0% +harmonic numbers and uh is substantially + + + align:start position:0% +harmonic numbers and uh is substantially +more more complicated uh for uh in my + + align:start position:0% +more more complicated uh for uh in my + + + align:start position:0% +more more complicated uh for uh in my +mind no + + align:start position:0% +mind no + + + align:start position:0% +mind no +reason uh and so we have a simpler + + align:start position:0% +reason uh and so we have a simpler + + + align:start position:0% +reason uh and so we have a simpler +analysis here that is simply going to be + + align:start position:0% +analysis here that is simply going to be + + + align:start position:0% +analysis here that is simply going to be +a matter of counting um we are picking + + align:start position:0% +a matter of counting um we are picking + + + align:start position:0% +a matter of counting um we are picking +the maximum number of + + align:start position:0% +the maximum number of + + + align:start position:0% +the maximum number of +uh uh of elements every time the best we + + align:start position:0% +uh uh of elements every time the best we + + + align:start position:0% +uh uh of elements every time the best we +can do it's a greedy heuristic we're + + align:start position:0% +can do it's a greedy heuristic we're + + + align:start position:0% +can do it's a greedy heuristic we're +trying to uh shrink our problem uh as + + align:start position:0% +trying to uh shrink our problem uh as + + + align:start position:0% +trying to uh shrink our problem uh as +much as possible initially we have X and + + align:start position:0% +much as possible initially we have X and + + + align:start position:0% +much as possible initially we have X and +then we're going to get a new problem + + align:start position:0% +then we're going to get a new problem + + + align:start position:0% +then we're going to get a new problem +let's call it x0 first for the initial + + align:start position:0% +let's call it x0 first for the initial + + + align:start position:0% +let's call it x0 first for the initial +problem we're going to get a new problem + + align:start position:0% +problem we're going to get a new problem + + + align:start position:0% +problem we're going to get a new problem +X1 and we're maximally + + align:start position:0% +X1 and we're maximally + + + align:start position:0% +X1 and we're maximally +shrinking uh uh X1 in relation to x0 in + + align:start position:0% +shrinking uh uh X1 in relation to x0 in + + + align:start position:0% +shrinking uh uh X1 in relation to x0 in +the sense that we're going to remove as + + align:start position:0% +the sense that we're going to remove as + + + align:start position:0% +the sense that we're going to remove as +many elements as we can because that is + + align:start position:0% +many elements as we can because that is + + + align:start position:0% +many elements as we can because that is +precisely our heuristic so the the big + + align:start position:0% +precisely our heuristic so the the big + + + align:start position:0% +precisely our heuristic so the the big +question is as we go from the bigger + + align:start position:0% +question is as we go from the bigger + + + align:start position:0% +question is as we go from the bigger +biggest problem that we have the + + align:start position:0% +biggest problem that we have the + + + align:start position:0% +biggest problem that we have the +original problem to smaller and smaller + + align:start position:0% +original problem to smaller and smaller + + + align:start position:0% +original problem to smaller and smaller +problems when do we end up with nothing + + align:start position:0% +problems when do we end up with nothing + + + align:start position:0% +problems when do we end up with nothing +when we end up with nothing that's when + + align:start position:0% +when we end up with nothing that's when + + + align:start position:0% +when we end up with nothing that's when +the number of iterations that + + align:start position:0% +the number of iterations that + + + align:start position:0% +the number of iterations that +corresponds to the number of Si that we + + align:start position:0% +corresponds to the number of Si that we + + + align:start position:0% +corresponds to the number of Si that we +picked is going to be the collection of + + align:start position:0% +picked is going to be the collection of + + + align:start position:0% +picked is going to be the collection of +Si in our solution and the cardinality + + align:start position:0% +Si in our solution and the cardinality + + + align:start position:0% +Si in our solution and the cardinality +of that is our cost right so that's + + align:start position:0% +of that is our cost right so that's + + + align:start position:0% +of that is our cost right so that's +that's all pretty straightforward uh + + align:start position:0% +that's all pretty straightforward uh + + + align:start position:0% +that's all pretty straightforward uh +hopefully so but what we need to do of + + align:start position:0% +hopefully so but what we need to do of + + + align:start position:0% +hopefully so but what we need to do of +course is is show a proof and the way + + align:start position:0% +course is is show a proof and the way + + + align:start position:0% +course is is show a proof and the way +we're going to do this is by a fairly + + align:start position:0% +we're going to do this is by a fairly + + + align:start position:0% +we're going to do this is by a fairly +straightforward counting + + align:start position:0% +straightforward counting + + + align:start position:0% +straightforward counting +argument assume there's a + + align:start position:0% + + + + align:start position:0% + +cover SE + + align:start position:0% +cover SE + + + align:start position:0% +cover SE +opt such that + + align:start position:0% +opt such that + + + align:start position:0% +opt such that +copt equals + + align:start position:0% +copt equals + + + align:start position:0% +copt equals +t Okay so the cardinality of copt equals + + align:start position:0% +t Okay so the cardinality of copt equals + + + align:start position:0% +t Okay so the cardinality of copt equals +T so I'm just assuming that this T + + align:start position:0% +T so I'm just assuming that this T + + + align:start position:0% +T so I'm just assuming that this T +subsets in my Optimum cover + + align:start position:0% +subsets in my Optimum cover + + + align:start position:0% +subsets in my Optimum cover +okay T sub sets in my Optimum cover now + + align:start position:0% +okay T sub sets in my Optimum cover now + + + align:start position:0% +okay T sub sets in my Optimum cover now +let X of + + align:start position:0% +let X of + + + align:start position:0% +let X of +K be the set of + + align:start position:0% + + + + align:start position:0% + +elements in iteration + + align:start position:0% + + + + align:start position:0% + +K and let's assume that x0 equals x so + + align:start position:0% +K and let's assume that x0 equals x so + + + align:start position:0% +K and let's assume that x0 equals x so +initially I'm at zero and I want to + + align:start position:0% +initially I'm at zero and I want to + + + align:start position:0% +initially I'm at zero and I want to +subscript this because I want to point + + align:start position:0% +subscript this because I want to point + + + align:start position:0% +subscript this because I want to point +to each of the problems that I'm going + + align:start position:0% +to each of the problems that I'm going + + + align:start position:0% +to each of the problems that I'm going +to have as I shrink this uh set down to + + align:start position:0% +to have as I shrink this uh set down to + + + align:start position:0% +to have as I shrink this uh set down to +nothing right now I know that for all K + + align:start position:0% +nothing right now I know that for all K + + + align:start position:0% +nothing right now I know that for all K +including of + + align:start position:0% +including of + + + align:start position:0% +including of +course x0 XK can be + + align:start position:0% +course x0 XK can be + + + align:start position:0% +course x0 XK can be +covered by T + + align:start position:0% +covered by T + + + align:start position:0% +covered by T +sets Okay I mean that's a kind of a + + align:start position:0% +sets Okay I mean that's a kind of a + + + align:start position:0% +sets Okay I mean that's a kind of a +vacuous statement because I assumed that + + align:start position:0% +vacuous statement because I assumed that + + + align:start position:0% +vacuous statement because I assumed that +x0 could be covered by T sets and x0 is + + align:start position:0% +x0 could be covered by T sets and x0 is + + + align:start position:0% +x0 could be covered by T sets and x0 is +only shrinking to X1 to X2 2 Etc and I'm + + align:start position:0% +only shrinking to X1 to X2 2 Etc and I'm + + + align:start position:0% +only shrinking to X1 to X2 2 Etc and I'm +just saying all of these things could be + + align:start position:0% +just saying all of these things could be + + + align:start position:0% +just saying all of these things could be +covered uh each of those uh intermediate + + align:start position:0% +covered uh each of those uh intermediate + + + align:start position:0% +covered uh each of those uh intermediate +problems as well can be covered by T in + + align:start position:0% +problems as well can be covered by T in + + + align:start position:0% +problems as well can be covered by T in +fact in the solution that we have in the + + align:start position:0% +fact in the solution that we have in the + + + align:start position:0% +fact in the solution that we have in the +optimal solution um it if if this these + + align:start position:0% +optimal solution um it if if this these + + + align:start position:0% +optimal solution um it if if this these +X zeros are coming from my heuristic but + + align:start position:0% +X zeros are coming from my heuristic but + + + align:start position:0% +X zeros are coming from my heuristic but +if they were coming from an Optimum + + align:start position:0% +if they were coming from an Optimum + + + align:start position:0% +if they were coming from an Optimum +solution uh then uh uh x0 would be + + align:start position:0% +solution uh then uh uh x0 would be + + + align:start position:0% +solution uh then uh uh x0 would be +covered by T X1 would be covered by T + + align:start position:0% +covered by T X1 would be covered by T + + + align:start position:0% +covered by T X1 would be covered by T +minus one and T minus 2 and so on and so + + align:start position:0% +minus one and T minus 2 and so on and so + + + align:start position:0% +minus one and T minus 2 and so on and so +forth but I I don't have an Optimum + + align:start position:0% +forth but I I don't have an Optimum + + + align:start position:0% +forth but I I don't have an Optimum +algorithm here I just have my heuristic + + align:start position:0% +algorithm here I just have my heuristic + + + align:start position:0% +algorithm here I just have my heuristic +algorithm and I'm just making a fairly + + align:start position:0% +algorithm and I'm just making a fairly + + + align:start position:0% +algorithm and I'm just making a fairly +vacuous statement as I said based on my + + align:start position:0% +vacuous statement as I said based on my + + + align:start position:0% +vacuous statement as I said based on my +definition that the original problem can + + align:start position:0% +definition that the original problem can + + + align:start position:0% +definition that the original problem can +be covered using T and therefore a + + align:start position:0% +be covered using T and therefore a + + + align:start position:0% +be covered using T and therefore a +smaller problem where I removed elements + + align:start position:0% +smaller problem where I removed elements + + + align:start position:0% +smaller problem where I removed elements +from it could also be covered using T + + align:start position:0% +from it could also be covered using T + + + align:start position:0% +from it could also be covered using T +okay so far so + + align:start position:0% +okay so far so + + + align:start position:0% +okay so far so +good um so + + align:start position:0% + + + + align:start position:0% + +now one of + + align:start position:0% + + + + align:start position:0% + +them + + align:start position:0% +them + + + align:start position:0% +them +covers what + + align:start position:0% +covers what + + + align:start position:0% +covers what +what can I say about one of them what + + align:start position:0% +what can I say about one of them what + + + align:start position:0% +what can I say about one of them what +what principle can I use to to make a + + align:start position:0% +what principle can I use to to make a + + + align:start position:0% +what principle can I use to to make a +claim about the number of elements that + + align:start position:0% +claim about the number of elements that + + + align:start position:0% +claim about the number of elements that +are covered + + align:start position:0% +are covered + + + align:start position:0% +are covered +by one of these T + + align:start position:0% + + + + align:start position:0% + +sets remember a a principle from way + + align:start position:0% +sets remember a a principle from way + + + align:start position:0% +sets remember a a principle from way +back + + align:start position:0% +back + + + align:start position:0% +back +6042 my favorite principle flopping I + + align:start position:0% +6042 my favorite principle flopping I + + + align:start position:0% +6042 my favorite principle flopping I +think + + align:start position:0% +think + + + align:start position:0% +think +flapping pigon hole pigon hole principle + + align:start position:0% +flapping pigon hole pigon hole principle + + + align:start position:0% +flapping pigon hole pigon hole principle +right right see you have to remember all + + align:start position:0% +right right see you have to remember all + + + align:start position:0% +right right see you have to remember all +of the material that you learned in MIT + + align:start position:0% +of the material that you learned in MIT + + + align:start position:0% +of the material that you learned in MIT +for the rest of your life okay you never + + align:start position:0% +for the rest of your life okay you never + + + align:start position:0% +for the rest of your life okay you never +know when it's going to be useful okay + + align:start position:0% +know when it's going to be useful okay + + + align:start position:0% +know when it's going to be useful okay +so here you go pigeon hole my favorite + + align:start position:0% +so here you go pigeon hole my favorite + + + align:start position:0% +so here you go pigeon hole my favorite +principle uh it's such a trivial + + align:start position:0% +principle uh it's such a trivial + + + align:start position:0% +principle uh it's such a trivial +principle but um so one of them + + align:start position:0% +principle but um so one of them + + + align:start position:0% +principle but um so one of them +covers at + + align:start position:0% +covers at + + + align:start position:0% +covers at +least XK / T I mean why is this even a + + align:start position:0% +least XK / T I mean why is this even a + + + align:start position:0% +least XK / T I mean why is this even a +principle right + + align:start position:0% + + + + align:start position:0% + +elements okay so that's it right that's + + align:start position:0% +elements okay so that's it right that's + + + align:start position:0% +elements okay so that's it right that's +the + + align:start position:0% +the + + + align:start position:0% +the +observation uh + + align:start position:0% +observation uh + + + align:start position:0% +observation uh +and now that + + align:start position:0% +and now that + + + align:start position:0% +and now that +implies that an algorithm because it's + + align:start position:0% +implies that an algorithm because it's + + + align:start position:0% +implies that an algorithm because it's +going to pick the maximum of these right + + align:start position:0% +going to pick the maximum of these right + + + align:start position:0% +going to pick the maximum of these right +the algorithm is going to pick the + + align:start position:0% +the algorithm is going to pick the + + + align:start position:0% +the algorithm is going to pick the +maximum of these so uh it's going to + + align:start position:0% +maximum of these so uh it's going to + + + align:start position:0% +maximum of these so uh it's going to +pick a + + align:start position:0% +pick a + + + align:start position:0% +pick a +set of current size + + align:start position:0% + + + + align:start position:0% + +greater than or equal to XK / T um + + align:start position:0% +greater than or equal to XK / T um + + + align:start position:0% +greater than or equal to XK / T um +otherwise the algorithm would be + + align:start position:0% +otherwise the algorithm would be + + + align:start position:0% +otherwise the algorithm would be +incorrect it's not doing what you told + + align:start position:0% +incorrect it's not doing what you told + + + align:start position:0% +incorrect it's not doing what you told +it to do right it's got to pick the + + align:start position:0% +it to do right it's got to pick the + + + align:start position:0% +it to do right it's got to pick the +maximum so keep chugging + + align:start position:0% +maximum so keep chugging + + + align:start position:0% +maximum so keep chugging +here and one + + align:start position:0% + + + + align:start position:0% + +real observation and then the rest of it + + align:start position:0% +real observation and then the rest of it + + + align:start position:0% +real observation and then the rest of it +is + + align:start position:0% + + + + align:start position:0% + +algebra so what I can say is that for + + align:start position:0% +algebra so what I can say is that for + + + align:start position:0% +algebra so what I can say is that for +all + + align:start position:0% +all + + + align:start position:0% +all +K XK + 1 which is shrinking is less than + + align:start position:0% +K XK + 1 which is shrinking is less than + + + align:start position:0% +K XK + 1 which is shrinking is less than +or equal to 1 - 1 + + align:start position:0% +or equal to 1 - 1 + + + align:start position:0% +or equal to 1 - 1 +/t + + align:start position:0% +/t + + + align:start position:0% +/t +XK okay that's the way I'm shrinking + + align:start position:0% +XK okay that's the way I'm shrinking + + + align:start position:0% +XK okay that's the way I'm shrinking +right this is again a fairly + + align:start position:0% +right this is again a fairly + + + align:start position:0% +right this is again a fairly +conservative + + align:start position:0% +conservative + + + align:start position:0% +conservative +statement because the fact of the matter + + align:start position:0% +statement because the fact of the matter + + + align:start position:0% +statement because the fact of the matter +is that I'm putting T in as a constant + + align:start position:0% +is that I'm putting T in as a constant + + + align:start position:0% +is that I'm putting T in as a constant +here right but T is actually in effect + + align:start position:0% +here right but T is actually in effect + + + align:start position:0% +here right but T is actually in effect +changing obviously way through the + + align:start position:0% +changing obviously way through the + + + align:start position:0% +changing obviously way through the +algorithm I don't need uh T sets to + + align:start position:0% +algorithm I don't need uh T sets to + + + align:start position:0% +algorithm I don't need uh T sets to +cover the X uh whatever it is XK over2 + + align:start position:0% +cover the X uh whatever it is XK over2 + + + align:start position:0% +cover the X uh whatever it is XK over2 +or whatever it is that I have right I + + align:start position:0% +or whatever it is that I have right I + + + align:start position:0% +or whatever it is that I have right I +need the T for x0 maybe uh I did a bad + + align:start position:0% +need the T for x0 maybe uh I did a bad + + + align:start position:0% +need the T for x0 maybe uh I did a bad +selection with my heuristic and I still + + align:start position:0% +selection with my heuristic and I still + + + align:start position:0% +selection with my heuristic and I still +need I still would need T which is + + align:start position:0% +need I still would need T which is + + + align:start position:0% +need I still would need T which is +Optimum remember for X1 but halfway + + align:start position:0% +Optimum remember for X1 but halfway + + + align:start position:0% +Optimum remember for X1 but halfway +through the algorithm after I picked a + + align:start position:0% +through the algorithm after I picked a + + + align:start position:0% +through the algorithm after I picked a +bunch of sets I'm still saying I need t + + align:start position:0% +bunch of sets I'm still saying I need t + + + align:start position:0% +bunch of sets I'm still saying I need t +Okay because I just need that for my + + align:start position:0% +Okay because I just need that for my + + + align:start position:0% +Okay because I just need that for my +proof right that's all I need for the + + align:start position:0% +proof right that's all I need for the + + + align:start position:0% +proof right that's all I need for the +proof in clrs this actually varies and + + align:start position:0% +proof in clrs this actually varies and + + + align:start position:0% +proof in clrs this actually varies and +and it turns into a harmonic series if + + align:start position:0% +and it turns into a harmonic series if + + + align:start position:0% +and it turns into a harmonic series if +we won't go there okay you can do the uh + + align:start position:0% +we won't go there okay you can do the uh + + + align:start position:0% +we won't go there okay you can do the uh +natural logarithm of n + one appr proof + + align:start position:0% +natural logarithm of n + one appr proof + + + align:start position:0% +natural logarithm of n + one appr proof +just doing this simpler analysis okay so + + align:start position:0% +just doing this simpler analysis okay so + + + align:start position:0% +just doing this simpler analysis okay so +you see what's happening here that's my + + align:start position:0% +you see what's happening here that's my + + + align:start position:0% +you see what's happening here that's my +shrinkage that's + + align:start position:0% +shrinkage that's + + + align:start position:0% +shrinkage that's +the recurrence if you will that tells me + + align:start position:0% +the recurrence if you will that tells me + + + align:start position:0% +the recurrence if you will that tells me +how my problem size is shrinking and + + align:start position:0% +how my problem size is shrinking and + + + align:start position:0% +how my problem size is shrinking and +when do I end what is my stopping point + + align:start position:0% + + + + align:start position:0% + +what's my stopping point + + align:start position:0% + + + + align:start position:0% + +mathematically when do we end this + + align:start position:0% +mathematically when do we end this + + + align:start position:0% +mathematically when do we end this +lecture when you give me the answer no + + align:start position:0% +lecture when you give me the answer no + + + align:start position:0% +lecture when you give me the answer no +not quite so I end when I got nothing to + + align:start position:0% +not quite so I end when I got nothing to + + + align:start position:0% +not quite so I end when I got nothing to +cover right so when one of these things + + align:start position:0% +cover right so when one of these things + + + align:start position:0% +cover right so when one of these things +is + + align:start position:0% + + + + align:start position:0% + +uh gets down + + align:start position:0% +uh gets down + + + align:start position:0% +uh gets down +to + + align:start position:0% +to + + + align:start position:0% +to +XK equal Z right when XK equals z I'm + + align:start position:0% + + + + align:start position:0% + +done I'm constantly taking stuff away + + align:start position:0% +done I'm constantly taking stuff away + + + align:start position:0% +done I'm constantly taking stuff away +when XK equals zero I'm going to be done + + align:start position:0% +when XK equals zero I'm going to be done + + + align:start position:0% +when XK equals zero I'm going to be done +okay and I I I'm going to move a little + + align:start position:0% +okay and I I I'm going to move a little + + + align:start position:0% +okay and I I I'm going to move a little +bit between discrete and continuous here + + align:start position:0% +bit between discrete and continuous here + + + align:start position:0% +bit between discrete and continuous here +it's it's all going to be fine but what + + align:start position:0% +it's it's all going to be fine but what + + + align:start position:0% +it's it's all going to be fine but what +uh I I have is if I just take that I can + + align:start position:0% +uh I I have is if I just take that I can + + + align:start position:0% +uh I I have is if I just take that I can +turn this this is a recurrence I want to + + align:start position:0% +turn this this is a recurrence I want to + + + align:start position:0% +turn this this is a recurrence I want to +turn that into a a series so I can say + + align:start position:0% +turn that into a a series so I can say + + + align:start position:0% +turn that into a a series so I can say +something like 1 - 1 / T raised to K * n + + align:start position:0% +something like 1 - 1 / T raised to K * n + + + align:start position:0% +something like 1 - 1 / T raised to K * n +and this is the cardinality of X which + + align:start position:0% +and this is the cardinality of X which + + + align:start position:0% +and this is the cardinality of X which +is the cardinality of + + align:start position:0% +is the cardinality of + + + align:start position:0% +is the cardinality of +x0 right so that's what I have up there + + align:start position:0% +x0 right so that's what I have up there + + + align:start position:0% +x0 right so that's what I have up there +and that's essentially what happens I + + align:start position:0% +and that's essentially what happens I + + + align:start position:0% +and that's essentially what happens I +constantly shrink as I go along and I + + align:start position:0% +constantly shrink as I go along and I + + + align:start position:0% +constantly shrink as I go along and I +have a constant rate of shrinkage here + + align:start position:0% +have a constant rate of shrinkage here + + + align:start position:0% +have a constant rate of shrinkage here +right which is the conservative part of + + align:start position:0% +right which is the conservative part of + + + align:start position:0% +right which is the conservative part of +it so keep that in mind but doesn't + + align:start position:0% +it so keep that in mind but doesn't + + + align:start position:0% +it so keep that in mind but doesn't +matter from an analysis standpoint okay + + align:start position:0% +matter from an analysis standpoint okay + + + align:start position:0% +matter from an analysis standpoint okay +so if you look at that and you say what + + align:start position:0% +so if you look at that and you say what + + + align:start position:0% +so if you look at that and you say what +happens here well I can just say that + + align:start position:0% +happens here well I can just say that + + + align:start position:0% +happens here well I can just say that +this is less than or equal to e raed to + + align:start position:0% +this is less than or equal to e raed to + + + align:start position:0% +this is less than or equal to e raed to +minus you knew you were going to get an + + align:start position:0% +minus you knew you were going to get an + + + align:start position:0% +minus you knew you were going to get an +e because you saw a natural logarithm + + align:start position:0% +e because you saw a natural logarithm + + + align:start position:0% +e because you saw a natural logarithm +here right um and so that's what we + + align:start position:0% +here right um and so that's what we + + + align:start position:0% +here right um and so that's what we +got and uh basically uh that's it uh you + + align:start position:0% +got and uh basically uh that's it uh you + + + align:start position:0% +got and uh basically uh that's it uh you +can uh you can do a little bit of + + align:start position:0% +can uh you can do a little bit of + + + align:start position:0% +can uh you can do a little bit of +algebra I'll just write this out for you + + align:start position:0% +algebra I'll just write this out for you + + + align:start position:0% +algebra I'll just write this out for you +but I won't really explain it uh you're + + align:start position:0% +but I won't really explain it uh you're + + + align:start position:0% +but I won't really explain it uh you're +going to have XK equals z you're done + + align:start position:0% +going to have XK equals z you're done + + + align:start position:0% +going to have XK equals z you're done +the cost of course is K right the cost + + align:start position:0% +the cost of course is K right the cost + + + align:start position:0% +the cost of course is K right the cost +is K because you've selected k subsets + + align:start position:0% +is K because you've selected k subsets + + + align:start position:0% +is K because you've selected k subsets +right that's your cost right so when it + + align:start position:0% +right that's your cost right so when it + + + align:start position:0% +right that's your cost right so when it +gets to the point you're done and the + + align:start position:0% +gets to the point you're done and the + + + align:start position:0% +gets to the point you're done and the +cost is K so what you need is um you + + align:start position:0% +cost is K so what you need is um you + + + align:start position:0% +cost is K so what you need is um you +need to say that e ra to minus KT / n is + + align:start position:0% +need to say that e ra to minus KT / n is + + + align:start position:0% +need to say that e ra to minus KT / n is +strictly less than one because that is + + align:start position:0% +strictly less than one because that is + + + align:start position:0% +strictly less than one because that is +effectively um when you have strictly + + align:start position:0% +effectively um when you have strictly + + + align:start position:0% +effectively um when you have strictly +less than one element it's discrete so + + align:start position:0% +less than one element it's discrete so + + + align:start position:0% +less than one element it's discrete so +that means you have zero elements left + + align:start position:0% +that means you have zero elements left + + + align:start position:0% +that means you have zero elements left +to cover that means you're done okay so + + align:start position:0% +to cover that means you're done okay so + + + align:start position:0% +to cover that means you're done okay so +so that's your condition for stopping so + + align:start position:0% +so that's your condition for stopping so + + + align:start position:0% +so that's your condition for stopping so +this + + align:start position:0% +this + + + align:start position:0% +this +means that eus KT * n is less strictly + + align:start position:0% +means that eus KT * n is less strictly + + + align:start position:0% +means that eus KT * n is less strictly +less than one and if you go do that uh + + align:start position:0% +less than one and if you go do that uh + + + align:start position:0% +less than one and if you go do that uh +you can you get k/ T um greater than + + align:start position:0% +you can you get k/ T um greater than + + + align:start position:0% +you can you get k/ T um greater than +just about greater than natural + + align:start position:0% +just about greater than natural + + + align:start position:0% +just about greater than natural +logarithm of m n the algorithm + + align:start position:0% +logarithm of m n the algorithm + + + align:start position:0% +logarithm of m n the algorithm +terminates if we just do a little + + align:start position:0% +terminates if we just do a little + + + align:start position:0% +terminates if we just do a little +manipulation and that implies that k / T + + align:start position:0% +manipulation and that implies that k / T + + + align:start position:0% +manipulation and that implies that k / T +less than or equal to natural logarithm + + align:start position:0% +less than or equal to natural logarithm + + + align:start position:0% +less than or equal to natural logarithm +of n + 1 + + align:start position:0% + + + + align:start position:0% + +um is valid right k/ T is is going to be + + align:start position:0% +um is valid right k/ T is is going to be + + + align:start position:0% +um is valid right k/ T is is going to be +less than or equal to Natural logorithm + + align:start position:0% +less than or equal to Natural logorithm + + + align:start position:0% +less than or equal to Natural logorithm +of n plus one because if the instant it + + align:start position:0% +of n plus one because if the instant it + + + align:start position:0% +of n plus one because if the instant it +becomes greater the algorithm terminates + + align:start position:0% +becomes greater the algorithm terminates + + + align:start position:0% +becomes greater the algorithm terminates +all right and that's how you got your + + align:start position:0% +all right and that's how you got your + + + align:start position:0% +all right and that's how you got your +proof over here because this is exactly + + align:start position:0% +proof over here because this is exactly + + + align:start position:0% +proof over here because this is exactly +what we want K is our C from way back + + align:start position:0% +what we want K is our C from way back + + + align:start position:0% +what we want K is our C from way back +where it's the cost of our heuristic or + + align:start position:0% +where it's the cost of our heuristic or + + + align:start position:0% +where it's the cost of our heuristic or +cost of our approximation T is the + + align:start position:0% +cost of our approximation T is the + + + align:start position:0% +cost of our approximation T is the +optimum cost um that's what I defined it + + align:start position:0% +optimum cost um that's what I defined it + + + align:start position:0% +optimum cost um that's what I defined it +as and this is a bound on k/t + + align:start position:0% +as and this is a bound on k/t + + + align:start position:0% +as and this is a bound on k/t +all right cool any questions on + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% +this + + + align:start position:0% +this +okay so this approximation ratio gets + + align:start position:0% +okay so this approximation ratio gets + + + align:start position:0% +okay so this approximation ratio gets +worse for larger problems just like this + + align:start position:0% +worse for larger problems just like this + + + align:start position:0% +worse for larger problems just like this +other approximation uh algorithm that we + + align:start position:0% +other approximation uh algorithm that we + + + align:start position:0% +other approximation uh algorithm that we +didn't actually prove from the very + + align:start position:0% +didn't actually prove from the very + + + align:start position:0% +didn't actually prove from the very +first problem that also got worse um it + + align:start position:0% +first problem that also got worse um it + + + align:start position:0% +first problem that also got worse um it +was uh it was the we had a log K factor + + align:start position:0% +was uh it was the we had a log K factor + + + align:start position:0% +was uh it was the we had a log K factor +for that and as your problem size + + align:start position:0% +for that and as your problem size + + + align:start position:0% +for that and as your problem size +increased obviously the approximation + + align:start position:0% +increased obviously the approximation + + + align:start position:0% +increased obviously the approximation +Factor increased inreased this is a + + align:start position:0% +Factor increased inreased this is a + + + align:start position:0% +Factor increased inreased this is a +little clearer um as to um as to what + + align:start position:0% +little clearer um as to um as to what + + + align:start position:0% +little clearer um as to um as to what +the increase looks like in relation to + + align:start position:0% +the increase looks like in relation to + + + align:start position:0% +the increase looks like in relation to +the original size of of n right so it's + + align:start position:0% +the original size of of n right so it's + + + align:start position:0% +the original size of of n right so it's +just natural logorithm of n plus one um + + align:start position:0% +just natural logorithm of n plus one um + + + align:start position:0% +just natural logorithm of n plus one um +so so far we've done approximation + + align:start position:0% +so so far we've done approximation + + + align:start position:0% +so so far we've done approximation +algorithms couple of different varieties + + align:start position:0% +algorithms couple of different varieties + + + align:start position:0% +algorithms couple of different varieties +we had a constant Factor one and then we + + align:start position:0% +we had a constant Factor one and then we + + + align:start position:0% +we had a constant Factor one and then we +had a a row of n that actually had a + + align:start position:0% +had a a row of n that actually had a + + + align:start position:0% +had a a row of n that actually had a +dependence on N um now let's move and + + align:start position:0% +dependence on N um now let's move and + + + align:start position:0% +dependence on N um now let's move and +we'll do one last example um on + + align:start position:0% +we'll do one last example um on + + + align:start position:0% +we'll do one last example um on +partition which um it turns out has a + + align:start position:0% +partition which um it turns out has a + + + align:start position:0% +partition which um it turns out has a +trivial constant Factor approximation + + align:start position:0% +trivial constant Factor approximation + + + align:start position:0% +trivial constant Factor approximation +scheme uh and it's this this obvious + + align:start position:0% +scheme uh and it's this this obvious + + + align:start position:0% +scheme uh and it's this this obvious +thing and we'll get to that in just a + + align:start position:0% +thing and we'll get to that in just a + + + align:start position:0% +thing and we'll get to that in just a +second uh but what is uh nice about + + align:start position:0% +second uh but what is uh nice about + + + align:start position:0% +second uh but what is uh nice about +partition is you can actually get a ptas + + align:start position:0% +partition is you can actually get a ptas + + + align:start position:0% +partition is you can actually get a ptas +right polinomial time approximation + + align:start position:0% +right polinomial time approximation + + + align:start position:0% +right polinomial time approximation +scheme and FP Tas fully polinomial time + + align:start position:0% +scheme and FP Tas fully polinomial time + + + align:start position:0% +scheme and FP Tas fully polinomial time +approximation scheme uh that uh uh + + align:start position:0% +approximation scheme uh that uh uh + + + align:start position:0% +approximation scheme uh that uh uh +essentially give you uh with higher and + + align:start position:0% +essentially give you uh with higher and + + + align:start position:0% +essentially give you uh with higher and +higher run times uh they're going to + + align:start position:0% +higher run times uh they're going to + + + align:start position:0% +higher run times uh they're going to +give you solutions that are closer and + + align:start position:0% +give you solutions that are closer and + + + align:start position:0% +give you solutions that are closer and +closer to Optimal right we want to do + + align:start position:0% +closer to Optimal right we want to do + + + align:start position:0% +closer to Optimal right we want to do +the FP Tas we'll do the P Tas right so + + align:start position:0% +the FP Tas we'll do the P Tas right so + + + align:start position:0% +the FP Tas we'll do the P Tas right so +partition is is a a trivial little + + align:start position:0% +partition is is a a trivial little + + + align:start position:0% +partition is is a a trivial little +problem to Define it's just you have a + + align:start position:0% +problem to Define it's just you have a + + + align:start position:0% +problem to Define it's just you have a +set and you want to partition it into + + align:start position:0% +set and you want to partition it into + + + align:start position:0% +set and you want to partition it into +two + + align:start position:0% +two + + + align:start position:0% +two +sets uh such that they're not unbalanced + + align:start position:0% +sets uh such that they're not unbalanced + + + align:start position:0% +sets uh such that they're not unbalanced +so your your cost is the + + align:start position:0% +so your your cost is the + + + align:start position:0% +so your your cost is the +imbalance uh between the two sets and + + align:start position:0% +imbalance uh between the two sets and + + + align:start position:0% +imbalance uh between the two sets and +you want to minimize that cost you'd + + align:start position:0% +you want to minimize that cost you'd + + + align:start position:0% +you want to minimize that cost you'd +love to have two sets that are exactly + + align:start position:0% +love to have two sets that are exactly + + + align:start position:0% +love to have two sets that are exactly +the same weight but if one of them is + + align:start position:0% +the same weight but if one of them is + + + align:start position:0% +the same weight but if one of them is +extremely uh + + align:start position:0% +extremely uh + + + align:start position:0% +extremely uh +unbalanced with respect to the other + + align:start position:0% +unbalanced with respect to the other + + + align:start position:0% +unbalanced with respect to the other +then you it's bad either way uh so so + + align:start position:0% +then you it's bad either way uh so so + + + align:start position:0% +then you it's bad either way uh so so +here we go with + + align:start position:0% + + + + align:start position:0% + +Partition + + align:start position:0% +Partition + + + align:start position:0% +Partition +sets of n + + align:start position:0% + + + + align:start position:0% + +items with + + align:start position:0% + + + + align:start position:0% + +weights + + align:start position:0% +weights + + + align:start position:0% +weights +S1 through SN + + align:start position:0% + + + + align:start position:0% + +assume S1 greater than + + align:start position:0% + + + + align:start position:0% + +S2 SN I without loss of generality so + + align:start position:0% +S2 SN I without loss of generality so + + + align:start position:0% +S2 SN I without loss of generality so +this is just an ordering thing I mean + + align:start position:0% +this is just an ordering thing I mean + + + align:start position:0% +this is just an ordering thing I mean +obviously there's some order I'm not + + align:start position:0% +obviously there's some order I'm not + + + align:start position:0% +obviously there's some order I'm not +even claiming uniqueness here I'm just + + align:start position:0% +even claiming uniqueness here I'm just + + + align:start position:0% +even claiming uniqueness here I'm just +saying just assume that this is the + + align:start position:0% +saying just assume that this is the + + + align:start position:0% +saying just assume that this is the +order the analysis is much better if you + + align:start position:0% +order the analysis is much better if you + + + align:start position:0% +order the analysis is much better if you +do + + align:start position:0% +do + + + align:start position:0% +do +this if you make this + + align:start position:0% +this if you make this + + + align:start position:0% +this if you make this +assumption and I want to + + align:start position:0% +assumption and I want to + + + align:start position:0% +assumption and I want to +partition + + align:start position:0% +partition + + + align:start position:0% +partition +into + + align:start position:0% +into + + + align:start position:0% +into +a and + + align:start position:0% +a and + + + align:start position:0% +a and +B to + + align:start position:0% + + + + align:start position:0% + +minimize + + align:start position:0% +minimize + + + align:start position:0% +minimize +Max of Sigma I belongs to a + + align:start position:0% +Max of Sigma I belongs to a + + + align:start position:0% +Max of Sigma I belongs to a +SI Sigma I belongs to + + align:start position:0% +SI Sigma I belongs to + + + align:start position:0% +SI Sigma I belongs to +B + + align:start position:0% +B + + + align:start position:0% +B +SI and this is the + + align:start position:0% +SI and this is the + + + align:start position:0% +SI and this is the +weight of a and this is the weight of + + align:start position:0% +weight of a and this is the weight of + + + align:start position:0% +weight of a and this is the weight of +B and so um + + align:start position:0% +B and so um + + + align:start position:0% +B and so um +there's only so much you can do um if + + align:start position:0% +there's only so much you can do um if + + + align:start position:0% +there's only so much you can do um if +you if you have 2 L equals Sigma I = 1 + + align:start position:0% +you if you have 2 L equals Sigma I = 1 + + + align:start position:0% +you if you have 2 L equals Sigma I = 1 +through n SI + + align:start position:0% +through n SI + + + align:start position:0% +through n SI +I uh so I'm just calling that to L the + + align:start position:0% +I uh so I'm just calling that to L the + + + align:start position:0% +I uh so I'm just calling that to L the +the the sum of all the weights then uh + + align:start position:0% +the the sum of all the weights then uh + + + align:start position:0% +the the sum of all the weights then uh +my Optimum solution uh is what it's a + + align:start position:0% +my Optimum solution uh is what it's a + + + align:start position:0% +my Optimum solution uh is what it's a +what is the lower Bond on the optimum + + align:start position:0% +what is the lower Bond on the optimum + + + align:start position:0% +what is the lower Bond on the optimum +solution if uh if it's 2 L what's the + + align:start position:0% +solution if uh if it's 2 L what's the + + + align:start position:0% +solution if uh if it's 2 L what's the +trivial lower + + align:start position:0% +trivial lower + + + align:start position:0% +trivial lower +Bond just L right so I could have L here + + align:start position:0% +Bond just L right so I could have L here + + + align:start position:0% +Bond just L right so I could have L here +and L there and if I had 2 L here and + + align:start position:0% +and L there and if I had 2 L here and + + + align:start position:0% +and L there and if I had 2 L here and +zero + + align:start position:0% +zero + + + align:start position:0% +zero +here uh then oh that's right yeah I want + + align:start position:0% +here uh then oh that's right yeah I want + + + align:start position:0% +here uh then oh that's right yeah I want +to minimize remember don't uh I maybe + + align:start position:0% +to minimize remember don't uh I maybe + + + align:start position:0% +to minimize remember don't uh I maybe +that's what threw you off it threw me + + align:start position:0% +that's what threw you off it threw me + + + align:start position:0% +that's what threw you off it threw me +off right here I see a Max here and and + + align:start position:0% +off right here I see a Max here and and + + + align:start position:0% +off right here I see a Max here and and +I got a little worried but uh I want to + + align:start position:0% +I got a little worried but uh I want to + + + align:start position:0% +I got a little worried but uh I want to +minimize the maximum of these two + + align:start position:0% +minimize the maximum of these two + + + align:start position:0% +minimize the maximum of these two +quantities okay and so um the best I + + align:start position:0% +quantities okay and so um the best I + + + align:start position:0% +quantities okay and so um the best I +could do is to keep them equal and if I + + align:start position:0% +could do is to keep them equal and if I + + + align:start position:0% +could do is to keep them equal and if I +get L for both of them that would + + align:start position:0% +get L for both of them that would + + + align:start position:0% +get L for both of them that would +minimize the maximum of the those two + + align:start position:0% +minimize the maximum of the those two + + + align:start position:0% +minimize the maximum of the those two +quantities if I had 2 L and zero then + + align:start position:0% +quantities if I had 2 L and zero then + + + align:start position:0% +quantities if I had 2 L and zero then +the maximum of those two quantities is 2 + + align:start position:0% +the maximum of those two quantities is 2 + + + align:start position:0% +the maximum of those two quantities is 2 +L and obviously I haven't done any + + align:start position:0% +L and obviously I haven't done any + + + align:start position:0% +L and obviously I haven't done any +minimization so now you see why there's + + align:start position:0% +minimization so now you see why there's + + + align:start position:0% +minimization so now you see why there's +a + + align:start position:0% + + + + align:start position:0% + +trivial Optimum + + align:start position:0% +trivial Optimum + + + align:start position:0% +trivial Optimum +solution is greater than or equal to + + align:start position:0% +solution is greater than or equal to + + + align:start position:0% +solution is greater than or equal to +l right and and now you see why there's + + align:start position:0% +l right and and now you see why there's + + + align:start position:0% +l right and and now you see why there's +a trivial two approximation algorithm uh + + align:start position:0% +a trivial two approximation algorithm uh + + + align:start position:0% +a trivial two approximation algorithm uh +because the worst I could do is 2 L + + align:start position:0% +because the worst I could do is 2 L + + + align:start position:0% +because the worst I could do is 2 L +right I could dump all of them on one + + align:start position:0% +right I could dump all of them on one + + + align:start position:0% +right I could dump all of them on one +side constant time and the other one is + + align:start position:0% +side constant time and the other one is + + + align:start position:0% +side constant time and the other one is +zero and my my cost is 2 L so I'm within + + align:start position:0% +zero and my my cost is 2 L so I'm within + + + align:start position:0% +zero and my my cost is 2 L so I'm within +a factor two in this problem trivially + + align:start position:0% +a factor two in this problem trivially + + + align:start position:0% +a factor two in this problem trivially +so unfortunately that's not the end of + + align:start position:0% +so unfortunately that's not the end of + + + align:start position:0% +so unfortunately that's not the end of +the lecture okay so we got to do better + + align:start position:0% +the lecture okay so we got to do better + + + align:start position:0% +the lecture okay so we got to do better +I mean clearly there's more here you'd + + align:start position:0% +I mean clearly there's more here you'd + + + align:start position:0% +I mean clearly there's more here you'd +like to get much closer this is a + + align:start position:0% +like to get much closer this is a + + + align:start position:0% +like to get much closer this is a +different kind of problem and it'd be + + align:start position:0% +different kind of problem and it'd be + + + align:start position:0% +different kind of problem and it'd be +wonderful if you could get with an + + align:start position:0% +wonderful if you could get with an + + + align:start position:0% +wonderful if you could get with an +Epsilon right I'm within 1% how long + + align:start position:0% +Epsilon right I'm within 1% how long + + + align:start position:0% +Epsilon right I'm within 1% how long +does it take me I'm within 0 1% + + align:start position:0% +does it take me I'm within 0 1% + + + align:start position:0% +does it take me I'm within 0 1% +guaranteed how long does it take me + + align:start position:0% +guaranteed how long does it take me + + + align:start position:0% +guaranteed how long does it take me +right that's what an approximation + + align:start position:0% +right that's what an approximation + + + align:start position:0% +right that's what an approximation +scheme is as opposed to just a plain + + align:start position:0% +scheme is as opposed to just a plain + + + align:start position:0% +scheme is as opposed to just a plain +algorithm so we're going to actually + + align:start position:0% +algorithm so we're going to actually + + + align:start position:0% +algorithm so we're going to actually +talk about um Eep Epsilon uh here and + + align:start position:0% +talk about um Eep Epsilon uh here and + + + align:start position:0% +talk about um Eep Epsilon uh here and +we're just doing a p + + align:start position:0% +we're just doing a p + + + align:start position:0% +we're just doing a p +test so we're going to see something + + align:start position:0% +test so we're going to see something + + + align:start position:0% +test so we're going to see something +that U is not polinomial in 1 / Epsilon + + align:start position:0% +that U is not polinomial in 1 / Epsilon + + + align:start position:0% +that U is not polinomial in 1 / Epsilon +it's polinomial in N but not polinomial + + align:start position:0% +it's polinomial in N but not polinomial + + + align:start position:0% +it's polinomial in N but not polinomial +in 1 / Epsilon but there is an fpts for + + align:start position:0% +in 1 / Epsilon but there is an fpts for + + + align:start position:0% +in 1 / Epsilon but there is an fpts for +this problem that uh you're not + + align:start position:0% +this problem that uh you're not + + + align:start position:0% +this problem that uh you're not +responsible for + + align:start position:0% + + + + align:start position:0% + +so this is going to be an interesting + + align:start position:0% +so this is going to be an interesting + + + align:start position:0% +so this is going to be an interesting +algorithm simply because uh we now have + + align:start position:0% +algorithm simply because uh we now have + + + align:start position:0% +algorithm simply because uh we now have +to do something with Epsilon it's going + + align:start position:0% +to do something with Epsilon it's going + + + align:start position:0% +to do something with Epsilon it's going +to have an extra input it's not going to + + align:start position:0% +to have an extra input it's not going to + + + align:start position:0% +to have an extra input it's not going to +be this simple juristic where I'm going + + align:start position:0% +be this simple juristic where I'm going + + + align:start position:0% +be this simple juristic where I'm going +to do maximum degree or maximum number + + align:start position:0% +to do maximum degree or maximum number + + + align:start position:0% +to do maximum degree or maximum number +of elements or anything like that right + + align:start position:0% +of elements or anything like that right + + + align:start position:0% +of elements or anything like that right +I want to take this Epsilon and actually + + align:start position:0% +I want to take this Epsilon and actually + + + align:start position:0% +I want to take this Epsilon and actually +do something with it right so how does + + align:start position:0% +do something with it right so how does + + + align:start position:0% +do something with it right so how does +this work + + align:start position:0% +this work + + + align:start position:0% +this work +well basically what happens in ptases or + + align:start position:0% +well basically what happens in ptases or + + + align:start position:0% +well basically what happens in ptases or +in a bunch of them is that you + + align:start position:0% +in a bunch of them is that you + + + align:start position:0% +in a bunch of them is that you +essentially do an exponential amount of + + align:start position:0% +essentially do an exponential amount of + + + align:start position:0% +essentially do an exponential amount of +work uh given a particular Epsilon to + + align:start position:0% +work uh given a particular Epsilon to + + + align:start position:0% +work uh given a particular Epsilon to +get a partial optimal solution so you + + align:start position:0% +get a partial optimal solution so you + + + align:start position:0% +get a partial optimal solution so you +can think + + align:start position:0% + + + + align:start position:0% + +of um you can think of Epsilon as + + align:start position:0% +of um you can think of Epsilon as + + + align:start position:0% +of um you can think of Epsilon as +essentially being one 1 divided m + one + + align:start position:0% +essentially being one 1 divided m + one + + + align:start position:0% +essentially being one 1 divided m + one +where m is some quantity and um as M + + align:start position:0% +where m is some quantity and um as M + + + align:start position:0% +where m is some quantity and um as M +grows uh the complexity of your + + align:start position:0% +grows uh the complexity of your + + + align:start position:0% +grows uh the complexity of your +algorithm is going to grow but obviously + + align:start position:0% +algorithm is going to grow but obviously + + + align:start position:0% +algorithm is going to grow but obviously +as M grows you're getting a Tighter and + + align:start position:0% +as M grows you're getting a Tighter and + + + align:start position:0% +as M grows you're getting a Tighter and +Tighter + + align:start position:0% +Tighter + + + align:start position:0% +Tighter +Epsilon you're getting guaranteed closer + + align:start position:0% +Epsilon you're getting guaranteed closer + + + align:start position:0% +Epsilon you're getting guaranteed closer +and closer to your Optimum right and so + + align:start position:0% +and closer to your Optimum right and so + + + align:start position:0% +and closer to your Optimum right and so +we're going to have two phases here in + + align:start position:0% +we're going to have two phases here in + + + align:start position:0% +we're going to have two phases here in +this particular approximation + + align:start position:0% +this particular approximation + + + align:start position:0% +this particular approximation +scheme uh the first phase + + align:start position:0% +scheme uh the first phase + + + align:start position:0% +scheme uh the first phase +is find an + + align:start position:0% +is find an + + + align:start position:0% +is find an +optimal + + align:start position:0% +optimal + + + align:start position:0% +optimal +partition a prime B + + align:start position:0% +partition a prime B + + + align:start position:0% +partition a prime B +Prime of S1 through S and uh we're just + + align:start position:0% +Prime of S1 through S and uh we're just + + + align:start position:0% +Prime of S1 through S and uh we're just +going to assume that it's exhaustive + + align:start position:0% +going to assume that it's exhaustive + + + align:start position:0% +going to assume that it's exhaustive +search which looks at all possible + + align:start position:0% +search which looks at all possible + + + align:start position:0% +search which looks at all possible +subsets and picks the best one okay and + + align:start position:0% +subsets and picks the best one okay and + + + align:start position:0% +subsets and picks the best one okay and +how many subsets are there for a a set + + align:start position:0% +how many subsets are there for a a set + + + align:start position:0% +how many subsets are there for a a set +of size M it's 2 raised to M so this is + + align:start position:0% +of size M it's 2 raised to M so this is + + + align:start position:0% +of size M it's 2 raised to M so this is +going to be an exponential order 2 + + align:start position:0% +going to be an exponential order 2 + + + align:start position:0% +going to be an exponential order 2 +raised to M algorithm okay I'm just + + align:start position:0% +raised to M algorithm okay I'm just + + + align:start position:0% +raised to M algorithm okay I'm just +going to find the optimum partition + + align:start position:0% +going to find the optimum partition + + + align:start position:0% +going to find the optimum partition +through exhaustive search for M right m + + align:start position:0% +through exhaustive search for M right m + + + align:start position:0% +through exhaustive search for M right m +is uh less than n right + + align:start position:0% + + + + align:start position:0% + +so I'm picking something that's a + + align:start position:0% +so I'm picking something that's a + + + align:start position:0% +so I'm picking something that's a +smaller problem I'm going to seed this + + align:start position:0% +smaller problem I'm going to seed this + + + align:start position:0% +smaller problem I'm going to seed this +so the way the scheme works is I'm + + align:start position:0% +so the way the scheme works is I'm + + + align:start position:0% +so the way the scheme works is I'm +seeding my actual algorithm my + + align:start position:0% +seeding my actual algorithm my + + + align:start position:0% +seeding my actual algorithm my +actualistic with uh an + + align:start position:0% +actualistic with uh an + + + align:start position:0% +actualistic with uh an +initial partial solution and uh + + align:start position:0% +initial partial solution and uh + + + align:start position:0% +initial partial solution and uh +depending on how much work I do to + + align:start position:0% +depending on how much work I do to + + + align:start position:0% +depending on how much work I do to +create the seed I'm going to end up + + align:start position:0% +create the seed I'm going to end up + + + align:start position:0% +create the seed I'm going to end up +having higher complexity and obviously + + align:start position:0% +having higher complexity and obviously + + + align:start position:0% +having higher complexity and obviously +that's a function of U small M right or + + align:start position:0% +that's a function of U small M right or + + + align:start position:0% +that's a function of U small M right or +1/ + + align:start position:0% +1/ + + + align:start position:0% +1/ +Epsilon um and so this + + align:start position:0% +Epsilon um and so this + + + align:start position:0% +Epsilon um and so this +takes uh this optimal T takes order 2 ra + + align:start position:0% +takes uh this optimal T takes order 2 ra + + + align:start position:0% +takes uh this optimal T takes order 2 ra +to M + + align:start position:0% +to M + + + align:start position:0% +to M +time and you can think of that as um + + align:start position:0% +time and you can think of that as um + + + align:start position:0% +time and you can think of that as um +order 2 ra to 1/ + + align:start position:0% +order 2 ra to 1/ + + + align:start position:0% +order 2 ra to 1/ +Epsilon and so that's why it's a ptas + + align:start position:0% +Epsilon and so that's why it's a ptas + + + align:start position:0% +Epsilon and so that's why it's a ptas +and not an + + align:start position:0% +and not an + + + align:start position:0% +and not an +fpas + + align:start position:0% +fpas + + + align:start position:0% +fpas +okay so this is ptas + + align:start position:0% + + + + align:start position:0% + +what else do we need to do well I don't + + align:start position:0% +what else do we need to do well I don't + + + align:start position:0% +what else do we need to do well I don't +actually have a solution yet because if + + align:start position:0% +actually have a solution yet because if + + + align:start position:0% +actually have a solution yet because if +m is really small and and by the way M + + align:start position:0% +m is really small and and by the way M + + + align:start position:0% +m is really small and and by the way M +can be zero as + + align:start position:0% +can be zero as + + + align:start position:0% +can be zero as +well right uh Epsilon would then be a + + align:start position:0% +well right uh Epsilon would then be a + + + align:start position:0% +well right uh Epsilon would then be a +two approximation one divided by uh this + + align:start position:0% +two approximation one divided by uh this + + + align:start position:0% +two approximation one divided by uh this +would be 1 half and so 1/ Epsilon is two + + align:start position:0% +would be 1 half and so 1/ Epsilon is two + + + align:start position:0% +would be 1 half and so 1/ Epsilon is two +so then you got your trivial algorithm + + align:start position:0% +so then you got your trivial algorithm + + + align:start position:0% +so then you got your trivial algorithm +that we had the two approximation scheme + + align:start position:0% +that we had the two approximation scheme + + + align:start position:0% +that we had the two approximation scheme +right so that makes + + align:start position:0% +right so that makes + + + align:start position:0% +right so that makes +sense so the second phase is uh you're + + align:start position:0% +sense so the second phase is uh you're + + + align:start position:0% +sense so the second phase is uh you're +going to start with your seed + + align:start position:0% +going to start with your seed + + + align:start position:0% +going to start with your seed +corresponding to uh A and B uh you're + + align:start position:0% +corresponding to uh A and B uh you're + + + align:start position:0% +corresponding to uh A and B uh you're +going to set them to a prime and B Prime + + align:start position:0% +going to set them to a prime and B Prime + + + align:start position:0% +going to set them to a prime and B Prime +and what I'm going to do is for i = m + + + align:start position:0% +and what I'm going to do is for i = m + + + + align:start position:0% +and what I'm going to do is for i = m + +1 to + + align:start position:0% +1 to + + + align:start position:0% +1 to +n + + align:start position:0% +n + + + align:start position:0% +n +if w + + align:start position:0% +if w + + + align:start position:0% +if w +a less than or equal to + + align:start position:0% + + + + align:start position:0% + +WB a equal a union + + align:start position:0% +WB a equal a union + + + align:start position:0% +WB a equal a union +I uh running out of the room + + align:start position:0% +I uh running out of the room + + + align:start position:0% +I uh running out of the room +else uh b + + align:start position:0% +else uh b + + + align:start position:0% +else uh b +equals + + align:start position:0% +equals + + + align:start position:0% +equals +B Union + + align:start position:0% +B Union + + + align:start position:0% +B Union +I okay so uh it's not that hard to see + + align:start position:0% +I okay so uh it's not that hard to see + + + align:start position:0% +I okay so uh it's not that hard to see +hopefully um all I'm doing here is I'm + + align:start position:0% +hopefully um all I'm doing here is I'm + + + align:start position:0% +hopefully um all I'm doing here is I'm +just going in a very greedy way I got my + + align:start position:0% +just going in a very greedy way I got my + + + align:start position:0% +just going in a very greedy way I got my +uh my initial a prime and B Prime I set + + align:start position:0% +uh my initial a prime and B Prime I set + + + align:start position:0% +uh my initial a prime and B Prime I set +them to A and B and I say oh I got this + + align:start position:0% +them to A and B and I say oh I got this + + + align:start position:0% +them to A and B and I say oh I got this +element here which one is bigger oh this + + align:start position:0% +element here which one is bigger oh this + + + align:start position:0% +element here which one is bigger oh this +one is bigger I'm going to put the + + align:start position:0% +one is bigger I'm going to put the + + + align:start position:0% +one is bigger I'm going to put the +element over here and then I look at it + + align:start position:0% +element over here and then I look at it + + + align:start position:0% +element over here and then I look at it +again got another element which one is + + align:start position:0% +again got another element which one is + + + align:start position:0% +again got another element which one is +bigger and I go this way that way that's + + align:start position:0% +bigger and I go this way that way that's + + + align:start position:0% +bigger and I go this way that way that's +that's pretty much it right so again all + + align:start position:0% +that's pretty much it right so again all + + + align:start position:0% +that's pretty much it right so again all +of these algorithms are really + + align:start position:0% +of these algorithms are really + + + align:start position:0% +of these algorithms are really +straightforward uh the the interesting + + align:start position:0% +straightforward uh the the interesting + + + align:start position:0% +straightforward uh the the interesting +part the fun Parts in showing the + + align:start position:0% +part the fun Parts in showing the + + + align:start position:0% +part the fun Parts in showing the +approximation + + align:start position:0% +approximation + + + align:start position:0% +approximation +guarantee so we good + + align:start position:0% +guarantee so we good + + + align:start position:0% +guarantee so we good +here + + align:start position:0% +here + + + align:start position:0% +here +yep all right so uh back to + + align:start position:0% +yep all right so uh back to + + + align:start position:0% +yep all right so uh back to +analysis one last time + + align:start position:0% + + + + align:start position:0% + +so let's see + + align:start position:0% +so let's see + + + align:start position:0% +so let's see +um we want to show that + + align:start position:0% +um we want to show that + + + align:start position:0% +um we want to show that +approx + + align:start position:0% + + + + align:start position:0% + +partition ah you know how to spell + + align:start position:0% +partition ah you know how to spell + + + align:start position:0% +partition ah you know how to spell +partition is + + align:start position:0% + + + + align:start position:0% + +P I guess I don't but you + + align:start position:0% +P I guess I don't but you + + + align:start position:0% +P I guess I don't but you +do uh let's assume that w a is greater + + align:start position:0% +do uh let's assume that w a is greater + + + align:start position:0% +do uh let's assume that w a is greater +than or equal to + + align:start position:0% +than or equal to + + + align:start position:0% +than or equal to +WB uh to to end with right so I'm just + + align:start position:0% +WB uh to to end with right so I'm just + + + align:start position:0% +WB uh to to end with right so I'm just +saying at the end here I'm just marking + + align:start position:0% +saying at the end here I'm just marking + + + align:start position:0% +saying at the end here I'm just marking +the one that was larger that came out of + + align:start position:0% +the one that was larger that came out of + + + align:start position:0% +the one that was larger that came out of +the max as a right without loss of + + align:start position:0% +the max as a right without loss of + + + align:start position:0% +the max as a right without loss of +generality just to make things easier I + + align:start position:0% +generality just to make things easier I + + + align:start position:0% +generality just to make things easier I +don't want to keep interchanging things + + align:start position:0% +don't want to keep interchanging things + + + align:start position:0% +don't want to keep interchanging things +so our approximation + + align:start position:0% + + + + align:start position:0% + +ratio is W divided by L right wa could + + align:start position:0% +ratio is W divided by L right wa could + + + align:start position:0% +ratio is W divided by L right wa could +at best be L if if I got a perfect + + align:start position:0% +at best be L if if I got a perfect + + + align:start position:0% +at best be L if if I got a perfect +partition perfectly balanced but it + + align:start position:0% +partition perfectly balanced but it + + + align:start position:0% +partition perfectly balanced but it +could be a little bit more and that's my + + align:start position:0% +could be a little bit more and that's my + + + align:start position:0% +could be a little bit more and that's my +approximation ratio okay so I I need to + + align:start position:0% +approximation ratio okay so I I need to + + + align:start position:0% +approximation ratio okay so I I need to +now figure out how the approximation + + align:start position:0% +now figure out how the approximation + + + align:start position:0% +now figure out how the approximation +ratio reflects on the runtime and is + + align:start position:0% +ratio reflects on the runtime and is + + + align:start position:0% +ratio reflects on the runtime and is +related to M and therefore Epsilon all + + align:start position:0% +related to M and therefore Epsilon all + + + align:start position:0% +related to M and therefore Epsilon all +right so what I'm going to do here is + + align:start position:0% +right so what I'm going to do here is + + + align:start position:0% +right so what I'm going to do here is +I'm going to look + + align:start position:0% + + + + align:start position:0% + +at a point in time + + align:start position:0% + + + + align:start position:0% + +where I have a and b and remember that W + + align:start position:0% +where I have a and b and remember that W + + + align:start position:0% +where I have a and b and remember that W +is defined to be greater than WB but + + align:start position:0% +is defined to be greater than WB but + + + align:start position:0% +is defined to be greater than WB but +here I'm looking at some point in time + + align:start position:0% +here I'm looking at some point in time + + + align:start position:0% +here I'm looking at some point in time +which is not necessarily at the um at + + align:start position:0% +which is not necessarily at the um at + + + align:start position:0% +which is not necessarily at the um at +the very end here it it could be but you + + align:start position:0% +the very end here it it could be but you + + + align:start position:0% +the very end here it it could be but you +can think of this as being I'm just + + align:start position:0% +can think of this as being I'm just + + + align:start position:0% +can think of this as being I'm just +going to say b + + align:start position:0% +going to say b + + + align:start position:0% +going to say b +or um + + align:start position:0% +or um + + + align:start position:0% +or um +intermediate B and this won't matter too + + align:start position:0% +intermediate B and this won't matter too + + + align:start position:0% +intermediate B and this won't matter too +much but I'm just being a little uh bit + + align:start position:0% +much but I'm just being a little uh bit + + + align:start position:0% +much but I'm just being a little uh bit +uh of a stickler here but I'll explain + + align:start position:0% +uh of a stickler here but I'll explain + + + align:start position:0% +uh of a stickler here but I'll explain +why I said that in just a minute but the + + align:start position:0% +why I said that in just a minute but the + + + align:start position:0% +why I said that in just a minute but the +point is I have a a situation where I + + align:start position:0% +point is I have a a situation where I + + + align:start position:0% +point is I have a a situation where I +know that the wa is greater than WB or + + align:start position:0% +know that the wa is greater than WB or + + + align:start position:0% +know that the wa is greater than WB or +greater than or equal to WB because I + + align:start position:0% +greater than or equal to WB because I + + + align:start position:0% +greater than or equal to WB because I +assumed it that's how I marked it and + + align:start position:0% +assumed it that's how I marked it and + + + align:start position:0% +assumed it that's how I marked it and +I'm I'm going to look at K is the last + + align:start position:0% +I'm I'm going to look at K is the last + + + align:start position:0% +I'm I'm going to look at K is the last +element + + align:start position:0% + + + + align:start position:0% + +added to a is it's is being added now + + align:start position:0% +added to a is it's is being added now + + + align:start position:0% +added to a is it's is being added now +this could have been + + align:start position:0% + + + + align:start position:0% + +added in the first phase or the second + + align:start position:0% +added in the first phase or the second + + + align:start position:0% +added in the first phase or the second +phase it's quite + + align:start position:0% +phase it's quite + + + align:start position:0% +phase it's quite +possible that for a given + + align:start position:0% +possible that for a given + + + align:start position:0% +possible that for a given +M that if it's large for example that + + align:start position:0% +M that if it's large for example that + + + align:start position:0% +M that if it's large for example that +the a that you you the a prime that you + + align:start position:0% +the a that you you the a prime that you + + + align:start position:0% +the a that you you the a prime that you +end up with uh is your a to begin with + + align:start position:0% +end up with uh is your a to begin with + + + align:start position:0% +end up with uh is your a to begin with +here and that you never + + align:start position:0% +here and that you never + + + align:start position:0% +here and that you never +execute uh this statement okay it's + + align:start position:0% +execute uh this statement okay it's + + + align:start position:0% +execute uh this statement okay it's +quite possible right um you you you got + + align:start position:0% +quite possible right um you you you got + + + align:start position:0% +quite possible right um you you you got +your uh initial seed and you never added + + align:start position:0% +your uh initial seed and you never added + + + align:start position:0% +your uh initial seed and you never added +to it and that was it because your M was + + align:start position:0% +to it and that was it because your M was + + + align:start position:0% +to it and that was it because your M was +large for example right so what I'm + + align:start position:0% +large for example right so what I'm + + + align:start position:0% +large for example right so what I'm +saying here is K is the last element + + align:start position:0% +saying here is K is the last element + + + align:start position:0% +saying here is K is the last element +added to a okay so there's clearly a + + align:start position:0% +added to a okay so there's clearly a + + + align:start position:0% +added to a okay so there's clearly a +last element I'm just marking that + + align:start position:0% +last element I'm just marking that + + + align:start position:0% +last element I'm just marking that +um and we know that a is greater than or + + align:start position:0% +um and we know that a is greater than or + + + align:start position:0% +um and we know that a is greater than or +equal to B now it may be true that if + + align:start position:0% +equal to B now it may be true that if + + + align:start position:0% +equal to B now it may be true that if +I'm looking at the snapshot when just + + align:start position:0% +I'm looking at the snapshot when just + + + align:start position:0% +I'm looking at the snapshot when just +after I add the K element to a I may not + + align:start position:0% +after I add the K element to a I may not + + + align:start position:0% +after I add the K element to a I may not +quite I may not be done yet in terms of + + align:start position:0% +quite I may not be done yet in terms of + + + align:start position:0% +quite I may not be done yet in terms of +I still have a few elements and I may be + + align:start position:0% +I still have a few elements and I may be + + + align:start position:0% +I still have a few elements and I may be +adding elements to B but regardless + + align:start position:0% +adding elements to B but regardless + + + align:start position:0% +adding elements to B but regardless +given my definition I know that b is + + align:start position:0% +given my definition I know that b is + + + align:start position:0% +given my definition I know that b is +less than the weight of B is less than + + align:start position:0% +less than the weight of B is less than + + + align:start position:0% +less than the weight of B is less than +the weight of a because even though um + + align:start position:0% +the weight of a because even though um + + + align:start position:0% +the weight of a because even though um +the last element overall may be added to + + align:start position:0% +the last element overall may be added to + + + align:start position:0% +the last element overall may be added to +B uh WB is is less than wa and I'm only + + align:start position:0% +B uh WB is is less than wa and I'm only + + + align:start position:0% +B uh WB is is less than wa and I'm only +looking at the last element added to + + align:start position:0% +looking at the last element added to + + + align:start position:0% +looking at the last element added to +added to a here okay so uh why all of + + align:start position:0% +added to a here okay so uh why all of + + + align:start position:0% +added to a here okay so uh why all of +this skull + + align:start position:0% +this skull + + + align:start position:0% +this skull +dugery + + align:start position:0% +dugery + + + align:start position:0% +dugery +well there's a there's a method here to + + align:start position:0% +well there's a there's a method here to + + + align:start position:0% +well there's a there's a method here to +the + + align:start position:0% +the + + + align:start position:0% +the +madness uh we're going to + + align:start position:0% +madness uh we're going to + + + align:start position:0% +madness uh we're going to +analyze what possibly happens in the + + align:start position:0% +analyze what possibly happens in the + + + align:start position:0% +analyze what possibly happens in the +first phase and the second phase and get + + align:start position:0% +first phase and the second phase and get + + + align:start position:0% +first phase and the second phase and get +our approximation + + align:start position:0% + + + + align:start position:0% + +ratio shouldn't take too + + align:start position:0% + + + + align:start position:0% + +long so there's two cases here that we + + align:start position:0% +long so there's two cases here that we + + + align:start position:0% +long so there's two cases here that we +need to analiz the first one is easy + + align:start position:0% +need to analiz the first one is easy + + + align:start position:0% +need to analiz the first one is easy +second one is a little more involved I'm + + align:start position:0% +second one is a little more involved I'm + + + align:start position:0% +second one is a little more involved I'm +going to now assume + + align:start position:0% +going to now assume + + + align:start position:0% +going to now assume +that uh K was the last element and was + + align:start position:0% +that uh K was the last element and was + + + align:start position:0% +that uh K was the last element and was +added in the first phase okay if K is + + align:start position:0% +added in the first phase okay if K is + + + align:start position:0% +added in the first phase okay if K is +added + + align:start position:0% +added + + + align:start position:0% +added +to + + align:start position:0% + + + + align:start position:0% + +a what can I say if K was added in the + + align:start position:0% +a what can I say if K was added in the + + + align:start position:0% +a what can I say if K was added in the +first phase to a and and that's the last + + align:start position:0% +first phase to a and and that's the last + + + align:start position:0% +first phase to a and and that's the last +element added throughout the algorithm + + align:start position:0% +element added throughout the algorithm + + + align:start position:0% +element added throughout the algorithm +by the time you get a partition what can + + align:start position:0% +by the time you get a partition what can + + + align:start position:0% +by the time you get a partition what can +you + + align:start position:0% + + + + align:start position:0% + +say what can you say about the solution + + align:start position:0% +say what can you say about the solution + + + align:start position:0% +say what can you say about the solution +what strong state M can you make about + + align:start position:0% +what strong state M can you make about + + + align:start position:0% +what strong state M can you make about +the + + align:start position:0% + + + + align:start position:0% + +solution what's the only interesting + + align:start position:0% +solution what's the only interesting + + + align:start position:0% +solution what's the only interesting +statement strong statement that you can + + align:start position:0% +statement strong statement that you can + + + align:start position:0% +statement strong statement that you can +make about a + + align:start position:0% +make about a + + + align:start position:0% +make about a +solution right so I I I got to a + + align:start position:0% +solution right so I I I got to a + + + align:start position:0% +solution right so I I I got to a +remember what the fa first phase is + + align:start position:0% +remember what the fa first phase is + + + align:start position:0% +remember what the fa first phase is +what's the first + + align:start position:0% +what's the first + + + align:start position:0% +what's the first +phase well it's optimal right so after + + align:start position:0% +phase well it's optimal right so after + + + align:start position:0% +phase well it's optimal right so after +that what happened to + + align:start position:0% +that what happened to + + + align:start position:0% +that what happened to +a well it didn't change right so what + + align:start position:0% +a well it didn't change right so what + + + align:start position:0% +a well it didn't change right so what +you got is Optimum right because W was + + align:start position:0% +you got is Optimum right because W was + + + align:start position:0% +you got is Optimum right because W was +defined to be greater than or equal to + + align:start position:0% +defined to be greater than or equal to + + + align:start position:0% +defined to be greater than or equal to +WB wa was Optimum for the smaller + + align:start position:0% +WB wa was Optimum for the smaller + + + align:start position:0% +WB wa was Optimum for the smaller +Problem whatever M was you never added + + align:start position:0% +Problem whatever M was you never added + + + align:start position:0% +Problem whatever M was you never added +anything else to it so you're done it's + + align:start position:0% +anything else to it so you're done it's + + + align:start position:0% +anything else to it so you're done it's +optimal so you're in this case your + + align:start position:0% +optimal so you're in this case your + + + align:start position:0% +optimal so you're in this case your +approximation ratio is one because you + + align:start position:0% +approximation ratio is one because you + + + align:start position:0% +approximation ratio is one because you +got the optimum solution right so if K + + align:start position:0% +got the optimum solution right so if K + + + align:start position:0% +got the optimum solution right so if K +is added to a in the first place this + + align:start position:0% +is added to a in the first place this + + + align:start position:0% +is added to a in the first place this +means AAL a + + align:start position:0% +means AAL a + + + align:start position:0% +means AAL a +prime we + + align:start position:0% +prime we + + + align:start position:0% +prime we +have an + + align:start position:0% +have an + + + align:start position:0% +have an +optimal partition + + align:start position:0% + + + + align:start position:0% + +since we can't + + align:start position:0% +since we can't + + + align:start position:0% +since we can't +do + + align:start position:0% + + + + align:start position:0% + +better + + align:start position:0% +better + + + align:start position:0% +better +than W + + align:start position:0% +than W + + + align:start position:0% +than W +Prime when we + + align:start position:0% + + + + align:start position:0% + +have n greater than M + + align:start position:0% +have n greater than M + + + align:start position:0% +have n greater than M +items and we + + align:start position:0% +items and we + + + align:start position:0% +items and we +know w + + align:start position:0% +know w + + + align:start position:0% +know w +Prime is + + align:start position:0% +Prime is + + + align:start position:0% +Prime is +optimal for the M + + align:start position:0% +optimal for the M + + + align:start position:0% +optimal for the M +items okay so so that's cool that's good + + align:start position:0% +items okay so so that's cool that's good + + + align:start position:0% +items okay so so that's cool that's good +so we we got an approximation ratio of + + align:start position:0% +so we we got an approximation ratio of + + + align:start position:0% +so we we got an approximation ratio of +of one there of uh uh and and remember + + align:start position:0% +of one there of uh uh and and remember + + + align:start position:0% +of one there of uh uh and and remember +that this is not taking overall + + align:start position:0% +that this is not taking overall + + + align:start position:0% +that this is not taking overall +exponential time necessarily it's just a + + align:start position:0% +exponential time necessarily it's just a + + + align:start position:0% +exponential time necessarily it's just a +case where I've picked some arbitrary M + + align:start position:0% +case where I've picked some arbitrary M + + + align:start position:0% +case where I've picked some arbitrary M +and it happens to be the case that + + align:start position:0% +and it happens to be the case that + + + align:start position:0% +and it happens to be the case that +a equals a prime at the end of the + + align:start position:0% +a equals a prime at the end of the + + + align:start position:0% +a equals a prime at the end of the +algorithm so I am taking exponential + + align:start position:0% +algorithm so I am taking exponential + + + align:start position:0% +algorithm so I am taking exponential +time in in M right M as in Mary but I'm + + align:start position:0% +time in in M right M as in Mary but I'm + + + align:start position:0% +time in in M right M as in Mary but I'm +not taking exponential time is is in N + + align:start position:0% +not taking exponential time is is in N + + + align:start position:0% +not taking exponential time is is in N +right n is in + + align:start position:0% + + + + align:start position:0% + +Nancy so the second part is where the + + align:start position:0% +Nancy so the second part is where the + + + align:start position:0% +Nancy so the second part is where the +approximation ratio comes + + align:start position:0% +approximation ratio comes + + + align:start position:0% +approximation ratio comes +in uh K is + + align:start position:0% + + + + align:start position:0% + +added to a in the second phase + + align:start position:0% + + + + align:start position:0% + +so here what we're going to do is we're + + align:start position:0% +so here what we're going to do is we're + + + align:start position:0% +so here what we're going to do is we're +going to say we + + align:start position:0% +going to say we + + + align:start position:0% +going to say we +know W A minus SK is less than or equal + + align:start position:0% +know W A minus SK is less than or equal + + + align:start position:0% +know W A minus SK is less than or equal +to + + align:start position:0% +to + + + align:start position:0% +to +WB right this is the second phase we're + + align:start position:0% +WB right this is the second phase we're + + + align:start position:0% +WB right this is the second phase we're +talking about here the only reason SK + + align:start position:0% +talking about here the only reason SK + + + align:start position:0% +talking about here the only reason SK +was added to a was because you decided + + align:start position:0% +was added to a was because you decided + + + align:start position:0% +was added to a was because you decided +that uh a was the side that was smaller + + align:start position:0% +that uh a was the side that was smaller + + + align:start position:0% +that uh a was the side that was smaller +right or perhaps equal right so that's + + align:start position:0% +right or perhaps equal right so that's + + + align:start position:0% +right or perhaps equal right so that's +the reason you added it into it so you + + align:start position:0% +the reason you added it into it so you + + + align:start position:0% +the reason you added it into it so you +know that W A minus SK is less than or + + align:start position:0% +know that W A minus SK is less than or + + + align:start position:0% +know that W A minus SK is less than or +equal to WB at at that time so think + + align:start position:0% +equal to WB at at that time so think + + + align:start position:0% +equal to WB at at that time so think +think of A and B here as being variables + + align:start position:0% +think of A and B here as being variables + + + align:start position:0% +think of A and B here as being variables +that are obviously changing right uh um + + align:start position:0% +that are obviously changing right uh um + + + align:start position:0% +that are obviously changing right uh um +but I what I'm saying here um is if you + + align:start position:0% +but I what I'm saying here um is if you + + + align:start position:0% +but I what I'm saying here um is if you +even if you look this is the algorithm + + align:start position:0% +even if you look this is the algorithm + + + align:start position:0% +even if you look this is the algorithm +where A and B you constantly look at + + align:start position:0% +where A and B you constantly look at + + + align:start position:0% +where A and B you constantly look at +them and decide which way to go but if + + align:start position:0% +them and decide which way to go but if + + + align:start position:0% +them and decide which way to go but if +you look at uh the the last step then + + align:start position:0% +you look at uh the the last step then + + + align:start position:0% +you look at uh the the last step then +you look at the final value + + align:start position:0% +you look at the final value + + + align:start position:0% +you look at the final value +then you can certainly make the + + align:start position:0% +then you can certainly make the + + + align:start position:0% +then you can certainly make the +statement for those final values that + + align:start position:0% +statement for those final values that + + + align:start position:0% +statement for those final values that +the wa which is the resultant value + + align:start position:0% +the wa which is the resultant value + + + align:start position:0% +the wa which is the resultant value +minus SK should have been less than or + + align:start position:0% +minus SK should have been less than or + + + align:start position:0% +minus SK should have been less than or +equal to WB uh and you had a smaller W + + align:start position:0% +equal to WB uh and you had a smaller W + + + align:start position:0% +equal to WB uh and you had a smaller W +to uh to begin with uh and you added SK + + align:start position:0% +to uh to begin with uh and you added SK + + + align:start position:0% +to uh to begin with uh and you added SK +to it and that happened in the in the + + align:start position:0% +to it and that happened in the in the + + + align:start position:0% +to it and that happened in the in the +second phase okay so this is why K was + + align:start position:0% +second phase okay so this is why K was + + + align:start position:0% +second phase okay so this is why K was +added this is + + align:start position:0% +added this is + + + align:start position:0% +added this is +why K was added to a + + align:start position:0% + + + + align:start position:0% + +I want to be a little careful here given + + align:start position:0% +I want to be a little careful here given + + + align:start position:0% +I want to be a little careful here given +that we're using we overloading A and B + + align:start position:0% +that we're using we overloading A and B + + + align:start position:0% +that we're using we overloading A and B +but I'll try and point out what each of + + align:start position:0% +but I'll try and point out what each of + + + align:start position:0% +but I'll try and point out what each of +these statements actually means and and + + align:start position:0% +these statements actually means and and + + + align:start position:0% +these statements actually means and and +uh ask questions if you're if you're + + align:start position:0% +uh ask questions if you're if you're + + + align:start position:0% +uh ask questions if you're if you're +confused um I know that w a - SK is less + + align:start position:0% +confused um I know that w a - SK is less + + + align:start position:0% +confused um I know that w a - SK is less +than or equal to 2 lus W all that's just + + align:start position:0% +than or equal to 2 lus W all that's just + + + align:start position:0% +than or equal to 2 lus W all that's just +a substitution because W A + WB equal 2 + + align:start position:0% +a substitution because W A + WB equal 2 + + + align:start position:0% +a substitution because W A + WB equal 2 +L + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then last little trick again it's + + align:start position:0% +and then last little trick again it's + + + align:start position:0% +and then last little trick again it's +it's algebra nothing profound here um we + + align:start position:0% +it's algebra nothing profound here um we + + + align:start position:0% +it's algebra nothing profound here um we +we have our assumption that we ordered + + align:start position:0% +we have our assumption that we ordered + + + align:start position:0% +we have our assumption that we ordered +these things um so you had S1 through uh + + align:start position:0% +these things um so you had S1 through uh + + + align:start position:0% +these things um so you had S1 through uh +SN excuse me the whole the whole thing + + align:start position:0% +SN excuse me the whole the whole thing + + + align:start position:0% +SN excuse me the whole the whole thing +was + + align:start position:0% +was + + + align:start position:0% +was +ordered um and so we can + + align:start position:0% + + + + align:start position:0% + +say + + align:start position:0% +say + + + align:start position:0% +say +that S1 S2 all the way to S is greater + + align:start position:0% +that S1 S2 all the way to S is greater + + + align:start position:0% +that S1 S2 all the way to S is greater +than or equal to + + align:start position:0% +than or equal to + + + align:start position:0% +than or equal to +SK uh we are actually doing this in + + align:start position:0% +SK uh we are actually doing this in + + + align:start position:0% +SK uh we are actually doing this in +order we taking the bigger elements and + + align:start position:0% +order we taking the bigger elements and + + + align:start position:0% +order we taking the bigger elements and +then deciding where they go so we sorted + + align:start position:0% +then deciding where they go so we sorted + + + align:start position:0% +then deciding where they go so we sorted +those things initially and so what we + + align:start position:0% +those things initially and so what we + + + align:start position:0% +those things initially and so what we +end up with when we look at SK we have + + align:start position:0% +end up with when we look at SK we have + + + align:start position:0% +end up with when we look at SK we have +taken care of values prior to SK that + + align:start position:0% +taken care of values prior to SK that + + + align:start position:0% +taken care of values prior to SK that +are all greater than or equal to SK + + align:start position:0% +are all greater than or equal to SK + + + align:start position:0% +are all greater than or equal to SK +right that's uh again using our initial + + align:start position:0% +right that's uh again using our initial + + + align:start position:0% +right that's uh again using our initial +assumption so what that means is 2 L + + align:start position:0% +assumption so what that means is 2 L + + + align:start position:0% +assumption so what that means is 2 L +is greater than or equal + + align:start position:0% +is greater than or equal + + + align:start position:0% +is greater than or equal +to m + 1 + + align:start position:0% +to m + 1 + + + align:start position:0% +to m + 1 +SK since K is greater than M right again + + align:start position:0% +SK since K is greater than M right again + + + align:start position:0% +SK since K is greater than M right again +this is not particularly tight um + + align:start position:0% +this is not particularly tight um + + + align:start position:0% +this is not particularly tight um +because M could be really pretty small + + align:start position:0% +because M could be really pretty small + + + align:start position:0% +because M could be really pretty small +in relation to n but I do know that I + + align:start position:0% +in relation to n but I do know that I + + + align:start position:0% +in relation to n but I do know that I +can make the statement that um since the + + align:start position:0% +can make the statement that um since the + + + align:start position:0% +can make the statement that um since the +values are decreasing that 2L which is + + align:start position:0% +values are decreasing that 2L which is + + + align:start position:0% +values are decreasing that 2L which is +the sum of all of those is greater than + + align:start position:0% +the sum of all of those is greater than + + + align:start position:0% +the sum of all of those is greater than +or equal to m + 1 * SK regardless of + + align:start position:0% +or equal to m + 1 * SK regardless of + + + align:start position:0% +or equal to m + 1 * SK regardless of +what m is + + align:start position:0% +what m is + + + align:start position:0% +what m is +right uh and so so that's pretty much it + + align:start position:0% +right uh and so so that's pretty much it + + + align:start position:0% +right uh and so so that's pretty much it +uh once you do that you have your + + align:start position:0% +uh once you do that you have your + + + align:start position:0% +uh once you do that you have your +approximation uh + + align:start position:0% +approximation uh + + + align:start position:0% +approximation uh +ratio uh let's leave that up there + + align:start position:0% +ratio uh let's leave that up there + + + align:start position:0% +ratio uh let's leave that up there +because that's the algorithm finish this + + align:start position:0% + + + + align:start position:0% + +off with a little + + align:start position:0% + + + + align:start position:0% + +algebra all right so w a divid by L is + + align:start position:0% +algebra all right so w a divid by L is + + + align:start position:0% +algebra all right so w a divid by L is +less than or equal to l + SK / 2 / L I'm + + align:start position:0% +less than or equal to l + SK / 2 / L I'm + + + align:start position:0% +less than or equal to l + SK / 2 / L I'm +basically substituting I have this and I + + align:start position:0% +basically substituting I have this and I + + + align:start position:0% +basically substituting I have this and I +have that and I'm playing around with + + align:start position:0% +have that and I'm playing around with + + + align:start position:0% +have that and I'm playing around with +it um and I got one + + + align:start position:0% +it um and I got one + + + + align:start position:0% +it um and I got one + +SK divided + + align:start position:0% +SK divided + + + align:start position:0% +SK divided +by uh 1 + SK ided 2 + + align:start position:0% +by uh 1 + SK ided 2 + + + align:start position:0% +by uh 1 + SK ided 2 +L um which + + align:start position:0% +L um which + + + align:start position:0% +L um which +is now this I can say is equal + + align:start position:0% +is now this I can say is equal + + + align:start position:0% +is now this I can say is equal +uh that's simply equal this I have less + + align:start position:0% +uh that's simply equal this I have less + + + align:start position:0% +uh that's simply equal this I have less +than or equal to and then I can go less + + align:start position:0% +than or equal to and then I can go less + + + align:start position:0% +than or equal to and then I can go less +than or equal to 1 + SK divided by m + 1 + + align:start position:0% +than or equal to 1 + SK divided by m + 1 + + + align:start position:0% +than or equal to 1 + SK divided by m + 1 +SK and then I got 1 + 1 / m + 1 which is + + align:start position:0% +SK and then I got 1 + 1 / m + 1 which is + + + align:start position:0% +SK and then I got 1 + 1 / m + 1 which is +of + + align:start position:0% +of + + + align:start position:0% +of +course 1 plus Epsilon right so all I did + + align:start position:0% +course 1 plus Epsilon right so all I did + + + align:start position:0% +course 1 plus Epsilon right so all I did +here was use this fact and and and + + align:start position:0% +here was use this fact and and and + + + align:start position:0% +here was use this fact and and and +essentially relate two to SK and once I + + align:start position:0% +essentially relate two to SK and once I + + + align:start position:0% +essentially relate two to SK and once I +could relate 2 L to SK um + + align:start position:0% +could relate 2 L to SK um + + + align:start position:0% +could relate 2 L to SK um +substituting for uh + + align:start position:0% +substituting for uh + + + align:start position:0% +substituting for uh +SK in in in here I I I ended up with the + + align:start position:0% +SK in in in here I I I ended up with the + + + align:start position:0% +SK in in in here I I I ended up with the +approximation ratio that I want wa over + + align:start position:0% +approximation ratio that I want wa over + + + align:start position:0% +approximation ratio that I want wa over +L is L plus SK ided two that simply + + align:start position:0% +L is L plus SK ided two that simply + + + align:start position:0% +L is L plus SK ided two that simply +comes from here um and you know plug + + align:start position:0% +comes from here um and you know plug + + + align:start position:0% +comes from here um and you know plug +that in divided by L and then um I have + + align:start position:0% +that in divided by L and then um I have + + + align:start position:0% +that in divided by L and then um I have +uh SK divided by 2L and then this part + + align:start position:0% +uh SK divided by 2L and then this part + + + align:start position:0% +uh SK divided by 2L and then this part +here 2L is going to uh get substituted + + align:start position:0% +here 2L is going to uh get substituted + + + align:start position:0% +here 2L is going to uh get substituted +by m+1 SK and uh voila I'm over here + + align:start position:0% +by m+1 SK and uh voila I'm over here + + + align:start position:0% +by m+1 SK and uh voila I'm over here +okay so um the story behind this uh + + align:start position:0% +okay so um the story behind this uh + + + align:start position:0% +okay so um the story behind this uh +particular uh problem was uh it was in + + align:start position:0% +particular uh problem was uh it was in + + + align:start position:0% +particular uh problem was uh it was in +the quiz and Eric I guess took the quiz + + align:start position:0% +the quiz and Eric I guess took the quiz + + + align:start position:0% +the quiz and Eric I guess took the quiz +did you actually take the quiz or edit + + align:start position:0% +did you actually take the quiz or edit + + + align:start position:0% +did you actually take the quiz or edit +the quiz and he says this problem is + + align:start position:0% +the quiz and he says this problem is + + + align:start position:0% +the quiz and he says this problem is +impossible um it was a it was a it was a + + align:start position:0% +impossible um it was a it was a it was a + + + align:start position:0% +impossible um it was a it was a it was a +problem he said this problem is + + align:start position:0% +problem he said this problem is + + + align:start position:0% +problem he said this problem is +impossible I had to Google it to find + + align:start position:0% +impossible I had to Google it to find + + + align:start position:0% +impossible I had to Google it to find +out the answer or something like that + + align:start position:0% +out the answer or something like that + + + align:start position:0% +out the answer or something like that +and I said well I'm going to give the + + align:start position:0% +and I said well I'm going to give the + + + align:start position:0% +and I said well I'm going to give the +answer in lecture right so there you go + + align:start position:0% +answer in lecture right so there you go + + + align:start position:0% +answer in lecture right so there you go +so remember this write it down four + + align:start position:0% +so remember this write it down four + + + align:start position:0% +so remember this write it down four +points for coming to lecture today right + + align:start position:0% +points for coming to lecture today right + + + align:start position:0% +points for coming to lecture today right +see you guys next time \ No newline at end of file diff --git a/MRdNlTEoIFE.txt b/MRdNlTEoIFE.txt new file mode 100644 index 0000000000000000000000000000000000000000..9e98e23463e63202fed0ab652fb58efc95333f55 --- /dev/null +++ b/MRdNlTEoIFE.txt @@ -0,0 +1,3499 @@ +align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +the next important part of turbulent + + align:start position:0% +the next important part of turbulent + + + align:start position:0% +the next important part of turbulent +plume theory that we need is the + + align:start position:0% +plume theory that we need is the + + + align:start position:0% +plume theory that we need is the +distribution of concentration + + align:start position:0% +distribution of concentration + + + align:start position:0% +distribution of concentration +of particles or droplets in this case + + align:start position:0% +of particles or droplets in this case + + + align:start position:0% +of particles or droplets in this case +that are + + align:start position:0% +that are + + + align:start position:0% +that are +injected with the fluid at the source + + align:start position:0% +injected with the fluid at the source + + + align:start position:0% +injected with the fluid at the source +so as we've just derived the + + align:start position:0% +so as we've just derived the + + + align:start position:0% +so as we've just derived the +concentration c in this case we could + + align:start position:0% +concentration c in this case we could + + + align:start position:0% +concentration c in this case we could +refer to infection quanta in infectious + + align:start position:0% +refer to infection quanta in infectious + + + align:start position:0% +refer to infection quanta in infectious +aerosols + + align:start position:0% +aerosols + + + align:start position:0% +aerosols +relative to that leaving the mouth which + + align:start position:0% +relative to that leaving the mouth which + + + align:start position:0% +relative to that leaving the mouth which +is + + align:start position:0% +is + + + align:start position:0% +is +we've called cq scales as + + align:start position:0% +we've called cq scales as + + + align:start position:0% +we've called cq scales as +square root of area of the mouth divided + + align:start position:0% +square root of area of the mouth divided + + + align:start position:0% +square root of area of the mouth divided +by alpha x where alpha is the turbulent + + align:start position:0% +by alpha x where alpha is the turbulent + + + align:start position:0% +by alpha x where alpha is the turbulent +entrainment coefficient + + align:start position:0% +entrainment coefficient + + + align:start position:0% +entrainment coefficient +around 0.1 or 0.15 and that leads to a + + align:start position:0% +around 0.1 or 0.15 and that leads to a + + + align:start position:0% +around 0.1 or 0.15 and that leads to a +jet which + + align:start position:0% +jet which + + + align:start position:0% +jet which +grows in size and grows in fluctuations + + align:start position:0% +grows in size and grows in fluctuations + + + align:start position:0% +grows in size and grows in fluctuations +as you see more and more eddies + + align:start position:0% +as you see more and more eddies + + + align:start position:0% +as you see more and more eddies +and eventually might even bend due to + + align:start position:0% +and eventually might even bend due to + + + align:start position:0% +and eventually might even bend due to +flows in the room or + + align:start position:0% +flows in the room or + + + align:start position:0% +flows in the room or +thermal buoyancy effects and i'd like to + + align:start position:0% +thermal buoyancy effects and i'd like to + + + align:start position:0% +thermal buoyancy effects and i'd like to +talk about + + align:start position:0% +talk about + + + align:start position:0% +talk about +the difference between short-range + + align:start position:0% +the difference between short-range + + + align:start position:0% +the difference between short-range +transmission due to really placing + + align:start position:0% +transmission due to really placing + + + align:start position:0% +transmission due to really placing +yourself + + align:start position:0% +yourself + + + align:start position:0% +yourself +in this jet and breathing that air + + align:start position:0% +in this jet and breathing that air + + + align:start position:0% +in this jet and breathing that air +directly which is more concentrated than + + align:start position:0% +directly which is more concentrated than + + + align:start position:0% +directly which is more concentrated than +the background + + align:start position:0% +the background + + + align:start position:0% +the background +and then compare that with the + + align:start position:0% +and then compare that with the + + + align:start position:0% +and then compare that with the +transmission in the well mixed room that + + align:start position:0% +transmission in the well mixed room that + + + align:start position:0% +transmission in the well mixed room that +we've been talking about all along + + align:start position:0% +we've been talking about all along + + + align:start position:0% +we've been talking about all along +so obviously if we're at position zero + + align:start position:0% +so obviously if we're at position zero + + + align:start position:0% +so obviously if we're at position zero +here right at the mouth + + align:start position:0% +here right at the mouth + + + align:start position:0% +here right at the mouth +this is the worst case scenario so if + + align:start position:0% +this is the worst case scenario so if + + + align:start position:0% +this is the worst case scenario so if +we're here + + align:start position:0% +we're here + + + align:start position:0% +we're here +let's say we're only uh you know one + + align:start position:0% +let's say we're only uh you know one + + + align:start position:0% +let's say we're only uh you know one +inch or one centimeter away and we put + + align:start position:0% +inch or one centimeter away and we put + + + align:start position:0% +inch or one centimeter away and we put +our mouth on top of the other person's + + align:start position:0% +our mouth on top of the other person's + + + align:start position:0% +our mouth on top of the other person's +mouth that is the worst case scenario + + align:start position:0% +mouth that is the worst case scenario + + + align:start position:0% +mouth that is the worst case scenario +of short range transmissioner okay that + + align:start position:0% +of short range transmissioner okay that + + + align:start position:0% +of short range transmissioner okay that +is relative to the background room we're + + align:start position:0% +is relative to the background room we're + + + align:start position:0% +is relative to the background room we're +getting a much worse situation there + + align:start position:0% +getting a much worse situation there + + + align:start position:0% +getting a much worse situation there +but if we ask ourselves how much worse + + align:start position:0% +but if we ask ourselves how much worse + + + align:start position:0% +but if we ask ourselves how much worse +is it so we know that + + align:start position:0% +is it so we know that + + + align:start position:0% +is it so we know that +um f d is the dilution factor that is + + align:start position:0% +um f d is the dilution factor that is + + + align:start position:0% +um f d is the dilution factor that is +the concentration + + align:start position:0% +the concentration + + + align:start position:0% +the concentration +kind of at the um is you know + + align:start position:0% +kind of at the um is you know + + + align:start position:0% +kind of at the um is you know +at the uh source relative to c + + align:start position:0% +at the uh source relative to c + + + align:start position:0% +at the uh source relative to c +sort of at infinity and the well makes + + align:start position:0% +sort of at infinity and the well makes + + + align:start position:0% +sort of at infinity and the well makes +room so let's just say far away okay so + + align:start position:0% +room so let's just say far away okay so + + + align:start position:0% +room so let's just say far away okay so +the average + + align:start position:0% +the average + + + align:start position:0% +the average +actually instead of seeing finish i call + + align:start position:0% +actually instead of seeing finish i call + + + align:start position:0% +actually instead of seeing finish i call +that c average + + align:start position:0% +that c average + + + align:start position:0% +that c average +um because it is the average + + align:start position:0% +um because it is the average + + + align:start position:0% +um because it is the average +concentration um in the room + + align:start position:0% +concentration um in the room + + + align:start position:0% +concentration um in the room +and we've seen that the dilution factor + + align:start position:0% +and we've seen that the dilution factor + + + align:start position:0% +and we've seen that the dilution factor +can be written as the flow rate of the + + align:start position:0% +can be written as the flow rate of the + + + align:start position:0% +can be written as the flow rate of the +breath + + align:start position:0% +breath + + + align:start position:0% +breath +divided by the + + align:start position:0% +divided by the + + + align:start position:0% +divided by the +sort of decay rate of the concentration + + align:start position:0% +sort of decay rate of the concentration + + + align:start position:0% +sort of decay rate of the concentration +field + + align:start position:0% +field + + + align:start position:0% +field +at the average at the appropriately + + align:start position:0% +at the average at the appropriately + + + align:start position:0% +at the average at the appropriately +defined mean radius + + align:start position:0% +defined mean radius + + + align:start position:0% +defined mean radius +divided by the volume of the room so + + align:start position:0% +divided by the volume of the room so + + + align:start position:0% +divided by the volume of the room so +that is telling us how much more + + align:start position:0% +that is telling us how much more + + + align:start position:0% +that is telling us how much more +concentrated + + align:start position:0% +concentrated + + + align:start position:0% +concentrated +the infection quanta or viruses are here + + align:start position:0% +the infection quanta or viruses are here + + + align:start position:0% +the infection quanta or viruses are here +versus the well-mixed room + + align:start position:0% +versus the well-mixed room + + + align:start position:0% +versus the well-mixed room +where they're really spread out + + align:start position:0% + + + + align:start position:0% + +okay now how big is this factor so this + + align:start position:0% +okay now how big is this factor so this + + + align:start position:0% +okay now how big is this factor so this +factor + + align:start position:0% +factor + + + align:start position:0% +factor +for the skagit choir which we've + + align:start position:0% +for the skagit choir which we've + + + align:start position:0% +for the skagit choir which we've +analyzed + + align:start position:0% +analyzed + + + align:start position:0% +analyzed +the skagit valley corral + + align:start position:0% +the skagit valley corral + + + align:start position:0% +the skagit valley corral +uh so that was a fairly large room 4.5 + + align:start position:0% +uh so that was a fairly large room 4.5 + + + align:start position:0% +uh so that was a fairly large room 4.5 +meter ceiling + + align:start position:0% +meter ceiling + + + align:start position:0% +meter ceiling +uh but it didn't have very good + + align:start position:0% +uh but it didn't have very good + + + align:start position:0% +uh but it didn't have very good +ventilation so that's sort of a + + align:start position:0% +ventilation so that's sort of a + + + align:start position:0% +ventilation so that's sort of a +similar to smaller rooms with better + + align:start position:0% +similar to smaller rooms with better + + + align:start position:0% +similar to smaller rooms with better +ventilation and in that case + + align:start position:0% +ventilation and in that case + + + align:start position:0% +ventilation and in that case +this number was 10 to the minus three + + align:start position:0% +this number was 10 to the minus three + + + align:start position:0% +this number was 10 to the minus three +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and in general you know fd for typical + + align:start position:0% +and in general you know fd for typical + + + align:start position:0% +and in general you know fd for typical +indoor spaces for offices classrooms and + + align:start position:0% +indoor spaces for offices classrooms and + + + align:start position:0% +indoor spaces for offices classrooms and +homes + + align:start position:0% +homes + + + align:start position:0% +homes +is on the order of 10 to the minus 2 to + + align:start position:0% +is on the order of 10 to the minus 2 to + + + align:start position:0% +is on the order of 10 to the minus 2 to +the 10 to the minus 4. so there's quite + + align:start position:0% +the 10 to the minus 4. so there's quite + + + align:start position:0% +the 10 to the minus 4. so there's quite +a significant difference if you are + + align:start position:0% +a significant difference if you are + + + align:start position:0% +a significant difference if you are +right + + align:start position:0% +right + + + align:start position:0% +right +at the point of somebody's mouth and + + align:start position:0% +at the point of somebody's mouth and + + + align:start position:0% +at the point of somebody's mouth and +breathing in their air versus being far + + align:start position:0% +breathing in their air versus being far + + + align:start position:0% +breathing in their air versus being far +away + + align:start position:0% +away + + + align:start position:0% +away +there really is a big difference to put + + align:start position:0% +there really is a big difference to put + + + align:start position:0% +there really is a big difference to put +in perspective + + align:start position:0% +in perspective + + + align:start position:0% +in perspective +we can ask ourselves well how long would + + align:start position:0% +we can ask ourselves well how long would + + + align:start position:0% +we can ask ourselves well how long would +you have to stay in the well-mixed room + + align:start position:0% +you have to stay in the well-mixed room + + + align:start position:0% +you have to stay in the well-mixed room +far away breathing the air to have the + + align:start position:0% +far away breathing the air to have the + + + align:start position:0% +far away breathing the air to have the +same exposure + + align:start position:0% +same exposure + + + align:start position:0% +same exposure +as if and dose of an infection quanta as + + align:start position:0% +as if and dose of an infection quanta as + + + align:start position:0% +as if and dose of an infection quanta as +if you put your mouth + + align:start position:0% +if you put your mouth + + + align:start position:0% +if you put your mouth +on top of somebody else and breathed in + + align:start position:0% +on top of somebody else and breathed in + + + align:start position:0% +on top of somebody else and breathed in +one lung full of air + + align:start position:0% +one lung full of air + + + align:start position:0% +one lung full of air +so if we just say that + + align:start position:0% +so if we just say that + + + align:start position:0% +so if we just say that +if we calculate it as a time scale + + align:start position:0% +if we calculate it as a time scale + + + align:start position:0% +if we calculate it as a time scale +taking in the volume of a single breath + + align:start position:0% +taking in the volume of a single breath + + + align:start position:0% +taking in the volume of a single breath +and then dividing that by cube breadth + + align:start position:0% +and then dividing that by cube breadth + + + align:start position:0% +and then dividing that by cube breadth +and + + align:start position:0% +and + + + align:start position:0% +and +the dilution factor that is the time you + + align:start position:0% +the dilution factor that is the time you + + + align:start position:0% +the dilution factor that is the time you +would have + + align:start position:0% +would have + + + align:start position:0% +would have +to spend breathing the background air + + align:start position:0% +to spend breathing the background air + + + align:start position:0% +to spend breathing the background air +in order to uh achieve the same uh + + align:start position:0% +in order to uh achieve the same uh + + + align:start position:0% +in order to uh achieve the same uh +in order to see the same dose and this + + align:start position:0% +in order to see the same dose and this + + + align:start position:0% +in order to see the same dose and this +quantity + + align:start position:0% +quantity + + + align:start position:0% +quantity +ends up being for the skag acquire that + + align:start position:0% +ends up being for the skag acquire that + + + align:start position:0% +ends up being for the skag acquire that +we've calculated around + + align:start position:0% +we've calculated around + + + align:start position:0% +we've calculated around +one hour so + + align:start position:0% +one hour so + + + align:start position:0% +one hour so +if 63 people were in the room and you + + align:start position:0% +if 63 people were in the room and you + + + align:start position:0% +if 63 people were in the room and you +know 53 or so + + align:start position:0% +know 53 or so + + + align:start position:0% +know 53 or so +were infected then that + + align:start position:0% +were infected then that + + + align:start position:0% +were infected then that +most likely happened through the + + align:start position:0% +most likely happened through the + + + align:start position:0% +most likely happened through the +airborne route as we've discussed + + align:start position:0% +airborne route as we've discussed + + + align:start position:0% +airborne route as we've discussed +because 53 people were mostly breathing + + align:start position:0% +because 53 people were mostly breathing + + + align:start position:0% +because 53 people were mostly breathing +the background error that was perhaps + + align:start position:0% +the background error that was perhaps + + + align:start position:0% +the background error that was perhaps +well mixed on the other hand you also + + align:start position:0% +well mixed on the other hand you also + + + align:start position:0% +well mixed on the other hand you also +could infect 53 people by taking turns + + align:start position:0% +could infect 53 people by taking turns + + + align:start position:0% +could infect 53 people by taking turns +one at a time + + align:start position:0% +one at a time + + + align:start position:0% +one at a time +putting their lips against the other + + align:start position:0% +putting their lips against the other + + + align:start position:0% +putting their lips against the other +person who's infected and just breathing + + align:start position:0% +person who's infected and just breathing + + + align:start position:0% +person who's infected and just breathing +in one + + align:start position:0% +in one + + + align:start position:0% +in one +full lung full of air then you would get + + align:start position:0% +full lung full of air then you would get + + + align:start position:0% +full lung full of air then you would get +you know a similar number of people + + align:start position:0% +you know a similar number of people + + + align:start position:0% +you know a similar number of people +infected on the order of + + align:start position:0% +infected on the order of + + + align:start position:0% +infected on the order of +uh hour or two which is the length of + + align:start position:0% +uh hour or two which is the length of + + + align:start position:0% +uh hour or two which is the length of +time of that choir practice + + align:start position:0% +time of that choir practice + + + align:start position:0% +time of that choir practice +but we know that didn't happen so that + + align:start position:0% +but we know that didn't happen so that + + + align:start position:0% +but we know that didn't happen so that +already tells us + + align:start position:0% +already tells us + + + align:start position:0% +already tells us +that short range transmission really + + align:start position:0% +that short range transmission really + + + align:start position:0% +that short range transmission really +can't explain what happened in this gag + + align:start position:0% +can't explain what happened in this gag + + + align:start position:0% +can't explain what happened in this gag +acquire and as we've discussed + + align:start position:0% +acquire and as we've discussed + + + align:start position:0% +acquire and as we've discussed +it has to be longer range airborne + + align:start position:0% +it has to be longer range airborne + + + align:start position:0% +it has to be longer range airborne +aerosol + + align:start position:0% +aerosol + + + align:start position:0% +aerosol +transmission but how much longer range + + align:start position:0% +transmission but how much longer range + + + align:start position:0% +transmission but how much longer range +we can also sample at different + + align:start position:0% +we can also sample at different + + + align:start position:0% +we can also sample at different +positions here so that's the absolute + + align:start position:0% +positions here so that's the absolute + + + align:start position:0% +positions here so that's the absolute +worst case scenario + + align:start position:0% +worst case scenario + + + align:start position:0% +worst case scenario +so let's consider as important numbers + + align:start position:0% +so let's consider as important numbers + + + align:start position:0% +so let's consider as important numbers +three feet and six feet so + + align:start position:0% +three feet and six feet so + + + align:start position:0% +three feet and six feet so +three feet corresponds to + + align:start position:0% +three feet corresponds to + + + align:start position:0% +three feet corresponds to +one meter which is the social distancing + + align:start position:0% +one meter which is the social distancing + + + align:start position:0% +one meter which is the social distancing +guideline of the world health + + align:start position:0% +guideline of the world health + + + align:start position:0% +guideline of the world health +organization today + + align:start position:0% +organization today + + + align:start position:0% +organization today +i would also argue that three or maybe + + align:start position:0% +i would also argue that three or maybe + + + align:start position:0% +i would also argue that three or maybe +two feet + + align:start position:0% +two feet + + + align:start position:0% +two feet +is kind of close to what you might call + + align:start position:0% +is kind of close to what you might call + + + align:start position:0% +is kind of close to what you might call +natural social distancing + + align:start position:0% +natural social distancing + + + align:start position:0% +natural social distancing +so if you don't impose social distancing + + align:start position:0% +so if you don't impose social distancing + + + align:start position:0% +so if you don't impose social distancing +most people prefer to have a little + + align:start position:0% +most people prefer to have a little + + + align:start position:0% +most people prefer to have a little +space bubble around them they don't want + + align:start position:0% +space bubble around them they don't want + + + align:start position:0% +space bubble around them they don't want +to be right up against somebody if they + + align:start position:0% +to be right up against somebody if they + + + align:start position:0% +to be right up against somebody if they +don't have to and they tend to stand + + align:start position:0% +don't have to and they tend to stand + + + align:start position:0% +don't have to and they tend to stand +two or three feet apart so somewhere in + + align:start position:0% +two or three feet apart so somewhere in + + + align:start position:0% +two or three feet apart so somewhere in +here is what i would call natural social + + align:start position:0% +here is what i would call natural social + + + align:start position:0% +here is what i would call natural social +distancing + + align:start position:0% +distancing + + + align:start position:0% +distancing +except in cases where you're in a crowd + + align:start position:0% +except in cases where you're in a crowd + + + align:start position:0% +except in cases where you're in a crowd +so if you're in a + + align:start position:0% +so if you're in a + + + align:start position:0% +so if you're in a +nightclub or bar or some crowded space + + align:start position:0% +nightclub or bar or some crowded space + + + align:start position:0% +nightclub or bar or some crowded space +where you're starting to press against + + align:start position:0% +where you're starting to press against + + + align:start position:0% +where you're starting to press against +people then you come closer you might be + + align:start position:0% +people then you come closer you might be + + + align:start position:0% +people then you come closer you might be +one foot or half a foot and you might + + align:start position:0% +one foot or half a foot and you might + + + align:start position:0% +one foot or half a foot and you might +start to get closer to this worst case + + align:start position:0% +start to get closer to this worst case + + + align:start position:0% +start to get closer to this worst case +but you know people tend to be about + + align:start position:0% +but you know people tend to be about + + + align:start position:0% +but you know people tend to be about +three feet apart so we can ask ourselves + + align:start position:0% +three feet apart so we can ask ourselves + + + align:start position:0% +three feet apart so we can ask ourselves +what happens there we can also look a + + align:start position:0% +what happens there we can also look a + + + align:start position:0% +what happens there we can also look a +little further the center for disease + + align:start position:0% +little further the center for disease + + + align:start position:0% +little further the center for disease +control in the united states + + align:start position:0% +control in the united states + + + align:start position:0% +control in the united states +has imposed a six-foot rule as we have + + align:start position:0% +has imposed a six-foot rule as we have + + + align:start position:0% +has imposed a six-foot rule as we have +discussed + + align:start position:0% +discussed + + + align:start position:0% +discussed +in fact it's been interpreted so + + align:start position:0% +in fact it's been interpreted so + + + align:start position:0% +in fact it's been interpreted so +strictly the united states that you can + + align:start position:0% +strictly the united states that you can + + + align:start position:0% +strictly the united states that you can +find + + align:start position:0% +find + + + align:start position:0% +find +floor stickers exactly six feet apart in + + align:start position:0% +floor stickers exactly six feet apart in + + + align:start position:0% +floor stickers exactly six feet apart in +all sorts of indoor spaces + + align:start position:0% +all sorts of indoor spaces + + + align:start position:0% +all sorts of indoor spaces +even when people are wearing masks and + + align:start position:0% +even when people are wearing masks and + + + align:start position:0% +even when people are wearing masks and +when we aren't sure exactly what the + + align:start position:0% +when we aren't sure exactly what the + + + align:start position:0% +when we aren't sure exactly what the +flows are like + + align:start position:0% +flows are like + + + align:start position:0% +flows are like +and we can ask ourselves what what what + + align:start position:0% +and we can ask ourselves what what what + + + align:start position:0% +and we can ask ourselves what what what +what is the sort of level of + + align:start position:0% +what is the sort of level of + + + align:start position:0% +what is the sort of level of +concentration + + align:start position:0% +concentration + + + align:start position:0% +concentration +uh there it's also worth noting + + align:start position:0% +uh there it's also worth noting + + + align:start position:0% +uh there it's also worth noting +uh that we can also look at a negative + + align:start position:0% +uh that we can also look at a negative + + + align:start position:0% +uh that we can also look at a negative +value how about + + align:start position:0% +value how about + + + align:start position:0% +value how about +minus three feet uh because it's + + align:start position:0% +minus three feet uh because it's + + + align:start position:0% +minus three feet uh because it's +important to note + + align:start position:0% +important to note + + + align:start position:0% +important to note +that respiratory just do not only + + align:start position:0% +that respiratory just do not only + + + align:start position:0% +that respiratory just do not only +increase + + align:start position:0% +increase + + + align:start position:0% +increase +your risk relative to the well-mixed + + align:start position:0% +your risk relative to the well-mixed + + + align:start position:0% +your risk relative to the well-mixed +ambient + + align:start position:0% +ambient + + + align:start position:0% +ambient +there must be regions where the risk is + + align:start position:0% +there must be regions where the risk is + + + align:start position:0% +there must be regions where the risk is +actually lower than the well-missed + + align:start position:0% +actually lower than the well-missed + + + align:start position:0% +actually lower than the well-missed +ambient because in the end the welming + + align:start position:0% +ambient because in the end the welming + + + align:start position:0% +ambient because in the end the welming +solution was obtained by mass + + align:start position:0% +solution was obtained by mass + + + align:start position:0% +solution was obtained by mass +balance so that means we've essentially + + align:start position:0% +balance so that means we've essentially + + + align:start position:0% +balance so that means we've essentially +counted all + + align:start position:0% +counted all + + + align:start position:0% +counted all +the infection quanta or virions in the + + align:start position:0% +the infection quanta or virions in the + + + align:start position:0% +the infection quanta or virions in the +room and if there's a higher + + align:start position:0% +room and if there's a higher + + + align:start position:0% +room and if there's a higher +concentration here + + align:start position:0% +concentration here + + + align:start position:0% +concentration here +there must be a lower concentration + + align:start position:0% +there must be a lower concentration + + + align:start position:0% +there must be a lower concentration +somewhere else to account for that + + align:start position:0% +somewhere else to account for that + + + align:start position:0% +somewhere else to account for that +so perhaps if you're standing behind + + align:start position:0% +so perhaps if you're standing behind + + + align:start position:0% +so perhaps if you're standing behind +somebody at a reasonable distance you + + align:start position:0% +somebody at a reasonable distance you + + + align:start position:0% +somebody at a reasonable distance you +actually have a lower concentration + + align:start position:0% +actually have a lower concentration + + + align:start position:0% +actually have a lower concentration +although there's still mixing going on + + align:start position:0% +although there's still mixing going on + + + align:start position:0% +although there's still mixing going on +and you will + + align:start position:0% +and you will + + + align:start position:0% +and you will +be exposed to the well-mixed room which + + align:start position:0% +be exposed to the well-mixed room which + + + align:start position:0% +be exposed to the well-mixed room which +then brings me to the way that we should + + align:start position:0% +then brings me to the way that we should + + + align:start position:0% +then brings me to the way that we should +really think about + + align:start position:0% +really think about + + + align:start position:0% +really think about +the role of short-range transmission + + align:start position:0% +the role of short-range transmission + + + align:start position:0% +the role of short-range transmission +versus long-range transmission and that + + align:start position:0% +versus long-range transmission and that + + + align:start position:0% +versus long-range transmission and that +is to compare the concentration of the + + align:start position:0% +is to compare the concentration of the + + + align:start position:0% +is to compare the concentration of the +respiratory jet + + align:start position:0% +respiratory jet + + + align:start position:0% +respiratory jet +to that of the well-mixed ambient that + + align:start position:0% +to that of the well-mixed ambient that + + + align:start position:0% +to that of the well-mixed ambient that +we calculated + + align:start position:0% +we calculated + + + align:start position:0% +we calculated +that's essentially the definition of + + align:start position:0% +that's essentially the definition of + + + align:start position:0% +that's essentially the definition of +when + + align:start position:0% +when + + + align:start position:0% +when +the there's a transition from short + + align:start position:0% +the there's a transition from short + + + align:start position:0% +the there's a transition from short +range to long range + + align:start position:0% +range to long range + + + align:start position:0% +range to long range +behavior so where will that occur it + + align:start position:0% +behavior so where will that occur it + + + align:start position:0% +behavior so where will that occur it +will typically be somewhere here + + align:start position:0% +will typically be somewhere here + + + align:start position:0% +will typically be somewhere here +so there's a certain position which + + align:start position:0% +so there's a certain position which + + + align:start position:0% +so there's a certain position which +we'll call + + align:start position:0% +we'll call + + + align:start position:0% +we'll call +xc and this will be defined by + + align:start position:0% +xc and this will be defined by + + + align:start position:0% +xc and this will be defined by +saying that c over the initial value + + align:start position:0% +saying that c over the initial value + + + align:start position:0% +saying that c over the initial value +is equal to the dilution factor so this + + align:start position:0% +is equal to the dilution factor so this + + + align:start position:0% +is equal to the dilution factor so this +is the point + + align:start position:0% +is the point + + + align:start position:0% +is the point +where if i you know follow this orange + + align:start position:0% +where if i you know follow this orange + + + align:start position:0% +where if i you know follow this orange +curve i just hit the concentration that + + align:start position:0% +curve i just hit the concentration that + + + align:start position:0% +curve i just hit the concentration that +is predicted for the background + + align:start position:0% +is predicted for the background + + + align:start position:0% +is predicted for the background +well mixed room which we have already + + align:start position:0% +well mixed room which we have already + + + align:start position:0% +well mixed room which we have already +calculated before + + align:start position:0% +calculated before + + + align:start position:0% +calculated before +so if you use our formula for c there + + align:start position:0% +so if you use our formula for c there + + + align:start position:0% +so if you use our formula for c there +you see you then get a formula for this + + align:start position:0% +you see you then get a formula for this + + + align:start position:0% +you see you then get a formula for this +this xc which is + + align:start position:0% +this xc which is + + + align:start position:0% +this xc which is +square root of the mouth area + + align:start position:0% +square root of the mouth area + + + align:start position:0% +square root of the mouth area +uh times lambda c of r bar so the decay + + align:start position:0% +uh times lambda c of r bar so the decay + + + align:start position:0% +uh times lambda c of r bar so the decay +rate of the concentration field the + + align:start position:0% +rate of the concentration field the + + + align:start position:0% +rate of the concentration field the +volume of the room + + align:start position:0% +volume of the room + + + align:start position:0% +volume of the room +and then alpha qb + + align:start position:0% + + + + align:start position:0% + +so i would argue that this is really the + + align:start position:0% +so i would argue that this is really the + + + align:start position:0% +so i would argue that this is really the +boundary which separates + + align:start position:0% +boundary which separates + + + align:start position:0% +boundary which separates +long-range airborne transmission + + align:start position:0% + + + + align:start position:0% + +by aerosols with short range + + align:start position:0% +by aerosols with short range + + + align:start position:0% +by aerosols with short range +transmission + + align:start position:0% +transmission + + + align:start position:0% +transmission +which also includes aerosols by the way + + align:start position:0% +which also includes aerosols by the way + + + align:start position:0% +which also includes aerosols by the way +so some of these aerosol droplets you + + align:start position:0% +so some of these aerosol droplets you + + + align:start position:0% +so some of these aerosol droplets you +definitely could be inhaling anywhere in + + align:start position:0% +definitely could be inhaling anywhere in + + + align:start position:0% +definitely could be inhaling anywhere in +here + + align:start position:0% +here + + + align:start position:0% +here +but if you go long range you're only + + align:start position:0% +but if you go long range you're only + + + align:start position:0% +but if you go long range you're only +talking about the aerosol droplets + + align:start position:0% +talking about the aerosol droplets + + + align:start position:0% +talking about the aerosol droplets +so this is really where the dividing + + align:start position:0% +so this is really where the dividing + + + align:start position:0% +so this is really where the dividing +line is and if you plug in numbers for + + align:start position:0% +line is and if you plug in numbers for + + + align:start position:0% +line is and if you plug in numbers for +different settings you'll find this is + + align:start position:0% +different settings you'll find this is + + + align:start position:0% +different settings you'll find this is +often larger than six feet in fact in + + align:start position:0% +often larger than six feet in fact in + + + align:start position:0% +often larger than six feet in fact in +some cases + + align:start position:0% +some cases + + + align:start position:0% +some cases +in many cases it's actually larger than + + align:start position:0% +in many cases it's actually larger than + + + align:start position:0% +in many cases it's actually larger than +the room it could be + + align:start position:0% +the room it could be + + + align:start position:0% +the room it could be +tens of meters even because this + + align:start position:0% +tens of meters even because this + + + align:start position:0% +tens of meters even because this +dilution factor can be of order + + align:start position:0% +dilution factor can be of order + + + align:start position:0% +dilution factor can be of order +uh you know a factor of a hundred or + + align:start position:0% +uh you know a factor of a hundred or + + + align:start position:0% +uh you know a factor of a hundred or +even ten thousand + + align:start position:0% +even ten thousand + + + align:start position:0% +even ten thousand +lower concentration in the well-mixed + + align:start position:0% +lower concentration in the well-mixed + + + align:start position:0% +lower concentration in the well-mixed +room than at the person's mouth so you + + align:start position:0% +room than at the person's mouth so you + + + align:start position:0% +room than at the person's mouth so you +have to go pretty far away to see it + + align:start position:0% +have to go pretty far away to see it + + + align:start position:0% +have to go pretty far away to see it +actually drop back down + + align:start position:0% +actually drop back down + + + align:start position:0% +actually drop back down +what that means is that when people are + + align:start position:0% +what that means is that when people are + + + align:start position:0% +what that means is that when people are +breathing in a room these breasts are + + align:start position:0% +breathing in a room these breasts are + + + align:start position:0% +breathing in a room these breasts are +crossing all over the place they're + + align:start position:0% +crossing all over the place they're + + + align:start position:0% +crossing all over the place they're +mixing + + align:start position:0% +mixing + + + align:start position:0% +mixing +and you really can't think about a + + align:start position:0% +and you really can't think about a + + + align:start position:0% +and you really can't think about a +turbulent plume lasting you know out to + + align:start position:0% +turbulent plume lasting you know out to + + + align:start position:0% +turbulent plume lasting you know out to +infinity because there's another person + + align:start position:0% +infinity because there's another person + + + align:start position:0% +infinity because there's another person +standing here + + align:start position:0% +standing here + + + align:start position:0% +standing here +there's ventilation flow there are + + align:start position:0% +there's ventilation flow there are + + + align:start position:0% +there's ventilation flow there are +thermal flows + + align:start position:0% +thermal flows + + + align:start position:0% +thermal flows +all the mechanisms we talked about + + align:start position:0% +all the mechanisms we talked about + + + align:start position:0% +all the mechanisms we talked about +mixing will take this jet and start to + + align:start position:0% +mixing will take this jet and start to + + + align:start position:0% +mixing will take this jet and start to +mix it around the room so it won't look + + align:start position:0% +mix it around the room so it won't look + + + align:start position:0% +mix it around the room so it won't look +like a perfect jet all the way + + align:start position:0% +like a perfect jet all the way + + + align:start position:0% +like a perfect jet all the way +but at least this gives us an estimate + + align:start position:0% +but at least this gives us an estimate + + + align:start position:0% +but at least this gives us an estimate +for these closer spacings here + + align:start position:0% +for these closer spacings here + + + align:start position:0% +for these closer spacings here +of sort of what our risk might be so + + align:start position:0% +of sort of what our risk might be so + + + align:start position:0% +of sort of what our risk might be so +using this concept + + align:start position:0% +using this concept + + + align:start position:0% +using this concept +you know i'll just mention this is + + align:start position:0% +you know i'll just mention this is + + + align:start position:0% +you know i'll just mention this is +typically much bigger than six feet + + align:start position:0% +typically much bigger than six feet + + + align:start position:0% +typically much bigger than six feet +we could estimate how much worse is it + + align:start position:0% +we could estimate how much worse is it + + + align:start position:0% +we could estimate how much worse is it +to be six feet or three feet away with + + align:start position:0% +to be six feet or three feet away with + + + align:start position:0% +to be six feet or three feet away with +yourself + + align:start position:0% +yourself + + + align:start position:0% +yourself +in a worst case scenario perfectly + + align:start position:0% +in a worst case scenario perfectly + + + align:start position:0% +in a worst case scenario perfectly +placed in a respiratory jet + + align:start position:0% +placed in a respiratory jet + + + align:start position:0% +placed in a respiratory jet +so what we're asking here is what if we + + align:start position:0% +so what we're asking here is what if we + + + align:start position:0% +so what we're asking here is what if we +were unlucky enough + + align:start position:0% +were unlucky enough + + + align:start position:0% +were unlucky enough +to be you know right here + + align:start position:0% +to be you know right here + + + align:start position:0% +to be you know right here +and breathing in for a long period of + + align:start position:0% +and breathing in for a long period of + + + align:start position:0% +and breathing in for a long period of +time + + align:start position:0% +time + + + align:start position:0% +time +so not just for a fleeting second but + + align:start position:0% +so not just for a fleeting second but + + + align:start position:0% +so not just for a fleeting second but +you're sitting there and just over + + align:start position:0% +you're sitting there and just over + + + align:start position:0% +you're sitting there and just over +and over you're just sitting here + + align:start position:0% +and over you're just sitting here + + + align:start position:0% +and over you're just sitting here +breathing in that person's breath + + align:start position:0% +breathing in that person's breath + + + align:start position:0% +breathing in that person's breath +it's not an unreasonable situation you + + align:start position:0% +it's not an unreasonable situation you + + + align:start position:0% +it's not an unreasonable situation you +could imagine at a meeting when two + + align:start position:0% +could imagine at a meeting when two + + + align:start position:0% +could imagine at a meeting when two +people are sitting at a table or maybe + + align:start position:0% +people are sitting at a table or maybe + + + align:start position:0% +people are sitting at a table or maybe +they're having dinner + + align:start position:0% +they're having dinner + + + align:start position:0% +they're having dinner +masks are off they are facing each other + + align:start position:0% +masks are off they are facing each other + + + align:start position:0% +masks are off they are facing each other +talking to each other and in fact that + + align:start position:0% +talking to each other and in fact that + + + align:start position:0% +talking to each other and in fact that +is a high risk situation in terms of + + align:start position:0% +is a high risk situation in terms of + + + align:start position:0% +is a high risk situation in terms of +this kind of transmission + + align:start position:0% +this kind of transmission + + + align:start position:0% +this kind of transmission +so let's see how much worse it actually + + align:start position:0% +so let's see how much worse it actually + + + align:start position:0% +so let's see how much worse it actually +could be well + + align:start position:0% +could be well + + + align:start position:0% +could be well +if you plug in the numbers then + + align:start position:0% +if you plug in the numbers then + + + align:start position:0% +if you plug in the numbers then +using a typical mouth area + + align:start position:0% +using a typical mouth area + + + align:start position:0% +using a typical mouth area +in this case the concentration + + align:start position:0% +in this case the concentration + + + align:start position:0% +in this case the concentration +uh drops to about six percent + + align:start position:0% +uh drops to about six percent + + + align:start position:0% +uh drops to about six percent +in this case the concentration since + + align:start position:0% +in this case the concentration since + + + align:start position:0% +in this case the concentration since +it's + + align:start position:0% +it's + + + align:start position:0% +it's +uh what goes as one over a distance is + + align:start position:0% +uh what goes as one over a distance is + + + align:start position:0% +uh what goes as one over a distance is +more like + + align:start position:0% +more like + + + align:start position:0% +more like +three percent so it's a very rough + + align:start position:0% +three percent so it's a very rough + + + align:start position:0% +three percent so it's a very rough +calculation + + align:start position:0% +calculation + + + align:start position:0% +calculation +but relative and i should say so + + align:start position:0% +but relative and i should say so + + + align:start position:0% +but relative and i should say so +relative to the highest concentration of + + align:start position:0% +relative to the highest concentration of + + + align:start position:0% +relative to the highest concentration of +reaching the mouth + + align:start position:0% +reaching the mouth + + + align:start position:0% +reaching the mouth +the plume has been diluted down to six + + align:start position:0% +the plume has been diluted down to six + + + align:start position:0% +the plume has been diluted down to six +percent or three percent + + align:start position:0% +percent or three percent + + + align:start position:0% +percent or three percent +as you go these distances notice there's + + align:start position:0% +as you go these distances notice there's + + + align:start position:0% +as you go these distances notice there's +not a massive difference + + align:start position:0% +not a massive difference + + + align:start position:0% +not a massive difference +between three and six + + align:start position:0% +between three and six + + + align:start position:0% +between three and six +and and it does make a very big + + align:start position:0% +and and it does make a very big + + + align:start position:0% +and and it does make a very big +difference in terms of decisions to + + align:start position:0% +difference in terms of decisions to + + + align:start position:0% +difference in terms of decisions to +reopen spaces and how people interact + + align:start position:0% +reopen spaces and how people interact + + + align:start position:0% +reopen spaces and how people interact +whether you're strictly six feet apart + + align:start position:0% +whether you're strictly six feet apart + + + align:start position:0% +whether you're strictly six feet apart +or perhaps you can be three so keep in + + align:start position:0% +or perhaps you can be three so keep in + + + align:start position:0% +or perhaps you can be three so keep in +mind that + + align:start position:0% +mind that + + + align:start position:0% +mind that +three to six percent dilution but what + + align:start position:0% +three to six percent dilution but what + + + align:start position:0% +three to six percent dilution but what +we're really interested in + + align:start position:0% +we're really interested in + + + align:start position:0% +we're really interested in +here is now how do these fractions + + align:start position:0% +here is now how do these fractions + + + align:start position:0% +here is now how do these fractions +compare + + align:start position:0% +compare + + + align:start position:0% +compare +with the well-mixed room and so for that + + align:start position:0% +with the well-mixed room and so for that + + + align:start position:0% +with the well-mixed room and so for that +i actually would like to do a different + + align:start position:0% +i actually would like to do a different + + + align:start position:0% +i actually would like to do a different +comparison + + align:start position:0% +comparison + + + align:start position:0% +comparison +as i'd like to do c over f d because f d + + align:start position:0% +as i'd like to do c over f d because f d + + + align:start position:0% +as i'd like to do c over f d because f d +relative to here is the concentration uh + + align:start position:0% +relative to here is the concentration uh + + + align:start position:0% +relative to here is the concentration uh +far away so i want c + + align:start position:0% +far away so i want c + + + align:start position:0% +far away so i want c +over c q i should say + + align:start position:0% + + + + align:start position:0% + +over over f d and so + + align:start position:0% +over over f d and so + + + align:start position:0% +over over f d and so +this also can be written as x + + align:start position:0% +this also can be written as x + + + align:start position:0% +this also can be written as x +c over x so it's basically how much + + align:start position:0% +c over x so it's basically how much + + + align:start position:0% +c over x so it's basically how much +farther is that cross or a point + + align:start position:0% +farther is that cross or a point + + + align:start position:0% +farther is that cross or a point +relative to where you're standing that's + + align:start position:0% +relative to where you're standing that's + + + align:start position:0% +relative to where you're standing that's +another way to think about it + + align:start position:0% +another way to think about it + + + align:start position:0% +another way to think about it +and this is then six + + align:start position:0% +and this is then six + + + align:start position:0% +and this is then six +to six hundred so this is the + + align:start position:0% +to six hundred so this is the + + + align:start position:0% +to six hundred so this is the +excess risk + + align:start position:0% +excess risk + + + align:start position:0% +excess risk +if you were to stand three feet away + + align:start position:0% +if you were to stand three feet away + + + align:start position:0% +if you were to stand three feet away +that's the excess risk you face from + + align:start position:0% +that's the excess risk you face from + + + align:start position:0% +that's the excess risk you face from +short-range transmission if you are 100 + + align:start position:0% +short-range transmission if you are 100 + + + align:start position:0% +short-range transmission if you are 100 +of the time breathing in + + align:start position:0% +of the time breathing in + + + align:start position:0% +of the time breathing in +the jet of the infected person you know + + align:start position:0% +the jet of the infected person you know + + + align:start position:0% +the jet of the infected person you know +pointing right at you all the time + + align:start position:0% +pointing right at you all the time + + + align:start position:0% +pointing right at you all the time +if you take this six-foot rule it's a + + align:start position:0% +if you take this six-foot rule it's a + + + align:start position:0% +if you take this six-foot rule it's a +little bit less strong + + align:start position:0% +little bit less strong + + + align:start position:0% +little bit less strong +you have a c over cq divided by fd + + align:start position:0% +you have a c over cq divided by fd + + + align:start position:0% +you have a c over cq divided by fd +that is more like three to three hundred + + align:start position:0% +that is more like three to three hundred + + + align:start position:0% +that is more like three to three hundred +okay it again depends on the details of + + align:start position:0% +okay it again depends on the details of + + + align:start position:0% +okay it again depends on the details of +the room + + align:start position:0% +the room + + + align:start position:0% +the room +but it still can be a significant factor + + align:start position:0% +but it still can be a significant factor + + + align:start position:0% +but it still can be a significant factor +so + + align:start position:0% +so + + + align:start position:0% +so +we will come back to thinking about how + + align:start position:0% +we will come back to thinking about how + + + align:start position:0% +we will come back to thinking about how +to handle short-range transmission in + + align:start position:0% +to handle short-range transmission in + + + align:start position:0% +to handle short-range transmission in +light of + + align:start position:0% +light of + + + align:start position:0% +light of +its interaction with long range but let + + align:start position:0% +its interaction with long range but let + + + align:start position:0% +its interaction with long range but let +me make one final comment on this + + align:start position:0% +me make one final comment on this + + + align:start position:0% +me make one final comment on this +discussion which is where is this + + align:start position:0% +discussion which is where is this + + + align:start position:0% +discussion which is where is this +crossover point so notice + + align:start position:0% +crossover point so notice + + + align:start position:0% +crossover point so notice +it scales with volume so + + align:start position:0% +it scales with volume so + + + align:start position:0% +it scales with volume so +something you may be wondering is don't + + align:start position:0% +something you may be wondering is don't + + + align:start position:0% +something you may be wondering is don't +we have airborne transmission + + align:start position:0% +we have airborne transmission + + + align:start position:0% +we have airborne transmission +and short range transmission outdoors + + align:start position:0% +and short range transmission outdoors + + + align:start position:0% +and short range transmission outdoors +also + + align:start position:0% +also + + + align:start position:0% +also +yes and that is actually covered by the + + align:start position:0% +yes and that is actually covered by the + + + align:start position:0% +yes and that is actually covered by the +theoretic arguments that we're making + + align:start position:0% +theoretic arguments that we're making + + + align:start position:0% +theoretic arguments that we're making +here although i as i said these jets + + align:start position:0% +here although i as i said these jets + + + align:start position:0% +here although i as i said these jets +really can't last forever + + align:start position:0% +really can't last forever + + + align:start position:0% +really can't last forever +but we can at least say to ourselves + + align:start position:0% +but we can at least say to ourselves + + + align:start position:0% +but we can at least say to ourselves +what happens as v goes to infinity + + align:start position:0% +what happens as v goes to infinity + + + align:start position:0% +what happens as v goes to infinity +so i like to call this the outdoor limit + + align:start position:0% +so i like to call this the outdoor limit + + + align:start position:0% +so i like to call this the outdoor limit +if you apply our safety criterion for a + + align:start position:0% +if you apply our safety criterion for a + + + align:start position:0% +if you apply our safety criterion for a +well-mixed room + + align:start position:0% +well-mixed room + + + align:start position:0% +well-mixed room +to a very big room think of for example + + align:start position:0% +to a very big room think of for example + + + align:start position:0% +to a very big room think of for example +a gymnasium + + align:start position:0% +a gymnasium + + + align:start position:0% +a gymnasium +or a sports stadium very very big room + + align:start position:0% +or a sports stadium very very big room + + + align:start position:0% +or a sports stadium very very big room +then if there's only one infected person + + align:start position:0% +then if there's only one infected person + + + align:start position:0% +then if there's only one infected person +then the dilution of those + + align:start position:0% +then the dilution of those + + + align:start position:0% +then the dilution of those +droplets in a massive space is almost + + align:start position:0% +droplets in a massive space is almost + + + align:start position:0% +droplets in a massive space is almost +it's like being outside you might as + + align:start position:0% +it's like being outside you might as + + + align:start position:0% +it's like being outside you might as +well be outside + + align:start position:0% +well be outside + + + align:start position:0% +well be outside +and what you find then is the crossover + + align:start position:0% +and what you find then is the crossover + + + align:start position:0% +and what you find then is the crossover +is very far away which means the + + align:start position:0% +is very far away which means the + + + align:start position:0% +is very far away which means the +long-range analysis + + align:start position:0% +long-range analysis + + + align:start position:0% +long-range analysis +is not even helpful it's not even valid + + align:start position:0% +is not even helpful it's not even valid + + + align:start position:0% +is not even helpful it's not even valid +really + + align:start position:0% +really + + + align:start position:0% +really +it's the short-range analysis you'd be + + align:start position:0% +it's the short-range analysis you'd be + + + align:start position:0% +it's the short-range analysis you'd be +thinking about okay now unfortunately + + align:start position:0% +thinking about okay now unfortunately + + + align:start position:0% +thinking about okay now unfortunately +the short-range analysis depends on many + + align:start position:0% +the short-range analysis depends on many + + + align:start position:0% +the short-range analysis depends on many +assumptions about how people are + + align:start position:0% +assumptions about how people are + + + align:start position:0% +assumptions about how people are +positioned how they're interacting what + + align:start position:0% +positioned how they're interacting what + + + align:start position:0% +positioned how they're interacting what +are the local flow fields + + align:start position:0% +are the local flow fields + + + align:start position:0% +are the local flow fields +but you have to deal with short-range + + align:start position:0% +but you have to deal with short-range + + + align:start position:0% +but you have to deal with short-range +transmission and social distancing can + + align:start position:0% +transmission and social distancing can + + + align:start position:0% +transmission and social distancing can +play a role + + align:start position:0% +play a role + + + align:start position:0% +play a role +in how you address that threat but once + + align:start position:0% +in how you address that threat but once + + + align:start position:0% +in how you address that threat but once +you get to smaller rooms + + align:start position:0% +you get to smaller rooms + + + align:start position:0% +you get to smaller rooms +and longer periods of time and + + align:start position:0% +and longer periods of time and + + + align:start position:0% +and longer periods of time and +then you actually find that this xc is + + align:start position:0% +then you actually find that this xc is + + + align:start position:0% +then you actually find that this xc is +on the order of the room size and then + + align:start position:0% +on the order of the room size and then + + + align:start position:0% +on the order of the room size and then +you really + + align:start position:0% +you really + + + align:start position:0% +you really +are going to be having significant + + align:start position:0% +are going to be having significant + + + align:start position:0% +are going to be having significant +effects of long-range transmission + + align:start position:0% +effects of long-range transmission + + + align:start position:0% +effects of long-range transmission +and i will argue that for most typical + + align:start position:0% +and i will argue that for most typical + + + align:start position:0% +and i will argue that for most typical +rooms + + align:start position:0% +rooms + + + align:start position:0% +rooms +that we inhabit indoors that the + + align:start position:0% +that we inhabit indoors that the + + + align:start position:0% +that we inhabit indoors that the +long-range airborne risk is the leading + + align:start position:0% +long-range airborne risk is the leading + + + align:start position:0% +long-range airborne risk is the leading +order + + align:start position:0% +order + + + align:start position:0% +order +first approximation and best + + align:start position:0% +first approximation and best + + + align:start position:0% +first approximation and best +approximation and the short range + + align:start position:0% +approximation and the short range + + + align:start position:0% +approximation and the short range +risk must be considered but it's a + + align:start position:0% +risk must be considered but it's a + + + align:start position:0% +risk must be considered but it's a +correction to that \ No newline at end of file diff --git a/MZSnYgdlV0A.txt b/MZSnYgdlV0A.txt new file mode 100644 index 0000000000000000000000000000000000000000..9926b60c2a98e73fc5d525e568e730be3152295c --- /dev/null +++ b/MZSnYgdlV0A.txt @@ -0,0 +1,4936 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help +MIT OpenCourseWare + +continue to offer high-quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: All +right, so it looks + +like we've got everybody here. + +It's about 1:11. + +Today in class, we are going +to end our project twos. + +Yay. + +We feeling good about this? + +Kinda? + +I'm feeling good about this. + +And we're going to +start project three. + +So we're going to start off with +our project two presentations. + +Again, we're going +to go through here. + +Each team has five minutes +to give their presentation. + +Slides. + +You can set up your +slides up here. + +We've carved out +enough time for today + +to be able to swap out +between computers and for us + +to ask a couple of questions +after each presentation. + +After all the +presentations are done, + +we're going to take a break. + +Instructors will kind +of talk to each other + +about what we saw in +the presentations, + +and we'll address some of +the feedback that we heard, + +some of the things that we +saw in the presentations. + +As a reminder, +presentations, we want + +to hear about what went +right, what went wrong, + +and also what would +you do differently? + +Then we're going to +start project three. + +And we're going to do +brainstorming in class. + +Basically, the +first week of class + +we're going to compress into +about 30 minutes of this class. + +We're going to +brainstorm, we're going + +to do our elevator pitches, and +then we're going to form teams. + +So we're going to do that +really, really quick. + +And it might require +rolling the die again. + +It might require moving you +from project to project. + +And that's going to be OK. + +We'll talk about why we're +doing that when we go. + +So I think that's +everything from me. + +Any questions? + +And if not, Sparkly +Redemption, come on down. + +PRESENTER 1: So what went right? + +The game got made. + +It isn't broken or sad or dead. + +Even though we had +to cut some things, + +I feel like the general +idea of you are a player + +and you pick up sparklies and +your sparklies change monster + +behavior slash your +power-up slash whatever + +got implemented pretty +well in a way that carried + +across our original idea. + +What went wrong? + +I guess we had to +drop some things. + +We had a person on our +team not get hit by a bus, + +but they did basically +not have as much time + +to work on the project +as much as we thought. + +So we had to adapt to that. + +On the other hand, I feel like +we adapted to that pretty well. + +So not good, but still +good, I think, personally. + +We were told to test +early and test often, + +which I think we actually kind +of did-- maybe not as early + +or as often as we could have. + +But we still tested even +when we had something + +that we felt wasn't +really testable + +but was still touchable. + +And I feel like that was +kind of interesting to do + +because people kept +telling us, you + +should totally be able to die. + +And we were like, +yes, we do think + +you should be able to die, but +we haven't implemented that. + +And so on and so forth. + +But on the other +hand, that meant + +we still got lots and lots +of good feedback and things + +to think about, like +stuff that we probably + +wouldn't have thought to +have implemented but still + +implemented because we +caught that early on. + +So yes, test early and test +often, even if it's annoying, + +is what I learned, and +I feel we all learned. + +And that might be +all I can think of. + +PROFESSOR: What would you +do differently next time? + +PRESENTER 1: What would I +do differently next time? + +Meet up with people. + +Well, not necessarily +physically, + +because we scheduled +meetings but then we + +decided maybe we don't +need to physically meet up + +because it's a pain +getting people onto campus + +if they don't live on campus, +which would have been fine. + +But then there were still +times we were like, well, + +we meant to meet up +but then we got iffy + +about scheduling a time, +and everyone got confused. + +And I feel like we managed +to work our way through it. + +But it was still +more of a hassle + +than it probably needed to be if +we just sat down and scheduled + +out a chunk of time +and listed things + +that we were going to get done. + +So differently would +be better about meeting + +with each other, +either physically + +or through the interwebs. + +PROFESSOR: Any +questions from anybody? + +OK. + +Which game engine +was that again? + +PRESENTER 1: Sparkly Redemption. + +It's the one-armed lady. + +PROFESSOR: What game +engine did you use? + +PRESENTER 1: Oh. + +Phaser. + +AUDIENCE: Anything to +say about the experience + +of working with Phaser? + +PRESENTER 1: So you do the +thing where you have a bug + +and you think it's +Phaser related, + +so you Google vague terms. + +And I've worked with +Flixel and Unity, + +so I know personally I'm used +to having long form posts pop up + +that you then dig through. + +But I feel like with Phaser +it was a bit of a mixed bag. + +And sometimes you +got relevant posts. + +Or sometimes you just went +to the Phaser examples + +and kept digging through it +until you found something + +vaguely relevant. + +So it wasn't terrible, +but it was still + +not quite what I was used to in +terms of figuring things out. + +PRESENTER 2: So we're +Lost Underground. + +One of the biggest things I +felt our team had a problem with + +was communication. + +Because at the very beginning, +we were really good. + +We all got really +pumped for this project, + +and we got together. + +We had the paper prototype. + +We edited it a bunch. + +We quickly got that over +to a digital prototype. + +And then it kind of stagnated. + +We had the play testing, and +we learned a lot from that. + +One of the most +interesting things + +is we added the darkness +mechanic, where you can only + +see a certain zone around you. + +And some people felt +like you shouldn't + +be able to see as much. + +People felt you should be +able to see more or less. + +Everyone had different opinions. + +But we liked the way it worked. + +But it didn't work the +way we wanted it to. + +People weren't concerned +about walking around at all. + +The whole point of the dark is +to be afraid of it, like oh, + +is there a monster +over there, but there + +could be something to +collect, and people + +weren't feeling that. + +And so we found out +from the play testing + +we needed to change it. + +And the best way to do +this was to shrink it + +so you could see even less, +to zoom out the camera so you + +feel really claustrophobic +and far away from everything. + +And I think that +really helped us. + +We also learned-- +what was really + +funny is we had +just a placeholder, + +a little coffee cup, +instead of a coin, which + +is what we originally went for. + +But every play tester +was like, oh, coffee. + +That's the coolest thing. + +I love the idea of +collecting coffee. + +And so one of the cool +things about play testing + +is if you don't say +anything, they will give you + +really useful information, +even though that's not + +what you intended at +all, which was really + +cool to experience firsthand. + +And so we decided to stick +with the coffee mechanic, + +and it ended up being a +little more silly than what + +we originally planned for. + +But like I said, +communication was really hard. + +Planning out who was going to +do what with a digital prototype + +was much more difficult +than with a paper prototype, + +I personally feel. + +Because code intermingles +in a way that paper doesn't. + +And so it becomes +really difficult + +when people are pushing +things and pulling things + +and then things break. + +And so that was really hard. + +A way to change +this, I feel like, + +would be to just make +sure everyone replies + +to their emails, and make +sure people are talking + +and everyone knows +what's going on. + +And I don't know the +best way to do this. + +Maybe an IRC chat, +where they constantly + +have that chat channel +there and people + +can look at it +when they want to. + +Because emails kind of get lost. + +And text messages people +forget to reply to. + +So something like that, +where it's constantly there + +and you can go look +at it and hopefully + +reply to it in a timely manner. + +Or maybe just have-- +one of the things + +I did in my other classes +is the very beginning, + +everyone had to write +up a contract of when + +you'd be working on things, +when you reply to things. + +And so we had to +sign and say, I will + +reply to any emails about +this at 9:00 PM every day. + +And so you can expect a +reply by my by 10:00 PM. + +And so because we +had this contract, + +we knew-- if I send an email +to this person before 9:00 PM, + +I will get a reply +an hour later, which + +was really useful when +people were a little hectic + +and they had other things to do. + +At least I knew I would +get that email back. + +So any questions? + +PROFESSOR: So same +question as before. + +What game engine did you use? + +PRESENTER 2: So we used Phaser. + +And any coding +questions, I'm going + +to direct to another team member +who was more heavily invested + +in it than I was. + +PROFESSOR: Anybody want +to speak up about coding? + +AUDIENCE: [INAUDIBLE] +curious about Phaser. + +PRESENTER 3: I thought Phaser +was an interesting engine + +to use. + +I think in terms of the +organization of the code, + +you have to do a lot of +thinking beforehand if you + +want to make it work well. + +I guess it could be a +little finicky when you just + +start building, because we +thought, OK, well, we'll + +add code, and then we'll +sort of architect it + +based on what we see happening. + +But then we came to realize +that our code wasn't + +going to be as separable +as we thought it might be. + +I also ran into a couple of +bugs that were in Phaser itself + +that I had to sort +of dance around. + +So I would say watch +out for the fact + +that there are still +some bugs in it. + +PRESENTER 4: Yeah, +just callback nastiness + +and having to think about +something will happen now-ish. + +Time isn't really now-now. + +It's like, now kind of +now, then kind of then, + +floating point numbers +that are somehow always + +floats and nothing +is ever actually + +equal to anything else. + +PROFESSOR: Is any +of that documented? + +PRESENTER 4: This +is just found out. + +That's JavaScript. + +But I thought we could get away +from JavaScript by wrapping + +that all in an engine, but no. + +PROFESSOR: Thank you. + +PRESENTER 5: Hello. + +We were Plunder Winds. + +So starting off with the good. + +I think our team was actually +pretty well organized, + +and our roles were well-defined. + +So from the very beginning, +we set up task lists and lines + +of communication. + +We set up a mailing +list and then + +assigned everybody +specific roles. + +And then from that, we +were able to-- none of us + +duplicated work. + +And we set up a good +architecture early on. + +And so we used Phaser. + +And unfortunately, there's +this one part of Phaser + +that's not really +well documented + +in any of the examples and +tutorials which is the state + +machine that Phaser has. + +Surprise, there's a +state machine in Phaser. + +And then once we discovered +that-- we discovered + +that early on and used it. + +And so that allowed us to +really architect our code well + +and separate out modules. + +And we also used a JavaScript +module thing, which basically + +made it so that all of our +coding efforts were really-- + +were really efficient, I think. + +And as for the bad, +five out of six, + +or basically our +entire team, came down + +with the flu the first week, +or over the first weekend. + +And that really +impacted our schedule. + +So originally we had wanted +to get a playable prototype + +by the first weekend so we +could get people touching it + +and start getting feedback. + +But the plans best +laid, it doesn't + +help if everyone gets sick. + +So we had a large +schedule impact. + +And the way we had to deal +with that was, like, there's + +one guy who was able to code +throughout the entire first + +week. + +And then the rest of us +were playing catch up. + +And so we didn't get +anything playable + +until the in-class +workshop on Wednesday. + +And I think that really +hurt us because we weren't + +able to get a lot of +important feedback + +until very late in the process. + +And so there were some +features that we kind of added. + +And we were like, this may +address player concerns. + +But we just didn't get +enough feedback or data + +to figure out whether or not +those concerns were actually + +really addressed. + +PROFESSOR: And anything +you'd do differently? + +PRESENTER 5: I think +we would not get sick. + +But also, we set up Asana +and everything on Monday. + +But then we learned, +like, oh, we + +have to do a sprint task +list and a product backlog + +on Wednesday. + +So I think there was +a bit of a weird issue + +there, where we already had +one task management system, + +and then we introduced +another one. + +And then we introduced scrum +boards and we were like, well, + +which one do we use? + +And then we just didn't +end up using any of them. + +PROFESSOR: Any questions? + +So my question, I think, +is you had the flu. + +A bunch of people were out. + +You didn't cut features. + +You tried to just catch up. + +Did you think about +cutting features? + +Do you feel like you ended +up cutting anything at all? + +PRESENTER 5: So I think our core +game was actually, like-- it + +was pretty simple to implement. + +And I just want to give +a shout-out to our team. + +You guys pulled +off an awesome job + +and implemented +everything by Wednesday. + +And so we did actually +manage to get a feature + +complete game by Wednesday. + +And then we started adding +tweaks, like interface tweaks + +and maybe a visual cue here +and there throughout the rest + +of the week. + +But in terms of +cutting features, + +we didn't really have any +complex time-intensive features + +that we would have benefited +from cutting, I don't think. + +PROFESSOR: Thank you. + +PRESENTER 6: So our project +was Beaver Evolution. + +And so I guess I'll first go +through three of the bigger + +design challenges +we came up with + +or that we encountered +during these two weeks. + +And our [? system ?] +was working with Phaser, + +which is kind of design, kind +of the project challenge. + +And so one thing +we ran into is we + +didn't realize there was +this thing called stages, + +and I think you guys +just mentioned that. + +But since everything is +turn-based, and in each turn + +you can make a choice +between building, populating, + +and evolving, and then +disaster might strike. + +So there was different +things that happen. + +So we thought it +could be very modular + +and we could use stages. + +But then we learned that +stages really start and stop + +every time you switch stages. + +So it doesn't take +the info about what + +happened in a previous +stage, which was + +really important to our game. + +So then we ended up having +to switch everything over + +to Phaser groups, so we could +hide groups and show groups. + +So that was one of +our first challenges, + +just kind of figuring +out how Phaser worked + +and what would be +best for our code. + +It turned out our +code was very modular + +because there were so +many different elements + +to each turn. + +So it was very easy +to split up the work. + +And that was helpful. + +Overall, we really liked Phaser. + +Our second challenge +is balancing the game, + +so making it not too easy to +win and not too hard to win. + +And we kind of changed that by +changing some of the winning + +conditions and then also +adding a few mechanics here + +and there to make +the game harder. + +Because often it +was just too easy. + +So for example, you +could just keep evolving. + +Or you could keep +populating your beavers. + +And then once you reached the +number of beavers you needed, + +you'd win. + +But we kind of changed +that by implementing + +a rule where you can't +populate every turn because you + +have to [INAUDIBLE]. + +So I guess the slide +is not really working. + +PRESENTER 7: Yeah. + +So I'm not sure why the +screen won't show our slides, + +but we can keep +talking about the game. + +So Rachel talked a +lot about the design + +challenges we ran +into for the game. + +And so I'll talk about some +of the project challenges + +that we ran into. + +I was assigned the role +of the product manager. + +So you remember the product +manager in the scrum roles + +is the person who's supposed to +sort of lead where the game is + +going and make sure that all +the design implementations are + +the way that they're +supposed to be and handle + +any changes that we need +to make to the code. + +So unfortunately, +we didn't explicitly + +assign a scrum master. + +So by taking on the role of +being the product manager, + +I also assumed some of the +roles of the scrum master. + +And I know that this +was stated to us + +in the lecture about scrum, +how we should definitely not + +do that. + +And we now see why. + +I unfortunately had to run +some of the meeting-- I + +unfortunately had to focus +on running the meeting + +as well as on making +sure that the design was + +going in the direction +it was supposed to go. + +So I definitely lost +some efficiency there. + +And we started off +very efficient. + +We were able to assign tasks, +and our product backlog, + +our sprint task lists, +were all very laid out. + +We had an early +meeting to make sure + +that everything was going well. + +But then by the end, I just sort +of started running out of time. + +We were unable to schedule a +meeting after the play testing + +session due to everybody's +schedules being very tight. + +And so some of the +changes that we + +wanted to implement after +the feedback from the testing + +session we were +unable to implement. + +But we were still able to +get a good game together. + +Our organization just sort of +fell apart towards the end. + +So those were probably +some of the biggest design + +problems we ran into. + +I would definitely next +time, for our next project, + +make sure that there's +a clear product + +manager and a clear scrum +master so that those two + +roles can be done very +efficiently and not overlap. + +PRESENTER 6: Yeah. + +And I'll just add +on, so our testing + +we really realized that +user experience could + +be improved between having all +the players know all the game + +mechanics and rules +coming into the game. + +So yeah, in addition to +not being able to meet up, + +not being able to +play all the features, + +we really just focused on +improving game experience + +by adding audio and by +adding smaller things. + +But I think earlier +in the game, we + +should have thought more +about user experience + +and making sure that +was a good flow. + +PROFESSOR: Are +there any questions? + +I think you covered everything. + +Thank you. + +PRESENTER 8: All right. + +We're Comcastic. + +So as you'll recall, +our game involves + +placing service centers +on a map and trying + +to cover all of the houses. + +So what went wrong-- setting +up Phaser took a long time. + +It was really hard for us to +actually start writing code. + +We were using TypeScript, +which was important, + +I think, for us, especially +as a documentation. + +But it took some time to +get a good set-up where + +you had a posted Phaser +where everybody could develop + +and you had +TypeScript integrated. + +And it would be nice if-- +future projects, I think, + +will be set up for that. + +But for the first +project, that was hard. + +Meetings-- it was really +hard to schedule meetings. + +We had seven people +when we started, + +and we went down to six. + +And even at six, it was still +hard to schedule meetings, + +mostly because of PSETs. + +I had one PSET, but everybody +else had a lot of PSETs, + +and it was a lot of +conflicting times. + +What went right-- so +Phaser itself, I think, + +really helped us develop fast. + +Once we got the hang of Phaser, +it was a lot easier to develop. + +It was pretty consistent. + +The code is pretty good. + +It was not hard to debug by just +looking at Phaser code for us. + +Also, I think we got the +synchronous communication down, + +because we really didn't +meet that often, especially + +as a whole group. + +So we were using +Trello, and it was + +really nice to just +sort of bounce an idea + +off Trello, just put +in [INAUDIBLE] feature, + +and then we would sort +of discuss it via Trello. + +I think that that's something +that we want to keep doing. + +Also balance-- I think +our balance is actually + +pretty good. + +It was sort of a coincidence +that our pieces-- + +so the components of our +balance are basically + +how the map looks, +where the houses are, + +and then also the service +centers you can place are. + +And you can imagine it'd be kind +of difficult to make these two + +match up, but I think our +first random attempts ended up + +working pretty well. + +What we would do differently-- +we would definitely + +stick to one communication tool +and stick to something simple. + +I think Trello was fine, +[? but even ?] GitHub issues + +would be good, and they would +integrate with the code. + +Definitely we want to keep +scheduling partial meetings + +with some of the group, +just the programmers, just + +a handful of people, whoever +can make it to one meeting. + +I think with students that ends +up being the best thing to do. + +And getting a [INAUDIBLE] +viable product out early on-- I + +think we underestimated how +important that was, even just + +getting a Phaser set up where +you have an empty game running + +quickly. + +Even that, if you get that done +in two hours versus two days, + +it makes a huge difference. + +PROFESSOR: Any +questions from anybody? + +AUDIENCE: [INAUDIBLE]. + +PRESENTER 8: Yes, +face-to-face meetings. + +Even Google Hangouts +actually weren't + +easy to get everybody +at one time. + +PROFESSOR: All right, thank you. + +PRESENTER 9: Hi. + +We're Modudice. + +That is our game. + +For those of you that +played it, it's sort of + +like a number-puzzle type game. + +You move around a dice. + +You add numbers, +a module of seven. + +And you want to make as many +sevens on the board as you can, + +and you get points. + +And so what went well for +us is our design meetings + +went quite well. + +We had two or +three of these that + +were basically dedicated +to figuring out, + +how do we do this better? + +And how do we answer some +of the questions that + +came up during testing? + +And I feel like those +went really well. + +We were able to get +good discussion. + +We actually came up with, +like, solid answers. + +And we were convinced, like, OK. + +This may not be +the best way to go, + +but it's definitely comparably +good to anything else. + +So we're going to +just stick with this. + +And we were able to make task +lists as a result of that. + +So we decide on something +and then say, OK, + +what do we need to do +to actually do this? + +And I think that went +across fairly well. + +And we did a lot of good +testing, especially the testing + +we did in class. + +And on top of that, +like, all of us + +just tested the game +with our friends, + +since it's, like, fairly +easy to play and sort of fun. + +So yeah, the testing +was really useful. + +And we actually did change +a lot as a cause of it. + +PRESENTER 10: I'd like +to add to the task list + +that I think we also did +a very good job in terms + +of prioritizing what +tasks were important. + +I'd like to say that we cut +two features-- the dice rolling + +animation and sound. + +And I think those were +really good feature cuts + +because they weren't +central to our game-play + +as a very fast-paced +browser game. + +And cutting them actually +saved us a lot of work + +and let us have the time +to spend on other features + +and stuff. + +PRESENTER 9: And Phaser +was good in the sense + +that it was something +that went well, + +because it was +easy to start with + +and it was fairly easy to use. + +Like, once you knew what you +needed to do with Phaser, + +it was pretty simple +to get it going. + +But it was also a bad +thing because it's Java. + +At least we did +it in JavaScript. + +So JavaScript is +hard to work with, + +hard to fix bugs and stuff. + +And I could see-- like, +Phaser was fine because it + +was a fairly small project. + +I could see Phaser being +absolutely horrible + +for large projects. + +Like, I would never +want to use it ever. + +PRESENTER 11: I actually +thought that it actually + +did not have a lot +of good documentation + +when we were trying things. + +I thought the community was +not the best for Phaser. + +PRESENTER 9: And so Git, +I think, is awesome. + +But a lot of people +weren't familiar with Git. + +And so the branching +was confusing. + +And that became an issue. + +So if you're going to use a +[? version control ?] like Git, + +make sure everyone +understands it. + +That's something we learned. + +And getting tasks +done separately-- + +we thought that would be +most efficient, since we're + +everywhere across campus, it's +hard to meet up and stuff. + +But I think it's actually +better to just at least start + +working together. + +When you have a set of tasks, +begin the work together, + +do as much as you can, +and make sure everyone's + +clear on how to do +what they need to do + +and what exactly they need +to do so that everyone feels + +like they are actually +contributing and working + +together on this. + +PRESENTER 12: I want to add +one more point on Phaser, + +in the sense that-- I feel like +Phaser-- we're trash-talking it + +right now, but I think Phaser +is good for a one-person project + +because it's very easy to +manage the stuff on your own. + +But with larger +groups, I just don't + +like reading through +JavaScript spaghetti code. + +So maybe we needed to find +a better way to organize + +our code with more people. + +But I just didn't like-- like, +I edited a piece of code, + +someone else edited it, +and I was like, wow, + +it's totally different from +what I expected it to be. + +PRESENTER 9: And +so yeah, next time + +it would definitely help +to have scrum meeting + +and work physically together, +so basically just spend + +more time together as opposed +to messaging on email and stuff. + +Make sure everyone +understands the source control + +and the engine. + +And like, have more people +really think about-- like, + +have everyone on the team really +think about design decisions. + +And then communicate, +communicate. + +More communication +definitely would hurt. + +PRESENTER 10: I would +like to add to that + +in terms of the communication. + +Because as a new +member of a team who + +joined the Modudice, not +the original Modudice team, + +we didn't actually host +an information session + +about what were the critical +things about the game, + +that we made it +the way we made it. + +So the new members, such +as me, had difficulty + +to put in variable input, at +least for the starting duration + +of the project, and then +we picked up later on. + +But if we had an information +session, something like that, + +it would be very helpful. + +PROFESSOR: Any +questions from anybody? + +AUDIENCE: Well, [INAUDIBLE]. + +When you said that your +design meetings-- this was + +all the way on your first +slide, were those online? + +Or were those in person? + +PRESENTER 9: It was in person. + +But those were mostly +focused, like-- so we + +had a lot of questions of how +to represent the dice in 2D + +and stuff like that. + +So the design +meetings were mostly + +focused on big +questions like that. + +PRESENTER 11: In +addition, I think + +we had [INAUDIBLE] meetings. + +And I thought that we should +just have multiple smaller + +ones, [INAUDIBLE]. + +PRESENTER 9: It ended up +going, like, two hours. + +PROFESSOR: Thank you. + +PRESENTER 13: So what was bad? + +We're going to start +with the bad things. + +The first decision +we made as a team + +was using Unity 2D, because +that was just the majority vote. + +Most people had worked with +Unity for the project before. + +But it ended up having +too many complications. + +And it was actually a good +thing that we switched + +to Phaser very early on. + +Like, two days into the +project we switched to Phaser. + +So Unity [INAUDIBLE]. + +Second thing, we weren't +paying too much attention + +to the assignments. + +Everyone was focusing +on the game development + +and making the game look good. + +And we weren't updating +the product backlog, + +and a change log [INAUDIBLE]. + +So we had to go back +and remember what + +we worked on in the past week. + +And it was very +asynchronized with that. + +Another thing is we put off a +lot of the work until the day + +before they were due. + +Like, the last project +we had a lot of things + +that could have been +done during the week, + +but the night before, +we always have + +hundreds of emails to sending +the emails around, trying + +to get everything +to actually work. + +And that was a thing that +cut off on our productivity. + +Another thing is that we didn't +really have a lot of meetings. + +We only had two meetings +throughout the entire project, + +which had a downside that we +weren't very synchronized. + +Even in some of those meetings, +some of us couldn't make it. + +So we had to update whoever +wasn't there with what + +happened in the meetings +and things like that. + +And we definitely could +have used more meetings + +to keep our work synchronized. + +The last part is CoffeeScript. + +CoffeeScript was a +good and a bad thing. + +I think it was a good +decision overall, + +but it definitely +had bad parts to it, + +which is that we had +to sort of-- there's + +a hack-ish with Phaser that +had to compile CoffeeScript + +to JavaScript, which caused +some problems with the + +[? gulping, ?] where it +would sometimes not work. + +And we had to run it twice. + +It generated JS files +which we had to not + +commit into the source +control because they + +were changed when the +CoffeeScript files would + +change. + +And so there was some +problems with it. + +But once we had +it up and running, + +it was so easy to write code +and just iterate on the code. + +It was also easy to read +other people's code, + +because it simplified +100 lines of JavaScript + +into two lines of CoffeeScript. + +I'm exaggerating. + +And then finally, also, it +optimized the JS when compiled, + +so it would run faster. + +PRESENTER 14: So talking about +now some things that went well + +in addition to +finding CoffeeScript, + +we had really great group +direction from the get-go. + +Even though we didn't +have a lot of meetings, + +I think one way we +still managed to make + +that work was we divided bigger +tasks into the sub-categories + +really quickly. + +And we also set +up a Google folder + +in which we kept everything. + +We didn't end up using +Trello or anything like that + +because we really found that a +Google folder with everything + +in it was the simplest for +us-- that along with just + +one chain email where we +sent everything really + +kept everything focused and +everybody in communication, + +in the loop, as +best as possible. + +So source control, we +used Git and GitHub. + +And we actually had a +great experience with that. + +I'm sorry some people didn't. + +Nothing ever broke, +and we barely + +had to merge because +I don't think + +we did very much branching, +which is the way I think + +we avoided any problems there. + +So iteration-- we +iterated our game a lot. + +We changed a lot of +things, because we'd + +play it and be like, +well, people keep dying, + +so how can we make that better? + +Another example is +with our sprites, + +as you can see up there-- +so the initial designs + +and then what we +changed them to. + +We actually had a +problem where somebody + +looked at our first +alien design and said, + +that looks like a piece +of the female anatomy. + +That is distracting. + +You need to change it. + +And we said, OK, you might +have a valid point there. + +Even if we don't think +so, maybe it does. + +Let's change it. + +So we iterated a lot. + +And then focus testing-- +we really actually + +implemented-- talking +about iteration, + +in our focus testing, +the two things we + +found were that new players +were dying really fast. + +It took them, like, +five times before they + +realized how to play the game. + +And then, in addition to +that, after five minutes, + +they were getting bored. + +So we actually +took that to heart, + +and we changed one of the main +premises of our game, which + +was this reloading +thing, that it + +would take a couple of seconds +before you could shoot again. + +And instead, we added +a short term goal + +of actually picking up ammo. + +So you can see-- it's +kind of hard to see. + +But the ammo-- the big +thing is just the animation. + +But if you can see on the +screen, there's a player, + +there's the ammo, +and there's a bug. + +And basically we changed that +whole way the player actually + +shot to make the game a little +more difficult over time + +but also starting easier, +by having everybody smaller + +and then the bugs get bigger. + +So a lot of changes +and iteration + +even based on our focus testing. + +What we would change-- +we'd start earlier. + +I know we talked +about a lot of changes + +we made were the night +before things were due. + +Pretty much all of our +documents changed the night + +before they were due. + +And it's kind of +frustrating, you + +know, having to stay up really +late the night before it's due + +when you've had the +whole week to do it. + +So just start earlier. + +I mean, we started pretty early, +but finish earlier, definitely. + +Hands off for the last +12 hours, kind of thing. + +And then we also talked +about this-- being + +focused on what's actually due. + +So one thing that was good +about having a lot of focus + +on our game was that we had a +viable product really early. + +But a lot of our other documents +kind of fell by the wayside, + +and they kind of came +up to one or two people + +to just fix them all the +night before they were due. + +So definitely focus on those +things and more accountability + +with that. + +And in conclusion, even though +we had some frustrations, + +it went pretty well. + +Our game ended up pretty +clean and creep and fun. + +So we really like it. + +Thanks, guys. + +[APPLAUSE] + +PROFESSOR: Questions? + +AUDIENCE: How did you +stumble upon CoffeeScript? + +What was the decision when you +were trying to [INAUDIBLE]? + +PRESENTER 13: Jen, you +want to take this one? + +AUDIENCE: If you could +come down [INAUDIBLE]. + +PRESENTER 15: I used +CoffeeScript a lot + +before I was really +familiar with the + +build systems and stuff. + +So I figured it'd be +best to kind of set + +up a build pipeline that +optimizes the [? alpha ?] + +JavaScript to make the game +run faster because [INAUDIBLE]. + +PRESENTER 13: And CoffeeScript +also has a lot of shortcuts. + +It's like Python. + +It's like using +Python to write Java. + +It's so good. + +Like that. + +PRESENTER 14: Any +other questions? + +PROFESSOR: Thanks. + +OK, feedback. + +And instructors, please +feel free to jump in + +if I'm missing anything. + +Oh, and I forgot to +copy all my notes. + +All right. + +So yeah, I was wrong. + +Ha, you caught me. + +Slides were intended to be +required for this project, + +but they were not. + +So you're not going to +get penalized for that. + +The issue for that +is slides and visuals + +are recommended to help your +presentations stay on topic. + +Basically, you had +some issues sometimes + +with keeping track of changes. + +We had some issues with +keeping track of our changes + +to our documents. + +So QA is important in +everything that we do in life. + +But for project three, +slides and visuals + +are recommended to help your +presentations stay on topic. + +And what we saw +presentation-wise, + +slide-wise, was perfect +for these five minute + +presentations. + +Quick, dirty, gets +the point across, + +gets the bullets across. + +Visuals, like images or +something, if you need it. + +For project four, that's +a 20-minute presentation. + +Visuals are more +important there. + +And we'll talk about those +presentation requirements + +later when we +start project four. + +So discussion on +meetings, things + +you should do in +project three-- address + +how you're going to meet in +your initial design meeting. + +The most important +thing you have, + +before you even start +designing your game, + +is to talk about who can meet +when, what is your schedule. + +You all have syllabuses +from your other classes. + +When are your PSETs due, +when are your recitations, + +all that stuff. + +Put it in your high-level +design document. + +It's actually one +thing that we use often + +in that one section where +we talk about team roles, + +is team meeting times. + +And I think I heard +this team mention that, + +that you've used in +previous classes. + +That's a very good tip. + +Use that. + +If others can't make +it to your meetings, + +is there a way you +can take video? + +Is there a way you +can archive what + +happened in the meeting for +those people who couldn't come? + +Here's something that I've +seen some local companies do-- + +drop in IRC. + +Basically, even something as +simple as keeping Skype open. + +Even better-- actually, my +notes weren't put in there. + +Even better, an +IRC solution that + +has some kind of +archival process + +in, so all the previous +chat can be saved. + +I know there are some solutions +out there that actually + +hook this into your GitHub or +Bitbucket or what you're using. + +Those solutions are out there. + +Try one of them. + +But again, even something +as simple as having + +Skype open and +online, you can always + +tell if one of your +team members is online. + +You can throw a +text and say, hey, + +can I get your feedback on this? + +Can you take a +look at this code? + +For your daily scrum, 15 +minute Hangouts probably + +is-- all you need is +15 minutes for doing + +that kind of daily scrum +meeting, so trying that out. + +Problems we saw with backfilling +your product management. + +Integrate your project +management from the beginning. + +We know that this was a +problem for this project + +because we introduced it +to you midway through. + +That's OK. + +You actually did-- +we mentioned this, + +you did some pretty good +use of product management. + +The goal for any +project management + +tool that we're +teaching in this class + +is that it should be helpful. + +It shouldn't be a hindrance. + +That said, we'd like you to +get some practice with it + +first before you +start throwing it out. + +So for project three, please +use the project management tools + +that we described as we've +described them to you. + +In particular, product +backlogs, sprint task lists, + +and the design change log, +and the vision statements, + +those high level +design documents. + +Scrum boards, mostly optional, +but we found them useful. + +They might not be useful for +how your team is distributed. + +It's up to you to +figure that out. + +For project four, we'll +give you the ability + +to create the system +that works for your team, + +so long as you give us what +information we're asking for. + +So you know you need +this information. + +You know you need a way +to manage your tasks. + +You know you need a way +to manage your features + +and to prioritize your +features to estimate. + +But how you actually do that +and how you actually save it, + +that can be up to +you for project four. + +We will want to see it actually +cause some improvements. + +And if it doesn't +cause improvements, + +let us know why and what kind +of problems you found with that. + +And again, the +design change log. + +This is a design diary. + +It's even better. + +It's your meeting minutes. + +You should be able to fill +it out in five minutes. + +Along with your task +list and backlog, + +it kind of shows the +history of the project. + +Take the time just to +spend those five minutes + +at the end of each meeting +to just throw something + +quick down so you know what +has changed in the past. + +Phillip, you want to +chime in on this one? + +Modular code doesn't mean your +tasks are actually separate. + +PHILLIP: Yeah. + +This is just +something that I got + +a sense of from watching +everyone's presentations today. + +A lot of folks, even the folks +who mentioned that the code was + +well separated and people +could code independently, + +it doesn't mean that +there are no benefits + +to actually still working side +by side, even if you're working + +on different parts of the code. + +And some teams mentioned that. + +So actually, again, being +on Google Hangout or Skype + +or IRC or whatever, if you're +working in your own rooms, + +or even better, a lot +of people mentioned + +scheduling those face-to-face +meetings-- it's OK for you + +to have a face-to-face +meeting, even + +if you're not +planning on working + +on the same batch of code. + +And you can actually still save +a lot of communication time-- + +if nothing else, just to tell +people what you're doing. + +So maybe it's not +speeding you up, + +but it might speed +everybody else up, + +and suddenly it helps +the communication. + +PROFESSOR: Form strike teams. + +You've got six people, maybe +seven people, and eight people + +on project four. + +Not everyone needs +to be touching code. + +There are other tasks +that need to get done. + +You can form up +into smaller teams. + +One team might just be working +on some kind of-- again, + +if it's modular, it's going +to have some dependencies. + +But if you can +modularize it out, great. + +But even better, especially +with project four, + +when you have longer time, one +team doing paper modification, + +doing UI elements, running +focus tests, while another team + +is writing code. + +Think about how you +can better utilize + +all the personal resources +and all the man hours + +you have without requiring +all these clashes + +with so many people +touching the code. + +It's that too many cooks in +the kitchen kind of thing-- + +not everybody needs to be doing +that, need to be touching that. + +Here's another thing we noticed. + +A lot of what you asked for +was basically more time-- just + +various different ways of saying +you wished you had more time, + +you wished you had +started earlier, + +you wish you had iterated +earlier, the flu hit. + +A lot of what you're +describing there + +are things you're not going +to have any control over ever. + +You never have control +over that stuff. + +What you need to do is +focus on those things + +that you can control. + +So if you have illnesses, if you +have major technical problems, + +the game is whatever +you decide the game is. + +You've actually got some freedom +in this class in that you've + +told us what the game is, and +we're actually even telling you + +in the last week, again, tell +us, what was this game actually + +supposed to be, so that +when things change midway + +through the project, +be flexible. + +Change what you're +delivering to us. + +Make it so that whatever +you're delivering to us + +runs, works, is playable. + +This isn't a design class. + +We're trying to teach +you some design skills. + +But it's not focused on design. + +So if the final game +isn't fun, it's sad, + +but it's OK, so long as it runs, +so long as it's playable, so + +long as it fits all the +requirements that we're asking + +of you from the beginning. + +I know it's weird. + +This is the only +class we do this in. + +Trust me. + +All right. + +So that's it. + +Any other questions +about project two? + +I think you all did +really, really well. + +Really happy to see how +the presentations went out. + +Yes? + +AUDIENCE: Is there any way +we can see what everyone did? + +PROFESSOR: What's that? + +AUDIENCE: Is there any way +we can see what everyone did? + +PROFESSOR: Oh, yeah. + +So one thing I highly +suggest, somebody on your team + +email the video +game mailing list. + +Video games, yeah. + +I did the plurals wrong. + +I never do that +right with mailing + +lists. videogames@mit.edu-- +email out a link to your game + +to your classmates if you want +people to play it and give you + +feedback on it. + +At the end of every +project do that. + +Actually, use that mailing +list as a resource for you + +to talk to each +other across teams. + +Hey, here's our game. + +We need a little bit +of feedback on this. + +My team is all sick. + +Can somebody please play this +and tell me what's wrong? + +Can you play this on +a different browser + +and tell me if it's broken? + +Take advantage of +that mailing list. + +Any other questions? + +Yeah. + +AUDIENCE: So +[INAUDIBLE] postmortem, + +will we get more feedback on +project one and project two, + +what the group grade was? + +PROFESSOR: So there +are no group grades. + +So what you're getting +is-- your grades, if you + +look at the grading rubric, 20% +of your grade is individual. + +The other 80% percent +is your group. + +So the grade that +you get is basically + +adjusted based on the +quality of the write-up. + +AUDIENCE: OK. + +And on project two, will we +get more feedback on everything + +we've done, so we can better +plan for project four? + +PROFESSOR: Yeah. + +So for project two, you're going +to get feedback on your design + +change log again. + +You're going to get feedback +on your task list and product + +backlog. + +We just gave you feedback +on the presentations + +and on those skills. + +You're going to do that +again for project three. + +You get your feedback on +the individual write-up. + +Is there anything +I'm missing there? + +And then game +functionality-- we're + +going to give you +more feedback on game + +functionality, because last +time we did that in class. + +This time we're actually +going to play your digitally + +released games. + +We'll give you some +design feedback + +there for product three. + +PHILLIP: Yeah. + +Because we could just show +the actual numerical grading + +proclamations that +we do, but that's + +meaningless without actually +explaining what it is. + +So what we'll try to do is focus +more on actual text feedback + +on what we thought were the +strengths or the weaknesses + +of whatever you've given us. + +PROFESSOR: That answer? + +Cool. + +Any other questions on grading? + +All right, give +yourselves a round + +of applause for +finalizing project two. + +[APPLAUSE] + +Let me double check to make +sure I didn't miss a break. + +No, we just took a break. + +Ha, ha. + +All right. + +So project three, you're going +to practice project management, + +meaning you're going to use +those tools that we talked + +to you about in the middle of +project two from the get-go, + +with a slightly larger team. + +Some of your teams were +five people this time, + +minimum is going to be six. + +We're going to make sure we +leave class today with at least + +six people on each team. + +And again, that's just +to get used to it. + +Project eight, your minimum +is going to be eight people. + +So with a larger +team, you're going + +to focus on design iteration +to maximize usability + +using user feedback through +independent user testing. + +So the keywords there-- +users, feedback, usability. + +Those are things +we're going to be + +looking at when we're +grading the functionality + +of your games. + +So for project management, +we mean create and use + +a product backlog and +a sprint task list. + +There's few turn-ins for that. + +For design iteration, +you're going + +to conduct focus testing and +user testing on your own. + +And I'll touch on this +again, but basically you're + +going to turn in two focus +test reports, one of which + +can happen in class +on a scheduled day. + +The other one must +happen outside of class + +with a group of people +who are not in class. + +So get people to test your game +and report back to us on that. + +And again, maximize usability. + +All the iteration that we +see you do on your games, + +you should be iterating on that +user interface or that user + +experience. + +So we are going to ask +you to make a little bit + +more complex game than before. + +But really what we're +trying to get you to do + +is make a complex game that +has a possibly problematic user + +interface. + +Give us an interface +that's good. + +Give us a user experience that +matches the user experience + +that you want to strive for +when you're designing the game. + +PHILLIP: Just a quick thing. + +We do have a couple +of lectures coming up + +on designing for that. + +But as Greg mentioned +earlier, this is not actually + +the design class. + +There is actually a different +design class that some of you + +have taken and are going to be +distributed among the teams. + +Or you might have taken, say, +Rob Miller's user interface + +class, which also has a lot of +those same sort of concepts. + +If you've taken any +of those classes, + +you should be identifying +yourself to your teams, + +because you probably +have actually + +practiced designing +for usability + +a lot more than a lot of the +other people in your group. + +And that's what we're +going to be looking for. + +But most importantly, +the testing + +that we've been +talking about, we + +are expecting you to +be able to do that. + +And that anyone of +you have already + +got the basic foundation of. + +PROFESSOR: So our design +constraint-- we're leveling up + +from planning for randomness. + +We want to see trade-offs +in decision making. + +So every decision +made by the player + +must have a positive +and negative outcome + +in their play state. + +So first off, what +does that mean to you? + +What do you think that means? + +Jenny? + +AUDIENCE: Good +things and bad things + +happen when you take steps. + +So you have to decide whether +the good things outweigh + +the bad things at your +current point in time? + +PROFESSOR: Yep. + +Basically it-- +opportunity costs. + +Risk management, future +risks, unknown risks. + +There should be some +unknowns and knowns there. + +So while the players +should know that there's + +going to be some positive +and some negative, + +they might not know the values +of those positive and negative + +outcomes. + +So there's some kind +of uncertainty going on + +in the game there. + +And then some of +the side effects-- + +sometimes when you +make a decision, + +there's going to be an immediate +change in player state. + +Sometimes it's going +to be a long term. + +It's going to chain or combo +up from previous decisions, + +causing problems +in later things. + +So easy way to think +about this, again, + +is of course strategy games. + +But you're also welcome +to apply this to any genre + +that you might +like to experiment + +with in this project. + +So here's some suggested goals. + +Think of project-- +yeah, go ahead. + +AUDIENCE: Do we still +have to use planning + +for randomness in this game? + +PROFESSOR: Yeah. + +So there should be some amount +of randomness in this game. + +So it's building onto it. + +So there should be some +kind of uncertainty. + +It's not the focus +of it anymore. + +So project two and +project one were focusing + +on just that randomness. + +Project three should have some +of the randomness in there. + +But really, what we want you +to focus on is trade-offs. + +So that's a tool +in your toolbox. + +Try it out. + +If it doesn't work, if there's +a reason it doesn't work, + +then don't use it. + +But there should be +some uncertainty there. + +And again, all this is +building up to project four. + +So things you should try +out in project three-- + +work with new people. + +The method we're going to +have to put you in teams + +is going to try to do that. + +So you'll be working +in different teams + +with different people. + +These are basically +auditions for project four. + +Use a new game engine. + +Did everybody use Phaser? + +Yeah. + +You're not using Phaser +for project three. + +So we're going to basically +want you to go back to that game + +engine tutorial, think +about the other game engines + +you have available. + +We had one team to use Unity, +and they had some issues + +why they wouldn't use Unity. + +And actually, those +issues will probably + +apply for project three as well. + +Maybe you don't +want to use Unity. + +Maybe it's too scary. + +Maybe it's a challenge. + +Figure it out. + +And the last one-- I +posted this to Stellar. + +It's a light read. + +Games For a New +Climate is basically + +our handbook for project four. + +Our client presented us +with this information. + +This is basically +how games are used + +for game based learning, +for climate change, + +for talking about planning for +future risks, the complexity + +of future risks. + +Take a flip through the book. + +Read it now. + +Start it now. + +Have it read by project four. + +Again, we don't have +required reading here, + +but you'll have a +better game, you'll + +have a better +product if you take + +a look at this and maybe even +do a little bit of research + +on your own, which +is actually going + +to be part of project four. + +We'll talk about that later. + +But if you want to make a +game that does this, you can. + +If you want to make a +game for project three + +that is a game to help a +policymaker understand the need + +to spend money, +time, or resources + +on disaster preparedness as +a result of climate change, + +feel free. + +Part of that trade-off +design challenge + +is actually inside +of that statement. + +The uncertainty is +inside of that statement. + +Project three +actually would turn + +into a possible +springboard and a way + +to recruit people +for project four. + +But again, you're +not necessarily + +going to have the same group. + +So it's up to you to +figure out if that's + +going to be useful for +you on this team or not. + +All right. + +And then the hard +requirements-- please + +read this handout on Stellar. + +I'll actually read the handout +on Stellar too this time. + +Sorry about that. + +Maximum play length, +again, is five minutes. + +Again, single player game. + +User interface tested for +legibility and usability. + +It must use and play +audio for the player. + +And then, like +previously, players + +can pick up and start +playing the game + +with no external instructions. + +So if there are instructions, +which there can be, + +it must be inside of the +game or at least inside + +of the frame of the +web page that you + +are using as a link +for us to play within. + +And then, of course, must be +delivered as a browser game, + +running on Chrome. + +And also, only in those engines +that w e used in the tutorial. + +Deliverables-- so actually, +this is Monday the 29th. + +Wednesday is the 1st. + +On Wednesday the 1st, we have +a guest lecture coming in. + +Swery65 is coming in to talk +to us about his new game. + +His lecture is probably +going to last about an hour. + +That means you're going to have +two hours in class on Wednesday + +to work in teams and create +a low fidelity prototype. + +It is not something you're +required to turn in. + +We are asking you to have +a playable game on Monday, + +the 6th. + +Whether that's digital or paper +is up to you, but we highly, + +highly, highly recommend making +a quick, low fidelity prototype + +on Wednesday in the two +hours you have, and then + +based on that prototype +create the product backlog. + +It's the best way that I've +found to make product backlogs. + +You might find a different way. + +That's OK, as long +as you make one. + +But on Monday, on the +6th, turn in the Stellar, + +your high level design doc, and +what your product backlog is. + +So what are all +the features that + +have been estimated, that have +been put in priority order? + +In class, you're going +to give a really quick-- + +AUDIENCE: Next slide. + +PROFESSOR: What's up? + +AUDIENCE: You're talking +about stuff on the next one. + +PROFESSOR: Oh, wow. + +I'm talking about +stuff on the next one. + +Thank you. + +That's weird. + +In class, two minute +presentations. + +Basically, just the core +of your game design idea. + +Let us know what you're making. + +And then we'll be able +to test your prototypes. + +I think-- let me look ahead. + +Yeah, so testing prototype +is not required on the 6th. + +But if you do it, please +we'll test them then. + +We will also test +on-- and this is + +where we actually +do want you to have + +a playable, digital version. + +Basically, let us know that you +have a playable game by October + +8. + +And turn in via Stellar +your sprint task list-- + +basically all the tasks +with time estimates + +that are going to happen +between Wednesday, October + +8 and Monday, October 15. + +And the project due is +the same kind of stuff + +that we did for this +project-- your game prototype + +builds, your post mortems, +your design change + +log, updated design document +if you have an updated design + +document. + +And again, two focus +test reports this time. + +One can be created in class +on either the 6th or the 8th. + +The other one should be +created outside of class + +with external testers. + +AUDIENCE: Question. + +PROFESSOR: Yes? + +AUDIENCE: Is that Monday the +13th or Wednesday the 15th? + +PROFESSOR: Oh, my lord. + +Did I really make that mistake? + +Can somebody check +on Stellar for me? + +So it should be Monday +the 13th, right? + +AUDIENCE: No, we +think it's Wednesday. + +PROFESSOR: Wednesday +the 15th is when we're + +having people turn stuff in? + +AUDIENCE: Yep. + +PROFESSOR: All right, holiday. + +Right? + +Is there a holiday that week? + +AUDIENCE: Yeah. + +PROFESSOR: OK. + +Stellar is the right place, +and I will update these slides + +before I post them to Stellar. + +AUDIENCE: Let me check +on the big schedule. + +It's Columbus Day. + +So Monday, there is no class. + +PROFESSOR: So Monday, no class. + +So Wednesday, the 15th. + +So you got a little +bit of extra time. + +But it's a holiday, so maybe +you don't have extra time. + +PHILLIP: But if you +get it done by Monday, + +then you can let your code +soak a little bit [INAUDIBLE]. + +PROFESSOR: All right. + +So we are going to +do brainstorming, + +and we're going to brainstorm +in groups that you are not + +currently working with, so +you can meet new people. + +You're going to get a card. + +It's going to have a number +on it-- one, two, three, five, + +eight, or 13. + +I'll hand out the +cards really quickly. + +Go to one of these stations, +erase whatever's on the board + +if you need to +erase on the board. + +If you're in five, +eight, or 13, you're + +going to have these easel pads. + +We are going to give you two +timed quick brainstorming + +sessions. + +Five minutes, small break, +another five minutes. + +When we break, change +whoever's writing things down + +so everybody has +a chance to speak. + +After this, each +brainstorm group + +is going to be allowed to +make two pitches to the larger + +class. + +What we're going +to ask you to do + +is write a title for the +game on a large Post-It, + +and we'll hand these out. + +One of these, yeah. + +We'll hand these out +when we get there. + +In your elevator pitch, +make sure to address + +the core mechanic of the +game and how it's applied + +to the design constraints. + +Games from project one that were +not selected for project two + +can be pitched if your +brainstorming group says + +that was actually +a pretty cool idea. + +Let's pitch that too. + +But it must be altered +for design constraints. + +And I'll give you a break +after that second brainstorming + +session to come up with these +pitches-- about 10 minutes, + +I think. + +Any questions about this? + +Psyched? + +Pumped? + +All right, I'm going +to hand these out. + +[SIDE CONVERSATION] + +PROFESSOR: Team one, +pitch one, come on down. + +And just like before, +you've got about a minute. + +Describe-- oops, wrong ones. + +Give us the name of the +pitch, the core mechanic, + +and how this pitch approaches +the design constraint. + +Pitch, go. + +PRESENTER 16: So our first +pitch is called Dragon's Lair. + +It bears no relation to the +previous Dragon's Lair idea. + +The idea we came up with is +that as a dragon, when you're + +acquiring gold, the +more gold you have, + +the more heroes want to +come in and mess you up + +to try and steal your stuff. + +So we thought that there's +a fun trade-off there + +between acquiring +more gold and becoming + +a more powerful dragon, +but at the same time + +having more and +more heroes wanting + +to come in and attack you. + +We also thought that +just in that, in itself, + +you don't quite get the idea +of meaningful decisions, + +because everybody's +just going to want + +to be a more powerful dragon and +prove themselves as, oh, I can + +handle more and more knights. + +So we thought it'd be +interesting to have + +this idea of not just +being an enemy to everyone. + +You can actually ally with some +of the villages in the game + +so you'll be making less +money, but then you'd + +have more people on your +side to help you defend. + +So the trade-off here is +between being nice to people + +in order to get more +defense or slaughtering them + +or just steal their money. + +PROFESSOR: Nice pitch. + +Number two. + +PRESENTER 17: All right, +so our second game + +is called caffeine worker. + +And it's based on the idea +that caffeine will pretty much + +simulate your [INAUDIBLE] +where you can actually + +get more work done under +less amount of sleep. + +But it also tends to +have side effects. + +So our game pretty much revolves +around you are a worker, + +and you want to get +these tasks done. + +And you want to get these done +as efficiently as possible. + +So we're going to have +something like a 24 hour clock. + +We're going to +have night and day. + +We're going to have a lot +of different sort of actions + +that you can sort of, like, +decide on executing, such + +as you can figure out how +many hours you want to sleep, + +how much caffeine +you want to take, + +and also you can also figure out +your eating schedule as well. + +So we don't really have +the nitty-gritty details, + +but we imagine that +this game will involve + +a lot of scheduling, a lot +of sort of-- I don't know, + +the trade-offs between sleeping +and eating and drinking coffee. + +But in the end, I +think what we want + +to do is that we want +to make this game + +sort of like a platformer, +where you are actual in control + +of the character +and for [INAUDIBLE] + +your tasks, something you need +to go from point A to point B. + +But these different sort of +attributes, how much caffeine + +you have over time, +how much sleep you + +have, whether you're eating +enough, whether you're happy + +or not-- those sort of +effect your motor skills + +as well as some +other implementations + +that we have yet to figure out. + +PROFESSOR: All right. + +Thank you. + +Thank you group one. + +Group two. + +Pitch one, category A. Remember, +it's one-minute pitches. + +PRESENTER 18: All right, +so here's the idea. + +You are an administrator at MIT. + +And your goal is the management +of MIT and promote MIT's ideals + +and maximize their +endowment and all that. + +And your goal is to carefully +trade-off the short-term + +versus long-term policy. + +For example, you've +got this plot of land. + +You could lease it to Pfizer +for 60 years and get 2 billion + +straight to the endowment. + +But then you can't +expand it till later. + +And do you want to appease +the students to get more + +in tuition? + +But maybe you need that +money, so you raise tuition, + +but you also get rid of +your unpopular flag policy + +at the same time. + +So you can play as many +different administrators. + +You can play as, +like, Dean Colombo. + +You can play as Kevin +Kraft from the Office + +of Student Citizenship. + +You can play as the +shady MIT corporation + +with this weird board +of self-voting members + +that no one really understands. + +That's our pitch one. + +[APPLAUSE] + +PROFESSOR: What's +the name of that one? + +PRESENTER 18: MIT +Simulator 2015. + +PRESENTER 19: Our second +idea is build a car. + +And we thought that +you could start out + +with a limited amount +of money, and we + +will send the car you +build after a turn + +through a simulator. + +And so you don't exactly know +which maze it's going to get. + +So depending on +the result of that, + +you have trade-offs of +how to spend your money, + +what parts to buy, +and build a car. + +PROFESSOR: Great. + +Group three. + +PRESENTER 20: Hi, everyone. + +I'm going to tell you about +Fight or Flight, which + +is from our first project. + +And if anyone played +the paper prototype, + +it's going to be +completely different. + +So the idea is that you're +playing this platformer, which + +is a map that has a bunch +of separate little rooms. + +So any given little room might +have four or five platforms. + +It's not really big. + +And so this whole +big map has a bunch + +of these little +rooms, all connected + +by different passageways. + +And you can get from different +places to different places. + +And all of these rooms +are potentially exploding. + +So this is some +sort of spaceship, + +and there's a meltdown. + +Or, I don't know, this +is, like, the tavern. + +And near a volcano, +things are filling + +with lava, or something. + +However you want to skin it. + +So each of the +rooms will give you + +some sort of warning +about whether or not + +it's about to explode. + +And then some time after the +warning starts, it explodes. + +And then if you're in +there, you're in trouble. + +So the trade-offs +in this game are + +that-- so the overall goal is +to get somewhere, is to get out, + +is to get from one side +of the map to the other. + +And in between, there's a +whole bunch of other people + +who want to fight you, +just for the heck of it. + +So they want to fight you, +you want to fight them. + +But the more you fight, +the more tired you get. + +And the more tired you +get, the slower you move. + +And the more slowly +you move, the harder + +it is to escape a room +once it starts exploding. + +So you can choose to +fight, and you're probably + +going to kill them, you +could kill the enemies + +because they're AI written +by people in this class. + +Versus, like, the player who +can actually just implement + +strategies and things. + +But if you do go and have fun +and try to kick everyone's ass + +and you succeed at +that, well, then you're + +panting in the middle of a +room that's about to explode. + +So fight or flight everyone. + +PRESENTER 21: The second +one is Jigsaw World, + +another platformer where you are +inside a jigsaw puzzle, where + +every time you get to the +end of a block section + +square thing-- they're oddly +shaped because it's a jigsaw + +puzzle-- you get a choice +of a new set of tiles + +to put on the end of the +one you've already gotten. + +Sometimes you have to +go back and pick one up + +off the beginning of your +puzzle and put it at the end. + +And various power-ups make +certain ones incompatible, + +like being able to fly. + +That means you can't swim. + +Being able to swim +means you can't jump-- + +all those kinds of things. + +You're kind of creating +your own world that you then + +have to navigate differently. + +Oh, yeah. + +And deconstruct it. + +You never get to see +the whole thing at once + +because it's falling apart as +you're taking it and moving it + +somewhere. + +PROFESSOR: Thank you. + +Group five. + +PRESENTER 22: So +our first idea is + +a game called The Gun +Wars, in which you're + +managing a defense company. + +And you're trading +off who you're + +going to sell your +product to amidst + +a bunch of different clients. + +So you could have +somebody go up to you, + +you get some information +on who they are, say, hey, + +this is James, seems +like an OK guy, + +and he wants to buy, +like, 10,000 missiles, + +air-to-surface +missiles or something. + +You have to surmise +him, figure out + +if that's somebody +you want to sell to, + +figure out at what +price you want to sell. + +And then there may be some +consequences for that. + +Maybe you sell to +Jimmy, and then he + +launches an attack on some +country you like or don't like. + +But more importantly, +maybe he does + +something your other +clients like or don't like. + +And so you lose other business. + +Or you get new business from +people that are Jimmy's friends + +and realize they can +buy weapons from you. + +So it's sort of a social +responsibility game. + +You're a defense contractor. + +You're managing some +pool of money, trying + +to make money off of contracts. + +And the trade-offs +come with who you're + +deciding to buy and sell from. + +PRESENTER 23: Our second idea +for the game is Bullet Craft. + +Bullet Craft is a fast-paced, +top-down shooter game + +that follows the simple +formula, the classic formula, + +that the player controls +the ship, moves around, + +[INAUDIBLE] that's +coming at him, + +and shoots the +enemies that spawns + +from the top of the screen. + +Well, you might ask, +where does trade-offs come + +into play for Bullet Craft? + +So there are +actually various ways + +we can augment the +game play so that we + +will incorporate trade-offs. + +For example, on +the micro level, we + +can have ammo limits +or overheating guns. + +And we can have a fuel limit +which if the player moves, + +he consumes fuel which +pollutes the environment, + +and the enemies become stronger +because of that pollution. + +At the macro level, +we could also + +have the player choosing +different types of weapons, + +spending their money on +different types of ships + +and even a crew. + +What I like about +Bullet Craft is + +it is very easy to implement, +and it's guaranteed to be fun, + +so that if we make +Bullet Craft, we + +are sure that we will be able +to make a successful game. + +PROFESSOR: Group eight. + +PRESENTER 24: So the first +idea we had is Daydream Inc. + +So in this game, you're like +a regular office worker. + +And you have to try +and not get fired. + +But the goal of the game is +to succeed in your daydreams. + +So there's basically two +mini-games within the game. + +There's surviving +the office life, + +and then there's +also your daydreams + +where you're fighting +your boss or something. + +And it's interesting +because you use tools + +from the office to build +weapons for your daydreams. + +So you might get a +stapler and a rubber band + +and make a staple gun or +something for your daydreams. + +So you have to spend both time +and research from the office + +life in the daydreams +without getting fired, + +so you can eventually +win the game. + +Also, if you become +CEO in the office life, + +so if you do really well +there too, you lose. + +PRESENTER 25: So our +second idea was Score High. + +So basically, you're +an MIT student. + +And you have a list of +maybe three classes. + +And you have some stats-- like, +your food, sleep, happiness, + +health. + +And the thing is, each of your +classes has PSETs and tests. + +And you have to get +to the tests on time, + +and you also have to turn +in your PSETs on time. + +And so how do you do that? + +So you run around +the maze, and you + +have to get to the right +building at the right time. + +But you also, when +you're there, actually + +have to take the tests. + +And depending on-- you +pick up different items. + +And say you drink 10 cups of +coffee, you're really jittery. + +Instead of seeing all of the +options for the multiple choice + +question, suddenly +you can't look at it, + +and you only see one question. + +And somehow you miss +the back of the page. + +So you fail the test, right? + +So the whole game is +about choosing-- you know, + +when am I going to drink coffee? + +Or maybe I'll buy +my friend coffee, + +and he'll give me +the PSET answers + +so I don't have to spend +five minutes doing the PSET. + +And managing those +trade-offs while also + +running around this +maze and getting + +everything done on time. + +And if you fail any of +your classes, you lose. + +PROFESSOR: Group +13, come on down. + +PRESENTER 26: Our first +idea is Ghost Face. + +The title's a working title. + +The idea is you're in a +maze, actually a maze. + +And you have very +limited visibility. + +You can only see +a certain radius + +that is much smaller than +the actual size of the maze. + +And there's ghosts +coming at you. + +And basically the idea is to get +to the other side of the maze, + +solving the maze, but you +only have limited disability. + +So you have to explore the maze +and remember which path was + +a good decision and +which path wasn't. + +So you have to trace back a lot. + +You can also add in more things. + +Like, you may have +a certain number + +of beacons, light +beacons, that you + +can place in different areas, +but a limited number of them. + +So you want to be-- you want +to make a decision as to what + +would be a strategically +good place to place a beacon + +and reveal an important and +critical part of the maze + +so that you can see +more of the maze. + +So that's our first idea. + +PRESENTER 27: So our second +idea revolves around DNA. + +We haven't found a +good title for it. + +But the idea is, let's +say there's an organism. + +And you have a certain +set of diseases + +that you want to +try to get rid of. + +And your goal is to somehow go +around finding other organisms + +that have their set of traits. + +What's the diseases +that you don't have, + +some other diseases +that you have. + +And play a game of +chance-- so whether it's + +worth it to spend your +time and energy eating + +or mating with +the other organism + +and seeing if those genes come +across to your [INAUDIBLE]. + +And the trade-off +is-- the trade-off is, + +do you want to mate with +this organism or not? + +We're still working on +the details of this, + +but the idea is this gene +competition [INAUDIBLE]. + +PRESENTER 28: And +random mutation. + +PRESENTER 27: Yeah, random +mutations [INAUDIBLE] + +PROFESSOR: OK. + +Thank you. + +All right. + +We're actually really +good on time today, + +so you'll actually have some +time to work in your teams + +after we get you all sorted out. + +So we heard about Dragon's Lair, +Caffeine Worker, MIT Simulator, + +Build a Car, Fight or Flight, +Jigsaw World, The Gun Wars, + +Bullet Craft, Daydream Inc., +Score High, Ghost Maze, + +and DNA. + +12 ideas-- actually, +a few of them + +could probably combine +pretty well together. + +So we're not really +throwing the ideas away. + +We're really just trying to +get together into groups of six + +around a base idea +we can start with. + +So if you've got a game +that you're really, really + +excited about working +on, come right down + +and put your name on it. + +And make sure your Post-It +has your name and the game + +engine you used in the +tutorial assignments. + +Let's see what we got. + +All right, raise your +hand if you still have + +your name tag, your Post-It. + +One, two, three, four. + +All right. + +We have Caffeine Worker +only has one person on. + +[? Zigamantias ?], you +have your name tag back. + +Nope, sit down. + +Just sit down. + +Jigsaw World. + +Sorry, Kathleen. + +All right. + +We've got one, two, +three, four, five, six. + +DNA is done. + +So DNA is Derek, Eduardo, Ava, +Harry, Trisha, and Lauren. + +One, two, three for Ghost Maze. + +Three for Score High. + +Two for Daydream. + +None for Gun Wars. + +Two for Bullet Craft. + +Three for Fight or Flight. + +One, two, three, +four for Build a Car. + +Two, three, four, five, six. + +Oh, cool. + +MIT Simulator. + +Don't get me in trouble. + +Norman, Jordan, James, +Peter, [? Szeun, ?] and Sam. + +Bullet Craft and +Daydream-- first off, + +does anybody who has +their name tag on them, + +are they all excited about +either of these two games? + +AUDIENCE: I am. + +PROFESSOR: You are? + +Is your name-- do you have +your name tag in your hand? + +OK, raise your hand if you have +your name tag in your hand. + +All right, come down here +and put your name on a game. + +I'm going to get them all. + +I think we have enough +to get every game to six. + +10, nine, eight, +seven, six-- hey, five. + +Cool. + +Thank you. + +All right, Fight or +Flight, Bullet Craft, + +Daydream I think +are all either going + +to go away or combine somehow. + +Score High, one, +two, three, four. + +One, two, three, four, +five on Ghost Maze. + +Just needs one more person. + +Five on Build a Car. + +Just needs one more person. + +Four on Dragon's Lair. + +One, two, three, +four, five, six. + +OK. + +Daydream is gone, +Bullet Craft is gone, + +Fight or Flight is gone. + +Move yourself to another team. + +All right, Ghost Maze +has six and is done. + +Score High has five, six. + +Done. + +AUDIENCE: Everything +is full, isn't it? + +PROFESSOR: Yes. + +So put yourself on one, +two, three, four, five, six. + +Put yourself on any of them. + +Five, four, three, +two-- thank you. + +So here are our final teams. + +We're going to do +one last shuffle. + +If anyone is like, I don't +want to really be on that one, + +they can move to another. + +For Dragon's Lair, we have Roy, +[? Mikael, ?] Liz, Zigamantis, + +Devon, Caleb, and Kathleen. + +You have a good mix +of Unity and Flixel, + +so I imagine you might +use Unity or Flixel. + +Build a Car, we have Rodrigo, +Anderson, Matt, [? Taj ?], + +Jeremy, and [INAUDIBLE]. + +We have Unity, Unity, Unity-- +three Unity, three Phaser. + +I wonder what +you're going to use. + +Score High, six. + +Miriam, [? Sen ?], Megan, +Kevin, Sabrina, and [? Zinue ?]. + +And we have Haxe, Haxe, Flixel. + +Oh, wow, lots of Flixel. + +And two Unity. + +So maybe one of those. + +Ghost Maze, [? Jutoshka ?], +[? Salaam ?], Daniel, Kevin, + +Justin, and Rachel. + +And Unity, Unity, HaxeFlixel. + +Ooh, it's going to +be kind of tough. + +We've got three Phaser, two +Unity, and one HaxeFlixel, + +so that's going to be a +hard decision to make. + +DNA, we've got seven-- Jenny, +Lauren, Ava, Tricia, Harry, + +Eduardo, Derek. + +HaxeFlixel, HaxeFlixel, +HaxeFlixel, Flixel, and one + +Unity. + +So probably one of the Flixels. + +[GROANING] + +You decide. + +MIT Simulator has Unity, Unity, +Unity, Unity, Unity, Unity, + +Unity. + +Four Unitys and two +Phasers, so probably Unity. + +And that is Norman, +Jordan, James, Peter, + +Sam, and [? Szeun. ?] We have +how many students are not + +in class today? + +Five or six students +not in class today. + +They are going to +have to-- what's up? + +AUDIENCE: Make them a team. + +AUDIENCE: Game to learn +how not to be late. + +PROFESSOR: That's +a good question. + +PHILLIP: [INAUDIBLE] +simultaneously on Wednesday, + +that might be possible. + +But if a few of them don't +come back on Wednesday, + +that may not work. + +PROFESSOR: So teams will +be finalized on Wednesday. + +These are the teams as +they stand right now. + +You have 40 minutes +to meet as a team + +to figure out if you +all match schedules, + +to talk about the +idea you just pitched, + +and make a really +quick lo-fi prototype, + +or write down that page +that you just said out loud + +on the spur of the moment. + +Figure out what is that +game that you're making. + +Work on that vision statement. + +And feel free to +grab your things + +and put your names +on it if you like. \ No newline at end of file diff --git a/MtK9rIbdlis.txt b/MtK9rIbdlis.txt new file mode 100644 index 0000000000000000000000000000000000000000..1acae1128ec390284f67eb26d7e9edf77b7bce0b --- /dev/null +++ b/MtK9rIbdlis.txt @@ -0,0 +1,1499 @@ +align:start position:0% + +we're gonna do a couple of results with + + align:start position:0% +we're gonna do a couple of results with + + + align:start position:0% +we're gonna do a couple of results with +this formula that connect even a little + + align:start position:0% +this formula that connect even a little + + + align:start position:0% +this formula that connect even a little +more with what we're doing maybe I'll + + align:start position:0% +more with what we're doing maybe I'll + + + align:start position:0% +more with what we're doing maybe I'll +leave that blackboard here because it up + + align:start position:0% +leave that blackboard here because it up + + + align:start position:0% +leave that blackboard here because it up +simple formulas come out of this which + + align:start position:0% +simple formulas come out of this which + + + align:start position:0% +simple formulas come out of this which +is very nice actually + + align:start position:0% + + + + align:start position:0% + +so one simple formula was that the total + + align:start position:0% +so one simple formula was that the total + + + align:start position:0% +so one simple formula was that the total +cross section we will wrote the formula + + align:start position:0% +cross section we will wrote the formula + + + align:start position:0% +cross section we will wrote the formula +for the differential cross section but + + align:start position:0% +for the differential cross section but + + + align:start position:0% +for the differential cross section but +the total cross section is the integral + + align:start position:0% +the total cross section is the integral + + + align:start position:0% +the total cross section is the integral +of F K of theta in this case the Omega + + align:start position:0% +of F K of theta in this case the Omega + + + align:start position:0% +of F K of theta in this case the Omega +so this is the integral of F K of theta + + align:start position:0% +so this is the integral of F K of theta + + + align:start position:0% +so this is the integral of F K of theta +star FK of theta the army gamma but we + + align:start position:0% +star FK of theta the army gamma but we + + + align:start position:0% +star FK of theta the army gamma but we +have FK of theta here that zero looks + + align:start position:0% +have FK of theta here that zero looks + + + align:start position:0% +have FK of theta here that zero looks +like theta is not good that's a zero and + + align:start position:0% +like theta is not good that's a zero and + + + align:start position:0% +like theta is not good that's a zero and +we can plug all this in so what do we + + align:start position:0% +we can plug all this in so what do we + + + align:start position:0% +we can plug all this in so what do we +have we do this because the answer is + + align:start position:0% +have we do this because the answer is + + + align:start position:0% +have we do this because the answer is +very simple we get a 4 PI over K squared + + align:start position:0% +very simple we get a 4 PI over K squared + + + align:start position:0% +very simple we get a 4 PI over K squared +we have a sum over L and L prime because + + align:start position:0% +we have a sum over L and L prime because + + + align:start position:0% +we have a sum over L and L prime because +we have two factors to L plus 1 to L + + align:start position:0% +we have two factors to L plus 1 to L + + + align:start position:0% +we have two factors to L plus 1 to L +prime plus 1 the phase shift for L prime + + align:start position:0% +prime plus 1 the phase shift for L prime + + + align:start position:0% +prime plus 1 the phase shift for L prime +and the phase shift for L so e to the + + align:start position:0% +and the phase shift for L so e to the + + + align:start position:0% +and the phase shift for L so e to the +minus I Delta L sine of Delta L so I + + align:start position:0% +minus I Delta L sine of Delta L so I + + + align:start position:0% +minus I Delta L sine of Delta L so I +guess I'm using L for this one and L + + align:start position:0% +guess I'm using L for this one and L + + + align:start position:0% +guess I'm using L for this one and L +prime for that one e to the I Delta L + + align:start position:0% +prime for that one e to the I Delta L + + + align:start position:0% +prime for that one e to the I Delta L +prime sine of + + align:start position:0% +prime sine of + + + align:start position:0% +prime sine of +delta L Prime but happily all that will + + align:start position:0% +delta L Prime but happily all that will + + + align:start position:0% +delta L Prime but happily all that will +not matter because then you have the + + align:start position:0% +not matter because then you have the + + + align:start position:0% +not matter because then you have the +integral over solid angle of why L star + + align:start position:0% +integral over solid angle of why L star + + + align:start position:0% +integral over solid angle of why L star +zero of Omega why L 0 of Omega Prime + + align:start position:0% +zero of Omega why L 0 of Omega Prime + + + align:start position:0% +zero of Omega why L 0 of Omega Prime +here ok seems like a lot of work but + + align:start position:0% +here ok seems like a lot of work but + + + align:start position:0% +here ok seems like a lot of work but +we're not doing nothing else and + + align:start position:0% +we're not doing nothing else and + + + align:start position:0% +we're not doing nothing else and +integrating this F of theta let's look + + align:start position:0% +integrating this F of theta let's look + + + align:start position:0% +integrating this F of theta let's look +at it for a second + + align:start position:0% +at it for a second + + + align:start position:0% +at it for a second +it's just that formula squared so + + align:start position:0% +it's just that formula squared so + + + align:start position:0% +it's just that formula squared so +basically you started one why you don't + + align:start position:0% +basically you started one why you don't + + + align:start position:0% +basically you started one why you don't +start the other but you have to + + align:start position:0% +start the other but you have to + + + align:start position:0% +start the other but you have to +integrate them and the orthonormality of + + align:start position:0% +integrate them and the orthonormality of + + + align:start position:0% +integrate them and the orthonormality of +our spherical harmonics means that this + + align:start position:0% +our spherical harmonics means that this + + + align:start position:0% +our spherical harmonics means that this +is Delta ll prime so you can set L prime + + align:start position:0% +is Delta ll prime so you can set L prime + + + align:start position:0% +is Delta ll prime so you can set L prime +equal to L this faces will can so this + + align:start position:0% +equal to L this faces will can so this + + + align:start position:0% +equal to L this faces will can so this +factor will be squared this square root + + align:start position:0% +factor will be squared this square root + + + align:start position:0% +factor will be squared this square root +will disappear and you have a simple + + align:start position:0% +will disappear and you have a simple + + + align:start position:0% +will disappear and you have a simple +formula that the cross-section is 4 PI + + align:start position:0% +formula that the cross-section is 4 PI + + + align:start position:0% +formula that the cross-section is 4 PI +over K squared sum to L plus 1 sine + + align:start position:0% +over K squared sum to L plus 1 sine + + + align:start position:0% +over K squared sum to L plus 1 sine +squared Delta L very nice formula for a + + align:start position:0% +squared Delta L very nice formula for a + + + align:start position:0% +squared Delta L very nice formula for a +physical observable what did you get + + align:start position:0% +physical observable what did you get + + + align:start position:0% +physical observable what did you get +that the cross-section is the sum of + + align:start position:0% +that the cross-section is the sum of + + + align:start position:0% +that the cross-section is the sum of +contributions the total cross-section is + + align:start position:0% +contributions the total cross-section is + + + align:start position:0% +contributions the total cross-section is +the sum of contributions from partial + + align:start position:0% +the sum of contributions from partial + + + align:start position:0% +the sum of contributions from partial +cross-sections from each partial wave + + align:start position:0% +cross-sections from each partial wave + + + align:start position:0% +cross-sections from each partial wave +that's not true for the differential + + align:start position:0% +that's not true for the differential + + + align:start position:0% +that's not true for the differential +cross-section because in the + + align:start position:0% +cross-section because in the + + + align:start position:0% +cross-section because in the +differential cross-section you don't + + align:start position:0% +differential cross-section you don't + + + align:start position:0% +differential cross-section you don't +integrate and as long as you don't + + align:start position:0% +integrate and as long as you don't + + + align:start position:0% +integrate and as long as you don't +integrate you have mixing between + + align:start position:0% +integrate you have mixing between + + + align:start position:0% +integrate you have mixing between +different else the different partial + + align:start position:0% +different else the different partial + + + align:start position:0% +different else the different partial +waves interfere in the differential + + align:start position:0% +waves interfere in the differential + + + align:start position:0% +waves interfere in the differential +cross-section but they will not + + align:start position:0% +cross-section but they will not + + + align:start position:0% +cross-section but they will not +interfere anymore in the total + + align:start position:0% +interfere anymore in the total + + + align:start position:0% +interfere anymore in the total +cross-section each partial wave + + align:start position:0% +cross-section each partial wave + + + align:start position:0% +cross-section each partial wave +contributes to the total cross-section + + align:start position:0% +contributes to the total cross-section + + + align:start position:0% +contributes to the total cross-section +that's why it's important + + align:start position:0% +that's why it's important + + + align:start position:0% +that's why it's important +to calculate this phase shifts you say + + align:start position:0% +to calculate this phase shifts you say + + + align:start position:0% +to calculate this phase shifts you say +oh just the face phases don't matter now + + align:start position:0% +oh just the face phases don't matter now + + + align:start position:0% +oh just the face phases don't matter now +the relative faces matter a lot those + + align:start position:0% +the relative faces matter a lot those + + + align:start position:0% +the relative faces matter a lot those +are the faces that enter here and the + + align:start position:0% +are the faces that enter here and the + + + align:start position:0% +are the faces that enter here and the +cross-section is expressed in terms of + + align:start position:0% +cross-section is expressed in terms of + + + align:start position:0% +cross-section is expressed in terms of +those phases oh there's one more result + + align:start position:0% +those phases oh there's one more result + + + align:start position:0% +those phases oh there's one more result +that is famous in scattering and has to + + align:start position:0% +that is famous in scattering and has to + + + align:start position:0% +that is famous in scattering and has to +do with the optical theorem the optical + + align:start position:0% +do with the optical theorem the optical + + + align:start position:0% +do with the optical theorem the optical +theorem is something you may have seen + + align:start position:0% +theorem is something you may have seen + + + align:start position:0% +theorem is something you may have seen +already in electromagnetism or in other + + align:start position:0% +already in electromagnetism or in other + + + align:start position:0% +already in electromagnetism or in other +fields it's a statement about + + align:start position:0% +fields it's a statement about + + + align:start position:0% +fields it's a statement about +probability of conservation of flux it's + + align:start position:0% +probability of conservation of flux it's + + + align:start position:0% +probability of conservation of flux it's +fairly non-trivial and it's a constraint + + align:start position:0% +fairly non-trivial and it's a constraint + + + align:start position:0% +fairly non-trivial and it's a constraint +on the scattering amplitude basically + + align:start position:0% +on the scattering amplitude basically + + + align:start position:0% +on the scattering amplitude basically +and we may discuss it in a problem of + + align:start position:0% +and we may discuss it in a problem of + + + align:start position:0% +and we may discuss it in a problem of +it's a statement that when you have an + + align:start position:0% +it's a statement that when you have an + + + align:start position:0% +it's a statement that when you have an +object the thing that you detect as the + + align:start position:0% +object the thing that you detect as the + + + align:start position:0% +object the thing that you detect as the +scattering cross-section is all these + + align:start position:0% +scattering cross-section is all these + + + align:start position:0% +scattering cross-section is all these +particles that were deflected from the + + align:start position:0% +particles that were deflected from the + + + align:start position:0% +particles that were deflected from the +object and they were deflected from the + + align:start position:0% +object and they were deflected from the + + + align:start position:0% +object and they were deflected from the +object because the object creates a + + align:start position:0% +object because the object creates a + + + align:start position:0% +object because the object creates a +shadow at least in electromagnetism that + + align:start position:0% +shadow at least in electromagnetism that + + + align:start position:0% +shadow at least in electromagnetism that +intuition is very clear you have a + + align:start position:0% +intuition is very clear you have a + + + align:start position:0% +intuition is very clear you have a +sphere here maybe a conducting sphere + + align:start position:0% +sphere here maybe a conducting sphere + + + align:start position:0% +sphere here maybe a conducting sphere +and observing so you shine light you + + align:start position:0% +and observing so you shine light you + + + align:start position:0% +and observing so you shine light you +create a shadow and that is the light + + align:start position:0% +create a shadow and that is the light + + + align:start position:0% +create a shadow and that is the light +that if you didn't have here it would + + align:start position:0% +that if you didn't have here it would + + + align:start position:0% +that if you didn't have here it would +have gone through but if it's here the + + align:start position:0% +have gone through but if it's here the + + + align:start position:0% +have gone through but if it's here the +shadow is responsible what you lost from + + align:start position:0% +shadow is responsible what you lost from + + + align:start position:0% +shadow is responsible what you lost from +the shadow is what you got scattered so + + align:start position:0% +the shadow is what you got scattered so + + + align:start position:0% +the shadow is what you got scattered so +whatever you get in the forward + + align:start position:0% +whatever you get in the forward + + + align:start position:0% +whatever you get in the forward +direction here you get nothing you get a + + align:start position:0% +direction here you get nothing you get a + + + align:start position:0% +direction here you get nothing you get a +shadow carries the information about the + + align:start position:0% +shadow carries the information about the + + + align:start position:0% +shadow carries the information about the +the wave that scatter it's a little more + + align:start position:0% +the wave that scatter it's a little more + + + align:start position:0% +the wave that scatter it's a little more +complicated than that mathematically + + align:start position:0% +complicated than that mathematically + + + align:start position:0% +complicated than that mathematically +when you do it because the total wave + + align:start position:0% +when you do it because the total wave + + + align:start position:0% +when you do it because the total wave +function in the forward Direction is a + + align:start position:0% +function in the forward Direction is a + + + align:start position:0% +function in the forward Direction is a +combination of the incoming wave + + align:start position:0% +combination of the incoming wave + + + align:start position:0% +combination of the incoming wave +function accustomed forward direction + + align:start position:0% +function accustomed forward direction + + + align:start position:0% +function accustomed forward direction +and the scattered wave function that has + + align:start position:0% +and the scattered wave function that has + + + align:start position:0% +and the scattered wave function that has +a forward direction so the theorem is + + align:start position:0% +a forward direction so the theorem is + + + align:start position:0% +a forward direction so the theorem is +quite interesting to prove and we proved + + align:start position:0% +quite interesting to prove and we proved + + + align:start position:0% +quite interesting to prove and we proved +it with flux conservation it gives you + + align:start position:0% +it with flux conservation it gives you + + + align:start position:0% +it with flux conservation it gives you +enormous insight into the physics but + + align:start position:0% +enormous insight into the physics but + + + align:start position:0% +enormous insight into the physics but +here is the power of algebra and the + + align:start position:0% +here is the power of algebra and the + + + align:start position:0% +here is the power of algebra and the +power of phase shifts you don't have to + + align:start position:0% +power of phase shifts you don't have to + + + align:start position:0% +power of phase shifts you don't have to +be brilliant to discover the optical + + align:start position:0% +be brilliant to discover the optical + + + align:start position:0% +be brilliant to discover the optical +theorem in this set up the physics has + + align:start position:0% +theorem in this set up the physics has + + + align:start position:0% +theorem in this set up the physics has +already done the mathematics of the + + align:start position:0% +already done the mathematics of the + + + align:start position:0% +already done the mathematics of the +faces has already done all the work for + + align:start position:0% +faces has already done all the work for + + + align:start position:0% +faces has already done all the work for +you + + align:start position:0% +you + + + align:start position:0% +you +let's see happen let's figure out how + + align:start position:0% +let's see happen let's figure out how + + + align:start position:0% +let's see happen let's figure out how +does the forward the scattering + + align:start position:0% +does the forward the scattering + + + align:start position:0% +does the forward the scattering +cross-section look in the forward + + align:start position:0% +cross-section look in the forward + + + align:start position:0% +cross-section look in the forward +direction so you have your object here + + align:start position:0% +direction so you have your object here + + + align:start position:0% +direction so you have your object here +you send in your waves get scatter but + + align:start position:0% +you send in your waves get scatter but + + + align:start position:0% +you send in your waves get scatter but +there is something in the forward + + align:start position:0% +there is something in the forward + + + align:start position:0% +there is something in the forward +direction that is FK at theta equals + + align:start position:0% +direction that is FK at theta equals + + + align:start position:0% +direction that is FK at theta equals +zero is the forward scattering word + + align:start position:0% +zero is the forward scattering word + + + align:start position:0% +zero is the forward scattering word +scattering and now this forward + + align:start position:0% +scattering and now this forward + + + align:start position:0% +scattering and now this forward +scattering is we can calculate it for + + align:start position:0% +scattering is we can calculate it for + + + align:start position:0% +scattering is we can calculate it for +that we need to know that yl0 + + align:start position:0% +that we need to know that yl0 + + + align:start position:0% +that we need to know that yl0 +of theta equals zero well why L zero of + + align:start position:0% +of theta equals zero well why L zero of + + + align:start position:0% +of theta equals zero well why L zero of +theta is actually 2 L plus 1 over 4 pi P + + align:start position:0% +theta is actually 2 L plus 1 over 4 pi P + + + align:start position:0% +theta is actually 2 L plus 1 over 4 pi P +L the Legendre polynomial of cosine + + align:start position:0% +L the Legendre polynomial of cosine + + + align:start position:0% +L the Legendre polynomial of cosine +theta so why L 0 at theta equals 0 is + + align:start position:0% +theta so why L 0 at theta equals 0 is + + + align:start position:0% +theta so why L 0 at theta equals 0 is +just square root of 2 L plus 1 over 4 pi + + align:start position:0% +just square root of 2 L plus 1 over 4 pi + + + align:start position:0% +just square root of 2 L plus 1 over 4 pi +and the Legendre polynomials are defined + + align:start position:0% +and the Legendre polynomials are defined + + + align:start position:0% +and the Legendre polynomials are defined +always so that PL at 1 is equal to 1 Oh + + align:start position:0% +always so that PL at 1 is equal to 1 Oh + + + align:start position:0% +always so that PL at 1 is equal to 1 Oh +pls + + align:start position:0% +pls + + + align:start position:0% +pls +at x equals 1 are always one so that's + + align:start position:0% +at x equals 1 are always one so that's + + + align:start position:0% +at x equals 1 are always one so that's +the spherical harmonic in the forward + + align:start position:0% +the spherical harmonic in the forward + + + align:start position:0% +the spherical harmonic in the forward +direction so you have here from that + + align:start position:0% +direction so you have here from that + + + align:start position:0% +direction so you have here from that +formula on the right 4 PI over K sum + + align:start position:0% +formula on the right 4 PI over K sum + + + align:start position:0% +formula on the right 4 PI over K sum +from l equals 0 this is an investigation + + align:start position:0% +from l equals 0 this is an investigation + + + align:start position:0% +from l equals 0 this is an investigation +of what happens to the forward + + align:start position:0% +of what happens to the forward + + + align:start position:0% +of what happens to the forward +scattering amplitude the yl0 gives you + + align:start position:0% +scattering amplitude the yl0 gives you + + + align:start position:0% +scattering amplitude the yl0 gives you +another square root of 2l plus 1 and a 4 + + align:start position:0% +another square root of 2l plus 1 and a 4 + + + align:start position:0% +another square root of 2l plus 1 and a 4 +square root of 4 pi as well and then you + + align:start position:0% +square root of 4 pi as well and then you + + + align:start position:0% +square root of 4 pi as well and then you +get e to the I Delta L sine Delta so + + align:start position:0% +get e to the I Delta L sine Delta so + + + align:start position:0% +get e to the I Delta L sine Delta so +look here here and these factors + + align:start position:0% +look here here and these factors + + + align:start position:0% +look here here and these factors +simplify so f K of theta equals 0 is 1 + + align:start position:0% +simplify so f K of theta equals 0 is 1 + + + align:start position:0% +simplify so f K of theta equals 0 is 1 +over K some of L 2 L plus 1 e to the I + + align:start position:0% +over K some of L 2 L plus 1 e to the I + + + align:start position:0% +over K some of L 2 L plus 1 e to the I +Delta Sonning Delta ok that's a nice + + align:start position:0% +Delta Sonning Delta ok that's a nice + + + align:start position:0% +Delta Sonning Delta ok that's a nice +formula maybe something it has to do + + align:start position:0% +formula maybe something it has to do + + + align:start position:0% +formula maybe something it has to do +with a cross section F in this forward + + align:start position:0% +with a cross section F in this forward + + + align:start position:0% +with a cross section F in this forward +direction has that formula and the cross + + align:start position:0% +direction has that formula and the cross + + + align:start position:0% +direction has that formula and the cross +section has this formula + + align:start position:0% + + + + align:start position:0% + +so how do I get to relay them I get to + + align:start position:0% +so how do I get to relay them I get to + + + align:start position:0% +so how do I get to relay them I get to +relate them if I said now I asked for + + align:start position:0% +relate them if I said now I asked for + + + align:start position:0% +relate them if I said now I asked for +the imaginary part of this FK for it + + align:start position:0% +the imaginary part of this FK for it + + + align:start position:0% +the imaginary part of this FK for it +because the imaginary part of this FK at + + align:start position:0% +because the imaginary part of this FK at + + + align:start position:0% +because the imaginary part of this FK at +theta equals zero is equal to one over K + + align:start position:0% +theta equals zero is equal to one over K + + + align:start position:0% +theta equals zero is equal to one over K +sum over L this 2l plus 1 and the + + align:start position:0% +sum over L this 2l plus 1 and the + + + align:start position:0% +sum over L this 2l plus 1 and the +imaginary part of that turns it into + + align:start position:0% +imaginary part of that turns it into + + + align:start position:0% +imaginary part of that turns it into +sine squared Delta because the imaginary + + align:start position:0% +sine squared Delta because the imaginary + + + align:start position:0% +sine squared Delta because the imaginary +part of the e to the I Delta is sine + + align:start position:0% +part of the e to the I Delta is sine + + + align:start position:0% +part of the e to the I Delta is sine +Delta so I get the sine squared Delta + + align:start position:0% +Delta so I get the sine squared Delta + + + align:start position:0% +Delta so I get the sine squared Delta +there and you say look at this sum is + + align:start position:0% +there and you say look at this sum is + + + align:start position:0% +there and you say look at this sum is +identical to the sum of the + + align:start position:0% +identical to the sum of the + + + align:start position:0% +identical to the sum of the +cross-section you have discovered a + + align:start position:0% +cross-section you have discovered a + + + align:start position:0% +cross-section you have discovered a +relation between the total cross-section + + align:start position:0% +relation between the total cross-section + + + align:start position:0% +relation between the total cross-section +and the imaginary part of the forward + + align:start position:0% +and the imaginary part of the forward + + + align:start position:0% +and the imaginary part of the forward +scattering amplitude so what is the + + align:start position:0% +scattering amplitude so what is the + + + align:start position:0% +scattering amplitude so what is the +final formula the final formula is that + + align:start position:0% +final formula the final formula is that + + + align:start position:0% +final formula the final formula is that +Sigma maybe I can do it here + + align:start position:0% +Sigma maybe I can do it here + + + align:start position:0% +Sigma maybe I can do it here +[Applause] + + align:start position:0% + + + + align:start position:0% + +Sigma is equal to well it differs from + + align:start position:0% +Sigma is equal to well it differs from + + + align:start position:0% +Sigma is equal to well it differs from +this from a 4 PI over K imaginary part + + align:start position:0% +this from a 4 PI over K imaginary part + + + align:start position:0% +this from a 4 PI over K imaginary part +of F of theta equals 0 FK this is the + + align:start position:0% +of F of theta equals 0 FK this is the + + + align:start position:0% +of F of theta equals 0 FK this is the +optical theorem which was discovered in + + align:start position:0% +optical theorem which was discovered in + + + align:start position:0% +optical theorem which was discovered in +the context of optics by thinking of the + + align:start position:0% +the context of optics by thinking of the + + + align:start position:0% +the context of optics by thinking of the +physics of shadows + + align:start position:0% + + + + align:start position:0% + +whatever is basically the shadow + + align:start position:0% +whatever is basically the shadow + + + align:start position:0% +whatever is basically the shadow +contains all that kind of information + + align:start position:0% +contains all that kind of information + + + align:start position:0% +contains all that kind of information +about all that was lost from the + + align:start position:0% +about all that was lost from the + + + align:start position:0% +about all that was lost from the +incoming beam so that's a nice it's not + + align:start position:0% +incoming beam so that's a nice it's not + + + align:start position:0% +incoming beam so that's a nice it's not +absolutely obvious how it works the + + align:start position:0% +absolutely obvious how it works the + + + align:start position:0% +absolutely obvious how it works the +process of interference between the + + align:start position:0% +process of interference between the + + + align:start position:0% +process of interference between the +incoming wave and the scattered wave and + + align:start position:0% +incoming wave and the scattered wave and + + + align:start position:0% +incoming wave and the scattered wave and +what they do and you have to look + + align:start position:0% +what they do and you have to look + + + align:start position:0% +what they do and you have to look +carefully of this thing so that explains + + align:start position:0% +carefully of this thing so that explains + + + align:start position:0% +carefully of this thing so that explains +why you need the imaginary part and why + + align:start position:0% +why you need the imaginary part and why + + + align:start position:0% +why you need the imaginary part and why +this factor show up but the intuition is + + align:start position:0% +this factor show up but the intuition is + + + align:start position:0% +this factor show up but the intuition is +nevertheless simple \ No newline at end of file diff --git a/NNhVVk244ZA.txt b/NNhVVk244ZA.txt new file mode 100644 index 0000000000000000000000000000000000000000..54e6afb50eea4a586d8c1e96b193071490f24cf8 --- /dev/null +++ b/NNhVVk244ZA.txt @@ -0,0 +1,1491 @@ +align:start position:0% + +many mathematical models involve high + + align:start position:0% +many mathematical models involve high + + + align:start position:0% +many mathematical models involve high +order derivatives but the MATLAB Oh de + + align:start position:0% +order derivatives but the MATLAB Oh de + + + align:start position:0% +order derivatives but the MATLAB Oh de +solvers only work with systems of + + align:start position:0% +solvers only work with systems of + + + align:start position:0% +solvers only work with systems of +first-order ordinary differential + + align:start position:0% +first-order ordinary differential + + + align:start position:0% +first-order ordinary differential +equations so we have to rewrite the + + align:start position:0% +equations so we have to rewrite the + + + align:start position:0% +equations so we have to rewrite the +models to just involve first order + + align:start position:0% +models to just involve first order + + + align:start position:0% +models to just involve first order +derivatives let's see how to do that + + align:start position:0% +derivatives let's see how to do that + + + align:start position:0% +derivatives let's see how to do that +with a very simple model the harmonic + + align:start position:0% +with a very simple model the harmonic + + + align:start position:0% +with a very simple model the harmonic +oscillator X double prime plus x equals + + align:start position:0% +oscillator X double prime plus x equals + + + align:start position:0% +oscillator X double prime plus x equals +zero this involves a second-order + + align:start position:0% +zero this involves a second-order + + + align:start position:0% +zero this involves a second-order +derivative so to write it as a first + + align:start position:0% +derivative so to write it as a first + + + align:start position:0% +derivative so to write it as a first +order system we introduce the vector Y + + align:start position:0% +order system we introduce the vector Y + + + align:start position:0% +order system we introduce the vector Y +which is if this is a vector with two + + align:start position:0% +which is if this is a vector with two + + + align:start position:0% +which is if this is a vector with two +components X and the derivative of X + + align:start position:0% +components X and the derivative of X + + + align:start position:0% +components X and the derivative of X +which is changing notation to let Y have + + align:start position:0% +which is changing notation to let Y have + + + align:start position:0% +which is changing notation to let Y have +two components X and X prime then the + + align:start position:0% +two components X and X prime then the + + + align:start position:0% +two components X and X prime then the +derivative of Y is the vector with X and + + align:start position:0% +derivative of Y is the vector with X and + + + align:start position:0% +derivative of Y is the vector with X and +X double prime so the differential + + align:start position:0% +X double prime so the differential + + + align:start position:0% +X double prime so the differential +equation now becomes Y 2 prime plus y1 + + align:start position:0% +equation now becomes Y 2 prime plus y1 + + + align:start position:0% +equation now becomes Y 2 prime plus y1 +equals 0 do you see how we've just + + align:start position:0% +equals 0 do you see how we've just + + + align:start position:0% +equals 0 do you see how we've just +rewritten this differential equation so + + align:start position:0% +rewritten this differential equation so + + + align:start position:0% +rewritten this differential equation so +y 2 plus y 2 prime is playing the role + + align:start position:0% +y 2 plus y 2 prime is playing the role + + + align:start position:0% +y 2 plus y 2 prime is playing the role +of X double Prime + + align:start position:0% +of X double Prime + + + align:start position:0% +of X double Prime +once you've done that everything else is + + align:start position:0% +once you've done that everything else is + + + align:start position:0% +once you've done that everything else is +easy the vector system is now y1 y2 + + align:start position:0% +easy the vector system is now y1 y2 + + + align:start position:0% +easy the vector system is now y1 y2 +prime is y2 minus y1 + + align:start position:0% +prime is y2 minus y1 + + + align:start position:0% +prime is y2 minus y1 +the first component says y1 prime is y 2 + + align:start position:0% +the first component says y1 prime is y 2 + + + align:start position:0% +the first component says y1 prime is y 2 +that's just saying that the derivative + + align:start position:0% +that's just saying that the derivative + + + align:start position:0% +that's just saying that the derivative +of the first component is the second + + align:start position:0% +of the first component is the second + + + align:start position:0% +of the first component is the second +here's the differential equation itself + + align:start position:0% +here's the differential equation itself + + + align:start position:0% +here's the differential equation itself +y2 prime is minus y1 is the actual + + align:start position:0% +y2 prime is minus y1 is the actual + + + align:start position:0% +y2 prime is minus y1 is the actual +harmonic oscillator differential + + align:start position:0% +harmonic oscillator differential + + + align:start position:0% +harmonic oscillator differential +equation when we write this as an + + align:start position:0% +equation when we write this as an + + + align:start position:0% +equation when we write this as an +autonomous function for MATLAB here's + + align:start position:0% +autonomous function for MATLAB here's + + + align:start position:0% +autonomous function for MATLAB here's +the autonomous function f is an + + align:start position:0% +the autonomous function f is an + + + align:start position:0% +the autonomous function f is an +autonomous + + align:start position:0% +autonomous + + + align:start position:0% +autonomous +function of T and Y and it doesn't + + align:start position:0% +function of T and Y and it doesn't + + + align:start position:0% +function of T and Y and it doesn't +depend upon T first gets a vector now + + align:start position:0% +depend upon T first gets a vector now + + + align:start position:0% +depend upon T first gets a vector now +the column vector the first component of + + align:start position:0% +the column vector the first component of + + + align:start position:0% +the column vector the first component of +F is y2 and the second component is + + align:start position:0% +F is y2 and the second component is + + + align:start position:0% +F is y2 and the second component is +minus minus y1 the first component here + + align:start position:0% +minus minus y1 the first component here + + + align:start position:0% +minus minus y1 the first component here +is just a matter of notation all the + + align:start position:0% +is just a matter of notation all the + + + align:start position:0% +is just a matter of notation all the +content is in the second component which + + align:start position:0% +content is in the second component which + + + align:start position:0% +content is in the second component which +expresses the differential equation now + + align:start position:0% +expresses the differential equation now + + + align:start position:0% +expresses the differential equation now +for some initial conditions suppose the + + align:start position:0% +for some initial conditions suppose the + + + align:start position:0% +for some initial conditions suppose the +initial conditions are that X of 0 is 0 + + align:start position:0% +initial conditions are that X of 0 is 0 + + + align:start position:0% +initial conditions are that X of 0 is 0 +and X prime of 0 is 1 in terms of the + + align:start position:0% +and X prime of 0 is 1 in terms of the + + + align:start position:0% +and X prime of 0 is 1 in terms of the +vector Y that's why 1 of 0 the first + + align:start position:0% +vector Y that's why 1 of 0 the first + + + align:start position:0% +vector Y that's why 1 of 0 the first +component is why it is 0 and the second + + align:start position:0% +component is why it is 0 and the second + + + align:start position:0% +component is why it is 0 and the second +component is 1 or in vector terms the + + align:start position:0% +component is 1 or in vector terms the + + + align:start position:0% +component is 1 or in vector terms the +initial vector is 0 1 that implies the + + align:start position:0% +initial vector is 0 1 that implies the + + + align:start position:0% +initial vector is 0 1 that implies the +solution is sine T and cosine T when we + + align:start position:0% +solution is sine T and cosine T when we + + + align:start position:0% +solution is sine T and cosine T when we +write the initial condition in MATLAB + + align:start position:0% +write the initial condition in MATLAB + + + align:start position:0% +write the initial condition in MATLAB +it's the column vector 0 1 let's bring + + align:start position:0% +it's the column vector 0 1 let's bring + + + align:start position:0% +it's the column vector 0 1 let's bring +up the MATLAB command window here's the + + align:start position:0% +up the MATLAB command window here's the + + + align:start position:0% +up the MATLAB command window here's the +differential equation y 1 prime is y 2 + + align:start position:0% +differential equation y 1 prime is y 2 + + + align:start position:0% +differential equation y 1 prime is y 2 +and Y 2 prime is minus y 1 here's the + + align:start position:0% +and Y 2 prime is minus y 1 here's the + + + align:start position:0% +and Y 2 prime is minus y 1 here's the +harmonic oscillator we're going to + + align:start position:0% +harmonic oscillator we're going to + + + align:start position:0% +harmonic oscillator we're going to +integrate from 0 to 2 pi because the + + align:start position:0% +integrate from 0 to 2 pi because the + + + align:start position:0% +integrate from 0 to 2 pi because the +trick fun functions and I'm going to ask + + align:start position:0% +trick fun functions and I'm going to ask + + + align:start position:0% +trick fun functions and I'm going to ask +for output steps of 2 PI over 36 which + + align:start position:0% +for output steps of 2 PI over 36 which + + + align:start position:0% +for output steps of 2 PI over 36 which +corresponds to every 10 degrees like the + + align:start position:0% +corresponds to every 10 degrees like the + + + align:start position:0% +corresponds to every 10 degrees like the +runways at an airport I'm going to need + + align:start position:0% +runways at an airport I'm going to need + + + align:start position:0% +runways at an airport I'm going to need +an initial condition Y naught is 0 and + + align:start position:0% +an initial condition Y naught is 0 and + + + align:start position:0% +an initial condition Y naught is 0 and +need a column vector 0 1 for the two + + align:start position:0% +need a column vector 0 1 for the two + + + align:start position:0% +need a column vector 0 1 for the two +components I'm gonna use OD 45 and if I + + align:start position:0% +components I'm gonna use OD 45 and if I + + + align:start position:0% +components I'm gonna use OD 45 and if I +call it with no output arguments OD 45 + + align:start position:0% +call it with no output arguments OD 45 + + + align:start position:0% +call it with no output arguments OD 45 +the differential equation F T span the + + align:start position:0% +the differential equation F T span the + + + align:start position:0% +the differential equation F T span the +time interval and why not the initial + + align:start position:0% +time interval and why not the initial + + + align:start position:0% +time interval and why not the initial +condition if I call OD 45 with no output + + align:start position:0% +condition if I call OD 45 with no output + + + align:start position:0% +condition if I call OD 45 with no output +arguments it just plots the solution + + align:start position:0% +arguments it just plots the solution + + + align:start position:0% +arguments it just plots the solution +automatically and here we get a graph of + + align:start position:0% +automatically and here we get a graph of + + + align:start position:0% +automatically and here we get a graph of +cosine T starting at 1 and sine T + + align:start position:0% +cosine T starting at 1 and sine T + + + align:start position:0% +cosine T starting at 1 and sine T +starting at 0 now if I go back to the + + align:start position:0% +starting at 0 now if I go back to the + + + align:start position:0% +starting at 0 now if I go back to the +command window and asked to capture the + + align:start position:0% +command window and asked to capture the + + + align:start position:0% +command window and asked to capture the +output in T and Y I then get vectors of + + align:start position:0% +output in T and Y I then get vectors of + + + align:start position:0% +output in T and Y I then get vectors of +output 37 steps a vector T and a 2 + + align:start position:0% +output 37 steps a vector T and a 2 + + + align:start position:0% +output 37 steps a vector T and a 2 +components Y the two columns containing + + align:start position:0% +components Y the two columns containing + + + align:start position:0% +components Y the two columns containing +sine and cosine and now I can plot them + + align:start position:0% +sine and cosine and now I can plot them + + + align:start position:0% +sine and cosine and now I can plot them +in the phase plane plot plot y 1 against + + align:start position:0% +in the phase plane plot plot y 1 against + + + align:start position:0% +in the phase plane plot plot y 1 against +Y 2 if I regularize the axes I get a + + align:start position:0% +Y 2 if I regularize the axes I get a + + + align:start position:0% +Y 2 if I regularize the axes I get a +nice plot of a circle with small circles + + align:start position:0% +nice plot of a circle with small circles + + + align:start position:0% +nice plot of a circle with small circles +every 10 degrees as I said like the + + align:start position:0% +every 10 degrees as I said like the + + + align:start position:0% +every 10 degrees as I said like the +runways at an airport the van der Pol + + align:start position:0% +runways at an airport the van der Pol + + + align:start position:0% +runways at an airport the van der Pol +oscillator was introduced in 1927 by a + + align:start position:0% +oscillator was introduced in 1927 by a + + + align:start position:0% +oscillator was introduced in 1927 by a +Dutch electrical engineer to model + + align:start position:0% +Dutch electrical engineer to model + + + align:start position:0% +Dutch electrical engineer to model +oscillations in a circuit involving + + align:start position:0% +oscillations in a circuit involving + + + align:start position:0% +oscillations in a circuit involving +vacuum tubes + + align:start position:0% +vacuum tubes + + + align:start position:0% +vacuum tubes +it has a nonlinear damping term it's + + align:start position:0% +it has a nonlinear damping term it's + + + align:start position:0% +it has a nonlinear damping term it's +since been I used a model phenomena in + + align:start position:0% +since been I used a model phenomena in + + + align:start position:0% +since been I used a model phenomena in +all kinds of fields including geology + + align:start position:0% +all kinds of fields including geology + + + align:start position:0% +all kinds of fields including geology +and neurology it exhibits chaotic + + align:start position:0% +and neurology it exhibits chaotic + + + align:start position:0% +and neurology it exhibits chaotic +behavior we're interested in it + + align:start position:0% +behavior we're interested in it + + + align:start position:0% +behavior we're interested in it +numerical numerical analysis because as + + align:start position:0% +numerical numerical analysis because as + + + align:start position:0% +numerical numerical analysis because as +the parameter mu increases the problem + + align:start position:0% +the parameter mu increases the problem + + + align:start position:0% +the parameter mu increases the problem +becomes increasingly stiff + + align:start position:0% +becomes increasingly stiff + + + align:start position:0% +becomes increasingly stiff +to write it as a first order system for + + align:start position:0% +to write it as a first order system for + + + align:start position:0% +to write it as a first order system for +use with the MATLAB Odie's solvers we + + align:start position:0% +use with the MATLAB Odie's solvers we + + + align:start position:0% +use with the MATLAB Odie's solvers we +introduced the vector Y containing X and + + align:start position:0% +introduced the vector Y containing X and + + + align:start position:0% +introduced the vector Y containing X and +X Prime + + align:start position:0% +X Prime + + + align:start position:0% +X Prime +so Y prime is X Prime and X double Prime + + align:start position:0% +so Y prime is X Prime and X double Prime + + + align:start position:0% +so Y prime is X Prime and X double Prime +and then the differential equation is + + align:start position:0% +and then the differential equation is + + + align:start position:0% +and then the differential equation is +written so that Y prime is the first + + align:start position:0% +written so that Y prime is the first + + + align:start position:0% +written so that Y prime is the first +component of Y prime is is y - and then + + align:start position:0% +component of Y prime is is y - and then + + + align:start position:0% +component of Y prime is is y - and then +the differential equation is written in + + align:start position:0% +the differential equation is written in + + + align:start position:0% +the differential equation is written in +the second component of Y here's the + + align:start position:0% +the second component of Y here's the + + + align:start position:0% +the second component of Y here's the +damping the nonlinear damping term - + + align:start position:0% +damping the nonlinear damping term - + + + align:start position:0% +damping the nonlinear damping term - +mock y1 when mil is 0 this is becomes + + align:start position:0% +mock y1 when mil is 0 this is becomes + + + align:start position:0% +mock y1 when mil is 0 this is becomes +the harmonic oscillator and here it is + + align:start position:0% +the harmonic oscillator and here it is + + + align:start position:0% +the harmonic oscillator and here it is +as the anonymous function let's run some + + align:start position:0% +as the anonymous function let's run some + + + align:start position:0% +as the anonymous function let's run some +experiments with the van der Pol + + align:start position:0% +experiments with the van der Pol + + + align:start position:0% +experiments with the van der Pol +oscillator first of all I have to define + + align:start position:0% +oscillator first of all I have to define + + + align:start position:0% +oscillator first of all I have to define +the value of mu and I'll take a modest + + align:start position:0% +the value of mu and I'll take a modest + + + align:start position:0% +the value of mu and I'll take a modest +value of mu mu equals 100 and now with + + align:start position:0% +value of mu mu equals 100 and now with + + + align:start position:0% +value of mu mu equals 100 and now with +me to set I can define the anonymous + + align:start position:0% +me to set I can define the anonymous + + + align:start position:0% +me to set I can define the anonymous +function it involves the value of mu and + + align:start position:0% +function it involves the value of mu and + + + align:start position:0% +function it involves the value of mu and +here is the van der Pol equation in the + + align:start position:0% +here is the van der Pol equation in the + + + align:start position:0% +here is the van der Pol equation in the +second component of F I'm going to + + align:start position:0% +second component of F I'm going to + + + align:start position:0% +second component of F I'm going to +gather statistics about how hard the Eau + + align:start position:0% +gather statistics about how hard the Eau + + + align:start position:0% +gather statistics about how hard the Eau +de sauver works and for that I'm going + + align:start position:0% +de sauver works and for that I'm going + + + align:start position:0% +de sauver works and for that I'm going +to use Eau de sete and tell it I want to + + align:start position:0% +to use Eau de sete and tell it I want to + + + align:start position:0% +to use Eau de sete and tell it I want to +turn on stats I need an initial + + align:start position:0% +turn on stats I need an initial + + + align:start position:0% +turn on stats I need an initial +condition + + align:start position:0% + + + + align:start position:0% + +now I'm going to run OD 45 on this + + align:start position:0% +now I'm going to run OD 45 on this + + + align:start position:0% +now I'm going to run OD 45 on this +problem and I with specifying just a + + align:start position:0% +problem and I with specifying just a + + + align:start position:0% +problem and I with specifying just a +starting value of T and a final value of + + align:start position:0% +starting value of T and a final value of + + + align:start position:0% +starting value of T and a final value of +T OD 45 is going to pick its own time + + align:start position:0% +T OD 45 is going to pick its own time + + + align:start position:0% +T OD 45 is going to pick its own time +stamps and I know with T final equals + + align:start position:0% +stamps and I know with T final equals + + + align:start position:0% +stamps and I know with T final equals +400 660 it's going to integrate over + + align:start position:0% +400 660 it's going to integrate over + + + align:start position:0% +400 660 it's going to integrate over +about two periods of the solution now we + + align:start position:0% +about two periods of the solution now we + + + align:start position:0% +about two periods of the solution now we +can watch it go for a while it's taken + + align:start position:0% +can watch it go for a while it's taken + + + align:start position:0% +can watch it go for a while it's taken +lots of steps and it's beginning to slow + + align:start position:0% +lots of steps and it's beginning to slow + + + align:start position:0% +lots of steps and it's beginning to slow +down as it takes more and more steps + + align:start position:0% + + + + align:start position:0% + +now this begins to get too painfully + + align:start position:0% +now this begins to get too painfully + + + align:start position:0% +now this begins to get too painfully +slow as it runs into a stiffness all I + + align:start position:0% +slow as it runs into a stiffness all I + + + align:start position:0% +slow as it runs into a stiffness all I +turn off the camera for a while here so + + align:start position:0% +turn off the camera for a while here so + + + align:start position:0% +turn off the camera for a while here so +you don't have to watch all these steps + + align:start position:0% +you don't have to watch all these steps + + + align:start position:0% +you don't have to watch all these steps +and I'll turn it back on it so we're + + align:start position:0% +and I'll turn it back on it so we're + + + align:start position:0% +and I'll turn it back on it so we're +trying to get up here to 460 then I'll + + align:start position:0% +trying to get up here to 460 then I'll + + + align:start position:0% +trying to get up here to 460 then I'll +turn it back on as we get close to the + + align:start position:0% +turn it back on as we get close to the + + + align:start position:0% +turn it back on as we get close to the +end + + align:start position:0% + + + + align:start position:0% + +okay well cameras been off about three + + align:start position:0% +okay well cameras been off about three + + + align:start position:0% +okay well cameras been off about three +minutes and you can see how far we've + + align:start position:0% +minutes and you can see how far we've + + + align:start position:0% +minutes and you can see how far we've +gotten we're nowheres near the end so + + align:start position:0% +gotten we're nowheres near the end so + + + align:start position:0% +gotten we're nowheres near the end so +I'm gonna press the stop button here and + + align:start position:0% + + + + align:start position:0% + +we'll go back to the command window and + + align:start position:0% +we'll go back to the command window and + + + align:start position:0% +we'll go back to the command window and +oh so we did gather this we didn't get + + align:start position:0% +oh so we did gather this we didn't get + + + align:start position:0% +oh so we did gather this we didn't get +to the end here let me back off on the + + align:start position:0% +to the end here let me back off on the + + + align:start position:0% +to the end here let me back off on the +time interval and try try this value + + align:start position:0% +time interval and try try this value + + + align:start position:0% +time interval and try try this value +here see how that works so this is + + align:start position:0% +here see how that works so this is + + + align:start position:0% +here see how that works so this is +better still take lots of steps but + + align:start position:0% +better still take lots of steps but + + + align:start position:0% +better still take lots of steps but +we'll be able to this will go over about + + align:start position:0% +we'll be able to this will go over about + + + align:start position:0% +we'll be able to this will go over about +one period we'll actually get to get to + + align:start position:0% +one period we'll actually get to get to + + + align:start position:0% +one period we'll actually get to get to +the end here + + align:start position:0% + + + + align:start position:0% + +I'll leave the camera on to ya till we + + align:start position:0% +I'll leave the camera on to ya till we + + + align:start position:0% +I'll leave the camera on to ya till we +finish + + align:start position:0% + + + + align:start position:0% + +okay so that took a little under a + + align:start position:0% +okay so that took a little under a + + + align:start position:0% +okay so that took a little under a +minute dead and it took nearly 15,000 + + align:start position:0% +minute dead and it took nearly 15,000 + + + align:start position:0% +minute dead and it took nearly 15,000 +steps so let's run up with a stiff + + align:start position:0% +steps so let's run up with a stiff + + + align:start position:0% +steps so let's run up with a stiff +solver there so it took half a second + + align:start position:0% +solver there so it took half a second + + + align:start position:0% +solver there so it took half a second +and only 500 steps so there's a modest + + align:start position:0% +and only 500 steps so there's a modest + + + align:start position:0% +and only 500 steps so there's a modest +example of stiffness here so let's + + align:start position:0% +example of stiffness here so let's + + + align:start position:0% +example of stiffness here so let's +examine the van der Pol equation using + + align:start position:0% +examine the van der Pol equation using + + + align:start position:0% +examine the van der Pol equation using +uh using the stiff solver let's capture + + align:start position:0% +uh using the stiff solver let's capture + + + align:start position:0% +uh using the stiff solver let's capture +the output and plot it does that plot + + align:start position:0% +the output and plot it does that plot + + + align:start position:0% +the output and plot it does that plot +wasn't very interesting I want to plot + + align:start position:0% +wasn't very interesting I want to plot + + + align:start position:0% +wasn't very interesting I want to plot +it a couple of different ways and again + + align:start position:0% +it a couple of different ways and again + + + align:start position:0% +it a couple of different ways and again +I want to go back up to the capture a + + align:start position:0% +I want to go back up to the capture a + + + align:start position:0% +I want to go back up to the capture a +couple periods + + align:start position:0% + + + + align:start position:0% + +let's plot one of the components as a + + align:start position:0% +let's plot one of the components as a + + + align:start position:0% +let's plot one of the components as a +function of time and here it is here's + + align:start position:0% +function of time and here it is here's + + + align:start position:0% +function of time and here it is here's +the van der Pol equation and you can see + + align:start position:0% +the van der Pol equation and you can see + + + align:start position:0% +the van der Pol equation and you can see +it has an initial transient and then it + + align:start position:0% +it has an initial transient and then it + + + align:start position:0% +it has an initial transient and then it +settles into this periodic oscillation + + align:start position:0% +settles into this periodic oscillation + + + align:start position:0% +settles into this periodic oscillation +with these really steep trend the steep + + align:start position:0% +with these really steep trend the steep + + + align:start position:0% +with these really steep trend the steep +spikes here and even this stiff solver + + align:start position:0% +spikes here and even this stiff solver + + + align:start position:0% +spikes here and even this stiff solver +is working hard and as the at these + + align:start position:0% +is working hard and as the at these + + + align:start position:0% +is working hard and as the at these +rapid changes we've got a lot of fair + + align:start position:0% +rapid changes we've got a lot of fair + + + align:start position:0% +rapid changes we've got a lot of fair +fair number of points in here as it is + + align:start position:0% +fair number of points in here as it is + + + align:start position:0% +fair number of points in here as it is +it chooses the step size and now let's + + align:start position:0% +it chooses the step size and now let's + + + align:start position:0% +it chooses the step size and now let's +go back to the command line and do a + + align:start position:0% +go back to the command line and do a + + + align:start position:0% +go back to the command line and do a +phase pane plot so here's the phase + + align:start position:0% +phase pane plot so here's the phase + + + align:start position:0% +phase pane plot so here's the phase +plane plot of this oscillator with + + align:start position:0% +plane plot of this oscillator with + + + align:start position:0% +plane plot of this oscillator with +damping and it's nowheres near a circle + + align:start position:0% +damping and it's nowheres near a circle + + + align:start position:0% +damping and it's nowheres near a circle +which would be with mu is zero and this + + align:start position:0% +which would be with mu is zero and this + + + align:start position:0% +which would be with mu is zero and this +is the characteristic behavior of the + + align:start position:0% +is the characteristic behavior of the + + + align:start position:0% +is the characteristic behavior of the +van der Mona van der Pol oscillator \ No newline at end of file diff --git a/NRygklHAoEw.txt b/NRygklHAoEw.txt new file mode 100644 index 0000000000000000000000000000000000000000..268dc78e46d6f7f426ea2633b522765286c83cc1 --- /dev/null +++ b/NRygklHAoEw.txt @@ -0,0 +1,15483 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu + + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu +all right start off with perception is a + + align:start position:0% +all right start off with perception is a + + + align:start position:0% +all right start off with perception is a +very difficult problem and there's a + + align:start position:0% +very difficult problem and there's a + + + align:start position:0% +very difficult problem and there's a +good reason why perception should be + + align:start position:0% +good reason why perception should be + + + align:start position:0% +good reason why perception should be +difficult right we get a very + + align:start position:0% +difficult right we get a very + + + align:start position:0% +difficult right we get a very +impoverished stimulus we get like you + + align:start position:0% +impoverished stimulus we get like you + + + align:start position:0% +impoverished stimulus we get like you +know a 2d array of values from a 3d + + align:start position:0% +know a 2d array of values from a 3d + + + align:start position:0% +know a 2d array of values from a 3d +scene given this impoverished simul is + + align:start position:0% +scene given this impoverished simul is + + + align:start position:0% +scene given this impoverished simul is +we have to understand a huge amount of + + align:start position:0% +we have to understand a huge amount of + + + align:start position:0% +we have to understand a huge amount of +stuff about the world we have to + + align:start position:0% +stuff about the world we have to + + + align:start position:0% +stuff about the world we have to +understand the 3d structure of the world + + align:start position:0% +understand the 3d structure of the world + + + align:start position:0% +understand the 3d structure of the world +if you look at any one pixel you have to + + align:start position:0% +if you look at any one pixel you have to + + + align:start position:0% +if you look at any one pixel you have to +understand the properties of the surface + + align:start position:0% +understand the properties of the surface + + + align:start position:0% +understand the properties of the surface +that produce the illumination they gave + + align:start position:0% +that produce the illumination they gave + + + align:start position:0% +that produce the illumination they gave +you that pixel you have to understand + + align:start position:0% +you that pixel you have to understand + + + align:start position:0% +you that pixel you have to understand +the color the texture you have to see + + align:start position:0% +the color the texture you have to see + + + align:start position:0% +the color the texture you have to see +the color of the light that hit that + + align:start position:0% +the color of the light that hit that + + + align:start position:0% +the color of the light that hit that +surface the roughness of the surface etc + + align:start position:0% +surface the roughness of the surface etc + + + align:start position:0% +surface the roughness of the surface etc +so you have a very small channel a very + + align:start position:0% +so you have a very small channel a very + + + align:start position:0% +so you have a very small channel a very +small window onto the world and you have + + align:start position:0% +small window onto the world and you have + + + align:start position:0% +small window onto the world and you have +to extract a tremendous amount of + + align:start position:0% +to extract a tremendous amount of + + + align:start position:0% +to extract a tremendous amount of +information so that you can survive and + + align:start position:0% +information so that you can survive and + + + align:start position:0% +information so that you can survive and +not get killed by cars regularly all + + align:start position:0% +not get killed by cars regularly all + + + align:start position:0% +not get killed by cars regularly all +right that's exactly the problem we're + + align:start position:0% +right that's exactly the problem we're + + + align:start position:0% +right that's exactly the problem we're +gonna talk about here which is how do we + + align:start position:0% +gonna talk about here which is how do we + + + align:start position:0% +gonna talk about here which is how do we +use our knowledge of the world to + + align:start position:0% +use our knowledge of the world to + + + align:start position:0% +use our knowledge of the world to +structure our perception to actually + + align:start position:0% +structure our perception to actually + + + align:start position:0% +structure our perception to actually +modify what we see in order to be able + + align:start position:0% +modify what we see in order to be able + + + align:start position:0% +modify what we see in order to be able +to solve this problem how do we take a + + align:start position:0% +to solve this problem how do we take a + + + align:start position:0% +to solve this problem how do we take a +small impoverished stimulus and extract + + align:start position:0% +small impoverished stimulus and extract + + + align:start position:0% +small impoverished stimulus and extract +a huge amount of information about the + + align:start position:0% +a huge amount of information about the + + + align:start position:0% +a huge amount of information about the +world around us so let's start with the + + align:start position:0% +world around us so let's start with the + + + align:start position:0% +world around us so let's start with the +few examples where knowledge about the + + align:start position:0% +few examples where knowledge about the + + + align:start position:0% +few examples where knowledge about the +world really practically changes what we + + align:start position:0% +world really practically changes what we + + + align:start position:0% +world really practically changes what we +see some Canadians I'm required to show + + align:start position:0% +see some Canadians I'm required to show + + + align:start position:0% +see some Canadians I'm required to show +you a Canadian flag in every talk here + + align:start position:0% +you a Canadian flag in every talk here + + + align:start position:0% +you a Canadian flag in every talk here +we are you can take this flag and you + + align:start position:0% +we are you can take this flag and you + + + align:start position:0% +we are you can take this flag and you +can give it to any of you you can give + + align:start position:0% +can give it to any of you you can give + + + align:start position:0% +can give it to any of you you can give +it to any kid and you can ask them + + align:start position:0% +it to any kid and you can ask them + + + align:start position:0% +it to any kid and you can ask them +here's a marker put big red marks around + + align:start position:0% +here's a marker put big red marks around + + + align:start position:0% +here's a marker put big red marks around +the regions on this flag or in the + + align:start position:0% +the regions on this flag or in the + + + align:start position:0% +the regions on this flag or in the +regions in this image that are red and + + align:start position:0% +regions in this image that are red and + + + align:start position:0% +regions in this image that are red and +it's pretty clear to all of us that + + align:start position:0% +it's pretty clear to all of us that + + + align:start position:0% +it's pretty clear to all of us that +there's a distinction between the red + + align:start position:0% +there's a distinction between the red + + + align:start position:0% +there's a distinction between the red +that's in the flag and the bars and in + + align:start position:0% +that's in the flag and the bars and in + + + align:start position:0% +that's in the flag and the bars and in +the maple leaf versus the red that's + + align:start position:0% +the maple leaf versus the red that's + + + align:start position:0% +the maple leaf versus the red that's +actually in the background and we can + + align:start position:0% +actually in the background and we can + + + align:start position:0% +actually in the background and we can +all tell those two apart except if you + + align:start position:0% +all tell those two apart except if you + + + align:start position:0% +all tell those two apart except if you +actually look at the pixel values you + + align:start position:0% +actually look at the pixel values you + + + align:start position:0% +actually look at the pixel values you +open them in Photoshop or or + + align:start position:0% +open them in Photoshop or or + + + align:start position:0% +open them in Photoshop or or +whatever other program you want you're + + align:start position:0% +whatever other program you want you're + + + align:start position:0% +whatever other program you want you're +gonna notice that those pixel values are + + align:start position:0% +gonna notice that those pixel values are + + + align:start position:0% +gonna notice that those pixel values are +actually not particularly different + + align:start position:0% +actually not particularly different + + + align:start position:0% +actually not particularly different +there's no threshold that you can choose + + align:start position:0% +there's no threshold that you can choose + + + align:start position:0% +there's no threshold that you can choose +that will separate the red on the flag + + align:start position:0% +that will separate the red on the flag + + + align:start position:0% +that will separate the red on the flag +from the red in the background so you're + + align:start position:0% +from the red in the background so you're + + + align:start position:0% +from the red in the background so you're +doing a huge amount of inference just to + + align:start position:0% +doing a huge amount of inference just to + + + align:start position:0% +doing a huge amount of inference just to +solve this trivial little problem of + + align:start position:0% +solve this trivial little problem of + + + align:start position:0% +solve this trivial little problem of +what color is where you're using + + align:start position:0% +what color is where you're using + + + align:start position:0% +what color is where you're using +knowledge about region + + align:start position:0% +knowledge about region + + + align:start position:0% +knowledge about region +knowledge is about flags knowledge about + + align:start position:0% +knowledge is about flags knowledge about + + + align:start position:0% +knowledge is about flags knowledge about +transparency in order to figure out that + + align:start position:0% +transparency in order to figure out that + + + align:start position:0% +transparency in order to figure out that +the red on the flag is different from + + align:start position:0% +the red on the flag is different from + + + align:start position:0% +the red on the flag is different from +the red in the background so this is a + + align:start position:0% +the red in the background so this is a + + + align:start position:0% +the red in the background so this is a +really practical way that your knowledge + + align:start position:0% +really practical way that your knowledge + + + align:start position:0% +really practical way that your knowledge +about the world really changes your + + align:start position:0% +about the world really changes your + + + align:start position:0% +about the world really changes your +perception you're not seeing the colors + + align:start position:0% +perception you're not seeing the colors + + + align:start position:0% +perception you're not seeing the colors +that are really there another nice + + align:start position:0% +that are really there another nice + + + align:start position:0% +that are really there another nice +example comes from a paper by Antonio de + + align:start position:0% +example comes from a paper by Antonio de + + + align:start position:0% +example comes from a paper by Antonio de +Alba so if you look at the scene it's + + align:start position:0% +Alba so if you look at the scene it's + + + align:start position:0% +Alba so if you look at the scene it's +pretty blurry and it has to be blurry + + align:start position:0% +pretty blurry and it has to be blurry + + + align:start position:0% +pretty blurry and it has to be blurry +because your visual system is so + + align:start position:0% +because your visual system is so + + + align:start position:0% +because your visual system is so +incredibly good we have to degrade the + + align:start position:0% +incredibly good we have to degrade the + + + align:start position:0% +incredibly good we have to degrade the +input for you to see how poor it + + align:start position:0% +input for you to see how poor it + + + align:start position:0% +input for you to see how poor it +actually is if we take away some + + align:start position:0% +actually is if we take away some + + + align:start position:0% +actually is if we take away some +information so this looks like a scene + + align:start position:0% +information so this looks like a scene + + + align:start position:0% +information so this looks like a scene +and the background looks like a building + + align:start position:0% +and the background looks like a building + + + align:start position:0% +and the background looks like a building +in the foreground you can see there's an + + align:start position:0% +in the foreground you can see there's an + + + align:start position:0% +in the foreground you can see there's an +80th Street and the thing on the street + + align:start position:0% +80th Street and the thing on the street + + + align:start position:0% +80th Street and the thing on the street +kind of looks like a car does that look + + align:start position:0% +kind of looks like a car does that look + + + align:start position:0% +kind of looks like a car does that look +like a car to everybody awesome we can + + align:start position:0% +like a car to everybody awesome we can + + + align:start position:0% +like a car to everybody awesome we can +look at a slightly different image we + + align:start position:0% +look at a slightly different image we + + + align:start position:0% +look at a slightly different image we +can look at a very similar scene again + + align:start position:0% +can look at a very similar scene again + + + align:start position:0% +can look at a very similar scene again +same building in the background same + + align:start position:0% +same building in the background same + + + align:start position:0% +same building in the background same +street in the foreground now there's + + align:start position:0% +street in the foreground now there's + + + align:start position:0% +street in the foreground now there's +kind of a blob in the foreground and it + + align:start position:0% +kind of a blob in the foreground and it + + + align:start position:0% +kind of a blob in the foreground and it +looks as if it's a person it looks like + + align:start position:0% +looks as if it's a person it looks like + + + align:start position:0% +looks as if it's a person it looks like +a person to everyone right awesome well + + align:start position:0% +a person to everyone right awesome well + + + align:start position:0% +a person to everyone right awesome well +the only problem is the blob on the left + + align:start position:0% +the only problem is the blob on the left + + + align:start position:0% +the only problem is the blob on the left +is exactly the same as the blob on the + + align:start position:0% +is exactly the same as the blob on the + + + align:start position:0% +is exactly the same as the blob on the +right it's difficult to believe me but + + align:start position:0% +right it's difficult to believe me but + + + align:start position:0% +right it's difficult to believe me but +you can find these two images online and + + align:start position:0% +you can find these two images online and + + + align:start position:0% +you can find these two images online and +in his paper you can open them up in + + align:start position:0% +in his paper you can open them up in + + + align:start position:0% +in his paper you can open them up in +your favorite image viewer you can zoom + + align:start position:0% +your favorite image viewer you can zoom + + + align:start position:0% +your favorite image viewer you can zoom +in and you'll see they are pixel wise + + align:start position:0% +in and you'll see they are pixel wise + + + align:start position:0% +in and you'll see they are pixel wise +completely identical so you just see a + + align:start position:0% +completely identical so you just see a + + + align:start position:0% +completely identical so you just see a +tremendous amount of information to put + + align:start position:0% +tremendous amount of information to put + + + align:start position:0% +tremendous amount of information to put +together the fact that buildings and + + align:start position:0% +together the fact that buildings and + + + align:start position:0% +together the fact that buildings and +streets when you see these horizontal + + align:start position:0% +streets when you see these horizontal + + + align:start position:0% +streets when you see these horizontal +streaks it means a car and when you see + + align:start position:0% +streaks it means a car and when you see + + + align:start position:0% +streaks it means a car and when you see +these vertical streaks it means people + + align:start position:0% +these vertical streaks it means people + + + align:start position:0% +these vertical streaks it means people +and this really changes how you see the + + align:start position:0% +and this really changes how you see the + + + align:start position:0% +and this really changes how you see the +world and it changes it to the point + + align:start position:0% +world and it changes it to the point + + + align:start position:0% +world and it changes it to the point +where you actually probably don't + + align:start position:0% +where you actually probably don't + + + align:start position:0% +where you actually probably don't +believe me that these two blobs are the + + align:start position:0% +believe me that these two blobs are the + + + align:start position:0% +believe me that these two blobs are the +same and I didn't believe it either + + align:start position:0% +same and I didn't believe it either + + + align:start position:0% +same and I didn't believe it either +until I realize in been a check so you + + align:start position:0% +until I realize in been a check so you + + + align:start position:0% +until I realize in been a check so you +can see lots of interesting effects + + align:start position:0% +can see lots of interesting effects + + + align:start position:0% +can see lots of interesting effects +where your high-level knowledge of the + + align:start position:0% +where your high-level knowledge of the + + + align:start position:0% +where your high-level knowledge of the +world is structuring your low-level + + align:start position:0% +world is structuring your low-level + + + align:start position:0% +world is structuring your low-level +perception and is actually overriding it + + align:start position:0% +perception and is actually overriding it + + + align:start position:0% +perception and is actually overriding it +you've seen this example with the hammer + + align:start position:0% +you've seen this example with the hammer + + + align:start position:0% +you've seen this example with the hammer +where you were unable to recognize + + align:start position:0% +where you were unable to recognize + + + align:start position:0% +where you were unable to recognize +what's going on in a small region but + + align:start position:0% +what's going on in a small region but + + + align:start position:0% +what's going on in a small region but +when I give you the rest of the context + + align:start position:0% +when I give you the rest of the context + + + align:start position:0% +when I give you the rest of the context +you can tell that it's a hammer and when + + align:start position:0% +you can tell that it's a hammer and when + + + align:start position:0% +you can tell that it's a hammer and when +you see the whole video you actually + + align:start position:0% +you see the whole video you actually + + + align:start position:0% +you see the whole video you actually +don't see the hammer disappear so you're + + align:start position:0% +don't see the hammer disappear so you're + + + align:start position:0% +don't see the hammer disappear so you're +filling in information from context and + + align:start position:0% +filling in information from context and + + + align:start position:0% +filling in information from context and +single images and you're filling in + + align:start position:0% +single images and you're filling in + + + align:start position:0% +single images and you're filling in +information from context in the whole + + align:start position:0% +information from context in the whole + + + align:start position:0% +information from context in the whole +videos but if we dig in what's going on + + align:start position:0% +videos but if we dig in what's going on + + + align:start position:0% +videos but if we dig in what's going on +here just a little bit more what's going + + align:start position:0% +here just a little bit more what's going + + + align:start position:0% +here just a little bit more what's going +on is somewhere inside your head there's + + align:start position:0% +on is somewhere inside your head there's + + + align:start position:0% +on is somewhere inside your head there's +something resembling a hammer detector + + align:start position:0% +something resembling a hammer detector + + + align:start position:0% +something resembling a hammer detector +right so you run a hammer detector and + + align:start position:0% +right so you run a hammer detector and + + + align:start position:0% +right so you run a hammer detector and +you ground that hammer detector over + + align:start position:0% +you ground that hammer detector over + + + align:start position:0% +you ground that hammer detector over +that little region and it said + + align:start position:0% +that little region and it said + + + align:start position:0% +that little region and it said +I'm not so sure I'm pretty not I'm not + + align:start position:0% +I'm not so sure I'm pretty not I'm not + + + align:start position:0% +I'm not so sure I'm pretty not I'm not +very confident about what I see in this + + align:start position:0% +very confident about what I see in this + + + align:start position:0% +very confident about what I see in this +little region and somewhere inside your + + align:start position:0% +little region and somewhere inside your + + + align:start position:0% +little region and somewhere inside your +head there's some detector or something + + align:start position:0% +head there's some detector or something + + + align:start position:0% +head there's some detector or something +that can recognize someone hammering + + align:start position:0% +that can recognize someone hammering + + + align:start position:0% +that can recognize someone hammering +something so if we look at sort of a + + align:start position:0% +something so if we look at sort of a + + + align:start position:0% +something so if we look at sort of a +more traditional computer vision + + align:start position:0% +more traditional computer vision + + + align:start position:0% +more traditional computer vision +pipeline what you would do is you would + + align:start position:0% +pipeline what you would do is you would + + + align:start position:0% +pipeline what you would do is you would +you run your hammer detector you take + + align:start position:0% +you run your hammer detector you take + + + align:start position:0% +you run your hammer detector you take +your hammer detector you would use that + + align:start position:0% +your hammer detector you would use that + + + align:start position:0% +your hammer detector you would use that +knowledge in order to recognize + + align:start position:0% +knowledge in order to recognize + + + align:start position:0% +knowledge in order to recognize +hammering in the scene and at the end + + align:start position:0% +hammering in the scene and at the end + + + align:start position:0% +hammering in the scene and at the end +you would say I'm really confused + + align:start position:0% +you would say I'm really confused + + + align:start position:0% +you would say I'm really confused +because my hammer detector didn't work + + align:start position:0% +because my hammer detector didn't work + + + align:start position:0% +because my hammer detector didn't work +very well the reason why you can + + align:start position:0% +very well the reason why you can + + + align:start position:0% +very well the reason why you can +actually do this is because you have a + + align:start position:0% +actually do this is because you have a + + + align:start position:0% +actually do this is because you have a +feedback you were able to recognize the + + align:start position:0% +feedback you were able to recognize the + + + align:start position:0% +feedback you were able to recognize the +hammering event as a whole and that lets + + align:start position:0% +hammering event as a whole and that lets + + + align:start position:0% +hammering event as a whole and that lets +you upgrade the scores of your hammer + + align:start position:0% +you upgrade the scores of your hammer + + + align:start position:0% +you upgrade the scores of your hammer +detector which is very unreliable in + + align:start position:0% +detector which is very unreliable in + + + align:start position:0% +detector which is very unreliable in +this case so feedback was really + + align:start position:0% +this case so feedback was really + + + align:start position:0% +this case so feedback was really +critical in being able to understand + + align:start position:0% +critical in being able to understand + + + align:start position:0% +critical in being able to understand +this scene unfortunately pretty much all + + align:start position:0% +this scene unfortunately pretty much all + + + align:start position:0% +this scene unfortunately pretty much all +of computer vision is feed-forward + + align:start position:0% +of computer vision is feed-forward + + + align:start position:0% +of computer vision is feed-forward +even though most of your visual system + + align:start position:0% +even though most of your visual system + + + align:start position:0% +even though most of your visual system +has for the most part feedback + + align:start position:0% +has for the most part feedback + + + align:start position:0% +has for the most part feedback +connections more feedback than + + align:start position:0% +connections more feedback than + + + align:start position:0% +connections more feedback than +feed-forward so in this talk we're gonna + + align:start position:0% +feed-forward so in this talk we're gonna + + + align:start position:0% +feed-forward so in this talk we're gonna +talk about that feedback and we're going + + align:start position:0% +talk about that feedback and we're going + + + align:start position:0% +talk about that feedback and we're going +to see a way that we're gonna build this + + align:start position:0% +to see a way that we're gonna build this + + + align:start position:0% +to see a way that we're gonna build this +feedback in a principled way that if we + + align:start position:0% +feedback in a principled way that if we + + + align:start position:0% +feedback in a principled way that if we +choose right detection for right + + align:start position:0% +choose right detection for right + + + align:start position:0% +choose right detection for right +algorithms and right representations + + align:start position:0% +algorithms and right representations + + + align:start position:0% +algorithms and right representations +from our low-level perception we're + + align:start position:0% +from our low-level perception we're + + + align:start position:0% +from our low-level perception we're +gonna be able to combine it with our + + align:start position:0% +gonna be able to combine it with our + + + align:start position:0% +gonna be able to combine it with our +high level perception of the world so + + align:start position:0% +high level perception of the world so + + + align:start position:0% +high level perception of the world so +we've seen that perception is very + + align:start position:0% +we've seen that perception is very + + + align:start position:0% +we've seen that perception is very +unreliable the top-down knowledge really + + align:start position:0% +unreliable the top-down knowledge really + + + align:start position:0% +unreliable the top-down knowledge really +affects your perception and that what + + align:start position:0% +affects your perception and that what + + + align:start position:0% +affects your perception and that what +you're going to see in a moment is that + + align:start position:0% +you're going to see in a moment is that + + + align:start position:0% +you're going to see in a moment is that +one integrated representation can be + + align:start position:0% +one integrated representation can be + + + align:start position:0% +one integrated representation can be +referred for many tasks the advantage of + + align:start position:0% +referred for many tasks the advantage of + + + align:start position:0% +referred for many tasks the advantage of +these feedbacks goes beyond just better + + align:start position:0% +these feedbacks goes beyond just better + + + align:start position:0% +these feedbacks goes beyond just better +vision it lets you solve a lot of + + align:start position:0% +vision it lets you solve a lot of + + + align:start position:0% +vision it lets you solve a lot of +different problems that look very very + + align:start position:0% +different problems that look very very + + + align:start position:0% +different problems that look very very +distinct but actually turn out to be + + align:start position:0% +distinct but actually turn out to be + + + align:start position:0% +distinct but actually turn out to be +very very similar so one problem is + + align:start position:0% +very very similar so one problem is + + + align:start position:0% +very very similar so one problem is +recognition I can give you a picture of + + align:start position:0% +recognition I can give you a picture of + + + align:start position:0% +recognition I can give you a picture of +a chair and I can tell you what is this + + align:start position:0% +a chair and I can tell you what is this + + + align:start position:0% +a chair and I can tell you what is this +and you can tell me it's a chair or I + + align:start position:0% +and you can tell me it's a chair or I + + + align:start position:0% +and you can tell me it's a chair or I +can give you a picture and I can give + + align:start position:0% +can give you a picture and I can give + + + align:start position:0% +can give you a picture and I can give +you a sentence this is a chair and you + + align:start position:0% +you a sentence this is a chair and you + + + align:start position:0% +you a sentence this is a chair and you +can tell me I believe you this is true + + align:start position:0% +can tell me I believe you this is true + + + align:start position:0% +can tell me I believe you this is true +there's also a completely different + + align:start position:0% +there's also a completely different + + + align:start position:0% +there's also a completely different +problem which is retrieval related to + + align:start position:0% +problem which is retrieval related to + + + align:start position:0% +problem which is retrieval related to +recognition right okay I know how about + + align:start position:0% +recognition right okay I know how about + + + align:start position:0% +recognition right okay I know how about +I give you a library of videos and ask + + align:start position:0% +I give you a library of videos and ask + + + align:start position:0% +I give you a library of videos and ask +you find me the video where the person + + align:start position:0% +you find me the video where the person + + + align:start position:0% +you find me the video where the person +was sitting on the chair and you can + + align:start position:0% +was sitting on the chair and you can + + + align:start position:0% +was sitting on the chair and you can +solve that problem you can also solve a + + align:start position:0% +solve that problem you can also solve a + + + align:start position:0% +solve that problem you can also solve a +problem like generation I can give you a + + align:start position:0% +problem like generation I can give you a + + + align:start position:0% +problem like generation I can give you a +video and I can tell you I don't know + + align:start position:0% +video and I can tell you I don't know + + + align:start position:0% +video and I can tell you I don't know +what's here please describe it to me + + align:start position:0% +what's here please describe it to me + + + align:start position:0% +what's here please describe it to me +right so if you see the scene you can + + align:start position:0% +right so if you see the scene you can + + + align:start position:0% +right so if you see the scene you can +say what's on the screen well there's a + + align:start position:0% +say what's on the screen well there's a + + + align:start position:0% +say what's on the screen well there's a +whole bunch of text on the screen you + + align:start position:0% +whole bunch of text on the screen you + + + align:start position:0% +whole bunch of text on the screen you +can also do question answering you can + + align:start position:0% +can also do question answering you can + + + align:start position:0% +can also do question answering you can +take an image like this I can ask you a + + align:start position:0% +take an image like this I can ask you a + + + align:start position:0% +take an image like this I can ask you a +question what's the color of the font + + align:start position:0% +question what's the color of the font + + + align:start position:0% +question what's the color of the font +and you can say the font is white so you + + align:start position:0% +and you can say the font is white so you + + + align:start position:0% +and you can say the font is white so you +were able to take some very high-level + + align:start position:0% +were able to take some very high-level + + + align:start position:0% +were able to take some very high-level +knowledge that's in my head that got + + align:start position:0% +knowledge that's in my head that got + + + align:start position:0% +knowledge that's in my head that got +transmitted to your head + + align:start position:0% +transmitted to your head + + + align:start position:0% +transmitted to your head +you were able to understand the purpose + + align:start position:0% +you were able to understand the purpose + + + align:start position:0% +you were able to understand the purpose +of this transmission connected to your + + align:start position:0% +of this transmission connected to your + + + align:start position:0% +of this transmission connected to your +perception figure out the knowledge that + + align:start position:0% +perception figure out the knowledge that + + + align:start position:0% +perception figure out the knowledge that +I wanted extracted from your perception + + align:start position:0% +I wanted extracted from your perception + + + align:start position:0% +I wanted extracted from your perception +and given back to me in a way that's + + align:start position:0% +and given back to me in a way that's + + + align:start position:0% +and given back to me in a way that's +meaningful to me even more than this you + + align:start position:0% +meaningful to me even more than this you + + + align:start position:0% +meaningful to me even more than this you +can disambiguate you can take a sentence + + align:start position:0% +can disambiguate you can take a sentence + + + align:start position:0% +can disambiguate you can take a sentence +that's extremely ambiguous about the + + align:start position:0% +that's extremely ambiguous about the + + + align:start position:0% +that's extremely ambiguous about the +world and figure out what I'm referring + + align:start position:0% +world and figure out what I'm referring + + + align:start position:0% +world and figure out what I'm referring +to + + align:start position:0% +to + + + align:start position:0% +to +and we do this all the time but that's + + align:start position:0% +and we do this all the time but that's + + + align:start position:0% +and we do this all the time but that's +really what makes human communication + + align:start position:0% +really what makes human communication + + + align:start position:0% +really what makes human communication +possible right the fact that most of + + align:start position:0% +possible right the fact that most of + + + align:start position:0% +possible right the fact that most of +what I say is extremely ambiguous + + align:start position:0% +what I say is extremely ambiguous + + + align:start position:0% +what I say is extremely ambiguous +that's why programming computers is a + + align:start position:0% +that's why programming computers is a + + + align:start position:0% +that's why programming computers is a +real pain but talking to people is + + align:start position:0% +real pain but talking to people is + + + align:start position:0% +real pain but talking to people is +generally easier depending on the person + + align:start position:0% +generally easier depending on the person + + + align:start position:0% +generally easier depending on the person +you can also acquire knowledge right you + + align:start position:0% +you can also acquire knowledge right you + + + align:start position:0% +you can also acquire knowledge right you +can look at a whole bunch of videos if + + align:start position:0% +can look at a whole bunch of videos if + + + align:start position:0% +can look at a whole bunch of videos if +you're a child you sort of perceive the + + align:start position:0% +you're a child you sort of perceive the + + + align:start position:0% +you're a child you sort of perceive the +world around you occasionally an adult + + align:start position:0% +world around you occasionally an adult + + + align:start position:0% +world around you occasionally an adult +comes drop the sentence here or there + + align:start position:0% +comes drop the sentence here or there + + + align:start position:0% +comes drop the sentence here or there +for you but what's important is that no + + align:start position:0% +for you but what's important is that no + + + align:start position:0% +for you but what's important is that no +adult ever really points out what the + + align:start position:0% +adult ever really points out what the + + + align:start position:0% +adult ever really points out what the +sentence is referring to you don't know + + align:start position:0% +sentence is referring to you don't know + + + align:start position:0% +sentence is referring to you don't know +that approach refers to this particular + + align:start position:0% +that approach refers to this particular + + + align:start position:0% +that approach refers to this particular +vector when someone was doing some + + align:start position:0% +vector when someone was doing some + + + align:start position:0% +vector when someone was doing some +action you don't know that Apple refers + + align:start position:0% +action you don't know that Apple refers + + + align:start position:0% +action you don't know that Apple refers +to this particular object class who + + align:start position:0% +to this particular object class who + + + align:start position:0% +to this particular object class who +knows what it could mean but you get + + align:start position:0% +knows what it could mean but you get + + + align:start position:0% +knows what it could mean but you get +enough data and you're able to + + align:start position:0% +enough data and you're able to + + + align:start position:0% +enough data and you're able to +disentangle your you're able to + + align:start position:0% +disentangle your you're able to + + + align:start position:0% +disentangle your you're able to +disentangle this problem of seeing + + align:start position:0% +disentangle this problem of seeing + + + align:start position:0% +disentangle this problem of seeing +weekly supervised videos paired with + + align:start position:0% +weekly supervised videos paired with + + + align:start position:0% +weekly supervised videos paired with +sentences and we'll see how you can do + + align:start position:0% +sentences and we'll see how you can do + + + align:start position:0% +sentences and we'll see how you can do +that pretty much everything I'll talk + + align:start position:0% +that pretty much everything I'll talk + + + align:start position:0% +that pretty much everything I'll talk +about is going to be about videos and + + align:start position:0% +about is going to be about videos and + + + align:start position:0% +about is going to be about videos and +I'll tell you a story about how I think + + align:start position:0% +I'll tell you a story about how I think + + + align:start position:0% +I'll tell you a story about how I think +we can do images as well there are a + + align:start position:0% +we can do images as well there are a + + + align:start position:0% +we can do images as well there are a +bunch of other problems that you can + + align:start position:0% +bunch of other problems that you can + + + align:start position:0% +bunch of other problems that you can +solve with this approach I'm sorry yes + + align:start position:0% +solve with this approach I'm sorry yes + + + align:start position:0% +solve with this approach I'm sorry yes +so rather than doing videos we're going + + align:start position:0% +so rather than doing videos we're going + + + align:start position:0% +so rather than doing videos we're going +to do images so one thing that you can + + align:start position:0% +to do images so one thing that you can + + + align:start position:0% +to do images so one thing that you can +do is you can write to do translation we + + align:start position:0% +do is you can write to do translation we + + + align:start position:0% +do is you can write to do translation we +haven't done this we're gonna be doing + + align:start position:0% +haven't done this we're gonna be doing + + + align:start position:0% +haven't done this we're gonna be doing +this in the fall we have two students + + align:start position:0% +this in the fall we have two students + + + align:start position:0% +this in the fall we have two students +and I'll tell you at the end what the + + align:start position:0% +and I'll tell you at the end what the + + + align:start position:0% +and I'll tell you at the end what the +story is for how you're going to do a + + align:start position:0% +story is for how you're going to do a + + + align:start position:0% +story is for how you're going to do a +task that sounds as if it's from + + align:start position:0% +task that sounds as if it's from + + + align:start position:0% +task that sounds as if it's from +language to language but you're gonna do + + align:start position:0% +language to language but you're gonna do + + + align:start position:0% +language to language but you're gonna do +it in the grounded way that involves + + align:start position:0% +it in the grounded way that involves + + + align:start position:0% +it in the grounded way that involves +vision even more than that you can do + + align:start position:0% +vision even more than that you can do + + + align:start position:0% +vision even more than that you can do +planning and I'll tell you about that at + + align:start position:0% +planning and I'll tell you about that at + + + align:start position:0% +planning and I'll tell you about that at +the end a little bit and finally you can + + align:start position:0% +the end a little bit and finally you can + + + align:start position:0% +the end a little bit and finally you can +also incorporate some theory of mind and + + align:start position:0% +also incorporate some theory of mind and + + + align:start position:0% +also incorporate some theory of mind and +that's actually the project that the + + align:start position:0% +that's actually the project that the + + + align:start position:0% +that's actually the project that the +students are doing as part of summer + + align:start position:0% +students are doing as part of summer + + + align:start position:0% +students are doing as part of summer +school and I'll say a few words about + + align:start position:0% +school and I'll say a few words about + + + align:start position:0% +school and I'll say a few words about +that what's important about this is the + + align:start position:0% +that what's important about this is the + + + align:start position:0% +that what's important about this is the +parts at the top we understand better + + align:start position:0% +parts at the top we understand better + + + align:start position:0% +parts at the top we understand better +we've published papers about them the + + align:start position:0% +we've published papers about them the + + + align:start position:0% +we've published papers about them the +parts at the bottom are sort of more + + align:start position:0% +parts at the bottom are sort of more + + + align:start position:0% +parts at the bottom are sort of more +future work and I'll say less about them + + align:start position:0% +future work and I'll say less about them + + + align:start position:0% +future work and I'll say less about them +well one important part about this is + + align:start position:0% +well one important part about this is + + + align:start position:0% +well one important part about this is +I've shown you all these tasks but you + + align:start position:0% +I've shown you all these tasks but you + + + align:start position:0% +I've shown you all these tasks but you +really have to believe me that humans + + align:start position:0% +really have to believe me that humans + + + align:start position:0% +really have to believe me that humans +perform these desks all the time every + + align:start position:0% +perform these desks all the time every + + + align:start position:0% +perform these desks all the time every +time you're sitting at a table and you + + align:start position:0% +time you're sitting at a table and you + + + align:start position:0% +time you're sitting at a table and you +ask someone gives me a cup that's a + + align:start position:0% +ask someone gives me a cup that's a + + + align:start position:0% +ask someone gives me a cup that's a +really hard vision language task there + + align:start position:0% +really hard vision language task there + + + align:start position:0% +really hard vision language task there +may be ten different cups inside of you + + align:start position:0% +may be ten different cups inside of you + + + align:start position:0% +may be ten different cups inside of you +on the table if you're sitting on one of + + align:start position:0% +on the table if you're sitting on one of + + + align:start position:0% +on the table if you're sitting on one of +the big round tables and you + + align:start position:0% +the big round tables and you + + + align:start position:0% +the big round tables and you +to figure out what object am I talking + + align:start position:0% +to figure out what object am I talking + + + align:start position:0% +to figure out what object am I talking +about what kind of cop am I talking + + align:start position:0% +about what kind of cop am I talking + + + align:start position:0% +about what kind of cop am I talking +about which cup would I be interested in + + align:start position:0% +about which cup would I be interested in + + + align:start position:0% +about which cup would I be interested in +if I drank out of the cup + + align:start position:0% +if I drank out of the cup + + + align:start position:0% +if I drank out of the cup +I would expect that you give me my cup + + align:start position:0% +I would expect that you give me my cup + + + align:start position:0% +I would expect that you give me my cup +not your cup otherwise let me know and + + align:start position:0% +not your cup otherwise let me know and + + + align:start position:0% +not your cup otherwise let me know and +we'll sit at different tables from now + + align:start position:0% +we'll sit at different tables from now + + + align:start position:0% +we'll sit at different tables from now +on if you ask if I ask you which chair + + align:start position:0% +on if you ask if I ask you which chair + + + align:start position:0% +on if you ask if I ask you which chair +should I sit in again you have to solve + + align:start position:0% +should I sit in again you have to solve + + + align:start position:0% +should I sit in again you have to solve +a pretty difficult problem where you + + align:start position:0% +a pretty difficult problem where you + + + align:start position:0% +a pretty difficult problem where you +look at chairs you figure out what I + + align:start position:0% +look at chairs you figure out what I + + + align:start position:0% +look at chairs you figure out what I +mean by which shirt should I sit in is + + align:start position:0% +mean by which shirt should I sit in is + + + align:start position:0% +mean by which shirt should I sit in is +it that there's a chair that's reserved + + align:start position:0% +it that there's a chair that's reserved + + + align:start position:0% +it that there's a chair that's reserved +for someone is that a chair is for a + + align:start position:0% +for someone is that a chair is for a + + + align:start position:0% +for someone is that a chair is for a +child and I'm an adult that kind of + + align:start position:0% +child and I'm an adult that kind of + + + align:start position:0% +child and I'm an adult that kind of +thing you can say something like this is + + align:start position:0% +thing you can say something like this is + + + align:start position:0% +thing you can say something like this is +an apple and when you say that to a + + align:start position:0% +an apple and when you say that to a + + + align:start position:0% +an apple and when you say that to a +child + + align:start position:0% +child + + + align:start position:0% +child +you're saying it for a particular reason + + align:start position:0% +you're saying it for a particular reason + + + align:start position:0% +you're saying it for a particular reason +to convey some idea you have to + + align:start position:0% +to convey some idea you have to + + + align:start position:0% +to convey some idea you have to +coordinate your games with the other + + align:start position:0% +coordinate your games with the other + + + align:start position:0% +coordinate your games with the other +person's case to make sure you're + + align:start position:0% +person's case to make sure you're + + + align:start position:0% +person's case to make sure you're +drawing their attention to the real + + align:start position:0% +drawing their attention to the real + + + align:start position:0% +drawing their attention to the real +object even more than that you can say + + align:start position:0% +object even more than that you can say + + + align:start position:0% +object even more than that you can say +very abstract things like to win this + + align:start position:0% +very abstract things like to win this + + + align:start position:0% +very abstract things like to win this +game you have to make a straight line + + align:start position:0% +game you have to make a straight line + + + align:start position:0% +game you have to make a straight line +out of these pieces that means that we + + align:start position:0% +out of these pieces that means that we + + + align:start position:0% +out of these pieces that means that we +both agree on what a pieces that I've + + align:start position:0% +both agree on what a pieces that I've + + + align:start position:0% +both agree on what a pieces that I've +drawn your attention to the right idea + + align:start position:0% +drawn your attention to the right idea + + + align:start position:0% +drawn your attention to the right idea +of a piece that we agree on what a + + align:start position:0% +of a piece that we agree on what a + + + align:start position:0% +of a piece that we agree on what a +straight line means on this particular + + align:start position:0% +straight line means on this particular + + + align:start position:0% +straight line means on this particular +board there's a lot of knowledge that + + align:start position:0% +board there's a lot of knowledge that + + + align:start position:0% +board there's a lot of knowledge that +goes into each of these but the + + align:start position:0% +goes into each of these but the + + + align:start position:0% +goes into each of these but the +important part is that they're each + + align:start position:0% +important part is that they're each + + + align:start position:0% +important part is that they're each +grounded in perception we have to agree + + align:start position:0% +grounded in perception we have to agree + + + align:start position:0% +grounded in perception we have to agree +on what we're seeing in front of each + + align:start position:0% +on what we're seeing in front of each + + + align:start position:0% +on what we're seeing in front of each +other in order to be able to exchange + + align:start position:0% +other in order to be able to exchange + + + align:start position:0% +other in order to be able to exchange +this information and pretty much + + align:start position:0% +this information and pretty much + + + align:start position:0% +this information and pretty much +everything that we do in daily + + align:start position:0% +everything that we do in daily + + + align:start position:0% +everything that we do in daily +communication is a language vision + + align:start position:0% +communication is a language vision + + + align:start position:0% +communication is a language vision +problem on some level all right so if we + + align:start position:0% +problem on some level all right so if we + + + align:start position:0% +problem on some level all right so if we +believe these problems are important we + + align:start position:0% +believe these problems are important we + + + align:start position:0% +believe these problems are important we +can make one other observation which is + + align:start position:0% +can make one other observation which is + + + align:start position:0% +can make one other observation which is +none of you got training in most of + + align:start position:0% +none of you got training in most of + + + align:start position:0% +none of you got training in most of +these problems no adult ever sat you + + align:start position:0% +these problems no adult ever sat you + + + align:start position:0% +these problems no adult ever sat you +down and said okay now you're four now + + align:start position:0% +down and said okay now you're four now + + + align:start position:0% +down and said okay now you're four now +I'm going to teach you how to ask + + align:start position:0% +I'm going to teach you how to ask + + + align:start position:0% +I'm going to teach you how to ask +questions about the real world right + + align:start position:0% +questions about the real world right + + + align:start position:0% +questions about the real world right +where no one stands you down and said + + align:start position:0% +where no one stands you down and said + + + align:start position:0% +where no one stands you down and said +okay now let's talk about language + + align:start position:0% +okay now let's talk about language + + + align:start position:0% +okay now let's talk about language +acquisition you're supposed to do + + align:start position:0% +acquisition you're supposed to do + + + align:start position:0% +acquisition you're supposed to do +gradient descent so what's important is + + align:start position:0% +gradient descent so what's important is + + + align:start position:0% +gradient descent so what's important is +you have some core ability that's shared + + align:start position:0% +you have some core ability that's shared + + + align:start position:0% +you have some core ability that's shared +across all of these tasks and you're + + align:start position:0% +across all of these tasks and you're + + + align:start position:0% +across all of these tasks and you're +able to acquire knowledge maybe in one + + align:start position:0% +able to acquire knowledge maybe in one + + + align:start position:0% +able to acquire knowledge maybe in one +of these tasks or across all of these + + align:start position:0% +of these tasks or across all of these + + + align:start position:0% +of these tasks or across all of these +tasks you're able to put it together and + + align:start position:0% +tasks you're able to put it together and + + + align:start position:0% +tasks you're able to put it together and +as soon as you have this knowledge you + + align:start position:0% +as soon as you have this knowledge you + + + align:start position:0% +as soon as you have this knowledge you +can use this for all these other tasks + + align:start position:0% +can use this for all these other tasks + + + align:start position:0% +can use this for all these other tasks +without having to learn anything else + + align:start position:0% +without having to learn anything else + + + align:start position:0% +without having to learn anything else +and that's what we're gonna see and the + + align:start position:0% +and that's what we're gonna see and the + + + align:start position:0% +and that's what we're gonna see and the +core of this that we're gonna focus on + + align:start position:0% +core of this that we're gonna focus on + + + align:start position:0% +core of this that we're gonna focus on +is recognition so we're going to build + + align:start position:0% +is recognition so we're going to build + + + align:start position:0% +is recognition so we're going to build +one component this is the engineering + + align:start position:0% +one component this is the engineering + + + align:start position:0% +one component this is the engineering +portion of the talk we're going to build + + align:start position:0% +portion of the talk we're going to build + + + align:start position:0% +portion of the talk we're going to build +one scoring function that takes a + + align:start position:0% +one scoring function that takes a + + + align:start position:0% +one scoring function that takes a +sentence in a video and gives you a + + align:start position:0% +sentence in a video and gives you a + + + align:start position:0% +sentence in a video and gives you a +score how well does this sentence match + + align:start position:0% +score how well does this sentence match + + + align:start position:0% +score how well does this sentence match +this video if the score is one it means + + align:start position:0% +this video if the score is one it means + + + align:start position:0% +this video if the score is one it means +the system really believes the sentence + + align:start position:0% +the system really believes the sentence + + + align:start position:0% +the system really believes the sentence +is depicted by the video if the score is + + align:start position:0% +is depicted by the video if the score is + + + align:start position:0% +is depicted by the video if the score is +zero means the system really believes + + align:start position:0% +zero means the system really believes + + + align:start position:0% +zero means the system really believes +the sentence does not occur anywhere in + + align:start position:0% +the sentence does not occur anywhere in + + + align:start position:0% +the sentence does not occur anywhere in +this video and this is the basic thing + + align:start position:0% +this video and this is the basic thing + + + align:start position:0% +this video and this is the basic thing +that's going to allow us to connect our + + align:start position:0% +that's going to allow us to connect our + + + align:start position:0% +that's going to allow us to connect our +our knowledge about what's going on in + + align:start position:0% +our knowledge about what's going on in + + + align:start position:0% +our knowledge about what's going on in +the world with our low-level perception + + align:start position:0% +the world with our low-level perception + + + align:start position:0% +the world with our low-level perception +and after we have this we're going to + + align:start position:0% +and after we have this we're going to + + + align:start position:0% +and after we have this we're going to +see how we reformulate everything in + + align:start position:0% +see how we reformulate everything in + + + align:start position:0% +see how we reformulate everything in +terms of this one function so we don't + + align:start position:0% +terms of this one function so we don't + + + align:start position:0% +terms of this one function so we don't +have to learn anything else about the + + align:start position:0% +have to learn anything else about the + + + align:start position:0% +have to learn anything else about the +world alright so we said we need this + + align:start position:0% +world alright so we said we need this + + + align:start position:0% +world alright so we said we need this +one function scoring function between + + align:start position:0% +one function scoring function between + + + align:start position:0% +one function scoring function between +sentences and videos so let's look at + + align:start position:0% +sentences and videos so let's look at + + + align:start position:0% +sentences and videos so let's look at +what we we need to have inside this + + align:start position:0% +what we we need to have inside this + + + align:start position:0% +what we we need to have inside this +function in the first place if I give + + align:start position:0% +function in the first place if I give + + + align:start position:0% +function in the first place if I give +you a video like this it's just a person + + align:start position:0% +you a video like this it's just a person + + + align:start position:0% +you a video like this it's just a person +riding a skateboard and I give you a + + align:start position:0% +riding a skateboard and I give you a + + + align:start position:0% +riding a skateboard and I give you a +sentence the person wrote the skateboard + + align:start position:0% +sentence the person wrote the skateboard + + + align:start position:0% +sentence the person wrote the skateboard +left word well I can ask you is this + + align:start position:0% +left word well I can ask you is this + + + align:start position:0% +left word well I can ask you is this +sentence true of this video and indeed + + align:start position:0% +sentence true of this video and indeed + + + align:start position:0% +sentence true of this video and indeed +it is true but let's think about what + + align:start position:0% +it is true but let's think about what + + + align:start position:0% +it is true but let's think about what +you have to do in order to be able to + + align:start position:0% +you have to do in order to be able to + + + align:start position:0% +you have to do in order to be able to +answer this question well you had to at + + align:start position:0% +answer this question well you had to at + + + align:start position:0% +answer this question well you had to at +some level decide there's a person there + + align:start position:0% +some level decide there's a person there + + + align:start position:0% +some level decide there's a person there +I'm not saying that you're doing this in + + align:start position:0% +I'm not saying that you're doing this in + + + align:start position:0% +I'm not saying that you're doing this in +this order in your brain I'm not saying + + align:start position:0% +this order in your brain I'm not saying + + + align:start position:0% +this order in your brain I'm not saying +that they have to be individual stages + + align:start position:0% +that they have to be individual stages + + + align:start position:0% +that they have to be individual stages +I'm not saying you have to have object + + align:start position:0% +I'm not saying you have to have object + + + align:start position:0% +I'm not saying you have to have object +detectors but at some point you have to + + align:start position:0% +detectors but at some point you have to + + + align:start position:0% +detectors but at some point you have to +decide there really is a person there + + align:start position:0% +decide there really is a person there + + + align:start position:0% +decide there really is a person there +somehow you also had to decide there's a + + align:start position:0% +somehow you also had to decide there's a + + + align:start position:0% +somehow you also had to decide there's a +skateboard there you had to look at + + align:start position:0% +skateboard there you had to look at + + + align:start position:0% +skateboard there you had to look at +these objects over time or at least in + + align:start position:0% +these objects over time or at least in + + + align:start position:0% +these objects over time or at least in +at least one or two frames to decide + + align:start position:0% +at least one or two frames to decide + + + align:start position:0% +at least one or two frames to decide +that they have a particular relationship + + align:start position:0% +that they have a particular relationship + + + align:start position:0% +that they have a particular relationship +so that the person isn't flying in the + + align:start position:0% +so that the person isn't flying in the + + + align:start position:0% +so that the person isn't flying in the +air the skateboard continues onwards and + + align:start position:0% +air the skateboard continues onwards and + + + align:start position:0% +air the skateboard continues onwards and +you have to look at this relationship + + align:start position:0% +you have to look at this relationship + + + align:start position:0% +you have to look at this relationship +and decide yeah okay this is writing and + + align:start position:0% +and decide yeah okay this is writing and + + + align:start position:0% +and decide yeah okay this is writing and +it's happening leftward so you have to + + align:start position:0% +it's happening leftward so you have to + + + align:start position:0% +it's happening leftward so you have to +have these components on some level + + align:start position:0% +have these components on some level + + + align:start position:0% +have these components on some level +you've got to see the objects you've got + + align:start position:0% +you've got to see the objects you've got + + + align:start position:0% +you've got to see the objects you've got +to see the relationships the static and + + align:start position:0% +to see the relationships the static and + + + align:start position:0% +to see the relationships the static and +the changing relationships between the + + align:start position:0% +the changing relationships between the + + + align:start position:0% +the changing relationships between the +objects you have to have some way of + + align:start position:0% +objects you have to have some way of + + + align:start position:0% +objects you have to have some way of +combining those together to form some + + align:start position:0% +combining those together to form some + + + align:start position:0% +combining those together to form some +kind of sentence you can represent that + + align:start position:0% +kind of sentence you can represent that + + + align:start position:0% +kind of sentence you can represent that +knowledge and that's what we're gonna do + + align:start position:0% +knowledge and that's what we're gonna do + + + align:start position:0% +knowledge and that's what we're gonna do +and everything I describe to you is this + + align:start position:0% +and everything I describe to you is this + + + align:start position:0% +and everything I describe to you is this +feed-forward system right we had objects + + align:start position:0% +feed-forward system right we had objects + + + align:start position:0% +feed-forward system right we had objects +we have tracks we take tracks and we + + align:start position:0% +we have tracks we take tracks and we + + + align:start position:0% +we have tracks we take tracks and we +build event events like ride and we take + + align:start position:0% +build event events like ride and we take + + + align:start position:0% +build event events like ride and we take +those events together and we form + + align:start position:0% +those events together and we form + + + align:start position:0% +those events together and we form +sentences out of them and this kind of + + align:start position:0% +sentences out of them and this kind of + + + align:start position:0% +sentences out of them and this kind of +just hurts oppression right it's easy to + + align:start position:0% +just hurts oppression right it's easy to + + + align:start position:0% +just hurts oppression right it's easy to +understand the system where what you do + + align:start position:0% +understand the system where what you do + + + align:start position:0% +understand the system where what you do +is you have objects tracks events and + + align:start position:0% +is you have objects tracks events and + + + align:start position:0% +is you have objects tracks events and +sentences and you use tracks in order to + + align:start position:0% +sentences and you use tracks in order to + + + align:start position:0% +sentences and you use tracks in order to +see if your events happened and your + + align:start position:0% +see if your events happened and your + + + align:start position:0% +see if your events happened and your +events in order to see if a particular + + align:start position:0% +events in order to see if a particular + + + align:start position:0% +events in order to see if a particular +sentence occurred so that's what we're + + align:start position:0% +sentence occurred so that's what we're + + + align:start position:0% +sentence occurred so that's what we're +going to describe first and then we're + + align:start position:0% +going to describe first and then we're + + + align:start position:0% +going to describe first and then we're +going to see how because we're gonna + + align:start position:0% +going to see how because we're gonna + + + align:start position:0% +going to see how because we're gonna +choose the right representations for + + align:start position:0% +choose the right representations for + + + align:start position:0% +choose the right representations for +each of these these feedbacks become + + align:start position:0% +each of these these feedbacks become + + + align:start position:0% +each of these these feedbacks become +completely trivial and very natural to + + align:start position:0% +completely trivial and very natural to + + + align:start position:0% +completely trivial and very natural to +implement all right we need to start + + align:start position:0% +implement all right we need to start + + + align:start position:0% +implement all right we need to start +with some object detection otherwise + + align:start position:0% +with some object detection otherwise + + + align:start position:0% +with some object detection otherwise +we're just gonna hallucinate objects all + + align:start position:0% +we're just gonna hallucinate objects all + + + align:start position:0% +we're just gonna hallucinate objects all +the time any off-the-shelf fog detector + + align:start position:0% +the time any off-the-shelf fog detector + + + align:start position:0% +the time any off-the-shelf fog detector +that you choose that will sometimes work + + align:start position:0% +that you choose that will sometimes work + + + align:start position:0% +that you choose that will sometimes work +here we ran a person detector in red in + + align:start position:0% +here we ran a person detector in red in + + + align:start position:0% +here we ran a person detector in red in +a + + align:start position:0% +a + + + align:start position:0% +a +detector and blue it'll sometimes give + + align:start position:0% +detector and blue it'll sometimes give + + + align:start position:0% +detector and blue it'll sometimes give +you false positives trees are often + + align:start position:0% +you false positives trees are often + + + align:start position:0% +you false positives trees are often +confused for people I guess we're both + + align:start position:0% +confused for people I guess we're both + + + align:start position:0% +confused for people I guess we're both +too vertical to long vertical lines and + + align:start position:0% +too vertical to long vertical lines and + + + align:start position:0% +too vertical to long vertical lines and +sometimes you get false negatives + + align:start position:0% +sometimes you get false negatives + + + align:start position:0% +sometimes you get false negatives +sometimes a bag is so deformable that + + align:start position:0% +sometimes a bag is so deformable that + + + align:start position:0% +sometimes a bag is so deformable that +you think the person's knee is the bag + + align:start position:0% +you think the person's knee is the bag + + + align:start position:0% +you think the person's knee is the bag +lest you think that object action is + + align:start position:0% +lest you think that object action is + + + align:start position:0% +lest you think that object action is +solved it actually isn't so if you look + + align:start position:0% +solved it actually isn't so if you look + + + align:start position:0% +solved it actually isn't so if you look +at something like the image net + + align:start position:0% +at something like the image net + + + align:start position:0% +at something like the image net +challenge most mostly people talk about + + align:start position:0% +challenge most mostly people talk about + + + align:start position:0% +challenge most mostly people talk about +the image classification but the stuff + + align:start position:0% +the image classification but the stuff + + + align:start position:0% +the image classification but the stuff +in light blue and they're saying that + + align:start position:0% +in light blue and they're saying that + + + align:start position:0% +in light blue and they're saying that +you know there's 10% error these days + + align:start position:0% +you know there's 10% error these days + + + align:start position:0% +you know there's 10% error these days +there's 5% error on this but that's + + align:start position:0% +there's 5% error on this but that's + + + align:start position:0% +there's 5% error on this but that's +really not what you're doing in the real + + align:start position:0% +really not what you're doing in the real + + + align:start position:0% +really not what you're doing in the real +world you're not classifying whole + + align:start position:0% +world you're not classifying whole + + + align:start position:0% +world you're not classifying whole +images when you see an image in the real + + align:start position:0% +images when you see an image in the real + + + align:start position:0% +images when you see an image in the real +world what you're doing is you're trying + + align:start position:0% +world what you're doing is you're trying + + + align:start position:0% +world what you're doing is you're trying +to figure out what objects are where and + + align:start position:0% +to figure out what objects are where and + + + align:start position:0% +to figure out what objects are where and +that's the red part that's the part + + align:start position:0% +that's the red part that's the part + + + align:start position:0% +that's the red part that's the part +where you have an average precision of + + align:start position:0% +where you have an average precision of + + + align:start position:0% +where you have an average precision of +50% in other words the object actor + + align:start position:0% +50% in other words the object actor + + + align:start position:0% +50% in other words the object actor +really really really sucks most of the + + align:start position:0% +really really really sucks most of the + + + align:start position:0% +really really really sucks most of the +time it's gonna be pretty wrong it's + + align:start position:0% +time it's gonna be pretty wrong it's + + + align:start position:0% +time it's gonna be pretty wrong it's +very very very far away from how + + align:start position:0% +very very very far away from how + + + align:start position:0% +very very very far away from how +accurate you are if your object actor + + align:start position:0% +accurate you are if your object actor + + + align:start position:0% +accurate you are if your object actor +was that bad + + align:start position:0% +was that bad + + + align:start position:0% +was that bad +you would die every time you cross the + + align:start position:0% +you would die every time you cross the + + + align:start position:0% +you would die every time you cross the +street all right so we believe that + + align:start position:0% +street all right so we believe that + + + align:start position:0% +street all right so we believe that +object action doesn't work well in order + + align:start position:0% +object action doesn't work well in order + + + align:start position:0% +object action doesn't work well in order +to fix this because somehow we have to + + align:start position:0% +to fix this because somehow we have to + + + align:start position:0% +to fix this because somehow we have to +be able to extract some knowledge about + + align:start position:0% +be able to extract some knowledge about + + + align:start position:0% +be able to extract some knowledge about +the video that's pretty robust for us to + + align:start position:0% +the video that's pretty robust for us to + + + align:start position:0% +the video that's pretty robust for us to +be able to track these objects and + + align:start position:0% +be able to track these objects and + + + align:start position:0% +be able to track these objects and +recognize these sentences we need to + + align:start position:0% +recognize these sentences we need to + + + align:start position:0% +recognize these sentences we need to +modify object actors a little bit we're + + align:start position:0% +modify object actors a little bit we're + + + align:start position:0% +modify object actors a little bit we're +gonna go into our object actor and + + align:start position:0% +gonna go into our object actor and + + + align:start position:0% +gonna go into our object actor and +normally they have a threshold right at + + align:start position:0% +normally they have a threshold right at + + + align:start position:0% +normally they have a threshold right at +some point they learn that if the score + + align:start position:0% +some point they learn that if the score + + + align:start position:0% +some point they learn that if the score +of this detection is above this level I + + align:start position:0% +of this detection is above this level I + + + align:start position:0% +of this detection is above this level I +should have confidence in it and if the + + align:start position:0% +should have confidence in it and if the + + + align:start position:0% +should have confidence in it and if the +score of this detection is below this + + align:start position:0% +score of this detection is below this + + + align:start position:0% +score of this detection is below this +level I shouldn't have confidence and + + align:start position:0% +level I shouldn't have confidence and + + + align:start position:0% +level I shouldn't have confidence and +then what we're gonna do is we remove + + align:start position:0% +then what we're gonna do is we remove + + + align:start position:0% +then what we're gonna do is we remove +that threshold + + align:start position:0% +that threshold + + + align:start position:0% +that threshold +we're until the object sector give me + + align:start position:0% +we're until the object sector give me + + + align:start position:0% +we're until the object sector give me +thousands or millions of detections in + + align:start position:0% +thousands or millions of detections in + + + align:start position:0% +thousands or millions of detections in +every frame we're going to take those + + align:start position:0% +every frame we're going to take those + + + align:start position:0% +every frame we're going to take those +detection and we're gonna figure out how + + align:start position:0% +detection and we're gonna figure out how + + + align:start position:0% +detection and we're gonna figure out how +to filter them later on all right the + + align:start position:0% +to filter them later on all right the + + + align:start position:0% +to filter them later on all right the +way we're gonna do this and this is the + + align:start position:0% +way we're gonna do this and this is the + + + align:start position:0% +way we're gonna do this and this is the +only flight that's going to have any + + align:start position:0% +only flight that's going to have any + + + align:start position:0% +only flight that's going to have any +equations and it's just going to be a + + align:start position:0% +equations and it's just going to be a + + + align:start position:0% +equations and it's just going to be a +linear combination all we're gonna do is + + align:start position:0% +linear combination all we're gonna do is + + + align:start position:0% +linear combination all we're gonna do is +we're gonna take every detection in + + align:start position:0% +we're gonna take every detection in + + + align:start position:0% +we're gonna take every detection in +every frame of this video we're gonna + + align:start position:0% +every frame of this video we're gonna + + + align:start position:0% +every frame of this video we're gonna +arrange them in a lattice in every + + align:start position:0% +arrange them in a lattice in every + + + align:start position:0% +arrange them in a lattice in every +column of this lattice we're going to + + align:start position:0% +column of this lattice we're going to + + + align:start position:0% +column of this lattice we're going to +have the detections for one particular + + align:start position:0% +have the detections for one particular + + + align:start position:0% +have the detections for one particular +frame and in that sense what we want is + + align:start position:0% +frame and in that sense what we want is + + + align:start position:0% +frame and in that sense what we want is +one detection for every object for every + + align:start position:0% +one detection for every object for every + + + align:start position:0% +one detection for every object for every +frame in other words we want the path + + align:start position:0% +frame in other words we want the path + + + align:start position:0% +frame in other words we want the path +through this lattice we want to select + + align:start position:0% +through this lattice we want to select + + + align:start position:0% +through this lattice we want to select +one detection in every column but we + + align:start position:0% +one detection in every column but we + + + align:start position:0% +one detection in every column but we +want tracks that have a particular + + align:start position:0% +want tracks that have a particular + + + align:start position:0% +want tracks that have a particular +property right if I'm approaching this + + align:start position:0% +property right if I'm approaching this + + + align:start position:0% +property right if I'm approaching this +microphone you know that you expect to + + align:start position:0% +microphone you know that you expect to + + + align:start position:0% +microphone you know that you expect to +see me kind of far away than getting + + align:start position:0% +see me kind of far away than getting + + + align:start position:0% +see me kind of far away than getting +closer than eventually I'm close to the + + align:start position:0% +closer than eventually I'm close to the + + + align:start position:0% +closer than eventually I'm close to the +microphone + + align:start position:0% +microphone + + + align:start position:0% +microphone +you don't expect me to be over there and + + align:start position:0% +you don't expect me to be over there and + + + align:start position:0% +you don't expect me to be over there and +then to appear over here as the five + + align:start position:0% +then to appear over here as the five + + + align:start position:0% +then to appear over here as the five +teleported so we want to build this + + align:start position:0% +teleported so we want to build this + + + align:start position:0% +teleported so we want to build this +intuition that objects move smoothly and + + align:start position:0% +intuition that objects move smoothly and + + + align:start position:0% +intuition that objects move smoothly and +that objects move according to how they + + align:start position:0% +that objects move according to how they + + + align:start position:0% +that objects move according to how they +previously moved right it's not like + + align:start position:0% +previously moved right it's not like + + + align:start position:0% +previously moved right it's not like +someone moves from one frame 10 pixels + + align:start position:0% +someone moves from one frame 10 pixels + + + align:start position:0% +someone moves from one frame 10 pixels +over the next frame they moves 10 pixels + + align:start position:0% +over the next frame they moves 10 pixels + + + align:start position:0% +over the next frame they moves 10 pixels +to the left and they keep oscillating + + align:start position:0% +to the left and they keep oscillating + + + align:start position:0% +to the left and they keep oscillating +between the two and that's what we're + + align:start position:0% +between the two and that's what we're + + + align:start position:0% +between the two and that's what we're +gonna do I'm not going to talk about how + + align:start position:0% +gonna do I'm not going to talk about how + + + align:start position:0% +gonna do I'm not going to talk about how +we compute this it's really trivial if + + align:start position:0% +we compute this it's really trivial if + + + align:start position:0% +we compute this it's really trivial if +you know about optical flow you can do + + align:start position:0% +you know about optical flow you can do + + + align:start position:0% +you know about optical flow you can do +it but basically what we want is a track + + align:start position:0% +it but basically what we want is a track + + + align:start position:0% +it but basically what we want is a track +where we don't hallucinate the objects + + align:start position:0% +where we don't hallucinate the objects + + + align:start position:0% +where we don't hallucinate the objects +so every node in our resulting + + align:start position:0% +so every node in our resulting + + + align:start position:0% +so every node in our resulting +detections should be strong if we ignore + + align:start position:0% +detections should be strong if we ignore + + + align:start position:0% +detections should be strong if we ignore +the strength of the object actor we're + + align:start position:0% +the strength of the object actor we're + + + align:start position:0% +the strength of the object actor we're +just gonna pretend that there are a + + align:start position:0% +just gonna pretend that there are a + + + align:start position:0% +just gonna pretend that there are a +whole bunch of people in front of us and + + align:start position:0% +whole bunch of people in front of us and + + + align:start position:0% +whole bunch of people in front of us and +every edge should also be strong in + + align:start position:0% +every edge should also be strong in + + + align:start position:0% +every edge should also be strong in +other words when we look at two + + align:start position:0% +other words when we look at two + + + align:start position:0% +other words when we look at two +detections from adjacent frames if I + + align:start position:0% +detections from adjacent frames if I + + + align:start position:0% +detections from adjacent frames if I +have a person over here in one frame and + + align:start position:0% +have a person over here in one frame and + + + align:start position:0% +have a person over here in one frame and +a person over here in another frame I + + align:start position:0% +a person over here in another frame I + + + align:start position:0% +a person over here in another frame I +shouldn't really think that that's a + + align:start position:0% +shouldn't really think that that's a + + + align:start position:0% +shouldn't really think that that's a +very good person track but if I have a + + align:start position:0% +very good person track but if I have a + + + align:start position:0% +very good person track but if I have a +person over here that kind of move to + + align:start position:0% +person over here that kind of move to + + + align:start position:0% +person over here that kind of move to +the right the previous frame and I have + + align:start position:0% +the right the previous frame and I have + + + align:start position:0% +the right the previous frame and I have +a new detection that's just slightly to + + align:start position:0% +a new detection that's just slightly to + + + align:start position:0% +a new detection that's just slightly to +the right of that one I should expect + + align:start position:0% +the right of that one I should expect + + + align:start position:0% +the right of that one I should expect +that that's a much better track so + + align:start position:0% +that that's a much better track so + + + align:start position:0% +that that's a much better track so +that's all we do and encoding this + + align:start position:0% +that's all we do and encoding this + + + align:start position:0% +that's all we do and encoding this +intuition is very very straightforward + + align:start position:0% +intuition is very very straightforward + + + align:start position:0% +intuition is very very straightforward +it's just a linear combination so the + + align:start position:0% +it's just a linear combination so the + + + align:start position:0% +it's just a linear combination so the +score of one path the score of the track + + align:start position:0% +score of one path the score of the track + + + align:start position:0% +score of one path the score of the track +of an object is just the sum of your + + align:start position:0% +of an object is just the sum of your + + + align:start position:0% +of an object is just the sum of your +confidence in the detection so in every + + align:start position:0% +confidence in the detection so in every + + + align:start position:0% +confidence in the detection so in every +detection every frame along with the + + align:start position:0% +detection every frame along with the + + + align:start position:0% +detection every frame along with the +confidence that the object track was + + align:start position:0% +confidence that the object track was + + + align:start position:0% +confidence that the object track was +actually coherent all right this is the + + align:start position:0% +actually coherent all right this is the + + + align:start position:0% +actually coherent all right this is the +only equation we're gonna see in this + + align:start position:0% +only equation we're gonna see in this + + + align:start position:0% +only equation we're gonna see in this +talk and it's just a linear combination + + align:start position:0% +talk and it's just a linear combination + + + align:start position:0% +talk and it's just a linear combination +but it will come back to haunt us in + + align:start position:0% +but it will come back to haunt us in + + + align:start position:0% +but it will come back to haunt us in +several times before at the end all + + align:start position:0% +several times before at the end all + + + align:start position:0% +several times before at the end all +right so we use dynamic programming we + + align:start position:0% +right so we use dynamic programming we + + + align:start position:0% +right so we use dynamic programming we +find the path through this lattice and + + align:start position:0% +find the path through this lattice and + + + align:start position:0% +find the path through this lattice and +this is a tracker and actually Viterbi + + align:start position:0% +this is a tracker and actually Viterbi + + + align:start position:0% +this is a tracker and actually Viterbi +did this in 1967 for radar this is not a + + align:start position:0% +did this in 1967 for radar this is not a + + + align:start position:0% +did this in 1967 for radar this is not a +new idea here we ran it for for just a + + align:start position:0% +new idea here we ran it for for just a + + + align:start position:0% +new idea here we ran it for for just a +computer vision task where we just + + align:start position:0% +computer vision task where we just + + + align:start position:0% +computer vision task where we just +wanted to track objects we ran a person + + align:start position:0% +wanted to track objects we ran a person + + + align:start position:0% +wanted to track objects we ran a person +detector in a motorcycle detector but we + + align:start position:0% +detector in a motorcycle detector but we + + + align:start position:0% +detector in a motorcycle detector but we +don't have a person standing up in a + + align:start position:0% +don't have a person standing up in a + + + align:start position:0% +don't have a person standing up in a +person sitting down detector so the + + align:start position:0% +person sitting down detector so the + + + align:start position:0% +person sitting down detector so the +tracker is good enough that it can keep + + align:start position:0% +tracker is good enough that it can keep + + + align:start position:0% +tracker is good enough that it can keep +the two people separate from each other + + align:start position:0% +the two people separate from each other + + + align:start position:0% +the two people separate from each other +despite the fact that they're actually + + align:start position:0% +despite the fact that they're actually + + + align:start position:0% +despite the fact that they're actually +pretty close in the video so you see we + + align:start position:0% +pretty close in the video so you see we + + + align:start position:0% +pretty close in the video so you see we +do a pretty decent job of tracking all + + align:start position:0% +do a pretty decent job of tracking all + + + align:start position:0% +do a pretty decent job of tracking all +the objects until they get pretty small + + align:start position:0% +the objects until they get pretty small + + + align:start position:0% +the objects until they get pretty small +in the field of view and the Apple + + align:start position:0% +in the field of view and the Apple + + + align:start position:0% +in the field of view and the Apple +detector doesn't work well anymore all + + align:start position:0% +detector doesn't work well anymore all + + + align:start position:0% +detector doesn't work well anymore all +right + + align:start position:0% +right + + + align:start position:0% +right +so now we have our the tracks of objects + + align:start position:0% +so now we have our the tracks of objects + + + align:start position:0% +so now we have our the tracks of objects +we can see object motion over time from + + align:start position:0% +we can see object motion over time from + + + align:start position:0% +we can see object motion over time from +a video and somehow we have to look at + + align:start position:0% +a video and somehow we have to look at + + + align:start position:0% +a video and somehow we have to look at +these tracks and determine what happened + + align:start position:0% +these tracks and determine what happened + + + align:start position:0% +these tracks and determine what happened +to them with someone riding with someone + + align:start position:0% +to them with someone riding with someone + + + align:start position:0% +to them with someone riding with someone +running with someone bouncing up and + + align:start position:0% +running with someone bouncing up and + + + align:start position:0% +running with someone bouncing up and +down in order to do this we're gonna get + + align:start position:0% +down in order to do this we're gonna get + + + align:start position:0% +down in order to do this we're gonna get +some features from our tracks you can + + align:start position:0% +some features from our tracks you can + + + align:start position:0% +some features from our tracks you can +look at the track in every frame and you + + align:start position:0% +look at the track in every frame and you + + + align:start position:0% +look at the track in every frame and you +can extract out a lot of information you + + align:start position:0% +can extract out a lot of information you + + + align:start position:0% +can extract out a lot of information you +can extract out the average color you + + align:start position:0% +can extract out the average color you + + + align:start position:0% +can extract out the average color you +can extract out the position the + + align:start position:0% +can extract out the position the + + + align:start position:0% +can extract out the position the +velocity acceleration aspect ratio + + align:start position:0% +velocity acceleration aspect ratio + + + align:start position:0% +velocity acceleration aspect ratio +anything that you want to get out of + + align:start position:0% +anything that you want to get out of + + + align:start position:0% +anything that you want to get out of +this frame knowing that this bounding + + align:start position:0% +this frame knowing that this bounding + + + align:start position:0% +this frame knowing that this bounding +box is there you can compute and the + + align:start position:0% +box is there you can compute and the + + + align:start position:0% +box is there you can compute and the +algorithm doesn't care all right there's + + align:start position:0% +algorithm doesn't care all right there's + + + align:start position:0% +algorithm doesn't care all right there's +one small problem though most of the + + align:start position:0% +one small problem though most of the + + + align:start position:0% +one small problem though most of the +time we need more complicated feature + + align:start position:0% +time we need more complicated feature + + + align:start position:0% +time we need more complicated feature +vectors so for example for ride it's not + + align:start position:0% +vectors so for example for ride it's not + + + align:start position:0% +vectors so for example for ride it's not +enough to have a feature vector that + + align:start position:0% +enough to have a feature vector that + + + align:start position:0% +enough to have a feature vector that +only includes the person you needed to + + align:start position:0% +only includes the person you needed to + + + align:start position:0% +only includes the person you needed to +look at the relative position between + + align:start position:0% +look at the relative position between + + + align:start position:0% +look at the relative position between +the person and the skateboard to + + align:start position:0% +the person and the skateboard to + + + align:start position:0% +the person and the skateboard to +determine that are actually going + + align:start position:0% +determine that are actually going + + + align:start position:0% +determine that are actually going +together and one isn't going right and + + align:start position:0% +together and one isn't going right and + + + align:start position:0% +together and one isn't going right and +the other one's going left so for that + + align:start position:0% +the other one's going left so for that + + + align:start position:0% +the other one's going left so for that +what we're gonna do is we're gonna build + + align:start position:0% +what we're gonna do is we're gonna build + + + align:start position:0% +what we're gonna do is we're gonna build +a feature vector for the agent of the + + align:start position:0% +a feature vector for the agent of the + + + align:start position:0% +a feature vector for the agent of the +action and in the case of ride and a + + align:start position:0% +action and in the case of ride and a + + + align:start position:0% +action and in the case of ride and a +feature vector for the instrument the + + align:start position:0% +feature vector for the instrument the + + + align:start position:0% +feature vector for the instrument the +skateboard we're just going to + + align:start position:0% +skateboard we're just going to + + + align:start position:0% +skateboard we're just going to +concatenate the two together so we get a + + align:start position:0% +concatenate the two together so we get a + + + align:start position:0% +concatenate the two together so we get a +bigger feature vector and then we're + + align:start position:0% +bigger feature vector and then we're + + + align:start position:0% +bigger feature vector and then we're +gonna have some extra features that tell + + align:start position:0% +gonna have some extra features that tell + + + align:start position:0% +gonna have some extra features that tell +us about the relationships between these + + align:start position:0% +us about the relationships between these + + + align:start position:0% +us about the relationships between these +two so we can include things like the + + align:start position:0% +two so we can include things like the + + + align:start position:0% +two so we can include things like the +distance the relative velocity the angle + + align:start position:0% +distance the relative velocity the angle + + + align:start position:0% +distance the relative velocity the angle +overlap anything that you want to + + align:start position:0% +overlap anything that you want to + + + align:start position:0% +overlap anything that you want to +compute between these two bounding boxes + + align:start position:0% +compute between these two bounding boxes + + + align:start position:0% +compute between these two bounding boxes +in this frame you're welcome to compute + + align:start position:0% +in this frame you're welcome to compute + + + align:start position:0% +in this frame you're welcome to compute +alright and if you build this feature + + align:start position:0% +alright and if you build this feature + + + align:start position:0% +alright and if you build this feature +vector between this person and the + + align:start position:0% +vector between this person and the + + + align:start position:0% +vector between this person and the +skateboard you could recognize the + + align:start position:0% +skateboard you could recognize the + + + align:start position:0% +skateboard you could recognize the +person wrote the skateboard in this + + align:start position:0% +person wrote the skateboard in this + + + align:start position:0% +person wrote the skateboard in this +video if you build a different feature + + align:start position:0% +video if you build a different feature + + + align:start position:0% +video if you build a different feature +vector for example between these two + + align:start position:0% +vector for example between these two + + + align:start position:0% +vector for example between these two +people you could recognize the person + + align:start position:0% +people you could recognize the person + + + align:start position:0% +people you could recognize the person +was approaching the other person or a + + align:start position:0% +was approaching the other person or a + + + align:start position:0% +was approaching the other person or a +person was leaving the other person if + + align:start position:0% +person was leaving the other person if + + + align:start position:0% +person was leaving the other person if +you build a feature vector between the + + align:start position:0% +you build a feature vector between the + + + align:start position:0% +you build a feature vector between the +skateboard and the other person you + + align:start position:0% +skateboard and the other person you + + + align:start position:0% +skateboard and the other person you +could recognize a skateboard is + + align:start position:0% +could recognize a skateboard is + + + align:start position:0% +could recognize a skateboard is +approaching the person etc so depending + + align:start position:0% +approaching the person etc so depending + + + align:start position:0% +approaching the person etc so depending +on which feature vector you build you + + align:start position:0% +on which feature vector you build you + + + align:start position:0% +on which feature vector you build you +can recognize different kinds of actions + + align:start position:0% +can recognize different kinds of actions + + + align:start position:0% +can recognize different kinds of actions +so when we have our tracks we know how + + align:start position:0% +so when we have our tracks we know how + + + align:start position:0% +so when we have our tracks we know how +the objects moved in these videos we get + + align:start position:0% +the objects moved in these videos we get + + + align:start position:0% +the objects moved in these videos we get +out some feature vectors from our tracks + + align:start position:0% +out some feature vectors from our tracks + + + align:start position:0% +out some feature vectors from our tracks +and what we need to do is decide what + + align:start position:0% +and what we need to do is decide what + + + align:start position:0% +and what we need to do is decide what +these feature vectors are actually doing + + align:start position:0% +these feature vectors are actually doing + + + align:start position:0% +these feature vectors are actually doing +is the person riding that skateboard the + + align:start position:0% +is the person riding that skateboard the + + + align:start position:0% +is the person riding that skateboard the +way we're going to do this is using + + align:start position:0% +way we're going to do this is using + + + align:start position:0% +way we're going to do this is using +hidden Markov models hidden Markov + + align:start position:0% +hidden Markov models hidden Markov + + + align:start position:0% +hidden Markov models hidden Markov +models are really simple all these to + + align:start position:0% +models are really simple all these to + + + align:start position:0% +models are really simple all these to +them is that there's a model of the + + align:start position:0% +them is that there's a model of the + + + align:start position:0% +them is that there's a model of the +world that follows a particular kind of + + align:start position:0% +world that follows a particular kind of + + + align:start position:0% +world that follows a particular kind of +dynamics in this case imagine that we + + align:start position:0% +dynamics in this case imagine that we + + + align:start position:0% +dynamics in this case imagine that we +have an action like approach I'm far + + align:start position:0% +have an action like approach I'm far + + + align:start position:0% +have an action like approach I'm far +away from the object I get closer to the + + align:start position:0% +away from the object I get closer to the + + + align:start position:0% +away from the object I get closer to the +object + + align:start position:0% +object + + + align:start position:0% +object +eventually and next to the object so + + align:start position:0% +eventually and next to the object so + + + align:start position:0% +eventually and next to the object so +this action for example has three states + + align:start position:0% +this action for example has three states + + + align:start position:0% +this action for example has three states +one was iswhen where I was far more as I + + align:start position:0% +one was iswhen where I was far more as I + + + align:start position:0% +one was iswhen where I was far more as I +was getting nearer one where I was very + + align:start position:0% +was getting nearer one where I was very + + + align:start position:0% +was getting nearer one where I was very +close and we have a particular + + align:start position:0% +close and we have a particular + + + align:start position:0% +close and we have a particular +transition between these states right we + + align:start position:0% +transition between these states right we + + + align:start position:0% +transition between these states right we +already said that I don't teleport so I + + align:start position:0% +already said that I don't teleport so I + + + align:start position:0% +already said that I don't teleport so I +shouldn't be able to go from being far + + align:start position:0% +shouldn't be able to go from being far + + + align:start position:0% +shouldn't be able to go from being far +away to being near so you should expect + + align:start position:0% +away to being near so you should expect + + + align:start position:0% +away to being near so you should expect +me to go from the first day to the + + align:start position:0% +me to go from the first day to the + + + align:start position:0% +me to go from the first day to the +second state unto the third state + + align:start position:0% +second state unto the third state + + + align:start position:0% +second state unto the third state +without going from the first to the last + + align:start position:0% +without going from the first to the last + + + align:start position:0% +without going from the first to the last +in each state you have something that + + align:start position:0% +in each state you have something that + + + align:start position:0% +in each state you have something that +you want to observe about me right you + + align:start position:0% +you want to observe about me right you + + + align:start position:0% +you want to observe about me right you +want to really see that I'm far away in + + align:start position:0% +want to really see that I'm far away in + + + align:start position:0% +want to really see that I'm far away in +the first date + + align:start position:0% +the first date + + + align:start position:0% +the first date +that I'm getting closer in the second + + align:start position:0% +that I'm getting closer in the second + + + align:start position:0% +that I'm getting closer in the second +and I'm actually there on the third so + + align:start position:0% +and I'm actually there on the third so + + + align:start position:0% +and I'm actually there on the third so +we have some model for what we expect to + + align:start position:0% +we have some model for what we expect to + + + align:start position:0% +we have some model for what we expect to +see in every state and we can connect + + align:start position:0% +see in every state and we can connect + + + align:start position:0% +see in every state and we can connect +this with our feature vectors so the + + align:start position:0% +this with our feature vectors so the + + + align:start position:0% +this with our feature vectors so the +idea is there's some hidden information + + align:start position:0% +idea is there's some hidden information + + + align:start position:0% +idea is there's some hidden information +behind the motion of these objects and + + align:start position:0% +behind the motion of these objects and + + + align:start position:0% +behind the motion of these objects and +we're going to assume that hidden + + align:start position:0% +we're going to assume that hidden + + + align:start position:0% +we're going to assume that hidden +information is represented within hmm + + align:start position:0% +information is represented within hmm + + + align:start position:0% +information is represented within hmm +and what we need to recover is the real + + align:start position:0% +and what we need to recover is the real + + + align:start position:0% +and what we need to recover is the real +state of these objects so if you see a + + align:start position:0% +state of these objects so if you see a + + + align:start position:0% +state of these objects so if you see a +video of me moving towards this + + align:start position:0% +video of me moving towards this + + + align:start position:0% +video of me moving towards this +microphone you have to recover some + + align:start position:0% +microphone you have to recover some + + + align:start position:0% +microphone you have to recover some +hidden information of which frames was I + + align:start position:0% +hidden information of which frames was I + + + align:start position:0% +hidden information of which frames was I +far away in which frames what I was at + + align:start position:0% +far away in which frames what I was at + + + align:start position:0% +far away in which frames what I was at +getting nearer and which frames was + + align:start position:0% +getting nearer and which frames was + + + align:start position:0% +getting nearer and which frames was +actually next to the object for now what + + align:start position:0% +actually next to the object for now what + + + align:start position:0% +actually next to the object for now what +we're gonna do is we're going to assume + + align:start position:0% +we're gonna do is we're going to assume + + + align:start position:0% +we're gonna do is we're going to assume +that we have one of these three Markov + + align:start position:0% +that we have one of these three Markov + + + align:start position:0% +that we have one of these three Markov +models for every different word so for + + align:start position:0% +models for every different word so for + + + align:start position:0% +models for every different word so for +every verb we have a different head + + align:start position:0% +every verb we have a different head + + + align:start position:0% +every verb we have a different head +Markov model there's one for approach + + align:start position:0% +Markov model there's one for approach + + + align:start position:0% +Markov model there's one for approach +just one for pickup there's one for ride + + align:start position:0% +just one for pickup there's one for ride + + + align:start position:0% +just one for pickup there's one for ride +etc and if you want to tell me what's + + align:start position:0% +etc and if you want to tell me what's + + + align:start position:0% +etc and if you want to tell me what's +going on in this video you just have a + + align:start position:0% +going on in this video you just have a + + + align:start position:0% +going on in this video you just have a +big library of hidden Markov models you + + align:start position:0% +big library of hidden Markov models you + + + align:start position:0% +big library of hidden Markov models you +apply every one to every video you have + + align:start position:0% +apply every one to every video you have + + + align:start position:0% +apply every one to every video you have +some threshold and anything above that + + align:start position:0% +some threshold and anything above that + + + align:start position:0% +some threshold and anything above that +threshold you say happen and you produce + + align:start position:0% +threshold you say happen and you produce + + + align:start position:0% +threshold you say happen and you produce +a sentence for it okay if we look at how + + align:start position:0% +a sentence for it okay if we look at how + + + align:start position:0% +a sentence for it okay if we look at how +you actually figure out what this hidden + + align:start position:0% +you actually figure out what this hidden + + + align:start position:0% +you actually figure out what this hidden +information is what's data am I in when + + align:start position:0% +information is what's data am I in when + + + align:start position:0% +information is what's data am I in when +I'm approaching this object it looks a + + align:start position:0% +I'm approaching this object it looks a + + + align:start position:0% +I'm approaching this object it looks a +lot like the tracker what you have is + + align:start position:0% +lot like the tracker what you have is + + + align:start position:0% +lot like the tracker what you have is +you have to make a choice in every frame + + align:start position:0% +you have to make a choice in every frame + + + align:start position:0% +you have to make a choice in every frame +your choice is which state is my action + + align:start position:0% +your choice is which state is my action + + + align:start position:0% +your choice is which state is my action +is it state 1 through 3 or some other + + align:start position:0% +is it state 1 through 3 or some other + + + align:start position:0% +is it state 1 through 3 or some other +state in the same way that in tracker + + align:start position:0% +state in the same way that in tracker + + + align:start position:0% +state in the same way that in tracker +you have to make a choice you have to + + align:start position:0% +you have to make a choice you have to + + + align:start position:0% +you have to make a choice you have to +choose which detection is the system in + + align:start position:0% +choose which detection is the system in + + + align:start position:0% +choose which detection is the system in +for each frame and here you also have + + align:start position:0% +for each frame and here you also have + + + align:start position:0% +for each frame and here you also have +edges edges tell you how likely am I to + + align:start position:0% +edges edges tell you how likely am I to + + + align:start position:0% +edges edges tell you how likely am I to +transition between different states in + + align:start position:0% +transition between different states in + + + align:start position:0% +transition between different states in +my action and every node also has a + + align:start position:0% +my action and every node also has a + + + align:start position:0% +my action and every node also has a +score it's the score of did you actually + + align:start position:0% +score it's the score of did you actually + + + align:start position:0% +score it's the score of did you actually +observe me doing what you're supposed to + + align:start position:0% +observe me doing what you're supposed to + + + align:start position:0% +observe me doing what you're supposed to +observe me doing in every action so if + + align:start position:0% +observe me doing in every action so if + + + align:start position:0% +observe me doing in every action so if +you're saying I'm in the first state did + + align:start position:0% +you're saying I'm in the first state did + + + align:start position:0% +you're saying I'm in the first state did +you actually see me stationary and far + + align:start position:0% +you actually see me stationary and far + + + align:start position:0% +you actually see me stationary and far +away from that object + + align:start position:0% +away from that object + + + align:start position:0% +away from that object +and what you want is a path through this + + align:start position:0% +and what you want is a path through this + + + align:start position:0% +and what you want is a path through this +lattice in the same way that we had a + + align:start position:0% +lattice in the same way that we had a + + + align:start position:0% +lattice in the same way that we had a +path before and a path just means you + + align:start position:0% +path before and a path just means you + + + align:start position:0% +path before and a path just means you +made a decision that I'm in state 1 and + + align:start position:0% +made a decision that I'm in state 1 and + + + align:start position:0% +made a decision that I'm in state 1 and +the first frame or in state 1 in the + + align:start position:0% +the first frame or in state 1 in the + + + align:start position:0% +the first frame or in state 1 in the +third frame etc and that's just the + + align:start position:0% +third frame etc and that's just the + + + align:start position:0% +third frame etc and that's just the +linear combination of course this is the + + align:start position:0% +linear combination of course this is the + + + align:start position:0% +linear combination of course this is the +same equation we saw before so here's an + + align:start position:0% +same equation we saw before so here's an + + + align:start position:0% +same equation we saw before so here's an +example of this sort of feed-forward + + align:start position:0% +example of this sort of feed-forward + + + align:start position:0% +example of this sort of feed-forward +pipeline in action we ran it over a few + + align:start position:0% +pipeline in action we ran it over a few + + + align:start position:0% +pipeline in action we ran it over a few +thousand videos it produces output like + + align:start position:0% +thousand videos it produces output like + + + align:start position:0% +thousand videos it produces output like +the person carried something the person + + align:start position:0% +the person carried something the person + + + align:start position:0% +the person carried something the person +went away the person walk the person had + + align:start position:0% +went away the person walk the person had + + + align:start position:0% +went away the person walk the person had +the bag it's pretty limited and it's + + align:start position:0% +the bag it's pretty limited and it's + + + align:start position:0% +the bag it's pretty limited and it's +vocabulary has 48 verbs about 30 + + align:start position:0% +vocabulary has 48 verbs about 30 + + + align:start position:0% +vocabulary has 48 verbs about 30 +different objects a few different + + align:start position:0% +different objects a few different + + + align:start position:0% +different objects a few different +prepositions and it even works when the + + align:start position:0% +prepositions and it even works when the + + + align:start position:0% +prepositions and it even works when the +camera moves so the person chased the + + align:start position:0% +camera moves so the person chased the + + + align:start position:0% +camera moves so the person chased the +car right or the person is slowly around + + align:start position:0% +car right or the person is slowly around + + + align:start position:0% +car right or the person is slowly around +rightward to the car and should also + + align:start position:0% +rightward to the car and should also + + + align:start position:0% +rightward to the car and should also +probably say the person had a really bad + + align:start position:0% +probably say the person had a really bad + + + align:start position:0% +probably say the person had a really bad +day that's for the future so we've seen + + align:start position:0% +day that's for the future so we've seen + + + align:start position:0% +day that's for the future so we've seen +this feed-forward pipeline we've seen + + align:start position:0% +this feed-forward pipeline we've seen + + + align:start position:0% +this feed-forward pipeline we've seen +that we can get objects we can get + + align:start position:0% +that we can get objects we can get + + + align:start position:0% +that we can get objects we can get +trucks we can look at our trucks get + + align:start position:0% +trucks we can look at our trucks get + + + align:start position:0% +trucks we can look at our trucks get +some features run event detectors take + + align:start position:0% +some features run event detectors take + + + align:start position:0% +some features run event detectors take +those events the hitters and produce + + align:start position:0% +those events the hitters and produce + + + align:start position:0% +those events the hitters and produce +some sentences and now what we're gonna + + align:start position:0% +some sentences and now what we're gonna + + + align:start position:0% +some sentences and now what we're gonna +do is we're going to break down the + + align:start position:0% +do is we're going to break down the + + + align:start position:0% +do is we're going to break down the +barriers between these and show you how + + align:start position:0% +barriers between these and show you how + + + align:start position:0% +barriers between these and show you how +you can have feedback in a really really + + align:start position:0% +you can have feedback in a really really + + + align:start position:0% +you can have feedback in a really really +simple way all right so first let's + + align:start position:0% +simple way all right so first let's + + + align:start position:0% +simple way all right so first let's +combine our event detector in our + + align:start position:0% +combine our event detector in our + + + align:start position:0% +combine our event detector in our +tracker because what that's gonna say is + + align:start position:0% +tracker because what that's gonna say is + + + align:start position:0% +tracker because what that's gonna say is +if you're looking for someone writing + + align:start position:0% +if you're looking for someone writing + + + align:start position:0% +if you're looking for someone writing +something well you should be bias toward + + align:start position:0% +something well you should be bias toward + + + align:start position:0% +something well you should be bias toward +seeing people that are writing something + + align:start position:0% +seeing people that are writing something + + + align:start position:0% +seeing people that are writing something +so in the occlusion example if you see + + align:start position:0% +so in the occlusion example if you see + + + align:start position:0% +so in the occlusion example if you see +someone go behind some large pillar + + align:start position:0% +someone go behind some large pillar + + + align:start position:0% +someone go behind some large pillar +well you might lose them but you have a + + align:start position:0% +well you might lose them but you have a + + + align:start position:0% +well you might lose them but you have a +bias that you should react wire someone + + align:start position:0% +bias that you should react wire someone + + + align:start position:0% +bias that you should react wire someone +riding a skateboard after they leave the + + align:start position:0% +riding a skateboard after they leave the + + + align:start position:0% +riding a skateboard after they leave the +pillar which you don't have if you just + + align:start position:0% +pillar which you don't have if you just + + + align:start position:0% +pillar which you don't have if you just +run the tracker independently from the + + align:start position:0% +run the tracker independently from the + + + align:start position:0% +run the tracker independently from the +event detector so the way we're going to + + align:start position:0% +event detector so the way we're going to + + + align:start position:0% +event detector so the way we're going to +put them together is very very easy + + align:start position:0% +put them together is very very easy + + + align:start position:0% +put them together is very very easy +there's a reason why these two look + + align:start position:0% +there's a reason why these two look + + + align:start position:0% +there's a reason why these two look +completely identical and why the + + align:start position:0% +completely identical and why the + + + align:start position:0% +completely identical and why the +inference algorithm between them is + + align:start position:0% +inference algorithm between them is + + + align:start position:0% +inference algorithm between them is +identical right now what we're doing is + + align:start position:0% +identical right now what we're doing is + + + align:start position:0% +identical right now what we're doing is +we have a tracker on the left or on your + + align:start position:0% +we have a tracker on the left or on your + + + align:start position:0% +we have a tracker on the left or on your +left and we have an event recognizer on + + align:start position:0% +left and we have an event recognizer on + + + align:start position:0% +left and we have an event recognizer on +the right right now we're running one + + align:start position:0% +the right right now we're running one + + + align:start position:0% +the right right now we're running one +and then we're feeding the output of one + + align:start position:0% +and then we're feeding the output of one + + + align:start position:0% +and then we're feeding the output of one +into the other + + align:start position:0% +into the other + + + align:start position:0% +into the other +basically we run one maximization and + + align:start position:0% +basically we run one maximization and + + + align:start position:0% +basically we run one maximization and +then we run another maximization and all + + align:start position:0% +then we run another maximization and all + + + align:start position:0% +then we run another maximization and all +we're gonna do is move the max on the + + align:start position:0% +we're gonna do is move the max on the + + + align:start position:0% +we're gonna do is move the max on the +right to the left and you get the exact + + align:start position:0% +right to the left and you get the exact + + + align:start position:0% +right to the left and you get the exact +same inference algorithm the intuition + + align:start position:0% +same inference algorithm the intuition + + + align:start position:0% +same inference algorithm the intuition +behind this is you have two lettuces and + + align:start position:0% +behind this is you have two lettuces and + + + align:start position:0% +behind this is you have two lettuces and +you can take the cross product of the + + align:start position:0% +you can take the cross product of the + + + align:start position:0% +you can take the cross product of the +lettuces basically for every try + + align:start position:0% +lettuces basically for every try + + + align:start position:0% +lettuces basically for every try +no you just look at all the event + + align:start position:0% +no you just look at all the event + + + align:start position:0% +no you just look at all the event +recognizers now it's and you make one + + align:start position:0% +recognizers now it's and you make one + + + align:start position:0% +recognizers now it's and you make one +big note for each of those and every + + align:start position:0% +big note for each of those and every + + + align:start position:0% +big note for each of those and every +node represents the fact that the + + align:start position:0% +node represents the fact that the + + + align:start position:0% +node represents the fact that the +tracker was in some state and the event + + align:start position:0% +tracker was in some state and the event + + + align:start position:0% +tracker was in some state and the event +recognizer was in some other state so we + + align:start position:0% +recognizer was in some other state so we + + + align:start position:0% +recognizer was in some other state so we +have a note that says the tracker chose + + align:start position:0% +have a note that says the tracker chose + + + align:start position:0% +have a note that says the tracker chose +the first detection the event recognizer + + align:start position:0% +the first detection the event recognizer + + + align:start position:0% +the first detection the event recognizer +was in the first state we have another + + align:start position:0% +was in the first state we have another + + + align:start position:0% +was in the first state we have another +note that says the tracker chose the + + align:start position:0% +note that says the tracker chose the + + + align:start position:0% +note that says the tracker chose the +second detection the event recognizer + + align:start position:0% +second detection the event recognizer + + + align:start position:0% +second detection the event recognizer +we're still in the first state and you + + align:start position:0% +we're still in the first state and you + + + align:start position:0% +we're still in the first state and you +do this for every detection then you do + + align:start position:0% +do this for every detection then you do + + + align:start position:0% +do this for every detection then you do +the same thing for the event recognizer + + align:start position:0% +the same thing for the event recognizer + + + align:start position:0% +the same thing for the event recognizer +being the second state etc so you're + + align:start position:0% +being the second state etc so you're + + + align:start position:0% +being the second state etc so you're +just taking a cross-product between all + + align:start position:0% +just taking a cross-product between all + + + align:start position:0% +just taking a cross-product between all +of the states does that make sense + + align:start position:0% +of the states does that make sense + + + align:start position:0% +of the states does that make sense +another way to say it is that we have + + align:start position:0% +another way to say it is that we have + + + align:start position:0% +another way to say it is that we have +two markov chains one that's observing + + align:start position:0% +two markov chains one that's observing + + + align:start position:0% +two markov chains one that's observing +the output from the object sector and + + align:start position:0% +the output from the object sector and + + + align:start position:0% +the output from the object sector and +another one that's observing the output + + align:start position:0% +another one that's observing the output + + + align:start position:0% +another one that's observing the output +of the middle of Markov chain and you do + + align:start position:0% +of the middle of Markov chain and you do + + + align:start position:0% +of the middle of Markov chain and you do +joint inference over them and the way + + align:start position:0% +joint inference over them and the way + + + align:start position:0% +joint inference over them and the way +you can do joint difference is by taking + + align:start position:0% +you can do joint difference is by taking + + + align:start position:0% +you can do joint difference is by taking +the cross product basically you have to + + align:start position:0% +the cross product basically you have to + + + align:start position:0% +the cross product basically you have to +hear Markov models right one that does + + align:start position:0% +hear Markov models right one that does + + + align:start position:0% +hear Markov models right one that does +tracking and one that does event + + align:start position:0% +tracking and one that does event + + + align:start position:0% +tracking and one that does event +recognition and all we're gonna do is + + align:start position:0% +recognition and all we're gonna do is + + + align:start position:0% +recognition and all we're gonna do is +joint differences on both of them so + + align:start position:0% +joint differences on both of them so + + + align:start position:0% +joint differences on both of them so +rather than trying to choose the best + + align:start position:0% +rather than trying to choose the best + + + align:start position:0% +rather than trying to choose the best +detection and then the best state for my + + align:start position:0% +detection and then the best state for my + + + align:start position:0% +detection and then the best state for my +event I'm gonna jointly figure out + + align:start position:0% +event I'm gonna jointly figure out + + + align:start position:0% +event I'm gonna jointly figure out +what's the best detection if I assume + + align:start position:0% +what's the best detection if I assume + + + align:start position:0% +what's the best detection if I assume +I'm in this state what's the best + + align:start position:0% +I'm in this state what's the best + + + align:start position:0% +I'm in this state what's the best +detection prime minister min I mean this + + align:start position:0% +detection prime minister min I mean this + + + align:start position:0% +detection prime minister min I mean this +other state and at the end I'll pick the + + align:start position:0% +other state and at the end I'll pick the + + + align:start position:0% +other state and at the end I'll pick the +best combination make sense so this is a + + align:start position:0% +best combination make sense so this is a + + + align:start position:0% +best combination make sense so this is a +way for your event recognizer to + + align:start position:0% +way for your event recognizer to + + + align:start position:0% +way for your event recognizer to +influence your tracker because now + + align:start position:0% +influence your tracker because now + + + align:start position:0% +influence your tracker because now +you're jointly choosing the best + + align:start position:0% +you're jointly choosing the best + + + align:start position:0% +you're jointly choosing the best +detection for both the tracker and the + + align:start position:0% +detection for both the tracker and the + + + align:start position:0% +detection for both the tracker and the +event tracking Euler so it was really + + align:start position:0% +event tracking Euler so it was really + + + align:start position:0% +event tracking Euler so it was really +really simple it's we put in a + + align:start position:0% +really simple it's we put in a + + + align:start position:0% +really simple it's we put in a +tremendous amount of feedback by just + + align:start position:0% +tremendous amount of feedback by just + + + align:start position:0% +tremendous amount of feedback by just +taking a cross-product so we can see + + align:start position:0% +taking a cross-product so we can see + + + align:start position:0% +taking a cross-product so we can see +this in action I'm going to show you the + + align:start position:0% +this in action I'm going to show you the + + + align:start position:0% +this in action I'm going to show you the +same video twice the person is not gonna + + align:start position:0% +same video twice the person is not gonna + + + align:start position:0% +same video twice the person is not gonna +move in this video at all what we told + + align:start position:0% +move in this video at all what we told + + + align:start position:0% +move in this video at all what we told +the system is that a ball will approach + + align:start position:0% +the system is that a ball will approach + + + align:start position:0% +the system is that a ball will approach +a person that's it we didn't tell them + + align:start position:0% +a person that's it we didn't tell them + + + align:start position:0% +a person that's it we didn't tell them +which person we didn't told them that we + + align:start position:0% +which person we didn't told them that we + + + align:start position:0% +which person we didn't told them that we +didn't tell the system that their which + + align:start position:0% +didn't tell the system that their which + + + align:start position:0% +didn't tell the system that their which +particular ball which direction is going + + align:start position:0% +particular ball which direction is going + + + align:start position:0% +particular ball which direction is going +to come from or anything like that the + + align:start position:0% +to come from or anything like that the + + + align:start position:0% +to come from or anything like that the +top detection in this frame happens to + + align:start position:0% +top detection in this frame happens to + + + align:start position:0% +top detection in this frame happens to +be the window it's a little hard to see + + align:start position:0% +be the window it's a little hard to see + + + align:start position:0% +be the window it's a little hard to see +it's quite a bit stronger than the + + align:start position:0% +it's quite a bit stronger than the + + + align:start position:0% +it's quite a bit stronger than the +person but because neither the window + + align:start position:0% +person but because neither the window + + + align:start position:0% +person but because neither the window +nor the person ever move in this + + align:start position:0% +nor the person ever move in this + + + align:start position:0% +nor the person ever move in this +scenario the tracker can't possibly help + + align:start position:0% +scenario the tracker can't possibly help + + + align:start position:0% +scenario the tracker can't possibly help +you you have no motion information the + + align:start position:0% +you you have no motion information the + + + align:start position:0% +you you have no motion information the +only way to override that window + + align:start position:0% +only way to override that window + + + align:start position:0% +only way to override that window +detection is to know something else + + align:start position:0% +detection is to know something else + + + align:start position:0% +detection is to know something else +about the world so we told you that the + + align:start position:0% +about the world so we told you that the + + + align:start position:0% +about the world so we told you that the +ball will approach and you can see that + + align:start position:0% +ball will approach and you can see that + + + align:start position:0% +ball will approach and you can see that +for the combined tracker in event + + align:start position:0% +for the combined tracker in event + + + align:start position:0% +for the combined tracker in event +recognizer + + align:start position:0% +recognizer + + + align:start position:0% +recognizer +indeed when the ball comes into + + align:start position:0% +indeed when the ball comes into + + + align:start position:0% +indeed when the ball comes into +view it'll make more sense so the reason + + align:start position:0% +view it'll make more sense so the reason + + + align:start position:0% +view it'll make more sense so the reason +why we actually coming back to the + + align:start position:0% +why we actually coming back to the + + + align:start position:0% +why we actually coming back to the +question that you asked why we don't run + + align:start position:0% +question that you asked why we don't run + + + align:start position:0% +question that you asked why we don't run +it over small windows is because we want + + align:start position:0% +it over small windows is because we want + + + align:start position:0% +it over small windows is because we want +this effect of knowledge that's much + + align:start position:0% +this effect of knowledge that's much + + + align:start position:0% +this effect of knowledge that's much +much later on in the video like the fact + + align:start position:0% +much later on in the video like the fact + + + align:start position:0% +much later on in the video like the fact +that the ball will enter approach that + + align:start position:0% +that the ball will enter approach that + + + align:start position:0% +that the ball will enter approach that +person as opposed to that window to + + align:start position:0% +person as opposed to that window to + + + align:start position:0% +person as opposed to that window to +actually help you much earlier in the + + align:start position:0% +actually help you much earlier in the + + + align:start position:0% +actually help you much earlier in the +video if you run it over small windows + + align:start position:0% +video if you run it over small windows + + + align:start position:0% +video if you run it over small windows +you lose that effect right so here you + + align:start position:0% +you lose that effect right so here you + + + align:start position:0% +you lose that effect right so here you +track the person correctly from the very + + align:start position:0% +track the person correctly from the very + + + align:start position:0% +track the person correctly from the very +first frame despite the fact that the + + align:start position:0% +first frame despite the fact that the + + + align:start position:0% +first frame despite the fact that the +ball only comes into view halfway + + align:start position:0% +ball only comes into view halfway + + + align:start position:0% +ball only comes into view halfway +through the video there are many more + + align:start position:0% +through the video there are many more + + + align:start position:0% +through the video there are many more +examples of this in this case this is a + + align:start position:0% +examples of this in this case this is a + + + align:start position:0% +examples of this in this case this is a +person carrying something here we told + + align:start position:0% +person carrying something here we told + + + align:start position:0% +person carrying something here we told +the system one person is carrying + + align:start position:0% +the system one person is carrying + + + align:start position:0% +the system one person is carrying +something and you'll see when the person + + align:start position:0% +something and you'll see when the person + + + align:start position:0% +something and you'll see when the person +moves we can detect the person and the + + align:start position:0% +moves we can detect the person and the + + + align:start position:0% +moves we can detect the person and the +bag the object texture fails much much + + align:start position:0% +bag the object texture fails much much + + + align:start position:0% +bag the object texture fails much much +earlier because the person is deformable + + align:start position:0% +earlier because the person is deformable + + + align:start position:0% +earlier because the person is deformable +so we see now we can combine together + + align:start position:0% +so we see now we can combine together + + + align:start position:0% +so we see now we can combine together +trackers and event recognizers and now + + align:start position:0% +trackers and event recognizers and now + + + align:start position:0% +trackers and event recognizers and now +we need to add sentences and the trick + + align:start position:0% +we need to add sentences and the trick + + + align:start position:0% +we need to add sentences and the trick +for adding sentences is going to be do + + align:start position:0% +for adding sentences is going to be do + + + align:start position:0% +for adding sentences is going to be do +more of the same we're going to do is + + align:start position:0% +more of the same we're going to do is + + + align:start position:0% +more of the same we're going to do is +we're going to take a tracker it's just + + align:start position:0% +we're going to take a tracker it's just + + + align:start position:0% +we're going to take a tracker it's just +exactly what we saw before and what we + + align:start position:0% +exactly what we saw before and what we + + + align:start position:0% +exactly what we saw before and what we +just did a moment ago is we combine it + + align:start position:0% +just did a moment ago is we combine it + + + align:start position:0% +just did a moment ago is we combine it +with an event recognizer well there's no + + align:start position:0% +with an event recognizer well there's no + + + align:start position:0% +with an event recognizer well there's no +reason why we can't add more trackers we + + align:start position:0% +reason why we can't add more trackers we + + + align:start position:0% +reason why we can't add more trackers we +actually kind of did that right we were + + align:start position:0% +actually kind of did that right we were + + + align:start position:0% +actually kind of did that right we were +tracking both a person and a ball a + + align:start position:0% +tracking both a person and a ball a + + + align:start position:0% +tracking both a person and a ball a +moment ago so we can take an even bigger + + align:start position:0% +moment ago so we can take an even bigger + + + align:start position:0% +moment ago so we can take an even bigger +cross-product have multiple trackers and + + align:start position:0% +cross-product have multiple trackers and + + + align:start position:0% +cross-product have multiple trackers and +have multiple words so all we're saying + + align:start position:0% +have multiple words so all we're saying + + + align:start position:0% +have multiple words so all we're saying +is I have say five trackers that are + + align:start position:0% +is I have say five trackers that are + + + align:start position:0% +is I have say five trackers that are +running I have five words that I want to + + align:start position:0% +running I have five words that I want to + + + align:start position:0% +running I have five words that I want to +detect or ten words that I want to + + align:start position:0% +detect or ten words that I want to + + + align:start position:0% +detect or ten words that I want to +detect and I want to make the choice for + + align:start position:0% +detect and I want to make the choice for + + + align:start position:0% +detect and I want to make the choice for +all of these five trackers jointly so + + align:start position:0% +all of these five trackers jointly so + + + align:start position:0% +all of these five trackers jointly so +that they match all of these ten words + + align:start position:0% +that they match all of these ten words + + + align:start position:0% +that they match all of these ten words +in this picture basically our words are + + align:start position:0% +in this picture basically our words are + + + align:start position:0% +in this picture basically our words are +kind of our sentence are kind of like + + align:start position:0% +kind of our sentence are kind of like + + + align:start position:0% +kind of our sentence are kind of like +bags of words right every word is + + align:start position:0% +bags of words right every word is + + + align:start position:0% +bags of words right every word is +combined with every tracker but we know + + align:start position:0% +combined with every tracker but we know + + + align:start position:0% +combined with every tracker but we know +if you look at the structure of a + + align:start position:0% +if you look at the structure of a + + + align:start position:0% +if you look at the structure of a +sentence like the tall person quickly + + align:start position:0% +sentence like the tall person quickly + + + align:start position:0% +sentence like the tall person quickly +rode the horse not every word refers to + + align:start position:0% +rode the horse not every word refers to + + + align:start position:0% +rode the horse not every word refers to +every object in the sentence right so + + align:start position:0% +every object in the sentence right so + + + align:start position:0% +every object in the sentence right so +you can run your object sector so over + + align:start position:0% +you can run your object sector so over + + + align:start position:0% +you can run your object sector so over +your video and you can look at your + + align:start position:0% +your video and you can look at your + + + align:start position:0% +your video and you can look at your +sentence and you can look at the nouns + + align:start position:0% +sentence and you can look at the nouns + + + align:start position:0% +sentence and you can look at the nouns +and say okay so I have people on horses + + align:start position:0% +and say okay so I have people on horses + + + align:start position:0% +and say okay so I have people on horses +inside the sentence and you can say okay + + align:start position:0% +inside the sentence and you can say okay + + + align:start position:0% +inside the sentence and you can say okay +well if I have people horses I need two + + align:start position:0% +well if I have people horses I need two + + + align:start position:0% +well if I have people horses I need two +trackers but you can look at a little + + align:start position:0% +trackers but you can look at a little + + + align:start position:0% +trackers but you can look at a little +bit more at your sentence and see that + + align:start position:0% +bit more at your sentence and see that + + + align:start position:0% +bit more at your sentence and see that +oh well it's the other horse so you + + align:start position:0% +oh well it's the other horse so you + + + align:start position:0% +oh well it's the other horse so you +analyze your sentence and you can + + align:start position:0% +analyze your sentence and you can + + + align:start position:0% +analyze your sentence and you can +determine there are three participants + + align:start position:0% +determine there are three participants + + + align:start position:0% +determine there are three participants +in the event described by the sentence + + align:start position:0% +in the event described by the sentence + + + align:start position:0% +in the event described by the sentence +there's a person and two horses once + + align:start position:0% +there's a person and two horses once + + + align:start position:0% +there's a person and two horses once +agent once the patient the the thing + + align:start position:0% +agent once the patient the the thing + + + align:start position:0% +agent once the patient the the thing +that's being ridden and wants source the + + align:start position:0% +that's being ridden and wants source the + + + align:start position:0% +that's being ridden and wants source the +thing that is being left does that make + + align:start position:0% +thing that is being left does that make + + + align:start position:0% +thing that is being left does that make +sense + + align:start position:0% +sense + + + align:start position:0% +sense +awesome so now given a sentence we know + + align:start position:0% +awesome so now given a sentence we know + + + align:start position:0% +awesome so now given a sentence we know +that we need n trackers and for every + + align:start position:0% +that we need n trackers and for every + + + align:start position:0% +that we need n trackers and for every +word we can have a hidden Markov model + + align:start position:0% +word we can have a hidden Markov model + + + align:start position:0% +word we can have a hidden Markov model +right we can have a hidden Markov model + + align:start position:0% +right we can have a hidden Markov model + + + align:start position:0% +right we can have a hidden Markov model +for a ride it's just another verb and we + + align:start position:0% +for a ride it's just another verb and we + + + align:start position:0% +for a ride it's just another verb and we +just have to be careful how we build a + + align:start position:0% +just have to be careful how we build a + + + align:start position:0% +just have to be careful how we build a +feature vector for a ride + + align:start position:0% +feature vector for a ride + + + align:start position:0% +feature vector for a ride +because if we build it in one way we're + + align:start position:0% +because if we build it in one way we're + + + align:start position:0% +because if we build it in one way we're +gonna detect the person rode the horse + + align:start position:0% +gonna detect the person rode the horse + + + align:start position:0% +gonna detect the person rode the horse +and if we build it in the opposite way + + align:start position:0% +and if we build it in the opposite way + + + align:start position:0% +and if we build it in the opposite way +by concatenative the vectors the other + + align:start position:0% +by concatenative the vectors the other + + + align:start position:0% +by concatenative the vectors the other +way around + + align:start position:0% +way around + + + align:start position:0% +way around +we're gonna detect the horse rode the + + align:start position:0% +we're gonna detect the horse rode the + + + align:start position:0% +we're gonna detect the horse rode the +person which is not what we want we can + + align:start position:0% +person which is not what we want we can + + + align:start position:0% +person which is not what we want we can +also detect all all this kind of a weird + + align:start position:0% +also detect all all this kind of a weird + + + align:start position:0% +also detect all all this kind of a weird +hidden Markov model right it has only a + + align:start position:0% +hidden Markov model right it has only a + + + align:start position:0% +hidden Markov model right it has only a +single state but it's still an markov + + align:start position:0% +single state but it's still an markov + + + align:start position:0% +single state but it's still an markov +model it just wants to see that this + + align:start position:0% +model it just wants to see that this + + + align:start position:0% +model it just wants to see that this +object is tall so maybe it's aspect + + align:start position:0% +object is tall so maybe it's aspect + + + align:start position:0% +object is tall so maybe it's aspect +ratio is more than the mean aspect ratio + + align:start position:0% +ratio is more than the mean aspect ratio + + + align:start position:0% +ratio is more than the mean aspect ratio +of objects of this class but nonetheless + + align:start position:0% +of objects of this class but nonetheless + + + align:start position:0% +of objects of this class but nonetheless +it still fits into this paradigm we can + + align:start position:0% +it still fits into this paradigm we can + + + align:start position:0% +it still fits into this paradigm we can +do the same thing for quickly we can + + align:start position:0% +do the same thing for quickly we can + + + align:start position:0% +do the same thing for quickly we can +have it a trimmer for that we can do a + + align:start position:0% +have it a trimmer for that we can do a + + + align:start position:0% +have it a trimmer for that we can do a +left where we can do away from away from + + align:start position:0% +left where we can do away from away from + + + align:start position:0% +left where we can do away from away from +looks a lot like leave right that's the + + align:start position:0% +looks a lot like leave right that's the + + + align:start position:0% +looks a lot like leave right that's the +same saying meaning and basically we end + + align:start position:0% +same saying meaning and basically we end + + + align:start position:0% +same saying meaning and basically we end +up with this bipartite graph at the top + + align:start position:0% +up with this bipartite graph at the top + + + align:start position:0% +up with this bipartite graph at the top +we have lattices that represent words + + align:start position:0% +we have lattices that represent words + + + align:start position:0% +we have lattices that represent words +each word has a hidden Markov model and + + align:start position:0% +each word has a hidden Markov model and + + + align:start position:0% +each word has a hidden Markov model and +in the middle we have lattices that + + align:start position:0% +in the middle we have lattices that + + + align:start position:0% +in the middle we have lattices that +represent trackers we can combine them + + align:start position:0% +represent trackers we can combine them + + + align:start position:0% +represent trackers we can combine them +together according to the links and you + + align:start position:0% +together according to the links and you + + + align:start position:0% +together according to the links and you +can get these links from your favorite + + align:start position:0% +can get these links from your favorite + + + align:start position:0% +can get these links from your favorite +dependency parser you can get them from + + align:start position:0% +dependency parser you can get them from + + + align:start position:0% +dependency parser you can get them from +Boris will start system any language + + align:start position:0% +Boris will start system any language + + + align:start position:0% +Boris will start system any language +analysis system will give you this so + + align:start position:0% +analysis system will give you this so + + + align:start position:0% +analysis system will give you this so +this is actually all the heavy lifting + + align:start position:0% +this is actually all the heavy lifting + + + align:start position:0% +this is actually all the heavy lifting +that we have to do everything from now + + align:start position:0% +that we have to do everything from now + + + align:start position:0% +that we have to do everything from now +on is kind of eye candy one thing that + + align:start position:0% +on is kind of eye candy one thing that + + + align:start position:0% +on is kind of eye candy one thing that +we really wanted to make sure that + + align:start position:0% +we really wanted to make sure that + + + align:start position:0% +we really wanted to make sure that +system was doing is that we could + + align:start position:0% +system was doing is that we could + + + align:start position:0% +system was doing is that we could +distinguish different sentences so we + + align:start position:0% +distinguish different sentences so we + + + align:start position:0% +distinguish different sentences so we +tried to come up with an experiment that + + align:start position:0% +tried to come up with an experiment that + + + align:start position:0% +tried to come up with an experiment that +is in some way maximally difficult where + + align:start position:0% +is in some way maximally difficult where + + + align:start position:0% +is in some way maximally difficult where +events are going to happen at the same + + align:start position:0% +events are going to happen at the same + + + align:start position:0% +events are going to happen at the same +time so you can't use time in order to + + align:start position:0% +time so you can't use time in order to + + + align:start position:0% +time so you can't use time in order to +distinguish them and the sentences only + + align:start position:0% +distinguish them and the sentences only + + + align:start position:0% +distinguish them and the sentences only +differ in one word or one lexical item + + align:start position:0% +differ in one word or one lexical item + + + align:start position:0% +differ in one word or one lexical item +so in this case we have a sentence like + + align:start position:0% +so in this case we have a sentence like + + + align:start position:0% +so in this case we have a sentence like +the person picked up an object and + + align:start position:0% +the person picked up an object and + + + align:start position:0% +the person picked up an object and +person put down an object this there are + + align:start position:0% +person put down an object this there are + + + align:start position:0% +person put down an object this there are +two systems that are running one is + + align:start position:0% +two systems that are running one is + + + align:start position:0% +two systems that are running one is +running on one sentence one is running + + align:start position:0% +running on one sentence one is running + + + align:start position:0% +running on one sentence one is running +on the other sentence you're gonna see + + align:start position:0% +on the other sentence you're gonna see + + + align:start position:0% +on the other sentence you're gonna see +the same video play twice side by side + + align:start position:0% +the same video play twice side by side + + + align:start position:0% +the same video play twice side by side +and you can already see that one system + + align:start position:0% +and you can already see that one system + + + align:start position:0% +and you can already see that one system +when we primed it to look for pickup it + + align:start position:0% +when we primed it to look for pickup it + + + align:start position:0% +when we primed it to look for pickup it +detect me picking up my backpack and + + align:start position:0% +detect me picking up my backpack and + + + align:start position:0% +detect me picking up my backpack and +then the other one had detected one of + + align:start position:0% +then the other one had detected one of + + + align:start position:0% +then the other one had detected one of +my lab mates + + align:start position:0% +my lab mates + + + align:start position:0% +my lab mates +picking up a bin so the only way it + + align:start position:0% +picking up a bin so the only way it + + + align:start position:0% +picking up a bin so the only way it +could focus its attention on the right + + align:start position:0% +could focus its attention on the right + + + align:start position:0% +could focus its attention on the right +object is if it understood the + + align:start position:0% +object is if it understood the + + + align:start position:0% +object is if it understood the +distinction between these two sentences + + align:start position:0% +distinction between these two sentences + + + align:start position:0% +distinction between these two sentences +Rafi was able to represent them so we + + align:start position:0% +Rafi was able to represent them so we + + + align:start position:0% +Rafi was able to represent them so we +can play this game many many times over + + align:start position:0% +can play this game many many times over + + + align:start position:0% +can play this game many many times over +we can have it pay attention to the + + align:start position:0% +we can have it pay attention to the + + + align:start position:0% +we can have it pay attention to the +subject is a backpack approaches + + align:start position:0% +subject is a backpack approaches + + + align:start position:0% +subject is a backpack approaches +something or is a chair approaching + + align:start position:0% +something or is a chair approaching + + + align:start position:0% +something or is a chair approaching +something we can have it pay attention + + align:start position:0% +something we can have it pay attention + + + align:start position:0% +something we can have it pay attention +to the color of an object is the red + + align:start position:0% +to the color of an object is the red + + + align:start position:0% +to the color of an object is the red +object approaching something or a blue + + align:start position:0% +object approaching something or a blue + + + align:start position:0% +object approaching something or a blue +object approaching something we can have + + align:start position:0% +object approaching something we can have + + + align:start position:0% +object approaching something we can have +it pay attention to a preposition is + + align:start position:0% +it pay attention to a preposition is + + + align:start position:0% +it pay attention to a preposition is +someone picking up an object to the left + + align:start position:0% +someone picking up an object to the left + + + align:start position:0% +someone picking up an object to the left +of something or to the right of + + align:start position:0% +of something or to the right of + + + align:start position:0% +of something or to the right of +something and we have many many dozens + + align:start position:0% +something and we have many many dozens + + + align:start position:0% +something and we have many many dozens +or hundreds of these and won't bore you + + align:start position:0% +or hundreds of these and won't bore you + + + align:start position:0% +or hundreds of these and won't bore you +with all of them but the important part + + align:start position:0% +with all of them but the important part + + + align:start position:0% +with all of them but the important part +is we can handle lots and lots of + + align:start position:0% +is we can handle lots and lots of + + + align:start position:0% +is we can handle lots and lots of +different parts of speech and we can + + align:start position:0% +different parts of speech and we can + + + align:start position:0% +different parts of speech and we can +still represent them and we can still be + + align:start position:0% +still represent them and we can still be + + + align:start position:0% +still represent them and we can still be +sensitive to these subtle distinctions + + align:start position:0% +sensitive to these subtle distinctions + + + align:start position:0% +sensitive to these subtle distinctions +in the meanings of the sentences all + + align:start position:0% +in the meanings of the sentences all + + + align:start position:0% +in the meanings of the sentences all +right so we did all the hard work and we + + align:start position:0% +right so we did all the hard work and we + + + align:start position:0% +right so we did all the hard work and we +actually built this recognizer the score + + align:start position:0% +actually built this recognizer the score + + + align:start position:0% +actually built this recognizer the score +of a sentence given a video and now it + + align:start position:0% +of a sentence given a video and now it + + + align:start position:0% +of a sentence given a video and now it +turns out that we can reformulate all of + + align:start position:0% +turns out that we can reformulate all of + + + align:start position:0% +turns out that we can reformulate all of +these other tasks in terms of this one + + align:start position:0% +these other tasks in terms of this one + + + align:start position:0% +these other tasks in terms of this one +score and it's going to do all the heavy + + align:start position:0% +score and it's going to do all the heavy + + + align:start position:0% +score and it's going to do all the heavy +lifting for us so when we tune the + + align:start position:0% +lifting for us so when we tune the + + + align:start position:0% +lifting for us so when we tune the +parameters of whatever goes into the + + align:start position:0% +parameters of whatever goes into the + + + align:start position:0% +parameters of whatever goes into the +scoring function we're gonna get the + + align:start position:0% +scoring function we're gonna get the + + + align:start position:0% +scoring function we're gonna get the +ability to do all these other tasks so + + align:start position:0% +ability to do all these other tasks so + + + align:start position:0% +ability to do all these other tasks so +let's look at retrieval it's a most + + align:start position:0% +let's look at retrieval it's a most + + + align:start position:0% +let's look at retrieval it's a most +straightforward kind of test right it's + + align:start position:0% +straightforward kind of test right it's + + + align:start position:0% +straightforward kind of test right it's +what YouTube does for you you go to + + align:start position:0% +what YouTube does for you you go to + + + align:start position:0% +what YouTube does for you you go to +youtube you type in a query and YouTube + + align:start position:0% +youtube you type in a query and YouTube + + + align:start position:0% +youtube you type in a query and YouTube +comes back with some answers so let's + + align:start position:0% +comes back with some answers so let's + + + align:start position:0% +comes back with some answers so let's +see what YouTube actually does if you + + align:start position:0% +see what YouTube actually does if you + + + align:start position:0% +see what YouTube actually does if you +look at YouTube and if you look at + + align:start position:0% +look at YouTube and if you look at + + + align:start position:0% +look at YouTube and if you look at +something like pick up you get men + + align:start position:0% +something like pick up you get men + + + align:start position:0% +something like pick up you get men +picking up women if you look at approach + + align:start position:0% +picking up women if you look at approach + + + align:start position:0% +picking up women if you look at approach +you get men picking up women if you look + + align:start position:0% +you get men picking up women if you look + + + align:start position:0% +you get men picking up women if you look +at put down once upon a time you did get + + align:start position:0% +at put down once upon a time you did get + + + align:start position:0% +at put down once upon a time you did get +men picking up women but rap is now more + + align:start position:0% +men picking up women but rap is now more + + + align:start position:0% +men picking up women but rap is now more +popular if you ask something more + + align:start position:0% +popular if you ask something more + + + align:start position:0% +popular if you ask something more +interesting the person approach the + + align:start position:0% +interesting the person approach the + + + align:start position:0% +interesting the person approach the +other person you don't get videos where + + align:start position:0% +other person you don't get videos where + + + align:start position:0% +other person you don't get videos where +people approach each other you get + + align:start position:0% +people approach each other you get + + + align:start position:0% +people approach each other you get +videos about how you should approach + + align:start position:0% +videos about how you should approach + + + align:start position:0% +videos about how you should approach +women I didn't select these I typed them + + align:start position:0% +women I didn't select these I typed them + + + align:start position:0% +women I didn't select these I typed them +in and this is just what happened if you + + align:start position:0% +in and this is just what happened if you + + + align:start position:0% +in and this is just what happened if you +type in like the person approach the cat + + align:start position:0% +type in like the person approach the cat + + + align:start position:0% +type in like the person approach the cat +you get lots of people playing with cats + + align:start position:0% +you get lots of people playing with cats + + + align:start position:0% +you get lots of people playing with cats +but no one approaching cats including a + + align:start position:0% +but no one approaching cats including a + + + align:start position:0% +but no one approaching cats including a +lynx that's kind of kind of scary and an + + align:start position:0% +lynx that's kind of kind of scary and an + + + align:start position:0% +lynx that's kind of kind of scary and an +Airbus landing and I have no idea what + + align:start position:0% +Airbus landing and I have no idea what + + + align:start position:0% +Airbus landing and I have no idea what +that means so what we did is we build + + align:start position:0% +that means so what we did is we build + + + align:start position:0% +that means so what we did is we build +the video retrieval system that actually + + align:start position:0% +the video retrieval system that actually + + + align:start position:0% +the video retrieval system that actually +understand what's going on in the videos + + align:start position:0% +understand what's going on in the videos + + + align:start position:0% +understand what's going on in the videos +as opposed to just looking at the tags + + align:start position:0% +as opposed to just looking at the tags + + + align:start position:0% +as opposed to just looking at the tags +that the people apply to these videos + + align:start position:0% +that the people apply to these videos + + + align:start position:0% +that the people apply to these videos +people don't describe what's going on + + align:start position:0% +people don't describe what's going on + + + align:start position:0% +people don't describe what's going on +people describe some high-level concept + + align:start position:0% +people describe some high-level concept + + + align:start position:0% +people describe some high-level concept +so we took a whole bunch of object + + align:start position:0% +so we took a whole bunch of object + + + align:start position:0% +so we took a whole bunch of object +detectors that are completely off the + + align:start position:0% +detectors that are completely off the + + + align:start position:0% +detectors that are completely off the +shelf + + align:start position:0% +shelf + + + align:start position:0% +shelf +people on four horses and we took ten + + align:start position:0% +people on four horses and we took ten + + + align:start position:0% +people on four horses and we took ten +Hollywood movies nominally they're all + + align:start position:0% +Hollywood movies nominally they're all + + + align:start position:0% +Hollywood movies nominally they're all +westerns they involve people on horses + + align:start position:0% +westerns they involve people on horses + + + align:start position:0% +westerns they involve people on horses +and the reason why we chose people on + + align:start position:0% +and the reason why we chose people on + + + align:start position:0% +and the reason why we chose people on +horses is because people horses tend to + + align:start position:0% +horses is because people horses tend to + + + align:start position:0% +horses is because people horses tend to +be fairly larger than the field of view + + align:start position:0% +be fairly larger than the field of view + + + align:start position:0% +be fairly larger than the field of view +and given that object actor suck so much + + align:start position:0% +and given that object actor suck so much + + + align:start position:0% +and given that object actor suck so much +we thought we should kind of help the + + align:start position:0% +we thought we should kind of help the + + + align:start position:0% +we thought we should kind of help the +system along as best we could so we + + align:start position:0% +system along as best we could so we + + + align:start position:0% +system along as best we could so we +build the system it's a system that + + align:start position:0% +build the system it's a system that + + + align:start position:0% +build the system it's a system that +knows about three verbs it knows about + + align:start position:0% +knows about three verbs it knows about + + + align:start position:0% +knows about three verbs it knows about +two nouns personnel horse it knows about + + align:start position:0% +two nouns personnel horse it knows about + + + align:start position:0% +two nouns personnel horse it knows about +some adverbs quickly and slowly it knows + + align:start position:0% +some adverbs quickly and slowly it knows + + + align:start position:0% +some adverbs quickly and slowly it knows +about some prepositions left or right + + align:start position:0% +about some prepositions left or right + + + align:start position:0% +about some prepositions left or right +words towards away from and given this + + align:start position:0% +words towards away from and given this + + + align:start position:0% +words towards away from and given this +template you can generate about two or + + align:start position:0% +template you can generate about two or + + + align:start position:0% +template you can generate about two or +three hundred different sentences so we + + align:start position:0% +three hundred different sentences so we + + + align:start position:0% +three hundred different sentences so we +can type in something like the person + + align:start position:0% +can type in something like the person + + + align:start position:0% +can type in something like the person +rode the horse and we can get a bunch of + + align:start position:0% +rode the horse and we can get a bunch of + + + align:start position:0% +rode the horse and we can get a bunch of +results so you can see we were 90 + + align:start position:0% +results so you can see we were 90 + + + align:start position:0% +results so you can see we were 90 +percent accurate in the top 10 results + + align:start position:0% +percent accurate in the top 10 results + + + align:start position:0% +percent accurate in the top 10 results +you can see these are really videos of + + align:start position:0% +you can see these are really videos of + + + align:start position:0% +you can see these are really videos of +people riding horses the way this works + + align:start position:0% +people riding horses the way this works + + + align:start position:0% +people riding horses the way this works +is we took one of these long videos we + + align:start position:0% +is we took one of these long videos we + + + align:start position:0% +is we took one of these long videos we +chopped it up into many small segments + + align:start position:0% +chopped it up into many small segments + + + align:start position:0% +chopped it up into many small segments +and we ran over each individual segment + + align:start position:0% +and we ran over each individual segment + + + align:start position:0% +and we ran over each individual segment +you could run it over the whole video + + align:start position:0% +you could run it over the whole video + + + align:start position:0% +you could run it over the whole video +but then it would just classified the + + align:start position:0% +but then it would just classified the + + + align:start position:0% +but then it would just classified the +whole video because it's an hmm we would + + align:start position:0% +whole video because it's an hmm we would + + + align:start position:0% +whole video because it's an hmm we would +sort of adapt to the length of the video + + align:start position:0% +sort of adapt to the length of the video + + + align:start position:0% +sort of adapt to the length of the video +we can also ask for other kinds of + + align:start position:0% +we can also ask for other kinds of + + + align:start position:0% +we can also ask for other kinds of +queries like the person rode the horse + + align:start position:0% +queries like the person rode the horse + + + align:start position:0% +queries like the person rode the horse +quickly you can see we got videos that + + align:start position:0% +quickly you can see we got videos that + + + align:start position:0% +quickly you can see we got videos that +really are quicker we can ask for + + align:start position:0% +really are quicker we can ask for + + + align:start position:0% +really are quicker we can ask for +something more ambitious like the person + + align:start position:0% +something more ambitious like the person + + + align:start position:0% +something more ambitious like the person +rode the horse quickly rightward and we + + align:start position:0% +rode the horse quickly rightward and we + + + align:start position:0% +rode the horse quickly rightward and we +get videos where people are riding + + align:start position:0% +get videos where people are riding + + + align:start position:0% +get videos where people are riding +horses right word all right so we we did + + align:start position:0% +horses right word all right so we we did + + + align:start position:0% +horses right word all right so we we did +the hard work of building this + + align:start position:0% +the hard work of building this + + + align:start position:0% +the hard work of building this +recognition system and we saw we can use + + align:start position:0% +recognition system and we saw we can use + + + align:start position:0% +recognition system and we saw we can use +it for another task which is retrieval + + align:start position:0% +it for another task which is retrieval + + + align:start position:0% +it for another task which is retrieval +but let's do something else let's + + align:start position:0% +but let's do something else let's + + + align:start position:0% +but let's do something else let's +regeneration someone asked about + + align:start position:0% +regeneration someone asked about + + + align:start position:0% +regeneration someone asked about +generation earlier generation is very + + align:start position:0% +generation earlier generation is very + + + align:start position:0% +generation earlier generation is very +similar to retrieval right in retrieval + + align:start position:0% +similar to retrieval right in retrieval + + + align:start position:0% +similar to retrieval right in retrieval +we had was we had a fixed sentence and + + align:start position:0% +we had was we had a fixed sentence and + + + align:start position:0% +we had was we had a fixed sentence and +we searched over all our videos to see + + align:start position:0% +we searched over all our videos to see + + + align:start position:0% +we searched over all our videos to see +which ones were the best match here we + + align:start position:0% +which ones were the best match here we + + + align:start position:0% +which ones were the best match here we +have a fixed video and we're gonna + + align:start position:0% +have a fixed video and we're gonna + + + align:start position:0% +have a fixed video and we're gonna +search over all our sentences the only + + align:start position:0% +search over all our sentences the only + + + align:start position:0% +search over all our sentences the only +trick is you have a language model so we + + align:start position:0% +trick is you have a language model so we + + + align:start position:0% +trick is you have a language model so we +can generate a huge number of sentences + + align:start position:0% +can generate a huge number of sentences + + + align:start position:0% +can generate a huge number of sentences +but we're going to see that's okay so we + + align:start position:0% +but we're going to see that's okay so we + + + align:start position:0% +but we're going to see that's okay so we +have a language model it's very very + + align:start position:0% +have a language model it's very very + + + align:start position:0% +have a language model it's very very +small model by Boris's standards or the + + align:start position:0% +small model by Boris's standards or the + + + align:start position:0% +small model by Boris's standards or the +bar the standard of NLP we have only + + align:start position:0% +bar the standard of NLP we have only + + + align:start position:0% +bar the standard of NLP we have only +four verbs to add to adjectives only + + align:start position:0% +four verbs to add to adjectives only + + + align:start position:0% +four verbs to add to adjectives only +four nouns some adverbs etc but the + + align:start position:0% +four nouns some adverbs etc but the + + + align:start position:0% +four nouns some adverbs etc but the +important part is even if we ignore + + align:start position:0% +important part is even if we ignore + + + align:start position:0% +important part is even if we ignore +recursion we have a tremendous number of + + align:start position:0% +recursion we have a tremendous number of + + + align:start position:0% +recursion we have a tremendous number of +sentences and this model is recursive so + + align:start position:0% +sentences and this model is recursive so + + + align:start position:0% +sentences and this model is recursive so +we can really generate + + align:start position:0% +we can really generate + + + align:start position:0% +we can really generate +an infinite number of sentences for men + + align:start position:0% +an infinite number of sentences for men + + + align:start position:0% +an infinite number of sentences for men +but nonetheless it turns out that you + + align:start position:0% +but nonetheless it turns out that you + + + align:start position:0% +but nonetheless it turns out that you +can search the space of sentences very + + align:start position:0% +can search the space of sentences very + + + align:start position:0% +can search the space of sentences very +very efficiently and actually find the + + align:start position:0% +very efficiently and actually find the + + + align:start position:0% +very efficiently and actually find the +global optimum and the intuition provide + + align:start position:0% +global optimum and the intuition provide + + + align:start position:0% +global optimum and the intuition provide +that's true is pretty straightforward + + align:start position:0% +that's true is pretty straightforward + + + align:start position:0% +that's true is pretty straightforward +you can think of your sentence as a + + align:start position:0% +you can think of your sentence as a + + + align:start position:0% +you can think of your sentence as a +constraint on what you can see in the + + align:start position:0% +constraint on what you can see in the + + + align:start position:0% +constraint on what you can see in the +world the longer your sentence the more + + align:start position:0% +world the longer your sentence the more + + + align:start position:0% +world the longer your sentence the more +constraints you have so the lower the + + align:start position:0% +constraints you have so the lower the + + + align:start position:0% +constraints you have so the lower the +overall scores so every time you add a + + align:start position:0% +overall scores so every time you add a + + + align:start position:0% +overall scores so every time you add a +word the score can't possibly increase + + align:start position:0% +word the score can't possibly increase + + + align:start position:0% +word the score can't possibly increase +right the score has to always decrease + + align:start position:0% +right the score has to always decrease + + + align:start position:0% +right the score has to always decrease +so basically you have this monotonically + + align:start position:0% +so basically you have this monotonically + + + align:start position:0% +so basically you have this monotonically +decreasing function over a lattice of + + align:start position:0% +decreasing function over a lattice of + + + align:start position:0% +decreasing function over a lattice of +sentences and if you ignore the fact + + align:start position:0% +sentences and if you ignore the fact + + + align:start position:0% +sentences and if you ignore the fact +that you only have to search sentences + + align:start position:0% +that you only have to search sentences + + + align:start position:0% +that you only have to search sentences +you can start off with individual words + + align:start position:0% +you can start off with individual words + + + align:start position:0% +you can start off with individual words +aggregate words together so you look at + + align:start position:0% +aggregate words together so you look at + + + align:start position:0% +aggregate words together so you look at +all one word phrases you can look at two + + align:start position:0% +all one word phrases you can look at two + + + align:start position:0% +all one word phrases you can look at two +word phrases three or phrases eventually + + align:start position:0% +word phrases three or phrases eventually + + + align:start position:0% +word phrases three or phrases eventually +eventually get out to real sentences but + + align:start position:0% +eventually get out to real sentences but + + + align:start position:0% +eventually get out to real sentences but +because this is a monotonically + + align:start position:0% +because this is a monotonically + + + align:start position:0% +because this is a monotonically +decreasing function this is a very quick + + align:start position:0% +decreasing function this is a very quick + + + align:start position:0% +decreasing function this is a very quick +search so you can start off with an + + align:start position:0% +search so you can start off with an + + + align:start position:0% +search so you can start off with an +empty set you can add a word so for + + align:start position:0% +empty set you can add a word so for + + + align:start position:0% +empty set you can add a word so for +example you cannot carry it you can look + + align:start position:0% +example you cannot carry it you can look + + + align:start position:0% +example you cannot carry it you can look +at all the ways that you can extend + + align:start position:0% +at all the ways that you can extend + + + align:start position:0% +at all the ways that you can extend +carried with another word or two so you + + align:start position:0% +carried with another word or two so you + + + align:start position:0% +carried with another word or two so you +get a phrase like the person carried and + + align:start position:0% +get a phrase like the person carried and + + + align:start position:0% +get a phrase like the person carried and +you could keep adding words to it until + + align:start position:0% +you could keep adding words to it until + + + align:start position:0% +you could keep adding words to it until +you get to the global optimum so given a + + align:start position:0% +you get to the global optimum so given a + + + align:start position:0% +you get to the global optimum so given a +video like this here you see me doing + + align:start position:0% +video like this here you see me doing + + + align:start position:0% +video like this here you see me doing +something you can produce a sentence + + align:start position:0% +something you can produce a sentence + + + align:start position:0% +something you can produce a sentence +like the person to the right of them and + + align:start position:0% +like the person to the right of them and + + + align:start position:0% +like the person to the right of them and +picked up the backpack and that that's + + align:start position:0% +picked up the backpack and that that's + + + align:start position:0% +picked up the backpack and that that's +pretty straightforward we built a + + align:start position:0% +pretty straightforward we built a + + + align:start position:0% +pretty straightforward we built a +generator in just a few lines of code as + + align:start position:0% +generator in just a few lines of code as + + + align:start position:0% +generator in just a few lines of code as +long as we had a recognition system so + + align:start position:0% +long as we had a recognition system so + + + align:start position:0% +long as we had a recognition system so +you have this problem question answering + + align:start position:0% +you have this problem question answering + + + align:start position:0% +you have this problem question answering +that you have to connect two sentences + + align:start position:0% +that you have to connect two sentences + + + align:start position:0% +that you have to connect two sentences +with the video and instead of doing that + + align:start position:0% +with the video and instead of doing that + + + align:start position:0% +with the video and instead of doing that +what we're gonna do is we're gonna make + + align:start position:0% +what we're gonna do is we're gonna make + + + align:start position:0% +what we're gonna do is we're gonna make +some connection between two sentences so + + align:start position:0% +some connection between two sentences so + + + align:start position:0% +some connection between two sentences so +we're gonna take our question we're + + align:start position:0% +we're gonna take our question we're + + + align:start position:0% +we're gonna take our question we're +gonna give it to something like Boris + + align:start position:0% +gonna give it to something like Boris + + + align:start position:0% +gonna give it to something like Boris +the system and it's gonna tell us this + + align:start position:0% +the system and it's gonna tell us this + + + align:start position:0% +the system and it's gonna tell us this +question like what did the person put on + + align:start position:0% +question like what did the person put on + + + align:start position:0% +question like what did the person put on +top of the red car if you wanted to + + align:start position:0% +top of the red car if you wanted to + + + align:start position:0% +top of the red car if you wanted to +answer it you have produced an answer + + align:start position:0% +answer it you have produced an answer + + + align:start position:0% +answer it you have produced an answer +like the person put some noun phrase on + + align:start position:0% +like the person put some noun phrase on + + + align:start position:0% +like the person put some noun phrase on +top of the red car so you can run the + + align:start position:0% +top of the red car so you can run the + + + align:start position:0% +top of the red car so you can run the +generation system exactly as was + + align:start position:0% +generation system exactly as was + + + align:start position:0% +generation system exactly as was +suggested you seed it with this you give + + align:start position:0% +suggested you seed it with this you give + + + align:start position:0% +suggested you seed it with this you give +it a constraint that would it has to + + align:start position:0% +it a constraint that would it has to + + + align:start position:0% +it a constraint that would it has to +produce next inside this empty gap is a + + align:start position:0% +produce next inside this empty gap is a + + + align:start position:0% +produce next inside this empty gap is a +noun phrase and you're gonna get out the + + align:start position:0% +noun phrase and you're gonna get out the + + + align:start position:0% +noun phrase and you're gonna get out the +answer another way to think about this + + align:start position:0% +answer another way to think about this + + + align:start position:0% +answer another way to think about this +is you have sort of a partial detector + + align:start position:0% +is you have sort of a partial detector + + + align:start position:0% +is you have sort of a partial detector +you look inside the video to see where + + align:start position:0% +you look inside the video to see where + + + align:start position:0% +you look inside the video to see where +it matches you choose the best region + + align:start position:0% +it matches you choose the best region + + + align:start position:0% +it matches you choose the best region +where it matches and then you complete + + align:start position:0% +where it matches and then you complete + + + align:start position:0% +where it matches and then you complete +your sentence when you get an answer + + align:start position:0% +your sentence when you get an answer + + + align:start position:0% +your sentence when you get an answer +like the person put the pair on top of + + align:start position:0% +like the person put the pair on top of + + + align:start position:0% +like the person put the pair on top of +the red car + + align:start position:0% +the red car + + + align:start position:0% +the red car +there's there's one small problem with + + align:start position:0% +there's there's one small problem with + + + align:start position:0% +there's there's one small problem with +question-answering and it differs from + + align:start position:0% +question-answering and it differs from + + + align:start position:0% +question-answering and it differs from +generation in one way so imagine that + + align:start position:0% +generation in one way so imagine that + + + align:start position:0% +generation in one way so imagine that +we're in a parking lot and there are a + + align:start position:0% +we're in a parking lot and there are a + + + align:start position:0% +we're in a parking lot and there are a +hundred white cars on the side this + + align:start position:0% +hundred white cars on the side this + + + align:start position:0% +hundred white cars on the side this +parking lot and you come to me desperate + + align:start position:0% +parking lot and you come to me desperate + + + align:start position:0% +parking lot and you come to me desperate +and you say I lost my keys and I say + + align:start position:0% +and you say I lost my keys and I say + + + align:start position:0% +and you say I lost my keys and I say +don't worry I know exactly where your + + align:start position:0% +don't worry I know exactly where your + + + align:start position:0% +don't worry I know exactly where your +keys are and you look at me and I say + + align:start position:0% +keys are and you look at me and I say + + + align:start position:0% +keys are and you look at me and I say +they're in the white car and then you + + align:start position:0% +they're in the white car and then you + + + align:start position:0% +they're in the white car and then you +think I'm a complete because + + align:start position:0% +think I'm a complete because + + + align:start position:0% +think I'm a complete because +that was totally worthless information + + align:start position:0% +that was totally worthless information + + + align:start position:0% +that was totally worthless information +right I told you something that's + + align:start position:0% +right I told you something that's + + + align:start position:0% +right I told you something that's +basically true it's a parking lot full + + align:start position:0% +basically true it's a parking lot full + + + align:start position:0% +basically true it's a parking lot full +of white cars but isn't actually giving + + align:start position:0% +of white cars but isn't actually giving + + + align:start position:0% +of white cars but isn't actually giving +you anything useful so to handle this in + + align:start position:0% +you anything useful so to handle this in + + + align:start position:0% +you anything useful so to handle this in +the same way that in generation we had + + align:start position:0% +the same way that in generation we had + + + align:start position:0% +the same way that in generation we had +this one parameter that we could tune to + + align:start position:0% +this one parameter that we could tune to + + + align:start position:0% +this one parameter that we could tune to +get more or less for both sentences + + align:start position:0% +get more or less for both sentences + + + align:start position:0% +get more or less for both sentences +we're gonna add only one parameter to + + align:start position:0% +we're gonna add only one parameter to + + + align:start position:0% +we're gonna add only one parameter to +question-answering which is kind of a + + align:start position:0% +question-answering which is kind of a + + + align:start position:0% +question-answering which is kind of a +truthfulness parameter which basically + + align:start position:0% +truthfulness parameter which basically + + + align:start position:0% +truthfulness parameter which basically +is going to say this sentence the person + + align:start position:0% +is going to say this sentence the person + + + align:start position:0% +is going to say this sentence the person +put a put an object on top of the red + + align:start position:0% +put a put an object on top of the red + + + align:start position:0% +put a put an object on top of the red +car in this video is very ambiguous + + align:start position:0% +car in this video is very ambiguous + + + align:start position:0% +car in this video is very ambiguous +right it could either be Danny that did + + align:start position:0% +right it could either be Danny that did + + + align:start position:0% +right it could either be Danny that did +it or it could be me that puts something + + align:start position:0% +it or it could be me that puts something + + + align:start position:0% +it or it could be me that puts something +on top of the red car so what we're + + align:start position:0% +on top of the red car so what we're + + + align:start position:0% +on top of the red car so what we're +gonna do is we're gonna take this + + align:start position:0% +gonna do is we're gonna take this + + + align:start position:0% +gonna do is we're gonna take this +candidate's answer we're gonna run it + + align:start position:0% +candidate's answer we're gonna run it + + + align:start position:0% +candidate's answer we're gonna run it +over the video and we're gonna see how + + align:start position:0% +over the video and we're gonna see how + + + align:start position:0% +over the video and we're gonna see how +many times it has really close matches + + align:start position:0% +many times it has really close matches + + + align:start position:0% +many times it has really close matches +in the video and depending on this one + + align:start position:0% +in the video and depending on this one + + + align:start position:0% +in the video and depending on this one +parameter we're gonna say you're allowed + + align:start position:0% +parameter we're gonna say you're allowed + + + align:start position:0% +parameter we're gonna say you're allowed +to say more things about the video to + + align:start position:0% +to say more things about the video to + + + align:start position:0% +to say more things about the video to +become more specific about what you're + + align:start position:0% +become more specific about what you're + + + align:start position:0% +become more specific about what you're +referring to but potentially slightly + + align:start position:0% +referring to but potentially slightly + + + align:start position:0% +referring to but potentially slightly +less true because the score will be + + align:start position:0% +less true because the score will be + + + align:start position:0% +less true because the score will be +lower in the same way that you were + + align:start position:0% +lower in the same way that you were + + + align:start position:0% +lower in the same way that you were +saying slightly more in the generation + + align:start position:0% +saying slightly more in the generation + + + align:start position:0% +saying slightly more in the generation +case at the risk of saying potentially + + align:start position:0% +case at the risk of saying potentially + + + align:start position:0% +case at the risk of saying potentially +something that's likely less true so + + align:start position:0% +something that's likely less true so + + + align:start position:0% +something that's likely less true so +this way you can ignore the sentence + + align:start position:0% +this way you can ignore the sentence + + + align:start position:0% +this way you can ignore the sentence +which is unhelpful and you can end up + + align:start position:0% +which is unhelpful and you can end up + + + align:start position:0% +which is unhelpful and you can end up +saying something like the person on the + + align:start position:0% +saying something like the person on the + + + align:start position:0% +saying something like the person on the +left of the car put an object on top of + + align:start position:0% +left of the car put an object on top of + + + align:start position:0% +left of the car put an object on top of +the red car so we can actually do that + + align:start position:0% +the red car so we can actually do that + + + align:start position:0% +the red car so we can actually do that +and the system produces that output we + + align:start position:0% +and the system produces that output we + + + align:start position:0% +and the system produces that output we +built one recognition approach and we + + align:start position:0% +built one recognition approach and we + + + align:start position:0% +built one recognition approach and we +did retrieval generation in question + + align:start position:0% +did retrieval generation in question + + + align:start position:0% +did retrieval generation in question +answering with it we can also do this + + align:start position:0% +answering with it we can also do this + + + align:start position:0% +answering with it we can also do this +ambiguity with it in this emigration we + + align:start position:0% +ambiguity with it in this emigration we + + + align:start position:0% +ambiguity with it in this emigration we +take a sentence like Danny approached + + align:start position:0% +take a sentence like Danny approached + + + align:start position:0% +take a sentence like Danny approached +the chair with the bag and you can + + align:start position:0% +the chair with the bag and you can + + + align:start position:0% +the chair with the bag and you can +imagine that this sentence could be + + align:start position:0% +imagine that this sentence could be + + + align:start position:0% +imagine that this sentence could be +multiple things it could mean Danny was + + align:start position:0% +multiple things it could mean Danny was + + + align:start position:0% +multiple things it could mean Danny was +actually carrying a bag in approaching a + + align:start position:0% +actually carrying a bag in approaching a + + + align:start position:0% +actually carrying a bag in approaching a +chair or it could mean there was a chair + + align:start position:0% +chair or it could mean there was a chair + + + align:start position:0% +chair or it could mean there was a chair +there was a bag on a chair and Danny was + + align:start position:0% +there was a bag on a chair and Danny was + + + align:start position:0% +there was a bag on a chair and Danny was +approaching it and there's the question + + align:start position:0% +approaching it and there's the question + + + align:start position:0% +approaching it and there's the question +of how do you decide which + + align:start position:0% +of how do you decide which + + + align:start position:0% +of how do you decide which +interpretation for the sentence + + align:start position:0% +interpretation for the sentence + + + align:start position:0% +interpretation for the sentence +corresponds to which video + + align:start position:0% + + + + align:start position:0% + +basically you can take your sentences + + align:start position:0% +basically you can take your sentences + + + align:start position:0% +basically you can take your sentences +and you can look at their parse trees + + align:start position:0% +and you can look at their parse trees + + + align:start position:0% +and you can look at their parse trees +and you're going to see that they're + + align:start position:0% +and you're going to see that they're + + + align:start position:0% +and you're going to see that they're +different essentially your language + + align:start position:0% +different essentially your language + + + align:start position:0% +different essentially your language +system is going to give you a slightly + + align:start position:0% +system is going to give you a slightly + + + align:start position:0% +system is going to give you a slightly +different internal representation for + + align:start position:0% +different internal representation for + + + align:start position:0% +different internal representation for +each of these and we already know that + + align:start position:0% +each of these and we already know that + + + align:start position:0% +each of these and we already know that +when we build our detectors for the + + align:start position:0% +when we build our detectors for the + + + align:start position:0% +when we build our detectors for the +sentence we take these kinds of + + align:start position:0% +sentence we take these kinds of + + + align:start position:0% +sentence we take these kinds of +relationships between the words as + + align:start position:0% +relationships between the words as + + + align:start position:0% +relationships between the words as +inputs so even though there's one + + align:start position:0% +inputs so even though there's one + + + align:start position:0% +inputs so even though there's one +sentence in English that describe both + + align:start position:0% +sentence in English that describe both + + + align:start position:0% +sentence in English that describe both +of these scenarios when we build + + align:start position:0% +of these scenarios when we build + + + align:start position:0% +of these scenarios when we build +detectors we're going to end up with two + + align:start position:0% +detectors we're going to end up with two + + + align:start position:0% +detectors we're going to end up with two +different detectors one for one + + align:start position:0% +different detectors one for one + + + align:start position:0% +different detectors one for one +represent one for one meaning one for + + align:start position:0% +represent one for one meaning one for + + + align:start position:0% +represent one for one meaning one for +the other meaning and then we can just + + align:start position:0% +the other meaning and then we can just + + + align:start position:0% +the other meaning and then we can just +run the detectors and figure out which + + align:start position:0% +run the detectors and figure out which + + + align:start position:0% +run the detectors and figure out which +meaning corresponds to which video and + + align:start position:0% +meaning corresponds to which video and + + + align:start position:0% +meaning corresponds to which video and +indeed that's what we did except that + + align:start position:0% +indeed that's what we did except that + + + align:start position:0% +indeed that's what we did except that +there are lots and lots of different + + align:start position:0% +there are lots and lots of different + + + align:start position:0% +there are lots and lots of different +potential ambiguities there are + + align:start position:0% +potential ambiguities there are + + + align:start position:0% +potential ambiguities there are +different kinds of attachment in the + + align:start position:0% +different kinds of attachment in the + + + align:start position:0% +different kinds of attachment in the +same cases with I won't go through all + + align:start position:0% +same cases with I won't go through all + + + align:start position:0% +same cases with I won't go through all +of them but for example you might not + + align:start position:0% +of them but for example you might not + + + align:start position:0% +of them but for example you might not +know where the bag is + + align:start position:0% +know where the bag is + + + align:start position:0% +know where the bag is +you might not know who's performing the + + align:start position:0% +you might not know who's performing the + + + align:start position:0% +you might not know who's performing the +action you might not be sure if both + + align:start position:0% +action you might not be sure if both + + + align:start position:0% +action you might not be sure if both +people are performing the action or only + + align:start position:0% +people are performing the action or only + + + align:start position:0% +people are performing the action or only +one person is performing the action + + align:start position:0% +one person is performing the action + + + align:start position:0% +one person is performing the action +there may be some problems with + + align:start position:0% +there may be some problems with + + + align:start position:0% +there may be some problems with +references so this is a very simple + + align:start position:0% +references so this is a very simple + + + align:start position:0% +references so this is a very simple +example like Danny picked up the bag and + + align:start position:0% +example like Danny picked up the bag and + + + align:start position:0% +example like Danny picked up the bag and +the chair it is yellow but this is the + + align:start position:0% +the chair it is yellow but this is the + + + align:start position:0% +the chair it is yellow but this is the +kind of thing that you would see if you + + align:start position:0% +kind of thing that you would see if you + + + align:start position:0% +kind of thing that you would see if you +had a long paragraph you would have some + + align:start position:0% +had a long paragraph you would have some + + + align:start position:0% +had a long paragraph you would have some +reference later on or earlier on to some + + align:start position:0% +reference later on or earlier on to some + + + align:start position:0% +reference later on or earlier on to some +person and you wouldn't be sure who who + + align:start position:0% +person and you wouldn't be sure who who + + + align:start position:0% +person and you wouldn't be sure who who +is the referent and it turns out that if + + align:start position:0% +is the referent and it turns out that if + + + align:start position:0% +is the referent and it turns out that if +you have sentences like this you can + + align:start position:0% +you have sentences like this you can + + + align:start position:0% +you have sentences like this you can +disintegrate them pretty reliably so + + align:start position:0% +disintegrate them pretty reliably so + + + align:start position:0% +disintegrate them pretty reliably so +what's important is it's just a case of + + align:start position:0% +what's important is it's just a case of + + + align:start position:0% +what's important is it's just a case of +parse streets we need a more interesting + + align:start position:0% +parse streets we need a more interesting + + + align:start position:0% +parse streets we need a more interesting +internal representation and an example + + align:start position:0% +internal representation and an example + + + align:start position:0% +internal representation and an example +of how we do this is we take a sentence + + align:start position:0% +of how we do this is we take a sentence + + + align:start position:0% +of how we do this is we take a sentence +and we make some first-order logic + + align:start position:0% +and we make some first-order logic + + + align:start position:0% +and we make some first-order logic +formula out of it right so you have some + + align:start position:0% +formula out of it right so you have some + + + align:start position:0% +formula out of it right so you have some +variables the chair is something like X + + align:start position:0% +variables the chair is something like X + + + align:start position:0% +variables the chair is something like X +you have Danny who moved it and I moved + + align:start position:0% +you have Danny who moved it and I moved + + + align:start position:0% +you have Danny who moved it and I moved +it or in the other case you have two + + align:start position:0% +it or in the other case you have two + + + align:start position:0% +it or in the other case you have two +separate chairs and I moved one and + + align:start position:0% +separate chairs and I moved one and + + + align:start position:0% +separate chairs and I moved one and +Danny moved the other and they're + + align:start position:0% +Danny moved the other and they're + + + align:start position:0% +Danny moved the other and they're +distinct chairs what we do is we first + + align:start position:0% +distinct chairs what we do is we first + + + align:start position:0% +distinct chairs what we do is we first +ignore the people so we just say there + + align:start position:0% +ignore the people so we just say there + + + align:start position:0% +ignore the people so we just say there +are two people and in one in both cases + + align:start position:0% +are two people and in one in both cases + + + align:start position:0% +are two people and in one in both cases +we're distinct from each other but we + + align:start position:0% +we're distinct from each other but we + + + align:start position:0% +we're distinct from each other but we +don't have person recognizers face + + align:start position:0% +don't have person recognizers face + + + align:start position:0% +don't have person recognizers face +recognition or anything like that then + + align:start position:0% +recognition or anything like that then + + + align:start position:0% +recognition or anything like that then +for each of these variables we build a + + align:start position:0% +for each of these variables we build a + + + align:start position:0% +for each of these variables we build a +tracker and for every constraint we have + + align:start position:0% +tracker and for every constraint we have + + + align:start position:0% +tracker and for every constraint we have +a word model and essentially you can go + + align:start position:0% +a word model and essentially you can go + + + align:start position:0% +a word model and essentially you can go +from this first-order logic formula to + + align:start position:0% +from this first-order logic formula to + + + align:start position:0% +from this first-order logic formula to +one of our detectors so it's exactly the + + align:start position:0% +one of our detectors so it's exactly the + + + align:start position:0% +one of our detectors so it's exactly the +same thing as the case where we had a + + align:start position:0% +same thing as the case where we had a + + + align:start position:0% +same thing as the case where we had a +sentence in a video and we just wanted + + align:start position:0% +sentence in a video and we just wanted + + + align:start position:0% +sentence in a video and we just wanted +to + + align:start position:0% +to + + + align:start position:0% +to +see is the sentence sure of the video + + align:start position:0% +see is the sentence sure of the video + + + align:start position:0% +see is the sentence sure of the video +except that now we have a sentence + + align:start position:0% +except that now we have a sentence + + + align:start position:0% +except that now we have a sentence +interpretation on the video so we've + + align:start position:0% +interpretation on the video so we've + + + align:start position:0% +interpretation on the video so we've +seen that if all you have a multiple + + align:start position:0% +seen that if all you have a multiple + + + align:start position:0% +seen that if all you have a multiple +interpretation of a sentence you can + + align:start position:0% +interpretation of a sentence you can + + + align:start position:0% +interpretation of a sentence you can +figure out which one belongs to which + + align:start position:0% +figure out which one belongs to which + + + align:start position:0% +figure out which one belongs to which +video so and we'll come back to this in + + align:start position:0% +video so and we'll come back to this in + + + align:start position:0% +video so and we'll come back to this in +a moment because it's actually quite + + align:start position:0% +a moment because it's actually quite + + + align:start position:0% +a moment because it's actually quite +useful so you can imagine a scenario + + align:start position:0% +useful so you can imagine a scenario + + + align:start position:0% +useful so you can imagine a scenario +where you want to talk to a robot and + + align:start position:0% +where you want to talk to a robot and + + + align:start position:0% +where you want to talk to a robot and +you want to give it a command you don't + + align:start position:0% +you want to give it a command you don't + + + align:start position:0% +you want to give it a command you don't +want to play 20 questions with it right + + align:start position:0% +want to play 20 questions with it right + + + align:start position:0% +want to play 20 questions with it right +you want to tell it something it should + + align:start position:0% +you want to tell it something it should + + + align:start position:0% +you want to tell it something it should +look at the environment that it should + + align:start position:0% +look at the environment that it should + + + align:start position:0% +look at the environment that it should +figure out you're referring to this + + align:start position:0% +figure out you're referring to this + + + align:start position:0% +figure out you're referring to this +chair and this is what I'm supposed to + + align:start position:0% +chair and this is what I'm supposed to + + + align:start position:0% +chair and this is what I'm supposed to +do so the other reason for + + align:start position:0% +do so the other reason for + + + align:start position:0% +do so the other reason for +disambiguation is going to be because + + align:start position:0% +disambiguation is going to be because + + + align:start position:0% +disambiguation is going to be because +you get a lot of ambiguities while + + align:start position:0% +you get a lot of ambiguities while + + + align:start position:0% +you get a lot of ambiguities while +you're acquiring language we're going to + + align:start position:0% +you're acquiring language we're going to + + + align:start position:0% +you're acquiring language we're going to +break down language acquisition into two + + align:start position:0% +break down language acquisition into two + + + align:start position:0% +break down language acquisition into two +parts one part is we want to learn the + + align:start position:0% +parts one part is we want to learn the + + + align:start position:0% +parts one part is we want to learn the +meanings of each of our words and + + align:start position:0% +meanings of each of our words and + + + align:start position:0% +meanings of each of our words and +another one is we want to learn how we + + align:start position:0% +another one is we want to learn how we + + + align:start position:0% +another one is we want to learn how we +take a sentence and we transform it into + + align:start position:0% +take a sentence and we transform it into + + + align:start position:0% +take a sentence and we transform it into +this internal representation that we use + + align:start position:0% +this internal representation that we use + + + align:start position:0% +this internal representation that we use +to actually build these detectors so if + + align:start position:0% +to actually build these detectors so if + + + align:start position:0% +to actually build these detectors so if +you look at the first one let's say you + + align:start position:0% +you look at the first one let's say you + + + align:start position:0% +you look at the first one let's say you +have a whole bunch of videos and every + + align:start position:0% +have a whole bunch of videos and every + + + align:start position:0% +have a whole bunch of videos and every +video comes with a sentence you don't + + align:start position:0% +video comes with a sentence you don't + + + align:start position:0% +video comes with a sentence you don't +know what the sentence is actually + + align:start position:0% +know what the sentence is actually + + + align:start position:0% +know what the sentence is actually +referring to in the video you know when + + align:start position:0% +referring to in the video you know when + + + align:start position:0% +referring to in the video you know when +children are born nobody gives mothers + + align:start position:0% +children are born nobody gives mothers + + + align:start position:0% +children are born nobody gives mothers +bounding boxes and tells them put this + + align:start position:0% +bounding boxes and tells them put this + + + align:start position:0% +bounding boxes and tells them put this +around the teddy bear so your child + + align:start position:0% +around the teddy bear so your child + + + align:start position:0% +around the teddy bear so your child +knows what you're referring to so we + + align:start position:0% +knows what you're referring to so we + + + align:start position:0% +knows what you're referring to so we +don't get those we have this more weekly + + align:start position:0% +don't get those we have this more weekly + + + align:start position:0% +don't get those we have this more weekly +supervised system but what's important + + align:start position:0% +supervised system but what's important + + + align:start position:0% +supervised system but what's important +is we get this data set and there are + + align:start position:0% +is we get this data set and there are + + + align:start position:0% +is we get this data set and there are +certain correlations in this data set + + align:start position:0% +certain correlations in this data set + + + align:start position:0% +certain correlations in this data set +right we know the chair occurs in some + + align:start position:0% +right we know the chair occurs in some + + + align:start position:0% +right we know the chair occurs in some +videos we know that backpack occurs in + + align:start position:0% +videos we know that backpack occurs in + + + align:start position:0% +videos we know that backpack occurs in +others just by looking at the sentence + + align:start position:0% +others just by looking at the sentence + + + align:start position:0% +others just by looking at the sentence +we know a pickup occurs in others so + + align:start position:0% +we know a pickup occurs in others so + + + align:start position:0% +we know a pickup occurs in others so +basically this is the same thing as + + align:start position:0% +basically this is the same thing as + + + align:start position:0% +basically this is the same thing as +training one big hidden Markov model + + align:start position:0% +training one big hidden Markov model + + + align:start position:0% +training one big hidden Markov model +except that now we have multiple hidden + + align:start position:0% +except that now we have multiple hidden + + + align:start position:0% +except that now we have multiple hidden +Markov models they have a small amount + + align:start position:0% +Markov models they have a small amount + + + align:start position:0% +Markov models they have a small amount +of dependency between them and I won't + + align:start position:0% +of dependency between them and I won't + + + align:start position:0% +of dependency between them and I won't +talk about this you have to take my word + + align:start position:0% +talk about this you have to take my word + + + align:start position:0% +talk about this you have to take my word +for it you can look at the paper but + + align:start position:0% +for it you can look at the paper but + + + align:start position:0% +for it you can look at the paper but +it's identical to the Baum Walsh + + align:start position:0% +it's identical to the Baum Walsh + + + align:start position:0% +it's identical to the Baum Walsh +algorithm essentially all you do is you + + align:start position:0% +algorithm essentially all you do is you + + + align:start position:0% +algorithm essentially all you do is you +take the gradient through all the + + align:start position:0% +take the gradient through all the + + + align:start position:0% +take the gradient through all the +parameters of these words and you can + + align:start position:0% +parameters of these words and you can + + + align:start position:0% +parameters of these words and you can +acquire their meanings there are lots of + + align:start position:0% +acquire their meanings there are lots of + + + align:start position:0% +acquire their meanings there are lots of +technical issues with this but that's a + + align:start position:0% +technical issues with this but that's a + + + align:start position:0% +technical issues with this but that's a +general idea so we can also look at + + align:start position:0% +general idea so we can also look at + + + align:start position:0% +general idea so we can also look at +learning syntax and this is something + + align:start position:0% +learning syntax and this is something + + + align:start position:0% +learning syntax and this is something +that we haven't done but we really want + + align:start position:0% +that we haven't done but we really want + + + align:start position:0% +that we haven't done but we really want +to do and this is where the semi Gration + + align:start position:0% +to do and this is where the semi Gration + + + align:start position:0% +to do and this is where the semi Gration +work really comes into play so if I give + + align:start position:0% +work really comes into play so if I give + + + align:start position:0% +work really comes into play so if I give +you a sentence like Danny approached the + + align:start position:0% +you a sentence like Danny approached the + + + align:start position:0% +you a sentence like Danny approached the +chair with the bag you feed into a + + align:start position:0% +chair with the bag you feed into a + + + align:start position:0% +chair with the bag you feed into a +parser something like Boris's start + + align:start position:0% +parser something like Boris's start + + + align:start position:0% +parser something like Boris's start +system + + align:start position:0% +system + + + align:start position:0% +system +you get potentially two parts treats + + align:start position:0% +you get potentially two parts treats + + + align:start position:0% +you get potentially two parts treats +right one for one interpretation and one + + align:start position:0% +right one for one interpretation and one + + + align:start position:0% +right one for one interpretation and one +for the other interpretation you take + + align:start position:0% +for the other interpretation you take + + + align:start position:0% +for the other interpretation you take +the video and you can select one of + + align:start position:0% +the video and you can select one of + + + align:start position:0% +the video and you can select one of +these parse trees that's the game we + + align:start position:0% +these parse trees that's the game we + + + align:start position:0% +these parse trees that's the game we +just played a moment ago but imagine + + align:start position:0% +just played a moment ago but imagine + + + align:start position:0% +just played a moment ago but imagine +that we take Boris this system and we + + align:start position:0% +that we take Boris this system and we + + + align:start position:0% +that we take Boris this system and we +brain damages a little bit or we take + + align:start position:0% +brain damages a little bit or we take + + + align:start position:0% +brain damages a little bit or we take +some deep network that does parsing and + + align:start position:0% +some deep network that does parsing and + + + align:start position:0% +some deep network that does parsing and +we just randomize a few of the + + align:start position:0% +we just randomize a few of the + + + align:start position:0% +we just randomize a few of the +parameters so now rather than getting a + + align:start position:0% +parameters so now rather than getting a + + + align:start position:0% +parameters so now rather than getting a +single or two part series for our two + + align:start position:0% +single or two part series for our two + + + align:start position:0% +single or two part series for our two +interpretations we get a hundred or a + + align:start position:0% +interpretations we get a hundred or a + + + align:start position:0% +interpretations we get a hundred or a +thousand different parts trees we can + + align:start position:0% +thousand different parts trees we can + + + align:start position:0% +thousand different parts trees we can +take each one of those and we can see + + align:start position:0% +take each one of those and we can see + + + align:start position:0% +take each one of those and we can see +how well does this match our video and + + align:start position:0% +how well does this match our video and + + + align:start position:0% +how well does this match our video and +we get some distribution over them maybe + + align:start position:0% +we get some distribution over them maybe + + + align:start position:0% +we get some distribution over them maybe +we won't get a single one that matches + + align:start position:0% +we won't get a single one that matches + + + align:start position:0% +we won't get a single one that matches +best maybe we'll get a few that match + + align:start position:0% +best maybe we'll get a few that match + + + align:start position:0% +best maybe we'll get a few that match +well and a bunch that match really + + align:start position:0% +well and a bunch that match really + + + align:start position:0% +well and a bunch that match really +really poorly so this provides a signal + + align:start position:0% +really poorly so this provides a signal + + + align:start position:0% +really poorly so this provides a signal +to actually train the parser essentially + + align:start position:0% +to actually train the parser essentially + + + align:start position:0% +to actually train the parser essentially +you have a parser that produces a + + align:start position:0% +you have a parser that produces a + + + align:start position:0% +you have a parser that produces a +distribution over parse trees you use + + align:start position:0% +distribution over parse trees you use + + + align:start position:0% +distribution over parse trees you use +the vision system to decide which of + + align:start position:0% +the vision system to decide which of + + + align:start position:0% +the vision system to decide which of +these parse trees are better than others + + align:start position:0% +these parse trees are better than others + + + align:start position:0% +these parse trees are better than others +and you feed this information back into + + align:start position:0% +and you feed this information back into + + + align:start position:0% +and you feed this information back into +the parser entry trainer we haven't done + + align:start position:0% +the parser entry trainer we haven't done + + + align:start position:0% +the parser entry trainer we haven't done +this but it's in the pipeline and + + align:start position:0% +this but it's in the pipeline and + + + align:start position:0% +this but it's in the pipeline and +eventually the idea is that we're gonna + + align:start position:0% +eventually the idea is that we're gonna + + + align:start position:0% +eventually the idea is that we're gonna +be able to close the loop and learn the + + align:start position:0% +be able to close the loop and learn the + + + align:start position:0% +be able to close the loop and learn the +meanings of the words while we end up + + align:start position:0% +meanings of the words while we end up + + + align:start position:0% +meanings of the words while we end up +learning the parser but that's further + + align:start position:0% +learning the parser but that's further + + + align:start position:0% +learning the parser but that's further +further down the line so unless you + + align:start position:0% +further down the line so unless you + + + align:start position:0% +further down the line so unless you +think that there's something remarkable + + align:start position:0% +think that there's something remarkable + + + align:start position:0% +think that there's something remarkable +about language learning in humans + + align:start position:0% +about language learning in humans + + + align:start position:0% +about language learning in humans +actually lots of animals learn language + + align:start position:0% +actually lots of animals learn language + + + align:start position:0% +actually lots of animals learn language +not just humans and here's a cute + + align:start position:0% +not just humans and here's a cute + + + align:start position:0% +not just humans and here's a cute +example of a dog that does something + + align:start position:0% +example of a dog that does something + + + align:start position:0% +example of a dog that does something +that our system can do and actually no + + align:start position:0% +that our system can do and actually no + + + align:start position:0% +that our system can do and actually no +language system out there can do so + + align:start position:0% +language system out there can do so + + + align:start position:0% +language system out there can do so +there's this paper but this is from PBS + + align:start position:0% +there's this paper but this is from PBS + + + align:start position:0% +there's this paper but this is from PBS +and what ended up happening is this dog + + align:start position:0% +and what ended up happening is this dog + + + align:start position:0% +and what ended up happening is this dog +knows the meaning of about a thousand + + align:start position:0% +knows the meaning of about a thousand + + + align:start position:0% +knows the meaning of about a thousand +different words because they're labeled + + align:start position:0% +different words because they're labeled + + + align:start position:0% +different words because they're labeled +that they have been attached to + + align:start position:0% +that they have been attached to + + + align:start position:0% +that they have been attached to +different toys so it has a thousand + + align:start position:0% +different toys so it has a thousand + + + align:start position:0% +different toys so it has a thousand +different toys each one has a unique + + align:start position:0% +different toys each one has a unique + + + align:start position:0% +different toys each one has a unique +name and if you get if you tell the dog + + align:start position:0% +name and if you get if you tell the dog + + + align:start position:0% +name and if you get if you tell the dog +give me blinky it knows exactly which + + align:start position:0% +give me blinky it knows exactly which + + + align:start position:0% +give me blinky it knows exactly which +toy blinky is and it has a hundred + + align:start position:0% +toy blinky is and it has a hundred + + + align:start position:0% +toy blinky is and it has a hundred +percent accuracy getting your blinky + + align:start position:0% +percent accuracy getting your blinky + + + align:start position:0% +percent accuracy getting your blinky +from its big big pile of toys so what + + align:start position:0% +from its big big pile of toys so what + + + align:start position:0% +from its big big pile of toys so what +they did is they took ten toys they put + + align:start position:0% +they did is they took ten toys they put + + + align:start position:0% +they did is they took ten toys they put +them behind the sofa and they added one + + align:start position:0% +them behind the sofa and they added one + + + align:start position:0% +them behind the sofa and they added one +additional toy that the dog has never + + align:start position:0% +additional toy that the dog has never + + + align:start position:0% +additional toy that the dog has never +seen before they tested the dog many + + align:start position:0% +seen before they tested the dog many + + + align:start position:0% +seen before they tested the dog many +times to make sure that doesn't have a + + align:start position:0% +times to make sure that doesn't have a + + + align:start position:0% +times to make sure that doesn't have a +novelty preference or anything like that + + align:start position:0% +novelty preference or anything like that + + + align:start position:0% +novelty preference or anything like that +and that they asked the dog bring me + + align:start position:0% +and that they asked the dog bring me + + + align:start position:0% +and that they asked the dog bring me +blinky and you can see the dog was asked + + align:start position:0% +blinky and you can see the dog was asked + + + align:start position:0% +blinky and you can see the dog was asked +it goes behind it quickly finds blinky + + align:start position:0% +it goes behind it quickly finds blinky + + + align:start position:0% +it goes behind it quickly finds blinky +it brings it back and there we go and + + align:start position:0% +it brings it back and there we go and + + + align:start position:0% +it brings it back and there we go and +the dog you know dog is really happy so + + align:start position:0% +the dog you know dog is really happy so + + + align:start position:0% +the dog you know dog is really happy so +now the dog is gonna be asked bring me + + align:start position:0% +now the dog is gonna be asked bring me + + + align:start position:0% +now the dog is gonna be asked bring me +this mute I you know bring me the + + align:start position:0% +this mute I you know bring me the + + + align:start position:0% +this mute I you know bring me the +professor whatever the toys called and + + align:start position:0% +professor whatever the toys called and + + + align:start position:0% +professor whatever the toys called and +it's a little ascertain okay so I'm + + align:start position:0% +it's a little ascertain okay so I'm + + + align:start position:0% +it's a little ascertain okay so I'm +gonna go behind and it's gonna look at + + align:start position:0% +gonna go behind and it's gonna look at + + + align:start position:0% +gonna go behind and it's gonna look at +all the objects it's the toy would the + + align:start position:0% +all the objects it's the toy would the + + + align:start position:0% +all the objects it's the toy would the +beard is the new one that it hasn't seen + + align:start position:0% +beard is the new one that it hasn't seen + + + align:start position:0% +beard is the new one that it hasn't seen +before and it was there in the previous + + align:start position:0% +before and it was there in the previous + + + align:start position:0% +before and it was there in the previous +trial so looks around and it's a little + + align:start position:0% +trial so looks around and it's a little + + + align:start position:0% +trial so looks around and it's a little +sir doesn't quite want to come back + + align:start position:0% +sir doesn't quite want to come back + + + align:start position:0% +sir doesn't quite want to come back +we're gonna see that we're gonna have to + + align:start position:0% +we're gonna see that we're gonna have to + + + align:start position:0% +we're gonna see that we're gonna have to +give it another instruction in a moment + + align:start position:0% +give it another instruction in a moment + + + align:start position:0% +give it another instruction in a moment +he's gonna call it back and ask the dog + + align:start position:0% +he's gonna call it back and ask the dog + + + align:start position:0% +he's gonna call it back and ask the dog +to do exactly the same task again this + + align:start position:0% +to do exactly the same task again this + + + align:start position:0% +to do exactly the same task again this +isn't telling it anything new it's just + + align:start position:0% +isn't telling it anything new it's just + + + align:start position:0% +isn't telling it anything new it's just +to give it some encouragement so looking + + align:start position:0% +to give it some encouragement so looking + + + align:start position:0% +to give it some encouragement so looking +around for some toy and it picks the + + align:start position:0% +around for some toy and it picks the + + + align:start position:0% +around for some toy and it picks the +you'll see in a moment it picks the toy + + align:start position:0% +you'll see in a moment it picks the toy + + + align:start position:0% +you'll see in a moment it picks the toy +that hasn't seen before because it's a + + align:start position:0% +that hasn't seen before because it's a + + + align:start position:0% +that hasn't seen before because it's a +new word and the dog is really happy and + + align:start position:0% +new word and the dog is really happy and + + + align:start position:0% +new word and the dog is really happy and +I think the human is even happier that + + align:start position:0% +I think the human is even happier that + + + align:start position:0% +I think the human is even happier that +this actually worked so but the + + align:start position:0% +this actually worked so but the + + + align:start position:0% +this actually worked so but the +important part is I mean there's this + + align:start position:0% +important part is I mean there's this + + + align:start position:0% +important part is I mean there's this +dog that we normally don't associate + + align:start position:0% +dog that we normally don't associate + + + align:start position:0% +dog that we normally don't associate +with having a huge amount of linguistic + + align:start position:0% +with having a huge amount of linguistic + + + align:start position:0% +with having a huge amount of linguistic +ability but it's learning language in a + + align:start position:0% +ability but it's learning language in a + + + align:start position:0% +ability but it's learning language in a +way that is far more advanced than + + align:start position:0% +way that is far more advanced than + + + align:start position:0% +way that is far more advanced than +anything that we have and it's learning + + align:start position:0% +anything that we have and it's learning + + + align:start position:0% +anything that we have and it's learning +it in a grounded way like it had to + + align:start position:0% +it in a grounded way like it had to + + + align:start position:0% +it in a grounded way like it had to +connect its knowledge about what it sees + + align:start position:0% +connect its knowledge about what it sees + + + align:start position:0% +connect its knowledge about what it sees +with these toys this new object that + + align:start position:0% +with these toys this new object that + + + align:start position:0% +with these toys this new object that +it's never seen before and understand + + align:start position:0% +it's never seen before and understand + + + align:start position:0% +it's never seen before and understand +that this this new label and dogs are + + align:start position:0% +that this this new label and dogs are + + + align:start position:0% +that this this new label and dogs are +not the only animal that can do this + + align:start position:0% +not the only animal that can do this + + + align:start position:0% +not the only animal that can do this +there are many other animals that can do + + align:start position:0% +there are many other animals that can do + + + align:start position:0% +there are many other animals that can do +this all right and of course children do + + align:start position:0% +this all right and of course children do + + + align:start position:0% +this all right and of course children do +this as well so there was a question + + align:start position:0% +this as well so there was a question + + + align:start position:0% +this as well so there was a question +about the fact that we're constantly do + + align:start position:0% +about the fact that we're constantly do + + + align:start position:0% +about the fact that we're constantly do +it using videos here and we're very + + align:start position:0% +it using videos here and we're very + + + align:start position:0% +it using videos here and we're very +focused on motion but of course in many + + align:start position:0% +focused on motion but of course in many + + + align:start position:0% +focused on motion but of course in many +of these sentences we were referring to + + align:start position:0% +of these sentences we were referring to + + + align:start position:0% +of these sentences we were referring to +objects that were static so we're not + + align:start position:0% +objects that were static so we're not + + + align:start position:0% +objects that were static so we're not +only sensitive to objects that are + + align:start position:0% +only sensitive to objects that are + + + align:start position:0% +only sensitive to objects that are +moving so for example when I said + + align:start position:0% +moving so for example when I said + + + align:start position:0% +moving so for example when I said +something like it was the person to the + + align:start position:0% +something like it was the person to the + + + align:start position:0% +something like it was the person to the +left of the car neither the person nor + + align:start position:0% +left of the car neither the person nor + + + align:start position:0% +left of the car neither the person nor +the car were moving in that question it + + align:start position:0% +the car were moving in that question it + + + align:start position:0% +the car were moving in that question it +was the pair that was moving but there's + + align:start position:0% +was the pair that was moving but there's + + + align:start position:0% +was the pair that was moving but there's +an interesting question what if you want + + align:start position:0% +an interesting question what if you want + + + align:start position:0% +an interesting question what if you want +to recognize actions in still images + + align:start position:0% +to recognize actions in still images + + + align:start position:0% +to recognize actions in still images +because after all we can do it we'd + + align:start position:0% +because after all we can do it we'd + + + align:start position:0% +because after all we can do it we'd +probably didn't involve looking at + + align:start position:0% +probably didn't involve looking at + + + align:start position:0% +probably didn't involve looking at +photos you know 200 million years ago in + + align:start position:0% +photos you know 200 million years ago in + + + align:start position:0% +photos you know 200 million years ago in +our visual system was being formed so + + align:start position:0% +our visual system was being formed so + + + align:start position:0% +our visual system was being formed so +somehow we take our video ability and we + + align:start position:0% +somehow we take our video ability and we + + + align:start position:0% +somehow we take our video ability and we +apply it to + + align:start position:0% +apply it to + + + align:start position:0% +apply it to +images and the way we're gonna do that + + align:start position:0% +images and the way we're gonna do that + + + align:start position:0% +images and the way we're gonna do that +is by taking an image and predicting a + + align:start position:0% +is by taking an image and predicting a + + + align:start position:0% +is by taking an image and predicting a +video from it we haven't done this but + + align:start position:0% +video from it we haven't done this but + + + align:start position:0% +video from it we haven't done this but +we've done the part where you can + + align:start position:0% +we've done the part where you can + + + align:start position:0% +we've done the part where you can +actually get predict in motion from + + align:start position:0% +actually get predict in motion from + + + align:start position:0% +actually get predict in motion from +single frames so the intuition about why + + align:start position:0% +single frames so the intuition about why + + + align:start position:0% +single frames so the intuition about why +this works is if you look at this image + + align:start position:0% +this works is if you look at this image + + + align:start position:0% +this works is if you look at this image +and I ask you how quickly is this + + align:start position:0% +and I ask you how quickly is this + + + align:start position:0% +and I ask you how quickly is this +baseball moving you can give me an + + align:start position:0% +baseball moving you can give me an + + + align:start position:0% +baseball moving you can give me an +answer not not very quickly right and if + + align:start position:0% +answer not not very quickly right and if + + + align:start position:0% +answer not not very quickly right and if +you look at this baseball you can decide + + align:start position:0% +you look at this baseball you can decide + + + align:start position:0% +you look at this baseball you can decide +that you know it's moving very quickly + + align:start position:0% +that you know it's moving very quickly + + + align:start position:0% +that you know it's moving very quickly +all right okay so the other story in + + align:start position:0% +all right okay so the other story in + + + align:start position:0% +all right okay so the other story in +this talk is that I'm becoming more and + + align:start position:0% +this talk is that I'm becoming more and + + + align:start position:0% +this talk is that I'm becoming more and +more American I start with the Canadian + + align:start position:0% +more American I start with the Canadian + + + align:start position:0% +more American I start with the Canadian +flag not a baseball all right so you can + + align:start position:0% +flag not a baseball all right so you can + + + align:start position:0% +flag not a baseball all right so you can +clearly do this task there's good + + align:start position:0% +clearly do this task there's good + + + align:start position:0% +clearly do this task there's good +neuroscience evidence that you that + + align:start position:0% +neuroscience evidence that you that + + + align:start position:0% +neuroscience evidence that you that +people are doing this fairly regularly + + align:start position:0% +people are doing this fairly regularly + + + align:start position:0% +people are doing this fairly regularly +kids can do this + + align:start position:0% +kids can do this + + + align:start position:0% +kids can do this +etc all right so now what we did is we + + align:start position:0% +etc all right so now what we did is we + + + align:start position:0% +etc all right so now what we did is we +went to YouTube and we got a whole bunch + + align:start position:0% +went to YouTube and we got a whole bunch + + + align:start position:0% +went to YouTube and we got a whole bunch +of videos videos that contain cars or + + align:start position:0% +of videos videos that contain cars or + + + align:start position:0% +of videos videos that contain cars or +different kinds of objects we have a + + align:start position:0% +different kinds of objects we have a + + + align:start position:0% +different kinds of objects we have a +different object classes and we ran a + + align:start position:0% +different object classes and we ran a + + + align:start position:0% +different object classes and we ran a +standard optical flow algorithm just off + + align:start position:0% +standard optical flow algorithm just off + + + align:start position:0% +standard optical flow algorithm just off +the shelf and this gives us an idea of + + align:start position:0% +the shelf and this gives us an idea of + + + align:start position:0% +the shelf and this gives us an idea of +how the motion actually happens inside + + align:start position:0% +how the motion actually happens inside + + + align:start position:0% +how the motion actually happens inside +this video then we discard the video and + + align:start position:0% +this video then we discard the video and + + + align:start position:0% +this video then we discard the video and +we only keep one of the frames and we + + align:start position:0% +we only keep one of the frames and we + + + align:start position:0% +we only keep one of the frames and we +train a deep network this is the only + + align:start position:0% +train a deep network this is the only + + + align:start position:0% +train a deep network this is the only +time deep networks appear on this talk + + align:start position:0% +time deep networks appear on this talk + + + align:start position:0% +time deep networks appear on this talk +that takes as input the image and + + align:start position:0% +that takes as input the image and + + + align:start position:0% +that takes as input the image and +predicts the optical flow it looks a lot + + align:start position:0% +predicts the optical flow it looks a lot + + + align:start position:0% +predicts the optical flow it looks a lot +like an auto encoder except the input + + align:start position:0% +like an auto encoder except the input + + + align:start position:0% +like an auto encoder except the input +and the output are different from each + + align:start position:0% +and the output are different from each + + + align:start position:0% +and the output are different from each +other and it turns out this works pretty + + align:start position:0% +other and it turns out this works pretty + + + align:start position:0% +other and it turns out this works pretty +well it has similar performance actually + + align:start position:0% +well it has similar performance actually + + + align:start position:0% +well it has similar performance actually +doing optical flow on the video with + + align:start position:0% +doing optical flow on the video with + + + align:start position:0% +doing optical flow on the video with +sort of a crappy earlier optical flow + + align:start position:0% +sort of a crappy earlier optical flow + + + align:start position:0% +sort of a crappy earlier optical flow +algorithm so up until now are things + + align:start position:0% +algorithm so up until now are things + + + align:start position:0% +algorithm so up until now are things +that we've done really about kind of + + align:start position:0% +that we've done really about kind of + + + align:start position:0% +that we've done really about kind of +what we're doing in the future + + align:start position:0% +what we're doing in the future + + + align:start position:0% +what we're doing in the future +so one thing that you can do is + + align:start position:0% +so one thing that you can do is + + + align:start position:0% +so one thing that you can do is +translation and you can cast translation + + align:start position:0% +translation and you can cast translation + + + align:start position:0% +translation and you can cast translation +as a visual language task even though it + + align:start position:0% +as a visual language task even though it + + + align:start position:0% +as a visual language task even though it +sounds like it has nothing to do with + + align:start position:0% +sounds like it has nothing to do with + + + align:start position:0% +sounds like it has nothing to do with +vision so if I give you a sentence in + + align:start position:0% +vision so if I give you a sentence in + + + align:start position:0% +vision so if I give you a sentence in +Chinese you can imagine scenarios for + + align:start position:0% +Chinese you can imagine scenarios for + + + align:start position:0% +Chinese you can imagine scenarios for +that sentence and then try to describe + + align:start position:0% +that sentence and then try to describe + + + align:start position:0% +that sentence and then try to describe +them with another language that you know + + align:start position:0% +them with another language that you know + + + align:start position:0% +them with another language that you know +this is very different from the way + + align:start position:0% +this is very different from the way + + + align:start position:0% +this is very different from the way +people do translation right now sorry + + align:start position:0% +people do translation right now sorry + + + align:start position:0% +people do translation right now sorry +now the way it works is you have a + + align:start position:0% +now the way it works is you have a + + + align:start position:0% +now the way it works is you have a +sentence like Sam was happy and you have + + align:start position:0% +sentence like Sam was happy and you have + + + align:start position:0% +sentence like Sam was happy and you have +a parallel corpus if you want to + + align:start position:0% +a parallel corpus if you want to + + + align:start position:0% +a parallel corpus if you want to +translate it into French you go off you + + align:start position:0% +translate it into French you go off you + + + align:start position:0% +translate it into French you go off you +get the Hansard corpus and you get a + + align:start position:0% +get the Hansard corpus and you get a + + + align:start position:0% +get the Hansard corpus and you get a +whole bunch of french and english + + align:start position:0% +whole bunch of french and english + + + align:start position:0% +whole bunch of french and english +sentences that are aligned with each + + align:start position:0% +sentences that are aligned with each + + + align:start position:0% +sentences that are aligned with each +other and you learn the correspondence + + align:start position:0% +other and you learn the correspondence + + + align:start position:0% +other and you learn the correspondence +between them here I translated into a + + align:start position:0% +between them here I translated into a + + + align:start position:0% +between them here I translated into a +rushon the important part is in English + + align:start position:0% +rushon the important part is in English + + + align:start position:0% +rushon the important part is in English +there's no assumption about the gender + + align:start position:0% +there's no assumption about the gender + + + align:start position:0% +there's no assumption about the gender +of Sam right Sam is both a male name and + + align:start position:0% +of Sam right Sam is both a male name and + + + align:start position:0% +of Sam right Sam is both a male name and +the female name but the problem is + + align:start position:0% +the female name but the problem is + + + align:start position:0% +the female name but the problem is +English Romanian Russian and French etc + + align:start position:0% +English Romanian Russian and French etc + + + align:start position:0% +English Romanian Russian and French etc +they really forced you to specify the + + align:start position:0% +they really forced you to specify the + + + align:start position:0% +they really forced you to specify the +gender of the people that are involved + + align:start position:0% +gender of the people that are involved + + + align:start position:0% +gender of the people that are involved +in these actions and you have to go + + align:start position:0% +in these actions and you have to go + + + align:start position:0% +in these actions and you have to go +through a certain amount of we really + + align:start position:0% +through a certain amount of we really + + + align:start position:0% +through a certain amount of we really +want to avoid specifying their gender so + + align:start position:0% +want to avoid specifying their gender so + + + align:start position:0% +want to avoid specifying their gender so +here we specify the genders male here we + + align:start position:0% +here we specify the genders male here we + + + align:start position:0% +here we specify the genders male here we +specify the gender as female and if all + + align:start position:0% +specify the gender as female and if all + + + align:start position:0% +specify the gender as female and if all +you have is the distal machine + + align:start position:0% +you have is the distal machine + + + align:start position:0% +you have is the distal machine +translation system you may get an + + align:start position:0% +translation system you may get an + + + align:start position:0% +translation system you may get an +arbitrary in one of these two and you + + align:start position:0% +arbitrary in one of these two and you + + + align:start position:0% +arbitrary in one of these two and you +may not know that you got an arbitrary + + align:start position:0% +may not know that you got an arbitrary + + + align:start position:0% +may not know that you got an arbitrary +one of these two and it may be a + + align:start position:0% +one of these two and it may be a + + + align:start position:0% +one of these two and it may be a +terrible faux pas at some point so this + + align:start position:0% +terrible faux pas at some point so this + + + align:start position:0% +terrible faux pas at some point so this +problem is not restricted to gender and + + align:start position:0% +problem is not restricted to gender and + + + align:start position:0% +problem is not restricted to gender and +it occurs all the time for example in + + align:start position:0% +it occurs all the time for example in + + + align:start position:0% +it occurs all the time for example in +Thai you specify your siblings by age + + align:start position:0% +Thai you specify your siblings by age + + + align:start position:0% +Thai you specify your siblings by age +not by their gender so if you have a + + align:start position:0% +not by their gender so if you have a + + + align:start position:0% +not by their gender so if you have a +sent English sentence like my brother + + align:start position:0% +sent English sentence like my brother + + + align:start position:0% +sent English sentence like my brother +the Dex translating that is quite + + align:start position:0% +the Dex translating that is quite + + + align:start position:0% +the Dex translating that is quite +difficult in English you specify + + align:start position:0% +difficult in English you specify + + + align:start position:0% +difficult in English you specify +relative time through the tenth system + + align:start position:0% +relative time through the tenth system + + + align:start position:0% +relative time through the tenth system +but Mandarin doesn't have the same kind + + align:start position:0% +but Mandarin doesn't have the same kind + + + align:start position:0% +but Mandarin doesn't have the same kind +of 10th system in this language that I + + align:start position:0% +of 10th system in this language that I + + + align:start position:0% +of 10th system in this language that I +never tried to pronounce after the first + + align:start position:0% +never tried to pronounce after the first + + + align:start position:0% +never tried to pronounce after the first +time that I tried you don't use relative + + align:start position:0% +time that I tried you don't use relative + + + align:start position:0% +time that I tried you don't use relative +direction so you don't say the bottle to + + align:start position:0% +direction so you don't say the bottle to + + + align:start position:0% +direction so you don't say the bottle to +the left of the laptop we all agree on a + + align:start position:0% +the left of the laptop we all agree on a + + + align:start position:0% +the left of the laptop we all agree on a +common reference frame like a hill or + + align:start position:0% +common reference frame like a hill or + + + align:start position:0% +common reference frame like a hill or +something and we or we agree on cardinal + + align:start position:0% +something and we or we agree on cardinal + + + align:start position:0% +something and we or we agree on cardinal +directions and you say the bottle to the + + align:start position:0% +directions and you say the bottle to the + + + align:start position:0% +directions and you say the bottle to the +north of something and these people are + + align:start position:0% +north of something and these people are + + + align:start position:0% +north of something and these people are +really really kidding because they + + align:start position:0% +really really kidding because they + + + align:start position:0% +really really kidding because they +constantly have to know where North is + + align:start position:0% +constantly have to know where North is + + + align:start position:0% +constantly have to know where North is +many languages don't distinguish blue + + align:start position:0% +many languages don't distinguish blue + + + align:start position:0% +many languages don't distinguish blue +and green historically this is not + + align:start position:0% +and green historically this is not + + + align:start position:0% +and green historically this is not +something that languages have done it's + + align:start position:0% +something that languages have done it's + + + align:start position:0% +something that languages have done it's +pretty new and for example Japanese + + align:start position:0% +pretty new and for example Japanese + + + align:start position:0% +pretty new and for example Japanese +didn't 100 years ago they only started + + align:start position:0% +didn't 100 years ago they only started + + + align:start position:0% +didn't 100 years ago they only started +distinguishing the two fairly recently + + align:start position:0% +distinguishing the two fairly recently + + + align:start position:0% +distinguishing the two fairly recently +when they start interacting with the + + align:start position:0% +when they start interacting with the + + + align:start position:0% +when they start interacting with the +West more and many languages don't set + + align:start position:0% +West more and many languages don't set + + + align:start position:0% +West more and many languages don't set +that boundary at exactly the same place + + align:start position:0% +that boundary at exactly the same place + + + align:start position:0% +that boundary at exactly the same place +so one language you may say blue in + + align:start position:0% +so one language you may say blue in + + + align:start position:0% +so one language you may say blue in +another language you may have to say + + align:start position:0% +another language you may have to say + + + align:start position:0% +another language you may have to say +green it's well Healy you specified the + + align:start position:0% +green it's well Healy you specified the + + + align:start position:0% +green it's well Healy you specified the +color of everything as the color of X so + + align:start position:0% +color of everything as the color of X so + + + align:start position:0% +color of everything as the color of X so +like in English we have orange but in + + align:start position:0% +like in English we have orange but in + + + align:start position:0% +like in English we have orange but in +Swahili I could say the of the back of + + align:start position:0% +Swahili I could say the of the back of + + + align:start position:0% +Swahili I could say the of the back of +my lap my cell phone and I expect you to + + align:start position:0% +my lap my cell phone and I expect you to + + + align:start position:0% +my lap my cell phone and I expect you to +know that's blue as long as you can see + + align:start position:0% +know that's blue as long as you can see + + + align:start position:0% +know that's blue as long as you can see +it in Turkish there is a relatively + + align:start position:0% +it in Turkish there is a relatively + + + align:start position:0% +it in Turkish there is a relatively +complicated evidentiary system so you + + align:start position:0% +complicated evidentiary system so you + + + align:start position:0% +complicated evidentiary system so you +have to fairly often tell me why you + + align:start position:0% +have to fairly often tell me why you + + + align:start position:0% +have to fairly often tell me why you +know something so if you saw somebody do + + align:start position:0% +know something so if you saw somebody do + + + align:start position:0% +know something so if you saw somebody do +something you have to mark that in the + + align:start position:0% +something you have to mark that in the + + + align:start position:0% +something you have to mark that in the +sentence as opposed to hearing it from + + align:start position:0% +sentence as opposed to hearing it from + + + align:start position:0% +sentence as opposed to hearing it from +from cells so if it + + align:start position:0% +from cells so if it + + + align:start position:0% +from cells so if it +here say you have to let me know there + + align:start position:0% +here say you have to let me know there + + + align:start position:0% +here say you have to let me know there +are much more complicated that than she + + align:start position:0% +are much more complicated that than she + + + align:start position:0% +are much more complicated that than she +ality systems where you have to tell me + + align:start position:0% +ality systems where you have to tell me + + + align:start position:0% +ality systems where you have to tell me +did you hear it did you see it did you + + align:start position:0% +did you hear it did you see it did you + + + align:start position:0% +did you hear it did you see it did you +feel it it can get pretty hairy so there + + align:start position:0% +feel it it can get pretty hairy so there + + + align:start position:0% +feel it it can get pretty hairy so there +are a lot of reasons why just doing the + + align:start position:0% +are a lot of reasons why just doing the + + + align:start position:0% +are a lot of reasons why just doing the +straight four sentence alignment can + + align:start position:0% +straight four sentence alignment can + + + align:start position:0% +straight four sentence alignment can +really fail on you and you can make some + + align:start position:0% +really fail on you and you can make some + + + align:start position:0% +really fail on you and you can make some +pretty terrible mistakes and more + + align:start position:0% +pretty terrible mistakes and more + + + align:start position:0% +pretty terrible mistakes and more +importantly you just won't to make these + + align:start position:0% +importantly you just won't to make these + + + align:start position:0% +importantly you just won't to make these +mistakes since that we've been thinking + + align:start position:0% +mistakes since that we've been thinking + + + align:start position:0% +mistakes since that we've been thinking +is sort of translation by imagination so + + align:start position:0% +is sort of translation by imagination so + + + align:start position:0% +is sort of translation by imagination so +you take a sentence and it's a + + align:start position:0% +you take a sentence and it's a + + + align:start position:0% +you take a sentence and it's a +generative model that we have that + + align:start position:0% +generative model that we have that + + + align:start position:0% +generative model that we have that +connects sentences and videos and what + + align:start position:0% +connects sentences and videos and what + + + align:start position:0% +connects sentences and videos and what +you do is you sample your sample a whole + + align:start position:0% +you do is you sample your sample a whole + + + align:start position:0% +you do is you sample your sample a whole +bunch of videos so basically you imagine + + align:start position:0% +bunch of videos so basically you imagine + + + align:start position:0% +bunch of videos so basically you imagine +what scenarios the sentence could be + + align:start position:0% +what scenarios the sentence could be + + + align:start position:0% +what scenarios the sentence could be +true of you get your collection the + + align:start position:0% +true of you get your collection the + + + align:start position:0% +true of you get your collection the +generator you search over sentences that + + align:start position:0% +generator you search over sentences that + + + align:start position:0% +generator you search over sentences that +describe these videos and you output a + + align:start position:0% +describe these videos and you output a + + + align:start position:0% +describe these videos and you output a +sentence that describes them well in + + align:start position:0% +sentence that describes them well in + + + align:start position:0% +sentence that describes them well in +aggregate so basically you just combine + + align:start position:0% +aggregate so basically you just combine + + + align:start position:0% +aggregate so basically you just combine +your ability to sample which comes from + + align:start position:0% +your ability to sample which comes from + + + align:start position:0% +your ability to sample which comes from +your recognizer and your ability to + + align:start position:0% +your recognizer and your ability to + + + align:start position:0% +your recognizer and your ability to +generate and you get a translation + + align:start position:0% +generate and you get a translation + + + align:start position:0% +generate and you get a translation +system so you do a language to language + + align:start position:0% +system so you do a language to language + + + align:start position:0% +system so you do a language to language +task mediated by your understanding of + + align:start position:0% +task mediated by your understanding of + + + align:start position:0% +task mediated by your understanding of +the real world something else that you + + align:start position:0% +the real world something else that you + + + align:start position:0% +the real world something else that you +can do is planning which I'll just say + + align:start position:0% +can do is planning which I'll just say + + + align:start position:0% +can do is planning which I'll just say +two words about all you do is put in a + + align:start position:0% +two words about all you do is put in a + + + align:start position:0% +two words about all you do is put in a +planning task what you have is you have + + align:start position:0% +planning task what you have is you have + + + align:start position:0% +planning task what you have is you have +a planning language I'm glad that wasn't + + align:start position:0% +a planning language I'm glad that wasn't + + + align:start position:0% +a planning language I'm glad that wasn't +my cell phone you have a planning + + align:start position:0% +my cell phone you have a planning + + + align:start position:0% +my cell phone you have a planning +language right so you have a fairly + + align:start position:0% +language right so you have a fairly + + + align:start position:0% +language right so you have a fairly +constrained vocabulary that you can use + + align:start position:0% +constrained vocabulary that you can use + + + align:start position:0% +constrained vocabulary that you can use +to describe your plans and this allows + + align:start position:0% +to describe your plans and this allows + + + align:start position:0% +to describe your plans and this allows +you to have efficient inference instead + + align:start position:0% +you to have efficient inference instead + + + align:start position:0% +you to have efficient inference instead +what you can imagine that I have two + + align:start position:0% +what you can imagine that I have two + + + align:start position:0% +what you can imagine that I have two +frames of a video real or imagined where + + align:start position:0% +frames of a video real or imagined where + + + align:start position:0% +frames of a video real or imagined where +I have the first world I'm far away from + + align:start position:0% +I have the first world I'm far away from + + + align:start position:0% +I have the first world I'm far away from +microphone I have the last world where + + align:start position:0% +microphone I have the last world where + + + align:start position:0% +microphone I have the last world where +I'm near the microphone and I have an + + align:start position:0% +I'm near the microphone and I have an + + + align:start position:0% +I'm near the microphone and I have an +observed video between the two people + + align:start position:0% +observed video between the two people + + + align:start position:0% +observed video between the two people +have worked and I've done some work on + + align:start position:0% +have worked and I've done some work on + + + align:start position:0% +have worked and I've done some work on +filling in partially observed videos so + + align:start position:0% +filling in partially observed videos so + + + align:start position:0% +filling in partially observed videos so +it's a very similar idea except that + + align:start position:0% +it's a very similar idea except that + + + align:start position:0% +it's a very similar idea except that +here we have a partially observed video + + align:start position:0% +here we have a partially observed video + + + align:start position:0% +here we have a partially observed video +and we know that this partially + + align:start position:0% +and we know that this partially + + + align:start position:0% +and we know that this partially +observable should be described by one or + + align:start position:0% +observable should be described by one or + + + align:start position:0% +observable should be described by one or +more sentences so we're gonna do the + + align:start position:0% +more sentences so we're gonna do the + + + align:start position:0% +more sentences so we're gonna do the +same kind of sampling process where we + + align:start position:0% +same kind of sampling process where we + + + align:start position:0% +same kind of sampling process where we +sample from this partially observed + + align:start position:0% +sample from this partially observed + + + align:start position:0% +sample from this partially observed +video and we try to describe with + + align:start position:0% +video and we try to describe with + + + align:start position:0% +video and we try to describe with +sentences and now you're doing planning + + align:start position:0% +sentences and now you're doing planning + + + align:start position:0% +sentences and now you're doing planning +you're coming up with a description of + + align:start position:0% +you're coming up with a description of + + + align:start position:0% +you're coming up with a description of +what happened in this missing chunk of + + align:start position:0% +what happened in this missing chunk of + + + align:start position:0% +what happened in this missing chunk of +the video but you're planning language + + align:start position:0% +the video but you're planning language + + + align:start position:0% +the video but you're planning language +is English so you get to take advantage + + align:start position:0% +is English so you get to take advantage + + + align:start position:0% +is English so you get to take advantage +of things like ambiguity which you + + align:start position:0% +of things like ambiguity which you + + + align:start position:0% +of things like ambiguity which you +couldn't take advantage of in + + align:start position:0% +couldn't take advantage of in + + + align:start position:0% +couldn't take advantage of in +in languages theory of mind the idea + + align:start position:0% +in languages theory of mind the idea + + + align:start position:0% +in languages theory of mind the idea +here is relatively straightforward as + + align:start position:0% +here is relatively straightforward as + + + align:start position:0% +here is relatively straightforward as +well so what we have right now basically + + align:start position:0% +well so what we have right now basically + + + align:start position:0% +well so what we have right now basically +are two in Markov models are two kinds + + align:start position:0% +are two in Markov models are two kinds + + + align:start position:0% +are two in Markov models are two kinds +of hidden Markov models right there's a + + align:start position:0% +of hidden Markov models right there's a + + + align:start position:0% +of hidden Markov models right there's a +video we have some hidden Markov models + + align:start position:0% +video we have some hidden Markov models + + + align:start position:0% +video we have some hidden Markov models +that are tracks and we have some hidden + + align:start position:0% +that are tracks and we have some hidden + + + align:start position:0% +that are tracks and we have some hidden +Markov model that look at the tracks and + + align:start position:0% +Markov model that look at the tracks and + + + align:start position:0% +Markov model that look at the tracks and +they do some inference about what's + + align:start position:0% +they do some inference about what's + + + align:start position:0% +they do some inference about what's +going on with the events in these videos + + align:start position:0% +going on with the events in these videos + + + align:start position:0% +going on with the events in these videos +so now imagine that I had a third kind a + + align:start position:0% +so now imagine that I had a third kind a + + + align:start position:0% +so now imagine that I had a third kind a +third kind of hidden Markov model that + + align:start position:0% +third kind of hidden Markov model that + + + align:start position:0% +third kind of hidden Markov model that +only looks at the trackers doesn't look + + align:start position:0% +only looks at the trackers doesn't look + + + align:start position:0% +only looks at the trackers doesn't look +at the words directly and what it does + + align:start position:0% +at the words directly and what it does + + + align:start position:0% +at the words directly and what it does +is it makes another assumption about the + + align:start position:0% +is it makes another assumption about the + + + align:start position:0% +is it makes another assumption about the +videos so first we assumed them objects + + align:start position:0% +videos so first we assumed them objects + + + align:start position:0% +videos so first we assumed them objects +were moving in a coherent way then we + + align:start position:0% +were moving in a coherent way then we + + + align:start position:0% +were moving in a coherent way then we +assumed that the objects were moving + + align:start position:0% +assumed that the objects were moving + + + align:start position:0% +assumed that the objects were moving +according to the dynamics of some hidden + + align:start position:0% +according to the dynamics of some hidden + + + align:start position:0% +according to the dynamics of some hidden +Markov models now we're gonna people + + align:start position:0% +Markov models now we're gonna people + + + align:start position:0% +Markov models now we're gonna people +move according to some that some + + align:start position:0% +move according to some that some + + + align:start position:0% +move according to some that some +dynamics of what's going on inside our + + align:start position:0% +dynamics of what's going on inside our + + + align:start position:0% +dynamics of what's going on inside our +heads so you can assume that I have a + + align:start position:0% +heads so you can assume that I have a + + + align:start position:0% +heads so you can assume that I have a +planner inside my head that tells me + + align:start position:0% +planner inside my head that tells me + + + align:start position:0% +planner inside my head that tells me +what I want to do and what I should do + + align:start position:0% +what I want to do and what I should do + + + align:start position:0% +what I want to do and what I should do +in the future to accomplish my goals and + + align:start position:0% +in the future to accomplish my goals and + + + align:start position:0% +in the future to accomplish my goals and +you can look at a sequence of my actions + + align:start position:0% +you can look at a sequence of my actions + + + align:start position:0% +you can look at a sequence of my actions +and try to infer if you believe this + + align:start position:0% +and try to infer if you believe this + + + align:start position:0% +and try to infer if you believe this +planner is running in my head what do + + align:start position:0% +planner is running in my head what do + + + align:start position:0% +planner is running in my head what do +you think I should do next + + align:start position:0% +you think I should do next + + + align:start position:0% +you think I should do next +now the nice part about the all many of + + align:start position:0% +now the nice part about the all many of + + + align:start position:0% +now the nice part about the all many of +these planners is that they look a lot + + align:start position:0% +these planners is that they look a lot + + + align:start position:0% +these planners is that they look a lot +like these inner Markov models and the + + align:start position:0% +like these inner Markov models and the + + + align:start position:0% +like these inner Markov models and the +inference algorithms look a lot like + + align:start position:0% +inference algorithms look a lot like + + + align:start position:0% +inference algorithms look a lot like +these models so basically you can do the + + align:start position:0% +these models so basically you can do the + + + align:start position:0% +these models so basically you can do the +same kind of trick by assuming that hmm + + align:start position:0% +same kind of trick by assuming that hmm + + + align:start position:0% +same kind of trick by assuming that hmm +like things are going on inside people's + + align:start position:0% +like things are going on inside people's + + + align:start position:0% +like things are going on inside people's +heads so you can do things like predict + + align:start position:0% +heads so you can do things like predict + + + align:start position:0% +heads so you can do things like predict +actions figure out what people want to + + align:start position:0% +actions figure out what people want to + + + align:start position:0% +actions figure out what people want to +do in the future what they did in the + + align:start position:0% +do in the future what they did in the + + + align:start position:0% +do in the future what they did in the +past that's what that's what the project + + align:start position:0% +past that's what that's what the project + + + align:start position:0% +past that's what that's what the project +is I want to show you another example of + + align:start position:0% +is I want to show you another example of + + + align:start position:0% +is I want to show you another example of +vision and language but a totally + + align:start position:0% +vision and language but a totally + + + align:start position:0% +vision and language but a totally +different domain that I won't talk about + + align:start position:0% +different domain that I won't talk about + + + align:start position:0% +different domain that I won't talk about +which is in the case of robots this is + + align:start position:0% +which is in the case of robots this is + + + align:start position:0% +which is in the case of robots this is +something that we built several years + + align:start position:0% +something that we built several years + + + align:start position:0% +something that we built several years +ago this is a robot that looks at a 3d + + align:start position:0% +ago this is a robot that looks at a 3d + + + align:start position:0% +ago this is a robot that looks at a 3d +lecture it's built out of Lincoln Logs + + align:start position:0% +lecture it's built out of Lincoln Logs + + + align:start position:0% +lecture it's built out of Lincoln Logs +they're big they're easier for the robot + + align:start position:0% +they're big they're easier for the robot + + + align:start position:0% +they're big they're easier for the robot +to manipulate than Legos the downside is + + align:start position:0% +to manipulate than Legos the downside is + + + align:start position:0% +to manipulate than Legos the downside is +they're all brown so it's very difficult + + align:start position:0% +they're all brown so it's very difficult + + + align:start position:0% +they're all brown so it's very difficult +to division on this but it actually will + + align:start position:0% +to division on this but it actually will + + + align:start position:0% +to division on this but it actually will +in a moment reconstruct the 3d structure + + align:start position:0% +in a moment reconstruct the 3d structure + + + align:start position:0% +in a moment reconstruct the 3d structure +of what it sees and we annotated in red + + align:start position:0% +of what it sees and we annotated in red + + + align:start position:0% +of what it sees and we annotated in red +what it what errors in May we didn't + + align:start position:0% +what it what errors in May we didn't + + + align:start position:0% +what it what errors in May we didn't +tell it this what it does is it measures + + align:start position:0% +tell it this what it does is it measures + + + align:start position:0% +tell it this what it does is it measures +its own confidence and it figures out + + align:start position:0% +its own confidence and it figures out + + + align:start position:0% +its own confidence and it figures out +occluded so it has too little + + align:start position:0% +occluded so it has too little + + + align:start position:0% +occluded so it has too little +information and it plans another view it + + align:start position:0% +information and it plans another view it + + + align:start position:0% +information and it plans another view it +goes it acquires it by measuring its own + + align:start position:0% +goes it acquires it by measuring its own + + + align:start position:0% +goes it acquires it by measuring its own +confidence this view is actually worse + + align:start position:0% +confidence this view is actually worse + + + align:start position:0% +confidence this view is actually worse +than the previous view but it's + + align:start position:0% +than the previous view but it's + + + align:start position:0% +than the previous view but it's +complimentary so it will actually gain + + align:start position:0% +complimentary so it will actually gain + + + align:start position:0% +complimentary so it will actually gain +the information that it's missing and + + align:start position:0% +the information that it's missing and + + + align:start position:0% +the information that it's missing and +all of this comes from the same kind of + + align:start position:0% +all of this comes from the same kind of + + + align:start position:0% +all of this comes from the same kind of +Jenner + + align:start position:0% +Jenner + + + align:start position:0% +Jenner +model trick that I showed you a moment + + align:start position:0% +model trick that I showed you a moment + + + align:start position:0% +model trick that I showed you a moment +ago similar model it just makes + + align:start position:0% +ago similar model it just makes + + + align:start position:0% +ago similar model it just makes +different assumptions about what's built + + align:start position:0% +different assumptions about what's built + + + align:start position:0% +different assumptions about what's built +into it so now because we have a nice + + align:start position:0% +into it so now because we have a nice + + + align:start position:0% +into it so now because we have a nice +generative model we can integrate the + + align:start position:0% +generative model we can integrate the + + + align:start position:0% +generative model we can integrate the +two views together you're gonna see in a + + align:start position:0% +two views together you're gonna see in a + + + align:start position:0% +two views together you're gonna see in a +moment it'll still make some mistakes + + align:start position:0% +moment it'll still make some mistakes + + + align:start position:0% +moment it'll still make some mistakes +and won't be completely confident + + align:start position:0% +and won't be completely confident + + + align:start position:0% +and won't be completely confident +because there are some regions that it + + align:start position:0% +because there are some regions that it + + + align:start position:0% +because there are some regions that it +can't see even from both views and then + + align:start position:0% +can't see even from both views and then + + + align:start position:0% +can't see even from both views and then +what we told it is okay fine for second + + align:start position:0% +what we told it is okay fine for second + + + align:start position:0% +what we told it is okay fine for second +view take just the first view here's a + + align:start position:0% +view take just the first view here's a + + + align:start position:0% +view take just the first view here's a +sentence or in this case a sentence + + align:start position:0% +sentence or in this case a sentence + + + align:start position:0% +sentence or in this case a sentence +fragment the fragment is something like + + align:start position:0% +fragment the fragment is something like + + + align:start position:0% +fragment the fragment is something like +there's a window to the left and + + align:start position:0% +there's a window to the left and + + + align:start position:0% +there's a window to the left and +perpendicular to this door it'll just a + + align:start position:0% +perpendicular to this door it'll just a + + + align:start position:0% +perpendicular to this door it'll just a +pure moment and integrating this one + + align:start position:0% +pure moment and integrating this one + + + align:start position:0% +pure moment and integrating this one +view that it saw that was an uncertain + + align:start position:0% +view that it saw that was an uncertain + + + align:start position:0% +view that it saw that was an uncertain +with uncertain about with that one + + align:start position:0% +with uncertain about with that one + + + align:start position:0% +with uncertain about with that one +sentence that's also very generic and + + align:start position:0% +sentence that's also very generic and + + + align:start position:0% +sentence that's also very generic and +apply to many determine that these two + + align:start position:0% +apply to many determine that these two + + + align:start position:0% +apply to many determine that these two +completely disambiguate the structure + + align:start position:0% +completely disambiguate the structure + + + align:start position:0% +completely disambiguate the structure +and now it's perfectly confident in + + align:start position:0% +and now it's perfectly confident in + + + align:start position:0% +and now it's perfectly confident in +what's going on and it can go and it can + + align:start position:0% +what's going on and it can go and it can + + + align:start position:0% +what's going on and it can go and it can +disassemble the structure for you we can + + align:start position:0% +disassemble the structure for you we can + + + align:start position:0% +disassemble the structure for you we can +play this game in many directions we can + + align:start position:0% +play this game in many directions we can + + + align:start position:0% +play this game in many directions we can +have the robot describes as structures + + align:start position:0% +have the robot describes as structures + + + align:start position:0% +have the robot describes as structures +to us we can give it a description and + + align:start position:0% +to us we can give it a description and + + + align:start position:0% +to us we can give it a description and +it can build the structure one robot can + + align:start position:0% +it can build the structure one robot can + + + align:start position:0% +it can build the structure one robot can +describe the structure in English to + + align:start position:0% +describe the structure in English to + + + align:start position:0% +describe the structure in English to +another robot who can build it for it + + align:start position:0% +another robot who can build it for it + + + align:start position:0% +another robot who can build it for it +and it's exactly the same kind of idea + + align:start position:0% +and it's exactly the same kind of idea + + + align:start position:0% +and it's exactly the same kind of idea +you connect your vision and your + + align:start position:0% +you connect your vision and your + + + align:start position:0% +you connect your vision and your +language model to something in the real + + align:start position:0% +language model to something in the real + + + align:start position:0% +language model to something in the real +world and then you can play many many + + align:start position:0% +world and then you can play many many + + + align:start position:0% +world and then you can play many many +different tricks with one internal + + align:start position:0% +different tricks with one internal + + + align:start position:0% +different tricks with one internal +representation without modifying it at + + align:start position:0% +representation without modifying it at + + + align:start position:0% +representation without modifying it at +all but I realized yesterday that I was + + align:start position:0% +all but I realized yesterday that I was + + + align:start position:0% +all but I realized yesterday that I was +the last speaker before the weekend so I + + align:start position:0% +the last speaker before the weekend so I + + + align:start position:0% +the last speaker before the weekend so I +want to end by leaving you as depressed + + align:start position:0% +want to end by leaving you as depressed + + + align:start position:0% +want to end by leaving you as depressed +as I possibly can and tell you all the + + align:start position:0% +as I possibly can and tell you all the + + + align:start position:0% +as I possibly can and tell you all the +wonderful things that don't work and how + + align:start position:0% +wonderful things that don't work and how + + + align:start position:0% +wonderful things that don't work and how +far away we are from understanding + + align:start position:0% +far away we are from understanding + + + align:start position:0% +far away we are from understanding +anything so first of all we can't + + align:start position:0% +anything so first of all we can't + + + align:start position:0% +anything so first of all we can't +generate the kind of coherent stories + + align:start position:0% +generate the kind of coherent stories + + + align:start position:0% +generate the kind of coherent stories +that Patrick looks at right really if + + align:start position:0% +that Patrick looks at right really if + + + align:start position:0% +that Patrick looks at right really if +you look at a long video what we can do + + align:start position:0% +you look at a long video what we can do + + + align:start position:0% +you look at a long video what we can do +is we can search or we can describe + + align:start position:0% +is we can search or we can describe + + + align:start position:0% +is we can search or we can describe +small events you know person pick + + align:start position:0% +small events you know person pick + + + align:start position:0% +small events you know person pick +something up they put it down but we can + + align:start position:0% +something up they put it down but we can + + + align:start position:0% +something up they put it down but we can +say is you know the thief heard the room + + align:start position:0% +say is you know the thief heard the room + + + align:start position:0% +say is you know the thief heard the room +and rummaged around and ran away with + + align:start position:0% +and rummaged around and ran away with + + + align:start position:0% +and rummaged around and ran away with +the gold right that's the kind of thing + + align:start position:0% +the gold right that's the kind of thing + + + align:start position:0% +the gold right that's the kind of thing +that you want to generate is the kind of + + align:start position:0% +that you want to generate is the kind of + + + align:start position:0% +that you want to generate is the kind of +thing that kids generate but we're not + + align:start position:0% +thing that kids generate but we're not + + + align:start position:0% +thing that kids generate but we're not +there yet + + align:start position:0% +there yet + + + align:start position:0% +there yet +not even close we also only reason in 2d + + align:start position:0% +not even close we also only reason in 2d + + + align:start position:0% +not even close we also only reason in 2d +there's no 3d reasoning here and that + + align:start position:0% +there's no 3d reasoning here and that + + + align:start position:0% +there's no 3d reasoning here and that +significantly hurts us although we have + + align:start position:0% +significantly hurts us although we have + + + align:start position:0% +significantly hurts us although we have +some ideas for how we might do 3d + + align:start position:0% +some ideas for how we might do 3d + + + align:start position:0% +some ideas for how we might do 3d +another important aspect is we don't + + align:start position:0% +another important aspect is we don't + + + align:start position:0% +another important aspect is we don't +thack relationships now that's fine as + + align:start position:0% +thack relationships now that's fine as + + + align:start position:0% +thack relationships now that's fine as +long as pickup means this kind of action + + align:start position:0% +long as pickup means this kind of action + + + align:start position:0% +long as pickup means this kind of action +where you see me standing next to an + + align:start position:0% +where you see me standing next to an + + + align:start position:0% +where you see me standing next to an +object and the object moving up but + + align:start position:0% +object and the object moving up but + + + align:start position:0% +object and the object moving up but +sometimes pickup means something totally + + align:start position:0% +sometimes pickup means something totally + + + align:start position:0% +sometimes pickup means something totally +different so you're gonna see this cat + + align:start position:0% +different so you're gonna see this cat + + + align:start position:0% +different so you're gonna see this cat +is gonna pick up that kitten in just a + + align:start position:0% +is gonna pick up that kitten in just a + + + align:start position:0% +is gonna pick up that kitten in just a +moment and you're gonna see if you pay + + align:start position:0% +moment and you're gonna see if you pay + + + align:start position:0% +moment and you're gonna see if you pay +attention to the motion of the cats that + + align:start position:0% +attention to the motion of the cats that + + + align:start position:0% +attention to the motion of the cats that +it doesn't look and picking something up + + align:start position:0% +it doesn't look and picking something up + + + align:start position:0% +it doesn't look and picking something up +it's not very good at picking up the + + align:start position:0% +it's not very good at picking up the + + + align:start position:0% +it's not very good at picking up the +kitten mind you I think this may be its + + align:start position:0% +kitten mind you I think this may be its + + + align:start position:0% +kitten mind you I think this may be its +first try right I think it's having a + + align:start position:0% +first try right I think it's having a + + + align:start position:0% +first try right I think it's having a +good day okay + + align:start position:0% +good day okay + + + align:start position:0% +good day okay +struggling a little bit so definitely + + align:start position:0% +struggling a little bit so definitely + + + align:start position:0% +struggling a little bit so definitely +picked it up but it didn't look anything + + align:start position:0% +picked it up but it didn't look anything + + + align:start position:0% +picked it up but it didn't look anything +like any of the other pickup examples I + + align:start position:0% +like any of the other pickup examples I + + + align:start position:0% +like any of the other pickup examples I +showed you but can separately + + align:start position:0% +showed you but can separately + + + align:start position:0% +showed you but can separately +you should totally recognize this if + + align:start position:0% +you should totally recognize this if + + + align:start position:0% +you should totally recognize this if +you've seen those other examples and + + align:start position:0% +you've seen those other examples and + + + align:start position:0% +you've seen those other examples and +kids can do this so the important part + + align:start position:0% +kids can do this so the important part + + + align:start position:0% +kids can do this so the important part +is you have to change how you reason you + + align:start position:0% +is you have to change how you reason you + + + align:start position:0% +is you have to change how you reason you +can't just reason about the relative + + align:start position:0% +can't just reason about the relative + + + align:start position:0% +can't just reason about the relative +motions of the objects you have to + + align:start position:0% +motions of the objects you have to + + + align:start position:0% +motions of the objects you have to +assume that there are some hidden forces + + align:start position:0% +assume that there are some hidden forces + + + align:start position:0% +assume that there are some hidden forces +going on and you have to reason about + + align:start position:0% +going on and you have to reason about + + + align:start position:0% +going on and you have to reason about +the contact relationships and the forces + + align:start position:0% +the contact relationships and the forces + + + align:start position:0% +the contact relationships and the forces +that the objects are undergoing happens + + align:start position:0% +that the objects are undergoing happens + + + align:start position:0% +that the objects are undergoing happens +if you try to recognize a helicopter + + align:start position:0% +if you try to recognize a helicopter + + + align:start position:0% +if you try to recognize a helicopter +picking something up it looks totally + + align:start position:0% +picking something up it looks totally + + + align:start position:0% +picking something up it looks totally +different from a human doing it but no + + align:start position:0% +different from a human doing it but no + + + align:start position:0% +different from a human doing it but no +one has any problems recognizing this + + align:start position:0% +one has any problems recognizing this + + + align:start position:0% +one has any problems recognizing this +segmentation is also a huge problem for + + align:start position:0% +segmentation is also a huge problem for + + + align:start position:0% +segmentation is also a huge problem for +many of these problems you have to pay + + align:start position:0% +many of these problems you have to pay + + + align:start position:0% +many of these problems you have to pay +attention to define boundaries of the + + align:start position:0% +attention to define boundaries of the + + + align:start position:0% +attention to define boundaries of the +objects in order to understand that that + + align:start position:0% +objects in order to understand that that + + + align:start position:0% +objects in order to understand that that +kitten was being rotated and then + + align:start position:0% +kitten was being rotated and then + + + align:start position:0% +kitten was being rotated and then +slightly lifted there's also a more + + align:start position:0% +slightly lifted there's also a more + + + align:start position:0% +slightly lifted there's also a more +philosophical problem apart and what it + + align:start position:0% +philosophical problem apart and what it + + + align:start position:0% +philosophical problem apart and what it +means for something to be an object + + align:start position:0% +means for something to be an object + + + align:start position:0% +means for something to be an object +you know we arbitrarily say that the cat + + align:start position:0% +you know we arbitrarily say that the cat + + + align:start position:0% +you know we arbitrarily say that the cat +is an object but I could refer to its + + align:start position:0% +is an object but I could refer to its + + + align:start position:0% +is an object but I could refer to its +paws I could refer to its ears I could + + align:start position:0% +paws I could refer to its ears I could + + + align:start position:0% +paws I could refer to its ears I could +refer to one small patch on its back as + + align:start position:0% +refer to one small patch on its back as + + + align:start position:0% +refer to one small patch on its back as +long as we all know what we're talking + + align:start position:0% +long as we all know what we're talking + + + align:start position:0% +long as we all know what we're talking +about that can be our object and that's + + align:start position:0% +about that can be our object and that's + + + align:start position:0% +about that can be our object and that's +a problem throughout computer vision it + + align:start position:0% +a problem throughout computer vision it + + + align:start position:0% +a problem throughout computer vision it +also occurs in a totally different + + align:start position:0% +also occurs in a totally different + + + align:start position:0% +also occurs in a totally different +problem so if you've ever seen Bongard + + align:start position:0% +problem so if you've ever seen Bongard + + + align:start position:0% +problem so if you've ever seen Bongard +problems there are these problems where + + align:start position:0% +problems there are these problems where + + + align:start position:0% +problems there are these problems where +you have these weird patches and you + + align:start position:0% +you have these weird patches and you + + + align:start position:0% +you have these weird patches and you +have to figure out what's in common + + align:start position:0% +have to figure out what's in common + + + align:start position:0% +have to figure out what's in common +between them and that's a case where you + + align:start position:0% +between them and that's a case where you + + + align:start position:0% +between them and that's a case where you +have to dig deep into your visual system + + align:start position:0% +have to dig deep into your visual system + + + align:start position:0% +have to dig deep into your visual system +to extract the completely different kind + + align:start position:0% +to extract the completely different kind + + + align:start position:0% +to extract the completely different kind +of information and this is an example + + align:start position:0% +of information and this is an example + + + align:start position:0% +of information and this is an example +that I prefer so in this task you can + + align:start position:0% +that I prefer so in this task you can + + + align:start position:0% +that I prefer so in this task you can +try to find the real dog right we can + + align:start position:0% +try to find the real dog right we can + + + align:start position:0% +try to find the real dog right we can +all spot it after you look for a little + + align:start position:0% +all spot it after you look for a little + + + align:start position:0% +all spot it after you look for a little +while right as anyway + + align:start position:0% +while right as anyway + + + align:start position:0% +while right as anyway +okay so you can all see it the + + align:start position:0% +okay so you can all see it the + + + align:start position:0% +okay so you can all see it the +interesting part is I mean I doubt you + + align:start position:0% +interesting part is I mean I doubt you + + + align:start position:0% +interesting part is I mean I doubt you +have ever had training detecting real + + align:start position:0% +have ever had training detecting real + + + align:start position:0% +have ever had training detecting real +dogs amongst masses of fake dogs but + + align:start position:0% +dogs amongst masses of fake dogs but + + + align:start position:0% +dogs amongst masses of fake dogs but +somehow you were able to adapt and + + align:start position:0% +somehow you were able to adapt and + + + align:start position:0% +somehow you were able to adapt and +extract the completely different kind of + + align:start position:0% +extract the completely different kind of + + + align:start position:0% +extract the completely different kind of +information from your visual system + + align:start position:0% +information from your visual system + + + align:start position:0% +information from your visual system +information that isn't captured by our + + align:start position:0% +information that isn't captured by our + + + align:start position:0% +information that isn't captured by our +feature vectors that talk about the + + align:start position:0% +feature vectors that talk about the + + + align:start position:0% +feature vectors that talk about the +color location velocity etc so you have + + align:start position:0% +color location velocity etc so you have + + + align:start position:0% +color location velocity etc so you have +this ability to extract out past + + align:start position:0% +this ability to extract out past + + + align:start position:0% +this ability to extract out past +specific information you can do things + + align:start position:0% +specific information you can do things + + + align:start position:0% +specific information you can do things +like theory of mine but you can do far + + align:start position:0% +like theory of mine but you can do far + + + align:start position:0% +like theory of mine but you can do far +more than assume people are writing a + + align:start position:0% +more than assume people are writing a + + + align:start position:0% +more than assume people are writing a +planner you can detect if I'm sad if I'm + + align:start position:0% +planner you can detect if I'm sad if I'm + + + align:start position:0% +planner you can detect if I'm sad if I'm +happy you can reason about whether two + + align:start position:0% +happy you can reason about whether two + + + align:start position:0% +happy you can reason about whether two +people are having a particular kind of + + align:start position:0% +people are having a particular kind of + + + align:start position:0% +people are having a particular kind of +interaction who's more powerful than the + + align:start position:0% +interaction who's more powerful than the + + + align:start position:0% +interaction who's more powerful than the +other person you also have a very strong + + align:start position:0% +other person you also have a very strong + + + align:start position:0% +other person you also have a very strong +physics model inside your head that + + align:start position:0% +physics model inside your head that + + + align:start position:0% +physics model inside your head that +underlies much of this and even more + + align:start position:0% +underlies much of this and even more + + + align:start position:0% +underlies much of this and even more +than that there's the concept of + + align:start position:0% +than that there's the concept of + + + align:start position:0% +than that there's the concept of +modification so walking quickly it looks + + align:start position:0% +modification so walking quickly it looks + + + align:start position:0% +modification so walking quickly it looks +very different from running quickly and + + align:start position:0% +very different from running quickly and + + + align:start position:0% +very different from running quickly and +the way you model these is quite + + align:start position:0% +the way you model these is quite + + + align:start position:0% +the way you model these is quite +complicated and the system that I + + align:start position:0% +complicated and the system that I + + + align:start position:0% +complicated and the system that I +present it doesn't do a good job of it + + align:start position:0% +present it doesn't do a good job of it + + + align:start position:0% +present it doesn't do a good job of it +but one of my favorite examples from my + + align:start position:0% +but one of my favorite examples from my + + + align:start position:0% +but one of my favorite examples from my +childhood long ago is is this one which + + align:start position:0% +childhood long ago is is this one which + + + align:start position:0% +childhood long ago is is this one which +is a kind of modification right so + + align:start position:0% +is a kind of modification right so + + + align:start position:0% +is a kind of modification right so +coyote is gonna draw this you're gonna + + align:start position:0% +coyote is gonna draw this you're gonna + + + align:start position:0% +coyote is gonna draw this you're gonna +see the roadrunner try to run through it + + align:start position:0% +see the roadrunner try to run through it + + + align:start position:0% +see the roadrunner try to run through it +and he makes it and you can imagine + + align:start position:0% +and he makes it and you can imagine + + + align:start position:0% +and he makes it and you can imagine +what's about to happen next + + align:start position:0% +what's about to happen next + + + align:start position:0% +what's about to happen next +coyotes not gonna have a good day so so + + align:start position:0% +coyotes not gonna have a good day so so + + + align:start position:0% +coyotes not gonna have a good day so so +this looks silly right and you would + + align:start position:0% +this looks silly right and you would + + + align:start position:0% +this looks silly right and you would +think to yourself I possibly applied + + align:start position:0% +think to yourself I possibly applied + + + align:start position:0% +think to yourself I possibly applied +this in the real world but actually this + + align:start position:0% +this in the real world but actually this + + + align:start position:0% +this in the real world but actually this +happens in the real world all the time a + + align:start position:0% +happens in the real world all the time a + + + align:start position:0% +happens in the real world all the time a +cage can be open for a mouse but close + + align:start position:0% +cage can be open for a mouse but close + + + align:start position:0% +cage can be open for a mouse but close +for an elephant so if you're gonna + + align:start position:0% +for an elephant so if you're gonna + + + align:start position:0% +for an elephant so if you're gonna +represent something like is something + + align:start position:0% +represent something like is something + + + align:start position:0% +represent something like is something +closed or not you have to be able to + + align:start position:0% +closed or not you have to be able to + + + align:start position:0% +closed or not you have to be able to +handle situations like this and that's + + align:start position:0% +handle situations like this and that's + + + align:start position:0% +handle situations like this and that's +why kids can understand really weird + + align:start position:0% +why kids can understand really weird + + + align:start position:0% +why kids can understand really weird +scenarios like this because they're not + + align:start position:0% +scenarios like this because they're not + + + align:start position:0% +scenarios like this because they're not +so outlandish there's also the problem + + align:start position:0% +so outlandish there's also the problem + + + align:start position:0% +so outlandish there's also the problem +Dority of English verbs things like + + align:start position:0% +Dority of English verbs things like + + + align:start position:0% +Dority of English verbs things like +absolve admire anger approve bark etc + + align:start position:0% +absolve admire anger approve bark etc + + + align:start position:0% +absolve admire anger approve bark etc +all of them require far more knowledge + + align:start position:0% +all of them require far more knowledge + + + align:start position:0% +all of them require far more knowledge +they require many of the things I've + + align:start position:0% +they require many of the things I've + + + align:start position:0% +they require many of the things I've +talked about before and actually far + + align:start position:0% +talked about before and actually far + + + align:start position:0% +talked about before and actually far +more than them and what's even worse is + + align:start position:0% +more than them and what's even worse is + + + align:start position:0% +more than them and what's even worse is +we also use language in pretty bizarre + + align:start position:0% +we also use language in pretty bizarre + + + align:start position:0% +we also use language in pretty bizarre +ways so there are some kinds of idioms + + align:start position:0% +ways so there are some kinds of idioms + + + align:start position:0% +ways so there are some kinds of idioms +in English like the market or bullish + + align:start position:0% +in English like the market or bullish + + + align:start position:0% +in English like the market or bullish +that you have to have seen before to + + align:start position:0% +that you have to have seen before to + + + align:start position:0% +that you have to have seen before to +understand right there's no reason to + + align:start position:0% +understand right there's no reason to + + + align:start position:0% +understand right there's no reason to +assume that bears are better or worse + + align:start position:0% +assume that bears are better or worse + + + align:start position:0% +assume that bears are better or worse +than Bulls when you apply them to the + + align:start position:0% +than Bulls when you apply them to the + + + align:start position:0% +than Bulls when you apply them to the +stock market but on the other hand Irv's + + align:start position:0% +stock market but on the other hand Irv's + + + align:start position:0% +stock market but on the other hand Irv's +certain things are very systematic I can + + align:start position:0% +certain things are very systematic I can + + + align:start position:0% +certain things are very systematic I can +have an up day or a down day because + + align:start position:0% +have an up day or a down day because + + + align:start position:0% +have an up day or a down day because +we've both + + align:start position:0% +we've both + + + align:start position:0% +we've both +as a culture agreed that up is good and + + align:start position:0% +as a culture agreed that up is good and + + + align:start position:0% +as a culture agreed that up is good and +down is bad some cultures have made the + + align:start position:0% +down is bad some cultures have made the + + + align:start position:0% +down is bad some cultures have made the +opposite choice but usually it's up is + + align:start position:0% +opposite choice but usually it's up is + + + align:start position:0% +opposite choice but usually it's up is +good down so an idea can be grand or it + + align:start position:0% +good down so an idea can be grand or it + + + align:start position:0% +good down so an idea can be grand or it +can be small because we've decided big + + align:start position:0% +can be small because we've decided big + + + align:start position:0% +can be small because we've decided big +things or better than small things + + align:start position:0% +things or better than small things + + + align:start position:0% +things or better than small things +something someone's mood can be dark or + + align:start position:0% +something someone's mood can be dark or + + + align:start position:0% +something someone's mood can be dark or +light and these are very systematic + + align:start position:0% +light and these are very systematic + + + align:start position:0% +light and these are very systematic +variations that underlie all of language + + align:start position:0% +variations that underlie all of language + + + align:start position:0% +variations that underlie all of language +and we constantly use metaphoric + + align:start position:0% +and we constantly use metaphoric + + + align:start position:0% +and we constantly use metaphoric +extension in order to describe what's + + align:start position:0% +extension in order to describe what's + + + align:start position:0% +extension in order to describe what's +going on around us and to talk about + + align:start position:0% +going on around us and to talk about + + + align:start position:0% +going on around us and to talk about +abstract things it really seems as it is + + align:start position:0% +abstract things it really seems as it is + + + align:start position:0% +abstract things it really seems as it is +kind of built into our model of the + + align:start position:0% +kind of built into our model of the + + + align:start position:0% +kind of built into our model of the +world and modeling this is kind of over + + align:start position:0% +world and modeling this is kind of over + + + align:start position:0% +world and modeling this is kind of over +the horizon and there are many many many + + align:start position:0% +the horizon and there are many many many + + + align:start position:0% +the horizon and there are many many many +other things that we're missing here so + + align:start position:0% +other things that we're missing here so + + + align:start position:0% +other things that we're missing here so +I just want to thank all my wonderful + + align:start position:0% +I just want to thank all my wonderful + + + align:start position:0% +I just want to thank all my wonderful +collaborators like worse Max Candice and + + align:start position:0% +collaborators like worse Max Candice and + + + align:start position:0% +collaborators like worse Max Candice and +people at MIT and people elsewhere + + align:start position:0% +people at MIT and people elsewhere + + + align:start position:0% +people at MIT and people elsewhere +but to recap what we saw is that we can + + align:start position:0% +but to recap what we saw is that we can + + + align:start position:0% +but to recap what we saw is that we can +get a little bit of traction on these + + align:start position:0% +get a little bit of traction on these + + + align:start position:0% +get a little bit of traction on these +problems we can build one system that + + align:start position:0% +problems we can build one system that + + + align:start position:0% +problems we can build one system that +does one simple problem just connects + + align:start position:0% +does one simple problem just connects + + + align:start position:0% +does one simple problem just connects +our perception with our high-level + + align:start position:0% +our perception with our high-level + + + align:start position:0% +our perception with our high-level +knowledge takes a video and a sentence + + align:start position:0% +knowledge takes a video and a sentence + + + align:start position:0% +knowledge takes a video and a sentence +and gives us a score and once we have + + align:start position:0% +and gives us a score and once we have + + + align:start position:0% +and gives us a score and once we have +this interesting connection this + + align:start position:0% +this interesting connection this + + + align:start position:0% +this interesting connection this +interesting feedback between these two + + align:start position:0% +interesting feedback between these two + + + align:start position:0% +interesting feedback between these two +very different looking systems it turns + + align:start position:0% +very different looking systems it turns + + + align:start position:0% +very different looking systems it turns +out that we can do many different and + + align:start position:0% +out that we can do many different and + + + align:start position:0% +out that we can do many different and +sometimes surprising + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/ObGYNQLG3us.txt b/ObGYNQLG3us.txt new file mode 100644 index 0000000000000000000000000000000000000000..6686c906b2314ac2cb392b8b480eb0b729f7418e --- /dev/null +++ b/ObGYNQLG3us.txt @@ -0,0 +1,4226 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help +MIT OpenCourseWare + +continue to offer high quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +GARY GENSLER: So we're +going to come back again + +today to blockchain economics. + +A lot of what we're going to +talk about today while again + +anchored in the +readings will also + +be relevant as we +now turn to after Sip + +week to act three where +we're going through use cases + +but also hopefully relevant as +you're starting to think, OK, + +what about this final +project and so forth + +and what do we need to do? + +Five or six of the groups +have come in either + +as an individual person or teams +of three or four have come in + +and bounced ideas off of me. + +So I want to thank all of +the groups that have come in, + +because you've helped +me also organize + +some of my talking +points for today + +as to what we're going through. + +And those of you +who haven't come in, + +feel free to set things +up if you find it helpful. + +It's not mandatory. + +But you can also +thank the six groups + +that have come in, +because now I'm + +trying to anticipate +your questions as well + +along the way. + +So, the overview of course our +reading and study questions + +will come through. + +There was the letter +to Jamie Dimon. + +So we're going to dive +into that one a little bit. + +I found it interesting when +I read it about a year ago. + +And then I thought, why not +throw it into to the mix here? + +The McKinsey report, +which, again, I + +found this to be true for years. + +It's not just this +class that you + +can find some consultant that's +put a generalized paper out, + +it does sort of +just skim the tops, + +but you're getting a +sense of how they're + +trying to gin up business. + +Their business model is to +write some of these reports. + +And some of you are going +to go into consulting + +and maybe even write these +reports at some point in time. + +But it's often a good way +to see what I'll call it + +just a survey, a +topical survey in how + +folks think about things. + +Quickly a little bit +on potential use cases. + +In the heart of +today's discussion + +and kind of the +heart for thinking + +about the final projects +is how to really assess + +the costs and benefits of +any potential use case. + +So I'll skip through +the study questions. + +But these are the key. + +I didn't see anybody go +in the discussion board. + +I looked. + +Did you see anything there? + +No. + +we did set it up. + +But what are the +potential benefits, + +and how do you assess +the cost of trusts? + +And that is going to be true +in every single project you + +look at. + +If you take anything +from this class, + +it's this core critical +reasoning of like-- + +and hopefully after +the Roubini paper + +last Tuesday, we're going +to come out of the doldrums + +and we're going to pull back +out of the minimalist side + +and get more in the middle. + +I might not get Alin lean +out of the minimalist side, + +I don't know. + +But it's interesting. + +Some groups come in and I find +the three or four people that + +are sitting there I ask. + +In and even amongst +the group, there's + +somebody who's a maximalist and +somebody who's a minimalist. + +So I think we're being +successful that we're not + +going to come out all +in the same place. + +So, of course, since we're +going to talk about the reading, + +let's jumped through, a +letter to Jamie Dimon. + +Anybody want to tell me what +you took from that letter? + +AUDIENCE: I really +loved this article. + +It is my favorite +reading so far. + +GARY GENSLER: Oh my +gosh, 12 classes. + +All right. + +AUDIENCE: So I though +that he really great + +job of stripping some of the +hyperbole, both the maximalist + +and the minimalist hyperbole +surrounding this out + +of it to lean on +really what it is + +and a very good explanation +of how it works. + +And then also, the +note of caution + +to see if these are the +dimensions around which-- + +you should wait til +you put a word in, + +but these are the +reasons why there's + +potentially big implications. + +GARY GENSLER: Right. + +And he wants to add to it. + +I'm going to hold-- there +was a hand before Alin? + +AUDIENCE: Yeah, no. + +I actually was going to +say something similar. + +But I thought he highlighted a +lot the trade-off between trust + +and the decentralized +properties of blockchain + +versus the cost you +must be willing to pay. + +GARY GENSLER: And remind +me your first name. + +AUDIENCE: Leonardo. + +GARY GENSLER: Leonardo. + +All right. + +AUDIENCE: I agree +with both of them. + +Also, very good +writing and style. + +One thing that I didn't +like is that at some point, + +he raised the +question, well, who + +needs censorship resistance? + +Because it seems like +this is the only benefit + +of these decentralized +applications. + +And he didn't answer +that question actually. + +He just gave two +vague broad answers, + +but didn't answer that question. + +So I think that's a +really good question. + +Who needs this stuff, anyway? + +GARY GENSLER: All right. + +Censorship resistance. + +We're going to come back to it. + +Stephanie. + +AUDIENCE: Yeah. + +So actually, I thought +censorship resistance was also + +one of the more interesting +parts of this letter. + +Because to me, when you read +through what they highlighted + +that Jamie Dimon had +said, one of the things + +was people who use Bitcoin +or Blockchain are criminals. + +And I didn't find that his +focus on censorship resistance + +really rebutted Jamie +Dimon's argument. + +GARY GENSLER: So-- + +Sean. + +AUDIENCE: Oh, I think that +censorship resistance is really + +interested in a way that +now I actually almost feel + +why we spend so much time and +energy on trying to understand + +public policy or +why is public policy + +such a big thing in response +to decentralized apps. + +I think this is a key question. + +GARY GENSLER: So I think of-- + +AUDIENCE: I just wanted to-- +well, I definitely agree. + +Because that was one of Dimon's +points, that, well, yeah, + +if you're a criminal, +this could be useful. + +And then he talked +about how it's + +worse than a lot of aspects +except censorship resistance. + +But I think the +analogy he used was + +the rise in encrypted messaging +that has just become-- + +it wasn't really +predictable that that + +would be such a big thing, +but now that's gotten + +use cases in the world. + +GARY GENSLER: So it +seems like people really + +like the writing, +not just the style + +but that it took on and +had a balanced approach. + +But you're highlighting, +wait a minute, + +he ends with +censorship resistance, + +but then doesn't +take it the next way. + +Like, what does that mean? + +And so I think +we're going to try + +to tease that out a little +bit, but I think of it + +as in two ways. + +It's the individual. + +Any one of us could be +blocked from doing something. + +We could not get a +service, we could not + +be allowed to take credit if +somebody is allocating credit. + +Think about Uber. + +If Uber were censoring, we +can't get a ride any longer. + +How many of us rate +everybody a five when + +we ride our Ubers +because we think, + +well, maybe they'll pick me up. + +If I rated everybody a three, +maybe they'll censor me. + +I don't know, but maybe you all +give more legitimate feedback. + +I just hit five. + +So it's the +individual censorship, + +but I think of it as +a second thing also, + +is barriers to entry, a +commercial more broad market + +barrier. + +And that in some ways, +the blockchain technology + +might allow to build something +where incumbents already + +have barriers to entry. + +They might have used public +policy to get the barriers, + +by the way. + +They might have regulatory +barriers as well. + +But more specifically, +he did define-- + +it was kind of +interesting-- crypto assets. + +And he was one that-- + +I'm trying to remember +the gentleman who wrote it + +because it was on Chain. + +It was the head of Chain. + +What's that? + +AUDIENCE: Adam Ludwin. + +GARY GENSLER: Adam Ludwin. + +But he too said, let's not +use the word cryptocurrency. + +Let's use the word +crypto assets. + +They enable a +decentralized application. + +And that was a key thing he was +trying to say to Jamie Dimon. + +It depends on how +much you believe + +in decentralized applications. + +If you don't see a value in +decentralized applications, + +Ludwin, said, all +right, I get it, + +I'll agree with you, Mr. Dimon. + +But there is a benefit for +decentralized applications + +and a mechanism to +allocate resources + +to a specific organization. + +So some incentive way, some +way to allocate resources. + +I would say this. + +We've studied money +a lot this semester, + +the medium of exchange, unit +of a cat, store of value. + +But it's also possible that +these crypto assets have + +some other benefit, that they're +not really truly competing + +with the US dollar or +competing with the Euro, + +but maybe they're competing +with-- who's my friend who's + +the gamer over here? + +Skins, yeah. + +What's your name again? + +AUDIENCE: Mike. + +GARY GENSLER: Mike. + +I'm going to be always +looking to my right for the-- + +but it could be an +incentive and be competing + +with skins, in a sense. + +And so I took that, +that, Mr. Dimon, + +don't think of it only +versus the Euro or the Dollar + +because maybe you're right. + +But it could have +something to do + +with decentralized applications. + +Kelly. + +AUDIENCE: To add to that, +Bitcoin is capitalism still. + +He should love it. + +GARY GENSLER: That +you should still + +love Bitcoin and capitalism, +and that the banks + +aren't going away. + +They will probably +still have banks. + +AUDIENCE: It is incredible +that he didn't use the word + +blockchain till the very +end to asterisk and say, + +you'll notice I +don't use blockchain, + +and I thought kind of a genius +way to separate [INAUDIBLE].. + +GARY GENSLER: Right. + +I'm not as genius as him +because the whole course + +is called Blockchain and Money. + +[LAUGHTER] + +Oh, well. + +So what are decentralized +applications, at least + +in this write-up? + +Anybody? + +Kelly? + +AUDIENCE: Basically, it just +says it allows you [INAUDIBLE] + +but without the trust part. + +GARY GENSLER: So you don't need +a centralized trusted party. + +That's what in the 1990s so many +people tried and failed with, + +in a sense. + +And the internet became this +way, in a decentralized way, + +to distribute packets +of information, + +even though there is +centralization on the internet + +as well, as we discussed +Tuesday and so forth. + +But this decentralized +application-- so + +in this context, he +was using it broader + +than just something +built on top of Ethereum + +through smart contracts. + +Because he even said Bitcoin +was a decentralized application. + +So he was using it in +the broader context, + +not in what some people +would call dapps. + +But a new model for creating +financing operating software. + +And this is what Christian +Catalini wrote about as well, + +that it might be that there's +a new way to finance a software + +development. + +Maybe raise some money +for the file sharing + +before you have +the file sharing. + +Might be an incentive +system as well. + +And then he talked about +two structural trade-offs + +from the design. + +Now, this blockchain design +has a lot of complexity. + +It has a lot of additional +cost, whether it's mining costs + +for proof of work +or some other cost + +to basically secure the data. + +And so there has +to be a trade-off. + +And what can pull you out of +the minimalist end of this + +is whether there's +some benefits as well. + +And we're going +to chat about that + +in five or 10 minutes again. + +And then the +censorship resistance. + +These are my words, not his. + +I really do think it's +the individual censorship, + +but also, what I'll +broadly call the market. + +Are there barriers to entry +in the current system that + +are, in essence, censoring +economic activity broadly, + +not individually? + +And I think, though, that +was not how he defined + +it-- and I agree with Alin. + +It would have been great if +he had written a few more + +paragraphs or another page. + +But I think it's not +just the individual, + +it's some barriers to entry +for whole market structures. + +And often, centralized +institutions, + +because they have such +a networking effect, + +it's hard to break in +when somebody is basically + +the hub of a hub and spokes +network for almost anything. + +How do you topple Facebook +at this point in time? + +Because it can censor other +market activity, as an example. + +So then we had the +McKinsey report. + +Anything that people took +from yet one more survey paper + +that you've had? + +Akira? + +It's just because I can see +your name on the board there. + +AUDIENCE: From [INAUDIBLE],, I +found the use case [INAUDIBLE] + +use case to be [INAUDIBLE]. + +And one thing I +found interesting + +is the switching costs. + +Because the incumbent +financial institutions + +have to think about not only the +benefit of the cost reduction, + +but also, we have to think about +[INAUDIBLE] costs, existing + +infrastructure, a lot of +the affect on the people + +watching [INAUDIBLE]. + +GARY GENSLER: So Akira's +raised a very important thing + +about switching costs. + +And we wrote about this, even +though I'm not detailing it + +again, in the joint paper that +Simon, Johnson, and Nihon, + +and Michael, and +Joan, and I wrote. + +Now, this the last time-- + +it's the third time you had to +come back and supposedly read + +a little bit more of +the Geneva Report. + +But we talked there about +the switching cost as well. + +And by the way, +to Alin's question + +from Tuesday about +interoperability, + +a lot of switching costs +relate to interoperability. + +If you're an +institution and you're + +thinking about putting in +place some blockchain solution, + +permissioned or permissionless, +but how does it communicate + +with the existing network? + +If the Australian +stock exchange is + +putting in a new back end +clearing and settlement system + +on a blockchain-- + +and they are and they're +using digital asset holding-- + +they have to think about, +well, all of our customers + +are currently communicating +with a legacy database system. + +And now we're creating +a blockchain system. + +How does that communicate? + +How does the old system +literally move information over + +into the new system? + +And all of those from +a business perspective + +are a question of how do +you operate or interoperate + +with the legacy system +and all the network. + +Because any blockchain +solution that you're + +going to come up +with is likely to be + +replacing some other economic +activity, and likely, + +you're not going to try to +replace the entire network. + +You're going to be surgical. + +You're going to decide-- + +I'm not trying to +give anything, Eric, + +but can I say what you +all are talking about it + +in your final project? + +You have intellectual +property, so I don't + +know if you wanted to share it. + +But do you want to say what-- + +AUDIENCE: Could you +elaborate a little more? + +In the point we were +discussing, I was kind of lost. + +GARY GENSLER: Well, +so Eric's group-- + +and Brotish, and +Catalina, and Ross-- + +are talking about maybe doing +a permissioned blockchain + +application for credit reports. + +Not credit reports for +the commercial side, + +but consumer credit. + +Basically, an-- uh-oh, Alf. + +Are you competing with them? + +Did I just-- + +AUDIENCE: No, no. + +GARY GENSLER: OK. + +All right. + +Maybe you are, so I +shouldn't say much more. + +No, it's all right. + +But I won't say anything more. + +AUDIENCE: Maybe it would +be interesting to point out + +the fundamental-- + +or one of the interesting +things that comes up + +from the discussion of +the topic we're engaging + +is how to approach a +blockchain solution + +from an entrepreneurial +perspective. + +Going back to the letter to-- + +GARY GENSLER: Jamie Dimon. + +AUDIENCE: To Jamie +Dimon reading, + +we're trying to get +rid of intermediaries + +or getting economic rents with +that differing kind of paradigm + +that justifies the costs of +using a blockchain approach + +to promote [INAUDIBLE]. + +But from an entrepreneurial +point of view, + +you would end up trying to get +some benefit from that kind + +of implementation. + +So you don't want to +replace intermediaries + +with another intermediary. + +So you would have to be +really creative in terms + +of how to come up with really +lowering costs and gaining + +some profits in the process. + +GARY GENSLER: So Eric's +raising that if you're just + +replacing one intermediary +with another intermediary, + +will you be successful +as an entrepreneur? + +Yes, if you're providing a +better service or a lower cost + +structure, lower economic rents. + +So I wouldn't doubt yourself. + +I would say, we might +be able to do it. + +In your use case-- +and apologies, + +maybe it's multiple use-- + +maybe it's two or three +groups thinking about it. + +There's a lot of market power +right now, and thus a lot + +of economic rents, but a lot of +market power and economic rents + +and credit reporting. + +Equifax, First Union, and +others earn a certain fees + +for all of those FICA scores. + +In the US, we use this. + +If you're getting +a job, somebody + +runs a credit report on you. + +If you're buying an automobile +and taking out an auto loan. + +It feels like each +of us probably + +have a credit report pulled +on us multiple times a year. + +Sometimes we don't even know it. + +But back to interoperability +and switching + +costs, just to pull +it all together. + +How could you convince the +commercial banks to use-- + +I'll call it Eric's +project, it's + +four people, but how could you +convince all the banks to use + +their project and how about +all the auto dealerships + +on the other side who right +now are very comfortable using + +First Union? + +Everybody's probably +paying a little bit extra. + +And there's a fat market +power, economic rents. + +And so that's part of +the switching costs + +that Akira mentioned. + +And to the +interoperability, I believe + +they'll be more +successful if they + +don't try to completely +change how data flows, + +that at some point +you need to know + +that you can't be +successful by biting off + +too much all at once. + +I'm sorry, Catalina. + +AUDIENCE: I was going to +say that, precisely, that + +is one of the +forms of blockchain + +he raised in the paper. + +And it's not changing one +intermediary for another. + +Financially, what they +say is that he's going + +to be more successful for-- + +blockchain's going to be more +successful in the permissioned + +than in the permissionless +because the incumbents are more + +willing to work on +the permissioned + +than with the permissionless. + +GARY GENSLER: In +essence, Catalina + +is saying you might be +more successful not trying + +to disrupt the entire +community, whatever + +that community in some +ecosystem, some business + +community, and do +it in a permissioned + +versus permissionless. + +But we're going to play +with that a little longer. + +Kelly. + +AUDIENCE: I feel like they +addressed the timeline of where + +the strategic value is. + +For example, they +said, currently + +the best way to reap the +benefits from blockchain + +are to focus on +this, this, and this. + +And then they say, however, +feasibility at scale, they say, + +is probably three +to five years away, + +exactly what you've been saying. + +So-- + +GARY GENSLER: Oh, my god. + +We could both be wrong. + +All right. + +Jack. + +AUDIENCE: Something else +I found interesting. + +There's a lot of talk right now +about robotics and supply chain + +using blockchain. + +And the McKinsey report +kind of touched on that. + +No matter how secure +the blockchain + +is, when you start involving +actual real products + +and assets, it could be +completely corrupted, + +even if the blockchain folds. + +GARY GENSLER: Right. + +And also, it's interesting-- + +I think, Jack, if I can +pick further on that. + +When you have something +on the blockchain, + +even if it arguably +should be there, + +it's a property +right and so forth, + +but it's an off-chain asset, +it's not just a digital asset, + +and secured and verified +on a blockchain. + +But in supply chain, it's often +an off-chain asset, and often + +a physical asset. + +Then there's +additional challenges. + +I think there's some really +interesting use cases, + +but it's a little bit +of a different place. + +James. + +And then I'm going to-- no? + +So McKinsey defines +a blockchain. + +And they point out +it doesn't have + +to necessarily disintermediate +to generate value. + +I thought that was an +interesting intuition. + +Don't always think that +you have to disintermediate + +to generate value. + +They might be right or +they might be wrong. + +But you might +actually still end up + +with something that's kind of-- + +as-- did Catalina say it? + +I can't remember +now who said it, + +but they also said +they gave a timescale. + +A short term value +might be predominantly-- + +Kelly did, sorry-- three +to five years away. + +How to capture value. + +Be pragmatic and +skeptical, but you + +need to go down to +a granular level. + +And that's also what +I'm going to ask + +you to do in the +final paper, is really + +to challenge yourself, +challenge your group + +to go down to the granular +level and say, wait, + +what transactions +are we actually going + +to change the flow? + +What ledger system +might we shift? + +And even though it's +the back office-- + +and to some people, +you might say, oh, + +my god, that's kind of the +boring side of business. + +But that's really what +blockchain is about. + +It's a database and ledger +management system also. + +And to be successful, +you have to get down + +to that granular level +and figure it out + +in terms of whatever +that current ecosystem is + +or the regulatory system. + +They said it's particularly +valuable in low trust + +environments. + +And that could be +where currently we + +can't trade directly and you've +created a new way to do peer + +to peer, or where +there's not currently + +a central intermediary. + +You can go right at it. + +You could be like this +bold group that says, + +I want to take on Transunion, +I want to take on Equifax. + +That's something which is a +central intermediary right now. + +But it is correct, we're +not really trading directly. + +It's not like when I walk into +the auto shop or to buy a car + +and I'm going to take a loan +out that I can transact. + +They want to validate that I +can pay back that darn loan. + +Yes? + +AUDIENCE: Just two points, +particularly the fact where + +your-- + +well, you can't +trade directly now, + +but there's a lot +of trade happening + +where you don't have +an intermediary, + +but some sort of +intermediary would help. + +I couldn't help but think +of ag markets in very-- + +GARY GENSLER: You're saying +ag, like agriculture? + +AUDIENCE: Agriculture markets in +very remote parts of the world, + +where actually being networked. + +And precisely, there's no trust. + +That kind of environment exists. + +So a good use case for +that, extreme remote parts + +of the world where internet +is there, but not necessarily + +financial institutions or +regulatory environments. + +GARY GENSLER: Right. + +And there are many parts, +particularly in the third world + +that are still unbanked. + +I've said this statistic before, +but the World Bank report + +on banking in 2017, half +of sub-Saharan African + +was still unbanked. + +But half of that half +has mobile phones. + +So it's just-- those gaps might +change, but then it will move. + +Yes, they might have +a banking account, + +but it would be not +something they can really + +do with agriculture. + +So two opportunities-- +and I'm going + +to come to the +question-- is like, + +do you go head-on against +a central intermediary + +and use this technology +to do it better? + +[PHONE RINGING] + +Look at that. + +I should turn this off. + +Head-on against a +central intermediary? + +Or some market structure +that has no really core + +intermediary, but you can +build a better trustless + +peer to peer network? + +AUDIENCE: Yeah, +[INAUDIBLE] that's + +when it comes to +private permission. + +Architectural blockchain, +it's highly likely + +to be more scalable. + +Why is that? + +GARY GENSLER: Highly likely +to be more scalable, yes. + +So permissioned blockchains, +they've made a trade-off. + +So Nakamoto's paper comes out. + +For a few years, people +don't really notice it. + +But then it starts +to get some lift + +and folks are looking +at it in 2013 to 2015. + +And the financial industry +starts to think about this + +and says, this actually +is pretty interesting. + +We're not sure what +it's going to do, + +but we're pretty interested. + +And they get attracted to +it because it might be a way + +to move data around, it might +be able to literally lower + +the costs of the back office. + +Many banks keeping the +same set of records-- + +I have an equity +trading business, + +you have an equity +trading business. + +We both have to confirm +and correct those records. + +But we keep full databases. + +What they found +attractive was real. + +But then remember, +Bitcoin can only + +do seven transactions a second. + +So all of those challenges of +scalability, privacy, security + +led them to think +about, was there + +a way that we could +literally toss + +some of the technical +things over the side? + +And most of them thought, we +don't need a native token. + +We don't need an +incentive structure. + +And if we limit the number +of nodes in the network, + +we can increase +scalability and we + +can get rid of proof of work. + +So my narrative +might not matter, + +but it's important +to understand it. + +The permissionless thing comes +along, and then they say, + +it's not scalable. + +What can we toss overboard +and make it scalable? + +And what they tossed overboard-- + +they didn't even feel they +needed the native token, + +and they tossed overboard +proof of work, consensus, + +and had a club deal. + +In the Australian +stock exchange example, + +they might only have +two or three nodes. + +But in some of these, +there's 15 or 20. + +So why is it more scalable? + +Fewer nodes and much more +efficient consensus mechanisms. + +But the trade-off is +you better damn well + +trust now those 15 or 20 nodes. + +And when we talk +about 51% attacks, + +you could revise a whole +permissioned blockchain + +if those 15 parties wanted to. + +Now, some people say, well, you +could just do a hash function. + +Remember that whole hashing. + +You could do a hash function of +a whole permissioned blockchain + +once a day, once a +week, once an hour + +and store it somewhere else. + +In fact, you could store the +hash of all of that on Bitcoin. + +You could use a +ledger like Bitcoin + +and just store it there. + +So there's some feedback loops. + +Does that help? + +Give you a sense? + +AUDIENCE: I was also just +going to build on that. + +So the power of a +permissioned blockchain + +is that, unlike Ethereum or +Bitcoin, it's not public. + +So there is no public ledger. + +You can make it public, +but it's permissioned, not + +permissionless. + +Because you need to have trusted +entities in this network. + +So this can also +be, you could say, + +a feature, not a bug +when it comes to scaling. + +Because essentially, +you control the scale. + +So you control these nodes. + +And then like +mentioned, these nodes + +are only relevant +because they are + +trusted pieces of this puzzle. + +Yeah. + +AUDIENCE: Right. + +I think it's easier +to get scale, + +but there is not a +large enough market + +to actually make +it scale or make + +it reach to the critical mass. + +GARY GENSLER: So are you +worried that there's not + +enough to get to +the critical mass? + +Now, I'm not sure-- + +so a permissionless blockchain +and a permissioned blockchain + +both can be open +to public users. + +You can have millions of people +use a permissioned blockchain, + +but only 15 have the right +to amend the records. + +So one might think +of who has a right + +to read it, who has a +right to write on it. + +Read, write. + +But also, absent even that, +it might provide a service, + +like file sharing +or some service. + +There might even be +a third list of who + +has a right to use the service. + +Now, usually to use a +service, you actually + +have to read the data. + +But you could partition and say, +how much can be read as well. + +Yes, and remind me +of your first name. + +I'm sorry. + +AUDIENCE: [INAUDIBLE] + +GARY GENSLER: [INAUDIBLE] + +AUDIENCE: Yeah. + +I really appreciate +your perspective + +from how you +envision [INAUDIBLE] + +permissioned projects. + +GARY GENSLER: The +pathway, you said? + +AUDIENCE: [INAUDIBLE] in +terms of its relationship with + +[INAUDIBLE]. + +Do you think it +would pave the way + +towards the true +decentralization eventually? + +Or you were just [INAUDIBLE] +Or you would just + +become irrelevant just as the +intranet compared to internet. + +GARY GENSLER: So [INAUDIBLE] +question is unanswerable, + +but I'll try to give my opinion +in 2018, and then we'll see. + +And it's being recorded, +so we'll see how I'll do. + +But the question +really is, what's + +the relationship for +permissioned and permissionless + +blockchains? + +And what is it going +to be longer term? + +I think today in 2018, because +of the scalability issues + +and some of the +privacy and security + +issues, the dominant place +that the investment will + +be is on the permissioned +side, especially + +with what's called enterprise +applications, the banks, + +the large institutions. + +There's not enough scalability +because 1,000 users a day + +or 1,500 users a +day on the big apps + +right now on the Ethereum +network, that's just not + +enough beyond gaming sites +and some small hobbyist type + +things, like CryptoKitties. + +It's fun, it's +interesting, but it's not + +truly scalable to 7 billion +people living around the globe. + +But I wouldn't-- and I've +said this to some IBM folks. + +And they have 1,000 people at +IBM in the hyper ledger team. + +Anybody who is a +blockchain minimalist-- + +you haven't heard this number? + +AUDIENCE: I've heard 2,500. + +GARY GENSLER: 2,500? + +All right. + +So it's more than I thought. + +So 1,000 to 2,500. + +I knew it was more than 1,000. + +IBM is throwing a +lot of money there. + +Now, they might be doing +that to protect their risk. + +They might be investing even +if all those 1,000 people + +ultimately produce nothing. + +But I think that five years from +now or seven years from now, + +the gap will close. + +I think that permissionless +systems will always + +have a lot of challenge about +governance, collective action. + +How you have collective +action is not just + +a matter of technical and +coding and smart scientist + +at MIT and elsewhere. + +I think that's going to +still be a challenge, + +and there will be trade-offs. + +So it might be +that they coexist, + +but I think the gap will close. + +And you said, well, will it +be like the intranet went away + +and the internet was there. + +There are some people +that believe that. + +And that might be-- + +I'm probably not there. + +I'm probably not +all the way there. + +But I think when +the gap closes, some + +of these permissioned systems +will not be as necessary. + +Zero knowledge +proofs, other ways + +that come along that +make it more usable. + +Yes, Zann. + +AUDIENCE: Totally understood. + +I'm a little bit skeptical on +the permissioned blockchains. + +One of the-- + +GARY GENSLER: Are +you skeptical-- + +if I can interrupt you-- + +and thus it moves you over +to traditional databases? + +Or skeptical and you're moved +over to permissionless open? + +So I don't know, which +way is it pushing you? + +AUDIENCE: Depending +on the use case. + +For enterprises, I think +traditional databases + +for the enterprise use case. + +Reading here, this +line killed me. + +It said, "Accenture developed +immutable blockchain + +in which the content +of individual blocks + +can be modified." + +It's a ridiculous statement +considering the definition + +of blockchain is anti-- + +this is the antithesis +of basically-- + +GARY GENSLER: Right. + +So Accenture created an +immutable blockchain that + +isn't immutable, is what you're +saying, it can be amended. + +So it's a backdoor I can change. + +And yet, the economics of it +is that a lot of times, people + +do want a backdoor. + +And the challenges-- and these +are the weaknesses as well, + +as Nouriel Roubini says. + +Why would you create a +system where if you forget + +your private key, +lose your private key, + +or the cave collapses-- that +you're hiding the private key + +in a cave and maybe it floods-- + +that you've lost your assets? + +Wouldn't you want a backdoor? + +But I respect-- you would say +this isn't even a blockchain. + +I'm trying to teach this +class in a little bit + +neutral between permissionless +and permissioned blockchains. + +But you need +something to get out + +of the traditional databases. + +And I've chosen, at least for +purposes of this class, that + +means you've got to +have an append-only log, + +you have to have time stamping. + +So the basis of multiple +people writing to the ledger, + +even if it's only three or five. + +But these are not +well-defined vocabulary terms. + +Alin. + +AUDIENCE: This is why we +should stop using them. + +And this is a +perfect opportunity + +to actually talk about +append-only ledgers + +because that's +actually meaningful-- + +a meaningful notion that's +been studied in computer + +science for decades. + +Or consensus +algorithms, which is + +another meaningful notion +studied in computer + +science for decades. + +And consensus algorithms on +append-only ledgers, sometimes + +referred to colloquially +as blockchain, + +and then we would know what +are we actually talking about. + +If we-- + +[LAUGHTER] + +GARY GENSLER: Well, +I will try to help. + +But we're only 80 people, +and there is a lot + +of people using these terms. + +And when you go outside +of this class or even + +when you read an open +letter to Jamie Dimon-- + +of the somewhere between 25 +and 50 readings you had so far + +this semester, they've +used the word blockchain + +in multiple ways. + +I'm agreeing with you. + +You're just asking me not to +ever use the word blockchain + +again? + +AUDIENCE: Yes. + +GARY GENSLER: Oh, my god. + +And he's sitting in the +center of the class. + +Let's keep going. + +So we're going to study these. + +This is just this list +that we've talked about. + +But in Act Three, we're going +to come to it after SIP week + +and start to go through +venture capital payment systems + +and so forth. + +It might be some of +what you're picking up + +for the final projects. + +But here-- and I stress the +word, potential use cases. + +Will these all work? + +Will they be places? + +In the non-financial space, +supply chain management + +I put on this list, but +it's kind of financial + +and I wanted to include it. + +Digital identity is both within +finance and outside of finance. + +Property and asset registries-- +you can call it finance, + +but I'm not going to +dig into that a lot + +in the rest of the semester. + +Medical records, internet +of things, and so forth. + +This isn't going +to be exhaustive. + +If you come on Tuesday, October +30, to the Bitcoin blockchain + +dinner that Simon +Johnson sponsors, + +we'll have somebody doing +election and voting. + +So there's a lot of other +interesting applications. + +I tend to be a little +doubtful about the voting + +because I think official sector +and governments want something + +so centralized in that. + +But maybe it will be +more decentralized. + +Maybe it's append-only +without a consensus. + +McKinsey, they broke it +down into six buckets. + +They had the record keeping +and the transaction-based. + +And a lot of these are +the similar buckets. + +It's just to give a +spur to all of it. + +So accessing costs and benefits. + +So we've talked about +what are the benefits. + +These are the questions +that I would be saying. + +And some of this was +in the Geneva Report, + +but rather than +trying to tease it out + +of all of the discussion, here +I would lay out four big buckets + +as to how I think about this and +how I might get your feedback. + +If you see other +ways to look at this, + +I want to learn from +you all as well. + +And when I say four, +this is the first bucket. + +Basically, what are the benefits +of using this technology? + +Whether it's this idea about +consumer credit or some of you + +have had ideas about +government procurement + +or payments, wherever you +are, what is the true benefit? + +You've got to find a pain point. + +Every entrepreneur always has +to find a pain point, something + +that you can be solving it +for a group of stakeholders. + +And who are the stakeholders +you're solving something for? + +Or if you're a company, is +it an internal pain point? + +Pain point is some +constraint to making + +more profits, more revenues. + +Or it's a friction, +it's a cost and you + +want to get rid of a cost. + +But what is the pain point +for providing a good service + +or making more money? + +How can you capture the value? + +As an entrepreneur, +if you do something + +for eleemosynary +purposes, meaning + +you don't care +about making money, + +I applaud that, that's terrific. + +You can even hand that in +for your final project. + +But I'm assuming that you're +going to be thinking like me, + +how do you capture value? + +Not only do something, but +also capture that value + +and get a little of somebody +else's economic rents + +if possible. + +Thirdly, what are the +competition doing? + +What are the competitors doing? + +Even if they're using +traditional databases, + +how are they addressing the +same pain point in anything + +you're doing? + +And why is blockchain +technology-- + +or, as Alin would +wish me to say, + +why are append-only longs +and consensus protocols-- + +what is the answer? + +What is it about append-only +logs with their time + +stamping, with their +final settlement, + +the finality of that +settlement, what about that? + +Or even a full consensus +protocol and a native currency. + +So I'd add a third thing because +permissionless would also + +have an incentive system +in a native currency. + +So what is it about append-only +logs, consensus protocol, + +and a native currency? + +How am I doing? + +AUDIENCE: I love this. + +GARY GENSLER: You love it, yeah. + +AUDIENCE: Talk like +this all the time. + +Don't forget it. + +GARY GENSLER: Yeah. + +Oh, my god. + +[LAUGHTER] + +Oh, I need this. + +But that's the core. + +And I talk about it +being the final project, + +but this is going on right +now. $28 billion dollars + +has been raised in +initial coin offerings + +and a few extra billion, +3 or 4 other billion + +has been raised by direct +venture capital in this world, + +but call it $30 billion. + +It's not fully mature, +but it's maturing, + +and a lot of venture capitalists +are saying, wait a minute, + +wait a minute, we're +past the hype stage. + +What pain point are +you trying to address? + +How are you creating value? + +What are the competitions doing? + +And why do you need append-only +logs, consensus protocols, + +and possibly native tokens? + +AUDIENCE: I just wanted to +follow-up on that point about + +the Accenture-- + +GARY GENSLER: You're +not going to tell me + +how to define something? + +All right, Kelly. + +AUDIENCE: The Accenture thing +he was talking about from the-- + +GARY GENSLER: It's +immutable but amendable. + +AUDIENCE: Right. + +So we ask ourselves +the question-- + +that seems a little bit-- + +it defeats the purpose, right? + +So I then ask myself, what value +is being created by doing that? + +If it's not necessarily +for their customers, + +where is the +internal value lying? + +GARY GENSLER: I don't know +what the application was. + +But I think that in every +application that we find, + +not just in blockchain +but in other applications, + +you have to ask absolute +final settlement. + +If you can never amend it, +if it is truly immutable, + +what cost does that also make? + +I assume that in +this application + +that was too great +a cost for them + +and they wanted +a backdoor, a way + +to amend that which was +supposed to be immutable. + +Again, I don't know +that application. + +But that is one of the-- + +I think it's a +feature of blockchain. + +But it's both a +feature and, to some, + +a bug that you cannot +amend something. + +AUDIENCE: Yeah. + +It says that one +of the benefits was + +that it allowed different +entities involved + +to draw on the same record. + +So yeah, of course, I can +see where that's valuable. + +But then it also +begs the question, + +if you want to change +it, then why not just + +use a traditional database? + +GARY GENSLER: Vitalik +Buterin in 2016 + +helped when an organization +called DAO, the DAO-- + +is it Decentralized +Autonomous Organization? + +Thank you for those who-- + +it was one of the largest at +the time initial coin offerings. + +It raised about $160 US million. + +And very quickly, right +in the smart contract-- + +it wasn't in the +base Ethereum layer, + +but I believe it was in +the smart contract on top, + +somebody saw what has +later been called a bug. + +I don't know if +it's truly a bug. + +It was programmed +in, in a sense, + +but there was a way that they +could see how to get in there. + +And they took about a +third of the tokens, + +so the equivalent of +about $50 million. + +But the way the +programming worked, + +there was about two weeks before +it actually was truly final. + +It was something in the code +also, and that wasn't a bug. + +And the whole Ethereum +community was debating it. + +And Vitalik Buterin said, +no, we can't let this happen. + +So in a sense, +they big footed it. + +They almost did what Essentia. + +Now, he might say, +no, actually, it + +was right at the 11th +hour and 59th minute + +because there was this +10-day or two-week period. + +But they basically, Vitalik +Buterin even did kind of what + +Essentia did at that moment. + +AUDIENCE: They forked +it then, right? + +GARY GENSLER: I don't even know. + +Was it a technical fork +because of how they did it? + +AUDIENCE: [INAUDIBLE] + +GARY GENSLER: Right +at that moment. + +AUDIENCE: Ethereum classic +still has the DAO-- + +GARY GENSLER: The +stolen $50 million + +or whatever, the +number of tokens. + +So that led to the fork. + +The majority of the +community went with Vitalik + +rather than what +the fork happened. + +So how immutable is immutable +if there's a broad consensus? + +Now that's the +backdoor, in a sense. + +Second-- was there another hand? + +I'm sorry, Brodish. + +AUDIENCE: I think +the [INAUDIBLE] + +GARY GENSLER: To address +Kelly's and Zann's. + +AUDIENCE: And the +word blockchain. + +GARY GENSLER: And +the word blockchain. + +All right. + +AUDIENCE: So I think when people +are talking about blockchain + +as a term, they're +essentially referring + +to a set of potential +benefits of this technology. + +And some of them can be relevant +for a particular use case. + +Some of them might +[INAUDIBLE],, some of them + +might actually [INAUDIBLE] +for that particular use case. + +So the way it can +be thought of is + +that we have an umbrella term +which talks about referring + +potential benefits. + +We take what is +[? referred ?] from that. + +It could be append-only, it +could be not append-only, + +it could be consensus, +it could be permission, + +permissionless, whatever. + +And then we cannot calibrate +with them and create a solution + +which is applicable for the +particular use case that I want + +to look at. + +That is why even if +it is not immutable, + +it is still a potential +use of blockchain, + +from my understanding. + +Because we are bringing up some +of the benefits of the umbrella + +term. + +GARY GENSLER: I +think you're correct, + +but I'm not going to go all +the way to where you are. + +I think you're correct +that, broadly speaking, + +many people are using +this term to promote + +their own innovation, the +innovation of their colleagues, + +and so forth. + +And yet, some want a +backdoor, like Essentia, + +and make it less immutable. + +And so all of a sudden, +if it has a big backdoor + +and you can amend, is it really +an append-only log any longer? + +What I do want to say is, in +this class, I am going to say, + +anything you're working +on for your final paper, + +it has to be at least a +permissioned or permissionless + +system. + +Thus it has to have a-- + +what's that? + +AUDIENCE: Not mine. + +GARY GENSLER: Not yours? + +But you're going to get there. + +You're going to +get there, Brodish. + +You're going to get there. + +Since I told you earlier +in the day, get to yes. + +But if it's a +traditional database, + +I'm saying stretch your minds, +try to figure out something. + +Even if it's got a +little bit of risk + +into it as to how you get +to using append-only logs, + +and even in a permissioned +closed loose private consensus, + +but some consensus. + +Think about whether +you use a token that + +gets the permissionless. + +Uh-oh. + +Eric's going to plead his case. + +AUDIENCE: I'm just going to try +to completely reconcile this. + +GARY GENSLER: And then +I need to keep going. + +AUDIENCE: Yeah. + +Those two apparently +divergent points-- + +GARY GENSLER: Right, +Brotish and Alin. + +AUDIENCE: Yeah. + +AUDIENCE: I actually +agree with Brotish. + +AUDIENCE: The point is that-- + +GARY GENSLER: That he +might agree with him. + +AUDIENCE: I'm +still in the middle + +because from a technical +standpoint, it's true. + +You have append-only log +in a consensus mechanism + +that make up the +original use case that + +brought the term blockchain. + +GARY GENSLER: Plus a +native token in that one. + +AUDIENCE: Yeah, of course. + +[INAUDIBLE] But to the +point, though, what + +happens if you want to +change or amend the log? + +Then is that really +a blockchain? + +That's exactly the reason +why the term [INAUDIBLE] + +later technologies came up. + +Because to a certain +purist extent, + +it's not an append-only +log because you're actually + +updating it from a +purist definition. + +That makes sense, of course. + +But then the nature of +a distributed database + +that's not located +in an intranet + +that governs the updates and +whatever changes you make it, + +it's the reason that make up +these ledger technologies that + +are blockchain +inspired, if you may. + +So it's OK, you can say +if you amend the log, + +then it's not blockchain. + +Right, but it's DLT, and the +DLT is blockchain inspired. + +So we can keep everything +in the neighborhood. + +GARY GENSLER: We're going +to keep this discussion + +and debate going. + +And we're probably +not all that far off. + +It's not about +vocabulary, it's also + +about I'm trying to spur you all +to get to yes, even if you're + +a minimalist. + +Think about some project that +uses the essence of this, + +and not just inspired. + +So then what are the specifics +of this append-only log + +and consensus use case +or blockchain use case? + +So what cost of +verification or networking + +are you actually reducing? + +Back to Catalini's work +about verification cost + +and networking costs that +we talked about on Tuesday. + +What is that cost you're +actually reducing? + +Which transactions +need to be recorded? + +What accounts or +transactions, you might say, + +need to be recorded on this log? + +What stakeholders need +to be able to write? + +If there's only one stakeholder +that needs to update something, + +I'm not really entirely +sure that you'd + +be in this distributed +decentralized place. + +So I list these questions +that weren't directly + +in the readings, but +I list these questions + +to say this is a way to start +to get your mind around where + +this technology, +however we label it, + +this technology can help. + +In essence, does it lower cost +of verification and networking? + +And if so, which ones? + +Which ones are you +trying to address? + +Which ones are you trying +to dig and basically create + +value for your startup? + +What transactions or accounts +are you trying to record? + +Transactions, like +changing property rights + +or moving around birth +records or land records + +or supply chain. + +But where's that? + +Which stakeholders actually need +to write to this distributed + +ledger? + +Because if it's only one party-- + +I'm still trying to get my head +around why the Australian Stock + +Exchange really +needs it, but OK. + +What is it that +multiple parties need + +to write to this shared +collective state of what + +is there? + +And then the last one is +also terribly important, + +is, what's the customer +user interface? + +And a lot of challenges +are basically like, + +currently we're not +in a place where + +a lot of blockchain +applications are distributed, + +applications have great +customer user interfaces. + +But that as well. + +Then what are the cost +of the transitions? + +Akira mentioned this +from the Geneva Report + +and the other readings. + +But what are the +costs and challenges? + +Well, of course, we still +have a bunch of scalability + +and performance issues. + +We have the privacy +issues and coordination. + +I'm not trying to hold us +all to that, by the way, + +for your final projects. + +If we're not going to get to +scalability for five or seven + +years, I'm not +going to say, well, + +then you all have to write +about permissioned systems. + +No. + +I'm OK if you say, +well, this is a pilot + +and somebody else +is going to solve + +through layer two or +zk-SNARKs or something, + +these other things. + +But I'd like you to +at least identify + +what are the issues +of scalability, + +performance, privacy, security, +those issues that might + +hold your implementation out. + +Can a permissioned +blockchain adequately + +addresses whatever +the use case is? + +And how can you actually +jump start broad adoption? + +That's your network challenges. + +How, when you start Uber, +can you get a lot of people + +to use your Uber app? + +But in this case, if I can +use that consumer credit-- + +I thought the consumer credit +idea was really a neat one. + +Maybe it could go right at the +heart of a lot of market power. + +But now, how do you get +all the auto dealers, + +how do you get +all the employers, + +how do you get the +banks to actually say, + +I want to get rid of First +Union and I want the Blockchain + +and Money final project team's-- + +and by the way, just replacing +one central monopolist + +with another central monopolist, +a lot of commercial banks + +aren't terribly +excited about that. + +Maybe you're going to have +to give some ownership. + +Maybe you'll have to give +50% of your ownership + +to the 20 banks that +are now a part of this. + +There are other ways to +build incentive systems. + +Maybe you put a +native token in there + +and you give them +the native token. + +So there may be +other incentive ways + +to beat the current monopolist. + +But having been around +commercial banks + +for a long time, they +really are looking for ways + +to replace their aggregators +and their back office, + +whether it's clearing, +settlement, exchanges, credit + +agencies. + +But they are deeply +understanding-- + +because they are pretty +ambitious and very + +good at making money +as well, they deeply + +understand that every idea +that's pitched to them + +is somebody who +currently is small + +but wants to get big +and gain market power. + +So they're also always +thinking about how + +to ensure that there's +a check to slow down + +your startup from gaining +market power 5, 10, + +and 15 years from now. + +They don't want you to be +the next Clearinghouse, + +like the Chicago Mercantile +Exchange or Intercontinental + +Exchange. + +They don't want you to be the +next central node of market + +power. + +So you might share +some of that with them, + +or you might find +an incentive system. + +And then what are the net? + +So key questions for companies +designing blockchains. + +This is something from MIT's +own Sloan Management Review. + +It was not a required +reading, but I + +thought it was a nice +little way to do it. + +What are you trying to do? + +Are you trying to +record something? + +Track something? + +Verify something? + +Aggregate something? + +This was in the Fall MIT Review. + +What value do you +want to capture? + +Literally, here's a +list of the things + +you might want to capture. + +Is it about contracts? + +Is it about permissioned? + +What is the value we're trying +to capture and for whom? + +Obviously, is it for suppliers +or customers and so forth? + +So it's another slice by +thoughtful people, MIT. + +That's a link to the reading +if you do want to read it. + +It was a well-written +five page article. + +I even held back on one reading. + +So the benefits of blockchain-- +we reviewed this last Tuesday, + +so I'm not going to +go through it again. + +But again, as you're +thinking about this + +and thinking about which +use cases and so forth, + +think of these costs +of verification. + +Which of these are you +really trying to hit? + +Or is it networking? + +And I changed the +networking a little bit, + +but a token incentive system, +which could be like the skins, + +rewards, and affinity, +identity could help + +you start it up or operate it. + +Or it could be +like CryptoKitties, + +where it's like a collectible. + +So that's another +way that you have + +token economics floating in. + +So this you've seen. + +I've flipped it +around, but basically, + +do you use a +traditional database? + +Do you think about a +private blockchain? + +Do you think about +a public blockchain? + +If you're over here, I really +ask you, Brodish, you've + +got to get to yes. + +You've got to get to here. + +You wouldn't want me +to just be teaching + +a traditional database, how do +you build something in Sloan, + +right? + +This is blockchained money. + +Or as Alin wants me to relabel +it, append-only logs, consensus + +protocols, and money. + +[LAUGHTER] + +AUDIENCE: And a native currency. + +GARY GENSLER: And +a native currency. + +But how many of +you would sign up? + +Would you recommend +that I list it + +in the course catalog that +way for next September? + +AUDIENCE: No. + +GARY GENSLER: Really? + +No, not really. + +All right. + +But if you want to really +juice, get to here. + +Put an append-only log +in there and some even + +private permissioned system. + +Or be bold. + +Try to get all the way to there. + +Don't stay there, please. + +All right. + +I've made my point. + +James. + +Where are you? + +Are you there or there? + +AUDIENCE: I think I'm in the +middle, private blockchain. + +GARY GENSLER: Ah, come on. + +AUDIENCE: [INAUDIBLE] + +GARY GENSLER: All right. + +Good. + +Yeah, but they're going +to get at least to there. + +They're not staying there, +they want to get a good grade. + +[LAUGHTER] + +No, no. + +Really, this is going to be fun. + +Listen, I get it. + +It's not just like any +Sloan class, where you + +have a final and everything. + +I've given you a hard test. + +There's $30 billion chasing +around to try to find uses. + +There's thousands-- 2,500 at IBM +or whatever-- there's thousands + +of people trying to do this. + +And there's no really true +market-wide applications + +right now. + +But that's the nature of what +we're doing here together. + +And I'm not asking +that somebody actually + +be able to go raise money +and actually start it. + +You don't have to code +it, except for you, Alin. + +But you don't have to +actually code this thing. + +But I'm really looking +for your business savvy, + +and it's more about +critical reasoning skills. + +And these four or five +pages, pull it off of Canvas + +and think about it, +think about how it fits + +in with your projects or not. + +Yes? + +AUDIENCE: Given that-- well, +the question in previous slides + +are helpful. + +But I still find it's hard to +decide whether we should really + +use blockchain +database [INAUDIBLE] + +traditional database. + +So is there a non-technical +model or framework that we can + +[INAUDIBLE] between those two? + +GARY GENSLER: I think of it-- + +I apologize if to go back to +the slides, so I'll try not to. + +But I think about it +as, are you moving + +around something of value? + +Do you need multiple +people to be + +able to help in that network? + +Because it's peer to peer. + +If it were the 80 or +90 of us in this room, + +you might be just +there right now, + +that there's a benefit +of that peer to peer + +movement of something of value. + +Or frankly, even back +to this, if there's + +a lot of economic rents. + +If there's market power +in this, if there's + +big market power and somebody +is just collecting lots, + +that might be your opportunity +because this is the technology + +that can get you there. + +And you might say, +well, I don't absolutely + +have to have an append-only +consensus native currency + +type of technology, but it's +how I get to peer to peer. + +So it might be +that that's the way + +that I'm going to +disrupt the party + +with the big economic rents. + +Like the letter to +Jamie Dimon, if there's + +a bunch of things +about censorship risk. + +And again, I don't know what +use cases you're thinking about. + +But I think if +you don't have one + +of these six, the +verification costs, + +it's unlikely you need an +append-only log and consensus + +in the whole mechanism. + +But I think if you do have +something here, hopefully not + +just economic rents +but market power, + +this might be the way you +get underneath it, by having + +a decentralized peer +to peer approach. + +So if that helps. + +And it could be something that +has no central authority right + +now, no central intermediary, +and it's just how + +to jump start something. + +I think in that +circumstance, it's + +more likely you +need a native token. + +I think if you're trying +to jump start a network-- + +and there's a lot of +collective action reasons + +that will still face you. + +Some of our colleagues, +Andy Lippman + +and others over at the Media +Lab, spent a lot of time + +a year, year and a half ago +on a medical records approach + +with Beth Israel +Hospital locally here. + +And if Andy were here, +he'd say, but I still + +have the collective +action issues. + +How do I get a +bunch of hospitals + +and a bunch of +doctors and how do I + +get all that collective +action to work together + +to use one database +system, if you wish? + +So I think to get over that +collective action issue, + +you start getting into, +well, this native token + +might be an interesting +way to do that. + +AUDIENCE: Right. + +It seemed that Uber satisfied +the things you just mentioned. + +GARY GENSLER: They did. + +They did. + +But would they have +done it differently + +if they started in +a different era? + +I don't know. + +It's remarkable that they +took on and just completely + +transformed the ride +share business, the taxi + +business, if you wish. + +But I'm pretty +confident of this, + +there will be +something that we don't + +envision right now that really +transforms the next thing. + +As my brother said +when he said, it + +might be five and +10 years from now + +and you won't even expect it. + +Who would have thought +the internet in the 1990s + +was going to go straight and +transform the taxi business? + +Nobody in the New +York Taxi business + +would have envisioned that, +which was one of the things + +that he mentioned. + +So why use blockchain +versus traditional database? + +We did that. + +I know, you got it got, Brodish? + +Right there? + +OK. + +No, I'm having some fun. + +So the trade-offs we've talked +about, so these are costs. + +This is the cost +of centralization + +versus decentralization. + +We've looked at +this slide before. + +I think this was an +earlier question. + +Over time, I think +what's going to happen + +is these graphs might +have different slopes. + +So it's just like, OK, +what if the slopes change? + +I think that the cost +of decentralization + +are going to come down. + +But that's more my +forecasting prognostication. + +And then you'll have +more applications + +that feel more comfortable +over using something + +around this space. + +Now, I could be wrong and +it could go the other way. + +Just saying. + +And this would be more of +the minimalist side and says, + +well, you can address some +of those centralization costs + +and it comes down the other way. + +So it's just a +visual way to think + +about what will happen +over time with innovation. + +But I think innovation +will pull down + +the slope towards that from +where we are today because + +of the newer technology, +this decentralized + +how can we do this. + +And I think there will be +more opportunities around it. + +All right. + +So on the 30th, we're +going to be talking + +about basically our first area. + +We're going to talk +about payments. + +We're going to talk +a lot about payments. + +I'm going to take two days +to talk about payments. + +So we're going to lay +out a lot about what's + +going on in finance outside of +append-only logs and consensus + +protocols and blockchain. + +But we're going to have +fun because what we all + +live together. + +And some of you actually +live in these countries. + +But whether it's Alipay, +[INAUDIBLE],, and M-Pesa, so + +all these initiatives. + +And then how could maybe +blockchain fit into it? + +In terms of the use cases, +these are all those use cases + +that we're going to be doing +from October 30 to December 6. + +But this gives you a sense, +what I call Act Three. + +And we're going to +really be trying + +to challenge each other about-- + +some weeks, I'm going +to give you a heads up, + +it's going to be a little thin. + +I'm going to be +looking for who's + +got really good use cases. + +If you have something to +bring into the classroom + +that you're saying, +hey, this reading + +list I put together +in late August-- + +and by November, it +might be that there's + +somebody that's actually +moved something further. + +So don't be bashful. + +Shoot it into me in time +and I'll distribute it + +to the whole class. + +But in a couple of places, +digital ID, for instance, + +I thought it was thin. + +There's the Estonia case, +but it's not really-- + +not sure it's a blockchain. + +I'm admitting in +advance, some of these + +are a little thin +but still good. + +And the readings for the 30th-- + +the Federal Reserve +Payment Study really + +shows a bunch of information. + +And you have to read the words, +just look at the few charts. + +But it's going to +give you trends. + +You're going to really see some +interesting trends in there. + +What the best mobile apps are, +and the global payment report, + +and things like that. + +Any questions on any of that? + +And then what did we talk about? + +Blockchain technology +can address costs + +through verification +and networking. + +The potential use cases-- +the devil is in the detail. + +It's true in most +things in life, + +but it really is these +natty little details + +about what transactions, +who am I going + +to try to disintermediate, where +am I going to create value, + +why use a permissioned +or permissionless + +blockchain rather than +a traditional database, + +and really get some value. + +I think you really have +to address this question, + +but I think there's +potential there. + +Or why a public blockchain +versus a private? + +Is a token going to help +you jump start something? + +And remember, there's two +different types of tokens. + +There's the broad +currency type token. + +That might be Bitcoin, and they +might have won the whole thing, + +or it'll be somebody else, or +there might be two or three. + +I personally don't think +there'll be hundreds of those. + +But then there might +be, in essence, + +use case-specific tokens. + +Right now we have 1,600, +and most will fail. + +So that's it. + +Any other queries or anything? + +Yeah? + +AUDIENCE: Once all the bitcoins +are mined in 2040 or 2030-- + +[INTERPOSING VOICES] + +AUDIENCE: 2040. + +GARY GENSLER: But by 2040, it's +a very slow inflation curve. + +It's probably a +slow inflation curve + +in the middle of the 2030s. + +AUDIENCE: The +incentives, if there + +will continue to be +incentives for node operators + +to continue operating +benevolently, if there's + +no further incentives-- + +GARY GENSLER: So the question +is, what happens in 20-- + +when there's very +few mining rewards? + +And the answer is-- + +I'm going to have some +fun with you here. + +I'm going to show +you one other thing. + +The answer is, yes, +because it's fees. + +And the fees in the system-- + +I apologize. + +It's just one thing that I +want to show you that's fun. + +The fees in the system-- + +so right now you can have +fees, if you remember how + +there are fees in the system. + +And instead of having +mining rewards, + +right now there are +very small fees. + +So for every transaction +you put into Bitcoin, + +you can actually say, +instead of taking at exactly + +that the inputs +equal the outputs, + +you have inputs greater than the +outputs, and the net is fees. + +And what is the case +there is that in 2030 + +or something like +that, I think the fees + +will continue to increase, +I think, if this takes off. + +The question is, +does it take off? + +So I just had some fun because +this day is an important day + +for me since you met him. + +So whom is whom? + +[LAUGHTER] + +I sent this picture +to Rob this morning + +because today is our birthday. + +[CHEERING, APPLAUSE] + +AUDIENCE: (SINGING) +Happy birthday to you-- + +GARY GENSLER: No, no, +no, no, no, no, no. + +That's all right. + +AUDIENCE: (SINGING) +Happy birthday to you. + +GARY GENSLER: No, no, no, no. + +AUDIENCE: (SINGING) Happy +birthday, dear Gary. + +Happy birthday to you. + +[APPLAUSE] + +GARY GENSLER: So who's who? + +AUDIENCE: You're in the white. + +GARY GENSLER: White in +striped shirt or not? + +OK. + +AUDIENCE: Solid. + +AUDIENCE: Your stripes. + +GARY GENSLER: All right. + +How many striped shirters? + +All right. + +How many solid shirters? + +Wow. + +So I sent it to +Rob this morning, + +and I sent it to +my three daughters, + +and I sent it to my girlfriend. + +I said, who is this? + +It's split view there, too. + +[LAUGHTER] + +I went with striped shirt, +but Rob said he doesn't know. + +[LAUGHTER] + +We were three years old there. + +So that's just a +goof around with you. + +All right. + +Thank you all. \ No newline at end of file diff --git a/Oi-JCJePLlc.txt b/Oi-JCJePLlc.txt new file mode 100644 index 0000000000000000000000000000000000000000..e9e6c9b8d2811b4161acf27882de3f94e3a4b9e6 --- /dev/null +++ b/Oi-JCJePLlc.txt @@ -0,0 +1,3436 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: Going to +get started right away. + +I want to make a comment +about energy time uncertainty + +relations. + +And we talked last +time about the fact + +that the energy time uncertainty +relation really tells you + +something about how +fast a state can change. + +So an interesting way +to try to evaluate + +that is to consider +a system that + +has to state that time +equals 0 and compute + +the overlap with a +state at time equals t. + +Now this overlap is a +very schematic thing. + +It's a bracket. + +It's a number. + +And you know what that means. + +You can keep in +mind what that is. + +It's an integral over space +possibly of psi star at t + +equals 0 x psi t x. + +It's a complete integral, +its inner product. + +So you may want to understand +this, because, in a sense, + +this is telling you how +quickly a state can change. + +At time equals 0, this +overlap is just 1. + +A little later, this +overlap is going to change + +and perhaps after some time +the overlap is going to be 0. + +And we're going to say that we +actually have changed a lot. + +So this number is very +interesting to compute. + +And in fact, we might +as well square it, + +because it's a complex number. + +So to understand better +what it is we'll square it. + +And we'll have to evaluate this. + +Now how could you evaluate this? + +Well, we'll assume that this +system that governs this time + +evolution has a time +independent Hamiltonian. + +Once this evolution is done by +a time independent Hamiltonian, + +you can wonder what it is. + +Now it's quite +interesting, and you + +will have to discuss +that in the homework + +because it will +actually help you + +prove that version of the +time energy uncertainty + +relationship that says that the +quickest time state can turn + +orthogonal to itself is +bounded by some amount. + +Cannot do it infinitely fast. + +So you want to know how +fast this can change. + +Now it's very surprising what +it depends on, this thing. + +Because suppose you had +an energy eigenstate, + +suppose psi at time equals +0 is an energy eigenstate. + +What would happen later on? + +Well, you know that +energy eigenstates + +evolve with a phase, +an exponential of e + +to the minus iht over h bar. + +So actually if you had +an energy eigenstate, + +this thing would remain +equal to 1 for all times. + +So if this is going +to be non-zero, + +it's because it's +going to have-- + +you have to have a state is +not an energy eigenstate. + +That you're going to have +an uncertainty in the energy + +and energy uncertainty. + +So the curious thing is that you +can evaluate this, and expand + +it as a power in t, and go, +say, to quadratic ordering + +in t evaluating what this is. + +And this only depends +on the uncertainty of h, + +and t, and things like that. + +So only the uncertainty of +h matters at this moment. + +So this would be quite +interested, I think, + +for you to figure out +and to explore in detail. + +That kind of analysis +has been the center + +of attention recently, having +to do with quantum computation. + +Because in a sense, +in a quantum computer, + +you want to change states +quickly and do operations. + +So how quickly you can +change a state is crucial. + +So in fact, the people that +proved these inequalities + +that you're going to find +say that this eventually + +will limit the speed +of a quantum computer, + +and more slow that computers +become twice as fast every year + +or so, and double the speed. + +So this limit +apparently, it's claimed, + +will allow 80 +duplications of the speed + +until you hit this limit +in a quantum computer + +due to quantum mechanics. + +So you will be investigating +this in next week's homework. + +Today we want to begin +quickly with an application + +of the uncertainty principal to +find exact bounds of energies + +for quantum systems, for ground +states of quantum systems. + +So this will be a very precise +application of the uncertainty + +principle. + +Then we'll turn to a +completion of these things + +that we've been +talking about having + +to do with linear algebra. + +We'll get to the main +theorems of the subject. + +In a sense, the most important +theorems of the subject. + +These are the spectral +theorem that tells you + +about what operators +can be diagonalized. + +And then a theorem that +leads to the concept + +of a complete set of +commuting observables. + +So really pretty key +mathematical ideas. + +And the way we're good to +do it, I think you will see, + +that we have gained a lot by +learning the linear algebra + +concepts in a +slightly abstract way. + +I do remember doing this +proof that we're going today + +in previous years, +and it was always + +considered the most complicated +lecture of the course. + +Just taking the +[? indices ?] went crazy, + +and lots of formulas, and +the notation was funny. + +And now we will do +the proof, and we'll + +write a few little things. + +And we'll just try to +imagine what's going on. + +And will be, I think, easier. + +I hope you will agree. + +So let's begin with an example +of a use of the uncertainty + +principle. + +So example. + +So this will be +maybe for 20 minutes. + +Consider this Hamiltonian for +a one dimensional particle + +that, in fact, you've +considered before, + +alpha x to the fourth, for which +you did some approximations. + +You know that the +expectation value + +of the energy in +the ground state. + +You've done it numerically. + +You've done it variationally. + +And variationally you knew +that the energy at every stage + +was smaller at a given bound. + +The uncertainty +principle is not going + +to give us an upper bound. + +It's going to give +us a lower bound. + +So it's a really +nice thing, because + +between the variational +principal and the uncertainty + +principle, we can narrow the +energy of this ground state + +to a window. + +In one of the problems that +you're doing for this week-- + +and I'm sorry only +today you really + +have all the tools after you +hear this discussion-- you + +do the same for the +harmonic oscillator. + +You do a variational estimate +for the ground state energy. + +You do the uncertainty principle +bound for ground state energy. + +And you will see +these two bounds meet. + +And therefore after you've +done this to bounds, + +you found the +ground state energy + +of the harmonic oscillator, +so it's kind of a neat thing. + +So we want to estimate +the ground state energy. + +So we first write some words. + +We just say H in +the ground state + +will be given by the +expectation value of p squared + +in the ground state plus +alpha times the expectation + +value of x to the fourth +in the ground state. + +Haven't made much +progress, but you + +have, because you're starting to +talk about the right variables. + +Now this thing to +that you have to know + +is that you have +a potential that + +is like this, sort +of a little flatter + +than x squared potential. + +And what can we say about +the expectation value + +of the momentum on +the ground state + +and the expectation value +of x in the ground state? + +Well, the expectation value +of x should be no big problem. + +This is a symmetric +potential, therefore + +wave functions in a one +dimensional quantum mechanics + +problems are either +symmetric or anti symmetric. + +It could not be anti +symmetric because it's + +a ground state and +kind of have a 0. + +So it's asymmetric. + +Has no nodes. + +So there's the wave +function of the ground + +state, the symmetric, +and the expectation value + +of x in the ground state is 0. + +Similarly, the expectation value +of the momentum in the ground + +state, what is it? + +Is? + +0 too. + +And you can imagine +just computing it. + +It would be the integral of psi. + +Psi is going to be a real +d dx h bar over i psi. + +This is a total derivative. + +If it's a bound state, +it's 0 at the ends. + +This is 0. + +So actually, we have a +little advantage here. + +We have some control +over what p squared is, + +because the uncertainty in p +in the ground state-- well, + +the uncertainty in p squared +is the expectation value + +of p squared minus the +expectation value of p squared. + +So in the ground +state, this is 0. + +So delta p squared +in the ground state + +is just p squared +on the ground state. + +Similarly, because +the expectation value + +of x is equal to 0, delta x +squared in the ground state + +is equal to expectation value of +x squared in the ground state. + +So actually, this expectation +of p squared is delta p. + +And we want to use the +uncertainty principle, + +so that's progress. + +We've related something we want +to estimate to an uncertainty. + +Small complication is that +we have an expectation + +value of x to the fourth. + +Now we learned-- maybe +I can continue here. + +We learned that the expectations +value for an operator squared + +is bigger than or equal +to the expectation + +value of the operator squared. + +So the expectation +value of x to the fourth + +is definitely bigger than the +expectation value of x squared + +squared. + +And this is true on any state. + +This was derived when +we did uncertainty. + +We proved that the +uncertainty squared + +is positive, because +the norm of a vector, + +and that gave you this thing. + +So here you think of the +operator as x squared. + +So the operator squared +is x to the fourth. + +And here's the operator +expectation value squared. + +So this is true for +the ground state. + +It's also here true for any +state, so is the ground state. + +And this x squared +now is delta x. + +So this is delta x on the +ground state to the fourth. + +So look what we have. + +We have that the expectation +value of H on the ground state + +is strictly equal to delta p +on the ground state squared + +over 2m plus alpha. + +And we cannot do a Priorean +equality here, so we have this. + +This is so far an equality. + +But because of this, this +thing is bigger than that. + +Well, alpha is supposed +to be positive. + +So this is bigger than delta +p ground state squared over + +2m plus alpha delta x on the +ground state to the fourth. + +OK, so far so good. + +We have a strict thing, this. + +And the order of the inequality +is already showing up. + +We're going to get, if +anything, a lower bound. + +You're going to be bigger +than or equal to something. + +So what is next? + +Next is the +uncertainty principle. + +We know that delta p delta +x is greater than or equal + +to h bar over 2 in any state. + +So the delta p ground state +and delta x on the ground state + +still should be equal to that. + +Therefore delta p ground +state is bigger than + +or equal than h over 2 delta x +in the ground state like that. + +So this inequality still +the right direction. + +So we can replace +this by something + +that is bigger than +this quantity day + +without disturbing the logic. + +So we have H ground +state now is greater + +than or equal to replace +the delta p by this thing + +here, h squared over 8, +because this is squared + +and there's another 2m delta x +ground state squared plus alpha + +delta x ground +state to the fourth. + +And that's it. + +We've obtained this inequality. + +So here you say, well, this +is good but how can I use it? + +I don't know what delta +x is in the ground state, + +so what have I gained? + +Well, let me do +a way of thinking + +about this that can help you. + +Plot the right hand side +as a function of delta + +x on the ground. + +So you don't know +how much it is, + +delta x on the ground +state, so just plot it. + +So if you plot this +function, there + +will be a divergence as +this delta x goes to 0, + +then it will be a minimum. + +It will be a positive minimum, +because this is all positive. + +And then it will go up again. + +So the right hand side as a +function of delta x is this. + +So here it comes. + +You see I don't know +what delta x is. + +Suppose delta x +happens to be this. + +Well, then I know +that the ground state + +energy is bigger +than that value. + +But maybe that's not delta x. + +Delta x may be is this +on the ground state. + +And then if it's that, well, +the ground state energy + +is bigger than this +value over here. + +Well, since I just +don't know what it is, + +the worst situation +is if delta x is here, + +and therefore definitely H must +be bigger than the lowest value + +that this can take. + +So the claim is that +H of gs, therefore + +is greater than or equal than +the minimum of this function + +h squared over 8m, and +I'll just write here + +delta x squared plus alpha delta +x to the fourth over delta x. + +The minimum of this function +over that space is the bound. + +So I just have to do a +calculus problem here. + +This is the minimum. + +I should take the derivative +with respect to delta x. + +Find delta x and substitute. + +Of course, I'm not +going to do that here, + +but I'll tell you a formula +that will do that for you. + +A over x squared +plus Bx to the fourth + +is minimized for x squared +is equal to 1 over 2-- + +it's pretty awful numbers. + +2 to the 1/3 A +over B to the 1/3. + +And its value at that point is +2 to the 1/3 times 3/2 times + +A to the 2/3 times B to the 1/3. + +A little bit of arithmetic. + +So for this function, +it turns out + +that A is whatever +coefficient is here. + +B is whatever +coefficient is there, + +so this is supposed +to be the answer. + +And you get H on +the ground state + +is greater than or equal to +2 to the 1/3 3/8 h squared + +square root of alpha over m to +the 2/3, which is about 0.4724 + +times h squared square root +of alpha over m to the 2/3. + +And that's our bound. + +How good or how +bad is the bound? + +It's OK. + +It's not fabulous. + +The real answer is done +numerically is 0.668. + +I think I remember +variational principal gave you + +something like 0.68 or 0.69. + +And this one says +it's bigger than 0.47. + +It gives you something. + +So the important thing is +that it's completely rigorous. + +Many times people use +the uncertainty principle + +to estimate ground +state energies. + +Those estimates +are very hand wavy. + +You might as well just +do dimensional analysis. + +You don't gain anything. + +You don't know the factors. + +But this is completely rigorous. + +I never made an approximation +or anything here. + +Every step was logical. + +Every inequality was exact. + +And therefore, this +is a solid result. + +This is definitely true. + +It doesn't tell you an +estimate of the answer. + +If you dimensional analysis, you +say the answer is this times 1, + +and that's as good as you can +do with dimensional analysis. + +It's not that bad. + +The answer turns out to be 0.7. + +But the uncertainty +principle really, + +if you're careful, sometimes, +not for every problem, + +you can do a rigorous thing +and find the rigorous answer. + +OK, so are there any questions? + +Your problem in +the homework will + +be to do this for the +harmonic oscillator + +and find the two bounds. + +Yes? + +AUDIENCE: How does +the answer change + +if we don't look at +the ground state? + +PROFESSOR: How do they what? + +PROFESSOR: How does +the answer change + +if we look at a state different +from the ground state? + +PROFESSOR: Different +from the ground state? + +So the question was +how would this change + +if I would try to do something +different from the ground + +state. + +I think for any +state, you would still + +be able to say that +the expectation + +value of the momentum is 0. + +Now the expectation value +of x still would be 0. + +So you can go through +some steps here. + +The problem here being +that I don't have a way + +to treat any other +state differently. + +So I would go ahead, +and I would have + +said for any stationary state, +or for any energy eigenstate, + +all of what I said is true. + +So I don't get a new one. + +These things people actually +keep working and writing papers + +on this stuff. + +People sometimes find bounds +that are a little original. + +Yes? + +AUDIENCE: How do you know +the momentum expectation is 0 + +again? + +PROFESSOR: The momentum +expectation for a bound state + +goes like this. + +So you want to figure +out what is psi p psi. + +And you do the following. + +That's integral. + +Now psi in these +problems can be chosen + +to be real, so I won't bother. + +It's psi of x h bar +over i d dx of psi. + +So this is equal to h bar over +2i the integral dx of d dx + +of psi squared. + +So at this moment, you say +well that's just h bar over 2i, + +the value of psi squared at +infinity and at minus infinity. + +And since it's a bound +state, it's 0 here, 0 there, + +and it's equal to 0. + +A state that would have +expectation value of momentum + +you would expect +it to be moving. + +So this state is +there is static. + +It's stationary It doesn't have +expectation value of momentum. + +Yes? + +AUDIENCE: Is the reason that +you can't get a better estimate + +for the things that are +on the ground state, + +because if you consider +the harmonic oscillator, + +the uncertainty delta x +[? delta p ?] from the ground + +state [INAUDIBLE] you +go up to higher states. + +PROFESSOR: Right, I +think that's another way. + +AUDIENCE: [INAUDIBLE] higher +state using the absolute. + +PROFESSOR: Yeah. + +That's a [INAUDIBLE]. + +So the ground state of the +harmonic oscillator saturates + +the uncertainty principal +and the others don't. + +So this argument, I think, +is just good for ground state + +energies. + +One more question. + +AUDIENCE: It appears that +this method really works. + +Doesn't particularly work well +if we have a potential that + +has an odd power, because we +can't use [? the packet ?], + +like x [INAUDIBLE] expectation +value x to the fourth + +is something, some +power, expectation. + +PROFESSOR: Right, if +it's an odd power, + +the method doesn't work well. + +But actually for an +odd power, the physics + +doesn't work well either, +because the system doesn't + +have ground states. + +And so let's say +that if you had x + +to the fourth plus some x +cubed, the physics could still + +make sense. + +But then it's not clear +I can do the same. + +Actually you can +do the same for x + +to the eighth and any sort +of powers of this type. + +But I don't think it +works for x to the sixth. + +You can try a few things. + +OK, so we leave the +uncertainty principle + +and begin to understand +more formerly the operators + +for which there's no uncertainty +and you can simultaneously + +diagonalize them. + +So we're going to find +operators like A and B, + +that they commute. + +And then sometimes +you can simultaneously + +diagonalize them. + +Yes? + +You have a question. + +AUDIENCE: So part of [INAUDIBLE] +we use here is [INAUDIBLE], + +right? + +PROFESSOR: Right. + +AUDIENCE: If we get an asset-- +is there any way that we + +can better our [INAUDIBLE] +principle based on the wave + +function with non saturated? + +Can we get an upper +bound for just + +[INAUDIBLE] principle +with an h bar over it? + +PROFESSOR: Can I +get an upper bound? + +I'm not sure I +understand your question. + +AUDIENCE: [INAUDIBLE] the fact +that the [INAUDIBLE] principle + +will not be saturated. + +Can you put the bound for +just taking [INAUDIBLE]? + +PROFESSOR: Yeah, certainly. + +You might have some +systems in which + +you know that this +uncertainty might + +be bigger than the one warranted +by the uncertainty principles. + +And you use that information. + +But on general grounds, +it's hard to know + +that a system might come +very close to satisfy + +the uncertainty principle +in its ground state. + +We don't know. + +There are systems that come +very close in the ground state + +to satisfy this and +some that are far. + +If they are far, you +must have some reason + +to understand that to use it. + +So I don't know. + +So let me turn now to +this issue of operators + +and diagonalization +of operators. + +Now you might be irritated +a little even by the title. + +Diagonalization of operation. + +You'll be talking about +diagonalization of matrices. + +Well, there's a +way to state what + +we mean by diagonalizing +an operator in such a way + +that we can talk later +about the matrix. + +So what is the point here? + +You have an operator, +and it's presumably + +an important operator +in your theory. + +You want to understand +this operator better. + +So you really are +faced with a dilemma. + +How do I get some insight +into this operator? + +Perhaps the simplest thing +you could do is to say, + +OK let me choose some ideal +basis of the vector space, + +such as that operator +is as simple as possible + +in that basis. + +So that's the origin +of this thing. + +Find a basis in the state +space, so the operator + +looks as simple as possible. + +So you say that you can +diagonalize an operator + +if you can find the basis +such that the operator has + +just diagonal entries. + +So let me just +write it like this. + +So if you can find a basis in +V where the matrix representing + +the operator is +diagonal, the operator + +is said to be diagonalizable. + +So to be diagonalizable +is just a statement + +that there is some basis +where you look at the matrix + +representation +operator, and you find + +that it takes form +as a diagonal. + +So let's try to understand +this conceptually + +and see what actually +it's telling us. + +It tells us actually a lot. + +Suppose t is diagonal in +some basis u1 up to un. + +So what does it mean +for it to be diagonal? + +Well, you may remember +all these definitions + +we had about matrix action. + +If T acting on a ui +is supposed to be + +Tki uk in some basis sum over k. + +You act on ui, and +you get a lot of u's. + +And these are the matrix +elements of the operator. + +Now the fact that +it's diagonalizable + +means that in some basis, the +u basis, this is diagonal. + +So ki in this sum only +happens to work out + +when k is equal to i. + +And that's one number and you +get back to the vector ui. + +So if it's diagonal +in this basis, + +you have the T on u1 is lambda +a number times u1 T on u2 + +is lambda 2 in u2. + +And Tun equal lambda n un. + +So what you learn is +that this basis vector-- + +so you learn something +that maybe you + +thought it's tautological. + +It's not tautological. + +You learn that if you have +a set of basis vectors + +in which the +operator is diagonal, + +these basis vectors are +eigenvectors of the operator. + +And then you learn something +that is quite important, + +that an operator is +diagonalizable if, + +and only if, it has +a set of eigenvectors + +that span the space. + +So the statement +is very important. + +An operator T is +that diagonalizable + +if it has a set of eigenvectors +that span the space. + +Span V. If and only if. + +If this double f. + +If and only if. + +So here it's diagonalizable, +and we have a basis, + +and it has a set of +these are eigenvectors. + +So diagonalizable +realizable really + +means that it has a +set of eigenvectors + +that span the space. + +On the other hand, if you have +the set of eigenvectors that + +span the space, you have a +set of u's that satisfy this, + +and then you read that, oh +yeah, this matrix is diagonal, + +so it's diagonalizable. + +So a simple statement, +but an important one, + +because there are examples of +matrices that immediately you + +know you're never going +to succeed to diagonalize. + +So here is one matrix, 0 0 1 0. + +This matrix has +eigenvalues, so you + +do the characteristic equation +lambda squared equals 0. + +So the only eigenvalue +is lambda equals 0. + +And let's see how +many eigenvectors + +you would have for +lambda equals 0. + +Well, you would have if +this is T, T on some vector + +a b must be equal to 0. + +So this is 0 1 0 0 on a b, +which is b and 0, must be zero. + +So b is equal to 0. + +So the only +eigenvector here-- I'll + +just write it here and then +move to the other side. + +The only eigenvector +for lambda equals 0, + +the only eigenvector +is with b equals 0. + +So it's 1 0. + +One eigenvector only. + +No more eigenvectors. + +By the theorem, +or by this claim, + +you know it's a two dimensional +vector space you just + +can't diagonalize this matrix. + +It's impossible. + +Can't be done. + +OK, a couple more +things that I wish to + +say about this process +of diagonalization. + +Well, the statement that +an operator is diagonal + +is a statement about the +existence of some basis. + +Now you can try to figure +out what that basis is, + +so typically what is the +problem that you face? + +Typically you have a +vector spaces V. Sorry? + +AUDIENCE: I have a question. + +PROFESSOR: Yes? + +If you had an infinite +dimensional space + +and you had an operator +whose eigenvectors do not + +span the space, can it +still have eigenvectors, + +or does it not have any then? + +PROFESSOR: No. + +You said it has +some eigenvectors, + +but they don't span the space. + +So it does have +some eigenvectors. + +AUDIENCE: So my question +is was what I just + +said a logical contradiction in +an infinite dimensional space? + +PROFESSOR: To have +just some eigenvectors? + +I think-- + +PROFESSOR: I'm looking +more specifically + +at a dagger for instance. + +PROFESSOR: Yes. + +AUDIENCE: In the +harmonic oscillator, + +you I think mentioned at some +point that it does not have-- + +PROFESSOR: So the +fact that you can' + +diagonalize this +thing already implies + +that it's even worse +in higher dimensions. + +So some operator +may be pretty nice, + +and you might still be +able to diagonalize it, + +so you're going to lack +eigenvectors in general. + +You're going to +lack lots of them. + +And there are going to +be blocks of Jordan. + +Blocks are called things that +are above the diagonal, things + +that you can't do much about. + +Let me then think concretely now +that you have a vector space, + +and you've chosen +some basis v1 vn. + +And then you look +at this operator T, + +and of course, you chose +an arbitrary basis. + +There's no reason why +its matrix representation + +would be diagonal. + +So T on the basis v-- Tij. + +Sometimes to be very explicit +we write Tij like that-- + +is not diagonal. + +Now if it's not +diagonal, the question + +is whether you can find a +basis where it is diagonal. + +And then you try, of +course, changing basis. + +And you change basis-- +you've discussed + +that in the homework-- +with a linear operator. + +So you use a linear +operator to produce + +another basis, an +invertible in your operator. + +So that you get these vectors +uk being equal to some operator + +A times vk. + +So this is going to be +the u1's up to un's are + +going to be another basis. + +The n vector here +is the operator + +acting with the n +vector on this thing. + +And then you prove, in the +homework, a relationship + +between these matrix elements +of T in the new basis, + +in the u basis. + +And the matrix elements +of T in the v basis. + +You have a +relationship like this, + +or you have more explicitly +Tij in the basis u + +is equal to A minus +1 ik Tkp of v Apj. + +So this is what happens. + +This is the new +operator in this basis. + +And typically what +you're trying to do + +is find this matrix A +that makes this thing + +into a diagonal matrix. + +Because we say in the u basis +the operator is diagonal. + +I want to emphasize that there's +a couple of ways in which you + +can think of diagonalization. + +Sort of a passive +and an active way. + +You can imagine the +operator, and you + +say look, this +operator I just need + +to find some basis in +which it is diagonal. + +So I'm looking for a basis. + +The other way of +thinking of this operator + +is to think that A minus +1 TA is another operator, + +and it's diagonal +in original basis. + +So it might have seem funny +to you, but let's stop again + +and say this again. + +You have an operator, and the +question of diagonalization + +is whether there is some basis +in which it looks diagonal, + +its matrix is diagonal. + +But the equivalent +question is whether there + +is an operator A +such that this is + +diagonal in the original basis. + +To make sure that you see +that, consider the following. + +So this is diagonal +in the original basis. + +So in order to see that, think +of Tui is equal to lambda i ui. + +We know that the +u's are supposed + +to be this basis of eigenvectors +where the matrix is diagonal, + +so here you got it. + +Here the i not summed. + +It's pretty important. + +There's a problem with +this eigenvalue notation. + +I don't know how +to do it better. + +If you have several eigenvalues, +you want to write this, + +but you don't want this to +think that you're acting on u1 + +and you get lambda 1 u1. + +Not the sum right here. + +OK, but they ui is +equal to A on vi. + +So therefore this +is lambda i A on vi. + +And then you'll +act with A minus 1. + +Act with A minus 1 from +the left with the operator. + +So you get A minus 1 TA vi +is equal to lambda i vi. + +So what do you see? + +You see an operator +that is actually + +diagonal in the v basis. + +So this operator is diagonal +in the original basis. + +That's another way of +thinking of the process + +of diagonalization. + +There's one last remark, +which is that the columns of A + +are the eigenvectors, in fact. + +Columns of A are +the eigenvectors. + +Well, how do you see that? + +It's really very simple. + +You can convince +yourself in many ways, + +but the uk are the eigenvectors. + +But what are uk's? + +I have it somewhere. + +There it is. + +A on vk. + +And A on vk is this +matrix representation + +is sum over i Aik vi. + +So now if this is +the original basis, + +the vi's are your +original basis, + +then you have the +following, that the vi's + +can be thought as the basis +vectors and represented + +by columns with a +1 in the ith entry. + +So this equation is saying +nothing more, or nothing less + +than uk, in terms of +matrices or columns, + +is equal to A1k v1 plus Ank +vn, which is just A1k A2k Ank. + +Because vi is the +ith basis vector. + +So 1 0's only in +the ith position. + +So these are the eigenvectors. + +And they're thought as linear +combinations of the vi's. + +The vi's are the +original basis vectors. + +So the eigenvectors +are these numbers. + +OK, we've talked +about diagonlization, + +but then there's a term that is +more crucial for our operators + +that we're interested in. + +We're talking about +Hermitian operators. + +So the term that is going +to be important for us + +is unitarily diagonalizable. + +What is a unitarily +diagonalizable operator? + +Two ways again of +thinking about this. + +And perhaps the first +way is the best. + +And I will say it. + +A matrix is set to be +unitarily diagonalizable + +if you have an orthonormal +basis of eigenvectors. + +Remember diagonalizable meant +a basis of eigenvectors. + +That's all it means. + +Unitarily diagonalizable +means orthonormal basis + +of eigenvectors. + +So T has an orthonormal +basis of eigenvectors. + +Now that's a very +clear statement. + +And it's a fabulous +thing if you can achieve, + +because you basically +have broken down the space + +into basis spaces, each one +of them with a simple thing + +before your operators. + +And they're orthonormal, +so it's the simplest + +possible calculational tool. + +So it's ideal if +you can have this. + +Now the way we think +of this is that you + +start with-- +concretely, you start + +with a T of some basis v +that is an orthonormal basis. + +Start with an orthonormal +basis, and then + +pass to another +orthonormal basis u. + +So you're going to pass to +another orthonormal basis + +u with some operator. + +But what you have +learned is that if you + +want to pass from v +orthonormal to another basis + +u, a vector that is +also orthonormal, + +the way to go from +one to the other + +is through a unitary operator. + +Only unitary operators pass you +from orthonormal to orthonormal + +basis. + +Therefore really, when +you start with your matrix + +in an orthonormal basis +that is not diagonal, + +the only thing you can +hope is that T of u + +will be equal to sum u dagger, +or u minus 1, T of v u. + +Remember, for a unitary +operator, where u is unitary, + +the inverse is the dagger. + +So you're doing a +unitary transformation, + +and you find the matrix that +is presumably then diagonal. + +So basically, unitarily +diagonalizable + +is the statement +that if you start + +with the operator in an +arbitrary orthonormal basis, + +then there's some unitary +operator that takes you + +to the privilege basis in which +your operator is diagonal, + +is still orthonormal. + +But maybe in a more simple +way, unitarily diagonalizable + +is just a statement +that you can find + +an orthonormal basis +of eigenvectors. + +Now the main theorem +of this subject, + +perhaps one of the +most important theorems + +of linear algebra, is +the characterization + +of which operators have such +a wonderful representation. + +What is the most +general operator T + +that will have an orthonormal +basis of eigenvectors? + +Now we probably have heard that +Hermitian operators do the job. + +Hermitian operators have that. + +But that's not the +most general ones. + +And given that you want +the complete result, + +let's give you the +complete result. + +The operators that have +this wonderful properties + +are called normal +operators, and they + +satisfy the following property. + +M is normal if M dagger, the +adjoint of it, commutes with M. + +So Hermitian +operators are normal, + +because M dagger is equal +to M, and they commute. + +Anti Hermitian mission +operators are also normal, + +because anti Hermitian +means that dagger + +is equal to minus M, and +it still commutes with M. + +Unitary operators have +U dagger U equal to U U + +dagger equals to 1. + +So U and U dagger +actually commute as well. + +So Hermitian, anti +Hermitian, unitary, they're + +all normal operators. + +What do we know about +normal operators? + +There's one important result +about normal operators, + +a lemma. + +If M is normal and +W is an eigenvector, + +such that MW is +equal to lambda W. + +Now normal operators need +not have real eigenvalues, + +because they include +unitary operators. + +So here I should write +Hermitian, anti Hermitian, + +and unitary are normal. + +So here is what a normal +operator is doing. + +You have a normal operator. + +It has an eigenvector +with some eigenvalue. + +Lambda is a complex +number in principle. + +Then the following +result is true, + +then M dagger omega is also +an eigenvector of M dagger. + +And it has eigenvalue +lambda star. + +Now this is not all +that easy to show. + +It's a few lines, and +it's done in the notes. + +I ask you to see. + +It's actually very elegant. + +What is the usual +strategy to prove things + +like that Is to say oh, I want +to show this is equal to that, + +so I want to show that +this binds that is 0. + +So I have a vector +that is zero what + +is the easiest way +to show that it's 0? + +If I can show it's norm is 0. + +So that's a typical +strategy that you + +use to prove equalities. + +You say, oh, it's a vector +that must be 0 as my equality. + +Let's see if it's 0. + +Let's find its norm, +and you get it. + +So that's a result. + +So with this stated, we +finally have the main result + +that we wanted to get to. + +And I will be very +sketchy on this. + +The notes are complete, +but I will be sketchy here. + +It's called the +spectral theorem. + +Let M be an operator in +a complex vector space. + +The vector space has +an orthonormal basis + +of eigenvectors of M if +and only if M is normal. + +So the normal operators are it. + +You want to have a complete set +of orthonormal eigenvectors. + +Well, this will only +happen if your operator + +is normal, end of story. + +Now there's two things +about this theorem + +is to show that if it's +diagonalizable, it is normal, + +and the other thing is to +show, that if it's normal, + +it can be diagonalized. + +Of course, you can +imagine the second one + +is harder than the first. + +Let me do the first +one for a few minutes. + +And then say a couple of +words about the second. + +And you may discuss +this in recitation. + +It's a little +mathematical, but it's all + +within the kind of +things that we do. + +And really it's fairly +physical in a sense. + +We're accustomed to do +such kinds of arguments. + +So suppose it's +unitarily diagonalizable, + +which means that M-- so +if you have U dagger, + +MU is equal to a +diagonal matrix, DM. + +I'm talking now matrices. + +So these are all matrices, +a diagonal matrix. + +There's no basis to the +notion of a diagonal operator, + +because if you have +a diagonal operator, + +it may not look diagonal +in another basis. + +Only the identity operator is +diagonal in all basis, but not + +the typical diagonal operator. + +So unitarily +diagonalizable, as we said, + +you make it-- it's +gone somewhere. + +Here. + +You act with an +inverse matrices, + +and you get the diagonal matrix. + +So from this, you find that +M is equal to U DM U dagger + +by acting with U on the left and +with U dagger from the right, + +you solve for M, and it's this. + +And then M dagger is the +dagger of these things. + +So it's U to DM dagger U dagger. + +The U's sort of +remain the same way, + +but the diagonal matrix +is not necessarily real, + +so you must put the +dagger in there. + +And now M dagger M. To check +that the matrix is normal + +that commutator should be 0. + +So M dagger M. You +do this times that. + +You get U DM dagger. + +U dagger U. That's one. + +DM U dagger. + +And M M dagger you multiply +the other direction + +you get U DM DM dagger U dagger. + +So the commutator of M dagger +M is equal to U DM dagger DM + +minus DM Dm dagger U dagger. + +But any two diagonal +matrices commute. + +They may not be that simple. + +Diagonal matrices are not +the identity matrices, + +but for sure they commute. + +You multiply elements along +with diagonal so this is 0. + +So certainly any unitarily +diagonalizable matrix + +is normal. + +Now the other part +of the proof, which + +I'm not going to speak about, +it's actually quite simple. + +And it's based on the fact that +any matrix in a complex vector + +space has at least +one eigenvalue. + +So what you do is you pick +out that eigenvalue and it's + +eigenvector, and +change the basis + +to use that eigenvector +instead of your other vectors. + +And then you look at the matrix. + +And after you use +that eigenvector, + +the matrix has a lot of 0's +here and a lot of 0's here. + +And then the matrix has been +reduced in dimension mansion, + +and then you go step by step. + +So basically, it's the +fact that any operator + +has at least one eigenvalue +and at least one eigenvector. + +It allows you to go down. + +And normality is analogous +to Hermiticity in some sense. + +And the statement that +you have an eigenvector + +generally tells you that this +thing is full of 0's, but then + +you don't know that +there are 0's here. + +And either normality +or Hermiticity + +shows that there are +0's here, and then you + +can proceed at lower dimensions. + +So you should look at +the proof because it + +will make clear to you that +you understand what's going on. + +OK but let's take it for granted +now you have these operators + +and can be diagonalized. + +Then we have the +next thing, which + +is simultaneous diagonalization. + +What is simultaneous +diagonalization? + +It's an awfully important thing. + +So we will now focus on +simultaneous diagonalization + +of Hermitian operators. + +So simultaneous diagonalization +of Hermitian ops. + +Now as we will emphasize +towards the end, + +this is perhaps one of +the most important ideas + +in quantum mechanics. + +It's this stuff that allows +you to label and understand + +your state system. + +Basically you need +to diagonalize + +more than one operator +most of the time. + +You can say OK, you found +the energy eigenstates. + +You're done. + +But if you find your +energy eigenstates + +and you think you're +done, maybe you + +are if you have all these +energy eigenstates tabulated. + +But if you have +a degeneracy, you + +have a lot of states that +have the same energy. + +And what's different about them? + +They're certainly +different because you've + +got several states, but +what's different about them? + +You may not know, +unless you figure out + +that they have different +physical properties. + +If they're different, something +must be different about them. + +So you need more +than one operator, + +and your facing the problem of +simultaneously diagonalizing + +things, because states cannot +be characterized just by one + +property, one observable. + +Would be simple if you could, +but life is not that simple. + +So you need more +than one observable, + +and then you ask +when can they be + +simultaneously diagonalizable. + +Well, the statement is clear. + +If you have two +operators, S and T that + +belong to the linear +operators in a vector space, + +they can be simultaneously +diagonalized + +if there is a basis for +which every basis vector is + +eigenstate of this and +an eigenstate of that. + +Common set of eigenstates. + +So they can be +simultaneously diagonalized. + +Diagonalizable is that there +is a basis where this basis is + +comprised of the +eigenvectors of the operator. + +So this time you require +more, that that basis + +be at the same time a basis +set of eigenvectors of this + +and a set of eigenvectors +of the second one. + +So a necessary condition for +simultaneous diagonalization + +is that they commute. + +Why is that? + +The fact that two operators +commute or they don't commute + +is an issue that is +basis independent. + +If they don't commute, +the order gives something + +different, and that you +can see in every basis. + +So if they don't commute +and they're simultaneously + +diagonalizable, there would +be a basis in which both + +are diagonal and they +still wouldn't commute. + +But you know that +diagonal matrices commute. + +So if two operators +don't commute, + +they must not +commute in any base, + +therefore there can't +be a basis in which both + +are at the same time diagonal. + +So you need, for +simultaneous diagonalizable, + +you need that S and P commute. + +Now that may not be enough, +because not all operators + +can be diagonalized. + +So the fact that they commute +is necessary, but not everything + +can be diagonalizable. + +Well, you've learned that +every normal operator, + +every Hermitian operator +is diagonalizable. + +And then you got now +a claim of something + +that could possibly be true. + +Is the fact that whenever you +have two Hermitian operators, + +each one can be +diagonalized by themselves. + +And they commute. + +There is a simultaneous +set of eigenvectors of 1 + +that are eigenvectors of +the first and eigenvectors + +of the second. + +So the statement is that +if S and T are commuting + +Hermitian operators, they can +be simultaneously diagonalized. + +So this theorem would +be quite easy to show + +if there would be +no degeneracies, + +and that's what we're +going to do first. + +But then we'll consider +the case of degeneracies. + +So I'm going to consider +the following possibilities. + +Perhaps neither one has +a degenerate spectrum. + +What does it mean a +degenerate spectrum? + +Same eigenvalue +repeated many times. + +But that is a wishful +thinking situation. + +So either both are +non degenerate, + +either one is non degenerate +and the other is degenerate, + +or both are degenerate. + +And that causes a very +interesting complication. + +So let's say there's +going to be two cases. + +It will suffice. + +In fact, it seems +that there are three, + +but two is enough to consider. + +There is no degeneracy +in T. So suppose + +one operator has no +degeneracy, and let's call + +it T. So that's one possibility. + +And then S may be degenerate, +or it may not be degenerate. + +And the second possibility +is that both S and T + +are degenerate. + +So I'll take care +of case one first. + +And then we'll discuss +case two, and that + +will complete our discussion. + +So suppose there's +no the degeneracy + +in the spectrum +of T. So case one. + +So what does that mean? + +It means that T +is non degenerate. + +There's a basis U1 +can be diagonalized + +to UM, orthonormal by +the spectral theorem. + +And there's eigenvectors T +U-- these are eigenvectors. + +Lambda I Ui. + +And lambda I is +different to lambda j + +for i different from j. + +So all the eigenvalues, +again, it's not summed here. + +All the eigenvalues +are different. + +So what do we have? + +Well, each of +those eigenvectors, + +each of the Ui's that +are eigenvectors, + +generate invariant subspaces. + +There are T invariant subspaces. + +So each one, each +vector U1 you can + +imagine multiplying by +all possible numbers, + +positive and negative. + +And that's an invariant +one dimensional subspace, + +because if you act with T, +it's a T invariant space, + +you get the number +times a vector there. + +So the question that +you must ask now + +is you want to know if these +are simultaneous eigenvectors. + +So you want to figure +out what about S. + +How does S work with this thing? + +So you can act with +S from the left. + +So you get STUi is +equal to lambda i SUi. + +So here each Ui generates +an invariant subspace Ui T + +invariant. + +But S and T commute, so you have +T SUi is equal to lambda i SUi. + +And look at that equation again. + +This says that +this vector belongs + +to the invariant subspace Ui, +because it satisfies exactly + +the property that T acting on +it is equal to lambda i Ui. + +And it couldn't belong to +any other of the subspaces, + +because all the +eigenvalues are different. + +So spaces that are in Ui are the +spaces-- vectors that are in Ui + +are precisely all those +vectors that are left invariant + +by the action of T. +They're scaled only. + +So this vector is also in Ui. + +If this vector is +in Ui, SUi must + +be some number Wi times Ui. + +And therefore you've shown that +Ui is also an eigenvector of S, + +possibly with a different +eigenvalue of course. + +Because the only +thing that you know + +is that SUi is in this space. + +You don't know how big it is. + +So then you've shown +that, indeed, these Ui's + +that were eigenstates of T +are also eigenstates of S. + +And therefore +that's the statement + +of simultaneously +diagonalizable. + +They have the common +set of eigenvectors. + +So that's this part. + +And it's relatively +straight forward. + +Now we have to do case two. + +Case two is the interesting one. + +This time you're going +to have degeneracy. + +We have to have a notation +that is good for degeneracy. + +So if S is degeneracies, +has degeneracies, + +what happens with this operator? + +It will have-- remember, +a degenerate operator + +has eigenstates that form higher +than one dimensional spaces. + +If you have different +eigenvalues, + +each one generates a one +dimensional operator invariant + +subspace. + +But if you have +degeneracies, there + +are operators-- there are +spaces of higher dimensions that + +are left invariant. + +So for example, let Uk +denote the S invariant + +subspace of some +dimension Dk, which + +is greater or equal than 1. + +I will go here first. + +We're going to define Uk to +be the set of all vectors + +so that SU is equal +to lambda k U. + +And this will have dimension +of Uk is going to be Dk. + +So look what's happening. + +Basically the fact is +that for some eigenvalues, + +say the kth eigenvalue, you +just get several eigenvectors. + +So if you get several +eigenvectors not just scaled + +off each other, +these eigenvectors + +correspond to that +eigenvalue span of space. + +It's a degenerate subspace. + +So you must imagine +that as having + +a subspace of some +dimensionality with some basis + +vectors that span this thing. + +And they all have +the same eigenvector. + +Now you should really +have visualized + +this in a simple way. + +You have this subspace like a +cone or something like that, + +in which every vector +is an eigenvector. + +So every vector, when it's +acted by S is just scaled up. + +And all of them are +scaled by the same amount. + +That is what this +statement says. + +And corresponding to this thing, +you have a basis of vectors, + +of these eigenvectors, +and we'll call + +them Uk1, the first one, +the second, up to U Dk1, + +because it's a +subspace that we say + +it has the dimensionality Dk. + +So look at this thing. + +Somebody tells you +there's an operator. + +It has degenerate spectrum. + +You should start imagining all +kind of invariant subspaces + +of some dimensionality. + +If it has degeneracy, it's +a degeneracy each time + +the Dk is greater than +1, because if it's + +one dimensional, it's +just one basis vector one + +eigenvector, end of the story. + +Now this thing, by +the spectral theorem, + +this is an orthonormal basis. + +There's no problem, when you +have a degenerate subspace, + +to find an orthonormal basis. + +The theorem guarantees it, +so these are all orthonormal. + +So at the end of the day, +you have a decomposition + +of the vector space, V as U1 +plus U2 plus maybe up to UM. + +And all of these vector +spaces like U's here, they + +may have some with just +no degeneracy, and some + +with degeneracy 2, +degeneracy 3, degeneracy 4. + +I don't know how +much degeneracy, + +but they might have +different degeneracy. + +Now what do we say next? + +Well, the fact that S +is a Hermitian operator + +says it just can +be diagonalized, + +and we're can find +all these spaces, + +and the basis for +the whole thing. + +So the basis would look U1 +of the first base up to U d1 + +of the first base. + +These are the basis +vectors of the first + +plus the basis +vectors of the second. + +All the basis vectors U1 +up to Udm of the mth space. + +All this is the list. + +This is the basis +of V. So I've listed + +the basis of V, which a basis +for U1, all these vectors. + +U2, all of this. + +So you see, we're not +calculating anything. + +We're just trying to +understand the picture. + +And why is this operator, +S, diagonal in this basis? + +It's clear. + +Because every vector here, every +vector is an eigenvector of S. + +So when you act with +S on any vector, + +you get that vector +times a number. + +But that vector is +orthogonal to all the rest. + +So when you have some +U and S and another U, + +this gives you a vector +proportional to U. + +And this is another vector. + +The matrix element is 0, +because they're all orthogonal. + +So it should be obvious why +this list produces something + +that is completely +orthogonal-- a diagonal matrix. + +So S, in this basis, looks +like the diagonal matrix + +in which you have lambda 1 d1 +times up to lambda m dm times. + +Now I'll have to go until +2:00 to get the punchline. + +I apologize, but we +can't stop right now. + +We're almost there, +believe it or not. + +Two more things. + +This basis is good, but +actually another basis + +would also be good. + +I'll write this other basis +would be a V1 acting on the U1 + +up to V1 acting on that U1 up to +a Vm acting on this U1 up to Vm + +acting on that U1. + +This is m. + +m. + +This is dm. + +And here it's not U1. + +It's Ud1. + +You see, in the first +collection of vectors, + +I act with an operator V1 up +to here with an operator Vm. + +All of them with Vk being +a unitary operator in Uk. + +In every subspace, there +are unitary operators. + +So you can have +these bases and act + +with a unitary operator +of the space U1 here. + +A unitary operator +with a space U2 here. + +A unitary operator +of the space Un here. + +Hope you're following. + +And what happens if this +operator is unitary, + +this is still an +orthonormal basis in U1. + +These are still +orthonormal basis in Um. + +And therefore this is +an orthonormal basis + +for the whole thing, because +anyway those different spaces + +are orthogonal to each other. + +It's an orthogonal +decomposition. + +Everything is orthogonal +to everything. + +So this basis would be equally +good to represent the operator. + +Yes? + +AUDIENCE: [INAUDIBLE] +arbitrary unitary operators? + +PROFESSOR: Arbitrary unitary +operators at this moment. + +Arbitrary. + +So here comes the catch +as to the main property + +that now you want to establish +is that the spaces Uk are also + +T invariant. + +You see, the spaces +Uk were defined + +to be S invariant subspaces. + +And now the main important +thing is that they are also T + +invariant because they +commute with that. + +So let's see why +that is the case. + +Suppose U belongs to Uk. + +And then let's look at the +vector-- examine the vector Tu. + +What happens to Tu? + +Well, you want to act on +S on Tu to understand it. + +But S and T commute, +so this is T SU. + +But since U belongs +to Uk, that's + +the space with +eigenvalue lambda k. + +So this is lambda k times +u, so you have Tu here. + +So Tu acted with S +gives you lambda k Tu. + +So Tu is in the +invariant subspace Uk. + +What's happening here is now +something very straightforward. + +You try to imagine how does +the matrix T look in the basis + +that we have here. + +Here is this basis. + +how does this matrix T look? + +Well, this matrix keeps +the invariant subspaces. + +So you have to think of +it blocked diagonally. + +If it acts on it-- here +are the first vectors + +that you're considering, the U1. + +Well if you act on it +with T of the U1 subspace, + +you stay in the U1 subspace. + +So you don't get anything else. + +So you must have +0's all over here. + +And you can have a matrix here. + +And if you act on the second +Uk U2, you get a vector in U2, + +so it's orthogonal to +all the other vectors. + +So you get a matrix here. + +And you get a matrix here. + +So actually you get a +blocked diagonal matrix + +in which the blocks +correspond to the degeneracy. + +So if there's a degeneracy +d1 here, it's a d1 times d1. + +And d2 times d2. + +So actually you +haven't simultaneously + +diagonalized them. + +That's the problem +of degeneracy. + +You haven't, but you +now have the tools, + +because this operator is +Hermitian, therefore it's + +Hermitian here, and +here, and here, and here. + +So you can diagonalize here. + +But what do you need +for diagonalizing here? + +You need a unitary matrix. + +Call it V1. + +For here you need +another unitary matrix. + +Call it V2. + +Vn. + +And then this matrix +becomes diagonal. + +But then what about +the old matrix? + +Well, we just explained here +that if you change the basis + +by unitary matrices, you +don't change the first matrix. + +So actually you succeeded. + +You now can diagonalize +this without destroying + +your earlier result. + +And you managed to +diagonalize the whole thing. + +So this is for two +operators in the notes. + +You'll see why it simply extends +for three, four, and five, + +or arbitrary number +of operators. + +See you next time. \ No newline at end of file diff --git a/OxJg8VJ-dBA.txt b/OxJg8VJ-dBA.txt new file mode 100644 index 0000000000000000000000000000000000000000..970219c3e18224e9688a291af09886bf570b7029 --- /dev/null +++ b/OxJg8VJ-dBA.txt @@ -0,0 +1,923 @@ +align:start position:0% + +visualization of standing waves that are + + align:start position:0% +visualization of standing waves that are + + + align:start position:0% +visualization of standing waves that are +electromagnetic requires that we see + + align:start position:0% +electromagnetic requires that we see + + + align:start position:0% +electromagnetic requires that we see +fields that are invisible and are + + align:start position:0% +fields that are invisible and are + + + align:start position:0% +fields that are invisible and are +varying at a frequency higher than we + + align:start position:0% +varying at a frequency higher than we + + + align:start position:0% +varying at a frequency higher than we +can actually perceive with our + + align:start position:0% + + + + align:start position:0% + +eyes the visualization of waves that are + + align:start position:0% +eyes the visualization of waves that are + + + align:start position:0% +eyes the visualization of waves that are +mechanical is + + align:start position:0% +mechanical is + + + align:start position:0% +mechanical is +easier here we've got a + + align:start position:0% +easier here we've got a + + + align:start position:0% +easier here we've got a +spring under tension + + align:start position:0% + + + + align:start position:0% + +the transverse deflections satisfy the + + align:start position:0% +the transverse deflections satisfy the + + + align:start position:0% +the transverse deflections satisfy the +wave + + align:start position:0% + + + + align:start position:0% + +equation the object in this + + align:start position:0% +equation the object in this + + + align:start position:0% +equation the object in this +demonstration is to see standing waves + + align:start position:0% +demonstration is to see standing waves + + + align:start position:0% +demonstration is to see standing waves +in the sinusoidal study State Professor + + align:start position:0% +in the sinusoidal study State Professor + + + align:start position:0% +in the sinusoidal study State Professor +Zan will provide a fixed termination at + + align:start position:0% +Zan will provide a fixed termination at + + + align:start position:0% +Zan will provide a fixed termination at +that end and I'll try and provide the + + align:start position:0% +that end and I'll try and provide the + + + align:start position:0% +that end and I'll try and provide the +sinusoidal + + align:start position:0% +sinusoidal + + + align:start position:0% +sinusoidal +exitation the first Mode's pretty + + align:start position:0% + + + + align:start position:0% + +easy here's the second + + align:start position:0% +easy here's the second + + + align:start position:0% +easy here's the second +mode little harder to + + align:start position:0% +mode little harder to + + + align:start position:0% +mode little harder to +do try that + + align:start position:0% +do try that + + + align:start position:0% +do try that +again at any + + align:start position:0% +again at any + + + align:start position:0% +again at any +location the the the response is + + align:start position:0% +location the the the response is + + + align:start position:0% +location the the the response is +sinusoidal we have a null in the middle + + align:start position:0% +sinusoidal we have a null in the middle + + + align:start position:0% +sinusoidal we have a null in the middle +because a wave incident on that + + align:start position:0% +because a wave incident on that + + + align:start position:0% +because a wave incident on that +termination comes back and interferes + + align:start position:0% +termination comes back and interferes + + + align:start position:0% +termination comes back and interferes +with the incident wave + + align:start position:0% + + + + align:start position:0% + +here are the actual plates and the + + align:start position:0% + + + + align:start position:0% + +short they're driven at the left by a + + align:start position:0% +short they're driven at the left by a + + + align:start position:0% +short they're driven at the left by a +radio frequency + + align:start position:0% +radio frequency + + + align:start position:0% +radio frequency +generator to see the lamp we've turned + + align:start position:0% +generator to see the lamp we've turned + + + align:start position:0% +generator to see the lamp we've turned +the lights + + align:start position:0% +the lights + + + align:start position:0% +the lights +down next the generator is turned on + + align:start position:0% +down next the generator is turned on + + + align:start position:0% +down next the generator is turned on +and the lamp is put in + + align:start position:0% +and the lamp is put in + + + align:start position:0% +and the lamp is put in +place I'm rubbing my feet on the carpet + + align:start position:0% +place I'm rubbing my feet on the carpet + + + align:start position:0% +place I'm rubbing my feet on the carpet +to generate static electricity to help + + align:start position:0% +to generate static electricity to help + + + align:start position:0% +to generate static electricity to help +ignite the + + align:start position:0% + + + + align:start position:0% + +lamp remember where there's light + + align:start position:0% +lamp remember where there's light + + + align:start position:0% +lamp remember where there's light +there's an oscillating electric + + align:start position:0% + + + + align:start position:0% + +field the dark areas are therefore where + + align:start position:0% +field the dark areas are therefore where + + + align:start position:0% +field the dark areas are therefore where +the electric field tends to null + + align:start position:0% + + + + align:start position:0% + +at the right end we also appear to have + + align:start position:0% +at the right end we also appear to have + + + align:start position:0% +at the right end we also appear to have +a + + align:start position:0% + + + + align:start position:0% + +null remember the right end is + + align:start position:0% + + + + align:start position:0% + +shorted we can see the nulls even better + + align:start position:0% +shorted we can see the nulls even better + + + align:start position:0% +shorted we can see the nulls even better +if the lights are turned out + + align:start position:0% + + + + align:start position:0% + +completely what we see is the magnitude + + align:start position:0% +completely what we see is the magnitude + + + align:start position:0% +completely what we see is the magnitude +or envelope of the standing wave of + + align:start position:0% +or envelope of the standing wave of + + + align:start position:0% +or envelope of the standing wave of +electric field we can think of the + + align:start position:0% +electric field we can think of the + + + align:start position:0% +electric field we can think of the +electric field between the plates as + + align:start position:0% +electric field between the plates as + + + align:start position:0% +electric field between the plates as +being analogous to the deflection of our + + align:start position:0% +being analogous to the deflection of our + + + align:start position:0% +being analogous to the deflection of our +spring + + align:start position:0% +spring + + + align:start position:0% +spring +ring the deflection like the electric + + align:start position:0% +ring the deflection like the electric + + + align:start position:0% +ring the deflection like the electric +field is pinned to zero at the right + + align:start position:0% +field is pinned to zero at the right + + + align:start position:0% +field is pinned to zero at the right +end the deflection like both the + + align:start position:0% +end the deflection like both the + + + align:start position:0% +end the deflection like both the +electric and magnetic fields is an + + align:start position:0% +electric and magnetic fields is an + + + align:start position:0% +electric and magnetic fields is an +oscillating function of + + align:start position:0% +oscillating function of + + + align:start position:0% +oscillating function of +time it remains zero at the null + + align:start position:0% + + + + align:start position:0% + +points we can measure the magnetic field + + align:start position:0% +points we can measure the magnetic field + + + align:start position:0% +points we can measure the magnetic field +with a one turn induction coil + + align:start position:0% +with a one turn induction coil + + + align:start position:0% +with a one turn induction coil +the coil voltage displayed on the + + align:start position:0% +the coil voltage displayed on the + + + align:start position:0% +the coil voltage displayed on the +scope indicates the magnetic field + + align:start position:0% +scope indicates the magnetic field + + + align:start position:0% +scope indicates the magnetic field +perpendicular to its + + align:start position:0% + + + + align:start position:0% + +axis first we put the coil at the null + + align:start position:0% +axis first we put the coil at the null + + + align:start position:0% +axis first we put the coil at the null +in electric + + align:start position:0% + + + + align:start position:0% + +field the magnetic field is indeed + + align:start position:0% +field the magnetic field is indeed + + + align:start position:0% +field the magnetic field is indeed +tangential to the + + align:start position:0% +tangential to the + + + align:start position:0% +tangential to the +plates and perpendicular to the + + align:start position:0% +plates and perpendicular to the + + + align:start position:0% +plates and perpendicular to the +direction of + + align:start position:0% + + + + align:start position:0% + +propagation the magnetic field should be + + align:start position:0% +propagation the magnetic field should be + + + align:start position:0% +propagation the magnetic field should be +a peak here at the null an electric + + align:start position:0% +a peak here at the null an electric + + + align:start position:0% +a peak here at the null an electric +field now moving toward the + + align:start position:0% +field now moving toward the + + + align:start position:0% +field now moving toward the +short where the electric field is + + align:start position:0% +short where the electric field is + + + align:start position:0% +short where the electric field is +maximum the magnetic field should null + + align:start position:0% + + + + align:start position:0% + +and then at the short it should peek + + align:start position:0% + + + + align:start position:0% + +again note that the phase shifts by 180° + + align:start position:0% +again note that the phase shifts by 180° + + + align:start position:0% +again note that the phase shifts by 180° +as we pass through the + + align:start position:0% + + + + align:start position:0% + +null watch the Peaks and intensity move + + align:start position:0% +null watch the Peaks and intensity move + + + align:start position:0% +null watch the Peaks and intensity move +by a quarter wavelength as the short is + + align:start position:0% +by a quarter wavelength as the short is + + + align:start position:0% +by a quarter wavelength as the short is +removed + + align:start position:0% + + + + align:start position:0% + +again with a short + + align:start position:0% + + + + align:start position:0% + +on and with a short + + align:start position:0% + + + + align:start position:0% + +removed it is the electric field + + align:start position:0% +removed it is the electric field + + + align:start position:0% +removed it is the electric field +intensity that is now the maximum at the + + align:start position:0% +intensity that is now the maximum at the + + + align:start position:0% +intensity that is now the maximum at the +right end we see this better with the + + align:start position:0% +right end we see this better with the + + + align:start position:0% +right end we see this better with the +lights out + + align:start position:0% + + + + align:start position:0% + +by measuring the distance between nulls + + align:start position:0% +by measuring the distance between nulls + + + align:start position:0% +by measuring the distance between nulls +and the electric field intensity we + + align:start position:0% +and the electric field intensity we + + + align:start position:0% +and the electric field intensity we +determine the half + + align:start position:0% + + + + align:start position:0% + +wavelength it appears to be about 70 + + align:start position:0% + + + + align:start position:0% + +CM electromagnetic waves propagate on + + align:start position:0% +CM electromagnetic waves propagate on + + + align:start position:0% +CM electromagnetic waves propagate on +the line at the velocity of light + + align:start position:0% +the line at the velocity of light + + + align:start position:0% +the line at the velocity of light +C so we can deduce the frequency of the + + align:start position:0% +C so we can deduce the frequency of the + + + align:start position:0% +C so we can deduce the frequency of the +source driving the plates at the Left + + align:start position:0% +source driving the plates at the Left + + + align:start position:0% +source driving the plates at the Left +End the frequency is equal to the + + align:start position:0% +End the frequency is equal to the + + + align:start position:0% +End the frequency is equal to the +velocity of light 3 * 10 8 + + align:start position:0% + + + + align:start position:0% + +m/s divided by the wavelength about 1.4 + + align:start position:0% + + + + align:start position:0% + +M so the frequency must be about 210 + + align:start position:0% +M so the frequency must be about 210 + + + align:start position:0% +M so the frequency must be about 210 +mahz + + align:start position:0% + + + + align:start position:0% + +this is the frequency that we should + + align:start position:0% +this is the frequency that we should + + + align:start position:0% +this is the frequency that we should +deduce from the oscilloscope trace for + + align:start position:0% +deduce from the oscilloscope trace for + + + align:start position:0% +deduce from the oscilloscope trace for +the magnetic + + align:start position:0% + + + + align:start position:0% + +probe the period is about 5.2 + + align:start position:0% +probe the period is about 5.2 + + + align:start position:0% +probe the period is about 5.2 +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +nond The frequencies about 195 + + align:start position:0% + + + + align:start position:0% + +mahz the agreement with the 210 megaherz + + align:start position:0% +mahz the agreement with the 210 megaherz + + + align:start position:0% +mahz the agreement with the 210 megaherz +we found from the wavelength + + align:start position:0% +we found from the wavelength + + + align:start position:0% +we found from the wavelength +is consistent with the accuracy of our + + align:start position:0% +is consistent with the accuracy of our + + + align:start position:0% +is consistent with the accuracy of our +measurements in visualizing + + align:start position:0% +measurements in visualizing + + + align:start position:0% +measurements in visualizing +electromagnetic standing waves we've + + align:start position:0% +electromagnetic standing waves we've + + + align:start position:0% +electromagnetic standing waves we've +used the light illumination to indicate + + align:start position:0% +used the light illumination to indicate + + + align:start position:0% +used the light illumination to indicate +the electric field intensity and the + + align:start position:0% +the electric field intensity and the + + + align:start position:0% +the electric field intensity and the +probe to measure the magnetic field + + align:start position:0% +probe to measure the magnetic field + + + align:start position:0% +probe to measure the magnetic field +intensity we've observed the + + align:start position:0% +intensity we've observed the + + + align:start position:0% +intensity we've observed the +distributions of En andh with open and + + align:start position:0% +distributions of En andh with open and + + + align:start position:0% +distributions of En andh with open and +shortcircuit terminations \ No newline at end of file diff --git a/PaYY0e9eE2A.txt b/PaYY0e9eE2A.txt new file mode 100644 index 0000000000000000000000000000000000000000..1d5fb90c5a34442205cefd710bee410a8e8c23f7 --- /dev/null +++ b/PaYY0e9eE2A.txt @@ -0,0 +1,6242 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +Audio quality for this video +is poor due to technical + +difficulties. + +PROFESSOR: OK, today, political +barriers to + +educational change. + +"One had to cram all this stuff +into one's mind, whether + +one liked it or not. + +This coercion had such a +determined effect that after I + +had passed the final examination +I found the + +consideration of any +scientific problems + +distasteful to me for an entire +year." Who said that? + +Einstein, so one of the greatest +scientists in the + +last 300 or 400 years. + +So that was the effect of +regular school and education + +on Einstein. + +And it's not just Einstein. + +It's a general pattern. + +So here, from Manchester, New +Hampshire, in the 1930's is + +how Bruce [? Betiset ?] +superintendent describes the + +children's approach to learning +and to reading and + +interest in knowledge. + +"In the traditional fourth +grades, when I asked children + +to tell me what they'd been +reading, they were hesitant, + +embarrassed, and diffident. + +In one fourth grade I cannot +find a single child who would + +admit that he had committed +the sin of reading. + +I did not have single volunteer +and when I tried to + +draft them, the children +stood up, shook + +their heads, sat down. + +In the four experimental fourth +grades the children + +fairly fought to tell me what +they had been reading. + +The hour closed-- in each case-- +with a dozen hands + +waved in the and little faces +crestfallen because we had not + +got around to hear what +they had to tell." + +So the contrast is +pretty strong. + +And the question is why do +experiments like what + +[? Betiset ?] did not survive? + +Whereas why does the education +system tend to have an effect + +such as Einstein described, +where he found the + +consideration of any +scientific problems + +distasteful an entire year? + +So reading is a particular +example-- which I'll give you + +another one [INAUDIBLE]-- + +of the change and the +effect of the + +formal educational system. + +So in revolutionary America-- + +so this is late 1770's-- + +Thomas Paine's Common Sense +sold 120,000 copies. + +And their population then +was three million. + +OK, so that's 1/100th of +the population now. + +So the equivalent of 120,000 +copies then was about 10 + +million or 12 million +copies today. + +Now if you actually look at +Thomas Paine's Common Sense, + +it's written in a language, +today, that we + +would call very biblical. + +When we read it you use English +and we speak English + +but you wouldn't expect 12 +million people to buy a book + +of that complexity +and subtlety. + +Now that expectation's is +confirmed by many a study + +about literacy and proficiency +in analyzing documents + +conducted across the +United States. + +So the latest one, it was in +2003, National Assessment of + +Adult Literacy. + +So this was published in 2005 +by the US government. + +So they America in 2003 and +they tested three kinds of + +proficiencies. + +Prose proficiency, which is +comparing viewpoints and two + +editorials as an example of +something where if you have + +prose proficiency you have +document proficiency, which is + +interpreting a table about +blood pressure and any + +physical activity. + +So taking information from +doctors and [INAUDIBLE]. + +And quantitative proficiency, +computing and comparing the + +cost and analysis +of food items. + +But none of these are very +advanced skills. + +OK now, the percentage of adults +who are proficient in + +each of these categories? + +13%. + +OK, now, 13% is a very, very +low number especially + +considering the level of +proficiency that's required, + +the threshold is pretty low. + +Whereas back in 1770's America +10 million, 12 million people + +equivalent today bought Thomas +Paine's Common Sense. + +And probably many of them were +not actually literate in the + +sense that they couldn't read. + +So that book was read to them. + +So there was a great hunger +for words and ideas and + +learning, which in many ways we +had not matched, despite or + +because of the vast extent of +the schooling system and + +educational system. + +So suppose you want +to change this. + +You want to improve +the situation. + +You'd like to make +education better. + +What are some of +the obstacles? + +So I'm going to discuss the +obstacles in ascending order + +of difficulty in overcoming. + +So another way to phrase, +ascending order of + +how local they are. + +So the first obstacle I'm going +to discuss is one that's + +local to personal psychology. + +It's local to how people +individually act. + +And then I'll move +to obstacles that + +are broader in scope. + +So the first obstacle is what +I'll call cognitive + +dissonance. + +So the way to see this in action +is suppose you go to + +someone and you say, well you +know, the way that that course + +is done could really +be improved if + +you do it this way. + +And you think you've made a +perfectly reasonable point, + +perfectly valid point. + +But somehow your point isn't +taken any notice of. + +Or it's met with resistance +and maybe even hostility. + +Now, why might that be? + +Well, there are many reasons. + +But one of them is you might +have phrased it badly. + +You might have cursed out +somebody's mother while you + +were doing it. + +There are all kinds of things +that you have a lot of control + +over and don't necessarily +have to do. + +But there are some reasons that +are harder to control. + +And that's in the psychology +of the person who's hearing + +what you're saying. + +So one of the obstacles is +this idea of cognitive + +dissonance. + +So let's see how that works. + +So cognitive dissonance was a +concept invented in the 1950's + +by Festinger, Leon Festinger, +psychology at Stanford. + +And he did the following +experiments. + +The experiments were, he had +people come and do this task + +where they basically just put +round pegs into round holes + +and-- he's a college student-- +put square pegs into square + +holes and triangle pegs +into triangle holes. + +So after they did the experiment +they were then + +split into two groups. + +Group A was just sent away. + +You know, they did the +experiment and they left and + +nothing more was heard from +them until a year later. + +Now Group B was told, oh, we +actually need people to help + +us recruit more volunteers +for this experiment. + +And obviously they might have +problems recruiting people to + +do the experiment because +it was so dull. + +All you do is put square +pegs into square holes. + +So they said would you +be willing to be-- + +in the experiment-- + +our assistant in helping +recruit people? + +So Group A, they +just went away. + +And Group B, they were offered +a position as experimenter's + +assistant and were paid +$20 for that. + +And Group C-- the same thing. + +They were offered a position as +experiment's assistant but + +they were only paid $1. + +This was in 1950-ish. + +So roughly speaking in today's +dollars, let me + +just translate those. + +So here's a way of estimating +the equation. + +So in 1950 we still have +the gold standard. + +And the gold standard +was $35 an ounce. + +So the world price of gold was +fixed by Fiat from Bretton + +Woods at $35 an ounce. + +Now it's maybe $70 an ounce. + +So inflation is about 25%. + +So this is about 400 today. + +And this is about $20. + +So then what happened was these +students then did their + +work, nothing, this, or that, +being an assistant. + +And then they were tested a year +later about their opinion + +of the experiment. + +So that was actually the +real experiment. + +So these students thought-- + +like all psychology +experiments-- + +they were actually helping +recruit people for an + +experiment. + +When actually, they were +the experiment. + +They were really the subject. + +So a year later they were asked +their opinion of the + +experiment, did you think +it was interesting? + +So these people, they obviously +thought it was + +boring because it +wasn't worth it. + +So a year later these people +were asked what they thought. + +And these people said boring. + +OK, now, what about +Groups B and C? + +What did they think? + +So take a minute or two, try +to predict what they were + +opinions about the experiment +were one year later. + +Question, yes? + +AUDIENCE: So did they have +a choice to participate? + +Were they forced to do this? + +PROFESSOR: No, I don't think +they were forced. + +It was the Group B who +agreed, or the Group + +C people who agreed. + +I'm pretty sure that's right. + +And I'm sure they +weren't forced. + +So yeah, find a neighbor or +two and see if you can + +predict, what did Groups B and +C think after a year or so? + +OK, so, what do you think +they thought? + +Yeah? + +AUDIENCE: Well, maybe Group C +liked the experiment better + +because they were only trying +to recruit, I think they + +wanted to but [INAUDIBLE]. + +PROFESSOR: OK, so Group +C maybe liked it more. + +So the question is, +who liked it more? + +So maybe Group C +liked it more. + +So they weren't getting enough +incentive in cash and they + +must have liked it. + +Any other thoughts, comments? + +Yeah? + +AUDIENCE: Well, it's possible +they didn't like it + +originally, but they convinced +themselves they liked it + +because they were doing this +work recruiting for not very + +much money. + +PROFESSOR: OK. + +So they must have convinced +themselves because they were + +getting enough cash +to be happy. + +AUDIENCE: I actually +have a question. + +PROFESSOR: Yeah? + +AUDIENCE: So did +[? all of them ?] take over? + +Or are we talking only about +those who did it? + +PROFESSOR: That I +don't remember. + +That's a good question. + +I think we're just talking +about the people + +who took the offer. + +AUDIENCE: OK, so it was +self selection? + +PROFESSOR: Yeah, there's +some self selection. + +AUDIENCE: But if a group came +from that, you probably should + +ask the question immediately +after the experiment before + +asking them to help assist and +then you set the control. + +[INAUDIBLE]. + +PROFESSOR: And they might +have done that. + +I don't remember all +the details of it. + +So they might have done that. + +And [? some wonder ?] if the +control was the Group A. But + +you're right, that's another +good control. + +And they might have done that. + +Other comments or questions? + +Predictions? + +Yeah? + +AUDIENCE: Is this a flat rate +or is this a per person? + +PROFESSOR: Oh, per person +they recruited? + +No, this was their salary. + +Yeah, that'd be pretty +lucrative, $20 a pop. + +Yeah? + +AUDIENCE: I was thinking B +probably wouldn't have liked + +it as much as C because they +probably would have thought, + +if they have to pay me $400 it's +really, really boring. + +PROFESSOR: OK, so B liked it +less on the theory that they + +were doing it just +for the money. + +They were thinking +to themselves-- + +AUDIENCE: Or also if the reason +they really have to pay + +them this much to get the +subjects it must really suck. + +PROFESSOR: Yeah? + +AUDIENCE: Well, and you can +look at it another way. + +You can say, they're paying +me this much money. + +There must be some intrinsic +importance to the work. + +So you could convince +yourself-- + +PROFESSOR: it could +go both ways. + +AUDIENCE: Right, exactly. + +PROFESSOR: They pay me +a lot so it must be + +really important work. + +They must have tons of +government funding for people. + +AUDIENCE: Yeah. + +PROFESSOR: All right. + +So it could be [INAUDIBLE]. + +Oh, comment? + +AUDIENCE: Well, I have to say, +I think the process of + +recruiting people would get +you to like it more. + +Because you'd have +to be selling it. + +And then the question is whether +you put more effort + +into that if you're getting +paid more money or not. + +PROFESSOR: OK, but the common +point is recruiting can help + +you like it? + +AUDIENCE: Yeah. + +PROFESSOR: OK, so I would say +to me, actually, you were + +right, actually, what happened +is that these people still + +found this boring. + +And these people liked it. + +And basically, at the time this +was counter intuitive. + +And the whole idea of cognitive +dissonance was built + +up to explain this +counter-intuitive result, + +which is why would you like it +more when you're paid less? + +It is sort of counter +intuitive. + +And it's exactly like you say, +which is that you reason to + +yourself well, if they're giving +me 400, yeah, sure, I'd + +sell my grandmother for 400. + +You know, that doesn't mean +that I don't like my + +grandmother. + +But $400 is $400. + +But if they only +give you $20-- + +that's option C-- + +no, of course you wouldn't +do that. + +There must be some reason +that you're doing that. + +So if you're participating in +the activity we'll say by + +doing but don't like it, +or at least you try to + +justify it to yourself. + +You need some kind +of justification. + +And the justification of Group +B is well, I'm doing it + +because it pays a +lot of money. + +The justification of Group C +can't be that because there + +isn't enough money. + +So it must be that it's an + +intrinsically worthwhile activity. + +So the opinion shifts. + +Now if you remember, I mentioned +cognitive dissonance + +as one of reasons to have +people vote when you're + +originally doing multiple-choice +questions. + +Give a muiltiple-choice question +to the students, say + +A, B, C, or D. The importance of +having them vote and make a + +public stand is that it commits +them to the question + +and to the answer. + +Now they have some public +appearance in the one of the + +A, B, C, D categories. + +And they want to know, +is this right? + +So the political organizers +know this. + +And these kind of ideas +are old hat now. + +We've seen things that +consciousness and psychology + +in marketing. + +So people will sometimes-- for +example-- come around and ask + +you well, would you mind putting +a sign in your front + +yard for this political +campaign? + +Well, at first they'll say, +would you like to give $100 to + +the campaign? + +And you say, no. + +I don't really know +who XYZ is. + +I sort of maybe support +him $100. + +[INAUDIBLE]. + +So you say no. + +They say, OK, well, would you +mind putting a sign in your + +front yard? + +So now, what have you done? + +Made a public commitment. + +All right, everybody who drives +by or walks by sees + +that sign for the candidate. + +So now studies are completely +consistent with this-- + +you now do it-- you now support +that candidate more. + +So turns out, what's the key +thing in changing your view? + +Is that you feel you +had a choice. + +So here, if you put a gun to +someone's head and say, put a + +sign in your front yard. + +And they put a sign in their +front yard, that doesn't + +change their view of +the candidate. + +The person could +refuse or not. + +It was up to them. + +If they chose to do it, well, +that opens a door to further + +commitment. + +So here, this is sort of like +putting a gun to their head. + +This is sort of like putting +a gun to their head. + +You don't really feel like +you have a choice. + +You're like, OK, whether it was +boring or not, who cares? + +Whereas here, you +took the choice. + +And the ones that did it +changed their view. + +So cognitive dissonance is +very, very powerful. + +Now, how does that relate to +peoples' response when you + +say, you'd like to change +the course? + +OK, and we'll come to that. + +Yes, question? + +AUDIENCE: Yeah, so again, +Group A then was + +never offered a choice? + +PROFESSOR: Yeah, they +were sent away. + +And they were asked a year +later to see what + +they thought of it. + +And they said, yeah, +it was boring. + +They're sort of control. + +I mean, you expect them +to say, it's boring. + +AUDIENCE: [INAUDIBLE] + +boring? + +PROFESSOR: Yeah, just to check +so no one could say, well, + +maybe people found it +really fascinating. + +You know, because they didn't. + +So now what happens when you say +to someone, oh, we really + +should change the way +this course is done. + +So now suppose you're at some +weak university like MIT or + +Cambridge or something +like that. + +Now, where do a lot of the +people who teach at these + +universities come from? + +Either that same university-- + +especially in England, that was +really notorious in the + +united justification [? for +it ?], which was that our + +system's so wacky and different, +only people who've + +been through that particular +system can + +possibly teach here. + +So how are the justifications? + +Either the people come from that +same place or come from a + +similar background, similar +university background. + +So now you're not criticizing +a system that + +they A, selected them. + +Right? + +The system selected them from +a whole bunch of people. + +And so by definition, it +must be a good system. + +Also, they've now had many +opportunities to make public + +commitments to the system of the +way things are taught, the + +way things are done. + +They've taught them in classes, +they've participated + +in curriculum discussions. + +They've selected the students +that come, recommended the + +students that would +be better or worse + +according to that system. + +So the result is that because +of years of cognitive + +dissonance working on people, +they are now very, very + +convinced that the way things +are done right now is great. + +And although it's called +cognitive dissonance, it's not + +necessarily a cognitive +belief. + +If you ask them, can you explain +why it's great they + +wouldn't necessarily give +you great reasons. + +And this can be very misleading +and can lead you + +into hot water. + +So for example, when you say, +well, really we should teach + +this course differently and put +in interactive questions + +so students learn them. + +You'll get responses that +are almost nonsense. + +They'll be things like, for +example, well, if we don't put + +everything on the chalkboard how +will students know what's + +going to be on the exam? + +And yeah, it's a valid +English sentence. + +But it's not a good argument +because there are other ways + +to communicate with students. + +You can put stuff on notes. + +You can say, read the book. + +There's tons of answers +to that problem. + +But these kind of things can be +offered as just a complete + +trump card. + +OK, these trumps have been +played, because no one can do + +anything interactive. + +Now, that level of thought +that's behind it, no way + +people would put that level of +thought into their research + +and be successful +with research. + +And how come that's OK +and can be sort of + +convincing in this area? + +Well, because it's really +not a cognitive + +response to be made. + +It's a belief response. + +You threaten and challenge a +person's core beliefs and + +they're going to come out +and react very strongly. + +And if you try to argue it just +on the rational level + +you'll, actually, pick +up angry people. + +And you won't anger yourself +because you wonder why you + +hate the progress. + +So one way to think about those +kinds of conversations + +is A, if they're difficult +conversations-- + +and actually, the reason I write +that there is there's an + +excellent book called Difficult +Conversations. + +written by-- + +I'm pretty sure-- it's from the + +Harvard Negotiation Project. + +And they said, look, every +interaction-- and I + +think this is right-- + +has three levels. + +So that would be the factual +level, which is just the ideas + +being exchanged, of should we +teach interactively or not? + +Is there enough time? + +There's the emotional level, +which is how we feel about + +these facts. + +And then there's the meaning. + +So what does this discussion +mean for people? + +So as an example, [INAUDIBLE], +the problem with a student + +who's worried about +their grade. + +Well, you can tell them, +factually, look-- + +about 3% on that problem set is +going to be 0.03% of your + +grade's total points, don't +even worry about it. + +All right, so that's +the factual level. + +You may often find that just the +factual discussion is just + +the tip of the iceberg +because there's all + +this stuff going on. + +So what could some +of this stuff be? + +Well, the emotional level is +they just feel really anxious + +about grades. + +Now, why might that be? + +Well, that's where the +meaning comes in. + +The meaning may be that they +feel that the grade measures + +how good they are. + +And they've always thought they +got into MIT by mistake. + +And now people are going +to find them out. + +If they ever get a bad grade +their cover will be blown. + +And everyone will know that +they don't belong. + +So it may have a really strong +meaning for them, which is + +rather emotional. + +Which means the fact [INAUDIBLE] +discussion + +[INAUDIBLE]. + +So it's a similar thing with +the discussion of change in + +education, is that people will +have a factual discussion that + +seems pointless and it's just +frustrating to you. + +Because actually there's +emotional investment in the + +way things are done. + +And meaning, it means +a lot to people. + +This system, it chose them. + +It's a system they're +committed to. + +And it's being criticized +by you. + +Therefore, you're going to get +a whole bunch of unrealized + +anger [INAUDIBLE]. + +Question? + +AUDIENCE: So when it comes to +changing a single class and + +adding some interactivity, +what are the downfalls + +avoiding the difficult +conversations by asking for + +forgiveness rather +than permission? + +PROFESSOR: Nate, that's +a good question. + +So asking for forgiveness rather +than permission, one of + +the downsides is-- + +I think, in small and moderate +doses that is a good idea. + +Because first of all, no +one's going to notice. + +Because they're too busy with +their own [INAUDIBLE] teaching + +that that's rather busybody +over what you're doing. + +So you have, definitely, +something right away that you + +might as well use. + +But if you want to make any +larger changes, like for + +example, take out something +that you think isn't so + +important in the curriculums-- +and make room for doing this-- + +and somebody downstream +really wants that. + +Well, it's important to have +done it beforehand, discuss it + +beforehand. + +Because otherwise, if there's +emotional and meaning + +investment in the way things are +done, they won't be able + +to listen and then +you surprise them + +with a factual change. + +They won't be able to listen +to your factual arguments + +then, because you activated the + +emotional and meaning responses. + +So you want to try to arrange, +[INAUDIBLE] those things + +beforehand and get all those +out in the open first. + +So I would say, for smaller +changes, yeah. + +For larger changes, it's +important to have people + +jointly figure out what to +do, which is true of + +any political change. + +And that's why when I +deliberately chose the title + +Political Barriers to +Educational Change. + +Because political barriers has +the implication that it's a + +political problem. + +It's a social problem. + +It's a collective problem. + +And any collective problems has +these issues of what you + +do by yourself versus what we do +in a group or [INAUDIBLE]. + +Question, yeah? + +AUDIENCE: So I'm just a little +bit confused about the idea of + +cognitive dissonance. + +So is that where the [INAUDIBLE] +between the + +responses of groups B and C? + +PROFESSOR: Mm-hmm. + +Yes, it's that. + +Oh, so where does the dissonance +come into it? + +I should've explained that. + +The dissonance is what +you try to reduce by + +changing your view. + +So in Group B there's really +no dissonance because the + +experiment's boring. + +And they did the recruiting +because they were paid. + +There's no dissonance. + +Here, the experiment is boring, +but they don't have + +the resolution that oh, I'm +being paid to do it. + +So they have to have some way +of reducing that dissonance. + +And they're going out and +recruiting people. + +So the way they do it is they +reduce the dissonance between + +the internal view and external +performance by changing their + +internal view. + +Thanks. + +AUDIENCE: Yeah. + +AUDIENCE: So I'm wondering +whether-- + +do you know how people talk +about how sometimes if you're + +trying to convince people to +do something you try to get + +them to feel like it +was their idea? + +And it seems like that would +be the opposite approach to + +what you were just saying, which +was that you try to get + +people on board in advance maybe +even so subtly that they + +don't even realize it. + +Because I think if you make +people feel like they're being + +threatened and furthermore that +like you're deceiving + +them, but they'll claim to be +always kind of on purpose + +because you felt like you were +backed into a corner. + +And even if they're not +committed to it, because it + +produces them as [INAUDIBLE], +or just because people don't + +like to be fooled, that they +don't like to feel like + +they're taken advantage of. + +PROFESSOR: Right. + +So that's why I would +say, yeah. + +Take advantage of the freedom +that you have that everyone + +sort of [INAUDIBLE] + +to make smaller changes +just on your own. + +AUDIENCE: Do you have ideas +for how you might go about + +[INAUDIBLE], if you see people +with [INAUDIBLE]? + +PROFESSOR: Yeah. + +And not so much convincing +things that + +it's their idea it's-- + +yeah, I don't want to phrase it +as people think this as a + +dishonest [INAUDIBLE]. + +AUDIENCE: Yeah, yeah. + +PROFESSOR: It's really you're +trying to find collective + +solutions to problems that you +both think are happening, or + +you all think are happening. + +So one way to go about that +is to say, well, look. + +Here is a problem I see. + +What do you think you +could do about it? + +They might agree with +you on the problem. + +By creating one problem, pretty +much generally people + +will say, yeah, the students +are fine with problem set. + +But when they have to go +do something with it, + +they can't do it. + +So you'll get a much wider +grievant on that statement + +than on what to do about it. + +But you can start there. + +Say, OK, well, what do you think +we should do about it? + +They may have some ideas. + +They may accept the idea +that, well, this + +is a serious problem. + +And it's not clear what +to do about it. + +But that right away gives you +some license to try to + +[? external?] + +[INAUDIBLE]. + +So you say, OK, well, +here's one thing + +I'm thinking of trying. + +Let's see how it works. + +So you're not saying, it must be +done this way, and this is + +the only way to do it, and +you're bad to not do it. + +Say, well I'm going +to try this. + +Let's see how it works. + +And I'm happy to share +the results with you. + +And you can use that, too. + +And so there's another related +point to that, which is the-- + +I don't know what percentage +to give it. + +So let's call it +a 10%, 10%, 8%. + +So 10%, 10%, 8% equals this. + +So 10% of people will +be early adopters. + +They're really curious +about new things. + +They want to try new things. + +Let's call them [INAUDIBLE]. + +There will be, say, 10% who no +matter what you do are just + +going to say, this +is terrible. + +So, the never adopters. + +And the 8% who are in the middle +who will wait to see + +and will sort of sit +on the fence but + +[INAUDIBLE], but open. + +They have other priorities, +but they're open to + +these kind of things. + +So my rough rule of thumb is, +when you're talking to + +someone, could be figure out +which category they're in. + +If they're in- this is true of +political discussions, right? + +You probably have some relatives +in the family where + +you just agree we're not going +to talk about politics. + +Right? + +So, I have them. + +I'm sure I'm in some people's +category of that , too. + +We just say, we're just not +going to talk about that. + +Because one or the two of us is +not going to adopt the view + +of the other no matter what is +said because you just think + +it's absurd. + +So if someone's in that +category, don't + +even spend any time. + +Just spend your time +[INAUDIBLE] + +category and say, OK, I'm +going to move on. + +If they're in this category, +you usually can figure that + +out pretty quickly, too. + +Work with them. + +And if they're in this category, +that's the people + +you can reach if you do +things in a good way. + +OK, now this is actually +pretty large. + +I think in the '70s this was +called the silent majority, + +was the code for this +[? this word. ?] + +Yeah. + +AUDIENCE: Are you ready +to be done with this? + +PROFESSOR: Yeah. + +AUDIENCE: Could you talk a +little bit-- maybe a little + +later-- about what sort +of scale changes + +you're talking about? + +And also along with that, how +much power each individual + +professor has to design +their own course. + +If you figure out what the +prerequisites are for the next + +course, then I don't see exactly +what the problem is + +doing whatever you want in your +course as long as you + +meet those-- as long +as you teach them. + +PROFESSOR: So the question is +what size scale change am I + +talking about? + +Well, it depends. + +How much freedom you +have depends on the + +change you want to do. + +For example, suppose you took to +heart some of the readings + +that were for today and you +thought that grading was + +really terrible and you want to +just dispense with grading + +completely. + +Well, even if you're teaching +all the right stuff, that will + +raise a lot of of ire. + +And people will come after you +for that even if you're + +teaching everything right and +you're doing all the prereq. + +Because it will trigger all +kinds of factual, emotional, + +meaning responses +in other people. + +And it'll go against many, +many-- and that's what I'm + +going to talk about next is-- + +features of American society +to think we must + +do things that way. + +So you have less freedom to do +something like that, even if + +you're meeting all +the prereqs. + +Now, if you want to, for +example, use different + +examples to teach the +same ideas, Everyone + +wants complete freedom. + +So it really depends what +you want to do. + +Then there's many scales where +you can make change. + +So you may find that there isn't +any way to do what I + +want to do and meet all the +prereqs for the next course, + +because it just means doing +way too much stuff. + +OK, well now you have +a problem of a + +bigger scale change. + +How do you get the whole group +of faculty or group of people + +in charge of that area or course +to change what was + +going on and changes the +prerequisites, change the + +overall curriculum. + +So now, you're definitely going +to be working with lots + +of other people. + +There's another sort of +dichotomy, which is is the + +course required or not? + +If the course isn't required, +you have much more freedom. + +[INAUDIBLE] + +so your course. + +If people don't like it, they +don't have to take it. + +And even if other people don't +like your course or don't + +think it's that important, +they're perfectly happy, + +generally, to let you teach +the course that they don't + +think is that important. + +Because they want to teach their +course, which you may + +think is not that important. + +But now the required courses +that every single undergrad + +that majors in the fields take, +those generally are + +guarded more with jealousy. + +And so changes in those are +harder and generally require + +more consent from other people +just because it's considered a + +shared core of the field. + +So that's the meaning. + +And by changing that, you're +complicitly perhaps + +threatening to share +core of the field. + +Does that answer +your question? + +OK, so what I'm going to talk +about after the break-- + +so this was the idea +of cognitive + +dissonance, and what role-- + +and maybe just a few, your +local group, maybe your + +department, maybe +your school-- + +difficulties and obstacles and +issues that come up when + +you're trying to make some kind +of educational change. + +What I'm going to talk about +after the break is + +society-wide features. + +All right. + +So American society or say, +European-American society in + +general, that impose really +large obstacles + +in educational change. + +In some ways, even bigger +than this one. + +And you definitely want to take +your time with this one. + +But it's also important to +take your time with even + +larger scale ones. + +And those will be Behaviorism, +Taylorism, and the history and + +the purpose of those schools. + +And we'll talk about those +after the break. + +It's 9:58 right now. + +So we'll start at 10:08 +according to that clock. + +The first barrier, cognitive +dissonancy is a-- + +to a personal psychology. + +But now we're going to look +at factors that span the + +individual. + +I mean, this spans the +individual in the sense that + +it's the common feature of our +psychology, maybe of this + +[INAUDIBLE] psychology. + +But let's see it in +individual people. + +But they're are also features +that are common across-- + +you could call them social +psychology or social + +tendencies. + +The first one is Behaviorism. + +Behaviorism is also a school +of psychology, which, + +basically in America, grew +out of Pavlov's work on + +conditioning dogs and working on +teaching patience by reward + +and punishment. + +And in psychology, what it was +is it was a focus on outputs. + +So it basically denied the +importance of studying what's + +going on inside the +human mind. + +It was correlated with what +was called the logical + +positivism in the +Vienna school. + +So in Europe, around the same +time and soon after, was the + +rise of quantum mechanics. + +So if you look at quantum +mechanics, quantum mechanics + +was created partly by the Vienna +logical positivists in + +math in [INAUDIBLE]. + +In quantum mechanics what's one +of the fundamental ideas + +is what's called an observer. + +You know, where it says, look. + +Don't talk about what's +not observable. + +The important thing is +what's observable. + +Everything is sort of rigid +around observance. + +All right, so behaviorist +psychology was + +almost in the same way. + +It says, look, don't talk +about the mind. + +We don't know what +the mind is. + +It has no separate existence. + +Let's just talk about +behaviors. + +How does what you do effect +what the organism does? + +It's a fine way of training +pigeons, but it's not a great + +way of understanding people. + +But you can see that it's +actually dominant in lots of + +American education. + +So Behaviorism was actually +strongest in America, It was + +eventually, I would say, +demolished as an intellectual + +movement basically +in this space. + +I guess the old linguistic +department was here. + +And Noam Chomsky in 1957, '59 +wrote the review of Skinner's + +book on Behaviorism. + +And that's considered the coup +de grace of Behaviorism. + +But even then, the +idea lives on. + +And it underlies so much of what +goes on in this school. + +And you can see that with +actually the lively examples + +of that, given the core. + +I'll give you one more +of that [INAUDIBLE]. + +So this was a study. + +This was fourth, fifth, +and sixth grade. + +And they were asked what's +six times three. + +Well, they weren't having a +problem with that, It's 18. + +They were asked to make +a story problem for 6 + +times 3 equals 18. + +80% of the students +could not do it. + +They couldn't make a valid +story problem. + +Now, what I mean by story +problem is a word problem. + +So they could actually do +the multiplication. + +That was no problem. + +But to make a problem which used +that multiplication, that + +was difficult for them. + +Most of the problems they came +up with were along this line. + +On Monday, Johnny +buys six apples. + +It's always Johnny, not John. + +I don't know why. + +On Tuesday, Johnny buys +three apples. + +So 6 times 3 equals 18. + +There's was a fundamental lack +of understanding of what's + +going on here behind +the equation. + +So the performance was fine. + +He said, what's 6 times 3? + +18. + +And so the observable +was [INAUDIBLE]. + +So by the [INAUDIBLE] standards +that was fine. + +There was no problem. + +And so much of it was +on the school. + +Bacon just looks at +the outreach. + +Whereas, if you actually look +into the [INAUDIBLE], that + +Behaviorists say you shouldn't +really do, and ask the tougher + +[? question, you'll ?] find +it actually has no meat. + +But it's just like tissue. + +AUDIENCE: Is the problem here +me, or is it we are looking + +for the wrong outputs? + +I don't see, per se, how asking +students to make a word + +problem is looking into the mind +any deeper than asking + +them 6 times 3 equals 18 because +it's an output that's + +closer to what we +want students to + +actually be able to do. + +PROFESSOR: The thing is if they +this, if they produce a + +correct story as a formula +too, then you wouldn't be + +happy either. + +So in some way you want +to know does this + +have meaning for them. + +So you could then say, well, +6 times 3 is 18. + +OK, they understood that. + +Now, I want them to +give me the right + +output of a story problem. + +Well, I have them memorize +a correct story problem. + +Whenever they see +multiplication, do this kind + +of story problem. + +And then, if you ask them the +question give me a story + +problem, they would produce +the right output. + +But you'd still be unhappy. + +You'd have to ask a different +question to figure out if it + +actually had any meat. + +Maybe for example you'd say, +well, multiplication's pretty + +similar to division, so let me +see if they could make a story + +problem for division. + +Or let me give them a +different question, + +which is this one. + +Suppose they hadn't had this +question before and hadn't + +been pigeon trained with it. + +So you could give them that +question and see if they + +understood what really +multiplication means. + +If they just write down 73, +you would say, OK, they + +understood that. + +And it would be kind of +pointless to try and have them + +memorize all questions +like this. + +But after they've seen this kind +of question, yeah, they + +might produce the +right output. + +If you just tell them, OK, +whenever you see this, one, + +two, three, four guys here and +four there, produce 73 here. + +Well, that's different from +really in understanding + +multiplication. + +So I would say output +is not sufficient. + +So you have to look +behind the output. + +Did that help answer +your question? + +AUDIENCE: Well, but I feel +like you're still looking + +[INAUDIBLE] but the difference +is the process you used to get + +the students to the point where +they can generate that. + +PROFESSOR: No. + +Well, you're looking at the +output, because that's all you + +can look at. + +But you're not saying if the +output is fine, it's-- + +you're making inferences about +what's going behind that. + +And that's what behaviorists +don't want. + +You're saying, oh, there's +understanding, there's + +meaning, there's reasoning going +on beyond the output. + +And that's what the Behaviorists +don't want to + +talk about. + +They just want to talk about +just the outputs. + +And that's a fundamental +problem. + +Because real understanding-- + +focus on just outputs leads +to rote learning. + +And I think that is one +explanation for why there's so + +much rote learning produced in +the American education system. + +AUDIENCE: Does anyone-- + +[INAUDIBLE] + +[? location ?] + +[INAUDIBLE] + +making the contributions +[INAUDIBLE] like understanding + +a problem, [INAUDIBLE]. + +So what's the operation for +that that's different from + +making up problem. + +Making up a problem requires +more understanding, right? + +PROFESSOR: Yeah. + +Making up a problem does +require a lot of + +understanding. + +AUDIENCE: [INAUDIBLE] + +So society wise, you only need +a person to solve the problem + +not make up a problem, right? + +PROFESSOR: Well, that's +not the purpose of-- + +so do mean prompt people +to just solve + +problems or make up problems? + +That can't be the premise +on [INAUDIBLE] + +democratic society. + +AUDIENCE: Right. + +OK. + +I agree with that. + +But why should [INAUDIBLE]? + +PROFESSOR: Pardon? + +AUDIENCE: Who's happy to +choose the computation? + +They know that 6 +times 3 is 18. + +[INAUDIBLE]. + +PROFESSOR: Well, +so it depends. + +So on the [INAUDIBLE] in many +schools there's tests that + +just test things like that. + +[INAUDIBLE] . + +So the No Child Left Behind Act +has pretty much mandated + +that children be tested +pretty regularly + +on their basic skills. + +And so there's a ton of +questions and things like that + +on these basic skills tests. + +So some people care. + +And these kind of tests are an +impediment to making any kind + +of educational change. + +Because if you start spending +time on things like that, + +well, then you have less time +to practice three-digit by + +five-digit multiplication. + +AUDIENCE: Now this +[INAUDIBLE]. + +We should say [INAUDIBLE] + +point first, and then from there +break it down to the + +[INAUDIBLE] + +much more [INAUDIBLE] +than [INAUDIBLE]. + +PROFESSOR: That may be true. + +So the comment was that maybe +it's better to try something + +not so hard as making +up a story problem. + +Identify-- + +AUDIENCE: [INAUDIBLE] the +[INAUDIBLE] that we need. + +PROFESSOR: It shouldn't +be that hard. + +AUDIENCE: I mean, we're +on a skill, right? + +PROFESSOR: It shouldn't be that +hard, but it is hard if + +you've just done drill. + +AUDIENCE: Yeah. + +If you start so low-- + +PROFESSOR: Yeah. + +I agree. + +So it's not saying that +all of a sudden now-- + +I'm not saying all of a sudden +now you should ask what we're + +doing with this question how +to make a story problem. + +But this is used as an example +to show how far away we are + +from where we'd like to be. + +So Behaviorism is, I would say +branded reward and punishment, + +pretty much rampant in +American society. + +In discussions of merit pay for +teachers, OK, should we + +give teachers higher pay if +their students do better on + +tests from No Child +Left Behind? + +So that is the assumption that +you want more output from the + +teacher in that [INAUDIBLE]. + +You just pay more money. + +You give them more +pigeon food. + +But there actually maybe other +reasons going on, there may be + +completely other factors +besides input output. + +For example, maybe teachers +think we shouldn't be teaching + +the test this way. + +Maybe there's all kinds of +social consideration which + +aren't included in just paying +people quote "meritly." So you + +could see how rampant it is +because when you say, oh no, + +we shouldn't do that +to teachers, people + +think you're crazy. + +They say, well, of course we +should-- and then they make a + +really, really long argument +for why we shouldn't. + +So the default is, yeah, +everything should be paid + +according to results and +rewards, and rewarding + +according to result. + +Yeah. + +AUDIENCE: I'm curious about what +you think-- because I do + +think that there is no question +that in our society + +things in which we give respect +to and value as a + +society do get paid more and +[INAUDIBLE] to have more + +perspective as we [INAUDIBLE] +our educational system is that + +we don't pay our teachers +anything and + +don't respect them. + +And that's why very few people +actually consider that as a + +real career. + +[INAUDIBLE] + +you know, [INAUDIBLE] +to actually consider + +teaching at my school. + +Very [INAUDIBLE] rate. + +And that's because it's +not respected. + +It's not considered a +challenging [INAUDIBLE]. + +But don't you think that the +amount of money that people + +get paid actually does in some +sense request our respect for + +them as a society? + +PROFESSOR: That I agree with. + +So there's the meaning +[INAUDIBLE]. + +Yeah, there's meaning associated +with the salary. + +So the problem, what's wrong +with merit pay is that the + +meaning is that you're competing +with other teachers. + +I'll give some money to the +schools and say, now dole it + +out among your teachers. + +And the one's who do best--- + +AUDIENCE: Yeah. + +No, I think that's +[INAUDIBLE]. + +PROFESSOR: But I agree with +you about increasing the + +overall salaries for teachers. + +And it's exactly right what +you say that it's not + +respected as a profession +in this country. + +And as you say, people who get a +Ph.D from MIT are not likely + +to teach in high school, +which is, I think, sad. + +But it doesn't have +to be that way. + +So in Europe-- + +so George Collier, one of the +greatest mathematicians of the + +century, he taught at +a Swiss high school. + +It was a considered a very +respectable position and + +profession. + +It's a serious profession. + +It's really important. + +Whereas, that's pretty +much unheard of here. + +And [INAUDIBLE]. + +So it's a combination of +respect and salary. + +And related to that, autonomy. + +So teachers here in America +generally have the least + +autonomy compared to, say, +Western European countries. + +So one way of measuring that +is just how much free time + +teachers have to do curriculum +[INAUDIBLE]. + +So think back to your +own high school. + +How many classes did +your teacher teach? + +Typically, six a day. + +I mean, I'm exhausted if I +teach two classes today. + +Because it really takes energy +to teach a class really well, + +think about it, prepare, answer +questions, follow up + +with what happened, and +make references. + +Teaching six times +a day is absurd. + +And all you can do is +just try to survive. + +So that's, again, another +barrier to educational change. + +So that is barrier number +two which is-- + +the second we'll call +the [INAUDIBLE]. + +So it's the focus on outputs +and reward and punishment. + +And then the next barrier is +another social wide factor + +called Taylorism. + +So Taylor-- + +it's related a bit +to Behaviorism. + +So Frederick Taylor was +a mechanical engineer. + +Let's see, when did he live? + +About 1850ish to about +1915 or 1920. + +1856 to 1915. + +So what he did-- + +he's the originator of time +and motion studies. + +So time and motion studies +watch how someone, for + +example, is riveting +bolts onto a car. + +And you watch every single +movement and you optimize it. + +And you say, oh, actually if +you have the screwdriver on + +this side, well then when the +car door comes down this way + +you can do this with much +shorter movement than trying + +to do that. + +So they said you can break every +task down with a lots of + +little little fragments +you can optimize. + +Now, this basically took the +whole country by storm in the + +1910s or so. + +Now, how did that happen? + +Well, this was a time of +industrial unrest. + +And unions were striking +demanded higher wages. + +And there was the Interstate +Commerce Commission, which + +regulated the railroad fares. + +And so the railroad attorney, +Louis Brandeis, later Supreme + +Court Justice, argued the in +front of the Interstate + +Commerce Commission, well, +actually we don't have to + +raise fares. + +And we can actually give the +unions some of what they want + +without doing any of +that provided we + +implement Taylor's system. + +So the idea of Taylor's system +was a way of basically trying + +to prevent the unions from +striking, but not distribute + +any of the wealth for +management, but just make + +things more efficient. + +So it was what we now call +the Cult of Efficiency. + +And this Cult of Efficiency I +would say probably could only + +happen in a frontier society, +like America. + +So there's a completely +fascinating book, which I + +highly recommend reading, The +Great Frontier, by Walter + +Prescott Webb. + +So what he looks at is he +looks at the effect on + +European society of the European +discovery of the + +Americas, so around 1500 BC. + +Columbus sailed and all the +explorers were going a sail. + +So what happened? + +Well, before 1500 Europe was +extremely crowded, lots of + +people, very few resources, very +little land, pretty much + +deforested, not much fuel. + +And so it was a hard +place to live. + +With the discovery of the new +world, that switched. + +There was now a ton of land +and not enough people, + +especially after the Indians +all got small pox and died. + +There was a ton of natural +resources-- wood, minerals, + +eventually oil. + +So around 1500, so the world +society changed. + +At least the European society. + +And with it, changed conceptions +of how society + +should work. + +And in the frontier societies, +basically everything was there + +for the taking. + +You just had to work +to get it. + +So in a frontier society, +basically work was a religion. + +That was the religion of +a frontier society. + +And you can still see +that in America. + +How many weeks of holidays +do people have completely + +guaranteed? + +I think zero. + +And whereas in-- for example, +England, I think it was four + +weeks, maybe statutory +minimum. + +In Germany, it's five +or six weeks. + +So in the frontier society, work +will be your religion. + +And it's likely to be placed +where ideas such as Taylorism + +will grow, and sprout, +and thrive. + +So Taylorism spread throughout +the entire country, including + +to the schools. + +And you can still see +it in school. + +School is considered +a factory. + +And the inputs are +the students. + +And we want to do that as +efficiently as possible. + +Think class size, giant +buildings to [INAUDIBLE] + +to produce more product +at the end. + +So this is one of the early +examples of a Taylor school. + +The Platoon School. + +So this was an elementary +school. + +What they did was they-- + +this is absurd. + +They enrolled 10% to 70% more +children than there were seats + +for in the classrooms. + +So [INAUDIBLE] + +efficiency. + +This is done by dumping the 10% +to 70% on the playground, + +into the auditorium +or basement. + +So by keeping all the children +rotating from room to room, + +teacher to teacher, so that +the same 10% to 70% + +[INAUDIBLE] way longer than 30 +consecutive minutes to get + +into classrooms. + +So even the 6-year-old children +have 6 or 7 teachers + +a day and as many as 12 +or 13 in some cities. + +And teachers handle as many as +400 people through the day and + +1,000 a week. + +So the terrorists came to the +school and said, hey, look, + +these schools-- it's all very +relevant to have small schools + +for people, but really, +it's not efficient. + +Look, there's all this +inefficiency you could squeeze + +out of the system. + +And so you can see probably +MIT's going to be going + +through something like that with +the budget cuts, all the + +[INAUDIBLE]. + +And trying to squeeze +the life-- + +I mean, the inefficiencies +out of the place. + +So what they said was they said, +oh, look, there are all + +these rooms that aren't +being used. + +You have the gym that's +not used all the time. + +There's the lunch room that's +only used at lunch time. + +That's crazy. + +There's an empty room there. + +There's the playground that's +only used at recess. + +What we should do is we +should rotate the + +kids all the way through. + +And you'll actually see +that in schools now. + +Many of them have lunch period +that starts at 10:00 AM, and + +the lunch period goes till +almost 2:00, because it's a + +much more efficient use +of the lunch room. + +But ironically, they had to +cancel recess, because recess + +is inefficient. + +Recess is not efficient for +doing standardized test + +problems, so you guys will +see that as well. + +So again, they called +it efficiency. + +That was back in the +'20s [INAUDIBLE]. + +It's from Raymond Callahan's +book called Education and the + +Cult of Efficiency: A Study of +the Social Forces that have + +Shaped the Administration +of Public School. + +It's about Taylorism in +the public schools. + +But it continues to today. + +In No Child Left Behind, +you can see is a + +perfect example of it. + +[INAUDIBLE] + +wrote, he said, "The long lines +of marching children + +that look to be like nothing +so much as the lines of + +uncompleted Ford cars in the +factory, moving always on with + +a screw put on or a [INAUDIBLE] +tighten as they + +passed-- standardized, +mechanical, pitiful. + +When the factory system carried +into the public + +school, which needs only the +closing time whistle to make + +complete [INAUDIBLE] with +giant, great industrial + +plants." + +So there you have another +fundamentally + +important social factor. + +[INAUDIBLE]. + +So behaviorism and Taylorism are +sort of lumped together. + +Which is the joining of the +school and the factory and the + +educational system and +the social order. + +So that I'll call the social +history of education. + +So education-- and America was +one of the leading countries + +in this, in making schools +free and required-- + +compulsory free education. + +[INAUDIBLE] public school. + +So this-- in Massachusetts, +actually-- our state was the + +leading state in American +[INAUDIBLE]. + +And so Horace Mann +in the 1840s-- + +he was one of the leading +educational reformers. + +And he was arguing +to businessmen. + +OK, you really should be willing +to have higher taxes + +to make schools free +and required. + +Now, why would businesses want +to part with their profits to + +pay for schools? + +But he says, look, there's all +these benefits from schools. + +The schooled workers are more +docile and quick in applying + +themselves to work. + +They had better domestic and +social habits, you know, + +punctuality and fidelity. + +They have higher punctuality +and fidelity in the + +performance of their duties. + +So basically, he was arguing +for school as a method of + +social control. + +Now, there was a strange feature +in my high school, + +which I never understood till +I actually read about this. + +History of Horace Mann called +the School of America, which + +was that-- so I experienced +this first-hand. + +One day in my high school, this +racist student attacked + +me and called me nasty names. + +And so when I fought back-- + +and we sort of fought to a draw, +which was good because + +he was trying to do +serious damage. + +As a result, the school policy +was that whoever was in the + +fight was suspended +for three days. + +So we were both automatically +suspended, and then had to go + +to court to figure out who +was really at fault. + +But by then, of course, +I'd already been + +suspended for two days. + +So I was suspended for three +days and I got to find out, + +what are the policies when +you miss school? + +So it was very interesting. + +So first of all, if you're late +to school three times in + +a quarter, then you fail +for that quarter. + +If you fail in the second +quarter of a semester, you + +fail the semester. + +If you fail in the second +semester of a course, you fail + +the entire year. + +And if you failed a required +course, like English-- + +math or English required-- then +you failed the entire + +year and had to repeat +the whole grade. + +OK, so they were very, very, +very sticklers about + +punctuality. + +But they didn't really +care what your + +grades were that much. + +You could get C's and D's on +tests and you'd do much better + +than if you missed four +days of school. + +Now, my teachers were +nice in this case. + +Said, no, don't worry +about it. + +Good thing you fought and +stood up for yourself. + +We won't do any of that stuff. + +So it was always puzzling to me +why punctuality was so much + +more important in this public +school, which was supposed to + +be one of the leading public +schools [INAUDIBLE], than the + +actual grades you got and +how much you learned. + +When I read the history +of Horace Mann, I + +thought, oh, yeah. + +That actually made +perfect sense. + +The purpose of the school wasn't +necessarily to teach + +people to think and +really understand. + +The social history behind it was +to produce people who are + +basically docile workers for the +factory system, which was + +just coming around +in the 1840s. + +So there were many comments +along those lines. + +One of the arguments also for +the school was similar. + +It was a resolution that the +best police for our cities, + +the lowest insurance of our +houses, the permanent security + +for our banks, the most +effective means of preventing + +pauperism, vice, and crime, and +the only sure defense of + +our country are our +common schools. + +They mean the public, free +schools that are required. + +So again, it's seen +as a defense + +of property, basically. + +This was true-- so when I say +America, it's not just + +America, actually. + +England in 1870 passed an +education act that required + +public schooling. + +[INAUDIBLE]. + +And the arguments in England +were almost exactly the same. + +"Would not the policemen be +better employed in assisting + +the work of the school master by +collecting [INAUDIBLE] for + +school attendance the willfully +neglected children + +who are [INAUDIBLE] recruits for +the great army of crime." + +We wanted to prevent the working +classes from engaging + +in those vain strikes which end +in 99 out of 100 leaving + +them in worse condition +than before. + +We wanted to keep them from +habits of waste and + +improvidence that some knowledge +of the succession of + +events in life, such as +education could supply. + +So in other words, education +has a class role. + +So that history of education, +it still permeates it. + +And people were very +open about this. + +These weren't secret documents +that people wrote in their + +conspiratory council. + +These were openly discussed, +saying this is why you should + +pay for schools. + +I would say it was even quite +a soph-- reached quite a + +sophisticated level. + +So William Whewell, he was +master of Trinity College, + +Cambridge, in the +1860s, I think. + +So when he was a university +professor, before becoming + +master at Trinity, he was +commenting on the difference + +between the European and the, +say, English and American + +educational system. + +And he said, well, actually, +they had [INAUDIBLE] + +problem in Europe. + +And the problem [INAUDIBLE]. + +So he was recommending the +teaching of mathematics. + +He said, "The mathematical +doctrines + +were fixed and permanent. + +No new system of geometry +can supersede the old. + +Not only so, but even the old +books remain in use." + +So now contrasting that, "The +fixed and constant nature of + +mathematics was not likely to +promote the critical spirit + +[INAUDIBLE] + +France and Germany, where too +much attention to the more + +provisional and contentious +observational sciences had + +been partly responsible for the +imminent general hostility + +to the existing institutions +in their country." + +So in other words, we should +teach mathematics because it + +has one answer. + +[INAUDIBLE] + +conclude about society, too. + +It has the one answer, which +is the society we have. + +Whereas, if you teach +observational sciences, social + +sciences, people might start +questioning way too much. + +So there was not just schools, +but what should we teach in + +our schools? + +So that history is very, very +hard to overcome because it's + +so deeply embedded into the +foundation of a school. + +We will find its purpose +is like that. + +Such purposes keep creeping +up whenever you + +try to change things. + +So there are all kinds of things +that are crazy in the + +schools that we do that you +don't necessarily need to do + +in the school. + +For example, grading. + +Why do schools have to grade? + +People think, oh, well, how +will other people know? + +If other people want to know +what students can do, let them + +worry about it. + +Why does the school +have to do that? + +Sure, it's school. + +It could tell students, look +you're not learning this idea + +very well, you could spend +more time on that. + +You're learning this +idea really good. + +You don't need to spend +any more time on that. + +That kind of evaluation, for +the student's benefit, is + +quite useful. + +But why should that be +publicized to other people? + +Well, those are two separate +questions, but they're + +automatically conflated +because-- partly, the purpose + +of the school is to get +people to accept their + +place in the society. + +There was a very interesting +experiment along those lines. + +I don't know if you know it. + +It was blues eyes, brown eyes. + +So this is related to tracking +and grading. + +So I don't think you could +do this experiment today. + +But what they was they took-- + +I think it was third graders. + +And they came into the +class and they said, + +OK, you third graders. + +We've just found out that the +blue-eyed children are more + +intelligent than brown-eyed +children. + +And so we're going to have +to teach them separately. + +So they then separated into two +classrooms and they taught + +them exactly the same stuff. + +And then they tested them a +while later and they found the + +blue-eyed children did much, +much better than the + +brown-eyed children. + +So sure, the test results +must have been correct. + +Actually what they did is +afterwards they said, + +actually, no we fucked up-- + +sorry. + +[LAUGHTER] + +We screwed up. + +And actually, we got +it backwards. + +It was the brown-eyed children +who were more intelligent than + +the blue-eyed children. + +So we had to switch +the classrooms. + +So they switched +the classrooms. + +And of course, they taught them +exactly the same stuff. + +And what do you think happened +[INAUDIBLE]? + +They flipped. + +That's an example +of the effect of + +tracking and grading. + +So what's the result of that is +that, well, students then + +accept their place. + +They think, oh, yeah. + +I am the dumb student. + +I am the bad reader. + +Oh, I'm just not so +good at math. + +It's my fault. + +Rather than-- well, it's +the way it's taught. + +It's that I came from a family +where we just didn't have much + +money, even for food. + +And the society just didn't +provide that, so I was + +hungry every day. + +So there's all kinds of social +explanations which you're + +taught not to look at. + +And even the very problems that +are done in school tend + +to reinforce the social +order that we have. + +So an example of that, to really +show how strong that + +tendency is, is look at the +problems that are done about + +percentages. + +The percentage problems are +always of the following form. + +Johnny has $1,000 which he lends +to Jane at 6% interest. + +How much interest does Jane +pay after two years? + +Well, there's many interesting +features about that. + +First of all, Johnny +makes the money. + +The guy has the money +and not the woman. + +The woman is the borrower. + +So now, with feminism, we've +made it so that Jane + +can have the money. + +But you haven't changed the +fundamental problem, which is + +that the problem is +reinforcing the + +idea of money lending. + +[INAUDIBLE]. + +What about the following +problem, which you never see, + +which is also [INAUDIBLE] + +interesting percentage problem? + +The hourly minimum wage +is $7 an hour. + +If somebody works 40 hours a +week, what's their salary? + +OK, it's this much. + +It's roughly $14,000 a year. + +What percentage of the +federal poverty line + +is $14,000 a year? + +That's an equally interesting +percentage problem, but it has + +a different social message. + +So the schools have chosen, +basically [INAUDIBLE] social + +pressures that push towards one +kind of problem, one kind + +of grading, one kind +of system. + +And this is despite what people + +know about these things. + +So blue eyes, brown eyes +experiment shows what's the + +detrimental effect +[INAUDIBLE]. + +Many people say, well, actually, +[INAUDIBLE]. + +Another example is tracking. + +So tracking where people +know that it's harmful. + +So a friend of mine in New +York, he went to an elite + +private school. + +It's a small, elite +private school. + +And one year they decided +to introduce tracking. + +So tracking is advanced math, +median math, OK math, and + +remedial math. + +And after a year, there was +a parental revolt and they + +abolished it. + +The parents said, this +is outrageous. + +We're not paying $25,000 a year +for you to tell our kid + +that our kid is not +intelligent. + +Get rid of it. + +Whereas, it's considered +perfectly acceptable to do + +that to kids in public +schools. + +So people know, yet +the thing goes on. + +So whenever you see something +like that happening, you can + +bet there's some really deeply +embedded social history-- + +the purposes of the schools. + +And related to the social +history is the social history + +of our society. + +So these tendencies, they're +not immutable. + +All social factors have changed +in the past and all of + +them can change again. + +But in order to change them, +It's important to be aware. + +You have a question? + +AUDIENCE: Yeah. + +I just had a question with the +whole concepts of getting the + +grades, which I can see is +a benefit in some ways. + +But I feel like [INAUDIBLE] + +to just stop grading children, +I feel like at least at the + +level of college acceptance, +there's still going to be some + +level of evaluating +the children. + +And eventually, it's just going +to be that some other + +form of evaluation is leading +to this separation, even if + +it's not just by numbers. + +Saying [INAUDIBLE]. + +And is there any way you could +really deal with it without + +having grades? + +PROFESSOR: Well, I think +you've identified the + +fundamental problem, which +is the competition. + +So it's sort of like +the water bed. + +If you sit on one side +of the water bed, the + +other side goes up. + +So if you reduce the competition +in one place, it + +might increase in other ways. + +So for example, you have no +grades in high schools, but + +then you have a really, really +high stakes university + +entrance exam, which is not + +necessarily the ideal solution. + +I think the ideal solution +is that you make good + +universities accessible +to all people. + +Or, for example, if you make +it so that you don't need a + +university degree to earn +a decent salary. + +AUDIENCE: But is that ever +going to be possible? + +PROFESSOR: Well, I always quote +Margaret Mead on that, + +"Never underestimate the power +of a small number of people + +[INAUDIBLE] + +to make social change." And not +just a small number, but + +people in general. + +So all things that we now think +are absurd and just + +horrible were once normal. + +Slavery was considered +absolutely normal. + +And in fact, the view of the +inferior races [INAUDIBLE]. + +But all these things that we +think are horrible now-- + +torture-- + +are now considered just beyond +the pale because of social + +[INAUDIBLE]. + +So my main point here is that +these are structural, + +fundamental, large issues. + +And they require structural and +large society-wide changes + +to fundamentally change them. + +But it goes both ways. + +The schools themselves produce +people who reinforce the + +social structures. + +So if people had come through +the blue eyes, brown eyes + +experiment and they feel +themselves that they are not + +worthy, they're less likely to +try and make a social change + +to make a just society. + +So it goes both ways. + +Improving the schools and the +educational system improves + +the society. + +Improving the society improves +the schools. + +AUDIENCE: I was wondering if +you could take advantage of + +that blue-eyed, brown-eyed +thing, like to say-- + +one could say something like, +oh, people in that class + +always did really well in their +future physics classes. + +And then everyone could just +be like, oh, great. + +[INAUDIBLE]. + +PROFESSOR: It's a great point. + +So the point was, could you +take advantage of the blue + +eyes, brown eyes experiment +to just tell people, look, + +everyone in my physics +class does great. + +And so just, actually, +make people do well? + +There is actually a fair amount +of data that does work. + +So [INAUDIBLE] wasn't phrased +in exactly that way, but the + +example I'm thinking of +is women's colleges. + +So a large portion of women in +science Ph.D's come from + +all-women's colleges. + +And I think that's partly +that effect. + +In the regular society, women +are generally told, look, + +[INAUDIBLE] the Barbie doll +that was taken off, + +[INAUDIBLE] + +Barbie doll that for a +while said, oh, math. + +Math is hard. + +I don't do math, or something +like that. + +That's what it taught. + +It's really amazing that they +thought they could do that. + +So there was huge outcry and +they had to take it-- some + +people did spoofs. + +They put that as a Ken doll and +they put a big, deep voice + +in the Barbie doll just +to play on that. + +But that social attitude does +permeate the society. + +And it's much less in the +all-women's colleges. + +So places like Swarthmore, Bryn +Mawr, and Smith where + +women are-- it's +just expected. + +Of course you're going to +do well in science. + +Everyone around here does +well in science. + +It's not considered +anything special. + +It's considered a good thing, +but it's not [INAUDIBLE] + +to women. + +So they already took away the +blue eyes or the brown eyes + +and just put everyone +[INAUDIBLE]. + +So I think that is a reason +for not criticizing kids. + +When you're raising young +children or teaching them + +things, don't criticize them. + +And same with grades +at a university. + +Grades should be so the students +can figure out what + +they need to learn more of, +but not as a way of making + +them feel bad. + +That's so hard to do when people +have been graded or + +degraded for so long. + +Question, yeah. + +AUDIENCE: So I wanted to go +back to your earlier point + +about competition, how it takes +it away from one place + +and it ends up another place. + +PROFESSOR: I don't say +it's conserved. + +But you have to think about +the whole system. + +Yeah, so I agree with +the question. + +AUDIENCE: [INAUDIBLE]. + +Not only it doesn't scale +because of limited resources. + +You can't keep everybody +in teacher one on one. + +It would be great if it +took, but the system + +won't work that way. + +We won't have enough teachers. + +So there's always going to be +competition for resources. + +I just want to-- + +PROFESSOR: Well, OK, so the +question of competition. + +So let me close with one quote, +and then I'll come to + +your question. + +OK, so it's a good question. + +So to continue the rest +of what Einstein said. + +So remember, before Einstein +said that one had to cram all + +this stuff into one's mind, +whether one liked it or not. + +"This [INAUDIBLE] + +effect that after I passed the +final exam, I found the + +consideration of any +scientific problems + +distasteful to me for +the entire year. + +It is, in fact, nothing short +of a miracle that the modern + +methods of instruction have +not entirely strangled the + +[? whole new ?] + +curiosity required. + +For this delicate little plant, +aside from stimulation, + +stands mainly in need +of freedom. + +Without this, it goes to wrack +and ruin without fail." + +So I hope that when you're out +in the world, when you're + +teaching and raising your +children, that you find ways + +to make more freedom +in education. + +So that when the students +actually that you produce + +improve the society, and they +then, can help you improve the + +schools and the rest of +the education system. + +OK, your question about +competition. + +It is a fundamental one. + +And about competition for + +resources, you have to really-- + +so make a radical analysis. + +So radical in Latin +means to the root. + +So you have to get to the +root of the problem. + +So the root of the problem, you +can see it in the extreme + +case of India where there are +so many people and so few + +comfortable jobs, and the route +to the comfortable job + +is in education. + +That's there's intense +competition for + +tutors and all this. + +Not because people want to +learn, but because that's the + +means to actually not starve +on the street. + +So what that shows is that not +everyone wants to learn with a + +tutor differential equations. + +But a lot of people are +learning differential + +equations with a tutor because +that means they'll get a + +degree, which means they can +work in investment bank, which + +means-- well, it used to +mean that they would be + +comfortable. + +So part of the issue is of +redistributing the wealth in + +the society, so that you're +comfortable whether or not you + +had a tutorial in differential +equations + +or one-on-one tutorial. + +Then, when the fears are taken +away, people are much more + +likely to do things for +intrinsic reasons. + +So the people who really +are interested in + +that, then do that. + +The people who are really +interested in teaching that + +will teach that. + +And you'll have a redirection +of social resources in much + +more productive way. + +But that requires, for example, +the value of, say, + +guaranteed income, guaranteed +health care. + +Maybe even guaranteed basic +schooling for everyone, so + +that those things are features +of competition. + +Yeah. + +AUDIENCE: But the system based +on competition is quite + +self-regulating, right? + +PROFESSOR: I don't +know about that. + +So a good example-- is the +system based on competition + +self-regulating? + +I'm not sure about that. + +I mean, the mortgage derivative +market is a great + +example that-- actually, what +happened was-- you can think + +of it in electrical +engineering terms. + +You had-- + +let's do it under +continuous time. + +So you had some sort of slow, +pokey banking system with + +feedback loops and the poles +were [INAUDIBLE]. + +[INAUDIBLE], nice +decay constant. + +And then, the competition to +make more money quickly-- + +well, one way to make more +money was to trade + +[INAUDIBLE]. + +What did that do? + +It increased the gaming of +feedback loops and [INAUDIBLE] + +the poles this way. + +And eventually, some of the +poles crossed the axis and you + +got huge nonlinear oscillations, +which grew to-- + +huge oscillations grew to +nonlinear [INAUDIBLE] and + +broke a whole bunch of the +world banking system. + +So it's actually not necessarily +true that + +competition is self-regulating, +because there + +are all these nonlinearities +and feedbacks and delays in + +the system, there's no +guarantee of that. + +And one of the harms of the +competition is it puts people + +against each other. + +And what'd you much rather +have is people working + +together and helping +each other. + +Because as studies quoted by +[INAUDIBLE] showed, that + +actually-- if you want it to go +a high level, [INAUDIBLE]. + +That's how it happens. + +Not through competition and +dog-eat-dog, but people + +cooperating and sharing +knowledge. + +And what we wanted to do, I +would say in our educational + +system, is shift it more towards +there and free people + +[INAUDIBLE] for creating +the [INAUDIBLE]. + +Instead of [INAUDIBLE]. + +AUDIENCE: So we don't determine +the pay of different + +people in the society +based on the + +competition, what do you propose? + +Do you propose that somebody +else decides [INAUDIBLE]? + +PROFESSOR: Well, we already +have all kinds of ways. + +I mean, you can have +regulations. + +You could, for example. + +Say, I mean, income tax is a +social way of deciding what's + +worthwhile and what's not. + +You could say, OK, we're going +to tax peoples' income the + +99%, beyond 200,000. + +[INAUDIBLE]. + +And we're going to use that +money to pay teachers more. + +That's a social choice because +saying the teachers' + +salaries are this. + +If you think it's a worthwhile +thing to do we could say look, + +we think bridge building +is really important it + +revitalizes the [INAUDIBLE]. + +We're going to pay people +to do that. + +Those are social choices, +just like anything. + +It doesn't have to +be permissive. + +All right? + +So we can change our educational +system that way. + +The barrier to it is that our +thoughts are limited by the + +educational system that +we went through. + +So in one way that's bad news, +because there was this giant + +feedback loop keeping things +the way they are. + +On the other hand, because +there's a feedback loop, the + +educational system affects the +society and vice versa. + +Well, it means you can work +anywhere on the feedback loop + +you want that you think +is interesting. + +You could try to improve +the society directly. + +You could try to improve the +educational system in + +[INAUDIBLE]. + +You can try to skip the feedback +wherever you see it. + +Insert something good in here. + +And you improve things for +everybody that way. + +OK, so if you could fill +out the question sheet. + +[INAUDIBLE] + +put on the website +who [INAUDIBLE] + +as well as referenced +[INAUDIBLE]. + +And next time we'll have a +summary of all of the second + +[INAUDIBLE] + +as well as questions from you. + +Because I know I have a few +questions that I have to + +answer plus [INAUDIBLE]. + +So we'll try to answer all your +questions [INAUDIBLE]. + +Answers from lecture +10 to questions + +generated in lecture 9. + +PROFESSOR: OK, lots of questions +from last time. + +So I won't answer all of them +because otherwise we'll + +probably spend the entire +time just on the + +questions from last time. + +Which maybe I should have +anticipated since it's a + +central topic and one that +connects to not just + +education, but directly to +society, the topic on + +political barriers to +educational change. + +So I'll answer some of those. + +But then I wanted to also give +you a chance to ask any + +questions that have been +unresolved that have come up + +in your teaching or that +you think might + +come up in your teaching. + +One of my old teachers, Don +[? Knuth, ?] always reserved + +the last session for +student questions. + +And I think it's a really good +philosophy to tie everything + +together, tie all the +loose ends up. + +So I call it your turn. + +OK, but part of your turn was +answering some of your + +questions from before. + +Is social education +a bad thing? + +And so the comment was, I'm +still not convinced social + +education is a bad thing. + +Obviously it gives a lot of +control to whoever gets to + +make the decision of what +constitutes a good citizen. + +But some of the social agendas +in public schooling were good. + +For example, diversity, +recycling. + +And that's true. + +So I don't want to be +misinterpreted as saying + +society is a bad thing. + +I think society naturally +educates people. + +You pick up your values from +people around you. + +Your parents give you +ethical norms. + +Schools give you +ethical norms. + +And I think it's exactly what +the question said, it said who + +gets to decide? + +Is it some group of elites who +decide or is it the whole + +society collectively deciding +what is good for everybody. + +And what's good for everybody +may not be one thing. + +It may be the decision is well, +different people need or + +want different things. + +And we think a good society is +based on the idea that people + +have freedom to follow +their interests. + +And also, some required work +that everyone need to learn, + +for example, reading. + +But then what you read +may be up to you. + +So yeah, I don't think all +social education is a bad + +thing at all. + +I think all education +is social. + +There's no way to avoid that. + +Inherently we're +social animals. + +And it's the question of what's +in that education? + +And it's the same +thing, political + +barriers educational change. + +It's not that politics is +inherently a bad thing. + +The question is, what kind +of politics do we have? + +And how can we make that +better and more humane? + +So for example, I think +recycling is a good example of + +making things more humane. + +OK, if competition demotivates +some people does it motivate + +other people? + +Does eliminating competition +reduce maximum performance? + +Other than the studies referred +to by Alfie Kohn, I'm + +not sure if the answer +to that is known. + +I mean, there's certainly +studies on how, for example, + +competition leads to +a lot of waste. + +The classic example in economics +is suppose you-- + +and this was actually +a real example-- + +give people 160 acres +of land-- + +I think that was the a 1/4 +plot-- or 640 acres of land + +way out in the west. + +And the rule is whoever gets +there first gets to claim that + +piece of land. + +And you get there and you stick +posts up and you put a + +fence there. + +That's roughly how the +Homestead Act worked. + +Well, the problem with +that is that it does + +cause a lot of waste. + +Which is that tons of people +might run out and + +chase after that land. + +And make a whole bunch of effort +buying train tickets, + +go on a wagon with their +whole family out west. + +But only one person +gets the land. + +So a whole bunch of people +actually put in a lot of + +wasted effort. + +So that's a classic example +of how competition + +can be quite wasteful. + +Other examples, where exclusive + +rights do that, or patents. + +So as is the case, a patent's +only given to one person-- + +or the inventor-- + +and you have 15 people +or 30 people + +trying to invent something. + +So the more the competition, in +this case, the more waste + +is going to happen. + +Because all these people are +going to invest funds. + +But only one person is going +to get the exclusive right. + +And the other people are +just left high and dry. + +So there's many examples where +eliminating competition will + +actually increase the amount of +social wealth contributed + +towards useful ends. + +But to the direct question of +whether it reduces maximum + +forms, I don't know +if that's known. + +The studies in Alfie Kohn's +article pointed to how + +competition reduces high-level +performance. + +For example, complex +cognitive tasks. + +Maximum performance, probably, +one would need to define that + +pretty closely. + +And then one could +do studies on it. + +OK, so there was an interesting +question about the + +understanding multiplication. + +So the understanding +multiplication example I gave, + +where people could multiply +6 by 3 and get 18 but then + +couldn't come up with a word +problem that used 6 by 3. + +Or they could, but the word +problem was Johnny buys 6 + +apples on Monday. + +He buys 3 apples on Tuesday. + +So 6 times 3 is 18. + +So that was, maybe, a bit +unfair to ask students. + +Because writing a story draws on +skills beyond mathematical + +understanding such as +imagination and language. + +So it's true, it does draw +on those skills. + +But I don't think those are +separate from mathematical + +understanding. + +If you can't explain the +mathematics that you in you, + +you don't really +understand it. + +When I was an undergraduate a +friend of mine and I used to + +torment the math +grad students. + +It was sort of unfair. + +And we were really curious +about math. + +We were fascinated by math. + +And we wanted to know what +people do in graduate school. + +And only later did +I realize we were + +actually tormenting them. + +We weren't doing it +intentionally. + +We would ask them, OK, what +are you working on? + +Sometimes we had classes with +them or we'd see them in the + +math lounge. + +And they would say, oh, blah, +blah, the theorem. + +And we were undergraduates +and young. + +And we didn't really know +what the theorem was. + +So we'd say, well, can you +give us an example? + +And that produced just deer +in the headlights. + +Example? + +Example? + +That was completely foreign and +not at all what they were + +thinking about. + +It was completely out +of their space. + +And later I actually realized +that that was actually a very + +fair question. + +And if you wanted to test +whether people understood what + +they were working on. + +And I found that things I can +give examples on I understand. + +The things I can't, I +don't understand. + +Another example that +is Feynman. + +He said, I have always found +that I don't understand + +anything unless I can give +a freshman lecture on it. + +Or equivalently, people +asked him to give + +a lecture on something. + +He said, no, I don't +understand. + +I don't understand +that well enough. + +I'll have to first work out +a freshman lecture on it. + +Then I can explain it better. + +And so there's famous lectures +of his where he's explained + +anti particles and spin. + +And he finally got it to a level +where he thinks it was + +actually suitable for a +freshman, so first-year + +college students. + +So it's a brilliant lecture. + +If you search for the Dirac +Memorial Lectures by Feynman + +you'll find that +lecture there. + +And it's fascinating. + +So it shows the level of how +hard work it is to actually + +understand something +of that level. + +And almost essential to that +process is examples. + +So examples, explaining, +understanding, I think those + +are intrinsic to mathematical +understanding. + +So it wasn't an unfair test. + +It was actually a test of +high-level mathematical + +understanding. + +One point was made, Swarthmore +was not a women's college. + +Yeah, that's true. + +I mentioned that women's +colleges were much more + +successful in producing women +Ph.D. students in science. + +And I listed Bryn +Mawr and Smith. + +And then I listed Swarthmore, +which was not correct. + +That was crosstalk between Bryn +Mawr is and Swarthmore. + +I grouped them all, Bryn +Mawr, Haverford, + +and Swarthmore together. + +So Swarthmore is a coeducational +college. + +And I meant Bryn +Mawr and Smith. + +And I was thinking of +Wellesley as well. + +So Wellesley is an all-women's +college, unless they've + +changed lately? + +No, OK. + +I mean every once in a while +colleges think of changing. + +But they're still all women. + +Now, people asked for references +and further + +information about that. + +So I'll put a link +on the website. + +But it's Barbara Whitten at the +Colorado College physics + +department, she's done the most +extensive studies on not + +just what makes for women being +successful in science, + +but in general, what makes +for students in + +say, physics majors. + +She was the chair of the +Colorado College physics + +department when I interviewed +there. + +What makes for a successful +undergraduate major program? + +So this is quite interesting +for people + +interested in teaching. + +Not just revising one course, +but revising an entire + +department curriculum. + +So she's done +cross-institutional studies of + +the culture of departments and +what facets of the culture are + +responsible for students +continuing on in science. + +And what she's found is that +the same features that help + +women continue in science +help everybody. + +So I highly recommend +her work. + +And I'll put a link to her web +page on our course web page. + +Barbara Whitten. + +I think it's W-I-T-T-E-N. But it +might be W-H-I-T-T-E-N, the + +Colorado College physics +department. + +OK, it's clear that I don't +like No Child Left Behind. + +But would I do if I were +the Secretary of + +Education in this country? + +Yeah, well, Hell would probably +freeze over before + +that happened. + +There's a long vetting process +before people become that. + +And you have to show your +loyalty to pretty much every + +aspect of the current system +before that happens, before + +you're appointed +to such a post. + +But if Hell froze over +what would I do? + +I think one of the fundamental +problems with education in + +America is the vast +inequalities + +in funding, in resources. + +So the wealthy school districts +have two, three, + +four times as much funds +per student as + +the poor school districts. + +And there's a good +part of that. + +I mean, the disparity is bad. + +But there's a reason +for the disparity. + +And the reason isn't all bad. + +The reason is that America +education is a local affair. + +It's controlled by local +authorities. + +So the constitution reserves +a bunch of powers for the + +federal government, printing +money, making war, various + +things like that. + +Then it says, OK, then the +states can do a bunch of stuff + +like, for example, +regulate voting. + +And then it says anything not +explicitly given to the + +national or state governments +is given to the people. + +Or in fact I think it says-- +this is the 10th or 11th + +commandment-- + +especially devolution. + +It says any powers not given to +the federal government go + +to the state. + +If they're given to the state. + +And if not given to the state +they go to the people. + +And so education is +in that category. + +It's nowhere mentioned in the +constitution, education. + +So it's not given +to the states. + +It's not given to the +federal government. + +So in America it's given to +the local authorities. + +Now the problem is that +different communities have + +different wealth bases. + +Because there's some +very rich suburbs. + +And for a while the cities +were wealthy. + +But then people fled. + +All the wealthy people fled the +cities in the 1950s during + +suburbanization. + +So the centers of cities +became very poor. + +So there's vast disparities +in wealth there. + +And I think one thing that the +federal government could do is + +actually just correct those. + +So there've been lawsuits along +those lines for forcing + +state governments to try to +correct that because there is + +some role for the states +in education. + +I'm not sure where that comes +from in the constitution. + +But there are state boards +of education. + +And I think it's Vermont and +New Jersey, there've been + +lawsuits in state courts to +force the states to equalize + +funding across school +districts. + +So somehow mitigating +the differential in + +property-tax revenues. + +And I think the federal +government + +could do that as well. + +So those lawsuits +are based on-- + +I'm pretty sure-- the 14th +Amendment, equal + +protection of the laws. + +Now, there's no reason the +federal government couldn't do + +that as well. + +So I would do that as +step number one. + +No strings attached, +here, let's just + +equalize the resources. + +And then we can worry +about what we're + +going to do after that. + +Whereas No Child Left Behind, +what it does, it makes the + +resources actually, +more unequal. + +Because it tests all +the schools. + +And the schools that are going +to do badly are the ones with + +less resources. + +And then they're going to get +punished for doing badly. + +So I would take the +opposite approach. + +Is there a particular country's +educational system + +that I particularly admire? + +That's a good question. + +Again, I think it's local. + +There's local educational +experiments that I admire a + +lot and occasionally +larger-scale ones. + +A whole country, not so much. + +I mean, there's states +in India, for + +example, for awhile Kerala-- + +I don't know if this is still +true-- but had an incredibly + +high literacy rate, I think +98%, Which was much higher + +than anywhere else in India +and matches literacy + +levels in the West. + +And this has many benefits. + +So for example, one study +about population is that + +population growth is slowed +down the most + +by educating women. + +And Kerala actually, that 98% +included women not just men. + +So I think that's an educational +system worth + +looking into. + +And places that I admire, +there are local pockets. + +The free schools in the 1960s. + +There's a few places like +that still in America. + +There's the Sudbury +Valley School. + +Maybe it's 50 miles +west of here. + +It's in the Sudbury Valley. + +And that's modeled on +Summerhill, one of the + +earliest free schools +in England. + +So actually, it has +its good and bad. + +So Summerhill, there's +no required classes. + +And there's no required +curriculum. + +And the students can +go to class or not + +and can play outside. + +So that would work +really well. + +I think that works really +well if all the + +teachers are really inspiring. + +Because then the students would +be automatically drawn + +in to learn stuff. + +But if the teachers aren't very +skilled then you have + +problems with that. + +So I think it worked +mixed there. + +But the potential is good and +the freedom is really good. + +And it teaches people +to be responsible. + +But it has its downsides. + +So I have a personal experience +with that. + +Which is when I was three. + +So I was born in England. + +And we lived there +for a few years. + +And then we moved +to New Jersey. + +And I guess I was four maybe, +my parents thought about + +sending me to England +to go to Summerhill + +because this was 1973. + +So it was in the middle +of lots of + +political change in America. + +Free schools were a big part +of the cultural discussion. + +And my parents believed +in those values, which + +I'm glad they did. + +And they thought, OK, let's see +about sending Sanjay to + +Summerhill. + +So we took a trip +back to England. + +And they visited. + +And the way they tell me what +happened, was that everything + +was fine except then they were +wandering around with the + +teacher on the tour. + +And they saw these marks +on the door. + +And they said, what are those +marks on the door? + +Because they believed in the +philosophy of letting children + +do what they want to do and +follow their interests. + +But they said, oh, what are +those marks on the door there? + +And they said, oh, +that's Johnny. + +He likes to stand over there and +throw knives at the door. + +So then my parents thought, +well, maybe that's just a + +little too unsupervised. + +Especially if the child is +across the Atlantic from us. + +And it's not really easy to see +how things are going and + +intervene if things aren't +going so well. + +So they decided not to send +me to Summerhill. + +But they sent me to progressive +nursery schools + +locally as well. + +And I have good memories +of those too. + +So yeah, I would say there's a +fundamental point in there, + +which is there's a difference +between freedom and license. + +And so this is a distinction +not often made. + +So license is the bad pole +and freedom is the good. + +This is how I'm splitting +the two parts. + +So license is just do +whatever you want. + +Take drugs. + +Be a prostitute. + +Do whatever you want. + +You're free. + +Well, that's not +really freedom. + +You're licensed. + +Whereas freedom-- + +in my mind-- has some intrinsic +regulation on it. + +You're free. + +You're a free creature. + +You have responsibility to +use that freedom well. + +And license doesn't have any +of that responsibility. + +So I think when one is designing +curricula like that + +you have to try to make the +norm such that freedom is + +promoted and not license. + +Now, to some extent, you can't +avoid a bit of license. + +Because, for example, the +Summerhill teachers say that + +when students come from regular +schools where they've + +been basically competing with +each other, basically feeling + +beaten down, some of them come +to Summerhill and just do + +nothing for a year. + +They just sit outside and play +on the swings and in the + +creek, just for a year. + +It takes them a year of +detoxification before they are + +ready to go back into +the classroom and + +learn things formally. + +So you could say that's +a bit of license. + +But maybe that's a bit +of necessary license. + +Or maybe they're actually just + +discovering how to use freedom. + +And it takes them a year because +they never had any + +practice with that. + +So I think it's important +to keep + +those two pieces separate. + +OK, so now there's so +many questions. + +OK so there's two that I +think are particularly + +important to discuss. + +So there was a comment that one +of the Alfie Kohn readings + +was off putting because he made +comments about people + +with different political views +than his and he seemed like a + +left-wing nut. + +And that, therefore, that +reading shouldn't be assigned. + +So yeah, I agree that if you +have quite a different + +political view than Alfie Kohn +it can be a bit off putting. + +But actually, I think +that's a good thing. + +Now why is that? + +It's because it's fundamentally +important to + +find views that challenge you +and read them anyway. + +So as you probably guessed, +most of my views are not + +mainstream. + +So I do that all the time +whether I like it or not, just + +when I open the paper, or if I +happen to watch television, + +which I actually don't +hardly at all. + +But if I open the newspaper or +read things, just right next + +to my office there was +a teaching magazine. + +I forget what is called. + +Prism maybe? + +I forget the name +of the magazine. + +But it's on the magazine +display. + +And I just was walking by. + +And turned my head this +way to read the title + +on the front cover. + +And it said cash incentives +are proving successful for + +promoting student learning. + +So this was against everything +I believed in. + +So if I have the time I'll +actually read the article. + +But I'm surrounded by things +I disagree with. + +And I think that's actually +pretty healthy. + +So if you disagree with +the article read + +it all the way through. + +And the law professor Cass +Sonstein from Chicago-- + +who's talked about as being +a possible Supreme + +Court nominee by Obama-- + +he's written eloquently about +the dangers of not doing that. + +Because it wasn't so possible +50 years ago. + +There was large-circulation +newspapers and maybe two, + +three in each town. + +And people read those. + +There was a common discourse +through that. + +But now, everyone can get their +own particular news on + +the internet. + +Right? + +You can get your own views from +this small journal or + +from that particular newspaper +or this person writing an + +article that you happen +to agree with. + +And the danger is of people +just collecting into small + +little micro communities, where +each community just + +agrees with itself and only +reads things and discusses + +things that they agree with. + +And that's very unhealthy for +democracy he points out, which + +I think is right. + +So I think it's very important +to actually seek out things + +you disagree with. + +And so if I happen to give you +a reading that at first you + +disagreed with it's not +such a bad thing. + +And it belongs, for sure, in +an academic curriculum. + +Because that's one of the +purposes of an academic + +curriculum. + +The word university comes from-- +it has Uni in it, one. + +So the idea is it's +one universe. + +All ideas are open discussion, +even ones we disagree with. + +OK, so let's see. + +OK, then the related one is, I +find it off putting when I put + +my personal biases and +opinions as absolute. + +For example, programming-- + +and this is related to +the last point-- + +programming LaTeX may +be easier and more + +convenient for me. + +But it's possible to develop +familiarity with other + +software and systems that +makes them close to + +equivalent, if not equivalent. + +That may be true. + +Though I think there's +fundamental reasons to + +wonder about it. + +Just because By not using a +system such as LaTeX or Tex. + +What's common about all of them +is that you program them. + +And by not using a system like +that, you give up the ability + +to program. + +And that is a huge loss. + +You can see it, how much +can computers do? + +The way computers are +so powerful is + +because we program them. + +And the fundamental recipe +for programming is-- + +at least when I teach it-- + +this-- + +So this is how the fundamental +idea of programming I think. + +So you do something and +then you do it again. + +And when you're doing it +again, you're like, + +oh, I just did this. + +Maybe I should write +a program. + +Nah, I'm too lazy. + +But then the third time +it happens again. + +And you're like, OK, +bloody hell, this + +time write a program. + +OK, so basically the recipe is +the third time you're about to + +do something, don't do it. + +Write a program to do it. + +So now you have a little mini +program that you can reuse. + +Now it's a new module. + +And you can use that module to +build still new programs. + +You can build a huge +power abstraction. + +So for example, in the +figure-drawing program you can + +actually write programs +that generate trees. + +And then you can write +a five-line script. + +And you say, OK, feed +that through my + +tree-generating program. + +And it'll make a tree that you +can use in your figures, in + +your talks, or in your books. + +So I'll post a few +examples of that. + +The input as five-line tree +and the output PDF. + +So the first time you write that +program it takes longer + +than doing it graphically, +no question. + +Which is why this second +part happens. + +Because you do it the slightly +hard way the first time. + +You don't realize the second +time you're like, oh, there's + +something in common here. + +[BUZZER SOUND] + +But it's too late. + +I just have to do it the +slightly hard way. + +The third time you think, OK, +finally I'm going to do it + +with the program. + +So I think there are fundamental +reasons to think + +that if you can program +your documents you'll + +also be more efficient. + +Now, that actually may end +up not being true. + +I suspect it is. + +But it may not be. + +But even if it isn't take +it as not an absolute. + +But as a suggestion to +try in your own work + +and in your own writing. + +And I don't mean it +as an absolute. + +OK, so now there's 10 +more questions. + +But I'm going to leave +them for now. + +And if at the end we haven't +used up all the time with + +questions I'll continue with +some of those questions. \ No newline at end of file diff --git a/PrErxYzSANo.txt b/PrErxYzSANo.txt new file mode 100644 index 0000000000000000000000000000000000000000..c366a882b6bd44062d52cbdf3bd8fae5e31e4ced --- /dev/null +++ b/PrErxYzSANo.txt @@ -0,0 +1,5299 @@ +align:start position:0% + +okay this uh lecture is uh applies to + + align:start position:0% +okay this uh lecture is uh applies to + + + align:start position:0% +okay this uh lecture is uh applies to +every Matrix and it comes really near + + align:start position:0% +every Matrix and it comes really near + + + align:start position:0% +every Matrix and it comes really near +the beginning of linear algebra uh + + align:start position:0% +the beginning of linear algebra uh + + + align:start position:0% +the beginning of linear algebra uh +elimination is the the powerful way to + + align:start position:0% +elimination is the the powerful way to + + + align:start position:0% +elimination is the the powerful way to +make the Matrix simpler get a lot of + + align:start position:0% +make the Matrix simpler get a lot of + + + align:start position:0% +make the Matrix simpler get a lot of +zeros in it is what is actually achieved + + align:start position:0% +zeros in it is what is actually achieved + + + align:start position:0% +zeros in it is what is actually achieved +by + + align:start position:0% +by + + + align:start position:0% +by +elimination uh but then it's a little + + align:start position:0% +elimination uh but then it's a little + + + align:start position:0% +elimination uh but then it's a little +question what have I done what how do I + + align:start position:0% +question what have I done what how do I + + + align:start position:0% +question what have I done what how do I +describe the answer and I think + + align:start position:0% +describe the answer and I think + + + align:start position:0% +describe the answer and I think +factorizations which you'll see are the + + align:start position:0% +factorizations which you'll see are the + + + align:start position:0% +factorizations which you'll see are the +fundamental theme in linear algebra or + + align:start position:0% +fundamental theme in linear algebra or + + + align:start position:0% +fundamental theme in linear algebra or +give a great uh description of + + align:start position:0% +give a great uh description of + + + align:start position:0% +give a great uh description of +elimination you can see what you've done + + align:start position:0% +elimination you can see what you've done + + + align:start position:0% +elimination you can see what you've done +and this + + align:start position:0% +and this + + + align:start position:0% +and this +factorization + + align:start position:0% +factorization + + + align:start position:0% +factorization +uh takes any Matrix a any rectangular + + align:start position:0% +uh takes any Matrix a any rectangular + + + align:start position:0% +uh takes any Matrix a any rectangular +Matrix Square rectangular and finds a + + align:start position:0% +Matrix Square rectangular and finds a + + + align:start position:0% +Matrix Square rectangular and finds a +column Matrix and a row Matrix that + + align:start position:0% +column Matrix and a row Matrix that + + + align:start position:0% +column Matrix and a row Matrix that +multiplies so it's maybe the first of + + align:start position:0% +multiplies so it's maybe the first of + + + align:start position:0% +multiplies so it's maybe the first of +our six factorizations that really + + align:start position:0% +our six factorizations that really + + + align:start position:0% +our six factorizations that really +organize the linear algebra course so + + align:start position:0% +organize the linear algebra course so + + + align:start position:0% +organize the linear algebra course so +ready to start on this so elimination is + + align:start position:0% +ready to start on this so elimination is + + + align:start position:0% +ready to start on this so elimination is +familiar but this fact factorization is + + align:start position:0% +familiar but this fact factorization is + + + align:start position:0% +familiar but this fact factorization is +more is newer okay uh so I'm going to + + align:start position:0% +more is newer okay uh so I'm going to + + + align:start position:0% +more is newer okay uh so I'm going to +take an example there is a matrix a 3x4 + + align:start position:0% +take an example there is a matrix a 3x4 + + + align:start position:0% +take an example there is a matrix a 3x4 +pretty arbitrary + + align:start position:0% +pretty arbitrary + + + align:start position:0% +pretty arbitrary +Matrix um so uh and I want to do + + align:start position:0% +Matrix um so uh and I want to do + + + align:start position:0% +Matrix um so uh and I want to do +elimination to it let me just describe + + align:start position:0% +elimination to it let me just describe + + + align:start position:0% +elimination to it let me just describe +elimination how it would start in words + + align:start position:0% +elimination how it would start in words + + + align:start position:0% +elimination how it would start in words +I would say I want to turn that three + + align:start position:0% +I would say I want to turn that three + + + align:start position:0% +I would say I want to turn that three +into a zero so I take three * Row one + + align:start position:0% +into a zero so I take three * Row one + + + align:start position:0% +into a zero so I take three * Row one +and subra ract from row two and that + + align:start position:0% +and subra ract from row two and that + + + align:start position:0% +and subra ract from row two and that +gives me a zero there and it gives me + + align:start position:0% +gives me a zero there and it gives me + + + align:start position:0% +gives me a zero there and it gives me +something else and I take four times Row + + align:start position:0% +something else and I take four times Row + + + align:start position:0% +something else and I take four times Row +one from Row three and that gives me a + + align:start position:0% +one from Row three and that gives me a + + + align:start position:0% +one from Row three and that gives me a +zero I think yeah uh the that this is + + align:start position:0% +zero I think yeah uh the that this is + + + align:start position:0% +zero I think yeah uh the that this is +the process that you repeat multiples + + align:start position:0% +the process that you repeat multiples + + + align:start position:0% +the process that you repeat multiples +and and the subtractions can go upwards + + align:start position:0% +and and the subtractions can go upwards + + + align:start position:0% +and and the subtractions can go upwards +here I can I could after I've taken + + align:start position:0% +here I can I could after I've taken + + + align:start position:0% +here I can I could after I've taken +three of these away from row two I have + + align:start position:0% +three of these away from row two I have + + + align:start position:0% +three of these away from row two I have +a new row two I can take some multiple + + align:start position:0% +a new row two I can take some multiple + + + align:start position:0% +a new row two I can take some multiple +of that row two away from Row + + align:start position:0% +of that row two away from Row + + + align:start position:0% +of that row two away from Row +one and produce that + + align:start position:0% +one and produce that + + + align:start position:0% +one and produce that +zero I I don't plan to discuss all the + + align:start position:0% +zero I I don't plan to discuss all the + + + align:start position:0% +zero I I don't plan to discuss all the +horrible details of elimination right + + align:start position:0% +horrible details of elimination right + + + align:start position:0% +horrible details of elimination right +here just this but I'll tell you the + + align:start position:0% +here just this but I'll tell you the + + + align:start position:0% +here just this but I'll tell you the +operations and for this Matrix I end up + + align:start position:0% +operations and for this Matrix I end up + + + align:start position:0% +operations and for this Matrix I end up +with that Matrix that this is what + + align:start position:0% +with that Matrix that this is what + + + align:start position:0% +with that Matrix that this is what +elimination goes to if we go the whole + + align:start position:0% +elimination goes to if we go the whole + + + align:start position:0% +elimination goes to if we go the whole +way we get a couple of columns so how do + + align:start position:0% +way we get a couple of columns so how do + + + align:start position:0% +way we get a couple of columns so how do +I how do I under understand this Matrix + + align:start position:0% +I how do I under understand this Matrix + + + align:start position:0% +I how do I under understand this Matrix +Z which came from a well let's see if I + + align:start position:0% +Z which came from a well let's see if I + + + align:start position:0% +Z which came from a well let's see if I +look at the rows I see two nonzero rows + + align:start position:0% +look at the rows I see two nonzero rows + + + align:start position:0% +look at the rows I see two nonzero rows +and that that turns out they turn out to + + align:start position:0% +and that that turns out they turn out to + + + align:start position:0% +and that that turns out they turn out to +be a basis for the row space the + + align:start position:0% +be a basis for the row space the + + + align:start position:0% +be a basis for the row space the +combinations of those two rows give me + + align:start position:0% +combinations of those two rows give me + + + align:start position:0% +combinations of those two rows give me +any all of the three rows of a and + + align:start position:0% +any all of the three rows of a and + + + align:start position:0% +any all of the three rows of a and +notice that there's a zero row so the + + align:start position:0% +notice that there's a zero row so the + + + align:start position:0% +notice that there's a zero row so the +rank is only two for this Matrix this + + align:start position:0% +rank is only two for this Matrix this + + + align:start position:0% +rank is only two for this Matrix this +Matrix has only two uh nonzero rows in + + align:start position:0% +Matrix has only two uh nonzero rows in + + + align:start position:0% +Matrix has only two uh nonzero rows in +when it after at the end of elimination + + align:start position:0% +when it after at the end of elimination + + + align:start position:0% +when it after at the end of elimination +and so so there are bases for the row + + align:start position:0% +and so so there are bases for the row + + + align:start position:0% +and so so there are bases for the row +space which is + + align:start position:0% +space which is + + + align:start position:0% +space which is +two-dimensional and the columns the + + align:start position:0% +two-dimensional and the columns the + + + align:start position:0% +two-dimensional and the columns the +first two so the first two columns here + + align:start position:0% +first two so the first two columns here + + + align:start position:0% +first two so the first two columns here +are that's the destination that's the + + align:start position:0% +are that's the destination that's the + + + align:start position:0% +are that's the destination that's the +goal of elimination to get these ones + + align:start position:0% +goal of elimination to get these ones + + + align:start position:0% +goal of elimination to get these ones +and zeros so they tell us that these two + + align:start position:0% +and zeros so they tell us that these two + + + align:start position:0% +and zeros so they tell us that these two +columns were and we'll call those those + + align:start position:0% +columns were and we'll call those those + + + align:start position:0% +columns were and we'll call those those +those are the First Independent columns + + align:start position:0% +those are the First Independent columns + + + align:start position:0% +those are the First Independent columns +these columns are independent of the + + align:start position:0% +these columns are independent of the + + + align:start position:0% +these columns are independent of the +previous ones but the last two columns + + align:start position:0% +previous ones but the last two columns + + + align:start position:0% +previous ones but the last two columns +are combinations of the first two so the + + align:start position:0% +are combinations of the first two so the + + + align:start position:0% +are combinations of the first two so the +column space of this Matrix is the same + + align:start position:0% +column space of this Matrix is the same + + + align:start position:0% +column space of this Matrix is the same +as the column space is sorry has the + + align:start position:0% +as the column space is sorry has the + + + align:start position:0% +as the column space is sorry has the +same + + align:start position:0% +same + + + align:start position:0% +same +same basis the same we we learn about + + align:start position:0% +same basis the same we we learn about + + + align:start position:0% +same basis the same we we learn about +the column space of this Matrix from the + + align:start position:0% +the column space of this Matrix from the + + + align:start position:0% +the column space of this Matrix from the +column space of this one so that's point + + align:start position:0% +column space of this one so that's point + + + align:start position:0% +column space of this one so that's point +two The Columns of + + align:start position:0% +two The Columns of + + + align:start position:0% +two The Columns of +a these first two columns are a basis + + align:start position:0% +a these first two columns are a basis + + + align:start position:0% +a these first two columns are a basis +for the column space of a because they + + align:start position:0% +for the column space of a because they + + + align:start position:0% +for the column space of a because they +became clearly the basis when we went to + + align:start position:0% +became clearly the basis when we went to + + + align:start position:0% +became clearly the basis when we went to +Z and finally the null space if we want + + align:start position:0% +Z and finally the null space if we want + + + align:start position:0% +Z and finally the null space if we want +to solve + + align:start position:0% +to solve + + + align:start position:0% +to solve +axal 0 we this makes us this moves us to + + align:start position:0% +axal 0 we this makes us this moves us to + + + align:start position:0% +axal 0 we this makes us this moves us to +solving ZX equals 0 that null space is + + align:start position:0% +solving ZX equals 0 that null space is + + + align:start position:0% +solving ZX equals 0 that null space is +null meaning zero and that that on the + + align:start position:0% +null meaning zero and that that on the + + + align:start position:0% +null meaning zero and that that on the +right hand side so to solve ZX equals + + align:start position:0% +right hand side so to solve ZX equals + + + align:start position:0% +right hand side so to solve ZX equals +zero uh is easy as and we'll do it in a + + align:start position:0% +zero uh is easy as and we'll do it in a + + + align:start position:0% +zero uh is easy as and we'll do it in a +minute and that will be the same + + align:start position:0% +minute and that will be the same + + + align:start position:0% +minute and that will be the same +Solutions as ax equals z so that's + + align:start position:0% +Solutions as ax equals z so that's + + + align:start position:0% +Solutions as ax equals z so that's +that's what elimination it chieves the + + align:start position:0% +that's what elimination it chieves the + + + align:start position:0% +that's what elimination it chieves the +uh these sub these subspaces have move + + align:start position:0% +uh these sub these subspaces have move + + + align:start position:0% +uh these sub these subspaces have move +in a simple one simple form or connected + + align:start position:0% +in a simple one simple form or connected + + + align:start position:0% +in a simple one simple form or connected +in a nice way from A to Z okay ready for + + align:start position:0% +in a nice way from A to Z okay ready for + + + align:start position:0% +in a nice way from A to Z okay ready for +the next slide yeah all right and I make + + align:start position:0% +the next slide yeah all right and I make + + + align:start position:0% +the next slide yeah all right and I make +it + + align:start position:0% + + + + align:start position:0% + +happen oh okay and now my new point is + + align:start position:0% +happen oh okay and now my new point is + + + align:start position:0% +happen oh okay and now my new point is +to see that elimination process which is + + align:start position:0% +to see that elimination process which is + + + align:start position:0% +to see that elimination process which is +has been taught in linear algebra for + + align:start position:0% +has been taught in linear algebra for + + + align:start position:0% +has been taught in linear algebra for +quite a long time I want to see it this + + align:start position:0% +quite a long time I want to see it this + + + align:start position:0% +quite a long time I want to see it this +step from the a that we started with to + + align:start position:0% +step from the a that we started with to + + + align:start position:0% +step from the a that we started with to +the elimination Matrix that we ended + + align:start position:0% +the elimination Matrix that we ended + + + align:start position:0% +the elimination Matrix that we ended +with tells me that this original Matrix + + align:start position:0% +with tells me that this original Matrix + + + align:start position:0% +with tells me that this original Matrix +factors into a column Matrix times a row + + align:start position:0% +factors into a column Matrix times a row + + + align:start position:0% +factors into a column Matrix times a row +Matrix C time R that's a that'll be then + + align:start position:0% +Matrix C time R that's a that'll be then + + + align:start position:0% +Matrix C time R that's a that'll be then +the first factorization in the linear + + align:start position:0% +the first factorization in the linear + + + align:start position:0% +the first factorization in the linear +algebra textbook it comes + + align:start position:0% +algebra textbook it comes + + + align:start position:0% +algebra textbook it comes +first and then the great factorizations + + align:start position:0% +first and then the great factorizations + + + align:start position:0% +first and then the great factorizations +of linear algebra like igen values and + + align:start position:0% +of linear algebra like igen values and + + + align:start position:0% +of linear algebra like igen values and +singular values are build out of this so + + align:start position:0% +singular values are build out of this so + + + align:start position:0% +singular values are build out of this so +but this is a factorization every Matrix + + align:start position:0% +but this is a factorization every Matrix + + + align:start position:0% +but this is a factorization every Matrix +a factors by doing that elimination into + + align:start position:0% +a factors by doing that elimination into + + + align:start position:0% +a factors by doing that elimination into +uh the column Matrix it has two + + align:start position:0% +uh the column Matrix it has two + + + align:start position:0% +uh the column Matrix it has two +independent columns just as a has and it + + align:start position:0% +independent columns just as a has and it + + + align:start position:0% +independent columns just as a has and it +has two independent rows just as a has + + align:start position:0% +has two independent rows just as a has + + + align:start position:0% +has two independent rows just as a has +and what does that tell us that tells us + + align:start position:0% +and what does that tell us that tells us + + + align:start position:0% +and what does that tell us that tells us +the two two equaling two there that the + + align:start position:0% +the two two equaling two there that the + + + align:start position:0% +the two two equaling two there that the +column Rank and the row rank are the + + align:start position:0% +column Rank and the row rank are the + + + align:start position:0% +column Rank and the row rank are the +same which is really the first wonderful + + align:start position:0% +same which is really the first wonderful + + + align:start position:0% +same which is really the first wonderful +fact in linear algebra that if I take + + align:start position:0% +fact in linear algebra that if I take + + + align:start position:0% +fact in linear algebra that if I take +any Matrix and if you just glance at + + align:start position:0% +any Matrix and if you just glance at + + + align:start position:0% +any Matrix and if you just glance at +that you can't see how many rows are + + align:start position:0% +that you can't see how many rows are + + + align:start position:0% +that you can't see how many rows are +independent how many columns are + + align:start position:0% +independent how many columns are + + + align:start position:0% +independent how many columns are +independent but the number is two in + + align:start position:0% +independent but the number is two in + + + align:start position:0% +independent but the number is two in +both cases always equal okay now I have + + align:start position:0% +both cases always equal okay now I have + + + align:start position:0% +both cases always equal okay now I have +to + + align:start position:0% +to + + + align:start position:0% +to +explain use Matrix notation to say what + + align:start position:0% +explain use Matrix notation to say what + + + align:start position:0% +explain use Matrix notation to say what +that R Matrix is okay so I start with a + + align:start position:0% +that R Matrix is okay so I start with a + + + align:start position:0% +that R Matrix is okay so I start with a +and I'm all I'll always use little r for + + align:start position:0% +and I'm all I'll always use little r for + + + align:start position:0% +and I'm all I'll always use little r for +the rank the number of independent + + align:start position:0% +the rank the number of independent + + + align:start position:0% +the rank the number of independent +columns and you remember that those go + + align:start position:0% +columns and you remember that those go + + + align:start position:0% +columns and you remember that those go +into C so I'm just able to tell you what + + align:start position:0% +into C so I'm just able to tell you what + + + align:start position:0% +into C so I'm just able to tell you what +the r factor + + align:start position:0% +the r factor + + + align:start position:0% +the r factor +is so that's the maybe the a + + align:start position:0% +is so that's the maybe the a + + + align:start position:0% +is so that's the maybe the a +key idea here that it's not not usually + + align:start position:0% +key idea here that it's not not usually + + + align:start position:0% +key idea here that it's not not usually +in textbooks what is that R well it + + align:start position:0% +in textbooks what is that R well it + + + align:start position:0% +in textbooks what is that R well it +starts with the identity Matrix and then + + align:start position:0% +starts with the identity Matrix and then + + + align:start position:0% +starts with the identity Matrix and then +it has a matrix F that that accounts for + + align:start position:0% +it has a matrix F that that accounts for + + + align:start position:0% +it has a matrix F that that accounts for +the dependent columns so the identity + + align:start position:0% +the dependent columns so the identity + + + align:start position:0% +the dependent columns so the identity +Matrix is sitting in the in the columns + + align:start position:0% +Matrix is sitting in the in the columns + + + align:start position:0% +Matrix is sitting in the in the columns +that are independent in a the first the + + align:start position:0% +that are independent in a the first the + + + align:start position:0% +that are independent in a the first the +first uh uh L R + + align:start position:0% +first uh uh L R + + + align:start position:0% +first uh uh L R +columns independent columns and then the + + align:start position:0% +columns independent columns and then the + + + align:start position:0% +columns independent columns and then the +F + + align:start position:0% +F + + + align:start position:0% +F +Matrix so the F Matrix the matrices + + align:start position:0% +Matrix so the F Matrix the matrices + + + align:start position:0% +Matrix so the F Matrix the matrices +there are dependent on the columns in C + + align:start position:0% +there are dependent on the columns in C + + + align:start position:0% +there are dependent on the columns in C +and that tells us that they're + + align:start position:0% +and that tells us that they're + + + align:start position:0% +and that tells us that they're +combinations so so what's what's there + + align:start position:0% +combinations so so what's what's there + + + align:start position:0% +combinations so so what's what's there +is uh those those columns of of the + + align:start position:0% +is uh those those columns of of the + + + align:start position:0% +is uh those those columns of of the +Matrix a have the form C * F so f is the + + align:start position:0% +Matrix a have the form C * F so f is the + + + align:start position:0% +Matrix a have the form C * F so f is the +Matrix that makes this correct and + + align:start position:0% +Matrix that makes this correct and + + + align:start position:0% +Matrix that makes this correct and +annoyingly + + align:start position:0% +annoyingly + + + align:start position:0% +annoyingly +there we may need to re reorder The + + align:start position:0% +there we may need to re reorder The + + + align:start position:0% +there we may need to re reorder The +Columns because in my nice example the + + align:start position:0% +Columns because in my nice example the + + + align:start position:0% +Columns because in my nice example the +independent columns came first columns + + align:start position:0% +independent columns came first columns + + + align:start position:0% +independent columns came first columns +one and two but I could if I move those + + align:start position:0% +one and two but I could if I move those + + + align:start position:0% +one and two but I could if I move those +off to the right then I need to get them + + align:start position:0% +off to the right then I need to get them + + + align:start position:0% +off to the right then I need to get them +back to the left again for my nice + + align:start position:0% +back to the left again for my nice + + + align:start position:0% +back to the left again for my nice +picture and it's that permutation P that + + align:start position:0% +picture and it's that permutation P that + + + align:start position:0% +picture and it's that permutation P that +does it don't pay a lot of attention to + + align:start position:0% +does it don't pay a lot of attention to + + + align:start position:0% +does it don't pay a lot of attention to +P here's the important part the the + + align:start position:0% +P here's the important part the the + + + align:start position:0% +P here's the important part the the +independent columns and then The Matrix + + align:start position:0% +independent columns and then The Matrix + + + align:start position:0% +independent columns and then The Matrix +that tells us how to get the dependent + + align:start position:0% +that tells us how to get the dependent + + + align:start position:0% +that tells us how to get the dependent +columns from the Independent columns by + + align:start position:0% +columns from the Independent columns by + + + align:start position:0% +columns from the Independent columns by +multiplying by F okay so that's the + + align:start position:0% +multiplying by F okay so that's the + + + align:start position:0% +multiplying by F okay so that's the +that's the factorization and now I want + + align:start position:0% +that's the factorization and now I want + + + align:start position:0% +that's the factorization and now I want +to use it oh I I did an example that + + align:start position:0% +to use it oh I I did an example that + + + align:start position:0% +to use it oh I I did an example that +involves P that requires a permutation + + align:start position:0% +involves P that requires a permutation + + + align:start position:0% +involves P that requires a permutation +yeah it's a good example to look at so + + align:start position:0% +yeah it's a good example to look at so + + + align:start position:0% +yeah it's a good example to look at so +there's our original Matrix a and if I + + align:start position:0% +there's our original Matrix a and if I + + + align:start position:0% +there's our original Matrix a and if I +look for the independent columns well + + align:start position:0% +look for the independent columns well + + + align:start position:0% +look for the independent columns well +column one is great okay column two is + + align:start position:0% +column one is great okay column two is + + + align:start position:0% +column one is great okay column two is +not so great because it's dependent it's + + align:start position:0% +not so great because it's dependent it's + + + align:start position:0% +not so great because it's dependent it's +just two * column 1 nothing new in + + align:start position:0% +just two * column 1 nothing new in + + + align:start position:0% +just two * column 1 nothing new in +column two so that's a dependent column + + align:start position:0% +column two so that's a dependent column + + + align:start position:0% +column two so that's a dependent column +and then column three we do have an + + align:start position:0% +and then column three we do have an + + + align:start position:0% +and then column three we do have an +independent column so the two + + align:start position:0% +independent column so the two + + + align:start position:0% +independent column so the two +independent columns go into C and that's + + align:start position:0% +independent columns go into C and that's + + + align:start position:0% +independent columns go into C and that's +the Matrix that multiplies R and you you + + align:start position:0% +the Matrix that multiplies R and you you + + + align:start position:0% +the Matrix that multiplies R and you you +see how a permutation May in this form + + align:start position:0% +see how a permutation May in this form + + + align:start position:0% +see how a permutation May in this form +the + + align:start position:0% +the + + + align:start position:0% +the +identity is over over on the fully on + + align:start position:0% +identity is over over on the fully on + + + align:start position:0% +identity is over over on the fully on +the left side that this has columns one + + align:start position:0% +the left side that this has columns one + + + align:start position:0% +the left side that this has columns one +and two as special but it's the + + align:start position:0% +and two as special but it's the + + + align:start position:0% +and two as special but it's the +permutation then that makes columns one + + align:start position:0% +permutation then that makes columns one + + + align:start position:0% +permutation then that makes columns one +and put puts them into columns one and + + align:start position:0% +and put puts them into columns one and + + + align:start position:0% +and put puts them into columns one and +three which are really the special + + align:start position:0% +three which are really the special + + + align:start position:0% +three which are really the special +independent columns for a that and that + + align:start position:0% +independent columns for a that and that + + + align:start position:0% +independent columns for a that and that +okay so that's just a word about p and + + align:start position:0% +okay so that's just a word about p and + + + align:start position:0% +okay so that's just a word about p and +from now on I'll try to forget there + + align:start position:0% +from now on I'll try to forget there + + + align:start position:0% +from now on I'll try to forget there +there might be a p Matrix okay if + + align:start position:0% +there might be a p Matrix okay if + + + align:start position:0% +there might be a p Matrix okay if +essential + + align:start position:0% +essential + + + align:start position:0% +essential +information what what does elimination + + align:start position:0% +information what what does elimination + + + align:start position:0% +information what what does elimination +accomplish after all these thousands of + + align:start position:0% +accomplish after all these thousands of + + + align:start position:0% +accomplish after all these thousands of +years that was vented in China uh more + + align:start position:0% +years that was vented in China uh more + + + align:start position:0% +years that was vented in China uh more +than 2,000 years ago the the information + + align:start position:0% +than 2,000 years ago the the information + + + align:start position:0% +than 2,000 years ago the the information +it is it tells us which columns are + + align:start position:0% +it is it tells us which columns are + + + align:start position:0% +it is it tells us which columns are +independent then there in the identity + + align:start position:0% +independent then there in the identity + + + align:start position:0% +independent then there in the identity +Matrix shows up in those columns and it + + align:start position:0% +Matrix shows up in those columns and it + + + align:start position:0% +Matrix shows up in those columns and it +also tells us the Matrix the how the + + align:start position:0% +also tells us the Matrix the how the + + + align:start position:0% +also tells us the Matrix the how the +dependent ones come from the IND dep + + align:start position:0% +dependent ones come from the IND dep + + + align:start position:0% +dependent ones come from the IND dep +dependent ones you multiply C by some + + align:start position:0% +dependent ones you multiply C by some + + + align:start position:0% +dependent ones you multiply C by some +Matrix F which elimination finds so + + align:start position:0% +Matrix F which elimination finds so + + + align:start position:0% +Matrix F which elimination finds so +elimination finds all these matrices as + + align:start position:0% +elimination finds all these matrices as + + + align:start position:0% +elimination finds all these matrices as +we saw in that example and now I want to + + align:start position:0% +we saw in that example and now I want to + + + align:start position:0% +we saw in that example and now I want to +use that to see what that Matrix right + + align:start position:0% +use that to see what that Matrix right + + + align:start position:0% +use that to see what that Matrix right +down here with with a slide or two uh + + align:start position:0% +down here with with a slide or two uh + + + align:start position:0% +down here with with a slide or two uh +just exactly what steps of elimination + + align:start position:0% +just exactly what steps of elimination + + + align:start position:0% +just exactly what steps of elimination +are are allowed so elimination has three + + align:start position:0% +are are allowed so elimination has three + + + align:start position:0% +are are allowed so elimination has three +simple steps and all of them are rever + + align:start position:0% +simple steps and all of them are rever + + + align:start position:0% +simple steps and all of them are rever +reversible uh like exchange two rows + + align:start position:0% +reversible uh like exchange two rows + + + align:start position:0% +reversible uh like exchange two rows +because if I had a zero on the top left + + align:start position:0% +because if I had a zero on the top left + + + align:start position:0% +because if I had a zero on the top left +corner I wouldn't want that so I would + + align:start position:0% +corner I wouldn't want that so I would + + + align:start position:0% +corner I wouldn't want that so I would +do a row exchange I I divide I can + + align:start position:0% +do a row exchange I I divide I can + + + align:start position:0% +do a row exchange I I divide I can +divide a row by a number if I had a two + + align:start position:0% +divide a row by a number if I had a two + + + align:start position:0% +divide a row by a number if I had a two +in the top left corner I'd rather have a + + align:start position:0% +in the top left corner I'd rather have a + + + align:start position:0% +in the top left corner I'd rather have a +one so I just divide that row by two and + + align:start position:0% +one so I just divide that row by two and + + + align:start position:0% +one so I just divide that row by two and +this is the main step to subtract a + + align:start position:0% +this is the main step to subtract a + + + align:start position:0% +this is the main step to subtract a +multiple of one row from another row + + align:start position:0% +multiple of one row from another row + + + align:start position:0% +multiple of one row from another row +that doesn't change the row space just + + align:start position:0% +that doesn't change the row space just + + + align:start position:0% +that doesn't change the row space just +changes the the rows themselves but + + align:start position:0% +changes the the rows themselves but + + + align:start position:0% +changes the the rows themselves but +their combinations have not changed all + + align:start position:0% +their combinations have not changed all + + + align:start position:0% +their combinations have not changed all +these uh three three steps are + + align:start position:0% +these uh three three steps are + + + align:start position:0% +these uh three three steps are +reversible if I exchange two rows I + + align:start position:0% +reversible if I exchange two rows I + + + align:start position:0% +reversible if I exchange two rows I +could exchange them again and I'd be + + align:start position:0% +could exchange them again and I'd be + + + align:start position:0% +could exchange them again and I'd be +back to where I started if I divide by + + align:start position:0% +back to where I started if I divide by + + + align:start position:0% +back to where I started if I divide by +seven then I could multiply by seven or + + align:start position:0% +seven then I could multiply by seven or + + + align:start position:0% +seven then I could multiply by seven or +divide by + + align:start position:0% +divide by + + + align:start position:0% +divide by +17th uh so so this is what + + align:start position:0% +17th uh so so this is what + + + align:start position:0% +17th uh so so this is what +is + + align:start position:0% + + + + align:start position:0% + +always if you get this topic in a linear + + align:start position:0% +always if you get this topic in a linear + + + align:start position:0% +always if you get this topic in a linear +algebra course this is the Matrix that + + align:start position:0% +algebra course this is the Matrix that + + + align:start position:0% +algebra course this is the Matrix that +you get to and what I want to do is + + align:start position:0% +you get to and what I want to do is + + + align:start position:0% +you get to and what I want to do is +understand that + + align:start position:0% +understand that + + + align:start position:0% +understand that +Matrix uh as coming as entering a + + align:start position:0% +Matrix uh as coming as entering a + + + align:start position:0% +Matrix uh as coming as entering a +factorization of a so I can use + + align:start position:0% +factorization of a so I can use + + + align:start position:0% +factorization of a so I can use +elimination this is so that but that's + + align:start position:0% +elimination this is so that but that's + + + align:start position:0% +elimination this is so that but that's +the picture of what I get as we saw all + + align:start position:0% +the picture of what I get as we saw all + + + align:start position:0% +the picture of what I get as we saw all +right so so that's this is the key fact + + align:start position:0% +right so so that's this is the key fact + + + align:start position:0% +right so so that's this is the key fact +we're we're sort of like ending the work + + align:start position:0% +we're we're sort of like ending the work + + + align:start position:0% +we're we're sort of like ending the work +of + + align:start position:0% +of + + + align:start position:0% +of +elimination it can get it'll find out + + align:start position:0% +elimination it can get it'll find out + + + align:start position:0% +elimination it can get it'll find out +how many independent columns there are + + align:start position:0% +how many independent columns there are + + + align:start position:0% +how many independent columns there are +how many independent rows and that + + align:start position:0% +how many independent rows and that + + + align:start position:0% +how many independent rows and that +numberb is the same because we're + + align:start position:0% +numberb is the same because we're + + + align:start position:0% +numberb is the same because we're +looking at the identity Matrix and then + + align:start position:0% +looking at the identity Matrix and then + + + align:start position:0% +looking at the identity Matrix and then +we we see how this is the simplification + + align:start position:0% +we we see how this is the simplification + + + align:start position:0% +we we see how this is the simplification +of the of the Matrix a okay so what can + + align:start position:0% +of the of the Matrix a okay so what can + + + align:start position:0% +of the of the Matrix a okay so what can +we do what do we learn from that oh so I + + align:start position:0% +we do what do we learn from that oh so I + + + align:start position:0% +we do what do we learn from that oh so I +I I put in a few slides just to say how + + align:start position:0% +I I put in a few slides just to say how + + + align:start position:0% +I I put in a few slides just to say how +would you code + + align:start position:0% +would you code + + + align:start position:0% +would you code +elimination uh and it's really neat it's + + align:start position:0% +elimination uh and it's really neat it's + + + align:start position:0% +elimination uh and it's really neat it's +so it's how how does elimination work + + align:start position:0% +so it's how how does elimination work + + + align:start position:0% +so it's how how does elimination work +well column by column so suppose we've + + align:start position:0% +well column by column so suppose we've + + + align:start position:0% +well column by column so suppose we've +got K columns done and we're ready for + + align:start position:0% +got K columns done and we're ready for + + + align:start position:0% +got K columns done and we're ready for +the next one like we may have seven + + align:start position:0% +the next one like we may have seven + + + align:start position:0% +the next one like we may have seven +columns taken care of we're ready for + + align:start position:0% +columns taken care of we're ready for + + + align:start position:0% +columns taken care of we're ready for +column eight so this is what column 7 + + align:start position:0% +column eight so this is what column 7 + + + align:start position:0% +column eight so this is what column 7 +looks like because it's that same if + + align:start position:0% +looks like because it's that same if + + + align:start position:0% +looks like because it's that same if +f0000 P picture it's those seven columns + + align:start position:0% +f0000 P picture it's those seven columns + + + align:start position:0% +f0000 P picture it's those seven columns +are finished and now here's one and I + + align:start position:0% +are finished and now here's one and I + + + align:start position:0% +are finished and now here's one and I +let U be the upper part upper half and L + + align:start position:0% +let U be the upper part upper half and L + + + align:start position:0% +let U be the upper part upper half and L +be the lower half U is the half that's + + align:start position:0% +be the lower half U is the half that's + + + align:start position:0% +be the lower half U is the half that's +or the part that's that's of the new + + align:start position:0% +or the part that's that's of the new + + + align:start position:0% +or the part that's that's of the new +column that's that goes up at the top + + align:start position:0% +column that's that goes up at the top + + + align:start position:0% +column that's that goes up at the top +and even with the zeros goes l + + align:start position:0% +and even with the zeros goes l + + + align:start position:0% +and even with the zeros goes l +so what what do we do in what does + + align:start position:0% +so what what do we do in what does + + + align:start position:0% +so what what do we do in what does +elimination do with this next column so + + align:start position:0% +elimination do with this next column so + + + align:start position:0% +elimination do with this next column so +I'm describing elimination again in a + + align:start position:0% +I'm describing elimination again in a + + + align:start position:0% +I'm describing elimination again in a +way you would code it uh I come to the + + align:start position:0% +way you would code it uh I come to the + + + align:start position:0% +way you would code it uh I come to the +new column all right and I want to know + + align:start position:0% +new column all right and I want to know + + + align:start position:0% +new column all right and I want to know +I'm I want something a picture like this + + align:start position:0% +I'm I want something a picture like this + + + align:start position:0% +I'm I want something a picture like this +with K moved up to k + + + align:start position:0% +with K moved up to k + + + + align:start position:0% +with K moved up to k + +one okay it's a lot to give you the all + + align:start position:0% +one okay it's a lot to give you the all + + + align:start position:0% +one okay it's a lot to give you the all +the details of elimination but there + + align:start position:0% +the details of elimination but there + + + align:start position:0% +the details of elimination but there +there everybody catches on to them by + + align:start position:0% +there everybody catches on to them by + + + align:start position:0% +there everybody catches on to them by +doing a few either on a computer or or + + align:start position:0% +doing a few either on a computer or or + + + align:start position:0% +doing a few either on a computer or or +by hand okay so our question is this is + + align:start position:0% +by hand okay so our question is this is + + + align:start position:0% +by hand okay so our question is this is +I want a picture like this after one + + align:start position:0% +I want a picture like this after one + + + align:start position:0% +I want a picture like this after one +with one more column in it and the + + align:start position:0% +with one more column in it and the + + + align:start position:0% +with one more column in it and the +question is is this new column going to + + align:start position:0% +question is is this new column going to + + + align:start position:0% +question is is this new column going to +feed into the identity well if if L is + + align:start position:0% +feed into the identity well if if L is + + + align:start position:0% +feed into the identity well if if L is +the zero Vector if if it's all if it's + + align:start position:0% +the zero Vector if if it's all if it's + + + align:start position:0% +the zero Vector if if it's all if it's +all zeros below the pivot then uh then + + align:start position:0% +all zeros below the pivot then uh then + + + align:start position:0% +all zeros below the pivot then uh then +this U will go along with f because we + + align:start position:0% +this U will go along with f because we + + + align:start position:0% +this U will go along with f because we +we're not getting anything new the we + + align:start position:0% +we're not getting anything new the we + + + align:start position:0% +we're not getting anything new the we +still have K nonzero rows so at this + + align:start position:0% +still have K nonzero rows so at this + + + align:start position:0% +still have K nonzero rows so at this +point we have K nonzero rows or or let's + + align:start position:0% +point we have K nonzero rows or or let's + + + align:start position:0% +point we have K nonzero rows or or let's +say whatever number we whatever number + + align:start position:0% +say whatever number we whatever number + + + align:start position:0% +say whatever number we whatever number +we have and if L is zero then the new + + align:start position:0% +we have and if L is zero then the new + + + align:start position:0% +we have and if L is zero then the new +column is dependent on the old columns + + align:start position:0% +column is dependent on the old columns + + + align:start position:0% +column is dependent on the old columns +and doesn't add anything new uh so so if + + align:start position:0% +and doesn't add anything new uh so so if + + + align:start position:0% +and doesn't add anything new uh so so if +again I'll just repeat if L is the zero + + align:start position:0% +again I'll just repeat if L is the zero + + + align:start position:0% +again I'll just repeat if L is the zero +Vector if I'm all zeros here then that + + align:start position:0% +Vector if I'm all zeros here then that + + + align:start position:0% +Vector if I'm all zeros here then that +will go in with f if it's not all zeros + + align:start position:0% +will go in with f if it's not all zeros + + + align:start position:0% +will go in with f if it's not all zeros +there then I then I'm going to do some + + align:start position:0% +there then I then I'm going to do some + + + align:start position:0% +there then I then I'm going to do some +row exchanges and some pivot steps uh I + + align:start position:0% +row exchanges and some pivot steps uh I + + + align:start position:0% +row exchanges and some pivot steps uh I +can I what I can do is clear out all of + + align:start position:0% +can I what I can do is clear out all of + + + align:start position:0% +can I what I can do is clear out all of +L except for one non zero that'll be the + + align:start position:0% +L except for one non zero that'll be the + + + align:start position:0% +L except for one non zero that'll be the +new pivot maybe the next I hope hope the + + align:start position:0% +new pivot maybe the next I hope hope the + + + align:start position:0% +new pivot maybe the next I hope hope the +next + + align:start position:0% +next + + + align:start position:0% +next +uh so if L is all Zer the new column is + + align:start position:0% +uh so if L is all Zer the new column is + + + align:start position:0% +uh so if L is all Zer the new column is +joins with f if L is not all zero the + + align:start position:0% +joins with f if L is not all zero the + + + align:start position:0% +joins with f if L is not all zero the +new column is independent so we we've + + align:start position:0% +new column is independent so we we've + + + align:start position:0% +new column is independent so we we've +hit another independent column and we uh + + align:start position:0% +hit another independent column and we uh + + + align:start position:0% +hit another independent column and we uh +do + + align:start position:0% +do + + + align:start position:0% +do +elimination on that column to to get it + + align:start position:0% +elimination on that column to to get it + + + align:start position:0% +elimination on that column to to get it +into the right form to be ready for + + align:start position:0% +into the right form to be ready for + + + align:start position:0% +into the right form to be ready for +column the column K plus 2 is coming + + align:start position:0% +column the column K plus 2 is coming + + + align:start position:0% +column the column K plus 2 is coming +next I I don't you the way to learn the + + align:start position:0% +next I I don't you the way to learn the + + + align:start position:0% +next I I don't you the way to learn the +steps of elimination is to is to do them + + align:start position:0% +steps of elimination is to is to do them + + + align:start position:0% +steps of elimination is to is to do them +on a few matrices and I won't do more + + align:start position:0% +on a few matrices and I won't do more + + + align:start position:0% +on a few matrices and I won't do more +here okay so just but but I want you to + + align:start position:0% +here okay so just but but I want you to + + + align:start position:0% +here okay so just but but I want you to +know what is elimination telling us so + + align:start position:0% +know what is elimination telling us so + + + align:start position:0% +know what is elimination telling us so +the result of elimination tells us which + + align:start position:0% +the result of elimination tells us which + + + align:start position:0% +the result of elimination tells us which +are the First Independent columns + + align:start position:0% +are the First Independent columns + + + align:start position:0% +are the First Independent columns +they're the ones that end up with a one + + align:start position:0% +they're the ones that end up with a one + + + align:start position:0% +they're the ones that end up with a one +with the identity Matrix there's and + + align:start position:0% +with the identity Matrix there's and + + + align:start position:0% +with the identity Matrix there's and +they're the and those first + + align:start position:0% +they're the and those first + + + align:start position:0% +they're the and those first +columns back in a are The Columns of C + + align:start position:0% +columns back in a are The Columns of C + + + align:start position:0% +columns back in a are The Columns of C +the row space is not change those + + align:start position:0% +the row space is not change those + + + align:start position:0% +the row space is not change those +operations of elimination don't change + + align:start position:0% +operations of elimination don't change + + + align:start position:0% +operations of elimination don't change +the row space but but they give us a + + align:start position:0% +the row space but but they give us a + + + align:start position:0% +the row space but but they give us a +nice picture so + + align:start position:0% +nice picture so + + + align:start position:0% +nice picture so +so so the th this thing is this slide is + + align:start position:0% +so so the th this thing is this slide is + + + align:start position:0% +so so the th this thing is this slide is +really telling us that the result of + + align:start position:0% +really telling us that the result of + + + align:start position:0% +really telling us that the result of +elimination is the identity Matrix the C + + align:start position:0% +elimination is the identity Matrix the C + + + align:start position:0% +elimination is the identity Matrix the C +Matrix + + align:start position:0% +Matrix + + + align:start position:0% +Matrix +and zeros in in the low in the lower + + align:start position:0% +and zeros in in the low in the lower + + + align:start position:0% +and zeros in in the low in the lower +rows we can see how many rows are + + align:start position:0% +rows we can see how many rows are + + + align:start position:0% +rows we can see how many rows are +independent by how many the the nonzero + + align:start position:0% +independent by how many the the nonzero + + + align:start position:0% +independent by how many the the nonzero +rows are all independent because they + + align:start position:0% +rows are all independent because they + + + align:start position:0% +rows are all independent because they +that identity is is makes that so so + + align:start position:0% +that identity is is makes that so so + + + align:start position:0% +that identity is is makes that so so +that's that's where we are uh at the end + + align:start position:0% +that's that's where we are uh at the end + + + align:start position:0% +that's that's where we are uh at the end +of + + align:start position:0% +of + + + align:start position:0% +of +elimination we have little r the rank + + align:start position:0% +elimination we have little r the rank + + + align:start position:0% +elimination we have little r the rank +then the the the dimension of of the row + + align:start position:0% +then the the the dimension of of the row + + + align:start position:0% +then the the the dimension of of the row +space the dimension of the column space + + align:start position:0% +space the dimension of the column space + + + align:start position:0% +space the dimension of the column space +is little r and we can + + align:start position:0% +is little r and we can + + + align:start position:0% +is little r and we can +see the basis for it in C and then we + + align:start position:0% +see the basis for it in C and then we + + + align:start position:0% +see the basis for it in C and then we +also have that Matrix F so we got to C + + align:start position:0% +also have that Matrix F so we got to C + + + align:start position:0% +also have that Matrix F so we got to C +and F and elimination + + align:start position:0% +and F and elimination + + + align:start position:0% +and F and elimination +finished by giving us a picture of the + + align:start position:0% +finished by giving us a picture of the + + + align:start position:0% +finished by giving us a picture of the +original Matrix much simplified lots of + + align:start position:0% +original Matrix much simplified lots of + + + align:start position:0% +original Matrix much simplified lots of +zeros okay oh all right and let's just + + align:start position:0% +zeros okay oh all right and let's just + + + align:start position:0% +zeros okay oh all right and let's just +apply it so here we go you this is the + + align:start position:0% +apply it so here we go you this is the + + + align:start position:0% +apply it so here we go you this is the +payoff do you rem remember our Matrix + + align:start position:0% +payoff do you rem remember our Matrix + + + align:start position:0% +payoff do you rem remember our Matrix +that had 13 27 that was my example at + + align:start position:0% +that had 13 27 that was my example at + + + align:start position:0% +that had 13 27 that was my example at +the very beginning but it had some + + align:start position:0% +the very beginning but it had some + + + align:start position:0% +the very beginning but it had some +combination of those two rows so this + + align:start position:0% +combination of those two rows so this + + + align:start position:0% +combination of those two rows so this +third row I've just forgotten because it + + align:start position:0% +third row I've just forgotten because it + + + align:start position:0% +third row I've just forgotten because it +turned out to be a combination of these + + align:start position:0% +turned out to be a combination of these + + + align:start position:0% +turned out to be a combination of these +and and gave us a row of zeros so these + + align:start position:0% +and and gave us a row of zeros so these + + + align:start position:0% +and and gave us a row of zeros so these +are the two equations in axal 0 we're + + align:start position:0% +are the two equations in axal 0 we're + + + align:start position:0% +are the two equations in axal 0 we're +looking for the n space this is what + + align:start position:0% +looking for the n space this is what + + + align:start position:0% +looking for the n space this is what +elimination is tells us how what how to + + align:start position:0% +elimination is tells us how what how to + + + align:start position:0% +elimination is tells us how what how to +do it's a step to simplify the equations + + align:start position:0% +do it's a step to simplify the equations + + + align:start position:0% +do it's a step to simplify the equations +from that messy looking two two + + align:start position:0% +from that messy looking two two + + + align:start position:0% +from that messy looking two two +equations to this simple pair of + + align:start position:0% +equations to this simple pair of + + + align:start position:0% +equations to this simple pair of +equations where the one and the one are + + align:start position:0% +equations where the one and the one are + + + align:start position:0% +equations where the one and the one are +in columns one and two and and nice + + align:start position:0% +in columns one and two and and nice + + + align:start position:0% +in columns one and two and and nice +numbers and the point is you can solve + + align:start position:0% +numbers and the point is you can solve + + + align:start position:0% +numbers and the point is you can solve +those without taking a linear out of a + + align:start position:0% +those without taking a linear out of a + + + align:start position:0% +those without taking a linear out of a +course but still take the course okay so + + align:start position:0% +course but still take the course okay so + + + align:start position:0% +course but still take the course okay so +I'm looking for solutions to that okay + + align:start position:0% +I'm looking for solutions to that okay + + + align:start position:0% +I'm looking for solutions to that okay +so I could find a solution if I said X3 + + align:start position:0% +so I could find a solution if I said X3 + + + align:start position:0% +so I could find a solution if I said X3 +to be one and X4 to be zero so X4 is + + align:start position:0% +to be one and X4 to be zero so X4 is + + + align:start position:0% +to be one and X4 to be zero so X4 is +zero that's gone X3 is 1 so X1 + 3 = 0 + + align:start position:0% +zero that's gone X3 is 1 so X1 + 3 = 0 + + + align:start position:0% +zero that's gone X3 is 1 so X1 + 3 = 0 +X2 + 4 = 0 so X1 and X2 are Min -3 and + + align:start position:0% +X2 + 4 = 0 so X1 and X2 are Min -3 and + + + align:start position:0% +X2 + 4 = 0 so X1 and X2 are Min -3 and +-4 and there's the one and the zero did + + align:start position:0% +-4 and there's the one and the zero did + + + align:start position:0% +-4 and there's the one and the zero did +you see that we produce that solution + + align:start position:0% +you see that we produce that solution + + + align:start position:0% +you see that we produce that solution +just by I it jumps out and let's see how + + align:start position:0% +just by I it jumps out and let's see how + + + align:start position:0% +just by I it jumps out and let's see how +the next one jumps out so we suppose we + + align:start position:0% +the next one jumps out so we suppose we + + + align:start position:0% +the next one jumps out so we suppose we +take those equations those are the + + align:start position:0% +take those equations those are the + + + align:start position:0% +take those equations those are the +simple form of this horrible horrible + + align:start position:0% +simple form of this horrible horrible + + + align:start position:0% +simple form of this horrible horrible +pair we got that we got it to a very + + align:start position:0% +pair we got that we got it to a very + + + align:start position:0% +pair we got that we got it to a very +simple form and now I want to know + + align:start position:0% +simple form and now I want to know + + + align:start position:0% +simple form and now I want to know +another solution and another different + + align:start position:0% +another solution and another different + + + align:start position:0% +another solution and another different +certainly different one will be to set + + align:start position:0% +certainly different one will be to set + + + align:start position:0% +certainly different one will be to set +X3 equals z so that's gone + + align:start position:0% +X3 equals z so that's gone + + + align:start position:0% +X3 equals z so that's gone +X4 equal to 1 so that's five and six and + + align:start position:0% +X4 equal to 1 so that's five and six and + + + align:start position:0% +X4 equal to 1 so that's five and six and +then I need X1 to be minus 5 and X2 to + + align:start position:0% +then I need X1 to be minus 5 and X2 to + + + align:start position:0% +then I need X1 to be minus 5 and X2 to +be minus 6 to cancel a five and six + + align:start position:0% +be minus 6 to cancel a five and six + + + align:start position:0% +be minus 6 to cancel a five and six +golden solution Simple Solution complete + + align:start position:0% +golden solution Simple Solution complete + + + align:start position:0% +golden solution Simple Solution complete +so I've got two solutions to ax equals z + + align:start position:0% +so I've got two solutions to ax equals z + + + align:start position:0% +so I've got two solutions to ax equals z +and the null space has the right + + align:start position:0% +and the null space has the right + + + align:start position:0% +and the null space has the right +Dimension two and I found a basis for + + align:start position:0% +Dimension two and I found a basis for + + + align:start position:0% +Dimension two and I found a basis for +that space and all other Solutions are + + align:start position:0% +that space and all other Solutions are + + + align:start position:0% +that space and all other Solutions are +combinations of these Simple Solutions + + align:start position:0% +combinations of these Simple Solutions + + + align:start position:0% +combinations of these Simple Solutions +The Simple Solutions have zeros and ones + + align:start position:0% +The Simple Solutions have zeros and ones + + + align:start position:0% +The Simple Solutions have zeros and ones +in the dependent + + align:start position:0% + + + + align:start position:0% + +columns I hope you can just see that + + align:start position:0% +columns I hope you can just see that + + + align:start position:0% +columns I hope you can just see that +after elimination when we get to a + + align:start position:0% +after elimination when we get to a + + + align:start position:0% +after elimination when we get to a +simple form like that it becomes a + + align:start position:0% +simple form like that it becomes a + + + align:start position:0% +simple form like that it becomes a +picnic to solve it the equations are + + align:start position:0% +picnic to solve it the equations are + + + align:start position:0% +picnic to solve it the equations are +easily solved just let X3 = 1 and X4 + + align:start position:0% +easily solved just let X3 = 1 and X4 + + + align:start position:0% +easily solved just let X3 = 1 and X4 +equal 0 and you get an answer let X3 + + align:start position:0% +equal 0 and you get an answer let X3 + + + align:start position:0% +equal 0 and you get an answer let X3 +equal 0 and X4 equal 1 you get another + + align:start position:0% +equal 0 and X4 equal 1 you get another + + + align:start position:0% +equal 0 and X4 equal 1 you get another +answer so so that was that's the point + + align:start position:0% +answer so so that was that's the point + + + align:start position:0% +answer so so that was that's the point +of elimination it's good to make the + + align:start position:0% +of elimination it's good to make the + + + align:start position:0% +of elimination it's good to make the +what was the point of learning this + + align:start position:0% +what was the point of learning this + + + align:start position:0% +what was the point of learning this +process or coding up this process it's + + align:start position:0% +process or coding up this process it's + + + align:start position:0% +process or coding up this process it's +not I have to admit that it's not uh um + + align:start position:0% +not I have to admit that it's not uh um + + + align:start position:0% +not I have to admit that it's not uh um +the most super efficient way to find the + + align:start position:0% +the most super efficient way to find the + + + align:start position:0% +the most super efficient way to find the +solution uh because it involves + + align:start position:0% +solution uh because it involves + + + align:start position:0% +solution uh because it involves +subtraction of rows of from rows + + align:start position:0% +subtraction of rows of from rows + + + align:start position:0% +subtraction of rows of from rows +above and as well as subtraction from + + align:start position:0% +above and as well as subtraction from + + + align:start position:0% +above and as well as subtraction from +rows below so it could be speed it + + align:start position:0% +rows below so it could be speed it + + + align:start position:0% +rows below so it could be speed it +up uh and it usually is for for square + + align:start position:0% +up uh and it usually is for for square + + + align:start position:0% +up uh and it usually is for for square +invertible + + align:start position:0% +invertible + + + align:start position:0% +invertible +matrices for let let me ask you this + + align:start position:0% +matrices for let let me ask you this + + + align:start position:0% +matrices for let let me ask you this +question if I had a square 4x4 + + align:start position:0% +question if I had a square 4x4 + + + align:start position:0% +question if I had a square 4x4 +invertible Matrix what would over here + + align:start position:0% +invertible Matrix what would over here + + + align:start position:0% +invertible Matrix what would over here +what would be the the uh reduced form + + align:start position:0% +what would be the the uh reduced form + + + align:start position:0% +what would be the the uh reduced form +after I do elimination + + align:start position:0% +after I do elimination + + + align:start position:0% +after I do elimination +well it would just be identity identity + + align:start position:0% +well it would just be identity identity + + + align:start position:0% +well it would just be identity identity +the identity Matrix if if I had a 4X for + + align:start position:0% +the identity Matrix if if I had a 4X for + + + align:start position:0% +the identity Matrix if if I had a 4X for +if I have an invertible Matrix + + align:start position:0% +if I have an invertible Matrix + + + align:start position:0% +if I have an invertible Matrix +elimination produces the identity Matrix + + align:start position:0% +elimination produces the identity Matrix + + + align:start position:0% +elimination produces the identity Matrix +so it really goes all the way to + + align:start position:0% +so it really goes all the way to + + + align:start position:0% +so it really goes all the way to +simplifying The Matrix and and you pay a + + align:start position:0% +simplifying The Matrix and and you pay a + + + align:start position:0% +simplifying The Matrix and and you pay a +little price if if to get all the way to + + align:start position:0% +little price if if to get all the way to + + + align:start position:0% +little price if if to get all the way to +the identity Matrix but to see the + + align:start position:0% +the identity Matrix but to see the + + + align:start position:0% +the identity Matrix but to see the +theory it's it's a right thing to do we + + align:start position:0% +theory it's it's a right thing to do we + + + align:start position:0% +theory it's it's a right thing to do we +won't do we wouldn't actually do it we + + align:start position:0% +won't do we wouldn't actually do it we + + + align:start position:0% +won't do we wouldn't actually do it we +would stop at a triangular Matrix and + + align:start position:0% +would stop at a triangular Matrix and + + + align:start position:0% +would stop at a triangular Matrix and +start solving from that point if we had + + align:start position:0% +start solving from that point if we had + + + align:start position:0% +start solving from that point if we had +to pay for the for the for the computer + + align:start position:0% +to pay for the for the for the computer + + + align:start position:0% +to pay for the for the for the computer +time all right and now here I've written + + align:start position:0% +time all right and now here I've written + + + align:start position:0% +time all right and now here I've written +in with Matrix notation what that last + + align:start position:0% +in with Matrix notation what that last + + + align:start position:0% +in with Matrix notation what that last +slide showed you and again what that + + align:start position:0% +slide showed you and again what that + + + align:start position:0% +slide showed you and again what that +last slide showed you is that once you + + align:start position:0% +last slide showed you is that once you + + + align:start position:0% +last slide showed you is that once you +have it have completed elimination it's + + align:start position:0% +have it have completed elimination it's + + + align:start position:0% +have it have completed elimination it's +a cinch to solve a x equals z yeah so so + + align:start position:0% +a cinch to solve a x equals z yeah so so + + + align:start position:0% +a cinch to solve a x equals z yeah so so +we we elimination puts a into that form + + align:start position:0% +we we elimination puts a into that form + + + align:start position:0% +we we elimination puts a into that form +and then the solutions X are in this + + align:start position:0% +and then the solutions X are in this + + + align:start position:0% +and then the solutions X are in this +form and If I multiply that by that I + + align:start position:0% +form and If I multiply that by that I + + + align:start position:0% +form and If I multiply that by that I +get + + align:start position:0% +get + + + align:start position:0% +get +zero so The Columns of X solve ax equals + + align:start position:0% +zero so The Columns of X solve ax equals + + + align:start position:0% +zero so The Columns of X solve ax equals +z I have found the null + + align:start position:0% +z I have found the null + + + align:start position:0% +z I have found the null +space I've computed the n space and + + align:start position:0% +space I've computed the n space and + + + align:start position:0% +space I've computed the n space and +uh what I wanted to do was to show that + + align:start position:0% +uh what I wanted to do was to show that + + + align:start position:0% +uh what I wanted to do was to show that +elimination does its job makes it simple + + align:start position:0% +elimination does its job makes it simple + + + align:start position:0% +elimination does its job makes it simple +it makes the null space jump out you + + align:start position:0% +it makes the null space jump out you + + + align:start position:0% +it makes the null space jump out you +just need the F it comes from + + align:start position:0% +just need the F it comes from + + + align:start position:0% +just need the F it comes from +elimination the possible + + align:start position:0% +elimination the possible + + + align:start position:0% +elimination the possible +permutations and you've got the answer + + align:start position:0% +permutations and you've got the answer + + + align:start position:0% +permutations and you've got the answer +you've got the the x is that solve ax + + align:start position:0% +you've got the the x is that solve ax + + + align:start position:0% +you've got the the x is that solve ax +equals z okay again uh it's not the the + + align:start position:0% +equals z okay again uh it's not the the + + + align:start position:0% +equals z okay again uh it's not the the +code that's used all the time in in + + align:start position:0% +code that's used all the time in in + + + align:start position:0% +code that's used all the time in in +Computing problems in physics or + + align:start position:0% +Computing problems in physics or + + + align:start position:0% +Computing problems in physics or +engineering but it's for math it + + align:start position:0% +engineering but it's for math it + + + align:start position:0% +engineering but it's for math it +elimination completed elimination as + + align:start position:0% +elimination completed elimination as + + + align:start position:0% +elimination completed elimination as +we've done really gets you to the point + + align:start position:0% +we've done really gets you to the point + + + align:start position:0% +we've done really gets you to the point +where you can read off the answer + + align:start position:0% +where you can read off the answer + + + align:start position:0% +where you can read off the answer +okay so that's the point really is to + + align:start position:0% +okay so that's the point really is to + + + align:start position:0% +okay so that's the point really is to +see how far elimination gets + + align:start position:0% +see how far elimination gets + + + align:start position:0% +see how far elimination gets +you okay oh here so here's the comment + + align:start position:0% +you okay oh here so here's the comment + + + align:start position:0% +you okay oh here so here's the comment +that I have just been making what the + + align:start position:0% +that I have just been making what the + + + align:start position:0% +that I have just been making what the +method that we pushed all the way to get + + align:start position:0% +method that we pushed all the way to get + + + align:start position:0% +method that we pushed all the way to get +the identity Matrix is not as efficient + + align:start position:0% +the identity Matrix is not as efficient + + + align:start position:0% +the identity Matrix is not as efficient +as + + align:start position:0% +as + + + align:start position:0% +as +gaus gaus the greatest mathematician of + + align:start position:0% +gaus gaus the greatest mathematician of + + + align:start position:0% +gaus gaus the greatest mathematician of +all time he uh knew he knew enough to + + align:start position:0% +all time he uh knew he knew enough to + + + align:start position:0% +all time he uh knew he knew enough to +stop when the Matrix was + + align:start position:0% +stop when the Matrix was + + + align:start position:0% +stop when the Matrix was +triangular instead of getting to a + + align:start position:0% +triangular instead of getting to a + + + align:start position:0% +triangular instead of getting to a +matrix that's could could well be + + align:start position:0% +matrix that's could could well be + + + align:start position:0% +matrix that's could could well be +diagonal uh he doesn't do the + + align:start position:0% +diagonal uh he doesn't do the + + + align:start position:0% +diagonal uh he doesn't do the +subtractions from upper rows he just + + align:start position:0% +subtractions from upper rows he just + + + align:start position:0% +subtractions from upper rows he just +goes from subtracts multiples of a row + + align:start position:0% +goes from subtracts multiples of a row + + + align:start position:0% +goes from subtracts multiples of a row +from lower rows and that makes the + + align:start position:0% +from lower rows and that makes the + + + align:start position:0% +from lower rows and that makes the +Matrix triangular and then solving is + + align:start position:0% +Matrix triangular and then solving is + + + align:start position:0% +Matrix triangular and then solving is +easy so just want you to and that's the + + align:start position:0% +easy so just want you to and that's the + + + align:start position:0% +easy so just want you to and that's the +the the oper the steps that you really + + align:start position:0% +the the oper the steps that you really + + + align:start position:0% +the the oper the steps that you really +everybody learns in linear algebra + + align:start position:0% +everybody learns in linear algebra + + + align:start position:0% +everybody learns in linear algebra +elimination from The Matrix from a + + align:start position:0% +elimination from The Matrix from a + + + align:start position:0% +elimination from The Matrix from a +square Matrix to a triangular one and + + align:start position:0% +square Matrix to a triangular one and + + + align:start position:0% +square Matrix to a triangular one and +then solution is a + + align:start position:0% +then solution is a + + + align:start position:0% +then solution is a +cinch okay + + align:start position:0% +cinch okay + + + align:start position:0% +cinch okay +all right I'm near the end I just want + + align:start position:0% +all right I'm near the end I just want + + + align:start position:0% +all right I'm near the end I just want +to + + align:start position:0% +to + + + align:start position:0% +to +express what I did in Matrix notation + + align:start position:0% +express what I did in Matrix notation + + + align:start position:0% +express what I did in Matrix notation +actually that's sort of the fundamental + + align:start position:0% +actually that's sort of the fundamental + + + align:start position:0% +actually that's sort of the fundamental +idea of this of this uh lecture that I'm + + align:start position:0% +idea of this of this uh lecture that I'm + + + align:start position:0% +idea of this of this uh lecture that I'm +sort of extra lecture on + + align:start position:0% +sort of extra lecture on + + + align:start position:0% +sort of extra lecture on +elimination um is to see what's + + align:start position:0% +elimination um is to see what's + + + align:start position:0% +elimination um is to see what's +happening in Matrix language we know if + + align:start position:0% +happening in Matrix language we know if + + + align:start position:0% +happening in Matrix language we know if +you take the course and you grind + + align:start position:0% +you take the course and you grind + + + align:start position:0% +you take the course and you grind +through a few examples of elimination + + align:start position:0% +through a few examples of elimination + + + align:start position:0% +through a few examples of elimination +then you know the steps my this lecture + + align:start position:0% +then you know the steps my this lecture + + + align:start position:0% +then you know the steps my this lecture +is about sit back don't panic with each + + align:start position:0% +is about sit back don't panic with each + + + align:start position:0% +is about sit back don't panic with each +step but what's the big picture and the + + align:start position:0% +step but what's the big picture and the + + + align:start position:0% +step but what's the big picture and the +big picture is that you started with a + + align:start position:0% +big picture is that you started with a + + + align:start position:0% +big picture is that you started with a +matrix like this so you see it's a it's + + align:start position:0% +matrix like this so you see it's a it's + + + align:start position:0% +matrix like this so you see it's a it's +a matrix with + + align:start position:0% +a matrix with + + + align:start position:0% +a matrix with +submatrices so this the rank this this + + align:start position:0% +submatrices so this the rank this this + + + align:start position:0% +submatrices so this the rank this this +Matrix W here is the is square and it's + + align:start position:0% +Matrix W here is the is square and it's + + + align:start position:0% +Matrix W here is the is square and it's +full its rank is it's got if if there if + + align:start position:0% +full its rank is it's got if if there if + + + align:start position:0% +full its rank is it's got if if there if +the whole Matrix a has R independent + + align:start position:0% +the whole Matrix a has R independent + + + align:start position:0% +the whole Matrix a has R independent +columns and R independent rows then we + + align:start position:0% +columns and R independent rows then we + + + align:start position:0% +columns and R independent rows then we +move them into this + + align:start position:0% +move them into this + + + align:start position:0% +move them into this +position + + align:start position:0% +position + + + align:start position:0% +position +W so so I want to start elimination + + align:start position:0% +W so so I want to start elimination + + + align:start position:0% +W so so I want to start elimination +again you'll see I'll get it in one + + align:start position:0% +again you'll see I'll get it in one + + + align:start position:0% +again you'll see I'll get it in one +quick line I want to start think about + + align:start position:0% +quick line I want to start think about + + + align:start position:0% +quick line I want to start think about +elimination but let me suppose that I'm + + align:start position:0% +elimination but let me suppose that I'm + + + align:start position:0% +elimination but let me suppose that I'm +starting with a matrix like my + + align:start position:0% +starting with a matrix like my + + + align:start position:0% +starting with a matrix like my +example that that has a a square + + align:start position:0% +example that that has a a square + + + align:start position:0% +example that that has a a square +invertible Matrix there and what does + + align:start position:0% +invertible Matrix there and what does + + + align:start position:0% +invertible Matrix there and what does +elimination + + align:start position:0% +elimination + + + align:start position:0% +elimination +do what does el well we know that this + + align:start position:0% +do what does el well we know that this + + + align:start position:0% +do what does el well we know that this +is the result so this is what goes in + + align:start position:0% +is the result so this is what goes in + + + align:start position:0% +is the result so this is what goes in +and this is what goes out just 2 by two + + align:start position:0% +and this is what goes out just 2 by two + + + align:start position:0% +and this is what goes out just 2 by two +block matrices I call them a block + + align:start position:0% +block matrices I call them a block + + + align:start position:0% +block matrices I call them a block +Matrix because these are blocks of + + align:start position:0% +Matrix because these are blocks of + + + align:start position:0% +Matrix because these are blocks of +numbers not just single numbers of + + align:start position:0% +numbers not just single numbers of + + + align:start position:0% +numbers not just single numbers of +course to understand the picture quite + + align:start position:0% +course to understand the picture quite + + + align:start position:0% +course to understand the picture quite +good to take just single numbers we + + align:start position:0% +good to take just single numbers we + + + align:start position:0% +good to take just single numbers we +might have the numbers 3 7 6 11 + + align:start position:0% +might have the numbers 3 7 6 11 + + + align:start position:0% +might have the numbers 3 7 6 11 +something like that and what does it + + align:start position:0% +something like that and what does it + + + align:start position:0% +something like that and what does it +reduce to okay and the point is + + align:start position:0% +reduce to okay and the point is + + + align:start position:0% +reduce to okay and the point is +elimination we we have we get the + + align:start position:0% +elimination we we have we get the + + + align:start position:0% +elimination we we have we get the +identity + + align:start position:0% +identity + + + align:start position:0% +identity +Matrix W goes to the identity + + align:start position:0% +Matrix W goes to the identity + + + align:start position:0% +Matrix W goes to the identity +Matrix so elimination is really + + align:start position:0% +Matrix so elimination is really + + + align:start position:0% +Matrix so elimination is really +inverting finding the inverse of w that + + align:start position:0% +inverting finding the inverse of w that + + + align:start position:0% +inverting finding the inverse of w that +that's what elimination is doing + + align:start position:0% +that's what elimination is doing + + + align:start position:0% +that's what elimination is doing +and that was my goal to find out what + + align:start position:0% +and that was my goal to find out what + + + align:start position:0% +and that was my goal to find out what +the heck is elimination doing as I take + + align:start position:0% +the heck is elimination doing as I take + + + align:start position:0% +the heck is elimination doing as I take +all these steps it's what it's doing is + + align:start position:0% +all these steps it's what it's doing is + + + align:start position:0% +all these steps it's what it's doing is +it's finding it's it's inverting that + + align:start position:0% +it's finding it's it's inverting that + + + align:start position:0% +it's finding it's it's inverting that +Matrix W but of course it's operating on + + align:start position:0% +Matrix W but of course it's operating on + + + align:start position:0% +Matrix W but of course it's operating on +whole + + align:start position:0% +whole + + + align:start position:0% +whole +rows + + align:start position:0% +rows + + + align:start position:0% +rows +so it it some some the subtractions from + + align:start position:0% +so it it some some the subtractions from + + + align:start position:0% +so it it some some the subtractions from +down here leave + + align:start position:0% + + + + align:start position:0% + +zeros and the and the steps up here + + align:start position:0% +zeros and the and the steps up here + + + align:start position:0% +zeros and the and the steps up here +multiply the W by its inverse to the the + + align:start position:0% +multiply the W by its inverse to the the + + + align:start position:0% +multiply the W by its inverse to the the +identity this is what we recognize + + align:start position:0% +identity this is what we recognize + + + align:start position:0% +identity this is what we recognize +that's the r Matrix after elimination + + align:start position:0% +that's the r Matrix after elimination + + + align:start position:0% +that's the r Matrix after elimination +it's got if if there are if there are + + align:start position:0% +it's got if if there are if there are + + + align:start position:0% +it's got if if there are if there are +dependent rows they turn into zero rows + + align:start position:0% +dependent rows they turn into zero rows + + + align:start position:0% +dependent rows they turn into zero rows +the independent columns turn into start + + align:start position:0% +the independent columns turn into start + + + align:start position:0% +the independent columns turn into start +with the identity after elimination + + align:start position:0% +with the identity after elimination + + + align:start position:0% +with the identity after elimination +that's the whole point that's the point + + align:start position:0% +that's the whole point that's the point + + + align:start position:0% +that's the whole point that's the point +of elimination to get from a general + + align:start position:0% +of elimination to get from a general + + + align:start position:0% +of elimination to get from a general +Matrix to that kind of a matrix okay and + + align:start position:0% +Matrix to that kind of a matrix okay and + + + align:start position:0% +Matrix to that kind of a matrix okay and +that's what it does that's the row + + align:start position:0% +that's what it does that's the row + + + align:start position:0% +that's what it does that's the row +reduced Echelon + + align:start position:0% +reduced Echelon + + + align:start position:0% +reduced Echelon +form that that elimination does so + + align:start position:0% +form that that elimination does so + + + align:start position:0% +form that that elimination does so +that's really this is the simplest + + align:start position:0% +that's really this is the simplest + + + align:start position:0% +that's really this is the simplest +explanation I could give now you might + + align:start position:0% +explanation I could give now you might + + + align:start position:0% +explanation I could give now you might +say wait a minute this is assuming that + + align:start position:0% +say wait a minute this is assuming that + + + align:start position:0% +say wait a minute this is assuming that +W up in that left corner is a nice + + align:start position:0% +W up in that left corner is a nice + + + align:start position:0% +W up in that left corner is a nice +Square invertible full rank Matrix then + + align:start position:0% +Square invertible full rank Matrix then + + + align:start position:0% +Square invertible full rank Matrix then +then we go here suppose it isn't suppose + + align:start position:0% +then we go here suppose it isn't suppose + + + align:start position:0% +then we go here suppose it isn't suppose +I have a zero up in the top left corner + + align:start position:0% +I have a zero up in the top left corner + + + align:start position:0% +I have a zero up in the top left corner +or something like that then what what + + align:start position:0% +or something like that then what what + + + align:start position:0% +or something like that then what what +what do I do well I do some row + + align:start position:0% +what do I do well I do some row + + + align:start position:0% +what do I do well I do some row +exchanges to get and maybe some column + + align:start position:0% +exchanges to get and maybe some column + + + align:start position:0% +exchanges to get and maybe some column +exchanges to to get to to this W to get + + align:start position:0% +exchanges to to get to to this W to get + + + align:start position:0% +exchanges to to get to to this W to get +to this + + align:start position:0% +to this + + + align:start position:0% +to this +invertible uh block pivot you could you + + align:start position:0% +invertible uh block pivot you could you + + + align:start position:0% +invertible uh block pivot you could you +could call it which which turns into ey + + align:start position:0% +could call it which which turns into ey + + + align:start position:0% +could call it which which turns into ey +so I have to so the next slide will show + + align:start position:0% +so I have to so the next slide will show + + + align:start position:0% +so I have to so the next slide will show +you the the possible steps I may have to + + align:start position:0% +you the the possible steps I may have to + + + align:start position:0% +you the the possible steps I may have to +use some permutation some reordering of + + align:start position:0% +use some permutation some reordering of + + + align:start position:0% +use some permutation some reordering of +the rows you got to be up for those it + + align:start position:0% +the rows you got to be up for those it + + + align:start position:0% +the rows you got to be up for those it +can have a reordering of the columns and + + align:start position:0% +can have a reordering of the columns and + + + align:start position:0% +can have a reordering of the columns and +that will get it into the position into + + align:start position:0% +that will get it into the position into + + + align:start position:0% +that will get it into the position into +what we want that gets it into what we + + align:start position:0% +what we want that gets it into what we + + + align:start position:0% +what we want that gets it into what we +want and then elimination gets us where + + align:start position:0% +want and then elimination gets us where + + + align:start position:0% +want and then elimination gets us where +we really want okay so so this is a this + + align:start position:0% +we really want okay so so this is a this + + + align:start position:0% +we really want okay so so this is a this +is we're at the end now this is the + + align:start position:0% +is we're at the end now this is the + + + align:start position:0% +is we're at the end now this is the +picture of elimination where written in + + align:start position:0% +picture of elimination where written in + + + align:start position:0% +picture of elimination where written in +its simplest Matrix form I I do + + align:start position:0% +its simplest Matrix form I I do + + + align:start position:0% +its simplest Matrix form I I do +permutations of rows I reorder the rows + + align:start position:0% +permutations of rows I reorder the rows + + + align:start position:0% +permutations of rows I reorder the rows +and the columns to get the first columns + + align:start position:0% +and the columns to get the first columns + + + align:start position:0% +and the columns to get the first columns +and the first rows to be + + align:start position:0% +and the first rows to be + + + align:start position:0% +and the first rows to be +independent and that that means that + + align:start position:0% +independent and that that means that + + + align:start position:0% +independent and that that means that +they have a r by R Matrix W that's + + align:start position:0% +they have a r by R Matrix W that's + + + align:start position:0% +they have a r by R Matrix W that's +invertible then H and J or whatever they + + align:start position:0% +invertible then H and J or whatever they + + + align:start position:0% +invertible then H and J or whatever they +are but then then the next step of + + align:start position:0% +are but then then the next step of + + + align:start position:0% +are but then then the next step of +elimination + + align:start position:0% +elimination + + + align:start position:0% +elimination +the two jobs of elimination are get + + align:start position:0% +the two jobs of elimination are get + + + align:start position:0% +the two jobs of elimination are get +things in the right order and get zeros + + align:start position:0% +things in the right order and get zeros + + + align:start position:0% +things in the right order and get zeros +produce zeros so here I'm supposing that + + align:start position:0% +produce zeros so here I'm supposing that + + + align:start position:0% +produce zeros so here I'm supposing that +I get them in the right order there and + + align:start position:0% +I get them in the right order there and + + + align:start position:0% +I get them in the right order there and +then I produce the zeros there and also + + align:start position:0% +then I produce the zeros there and also + + + align:start position:0% +then I produce the zeros there and also +produce a bunch of zeros in that + + align:start position:0% +produce a bunch of zeros in that + + + align:start position:0% +produce a bunch of zeros in that +identity Matrix and this is the F this + + align:start position:0% +identity Matrix and this is the F this + + + align:start position:0% +identity Matrix and this is the F this +is our friend F which we're giving we're + + align:start position:0% +is our friend F which we're giving we're + + + align:start position:0% +is our friend F which we're giving we're +shining a light in this lecture on this + + align:start position:0% +shining a light in this lecture on this + + + align:start position:0% +shining a light in this lecture on this +Matrix F that that got really ignored + + align:start position:0% +Matrix F that that got really ignored + + + align:start position:0% +Matrix F that that got really ignored +for a thousand years so there you go I'm + + align:start position:0% +for a thousand years so there you go I'm + + + align:start position:0% +for a thousand years so there you go I'm +not sure if were through for I I feel + + align:start position:0% +not sure if were through for I I feel + + + align:start position:0% +not sure if were through for I I feel +I'm through I've see it says 14 of 16 so + + align:start position:0% +I'm through I've see it says 14 of 16 so + + + align:start position:0% +I'm through I've see it says 14 of 16 so +there must be some brilliant ideas on + + align:start position:0% +there must be some brilliant ideas on + + + align:start position:0% +there must be some brilliant ideas on +the last last things so interesting + + align:start position:0% +the last last things so interesting + + + align:start position:0% +the last last things so interesting +point the question is where is that W + + align:start position:0% +point the question is where is that W + + + align:start position:0% +point the question is where is that W +that Matrix of of um that invertible R + + align:start position:0% +that Matrix of of um that invertible R + + + align:start position:0% +that Matrix of of um that invertible R +byr Matrix that that is the basis for + + align:start position:0% +byr Matrix that that is the basis for + + + align:start position:0% +byr Matrix that that is the basis for +elimination that W up in the corner and + + align:start position:0% +elimination that W up in the corner and + + + align:start position:0% +elimination that W up in the corner and +and the theorem is that if I find R + + align:start position:0% +and the theorem is that if I find R + + + align:start position:0% +and the theorem is that if I find R +independent rows which there are in the + + align:start position:0% +independent rows which there are in the + + + align:start position:0% +independent rows which there are in the +row + + align:start position:0% +row + + + align:start position:0% +row +space if i cho if I find our independent + + align:start position:0% +space if i cho if I find our independent + + + align:start position:0% +space if i cho if I find our independent +columns so suppose the rows are in a row + + align:start position:0% +columns so suppose the rows are in a row + + + align:start position:0% +columns so suppose the rows are in a row +in a matrix B with r rows the columns + + align:start position:0% +in a matrix B with r rows the columns + + + align:start position:0% +in a matrix B with r rows the columns +are in a matrix c as before with r + + align:start position:0% +are in a matrix c as before with r + + + align:start position:0% +are in a matrix c as before with r +independent columns then where B meets C + + align:start position:0% +independent columns then where B meets C + + + align:start position:0% +independent columns then where B meets C +can you see this on my so B is coming + + align:start position:0% +can you see this on my so B is coming + + + align:start position:0% +can you see this on my so B is coming +along as independent rows C is our + + align:start position:0% +along as independent rows C is our + + + align:start position:0% +along as independent rows C is our +independent columns and where they + + align:start position:0% +independent columns and where they + + + align:start position:0% +independent columns and where they +meet I claim is an R byr Matrix that's + + align:start position:0% +meet I claim is an R byr Matrix that's + + + align:start position:0% +meet I claim is an R byr Matrix that's +invertible indep it has independent rows + + align:start position:0% +invertible indep it has independent rows + + + align:start position:0% +invertible indep it has independent rows +in independent columns so for me this + + align:start position:0% +in independent columns so for me this + + + align:start position:0% +in independent columns so for me this +was the real math uh principle that that + + align:start position:0% +was the real math uh principle that that + + + align:start position:0% +was the real math uh principle that that +wasn't so I wasn't so sure about but but + + align:start position:0% +wasn't so I wasn't so sure about but but + + + align:start position:0% +wasn't so I wasn't so sure about but but +it works okay oh oh just to tell you uh + + align:start position:0% +it works okay oh oh just to tell you uh + + + align:start position:0% +it works okay oh oh just to tell you uh +that the paper is in a journal called + + align:start position:0% +that the paper is in a journal called + + + align:start position:0% +that the paper is in a journal called +mathematics magazine it's almost + + align:start position:0% +mathematics magazine it's almost + + + align:start position:0% +mathematics magazine it's almost +published as I make this recording uh + + align:start position:0% +published as I make this recording uh + + + align:start position:0% +published as I make this recording uh +it's the mass Association of America and + + align:start position:0% +it's the mass Association of America and + + + align:start position:0% +it's the mass Association of America and +then there's also a website that has a + + align:start position:0% +then there's also a website that has a + + + align:start position:0% +then there's also a website that has a +lot of math + + align:start position:0% +lot of math + + + align:start position:0% +lot of math +papers put put in there before + + align:start position:0% +papers put put in there before + + + align:start position:0% +papers put put in there before +publication and they have some crazy + + align:start position:0% +publication and they have some crazy + + + align:start position:0% +publication and they have some crazy +long number to identify them but + + align:start position:0% +long number to identify them but + + + align:start position:0% +long number to identify them but +it's this is the linear algebra textbook + + align:start position:0% +it's this is the linear algebra textbook + + + align:start position:0% +it's this is the linear algebra textbook +that that uses this lecture actually + + align:start position:0% +that that uses this lecture actually + + + align:start position:0% +that that uses this lecture actually +this lecture is not in the textbook it's + + align:start position:0% +this lecture is not in the textbook it's + + + align:start position:0% +this lecture is not in the textbook it's +uh separate + + align:start position:0% +uh separate + + + align:start position:0% +uh separate +because + + align:start position:0% +because + + + align:start position:0% +because +the I didn't want to fill the textbook + + align:start position:0% +the I didn't want to fill the textbook + + + align:start position:0% +the I didn't want to fill the textbook +by this complicated thing + + align:start position:0% +by this complicated thing + + + align:start position:0% +by this complicated thing +where the idea is + + align:start position:0% +where the idea is + + + align:start position:0% +where the idea is +simple where you you simplify your + + align:start position:0% +simple where you you simplify your + + + align:start position:0% +simple where you you simplify your +Matrix a by elimination and then you can + + align:start position:0% +Matrix a by elimination and then you can + + + align:start position:0% +Matrix a by elimination and then you can +read off all four + + align:start position:0% +read off all four + + + align:start position:0% +read off all four +subspaces and all four fundamental + + align:start position:0% +subspaces and all four fundamental + + + align:start position:0% +subspaces and all four fundamental +subspaces and the idea is to say what is + + align:start position:0% +subspaces and the idea is to say what is + + + align:start position:0% +subspaces and the idea is to say what is +elimination actually doing to to put in + + align:start position:0% +elimination actually doing to to put in + + + align:start position:0% +elimination actually doing to to put in +a little more of the details which are + + align:start position:0% +a little more of the details which are + + + align:start position:0% +a little more of the details which are +in this talk but not appropriate for uh + + align:start position:0% +in this talk but not appropriate for uh + + + align:start position:0% +in this talk but not appropriate for uh +to necessarily to go into the textbook + + align:start position:0% +to necessarily to go into the textbook + + + align:start position:0% +to necessarily to go into the textbook +so there I there it is + + align:start position:0% +so there I there it is + + + align:start position:0% +so there I there it is +um uh the paper that that takes these + + align:start position:0% +um uh the paper that that takes these + + + align:start position:0% +um uh the paper that that takes these +steps is in a journal that many + + align:start position:0% +steps is in a journal that many + + + align:start position:0% +steps is in a journal that many +libraries will uh take well thanks for + + align:start position:0% +libraries will uh take well thanks for + + + align:start position:0% +libraries will uh take well thanks for +patience with this uh unusual step I + + align:start position:0% +patience with this uh unusual step I + + + align:start position:0% +patience with this uh unusual step I +didn't know it was going to happen but + + align:start position:0% +didn't know it was going to happen but + + + align:start position:0% +didn't know it was going to happen but +it just I was never happy with with + + align:start position:0% +it just I was never happy with with + + + align:start position:0% +it just I was never happy with with +elimination without having a matrix + + align:start position:0% +elimination without having a matrix + + + align:start position:0% +elimination without having a matrix +description what happens with the Matrix + + align:start position:0% +description what happens with the Matrix + + + align:start position:0% +description what happens with the Matrix +pieces of the of my overall Matrix a and + + align:start position:0% +pieces of the of my overall Matrix a and + + + align:start position:0% +pieces of the of my overall Matrix a and +that's what this lecture was about so + + align:start position:0% +that's what this lecture was about so + + + align:start position:0% +that's what this lecture was about so +thanks for joining and uh best wishes in + + align:start position:0% +thanks for joining and uh best wishes in + + + align:start position:0% +thanks for joining and uh best wishes in +linear algebra it's a beautiful subject + + align:start position:0% +linear algebra it's a beautiful subject + + + align:start position:0% +linear algebra it's a beautiful subject +thanks \ No newline at end of file diff --git a/Q7-mCKOzNUI.txt b/Q7-mCKOzNUI.txt new file mode 100644 index 0000000000000000000000000000000000000000..d27d3cd10efac9b03c1d637150b23b4b06ebb82c --- /dev/null +++ b/Q7-mCKOzNUI.txt @@ -0,0 +1,9707 @@ +align:start position:0% + +Okay. So today we are going to turn from + + align:start position:0% +Okay. So today we are going to turn from + + + align:start position:0% +Okay. So today we are going to turn from +the consumer side of the story to the + + align:start position:0% +the consumer side of the story to the + + + align:start position:0% +the consumer side of the story to the +producer side of the story. Once again + + align:start position:0% +producer side of the story. Once again + + + align:start position:0% +producer side of the story. Once again +in the first lecture we talked about + + align:start position:0% +in the first lecture we talked about + + + align:start position:0% +in the first lecture we talked about +supply and demand curves. The last few + + align:start position:0% +supply and demand curves. The last few + + + align:start position:0% +supply and demand curves. The last few +lectures we developed where demand + + align:start position:0% +lectures we developed where demand + + + align:start position:0% +lectures we developed where demand +curves come from. Now we're develop + + align:start position:0% +curves come from. Now we're develop + + + align:start position:0% +curves come from. Now we're develop +where supply curves come from. So we're + + align:start position:0% +where supply curves come from. So we're + + + align:start position:0% +where supply curves come from. So we're +going to flip and explain where supply + + align:start position:0% +going to flip and explain where supply + + + align:start position:0% +going to flip and explain where supply +curves come from. + + align:start position:0% +curves come from. + + + align:start position:0% +curves come from. +So, and to do so, we're going to start + + align:start position:0% +So, and to do so, we're going to start + + + align:start position:0% +So, and to do so, we're going to start +by talking about production + + align:start position:0% + + + + align:start position:0% + +functions. Now, we all know + + align:start position:0% +functions. Now, we all know + + + align:start position:0% +functions. Now, we all know +what firms, what consumers want. They + + align:start position:0% +what firms, what consumers want. They + + + align:start position:0% +what firms, what consumers want. They +want to figure out the bundle of goods + + align:start position:0% +want to figure out the bundle of goods + + + align:start position:0% +want to figure out the bundle of goods +that makes them as well off as possible + + align:start position:0% +that makes them as well off as possible + + + align:start position:0% +that makes them as well off as possible +given their budget constraint. What do + + align:start position:0% +given their budget constraint. What do + + + align:start position:0% +given their budget constraint. What do +firms want? + + align:start position:0% +firms want? + + + align:start position:0% +firms want? +Firms want to maximize their profits. So + + align:start position:0% +Firms want to maximize their profits. So + + + align:start position:0% +Firms want to maximize their profits. So +just like consumers want to maximize + + align:start position:0% +just like consumers want to maximize + + + align:start position:0% +just like consumers want to maximize +their utility, firms want to maximize + + align:start position:0% +their utility, firms want to maximize + + + align:start position:0% +their utility, firms want to maximize +their profits. And firm profits will + + align:start position:0% +their profits. And firm profits will + + + align:start position:0% +their profits. And firm profits will +depend so they want to maximize + + align:start position:0% +depend so they want to maximize + + + align:start position:0% +depend so they want to maximize +profits. And profits will depend on + + align:start position:0% +profits. And profits will depend on + + + align:start position:0% +profits. And profits will depend on +three things. They'll depend on consumer + + align:start position:0% +three things. They'll depend on consumer + + + align:start position:0% +three things. They'll depend on consumer +demand. + + align:start position:0% + + + + align:start position:0% + +They'll depend on the cost of + + align:start position:0% + + + + align:start position:0% + +production and they will depend on + + align:start position:0% + + + + align:start position:0% + +competition. Now the first two, the + + align:start position:0% +competition. Now the first two, the + + + align:start position:0% +competition. Now the first two, the +first and the third are things which are + + align:start position:0% +first and the third are things which are + + + align:start position:0% +first and the third are things which are +largely out of the firm's control. Not + + align:start position:0% +largely out of the firm's control. Not + + + align:start position:0% +largely out of the firm's control. Not +totally out of the firm's control. We'll + + align:start position:0% +totally out of the firm's control. We'll + + + align:start position:0% +totally out of the firm's control. We'll +come back to how things like advertising + + align:start position:0% +come back to how things like advertising + + + align:start position:0% +come back to how things like advertising +might affect demand and how things like + + align:start position:0% +might affect demand and how things like + + + align:start position:0% +might affect demand and how things like +monopolies might affect competition. But + + align:start position:0% +monopolies might affect competition. But + + + align:start position:0% +monopolies might affect competition. But +in the standard model, view them as sort + + align:start position:0% +in the standard model, view them as sort + + + align:start position:0% +in the standard model, view them as sort +of out of the firm's control. Take them + + align:start position:0% +of out of the firm's control. Take them + + + align:start position:0% +of out of the firm's control. Take them +as given. What the firm controls is the + + align:start position:0% +as given. What the firm controls is the + + + align:start position:0% +as given. What the firm controls is the +cost of production. That's what they can + + align:start position:0% +cost of production. That's what they can + + + align:start position:0% +cost of production. That's what they can +that's what's under their + + align:start position:0% +that's what's under their + + + align:start position:0% +that's what's under their +control. So from the firm's + + align:start position:0% +control. So from the firm's + + + align:start position:0% +control. So from the firm's +perspective, maximizing profits is the + + align:start position:0% +perspective, maximizing profits is the + + + align:start position:0% +perspective, maximizing profits is the +same as minimizing costs. + + align:start position:0% + + + + align:start position:0% + +Okay, the way to maximize profits is to + + align:start position:0% +Okay, the way to maximize profits is to + + + align:start position:0% +Okay, the way to maximize profits is to +minimize costs and that's how the firm + + align:start position:0% +minimize costs and that's how the firm + + + align:start position:0% +minimize costs and that's how the firm +produces as efficiently as possible by + + align:start position:0% +produces as efficiently as possible by + + + align:start position:0% +produces as efficiently as possible by +minimizing + + align:start position:0% +minimizing + + + align:start position:0% +minimizing +costs. Okay, once again in the real + + align:start position:0% +costs. Okay, once again in the real + + + align:start position:0% +costs. Okay, once again in the real +world there's complications but in the + + align:start position:0% +world there's complications but in the + + + align:start position:0% +world there's complications but in the +model and what'll explain most the real + + align:start position:0% +model and what'll explain most the real + + + align:start position:0% +model and what'll explain most the real +world we just say + + align:start position:0% +world we just say + + + align:start position:0% +world we just say +firms their goal is to minimize + + align:start position:0% +firms their goal is to minimize + + + align:start position:0% +firms their goal is to minimize +costs. Now to understand how to minimize + + align:start position:0% +costs. Now to understand how to minimize + + + align:start position:0% +costs. Now to understand how to minimize +costs we have to understand where a + + align:start position:0% +costs we have to understand where a + + + align:start position:0% +costs we have to understand where a +firm's costs come from. + + align:start position:0% +firm's costs come from. + + + align:start position:0% +firm's costs come from. +understand that we have to understand + + align:start position:0% +understand that we have to understand + + + align:start position:0% +understand that we have to understand +what firms actually + + align:start position:0% +what firms actually + + + align:start position:0% +what firms actually +do. So in this course, firms are simply + + align:start position:0% +do. So in this course, firms are simply + + + align:start position:0% +do. So in this course, firms are simply +black boxes for much of the course. + + align:start position:0% +black boxes for much of the course. + + + align:start position:0% +black boxes for much of the course. +They're simply boxes where inputs go in + + align:start position:0% +They're simply boxes where inputs go in + + + align:start position:0% +They're simply boxes where inputs go in +and outputs come out and in the middle + + align:start position:0% +and outputs come out and in the middle + + + align:start position:0% +and outputs come out and in the middle +is something called a production + + align:start position:0% +is something called a production + + + align:start position:0% +is something called a production +function. Okay, that production function + + align:start position:0% +function. Okay, that production function + + + align:start position:0% +function. Okay, that production function +is the magic that makes is the magic of + + align:start position:0% +is the magic that makes is the magic of + + + align:start position:0% +is the magic that makes is the magic of +the firm. Okay. And technically what a + + align:start position:0% +the firm. Okay. And technically what a + + + align:start position:0% +the firm. Okay. And technically what a +production function is, what a + + align:start position:0% +production function is, what a + + + align:start position:0% +production function is, what a +production function is, it's a + + align:start position:0% +production function is, it's a + + + align:start position:0% +production function is, it's a +description of what is technically + + align:start position:0% + + + + align:start position:0% + +feasible for the firm to produce. Okay, + + align:start position:0% +feasible for the firm to produce. Okay, + + + align:start position:0% +feasible for the firm to produce. Okay, +that's their production function. What + + align:start position:0% +that's their production function. What + + + align:start position:0% +that's their production function. What +is technically feasible for them to + + align:start position:0% +is technically feasible for them to + + + align:start position:0% +is technically feasible for them to +produce. + + align:start position:0% +produce. + + + align:start position:0% +produce. +Okay. And essentially what this + + align:start position:0% +Okay. And essentially what this + + + align:start position:0% +Okay. And essentially what this +production function does is it takes as + + align:start position:0% +production function does is it takes as + + + align:start position:0% +production function does is it takes as +inputs two things. Takes as inputs uh + + align:start position:0% +inputs two things. Takes as inputs uh + + + align:start position:0% +inputs two things. Takes as inputs uh +factors of production. It takes factors + + align:start position:0% +factors of production. It takes factors + + + align:start position:0% +factors of production. It takes factors +of + + align:start position:0% +of + + + align:start position:0% +of +production what we call factors of + + align:start position:0% +production what we call factors of + + + align:start position:0% +production what we call factors of +production. I'll come back to what those + + align:start position:0% +production. I'll come back to what those + + + align:start position:0% +production. I'll come back to what those +are in a + + align:start position:0% +are in a + + + align:start position:0% +are in a +minute. Takes factors of production. It + + align:start position:0% +minute. Takes factors of production. It + + + align:start position:0% +minute. Takes factors of production. It +puts it through a production + + align:start position:0% +puts it through a production + + + align:start position:0% +puts it through a production +function which is a black box will + + align:start position:0% +function which is a black box will + + + align:start position:0% +function which is a black box will +express as a mathematical function and + + align:start position:0% +express as a mathematical function and + + + align:start position:0% +express as a mathematical function and +out comes a production of goods and + + align:start position:0% + + + + align:start position:0% + +services. Okay. And that's the way we + + align:start position:0% +services. Okay. And that's the way we + + + align:start position:0% +services. Okay. And that's the way we +model the supply + + align:start position:0% +model the supply + + + align:start position:0% +model the supply +side. So what are these factors of + + align:start position:0% +side. So what are these factors of + + + align:start position:0% +side. So what are these factors of +production? These factors of production + + align:start position:0% +production? These factors of production + + + align:start position:0% +production? These factors of production +are what we call inputs into the + + align:start position:0% +are what we call inputs into the + + + align:start position:0% +are what we call inputs into the +production process. The + + align:start position:0% +production process. The + + + align:start position:0% +production process. The +inputs into production are of two types. + + align:start position:0% +inputs into production are of two types. + + + align:start position:0% +inputs into production are of two types. +To make life easy, once again, obviously + + align:start position:0% +To make life easy, once again, obviously + + + align:start position:0% +To make life easy, once again, obviously +in the real world there's a million + + align:start position:0% +in the real world there's a million + + + align:start position:0% +in the real world there's a million +types of inputs in a production. But to + + align:start position:0% +types of inputs in a production. But to + + + align:start position:0% +types of inputs in a production. But to +make life easy, we'll start with a model + + align:start position:0% +make life easy, we'll start with a model + + + align:start position:0% +make life easy, we'll start with a model +with two types of inputs in a + + align:start position:0% +with two types of inputs in a + + + align:start position:0% +with two types of inputs in a +production. + + align:start position:0% +production. + + + align:start position:0% +production. +Labor and + + align:start position:0% + + + + align:start position:0% + +capital. Labor and + + align:start position:0% +capital. Labor and + + + align:start position:0% +capital. Labor and +capital. Okay. Labor. It's clear what + + align:start position:0% +capital. Okay. Labor. It's clear what + + + align:start position:0% +capital. Okay. Labor. It's clear what +labor is. It's the amount of hours that + + align:start position:0% +labor is. It's the amount of hours that + + + align:start position:0% +labor is. It's the amount of hours that +people work at your firm. + + align:start position:0% +people work at your firm. + + + align:start position:0% +people work at your firm. +Okay. So, labor is literally how many + + align:start position:0% +Okay. So, labor is literally how many + + + align:start position:0% +Okay. So, labor is literally how many +hours are devoted towards work uh at + + align:start position:0% +hours are devoted towards work uh at + + + align:start position:0% +hours are devoted towards work uh at +your + + align:start position:0% +your + + + align:start position:0% +your +firm. Hours are + + align:start position:0% +firm. Hours are + + + align:start position:0% +firm. Hours are +provided by + + align:start position:0% +provided by + + + align:start position:0% +provided by +individuals in the labor market. So now + + align:start position:0% +individuals in the labor market. So now + + + align:start position:0% +individuals in the labor market. So now +people on the other side of the equation + + align:start position:0% +people on the other side of the equation + + + align:start position:0% +people on the other side of the equation +instead of people wanting pizza and + + align:start position:0% +instead of people wanting pizza and + + + align:start position:0% +instead of people wanting pizza and +cookies, now people are inputs into + + align:start position:0% +cookies, now people are inputs into + + + align:start position:0% +cookies, now people are inputs into +production because they produce the + + align:start position:0% +production because they produce the + + + align:start position:0% +production because they produce the +labor. So people produce labor. they + + align:start position:0% +labor. So people produce labor. they + + + align:start position:0% +labor. So people produce labor. they +work at your firm and the price they + + align:start position:0% +work at your firm and the price they + + + align:start position:0% +work at your firm and the price they +demand for that labor is the + + align:start position:0% +demand for that labor is the + + + align:start position:0% +demand for that labor is the +wage. That is the price that they demand + + align:start position:0% +wage. That is the price that they demand + + + align:start position:0% +wage. That is the price that they demand +for their labor. Where does the wage + + align:start position:0% +for their labor. Where does the wage + + + align:start position:0% +for their labor. Where does the wage +come from? We'll talk about that in a + + align:start position:0% +come from? We'll talk about that in a + + + align:start position:0% +come from? We'll talk about that in a +few lectures. Right now, we're going to + + align:start position:0% +few lectures. Right now, we're going to + + + align:start position:0% +few lectures. Right now, we're going to +take the wage as given. Just in previous + + align:start position:0% +take the wage as given. Just in previous + + + align:start position:0% +take the wage as given. Just in previous +lectures, we took the price of cookies + + align:start position:0% +lectures, we took the price of cookies + + + align:start position:0% +lectures, we took the price of cookies +and the price of pizza as + + align:start position:0% +and the price of pizza as + + + align:start position:0% +and the price of pizza as +given. And we'll tell you later where + + align:start position:0% +given. And we'll tell you later where + + + align:start position:0% +given. And we'll tell you later where +they come from. Now, we're just going to + + align:start position:0% +they come from. Now, we're just going to + + + align:start position:0% +they come from. Now, we're just going to +take the wage as given. I'll tell you + + align:start position:0% +take the wage as given. I'll tell you + + + align:start position:0% +take the wage as given. I'll tell you +later where that comes from. By + + align:start position:0% +later where that comes from. By + + + align:start position:0% +later where that comes from. By +proceeding in steps, we make it feasible + + align:start position:0% +proceeding in steps, we make it feasible + + + align:start position:0% +proceeding in steps, we make it feasible +to model this in a in a reasonable way. + + align:start position:0% +to model this in a in a reasonable way. + + + align:start position:0% +to model this in a in a reasonable way. +Okay, capital is more confusing. Okay, + + align:start position:0% +Okay, capital is more confusing. Okay, + + + align:start position:0% +Okay, capital is more confusing. Okay, +capital is more confusing. This is + + align:start position:0% +capital is more confusing. This is + + + align:start position:0% +capital is more confusing. This is +basically think of it as everything else + + align:start position:0% +basically think of it as everything else + + + align:start position:0% +basically think of it as everything else +that goes in production. The machines, + + align:start position:0% +that goes in production. The machines, + + + align:start position:0% +that goes in production. The machines, +the buildings, the land you build on. + + align:start position:0% +the buildings, the land you build on. + + + align:start position:0% +the buildings, the land you build on. +Think of it roughly as machines. Think + + align:start position:0% +Think of it roughly as machines. Think + + + align:start position:0% +Think of it roughly as machines. Think +of this black box as being workers and + + align:start position:0% +of this black box as being workers and + + + align:start position:0% +of this black box as being workers and +machines come together to produce + + align:start position:0% +machines come together to produce + + + align:start position:0% +machines come together to produce +something. The workers we call labor. + + align:start position:0% +something. The workers we call labor. + + + align:start position:0% +something. The workers we call labor. +Labor. The machines we call + + align:start position:0% +Labor. The machines we call + + + align:start position:0% +Labor. The machines we call +capital. And the price of capital we're + + align:start position:0% +capital. And the price of capital we're + + + align:start position:0% +capital. And the price of capital we're +going to call the rental + + align:start position:0% + + + + align:start position:0% + +rate. In other words, think of whatever + + align:start position:0% +rate. In other words, think of whatever + + + align:start position:0% +rate. In other words, think of whatever +you use in production as rented. You + + align:start position:0% +you use in production as rented. You + + + align:start position:0% +you use in production as rented. You +rent a machine. You rent a building. + + align:start position:0% +rent a machine. You rent a building. + + + align:start position:0% +rent a machine. You rent a building. +Okay? In substance, workers, the wage is + + align:start position:0% +Okay? In substance, workers, the wage is + + + align:start position:0% +Okay? In substance, workers, the wage is +the price you pay to rent an hour of a + + align:start position:0% +the price you pay to rent an hour of a + + + align:start position:0% +the price you pay to rent an hour of a +worker's time, right? That's the way. + + align:start position:0% +worker's time, right? That's the way. + + + align:start position:0% +worker's time, right? That's the way. +It's what the wage is. The price for + + align:start position:0% +It's what the wage is. The price for + + + align:start position:0% +It's what the wage is. The price for +renting an hour of a worker's time. And + + align:start position:0% +renting an hour of a worker's time. And + + + align:start position:0% +renting an hour of a worker's time. And +the rental rate is the price for renting + + align:start position:0% +the rental rate is the price for renting + + + align:start position:0% +the rental rate is the price for renting +a unit of + + align:start position:0% +a unit of + + + align:start position:0% +a unit of +capital. Okay. Now, later on we'll talk + + align:start position:0% +capital. Okay. Now, later on we'll talk + + + align:start position:0% +capital. Okay. Now, later on we'll talk +about where that comes from, the fact + + align:start position:0% +about where that comes from, the fact + + + align:start position:0% +about where that comes from, the fact +that firms actually own machines, etc. + + align:start position:0% +that firms actually own machines, etc. + + + align:start position:0% +that firms actually own machines, etc. +But for now, this makes it easy and + + align:start position:0% +But for now, this makes it easy and + + + align:start position:0% +But for now, this makes it easy and +allows for a parallel analysis between + + align:start position:0% +allows for a parallel analysis between + + + align:start position:0% +allows for a parallel analysis between +workers and machines. They're both + + align:start position:0% +workers and machines. They're both + + + align:start position:0% +workers and machines. They're both +things you + + align:start position:0% +things you + + + align:start position:0% +things you +rent. Okay. + + align:start position:0% +rent. Okay. + + + align:start position:0% +rent. Okay. +Now the production function is a + + align:start position:0% +Now the production function is a + + + align:start position:0% +Now the production function is a +function + + align:start position:0% +function + + + align:start position:0% +function +Q that + + align:start position:0% +Q that + + + align:start position:0% +Q that +basically converts I'm sorry it's a + + align:start position:0% +basically converts I'm sorry it's a + + + align:start position:0% +basically converts I'm sorry it's a +function f I'm sorry it's a function f + + align:start position:0% +function f I'm sorry it's a function f + + + align:start position:0% +function f I'm sorry it's a function f +that converts labor and capital into + + align:start position:0% +that converts labor and capital into + + + align:start position:0% +that converts labor and capital into +outputs. So the production function f + + align:start position:0% +outputs. So the production function f + + + align:start position:0% +outputs. So the production function f +converts labor and capital into output + + align:start position:0% +converts labor and capital into output + + + align:start position:0% +converts labor and capital into output +just like utility function. And once + + align:start position:0% +just like utility function. And once + + + align:start position:0% +just like utility function. And once +again there's going to be enormous + + align:start position:0% +again there's going to be enormous + + + align:start position:0% +again there's going to be enormous +parallels to the consumer theory. That's + + align:start position:0% +parallels to the consumer theory. That's + + + align:start position:0% +parallels to the consumer theory. That's +what I drilled into you developing the + + align:start position:0% +what I drilled into you developing the + + + align:start position:0% +what I drilled into you developing the +intuition of consumer theory. That same + + align:start position:0% +intuition of consumer theory. That same + + + align:start position:0% +intuition of consumer theory. That same +intuition is going to carry over here to + + align:start position:0% +intuition is going to carry over here to + + + align:start position:0% +intuition is going to carry over here to +producer theory. So just like the + + align:start position:0% +producer theory. So just like the + + + align:start position:0% +producer theory. So just like the +utility function is a mathematical + + align:start position:0% +utility function is a mathematical + + + align:start position:0% +utility function is a mathematical +representation of how goods turn into + + align:start position:0% +representation of how goods turn into + + + align:start position:0% +representation of how goods turn into +happiness, the production function which + + align:start position:0% +happiness, the production function which + + + align:start position:0% +happiness, the production function which +in some sense easy to understand is a + + align:start position:0% +in some sense easy to understand is a + + + align:start position:0% +in some sense easy to understand is a +mathematical representation of how + + align:start position:0% +mathematical representation of how + + + align:start position:0% +mathematical representation of how +inputs turn to outputs. Sort of easy to + + align:start position:0% +inputs turn to outputs. Sort of easy to + + + align:start position:0% +inputs turn to outputs. Sort of easy to +understand. Utility function is a vague + + align:start position:0% +understand. Utility function is a vague + + + align:start position:0% +understand. Utility function is a vague +thing. A production function is a + + align:start position:0% +thing. A production function is a + + + align:start position:0% +thing. A production function is a +technology. We all know that. Okay, it's + + align:start position:0% +technology. We all know that. Okay, it's + + + align:start position:0% +technology. We all know that. Okay, it's +the 20 007 contest. You've got some + + align:start position:0% +the 20 007 contest. You've got some + + + align:start position:0% +the 20 007 contest. You've got some +inputs and you produce an output. + + align:start position:0% +inputs and you produce an output. + + + align:start position:0% +inputs and you produce an output. +Okay, so production function is just the + + align:start position:0% +Okay, so production function is just the + + + align:start position:0% +Okay, so production function is just the +technology that translates the inputs to + + align:start position:0% +technology that translates the inputs to + + + align:start position:0% +technology that translates the inputs to +the + + align:start position:0% +the + + + align:start position:0% +the +outputs. Let me highlight one thing. + + align:start position:0% +outputs. Let me highlight one thing. + + + align:start position:0% +outputs. Let me highlight one thing. +Little Q I'm going to distinguish here + + align:start position:0% +Little Q I'm going to distinguish here + + + align:start position:0% +Little Q I'm going to distinguish here +and if I get this wrong, you can catch + + align:start position:0% +and if I get this wrong, you can catch + + + align:start position:0% +and if I get this wrong, you can catch +me. Little Q refers to a specific firm. + + align:start position:0% +me. Little Q refers to a specific firm. + + + align:start position:0% +me. Little Q refers to a specific firm. +Big Q refers to the market. So I did my + + align:start position:0% +Big Q refers to the market. So I did my + + + align:start position:0% +Big Q refers to the market. So I did my +supply and demand curves where I had big + + align:start position:0% +supply and demand curves where I had big + + + align:start position:0% +supply and demand curves where I had big +Q. That refers to the whole market. + + align:start position:0% +Q. That refers to the whole market. + + + align:start position:0% +Q. That refers to the whole market. +Little Q refers to a given firm within + + align:start position:0% +Little Q refers to a given firm within + + + align:start position:0% +Little Q refers to a given firm within +the market. Okay? and we'll go over that + + align:start position:0% +the market. Okay? and we'll go over that + + + align:start position:0% +the market. Okay? and we'll go over that +throughout. Okay. Now, these + + align:start position:0% +throughout. Okay. Now, these + + + align:start position:0% +throughout. Okay. Now, these +inputs can be what we call + + align:start position:0% + + + + align:start position:0% + +variable or + + align:start position:0% +variable or + + + align:start position:0% +variable or +fixed. And what do we mean by what do we + + align:start position:0% +fixed. And what do we mean by what do we + + + align:start position:0% +fixed. And what do we mean by what do we +mean by that? A varial input is an input + + align:start position:0% +mean by that? A varial input is an input + + + align:start position:0% +mean by that? A varial input is an input +that can be easily + + align:start position:0% +that can be easily + + + align:start position:0% +that can be easily +changed. A fixed input is one that is + + align:start position:0% +changed. A fixed input is one that is + + + align:start position:0% +changed. A fixed input is one that is +hard to change at least in the near + + align:start position:0% +hard to change at least in the near + + + align:start position:0% +hard to change at least in the near +term. + + align:start position:0% +term. + + + align:start position:0% +term. +So the key distinction between whether + + align:start position:0% +So the key distinction between whether + + + align:start position:0% +So the key distinction between whether +an input is variable or fixed is whether + + align:start position:0% +an input is variable or fixed is whether + + + align:start position:0% +an input is variable or fixed is whether +you're talking about the short + + align:start position:0% + + + + align:start position:0% + +run or the long + + align:start position:0% +run or the long + + + align:start position:0% +run or the long +run. The short run is + + align:start position:0% +run. The short run is + + + align:start position:0% +run. The short run is +defined as a period of time over which + + align:start position:0% +defined as a period of time over which + + + align:start position:0% +defined as a period of time over which +only some good some inputs are variable + + align:start position:0% +only some good some inputs are variable + + + align:start position:0% +only some good some inputs are variable +and others are fixed. + + align:start position:0% +and others are fixed. + + + align:start position:0% +and others are fixed. +The long run is defined as a period of + + align:start position:0% +The long run is defined as a period of + + + align:start position:0% +The long run is defined as a period of +time of which all inputs are + + align:start position:0% +time of which all inputs are + + + align:start position:0% +time of which all inputs are +variable. That's it. That's the + + align:start position:0% +variable. That's it. That's the + + + align:start position:0% +variable. That's it. That's the +definition. I'm not going to tell you + + align:start position:0% +definition. I'm not going to tell you + + + align:start position:0% +definition. I'm not going to tell you +the short run is six months and three + + align:start position:0% +the short run is six months and three + + + align:start position:0% +the short run is six months and three +days and four hours and long runs past + + align:start position:0% +days and four hours and long runs past + + + align:start position:0% +days and four hours and long runs past +that. I can't tell you that. I can't + + align:start position:0% +that. I can't tell you that. I can't + + + align:start position:0% +that. I can't tell you that. I can't +tell you what they represent except + + align:start position:0% +tell you what they represent except + + + align:start position:0% +tell you what they represent except +theoretically. Theoretically, we define + + align:start position:0% +theoretically. Theoretically, we define + + + align:start position:0% +theoretically. Theoretically, we define +the short run as a period of time which + + align:start position:0% +the short run as a period of time which + + + align:start position:0% +the short run as a period of time which +some inputs are fixed and some are + + align:start position:0% +some inputs are fixed and some are + + + align:start position:0% +some inputs are fixed and some are +variable. The long run is a period of + + align:start position:0% +variable. The long run is a period of + + + align:start position:0% +variable. The long run is a period of +time over which everything's variable. + + align:start position:0% +time over which everything's variable. + + + align:start position:0% +time over which everything's variable. +Think of the short run as days and the + + align:start position:0% +Think of the short run as days and the + + + align:start position:0% +Think of the short run as days and the +long run as decades and sort of where in + + align:start position:0% +long run as decades and sort of where in + + + align:start position:0% +long run as decades and sort of where in +between days and decades things lay in + + align:start position:0% +between days and decades things lay in + + + align:start position:0% +between days and decades things lay in +depends. Okay. So what we are going to + + align:start position:0% +depends. Okay. So what we are going to + + + align:start position:0% +depends. Okay. So what we are going to +do is we are going to assume that labor + + align:start position:0% +do is we are going to assume that labor + + + align:start position:0% +do is we are going to assume that labor +is variable and capital is + + align:start position:0% +is variable and capital is + + + align:start position:0% +is variable and capital is +fixed. That is labor is something you + + align:start position:0% +fixed. That is labor is something you + + + align:start position:0% +fixed. That is labor is something you +can adjust at any point in time. You can + + align:start position:0% +can adjust at any point in time. You can + + + align:start position:0% +can adjust at any point in time. You can +always fire somebody and hire someone + + align:start position:0% +always fire somebody and hire someone + + + align:start position:0% +always fire somebody and hire someone +the next day. Okay. Now, in reality, + + align:start position:0% +the next day. Okay. Now, in reality, + + + align:start position:0% +the next day. Okay. Now, in reality, +that's difficult, but in in theory, you + + align:start position:0% +that's difficult, but in in theory, you + + + align:start position:0% +that's difficult, but in in theory, you +can. Capital is harder to change. You + + align:start position:0% +can. Capital is harder to change. You + + + align:start position:0% +can. Capital is harder to change. You +got to build a new machine. You got to + + align:start position:0% +got to build a new machine. You got to + + + align:start position:0% +got to build a new machine. You got to +build a new building, etc. That's slower + + align:start position:0% +build a new building, etc. That's slower + + + align:start position:0% +build a new building, etc. That's slower +to change. So, we're going to call labor + + align:start position:0% +to change. So, we're going to call labor + + + align:start position:0% +to change. So, we're going to call labor +the variable input and capital the fixed + + align:start position:0% +the variable input and capital the fixed + + + align:start position:0% +the variable input and capital the fixed +input. So, in the short + + align:start position:0% +input. So, in the short + + + align:start position:0% +input. So, in the short +run, we get that labor will be variable + + align:start position:0% +run, we get that labor will be variable + + + align:start position:0% +run, we get that labor will be variable +and capital will be + + align:start position:0% +and capital will be + + + align:start position:0% +and capital will be +fixed. But in the long run, they're both + + align:start position:0% +fixed. But in the long run, they're both + + + align:start position:0% +fixed. But in the long run, they're both +variable. Now, of course, once again, in + + align:start position:0% +variable. Now, of course, once again, in + + + align:start position:0% +variable. Now, of course, once again, in +reality, this isn't so distinct. This + + align:start position:0% +reality, this isn't so distinct. This + + + align:start position:0% +reality, this isn't so distinct. This +isn't so clean. You can't just fire + + align:start position:0% +isn't so clean. You can't just fire + + + align:start position:0% +isn't so clean. You can't just fire +workers right away and replace them the + + align:start position:0% +workers right away and replace them the + + + align:start position:0% +workers right away and replace them the +next day, especially in this labor + + align:start position:0% +next day, especially in this labor + + + align:start position:0% +next day, especially in this labor +market with a lot of labor shortage. And + + align:start position:0% +market with a lot of labor shortage. And + + + align:start position:0% +market with a lot of labor shortage. And +you can build machines pretty quickly. + + align:start position:0% +you can build machines pretty quickly. + + + align:start position:0% +you can build machines pretty quickly. +Okay, so the short run long run + + align:start position:0% +Okay, so the short run long run + + + align:start position:0% +Okay, so the short run long run +distinction is obviously not perfect, + + align:start position:0% +distinction is obviously not perfect, + + + align:start position:0% +distinction is obviously not perfect, +but it allows us to essentially + + align:start position:0% +but it allows us to essentially + + + align:start position:0% +but it allows us to essentially +distinguish the the concept of things + + align:start position:0% +distinguish the the concept of things + + + align:start position:0% +distinguish the the concept of things +you can change quickly versus things you + + align:start position:0% +you can change quickly versus things you + + + align:start position:0% +you can change quickly versus things you +can't. Okay, let me pause there. There's + + align:start position:0% +can't. Okay, let me pause there. There's + + + align:start position:0% +can't. Okay, let me pause there. There's +a lot of definitions questions about + + align:start position:0% + + + + align:start position:0% + +that. Yeah. + + align:start position:0% + + + + align:start position:0% + +No Q. No, it should not. Q Q is a Q + + align:start position:0% +No Q. No, it should not. Q Q is a Q + + + align:start position:0% +No Q. No, it should not. Q Q is a Q +could be L plus K. That would be a + + align:start position:0% +could be L plus K. That would be a + + + align:start position:0% +could be L plus K. That would be a +particular form of F. But just like you + + align:start position:0% +particular form of F. But just like you + + + align:start position:0% +particular form of F. But just like you +can't tell me what form my utility + + align:start position:0% +can't tell me what form my utility + + + align:start position:0% +can't tell me what form my utility +function is, I can't tell you what form + + align:start position:0% +function is, I can't tell you what form + + + align:start position:0% +function is, I can't tell you what form +your production function is. This is + + align:start position:0% +your production function is. This is + + + align:start position:0% +your production function is. This is +some rich function of how you translate + + align:start position:0% +some rich function of how you translate + + + align:start position:0% +some rich function of how you translate +L and K to Q. So if Q is just L plus K, + + align:start position:0% +L and K to Q. So if Q is just L plus K, + + + align:start position:0% +L and K to Q. So if Q is just L plus K, +that would be a predictable production + + align:start position:0% +that would be a predictable production + + + align:start position:0% +that would be a predictable production +function, which would imply that another + + align:start position:0% +function, which would imply that another + + + align:start position:0% +function, which would imply that another +unit of labor, another unit of capital + + align:start position:0% +unit of labor, another unit of capital + + + align:start position:0% +unit of labor, another unit of capital +deliver. But what if a machine is five + + align:start position:0% +deliver. But what if a machine is five + + + align:start position:0% +deliver. But what if a machine is five +times as good as a worker? Then it' be + + align:start position:0% +times as good as a worker? Then it' be + + + align:start position:0% +times as good as a worker? Then it' be +L+ 5K. What if what if the effect of + + align:start position:0% +L+ 5K. What if what if the effect of + + + align:start position:0% +L+ 5K. What if what if the effect of +machines and workers varies based on how + + align:start position:0% +machines and workers varies based on how + + + align:start position:0% +machines and workers varies based on how +many machines and workers you have? Then + + align:start position:0% +many machines and workers you have? Then + + + align:start position:0% +many machines and workers you have? Then +it's a richer function. So just like + + align:start position:0% +it's a richer function. So just like + + + align:start position:0% +it's a richer function. So just like +utility isn't just cookies plus slices, + + align:start position:0% +utility isn't just cookies plus slices, + + + align:start position:0% +utility isn't just cookies plus slices, +it's some function of cookies and + + align:start position:0% +it's some function of cookies and + + + align:start position:0% +it's some function of cookies and +slices. Production is some function of + + align:start position:0% +slices. Production is some function of + + + align:start position:0% +slices. Production is some function of +labor and capital. All right, good + + align:start position:0% +labor and capital. All right, good + + + align:start position:0% +labor and capital. All right, good +question. Other + + align:start position:0% +question. Other + + + align:start position:0% +question. Other +questions? Okay, so now let's talk about + + align:start position:0% +questions? Okay, so now let's talk about + + + align:start position:0% +questions? Okay, so now let's talk about +the short run. Let's talk about shortrun + + align:start position:0% +the short run. Let's talk about shortrun + + + align:start position:0% +the short run. Let's talk about shortrun +production. And how do we think about a + + align:start position:0% +production. And how do we think about a + + + align:start position:0% +production. And how do we think about a +firm's shortrun production + + align:start position:0% +firm's shortrun production + + + align:start position:0% +firm's shortrun production +decisions? How do we think about a + + align:start position:0% +decisions? How do we think about a + + + align:start position:0% +decisions? How do we think about a +firm's shortrun production + + align:start position:0% +firm's shortrun production + + + align:start position:0% +firm's shortrun production +decisions? Well, in the short run, + + align:start position:0% +decisions? Well, in the short run, + + + align:start position:0% +decisions? Well, in the short run, +capital's fixed. So, we can write our + + align:start position:0% +capital's fixed. So, we can write our + + + align:start position:0% +capital's fixed. So, we can write our +production function as Q= F of L and K + + align:start position:0% +production function as Q= F of L and K + + + align:start position:0% +production function as Q= F of L and K +bar. Capital's fixed in the short run. + + align:start position:0% +bar. Capital's fixed in the short run. + + + align:start position:0% +bar. Capital's fixed in the short run. +Okay, that's definitional. + + align:start position:0% +Okay, that's definitional. + + + align:start position:0% +Okay, that's definitional. +So what the firm is trying to ask is + + align:start position:0% +So what the firm is trying to ask is + + + align:start position:0% +So what the firm is trying to ask is +look I can't change the machines I have + + align:start position:0% +look I can't change the machines I have + + + align:start position:0% +look I can't change the machines I have +that's fixed in the future I could + + align:start position:0% +that's fixed in the future I could + + + align:start position:0% +that's fixed in the future I could +change it but for my decision today I've + + align:start position:0% +change it but for my decision today I've + + + align:start position:0% +change it but for my decision today I've +gone to work today September 20th I + + align:start position:0% +gone to work today September 20th I + + + align:start position:0% +gone to work today September 20th I +showed up at work I have a decision to + + align:start position:0% +showed up at work I have a decision to + + + align:start position:0% +showed up at work I have a decision to +make today which is how many workers do + + align:start position:0% +make today which is how many workers do + + + align:start position:0% +make today which is how many workers do +I want today well the key input that + + align:start position:0% +I want today well the key input that + + + align:start position:0% +I want today well the key input that +decision is going to be the marginal + + align:start position:0% +decision is going to be the marginal + + + align:start position:0% +decision is going to be the marginal +product of + + align:start position:0% +product of + + + align:start position:0% +product of +labor which is how valuable is the next + + align:start position:0% +labor which is how valuable is the next + + + align:start position:0% +labor which is how valuable is the next +worker in terms of delivering output + + align:start position:0% +worker in terms of delivering output + + + align:start position:0% +worker in terms of delivering output +which is going to be DQ + + align:start position:0% + + + + align:start position:0% + +DL that is what is the marginal effect + + align:start position:0% +DL that is what is the marginal effect + + + align:start position:0% +DL that is what is the marginal effect +of the next worker. Remember this course + + align:start position:0% +of the next worker. Remember this course + + + align:start position:0% +of the next worker. Remember this course +always works on marginal decisions. What + + align:start position:0% +always works on marginal decisions. What + + + align:start position:0% +always works on marginal decisions. What +is the marginal effect of the next + + align:start position:0% +is the marginal effect of the next + + + align:start position:0% +is the marginal effect of the next +worker on output + + align:start position:0% +worker on output + + + align:start position:0% +worker on output +produced? + + align:start position:0% +produced? + + + align:start position:0% +produced? +Okay, we are going to + + align:start position:0% +Okay, we are going to + + + align:start position:0% +Okay, we are going to +assume that in the relevant range + + align:start position:0% +assume that in the relevant range + + + align:start position:0% +assume that in the relevant range +dqdl is + + align:start position:0% + + + + align:start position:0% + +negative that is we are going to assume + + align:start position:0% +negative that is we are going to assume + + + align:start position:0% +negative that is we are going to assume +diminishing marginal + + align:start position:0% +diminishing marginal + + + align:start position:0% +diminishing marginal +products. This does not mean diminishing + + align:start position:0% +products. This does not mean diminishing + + + align:start position:0% +products. This does not mean diminishing +total product. This does not mean once + + align:start position:0% +total product. This does not mean once + + + align:start position:0% +total product. This does not mean once +again like with consumers more is + + align:start position:0% +again like with consumers more is + + + align:start position:0% +again like with consumers more is +generally better. More workers are + + align:start position:0% +generally better. More workers are + + + align:start position:0% +generally better. More workers are +better. But each worker given fixed + + align:start position:0% +better. But each worker given fixed + + + align:start position:0% +better. But each worker given fixed +capital adds less to + + align:start position:0% +capital adds less to + + + align:start position:0% +capital adds less to +output. Okay. Now this is hard to think + + align:start position:0% +output. Okay. Now this is hard to think + + + align:start position:0% +output. Okay. Now this is hard to think +about and harder than it's easier with + + align:start position:0% +about and harder than it's easier with + + + align:start position:0% +about and harder than it's easier with +pizza slices to have this intuition but + + align:start position:0% +pizza slices to have this intuition but + + + align:start position:0% +pizza slices to have this intuition but +same intuition as pizza slices. So let's + + align:start position:0% +same intuition as pizza slices. So let's + + + align:start position:0% +same intuition as pizza slices. So let's +do an example illustrates it. Let's + + align:start position:0% +do an example illustrates it. Let's + + + align:start position:0% +do an example illustrates it. Let's +think about digging a hole. You want to + + align:start position:0% +think about digging a hole. You want to + + + align:start position:0% +think about digging a hole. You want to +dig a hole and you have one piece of + + align:start position:0% +dig a hole and you have one piece of + + + align:start position:0% +dig a hole and you have one piece of +capital, a + + align:start position:0% +capital, a + + + align:start position:0% +capital, a +shovel. And that can't be changed in the + + align:start position:0% +shovel. And that can't be changed in the + + + align:start position:0% +shovel. And that can't be changed in the +short run. All you can change is how + + align:start position:0% +short run. All you can change is how + + + align:start position:0% +short run. All you can change is how +many people you have working on digging + + align:start position:0% +many people you have working on digging + + + align:start position:0% +many people you have working on digging +the hole. So you hire the first person + + align:start position:0% +the hole. So you hire the first person + + + align:start position:0% +the hole. So you hire the first person +and they're digging. You hire a second + + align:start position:0% +and they're digging. You hire a second + + + align:start position:0% +and they're digging. You hire a second +person, you clearly you'll get faster, + + align:start position:0% +person, you clearly you'll get faster, + + + align:start position:0% +person, you clearly you'll get faster, +more productive digging. But will it be + + align:start position:0% +more productive digging. But will it be + + + align:start position:0% +more productive digging. But will it be +twice as fast? Well, maybe if you can + + align:start position:0% +twice as fast? Well, maybe if you can + + + align:start position:0% +twice as fast? Well, maybe if you can +get them to if you can get them to + + align:start position:0% +get them to if you can get them to + + + align:start position:0% +get them to if you can get them to +alternate shifts. One more 12, one to + + align:start position:0% +alternate shifts. One more 12, one to + + + align:start position:0% +alternate shifts. One more 12, one to +other 12. How about the third worker? + + align:start position:0% +other 12. How about the third worker? + + + align:start position:0% +other 12. How about the third worker? +Will be three times as fast? Maybe, but + + align:start position:0% +Will be three times as fast? Maybe, but + + + align:start position:0% +Will be three times as fast? Maybe, but +probably not. By the time you're the + + align:start position:0% +probably not. By the time you're the + + + align:start position:0% +probably not. By the time you're the +hundth worker, there's only one shovel. + + align:start position:0% +hundth worker, there's only one shovel. + + + align:start position:0% +hundth worker, there's only one shovel. +What are they going to do? They're sort + + align:start position:0% +What are they going to do? They're sort + + + align:start position:0% +What are they going to do? They're sort +of sitting around. You can rotate them + + align:start position:0% +of sitting around. You can rotate them + + + align:start position:0% +of sitting around. You can rotate them +really quickly. And you're certainly + + align:start position:0% +really quickly. And you're certainly + + + align:start position:0% +really quickly. And you're certainly +better off with a 100 workers than with + + align:start position:0% +better off with a 100 workers than with + + + align:start position:0% +better off with a 100 workers than with +90 workers because you can rotate it + + align:start position:0% +90 workers because you can rotate it + + + align:start position:0% +90 workers because you can rotate it +more quickly. But clearly the hundth + + align:start position:0% +more quickly. But clearly the hundth + + + align:start position:0% +more quickly. But clearly the hundth +worker is not as valuable as the second + + align:start position:0% +worker is not as valuable as the second + + + align:start position:0% +worker is not as valuable as the second +worker in terms of digging that + + align:start position:0% +worker in terms of digging that + + + align:start position:0% +worker in terms of digging that +hole. So the idea of diminished marginal + + align:start position:0% +hole. So the idea of diminished marginal + + + align:start position:0% +hole. So the idea of diminished marginal +product is given that you only have one + + align:start position:0% +product is given that you only have one + + + align:start position:0% +product is given that you only have one +shovel, giving you fixed capital, each + + align:start position:0% +shovel, giving you fixed capital, each + + + align:start position:0% +shovel, giving you fixed capital, each +additional worker does less and less + + align:start position:0% +additional worker does less and less + + + align:start position:0% +additional worker does less and less +good. Okay, it's not quite as simple as + + align:start position:0% +good. Okay, it's not quite as simple as + + + align:start position:0% +good. Okay, it's not quite as simple as +an intuition as diminishing margin + + align:start position:0% +an intuition as diminishing margin + + + align:start position:0% +an intuition as diminishing margin +utility, which I think is sort of na + + align:start position:0% +utility, which I think is sort of na + + + align:start position:0% +utility, which I think is sort of na +natural, but the and and you know it's + + align:start position:0% +natural, but the and and you know it's + + + align:start position:0% +natural, but the and and you know it's +not always true. Like I said, you can + + align:start position:0% +not always true. Like I said, you can + + + align:start position:0% +not always true. Like I said, you can +imagine the second worker might be as + + align:start position:0% +imagine the second worker might be as + + + align:start position:0% +imagine the second worker might be as +good as the first worker, but in + + align:start position:0% +good as the first worker, but in + + + align:start position:0% +good as the first worker, but in +general, each additional worker will add + + align:start position:0% +general, each additional worker will add + + + align:start position:0% +general, each additional worker will add +less and less value if they're working + + align:start position:0% +less and less value if they're working + + + align:start position:0% +less and less value if they're working +with the same number of + + align:start position:0% +with the same number of + + + align:start position:0% +with the same number of +machines. Okay? Now, in the long run, + + align:start position:0% +machines. Okay? Now, in the long run, + + + align:start position:0% +machines. Okay? Now, in the long run, +you could take more advantage. You could + + align:start position:0% +you could take more advantage. You could + + + align:start position:0% +you could take more advantage. You could +add wheelbarrows and more shovels, and + + align:start position:0% +add wheelbarrows and more shovels, and + + + align:start position:0% +add wheelbarrows and more shovels, and +you could add sorts of capital and then + + align:start position:0% +you could add sorts of capital and then + + + align:start position:0% +you could add sorts of capital and then +make each worker more productive. But in + + align:start position:0% +make each worker more productive. But in + + + align:start position:0% +make each worker more productive. But in +in the short run, with only one piece of + + align:start position:0% +in the short run, with only one piece of + + + align:start position:0% +in the short run, with only one piece of +capital, that one shovel, there is uh + + align:start position:0% +capital, that one shovel, there is uh + + + align:start position:0% +capital, that one shovel, there is uh +nothing else you can do. Yeah. + + align:start position:0% + + + + align:start position:0% + +I'm sorry. Yeah, I'm sorry. It's + + align:start position:0% +I'm sorry. Yeah, I'm sorry. It's + + + align:start position:0% +I'm sorry. Yeah, I'm sorry. It's +diminishing. Shouldn't say negative. + + align:start position:0% +diminishing. Shouldn't say negative. + + + align:start position:0% +diminishing. Shouldn't say negative. +It's diminishing. My bad. It's + + align:start position:0% +It's diminishing. My bad. It's + + + align:start position:0% +It's diminishing. My bad. It's +diminishing. My bad. It's not negative. + + align:start position:0% +diminishing. My bad. It's not negative. + + + align:start position:0% +diminishing. My bad. It's not negative. +It's diminishing. Sorry about that. So, + + align:start position:0% +It's diminishing. Sorry about that. So, + + + align:start position:0% +It's diminishing. Sorry about that. So, +we have diminishing marginal product. DQ + + align:start position:0% +we have diminishing marginal product. DQ + + + align:start position:0% +we have diminishing marginal product. DQ +square or DL square is negative, but + + align:start position:0% +square or DL square is negative, but + + + align:start position:0% +square or DL square is negative, but +DQDL is positive. Each additional worker + + align:start position:0% +DQDL is positive. Each additional worker + + + align:start position:0% +DQDL is positive. Each additional worker +adds value. Add less and less and less. + + align:start position:0% +adds value. Add less and less and less. + + + align:start position:0% +adds value. Add less and less and less. +Thank you for catching + + align:start position:0% +Thank you for catching + + + align:start position:0% +Thank you for catching +that. Okay, other questions. + + align:start position:0% +that. Okay, other questions. + + + align:start position:0% +that. Okay, other questions. +So diminishing marginal product in the + + align:start position:0% +So diminishing marginal product in the + + + align:start position:0% +So diminishing marginal product in the +short run. That's all we're really going + + align:start position:0% +short run. That's all we're really going + + + align:start position:0% +short run. That's all we're really going +to say about the short run. The more + + align:start position:0% +to say about the short run. The more + + + align:start position:0% +to say about the short run. The more +interesting case is the long run. So now + + align:start position:0% +interesting case is the long run. So now + + + align:start position:0% +interesting case is the long run. So now +let's talk about long run + + align:start position:0% + + + + align:start position:0% + +production. The long run's more + + align:start position:0% +production. The long run's more + + + align:start position:0% +production. The long run's more +interesting because now you can vary + + align:start position:0% +interesting because now you can vary + + + align:start position:0% +interesting because now you can vary +both capital and labor. So now the + + align:start position:0% +both capital and labor. So now the + + + align:start position:0% +both capital and labor. So now the +problem's going to look just like the + + align:start position:0% +problem's going to look just like the + + + align:start position:0% +problem's going to look just like the +consumer choice problem. Consumer + + align:start position:0% +consumer choice problem. Consumer + + + align:start position:0% +consumer choice problem. Consumer +choice, we never said you couldn't + + align:start position:0% +choice, we never said you couldn't + + + align:start position:0% +choice, we never said you couldn't +affect number of pizza. You can only + + align:start position:0% +affect number of pizza. You can only + + + align:start position:0% +affect number of pizza. You can only +change cookies. That's what I've just + + align:start position:0% +change cookies. That's what I've just + + + align:start position:0% +change cookies. That's what I've just +done here. I've said you can't change + + align:start position:0% +done here. I've said you can't change + + + align:start position:0% +done here. I've said you can't change +pizza, you can only change cookies. And + + align:start position:0% +pizza, you can only change cookies. And + + + align:start position:0% +pizza, you can only change cookies. And +just as in that case, given a fixed + + align:start position:0% +just as in that case, given a fixed + + + align:start position:0% +just as in that case, given a fixed +amount of pizza, each additional cookie + + align:start position:0% +amount of pizza, each additional cookie + + + align:start position:0% +amount of pizza, each additional cookie +does less and less. Okay? Now, we're + + align:start position:0% +does less and less. Okay? Now, we're + + + align:start position:0% +does less and less. Okay? Now, we're +going to vary both. And guess what? + + align:start position:0% +going to vary both. And guess what? + + + align:start position:0% +going to vary both. And guess what? +We're going to choose a familiar form + + align:start position:0% +We're going to choose a familiar form + + + align:start position:0% +We're going to choose a familiar form +for the production function. Let's + + align:start position:0% +for the production function. Let's + + + align:start position:0% +for the production function. Let's +assume Q equals the square root of L* + + align:start position:0% +assume Q equals the square root of L* + + + align:start position:0% +assume Q equals the square root of L* +K. Let's assume Q equals the square root + + align:start position:0% +K. Let's assume Q equals the square root + + + align:start position:0% +K. Let's assume Q equals the square root +of L* K. familiar form but once again a + + align:start position:0% +of L* K. familiar form but once again a + + + align:start position:0% +of L* K. familiar form but once again a +useful form in this context just as it + + align:start position:0% +useful form in this context just as it + + + align:start position:0% +useful form in this context just as it +was in consumer + + align:start position:0% +was in consumer + + + align:start position:0% +was in consumer +theory and let's go to figure + + align:start position:0% + + + + align:start position:0% + +51 this + + align:start position:0% +51 this + + + align:start position:0% +51 this +illustrates a set of combinations of K + + align:start position:0% +illustrates a set of combinations of K + + + align:start position:0% +illustrates a set of combinations of K +and L which deliver the same amount of + + align:start position:0% +and L which deliver the same amount of + + + align:start position:0% +and L which deliver the same amount of +Q look familiar it should look familiar + + align:start position:0% +Q look familiar it should look familiar + + + align:start position:0% +Q look familiar it should look familiar +these look like indifference curves but + + align:start position:0% +these look like indifference curves but + + + align:start position:0% +these look like indifference curves but +in this context we call them Isoquants + + align:start position:0% +in this context we call them Isoquants + + + align:start position:0% +in this context we call them Isoquants +because we like making up cool words. + + align:start position:0% +because we like making up cool words. + + + align:start position:0% +because we like making up cool words. +Isoquants. An isoquant is the + + align:start position:0% +Isoquants. An isoquant is the + + + align:start position:0% +Isoquants. An isoquant is the +combination of K and L that delivers the + + align:start position:0% +combination of K and L that delivers the + + + align:start position:0% +combination of K and L that delivers the +same + + align:start position:0% +same + + + align:start position:0% +same +output. So all the features of + + align:start position:0% +output. So all the features of + + + align:start position:0% +output. So all the features of +indifference curves that we liked apply + + align:start position:0% +indifference curves that we liked apply + + + align:start position:0% +indifference curves that we liked apply +to + + align:start position:0% +to + + + align:start position:0% +to +isoquants. Okay. Further out is + + align:start position:0% +isoquants. Okay. Further out is + + + align:start position:0% +isoquants. Okay. Further out is +better. They slope down. They don't + + align:start position:0% +better. They slope down. They don't + + + align:start position:0% +better. They slope down. They don't +cross. Okay. And basically what it's + + align:start position:0% +cross. Okay. And basically what it's + + + align:start position:0% +cross. Okay. And basically what it's +saying + + align:start position:0% +saying + + + align:start position:0% +saying +is it's about opportunity cost. That + + align:start position:0% +is it's about opportunity cost. That + + + align:start position:0% +is it's about opportunity cost. That +basically as you have more capital for a + + align:start position:0% +basically as you have more capital for a + + + align:start position:0% +basically as you have more capital for a +given for a given amount of money you + + align:start position:0% +given for a given amount of money you + + + align:start position:0% +given for a given amount of money you +want to spend and less labor that's + + align:start position:0% +want to spend and less labor that's + + + align:start position:0% +want to spend and less labor that's +going to affect how much you produce. If + + align:start position:0% +going to affect how much you produce. If + + + align:start position:0% +going to affect how much you produce. If +it if the amount you produce stays + + align:start position:0% +it if the amount you produce stays + + + align:start position:0% +it if the amount you produce stays +constant, you switch capital and labor. + + align:start position:0% +constant, you switch capital and labor. + + + align:start position:0% +constant, you switch capital and labor. +You stay in the same isoquant. If you + + align:start position:0% +You stay in the same isoquant. If you + + + align:start position:0% +You stay in the same isoquant. If you +can produce more, you move out to a + + align:start position:0% +can produce more, you move out to a + + + align:start position:0% +can produce more, you move out to a +higher + + align:start position:0% +higher + + + align:start position:0% +higher +isoquant. + + align:start position:0% +isoquant. + + + align:start position:0% +isoquant. +Okay. Now here's a good question. It + + align:start position:0% +Okay. Now here's a good question. It + + + align:start position:0% +Okay. Now here's a good question. It +relates to the earlier question was + + align:start position:0% +relates to the earlier question was + + + align:start position:0% +relates to the earlier question was +asked about K plus + + align:start position:0% +asked about K plus + + + align:start position:0% +asked about K plus +L. What determines the shape of these + + align:start position:0% +L. What determines the shape of these + + + align:start position:0% +L. What determines the shape of these +isoquants. What determines their shape? + + align:start position:0% +isoquants. What determines their shape? + + + align:start position:0% +isoquants. What determines their shape? +What underlying sort of notion? It's a + + align:start position:0% +What underlying sort of notion? It's a + + + align:start position:0% +What underlying sort of notion? It's a +hard question. See if anyone's the + + align:start position:0% +hard question. See if anyone's the + + + align:start position:0% +hard question. See if anyone's the +intuition. When are when are these + + align:start position:0% +intuition. When are when are these + + + align:start position:0% +intuition. When are when are these +isoquants going to + + align:start position:0% +isoquants going to + + + align:start position:0% +isoquants going to +be more bendy and when are they going to + + align:start position:0% +be more bendy and when are they going to + + + align:start position:0% +be more bendy and when are they going to +be when are they going to be straighter + + align:start position:0% +be when are they going to be straighter + + + align:start position:0% +be when are they going to be straighter +and when are they going to be more bent? + + align:start position:0% +and when are they going to be more bent? + + + align:start position:0% +and when are they going to be more bent? +What's going to determine + + align:start position:0% +What's going to determine + + + align:start position:0% +What's going to determine +that? Yeah. + + align:start position:0% + + + + align:start position:0% + +Exactly. It's going to depend on the + + align:start position:0% +Exactly. It's going to depend on the + + + align:start position:0% +Exactly. It's going to depend on the +substitutability of the different + + align:start position:0% +substitutability of the different + + + align:start position:0% +substitutability of the different +inputs. The more + + align:start position:0% +inputs. The more + + + align:start position:0% +inputs. The more +substitutable, the straighter is the + + align:start position:0% +substitutable, the straighter is the + + + align:start position:0% +substitutable, the straighter is the +isoquant. The less substitutable, the + + align:start position:0% +isoquant. The less substitutable, the + + + align:start position:0% +isoquant. The less substitutable, the +more bent is the isoquant. So for + + align:start position:0% +more bent is the isoquant. So for + + + align:start position:0% +more bent is the isoquant. So for +example, let's look at figure + + align:start position:0% +example, let's look at figure + + + align:start position:0% +example, let's look at figure +52A. Here we have the production + + align:start position:0% +52A. Here we have the production + + + align:start position:0% +52A. Here we have the production +function that was that was suggested + + align:start position:0% +function that was that was suggested + + + align:start position:0% +function that was that was suggested +earlier. I like to think it's a + + align:start position:0% +earlier. I like to think it's a + + + align:start position:0% +earlier. I like to think it's a +production function between this is one + + align:start position:0% +production function between this is one + + + align:start position:0% +production function between this is one +where goods are perfectly substitutable. + + align:start position:0% +where goods are perfectly substitutable. + + + align:start position:0% +where goods are perfectly substitutable. +Okay, I think it's a production function + + align:start position:0% +Okay, I think it's a production function + + + align:start position:0% +Okay, I think it's a production function +between Harvard graduates and Beanie + + align:start position:0% +between Harvard graduates and Beanie + + + align:start position:0% +between Harvard graduates and Beanie +Babies. Okay, perfectly nothing on that. + + align:start position:0% +Babies. Okay, perfectly nothing on that. + + + align:start position:0% +Babies. Okay, perfectly nothing on that. +Come on guys, work with me here. Okay, + + align:start position:0% +Come on guys, work with me here. Okay, + + + align:start position:0% +Come on guys, work with me here. Okay, +this is the this perfectly + + align:start position:0% +this is the this perfectly + + + align:start position:0% +this is the this perfectly +substitutable. Okay, and bas No, no, + + align:start position:0% +substitutable. Okay, and bas No, no, + + + align:start position:0% +substitutable. Okay, and bas No, no, +don't mean to offend the Harvard the + + align:start position:0% +don't mean to offend the Harvard the + + + align:start position:0% +don't mean to offend the Harvard the +Harvard students in the class, they're + + align:start position:0% +Harvard students in the class, they're + + + align:start position:0% +Harvard students in the class, they're +smart. They came over here to take + + align:start position:0% +smart. They came over here to take + + + align:start position:0% +smart. They came over here to take +classes, so they're exempted. Okay, but + + align:start position:0% +classes, so they're exempted. Okay, but + + + align:start position:0% +classes, so they're exempted. Okay, but +basically the idea is these inputs are + + align:start position:0% +basically the idea is these inputs are + + + align:start position:0% +basically the idea is these inputs are +perfectly + + align:start position:0% +perfectly + + + align:start position:0% +perfectly +substitutable. So it doesn't matter if + + align:start position:0% +substitutable. So it doesn't matter if + + + align:start position:0% +substitutable. So it doesn't matter if +you have a unit of labor capital as long + + align:start position:0% +you have a unit of labor capital as long + + + align:start position:0% +you have a unit of labor capital as long +as you have just matters the total + + align:start position:0% +as you have just matters the total + + + align:start position:0% +as you have just matters the total +number of units you have in that term as + + align:start position:0% +number of units you have in that term as + + + align:start position:0% +number of units you have in that term as +your production that would lead to these + + align:start position:0% +your production that would lead to these + + + align:start position:0% +your production that would lead to these +straight downward sloping + + align:start position:0% +straight downward sloping + + + align:start position:0% +straight downward sloping +isoquants. On the other hand, consider + + align:start position:0% +isoquants. On the other hand, consider + + + align:start position:0% +isoquants. On the other hand, consider +something like figure 52B on the other + + align:start position:0% +something like figure 52B on the other + + + align:start position:0% +something like figure 52B on the other +side of the + + align:start position:0% +side of the + + + align:start position:0% +side of the +page. These would be nonsubstitutable + + align:start position:0% +page. These would be nonsubstitutable + + + align:start position:0% +page. These would be nonsubstitutable +inputs so that the production function + + align:start position:0% +inputs so that the production function + + + align:start position:0% +inputs so that the production function +is Q equals the min of X and Y. For + + align:start position:0% +is Q equals the min of X and Y. For + + + align:start position:0% +is Q equals the min of X and Y. For +example, think of these like cereal and + + align:start position:0% +example, think of these like cereal and + + + align:start position:0% +example, think of these like cereal and +cereal boxes. Okay? Doesn't matter how + + align:start position:0% +cereal boxes. Okay? Doesn't matter how + + + align:start position:0% +cereal boxes. Okay? Doesn't matter how +much for every amount of cereal you got, + + align:start position:0% +much for every amount of cereal you got, + + + align:start position:0% +much for every amount of cereal you got, +you got to have a box. If you only have + + align:start position:0% +you got to have a box. If you only have + + + align:start position:0% +you got to have a box. If you only have +one box, it doesn't matter how much + + align:start position:0% +one box, it doesn't matter how much + + + align:start position:0% +one box, it doesn't matter how much +cereal you have, it's just going to sit + + align:start position:0% +cereal you have, it's just going to sit + + + align:start position:0% +cereal you have, it's just going to sit +there. Okay? You need more boxes. Okay? + + align:start position:0% +there. Okay? You need more boxes. Okay? + + + align:start position:0% +there. Okay? You need more boxes. Okay? +So, just like the indifference curves + + align:start position:0% +So, just like the indifference curves + + + align:start position:0% +So, just like the indifference curves +for this case were left shoe, right + + align:start position:0% +for this case were left shoe, right + + + align:start position:0% +for this case were left shoe, right +shoe. This is you think of serial serial + + align:start position:0% +shoe. This is you think of serial serial + + + align:start position:0% +shoe. This is you think of serial serial +boxes things which are + + align:start position:0% +boxes things which are + + + align:start position:0% +boxes things which are +nonsubstitutable. They can't substitute + + align:start position:0% +nonsubstitutable. They can't substitute + + + align:start position:0% +nonsubstitutable. They can't substitute +for each other at all. And in that case + + align:start position:0% +for each other at all. And in that case + + + align:start position:0% +for each other at all. And in that case +you get these squared uh squared + + align:start position:0% +you get these squared uh squared + + + align:start position:0% +you get these squared uh squared +isoquants. + + align:start position:0% +isoquants. + + + align:start position:0% +isoquants. +Okay, questions about that uh + + align:start position:0% + + + + align:start position:0% + +intuition. So it's the degree of + + align:start position:0% +intuition. So it's the degree of + + + align:start position:0% +intuition. So it's the degree of +substitutability which determines the + + align:start position:0% +substitutability which determines the + + + align:start position:0% +substitutability which determines the +shape of these isoquants. more + + align:start position:0% +shape of these isoquants. more + + + align:start position:0% +shape of these isoquants. more +generally just we'll generally be in + + align:start position:0% +generally just we'll generally be in + + + align:start position:0% +generally just we'll generally be in +between as I said nothing's ever at the + + align:start position:0% +between as I said nothing's ever at the + + + align:start position:0% +between as I said nothing's ever at the +extremes we'll generally be in between + + align:start position:0% +extremes we'll generally be in between + + + align:start position:0% +extremes we'll generally be in between +these two cases and we'll have an + + align:start position:0% +these two cases and we'll have an + + + align:start position:0% +these two cases and we'll have an +isoquant that looks like figure + + align:start position:0% +isoquant that looks like figure + + + align:start position:0% +isoquant that looks like figure +53 and along that isoquant we have the + + align:start position:0% +53 and along that isoquant we have the + + + align:start position:0% +53 and along that isoquant we have the +slope which is the + + align:start position:0% +slope which is the + + + align:start position:0% +slope which is the +marginal the marginal rate of technical + + align:start position:0% +marginal the marginal rate of technical + + + align:start position:0% +marginal the marginal rate of technical +substitution just to really mess you up + + align:start position:0% +substitution just to really mess you up + + + align:start position:0% +substitution just to really mess you up +with consumers your margin rate + + align:start position:0% +with consumers your margin rate + + + align:start position:0% +with consumers your margin rate +substitution margin rate of + + align:start position:0% +substitution margin rate of + + + align:start position:0% +substitution margin rate of +transformation MRS and MRT now I'm going + + align:start position:0% +transformation MRS and MRT now I'm going + + + align:start position:0% +transformation MRS and MRT now I'm going +to have MRTS okay which is the margin + + align:start position:0% +to have MRTS okay which is the margin + + + align:start position:0% +to have MRTS okay which is the margin +rate of technical + + align:start position:0% +rate of technical + + + align:start position:0% +rate of technical +substitution okay that is the margin + + align:start position:0% +substitution okay that is the margin + + + align:start position:0% +substitution okay that is the margin +rate of technical substitution is the + + align:start position:0% +rate of technical substitution is the + + + align:start position:0% +rate of technical substitution is the +rate at which effectively you can trade + + align:start position:0% +rate at which effectively you can trade + + + align:start position:0% +rate at which effectively you can trade +off labor and capital to produce the + + align:start position:0% +off labor and capital to produce the + + + align:start position:0% +off labor and capital to produce the +same quantity of + + align:start position:0% +same quantity of + + + align:start position:0% +same quantity of +good so and essentially we can relate + + align:start position:0% +good so and essentially we can relate + + + align:start position:0% +good so and essentially we can relate +this just as we can relate the MRS to + + align:start position:0% +this just as we can relate the MRS to + + + align:start position:0% +this just as we can relate the MRS to +margin utilities yeah I'm sorry go ahead + + align:start position:0% + + + + align:start position:0% + +Roger of technical + + align:start position:0% +Roger of technical + + + align:start position:0% +Roger of technical +substitution margin of technical + + align:start position:0% +substitution margin of technical + + + align:start position:0% +substitution margin of technical +substitution. Remember when we developed + + align:start position:0% +substitution. Remember when we developed + + + align:start position:0% +substitution. Remember when we developed +the margin rate of substitution I used a + + align:start position:0% +the margin rate of substitution I used a + + + align:start position:0% +the margin rate of substitution I used a +little proof to show you how it relates + + align:start position:0% +little proof to show you how it relates + + + align:start position:0% +little proof to show you how it relates +to margin utilities. We can use the same + + align:start position:0% +to margin utilities. We can use the same + + + align:start position:0% +to margin utilities. We can use the same +proof here which is let's ask let's ask + + align:start position:0% +proof here which is let's ask let's ask + + + align:start position:0% +proof here which is let's ask let's ask +what happens you have a marginal + + align:start position:0% +what happens you have a marginal + + + align:start position:0% +what happens you have a marginal +increase in labor and a marginal + + align:start position:0% +increase in labor and a marginal + + + align:start position:0% +increase in labor and a marginal +decrease in capital so that you stay on + + align:start position:0% +decrease in capital so that you stay on + + + align:start position:0% +decrease in capital so that you stay on +the same line. Okay. Well, we know the + + align:start position:0% +the same line. Okay. Well, we know the + + + align:start position:0% +the same line. Okay. Well, we know the +So, we're asking where DL time MPL, the + + align:start position:0% +So, we're asking where DL time MPL, the + + + align:start position:0% +So, we're asking where DL time MPL, the +marginal product of + + align:start position:0% +marginal product of + + + align:start position:0% +marginal product of +labor, plus DK time MPK, just as a + + align:start position:0% +labor, plus DK time MPK, just as a + + + align:start position:0% +labor, plus DK time MPK, just as a +marginal product of labor, there's a + + align:start position:0% +marginal product of labor, there's a + + + align:start position:0% +marginal product of labor, there's a +marginal product of + + align:start position:0% +marginal product of + + + align:start position:0% +marginal product of +capital. Okay, same intuition. It's + + align:start position:0% +capital. Okay, same intuition. It's + + + align:start position:0% +capital. Okay, same intuition. It's +diminishing. One worker each additional + + align:start position:0% +diminishing. One worker each additional + + + align:start position:0% +diminishing. One worker each additional +shovel does less and less good. Okay, + + align:start position:0% +shovel does less and less good. Okay, + + + align:start position:0% +shovel does less and less good. Okay, +same concept there. That's equal to zero + + align:start position:0% +same concept there. That's equal to zero + + + align:start position:0% +same concept there. That's equal to zero +along that indifference curve. It's an + + align:start position:0% +along that indifference curve. It's an + + + align:start position:0% +along that indifference curve. It's an +incremental step along that indifference + + align:start position:0% +incremental step along that indifference + + + align:start position:0% +incremental step along that indifference +curve. So solving this, this says that + + align:start position:0% +curve. So solving this, this says that + + + align:start position:0% +curve. So solving this, this says that +this the slope of that indifference + + align:start position:0% +this the slope of that indifference + + + align:start position:0% +this the slope of that indifference +curve DK + + align:start position:0% +curve DK + + + align:start position:0% +curve DK +DL okay is equal to the + + align:start position:0% +DL okay is equal to the + + + align:start position:0% +DL okay is equal to the +MRTS which is equal to + + align:start position:0% +MRTS which is equal to + + + align:start position:0% +MRTS which is equal to +minus + + align:start position:0% +minus + + + align:start position:0% +minus +MPL over + + align:start position:0% + + + + align:start position:0% + +MPK. The slope of the indifference curve + + align:start position:0% +MPK. The slope of the indifference curve + + + align:start position:0% +MPK. The slope of the indifference curve +is minus MPL over MK APK. Once again, + + align:start position:0% +is minus MPL over MK APK. Once again, + + + align:start position:0% +is minus MPL over MK APK. Once again, +looks should look familiar from consumer + + align:start position:0% +looks should look familiar from consumer + + + align:start position:0% +looks should look familiar from consumer +theory. Okay, it's the ratio of the + + align:start position:0% +theory. Okay, it's the ratio of the + + + align:start position:0% +theory. Okay, it's the ratio of the +marginal products that determines the + + align:start position:0% +marginal products that determines the + + + align:start position:0% +marginal products that determines the +slope of the indifference curve. + + align:start position:0% +slope of the indifference curve. + + + align:start position:0% +slope of the indifference curve. +Okay. So for + + align:start position:0% +Okay. So for + + + align:start position:0% +Okay. So for +example, let's take our production + + align:start position:0% +example, let's take our production + + + align:start position:0% +example, let's take our production +function we're using here, which is uh + + align:start position:0% +function we're using here, which is uh + + + align:start position:0% +function we're using here, which is uh +square root of L * K. That's our + + align:start position:0% +square root of L * K. That's our + + + align:start position:0% +square root of L * K. That's our +production function. Okay. Let's solve + + align:start position:0% +production function. Okay. Let's solve + + + align:start position:0% +production function. Okay. Let's solve +for the marginal rate of technical + + align:start position:0% +for the marginal rate of technical + + + align:start position:0% +for the marginal rate of technical +substitution. Well, we know what's the + + align:start position:0% +substitution. Well, we know what's the + + + align:start position:0% +substitution. Well, we know what's the +marginal product of labor. The marginal + + align:start position:0% +marginal product of labor. The marginal + + + align:start position:0% +marginal product of labor. The marginal +product of labor is the + + align:start position:0% +product of labor is the + + + align:start position:0% +product of labor is the +derivative of this production + + align:start position:0% +derivative of this production + + + align:start position:0% +derivative of this production +function with respect to + + align:start position:0% +function with respect to + + + align:start position:0% +function with respect to +L. Okay, take the der of that production + + align:start position:0% +L. Okay, take the der of that production + + + align:start position:0% +L. Okay, take the der of that production +function with respect to L and you get + + align:start position:0% +function with respect to L and you get + + + align:start position:0% +function with respect to L and you get +0.5 * K over square root of K * + + align:start position:0% +0.5 * K over square root of K * + + + align:start position:0% +0.5 * K over square root of K * +L. The marginal product of capital is + + align:start position:0% +L. The marginal product of capital is + + + align:start position:0% +L. The marginal product of capital is +the derivative of this production + + align:start position:0% +the derivative of this production + + + align:start position:0% +the derivative of this production +function with respect to + + align:start position:0% +function with respect to + + + align:start position:0% +function with respect to +K. You take that derivative, you get 0.5 + + align:start position:0% +K. You take that derivative, you get 0.5 + + + align:start position:0% +K. You take that derivative, you get 0.5 +* + + align:start position:0% +* + + + align:start position:0% +* +L over K * + + align:start position:0% +L over K * + + + align:start position:0% +L over K * +L. So that the marginal rate of + + align:start position:0% +L. So that the marginal rate of + + + align:start position:0% +L. So that the marginal rate of +technical substitution is the ratio of + + align:start position:0% +technical substitution is the ratio of + + + align:start position:0% +technical substitution is the ratio of +these two the opposite ratio which + + align:start position:0% +these two the opposite ratio which + + + align:start position:0% +these two the opposite ratio which +equals minus K over L. + + align:start position:0% +equals minus K over L. + + + align:start position:0% +equals minus K over L. +In this case once again I don't want to + + align:start position:0% +In this case once again I don't want to + + + align:start position:0% +In this case once again I don't want to +confuse people this is the this is for + + align:start position:0% +confuse people this is the this is for + + + align:start position:0% +confuse people this is the this is for +for this production function that's a + + align:start position:0% +for this production function that's a + + + align:start position:0% +for this production function that's a +marginary touchal substitution just like + + align:start position:0% +marginary touchal substitution just like + + + align:start position:0% +marginary touchal substitution just like +for this utility function I got a + + align:start position:0% +for this utility function I got a + + + align:start position:0% +for this utility function I got a +particular margin of substitution okay + + align:start position:0% +particular margin of substitution okay + + + align:start position:0% +particular margin of substitution okay +that is I'm just showing you how to + + align:start position:0% +that is I'm just showing you how to + + + align:start position:0% +that is I'm just showing you how to +develop it for a given production + + align:start position:0% +develop it for a given production + + + align:start position:0% +develop it for a given production +function and that gives you something + + align:start position:0% +function and that gives you something + + + align:start position:0% +function and that gives you something +like figure + + align:start position:0% +like figure + + + align:start position:0% +like figure +53 okay figure 53 shows you the marginal + + align:start position:0% +53 okay figure 53 shows you the marginal + + + align:start position:0% +53 okay figure 53 shows you the marginal +rate technical substitution for this + + align:start position:0% +rate technical substitution for this + + + align:start position:0% +rate technical substitution for this +production function and you can see that + + align:start position:0% +production function and you can see that + + + align:start position:0% +production function and you can see that +at for example a point like A you have + + align:start position:0% +at for example a point like A you have + + + align:start position:0% +at for example a point like A you have +an MRTS of + + align:start position:0% +an MRTS of + + + align:start position:0% +an MRTS of +minus4. That means that you have very + + align:start position:0% +minus4. That means that you have very + + + align:start position:0% +minus4. That means that you have very +little labor and a lot of capital. That + + align:start position:0% +little labor and a lot of capital. That + + + align:start position:0% +little labor and a lot of capital. That +means you give up four units of capital + + align:start position:0% +means you give up four units of capital + + + align:start position:0% +means you give up four units of capital +to get one more worker. Why? Because + + align:start position:0% +to get one more worker. Why? Because + + + align:start position:0% +to get one more worker. Why? Because +marginal products are diminishing. When + + align:start position:0% +marginal products are diminishing. When + + + align:start position:0% +marginal products are diminishing. When +you've got four shovels and one worker, + + align:start position:0% +you've got four shovels and one worker, + + + align:start position:0% +you've got four shovels and one worker, +you'd happily give up shovels to get + + align:start position:0% +you'd happily give up shovels to get + + + align:start position:0% +you'd happily give up shovels to get +more workers. Okay? So, you want to move + + align:start position:0% +more workers. Okay? So, you want to move + + + align:start position:0% +more workers. Okay? So, you want to move +to the right. Likewise, at point C, + + align:start position:0% +to the right. Likewise, at point C, + + + align:start position:0% +to the right. Likewise, at point C, +you've got four workers and one shovel. + + align:start position:0% +you've got four workers and one shovel. + + + align:start position:0% +you've got four workers and one shovel. +that's doing you no good. You'd happily + + align:start position:0% +that's doing you no good. You'd happily + + + align:start position:0% +that's doing you no good. You'd happily +give up a worker to get a shovel. So you + + align:start position:0% +give up a worker to get a shovel. So you + + + align:start position:0% +give up a worker to get a shovel. So you +want to move to the + + align:start position:0% +want to move to the + + + align:start position:0% +want to move to the +left. Okay, so basically um that is how + + align:start position:0% +left. Okay, so basically um that is how + + + align:start position:0% +left. Okay, so basically um that is how +we end up with with this marginal rate + + align:start position:0% +we end up with with this marginal rate + + + align:start position:0% +we end up with with this marginal rate +of technical substitution. Okay, + + align:start position:0% +of technical substitution. Okay, + + + align:start position:0% +of technical substitution. Okay, +questions about + + align:start position:0% + + + + align:start position:0% + +that? Okay, once again parallel to + + align:start position:0% +that? Okay, once again parallel to + + + align:start position:0% +that? Okay, once again parallel to +consumer + + align:start position:0% +consumer + + + align:start position:0% +consumer +theory. Now, now I'm going to talk about + + align:start position:0% +theory. Now, now I'm going to talk about + + + align:start position:0% +theory. Now, now I'm going to talk about +two things which are are not parallel to + + align:start position:0% +two things which are are not parallel to + + + align:start position:0% +two things which are are not parallel to +consumer theory. Let me just say by way + + align:start position:0% +consumer theory. Let me just say by way + + + align:start position:0% +consumer theory. Let me just say by way +of introduction, producer theory is one + + align:start position:0% +of introduction, producer theory is one + + + align:start position:0% +of introduction, producer theory is one +step harder than consumer theory. It's + + align:start position:0% +step harder than consumer theory. It's + + + align:start position:0% +step harder than consumer theory. It's +all the fun stuff for consumer theory + + align:start position:0% +all the fun stuff for consumer theory + + + align:start position:0% +all the fun stuff for consumer theory +plus one additional step. Okay? And + + align:start position:0% +plus one additional step. Okay? And + + + align:start position:0% +plus one additional step. Okay? And +we'll talk about that step starting uh + + align:start position:0% +we'll talk about that step starting uh + + + align:start position:0% +we'll talk about that step starting uh +two lectures from now. But for right + + align:start position:0% +two lectures from now. But for right + + + align:start position:0% +two lectures from now. But for right +now, it's parallel consumer theory. But + + align:start position:0% +now, it's parallel consumer theory. But + + + align:start position:0% +now, it's parallel consumer theory. But +here's a couple of wrinkles that arise + + align:start position:0% +here's a couple of wrinkles that arise + + + align:start position:0% +here's a couple of wrinkles that arise +in the context of production that you + + align:start position:0% +in the context of production that you + + + align:start position:0% +in the context of production that you +don't get in the context of + + align:start position:0% +don't get in the context of + + + align:start position:0% +don't get in the context of +consumption. The first wrinkle is what + + align:start position:0% +consumption. The first wrinkle is what + + + align:start position:0% +consumption. The first wrinkle is what +we + + align:start position:0% +we + + + align:start position:0% +we +call returns to scale. + + align:start position:0% +call returns to scale. + + + align:start position:0% +call returns to scale. +returns to + + align:start position:0% +returns to + + + align:start position:0% +returns to +scale. + + align:start position:0% +scale. + + + align:start position:0% +scale. +Okay, returns to scale are the notion of + + align:start position:0% +Okay, returns to scale are the notion of + + + align:start position:0% +Okay, returns to scale are the notion of +what + + align:start position:0% +what + + + align:start position:0% +what +happens when I increase all inputs + + align:start position:0% +happens when I increase all inputs + + + align:start position:0% +happens when I increase all inputs +proportionally. It's not sort of an + + align:start position:0% +proportionally. It's not sort of an + + + align:start position:0% +proportionally. It's not sort of an +interesting question for consumer + + align:start position:0% +interesting question for consumer + + + align:start position:0% +interesting question for consumer +theory, but it's interesting producer + + align:start position:0% +theory, but it's interesting producer + + + align:start position:0% +theory, but it's interesting producer +theory because I want to say what + + align:start position:0% +theory because I want to say what + + + align:start position:0% +theory because I want to say what +happens if the firm gets bigger. When + + align:start position:0% +happens if the firm gets bigger. When + + + align:start position:0% +happens if the firm gets bigger. When +you say in your mind, what happens when + + align:start position:0% +you say in your mind, what happens when + + + align:start position:0% +you say in your mind, what happens when +a firm gets bigger? You're thinking what + + align:start position:0% +a firm gets bigger? You're thinking what + + + align:start position:0% +a firm gets bigger? You're thinking what +happens when it just when everything + + align:start position:0% +happens when it just when everything + + + align:start position:0% +happens when it just when everything +increases, when all inputs increase + + align:start position:0% +increases, when all inputs increase + + + align:start position:0% +increases, when all inputs increase +proportionally is our notion of how a + + align:start position:0% +proportionally is our notion of how a + + + align:start position:0% +proportionally is our notion of how a +firm gets bigger. + + align:start position:0% +firm gets bigger. + + + align:start position:0% +firm gets bigger. +And so that's what we call return to + + align:start position:0% +And so that's what we call return to + + + align:start position:0% +And so that's what we call return to +scale. Scale is basically when you scale + + align:start position:0% +scale. Scale is basically when you scale + + + align:start position:0% +scale. Scale is basically when you scale +up everything or scale down everything + + align:start position:0% +up everything or scale down everything + + + align:start position:0% +up everything or scale down everything +equally. + + align:start position:0% +equally. + + + align:start position:0% +equally. +So the question is how does output + + align:start position:0% +So the question is how does output + + + align:start position:0% +So the question is how does output +respond? For example, it could be that + + align:start position:0% +respond? For example, it could be that + + + align:start position:0% +respond? For example, it could be that +when you double inputs, you double + + align:start position:0% +when you double inputs, you double + + + align:start position:0% +when you double inputs, you double +outputs. It could be that f of 2 L comma + + align:start position:0% +outputs. It could be that f of 2 L comma + + + align:start position:0% +outputs. It could be that f of 2 L comma +2 k equals 2 * f of l k. + + align:start position:0% +2 k equals 2 * f of l k. + + + align:start position:0% +2 k equals 2 * f of l k. +We'll call this a constant + + align:start position:0% +We'll call this a constant + + + align:start position:0% +We'll call this a constant +returnsto-scale production + + align:start position:0% +returnsto-scale production + + + align:start position:0% +returnsto-scale production +function. Double output, double inputs, + + align:start position:0% +function. Double output, double inputs, + + + align:start position:0% +function. Double output, double inputs, +double outputs. Sort of a natural + + align:start position:0% +double outputs. Sort of a natural + + + align:start position:0% +double outputs. Sort of a natural +intuition, but it doesn't have to be the + + align:start position:0% +intuition, but it doesn't have to be the + + + align:start position:0% +intuition, but it doesn't have to be the +case. Indeed, + + align:start position:0% +case. Indeed, + + + align:start position:0% +case. Indeed, +typically we assume firms have we call + + align:start position:0% +typically we assume firms have we call + + + align:start position:0% +typically we assume firms have we call +diminishing returns to scale. Decreasing + + align:start position:0% +diminishing returns to scale. Decreasing + + + align:start position:0% +diminishing returns to scale. Decreasing +returns to scale. I'm sorry. Decreasing + + align:start position:0% +returns to scale. I'm sorry. Decreasing + + + align:start position:0% +returns to scale. I'm sorry. Decreasing +returns to scale where f of 2 L comma 2k + + align:start position:0% +returns to scale where f of 2 L comma 2k + + + align:start position:0% +returns to scale where f of 2 L comma 2k +is less than 2 * f of l and k. That is + + align:start position:0% +is less than 2 * f of l and k. That is + + + align:start position:0% +is less than 2 * f of l and k. That is +when you double inputs, you get less + + align:start position:0% +when you double inputs, you get less + + + align:start position:0% +when you double inputs, you get less +than twice as much + + align:start position:0% +than twice as much + + + align:start position:0% +than twice as much +outputs. Why is that? Well, think about + + align:start position:0% +outputs. Why is that? Well, think about + + + align:start position:0% +outputs. Why is that? Well, think about +the idea that basically uh if you you're + + align:start position:0% +the idea that basically uh if you you're + + + align:start position:0% +the idea that basically uh if you you're +still trying to dig a hole. There's one + + align:start position:0% +still trying to dig a hole. There's one + + + align:start position:0% +still trying to dig a hole. There's one +guy with one shovel. You got two guys + + align:start position:0% +guy with one shovel. You got two guys + + + align:start position:0% +guy with one shovel. You got two guys +with two shovels. They're in each + + align:start position:0% +with two shovels. They're in each + + + align:start position:0% +with two shovels. They're in each +other's way. they can't quite work as + + align:start position:0% +other's way. they can't quite work as + + + align:start position:0% +other's way. they can't quite work as +efficiently as one guy with one shovel + + align:start position:0% +efficiently as one guy with one shovel + + + align:start position:0% +efficiently as one guy with one shovel +because you're still trying to dig one + + align:start position:0% +because you're still trying to dig one + + + align:start position:0% +because you're still trying to dig one +hole. Okay? So, it's a decrease in + + align:start position:0% +hole. Okay? So, it's a decrease in + + + align:start position:0% +hole. Okay? So, it's a decrease in +return to scale doubling the enterprise + + align:start position:0% +return to scale doubling the enterprise + + + align:start position:0% +return to scale doubling the enterprise +or if you go to four guys with four + + align:start position:0% +or if you go to four guys with four + + + align:start position:0% +or if you go to four guys with four +shovels, they're definitely going to be + + align:start position:0% +shovels, they're definitely going to be + + + align:start position:0% +shovels, they're definitely going to be +just be way. They have to sit around for + + align:start position:0% +just be way. They have to sit around for + + + align:start position:0% +just be way. They have to sit around for +a while. So, doubling the enterprise + + align:start position:0% +a while. So, doubling the enterprise + + + align:start position:0% +a while. So, doubling the enterprise +doesn't double production. Of course, we + + align:start position:0% +doesn't double production. Of course, we + + + align:start position:0% +doesn't double production. Of course, we +can also consider cases of increasing + + align:start position:0% +can also consider cases of increasing + + + align:start position:0% +can also consider cases of increasing +returns to scale where f of 2L con + + align:start position:0% +returns to scale where f of 2L con + + + align:start position:0% +returns to scale where f of 2L con +2k is greater than 2 * f of l and + + align:start position:0% +2k is greater than 2 * f of l and + + + align:start position:0% +2k is greater than 2 * f of l and +k. Increase in returns to + + align:start position:0% +k. Increase in returns to + + + align:start position:0% +k. Increase in returns to +scale that would might arise through + + align:start position:0% +scale that would might arise through + + + align:start position:0% +scale that would might arise through +something like the fact that when the + + align:start position:0% +something like the fact that when the + + + align:start position:0% +something like the fact that when the +firm gets bigger, it can specialize + + align:start position:0% +firm gets bigger, it can specialize + + + align:start position:0% +firm gets bigger, it can specialize +more. So maybe as a firm gets bigger and + + align:start position:0% +more. So maybe as a firm gets bigger and + + + align:start position:0% +more. So maybe as a firm gets bigger and +bigger, it can get better and better at + + align:start position:0% +bigger, it can get better and better at + + + align:start position:0% +bigger, it can get better and better at +what it does and production can become + + align:start position:0% +what it does and production can become + + + align:start position:0% +what it does and production can become +more and more efficient. + + align:start position:0% +more and more efficient. + + + align:start position:0% +more and more efficient. +Okay. So these this is an important + + align:start position:0% +Okay. So these this is an important + + + align:start position:0% +Okay. So these this is an important +concept because basically this is how we + + align:start position:0% +concept because basically this is how we + + + align:start position:0% +concept because basically this is how we +think about economies growing. This is + + align:start position:0% +think about economies growing. This is + + + align:start position:0% +think about economies growing. This is +the core of any model of economic + + align:start position:0% +the core of any model of economic + + + align:start position:0% +the core of any model of economic +growth. If you take macroeconomics about + + align:start position:0% +growth. If you take macroeconomics about + + + align:start position:0% +growth. If you take macroeconomics about +economic growth the core of any model of + + align:start position:0% +economic growth the core of any model of + + + align:start position:0% +economic growth the core of any model of +economic growth is what is the returns + + align:start position:0% +economic growth is what is the returns + + + align:start position:0% +economic growth is what is the returns +to scale for the + + align:start position:0% +to scale for the + + + align:start position:0% +to scale for the +economy. Typically economists do not + + align:start position:0% +economy. Typically economists do not + + + align:start position:0% +economy. Typically economists do not +believe that there's everywhere and + + align:start position:0% +believe that there's everywhere and + + + align:start position:0% +believe that there's everywhere and +always increasing returns to scale. We + + align:start position:0% +always increasing returns to scale. We + + + align:start position:0% +always increasing returns to scale. We +typically believe returns to scale may + + align:start position:0% +typically believe returns to scale may + + + align:start position:0% +typically believe returns to scale may +increase initially as you specialize the + + align:start position:0% +increase initially as you specialize the + + + align:start position:0% +increase initially as you specialize the +firm but eventually have to decrease. + + align:start position:0% +firm but eventually have to decrease. + + + align:start position:0% +firm but eventually have to decrease. +And the reason we believe that or at + + align:start position:0% +And the reason we believe that or at + + + align:start position:0% +And the reason we believe that or at +least believed that was that if there + + align:start position:0% +least believed that was that if there + + + align:start position:0% +least believed that was that if there +was always and forever increasing + + align:start position:0% +was always and forever increasing + + + align:start position:0% +was always and forever increasing +returns to scale, how many firms would + + align:start position:0% +returns to scale, how many firms would + + + align:start position:0% +returns to scale, how many firms would +there be in the + + align:start position:0% +there be in the + + + align:start position:0% +there be in the +economy? One. Because it could always + + align:start position:0% +economy? One. Because it could always + + + align:start position:0% +economy? One. Because it could always +just do better by getting bigger and + + align:start position:0% +just do better by getting bigger and + + + align:start position:0% +just do better by getting bigger and +bigger and bigger. Now, it turns out for + + align:start position:0% +bigger and bigger. Now, it turns out for + + + align:start position:0% +bigger and bigger. Now, it turns out for +search engines, maybe that's not such a + + align:start position:0% +search engines, maybe that's not such a + + + align:start position:0% +search engines, maybe that's not such a +bad description. We'll see in the trial + + align:start position:0% +bad description. We'll see in the trial + + + align:start position:0% +bad description. We'll see in the trial +that's going on now where Google may get + + align:start position:0% +that's going on now where Google may get + + + align:start position:0% +that's going on now where Google may get +broken up. So it may be that increasing + + align:start position:0% +broken up. So it may be that increasing + + + align:start position:0% +broken up. So it may be that increasing +returns to scale may last longer than we + + align:start position:0% +returns to scale may last longer than we + + + align:start position:0% +returns to scale may last longer than we +thought as economists but typically we + + align:start position:0% +thought as economists but typically we + + + align:start position:0% +thought as economists but typically we +think of firms as maybe initially having + + align:start position:0% +think of firms as maybe initially having + + + align:start position:0% +think of firms as maybe initially having +increasing return insurance to scale and + + align:start position:0% +increasing return insurance to scale and + + + align:start position:0% +increasing return insurance to scale and +then eventually as they mature having + + align:start position:0% +then eventually as they mature having + + + align:start position:0% +then eventually as they mature having +decreasing returns to + + align:start position:0% +decreasing returns to + + + align:start position:0% +decreasing returns to +scale. Okay, questions about + + align:start position:0% +scale. Okay, questions about + + + align:start position:0% +scale. Okay, questions about +that. Yeah. + + align:start position:0% + + + + align:start position:0% + +Well, I'm going to get to that in a + + align:start position:0% +Well, I'm going to get to that in a + + + align:start position:0% +Well, I'm going to get to that in a +second. Not necessarily. And I'm going + + align:start position:0% +second. Not necessarily. And I'm going + + + align:start position:0% +second. Not necessarily. And I'm going +to get I'm going to get to that in one + + align:start position:0% +to get I'm going to get to that in one + + + align:start position:0% +to get I'm going to get to that in one +second. + + align:start position:0% +second. + + + align:start position:0% +second. +Okay, I want to because we haven't + + align:start position:0% +Okay, I want to because we haven't + + + align:start position:0% +Okay, I want to because we haven't +talked about innovation yet and that's a + + align:start position:0% +talked about innovation yet and that's a + + + align:start position:0% +talked about innovation yet and that's a +missing piece of this that I want to + + align:start position:0% +missing piece of this that I want to + + + align:start position:0% +missing piece of this that I want to +turn to next. But other questions? So + + align:start position:0% +turn to next. But other questions? So + + + align:start position:0% +turn to next. But other questions? So +I'm going to turn to last before I do I + + align:start position:0% +I'm going to turn to last before I do I + + + align:start position:0% +I'm going to turn to last before I do I +just want to review where we are. So + + align:start position:0% +just want to review where we are. So + + + align:start position:0% +just want to review where we are. So +basically just like we have utility + + align:start position:0% +basically just like we have utility + + + align:start position:0% +basically just like we have utility +function and production function it + + align:start position:0% +function and production function it + + + align:start position:0% +function and production function it +translates your inputs into your + + align:start position:0% +translates your inputs into your + + + align:start position:0% +translates your inputs into your +outputs. In the short run labor's fixed, + + align:start position:0% +outputs. In the short run labor's fixed, + + + align:start position:0% +outputs. In the short run labor's fixed, +capital's not this is just the only + + align:start position:0% +capital's not this is just the only + + + align:start position:0% +capital's not this is just the only +reason I tell you short run case is to + + align:start position:0% +reason I tell you short run case is to + + + align:start position:0% +reason I tell you short run case is to +develop the intuition of diminishing + + align:start position:0% +develop the intuition of diminishing + + + align:start position:0% +develop the intuition of diminishing +marginal products. The ancient case the + + align:start position:0% +marginal products. The ancient case the + + + align:start position:0% +marginal products. The ancient case the +long run was where it's just like + + align:start position:0% +long run was where it's just like + + + align:start position:0% +long run was where it's just like +consumer theory. You're just like + + align:start position:0% +consumer theory. You're just like + + + align:start position:0% +consumer theory. You're just like +consumer theory. You're trading off + + align:start position:0% +consumer theory. You're trading off + + + align:start position:0% +consumer theory. You're trading off +pizza pizza and cookies to make you + + align:start position:0% +pizza pizza and cookies to make you + + + align:start position:0% +pizza pizza and cookies to make you +happy. Here you're trading off labor and + + align:start position:0% +happy. Here you're trading off labor and + + + align:start position:0% +happy. Here you're trading off labor and +capital to make a good. Okay. And it's + + align:start position:0% +capital to make a good. Okay. And it's + + + align:start position:0% +capital to make a good. Okay. And it's +the same mathematics we saw + + align:start position:0% +the same mathematics we saw + + + align:start position:0% +the same mathematics we saw +before. All + + align:start position:0% +before. All + + + align:start position:0% +before. All +right. And likewise, just as we had + + align:start position:0% +right. And likewise, just as we had + + + align:start position:0% +right. And likewise, just as we had +marginal rates of substitution + + align:start position:0% +marginal rates of substitution + + + align:start position:0% +marginal rates of substitution +determining the slope of the difference + + align:start position:0% +determining the slope of the difference + + + align:start position:0% +determining the slope of the difference +curve, we have these marginal rates of + + align:start position:0% +curve, we have these marginal rates of + + + align:start position:0% +curve, we have these marginal rates of +technical substitution determining the + + align:start position:0% +technical substitution determining the + + + align:start position:0% +technical substitution determining the +slope of the isoquant. + + align:start position:0% +slope of the isoquant. + + + align:start position:0% +slope of the isoquant. +Now let me come to the question here and + + align:start position:0% +Now let me come to the question here and + + + align:start position:0% +Now let me come to the question here and +talk about a last topic which is + + align:start position:0% + + + + align:start position:0% + +productivity. One of the most exciting + + align:start position:0% +productivity. One of the most exciting + + + align:start position:0% +productivity. One of the most exciting +topics in economics is thinking about + + align:start position:0% +topics in economics is thinking about + + + align:start position:0% +topics in economics is thinking about +productivity. Okay. One of the most + + align:start position:0% +productivity. Okay. One of the most + + + align:start position:0% +productivity. Okay. One of the most +famous and the idea of productivity + + align:start position:0% +famous and the idea of productivity + + + align:start position:0% +famous and the idea of productivity +comes actually from a very famous + + align:start position:0% +comes actually from a very famous + + + align:start position:0% +comes actually from a very famous +application from + + align:start position:0% +application from + + + align:start position:0% +application from +1798 of the idea of uh decreasing + + align:start position:0% +1798 of the idea of uh decreasing + + + align:start position:0% +1798 of the idea of uh decreasing +returns to scale or diminishing marginal + + align:start position:0% +returns to scale or diminishing marginal + + + align:start position:0% +returns to scale or diminishing marginal +product. Thomas Malfus was a very I + + align:start position:0% +product. Thomas Malfus was a very I + + + align:start position:0% +product. Thomas Malfus was a very I +think probably pretty depressed + + align:start position:0% +think probably pretty depressed + + + align:start position:0% +think probably pretty depressed +philosopher given all the stuff he wrote + + align:start position:0% +philosopher given all the stuff he wrote + + + align:start position:0% +philosopher given all the stuff he wrote +uh back in the + + align:start position:0% +uh back in the + + + align:start position:0% +uh back in the +1700s and he said look think about the + + align:start position:0% +1700s and he said look think about the + + + align:start position:0% +1700s and he said look think about the +production of + + align:start position:0% +production of + + + align:start position:0% +production of +agriculture there's essentially two + + align:start position:0% +agriculture there's essentially two + + + align:start position:0% +agriculture there's essentially two +inputs there's people and land the + + align:start position:0% +inputs there's people and land the + + + align:start position:0% +inputs there's people and land the +people harvest the land he said in the + + align:start position:0% +people harvest the land he said in the + + + align:start position:0% +people harvest the land he said in the +the difference between capital and land + + align:start position:0% +the difference between capital and land + + + align:start position:0% +the difference between capital and land +is land is always fixed even in the long + + align:start position:0% +is land is always fixed even in the long + + + align:start position:0% +is land is always fixed even in the long +run there's only so much land we got the + + align:start position:0% +run there's only so much land we got the + + + align:start position:0% +run there's only so much land we got the +earth unless we go colonize another + + align:start position:0% +earth unless we go colonize another + + + align:start position:0% +earth unless we go colonize another +planet which I don't think he was + + align:start position:0% +planet which I don't think he was + + + align:start position:0% +planet which I don't think he was +thinking about back then there's a fixed + + align:start position:0% +thinking about back then there's a fixed + + + align:start position:0% +thinking about back then there's a fixed +amount of land so that means that the + + align:start position:0% +amount of land so that means that the + + + align:start position:0% +amount of land so that means that the +marginal product of labor must be + + align:start position:0% +marginal product of labor must be + + + align:start position:0% +marginal product of labor must be +everywhere + + align:start position:0% +everywhere + + + align:start position:0% +everywhere +diminishing that means that + + align:start position:0% +diminishing that means that + + + align:start position:0% +diminishing that means that +eventually we're going to starve there's + + align:start position:0% +eventually we're going to starve there's + + + align:start position:0% +eventually we're going to starve there's +only so much land as population grows + + align:start position:0% +only so much land as population grows + + + align:start position:0% +only so much land as population grows +each worker's producing less and less + + align:start position:0% +each worker's producing less and less + + + align:start position:0% +each worker's producing less and less +and less on the same amount of land and + + align:start position:0% +and less on the same amount of land and + + + align:start position:0% +and less on the same amount of land and +eventually we starve through the + + align:start position:0% +eventually we starve through the + + + align:start position:0% +eventually we starve through the +principle diminished marginal product he + + align:start position:0% +principle diminished marginal product he + + + align:start position:0% +principle diminished marginal product he +didn't put it that way but that was + + align:start position:0% +didn't put it that way but that was + + + align:start position:0% +didn't put it that way but that was +intuition basically a fixed amount of + + align:start position:0% +intuition basically a fixed amount of + + + align:start position:0% +intuition basically a fixed amount of +land ever growing population each worker + + align:start position:0% +land ever growing population each worker + + + align:start position:0% +land ever growing population each worker +produces less and less and less until + + align:start position:0% +produces less and less and less until + + + align:start position:0% +produces less and less and less until +you can't feed yourself until you + + align:start position:0% +you can't feed yourself until you + + + align:start position:0% +you can't feed yourself until you +produce less than actually needed to + + align:start position:0% +produce less than actually needed to + + + align:start position:0% +produce less than actually needed to +feed yourself and people start to die + + align:start position:0% +feed yourself and people start to die + + + align:start position:0% +feed yourself and people start to die +off. So Mthus actually said that there + + align:start position:0% +off. So Mthus actually said that there + + + align:start position:0% +off. So Mthus actually said that there +would be cycle the world would be would + + align:start position:0% +would be cycle the world would be would + + + align:start position:0% +would be cycle the world would be would +be marked by cycles of starvation that + + align:start position:0% +be marked by cycles of starvation that + + + align:start position:0% +be marked by cycles of starvation that +essentially population would grow we'd + + align:start position:0% +essentially population would grow we'd + + + align:start position:0% +essentially population would grow we'd +be unable to lose enough food. We'd all + + align:start position:0% +be unable to lose enough food. We'd all + + + align:start position:0% +be unable to lose enough food. We'd all +a bunch of us would die off then we'd + + align:start position:0% +a bunch of us would die off then we'd + + + align:start position:0% +a bunch of us would die off then we'd +have a small enough population we'd have + + align:start position:0% +have a small enough population we'd have + + + align:start position:0% +have a small enough population we'd have +marginal product of labor that could + + align:start position:0% +marginal product of labor that could + + + align:start position:0% +marginal product of labor that could +support production and we go back to + + align:start position:0% +support production and we go back to + + + align:start position:0% +support production and we go back to +producing food again till we all died + + align:start position:0% +producing food again till we all died + + + align:start position:0% +producing food again till we all died +off again. really not a very happy uh + + align:start position:0% +off again. really not a very happy uh + + + align:start position:0% +off again. really not a very happy uh +picture of the + + align:start position:0% +picture of the + + + align:start position:0% +picture of the +future. Now, since Mthus wrote that + + align:start position:0% +future. Now, since Mthus wrote that + + + align:start position:0% +future. Now, since Mthus wrote that +book, the world population increased + + align:start position:0% +book, the world population increased + + + align:start position:0% +book, the world population increased +roughly a + + align:start position:0% +roughly a + + + align:start position:0% +roughly a +thousand%. Okay, roughly a thousand% + + align:start position:0% +thousand%. Okay, roughly a thousand% + + + align:start position:0% +thousand%. Okay, roughly a thousand% +increase in world population and we are + + align:start position:0% +increase in world population and we are + + + align:start position:0% +increase in world population and we are +fatter than + + align:start position:0% +fatter than + + + align:start position:0% +fatter than +ever. Okay, so what did Mthus get wrong? + + align:start position:0% +ever. Okay, so what did Mthus get wrong? + + + align:start position:0% +ever. Okay, so what did Mthus get wrong? +I mean, not there's not starvation and + + align:start position:0% +I mean, not there's not starvation and + + + align:start position:0% +I mean, not there's not starvation and +let me be clear, there's horrible + + align:start position:0% +let me be clear, there's horrible + + + align:start position:0% +let me be clear, there's horrible +problem starvation around the world. + + align:start position:0% +problem starvation around the world. + + + align:start position:0% +problem starvation around the world. +Although let me also be clear the famous + + align:start position:0% +Although let me also be clear the famous + + + align:start position:0% +Although let me also be clear the famous +economist of Marchen effectively won the + + align:start position:0% +economist of Marchen effectively won the + + + align:start position:0% +economist of Marchen effectively won the +nob Nobel prize for an important + + align:start position:0% +nob Nobel prize for an important + + + align:start position:0% +nob Nobel prize for an important +observation which is that there's never + + align:start position:0% +observation which is that there's never + + + align:start position:0% +observation which is that there's never +been a famine in a + + align:start position:0% +been a famine in a + + + align:start position:0% +been a famine in a +democracy. So we think about famines and + + align:start position:0% +democracy. So we think about famines and + + + align:start position:0% +democracy. So we think about famines and +starvation all over the world. Remember + + align:start position:0% +starvation all over the world. Remember + + + align:start position:0% +starvation all over the world. Remember +that's a political failure not + + align:start position:0% +that's a political failure not + + + align:start position:0% +that's a political failure not +technological failure. There's never + + align:start position:0% +technological failure. There's never + + + align:start position:0% +technological failure. There's never +been a famine in democracy. Famines only + + align:start position:0% +been a famine in democracy. Famines only + + + align:start position:0% +been a famine in democracy. Famines only +happen when corrupt governments uh don't + + align:start position:0% +happen when corrupt governments uh don't + + + align:start position:0% +happen when corrupt governments uh don't +spread the food they need to the people + + align:start position:0% +spread the food they need to the people + + + align:start position:0% +spread the food they need to the people +who need to get it. So fundamentally we + + align:start position:0% +who need to get it. So fundamentally we + + + align:start position:0% +who need to get it. So fundamentally we +have enough food despite the fact + + align:start position:0% +have enough food despite the fact + + + align:start position:0% +have enough food despite the fact +population has gone up 10 times. gone up + + align:start position:0% +population has gone up 10 times. gone up + + + align:start position:0% +population has gone up 10 times. gone up +a thousand% sorry 100 times. So what is + + align:start position:0% +a thousand% sorry 100 times. So what is + + + align:start position:0% +a thousand% sorry 100 times. So what is +it? What's happened? What's changed? + + align:start position:0% +it? What's happened? What's changed? + + + align:start position:0% +it? What's happened? What's changed? +What did Mthus mix miss? Yeah. + + align:start position:0% +What did Mthus mix miss? Yeah. + + + align:start position:0% +What did Mthus mix miss? Yeah. +Technology. Mus the fact that we are + + align:start position:0% +Technology. Mus the fact that we are + + + align:start position:0% +Technology. Mus the fact that we are +missing a key component of how we write + + align:start position:0% +missing a key component of how we write + + + align:start position:0% +missing a key component of how we write +down our production function. We because + + align:start position:0% +down our production function. We because + + + align:start position:0% +down our production function. We because +there's actually productivity + + align:start position:0% +there's actually productivity + + + align:start position:0% +there's actually productivity +improvements in agriculture. What were + + align:start position:0% +improvements in agriculture. What were + + + align:start position:0% +improvements in agriculture. What were +they? Well, + + align:start position:0% +they? Well, + + + align:start position:0% +they? Well, +fertilizers, machines, + + align:start position:0% +fertilizers, machines, + + + align:start position:0% +fertilizers, machines, +um basically in the long run we have and + + align:start position:0% +um basically in the long run we have and + + + align:start position:0% +um basically in the long run we have and +eventually uh disease resistant seeds, + + align:start position:0% +eventually uh disease resistant seeds, + + + align:start position:0% +eventually uh disease resistant seeds, +better land management practices. He + + align:start position:0% +better land management practices. He + + + align:start position:0% +better land management practices. He +missed all the changes. He was right + + align:start position:0% +missed all the changes. He was right + + + align:start position:0% +missed all the changes. He was right +that the amount of land is fixed, but he + + align:start position:0% +that the amount of land is fixed, but he + + + align:start position:0% +that the amount of land is fixed, but he +missed the fact that the way we used + + align:start position:0% +missed the fact that the way we used + + + align:start position:0% +missed the fact that the way we used +land will get more and more productive + + align:start position:0% +land will get more and more productive + + + align:start position:0% +land will get more and more productive +over time. He missed all the technology + + align:start position:0% +over time. He missed all the technology + + + align:start position:0% +over time. He missed all the technology +that was going to come. He missed the + + align:start position:0% +that was going to come. He missed the + + + align:start position:0% +that was going to come. He missed the +productivity improvements that we were + + align:start position:0% +productivity improvements that we were + + + align:start position:0% +productivity improvements that we were +going to + + align:start position:0% +going to + + + align:start position:0% +going to +see. Okay. + + align:start position:0% +see. Okay. + + + align:start position:0% +see. Okay. +actually world food consumption per + + align:start position:0% +actually world food consumption per + + + align:start position:0% +actually world food consumption per +capita is actually up since 1950 despite + + align:start position:0% +capita is actually up since 1950 despite + + + align:start position:0% +capita is actually up since 1950 despite +the fact that world population has + + align:start position:0% +the fact that world population has + + + align:start position:0% +the fact that world population has +grown. So what this says is really we + + align:start position:0% +grown. So what this says is really we + + + align:start position:0% +grown. So what this says is really we +should really think about writing + + align:start position:0% +should really think about writing + + + align:start position:0% +should really think about writing +production functions as Q uh equals A + + align:start position:0% +production functions as Q uh equals A + + + align:start position:0% +production functions as Q uh equals A +time F of L and K where A is a + + align:start position:0% +time F of L and K where A is a + + + align:start position:0% +time F of L and K where A is a +productivity factor. + + align:start position:0% + + + + align:start position:0% + +Okay, basically there's an extra piece + + align:start position:0% +Okay, basically there's an extra piece + + + align:start position:0% +Okay, basically there's an extra piece +which makes the world more + + align:start position:0% +which makes the world more + + + align:start position:0% +which makes the world more +productive. Okay, this is not just true + + align:start position:0% +productive. Okay, this is not just true + + + align:start position:0% +productive. Okay, this is not just true +in + + align:start position:0% +in + + + align:start position:0% +in +agriculture. Let's think of one of the + + align:start position:0% +agriculture. Let's think of one of the + + + align:start position:0% +agriculture. Let's think of one of the +most famous examples which is car + + align:start position:0% +most famous examples which is car + + + align:start position:0% +most famous examples which is car +production. Okay, basically before the + + align:start position:0% +production. Okay, basically before the + + + align:start position:0% +production. Okay, basically before the +1900s, cars were made like other + + align:start position:0% +1900s, cars were made like other + + + align:start position:0% +1900s, cars were made like other +customized goods. A single person or a + + align:start position:0% +customized goods. A single person or a + + + align:start position:0% +customized goods. A single person or a +couple people make it together. And then + + align:start position:0% +couple people make it together. And then + + + align:start position:0% +couple people make it together. And then +Henry Ford introduced the assembly line + + align:start position:0% +Henry Ford introduced the assembly line + + + align:start position:0% +Henry Ford introduced the assembly line +where basically you had interchangeable + + align:start position:0% +where basically you had interchangeable + + + align:start position:0% +where basically you had interchangeable +parts and you had a conveyor belt or + + align:start position:0% +parts and you had a conveyor belt or + + + align:start position:0% +parts and you had a conveyor belt or +assembly line where people could just + + align:start position:0% +assembly line where people could just + + + align:start position:0% +assembly line where people could just +specialize in putting this this screwing + + align:start position:0% +specialize in putting this this screwing + + + align:start position:0% +specialize in putting this this screwing +this bolt in over and over and over + + align:start position:0% +this bolt in over and over and over + + + align:start position:0% +this bolt in over and over and over +again and they could do it much faster + + align:start position:0% +again and they could do it much faster + + + align:start position:0% +again and they could do it much faster +and they could specialize in it. Now + + align:start position:0% +and they could specialize in it. Now + + + align:start position:0% +and they could specialize in it. Now +this seems pretty obvious at the time + + align:start position:0% +this seems pretty obvious at the time + + + align:start position:0% +this seems pretty obvious at the time +but it was very pretty obvious now. It's + + align:start position:0% +but it was very pretty obvious now. It's + + + align:start position:0% +but it was very pretty obvious now. It's +pretty radical at the time. He actually + + align:start position:0% +pretty radical at the time. He actually + + + align:start position:0% +pretty radical at the time. He actually +cut the car cost of car production in + + align:start position:0% +cut the car cost of car production in + + + align:start position:0% +cut the car cost of car production in +half almost + + align:start position:0% +half almost + + + align:start position:0% +half almost +overnight. That was a massive + + align:start position:0% +overnight. That was a massive + + + align:start position:0% +overnight. That was a massive +productivity improvement. the same + + align:start position:0% +productivity improvement. the same + + + align:start position:0% +productivity improvement. the same +number of workers could produce many + + align:start position:0% +number of workers could produce many + + + align:start position:0% +number of workers could produce many +more many same number of workers and + + align:start position:0% +more many same number of workers and + + + align:start position:0% +more many same number of workers and +same number of machines you can produce + + align:start position:0% +same number of machines you can produce + + + align:start position:0% +same number of machines you can produce +many many more + + align:start position:0% +many many more + + + align:start position:0% +many many more +cars. Okay. Now, but this innovation + + align:start position:0% +cars. Okay. Now, but this innovation + + + align:start position:0% +cars. Okay. Now, but this innovation +didn't just end with Henry Ford. Okay. + + align:start position:0% +didn't just end with Henry Ford. Okay. + + + align:start position:0% +didn't just end with Henry Ford. Okay. +Um the Indian company Tata produces the + + align:start position:0% +Um the Indian company Tata produces the + + + align:start position:0% +Um the Indian company Tata produces the +Nano which is a $2,500 car. How is the + + align:start position:0% +Nano which is a $2,500 car. How is the + + + align:start position:0% +Nano which is a $2,500 car. How is the +Nano so cheap? Well, it's basically much + + align:start position:0% +Nano so cheap? Well, it's basically much + + + align:start position:0% +Nano so cheap? Well, it's basically much +lighter than other cars. It's much + + align:start position:0% +lighter than other cars. It's much + + + align:start position:0% +lighter than other cars. It's much +smaller, but they do things like putting + + align:start position:0% +smaller, but they do things like putting + + + align:start position:0% +smaller, but they do things like putting +the wheels way out on the edge instead + + align:start position:0% +the wheels way out on the edge instead + + + align:start position:0% +the wheels way out on the edge instead +of under the car to create more room for + + align:start position:0% +of under the car to create more room for + + + align:start position:0% +of under the car to create more room for +people to sit in. Okay? And they + + align:start position:0% +people to sit in. Okay? And they + + + align:start position:0% +people to sit in. Okay? And they +minimize the parts that are used to make + + align:start position:0% +minimize the parts that are used to make + + + align:start position:0% +minimize the parts that are used to make +it easy to exchange and easier to + + align:start position:0% +it easy to exchange and easier to + + + align:start position:0% +it easy to exchange and easier to +repair. Innovation is going on. And of + + align:start position:0% +repair. Innovation is going on. And of + + + align:start position:0% +repair. Innovation is going on. And of +course, we're seeing perhaps most one of + + align:start position:0% +course, we're seeing perhaps most one of + + + align:start position:0% +course, we're seeing perhaps most one of +the most major innovations in our in + + align:start position:0% +the most major innovations in our in + + + align:start position:0% +the most major innovations in our in +automobile industry in decades, which is + + align:start position:0% +automobile industry in decades, which is + + + align:start position:0% +automobile industry in decades, which is +the electrification of the automobile + + align:start position:0% +the electrification of the automobile + + + align:start position:0% +the electrification of the automobile +fleet. And if you don't think Tesla's + + align:start position:0% +fleet. And if you don't think Tesla's + + + align:start position:0% +fleet. And if you don't think Tesla's +more innovative than an old Ford, you + + align:start position:0% +more innovative than an old Ford, you + + + align:start position:0% +more innovative than an old Ford, you +haven't seen a Tesla, okay? despite what + + align:start position:0% +haven't seen a Tesla, okay? despite what + + + align:start position:0% +haven't seen a Tesla, okay? despite what +we think about Elon Musk. It's a pretty + + align:start position:0% +we think about Elon Musk. It's a pretty + + + align:start position:0% +we think about Elon Musk. It's a pretty +cool car. Okay. So, basically we are + + align:start position:0% +cool car. Okay. So, basically we are + + + align:start position:0% +cool car. Okay. So, basically we are +seeing continuous continuous um uh + + align:start position:0% +seeing continuous continuous um uh + + + align:start position:0% +seeing continuous continuous um uh +productivity improvements and that's + + align:start position:0% +productivity improvements and that's + + + align:start position:0% +productivity improvements and that's +what the standard model + + align:start position:0% +what the standard model + + + align:start position:0% +what the standard model +misses. Okay. is that basically now this + + align:start position:0% +misses. Okay. is that basically now this + + + align:start position:0% +misses. Okay. is that basically now this +has + + align:start position:0% +has + + + align:start position:0% +has +become a really important area in + + align:start position:0% +become a really important area in + + + align:start position:0% +become a really important area in +economics because ultimately a or + + align:start position:0% +economics because ultimately a or + + + align:start position:0% +economics because ultimately a or +product improvements become one of the + + align:start position:0% +product improvements become one of the + + + align:start position:0% +product improvements become one of the +key determinants for countries in their + + align:start position:0% +key determinants for countries in their + + + align:start position:0% +key determinants for countries in their +standard of + + align:start position:0% +standard of + + + align:start position:0% +standard of +living. Okay. So with standard of living + + align:start position:0% +living. Okay. So with standard of living + + + align:start position:0% +living. Okay. So with standard of living +think of it as how much stuff do we get + + align:start position:0% +think of it as how much stuff do we get + + + align:start position:0% +think of it as how much stuff do we get +to consume per person? Think of it as + + align:start position:0% +to consume per person? Think of it as + + + align:start position:0% +to consume per person? Think of it as +our standard of living. How much stuff + + align:start position:0% +our standard of living. How much stuff + + + align:start position:0% +our standard of living. How much stuff +do we have per person? Okay. What's + + align:start position:0% +do we have per person? Okay. What's + + + align:start position:0% +do we have per person? Okay. What's +going to determine that? three things. + + align:start position:0% +going to determine that? three things. + + + align:start position:0% +going to determine that? three things. +How hard we + + align:start position:0% +How hard we + + + align:start position:0% +How hard we +work, how many machines we + + align:start position:0% +work, how many machines we + + + align:start position:0% +work, how many machines we +have, and how productive we are with + + align:start position:0% +have, and how productive we are with + + + align:start position:0% +have, and how productive we are with +those + + align:start position:0% +those + + + align:start position:0% +those +inputs. Those are three things that'll + + align:start position:0% +inputs. Those are three things that'll + + + align:start position:0% +inputs. Those are three things that'll +determine how much stuff we have. What's + + align:start position:0% +determine how much stuff we have. What's + + + align:start position:0% +determine how much stuff we have. What's +great about productivity is these two + + align:start position:0% +great about productivity is these two + + + align:start position:0% +great about productivity is these two +are expensive. Working harder is costly. + + align:start position:0% +are expensive. Working harder is costly. + + + align:start position:0% +are expensive. Working harder is costly. +You got to work harder. It sucks. + + align:start position:0% +You got to work harder. It sucks. + + + align:start position:0% +You got to work harder. It sucks. +Capital, you got to build a machine. You + + align:start position:0% +Capital, you got to build a machine. You + + + align:start position:0% +Capital, you got to build a machine. You +need to use stuff to build a machine. + + align:start position:0% +need to use stuff to build a machine. + + + align:start position:0% +need to use stuff to build a machine. +Productivity, boom, you got more. A + + align:start position:0% +Productivity, boom, you got more. A + + + align:start position:0% +Productivity, boom, you got more. A +brilliant idea and suddenly, boom, you + + align:start position:0% +brilliant idea and suddenly, boom, you + + + align:start position:0% +brilliant idea and suddenly, boom, you +got more stuff for everyone. + + align:start position:0% +got more stuff for everyone. + + + align:start position:0% +got more stuff for everyone. +So productivity is is the magic that + + align:start position:0% +So productivity is is the magic that + + + align:start position:0% +So productivity is is the magic that +makes economic growth happen almost + + align:start position:0% +makes economic growth happen almost + + + align:start position:0% +makes economic growth happen almost +costlessly. Okay? And as a result, + + align:start position:0% +costlessly. Okay? And as a result, + + + align:start position:0% +costlessly. Okay? And as a result, +productivity is the central determinant + + align:start position:0% +productivity is the central determinant + + + align:start position:0% +productivity is the central determinant +of our standard of + + align:start position:0% +of our standard of + + + align:start position:0% +of our standard of +living. And it turns out productivity + + align:start position:0% +living. And it turns out productivity + + + align:start position:0% +living. And it turns out productivity +has changed. From World War II until + + align:start position:0% +has changed. From World War II until + + + align:start position:0% +has changed. From World War II until +about + + align:start position:0% +about + + + align:start position:0% +about +1973, US productivity grew at about 2 + + align:start position:0% +1973, US productivity grew at about 2 + + + align:start position:0% +1973, US productivity grew at about 2 +and a half% a year. What that meant was + + align:start position:0% +and a half% a year. What that meant was + + + align:start position:0% +and a half% a year. What that meant was +working just as hard with just as many + + align:start position:0% +working just as hard with just as many + + + align:start position:0% +working just as hard with just as many +machines, we could each consume two and + + align:start position:0% +machines, we could each consume two and + + + align:start position:0% +machines, we could each consume two and +a half% more stuff every single + + align:start position:0% +a half% more stuff every single + + + align:start position:0% +a half% more stuff every single +year, just magically through the growth + + align:start position:0% +year, just magically through the growth + + + align:start position:0% +year, just magically through the growth +in productivity. Okay. However, from + + align:start position:0% +in productivity. Okay. However, from + + + align:start position:0% +in productivity. Okay. However, from +1973 until the 1990s, that fell to less + + align:start position:0% +1973 until the 1990s, that fell to less + + + align:start position:0% +1973 until the 1990s, that fell to less +than 1% a year, which meant if we wanted + + align:start position:0% +than 1% a year, which meant if we wanted + + + align:start position:0% +than 1% a year, which meant if we wanted +more stuff, we had to work harder, get + + align:start position:0% +more stuff, we had to work harder, get + + + align:start position:0% +more stuff, we had to work harder, get +more machines. + + align:start position:0% +more machines. + + + align:start position:0% +more machines. +Now one question people were asking was + + align:start position:0% +Now one question people were asking was + + + align:start position:0% +Now one question people were asking was +basically you know the IT revolution + + align:start position:0% +basically you know the IT revolution + + + align:start position:0% +basically you know the IT revolution +started in the late 80s but productivity + + align:start position:0% +started in the late 80s but productivity + + + align:start position:0% +started in the late 80s but productivity +didn't increase people were saying well + + align:start position:0% +didn't increase people were saying well + + + align:start position:0% +didn't increase people were saying well +where's the IT revolution there's a + + align:start position:0% +where's the IT revolution there's a + + + align:start position:0% +where's the IT revolution there's a +great saying saying you can see the IT + + align:start position:0% +great saying saying you can see the IT + + + align:start position:0% +great saying saying you can see the IT +revolution everywhere in life except the + + align:start position:0% +revolution everywhere in life except the + + + align:start position:0% +revolution everywhere in life except the +productivity numbers but then suddenly + + align:start position:0% +productivity numbers but then suddenly + + + align:start position:0% +productivity numbers but then suddenly +there was a boom from the mid 90s to the + + align:start position:0% +there was a boom from the mid 90s to the + + + align:start position:0% +there was a boom from the mid 90s to the +mid 2000s productivity jumped up again + + align:start position:0% +mid 2000s productivity jumped up again + + + align:start position:0% +mid 2000s productivity jumped up again +we thought aha the IT revolution is here + + align:start position:0% +we thought aha the IT revolution is here + + + align:start position:0% +we thought aha the IT revolution is here +productivity rose to about 2.3% a year + + align:start position:0% +productivity rose to about 2.3% a year + + + align:start position:0% +productivity rose to about 2.3% a year +but after 2005 it stopped and + + align:start position:0% +but after 2005 it stopped and + + + align:start position:0% +but after 2005 it stopped and +productivity is back down again to a + + align:start position:0% +productivity is back down again to a + + + align:start position:0% +productivity is back down again to a +little more than 1% a + + align:start position:0% +little more than 1% a + + + align:start position:0% +little more than 1% a +year. So, we're basically not really + + align:start position:0% +year. So, we're basically not really + + + align:start position:0% +year. So, we're basically not really +growing. We're not really innovating and + + align:start position:0% +growing. We're not really innovating and + + + align:start position:0% +growing. We're not really innovating and +developing and allow our standard of + + align:start position:0% +developing and allow our standard of + + + align:start position:0% +developing and allow our standard of +living to grow as fast as it used + + align:start position:0% +living to grow as fast as it used + + + align:start position:0% +living to grow as fast as it used +to. + + align:start position:0% +to. + + + align:start position:0% +to. +Okay, this raises three key questions. + + align:start position:0% +Okay, this raises three key questions. + + + align:start position:0% +Okay, this raises three key questions. +The first question + + align:start position:0% + + + + align:start position:0% + +is, you know, why why not long lasting + + align:start position:0% +is, you know, why why not long lasting + + + align:start position:0% +is, you know, why why not long lasting +effects of ET of it + + align:start position:0% + + + + align:start position:0% + +ET? Why did the IT revolution sort of + + align:start position:0% +ET? Why did the IT revolution sort of + + + align:start position:0% +ET? Why did the IT revolution sort of +cause this brief burst and then + + align:start position:0% +cause this brief burst and then + + + align:start position:0% +cause this brief burst and then +eventually kind of wear + + align:start position:0% +eventually kind of wear + + + align:start position:0% +eventually kind of wear +off? Is it because basically all our + + align:start position:0% +off? Is it because basically all our + + + align:start position:0% +off? Is it because basically all our +innovation is watching Tik Tok and not + + align:start position:0% +innovation is watching Tik Tok and not + + + align:start position:0% +innovation is watching Tik Tok and not +in making stuff? I don't know. But + + align:start position:0% +in making stuff? I don't know. But + + + align:start position:0% +in making stuff? I don't know. But +that's sort of one question we have, + + align:start position:0% +that's sort of one question we have, + + + align:start position:0% +that's sort of one question we have, +which is why is this incredible? You + + align:start position:0% +which is why is this incredible? You + + + align:start position:0% +which is why is this incredible? You +guys have no idea how different life is + + align:start position:0% +guys have no idea how different life is + + + align:start position:0% +guys have no idea how different life is +now than it was 25 years ago in terms of + + align:start position:0% +now than it was 25 years ago in terms of + + + align:start position:0% +now than it was 25 years ago in terms of +the internet and everything you have, + + align:start position:0% +the internet and everything you have, + + + align:start position:0% +the internet and everything you have, +but somehow we're not that much more + + align:start position:0% +but somehow we're not that much more + + + align:start position:0% +but somehow we're not that much more +productive as an economy. The question + + align:start position:0% +productive as an economy. The question + + + align:start position:0% +productive as an economy. The question +is why + + align:start position:0% +is why + + + align:start position:0% +is why +not? The second question this + + align:start position:0% +not? The second question this + + + align:start position:0% +not? The second question this +raises is where does productivity come + + align:start position:0% +raises is where does productivity come + + + align:start position:0% +raises is where does productivity come +from? Where does what's the where does A + + align:start position:0% +from? Where does what's the where does A + + + align:start position:0% +from? Where does what's the where does A +come from? + + align:start position:0% +come from? + + + align:start position:0% +come from? +And here this is a rich field of study + + align:start position:0% +And here this is a rich field of study + + + align:start position:0% +And here this is a rich field of study +because I said it was free. It's not + + align:start position:0% +because I said it was free. It's not + + + align:start position:0% +because I said it was free. It's not +free. It's not magical. Productivity is + + align:start position:0% +free. It's not magical. Productivity is + + + align:start position:0% +free. It's not magical. Productivity is +through real things. In the case of + + align:start position:0% +through real things. In the case of + + + align:start position:0% +through real things. In the case of +Henry Ford is through a brilliant + + align:start position:0% +Henry Ford is through a brilliant + + + align:start position:0% +Henry Ford is through a brilliant +insight. So one place A comes from is + + align:start position:0% + + + + align:start position:0% + +education. As we educate people and make + + align:start position:0% +education. As we educate people and make + + + align:start position:0% +education. As we educate people and make +them smarter, make them more creative, + + align:start position:0% +them smarter, make them more creative, + + + align:start position:0% +them smarter, make them more creative, +they'll think of cool new + + align:start position:0% +they'll think of cool new + + + align:start position:0% +they'll think of cool new +ideas. Okay. Productivity comes from + + align:start position:0% +ideas. Okay. Productivity comes from + + + align:start position:0% +ideas. Okay. Productivity comes from +firm research and development. + + align:start position:0% +firm research and development. + + + align:start position:0% +firm research and development. +As firms do research and development, + + align:start position:0% +As firms do research and development, + + + align:start position:0% +As firms do research and development, +stuff that many of you may go on and do + + align:start position:0% +stuff that many of you may go on and do + + + align:start position:0% +stuff that many of you may go on and do +with your + + align:start position:0% +with your + + + align:start position:0% +with your +lives, okay, they think up new + + align:start position:0% +lives, okay, they think up new + + + align:start position:0% +lives, okay, they think up new +ideas, okay, and they develop new + + align:start position:0% +ideas, okay, and they develop new + + + align:start position:0% +ideas, okay, and they develop new +products. It also comes from public + + align:start position:0% +products. It also comes from public + + + align:start position:0% +products. It also comes from public +research and + + align:start position:0% +research and + + + align:start position:0% +research and +development like the National Science + + align:start position:0% +development like the National Science + + + align:start position:0% +development like the National Science +Foundation. Some of you may have may may + + align:start position:0% +Foundation. Some of you may have may may + + + align:start position:0% +Foundation. Some of you may have may may +eventually get funding from the National + + align:start position:0% +eventually get funding from the National + + + align:start position:0% +eventually get funding from the National +SC may already have or may eventually + + align:start position:0% +SC may already have or may eventually + + + align:start position:0% +SC may already have or may eventually +get funding from the National Science + + align:start position:0% +get funding from the National Science + + + align:start position:0% +get funding from the National Science +Foundation for educations. The National + + align:start position:0% +Foundation for educations. The National + + + align:start position:0% +Foundation for educations. The National +Science Foundation funds a lot of + + align:start position:0% +Science Foundation funds a lot of + + + align:start position:0% +Science Foundation funds a lot of +research. The National Institutes of + + align:start position:0% +research. The National Institutes of + + + align:start position:0% +research. The National Institutes of +Health fund a lot of research. This + + align:start position:0% +Health fund a lot of research. This + + + align:start position:0% +Health fund a lot of research. This +turns out to be particularly critical + + align:start position:0% +turns out to be particularly critical + + + align:start position:0% +turns out to be particularly critical +because that's a lot of the basic + + align:start position:0% +because that's a lot of the basic + + + align:start position:0% +because that's a lot of the basic +research that gets done. Firms do what + + align:start position:0% +research that gets done. Firms do what + + + align:start position:0% +research that gets done. Firms do what +we often call applied research. They + + align:start position:0% +we often call applied research. They + + + align:start position:0% +we often call applied research. They +take basic ideas and turn them into + + align:start position:0% +take basic ideas and turn them into + + + align:start position:0% +take basic ideas and turn them into +products. But the basic research is + + align:start position:0% +products. But the basic research is + + + align:start position:0% +products. But the basic research is +often funded by government. And so + + align:start position:0% +often funded by government. And so + + + align:start position:0% +often funded by government. And so +that's where that comes from. So + + align:start position:0% +that's where that comes from. So + + + align:start position:0% +that's where that comes from. So +basically it there are things we can do + + align:start position:0% +basically it there are things we can do + + + align:start position:0% +basically it there are things we can do +as society to increase our productivity. + + align:start position:0% +as society to increase our productivity. + + + align:start position:0% +as society to increase our productivity. +We don't just sit back and let it + + align:start position:0% +We don't just sit back and let it + + + align:start position:0% +We don't just sit back and let it +happen. Having more educated population, + + align:start position:0% +happen. Having more educated population, + + + align:start position:0% +happen. Having more educated population, +more investments in R&D, the research + + align:start position:0% +more investments in R&D, the research + + + align:start position:0% +more investments in R&D, the research +and development by the way is R&D. Those + + align:start position:0% +and development by the way is R&D. Those + + + align:start position:0% +and development by the way is R&D. Those +can really make a difference in terms of + + align:start position:0% +can really make a difference in terms of + + + align:start position:0% +can really make a difference in terms of +how fast we + + align:start position:0% +how fast we + + + align:start position:0% +how fast we +grow. Third + + align:start position:0% +grow. Third + + + align:start position:0% +grow. Third +question, third + + align:start position:0% +question, third + + + align:start position:0% +question, third +point. How should we spend + + align:start position:0% +point. How should we spend + + + align:start position:0% +point. How should we spend +productivity? And here's what I mean by + + align:start position:0% +productivity? And here's what I mean by + + + align:start position:0% +productivity? And here's what I mean by +that. Imagine you have a cool new idea + + align:start position:0% +that. Imagine you have a cool new idea + + + align:start position:0% +that. Imagine you have a cool new idea +that can make things more efficient. + + align:start position:0% +that can make things more efficient. + + + align:start position:0% +that can make things more efficient. +Take Henry Ford's idea. He could do two + + align:start position:0% +Take Henry Ford's idea. He could do two + + + align:start position:0% +Take Henry Ford's idea. He could do two +things with that. One is he could make + + align:start position:0% +things with that. One is he could make + + + align:start position:0% +things with that. One is he could make +more cars. Two is he give people more + + align:start position:0% +more cars. Two is he give people more + + + align:start position:0% +more cars. Two is he give people more +time off. Right? If A goes up, you can + + align:start position:0% +time off. Right? If A goes up, you can + + + align:start position:0% +time off. Right? If A goes up, you can +reduce L and end up with the same amount + + align:start position:0% +reduce L and end up with the same amount + + + align:start position:0% +reduce L and end up with the same amount +of + + align:start position:0% +of + + + align:start position:0% +of +output. There's no reason an increase in + + align:start position:0% +output. There's no reason an increase in + + + align:start position:0% +output. There's no reason an increase in +A has to go into more Q. An increase in + + align:start position:0% +A has to go into more Q. An increase in + + + align:start position:0% +A has to go into more Q. An increase in +A could go into less L, which people + + align:start position:0% +A could go into less L, which people + + + align:start position:0% +A could go into less L, which people +like. They like time off. One thing + + align:start position:0% +like. They like time off. One thing + + + align:start position:0% +like. They like time off. One thing +we'll learn in this class, the hardest + + align:start position:0% +we'll learn in this class, the hardest + + + align:start position:0% +we'll learn in this class, the hardest +thing I teach in this class at MIT, the + + align:start position:0% +thing I teach in this class at MIT, the + + + align:start position:0% +thing I teach in this class at MIT, the +single hardest thing is in the real + + align:start position:0% +single hardest thing is in the real + + + align:start position:0% +single hardest thing is in the real +world, people actually don't like work. + + align:start position:0% +world, people actually don't like work. + + + align:start position:0% +world, people actually don't like work. +And we find this hard to believe, guys, + + align:start position:0% +And we find this hard to believe, guys, + + + align:start position:0% +And we find this hard to believe, guys, +but in the real world, people would + + align:start position:0% +but in the real world, people would + + + align:start position:0% +but in the real world, people would +rather not be at work than at work. + + align:start position:0% +rather not be at work than at work. + + + align:start position:0% +rather not be at work than at work. +Okay? And basically people would rather + + align:start position:0% +Okay? And basically people would rather + + + align:start position:0% +Okay? And basically people would rather +say well gee if you can make cars + + align:start position:0% +say well gee if you can make cars + + + align:start position:0% +say well gee if you can make cars +quicker why am I why am I working so + + align:start position:0% +quicker why am I why am I working so + + + align:start position:0% +quicker why am I why am I working so +hard and the answer is we don't know you + + align:start position:0% +hard and the answer is we don't know you + + + align:start position:0% +hard and the answer is we don't know you +know there's no clear question about how + + align:start position:0% +know there's no clear question about how + + + align:start position:0% +know there's no clear question about how +to spend productivity indeed the US and + + align:start position:0% +to spend productivity indeed the US and + + + align:start position:0% +to spend productivity indeed the US and +Europe have made radically different + + align:start position:0% +Europe have made radically different + + + align:start position:0% +Europe have made radically different +choices on this front decades since + + align:start position:0% +choices on this front decades since + + + align:start position:0% +choices on this front decades since +World War II where productivity has + + align:start position:0% +World War II where productivity has + + + align:start position:0% +World War II where productivity has +risen the US has largely put that into + + align:start position:0% +risen the US has largely put that into + + + align:start position:0% +risen the US has largely put that into +more + + align:start position:0% +more + + + align:start position:0% +more +goods Europe has largely put a lot of it + + align:start position:0% +goods Europe has largely put a lot of it + + + align:start position:0% +goods Europe has largely put a lot of it +into more leisure so a starting worker + + align:start position:0% +into more leisure so a starting worker + + + align:start position:0% +into more leisure so a starting worker +in Europe gets six weeks off a starting + + align:start position:0% +in Europe gets six weeks off a starting + + + align:start position:0% +in Europe gets six weeks off a starting +worker in the US gets two weeks off. + + align:start position:0% +worker in the US gets two weeks off. + + + align:start position:0% +worker in the US gets two weeks off. +Basically, people in Europe work from + + align:start position:0% +Basically, people in Europe work from + + + align:start position:0% +Basically, people in Europe work from +about 25 to 60 and then stop. People in + + align:start position:0% +about 25 to 60 and then stop. People in + + + align:start position:0% +about 25 to 60 and then stop. People in +the US work from like 20 to to 65. We + + align:start position:0% +the US work from like 20 to to 65. We + + + align:start position:0% +the US work from like 20 to to 65. We +work a lot more hours per week. The US + + align:start position:0% +work a lot more hours per week. The US + + + align:start position:0% +work a lot more hours per week. The US +has decided we want lot well, it's been + + align:start position:0% +has decided we want lot well, it's been + + + align:start position:0% +has decided we want lot well, it's been +decided, I don't want to say necessarily + + align:start position:0% +decided, I don't want to say necessarily + + + align:start position:0% +decided, I don't want to say necessarily +a conscious decision, but our society is + + align:start position:0% +a conscious decision, but our society is + + + align:start position:0% +a conscious decision, but our society is +one which evolved to be that all the + + align:start position:0% +one which evolved to be that all the + + + align:start position:0% +one which evolved to be that all the +productive improvements go into more + + align:start position:0% +productive improvements go into more + + + align:start position:0% +productive improvements go into more +stuff. Whereas in Europe, a lot of it + + align:start position:0% +stuff. Whereas in Europe, a lot of it + + + align:start position:0% +stuff. Whereas in Europe, a lot of it +goes into more time off. What's the + + align:start position:0% +goes into more time off. What's the + + + align:start position:0% +goes into more time off. What's the +better thing to have? Good question. + + align:start position:0% +better thing to have? Good question. + + + align:start position:0% +better thing to have? Good question. +Okay. When I was young, I probably + + align:start position:0% +Okay. When I was young, I probably + + + align:start position:0% +Okay. When I was young, I probably +thought stuff. Now that I'm older, I + + align:start position:0% +thought stuff. Now that I'm older, I + + + align:start position:0% +thought stuff. Now that I'm older, I +might think time off. Okay, but that's + + align:start position:0% +might think time off. Okay, but that's + + + align:start position:0% +might think time off. Okay, but that's +something we need to be conscious of + + align:start position:0% +something we need to be conscious of + + + align:start position:0% +something we need to be conscious of +that our society that societies can take + + align:start position:0% +that our society that societies can take + + + align:start position:0% +that our society that societies can take +different paths. The pandemic may have + + align:start position:0% +different paths. The pandemic may have + + + align:start position:0% +different paths. The pandemic may have +shook this up in the US. The pandemic + + align:start position:0% +shook this up in the US. The pandemic + + + align:start position:0% +shook this up in the US. The pandemic +was the first chance that people had to + + align:start position:0% +was the first chance that people had to + + + align:start position:0% +was the first chance that people had to +actually be at home and say, "Wait a + + align:start position:0% +actually be at home and say, "Wait a + + + align:start position:0% +actually be at home and say, "Wait a +second, maybe I don't want to work that + + align:start position:0% +second, maybe I don't want to work that + + + align:start position:0% +second, maybe I don't want to work that +hard." And there was a huge reduction in + + align:start position:0% +hard." And there was a huge reduction in + + + align:start position:0% +hard." And there was a huge reduction in +labor supply after the pandemic. A lot + + align:start position:0% +labor supply after the pandemic. A lot + + + align:start position:0% +labor supply after the pandemic. A lot +of people retired early. People aren't + + align:start position:0% +of people retired early. People aren't + + + align:start position:0% +of people retired early. People aren't +working as hard. People want to be in + + align:start position:0% +working as hard. People want to be in + + + align:start position:0% +working as hard. People want to be in +better jobs. People want to work from + + align:start position:0% +better jobs. People want to work from + + + align:start position:0% +better jobs. People want to work from +home. So the pandemic really shook + + align:start position:0% +home. So the pandemic really shook + + + align:start position:0% +home. So the pandemic really shook +things up in terms of people maybe + + align:start position:0% +things up in terms of people maybe + + + align:start position:0% +things up in terms of people maybe +starting to value their leisure uh more + + align:start position:0% +starting to value their leisure uh more + + + align:start position:0% +starting to value their leisure uh more +than maybe they did before. Okay, so + + align:start position:0% +than maybe they did before. Okay, so + + + align:start position:0% +than maybe they did before. Okay, so +that's the third + + align:start position:0% +that's the third + + + align:start position:0% +that's the third +question. The + + align:start position:0% +question. The + + + align:start position:0% +question. The +fourth + + align:start position:0% +fourth + + + align:start position:0% +fourth +is who gets + + align:start position:0% + + + + align:start position:0% + +a that is which group in society + + align:start position:0% +a that is which group in society + + + align:start position:0% +a that is which group in society +benefits from more productive + + align:start position:0% +benefits from more productive + + + align:start position:0% +benefits from more productive +economy. + + align:start position:0% +economy. + + + align:start position:0% +economy. +Okay. So basically + + align:start position:0% +Okay. So basically + + + align:start position:0% +Okay. So basically +um if you look at the period from World + + align:start position:0% +um if you look at the period from World + + + align:start position:0% +um if you look at the period from World +War II till + + align:start position:0% + + + + align:start position:0% + +1973 the average US income grew by 2 and + + align:start position:0% +1973 the average US income grew by 2 and + + + align:start position:0% +1973 the average US income grew by 2 and +a half% a year because of productivity. + + align:start position:0% +a half% a year because of productivity. + + + align:start position:0% +a half% a year because of productivity. +It turns out pretty much every group in + + align:start position:0% +It turns out pretty much every group in + + + align:start position:0% +It turns out pretty much every group in +society saw that increase. The poorest + + align:start position:0% +society saw that increase. The poorest + + + align:start position:0% +society saw that increase. The poorest +people saw their incomes go up about two + + align:start position:0% +people saw their incomes go up about two + + + align:start position:0% +people saw their incomes go up about two +and a half% a year. The richest people + + align:start position:0% +and a half% a year. The richest people + + + align:start position:0% +and a half% a year. The richest people +saw their incomes go up to about two and + + align:start position:0% +saw their incomes go up to about two and + + + align:start position:0% +saw their incomes go up to about two and +a half% a year. Since the mid1 1970s + + align:start position:0% +a half% a year. Since the mid1 1970s + + + align:start position:0% +a half% a year. Since the mid1 1970s +that has changed + + align:start position:0% +that has changed + + + align:start position:0% +that has changed +radically. Since the mid1 1970s + + align:start position:0% +radically. Since the mid1 1970s + + + align:start position:0% +radically. Since the mid1 1970s +virtually all of the benefit of + + align:start position:0% +virtually all of the benefit of + + + align:start position:0% +virtually all of the benefit of +increased productivity has gone to gone + + align:start position:0% +increased productivity has gone to gone + + + align:start position:0% +increased productivity has gone to gone +to the richest members of society, the + + align:start position:0% +to the richest members of society, the + + + align:start position:0% +to the richest members of society, the +people that own the capital and not to + + align:start position:0% +people that own the capital and not to + + + align:start position:0% +people that own the capital and not to +the + + align:start position:0% +the + + + align:start position:0% +the +workers. Okay. Basically, if you look at + + align:start position:0% +workers. Okay. Basically, if you look at + + + align:start position:0% +workers. Okay. Basically, if you look at +the purchasing power of a typical wage + + align:start position:0% +the purchasing power of a typical wage + + + align:start position:0% +the purchasing power of a typical wage +today, it's not much higher than what + + align:start position:0% +today, it's not much higher than what + + + align:start position:0% +today, it's not much higher than what +you could buy with that wage in + + align:start position:0% +you could buy with that wage in + + + align:start position:0% +you could buy with that wage in +1980. That is and we're the wage itself + + align:start position:0% +1980. That is and we're the wage itself + + + align:start position:0% +1980. That is and we're the wage itself +is higher, but goods cost more. We'll + + align:start position:0% +is higher, but goods cost more. We'll + + + align:start position:0% +is higher, but goods cost more. We'll +come back and talk more about inflation + + align:start position:0% +come back and talk more about inflation + + + align:start position:0% +come back and talk more about inflation +and things. The bottom line is the + + align:start position:0% +and things. The bottom line is the + + + align:start position:0% +and things. The bottom line is the +average worker can't buy that much more + + align:start position:0% +average worker can't buy that much more + + + align:start position:0% +average worker can't buy that much more +stuff than they could in + + align:start position:0% +stuff than they could in + + + align:start position:0% +stuff than they could in +1980. Meanwhile, the wealthiest have + + align:start position:0% +1980. Meanwhile, the wealthiest have + + + align:start position:0% +1980. Meanwhile, the wealthiest have +gotten incredibly wealthy. Um the share + + align:start position:0% +gotten incredibly wealthy. Um the share + + + align:start position:0% +gotten incredibly wealthy. Um the share +of wealth uh in the US um the share of + + align:start position:0% +of wealth uh in the US um the share of + + + align:start position:0% +of wealth uh in the US um the share of +income controlled by the top 1% of + + align:start position:0% +income controlled by the top 1% of + + + align:start position:0% +income controlled by the top 1% of +people in the US uh was uh 26% in + + align:start position:0% +people in the US uh was uh 26% in + + + align:start position:0% +people in the US uh was uh 26% in +1989. Uh and it's 35% today. + + align:start position:0% +1989. Uh and it's 35% today. + + + align:start position:0% +1989. Uh and it's 35% today. +Even more in 2021 + + align:start position:0% +Even more in 2021 + + + align:start position:0% +Even more in 2021 +uh in the coming back from the pandemic + + align:start position:0% +uh in the coming back from the pandemic + + + align:start position:0% +uh in the coming back from the pandemic +in the year you know in the year after + + align:start position:0% +in the year you know in the year after + + + align:start position:0% +in the year you know in the year after +the pandemic as we readjusted to life + + align:start position:0% +the pandemic as we readjusted to life + + + align:start position:0% +the pandemic as we readjusted to life +the top 1% of earners saw their incomes + + align:start position:0% +the top 1% of earners saw their incomes + + + align:start position:0% +the top 1% of earners saw their incomes +increase by + + align:start position:0% +increase by + + + align:start position:0% +increase by +9% while everyone else saw their incomes + + align:start position:0% +9% while everyone else saw their incomes + + + align:start position:0% +9% while everyone else saw their incomes +decrease. So the top 1% of earners were + + align:start position:0% +decrease. So the top 1% of earners were + + + align:start position:0% +decrease. So the top 1% of earners were +the only group that actually saw their + + align:start position:0% +the only group that actually saw their + + + align:start position:0% +the only group that actually saw their +income increase. Everyone else saw + + align:start position:0% +income increase. Everyone else saw + + + align:start position:0% +income increase. Everyone else saw +income decrease because inflation aid + + align:start position:0% +income decrease because inflation aid + + + align:start position:0% +income decrease because inflation aid +into people's wages. + + align:start position:0% +into people's wages. + + + align:start position:0% +into people's wages. +The bottom line is we also a doesn't + + align:start position:0% +The bottom line is we also a doesn't + + + align:start position:0% +The bottom line is we also a doesn't +magically go to everyone. Okay, it's not + + align:start position:0% +magically go to everyone. Okay, it's not + + + align:start position:0% +magically go to everyone. Okay, it's not +like a more productive economy so + + align:start position:0% +like a more productive economy so + + + align:start position:0% +like a more productive economy so +everyone benefits. That's determined by + + align:start position:0% +everyone benefits. That's determined by + + + align:start position:0% +everyone benefits. That's determined by +a set of decisions made by individual + + align:start position:0% +a set of decisions made by individual + + + align:start position:0% +a set of decisions made by individual +actors in the economy and by the + + align:start position:0% +actors in the economy and by the + + + align:start position:0% +actors in the economy and by the +government. And that's what we'll talk + + align:start position:0% +government. And that's what we'll talk + + + align:start position:0% +government. And that's what we'll talk +about later semester is how does the + + align:start position:0% +about later semester is how does the + + + align:start position:0% +about later semester is how does the +government think about those decisions + + align:start position:0% +government think about those decisions + + + align:start position:0% +government think about those decisions +or how do we think as society about how + + align:start position:0% +or how do we think as society about how + + + align:start position:0% +or how do we think as society about how +to spend the extra resources we get when + + align:start position:0% +to spend the extra resources we get when + + + align:start position:0% +to spend the extra resources we get when +the economy gets more productive. Okay. + + align:start position:0% +the economy gets more productive. Okay. + + + align:start position:0% +the economy gets more productive. Okay. +Okay. And that comes to the topic of + + align:start position:0% +Okay. And that comes to the topic of + + + align:start position:0% +Okay. And that comes to the topic of +economic fairness which we won't spend + + align:start position:0% +economic fairness which we won't spend + + + align:start position:0% +economic fairness which we won't spend +nearly enough time on but we will come + + align:start position:0% +nearly enough time on but we will come + + + align:start position:0% +nearly enough time on but we will come +back to towards the end of the semester. + + align:start position:0% +back to towards the end of the semester. + + + align:start position:0% +back to towards the end of the semester. +Okay. Questions about + + align:start position:0% +Okay. Questions about + + + align:start position:0% +Okay. Questions about +that? All right. Why don't we stop there + + align:start position:0% +that? All right. Why don't we stop there + + + align:start position:0% +that? All right. Why don't we stop there +and uh there's there's no section + + align:start position:0% +and uh there's there's no section + + + align:start position:0% +and uh there's there's no section +Friday, right? No section Friday. + + align:start position:0% +Friday, right? No section Friday. + + + align:start position:0% +Friday, right? No section Friday. +Remember the first problem set is due + + align:start position:0% +Remember the first problem set is due + + + align:start position:0% +Remember the first problem set is due +next Friday and the section you go to + + align:start position:0% +next Friday and the section you go to + + + align:start position:0% +next Friday and the section you go to +next Friday is the one you're going to + + align:start position:0% +next Friday is the one you're going to + + + align:start position:0% +next Friday is the one you're going to +stay in for the semester. Okay. Thank + + align:start position:0% +stay in for the semester. Okay. Thank + + + align:start position:0% +stay in for the semester. Okay. Thank +you. \ No newline at end of file diff --git a/QDIdZR9G2UU.txt b/QDIdZR9G2UU.txt new file mode 100644 index 0000000000000000000000000000000000000000..57517aaccb0de3eee30a28630b2afbe7f89b10c8 --- /dev/null +++ b/QDIdZR9G2UU.txt @@ -0,0 +1,1123 @@ +align:start position:0% + +hello and welcome back to 8701 so in + + align:start position:0% +hello and welcome back to 8701 so in + + + align:start position:0% +hello and welcome back to 8701 so in +this class you want to talk about + + align:start position:0% +this class you want to talk about + + + align:start position:0% +this class you want to talk about +the range of forces and specifically how + + align:start position:0% +the range of forces and specifically how + + + align:start position:0% +the range of forces and specifically how +the range of forces depend on the mass + + align:start position:0% +the range of forces depend on the mass + + + align:start position:0% +the range of forces depend on the mass +of the particle involved + + align:start position:0% +of the particle involved + + + align:start position:0% +of the particle involved +in transmitting the force we have seen + + align:start position:0% +in transmitting the force we have seen + + + align:start position:0% +in transmitting the force we have seen +this table before you know that the + + align:start position:0% +this table before you know that the + + + align:start position:0% +this table before you know that the +different forces the strong force the + + align:start position:0% +different forces the strong force the + + + align:start position:0% +different forces the strong force the +electromagnetic force + + align:start position:0% +electromagnetic force + + + align:start position:0% +electromagnetic force +and the weak force and the boson + + align:start position:0% +and the weak force and the boson + + + align:start position:0% +and the weak force and the boson +which carries carries the force + + align:start position:0% +which carries carries the force + + + align:start position:0% +which carries carries the force +on gluons photons in the w and the z + + align:start position:0% +on gluons photons in the w and the z + + + align:start position:0% +on gluons photons in the w and the z +bowser + + align:start position:0% +bowser + + + align:start position:0% +bowser +but now we want to actually just look + + align:start position:0% +but now we want to actually just look + + + align:start position:0% +but now we want to actually just look +into the aspect of + + align:start position:0% +into the aspect of + + + align:start position:0% +into the aspect of +of the range and how mass is interplay + + align:start position:0% +of the range and how mass is interplay + + + align:start position:0% +of the range and how mass is interplay +here + + align:start position:0% +here + + + align:start position:0% +here +so you all know the electromagnetic + + align:start position:0% +so you all know the electromagnetic + + + align:start position:0% +so you all know the electromagnetic +potential usual point charge given by + + align:start position:0% +potential usual point charge given by + + + align:start position:0% +potential usual point charge given by +the maximum equation + + align:start position:0% +the maximum equation + + + align:start position:0% +the maximum equation +we have seen this equation before + + align:start position:0% + + + + align:start position:0% + +and the time independent potential here + + align:start position:0% +and the time independent potential here + + + align:start position:0% +and the time independent potential here +you also know that the massless proton + + align:start position:0% +you also know that the massless proton + + + align:start position:0% +you also know that the massless proton +gives rise to an infinite range of the + + align:start position:0% +gives rise to an infinite range of the + + + align:start position:0% +gives rise to an infinite range of the +electromagnetic interaction + + align:start position:0% +electromagnetic interaction + + + align:start position:0% +electromagnetic interaction +but the question now is how would this + + align:start position:0% +but the question now is how would this + + + align:start position:0% +but the question now is how would this +change how would this be modified + + align:start position:0% +change how would this be modified + + + align:start position:0% +change how would this be modified +if the photon were massive + + align:start position:0% +if the photon were massive + + + align:start position:0% +if the photon were massive +so to do this + + align:start position:0% + + + + align:start position:0% + +we have to generalize this a little bit + + align:start position:0% +we have to generalize this a little bit + + + align:start position:0% +we have to generalize this a little bit +first of all we have to look at the + + align:start position:0% +first of all we have to look at the + + + align:start position:0% +first of all we have to look at the +time dependent equation or the wave + + align:start position:0% +time dependent equation or the wave + + + align:start position:0% +time dependent equation or the wave +equation + + align:start position:0% +equation + + + align:start position:0% +equation +this is wave equation + + align:start position:0% +this is wave equation + + + align:start position:0% +this is wave equation +we have also seen this before + + align:start position:0% + + + + align:start position:0% + +wave equation + + align:start position:0% + + + + align:start position:0% + +and by adding a mass term so we are + + align:start position:0% +and by adding a mass term so we are + + + align:start position:0% +and by adding a mass term so we are +using here + + align:start position:0% +using here + + + align:start position:0% +using here +an equation um which has to be fulfilled + + align:start position:0% +an equation um which has to be fulfilled + + + align:start position:0% +an equation um which has to be fulfilled +by all particles + + align:start position:0% +by all particles + + + align:start position:0% +by all particles +um it's a relation between energy + + align:start position:0% +um it's a relation between energy + + + align:start position:0% +um it's a relation between energy +momentum and mass + + align:start position:0% +momentum and mass + + + align:start position:0% +momentum and mass +the uh we have discussed this in the + + align:start position:0% +the uh we have discussed this in the + + + align:start position:0% +the uh we have discussed this in the +context of special relativity + + align:start position:0% +context of special relativity + + + align:start position:0% +context of special relativity +before what we are trying to do now is + + align:start position:0% +before what we are trying to do now is + + + align:start position:0% +before what we are trying to do now is +build a + + align:start position:0% +build a + + + align:start position:0% +build a +schrodinger-like equation by using the + + align:start position:0% +schrodinger-like equation by using the + + + align:start position:0% +schrodinger-like equation by using the +quantum mechanical operators + + align:start position:0% +quantum mechanical operators + + + align:start position:0% +quantum mechanical operators +for energy and momentum so we just add + + align:start position:0% +for energy and momentum so we just add + + + align:start position:0% +for energy and momentum so we just add +this here + + align:start position:0% +this here + + + align:start position:0% +this here +and find a new equation which is called + + align:start position:0% +and find a new equation which is called + + + align:start position:0% +and find a new equation which is called +the klein gordon equation + + align:start position:0% + + + + align:start position:0% + +that's equation + + align:start position:0% + + + + align:start position:0% + +so this equation has to be in all + + align:start position:0% +so this equation has to be in all + + + align:start position:0% +so this equation has to be in all +particle waves + + align:start position:0% +particle waves + + + align:start position:0% +particle waves +or particles have to fulfill this + + align:start position:0% +or particles have to fulfill this + + + align:start position:0% +or particles have to fulfill this +equation + + align:start position:0% +equation + + + align:start position:0% +equation +um so the question is you know what kind + + align:start position:0% +um so the question is you know what kind + + + align:start position:0% +um so the question is you know what kind +of solutions + + align:start position:0% +of solutions + + + align:start position:0% +of solutions +does this kind of equation have how does + + align:start position:0% +does this kind of equation have how does + + + align:start position:0% +does this kind of equation have how does +this look like + + align:start position:0% +this look like + + + align:start position:0% +this look like +and if you now you know start from + + align:start position:0% +and if you now you know start from + + + align:start position:0% +and if you now you know start from +again a time independent equation + + align:start position:0% +again a time independent equation + + + align:start position:0% +again a time independent equation +you find solutions which look like this + + align:start position:0% +you find solutions which look like this + + + align:start position:0% +you find solutions which look like this +right and you see again very similar + + align:start position:0% +right and you see again very similar + + + align:start position:0% +right and you see again very similar +than to before the charge over some + + align:start position:0% +than to before the charge over some + + + align:start position:0% +than to before the charge over some +constant as a function of radius + + align:start position:0% +constant as a function of radius + + + align:start position:0% +constant as a function of radius +but you also see this exponential term + + align:start position:0% +but you also see this exponential term + + + align:start position:0% +but you also see this exponential term +and what we see here is this potential + + align:start position:0% +and what we see here is this potential + + + align:start position:0% +and what we see here is this potential +this form of potential is called you + + align:start position:0% +this form of potential is called you + + + align:start position:0% +this form of potential is called you +cover potential + + align:start position:0% +cover potential + + + align:start position:0% +cover potential +and what's nicely shown in this plot + + align:start position:0% +and what's nicely shown in this plot + + + align:start position:0% +and what's nicely shown in this plot +here is again + + align:start position:0% +here is again + + + align:start position:0% +here is again +the potential as a function of radius in + + align:start position:0% +the potential as a function of radius in + + + align:start position:0% +the potential as a function of radius in +units of + + align:start position:0% +units of + + + align:start position:0% +units of +femtometers the dependency of the mass + + align:start position:0% +femtometers the dependency of the mass + + + align:start position:0% +femtometers the dependency of the mass +on the + + align:start position:0% +on the + + + align:start position:0% +on the +of the range of the force on the mass so + + align:start position:0% +of the range of the force on the mass so + + + align:start position:0% +of the range of the force on the mass so +you see here as an example for the mass + + align:start position:0% +you see here as an example for the mass + + + align:start position:0% +you see here as an example for the mass +equal to zero + + align:start position:0% +equal to zero + + + align:start position:0% +equal to zero +mark mass equal to one jv and mass equal + + align:start position:0% +mark mass equal to one jv and mass equal + + + align:start position:0% +mark mass equal to one jv and mass equal +to 10gb and you can easily see + + align:start position:0% +to 10gb and you can easily see + + + align:start position:0% +to 10gb and you can easily see +the range of the force is reduced by the + + align:start position:0% +the range of the force is reduced by the + + + align:start position:0% +the range of the force is reduced by the +fact that + + align:start position:0% +fact that + + + align:start position:0% +fact that +the particle actually had mass now + + align:start position:0% +the particle actually had mass now + + + align:start position:0% +the particle actually had mass now +the gauge both on the both end of the + + align:start position:0% +the gauge both on the both end of the + + + align:start position:0% +the gauge both on the both end of the +weak interaction the w and the z + + align:start position:0% +weak interaction the w and the z + + + align:start position:0% +weak interaction the w and the z +position are quite massive + + align:start position:0% +position are quite massive + + + align:start position:0% +position are quite massive +they have masses in the order of 80 90 + + align:start position:0% +they have masses in the order of 80 90 + + + align:start position:0% +they have masses in the order of 80 90 +or the order of 100 geb + + align:start position:0% +or the order of 100 geb + + + align:start position:0% +or the order of 100 geb +so you can see that the masses actually + + align:start position:0% +so you can see that the masses actually + + + align:start position:0% +so you can see that the masses actually +leads to reduction of the strength of + + align:start position:0% +leads to reduction of the strength of + + + align:start position:0% +leads to reduction of the strength of +the of the range of this force + + align:start position:0% +the of the range of this force + + + align:start position:0% +the of the range of this force +and we find you just not look + + align:start position:0% +and we find you just not look + + + align:start position:0% +and we find you just not look +don't look at the gravitational part + + align:start position:0% +don't look at the gravitational part + + + align:start position:0% +don't look at the gravitational part +here it's not + + align:start position:0% +here it's not + + + align:start position:0% +here it's not +part of the standard model if you look + + align:start position:0% +part of the standard model if you look + + + align:start position:0% +part of the standard model if you look +at electromagnetic interaction where the + + align:start position:0% +at electromagnetic interaction where the + + + align:start position:0% +at electromagnetic interaction where the +range is + + align:start position:0% +range is + + + align:start position:0% +range is +infinite we find that the range of the + + align:start position:0% +infinite we find that the range of the + + + align:start position:0% +infinite we find that the range of the +weak interaction is 10 to the minus 18 + + align:start position:0% +weak interaction is 10 to the minus 18 + + + align:start position:0% +weak interaction is 10 to the minus 18 +meters so this is greatly reduced + + align:start position:0% +meters so this is greatly reduced + + + align:start position:0% +meters so this is greatly reduced +because of the masses of the particle if + + align:start position:0% +because of the masses of the particle if + + + align:start position:0% +because of the masses of the particle if +we just look at the + + align:start position:0% +we just look at the + + + align:start position:0% +we just look at the +you know charge itself we would find + + align:start position:0% +you know charge itself we would find + + + align:start position:0% +you know charge itself we would find +that the weak interaction and the + + align:start position:0% +that the weak interaction and the + + + align:start position:0% +that the weak interaction and the +electromagnetic interaction are actually + + align:start position:0% +electromagnetic interaction are actually + + + align:start position:0% +electromagnetic interaction are actually +quite comparable + + align:start position:0% +quite comparable + + + align:start position:0% +quite comparable +we will also talk about the strong + + align:start position:0% +we will also talk about the strong + + + align:start position:0% +we will also talk about the strong +interaction this year here + + align:start position:0% +interaction this year here + + + align:start position:0% +interaction this year here +there's a strong interaction that the + + align:start position:0% +there's a strong interaction that the + + + align:start position:0% +there's a strong interaction that the +coupling + + align:start position:0% +coupling + + + align:start position:0% +coupling +and alpha is in the order one so when we + + align:start position:0% +and alpha is in the order one so when we + + + align:start position:0% +and alpha is in the order one so when we +talked about finding diagrams we talked + + align:start position:0% +talked about finding diagrams we talked + + + align:start position:0% +talked about finding diagrams we talked +about perturbation theory + + align:start position:0% +about perturbation theory + + + align:start position:0% +about perturbation theory +now if you do a perturbation series for + + align:start position:0% + + + + align:start position:0% + +a interaction of cup of order of one + + align:start position:0% +a interaction of cup of order of one + + + align:start position:0% +a interaction of cup of order of one +couplings of order one your vertices in + + align:start position:0% +couplings of order one your vertices in + + + align:start position:0% +couplings of order one your vertices in +the other one + + align:start position:0% +the other one + + + align:start position:0% +the other one +you'll see that perturbation theory + + align:start position:0% +you'll see that perturbation theory + + + align:start position:0% +you'll see that perturbation theory +might break down + + align:start position:0% +might break down + + + align:start position:0% +might break down +so okay so what we have seen in this + + align:start position:0% +so okay so what we have seen in this + + + align:start position:0% +so okay so what we have seen in this +lecture um + + align:start position:0% +lecture um + + + align:start position:0% +lecture um +is how a mass or how masses um + + align:start position:0% +is how a mass or how masses um + + + align:start position:0% +is how a mass or how masses um +reduce the range of a force uh we have + + align:start position:0% +reduce the range of a force uh we have + + + align:start position:0% +reduce the range of a force uh we have +simply built + + align:start position:0% +simply built + + + align:start position:0% +simply built +klein gordon equation here + + align:start position:0% +klein gordon equation here + + + align:start position:0% +klein gordon equation here +looked at a solution and found that + + align:start position:0% +looked at a solution and found that + + + align:start position:0% +looked at a solution and found that +there is this diminishing + + align:start position:0% +there is this diminishing + + + align:start position:0% +there is this diminishing +of um the range of the force + + align:start position:0% + + + + align:start position:0% + +later um we will look at one additional + + align:start position:0% +later um we will look at one additional + + + align:start position:0% +later um we will look at one additional +complication and another equation which + + align:start position:0% +complication and another equation which + + + align:start position:0% +complication and another equation which +has been + + align:start position:0% +has been + + + align:start position:0% +has been +hit by particles which is so-called + + align:start position:0% +hit by particles which is so-called + + + align:start position:0% +hit by particles which is so-called +direct equation which has to be + + align:start position:0% +direct equation which has to be + + + align:start position:0% +direct equation which has to be +fulfilled + + align:start position:0% +fulfilled + + + align:start position:0% +fulfilled +or hold up by by fermions + + align:start position:0% +or hold up by by fermions + + + align:start position:0% +or hold up by by fermions +but that's beyond of the scope of this + + align:start position:0% +but that's beyond of the scope of this + + + align:start position:0% +but that's beyond of the scope of this +of this club we'll look at this later in + + align:start position:0% +of this club we'll look at this later in + + + align:start position:0% +of this club we'll look at this later in +more detail + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/RdrCzc3DxLg.txt b/RdrCzc3DxLg.txt new file mode 100644 index 0000000000000000000000000000000000000000..eb7ed8bdbcd359a6853be167360fba3115f81237 --- /dev/null +++ b/RdrCzc3DxLg.txt @@ -0,0 +1,13867 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +this class we've talked about a lot of + + align:start position:0% +this class we've talked about a lot of + + + align:start position:0% +this class we've talked about a lot of +examples which were over and over again + + align:start position:0% +examples which were over and over again + + + align:start position:0% +examples which were over and over again +the same three concepts and then we + + align:start position:0% +the same three concepts and then we + + + align:start position:0% +the same three concepts and then we +talked about the general theory which is + + align:start position:0% +talked about the general theory which is + + + align:start position:0% +talked about the general theory which is +you know new because it's on Metric + + align:start position:0% +you know new because it's on Metric + + + align:start position:0% +you know new because it's on Metric +spaces + + align:start position:0% +spaces + + + align:start position:0% +spaces +but it's very similar to the stuff we've + + align:start position:0% +but it's very similar to the stuff we've + + + align:start position:0% +but it's very similar to the stuff we've +already seen for you for the in space + + align:start position:0% +already seen for you for the in space + + + align:start position:0% +already seen for you for the in space +right + + align:start position:0% +right + + + align:start position:0% +right +compact sets will be slightly different + + align:start position:0% +compact sets will be slightly different + + + align:start position:0% +compact sets will be slightly different +it's not the compact sets don't exist in + + align:start position:0% +it's not the compact sets don't exist in + + + align:start position:0% +it's not the compact sets don't exist in +euclidean space it's that they're pretty + + align:start position:0% +euclidean space it's that they're pretty + + + align:start position:0% +euclidean space it's that they're pretty +nice there so I hope to highlight why + + align:start position:0% +nice there so I hope to highlight why + + + align:start position:0% +nice there so I hope to highlight why +it's so nice when you put in space but + + align:start position:0% +it's so nice when you put in space but + + + align:start position:0% +it's so nice when you put in space but +also highlight the definitions that will + + align:start position:0% +also highlight the definitions that will + + + align:start position:0% +also highlight the definitions that will +become more difficult to manage on + + align:start position:0% +become more difficult to manage on + + + align:start position:0% +become more difficult to manage on +Metric spaces + + align:start position:0% +Metric spaces + + + align:start position:0% +Metric spaces +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so what is so like + + align:start position:0% +so what is so like + + + align:start position:0% +so what is so like +amazing about compact sets well if you + + align:start position:0% +amazing about compact sets well if you + + + align:start position:0% +amazing about compact sets well if you +looked up you know what's the + + align:start position:0% +looked up you know what's the + + + align:start position:0% +looked up you know what's the +integration behind compact sets the + + align:start position:0% +integration behind compact sets the + + + align:start position:0% +integration behind compact sets the +first thing you'll see on stack exchange + + align:start position:0% +first thing you'll see on stack exchange + + + align:start position:0% +first thing you'll see on stack exchange +is a conversation about ins now we have + + align:start position:0% +is a conversation about ins now we have + + + align:start position:0% +is a conversation about ins now we have +finiteness in two senses one in terms of + + align:start position:0% +finiteness in two senses one in terms of + + + align:start position:0% +finiteness in two senses one in terms of +like integrals one is an integral finite + + align:start position:0% +like integrals one is an integral finite + + + align:start position:0% +like integrals one is an integral finite +and secondly we have it in terms of + + align:start position:0% +and secondly we have it in terms of + + + align:start position:0% +and secondly we have it in terms of +finite sets we can consider you know + + align:start position:0% +finite sets we can consider you know + + + align:start position:0% +finite sets we can consider you know +what sort of statements can I make about + + align:start position:0% +what sort of statements can I make about + + + align:start position:0% +what sort of statements can I make about +climate sets these two Notions Drive the + + align:start position:0% +climate sets these two Notions Drive the + + + align:start position:0% +climate sets these two Notions Drive the +understanding of compact sets and so + + align:start position:0% +understanding of compact sets and so + + + align:start position:0% +understanding of compact sets and so +today my goal is to start off with + + align:start position:0% +today my goal is to start off with + + + align:start position:0% +today my goal is to start off with +motivation using norms to describe + + align:start position:0% +motivation using norms to describe + + + align:start position:0% +motivation using norms to describe +finiteness and then I'm going to talk + + align:start position:0% +finiteness and then I'm going to talk + + + align:start position:0% +finiteness and then I'm going to talk +about finite and or finally sets and the + + align:start position:0% +about finite and or finally sets and the + + + align:start position:0% +about finite and or finally sets and the +analysis we can do all of those + + align:start position:0% +analysis we can do all of those + + + align:start position:0% +analysis we can do all of those +okay so let's start with norms + + align:start position:0% + + + + align:start position:0% + +so to define a norm which you might have + + align:start position:0% +so to define a norm which you might have + + + align:start position:0% +so to define a norm which you might have +heard about before either in this class + + align:start position:0% +heard about before either in this class + + + align:start position:0% +heard about before either in this class +or in 1802 + + align:start position:0% +or in 1802 + + + align:start position:0% +or in 1802 +um we're going to need the notion of a + + align:start position:0% +um we're going to need the notion of a + + + align:start position:0% +um we're going to need the notion of a +vector space and so let's define what + + align:start position:0% +vector space and so let's define what + + + align:start position:0% +vector space and so let's define what +that is now + + align:start position:0% + + + + align:start position:0% + +a vectors based + + align:start position:0% + + + + align:start position:0% + +is a fat V + + align:start position:0% +is a fat V + + + align:start position:0% +is a fat V +with addition + + align:start position:0% + + + + align:start position:0% + +which takes in two vectors so B cross B + + align:start position:0% +which takes in two vectors so B cross B + + + align:start position:0% +which takes in two vectors so B cross B +it Maps it to another Vector so when I + + align:start position:0% +it Maps it to another Vector so when I + + + align:start position:0% +it Maps it to another Vector so when I +add two vectors I get another vector and + + align:start position:0% +add two vectors I get another vector and + + + align:start position:0% +add two vectors I get another vector and +secondly multiplication If I multiply by + + align:start position:0% +secondly multiplication If I multiply by + + + align:start position:0% +secondly multiplication If I multiply by +let's say a real number + + align:start position:0% +let's say a real number + + + align:start position:0% +let's say a real number +on a vector I should get another Vector + + align:start position:0% +on a vector I should get another Vector + + + align:start position:0% +on a vector I should get another Vector +back out + + align:start position:0% +back out + + + align:start position:0% +back out +so this is very fancy notation but + + align:start position:0% +so this is very fancy notation but + + + align:start position:0% +so this is very fancy notation but +essentially what this is saying again is + + align:start position:0% +essentially what this is saying again is + + + align:start position:0% +essentially what this is saying again is +that if I have two vectors I can add + + align:start position:0% +that if I have two vectors I can add + + + align:start position:0% +that if I have two vectors I can add +them together and get another and If I + + align:start position:0% +them together and get another and If I + + + align:start position:0% +them together and get another and If I +multiply by a real number I'll get + + align:start position:0% +multiply by a real number I'll get + + + align:start position:0% +multiply by a real number I'll get +another vector + + align:start position:0% +another vector + + + align:start position:0% +another vector +specifically + + align:start position:0% +specifically + + + align:start position:0% +specifically +a vector space is a set V with these two + + align:start position:0% +a vector space is a set V with these two + + + align:start position:0% +a vector space is a set V with these two +operations on it with nice properties + + align:start position:0% + + + + align:start position:0% + +so those nice properties that we wanted + + align:start position:0% +so those nice properties that we wanted + + + align:start position:0% +so those nice properties that we wanted +to define or want to have are as follows + + align:start position:0% +to define or want to have are as follows + + + align:start position:0% +to define or want to have are as follows +I'll just date a few of them just to + + align:start position:0% +I'll just date a few of them just to + + + align:start position:0% +I'll just date a few of them just to +point out why they're so nice but + + align:start position:0% +point out why they're so nice but + + + align:start position:0% +point out why they're so nice but +essentially it's the field axioms we + + align:start position:0% +essentially it's the field axioms we + + + align:start position:0% +essentially it's the field axioms we +want this Vector space to be one + + align:start position:0% +want this Vector space to be one + + + align:start position:0% +want this Vector space to be one +commutative + + align:start position:0% +commutative + + + align:start position:0% +commutative +so when I add the addition the order in + + align:start position:0% +so when I add the addition the order in + + + align:start position:0% +so when I add the addition the order in +which I add two things doesn't matter + + align:start position:0% +which I add two things doesn't matter + + + align:start position:0% +which I add two things doesn't matter +tattoo + + align:start position:0% +tattoo + + + align:start position:0% +tattoo +to associative + + align:start position:0% + + + + align:start position:0% + +meaning that a plus b plus C is a plus b + + align:start position:0% +meaning that a plus b plus C is a plus b + + + align:start position:0% +meaning that a plus b plus C is a plus b +plus c + + align:start position:0% +plus c + + + align:start position:0% +plus c +we want there to be a distributive law + + align:start position:0% + + + + align:start position:0% + +reputative + + align:start position:0% + + + + align:start position:0% + +and I'll just do one more + + align:start position:0% +and I'll just do one more + + + align:start position:0% +and I'll just do one more +we have the identity + + align:start position:0% +we have the identity + + + align:start position:0% +we have the identity +by which I mean + + align:start position:0% + + + + align:start position:0% + +zero and one + + align:start position:0% +zero and one + + + align:start position:0% +zero and one +are sorry I should say zero is in your + + align:start position:0% +are sorry I should say zero is in your + + + align:start position:0% +are sorry I should say zero is in your +vector space + + align:start position:0% +vector space + + + align:start position:0% +vector space +and minus V is in your vector space so I + + align:start position:0% +and minus V is in your vector space so I + + + align:start position:0% +and minus V is in your vector space so I +can always get back to zero there's a + + align:start position:0% +can always get back to zero there's a + + + align:start position:0% +can always get back to zero there's a +few more axioms than this to define a + + align:start position:0% +few more axioms than this to define a + + + align:start position:0% +few more axioms than this to define a +vector space this is mostly covered in + + align:start position:0% +vector space this is mostly covered in + + + align:start position:0% +vector space this is mostly covered in +1806. + + align:start position:0% +1806. + + + align:start position:0% +1806. +um but + + align:start position:0% +um but + + + align:start position:0% +um but +I'll just need a few of them right now + + align:start position:0% +I'll just need a few of them right now + + + align:start position:0% +I'll just need a few of them right now +now the reason that Becker spaces are so + + align:start position:0% +now the reason that Becker spaces are so + + + align:start position:0% +now the reason that Becker spaces are so +helpful is because of this notion of + + align:start position:0% +helpful is because of this notion of + + + align:start position:0% +helpful is because of this notion of +addition right as we've talked about + + align:start position:0% +addition right as we've talked about + + + align:start position:0% +addition right as we've talked about +before for metric spaces there's not too + + align:start position:0% +before for metric spaces there's not too + + + align:start position:0% +before for metric spaces there's not too +much more we can do we can't state facts + + align:start position:0% +much more we can do we can't state facts + + + align:start position:0% +much more we can do we can't state facts +about how you add two elements in a + + align:start position:0% +about how you add two elements in a + + + align:start position:0% +about how you add two elements in a +metric space because it doesn't always + + align:start position:0% +metric space because it doesn't always + + + align:start position:0% +metric space because it doesn't always +make sense we don't have addition always + + align:start position:0% +make sense we don't have addition always + + + align:start position:0% +make sense we don't have addition always +defined + + align:start position:0% +defined + + + align:start position:0% +defined +um so just to recap uh today we're + + align:start position:0% +um so just to recap uh today we're + + + align:start position:0% +um so just to recap uh today we're +talking about compact sets and I just + + align:start position:0% +talking about compact sets and I just + + + align:start position:0% +talking about compact sets and I just +somewhat rigorously Define what a vector + + align:start position:0% +somewhat rigorously Define what a vector + + + align:start position:0% +somewhat rigorously Define what a vector +space is yes didn't miss too much + + align:start position:0% +space is yes didn't miss too much + + + align:start position:0% +space is yes didn't miss too much +um all right so now that we have this + + align:start position:0% +um all right so now that we have this + + + align:start position:0% +um all right so now that we have this +definition of a vector space we're not + + align:start position:0% +definition of a vector space we're not + + + align:start position:0% +definition of a vector space we're not +going to Define what a norm is + + align:start position:0% + + + + align:start position:0% + +Norm + + align:start position:0% + + + + align:start position:0% + +a norm + + align:start position:0% +a norm + + + align:start position:0% +a norm +is essentially going to be like a metric + + align:start position:0% +is essentially going to be like a metric + + + align:start position:0% +is essentially going to be like a metric +on your vector space + + align:start position:0% +on your vector space + + + align:start position:0% +on your vector space +y map + + align:start position:0% + + + + align:start position:0% + +that's denoted like this which will make + + align:start position:0% +that's denoted like this which will make + + + align:start position:0% +that's denoted like this which will make +a bit more sense in a moment + + align:start position:0% +a bit more sense in a moment + + + align:start position:0% +a bit more sense in a moment +with + + align:start position:0% +with + + + align:start position:0% +with +a map taking in vectors + + align:start position:0% +a map taking in vectors + + + align:start position:0% +a map taking in vectors +in a vector space V it's bidding out a + + align:start position:0% +in a vector space V it's bidding out a + + + align:start position:0% +in a vector space V it's bidding out a +positive number and in particular we + + align:start position:0% +positive number and in particular we + + + align:start position:0% +positive number and in particular we +want this normally satisfy three + + align:start position:0% +want this normally satisfy three + + + align:start position:0% +want this normally satisfy three +properties just like we did for metric + + align:start position:0% +properties just like we did for metric + + + align:start position:0% +properties just like we did for metric +spaces + + align:start position:0% +spaces + + + align:start position:0% +spaces +one + + align:start position:0% +one + + + align:start position:0% +one +of course we want positive definiteness + + align:start position:0% + + + + align:start position:0% + +where here you want + + align:start position:0% +where here you want + + + align:start position:0% +where here you want +B bigger than or equal to zero for all + + align:start position:0% +B bigger than or equal to zero for all + + + align:start position:0% +B bigger than or equal to zero for all +we + + align:start position:0% +we + + + align:start position:0% +we +and + + align:start position:0% +and + + + align:start position:0% +and +the norm of B is equal to zero if only + + align:start position:0% +the norm of B is equal to zero if only + + + align:start position:0% +the norm of B is equal to zero if only +if V equals zero + + align:start position:0% +if V equals zero + + + align:start position:0% +if V equals zero +that's the definition of positive + + align:start position:0% +that's the definition of positive + + + align:start position:0% +that's the definition of positive +definite X now why didn't this work on + + align:start position:0% +definite X now why didn't this work on + + + align:start position:0% +definite X now why didn't this work on +Metric spaces + + align:start position:0% +Metric spaces + + + align:start position:0% +Metric spaces +because there we didn't have a notion of + + align:start position:0% +because there we didn't have a notion of + + + align:start position:0% +because there we didn't have a notion of +what it meant for the number zero to be + + align:start position:0% +what it meant for the number zero to be + + + align:start position:0% +what it meant for the number zero to be +in your vector space But Here We Do + + align:start position:0% +in your vector space But Here We Do + + + align:start position:0% +in your vector space But Here We Do +right in a vector space we're assuming + + align:start position:0% +right in a vector space we're assuming + + + align:start position:0% +right in a vector space we're assuming +that we have an element zero in our + + align:start position:0% +that we have an element zero in our + + + align:start position:0% +that we have an element zero in our +Vector space + + align:start position:0% +Vector space + + + align:start position:0% +Vector space +so we're all good there positive + + align:start position:0% +so we're all good there positive + + + align:start position:0% +so we're all good there positive +definite and this is actually the same + + align:start position:0% +definite and this is actually the same + + + align:start position:0% +definite and this is actually the same +secondly we have homogeneity + + align:start position:0% + + + + align:start position:0% + +which essentially just states that we + + align:start position:0% +which essentially just states that we + + + align:start position:0% +which essentially just states that we +can pull out constants + + align:start position:0% +can pull out constants + + + align:start position:0% +can pull out constants +so the norm of Lambda V where Lambda is + + align:start position:0% +so the norm of Lambda V where Lambda is + + + align:start position:0% +so the norm of Lambda V where Lambda is +just a constant and V is a vector + + align:start position:0% +just a constant and V is a vector + + + align:start position:0% +just a constant and V is a vector +is equal to the absolute value of Lambda + + align:start position:0% +is equal to the absolute value of Lambda + + + align:start position:0% +is equal to the absolute value of Lambda +times V Capital normal V + + align:start position:0% +times V Capital normal V + + + align:start position:0% +times V Capital normal V +and finally + + align:start position:0% + + + + align:start position:0% + +we have the triangle inequality + + align:start position:0% + + + + align:start position:0% + +but here we don't need to have three + + align:start position:0% +but here we don't need to have three + + + align:start position:0% +but here we don't need to have three +vectors because this one's just defined + + align:start position:0% +vectors because this one's just defined + + + align:start position:0% +vectors because this one's just defined +in terms of one so all we need is that V + + align:start position:0% +in terms of one so all we need is that V + + + align:start position:0% +in terms of one so all we need is that V +plus W + + align:start position:0% +plus W + + + align:start position:0% +plus W +is less than or equal to the norm of V + + align:start position:0% +is less than or equal to the norm of V + + + align:start position:0% +is less than or equal to the norm of V +plus the norm of w + + align:start position:0% + + + + align:start position:0% + +this is it these are the three three + + align:start position:0% +this is it these are the three three + + + align:start position:0% +this is it these are the three three +properties that Define what a norm space + + align:start position:0% +properties that Define what a norm space + + + align:start position:0% +properties that Define what a norm space +is and in fact you can see right here + + align:start position:0% +is and in fact you can see right here + + + align:start position:0% +is and in fact you can see right here +like the setup of this is very very + + align:start position:0% +like the setup of this is very very + + + align:start position:0% +like the setup of this is very very +similar to metric spaces the only + + align:start position:0% +similar to metric spaces the only + + + align:start position:0% +similar to metric spaces the only +difference being that we now know what + + align:start position:0% +difference being that we now know what + + + align:start position:0% +difference being that we now know what +it means to multiply by constants we now + + align:start position:0% +it means to multiply by constants we now + + + align:start position:0% +it means to multiply by constants we now +know what it means for a vector to be + + align:start position:0% +know what it means for a vector to be + + + align:start position:0% +know what it means for a vector to be +zero and we have addition defined on our + + align:start position:0% +zero and we have addition defined on our + + + align:start position:0% +zero and we have addition defined on our +space + + align:start position:0% +space + + + align:start position:0% +space +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now + + align:start position:0% +now + + + align:start position:0% +now +let's look at some example of norms + + align:start position:0% +let's look at some example of norms + + + align:start position:0% +let's look at some example of norms +uh and the examples that we're going to + + align:start position:0% +uh and the examples that we're going to + + + align:start position:0% +uh and the examples that we're going to +look at are in fact going to be very + + align:start position:0% +look at are in fact going to be very + + + align:start position:0% +look at are in fact going to be very +similar to metrics themselves + + align:start position:0% +similar to metrics themselves + + + align:start position:0% +similar to metrics themselves +so + + align:start position:0% +so + + + align:start position:0% +so +example one + + align:start position:0% + + + + align:start position:0% + +uh suppose + + align:start position:0% +uh suppose + + + align:start position:0% +uh suppose +we're looking at this set of continuous + + align:start position:0% +we're looking at this set of continuous + + + align:start position:0% +we're looking at this set of continuous +functions on the interval A to B or + + align:start position:0% +functions on the interval A to B or + + + align:start position:0% +functions on the interval A to B or +actually I'll just do zero to one for + + align:start position:0% +actually I'll just do zero to one for + + + align:start position:0% +actually I'll just do zero to one for +now so that it's simpler + + align:start position:0% +now so that it's simpler + + + align:start position:0% +now so that it's simpler +and then consider + + align:start position:0% +and then consider + + + align:start position:0% +and then consider +the norm acting on this C naught zero to + + align:start position:0% +the norm acting on this C naught zero to + + + align:start position:0% +the norm acting on this C naught zero to +one + + align:start position:0% +one + + + align:start position:0% +one +two positive or non-negative numbers + + align:start position:0% +two positive or non-negative numbers + + + align:start position:0% +two positive or non-negative numbers +with + + align:start position:0% +with + + + align:start position:0% +with +the norm of a function f being equal to + + align:start position:0% +the norm of a function f being equal to + + + align:start position:0% +the norm of a function f being equal to +the supper mom of all X + + align:start position:0% +the supper mom of all X + + + align:start position:0% +the supper mom of all X +and zero to one + + align:start position:0% +and zero to one + + + align:start position:0% +and zero to one +of absolute value f of x + + align:start position:0% +of absolute value f of x + + + align:start position:0% +of absolute value f of x +I claim that this is a factored Norm + + align:start position:0% +I claim that this is a factored Norm + + + align:start position:0% +I claim that this is a factored Norm +so let's show the three properties + + align:start position:0% +so let's show the three properties + + + align:start position:0% +so let's show the three properties +screws + + align:start position:0% +screws + + + align:start position:0% +screws +well + + align:start position:0% +well + + + align:start position:0% +well +the first one positive definiteness this + + align:start position:0% +the first one positive definiteness this + + + align:start position:0% +the first one positive definiteness this +one's mostly done we know that it's + + align:start position:0% +one's mostly done we know that it's + + + align:start position:0% +one's mostly done we know that it's +positive or non-negative + + align:start position:0% + + + + align:start position:0% + +more accurately it's not negative but + + align:start position:0% +more accurately it's not negative but + + + align:start position:0% +more accurately it's not negative but +let's look at the case where it is equal + + align:start position:0% +let's look at the case where it is equal + + + align:start position:0% +let's look at the case where it is equal +to zero + + align:start position:0% +to zero + + + align:start position:0% +to zero +so if the norm of f equals zero which + + align:start position:0% +so if the norm of f equals zero which + + + align:start position:0% +so if the norm of f equals zero which +again under under the definition this is + + align:start position:0% +again under under the definition this is + + + align:start position:0% +again under under the definition this is +the supper mom of X and zero and one + + align:start position:0% +the supper mom of X and zero and one + + + align:start position:0% +the supper mom of X and zero and one +of absolute value f of x + + align:start position:0% +of absolute value f of x + + + align:start position:0% +of absolute value f of x +this implies that the function must be + + align:start position:0% +this implies that the function must be + + + align:start position:0% +this implies that the function must be +zero everywhere right assume it wasn't + + align:start position:0% +zero everywhere right assume it wasn't + + + align:start position:0% +zero everywhere right assume it wasn't +zero at one point then the supplement + + align:start position:0% +zero at one point then the supplement + + + align:start position:0% +zero at one point then the supplement +would be that maximum value + + align:start position:0% +would be that maximum value + + + align:start position:0% +would be that maximum value +so that's implies that F must be equal + + align:start position:0% +so that's implies that F must be equal + + + align:start position:0% +so that's implies that F must be equal +to this is true if and only if + + align:start position:0% +to this is true if and only if + + + align:start position:0% +to this is true if and only if +f equals zero everywhere + + align:start position:0% + + + + align:start position:0% + +so we're good on that front + + align:start position:0% +so we're good on that front + + + align:start position:0% +so we're good on that front +secondly homogeneity this one isn't that + + align:start position:0% +secondly homogeneity this one isn't that + + + align:start position:0% +secondly homogeneity this one isn't that +bad as well because then we have + + align:start position:0% +bad as well because then we have + + + align:start position:0% +bad as well because then we have +the norm of Lambda f + + align:start position:0% +the norm of Lambda f + + + align:start position:0% +the norm of Lambda f +being equal to the supper mom + + align:start position:0% +being equal to the supper mom + + + align:start position:0% +being equal to the supper mom +of Lambda f of x + + align:start position:0% +of Lambda f of x + + + align:start position:0% +of Lambda f of x +and of course we can pull out the Lambda + + align:start position:0% +and of course we can pull out the Lambda + + + align:start position:0% +and of course we can pull out the Lambda +now because it's just a constant times + + align:start position:0% +now because it's just a constant times + + + align:start position:0% +now because it's just a constant times +the function so this is in fact equal to + + align:start position:0% +the function so this is in fact equal to + + + align:start position:0% +the function so this is in fact equal to +the supper mom of Lambda times f of x + + align:start position:0% +the supper mom of Lambda times f of x + + + align:start position:0% +the supper mom of Lambda times f of x +and then we can pull out Lambda so then + + align:start position:0% +and then we can pull out Lambda so then + + + align:start position:0% +and then we can pull out Lambda so then +this would be Lambda times except for + + align:start position:0% +this would be Lambda times except for + + + align:start position:0% +this would be Lambda times except for +Mom + + align:start position:0% +Mom + + + align:start position:0% +Mom +of f of x + + align:start position:0% + + + + align:start position:0% + +which is absolute value Lambda times the + + align:start position:0% +which is absolute value Lambda times the + + + align:start position:0% +which is absolute value Lambda times the +norm of that + + align:start position:0% +norm of that + + + align:start position:0% +norm of that +so all good on the product homogeneity + + align:start position:0% + + + + align:start position:0% + +and I won't prove it again + + align:start position:0% +and I won't prove it again + + + align:start position:0% +and I won't prove it again +actually I'll just date it because why + + align:start position:0% +actually I'll just date it because why + + + align:start position:0% +actually I'll just date it because why +not oh because we're going to look at + + align:start position:0% +not oh because we're going to look at + + + align:start position:0% +not oh because we're going to look at +one more example after this anyways so + + align:start position:0% +one more example after this anyways so + + + align:start position:0% +one more example after this anyways so +for the triangle inequality + + align:start position:0% + + + + align:start position:0% + +here we have that + + align:start position:0% +here we have that + + + align:start position:0% +here we have that +f of x plus G of x + + align:start position:0% +f of x plus G of x + + + align:start position:0% +f of x plus G of x +or I should say minus right no G plus + + align:start position:0% +or I should say minus right no G plus + + + align:start position:0% +or I should say minus right no G plus +that's fine uh this is less than or + + align:start position:0% +that's fine uh this is less than or + + + align:start position:0% +that's fine uh this is less than or +equal to absolute value f of x + + align:start position:0% +equal to absolute value f of x + + + align:start position:0% +equal to absolute value f of x +plus absolute value G of x + + align:start position:0% +plus absolute value G of x + + + align:start position:0% +plus absolute value G of x +and then on this right hand side I can + + align:start position:0% +and then on this right hand side I can + + + align:start position:0% +and then on this right hand side I can +apply this up from out great so applying + + align:start position:0% +apply this up from out great so applying + + + align:start position:0% +apply this up from out great so applying +this up problem on the right hand side + + align:start position:0% +this up problem on the right hand side + + + align:start position:0% +this up problem on the right hand side +is a f and g + + align:start position:0% +is a f and g + + + align:start position:0% +is a f and g +will get that + + align:start position:0% +will get that + + + align:start position:0% +will get that +is nothing equal to the suffering um + + align:start position:0% +is nothing equal to the suffering um + + + align:start position:0% +is nothing equal to the suffering um +of f of x + + align:start position:0% +of f of x + + + align:start position:0% +of f of x +plus this up remote + + align:start position:0% +plus this up remote + + + align:start position:0% +plus this up remote +G of x + + align:start position:0% +G of x + + + align:start position:0% +G of x +which is of course + + align:start position:0% +which is of course + + + align:start position:0% +which is of course +the norm of f plus the norm of G + + align:start position:0% +the norm of f plus the norm of G + + + align:start position:0% +the norm of f plus the norm of G +and then I can take this upper of the + + align:start position:0% +and then I can take this upper of the + + + align:start position:0% +and then I can take this upper of the +left hand side to complete the group + + align:start position:0% +left hand side to complete the group + + + align:start position:0% +left hand side to complete the group +right so that's the voices having to + + align:start position:0% +right so that's the voices having to + + + align:start position:0% +right so that's the voices having to +choose the extreme value theorem in the + + align:start position:0% +choose the extreme value theorem in the + + + align:start position:0% +choose the extreme value theorem in the +proof here all we used was bounds using + + align:start position:0% +proof here all we used was bounds using + + + align:start position:0% +proof here all we used was bounds using +the second amount + + align:start position:0% +the second amount + + + align:start position:0% +the second amount +which is how we've done the other group + + align:start position:0% +which is how we've done the other group + + + align:start position:0% +which is how we've done the other group +this is just a slightly more elegant way + + align:start position:0% +this is just a slightly more elegant way + + + align:start position:0% +this is just a slightly more elegant way +to do that + + align:start position:0% +to do that + + + align:start position:0% +to do that +all right so that's it of this example + + align:start position:0% +all right so that's it of this example + + + align:start position:0% +all right so that's it of this example +and this is again essentially what we + + align:start position:0% +and this is again essentially what we + + + align:start position:0% +and this is again essentially what we +looked at last time when we were looking + + align:start position:0% +looked at last time when we were looking + + + align:start position:0% +looked at last time when we were looking +at the metric except there we were + + align:start position:0% +at the metric except there we were + + + align:start position:0% +at the metric except there we were +looking at the distances between two uh + + align:start position:0% +looking at the distances between two uh + + + align:start position:0% +looking at the distances between two uh +between two functions itself here we can + + align:start position:0% +between two functions itself here we can + + + align:start position:0% +between two functions itself here we can +just look at the norm of a single + + align:start position:0% +just look at the norm of a single + + + align:start position:0% +just look at the norm of a single +function + + align:start position:0% +function + + + align:start position:0% +function +all right + + align:start position:0% +all right + + + align:start position:0% +all right +let's look at one more example which + + align:start position:0% +let's look at one more example which + + + align:start position:0% +let's look at one more example which +would be again to what we were looking + + align:start position:0% +would be again to what we were looking + + + align:start position:0% +would be again to what we were looking +at before + + align:start position:0% + + + + align:start position:0% + +so I'm going to define the L1 + + align:start position:0% + + + + align:start position:0% + +this notation will come up a bit later + + align:start position:0% +this notation will come up a bit later + + + align:start position:0% +this notation will come up a bit later +in lecture five + + align:start position:0% +in lecture five + + + align:start position:0% +in lecture five +but here we have + + align:start position:0% +but here we have + + + align:start position:0% +but here we have +the norm acting on C naught again so + + align:start position:0% +the norm acting on C naught again so + + + align:start position:0% +the norm acting on C naught again so +continuous functions on zero to one + + align:start position:0% +continuous functions on zero to one + + + align:start position:0% +continuous functions on zero to one +and spitting out + + align:start position:0% +and spitting out + + + align:start position:0% +and spitting out +a non-negative number + + align:start position:0% +a non-negative number + + + align:start position:0% +a non-negative number +where here specifically the norm of a + + align:start position:0% +where here specifically the norm of a + + + align:start position:0% +where here specifically the norm of a +function f let's see L1 + + align:start position:0% + + + + align:start position:0% + +is equal to the integral from zero to + + align:start position:0% +is equal to the integral from zero to + + + align:start position:0% +is equal to the integral from zero to +one of absolute value f of x DX + + align:start position:0% +one of absolute value f of x DX + + + align:start position:0% +one of absolute value f of x DX +and now let's just talk through why this + + align:start position:0% +and now let's just talk through why this + + + align:start position:0% +and now let's just talk through why this +why this is in fact a norm + + align:start position:0% +why this is in fact a norm + + + align:start position:0% +why this is in fact a norm +one positive definition we've already + + align:start position:0% +one positive definition we've already + + + align:start position:0% +one positive definition we've already +talked about in regards to metrics right + + align:start position:0% +talked about in regards to metrics right + + + align:start position:0% +talked about in regards to metrics right +this is definitely going to be positive + + align:start position:0% +this is definitely going to be positive + + + align:start position:0% +this is definitely going to be positive +or non-negative because its absolute + + align:start position:0% +or non-negative because its absolute + + + align:start position:0% +or non-negative because its absolute +values on the inside here and we're + + align:start position:0% +values on the inside here and we're + + + align:start position:0% +values on the inside here and we're +integrating over zero to one + + align:start position:0% +integrating over zero to one + + + align:start position:0% +integrating over zero to one +but the fact that it's positive + + align:start position:0% +but the fact that it's positive + + + align:start position:0% +but the fact that it's positive +definiteness comes from continuity + + align:start position:0% +definiteness comes from continuity + + + align:start position:0% +definiteness comes from continuity +right because if at any point this is + + align:start position:0% +right because if at any point this is + + + align:start position:0% +right because if at any point this is +bigger than zero there must be a point + + align:start position:0% +bigger than zero there must be a point + + + align:start position:0% +bigger than zero there must be a point +in which f of x is not zero + + align:start position:0% +in which f of x is not zero + + + align:start position:0% +in which f of x is not zero +homogeneity follows from homogeneity of + + align:start position:0% +homogeneity follows from homogeneity of + + + align:start position:0% +homogeneity follows from homogeneity of +the integral right because we can pull + + align:start position:0% +the integral right because we can pull + + + align:start position:0% +the integral right because we can pull +out constants if you multiply that by f + + align:start position:0% +out constants if you multiply that by f + + + align:start position:0% +out constants if you multiply that by f +and finally the Triangular inequality is + + align:start position:0% +and finally the Triangular inequality is + + + align:start position:0% +and finally the Triangular inequality is +precisely the same as before because we + + align:start position:0% +precisely the same as before because we + + + align:start position:0% +precisely the same as before because we +can apply the triangle inequality to + + align:start position:0% +can apply the triangle inequality to + + + align:start position:0% +can apply the triangle inequality to +let's say f plus G + + align:start position:0% +let's say f plus G + + + align:start position:0% +let's say f plus G +and then separate out using linearity of + + align:start position:0% +and then separate out using linearity of + + + align:start position:0% +and then separate out using linearity of +the integral so again three segments are + + align:start position:0% +the integral so again three segments are + + + align:start position:0% +the integral so again three segments are +very analogous + + align:start position:0% +very analogous + + + align:start position:0% +very analogous +uh so you might be wondering + + align:start position:0% +uh so you might be wondering + + + align:start position:0% +uh so you might be wondering +why do we care right why are we looking + + align:start position:0% +why do we care right why are we looking + + + align:start position:0% +why do we care right why are we looking +at Norm sets or Norm spaces + + align:start position:0% +at Norm sets or Norm spaces + + + align:start position:0% +at Norm sets or Norm spaces +oh I should say if you have a vector + + align:start position:0% +oh I should say if you have a vector + + + align:start position:0% +oh I should say if you have a vector +space what's the norm on it that is + + align:start position:0% +space what's the norm on it that is + + + align:start position:0% +space what's the norm on it that is +called a normed space + + align:start position:0% +called a normed space + + + align:start position:0% +called a normed space +I'll write that down in fact + + align:start position:0% +I'll write that down in fact + + + align:start position:0% +I'll write that down in fact +definition + + align:start position:0% + + + + align:start position:0% + +a vector space V with Norm absolute + + align:start position:0% +a vector space V with Norm absolute + + + align:start position:0% +a vector space V with Norm absolute +values + + align:start position:0% +values + + + align:start position:0% +values +is called a norm space + + align:start position:0% + + + + align:start position:0% + +just like a metric space + + align:start position:0% +just like a metric space + + + align:start position:0% +just like a metric space +so why do we even care + + align:start position:0% +so why do we even care + + + align:start position:0% +so why do we even care +well firstly + + align:start position:0% +well firstly + + + align:start position:0% +well firstly +18102 talks about this concept quite a + + align:start position:0% +18102 talks about this concept quite a + + + align:start position:0% +18102 talks about this concept quite a +bit further as you can know you know + + align:start position:0% +bit further as you can know you know + + + align:start position:0% +bit further as you can know you know +we're doing all of this on Vector spaces + + align:start position:0% +we're doing all of this on Vector spaces + + + align:start position:0% +we're doing all of this on Vector spaces +and what this lets us do essentially is + + align:start position:0% +and what this lets us do essentially is + + + align:start position:0% +and what this lets us do essentially is +linear algebra once we start studying + + align:start position:0% +linear algebra once we start studying + + + align:start position:0% +linear algebra once we start studying +Norms we can look at in your algebra on + + align:start position:0% +Norms we can look at in your algebra on + + + align:start position:0% +Norms we can look at in your algebra on +Vector spaces and in fact look at + + align:start position:0% +Vector spaces and in fact look at + + + align:start position:0% +Vector spaces and in fact look at +infinite dimensional Vector spaces + + align:start position:0% +infinite dimensional Vector spaces + + + align:start position:0% +infinite dimensional Vector spaces +that's the major difference if that + + align:start position:0% +that's the major difference if that + + + align:start position:0% +that's the major difference if that +terminology does not + + align:start position:0% +terminology does not + + + align:start position:0% +terminology does not +makes sense because y'all haven't done + + align:start position:0% +makes sense because y'all haven't done + + + align:start position:0% +makes sense because y'all haven't done +uh linear art workouts necessarily + + align:start position:0% +uh linear art workouts necessarily + + + align:start position:0% +uh linear art workouts necessarily +totally fair don't worry about it uh + + align:start position:0% +totally fair don't worry about it uh + + + align:start position:0% +totally fair don't worry about it uh +it's just what happens in 18102 which in + + align:start position:0% +it's just what happens in 18102 which in + + + align:start position:0% +it's just what happens in 18102 which in +the class I highly recommend + + align:start position:0% +the class I highly recommend + + + align:start position:0% +the class I highly recommend +um but secondly + + align:start position:0% +um but secondly + + + align:start position:0% +um but secondly +you know + + align:start position:0% +you know + + + align:start position:0% +you know +the process of figuring out that a norm + + align:start position:0% +the process of figuring out that a norm + + + align:start position:0% +the process of figuring out that a norm +is in fact a norm is very similar to + + align:start position:0% +is in fact a norm is very similar to + + + align:start position:0% +is in fact a norm is very similar to +showing that a metric is in fact a + + align:start position:0% +showing that a metric is in fact a + + + align:start position:0% +showing that a metric is in fact a +metric it's just checking all three + + align:start position:0% +metric it's just checking all three + + + align:start position:0% +metric it's just checking all three +properties and going through the details + + align:start position:0% +properties and going through the details + + + align:start position:0% +properties and going through the details +so that's the second reason why I bring + + align:start position:0% +so that's the second reason why I bring + + + align:start position:0% +so that's the second reason why I bring +it up here + + align:start position:0% +it up here + + + align:start position:0% +it up here +but the third reason in particular with + + align:start position:0% +but the third reason in particular with + + + align:start position:0% +but the third reason in particular with +compact sets is this going to help us + + align:start position:0% +compact sets is this going to help us + + + align:start position:0% +compact sets is this going to help us +understand this notion of finite masks + + align:start position:0% +understand this notion of finite masks + + + align:start position:0% +understand this notion of finite masks +so for instance one question we could + + align:start position:0% +so for instance one question we could + + + align:start position:0% +so for instance one question we could +ask + + align:start position:0% +ask + + + align:start position:0% +ask +question + + align:start position:0% + + + + align:start position:0% + +when is + + align:start position:0% + + + + align:start position:0% + +the L1 or monopuncture + + align:start position:0% + + + + align:start position:0% + +well here it's pretty straightforward + + align:start position:0% +well here it's pretty straightforward + + + align:start position:0% +well here it's pretty straightforward +right because here we're only looking at + + align:start position:0% +right because here we're only looking at + + + align:start position:0% +right because here we're only looking at +functions on zero to one so if it's + + align:start position:0% +functions on zero to one so if it's + + + align:start position:0% +functions on zero to one so if it's +continuous on zero to one we know that + + align:start position:0% +continuous on zero to one we know that + + + align:start position:0% +continuous on zero to one we know that +it has the maximum value and we know + + align:start position:0% +it has the maximum value and we know + + + align:start position:0% +it has the maximum value and we know +that it's that this term is always going + + align:start position:0% +that it's that this term is always going + + + align:start position:0% +that it's that this term is always going +to be finite + + align:start position:0% +to be finite + + + align:start position:0% +to be finite +but I guess I should say more rigorously + + align:start position:0% +but I guess I should say more rigorously + + + align:start position:0% +but I guess I should say more rigorously +you know this is clear + + align:start position:0% +you know this is clear + + + align:start position:0% +you know this is clear +if we're on zero to one + + align:start position:0% +if we're on zero to one + + + align:start position:0% +if we're on zero to one +but what about + + align:start position:0% +but what about + + + align:start position:0% +but what about +what about when you're looking at + + align:start position:0% +what about when you're looking at + + + align:start position:0% +what about when you're looking at +functions on r + + align:start position:0% + + + + align:start position:0% + +well here we can similarly Define L1 + + align:start position:0% +well here we can similarly Define L1 + + + align:start position:0% +well here we can similarly Define L1 +functions on r + + align:start position:0% +functions on r + + + align:start position:0% +functions on r +to be the set of functions + + align:start position:0% +to be the set of functions + + + align:start position:0% +to be the set of functions +this is like Lucy + + align:start position:0% +this is like Lucy + + + align:start position:0% +this is like Lucy +functions f + + align:start position:0% +functions f + + + align:start position:0% +functions f +such that the integral from minus + + align:start position:0% +such that the integral from minus + + + align:start position:0% +such that the integral from minus +infinity to Infinity + + align:start position:0% +infinity to Infinity + + + align:start position:0% +infinity to Infinity +of f of x DX + + align:start position:0% +of f of x DX + + + align:start position:0% +of f of x DX +is less than infinity + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +then this turns into a question + + align:start position:0% +then this turns into a question + + + align:start position:0% +then this turns into a question +of when are these integrals in fact + + align:start position:0% +of when are these integrals in fact + + + align:start position:0% +of when are these integrals in fact +finite + + align:start position:0% +finite + + + align:start position:0% +finite +and there's a few answers to this + + align:start position:0% +and there's a few answers to this + + + align:start position:0% +and there's a few answers to this +but the one that I want to point out + + align:start position:0% +but the one that I want to point out + + + align:start position:0% +but the one that I want to point out +is perhaps the most natural + + align:start position:0% +is perhaps the most natural + + + align:start position:0% +is perhaps the most natural +the L1 Norm of a function f on r + + align:start position:0% +the L1 Norm of a function f on r + + + align:start position:0% +the L1 Norm of a function f on r +will be finite + + align:start position:0% + + + + align:start position:0% + +if + + align:start position:0% +if + + + align:start position:0% +if +f is zero + + align:start position:0% +f is zero + + + align:start position:0% +f is zero +outside of some interval + + align:start position:0% +outside of some interval + + + align:start position:0% +outside of some interval +so let's just say + + align:start position:0% +so let's just say + + + align:start position:0% +so let's just say +the intervals minus end to end + + align:start position:0% + + + + align:start position:0% + +right if I have a function + + align:start position:0% +right if I have a function + + + align:start position:0% +right if I have a function +that is oscillating wildly in between + + align:start position:0% +that is oscillating wildly in between + + + align:start position:0% +that is oscillating wildly in between +two points that doesn't matter as long + + align:start position:0% +two points that doesn't matter as long + + + align:start position:0% +two points that doesn't matter as long +as at a certain point let's say from n + + align:start position:0% +as at a certain point let's say from n + + + align:start position:0% +as at a certain point let's say from n +to minus n + + align:start position:0% +to minus n + + + align:start position:0% +to minus n +it goes to zero right then we're going + + align:start position:0% +it goes to zero right then we're going + + + align:start position:0% +it goes to zero right then we're going +to know that the integral is in fact + + align:start position:0% +to know that the integral is in fact + + + align:start position:0% +to know that the integral is in fact +finite + + align:start position:0% +finite + + + align:start position:0% +finite +this is not an if and only if statement + + align:start position:0% +this is not an if and only if statement + + + align:start position:0% +this is not an if and only if statement +of course we could have functions I + + align:start position:0% +of course we could have functions I + + + align:start position:0% +of course we could have functions I +could gaussian + + align:start position:0% + + + + align:start position:0% + +so note + + align:start position:0% +so note + + + align:start position:0% +so note +not this statement is not if and only if + + align:start position:0% +not this statement is not if and only if + + + align:start position:0% +not this statement is not if and only if +we can have functions like e to the + + align:start position:0% +we can have functions like e to the + + + align:start position:0% +we can have functions like e to the +minus x squared where here it never + + align:start position:0% +minus x squared where here it never + + + align:start position:0% +minus x squared where here it never +quite goes to zero + + align:start position:0% +quite goes to zero + + + align:start position:0% +quite goes to zero +but rapidly decays to zero + + align:start position:0% +but rapidly decays to zero + + + align:start position:0% +but rapidly decays to zero +so note that the L1 functions are not + + align:start position:0% +so note that the L1 functions are not + + + align:start position:0% +so note that the L1 functions are not +simply ones that eventually go to zero + + align:start position:0% +simply ones that eventually go to zero + + + align:start position:0% +simply ones that eventually go to zero +but this is a pretty good answer to our + + align:start position:0% +but this is a pretty good answer to our + + + align:start position:0% +but this is a pretty good answer to our +question right this is a big set of + + align:start position:0% +question right this is a big set of + + + align:start position:0% +question right this is a big set of +functions I could just take functions + + align:start position:0% +functions I could just take functions + + + align:start position:0% +functions I could just take functions +that are continuous and then eventually + + align:start position:0% +that are continuous and then eventually + + + align:start position:0% +that are continuous and then eventually +go to zero that's a pretty big set + + align:start position:0% + + + + align:start position:0% + +um to be more explicit here + + align:start position:0% +um to be more explicit here + + + align:start position:0% +um to be more explicit here +this is how it's defined on R but we can + + align:start position:0% +this is how it's defined on R but we can + + + align:start position:0% +this is how it's defined on R but we can +be even more General than functions on r + + align:start position:0% +be even more General than functions on r + + + align:start position:0% +be even more General than functions on r +so + + align:start position:0% +so + + + align:start position:0% +so +uh if a function satisfies this we say + + align:start position:0% +uh if a function satisfies this we say + + + align:start position:0% +uh if a function satisfies this we say +that it has compact supports + + align:start position:0% + + + + align:start position:0% + +but but what is the support of a + + align:start position:0% +but but what is the support of a + + + align:start position:0% +but but what is the support of a +function + + align:start position:0% +function + + + align:start position:0% +function +well + + align:start position:0% +well + + + align:start position:0% +well +definition + + align:start position:0% + + + + align:start position:0% + +consider + + align:start position:0% +consider + + + align:start position:0% +consider +sum X + + align:start position:0% + + + + align:start position:0% + +function + + align:start position:0% +function + + + align:start position:0% +function +on r + + align:start position:0% + + + + align:start position:0% + +and then consider the set + + align:start position:0% + + + + align:start position:0% + +where it's non-zero + + align:start position:0% +where it's non-zero + + + align:start position:0% +where it's non-zero +so the X such that f of x + + align:start position:0% +so the X such that f of x + + + align:start position:0% +so the X such that f of x +is non-zero + + align:start position:0% + + + + align:start position:0% + +one question I could ask you before I + + align:start position:0% +one question I could ask you before I + + + align:start position:0% +one question I could ask you before I +get into what the actual definition is + + align:start position:0% +get into what the actual definition is + + + align:start position:0% +get into what the actual definition is +that we're looking at is is this set + + align:start position:0% +that we're looking at is is this set + + + align:start position:0% +that we're looking at is is this set +open or is it closed + + align:start position:0% + + + + align:start position:0% + +any ideas + + align:start position:0% + + + + align:start position:0% + +yeah it's open uh we can write this + + align:start position:0% +yeah it's open uh we can write this + + + align:start position:0% +yeah it's open uh we can write this +equivalently as F inverse of the + + align:start position:0% +equivalently as F inverse of the + + + align:start position:0% +equivalently as F inverse of the +complement of zero + + align:start position:0% +complement of zero + + + align:start position:0% +complement of zero +right we're looking at the points such + + align:start position:0% +right we're looking at the points such + + + align:start position:0% +right we're looking at the points such +that the image of them is non-zero and + + align:start position:0% +that the image of them is non-zero and + + + align:start position:0% +that the image of them is non-zero and +we know that the set the singular set + + align:start position:0% +we know that the set the singular set + + + align:start position:0% +we know that the set the singular set +zero is a closed set which means that + + align:start position:0% +zero is a closed set which means that + + + align:start position:0% +zero is a closed set which means that +the complement is open + + align:start position:0% +the complement is open + + + align:start position:0% +the complement is open +and the inverse image of an open set is + + align:start position:0% +and the inverse image of an open set is + + + align:start position:0% +and the inverse image of an open set is +open + + align:start position:0% +open + + + align:start position:0% +open +so this is open + + align:start position:0% + + + + align:start position:0% + +and then we Define + + align:start position:0% + + + + align:start position:0% + +the support of a function + + align:start position:0% + + + + align:start position:0% + +to be the closure of this set so I + + align:start position:0% +to be the closure of this set so I + + + align:start position:0% +to be the closure of this set so I +should say x such that f of x + + align:start position:0% +should say x such that f of x + + + align:start position:0% +should say x such that f of x +is not zero + + align:start position:0% +is not zero + + + align:start position:0% +is not zero +we need to find the support of the + + align:start position:0% +we need to find the support of the + + + align:start position:0% +we need to find the support of the +function to be the closure of this set + + align:start position:0% +function to be the closure of this set + + + align:start position:0% +function to be the closure of this set +now I have to Define what closure is + + align:start position:0% +now I have to Define what closure is + + + align:start position:0% +now I have to Define what closure is +what closure is is the smallest closed + + align:start position:0% +what closure is is the smallest closed + + + align:start position:0% +what closure is is the smallest closed +set that contains it all this is doing + + align:start position:0% +set that contains it all this is doing + + + align:start position:0% +set that contains it all this is doing +is adding the boundary points right so + + align:start position:0% +is adding the boundary points right so + + + align:start position:0% +is adding the boundary points right so +if I have a function + + align:start position:0% +if I have a function + + + align:start position:0% +if I have a function +here's a little aside + + align:start position:0% +here's a little aside + + + align:start position:0% +here's a little aside +if I have a function that's non-zero + + align:start position:0% +if I have a function that's non-zero + + + align:start position:0% +if I have a function that's non-zero +from + + align:start position:0% +from + + + align:start position:0% +from +non-zero from minus eight to a sorry + + align:start position:0% +non-zero from minus eight to a sorry + + + align:start position:0% +non-zero from minus eight to a sorry +minus a yeah let's say minus a to a + + align:start position:0% + + + + align:start position:0% + +minus h a + + align:start position:0% +minus h a + + + align:start position:0% +minus h a +and I can just draw out a little picture + + align:start position:0% +and I can just draw out a little picture + + + align:start position:0% +and I can just draw out a little picture +a function that + + align:start position:0% +a function that + + + align:start position:0% +a function that +acts like this for minus a to a + + align:start position:0% + + + + align:start position:0% + +then the support will be + + align:start position:0% +then the support will be + + + align:start position:0% +then the support will be +adding the boundary points + + align:start position:0% +adding the boundary points + + + align:start position:0% +adding the boundary points +so let's look if you think anyone who's + + align:start position:0% +so let's look if you think anyone who's + + + align:start position:0% +so let's look if you think anyone who's +just watching the board right now but + + align:start position:0% +just watching the board right now but + + + align:start position:0% +just watching the board right now but +verbally that's what's happening we're + + align:start position:0% +verbally that's what's happening we're + + + align:start position:0% +verbally that's what's happening we're +just adding the boundary point to our + + align:start position:0% +just adding the boundary point to our + + + align:start position:0% +just adding the boundary point to our +entry rules and this is a closed setup + + align:start position:0% +entry rules and this is a closed setup + + + align:start position:0% +entry rules and this is a closed setup +so when I say that a function has + + align:start position:0% +so when I say that a function has + + + align:start position:0% +so when I say that a function has +compact support + + align:start position:0% +compact support + + + align:start position:0% +compact support +I mean that the support of the function + + align:start position:0% +I mean that the support of the function + + + align:start position:0% +I mean that the support of the function +is a compact set + + align:start position:0% +is a compact set + + + align:start position:0% +is a compact set +I haven't defined what a compacts that + + align:start position:0% +I haven't defined what a compacts that + + + align:start position:0% +I haven't defined what a compacts that +is I'm going to do that in just a moment + + align:start position:0% +is I'm going to do that in just a moment + + + align:start position:0% +is I'm going to do that in just a moment +but this is how it's connected to the + + align:start position:0% +but this is how it's connected to the + + + align:start position:0% +but this is how it's connected to the +notion of finite Nets right again the + + align:start position:0% +notion of finite Nets right again the + + + align:start position:0% +notion of finite Nets right again the +way that we got here was asking a very + + align:start position:0% +way that we got here was asking a very + + + align:start position:0% +way that we got here was asking a very +simple question if I have a function on + + align:start position:0% +simple question if I have a function on + + + align:start position:0% +simple question if I have a function on +the real numbers when is its integral + + align:start position:0% +the real numbers when is its integral + + + align:start position:0% +the real numbers when is its integral +going to be finite + + align:start position:0% +going to be finite + + + align:start position:0% +going to be finite +and a nice answer is if it eventually + + align:start position:0% +and a nice answer is if it eventually + + + align:start position:0% +and a nice answer is if it eventually +goes to zero + + align:start position:0% +goes to zero + + + align:start position:0% +goes to zero +and that is somehow connected to the + + align:start position:0% +and that is somehow connected to the + + + align:start position:0% +and that is somehow connected to the +notion of a compact set + + align:start position:0% +notion of a compact set + + + align:start position:0% +notion of a compact set +so any questions thus far I know I'm + + align:start position:0% +so any questions thus far I know I'm + + + align:start position:0% +so any questions thus far I know I'm +being very hypothetical here like I know + + align:start position:0% +being very hypothetical here like I know + + + align:start position:0% +being very hypothetical here like I know +that I'm + + align:start position:0% +that I'm + + + align:start position:0% +that I'm +talking about a definition without + + align:start position:0% +talking about a definition without + + + align:start position:0% +talking about a definition without +saying what it is quite yet + + align:start position:0% +saying what it is quite yet + + + align:start position:0% +saying what it is quite yet +but this is how this is the logic that + + align:start position:0% +but this is how this is the logic that + + + align:start position:0% +but this is how this is the logic that +we're following + + align:start position:0% +we're following + + + align:start position:0% +we're following +any questions + + align:start position:0% + + + + align:start position:0% + +cool + + align:start position:0% +cool + + + align:start position:0% +cool +all right so let's look at some analysis + + align:start position:0% +all right so let's look at some analysis + + + align:start position:0% +all right so let's look at some analysis +on finite sets + + align:start position:0% +on finite sets + + + align:start position:0% +on finite sets +so this is the first part one more now + + align:start position:0% +so this is the first part one more now + + + align:start position:0% +so this is the first part one more now +we're looking at finite sets so + + align:start position:0% + + + + align:start position:0% + +let a be a subset of metric Space X with + + align:start position:0% +let a be a subset of metric Space X with + + + align:start position:0% +let a be a subset of metric Space X with +metric d + + align:start position:0% +metric d + + + align:start position:0% +metric d +um and suppose that a is finite + + align:start position:0% + + + + align:start position:0% + +then I claim that we have three + + align:start position:0% +then I claim that we have three + + + align:start position:0% +then I claim that we have three +properties of a + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +one + + align:start position:0% +one + + + align:start position:0% +one +let me switch + + align:start position:0% +let me switch + + + align:start position:0% +let me switch +every + + align:start position:0% +every + + + align:start position:0% +every +conversion sequence + + align:start position:0% +conversion sequence + + + align:start position:0% +conversion sequence +actually I'll just say every sequence + + align:start position:0% + + + + align:start position:0% + +of points of a + + align:start position:0% + + + + align:start position:0% + +so let's say x i + + align:start position:0% +so let's say x i + + + align:start position:0% +so let's say x i +continued in a + + align:start position:0% +continued in a + + + align:start position:0% +continued in a +has a convergence subsequence + + align:start position:0% + + + + align:start position:0% + +and I'm going to prove these things + + align:start position:0% +and I'm going to prove these things + + + align:start position:0% +and I'm going to prove these things +right if you're looking at this and + + align:start position:0% +right if you're looking at this and + + + align:start position:0% +right if you're looking at this and +wondering how are these statements true + + align:start position:0% +wondering how are these statements true + + + align:start position:0% +wondering how are these statements true +I'm going to quickly prove that one + + align:start position:0% +I'm going to quickly prove that one + + + align:start position:0% +I'm going to quickly prove that one +um but they aren't too hard to show + + align:start position:0% +um but they aren't too hard to show + + + align:start position:0% +um but they aren't too hard to show +two + + align:start position:0% +two + + + align:start position:0% +two +uh a is closed and bounded + + align:start position:0% + + + + align:start position:0% + +and three + + align:start position:0% +and three + + + align:start position:0% +and three +if f is a function on a so f is equal to + + align:start position:0% +if f is a function on a so f is equal to + + + align:start position:0% +if f is a function on a so f is equal to +x h r + + align:start position:0% + + + + align:start position:0% + +then f + + align:start position:0% +then f + + + align:start position:0% +then f +as a maximum and a minimum + + align:start position:0% + + + + align:start position:0% + +these are three properties of finite + + align:start position:0% +these are three properties of finite + + + align:start position:0% +these are three properties of finite +sets and let's actually prove these + + align:start position:0% +sets and let's actually prove these + + + align:start position:0% +sets and let's actually prove these +three properties right it's pretty nice + + align:start position:0% +three properties right it's pretty nice + + + align:start position:0% +three properties right it's pretty nice +to show them + + align:start position:0% +to show them + + + align:start position:0% +to show them +three + + align:start position:0% +three + + + align:start position:0% +three +okay so let's print these three + + align:start position:0% +okay so let's print these three + + + align:start position:0% +okay so let's print these three +properties + + align:start position:0% +properties + + + align:start position:0% +properties +true + + align:start position:0% +true + + + align:start position:0% +true +consider some sequence x i then a + + align:start position:0% + + + + align:start position:0% + +how can we find a convergent subsequent + + align:start position:0% +how can we find a convergent subsequent + + + align:start position:0% +how can we find a convergent subsequent +instead well because there's only + + align:start position:0% +instead well because there's only + + + align:start position:0% +instead well because there's only +finitely many points we can consider and + + align:start position:0% +finitely many points we can consider and + + + align:start position:0% +finitely many points we can consider and +a and a sequence has infinitely many + + align:start position:0% +a and a sequence has infinitely many + + + align:start position:0% +a and a sequence has infinitely many +terms we know that one of those terms + + align:start position:0% +terms we know that one of those terms + + + align:start position:0% +terms we know that one of those terms +must be repeated infinitely many times + + align:start position:0% +must be repeated infinitely many times + + + align:start position:0% +must be repeated infinitely many times +right well let's just say + + align:start position:0% +right well let's just say + + + align:start position:0% +right well let's just say +there exists and XJ + + align:start position:0% +there exists and XJ + + + align:start position:0% +there exists and XJ +in a + + align:start position:0% +in a + + + align:start position:0% +in a +with + + align:start position:0% +with + + + align:start position:0% +with +x j infinitely many times + + align:start position:0% + + + + align:start position:0% + +and because it's infinitely many because + + align:start position:0% +and because it's infinitely many because + + + align:start position:0% +and because it's infinitely many because +it appears infinitely many times this is + + align:start position:0% +it appears infinitely many times this is + + + align:start position:0% +it appears infinitely many times this is +going to imply + + align:start position:0% +going to imply + + + align:start position:0% +going to imply +the sequence of X and K's + + align:start position:0% +the sequence of X and K's + + + align:start position:0% +the sequence of X and K's +which are simply the points in our + + align:start position:0% +which are simply the points in our + + + align:start position:0% +which are simply the points in our +sequence which are equal to x j + + align:start position:0% +sequence which are equal to x j + + + align:start position:0% +sequence which are equal to x j +this is a convergent subsequence + + align:start position:0% + + + + align:start position:0% + +the fact that it's convergent is simply + + align:start position:0% +the fact that it's convergent is simply + + + align:start position:0% +the fact that it's convergent is simply +stating that if I have a sequence that's + + align:start position:0% +stating that if I have a sequence that's + + + align:start position:0% +stating that if I have a sequence that's +the same point over and over and over + + align:start position:0% +the same point over and over and over + + + align:start position:0% +the same point over and over and over +again is going to converge to that point + + align:start position:0% +again is going to converge to that point + + + align:start position:0% +again is going to converge to that point +right + + align:start position:0% +right + + + align:start position:0% +right +so again to reiterate here we had a + + align:start position:0% +so again to reiterate here we had a + + + align:start position:0% +so again to reiterate here we had a +finite set + + align:start position:0% +finite set + + + align:start position:0% +finite set +and we had a sequence on our finite set + + align:start position:0% +and we had a sequence on our finite set + + + align:start position:0% +and we had a sequence on our finite set +and we wanted to say that it has a + + align:start position:0% +and we wanted to say that it has a + + + align:start position:0% +and we wanted to say that it has a +convergent subsequence + + align:start position:0% +convergent subsequence + + + align:start position:0% +convergent subsequence +we know that this has to be true because + + align:start position:0% +we know that this has to be true because + + + align:start position:0% +we know that this has to be true because +there is at least one term in our set a + + align:start position:0% +there is at least one term in our set a + + + align:start position:0% +there is at least one term in our set a +that's repeated infinitely many times in + + align:start position:0% +that's repeated infinitely many times in + + + align:start position:0% +that's repeated infinitely many times in +our sequence and then we can just choose + + align:start position:0% +our sequence and then we can just choose + + + align:start position:0% +our sequence and then we can just choose +the subsequence to be that point over + + align:start position:0% +the subsequence to be that point over + + + align:start position:0% +the subsequence to be that point over +and over and over again + + align:start position:0% +and over and over again + + + align:start position:0% +and over and over again +so that's our convergent subsequence + + align:start position:0% +so that's our convergent subsequence + + + align:start position:0% +so that's our convergent subsequence +two + + align:start position:0% +two + + + align:start position:0% +two +how do we need to know that it's closed + + align:start position:0% +how do we need to know that it's closed + + + align:start position:0% +how do we need to know that it's closed +and bounded + + align:start position:0% +and bounded + + + align:start position:0% +and bounded +well closure + + align:start position:0% + + + + align:start position:0% + +close your photos from last time + + align:start position:0% +close your photos from last time + + + align:start position:0% +close your photos from last time +because we showed that a single if I'm + + align:start position:0% +because we showed that a single if I'm + + + align:start position:0% +because we showed that a single if I'm +looking at a single point we know that + + align:start position:0% +looking at a single point we know that + + + align:start position:0% +looking at a single point we know that +that is a closed set and we know that a + + align:start position:0% +that is a closed set and we know that a + + + align:start position:0% +that is a closed set and we know that a +union of closed sets a finite unit + + align:start position:0% +union of closed sets a finite unit + + + align:start position:0% +union of closed sets a finite unit +approach that is closed + + align:start position:0% +approach that is closed + + + align:start position:0% +approach that is closed +so we know that it's closed + + align:start position:0% +so we know that it's closed + + + align:start position:0% +so we know that it's closed +the fact that it's bounded + + align:start position:0% + + + + align:start position:0% + +comes from looking at uh + + align:start position:0% +comes from looking at uh + + + align:start position:0% +comes from looking at uh +comes from the fact that there's only + + align:start position:0% +comes from the fact that there's only + + + align:start position:0% +comes from the fact that there's only +finally many points so what we can + + align:start position:0% +finally many points so what we can + + + align:start position:0% +finally many points so what we can +consider is fix any point p + + align:start position:0% +consider is fix any point p + + + align:start position:0% +consider is fix any point p +in your metric Space X + + align:start position:0% + + + + align:start position:0% + +so any point + + align:start position:0% +so any point + + + align:start position:0% +so any point +and consider + + align:start position:0% +and consider + + + align:start position:0% +and consider +our bound B + + align:start position:0% + + + + align:start position:0% + +to be the maximum + + align:start position:0% +to be the maximum + + + align:start position:0% +to be the maximum +of the distances from E to x i where x i + + align:start position:0% + + + + align:start position:0% + +is then you say a + + align:start position:0% +is then you say a + + + align:start position:0% +is then you say a +and here we know that this maximum + + align:start position:0% +and here we know that this maximum + + + align:start position:0% +and here we know that this maximum +actually exists right because it's a + + align:start position:0% +actually exists right because it's a + + + align:start position:0% +actually exists right because it's a +finite set so if I'm looking at the + + align:start position:0% +finite set so if I'm looking at the + + + align:start position:0% +finite set so if I'm looking at the +maximum of finite thing + + align:start position:0% +maximum of finite thing + + + align:start position:0% +maximum of finite thing +this down will be finite + + align:start position:0% +this down will be finite + + + align:start position:0% +this down will be finite +so this implies that it's closed and + + align:start position:0% +so this implies that it's closed and + + + align:start position:0% +so this implies that it's closed and +it's bounded right we were able to find + + align:start position:0% +it's bounded right we were able to find + + + align:start position:0% +it's bounded right we were able to find +an upper bound on our set + + align:start position:0% +an upper bound on our set + + + align:start position:0% +an upper bound on our set +cool + + align:start position:0% +cool + + + align:start position:0% +cool +and lastly three + + align:start position:0% +and lastly three + + + align:start position:0% +and lastly three +the fact that a function + + align:start position:0% +the fact that a function + + + align:start position:0% +the fact that a function +on a to R + + align:start position:0% + + + + align:start position:0% + +has a maximum min + + align:start position:0% + + + + align:start position:0% + +follows from the fact that we can just + + align:start position:0% +follows from the fact that we can just + + + align:start position:0% +follows from the fact that we can just +consider the set F of a + + align:start position:0% +consider the set F of a + + + align:start position:0% +consider the set F of a +this would be a finite set in r + + align:start position:0% + + + + align:start position:0% + +and because that's fine I can order them + + align:start position:0% +and because that's fine I can order them + + + align:start position:0% +and because that's fine I can order them +right so I can just choose the point + + align:start position:0% +right so I can just choose the point + + + align:start position:0% +right so I can just choose the point +where it's the maximum is achieved and + + align:start position:0% +where it's the maximum is achieved and + + + align:start position:0% +where it's the maximum is achieved and +choose the point where the minimum is + + align:start position:0% +choose the point where the minimum is + + + align:start position:0% +choose the point where the minimum is +achieved the thing that's important to + + align:start position:0% +achieved the thing that's important to + + + align:start position:0% +achieved the thing that's important to +note is that the maximum and the minimum + + align:start position:0% +note is that the maximum and the minimum + + + align:start position:0% +note is that the maximum and the minimum +is achieved at a single or at least a + + align:start position:0% +is achieved at a single or at least a + + + align:start position:0% +is achieved at a single or at least a +point of your set a + + align:start position:0% +point of your set a + + + align:start position:0% +point of your set a +but yeah these are the three properties + + align:start position:0% +but yeah these are the three properties + + + align:start position:0% +but yeah these are the three properties +of finite sets that we can do analysis + + align:start position:0% +of finite sets that we can do analysis + + + align:start position:0% +of finite sets that we can do analysis +on and notice here that we're not + + align:start position:0% +on and notice here that we're not + + + align:start position:0% +on and notice here that we're not +assuming that the sequence is convergent + + align:start position:0% +assuming that the sequence is convergent + + + align:start position:0% +assuming that the sequence is convergent +we're not assuming that the function f + + align:start position:0% +we're not assuming that the function f + + + align:start position:0% +we're not assuming that the function f +is continuous everything is super nice + + align:start position:0% +is continuous everything is super nice + + + align:start position:0% +is continuous everything is super nice +when we're looking at + + align:start position:0% +when we're looking at + + + align:start position:0% +when we're looking at +um finite sets + + align:start position:0% +um finite sets + + + align:start position:0% +um finite sets +now these three properties are ones that + + align:start position:0% +now these three properties are ones that + + + align:start position:0% +now these three properties are ones that +we're in fact going to show or true + + align:start position:0% +we're in fact going to show or true + + + align:start position:0% +we're in fact going to show or true +about compact sets either we're going to + + align:start position:0% +about compact sets either we're going to + + + align:start position:0% +about compact sets either we're going to +show that they're true or we're simply + + align:start position:0% +show that they're true or we're simply + + + align:start position:0% +show that they're true or we're simply +going to Define them to be so + + align:start position:0% + + + + align:start position:0% + +let's go ahead and do that so this is it + + align:start position:0% +let's go ahead and do that so this is it + + + align:start position:0% +let's go ahead and do that so this is it +for the motivation about compact status + + align:start position:0% +for the motivation about compact status + + + align:start position:0% +for the motivation about compact status +I'm going to Define what a compact set + + align:start position:0% +I'm going to Define what a compact set + + + align:start position:0% +I'm going to Define what a compact set +is now and prove some nice facts about + + align:start position:0% +is now and prove some nice facts about + + + align:start position:0% +is now and prove some nice facts about +it but before I do so again any + + align:start position:0% +it but before I do so again any + + + align:start position:0% +it but before I do so again any +questions about what I've done so far + + align:start position:0% +questions about what I've done so far + + + align:start position:0% +questions about what I've done so far +a lot of motivation before we've + + align:start position:0% +a lot of motivation before we've + + + align:start position:0% +a lot of motivation before we've +actually defined what we're looking at + + align:start position:0% +actually defined what we're looking at + + + align:start position:0% +actually defined what we're looking at +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so go ahead and erase the reports and + + align:start position:0% +so go ahead and erase the reports and + + + align:start position:0% +so go ahead and erase the reports and +I'll move on to the definitions of + + align:start position:0% +I'll move on to the definitions of + + + align:start position:0% +I'll move on to the definitions of +compact sets + + align:start position:0% + + + + align:start position:0% + +or the definition of compact sets we're + + align:start position:0% +or the definition of compact sets we're + + + align:start position:0% +or the definition of compact sets we're +going to have two of them + + align:start position:0% +going to have two of them + + + align:start position:0% +going to have two of them +uh I'll explain why I've already have + + align:start position:0% +uh I'll explain why I've already have + + + align:start position:0% +uh I'll explain why I've already have +two of them in a moment + + align:start position:0% +two of them in a moment + + + align:start position:0% +two of them in a moment +but really + + align:start position:0% + + + + align:start position:0% + +um we're going to show that on + + align:start position:0% +um we're going to show that on + + + align:start position:0% +um we're going to show that on +metriculation Fair the same + + align:start position:0% +metriculation Fair the same + + + align:start position:0% +metriculation Fair the same +uh but before I Define what a compact + + align:start position:0% +uh but before I Define what a compact + + + align:start position:0% +uh but before I Define what a compact +set is I just have to say what a cover + + align:start position:0% +set is I just have to say what a cover + + + align:start position:0% +set is I just have to say what a cover +is + + align:start position:0% +is + + + align:start position:0% +is +so + + align:start position:0% +so + + + align:start position:0% +so +so a cover + + align:start position:0% + + + + align:start position:0% + +of asex + + align:start position:0% +of asex + + + align:start position:0% +of asex +a + + align:start position:0% +a + + + align:start position:0% +a +is simply + + align:start position:0% +is simply + + + align:start position:0% +is simply +a union of sets + + align:start position:0% + + + + align:start position:0% + +let's see those sets are called + + align:start position:0% +let's see those sets are called + + + align:start position:0% +let's see those sets are called +UI + + align:start position:0% + + + + align:start position:0% + +such + + align:start position:0% +such + + + align:start position:0% +such +uh + + align:start position:0% +uh + + + align:start position:0% +uh +such that a is contained to the union + + align:start position:0% + + + + align:start position:0% + +so I should say a collection of sites + + align:start position:0% +so I should say a collection of sites + + + align:start position:0% +so I should say a collection of sites +rather than it's a collection of sets + + align:start position:0% +rather than it's a collection of sets + + + align:start position:0% +rather than it's a collection of sets +such that a is contained in there + + align:start position:0% +such that a is contained in there + + + align:start position:0% +such that a is contained in there +all right + + align:start position:0% +all right + + + align:start position:0% +all right +this is the definition of a cover + + align:start position:0% +this is the definition of a cover + + + align:start position:0% +this is the definition of a cover +and an open cover + + align:start position:0% + + + + align:start position:0% + +is the same exact thing + + align:start position:0% +is the same exact thing + + + align:start position:0% +is the same exact thing +except then I'm going to assume that my + + align:start position:0% +except then I'm going to assume that my + + + align:start position:0% +except then I'm going to assume that my +uis are open + + align:start position:0% + + + + align:start position:0% + +so so same definition as a cover I'm + + align:start position:0% +so so same definition as a cover I'm + + + align:start position:0% +so so same definition as a cover I'm +just assuming that the sets that are + + align:start position:0% +just assuming that the sets that are + + + align:start position:0% +just assuming that the sets that are +covering by set a are open + + align:start position:0% + + + + align:start position:0% + +all right so let's define what + + align:start position:0% +all right so let's define what + + + align:start position:0% +all right so let's define what +uh compact is and this will become a + + align:start position:0% +uh compact is and this will become a + + + align:start position:0% +uh compact is and this will become a +apparent why I Define this first + + align:start position:0% +apparent why I Define this first + + + align:start position:0% +apparent why I Define this first +finish it + + align:start position:0% + + + + align:start position:0% + +I set a + + align:start position:0% +I set a + + + align:start position:0% +I set a +contained in a metric Space X + + align:start position:0% +contained in a metric Space X + + + align:start position:0% +contained in a metric Space X +is compact + + align:start position:0% + + + + align:start position:0% + +or I'm gonna because we're gonna have + + align:start position:0% +or I'm gonna because we're gonna have + + + align:start position:0% +or I'm gonna because we're gonna have +two definitions we're going to be + + align:start position:0% +two definitions we're going to be + + + align:start position:0% +two definitions we're going to be +careful here I'm going to say it's + + align:start position:0% +careful here I'm going to say it's + + + align:start position:0% +careful here I'm going to say it's +topologically compact + + align:start position:0% + + + + align:start position:0% + +compact + + align:start position:0% + + + + align:start position:0% + +if every open cover + + align:start position:0% + + + + align:start position:0% + +so if every open cover of a + + align:start position:0% +so if every open cover of a + + + align:start position:0% +so if every open cover of a +has a finite subcover + + align:start position:0% + + + + align:start position:0% + +now what do I mean by finite subcover I + + align:start position:0% +now what do I mean by finite subcover I + + + align:start position:0% +now what do I mean by finite subcover I +mean that I could just choose finitely + + align:start position:0% +mean that I could just choose finitely + + + align:start position:0% +mean that I could just choose finitely +many of these uis still cover our set + + align:start position:0% +many of these uis still cover our set + + + align:start position:0% +many of these uis still cover our set +all right + + align:start position:0% +all right + + + align:start position:0% +all right +and notice that this only depends on + + align:start position:0% +and notice that this only depends on + + + align:start position:0% +and notice that this only depends on +open says which is why it's called the + + align:start position:0% +open says which is why it's called the + + + align:start position:0% +open says which is why it's called the +topological compactness right this + + align:start position:0% +topological compactness right this + + + align:start position:0% +topological compactness right this +compact this definition of compactness + + align:start position:0% +compact this definition of compactness + + + align:start position:0% +compact this definition of compactness +only requires that we know what open + + align:start position:0% +only requires that we know what open + + + align:start position:0% +only requires that we know what open +sets are which is why we can do them in + + align:start position:0% +sets are which is why we can do them in + + + align:start position:0% +sets are which is why we can do them in +topology + + align:start position:0% +topology + + + align:start position:0% +topology +18901. + + align:start position:0% +18901. + + + align:start position:0% +18901. +all right our second definition is going + + align:start position:0% +all right our second definition is going + + + align:start position:0% +all right our second definition is going +to be one that has a much closer + + align:start position:0% +to be one that has a much closer + + + align:start position:0% +to be one that has a much closer +connection to finite sets + + align:start position:0% +connection to finite sets + + + align:start position:0% +connection to finite sets +at least apparently + + align:start position:0% +at least apparently + + + align:start position:0% +at least apparently +or or like it'll be more apparent + + align:start position:0% +or or like it'll be more apparent + + + align:start position:0% +or or like it'll be more apparent +so + + align:start position:0% +so + + + align:start position:0% +so +suppose again that we have a second a + + align:start position:0% +suppose again that we have a second a + + + align:start position:0% +suppose again that we have a second a +and X + + align:start position:0% +and X + + + align:start position:0% +and X +and this will be + + align:start position:0% +and this will be + + + align:start position:0% +and this will be +sequentially compact + + align:start position:0% + + + + align:start position:0% + +compact + + align:start position:0% + + + + align:start position:0% + +if every sequence has a con + + align:start position:0% +if every sequence has a con + + + align:start position:0% +if every sequence has a con +if + + align:start position:0% +if + + + align:start position:0% +if +every + + align:start position:0% +every + + + align:start position:0% +every +sequence of a + + align:start position:0% + + + + align:start position:0% + +has a convergence subsequence + + align:start position:0% + + + + align:start position:0% + +and now this should become apparent how + + align:start position:0% +and now this should become apparent how + + + align:start position:0% +and now this should become apparent how +directly relates to finite sets right + + align:start position:0% +directly relates to finite sets right + + + align:start position:0% +directly relates to finite sets right +because there we have sequences and we + + align:start position:0% +because there we have sequences and we + + + align:start position:0% +because there we have sequences and we +knew that every single sequence had a + + align:start position:0% +knew that every single sequence had a + + + align:start position:0% +knew that every single sequence had a +con uh how to convergent subsequence + + align:start position:0% +con uh how to convergent subsequence + + + align:start position:0% +con uh how to convergent subsequence +right + + align:start position:0% +right + + + align:start position:0% +right +so these are these are our two + + align:start position:0% +so these are these are our two + + + align:start position:0% +so these are these are our two +definitions of uh of compactness they + + align:start position:0% +definitions of uh of compactness they + + + align:start position:0% +definitions of uh of compactness they +are not equivalent always in fact in + + align:start position:0% +are not equivalent always in fact in + + + align:start position:0% +are not equivalent always in fact in +topological spaces these are very + + align:start position:0% +topological spaces these are very + + + align:start position:0% +topological spaces these are very +different + + align:start position:0% +different + + + align:start position:0% +different +um but on Metric spaces our ultimate + + align:start position:0% +um but on Metric spaces our ultimate + + + align:start position:0% +um but on Metric spaces our ultimate +goal for this class is to show that + + align:start position:0% +goal for this class is to show that + + + align:start position:0% +goal for this class is to show that +they're the same + + align:start position:0% +they're the same + + + align:start position:0% +they're the same +um but before we get to that on Metric + + align:start position:0% +um but before we get to that on Metric + + + align:start position:0% +um but before we get to that on Metric +spaces let's just talk about this on the + + align:start position:0% +spaces let's just talk about this on the + + + align:start position:0% +spaces let's just talk about this on the +real numbers because on the real numbers + + align:start position:0% +real numbers because on the real numbers + + + align:start position:0% +real numbers because on the real numbers +there's quite a bit we can actually say + + align:start position:0% +there's quite a bit we can actually say + + + align:start position:0% +there's quite a bit we can actually say +um I just want to know one's + + align:start position:0% +um I just want to know one's + + + align:start position:0% +um I just want to know one's +monotational thing + + align:start position:0% + + + + align:start position:0% + +as opposed to running compact set every + + align:start position:0% +as opposed to running compact set every + + + align:start position:0% +as opposed to running compact set every +single time I'm just going to use a + + align:start position:0% +single time I'm just going to use a + + + align:start position:0% +single time I'm just going to use a +is a subset of x if it's compact where + + align:start position:0% +is a subset of x if it's compact where + + + align:start position:0% +is a subset of x if it's compact where +here I have uh two subsets inside of + + align:start position:0% +here I have uh two subsets inside of + + + align:start position:0% +here I have uh two subsets inside of +each other and if you're using latex to + + align:start position:0% +each other and if you're using latex to + + + align:start position:0% +each other and if you're using latex to +type up your pieces + + align:start position:0% +type up your pieces + + + align:start position:0% +type up your pieces +this is just + + align:start position:0% +this is just + + + align:start position:0% +this is just +slash capital S subset + + align:start position:0% +slash capital S subset + + + align:start position:0% +slash capital S subset +so + + align:start position:0% +so + + + align:start position:0% +so +no worries there but that's the + + align:start position:0% +no worries there but that's the + + + align:start position:0% +no worries there but that's the +limitation for compact subsets that I'll + + align:start position:0% +limitation for compact subsets that I'll + + + align:start position:0% +limitation for compact subsets that I'll +be using and it's in fact a common one + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +what sites do we know that are + + align:start position:0% +what sites do we know that are + + + align:start position:0% +what sites do we know that are +sequentially compact from the real + + align:start position:0% +sequentially compact from the real + + + align:start position:0% +sequentially compact from the real +numbers you might have an answer for + + align:start position:0% +numbers you might have an answer for + + + align:start position:0% +numbers you might have an answer for +this already in your head especially if + + align:start position:0% +this already in your head especially if + + + align:start position:0% +this already in your head especially if +you've heard your resolution notes but + + align:start position:0% +you've heard your resolution notes but + + + align:start position:0% +you've heard your resolution notes but +we'll go through them + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +an immediate example that we can + + align:start position:0% +an immediate example that we can + + + align:start position:0% +an immediate example that we can +consider which is pretty nice is simply + + align:start position:0% +consider which is pretty nice is simply + + + align:start position:0% +consider which is pretty nice is simply +the set of real numbers themselves so + + align:start position:0% +the set of real numbers themselves so + + + align:start position:0% +the set of real numbers themselves so +let's do that + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +example + + align:start position:0% +example + + + align:start position:0% +example +consider the entire set of real numbers + + align:start position:0% +consider the entire set of real numbers + + + align:start position:0% +consider the entire set of real numbers +contained in r + + align:start position:0% + + + + align:start position:0% + +any guesses whether this will be compact + + align:start position:0% +any guesses whether this will be compact + + + align:start position:0% +any guesses whether this will be compact +or not + + align:start position:0% + + + + align:start position:0% + +yeah it will not be a compact set + + align:start position:0% + + + + align:start position:0% + +it's not going to be compact in either + + align:start position:0% +it's not going to be compact in either + + + align:start position:0% +it's not going to be compact in either +sense of Loop in either sense of the + + align:start position:0% +sense of Loop in either sense of the + + + align:start position:0% +sense of Loop in either sense of the +terms + + align:start position:0% + + + + align:start position:0% + +uh proof + + align:start position:0% +uh proof + + + align:start position:0% +uh proof +the proof of sequential compactness is + + align:start position:0% +the proof of sequential compactness is + + + align:start position:0% +the proof of sequential compactness is +not that bad right I can just choose the + + align:start position:0% +not that bad right I can just choose the + + + align:start position:0% +not that bad right I can just choose the +sequence that I'm considering + + align:start position:0% +sequence that I'm considering + + + align:start position:0% +sequence that I'm considering +I said + + align:start position:0% +I said + + + align:start position:0% +I said +accent + + align:start position:0% +accent + + + align:start position:0% +accent +to Simply Be + + align:start position:0% +to Simply Be + + + align:start position:0% +to Simply Be +equal to n for every natural number + + align:start position:0% + + + + align:start position:0% + +firstly this is non-convergent which is + + align:start position:0% +firstly this is non-convergent which is + + + align:start position:0% +firstly this is non-convergent which is +how we should expect right + + align:start position:0% +how we should expect right + + + align:start position:0% +how we should expect right +if the sequence that I'm considering is + + align:start position:0% +if the sequence that I'm considering is + + + align:start position:0% +if the sequence that I'm considering is +convergent then every subsequence will + + align:start position:0% +convergent then every subsequence will + + + align:start position:0% +convergent then every subsequence will +be convergent so start off with the + + align:start position:0% +be convergent so start off with the + + + align:start position:0% +be convergent so start off with the +Divergent set for a Divergent sequence + + align:start position:0% +Divergent set for a Divergent sequence + + + align:start position:0% +Divergent set for a Divergent sequence +but furthermore any subsequence of this + + align:start position:0% +but furthermore any subsequence of this + + + align:start position:0% +but furthermore any subsequence of this +I choose is going to go off to Infinity + + align:start position:0% +I choose is going to go off to Infinity + + + align:start position:0% +I choose is going to go off to Infinity +right so no subsequence of this will + + align:start position:0% +right so no subsequence of this will + + + align:start position:0% +right so no subsequence of this will +converge + + align:start position:0% +converge + + + align:start position:0% +converge +so this shows not sequentially impact + + align:start position:0% + + + + align:start position:0% + +but furthermore how do we show that the + + align:start position:0% +but furthermore how do we show that the + + + align:start position:0% +but furthermore how do we show that the +entire set of row numbers is non-compact + + align:start position:0% +entire set of row numbers is non-compact + + + align:start position:0% +entire set of row numbers is non-compact +topologically + + align:start position:0% +topologically + + + align:start position:0% +topologically +just choose a open cover that's nice so + + align:start position:0% +just choose a open cover that's nice so + + + align:start position:0% +just choose a open cover that's nice so +consider + + align:start position:0% + + + + align:start position:0% + +consider the cover the open cover + + align:start position:0% + + + + align:start position:0% + +given by the union of open intervals + + align:start position:0% +given by the union of open intervals + + + align:start position:0% +given by the union of open intervals +minus n + + align:start position:0% +minus n + + + align:start position:0% +minus n +or n in the natural numbers + + align:start position:0% + + + + align:start position:0% + +so here I'm just considering nested open + + align:start position:0% +so here I'm just considering nested open + + + align:start position:0% +so here I'm just considering nested open +intervals right one instead of the other + + align:start position:0% +intervals right one instead of the other + + + align:start position:0% +intervals right one instead of the other +instead of the other + + align:start position:0% +instead of the other + + + align:start position:0% +instead of the other +we know that this is going to contain + + align:start position:0% +we know that this is going to contain + + + align:start position:0% +we know that this is going to contain +the real numbers + + align:start position:0% +the real numbers + + + align:start position:0% +the real numbers +any row number that you choose is going + + align:start position:0% +any row number that you choose is going + + + align:start position:0% +any row number that you choose is going +to be in one of these open intervals + + align:start position:0% +to be in one of these open intervals + + + align:start position:0% +to be in one of these open intervals +right just choose one large enough + + align:start position:0% +right just choose one large enough + + + align:start position:0% +right just choose one large enough +but does there exist a finite sub + + align:start position:0% +but does there exist a finite sub + + + align:start position:0% +but does there exist a finite sub +coverage + + align:start position:0% +coverage + + + align:start position:0% +coverage +the answer is no suppose + + align:start position:0% + + + + align:start position:0% + +there existed a subsequence NK such that + + align:start position:0% +there existed a subsequence NK such that + + + align:start position:0% +there existed a subsequence NK such that +the union of NK in the natural numbers + + align:start position:0% +the union of NK in the natural numbers + + + align:start position:0% +the union of NK in the natural numbers +I should say the union of k equal to one + + align:start position:0% +I should say the union of k equal to one + + + align:start position:0% +I should say the union of k equal to one +to some m + + align:start position:0% +to some m + + + align:start position:0% +to some m +of minus NK to NK + + align:start position:0% +of minus NK to NK + + + align:start position:0% +of minus NK to NK +so this is our finite shelf cover + + align:start position:0% +so this is our finite shelf cover + + + align:start position:0% +so this is our finite shelf cover +suppose that this contains a real + + align:start position:0% +suppose that this contains a real + + + align:start position:0% +suppose that this contains a real +numbers + + align:start position:0% + + + + align:start position:0% + +this cannot be the case + + align:start position:0% +this cannot be the case + + + align:start position:0% +this cannot be the case +right choose choose the largest possible + + align:start position:0% +right choose choose the largest possible + + + align:start position:0% +right choose choose the largest possible +NK right + + align:start position:0% +NK right + + + align:start position:0% +NK right +if it's just the largest possible NK + + align:start position:0% +if it's just the largest possible NK + + + align:start position:0% +if it's just the largest possible NK +then I know that there exists a real + + align:start position:0% +then I know that there exists a real + + + align:start position:0% +then I know that there exists a real +number larger than that and so then I + + align:start position:0% +number larger than that and so then I + + + align:start position:0% +number larger than that and so then I +know that the real numbers is are not + + align:start position:0% +know that the real numbers is are not + + + align:start position:0% +know that the real numbers is are not +contained in this finite sub cupboards + + align:start position:0% +contained in this finite sub cupboards + + + align:start position:0% +contained in this finite sub cupboards +and this is true for every possible + + align:start position:0% +and this is true for every possible + + + align:start position:0% +and this is true for every possible +finite subcover + + align:start position:0% +finite subcover + + + align:start position:0% +finite subcover +um realistically we only + + align:start position:0% +um realistically we only + + + align:start position:0% +um realistically we only +uh yeah so in statements like this you + + align:start position:0% +uh yeah so in statements like this you + + + align:start position:0% +uh yeah so in statements like this you +need to show it's false for every + + align:start position:0% +need to show it's false for every + + + align:start position:0% +need to show it's false for every +subtopper of the open coverage chose to + + align:start position:0% +subtopper of the open coverage chose to + + + align:start position:0% +subtopper of the open coverage chose to +choose + + align:start position:0% +choose + + + align:start position:0% +choose +okay but this shows both not compact + + align:start position:0% + + + + align:start position:0% + +any questions here these examples are + + align:start position:0% +any questions here these examples are + + + align:start position:0% +any questions here these examples are +very important to + + align:start position:0% +very important to + + + align:start position:0% +very important to +understand so I'm happy to reiterate any + + align:start position:0% +understand so I'm happy to reiterate any + + + align:start position:0% +understand so I'm happy to reiterate any +points about them + + align:start position:0% + + + + align:start position:0% + +cool + + align:start position:0% + + + + align:start position:0% + +what about instead of considering all + + align:start position:0% +what about instead of considering all + + + align:start position:0% +what about instead of considering all +the real numbers we consider just nice + + align:start position:0% +the real numbers we consider just nice + + + align:start position:0% +the real numbers we consider just nice +intervals let's consider one that's half + + align:start position:0% +intervals let's consider one that's half + + + align:start position:0% +intervals let's consider one that's half +open + + align:start position:0% +open + + + align:start position:0% +open +and half closed so zero to one but not + + align:start position:0% +and half closed so zero to one but not + + + align:start position:0% +and half closed so zero to one but not +exiting zero + + align:start position:0% +exiting zero + + + align:start position:0% +exiting zero +this is also not compact + + align:start position:0% + + + + align:start position:0% + +and we can kind of guess this right + + align:start position:0% +and we can kind of guess this right + + + align:start position:0% +and we can kind of guess this right +because I'm claiming that topological + + align:start position:0% +because I'm claiming that topological + + + align:start position:0% +because I'm claiming that topological +compactness and potential compactness + + align:start position:0% +compactness and potential compactness + + + align:start position:0% +compactness and potential compactness +are going to be false for metric spaces + + align:start position:0% +are going to be false for metric spaces + + + align:start position:0% +are going to be false for metric spaces +and we know that the set is not + + align:start position:0% +and we know that the set is not + + + align:start position:0% +and we know that the set is not +sequentially compact + + align:start position:0% +sequentially compact + + + align:start position:0% +sequentially compact +how do we know that because zero has not + + align:start position:0% +how do we know that because zero has not + + + align:start position:0% +how do we know that because zero has not +been changed so just consider + + align:start position:0% +been changed so just consider + + + align:start position:0% +been changed so just consider +does that exercise + + align:start position:0% +does that exercise + + + align:start position:0% +does that exercise +to be 1 over n for n in the natural + + align:start position:0% +to be 1 over n for n in the natural + + + align:start position:0% +to be 1 over n for n in the natural +numbers + + align:start position:0% + + + + align:start position:0% + +this is a sequence that converges in R + + align:start position:0% +this is a sequence that converges in R + + + align:start position:0% +this is a sequence that converges in R +right what's it going to converge to + + align:start position:0% +right what's it going to converge to + + + align:start position:0% +right what's it going to converge to +zero uh so xn + + align:start position:0% +zero uh so xn + + + align:start position:0% +zero uh so xn +so the sequence does converge to zero it + + align:start position:0% +so the sequence does converge to zero it + + + align:start position:0% +so the sequence does converge to zero it +doesn't converge in our subset but it + + align:start position:0% +doesn't converge in our subset but it + + + align:start position:0% +doesn't converge in our subset but it +does converge + + align:start position:0% +does converge + + + align:start position:0% +does converge +what this tells us is that every + + align:start position:0% +what this tells us is that every + + + align:start position:0% +what this tells us is that every +possible subspeed with X and K + + align:start position:0% +possible subspeed with X and K + + + align:start position:0% +possible subspeed with X and K +also converges to zero but this is not + + align:start position:0% +also converges to zero but this is not + + + align:start position:0% +also converges to zero but this is not +in our open interval zero to one which + + align:start position:0% +in our open interval zero to one which + + + align:start position:0% +in our open interval zero to one which +implies not sequentially compact + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +how do we show it's not topologically + + align:start position:0% +how do we show it's not topologically + + + align:start position:0% +how do we show it's not topologically +compact well we just choose an open + + align:start position:0% +compact well we just choose an open + + + align:start position:0% +compact well we just choose an open +cover that works out in our favor again + + align:start position:0% +cover that works out in our favor again + + + align:start position:0% +cover that works out in our favor again +consider + + align:start position:0% + + + + align:start position:0% + +here the one I'm going to consider is + + align:start position:0% +here the one I'm going to consider is + + + align:start position:0% +here the one I'm going to consider is +the open cover + + align:start position:0% +the open cover + + + align:start position:0% +the open cover +five one over n to two + + align:start position:0% +five one over n to two + + + align:start position:0% +five one over n to two +why do I go to 2 so that I know that it + + align:start position:0% +why do I go to 2 so that I know that it + + + align:start position:0% +why do I go to 2 so that I know that it +contains one right if I'm going to cover + + align:start position:0% +contains one right if I'm going to cover + + + align:start position:0% +contains one right if I'm going to cover +it in open intervals it has to contain + + align:start position:0% +it in open intervals it has to contain + + + align:start position:0% +it in open intervals it has to contain +one so I'm going to go slightly past it + + align:start position:0% +one so I'm going to go slightly past it + + + align:start position:0% +one so I'm going to go slightly past it +in fact you can choose this to be this + + align:start position:0% +in fact you can choose this to be this + + + align:start position:0% +in fact you can choose this to be this +2v 1.5 if you really wanted to + + align:start position:0% +2v 1.5 if you really wanted to + + + align:start position:0% +2v 1.5 if you really wanted to +from n equal to one to Infinity + + align:start position:0% +from n equal to one to Infinity + + + align:start position:0% +from n equal to one to Infinity +I know that this contains my open + + align:start position:0% +I know that this contains my open + + + align:start position:0% +I know that this contains my open +interval 0 to 1. how do I know this is + + align:start position:0% +interval 0 to 1. how do I know this is + + + align:start position:0% +interval 0 to 1. how do I know this is +true choose any point we know that there + + align:start position:0% +true choose any point we know that there + + + align:start position:0% +true choose any point we know that there +exists and large enough such that that + + align:start position:0% +exists and large enough such that that + + + align:start position:0% +exists and large enough such that that +point is in one of these open intervals + + align:start position:0% +point is in one of these open intervals + + + align:start position:0% +point is in one of these open intervals +but again + + align:start position:0% +but again + + + align:start position:0% +but again +if you choose any finite sub cover of + + align:start position:0% +if you choose any finite sub cover of + + + align:start position:0% +if you choose any finite sub cover of +this + + align:start position:0% +this + + + align:start position:0% +this +there's going to exist a number between + + align:start position:0% +there's going to exist a number between + + + align:start position:0% +there's going to exist a number between +zero and that largest NK + + align:start position:0% +zero and that largest NK + + + align:start position:0% +zero and that largest NK +that doesn't exist in our in our phonics + + align:start position:0% +that doesn't exist in our in our phonics + + + align:start position:0% +that doesn't exist in our in our phonics +sub cover + + align:start position:0% +sub cover + + + align:start position:0% +sub cover +so I can write this out again but it's + + align:start position:0% +so I can write this out again but it's + + + align:start position:0% +so I can write this out again but it's +the same as this one right here the + + align:start position:0% +the same as this one right here the + + + align:start position:0% +the same as this one right here the +issue was any finite subcover I have I + + align:start position:0% +issue was any finite subcover I have I + + + align:start position:0% +issue was any finite subcover I have I +can choose the row number larger than + + align:start position:0% +can choose the row number larger than + + + align:start position:0% +can choose the row number larger than +that maximum number + + align:start position:0% +that maximum number + + + align:start position:0% +that maximum number +here any finite subcover I have will + + align:start position:0% +here any finite subcover I have will + + + align:start position:0% +here any finite subcover I have will +have a finite lower bound and I can find + + align:start position:0% +have a finite lower bound and I can find + + + align:start position:0% +have a finite lower bound and I can find +a row number smaller than that + + align:start position:0% +a row number smaller than that + + + align:start position:0% +a row number smaller than that +so this implies not topologically + + align:start position:0% +so this implies not topologically + + + align:start position:0% +so this implies not topologically +compact + + align:start position:0% + + + + align:start position:0% + +which is all great right these are all + + align:start position:0% +which is all great right these are all + + + align:start position:0% +which is all great right these are all +things that we want to be true about our + + align:start position:0% +things that we want to be true about our + + + align:start position:0% +things that we want to be true about our +about our + + align:start position:0% +about our + + + align:start position:0% +about our +definitions because if they weren't true + + align:start position:0% +definitions because if they weren't true + + + align:start position:0% +definitions because if they weren't true +then they wouldn't be equivalent which + + align:start position:0% +then they wouldn't be equivalent which + + + align:start position:0% +then they wouldn't be equivalent which +is what we're hoping to show + + align:start position:0% +is what we're hoping to show + + + align:start position:0% +is what we're hoping to show +uh drones this one I'll use this one + + align:start position:0% + + + + align:start position:0% + +so now we're going to look at an example + + align:start position:0% +so now we're going to look at an example + + + align:start position:0% +so now we're going to look at an example +that is compass but notice that's going + + align:start position:0% +that is compass but notice that's going + + + align:start position:0% +that is compass but notice that's going +to be a little bit harder to show at + + align:start position:0% +to be a little bit harder to show at + + + align:start position:0% +to be a little bit harder to show at +least on the face of it + + align:start position:0% +least on the face of it + + + align:start position:0% +least on the face of it +because when here for these examples we + + align:start position:0% +because when here for these examples we + + + align:start position:0% +because when here for these examples we +only had to come up with examples of + + align:start position:0% +only had to come up with examples of + + + align:start position:0% +only had to come up with examples of +sequences and of open covers that failed + + align:start position:0% +sequences and of open covers that failed + + + align:start position:0% +sequences and of open covers that failed +to be sequentially in topological + + align:start position:0% +to be sequentially in topological + + + align:start position:0% +to be sequentially in topological +patents so when we're looking at an + + align:start position:0% +patents so when we're looking at an + + + align:start position:0% +patents so when we're looking at an +actual compact set we're going to have + + align:start position:0% +actual compact set we're going to have + + + align:start position:0% +actual compact set we're going to have +to consider every open cover and every + + align:start position:0% +to consider every open cover and every + + + align:start position:0% +to consider every open cover and every +sequence + + align:start position:0% + + + + align:start position:0% + +which would be a little bit harder + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +example + + align:start position:0% + + + + align:start position:0% + +here I'm just going to add in the point + + align:start position:0% +here I'm just going to add in the point + + + align:start position:0% +here I'm just going to add in the point +zero zero to one + + align:start position:0% +zero zero to one + + + align:start position:0% +zero zero to one +this is a compact + + align:start position:0% + + + + align:start position:0% + +so this is a compact subset of the real + + align:start position:0% +so this is a compact subset of the real + + + align:start position:0% +so this is a compact subset of the real +numbers + + align:start position:0% +numbers + + + align:start position:0% +numbers +have we actually showed this well I'm + + align:start position:0% +have we actually showed this well I'm + + + align:start position:0% +have we actually showed this well I'm +going to show topologically compact but + + align:start position:0% +going to show topologically compact but + + + align:start position:0% +going to show topologically compact but +how do we show sequentially compact + + align:start position:0% + + + + align:start position:0% + +sequentially compact I'm not actually + + align:start position:0% +sequentially compact I'm not actually + + + align:start position:0% +sequentially compact I'm not actually +going to show right now + + align:start position:0% +going to show right now + + + align:start position:0% +going to show right now +um but I'll make a note of it consider + + align:start position:0% + + + + align:start position:0% + +the sequence xn + + align:start position:0% + + + + align:start position:0% + +which is contained in zero to one + + align:start position:0% + + + + align:start position:0% + +how do I know that this has convergence + + align:start position:0% +how do I know that this has convergence + + + align:start position:0% +how do I know that this has convergence +settings + + align:start position:0% + + + + align:start position:0% + +this is a fact from 18100a it's + + align:start position:0% +this is a fact from 18100a it's + + + align:start position:0% +this is a fact from 18100a it's +but does anyone remember the name of it + + align:start position:0% + + + + align:start position:0% + +no worries it's one of the ones that's + + align:start position:0% +no worries it's one of the ones that's + + + align:start position:0% +no worries it's one of the ones that's +not used too often but it's a + + align:start position:0% +not used too often but it's a + + + align:start position:0% +not used too often but it's a +bosonovirus drop serum the Bolzano virus + + align:start position:0% +bosonovirus drop serum the Bolzano virus + + + align:start position:0% +bosonovirus drop serum the Bolzano virus +Rock theorem tells us + + align:start position:0% + + + + align:start position:0% + +so Bolzano + + align:start position:0% +so Bolzano + + + align:start position:0% +so Bolzano +virus drugs + + align:start position:0% + + + + align:start position:0% + +tells us + + align:start position:0% + + + + align:start position:0% + +there exists + + align:start position:0% +there exists + + + align:start position:0% +there exists +uh finite or a convergence subsequence + + align:start position:0% + + + + align:start position:0% + +we're here the only assumptions + + align:start position:0% +we're here the only assumptions + + + align:start position:0% +we're here the only assumptions +bosonovirus drop has + + align:start position:0% +bosonovirus drop has + + + align:start position:0% +bosonovirus drop has +is that your set be closed and open + + align:start position:0% +is that your set be closed and open + + + align:start position:0% +is that your set be closed and open +closed and dotted + + align:start position:0% + + + + align:start position:0% + +so again to reiterate horizontal virus + + align:start position:0% +so again to reiterate horizontal virus + + + align:start position:0% +so again to reiterate horizontal virus +drops that is if I have a closed and + + align:start position:0% +drops that is if I have a closed and + + + align:start position:0% +drops that is if I have a closed and +bounded subset of a metric space or not + + align:start position:0% +bounded subset of a metric space or not + + + align:start position:0% +bounded subset of a metric space or not +a metric space I should say of the real + + align:start position:0% +a metric space I should say of the real + + + align:start position:0% +a metric space I should say of the real +numbers if I have a closed and bounded + + align:start position:0% +numbers if I have a closed and bounded + + + align:start position:0% +numbers if I have a closed and bounded +subset of the real numbers + + align:start position:0% +subset of the real numbers + + + align:start position:0% +subset of the real numbers +bosonovirus Rock says that every + + align:start position:0% +bosonovirus Rock says that every + + + align:start position:0% +bosonovirus Rock says that every +sequence has a convergence subsequence + + align:start position:0% +sequence has a convergence subsequence + + + align:start position:0% +sequence has a convergence subsequence +unfortunately uh unless y'all would like + + align:start position:0% +unfortunately uh unless y'all would like + + + align:start position:0% +unfortunately uh unless y'all would like +me to next lecture I will not be + + align:start position:0% +me to next lecture I will not be + + + align:start position:0% +me to next lecture I will not be +presenting this group this is one that + + align:start position:0% +presenting this group this is one that + + + align:start position:0% +presenting this group this is one that +I'm going to Black Box for the moment + + align:start position:0% +I'm going to Black Box for the moment + + + align:start position:0% +I'm going to Black Box for the moment +being because it's one that we did in + + align:start position:0% +being because it's one that we did in + + + align:start position:0% +being because it's one that we did in +100 days but if y'all would like YouTube + + align:start position:0% +100 days but if y'all would like YouTube + + + align:start position:0% +100 days but if y'all would like YouTube +feel free to send me an email and I'm + + align:start position:0% +feel free to send me an email and I'm + + + align:start position:0% +feel free to send me an email and I'm +happy to do it next time all right + + align:start position:0% +happy to do it next time all right + + + align:start position:0% +happy to do it next time all right +but the one that I think is slightly + + align:start position:0% +but the one that I think is slightly + + + align:start position:0% +but the one that I think is slightly +more interesting is to finite Club cover + + align:start position:0% +more interesting is to finite Club cover + + + align:start position:0% +more interesting is to finite Club cover +right you want to show that for every + + align:start position:0% +right you want to show that for every + + + align:start position:0% +right you want to show that for every +open cover of the closed and bounded set + + align:start position:0% +open cover of the closed and bounded set + + + align:start position:0% +open cover of the closed and bounded set +zero to one + + align:start position:0% +zero to one + + + align:start position:0% +zero to one +we want to show the lyrics to Spanish + + align:start position:0% +we want to show the lyrics to Spanish + + + align:start position:0% +we want to show the lyrics to Spanish +club cover and I think that's slightly + + align:start position:0% +club cover and I think that's slightly + + + align:start position:0% +club cover and I think that's slightly +more interesting + + align:start position:0% +more interesting + + + align:start position:0% +more interesting +so let me go through that group + + align:start position:0% + + + + align:start position:0% + +lunch + + align:start position:0% +lunch + + + align:start position:0% +lunch +zero to one + + align:start position:0% +zero to one + + + align:start position:0% +zero to one +if you can change in the union of uis + + align:start position:0% +if you can change in the union of uis + + + align:start position:0% +if you can change in the union of uis +from I equal to 1 to Infinity + + align:start position:0% +from I equal to 1 to Infinity + + + align:start position:0% +from I equal to 1 to Infinity +and I'm going to assume that this is an + + align:start position:0% +and I'm going to assume that this is an + + + align:start position:0% +and I'm going to assume that this is an +open cover + + align:start position:0% +open cover + + + align:start position:0% +open cover +so each of these uis are open + + align:start position:0% +so each of these uis are open + + + align:start position:0% +so each of these uis are open +in fact I can assume slightly more + + align:start position:0% +in fact I can assume slightly more + + + align:start position:0% +in fact I can assume slightly more +because last time what we talked about + + align:start position:0% +because last time what we talked about + + + align:start position:0% +because last time what we talked about +is that every every open set in a metric + + align:start position:0% +is that every every open set in a metric + + + align:start position:0% +is that every every open set in a metric +space is covered in um + + align:start position:0% +space is covered in um + + + align:start position:0% +space is covered in um +can be covered in uh + + align:start position:0% +can be covered in uh + + + align:start position:0% +can be covered in uh +involves right in open balls this is the + + align:start position:0% +involves right in open balls this is the + + + align:start position:0% +involves right in open balls this is the +fact that is showing up on your second + + align:start position:0% +fact that is showing up on your second + + + align:start position:0% +fact that is showing up on your second +column set but is one that I feel like + + align:start position:0% +column set but is one that I feel like + + + align:start position:0% +column set but is one that I feel like +is generally safe to assume so if you + + align:start position:0% +is generally safe to assume so if you + + + align:start position:0% +is generally safe to assume so if you +prefer you can think about this as an + + align:start position:0% +prefer you can think about this as an + + + align:start position:0% +prefer you can think about this as an +open cover by open intervals + + align:start position:0% +open cover by open intervals + + + align:start position:0% +open cover by open intervals +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now how do I show that there is this + + align:start position:0% +now how do I show that there is this + + + align:start position:0% +now how do I show that there is this +product + + align:start position:0% + + + + align:start position:0% + +so to do so what I'll do is I'll + + align:start position:0% +so to do so what I'll do is I'll + + + align:start position:0% +so to do so what I'll do is I'll +consider + + align:start position:0% + + + + align:start position:0% + +consider the following set + + align:start position:0% +consider the following set + + + align:start position:0% +consider the following set +consider the set of elements C such that + + align:start position:0% +consider the set of elements C such that + + + align:start position:0% +consider the set of elements C such that +the integral of zero to T or I should + + align:start position:0% +the integral of zero to T or I should + + + align:start position:0% +the integral of zero to T or I should +say C between 0 and 1. + + align:start position:0% +say C between 0 and 1. + + + align:start position:0% +say C between 0 and 1. +such that equals zero to one such as + + align:start position:0% +such that equals zero to one such as + + + align:start position:0% +such that equals zero to one such as +that the interval here is the + + align:start position:0% +that the interval here is the + + + align:start position:0% +that the interval here is the +has a finite step cover + + align:start position:0% + + + + align:start position:0% + +right so I'm going to consider the + + align:start position:0% +right so I'm going to consider the + + + align:start position:0% +right so I'm going to consider the +subset of elements C between zero to one + + align:start position:0% +subset of elements C between zero to one + + + align:start position:0% +subset of elements C between zero to one +such as that the closed interval 0 to C + + align:start position:0% +such as that the closed interval 0 to C + + + align:start position:0% +such as that the closed interval 0 to C +has a finite subcover + + align:start position:0% +has a finite subcover + + + align:start position:0% +has a finite subcover +what is my goal here my goal is to show + + align:start position:0% +what is my goal here my goal is to show + + + align:start position:0% +what is my goal here my goal is to show +the separate number of such C is one + + align:start position:0% +the separate number of such C is one + + + align:start position:0% +the separate number of such C is one +right because if I show that that c is + + align:start position:0% +right because if I show that that c is + + + align:start position:0% +right because if I show that that c is +one then I'm done + + align:start position:0% +one then I'm done + + + align:start position:0% +one then I'm done +right + + align:start position:0% +right + + + align:start position:0% +right +but how do we know that the supper mom + + align:start position:0% +but how do we know that the supper mom + + + align:start position:0% +but how do we know that the supper mom +exists + + align:start position:0% + + + + align:start position:0% + +question + + align:start position:0% +question + + + align:start position:0% +question +how do we know + + align:start position:0% + + + + align:start position:0% + +the supper mom exists + + align:start position:0% +the supper mom exists + + + align:start position:0% +the supper mom exists +in particular the supper mom of the set + + align:start position:0% + + + + align:start position:0% + +this is a property of real numbers and I + + align:start position:0% +this is a property of real numbers and I + + + align:start position:0% +this is a property of real numbers and I +want to recall this because it's one + + align:start position:0% +want to recall this because it's one + + + align:start position:0% +want to recall this because it's one +that you know it's been months at this + + align:start position:0% +that you know it's been months at this + + + align:start position:0% +that you know it's been months at this +point if you've done really now with + + align:start position:0% +point if you've done really now with + + + align:start position:0% +point if you've done really now with +this it's one that you might have + + align:start position:0% +this it's one that you might have + + + align:start position:0% +this it's one that you might have +forgotten + + align:start position:0% +forgotten + + + align:start position:0% +forgotten +this is a bounded set right + + align:start position:0% +this is a bounded set right + + + align:start position:0% +this is a bounded set right +it's bounded because it's just a subset + + align:start position:0% +it's bounded because it's just a subset + + + align:start position:0% +it's bounded because it's just a subset +of zero to one + + align:start position:0% +of zero to one + + + align:start position:0% +of zero to one +but it's also + + align:start position:0% +but it's also + + + align:start position:0% +but it's also +um + + align:start position:0% +um + + + align:start position:0% +um +yeah it's a bounded subset of zero + + align:start position:0% +yeah it's a bounded subset of zero + + + align:start position:0% +yeah it's a bounded subset of zero +numbers which means that we have the + + align:start position:0% +numbers which means that we have the + + + align:start position:0% +numbers which means that we have the +least upper bound property which + + align:start position:0% +least upper bound property which + + + align:start position:0% +least upper bound property which +guarantees that the subaruom exists + + align:start position:0% +guarantees that the subaruom exists + + + align:start position:0% +guarantees that the subaruom exists +that's how we Define the real numbers so + + align:start position:0% +that's how we Define the real numbers so + + + align:start position:0% +that's how we Define the real numbers so +that's the answer to the question + + align:start position:0% +that's the answer to the question + + + align:start position:0% +that's the answer to the question +we know that a suburbum exists by the + + align:start position:0% +we know that a suburbum exists by the + + + align:start position:0% +we know that a suburbum exists by the +least upper bound property + + align:start position:0% + + + + align:start position:0% + +and because I know that one exists I + + align:start position:0% +and because I know that one exists I + + + align:start position:0% +and because I know that one exists I +might as well give it a name so I'm + + align:start position:0% +might as well give it a name so I'm + + + align:start position:0% +might as well give it a name so I'm +going to call this down + + align:start position:0% +going to call this down + + + align:start position:0% +going to call this down +C Prime and I want to show that c Prime + + align:start position:0% +C Prime and I want to show that c Prime + + + align:start position:0% +C Prime and I want to show that c Prime +is in fact equal to one + + align:start position:0% +is in fact equal to one + + + align:start position:0% +is in fact equal to one +suppose + + align:start position:0% + + + + align:start position:0% + +for the sake of contradiction + + align:start position:0% +for the sake of contradiction + + + align:start position:0% +for the sake of contradiction +that c Prime was less than one + + align:start position:0% +that c Prime was less than one + + + align:start position:0% +that c Prime was less than one +what would this tell us + + align:start position:0% +what would this tell us + + + align:start position:0% +what would this tell us +well let's consider + + align:start position:0% +well let's consider + + + align:start position:0% +well let's consider +let's consider this rhetorically because + + align:start position:0% +let's consider this rhetorically because + + + align:start position:0% +let's consider this rhetorically because +this will be the easiest way to do + + align:start position:0% +this will be the easiest way to do + + + align:start position:0% +this will be the easiest way to do +happening + + align:start position:0% +happening + + + align:start position:0% +happening +here we have the interval from zero to + + align:start position:0% +here we have the interval from zero to + + + align:start position:0% +here we have the interval from zero to +one and I have some C Prime less than + + align:start position:0% +one and I have some C Prime less than + + + align:start position:0% +one and I have some C Prime less than +that + + align:start position:0% +that + + + align:start position:0% +that +right + + align:start position:0% +right + + + align:start position:0% +right +and I'm covering the interval from 0 to + + align:start position:0% +and I'm covering the interval from 0 to + + + align:start position:0% +and I'm covering the interval from 0 to +C Prime + + align:start position:0% +C Prime + + + align:start position:0% +C Prime +and finitely many open intervals so + + align:start position:0% +and finitely many open intervals so + + + align:start position:0% +and finitely many open intervals so +maybe it looks something like that + + align:start position:0% +maybe it looks something like that + + + align:start position:0% +maybe it looks something like that +Union with that Union with that + + align:start position:0% +Union with that Union with that + + + align:start position:0% +Union with that Union with that +unioned with something like that + + align:start position:0% +unioned with something like that + + + align:start position:0% +unioned with something like that +the issue is that when I'm covering this + + align:start position:0% +the issue is that when I'm covering this + + + align:start position:0% +the issue is that when I'm covering this +in open intervals + + align:start position:0% +in open intervals + + + align:start position:0% +in open intervals +I cannot + + align:start position:0% +I cannot + + + align:start position:0% +I cannot +um + + align:start position:0% +um + + + align:start position:0% +um +C Prime cannot be the ninth sum of such + + align:start position:0% +C Prime cannot be the ninth sum of such + + + align:start position:0% +C Prime cannot be the ninth sum of such +elements how do we rigorously see this + + align:start position:0% +elements how do we rigorously see this + + + align:start position:0% +elements how do we rigorously see this +this is the point that I want to be + + align:start position:0% +this is the point that I want to be + + + align:start position:0% +this is the point that I want to be +careful about + + align:start position:0% +careful about + + + align:start position:0% +careful about +the fact that there exists this wiggle + + align:start position:0% +the fact that there exists this wiggle + + + align:start position:0% +the fact that there exists this wiggle +room between them follows from openness + + align:start position:0% +room between them follows from openness + + + align:start position:0% +room between them follows from openness +so notice + + align:start position:0% +so notice + + + align:start position:0% +so notice +then that c prime or the interval + + align:start position:0% +then that c prime or the interval + + + align:start position:0% +then that c prime or the interval +yeah that c Prime is an element of the + + align:start position:0% +yeah that c Prime is an element of the + + + align:start position:0% +yeah that c Prime is an element of the +Union + + align:start position:0% +Union + + + align:start position:0% +Union +of this cupboard so k equal to 1 to m + + align:start position:0% +of this cupboard so k equal to 1 to m + + + align:start position:0% +of this cupboard so k equal to 1 to m +right so I take this oh I take this + + align:start position:0% +right so I take this oh I take this + + + align:start position:0% +right so I take this oh I take this +planet cover + + align:start position:0% +planet cover + + + align:start position:0% +planet cover +from zero to C Prime and then C Prime is + + align:start position:0% +from zero to C Prime and then C Prime is + + + align:start position:0% +from zero to C Prime and then C Prime is +an element of that + + align:start position:0% +an element of that + + + align:start position:0% +an element of that +what this tells us + + align:start position:0% +what this tells us + + + align:start position:0% +what this tells us +this set is open + + align:start position:0% + + + + align:start position:0% + +so there exists an Epsilon bigger than + + align:start position:0% +so there exists an Epsilon bigger than + + + align:start position:0% +so there exists an Epsilon bigger than +zero + + align:start position:0% +zero + + + align:start position:0% +zero +such that the ball of radius Epsilon + + align:start position:0% +such that the ball of radius Epsilon + + + align:start position:0% +such that the ball of radius Epsilon +around C Prime + + align:start position:0% +around C Prime + + + align:start position:0% +around C Prime +uh is contained in our theft so it's + + align:start position:0% +uh is contained in our theft so it's + + + align:start position:0% +uh is contained in our theft so it's +contained + + align:start position:0% + + + + align:start position:0% + +in the union of these UI + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +this is the definition of opening we + + align:start position:0% +this is the definition of opening we + + + align:start position:0% +this is the definition of opening we +have a union of open set so I know that + + align:start position:0% +have a union of open set so I know that + + + align:start position:0% +have a union of open set so I know that +it's open C Prime is an element of this + + align:start position:0% +it's open C Prime is an element of this + + + align:start position:0% +it's open C Prime is an element of this +open set so there exists a ball of + + align:start position:0% +open set so there exists a ball of + + + align:start position:0% +open set so there exists a ball of +radius Epsilon around that c Prime + + align:start position:0% +radius Epsilon around that c Prime + + + align:start position:0% +radius Epsilon around that c Prime +but then + + align:start position:0% +but then + + + align:start position:0% +but then +notice that c prime plus Epsilon over + + align:start position:0% +notice that c prime plus Epsilon over + + + align:start position:0% +notice that c prime plus Epsilon over +two + + align:start position:0% +two + + + align:start position:0% +two +is bigger than C Prime + + align:start position:0% +is bigger than C Prime + + + align:start position:0% +is bigger than C Prime +but it also has a 5x October right + + align:start position:0% +but it also has a 5x October right + + + align:start position:0% +but it also has a 5x October right +because the phonic subcover that works + + align:start position:0% +because the phonic subcover that works + + + align:start position:0% +because the phonic subcover that works +for C Prime will also work for C prime + + align:start position:0% +for C Prime will also work for C prime + + + align:start position:0% +for C Prime will also work for C prime +plus Epsilon over two + + align:start position:0% +plus Epsilon over two + + + align:start position:0% +plus Epsilon over two +so this is a contradiction right because + + align:start position:0% +so this is a contradiction right because + + + align:start position:0% +so this is a contradiction right because +this implies that we have an element + + align:start position:0% +this implies that we have an element + + + align:start position:0% +this implies that we have an element +bigger than the supper mom + + align:start position:0% +bigger than the supper mom + + + align:start position:0% +bigger than the supper mom +especially that it has a finite subcover + + align:start position:0% +especially that it has a finite subcover + + + align:start position:0% +especially that it has a finite subcover +and that's our contradiction + + align:start position:0% + + + + align:start position:0% + +and so what does this implies this + + align:start position:0% +and so what does this implies this + + + align:start position:0% +and so what does this implies this +implies at C time + + align:start position:0% +implies at C time + + + align:start position:0% +implies at C time +must equal to one which is what we + + align:start position:0% +must equal to one which is what we + + + align:start position:0% +must equal to one which is what we +wanted to show + + align:start position:0% +wanted to show + + + align:start position:0% +wanted to show +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so I'll move this up so you all can see + + align:start position:0% +so I'll move this up so you all can see + + + align:start position:0% +so I'll move this up so you all can see +uh any questions about this group feel + + align:start position:0% +uh any questions about this group feel + + + align:start position:0% +uh any questions about this group feel +free to shout them out as I'm erasing + + align:start position:0% +free to shout them out as I'm erasing + + + align:start position:0% +free to shout them out as I'm erasing +the board if any files + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so this shows that zero to one + + align:start position:0% +so this shows that zero to one + + + align:start position:0% +so this shows that zero to one +is going to be or the closest interval 0 + + align:start position:0% +is going to be or the closest interval 0 + + + align:start position:0% +is going to be or the closest interval 0 +to 1 is Compact and in fact I'll make a + + align:start position:0% +to 1 is Compact and in fact I'll make a + + + align:start position:0% +to 1 is Compact and in fact I'll make a +small remarks + + align:start position:0% +small remarks + + + align:start position:0% +small remarks +which is uh let me just get somebody + + align:start position:0% +which is uh let me just get somebody + + + align:start position:0% +which is uh let me just get somebody +drop and I'll see this out loud the new + + align:start position:0% +drop and I'll see this out loud the new + + + align:start position:0% +drop and I'll see this out loud the new +like remark thing to note is that this + + align:start position:0% +like remark thing to note is that this + + + align:start position:0% +like remark thing to note is that this +would have worked for any closed + + align:start position:0% +would have worked for any closed + + + align:start position:0% +would have worked for any closed +interval A to B right + + align:start position:0% + + + + align:start position:0% + +uh the proof would work by choosing + + align:start position:0% +uh the proof would work by choosing + + + align:start position:0% +uh the proof would work by choosing +uh or considering the set of C between a + + align:start position:0% +uh or considering the set of C between a + + + align:start position:0% +uh or considering the set of C between a +to B such that the interval A to B has a + + align:start position:0% +to B such that the interval A to B has a + + + align:start position:0% +to B such that the interval A to B has a +final cover and the proof would work + + align:start position:0% +final cover and the proof would work + + + align:start position:0% +final cover and the proof would work +exactly the same mark + + align:start position:0% + + + + align:start position:0% + +A to B + + align:start position:0% +A to B + + + align:start position:0% +A to B +is compact + + align:start position:0% + + + + align:start position:0% + +in fact if I'm considering this an RN + + align:start position:0% + + + + align:start position:0% + +so let's say in R2 + + align:start position:0% +so let's say in R2 + + + align:start position:0% +so let's say in R2 +I know that + + align:start position:0% +I know that + + + align:start position:0% +I know that +a b Cross C D is compact + + align:start position:0% + + + + align:start position:0% + +the proof of the second statement would + + align:start position:0% +the proof of the second statement would + + + align:start position:0% +the proof of the second statement would +also work out the same way one we can + + align:start position:0% +also work out the same way one we can + + + align:start position:0% +also work out the same way one we can +prove it directly I can prove + + align:start position:0% +prove it directly I can prove + + + align:start position:0% +prove it directly I can prove +uh of course the final compactness I can + + align:start position:0% +uh of course the final compactness I can + + + align:start position:0% +uh of course the final compactness I can +apply horizontal virus drops again + + align:start position:0% +apply horizontal virus drops again + + + align:start position:0% +apply horizontal virus drops again +for topological compactness I can just + + align:start position:0% +for topological compactness I can just + + + align:start position:0% +for topological compactness I can just +consider the sets I can just do one + + align:start position:0% +consider the sets I can just do one + + + align:start position:0% +consider the sets I can just do one +element at a time just choose one after + + align:start position:0% +element at a time just choose one after + + + align:start position:0% +element at a time just choose one after +the 75 and go through the proof uh these + + align:start position:0% +the 75 and go through the proof uh these + + + align:start position:0% +the 75 and go through the proof uh these +two problems are to like show these two + + align:start position:0% +two problems are to like show these two + + + align:start position:0% +two problems are to like show these two +things rigorously or on your problem set + + align:start position:0% +things rigorously or on your problem set + + + align:start position:0% +things rigorously or on your problem set +which is an optional problem but it is a + + align:start position:0% +which is an optional problem but it is a + + + align:start position:0% +which is an optional problem but it is a +helpful thing to work through so if + + align:start position:0% +helpful thing to work through so if + + + align:start position:0% +helpful thing to work through so if +you're interested in working through it + + align:start position:0% +you're interested in working through it + + + align:start position:0% +you're interested in working through it +I would highly recommend this problem + + align:start position:0% +I would highly recommend this problem + + + align:start position:0% +I would highly recommend this problem +um but it in fact uh + + align:start position:0% +um but it in fact uh + + + align:start position:0% +um but it in fact uh +gives us the next direction to go right + + align:start position:0% +gives us the next direction to go right + + + align:start position:0% +gives us the next direction to go right +because what can we know about all of + + align:start position:0% +because what can we know about all of + + + align:start position:0% +because what can we know about all of +these sets they are both closed and + + align:start position:0% +these sets they are both closed and + + + align:start position:0% +these sets they are both closed and +bounded + + align:start position:0% +bounded + + + align:start position:0% +bounded +which by the was on a fire stress + + align:start position:0% +which by the was on a fire stress + + + align:start position:0% +which by the was on a fire stress +theorem is a good thing right because + + align:start position:0% +theorem is a good thing right because + + + align:start position:0% +theorem is a good thing right because +the bazanovirus about zero which is over + + align:start position:0% +the bazanovirus about zero which is over + + + align:start position:0% +the bazanovirus about zero which is over +there it says that if your set is closed + + align:start position:0% +there it says that if your set is closed + + + align:start position:0% +there it says that if your set is closed +and bounded it has a convergent + + align:start position:0% +and bounded it has a convergent + + + align:start position:0% +and bounded it has a convergent +subsequence + + align:start position:0% +subsequence + + + align:start position:0% +subsequence +so it would be great if topologically + + align:start position:0% +so it would be great if topologically + + + align:start position:0% +so it would be great if topologically +compact sets an RN are both closed and + + align:start position:0% +compact sets an RN are both closed and + + + align:start position:0% +compact sets an RN are both closed and +bounded right because that will + + align:start position:0% +bounded right because that will + + + align:start position:0% +bounded right because that will +be halfway to proving that the two are + + align:start position:0% +be halfway to proving that the two are + + + align:start position:0% +be halfway to proving that the two are +the same at least on euclidean space + + align:start position:0% +the same at least on euclidean space + + + align:start position:0% +the same at least on euclidean space +and so let's actually start proving that + + align:start position:0% +and so let's actually start proving that + + + align:start position:0% +and so let's actually start proving that +because in fact that will be true + + align:start position:0% +because in fact that will be true + + + align:start position:0% +because in fact that will be true +so proposition + + align:start position:0% +so proposition + + + align:start position:0% +so proposition +now we're going back to proofs + + align:start position:0% +now we're going back to proofs + + + align:start position:0% +now we're going back to proofs +or the general theory + + align:start position:0% +or the general theory + + + align:start position:0% +or the general theory +compact that's + + align:start position:0% + + + + align:start position:0% + +those demanded + + align:start position:0% + + + + align:start position:0% + +let's prove this + + align:start position:0% + + + + align:start position:0% + +proof + + align:start position:0% +proof + + + align:start position:0% +proof +the fact that it's bounded is not too + + align:start position:0% +the fact that it's bounded is not too + + + align:start position:0% +the fact that it's bounded is not too +bad sorry let me just yeah the fact that + + align:start position:0% +bad sorry let me just yeah the fact that + + + align:start position:0% +bad sorry let me just yeah the fact that +it's bounded is not competition just fix + + align:start position:0% +it's bounded is not competition just fix + + + align:start position:0% +it's bounded is not competition just fix +the proof of bounded just fix any point + + align:start position:0% +the proof of bounded just fix any point + + + align:start position:0% +the proof of bounded just fix any point +p and X + + align:start position:0% + + + + align:start position:0% + +oh sorry I should be more careful + + align:start position:0% +oh sorry I should be more careful + + + align:start position:0% +oh sorry I should be more careful +I should say let + + align:start position:0% +I should say let + + + align:start position:0% +I should say let +a be a compact subset of x + + align:start position:0% +a be a compact subset of x + + + align:start position:0% +a be a compact subset of x +now we're going to groove close to + + align:start position:0% +now we're going to groove close to + + + align:start position:0% +now we're going to groove close to +boundedness of the set a + + align:start position:0% +boundedness of the set a + + + align:start position:0% +boundedness of the set a +poundedness is nice + + align:start position:0% +poundedness is nice + + + align:start position:0% +poundedness is nice +just consider it's a union + + align:start position:0% +just consider it's a union + + + align:start position:0% +just consider it's a union +or I should say fix + + align:start position:0% +or I should say fix + + + align:start position:0% +or I should say fix +p and X + + align:start position:0% + + + + align:start position:0% + +the Union + + align:start position:0% + + + + align:start position:0% + +of the balls of radius I around p + + align:start position:0% +of the balls of radius I around p + + + align:start position:0% +of the balls of radius I around p +right + + align:start position:0% + + + + align:start position:0% + +then what we know about this Union + + align:start position:0% + + + + align:start position:0% + +we know if we choose our P correctly + + align:start position:0% +we know if we choose our P correctly + + + align:start position:0% +we know if we choose our P correctly +that this is going to contain our set a + + align:start position:0% +that this is going to contain our set a + + + align:start position:0% +that this is going to contain our set a +right because again we're assuming uh oh + + align:start position:0% +right because again we're assuming uh oh + + + align:start position:0% +right because again we're assuming uh oh +or this is just because we're taking the + + align:start position:0% +or this is just because we're taking the + + + align:start position:0% +or this is just because we're taking the +unions of infinitely large balls + + align:start position:0% +unions of infinitely large balls + + + align:start position:0% +unions of infinitely large balls +right + + align:start position:0% +right + + + align:start position:0% +right +but this is compact right so I know + + align:start position:0% + + + + align:start position:0% + +there exists a finite subcover + + align:start position:0% + + + + align:start position:0% + +in the finite silk cover will look like + + align:start position:0% +in the finite silk cover will look like + + + align:start position:0% +in the finite silk cover will look like +this + + align:start position:0% +this + + + align:start position:0% +this +a is the Union uh a is a subset of the + + align:start position:0% +a is the Union uh a is a subset of the + + + align:start position:0% +a is the Union uh a is a subset of the +Union from I equal one to let's say m of + + align:start position:0% +Union from I equal one to let's say m of + + + align:start position:0% +Union from I equal one to let's say m of +balls of radius I around p + + align:start position:0% +balls of radius I around p + + + align:start position:0% +balls of radius I around p +foreign + + align:start position:0% +foreign + + + align:start position:0% +foreign +but each of these balls are contained in + + align:start position:0% +but each of these balls are contained in + + + align:start position:0% +but each of these balls are contained in +one another right as I make the radius + + align:start position:0% +one another right as I make the radius + + + align:start position:0% +one another right as I make the radius +larger it's going to be contained to the + + align:start position:0% +larger it's going to be contained to the + + + align:start position:0% +larger it's going to be contained to the +next one so this is a subset of the ball + + align:start position:0% +next one so this is a subset of the ball + + + align:start position:0% +next one so this is a subset of the ball +of radius m + + align:start position:0% +of radius m + + + align:start position:0% +of radius m +P or in fact is equal to I should say + + align:start position:0% +P or in fact is equal to I should say + + + align:start position:0% +P or in fact is equal to I should say +so what this tells us is our set a is + + align:start position:0% +so what this tells us is our set a is + + + align:start position:0% +so what this tells us is our set a is +bounded right this is the definition of + + align:start position:0% +bounded right this is the definition of + + + align:start position:0% +bounded right this is the definition of +bad events there exists Point p in a + + align:start position:0% +bad events there exists Point p in a + + + align:start position:0% +bad events there exists Point p in a +finite radius such that a is contained + + align:start position:0% +finite radius such that a is contained + + + align:start position:0% +finite radius such that a is contained +in a bowl a round p of that radius so + + align:start position:0% +in a bowl a round p of that radius so + + + align:start position:0% +in a bowl a round p of that radius so +that implies that dependence + + align:start position:0% +that implies that dependence + + + align:start position:0% +that implies that dependence +and notice here nowhere did I use the + + align:start position:0% +and notice here nowhere did I use the + + + align:start position:0% +and notice here nowhere did I use the +real numbers in fact this statement is + + align:start position:0% +real numbers in fact this statement is + + + align:start position:0% +real numbers in fact this statement is +going to be true about compact sets in a + + align:start position:0% +going to be true about compact sets in a + + + align:start position:0% +going to be true about compact sets in a +metric space + + align:start position:0% +metric space + + + align:start position:0% +metric space +so + + align:start position:0% +so + + + align:start position:0% +so +good things there + + align:start position:0% +good things there + + + align:start position:0% +good things there +left to proved filter now + + align:start position:0% + + + + align:start position:0% + +or I should take the list + + align:start position:0% +or I should take the list + + + align:start position:0% +or I should take the list +proving closeness is going to be a + + align:start position:0% +proving closeness is going to be a + + + align:start position:0% +proving closeness is going to be a +little bit harder as one would expect + + align:start position:0% +little bit harder as one would expect + + + align:start position:0% +little bit harder as one would expect +right there should be at some point in + + align:start position:0% +right there should be at some point in + + + align:start position:0% +right there should be at some point in +this proof that becomes quite a bit + + align:start position:0% +this proof that becomes quite a bit + + + align:start position:0% +this proof that becomes quite a bit +harder + + align:start position:0% +harder + + + align:start position:0% +harder +to prove closure what we're going to + + align:start position:0% +to prove closure what we're going to + + + align:start position:0% +to prove closure what we're going to +want to do is show that uh + + align:start position:0% +want to do is show that uh + + + align:start position:0% +want to do is show that uh +are not including a + + align:start position:0% +are not including a + + + align:start position:0% +are not including a +is opening + + align:start position:0% +is opening + + + align:start position:0% +is opening +realistically if you feel comfortable + + align:start position:0% +realistically if you feel comfortable + + + align:start position:0% +realistically if you feel comfortable +enough with it now you can replace this + + align:start position:0% +enough with it now you can replace this + + + align:start position:0% +enough with it now you can replace this +r with any metric space the proof that I + + align:start position:0% +r with any metric space the proof that I + + + align:start position:0% +r with any metric space the proof that I +present today will be on will be true + + align:start position:0% +present today will be on will be true + + + align:start position:0% +present today will be on will be true +for any metric space + + align:start position:0% +for any metric space + + + align:start position:0% +for any metric space +and now let me draw a picture of what's + + align:start position:0% +and now let me draw a picture of what's + + + align:start position:0% +and now let me draw a picture of what's +what we're going to do essentially in + + align:start position:0% +what we're going to do essentially in + + + align:start position:0% +what we're going to do essentially in +our group + + align:start position:0% + + + + align:start position:0% + +so let's say that this blog is our + + align:start position:0% +so let's say that this blog is our + + + align:start position:0% +so let's say that this blog is our +metric SpaceX + + align:start position:0% +metric SpaceX + + + align:start position:0% +metric SpaceX +and I'm going to consider my set a + + align:start position:0% + + + + align:start position:0% + +should be this yellow blogs + + align:start position:0% +should be this yellow blogs + + + align:start position:0% +should be this yellow blogs +I want to show that x minus a I either + + align:start position:0% +I want to show that x minus a I either + + + align:start position:0% +I want to show that x minus a I either +region outside of a is going to be open + + align:start position:0% +region outside of a is going to be open + + + align:start position:0% +region outside of a is going to be open +so let's consider some p + + align:start position:0% +so let's consider some p + + + align:start position:0% +so let's consider some p +out here + + align:start position:0% +out here + + + align:start position:0% +out here +how do I show that there exists a ball + + align:start position:0% +how do I show that there exists a ball + + + align:start position:0% +how do I show that there exists a ball +around around theophrenius Epsilon + + align:start position:0% +around around theophrenius Epsilon + + + align:start position:0% +around around theophrenius Epsilon +such that + + align:start position:0% +such that + + + align:start position:0% +such that +such that it doesn't intersect with a + + align:start position:0% +such that it doesn't intersect with a + + + align:start position:0% +such that it doesn't intersect with a +that's what we want to show for openness + + align:start position:0% +that's what we want to show for openness + + + align:start position:0% +that's what we want to show for openness +right + + align:start position:0% +right + + + align:start position:0% +right +well what I can do is compare P to every + + align:start position:0% +well what I can do is compare P to every + + + align:start position:0% +well what I can do is compare P to every +single Q in a + + align:start position:0% +single Q in a + + + align:start position:0% +single Q in a +so let's say q1 + + align:start position:0% +so let's say q1 + + + align:start position:0% +so let's say q1 +Q2 + + align:start position:0% + + + + align:start position:0% + +Q3 + + align:start position:0% +Q3 + + + align:start position:0% +Q3 +and I what I can do is just cover this + + align:start position:0% +and I what I can do is just cover this + + + align:start position:0% +and I what I can do is just cover this +and the ball of half of that radius so + + align:start position:0% +and the ball of half of that radius so + + + align:start position:0% +and the ball of half of that radius so +let's say that's a ball around G of half + + align:start position:0% +let's say that's a ball around G of half + + + align:start position:0% +let's say that's a ball around G of half +the radius + + align:start position:0% +the radius + + + align:start position:0% +the radius +and another bottle of half this radius + + align:start position:0% +and another bottle of half this radius + + + align:start position:0% +and another bottle of half this radius +and so on and so forth my goal is to + + align:start position:0% +and so on and so forth my goal is to + + + align:start position:0% +and so on and so forth my goal is to +take the intersection of all of these + + align:start position:0% +take the intersection of all of these + + + align:start position:0% +take the intersection of all of these +such that they don't intersect with a + + align:start position:0% +such that they don't intersect with a + + + align:start position:0% +such that they don't intersect with a +right I know that P I know that this + + align:start position:0% +right I know that P I know that this + + + align:start position:0% +right I know that P I know that this +ball will intersect with q1 and so on + + align:start position:0% +ball will intersect with q1 and so on + + + align:start position:0% +ball will intersect with q1 and so on +and so forth + + align:start position:0% +and so forth + + + align:start position:0% +and so forth +the issue here though the issue that + + align:start position:0% +the issue here though the issue that + + + align:start position:0% +the issue here though the issue that +we're going to have to work around is + + align:start position:0% +we're going to have to work around is + + + align:start position:0% +we're going to have to work around is +the fact that the intersection of + + align:start position:0% +the fact that the intersection of + + + align:start position:0% +the fact that the intersection of +infinitely many open sets is not + + align:start position:0% +infinitely many open sets is not + + + align:start position:0% +infinitely many open sets is not +inherently an open set right we know + + align:start position:0% +inherently an open set right we know + + + align:start position:0% +inherently an open set right we know +that the intersection of finitely many + + align:start position:0% +that the intersection of finitely many + + + align:start position:0% +that the intersection of finitely many +sets is finite or is open + + align:start position:0% +sets is finite or is open + + + align:start position:0% +sets is finite or is open +um but we don't know that the + + align:start position:0% +um but we don't know that the + + + align:start position:0% +um but we don't know that the +intersection of infinitely many steps is + + align:start position:0% +intersection of infinitely many steps is + + + align:start position:0% +intersection of infinitely many steps is +open and that's the issue + + align:start position:0% +open and that's the issue + + + align:start position:0% +open and that's the issue +so in our proof of showing openness + + align:start position:0% +so in our proof of showing openness + + + align:start position:0% +so in our proof of showing openness +we're going to essentially use + + align:start position:0% +we're going to essentially use + + + align:start position:0% +we're going to essentially use +topological compactiveness to go from + + align:start position:0% +topological compactiveness to go from + + + align:start position:0% +topological compactiveness to go from +this definition to or to complete to get + + align:start position:0% +this definition to or to complete to get + + + align:start position:0% +this definition to or to complete to get +a finite set of cover + + align:start position:0% +a finite set of cover + + + align:start position:0% +a finite set of cover +and that'll be enough for our proof so + + align:start position:0% +and that'll be enough for our proof so + + + align:start position:0% +and that'll be enough for our proof so +that's the outline of how this group is + + align:start position:0% +that's the outline of how this group is + + + align:start position:0% +that's the outline of how this group is +going to go but let's do it 10 times + + align:start position:0% +going to go but let's do it 10 times + + + align:start position:0% +going to go but let's do it 10 times +this rigorous fees + + align:start position:0% + + + + align:start position:0% + +so fix your point to be it in x minus a + + align:start position:0% + + + + align:start position:0% + +and what we're going to do is start + + align:start position:0% +and what we're going to do is start + + + align:start position:0% +and what we're going to do is start +constructing an open calibrator with set + + align:start position:0% +constructing an open calibrator with set + + + align:start position:0% +constructing an open calibrator with set +a + + align:start position:0% +a + + + align:start position:0% +a +and go from there + + align:start position:0% + + + + align:start position:0% + +and this proof will highlight why where + + align:start position:0% +and this proof will highlight why where + + + align:start position:0% +and this proof will highlight why where +we use topological Compact and it's very + + align:start position:0% +we use topological Compact and it's very + + + align:start position:0% +we use topological Compact and it's very +directly + + align:start position:0% +directly + + + align:start position:0% +directly +foreign + + align:start position:0% + + + + align:start position:0% + +x minus a or again you can just let this + + align:start position:0% +x minus a or again you can just let this + + + align:start position:0% +x minus a or again you can just let this +be the real numbers if you prefer + + align:start position:0% +be the real numbers if you prefer + + + align:start position:0% +be the real numbers if you prefer +and consider + + align:start position:0% + + + + align:start position:0% + +for all Q and A + + align:start position:0% + + + + align:start position:0% + +I'm going to consider the open cover of + + align:start position:0% +I'm going to consider the open cover of + + + align:start position:0% +I'm going to consider the open cover of +a + + align:start position:0% +a + + + align:start position:0% +a +by + + align:start position:0% +by + + + align:start position:0% +by +I'm going to consider VQ to be all + + align:start position:0% +I'm going to consider VQ to be all + + + align:start position:0% +I'm going to consider VQ to be all +around P of radius distance from P to Q + + align:start position:0% +around P of radius distance from P to Q + + + align:start position:0% +around P of radius distance from P to Q +over t + + align:start position:0% +over t + + + align:start position:0% +over t +and w q + + align:start position:0% +and w q + + + align:start position:0% +and w q +to be the ball around Q of the same + + align:start position:0% +to be the ball around Q of the same + + + align:start position:0% +to be the ball around Q of the same +radius + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +so what I'm doing now is I'm creating + + align:start position:0% +so what I'm doing now is I'm creating + + + align:start position:0% +so what I'm doing now is I'm creating +both an open cover of a and an open + + align:start position:0% +both an open cover of a and an open + + + align:start position:0% +both an open cover of a and an open +cover of P + + align:start position:0% +cover of P + + + align:start position:0% +cover of P +or sorry and + + align:start position:0% +or sorry and + + + align:start position:0% +or sorry and +yeah an open cover you want to find a + + align:start position:0% +yeah an open cover you want to find a + + + align:start position:0% +yeah an open cover you want to find a +neighborhood + + align:start position:0% + + + + align:start position:0% + +so is this effect an open cover of a + + align:start position:0% + + + + align:start position:0% + +is a a subset of the Union of w cubes + + align:start position:0% +is a a subset of the Union of w cubes + + + align:start position:0% +is a a subset of the Union of w cubes +for Q and A + + align:start position:0% + + + + align:start position:0% + +the answer is yes it's pretty much on + + align:start position:0% +the answer is yes it's pretty much on + + + align:start position:0% +the answer is yes it's pretty much on +the face of it right because every + + align:start position:0% +the face of it right because every + + + align:start position:0% +the face of it right because every +element Q is in WQ + + align:start position:0% +element Q is in WQ + + + align:start position:0% +element Q is in WQ +so the answer is yes + + align:start position:0% +so the answer is yes + + + align:start position:0% +so the answer is yes +and so what this tells us is I can + + align:start position:0% +and so what this tells us is I can + + + align:start position:0% +and so what this tells us is I can +choose a finite subform + + align:start position:0% +choose a finite subform + + + align:start position:0% +choose a finite subform +because a is we're assuming is compact + + align:start position:0% +because a is we're assuming is compact + + + align:start position:0% +because a is we're assuming is compact +so a is the subset of + + align:start position:0% +so a is the subset of + + + align:start position:0% +so a is the subset of +I equal to one so let's say m + + align:start position:0% +I equal to one so let's say m + + + align:start position:0% +I equal to one so let's say m +of w q i which I'll again write out + + align:start position:0% +of w q i which I'll again write out + + + align:start position:0% +of w q i which I'll again write out +what this is this is unit from I4 one to + + align:start position:0% +what this is this is unit from I4 one to + + + align:start position:0% +what this is this is unit from I4 one to +m + + align:start position:0% +m + + + align:start position:0% +m +of Falls around q i of radius distance P + + align:start position:0% +of Falls around q i of radius distance P + + + align:start position:0% +of Falls around q i of radius distance P +to P to q i over 2. + + align:start position:0% +to P to q i over 2. + + + align:start position:0% +to P to q i over 2. +everyone follow so far + + align:start position:0% +everyone follow so far + + + align:start position:0% +everyone follow so far +now the goal is to claim that the + + align:start position:0% +now the goal is to claim that the + + + align:start position:0% +now the goal is to claim that the +intersection of now the corresponding + + align:start position:0% +intersection of now the corresponding + + + align:start position:0% +intersection of now the corresponding +vqis is going to be uh is not going to + + align:start position:0% +vqis is going to be uh is not going to + + + align:start position:0% +vqis is going to be uh is not going to +intersect a + + align:start position:0% + + + + align:start position:0% + +so I claim that that is true + + align:start position:0% +so I claim that that is true + + + align:start position:0% +so I claim that that is true +claim + + align:start position:0% +claim + + + align:start position:0% +claim +the intersection of vqi from I equal 1 + + align:start position:0% +the intersection of vqi from I equal 1 + + + align:start position:0% +the intersection of vqi from I equal 1 +to m + + align:start position:0% +to m + + + align:start position:0% +to m +uh does not contain + + align:start position:0% + + + + align:start position:0% + +does not intersect + + align:start position:0% + + + + align:start position:0% + +hey + + align:start position:0% +hey + + + align:start position:0% +hey +how do I know that this is true + + align:start position:0% +how do I know that this is true + + + align:start position:0% +how do I know that this is true +well suppose I'll just leave this + + align:start position:0% +well suppose I'll just leave this + + + align:start position:0% +well suppose I'll just leave this +verbally + + align:start position:0% +verbally + + + align:start position:0% +verbally +suppose that there existed an element of + + align:start position:0% +suppose that there existed an element of + + + align:start position:0% +suppose that there existed an element of +this intersection that was also in a + + align:start position:0% +this intersection that was also in a + + + align:start position:0% +this intersection that was also in a +then that would have to be in one of + + align:start position:0% +then that would have to be in one of + + + align:start position:0% +then that would have to be in one of +these balls right the ball from Qi to p + + align:start position:0% +these balls right the ball from Qi to p + + + align:start position:0% +these balls right the ball from Qi to p +of half the Radian + + align:start position:0% +of half the Radian + + + align:start position:0% +of half the Radian +we know that this cannot be true by the + + align:start position:0% +we know that this cannot be true by the + + + align:start position:0% +we know that this cannot be true by the +triangle inequality right because this + + align:start position:0% +triangle inequality right because this + + + align:start position:0% +triangle inequality right because this +ball is open and we know that it must + + align:start position:0% +ball is open and we know that it must + + + align:start position:0% +ball is open and we know that it must +you can if it's contained in one of + + align:start position:0% +you can if it's contained in one of + + + align:start position:0% +you can if it's contained in one of +these balls it's not going to intersect + + align:start position:0% +these balls it's not going to intersect + + + align:start position:0% +these balls it's not going to intersect +the neighborhood of P + + align:start position:0% +the neighborhood of P + + + align:start position:0% +the neighborhood of P +right I would highly suggest working + + align:start position:0% +right I would highly suggest working + + + align:start position:0% +right I would highly suggest working +through this detail it's a very like + + align:start position:0% +through this detail it's a very like + + + align:start position:0% +through this detail it's a very like +specific point but it's one to like + + align:start position:0% +specific point but it's one to like + + + align:start position:0% +specific point but it's one to like +double check and make sure you fully + + align:start position:0% +double check and make sure you fully + + + align:start position:0% +double check and make sure you fully +understand + + align:start position:0% +understand + + + align:start position:0% +understand +but what this is telling us is that one + + align:start position:0% +but what this is telling us is that one + + + align:start position:0% +but what this is telling us is that one +the set doesn't intersect a + + align:start position:0% +the set doesn't intersect a + + + align:start position:0% +the set doesn't intersect a +two our Point p is definitely in this + + align:start position:0% +two our Point p is definitely in this + + + align:start position:0% +two our Point p is definitely in this +intersection because it's in all the + + align:start position:0% +intersection because it's in all the + + + align:start position:0% +intersection because it's in all the +balls + + align:start position:0% +balls + + + align:start position:0% +balls +in three + + align:start position:0% +in three + + + align:start position:0% +in three +this tells us that we're done + + align:start position:0% +this tells us that we're done + + + align:start position:0% +this tells us that we're done +because this set + + align:start position:0% +because this set + + + align:start position:0% +because this set +is a finite intersection of open sets so + + align:start position:0% +is a finite intersection of open sets so + + + align:start position:0% +is a finite intersection of open sets so +this is open + + align:start position:0% +this is open + + + align:start position:0% +this is open +so we're done because we found an open + + align:start position:0% +so we're done because we found an open + + + align:start position:0% +so we're done because we found an open +neighborhood around P that doesn't + + align:start position:0% +neighborhood around P that doesn't + + + align:start position:0% +neighborhood around P that doesn't +intersect with a and that tells us that + + align:start position:0% +intersect with a and that tells us that + + + align:start position:0% +intersect with a and that tells us that +a is a closed set + + align:start position:0% +a is a closed set + + + align:start position:0% +a is a closed set +so we're done this implies closing this + + align:start position:0% + + + + align:start position:0% + +any questions this proof was extremely + + align:start position:0% +any questions this proof was extremely + + + align:start position:0% +any questions this proof was extremely +difficult + + align:start position:0% +difficult + + + align:start position:0% +difficult +uh especially if you don't have much + + align:start position:0% +uh especially if you don't have much + + + align:start position:0% +uh especially if you don't have much +experience with + + align:start position:0% +experience with + + + align:start position:0% +experience with +uh topology specifically + + align:start position:0% +uh topology specifically + + + align:start position:0% +uh topology specifically +but I hope that the picture helps quite + + align:start position:0% +but I hope that the picture helps quite + + + align:start position:0% +but I hope that the picture helps quite +a bit + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so we've shown like compact sets are + + align:start position:0% +so we've shown like compact sets are + + + align:start position:0% +so we've shown like compact sets are +both closed and bounded + + align:start position:0% +both closed and bounded + + + align:start position:0% +both closed and bounded +um now is the Congress true are those + + align:start position:0% +um now is the Congress true are those + + + align:start position:0% +um now is the Congress true are those +sets are closed and bounded sets compact + + align:start position:0% +sets are closed and bounded sets compact + + + align:start position:0% +sets are closed and bounded sets compact +uh the answer will be not all the time + + align:start position:0% +uh the answer will be not all the time + + + align:start position:0% +uh the answer will be not all the time +in fact it will be true for the real + + align:start position:0% +in fact it will be true for the real + + + align:start position:0% +in fact it will be true for the real +numbers but it will not be true all of + + align:start position:0% +numbers but it will not be true all of + + + align:start position:0% +numbers but it will not be true all of +the time + + align:start position:0% +the time + + + align:start position:0% +the time +to prove that it's true for real numbers + + align:start position:0% +to prove that it's true for real numbers + + + align:start position:0% +to prove that it's true for real numbers +because again we're looking at uh + + align:start position:0% +because again we're looking at uh + + + align:start position:0% +because again we're looking at uh +compact subsets of R today + + align:start position:0% +compact subsets of R today + + + align:start position:0% +compact subsets of R today +uh it's not too bad I'll just note one + + align:start position:0% +uh it's not too bad I'll just note one + + + align:start position:0% +uh it's not too bad I'll just note one +small level + + align:start position:0% + + + + align:start position:0% + +um if f + + align:start position:0% +um if f + + + align:start position:0% +um if f +is a subset of a compact set K should + + align:start position:0% +is a subset of a compact set K should + + + align:start position:0% +is a subset of a compact set K should +say an X + + align:start position:0% +say an X + + + align:start position:0% +say an X +is closed so here I'm assuming that f is + + align:start position:0% +is closed so here I'm assuming that f is + + + align:start position:0% +is closed so here I'm assuming that f is +closed + + align:start position:0% +closed + + + align:start position:0% +closed +then f is itself compact + + align:start position:0% +then f is itself compact + + + align:start position:0% +then f is itself compact +I wrote this out notationally but what + + align:start position:0% +I wrote this out notationally but what + + + align:start position:0% +I wrote this out notationally but what +this tells you again in words is that a + + align:start position:0% +this tells you again in words is that a + + + align:start position:0% +this tells you again in words is that a +subset of a compact metric space Sorry + + align:start position:0% +subset of a compact metric space Sorry + + + align:start position:0% +subset of a compact metric space Sorry +of a compact occlude subset of a compact + + align:start position:0% +of a compact occlude subset of a compact + + + align:start position:0% +of a compact occlude subset of a compact +set is compact itself + + align:start position:0% +set is compact itself + + + align:start position:0% +set is compact itself +let's go through the proof + + align:start position:0% +let's go through the proof + + + align:start position:0% +let's go through the proof +group + + align:start position:0% +group + + + align:start position:0% +group +well because f is closed + + align:start position:0% +well because f is closed + + + align:start position:0% +well because f is closed +we know that the complement is open + + align:start position:0% +we know that the complement is open + + + align:start position:0% +we know that the complement is open +that's the definition of those so in + + align:start position:0% +that's the definition of those so in + + + align:start position:0% +that's the definition of those so in +fact this decision only F complement + + align:start position:0% +fact this decision only F complement + + + align:start position:0% +fact this decision only F complement +is open + + align:start position:0% + + + + align:start position:0% + +and we want to show political + + align:start position:0% +and we want to show political + + + align:start position:0% +and we want to show political +compactness of f so + + align:start position:0% +compactness of f so + + + align:start position:0% +compactness of f so +let u i + + align:start position:0% +let u i + + + align:start position:0% +let u i +be an open cover of x + + align:start position:0% + + + + align:start position:0% + +we want to go from this to a compact or + + align:start position:0% +we want to go from this to a compact or + + + align:start position:0% +we want to go from this to a compact or +to a finite subcover right that'll show + + align:start position:0% +to a finite subcover right that'll show + + + align:start position:0% +to a finite subcover right that'll show +compactions of that + + align:start position:0% +compactions of that + + + align:start position:0% +compactions of that +well how do we go from this to a how do + + align:start position:0% +well how do we go from this to a how do + + + align:start position:0% +well how do we go from this to a how do +we go from this to using the fact that K + + align:start position:0% +we go from this to using the fact that K + + + align:start position:0% +we go from this to using the fact that K +is + + align:start position:0% +is + + + align:start position:0% +is +well let's draw out the picture + + align:start position:0% +well let's draw out the picture + + + align:start position:0% +well let's draw out the picture +here we have our set X which doesn't + + align:start position:0% +here we have our set X which doesn't + + + align:start position:0% +here we have our set X which doesn't +really matter too much in this position + + align:start position:0% +really matter too much in this position + + + align:start position:0% +really matter too much in this position +here we have K which we know is compact + + align:start position:0% +here we have K which we know is compact + + + align:start position:0% +here we have K which we know is compact +and let's consider rset f + + align:start position:0% +and let's consider rset f + + + align:start position:0% +and let's consider rset f +what we've done now + + align:start position:0% +what we've done now + + + align:start position:0% +what we've done now +is we've covered our X + + align:start position:0% +is we've covered our X + + + align:start position:0% +is we've covered our X +in an open cover + + align:start position:0% + + + + align:start position:0% + +and in fact how do we go from this to an + + align:start position:0% +and in fact how do we go from this to an + + + align:start position:0% +and in fact how do we go from this to an +open cover of K + + align:start position:0% +open cover of K + + + align:start position:0% +open cover of K +well we know that F complement + + align:start position:0% + + + + align:start position:0% + +everything outside of f + + align:start position:0% + + + + align:start position:0% + +is going to be open so what this tells + + align:start position:0% +is going to be open so what this tells + + + align:start position:0% +is going to be open so what this tells +us is that k + + align:start position:0% +us is that k + + + align:start position:0% +us is that k +is contained in the union of these uis + + align:start position:0% +is contained in the union of these uis + + + align:start position:0% +is contained in the union of these uis +from I equal 1 to let's say infinity + + align:start position:0% +from I equal 1 to let's say infinity + + + align:start position:0% +from I equal 1 to let's say infinity +Union with f complement + + align:start position:0% + + + + align:start position:0% + +and this is an open cover okay this is + + align:start position:0% +and this is an open cover okay this is + + + align:start position:0% +and this is an open cover okay this is +the open cover that we're interested in + + align:start position:0% +the open cover that we're interested in + + + align:start position:0% +the open cover that we're interested in +right + + align:start position:0% +right + + + align:start position:0% +right +so we want to go from this to a finite + + align:start position:0% +so we want to go from this to a finite + + + align:start position:0% +so we want to go from this to a finite +subcover of f + + align:start position:0% +subcover of f + + + align:start position:0% +subcover of f +or do a finite step cover + + align:start position:0% +or do a finite step cover + + + align:start position:0% +or do a finite step cover +and we know that we can do so because K + + align:start position:0% +and we know that we can do so because K + + + align:start position:0% +and we know that we can do so because K +is compact so because + + align:start position:0% +is compact so because + + + align:start position:0% +is compact so because +case compact we know that k + + align:start position:0% +case compact we know that k + + + align:start position:0% +case compact we know that k +is contained in the union from I equal 1 + + align:start position:0% +is contained in the union from I equal 1 + + + align:start position:0% +is contained in the union from I equal 1 +to M of UI + + align:start position:0% +to M of UI + + + align:start position:0% +to M of UI +potentially unions is f complement it's + + align:start position:0% +potentially unions is f complement it's + + + align:start position:0% +potentially unions is f complement it's +not going to hurt to Union One More set + + align:start position:0% +not going to hurt to Union One More set + + + align:start position:0% +not going to hurt to Union One More set +so keep it pronounced + + align:start position:0% +so keep it pronounced + + + align:start position:0% +so keep it pronounced +and what we know is that f is a subset + + align:start position:0% +and what we know is that f is a subset + + + align:start position:0% +and what we know is that f is a subset +of K + + align:start position:0% +of K + + + align:start position:0% +of K +so we've gone from an open cover of f to + + align:start position:0% +so we've gone from an open cover of f to + + + align:start position:0% +so we've gone from an open cover of f to +an open cover of K + + align:start position:0% +an open cover of K + + + align:start position:0% +an open cover of K +we've gone from that open cover of K to + + align:start position:0% +we've gone from that open cover of K to + + + align:start position:0% +we've gone from that open cover of K to +a finite subcover + + align:start position:0% +a finite subcover + + + align:start position:0% +a finite subcover +and we mentioned that finite subcover of + + align:start position:0% +and we mentioned that finite subcover of + + + align:start position:0% +and we mentioned that finite subcover of +K is also going to cover F so we're done + + align:start position:0% +K is also going to cover F so we're done + + + align:start position:0% +K is also going to cover F so we're done +right because we showed that every open + + align:start position:0% +right because we showed that every open + + + align:start position:0% +right because we showed that every open +cover of f + + align:start position:0% +cover of f + + + align:start position:0% +cover of f +well I'll always take one more line to + + align:start position:0% +well I'll always take one more line to + + + align:start position:0% +well I'll always take one more line to +be extra clear f is therefore contained + + align:start position:0% +be extra clear f is therefore contained + + + align:start position:0% +be extra clear f is therefore contained +in the union from time to 1 to M of UI + + align:start position:0% +in the union from time to 1 to M of UI + + + align:start position:0% +in the union from time to 1 to M of UI +because no element of f is in F + + align:start position:0% +because no element of f is in F + + + align:start position:0% +because no element of f is in F +complement + + align:start position:0% +complement + + + align:start position:0% +complement +so we've gone from an open cover of f to + + align:start position:0% +so we've gone from an open cover of f to + + + align:start position:0% +so we've gone from an open cover of f to +a 5x number which implies topological + + align:start position:0% +a 5x number which implies topological + + + align:start position:0% +a 5x number which implies topological +compactions right that's the definition + + align:start position:0% +compactions right that's the definition + + + align:start position:0% +compactions right that's the definition +of topological compatibles + + align:start position:0% + + + + align:start position:0% + +and we're going to use this very + + align:start position:0% +and we're going to use this very + + + align:start position:0% +and we're going to use this very +directly to show that + + align:start position:0% +directly to show that + + + align:start position:0% +directly to show that +closed and bounded sets and euclidean's + + align:start position:0% +closed and bounded sets and euclidean's + + + align:start position:0% +closed and bounded sets and euclidean's +base are compact + + align:start position:0% + + + + align:start position:0% + +how do we do that + + align:start position:0% +how do we do that + + + align:start position:0% +how do we do that +well we're just going to shove our + + align:start position:0% +well we're just going to shove our + + + align:start position:0% +well we're just going to shove our +compact set in a closed intervals + + align:start position:0% +compact set in a closed intervals + + + align:start position:0% +compact set in a closed intervals +supposing interval + + align:start position:0% +supposing interval + + + align:start position:0% +supposing interval +so + + align:start position:0% +so + + + align:start position:0% +so +uh where + + align:start position:0% +uh where + + + align:start position:0% +uh where +we go + + align:start position:0% +we go + + + align:start position:0% +we go +proposition + + align:start position:0% + + + + align:start position:0% + +compact subsets of r + + align:start position:0% + + + + align:start position:0% + +are precisely closed and bonded sets + + align:start position:0% + + + + align:start position:0% + +of r + + align:start position:0% +of r + + + align:start position:0% +of r +right this is the theme we've proven one + + align:start position:0% +right this is the theme we've proven one + + + align:start position:0% +right this is the theme we've proven one +of the directions so far I've shown that + + align:start position:0% +of the directions so far I've shown that + + + align:start position:0% +of the directions so far I've shown that +compact complies because we found it + + align:start position:0% +compact complies because we found it + + + align:start position:0% +compact complies because we found it +let's show the other direction that has + + align:start position:0% +let's show the other direction that has + + + align:start position:0% +let's show the other direction that has +been bounded complied compact + + align:start position:0% +been bounded complied compact + + + align:start position:0% +been bounded complied compact +proof + + align:start position:0% + + + + align:start position:0% + +let + + align:start position:0% +let + + + align:start position:0% +let +a be a subset of r + + align:start position:0% +a be a subset of r + + + align:start position:0% +a be a subset of r +B because the mountain is + + align:start position:0% + + + + align:start position:0% + +because a is closed and bounded we know + + align:start position:0% +because a is closed and bounded we know + + + align:start position:0% +because a is closed and bounded we know +that a + + align:start position:0% +that a + + + align:start position:0% +that a +must be contained in some minus n to M's + + align:start position:0% +must be contained in some minus n to M's + + + align:start position:0% +must be contained in some minus n to M's +because because of boundedness + + align:start position:0% +because because of boundedness + + + align:start position:0% +because because of boundedness +and here and it's fine + + align:start position:0% +and here and it's fine + + + align:start position:0% +and here and it's fine +and now what can we do to complete to + + align:start position:0% +and now what can we do to complete to + + + align:start position:0% +and now what can we do to complete to +show that a is compact from here + + align:start position:0% +show that a is compact from here + + + align:start position:0% +show that a is compact from here +we can use the Lemma we just stated a is + + align:start position:0% +we can use the Lemma we just stated a is + + + align:start position:0% +we can use the Lemma we just stated a is +the code of this + + align:start position:0% +the code of this + + + align:start position:0% +the code of this +so by closing this this implies + + align:start position:0% +so by closing this this implies + + + align:start position:0% +so by closing this this implies +that a is compact + + align:start position:0% +that a is compact + + + align:start position:0% +that a is compact +because it's a closed subset + + align:start position:0% +because it's a closed subset + + + align:start position:0% +because it's a closed subset +of a closed and of a compact + + align:start position:0% +of a closed and of a compact + + + align:start position:0% +of a closed and of a compact +it is a closed subset of a compact set + + align:start position:0% +it is a closed subset of a compact set + + + align:start position:0% +it is a closed subset of a compact set +and the fact that minus n to n is + + align:start position:0% +and the fact that minus n to n is + + + align:start position:0% +and the fact that minus n to n is +compact is precisely the proof we did + + align:start position:0% +compact is precisely the proof we did + + + align:start position:0% +compact is precisely the proof we did +earlier right so I won't go through that + + align:start position:0% +earlier right so I won't go through that + + + align:start position:0% +earlier right so I won't go through that +group again but this implies the result + + align:start position:0% +group again but this implies the result + + + align:start position:0% +group again but this implies the result +that we wanted so we're done + + align:start position:0% + + + + align:start position:0% + +this statement + + align:start position:0% +this statement + + + align:start position:0% +this statement +uh I'll move it back down in case you + + align:start position:0% +uh I'll move it back down in case you + + + align:start position:0% +uh I'll move it back down in case you +want to see it again this statement is + + align:start position:0% +want to see it again this statement is + + + align:start position:0% +want to see it again this statement is +known as the Hannibal serum + + align:start position:0% + + + + align:start position:0% + +it's not like on the face of it the most + + align:start position:0% +it's not like on the face of it the most + + + align:start position:0% +it's not like on the face of it the most +easy thing to show + + align:start position:0% +easy thing to show + + + align:start position:0% +easy thing to show +um but I mean we're able to cover it in + + align:start position:0% +um but I mean we're able to cover it in + + + align:start position:0% +um but I mean we're able to cover it in +a lecture so + + align:start position:0% + + + + align:start position:0% + +um but the issue is is that this stigma + + align:start position:0% +um but the issue is is that this stigma + + + align:start position:0% +um but the issue is is that this stigma +is not going to be true about metric + + align:start position:0% +is not going to be true about metric + + + align:start position:0% +is not going to be true about metric +spaces right we are not going to have + + align:start position:0% +spaces right we are not going to have + + + align:start position:0% +spaces right we are not going to have +that closed and bounded sets are the + + align:start position:0% +that closed and bounded sets are the + + + align:start position:0% +that closed and bounded sets are the +same as compact set and electric space + + align:start position:0% +same as compact set and electric space + + + align:start position:0% +same as compact set and electric space +but it's so important on euclidean space + + align:start position:0% +but it's so important on euclidean space + + + align:start position:0% +but it's so important on euclidean space +that I wanted to bring this group up + + align:start position:0% +that I wanted to bring this group up + + + align:start position:0% +that I wanted to bring this group up +today + + align:start position:0% +today + + + align:start position:0% +today +because it does give a good example of + + align:start position:0% +because it does give a good example of + + + align:start position:0% +because it does give a good example of +you know + + align:start position:0% +you know + + + align:start position:0% +you know +how we uh + + align:start position:0% +how we uh + + + align:start position:0% +how we uh +how we think about things in euclidean + + align:start position:0% +how we think about things in euclidean + + + align:start position:0% +how we think about things in euclidean +space and why metric spaces are so + + align:start position:0% +space and why metric spaces are so + + + align:start position:0% +space and why metric spaces are so +important + + align:start position:0% +important + + + align:start position:0% +important +all right so now what we're going to do + + align:start position:0% +all right so now what we're going to do + + + align:start position:0% +all right so now what we're going to do +is show that closed and bounded is the + + align:start position:0% +is show that closed and bounded is the + + + align:start position:0% +is show that closed and bounded is the +same as sequentially continuous or sorry + + align:start position:0% +same as sequentially continuous or sorry + + + align:start position:0% +same as sequentially continuous or sorry +sequentially compact in euclidean space + + align:start position:0% +sequentially compact in euclidean space + + + align:start position:0% +sequentially compact in euclidean space +and that'll prove that the same all + + align:start position:0% +and that'll prove that the same all + + + align:start position:0% +and that'll prove that the same all +three are equivalent + + align:start position:0% +three are equivalent + + + align:start position:0% +three are equivalent +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so note + + align:start position:0% +so note + + + align:start position:0% +so note +proposition + + align:start position:0% +proposition + + + align:start position:0% +proposition +or I guess I should say zero zero + + align:start position:0% +or I guess I should say zero zero + + + align:start position:0% +or I guess I should say zero zero +five Bolzano by our gods + + align:start position:0% + + + + align:start position:0% + +I'm just going to State it again + + align:start position:0% + + + + align:start position:0% + +slow has been mounted + + align:start position:0% + + + + align:start position:0% + +and five sequently continuous + + align:start position:0% + + + + align:start position:0% + +oh sorry not sequentially continuous + + align:start position:0% +oh sorry not sequentially continuous + + + align:start position:0% +oh sorry not sequentially continuous +sequentially + + align:start position:0% + + + + align:start position:0% + +so to show that sequentially compact is + + align:start position:0% +so to show that sequentially compact is + + + align:start position:0% +so to show that sequentially compact is +the same as compact subsets + + align:start position:0% +the same as compact subsets + + + align:start position:0% +the same as compact subsets +or it's the same definition as compact + + align:start position:0% +or it's the same definition as compact + + + align:start position:0% +or it's the same definition as compact +substance of R we want to prove the + + align:start position:0% +substance of R we want to prove the + + + align:start position:0% +substance of R we want to prove the +other direction + + align:start position:0% +other direction + + + align:start position:0% +other direction +right + + align:start position:0% +right + + + align:start position:0% +right +uh + + align:start position:0% +uh + + + align:start position:0% +uh +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +actually + + align:start position:0% +actually + + + align:start position:0% +actually +yeah yeah + + align:start position:0% +yeah yeah + + + align:start position:0% +yeah yeah +so let's prove the other direction + + align:start position:0% +so let's prove the other direction + + + align:start position:0% +so let's prove the other direction +uh + + align:start position:0% +uh + + + align:start position:0% +uh +proposition + + align:start position:0% + + + + align:start position:0% + +sequentially compact + + align:start position:0% + + + + align:start position:0% + +implies closed and bounded + + align:start position:0% + + + + align:start position:0% + +well firstly + + align:start position:0% + + + + align:start position:0% + +uh to show Closure + + align:start position:0% +uh to show Closure + + + align:start position:0% +uh to show Closure +I should + + align:start position:0% + + + + align:start position:0% + +what I'll note is that this is going to + + align:start position:0% +what I'll note is that this is going to + + + align:start position:0% +what I'll note is that this is going to +show up on your second problem set + + align:start position:0% + + + + align:start position:0% + +on problems that two you'll show that + + align:start position:0% +on problems that two you'll show that + + + align:start position:0% +on problems that two you'll show that +closed sets are the same as ones which + + align:start position:0% +closed sets are the same as ones which + + + align:start position:0% +closed sets are the same as ones which +contain all of their limit points right + + align:start position:0% +contain all of their limit points right + + + align:start position:0% +contain all of their limit points right +meaning if I take a sequence and I know + + align:start position:0% +meaning if I take a sequence and I know + + + align:start position:0% +meaning if I take a sequence and I know +that it converges the thing it converges + + align:start position:0% +that it converges the thing it converges + + + align:start position:0% +that it converges the thing it converges +to must be in your closed set + + align:start position:0% +to must be in your closed set + + + align:start position:0% +to must be in your closed set +this is the fact that you'll prove under + + align:start position:0% +this is the fact that you'll prove under + + + align:start position:0% +this is the fact that you'll prove under +the second problem set so I won't write + + align:start position:0% +the second problem set so I won't write + + + align:start position:0% +the second problem set so I won't write +it out right now + + align:start position:0% +it out right now + + + align:start position:0% +it out right now +but what this tells you + + align:start position:0% +but what this tells you + + + align:start position:0% +but what this tells you +is that by segmental compactness + + align:start position:0% +is that by segmental compactness + + + align:start position:0% +is that by segmental compactness +if I take a sequence that converges to + + align:start position:0% +if I take a sequence that converges to + + + align:start position:0% +if I take a sequence that converges to +any point of your compact uh or that + + align:start position:0% +any point of your compact uh or that + + + align:start position:0% +any point of your compact uh or that +converges anywhere then it's going to + + align:start position:0% +converges anywhere then it's going to + + + align:start position:0% +converges anywhere then it's going to +have a con sorry let me say this again + + align:start position:0% +have a con sorry let me say this again + + + align:start position:0% +have a con sorry let me say this again +if I take a sequence in my code set I + + align:start position:0% +if I take a sequence in my code set I + + + align:start position:0% +if I take a sequence in my code set I +know that it's going to + + align:start position:0% +know that it's going to + + + align:start position:0% +know that it's going to +if I take a sequence I know that it's + + align:start position:0% +if I take a sequence I know that it's + + + align:start position:0% +if I take a sequence I know that it's +going to have a convergent subsequence + + align:start position:0% +going to have a convergent subsequence + + + align:start position:0% +going to have a convergent subsequence +which tells us it contains all of its + + align:start position:0% +which tells us it contains all of its + + + align:start position:0% +which tells us it contains all of its +Summit points which tells us that it's + + align:start position:0% +Summit points which tells us that it's + + + align:start position:0% +Summit points which tells us that it's +closed right this is the fact that I + + align:start position:0% +closed right this is the fact that I + + + align:start position:0% +closed right this is the fact that I +will leave to you to show because I + + align:start position:0% +will leave to you to show because I + + + align:start position:0% +will leave to you to show because I +believe that you all can do it + + align:start position:0% +believe that you all can do it + + + align:start position:0% +believe that you all can do it +um + + align:start position:0% +um + + + align:start position:0% +um +do + + align:start position:0% + + + + align:start position:0% + +two to show boundedness + + align:start position:0% + + + + align:start position:0% + +it's going to be a little bit easier to + + align:start position:0% +it's going to be a little bit easier to + + + align:start position:0% +it's going to be a little bit easier to +do because assume + + align:start position:0% + + + + align:start position:0% + +a + + align:start position:0% +a + + + align:start position:0% +a +is unbounded + + align:start position:0% + + + + align:start position:0% + +where a here is the sequentially compact + + align:start position:0% +where a here is the sequentially compact + + + align:start position:0% +where a here is the sequentially compact +set I'm considering + + align:start position:0% +set I'm considering + + + align:start position:0% +set I'm considering +then what this tells us is I can find a + + align:start position:0% +then what this tells us is I can find a + + + align:start position:0% +then what this tells us is I can find a +sequence x i + + align:start position:0% +sequence x i + + + align:start position:0% +sequence x i +which goes to Infinity + + align:start position:0% +which goes to Infinity + + + align:start position:0% +which goes to Infinity +and this is a subset of a + + align:start position:0% + + + + align:start position:0% + +right so if I'm assuming my set a is + + align:start position:0% +right so if I'm assuming my set a is + + + align:start position:0% +right so if I'm assuming my set a is +unbounded I can find a sequence which + + align:start position:0% +unbounded I can find a sequence which + + + align:start position:0% +unbounded I can find a sequence which +goes off to Infinity + + align:start position:0% +goes off to Infinity + + + align:start position:0% +goes off to Infinity +what this tells us is that there's not + + align:start position:0% +what this tells us is that there's not + + + align:start position:0% +what this tells us is that there's not +going to be any convergent subsequence + + align:start position:0% +going to be any convergent subsequence + + + align:start position:0% +going to be any convergent subsequence +of the set of the sequence right this is + + align:start position:0% +of the set of the sequence right this is + + + align:start position:0% +of the set of the sequence right this is +the same thing as we did before right we + + align:start position:0% +the same thing as we did before right we + + + align:start position:0% +the same thing as we did before right we +wanted to show the real numbers but not + + align:start position:0% +wanted to show the real numbers but not + + + align:start position:0% +wanted to show the real numbers but not +potentially compact just take a sequence + + align:start position:0% +potentially compact just take a sequence + + + align:start position:0% +potentially compact just take a sequence +that goes off to infinity and we're done + + align:start position:0% +that goes off to infinity and we're done + + + align:start position:0% +that goes off to infinity and we're done +and that's the same is true here + + align:start position:0% + + + + align:start position:0% + +every + + align:start position:0% +every + + + align:start position:0% +every +subsequence + + align:start position:0% + + + + align:start position:0% + +of x i or x n + + align:start position:0% +of x i or x n + + + align:start position:0% +of x i or x n +diverges + + align:start position:0% + + + + align:start position:0% + +which is a concrete contradiction + + align:start position:0% +which is a concrete contradiction + + + align:start position:0% +which is a concrete contradiction +or sorry not a contradiction we showed + + align:start position:0% +or sorry not a contradiction we showed + + + align:start position:0% +or sorry not a contradiction we showed +that unbounded implies not sequentially + + align:start position:0% +that unbounded implies not sequentially + + + align:start position:0% +that unbounded implies not sequentially +compact so we know that the Congress is + + align:start position:0% +compact so we know that the Congress is + + + align:start position:0% +compact so we know that the Congress is +true sequentially Compact and quite + + align:start position:0% +true sequentially Compact and quite + + + align:start position:0% +true sequentially Compact and quite +founded so we've proven the + + align:start position:0% +founded so we've proven the + + + align:start position:0% +founded so we've proven the +contrapositive + + align:start position:0% +contrapositive + + + align:start position:0% +contrapositive +all right and this shows host and + + align:start position:0% +all right and this shows host and + + + align:start position:0% +all right and this shows host and +bounded + + align:start position:0% + + + + align:start position:0% + +so I know that I'm leaving part of the + + align:start position:0% +so I know that I'm leaving part of the + + + align:start position:0% +so I know that I'm leaving part of the +proof left to you but I would highly + + align:start position:0% +proof left to you but I would highly + + + align:start position:0% +proof left to you but I would highly +recommend working through it + + align:start position:0% +recommend working through it + + + align:start position:0% +recommend working through it +working through that portion yourself + + align:start position:0% +working through that portion yourself + + + align:start position:0% +working through that portion yourself +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh and in fact we'll talk more about it + + align:start position:0% +uh and in fact we'll talk more about it + + + align:start position:0% +uh and in fact we'll talk more about it +on Thursday + + align:start position:0% +on Thursday + + + align:start position:0% +on Thursday +so what things do I want to know now + + align:start position:0% +so what things do I want to know now + + + align:start position:0% +so what things do I want to know now +we've shown compact subsets are the same + + align:start position:0% +we've shown compact subsets are the same + + + align:start position:0% +we've shown compact subsets are the same +as closed and bounded sets in r + + align:start position:0% +as closed and bounded sets in r + + + align:start position:0% +as closed and bounded sets in r +and we've in fact showed that closed and + + align:start position:0% +and we've in fact showed that closed and + + + align:start position:0% +and we've in fact showed that closed and +bounded is the same as sequential + + align:start position:0% +bounded is the same as sequential + + + align:start position:0% +bounded is the same as sequential +so in the case of euclidean space we're + + align:start position:0% +so in the case of euclidean space we're + + + align:start position:0% +so in the case of euclidean space we're +all done right you've done what I've set + + align:start position:0% +all done right you've done what I've set + + + align:start position:0% +all done right you've done what I've set +off to do I want to show that + + align:start position:0% +off to do I want to show that + + + align:start position:0% +off to do I want to show that +topological compactness is the system + + align:start position:0% +topological compactness is the system + + + align:start position:0% +topological compactness is the system +consciously compact in r great the issue + + align:start position:0% +consciously compact in r great the issue + + + align:start position:0% +consciously compact in r great the issue +again + + align:start position:0% +again + + + align:start position:0% +again +is posed and bounded sets are not always + + align:start position:0% +is posed and bounded sets are not always + + + align:start position:0% +is posed and bounded sets are not always +the same as compact subsets of R because + + align:start position:0% +the same as compact subsets of R because + + + align:start position:0% +the same as compact subsets of R because +here we inherently used the fact that I + + align:start position:0% +here we inherently used the fact that I + + + align:start position:0% +here we inherently used the fact that I +can shove a into a compact subset right + + align:start position:0% +can shove a into a compact subset right + + + align:start position:0% +can shove a into a compact subset right +I can set a to be a subset of minus n to + + align:start position:0% +I can set a to be a subset of minus n to + + + align:start position:0% +I can set a to be a subset of minus n to +n if it's bounded + + align:start position:0% +n if it's bounded + + + align:start position:0% +n if it's bounded +this fact is not going to be true about + + align:start position:0% +this fact is not going to be true about + + + align:start position:0% +this fact is not going to be true about +metric spaces right because what is + + align:start position:0% +metric spaces right because what is + + + align:start position:0% +metric spaces right because what is +minus end to n mean in a metric space it + + align:start position:0% +minus end to n mean in a metric space it + + + align:start position:0% +minus end to n mean in a metric space it +doesn't make sense + + align:start position:0% +doesn't make sense + + + align:start position:0% +doesn't make sense +but + + align:start position:0% +but + + + align:start position:0% +but +um + + align:start position:0% +um + + + align:start position:0% +um +but I'll make one small note + + align:start position:0% + + + + align:start position:0% + +metric spaces + + align:start position:0% + + + + align:start position:0% + +with + + align:start position:0% +with + + + align:start position:0% +with +the following the following game + + align:start position:0% + + + + align:start position:0% + +was the fact that exposed and bounded + + align:start position:0% + + + + align:start position:0% + +implies compact + + align:start position:0% + + + + align:start position:0% + +if I have those amounted implies compact + + align:start position:0% +if I have those amounted implies compact + + + align:start position:0% +if I have those amounted implies compact +this is then I'd say that the metric + + align:start position:0% +this is then I'd say that the metric + + + align:start position:0% +this is then I'd say that the metric +space + + align:start position:0% + + + + align:start position:0% + +has the kind of real property + + align:start position:0% + + + + align:start position:0% + +property + + align:start position:0% +property + + + align:start position:0% +property +so it's not true all the time but if + + align:start position:0% +so it's not true all the time but if + + + align:start position:0% +so it's not true all the time but if +it's if it's true that closed and + + align:start position:0% +it's if it's true that closed and + + + align:start position:0% +it's if it's true that closed and +bounded implies topologically compact + + align:start position:0% +bounded implies topologically compact + + + align:start position:0% +bounded implies topologically compact +then it's a specific name it's a + + align:start position:0% +then it's a specific name it's a + + + align:start position:0% +then it's a specific name it's a +spectral name known as anagram which + + align:start position:0% +spectral name known as anagram which + + + align:start position:0% +spectral name known as anagram which +makes sense because the theorem is + + align:start position:0% +makes sense because the theorem is + + + align:start position:0% +makes sense because the theorem is +called the high number of theorem + + align:start position:0% +called the high number of theorem + + + align:start position:0% +called the high number of theorem +um but that's what's going to fill for + + align:start position:0% +um but that's what's going to fill for + + + align:start position:0% +um but that's what's going to fill for +metric space is notice that we should + + align:start position:0% +metric space is notice that we should + + + align:start position:0% +metric space is notice that we should +have we should get that that's going to + + align:start position:0% +have we should get that that's going to + + + align:start position:0% +have we should get that that's going to +be the case because sequential + + align:start position:0% +be the case because sequential + + + align:start position:0% +be the case because sequential +compactness once you've worked through + + align:start position:0% +compactness once you've worked through + + + align:start position:0% +compactness once you've worked through +once you fully looked through this + + align:start position:0% +once you fully looked through this + + + align:start position:0% +once you fully looked through this +the proof of sequential compactness + + align:start position:0% +the proof of sequential compactness + + + align:start position:0% +the proof of sequential compactness +being the same as close to invalided + + align:start position:0% +being the same as close to invalided + + + align:start position:0% +being the same as close to invalided +that's going to work out in metric space + + align:start position:0% +that's going to work out in metric space + + + align:start position:0% +that's going to work out in metric space +as well so we should guess that if + + align:start position:0% +as well so we should guess that if + + + align:start position:0% +as well so we should guess that if +anything is going to break + + align:start position:0% +anything is going to break + + + align:start position:0% +anything is going to break +is going to be closed and bounded by + + align:start position:0% +is going to be closed and bounded by + + + align:start position:0% +is going to be closed and bounded by +topologically + + align:start position:0% +topologically + + + align:start position:0% +topologically +come back okay + + align:start position:0% +come back okay + + + align:start position:0% +come back okay +so that's it for today I do want to + + align:start position:0% +so that's it for today I do want to + + + align:start position:0% +so that's it for today I do want to +iterate that this is not meant to be + + align:start position:0% +iterate that this is not meant to be + + + align:start position:0% +iterate that this is not meant to be +like the easiest portion of this class + + align:start position:0% +like the easiest portion of this class + + + align:start position:0% +like the easiest portion of this class +this is this is in fact one of the + + align:start position:0% +this is this is in fact one of the + + + align:start position:0% +this is this is in fact one of the +hardest portions of this class + + align:start position:0% +hardest portions of this class + + + align:start position:0% +hardest portions of this class +but it's in fact part of the + + align:start position:0% +but it's in fact part of the + + + align:start position:0% +but it's in fact part of the +most important if you ask any analysis + + align:start position:0% +most important if you ask any analysis + + + align:start position:0% +most important if you ask any analysis +Professor what's the major difference + + align:start position:0% +Professor what's the major difference + + + align:start position:0% +Professor what's the major difference +between 100 B and 100a + + align:start position:0% +between 100 B and 100a + + + align:start position:0% +between 100 B and 100a +it's experienced with compact effects + + align:start position:0% +it's experienced with compact effects + + + align:start position:0% +it's experienced with compact effects +it's hard and it's kind of brutal + + align:start position:0% +it's hard and it's kind of brutal + + + align:start position:0% +it's hard and it's kind of brutal +sometimes but it is worthwhile to do \ No newline at end of file diff --git a/SFB2Fxel6iM.txt b/SFB2Fxel6iM.txt new file mode 100644 index 0000000000000000000000000000000000000000..ae48b0f3b9c9f9af8b2067d5e7cc473cb6f4bb92 --- /dev/null +++ b/SFB2Fxel6iM.txt @@ -0,0 +1,5715 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% +of MIT courses visit mitop courseware at + + + align:start position:0% +of MIT courses visit mitop courseware at +ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +hi today's lecture starts off what + + align:start position:0% +hi today's lecture starts off what + + + align:start position:0% +hi today's lecture starts off what +probably is the single most important + + align:start position:0% +probably is the single most important + + + align:start position:0% +probably is the single most important +topic in the entire course not just + + align:start position:0% +topic in the entire course not just + + + align:start position:0% +topic in the entire course not just +today but in the entire course and it's + + align:start position:0% +today but in the entire course and it's + + + align:start position:0% +today but in the entire course and it's +a uh rather sneaky thing in the sense + + align:start position:0% +a uh rather sneaky thing in the sense + + + align:start position:0% +a uh rather sneaky thing in the sense +that it takes a while to grow into it + + align:start position:0% +that it takes a while to grow into it + + + align:start position:0% +that it takes a while to grow into it +things have been going so smoothly so + + align:start position:0% +things have been going so smoothly so + + + align:start position:0% +things have been going so smoothly so +far that perhaps this point is going to + + align:start position:0% +far that perhaps this point is going to + + + align:start position:0% +far that perhaps this point is going to +be a little bit subtle to make and we'll + + align:start position:0% +be a little bit subtle to make and we'll + + + align:start position:0% +be a little bit subtle to make and we'll +try to lead into a grad ually there are + + align:start position:0% +try to lead into a grad ually there are + + + align:start position:0% +try to lead into a grad ually there are +probably uh 10 different ways to + + align:start position:0% +probably uh 10 different ways to + + + align:start position:0% +probably uh 10 different ways to +introduce this topic and whichever one + + align:start position:0% +introduce this topic and whichever one + + + align:start position:0% +introduce this topic and whichever one +you pick I think any one of the other + + align:start position:0% +you pick I think any one of the other + + + align:start position:0% +you pick I think any one of the other +nine would have been better but without + + align:start position:0% +nine would have been better but without + + + align:start position:0% +nine would have been better but without +any further Ado let me talk about + + align:start position:0% +any further Ado let me talk about + + + align:start position:0% +any further Ado let me talk about +today's lesson in terms of something + + align:start position:0% +today's lesson in terms of something + + + align:start position:0% +today's lesson in terms of something +called the directional derivative and + + align:start position:0% +called the directional derivative and + + + align:start position:0% +called the directional derivative and +indicate in a manner of speaking that + + align:start position:0% +indicate in a manner of speaking that + + + align:start position:0% +indicate in a manner of speaking that +when we deal with functions of several + + align:start position:0% +when we deal with functions of several + + + align:start position:0% +when we deal with functions of several +variables especially in the case that n + + align:start position:0% +variables especially in the case that n + + + align:start position:0% +variables especially in the case that n +equals 2 there is a very obvious geomet + + align:start position:0% +equals 2 there is a very obvious geomet + + + align:start position:0% +equals 2 there is a very obvious geomet +rcal interpretation one that we made + + align:start position:0% +rcal interpretation one that we made + + + align:start position:0% +rcal interpretation one that we made +some use of in the previous lecture but + + align:start position:0% +some use of in the previous lecture but + + + align:start position:0% +some use of in the previous lecture but +which I hope to make more use of in this + + align:start position:0% +which I hope to make more use of in this + + + align:start position:0% +which I hope to make more use of in this +particular lecture let's take a look and + + align:start position:0% +particular lecture let's take a look and + + + align:start position:0% +particular lecture let's take a look and +see what the situation is let's suppose + + align:start position:0% +see what the situation is let's suppose + + + align:start position:0% +see what the situation is let's suppose +I'm given that W is a function of the + + align:start position:0% +I'm given that W is a function of the + + + align:start position:0% +I'm given that W is a function of the +two independent variables X and Y and I + + align:start position:0% +two independent variables X and Y and I + + + align:start position:0% +two independent variables X and Y and I +have that W is therefore some function + + align:start position:0% +have that W is therefore some function + + + align:start position:0% +have that W is therefore some function +of X and Y and I can now talk about the + + align:start position:0% +of X and Y and I can now talk about the + + + align:start position:0% +of X and Y and I can now talk about the +graph of w which we assume is some + + align:start position:0% +graph of w which we assume is some + + + align:start position:0% +graph of w which we assume is some +surface okay and I've drawn it in this + + align:start position:0% +surface okay and I've drawn it in this + + + align:start position:0% +surface okay and I've drawn it in this +particular way I take some point a comma + + align:start position:0% +particular way I take some point a comma + + + align:start position:0% +particular way I take some point a comma +B in the XY plane on which f is + + align:start position:0% +B in the XY plane on which f is + + + align:start position:0% +B in the XY plane on which f is +defined and uh at that particular point + + align:start position:0% +defined and uh at that particular point + + + align:start position:0% +defined and uh at that particular point +I go to the corresponding point on the + + align:start position:0% +I go to the corresponding point on the + + + align:start position:0% +I go to the corresponding point on the +surface which I call p 0 which has + + align:start position:0% +surface which I call p 0 which has + + + align:start position:0% +surface which I call p 0 which has +coordinates what a b and c where C is + + align:start position:0% +coordinates what a b and c where C is + + + align:start position:0% +coordinates what a b and c where C is +simply F of a comma B that of course is + + align:start position:0% +simply F of a comma B that of course is + + + align:start position:0% +simply F of a comma B that of course is +how you graph a function of two + + align:start position:0% +how you graph a function of two + + + align:start position:0% +how you graph a function of two +independent variables the W coordinate + + align:start position:0% +independent variables the W coordinate + + + align:start position:0% +independent variables the W coordinate +so to speak is simply the functional + + align:start position:0% +so to speak is simply the functional + + + align:start position:0% +so to speak is simply the functional +value of the X and Y + + align:start position:0% +value of the X and Y + + + align:start position:0% +value of the X and Y +coordinates now what we did last time + + align:start position:0% +coordinates now what we did last time + + + align:start position:0% +coordinates now what we did last time +was we essentially said look at if we + + align:start position:0% +was we essentially said look at if we + + + align:start position:0% +was we essentially said look at if we +were to slice this + + align:start position:0% +were to slice this + + + align:start position:0% +were to slice this +Surface by a plane which was either + + align:start position:0% +Surface by a plane which was either + + + align:start position:0% +Surface by a plane which was either +parallel to the Wy plane or to the WX + + align:start position:0% +parallel to the Wy plane or to the WX + + + align:start position:0% +parallel to the Wy plane or to the WX +plane we get special curves of + + align:start position:0% +plane we get special curves of + + + align:start position:0% +plane we get special curves of +intersection and we use this to indicate + + align:start position:0% +intersection and we use this to indicate + + + align:start position:0% +intersection and we use this to indicate +the idea of partial derivatives now + + align:start position:0% +the idea of partial derivatives now + + + align:start position:0% +the idea of partial derivatives now +without too much imagination I think it + + align:start position:0% +without too much imagination I think it + + + align:start position:0% +without too much imagination I think it +should be very easy for you to visualize + + align:start position:0% +should be very easy for you to visualize + + + align:start position:0% +should be very easy for you to visualize +a arbitrary surface over your heads + + align:start position:0% +a arbitrary surface over your heads + + + align:start position:0% +a arbitrary surface over your heads +you're standing at a particular point on + + align:start position:0% +you're standing at a particular point on + + + align:start position:0% +you're standing at a particular point on +the floor at that point on the floor you + + align:start position:0% +the floor at that point on the floor you + + + align:start position:0% +the floor at that point on the floor you +visualize a coordinate axis which we'll + + align:start position:0% +visualize a coordinate axis which we'll + + + align:start position:0% +visualize a coordinate axis which we'll +call the X and Y axis now obviously you + + align:start position:0% +call the X and Y axis now obviously you + + + align:start position:0% +call the X and Y axis now obviously you +can move out from the point at which + + align:start position:0% +can move out from the point at which + + + align:start position:0% +can move out from the point at which +you're standing along the x axis you can + + align:start position:0% +you're standing along the x axis you can + + + align:start position:0% +you're standing along the x axis you can +move out in a direction along the Y AIS + + align:start position:0% +move out in a direction along the Y AIS + + + align:start position:0% +move out in a direction along the Y AIS +you can visualize that how rapidly the + + align:start position:0% +you can visualize that how rapidly the + + + align:start position:0% +you can visualize that how rapidly the +height above your head is changing As + + align:start position:0% +height above your head is changing As + + + align:start position:0% +height above your head is changing As +you move out certainly will depend on + + align:start position:0% +you move out certainly will depend on + + + align:start position:0% +you move out certainly will depend on +whether you're moving along the x- Axis + + align:start position:0% +whether you're moving along the x- Axis + + + align:start position:0% +whether you're moving along the x- Axis +or the Y AIS but the key point at least + + align:start position:0% +or the Y AIS but the key point at least + + + align:start position:0% +or the Y AIS but the key point at least +the key point from the point of view of + + align:start position:0% +the key point from the point of view of + + + align:start position:0% +the key point from the point of view of +today's lecture is the fact that why + + align:start position:0% +today's lecture is the fact that why + + + align:start position:0% +today's lecture is the fact that why +were you restricted to either of these + + align:start position:0% +were you restricted to either of these + + + align:start position:0% +were you restricted to either of these +two directions why couldn't you have + + align:start position:0% +two directions why couldn't you have + + + align:start position:0% +two directions why couldn't you have +moved in any one of infinitely many + + align:start position:0% +moved in any one of infinitely many + + + align:start position:0% +moved in any one of infinitely many +different directions namely from the + + align:start position:0% +different directions namely from the + + + align:start position:0% +different directions namely from the +point at which you're originating you + + align:start position:0% +point at which you're originating you + + + align:start position:0% +point at which you're originating you +can move in any direction at all because + + align:start position:0% +can move in any direction at all because + + + align:start position:0% +can move in any direction at all because +we're assuming at least that the floor + + align:start position:0% +we're assuming at least that the floor + + + align:start position:0% +we're assuming at least that the floor +on which you're standing is uh + + align:start position:0% +on which you're standing is uh + + + align:start position:0% +on which you're standing is uh +continuous it's unbroken you can move in + + align:start position:0% +continuous it's unbroken you can move in + + + align:start position:0% +continuous it's unbroken you can move in +these directions and the idea that you + + align:start position:0% +these directions and the idea that you + + + align:start position:0% +these directions and the idea that you +sort of get can be shown pictorially by + + align:start position:0% +sort of get can be shown pictorially by + + + align:start position:0% +sort of get can be shown pictorially by +saying look + + align:start position:0% +saying look + + + align:start position:0% +saying look +at let's assume that we're at the point + + align:start position:0% +at let's assume that we're at the point + + + align:start position:0% +at let's assume that we're at the point +a comma B we have this surface over our + + align:start position:0% +a comma B we have this surface over our + + + align:start position:0% +a comma B we have this surface over our +head just as we did before but now + + align:start position:0% +head just as we did before but now + + + align:start position:0% +head just as we did before but now +instead of picking a direction either + + align:start position:0% +instead of picking a direction either + + + align:start position:0% +instead of picking a direction either +parallel to the WX plane or to the Wy + + align:start position:0% +parallel to the WX plane or to the Wy + + + align:start position:0% +parallel to the WX plane or to the Wy +plane let's pick some arbitrary + + align:start position:0% +plane let's pick some arbitrary + + + align:start position:0% +plane let's pick some arbitrary +Direction s in which to move and now + + align:start position:0% +Direction s in which to move and now + + + align:start position:0% +Direction s in which to move and now +what I'm saying is if I now take the + + align:start position:0% +what I'm saying is if I now take the + + + align:start position:0% +what I'm saying is if I now take the +plane that passes is through + + align:start position:0% +plane that passes is through + + + align:start position:0% +plane that passes is through +this direction s perpendicular to the XY + + align:start position:0% +this direction s perpendicular to the XY + + + align:start position:0% +this direction s perpendicular to the XY +plane that plane will also intersect + + align:start position:0% +plane that plane will also intersect + + + align:start position:0% +plane that plane will also intersect +this surface passing through the point p + + align:start position:0% +this surface passing through the point p + + + align:start position:0% +this surface passing through the point p +0 I get a curve of intersection and I + + align:start position:0% +0 I get a curve of intersection and I + + + align:start position:0% +0 I get a curve of intersection and I +can talk about the slope of that + + align:start position:0% +can talk about the slope of that + + + align:start position:0% +can talk about the slope of that +particular curve see ultimately this is + + align:start position:0% +particular curve see ultimately this is + + + align:start position:0% +particular curve see ultimately this is +what we're going to be talking about now + + align:start position:0% +what we're going to be talking about now + + + align:start position:0% +what we're going to be talking about now +what is the slope of that particular + + align:start position:0% +what is the slope of that particular + + + align:start position:0% +what is the slope of that particular +curve well it's a derivative it's a + + align:start position:0% +curve well it's a derivative it's a + + + align:start position:0% +curve well it's a derivative it's a +derivative of w with respect to S where + + align:start position:0% +derivative of w with respect to S where + + + align:start position:0% +derivative of w with respect to S where +all of a sudden we've now Chen the S + + align:start position:0% +all of a sudden we've now Chen the S + + + align:start position:0% +all of a sudden we've now Chen the S +Direction over here to be what we're + + align:start position:0% +Direction over here to be what we're + + + align:start position:0% +Direction over here to be what we're +going to take our derivative with + + align:start position:0% +going to take our derivative with + + + align:start position:0% +going to take our derivative with +respect to in other words it seems to + + align:start position:0% +respect to in other words it seems to + + + align:start position:0% +respect to in other words it seems to +make sense to talk about the derivative + + align:start position:0% +make sense to talk about the derivative + + + align:start position:0% +make sense to talk about the derivative +of f in the direction of s evaluated at + + align:start position:0% +of f in the direction of s evaluated at + + + align:start position:0% +of f in the direction of s evaluated at +the point a comma B in other words just + + align:start position:0% +the point a comma B in other words just + + + align:start position:0% +the point a comma B in other words just +like we talked about F subx of a comma B + + align:start position:0% +like we talked about F subx of a comma B + + + align:start position:0% +like we talked about F subx of a comma B +and F suby of a comma B why can't we + + align:start position:0% +and F suby of a comma B why can't we + + + align:start position:0% +and F suby of a comma B why can't we +talk about the derivative of f evaluated + + align:start position:0% +talk about the derivative of f evaluated + + + align:start position:0% +talk about the derivative of f evaluated +at a comma B in the direction of s and + + align:start position:0% +at a comma B in the direction of s and + + + align:start position:0% +at a comma B in the direction of s and +if we want to correlate this with the + + align:start position:0% +if we want to correlate this with the + + + align:start position:0% +if we want to correlate this with the +notation in the text observe that we + + align:start position:0% +notation in the text observe that we + + + align:start position:0% +notation in the text observe that we +call that + + align:start position:0% +call that + + + align:start position:0% +call that +dwds by the way notice not the partial + + align:start position:0% +dwds by the way notice not the partial + + + align:start position:0% +dwds by the way notice not the partial +of w with respect to S but the + + align:start position:0% +of w with respect to S but the + + + align:start position:0% +of w with respect to S but the +derivative of w with respect to S + + align:start position:0% +derivative of w with respect to S + + + align:start position:0% +derivative of w with respect to S +remember the partials were essentially + + align:start position:0% +remember the partials were essentially + + + align:start position:0% +remember the partials were essentially +defined in terms of holding either X or + + align:start position:0% +defined in terms of holding either X or + + + align:start position:0% +defined in terms of holding either X or +Y constant notice that in our general + + align:start position:0% +Y constant notice that in our general + + + align:start position:0% +Y constant notice that in our general +directional derivative idea neither X + + align:start position:0% +directional derivative idea neither X + + + align:start position:0% +directional derivative idea neither X +nor Y is being held constant no notice + + align:start position:0% +nor Y is being held constant no notice + + + align:start position:0% +nor Y is being held constant no notice +that X and Y are varying as we move + + align:start position:0% +that X and Y are varying as we move + + + align:start position:0% +that X and Y are varying as we move +along s notice also by the way that once + + align:start position:0% +along s notice also by the way that once + + + align:start position:0% +along s notice also by the way that once +X and Y are restricted to move along s + + align:start position:0% +X and Y are restricted to move along s + + + align:start position:0% +X and Y are restricted to move along s +they are no longer independent variables + + align:start position:0% +they are no longer independent variables + + + align:start position:0% +they are no longer independent variables +it's a rather rather interesting point + + align:start position:0% +it's a rather rather interesting point + + + align:start position:0% +it's a rather rather interesting point +we talk about W being a function of the + + align:start position:0% +we talk about W being a function of the + + + align:start position:0% +we talk about W being a function of the +two independent variables X and Y but as + + align:start position:0% +two independent variables X and Y but as + + + align:start position:0% +two independent variables X and Y but as +soon as we pick that direction s in the + + align:start position:0% +soon as we pick that direction s in the + + + align:start position:0% +soon as we pick that direction s in the +XY plane X and Y have to be very + + align:start position:0% +XY plane X and Y have to be very + + + align:start position:0% +XY plane X and Y have to be very +specially related namely according to + + align:start position:0% +specially related namely according to + + + align:start position:0% +specially related namely according to +the equation of a straight line that + + align:start position:0% +the equation of a straight line that + + + align:start position:0% +the equation of a straight line that +determines s for that point to be on the + + align:start position:0% +determines s for that point to be on the + + + align:start position:0% +determines s for that point to be on the +line and that's why we talk about the + + align:start position:0% +line and that's why we talk about the + + + align:start position:0% +line and that's why we talk about the +WDS W is a function of a single variable + + align:start position:0% +WDS W is a function of a single variable + + + align:start position:0% +WDS W is a function of a single variable +once you restrict yourself to the + + align:start position:0% +once you restrict yourself to the + + + align:start position:0% +once you restrict yourself to the +particular direction s at any rate the + + align:start position:0% +particular direction s at any rate the + + + align:start position:0% +particular direction s at any rate the +question that we want to come to grips + + align:start position:0% +question that we want to come to grips + + + align:start position:0% +question that we want to come to grips +with is how do you find + + align:start position:0% +with is how do you find + + + align:start position:0% +with is how do you find +dwds well here again is the beauty of + + align:start position:0% +dwds well here again is the beauty of + + + align:start position:0% +dwds well here again is the beauty of +our logical structure by definition this + + align:start position:0% +our logical structure by definition this + + + align:start position:0% +our logical structure by definition this +is the same definition we knew early in + + align:start position:0% +is the same definition we knew early in + + + align:start position:0% +is the same definition we knew early in +part one of our course dwds by + + align:start position:0% +part one of our course dwds by + + + align:start position:0% +part one of our course dwds by +definition is the limit as Delta Del s + + align:start position:0% +definition is the limit as Delta Del s + + + align:start position:0% +definition is the limit as Delta Del s +approaches zero Delta W / Delta s now + + align:start position:0% +approaches zero Delta W / Delta s now + + + align:start position:0% +approaches zero Delta W / Delta s now +the thing is what's very difficult to + + align:start position:0% +the thing is what's very difficult to + + + align:start position:0% +the thing is what's very difficult to +compute in real life is Delta W after + + align:start position:0% +compute in real life is Delta W after + + + align:start position:0% +compute in real life is Delta W after +all this W being f ofx y f can be a very + + align:start position:0% +all this W being f ofx y f can be a very + + + align:start position:0% +all this W being f ofx y f can be a very +very complicated surface and to actually + + align:start position:0% +very complicated surface and to actually + + + align:start position:0% +very complicated surface and to actually +find the true change in W well heck we + + align:start position:0% +find the true change in W well heck we + + + align:start position:0% +find the true change in W well heck we +already saw this in part one when we + + align:start position:0% +already saw this in part one when we + + + align:start position:0% +already saw this in part one when we +compared this Delta y with Delta y tan + + align:start position:0% +compared this Delta y with Delta y tan + + + align:start position:0% +compared this Delta y with Delta y tan +to actually find the change in y was a + + align:start position:0% +to actually find the change in y was a + + + align:start position:0% +to actually find the change in y was a +much more difficult job than to find the + + align:start position:0% +much more difficult job than to find the + + + align:start position:0% +much more difficult job than to find the +change in y to the tangent line what + + align:start position:0% +change in y to the tangent line what + + + align:start position:0% +change in y to the tangent line what +we're saying here is look at we already + + align:start position:0% +we're saying here is look at we already + + + align:start position:0% +we're saying here is look at we already +know how to find the change in W not to + + align:start position:0% +know how to find the change in W not to + + + align:start position:0% +know how to find the change in W not to +the surface but to the plane which is + + align:start position:0% +the surface but to the plane which is + + + align:start position:0% +the surface but to the plane which is +tangent to the surface at our Point P + + align:start position:0% +tangent to the surface at our Point P + + + align:start position:0% +tangent to the surface at our Point P +Sub 0 in other words we have already + + align:start position:0% +Sub 0 in other words we have already + + + align:start position:0% +Sub 0 in other words we have already +discussed that Delta W1 is the partial + + align:start position:0% +discussed that Delta W1 is the partial + + + align:start position:0% +discussed that Delta W1 is the partial +of eff respect to X evaluated a comma B + + align:start position:0% +of eff respect to X evaluated a comma B + + + align:start position:0% +of eff respect to X evaluated a comma B +* Delta X plus the partial of effort + + align:start position:0% +* Delta X plus the partial of effort + + + align:start position:0% +* Delta X plus the partial of effort +respect to y * a at the point a comma B + + align:start position:0% +respect to y * a at the point a comma B + + + align:start position:0% +respect to y * a at the point a comma B +times Delta Y and now what we say is and + + align:start position:0% +times Delta Y and now what we say is and + + + align:start position:0% +times Delta Y and now what we say is and +I've written this to accentuate it + + align:start position:0% +I've written this to accentuate it + + + align:start position:0% +I've written this to accentuate it +because I have to talk very strongly + + align:start position:0% +because I have to talk very strongly + + + align:start position:0% +because I have to talk very strongly +about this it's a point that if I don't + + align:start position:0% +about this it's a point that if I don't + + + align:start position:0% +about this it's a point that if I don't +make you will most of you at least will + + align:start position:0% +make you will most of you at least will + + + align:start position:0% +make you will most of you at least will +allow me to slip over this and not even + + align:start position:0% +allow me to slip over this and not even + + + align:start position:0% +allow me to slip over this and not even +notice that I've missed something very + + align:start position:0% +notice that I've missed something very + + + align:start position:0% +notice that I've missed something very +very crucial but let me assume that I + + align:start position:0% +very crucial but let me assume that I + + + align:start position:0% +very crucial but let me assume that I +can approximate Delta W by Delta W Tan + + align:start position:0% +can approximate Delta W by Delta W Tan + + + align:start position:0% +can approximate Delta W by Delta W Tan +in other words let's suppose that Delta + + align:start position:0% +in other words let's suppose that Delta + + + align:start position:0% +in other words let's suppose that Delta +W is a reasonable or Delta W tan is a + + align:start position:0% +W is a reasonable or Delta W tan is a + + + align:start position:0% +W is a reasonable or Delta W tan is a +reasonable approximation for Delta W you + + align:start position:0% +reasonable approximation for Delta W you + + + align:start position:0% +reasonable approximation for Delta W you +say well you know what's such a big + + align:start position:0% +say well you know what's such a big + + + align:start position:0% +say well you know what's such a big +assumption about that and I'm going to + + align:start position:0% +assumption about that and I'm going to + + + align:start position:0% +assumption about that and I'm going to +save that for the very last part of the + + align:start position:0% +save that for the very last part of the + + + align:start position:0% +save that for the very last part of the +lecture because my belief is that the + + align:start position:0% +lecture because my belief is that the + + + align:start position:0% +lecture because my belief is that the +subtlety is so great that I would like + + align:start position:0% +subtlety is so great that I would like + + + align:start position:0% +subtlety is so great that I would like +to leave that for the very end and go + + align:start position:0% +to leave that for the very end and go + + + align:start position:0% +to leave that for the very end and go +through as if the subtlety didn't exist + + align:start position:0% +through as if the subtlety didn't exist + + + align:start position:0% +through as if the subtlety didn't exist +so you get the computational feeling as + + align:start position:0% +so you get the computational feeling as + + + align:start position:0% +so you get the computational feeling as +to what's going on here but here's the + + align:start position:0% +to what's going on here but here's the + + + align:start position:0% +to what's going on here but here's the +interesting point notice that Delta W is + + align:start position:0% +interesting point notice that Delta W is + + + align:start position:0% +interesting point notice that Delta W is +a change in W As you move from the point + + align:start position:0% +a change in W As you move from the point + + + align:start position:0% +a change in W As you move from the point +a comma B to some other point in the + + align:start position:0% +a comma B to some other point in the + + + align:start position:0% +a comma B to some other point in the +plane it's a change in height now + + align:start position:0% +plane it's a change in height now + + + align:start position:0% +plane it's a change in height now +obviously that change in W is going to + + align:start position:0% +obviously that change in W is going to + + + align:start position:0% +obviously that change in W is going to +depend very strongly on what direction + + align:start position:0% +depend very strongly on what direction + + + align:start position:0% +depend very strongly on what direction +you're moving in on the other hand how + + align:start position:0% +you're moving in on the other hand how + + + align:start position:0% +you're moving in on the other hand how +was Delta wtan computed Delta W tan was + + align:start position:0% +was Delta wtan computed Delta W tan was + + + align:start position:0% +was Delta wtan computed Delta W tan was +computed just by knowing two special + + align:start position:0% +computed just by knowing two special + + + align:start position:0% +computed just by knowing two special +partial derivatives are two special + + align:start position:0% +partial derivatives are two special + + + align:start position:0% +partial derivatives are two special +directional derivatives known as the + + align:start position:0% +directional derivatives known as the + + + align:start position:0% +directional derivatives known as the +partial derivatives you see notied that + + align:start position:0% +partial derivatives you see notied that + + + align:start position:0% +partial derivatives you see notied that +to get Delta W10 I have made the + + align:start position:0% +to get Delta W10 I have made the + + + align:start position:0% +to get Delta W10 I have made the +assumption that all I have to know is + + align:start position:0% +assumption that all I have to know is + + + align:start position:0% +assumption that all I have to know is +what's happening in the X Direction and + + align:start position:0% +what's happening in the X Direction and + + + align:start position:0% +what's happening in the X Direction and +what's happening in the y direction + + align:start position:0% +what's happening in the y direction + + + align:start position:0% +what's happening in the y direction +everything else being determined from + + align:start position:0% +everything else being determined from + + + align:start position:0% +everything else being determined from +the function evaluated at a comma B so + + align:start position:0% +the function evaluated at a comma B so + + + align:start position:0% +the function evaluated at a comma B so +this is really a very strong assumption + + align:start position:0% +this is really a very strong assumption + + + align:start position:0% +this is really a very strong assumption +that Delta W is determined pretty + + align:start position:0% +that Delta W is determined pretty + + + align:start position:0% +that Delta W is determined pretty +closely by Delta W tan and it turns out + + align:start position:0% +closely by Delta W tan and it turns out + + + align:start position:0% +closely by Delta W tan and it turns out +to be almost universally true and we're + + align:start position:0% +to be almost universally true and we're + + + align:start position:0% +to be almost universally true and we're +going to save that part as I say for the + + align:start position:0% +going to save that part as I say for the + + + align:start position:0% +going to save that part as I say for the +end but for now let's suppose that we + + align:start position:0% +end but for now let's suppose that we + + + align:start position:0% +end but for now let's suppose that we +are allowed to replace Delta W by Delta + + align:start position:0% +are allowed to replace Delta W by Delta + + + align:start position:0% +are allowed to replace Delta W by Delta +W10 if we do that and we go back to our + + align:start position:0% +W10 if we do that and we go back to our + + + align:start position:0% +W10 if we do that and we go back to our +definition for + + align:start position:0% +definition for + + + align:start position:0% +definition for +dwds namely the limit as Delta s + + align:start position:0% +dwds namely the limit as Delta s + + + align:start position:0% +dwds namely the limit as Delta s +approaches zero Delta W / Delta s we now + + align:start position:0% +approaches zero Delta W / Delta s we now + + + align:start position:0% +approaches zero Delta W / Delta s we now +replace Delta W by Delta W tan and + + align:start position:0% +replace Delta W by Delta W tan and + + + align:start position:0% +replace Delta W by Delta W tan and +divide through by Delta s to find Delta + + align:start position:0% +divide through by Delta s to find Delta + + + align:start position:0% +divide through by Delta s to find Delta +W over Delta s we + + align:start position:0% +W over Delta s we + + + align:start position:0% +W over Delta s we +have assuming that this is a legal + + align:start position:0% +have assuming that this is a legal + + + align:start position:0% +have assuming that this is a legal +substitution that Delta W over Delta s + + align:start position:0% +substitution that Delta W over Delta s + + + align:start position:0% +substitution that Delta W over Delta s +is the partial of f respect to X of + + align:start position:0% +is the partial of f respect to X of + + + align:start position:0% +is the partial of f respect to X of +evaluated a comma B time Delta x / Delta + + align:start position:0% +evaluated a comma B time Delta x / Delta + + + align:start position:0% +evaluated a comma B time Delta x / Delta +S Plus the partial of f respect to Y + + align:start position:0% +S Plus the partial of f respect to Y + + + align:start position:0% +S Plus the partial of f respect to Y +evaluated a comma btimes the partial of + + align:start position:0% +evaluated a comma btimes the partial of + + + align:start position:0% +evaluated a comma btimes the partial of +times the change in y divided by the + + align:start position:0% +times the change in y divided by the + + + align:start position:0% +times the change in y divided by the +change in s Delta y ided Delta s now + + align:start position:0% +change in s Delta y ided Delta s now + + + align:start position:0% +change in s Delta y ided Delta s now +remember in the S Direction X and Y are + + align:start position:0% +remember in the S Direction X and Y are + + + align:start position:0% +remember in the S Direction X and Y are +not independent variables in fact how + + align:start position:0% +not independent variables in fact how + + + align:start position:0% +not independent variables in fact how +are they related let's isolate our + + align:start position:0% +are they related let's isolate our + + + align:start position:0% +are they related let's isolate our +little diagram here so that we see in + + align:start position:0% +little diagram here so that we see in + + + align:start position:0% +little diagram here so that we see in +what direction we're moving here we're + + align:start position:0% +what direction we're moving here we're + + + align:start position:0% +what direction we're moving here we're +starting at the point a comma B and by + + align:start position:0% +starting at the point a comma B and by + + + align:start position:0% +starting at the point a comma B and by +the way to get the proper orientation + + align:start position:0% +the way to get the proper orientation + + + align:start position:0% +the way to get the proper orientation +here as I've drawn the XY plane here + + align:start position:0% +here as I've drawn the XY plane here + + + align:start position:0% +here as I've drawn the XY plane here +imagine the surface coming out from the + + align:start position:0% +imagine the surface coming out from the + + + align:start position:0% +imagine the surface coming out from the +Blackboard in other words the height is + + align:start position:0% +Blackboard in other words the height is + + + align:start position:0% +Blackboard in other words the height is +really being measured away from the + + align:start position:0% +really being measured away from the + + + align:start position:0% +really being measured away from the +Blackboard here that's where my Surface + + align:start position:0% +Blackboard here that's where my Surface + + + align:start position:0% +Blackboard here that's where my Surface +is I move in the direction of s here is + + align:start position:0% +is I move in the direction of s here is + + + align:start position:0% +is I move in the direction of s here is +a Delta X here is a Delta y s has a + + align:start position:0% +a Delta X here is a Delta y s has a + + + align:start position:0% +a Delta X here is a Delta y s has a +constant Direction a constant slope it's + + align:start position:0% +constant Direction a constant slope it's + + + align:start position:0% +constant Direction a constant slope it's +a straight line call the angle that it + + align:start position:0% +a straight line call the angle that it + + + align:start position:0% +a straight line call the angle that it +makes with the Positive xais Fe no noce + + align:start position:0% +makes with the Positive xais Fe no noce + + + align:start position:0% +makes with the Positive xais Fe no noce +that no matter how big Delta X and Delta + + align:start position:0% +that no matter how big Delta X and Delta + + + align:start position:0% +that no matter how big Delta X and Delta +y are they are related by similar + + align:start position:0% +y are they are related by similar + + + align:start position:0% +y are they are related by similar +triangles to what that Delta x divided + + align:start position:0% +triangles to what that Delta x divided + + + align:start position:0% +triangles to what that Delta x divided +Delta s will always be cosine V and + + align:start position:0% +Delta s will always be cosine V and + + + align:start position:0% +Delta s will always be cosine V and +Delta y / Delta s will always be sin Fe + + align:start position:0% +Delta y / Delta s will always be sin Fe + + + align:start position:0% +Delta y / Delta s will always be sin Fe +and therefore if I replace Delta x / + + align:start position:0% +and therefore if I replace Delta x / + + + align:start position:0% +and therefore if I replace Delta x / +Delta s by cosine Fe Delta y / Delta s + + align:start position:0% +Delta s by cosine Fe Delta y / Delta s + + + align:start position:0% +Delta s by cosine Fe Delta y / Delta s +by sin Fe I obtain that what Delta W / + + align:start position:0% +by sin Fe I obtain that what Delta W / + + + align:start position:0% +by sin Fe I obtain that what Delta W / +Delta s is is equal to the partial of + + align:start position:0% +Delta s is is equal to the partial of + + + align:start position:0% +Delta s is is equal to the partial of +effort respect to X evaluated at Point a + + align:start position:0% +effort respect to X evaluated at Point a + + + align:start position:0% +effort respect to X evaluated at Point a +comma B time the cosine of Fe plus the + + align:start position:0% +comma B time the cosine of Fe plus the + + + align:start position:0% +comma B time the cosine of Fe plus the +partial of effort respect to Y evaluated + + align:start position:0% +partial of effort respect to Y evaluated + + + align:start position:0% +partial of effort respect to Y evaluated +a comma B times the sign of Fe where Fe + + align:start position:0% +a comma B times the sign of Fe where Fe + + + align:start position:0% +a comma B times the sign of Fe where Fe +is the what the angle that the direction + + align:start position:0% +is the what the angle that the direction + + + align:start position:0% +is the what the angle that the direction +s makes with the Positive x-axis at any + + align:start position:0% +s makes with the Positive x-axis at any + + + align:start position:0% +s makes with the Positive x-axis at any +rate notice by the way that these things + + align:start position:0% +rate notice by the way that these things + + + align:start position:0% +rate notice by the way that these things +are all constants once s is chosen once + + align:start position:0% +are all constants once s is chosen once + + + align:start position:0% +are all constants once s is chosen once +the point a comma B is fixed therefore + + align:start position:0% +the point a comma B is fixed therefore + + + align:start position:0% +the point a comma B is fixed therefore +when I pass to the Limit nothing really + + align:start position:0% +when I pass to the Limit nothing really + + + align:start position:0% +when I pass to the Limit nothing really +changes is in other words this thing + + align:start position:0% +changes is in other words this thing + + + align:start position:0% +changes is in other words this thing +that I'm calling the directional + + align:start position:0% +that I'm calling the directional + + + align:start position:0% +that I'm calling the directional +derivative F of f in the direction of s + + align:start position:0% +derivative F of f in the direction of s + + + align:start position:0% +derivative F of f in the direction of s +evaluated at a comma B turns out to be + + align:start position:0% +evaluated at a comma B turns out to be + + + align:start position:0% +evaluated at a comma B turns out to be +what the partial of effort respect to X + + align:start position:0% +what the partial of effort respect to X + + + align:start position:0% +what the partial of effort respect to X +at the point a comma B time cosine Fe + + align:start position:0% +at the point a comma B time cosine Fe + + + align:start position:0% +at the point a comma B time cosine Fe +plus the partial of effort respect to Y + + align:start position:0% +plus the partial of effort respect to Y + + + align:start position:0% +plus the partial of effort respect to Y +evaluated a comma B times the sign of + + align:start position:0% +evaluated a comma B times the sign of + + + align:start position:0% +evaluated a comma B times the sign of +fee and what I'd like you to notice is + + align:start position:0% +fee and what I'd like you to notice is + + + align:start position:0% +fee and what I'd like you to notice is +that in these two terms one factor of + + align:start position:0% +that in these two terms one factor of + + + align:start position:0% +that in these two terms one factor of +each term is determined solely by the + + align:start position:0% +each term is determined solely by the + + + align:start position:0% +each term is determined solely by the +point a comma B in other words + + align:start position:0% +point a comma B in other words + + + align:start position:0% +point a comma B in other words +notice that these two factors here are + + align:start position:0% +notice that these two factors here are + + + align:start position:0% +notice that these two factors here are +just partial derivatives and have + + align:start position:0% +just partial derivatives and have + + + align:start position:0% +just partial derivatives and have +nothing to do with Direction they're + + align:start position:0% +nothing to do with Direction they're + + + align:start position:0% +nothing to do with Direction they're +determined solely by the choice of the + + align:start position:0% +determined solely by the choice of the + + + align:start position:0% +determined solely by the choice of the +function f and the point a comma B on + + align:start position:0% +function f and the point a comma B on + + + align:start position:0% +function f and the point a comma B on +the other hand notice that these two + + align:start position:0% +the other hand notice that these two + + + align:start position:0% +the other hand notice that these two +factors cosine Fe and sin Fe have + + align:start position:0% +factors cosine Fe and sin Fe have + + + align:start position:0% +factors cosine Fe and sin Fe have +nothing to do with f and have to do only + + align:start position:0% +nothing to do with f and have to do only + + + align:start position:0% +nothing to do with f and have to do only +with the direction s itself which again + + align:start position:0% +with the direction s itself which again + + + align:start position:0% +with the direction s itself which again +should make intuitive sense to you that + + align:start position:0% +should make intuitive sense to you that + + + align:start position:0% +should make intuitive sense to you that +if you're asking in terms of the surface + + align:start position:0% +if you're asking in terms of the surface + + + align:start position:0% +if you're asking in terms of the surface +being up over your head for a + + align:start position:0% +being up over your head for a + + + align:start position:0% +being up over your head for a +directional derivative obviously once + + align:start position:0% +directional derivative obviously once + + + align:start position:0% +directional derivative obviously once +the surface is given the directional + + align:start position:0% +the surface is given the directional + + + align:start position:0% +the surface is given the directional +derivative should depend on two things + + align:start position:0% +derivative should depend on two things + + + align:start position:0% +derivative should depend on two things +one what point you start at and the + + align:start position:0% +one what point you start at and the + + + align:start position:0% +one what point you start at and the +other what direction you move in once + + align:start position:0% +other what direction you move in once + + + align:start position:0% +other what direction you move in once +you've started at that particular point + + align:start position:0% +you've started at that particular point + + + align:start position:0% +you've started at that particular point +and what direction you move in has + + align:start position:0% +and what direction you move in has + + + align:start position:0% +and what direction you move in has +nothing to do with what the surface + + align:start position:0% +nothing to do with what the surface + + + align:start position:0% +nothing to do with what the surface +looks like over your head at any rate + + align:start position:0% +looks like over your head at any rate + + + align:start position:0% +looks like over your head at any rate +what we now do is invoke our DOT product + + align:start position:0% +what we now do is invoke our DOT product + + + align:start position:0% +what we now do is invoke our DOT product +notation in other words this little + + align:start position:0% +notation in other words this little + + + align:start position:0% +notation in other words this little +trick that we talked about when we do + + align:start position:0% +trick that we talked about when we do + + + align:start position:0% +trick that we talked about when we do +products this particular sum can be + + align:start position:0% +products this particular sum can be + + + align:start position:0% +products this particular sum can be +written + + align:start position:0% +written + + + align:start position:0% +written +very suggestively as the dot product of + + align:start position:0% +very suggestively as the dot product of + + + align:start position:0% +very suggestively as the dot product of +two vectors namely I will write this as + + align:start position:0% +two vectors namely I will write this as + + + align:start position:0% +two vectors namely I will write this as +what the vector whose components are F + + align:start position:0% +what the vector whose components are F + + + align:start position:0% +what the vector whose components are F +subx and F suby dotted with the vector + + align:start position:0% +subx and F suby dotted with the vector + + + align:start position:0% +subx and F suby dotted with the vector +whose components are cosine Fe and sin + + align:start position:0% +whose components are cosine Fe and sin + + + align:start position:0% +whose components are cosine Fe and sin +Fe because remember when you dot two + + align:start position:0% +Fe because remember when you dot two + + + align:start position:0% +Fe because remember when you dot two +vectors in cartisian coordinates you + + align:start position:0% +vectors in cartisian coordinates you + + + align:start position:0% +vectors in cartisian coordinates you +multiply them coefficient by coefficient + + align:start position:0% +multiply them coefficient by coefficient + + + align:start position:0% +multiply them coefficient by coefficient +to make a long story short + + align:start position:0% +to make a long story short + + + align:start position:0% +to make a long story short +dwds is what it's this Vector F sub + + align:start position:0% +dwds is what it's this Vector F sub + + + align:start position:0% +dwds is what it's this Vector F sub +whose I component is f subx evaluated a + + align:start position:0% +whose I component is f subx evaluated a + + + align:start position:0% +whose I component is f subx evaluated a +comma B whose J component is f suby + + align:start position:0% +comma B whose J component is f suby + + + align:start position:0% +comma B whose J component is f suby +evaluated a comma B I call that Vector G + + align:start position:0% +evaluated a comma B I call that Vector G + + + align:start position:0% +evaluated a comma B I call that Vector G +of a comma B I'm going to give that a + + align:start position:0% +of a comma B I'm going to give that a + + + align:start position:0% +of a comma B I'm going to give that a +special name a little bit later but for + + align:start position:0% +special name a little bit later but for + + + align:start position:0% +special name a little bit later but for +now it's very important to notice that + + align:start position:0% +now it's very important to notice that + + + align:start position:0% +now it's very important to notice that +this is not a number it's an ordered + + align:start position:0% +this is not a number it's an ordered + + + align:start position:0% +this is not a number it's an ordered +pair of numbers in other words it's a + + align:start position:0% +pair of numbers in other words it's a + + + align:start position:0% +pair of numbers in other words it's a +vector and if you want to think of this + + align:start position:0% +vector and if you want to think of this + + + align:start position:0% +vector and if you want to think of this +as a vector what we saying is what think + + align:start position:0% +as a vector what we saying is what think + + + align:start position:0% +as a vector what we saying is what think +of the vector whose I component is the + + align:start position:0% +of the vector whose I component is the + + + align:start position:0% +of the vector whose I component is the +partial of f respect to X evaluated a + + align:start position:0% +partial of f respect to X evaluated a + + + align:start position:0% +partial of f respect to X evaluated a +comma B whose J component is f suby + + align:start position:0% +comma B whose J component is f suby + + + align:start position:0% +comma B whose J component is f suby +evaluated a comma B notice that these + + align:start position:0% +evaluated a comma B notice that these + + + align:start position:0% +evaluated a comma B notice that these +are numbers because A and B are fixed + + align:start position:0% +are numbers because A and B are fixed + + + align:start position:0% +are numbers because A and B are fixed +constants here therefore this Vector G + + align:start position:0% +constants here therefore this Vector G + + + align:start position:0% +constants here therefore this Vector G +of a comma B is a constant vector and + + align:start position:0% +of a comma B is a constant vector and + + + align:start position:0% +of a comma B is a constant vector and +it's in the XY plane it's a twouble on + + align:start position:0% +it's in the XY plane it's a twouble on + + + align:start position:0% +it's in the XY plane it's a twouble on +the other hand the other Vector cosine + + align:start position:0% +the other hand the other Vector cosine + + + align:start position:0% +the other hand the other Vector cosine +Fe sin Fe hopefully you recognize by now + + align:start position:0% +Fe sin Fe hopefully you recognize by now + + + align:start position:0% +Fe sin Fe hopefully you recognize by now +is nothing more than the unit Vector in + + align:start position:0% +is nothing more than the unit Vector in + + + align:start position:0% +is nothing more than the unit Vector in +the direction of s you see this is the + + align:start position:0% +the direction of s you see this is the + + + align:start position:0% +the direction of s you see this is the +unit Vector in the direction of s so if + + align:start position:0% +unit Vector in the direction of s so if + + + align:start position:0% +unit Vector in the direction of s so if +I now abbr use my abbreviation dwds + + align:start position:0% +I now abbr use my abbreviation dwds + + + align:start position:0% +I now abbr use my abbreviation dwds +evaluated at a comma B in other words + + align:start position:0% +evaluated at a comma B in other words + + + align:start position:0% +evaluated at a comma B in other words +the directional derivative of w in the + + align:start position:0% +the directional derivative of w in the + + + align:start position:0% +the directional derivative of w in the +direction of s evaluated a comma B is + + align:start position:0% +direction of s evaluated a comma B is + + + align:start position:0% +direction of s evaluated a comma B is +just my Vector G of a comma B dotted + + align:start position:0% +just my Vector G of a comma B dotted + + + align:start position:0% +just my Vector G of a comma B dotted +with the unit Vector in the direction of + + align:start position:0% +with the unit Vector in the direction of + + + align:start position:0% +with the unit Vector in the direction of +s now observe two things first of all + + align:start position:0% +s now observe two things first of all + + + align:start position:0% +s now observe two things first of all +when you dot this is a constant I can't + + align:start position:0% +when you dot this is a constant I can't + + + align:start position:0% +when you dot this is a constant I can't +change this once A and B are given this + + align:start position:0% +change this once A and B are given this + + + align:start position:0% +change this once A and B are given this +is fixed so all I can vary is U Subs but + + align:start position:0% +is fixed so all I can vary is U Subs but + + + align:start position:0% +is fixed so all I can vary is U Subs but +U Subs is a unit Vector so the only way + + align:start position:0% +U Subs is a unit Vector so the only way + + + align:start position:0% +U Subs is a unit Vector so the only way +I can vary U Subs is to change its + + align:start position:0% +I can vary U Subs is to change its + + + align:start position:0% +I can vary U Subs is to change its +direction notice that for two vectors of + + align:start position:0% +direction notice that for two vectors of + + + align:start position:0% +direction notice that for two vectors of +constant magnitude their dot product is + + align:start position:0% +constant magnitude their dot product is + + + align:start position:0% +constant magnitude their dot product is +maximum when the two vectors are + + align:start position:0% +maximum when the two vectors are + + + align:start position:0% +maximum when the two vectors are +parallel in other words this will be as + + align:start position:0% +parallel in other words this will be as + + + align:start position:0% +parallel in other words this will be as +big as possible when U Subs is chosen to + + align:start position:0% +big as possible when U Subs is chosen to + + + align:start position:0% +big as possible when U Subs is chosen to +be in the direction of my Vector G in + + align:start position:0% +be in the direction of my Vector G in + + + align:start position:0% +be in the direction of my Vector G in +other words the WDS at a comma B is + + align:start position:0% +other words the WDS at a comma B is + + + align:start position:0% +other words the WDS at a comma B is +maximum in the direction of G of a comma + + align:start position:0% +maximum in the direction of G of a comma + + + align:start position:0% +maximum in the direction of G of a comma +B that's the first thing to observe the + + align:start position:0% +B that's the first thing to observe the + + + align:start position:0% +B that's the first thing to observe the +second thing is is that when they act + + align:start position:0% +second thing is is that when they act + + + align:start position:0% +second thing is is that when they act +parallel the cosine of the angle between + + align:start position:0% +parallel the cosine of the angle between + + + align:start position:0% +parallel the cosine of the angle between +them is one so the magnitude of this + + align:start position:0% +them is one so the magnitude of this + + + align:start position:0% +them is one so the magnitude of this +Vector will just be the product of these + + align:start position:0% +Vector will just be the product of these + + + align:start position:0% +Vector will just be the product of these +two magnitudes but the magnitude of U + + align:start position:0% +two magnitudes but the magnitude of U + + + align:start position:0% +two magnitudes but the magnitude of U +Subs U Subs being a unit Vector is one + + align:start position:0% +Subs U Subs being a unit Vector is one + + + align:start position:0% +Subs U Subs being a unit Vector is one +therefore the maximum magnitude not only + + align:start position:0% +therefore the maximum magnitude not only + + + align:start position:0% +therefore the maximum magnitude not only +occurs in the direction of G but it is + + align:start position:0% +occurs in the direction of G but it is + + + align:start position:0% +occurs in the direction of G but it is +also numerically equal to the magnitude + + align:start position:0% +also numerically equal to the magnitude + + + align:start position:0% +also numerically equal to the magnitude +of G in other words the maximum value of + + align:start position:0% +of G in other words the maximum value of + + + align:start position:0% +of G in other words the maximum value of +dwds evaluated a comma B not only occurs + + align:start position:0% +dwds evaluated a comma B not only occurs + + + align:start position:0% +dwds evaluated a comma B not only occurs +in the direction of the vector G but + + align:start position:0% +in the direction of the vector G but + + + align:start position:0% +in the direction of the vector G but +that maximum magnitude is the magnitude + + align:start position:0% +that maximum magnitude is the magnitude + + + align:start position:0% +that maximum magnitude is the magnitude +of G evaluated at a comma B for that + + align:start position:0% +of G evaluated at a comma B for that + + + align:start position:0% +of G evaluated at a comma B for that +reason G of a comma B is given a very + + align:start position:0% +reason G of a comma B is given a very + + + align:start position:0% +reason G of a comma B is given a very +important name and I decided to hold off + + align:start position:0% +important name and I decided to hold off + + + align:start position:0% +important name and I decided to hold off +on the name until as late as possible so + + align:start position:0% +on the name until as late as possible so + + + align:start position:0% +on the name until as late as possible so +that the name wouldn't frighten you but + + align:start position:0% +that the name wouldn't frighten you but + + + align:start position:0% +that the name wouldn't frighten you but +the name is the gradient Vector in other + + align:start position:0% +the name is the gradient Vector in other + + + align:start position:0% +the name is the gradient Vector in other +words the vector G of a comma B is + + align:start position:0% +words the vector G of a comma B is + + + align:start position:0% +words the vector G of a comma B is +called the gradient of F at a comma B + + align:start position:0% +called the gradient of F at a comma B + + + align:start position:0% +called the gradient of F at a comma B +and it's usually written in this + + align:start position:0% +and it's usually written in this + + + align:start position:0% +and it's usually written in this +notation an upside down Delta it's + + align:start position:0% +notation an upside down Delta it's + + + align:start position:0% +notation an upside down Delta it's +called Dell usually with an arrow over + + align:start position:0% +called Dell usually with an arrow over + + + align:start position:0% +called Dell usually with an arrow over +it or in boldfaced print in a text and + + align:start position:0% +it or in boldfaced print in a text and + + + align:start position:0% +it or in boldfaced print in a text and +it's written this way and it's read what + + align:start position:0% +it's written this way and it's read what + + + align:start position:0% +it's written this way and it's read what +the gradient of f evaluated a comma B + + align:start position:0% +the gradient of f evaluated a comma B + + + align:start position:0% +the gradient of f evaluated a comma B +what is the gradient of f evaluated a + + align:start position:0% +what is the gradient of f evaluated a + + + align:start position:0% +what is the gradient of f evaluated a +comma B it's the vector which gives you + + align:start position:0% +comma B it's the vector which gives you + + + align:start position:0% +comma B it's the vector which gives you +the hint as to how to compute the + + align:start position:0% +the hint as to how to compute the + + + align:start position:0% +the hint as to how to compute the +directional derivative in any direction + + align:start position:0% +directional derivative in any direction + + + align:start position:0% +directional derivative in any direction +that you wish namely in terms of the + + align:start position:0% +that you wish namely in terms of the + + + align:start position:0% +that you wish namely in terms of the +gradient Vector the directional + + align:start position:0% +gradient Vector the directional + + + align:start position:0% +gradient Vector the directional +derivative of f of f in the direction of + + align:start position:0% +derivative of f of f in the direction of + + + align:start position:0% +derivative of f of f in the direction of +s evaluated a comma B is the gradient of + + align:start position:0% +s evaluated a comma B is the gradient of + + + align:start position:0% +s evaluated a comma B is the gradient of +f evaluated a comma B dotted with the + + align:start position:0% +f evaluated a comma B dotted with the + + + align:start position:0% +f evaluated a comma B dotted with the +unit Vector in the direction s by the + + align:start position:0% +unit Vector in the direction s by the + + + align:start position:0% +unit Vector in the direction s by the +way you may recall that when you dot a + + align:start position:0% +way you may recall that when you dot a + + + align:start position:0% +way you may recall that when you dot a +vector with a unit Vector you get the + + align:start position:0% +vector with a unit Vector you get the + + + align:start position:0% +vector with a unit Vector you get the +projection of that Vector in the + + align:start position:0% +projection of that Vector in the + + + align:start position:0% +projection of that Vector in the +direction of the unit Vector in other + + align:start position:0% +direction of the unit Vector in other + + + align:start position:0% +direction of the unit Vector in other +words the directional derivative another + + align:start position:0% +words the directional derivative another + + + align:start position:0% +words the directional derivative another +way of looking at this physically is + + align:start position:0% +way of looking at this physically is + + + align:start position:0% +way of looking at this physically is +nothing more than the projection of the + + align:start position:0% +nothing more than the projection of the + + + align:start position:0% +nothing more than the projection of the +gradient Vector onto the given direction + + align:start position:0% +gradient Vector onto the given direction + + + align:start position:0% +gradient Vector onto the given direction +in which you moving and the important + + align:start position:0% +in which you moving and the important + + + align:start position:0% +in which you moving and the important +point is that this particular definition + + align:start position:0% +point is that this particular definition + + + align:start position:0% +point is that this particular definition +does not depend on our coordinate system + + align:start position:0% +does not depend on our coordinate system + + + align:start position:0% +does not depend on our coordinate system +what is interesting is that in cartisian + + align:start position:0% +what is interesting is that in cartisian + + + align:start position:0% +what is interesting is that in cartisian +coordinates there is a very simple way + + align:start position:0% +coordinates there is a very simple way + + + align:start position:0% +coordinates there is a very simple way +of computing the gradient Vector namely + + align:start position:0% +of computing the gradient Vector namely + + + align:start position:0% +of computing the gradient Vector namely +the I component of the gradient Vector + + align:start position:0% +the I component of the gradient Vector + + + align:start position:0% +the I component of the gradient Vector +is just a partial of f with respect to X + + align:start position:0% +is just a partial of f with respect to X + + + align:start position:0% +is just a partial of f with respect to X +and the J component is just a partial of + + align:start position:0% +and the J component is just a partial of + + + align:start position:0% +and the J component is just a partial of +f with respect to Y but that was a very + + align:start position:0% +f with respect to Y but that was a very + + + align:start position:0% +f with respect to Y but that was a very +special case because you see I and X + + align:start position:0% +special case because you see I and X + + + align:start position:0% +special case because you see I and X +happen to have the same direction as do + + align:start position:0% +happen to have the same direction as do + + + align:start position:0% +happen to have the same direction as do +y and J for arbitrary coordinate systems + + align:start position:0% +y and J for arbitrary coordinate systems + + + align:start position:0% +y and J for arbitrary coordinate systems +this need not be true and I'm going to + + align:start position:0% +this need not be true and I'm going to + + + align:start position:0% +this need not be true and I'm going to +drill you on that in the exercises but + + align:start position:0% +drill you on that in the exercises but + + + align:start position:0% +drill you on that in the exercises but +in other words what I'm saying is + + align:start position:0% +in other words what I'm saying is + + + align:start position:0% +in other words what I'm saying is +remember the gradient Vector in terms of + + align:start position:0% +remember the gradient Vector in terms of + + + align:start position:0% +remember the gradient Vector in terms of +a maximum directional derivative don't + + align:start position:0% +a maximum directional derivative don't + + + align:start position:0% +a maximum directional derivative don't +memorize it as a formula because if you + + align:start position:0% +memorize it as a formula because if you + + + align:start position:0% +memorize it as a formula because if you +do you're going to get in trouble for + + align:start position:0% +do you're going to get in trouble for + + + align:start position:0% +do you're going to get in trouble for +example if I were to give my Surface in + + align:start position:0% +example if I were to give my Surface in + + + align:start position:0% +example if I were to give my Surface in +polar coordinates say w is some function + + align:start position:0% +polar coordinates say w is some function + + + align:start position:0% +polar coordinates say w is some function +of r and Theta then it turns out and + + align:start position:0% +of r and Theta then it turns out and + + + align:start position:0% +of r and Theta then it turns out and +there's an excise on this in the notes + + align:start position:0% +there's an excise on this in the notes + + + align:start position:0% +there's an excise on this in the notes +that the gradient of f is the partial of + + align:start position:0% +that the gradient of f is the partial of + + + align:start position:0% +that the gradient of f is the partial of +w with respect to R time U subr plus and + + align:start position:0% +w with respect to R time U subr plus and + + + align:start position:0% +w with respect to R time U subr plus and +here's the big difference 1 / R time the + + align:start position:0% +here's the big difference 1 / R time the + + + align:start position:0% +here's the big difference 1 / R time the +partial of w with respect to Theta time + + align:start position:0% +partial of w with respect to Theta time + + + align:start position:0% +partial of w with respect to Theta time +U sub Theta in other words the gradient + + align:start position:0% +U sub Theta in other words the gradient + + + align:start position:0% +U sub Theta in other words the gradient +Vector is not the partial of w with + + align:start position:0% +Vector is not the partial of w with + + + align:start position:0% +Vector is not the partial of w with +respect to R * U subr plus the partial + + align:start position:0% +respect to R * U subr plus the partial + + + align:start position:0% +respect to R * U subr plus the partial +of w with respect to Theta time U sub + + align:start position:0% +of w with respect to Theta time U sub + + + align:start position:0% +of w with respect to Theta time U sub +Theta in other words you don't just + + align:start position:0% +Theta in other words you don't just + + + align:start position:0% +Theta in other words you don't just +mechanically differentiate respect to + + align:start position:0% +mechanically differentiate respect to + + + align:start position:0% +mechanically differentiate respect to +these variables and the key reason that + + align:start position:0% +these variables and the key reason that + + + align:start position:0% +these variables and the key reason that +you can't do this well look at let's + + align:start position:0% +you can't do this well look at let's + + + align:start position:0% +you can't do this well look at let's +just look at this little Di + + align:start position:0% +just look at this little Di + + + align:start position:0% +just look at this little Di +and I think the whole idea will become + + align:start position:0% +and I think the whole idea will become + + + align:start position:0% +and I think the whole idea will become +very clear remember that in polar + + align:start position:0% +very clear remember that in polar + + + align:start position:0% +very clear remember that in polar +coordinates R is denoted this way U sub + + align:start position:0% +coordinates R is denoted this way U sub + + + align:start position:0% +coordinates R is denoted this way U sub +Theta is at right angles to R notice + + align:start position:0% +Theta is at right angles to R notice + + + align:start position:0% +Theta is at right angles to R notice +that U sub Theta is not in the direction + + align:start position:0% +that U sub Theta is not in the direction + + + align:start position:0% +that U sub Theta is not in the direction +of theta notice that the direction of + + align:start position:0% +of theta notice that the direction of + + + align:start position:0% +of theta notice that the direction of +theta is sort of the tangent to this + + align:start position:0% +theta is sort of the tangent to this + + + align:start position:0% +theta is sort of the tangent to this +circle of radius r at this point if I + + align:start position:0% +circle of radius r at this point if I + + + align:start position:0% +circle of radius r at this point if I +call this increment D Theta notice that + + align:start position:0% +call this increment D Theta notice that + + + align:start position:0% +call this increment D Theta notice that +this AR length is r d Theta so the + + align:start position:0% +this AR length is r d Theta so the + + + align:start position:0% +this AR length is r d Theta so the +vector in the direction of U sub Theta + + align:start position:0% +vector in the direction of U sub Theta + + + align:start position:0% +vector in the direction of U sub Theta +is r d Theta not D Theta I don't know if + + align:start position:0% +is r d Theta not D Theta I don't know if + + + align:start position:0% +is r d Theta not D Theta I don't know if +you noticed that but coming back up here + + align:start position:0% +you noticed that but coming back up here + + + align:start position:0% +you noticed that but coming back up here +for a moment notice that this was okay + + align:start position:0% +for a moment notice that this was okay + + + align:start position:0% +for a moment notice that this was okay +here because R was in the same direction + + align:start position:0% +here because R was in the same direction + + + align:start position:0% +here because R was in the same direction +as yabar notice however that it's r d + + align:start position:0% +as yabar notice however that it's r d + + + align:start position:0% +as yabar notice however that it's r d +Theta which is in the U sub Theta + + align:start position:0% +Theta which is in the U sub Theta + + + align:start position:0% +Theta which is in the U sub Theta +direction again I leave most of these + + align:start position:0% +direction again I leave most of these + + + align:start position:0% +direction again I leave most of these +details for the notes but I feel that if + + align:start position:0% +details for the notes but I feel that if + + + align:start position:0% +details for the notes but I feel that if +I don't say these things to you it + + align:start position:0% +I don't say these things to you it + + + align:start position:0% +I don't say these things to you it +becomes very easy to miss these points + + align:start position:0% +becomes very easy to miss these points + + + align:start position:0% +becomes very easy to miss these points +when we talk about them or write about + + align:start position:0% +when we talk about them or write about + + + align:start position:0% +when we talk about them or write about +them that somehow I hope that by you're + + align:start position:0% +them that somehow I hope that by you're + + + align:start position:0% +them that somehow I hope that by you're +hearing me say this you'll be keyed in + + align:start position:0% +hearing me say this you'll be keyed in + + + align:start position:0% +hearing me say this you'll be keyed in +when you come to these Concepts in the + + align:start position:0% +when you come to these Concepts in the + + + align:start position:0% +when you come to these Concepts in the +uh unit that we're studying but I think + + align:start position:0% +uh unit that we're studying but I think + + + align:start position:0% +uh unit that we're studying but I think +the best way to augment what we're doing + + align:start position:0% +the best way to augment what we're doing + + + align:start position:0% +the best way to augment what we're doing +is by means of a specific example let us + + align:start position:0% +is by means of a specific example let us + + + align:start position:0% +is by means of a specific example let us +suppose that we're given the surface wal + + align:start position:0% +suppose that we're given the surface wal + + + align:start position:0% +suppose that we're given the surface wal +f ofx y where f ofx y is X 5th plus X + + align:start position:0% +f ofx y where f ofx y is X 5th plus X + + + align:start position:0% +f ofx y where f ofx y is X 5th plus X +Cub y + y 5 and we want to compute the + + align:start position:0% +Cub y + y 5 and we want to compute the + + + align:start position:0% +Cub y + y 5 and we want to compute the +directional derivative of F at the Point + + align:start position:0% +directional derivative of F at the Point + + + align:start position:0% +directional derivative of F at the Point +1 comma 1 in the direction let's call it + + align:start position:0% +1 comma 1 in the direction let's call it + + + align:start position:0% +1 comma 1 in the direction let's call it +S Sub one where S Sub one is the + + align:start position:0% +S Sub one where S Sub one is the + + + align:start position:0% +S Sub one where S Sub one is the +direction that goes from the point 1 + + align:start position:0% +direction that goes from the point 1 + + + align:start position:0% +direction that goes from the point 1 +comma 1 to the point 4 comma 5 now what + + align:start position:0% +comma 1 to the point 4 comma 5 now what + + + align:start position:0% +comma 1 to the point 4 comma 5 now what +we're saying is and I guess maybe if we + + align:start position:0% +we're saying is and I guess maybe if we + + + align:start position:0% +we're saying is and I guess maybe if we +look at these two diagrams concurrently + + align:start position:0% +look at these two diagrams concurrently + + + align:start position:0% +look at these two diagrams concurrently +or what uh have you maybe this will be + + align:start position:0% +or what uh have you maybe this will be + + + align:start position:0% +or what uh have you maybe this will be +easier to see here we are at the point 1 + + align:start position:0% +easier to see here we are at the point 1 + + + align:start position:0% +easier to see here we are at the point 1 +comma 1 we want to see how fast the + + align:start position:0% +comma 1 we want to see how fast the + + + align:start position:0% +comma 1 we want to see how fast the +slope over our head the the the W value + + align:start position:0% +slope over our head the the the W value + + + align:start position:0% +slope over our head the the the W value +is changing in the direction direction + + align:start position:0% +is changing in the direction direction + + + align:start position:0% +is changing in the direction direction +of S1 where S1 is chosen to be what + + align:start position:0% +of S1 where S1 is chosen to be what + + + align:start position:0% +of S1 where S1 is chosen to be what +we're moving from the point 1 comma 1 on + + align:start position:0% +we're moving from the point 1 comma 1 on + + + align:start position:0% +we're moving from the point 1 comma 1 on +the XY plane to the point 4 comma 5 see + + align:start position:0% +the XY plane to the point 4 comma 5 see + + + align:start position:0% +the XY plane to the point 4 comma 5 see +we're moving in this direction and we + + align:start position:0% +we're moving in this direction and we + + + align:start position:0% +we're moving in this direction and we +want to see how fast W is changing over + + align:start position:0% +want to see how fast W is changing over + + + align:start position:0% +want to see how fast W is changing over +our heads which geometrically means you + + align:start position:0% +our heads which geometrically means you + + + align:start position:0% +our heads which geometrically means you +draw This Plane intersect it with the + + align:start position:0% +draw This Plane intersect it with the + + + align:start position:0% +draw This Plane intersect it with the +particular surface here and this point p + + align:start position:0% +particular surface here and this point p + + + align:start position:0% +particular surface here and this point p +0 what we really want geometrically is + + align:start position:0% +0 what we really want geometrically is + + + align:start position:0% +0 what we really want geometrically is +what the slope of the line tangent to + + align:start position:0% +what the slope of the line tangent to + + + align:start position:0% +what the slope of the line tangent to +this curve in the ws1 plane tangent to + + align:start position:0% +this curve in the ws1 plane tangent to + + + align:start position:0% +this curve in the ws1 plane tangent to +this curve at the point p 0 and my claim + + align:start position:0% +this curve at the point p 0 and my claim + + + align:start position:0% +this curve at the point p 0 and my claim +is is that this can be done very very + + align:start position:0% +is is that this can be done very very + + + align:start position:0% +is is that this can be done very very +easy from a mechanical point of view now + + align:start position:0% +easy from a mechanical point of view now + + + align:start position:0% +easy from a mechanical point of view now +that we have a gradient Vector behind us + + align:start position:0% +that we have a gradient Vector behind us + + + align:start position:0% +that we have a gradient Vector behind us +namely what we do is given what w looks + + align:start position:0% +namely what we do is given what w looks + + + align:start position:0% +namely what we do is given what w looks +like as a function of X and Y we take + + align:start position:0% +like as a function of X and Y we take + + + align:start position:0% +like as a function of X and Y we take +the partial of w with respect to both X + + align:start position:0% +the partial of w with respect to both X + + + align:start position:0% +the partial of w with respect to both X +and Y which hopefully you can all do + + align:start position:0% +and Y which hopefully you can all do + + + align:start position:0% +and Y which hopefully you can all do +quite mechanically now based on our last + + align:start position:0% +quite mechanically now based on our last + + + align:start position:0% +quite mechanically now based on our last +units work we differentiate first + + align:start position:0% +units work we differentiate first + + + align:start position:0% +units work we differentiate first +holding y constant then holding x + + align:start position:0% +holding y constant then holding x + + + align:start position:0% +holding y constant then holding x +constant at any rate we obtain what that + + align:start position:0% +constant at any rate we obtain what that + + + align:start position:0% +constant at any rate we obtain what that +the partial of w with respect to X is 5 + + align:start position:0% +the partial of w with respect to X is 5 + + + align:start position:0% +the partial of w with respect to X is 5 +x 4 + 3x^2 Y and so if we compute that + + align:start position:0% +x 4 + 3x^2 Y and so if we compute that + + + align:start position:0% +x 4 + 3x^2 Y and so if we compute that +at the point one comma 1 when X and Y + + align:start position:0% +at the point one comma 1 when X and Y + + + align:start position:0% +at the point one comma 1 when X and Y +are both one this simply turns out to be + + align:start position:0% +are both one this simply turns out to be + + + align:start position:0% +are both one this simply turns out to be +a in a similar way the partial of w with + + align:start position:0% +a in a similar way the partial of w with + + + align:start position:0% +a in a similar way the partial of w with +respect to Y is X Cub + 6 y 5th so if we + + align:start position:0% +respect to Y is X Cub + 6 y 5th so if we + + + align:start position:0% +respect to Y is X Cub + 6 y 5th so if we +compute that at the point 1 comma 1 that + + align:start position:0% +compute that at the point 1 comma 1 that + + + align:start position:0% +compute that at the point 1 comma 1 that +turns out to be seven in other words + + align:start position:0% +turns out to be seven in other words + + + align:start position:0% +turns out to be seven in other words +then by definition of our gradient which + + align:start position:0% +then by definition of our gradient which + + + align:start position:0% +then by definition of our gradient which +is the partial of f with respect to X + + align:start position:0% +is the partial of f with respect to X + + + align:start position:0% +is the partial of f with respect to X +evaluated at 1 comma 1 * I plus the + + align:start position:0% +evaluated at 1 comma 1 * I plus the + + + align:start position:0% +evaluated at 1 comma 1 * I plus the +partial of f with respect to Y evaluated + + align:start position:0% +partial of f with respect to Y evaluated + + + align:start position:0% +partial of f with respect to Y evaluated +at 1 comma y * J the gradient of F at 1 + + align:start position:0% +at 1 comma y * J the gradient of F at 1 + + + align:start position:0% +at 1 comma y * J the gradient of F at 1 +comma 1 is just 8 I + 7 J very easy to + + align:start position:0% +comma 1 is just 8 I + 7 J very easy to + + + align:start position:0% +comma 1 is just 8 I + 7 J very easy to +write down mechanically when you're + + align:start position:0% +write down mechanically when you're + + + align:start position:0% +write down mechanically when you're +using cartisian coordinates now let me + + align:start position:0% +using cartisian coordinates now let me + + + align:start position:0% +using cartisian coordinates now let me +make a brief aside an interruption here + + align:start position:0% +make a brief aside an interruption here + + + align:start position:0% +make a brief aside an interruption here +the idea is to emphasize what the + + align:start position:0% +the idea is to emphasize what the + + + align:start position:0% +the idea is to emphasize what the +gradient Vector means what this tells me + + align:start position:0% +gradient Vector means what this tells me + + + align:start position:0% +gradient Vector means what this tells me +is that if I were to leave the point 1 + + align:start position:0% +is that if I were to leave the point 1 + + + align:start position:0% +is that if I were to leave the point 1 +comma 1 in the direction of the vector + + align:start position:0% +comma 1 in the direction of the vector + + + align:start position:0% +comma 1 in the direction of the vector +8i + 4 J if I were to leave in that + + align:start position:0% +8i + 4 J if I were to leave in that + + + align:start position:0% +8i + 4 J if I were to leave in that +direction that would be the direction in + + align:start position:0% +direction that would be the direction in + + + align:start position:0% +direction that would be the direction in +which the directional derivative would + + align:start position:0% +which the directional derivative would + + + align:start position:0% +which the directional derivative would +be maximum and moreover that maximum + + align:start position:0% +be maximum and moreover that maximum + + + align:start position:0% +be maximum and moreover that maximum +directional derivative would just be the + + align:start position:0% +directional derivative would just be the + + + align:start position:0% +directional derivative would just be the +magnitude of this gradient Vector the + + align:start position:0% +magnitude of this gradient Vector the + + + align:start position:0% +magnitude of this gradient Vector the +magnitude of that gradient Vector is + + align:start position:0% +magnitude of that gradient Vector is + + + align:start position:0% +magnitude of that gradient Vector is +just the square root of 8^2 + 7^2 uh + + align:start position:0% +just the square root of 8^2 + 7^2 uh + + + align:start position:0% +just the square root of 8^2 + 7^2 uh +which is the sare root of 113 in other + + align:start position:0% +which is the sare root of 113 in other + + + align:start position:0% +which is the sare root of 113 in other +words what this tells us is that the + + align:start position:0% +words what this tells us is that the + + + align:start position:0% +words what this tells us is that the +maximum directional derivative leaving + + align:start position:0% +maximum directional derivative leaving + + + align:start position:0% +maximum directional derivative leaving +the point1 comma 1 is the square < TK of + + align:start position:0% +the point1 comma 1 is the square < TK of + + + align:start position:0% +the point1 comma 1 is the square < TK of +113 and it occurs in the direction 8 I + + + align:start position:0% +113 and it occurs in the direction 8 I + + + + align:start position:0% +113 and it occurs in the direction 8 I + +7 J as you leave the point1 comma 1 at + + align:start position:0% +7 J as you leave the point1 comma 1 at + + + align:start position:0% +7 J as you leave the point1 comma 1 at +any rate getting back to the mainstream + + align:start position:0% +any rate getting back to the mainstream + + + align:start position:0% +any rate getting back to the mainstream +of the problem what we want is a + + align:start position:0% +of the problem what we want is a + + + align:start position:0% +of the problem what we want is a +directional derivative in the direction + + align:start position:0% +directional derivative in the direction + + + align:start position:0% +directional derivative in the direction +of + + align:start position:0% +of + + + align:start position:0% +of +S1 that means what we take our gradient + + align:start position:0% +S1 that means what we take our gradient + + + align:start position:0% +S1 that means what we take our gradient +Vector which is 8A 7 and Dot that with + + align:start position:0% +Vector which is 8A 7 and Dot that with + + + align:start position:0% +Vector which is 8A 7 and Dot that with +the unit Vector in the direction of S1 + + align:start position:0% +the unit Vector in the direction of S1 + + + align:start position:0% +the unit Vector in the direction of S1 +you may recall from this diagram here + + align:start position:0% +you may recall from this diagram here + + + align:start position:0% +you may recall from this diagram here +that the vector in the direction of S1 + + align:start position:0% +that the vector in the direction of S1 + + + align:start position:0% +that the vector in the direction of S1 +has its I component equal to three its J + + align:start position:0% +has its I component equal to three its J + + + align:start position:0% +has its I component equal to three its J +component equal to four this makes this + + align:start position:0% +component equal to four this makes this + + + align:start position:0% +component equal to four this makes this +a 345 right triangle so the unit Vector + + align:start position:0% +a 345 right triangle so the unit Vector + + + align:start position:0% +a 345 right triangle so the unit Vector +in this direction has as its components + + align:start position:0% +in this direction has as its components + + + align:start position:0% +in this direction has as its components +three 3 fths and 4 Fs in other words the + + align:start position:0% +three 3 fths and 4 Fs in other words the + + + align:start position:0% +three 3 fths and 4 Fs in other words the +directional derivative of F at the point + + align:start position:0% +directional derivative of F at the point + + + align:start position:0% +directional derivative of F at the point +1 comma 1 in the given Direction S1 is + + align:start position:0% +1 comma 1 in the given Direction S1 is + + + align:start position:0% +1 comma 1 in the given Direction S1 is +just the gradient dotted with the unit + + align:start position:0% +just the gradient dotted with the unit + + + align:start position:0% +just the gradient dotted with the unit +Vector 35ths I plus 45ths J just + + align:start position:0% +Vector 35ths I plus 45ths J just + + + align:start position:0% +Vector 35ths I plus 45ths J just +mechanically carrying out this operation + + align:start position:0% +mechanically carrying out this operation + + + align:start position:0% +mechanically carrying out this operation +leads to 52 over5 and by the + + align:start position:0% +leads to 52 over5 and by the + + + align:start position:0% +leads to 52 over5 and by the +way this had better turn out to + + align:start position:0% + + + + align:start position:0% + +be less than this because this is what + + align:start position:0% +be less than this because this is what + + + align:start position:0% +be less than this because this is what +the maximum value that the directional + + align:start position:0% +the maximum value that the directional + + + align:start position:0% +the maximum value that the directional +derivative can have in other words if we + + align:start position:0% +derivative can have in other words if we + + + align:start position:0% +derivative can have in other words if we +haven't made a mistake here one of the + + align:start position:0% +haven't made a mistake here one of the + + + align:start position:0% +haven't made a mistake here one of the +checkpoints is what that you can't get a + + align:start position:0% +checkpoints is what that you can't get a + + + align:start position:0% +checkpoints is what that you can't get a +the vector can't project to be any + + align:start position:0% +the vector can't project to be any + + + align:start position:0% +the vector can't project to be any +longer than what it really uh is in this + + align:start position:0% +longer than what it really uh is in this + + + align:start position:0% +longer than what it really uh is in this +I mean it can't be + + align:start position:0% +I mean it can't be + + + align:start position:0% +I mean it can't be +more than the gradient Vector but at any + + align:start position:0% +more than the gradient Vector but at any + + + align:start position:0% +more than the gradient Vector but at any +rate let's now conclude the lecture by + + align:start position:0% +rate let's now conclude the lecture by + + + align:start position:0% +rate let's now conclude the lecture by +coming to the part which is probably the + + align:start position:0% +coming to the part which is probably the + + + align:start position:0% +coming to the part which is probably the +hardest thing that we're going to + + align:start position:0% +hardest thing that we're going to + + + align:start position:0% +hardest thing that we're going to +encounter in the whole course in a way I + + align:start position:0% +encounter in the whole course in a way I + + + align:start position:0% +encounter in the whole course in a way I +feel a little bit like the man who fell + + align:start position:0% +feel a little bit like the man who fell + + + align:start position:0% +feel a little bit like the man who fell +off the Empire State Building and when + + align:start position:0% +off the Empire State Building and when + + + align:start position:0% +off the Empire State Building and when +he went past the 40th floor somebody + + align:start position:0% +he went past the 40th floor somebody + + + align:start position:0% +he went past the 40th floor somebody +said how you doing and he said so far so + + align:start position:0% +said how you doing and he said so far so + + + align:start position:0% +said how you doing and he said so far so +good and that is we've taken some + + align:start position:0% +good and that is we've taken some + + + align:start position:0% +good and that is we've taken some +tremendous Liberties here and the + + align:start position:0% +tremendous Liberties here and the + + + align:start position:0% +tremendous Liberties here and the +biggest Liberty that we've taken and + + align:start position:0% +biggest Liberty that we've taken and + + + align:start position:0% +biggest Liberty that we've taken and +it's not just a liberty it's the kind of + + align:start position:0% +it's not just a liberty it's the kind of + + + align:start position:0% +it's not just a liberty it's the kind of +a liberty that to solve involves the + + align:start position:0% +a liberty that to solve involves the + + + align:start position:0% +a liberty that to solve involves the +foundations of our entire course we are + + align:start position:0% +foundations of our entire course we are + + + align:start position:0% +foundations of our entire course we are +now at the Grassroots of what functions + + align:start position:0% +now at the Grassroots of what functions + + + align:start position:0% +now at the Grassroots of what functions +at least the calculus of functions of + + align:start position:0% +at least the calculus of functions of + + + align:start position:0% +at least the calculus of functions of +several variables is all about and + + align:start position:0% +several variables is all about and + + + align:start position:0% +several variables is all about and +that's this trouble spot first of all + + align:start position:0% +that's this trouble spot first of all + + + align:start position:0% +that's this trouble spot first of all +does Delta W10 exist that's the first + + align:start position:0% +does Delta W10 exist that's the first + + + align:start position:0% +does Delta W10 exist that's the first +question namely how do you know that + + align:start position:0% +question namely how do you know that + + + align:start position:0% +question namely how do you know that +there is a tangent plane just because + + align:start position:0% +there is a tangent plane just because + + + align:start position:0% +there is a tangent plane just because +the surface happens to be smooth when + + align:start position:0% +the surface happens to be smooth when + + + align:start position:0% +the surface happens to be smooth when +you cut it by a plane parallel to the Wy + + align:start position:0% +you cut it by a plane parallel to the Wy + + + align:start position:0% +you cut it by a plane parallel to the Wy +plane and smooth when you cut it by a + + align:start position:0% +plane and smooth when you cut it by a + + + align:start position:0% +plane and smooth when you cut it by a +plane parallel to the WX plane how do + + align:start position:0% +plane parallel to the WX plane how do + + + align:start position:0% +plane parallel to the WX plane how do +you know that it's going to be smooth + + align:start position:0% +you know that it's going to be smooth + + + align:start position:0% +you know that it's going to be smooth +for any given + + align:start position:0% +for any given + + + align:start position:0% +for any given +Direction so that's the first + + align:start position:0% +Direction so that's the first + + + align:start position:0% +Direction so that's the first +intellectual question that comes up in + + align:start position:0% +intellectual question that comes up in + + + align:start position:0% +intellectual question that comes up in +the reading assignment that has to be + + align:start position:0% +the reading assignment that has to be + + + align:start position:0% +the reading assignment that has to be +solved effectively first of all does + + align:start position:0% +solved effectively first of all does + + + align:start position:0% +solved effectively first of all does +Delta W tan exist meaningfully and + + align:start position:0% +Delta W tan exist meaningfully and + + + align:start position:0% +Delta W tan exist meaningfully and +secondly if it does exist how is it + + align:start position:0% +secondly if it does exist how is it + + + align:start position:0% +secondly if it does exist how is it +related to Delta W and now we come to + + align:start position:0% +related to Delta W and now we come to + + + align:start position:0% +related to Delta W and now we come to +that key theorem the proof of which is + + align:start position:0% +that key theorem the proof of which is + + + align:start position:0% +that key theorem the proof of which is +quite hairy it's done in the text it's + + align:start position:0% +quite hairy it's done in the text it's + + + align:start position:0% +quite hairy it's done in the text it's +uh also done as an optional exercise to + + align:start position:0% +uh also done as an optional exercise to + + + align:start position:0% +uh also done as an optional exercise to +help you generalize What's Done in the + + align:start position:0% +help you generalize What's Done in the + + + align:start position:0% +help you generalize What's Done in the +text and it's the counterpart of what + + align:start position:0% +text and it's the counterpart of what + + + align:start position:0% +text and it's the counterpart of what +happens with differentials in functions + + align:start position:0% +happens with differentials in functions + + + align:start position:0% +happens with differentials in functions +of a single real variable but the key + + align:start position:0% +of a single real variable but the key + + + align:start position:0% +of a single real variable but the key +theorem which I'll State here without + + align:start position:0% +theorem which I'll State here without + + + align:start position:0% +theorem which I'll State here without +proof is simply this suppose that W is a + + align:start position:0% +proof is simply this suppose that W is a + + + align:start position:0% +proof is simply this suppose that W is a +function of X and Y and that F subx and + + align:start position:0% +function of X and Y and that F subx and + + + align:start position:0% +function of X and Y and that F subx and +F suby both happen to exist in some + + align:start position:0% +F suby both happen to exist in some + + + align:start position:0% +F suby both happen to exist in some +neighborhood of the point a comma B all + + align:start position:0% +neighborhood of the point a comma B all + + + align:start position:0% +neighborhood of the point a comma B all +right so far so good now here is the key + + align:start position:0% +right so far so good now here is the key + + + align:start position:0% +right so far so good now here is the key +additional hypothesis suppose also that + + align:start position:0% +additional hypothesis suppose also that + + + align:start position:0% +additional hypothesis suppose also that +F subx and F suby happen to be + + align:start position:0% +F subx and F suby happen to be + + + align:start position:0% +F subx and F suby happen to be +continuous at a comma B my claim is is + + align:start position:0% +continuous at a comma B my claim is is + + + align:start position:0% +continuous at a comma B my claim is is +that if this additional hypothesis is + + align:start position:0% +that if this additional hypothesis is + + + align:start position:0% +that if this additional hypothesis is +obeyed the tangent plane will exist in + + align:start position:0% +obeyed the tangent plane will exist in + + + align:start position:0% +obeyed the tangent plane will exist in +other words it's not enough for the + + align:start position:0% +other words it's not enough for the + + + align:start position:0% +other words it's not enough for the +directional derivative to exist in the X + + align:start position:0% +directional derivative to exist in the X + + + align:start position:0% +directional derivative to exist in the X +and Y directions in order to guarantee + + align:start position:0% +and Y directions in order to guarantee + + + align:start position:0% +and Y directions in order to guarantee +that the directional derivative will + + align:start position:0% +that the directional derivative will + + + align:start position:0% +that the directional derivative will +exist in every direction but it is + + align:start position:0% +exist in every direction but it is + + + align:start position:0% +exist in every direction but it is +enough provided that these directional + + align:start position:0% +enough provided that these directional + + + align:start position:0% +enough provided that these directional +derivatives happen to be continuous and + + align:start position:0% +derivatives happen to be continuous and + + + align:start position:0% +derivatives happen to be continuous and +by the way if these conditions are met + + align:start position:0% +by the way if these conditions are met + + + align:start position:0% +by the way if these conditions are met +we say that f is a continuously + + align:start position:0% +we say that f is a continuously + + + align:start position:0% +we say that f is a continuously +differentiable function of X and Y but + + align:start position:0% +differentiable function of X and Y but + + + align:start position:0% +differentiable function of X and Y but +I'll talk about that more next time or + + align:start position:0% +I'll talk about that more next time or + + + align:start position:0% +I'll talk about that more next time or +in the notes or in the exercises we're + + align:start position:0% +in the notes or in the exercises we're + + + align:start position:0% +in the notes or in the exercises we're +going to make a big issue over this + + align:start position:0% +going to make a big issue over this + + + align:start position:0% +going to make a big issue over this +sooner or later but for now what I do + + align:start position:0% +sooner or later but for now what I do + + + align:start position:0% +sooner or later but for now what I do +want to do is just end with what the key + + align:start position:0% +want to do is just end with what the key + + + align:start position:0% +want to do is just end with what the key +theorem is the key theorem says look at + + align:start position:0% +theorem is the key theorem says look at + + + align:start position:0% +theorem is the key theorem says look at +just like with one variable if these + + align:start position:0% +just like with one variable if these + + + align:start position:0% +just like with one variable if these +conditions are met then there is a very + + align:start position:0% +conditions are met then there is a very + + + align:start position:0% +conditions are met then there is a very +reasonable approximation to Delta W by + + align:start position:0% +reasonable approximation to Delta W by + + + align:start position:0% +reasonable approximation to Delta W by +Delta W1 namely what the theorem says is + + align:start position:0% +Delta W1 namely what the theorem says is + + + align:start position:0% +Delta W1 namely what the theorem says is +in this case Delta W will be the partial + + align:start position:0% +in this case Delta W will be the partial + + + align:start position:0% +in this case Delta W will be the partial +of f respect to X evaluated a comma B * + + align:start position:0% +of f respect to X evaluated a comma B * + + + align:start position:0% +of f respect to X evaluated a comma B * +Delta X plus the partial of effort + + align:start position:0% +Delta X plus the partial of effort + + + align:start position:0% +Delta X plus the partial of effort +respect to Y evaluated a comma B * Delta + + align:start position:0% +respect to Y evaluated a comma B * Delta + + + align:start position:0% +respect to Y evaluated a comma B * Delta +Y and notice of course that this is the + + align:start position:0% +Y and notice of course that this is the + + + align:start position:0% +Y and notice of course that this is the +thing that we've been calling Delta + + align:start position:0% + + + + align:start position:0% + +y1 plus an error and the error has the + + align:start position:0% +y1 plus an error and the error has the + + + align:start position:0% +y1 plus an error and the error has the +form K1 Delta X Plus K2 Delta Y where K1 + + align:start position:0% +form K1 Delta X Plus K2 Delta Y where K1 + + + align:start position:0% +form K1 Delta X Plus K2 Delta Y where K1 +and K2 both approach zero as Delta X and + + align:start position:0% +and K2 both approach zero as Delta X and + + + align:start position:0% +and K2 both approach zero as Delta X and +Delta y approach zero and this is very + + align:start position:0% +Delta y approach zero and this is very + + + align:start position:0% +Delta y approach zero and this is very +very crucial it's not enough as we're + + align:start position:0% +very crucial it's not enough as we're + + + align:start position:0% +very crucial it's not enough as we're +going to see in the very next lecture + + align:start position:0% +going to see in the very next lecture + + + align:start position:0% +going to see in the very next lecture +that Delta X Delta y approach zero it's + + align:start position:0% +that Delta X Delta y approach zero it's + + + align:start position:0% +that Delta X Delta y approach zero it's +that these things go to zero as Delta X + + align:start position:0% +that these things go to zero as Delta X + + + align:start position:0% +that these things go to zero as Delta X +and Delta y go to zero consequently + + align:start position:0% +and Delta y go to zero consequently + + + align:start position:0% +and Delta y go to zero consequently +these terms go to zero faster they go to + + align:start position:0% +these terms go to zero faster they go to + + + align:start position:0% +these terms go to zero faster they go to +zero as a second order infinit tesmo and + + align:start position:0% +zero as a second order infinit tesmo and + + + align:start position:0% +zero as a second order infinit tesmo and +what this really says is look for very + + align:start position:0% +what this really says is look for very + + + align:start position:0% +what this really says is look for very +small values of Delta X and Delta y even + + align:start position:0% +small values of Delta X and Delta y even + + + align:start position:0% +small values of Delta X and Delta y even +when you're dealing with zero over zero + + align:start position:0% +when you're dealing with zero over zero + + + align:start position:0% +when you're dealing with zero over zero +forms if you pick a sufficiently small + + align:start position:0% +forms if you pick a sufficiently small + + + align:start position:0% +forms if you pick a sufficiently small +neighborhood of the point a comma B and + + align:start position:0% +neighborhood of the point a comma B and + + + align:start position:0% +neighborhood of the point a comma B and +that's the key point a efficiently small + + align:start position:0% +that's the key point a efficiently small + + + align:start position:0% +that's the key point a efficiently small +neighborhood of the point a comma B then + + align:start position:0% +neighborhood of the point a comma B then + + + align:start position:0% +neighborhood of the point a comma B then +Delta W is approximately equal to Delta + + align:start position:0% +Delta W is approximately equal to Delta + + + align:start position:0% +Delta W is approximately equal to Delta +W10 and by the way this holds also in + + align:start position:0% +W10 and by the way this holds also in + + + align:start position:0% +W10 and by the way this holds also in +several variables in other words I + + align:start position:0% +several variables in other words I + + + align:start position:0% +several variables in other words I +picked the case and equals 2 here simply + + align:start position:0% +picked the case and equals 2 here simply + + + align:start position:0% +picked the case and equals 2 here simply +so that we could utilize the geometry + + align:start position:0% +so that we could utilize the geometry + + + align:start position:0% +so that we could utilize the geometry +namely what we're saying is in terms of + + align:start position:0% +namely what we're saying is in terms of + + + align:start position:0% +namely what we're saying is in terms of +the geometry if F happens to be a + + align:start position:0% +the geometry if F happens to be a + + + align:start position:0% +the geometry if F happens to be a +continuously differentiable function of + + align:start position:0% +continuously differentiable function of + + + align:start position:0% +continuously differentiable function of +X and Y and we look at the surface wal f + + align:start position:0% +X and Y and we look at the surface wal f + + + align:start position:0% +X and Y and we look at the surface wal f +ofx y above the point a comma B what + + align:start position:0% +ofx y above the point a comma B what + + + align:start position:0% +ofx y above the point a comma B what +we're saying is that in a neighborhood + + align:start position:0% +we're saying is that in a neighborhood + + + align:start position:0% +we're saying is that in a neighborhood +of that point there is well first of all + + align:start position:0% +of that point there is well first of all + + + align:start position:0% +of that point there is well first of all +we're saying what a tangent plane exists + + align:start position:0% +we're saying what a tangent plane exists + + + align:start position:0% +we're saying what a tangent plane exists +to the surface above that point and that + + align:start position:0% +to the surface above that point and that + + + align:start position:0% +to the surface above that point and that +in a neighborhood of that point of + + align:start position:0% +in a neighborhood of that point of + + + align:start position:0% +in a neighborhood of that point of +tangency the tangent plane is an + + align:start position:0% +tangency the tangent plane is an + + + align:start position:0% +tangency the tangent plane is an +excellent approximation for the true + + align:start position:0% +excellent approximation for the true + + + align:start position:0% +excellent approximation for the true +change in W now what happens is if n is + + align:start position:0% +change in W now what happens is if n is + + + align:start position:0% +change in W now what happens is if n is +greater than two we can no longer use + + align:start position:0% +greater than two we can no longer use + + + align:start position:0% +greater than two we can no longer use +the geometric interpretation but what is + + align:start position:0% +the geometric interpretation but what is + + + align:start position:0% +the geometric interpretation but what is +important is that the analytic proof + + align:start position:0% +important is that the analytic proof + + + align:start position:0% +important is that the analytic proof +never makes use of the picture and the + + align:start position:0% +never makes use of the picture and the + + + align:start position:0% +never makes use of the picture and the +key point is and I'm going to exploit + + align:start position:0% +key point is and I'm going to exploit + + + align:start position:0% +key point is and I'm going to exploit +this in future lectures the really key + + align:start position:0% +this in future lectures the really key + + + align:start position:0% +this in future lectures the really key +point is that the Delta W10 never gets + + align:start position:0% +point is that the Delta W10 never gets + + + align:start position:0% +point is that the Delta W10 never gets +messy that the variables Delta X Delta y + + align:start position:0% +messy that the variables Delta X Delta y + + + align:start position:0% +messy that the variables Delta X Delta y +Etc all occur as linear terms and this + + align:start position:0% +Etc all occur as linear terms and this + + + align:start position:0% +Etc all occur as linear terms and this +is why the so-called linear algebra + + align:start position:0% +is why the so-called linear algebra + + + align:start position:0% +is why the so-called linear algebra +subject becomes so important in the + + align:start position:0% +subject becomes so important in the + + + align:start position:0% +subject becomes so important in the +study of functions of several variables + + align:start position:0% +study of functions of several variables + + + align:start position:0% +study of functions of several variables +at any rate I think this is enough for + + align:start position:0% +at any rate I think this is enough for + + + align:start position:0% +at any rate I think this is enough for +one lesson and in our next lesson what + + align:start position:0% +one lesson and in our next lesson what + + + align:start position:0% +one lesson and in our next lesson what +we will do is show how using this key + + align:start position:0% +we will do is show how using this key + + + align:start position:0% +we will do is show how using this key +theorem has its analog in something + + align:start position:0% +theorem has its analog in something + + + align:start position:0% +theorem has its analog in something +called The Chain rule just as it did in + + align:start position:0% +called The Chain rule just as it did in + + + align:start position:0% +called The Chain rule just as it did in +the case of part one when we studied + + align:start position:0% +the case of part one when we studied + + + align:start position:0% +the case of part one when we studied +functions of a single independent + + align:start position:0% +functions of a single independent + + + align:start position:0% +functions of a single independent +variable at any rate then until next + + align:start position:0% +variable at any rate then until next + + + align:start position:0% +variable at any rate then until next +time + + align:start position:0% +time + + + align:start position:0% +time +goodbye funding for the publication of + + align:start position:0% +goodbye funding for the publication of + + + align:start position:0% +goodbye funding for the publication of +this video was provided by the Gabriella + + align:start position:0% +this video was provided by the Gabriella + + + align:start position:0% +this video was provided by the Gabriella +and Paul rosenbom + + align:start position:0% +and Paul rosenbom + + + align:start position:0% +and Paul rosenbom +foundation help ocw continue to provide + + align:start position:0% +foundation help ocw continue to provide + + + align:start position:0% +foundation help ocw continue to provide +free and open access to MIT courses by + + align:start position:0% +free and open access to MIT courses by + + + align:start position:0% +free and open access to MIT courses by +making a donation at ocw.mit.edu/donate \ No newline at end of file diff --git a/S_Egep9GOpQ.txt b/S_Egep9GOpQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..92e4e5ed33f7787029450dd74cde13014613f1c6 --- /dev/null +++ b/S_Egep9GOpQ.txt @@ -0,0 +1,382 @@ +Hi. + +In this problem, we'll be going +over practice with the + +calculation of conditional +probabilities. + +We'll start with a game where +our friend Alice will be + +tossing a coin with certain +bias of having a head, and + +tosses this coin twice. + +And we're interested in +knowing, what's the + +probability that both +coin tosses will + +end up being a head? + +The first step we're going to +do is to convert the problem + +into a mathematical form +by defining two + +events as the following. + +Event A is where the first +coin toss is a head. + +And similarly, event B will be +having the second coin toss + +also being a head. + +Having these two events will +allow us to say, well, the + +event that A intersection B will +be the event that both + +coin tosses are a head. + +And we'd like to know the +probability of such an event. + +In particular, the probability +of A and B will be calculated + +under two types of +information. + +In the first case, we'll be +conditioning on that we know + +the first coin toss is a head. + +I'd like to know what the +probability of A and B is. + +In the second case, we know that +at least one of the two + +coin tosses is a head expressed +in the form A union + +B. + +And under this conditioning, +what is the probability of A + +and B, A intersection B? + +So Alice, in this problem, +says-- well, her guess will be + +that the first quantity +is no smaller + +than the second quantity. + +Namely, knowing that the first +coin toss is a head somehow + +more strongly implies that both +coin tosses will be a + +head, compared to the case that +we only know at least one + +of the two coin tosses +is a head. + +And we'd like to verify if this + +inequality is indeed true. + +To do so, let's just use the +basic calculation of + +conditional probability. + +Now, from the lectures, you've +already learned that to + +calculate this quantity, we'll +write out a fraction where the + +numerator is the probability of +the intersection of these + +two events. + +So we have A intersect B +intersection A divided by the + +probability of the event that +we're conditioning on, which + +is A. + +Now, the top quantity, since +we know that A and B is a + +subset of event A, then taking +the intersection of these two + +quantities will just give +us the first event. + +So we have A and B. And the +bottom is still probability of + +A. + +Let's do the same thing for +the second quantity here. + +We have the top probability of A +and B intersection the event + +A union B, and on the bottom, +probability of the event A and + +B. Again, we see the event A and +B is a subset of the event + +A union B. So the top will be +A and B. And the bottom-- + +A union B. + +OK, now let's stop +for a little bit. + +We've computed the probability +for each expression in the + +following fractional form. + +And we observed that for +both fractions, the + +numerator is the same. + +So the numerator is a +probability of A and B. And + +the denominator in the first +case is probably of A, and the + +second case, probably +of A union B. + +Since we know that A is a subset +of the event A union B, + +and by the monotonicity of +probabilities, we know that + +the probability of A is hence no +greater than a probability + +of A union B. Substituting +this back into these + +expressions, we know that +because they lie in the + +denominators, the first +expression is indeed no + +smaller than the second +expression. + +So our friend Alice +was correct. + +So throughout this problem, we +never used the fact that the + +probability of a particular coin +toss results, let's say, + +in a head is a certain number. + +Actually, this bias for the +coin is irrelevant. + +Whether the coin is fair +or unfair, this + +fact is always true. + +So indeed, it does +not depend on the + +probability of the coin. + +But if you're really curious +what happens when the coin is + +fair, we can plug +in the numbers. + +And here, we're assuming the +coin is fair, which means + +probability of having +a head is 1/2. + +Then, we'll see after going +through the calculations that + +the first probability is 1/2, +whereas the second probability + +is 1/3, which means, in this +case, the [? dominance ?] + +actually is strict. + +So the first one is strictly +greater than + +the second one, OK? + +So this completes the first +part of the problem. + +How do we generalize this into +more general settings? + +There are multiple ways, +but we'll go over + +one particular form. + +And to do so, we'll be defining +three events somewhat + +more abstractly. + +Let's say we have +three events-- + +C, D, and E. Imagine any event, +but all three events + +have to satisfy the following +condition. + +First, event D will be a subset +of E. And second, the + +intersection of C and +D is equal to the + +intersection of C and E, OK? + +So this will be our +choice events. + +And let's see a particular +example. + +Let's say you have a sample +space here and some event E. + +Now, by the first condition, D +will have to lie somewhere in + +E. For the second condition, +we'll pick some event C such + +that this is true. + +And one way to do so is simply +picking C that lies within + +both D and E. And you can see +C intersection D will be C. + +And C intersection E will still +be C. Hence, the second + +equality is true. + +So if both equalities are true, +we have the following + +relationship, that the +probability of C conditional + +on D will be no smaller than +the probability of C + +conditional on event E. And this +will be the more general + +form of the inequality +that we saw before. + + + +So first of all, the +way to prove this + +is in fact the same. + +We simply write out the +value of this using + +the fractional form. + +And based on these two facts, +we can arrive at this + +equation, which I shall +now go over. + +But just to see why this form +is more general, in fact, if + +we-- say we let C be the event +A intersection B, D be the + +event A, and E be the event A +and B where A and B are the + +events that we defined +earlier. + +We can verify that, indeed, +these conditions are true, + +namely D is a subset of E. +Because A is a subset of A + +union B, and C is a subset of +both D and E. And hence, + +condition two is also true. + +And if that's the case, we +will actually recover the + +result we got earlier for events +A and B. And hence, + +this equation here is +a more general form. + +So that's the end +of the problem. + +See you next time. \ No newline at end of file diff --git a/Sa1DMeTf8U8.txt b/Sa1DMeTf8U8.txt new file mode 100644 index 0000000000000000000000000000000000000000..ad7eb91718c02185dde1dd533eb357d830370678 --- /dev/null +++ b/Sa1DMeTf8U8.txt @@ -0,0 +1,907 @@ +align:start position:0% + +welcome back to a20 special relativity + + align:start position:0% +welcome back to a20 special relativity + + + align:start position:0% +welcome back to a20 special relativity +in this last example of relativistic + + align:start position:0% +in this last example of relativistic + + + align:start position:0% +in this last example of relativistic +kinematics we want to investigate + + align:start position:0% +kinematics we want to investigate + + + align:start position:0% +kinematics we want to investigate +scattering in the specific cases + + align:start position:0% +scattering in the specific cases + + + align:start position:0% +scattering in the specific cases +scattering of a photon on an electron at + + align:start position:0% +scattering of a photon on an electron at + + + align:start position:0% +scattering of a photon on an electron at +rest + + align:start position:0% +rest + + + align:start position:0% +rest +so we have as an initial state a photon + + align:start position:0% +so we have as an initial state a photon + + + align:start position:0% +so we have as an initial state a photon +an electron at rest + + align:start position:0% +an electron at rest + + + align:start position:0% +an electron at rest +and then the photon is scattered and we + + align:start position:0% +and then the photon is scattered and we + + + align:start position:0% +and then the photon is scattered and we +also observe a scattered electron + + align:start position:0% +also observe a scattered electron + + + align:start position:0% +also observe a scattered electron +there is one important piece of physics + + align:start position:0% +there is one important piece of physics + + + align:start position:0% +there is one important piece of physics +here which we add without further + + align:start position:0% +here which we add without further + + + align:start position:0% +here which we add without further +explanation which is the planck einstein + + align:start position:0% +explanation which is the planck einstein + + + align:start position:0% +explanation which is the planck einstein +relation which relates the energy of the + + align:start position:0% +relation which relates the energy of the + + + align:start position:0% +relation which relates the energy of the +photon to the frequency of the photon or + + align:start position:0% +photon to the frequency of the photon or + + + align:start position:0% +photon to the frequency of the photon or +the wavelength + + align:start position:0% +the wavelength + + + align:start position:0% +the wavelength +this is + + align:start position:0% +this is + + + align:start position:0% +this is +fundamentally important in + + align:start position:0% +fundamentally important in + + + align:start position:0% +fundamentally important in +quantum physics + + align:start position:0% +quantum physics + + + align:start position:0% +quantum physics +and + + align:start position:0% +and + + + align:start position:0% +and +can be explained or tested with the + + align:start position:0% +can be explained or tested with the + + + align:start position:0% +can be explained or tested with the +photoelectric effect for which einstein + + align:start position:0% +photoelectric effect for which einstein + + + align:start position:0% +photoelectric effect for which einstein +received the nobel prize + + align:start position:0% +received the nobel prize + + + align:start position:0% +received the nobel prize +so what we want to do here is find the + + align:start position:0% +so what we want to do here is find the + + + align:start position:0% +so what we want to do here is find the +wavelength shift so delta lambda + + align:start position:0% +wavelength shift so delta lambda + + + align:start position:0% +wavelength shift so delta lambda +which is the wavelength of the incoming + + align:start position:0% +which is the wavelength of the incoming + + + align:start position:0% +which is the wavelength of the incoming +photon minus the wavelength of the + + align:start position:0% +photon minus the wavelength of the + + + align:start position:0% +photon minus the wavelength of the +outgoing photon + + align:start position:0% +outgoing photon + + + align:start position:0% +outgoing photon +as a function of the scattering angle + + align:start position:0% +as a function of the scattering angle + + + align:start position:0% +as a function of the scattering angle +theta as shown in this picture here + + align:start position:0% +theta as shown in this picture here + + + align:start position:0% +theta as shown in this picture here +okay so again this is an activity i want + + align:start position:0% +okay so again this is an activity i want + + + align:start position:0% +okay so again this is an activity i want +you to to to work on and and try to find + + align:start position:0% +you to to to work on and and try to find + + + align:start position:0% +you to to to work on and and try to find +out this the algebra here is not trivial + + align:start position:0% +out this the algebra here is not trivial + + + align:start position:0% +out this the algebra here is not trivial +but knowing how to set up a problem like + + align:start position:0% +but knowing how to set up a problem like + + + align:start position:0% +but knowing how to set up a problem like +this is important + + align:start position:0% +this is important + + + align:start position:0% +this is important +so let's try + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +the way to set this up is to write this + + align:start position:0% +the way to set this up is to write this + + + align:start position:0% +the way to set this up is to write this +four vector relation or you could just + + align:start position:0% +four vector relation or you could just + + + align:start position:0% +four vector relation or you could just +simply write down energy conservation + + align:start position:0% +simply write down energy conservation + + + align:start position:0% +simply write down energy conservation +and momentum conservation so you have an + + align:start position:0% +and momentum conservation so you have an + + + align:start position:0% +and momentum conservation so you have an +initial state the before + + align:start position:0% +initial state the before + + + align:start position:0% +initial state the before +and the final state the after so you + + align:start position:0% +and the final state the after so you + + + align:start position:0% +and the final state the after so you +simply add the four vectors of the + + align:start position:0% +simply add the four vectors of the + + + align:start position:0% +simply add the four vectors of the +initial electron and photon + + align:start position:0% +initial electron and photon + + + align:start position:0% +initial electron and photon +um and set this equal to the scattered + + align:start position:0% +um and set this equal to the scattered + + + align:start position:0% +um and set this equal to the scattered +electron and the scattered folder + + align:start position:0% +electron and the scattered folder + + + align:start position:0% +electron and the scattered folder +now we are interested in + + align:start position:0% +now we are interested in + + + align:start position:0% +now we are interested in +a quantity delta lambda which is related + + align:start position:0% +a quantity delta lambda which is related + + + align:start position:0% +a quantity delta lambda which is related +to the change in energy of the photon + + align:start position:0% +to the change in energy of the photon + + + align:start position:0% +to the change in energy of the photon +so therefore you bring the four vector + + align:start position:0% +so therefore you bring the four vector + + + align:start position:0% +so therefore you bring the four vector +of the four scattered photon over here + + align:start position:0% +of the four scattered photon over here + + + align:start position:0% +of the four scattered photon over here +to this side + + align:start position:0% +to this side + + + align:start position:0% +to this side +um and build the square which allows us + + align:start position:0% +um and build the square which allows us + + + align:start position:0% +um and build the square which allows us +then to use + + align:start position:0% +then to use + + + align:start position:0% +then to use +our invariant information in this within + + align:start position:0% +our invariant information in this within + + + align:start position:0% +our invariant information in this within +the scattering process + + align:start position:0% +the scattering process + + + align:start position:0% +the scattering process +um + + align:start position:0% +um + + + align:start position:0% +um +when we explore the squared here + + align:start position:0% +when we explore the squared here + + + align:start position:0% +when we explore the squared here +um we find the photon for vectors + + align:start position:0% +um we find the photon for vectors + + + align:start position:0% +um we find the photon for vectors +squared + + align:start position:0% +squared + + + align:start position:0% +squared +um for the scattered and the unscattered + + align:start position:0% +um for the scattered and the unscattered + + + align:start position:0% +um for the scattered and the unscattered +photon minus two times the product of + + align:start position:0% +photon minus two times the product of + + + align:start position:0% +photon minus two times the product of +the two four vectors now the mass of the + + align:start position:0% +the two four vectors now the mass of the + + + align:start position:0% +the two four vectors now the mass of the +photon is zero and then hence the + + align:start position:0% +photon is zero and then hence the + + + align:start position:0% +photon is zero and then hence the +invariant mass is zero two so this + + align:start position:0% +invariant mass is zero two so this + + + align:start position:0% +invariant mass is zero two so this +invariant four vector + + align:start position:0% +invariant four vector + + + align:start position:0% +invariant four vector +is zero so this cancels and this cancels + + align:start position:0% +is zero so this cancels and this cancels + + + align:start position:0% +is zero so this cancels and this cancels +and then we know that the mass of the + + align:start position:0% +and then we know that the mass of the + + + align:start position:0% +and then we know that the mass of the +electron is the mass of the electron the + + align:start position:0% +electron is the mass of the electron the + + + align:start position:0% +electron is the mass of the electron the +initial momentum of the electron is zero + + align:start position:0% +initial momentum of the electron is zero + + + align:start position:0% +initial momentum of the electron is zero +and we just for the further not to get + + align:start position:0% +and we just for the further not to get + + + align:start position:0% +and we just for the further not to get +confused we set c equal to 0 to 1. + + align:start position:0% +confused we set c equal to 0 to 1. + + + align:start position:0% +confused we set c equal to 0 to 1. +so then we just go through a sequence of + + align:start position:0% +so then we just go through a sequence of + + + align:start position:0% +so then we just go through a sequence of +algebra here + + align:start position:0% + + + + align:start position:0% + +making use of + + align:start position:0% +making use of + + + align:start position:0% +making use of +information that those guys here are + + align:start position:0% +information that those guys here are + + + align:start position:0% +information that those guys here are +simply the mass of the electron um we + + align:start position:0% +simply the mass of the electron um we + + + align:start position:0% +simply the mass of the electron um we +move things around a little bit and then + + align:start position:0% +move things around a little bit and then + + + align:start position:0% +move things around a little bit and then +find this equation here which relates + + align:start position:0% +find this equation here which relates + + + align:start position:0% +find this equation here which relates +um the the energies of the two photons + + align:start position:0% +um the the energies of the two photons + + + align:start position:0% +um the the energies of the two photons +we are the scattering angle which we get + + align:start position:0% +we are the scattering angle which we get + + + align:start position:0% +we are the scattering angle which we get +from the scalar product of the + + align:start position:0% +from the scalar product of the + + + align:start position:0% +from the scalar product of the +three momenta of the photon + + align:start position:0% +three momenta of the photon + + + align:start position:0% +three momenta of the photon +to the change in electron + + align:start position:0% +to the change in electron + + + align:start position:0% +to the change in electron +energy + + align:start position:0% +energy + + + align:start position:0% +energy +which is the energy of the electron + + align:start position:0% +which is the energy of the electron + + + align:start position:0% +which is the energy of the electron +minus the mass + + align:start position:0% +minus the mass + + + align:start position:0% +minus the mass +okay and then we start using the + + align:start position:0% +okay and then we start using the + + + align:start position:0% +okay and then we start using the +einstein relation here + + align:start position:0% +einstein relation here + + + align:start position:0% +einstein relation here +and again a little bit of algebra then + + align:start position:0% +and again a little bit of algebra then + + + align:start position:0% +and again a little bit of algebra then +brings us to delta lambda equal + + align:start position:0% +brings us to delta lambda equal + + + align:start position:0% +brings us to delta lambda equal +h over me times 1 minus cosine theta + + align:start position:0% +h over me times 1 minus cosine theta + + + align:start position:0% +h over me times 1 minus cosine theta +so this relates the + + align:start position:0% +so this relates the + + + align:start position:0% +so this relates the +shift in wavelength to the scattering + + align:start position:0% +shift in wavelength to the scattering + + + align:start position:0% +shift in wavelength to the scattering +angle of the photon + + align:start position:0% +angle of the photon + + + align:start position:0% +angle of the photon +important if you want to recall this + + align:start position:0% +important if you want to recall this + + + align:start position:0% +important if you want to recall this +the most important part to this problem + + align:start position:0% +the most important part to this problem + + + align:start position:0% +the most important part to this problem +is setting up + + align:start position:0% +is setting up + + + align:start position:0% +is setting up +this first equation here which relates + + align:start position:0% +this first equation here which relates + + + align:start position:0% +this first equation here which relates +the energy and the momentum or the four + + align:start position:0% +the energy and the momentum or the four + + + align:start position:0% +the energy and the momentum or the four +vector of those particles before and + + align:start position:0% +vector of those particles before and + + + align:start position:0% +vector of those particles before and +after the collision + + align:start position:0% +after the collision + + + align:start position:0% +after the collision +and again and then you know it takes a + + align:start position:0% +and again and then you know it takes a + + + align:start position:0% +and again and then you know it takes a +little bit of practice but the way to + + align:start position:0% +little bit of practice but the way to + + + align:start position:0% +little bit of practice but the way to +approach most of those problems is to + + align:start position:0% +approach most of those problems is to + + + align:start position:0% +approach most of those problems is to +make use of + + align:start position:0% +make use of + + + align:start position:0% +make use of +um the invariant for vector + + align:start position:0% +um the invariant for vector + + + align:start position:0% +um the invariant for vector +squared + + align:start position:0% +squared + + + align:start position:0% +squared +or the invariant mass of the objects + + align:start position:0% +or the invariant mass of the objects + + + align:start position:0% +or the invariant mass of the objects +involved as we know the masses of the + + align:start position:0% +involved as we know the masses of the + + + align:start position:0% +involved as we know the masses of the +object involved + + align:start position:0% +object involved + + + align:start position:0% +object involved +okay + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/TIQ3xN38jgM.txt b/TIQ3xN38jgM.txt new file mode 100644 index 0000000000000000000000000000000000000000..b2a9cf273908d07671d9351e3818d6fd84da2766 --- /dev/null +++ b/TIQ3xN38jgM.txt @@ -0,0 +1,627 @@ +align:start position:0% + +the point of switching from relational + + align:start position:0% +the point of switching from relational + + + align:start position:0% +the point of switching from relational +language to graph theor radical language + + align:start position:0% +language to graph theor radical language + + + align:start position:0% +language to graph theor radical language +is really so that we can talk about + + align:start position:0% +is really so that we can talk about + + + align:start position:0% +is really so that we can talk about +paths and connections so let's look at + + align:start position:0% +paths and connections so let's look at + + + align:start position:0% +paths and connections so let's look at +the topic of graph connectivity in + + align:start position:0% +the topic of graph connectivity in + + + align:start position:0% +the topic of graph connectivity in +general two vertices uh in a simple + + align:start position:0% +general two vertices uh in a simple + + + align:start position:0% +general two vertices uh in a simple +graph or for that matter a directed + + align:start position:0% +graph or for that matter a directed + + + align:start position:0% +graph or for that matter a directed +graph are said to be connected if and + + align:start position:0% +graph are said to be connected if and + + + align:start position:0% +graph are said to be connected if and +only if there's a path between them in a + + align:start position:0% +only if there's a path between them in a + + + align:start position:0% +only if there's a path between them in a +directed graph the path would have a + + align:start position:0% +directed graph the path would have a + + + align:start position:0% +directed graph the path would have a +direction in a simple graph it pads + + align:start position:0% +direction in a simple graph it pads + + + align:start position:0% +direction in a simple graph it pads +don't have Direction so a is connected + + align:start position:0% +don't have Direction so a is connected + + + align:start position:0% +don't have Direction so a is connected +to B if and only if B is connected to a + + align:start position:0% +to B if and only if B is connected to a + + + align:start position:0% +to B if and only if B is connected to a +it's a + + align:start position:0% +it's a + + + align:start position:0% +it's a +symmetric relation so two vertices are + + align:start position:0% +symmetric relation so two vertices are + + + align:start position:0% +symmetric relation so two vertices are +connected if and only if there's a path + + align:start position:0% +connected if and only if there's a path + + + align:start position:0% +connected if and only if there's a path +between them that's equivalent of course + + align:start position:0% +between them that's equivalent of course + + + align:start position:0% +between them that's equivalent of course +to saying if and only if there's a walk + + align:start position:0% +to saying if and only if there's a walk + + + align:start position:0% +to saying if and only if there's a walk +between them we include length zero + + align:start position:0% +between them we include length zero + + + align:start position:0% +between them we include length zero +paths and length zero walks so every + + align:start position:0% +paths and length zero walks so every + + + align:start position:0% +paths and length zero walks so every +vertex is considered to be connected to + + align:start position:0% +vertex is considered to be connected to + + + align:start position:0% +vertex is considered to be connected to +itself a whole graph is said to be + + align:start position:0% +itself a whole graph is said to be + + + align:start position:0% +itself a whole graph is said to be +connected if all of its vertex are + + align:start position:0% +connected if all of its vertex are + + + align:start position:0% +connected if all of its vertex are +connected to each + + align:start position:0% +connected to each + + + align:start position:0% +connected to each +other now so every graph you can think + + align:start position:0% +other now so every graph you can think + + + align:start position:0% +other now so every graph you can think +of as broken up into the mutually + + align:start position:0% +of as broken up into the mutually + + + align:start position:0% +of as broken up into the mutually +connected pieces or subgraphs which are + + align:start position:0% +connected pieces or subgraphs which are + + + align:start position:0% +connected pieces or subgraphs which are +called its connected components so let's + + align:start position:0% +called its connected components so let's + + + align:start position:0% +called its connected components so let's +look at a simple example uh let's look + + align:start position:0% +look at a simple example uh let's look + + + align:start position:0% +look at a simple example uh let's look +at the connections between MIT buildings + + align:start position:0% +at the connections between MIT buildings + + + align:start position:0% +at the connections between MIT buildings +where we draw an edge between building + + align:start position:0% +where we draw an edge between building + + + align:start position:0% +where we draw an edge between building +10 and Building 13 if there's a door + + align:start position:0% +10 and Building 13 if there's a door + + + align:start position:0% +10 and Building 13 if there's a door +between them or a corridor between them + + align:start position:0% +between them or a corridor between them + + + align:start position:0% +between them or a corridor between them +so there's a corridor between building + + align:start position:0% +so there's a corridor between building + + + align:start position:0% +so there's a corridor between building +10 and building four but not between + + align:start position:0% +10 and building four but not between + + + align:start position:0% +10 and building four but not between +building 10 and building 12 to get to 12 + + align:start position:0% +building 10 and building 12 to get to 12 + + + align:start position:0% +building 10 and building 12 to get to 12 +you have to go through + + align:start position:0% +you have to go through + + + align:start position:0% +you have to go through +four um that's the main building numbers + + align:start position:0% +four um that's the main building numbers + + + align:start position:0% +four um that's the main building numbers +off the MIT infinite Corridor East + + align:start position:0% +off the MIT infinite Corridor East + + + align:start position:0% +off the MIT infinite Corridor East +Campus of course isn't connected to + + align:start position:0% +Campus of course isn't connected to + + + align:start position:0% +Campus of course isn't connected to +anything so it's a single isolated + + align:start position:0% +anything so it's a single isolated + + + align:start position:0% +anything so it's a single isolated +Vortex and then there's the medical + + align:start position:0% +Vortex and then there's the medical + + + align:start position:0% +Vortex and then there's the medical +center in E17 and e25 which are a a + + align:start position:0% +center in E17 and e25 which are a a + + + align:start position:0% +center in E17 and e25 which are a a +sequence of four buildings that are + + align:start position:0% +sequence of four buildings that are + + + align:start position:0% +sequence of four buildings that are +connected as indicated but not connected + + align:start position:0% +connected as indicated but not connected + + + align:start position:0% +connected as indicated but not connected +at all to East Campus or the infinite + + align:start position:0% +at all to East Campus or the infinite + + + align:start position:0% +at all to East Campus or the infinite +carer that is you have to go outside to + + align:start position:0% +carer that is you have to go outside to + + + align:start position:0% +carer that is you have to go outside to +get from East Campus to the infinite + + align:start position:0% +get from East Campus to the infinite + + + align:start position:0% +get from East Campus to the infinite +caror or from the infinite caror to the + + align:start position:0% +caror or from the infinite caror to the + + + align:start position:0% +caror or from the infinite caror to the +medical center unless you sneak through + + align:start position:0% +medical center unless you sneak through + + + align:start position:0% +medical center unless you sneak through +the basement which and and other + + align:start position:0% +the basement which and and other + + + align:start position:0% +the basement which and and other +restricted areas so this is one graph + + align:start position:0% +restricted areas so this is one graph + + + align:start position:0% +restricted areas so this is one graph +it's not three graphs this is one graph + + align:start position:0% +it's not three graphs this is one graph + + + align:start position:0% +it's not three graphs this is one graph +which has three parts part s uh and so + + align:start position:0% +which has three parts part s uh and so + + + align:start position:0% +which has three parts part s uh and so +it has three connected + + align:start position:0% +it has three connected + + + align:start position:0% +it has three connected +components in general the more connected + + align:start position:0% +components in general the more connected + + + align:start position:0% +components in general the more connected +components a graph has the more broken + + align:start position:0% +components a graph has the more broken + + + align:start position:0% +components a graph has the more broken +up it is that's a way to remember it the + + align:start position:0% +up it is that's a way to remember it the + + + align:start position:0% +up it is that's a way to remember it the +formal definition of the connected + + align:start position:0% +formal definition of the connected + + + align:start position:0% +formal definition of the connected +component of a Vertex V is simply all of + + align:start position:0% +component of a Vertex V is simply all of + + + align:start position:0% +component of a Vertex V is simply all of +the vertices W that are connected to V + + align:start position:0% +the vertices W that are connected to V + + + align:start position:0% +the vertices W that are connected to V +and if you uh look at these connected + + align:start position:0% +and if you uh look at these connected + + + align:start position:0% +and if you uh look at these connected +components they Define an equivalence + + align:start position:0% +components they Define an equivalence + + + align:start position:0% +components they Define an equivalence +relation on the vertices of course + + align:start position:0% +relation on the vertices of course + + + align:start position:0% +relation on the vertices of course +because uh a connected component is a + + align:start position:0% +because uh a connected component is a + + + align:start position:0% +because uh a connected component is a +block of the equivalence + + align:start position:0% +block of the equivalence + + + align:start position:0% +block of the equivalence +relation it's a block of the partition + + align:start position:0% +relation it's a block of the partition + + + align:start position:0% +relation it's a block of the partition +associated with the equivalence + + align:start position:0% +associated with the equivalence + + + align:start position:0% +associated with the equivalence +relation um another way to say to Define + + align:start position:0% +relation um another way to say to Define + + + align:start position:0% +relation um another way to say to Define +this the set of w that are connected to + + align:start position:0% +this the set of w that are connected to + + + align:start position:0% +this the set of w that are connected to +V is simply it's taking the image of V + + align:start position:0% +V is simply it's taking the image of V + + + align:start position:0% +V is simply it's taking the image of V +under the uh uh greater than or equal to + + align:start position:0% +under the uh uh greater than or equal to + + + align:start position:0% +under the uh uh greater than or equal to +zero walk relation e we is our notation + + align:start position:0% +zero walk relation e we is our notation + + + align:start position:0% +zero walk relation e we is our notation +for the walk relation in the graph whose + + align:start position:0% +for the walk relation in the graph whose + + + align:start position:0% +for the walk relation in the graph whose +edges are e including walks of length + + align:start position:0% +edges are e including walks of length + + + align:start position:0% +edges are e including walks of length +zero + + align:start position:0% +zero + + + align:start position:0% +zero +so a graph is connected then means it + + align:start position:0% +so a graph is connected then means it + + + align:start position:0% +so a graph is connected then means it +really has only one connected + + align:start position:0% +really has only one connected + + + align:start position:0% +really has only one connected +component \ No newline at end of file diff --git a/US_75CwRIUM.txt b/US_75CwRIUM.txt new file mode 100644 index 0000000000000000000000000000000000000000..53f7a496d52b728a73bcf70433cd007f6249e937 --- /dev/null +++ b/US_75CwRIUM.txt @@ -0,0 +1,8944 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay let's get + + align:start position:0% +ocw.mit.edu okay let's get + + + align:start position:0% +ocw.mit.edu okay let's get +started uh one an announcement one + + align:start position:0% +started uh one an announcement one + + + align:start position:0% +started uh one an announcement one +announcement test + + align:start position:0% +announcement test + + + align:start position:0% +announcement test +three it's a celebration of learning + + align:start position:0% +three it's a celebration of learning + + + align:start position:0% +three it's a celebration of learning +it's going to be on Wednesday which + + align:start position:0% +it's going to be on Wednesday which + + + align:start position:0% +it's going to be on Wednesday which +means no lecture no lecture Wednesday + + align:start position:0% +means no lecture no lecture Wednesday + + + align:start position:0% +means no lecture no lecture Wednesday +instead the + + align:start position:0% +instead the + + + align:start position:0% +instead the +celebration um please go to your rooms + + align:start position:0% +celebration um please go to your rooms + + + align:start position:0% +celebration um please go to your rooms +as assigned here if you're writing at + + align:start position:0% +as assigned here if you're writing at + + + align:start position:0% +as assigned here if you're writing at +11:00 you're probably in this room right + + align:start position:0% +11:00 you're probably in this room right + + + align:start position:0% +11:00 you're probably in this room right +now and those are the room assignments + + align:start position:0% +now and those are the room assignments + + + align:start position:0% +now and those are the room assignments +uh they're the same as for test two but + + align:start position:0% +uh they're the same as for test two but + + + align:start position:0% +uh they're the same as for test two but +not the same as for test one we moved + + align:start position:0% +not the same as for test one we moved + + + align:start position:0% +not the same as for test one we moved +more people out of of uh 10250 give a + + align:start position:0% +more people out of of uh 10250 give a + + + align:start position:0% +more people out of of uh 10250 give a +little more room here and there's plenty + + align:start position:0% +little more room here and there's plenty + + + align:start position:0% +little more room here and there's plenty +of room in these others uh those that + + align:start position:0% +of room in these others uh those that + + + align:start position:0% +of room in these others uh those that +write at 1:00 do not go to the normal + + align:start position:0% +write at 1:00 do not go to the normal + + + align:start position:0% +write at 1:00 do not go to the normal +lecture room 6120 we're writing in + + align:start position:0% +lecture room 6120 we're writing in + + + align:start position:0% +lecture room 6120 we're writing in +26100 um and the coverage is right here + + align:start position:0% +26100 um and the coverage is right here + + + align:start position:0% +26100 um and the coverage is right here +so uh that's uh up on the uh the website + + align:start position:0% +so uh that's uh up on the uh the website + + + align:start position:0% +so uh that's uh up on the uh the website +so you should know what we're going to + + align:start position:0% +so you should know what we're going to + + + align:start position:0% +so you should know what we're going to +be um examining you on and uh the same + + align:start position:0% +be um examining you on and uh the same + + + align:start position:0% +be um examining you on and uh the same +comments that I've made before you know + + align:start position:0% +comments that I've made before you know + + + align:start position:0% +comments that I've made before you know +I want to give you feedback let you know + + align:start position:0% +I want to give you feedback let you know + + + align:start position:0% +I want to give you feedback let you know +how you're doing whether your study uh + + align:start position:0% +how you're doing whether your study uh + + + align:start position:0% +how you're doing whether your study uh +methods are effective or not it's not an + + align:start position:0% +methods are effective or not it's not an + + + align:start position:0% +methods are effective or not it's not an +attempt to retest your admission to MIT + + align:start position:0% +attempt to retest your admission to MIT + + + align:start position:0% +attempt to retest your admission to MIT +or anything like that if you've done + + align:start position:0% +or anything like that if you've done + + + align:start position:0% +or anything like that if you've done +your work you should do very well and if + + align:start position:0% +your work you should do very well and if + + + align:start position:0% +your work you should do very well and if +you haven't done your work um you + + align:start position:0% +you haven't done your work um you + + + align:start position:0% +you haven't done your work um you +shouldn't do very well and we'll be able + + align:start position:0% +shouldn't do very well and we'll be able + + + align:start position:0% +shouldn't do very well and we'll be able +to tell you so um so just remember what + + align:start position:0% +to tell you so um so just remember what + + + align:start position:0% +to tell you so um so just remember what +we've said in the past please take some + + align:start position:0% +we've said in the past please take some + + + align:start position:0% +we've said in the past please take some +time read the whole exam um do the easy + + align:start position:0% +time read the whole exam um do the easy + + + align:start position:0% +time read the whole exam um do the easy +questions for you the ones that you find + + align:start position:0% +questions for you the ones that you find + + + align:start position:0% +questions for you the ones that you find +easiest do those first um but let's + + align:start position:0% +easiest do those first um but let's + + + align:start position:0% +easiest do those first um but let's +let's be honest you know this isn't high + + align:start position:0% +let's be honest you know this isn't high + + + align:start position:0% +let's be honest you know this isn't high +school anymore so I mean I had some + + align:start position:0% +school anymore so I mean I had some + + + align:start position:0% +school anymore so I mean I had some +people tell me after the second test you + + align:start position:0% +people tell me after the second test you + + + align:start position:0% +people tell me after the second test you +know I had had my age sheet but I hardly + + align:start position:0% +know I had had my age sheet but I hardly + + + align:start position:0% +know I had had my age sheet but I hardly +used it well think about it do you think + + align:start position:0% +used it well think about it do you think + + + align:start position:0% +used it well think about it do you think +I'm going to give you an age sheet and + + align:start position:0% +I'm going to give you an age sheet and + + + align:start position:0% +I'm going to give you an age sheet and +then give you a question that requires + + align:start position:0% +then give you a question that requires + + + align:start position:0% +then give you a question that requires +you to take something off the AG sheet + + align:start position:0% +you to take something off the AG sheet + + + align:start position:0% +you to take something off the AG sheet +and transfer it to the answer paper it's + + align:start position:0% +and transfer it to the answer paper it's + + + align:start position:0% +and transfer it to the answer paper it's +not pattern recognition I mean this + + align:start position:0% +not pattern recognition I mean this + + + align:start position:0% +not pattern recognition I mean this +isn't medical school for crying out loud + + align:start position:0% +isn't medical school for crying out loud + + + align:start position:0% +isn't medical school for crying out loud +you know you got to think here you got + + align:start position:0% +you know you got to think here you got + + + align:start position:0% +you know you got to think here you got +to think right so you know and this is + + align:start position:0% +to think right so you know and this is + + + align:start position:0% +to think right so you know and this is +now the third test it's going to be + + align:start position:0% +now the third test it's going to be + + + align:start position:0% +now the third test it's going to be +more and more thinking and less and less + + align:start position:0% +more and more thinking and less and less + + + align:start position:0% +more and more thinking and less and less +Road although we'll have some confidence + + align:start position:0% +Road although we'll have some confidence + + + align:start position:0% +Road although we'll have some confidence +builders on there I don't want to uh uh + + align:start position:0% +builders on there I don't want to uh uh + + + align:start position:0% +builders on there I don't want to uh uh +knock people off their off their balance + + align:start position:0% +knock people off their off their balance + + + align:start position:0% +knock people off their off their balance +um so work uh work + + align:start position:0% +um so work uh work + + + align:start position:0% +um so work uh work +parametrically uh try not to immediately + + align:start position:0% +parametrically uh try not to immediately + + + align:start position:0% +parametrically uh try not to immediately +start punching in numbers and uh if you + + align:start position:0% +start punching in numbers and uh if you + + + align:start position:0% +start punching in numbers and uh if you +don't know how to do a question in great + + align:start position:0% +don't know how to do a question in great + + + align:start position:0% +don't know how to do a question in great +detail write me an outline tell me what + + align:start position:0% +detail write me an outline tell me what + + + align:start position:0% +detail write me an outline tell me what +you'd do you'd equate some energies or + + align:start position:0% +you'd do you'd equate some energies or + + + align:start position:0% +you'd do you'd equate some energies or +you'd minimize something or maximize + + align:start position:0% +you'd minimize something or maximize + + + align:start position:0% +you'd minimize something or maximize +something give us a sense that you have + + align:start position:0% +something give us a sense that you have + + + align:start position:0% +something give us a sense that you have +uh a grasp of the material and + + align:start position:0% +uh a grasp of the material and + + + align:start position:0% +uh a grasp of the material and +um keep your eyes on your own paper and + + align:start position:0% +um keep your eyes on your own paper and + + + align:start position:0% +um keep your eyes on your own paper and +our effort is going to be to get those + + align:start position:0% +our effort is going to be to get those + + + align:start position:0% +our effort is going to be to get those +graded on Wednesday and back to you in + + align:start position:0% +graded on Wednesday and back to you in + + + align:start position:0% +graded on Wednesday and back to you in +recitation on on Thursday + + align:start position:0% +recitation on on Thursday + + + align:start position:0% +recitation on on Thursday +so I think that's uh and remember please + + align:start position:0% +so I think that's uh and remember please + + + align:start position:0% +so I think that's uh and remember please +bring bring your five items uh we we're + + align:start position:0% +bring bring your five items uh we we're + + + align:start position:0% +bring bring your five items uh we we're +having more and more people showing up + + align:start position:0% +having more and more people showing up + + + align:start position:0% +having more and more people showing up +minus periodic table table of constants + + align:start position:0% +minus periodic table table of constants + + + align:start position:0% +minus periodic table table of constants +uh something to write with I've had + + align:start position:0% +uh something to write with I've had + + + align:start position:0% +uh something to write with I've had +people ask me for for pens for + + align:start position:0% +people ask me for for pens for + + + align:start position:0% +people ask me for for pens for +calculators uh no one has asked me yet + + align:start position:0% +calculators uh no one has asked me yet + + + align:start position:0% +calculators uh no one has asked me yet +for an AG sheet so I haven't haven't had + + align:start position:0% +for an AG sheet so I haven't haven't had + + + align:start position:0% +for an AG sheet so I haven't haven't had +to help anybody on that one okay good + + align:start position:0% +to help anybody on that one okay good + + + align:start position:0% +to help anybody on that one okay good +well today what I want to do is uh um + + align:start position:0% +well today what I want to do is uh um + + + align:start position:0% +well today what I want to do is uh um +start a new unit uh I want to talk today + + align:start position:0% +start a new unit uh I want to talk today + + + align:start position:0% +start a new unit uh I want to talk today +about organic chemistry now this is this + + align:start position:0% +about organic chemistry now this is this + + + align:start position:0% +about organic chemistry now this is this +is going to be the the most minimal + + align:start position:0% +is going to be the the most minimal + + + align:start position:0% +is going to be the the most minimal +introduction to organic chemistry the + + align:start position:0% +introduction to organic chemistry the + + + align:start position:0% +introduction to organic chemistry the +reason we talk about organic chemistry + + align:start position:0% +reason we talk about organic chemistry + + + align:start position:0% +reason we talk about organic chemistry +at all is in order to prepare ourselves + + align:start position:0% +at all is in order to prepare ourselves + + + align:start position:0% +at all is in order to prepare ourselves +for more solid state chemistry + + align:start position:0% +for more solid state chemistry + + + align:start position:0% +for more solid state chemistry +specifically I'm going to talk about + + align:start position:0% +specifically I'm going to talk about + + + align:start position:0% +specifically I'm going to talk about +polymers and ultimately we're going to + + align:start position:0% +polymers and ultimately we're going to + + + align:start position:0% +polymers and ultimately we're going to +talk about biochemistry because even + + align:start position:0% +talk about biochemistry because even + + + align:start position:0% +talk about biochemistry because even +though this is solid state chemistry we + + align:start position:0% +though this is solid state chemistry we + + + align:start position:0% +though this is solid state chemistry we +as living beings are solid state devices + + align:start position:0% +as living beings are solid state devices + + + align:start position:0% +as living beings are solid state devices +we're made of soft matter this is a + + align:start position:0% +we're made of soft matter this is a + + + align:start position:0% +we're made of soft matter this is a +polymer right this is a uh semiconductor + + align:start position:0% +polymer right this is a uh semiconductor + + + align:start position:0% +polymer right this is a uh semiconductor +band gap of two to three electron volts + + align:start position:0% +band gap of two to three electron volts + + + align:start position:0% +band gap of two to three electron volts +but it's not made out of 35 + + align:start position:0% +but it's not made out of 35 + + + align:start position:0% +but it's not made out of 35 +semiconductor Nature's figured out a way + + align:start position:0% +semiconductor Nature's figured out a way + + + align:start position:0% +semiconductor Nature's figured out a way +of doing this + + align:start position:0% +of doing this + + + align:start position:0% +of doing this +without + + align:start position:0% +without + + + align:start position:0% +without +inorganic means + + align:start position:0% +inorganic means + + + align:start position:0% +inorganic means +so we need to know a little bit but if + + align:start position:0% +so we need to know a little bit but if + + + align:start position:0% +so we need to know a little bit but if +you really want to know organic + + align:start position:0% +you really want to know organic + + + align:start position:0% +you really want to know organic +chemistry you're going to have to take + + align:start position:0% +chemistry you're going to have to take + + + align:start position:0% +chemistry you're going to have to take +512 so I can't teach you in 50 minutes + + align:start position:0% +512 so I can't teach you in 50 minutes + + + align:start position:0% +512 so I can't teach you in 50 minutes +what people teach in one semester so + + align:start position:0% +what people teach in one semester so + + + align:start position:0% +what people teach in one semester so +let's get a few definitions under our + + align:start position:0% +let's get a few definitions under our + + + align:start position:0% +let's get a few definitions under our +belts uh organic chemistry is the + + align:start position:0% +belts uh organic chemistry is the + + + align:start position:0% +belts uh organic chemistry is the +chemistry of compounds containing both + + align:start position:0% +chemistry of compounds containing both + + + align:start position:0% +chemistry of compounds containing both +carbon and hydrogen not just carbon + + align:start position:0% +carbon and hydrogen not just carbon + + + align:start position:0% +carbon and hydrogen not just carbon +carbon and hydrogen so Diamond graphite + + align:start position:0% +carbon and hydrogen so Diamond graphite + + + align:start position:0% +carbon and hydrogen so Diamond graphite +are not organic because they contain + + align:start position:0% +are not organic because they contain + + + align:start position:0% +are not organic because they contain +carbon but not hydrogen and what what + + align:start position:0% +carbon but not hydrogen and what what + + + align:start position:0% +carbon but not hydrogen and what what +makes these two elements special that + + align:start position:0% +makes these two elements special that + + + align:start position:0% +makes these two elements special that +that uh they figure so prominently in + + align:start position:0% +that uh they figure so prominently in + + + align:start position:0% +that uh they figure so prominently in +living uh organisms first of all + + align:start position:0% +living uh organisms first of all + + + align:start position:0% +living uh organisms first of all +hydrogen hydrogen is the element with + + align:start position:0% +hydrogen hydrogen is the element with + + + align:start position:0% +hydrogen hydrogen is the element with +the lowest atomic number lowest atomic + + align:start position:0% +the lowest atomic number lowest atomic + + + align:start position:0% +the lowest atomic number lowest atomic +number and when it loses its electron it + + align:start position:0% +number and when it loses its electron it + + + align:start position:0% +number and when it loses its electron it +changes character dramatically we talked + + align:start position:0% +changes character dramatically we talked + + + align:start position:0% +changes character dramatically we talked +about this in recent uh lectures where + + align:start position:0% +about this in recent uh lectures where + + + align:start position:0% +about this in recent uh lectures where +we have simply a + + align:start position:0% +we have simply a + + + align:start position:0% +we have simply a +proton if it's capable of forming Cove + + align:start position:0% +proton if it's capable of forming Cove + + + align:start position:0% +proton if it's capable of forming Cove +valent bonds but when it finds itself in + + align:start position:0% +valent bonds but when it finds itself in + + + align:start position:0% +valent bonds but when it finds itself in +a compound forming a calent bond with + + align:start position:0% +a compound forming a calent bond with + + + align:start position:0% +a compound forming a calent bond with +something it's strongly electronegative + + align:start position:0% +something it's strongly electronegative + + + align:start position:0% +something it's strongly electronegative +it's so denuded of electrons even in the + + align:start position:0% +it's so denuded of electrons even in the + + + align:start position:0% +it's so denuded of electrons even in the +Cove valent bond that that protonic + + align:start position:0% +Cove valent bond that that protonic + + + align:start position:0% +Cove valent bond that that protonic +entity can start mischief and form + + align:start position:0% +entity can start mischief and form + + + align:start position:0% +entity can start mischief and form +hydrogen bonds carbon carbon's dead + + align:start position:0% +hydrogen bonds carbon carbon's dead + + + align:start position:0% +hydrogen bonds carbon carbon's dead +center four veence electrons so it's + + align:start position:0% +center four veence electrons so it's + + + align:start position:0% +center four veence electrons so it's +nowhere near metallic it's nowhere near + + align:start position:0% +nowhere near metallic it's nowhere near + + + align:start position:0% +nowhere near metallic it's nowhere near +non-metallic so it's got an intermediate + + align:start position:0% +non-metallic so it's got an intermediate + + + align:start position:0% +non-metallic so it's got an intermediate +value of average veence electron energy + + align:start position:0% +value of average veence electron energy + + + align:start position:0% +value of average veence electron energy +it's very unlikely that carbon is going + + align:start position:0% +it's very unlikely that carbon is going + + + align:start position:0% +it's very unlikely that carbon is going +to acquire four electrons and become C4 + + align:start position:0% +to acquire four electrons and become C4 + + + align:start position:0% +to acquire four electrons and become C4 +minus or lose four electrons and become + + align:start position:0% +minus or lose four electrons and become + + + align:start position:0% +minus or lose four electrons and become +C4 plus it's prominently a Cove valent + + align:start position:0% +C4 plus it's prominently a Cove valent + + + align:start position:0% +C4 plus it's prominently a Cove valent +player but it's very small and because + + align:start position:0% +player but it's very small and because + + + align:start position:0% +player but it's very small and because +it's small it can form multiple bonds it + + align:start position:0% +it's small it can form multiple bonds it + + + align:start position:0% +it's small it can form multiple bonds it +forms multiple bonds we've already seen + + align:start position:0% +forms multiple bonds we've already seen + + + align:start position:0% +forms multiple bonds we've already seen +evidence where it forms Sigma and Pi + + align:start position:0% +evidence where it forms Sigma and Pi + + + align:start position:0% +evidence where it forms Sigma and Pi +bonds so it can form double bonds and + + align:start position:0% +bonds so it can form double bonds and + + + align:start position:0% +bonds so it can form double bonds and +triple bonds not only with itself but + + align:start position:0% +triple bonds not only with itself but + + + align:start position:0% +triple bonds not only with itself but +with other elements notably nitrogen + + align:start position:0% +with other elements notably nitrogen + + + align:start position:0% +with other elements notably nitrogen +oxygen phosphorus and sulfur and even + + align:start position:0% +oxygen phosphorus and sulfur and even + + + align:start position:0% +oxygen phosphorus and sulfur and even +those silicon and germanium hybridized + + align:start position:0% +those silicon and germanium hybridized + + + align:start position:0% +those silicon and germanium hybridized +because they're not small silicon does + + align:start position:0% +because they're not small silicon does + + + align:start position:0% +because they're not small silicon does +not form double bonds you will not see + + align:start position:0% +not form double bonds you will not see + + + align:start position:0% +not form double bonds you will not see +silicon analoges to carbon + + align:start position:0% +silicon analoges to carbon + + + align:start position:0% +silicon analoges to carbon +compounds throughout yeah silicon sp3 + + align:start position:0% +compounds throughout yeah silicon sp3 + + + align:start position:0% +compounds throughout yeah silicon sp3 +hybridizes and uh single Crystal silicon + + align:start position:0% +hybridizes and uh single Crystal silicon + + + align:start position:0% +hybridizes and uh single Crystal silicon +has the same crystal structure as single + + align:start position:0% +has the same crystal structure as single + + + align:start position:0% +has the same crystal structure as single +crystal diamond but that's pretty much + + align:start position:0% +crystal diamond but that's pretty much + + + align:start position:0% +crystal diamond but that's pretty much +where the similarity ends it's uh pretty + + align:start position:0% +where the similarity ends it's uh pretty + + + align:start position:0% +where the similarity ends it's uh pretty +much sp3 hybridization and that's the + + align:start position:0% +much sp3 hybridization and that's the + + + align:start position:0% +much sp3 hybridization and that's the +end of the story so these two have very + + align:start position:0% +end of the story so these two have very + + + align:start position:0% +end of the story so these two have very +special qualities that make them uh so + + align:start position:0% +special qualities that make them uh so + + + align:start position:0% +special qualities that make them uh so +important and I mean the other thing + + align:start position:0% +important and I mean the other thing + + + align:start position:0% +important and I mean the other thing +that carbon can do is it can it can + + align:start position:0% +that carbon can do is it can it can + + + align:start position:0% +that carbon can do is it can it can +continue to link with itself and form + + align:start position:0% +continue to link with itself and form + + + align:start position:0% +continue to link with itself and form +chains and various other structures and + + align:start position:0% +chains and various other structures and + + + align:start position:0% +chains and various other structures and +we're going to meet a few of those today + + align:start position:0% +we're going to meet a few of those today + + + align:start position:0% +we're going to meet a few of those today +um there are millions of organic + + align:start position:0% +um there are millions of organic + + + align:start position:0% +um there are millions of organic +compounds Millions let say billions + + align:start position:0% +compounds Millions let say billions + + + align:start position:0% +compounds Millions let say billions +billions and billions but I'm not going + + align:start position:0% +billions and billions but I'm not going + + + align:start position:0% +billions and billions but I'm not going +to cover all that we're going to cover + + align:start position:0% +to cover all that we're going to cover + + + align:start position:0% +to cover all that we're going to cover +the ones that are most uh gerine to our + + align:start position:0% +the ones that are most uh gerine to our + + + align:start position:0% +the ones that are most uh gerine to our +subsequent discussions of polymers and + + align:start position:0% +subsequent discussions of polymers and + + + align:start position:0% +subsequent discussions of polymers and +uh biochemistry + + align:start position:0% +uh biochemistry + + + align:start position:0% +uh biochemistry +so let's first of all go through the the + + align:start position:0% +so let's first of all go through the the + + + align:start position:0% +so let's first of all go through the the +taxonomy so I mean I've posted all this + + align:start position:0% +taxonomy so I mean I've posted all this + + + align:start position:0% +taxonomy so I mean I've posted all this +at the website and it's in the reading + + align:start position:0% +at the website and it's in the reading + + + align:start position:0% +at the website and it's in the reading +I've tried to characterize this in a way + + align:start position:0% +I've tried to characterize this in a way + + + align:start position:0% +I've tried to characterize this in a way +that uh or categorize it so that it it + + align:start position:0% +that uh or categorize it so that it it + + + align:start position:0% +that uh or categorize it so that it it +uh it makes some uh simple sense as + + align:start position:0% +uh it makes some uh simple sense as + + + align:start position:0% +uh it makes some uh simple sense as +opposed to just standing here and + + align:start position:0% +opposed to just standing here and + + + align:start position:0% +opposed to just standing here and +barking out a Litany of uh of facts to + + align:start position:0% +barking out a Litany of uh of facts to + + + align:start position:0% +barking out a Litany of uh of facts to +you so the first thing I want to do is + + align:start position:0% +you so the first thing I want to do is + + + align:start position:0% +you so the first thing I want to do is +look at the leftand column called the + + align:start position:0% +look at the leftand column called the + + + align:start position:0% +look at the leftand column called the +alanes and these are hydrocarbons the + + align:start position:0% +alanes and these are hydrocarbons the + + + align:start position:0% +alanes and these are hydrocarbons the +whole thing we're going to look at is + + align:start position:0% +whole thing we're going to look at is + + + align:start position:0% +whole thing we're going to look at is +hydrocarbons for starters + + align:start position:0% + + + + align:start position:0% + +and these as the name implies are + + align:start position:0% +and these as the name implies are + + + align:start position:0% +and these as the name implies are +compounds that consist of only carbon + + align:start position:0% +compounds that consist of only carbon + + + align:start position:0% +compounds that consist of only carbon +and hydrogen + + align:start position:0% +and hydrogen + + + align:start position:0% +and hydrogen +compounds compounds cons containing + + align:start position:0% +compounds compounds cons containing + + + align:start position:0% +compounds compounds cons containing +only hyrogen and + + align:start position:0% +only hyrogen and + + + align:start position:0% +only hyrogen and +carbon and the first group that we're + + align:start position:0% +carbon and the first group that we're + + + align:start position:0% +carbon and the first group that we're +going to look at is the alkanes as you + + align:start position:0% +going to look at is the alkanes as you + + + align:start position:0% +going to look at is the alkanes as you +can see in the in the uh uh slide and + + align:start position:0% +can see in the in the uh uh slide and + + + align:start position:0% +can see in the in the uh uh slide and +these are character cized by sp3 + + align:start position:0% +these are character cized by sp3 + + + align:start position:0% +these are character cized by sp3 +hybridization on the carbon all the + + align:start position:0% +hybridization on the carbon all the + + + align:start position:0% +hybridization on the carbon all the +carbons are sp3 hybridized and so that + + align:start position:0% +carbons are sp3 hybridized and so that + + + align:start position:0% +carbons are sp3 hybridized and so that +gives us the maximum possible number of + + align:start position:0% +gives us the maximum possible number of + + + align:start position:0% +gives us the maximum possible number of +bonds maximum number of carbon hydrogen + + align:start position:0% +bonds maximum number of carbon hydrogen + + + align:start position:0% +bonds maximum number of carbon hydrogen +linkages maximum number of carbon + + align:start position:0% +linkages maximum number of carbon + + + align:start position:0% +linkages maximum number of carbon +hydrogen linkages and so the the + + align:start position:0% +hydrogen linkages and so the the + + + align:start position:0% +hydrogen linkages and so the the +chemical term for such compounds is + + align:start position:0% +chemical term for such compounds is + + + align:start position:0% +chemical term for such compounds is +saturated these are saturated + + align:start position:0% +saturated these are saturated + + + align:start position:0% +saturated these are saturated +hydrocarbons and and all of these bonds + + align:start position:0% +hydrocarbons and and all of these bonds + + + align:start position:0% +hydrocarbons and and all of these bonds +are Sigma bonds all the bonds are Sigma + + align:start position:0% +are Sigma bonds all the bonds are Sigma + + + align:start position:0% +are Sigma bonds all the bonds are Sigma +bonds because they're all single bonds + + align:start position:0% +bonds because they're all single bonds + + + align:start position:0% +bonds because they're all single bonds +all Sigma bonds so these are the + + align:start position:0% +all Sigma bonds so these are the + + + align:start position:0% +all Sigma bonds so these are the +characteristics and the general formula + + align:start position:0% +characteristics and the general formula + + + align:start position:0% +characteristics and the general formula +if you go through the the math is going + + align:start position:0% +if you go through the the math is going + + + align:start position:0% +if you go through the the math is going +to be C some subn number whatever the + + align:start position:0% +to be C some subn number whatever the + + + align:start position:0% +to be C some subn number whatever the +number of carbons in the in the molecule + + align:start position:0% +number of carbons in the in the molecule + + + align:start position:0% +number of carbons in the in the molecule +and then if we go through sp3 + + align:start position:0% +and then if we go through sp3 + + + align:start position:0% +and then if we go through sp3 +hybridization and put hydrogens at all + + align:start position:0% +hybridization and put hydrogens at all + + + align:start position:0% +hybridization and put hydrogens at all +the non-carbon linkages it'll be h two + + align:start position:0% +the non-carbon linkages it'll be h two + + + align:start position:0% +the non-carbon linkages it'll be h two +times the c number plus two and so these + + align:start position:0% +times the c number plus two and so these + + + align:start position:0% +times the c number plus two and so these +are called + + align:start position:0% +are called + + + align:start position:0% +are called +alkanes and this is the the way you + + align:start position:0% +alkanes and this is the the way you + + + align:start position:0% +alkanes and this is the the way you +build the name a nomenclature is + + align:start position:0% +build the name a nomenclature is + + + align:start position:0% +build the name a nomenclature is +to it's going to have an A ending which + + align:start position:0% +to it's going to have an A ending which + + + align:start position:0% +to it's going to have an A ending which +is going to indicate that we're talking + + align:start position:0% +is going to indicate that we're talking + + + align:start position:0% +is going to indicate that we're talking +about sp3 + + align:start position:0% +about sp3 + + + align:start position:0% +about sp3 +hybridized uh + + align:start position:0% +hybridized uh + + + align:start position:0% +hybridized uh +hydrocarbons and then in order to + + align:start position:0% +hydrocarbons and then in order to + + + align:start position:0% +hydrocarbons and then in order to +indicate the number of carbons we call + + align:start position:0% +indicate the number of carbons we call + + + align:start position:0% +indicate the number of carbons we call +out we call out the carbon number by the + + align:start position:0% +out we call out the carbon number by the + + + align:start position:0% +out we call out the carbon number by the +prefix so this prefix identifies the + + align:start position:0% +prefix so this prefix identifies the + + + align:start position:0% +prefix so this prefix identifies the +carbon number and uh they're showing + + align:start position:0% +carbon number and uh they're showing + + + align:start position:0% +carbon number and uh they're showing +here actually let's take a look at a set + + align:start position:0% +here actually let's take a look at a set + + + align:start position:0% +here actually let's take a look at a set +of those this is right out of your right + + align:start position:0% +of those this is right out of your right + + + align:start position:0% +of those this is right out of your right +out of your reading and there they are + + align:start position:0% +out of your reading and there they are + + + align:start position:0% +out of your reading and there they are +one two three and so on and it's uh it's + + align:start position:0% +one two three and so on and it's uh it's + + + align:start position:0% +one two three and so on and it's uh it's +basically + + align:start position:0% +basically + + + align:start position:0% +basically +meth + + align:start position:0% +meth + + + align:start position:0% +meth +F prob 3 but is four and these are all + + align:start position:0% +F prob 3 but is four and these are all + + + align:start position:0% +F prob 3 but is four and these are all +historical and you can go into the + + align:start position:0% +historical and you can go into the + + + align:start position:0% +historical and you can go into the +reading and figure out but IC acid is + + align:start position:0% +reading and figure out but IC acid is + + + align:start position:0% +reading and figure out but IC acid is +one of the elements in rancid butter and + + align:start position:0% +one of the elements in rancid butter and + + + align:start position:0% +one of the elements in rancid butter and +so on so there's there's some historical + + align:start position:0% +so on so there's there's some historical + + + align:start position:0% +so on so there's there's some historical +reasons but after you get to four it's + + align:start position:0% +reasons but after you get to four it's + + + align:start position:0% +reasons but after you get to four it's +strictly the Latin ordinals from here on + + align:start position:0% +strictly the Latin ordinals from here on + + + align:start position:0% +strictly the Latin ordinals from here on +it's this is pent and what do we have we + + align:start position:0% +it's this is pent and what do we have we + + + align:start position:0% +it's this is pent and what do we have we +have hex + + align:start position:0% +have hex + + + align:start position:0% +have hex +hept known deck and so on so just go + + align:start position:0% +hept known deck and so on so just go + + + align:start position:0% +hept known deck and so on so just go +back to your Latin and you're going to + + align:start position:0% +back to your Latin and you're going to + + + align:start position:0% +back to your Latin and you're going to +be fine uh I'm not going to expect you + + align:start position:0% +be fine uh I'm not going to expect you + + + align:start position:0% +be fine uh I'm not going to expect you +to pull these out of out of memory I + + align:start position:0% +to pull these out of out of memory I + + + align:start position:0% +to pull these out of out of memory I +would tell you you know + + align:start position:0% +would tell you you know + + + align:start position:0% +would tell you you know +C5 well what's you forgot your Latin um + + align:start position:0% +C5 well what's you forgot your Latin um + + + align:start position:0% +C5 well what's you forgot your Latin um +was it a requirement an admission + + align:start position:0% +was it a requirement an admission + + + align:start position:0% +was it a requirement an admission +requirement how many semesters of Latin + + align:start position:0% +requirement how many semesters of Latin + + + align:start position:0% +requirement how many semesters of Latin +did you need in high school to get into + + align:start position:0% +did you need in high school to get into + + + align:start position:0% +did you need in high school to get into +MIT none okay so I think I better keep + + align:start position:0% +MIT none okay so I think I better keep + + + align:start position:0% +MIT none okay so I think I better keep +that in mind so I will tell you pentane + + align:start position:0% +that in mind so I will tell you pentane + + + align:start position:0% +that in mind so I will tell you pentane +and I'll give you the formula C5 + + align:start position:0% +and I'll give you the formula C5 + + + align:start position:0% +and I'll give you the formula C5 +h12 all right so these are also called + + align:start position:0% +h12 all right so these are also called + + + align:start position:0% +h12 all right so these are also called +they're called straight chain molecules + + align:start position:0% +they're called straight chain molecules + + + align:start position:0% +they're called straight chain molecules +because if we look at them a little bit + + align:start position:0% +because if we look at them a little bit + + + align:start position:0% +because if we look at them a little bit +more carefully we'll see the following + + align:start position:0% +more carefully we'll see the following + + + align:start position:0% +more carefully we'll see the following +let's have a look at what they look like + + align:start position:0% +let's have a look at what they look like + + + align:start position:0% +let's have a look at what they look like +oh before I go I just wanted to you know + + align:start position:0% +oh before I go I just wanted to you know + + + align:start position:0% +oh before I go I just wanted to you know +hearken back and show that there's some + + align:start position:0% +hearken back and show that there's some + + + align:start position:0% +hearken back and show that there's some +some uh overarching theme here so these + + align:start position:0% +some uh overarching theme here so these + + + align:start position:0% +some uh overarching theme here so these +are these are three hydrocarbons that + + align:start position:0% +are these are three hydrocarbons that + + + align:start position:0% +are these are three hydrocarbons that +I've chosen propane which uh we know is + + align:start position:0% +I've chosen propane which uh we know is + + + align:start position:0% +I've chosen propane which uh we know is +used as a as a fuel in uh among other + + align:start position:0% +used as a as a fuel in uh among other + + + align:start position:0% +used as a as a fuel in uh among other +things transportation and even in uh + + align:start position:0% +things transportation and even in uh + + + align:start position:0% +things transportation and even in uh +domestic barbecue grills and it's a + + align:start position:0% +domestic barbecue grills and it's a + + + align:start position:0% +domestic barbecue grills and it's a +gaset room temperature these are all the + + align:start position:0% +gaset room temperature these are all the + + + align:start position:0% +gaset room temperature these are all the +same they're long chains with hydrogen + + align:start position:0% +same they're long chains with hydrogen + + + align:start position:0% +same they're long chains with hydrogen +around them okay these are all symmetric + + align:start position:0% +around them okay these are all symmetric + + + align:start position:0% +around them okay these are all symmetric +molecules ules octane which is the + + align:start position:0% +molecules ules octane which is the + + + align:start position:0% +molecules ules octane which is the +principal constituent of gasoline is a + + align:start position:0% +principal constituent of gasoline is a + + + align:start position:0% +principal constituent of gasoline is a +liquid at room temperature and icosane + + align:start position:0% +liquid at room temperature and icosane + + + align:start position:0% +liquid at room temperature and icosane +is a solid at room temperature so all of + + align:start position:0% +is a solid at room temperature so all of + + + align:start position:0% +is a solid at room temperature so all of +these have their symmetric molecules and + + align:start position:0% +these have their symmetric molecules and + + + align:start position:0% +these have their symmetric molecules and +the only thing that's happening as you + + align:start position:0% +the only thing that's happening as you + + + align:start position:0% +the only thing that's happening as you +go to larger and larger molecules is + + align:start position:0% +go to larger and larger molecules is + + + align:start position:0% +go to larger and larger molecules is +you're increasing + + align:start position:0% +you're increasing + + + align:start position:0% +you're increasing +polarizability your Vander va's bonds + + align:start position:0% +polarizability your Vander va's bonds + + + align:start position:0% +polarizability your Vander va's bonds +between molecules of the same uh + + align:start position:0% +between molecules of the same uh + + + align:start position:0% +between molecules of the same uh +identity increases and you can see that + + align:start position:0% +identity increases and you can see that + + + align:start position:0% +identity increases and you can see that +as the molecular length increases the uh + + align:start position:0% +as the molecular length increases the uh + + + align:start position:0% +as the molecular length increases the uh +uh element the Ule rather converts from + + align:start position:0% +uh element the Ule rather converts from + + + align:start position:0% +uh element the Ule rather converts from +gas to liquid to solid so something to + + align:start position:0% +gas to liquid to solid so something to + + + align:start position:0% +gas to liquid to solid so something to +keep in mind so here's uh these are the + + align:start position:0% +keep in mind so here's uh these are the + + + align:start position:0% +keep in mind so here's uh these are the +the ball and stick images methane we've + + align:start position:0% +the ball and stick images methane we've + + + align:start position:0% +the ball and stick images methane we've +met before there's the sp3 hybridization + + align:start position:0% +met before there's the sp3 hybridization + + + align:start position:0% +met before there's the sp3 hybridization +four bonds 109 degrees apart in the case + + align:start position:0% +four bonds 109 degrees apart in the case + + + align:start position:0% +four bonds 109 degrees apart in the case +of ethane this is c2h6 one of the four + + align:start position:0% +of ethane this is c2h6 one of the four + + + align:start position:0% +of ethane this is c2h6 one of the four +bonds is a carbon carbon Bond it's a + + align:start position:0% +bonds is a carbon carbon Bond it's a + + + align:start position:0% +bonds is a carbon carbon Bond it's a +sigma Bond okay and then we go to + + align:start position:0% +sigma Bond okay and then we go to + + + align:start position:0% +sigma Bond okay and then we go to +propane so now we've got C3 so that's + + align:start position:0% +propane so now we've got C3 so that's + + + align:start position:0% +propane so now we've got C3 so that's +that's what's queuing Us in on which of + + align:start position:0% +that's what's queuing Us in on which of + + + align:start position:0% +that's what's queuing Us in on which of +these to choose but I want you to note + + align:start position:0% +these to choose but I want you to note + + + align:start position:0% +these to choose but I want you to note +that at propane this sp3 hybridization + + align:start position:0% +that at propane this sp3 hybridization + + + align:start position:0% +that at propane this sp3 hybridization +requires that as we add more and more + + align:start position:0% +requires that as we add more and more + + + align:start position:0% +requires that as we add more and more +carbons we're going to put one more + + align:start position:0% +carbons we're going to put one more + + + align:start position:0% +carbons we're going to put one more +carbon we're going to put it up here you + + align:start position:0% +carbon we're going to put it up here you + + + align:start position:0% +carbon we're going to put it up here you +can see that even though this thing is + + align:start position:0% +can see that even though this thing is + + + align:start position:0% +can see that even though this thing is +straight it in fact at the local level + + align:start position:0% +straight it in fact at the local level + + + align:start position:0% +straight it in fact at the local level +is a zigzagging at the local level + + align:start position:0% +is a zigzagging at the local level + + + align:start position:0% +is a zigzagging at the local level +there's some zigzagging so we want to + + align:start position:0% +there's some zigzagging so we want to + + + align:start position:0% +there's some zigzagging so we want to +keep that in mind the the sp3 + + align:start position:0% +keep that in mind the the sp3 + + + align:start position:0% +keep that in mind the the sp3 +hybridization + + align:start position:0% +hybridization + + + align:start position:0% +hybridization +sp3 + + align:start position:0% +sp3 + + + align:start position:0% +sp3 +um + + align:start position:0% +um + + + align:start position:0% +um +hybridization gives bonding along the + + align:start position:0% +hybridization gives bonding along the + + + align:start position:0% +hybridization gives bonding along the +chain that in fact zigzags this is 109 + + align:start position:0% +chain that in fact zigzags this is 109 + + + align:start position:0% +chain that in fact zigzags this is 109 +degree angle and you know so if you're + + align:start position:0% +degree angle and you know so if you're + + + align:start position:0% +degree angle and you know so if you're +up really close you say well this is + + align:start position:0% +up really close you say well this is + + + align:start position:0% +up really close you say well this is +clearly bent but if you make this long + + align:start position:0% +clearly bent but if you make this long + + + align:start position:0% +clearly bent but if you make this long +enough and you get far enough back and + + align:start position:0% +enough and you get far enough back and + + + align:start position:0% +enough and you get far enough back and +in a general sense this is termed a + + align:start position:0% +in a general sense this is termed a + + + align:start position:0% +in a general sense this is termed a +straight this is termed a straight chain + + align:start position:0% +straight this is termed a straight chain + + + align:start position:0% +straight this is termed a straight chain +it's a straight chain hydrocarbon + + align:start position:0% +it's a straight chain hydrocarbon + + + align:start position:0% +it's a straight chain hydrocarbon +there's there's one other thing that uh + + align:start position:0% +there's there's one other thing that uh + + + align:start position:0% +there's there's one other thing that uh +is is similar to what we've seen in the + + align:start position:0% +is is similar to what we've seen in the + + + align:start position:0% +is is similar to what we've seen in the +past in the case of uh of silicates and + + align:start position:0% +past in the case of uh of silicates and + + + align:start position:0% +past in the case of uh of silicates and +that's shown here the as long as we've + + align:start position:0% +that's shown here the as long as we've + + + align:start position:0% +that's shown here the as long as we've +got + + align:start position:0% +got + + + align:start position:0% +got +109° uh along this axis between the + + align:start position:0% +109° uh along this axis between the + + + align:start position:0% +109° uh along this axis between the +other bonds there's no specification + + align:start position:0% +other bonds there's no specification + + + align:start position:0% +other bonds there's no specification +what happens down here so this this + + align:start position:0% +what happens down here so this this + + + align:start position:0% +what happens down here so this this +should remind you of what happens in a + + align:start position:0% +should remind you of what happens in a + + + align:start position:0% +should remind you of what happens in a +silicate when the oxygens don't all line + + align:start position:0% +silicate when the oxygens don't all line + + + align:start position:0% +silicate when the oxygens don't all line +up and so it's possible to get disorder + + align:start position:0% +up and so it's possible to get disorder + + + align:start position:0% +up and so it's possible to get disorder +and so here you see one case where you + + align:start position:0% +and so here you see one case where you + + + align:start position:0% +and so here you see one case where you +have the the hydrogens on adjacent + + align:start position:0% +have the the hydrogens on adjacent + + + align:start position:0% +have the the hydrogens on adjacent +carbons not facing one another whereas + + align:start position:0% +carbons not facing one another whereas + + + align:start position:0% +carbons not facing one another whereas +here they're lined up so if I were to + + align:start position:0% +here they're lined up so if I were to + + + align:start position:0% +here they're lined up so if I were to +look on end from the left down the chain + + align:start position:0% +look on end from the left down the chain + + + align:start position:0% +look on end from the left down the chain +I would only see one the all of the + + align:start position:0% +I would only see one the all of the + + + align:start position:0% +I would only see one the all of the +hydrogens are lined up and we call this + + align:start position:0% +hydrogens are lined up and we call this + + + align:start position:0% +hydrogens are lined up and we call this +configuration an eclipse configuration + + align:start position:0% +configuration an eclipse configuration + + + align:start position:0% +configuration an eclipse configuration +this is slightly high energy whereas + + align:start position:0% +this is slightly high energy whereas + + + align:start position:0% +this is slightly high energy whereas +this is little bit lower energy + + align:start position:0% +this is little bit lower energy + + + align:start position:0% +this is little bit lower energy +staggered and what's the effect of that + + align:start position:0% +staggered and what's the effect of that + + + align:start position:0% +staggered and what's the effect of that +the effect is not to give us a straight + + align:start position:0% +the effect is not to give us a straight + + + align:start position:0% +the effect is not to give us a straight +chain that goes in a Bel line for that + + align:start position:0% +chain that goes in a Bel line for that + + + align:start position:0% +chain that goes in a Bel line for that +you'd have to have the eclipse + + align:start position:0% +you'd have to have the eclipse + + + align:start position:0% +you'd have to have the eclipse +configuration here's two examples of C7 + + align:start position:0% +configuration here's two examples of C7 + + + align:start position:0% +configuration here's two examples of C7 + + align:start position:0% + + + align:start position:0% +h36 they're both straight chain but + + align:start position:0% +h36 they're both straight chain but + + + align:start position:0% +h36 they're both straight chain but +because one's twisting a little bit more + + align:start position:0% +because one's twisting a little bit more + + + align:start position:0% +because one's twisting a little bit more +than the other and here I'm talking + + align:start position:0% +than the other and here I'm talking + + + align:start position:0% +than the other and here I'm talking +about just the carbon carbon Bond + + align:start position:0% +about just the carbon carbon Bond + + + align:start position:0% +about just the carbon carbon Bond +twisting these are both terms straight + + align:start position:0% +twisting these are both terms straight + + + align:start position:0% +twisting these are both terms straight +chain but they have different + + align:start position:0% +chain but they have different + + + align:start position:0% +chain but they have different +conformations so this is starting to + + align:start position:0% +conformations so this is starting to + + + align:start position:0% +conformations so this is starting to +make you think about the the plurality + + align:start position:0% +make you think about the the plurality + + + align:start position:0% +make you think about the the plurality +of possibilities even within the same + + align:start position:0% +of possibilities even within the same + + + align:start position:0% +of possibilities even within the same +chemical composition that would be + + align:start position:0% +chemical composition that would be + + + align:start position:0% +chemical composition that would be +present in polymers here we've only got + + align:start position:0% +present in polymers here we've only got + + + align:start position:0% +present in polymers here we've only got +17 imagine if instead of 17 it became + + align:start position:0% +17 imagine if instead of 17 it became + + + align:start position:0% +17 imagine if instead of 17 it became +177,000 what this can do so this is a + + align:start position:0% +177,000 what this can do so this is a + + + align:start position:0% +177,000 what this can do so this is a +example of of what we mean by Straight + + align:start position:0% +example of of what we mean by Straight + + + align:start position:0% +example of of what we mean by Straight +chain but it doesn't mean that it's a a + + align:start position:0% +chain but it doesn't mean that it's a a + + + align:start position:0% +chain but it doesn't mean that it's a a +rodlike uh uh entity okay but I can now + + align:start position:0% +rodlike uh uh entity okay but I can now + + + align:start position:0% +rodlike uh uh entity okay but I can now +show you something that's not a straight + + align:start position:0% +show you something that's not a straight + + + align:start position:0% +show you something that's not a straight +chain so let's also look at something + + align:start position:0% +chain so let's also look at something + + + align:start position:0% +chain so let's also look at something +called a branch + + align:start position:0% +called a branch + + + align:start position:0% +called a branch +chain Branch chain now that's different + + align:start position:0% +chain Branch chain now that's different + + + align:start position:0% +chain Branch chain now that's different +and I'm let's go to look at one I'm + + align:start position:0% +and I'm let's go to look at one I'm + + + align:start position:0% +and I'm let's go to look at one I'm +going to look at + + align:start position:0% +going to look at + + + align:start position:0% +going to look at +butane butane you know that's a gas at + + align:start position:0% +butane butane you know that's a gas at + + + align:start position:0% +butane butane you know that's a gas at +room temperature used to be used as a uh + + align:start position:0% +room temperature used to be used as a uh + + + align:start position:0% +room temperature used to be used as a uh +fuel for uh cigarette lighters but I + + align:start position:0% +fuel for uh cigarette lighters but I + + + align:start position:0% +fuel for uh cigarette lighters but I +guess that's not PC anymore so I don't + + align:start position:0% +guess that's not PC anymore so I don't + + + align:start position:0% +guess that's not PC anymore so I don't +know oh now you can use it for uh + + align:start position:0% +know oh now you can use it for uh + + + align:start position:0% +know oh now you can use it for uh +lighting candles right can use it for + + align:start position:0% +lighting candles right can use it for + + + align:start position:0% +lighting candles right can use it for +lighting C I can say that can I light + + align:start position:0% +lighting C I can say that can I light + + + align:start position:0% +lighting C I can say that can I light +candles all right so let's look at + + align:start position:0% +candles all right so let's look at + + + align:start position:0% +candles all right so let's look at +butane so that's number four + + align:start position:0% +butane so that's number four + + + align:start position:0% +butane so that's number four +so all right so I'm just to Smo smooth + + align:start position:0% +so all right so I'm just to Smo smooth + + + align:start position:0% +so all right so I'm just to Smo smooth +things along it's possible to just write + + align:start position:0% +things along it's possible to just write + + + align:start position:0% +things along it's possible to just write +them in a straight line even though we + + align:start position:0% +them in a straight line even though we + + + align:start position:0% +them in a straight line even though we +know these are 100 + + align:start position:0% +know these are 100 + + + align:start position:0% +know these are 100 +9° and we know that if there's nothing + + align:start position:0% +9° and we know that if there's nothing + + + align:start position:0% +9° and we know that if there's nothing +put at the end of the stick we assume + + align:start position:0% +put at the end of the stick we assume + + + align:start position:0% +put at the end of the stick we assume +it's hydrogen so all of these are + + align:start position:0% +it's hydrogen so all of these are + + + align:start position:0% +it's hydrogen so all of these are +hydrogen carbon hydrogen linkages so + + align:start position:0% +hydrogen carbon hydrogen linkages so + + + align:start position:0% +hydrogen carbon hydrogen linkages so +I've got 1 two 3 four carbons and I've + + align:start position:0% +I've got 1 two 3 four carbons and I've + + + align:start position:0% +I've got 1 two 3 four carbons and I've +got 1 2 3 4 5 6 7 8 9 10 so this is as + + align:start position:0% +got 1 2 3 4 5 6 7 8 9 10 so this is as + + + align:start position:0% +got 1 2 3 4 5 6 7 8 9 10 so this is as +it should be C4 h10 and certainly this + + align:start position:0% +it should be C4 h10 and certainly this + + + align:start position:0% +it should be C4 h10 and certainly this +is this is identical to something that + + align:start position:0% +is this is identical to something that + + + align:start position:0% +is this is identical to something that +could be represented as follows + + align:start position:0% +could be represented as follows + + + align:start position:0% +could be represented as follows +all right so now I'm going to have the + + align:start position:0% +all right so now I'm going to have the + + + align:start position:0% +all right so now I'm going to have the +four outlining a tetrahedron so there's + + align:start position:0% +four outlining a tetrahedron so there's + + + align:start position:0% +four outlining a tetrahedron so there's +one two 3 4 1 2 3 4 1 2 3 4 remember + + align:start position:0% +one two 3 4 1 2 3 4 1 2 3 4 remember + + + align:start position:0% +one two 3 4 1 2 3 4 1 2 3 4 remember +when you're in carbon chemistry four + + align:start position:0% +when you're in carbon chemistry four + + + align:start position:0% +when you're in carbon chemistry four +sticks four sticks off of every carbon + + align:start position:0% +sticks four sticks off of every carbon + + + align:start position:0% +sticks four sticks off of every carbon +that's what you're checking okay so this + + align:start position:0% +that's what you're checking okay so this + + + align:start position:0% +that's what you're checking okay so this +is this is the the linear but there's + + align:start position:0% +is this is the the linear but there's + + + align:start position:0% +is this is the the linear but there's +another way there's another way we can + + align:start position:0% +another way there's another way we can + + + align:start position:0% +another way there's another way we can +do this we can do the following we can + + align:start position:0% +do this we can do the following we can + + + align:start position:0% +do this we can do the following we can +put + + align:start position:0% + + + + align:start position:0% + +and off one of the carbons I can put a + + align:start position:0% +and off one of the carbons I can put a + + + align:start position:0% +and off one of the carbons I can put a +branch put a branch and then I've got to + + align:start position:0% +branch put a branch and then I've got to + + + align:start position:0% +branch put a branch and then I've got to +use the four Stick rule so one two three + + align:start position:0% +use the four Stick rule so one two three + + + align:start position:0% +use the four Stick rule so one two three +one two so one two 3 four this has one + + align:start position:0% +one two so one two 3 four this has one + + + align:start position:0% +one two so one two 3 four this has one +two three four so now let's count 1 2 3 + + align:start position:0% +two three four so now let's count 1 2 3 + + + align:start position:0% +two three four so now let's count 1 2 3 +4 four + + align:start position:0% +4 four + + + align:start position:0% +4 four +carbons and 3 6 9 10 10 + + align:start position:0% +carbons and 3 6 9 10 10 + + + align:start position:0% +carbons and 3 6 9 10 10 +hydrogens so on a formula basis this is + + align:start position:0% +hydrogens so on a formula basis this is + + + align:start position:0% +hydrogens so on a formula basis this is +also a butane but it's a different and + + align:start position:0% +also a butane but it's a different and + + + align:start position:0% +also a butane but it's a different and +know as as as as solid state chemists + + align:start position:0% +know as as as as solid state chemists + + + align:start position:0% +know as as as as solid state chemists +we're we're very much attuned to + + align:start position:0% +we're we're very much attuned to + + + align:start position:0% +we're we're very much attuned to +molecular structure and this molecular + + align:start position:0% +molecular structure and this molecular + + + align:start position:0% +molecular structure and this molecular +structure the linear one is different + + align:start position:0% +structure the linear one is different + + + align:start position:0% +structure the linear one is different +from this one this is a branched one so + + align:start position:0% +from this one this is a branched one so + + + align:start position:0% +from this one this is a branched one so +this one's called + + align:start position:0% +this one's called + + + align:start position:0% +this one's called +isobutane + + align:start position:0% + + + + align:start position:0% + +isobutane and the other way to look at + + align:start position:0% +isobutane and the other way to look at + + + align:start position:0% +isobutane and the other way to look at +it is well the backbone is only three + + align:start position:0% +it is well the backbone is only three + + + align:start position:0% +it is well the backbone is only three +carbons so if the backbone's only three + + align:start position:0% +carbons so if the backbone's only three + + + align:start position:0% +carbons so if the backbone's only three +carbons according to this rule this + + align:start position:0% +carbons according to this rule this + + + align:start position:0% +carbons according to this rule this +should be some kind of a + + align:start position:0% +should be some kind of a + + + align:start position:0% +should be some kind of a +propane this another way to name this is + + align:start position:0% +propane this another way to name this is + + + align:start position:0% +propane this another way to name this is +to call it a propane all right but it's + + align:start position:0% +to call it a propane all right but it's + + + align:start position:0% +to call it a propane all right but it's +got instead of just hydrogens one of the + + align:start position:0% +got instead of just hydrogens one of the + + + align:start position:0% +got instead of just hydrogens one of the +propane side groups instead of being a + + align:start position:0% +propane side groups instead of being a + + + align:start position:0% +propane side groups instead of being a +simple hydrogen has this ch3 which is a + + align:start position:0% +simple hydrogen has this ch3 which is a + + + align:start position:0% +simple hydrogen has this ch3 which is a +methyl group so we could call this one a + + align:start position:0% +methyl group so we could call this one a + + + align:start position:0% +methyl group so we could call this one a +methyl methyl propane and we could + + align:start position:0% +methyl methyl propane and we could + + + align:start position:0% +methyl methyl propane and we could +further number the carbons number the + + align:start position:0% +further number the carbons number the + + + align:start position:0% +further number the carbons number the +carbons from left to right so this the + + align:start position:0% +carbons from left to right so this the + + + align:start position:0% +carbons from left to right so this the +first one is the number one carbon + + align:start position:0% +first one is the number one carbon + + + align:start position:0% +first one is the number one carbon +second is number two the third is number + + align:start position:0% +second is number two the third is number + + + align:start position:0% +second is number two the third is number +three three and the methyl group is + + align:start position:0% +three three and the methyl group is + + + align:start position:0% +three three and the methyl group is +attached to the one in the second so + + align:start position:0% +attached to the one in the second so + + + align:start position:0% +attached to the one in the second so +this is two methyl propane and what we + + align:start position:0% +this is two methyl propane and what we + + + align:start position:0% +this is two methyl propane and what we +have here is two identical chemical + + align:start position:0% +have here is two identical chemical + + + align:start position:0% +have here is two identical chemical +formulas but two different structures + + align:start position:0% +formulas but two different structures + + + align:start position:0% +formulas but two different structures +and so and we all have sing Sigma bonds + + align:start position:0% +and so and we all have sing Sigma bonds + + + align:start position:0% +and so and we all have sing Sigma bonds +everywhere so we call these isomers + + align:start position:0% +everywhere so we call these isomers + + + align:start position:0% +everywhere so we call these isomers +these are called + + align:start position:0% +these are called + + + align:start position:0% +these are called +isomers but they're an isomer of a + + align:start position:0% +isomers but they're an isomer of a + + + align:start position:0% +isomers but they're an isomer of a +particular kind they both have the same + + align:start position:0% +particular kind they both have the same + + + align:start position:0% +particular kind they both have the same +chemical formula but what we can can do + + align:start position:0% +chemical formula but what we can can do + + + align:start position:0% +chemical formula but what we can can do +is we can look at the uh constitutive + + align:start position:0% +is we can look at the uh constitutive + + + align:start position:0% +is we can look at the uh constitutive +groups here so what we can do is say um + + align:start position:0% +groups here so what we can do is say um + + + align:start position:0% +groups here so what we can do is say um +here we + + align:start position:0% +here we + + + align:start position:0% +here we +have here's a + + align:start position:0% + + + + align:start position:0% + +ch3 here's a + + align:start position:0% +ch3 here's a + + + align:start position:0% +ch3 here's a +ch3 and here's a + + align:start position:0% +ch3 and here's a + + + align:start position:0% +ch3 and here's a +ch3 and that leaves this one which is a + + align:start position:0% +ch3 and that leaves this one which is a + + + align:start position:0% +ch3 and that leaves this one which is a +CH whereas over here I've + + align:start position:0% +CH whereas over here I've + + + align:start position:0% +CH whereas over here I've +got + + align:start position:0% +got + + + align:start position:0% +got +ch3 a ch3 + + align:start position:0% + + + + align:start position:0% + +and in the middle two + + align:start position:0% + + + + align:start position:0% + +ch2s these are these are units some + + align:start position:0% +ch2s these are these are units some + + + align:start position:0% +ch2s these are these are units some +people call them uh constitutive groups + + align:start position:0% +people call them uh constitutive groups + + + align:start position:0% +people call them uh constitutive groups +con constitutive groups so here the + + align:start position:0% +con constitutive groups so here the + + + align:start position:0% +con constitutive groups so here the +constitutive groups are different from + + align:start position:0% +constitutive groups are different from + + + align:start position:0% +constitutive groups are different from +the con constitutive groups in the + + align:start position:0% +the con constitutive groups in the + + + align:start position:0% +the con constitutive groups in the +linear configuration and so these are + + align:start position:0% +linear configuration and so these are + + + align:start position:0% +linear configuration and so these are +called + + align:start position:0% +called + + + align:start position:0% +called +constitutional + + align:start position:0% +constitutional + + + align:start position:0% +constitutional +constitutional + + align:start position:0% +constitutional + + + align:start position:0% +constitutional +isomers constitutional isomers because + + align:start position:0% +isomers constitutional isomers because + + + align:start position:0% +isomers constitutional isomers because +they have + + align:start position:0% + + + + align:start position:0% + +identical identical + + align:start position:0% +identical identical + + + align:start position:0% +identical identical +chemistry but + + align:start position:0% +chemistry but + + + align:start position:0% +chemistry but +different different constitutive + + align:start position:0% + + + + align:start position:0% + +groups or constituent + + align:start position:0% + + + + align:start position:0% + +groups and so we can see + + align:start position:0% +groups and so we can see + + + align:start position:0% +groups and so we can see +this uh other thing that I need to + + align:start position:0% +this uh other thing that I need to + + + align:start position:0% +this uh other thing that I need to +introduce you + + align:start position:0% + + + + align:start position:0% + +to okay so this is the the same this is + + align:start position:0% +to okay so this is the the same this is + + + align:start position:0% +to okay so this is the the same this is +just the uh methyl propane and the + + align:start position:0% +just the uh methyl propane and the + + + align:start position:0% +just the uh methyl propane and the +straight straight chain butane uh down + + align:start position:0% +straight straight chain butane uh down + + + align:start position:0% +straight straight chain butane uh down +towards the bottom there's a uh + + align:start position:0% +towards the bottom there's a uh + + + align:start position:0% +towards the bottom there's a uh +something called ethyl and that's a + + align:start position:0% +something called ethyl and that's a + + + align:start position:0% +something called ethyl and that's a +radical so we need to know the radical + + align:start position:0% +radical so we need to know the radical + + + align:start position:0% +radical so we need to know the radical +terminology the radical is a + + align:start position:0% + + + + align:start position:0% + +species it's a species with one or more + + align:start position:0% +species it's a species with one or more + + + align:start position:0% +species it's a species with one or more +unpaired electrons with one in some + + align:start position:0% +unpaired electrons with one in some + + + align:start position:0% +unpaired electrons with one in some +cases more unpaired + + align:start position:0% + + + + align:start position:0% + +electrons so paired electrons living in + + align:start position:0% +electrons so paired electrons living in + + + align:start position:0% +electrons so paired electrons living in +a in an orbital that's a broken bond so + + align:start position:0% +a in an orbital that's a broken bond so + + + align:start position:0% +a in an orbital that's a broken bond so +this is very highly reactive this highly + + align:start position:0% +this is very highly reactive this highly + + + align:start position:0% +this is very highly reactive this highly +reactive okay so this + + align:start position:0% +reactive okay so this + + + align:start position:0% +reactive okay so this +is if you like think of it as a broken + + align:start position:0% +is if you like think of it as a broken + + + align:start position:0% +is if you like think of it as a broken +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +bond highly + + align:start position:0% + + + + align:start position:0% + +reactive so we need to know these and + + align:start position:0% +reactive so we need to know these and + + + align:start position:0% +reactive so we need to know these and +the ones that we need to know uh are + + align:start position:0% +the ones that we need to know uh are + + + align:start position:0% +the ones that we need to know uh are +these little units that I've just been + + align:start position:0% +these little units that I've just been + + + align:start position:0% +these little units that I've just been +drawing these little units so if I take + + align:start position:0% +drawing these little units so if I take + + + align:start position:0% +drawing these little units so if I take +if I take methane methane with four + + align:start position:0% +if I take methane methane with four + + + align:start position:0% +if I take methane methane with four +hydrogens and I break one of the + + align:start position:0% +hydrogens and I break one of the + + + align:start position:0% +hydrogens and I break one of the +hydrogens off and now I have a single + + align:start position:0% +hydrogens off and now I have a single + + + align:start position:0% +hydrogens off and now I have a single +electron sitting here this is capable of + + align:start position:0% +electron sitting here this is capable of + + + align:start position:0% +electron sitting here this is capable of +being attached to some other species in + + align:start position:0% +being attached to some other species in + + + align:start position:0% +being attached to some other species in +this case it was attached to the carbon + + align:start position:0% +this case it was attached to the carbon + + + align:start position:0% +this case it was attached to the carbon +backbone so this radical that comes from + + align:start position:0% +backbone so this radical that comes from + + + align:start position:0% +backbone so this radical that comes from +methane is called the methyl + + align:start position:0% +methane is called the methyl + + + align:start position:0% +methane is called the methyl +radical methyl radical another way to + + align:start position:0% +radical methyl radical another way to + + + align:start position:0% +radical methyl radical another way to +denote it + + align:start position:0% +denote it + + + align:start position:0% +denote it +is with the dot up here indicating that + + align:start position:0% +is with the dot up here indicating that + + + align:start position:0% +is with the dot up here indicating that +there's an unpaired electron obviously + + align:start position:0% +there's an unpaired electron obviously + + + align:start position:0% +there's an unpaired electron obviously +the unpaired electron is on the carbon + + align:start position:0% +the unpaired electron is on the carbon + + + align:start position:0% +the unpaired electron is on the carbon +but in the nomenclature of organic + + align:start position:0% +but in the nomenclature of organic + + + align:start position:0% +but in the nomenclature of organic +chemistry people are + + align:start position:0% +chemistry people are + + + align:start position:0% +chemistry people are +fairly quick to make the necessary + + align:start position:0% +fairly quick to make the necessary + + + align:start position:0% +fairly quick to make the necessary +change so if you see that no one's + + align:start position:0% +change so if you see that no one's + + + align:start position:0% +change so if you see that no one's +suggesting that the electrons attach to + + align:start position:0% +suggesting that the electrons attach to + + + align:start position:0% +suggesting that the electrons attach to +the hydrogen it's just a it's just a + + align:start position:0% +the hydrogen it's just a it's just a + + + align:start position:0% +the hydrogen it's just a it's just a +short uh short uh hand for it this one + + align:start position:0% +short uh short uh hand for it this one + + + align:start position:0% +short uh short uh hand for it this one +here the ch2 the ch2 that we see over in + + align:start position:0% +here the ch2 the ch2 that we see over in + + + align:start position:0% +here the ch2 the ch2 that we see over in +the straight chain butane this one is + + align:start position:0% +the straight chain butane this one is + + + align:start position:0% +the straight chain butane this one is +called in this case there's hydrogen's + + align:start position:0% +called in this case there's hydrogen's + + + align:start position:0% +called in this case there's hydrogen's +above and below so there's two unpaired + + align:start position:0% +above and below so there's two unpaired + + + align:start position:0% +above and below so there's two unpaired +electrons here so they can then link up + + align:start position:0% +electrons here so they can then link up + + + align:start position:0% +electrons here so they can then link up +with uh carbons on either side so that + + align:start position:0% +with uh carbons on either side so that + + + align:start position:0% +with uh carbons on either side so that +would be designated as follows or if you + + align:start position:0% +would be designated as follows or if you + + + align:start position:0% +would be designated as follows or if you +want + + align:start position:0% +want + + + align:start position:0% +want +ch2 with two dots and this is called + + align:start position:0% +ch2 with two dots and this is called + + + align:start position:0% +ch2 with two dots and this is called +methylene this is called this is the + + align:start position:0% +methylene this is called this is the + + + align:start position:0% +methylene this is called this is the +methylene radical and then the only + + align:start position:0% +methylene radical and then the only + + + align:start position:0% +methylene radical and then the only +other one that I really care about in + + align:start position:0% +other one that I really care about in + + + align:start position:0% +other one that I really care about in +the uh alkanes is the one that comes + + align:start position:0% +the uh alkanes is the one that comes + + + align:start position:0% +the uh alkanes is the one that comes +from ethane c2h6 is ethane and so the + + align:start position:0% +from ethane c2h6 is ethane and so the + + + align:start position:0% +from ethane c2h6 is ethane and so the +radical from this would be C2 H5 and + + align:start position:0% +radical from this would be C2 H5 and + + + align:start position:0% +radical from this would be C2 H5 and +this is called the ethyl radical and + + align:start position:0% +this is called the ethyl radical and + + + align:start position:0% +this is called the ethyl radical and +we'll come across some compounds uh one + + align:start position:0% +we'll come across some compounds uh one + + + align:start position:0% +we'll come across some compounds uh one +that we meet socially is ethyl alcohol + + align:start position:0% +that we meet socially is ethyl alcohol + + + align:start position:0% +that we meet socially is ethyl alcohol +where we put the alcohol functional + + align:start position:0% +where we put the alcohol functional + + + align:start position:0% +where we put the alcohol functional +group on the end of the ethyl so that + + align:start position:0% +group on the end of the ethyl so that + + + align:start position:0% +group on the end of the ethyl so that +that gives you an introduction to to + + align:start position:0% +that gives you an introduction to to + + + align:start position:0% +that gives you an introduction to to +alkan so now let's go back and and look + + align:start position:0% +alkan so now let's go back and and look + + + align:start position:0% +alkan so now let's go back and and look +at uh the next uh column that's the + + align:start position:0% +at uh the next uh column that's the + + + align:start position:0% +at uh the next uh column that's the +alkenes so now we're going to look at + + align:start position:0% +alkenes so now we're going to look at + + + align:start position:0% +alkenes so now we're going to look at +unsaturated + + align:start position:0% +unsaturated + + + align:start position:0% +unsaturated +unsaturated hydrocarbons and the first + + align:start position:0% +unsaturated hydrocarbons and the first + + + align:start position:0% +unsaturated hydrocarbons and the first +example is the alkenes and these are + + align:start position:0% +example is the alkenes and these are + + + align:start position:0% +example is the alkenes and these are +characterized by + + align:start position:0% +characterized by + + + align:start position:0% +characterized by +SP2 hybridization so that means at least + + align:start position:0% +SP2 hybridization so that means at least + + + align:start position:0% +SP2 hybridization so that means at least +in one place it only takes one at least + + align:start position:0% +in one place it only takes one at least + + + align:start position:0% +in one place it only takes one at least +in one place in the molecule there's a + + align:start position:0% +in one place in the molecule there's a + + + align:start position:0% +in one place in the molecule there's a +carbon carbon double bond and that will + + align:start position:0% +carbon carbon double bond and that will + + + align:start position:0% +carbon carbon double bond and that will +give you if all we have is the one + + align:start position:0% +give you if all we have is the one + + + align:start position:0% +give you if all we have is the one +carbon carbon double bond it will give + + align:start position:0% +carbon carbon double bond it will give + + + align:start position:0% +carbon carbon double bond it will give +us the chemical formula CN h2n and + + align:start position:0% +us the chemical formula CN h2n and + + + align:start position:0% +us the chemical formula CN h2n and +clearly n must be greater than equal to + + align:start position:0% +clearly n must be greater than equal to + + + align:start position:0% +clearly n must be greater than equal to +greater than or equal to two so the + + align:start position:0% +greater than or equal to two so the + + + align:start position:0% +greater than or equal to two so the +simplest one is c2h4 which we've seen + + align:start position:0% +simplest one is c2h4 which we've seen + + + align:start position:0% +simplest one is c2h4 which we've seen +already when we talked about uh Sigma + + align:start position:0% +already when we talked about uh Sigma + + + align:start position:0% +already when we talked about uh Sigma +and Pi bonding this is + + align:start position:0% +and Pi bonding this is + + + align:start position:0% +and Pi bonding this is +ethylene and hydrogens here we have SP2 + + align:start position:0% +ethylene and hydrogens here we have SP2 + + + align:start position:0% +ethylene and hydrogens here we have SP2 +hybridization so we have one Sigma Bond + + align:start position:0% +hybridization so we have one Sigma Bond + + + align:start position:0% +hybridization so we have one Sigma Bond +and one Pi Bond so the carbons and the + + align:start position:0% +and one Pi Bond so the carbons and the + + + align:start position:0% +and one Pi Bond so the carbons and the +hydrogen's lie in a plane this is + + align:start position:0% +hydrogen's lie in a plane this is + + + align:start position:0% +hydrogen's lie in a plane this is +120° we've seen all of that before the + + align:start position:0% +120° we've seen all of that before the + + + align:start position:0% +120° we've seen all of that before the +ethylene is the common name for it but + + align:start position:0% +ethylene is the common name for it but + + + align:start position:0% +ethylene is the common name for it but +the the the name + + align:start position:0% + + + + align:start position:0% + +that's regulated by the international + + align:start position:0% +that's regulated by the international + + + align:start position:0% +that's regulated by the international +Union of pure and applied chemistry is + + align:start position:0% +Union of pure and applied chemistry is + + + align:start position:0% +Union of pure and applied chemistry is +following this nomenclature we take the + + align:start position:0% +following this nomenclature we take the + + + align:start position:0% +following this nomenclature we take the +eth because c number is two and we add + + align:start position:0% +eth because c number is two and we add + + + align:start position:0% +eth because c number is two and we add +so the formal name for this is ethine + + align:start position:0% +so the formal name for this is ethine + + + align:start position:0% +so the formal name for this is ethine +not ethylene but uh you you can use + + align:start position:0% +not ethylene but uh you you can use + + + align:start position:0% +not ethylene but uh you you can use +either one no one's going to I get very + + align:start position:0% +either one no one's going to I get very + + + align:start position:0% +either one no one's going to I get very +agitated about it and then for n greater + + align:start position:0% +agitated about it and then for n greater + + + align:start position:0% +agitated about it and then for n greater +than two for n greater than two the + + align:start position:0% +than two for n greater than two the + + + align:start position:0% +than two for n greater than two the +position of the double bond is is not + + align:start position:0% +position of the double bond is is not + + + align:start position:0% +position of the double bond is is not +fixed position of double bond not fixed + + align:start position:0% +fixed position of double bond not fixed + + + align:start position:0% +fixed position of double bond not fixed +so we can show examples of that let's + + align:start position:0% +so we can show examples of that let's + + + align:start position:0% +so we can show examples of that let's +look at here's one + + align:start position:0% +look at here's one + + + align:start position:0% +look at here's one +buttine + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +C4 h8 so one is to put the double bond + + align:start position:0% +C4 h8 so one is to put the double bond + + + align:start position:0% +C4 h8 so one is to put the double bond +at the very + + align:start position:0% +at the very + + + align:start position:0% +at the very +end so I've just got one double bond in + + align:start position:0% +end so I've just got one double bond in + + + align:start position:0% +end so I've just got one double bond in +it there's the 120° hydrogen hydrogen + + align:start position:0% +it there's the 120° hydrogen hydrogen + + + align:start position:0% +it there's the 120° hydrogen hydrogen +Now 1 2 3 4 1 2 3 4 1 two 3 4 so this is + + align:start position:0% +Now 1 2 3 4 1 2 3 4 1 two 3 4 so this is + + + align:start position:0% +Now 1 2 3 4 1 2 3 4 1 two 3 4 so this is +c4h8 and this is called + + align:start position:0% +c4h8 and this is called + + + align:start position:0% +c4h8 and this is called +one buttine because the double bond is + + align:start position:0% +one buttine because the double bond is + + + align:start position:0% +one buttine because the double bond is +off of the the first carbon or we can + + align:start position:0% +off of the the first carbon or we can + + + align:start position:0% +off of the the first carbon or we can +put the double bond somewhere along the + + align:start position:0% +put the double bond somewhere along the + + + align:start position:0% +put the double bond somewhere along the +line so we can do this + + align:start position:0% +line so we can do this + + + align:start position:0% +line so we can do this +so the double bond is not at the very + + align:start position:0% +so the double bond is not at the very + + + align:start position:0% +so the double bond is not at the very +end so we have a methyl group at the end + + align:start position:0% +end so we have a methyl group at the end + + + align:start position:0% +end so we have a methyl group at the end +1 2 3 4 1 two 3 + + align:start position:0% +1 2 3 4 1 two 3 + + + align:start position:0% +1 2 3 4 1 two 3 +4 so this would then be called + + align:start position:0% +4 so this would then be called + + + align:start position:0% +4 so this would then be called +two two buttine two buttine indicating + + align:start position:0% +two two buttine two buttine indicating + + + align:start position:0% +two two buttine two buttine indicating +that the double bond comes off of the + + align:start position:0% +that the double bond comes off of the + + + align:start position:0% +that the double bond comes off of the +number two uh carbon so one buttine and + + align:start position:0% +number two uh carbon so one buttine and + + + align:start position:0% +number two uh carbon so one buttine and +two buttine turn out to be + + align:start position:0% +two buttine turn out to be + + + align:start position:0% +two buttine turn out to be +constitutional isomers because they got + + align:start position:0% +constitutional isomers because they got + + + align:start position:0% +constitutional isomers because they got +the same chemical formula but they have + + align:start position:0% +the same chemical formula but they have + + + align:start position:0% +the same chemical formula but they have +a different mix of uh uh constituent + + align:start position:0% +a different mix of uh uh constituent + + + align:start position:0% +a different mix of uh uh constituent +groups so let's label this as + + align:start position:0% +groups so let's label this as + + + align:start position:0% +groups so let's label this as +constitutional these are both + + align:start position:0% +constitutional these are both + + + align:start position:0% +constitutional these are both +constitutional + + align:start position:0% +constitutional + + + align:start position:0% +constitutional +isomers but we can zoom in a little bit + + align:start position:0% +isomers but we can zoom in a little bit + + + align:start position:0% +isomers but we can zoom in a little bit +more on two buttin and be introduced to + + align:start position:0% +more on two buttin and be introduced to + + + align:start position:0% +more on two buttin and be introduced to +yet another uh type of of isomer so I'm + + align:start position:0% +yet another uh type of of isomer so I'm + + + align:start position:0% +yet another uh type of of isomer so I'm +going to redraw this because this has + + align:start position:0% +going to redraw this because this has + + + align:start position:0% +going to redraw this because this has +been drawn at right angles it's + + align:start position:0% +been drawn at right angles it's + + + align:start position:0% +been drawn at right angles it's +colloquial we know this thing is + + align:start position:0% +colloquial we know this thing is + + + align:start position:0% +colloquial we know this thing is +zigzagging and whatnot so I want to + + align:start position:0% +zigzagging and whatnot so I want to + + + align:start position:0% +zigzagging and whatnot so I want to +redraw the two buttin and so I'll be by + + align:start position:0% +redraw the two buttin and so I'll be by + + + align:start position:0% +redraw the two buttin and so I'll be by +putting the double bond and then that + + align:start position:0% +putting the double bond and then that + + + align:start position:0% +putting the double bond and then that +means that I have to have 120° angles + + align:start position:0% +means that I have to have 120° angles + + + align:start position:0% +means that I have to have 120° angles +and what turns out here is that the + + align:start position:0% +and what turns out here is that the + + + align:start position:0% +and what turns out here is that the +double bond goes to uh carbon which has + + align:start position:0% +double bond goes to uh carbon which has + + + align:start position:0% +double bond goes to uh carbon which has +a hydrogen on one side and on the other + + align:start position:0% +a hydrogen on one side and on the other + + + align:start position:0% +a hydrogen on one side and on the other +side it has a methyl + + align:start position:0% +side it has a methyl + + + align:start position:0% +side it has a methyl +group right and the same thing here so + + align:start position:0% +group right and the same thing here so + + + align:start position:0% +group right and the same thing here so +now I have a choice what I can do is I + + align:start position:0% +now I have a choice what I can do is I + + + align:start position:0% +now I have a choice what I can do is I +can put the methyl group up here and the + + align:start position:0% +can put the methyl group up here and the + + + align:start position:0% +can put the methyl group up here and the +hydrogen all I've done is redraw this + + align:start position:0% +hydrogen all I've done is redraw this + + + align:start position:0% +hydrogen all I've done is redraw this +all I've done is redraw the the the two + + align:start position:0% + + + + align:start position:0% + +buttine and I think you can see that I + + align:start position:0% +buttine and I think you can see that I + + + align:start position:0% +buttine and I think you can see that I +can put a um a symmetry plane here I can + + align:start position:0% +can put a um a symmetry plane here I can + + + align:start position:0% +can put a um a symmetry plane here I can +put a symmetry plane and what do I what + + align:start position:0% +put a symmetry plane and what do I what + + + align:start position:0% +put a symmetry plane and what do I what +do I have I've got all of my I've got + + align:start position:0% +do I have I've got all of my I've got + + + align:start position:0% +do I have I've got all of my I've got +both of my methyl groups above the + + align:start position:0% +both of my methyl groups above the + + + align:start position:0% +both of my methyl groups above the +carbon carbon double bond and both of + + align:start position:0% +carbon carbon double bond and both of + + + align:start position:0% +carbon carbon double bond and both of +the hydrogen's below the carbon carbon + + align:start position:0% +the hydrogen's below the carbon carbon + + + align:start position:0% +the hydrogen's below the carbon carbon +double bond but another way I could have + + align:start position:0% +double bond but another way I could have + + + align:start position:0% +double bond but another way I could have +uh set up this structure again there's + + align:start position:0% +uh set up this structure again there's + + + align:start position:0% +uh set up this structure again there's +the carbon carbon double bond let's put + + align:start position:0% +the carbon carbon double bond let's put + + + align:start position:0% +the carbon carbon double bond let's put +the 120 degree angles we'll put the + + align:start position:0% +the 120 degree angles we'll put the + + + align:start position:0% +the 120 degree angles we'll put the +methyl group above the carboncarbon bond + + align:start position:0% +methyl group above the carboncarbon bond + + + align:start position:0% +methyl group above the carboncarbon bond +on the left side but below the carbon + + align:start position:0% +on the left side but below the carbon + + + align:start position:0% +on the left side but below the carbon +carbon Bond on the right side and then + + align:start position:0% +carbon Bond on the right side and then + + + align:start position:0% +carbon Bond on the right side and then +we'll do the + + align:start position:0% +we'll do the + + + align:start position:0% +we'll do the +complimentary uh positioning with the + + align:start position:0% +complimentary uh positioning with the + + + align:start position:0% +complimentary uh positioning with the +hydrogens so in the case on the right + + align:start position:0% +hydrogens so in the case on the right + + + align:start position:0% +hydrogens so in the case on the right +which is also a two buttine it's also a + + align:start position:0% +which is also a two buttine it's also a + + + align:start position:0% +which is also a two buttine it's also a +two + + align:start position:0% +two + + + align:start position:0% +two +buttine but we can see as 309 wers we + + align:start position:0% +buttine but we can see as 309 wers we + + + align:start position:0% +buttine but we can see as 309 wers we +look at structure structure is really + + align:start position:0% +look at structure structure is really + + + align:start position:0% +look at structure structure is really +important to us and we say okay same + + align:start position:0% +important to us and we say okay same + + + align:start position:0% +important to us and we say okay same +constituent groups but boy you can tell + + align:start position:0% +constituent groups but boy you can tell + + + align:start position:0% +constituent groups but boy you can tell +what the electron distribution is going + + align:start position:0% +what the electron distribution is going + + + align:start position:0% +what the electron distribution is going +to be different in the one on the left + + align:start position:0% +to be different in the one on the left + + + align:start position:0% +to be different in the one on the left +from the one on the right so you start + + align:start position:0% +from the one on the right so you start + + + align:start position:0% +from the one on the right so you start +thinking well what about their + + align:start position:0% +thinking well what about their + + + align:start position:0% +thinking well what about their +properties guess what they have + + align:start position:0% +properties guess what they have + + + align:start position:0% +properties guess what they have +different melting points they have + + align:start position:0% +different melting points they have + + + align:start position:0% +different melting points they have +different boiling points they have + + align:start position:0% +different boiling points they have + + + align:start position:0% +different boiling points they have +different density you can see they're + + align:start position:0% +different density you can see they're + + + align:start position:0% +different density you can see they're +going to pack differently so all of this + + align:start position:0% +going to pack differently so all of this + + + align:start position:0% +going to pack differently so all of this +and yet they have the same chemical + + align:start position:0% +and yet they have the same chemical + + + align:start position:0% +and yet they have the same chemical +formula so we have to distinguish these + + align:start position:0% +formula so we have to distinguish these + + + align:start position:0% +formula so we have to distinguish these +two they're not different + + align:start position:0% +two they're not different + + + align:start position:0% +two they're not different +by their constitution but they are + + align:start position:0% +by their constitution but they are + + + align:start position:0% +by their constitution but they are +different by their spatial layout and + + align:start position:0% +different by their spatial layout and + + + align:start position:0% +different by their spatial layout and +the term that we use to talk about + + align:start position:0% +the term that we use to talk about + + + align:start position:0% +the term that we use to talk about +isomers that are different in their + + align:start position:0% +isomers that are different in their + + + align:start position:0% +isomers that are different in their +spatial layout spatial Arrangement is + + align:start position:0% +spatial layout spatial Arrangement is + + + align:start position:0% +spatial layout spatial Arrangement is +Stereo isomer stereo + + align:start position:0% +Stereo isomer stereo + + + align:start position:0% +Stereo isomer stereo +isomer they are constitutionally + + align:start position:0% +isomer they are constitutionally + + + align:start position:0% +isomer they are constitutionally +identical but structurally different + + align:start position:0% +identical but structurally different + + + align:start position:0% +identical but structurally different +okay constitutionally identical + + align:start position:0% + + + + align:start position:0% + +identical Constitution different + + align:start position:0% +identical Constitution different + + + align:start position:0% +identical Constitution different +spatial + + align:start position:0% + + + + align:start position:0% + +Arrangement and so we've got labels on + + align:start position:0% +Arrangement and so we've got labels on + + + align:start position:0% +Arrangement and so we've got labels on +this the the one on the right to + + align:start position:0% +this the the one on the right to + + + align:start position:0% +this the the one on the right to +indicate that the various groups are on + + align:start position:0% +indicate that the various groups are on + + + align:start position:0% +indicate that the various groups are on +opposite sides of the double bond is + + align:start position:0% +opposite sides of the double bond is + + + align:start position:0% +opposite sides of the double bond is +called trans trans so the structure on + + align:start position:0% +called trans trans so the structure on + + + align:start position:0% +called trans trans so the structure on +the right is trans Tu butine where the + + align:start position:0% +the right is trans Tu butine where the + + + align:start position:0% +the right is trans Tu butine where the +one on the left is s + + align:start position:0% +one on the left is s + + + align:start position:0% +one on the left is s +to buttine so now we've met stereo + + align:start position:0% +to buttine so now we've met stereo + + + align:start position:0% +to buttine so now we've met stereo +isomer and we know what the oh there's + + align:start position:0% +isomer and we know what the oh there's + + + align:start position:0% +isomer and we know what the oh there's +one other thing we can have more than + + align:start position:0% +one other thing we can have more than + + + align:start position:0% +one other thing we can have more than +one double bond as well we can have more + + align:start position:0% +one double bond as well we can have more + + + align:start position:0% +one double bond as well we can have more +than one double + + align:start position:0% +than one double + + + align:start position:0% +than one double +bond in an + + align:start position:0% +bond in an + + + align:start position:0% +bond in an +alken more than one double bond in an + + align:start position:0% +alken more than one double bond in an + + + align:start position:0% +alken more than one double bond in an +Aline and we'll meet a few of these as + + align:start position:0% +Aline and we'll meet a few of these as + + + align:start position:0% +Aline and we'll meet a few of these as +well when we talk about polymers if we + + align:start position:0% +well when we talk about polymers if we + + + align:start position:0% +well when we talk about polymers if we +have two this is called a dine + + align:start position:0% +have two this is called a dine + + + align:start position:0% +have two this is called a dine +and if we have three it's called + + align:start position:0% +and if we have three it's called + + + align:start position:0% +and if we have three it's called +a triene and we'll look at one of these + + align:start position:0% +a triene and we'll look at one of these + + + align:start position:0% +a triene and we'll look at one of these +so so for example we could do something + + align:start position:0% +so so for example we could do something + + + align:start position:0% +so so for example we could do something +like this suppose I gave you ch2 you + + align:start position:0% +like this suppose I gave you ch2 you + + + align:start position:0% +like this suppose I gave you ch2 you +don't mind that I'm going to put the H + + align:start position:0% +don't mind that I'm going to put the H + + + align:start position:0% +don't mind that I'm going to put the H +on the inside you you'll forgive me I + + align:start position:0% +on the inside you you'll forgive me I + + + align:start position:0% +on the inside you you'll forgive me I +mean this is okay right so you know the + + align:start position:0% +mean this is okay right so you know the + + + align:start position:0% +mean this is okay right so you know the +hes are outboard but we're just going to + + align:start position:0% +hes are outboard but we're just going to + + + align:start position:0% +hes are outboard but we're just going to +go with it C all + + align:start position:0% +go with it C all + + + align:start position:0% +go with it C all +right what else + + align:start position:0% + + + + align:start position:0% + +CH yeah + + align:start position:0% + + + + align:start position:0% + +okay so what are we going to do with + + align:start position:0% +okay so what are we going to do with + + + align:start position:0% +okay so what are we going to do with +this one I'm not going to give you this + + align:start position:0% +this one I'm not going to give you this + + + align:start position:0% +this one I'm not going to give you this +to to name I just want you to see how it + + align:start position:0% +to to name I just want you to see how it + + + align:start position:0% +to to name I just want you to see how it +works and I'll I'll make sure that we + + align:start position:0% +works and I'll I'll make sure that we + + + align:start position:0% +works and I'll I'll make sure that we +focus on the chemistry but just for the + + align:start position:0% +focus on the chemistry but just for the + + + align:start position:0% +focus on the chemistry but just for the +record one two three four five five so + + align:start position:0% +record one two three four five five so + + + align:start position:0% +record one two three four five five so +it's got to be pent is something + + align:start position:0% +it's got to be pent is something + + + align:start position:0% +it's got to be pent is something +pent and it's got to be an e and e + + align:start position:0% +pent and it's got to be an e and e + + + align:start position:0% +pent and it's got to be an e and e +because there's at least one double bond + + align:start position:0% +because there's at least one double bond + + + align:start position:0% +because there's at least one double bond +here and there are two so this is going + + align:start position:0% +here and there are two so this is going + + + align:start position:0% +here and there are two so this is going +to be a + + align:start position:0% +to be a + + + align:start position:0% +to be a +Penta die + + align:start position:0% +Penta die + + + align:start position:0% +Penta die +a pentadine and furthermore we can say + + align:start position:0% +a pentadine and furthermore we can say + + + align:start position:0% +a pentadine and furthermore we can say +this is this is uh carbon number one + + align:start position:0% +this is this is uh carbon number one + + + align:start position:0% +this is this is uh carbon number one +carbon number two number three number + + align:start position:0% +carbon number two number three number + + + align:start position:0% +carbon number two number three number +four number five and the double bonds + + align:start position:0% +four number five and the double bonds + + + align:start position:0% +four number five and the double bonds +issue from carbon number one and carbon + + align:start position:0% +issue from carbon number one and carbon + + + align:start position:0% +issue from carbon number one and carbon +number three so we could call this 1 + + align:start position:0% +number three so we could call this 1 + + + align:start position:0% +number three so we could call this 1 +three + + align:start position:0% +three + + + align:start position:0% +three +pentadine so now you see how how all of + + align:start position:0% +pentadine so now you see how how all of + + + align:start position:0% +pentadine so now you see how how all of +this works and it's not so bad uh + + align:start position:0% +this works and it's not so bad uh + + + align:start position:0% +this works and it's not so bad uh +radicals what happens if we want to use + + align:start position:0% +radicals what happens if we want to use + + + align:start position:0% +radicals what happens if we want to use +just a piece of one of these so the only + + align:start position:0% +just a piece of one of these so the only + + + align:start position:0% +just a piece of one of these so the only +one that's that comes up that uh well + + align:start position:0% +one that's that comes up that uh well + + + align:start position:0% +one that's that comes up that uh well +there's two actually uh one of them + + align:start position:0% +there's two actually uh one of them + + + align:start position:0% +there's two actually uh one of them +comes from from ethylene or eth so I'm + + align:start position:0% +comes from from ethylene or eth so I'm + + + align:start position:0% +comes from from ethylene or eth so I'm +going to put the hydrogens to indicate + + align:start position:0% +going to put the hydrogens to indicate + + + align:start position:0% +going to put the hydrogens to indicate +when I don't have one so I'm going to + + align:start position:0% +when I don't have one so I'm going to + + + align:start position:0% +when I don't have one so I'm going to +break this Bond throw away the hydrogen + + align:start position:0% +break this Bond throw away the hydrogen + + + align:start position:0% +break this Bond throw away the hydrogen +and use this so this is the radical that + + align:start position:0% +and use this so this is the radical that + + + align:start position:0% +and use this so this is the radical that +comes + + align:start position:0% +comes + + + align:start position:0% +comes +from + + align:start position:0% +from + + + align:start position:0% +from +ethylene well you might say well why + + align:start position:0% +ethylene well you might say well why + + + align:start position:0% +ethylene well you might say well why +don't we call this since the formal name + + align:start position:0% +don't we call this since the formal name + + + align:start position:0% +don't we call this since the formal name +I'm going to use the UPAC name ethine + + align:start position:0% +I'm going to use the UPAC name ethine + + + align:start position:0% +I'm going to use the UPAC name ethine +well we can't say ethyl because ethyl's + + align:start position:0% +well we can't say ethyl because ethyl's + + + align:start position:0% +well we can't say ethyl because ethyl's +already taken ethyl is the the uh the + + align:start position:0% +already taken ethyl is the the uh the + + + align:start position:0% +already taken ethyl is the the uh the +one that's used over here for + + align:start position:0% +one that's used over here for + + + align:start position:0% +one that's used over here for +c2h5 so we need to distinguish this and + + align:start position:0% +c2h5 so we need to distinguish this and + + + align:start position:0% +c2h5 so we need to distinguish this and +the name for this radical when we take + + align:start position:0% +the name for this radical when we take + + + align:start position:0% +the name for this radical when we take +ethylene or ethine is called + + align:start position:0% +ethylene or ethine is called + + + align:start position:0% +ethylene or ethine is called +vinyl vinyl and we'll meet this one + + align:start position:0% +vinyl vinyl and we'll meet this one + + + align:start position:0% +vinyl vinyl and we'll meet this one +because if we want we could then stick + + align:start position:0% +because if we want we could then stick + + + align:start position:0% +because if we want we could then stick +onto there react it with chlorine and + + align:start position:0% +onto there react it with chlorine and + + + align:start position:0% +onto there react it with chlorine and +then + + align:start position:0% + + + + align:start position:0% + +make this is vinyl chloride and then + + align:start position:0% +make this is vinyl chloride and then + + + align:start position:0% +make this is vinyl chloride and then +later on we'll polymerize this and we'll + + align:start position:0% +later on we'll polymerize this and we'll + + + align:start position:0% +later on we'll polymerize this and we'll +make poly vinyl chloride so vinyl is the + + align:start position:0% +make poly vinyl chloride so vinyl is the + + + align:start position:0% +make poly vinyl chloride so vinyl is the +radical that comes from the uh uh + + align:start position:0% +radical that comes from the uh uh + + + align:start position:0% +radical that comes from the uh uh +compound uh ethylene or ethine and then + + align:start position:0% +compound uh ethylene or ethine and then + + + align:start position:0% +compound uh ethylene or ethine and then +there's one other one that comes up in + + align:start position:0% +there's one other one that comes up in + + + align:start position:0% +there's one other one that comes up in +the life science is a fair bit if we + + align:start position:0% +the life science is a fair bit if we + + + align:start position:0% +the life science is a fair bit if we +look at uh propene or + + align:start position:0% +look at uh propene or + + + align:start position:0% +look at uh propene or +propylene so that should be it's got to + + align:start position:0% +propylene so that should be it's got to + + + align:start position:0% +propylene so that should be it's got to +have a three so one two three all right + + align:start position:0% +have a three so one two three all right + + + align:start position:0% +have a three so one two three all right +so this is + + align:start position:0% + + + + align:start position:0% + +if I lose one of the hydrogens here and + + align:start position:0% +if I lose one of the hydrogens here and + + + align:start position:0% +if I lose one of the hydrogens here and +make this into a radical the radical + + align:start position:0% +make this into a radical the radical + + + align:start position:0% +make this into a radical the radical +that comes from propan can't be propy + + align:start position:0% +that comes from propan can't be propy + + + align:start position:0% +that comes from propan can't be propy +because that's going to be C3 uh H7 so + + align:start position:0% +because that's going to be C3 uh H7 so + + + align:start position:0% +because that's going to be C3 uh H7 so +here this will be called + + align:start position:0% +here this will be called + + + align:start position:0% +here this will be called +alil alil and as I say this comes up + + align:start position:0% +alil alil and as I say this comes up + + + align:start position:0% +alil alil and as I say this comes up +sometimes in the Life Sciences so we may + + align:start position:0% +sometimes in the Life Sciences so we may + + + align:start position:0% +sometimes in the Life Sciences so we may +find ourselves referring to that so I'm + + align:start position:0% +find ourselves referring to that so I'm + + + align:start position:0% +find ourselves referring to that so I'm +giving you the the uh the direct path + + align:start position:0% +giving you the the uh the direct path + + + align:start position:0% +giving you the the uh the direct path +the short course in um + + align:start position:0% +the short course in um + + + align:start position:0% +the short course in um +in organic nomenclature for our future + + align:start position:0% +in organic nomenclature for our future + + + align:start position:0% +in organic nomenclature for our future +work on polymers and on uh biochemistry + + align:start position:0% +work on polymers and on uh biochemistry + + + align:start position:0% +work on polymers and on uh biochemistry +the last one let's look at the right + + align:start position:0% +the last one let's look at the right + + + align:start position:0% +the last one let's look at the right +hand column which is also unsaturated + + align:start position:0% +hand column which is also unsaturated + + + align:start position:0% +hand column which is also unsaturated +that's the + + align:start position:0% +that's the + + + align:start position:0% +that's the +alyes the + + align:start position:0% +alyes the + + + align:start position:0% +alyes the +alkin and these are characterized by SP + + align:start position:0% +alkin and these are characterized by SP + + + align:start position:0% +alkin and these are characterized by SP +hybridization so SP hybridization so + + align:start position:0% +hybridization so SP hybridization so + + + align:start position:0% +hybridization so SP hybridization so +these then are going to be hydrocarbons + + align:start position:0% +these then are going to be hydrocarbons + + + align:start position:0% +these then are going to be hydrocarbons +containing at least one carbon carbon + + align:start position:0% +containing at least one carbon carbon + + + align:start position:0% +containing at least one carbon carbon +triple bond this has the capability of + + align:start position:0% +triple bond this has the capability of + + + align:start position:0% +triple bond this has the capability of +carbon carbon triple bonding and has the + + align:start position:0% +carbon carbon triple bonding and has the + + + align:start position:0% +carbon carbon triple bonding and has the +general formula CN h 2nus 2 for n + + align:start position:0% +general formula CN h 2nus 2 for n + + + align:start position:0% +general formula CN h 2nus 2 for n +greater than equal to two and the main + + align:start position:0% +greater than equal to two and the main + + + align:start position:0% +greater than equal to two and the main +one that comes up that that you you're + + align:start position:0% +one that comes up that that you you're + + + align:start position:0% +one that comes up that that you you're +apt to meet is simply + + align:start position:0% +apt to meet is simply + + + align:start position:0% +apt to meet is simply +c2h2 which has the triple bond between + + align:start position:0% +c2h2 which has the triple bond between + + + align:start position:0% +c2h2 which has the triple bond between +the carbons and the SP gives us 180 + + align:start position:0% +the carbons and the SP gives us 180 + + + align:start position:0% +the carbons and the SP gives us 180 +degrees is a linear molecule and this + + align:start position:0% +degrees is a linear molecule and this + + + align:start position:0% +degrees is a linear molecule and this +according to the nomenclature should be + + align:start position:0% +according to the nomenclature should be + + + align:start position:0% +according to the nomenclature should be +ethine because it's one of the alkin but + + align:start position:0% +ethine because it's one of the alkin but + + + align:start position:0% +ethine because it's one of the alkin but +you know this molecule as acetylene + + align:start position:0% +you know this molecule as acetylene + + + align:start position:0% +you know this molecule as acetylene +which is used as a fuel in such things + + align:start position:0% +which is used as a fuel in such things + + + align:start position:0% +which is used as a fuel in such things +as welding torches and obviously the + + align:start position:0% +as welding torches and obviously the + + + align:start position:0% +as welding torches and obviously the +carbon carbon triple bond has enormous + + align:start position:0% +carbon carbon triple bond has enormous + + + align:start position:0% +carbon carbon triple bond has enormous +energy in it so that's uh one example + + align:start position:0% +energy in it so that's uh one example + + + align:start position:0% +energy in it so that's uh one example +okay there's a few others few others one + + align:start position:0% +okay there's a few others few others one + + + align:start position:0% +okay there's a few others few others one +is the aromatic hydrocarbons we need to + + align:start position:0% +is the aromatic hydrocarbons we need to + + + align:start position:0% +is the aromatic hydrocarbons we need to +know those because we're going to meet + + align:start position:0% +know those because we're going to meet + + + align:start position:0% +know those because we're going to meet +those again aromatic + + align:start position:0% +those again aromatic + + + align:start position:0% +those again aromatic +hydrocarbons um and the UPAC name is + + align:start position:0% +hydrocarbons um and the UPAC name is + + + align:start position:0% +hydrocarbons um and the UPAC name is +arines these are + + align:start position:0% +arines these are + + + align:start position:0% +arines these are +arines and the prototypical one is + + align:start position:0% +arines and the prototypical one is + + + align:start position:0% +arines and the prototypical one is +Benzene Benzene is the is the main one + + align:start position:0% +Benzene Benzene is the is the main one + + + align:start position:0% +Benzene Benzene is the is the main one +that we need to know and its chemical + + align:start position:0% +that we need to know and its chemical + + + align:start position:0% +that we need to know and its chemical +formula is c6h6 so it qualifies as a + + align:start position:0% +formula is c6h6 so it qualifies as a + + + align:start position:0% +formula is c6h6 so it qualifies as a +hydrocarbon and people were mystified by + + align:start position:0% +hydrocarbon and people were mystified by + + + align:start position:0% +hydrocarbon and people were mystified by +its chemical structure and it was + + align:start position:0% +its chemical structure and it was + + + align:start position:0% +its chemical structure and it was +Kay keko in + + align:start position:0% +Kay keko in + + + align:start position:0% +Kay keko in +1865 who proposed the following St + + align:start position:0% +1865 who proposed the following St + + + align:start position:0% +1865 who proposed the following St +structure he + + align:start position:0% +structure he + + + align:start position:0% +structure he +proposed uh a hexagon of carbons with + + align:start position:0% +proposed uh a hexagon of carbons with + + + align:start position:0% +proposed uh a hexagon of carbons with +hydrogens off the corners and then + + align:start position:0% +hydrogens off the corners and then + + + align:start position:0% +hydrogens off the corners and then +alternating double and single bonds so + + align:start position:0% +alternating double and single bonds so + + + align:start position:0% +alternating double and single bonds so +double single double single double + + align:start position:0% +double single double single double + + + align:start position:0% +double single double single double +single and this is the way things lay + + align:start position:0% +single and this is the way things lay + + + align:start position:0% +single and this is the way things lay +until the 20th century when in the light + + align:start position:0% +until the 20th century when in the light + + + align:start position:0% +until the 20th century when in the light +of data it became known from spectral + + align:start position:0% +of data it became known from spectral + + + align:start position:0% +of data it became known from spectral +evidence that first of all that all all + + align:start position:0% +evidence that first of all that all all + + + align:start position:0% +evidence that first of all that all all +carbons lie in the same plane all + + align:start position:0% +carbons lie in the same plane all + + + align:start position:0% +carbons lie in the same plane all +carbons lie in the same plane and you + + align:start position:0% +carbons lie in the same plane and you + + + align:start position:0% +carbons lie in the same plane and you +can't have that if you've got + + align:start position:0% +can't have that if you've got + + + align:start position:0% +can't have that if you've got +alternating double and single bonds + + align:start position:0% +alternating double and single bonds + + + align:start position:0% +alternating double and single bonds +because the single bonds are going to be + + align:start position:0% +because the single bonds are going to be + + + align:start position:0% +because the single bonds are going to be +coming out at at uh something other than + + align:start position:0% +coming out at at uh something other than + + + align:start position:0% +coming out at at uh something other than +120° and then the second thing that + + align:start position:0% +120° and then the second thing that + + + align:start position:0% +120° and then the second thing that +mystified people was the finding that + + align:start position:0% +mystified people was the finding that + + + align:start position:0% +mystified people was the finding that +all carbon carbon bonds all carbon + + align:start position:0% +all carbon carbon bonds all carbon + + + align:start position:0% +all carbon carbon bonds all carbon +carbon bonds in Benzene are the same + + align:start position:0% +carbon bonds in Benzene are the same + + + align:start position:0% +carbon bonds in Benzene are the same +length + + align:start position:0% +length + + + align:start position:0% +length +all carbon carbon bonds are the same + + align:start position:0% +all carbon carbon bonds are the same + + + align:start position:0% +all carbon carbon bonds are the same +length so if the kcoa structure is + + align:start position:0% +length so if the kcoa structure is + + + align:start position:0% +length so if the kcoa structure is +correct you have the situation where the + + align:start position:0% +correct you have the situation where the + + + align:start position:0% +correct you have the situation where the +double bond is the same length as a + + align:start position:0% +double bond is the same length as a + + + align:start position:0% +double bond is the same length as a +single Bond and that doesn't that + + align:start position:0% +single Bond and that doesn't that + + + align:start position:0% +single Bond and that doesn't that +doesn't sit well and so we had to wait + + align:start position:0% +doesn't sit well and so we had to wait + + + align:start position:0% +doesn't sit well and so we had to wait +until lonus + + align:start position:0% +until lonus + + + align:start position:0% +until lonus +Pauling who in + + align:start position:0% +Pauling who in + + + align:start position:0% +Pauling who in +1931 uh proposed that in fact there are + + align:start position:0% +1931 uh proposed that in fact there are + + + align:start position:0% +1931 uh proposed that in fact there are +two structures there are two structures + + align:start position:0% +two structures there are two structures + + + align:start position:0% +two structures there are two structures +that uh um involve alternating between + + align:start position:0% +that uh um involve alternating between + + + align:start position:0% +that uh um involve alternating between +the structure that I've drawn here + + align:start position:0% +the structure that I've drawn here + + + align:start position:0% +the structure that I've drawn here +and the complimentary structure where + + align:start position:0% +and the complimentary structure where + + + align:start position:0% +and the complimentary structure where +the the double bonds move to where the + + align:start position:0% +the the double bonds move to where the + + + align:start position:0% +the the double bonds move to where the +single bonds are in the uh existing + + align:start position:0% +single bonds are in the uh existing + + + align:start position:0% +single bonds are in the uh existing +structure so now we have two of these + + align:start position:0% +structure so now we have two of these + + + align:start position:0% +structure so now we have two of these +and he said each of these is a hybrid + + align:start position:0% +and he said each of these is a hybrid + + + align:start position:0% +and he said each of these is a hybrid +remember Pauling was the one who + + align:start position:0% +remember Pauling was the one who + + + align:start position:0% +remember Pauling was the one who +described hybridization in carbon in the + + align:start position:0% +described hybridization in carbon in the + + + align:start position:0% +described hybridization in carbon in the +first place so these are hybrids but + + align:start position:0% +first place so these are hybrids but + + + align:start position:0% +first place so these are hybrids but +they're hybrids of a different type it's + + align:start position:0% +they're hybrids of a different type it's + + + align:start position:0% +they're hybrids of a different type it's +a it's a mixing and in fact he proposed + + align:start position:0% +a it's a mixing and in fact he proposed + + + align:start position:0% +a it's a mixing and in fact he proposed +that the structure resonate between the + + align:start position:0% +that the structure resonate between the + + + align:start position:0% +that the structure resonate between the +two so these are resonant + + align:start position:0% +two so these are resonant + + + align:start position:0% +two so these are resonant +hybrids resonant hybrids and sure enough + + align:start position:0% +hybrids resonant hybrids and sure enough + + + align:start position:0% +hybrids resonant hybrids and sure enough +it's been found + + align:start position:0% +it's been found + + + align:start position:0% +it's been found +that uh the carbon carbon Bond length is + + align:start position:0% +that uh the carbon carbon Bond length is + + + align:start position:0% +that uh the carbon carbon Bond length is +on the order of about 1.47 angstroms the + + align:start position:0% +on the order of about 1.47 angstroms the + + + align:start position:0% +on the order of about 1.47 angstroms the +carbon carbon double bond is + + align:start position:0% +carbon carbon double bond is + + + align:start position:0% +carbon carbon double bond is +1.33 angstroms generally if you look in + + align:start position:0% +1.33 angstroms generally if you look in + + + align:start position:0% +1.33 angstroms generally if you look in +some of these uh alkanes but in Benzene + + align:start position:0% +some of these uh alkanes but in Benzene + + + align:start position:0% +some of these uh alkanes but in Benzene +the carbon carbon in benzene + + align:start position:0% +the carbon carbon in benzene + + + align:start position:0% +the carbon carbon in benzene +in Benzene was found to be on the order + + align:start position:0% +in Benzene was found to be on the order + + + align:start position:0% +in Benzene was found to be on the order +of about + + align:start position:0% +of about + + + align:start position:0% +of about +1.39 angstroms which puts it in between + + align:start position:0% +1.39 angstroms which puts it in between + + + align:start position:0% +1.39 angstroms which puts it in between +so if you take an average we've got + + align:start position:0% +so if you take an average we've got + + + align:start position:0% +so if you take an average we've got +three double bonds and three single + + align:start position:0% +three double bonds and three single + + + align:start position:0% +three double bonds and three single +bonds this is + + align:start position:0% +bonds this is + + + align:start position:0% +bonds this is +consistent consistent with the notion of + + align:start position:0% +consistent consistent with the notion of + + + align:start position:0% +consistent consistent with the notion of +bond + + align:start position:0% +bond + + + align:start position:0% +bond +order bond order 1.5 and so today what + + align:start position:0% +order bond order 1.5 and so today what + + + align:start position:0% +order bond order 1.5 and so today what +people do to represent Benzene is rather + + align:start position:0% +people do to represent Benzene is rather + + + align:start position:0% +people do to represent Benzene is rather +than drawing these two structures or one + + align:start position:0% +than drawing these two structures or one + + + align:start position:0% +than drawing these two structures or one +of them and say figure out the rest for + + align:start position:0% +of them and say figure out the rest for + + + align:start position:0% +of them and say figure out the rest for +you is to use a a molecular orbital + + align:start position:0% +you is to use a a molecular orbital + + + align:start position:0% +you is to use a a molecular orbital +representation molecular orbital + + align:start position:0% +representation molecular orbital + + + align:start position:0% +representation molecular orbital +representation is as follows we draw the + + align:start position:0% +representation is as follows we draw the + + + align:start position:0% +representation is as follows we draw the +hexagon and a circle inside so this + + align:start position:0% +hexagon and a circle inside so this + + + align:start position:0% +hexagon and a circle inside so this +indicates the the resonant hybrid that + + align:start position:0% +indicates the the resonant hybrid that + + + align:start position:0% +indicates the the resonant hybrid that +is uh present + + align:start position:0% +is uh present + + + align:start position:0% +is uh present +in uh Benzene and it's also present in a + + align:start position:0% +in uh Benzene and it's also present in a + + + align:start position:0% +in uh Benzene and it's also present in a +few other + + align:start position:0% +few other + + + align:start position:0% +few other +aromatics and the other thing is that uh + + align:start position:0% +aromatics and the other thing is that uh + + + align:start position:0% +aromatics and the other thing is that uh +what happens in terms of electronic + + align:start position:0% +what happens in terms of electronic + + + align:start position:0% +what happens in terms of electronic +structure I'm going to try to draw this + + align:start position:0% +structure I'm going to try to draw this + + + align:start position:0% +structure I'm going to try to draw this +my drawing isn't the best but you're + + align:start position:0% +my drawing isn't the best but you're + + + align:start position:0% +my drawing isn't the best but you're +stuck with me what I want to do is to + + align:start position:0% +stuck with me what I want to do is to + + + align:start position:0% +stuck with me what I want to do is to +try to look at the what happens in terms + + align:start position:0% +try to look at the what happens in terms + + + align:start position:0% +try to look at the what happens in terms +of the single and double bonds from the + + align:start position:0% +of the single and double bonds from the + + + align:start position:0% +of the single and double bonds from the +standpoint of + + align:start position:0% +standpoint of + + + align:start position:0% +standpoint of +formation uh with the various orbitals + + align:start position:0% +formation uh with the various orbitals + + + align:start position:0% +formation uh with the various orbitals +involved and in particular I want to + + align:start position:0% +involved and in particular I want to + + + align:start position:0% +involved and in particular I want to +look at what happens with the pi orbital + + align:start position:0% +look at what happens with the pi orbital + + + align:start position:0% +look at what happens with the pi orbital +so 1 two 3 four five six well let's say + + align:start position:0% +so 1 two 3 four five six well let's say + + + align:start position:0% +so 1 two 3 four five six well let's say +for argument sake that the the double + + align:start position:0% +for argument sake that the the double + + + align:start position:0% +for argument sake that the the double +bond is where I've drawn it so this + + align:start position:0% +bond is where I've drawn it so this + + + align:start position:0% +bond is where I've drawn it so this +means this is formed by the combination + + align:start position:0% +means this is formed by the combination + + + align:start position:0% +means this is formed by the combination +of a sigma Bond and a pi Bond so the pi + + align:start position:0% +of a sigma Bond and a pi Bond so the pi + + + align:start position:0% +of a sigma Bond and a pi Bond so the pi +Bond involves the smearing of these two + + align:start position:0% +Bond involves the smearing of these two + + + align:start position:0% +Bond involves the smearing of these two +Pi + + align:start position:0% +Pi + + + align:start position:0% +Pi +orbitals so let's indicate that with a + + align:start position:0% +orbitals so let's indicate that with a + + + align:start position:0% +orbitals so let's indicate that with a +little bit of fuchsia chalk so there's a + + align:start position:0% +little bit of fuchsia chalk so there's a + + + align:start position:0% +little bit of fuchsia chalk so there's a +single Bond next door now there's a + + align:start position:0% +single Bond next door now there's a + + + align:start position:0% +single Bond next door now there's a +double bond and this double bond + + align:start position:0% +double bond and this double bond + + + align:start position:0% +double bond and this double bond +involves the smearing again of + + align:start position:0% +involves the smearing again of + + + align:start position:0% +involves the smearing again of +two Pi orbitals P orbitals excuse me to + + align:start position:0% +two Pi orbitals P orbitals excuse me to + + + align:start position:0% +two Pi orbitals P orbitals excuse me to +form a pi Bond and then lastly there's a + + align:start position:0% +form a pi Bond and then lastly there's a + + + align:start position:0% +form a pi Bond and then lastly there's a +a double bond across the the lower left + + align:start position:0% +a double bond across the the lower left + + + align:start position:0% +a double bond across the the lower left +here + + align:start position:0% +here + + + align:start position:0% +here +and so the pi orbital is formed but when + + align:start position:0% +and so the pi orbital is formed but when + + + align:start position:0% +and so the pi orbital is formed but when +we realize that all six of these bonds + + align:start position:0% +we realize that all six of these bonds + + + align:start position:0% +we realize that all six of these bonds +are found to be identical in length then + + align:start position:0% +are found to be identical in length then + + + align:start position:0% +are found to be identical in length then +everything is brought together so that + + align:start position:0% +everything is brought together so that + + + align:start position:0% +everything is brought together so that +we have equal spacing at which point the + + align:start position:0% +we have equal spacing at which point the + + + align:start position:0% +we have equal spacing at which point the +electrons all all six of these end up + + align:start position:0% +electrons all all six of these end up + + + align:start position:0% +electrons all all six of these end up +smearing hence this concept of + + align:start position:0% + + + + align:start position:0% + +electron + + align:start position:0% +electron + + + align:start position:0% +electron +delocalization in other words the + + align:start position:0% +delocalization in other words the + + + align:start position:0% +delocalization in other words the +electron is no longer confined to + + align:start position:0% +electron is no longer confined to + + + align:start position:0% +electron is no longer confined to +alternating pairs of P orbitals but + + align:start position:0% +alternating pairs of P orbitals but + + + align:start position:0% +alternating pairs of P orbitals but +rather it's moving amongst all six so + + align:start position:0% +rather it's moving amongst all six so + + + align:start position:0% +rather it's moving amongst all six so +this can move through the entire + + align:start position:0% +this can move through the entire + + + align:start position:0% +this can move through the entire +structure right and you can imagine if + + align:start position:0% +structure right and you can imagine if + + + align:start position:0% +structure right and you can imagine if +we then go back to graphite go back to + + align:start position:0% +we then go back to graphite go back to + + + align:start position:0% +we then go back to graphite go back to +graphite then the electrons can move + + align:start position:0% +graphite then the electrons can move + + + align:start position:0% +graphite then the electrons can move +through the entire solid which explains + + align:start position:0% +through the entire solid which explains + + + align:start position:0% +through the entire solid which explains +the observed electronic conductivity in + + align:start position:0% +the observed electronic conductivity in + + + align:start position:0% +the observed electronic conductivity in +graphite and I think I've got a a sketch + + align:start position:0% +graphite and I think I've got a a sketch + + + align:start position:0% +graphite and I think I've got a a sketch +right here to + + align:start position:0% +right here to + + + align:start position:0% +right here to +indicate uh oh that's the that's just + + align:start position:0% +indicate uh oh that's the that's just + + + align:start position:0% +indicate uh oh that's the that's just +the stick ball model of the stereo + + align:start position:0% +the stick ball model of the stereo + + + align:start position:0% +the stick ball model of the stereo +isomer okay so there's a there's a + + align:start position:0% +isomer okay so there's a there's a + + + align:start position:0% +isomer okay so there's a there's a +diagram from a book and it's uh okay so + + align:start position:0% +diagram from a book and it's uh okay so + + + align:start position:0% +diagram from a book and it's uh okay so +the the artist that worked for the + + align:start position:0% +the the artist that worked for the + + + align:start position:0% +the the artist that worked for the +publisher did a better drawing than I + + align:start position:0% +publisher did a better drawing than I + + + align:start position:0% +publisher did a better drawing than I +did all right I I I accept that I accept + + align:start position:0% +did all right I I I accept that I accept + + + align:start position:0% +did all right I I I accept that I accept +that but you can see that the the + + align:start position:0% +that but you can see that the the + + + align:start position:0% +that but you can see that the the +delocalization of the electrons here and + + align:start position:0% +delocalization of the electrons here and + + + align:start position:0% +delocalization of the electrons here and +it doesn't just apply to something like + + align:start position:0% +it doesn't just apply to something like + + + align:start position:0% +it doesn't just apply to something like +Benzene it can apply in a straight line + + align:start position:0% +Benzene it can apply in a straight line + + + align:start position:0% +Benzene it can apply in a straight line +and the the recipe is for a + + align:start position:0% +and the the recipe is for a + + + align:start position:0% +and the the recipe is for a +conjugated + + align:start position:0% +conjugated + + + align:start position:0% +conjugated +conjugated + + align:start position:0% +conjugated + + + align:start position:0% +conjugated +electron system + + align:start position:0% +electron system + + + align:start position:0% +electron system +and what they mean by that is + + align:start position:0% +and what they mean by that is + + + align:start position:0% +and what they mean by that is +alternating between uh double or + + align:start position:0% +alternating between uh double or + + + align:start position:0% +alternating between uh double or +triple and a single double or triple and + + align:start position:0% +triple and a single double or triple and + + + align:start position:0% +triple and a single double or triple and +then a single so whenever you have + + align:start position:0% +then a single so whenever you have + + + align:start position:0% +then a single so whenever you have +multiple Bond single Bond multiple Bond + + align:start position:0% +multiple Bond single Bond multiple Bond + + + align:start position:0% +multiple Bond single Bond multiple Bond +single Bond you have the possibility of + + align:start position:0% +single Bond you have the possibility of + + + align:start position:0% +single Bond you have the possibility of +of pulling everything in tight enough + + align:start position:0% +of pulling everything in tight enough + + + align:start position:0% +of pulling everything in tight enough +that the electrons can move from one + + align:start position:0% +that the electrons can move from one + + + align:start position:0% +that the electrons can move from one +multiple bond to the next multiple Bond + + align:start position:0% +multiple bond to the next multiple Bond + + + align:start position:0% +multiple bond to the next multiple Bond +so this is a conjugated structure and + + align:start position:0% +so this is a conjugated structure and + + + align:start position:0% +so this is a conjugated structure and +here's one that's showing it's uh this + + align:start position:0% +here's one that's showing it's uh this + + + align:start position:0% +here's one that's showing it's uh this +is a straight line molecule and this one + + align:start position:0% +is a straight line molecule and this one + + + align:start position:0% +is a straight line molecule and this one +is a uh I've just shown you a multiple + + align:start position:0% +is a uh I've just shown you a multiple + + + align:start position:0% +is a uh I've just shown you a multiple +Bond and an Aline so this is a 13 badine + + align:start position:0% +Bond and an Aline so this is a 13 badine + + + align:start position:0% +Bond and an Aline so this is a 13 badine +where you have double bond single Bond + + align:start position:0% +where you have double bond single Bond + + + align:start position:0% +where you have double bond single Bond +double + + align:start position:0% +double + + + align:start position:0% +double +bond + + align:start position:0% +bond + + + align:start position:0% +bond +badine one three and what can happen is + + align:start position:0% +badine one three and what can happen is + + + align:start position:0% +badine one three and what can happen is +this can pull in so that we have a + + align:start position:0% +this can pull in so that we have a + + + align:start position:0% +this can pull in so that we have a +double bond here so this is two this is + + align:start position:0% +double bond here so this is two this is + + + align:start position:0% +double bond here so this is two this is +a double bond this is one two 2 * 2 2 * + + align:start position:0% +a double bond this is one two 2 * 2 2 * + + + align:start position:0% +a double bond this is one two 2 * 2 2 * +2 + 1 we have this is essentially 5/3 + + align:start position:0% +2 + 1 we have this is essentially 5/3 + + + align:start position:0% +2 + 1 we have this is essentially 5/3 +average average bond order through this + + align:start position:0% +average average bond order through this + + + align:start position:0% +average average bond order through this +linear molecule and that's what you see + + align:start position:0% +linear molecule and that's what you see + + + align:start position:0% +linear molecule and that's what you see +up here so you can imagine that + + align:start position:0% +up here so you can imagine that + + + align:start position:0% +up here so you can imagine that +happening in in other systems where we + + align:start position:0% +happening in in other systems where we + + + align:start position:0% +happening in in other systems where we +have alternating single bonds double + + align:start position:0% +have alternating single bonds double + + + align:start position:0% +have alternating single bonds double +bonds single bonds double bonds or can + + align:start position:0% +bonds single bonds double bonds or can + + + align:start position:0% +bonds single bonds double bonds or can +be even single bonds and triple bonds + + align:start position:0% +be even single bonds and triple bonds + + + align:start position:0% +be even single bonds and triple bonds +multiple single multiple single pulls + + align:start position:0% +multiple single multiple single pulls + + + align:start position:0% +multiple single multiple single pulls +everything in um and all of these will + + align:start position:0% +everything in um and all of these will + + + align:start position:0% +everything in um and all of these will +be called resonance hybrids when they + + align:start position:0% +be called resonance hybrids when they + + + align:start position:0% +be called resonance hybrids when they +allow the electrons to uh to move as + + align:start position:0% +allow the electrons to uh to move as + + + align:start position:0% +allow the electrons to uh to move as +they do um last thing is the + + align:start position:0% +they do um last thing is the + + + align:start position:0% +they do um last thing is the +radical last thing is the radical the + + align:start position:0% +radical last thing is the radical the + + + align:start position:0% +radical last thing is the radical the +radical here if we + + align:start position:0% + + + + align:start position:0% + +take Benzene and I'm going to indicate + + align:start position:0% +take Benzene and I'm going to indicate + + + align:start position:0% +take Benzene and I'm going to indicate +that this is the this is the one that's + + align:start position:0% +that this is the this is the one that's + + + align:start position:0% +that this is the this is the one that's +got the missing electron okay so there's + + align:start position:0% +got the missing electron okay so there's + + + align:start position:0% +got the missing electron okay so there's +only one electron in the orbital this + + align:start position:0% +only one electron in the orbital this + + + align:start position:0% +only one electron in the orbital this +radical which is C6 H5 is called + + align:start position:0% +radical which is C6 H5 is called + + + align:start position:0% +radical which is C6 H5 is called +fennel fennel + + align:start position:0% + + + + align:start position:0% + +so we could take something like let's + + align:start position:0% +so we could take something like let's + + + align:start position:0% +so we could take something like let's +build two of these let's take uh here's + + align:start position:0% +build two of these let's take uh here's + + + align:start position:0% +build two of these let's take uh here's +a + + align:start position:0% +a + + + align:start position:0% +a +here's here's + + align:start position:0% +here's here's + + + align:start position:0% +here's here's +Ethan and I'm going to break one of + + align:start position:0% +Ethan and I'm going to break one of + + + align:start position:0% +Ethan and I'm going to break one of +these off and I'm going to attach it + + align:start position:0% +these off and I'm going to attach it + + + align:start position:0% +these off and I'm going to attach it +to fennel so I can either call this + + align:start position:0% +to fennel so I can either call this + + + align:start position:0% +to fennel so I can either call this +vinyl + + align:start position:0% +vinyl + + + align:start position:0% +vinyl +Benzene vinyl Benzene or we could call + + align:start position:0% +Benzene vinyl Benzene or we could call + + + align:start position:0% +Benzene vinyl Benzene or we could call +it fenel or pheny um + + align:start position:0% +it fenel or pheny um + + + align:start position:0% +it fenel or pheny um +ethine right who's to say mean are you + + align:start position:0% +ethine right who's to say mean are you + + + align:start position:0% +ethine right who's to say mean are you +benzo Centric so you say that this is uh + + align:start position:0% +benzo Centric so you say that this is uh + + + align:start position:0% +benzo Centric so you say that this is uh +this is vinyl ATT attached onto Benzene + + align:start position:0% +this is vinyl ATT attached onto Benzene + + + align:start position:0% +this is vinyl ATT attached onto Benzene +or maybe you're etheno Centric and so + + align:start position:0% +or maybe you're etheno Centric and so + + + align:start position:0% +or maybe you're etheno Centric and so +you say this is a a pheny attached on to + + align:start position:0% +you say this is a a pheny attached on to + + + align:start position:0% +you say this is a a pheny attached on to +thing but neither one of these These are + + align:start position:0% +thing but neither one of these These are + + + align:start position:0% +thing but neither one of these These are +both correct by the way but we don't use + + align:start position:0% +both correct by the way but we don't use + + + align:start position:0% +both correct by the way but we don't use +this this compound is called + + align:start position:0% +this this compound is called + + + align:start position:0% +this this compound is called +styrene and what we're going to do later + + align:start position:0% +styrene and what we're going to do later + + + align:start position:0% +styrene and what we're going to do later +on is break this double Bond and we're + + align:start position:0% +on is break this double Bond and we're + + + align:start position:0% +on is break this double Bond and we're +going to make polystyrene so that's + + align:start position:0% +going to make polystyrene so that's + + + align:start position:0% +going to make polystyrene so that's +styrene and two others that I'd like you + + align:start position:0% +styrene and two others that I'd like you + + + align:start position:0% +styrene and two others that I'd like you +to be familiar with are we can take and + + align:start position:0% +to be familiar with are we can take and + + + align:start position:0% +to be familiar with are we can take and +just simply add methyl groups so if we + + align:start position:0% +just simply add methyl groups so if we + + + align:start position:0% +just simply add methyl groups so if we +take Benzene and add one methyl group + + align:start position:0% +take Benzene and add one methyl group + + + align:start position:0% +take Benzene and add one methyl group +this would be methyl Benzene or we could + + align:start position:0% +this would be methyl Benzene or we could + + + align:start position:0% +this would be methyl Benzene or we could +call This + + align:start position:0% +call This + + + align:start position:0% +call This +talline And there's the last one I'll + + align:start position:0% +talline And there's the last one I'll + + + align:start position:0% +talline And there's the last one I'll +introduce you to and that's two methyl + + align:start position:0% +introduce you to and that's two methyl + + + align:start position:0% +introduce you to and that's two methyl +groups two methyl groups so this is + + align:start position:0% +groups two methyl groups so this is + + + align:start position:0% +groups two methyl groups so this is +dimethylbenzene or it's called called uh + + align:start position:0% + + + + align:start position:0% + +xylene and this whole sequence of + + align:start position:0% +xylene and this whole sequence of + + + align:start position:0% +xylene and this whole sequence of +benzene let's just put Benzene up here + + align:start position:0% +benzene let's just put Benzene up here + + + align:start position:0% +benzene let's just put Benzene up here +for completeness so + + align:start position:0% +for completeness so + + + align:start position:0% +for completeness so +Benzene toine zylene this + + align:start position:0% +Benzene toine zylene this + + + align:start position:0% +Benzene toine zylene this +btx is used as additives to a jet engine + + align:start position:0% +btx is used as additives to a jet engine + + + align:start position:0% +btx is used as additives to a jet engine +fuel to uh improve the octane number and + + align:start position:0% +fuel to uh improve the octane number and + + + align:start position:0% +fuel to uh improve the octane number and +improve + + align:start position:0% +improve + + + align:start position:0% +improve +performance so let's move to that + + align:start position:0% +performance so let's move to that + + + align:start position:0% +performance so let's move to that +so first of all a little bit about k k + + align:start position:0% +so first of all a little bit about k k + + + align:start position:0% +so first of all a little bit about k k +is an interesting person he uh entered + + align:start position:0% +is an interesting person he uh entered + + + align:start position:0% +is an interesting person he uh entered +the University of Geeson to study + + align:start position:0% +the University of Geeson to study + + + align:start position:0% +the University of Geeson to study +architecture but then he switched over + + align:start position:0% +architecture but then he switched over + + + align:start position:0% +architecture but then he switched over +to chemistry and after his PhD he moved + + align:start position:0% +to chemistry and after his PhD he moved + + + align:start position:0% +to chemistry and after his PhD he moved +to uh Britain he took a job at St + + align:start position:0% +to uh Britain he took a job at St + + + align:start position:0% +to uh Britain he took a job at St +Bartholomew's Hospital in London and he + + align:start position:0% +Bartholomew's Hospital in London and he + + + align:start position:0% +Bartholomew's Hospital in London and he +would fall asleep on the bus going back + + align:start position:0% +would fall asleep on the bus going back + + + align:start position:0% +would fall asleep on the bus going back +to his flat and The Story Goes that one + + align:start position:0% +to his flat and The Story Goes that one + + + align:start position:0% +to his flat and The Story Goes that one +day he fell asleep on the bus missed his + + align:start position:0% +day he fell asleep on the bus missed his + + + align:start position:0% +day he fell asleep on the bus missed his +stop woke up far beyond where he was + + align:start position:0% +stop woke up far beyond where he was + + + align:start position:0% +stop woke up far beyond where he was +supposed to get off and during the + + align:start position:0% +supposed to get off and during the + + + align:start position:0% +supposed to get off and during the +course of that bus ride it it occurred + + align:start position:0% +course of that bus ride it it occurred + + + align:start position:0% +course of that bus ride it it occurred +to him in a dream that the way to + + align:start position:0% +to him in a dream that the way to + + + align:start position:0% +to him in a dream that the way to +describe the structures of some of the + + align:start position:0% +describe the structures of some of the + + + align:start position:0% +describe the structures of some of the +carbon compounds that were known at that + + align:start position:0% +carbon compounds that were known at that + + + align:start position:0% +carbon compounds that were known at that +time people could characterize them by + + align:start position:0% +time people could characterize them by + + + align:start position:0% +time people could characterize them by +their molecular weight so they knew what + + align:start position:0% +their molecular weight so they knew what + + + align:start position:0% +their molecular weight so they knew what +the structure was but nobody until that + + align:start position:0% +the structure was but nobody until that + + + align:start position:0% +the structure was but nobody until that +time had the vision to suggest that + + align:start position:0% +time had the vision to suggest that + + + align:start position:0% +time had the vision to suggest that +carbon could link to itself and form a + + align:start position:0% +carbon could link to itself and form a + + + align:start position:0% +carbon could link to itself and form a +chain so this is where he first proposes + + align:start position:0% +chain so this is where he first proposes + + + align:start position:0% +chain so this is where he first proposes +chains in 1855 then he got a a job as a + + align:start position:0% +chains in 1855 then he got a a job as a + + + align:start position:0% +chains in 1855 then he got a a job as a +faculty member at the University of Kent + + align:start position:0% +faculty member at the University of Kent + + + align:start position:0% +faculty member at the University of Kent +went back to Continental Europe and one + + align:start position:0% +went back to Continental Europe and one + + + align:start position:0% +went back to Continental Europe and one +night he fell asleep by the fireplace + + align:start position:0% +night he fell asleep by the fireplace + + + align:start position:0% +night he fell asleep by the fireplace +and he was dreaming about the Benzene + + align:start position:0% +and he was dreaming about the Benzene + + + align:start position:0% +and he was dreaming about the Benzene +molecule this guy really took his work + + align:start position:0% +molecule this guy really took his work + + + align:start position:0% +molecule this guy really took his work +home with him okay and uh so the The + + align:start position:0% +home with him okay and uh so the The + + + align:start position:0% +home with him okay and uh so the The +Story Goes that he had this vision of a + + align:start position:0% +Story Goes that he had this vision of a + + + align:start position:0% +Story Goes that he had this vision of a +snake biting its tail and spinning in + + align:start position:0% +snake biting its tail and spinning in + + + align:start position:0% +snake biting its tail and spinning in +the dream and that's where he came up + + align:start position:0% +the dream and that's where he came up + + + align:start position:0% +the dream and that's where he came up +with the idea of this Kola structure of + + align:start position:0% +with the idea of this Kola structure of + + + align:start position:0% +with the idea of this Kola structure of +folding remember he already had the + + align:start position:0% +folding remember he already had the + + + align:start position:0% +folding remember he already had the +courage to put carbons in a line so now + + align:start position:0% +courage to put carbons in a line so now + + + align:start position:0% +courage to put carbons in a line so now +he's going to fold that line over onto + + align:start position:0% +he's going to fold that line over onto + + + align:start position:0% +he's going to fold that line over onto +itself and so he's really been consider + + align:start position:0% +itself and so he's really been consider + + + align:start position:0% +itself and so he's really been consider +considered the father of uh structural + + align:start position:0% +considered the father of uh structural + + + align:start position:0% +considered the father of uh structural +chemistry and so I I try to abstract um + + align:start position:0% +chemistry and so I I try to abstract um + + + align:start position:0% +chemistry and so I I try to abstract um +you know just just keep the noise down + + align:start position:0% +you know just just keep the noise down + + + align:start position:0% +you know just just keep the noise down +we three more minutes and then then + + align:start position:0% +we three more minutes and then then + + + align:start position:0% +we three more minutes and then then +you're gone so what's his formula for + + align:start position:0% +you're gone so what's his formula for + + + align:start position:0% +you're gone so what's his formula for +Success well he moved into chemistry + + align:start position:0% +Success well he moved into chemistry + + + align:start position:0% +Success well he moved into chemistry +from another field so sometimes this + + align:start position:0% +from another field so sometimes this + + + align:start position:0% +from another field so sometimes this +cross fertilization is good and the + + align:start position:0% +cross fertilization is good and the + + + align:start position:0% +cross fertilization is good and the +other thing is he's a dreamer and I + + align:start position:0% +other thing is he's a dreamer and I + + + align:start position:0% +other thing is he's a dreamer and I +always tell people you got to keep + + align:start position:0% +always tell people you got to keep + + + align:start position:0% +always tell people you got to keep +dreaming when you stop dreaming you + + align:start position:0% +dreaming when you stop dreaming you + + + align:start position:0% +dreaming when you stop dreaming you +stop thinking big but if you're going to + + align:start position:0% +stop thinking big but if you're going to + + + align:start position:0% +stop thinking big but if you're going to +dream you have to get some + + align:start position:0% +dream you have to get some + + + align:start position:0% +dream you have to get some +sleep I know people in this room don't + + align:start position:0% +sleep I know people in this room don't + + + align:start position:0% +sleep I know people in this room don't +sleep enough so I'm I'm going to + + align:start position:0% +sleep enough so I'm I'm going to + + + align:start position:0% +sleep enough so I'm I'm going to +challenge you to get some sleep + + align:start position:0% +challenge you to get some sleep + + + align:start position:0% +challenge you to get some sleep +especially get a little bit of sleep on + + align:start position:0% +especially get a little bit of sleep on + + + align:start position:0% +especially get a little bit of sleep on +Tuesday night I think you'll perform + + align:start position:0% +Tuesday night I think you'll perform + + + align:start position:0% +Tuesday night I think you'll perform +better on Wednesday if you've had some + + align:start position:0% +better on Wednesday if you've had some + + + align:start position:0% +better on Wednesday if you've had some +sleep on Tuesday night the last thing I + + align:start position:0% +sleep on Tuesday night the last thing I + + + align:start position:0% +sleep on Tuesday night the last thing I +want to talk about is uh anti- knocking + + align:start position:0% +want to talk about is uh anti- knocking + + + align:start position:0% +want to talk about is uh anti- knocking +agents in automobiles and also an + + align:start position:0% +agents in automobiles and also an + + + align:start position:0% +agents in automobiles and also an +aircraft um if we took only straight + + align:start position:0% +aircraft um if we took only straight + + + align:start position:0% +aircraft um if we took only straight +chain alkanes for gasoline they would + + align:start position:0% +chain alkanes for gasoline they would + + + align:start position:0% +chain alkanes for gasoline they would +burn very unevenly remember in in a + + align:start position:0% +burn very unevenly remember in in a + + + align:start position:0% +burn very unevenly remember in in a +internal combustion engine you ad met + + align:start position:0% +internal combustion engine you ad met + + + align:start position:0% +internal combustion engine you ad met +fuel as Vapor you compress and then you + + align:start position:0% +fuel as Vapor you compress and then you + + + align:start position:0% +fuel as Vapor you compress and then you +ignite but after a number of firings the + + align:start position:0% +ignite but after a number of firings the + + + align:start position:0% +ignite but after a number of firings the +engine chamber is hot and if the fuel is + + align:start position:0% +engine chamber is hot and if the fuel is + + + align:start position:0% +engine chamber is hot and if the fuel is +too reactive it'll ignite by itself as + + align:start position:0% +too reactive it'll ignite by itself as + + + align:start position:0% +too reactive it'll ignite by itself as +you're on the compression cycle and you + + align:start position:0% +you're on the compression cycle and you + + + align:start position:0% +you're on the compression cycle and you +want staged compression it has to be + + align:start position:0% +want staged compression it has to be + + + align:start position:0% +want staged compression it has to be +done in concert on que not before it's + + align:start position:0% +done in concert on que not before it's + + + align:start position:0% +done in concert on que not before it's +time so uh this unprovoked uh firing is + + align:start position:0% +time so uh this unprovoked uh firing is + + + align:start position:0% +time so uh this unprovoked uh firing is +called knocking and you'll hear that + + align:start position:0% +called knocking and you'll hear that + + + align:start position:0% +called knocking and you'll hear that +sometimes when you accelerate up a hill + + align:start position:0% +sometimes when you accelerate up a hill + + + align:start position:0% +sometimes when you accelerate up a hill +you'll hear this pinging sound well this + + align:start position:0% +you'll hear this pinging sound well this + + + align:start position:0% +you'll hear this pinging sound well this +is knocking so the figure of Merit that + + align:start position:0% +is knocking so the figure of Merit that + + + align:start position:0% +is knocking so the figure of Merit that +was introduced in 1927 is called the + + align:start position:0% +was introduced in 1927 is called the + + + align:start position:0% +was introduced in 1927 is called the +octane number so it has an ISO octane + + align:start position:0% +octane number so it has an ISO octane + + + align:start position:0% +octane number so it has an ISO octane +see it's trimethyl pentane well you know + + align:start position:0% +see it's trimethyl pentane well you know + + + align:start position:0% +see it's trimethyl pentane well you know +that's five carbons and three the other + + align:start position:0% +that's five carbons and three the other + + + align:start position:0% +that's five carbons and three the other +three carbons to make octane or our side + + align:start position:0% +three carbons to make octane or our side + + + align:start position:0% +three carbons to make octane or our side +groups and they're off of the two two + + align:start position:0% +groups and they're off of the two two + + + align:start position:0% +groups and they're off of the two two +and the four and then compare that to + + align:start position:0% +and the four and then compare that to + + + align:start position:0% +and the four and then compare that to +heptane which is absolutely abysmal so + + align:start position:0% +heptane which is absolutely abysmal so + + + align:start position:0% +heptane which is absolutely abysmal so +this is 100 this is zero and then you + + align:start position:0% +this is 100 this is zero and then you + + + align:start position:0% +this is 100 this is zero and then you +take whatever your gasoline is and you + + align:start position:0% +take whatever your gasoline is and you + + + align:start position:0% +take whatever your gasoline is and you +compare it against this uh standard + + align:start position:0% +compare it against this uh standard + + + align:start position:0% +compare it against this uh standard +solution this case it's 90% of the + + align:start position:0% +solution this case it's 90% of the + + + align:start position:0% +solution this case it's 90% of the +trimethyl pentane 10% heptane it ends up + + align:start position:0% +trimethyl pentane 10% heptane it ends up + + + align:start position:0% +trimethyl pentane 10% heptane it ends up +with an octane number of 90 anything + + align:start position:0% +with an octane number of 90 anything + + + align:start position:0% +with an octane number of 90 anything +else that performs in the same manner so + + align:start position:0% +else that performs in the same manner so + + + align:start position:0% +else that performs in the same manner so +when you go to the Gas Pump and it says + + align:start position:0% +when you go to the Gas Pump and it says + + + align:start position:0% +when you go to the Gas Pump and it says +octane 89 or whatever that's that's + + align:start position:0% +octane 89 or whatever that's that's + + + align:start position:0% +octane 89 or whatever that's that's +where it's coming from and you can use + + align:start position:0% +where it's coming from and you can use + + + align:start position:0% +where it's coming from and you can use +additives to increase octane in fact + + align:start position:0% +additives to increase octane in fact + + + align:start position:0% +additives to increase octane in fact +what you're trying to do is to repress + + align:start position:0% +what you're trying to do is to repress + + + align:start position:0% +what you're trying to do is to repress +ignition high octane fuel Burns less + + align:start position:0% +ignition high octane fuel Burns less + + + align:start position:0% +ignition high octane fuel Burns less +well but it burns on Q that's the thing + + align:start position:0% +well but it burns on Q that's the thing + + + align:start position:0% +well but it burns on Q that's the thing +so you could add tetraethyl Leed which + + align:start position:0% +so you could add tetraethyl Leed which + + + align:start position:0% +so you could add tetraethyl Leed which +was added for years it's now banned or + + align:start position:0% +was added for years it's now banned or + + + align:start position:0% +was added for years it's now banned or +ethyl alcohol ethyl alcohol will raise + + align:start position:0% +ethyl alcohol ethyl alcohol will raise + + + align:start position:0% +ethyl alcohol ethyl alcohol will raise +the octane rating and the way to make a + + align:start position:0% +the octane rating and the way to make a + + + align:start position:0% +the octane rating and the way to make a +mix of branched and cyclic alkanes is + + align:start position:0% +mix of branched and cyclic alkanes is + + + align:start position:0% +mix of branched and cyclic alkanes is +catalysis you use a catalyst of alumina + + align:start position:0% +catalysis you use a catalyst of alumina + + + align:start position:0% +catalysis you use a catalyst of alumina +silica 450 550° C it's called catalytic + + align:start position:0% +silica 450 550° C it's called catalytic + + + align:start position:0% +silica 450 550° C it's called catalytic +cracking and so by catalysis we can + + align:start position:0% +cracking and so by catalysis we can + + + align:start position:0% +cracking and so by catalysis we can +direct the synthesis to get the right + + align:start position:0% +direct the synthesis to get the right + + + align:start position:0% +direct the synthesis to get the right +mix of the right structures and thereby + + align:start position:0% +mix of the right structures and thereby + + + align:start position:0% +mix of the right structures and thereby +improve performance good luck on + + align:start position:0% +improve performance good luck on + + + align:start position:0% +improve performance good luck on +Wednesday \ No newline at end of file diff --git a/UYe98CcxPbs.txt b/UYe98CcxPbs.txt new file mode 100644 index 0000000000000000000000000000000000000000..c668e738d38f0133d7db792c27911c347ccf92d2 --- /dev/null +++ b/UYe98CcxPbs.txt @@ -0,0 +1,7467 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu today we're going to see how + + align:start position:0% +ocw.mit.edu today we're going to see how + + + align:start position:0% +ocw.mit.edu today we're going to see how +to use what we saw last time about + + align:start position:0% +to use what we saw last time about + + + align:start position:0% +to use what we saw last time about +partial derivatives + + align:start position:0% + + + + align:start position:0% + +to handle minimization or maximization + + align:start position:0% +to handle minimization or maximization + + + align:start position:0% +to handle minimization or maximization +problems involving functions of several + + align:start position:0% +problems involving functions of several + + + align:start position:0% +problems involving functions of several +variables + + align:start position:0% +variables + + + align:start position:0% +variables +so before that so remember last time we + + align:start position:0% +so before that so remember last time we + + + align:start position:0% +so before that so remember last time we +said that when we have a function say of + + align:start position:0% +said that when we have a function say of + + + align:start position:0% +said that when we have a function say of +two variables X and Y then we have + + align:start position:0% +two variables X and Y then we have + + + align:start position:0% +two variables X and Y then we have +actually two different + + align:start position:0% +actually two different + + + align:start position:0% +actually two different +derivatives partial F partial X also + + align:start position:0% +derivatives partial F partial X also + + + align:start position:0% +derivatives partial F partial X also +called f subx is the derivative with + + align:start position:0% +called f subx is the derivative with + + + align:start position:0% +called f subx is the derivative with +respect to X keeping y constant + + align:start position:0% + + + + align:start position:0% + +and we have partial F partial + + align:start position:0% +and we have partial F partial + + + align:start position:0% +and we have partial F partial +y also called f sub + + align:start position:0% + + + + align:start position:0% + +y where we VAR Y and we treat X as a + + align:start position:0% + + + + align:start position:0% + +constant okay and now one thing I didn't + + align:start position:0% +constant okay and now one thing I didn't + + + align:start position:0% +constant okay and now one thing I didn't +have time to tell you about but + + align:start position:0% +have time to tell you about but + + + align:start position:0% +have time to tell you about but +hopefully you heard about in recitation + + align:start position:0% +hopefully you heard about in recitation + + + align:start position:0% +hopefully you heard about in recitation +yesterday is the approximation + + align:start position:0% +yesterday is the approximation + + + align:start position:0% +yesterday is the approximation +formula that tells you what + + align:start position:0% +formula that tells you what + + + align:start position:0% +formula that tells you what +happens if you vary both X and + + align:start position:0% + + + + align:start position:0% + +Y + + align:start position:0% +Y + + + align:start position:0% +Y +so F subx tells us what happens if we + + align:start position:0% +so F subx tells us what happens if we + + + align:start position:0% +so F subx tells us what happens if we +change x a little bit by some small + + align:start position:0% +change x a little bit by some small + + + align:start position:0% +change x a little bit by some small +amount Delta x f sub y tells us how F + + align:start position:0% +amount Delta x f sub y tells us how F + + + align:start position:0% +amount Delta x f sub y tells us how F +changes if we change y by a small amount + + align:start position:0% +changes if we change y by a small amount + + + align:start position:0% +changes if we change y by a small amount +Delta y if we do both at the same time + + align:start position:0% +Delta y if we do both at the same time + + + align:start position:0% +Delta y if we do both at the same time +then the two effects will add up with + + align:start position:0% +then the two effects will add up with + + + align:start position:0% +then the two effects will add up with +each + + align:start position:0% +each + + + align:start position:0% +each +right because you can imagine that first + + align:start position:0% +right because you can imagine that first + + + align:start position:0% +right because you can imagine that first +you will change X and then you will + + align:start position:0% +you will change X and then you will + + + align:start position:0% +you will change X and then you will +change y or the other way around it + + align:start position:0% +change y or the other way around it + + + align:start position:0% +change y or the other way around it +doesn't really matter + + align:start position:0% + + + + align:start position:0% + +so if we + + align:start position:0% +so if we + + + align:start position:0% +so if we +change + + align:start position:0% +change + + + align:start position:0% +change +X by a certain amount Delta X and if we + + align:start position:0% +X by a certain amount Delta X and if we + + + align:start position:0% +X by a certain amount Delta X and if we +change y by the amount Delta Y and let's + + align:start position:0% +change y by the amount Delta Y and let's + + + align:start position:0% +change y by the amount Delta Y and let's +say that we have zal f ofx y then and + + align:start position:0% +say that we have zal f ofx y then and + + + align:start position:0% +say that we have zal f ofx y then and +that + + align:start position:0% +that + + + align:start position:0% +that +changes by an amount which is + + align:start position:0% +changes by an amount which is + + + align:start position:0% +changes by an amount which is +approximately f subx * Delta X Plus F + + align:start position:0% +approximately f subx * Delta X Plus F + + + align:start position:0% +approximately f subx * Delta X Plus F +sub y * Delta + + align:start position:0% +sub y * Delta + + + align:start position:0% +sub y * Delta +y okay and that's one of the most + + align:start position:0% +y okay and that's one of the most + + + align:start position:0% +y okay and that's one of the most +important formulas about partial + + align:start position:0% +important formulas about partial + + + align:start position:0% +important formulas about partial +derivatives okay so the intuition for + + align:start position:0% +derivatives okay so the intuition for + + + align:start position:0% +derivatives okay so the intuition for +this again is just the two effects add + + align:start position:0% +this again is just the two effects add + + + align:start position:0% +this again is just the two effects add +up if I change X by a small amount and + + align:start position:0% +up if I change X by a small amount and + + + align:start position:0% +up if I change X by a small amount and +then I change y well first changing X + + align:start position:0% +then I change y well first changing X + + + align:start position:0% +then I change y well first changing X +will modify f how much does it modify f + + align:start position:0% +will modify f how much does it modify f + + + align:start position:0% +will modify f how much does it modify f +the answer is the rate of change is f + + align:start position:0% +the answer is the rate of change is f + + + align:start position:0% +the answer is the rate of change is f +subx and if I change y then the rate of + + align:start position:0% +subx and if I change y then the rate of + + + align:start position:0% +subx and if I change y then the rate of +change of f when I change Y is f sub y + + align:start position:0% +change of f when I change Y is f sub y + + + align:start position:0% +change of f when I change Y is f sub y +so Al together I get this change in the + + align:start position:0% +so Al together I get this change in the + + + align:start position:0% +so Al together I get this change in the +value of F and of course that's only an + + align:start position:0% +value of F and of course that's only an + + + align:start position:0% +value of F and of course that's only an +approximation formula actually there + + align:start position:0% +approximation formula actually there + + + align:start position:0% +approximation formula actually there +would be higher order terms involving + + align:start position:0% +would be higher order terms involving + + + align:start position:0% +would be higher order terms involving +second and third derivatives and so + + align:start position:0% + + + + align:start position:0% + +on so one way to justify this + + align:start position:0% + + + + align:start position:0% + +sorry I was distracted by microphone + + align:start position:0% +sorry I was distracted by microphone + + + align:start position:0% +sorry I was distracted by microphone +problem okay + + align:start position:0% +problem okay + + + align:start position:0% +problem okay +so how do we + + align:start position:0% +so how do we + + + align:start position:0% +so how do we +justify this + + align:start position:0% +justify this + + + align:start position:0% +justify this +formula well one way to think about it + + align:start position:0% +formula well one way to think about it + + + align:start position:0% +formula well one way to think about it +is in terms of tangent plane + + align:start position:0% + + + + align:start position:0% + +oximation so let's think about the + + align:start position:0% +oximation so let's think about the + + + align:start position:0% +oximation so let's think about the +tangent plane to the graph of the + + align:start position:0% +tangent plane to the graph of the + + + align:start position:0% +tangent plane to the graph of the +function + + align:start position:0% +function + + + align:start position:0% +function +f okay so I have some pictures to show + + align:start position:0% +f okay so I have some pictures to show + + + align:start position:0% +f okay so I have some pictures to show +you it will be easier if I show the + + align:start position:0% +you it will be easier if I show the + + + align:start position:0% +you it will be easier if I show the +pictures okay so + + align:start position:0% +pictures okay so + + + align:start position:0% +pictures okay so +remember partial F partial + + align:start position:0% +remember partial F partial + + + align:start position:0% +remember partial F partial +X was obtained by looking at the + + align:start position:0% +X was obtained by looking at the + + + align:start position:0% +X was obtained by looking at the +situation where Y is held constant so + + align:start position:0% +situation where Y is held constant so + + + align:start position:0% +situation where Y is held constant so +that means I'm slicing the graph of f by + + align:start position:0% +that means I'm slicing the graph of f by + + + align:start position:0% +that means I'm slicing the graph of f by +a plane that's parallel to the XZ plane + + align:start position:0% +a plane that's parallel to the XZ plane + + + align:start position:0% +a plane that's parallel to the XZ plane +and then when I change x z changes and + + align:start position:0% +and then when I change x z changes and + + + align:start position:0% +and then when I change x z changes and +the slope of that is going to be the + + align:start position:0% +the slope of that is going to be the + + + align:start position:0% +the slope of that is going to be the +derivative with respect to + + align:start position:0% +derivative with respect to + + + align:start position:0% +derivative with respect to +X so now if I do the same in the other + + align:start position:0% +X so now if I do the same in the other + + + align:start position:0% +X so now if I do the same in the other +direction then I will have similarly the + + align:start position:0% +direction then I will have similarly the + + + align:start position:0% +direction then I will have similarly the +slope in a slice now parallel to the YZ + + align:start position:0% +slope in a slice now parallel to the YZ + + + align:start position:0% +slope in a slice now parallel to the YZ +plane that will be partial F partial y + + align:start position:0% +plane that will be partial F partial y + + + align:start position:0% +plane that will be partial F partial y +so in fact in each case I have a line + + align:start position:0% +so in fact in each case I have a line + + + align:start position:0% +so in fact in each case I have a line +and that line is tangent to the surface + + align:start position:0% +and that line is tangent to the surface + + + align:start position:0% +and that line is tangent to the surface +so now if I have two lines tangent to + + align:start position:0% +so now if I have two lines tangent to + + + align:start position:0% +so now if I have two lines tangent to +the surface well then together the + + align:start position:0% +the surface well then together the + + + align:start position:0% +the surface well then together the +determine for me the tangent plane to + + align:start position:0% +determine for me the tangent plane to + + + align:start position:0% +determine for me the tangent plane to +the + + align:start position:0% +the + + + align:start position:0% +the +surface okay so let's try to see how + + align:start position:0% +surface okay so let's try to see how + + + align:start position:0% +surface okay so let's try to see how +that + + align:start position:0% +that + + + align:start position:0% +that +works + + align:start position:0% + + + + align:start position:0% + +so we + + align:start position:0% +so we + + + align:start position:0% +so we +know that F subx and F sub y are + + align:start position:0% +know that F subx and F sub y are + + + align:start position:0% +know that F subx and F sub y are +slopes are the slopes of two tangent + + align:start position:0% +slopes are the slopes of two tangent + + + align:start position:0% +slopes are the slopes of two tangent +lines + + align:start position:0% + + + + align:start position:0% + +to this plane sorry two tangent lines to + + align:start position:0% +to this plane sorry two tangent lines to + + + align:start position:0% +to this plane sorry two tangent lines to +the graph and let's write down the + + align:start position:0% +the graph and let's write down the + + + align:start position:0% +the graph and let's write down the +equations of these lines I'm not going + + align:start position:0% +equations of these lines I'm not going + + + align:start position:0% +equations of these lines I'm not going +to write parametric equations I'm going + + align:start position:0% +to write parametric equations I'm going + + + align:start position:0% +to write parametric equations I'm going +to write them in terms of XYZ + + align:start position:0% +to write them in terms of XYZ + + + align:start position:0% +to write them in terms of XYZ +coordinates + + align:start position:0% +coordinates + + + align:start position:0% +coordinates +so let's say that partial F of a partial + + align:start position:0% +so let's say that partial F of a partial + + + align:start position:0% +so let's say that partial F of a partial +X at a given point is equal to + + align:start position:0% +X at a given point is equal to + + + align:start position:0% +X at a given point is equal to +a then that means that we have a + + align:start position:0% +a then that means that we have a + + + align:start position:0% +a then that means that we have a +line given by the following + + align:start position:0% +line given by the following + + + align:start position:0% +line given by the following +conditions so I'm going to keep y + + align:start position:0% +conditions so I'm going to keep y + + + align:start position:0% +conditions so I'm going to keep y +constant equal to + + align:start position:0% +constant equal to + + + align:start position:0% +constant equal to +y0 and I'm going to change X and as I + + align:start position:0% +y0 and I'm going to change X and as I + + + align:start position:0% +y0 and I'm going to change X and as I +change x z will change at a + + align:start position:0% +change x z will change at a + + + align:start position:0% +change x z will change at a +rate uh that's equal to a so that would + + align:start position:0% +rate uh that's equal to a so that would + + + align:start position:0% +rate uh that's equal to a so that would +be Z equals z0 plus a * the change in x + + align:start position:0% +be Z equals z0 plus a * the change in x + + + align:start position:0% +be Z equals z0 plus a * the change in x +X - + + align:start position:0% +X - + + + align:start position:0% +X - +x0 okay that is how you would describe + + align:start position:0% +x0 okay that is how you would describe + + + align:start position:0% +x0 okay that is how you would describe +the + + align:start position:0% +the + + + align:start position:0% +the +line that's I guess the one that's + + align:start position:0% +line that's I guess the one that's + + + align:start position:0% +line that's I guess the one that's +ploted in green here that's the + + align:start position:0% +ploted in green here that's the + + + align:start position:0% +ploted in green here that's the +intersection with a slice parall to the + + align:start position:0% +intersection with a slice parall to the + + + align:start position:0% +intersection with a slice parall to the +XZ plane I hold y constant equal to y0 + + align:start position:0% +XZ plane I hold y constant equal to y0 + + + align:start position:0% +XZ plane I hold y constant equal to y0 +and Z is a function of X that varies + + align:start position:0% +and Z is a function of X that varies + + + align:start position:0% +and Z is a function of X that varies +with a rate of + + align:start position:0% +with a rate of + + + align:start position:0% +with a rate of +a okay + + align:start position:0% +a okay + + + align:start position:0% +a okay +and now if I look similarly at the other + + align:start position:0% + + + + align:start position:0% + +slice let's say that the partial with + + align:start position:0% +slice let's say that the partial with + + + align:start position:0% +slice let's say that the partial with +respect to Y is equal to B then I get + + align:start position:0% +respect to Y is equal to B then I get + + + align:start position:0% +respect to Y is equal to B then I get +another line which is obtained by the + + align:start position:0% +another line which is obtained by the + + + align:start position:0% +another line which is obtained by the +fact that Z now will depend on + + align:start position:0% +fact that Z now will depend on + + + align:start position:0% +fact that Z now will depend on +Y and the rate of change with respect to + + align:start position:0% +Y and the rate of change with respect to + + + align:start position:0% +Y and the rate of change with respect to +Y will be + + align:start position:0% +Y will be + + + align:start position:0% +Y will be +B while X is held constant equal to x0 + + align:start position:0% +B while X is held constant equal to x0 + + + align:start position:0% +B while X is held constant equal to x0 +so these two lines are both going to be + + align:start position:0% +so these two lines are both going to be + + + align:start position:0% +so these two lines are both going to be +in the tangent plane to the surface + + align:start position:0% + + + + align:start position:0% + +so they're both tangent to the graph of + + align:start position:0% +so they're both tangent to the graph of + + + align:start position:0% +so they're both tangent to the graph of +F and well together they determine a + + align:start position:0% + + + + align:start position:0% + +plane and that plane is just given by + + align:start position:0% +plane and that plane is just given by + + + align:start position:0% +plane and that plane is just given by +the formula Z = Z 0 + a * x - x0 + B * + + align:start position:0% +the formula Z = Z 0 + a * x - x0 + B * + + + align:start position:0% +the formula Z = Z 0 + a * x - x0 + B * +Yus + + align:start position:0% +Yus + + + align:start position:0% +Yus +y0 right if + + align:start position:0% +y0 right if + + + align:start position:0% +y0 right if +you look at what happens so this is the + + align:start position:0% +you look at what happens so this is the + + + align:start position:0% +you look at what happens so this is the +equation of a + + align:start position:0% +equation of a + + + align:start position:0% +equation of a +plane Z equals constant * X Plus + + align:start position:0% +plane Z equals constant * X Plus + + + align:start position:0% +plane Z equals constant * X Plus +constant * y plus constant and if you + + align:start position:0% +constant * y plus constant and if you + + + align:start position:0% +constant * y plus constant and if you +look at what happens if I hold y + + align:start position:0% +look at what happens if I hold y + + + align:start position:0% +look at what happens if I hold y +constant and Vary X I recover the first + + align:start position:0% +constant and Vary X I recover the first + + + align:start position:0% +constant and Vary X I recover the first +line if I hold x constant and very y I + + align:start position:0% +line if I hold x constant and very y I + + + align:start position:0% +line if I hold x constant and very y I +get the second + + align:start position:0% +get the second + + + align:start position:0% +get the second +line okay another way to do it of course + + align:start position:0% +line okay another way to do it of course + + + align:start position:0% +line okay another way to do it of course +would be to write actually parametric + + align:start position:0% +would be to write actually parametric + + + align:start position:0% +would be to write actually parametric +equations of these lines get vectors + + align:start position:0% +equations of these lines get vectors + + + align:start position:0% +equations of these lines get vectors +along them and then take the cross + + align:start position:0% +along them and then take the cross + + + align:start position:0% +along them and then take the cross +product to get the normal Vector to the + + align:start position:0% +product to get the normal Vector to the + + + align:start position:0% +product to get the normal Vector to the +plane and then get this equation for the + + align:start position:0% +plane and then get this equation for the + + + align:start position:0% +plane and then get this equation for the +plane using the normal Vector that also + + align:start position:0% +plane using the normal Vector that also + + + align:start position:0% +plane using the normal Vector that also +works and it gives you the same formula + + align:start position:0% +works and it gives you the same formula + + + align:start position:0% +works and it gives you the same formula +so you know if you're + + align:start position:0% +so you know if you're + + + align:start position:0% +so you know if you're +curious exercise do it again using + + align:start position:0% +curious exercise do it again using + + + align:start position:0% +curious exercise do it again using +parametrics and using cross product to + + align:start position:0% +parametrics and using cross product to + + + align:start position:0% +parametrics and using cross product to +get the plane equation + + align:start position:0% +get the plane equation + + + align:start position:0% +get the plane equation +okay so that's how we get the tangent + + align:start position:0% +okay so that's how we get the tangent + + + align:start position:0% +okay so that's how we get the tangent +plane and now what this approximation + + align:start position:0% +plane and now what this approximation + + + align:start position:0% +plane and now what this approximation +formula here says is that in fact the + + align:start position:0% +formula here says is that in fact the + + + align:start position:0% +formula here says is that in fact the +graph of the function is close to the + + align:start position:0% +graph of the function is close to the + + + align:start position:0% +graph of the function is close to the +tangent plane okay if we were moving on + + align:start position:0% +tangent plane okay if we were moving on + + + align:start position:0% +tangent plane okay if we were moving on +the tangent plane this would be an + + align:start position:0% +the tangent plane this would be an + + + align:start position:0% +the tangent plane this would be an +actual equality Delta Z would be a + + align:start position:0% +actual equality Delta Z would be a + + + align:start position:0% +actual equality Delta Z would be a +linear function of Delta X and Delta Y + + align:start position:0% +linear function of Delta X and Delta Y + + + align:start position:0% +linear function of Delta X and Delta Y +and the graph of the function is near + + align:start position:0% +and the graph of the function is near + + + align:start position:0% +and the graph of the function is near +the tangent plane but it's not quite the + + align:start position:0% +the tangent plane but it's not quite the + + + align:start position:0% +the tangent plane but it's not quite the +same so it's only an approximation for + + align:start position:0% +same so it's only an approximation for + + + align:start position:0% +same so it's only an approximation for +small Delta X and small Delta y + + align:start position:0% + + + + align:start position:0% + +so the approximation + + align:start position:0% +so the approximation + + + align:start position:0% +so the approximation +formula + + align:start position:0% +formula + + + align:start position:0% +formula +says the graph of + + align:start position:0% + + + + align:start position:0% + +f is close to its tangent + + align:start position:0% + + + + align:start position:0% + +plane okay and we can use that formula + + align:start position:0% +plane okay and we can use that formula + + + align:start position:0% +plane okay and we can use that formula +of here now to estimate how the value of + + align:start position:0% +of here now to estimate how the value of + + + align:start position:0% +of here now to estimate how the value of +f changes if I change X and Y at the + + align:start position:0% +f changes if I change X and Y at the + + + align:start position:0% +f changes if I change X and Y at the +same + + align:start position:0% + + + + align:start position:0% + +time okay questions about + + align:start position:0% + + + + align:start position:0% + +that okay so now that we've CAU up with + + align:start position:0% +that okay so now that we've CAU up with + + + align:start position:0% +that okay so now that we've CAU up with +what we were supposed to see on + + align:start position:0% +what we were supposed to see on + + + align:start position:0% +what we were supposed to see on +Tuesday I can tell + + align:start position:0% +Tuesday I can tell + + + align:start position:0% +Tuesday I can tell +you now about Max and Min problems + + align:start position:0% + + + + align:start position:0% + +so that's going to be an application of + + align:start position:0% +so that's going to be an application of + + + align:start position:0% +so that's going to be an application of +partial + + align:start position:0% + + + + align:start position:0% + +derivatives to look + + align:start position:0% +derivatives to look + + + align:start position:0% +derivatives to look +at optimization problems + + align:start position:0% + + + + align:start position:0% + +okay so maybe you know 10 years from now + + align:start position:0% +okay so maybe you know 10 years from now + + + align:start position:0% +okay so maybe you know 10 years from now +when you have a real job your job might + + align:start position:0% +when you have a real job your job might + + + align:start position:0% +when you have a real job your job might +be to actually minimize the cost of + + align:start position:0% +be to actually minimize the cost of + + + align:start position:0% +be to actually minimize the cost of +something or maximize the profit of + + align:start position:0% +something or maximize the profit of + + + align:start position:0% +something or maximize the profit of +something or um whatever but typically + + align:start position:0% +something or um whatever but typically + + + align:start position:0% +something or um whatever but typically +the function that you will have to you + + align:start position:0% +the function that you will have to you + + + align:start position:0% +the function that you will have to you +know strive to minimize or maximize will + + align:start position:0% +know strive to minimize or maximize will + + + align:start position:0% +know strive to minimize or maximize will +depend on several variables so if you + + align:start position:0% +depend on several variables so if you + + + align:start position:0% +depend on several variables so if you +have a function of one variable um you + + align:start position:0% +have a function of one variable um you + + + align:start position:0% +have a function of one variable um you +know that to find its minimum or it's + + align:start position:0% +know that to find its minimum or it's + + + align:start position:0% +know that to find its minimum or it's +maximum you look at the derivative and + + align:start position:0% +maximum you look at the derivative and + + + align:start position:0% +maximum you look at the derivative and +you set that equal to zero and you try + + align:start position:0% +you set that equal to zero and you try + + + align:start position:0% +you set that equal to zero and you try +to then look at what happens to the + + align:start position:0% +to then look at what happens to the + + + align:start position:0% +to then look at what happens to the +function so here it's going to be kind + + align:start position:0% +function so here it's going to be kind + + + align:start position:0% +function so here it's going to be kind +of + + align:start position:0% +of + + + align:start position:0% +of +similar except of course we have several + + align:start position:0% + + + + align:start position:0% + +derivatives okay + + align:start position:0% +derivatives okay + + + align:start position:0% +derivatives okay +so for today we'll think about a + + align:start position:0% +so for today we'll think about a + + + align:start position:0% +so for today we'll think about a +function of two variables but it works + + align:start position:0% +function of two variables but it works + + + align:start position:0% +function of two variables but it works +exactly the same if you have three + + align:start position:0% +exactly the same if you have three + + + align:start position:0% +exactly the same if you have three +variables 10 variables a million + + align:start position:0% +variables 10 variables a million + + + align:start position:0% +variables 10 variables a million +variables + + align:start position:0% + + + + align:start position:0% + +so the first observation is + + align:start position:0% + + + + align:start position:0% + +that so if we have a local + + align:start position:0% +that so if we have a local + + + align:start position:0% +that so if we have a local +minimum or a local + + align:start position:0% +minimum or a local + + + align:start position:0% +minimum or a local +maximum then both partial + + align:start position:0% + + + + align:start position:0% + +derivative so partial F partial X and + + align:start position:0% +derivative so partial F partial X and + + + align:start position:0% +derivative so partial F partial X and +partial F partial y are both zero at the + + align:start position:0% +partial F partial y are both zero at the + + + align:start position:0% +partial F partial y are both zero at the +same time so why is that well let's say + + align:start position:0% +same time so why is that well let's say + + + align:start position:0% +same time so why is that well let's say +that f subx is zero that means when I + + align:start position:0% +that f subx is zero that means when I + + + align:start position:0% +that f subx is zero that means when I +vary X well to first order the function + + align:start position:0% +vary X well to first order the function + + + align:start position:0% +vary X well to first order the function +doesn't change maybe that's because it's + + align:start position:0% +doesn't change maybe that's because it's + + + align:start position:0% +doesn't change maybe that's because it's +going through if I look only at the + + align:start position:0% +going through if I look only at the + + + align:start position:0% +going through if I look only at the +slice parallel to the x-axis then maybe + + align:start position:0% +slice parallel to the x-axis then maybe + + + align:start position:0% +slice parallel to the x-axis then maybe +I'm going through the minimum but then + + align:start position:0% +I'm going through the minimum but then + + + align:start position:0% +I'm going through the minimum but then +if parti F parti Y is not zero then + + align:start position:0% +if parti F parti Y is not zero then + + + align:start position:0% +if parti F parti Y is not zero then +actually by changing y I could still + + align:start position:0% +actually by changing y I could still + + + align:start position:0% +actually by changing y I could still +make the value larger or smaller so that + + align:start position:0% +make the value larger or smaller so that + + + align:start position:0% +make the value larger or smaller so that +wouldn't be an actual maximum or minimum + + align:start position:0% +wouldn't be an actual maximum or minimum + + + align:start position:0% +wouldn't be an actual maximum or minimum +it would only be uh maximum or minimum + + align:start position:0% +it would only be uh maximum or minimum + + + align:start position:0% +it would only be uh maximum or minimum +if I stay in the slice but if I allow + + align:start position:0% +if I stay in the slice but if I allow + + + align:start position:0% +if I stay in the slice but if I allow +myself to change y that doesn't work so + + align:start position:0% +myself to change y that doesn't work so + + + align:start position:0% +myself to change y that doesn't work so +I need actually to know that if I change + + align:start position:0% +I need actually to know that if I change + + + align:start position:0% +I need actually to know that if I change +y the value will not change either to + + align:start position:0% +y the value will not change either to + + + align:start position:0% +y the value will not change either to +first order so that's why I also need + + align:start position:0% +first order so that's why I also need + + + align:start position:0% +first order so that's why I also need +partial F partial y to be zero now let's + + align:start position:0% +partial F partial y to be zero now let's + + + align:start position:0% +partial F partial y to be zero now let's +say that they're both zero well why is + + align:start position:0% +say that they're both zero well why is + + + align:start position:0% +say that they're both zero well why is +that enough it's essentially enough + + align:start position:0% +that enough it's essentially enough + + + align:start position:0% +that enough it's essentially enough +because of this formula telling me that + + align:start position:0% +because of this formula telling me that + + + align:start position:0% +because of this formula telling me that +if both of these guys are zero then to + + align:start position:0% +if both of these guys are zero then to + + + align:start position:0% +if both of these guys are zero then to +first order the function doesn't change + + align:start position:0% +first order the function doesn't change + + + align:start position:0% +first order the function doesn't change +and then of course there will be maybe + + align:start position:0% +and then of course there will be maybe + + + align:start position:0% +and then of course there will be maybe +quadratic terms that will actually turn + + align:start position:0% +quadratic terms that will actually turn + + + align:start position:0% +quadratic terms that will actually turn +that you know this won't really say that + + align:start position:0% +that you know this won't really say that + + + align:start position:0% +that you know this won't really say that +your function is actually constant it + + align:start position:0% +your function is actually constant it + + + align:start position:0% +your function is actually constant it +will just tell you that maybe U it will + + align:start position:0% +will just tell you that maybe U it will + + + align:start position:0% +will just tell you that maybe U it will +be actually quadratic or higher order in + + align:start position:0% +be actually quadratic or higher order in + + + align:start position:0% +be actually quadratic or higher order in +Delta X and Delta y That's what you + + align:start position:0% +Delta X and Delta y That's what you + + + align:start position:0% +Delta X and Delta y That's what you +expect to have at a maximum or a + + align:start position:0% +expect to have at a maximum or a + + + align:start position:0% +expect to have at a maximum or a +minimum + + align:start position:0% +minimum + + + align:start position:0% +minimum +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so we + + align:start position:0% + + + + align:start position:0% + +have okay so that condition is the same + + align:start position:0% +have okay so that condition is the same + + + align:start position:0% +have okay so that condition is the same +thing as saying that the tangent plane + + align:start position:0% + + + + align:start position:0% + +to the + + align:start position:0% + + + + align:start position:0% + +graph is actually going to be + + align:start position:0% + + + + align:start position:0% + +horizontal okay and that's what you want + + align:start position:0% +horizontal okay and that's what you want + + + align:start position:0% +horizontal okay and that's what you want +to have say you have a minimum well see + + align:start position:0% +to have say you have a minimum well see + + + align:start position:0% +to have say you have a minimum well see +that the tangent plane at this point at + + align:start position:0% +that the tangent plane at this point at + + + align:start position:0% +that the tangent plane at this point at +the bottom of the graph is going to be + + align:start position:0% +the bottom of the graph is going to be + + + align:start position:0% +the bottom of the graph is going to be +horizontal + + align:start position:0% + + + + align:start position:0% + +and you can see that on this equation of + + align:start position:0% +and you can see that on this equation of + + + align:start position:0% +and you can see that on this equation of +a tangent plane when both these + + align:start position:0% +a tangent plane when both these + + + align:start position:0% +a tangent plane when both these +coefficients are zero that's when the + + align:start position:0% +coefficients are zero that's when the + + + align:start position:0% +coefficients are zero that's when the +equation becomes Z equals constant a + + align:start position:0% +equation becomes Z equals constant a + + + align:start position:0% +equation becomes Z equals constant a +horizontal + + align:start position:0% +horizontal + + + align:start position:0% +horizontal +plane okay does that make + + align:start position:0% + + + + align:start position:0% + +sense okay so we'll have a name for this + + align:start position:0% +sense okay so we'll have a name for this + + + align:start position:0% +sense okay so we'll have a name for this +kind of point because actually what + + align:start position:0% +kind of point because actually what + + + align:start position:0% +kind of point because actually what +we'll see very soon is that these + + align:start position:0% +we'll see very soon is that these + + + align:start position:0% +we'll see very soon is that these +conditions are necessary but they're not + + align:start position:0% +conditions are necessary but they're not + + + align:start position:0% +conditions are necessary but they're not +sufficient there's actually other kinds + + align:start position:0% +sufficient there's actually other kinds + + + align:start position:0% +sufficient there's actually other kinds +of points where the partial derivatives + + align:start position:0% +of points where the partial derivatives + + + align:start position:0% +of points where the partial derivatives +are zero so let's give a name to + + align:start position:0% +are zero so let's give a name to + + + align:start position:0% +are zero so let's give a name to +this we + + align:start position:0% +this we + + + align:start position:0% +this we +say definition we say that + + align:start position:0% +say definition we say that + + + align:start position:0% +say definition we say that +X let's say x0 y0 is a critical point of + + align:start position:0% + + + + align:start position:0% + +f if + + align:start position:0% + + + + align:start position:0% + +the partial derivative with respect to X + + align:start position:0% +the partial derivative with respect to X + + + align:start position:0% +the partial derivative with respect to X +and the partial derivative with respect + + align:start position:0% +and the partial derivative with respect + + + align:start position:0% +and the partial derivative with respect +to + + align:start position:0% + + + + align:start position:0% + +Y are both + + align:start position:0% +Y are both + + + align:start position:0% +Y are both +zero okay more generally you would want + + align:start position:0% +zero okay more generally you would want + + + align:start position:0% +zero okay more generally you would want +all the partial derivatives no matter + + align:start position:0% +all the partial derivatives no matter + + + align:start position:0% +all the partial derivatives no matter +how many variables you have you want all + + align:start position:0% +how many variables you have you want all + + + align:start position:0% +how many variables you have you want all +the partials to be zero at the same + + align:start position:0% + + + + align:start position:0% + +time + + align:start position:0% +time + + + align:start position:0% +time +okay so let's see and + + align:start position:0% + + + + align:start position:0% + +example so let's + + align:start position:0% + + + + align:start position:0% + +say I give you the function f of XY + + align:start position:0% +say I give you the function f of XY + + + align:start position:0% +say I give you the function f of XY +equals x 2 - 2x y + 3 y^ + + align:start position:0% +equals x 2 - 2x y + 3 y^ + + + align:start position:0% +equals x 2 - 2x y + 3 y^ +2 + + + align:start position:0% +2 + + + + align:start position:0% +2 + +2x - 2 + + align:start position:0% +2x - 2 + + + align:start position:0% +2x - 2 +y + + align:start position:0% +y + + + align:start position:0% +y +okay and let's try to figure out whether + + align:start position:0% +okay and let's try to figure out whether + + + align:start position:0% +okay and let's try to figure out whether +we can minimize or maximize + + align:start position:0% +we can minimize or maximize + + + align:start position:0% +we can minimize or maximize +this well so what we start doing + + align:start position:0% +this well so what we start doing + + + align:start position:0% +this well so what we start doing +immediately is taking the partial + + align:start position:0% +immediately is taking the partial + + + align:start position:0% +immediately is taking the partial +derivatives okay so what is f + + align:start position:0% + + + + align:start position:0% + +subx starts with + + align:start position:0% +subx starts with + + + align:start position:0% +subx starts with +2x + + align:start position:0% +2x + + + align:start position:0% +2x +minus 2 y + 0 + + + align:start position:0% +minus 2 y + 0 + + + + align:start position:0% +minus 2 y + 0 + +2 okay remember that Y is a constant so + + align:start position:0% +2 okay remember that Y is a constant so + + + align:start position:0% +2 okay remember that Y is a constant so +this differentiates to + + align:start position:0% +this differentiates to + + + align:start position:0% +this differentiates to +zero now if we do F sub + + align:start position:0% +zero now if we do F sub + + + align:start position:0% +zero now if we do F sub +y that's going to be well 0 - + + align:start position:0% +y that's going to be well 0 - + + + align:start position:0% +y that's going to be well 0 - +2x + 6 + + align:start position:0% +2x + 6 + + + align:start position:0% +2x + 6 +Yus + + align:start position:0% +Yus + + + align:start position:0% +Yus +2 and what we want to do is set these + + align:start position:0% +2 and what we want to do is set these + + + align:start position:0% +2 and what we want to do is set these +things equal to zero and we want to + + align:start position:0% +things equal to zero and we want to + + + align:start position:0% +things equal to zero and we want to +solve these two equations at the same + + align:start position:0% +solve these two equations at the same + + + align:start position:0% +solve these two equations at the same +time okay so an important thing to + + align:start position:0% +time okay so an important thing to + + + align:start position:0% +time okay so an important thing to +remember I mean maybe I should have told + + align:start position:0% +remember I mean maybe I should have told + + + align:start position:0% +remember I mean maybe I should have told +you couple of weeks ago already if you + + align:start position:0% +you couple of weeks ago already if you + + + align:start position:0% +you couple of weeks ago already if you +have two equations to solve well it's + + align:start position:0% +have two equations to solve well it's + + + align:start position:0% +have two equations to solve well it's +very good to try to simplify them by + + align:start position:0% +very good to try to simplify them by + + + align:start position:0% +very good to try to simplify them by +adding them together or whatever but you + + align:start position:0% +adding them together or whatever but you + + + align:start position:0% +adding them together or whatever but you +you must keep two equations okay if you + + align:start position:0% +you must keep two equations okay if you + + + align:start position:0% +you must keep two equations okay if you +have two equations you shouldn't end up + + align:start position:0% +have two equations you shouldn't end up + + + align:start position:0% +have two equations you shouldn't end up +with just one equation out of + + align:start position:0% +with just one equation out of + + + align:start position:0% +with just one equation out of +nowhere okay so for example here we can + + align:start position:0% +nowhere okay so for example here we can + + + align:start position:0% +nowhere okay so for example here we can +certainly simplify things by summing + + align:start position:0% +certainly simplify things by summing + + + align:start position:0% +certainly simplify things by summing +them together see if we add + + align:start position:0% + + + + align:start position:0% + +them together well the x is cancel and + + align:start position:0% +them together well the x is cancel and + + + align:start position:0% +them together well the x is cancel and +the constants cancel and in fact we just + + align:start position:0% +the constants cancel and in fact we just + + + align:start position:0% +the constants cancel and in fact we just +left with 4 y = z that's pretty good + + align:start position:0% +left with 4 y = z that's pretty good + + + align:start position:0% +left with 4 y = z that's pretty good +that tells us why should should be zero + + align:start position:0% +that tells us why should should be zero + + + align:start position:0% +that tells us why should should be zero +but then we should of course go back to + + align:start position:0% +but then we should of course go back to + + + align:start position:0% +but then we should of course go back to +these and see what else we know well now + + align:start position:0% +these and see what else we know well now + + + align:start position:0% +these and see what else we know well now +it tells us so if you put y equal 0 it + + align:start position:0% +it tells us so if you put y equal 0 it + + + align:start position:0% +it tells us so if you put y equal 0 it +tells you 2x + 2 = + + align:start position:0% + + + + align:start position:0% + +0 that tells you xals minus one okay so + + align:start position:0% +0 that tells you xals minus one okay so + + + align:start position:0% +0 that tells you xals minus one okay so +we have one critical + + align:start position:0% + + + + align:start position:0% + +point that's XY + + align:start position:0% +point that's XY + + + align:start position:0% +point that's XY +equal min-1 and z + + align:start position:0% + + + + align:start position:0% + +okay any questions so + + align:start position:0% + + + + align:start position:0% + +far no well you should have a question + + align:start position:0% +far no well you should have a question + + + align:start position:0% +far no well you should have a question +question should be how do we know if + + align:start position:0% +question should be how do we know if + + + align:start position:0% +question should be how do we know if +it's a maximum or a + + align:start position:0% + + + + align:start position:0% + +minimum well yeah so if we had a + + align:start position:0% +minimum well yeah so if we had a + + + align:start position:0% +minimum well yeah so if we had a +function of one variable we would decide + + align:start position:0% +function of one variable we would decide + + + align:start position:0% +function of one variable we would decide +Things based on the second derivative + + align:start position:0% +Things based on the second derivative + + + align:start position:0% +Things based on the second derivative +and in fact we'll see tomorrow how to do + + align:start position:0% +and in fact we'll see tomorrow how to do + + + align:start position:0% +and in fact we'll see tomorrow how to do +things based on the second derivative + + align:start position:0% +things based on the second derivative + + + align:start position:0% +things based on the second derivative +but that's kind of tricky because + + align:start position:0% +but that's kind of tricky because + + + align:start position:0% +but that's kind of tricky because +there's a lot of second derivatives I + + align:start position:0% +there's a lot of second derivatives I + + + align:start position:0% +there's a lot of second derivatives I +mean we already have two first + + align:start position:0% +mean we already have two first + + + align:start position:0% +mean we already have two first +derivatives you can imagine that if you + + align:start position:0% +derivatives you can imagine that if you + + + align:start position:0% +derivatives you can imagine that if you +keep taking partials you may end up + + align:start position:0% +keep taking partials you may end up + + + align:start position:0% +keep taking partials you may end up +with you know more and + + align:start position:0% +with you know more and + + + align:start position:0% +with you know more and +more uh so we'll have to figure out + + align:start position:0% +more uh so we'll have to figure out + + + align:start position:0% +more uh so we'll have to figure out +carefully what the condition should be + + align:start position:0% +carefully what the condition should be + + + align:start position:0% +carefully what the condition should be +so we'll do that + + align:start position:0% +so we'll do that + + + align:start position:0% +so we'll do that +tomorrow for now let's just try to look + + align:start position:0% +tomorrow for now let's just try to look + + + align:start position:0% +tomorrow for now let's just try to look +a bit + + align:start position:0% +a bit + + + align:start position:0% +a bit +at you know how do we understand this + + align:start position:0% +at you know how do we understand this + + + align:start position:0% +at you know how do we understand this +things by + + align:start position:0% + + + + align:start position:0% + +hand + + align:start position:0% + + + + align:start position:0% + +so in fact let me point out to you + + align:start position:0% +so in fact let me point out to you + + + align:start position:0% +so in fact let me point out to you +immediately that there's more than + + align:start position:0% +immediately that there's more than + + + align:start position:0% +immediately that there's more than +Maxima and Minima so remember we + + align:start position:0% +Maxima and Minima so remember we + + + align:start position:0% +Maxima and Minima so remember we +saw you know the example of x2+ y^2 that + + align:start position:0% +saw you know the example of x2+ y^2 that + + + align:start position:0% +saw you know the example of x2+ y^2 that +has a critical point that critical point + + align:start position:0% +has a critical point that critical point + + + align:start position:0% +has a critical point that critical point +is obviously a + + align:start position:0% +is obviously a + + + align:start position:0% +is obviously a +minimum and of course it could be a + + align:start position:0% +minimum and of course it could be a + + + align:start position:0% +minimum and of course it could be a +local minimum because it could be that + + align:start position:0% +local minimum because it could be that + + + align:start position:0% +local minimum because it could be that +you know if you have a more complicated + + align:start position:0% +you know if you have a more complicated + + + align:start position:0% +you know if you have a more complicated +function there's indeed a minimum here + + align:start position:0% +function there's indeed a minimum here + + + align:start position:0% +function there's indeed a minimum here +but then elsewhere the function drops to + + align:start position:0% +but then elsewhere the function drops to + + + align:start position:0% +but then elsewhere the function drops to +a lower value so we call that just we + + align:start position:0% +a lower value so we call that just we + + + align:start position:0% +a lower value so we call that just we +call that just a local minimum to say + + align:start position:0% +call that just a local minimum to say + + + align:start position:0% +call that just a local minimum to say +that it's a minimum if you stick two + + align:start position:0% +that it's a minimum if you stick two + + + align:start position:0% +that it's a minimum if you stick two +values that are close enough to that + + align:start position:0% +values that are close enough to that + + + align:start position:0% +values that are close enough to that +point of course you also have a local + + align:start position:0% +point of course you also have a local + + + align:start position:0% +point of course you also have a local +maximum well I didn't plot it but it's + + align:start position:0% +maximum well I didn't plot it but it's + + + align:start position:0% +maximum well I didn't plot it but it's +easy to plot okay that's a local + + align:start position:0% +easy to plot okay that's a local + + + align:start position:0% +easy to plot okay that's a local +maximum but there's a third example of + + align:start position:0% +maximum but there's a third example of + + + align:start position:0% +maximum but there's a third example of +critical point and that's a saddle point + + align:start position:0% +critical point and that's a saddle point + + + align:start position:0% +critical point and that's a saddle point +okay so the saddle point it's a new + + align:start position:0% +okay so the saddle point it's a new + + + align:start position:0% +okay so the saddle point it's a new +phenomenon that you don't really see + + align:start position:0% +phenomenon that you don't really see + + + align:start position:0% +phenomenon that you don't really see +in a single variable calculus it's a + + align:start position:0% +in a single variable calculus it's a + + + align:start position:0% +in a single variable calculus it's a +critical point that's neither a minimum + + align:start position:0% +critical point that's neither a minimum + + + align:start position:0% +critical point that's neither a minimum +nor a maximum because depending on which + + align:start position:0% +nor a maximum because depending on which + + + align:start position:0% +nor a maximum because depending on which +direction you look in it's either one or + + align:start position:0% +direction you look in it's either one or + + + align:start position:0% +direction you look in it's either one or +the other so here see the point in the + + align:start position:0% +the other so here see the point in the + + + align:start position:0% +the other so here see the point in the +middle at the origin is a settle Point + + align:start position:0% +middle at the origin is a settle Point + + + align:start position:0% +middle at the origin is a settle Point +um just you know if you look at the + + align:start position:0% +um just you know if you look at the + + + align:start position:0% +um just you know if you look at the +tangent plane to this graph you'll see + + align:start position:0% +tangent plane to this graph you'll see + + + align:start position:0% +tangent plane to this graph you'll see +that it's actually horizontal + + align:start position:0% +that it's actually horizontal + + + align:start position:0% +that it's actually horizontal +at the origin you have this mountain + + align:start position:0% +at the origin you have this mountain + + + align:start position:0% +at the origin you have this mountain +pass you know at a mountain pass um the + + align:start position:0% +pass you know at a mountain pass um the + + + align:start position:0% +pass you know at a mountain pass um the +ground is horizontal but depending on in + + align:start position:0% +ground is horizontal but depending on in + + + align:start position:0% +ground is horizontal but depending on in +which direction you go you go up or + + align:start position:0% +which direction you go you go up or + + + align:start position:0% +which direction you go you go up or +down so we say that a point is a settle + + align:start position:0% +down so we say that a point is a settle + + + align:start position:0% +down so we say that a point is a settle +point if it's neither a minimum nor a + + align:start position:0% +point if it's neither a minimum nor a + + + align:start position:0% +point if it's neither a minimum nor a +maximum Okay so + + align:start position:0% + + + + align:start position:0% + +possibilities could be a local mean a + + align:start position:0% +possibilities could be a local mean a + + + align:start position:0% +possibilities could be a local mean a +local Max or a + + align:start position:0% + + + + align:start position:0% + +s okay so tomorrow we'll see how to + + align:start position:0% +s okay so tomorrow we'll see how to + + + align:start position:0% +s okay so tomorrow we'll see how to +decide which one it is in general using + + align:start position:0% +decide which one it is in general using + + + align:start position:0% +decide which one it is in general using +second + + align:start position:0% +second + + + align:start position:0% +second +derivatives uh for this time let's just + + align:start position:0% +derivatives uh for this time let's just + + + align:start position:0% +derivatives uh for this time let's just +try to do it you know by hand + + align:start position:0% +try to do it you know by hand + + + align:start position:0% +try to do it you know by hand +so I just want to + + align:start position:0% +so I just want to + + + align:start position:0% +so I just want to +observe in fact I can try to you know + + align:start position:0% +observe in fact I can try to you know + + + align:start position:0% +observe in fact I can try to you know +these examples that I have here they x + + + align:start position:0% +these examples that I have here they x + + + + align:start position:0% +these examples that I have here they x + +y s y^ sare - x there sums or + + align:start position:0% +y s y^ sare - x there sums or + + + align:start position:0% +y s y^ sare - x there sums or +differences of squares and if we know + + align:start position:0% +differences of squares and if we know + + + align:start position:0% +differences of squares and if we know +that we can put think as a sum of + + align:start position:0% +that we can put think as a sum of + + + align:start position:0% +that we can put think as a sum of +squares for example will be done so + + align:start position:0% +squares for example will be done so + + + align:start position:0% +squares for example will be done so +let's try to express this maybe as the + + align:start position:0% +let's try to express this maybe as the + + + align:start position:0% +let's try to express this maybe as the +square of + + align:start position:0% +square of + + + align:start position:0% +square of +something well so the problem the main + + align:start position:0% +something well so the problem the main + + + align:start position:0% +something well so the problem the main +problem is this 2x y but observe we know + + align:start position:0% +problem is this 2x y but observe we know + + + align:start position:0% +problem is this 2x y but observe we know +something that starts with x^2 - 2x y + + align:start position:0% +something that starts with x^2 - 2x y + + + align:start position:0% +something that starts with x^2 - 2x y +that is actually the square of something + + align:start position:0% +that is actually the square of something + + + align:start position:0% +that is actually the square of something +else right it would be x s - 2x y + + align:start position:0% +else right it would be x s - 2x y + + + align:start position:0% +else right it would be x s - 2x y +well plus y^2 not plus 3 + + align:start position:0% +well plus y^2 not plus 3 + + + align:start position:0% +well plus y^2 not plus 3 +y^2 + + align:start position:0% +y^2 + + + align:start position:0% +y^2 +so let's try to do that so we're going + + align:start position:0% +so let's try to do that so we're going + + + align:start position:0% +so let's try to do that so we're going +to complete the + + align:start position:0% + + + + align:start position:0% + +square + + align:start position:0% +square + + + align:start position:0% +square +so I'm going to say it's x - y^ + + align:start position:0% +so I'm going to say it's x - y^ + + + align:start position:0% +so I'm going to say it's x - y^ +2 and then so that gives me the first + + align:start position:0% +2 and then so that gives me the first + + + align:start position:0% +2 and then so that gives me the first +two terms and also a y squ while I still + + align:start position:0% +two terms and also a y squ while I still + + + align:start position:0% +two terms and also a y squ while I still +need to add two more y squares + + align:start position:0% + + + + align:start position:0% + +and I also need to add of course the 2X + + align:start position:0% +and I also need to add of course the 2X + + + align:start position:0% +and I also need to add of course the 2X +and minus 2 + + align:start position:0% + + + + align:start position:0% + +y it's simpler it's still not simple + + align:start position:0% +y it's simpler it's still not simple + + + align:start position:0% +y it's simpler it's still not simple +enough for my taste I can actually do + + align:start position:0% +enough for my taste I can actually do + + + align:start position:0% +enough for my taste I can actually do +better see I mean now what's so these + + align:start position:0% +better see I mean now what's so these + + + align:start position:0% +better see I mean now what's so these +guys look like a sum of squares but here + + align:start position:0% +guys look like a sum of squares but here + + + align:start position:0% +guys look like a sum of squares but here +I have this extra stuff but oh 2x - 2 y + + align:start position:0% +I have this extra stuff but oh 2x - 2 y + + + align:start position:0% +I have this extra stuff but oh 2x - 2 y +well that's twice x - y it looks like + + align:start position:0% +well that's twice x - y it looks like + + + align:start position:0% +well that's twice x - y it looks like +maybe we can modify this and make this + + align:start position:0% +maybe we can modify this and make this + + + align:start position:0% +maybe we can modify this and make this +into another + + align:start position:0% +into another + + + align:start position:0% +into another +Square okay so in fact I can simplify + + align:start position:0% +Square okay so in fact I can simplify + + + align:start position:0% +Square okay so in fact I can simplify +this further to x - y + 1 s see if it + + align:start position:0% +this further to x - y + 1 s see if it + + + align:start position:0% +this further to x - y + 1 s see if it +would start like maybe I should put + + align:start position:0% +would start like maybe I should put + + + align:start position:0% +would start like maybe I should put +parenthesis here that would be x - y^ 2 + + align:start position:0% +parenthesis here that would be x - y^ 2 + + + align:start position:0% +parenthesis here that would be x - y^ 2 +plus t x - Y and then there's a plus one + + align:start position:0% +plus t x - Y and then there's a plus one + + + align:start position:0% +plus t x - Y and then there's a plus one +well we don't have that plus one so + + align:start position:0% +well we don't have that plus one so + + + align:start position:0% +well we don't have that plus one so +let's remove it by subtracting + + align:start position:0% +let's remove it by subtracting + + + align:start position:0% +let's remove it by subtracting +one okay oh so let me that minus one + + align:start position:0% +one okay oh so let me that minus one + + + align:start position:0% +one okay oh so let me that minus one +here and I still have my 2 + + align:start position:0% +here and I still have my 2 + + + align:start position:0% +here and I still have my 2 +y^2 okay do you see why this is the same + + align:start position:0% +y^2 okay do you see why this is the same + + + align:start position:0% +y^2 okay do you see why this is the same +function as that + + align:start position:0% +function as that + + + align:start position:0% +function as that +one + + align:start position:0% + + + + align:start position:0% + +yeah so again you know if I expand x - y + + align:start position:0% +yeah so again you know if I expand x - y + + + align:start position:0% +yeah so again you know if I expand x - y ++ 1 2 I get x - y^ 2 + twice x - y + + align:start position:0% ++ 1 2 I get x - y^ 2 + twice x - y + + + align:start position:0% ++ 1 2 I get x - y^ 2 + twice x - y +That's both guys plus one but I will + + align:start position:0% +That's both guys plus one but I will + + + align:start position:0% +That's both guys plus one but I will +have a minus one they will cancel out + + align:start position:0% +have a minus one they will cancel out + + + align:start position:0% +have a minus one they will cancel out +and then I have a plus 2 y^2 + + align:start position:0% + + + + align:start position:0% + +okay so now what I know see this is a + + align:start position:0% +okay so now what I know see this is a + + + align:start position:0% +okay so now what I know see this is a +sum of two squares minus + + align:start position:0% +sum of two squares minus + + + align:start position:0% +sum of two squares minus +one and this critical point x y = - 1 0 + + align:start position:0% +one and this critical point x y = - 1 0 + + + align:start position:0% +one and this critical point x y = - 1 0 +that's exactly when this is zero and + + align:start position:0% +that's exactly when this is zero and + + + align:start position:0% +that's exactly when this is zero and +that is zero so that's the smallest + + align:start position:0% + + + + align:start position:0% + +value this is + + align:start position:0% +value this is + + + align:start position:0% +value this is +always greater or equal to zero same + + align:start position:0% +always greater or equal to zero same + + + align:start position:0% +always greater or equal to zero same +with that one so that's always at least + + align:start position:0% +with that one so that's always at least + + + align:start position:0% +with that one so that's always at least +minus one and minus one happens to be + + align:start position:0% +minus one and minus one happens to be + + + align:start position:0% +minus one and minus one happens to be +the value at the critical + + align:start position:0% +the value at the critical + + + align:start position:0% +the value at the critical +point so it's a + + align:start position:0% + + + + align:start position:0% + +minimum okay now of course here I was + + align:start position:0% +minimum okay now of course here I was + + + align:start position:0% +minimum okay now of course here I was +very + + align:start position:0% +very + + + align:start position:0% +very +lucky in general I couldn't expect + + align:start position:0% +lucky in general I couldn't expect + + + align:start position:0% +lucky in general I couldn't expect +things to simplify that much in fact I + + align:start position:0% +things to simplify that much in fact I + + + align:start position:0% +things to simplify that much in fact I +cheated I started from that I expanded + + align:start position:0% +cheated I started from that I expanded + + + align:start position:0% +cheated I started from that I expanded +and then that's how I got my + + align:start position:0% + + + + align:start position:0% + +example Okay so + + align:start position:0% +example Okay so + + + align:start position:0% +example Okay so +the general method will be a bit + + align:start position:0% +the general method will be a bit + + + align:start position:0% +the general method will be a bit +different but you will see it will + + align:start position:0% +different but you will see it will + + + align:start position:0% +different but you will see it will +actually also involve completing squares + + align:start position:0% +actually also involve completing squares + + + align:start position:0% +actually also involve completing squares +just there's more to it than what we've + + align:start position:0% +just there's more to it than what we've + + + align:start position:0% +just there's more to it than what we've +seen okay + + align:start position:0% +seen okay + + + align:start position:0% +seen okay +so we'll come back to this + + align:start position:0% + + + + align:start position:0% + +tomorrow uh sorry oh do I how do I know + + align:start position:0% +tomorrow uh sorry oh do I how do I know + + + align:start position:0% +tomorrow uh sorry oh do I how do I know +that this + + align:start position:0% + + + + align:start position:0% + +equals uh Y is what negative one sorry + + align:start position:0% +equals uh Y is what negative one sorry + + + align:start position:0% +equals uh Y is what negative one sorry +like how do + + align:start position:0% + + + + align:start position:0% + +you that whole function + + align:start position:0% +you that whole function + + + align:start position:0% +you that whole function +iser how do I know that that whole + + align:start position:0% +iser how do I know that that whole + + + align:start position:0% +iser how do I know that that whole +function is greater or equal to negative + + align:start position:0% +function is greater or equal to negative + + + align:start position:0% +function is greater or equal to negative +one well I wrote F of XY as something + + align:start position:0% +one well I wrote F of XY as something + + + align:start position:0% +one well I wrote F of XY as something +squar + 2 y^ 2us + + align:start position:0% +squar + 2 y^ 2us + + + align:start position:0% +squar + 2 y^ 2us +1 okay this squared it's always a + + align:start position:0% +1 okay this squared it's always a + + + align:start position:0% +1 okay this squared it's always a +positive number non + + align:start position:0% +positive number non + + + align:start position:0% +positive number non +negative right it's a square the square + + align:start position:0% +negative right it's a square the square + + + align:start position:0% +negative right it's a square the square +of something is always always non + + align:start position:0% +of something is always always non + + + align:start position:0% +of something is always always non +negative similarly y^2 is also always + + align:start position:0% +negative similarly y^2 is also always + + + align:start position:0% +negative similarly y^2 is also always +non- negative so if you add something + + align:start position:0% +non- negative so if you add something + + + align:start position:0% +non- negative so if you add something +that's at least zero plus something + + align:start position:0% +that's at least zero plus something + + + align:start position:0% +that's at least zero plus something +that's at least zero and you subtract + + align:start position:0% +that's at least zero and you subtract + + + align:start position:0% +that's at least zero and you subtract +one you get always at least minus + + align:start position:0% +one you get always at least minus + + + align:start position:0% +one you get always at least minus +one and in fact the only way that you + + align:start position:0% +one and in fact the only way that you + + + align:start position:0% +one and in fact the only way that you +can getus one is if both of these guys + + align:start position:0% +can getus one is if both of these guys + + + align:start position:0% +can getus one is if both of these guys +are zero at the same + + align:start position:0% + + + + align:start position:0% + +time + + align:start position:0% +time + + + align:start position:0% +time +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that's how I get my minimum + + align:start position:0% + + + + align:start position:0% + +so more about this + + align:start position:0% + + + + align:start position:0% + +tomorrow so in fact what I would like to + + align:start position:0% +tomorrow so in fact what I would like to + + + align:start position:0% +tomorrow so in fact what I would like to +tell you about now + + align:start position:0% +tell you about now + + + align:start position:0% +tell you about now +instead is a nice application of minmax + + align:start position:0% +instead is a nice application of minmax + + + align:start position:0% +instead is a nice application of minmax +problems that maybe you don't think of + + align:start position:0% +problems that maybe you don't think of + + + align:start position:0% +problems that maybe you don't think of +as a min Max problem but you will see + + align:start position:0% +as a min Max problem but you will see + + + align:start position:0% +as a min Max problem but you will see +because I mean you don't think it that + + align:start position:0% +because I mean you don't think it that + + + align:start position:0% +because I mean you don't think it that +way because probably your calculator can + + align:start position:0% +way because probably your calculator can + + + align:start position:0% +way because probably your calculator can +do it for you or if not your computer + + align:start position:0% +do it for you or if not your computer + + + align:start position:0% +do it for you or if not your computer +can do it for you but it's actually + + align:start position:0% +can do it for you but it's actually + + + align:start position:0% +can do it for you but it's actually +something where the theory is based on + + align:start position:0% +something where the theory is based on + + + align:start position:0% +something where the theory is based on +minimization in two variables so very + + align:start position:0% +minimization in two variables so very + + + align:start position:0% +minimization in two variables so very +often in experimental Sciences you have + + align:start position:0% +often in experimental Sciences you have + + + align:start position:0% +often in experimental Sciences you have +to do something called list squares + + align:start position:0% +to do something called list squares + + + align:start position:0% +to do something called list squares +interpolation and what is that about + + align:start position:0% + + + + align:start position:0% + +well it's the idea that + + align:start position:0% +well it's the idea that + + + align:start position:0% +well it's the idea that +maybe you do some experiment and you + + align:start position:0% +maybe you do some experiment and you + + + align:start position:0% +maybe you do some experiment and you +know you record some data so you have + + align:start position:0% +know you record some data so you have + + + align:start position:0% +know you record some data so you have +some data X and some other data Y and I + + align:start position:0% +some data X and some other data Y and I + + + align:start position:0% +some data X and some other data Y and I +don't know maybe for example X is U you + + align:start position:0% +don't know maybe for example X is U you + + + align:start position:0% +don't know maybe for example X is U you +know maybe you're measuring frogs and + + align:start position:0% +know maybe you're measuring frogs and + + + align:start position:0% +know maybe you're measuring frogs and +you're trying to measure how big the + + align:start position:0% +you're trying to measure how big the + + + align:start position:0% +you're trying to measure how big the +frog leg is compared to the eyes of a + + align:start position:0% +frog leg is compared to the eyes of a + + + align:start position:0% +frog leg is compared to the eyes of a +frog or whatever or you know trying to + + align:start position:0% +frog or whatever or you know trying to + + + align:start position:0% +frog or whatever or you know trying to +measure something and you know if you're + + align:start position:0% +measure something and you know if you're + + + align:start position:0% +measure something and you know if you're +doing + + align:start position:0% +doing + + + align:start position:0% +doing +then it could be you know how much you + + align:start position:0% +then it could be you know how much you + + + align:start position:0% +then it could be you know how much you +put of some reactant and the output how + + align:start position:0% +put of some reactant and the output how + + + align:start position:0% +put of some reactant and the output how +much of the output product that you + + align:start position:0% +much of the output product that you + + + align:start position:0% +much of the output product that you +wanted to synthesize is generated or all + + align:start position:0% +wanted to synthesize is generated or all + + + align:start position:0% +wanted to synthesize is generated or all +sorts of + + align:start position:0% +sorts of + + + align:start position:0% +sorts of +things uh make up your own example but + + align:start position:0% +things uh make up your own example but + + + align:start position:0% +things uh make up your own example but +so you know you measure basically for + + align:start position:0% +so you know you measure basically for + + + align:start position:0% +so you know you measure basically for +various values of X what the value of y + + align:start position:0% +various values of X what the value of y + + + align:start position:0% +various values of X what the value of y +ends up being and then you know you + + align:start position:0% +ends up being and then you know you + + + align:start position:0% +ends up being and then you know you +would like to claim oh well these points + + align:start position:0% +would like to claim oh well these points + + + align:start position:0% +would like to claim oh well these points +are kind of aligned and of course to a + + align:start position:0% +are kind of aligned and of course to a + + + align:start position:0% +are kind of aligned and of course to a +mathematician they're not aligned but to + + align:start position:0% +mathematician they're not aligned but to + + + align:start position:0% +mathematician they're not aligned but to +an experimental scientist that's + + align:start position:0% +an experimental scientist that's + + + align:start position:0% +an experimental scientist that's +evidence that there's a Rel between the + + align:start position:0% +evidence that there's a Rel between the + + + align:start position:0% +evidence that there's a Rel between the +two and so you want to claim and you + + align:start position:0% +two and so you want to claim and you + + + align:start position:0% +two and so you want to claim and you +know in your paper you will actually + + align:start position:0% +know in your paper you will actually + + + align:start position:0% +know in your paper you will actually +draw a nice little line like that see + + align:start position:0% +draw a nice little line like that see + + + align:start position:0% +draw a nice little line like that see +these two functions depend linearly on + + align:start position:0% +these two functions depend linearly on + + + align:start position:0% +these two functions depend linearly on +each other okay so the question is how + + align:start position:0% +each other okay so the question is how + + + align:start position:0% +each other okay so the question is how +do we come up with that nice line that + + align:start position:0% +do we come up with that nice line that + + + align:start position:0% +do we come up with that nice line that +passes smack in the middle of the + + align:start position:0% +passes smack in the middle of the + + + align:start position:0% +passes smack in the middle of the +points + + align:start position:0% +points + + + align:start position:0% +points +so the question is + + align:start position:0% +so the question is + + + align:start position:0% +so the question is +given experimental data + + align:start position:0% + + + + align:start position:0% + +x i y + + align:start position:0% +x i y + + + align:start position:0% +x i y +i so maybe I should actually be more + + align:start position:0% +i so maybe I should actually be more + + + align:start position:0% +i so maybe I should actually be more +precise so you're given some + + align:start position:0% +precise so you're given some + + + align:start position:0% +precise so you're given some +experimental data you have you know data + + align:start position:0% +experimental data you have you know data + + + align:start position:0% +experimental data you have you know data +point X1 y1 X2 Y2 and so on xn + + align:start position:0% +point X1 y1 X2 Y2 and so on xn + + + align:start position:0% +point X1 y1 X2 Y2 and so on xn +YN the question would be + + align:start position:0% +YN the question would be + + + align:start position:0% +YN the question would be +find the best + + align:start position:0% + + + + align:start position:0% + +fit line + + align:start position:0% + + + + align:start position:0% + +of the form yal ax plus b that + + align:start position:0% +of the form yal ax plus b that + + + align:start position:0% +of the form yal ax plus b that +somehow in you know approximates very + + align:start position:0% +somehow in you know approximates very + + + align:start position:0% +somehow in you know approximates very +well this + + align:start position:0% +well this + + + align:start position:0% +well this +data so you know you can also use that + + align:start position:0% +data so you know you can also use that + + + align:start position:0% +data so you know you can also use that +by the way to predict various things for + + align:start position:0% +by the way to predict various things for + + + align:start position:0% +by the way to predict various things for +example if you look at your new homework + + align:start position:0% +example if you look at your new homework + + + align:start position:0% +example if you look at your new homework +actually the first problem asks you to + + align:start position:0% +actually the first problem asks you to + + + align:start position:0% +actually the first problem asks you to +predict how many iPods will be on this + + align:start position:0% +predict how many iPods will be on this + + + align:start position:0% +predict how many iPods will be on this +planet in 10 + + align:start position:0% +planet in 10 + + + align:start position:0% +planet in 10 +years okay uh looking at you know past + + align:start position:0% +years okay uh looking at you know past + + + align:start position:0% +years okay uh looking at you know past +sales and how they behave um one thing + + align:start position:0% +sales and how they behave um one thing + + + align:start position:0% +sales and how they behave um one thing +by the way before you you know lose all + + align:start position:0% +by the way before you you know lose all + + + align:start position:0% +by the way before you you know lose all +the money you don't have yet uh you + + align:start position:0% +the money you don't have yet uh you + + + align:start position:0% +the money you don't have yet uh you +cannot use that to predict the stock + + align:start position:0% +cannot use that to predict the stock + + + align:start position:0% +cannot use that to predict the stock +market + + align:start position:0% +market + + + align:start position:0% +market +okay so don't try to use that to make + + align:start position:0% +okay so don't try to use that to make + + + align:start position:0% +okay so don't try to use that to make +money it doesn't + + align:start position:0% + + + + align:start position:0% + +work + + align:start position:0% + + + + align:start position:0% + +so one tricky thing here that I want to + + align:start position:0% +so one tricky thing here that I want to + + + align:start position:0% +so one tricky thing here that I want to +draw your attention to is what are the + + align:start position:0% +draw your attention to is what are the + + + align:start position:0% +draw your attention to is what are the +unknowns here + + align:start position:0% + + + + align:start position:0% + +so the natural answer would be to say + + align:start position:0% +so the natural answer would be to say + + + align:start position:0% +so the natural answer would be to say +well the unknowns are X and Y that's not + + align:start position:0% +well the unknowns are X and Y that's not + + + align:start position:0% +well the unknowns are X and Y that's not +actually the case okay we're not trying + + align:start position:0% +actually the case okay we're not trying + + + align:start position:0% +actually the case okay we're not trying +to solve for some X and Y I mean we have + + align:start position:0% +to solve for some X and Y I mean we have + + + align:start position:0% +to solve for some X and Y I mean we have +some values given to us and when we look + + align:start position:0% +some values given to us and when we look + + + align:start position:0% +some values given to us and when we look +for when we're looking for that line we + + align:start position:0% +for when we're looking for that line we + + + align:start position:0% +for when we're looking for that line we +don't really care about a particular + + align:start position:0% +don't really care about a particular + + + align:start position:0% +don't really care about a particular +value of x what we care about is + + align:start position:0% +value of x what we care about is + + + align:start position:0% +value of x what we care about is +actually these coefficients A and + + align:start position:0% +actually these coefficients A and + + + align:start position:0% +actually these coefficients A and +B that will tell us what the relation is + + align:start position:0% +B that will tell us what the relation is + + + align:start position:0% +B that will tell us what the relation is +between X and Y so in fact we are trying + + align:start position:0% +between X and Y so in fact we are trying + + + align:start position:0% +between X and Y so in fact we are trying +to solve for for A and B that will give + + align:start position:0% +to solve for for A and B that will give + + + align:start position:0% +to solve for for A and B that will give +us the nicest possible line through + + align:start position:0% +us the nicest possible line through + + + align:start position:0% +us the nicest possible line through +these + + align:start position:0% +these + + + align:start position:0% +these +points okay so the + + align:start position:0% +points okay so the + + + align:start position:0% +points okay so the +unknowns in our equations will have to + + align:start position:0% +unknowns in our equations will have to + + + align:start position:0% +unknowns in our equations will have to +be a and b not X and Y + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so the question really is find the + + align:start position:0% +so the question really is find the + + + align:start position:0% +so the question really is find the +best A and + + align:start position:0% +best A and + + + align:start position:0% +best A and +B and of course we have to decide what + + align:start position:0% +B and of course we have to decide what + + + align:start position:0% +B and of course we have to decide what +we mean by + + align:start position:0% +we mean by + + + align:start position:0% +we mean by +best so best will mean that we minimize + + align:start position:0% +best so best will mean that we minimize + + + align:start position:0% +best so best will mean that we minimize +some function of A and B that measures + + align:start position:0% +some function of A and B that measures + + + align:start position:0% +some function of A and B that measures +the total error that we are making when + + align:start position:0% +the total error that we are making when + + + align:start position:0% +the total error that we are making when +we're choosing this line compared to the + + align:start position:0% +we're choosing this line compared to the + + + align:start position:0% +we're choosing this line compared to the +experimental data so maybe roughly + + align:start position:0% +experimental data so maybe roughly + + + align:start position:0% +experimental data so maybe roughly +speaking it should measure how far these + + align:start position:0% +speaking it should measure how far these + + + align:start position:0% +speaking it should measure how far these +points are from the + + align:start position:0% +points are from the + + + align:start position:0% +points are from the +line but now there's various ways to do + + align:start position:0% +line but now there's various ways to do + + + align:start position:0% +line but now there's various ways to do +it and some of them are I mean they're + + align:start position:0% +it and some of them are I mean they're + + + align:start position:0% +it and some of them are I mean they're +all actually you know a lot of them are + + align:start position:0% +all actually you know a lot of them are + + + align:start position:0% +all actually you know a lot of them are +valid they give you different + + align:start position:0% +valid they give you different + + + align:start position:0% +valid they give you different +answers you have to decide what it is + + align:start position:0% +answers you have to decide what it is + + + align:start position:0% +answers you have to decide what it is +that you prefer + + align:start position:0% +that you prefer + + + align:start position:0% +that you prefer +so for example you could measure the + + align:start position:0% +so for example you could measure the + + + align:start position:0% +so for example you could measure the +distance to the line you know by + + align:start position:0% +distance to the line you know by + + + align:start position:0% +distance to the line you know by +projecting + + align:start position:0% +projecting + + + align:start position:0% +projecting +perpendicularly or you could measure + + align:start position:0% +perpendicularly or you could measure + + + align:start position:0% +perpendicularly or you could measure +instead the difference between for a + + align:start position:0% +instead the difference between for a + + + align:start position:0% +instead the difference between for a +given value of x the difference between + + align:start position:0% +given value of x the difference between + + + align:start position:0% +given value of x the difference between +the experimental value of y and the + + align:start position:0% +the experimental value of y and the + + + align:start position:0% +the experimental value of y and the +predicted one and that's often more + + align:start position:0% +predicted one and that's often more + + + align:start position:0% +predicted one and that's often more +relevant because you know these guys are + + align:start position:0% +relevant because you know these guys are + + + align:start position:0% +relevant because you know these guys are +actually maybe expressing different + + align:start position:0% +actually maybe expressing different + + + align:start position:0% +actually maybe expressing different +units they're not the same type of + + align:start position:0% +units they're not the same type of + + + align:start position:0% +units they're not the same type of +quantity so you can't actually combine + + align:start position:0% +quantity so you can't actually combine + + + align:start position:0% +quantity so you can't actually combine +them arbitrarily but + + align:start position:0% +them arbitrarily but + + + align:start position:0% +them arbitrarily but +um anyway so the convention is usually + + align:start position:0% +um anyway so the convention is usually + + + align:start position:0% +um anyway so the convention is usually +we measure distance in this way next you + + align:start position:0% +we measure distance in this way next you + + + align:start position:0% +we measure distance in this way next you +could try to minimize the largest + + align:start position:0% +could try to minimize the largest + + + align:start position:0% +could try to minimize the largest +distance you know say we look at where's + + align:start position:0% +distance you know say we look at where's + + + align:start position:0% +distance you know say we look at where's +the largest error and we make that the + + align:start position:0% +the largest error and we make that the + + + align:start position:0% +the largest error and we make that the +smallest possible the drawback of doing + + align:start position:0% +smallest possible the drawback of doing + + + align:start position:0% +smallest possible the drawback of doing +that is experimentally very often you + + align:start position:0% +that is experimentally very often you + + + align:start position:0% +that is experimentally very often you +have one data point that's not good + + align:start position:0% +have one data point that's not good + + + align:start position:0% +have one data point that's not good +because maybe you know you fell asleep + + align:start position:0% +because maybe you know you fell asleep + + + align:start position:0% +because maybe you know you fell asleep +in front of the experiment and so you + + align:start position:0% +in front of the experiment and so you + + + align:start position:0% +in front of the experiment and so you +didn't measure the right thing so you + + align:start position:0% +didn't measure the right thing so you + + + align:start position:0% +didn't measure the right thing so you +you tend to want to you know not give + + align:start position:0% +you tend to want to you know not give + + + align:start position:0% +you tend to want to you know not give +too much importance to some data point + + align:start position:0% +too much importance to some data point + + + align:start position:0% +too much importance to some data point +that's far away from the others so maybe + + align:start position:0% +that's far away from the others so maybe + + + align:start position:0% +that's far away from the others so maybe +instead you want to measure you know the + + align:start position:0% +instead you want to measure you know the + + + align:start position:0% +instead you want to measure you know the +average + + align:start position:0% +average + + + align:start position:0% +average +distance or maybe you want to actually + + align:start position:0% +distance or maybe you want to actually + + + align:start position:0% +distance or maybe you want to actually +give more weight to things that are + + align:start position:0% +give more weight to things that are + + + align:start position:0% +give more weight to things that are +further away and then you don't want to + + align:start position:0% +further away and then you don't want to + + + align:start position:0% +further away and then you don't want to +do the distance but the square of the + + align:start position:0% +do the distance but the square of the + + + align:start position:0% +do the distance but the square of the +distance so there's various possible + + align:start position:0% +distance so there's various possible + + + align:start position:0% +distance so there's various possible +answers but one one of them gives us + + align:start position:0% +answers but one one of them gives us + + + align:start position:0% +answers but one one of them gives us +actually a particularly nice formula for + + align:start position:0% +actually a particularly nice formula for + + + align:start position:0% +actually a particularly nice formula for +a and b and so that's why it's the + + align:start position:0% +a and b and so that's why it's the + + + align:start position:0% +a and b and so that's why it's the +universally used one okay and so here it + + align:start position:0% +universally used one okay and so here it + + + align:start position:0% +universally used one okay and so here it +says list + + align:start position:0% +says list + + + align:start position:0% +says list +squares uh so that that's because we'll + + align:start position:0% +squares uh so that that's because we'll + + + align:start position:0% +squares uh so that that's because we'll +measure actually the sum of the squares + + align:start position:0% +measure actually the sum of the squares + + + align:start position:0% +measure actually the sum of the squares +of the + + align:start position:0% +of the + + + align:start position:0% +of the +errors and why do we do that well part + + align:start position:0% +errors and why do we do that well part + + + align:start position:0% +errors and why do we do that well part +of it is because actually it looks good + + align:start position:0% +of it is because actually it looks good + + + align:start position:0% +of it is because actually it looks good +I mean you know when you see these + + align:start position:0% +I mean you know when you see these + + + align:start position:0% +I mean you know when you see these +plots in you know scientific papers they + + align:start position:0% +plots in you know scientific papers they + + + align:start position:0% +plots in you know scientific papers they +really look like the line is indeed the + + align:start position:0% +really look like the line is indeed the + + + align:start position:0% +really look like the line is indeed the +ideal line and the second reason is + + align:start position:0% +ideal line and the second reason is + + + align:start position:0% +ideal line and the second reason is +because actually the minimization + + align:start position:0% +because actually the minimization + + + align:start position:0% +because actually the minimization +problem that we will get is particularly + + align:start position:0% +problem that we will get is particularly + + + align:start position:0% +problem that we will get is particularly +simple well posed and it's easy to solve + + align:start position:0% +simple well posed and it's easy to solve + + + align:start position:0% +simple well posed and it's easy to solve +so we'll have a nice formula for the + + align:start position:0% +so we'll have a nice formula for the + + + align:start position:0% +so we'll have a nice formula for the +best a and the best + + align:start position:0% +best a and the best + + + align:start position:0% +best a and the best +B so you know if you have a method + + align:start position:0% +B so you know if you have a method + + + align:start position:0% +B so you know if you have a method +that's simple and gives you a good + + align:start position:0% +that's simple and gives you a good + + + align:start position:0% +that's simple and gives you a good +answer then that's probably the good one + + align:start position:0% +answer then that's probably the good one + + + align:start position:0% +answer then that's probably the good one +so okay so we have to Define best and + + align:start position:0% +so okay so we have to Define best and + + + align:start position:0% +so okay so we have to Define best and +here it's in the sense + + align:start position:0% +here it's in the sense + + + align:start position:0% +here it's in the sense +of + + align:start position:0% + + + + align:start position:0% + +minimizing the total square + + align:start position:0% + + + + align:start position:0% + +l so or maybe I should say total square + + align:start position:0% +l so or maybe I should say total square + + + align:start position:0% +l so or maybe I should say total square +deviation me do that + + align:start position:0% + + + + align:start position:0% + +instead okay so what do I mean by that + + align:start position:0% +instead okay so what do I mean by that + + + align:start position:0% +instead okay so what do I mean by that +so the + + align:start position:0% + + + + align:start position:0% + +deviation for each data + + align:start position:0% + + + + align:start position:0% + +point is the difference between what you + + align:start position:0% +point is the difference between what you + + + align:start position:0% +point is the difference between what you +have measured and what you are + + align:start position:0% +have measured and what you are + + + align:start position:0% +have measured and what you are +predicting by your + + align:start position:0% +predicting by your + + + align:start position:0% +predicting by your +model okay so that's the difference + + align:start position:0% +model okay so that's the difference + + + align:start position:0% +model okay so that's the difference +between Yi and ax I plus + + align:start position:0% + + + + align:start position:0% + +b + + align:start position:0% +b + + + align:start position:0% +b +okay so + + align:start position:0% + + + + align:start position:0% + +now what we'll do is we'll try to + + align:start position:0% + + + + align:start position:0% + +minimize the function capital D which is + + align:start position:0% +minimize the function capital D which is + + + align:start position:0% +minimize the function capital D which is +just the sum for all the data points of + + align:start position:0% +just the sum for all the data points of + + + align:start position:0% +just the sum for all the data points of +the square of a deviation + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so let me emphasize again this is a + + align:start position:0% +so let me emphasize again this is a + + + align:start position:0% +so let me emphasize again this is a +function of A and B I mean of course + + align:start position:0% +function of A and B I mean of course + + + align:start position:0% +function of A and B I mean of course +there's a lot of letters in here but x i + + align:start position:0% +there's a lot of letters in here but x i + + + align:start position:0% +there's a lot of letters in here but x i +and Yi in real life there will be + + align:start position:0% +and Yi in real life there will be + + + align:start position:0% +and Yi in real life there will be +numbers given to you there will be the + + align:start position:0% +numbers given to you there will be the + + + align:start position:0% +numbers given to you there will be the +numbers that you have measured you've + + align:start position:0% +numbers that you have measured you've + + + align:start position:0% +numbers that you have measured you've +measured all of this data they are just + + align:start position:0% +measured all of this data they are just + + + align:start position:0% +measured all of this data they are just +going to be numbers you put them in + + align:start position:0% +going to be numbers you put them in + + + align:start position:0% +going to be numbers you put them in +there and you get a function of a and + + align:start position:0% +there and you get a function of a and + + + align:start position:0% +there and you get a function of a and +b okay + + align:start position:0% + + + + align:start position:0% + +any + + align:start position:0% + + + + align:start position:0% + +questions + + align:start position:0% +questions + + + align:start position:0% +questions +um yes + + align:start position:0% +um yes + + + align:start position:0% +um yes +no + + align:start position:0% +no + + + align:start position:0% +no +okay so how do we minimize this function + + align:start position:0% +okay so how do we minimize this function + + + align:start position:0% +okay so how do we minimize this function +of a and b well let's use our new + + align:start position:0% +of a and b well let's use our new + + + align:start position:0% +of a and b well let's use our new +knowledge let's actually look for a + + align:start position:0% +knowledge let's actually look for a + + + align:start position:0% +knowledge let's actually look for a +critical point + + align:start position:0% + + + + align:start position:0% + +so we want to + + align:start position:0% +so we want to + + + align:start position:0% +so we want to +solve for partial D over partial aals Z + + align:start position:0% +solve for partial D over partial aals Z + + + align:start position:0% +solve for partial D over partial aals Z +and partial D over partial b equals z + + align:start position:0% +and partial D over partial b equals z + + + align:start position:0% +and partial D over partial b equals z +that's how we look for critical + + align:start position:0% +that's how we look for critical + + + align:start position:0% +that's how we look for critical +points + + align:start position:0% +points + + + align:start position:0% +points +so let's take the derivative of this + + align:start position:0% +so let's take the derivative of this + + + align:start position:0% +so let's take the derivative of this +with respect to + + align:start position:0% +with respect to + + + align:start position:0% +with respect to +a well so it's going to be well the + + align:start position:0% +a well so it's going to be well the + + + align:start position:0% +a well so it's going to be well the +derivative of a sum is sum of the + + align:start position:0% +derivative of a sum is sum of the + + + align:start position:0% +derivative of a sum is sum of the +derivatives and now we have to take the + + align:start position:0% +derivatives and now we have to take the + + + align:start position:0% +derivatives and now we have to take the +derivative of this quantity squared so + + align:start position:0% +derivative of this quantity squared so + + + align:start position:0% +derivative of this quantity squared so +okay remember how we take the derivative + + align:start position:0% +okay remember how we take the derivative + + + align:start position:0% +okay remember how we take the derivative +of a square we take twice this quantity + + align:start position:0% +of a square we take twice this quantity + + + align:start position:0% +of a square we take twice this quantity +times the derivative of what we're + + align:start position:0% +times the derivative of what we're + + + align:start position:0% +times the derivative of what we're +squaring so we'll get 2 + + align:start position:0% + + + + align:start position:0% + +* minus Yi sorry y IUS ax i + + align:start position:0% +* minus Yi sorry y IUS ax i + + + align:start position:0% +* minus Yi sorry y IUS ax i +b times the derivative of this with + + align:start position:0% +b times the derivative of this with + + + align:start position:0% +b times the derivative of this with +respect to a what's the derivative of + + align:start position:0% +respect to a what's the derivative of + + + align:start position:0% +respect to a what's the derivative of +this with respect to a negative x i + + align:start position:0% +this with respect to a negative x i + + + align:start position:0% +this with respect to a negative x i +exactly okay and so we'll want this to + + align:start position:0% +exactly okay and so we'll want this to + + + align:start position:0% +exactly okay and so we'll want this to +be + + align:start position:0% +be + + + align:start position:0% +be +zero and partial D over partial B we do + + align:start position:0% +zero and partial D over partial B we do + + + align:start position:0% +zero and partial D over partial B we do +the same thing but differentiating with + + align:start position:0% +the same thing but differentiating with + + + align:start position:0% +the same thing but differentiating with +respect to b instead of with respect to + + align:start position:0% +respect to b instead of with respect to + + + align:start position:0% +respect to b instead of with respect to +a so again sum of squares twice y i + + align:start position:0% +a so again sum of squares twice y i + + + align:start position:0% +a so again sum of squares twice y i +minus a x i plus b times derivative of + + align:start position:0% +minus a x i plus b times derivative of + + + align:start position:0% +minus a x i plus b times derivative of +this with respect to B is + + align:start position:0% +this with respect to B is + + + align:start position:0% +this with respect to B is +is I think negative one + + align:start position:0% +is I think negative one + + + align:start position:0% +is I think negative one +okay so that's the equations we have to + + align:start position:0% +okay so that's the equations we have to + + + align:start position:0% +okay so that's the equations we have to +solve well let's reorganize this a + + align:start position:0% +solve well let's reorganize this a + + + align:start position:0% +solve well let's reorganize this a +little + + align:start position:0% + + + + align:start position:0% + +bit + + align:start position:0% + + + + align:start position:0% + +so the first equation + + align:start position:0% + + + + align:start position:0% + +so see there's A's and there's B's in + + align:start position:0% +so see there's A's and there's B's in + + + align:start position:0% +so see there's A's and there's B's in +these equations I'm going to just look + + align:start position:0% +these equations I'm going to just look + + + align:start position:0% +these equations I'm going to just look +at the coefficients of A and B if you + + align:start position:0% +at the coefficients of A and B if you + + + align:start position:0% +at the coefficients of A and B if you +have good eyes you can see probably that + + align:start position:0% +have good eyes you can see probably that + + + align:start position:0% +have good eyes you can see probably that +these are actually linear equations in A + + align:start position:0% +these are actually linear equations in A + + + align:start position:0% +these are actually linear equations in A +and B although there's a lot of clutter + + align:start position:0% +and B although there's a lot of clutter + + + align:start position:0% +and B although there's a lot of clutter +with all these x's and Y all over the + + align:start position:0% +with all these x's and Y all over the + + + align:start position:0% +with all these x's and Y all over the +place okay so let's actually try to + + align:start position:0% +place okay so let's actually try to + + + align:start position:0% +place okay so let's actually try to +expand things and make that more + + align:start position:0% +expand things and make that more + + + align:start position:0% +expand things and make that more +apparent + + align:start position:0% +apparent + + + align:start position:0% +apparent +so first thing I will do is I will + + align:start position:0% +so first thing I will do is I will + + + align:start position:0% +so first thing I will do is I will +actually get rid of these factors of two + + align:start position:0% +actually get rid of these factors of two + + + align:start position:0% +actually get rid of these factors of two +that are just you know not very + + align:start position:0% +that are just you know not very + + + align:start position:0% +that are just you know not very +important I can simplify things by + + align:start position:0% +important I can simplify things by + + + align:start position:0% +important I can simplify things by +two and next I'm going to look at the + + align:start position:0% +two and next I'm going to look at the + + + align:start position:0% +two and next I'm going to look at the +coefficient of a well I will get + + align:start position:0% +coefficient of a well I will get + + + align:start position:0% +coefficient of a well I will get +basically a * x i + + align:start position:0% +basically a * x i + + + align:start position:0% +basically a * x i +2 well let me just do it + + align:start position:0% +2 well let me just do it + + + align:start position:0% +2 well let me just do it +and and it should be + + align:start position:0% +and and it should be + + + align:start position:0% +and and it should be +clear so I claim when we simp simplify + + align:start position:0% +clear so I claim when we simp simplify + + + align:start position:0% +clear so I claim when we simp simplify +this we get x i 2 * + + align:start position:0% + + + + align:start position:0% + +a plus x i * + + align:start position:0% + + + + align:start position:0% + +B minus x i + + align:start position:0% + + + + align:start position:0% + +Yi and we set this equal to + + align:start position:0% +Yi and we set this equal to + + + align:start position:0% +Yi and we set this equal to +zero okay do you agree that this is what + + align:start position:0% +zero okay do you agree that this is what + + + align:start position:0% +zero okay do you agree that this is what +we get when we expand that product + + align:start position:0% + + + + align:start position:0% + +yeah kind + + align:start position:0% +yeah kind + + + align:start position:0% +yeah kind +of okay let's do the other + + align:start position:0% +of okay let's do the other + + + align:start position:0% +of okay let's do the other +one so we just multiply by minus one so + + align:start position:0% +one so we just multiply by minus one so + + + align:start position:0% +one so we just multiply by minus one so +we take the opposite of that it will be + + align:start position:0% +we take the opposite of that it will be + + + align:start position:0% +we take the opposite of that it will be +a x i plus b and we'll write that as X X + + align:start position:0% +a x i plus b and we'll write that as X X + + + align:start position:0% +a x i plus b and we'll write that as X X +I A Plus B minus + + align:start position:0% + + + + align:start position:0% + +Yi + + align:start position:0% +Yi + + + align:start position:0% +Yi +and oh sorry I forgot the N + + align:start position:0% +and oh sorry I forgot the N + + + align:start position:0% +and oh sorry I forgot the N +here and let me just reorganize that by + + align:start position:0% +here and let me just reorganize that by + + + align:start position:0% +here and let me just reorganize that by +actually putting you know all the A's + + align:start position:0% +actually putting you know all the A's + + + align:start position:0% +actually putting you know all the A's +together that means actually I will have + + align:start position:0% +together that means actually I will have + + + align:start position:0% +together that means actually I will have +sum of all the x i squ * a plus sum of x + + align:start position:0% +sum of all the x i squ * a plus sum of x + + + align:start position:0% +sum of all the x i squ * a plus sum of x +i * B minus sum of x i y i equal Z + + align:start position:0% + + + + align:start position:0% + +so if I Rite this it + + align:start position:0% + + + + align:start position:0% + +becomes sum of x i 2 * a plus sum of the + + align:start position:0% +becomes sum of x i 2 * a plus sum of the + + + align:start position:0% +becomes sum of x i 2 * a plus sum of the +x + + align:start position:0% +x + + + align:start position:0% +x +i * + + align:start position:0% +i * + + + align:start position:0% +i * +B minus let me move the other guys to + + align:start position:0% +B minus let me move the other guys to + + + align:start position:0% +B minus let me move the other guys to +the other side equals sum of + + align:start position:0% +the other side equals sum of + + + align:start position:0% +the other side equals sum of +x i + + align:start position:0% +x i + + + align:start position:0% +x i +Yi and that one + + align:start position:0% +Yi and that one + + + align:start position:0% +Yi and that one +becomes sum of x i * a plus how many B's + + align:start position:0% +becomes sum of x i * a plus how many B's + + + align:start position:0% +becomes sum of x i * a plus how many B's +do I get from this + + align:start position:0% +do I get from this + + + align:start position:0% +do I get from this +one well I get one for each data point + + align:start position:0% +one well I get one for each data point + + + align:start position:0% +one well I get one for each data point +when I sum them together I will get n + + align:start position:0% +when I sum them together I will get n + + + align:start position:0% +when I sum them together I will get n +very good so n * b equals sum of + + align:start position:0% +very good so n * b equals sum of + + + align:start position:0% +very good so n * b equals sum of +Yi okay now this quantities they look + + align:start position:0% +Yi okay now this quantities they look + + + align:start position:0% +Yi okay now this quantities they look +scary but they're actually just numbers + + align:start position:0% +scary but they're actually just numbers + + + align:start position:0% +scary but they're actually just numbers +right so for example for this one you + + align:start position:0% +right so for example for this one you + + + align:start position:0% +right so for example for this one you +look at all your data points for each of + + align:start position:0% +look at all your data points for each of + + + align:start position:0% +look at all your data points for each of +them you take the value of x and you + + align:start position:0% +them you take the value of x and you + + + align:start position:0% +them you take the value of x and you +just sum all these numbers + + align:start position:0% + + + + align:start position:0% + +together so what you get actually is a + + align:start position:0% +together so what you get actually is a + + + align:start position:0% +together so what you get actually is a +linear system in a and + + align:start position:0% +linear system in a and + + + align:start position:0% +linear system in a and +b a 2 by two linear + + align:start position:0% + + + + align:start position:0% + +system and so now we can solve this for + + align:start position:0% +system and so now we can solve this for + + + align:start position:0% +system and so now we can solve this for +a and + + align:start position:0% +a and + + + align:start position:0% +a and +b so in practice of course first you + + align:start position:0% +b so in practice of course first you + + + align:start position:0% +b so in practice of course first you +plug in the numbers for x i and Yi and + + align:start position:0% +plug in the numbers for x i and Yi and + + + align:start position:0% +plug in the numbers for x i and Yi and +then you solve the system that you + + align:start position:0% +then you solve the system that you + + + align:start position:0% +then you solve the system that you +get okay and we know how to solve 2 by + + align:start position:0% +get okay and we know how to solve 2 by + + + align:start position:0% +get okay and we know how to solve 2 by +two linear systems I + + align:start position:0% +two linear systems I + + + align:start position:0% +two linear systems I +hope okay so that's how we find the best + + align:start position:0% +hope okay so that's how we find the best + + + align:start position:0% +hope okay so that's how we find the best +fit line now why is that going to be the + + align:start position:0% +fit line now why is that going to be the + + + align:start position:0% +fit line now why is that going to be the +best one instead of the worst one you + + align:start position:0% +best one instead of the worst one you + + + align:start position:0% +best one instead of the worst one you +know we just solve for a critical point + + align:start position:0% +know we just solve for a critical point + + + align:start position:0% +know we just solve for a critical point +that could actually be a maximum of this + + align:start position:0% +that could actually be a maximum of this + + + align:start position:0% +that could actually be a maximum of this +error function D well so we'll have + + align:start position:0% +error function D well so we'll have + + + align:start position:0% +error function D well so we'll have +actually the answer to that next time uh + + align:start position:0% +actually the answer to that next time uh + + + align:start position:0% +actually the answer to that next time uh +but trust me if you really want to go + + align:start position:0% +but trust me if you really want to go + + + align:start position:0% +but trust me if you really want to go +through the second derivative test that + + align:start position:0% +through the second derivative test that + + + align:start position:0% +through the second derivative test that +we'll see tomorrow and apply it in this + + align:start position:0% +we'll see tomorrow and apply it in this + + + align:start position:0% +we'll see tomorrow and apply it in this +case it's quite hard to check but you + + align:start position:0% +case it's quite hard to check but you + + + align:start position:0% +case it's quite hard to check but you +can see it's actually a + + align:start position:0% +can see it's actually a + + + align:start position:0% +can see it's actually a +minimum so I'll just + + align:start position:0% + + + + align:start position:0% + +say we can show that it's a minimum + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now even for the linear case is the one + + align:start position:0% +now even for the linear case is the one + + + align:start position:0% +now even for the linear case is the one +that we the most familiar with list + + align:start position:0% +that we the most familiar with list + + + align:start position:0% +that we the most familiar with list +squares interpolation actually works in + + align:start position:0% +squares interpolation actually works in + + + align:start position:0% +squares interpolation actually works in +much more general + + align:start position:0% +much more general + + + align:start position:0% +much more general +settings okay + + align:start position:0% + + + + align:start position:0% + +because instead of fitting for the back + + align:start position:0% +because instead of fitting for the back + + + align:start position:0% +because instead of fitting for the back +line if you think that there's a + + align:start position:0% +line if you think that there's a + + + align:start position:0% +line if you think that there's a +different kind of relation then maybe + + align:start position:0% +different kind of relation then maybe + + + align:start position:0% +different kind of relation then maybe +you can fit you know in using a + + align:start position:0% +you can fit you know in using a + + + align:start position:0% +you can fit you know in using a +different kind of formula so let me + + align:start position:0% +different kind of formula so let me + + + align:start position:0% +different kind of formula so let me +actually illustrate that with an + + align:start position:0% +actually illustrate that with an + + + align:start position:0% +actually illustrate that with an +example so I don't know if you're + + align:start position:0% +example so I don't know if you're + + + align:start position:0% +example so I don't know if you're +familiar with Mo's law it's something + + align:start position:0% +familiar with Mo's law it's something + + + align:start position:0% +familiar with Mo's law it's something +that's supposed to tell you how quickly + + align:start position:0% +that's supposed to tell you how quickly + + + align:start position:0% +that's supposed to tell you how quickly +basically computer chips become smarter + + align:start position:0% +basically computer chips become smarter + + + align:start position:0% +basically computer chips become smarter +faster and faster over time + + align:start position:0% +faster and faster over time + + + align:start position:0% +faster and faster over time +it's a law that says things about the + + align:start position:0% +it's a law that says things about the + + + align:start position:0% +it's a law that says things about the +number of transistors that you can fit + + align:start position:0% +number of transistors that you can fit + + + align:start position:0% +number of transistors that you can fit +onto a computer chip so here I have some + + align:start position:0% +onto a computer chip so here I have some + + + align:start position:0% +onto a computer chip so here I have some +data + + align:start position:0% +data + + + align:start position:0% +data +about oh why + + align:start position:0% +about oh why + + + align:start position:0% +about oh why +okay + + align:start position:0% + + + + align:start position:0% + +so okay + + align:start position:0% +so okay + + + align:start position:0% +so okay +better so here's data about the number + + align:start position:0% +better so here's data about the number + + + align:start position:0% +better so here's data about the number +of transistors + + align:start position:0% +of transistors + + + align:start position:0% +of transistors +on uh you know standard PC processor as + + align:start position:0% +on uh you know standard PC processor as + + + align:start position:0% +on uh you know standard PC processor as +a function of time and well you know if + + align:start position:0% +a function of time and well you know if + + + align:start position:0% +a function of time and well you know if +you try to do the best line fit well + + align:start position:0% +you try to do the best line fit well + + + align:start position:0% +you try to do the best line fit well +you'll see quickly that it doesn't seem + + align:start position:0% +you'll see quickly that it doesn't seem + + + align:start position:0% +you'll see quickly that it doesn't seem +to follow a linear Trend + + align:start position:0% +to follow a linear Trend + + + align:start position:0% +to follow a linear Trend +okay on the other hand if you plot the + + align:start position:0% +okay on the other hand if you plot the + + + align:start position:0% +okay on the other hand if you plot the +diagram in a log scale you know with so + + align:start position:0% +diagram in a log scale you know with so + + + align:start position:0% +diagram in a log scale you know with so +the log of a number of transistors as a + + align:start position:0% +the log of a number of transistors as a + + + align:start position:0% +the log of a number of transistors as a +function of time then you get a much + + align:start position:0% +function of time then you get a much + + + align:start position:0% +function of time then you get a much +better + + align:start position:0% +better + + + align:start position:0% +better +line okay and so in fact that means that + + align:start position:0% +line okay and so in fact that means that + + + align:start position:0% +line okay and so in fact that means that +you had an exponential relation between + + align:start position:0% +you had an exponential relation between + + + align:start position:0% +you had an exponential relation between +the the number of transistors and time + + align:start position:0% +the the number of transistors and time + + + align:start position:0% +the the number of transistors and time +and so actually that's what most law + + align:start position:0% +and so actually that's what most law + + + align:start position:0% +and so actually that's what most law +says it says that the number of + + align:start position:0% +says it says that the number of + + + align:start position:0% +says it says that the number of +transistors on the chip doubles every so + + align:start position:0% +transistors on the chip doubles every so + + + align:start position:0% +transistors on the chip doubles every so +depending on the version every 18 months + + align:start position:0% +depending on the version every 18 months + + + align:start position:0% +depending on the version every 18 months +or every two years uh they keep changing + + align:start position:0% +or every two years uh they keep changing + + + align:start position:0% +or every two years uh they keep changing +the + + align:start position:0% +the + + + align:start position:0% +the +statement + + align:start position:0% +statement + + + align:start position:0% +statement +but so how do we find that best + + align:start position:0% +but so how do we find that best + + + align:start position:0% +but so how do we find that best +exponential + + align:start position:0% + + + + align:start position:0% + +fit well so an exponential fit would be + + align:start position:0% +fit well so an exponential fit would be + + + align:start position:0% +fit well so an exponential fit would be +something of the form y equals a + + align:start position:0% +something of the form y equals a + + + align:start position:0% +something of the form y equals a +constant time exponential of a * + + align:start position:0% +constant time exponential of a * + + + align:start position:0% +constant time exponential of a * +X okay that's what we want to look at + + align:start position:0% +X okay that's what we want to look at + + + align:start position:0% +X okay that's what we want to look at +well we could try to minimize a square + + align:start position:0% +well we could try to minimize a square + + + align:start position:0% +well we could try to minimize a square +error like we it before but doesn't work + + align:start position:0% +error like we it before but doesn't work + + + align:start position:0% +error like we it before but doesn't work +well at all the equations that you get + + align:start position:0% +well at all the equations that you get + + + align:start position:0% +well at all the equations that you get +are very complicated you can't solve + + align:start position:0% +are very complicated you can't solve + + + align:start position:0% +are very complicated you can't solve +them but remember what I showed you on + + align:start position:0% +them but remember what I showed you on + + + align:start position:0% +them but remember what I showed you on +this log + + align:start position:0% +this log + + + align:start position:0% +this log +plot right if you plot the log of Y as a + + align:start position:0% +plot right if you plot the log of Y as a + + + align:start position:0% +plot right if you plot the log of Y as a +function of X then suddenly it becomes a + + align:start position:0% +function of X then suddenly it becomes a + + + align:start position:0% +function of X then suddenly it becomes a +linear relation so observe this is the + + align:start position:0% +linear relation so observe this is the + + + align:start position:0% +linear relation so observe this is the +same as Ln of y equals Ln of C plus a x + + align:start position:0% +same as Ln of y equals Ln of C plus a x + + + align:start position:0% +same as Ln of y equals Ln of C plus a x +and that is a linear best + + align:start position:0% +and that is a linear best + + + align:start position:0% +and that is a linear best +fit + + align:start position:0% +fit + + + align:start position:0% +fit +so what you + + align:start position:0% + + + + align:start position:0% + +do is you just look for the the best + + align:start position:0% +do is you just look for the the best + + + align:start position:0% +do is you just look for the the best +straight line fit for the log of + + align:start position:0% +straight line fit for the log of + + + align:start position:0% +straight line fit for the log of +Y + + align:start position:0% + + + + align:start position:0% + +so that's something we already know but + + align:start position:0% +so that's something we already know but + + + align:start position:0% +so that's something we already know but +you can also do other examples for + + align:start position:0% +you can also do other examples for + + + align:start position:0% +you can also do other examples for +example let's say that you know we have + + align:start position:0% +example let's say that you know we have + + + align:start position:0% +example let's say that you know we have +something more complicated let's say + + align:start position:0% +something more complicated let's say + + + align:start position:0% +something more complicated let's say +that we have actually a + + align:start position:0% +that we have actually a + + + align:start position:0% +that we have actually a +quadratic law so for example Y is of the + + align:start position:0% +quadratic law so for example Y is of the + + + align:start position:0% +quadratic law so for example Y is of the +form a X2 plus BX plus c + + align:start position:0% +form a X2 plus BX plus c + + + align:start position:0% +form a X2 plus BX plus c +and of course you you're trying to find + + align:start position:0% +and of course you you're trying to find + + + align:start position:0% +and of course you you're trying to find +you know somehow the + + align:start position:0% +you know somehow the + + + align:start position:0% +you know somehow the +best so that would mean here fitting the + + align:start position:0% +best so that would mean here fitting the + + + align:start position:0% +best so that would mean here fitting the +best Parabola for your data + + align:start position:0% +best Parabola for your data + + + align:start position:0% +best Parabola for your data +points well to do that you would need to + + align:start position:0% +points well to do that you would need to + + + align:start position:0% +points well to do that you would need to +find a b and c okay and now you would + + align:start position:0% +find a b and c okay and now you would + + + align:start position:0% +find a b and c okay and now you would +have actually a + + align:start position:0% +have actually a + + + align:start position:0% +have actually a +function of a b and c which would be the + + align:start position:0% +function of a b and c which would be the + + + align:start position:0% +function of a b and c which would be the +sum of the all data points of the square + + align:start position:0% +sum of the all data points of the square + + + align:start position:0% +sum of the all data points of the square +deviation + + align:start position:0% + + + + align:start position:0% + +and if you try to solve for critical + + align:start position:0% +and if you try to solve for critical + + + align:start position:0% +and if you try to solve for critical +points so now you will have three + + align:start position:0% +points so now you will have three + + + align:start position:0% +points so now you will have three +equations involving a b and c and in + + align:start position:0% +equations involving a b and c and in + + + align:start position:0% +equations involving a b and c and in +fact you will find a 3 by3 linear system + + align:start position:0% +fact you will find a 3 by3 linear system + + + align:start position:0% +fact you will find a 3 by3 linear system +and it works just the same way just you + + align:start position:0% +and it works just the same way just you + + + align:start position:0% +and it works just the same way just you +have a little bit more + + align:start position:0% +have a little bit more + + + align:start position:0% +have a little bit more +data + + align:start position:0% +data + + + align:start position:0% +data +so + + align:start position:0% +so + + + align:start position:0% +so +basically you see that these best fit + + align:start position:0% +basically you see that these best fit + + + align:start position:0% +basically you see that these best fit +problems are an example of you know + + align:start position:0% +problems are an example of you know + + + align:start position:0% +problems are an example of you know +minimization problem that maybe you + + align:start position:0% +minimization problem that maybe you + + + align:start position:0% +minimization problem that maybe you +didn't expect to see minimization + + align:start position:0% +didn't expect to see minimization + + + align:start position:0% +didn't expect to see minimization +problems come in but that's really the + + align:start position:0% +problems come in but that's really the + + + align:start position:0% +problems come in but that's really the +way to handle these + + align:start position:0% + + + + align:start position:0% + +questions okay so tomorrow we'll go back + + align:start position:0% +questions okay so tomorrow we'll go back + + + align:start position:0% +questions okay so tomorrow we'll go back +to the question of how do we decide + + align:start position:0% +to the question of how do we decide + + + align:start position:0% +to the question of how do we decide +whether it's a minimum or a maximum and + + align:start position:0% +whether it's a minimum or a maximum and + + + align:start position:0% +whether it's a minimum or a maximum and +we'll continue exploring functions of + + align:start position:0% +we'll continue exploring functions of + + + align:start position:0% +we'll continue exploring functions of +several variables \ No newline at end of file diff --git a/Unvy1L_NH0c.txt b/Unvy1L_NH0c.txt new file mode 100644 index 0000000000000000000000000000000000000000..40e33af42285f83ee5779bb2b89900778db6c18a --- /dev/null +++ b/Unvy1L_NH0c.txt @@ -0,0 +1,12131 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +so so far we've talked about just + + align:start position:0% +so so far we've talked about just + + + align:start position:0% +so so far we've talked about just +examples of running things forward + + align:start position:0% +examples of running things forward + + + align:start position:0% +examples of running things forward +I've hoped I've given you some examples + + align:start position:0% +I've hoped I've given you some examples + + + align:start position:0% +I've hoped I've given you some examples +of different procedures that you can run + + align:start position:0% +of different procedures that you can run + + + align:start position:0% +of different procedures that you can run +forward to get some interesting stuff + + align:start position:0% +forward to get some interesting stuff + + + align:start position:0% +forward to get some interesting stuff +whether it's a mixture of gaussians + + align:start position:0% +whether it's a mixture of gaussians + + + align:start position:0% +whether it's a mixture of gaussians +whether it's a mcwhirter it's sort of + + align:start position:0% +whether it's a mcwhirter it's sort of + + + align:start position:0% +whether it's a mcwhirter it's sort of +this mixture of gaussian plus uniform + + align:start position:0% +this mixture of gaussian plus uniform + + + align:start position:0% +this mixture of gaussian plus uniform +whether it's just flipping a coin but + + align:start position:0% +whether it's just flipping a coin but + + + align:start position:0% +whether it's just flipping a coin but +the question is ok I've written down my + + align:start position:0% +the question is ok I've written down my + + + align:start position:0% +the question is ok I've written down my +Ford model and hopefully you saw that it + + align:start position:0% +Ford model and hopefully you saw that it + + + align:start position:0% +Ford model and hopefully you saw that it +wasn't even if it was a little bit + + align:start position:0% +wasn't even if it was a little bit + + + align:start position:0% +wasn't even if it was a little bit +broken and even if you didn't get the + + align:start position:0% +broken and even if you didn't get the + + + align:start position:0% +broken and even if you didn't get the +full details it wasn't that hard to + + align:start position:0% +full details it wasn't that hard to + + + align:start position:0% +full details it wasn't that hard to +write it down right someone could say + + align:start position:0% +write it down right someone could say + + + align:start position:0% +write it down right someone could say +listen I think the way the bombing works + + align:start position:0% +listen I think the way the bombing works + + + align:start position:0% +listen I think the way the bombing works +is this you're gonna put a gaussian I'm + + align:start position:0% +is this you're gonna put a gaussian I'm + + + align:start position:0% +is this you're gonna put a gaussian I'm +gonna put another gaussian maybe or + + align:start position:0% +gonna put another gaussian maybe or + + + align:start position:0% +gonna put another gaussian maybe or +maybe you're gonna put three I don't + + align:start position:0% +maybe you're gonna put three I don't + + + align:start position:0% +maybe you're gonna put three I don't +know how many and you can write that + + align:start position:0% +know how many and you can write that + + + align:start position:0% +know how many and you can write that +down and then you say okay I actually + + align:start position:0% +down and then you say okay I actually + + + align:start position:0% +down and then you say okay I actually +want to do inference on that and that's + + align:start position:0% +want to do inference on that and that's + + + align:start position:0% +want to do inference on that and that's +when it becomes a little bit painful to + + align:start position:0% +when it becomes a little bit painful to + + + align:start position:0% +when it becomes a little bit painful to +do and if only there was a way of + + align:start position:0% +do and if only there was a way of + + + align:start position:0% +do and if only there was a way of +running forward your model and just sort + + align:start position:0% +running forward your model and just sort + + + align:start position:0% +running forward your model and just sort +of having written the forward direction + + align:start position:0% +of having written the forward direction + + + align:start position:0% +of having written the forward direction +you can do inference and it looks like + + align:start position:0% +you can do inference and it looks like + + + align:start position:0% +you can do inference and it looks like +we're talking about something completely + + align:start position:0% +we're talking about something completely + + + align:start position:0% +we're talking about something completely +different but actually it's not ok we're + + align:start position:0% +different but actually it's not ok we're + + + align:start position:0% +different but actually it's not ok we're +basically going to run our models but + + align:start position:0% +basically going to run our models but + + + align:start position:0% +basically going to run our models but +we're going to run our models in a way + + align:start position:0% +we're going to run our models in a way + + + align:start position:0% +we're going to run our models in a way +that it's going to do inference so let's + + align:start position:0% +that it's going to do inference so let's + + + align:start position:0% +that it's going to do inference so let's +see how would we possibly do that + + align:start position:0% +see how would we possibly do that + + + align:start position:0% +see how would we possibly do that +so the basic syntax for any sort of + + align:start position:0% +so the basic syntax for any sort of + + + align:start position:0% +so the basic syntax for any sort of +query any sort of inference in Church is + + align:start position:0% +query any sort of inference in Church is + + + align:start position:0% +query any sort of inference in Church is +by stating the following procedure you + + align:start position:0% +by stating the following procedure you + + + align:start position:0% +by stating the following procedure you +start out with saying query where query + + align:start position:0% +start out with saying query where query + + + align:start position:0% +start out with saying query where query +is not itself a command it's just there + + align:start position:0% +is not itself a command it's just there + + + align:start position:0% +is not itself a command it's just there +are all sorts of queries there's + + align:start position:0% +are all sorts of queries there's + + + align:start position:0% +are all sorts of queries there's +rejection query + + align:start position:0% +rejection query + + + align:start position:0% +rejection query +there's MH query metropolis Hastings + + align:start position:0% +there's MH query metropolis Hastings + + + align:start position:0% +there's MH query metropolis Hastings +there's explicit enumeration but the + + align:start position:0% +there's explicit enumeration but the + + + align:start position:0% +there's explicit enumeration but the +point is you would write down that + + align:start position:0% +point is you would write down that + + + align:start position:0% +point is you would write down that +particular query then you would write + + align:start position:0% +particular query then you would write + + + align:start position:0% +particular query then you would write +down the generative model this is a list + + align:start position:0% +down the generative model this is a list + + + align:start position:0% +down the generative model this is a list +of things the way that you think the + + align:start position:0% +of things the way that you think the + + + align:start position:0% +of things the way that you think the +world works so here for example you + + align:start position:0% +world works so here for example you + + + align:start position:0% +world works so here for example you +would put in the London bombing example + + align:start position:0% +would put in the London bombing example + + + align:start position:0% +would put in the London bombing example +you would put in the list of things like + + align:start position:0% +you would put in the list of things like + + + align:start position:0% +you would put in the list of things like +I don't know it's either uniform or not + + align:start position:0% +I don't know it's either uniform or not + + + align:start position:0% +I don't know it's either uniform or not +uniform that's either Gaussian and + + align:start position:0% +uniform that's either Gaussian and + + + align:start position:0% +uniform that's either Gaussian and +allgäu so I'm gonna put some you know + + align:start position:0% +allgäu so I'm gonna put some you know + + + align:start position:0% +allgäu so I'm gonna put some you know +uncertainty and priors and things like + + align:start position:0% +uncertainty and priors and things like + + + align:start position:0% +uncertainty and priors and things like +that + + align:start position:0% +that + + + align:start position:0% +that +once you finish defining your forward + + align:start position:0% +once you finish defining your forward + + + align:start position:0% +once you finish defining your forward +model of how you think the world works + + align:start position:0% +model of how you think the world works + + + align:start position:0% +model of how you think the world works +you're going to ask you to predict + + align:start position:0% +you're going to ask you to predict + + + align:start position:0% +you're going to ask you to predict +or thing you're going to sort of the + + align:start position:0% +or thing you're going to sort of the + + + align:start position:0% +or thing you're going to sort of the +last statement the penultimate statement + + align:start position:0% +last statement the penultimate statement + + + align:start position:0% +last statement the penultimate statement +that you're going to give it is what we + + align:start position:0% +that you're going to give it is what we + + + align:start position:0% +that you're going to give it is what we +want to know like for example in this + + align:start position:0% +want to know like for example in this + + + align:start position:0% +want to know like for example in this +particular case suppose that before I + + align:start position:0% +particular case suppose that before I + + + align:start position:0% +particular case suppose that before I +started I say I'm going to I don't know + + align:start position:0% +started I say I'm going to I don't know + + + align:start position:0% +started I say I'm going to I don't know +if the bombing is targeted or not I'm + + align:start position:0% +if the bombing is targeted or not I'm + + + align:start position:0% +if the bombing is targeted or not I'm +50/50 either way I don't have to be but + + align:start position:0% +50/50 either way I don't have to be but + + + align:start position:0% +50/50 either way I don't have to be but +let's say in 5050 either way so I say + + align:start position:0% +let's say in 5050 either way so I say + + + align:start position:0% +let's say in 5050 either way so I say +I'm gonna flip a coin + + align:start position:0% +I'm gonna flip a coin + + + align:start position:0% +I'm gonna flip a coin +it's either targeted or it's not + + align:start position:0% +it's either targeted or it's not + + + align:start position:0% +it's either targeted or it's not +targeted and that's going to come up + + align:start position:0% +targeted and that's going to come up + + + align:start position:0% +targeted and that's going to come up +either true or false + + align:start position:0% +either true or false + + + align:start position:0% +either true or false +and what you're going to basically say + + align:start position:0% +and what you're going to basically say + + + align:start position:0% +and what you're going to basically say +you're going to query on that right you + + align:start position:0% +you're going to query on that right you + + + align:start position:0% +you're going to query on that right you +want to say did the coin come up to or + + align:start position:0% +want to say did the coin come up to or + + + align:start position:0% +want to say did the coin come up to or +false given the data okay so the last + + align:start position:0% +false given the data okay so the last + + + align:start position:0% +false given the data okay so the last +thing the ultimate statement that you're + + align:start position:0% +thing the ultimate statement that you're + + + align:start position:0% +thing the ultimate statement that you're +going to write is basically the + + align:start position:0% +going to write is basically the + + + align:start position:0% +going to write is basically the +conditional statement and the + + align:start position:0% +conditional statement and the + + + align:start position:0% +conditional statement and the +conditional statement is basically the + + align:start position:0% +conditional statement is basically the + + + align:start position:0% +conditional statement is basically the +thing that has to evaluate as true okay + + align:start position:0% +thing that has to evaluate as true okay + + + align:start position:0% +thing that has to evaluate as true okay +the usual thing that we would write down + + align:start position:0% +the usual thing that we would write down + + + align:start position:0% +the usual thing that we would write down +there I'll give you some examples of + + align:start position:0% +there I'll give you some examples of + + + align:start position:0% +there I'll give you some examples of +that but what we would usually write as + + align:start position:0% +that but what we would usually write as + + + align:start position:0% +that but what we would usually write as +something like given that the observed + + align:start position:0% +something like given that the observed + + + align:start position:0% +something like given that the observed +data matches the sample data from my + + align:start position:0% +data matches the sample data from my + + + align:start position:0% +data matches the sample data from my +model okay so if you want to do + + align:start position:0% +model okay so if you want to do + + + align:start position:0% +model okay so if you want to do +something like you know the probability + + align:start position:0% +something like you know the probability + + + align:start position:0% +something like you know the probability +of a particular hypothesis given the + + align:start position:0% +of a particular hypothesis given the + + + align:start position:0% +of a particular hypothesis given the +data this is the way that you would say + + align:start position:0% +data this is the way that you would say + + + align:start position:0% +data this is the way that you would say +this is my data this is what I know and + + align:start position:0% +this is my data this is what I know and + + + align:start position:0% +this is my data this is what I know and +the way that it would know it's you're + + align:start position:0% +the way that it would know it's you're + + + align:start position:0% +the way that it would know it's you're +sort of running down a program and + + align:start position:0% +sort of running down a program and + + + align:start position:0% +sort of running down a program and +you're constraining it to give you a + + align:start position:0% +you're constraining it to give you a + + + align:start position:0% +you're constraining it to give you a +sample that matches the actual thing + + align:start position:0% +sample that matches the actual thing + + + align:start position:0% +sample that matches the actual thing +that you see in the London bombing + + align:start position:0% +that you see in the London bombing + + + align:start position:0% +that you see in the London bombing +example what you would do is you would + + align:start position:0% +example what you would do is you would + + + align:start position:0% +example what you would do is you would +write something like query a bunch of + + align:start position:0% +write something like query a bunch of + + + align:start position:0% +write something like query a bunch of +defines targeted bombing random bombing + + align:start position:0% +defines targeted bombing random bombing + + + align:start position:0% +defines targeted bombing random bombing +things like that I want to know is it + + align:start position:0% +things like that I want to know is it + + + align:start position:0% +things like that I want to know is it +targeted or random what how did the coin + + align:start position:0% +targeted or random what how did the coin + + + align:start position:0% +targeted or random what how did the coin +fall and what you're going to do is + + align:start position:0% +fall and what you're going to do is + + + align:start position:0% +fall and what you're going to do is +you're going to say listen run this + + align:start position:0% +you're going to say listen run this + + + align:start position:0% +you're going to say listen run this +model forward under the following + + align:start position:0% +model forward under the following + + + align:start position:0% +model forward under the following +condition if I just ran it forward I + + align:start position:0% +condition if I just ran it forward I + + + align:start position:0% +condition if I just ran it forward I +would either get targeted or not it + + align:start position:0% +would either get targeted or not it + + + align:start position:0% +would either get targeted or not it +would be 50/50 under the condition that + + align:start position:0% +would be 50/50 under the condition that + + + align:start position:0% +would be 50/50 under the condition that +whatever this model samples has to match + + align:start position:0% +whatever this model samples has to match + + + align:start position:0% +whatever this model samples has to match +the actual data so I'm going to run it + + align:start position:0% +the actual data so I'm going to run it + + + align:start position:0% +the actual data so I'm going to run it +forward but it has to the thing that + + align:start position:0% +forward but it has to the thing that + + + align:start position:0% +forward but it has to the thing that +needs to evaluate is true is that the + + align:start position:0% +needs to evaluate is true is that the + + + align:start position:0% +needs to evaluate is true is that the +samples I got from the model are equal + + align:start position:0% +samples I got from the model are equal + + + align:start position:0% +samples I got from the model are equal +to the actual data that I got okay + + align:start position:0% +to the actual data that I got okay + + + align:start position:0% +to the actual data that I got okay +now once you do that once you define + + align:start position:0% +now once you do that once you define + + + align:start position:0% +now once you do that once you define +that particular thing what you've done + + align:start position:0% +that particular thing what you've done + + + align:start position:0% +that particular thing what you've done +is change the probability distribution + + align:start position:0% +is change the probability distribution + + + align:start position:0% +is change the probability distribution +that the genitive model describes okay + + align:start position:0% +that the genitive model describes okay + + + align:start position:0% +that the genitive model describes okay +remember how we talked earlier I was + + align:start position:0% +remember how we talked earlier I was + + + align:start position:0% +remember how we talked earlier I was +sort of trying to hammer it home that + + align:start position:0% +sort of trying to hammer it home that + + + align:start position:0% +sort of trying to hammer it home that +anything that you write down is Church + + align:start position:0% +anything that you write down is Church + + + align:start position:0% +anything that you write down is Church +is actually a probability distribution + + align:start position:0% +is actually a probability distribution + + + align:start position:0% +is actually a probability distribution +right you write down the program and you + + align:start position:0% +right you write down the program and you + + + align:start position:0% +right you write down the program and you +run it an infinite number of times and + + align:start position:0% +run it an infinite number of times and + + + align:start position:0% +run it an infinite number of times and +you get some distribution your + + align:start position:0% +you get some distribution your + + + align:start position:0% +you get some distribution your +generative model describes a particular + + align:start position:0% +generative model describes a particular + + + align:start position:0% +generative model describes a particular +distribution if you condition + + align:start position:0% +distribution if you condition + + + align:start position:0% +distribution if you condition +that model on something you get a + + align:start position:0% +that model on something you get a + + + align:start position:0% +that model on something you get a +different distribution okay and that + + align:start position:0% +different distribution okay and that + + + align:start position:0% +different distribution okay and that +different distribution is now what + + align:start position:0% +different distribution is now what + + + align:start position:0% +different distribution is now what +you're going to sample from okay you're + + align:start position:0% +you're going to sample from okay you're + + + align:start position:0% +you're going to sample from okay you're +going to sample from the posterior you + + align:start position:0% +going to sample from the posterior you + + + align:start position:0% +going to sample from the posterior you +have some prior you condition it on some + + align:start position:0% +have some prior you condition it on some + + + align:start position:0% +have some prior you condition it on some +data and you're going to sample from the + + align:start position:0% +data and you're going to sample from the + + + align:start position:0% +data and you're going to sample from the +posterior and something from the + + align:start position:0% +posterior and something from the + + + align:start position:0% +posterior and something from the +posterior can be something like and + + align:start position:0% +posterior can be something like and + + + align:start position:0% +posterior can be something like and +we'll get at some examples like I know + + align:start position:0% +we'll get at some examples like I know + + + align:start position:0% +we'll get at some examples like I know +how the world works in terms of their + + align:start position:0% +how the world works in terms of their + + + align:start position:0% +how the world works in terms of their +objects and I know how light works and I + + align:start position:0% +objects and I know how light works and I + + + align:start position:0% +objects and I know how light works and I +know how vision works I don't know how + + align:start position:0% +know how vision works I don't know how + + + align:start position:0% +know how vision works I don't know how +the particular what the particular + + align:start position:0% +the particular what the particular + + + align:start position:0% +the particular what the particular +objects in this world are that's what I + + align:start position:0% +objects in this world are that's what I + + + align:start position:0% +objects in this world are that's what I +want to know I condition on their + + align:start position:0% +want to know I condition on their + + + align:start position:0% +want to know I condition on their +retinal display being equal to something + + align:start position:0% +retinal display being equal to something + + + align:start position:0% +retinal display being equal to something +and now my posterior probability + + align:start position:0% +and now my posterior probability + + + align:start position:0% +and now my posterior probability +distribution is going to basically + + align:start position:0% +distribution is going to basically + + + align:start position:0% +distribution is going to basically +sample from say your face or these + + align:start position:0% +sample from say your face or these + + + align:start position:0% +sample from say your face or these +objects or these chairs okay but the + + align:start position:0% +objects or these chairs okay but the + + + align:start position:0% +objects or these chairs okay but the +same thing could work for example if + + align:start position:0% +same thing could work for example if + + + align:start position:0% +same thing could work for example if +you're trying to query a sentence you're + + align:start position:0% +you're trying to query a sentence you're + + + align:start position:0% +you're trying to query a sentence you're +trying to parse a sentence from sound or + + align:start position:0% +trying to parse a sentence from sound or + + + align:start position:0% +trying to parse a sentence from sound or +you're trying to you know learn how a + + align:start position:0% +you're trying to you know learn how a + + + align:start position:0% +you're trying to you know learn how a +model is you're trying to predict how + + align:start position:0% +model is you're trying to predict how + + + align:start position:0% +model is you're trying to predict how +the next step in a physics engine is + + align:start position:0% +the next step in a physics engine is + + + align:start position:0% +the next step in a physics engine is +going to work or many many many many + + align:start position:0% +going to work or many many many many + + + align:start position:0% +going to work or many many many many +different other things that you can find + + align:start position:0% +different other things that you can find + + + align:start position:0% +different other things that you can find +in problem on zorg okay so like I said + + align:start position:0% +in problem on zorg okay so like I said + + + align:start position:0% +in problem on zorg okay so like I said +the what we know is the condition and if + + align:start position:0% +the what we know is the condition and if + + + align:start position:0% +the what we know is the condition and if +you saw the condition to true that's a + + align:start position:0% +you saw the condition to true that's a + + + align:start position:0% +you saw the condition to true that's a +sampling from the generative model + + align:start position:0% +sampling from the generative model + + + align:start position:0% +sampling from the generative model +because you're always you're always + + align:start position:0% +because you're always you're always + + + align:start position:0% +because you're always you're always +going to evaluate as a true now how + + align:start position:0% +going to evaluate as a true now how + + + align:start position:0% +going to evaluate as a true now how +could you possibly implement this sort + + align:start position:0% +could you possibly implement this sort + + + align:start position:0% +could you possibly implement this sort +of magical procedure so how could you + + align:start position:0% +of magical procedure so how could you + + + align:start position:0% +of magical procedure so how could you +take some probability distribution and + + align:start position:0% +take some probability distribution and + + + align:start position:0% +take some probability distribution and +change it into a different probability + + align:start position:0% +change it into a different probability + + + align:start position:0% +change it into a different probability +distribution that does what you want it + + align:start position:0% +distribution that does what you want it + + + align:start position:0% +distribution that does what you want it +to do okay and the way that you would do + + align:start position:0% +to do okay and the way that you would do + + + align:start position:0% +to do okay and the way that you would do +that there are many many different ways + + align:start position:0% +that there are many many different ways + + + align:start position:0% +that there are many many different ways +of doing that but the easiest way of + + align:start position:0% +of doing that but the easiest way of + + + align:start position:0% +of doing that but the easiest way of +doing that is by something called + + align:start position:0% +doing that is by something called + + + align:start position:0% +doing that is by something called +rejection query and rejection query how + + align:start position:0% +rejection query and rejection query how + + + align:start position:0% +rejection query and rejection query how +many of you have know about rejection + + align:start position:0% +many of you have know about rejection + + + align:start position:0% +many of you have know about rejection +sampling how many of you don't know + + align:start position:0% +sampling how many of you don't know + + + align:start position:0% +sampling how many of you don't know +about rejection sampling okay the way + + align:start position:0% +about rejection sampling okay the way + + + align:start position:0% +about rejection sampling okay the way +rejection sampling works is that I have + + align:start position:0% +rejection sampling works is that I have + + + align:start position:0% +rejection sampling works is that I have +some sort of distribution that I'm + + align:start position:0% +some sort of distribution that I'm + + + align:start position:0% +some sort of distribution that I'm +trying to sample from okay and suppose + + align:start position:0% +trying to sample from okay and suppose + + + align:start position:0% +trying to sample from okay and suppose +that it's really hard to sample from the + + align:start position:0% +that it's really hard to sample from the + + + align:start position:0% +that it's really hard to sample from the +distribution exactly okay so suppose + + align:start position:0% +distribution exactly okay so suppose + + + align:start position:0% +distribution exactly okay so suppose +let's say that my distribution is this + + align:start position:0% +let's say that my distribution is this + + + align:start position:0% +let's say that my distribution is this +circle okay and I can't for whatever + + align:start position:0% +circle okay and I can't for whatever + + + align:start position:0% +circle okay and I can't for whatever +reason it's really really hard to sample + + align:start position:0% +reason it's really really hard to sample + + + align:start position:0% +reason it's really really hard to sample +from that circle okay I don't want to + + align:start position:0% +from that circle okay I don't want to + + + align:start position:0% +from that circle okay I don't want to +try to define the the probability + + align:start position:0% +try to define the the probability + + + align:start position:0% +try to define the the probability +distribution that describes this circle + + align:start position:0% +distribution that describes this circle + + + align:start position:0% +distribution that describes this circle +it's really hard to sample from it this + + align:start position:0% +it's really hard to sample from it this + + + align:start position:0% +it's really hard to sample from it this +is trivial but there are probably + + align:start position:0% +is trivial but there are probably + + + align:start position:0% +is trivial but there are probably +distributions that are really hard to + + align:start position:0% +distributions that are really hard to + + + align:start position:0% +distributions that are really hard to +sample from okay what do you do + + align:start position:0% +sample from okay what do you do + + + align:start position:0% +sample from okay what do you do +you can constructively + + align:start position:0% +you can constructively + + + align:start position:0% +you can constructively +a single distribution that you can + + align:start position:0% +a single distribution that you can + + + align:start position:0% +a single distribution that you can +sample from let's say that it's really + + align:start position:0% +sample from let's say that it's really + + + align:start position:0% +sample from let's say that it's really +really simple for me to sample from a + + align:start position:0% +really simple for me to sample from a + + + align:start position:0% +really simple for me to sample from a +uniform square that encompasses this + + align:start position:0% +uniform square that encompasses this + + + align:start position:0% +uniform square that encompasses this +circle okay so now I have some + + align:start position:0% +circle okay so now I have some + + + align:start position:0% +circle okay so now I have some +probability distribution there's a + + align:start position:0% +probability distribution there's a + + + align:start position:0% +probability distribution there's a +uniform distribution over the square + + align:start position:0% +uniform distribution over the square + + + align:start position:0% +uniform distribution over the square +that I can sample from what does it mean + + align:start position:0% +that I can sample from what does it mean + + + align:start position:0% +that I can sample from what does it mean +I can sample from it it means each time + + align:start position:0% +I can sample from it it means each time + + + align:start position:0% +I can sample from it it means each time +I run a procedure I get some point in + + align:start position:0% +I run a procedure I get some point in + + + align:start position:0% +I run a procedure I get some point in +this square but I don't want the points + + align:start position:0% +this square but I don't want the points + + + align:start position:0% +this square but I don't want the points +from the square I want only points from + + align:start position:0% +from the square I want only points from + + + align:start position:0% +from the square I want only points from +the circle okay so what I would do is + + align:start position:0% +the circle okay so what I would do is + + + align:start position:0% +the circle okay so what I would do is +basically sample from the square and + + align:start position:0% +basically sample from the square and + + + align:start position:0% +basically sample from the square and +each time it falls outside the square + + align:start position:0% +each time it falls outside the square + + + align:start position:0% +each time it falls outside the square +I'm gonna say throw that out okay that's + + align:start position:0% +I'm gonna say throw that out okay that's + + + align:start position:0% +I'm gonna say throw that out okay that's +called rejection sampling because you + + align:start position:0% +called rejection sampling because you + + + align:start position:0% +called rejection sampling because you +sample from some sort of procedure that + + align:start position:0% +sample from some sort of procedure that + + + align:start position:0% +sample from some sort of procedure that +you know how to sample from then you + + align:start position:0% +you know how to sample from then you + + + align:start position:0% +you know how to sample from then you +check that sample and if that sample + + align:start position:0% +check that sample and if that sample + + + align:start position:0% +check that sample and if that sample +didn't meet your desire up you throw it + + align:start position:0% +didn't meet your desire up you throw it + + + align:start position:0% +didn't meet your desire up you throw it +away and what you're left with is the + + align:start position:0% +away and what you're left with is the + + + align:start position:0% +away and what you're left with is the +circle is the distribution that you're + + align:start position:0% +circle is the distribution that you're + + + align:start position:0% +circle is the distribution that you're +trying to get so it might be how what is + + align:start position:0% +trying to get so it might be how what is + + + align:start position:0% +trying to get so it might be how what is +the simple thing and what is the hard + + align:start position:0% +the simple thing and what is the hard + + + align:start position:0% +the simple thing and what is the hard +thing in what we're describing so far + + align:start position:0% +thing in what we're describing so far + + + align:start position:0% +thing in what we're describing so far +the simple thing is a generative model + + align:start position:0% +the simple thing is a generative model + + + align:start position:0% +the simple thing is a generative model +it's relatively easy to sample from the + + align:start position:0% +it's relatively easy to sample from the + + + align:start position:0% +it's relatively easy to sample from the +generative model we just wrote it down + + align:start position:0% +generative model we just wrote it down + + + align:start position:0% +generative model we just wrote it down +so we know how to sample from it but + + align:start position:0% +so we know how to sample from it but + + + align:start position:0% +so we know how to sample from it but +we're looking for something else we're + + align:start position:0% +we're looking for something else we're + + + align:start position:0% +we're looking for something else we're +looking for some sort of different + + align:start position:0% +looking for some sort of different + + + align:start position:0% +looking for some sort of different +program we're looking from some sort of + + align:start position:0% +program we're looking from some sort of + + + align:start position:0% +program we're looking from some sort of +setting of a program that would generate + + align:start position:0% +setting of a program that would generate + + + align:start position:0% +setting of a program that would generate +the data that I saw not just the + + align:start position:0% +the data that I saw not just the + + + align:start position:0% +the data that I saw not just the +generative note model that I wrote the + + align:start position:0% +generative note model that I wrote the + + + align:start position:0% +generative note model that I wrote the +way that we would do that is in + + align:start position:0% +way that we would do that is in + + + align:start position:0% +way that we would do that is in +rejection query we would sample from the + + align:start position:0% +rejection query we would sample from the + + + align:start position:0% +rejection query we would sample from the +generative model we would check does + + align:start position:0% +generative model we would check does + + + align:start position:0% +generative model we would check does +that fit what we know okay suppose I + + align:start position:0% +that fit what we know okay suppose I + + + align:start position:0% +that fit what we know okay suppose I +just sampled something and then I check + + align:start position:0% +just sampled something and then I check + + + align:start position:0% +just sampled something and then I check +does that apply to the condition that I + + align:start position:0% +does that apply to the condition that I + + + align:start position:0% +does that apply to the condition that I +want so let's say I have here a + + align:start position:0% +want so let's say I have here a + + + align:start position:0% +want so let's say I have here a +particular world that what it wants to + + align:start position:0% +particular world that what it wants to + + + align:start position:0% +particular world that what it wants to +do it's a sort of a silly world but + + align:start position:0% +do it's a sort of a silly world but + + + align:start position:0% +do it's a sort of a silly world but +let's just make sure it works given the + + align:start position:0% +let's just make sure it works given the + + + align:start position:0% +let's just make sure it works given the +last time okay so what I'm going to do + + align:start position:0% +last time okay so what I'm going to do + + + align:start position:0% +last time okay so what I'm going to do +is I'm going to describe a world in + + align:start position:0% +is I'm going to describe a world in + + + align:start position:0% +is I'm going to describe a world in +which there's Legolas Gimli and Aaron + + align:start position:0% +which there's Legolas Gimli and Aaron + + + align:start position:0% +which there's Legolas Gimli and Aaron +anyone get Lord of the Ring references + + align:start position:0% +anyone get Lord of the Ring references + + + align:start position:0% +anyone get Lord of the Ring references +or something like that okay each one of + + align:start position:0% +or something like that okay each one of + + + align:start position:0% +or something like that okay each one of +them is going to take out a particular + + align:start position:0% +them is going to take out a particular + + + align:start position:0% +them is going to take out a particular +number of orcs okay and let's say that + + align:start position:0% +number of orcs okay and let's say that + + + align:start position:0% +number of orcs okay and let's say that +my generative model is I don't know how + + align:start position:0% +my generative model is I don't know how + + + align:start position:0% +my generative model is I don't know how +many each one of them took out let's say + + align:start position:0% +many each one of them took out let's say + + + align:start position:0% +many each one of them took out let's say +that they take anything between 0 and 20 + + align:start position:0% +that they take anything between 0 and 20 + + + align:start position:0% +that they take anything between 0 and 20 +ok they're having a brawl each one of + + align:start position:0% +ok they're having a brawl each one of + + + align:start position:0% +ok they're having a brawl each one of +them is going to take out some one + + align:start position:0% +them is going to take out some one + + + align:start position:0% +them is going to take out some one +boards so we're going to define the + + align:start position:0% +boards so we're going to define the + + + align:start position:0% +boards so we're going to define the +orcs that legolas took out to some + + align:start position:0% +orcs that legolas took out to some + + + align:start position:0% +orcs that legolas took out to some +random integer 20 okay we're going to + + align:start position:0% +random integer 20 okay we're going to + + + align:start position:0% +random integer 20 okay we're going to +take Ghibli's the same a ones the same + + align:start position:0% +take Ghibli's the same a ones the same + + + align:start position:0% +take Ghibli's the same a ones the same +and now what we're interested in is how + + align:start position:0% +and now what we're interested in is how + + + align:start position:0% +and now what we're interested in is how +many and what we're going to also define + + align:start position:0% +many and what we're going to also define + + + align:start position:0% +many and what we're going to also define +the total number of orcs that they took + + align:start position:0% +the total number of orcs that they took + + + align:start position:0% +the total number of orcs that they took +out as just plus each one of these + + align:start position:0% +out as just plus each one of these + + + align:start position:0% +out as just plus each one of these +things okay so we're going to look at + + align:start position:0% +things okay so we're going to look at + + + align:start position:0% +things okay so we're going to look at +the pile of orcs that they took out in + + align:start position:0% +the pile of orcs that they took out in + + + align:start position:0% +the pile of orcs that they took out in +the end + + align:start position:0% +the end + + + align:start position:0% +the end +that's my generative model that's it + + align:start position:0% +that's my generative model that's it + + + align:start position:0% +that's my generative model that's it +what I'm going to wonder about is how + + align:start position:0% +what I'm going to wonder about is how + + + align:start position:0% +what I'm going to wonder about is how +many orcs that Gimli take out okay not + + align:start position:0% +many orcs that Gimli take out okay not + + + align:start position:0% +many orcs that Gimli take out okay not +knowing anything + + align:start position:0% +knowing anything + + + align:start position:0% +knowing anything +how many orcs did give me take out okay + + align:start position:0% +how many orcs did give me take out okay + + + align:start position:0% +how many orcs did give me take out okay +should we just switch to kill or + + align:start position:0% +should we just switch to kill or + + + align:start position:0% +should we just switch to kill or +something I feel bad for the orcs but + + align:start position:0% +something I feel bad for the orcs but + + + align:start position:0% +something I feel bad for the orcs but +okay + + align:start position:0% +okay + + + align:start position:0% +okay +how many orcs did Gimli take out well we + + align:start position:0% +how many orcs did Gimli take out well we + + + align:start position:0% +how many orcs did Gimli take out well we +don't know right we just said we don't + + align:start position:0% +don't know right we just said we don't + + + align:start position:0% +don't know right we just said we don't +know it's a random integer between 0 and + + align:start position:0% +know it's a random integer between 0 and + + + align:start position:0% +know it's a random integer between 0 and +20 it's anyone's guess if I just ran + + align:start position:0% +20 it's anyone's guess if I just ran + + + align:start position:0% +20 it's anyone's guess if I just ran +this model forward it would give me any + + align:start position:0% +this model forward it would give me any + + + align:start position:0% +this model forward it would give me any +number between 0 and 20 if I ran it a + + align:start position:0% +number between 0 and 20 if I ran it a + + + align:start position:0% +number between 0 and 20 if I ran it a +thousand times over to get a uniform + + align:start position:0% +thousand times over to get a uniform + + + align:start position:0% +thousand times over to get a uniform +distribution over 0 in 20 now I'm going + + align:start position:0% +distribution over 0 in 20 now I'm going + + + align:start position:0% +distribution over 0 in 20 now I'm going +to give you a condition it's a simple + + align:start position:0% +to give you a condition it's a simple + + + align:start position:0% +to give you a condition it's a simple +condition the total number of orcs that + + align:start position:0% +condition the total number of orcs that + + + align:start position:0% +condition the total number of orcs that +they all took out is greater than 45 + + align:start position:0% +they all took out is greater than 45 + + + align:start position:0% +they all took out is greater than 45 +okay altogether Gimli heroine Legolas + + align:start position:0% +okay altogether Gimli heroine Legolas + + + align:start position:0% +okay altogether Gimli heroine Legolas +took out more than 45 orcs ok now how + + align:start position:0% +took out more than 45 orcs ok now how + + + align:start position:0% +took out more than 45 orcs ok now how +many orcs do you think that Gimli took + + align:start position:0% +many orcs do you think that Gimli took + + + align:start position:0% +many orcs do you think that Gimli took +out ok + + align:start position:0% +out ok + + + align:start position:0% +out ok +now the point is that you would somehow + + align:start position:0% +now the point is that you would somehow + + + align:start position:0% +now the point is that you would somehow +shift your distribution right this is a + + align:start position:0% +shift your distribution right this is a + + + align:start position:0% +shift your distribution right this is a +very simple problem you could probably + + align:start position:0% +very simple problem you could probably + + + align:start position:0% +very simple problem you could probably +write it down on a notepad but you're + + align:start position:0% +write it down on a notepad but you're + + + align:start position:0% +write it down on a notepad but you're +trying to do the posterior of the number + + align:start position:0% +trying to do the posterior of the number + + + align:start position:0% +trying to do the posterior of the number +of words that Gimli took out given + + align:start position:0% +of words that Gimli took out given + + + align:start position:0% +of words that Gimli took out given +conditioned on the fact that all them + + align:start position:0% +conditioned on the fact that all them + + + align:start position:0% +conditioned on the fact that all them +together took out more than 45 is this + + align:start position:0% +together took out more than 45 is this + + + align:start position:0% +together took out more than 45 is this +making sense ok how would I write down + + align:start position:0% +making sense ok how would I write down + + + align:start position:0% +making sense ok how would I write down +that as a rejection query and without + + align:start position:0% +that as a rejection query and without + + + align:start position:0% +that as a rejection query and without +using anything without using any syntax + + align:start position:0% +using anything without using any syntax + + + align:start position:0% +using anything without using any syntax +that you haven't seen already ok without + + align:start position:0% +that you haven't seen already ok without + + + align:start position:0% +that you haven't seen already ok without +using anything like query yet I'm just + + align:start position:0% +using anything like query yet I'm just + + + align:start position:0% +using anything like query yet I'm just +going to use basically recursion to + + align:start position:0% +going to use basically recursion to + + + align:start position:0% +going to use basically recursion to +write down a rejection query for that ok + + align:start position:0% +write down a rejection query for that ok + + + align:start position:0% +write down a rejection query for that ok +and later on you can use the rejection + + align:start position:0% +and later on you can use the rejection + + + align:start position:0% +and later on you can use the rejection +query but what I would do is I would + + align:start position:0% +query but what I would do is I would + + + align:start position:0% +query but what I would do is I would +just say here's a procedure that's going + + align:start position:0% +just say here's a procedure that's going + + + align:start position:0% +just say here's a procedure that's going +to give me back the number of orcs that + + align:start position:0% +to give me back the number of orcs that + + + align:start position:0% +to give me back the number of orcs that +Gimli took out conditioned on it being + + align:start position:0% +Gimli took out conditioned on it being + + + align:start position:0% +Gimli took out conditioned on it being +more than 45 unconditioned on everyone + + align:start position:0% +more than 45 unconditioned on everyone + + + align:start position:0% +more than 45 unconditioned on everyone +taking out more than 45 so I just run I + + align:start position:0% +taking out more than 45 so I just run I + + + align:start position:0% +taking out more than 45 so I just run I +write down a particular generative model + + align:start position:0% +write down a particular generative model + + + align:start position:0% +write down a particular generative model +like I know that Legolas took out + + align:start position:0% +like I know that Legolas took out + + + align:start position:0% +like I know that Legolas took out +somewhere between 0 and 20 again they + + align:start position:0% +somewhere between 0 and 20 again they + + + align:start position:0% +somewhere between 0 and 20 again they +took out some routines there in 20 + + align:start position:0% +took out some routines there in 20 + + + align:start position:0% +took out some routines there in 20 +I went took out somewhere between 0 and + + align:start position:0% +I went took out somewhere between 0 and + + + align:start position:0% +I went took out somewhere between 0 and +20 and they all took out the number + + align:start position:0% +20 and they all took out the number + + + align:start position:0% +20 and they all took out the number +total orcs now I say this if the total + + align:start position:0% +total orcs now I say this if the total + + + align:start position:0% +total orcs now I say this if the total +number of orcs is greater than 45 + + align:start position:0% +number of orcs is greater than 45 + + + align:start position:0% +number of orcs is greater than 45 +that's a good sample right so I'm going + + align:start position:0% +that's a good sample right so I'm going + + + align:start position:0% +that's a good sample right so I'm going +to go through this I'm going to sample + + align:start position:0% +to go through this I'm going to sample + + + align:start position:0% +to go through this I'm going to sample +my program I'm going to get Gimli did I + + align:start position:0% +my program I'm going to get Gimli did I + + + align:start position:0% +my program I'm going to get Gimli did I +don't know 15 Legolas did 10 so now say + + align:start position:0% +don't know 15 Legolas did 10 so now say + + + align:start position:0% +don't know 15 Legolas did 10 so now say +Aaron did 20 or something like that so + + align:start position:0% +Aaron did 20 or something like that so + + + align:start position:0% +Aaron did 20 or something like that so +now we got to 45 okay is that a good + + align:start position:0% +now we got to 45 okay is that a good + + + align:start position:0% +now we got to 45 okay is that a good +world + + align:start position:0% +world + + + align:start position:0% +world +yes we're over 45 fine give me back + + align:start position:0% +yes we're over 45 fine give me back + + + align:start position:0% +yes we're over 45 fine give me back +whatever well it was forgive me I don't + + align:start position:0% +whatever well it was forgive me I don't + + + align:start position:0% +whatever well it was forgive me I don't +even know what it was give me that back + + align:start position:0% +even know what it was give me that back + + + align:start position:0% +even know what it was give me that back +okay suppose it didn't add up to 45 try + + align:start position:0% +okay suppose it didn't add up to 45 try + + + align:start position:0% +okay suppose it didn't add up to 45 try +again + + align:start position:0% +again + + + align:start position:0% +again +okay this is basically the circle and + + align:start position:0% +okay this is basically the circle and + + + align:start position:0% +okay this is basically the circle and +square example from before the if + + align:start position:0% +square example from before the if + + + align:start position:0% +square example from before the if +statement is telling us if this matches + + align:start position:0% +statement is telling us if this matches + + + align:start position:0% +statement is telling us if this matches +my condition sample randomly from the + + align:start position:0% +my condition sample randomly from the + + + align:start position:0% +my condition sample randomly from the +world sample from the square sample from + + align:start position:0% +world sample from the square sample from + + + align:start position:0% +world sample from the square sample from +the generative model if the thing that + + align:start position:0% +the generative model if the thing that + + + align:start position:0% +the generative model if the thing that +you got matches the condition that you + + align:start position:0% +you got matches the condition that you + + + align:start position:0% +you got matches the condition that you +want give me back the sample give me + + align:start position:0% +want give me back the sample give me + + + align:start position:0% +want give me back the sample give me +back that answer if it didn't try again + + align:start position:0% +back that answer if it didn't try again + + + align:start position:0% +back that answer if it didn't try again +okay and now if we do this and we repeat + + align:start position:0% +okay and now if we do this and we repeat + + + align:start position:0% +okay and now if we do this and we repeat +this procedure a thousand times then + + align:start position:0% +this procedure a thousand times then + + + align:start position:0% +this procedure a thousand times then +what we would do is that Gimli probably + + align:start position:0% +what we would do is that Gimli probably + + + align:start position:0% +what we would do is that Gimli probably +it's no longer uniform distribution it's + + align:start position:0% +it's no longer uniform distribution it's + + + align:start position:0% +it's no longer uniform distribution it's +greater than you know five or whatever + + align:start position:0% +greater than you know five or whatever + + + align:start position:0% +greater than you know five or whatever +it's going to be zero on that because if + + align:start position:0% +it's going to be zero on that because if + + + align:start position:0% +it's going to be zero on that because if +you didn't if you took out zero they're + + align:start position:0% +you didn't if you took out zero they're + + + align:start position:0% +you didn't if you took out zero they're +never gonna get to 45 right and it's + + align:start position:0% +never gonna get to 45 right and it's + + + align:start position:0% +never gonna get to 45 right and it's +probably going to be sort of skewed in + + align:start position:0% +probably going to be sort of skewed in + + + align:start position:0% +probably going to be sort of skewed in +this direction okay so that's the + + align:start position:0% +this direction okay so that's the + + + align:start position:0% +this direction okay so that's the +posterior distribution on how many orcs + + align:start position:0% +posterior distribution on how many orcs + + + align:start position:0% +posterior distribution on how many orcs +Gimli took you out conditioned on all of + + align:start position:0% +Gimli took you out conditioned on all of + + + align:start position:0% +Gimli took you out conditioned on all of +them taking out more than 45 that's + + align:start position:0% +them taking out more than 45 that's + + + align:start position:0% +them taking out more than 45 that's +amazing you guys you've just written + + align:start position:0% +amazing you guys you've just written + + + align:start position:0% +amazing you guys you've just written +down or if you just understood rejection + + align:start position:0% +down or if you just understood rejection + + + align:start position:0% +down or if you just understood rejection +query okay you've just written down in + + align:start position:0% +query okay you've just written down in + + + align:start position:0% +query okay you've just written down in +very few very simple lines of code a + + align:start position:0% +very few very simple lines of code a + + + align:start position:0% +very few very simple lines of code a +sampling with rejection and in fact you + + align:start position:0% +sampling with rejection and in fact you + + + align:start position:0% +sampling with rejection and in fact you +can define all of conditioning using + + align:start position:0% +can define all of conditioning using + + + align:start position:0% +can define all of conditioning using +this thing okay you don't have to get + + align:start position:0% +this thing okay you don't have to get + + + align:start position:0% +this thing okay you don't have to get +fancy with metropolis Hastings and + + align:start position:0% +fancy with metropolis Hastings and + + + align:start position:0% +fancy with metropolis Hastings and +things like that if you're just trying + + align:start position:0% +things like that if you're just trying + + + align:start position:0% +things like that if you're just trying +to sort of prove things if you're into + + align:start position:0% +to sort of prove things if you're into + + + align:start position:0% +to sort of prove things if you're into +computer science and things like that + + align:start position:0% +computer science and things like that + + + align:start position:0% +computer science and things like that +you can just define conditioning using + + align:start position:0% +you can just define conditioning using + + + align:start position:0% +you can just define conditioning using +this okay + + align:start position:0% +this okay + + + align:start position:0% +this okay +you're saying I have some probability + + align:start position:0% +you're saying I have some probability + + + align:start position:0% +you're saying I have some probability +distribution I'm trying to condition it + + align:start position:0% +distribution I'm trying to condition it + + + align:start position:0% +distribution I'm trying to condition it +I get a different probability + + align:start position:0% +I get a different probability + + + align:start position:0% +I get a different probability +distribution the posterior how + + align:start position:0% +distribution the posterior how + + + align:start position:0% +distribution the posterior how +well-behaved is it can I write it down + + align:start position:0% +well-behaved is it can I write it down + + + align:start position:0% +well-behaved is it can I write it down +things like that you can prove it all + + align:start position:0% +things like that you can prove it all + + + align:start position:0% +things like that you can prove it all +the sort of things that you want to + + align:start position:0% +the sort of things that you want to + + + align:start position:0% +the sort of things that you want to +prove you can prove using something like + + align:start position:0% +prove you can prove using something like + + + align:start position:0% +prove you can prove using something like +this construction okay why shouldn't you + + align:start position:0% +this construction okay why shouldn't you + + + align:start position:0% +this construction okay why shouldn't you +use that okay so you can do that if + + align:start position:0% +use that okay so you can do that if + + + align:start position:0% +use that okay so you can do that if +you're in the theoretical computer + + align:start position:0% +you're in the theoretical computer + + + align:start position:0% +you're in the theoretical computer +science what is bad about how rejection + + align:start position:0% +science what is bad about how rejection + + + align:start position:0% +science what is bad about how rejection +query can anyone does anyone know can + + align:start position:0% +query can anyone does anyone know can + + + align:start position:0% +query can anyone does anyone know can +guess sorry costly in what sense + + align:start position:0% +guess sorry costly in what sense + + + align:start position:0% +guess sorry costly in what sense +[Music] + + align:start position:0% + + + + align:start position:0% + +right exactly depending on the condition + + align:start position:0% +right exactly depending on the condition + + + align:start position:0% +right exactly depending on the condition +it might be a very very bad idea here I + + align:start position:0% +it might be a very very bad idea here I + + + align:start position:0% +it might be a very very bad idea here I +could sort of do the condition right + + align:start position:0% +could sort of do the condition right + + + align:start position:0% +could sort of do the condition right +because I ran the model forward and + + align:start position:0% +because I ran the model forward and + + + align:start position:0% +because I ran the model forward and +sometimes I goat over 45 so yeah why is + + align:start position:0% +sometimes I goat over 45 so yeah why is + + + align:start position:0% +sometimes I goat over 45 so yeah why is +rejection query is a particularly bad + + align:start position:0% +rejection query is a particularly bad + + + align:start position:0% +rejection query is a particularly bad +example because your condition might be + + align:start position:0% +example because your condition might be + + + align:start position:0% +example because your condition might be +really really really hard to satisfy + + align:start position:0% +really really really hard to satisfy + + + align:start position:0% +really really really hard to satisfy +okay so if for example I changed this to + + align:start position:0% +okay so if for example I changed this to + + + align:start position:0% +okay so if for example I changed this to +59 okay what will happen now we can sort + + align:start position:0% +59 okay what will happen now we can sort + + + align:start position:0% +59 okay what will happen now we can sort +of look at this or we can say you know I + + align:start position:0% +of look at this or we can say you know I + + + align:start position:0% +of look at this or we can say you know I +think because of the way I wrote this + + align:start position:0% +think because of the way I wrote this + + + align:start position:0% +think because of the way I wrote this +it'll never reach that but thanks for + + align:start position:0% +it'll never reach that but thanks for + + + align:start position:0% +it'll never reach that but thanks for +that point but suppose it was let's + + align:start position:0% +that point but suppose it was let's + + + align:start position:0% +that point but suppose it was let's +change this to this okay don't run this + + align:start position:0% +change this to this okay don't run this + + + align:start position:0% +change this to this okay don't run this +by the way because it will never stop + + align:start position:0% +by the way because it will never stop + + + align:start position:0% +by the way because it will never stop +but or it'll take a long time so now + + align:start position:0% +but or it'll take a long time so now + + + align:start position:0% +but or it'll take a long time so now +it's only going to be fulfilled if each + + align:start position:0% +it's only going to be fulfilled if each + + + align:start position:0% +it's only going to be fulfilled if each +one of them took out 20 orcs right they + + align:start position:0% +one of them took out 20 orcs right they + + + align:start position:0% +one of them took out 20 orcs right they +would only to take out 20 orcs for the + + align:start position:0% +would only to take out 20 orcs for the + + + align:start position:0% +would only to take out 20 orcs for the +total number of orcs to be equal to 60 + + align:start position:0% +total number of orcs to be equal to 60 + + + align:start position:0% +total number of orcs to be equal to 60 +yes + + align:start position:0% +yes + + + align:start position:0% +yes +when is that going to happen it's going + + align:start position:0% +when is that going to happen it's going + + + align:start position:0% +when is that going to happen it's going +to happen one in 20 times one in 20 + + align:start position:0% +to happen one in 20 times one in 20 + + + align:start position:0% +to happen one in 20 times one in 20 +times one in twenty you're going to + + align:start position:0% +times one in twenty you're going to + + + align:start position:0% +times one in twenty you're going to +waste a lot of tons a lot of samples on + + align:start position:0% +waste a lot of tons a lot of samples on + + + align:start position:0% +waste a lot of tons a lot of samples on +something that's never going to happen + + align:start position:0% +something that's never going to happen + + + align:start position:0% +something that's never going to happen +and it doesn't even matter that much + + align:start position:0% +and it doesn't even matter that much + + + align:start position:0% +and it doesn't even matter that much +okay so and you can easily look at this + + align:start position:0% +okay so and you can easily look at this + + + align:start position:0% +okay so and you can easily look at this +and you can sort of say well obviously + + align:start position:0% +and you can sort of say well obviously + + + align:start position:0% +and you can sort of say well obviously +you Gimli took out more than this + + align:start position:0% +you Gimli took out more than this + + + align:start position:0% +you Gimli took out more than this +because I can you know I'm not a program + + align:start position:0% +because I can you know I'm not a program + + + align:start position:0% +because I can you know I'm not a program +and I can figure it out but oftentimes + + align:start position:0% +and I can figure it out but oftentimes + + + align:start position:0% +and I can figure it out but oftentimes +you will find that you can't exactly say + + align:start position:0% +you will find that you can't exactly say + + + align:start position:0% +you will find that you can't exactly say +you know you look at some convoluted + + align:start position:0% +you know you look at some convoluted + + + align:start position:0% +you know you look at some convoluted +program and you won't exactly know how + + align:start position:0% +program and you won't exactly know how + + + align:start position:0% +program and you won't exactly know how +this should look or whether it's easy or + + align:start position:0% +this should look or whether it's easy or + + + align:start position:0% +this should look or whether it's easy or +whether it's hard but in that sense + + align:start position:0% +whether it's hard but in that sense + + + align:start position:0% +whether it's hard but in that sense +rejection query is probably a bad idea + + align:start position:0% +rejection query is probably a bad idea + + + align:start position:0% +rejection query is probably a bad idea +another example of why it's a bad idea + + align:start position:0% +another example of why it's a bad idea + + + align:start position:0% +another example of why it's a bad idea +is something like precision so let's see + + align:start position:0% +is something like precision so let's see + + + align:start position:0% +is something like precision so let's see +don't run this because it'll take + + align:start position:0% +don't run this because it'll take + + + align:start position:0% +don't run this because it'll take +forever let's do an estimate of Pi and + + align:start position:0% +forever let's do an estimate of Pi and + + + align:start position:0% +forever let's do an estimate of Pi and +again I was sort of going to give this + + align:start position:0% +again I was sort of going to give this + + + align:start position:0% +again I was sort of going to give this +as an exercise but since we don't have a + + align:start position:0% +as an exercise but since we don't have a + + + align:start position:0% +as an exercise but since we don't have a +lot of time here's one thing that you + + align:start position:0% +lot of time here's one thing that you + + + align:start position:0% +lot of time here's one thing that you +could do with rejection query or you + + align:start position:0% +could do with rejection query or you + + + align:start position:0% +could do with rejection query or you +could do with any sort of query okay you + + align:start position:0% +could do with any sort of query okay you + + + align:start position:0% +could do with any sort of query okay you +could try to estimate pipe okay + + align:start position:0% +could try to estimate pipe okay + + + align:start position:0% +could try to estimate pipe okay +literally using that example that I just + + align:start position:0% +literally using that example that I just + + + align:start position:0% +literally using that example that I just +did you could try to say okay sample + + align:start position:0% +did you could try to say okay sample + + + align:start position:0% +did you could try to say okay sample +from some square only except the X's + + align:start position:0% +from some square only except the X's + + + align:start position:0% +from some square only except the X's +that are in the circle and then sort of + + align:start position:0% +that are in the circle and then sort of + + + align:start position:0% +that are in the circle and then sort of +try to estimate how many samples you've + + align:start position:0% +try to estimate how many samples you've + + + align:start position:0% +try to estimate how many samples you've +got in the circle out of the total + + align:start position:0% +got in the circle out of the total + + + align:start position:0% +got in the circle out of the total +number of samples you took so run a + + align:start position:0% +number of samples you took so run a + + + align:start position:0% +number of samples you took so run a +thousand samples and see how many of + + align:start position:0% +thousand samples and see how many of + + + align:start position:0% +thousand samples and see how many of +those following the square and if you + + align:start position:0% +those following the square and if you + + + align:start position:0% +those following the square and if you +run a thousand you'll get three points + + align:start position:0% +run a thousand you'll get three points + + + align:start position:0% +run a thousand you'll get three points +something you can try this III did as an + + align:start position:0% +something you can try this III did as an + + + align:start position:0% +something you can try this III did as an +exercise for you you can see I sort of + + align:start position:0% +exercise for you you can see I sort of + + + align:start position:0% +exercise for you you can see I sort of +set up some of the syntax if you want to + + align:start position:0% +set up some of the syntax if you want to + + + align:start position:0% +set up some of the syntax if you want to +try this out later please do you run + + align:start position:0% +try this out later please do you run + + + align:start position:0% +try this out later please do you run +10,000 samples it's like 3.1 I think if + + align:start position:0% +10,000 samples it's like 3.1 I think if + + + align:start position:0% +10,000 samples it's like 3.1 I think if +you do 100,000 to probably do 3.14 maybe + + align:start position:0% +you do 100,000 to probably do 3.14 maybe + + + align:start position:0% +you do 100,000 to probably do 3.14 maybe +not that much better like a hundred + + align:start position:0% +not that much better like a hundred + + + align:start position:0% +not that much better like a hundred +thousand samples seriously to get 3.14 + + align:start position:0% +thousand samples seriously to get 3.14 + + + align:start position:0% +thousand samples seriously to get 3.14 +we all know it's 3.1415 like sometimes + + align:start position:0% +we all know it's 3.1415 like sometimes + + + align:start position:0% +we all know it's 3.1415 like sometimes +if you can use math you should use math + + align:start position:0% +if you can use math you should use math + + + align:start position:0% +if you can use math you should use math +in some cases on the other hand this is + + align:start position:0% +in some cases on the other hand this is + + + align:start position:0% +in some cases on the other hand this is +by the way about a reason why you should + + align:start position:0% +by the way about a reason why you should + + + align:start position:0% +by the way about a reason why you should +probably not use query in general when + + align:start position:0% +probably not use query in general when + + + align:start position:0% +probably not use query in general when +you can use math or not use sampling + + align:start position:0% +you can use math or not use sampling + + + align:start position:0% +you can use math or not use sampling +sorry we can solve it analytically if + + align:start position:0% +sorry we can solve it analytically if + + + align:start position:0% +sorry we can solve it analytically if +you're interested in precision and + + align:start position:0% +you're interested in precision and + + + align:start position:0% +you're interested in precision and +things like that but suppose you're not + + align:start position:0% +things like that but suppose you're not + + + align:start position:0% +things like that but suppose you're not +interested in precision I'm actually + + align:start position:0% +interested in precision I'm actually + + + align:start position:0% +interested in precision I'm actually +going to try and and help that so you + + align:start position:0% +going to try and and help that so you + + + align:start position:0% +going to try and and help that so you +can actually get a pretty good estimate + + align:start position:0% +can actually get a pretty good estimate + + + align:start position:0% +can actually get a pretty good estimate +from about ten samples right if you just + + align:start position:0% +from about ten samples right if you just + + + align:start position:0% +from about ten samples right if you just +do ten samples on this thing you'll + + align:start position:0% +do ten samples on this thing you'll + + + align:start position:0% +do ten samples on this thing you'll +probably hit something like three as an + + align:start position:0% +probably hit something like three as an + + + align:start position:0% +probably hit something like three as an +estimate you can probably you can do the + + align:start position:0% +estimate you can probably you can do the + + + align:start position:0% +estimate you can probably you can do the +histogram for where it will fall or fall + + align:start position:0% +histogram for where it will fall or fall + + + align:start position:0% +histogram for where it will fall or fall +between two most of the samples like 70% + + align:start position:0% +between two most of the samples like 70% + + + align:start position:0% +between two most of the samples like 70% +of the samples are fall between 2.8 and + + align:start position:0% +of the samples are fall between 2.8 and + + + align:start position:0% +of the samples are fall between 2.8 and +3.6 if that's all you care about and + + align:start position:0% +3.6 if that's all you care about and + + + align:start position:0% +3.6 if that's all you care about and +that way it might be what all your + + align:start position:0% +that way it might be what all your + + + align:start position:0% +that way it might be what all your +vision system cares about or you know + + align:start position:0% +vision system cares about or you know + + + align:start position:0% +vision system cares about or you know +different things that might require + + align:start position:0% +different things that might require + + + align:start position:0% +different things that might require +sampling then that's fine and I'm not + + align:start position:0% +sampling then that's fine and I'm not + + + align:start position:0% +sampling then that's fine and I'm not +going to go too much into this because + + align:start position:0% +going to go too much into this because + + + align:start position:0% +going to go too much into this because +like I said the dream of Kabbalistic + + align:start position:0% +like I said the dream of Kabbalistic + + + align:start position:0% +like I said the dream of Kabbalistic +programming is sort of to free you from + + align:start position:0% +programming is sort of to free you from + + + align:start position:0% +programming is sort of to free you from +thinking too much about the sampling but + + align:start position:0% +thinking too much about the sampling but + + + align:start position:0% +thinking too much about the sampling but +those of you that are interested in + + align:start position:0% +those of you that are interested in + + + align:start position:0% +those of you that are interested in +sampling that are interested in + + align:start position:0% +sampling that are interested in + + + align:start position:0% +sampling that are interested in +algorithmic learning and things like + + align:start position:0% +algorithmic learning and things like + + + align:start position:0% +algorithmic learning and things like +that there's been a lot of research on + + align:start position:0% +that there's been a lot of research on + + + align:start position:0% +that there's been a lot of research on +exactly that when are we okay with just + + align:start position:0% +exactly that when are we okay with just + + + align:start position:0% +exactly that when are we okay with just +taking one sample we write down some + + align:start position:0% +taking one sample we write down some + + + align:start position:0% +taking one sample we write down some +sort of model and we see how well the + + align:start position:0% +sort of model and we see how well the + + + align:start position:0% +sort of model and we see how well the +model does by taking one sample ten + + align:start position:0% +model does by taking one sample ten + + + align:start position:0% +model does by taking one sample ten +samples what's the precision that you + + align:start position:0% +samples what's the precision that you + + + align:start position:0% +samples what's the precision that you +can get and does a precision match + + align:start position:0% +can get and does a precision match + + + align:start position:0% +can get and does a precision match +people trying to perform a similar task + + align:start position:0% +people trying to perform a similar task + + + align:start position:0% +people trying to perform a similar task +of estimating that thing + + align:start position:0% +of estimating that thing + + + align:start position:0% +of estimating that thing +again like the sampling hypothesis not + + align:start position:0% +again like the sampling hypothesis not + + + align:start position:0% +again like the sampling hypothesis not +sampling hypothesis for neuron sampling + + align:start position:0% +sampling hypothesis for neuron sampling + + + align:start position:0% +sampling hypothesis for neuron sampling +hypothesis for the way people answer + + align:start position:0% +hypothesis for the way people answer + + + align:start position:0% +hypothesis for the way people answer +questions is that they sample one or two + + align:start position:0% +questions is that they sample one or two + + + align:start position:0% +questions is that they sample one or two +or a few a number of points from their + + align:start position:0% +or a few a number of points from their + + + align:start position:0% +or a few a number of points from their +generative model not that many and you + + align:start position:0% +generative model not that many and you + + + align:start position:0% +generative model not that many and you +can sort of see the claim is that you + + align:start position:0% +can sort of see the claim is that you + + + align:start position:0% +can sort of see the claim is that you +can sort of see that they get better + + align:start position:0% +can sort of see that they get better + + + align:start position:0% +can sort of see that they get better +with time that they probably don't take + + align:start position:0% +with time that they probably don't take + + + align:start position:0% +with time that they probably don't take +that much if you give them more time to + + align:start position:0% +that much if you give them more time to + + + align:start position:0% +that much if you give them more time to +think it looks a bit like a sampling + + align:start position:0% +think it looks a bit like a sampling + + + align:start position:0% +think it looks a bit like a sampling +procedure that takes more samples and it + + align:start position:0% +procedure that takes more samples and it + + + align:start position:0% +procedure that takes more samples and it +seems like you can get away with quite a + + align:start position:0% +seems like you can get away with quite a + + + align:start position:0% +seems like you can get away with quite a +lot if you just do ten samples or + + align:start position:0% +lot if you just do ten samples or + + + align:start position:0% +lot if you just do ten samples or +hundred samples for pie and there's this + + align:start position:0% +hundred samples for pie and there's this + + + align:start position:0% +hundred samples for pie and there's this +xkcd cartoon that I quite like which is + + align:start position:0% +xkcd cartoon that I quite like which is + + + align:start position:0% +xkcd cartoon that I quite like which is +this is the way fizzy sorry not xxxx CD + + align:start position:0% +this is the way fizzy sorry not xxxx CD + + + align:start position:0% +this is the way fizzy sorry not xxxx CD +it's SMBC + + align:start position:0% +it's SMBC + + + align:start position:0% +it's SMBC +cartoon which is unlike why shouldn't + + align:start position:0% +cartoon which is unlike why shouldn't + + + align:start position:0% +cartoon which is unlike why shouldn't +physicists teach geometry and they're + + align:start position:0% +physicists teach geometry and they're + + + align:start position:0% +physicists teach geometry and they're +like well you know how do I remember the + + align:start position:0% +like well you know how do I remember the + + + align:start position:0% +like well you know how do I remember the +number the number pi the value of pi + + align:start position:0% +number the number pi the value of pi + + + align:start position:0% +number the number pi the value of pi +it's quite simple I look at my fingers + + align:start position:0% +it's quite simple I look at my fingers + + + align:start position:0% +it's quite simple I look at my fingers +and there's five of them and that's + + align:start position:0% +and there's five of them and that's + + + align:start position:0% +and there's five of them and that's +about pi yeah what else could we do if + + align:start position:0% +about pi yeah what else could we do if + + + align:start position:0% +about pi yeah what else could we do if +we don't want to use rejection query if + + align:start position:0% +we don't want to use rejection query if + + + align:start position:0% +we don't want to use rejection query if +we don't want to use a rejection + + align:start position:0% +we don't want to use a rejection + + + align:start position:0% +we don't want to use a rejection +sampling suppose we don't we probably + + align:start position:0% +sampling suppose we don't we probably + + + align:start position:0% +sampling suppose we don't we probably +don't we could try to do exhaustive + + align:start position:0% +don't we could try to do exhaustive + + + align:start position:0% +don't we could try to do exhaustive +enumeration if our model is small enough + + align:start position:0% +enumeration if our model is small enough + + + align:start position:0% +enumeration if our model is small enough +we can just consider all the + + align:start position:0% +we can just consider all the + + + align:start position:0% +we can just consider all the +possibilities and explicitly score them + + align:start position:0% +possibilities and explicitly score them + + + align:start position:0% +possibilities and explicitly score them +the other thing that we can do is + + align:start position:0% +the other thing that we can do is + + + align:start position:0% +the other thing that we can do is +something like metropolis Hastings how + + align:start position:0% +something like metropolis Hastings how + + + align:start position:0% +something like metropolis Hastings how +many of you are familiar with metropolis + + align:start position:0% +many of you are familiar with metropolis + + + align:start position:0% +many of you are familiar with metropolis +Hastings okay well why don't we raise + + align:start position:0% +Hastings okay well why don't we raise + + + align:start position:0% +Hastings okay well why don't we raise +our hands that the degree that we are + + align:start position:0% +our hands that the degree that we are + + + align:start position:0% +our hands that the degree that we are +familiar with the metropolis Hastings + + align:start position:0% +familiar with the metropolis Hastings + + + align:start position:0% +familiar with the metropolis Hastings +we're here is like really familiar + + align:start position:0% +we're here is like really familiar + + + align:start position:0% +we're here is like really familiar +here's not true okay metropolis Hastings + + align:start position:0% +here's not true okay metropolis Hastings + + + align:start position:0% +here's not true okay metropolis Hastings +I'm not going to go too much into the + + align:start position:0% +I'm not going to go too much into the + + + align:start position:0% +I'm not going to go too much into the +details I'll just be doing it a + + align:start position:0% +details I'll just be doing it a + + + align:start position:0% +details I'll just be doing it a +disservice but the way to think about it + + align:start position:0% +disservice but the way to think about it + + + align:start position:0% +disservice but the way to think about it +is to say instead of just sampling at + + align:start position:0% +is to say instead of just sampling at + + + align:start position:0% +is to say instead of just sampling at +random from the entire space of things + + align:start position:0% +random from the entire space of things + + + align:start position:0% +random from the entire space of things +that could be really really bad + + align:start position:0% +that could be really really bad + + + align:start position:0% +that could be really really bad +equally I'm going to try and sample from + + align:start position:0% +equally I'm going to try and sample from + + + align:start position:0% +equally I'm going to try and sample from +something that I think is likely to be + + align:start position:0% +something that I think is likely to be + + + align:start position:0% +something that I think is likely to be +good okay and the way I'm going to do + + align:start position:0% +good okay and the way I'm going to do + + + align:start position:0% +good okay and the way I'm going to do +that is I'm going to construct basically + + align:start position:0% +that is I'm going to construct basically + + + align:start position:0% +that is I'm going to construct basically +what's the best way sorry to explain + + align:start position:0% +what's the best way sorry to explain + + + align:start position:0% +what's the best way sorry to explain +this is to say I am I am in a particular + + align:start position:0% +this is to say I am I am in a particular + + + align:start position:0% +this is to say I am I am in a particular +point in the space okay I've got my + + align:start position:0% +point in the space okay I've got my + + + align:start position:0% +point in the space okay I've got my +sample I already have it what should I + + align:start position:0% +sample I already have it what should I + + + align:start position:0% +sample I already have it what should I +do now rejection sampling just says well + + align:start position:0% +do now rejection sampling just says well + + + align:start position:0% +do now rejection sampling just says well +just sample another one from the + + align:start position:0% +just sample another one from the + + + align:start position:0% +just sample another one from the +generative model right and see if that + + align:start position:0% +generative model right and see if that + + + align:start position:0% +generative model right and see if that +works that's a bad idea well you should + + align:start position:0% +works that's a bad idea well you should + + + align:start position:0% +works that's a bad idea well you should +actually do is try to use the sample + + align:start position:0% +actually do is try to use the sample + + + align:start position:0% +actually do is try to use the sample +that you already have and how good it is + + align:start position:0% +that you already have and how good it is + + + align:start position:0% +that you already have and how good it is +as + + align:start position:0% +as + + + align:start position:0% +as +to inform your next move so now what + + align:start position:0% +to inform your next move so now what + + + align:start position:0% +to inform your next move so now what +you're going to do is you're in this + + align:start position:0% +you're going to do is you're in this + + + align:start position:0% +you're going to do is you're in this +particular point in space and you're + + align:start position:0% +particular point in space and you're + + + align:start position:0% +particular point in space and you're +going to move to a different point in + + align:start position:0% +going to move to a different point in + + + align:start position:0% +going to move to a different point in +space that depends on the point that you + + align:start position:0% +space that depends on the point that you + + + align:start position:0% +space that depends on the point that you +are now so for example if you're in some + + align:start position:0% +are now so for example if you're in some + + + align:start position:0% +are now so for example if you're in some +2-dimensional space and you're over here + + align:start position:0% +2-dimensional space and you're over here + + + align:start position:0% +2-dimensional space and you're over here +you're not going to sample from this + + align:start position:0% +you're not going to sample from this + + + align:start position:0% +you're not going to sample from this +square you're going to sample from a + + align:start position:0% +square you're going to sample from a + + + align:start position:0% +square you're going to sample from a +point next to it + + align:start position:0% +point next to it + + + align:start position:0% +point next to it +what's it that's your proposal okay the + + align:start position:0% +what's it that's your proposal okay the + + + align:start position:0% +what's it that's your proposal okay the +way that you sample is called you sample + + align:start position:0% +way that you sample is called you sample + + + align:start position:0% +way that you sample is called you sample +according to your proposal distribution + + align:start position:0% +according to your proposal distribution + + + align:start position:0% +according to your proposal distribution +your proposal distribution tells you + + align:start position:0% +your proposal distribution tells you + + + align:start position:0% +your proposal distribution tells you +where you should sample next okay so + + align:start position:0% +where you should sample next okay so + + + align:start position:0% +where you should sample next okay so +you're here in the space of all possible + + align:start position:0% +you're here in the space of all possible + + + align:start position:0% +you're here in the space of all possible +programs or your theory space metropolis + + align:start position:0% +programs or your theory space metropolis + + + align:start position:0% +programs or your theory space metropolis +Hastings is more than just programs + + align:start position:0% +Hastings is more than just programs + + + align:start position:0% +Hastings is more than just programs +right anything you're in the space of + + align:start position:0% +right anything you're in the space of + + + align:start position:0% +right anything you're in the space of +possible things they're trying to sample + + align:start position:0% +possible things they're trying to sample + + + align:start position:0% +possible things they're trying to sample +from you're here you got one sample and + + align:start position:0% +from you're here you got one sample and + + + align:start position:0% +from you're here you got one sample and +now you're sort of looking around and + + align:start position:0% +now you're sort of looking around and + + + align:start position:0% +now you're sort of looking around and +you take another sample you do that + + align:start position:0% +you take another sample you do that + + + align:start position:0% +you take another sample you do that +according to your proposal distribution + + align:start position:0% +according to your proposal distribution + + + align:start position:0% +according to your proposal distribution +you jump there and you evaluate this + + align:start position:0% +you jump there and you evaluate this + + + align:start position:0% +you jump there and you evaluate this +point and the way that you evaluate it + + align:start position:0% +point and the way that you evaluate it + + + align:start position:0% +point and the way that you evaluate it +is you just look how well does this + + align:start position:0% +is you just look how well does this + + + align:start position:0% +is you just look how well does this +thing fit the data okay and we can get + + align:start position:0% +thing fit the data okay and we can get + + + align:start position:0% +thing fit the data okay and we can get +into that but the ways you sort of you + + align:start position:0% +into that but the ways you sort of you + + + align:start position:0% +into that but the ways you sort of you +score your model according to the data + + align:start position:0% +score your model according to the data + + + align:start position:0% +score your model according to the data +and you say well this one fits the data + + align:start position:0% +and you say well this one fits the data + + + align:start position:0% +and you say well this one fits the data +pretty well how well does this one fit + + align:start position:0% +pretty well how well does this one fit + + + align:start position:0% +pretty well how well does this one fit +the data + + align:start position:0% +the data + + + align:start position:0% +the data +not so great so I should probably move + + align:start position:0% +not so great so I should probably move + + + align:start position:0% +not so great so I should probably move +over there okay I should move to that + + align:start position:0% +over there okay I should move to that + + + align:start position:0% +over there okay I should move to that +point in program space I'm gonna move + + align:start position:0% +point in program space I'm gonna move + + + align:start position:0% +point in program space I'm gonna move +over here okay now I sample another + + align:start position:0% +over here okay now I sample another + + + align:start position:0% +over here okay now I sample another +point I go over here how well does this + + align:start position:0% +point I go over here how well does this + + + align:start position:0% +point I go over here how well does this +do not as great but I might still accept + + align:start position:0% +do not as great but I might still accept + + + align:start position:0% +do not as great but I might still accept +it okay the point is you're going to + + align:start position:0% +it okay the point is you're going to + + + align:start position:0% +it okay the point is you're going to +accept and reject new points new + + align:start position:0% +accept and reject new points new + + + align:start position:0% +accept and reject new points new +executions of the program according to + + align:start position:0% +executions of the program according to + + + align:start position:0% +executions of the program according to +how well they predict the data according + + align:start position:0% +how well they predict the data according + + + align:start position:0% +how well they predict the data according +to how well they answer the condition if + + align:start position:0% +to how well they answer the condition if + + + align:start position:0% +to how well they answer the condition if +the condition is a simple true/false + + align:start position:0% +the condition is a simple true/false + + + align:start position:0% +the condition is a simple true/false +that just means that you have an + + align:start position:0% +that just means that you have an + + + align:start position:0% +that just means that you have an +absolute yes or no but many of these + + align:start position:0% +absolute yes or no but many of these + + + align:start position:0% +absolute yes or no but many of these +conditions are going to be something + + align:start position:0% +conditions are going to be something + + + align:start position:0% +conditions are going to be something +like well it's good if it matches it you + + align:start position:0% +like well it's good if it matches it you + + + align:start position:0% +like well it's good if it matches it you +know you get some likelihood you get + + align:start position:0% +know you get some likelihood you get + + + align:start position:0% +know you get some likelihood you get +some score from the likelihood and the + + align:start position:0% +some score from the likelihood and the + + + align:start position:0% +some score from the likelihood and the +prior so you can score this new point in + + align:start position:0% +prior so you can score this new point in + + + align:start position:0% +prior so you can score this new point in +program space and either accept or + + align:start position:0% +program space and either accept or + + + align:start position:0% +program space and either accept or +reject it and this thing of moving + + align:start position:0% +reject it and this thing of moving + + + align:start position:0% +reject it and this thing of moving +around in program space and sampling + + align:start position:0% +around in program space and sampling + + + align:start position:0% +around in program space and sampling +according to some new proposal + + align:start position:0% +according to some new proposal + + + align:start position:0% +according to some new proposal +distribution and accepting or rejecting + + align:start position:0% +distribution and accepting or rejecting + + + align:start position:0% +distribution and accepting or rejecting +and moving around like that is a lot + + align:start position:0% +and moving around like that is a lot + + + align:start position:0% +and moving around like that is a lot +more efficient in most cases than + + align:start position:0% +more efficient in most cases than + + + align:start position:0% +more efficient in most cases than +rejection sampling and in the limit if + + align:start position:0% +rejection sampling and in the limit if + + + align:start position:0% +rejection sampling and in the limit if +you keep on doing this if you keep on + + align:start position:0% +you keep on doing this if you keep on + + + align:start position:0% +you keep on doing this if you keep on +walking around walking around taking + + align:start position:0% +walking around walking around taking + + + align:start position:0% +walking around walking around taking +samples accepting or rejecting them + + align:start position:0% +samples accepting or rejecting them + + + align:start position:0% +samples accepting or rejecting them +depending on how well this new + + align:start position:0% +depending on how well this new + + + align:start position:0% +depending on how well this new +point in program space does what you'll + + align:start position:0% +point in program space does what you'll + + + align:start position:0% +point in program space does what you'll +end up with is the posterior + + align:start position:0% +end up with is the posterior + + + align:start position:0% +end up with is the posterior +distribution that you're trying to + + align:start position:0% +distribution that you're trying to + + + align:start position:0% +distribution that you're trying to +sample from okay and I should say like + + align:start position:0% +sample from okay and I should say like + + + align:start position:0% +sample from okay and I should say like +what is the point in program space it + + align:start position:0% +what is the point in program space it + + + align:start position:0% +what is the point in program space it +just means like a program that I have + + align:start position:0% +just means like a program that I have + + + align:start position:0% +just means like a program that I have +completely evaluated like in the case of + + align:start position:0% +completely evaluated like in the case of + + + align:start position:0% +completely evaluated like in the case of +the London bombing it would be the + + align:start position:0% +the London bombing it would be the + + + align:start position:0% +the London bombing it would be the +center what I have two gaussians and + + align:start position:0% +center what I have two gaussians and + + + align:start position:0% +center what I have two gaussians and +this one's center is here and this one + + align:start position:0% +this one's center is here and this one + + + align:start position:0% +this one's center is here and this one +Center is here I've sort of walked + + align:start position:0% +Center is here I've sort of walked + + + align:start position:0% +Center is here I've sort of walked +through all the things that I can sample + + align:start position:0% +through all the things that I can sample + + + align:start position:0% +through all the things that I can sample +I've gotten one particular run of the + + align:start position:0% +I've gotten one particular run of the + + + align:start position:0% +I've gotten one particular run of the +program okay and I try to move to + + align:start position:0% +program okay and I try to move to + + + align:start position:0% +program okay and I try to move to +somewhere else like I might change the + + align:start position:0% +somewhere else like I might change the + + + align:start position:0% +somewhere else like I might change the +center of this Gaussian or I might say + + align:start position:0% +center of this Gaussian or I might say + + + align:start position:0% +center of this Gaussian or I might say +well you know what actually there aren't + + align:start position:0% +well you know what actually there aren't + + + align:start position:0% +well you know what actually there aren't +two gaussians there's let's run it again + + align:start position:0% +two gaussians there's let's run it again + + + align:start position:0% +two gaussians there's let's run it again +let's both point again there is actually + + align:start position:0% +let's both point again there is actually + + + align:start position:0% +let's both point again there is actually +ten okay so what I do the way I changed + + align:start position:0% +ten okay so what I do the way I changed + + + align:start position:0% +ten okay so what I do the way I changed +the way I move around in program space + + align:start position:0% +the way I move around in program space + + + align:start position:0% +the way I move around in program space +is to go to a particular point along the + + align:start position:0% +is to go to a particular point along the + + + align:start position:0% +is to go to a particular point along the +tree of the evaluation and say what if I + + align:start position:0% +tree of the evaluation and say what if I + + + align:start position:0% +tree of the evaluation and say what if I +change that + + align:start position:0% +change that + + + align:start position:0% +change that +what would I end up with a sort of + + align:start position:0% +what would I end up with a sort of + + + align:start position:0% +what would I end up with a sort of +resample okay and i resample i end up + + align:start position:0% +resample okay and i resample i end up + + + align:start position:0% +resample okay and i resample i end up +with some other program and I basically + + align:start position:0% +with some other program and I basically + + + align:start position:0% +with some other program and I basically +say how good is that yes no and I accept + + align:start position:0% +say how good is that yes no and I accept + + + align:start position:0% +say how good is that yes no and I accept +or reject that as I said I'm doing this + + align:start position:0% +or reject that as I said I'm doing this + + + align:start position:0% +or reject that as I said I'm doing this +a little bit of a disservice but you + + align:start position:0% +a little bit of a disservice but you + + + align:start position:0% +a little bit of a disservice but you +should if you keep that mental image in + + align:start position:0% +should if you keep that mental image in + + + align:start position:0% +should if you keep that mental image in +your head of something bouncing around + + align:start position:0% +your head of something bouncing around + + + align:start position:0% +your head of something bouncing around +and accepting or rejecting new proposals + + align:start position:0% +and accepting or rejecting new proposals + + + align:start position:0% +and accepting or rejecting new proposals +according to how well they do compared + + align:start position:0% +according to how well they do compared + + + align:start position:0% +according to how well they do compared +to one another in sort of pairwise + + align:start position:0% +to one another in sort of pairwise + + + align:start position:0% +to one another in sort of pairwise +fashion you won't go far wrong what this + + align:start position:0% +fashion you won't go far wrong what this + + + align:start position:0% +fashion you won't go far wrong what this +also tells you is that it's a little bit + + align:start position:0% +also tells you is that it's a little bit + + + align:start position:0% +also tells you is that it's a little bit +important where you start out with right + + align:start position:0% +important where you start out with right + + + align:start position:0% +important where you start out with right +so if I start out in this particular + + align:start position:0% +so if I start out in this particular + + + align:start position:0% +so if I start out in this particular +point in program space or in any space + + align:start position:0% +point in program space or in any space + + + align:start position:0% +point in program space or in any space +and I look locally I might accept a + + align:start position:0% +and I look locally I might accept a + + + align:start position:0% +and I look locally I might accept a +reject and things like that but actually + + align:start position:0% +reject and things like that but actually + + + align:start position:0% +reject and things like that but actually +the really good stuff is over here right + + align:start position:0% +the really good stuff is over here right + + + align:start position:0% +the really good stuff is over here right +the high probability stuff is over here + + align:start position:0% +the high probability stuff is over here + + + align:start position:0% +the high probability stuff is over here +but it'll take me a long time to get to + + align:start position:0% +but it'll take me a long time to get to + + + align:start position:0% +but it'll take me a long time to get to +that right because I started out here + + align:start position:0% +that right because I started out here + + + align:start position:0% +that right because I started out here +does I want to sort of understand what I + + align:start position:0% +does I want to sort of understand what I + + + align:start position:0% +does I want to sort of understand what I +mean when I say here so supposing you + + align:start position:0% +mean when I say here so supposing you + + + align:start position:0% +mean when I say here so supposing you +have a random square okay and you're + + align:start position:0% +have a random square okay and you're + + + align:start position:0% +have a random square okay and you're +trying to sample from a probability + + align:start position:0% +trying to sample from a probability + + + align:start position:0% +trying to sample from a probability +distribution over the square and in the + + align:start position:0% +distribution over the square and in the + + + align:start position:0% +distribution over the square and in the +corners they're sort of much less + + align:start position:0% +corners they're sort of much less + + + align:start position:0% +corners they're sort of much less +probability but you started out in the + + align:start position:0% +probability but you started out in the + + + align:start position:0% +probability but you started out in the +corner for whatever reason and I are + + align:start position:0% +corner for whatever reason and I are + + + align:start position:0% +corner for whatever reason and I are +trying to figure out like how to get to + + align:start position:0% +trying to figure out like how to get to + + + align:start position:0% +trying to figure out like how to get to +those good samples in the center but you + + align:start position:0% +those good samples in the center but you + + + align:start position:0% +those good samples in the center but you +can only move locally so the fact that + + align:start position:0% +can only move locally so the fact that + + + align:start position:0% +can only move locally so the fact that +you started you will eventually get to + + align:start position:0% +you started you will eventually get to + + + align:start position:0% +you started you will eventually get to +the center if you run this on long + + align:start position:0% +the center if you run this on long + + + align:start position:0% +the center if you run this on long +enough you will eventually get to those + + align:start position:0% +enough you will eventually get to those + + + align:start position:0% +enough you will eventually get to those +good probability spaces but it depends a + + align:start position:0% +good probability spaces but it depends a + + + align:start position:0% +good probability spaces but it depends a +lot on where you started out with okay + + align:start position:0% +lot on where you started out with okay + + + align:start position:0% +lot on where you started out with okay +and that just means that oftentimes + + align:start position:0% +and that just means that oftentimes + + + align:start position:0% +and that just means that oftentimes +you'll hear in metropolis Hastings and + + align:start position:0% +you'll hear in metropolis Hastings and + + + align:start position:0% +you'll hear in metropolis Hastings and +I'm seeing things like that you'll hear + + align:start position:0% +I'm seeing things like that you'll hear + + + align:start position:0% +I'm seeing things like that you'll hear +about burn-in which is just to say we + + align:start position:0% +about burn-in which is just to say we + + + align:start position:0% +about burn-in which is just to say we +want to sort of get rid of the + + align:start position:0% +want to sort of get rid of the + + + align:start position:0% +want to sort of get rid of the +initial X samples because those samples + + align:start position:0% +initial X samples because those samples + + + align:start position:0% +initial X samples because those samples +are going to be biased they're going to + + align:start position:0% +are going to be biased they're going to + + + align:start position:0% +are going to be biased they're going to +depend on where we started out with and + + align:start position:0% +depend on where we started out with and + + + align:start position:0% +depend on where we started out with and +the hope is that after examples were no + + align:start position:0% +the hope is that after examples were no + + + align:start position:0% +the hope is that after examples were no +longer biased we no longer remember + + align:start position:0% +longer biased we no longer remember + + + align:start position:0% +longer biased we no longer remember +where we started from we're just sort of + + align:start position:0% +where we started from we're just sort of + + + align:start position:0% +where we started from we're just sort of +sampling around in the space so we + + align:start position:0% +sampling around in the space so we + + + align:start position:0% +sampling around in the space so we +metropolis Hastings works and this is + + align:start position:0% +metropolis Hastings works and this is + + + align:start position:0% +metropolis Hastings works and this is +the backbone of inference in church is + + align:start position:0% +the backbone of inference in church is + + + align:start position:0% +the backbone of inference in church is +you would write down something like mhm + + align:start position:0% +you would write down something like mhm + + + align:start position:0% +you would write down something like mhm +query then you would write down the + + align:start position:0% +query then you would write down the + + + align:start position:0% +query then you would write down the +number of samples that you want from + + align:start position:0% +number of samples that you want from + + + align:start position:0% +number of samples that you want from +your posterior distribution you would + + align:start position:0% +your posterior distribution you would + + + align:start position:0% +your posterior distribution you would +write down the lag the lag is just to + + align:start position:0% +write down the lag the lag is just to + + + align:start position:0% +write down the lag the lag is just to +say like forget every X steps if you + + align:start position:0% +say like forget every X steps if you + + + align:start position:0% +say like forget every X steps if you +want to talk about this we can talk + + align:start position:0% +want to talk about this we can talk + + + align:start position:0% +want to talk about this we can talk +about it later it's not particularly + + align:start position:0% +about it later it's not particularly + + + align:start position:0% +about it later it's not particularly +interesting these are just two numbers + + align:start position:0% +interesting these are just two numbers + + + align:start position:0% +interesting these are just two numbers +and if you make them bigger you will get + + align:start position:0% +and if you make them bigger you will get + + + align:start position:0% +and if you make them bigger you will get +more samples you will get a better + + align:start position:0% +more samples you will get a better + + + align:start position:0% +more samples you will get a better +estimate of your posterior distribution + + align:start position:0% +estimate of your posterior distribution + + + align:start position:0% +estimate of your posterior distribution +you write down some generative model you + + align:start position:0% +you write down some generative model you + + + align:start position:0% +you write down some generative model you +write down what you want to know and you + + align:start position:0% +write down what you want to know and you + + + align:start position:0% +write down what you want to know and you +write down what you actually know and + + align:start position:0% +write down what you actually know and + + + align:start position:0% +write down what you actually know and +you do a random walk in the program + + align:start position:0% +you do a random walk in the program + + + align:start position:0% +you do a random walk in the program +evaluation space as I said this like Jo + + align:start position:0% +evaluation space as I said this like Jo + + + align:start position:0% +evaluation space as I said this like Jo +said what's nice about this is that it's + + align:start position:0% +said what's nice about this is that it's + + + align:start position:0% +said what's nice about this is that it's +very very very very general this will + + align:start position:0% +very very very very general this will + + + align:start position:0% +very very very very general this will +work on any program more or less defined + + align:start position:0% +work on any program more or less defined + + + align:start position:0% +work on any program more or less defined +correctly you need to make some + + align:start position:0% +correctly you need to make some + + + align:start position:0% +correctly you need to make some +decisions like how many samples you want + + align:start position:0% +decisions like how many samples you want + + + align:start position:0% +decisions like how many samples you want +to take what the lag is what the burn-in + + align:start position:0% +to take what the lag is what the burn-in + + + align:start position:0% +to take what the lag is what the burn-in +is you can do all sorts of fanciness you + + align:start position:0% +is you can do all sorts of fanciness you + + + align:start position:0% +is you can do all sorts of fanciness you +can do particle filtering you could run + + align:start position:0% +can do particle filtering you could run + + + align:start position:0% +can do particle filtering you could run +several chains you can do tempered + + align:start position:0% +several chains you can do tempered + + + align:start position:0% +several chains you can do tempered +annealing you could you can do lots of + + align:start position:0% +annealing you could you can do lots of + + + align:start position:0% +annealing you could you can do lots of +different things that I just said it + + align:start position:0% +different things that I just said it + + + align:start position:0% +different things that I just said it +might not make a lot of sense but the + + align:start position:0% +might not make a lot of sense but the + + + align:start position:0% +might not make a lot of sense but the +point is that this procedure could be + + align:start position:0% +point is that this procedure could be + + + align:start position:0% +point is that this procedure could be +made more or less fancy one of the + + align:start position:0% +made more or less fancy one of the + + + align:start position:0% +made more or less fancy one of the +problems with it is it takes awhile like + + align:start position:0% +problems with it is it takes awhile like + + + align:start position:0% +problems with it is it takes awhile like +joe said there's a lot of better + + align:start position:0% +joe said there's a lot of better + + + align:start position:0% +joe said there's a lot of better +algorithms if you know what your + + align:start position:0% +algorithms if you know what your + + + align:start position:0% +algorithms if you know what your +presentation is and it's something like + + align:start position:0% +presentation is and it's something like + + + align:start position:0% +presentation is and it's something like +a feed-forward neural network you + + align:start position:0% +a feed-forward neural network you + + + align:start position:0% +a feed-forward neural network you +probably shouldn't do metropolis + + align:start position:0% +probably shouldn't do metropolis + + + align:start position:0% +probably shouldn't do metropolis +Hastings on there's a lot of very fast + + align:start position:0% +Hastings on there's a lot of very fast + + + align:start position:0% +Hastings on there's a lot of very fast +things that you could do like gradient + + align:start position:0% +things that you could do like gradient + + + align:start position:0% +things that you could do like gradient +descent and you don't need to wait + + align:start position:0% +descent and you don't need to wait + + + align:start position:0% +descent and you don't need to wait +around for this thing to happen ok let's + + align:start position:0% +around for this thing to happen ok let's + + + align:start position:0% +around for this thing to happen ok let's +see so I think we have enough time to + + align:start position:0% +see so I think we have enough time to + + + align:start position:0% +see so I think we have enough time to +give you some examples of inference + + align:start position:0% +give you some examples of inference + + + align:start position:0% +give you some examples of inference +let's walk through some coin testing + + align:start position:0% +let's walk through some coin testing + + + align:start position:0% +let's walk through some coin testing +examples a bit of intuitive physics and + + align:start position:0% +examples a bit of intuitive physics and + + + align:start position:0% +examples a bit of intuitive physics and +a little bit of social reasoning so + + align:start position:0% +a little bit of social reasoning so + + + align:start position:0% +a little bit of social reasoning so +suppose that I took a coin and I flipped + + align:start position:0% +suppose that I took a coin and I flipped + + + align:start position:0% +suppose that I took a coin and I flipped +it ok and it came up heads what do you + + align:start position:0% +it ok and it came up heads what do you + + + align:start position:0% +it ok and it came up heads what do you +think is this coin weird no it's okay to + + align:start position:0% +think is this coin weird no it's okay to + + + align:start position:0% +think is this coin weird no it's okay to +say no what if I flipped it on my gold + + align:start position:0% +say no what if I flipped it on my gold + + + align:start position:0% +say no what if I flipped it on my gold +heads five times in a row do people + + align:start position:0% +heads five times in a row do people + + + align:start position:0% +heads five times in a row do people +think it's weird if you think it's weird + + align:start position:0% +think it's weird if you think it's weird + + + align:start position:0% +think it's weird if you think it's weird +sort of right raise your handle degree + + align:start position:0% +sort of right raise your handle degree + + + align:start position:0% +sort of right raise your handle degree +that + + align:start position:0% +that + + + align:start position:0% +that +weird is it weird that it's five right + + align:start position:0% +weird is it weird that it's five right + + + align:start position:0% +weird is it weird that it's five right +if I flip it ten times and it came up + + align:start position:0% +if I flip it ten times and it came up + + + align:start position:0% +if I flip it ten times and it came up +heads raise your hands to the degree + + align:start position:0% +heads raise your hands to the degree + + + align:start position:0% +heads raise your hands to the degree +that it's weird 15 times in a row heads + + align:start position:0% +that it's weird 15 times in a row heads + + + align:start position:0% +that it's weird 15 times in a row heads +20 time in a row heads okay we more or + + align:start position:0% +20 time in a row heads okay we more or + + + align:start position:0% +20 time in a row heads okay we more or +less asymptotes at somewhere between 10 + + align:start position:0% +less asymptotes at somewhere between 10 + + + align:start position:0% +less asymptotes at somewhere between 10 +and 15 which is exactly right and the + + align:start position:0% +and 15 which is exactly right and the + + + align:start position:0% +and 15 which is exactly right and the +point here is something like you know we + + align:start position:0% +point here is something like you know we + + + align:start position:0% +point here is something like you know we +have a particular prior over what we + + align:start position:0% +have a particular prior over what we + + + align:start position:0% +have a particular prior over what we +think the weight of the coin is we're + + align:start position:0% +think the weight of the coin is we're + + + align:start position:0% +think the weight of the coin is we're +pretty sure that the coin is not biased + + align:start position:0% +pretty sure that the coin is not biased + + + align:start position:0% +pretty sure that the coin is not biased +we're pretty sure that the coin is + + align:start position:0% +we're pretty sure that the coin is + + + align:start position:0% +we're pretty sure that the coin is +supposed to be equal weighted but then + + align:start position:0% +supposed to be equal weighted but then + + + align:start position:0% +supposed to be equal weighted but then +we get more and more evidence and we + + align:start position:0% +we get more and more evidence and we + + + align:start position:0% +we get more and more evidence and we +sort of figure out that wait a minute no + + align:start position:0% +sort of figure out that wait a minute no + + + align:start position:0% +sort of figure out that wait a minute no +this might be a trick coin this might be + + align:start position:0% +this might be a trick coin this might be + + + align:start position:0% +this might be a trick coin this might be +weird and the point of the first example + + align:start position:0% +weird and the point of the first example + + + align:start position:0% +weird and the point of the first example +is too short of showing you you know the + + align:start position:0% +is too short of showing you you know the + + + align:start position:0% +is too short of showing you you know the +basics of conditioning and inference and + + align:start position:0% +basics of conditioning and inference and + + + align:start position:0% +basics of conditioning and inference and +things like that using the coin example + + align:start position:0% +things like that using the coin example + + + align:start position:0% +things like that using the coin example +so what we would do is we would take in + + align:start position:0% +so what we would do is we would take in + + + align:start position:0% +so what we would do is we would take in +and again as I said I'm slightly going + + align:start position:0% +and again as I said I'm slightly going + + + align:start position:0% +and again as I said I'm slightly going +to rush this but I'll still try to + + align:start position:0% +to rush this but I'll still try to + + + align:start position:0% +to rush this but I'll still try to +explain it which is we're going to + + align:start position:0% +explain it which is we're going to + + + align:start position:0% +explain it which is we're going to +define some observed data suppose our + + align:start position:0% +define some observed data suppose our + + + align:start position:0% +define some observed data suppose our +observed data is that we got five heads + + align:start position:0% +observed data is that we got five heads + + + align:start position:0% +observed data is that we got five heads +in a row okay is that five yes it's fine + + align:start position:0% +in a row okay is that five yes it's fine + + + align:start position:0% +in a row okay is that five yes it's fine +and now we're going to say okay we're + + align:start position:0% +and now we're going to say okay we're + + + align:start position:0% +and now we're going to say okay we're +going to define something we're going to + + align:start position:0% +going to define something we're going to + + + align:start position:0% +going to define something we're going to +define an inference procedure we're + + align:start position:0% +define an inference procedure we're + + + align:start position:0% +define an inference procedure we're +gonna call it samples the way it's going + + align:start position:0% +gonna call it samples the way it's going + + + align:start position:0% +gonna call it samples the way it's going +to work is that it's going to give us + + align:start position:0% +to work is that it's going to give us + + + align:start position:0% +to work is that it's going to give us +10,000 it's going to give us a thousand + + align:start position:0% +10,000 it's going to give us a thousand + + + align:start position:0% +10,000 it's going to give us a thousand +samples back right we said we're going + + align:start position:0% +samples back right we said we're going + + + align:start position:0% +samples back right we said we're going +to write mhm query the number of samples + + align:start position:0% +to write mhm query the number of samples + + + align:start position:0% +to write mhm query the number of samples +and now we're going to define a + + align:start position:0% +and now we're going to define a + + + align:start position:0% +and now we're going to define a +generative model we're going to end up + + align:start position:0% +generative model we're going to end up + + + align:start position:0% +generative model we're going to end up +with a quit the thing that we're + + align:start position:0% +with a quit the thing that we're + + + align:start position:0% +with a quit the thing that we're +actually interested in under a certain + + align:start position:0% +actually interested in under a certain + + + align:start position:0% +actually interested in under a certain +condition so what's our model for the + + align:start position:0% +condition so what's our model for the + + + align:start position:0% +condition so what's our model for the +world for this simple world we're going + + align:start position:0% +world for this simple world we're going + + + align:start position:0% +world for this simple world we're going +to say let's like my prior on this being + + align:start position:0% +to say let's like my prior on this being + + + align:start position:0% +to say let's like my prior on this being +a fair coin is very high okay one means + + align:start position:0% +a fair coin is very high okay one means + + + align:start position:0% +a fair coin is very high okay one means +I'm absolutely sure it's a fair coin + + align:start position:0% +I'm absolutely sure it's a fair coin + + + align:start position:0% +I'm absolutely sure it's a fair coin +zero means it's not a fair coin and + + align:start position:0% +zero means it's not a fair coin and + + + align:start position:0% +zero means it's not a fair coin and +we're going to put in a little big prior + + align:start position:0% +we're going to put in a little big prior + + + align:start position:0% +we're going to put in a little big prior +and it being a fair coin it's going to + + align:start position:0% +and it being a fair coin it's going to + + + align:start position:0% +and it being a fair coin it's going to +be 0.999 and then we're going to + + align:start position:0% +be 0.999 and then we're going to + + + align:start position:0% +be 0.999 and then we're going to +basically say you know somewhere in the + + align:start position:0% +basically say you know somewhere in the + + + align:start position:0% +basically say you know somewhere in the +beginning the way I think the world + + align:start position:0% +beginning the way I think the world + + + align:start position:0% +beginning the way I think the world +works is that you're going to pull up a + + align:start position:0% +works is that you're going to pull up a + + + align:start position:0% +works is that you're going to pull up a +new coin off the mint and you're going + + align:start position:0% +new coin off the mint and you're going + + + align:start position:0% +new coin off the mint and you're going +to say is it a fair coin or not okay + + align:start position:0% +to say is it a fair coin or not okay + + + align:start position:0% +to say is it a fair coin or not okay +one in a thousand is fair 999 out of + + align:start position:0% +one in a thousand is fair 999 out of + + + align:start position:0% +one in a thousand is fair 999 out of +sorry 999 out of a thousand a fair one + + align:start position:0% +sorry 999 out of a thousand a fair one + + + align:start position:0% +sorry 999 out of a thousand a fair one +is not so we're basically saying this + + align:start position:0% +is not so we're basically saying this + + + align:start position:0% +is not so we're basically saying this +right we're going to say is it a fair + + align:start position:0% +right we're going to say is it a fair + + + align:start position:0% +right we're going to say is it a fair +coin and this is going to come up true + + align:start position:0% +coin and this is going to come up true + + + align:start position:0% +coin and this is going to come up true +999 times out of a thousand and it's + + align:start position:0% +999 times out of a thousand and it's + + + align:start position:0% +999 times out of a thousand and it's +going to come up false one time out of a + + align:start position:0% +going to come up false one time out of a + + + align:start position:0% +going to come up false one time out of a +thousand because what we're basically + + align:start position:0% +thousand because what we're basically + + + align:start position:0% +thousand because what we're basically +doing here is just flipping a coin + + align:start position:0% +doing here is just flipping a coin + + + align:start position:0% +doing here is just flipping a coin +we're flipping a coin with a bias of + + align:start position:0% +we're flipping a coin with a bias of + + + align:start position:0% +we're flipping a coin with a bias of +this prior okay so what we have here is + + align:start position:0% +this prior okay so what we have here is + + + align:start position:0% +this prior okay so what we have here is +this thing is going to come up this + + align:start position:0% +this thing is going to come up this + + + align:start position:0% +this thing is going to come up this +thing fair coin is going to come up + + align:start position:0% +thing fair coin is going to come up + + + align:start position:0% +thing fair coin is going to come up +without any knowledge without any data + + align:start position:0% +without any knowledge without any data + + + align:start position:0% +without any knowledge without any data +without seeing anything just you took a + + align:start position:0% +without seeing anything just you took a + + + align:start position:0% +without seeing anything just you took a +coin off the mint 999 times out of 1,000 + + align:start position:0% +coin off the mint 999 times out of 1,000 + + + align:start position:0% +coin off the mint 999 times out of 1,000 +you think it's going to be fair without + + align:start position:0% +you think it's going to be fair without + + + align:start position:0% +you think it's going to be fair without +seeing any data now you're going to + + align:start position:0% +seeing any data now you're going to + + + align:start position:0% +seeing any data now you're going to +create a coin okay the coin is going to + + align:start position:0% +create a coin okay the coin is going to + + + align:start position:0% +create a coin okay the coin is going to +take in some weight this it's this + + align:start position:0% +take in some weight this it's this + + + align:start position:0% +take in some weight this it's this +procedure that you can flip and actually + + align:start position:0% +procedure that you can flip and actually + + + align:start position:0% +procedure that you can flip and actually +get heads or tails and the way this coin + + align:start position:0% +get heads or tails and the way this coin + + + align:start position:0% +get heads or tails and the way this coin +is going to work is that if it's fair + + align:start position:0% +is going to work is that if it's fair + + + align:start position:0% +is going to work is that if it's fair +it's going to have a weight of 0.5 okay + + align:start position:0% +it's going to have a weight of 0.5 okay + + + align:start position:0% +it's going to have a weight of 0.5 okay +if it's unfair and this is a very simple + + align:start position:0% +if it's unfair and this is a very simple + + + align:start position:0% +if it's unfair and this is a very simple +example it's going to have a weight of + + align:start position:0% +example it's going to have a weight of + + + align:start position:0% +example it's going to have a weight of +0.9 5 okay so the fair coin comes up + + align:start position:0% +0.9 5 okay so the fair coin comes up + + + align:start position:0% +0.9 5 okay so the fair coin comes up +heads or tails equally likely the unfair + + align:start position:0% +heads or tails equally likely the unfair + + + align:start position:0% +heads or tails equally likely the unfair +coin the trick coin comes up heads + + align:start position:0% +coin the trick coin comes up heads + + + align:start position:0% +coin the trick coin comes up heads +almost all the time okay and again you + + align:start position:0% +almost all the time okay and again you + + + align:start position:0% +almost all the time okay and again you +can define like a different hypothesis + + align:start position:0% +can define like a different hypothesis + + + align:start position:0% +can define like a different hypothesis +it doesn't really matter but the point + + align:start position:0% +it doesn't really matter but the point + + + align:start position:0% +it doesn't really matter but the point +is I defined some sort of coin and now I + + align:start position:0% +is I defined some sort of coin and now I + + + align:start position:0% +is I defined some sort of coin and now I +define some sort of hypothesized data or + + align:start position:0% +define some sort of hypothesized data or + + + align:start position:0% +define some sort of hypothesized data or +the hypothesize data is just I sample + + align:start position:0% +the hypothesize data is just I sample + + + align:start position:0% +the hypothesize data is just I sample +from this coin that I just made okay and + + align:start position:0% +from this coin that I just made okay and + + + align:start position:0% +from this coin that I just made okay and +what I want to know is is this a fair + + align:start position:0% +what I want to know is is this a fair + + + align:start position:0% +what I want to know is is this a fair +coin yes or no condition the last + + align:start position:0% +coin yes or no condition the last + + + align:start position:0% +coin yes or no condition the last +statement is conditioned on this sample + + align:start position:0% +statement is conditioned on this sample + + + align:start position:0% +statement is conditioned on this sample +data this illusory data this imagined + + align:start position:0% +data this illusory data this imagined + + + align:start position:0% +data this illusory data this imagined +data being equal to the observed data + + align:start position:0% +data being equal to the observed data + + + align:start position:0% +data being equal to the observed data +okay so now you're trying to figure out + + align:start position:0% +okay so now you're trying to figure out + + + align:start position:0% +okay so now you're trying to figure out +right you have some sort of program and + + align:start position:0% +right you have some sort of program and + + + align:start position:0% +right you have some sort of program and +you're trying to figure out did this + + align:start position:0% +you're trying to figure out did this + + + align:start position:0% +you're trying to figure out did this +come out to be a fair coin or not right + + align:start position:0% +come out to be a fair coin or not right + + + align:start position:0% +come out to be a fair coin or not right +when I did this here if I didn't + + align:start position:0% +when I did this here if I didn't + + + align:start position:0% +when I did this here if I didn't +condition on anything then it just + + align:start position:0% +condition on anything then it just + + + align:start position:0% +condition on anything then it just +should give me back 999 times out of a + + align:start position:0% +should give me back 999 times out of a + + + align:start position:0% +should give me back 999 times out of a +thousand should give me back yes this is + + align:start position:0% +thousand should give me back yes this is + + + align:start position:0% +thousand should give me back yes this is +a fair coin but I've now conditioned on + + align:start position:0% +a fair coin but I've now conditioned on + + + align:start position:0% +a fair coin but I've now conditioned on +some data and the data is that it came + + align:start position:0% +some data and the data is that it came + + + align:start position:0% +some data and the data is that it came +up five times heads in a row and if you + + align:start position:0% +up five times heads in a row and if you + + + align:start position:0% +up five times heads in a row and if you +do a histogram for that then you'll find + + align:start position:0% +do a histogram for that then you'll find + + + align:start position:0% +do a histogram for that then you'll find +that it's still very likely to be a fair + + align:start position:0% +that it's still very likely to be a fair + + + align:start position:0% +that it's still very likely to be a fair +coin because the prior is so strong okay + + align:start position:0% +coin because the prior is so strong okay + + + align:start position:0% +coin because the prior is so strong okay +but now we can change that we can change + + align:start position:0% +but now we can change that we can change + + + align:start position:0% +but now we can change that we can change +the data to be you know add a few more + + align:start position:0% +the data to be you know add a few more + + + align:start position:0% +the data to be you know add a few more +heads here and I think we're now more or + + align:start position:0% +heads here and I think we're now more or + + + align:start position:0% +heads here and I think we're now more or +less a ten and it's starting to be like + + align:start position:0% +less a ten and it's starting to be like + + + align:start position:0% +less a ten and it's starting to be like +well is it a fair coin yes or no well + + align:start position:0% +well is it a fair coin yes or no well + + + align:start position:0% +well is it a fair coin yes or no well +it's it's a fair coin I'm like sixty + + align:start position:0% +it's it's a fair coin I'm like sixty + + + align:start position:0% +it's it's a fair coin I'm like sixty +percent sure that it's a fair coin now + + align:start position:0% +percent sure that it's a fair coin now + + + align:start position:0% +percent sure that it's a fair coin now +what if I flipped it I don't know like + + align:start position:0% + + + + align:start position:0% + +20 times or something like that and I + + align:start position:0% +20 times or something like that and I + + + align:start position:0% +20 times or something like that and I +came up with that and it's basically + + align:start position:0% +came up with that and it's basically + + + align:start position:0% +came up with that and it's basically +saying that it's 100% not a fair coin + + align:start position:0% +saying that it's 100% not a fair coin + + + align:start position:0% +saying that it's 100% not a fair coin +and the way that you can this is false + + align:start position:0% +and the way that you can this is false + + + align:start position:0% +and the way that you can this is false +it's basically saying like is it a fair + + align:start position:0% +it's basically saying like is it a fair + + + align:start position:0% +it's basically saying like is it a fair +coin no there is no way that if I ran my + + align:start position:0% +coin no there is no way that if I ran my + + + align:start position:0% +coin no there is no way that if I ran my +generative model even though the prior + + align:start position:0% +generative model even though the prior + + + align:start position:0% +generative model even though the prior +is strong even though if I just ran my + + align:start position:0% +is strong even though if I just ran my + + + align:start position:0% +is strong even though if I just ran my +generative model without any condition + + align:start position:0% +generative model without any condition + + + align:start position:0% +generative model without any condition +usually would be a fair coin there's no + + align:start position:0% +usually would be a fair coin there's no + + + align:start position:0% +usually would be a fair coin there's no +way that I would run my generative model + + align:start position:0% +way that I would run my generative model + + + align:start position:0% +way that I would run my generative model +and sample it twenty times that coin + + align:start position:0% +and sample it twenty times that coin + + + align:start position:0% +and sample it twenty times that coin +flip and it would come up heads all the + + align:start position:0% +flip and it would come up heads all the + + + align:start position:0% +flip and it would come up heads all the +time when the alternative is that it's + + align:start position:0% +time when the alternative is that it's + + + align:start position:0% +time when the alternative is that it's +going to come up heads so now you can + + align:start position:0% +going to come up heads so now you can + + + align:start position:0% +going to come up heads so now you can +sort of play around with this coin this + + align:start position:0% +sort of play around with this coin this + + + align:start position:0% +sort of play around with this coin this +is a nice example and by the way Josh + + align:start position:0% +is a nice example and by the way Josh + + + align:start position:0% +is a nice example and by the way Josh +you're like this some version of this + + align:start position:0% +you're like this some version of this + + + align:start position:0% +you're like this some version of this +not much more complicated than that was + + align:start position:0% +not much more complicated than that was + + + align:start position:0% +not much more complicated than that was +a cognition paper a few years ago where + + align:start position:0% +a cognition paper a few years ago where + + + align:start position:0% +a cognition paper a few years ago where +basically you gave people different + + align:start position:0% +basically you gave people different + + + align:start position:0% +basically you gave people different +sequences of coins different sequences + + align:start position:0% +sequences of coins different sequences + + + align:start position:0% +sequences of coins different sequences +of numbers and you started to see where + + align:start position:0% +of numbers and you started to see where + + + align:start position:0% +of numbers and you started to see where +does it become weird what hypothesis do + + align:start position:0% +does it become weird what hypothesis do + + + align:start position:0% +does it become weird what hypothesis do +they think is likely and all that they + + align:start position:0% +they think is likely and all that they + + + align:start position:0% +they think is likely and all that they +did was they gave it a more interesting + + align:start position:0% +did was they gave it a more interesting + + + align:start position:0% +did was they gave it a more interesting +hypothesis space right instead of saying + + align:start position:0% +hypothesis space right instead of saying + + + align:start position:0% +hypothesis space right instead of saying +it's either a fair coin or a coin that's + + align:start position:0% +it's either a fair coin or a coin that's + + + align:start position:0% +it's either a fair coin or a coin that's +95 percent heads they gave you a more + + align:start position:0% +95 percent heads they gave you a more + + + align:start position:0% +95 percent heads they gave you a more +general hypothesis space like it could + + align:start position:0% +general hypothesis space like it could + + + align:start position:0% +general hypothesis space like it could +be a coin that comes up mostly heads + + align:start position:0% +be a coin that comes up mostly heads + + + align:start position:0% +be a coin that comes up mostly heads +mostly tails maybe it's a coin that does + + align:start position:0% +mostly tails maybe it's a coin that does + + + align:start position:0% +mostly tails maybe it's a coin that does +heads tails heads tails heads tails head + + align:start position:0% +heads tails heads tails heads tails head + + + align:start position:0% +heads tails heads tails heads tails head +so or you can define the sort of + + align:start position:0% +so or you can define the sort of + + + align:start position:0% +so or you can define the sort of +alternative procedure but that we but + + align:start position:0% +alternative procedure but that we but + + + align:start position:0% +alternative procedure but that we but +that you would change over here the rest + + align:start position:0% +that you would change over here the rest + + + align:start position:0% +that you would change over here the rest +of this would stay more or less the same + + align:start position:0% +of this would stay more or less the same + + + align:start position:0% +of this would stay more or less the same +okay that's a very simple way of getting + + align:start position:0% +okay that's a very simple way of getting + + + align:start position:0% +okay that's a very simple way of getting +some hypothesis test let's do some very + + align:start position:0% +some hypothesis test let's do some very + + + align:start position:0% +some hypothesis test let's do some very +simple intuitive physics let's try + + align:start position:0% +simple intuitive physics let's try + + + align:start position:0% +simple intuitive physics let's try +something like this so in church you can + + align:start position:0% +something like this so in church you can + + + align:start position:0% +something like this so in church you can +do you can basically animate physics + + align:start position:0% +do you can basically animate physics + + + align:start position:0% +do you can basically animate physics +forward which what that means is I guess + + align:start position:0% +forward which what that means is I guess + + + align:start position:0% +forward which what that means is I guess +I hadn't counted them like when it's a + + align:start position:0% +I hadn't counted them like when it's a + + + align:start position:0% +I hadn't counted them like when it's a +full screen it sort of does that but + + align:start position:0% +full screen it sort of does that but + + + align:start position:0% +full screen it sort of does that but +what you can do is you can define + + align:start position:0% +what you can do is you can define + + + align:start position:0% +what you can do is you can define +basically a two-dimensional world when + + align:start position:0% +basically a two-dimensional world when + + + align:start position:0% +basically a two-dimensional world when +you say listen here's a two-dimensional + + align:start position:0% +you say listen here's a two-dimensional + + + align:start position:0% +you say listen here's a two-dimensional +world it's this big I'm going to add + + align:start position:0% +world it's this big I'm going to add + + + align:start position:0% +world it's this big I'm going to add +some shape so I'm going to put the + + align:start position:0% +some shape so I'm going to put the + + + align:start position:0% +some shape so I'm going to put the +shapes in random locations I'm going to + + align:start position:0% +shapes in random locations I'm going to + + + align:start position:0% +shapes in random locations I'm going to +set gravity to something and then I'm + + align:start position:0% +set gravity to something and then I'm + + + align:start position:0% +set gravity to something and then I'm +going to run it forward what happens + + align:start position:0% +going to run it forward what happens + + + align:start position:0% +going to run it forward what happens +sorry come on - for running okay oh of + + align:start position:0% +sorry come on - for running okay oh of + + + align:start position:0% +sorry come on - for running okay oh of +course + + align:start position:0% +course + + + align:start position:0% +course +thank you trivial thank you is that + + align:start position:0% +thank you trivial thank you is that + + + align:start position:0% +thank you trivial thank you is that +better everybody yep okay so I have this + + align:start position:0% +better everybody yep okay so I have this + + + align:start position:0% +better everybody yep okay so I have this +thing and I'm gonna hit simulate to try + + align:start position:0% +thing and I'm gonna hit simulate to try + + + align:start position:0% +thing and I'm gonna hit simulate to try +and see what happens okay so I basically + + align:start position:0% +and see what happens okay so I basically + + + align:start position:0% +and see what happens okay so I basically +have these things I guess in this case I + + align:start position:0% +have these things I guess in this case I + + + align:start position:0% +have these things I guess in this case I +didn't put any randomness on where they + + align:start position:0% +didn't put any randomness on where they + + + align:start position:0% +didn't put any randomness on where they +actually are but you could easily + + align:start position:0% +actually are but you could easily + + + align:start position:0% +actually are but you could easily +imagine putting some randomness + + align:start position:0% +imagine putting some randomness + + + align:start position:0% +imagine putting some randomness +where these blocks start out with where + + align:start position:0% +where these blocks start out with where + + + align:start position:0% +where these blocks start out with where +these blocks are but the point is you + + align:start position:0% +these blocks are but the point is you + + + align:start position:0% +these blocks are but the point is you +can this is just running it forward in + + align:start position:0% +can this is just running it forward in + + + align:start position:0% +can this is just running it forward in +physics now what is that good for well + + align:start position:0% +physics now what is that good for well + + + align:start position:0% +physics now what is that good for well +you could for example define a tower a + + align:start position:0% +you could for example define a tower a + + + align:start position:0% +you could for example define a tower a +tower is just defining a bunch of blocks + + align:start position:0% +tower is just defining a bunch of blocks + + + align:start position:0% +tower is just defining a bunch of blocks +one on top of the other and now you can + + align:start position:0% +one on top of the other and now you can + + + align:start position:0% +one on top of the other and now you can +run it forward right see what happens + + align:start position:0% +run it forward right see what happens + + + align:start position:0% +run it forward right see what happens +what do you think is this gonna fall or + + align:start position:0% +what do you think is this gonna fall or + + + align:start position:0% +what do you think is this gonna fall or +not yes no let's see you can simulate + + align:start position:0% +not yes no let's see you can simulate + + + align:start position:0% +not yes no let's see you can simulate +that forward it fell okay very nice now + + align:start position:0% +that forward it fell okay very nice now + + + align:start position:0% +that forward it fell okay very nice now +what can we do with that now we can + + align:start position:0% +what can we do with that now we can + + + align:start position:0% +what can we do with that now we can +define and I know as I said I'm going to + + align:start position:0% +define and I know as I said I'm going to + + + align:start position:0% +define and I know as I said I'm going to +zoom through this what we can define is + + align:start position:0% +zoom through this what we can define is + + + align:start position:0% +zoom through this what we can define is +basically a bunch of towers like this + + align:start position:0% +basically a bunch of towers like this + + + align:start position:0% +basically a bunch of towers like this +each one of them is just saying the + + align:start position:0% +each one of them is just saying the + + + align:start position:0% +each one of them is just saying the +blocks or like that and all I'm going to + + align:start position:0% +blocks or like that and all I'm going to + + + align:start position:0% +blocks or like that and all I'm going to +do is slightly perturb them and see if + + align:start position:0% +do is slightly perturb them and see if + + + align:start position:0% +do is slightly perturb them and see if +they fall down and I'm gonna do that a + + align:start position:0% +they fall down and I'm gonna do that a + + + align:start position:0% +they fall down and I'm gonna do that a +thousand times for each Tower okay and + + align:start position:0% +thousand times for each Tower okay and + + + align:start position:0% +thousand times for each Tower okay and +I'm gonna do that for a bunch of towers + + align:start position:0% +I'm gonna do that for a bunch of towers + + + align:start position:0% +I'm gonna do that for a bunch of towers +some of them are stable some of them are + + align:start position:0% +some of them are stable some of them are + + + align:start position:0% +some of them are stable some of them are +not stable so you can write down some + + align:start position:0% +not stable so you can write down some + + + align:start position:0% +not stable so you can write down some +church code which is basically like this + + align:start position:0% +church code which is basically like this + + + align:start position:0% +church code which is basically like this +is my world there's some ground the + + align:start position:0% +is my world there's some ground the + + + align:start position:0% +is my world there's some ground the +ground is just a rectangle here's a + + align:start position:0% +ground is just a rectangle here's a + + + align:start position:0% +ground is just a rectangle here's a +tower a stable tower okay the stable + + align:start position:0% +tower a stable tower okay the stable + + + align:start position:0% +tower a stable tower okay the stable +tower all that it means is that I'm + + align:start position:0% +tower all that it means is that I'm + + + align:start position:0% +tower all that it means is that I'm +creating some blocks in this particular + + align:start position:0% +creating some blocks in this particular + + + align:start position:0% +creating some blocks in this particular +order here's an almost stable tower it's + + align:start position:0% +order here's an almost stable tower it's + + + align:start position:0% +order here's an almost stable tower it's +blocks in this order here's an unstable + + align:start position:0% +blocks in this order here's an unstable + + + align:start position:0% +blocks in this order here's an unstable +tower it's books in that order and now + + align:start position:0% +tower it's books in that order and now + + + align:start position:0% +tower it's books in that order and now +what I'm going to do is I'm going to run + + align:start position:0% +what I'm going to do is I'm going to run + + + align:start position:0% +what I'm going to do is I'm going to run +this tower many times and I'm going to + + align:start position:0% +this tower many times and I'm going to + + + align:start position:0% +this tower many times and I'm going to +count up the number of times that it + + align:start position:0% +count up the number of times that it + + + align:start position:0% +count up the number of times that it +actually fell and if you do that you'll + + align:start position:0% +actually fell and if you do that you'll + + + align:start position:0% +actually fell and if you do that you'll +see that the stable tower didn't fall + + align:start position:0% +see that the stable tower didn't fall + + + align:start position:0% +see that the stable tower didn't fall +down this is just saying like did it + + align:start position:0% +down this is just saying like did it + + + align:start position:0% +down this is just saying like did it +fall down false true this one didn't + + align:start position:0% +fall down false true this one didn't + + + align:start position:0% +fall down false true this one didn't +fall down any other time this one fell + + align:start position:0% +fall down any other time this one fell + + + align:start position:0% +fall down any other time this one fell +down some of the time this one fell down + + align:start position:0% +down some of the time this one fell down + + + align:start position:0% +down some of the time this one fell down +all the time it's a toy example but it's + + align:start position:0% +all the time it's a toy example but it's + + + align:start position:0% +all the time it's a toy example but it's +actually a toy example of a very nice + + align:start position:0% +actually a toy example of a very nice + + + align:start position:0% +actually a toy example of a very nice +and interesting paper that came out very + + align:start position:0% +and interesting paper that came out very + + + align:start position:0% +and interesting paper that came out very +recently and shows something deep about + + align:start position:0% +recently and shows something deep about + + + align:start position:0% +recently and shows something deep about +intuitive physics they've done it also + + align:start position:0% +intuitive physics they've done it also + + + align:start position:0% +intuitive physics they've done it also +there's an interesting example for sort + + align:start position:0% +there's an interesting example for sort + + + align:start position:0% +there's an interesting example for sort +of we can ask yeah how hard it was to + + align:start position:0% +of we can ask yeah how hard it was to + + + align:start position:0% +of we can ask yeah how hard it was to +implement this thing this is an + + align:start position:0% +implement this thing this is an + + + align:start position:0% +implement this thing this is an +implementation of liquid physics in in + + align:start position:0% +implementation of liquid physics in in + + + align:start position:0% +implementation of liquid physics in in +not so much Church as web ppl and what + + align:start position:0% +not so much Church as web ppl and what + + + align:start position:0% +not so much Church as web ppl and what +they were trying to do here is to sort + + align:start position:0% +they were trying to do here is to sort + + + align:start position:0% +they were trying to do here is to sort +of say well this is a bunch of water ok + + align:start position:0% +of say well this is a bunch of water ok + + + align:start position:0% +of say well this is a bunch of water ok +physics is frozen right now I imagine + + align:start position:0% +physics is frozen right now I imagine + + + align:start position:0% +physics is frozen right now I imagine +that this is a big glob of water this is + + align:start position:0% +that this is a big glob of water this is + + + align:start position:0% +that this is a big glob of water this is +a cup over here and this is some barrier + + align:start position:0% +a cup over here and this is some barrier + + + align:start position:0% +a cup over here and this is some barrier +okay so if the water falls down on the + + align:start position:0% +okay so if the water falls down on the + + + align:start position:0% +okay so if the water falls down on the +barrier it's going to go every which way + + align:start position:0% +barrier it's going to go every which way + + + align:start position:0% +barrier it's going to go every which way +so let's see if we run it + + align:start position:0% + + + + align:start position:0% + +moment yeah so if we run it one of the + + align:start position:0% +moment yeah so if we run it one of the + + + align:start position:0% +moment yeah so if we run it one of the +questions that we can ask here and this + + align:start position:0% +questions that we can ask here and this + + + align:start position:0% +questions that we can ask here and this +is sort of been an example what I'm + + align:start position:0% +is sort of been an example what I'm + + + align:start position:0% +is sort of been an example what I'm +trying to show you here is that this is + + align:start position:0% +trying to show you here is that this is + + + align:start position:0% +trying to show you here is that this is +an active area of research even though + + align:start position:0% +an active area of research even though + + + align:start position:0% +an active area of research even though +it's sort of like church it's 2d physics + + align:start position:0% +it's sort of like church it's 2d physics + + + align:start position:0% +it's sort of like church it's 2d physics +it's simple but people have been doing + + align:start position:0% +it's simple but people have been doing + + + align:start position:0% +it's simple but people have been doing +what they've been porting in is a liquid + + align:start position:0% +what they've been porting in is a liquid + + + align:start position:0% +what they've been porting in is a liquid +physics thing into church that took them + + align:start position:0% +physics thing into church that took them + + + align:start position:0% +physics thing into church that took them +a little bit of time I think it was you + + align:start position:0% +a little bit of time I think it was you + + + align:start position:0% +a little bit of time I think it was you +probably want to talk to people who know + + align:start position:0% +probably want to talk to people who know + + + align:start position:0% +probably want to talk to people who know +what they're doing and that rather than + + align:start position:0% +what they're doing and that rather than + + + align:start position:0% +what they're doing and that rather than +saving your like save yourself some time + + align:start position:0% +saving your like save yourself some time + + + align:start position:0% +saving your like save yourself some time +and talk to people in no Goodman's group + + align:start position:0% +and talk to people in no Goodman's group + + + align:start position:0% +and talk to people in no Goodman's group +but what they did is they poured it in a + + align:start position:0% +but what they did is they poured it in a + + + align:start position:0% +but what they did is they poured it in a +liquid physics implementation into + + align:start position:0% +liquid physics implementation into + + + align:start position:0% +liquid physics implementation into +Church and they sort of said okay now we + + align:start position:0% +Church and they sort of said okay now we + + + align:start position:0% +Church and they sort of said okay now we +have some liquid physics and we can try + + align:start position:0% +have some liquid physics and we can try + + + align:start position:0% +have some liquid physics and we can try +to ask some questions like suppose that + + align:start position:0% +to ask some questions like suppose that + + + align:start position:0% +to ask some questions like suppose that +this glob is going to fall down we set + + align:start position:0% +this glob is going to fall down we set + + + align:start position:0% +this glob is going to fall down we set +it down over here it's going to fall + + align:start position:0% +it down over here it's going to fall + + + align:start position:0% +it down over here it's going to fall +down + + align:start position:0% +down + + + align:start position:0% +down +where should we put this block in order + + align:start position:0% +where should we put this block in order + + + align:start position:0% +where should we put this block in order +to get as much of the liquid into that + + align:start position:0% +to get as much of the liquid into that + + + align:start position:0% +to get as much of the liquid into that +cup okay that's an interesting question + + align:start position:0% +cup okay that's an interesting question + + + align:start position:0% +cup okay that's an interesting question +right it shows something about intuitive + + align:start position:0% +right it shows something about intuitive + + + align:start position:0% +right it shows something about intuitive +physics of liquids and things like that + + align:start position:0% +physics of liquids and things like that + + + align:start position:0% +physics of liquids and things like that +more than just objects so the way that + + align:start position:0% +more than just objects so the way that + + + align:start position:0% +more than just objects so the way that +you would do that is even in a simple + + align:start position:0% +you would do that is even in a simple + + + align:start position:0% +you would do that is even in a simple +world like this you would basically say + + align:start position:0% +world like this you would basically say + + + align:start position:0% +world like this you would basically say +fine put this thing somewhere randomly + + align:start position:0% +fine put this thing somewhere randomly + + + align:start position:0% +fine put this thing somewhere randomly +uniform conditioned on getting as much + + align:start position:0% +uniform conditioned on getting as much + + + align:start position:0% +uniform conditioned on getting as much +water into this thing as possible and + + align:start position:0% +water into this thing as possible and + + + align:start position:0% +water into this thing as possible and +then try to figure out where this book + + align:start position:0% +then try to figure out where this book + + + align:start position:0% +then try to figure out where this book +should go okay so you start our uniform + + align:start position:0% +should go okay so you start our uniform + + + align:start position:0% +should go okay so you start our uniform +condition on as much water as possible + + align:start position:0% +condition on as much water as possible + + + align:start position:0% +condition on as much water as possible +you'll get some posterior distribution + + align:start position:0% +you'll get some posterior distribution + + + align:start position:0% +you'll get some posterior distribution +of where to place this block and just to + + align:start position:0% +of where to place this block and just to + + + align:start position:0% +of where to place this block and just to +show you what that looks like let's try + + align:start position:0% +show you what that looks like let's try + + + align:start position:0% +show you what that looks like let's try +to + + align:start position:0% + + + + align:start position:0% + +so suppose that we actually tried to run + + align:start position:0% +so suppose that we actually tried to run + + + align:start position:0% +so suppose that we actually tried to run +this yeah so in this case you don't want + + align:start position:0% +this yeah so in this case you don't want + + + align:start position:0% +this yeah so in this case you don't want +the block to go there for example right + + align:start position:0% +the block to go there for example right + + + align:start position:0% +the block to go there for example right +because most of the water is going to + + align:start position:0% +because most of the water is going to + + + align:start position:0% +because most of the water is going to +slosh over there what if we put it over + + align:start position:0% +slosh over there what if we put it over + + + align:start position:0% +slosh over there what if we put it over +there it's a little bit better that's + + align:start position:0% +there it's a little bit better that's + + + align:start position:0% +there it's a little bit better that's +not so great you could do this you could + + align:start position:0% +not so great you could do this you could + + + align:start position:0% +not so great you could do this you could +run in many many different times at this + + align:start position:0% +run in many many different times at this + + + align:start position:0% +run in many many different times at this +point I hope most of you even if you + + align:start position:0% +point I hope most of you even if you + + + align:start position:0% +point I hope most of you even if you +don't quite know what you're doing you + + align:start position:0% +don't quite know what you're doing you + + + align:start position:0% +don't quite know what you're doing you +can see how you would go about writing + + align:start position:0% +can see how you would go about writing + + + align:start position:0% +can see how you would go about writing +the program to figure this out right you + + align:start position:0% +the program to figure this out right you + + + align:start position:0% +the program to figure this out right you +would write down the physics world + + align:start position:0% +would write down the physics world + + + align:start position:0% +would write down the physics world +assume most of that is taken care of for + + align:start position:0% +assume most of that is taken care of for + + + align:start position:0% +assume most of that is taken care of for +you all you need to do is sort of figure + + align:start position:0% +you all you need to do is sort of figure + + + align:start position:0% +you all you need to do is sort of figure +out where to place this bloke put some + + align:start position:0% +out where to place this bloke put some + + + align:start position:0% +out where to place this bloke put some +uniform distribution on it in this area + + align:start position:0% +uniform distribution on it in this area + + + align:start position:0% +uniform distribution on it in this area +condition on most of the water landing + + align:start position:0% +condition on most of the water landing + + + align:start position:0% +condition on most of the water landing +here and then just sample and figure out + + align:start position:0% +here and then just sample and figure out + + + align:start position:0% +here and then just sample and figure out +where this thing should be in the world + + align:start position:0% +where this thing should be in the world + + + align:start position:0% +where this thing should be in the world +that's pretty cool + + align:start position:0% +that's pretty cool + + + align:start position:0% +that's pretty cool +so here's another example that was + + align:start position:0% +so here's another example that was + + + align:start position:0% +so here's another example that was +intuitive physics let's move on to + + align:start position:0% +intuitive physics let's move on to + + + align:start position:0% +intuitive physics let's move on to +intuitive psychology which Josh was sort + + align:start position:0% +intuitive psychology which Josh was sort + + + align:start position:0% +intuitive psychology which Josh was sort +of getting at at the end of his lecture + + align:start position:0% +of getting at at the end of his lecture + + + align:start position:0% +of getting at at the end of his lecture +and here's a very simple very very + + align:start position:0% +and here's a very simple very very + + + align:start position:0% +and here's a very simple very very +simple question which is something like + + align:start position:0% +simple question which is something like + + + align:start position:0% +simple question which is something like +that okay suppose that you see an agent + + align:start position:0% +that okay suppose that you see an agent + + + align:start position:0% +that okay suppose that you see an agent +this guy with googly eye can people see + + align:start position:0% +this guy with googly eye can people see + + + align:start position:0% +this guy with googly eye can people see +him from way down there there's a guy + + align:start position:0% +him from way down there there's a guy + + + align:start position:0% +him from way down there there's a guy +with googly eyes doesn't matter + + align:start position:0% +with googly eyes doesn't matter + + + align:start position:0% +with googly eyes doesn't matter +it's me okay I'm right here there's a + + align:start position:0% +it's me okay I'm right here there's a + + + align:start position:0% +it's me okay I'm right here there's a +banana over there there's an apple over + + align:start position:0% +banana over there there's an apple over + + + align:start position:0% +banana over there there's an apple over +here okay and now there's there so + + align:start position:0% +here okay and now there's there so + + + align:start position:0% +here okay and now there's there so +there's the banana over there Apple over + + align:start position:0% +there's the banana over there Apple over + + + align:start position:0% +there's the banana over there Apple over +there and I start walking over here okay + + align:start position:0% +there and I start walking over here okay + + + align:start position:0% +there and I start walking over here okay +and not someone asked you why did Tomer + + align:start position:0% +and not someone asked you why did Tomer + + + align:start position:0% +and not someone asked you why did Tomer +go over there and you say well I guess + + align:start position:0% +go over there and you say well I guess + + + align:start position:0% +go over there and you say well I guess +he wanted the banana you say ah but you + + align:start position:0% +he wanted the banana you say ah but you + + + align:start position:0% +he wanted the banana you say ah but you +don't have access to his goals how do + + align:start position:0% +don't have access to his goals how do + + + align:start position:0% +don't have access to his goals how do +you know he wanted the banana you say + + align:start position:0% +you know he wanted the banana you say + + + align:start position:0% +you know he wanted the banana you say +well cuz he went to the banana no ID + + align:start position:0% +well cuz he went to the banana no ID + + + align:start position:0% +well cuz he went to the banana no ID +well you know just + + align:start position:0% +well you know just + + + align:start position:0% +well you know just +you're just being circular right how + + align:start position:0% +you're just being circular right how + + + align:start position:0% +you're just being circular right how +would you actually solve a test like + + align:start position:0% +would you actually solve a test like + + + align:start position:0% +would you actually solve a test like +this it's sort of trivial and you could + + align:start position:0% +this it's sort of trivial and you could + + + align:start position:0% +this it's sort of trivial and you could +solve it through something like queues + + align:start position:0% +solve it through something like queues + + + align:start position:0% +solve it through something like queues +you could say something like well you + + align:start position:0% +you could say something like well you + + + align:start position:0% +you could say something like well you +know the thing that you approach is your + + align:start position:0% +know the thing that you approach is your + + + align:start position:0% +know the thing that you approach is your +goal but another thing that you could do + + align:start position:0% +goal but another thing that you could do + + + align:start position:0% +goal but another thing that you could do +is you could say well I assume that the + + align:start position:0% +is you could say well I assume that the + + + align:start position:0% +is you could say well I assume that the +way Tomer works is that he has goals I + + align:start position:0% +way Tomer works is that he has goals I + + + align:start position:0% +way Tomer works is that he has goals I +don't know what his goals are but I + + align:start position:0% +don't know what his goals are but I + + + align:start position:0% +don't know what his goals are but I +assume he has goals and I assume that he + + align:start position:0% +assume he has goals and I assume that he + + + align:start position:0% +assume he has goals and I assume that he +can plan to reach those goals okay in + + align:start position:0% +can plan to reach those goals okay in + + + align:start position:0% +can plan to reach those goals okay in +some sort of semi efficient matter and + + align:start position:0% +some sort of semi efficient matter and + + + align:start position:0% +some sort of semi efficient matter and +he has some beliefs about the world and + + align:start position:0% +he has some beliefs about the world and + + + align:start position:0% +he has some beliefs about the world and +he's going to carry out some sort of + + align:start position:0% +he's going to carry out some sort of + + + align:start position:0% +he's going to carry out some sort of +planning procedure in order to get to + + align:start position:0% +planning procedure in order to get to + + + align:start position:0% +planning procedure in order to get to +his goals and if Tomer wanted the banana + + align:start position:0% +his goals and if Tomer wanted the banana + + + align:start position:0% +his goals and if Tomer wanted the banana +the action he should take + + align:start position:0% +the action he should take + + + align:start position:0% +the action he should take +do this it would be very unlikely for + + align:start position:0% +do this it would be very unlikely for + + + align:start position:0% +do this it would be very unlikely for +him to do this right if he wanted the + + align:start position:0% +him to do this right if he wanted the + + + align:start position:0% +him to do this right if he wanted the +Apple he would do that not that so you + + align:start position:0% +Apple he would do that not that so you + + + align:start position:0% +Apple he would do that not that so you +could sort of use this planning + + align:start position:0% +could sort of use this planning + + + align:start position:0% +could sort of use this planning +procedure to set the knobs on your + + align:start position:0% +procedure to set the knobs on your + + + align:start position:0% +procedure to set the knobs on your +procedure think of it like a generative + + align:start position:0% +procedure think of it like a generative + + + align:start position:0% +procedure think of it like a generative +model your generative model is something + + align:start position:0% +model your generative model is something + + + align:start position:0% +model your generative model is something +that goes from goals or utilities and + + align:start position:0% +that goes from goals or utilities and + + + align:start position:0% +that goes from goals or utilities and +beliefs to something like actions okay + + align:start position:0% +beliefs to something like actions okay + + + align:start position:0% +beliefs to something like actions okay +and you define the goals let's say you + + align:start position:0% +and you define the goals let's say you + + + align:start position:0% +and you define the goals let's say you +don't know what my goals are so you + + align:start position:0% +don't know what my goals are so you + + + align:start position:0% +don't know what my goals are so you +place some distribution over them + + align:start position:0% +place some distribution over them + + + align:start position:0% +place some distribution over them +and then you get to see my actions and + + align:start position:0% +and then you get to see my actions and + + + align:start position:0% +and then you get to see my actions and +you basically try to say well in program + + align:start position:0% +you basically try to say well in program + + + align:start position:0% +you basically try to say well in program +space what would be the setting of the + + align:start position:0% +space what would be the setting of the + + + align:start position:0% +space what would be the setting of the +goals of Tomer such that it would have + + align:start position:0% +goals of Tomer such that it would have + + + align:start position:0% +goals of Tomer such that it would have +produced the observed actions and if you + + align:start position:0% +produced the observed actions and if you + + + align:start position:0% +produced the observed actions and if you +write down a model for that you'll find + + align:start position:0% +write down a model for that you'll find + + + align:start position:0% +write down a model for that you'll find +that if I set the goal for Tomer as + + align:start position:0% +that if I set the goal for Tomer as + + + align:start position:0% +that if I set the goal for Tomer as +banana + + align:start position:0% +banana + + + align:start position:0% +banana +I'll get the observed action which is he + + align:start position:0% +I'll get the observed action which is he + + + align:start position:0% +I'll get the observed action which is he +walked towards the banana similarly for + + align:start position:0% +walked towards the banana similarly for + + + align:start position:0% +walked towards the banana similarly for +belief if you know something like you + + align:start position:0% +belief if you know something like you + + + align:start position:0% +belief if you know something like you +know you know there are two boxes here + + align:start position:0% +know you know there are two boxes here + + + align:start position:0% +know you know there are two boxes here +you don't know what's inside them you + + align:start position:0% +you don't know what's inside them you + + + align:start position:0% +you don't know what's inside them you +know it's either a banana or an apple + + align:start position:0% +know it's either a banana or an apple + + + align:start position:0% +know it's either a banana or an apple +and you know that I really love bananas + + align:start position:0% +and you know that I really love bananas + + + align:start position:0% +and you know that I really love bananas +and I hate apples and you see me walking + + align:start position:0% +and I hate apples and you see me walking + + + align:start position:0% +and I hate apples and you see me walking +towards this box you can infer that ah + + align:start position:0% +towards this box you can infer that ah + + + align:start position:0% +towards this box you can infer that ah +he probably thought there was a banana + + align:start position:0% +he probably thought there was a banana + + + align:start position:0% +he probably thought there was a banana +inside or he knew there was a banana + + align:start position:0% +inside or he knew there was a banana + + + align:start position:0% +inside or he knew there was a banana +inside and again if you had some sort of + + align:start position:0% +inside and again if you had some sort of + + + align:start position:0% +inside and again if you had some sort of +planning procedure and he would say okay + + align:start position:0% +planning procedure and he would say okay + + + align:start position:0% +planning procedure and he would say okay +would make sense for me to set his + + align:start position:0% +would make sense for me to set his + + + align:start position:0% +would make sense for me to set his +belief to be banana because the outcome + + align:start position:0% +belief to be banana because the outcome + + + align:start position:0% +belief to be banana because the outcome +of that if I run the model forward with + + align:start position:0% +of that if I run the model forward with + + + align:start position:0% +of that if I run the model forward with +those settings would be for him to walk + + align:start position:0% +those settings would be for him to walk + + + align:start position:0% +those settings would be for him to walk +in that direction and let me show you + + align:start position:0% +in that direction and let me show you + + + align:start position:0% +in that direction and let me show you +just one one example of what that sort + + align:start position:0% +just one one example of what that sort + + + align:start position:0% +just one one example of what that sort +of model would look like so this would + + align:start position:0% +of model would look like so this would + + + align:start position:0% +of model would look like so this would +be under intuitive psychology those of + + align:start position:0% +be under intuitive psychology those of + + + align:start position:0% +be under intuitive psychology those of +you who are interested in sort of + + align:start position:0% +you who are interested in sort of + + + align:start position:0% +you who are interested in sort of +inference over inference and you know + + align:start position:0% +inference over inference and you know + + + align:start position:0% +inference over inference and you know +how do agents reason about other agents + + align:start position:0% +how do agents reason about other agents + + + align:start position:0% +how do agents reason about other agents +or goal inference or things like that + + align:start position:0% +or goal inference or things like that + + + align:start position:0% +or goal inference or things like that +you might want to take a look at this + + align:start position:0% +you might want to take a look at this + + + align:start position:0% +you might want to take a look at this +section and this is this is sort of + + align:start position:0% +section and this is this is sort of + + + align:start position:0% +section and this is this is sort of +super simple there's no there's no + + align:start position:0% +super simple there's no there's no + + + align:start position:0% +super simple there's no there's no +probabilities exactly in the sense of + + align:start position:0% +probabilities exactly in the sense of + + + align:start position:0% +probabilities exactly in the sense of +like it's going to be either this goal + + align:start position:0% +like it's going to be either this goal + + + align:start position:0% +like it's going to be either this goal +or that go it's obviously something that + + align:start position:0% +or that go it's obviously something that + + + align:start position:0% +or that go it's obviously something that +can be modified if you want to there's + + align:start position:0% +can be modified if you want to there's + + + align:start position:0% +can be modified if you want to there's +that one more let's see what's going on + + align:start position:0% +that one more let's see what's going on + + + align:start position:0% +that one more let's see what's going on +here when we make that a bit bigger okay + + align:start position:0% +here when we make that a bit bigger okay + + + align:start position:0% +here when we make that a bit bigger okay +what's going on here what I've got what + + align:start position:0% +what's going on here what I've got what + + + align:start position:0% +what's going on here what I've got what +I try to write down is a model in which + + align:start position:0% +I try to write down is a model in which + + + align:start position:0% +I try to write down is a model in which +someone went for an apple and you're + + align:start position:0% +someone went for an apple and you're + + + align:start position:0% +someone went for an apple and you're +trying to figure out what did he go for + + align:start position:0% +trying to figure out what did he go for + + + align:start position:0% +trying to figure out what did he go for +sorry why did he go for that + + align:start position:0% +sorry why did he go for that + + + align:start position:0% +sorry why did he go for that +yes sorry it really should be over here + + align:start position:0% + + + + align:start position:0% + +now though let me start out actually + + align:start position:0% +now though let me start out actually + + + align:start position:0% +now though let me start out actually +with something like planning okay let's + + align:start position:0% +with something like planning okay let's + + + align:start position:0% +with something like planning okay let's +write down let's write down the forward + + align:start position:0% +write down let's write down the forward + + + align:start position:0% +write down let's write down the forward +model that's before we do inference + + align:start position:0% +model that's before we do inference + + + align:start position:0% +model that's before we do inference +right we said before we do inference + + align:start position:0% +right we said before we do inference + + + align:start position:0% +right we said before we do inference +let's write down the how we think the + + align:start position:0% +let's write down the how we think the + + + align:start position:0% +let's write down the how we think the +world works nothing that I said the way + + align:start position:0% +world works nothing that I said the way + + + align:start position:0% +world works nothing that I said the way +the world works is that Tomer has some + + align:start position:0% +the world works is that Tomer has some + + + align:start position:0% +the world works is that Tomer has some +goals and some beliefs and given his + + align:start position:0% +goals and some beliefs and given his + + + align:start position:0% +goals and some beliefs and given his +goals he'll take some action to achieve + + align:start position:0% +goals he'll take some action to achieve + + + align:start position:0% +goals he'll take some action to achieve +his goals let's write down to that part + + align:start position:0% +his goals let's write down to that part + + + align:start position:0% +his goals let's write down to that part +that's the forward part if we can write + + align:start position:0% +that's the forward part if we can write + + + align:start position:0% +that's the forward part if we can write +down the forward part the inference part + + align:start position:0% +down the forward part the inference part + + + align:start position:0% +down the forward part the inference part +comes for free okay we just put that in + + align:start position:0% +comes for free okay we just put that in + + + align:start position:0% +comes for free okay we just put that in +an mhm query and say what's the goal + + align:start position:0% +an mhm query and say what's the goal + + + align:start position:0% +an mhm query and say what's the goal +that made the observed thing happen so + + align:start position:0% +that made the observed thing happen so + + + align:start position:0% +that made the observed thing happen so +what we would do is we would write down + + align:start position:0% +what we would do is we would write down + + + align:start position:0% +what we would do is we would write down +something like what goal should I take + + align:start position:0% +something like what goal should I take + + + align:start position:0% +something like what goal should I take +I'm sorry what action should tomar take + + align:start position:0% +I'm sorry what action should tomar take + + + align:start position:0% +I'm sorry what action should tomar take +choose an action it's a procedure it's a + + align:start position:0% +choose an action it's a procedure it's a + + + align:start position:0% +choose an action it's a procedure it's a +procedure that it takes in a particular + + align:start position:0% +procedure that it takes in a particular + + + align:start position:0% +procedure that it takes in a particular +goal here it's a particular condition + + align:start position:0% +goal here it's a particular condition + + + align:start position:0% +goal here it's a particular condition +that I can satisfy but it could be a + + align:start position:0% +that I can satisfy but it could be a + + + align:start position:0% +that I can satisfy but it could be a +utility it could be anything but it's + + align:start position:0% +utility it could be anything but it's + + + align:start position:0% +utility it could be anything but it's +what actually what action should I take + + align:start position:0% +what actually what action should I take + + + align:start position:0% +what actually what action should I take +given a particular goal given how I + + align:start position:0% +given a particular goal given how I + + + align:start position:0% +given a particular goal given how I +think the world works that's a + + align:start position:0% +think the world works that's a + + + align:start position:0% +think the world works that's a +transition function okay if I take this + + align:start position:0% +transition function okay if I take this + + + align:start position:0% +transition function okay if I take this +action what will happen I need to know + + align:start position:0% +action what will happen I need to know + + + align:start position:0% +action what will happen I need to know +that if I go in if I go left from your + + align:start position:0% +that if I go in if I go left from your + + + align:start position:0% +that if I go in if I go left from your +perspective I'll get to the banana right + + align:start position:0% +perspective I'll get to the banana right + + + align:start position:0% +perspective I'll get to the banana right +that's the transition function for the + + align:start position:0% +that's the transition function for the + + + align:start position:0% +that's the transition function for the +world and I need some initial state and + + align:start position:0% +world and I need some initial state and + + + align:start position:0% +world and I need some initial state and +now I sample some action okay I just I + + align:start position:0% +now I sample some action okay I just I + + + align:start position:0% +now I sample some action okay I just I +do actually at random I either go left + + align:start position:0% +do actually at random I either go left + + + align:start position:0% +do actually at random I either go left +or either go right I sample it from some + + align:start position:0% +or either go right I sample it from some + + + align:start position:0% +or either go right I sample it from some +action prior suppose it's completely + + align:start position:0% +action prior suppose it's completely + + + align:start position:0% +action prior suppose it's completely +uniform okay define action it's sampled + + align:start position:0% +uniform okay define action it's sampled + + + align:start position:0% +uniform okay define action it's sampled +from action prior and suppose my prior + + align:start position:0% +from action prior and suppose my prior + + + align:start position:0% +from action prior and suppose my prior +is go left to go right with equal + + align:start position:0% +is go left to go right with equal + + + align:start position:0% +is go left to go right with equal +probability everyone with me so far + + align:start position:0% +probability everyone with me so far + + + align:start position:0% +probability everyone with me so far +okay we're trying to get a procedure + + align:start position:0% +okay we're trying to get a procedure + + + align:start position:0% +okay we're trying to get a procedure +that will give us an action what + + align:start position:0% +that will give us an action what + + + align:start position:0% +that will give us an action what +actually should I take imagine you took + + align:start position:0% +actually should I take imagine you took + + + align:start position:0% +actually should I take imagine you took +an action doesn't matter which one now + + align:start position:0% +an action doesn't matter which one now + + + align:start position:0% +an action doesn't matter which one now +did this action what what action did you + + align:start position:0% +did this action what what action did you + + + align:start position:0% +did this action what what action did you +end up with conditioned on that action + + align:start position:0% +end up with conditioned on that action + + + align:start position:0% +end up with conditioned on that action +getting you to your goal okay this is a + + align:start position:0% +getting you to your goal okay this is a + + + align:start position:0% +getting you to your goal okay this is a +rejection query right I'm trying to + + align:start position:0% +rejection query right I'm trying to + + + align:start position:0% +rejection query right I'm trying to +sample an action conditioned on that + + align:start position:0% +sample an action conditioned on that + + + align:start position:0% +sample an action conditioned on that +action getting me to my goal so let's + + align:start position:0% +action getting me to my goal so let's + + + align:start position:0% +action getting me to my goal so let's +say I sample the action i hypothesize + + align:start position:0% +say I sample the action i hypothesize + + + align:start position:0% +say I sample the action i hypothesize +that I go that way did I satisfy my goal + + align:start position:0% +that I go that way did I satisfy my goal + + + align:start position:0% +that I go that way did I satisfy my goal +no I ended up with the Apple do it again + + align:start position:0% +no I ended up with the Apple do it again + + + align:start position:0% +no I ended up with the Apple do it again +run it again write it again now I + + align:start position:0% +run it again write it again now I + + + align:start position:0% +run it again write it again now I +sampled the action go here did I end up + + align:start position:0% +sampled the action go here did I end up + + + align:start position:0% +sampled the action go here did I end up +with a banana yes okay so what action + + align:start position:0% +with a banana yes okay so what action + + + align:start position:0% +with a banana yes okay so what action +did I take I went from your perspective + + align:start position:0% +did I take I went from your perspective + + + align:start position:0% +did I take I went from your perspective +left returned that + + align:start position:0% +left returned that + + + align:start position:0% +left returned that +okay we've just written down a procedure + + align:start position:0% +okay we've just written down a procedure + + + align:start position:0% +okay we've just written down a procedure +for planning and it can be made much + + align:start position:0% +for planning and it can be made much + + + align:start position:0% +for planning and it can be made much +more complex than that in a few short + + align:start position:0% +more complex than that in a few short + + + align:start position:0% +more complex than that in a few short +steps by complex I don't mean that it's + + align:start position:0% +steps by complex I don't mean that it's + + + align:start position:0% +steps by complex I don't mean that it's +hard for you to follow I mean that it + + align:start position:0% +hard for you to follow I mean that it + + + align:start position:0% +hard for you to follow I mean that it +can take in multiple worlds multiple + + align:start position:0% +can take in multiple worlds multiple + + + align:start position:0% +can take in multiple worlds multiple +steps utilities probabilities things + + align:start position:0% +steps utilities probabilities things + + + align:start position:0% +steps utilities probabilities things +like that and it'll spit out a sequence + + align:start position:0% +like that and it'll spit out a sequence + + + align:start position:0% +like that and it'll spit out a sequence +of actions for you to go from X to Y to + + align:start position:0% +of actions for you to go from X to Y to + + + align:start position:0% +of actions for you to go from X to Y to +get to your goal okay and it's written + + align:start position:0% +get to your goal okay and it's written + + + align:start position:0% +get to your goal okay and it's written +as sort of planning as inference now + + align:start position:0% +as sort of planning as inference now + + + align:start position:0% +as sort of planning as inference now +there are many different types of + + align:start position:0% +there are many different types of + + + align:start position:0% +there are many different types of +planning procedures you could write down + + align:start position:0% +planning procedures you could write down + + + align:start position:0% +planning procedures you could write down +markov decision planning processes you + + align:start position:0% +markov decision planning processes you + + + align:start position:0% +markov decision planning processes you +could write down rapid random trees and + + align:start position:0% +could write down rapid random trees and + + + align:start position:0% +could write down rapid random trees and +just throwing out names there for those + + align:start position:0% +just throwing out names there for those + + + align:start position:0% +just throwing out names there for those +of you interested in these things + + align:start position:0% +of you interested in these things + + + align:start position:0% +of you interested in these things +there's lots of ways of doing planning + + align:start position:0% +there's lots of ways of doing planning + + + align:start position:0% +there's lots of ways of doing planning +this is one particular way of doing + + align:start position:0% +this is one particular way of doing + + + align:start position:0% +this is one particular way of doing +planning you could have done many + + align:start position:0% +planning you could have done many + + + align:start position:0% +planning you could have done many +different ways but the point is that we + + align:start position:0% +different ways but the point is that we + + + align:start position:0% +different ways but the point is that we +assume you can even sort of wrap this up + + align:start position:0% +assume you can even sort of wrap this up + + + align:start position:0% +assume you can even sort of wrap this up +in something like I as the observer I as + + align:start position:0% +in something like I as the observer I as + + + align:start position:0% +in something like I as the observer I as +you don't need to know exactly how to + + align:start position:0% +you don't need to know exactly how to + + + align:start position:0% +you don't need to know exactly how to +more works I just need to know that + + align:start position:0% +more works I just need to know that + + + align:start position:0% +more works I just need to know that +there is some procedure such that if I + + align:start position:0% +there is some procedure such that if I + + + align:start position:0% +there is some procedure such that if I +put into it a goal and somehow how the + + align:start position:0% +put into it a goal and somehow how the + + + align:start position:0% +put into it a goal and somehow how the +world works it'll spit out some rational + + align:start position:0% +world works it'll spit out some rational + + + align:start position:0% +world works it'll spit out some rational +action okay it's preferable that I know + + align:start position:0% +action okay it's preferable that I know + + + align:start position:0% +action okay it's preferable that I know +I mean I have some idea of how it works + + align:start position:0% +I mean I have some idea of how it works + + + align:start position:0% +I mean I have some idea of how it works +it doesn't need to be the right one + + align:start position:0% +it doesn't need to be the right one + + + align:start position:0% +it doesn't need to be the right one +doesn't need to be the one that I + + align:start position:0% +doesn't need to be the one that I + + + align:start position:0% +doesn't need to be the one that I +actually use but you need to have some + + align:start position:0% +actually use but you need to have some + + + align:start position:0% +actually use but you need to have some +sort of sense that I am planning some no + + align:start position:0% +sort of sense that I am planning some no + + + align:start position:0% +sort of sense that I am planning some no +this is one way to plan okay and now + + align:start position:0% +this is one way to plan okay and now + + + align:start position:0% +this is one way to plan okay and now +this is just showing you I put some + + align:start position:0% +this is just showing you I put some + + + align:start position:0% +this is just showing you I put some +uniform prior on the action prior I + + align:start position:0% +uniform prior on the action prior I + + + align:start position:0% +uniform prior on the action prior I +either go left or right the transition + + align:start position:0% +either go left or right the transition + + + align:start position:0% +either go left or right the transition +function of the world is such that if + + align:start position:0% +function of the world is such that if + + + align:start position:0% +function of the world is such that if +you go left you get an apple if you go + + align:start position:0% +you go left you get an apple if you go + + + align:start position:0% +you go left you get an apple if you go +right you get a banana so that's for my + + align:start position:0% +right you get a banana so that's for my + + + align:start position:0% +right you get a banana so that's for my +perspective I guess if you do anything + + align:start position:0% +perspective I guess if you do anything + + + align:start position:0% +perspective I guess if you do anything +else you get nothing and then you sort + + align:start position:0% +else you get nothing and then you sort + + + align:start position:0% +else you get nothing and then you sort +of just say my goal is did I get to the + + align:start position:0% +of just say my goal is did I get to the + + + align:start position:0% +of just say my goal is did I get to the +Apple let's say or did I get to the + + align:start position:0% +Apple let's say or did I get to the + + + align:start position:0% +Apple let's say or did I get to the +banana sorry I put that into the choose + + align:start position:0% +banana sorry I put that into the choose + + + align:start position:0% +banana sorry I put that into the choose +action and I'll end up going left + + align:start position:0% +action and I'll end up going left + + + align:start position:0% +action and I'll end up going left +because my goal was to get to the apple + + align:start position:0% +because my goal was to get to the apple + + + align:start position:0% +because my goal was to get to the apple +the Apple was on the left I'm going to + + align:start position:0% +the Apple was on the left I'm going to + + + align:start position:0% +the Apple was on the left I'm going to +choose an action I'm going to go through + + align:start position:0% +choose an action I'm going to go through + + + align:start position:0% +choose an action I'm going to go through +life this whole thing is just to say + + align:start position:0% +life this whole thing is just to say + + + align:start position:0% +life this whole thing is just to say +it's to show you that in fact this works + + align:start position:0% +it's to show you that in fact this works + + + align:start position:0% +it's to show you that in fact this works +the form you sample it forward it'll + + align:start position:0% +the form you sample it forward it'll + + + align:start position:0% +the form you sample it forward it'll +give you the right action you can now + + align:start position:0% +give you the right action you can now + + + align:start position:0% +give you the right action you can now +wrap up this whole thing in something + + align:start position:0% +wrap up this whole thing in something + + + align:start position:0% +wrap up this whole thing in something +that does goal inference that doesn't + + align:start position:0% +that does goal inference that doesn't + + + align:start position:0% +that does goal inference that doesn't +know that my goal was this that puts a + + align:start position:0% +know that my goal was this that puts a + + + align:start position:0% +know that my goal was this that puts a +uniform prior on this thing and then + + align:start position:0% +uniform prior on this thing and then + + + align:start position:0% +uniform prior on this thing and then +runs forward many many different samples + + align:start position:0% +runs forward many many different samples + + + align:start position:0% +runs forward many many different samples +and comes to the conclusion well it must + + align:start position:0% +and comes to the conclusion well it must + + + align:start position:0% +and comes to the conclusion well it must +have been the Apple because he went left + + align:start position:0% +have been the Apple because he went left + + + align:start position:0% +have been the Apple because he went left +okay and again this this example is + + align:start position:0% +okay and again this this example is + + + align:start position:0% +okay and again this this example is +fully written out for you over here as + + align:start position:0% +fully written out for you over here as + + + align:start position:0% +fully written out for you over here as +well as the belief inference + + align:start position:0% +well as the belief inference + + + align:start position:0% +well as the belief inference +this is an example of implicature how + + align:start position:0% +this is an example of implicature how + + + align:start position:0% +this is an example of implicature how +many of you knows what what implicature + + align:start position:0% +many of you knows what what implicature + + + align:start position:0% +many of you knows what what implicature +means like gracing implicature + + align:start position:0% +means like gracing implicature + + + align:start position:0% +means like gracing implicature +implicature okay it's a sort of thing + + align:start position:0% +implicature okay it's a sort of thing + + + align:start position:0% +implicature okay it's a sort of thing +where I say you know someone tells me + + align:start position:0% +where I say you know someone tells me + + + align:start position:0% +where I say you know someone tells me +hey are you going to the party tonight + + align:start position:0% +hey are you going to the party tonight + + + align:start position:0% +hey are you going to the party tonight +and I say I'm washing my hair right or + + align:start position:0% +and I say I'm washing my hair right or + + + align:start position:0% +and I say I'm washing my hair right or +you say something like you know how good + + align:start position:0% +you say something like you know how good + + + align:start position:0% +you say something like you know how good +of a lecturer was John and I say well he + + align:start position:0% +of a lecturer was John and I say well he + + + align:start position:0% +of a lecturer was John and I say well he +was speaking English right I'm not + + align:start position:0% +was speaking English right I'm not + + + align:start position:0% +was speaking English right I'm not +exactly telling you he was a bad + + align:start position:0% +exactly telling you he was a bad + + + align:start position:0% +exactly telling you he was a bad +lecturer right but if he was a good one + + align:start position:0% +lecturer right but if he was a good one + + + align:start position:0% +lecturer right but if he was a good one +I would say it right the fact that I + + align:start position:0% +I would say it right the fact that I + + + align:start position:0% +I would say it right the fact that I +didn't say it the fact that I chose to + + align:start position:0% +didn't say it the fact that I chose to + + + align:start position:0% +didn't say it the fact that I chose to +say something else implies that he + + align:start position:0% +say something else implies that he + + + align:start position:0% +say something else implies that he +probably wasn't a good lecturer and sort + + align:start position:0% +probably wasn't a good lecturer and sort + + + align:start position:0% +probably wasn't a good lecturer and sort +of happens a lot and the way that it + + align:start position:0% +of happens a lot and the way that it + + + align:start position:0% +of happens a lot and the way that it +works is that and this happens a lot in + + align:start position:0% +works is that and this happens a lot in + + + align:start position:0% +works is that and this happens a lot in +sort of language games social games + + align:start position:0% +sort of language games social games + + + align:start position:0% +sort of language games social games +reasoning about reasoning is that I'm + + align:start position:0% +reasoning about reasoning is that I'm + + + align:start position:0% +reasoning about reasoning is that I'm +the speaker you're the listener I have + + align:start position:0% +the speaker you're the listener I have + + + align:start position:0% +the speaker you're the listener I have +some model of you you have some model of + + align:start position:0% +some model of you you have some model of + + + align:start position:0% +some model of you you have some model of +me I know that you know that I would + + align:start position:0% +me I know that you know that I would + + + align:start position:0% +me I know that you know that I would +have said he was a good lecturer right I + + align:start position:0% +have said he was a good lecturer right I + + + align:start position:0% +have said he was a good lecturer right I +know that you know that if I wanted to I + + align:start position:0% +know that you know that if I wanted to I + + + align:start position:0% +know that you know that if I wanted to I +would have said that and I'm not so I + + align:start position:0% +would have said that and I'm not so I + + + align:start position:0% +would have said that and I'm not so I +know that you know that I know that and + + align:start position:0% +know that you know that I know that and + + + align:start position:0% +know that you know that I know that and +it works out such that you realize that + + align:start position:0% +it works out such that you realize that + + + align:start position:0% +it works out such that you realize that +he's not a good lecturer and that sounds + + align:start position:0% +he's not a good lecturer and that sounds + + + align:start position:0% +he's not a good lecturer and that sounds +sort of convoluted but it's actually not + + align:start position:0% +sort of convoluted but it's actually not + + + align:start position:0% +sort of convoluted but it's actually not +that bad and I want to show you an + + align:start position:0% +that bad and I want to show you an + + + align:start position:0% +that bad and I want to show you an +example of how that works and this + + align:start position:0% +example of how that works and this + + + align:start position:0% +example of how that works and this +particular example is based on the some + + align:start position:0% +particular example is based on the some + + + align:start position:0% +particular example is based on the some +not all example so this is a sort of + + align:start position:0% +not all example so this is a sort of + + + align:start position:0% +not all example so this is a sort of +thing like you know someone you're a TA + + align:start position:0% +thing like you know someone you're a TA + + + align:start position:0% +thing like you know someone you're a TA +in a class or something like that + + align:start position:0% +in a class or something like that + + + align:start position:0% +in a class or something like that +or I'm a TA in a class and someone asks + + align:start position:0% +or I'm a TA in a class and someone asks + + + align:start position:0% +or I'm a TA in a class and someone asks +me you know you know what how did the + + align:start position:0% +me you know you know what how did the + + + align:start position:0% +me you know you know what how did the +students do on the test and I say some + + align:start position:0% +students do on the test and I say some + + + align:start position:0% +students do on the test and I say some +of the students pass the test do you + + align:start position:0% +of the students pass the test do you + + + align:start position:0% +of the students pass the test do you +think I mean all the students pass the + + align:start position:0% +think I mean all the students pass the + + + align:start position:0% +think I mean all the students pass the +test no now why not because some in a + + align:start position:0% +test no now why not because some in a + + + align:start position:0% +test no now why not because some in a +sense also means all right all the + + align:start position:0% +sense also means all right all the + + + align:start position:0% +sense also means all right all the +students is true if some is something + + align:start position:0% +students is true if some is something + + + align:start position:0% +students is true if some is something +like a logical thing that means greater + + align:start position:0% +like a logical thing that means greater + + + align:start position:0% +like a logical thing that means greater +than five or greater than zero or + + align:start position:0% +than five or greater than zero or + + + align:start position:0% +than five or greater than zero or +greater than one whatever it is it can + + align:start position:0% +greater than one whatever it is it can + + + align:start position:0% +greater than one whatever it is it can +include all but if it was all I would + + align:start position:0% +include all but if it was all I would + + + align:start position:0% +include all but if it was all I would +have said all right and if it was one I + + align:start position:0% +have said all right and if it was one I + + + align:start position:0% +have said all right and if it was one I +would have said one so people are likely + + align:start position:0% +would have said one so people are likely + + + align:start position:0% +would have said one so people are likely +to infer from me saying some that I'm + + align:start position:0% +to infer from me saying some that I'm + + + align:start position:0% +to infer from me saying some that I'm +probably mean you know if there's a + + align:start position:0% +probably mean you know if there's a + + + align:start position:0% +probably mean you know if there's a +hundred students and I say some they can + + align:start position:0% +hundred students and I say some they can + + + align:start position:0% +hundred students and I say some they can +give you a distribution over what I mean + + align:start position:0% +give you a distribution over what I mean + + + align:start position:0% +give you a distribution over what I mean +by that and that distribution depends on + + align:start position:0% +by that and that distribution depends on + + + align:start position:0% +by that and that distribution depends on +the alternatives the alternative words I + + align:start position:0% +the alternatives the alternative words I + + + align:start position:0% +the alternatives the alternative words I +could have used which they know I didn't + + align:start position:0% +could have used which they know I didn't + + + align:start position:0% +could have used which they know I didn't +but they know I could have okay there's + + align:start position:0% +but they know I could have okay there's + + + align:start position:0% +but they know I could have okay there's +a nice example of scalar implicature and + + align:start position:0% +a nice example of scalar implicature and + + + align:start position:0% +a nice example of scalar implicature and +how it would work in probe mons what I + + align:start position:0% +how it would work in probe mons what I + + + align:start position:0% +how it would work in probe mons what I +want to show you is a slightly different + + align:start position:0% +want to show you is a slightly different + + + align:start position:0% +want to show you is a slightly different +example + + align:start position:0% +example + + + align:start position:0% +example +which is its again a London bombing + + align:start position:0% +which is its again a London bombing + + + align:start position:0% +which is its again a London bombing +example but the way it would work is + + align:start position:0% +example but the way it would work is + + + align:start position:0% +example but the way it would work is +something like this so imagine here's + + align:start position:0% +something like this so imagine here's + + + align:start position:0% +something like this so imagine here's +the background for it + + align:start position:0% +the background for it + + + align:start position:0% +the background for it +for implicature and I came up with this + + align:start position:0% +for implicature and I came up with this + + + align:start position:0% +for implicature and I came up with this +yesterday I'm not quite sure it'll work + + align:start position:0% +yesterday I'm not quite sure it'll work + + + align:start position:0% +yesterday I'm not quite sure it'll work +but we'll see imagine that things work + + align:start position:0% +but we'll see imagine that things work + + + align:start position:0% +but we'll see imagine that things work +like this okay + + align:start position:0% +like this okay + + + align:start position:0% +like this okay +the City of London is being bombed again + + align:start position:0% +the City of London is being bombed again + + + align:start position:0% +the City of London is being bombed again +sorry for the slightly dire things city + + align:start position:0% +sorry for the slightly dire things city + + + align:start position:0% +sorry for the slightly dire things city +of London is being bombed and there are + + align:start position:0% +of London is being bombed and there are + + + align:start position:0% +of London is being bombed and there are +sort of three places it could be bombed + + align:start position:0% +sort of three places it could be bombed + + + align:start position:0% +sort of three places it could be bombed +okay again it's this uniform square it + + align:start position:0% +okay again it's this uniform square it + + + align:start position:0% +okay again it's this uniform square it +could be bombed in this in the red sari + + align:start position:0% +could be bombed in this in the red sari + + + align:start position:0% +could be bombed in this in the red sari +in the blue part okay anywhere here if + + align:start position:0% +in the blue part okay anywhere here if + + + align:start position:0% +in the blue part okay anywhere here if +it's bombed there in the blue part I + + align:start position:0% +it's bombed there in the blue part I + + + align:start position:0% +it's bombed there in the blue part I +would say it was bombed outside London + + align:start position:0% +would say it was bombed outside London + + + align:start position:0% +would say it was bombed outside London +okay that means outside it doesn't + + align:start position:0% +okay that means outside it doesn't + + + align:start position:0% +okay that means outside it doesn't +include these things it's just outside + + align:start position:0% +include these things it's just outside + + + align:start position:0% +include these things it's just outside +London if it was bombed anywhere between + + align:start position:0% +London if it was bombed anywhere between + + + align:start position:0% +London if it was bombed anywhere between +you know in this red square so imagine + + align:start position:0% +you know in this red square so imagine + + + align:start position:0% +you know in this red square so imagine +that this Square something like I don't + + align:start position:0% +that this Square something like I don't + + + align:start position:0% +that this Square something like I don't +know zero to two and over here at zero + + align:start position:0% +know zero to two and over here at zero + + + align:start position:0% +know zero to two and over here at zero +to one anywhere in the Red Square is + + align:start position:0% +to one anywhere in the Red Square is + + + align:start position:0% +to one anywhere in the Red Square is +called London okay if a bomb fell there + + align:start position:0% +called London okay if a bomb fell there + + + align:start position:0% +called London okay if a bomb fell there +I would say a bomb during the Blitz + + align:start position:0% +I would say a bomb during the Blitz + + + align:start position:0% +I would say a bomb during the Blitz +dropped on London okay someone asked me + + align:start position:0% +dropped on London okay someone asked me + + + align:start position:0% +dropped on London okay someone asked me +like where did the bomb fall I would say + + align:start position:0% +like where did the bomb fall I would say + + + align:start position:0% +like where did the bomb fall I would say +in London but that includes this whole + + align:start position:0% +in London but that includes this whole + + + align:start position:0% +in London but that includes this whole +thing okay it also includes Big Ben okay + + align:start position:0% +thing okay it also includes Big Ben okay + + + align:start position:0% +thing okay it also includes Big Ben okay +Big Ben is in London okay you can maybe + + align:start position:0% +Big Ben is in London okay you can maybe + + + align:start position:0% +Big Ben is in London okay you can maybe +some of you can see what I'm getting at + + align:start position:0% +some of you can see what I'm getting at + + + align:start position:0% +some of you can see what I'm getting at +so if it fell on Big Ben I can say it + + align:start position:0% +so if it fell on Big Ben I can say it + + + align:start position:0% +so if it fell on Big Ben I can say it +fell on Big Ben I can say it fell in + + align:start position:0% +fell on Big Ben I can say it fell in + + + align:start position:0% +fell on Big Ben I can say it fell in +London because that's also true if it + + align:start position:0% +London because that's also true if it + + + align:start position:0% +London because that's also true if it +fell here I would say it fell in London + + align:start position:0% +fell here I would say it fell in London + + + align:start position:0% +fell here I would say it fell in London +if it fell here I would say outside + + align:start position:0% +if it fell here I would say outside + + + align:start position:0% +if it fell here I would say outside +London now there's a general and a staff + + align:start position:0% +London now there's a general and a staff + + + align:start position:0% +London now there's a general and a staff +sergeant walks up to him and he says you + + align:start position:0% +sergeant walks up to him and he says you + + + align:start position:0% +sergeant walks up to him and he says you +know bomb fell in London during the + + align:start position:0% +know bomb fell in London during the + + + align:start position:0% +know bomb fell in London during the +Blitz and the general says where did it + + align:start position:0% +Blitz and the general says where did it + + + align:start position:0% +Blitz and the general says where did it +fall and he says it fell in London + + align:start position:0% +fall and he says it fell in London + + + align:start position:0% +fall and he says it fell in London +I never says okay he looks outside his + + align:start position:0% +I never says okay he looks outside his + + + align:start position:0% +I never says okay he looks outside his +window and he says good god it hit Big + + align:start position:0% +window and he says good god it hit Big + + + align:start position:0% +window and he says good god it hit Big +Ben yes I said it fell in London that's + + align:start position:0% +Ben yes I said it fell in London that's + + + align:start position:0% +Ben yes I said it fell in London that's +very weird right we don't expect people + + align:start position:0% +very weird right we don't expect people + + + align:start position:0% +very weird right we don't expect people +to do that and sort of gracing + + align:start position:0% +to do that and sort of gracing + + + align:start position:0% +to do that and sort of gracing +implicature says we shouldn't do that + + align:start position:0% +implicature says we shouldn't do that + + + align:start position:0% +implicature says we shouldn't do that +but grace said it in a way that's like + + align:start position:0% +but grace said it in a way that's like + + + align:start position:0% +but grace said it in a way that's like +you should give the maximal amount of + + align:start position:0% +you should give the maximal amount of + + + align:start position:0% +you should give the maximal amount of +helpful information and not hold out + + align:start position:0% +helpful information and not hold out + + + align:start position:0% +helpful information and not hold out +other things how would that fall out of + + align:start position:0% +other things how would that fall out of + + + align:start position:0% +other things how would that fall out of +a particular model well the way would + + align:start position:0% +a particular model well the way would + + + align:start position:0% +a particular model well the way would +fall out is something like this and all + + align:start position:0% +fall out is something like this and all + + + align:start position:0% +fall out is something like this and all +again I'll show you the code for that + + align:start position:0% +again I'll show you the code for that + + + align:start position:0% +again I'll show you the code for that +it's something like there's the speaker + + align:start position:0% +it's something like there's the speaker + + + align:start position:0% +it's something like there's the speaker +the speaker is the staff sergeant he + + align:start position:0% +the speaker is the staff sergeant he + + + align:start position:0% +the speaker is the staff sergeant he +could choose one of three words outside + + align:start position:0% +could choose one of three words outside + + + align:start position:0% +could choose one of three words outside +London in London dropped on Big Ben okay + + align:start position:0% +London in London dropped on Big Ben okay + + + align:start position:0% +London in London dropped on Big Ben okay +let's say Ben London outside something + + align:start position:0% +let's say Ben London outside something + + + align:start position:0% +let's say Ben London outside something +like that he could choose one of three + + align:start position:0% +like that he could choose one of three + + + align:start position:0% +like that he could choose one of three +now the fact that he decided to say + + align:start position:0% +now the fact that he decided to say + + + align:start position:0% +now the fact that he decided to say +outside London sorry the fact they + + align:start position:0% +outside London sorry the fact they + + + align:start position:0% +outside London sorry the fact they +decided to say London couldn't + + align:start position:0% +decided to say London couldn't + + + align:start position:0% +decided to say London couldn't +big them but if it was Ben he could have + + align:start position:0% +big them but if it was Ben he could have + + + align:start position:0% +big them but if it was Ben he could have +also said Ben he didn't which implies + + align:start position:0% +also said Ben he didn't which implies + + + align:start position:0% +also said Ben he didn't which implies +that it probably fell over here so the + + align:start position:0% +that it probably fell over here so the + + + align:start position:0% +that it probably fell over here so the +last model that I wanted to show you was + + align:start position:0% +last model that I wanted to show you was + + + align:start position:0% +last model that I wanted to show you was +exactly that you sort of say listen + + align:start position:0% +exactly that you sort of say listen + + + align:start position:0% +exactly that you sort of say listen +there's some prior right the Boehm sort + + align:start position:0% +there's some prior right the Boehm sort + + + align:start position:0% +there's some prior right the Boehm sort +of fall anywhere and there's some + + align:start position:0% +of fall anywhere and there's some + + + align:start position:0% +of fall anywhere and there's some +distance here and you can get the words + + align:start position:0% +distance here and you can get the words + + + align:start position:0% +distance here and you can get the words +that you'll say let's say you start out + + align:start position:0% +that you'll say let's say you start out + + + align:start position:0% +that you'll say let's say you start out +with just random gibberish okay you can + + align:start position:0% +with just random gibberish okay you can + + + align:start position:0% +with just random gibberish okay you can +say either Ben or outside or inside + + align:start position:0% +say either Ben or outside or inside + + + align:start position:0% +say either Ben or outside or inside +doesn't matter like you regardless of + + align:start position:0% +doesn't matter like you regardless of + + + align:start position:0% +doesn't matter like you regardless of +what the world actually was this is just + + align:start position:0% +what the world actually was this is just + + + align:start position:0% +what the world actually was this is just +defining like what each one of these + + align:start position:0% +defining like what each one of these + + + align:start position:0% +defining like what each one of these +words mean the hit London means to be + + align:start position:0% +words mean the hit London means to be + + + align:start position:0% +words mean the hit London means to be +inside that small square I said the hit + + align:start position:0% +inside that small square I said the hit + + + align:start position:0% +inside that small square I said the hit +Ben means to be inside that smaller + + align:start position:0% +Ben means to be inside that smaller + + + align:start position:0% +Ben means to be inside that smaller +square inside London the hit outside + + align:start position:0% +square inside London the hit outside + + + align:start position:0% +square inside London the hit outside +means to hit outside okay that's what + + align:start position:0% +means to hit outside okay that's what + + + align:start position:0% +means to hit outside okay that's what +they mean it just gives you back a true + + align:start position:0% +they mean it just gives you back a true + + + align:start position:0% +they mean it just gives you back a true +or false on a particular point in a two + + align:start position:0% +or false on a particular point in a two + + + align:start position:0% +or false on a particular point in a two +dimensional space is it true or is it + + align:start position:0% +dimensional space is it true or is it + + + align:start position:0% +dimensional space is it true or is it +false that this is this happen now you + + align:start position:0% +false that this is this happen now you + + + align:start position:0% +false that this is this happen now you +have a speaker and listener model and + + align:start position:0% +have a speaker and listener model and + + + align:start position:0% +have a speaker and listener model and +the way that the speaker works is that + + align:start position:0% +the way that the speaker works is that + + + align:start position:0% +the way that the speaker works is that +he has a particular state in mind like + + align:start position:0% +he has a particular state in mind like + + + align:start position:0% +he has a particular state in mind like +he's looking at a woman at the sit of + + align:start position:0% +he's looking at a woman at the sit of + + + align:start position:0% +he's looking at a woman at the sit of +the world the bomb fell here and he + + align:start position:0% +the world the bomb fell here and he + + + align:start position:0% +the world the bomb fell here and he +needs to communicate something okay and + + align:start position:0% +needs to communicate something okay and + + + align:start position:0% +needs to communicate something okay and +he's reasoning about the others about + + align:start position:0% +he's reasoning about the others about + + + align:start position:0% +he's reasoning about the others about +the listener to a particular depth okay + + align:start position:0% +the listener to a particular depth okay + + + align:start position:0% +the listener to a particular depth okay +what he's going to do is he's going to + + align:start position:0% +what he's going to do is he's going to + + + align:start position:0% +what he's going to do is he's going to +choose a word randomly because our prior + + align:start position:0% +choose a word randomly because our prior + + + align:start position:0% +choose a word randomly because our prior +is rather kinda like before we chose an + + align:start position:0% +is rather kinda like before we chose an + + + align:start position:0% +is rather kinda like before we chose an +action at random and we saw if it worked + + align:start position:0% +action at random and we saw if it worked + + + align:start position:0% +action at random and we saw if it worked +his when to choose a word at random and + + align:start position:0% +his when to choose a word at random and + + + align:start position:0% +his when to choose a word at random and +he's going to choose the words such that + + align:start position:0% +he's going to choose the words such that + + + align:start position:0% +he's going to choose the words such that +it's going to cause the right state in + + align:start position:0% +it's going to cause the right state in + + + align:start position:0% +it's going to cause the right state in +the listener so he needs a model of the + + align:start position:0% +the listener so he needs a model of the + + + align:start position:0% +the listener so he needs a model of the +listener what's the listener the + + align:start position:0% +listener what's the listener the + + + align:start position:0% +listener what's the listener the +listener is someone who takes in a word + + align:start position:0% +listener is someone who takes in a word + + + align:start position:0% +listener is someone who takes in a word +and tries to figure out the state he + + align:start position:0% +and tries to figure out the state he + + + align:start position:0% +and tries to figure out the state he +doesn't know what happened where did the + + align:start position:0% +doesn't know what happened where did the + + + align:start position:0% +doesn't know what happened where did the +bomb fall someone gives him a word he's + + align:start position:0% +bomb fall someone gives him a word he's + + + align:start position:0% +bomb fall someone gives him a word he's +trying to figure out the state so he's + + align:start position:0% +trying to figure out the state so he's + + + align:start position:0% +trying to figure out the state so he's +drawing his state from the prior and + + align:start position:0% +drawing his state from the prior and + + + align:start position:0% +drawing his state from the prior and +it's prior is it could be anywhere it + + align:start position:0% +it's prior is it could be anywhere it + + + align:start position:0% +it's prior is it could be anywhere it +could be anywhere in the square where + + align:start position:0% +could be anywhere in the square where + + + align:start position:0% +could be anywhere in the square where +did that actually fall well it fell here + + align:start position:0% +did that actually fall well it fell here + + + align:start position:0% +did that actually fall well it fell here +let's say given that I got this + + align:start position:0% +let's say given that I got this + + + align:start position:0% +let's say given that I got this +particular word but this word was + + align:start position:0% +particular word but this word was + + + align:start position:0% +particular word but this word was +generated by a speaker which I need a + + align:start position:0% +generated by a speaker which I need a + + + align:start position:0% +generated by a speaker which I need a +model of so there's this model of the + + align:start position:0% +model of so there's this model of the + + + align:start position:0% +model of so there's this model of the +speaker understanding the listener or + + align:start position:0% +speaker understanding the listener or + + + align:start position:0% +speaker understanding the listener or +model the listener understanding the + + align:start position:0% +model the listener understanding the + + + align:start position:0% +model the listener understanding the +speaker up to a particular depth okay + + align:start position:0% +speaker up to a particular depth okay + + + align:start position:0% +speaker up to a particular depth okay +and they need to bottom out at some + + align:start position:0% +and they need to bottom out at some + + + align:start position:0% +and they need to bottom out at some +point and it's not that hard right like + + align:start position:0% +point and it's not that hard right like + + + align:start position:0% +point and it's not that hard right like +I mean it takes some time to wrap your + + align:start position:0% +I mean it takes some time to wrap your + + + align:start position:0% +I mean it takes some time to wrap your +head around it but it's written about + + align:start position:0% +head around it but it's written about + + + align:start position:0% +head around it but it's written about +eight lines of code and that's why I + + align:start position:0% +eight lines of code and that's why I + + + align:start position:0% +eight lines of code and that's why I +said the church + + align:start position:0% +said the church + + + align:start position:0% +said the church +remember that caveat I gave you of like + + align:start position:0% +remember that caveat I gave you of like + + + align:start position:0% +remember that caveat I gave you of like +it's a toy it's not a toy language it's + + align:start position:0% +it's a toy it's not a toy language it's + + + align:start position:0% +it's a toy it's not a toy language it's +under development but it's actually been + + align:start position:0% +under development but it's actually been + + + align:start position:0% +under development but it's actually been +doing some pretty interesting stuff this + + align:start position:0% +doing some pretty interesting stuff this + + + align:start position:0% +doing some pretty interesting stuff this +is one of those things these sort of + + align:start position:0% +is one of those things these sort of + + + align:start position:0% +is one of those things these sort of +language games are really hard to write + + align:start position:0% +language games are really hard to write + + + align:start position:0% +language games are really hard to write +in many other models really hard to + + align:start position:0% +in many other models really hard to + + + align:start position:0% +in many other models really hard to +write and here it's kind of trivial + + align:start position:0% +write and here it's kind of trivial + + + align:start position:0% +write and here it's kind of trivial +you can sort of see where to play with + + align:start position:0% +you can sort of see where to play with + + + align:start position:0% +you can sort of see where to play with +that I came up with this example + + align:start position:0% +that I came up with this example + + + align:start position:0% +that I came up with this example +yesterday and it's actually like asked + + align:start position:0% +yesterday and it's actually like asked + + + align:start position:0% +yesterday and it's actually like asked +andreas which is my go-to guy for these + + align:start position:0% +andreas which is my go-to guy for these + + + align:start position:0% +andreas which is my go-to guy for these +things and II thought it was interesting + + align:start position:0% +things and II thought it was interesting + + + align:start position:0% +things and II thought it was interesting +so you would run that and let's say that + + align:start position:0% +so you would run that and let's say that + + + align:start position:0% +so you would run that and let's say that +the the the speaker said it hit London + + align:start position:0% +the the the speaker said it hit London + + + align:start position:0% +the the the speaker said it hit London +what should the listener understand + + align:start position:0% +what should the listener understand + + + align:start position:0% +what should the listener understand +where is this distribution over it and + + align:start position:0% +where is this distribution over it and + + + align:start position:0% +where is this distribution over it and +I've sort of just sampled from it I've + + align:start position:0% +I've sort of just sampled from it I've + + + align:start position:0% +I've sort of just sampled from it I've +sampled from his distribution over where + + align:start position:0% +sampled from his distribution over where + + + align:start position:0% +sampled from his distribution over where +he thinks it fell and you can sort of + + align:start position:0% +he thinks it fell and you can sort of + + + align:start position:0% +he thinks it fell and you can sort of +notice I just did a few samples but you + + align:start position:0% +notice I just did a few samples but you + + + align:start position:0% +notice I just did a few samples but you +can sort of notice the suspicious gap + + align:start position:0% +can sort of notice the suspicious gap + + + align:start position:0% +can sort of notice the suspicious gap +over here and if I sample a hundred + + align:start position:0% +over here and if I sample a hundred + + + align:start position:0% +over here and if I sample a hundred +points you'll notice that it's basically + + align:start position:0% +points you'll notice that it's basically + + + align:start position:0% +points you'll notice that it's basically +it's going to be in London so between 1 + + align:start position:0% +it's going to be in London so between 1 + + + align:start position:0% +it's going to be in London so between 1 +and 1 + + align:start position:0% +and 1 + + + align:start position:0% +and 1 +let's might take it a minute but what + + align:start position:0% +let's might take it a minute but what + + + align:start position:0% +let's might take it a minute but what +you'll end up seeing is that it's + + align:start position:0% +you'll end up seeing is that it's + + + align:start position:0% +you'll end up seeing is that it's +probably anywhere in London if someone + + align:start position:0% +probably anywhere in London if someone + + + align:start position:0% +probably anywhere in London if someone +said to you it fell in London + + align:start position:0% +said to you it fell in London + + + align:start position:0% +said to you it fell in London +then you infer that it's anywhere in + + align:start position:0% +then you infer that it's anywhere in + + + align:start position:0% +then you infer that it's anywhere in +London except Big Ben because it was big + + align:start position:0% +London except Big Ben because it was big + + + align:start position:0% +London except Big Ben because it was big +then you would have said big then it's + + align:start position:0% +then you would have said big then it's + + + align:start position:0% +then you would have said big then it's +not perfect I mean there's some samples + + align:start position:0% +not perfect I mean there's some samples + + + align:start position:0% +not perfect I mean there's some samples +that get there it's actually some + + align:start position:0% +that get there it's actually some + + + align:start position:0% +that get there it's actually some +shifting distribution but yeah if you + + align:start position:0% +shifting distribution but yeah if you + + + align:start position:0% +shifting distribution but yeah if you +took like some heat map of this thing + + align:start position:0% +took like some heat map of this thing + + + align:start position:0% +took like some heat map of this thing +what you would end up with is that + + align:start position:0% +what you would end up with is that + + + align:start position:0% +what you would end up with is that +there's some sort of suspicious + + align:start position:0% +there's some sort of suspicious + + + align:start position:0% +there's some sort of suspicious +emptiness over here in this case there's + + align:start position:0% +emptiness over here in this case there's + + + align:start position:0% +emptiness over here in this case there's +also a bit of an emptiness over there + + align:start position:0% +also a bit of an emptiness over there + + + align:start position:0% +also a bit of an emptiness over there +but in the limit + + align:start position:0% +but in the limit + + + align:start position:0% +but in the limit +you'll get that so we did Plan B which + + align:start position:0% +you'll get that so we did Plan B which + + + align:start position:0% +you'll get that so we did Plan B which +was to zoom through a few things very + + align:start position:0% +was to zoom through a few things very + + + align:start position:0% +was to zoom through a few things very +quickly I'm sure you guys didn't fully + + align:start position:0% +quickly I'm sure you guys didn't fully + + + align:start position:0% +quickly I'm sure you guys didn't fully +grope the details and that's ok what I + + align:start position:0% +grope the details and that's ok what I + + + align:start position:0% +grope the details and that's ok what I +wanted to do with Plan B was to give you + + align:start position:0% +wanted to do with Plan B was to give you + + + align:start position:0% +wanted to do with Plan B was to give you +a taste of what is possible and how you + + align:start position:0% +a taste of what is possible and how you + + + align:start position:0% +a taste of what is possible and how you +would go about writing models the + + align:start position:0% +would go about writing models the + + + align:start position:0% +would go about writing models the +important things to remember here is + + align:start position:0% +important things to remember here is + + + align:start position:0% +important things to remember here is +that probabilistic programs are great + + align:start position:0% +that probabilistic programs are great + + + align:start position:0% +that probabilistic programs are great +tools for capturing lots of rich + + align:start position:0% +tools for capturing lots of rich + + + align:start position:0% +tools for capturing lots of rich +structure anything from physics to + + align:start position:0% +structure anything from physics to + + + align:start position:0% +structure anything from physics to +psychology to language games to grammars + + align:start position:0% +psychology to language games to grammars + + + align:start position:0% +psychology to language games to grammars +to vision churches a particularly useful + + align:start position:0% +to vision churches a particularly useful + + + align:start position:0% +to vision churches a particularly useful +language for teaching yourselves about + + align:start position:0% +language for teaching yourselves about + + + align:start position:0% +language for teaching yourselves about +these things there's a lot of different + + align:start position:0% +these things there's a lot of different + + + align:start position:0% +these things there's a lot of different +models they can play with on promod org + + align:start position:0% +models they can play with on promod org + + + align:start position:0% +models they can play with on promod org +you can write down a generative model + + align:start position:0% +you can write down a generative model + + + align:start position:0% +you can write down a generative model +very easily to describe how you think + + align:start position:0% +very easily to describe how you think + + + align:start position:0% +very easily to describe how you think +the world works and then you can put + + align:start position:0% +the world works and then you can put + + + align:start position:0% +the world works and then you can put +that in an inference engine and try to + + align:start position:0% +that in an inference engine and try to + + + align:start position:0% +that in an inference engine and try to +figure out what you actually saw ok so + + align:start position:0% +figure out what you actually saw ok so + + + align:start position:0% +figure out what you actually saw ok so +thank you + + align:start position:0% +thank you + + + align:start position:0% +thank you +[Applause] \ No newline at end of file diff --git a/V4uZz6OO2bM.txt b/V4uZz6OO2bM.txt new file mode 100644 index 0000000000000000000000000000000000000000..c1a3a167a34b6430063fa501f353485dba75aca1 --- /dev/null +++ b/V4uZz6OO2bM.txt @@ -0,0 +1,539 @@ +align:start position:0% + +so this gets me to my + + align:start position:0% +so this gets me to my + + + align:start position:0% +so this gets me to my +my brief why this matters for take so + + align:start position:0% +my brief why this matters for take so + + + align:start position:0% +my brief why this matters for take so +you know you say why is + + align:start position:0% +you know you say why is + + + align:start position:0% +you know you say why is +why would i care which one of these co2 + + align:start position:0% +why would i care which one of these co2 + + + align:start position:0% +why would i care which one of these co2 +takes + + align:start position:0% +takes + + + align:start position:0% +takes +right okay well it turns out that + + align:start position:0% +right okay well it turns out that + + + align:start position:0% +right okay well it turns out that +as long as we're not at absolute zero + + align:start position:0% +as long as we're not at absolute zero + + + align:start position:0% +as long as we're not at absolute zero +this molecule is moving + + align:start position:0% +this molecule is moving + + + align:start position:0% +this molecule is moving +and and so obviously that's related to + + align:start position:0% +and and so obviously that's related to + + + align:start position:0% +and and so obviously that's related to +this + + align:start position:0% + + + + align:start position:0% + +it's not obvious but cars + + align:start position:0% +it's not obvious but cars + + + align:start position:0% +it's not obvious but cars +in the u.s are now the number one + + align:start position:0% +in the u.s are now the number one + + + align:start position:0% +in the u.s are now the number one +emitter of co2 they're the number one + + align:start position:0% +emitter of co2 they're the number one + + + align:start position:0% +emitter of co2 they're the number one +cause + + align:start position:0% +cause + + + align:start position:0% +cause +of co2 emissions um and + + align:start position:0% +of co2 emissions um and + + + align:start position:0% +of co2 emissions um and +here's a nice little corner somewhere um + + align:start position:0% +here's a nice little corner somewhere um + + + align:start position:0% +here's a nice little corner somewhere um +and and so this is coming out now from + + align:start position:0% +and and so this is coming out now from + + + align:start position:0% +and and so this is coming out now from +the transportation sector you have the + + align:start position:0% +the transportation sector you have the + + + align:start position:0% +the transportation sector you have the +most more of the co2 comes from that + + align:start position:0% +most more of the co2 comes from that + + + align:start position:0% +most more of the co2 comes from that +than any other sector + + align:start position:0% +than any other sector + + + align:start position:0% +than any other sector +why does it matter well and why does + + align:start position:0% +why does it matter well and why does + + + align:start position:0% +why does it matter well and why does +this structure why does this lewis + + align:start position:0% +this structure why does this lewis + + + align:start position:0% +this structure why does this lewis +structure + + align:start position:0% +structure + + + align:start position:0% +structure +matter well it has to do with how it + + align:start position:0% +matter well it has to do with how it + + + align:start position:0% +matter well it has to do with how it +moves + + align:start position:0% +moves + + + align:start position:0% +moves +because you see i showed you this before + + align:start position:0% +because you see i showed you this before + + + align:start position:0% +because you see i showed you this before +and and i didn't complete it because we + + align:start position:0% +and and i didn't complete it because we + + + align:start position:0% +and and i didn't complete it because we +were talking about electron transitions + + align:start position:0% +were talking about electron transitions + + + align:start position:0% +were talking about electron transitions +and then i gave you the example of ozone + + align:start position:0% +and then i gave you the example of ozone + + + align:start position:0% +and then i gave you the example of ozone +being really important + + align:start position:0% +being really important + + + align:start position:0% +being really important +for absorbing in the uv and i showed you + + align:start position:0% +for absorbing in the uv and i showed you + + + align:start position:0% +for absorbing in the uv and i showed you +the chemistry of ozone degradation with + + align:start position:0% +the chemistry of ozone degradation with + + + align:start position:0% +the chemistry of ozone degradation with +cfcs but you see + + align:start position:0% +cfcs but you see + + + align:start position:0% +cfcs but you see +there's look at this absorption out here + + align:start position:0% +there's look at this absorption out here + + + align:start position:0% +there's look at this absorption out here +there's co2 + + align:start position:0% +there's co2 + + + align:start position:0% +there's co2 +right and so there's the sunlight above + + align:start position:0% +right and so there's the sunlight above + + + align:start position:0% +right and so there's the sunlight above +the atmosphere here it is + + align:start position:0% +the atmosphere here it is + + + align:start position:0% +the atmosphere here it is +on earth and you can see co2 there and + + align:start position:0% +on earth and you can see co2 there and + + + align:start position:0% +on earth and you can see co2 there and +but see + + align:start position:0% +but see + + + align:start position:0% +but see +the the reason co2 absorbs there + + align:start position:0% +the the reason co2 absorbs there + + + align:start position:0% +the the reason co2 absorbs there +has to do with how it moves right it has + + align:start position:0% +has to do with how it moves right it has + + + align:start position:0% +has to do with how it moves right it has +to do + + align:start position:0% +to do + + + align:start position:0% +to do +with its vibrations now that's not + + align:start position:0% +with its vibrations now that's not + + + align:start position:0% +with its vibrations now that's not +something that you need to know but i + + align:start position:0% +something that you need to know but i + + + align:start position:0% +something that you need to know but i +wanted just to to tell you know for like + + align:start position:0% +wanted just to to tell you know for like + + + align:start position:0% +wanted just to to tell you know for like +a test or something but i wanted to tell + + align:start position:0% +a test or something but i wanted to tell + + + align:start position:0% +a test or something but i wanted to tell +you about it because + + align:start position:0% +you about it because + + + align:start position:0% +you about it because +it is directly related to what we just + + align:start position:0% +it is directly related to what we just + + + align:start position:0% +it is directly related to what we just +did right those vibrations + + align:start position:0% +did right those vibrations + + + align:start position:0% +did right those vibrations +and by the way that first mode that + + align:start position:0% +and by the way that first mode that + + + align:start position:0% +and by the way that first mode that +first mode is the one out here + + align:start position:0% +first mode is the one out here + + + align:start position:0% +first mode is the one out here +doing all the ir absorption right this + + align:start position:0% +doing all the ir absorption right this + + + align:start position:0% +doing all the ir absorption right this +one + + align:start position:0% +one + + + align:start position:0% +one +and you can see right away like if this + + align:start position:0% +and you can see right away like if this + + + align:start position:0% +and you can see right away like if this +thing is is wiggling + + align:start position:0% +thing is is wiggling + + + align:start position:0% +thing is is wiggling +um it's going to wiggle very differently + + align:start position:0% +um it's going to wiggle very differently + + + align:start position:0% +um it's going to wiggle very differently +right it's going to wiggle very + + align:start position:0% +right it's going to wiggle very + + + align:start position:0% +right it's going to wiggle very +differently + + align:start position:0% +differently + + + align:start position:0% +differently +whether it has two double bonds on + + align:start position:0% +whether it has two double bonds on + + + align:start position:0% +whether it has two double bonds on +either side of the carbon or a triple in + + align:start position:0% +either side of the carbon or a triple in + + + align:start position:0% +either side of the carbon or a triple in +a single + + align:start position:0% +a single + + + align:start position:0% +a single +right and so that alone tells you + + align:start position:0% +right and so that alone tells you + + + align:start position:0% +right and so that alone tells you +something really important about how it + + align:start position:0% +something really important about how it + + + align:start position:0% +something really important about how it +interacts + + align:start position:0% +interacts + + + align:start position:0% +interacts +in our atmosphere with uh with thermal + + align:start position:0% +in our atmosphere with uh with thermal + + + align:start position:0% +in our atmosphere with uh with thermal +with radiant heat + + align:start position:0% +with radiant heat + + + align:start position:0% +with radiant heat +right with ir radiation + + align:start position:0% +right with ir radiation + + + align:start position:0% +right with ir radiation +okay that's my why this matters \ No newline at end of file diff --git a/Vsxfd97trIk.txt b/Vsxfd97trIk.txt new file mode 100644 index 0000000000000000000000000000000000000000..edec8e875acc4ef3040dc89aaef1552edb63f799 --- /dev/null +++ b/Vsxfd97trIk.txt @@ -0,0 +1,1947 @@ +align:start position:0% + +so what do we do in + + align:start position:0% +so what do we do in + + + align:start position:0% +so what do we do in +practice uh the simple approach is to + + align:start position:0% +practice uh the simple approach is to + + + align:start position:0% +practice uh the simple approach is to +calculate the upper bound this is known + + align:start position:0% +calculate the upper bound this is known + + + align:start position:0% +calculate the upper bound this is known +as the expected value of perfect + + align:start position:0% +as the expected value of perfect + + + align:start position:0% +as the expected value of perfect +information so this is where I'm I want + + align:start position:0% +information so this is where I'm I want + + + align:start position:0% +information so this is where I'm I want +to be leading you in this in this + + align:start position:0% +to be leading you in this in this + + + align:start position:0% +to be leading you in this in this +exercise so the expected value of + + align:start position:0% +exercise so the expected value of + + + align:start position:0% +exercise so the expected value of +perfect information is totally + + align:start position:0% +perfect information is totally + + + align:start position:0% +perfect information is totally +hypothetical it does not + + align:start position:0% +hypothetical it does not + + + align:start position:0% +hypothetical it does not +exist but it simplifies the analysis and + + align:start position:0% +exist but it simplifies the analysis and + + + align:start position:0% +exist but it simplifies the analysis and +gives you an upper bound which is useful + + align:start position:0% +gives you an upper bound which is useful + + + align:start position:0% +gives you an upper bound which is useful +because we can definitely exclude some + + align:start position:0% +because we can definitely exclude some + + + align:start position:0% +because we can definitely exclude some +tests if they don't meet if they um + + align:start position:0% +tests if they don't meet if they um + + + align:start position:0% +tests if they don't meet if they um +exceed the upper bound of the possible + + align:start position:0% +exceed the upper bound of the possible + + + align:start position:0% +exceed the upper bound of the possible +value so the concept is that there is a + + align:start position:0% +value so the concept is that there is a + + + align:start position:0% +value so the concept is that there is a +perfect test with exactly which event is + + align:start position:0% +perfect test with exactly which event is + + + align:start position:0% +perfect test with exactly which event is +going to occur I will call this I am + + align:start position:0% +going to occur I will call this I am + + + align:start position:0% +going to occur I will call this I am +calling this a Cassandra machine the + + align:start position:0% +calling this a Cassandra machine the + + + align:start position:0% +calling this a Cassandra machine the +Greek mythology not that anybody should + + align:start position:0% +Greek mythology not that anybody should + + + align:start position:0% +Greek mythology not that anybody should +necessarily know it um is that this lady + + align:start position:0% +necessarily know it um is that this lady + + + align:start position:0% +necessarily know it um is that this lady +called Cassandra who had the gift so to + + align:start position:0% +called Cassandra who had the gift so to + + + align:start position:0% +called Cassandra who had the gift so to +speak of always seeing what the future + + align:start position:0% +speak of always seeing what the future + + + align:start position:0% +speak of always seeing what the future +would be and with the curse that nobody + + align:start position:0% +would be and with the curse that nobody + + + align:start position:0% +would be and with the curse that nobody +would ever believe her it was all about + + align:start position:0% +would ever believe her it was all about + + + align:start position:0% +would ever believe her it was all about +the uh um the battle for Troy um and she + + align:start position:0% +the uh um the battle for Troy um and she + + + align:start position:0% +the uh um the battle for Troy um and she +could predict that somebody would die + + align:start position:0% +could predict that somebody would die + + + align:start position:0% +could predict that somebody would die +but nobody would believe her and so on + + align:start position:0% +but nobody would believe her and so on + + + align:start position:0% +but nobody would believe her and so on +so that was the thing that she could + + align:start position:0% +so that was the thing that she could + + + align:start position:0% +so that was the thing that she could +predict absolutely so this is the + + align:start position:0% +predict absolutely so this is the + + + align:start position:0% +predict absolutely so this is the +Cassandra machine that it it it predicts + + align:start position:0% +Cassandra machine that it it it predicts + + + align:start position:0% +Cassandra machine that it it it predicts +absolutely now of + + align:start position:0% +absolutely now of + + + align:start position:0% +absolutely now of +course that is does not exist but what + + align:start position:0% +course that is does not exist but what + + + align:start position:0% +course that is does not exist but what +is the benefit of + + align:start position:0% +is the benefit of + + + align:start position:0% +is the benefit of +it so the Cassandra machine is this + + align:start position:0% +it so the Cassandra machine is this + + + align:start position:0% +it so the Cassandra machine is this +black box which predicts exactly what + + align:start position:0% +black box which predicts exactly what + + + align:start position:0% +black box which predicts exactly what +test result will occur it produces the + + align:start position:0% +test result will occur it produces the + + + align:start position:0% +test result will occur it produces the +best possible + + align:start position:0% +best possible + + + align:start position:0% +best possible +information therefore I mean it's + + align:start position:0% +information therefore I mean it's + + + align:start position:0% +information therefore I mean it's +absolutely true so if you had the best + + align:start position:0% +absolutely true so if you had the best + + + align:start position:0% +absolutely true so if you had the best +possible information that is if you + + align:start position:0% +possible information that is if you + + + align:start position:0% +possible information that is if you +ended up with no uncertainty you could + + align:start position:0% +ended up with no uncertainty you could + + + align:start position:0% +ended up with no uncertainty you could +make the best decisions and you would + + align:start position:0% +make the best decisions and you would + + + align:start position:0% +make the best decisions and you would +have the maximum gain over the decision + + align:start position:0% +have the maximum gain over the decision + + + align:start position:0% +have the maximum gain over the decision +you'd make without the + + align:start position:0% +you'd make without the + + + align:start position:0% +you'd make without the +information therefore it gives you the + + align:start position:0% +information therefore it gives you the + + + align:start position:0% +information therefore it gives you the +upper limit on the value of the test so + + align:start position:0% +upper limit on the value of the test so + + + align:start position:0% +upper limit on the value of the test so +what we can do if we can't get the real + + align:start position:0% +what we can do if we can't get the real + + + align:start position:0% +what we can do if we can't get the real +value we can at least set some limits on + + align:start position:0% +value we can at least set some limits on + + + align:start position:0% +value we can at least set some limits on +it and this is what the Cassandra + + align:start position:0% +it and this is what the Cassandra + + + align:start position:0% +it and this is what the Cassandra +machine this hypothetical thing does the + + align:start position:0% +machine this hypothetical thing does the + + + align:start position:0% +machine this hypothetical thing does the +further beauty of it is that the + + align:start position:0% +further beauty of it is that the + + + align:start position:0% +further beauty of it is that the +calculation for this expected value of + + align:start position:0% +calculation for this expected value of + + + align:start position:0% +calculation for this expected value of +perfect information is almost trivial + + align:start position:0% +perfect information is almost trivial + + + align:start position:0% +perfect information is almost trivial +the first time you try to do it you'll + + align:start position:0% +the first time you try to do it you'll + + + align:start position:0% +the first time you try to do it you'll +flounder around a bit because you're not + + align:start position:0% +flounder around a bit because you're not + + + align:start position:0% +flounder around a bit because you're not +used to it but basically it's a very + + align:start position:0% +used to it but basically it's a very + + + align:start position:0% +used to it but basically it's a very +simple um device and is pretty + + align:start position:0% +simple um device and is pretty + + + align:start position:0% +simple um device and is pretty +transparent + + align:start position:0% +transparent + + + align:start position:0% +transparent +so let me give you an + + align:start position:0% +so let me give you an + + + align:start position:0% +so let me give you an +example so uh remember this is the + + align:start position:0% +example so uh remember this is the + + + align:start position:0% +example so uh remember this is the +raincoat problem that you getting up in + + align:start position:0% +raincoat problem that you getting up in + + + align:start position:0% +raincoat problem that you getting up in +the morning and should you decide to + + align:start position:0% +the morning and should you decide to + + + align:start position:0% +the morning and should you decide to +take the rain cat or not there may be a + + align:start position:0% +take the rain cat or not there may be a + + + align:start position:0% +take the rain cat or not there may be a +chance of rain uh rain or no rain as in + + align:start position:0% +chance of rain uh rain or no rain as in + + + align:start position:0% +chance of rain uh rain or no rain as in +the diagram uh there's a a prior + + align:start position:0% +the diagram uh there's a a prior + + + align:start position:0% +the diagram uh there's a a prior +assessment the probability is 04 or 6 of + + align:start position:0% +assessment the probability is 04 or 6 of + + + align:start position:0% +assessment the probability is 04 or 6 of +rain or no rain and there is these + + align:start position:0% +rain or no rain and there is these + + + align:start position:0% +rain or no rain and there is these +values of the situation in the end of + + align:start position:0% +values of the situation in the end of + + + align:start position:0% +values of the situation in the end of +five - 2 - 10 and four values that I've + + align:start position:0% +five - 2 - 10 and four values that I've + + + align:start position:0% +five - 2 - 10 and four values that I've +invented just to give us numbers to play + + align:start position:0% +invented just to give us numbers to play + + + align:start position:0% +invented just to give us numbers to play +with but um uh that's the original + + align:start position:0% +with but um uh that's the original + + + align:start position:0% +with but um uh that's the original +problem now uh just to set ourselves + + align:start position:0% +problem now uh just to set ourselves + + + align:start position:0% +problem now uh just to set ourselves +back into this + + align:start position:0% +back into this + + + align:start position:0% +back into this +context what the better choice at this + + align:start position:0% +context what the better choice at this + + + align:start position:0% +context what the better choice at this +point is + + align:start position:0% +point is + + + align:start position:0% +point is +what so how do we remind you how it is + + align:start position:0% +what so how do we remind you how it is + + + align:start position:0% +what so how do we remind you how it is +if we take the rain code which is a top + + align:start position:0% +if we take the rain code which is a top + + + align:start position:0% +if we take the rain code which is a top +decision we have a 04 chance of having + + align:start position:0% +decision we have a 04 chance of having + + + align:start position:0% +decision we have a 04 chance of having +five which is averages to two we have + + align:start position:0% +five which is averages to two we have + + + align:start position:0% +five which is averages to two we have +a06 chance of uh getting a minus um two + + align:start position:0% +a06 chance of uh getting a minus um two + + + align:start position:0% +a06 chance of uh getting a minus um two +which is a minus 1.2 2us 1.2 is + + align:start position:0% +which is a minus 1.2 2us 1.2 is + + + align:start position:0% +which is a minus 1.2 2us 1.2 is +0.8 conversely if I don't take the + + align:start position:0% +0.8 conversely if I don't take the + + + align:start position:0% +0.8 conversely if I don't take the +raincoat I have a probability of four of + + align:start position:0% +raincoat I have a probability of four of + + + align:start position:0% +raincoat I have a probability of four of +the minus 10 that's minus four a + + align:start position:0% +the minus 10 that's minus four a + + + align:start position:0% +the minus 10 that's minus four a +probability of0 6 of four two points um + + align:start position:0% +probability of0 6 of four two points um + + + align:start position:0% +probability of0 6 of four two points um +2.4 so it's a negative number so my best + + align:start position:0% +2.4 so it's a negative number so my best + + + align:start position:0% +2.4 so it's a negative number so my best +uh choice is to take the rain code + + align:start position:0% +uh choice is to take the rain code + + + align:start position:0% +uh choice is to take the rain code +right so I hope that you're all now back + + align:start position:0% +right so I hope that you're all now back + + + align:start position:0% +right so I hope that you're all now back +into this particular Groove + + align:start position:0% + + + + align:start position:0% + +now so uh the setup for the + + align:start position:0% +now so uh the setup for the + + + align:start position:0% +now so uh the setup for the +probabilities uh for the + + align:start position:0% +probabilities uh for the + + + align:start position:0% +probabilities uh for the +evpi so it's either going to say it's + + align:start position:0% +evpi so it's either going to say it's + + + align:start position:0% +evpi so it's either going to say it's +going to rain or not rain that is the + + align:start position:0% +going to rain or not rain that is the + + + align:start position:0% +going to rain or not rain that is the +perfect machine you press the button say + + align:start position:0% +perfect machine you press the button say + + + align:start position:0% +perfect machine you press the button say +truth please and it'll say Cassandra + + align:start position:0% +truth please and it'll say Cassandra + + + align:start position:0% +truth please and it'll say Cassandra +machine says rain or we'll say the + + align:start position:0% +machine says rain or we'll say the + + + align:start position:0% +machine says rain or we'll say the +contrary and because I've only given it + + align:start position:0% +contrary and because I've only given it + + + align:start position:0% +contrary and because I've only given it +two + + align:start position:0% +two + + + align:start position:0% +two +choices now what are the probabilities + + align:start position:0% +choices now what are the probabilities + + + align:start position:0% +choices now what are the probabilities +going to say that well your best + + align:start position:0% +going to say that well your best + + + align:start position:0% +going to say that well your best +estimate of these + + align:start position:0% +estimate of these + + + align:start position:0% +estimate of these +probabilities is what you have started + + align:start position:0% +probabilities is what you have started + + + align:start position:0% +probabilities is what you have started +with before you thought there was a 40% + + align:start position:0% +with before you thought there was a 40% + + + align:start position:0% +with before you thought there was a 40% +chance of getting rain so 40% of the + + align:start position:0% +chance of getting rain so 40% of the + + + align:start position:0% +chance of getting rain so 40% of the +time it's going to tell you it's going + + align:start position:0% +time it's going to tell you it's going + + + align:start position:0% +time it's going to tell you it's going +to rain and conversely so that you a + + align:start position:0% +to rain and conversely so that you a + + + align:start position:0% +to rain and conversely so that you a +priori you have your best estimates for + + align:start position:0% +priori you have your best estimates for + + + align:start position:0% +priori you have your best estimates for +the value of the outcome is what your + + align:start position:0% +the value of the outcome is what your + + + align:start position:0% +the value of the outcome is what your +prior else were now in general once you + + align:start position:0% +prior else were now in general once you + + + align:start position:0% +prior else were now in general once you +know what + + align:start position:0% +know what + + + align:start position:0% +know what +the UN resolution of the uncertainty is + + align:start position:0% +the UN resolution of the uncertainty is + + + align:start position:0% +the UN resolution of the uncertainty is +you will the best decision is pretty + + align:start position:0% +you will the best decision is pretty + + + align:start position:0% +you will the best decision is pretty +obvious if you knew it would rain uh + + align:start position:0% +obvious if you knew it would rain uh + + + align:start position:0% +obvious if you knew it would rain uh +going back here if you knew it was going + + align:start position:0% +going back here if you knew it was going + + + align:start position:0% +going back here if you knew it was going +to rain you're comparing five versus 10 + + align:start position:0% +to rain you're comparing five versus 10 + + + align:start position:0% +to rain you're comparing five versus 10 +well you take the rain code if you knew + + align:start position:0% +well you take the rain code if you knew + + + align:start position:0% +well you take the rain code if you knew +for sure it wasn't going to rain you + + align:start position:0% +for sure it wasn't going to rain you + + + align:start position:0% +for sure it wasn't going to rain you +compare minus two and four and you don't + + align:start position:0% +compare minus two and four and you don't + + + align:start position:0% +compare minus two and four and you don't +take the rain code so the um you don't + + align:start position:0% +take the rain code so the um you don't + + + align:start position:0% +take the rain code so the um you don't +have to do any complicated calculations + + align:start position:0% +have to do any complicated calculations + + + align:start position:0% +have to do any complicated calculations +of the + + align:start position:0% +of the + + + align:start position:0% +of the +possibilities uh you would have a + + align:start position:0% +possibilities uh you would have a + + + align:start position:0% +possibilities uh you would have a +probability of 04 that would take the + + align:start position:0% +probability of 04 that would take the + + + align:start position:0% +probability of 04 that would take the +rain Cod to get it to five and the + + align:start position:0% +rain Cod to get it to five and the + + + align:start position:0% +rain Cod to get it to five and the +probability of 0 six of not taking uh of + + align:start position:0% +probability of 0 six of not taking uh of + + + align:start position:0% +probability of 0 six of not taking uh of +not taking the rain code and getting a + + align:start position:0% +not taking the rain code and getting a + + + align:start position:0% +not taking the rain code and getting a +result of four so you can write down + + align:start position:0% +result of four so you can write down + + + align:start position:0% +result of four so you can write down +your best decisions uh pretty + + align:start position:0% +your best decisions uh pretty + + + align:start position:0% +your best decisions uh pretty +automatically now um the expected value + + align:start position:0% +automatically now um the expected value + + + align:start position:0% +automatically now um the expected value +after this case as I'm running this + + align:start position:0% +after this case as I'm running this + + + align:start position:0% +after this case as I'm running this +calculation of uh doing the 04 time the + + align:start position:0% +calculation of uh doing the 04 time the + + + align:start position:0% +calculation of uh doing the 04 time the +result of five and the0 six of four your + + align:start position:0% +result of five and the0 six of four your + + + align:start position:0% +result of five and the0 six of four your +perfect value is + + align:start position:0% +perfect value is + + + align:start position:0% +perfect value is +4.4 now the expected value perfect + + align:start position:0% +4.4 now the expected value perfect + + + align:start position:0% +4.4 now the expected value perfect +information is the value of the + + align:start position:0% +information is the value of the + + + align:start position:0% +information is the value of the +increment not the value that at at the + + align:start position:0% +increment not the value that at at the + + + align:start position:0% +increment not the value that at at the +end of it it's the value of the + + align:start position:0% +end of it it's the value of the + + + align:start position:0% +end of it it's the value of the +increment as what did you get from it so + + align:start position:0% +increment as what did you get from it so + + + align:start position:0% +increment as what did you get from it so +the expected value after the test was + + align:start position:0% +the expected value after the test was + + + align:start position:0% +the expected value after the test was +4.4 the expected value before the test + + align:start position:0% +4.4 the expected value before the test + + + align:start position:0% +4.4 the expected value before the test +was 0 .8 the expected value of perfect + + align:start position:0% +was 0 .8 the expected value of perfect + + + align:start position:0% +was 0 .8 the expected value of perfect +information in this case is uh + + align:start position:0% + + + + align:start position:0% + +3.6 all right + + align:start position:0% +3.6 all right + + + align:start position:0% +3.6 all right +so the the nice thing about it is the + + align:start position:0% +so the the nice thing about it is the + + + align:start position:0% +so the the nice thing about it is the +prior the expected value of simple + + align:start position:0% +prior the expected value of simple + + + align:start position:0% +prior the expected value of simple +perfect information is simple to + + align:start position:0% +perfect information is simple to + + + align:start position:0% +perfect information is simple to +calculate the prior probability must + + align:start position:0% +calculate the prior probability must + + + align:start position:0% +calculate the prior probability must +equal the probability that you of the + + align:start position:0% +equal the probability that you of the + + + align:start position:0% +equal the probability that you of the +perfect test + + align:start position:0% +perfect test + + + align:start position:0% +perfect test +result once you've run the perfect test + + align:start position:0% +result once you've run the perfect test + + + align:start position:0% +result once you've run the perfect test +test the posterior probabilities are + + align:start position:0% +test the posterior probabilities are + + + align:start position:0% +test the posterior probabilities are +either zero or one that either this + + align:start position:0% +either zero or one that either this + + + align:start position:0% +either zero or one that either this +happens or it doesn't happen there's no + + align:start position:0% +happens or it doesn't happen there's no + + + align:start position:0% +happens or it doesn't happen there's no +doubt about that once you know that + + align:start position:0% +doubt about that once you know that + + + align:start position:0% +doubt about that once you know that +there's a whole lot of zero + + align:start position:0% +there's a whole lot of zero + + + align:start position:0% +there's a whole lot of zero +probabilities on and there's a one + + align:start position:0% +probabilities on and there's a one + + + align:start position:0% +probabilities on and there's a one +probability you know what you're going + + align:start position:0% +probability you know what you're going + + + align:start position:0% +probability you know what you're going +to choose and pretty much you can uh + + align:start position:0% +to choose and pretty much you can uh + + + align:start position:0% +to choose and pretty much you can uh +write the expected value perfect + + align:start position:0% +write the expected value perfect + + + align:start position:0% +write the expected value perfect +information formula directly there's no + + align:start position:0% +information formula directly there's no + + + align:start position:0% +information formula directly there's no +need to use Bas + + align:start position:0% + + + + align:start position:0% + +theorem so Robert since you asked a + + align:start position:0% +theorem so Robert since you asked a + + + align:start position:0% +theorem so Robert since you asked a +question before I'm not trying to put + + align:start position:0% +question before I'm not trying to put + + + align:start position:0% +question before I'm not trying to put +you on the spot but since you've been + + align:start position:0% +you on the spot but since you've been + + + align:start position:0% +you on the spot but since you've been +doing it and I'm showing you this + + align:start position:0% +doing it and I'm showing you this + + + align:start position:0% +doing it and I'm showing you this +um why did you not use this approach if + + align:start position:0% +um why did you not use this approach if + + + align:start position:0% +um why did you not use this approach if +you if you knew about it or maybe you + + align:start position:0% +you if you knew about it or maybe you + + + align:start position:0% +you if you knew about it or maybe you +didn't know about it so what what is a + + align:start position:0% +didn't know about it so what what is a + + + align:start position:0% +didn't know about it so what what is a +um can you have a discussion about this + + align:start position:0% +um can you have a discussion about this + + + align:start position:0% +um can you have a discussion about this +please or your response to this if I'm + + align:start position:0% +please or your response to this if I'm + + + align:start position:0% +please or your response to this if I'm +not embarrassing you or putting you in + + align:start position:0% +not embarrassing you or putting you in + + + align:start position:0% +not embarrassing you or putting you in +the spot which I don't need to oh that's + + align:start position:0% +the spot which I don't need to oh that's + + + align:start position:0% +the spot which I don't need to oh that's +fine I I actually haven't heard this uh + + align:start position:0% +fine I I actually haven't heard this uh + + + align:start position:0% +fine I I actually haven't heard this uh +perfect information + + align:start position:0% +perfect information + + + align:start position:0% +perfect information +idea um yeah so that's probably the main + + align:start position:0% +idea um yeah so that's probably the main + + + align:start position:0% +idea um yeah so that's probably the main +reason I didn't use it but the other one + + align:start position:0% +reason I didn't use it but the other one + + + align:start position:0% +reason I didn't use it but the other one +was like at Chevron we we kind of have a + + align:start position:0% +was like at Chevron we we kind of have a + + + align:start position:0% +was like at Chevron we we kind of have a +defined procedure in terms of how we + + align:start position:0% +defined procedure in terms of how we + + + align:start position:0% +defined procedure in terms of how we +justify value of information so that + + align:start position:0% +justify value of information so that + + + align:start position:0% +justify value of information so that +that procedure was utilizing the + + align:start position:0% +that procedure was utilizing the + + + align:start position:0% +that procedure was utilizing the +conditional + + align:start position:0% +conditional + + + align:start position:0% +conditional +probabilities uh but myself I was + + align:start position:0% +probabilities uh but myself I was + + + align:start position:0% +probabilities uh but myself I was +personally a bit uncomfortable because + + align:start position:0% +personally a bit uncomfortable because + + + align:start position:0% +personally a bit uncomfortable because +it like you were saying it's hard to + + align:start position:0% +it like you were saying it's hard to + + + align:start position:0% +it like you were saying it's hard to +figure out what the percentages would be + + align:start position:0% +figure out what the percentages would be + + + align:start position:0% +figure out what the percentages would be +for either a good medium or bad outcome + + align:start position:0% +for either a good medium or bad outcome + + + align:start position:0% +for either a good medium or bad outcome +so it it was it was pretty challenging + + align:start position:0% +so it it was it was pretty challenging + + + align:start position:0% +so it it was it was pretty challenging +to actually apply and I think at the end + + align:start position:0% +to actually apply and I think at the end + + + align:start position:0% +to actually apply and I think at the end +people weren't super confident in it + + align:start position:0% +people weren't super confident in it + + + align:start position:0% +people weren't super confident in it +like you were + + align:start position:0% +like you were + + + align:start position:0% +like you were +saying well I think that that's right so + + align:start position:0% +saying well I think that that's right so + + + align:start position:0% +saying well I think that that's right so +um about 30 or 40 years ago I mean I can + + align:start position:0% +um about 30 or 40 years ago I mean I can + + + align:start position:0% +um about 30 or 40 years ago I mean I can +I'm old enough to remember that there + + align:start position:0% +I'm old enough to remember that there + + + align:start position:0% +I'm old enough to remember that there +was a phase where decision analysis was + + align:start position:0% +was a phase where decision analysis was + + + align:start position:0% +was a phase where decision analysis was +really taught a lot in Business Schools + + align:start position:0% +really taught a lot in Business Schools + + + align:start position:0% +really taught a lot in Business Schools +which is since gone by uh and compies + + align:start position:0% +which is since gone by uh and compies + + + align:start position:0% +which is since gone by uh and compies +picked up on that because it was + + align:start position:0% +picked up on that because it was + + + align:start position:0% +picked up on that because it was +certainly better than not looking at + + align:start position:0% +certainly better than not looking at + + + align:start position:0% +certainly better than not looking at +uncertainty and it was nice to have this + + align:start position:0% +uncertainty and it was nice to have this + + + align:start position:0% +uncertainty and it was nice to have this +notion of a bay rule Baye theorem and uh + + align:start position:0% +notion of a bay rule Baye theorem and uh + + + align:start position:0% +notion of a bay rule Baye theorem and uh +people thought of these cells he being + + align:start position:0% +people thought of these cells he being + + + align:start position:0% +people thought of these cells he being +basian or not and so there's a whole + + align:start position:0% +basian or not and so there's a whole + + + align:start position:0% +basian or not and so there's a whole +history about why this was the correct + + align:start position:0% +history about why this was the correct + + + align:start position:0% +history about why this was the correct +Improvement and + + align:start position:0% +Improvement and + + + align:start position:0% +Improvement and +approach not thinking about the fact + + align:start position:0% +approach not thinking about the fact + + + align:start position:0% +approach not thinking about the fact +that these other issues that probably + + align:start position:0% +that these other issues that probably + + + align:start position:0% +that these other issues that probably +the associates probabilities and the + + align:start position:0% +the associates probabilities and the + + + align:start position:0% +the associates probabilities and the +probability of occurrence and so forth + + align:start position:0% +probability of occurrence and so forth + + + align:start position:0% +probability of occurrence and so forth +which are the part of that special + + align:start position:0% +which are the part of that special + + + align:start position:0% +which are the part of that special +factor for the uh operation of the base + + align:start position:0% +factor for the uh operation of the base + + + align:start position:0% +factor for the uh operation of the base +theorem are just basically hard to get + + align:start position:0% +theorem are just basically hard to get + + + align:start position:0% +theorem are just basically hard to get +hard to document and hard to prove so + + align:start position:0% +hard to document and hard to prove so + + + align:start position:0% +hard to document and hard to prove so +that I think that you are reflecting + + align:start position:0% +that I think that you are reflecting + + + align:start position:0% +that I think that you are reflecting +which may Exist Elsewhere I'm not + + align:start position:0% +which may Exist Elsewhere I'm not + + + align:start position:0% +which may Exist Elsewhere I'm not +pointing a finger at Chevron but um that + + align:start position:0% +pointing a finger at Chevron but um that + + + align:start position:0% +pointing a finger at Chevron but um that +they have an estab they have a decision + + align:start position:0% +they have an estab they have a decision + + + align:start position:0% +they have an estab they have a decision +analysis manual they have an approach a + + align:start position:0% +analysis manual they have an approach a + + + align:start position:0% +analysis manual they have an approach a +procedure and so forth but uh it doesn't + + align:start position:0% +procedure and so forth but uh it doesn't + + + align:start position:0% +procedure and so forth but uh it doesn't +um it doesn't really fly and as you + + align:start position:0% +um it doesn't really fly and as you + + + align:start position:0% +um it doesn't really fly and as you +suggest that a lot of people don't + + align:start position:0% +suggest that a lot of people don't + + + align:start position:0% +suggest that a lot of people don't +believe in it and I would be bor one of + + align:start position:0% +believe in it and I would be bor one of + + + align:start position:0% +believe in it and I would be bor one of +those if I were in Chevron uh is because + + align:start position:0% +those if I were in Chevron uh is because + + + align:start position:0% +those if I were in Chevron uh is because +I it's such a spongy the calculation is + + align:start position:0% +I it's such a spongy the calculation is + + + align:start position:0% +I it's such a spongy the calculation is +correct but the the data are spongy and + + align:start position:0% +correct but the the data are spongy and + + + align:start position:0% +correct but the the data are spongy and +it's a Geo garbage in garbage out kind + + align:start position:0% +it's a Geo garbage in garbage out kind + + + align:start position:0% +it's a Geo garbage in garbage out kind +of a situation I think so I understand + + align:start position:0% +of a situation I think so I understand + + + align:start position:0% +of a situation I think so I understand +that you're encouraged to do that and + + align:start position:0% +that you're encouraged to do that and + + + align:start position:0% +that you're encouraged to do that and +this uh EVP + + align:start position:0% +this uh EVP + + + align:start position:0% +this uh EVP +is Trivial mathematically I mean you you + + align:start position:0% +is Trivial mathematically I mean you you + + + align:start position:0% +is Trivial mathematically I mean you you +don't have + + align:start position:0% +don't have + + + align:start position:0% +don't have +to be smart or think through the + + align:start position:0% +to be smart or think through the + + + align:start position:0% +to be smart or think through the +complexities but it gives you an upper + + align:start position:0% +complexities but it gives you an upper + + + align:start position:0% +complexities but it gives you an upper +bound and that is the useful aspect of + + align:start position:0% +bound and that is the useful aspect of + + + align:start position:0% +bound and that is the useful aspect of +it and I thank you for noting that is + + align:start position:0% +it and I thank you for noting that is + + + align:start position:0% +it and I thank you for noting that is +not the usual way of approaching things + + align:start position:0% +not the usual way of approaching things + + + align:start position:0% +not the usual way of approaching things +um uh but I think that it's a a + + align:start position:0% +um uh but I think that it's a a + + + align:start position:0% +um uh but I think that it's a a +reasonable way to do it and productive + + align:start position:0% +reasonable way to do it and productive + + + align:start position:0% +reasonable way to do it and productive +and I would encourage you to take the + + align:start position:0% +and I would encourage you to take the + + + align:start position:0% +and I would encourage you to take the +message back now I can see that they're + + align:start position:0% +message back now I can see that they're + + + align:start position:0% +message back now I can see that they're +not going to change the proced + + align:start position:0% +not going to change the proced + + + align:start position:0% +not going to change the proced +procedures for you and so what people do + + align:start position:0% +procedures for you and so what people do + + + align:start position:0% +procedures for you and so what people do +in the case of the procedure is wrong + + align:start position:0% +in the case of the procedure is wrong + + + align:start position:0% +in the case of the procedure is wrong +they sort of try to ignore it which is + + align:start position:0% +they sort of try to ignore it which is + + + align:start position:0% +they sort of try to ignore it which is +what you reflected \ No newline at end of file diff --git a/Vw4Gw9No008.txt b/Vw4Gw9No008.txt new file mode 100644 index 0000000000000000000000000000000000000000..4e13d773d0ffc257c784541d72f52945d081c6d5 --- /dev/null +++ b/Vw4Gw9No008.txt @@ -0,0 +1,8499 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay so uh this is a big day + + align:start position:0% +ocw.mit.edu okay so uh this is a big day + + + align:start position:0% +ocw.mit.edu okay so uh this is a big day +part one of the course is completed and + + align:start position:0% +part one of the course is completed and + + + align:start position:0% +part one of the course is completed and +I have your quizzes for you and was a + + align:start position:0% +I have your quizzes for you and was a + + + align:start position:0% +I have your quizzes for you and was a +very successful result I'm very pleased + + align:start position:0% +very successful result I'm very pleased + + + align:start position:0% +very successful result I'm very pleased +I hope you are too um quiz average of 85 + + align:start position:0% +I hope you are too um quiz average of 85 + + + align:start position:0% +I hope you are too um quiz average of 85 +that's on the first part of the course + + align:start position:0% +that's on the first part of the course + + + align:start position:0% +that's on the first part of the course +and then the second part so this is sex + + align:start position:0% +and then the second part so this is sex + + + align:start position:0% +and then the second part so this is sex +chapter 3 now uh starts with in one + + align:start position:0% +chapter 3 now uh starts with in one + + + align:start position:0% +chapter 3 now uh starts with in one +dimension with an equation of a type + + align:start position:0% +dimension with an equation of a type + + + align:start position:0% +dimension with an equation of a type +that we've already seen a little bit so + + align:start position:0% +that we've already seen a little bit so + + + align:start position:0% +that we've already seen a little bit so +there's some some more things to say + + align:start position:0% +there's some some more things to say + + + align:start position:0% +there's some some more things to say +about the equation and the framework but + + align:start position:0% +about the equation and the framework but + + + align:start position:0% +about the equation and the framework but +then uh we get to make a start on + + align:start position:0% +then uh we get to make a start on + + + align:start position:0% +then uh we get to make a start on +the finite element approach to solving + + align:start position:0% +the finite element approach to solving + + + align:start position:0% +the finite element approach to solving +it we could of course in 1D finite + + align:start position:0% +it we could of course in 1D finite + + + align:start position:0% +it we could of course in 1D finite +differences are probably the way to go + + align:start position:0% +differences are probably the way to go + + + align:start position:0% +differences are probably the way to go +actually uh in one dimension uh the the + + align:start position:0% +actually uh in one dimension uh the the + + + align:start position:0% +actually uh in one dimension uh the the +special um success of finite elements + + align:start position:0% +special um success of finite elements + + + align:start position:0% +special um success of finite elements +doesn't really show up that much because + + align:start position:0% +doesn't really show up that much because + + + align:start position:0% +doesn't really show up that much because +finite elements have have been I mean + + align:start position:0% +finite elements have have been I mean + + + align:start position:0% +finite elements have have been I mean +one great reason for their success is + + align:start position:0% +one great reason for their success is + + + align:start position:0% +one great reason for their success is +the that they handle different + + align:start position:0% +the that they handle different + + + align:start position:0% +the that they handle different +geometries they're flexible you could + + align:start position:0% +geometries they're flexible you could + + + align:start position:0% +geometries they're flexible you could +have regions in the plane + + align:start position:0% +have regions in the plane + + + align:start position:0% +have regions in the plane +three-dimensional bodies of different + + align:start position:0% +three-dimensional bodies of different + + + align:start position:0% +three-dimensional bodies of different +shapes finite differences doesn't really + + align:start position:0% +shapes finite differences doesn't really + + + align:start position:0% +shapes finite differences doesn't really +know what to do at a curved boundary in + + align:start position:0% +know what to do at a curved boundary in + + + align:start position:0% +know what to do at a curved boundary in +uh in two or 3D uh finite elements copes + + align:start position:0% +uh in two or 3D uh finite elements copes + + + align:start position:0% +uh in two or 3D uh finite elements copes +much better so we'll make a start today + + align:start position:0% +much better so we'll make a start today + + + align:start position:0% +much better so we'll make a start today +more tomorrow or Friday on + + align:start position:0% +more tomorrow or Friday on + + + align:start position:0% +more tomorrow or Friday on +onedimensional finite elements and + + align:start position:0% +onedimensional finite elements and + + + align:start position:0% +onedimensional finite elements and +then at uh a couple of weeks later uh + + align:start position:0% +then at uh a couple of weeks later uh + + + align:start position:0% +then at uh a couple of weeks later uh +will be the real thing 2D and 3D okay so + + align:start position:0% +will be the real thing 2D and 3D okay so + + + align:start position:0% +will be the real thing 2D and 3D okay so +ready to go on chapter three so that's + + align:start position:0% +ready to go on chapter three so that's + + + align:start position:0% +ready to go on chapter three so that's +our equation and everybody sees right + + align:start position:0% +our equation and everybody sees right + + + align:start position:0% +our equation and everybody sees right +away what's the the framework that + + align:start position:0% +away what's the the framework that + + + align:start position:0% +away what's the the framework that +that's a transpose in some way this is a + + align:start position:0% +that's a transpose in some way this is a + + + align:start position:0% +that's a transpose in some way this is a +transpose + + align:start position:0% +transpose + + + align:start position:0% +transpose +CA but what's new of course is that + + align:start position:0% +CA but what's new of course is that + + + align:start position:0% +CA but what's new of course is that +we're dealing with functions not + + align:start position:0% +we're dealing with functions not + + + align:start position:0% +we're dealing with functions not +vectors so we're deal dealing with you + + align:start position:0% +vectors so we're deal dealing with you + + + align:start position:0% +vectors so we're deal dealing with you +could say operators not matrices + + align:start position:0% +could say operators not matrices + + + align:start position:0% +could say operators not matrices +and + + align:start position:0% +and + + + align:start position:0% +and +nevertheless the big picture is still as + + align:start position:0% +nevertheless the big picture is still as + + + align:start position:0% +nevertheless the big picture is still as +it was so let me take U of x to be the + + align:start position:0% +it was so let me take U of x to be the + + + align:start position:0% +it was so let me take U of x to be the +displacements again so I'm thinking more + + align:start position:0% +displacements again so I'm thinking more + + + align:start position:0% +displacements again so I'm thinking more +of mechanics than Electronics here + + align:start position:0% +of mechanics than Electronics here + + + align:start position:0% +of mechanics than Electronics here +displacements and then we have du the E + + align:start position:0% +displacements and then we have du the E + + + align:start position:0% +displacements and then we have du the E +of X will be Dux that'll be the + + align:start position:0% +of X will be Dux that'll be the + + + align:start position:0% +of X will be Dux that'll be the +stretching the + + align:start position:0% +stretching the + + + align:start position:0% +stretching the +elongation and of + + align:start position:0% +elongation and of + + + align:start position:0% +elongation and of +course at that step you already see the + + align:start position:0% +course at that step you already see the + + + align:start position:0% +course at that step you already see the +big new item that the fact that the a + + align:start position:0% +big new item that the fact that the a + + + align:start position:0% +big new item that the fact that the a +the one that gets us from U to + + align:start position:0% +the one that gets us from U to + + + align:start position:0% +the one that gets us from U to +DX instead of being a difference Matrix + + align:start position:0% +DX instead of being a difference Matrix + + + align:start position:0% +DX instead of being a difference Matrix +which it has been our Matrix a is now a + + align:start position:0% +which it has been our Matrix a is now a + + + align:start position:0% +which it has been our Matrix a is now a +derivative a is d by + + align:start position:0% +derivative a is d by + + + align:start position:0% +derivative a is d by +DX so that's we + + align:start position:0% +DX so that's we + + + align:start position:0% +DX so that's we +haven't maybe I'll just take out that + + align:start position:0% +haven't maybe I'll just take out that + + + align:start position:0% +haven't maybe I'll just take out that +Arrow so you so a is d by DX now + + align:start position:0% +Arrow so you so a is d by DX now + + + align:start position:0% +Arrow so you so a is d by DX now +okay uh so + + align:start position:0% +okay uh so + + + align:start position:0% +okay uh so +that's but it's if we dealt okay with + + align:start position:0% +that's but it's if we dealt okay with + + + align:start position:0% +that's but it's if we dealt okay with +difference matrices we're going to deal + + align:start position:0% +difference matrices we're going to deal + + + align:start position:0% +difference matrices we're going to deal +okay with derivative then of course this + + align:start position:0% +okay with derivative then of course this + + + align:start position:0% +okay with derivative then of course this +is be this is the the C part that + + align:start position:0% +is be this is the the C part that + + + align:start position:0% +is be this is the the C part that +produces W of X and it's a + + align:start position:0% +produces W of X and it's a + + + align:start position:0% +produces W of X and it's a +multiplication by this this uh possibly + + align:start position:0% +multiplication by this this uh possibly + + + align:start position:0% +multiplication by this this uh possibly +varying possibly jumping uh stiffness + + align:start position:0% +varying possibly jumping uh stiffness + + + align:start position:0% +varying possibly jumping uh stiffness +constant C ofx so w of X is C of x e of + + align:start position:0% +constant C ofx so w of X is C of x e of + + + align:start position:0% +constant C ofx so w of X is C of x e of +X that's our old W equals CE this is + + align:start position:0% +X that's our old W equals CE this is + + + align:start position:0% +X that's our old W equals CE this is +hooks law I'll put hooks law but that's + + align:start position:0% +hooks law I'll put hooks law but that's + + + align:start position:0% +hooks law I'll put hooks law but that's +or + + align:start position:0% +or + + + align:start position:0% +or +whoever law it is we've got a it's like + + align:start position:0% +whoever law it is we've got a it's like + + + align:start position:0% +whoever law it is we've got a it's like +a diagonal matrix I hope you see that + + align:start position:0% +a diagonal matrix I hope you see that + + + align:start position:0% +a diagonal matrix I hope you see that +it's like a diagonal matrix U this + + align:start position:0% +it's like a diagonal matrix U this + + + align:start position:0% +it's like a diagonal matrix U this +function U is kind of like a a a vector + + align:start position:0% +function U is kind of like a a a vector + + + align:start position:0% +function U is kind of like a a a vector +but a continuous a Continuum Vector + + align:start position:0% +but a continuous a Continuum Vector + + + align:start position:0% +but a continuous a Continuum Vector +instead of just fixed finite number of + + align:start position:0% +instead of just fixed finite number of + + + align:start position:0% +instead of just fixed finite number of +values then at each value we used to + + align:start position:0% +values then at each value we used to + + + align:start position:0% +values then at each value we used to +multiply by CI now our values have are + + align:start position:0% +multiply by CI now our values have are + + + align:start position:0% +multiply by CI now our values have are +continuous with the X so we multiply by + + align:start position:0% +continuous with the X so we multiply by + + + align:start position:0% +continuous with the X so we multiply by +C of X and then you got you're going to + + align:start position:0% +C of X and then you got you're going to + + + align:start position:0% +C of X and then you got you're going to +expect that going up here there's going + + align:start position:0% +expect that going up here there's going + + + align:start position:0% +expect that going up here there's going +to be an a transpose + + align:start position:0% + + + + align:start position:0% + +WF and of + + align:start position:0% +WF and of + + + align:start position:0% +WF and of +course that a transpose we have to + + align:start position:0% +course that a transpose we have to + + + align:start position:0% +course that a transpose we have to +identify and that's the first point of + + align:start position:0% +identify and that's the first point of + + + align:start position:0% +identify and that's the first point of +the lecture really to identify what is a + + align:start position:0% +the lecture really to identify what is a + + + align:start position:0% +the lecture really to identify what is a +transpose what do I mean by a + + align:start position:0% +transpose what do I mean by a + + + align:start position:0% +transpose what do I mean by a +transpose and I better say right away + + align:start position:0% +transpose and I better say right away + + + align:start position:0% +transpose and I better say right away +that you never I that I'm a little uh + + align:start position:0% +that you never I that I'm a little uh + + + align:start position:0% +that you never I that I'm a little uh +the notation writing a transpose of a + + align:start position:0% +the notation writing a transpose of a + + + align:start position:0% +the notation writing a transpose of a +derivative is like that's not legal you + + align:start position:0% +derivative is like that's not legal you + + + align:start position:0% +derivative is like that's not legal you +know it's not sort of because we think + + align:start position:0% +know it's not sort of because we think + + + align:start position:0% +know it's not sort of because we think +of the transpose of a matrix you sort of + + align:start position:0% +of the transpose of a matrix you sort of + + + align:start position:0% +of the transpose of a matrix you sort of +flip it over uh the main diagonal but + + align:start position:0% +flip it over uh the main diagonal but + + + align:start position:0% +flip it over uh the main diagonal but +obviously that's not there's got to be + + align:start position:0% +obviously that's not there's got to be + + + align:start position:0% +obviously that's not there's got to be +something more to it than that + + align:start position:0% +something more to it than that + + + align:start position:0% +something more to it than that +and so that's a central ke math part of + + align:start position:0% +and so that's a central ke math part of + + + align:start position:0% +and so that's a central ke math part of +this lecture is what is what's really + + align:start position:0% +this lecture is what is what's really + + + align:start position:0% +this lecture is what is what's really +going on when you + + align:start position:0% +going on when you + + + align:start position:0% +going on when you +transpose because then we can copy + + align:start position:0% +transpose because then we can copy + + + align:start position:0% +transpose because then we can copy +what's going on and it's quite important + + align:start position:0% +what's going on and it's quite important + + + align:start position:0% +what's going on and it's quite important +to get it because this the transpose + + align:start position:0% +to get it because this the transpose + + + align:start position:0% +to get it because this the transpose +well other notations and other words for + + align:start position:0% +well other notations and other words for + + + align:start position:0% +well other notations and other words for +it would be uh a notation might be a + + align:start position:0% +it would be uh a notation might be a + + + align:start position:0% +it would be uh a notation might be a +star star is would be way more common + + align:start position:0% +star star is would be way more common + + + align:start position:0% +star star is would be way more common +than transpose I I'll just stay with + + align:start position:0% +than transpose I I'll just stay with + + + align:start position:0% +than transpose I I'll just stay with +transpose because I want to keep + + align:start position:0% +transpose because I want to keep + + + align:start position:0% +transpose because I want to keep +pressing the parallel with a transpose + + align:start position:0% +pressing the parallel with a transpose + + + align:start position:0% +pressing the parallel with a transpose +CA but and and the name for it would be + + align:start position:0% +CA but and and the name for it would be + + + align:start position:0% +CA but and and the name for it would be +the adjoint and and adjoint methods an + + align:start position:0% +the adjoint and and adjoint methods an + + + align:start position:0% +the adjoint and and adjoint methods an +adjoint operator those those appear a + + align:start position:0% +adjoint operator those those appear a + + + align:start position:0% +adjoint operator those those appear a +lot and you'll see them appear in finite + + align:start position:0% +lot and you'll see them appear in finite + + + align:start position:0% +lot and you'll see them appear in finite +elements so this is this is + + align:start position:0% + + + + align:start position:0% + +a good good bit good thing to catch on + + align:start position:0% +a good good bit good thing to catch on + + + align:start position:0% +a good good bit good thing to catch on +to why why should the D the the + + align:start position:0% +to why why should the D the the + + + align:start position:0% +to why why should the D the the +transpose or the adjoint of the + + align:start position:0% +transpose or the adjoint of the + + + align:start position:0% +transpose or the adjoint of the +derivative be minus the derivative and + + align:start position:0% +derivative be minus the derivative and + + + align:start position:0% +derivative be minus the derivative and +by the way just while we're fixing this + + align:start position:0% +by the way just while we're fixing this + + + align:start position:0% +by the way just while we're fixing this +this is a key fact then uh which which + + align:start position:0% +this is a key fact then uh which which + + + align:start position:0% +this is a key fact then uh which which +is certainly like we have a very strong + + align:start position:0% +is certainly like we have a very strong + + + align:start position:0% +is certainly like we have a very strong +hint from Center differences right if I + + align:start position:0% +hint from Center differences right if I + + + align:start position:0% +hint from Center differences right if I +if I think of derivatives if I associate + + align:start position:0% +if I think of derivatives if I associate + + + align:start position:0% +if I think of derivatives if I associate +them with differences the center + + align:start position:0% +them with differences the center + + + align:start position:0% +them with differences the center +difference Matrix so the a matrix maybe + + align:start position:0% +difference Matrix so the a matrix maybe + + + align:start position:0% +difference Matrix so the a matrix maybe +centered would be just just to remind us + + align:start position:0% +centered would be just just to remind us + + + align:start position:0% +centered would be just just to remind us +you know it's a center difference has + + align:start position:0% +you know it's a center difference has + + + align:start position:0% +you know it's a center difference has +ones and minus one one zeros on the + + align:start position:0% +ones and minus one one zeros on the + + + align:start position:0% +ones and minus one one zeros on the +diagonal right minus one one takes that + + align:start position:0% +diagonal right minus one one takes that + + + align:start position:0% +diagonal right minus one one takes that +difference at every at every uh + + align:start position:0% +difference at every at every uh + + + align:start position:0% +difference at every at every uh +row except possibly boundary rows and + + align:start position:0% +row except possibly boundary rows and + + + align:start position:0% +row except possibly boundary rows and +and of course as soon as you look at + + align:start position:0% +and of course as soon as you look at + + + align:start position:0% +and of course as soon as you look at +that Matrix you see yeah it's + + align:start position:0% +that Matrix you see yeah it's + + + align:start position:0% +that Matrix you see yeah it's +anti-symmetric that's an anti-symmetric + + align:start position:0% +anti-symmetric that's an anti-symmetric + + + align:start position:0% +anti-symmetric that's an anti-symmetric +Matrix so a transpose is minus a for the + + align:start position:0% +Matrix so a transpose is minus a for the + + + align:start position:0% +Matrix so a transpose is minus a for the +the for Center differences and therefore + + align:start position:0% +the for Center differences and therefore + + + align:start position:0% +the for Center differences and therefore +we're not so surprised to see a minus + + align:start position:0% +we're not so surprised to see a minus + + + align:start position:0% +we're not so surprised to see a minus +sign appear when we go to the continuous + + align:start position:0% +sign appear when we go to the continuous + + + align:start position:0% +sign appear when we go to the continuous +case the derivatives but we still have + + align:start position:0% +case the derivatives but we still have + + + align:start position:0% +case the derivatives but we still have +to say what it means + + align:start position:0% +to say what it means + + + align:start position:0% +to say what it means +what so that's what I'll do next okay so + + align:start position:0% +what so that's what I'll do next okay so + + + align:start position:0% +what so that's what I'll do next okay so +this is a good thing to know and I was + + align:start position:0% +this is a good thing to know and I was + + + align:start position:0% +this is a good thing to know and I was +just going to comment what would be the + + align:start position:0% +just going to comment what would be the + + + align:start position:0% +just going to comment what would be the +transpose of the second derivative just + + align:start position:0% +transpose of the second derivative just + + + align:start position:0% +transpose of the second derivative just +I won't even write this down if the + + align:start position:0% +I won't even write this down if the + + + align:start position:0% +I won't even write this down if the +transpose of the if the itive transposed + + align:start position:0% +transpose of the if the itive transposed + + + align:start position:0% +transpose of the if the itive transposed +sort of flips its sign to minus what + + align:start position:0% +sort of flips its sign to minus what + + + align:start position:0% +sort of flips its sign to minus what +would be what would you guess for the + + align:start position:0% +would be what would you guess for the + + + align:start position:0% +would be what would you guess for the +SEC transpose of second derivative our + + align:start position:0% +SEC transpose of second derivative our + + + align:start position:0% +SEC transpose of second derivative our +more familiar DC by dx^ S well we'll + + align:start position:0% +more familiar DC by dx^ S well we'll + + + align:start position:0% +more familiar DC by dx^ S well we'll +have two minus signs so it'll come out + + align:start position:0% +have two minus signs so it'll come out + + + align:start position:0% +have two minus signs so it'll come out +plus so that so second derivatives even + + align:start position:0% +plus so that so second derivatives even + + + align:start position:0% +plus so that so second derivatives even +order derivatives are sort of like + + align:start position:0% +order derivatives are sort of like + + + align:start position:0% +order derivatives are sort of like +symmetric guys odd order derivatives + + align:start position:0% +symmetric guys odd order derivatives + + + align:start position:0% +symmetric guys odd order derivatives +first and third and fifth derivatives + + align:start position:0% +first and third and fifth derivatives + + + align:start position:0% +first and third and fifth derivatives +well God forbid ever meet a fifth + + align:start position:0% +well God forbid ever meet a fifth + + + align:start position:0% +well God forbid ever meet a fifth +derivative but F first derivative anyway + + align:start position:0% +derivative but F first derivative anyway + + + align:start position:0% +derivative but F first derivative anyway +uh is + + align:start position:0% +uh is + + + align:start position:0% +uh is +anti-symmetric except for boundary + + align:start position:0% +anti-symmetric except for boundary + + + align:start position:0% +anti-symmetric except for boundary +conditions so I really have to emphasize + + align:start position:0% +conditions so I really have to emphasize + + + align:start position:0% +conditions so I really have to emphasize +that the boundary conditions come in and + + align:start position:0% +that the boundary conditions come in and + + + align:start position:0% +that the boundary conditions come in and +and you'll see them come in they have to + + align:start position:0% +and you'll see them come in they have to + + + align:start position:0% +and you'll see them come in they have to +come in okay so how what meaning can I + + align:start position:0% +come in okay so how what meaning can I + + + align:start position:0% +come in okay so how what meaning can I +assign to the transpose or or what's the + + align:start position:0% +assign to the transpose or or what's the + + + align:start position:0% +assign to the transpose or or what's the +or what yeah what was the real real + + align:start position:0% +or what yeah what was the real real + + + align:start position:0% +or what yeah what was the real real +thing happening when we flipped a matrix + + align:start position:0% +thing happening when we flipped a matrix + + + align:start position:0% +thing happening when we flipped a matrix +across its diagonal I claim that the + + align:start position:0% +across its diagonal I claim that the + + + align:start position:0% +across its diagonal I claim that the +real the the we we really + + align:start position:0% +real the the we we really + + + align:start position:0% +real the the we we really +Define the + + align:start position:0% +Define the + + + align:start position:0% +Define the +transpose + + align:start position:0% +transpose + + + align:start position:0% +transpose +by this + + align:start position:0% +by this + + + align:start position:0% +by this +rule by we know what inner products are + + align:start position:0% +rule by we know what inner products are + + + align:start position:0% +rule by we know what inner products are +I'll do vectors first we know what inner + + align:start position:0% +I'll do vectors first we know what inner + + + align:start position:0% +I'll do vectors first we know what inner +products dot products we know what the + + align:start position:0% +products dot products we know what the + + + align:start position:0% +products dot products we know what the +dot product of two vectors is so so if I + + align:start position:0% +dot product of two vectors is so so if I + + + align:start position:0% +dot product of two vectors is so so if I +have a this is the transpose of a how am + + align:start position:0% +have a this is the transpose of a how am + + + align:start position:0% +have a this is the transpose of a how am +I going to define the transpose of a + + align:start position:0% +I going to define the transpose of a + + + align:start position:0% +I going to define the transpose of a +well I look at the dot product of au + + align:start position:0% +well I look at the dot product of au + + + align:start position:0% +well I look at the dot product of au +with + + align:start position:0% +with + + + align:start position:0% +with +W I'll use a DOT here for once and then + + align:start position:0% +W I'll use a DOT here for once and then + + + align:start position:0% +W I'll use a DOT here for once and then +I may erase it and replace it if I if I + + align:start position:0% +I may erase it and replace it if I if I + + + align:start position:0% +I may erase it and replace it if I if I +look at the dotproduct of au with W then + + align:start position:0% +look at the dotproduct of au with W then + + + align:start position:0% +look at the dotproduct of au with W then +that equals for All U and W all vectors + + align:start position:0% +that equals for All U and W all vectors + + + align:start position:0% +that equals for All U and W all vectors +U and W that equals the dotproduct of U + + align:start position:0% +U and W that equals the dotproduct of U + + + align:start position:0% +U and W that equals the dotproduct of U +with + + align:start position:0% + + + + align:start position:0% + +something cuz it just you is coming if I + + align:start position:0% +something cuz it just you is coming if I + + + align:start position:0% +something cuz it just you is coming if I +write out what the dotproduct is I see + + align:start position:0% +write out what the dotproduct is I see + + + align:start position:0% +write out what the dotproduct is I see +U1 multiplies something U2 multiplies + + align:start position:0% +U1 multiplies something U2 multiplies + + + align:start position:0% +U1 multiplies something U2 multiplies +something and that's and what do I what + + align:start position:0% +something and that's and what do I what + + + align:start position:0% +something and that's and what do I what +what goes in that little + + align:start position:0% + + + + align:start position:0% + +space this is just an identity I mean + + align:start position:0% +space this is just an identity I mean + + + align:start position:0% +space this is just an identity I mean +it's like you'll say no no big deal but + + align:start position:0% +it's like you'll say no no big deal but + + + align:start position:0% +it's like you'll say no no big deal but +I'm saying there is a at least a small + + align:start position:0% +I'm saying there is a at least a small + + + align:start position:0% +I'm saying there is a at least a small +deal here okay + + align:start position:0% +deal here okay + + + align:start position:0% +deal here okay +so now if I write it this way you'll + + align:start position:0% +so now if I write it this way you'll + + + align:start position:0% +so now if I write it this way you'll +tell me write away this should be the + + align:start position:0% +tell me write away this should be the + + + align:start position:0% +tell me write away this should be the +same as U transpose times something and + + align:start position:0% +same as U transpose times something and + + + align:start position:0% +same as U transpose times something and +again so I'm asking for the same + + align:start position:0% +again so I'm asking for the same + + + align:start position:0% +again so I'm asking for the same +something on both both lines what is + + align:start position:0% +something on both both lines what is + + + align:start position:0% +something on both both lines what is +that + + align:start position:0% +that + + + align:start position:0% +that +something a transpose W whatever a + + align:start position:0% +something a transpose W whatever a + + + align:start position:0% +something a transpose W whatever a +transpose + + align:start position:0% +transpose + + + align:start position:0% +transpose +is it's the Matrix that makes this right + + align:start position:0% +is it's the Matrix that makes this right + + + align:start position:0% +is it's the Matrix that makes this right +that's really my message that a + + align:start position:0% +that's really my message that a + + + align:start position:0% +that's really my message that a +transpose is the reason we flip the + + align:start position:0% +transpose is the reason we flip the + + + align:start position:0% +transpose is the reason we flip the +Matrix across the diagonal is that it + + align:start position:0% +Matrix across the diagonal is that it + + + align:start position:0% +Matrix across the diagonal is that it +makes that equation correct + + align:start position:0% +makes that equation correct + + + align:start position:0% +makes that equation correct +and it and and and I'm writing the same + + align:start position:0% +and it and and and I'm writing the same + + + align:start position:0% +and it and and and I'm writing the same +thing here okay so again if we knew what + + align:start position:0% +thing here okay so again if we knew what + + + align:start position:0% +thing here okay so again if we knew what +dot products were what what inner + + align:start position:0% +dot products were what what inner + + + align:start position:0% +dot products were what what inner +products of vectors were then a + + align:start position:0% +products of vectors were then a + + + align:start position:0% +products of vectors were then a +transpose is the is the Matrix that + + align:start position:0% +transpose is the is the Matrix that + + + align:start position:0% +transpose is the is the Matrix that +makes this identity correct and of + + align:start position:0% +makes this identity correct and of + + + align:start position:0% +makes this identity correct and of +course if you if you write it all out in + + align:start position:0% +course if you if you write it all out in + + + align:start position:0% +course if you if you write it all out in +terms of IG every component you find it + + align:start position:0% +terms of IG every component you find it + + + align:start position:0% +terms of IG every component you find it +is correct okay so that defines the + + align:start position:0% +is correct okay so that defines the + + + align:start position:0% +is correct okay so that defines the +transpose of a matrix + + align:start position:0% +transpose of a matrix + + + align:start position:0% +transpose of a matrix +and and of course it coincides with + + align:start position:0% +and and of course it coincides with + + + align:start position:0% +and and of course it coincides with +flipping across the diagonal now how + + align:start position:0% +flipping across the diagonal now how + + + align:start position:0% +flipping across the diagonal now how +about the transpose of a + + align:start position:0% +about the transpose of a + + + align:start position:0% +about the transpose of a +derivative okay so I'm going to follow + + align:start position:0% +derivative okay so I'm going to follow + + + align:start position:0% +derivative okay so I'm going to follow +the same + + align:start position:0% +the same + + + align:start position:0% +the same +rule I here a is now going to be the + + align:start position:0% +rule I here a is now going to be the + + + align:start position:0% +rule I here a is now going to be the +derivative and a transpose is going to + + align:start position:0% +derivative and a transpose is going to + + + align:start position:0% +derivative and a transpose is going to +be whatever it takes to make this true + + align:start position:0% +be whatever it takes to make this true + + + align:start position:0% +be whatever it takes to make this true +but what do I mean now I have functions + + align:start position:0% +but what do I mean now I have functions + + + align:start position:0% +but what do I mean now I have functions +so I have to think again what do I mean + + align:start position:0% +so I have to think again what do I mean + + + align:start position:0% +so I have to think again what do I mean +by the inner product the dot product so + + align:start position:0% +by the inner product the dot product so + + + align:start position:0% +by the inner product the dot product so +I need for this to make sense I I need + + align:start position:0% +I need for this to make sense I I need + + + align:start position:0% +I need for this to make sense I I need +to say and it's very important thing + + align:start position:0% +to say and it's very important thing + + + align:start position:0% +to say and it's very important thing +anyway and it's the right Natural Choice + + align:start position:0% +anyway and it's the right Natural Choice + + + align:start position:0% +anyway and it's the right Natural Choice +I need to need I need to say the dot + + align:start position:0% +I need to need I need to say the dot + + + align:start position:0% +I need to need I need to say the dot +product or the inner product is a better + + align:start position:0% +product or the inner product is a better + + + align:start position:0% +product or the inner product is a better +word of + + align:start position:0% + + + + align:start position:0% + +functions of two functions say e of X + + align:start position:0% +functions of two functions say e of X + + + align:start position:0% +functions of two functions say e of X +and W ofx if I have two + + align:start position:0% +and W ofx if I have two + + + align:start position:0% +and W ofx if I have two +functions what do I mean by their inner + + align:start position:0% +functions what do I mean by their inner + + + align:start position:0% +functions what do I mean by their inner +product + + align:start position:0% +product + + + align:start position:0% +product +well I just really I just think back + + align:start position:0% +well I just really I just think back + + + align:start position:0% +well I just really I just think back +what did I what did we mean in the in + + align:start position:0% +what did I what did we mean in the in + + + align:start position:0% +what did I what did we mean in the in +the finite dimensional case I multiplied + + align:start position:0% +the finite dimensional case I multiplied + + + align:start position:0% +the finite dimensional case I multiplied +each e by a w each component of e by a w + + align:start position:0% +each e by a w each component of e by a w + + + align:start position:0% +each e by a w each component of e by a w +and I added so what am I going to do + + align:start position:0% +and I added so what am I going to do + + + align:start position:0% +and I added so what am I going to do +here and maybe my notation should be + + align:start position:0% +here and maybe my notation should be + + + align:start position:0% +here and maybe my notation should be +this with should be parentheses with a + + align:start position:0% +this with should be parentheses with a + + + align:start position:0% +this with should be parentheses with a +comma would be better than a DOT I think + + align:start position:0% +comma would be better than a DOT I think + + + align:start position:0% +comma would be better than a DOT I think +for functions so those are I have a + + align:start position:0% +for functions so those are I have a + + + align:start position:0% +for functions so those are I have a +function I'm in function space now you + + align:start position:0% +function I'm in function space now you + + + align:start position:0% +function I'm in function space now you +know move we moved out of RN today into + + align:start position:0% +know move we moved out of RN today into + + + align:start position:0% +know move we moved out of RN today into +function space our our vectors have + + align:start position:0% +function space our our vectors have + + + align:start position:0% +function space our our vectors have +become functions and now what's the + + align:start position:0% +become functions and now what's the + + + align:start position:0% +become functions and now what's the +dotproduct of two vectors well what do + + align:start position:0% +dotproduct of two vectors well what do + + + align:start position:0% +dotproduct of two vectors well what do +you what what am I going to do you you + + align:start position:0% +you what what am I going to do you you + + + align:start position:0% +you what what am I going to do you you +can I'm I'm going to do what I have to + + align:start position:0% +can I'm I'm going to do what I have to + + + align:start position:0% +can I'm I'm going to do what I have to +do I'm going to multiply each e by each + + align:start position:0% +do I'm going to multiply each e by each + + + align:start position:0% +do I'm going to multiply each e by each +W by its corresponding + + align:start position:0% +W by its corresponding + + + align:start position:0% +W by its corresponding +W and now they depend on this continuous + + align:start position:0% +W and now they depend on this continuous + + + align:start position:0% +W and now they depend on this continuous +variable X and now what am I so that's e + + align:start position:0% +variable X and now what am I so that's e + + + align:start position:0% +variable X and now what am I so that's e +ofx * W ofx and what do I do + + align:start position:0% +ofx * W ofx and what do I do + + + align:start position:0% +ofx * W ofx and what do I do +now + + align:start position:0% +now + + + align:start position:0% +now +integrate here I added EI * wi of course + + align:start position:0% +integrate here I added EI * wi of course + + + align:start position:0% +integrate here I added EI * wi of course +over here I have functions I integrate + + align:start position:0% +over here I have functions I integrate + + + align:start position:0% +over here I have functions I integrate +DX over whatever the region of the + + align:start position:0% +DX over whatever the region of the + + + align:start position:0% +DX over whatever the region of the +problem is and in our examples in 1D + + align:start position:0% +problem is and in our examples in 1D + + + align:start position:0% +problem is and in our examples in 1D +it'll be 0 to one if if these are + + align:start position:0% +it'll be 0 to one if if these are + + + align:start position:0% +it'll be 0 to one if if these are +functions of two variables I'd be + + align:start position:0% +functions of two variables I'd be + + + align:start position:0% +functions of two variables I'd be +integrating over some 2D region but + + align:start position:0% +integrating over some 2D region but + + + align:start position:0% +integrating over some 2D region but +we're in 1D today okay so now I'm you + + align:start position:0% +we're in 1D today okay so now I'm you + + + align:start position:0% +we're in 1D today okay so now I'm you +see that I'm like prepared to say this + + align:start position:0% +see that I'm like prepared to say this + + + align:start position:0% +see that I'm like prepared to say this +this now makes sense this this I I now + + align:start position:0% +this now makes sense this this I I now + + + align:start position:0% +this now makes sense this this I I now +want + + align:start position:0% +want + + + align:start position:0% +want +to mik still going yeah okay uh I I now + + align:start position:0% +to mik still going yeah okay uh I I now + + + align:start position:0% +to mik still going yeah okay uh I I now +want to say I want I'm going to let a be + + align:start position:0% +want to say I want I'm going to let a be + + + align:start position:0% +want to say I want I'm going to let a be +the derivative I'm and I'm going to + + align:start position:0% +the derivative I'm and I'm going to + + + align:start position:0% +the derivative I'm and I'm going to +figure out what a transpose has to be so + + align:start position:0% +figure out what a transpose has to be so + + + align:start position:0% +figure out what a transpose has to be so +if a is the derivative so so now I'm G + + align:start position:0% +if a is the derivative so so now I'm G + + + align:start position:0% +if a is the derivative so so now I'm G +to now is this key step why is the + + align:start position:0% +to now is this key step why is the + + + align:start position:0% +to now is this key step why is the +transpose that okay so I look + + align:start position:0% +transpose that okay so I look + + + align:start position:0% +transpose that okay so I look +at the derivative D DX with + + align:start position:0% +at the derivative D DX with + + + align:start position:0% +at the derivative D DX with +W so that's this integral from 0 to one + + align:start position:0% +W so that's this integral from 0 to one + + + align:start position:0% +W so that's this integral from 0 to one +of + + align:start position:0% +of + + + align:start position:0% +of +DX W of X + + align:start position:0% +DX W of X + + + align:start position:0% +DX W of X +DX and now I want + + align:start position:0% +DX and now I want + + + align:start position:0% +DX and now I want +to so that's my left side now I want to + + align:start position:0% +to so that's my left side now I want to + + + align:start position:0% +to so that's my left side now I want to +get U by + + align:start position:0% +get U by + + + align:start position:0% +get U by +itself I want to get the do dotproduct + + align:start position:0% +itself I want to get the do dotproduct + + + align:start position:0% +itself I want to get the do dotproduct +so I want to get another integral + + align:start position:0% +so I want to get another integral + + + align:start position:0% +so I want to get another integral +here that has U of X by itself times + + align:start position:0% +here that has U of X by itself times + + + align:start position:0% +here that has U of X by itself times +times something and that something is + + align:start position:0% +times something and that something is + + + align:start position:0% +times something and that something is +what I'm looking for that something will + + align:start position:0% +what I'm looking for that something will + + + align:start position:0% +what I'm looking for that something will +be a transpose + + align:start position:0% +be a transpose + + + align:start position:0% +be a transpose +W right + + align:start position:0% +W right + + + align:start position:0% +W right +right do you see what I'm doing this is + + align:start position:0% +right do you see what I'm doing this is + + + align:start position:0% +right do you see what I'm doing this is +this is the dot this is + + align:start position:0% +this is the dot this is + + + align:start position:0% +this is the dot this is +auw so I've WR written out what Au inner + + align:start position:0% +auw so I've WR written out what Au inner + + + align:start position:0% +auw so I've WR written out what Au inner +product with W is and now I want to get + + align:start position:0% +product with W is and now I want to get + + + align:start position:0% +product with W is and now I want to get +U out by itself and what it multiplies + + align:start position:0% +U out by itself and what it multiplies + + + align:start position:0% +U out by itself and what it multiplies +here will be the a transpose W and my + + align:start position:0% +here will be the a transpose W and my + + + align:start position:0% +here will be the a transpose W and my +rule will be will be extended to the + + align:start position:0% +rule will be will be extended to the + + + align:start position:0% +rule will be will be extended to the +function case and I'll be ready to + + align:start position:0% +function case and I'll be ready to + + + align:start position:0% +function case and I'll be ready to +go now do you recognize this is a basic + + align:start position:0% +go now do you recognize this is a basic + + + align:start position:0% +go now do you recognize this is a basic +calculus step what what what rule of + + align:start position:0% +calculus step what what what rule of + + + align:start position:0% +calculus step what what what rule of +calculus am I am I going to use we're + + align:start position:0% +calculus am I am I going to use we're + + + align:start position:0% +calculus am I am I going to use we're +back to + + align:start position:0% +back to + + + align:start position:0% +back to +1801 I have the integral of a derivative + + align:start position:0% +1801 I have the integral of a derivative + + + align:start position:0% +1801 I have the integral of a derivative +time W and what do I want to do I want + + align:start position:0% +time W and what do I want to do I want + + + align:start position:0% +time W and what do I want to do I want +to get the derivative off of + + align:start position:0% +to get the derivative off of + + + align:start position:0% +to get the derivative off of +you what happens what's it called + + align:start position:0% +you what happens what's it called + + + align:start position:0% +you what happens what's it called +integration by parts very important + + align:start position:0% +integration by parts very important + + + align:start position:0% +integration by parts very important +thing very important if you you miss its + + align:start position:0% +thing very important if you you miss its + + + align:start position:0% +thing very important if you you miss its +importance in in in calculus it gets + + align:start position:0% +importance in in in calculus it gets + + + align:start position:0% +importance in in in calculus it gets +sometimes introduced as a rule or a + + align:start position:0% +sometimes introduced as a rule or a + + + align:start position:0% +sometimes introduced as a rule or a +trick to find some goofy integral but + + align:start position:0% +trick to find some goofy integral but + + + align:start position:0% +trick to find some goofy integral but +it's it's really the real thing so what + + align:start position:0% +it's it's really the real thing so what + + + align:start position:0% +it's it's really the real thing so what +is integration by parts what's the rule + + align:start position:0% +is integration by parts what's the rule + + + align:start position:0% +is integration by parts what's the rule +you you take the derivative off of of U + + align:start position:0% +you you take the derivative off of of U + + + align:start position:0% +you you take the derivative off of of U +you put it on to the other one just what + + align:start position:0% +you put it on to the other one just what + + + align:start position:0% +you put it on to the other one just what +we hope for and then you also have to + + align:start position:0% +we hope for and then you also have to + + + align:start position:0% +we hope for and then you also have to +remember that there is + + align:start position:0% + + + + align:start position:0% + +a minus sign right integration by parts + + align:start position:0% +a minus sign right integration by parts + + + align:start position:0% +a minus sign right integration by parts +has a minus sign and let mean usually + + align:start position:0% +has a minus sign and let mean usually + + + align:start position:0% +has a minus sign and let mean usually +you'd see it out there but here I've + + align:start position:0% +you'd see it out there but here I've + + + align:start position:0% +you'd see it out there but here I've +left more room for it there DX so I have + + align:start position:0% +left more room for it there DX so I have + + + align:start position:0% +left more room for it there DX so I have +identified + + align:start position:0% +identified + + + align:start position:0% +identified +now a transpose w a transpose W had if + + align:start position:0% +now a transpose w a transpose W had if + + + align:start position:0% +now a transpose w a transpose W had if +this is au in a product with w + + align:start position:0% +this is au in a product with w + + + align:start position:0% +this is au in a product with w +that and then this is u in product with + + align:start position:0% +that and then this is u in product with + + + align:start position:0% +that and then this is u in product with +a transposed W it had to be what it was + + align:start position:0% +a transposed W it had to be what it was + + + align:start position:0% +a transposed W it had to be what it was +so that one integration by parts brought + + align:start position:0% +so that one integration by parts brought + + + align:start position:0% +so that one integration by parts brought +out a minus sign if I was looking at + + align:start position:0% +out a minus sign if I was looking at + + + align:start position:0% +out a minus sign if I was looking at +second derivatives there would probably + + align:start position:0% +second derivatives there would probably + + + align:start position:0% +second derivatives there would probably +be somewhere two integration by parts + + align:start position:0% +be somewhere two integration by parts + + + align:start position:0% +be somewhere two integration by parts +I'd have minus twice I'd be back to plus + + align:start position:0% +I'd have minus twice I'd be back to plus + + + align:start position:0% +I'd have minus twice I'd be back to plus +and you're going to ask about boundary + + align:start position:0% +and you're going to ask about boundary + + + align:start position:0% +and you're going to ask about boundary +conditions and you're right to ask about + + align:start position:0% +conditions and you're right to ask about + + + align:start position:0% +conditions and you're right to ask about +boundary conditions I even circled that + + align:start position:0% +boundary conditions I even circled that + + + align:start position:0% +boundary conditions I even circled that +because it's that it's so important so + + align:start position:0% +because it's that it's so important so + + + align:start position:0% +because it's that it's so important so +what we've done + + align:start position:0% +what we've done + + + align:start position:0% +what we've done +so far is sort of to get the interior of + + align:start position:0% +so far is sort of to get the interior of + + + align:start position:0% +so far is sort of to get the interior of +the interval right inside between zero + + align:start position:0% +the interval right inside between zero + + + align:start position:0% +the interval right inside between zero +and one if a is the derivative then a + + align:start position:0% +and one if a is the derivative then a + + + align:start position:0% +and one if a is the derivative then a +transposes minus the derivative that's + + align:start position:0% +transposes minus the derivative that's + + + align:start position:0% +transposes minus the derivative that's +that's all we've done we have not got + + align:start position:0% +that's all we've done we have not got + + + align:start position:0% +that's all we've done we have not got +the boundary conditions yet and and + + align:start position:0% +the boundary conditions yet and and + + + align:start position:0% +the boundary conditions yet and and +that's we we can't go on without that + + align:start position:0% +that's we we can't go on without that + + + align:start position:0% +that's we we can't go on without that +okay so so I'm ready now to say + + align:start position:0% +okay so so I'm ready now to say + + + align:start position:0% +okay so so I'm ready now to say +something about boundary + + align:start position:0% +something about boundary + + + align:start position:0% +something about boundary +conditions and it will bring up this + + align:start position:0% +conditions and it will bring up this + + + align:start position:0% +conditions and it will bring up this +Square Square versus rectangular also so + + align:start position:0% +Square Square versus rectangular also so + + + align:start position:0% +Square Square versus rectangular also so +this is this is a good this is like + + align:start position:0% +this is this is a good this is like + + + align:start position:0% +this is this is a good this is like +we're we're getting the kind of the + + align:start position:0% +we're we're getting the kind of the + + + align:start position:0% +we're we're getting the kind of the +rules straight before we tackle finite + + align:start position:0% +rules straight before we tackle finite + + + align:start position:0% +rules straight before we tackle finite +elements okay let me take an example of + + align:start position:0% +elements okay let me take an example of + + + align:start position:0% +elements okay let me take an example of +a matrix and it's transpose just so you + + align:start position:0% +a matrix and it's transpose just so you + + + align:start position:0% +a matrix and it's transpose just so you +see how boundary can suppose I have + + align:start position:0% +see how boundary can suppose I have + + + align:start position:0% +see how boundary can suppose I have +suppose I have a free fixed + + align:start position:0% +suppose I have a free fixed + + + align:start position:0% +suppose I have a free fixed +problem suppose I have a free fixed line + + align:start position:0% +problem suppose I have a free fixed line + + + align:start position:0% +problem suppose I have a free fixed line +of Springs what's the Matrix a for that + + align:start position:0% +of Springs what's the Matrix a for that + + + align:start position:0% +of Springs what's the Matrix a for that +well yeah question + + align:start position:0% + + + + align:start position:0% + +yes yeah yeah right that's sorry that's + + align:start position:0% +yes yeah yeah right that's sorry that's + + + align:start position:0% +yes yeah yeah right that's sorry that's +yes when I learned it it was also that + + align:start position:0% +yes when I learned it it was also that + + + align:start position:0% +yes when I learned it it was also that +stupid term so you would like me to put + + align:start position:0% +stupid term so you would like me to put + + + align:start position:0% +stupid term so you would like me to put +plus can I put plus whatever what do you + + align:start position:0% +plus can I put plus whatever what do you + + + align:start position:0% +plus can I put plus whatever what do you +want me to call that an integrated term + + align:start position:0% +want me to call that an integrated term + + + align:start position:0% +want me to call that an integrated term +it would be yeah why don't I even I even + + align:start position:0% +it would be yeah why don't I even I even + + + align:start position:0% +it would be yeah why don't I even I even +remember what it is as you do better + + align:start position:0% +remember what it is as you do better + + + align:start position:0% +remember what it is as you do better +than me U time w at the at the is that + + align:start position:0% +than me U time w at the at the is that + + + align:start position:0% +than me U time w at the at the is that +good yeah thank you sorry sorry yeah + + align:start position:0% +good yeah thank you sorry sorry yeah + + + align:start position:0% +good yeah thank you sorry sorry yeah +yeah yeah yeah so it's really this part + + align:start position:0% +yeah yeah yeah so it's really this part + + + align:start position:0% +yeah yeah yeah so it's really this part +that I'm now coming to it's the boundary + + align:start position:0% +that I'm now coming to it's the boundary + + + align:start position:0% +that I'm now coming to it's the boundary +part that I'm now coming to and and let + + align:start position:0% +part that I'm now coming to and and let + + + align:start position:0% +part that I'm now coming to and and let +me say so I I you I'm glad you asked the + + align:start position:0% +me say so I I you I'm glad you asked the + + + align:start position:0% +me say so I I you I'm glad you asked the +question because I made it seem + + align:start position:0% +question because I made it seem + + + align:start position:0% +question because I made it seem +unimportant where that's not true at all + + align:start position:0% +unimportant where that's not true at all + + + align:start position:0% +unimportant where that's not true at all +the boundary condition is part of the + + align:start position:0% +the boundary condition is part of the + + + align:start position:0% +the boundary condition is part of the +definition of a and part of the + + align:start position:0% +definition of a and part of the + + + align:start position:0% +definition of a and part of the +definition of a transpose just the way + + align:start position:0% +definition of a transpose just the way + + + align:start position:0% +definition of a transpose just the way +I'm about to say free fixed I had to + + align:start position:0% +I'm about to say free fixed I had to + + + align:start position:0% +I'm about to say free fixed I had to +tell you that for you to know what a was + + align:start position:0% +tell you that for you to know what a was + + + align:start position:0% +tell you that for you to know what a was +if I until I tell you the boundary + + align:start position:0% +if I until I tell you the boundary + + + align:start position:0% +if I until I tell you the boundary +condition you don't know what the + + align:start position:0% +condition you don't know what the + + + align:start position:0% +condition you don't know what the +boundary rows are you don't know you + + align:start position:0% +boundary rows are you don't know you + + + align:start position:0% +boundary rows are you don't know you +only know the inside of the Matrix or + + align:start position:0% +only know the inside of the Matrix or + + + align:start position:0% +only know the inside of the Matrix or +one possible inside so I'm thinking my + + align:start position:0% +one possible inside so I'm thinking my + + + align:start position:0% +one possible inside so I'm thinking my +inside is going to be minus one one - + + align:start position:0% +inside is going to be minus one one - + + + align:start position:0% +inside is going to be minus one one - +one one so on as a as + + align:start position:0% +one one so on as a as + + + align:start position:0% +one one so on as a as +a as a giving me finite different is + + align:start position:0% +a as a giving me finite different is + + + align:start position:0% +a as a giving me finite different is +minus one one but what so oh no let's + + align:start position:0% +minus one one but what so oh no let's + + + align:start position:0% +minus one one but what so oh no let's +see so I'm doing free fixed is that + + align:start position:0% +see so I'm doing free fixed is that + + + align:start position:0% +see so I'm doing free fixed is that +right am I doing free + + align:start position:0% +right am I doing free + + + align:start position:0% +right am I doing free +fixed okay okay so I'm taking free am I + + align:start position:0% +fixed okay okay so I'm taking free am I + + + align:start position:0% +fixed okay okay so I'm taking free am I +taking free at the Left + + align:start position:0% +taking free at the Left + + + align:start position:0% +taking free at the Left +End yes all right so so if I'm free at + + align:start position:0% +End yes all right so so if I'm free at + + + align:start position:0% +End yes all right so so if I'm free at +the Left End and fixed at the Right End + + align:start position:0% +the Left End and fixed at the Right End + + + align:start position:0% +the Left End and fixed at the Right End +what's my + + align:start position:0% +what's my + + + align:start position:0% +what's my +a we're getting better at this right uh + + align:start position:0% +a we're getting better at this right uh + + + align:start position:0% +a we're getting better at this right uh +minus1 one - one oneus one one minus one + + align:start position:0% +minus1 one - one oneus one one minus one + + + align:start position:0% +minus1 one - one oneus one one minus one +and the one here gets chopped + + align:start position:0% +and the one here gets chopped + + + align:start position:0% +and the one here gets chopped +off that we you could say if you want + + align:start position:0% +off that we you could say if you want + + + align:start position:0% +off that we you could say if you want +the fifth row of a + + align:start position:0% +the fifth row of a + + + align:start position:0% +the fifth row of a +notot remembering a notot as the hint on + + align:start position:0% +notot remembering a notot as the hint on + + + align:start position:0% +notot remembering a notot as the hint on +the quiz where it had five rows for the + + align:start position:0% +the quiz where it had five rows for the + + + align:start position:0% +the quiz where it had five rows for the +full thing free free and then when an N + + align:start position:0% +full thing free free and then when an N + + + align:start position:0% +full thing free free and then when an N +got fixed the fifth column sorry I + + align:start position:0% +got fixed the fifth column sorry I + + + align:start position:0% +got fixed the fifth column sorry I +should say say fifth column got got + + align:start position:0% +should say say fifth column got got + + + align:start position:0% +should say say fifth column got got +removed and that's my fix free fixed m + + align:start position:0% +removed and that's my fix free fixed m + + + align:start position:0% +removed and that's my fix free fixed m +Matrix at the left hand end at the zero + + align:start position:0% +Matrix at the left hand end at the zero + + + align:start position:0% +Matrix at the left hand end at the zero +end it's got the difference in there + + align:start position:0% +end it's got the difference in there + + + align:start position:0% +end it's got the difference in there +difference difference difference but + + align:start position:0% +difference difference difference but + + + align:start position:0% +difference difference difference but +here at the right hand end it's the the + + align:start position:0% +here at the right hand end it's the the + + + align:start position:0% +here at the right hand end it's the the +fixing the setting U whatever it would + + align:start position:0% +fixing the setting U whatever it would + + + align:start position:0% +fixing the setting U whatever it would +be u5 to zero or maybe it's u4 if this + + align:start position:0% +be u5 to zero or maybe it's u4 if this + + + align:start position:0% +be u5 to zero or maybe it's u4 if this +is you not one two 3 setting u4 to zero + + align:start position:0% +is you not one two 3 setting u4 to zero + + + align:start position:0% +is you not one two 3 setting u4 to zero +knock that out okay I all I want to do + + align:start position:0% +knock that out okay I all I want to do + + + align:start position:0% +knock that out okay I all I want to do +is transpose + + align:start position:0% +is transpose + + + align:start position:0% +is transpose +that and you'll see something you may we + + align:start position:0% +that and you'll see something you may we + + + align:start position:0% +that and you'll see something you may we +maybe didn't notice before so I + + align:start position:0% +maybe didn't notice before so I + + + align:start position:0% +maybe didn't notice before so I +transpose it that's Min -11 becomes a + + align:start position:0% +transpose it that's Min -11 becomes a + + + align:start position:0% +transpose it that's Min -11 becomes a +column Min -11 becomes a column minus + + align:start position:0% +column Min -11 becomes a column minus + + + align:start position:0% +column Min -11 becomes a column minus +one one becomes a column minus one is + + align:start position:0% +one one becomes a column minus one is + + + align:start position:0% +one one becomes a column minus one is +all the RIS that row becomes a so this + + align:start position:0% +all the RIS that row becomes a so this + + + align:start position:0% +all the RIS that row becomes a so this +was yeah okay so have I got it + + align:start position:0% + + + + align:start position:0% + +right yes what's happened + + align:start position:0% +right yes what's happened + + + align:start position:0% +right yes what's happened +here a transpose what are the boundary + + align:start position:0% +here a transpose what are the boundary + + + align:start position:0% +here a transpose what are the boundary +conditions going with a + + align:start position:0% +conditions going with a + + + align:start position:0% +conditions going with a +transpose the boundary conditions that + + align:start position:0% +transpose the boundary conditions that + + + align:start position:0% +transpose the boundary conditions that +went with a were the yeah let me say + + align:start position:0% +went with a were the yeah let me say + + + align:start position:0% +went with a were the yeah let me say +first what were the boundary conditions + + align:start position:0% +first what were the boundary conditions + + + align:start position:0% +first what were the boundary conditions +with a those are going to be boundary + + align:start position:0% +with a those are going to be boundary + + + align:start position:0% +with a those are going to be boundary +conditions on U so so a + + align:start position:0% +conditions on U so so a + + + align:start position:0% +conditions on U so so a +has boundary conditions on + + align:start position:0% +has boundary conditions on + + + align:start position:0% +has boundary conditions on +U and a + + align:start position:0% +U and a + + + align:start position:0% +U and a +transpose has boundary conditions on + + align:start position:0% +transpose has boundary conditions on + + + align:start position:0% +transpose has boundary conditions on +W because a transpose a on W and a acts + + align:start position:0% +W because a transpose a on W and a acts + + + align:start position:0% +W because a transpose a on W and a acts +on U so it's that's there was no choice + + align:start position:0% +on U so it's that's there was no choice + + + align:start position:0% +on U so it's that's there was no choice +so now what was the boundary condition + + align:start position:0% +so now what was the boundary condition + + + align:start position:0% +so now what was the boundary condition +here the boundary condition was u4 + + align:start position:0% +here the boundary condition was u4 + + + align:start position:0% +here the boundary condition was u4 +equals z right that was what I meant by + + align:start position:0% +equals z right that was what I meant by + + + align:start position:0% +equals z right that was what I meant by +that guy getting fixed now and no + + align:start position:0% +that guy getting fixed now and no + + + align:start position:0% +that guy getting fixed now and no +boundary condition at at u0 it was free + + align:start position:0% +boundary condition at at u0 it was free + + + align:start position:0% +boundary condition at at u0 it was free +now what are the boundary conditions + + align:start position:0% +now what are the boundary conditions + + + align:start position:0% +now what are the boundary conditions +that go with a transposed and remember a + + align:start position:0% +that go with a transposed and remember a + + + align:start position:0% +that go with a transposed and remember a +transposes multiplying W I'm going to + + align:start position:0% +transposes multiplying W I'm going to + + + align:start position:0% +transposes multiplying W I'm going to +put W here so what's what are the + + align:start position:0% +put W here so what's what are the + + + align:start position:0% +put W here so what's what are the +boundary conditions that go with with + + align:start position:0% +boundary conditions that go with with + + + align:start position:0% +boundary conditions that go with with +with a transpose this thing nothing got + + align:start position:0% +with a transpose this thing nothing got + + + align:start position:0% +with a transpose this thing nothing got +knocked off the boundary condition came + + align:start position:0% +knocked off the boundary condition came + + + align:start position:0% +knocked off the boundary condition came +up here for a transpose the boundary + + align:start position:0% +up here for a transpose the boundary + + + align:start position:0% +up here for a transpose the boundary +condition was + + align:start position:0% +condition was + + + align:start position:0% +condition was +w0 equals z that that got knocked out w0 + + align:start position:0% +w0 equals z that that got knocked out w0 + + + align:start position:0% +w0 equals z that that got knocked out w0 +to + + align:start position:0% + + + + align:start position:0% + +b0 no surprise free fix this is the free + + align:start position:0% +b0 no surprise free fix this is the free + + + align:start position:0% +b0 no surprise free fix this is the free +end at the left this is the fixed end at + + align:start position:0% +end at the left this is the fixed end at + + + align:start position:0% +end at the left this is the fixed end at +the right it just + + align:start position:0% +the right it just + + + align:start position:0% +the right it just +did you ever notice that the Matrix does + + align:start position:0% +did you ever notice that the Matrix does + + + align:start position:0% +did you ever notice that the Matrix does +it for you I mean the M but when you + + align:start position:0% +it for you I mean the M but when you + + + align:start position:0% +it for you I mean the M but when you +transpose that Matrix it just + + align:start position:0% +transpose that Matrix it just + + + align:start position:0% +transpose that Matrix it just +automatically built in the the correct + + align:start position:0% +automatically built in the the correct + + + align:start position:0% +automatically built in the the correct +boundary conditions on W by you're + + align:start position:0% +boundary conditions on W by you're + + + align:start position:0% +boundary conditions on W by you're +started with the conditions on U you + + align:start position:0% +started with the conditions on U you + + + align:start position:0% +started with the conditions on U you +transpose The Matrix and you discovered + + align:start position:0% +transpose The Matrix and you discovered + + + align:start position:0% +transpose The Matrix and you discovered +what the boundary conditions on W are + + align:start position:0% +what the boundary conditions on W are + + + align:start position:0% +what the boundary conditions on W are +and I'm going to do the same for the the + + align:start position:0% +and I'm going to do the same for the the + + + align:start position:0% +and I'm going to do the same for the the +uh continuous problem + + align:start position:0% +uh continuous problem + + + align:start position:0% +uh continuous problem +I'm going to do the same for the + + align:start position:0% +I'm going to do the same for the + + + align:start position:0% +I'm going to do the same for the +continuous problem so the continuous + + align:start position:0% +continuous problem so the continuous + + + align:start position:0% +continuous problem so the continuous +continuous freef + + align:start position:0% + + + + align:start position:0% + +fixed okay what's the boundary condition + + align:start position:0% +fixed okay what's the boundary condition + + + align:start position:0% +fixed okay what's the boundary condition +on + + align:start position:0% + + + + align:start position:0% + +you if it's free fix I I just want you + + align:start position:0% +you if it's free fix I I just want you + + + align:start position:0% +you if it's free fix I I just want you +to repeat this on the interval 0 to one + + align:start position:0% +to repeat this on the interval 0 to one + + + align:start position:0% +to repeat this on the interval 0 to one +for functions U of x w ofx instead of + + align:start position:0% +for functions U of x w ofx instead of + + + align:start position:0% +for functions U of x w ofx instead of +for vectors what's the boundary + + align:start position:0% +for vectors what's the boundary + + + align:start position:0% +for vectors what's the boundary +condition on you if I have a free fixed + + align:start position:0% +condition on you if I have a free fixed + + + align:start position:0% +condition on you if I have a free fixed +problem + + align:start position:0% +problem + + + align:start position:0% +problem +U + + align:start position:0% +U + + + align:start position:0% +U +of 1 equals + + align:start position:0% +of 1 equals + + + align:start position:0% +of 1 equals +z right U of one equals + + align:start position:0% +z right U of one equals + + + align:start position:0% +z right U of one equals +z what's the boundary so this is the + + align:start position:0% +z what's the boundary so this is the + + + align:start position:0% +z what's the boundary so this is the +boundary condition that goes with a in + + align:start position:0% +boundary condition that goes with a in + + + align:start position:0% +boundary condition that goes with a in +the free fixed case and what's the bound + + align:start position:0% +the free fixed case and what's the bound + + + align:start position:0% +the free fixed case and what's the bound +and and this this is part maybe I say + + align:start position:0% +and and this this is part maybe I say + + + align:start position:0% +and and this this is part maybe I say +this this is part of + + align:start position:0% +this this is part of + + + align:start position:0% +this this is part of +a that that was that that is part of + + align:start position:0% +a that that was that that is part of + + + align:start position:0% +a that that was that that is part of +a I don't know what a is until I know + + align:start position:0% +a I don't know what a is until I know + + + align:start position:0% +a I don't know what a is until I know +its boundary condition just the way I + + align:start position:0% +its boundary condition just the way I + + + align:start position:0% +its boundary condition just the way I +don't know what this Matrix is it could + + align:start position:0% +don't know what this Matrix is it could + + + align:start position:0% +don't know what this Matrix is it could +have been a it could have lost one + + align:start position:0% +have been a it could have lost one + + + align:start position:0% +have been a it could have lost one +column it could have lost two columns + + align:start position:0% +column it could have lost two columns + + + align:start position:0% +column it could have lost two columns +whatever I don't know until I've told + + align:start position:0% +whatever I don't know until I've told + + + align:start position:0% +whatever I don't know until I've told +you the boundary condition on U and then + + align:start position:0% +you the boundary condition on U and then + + + align:start position:0% +you the boundary condition on U and then +transposing is going to tell me + + align:start position:0% +transposing is going to tell me + + + align:start position:0% +transposing is going to tell me +automatically without any further input + + align:start position:0% +automatically without any further input + + + align:start position:0% +automatically without any further input +the boundary condition that goes on the + + align:start position:0% +the boundary condition that goes on the + + + align:start position:0% +the boundary condition that goes on the +Ed joint so what's the boundary + + align:start position:0% +Ed joint so what's the boundary + + + align:start position:0% +Ed joint so what's the boundary +condition on W that goes with that's + + align:start position:0% +condition on W that goes with that's + + + align:start position:0% +condition on W that goes with that's +part of a transpose well well you're + + align:start position:0% +part of a transpose well well you're + + + align:start position:0% +part of a transpose well well you're +going to tell + + align:start position:0% +going to tell + + + align:start position:0% +going to tell +me tell me W of0 should be zero okay it + + align:start position:0% +me tell me W of0 should be zero okay it + + + align:start position:0% +me tell me W of0 should be zero okay it +came out automatically naturally this is + + align:start position:0% +came out automatically naturally this is + + + align:start position:0% +came out automatically naturally this is +a big distinction between boundary + + align:start position:0% +a big distinction between boundary + + + align:start position:0% +a big distinction between boundary +conditions this would be I would call + + align:start position:0% +conditions this would be I would call + + + align:start position:0% +conditions this would be I would call +that an essential boundary condition I I + + align:start position:0% +that an essential boundary condition I I + + + align:start position:0% +that an essential boundary condition I I +push it I had to start with it I had to + + align:start position:0% +push it I had to start with it I had to + + + align:start position:0% +push it I had to start with it I had to +decide on that and then this I call a + + align:start position:0% +decide on that and then this I call a + + + align:start position:0% +decide on that and then this I call a +natural boundary condition or there are + + align:start position:0% +natural boundary condition or there are + + + align:start position:0% +natural boundary condition or there are +even two guys' names who uh who which + + align:start position:0% +even two guys' names who uh who which + + + align:start position:0% +even two guys' names who uh who which +are associated with these two types so + + align:start position:0% +are associated with these two types so + + + align:start position:0% +are associated with these two types so +maybe good CH first chance to just + + align:start position:0% +maybe good CH first chance to just + + + align:start position:0% +maybe good CH first chance to just +mention these names because you'll often + + align:start position:0% +mention these names because you'll often + + + align:start position:0% +mention these names because you'll often +see in in a reading some paper maybe on + + align:start position:0% +see in in a reading some paper maybe on + + + align:start position:0% +see in in a reading some paper maybe on +a sort + + align:start position:0% +a sort + + + align:start position:0% +a sort +of a little on the mathematical side to + + align:start position:0% +of a little on the mathematical side to + + + align:start position:0% +of a little on the mathematical side to +see the word used the guy's name with + + align:start position:0% +see the word used the guy's name with + + + align:start position:0% +see the word used the guy's name with +this sort of boundary condition is a + + align:start position:0% +this sort of boundary condition is a + + + align:start position:0% +this sort of boundary condition is a +French name not so easy to say + + align:start position:0% +French name not so easy to say + + + align:start position:0% +French name not so easy to say +directly I'll say it more often in the + + align:start position:0% +directly I'll say it more often in the + + + align:start position:0% +directly I'll say it more often in the +future anyway + + align:start position:0% +future anyway + + + align:start position:0% +future anyway +that I I would call that a derl + + align:start position:0% +that I I would call that a derl + + + align:start position:0% +that I I would call that a derl +condition and you would say it's a fixed + + align:start position:0% +condition and you would say it's a fixed + + + align:start position:0% +condition and you would say it's a fixed +boundary condition and if you were doing + + align:start position:0% +boundary condition and if you were doing + + + align:start position:0% +boundary condition and if you were doing +heat flow you would say it's a fixed + + align:start position:0% +heat flow you would say it's a fixed + + + align:start position:0% +heat flow you would say it's a fixed +temperature whatever fixed is the fixed + + align:start position:0% +temperature whatever fixed is the fixed + + + align:start position:0% +temperature whatever fixed is the fixed +is the is really the word to remember + + align:start position:0% +is the is really the word to remember + + + align:start position:0% +is the is really the word to remember +there okay and then I guess I better + + align:start position:0% +there okay and then I guess I better + + + align:start position:0% +there okay and then I guess I better +give Germany a shot here too uh so the + + align:start position:0% +give Germany a shot here too uh so the + + + align:start position:0% +give Germany a shot here too uh so the +boundary the boundary condition the the + + align:start position:0% +boundary the boundary condition the the + + + align:start position:0% +boundary the boundary condition the the +natural boundary condition is associated + + align:start position:0% +natural boundary condition is associated + + + align:start position:0% +natural boundary condition is associated +with the name of Nora + + align:start position:0% + + + + align:start position:0% + +so if I + + align:start position:0% +so if I + + + align:start position:0% +so if I +said a DeRay problem a total derl + + align:start position:0% +said a DeRay problem a total derl + + + align:start position:0% +said a DeRay problem a total derl +problem I would be speaking about fixed + + align:start position:0% +problem I would be speaking about fixed + + + align:start position:0% +problem I would be speaking about fixed +fixed and if I spoke about a Nyon + + align:start position:0% +fixed and if I spoke about a Nyon + + + align:start position:0% +fixed and if I spoke about a Nyon +problem I would be talking about free + + align:start position:0% +problem I would be talking about free + + + align:start position:0% +problem I would be talking about free +free and this problem is derl at one end + + align:start position:0% +free and this problem is derl at one end + + + align:start position:0% +free and this problem is derl at one end +Nyon at the other anyway so essential + + align:start position:0% +Nyon at the other anyway so essential + + + align:start position:0% +Nyon at the other anyway so essential +and and natural and now of course I + + align:start position:0% +and and natural and now of course I + + + align:start position:0% +and and natural and now of course I +guess I'm hoping that that's going to + + align:start position:0% +guess I'm hoping that that's going to + + + align:start position:0% +guess I'm hoping that that's going to +make this that that is going to make + + align:start position:0% +make this that that is going to make + + + align:start position:0% +make this that that is going to make +this boundary term uh go + + align:start position:0% +this boundary term uh go + + + align:start position:0% +this boundary term uh go +away + + align:start position:0% +away + + + align:start position:0% +away +H okay now I'm paying attention to this + + align:start position:0% +H okay now I'm paying attention to this + + + align:start position:0% +H okay now I'm paying attention to this +thing that you made me write UW okay + + align:start position:0% +thing that you made me write UW okay + + + align:start position:0% +thing that you made me write UW okay +what happens there u + + align:start position:0% +what happens there u + + + align:start position:0% +what happens there u +w oh all right this this isn't bad + + align:start position:0% +w oh all right this this isn't bad + + + align:start position:0% +w oh all right this this isn't bad +because it shows that there's a boundary + + align:start position:0% +because it shows that there's a boundary + + + align:start position:0% +because it shows that there's a boundary +conditions I've got some little deals + + align:start position:0% +conditions I've got some little deals + + + align:start position:0% +conditions I've got some little deals +going + + align:start position:0% +going + + + align:start position:0% +going +yeah but do you see yeah + + align:start position:0% +yeah but do you see yeah + + + align:start position:0% +yeah but do you see yeah +uh so do you see that that becomes + + align:start position:0% +uh so do you see that that becomes + + + align:start position:0% +uh so do you see that that becomes +zero why is it zero at the top end at at + + align:start position:0% +zero why is it zero at the top end at at + + + align:start position:0% +zero why is it zero at the top end at at +one when I take U * w at one why do I + + align:start position:0% +one when I take U * w at one why do I + + + align:start position:0% +one when I take U * w at one why do I +get + + align:start position:0% +get + + + align:start position:0% +get +zero because which one U of one is zero + + align:start position:0% +zero because which one U of one is zero + + + align:start position:0% +zero because which one U of one is zero +good and at the bottom end when I take + + align:start position:0% +good and at the bottom end when I take + + + align:start position:0% +good and at the bottom end when I take +UW at the at the other boundary why do I + + align:start position:0% +UW at the at the other boundary why do I + + + align:start position:0% +UW at the at the other boundary why do I +get zero because of w do you see that W + + align:start position:0% +get zero because of w do you see that W + + + align:start position:0% +get zero because of w do you see that W +was needed it that that W of Z was + + align:start position:0% +was needed it that that W of Z was + + + align:start position:0% +was needed it that that W of Z was +needed because there was no controlling + + align:start position:0% +needed because there was no controlling + + + align:start position:0% +needed because there was no controlling +U of zero I had no control of you at the + + align:start position:0% +U of zero I had no control of you at the + + + align:start position:0% +U of zero I had no control of you at the +leftand end because it was free so the + + align:start position:0% +leftand end because it was free so the + + + align:start position:0% +leftand end because it was free so the +the control has to come from W and so w + + align:start position:0% +the control has to come from W and so w + + + align:start position:0% +the control has to come from W and so w +naturally had to be zero because I + + align:start position:0% +naturally had to be zero because I + + + align:start position:0% +naturally had to be zero because I +wasn't controlling you at that left end + + align:start position:0% +wasn't controlling you at that left end + + + align:start position:0% +wasn't controlling you at that left end +free end yeah so it's so one way or the + + align:start position:0% +free end yeah so it's so one way or the + + + align:start position:0% +free end yeah so it's so one way or the +other the the uh integration by part is + + align:start position:0% +other the the uh integration by part is + + + align:start position:0% +other the the uh integration by part is +the key yeah so that that I'll I'll uh + + align:start position:0% +the key yeah so that that I'll I'll uh + + + align:start position:0% +the key yeah so that that I'll I'll uh +so that said what I critically wanted to + + align:start position:0% +so that said what I critically wanted to + + + align:start position:0% +so that said what I critically wanted to +say about uh + + align:start position:0% +say about uh + + + align:start position:0% +say about uh +transposing taking the ad + + align:start position:0% +transposing taking the ad + + + align:start position:0% +transposing taking the ad +joint except I was just going to add a + + align:start position:0% +joint except I was just going to add a + + + align:start position:0% +joint except I was just going to add a +comment about this square a versus + + align:start position:0% +comment about this square a versus + + + align:start position:0% +comment about this square a versus +rectangular because that's and this was + + align:start position:0% +rectangular because that's and this was + + + align:start position:0% +rectangular because that's and this was +a case of square right this was a case + + align:start position:0% +a case of square right this was a case + + + align:start position:0% +a case of square right this was a case +this free fixed case this example I + + align:start position:0% +this free fixed case this example I + + + align:start position:0% +this free fixed case this example I +happen to pick was square a not the free + + align:start position:0% +happen to pick was square a not the free + + + align:start position:0% +happen to pick was square a not the free +free guy that was a hint on the quiz was + + align:start position:0% +free guy that was a hint on the quiz was + + + align:start position:0% +free guy that was a hint on the quiz was +rectangular the fixed fix which was also + + align:start position:0% +rectangular the fixed fix which was also + + + align:start position:0% +rectangular the fixed fix which was also +on the quiz was also rectangular right + + align:start position:0% +on the quiz was also rectangular right + + + align:start position:0% +on the quiz was also rectangular right +it was what four 4 by3 or something this + + align:start position:0% +it was what four 4 by3 or something this + + + align:start position:0% +it was what four 4 by3 or something this +is this a is + + align:start position:0% +is this a is + + + align:start position:0% +is this a is +4x4 and and what + + align:start position:0% +4x4 and and what + + + align:start position:0% +4x4 and and what +is what is specially nice when it's + + align:start position:0% +is what is specially nice when it's + + + align:start position:0% +is what is specially nice when it's +Square it just uh it just if if our + + align:start position:0% +Square it just uh it just if if our + + + align:start position:0% +Square it just uh it just if if our +problem happens to give a square Matrix + + align:start position:0% +problem happens to give a square Matrix + + + align:start position:0% +problem happens to give a square Matrix +in the trust case if the number of + + align:start position:0% +in the trust case if the number of + + + align:start position:0% +in the trust case if the number of +displacement unknowns happens to equal + + align:start position:0% +displacement unknowns happens to equal + + + align:start position:0% +displacement unknowns happens to equal +the number of bars so m equals N I have + + align:start position:0% +the number of bars so m equals N I have + + + align:start position:0% +the number of bars so m equals N I have +a square Matrix a and uh this guy's + + align:start position:0% +a square Matrix a and uh this guy's + + + align:start position:0% +a square Matrix a and uh this guy's +invertible so it's all good you oh well + + align:start position:0% +invertible so it's all good you oh well + + + align:start position:0% +invertible so it's all good you oh well +that's maybe the whole point that if + + align:start position:0% +that's maybe the whole point that if + + + align:start position:0% +that's maybe the whole point that if +it's rectangular I wouldn't talk about + + align:start position:0% +it's rectangular I wouldn't talk about + + + align:start position:0% +it's rectangular I wouldn't talk about +its inverse but this is a square Matrix + + align:start position:0% +its inverse but this is a square Matrix + + + align:start position:0% +its inverse but this is a square Matrix +so I can it has a itself has an inverse + + align:start position:0% +so I can it has a itself has an inverse + + + align:start position:0% +so I can it has a itself has an inverse +instead of having as I usually have to + + align:start position:0% +instead of having as I usually have to + + + align:start position:0% +instead of having as I usually have to +deal with a transpose CA all all at once + + align:start position:0% +deal with a transpose CA all all at once + + + align:start position:0% +deal with a transpose CA all all at once +let me put this comment because it's + + align:start position:0% +let me put this comment because it's + + + align:start position:0% +let me put this comment because it's +just a small one uh up + + align:start position:0% +just a small one uh up + + + align:start position:0% +just a small one uh up +here right under these words Square + + align:start position:0% +here right under these words Square + + + align:start position:0% +here right under these words Square +versus rectangular square + + align:start position:0% +versus rectangular square + + + align:start position:0% +versus rectangular square +a and let's say + + align:start position:0% +a and let's say + + + align:start position:0% +a and let's say +invertible otherwise we're in the + + align:start position:0% +invertible otherwise we're in the + + + align:start position:0% +invertible otherwise we're in the +unstable case so you know what I mean + + align:start position:0% +unstable case so you know what I mean + + + align:start position:0% +unstable case so you know what I mean +the number of in the in the network + + align:start position:0% +the number of in the in the network + + + align:start position:0% +the number of in the in the network +problems the number of nodes equals + + align:start position:0% +problems the number of nodes equals + + + align:start position:0% +problems the number of nodes equals +number + + align:start position:0% +number + + + align:start position:0% +number +of well yeah it matches the number of + + align:start position:0% +of well yeah it matches the number of + + + align:start position:0% +of well yeah it matches the number of +edges in the in the uh in the spring + + align:start position:0% +edges in the in the uh in the spring + + + align:start position:0% +edges in the in the uh in the spring +problem we have free fix + + align:start position:0% +problem we have free fix + + + align:start position:0% +problem we have free fix +situation anyway a a comes out square + + align:start position:0% +situation anyway a a comes out square + + + align:start position:0% +situation anyway a a comes out square +whatever the application if it it it if + + align:start position:0% +whatever the application if it it it if + + + align:start position:0% +whatever the application if it it it if +it comes out square what is specially + + align:start position:0% +it comes out square what is specially + + + align:start position:0% +it comes out square what is specially +good if it comes out square what's + + align:start position:0% +good if it comes out square what's + + + align:start position:0% +good if it comes out square what's +specially good is that it has an inverse + + align:start position:0% +specially good is that it has an inverse + + + align:start position:0% +specially good is that it has an inverse +so that in this Square case this K + + align:start position:0% +so that in this Square case this K + + + align:start position:0% +so that in this Square case this K +inverse is a transpose C A inverse can + + align:start position:0% +inverse is a transpose C A inverse can + + + align:start position:0% +inverse is a transpose C A inverse can +be + + align:start position:0% +be + + + align:start position:0% +be +split can is a this is this allows us to + + align:start position:0% +split can is a this is this allows us to + + + align:start position:0% +split can is a this is this allows us to +separate to do + + align:start position:0% +separate to do + + + align:start position:0% +separate to do +what you better not do otherwise + + align:start position:0% + + + + align:start position:0% + +right in other words we are three steps + + align:start position:0% +right in other words we are three steps + + + align:start position:0% +right in other words we are three steps +which usually Munch Mash together and we + + align:start position:0% +which usually Munch Mash together and we + + + align:start position:0% +which usually Munch Mash together and we +can't separate them and we have to deal + + align:start position:0% +can't separate them and we have to deal + + + align:start position:0% +can't separate them and we have to deal +with the whole Matrix at once in this + + align:start position:0% +with the whole Matrix at once in this + + + align:start position:0% +with the whole Matrix at once in this +Square case they separate and so that's + + align:start position:0% +Square case they separate and so that's + + + align:start position:0% +Square case they separate and so that's +just like worth noticing it means that + + align:start position:0% +just like worth noticing it means that + + + align:start position:0% +just like worth noticing it means that +we can it means that we can go we can + + align:start position:0% +we can it means that we can go we can + + + align:start position:0% +we can it means that we can go we can +solve backwards we can solve these three + + align:start position:0% +solve backwards we can solve these three + + + align:start position:0% +solve backwards we can solve these three +one at a time the inverses can be done + + align:start position:0% +one at a time the inverses can be done + + + align:start position:0% +one at a time the inverses can be done +separately when a or a and a transpose + + align:start position:0% +separately when a or a and a transpose + + + align:start position:0% +separately when a or a and a transpose +are square then from this equation I can + + align:start position:0% +are square then from this equation I can + + + align:start position:0% +are square then from this equation I can +find W from this from knowing W I can + + align:start position:0% +find W from this from knowing W I can + + + align:start position:0% +find W from this from knowing W I can +find e just by inverting C by knowing e + + align:start position:0% +find e just by inverting C by knowing e + + + align:start position:0% +find e just by inverting C by knowing e +I can find U just by inverting a you see + + align:start position:0% +I can find U just by inverting a you see + + + align:start position:0% +I can find U just by inverting a you see +the three steps you could invert that + + align:start position:0% +the three steps you could invert that + + + align:start position:0% +the three steps you could invert that +then you can invert the middle step then + + align:start position:0% +then you can invert the middle step then + + + align:start position:0% +then you can invert the middle step then +you can invert a and You've Got U so the + + align:start position:0% +you can invert a and You've Got U so the + + + align:start position:0% +you can invert a and You've Got U so the +square case is like worth noticing it's + + align:start position:0% +square case is like worth noticing it's + + + align:start position:0% +square case is like worth noticing it's +special enough that in this case uh we + + align:start position:0% +special enough that in this case uh we + + + align:start position:0% +special enough that in this case uh we +would have an easy problem and this case + + align:start position:0% +would have an easy problem and this case + + + align:start position:0% +would have an easy problem and this case +is called in the for for trusses and + + align:start position:0% +is called in the for for trusses and + + + align:start position:0% +is called in the for for trusses and +mechanics is called there's a name for + + align:start position:0% +mechanics is called there's a name for + + + align:start position:0% +mechanics is called there's a name for +this and unfortunately it's a little + + align:start position:0% +this and unfortunately it's a little + + + align:start position:0% +this and unfortunately it's a little +long + + align:start position:0% +long + + + align:start position:0% +long +statically that's not the keyw + + align:start position:0% +statically that's not the keyw + + + align:start position:0% +statically that's not the keyw +determinant is the + + align:start position:0% + + + + align:start position:0% + +keyw statically + + align:start position:0% +keyw statically + + + align:start position:0% +keyw statically +determinant that that's goes with + + align:start position:0% +determinant that that's goes with + + + align:start position:0% +determinant that that's goes with +square and you can guess what the + + align:start position:0% +square and you can guess what the + + + align:start position:0% +square and you can guess what the +rectangular Matrix a what word would I + + align:start position:0% +rectangular Matrix a what word would I + + + align:start position:0% +rectangular Matrix a what word would I +use what's the opposite of determinant + + align:start position:0% +use what's the opposite of determinant + + + align:start position:0% +use what's the opposite of determinant +it's got to be + + align:start position:0% +it's got to be + + + align:start position:0% +it's got to be +indeterminate rectangular a will be + + align:start position:0% +indeterminate rectangular a will be + + + align:start position:0% +indeterminate rectangular a will be +indeterminant and and all I mean all + + align:start position:0% +indeterminant and and all I mean all + + + align:start position:0% +indeterminant and and all I mean all +that is referring to is the fact + + align:start position:0% +that is referring to is the fact + + + align:start position:0% +that is referring to is the fact +that in the determinant case the + + align:start position:0% +that in the determinant case the + + + align:start position:0% +that in the determinant case the +forces determine the + + align:start position:0% +forces determine the + + + align:start position:0% +forces determine the +stresses just you don't have to take out + + align:start position:0% +stresses just you don't have to take out + + + align:start position:0% +stresses just you don't have to take out +get the whole all three together mix + + align:start position:0% +get the whole all three together mix + + + align:start position:0% +get the whole all three together mix +them in invert go backwards all that you + + align:start position:0% +them in invert go backwards all that you + + + align:start position:0% +them in invert go backwards all that you +just can do them one at a time in this + + align:start position:0% +just can do them one at a time in this + + + align:start position:0% +just can do them one at a time in this +determinant case so I'm just oh and and + + align:start position:0% +determinant case so I'm just oh and and + + + align:start position:0% +determinant case so I'm just oh and and +now I guess I better say uh so here's + + align:start position:0% +now I guess I better say uh so here's + + + align:start position:0% +now I guess I better say uh so here's +the Matrix case but now in this chapter + + align:start position:0% +the Matrix case but now in this chapter + + + align:start position:0% +the Matrix case but now in this chapter +I always have to do the The Continuous + + align:start position:0% +I always have to do the The Continuous + + + align:start position:0% +I always have to do the The Continuous +part so what would be so let me stay + + align:start position:0% +part so what would be so let me stay + + + align:start position:0% +part so what would be so let me stay +with free fix and what's this what is + + align:start position:0% +with free fix and what's this what is + + + align:start position:0% +with free fix and what's this what is +this balance + + align:start position:0% +this balance + + + align:start position:0% +this balance +equation so this is my B this is my + + align:start position:0% +equation so this is my B this is my + + + align:start position:0% +equation so this is my B this is my +force + + align:start position:0% +force + + + align:start position:0% +force +balance I I + + align:start position:0% +balance I I + + + align:start position:0% +balance I I +didn't I didn't give it + + align:start position:0% +didn't I didn't give it + + + align:start position:0% +didn't I didn't give it +a its moment but its moment has come now + + align:start position:0% +a its moment but its moment has come now + + + align:start position:0% +a its moment but its moment has come now +so the force balance equation is minus + + align:start position:0% +so the force balance equation is minus + + + align:start position:0% +so the force balance equation is minus +dwdx + + align:start position:0% +dwdx + + + align:start position:0% +dwdx +because a transposes minus a derivative + + align:start position:0% +because a transposes minus a derivative + + + align:start position:0% +because a transposes minus a derivative +equal F ofx and my my free boundary + + align:start position:0% +equal F ofx and my my free boundary + + + align:start position:0% +equal F ofx and my my free boundary +condition my free end gave me W of what + + align:start position:0% +condition my free end gave me W of what + + + align:start position:0% +condition my free end gave me W of what +was + + align:start position:0% +was + + + align:start position:0% +was +it the the noyon guy gave me W of 0 + + align:start position:0% +it the the noyon guy gave me W of 0 + + + align:start position:0% +it the the noyon guy gave me W of 0 +equals + + align:start position:0% +equals + + + align:start position:0% +equals +0 and what's the + + align:start position:0% +0 and what's the + + + align:start position:0% +0 and what's the +point do do you see what I'm saying I'm + + align:start position:0% +point do do you see what I'm saying I'm + + + align:start position:0% +point do do you see what I'm saying I'm +saying that this free fixed is a + + align:start position:0% +saying that this free fixed is a + + + align:start position:0% +saying that this free fixed is a +beautiful example of + + align:start position:0% +beautiful example of + + + align:start position:0% +beautiful example of +determinant Square Matrix a in The + + align:start position:0% +determinant Square Matrix a in The + + + align:start position:0% +determinant Square Matrix a in The +Matrix case and the parallel in the + + align:start position:0% +Matrix case and the parallel in the + + + align:start position:0% +Matrix case and the parallel in the +continuous cases what I can solve that + + align:start position:0% +continuous cases what I can solve that + + + align:start position:0% +continuous cases what I can solve that +for w + + align:start position:0% +for w + + + align:start position:0% +for w +ofx I can solve directly for w + + align:start position:0% + + + + align:start position:0% + +ofx without involving you see I didn't + + align:start position:0% +ofx without involving you see I didn't + + + align:start position:0% +ofx without involving you see I didn't +have to know C of X I didn't even I + + align:start position:0% +have to know C of X I didn't even I + + + align:start position:0% +have to know C of X I didn't even I +don't haven't even got that far I'm just + + align:start position:0% +don't haven't even got that far I'm just + + + align:start position:0% +don't haven't even got that far I'm just +going backwards now I can solve this + + align:start position:0% +going backwards now I can solve this + + + align:start position:0% +going backwards now I can solve this +just just the way I can + + align:start position:0% +just just the way I can + + + align:start position:0% +just just the way I can +invert uh that + + align:start position:0% +invert uh that + + + align:start position:0% +invert uh that +Matrix inverting The Matrix here is the + + align:start position:0% +Matrix inverting The Matrix here is the + + + align:start position:0% +Matrix inverting The Matrix here is the +same as solving the equation you you see + + align:start position:0% +same as solving the equation you you see + + + align:start position:0% +same as solving the equation you you see +I have a first order first Der I mean + + align:start position:0% +I have a first order first Der I mean + + + align:start position:0% +I have a first order first Der I mean +it's a trivial equation right it's the + + align:start position:0% +it's a trivial equation right it's the + + + align:start position:0% +it's a trivial equation right it's the +equation you solved in the final problem + + align:start position:0% +equation you solved in the final problem + + + align:start position:0% +equation you solved in the final problem +of the quiz where F was a Delta function + + align:start position:0% +of the quiz where F was a Delta function + + + align:start position:0% +of the quiz where F was a Delta function +it was simple + + align:start position:0% +it was simple + + + align:start position:0% +it was simple +because it was a square determinant + + align:start position:0% +because it was a square determinant + + + align:start position:0% +because it was a square determinant +problem with one condition on W when + + align:start position:0% +problem with one condition on W when + + + align:start position:0% +problem with one condition on W when +both conditions are on you then then + + align:start position:0% +both conditions are on you then then + + + align:start position:0% +both conditions are on you then then +you've you've got to it's not Square + + align:start position:0% +you've you've got to it's not Square + + + align:start position:0% +you've you've got to it's not Square +anymore okay for that + + align:start position:0% +anymore okay for that + + + align:start position:0% +anymore okay for that +point determinate versus indeterminate + + align:start position:0% +point determinate versus indeterminate + + + align:start position:0% +point determinate versus indeterminate +okay so that's uh that's sort of and I + + align:start position:0% +okay so that's uh that's sort of and I + + + align:start position:0% +okay so that's uh that's sort of and I +could do examples you know I could maybe + + align:start position:0% +could do examples you know I could maybe + + + align:start position:0% +could do examples you know I could maybe +I've asked you on the homework to take a + + align:start position:0% +I've asked you on the homework to take a + + + align:start position:0% +I've asked you on the homework to take a +particular F ofx I hope it was a free + + align:start position:0% +particular F ofx I hope it was a free + + + align:start position:0% +particular F ofx I hope it was a free +fixed problem if I was feeling good that + + align:start position:0% +fixed problem if I was feeling good that + + + align:start position:0% +fixed problem if I was feeling good that +day because was free fixed you'll be + + align:start position:0% +day because was free fixed you'll be + + + align:start position:0% +day because was free fixed you'll be +able to get W of X right away if it was + + align:start position:0% +able to get W of X right away if it was + + + align:start position:0% +able to get W of X right away if it was +fixed fixed then I apologize it's going + + align:start position:0% +fixed fixed then I apologize it's going + + + align:start position:0% +fixed fixed then I apologize it's going +to take you a little bit longer to get + + align:start position:0% +to take you a little bit longer to get + + + align:start position:0% +to take you a little bit longer to get +to double to to get to youu yeah okay + + align:start position:0% +to double to to get to youu yeah okay + + + align:start position:0% +to double to to get to youu yeah okay +but this of course one I mean I just + + align:start position:0% +but this of course one I mean I just + + + align:start position:0% +but this of course one I mean I just +integrate inverting a difference Matrix + + align:start position:0% +integrate inverting a difference Matrix + + + align:start position:0% +integrate inverting a difference Matrix +is just integrating a function + + align:start position:0% +is just integrating a function + + + align:start position:0% +is just integrating a function +yeah good okay so there there that's + + align:start position:0% +yeah good okay so there there that's + + + align:start position:0% +yeah good okay so there there that's +these are sort of this this lecture so + + align:start position:0% +these are sort of this this lecture so + + + align:start position:0% +these are sort of this this lecture so +far was the transition + + align:start position:0% + + + + align:start position:0% + +from vectors and matrices to functions + + align:start position:0% +from vectors and matrices to functions + + + align:start position:0% +from vectors and matrices to functions +and continuous problems and then of + + align:start position:0% +and continuous problems and then of + + + align:start position:0% +and continuous problems and then of +course we're going to get deep into that + + align:start position:0% +course we're going to get deep into that + + + align:start position:0% +course we're going to get deep into that +because we got partial differential + + align:start position:0% +because we got partial differential + + + align:start position:0% +because we got partial differential +equations ahead but today let's stay in + + align:start position:0% +equations ahead but today let's stay in + + + align:start position:0% +equations ahead but today let's stay in +one dimension and introduce finite + + align:start position:0% +one dimension and introduce finite + + + align:start position:0% +one dimension and introduce finite +elements + + align:start position:0% +elements + + + align:start position:0% +elements +okay ready for finite elements so that's + + align:start position:0% +okay ready for finite elements so that's + + + align:start position:0% +okay ready for finite elements so that's +now a major step finite differences I I + + align:start position:0% +now a major step finite differences I I + + + align:start position:0% +now a major step finite differences I I +maybe I'll mention this probably in this + + align:start position:0% +maybe I'll mention this probably in this + + + align:start position:0% +maybe I'll mention this probably in this +afternoon's review session uh where I'll + + align:start position:0% +afternoon's review session uh where I'll + + + align:start position:0% +afternoon's review session uh where I'll +just be open to homework problems I'll + + align:start position:0% +just be open to homework problems I'll + + + align:start position:0% +just be open to homework problems I'll +say something more about trust examples + + align:start position:0% +say something more about trust examples + + + align:start position:0% +say something more about trust examples +and I might say something about finite + + align:start position:0% +and I might say something about finite + + + align:start position:0% +and I might say something about finite +differences for this but really it's + + align:start position:0% +differences for this but really it's + + + align:start position:0% +differences for this but really it's +finite elements that that get introduced + + align:start position:0% +finite elements that that get introduced + + + align:start position:0% +finite elements that that get introduced +right now so let me do that okay find + + align:start position:0% +right now so let me do that okay find + + + align:start position:0% +right now so let me do that okay find +out elements get introduced now + + align:start position:0% +out elements get introduced now + + + align:start position:0% +out elements get introduced now +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay so the prep the the getting ready + + align:start position:0% +okay so the prep the the getting ready + + + align:start position:0% +okay so the prep the the getting ready +for finite elements is to get hold of + + align:start position:0% +for finite elements is to get hold of + + + align:start position:0% +for finite elements is to get hold of +something called the weak + + align:start position:0% +something called the weak + + + align:start position:0% +something called the weak +form of the + + align:start position:0% +form of the + + + align:start position:0% +form of the +equation of the of the + + align:start position:0% + + + + align:start position:0% + +equation so that's going to be a a + + align:start position:0% +equation so that's going to be a a + + + align:start position:0% +equation so that's going to be a a +continuous a statement of the the finite + + align:start position:0% +continuous a statement of the the finite + + + align:start position:0% +continuous a statement of the the finite +elements aren't appearing yet this + + align:start position:0% +elements aren't appearing yet this + + + align:start position:0% +elements aren't appearing yet this +matrices are not appearing yet I'm + + align:start position:0% +matrices are not appearing yet I'm + + + align:start position:0% +matrices are not appearing yet I'm +talking about the + + align:start position:0% +talking about the + + + align:start position:0% +talking about the +differential equation but what is what + + align:start position:0% +differential equation but what is what + + + align:start position:0% +differential equation but what is what +do I mean by this weak form okay let me + + align:start position:0% +do I mean by this weak form okay let me + + + align:start position:0% +do I mean by this weak form okay let me +just go go for it directly you see the + + align:start position:0% +just go go for it directly you see the + + + align:start position:0% +just go go for it directly you see the +equation up there let me copy it so + + align:start position:0% +equation up there let me copy it so + + + align:start position:0% +equation up there let me copy it so +here's the strong + + align:start position:0% + + + + align:start position:0% + +form the strong form is the you would + + align:start position:0% +form the strong form is the you would + + + align:start position:0% +form the strong form is the you would +say is the ordinary equation the strong + + align:start position:0% +say is the ordinary equation the strong + + + align:start position:0% +say is the ordinary equation the strong +form is is what our equation is minus d + + align:start position:0% +form is is what our equation is minus d + + + align:start position:0% +form is is what our equation is minus d +by + + align:start position:0% +by + + + align:start position:0% +by +DX of C ofx + + align:start position:0% +DX of C ofx + + + align:start position:0% +DX of C ofx +Dux equal F + + align:start position:0% + + + + align:start position:0% + +ofx okay that's the strong form that's + + align:start position:0% +ofx okay that's the strong form that's + + + align:start position:0% +ofx okay that's the strong form that's +the equation now how do I get to the + + align:start position:0% +the equation now how do I get to the + + + align:start position:0% +the equation now how do I get to the +weak form let me let me just go to it + + align:start position:0% +weak form let me let me just go to it + + + align:start position:0% +weak form let me let me just go to it +directly and then we'll over the next + + align:start position:0% +directly and then we'll over the next + + + align:start position:0% +directly and then we'll over the next +days we'll see why it's so natural and + + align:start position:0% +days we'll see why it's so natural and + + + align:start position:0% +days we'll see why it's so natural and +important if I go for it directly what I + + align:start position:0% +important if I go for it directly what I + + + align:start position:0% +important if I go for it directly what I +do is this I multiply both sides of the + + align:start position:0% +do is this I multiply both sides of the + + + align:start position:0% +do is this I multiply both sides of the +equation by something I'll call a test + + align:start position:0% +equation by something I'll call a test + + + align:start position:0% +equation by something I'll call a test +function and I'll try to systematically + + align:start position:0% +function and I'll try to systematically + + + align:start position:0% +function and I'll try to systematically +use the letter V for the test functions + + align:start position:0% +use the letter V for the test functions + + + align:start position:0% +use the letter V for the test functions +U will be uh um solution V isn't the + + align:start position:0% +U will be uh um solution V isn't the + + + align:start position:0% +U will be uh um solution V isn't the +solution V is like any function that I + + align:start position:0% +solution V is like any function that I + + + align:start position:0% +solution V is like any function that I +that I test this equation this way I'm + + align:start position:0% +that I test this equation this way I'm + + + align:start position:0% +that I test this equation this way I'm +just multiplying both sides by the same + + align:start position:0% +just multiplying both sides by the same + + + align:start position:0% +just multiplying both sides by the same +thing some V ofx any V + + align:start position:0% +thing some V ofx any V + + + align:start position:0% +thing some V ofx any V +ofx we'll see if there are any + + align:start position:0% +ofx we'll see if there are any + + + align:start position:0% +ofx we'll see if there are any +limitations okay and I + + align:start position:0% + + + + align:start position:0% + +integrate + + align:start position:0% + + + + align:start position:0% + +DX okay so you're going to say no no + + align:start position:0% +DX okay so you're going to say no no + + + align:start position:0% +DX okay so you're going to say no no +problem I integrate from 0 to + + align:start position:0% +problem I integrate from 0 to + + + align:start position:0% +problem I integrate from 0 to +one all right so this is like um + + align:start position:0% +one all right so this is like um + + + align:start position:0% +one all right so this is like um +this would be true for so so the we so + + align:start position:0% +this would be true for so so the we so + + + align:start position:0% +this would be true for so so the we so +now I I'll erase the word strong form + + align:start position:0% +now I I'll erase the word strong form + + + align:start position:0% +now I I'll erase the word strong form +because the strong form isn't on the + + align:start position:0% +because the strong form isn't on the + + + align:start position:0% +because the strong form isn't on the +board + + align:start position:0% +board + + + align:start position:0% +board +anymore it's the weak form now that + + align:start position:0% +anymore it's the weak form now that + + + align:start position:0% +anymore it's the weak form now that +we're looking at and this is for any V + + align:start position:0% +we're looking at and this is for any V + + + align:start position:0% +we're looking at and this is for any V +for any and I'll put any in quotes just + + align:start position:0% +for any and I'll put any in quotes just + + + align:start position:0% +for any and I'll put any in quotes just +because I have I have to I'll eventually + + align:start position:0% +because I have I have to I'll eventually + + + align:start position:0% +because I have I have to I'll eventually +I'll say a little more about this for + + align:start position:0% +I'll say a little more about this for + + + align:start position:0% +I'll say a little more about this for +any I I'll write the equation this + + align:start position:0% +any I I'll write the equation this + + + align:start position:0% +any I I'll write the equation this +way and and you might think okay if I + + align:start position:0% +way and and you might think okay if I + + + align:start position:0% +way and and you might think okay if I +test if I if this has to hold for every + + align:start position:0% +test if I if this has to hold for every + + + align:start position:0% +test if I if this has to hold for every +V of + + align:start position:0% +V of + + + align:start position:0% +V of +X yeah I could like let V ofx be + + align:start position:0% +X yeah I could like let V ofx be + + + align:start position:0% +X yeah I could like let V ofx be +concentrated in a little area and and + + align:start position:0% +concentrated in a little area and and + + + align:start position:0% +concentrated in a little area and and +this would have to hold then I could try + + align:start position:0% +this would have to hold then I could try + + + align:start position:0% +this would have to hold then I could try +another V of X concentrated in around + + align:start position:0% +another V of X concentrated in around + + + align:start position:0% +another V of X concentrated in around +other + + align:start position:0% +other + + + align:start position:0% +other +points you can maybe + + align:start position:0% +points you can maybe + + + align:start position:0% +points you can maybe +feel that if this holds for every V ofx + + align:start position:0% +feel that if this holds for every V ofx + + + align:start position:0% +feel that if this holds for every V ofx +then I can get back to the strong form + + align:start position:0% +then I can get back to the strong form + + + align:start position:0% +then I can get back to the strong form +if this holds for every V ofx then + + align:start position:0% +if this holds for every V ofx then + + + align:start position:0% +if this holds for every V ofx then +somehow that had better be the same as + + align:start position:0% +somehow that had better be the same as + + + align:start position:0% +somehow that had better be the same as +that because if this was F ofx if this + + align:start position:0% +that because if this was F ofx if this + + + align:start position:0% +that because if this was F ofx if this +was F ofx + one and this is f ofx + + align:start position:0% +was F ofx + one and this is f ofx + + + align:start position:0% +was F ofx + one and this is f ofx +then i' I wouldn't have the equality + + align:start position:0% +then i' I wouldn't have the equality + + + align:start position:0% +then i' I wouldn't have the equality +anymore shall I just say that again it's + + align:start position:0% +anymore shall I just say that again it's + + + align:start position:0% +anymore shall I just say that again it's +just like at this point it's just a + + align:start position:0% +just like at this point it's just a + + + align:start position:0% +just like at this point it's just a +feeling that if this is true for every V + + align:start position:0% +feeling that if this is true for every V + + + align:start position:0% +feeling that if this is true for every V +ofx then that part had better equal that + + align:start position:0% +ofx then that part had better equal that + + + align:start position:0% +ofx then that part had better equal that +part I'll have a way that'll be my way + + align:start position:0% +part I'll have a way that'll be my way + + + align:start position:0% +part I'll have a way that'll be my way +back to the strong form it's a little + + align:start position:0% +back to the strong form it's a little + + + align:start position:0% +back to the strong form it's a little +bit like climbing a hill going downhill + + align:start position:0% +bit like climbing a hill going downhill + + + align:start position:0% +bit like climbing a hill going downhill +was easy I just multiplied by V and + + align:start position:0% +was easy I just multiplied by V and + + + align:start position:0% +was easy I just multiplied by V and +integrated nobody objected to that I'm + + align:start position:0% +integrated nobody objected to that I'm + + + align:start position:0% +integrated nobody objected to that I'm +saying I'll be able to get back to the + + align:start position:0% +saying I'll be able to get back to the + + + align:start position:0% +saying I'll be able to get back to the +strong form uh with a little patience + + align:start position:0% +strong form uh with a little patience + + + align:start position:0% +strong form uh with a little patience +but I like the weak form that's the + + align:start position:0% +but I like the weak form that's the + + + align:start position:0% +but I like the weak form that's the +whole point you gotta begin to like the + + align:start position:0% +whole point you gotta begin to like the + + + align:start position:0% +whole point you gotta begin to like the +weak + + align:start position:0% +weak + + + align:start position:0% +weak +form you begin to take it in and think + + align:start position:0% +form you begin to take it in and think + + + align:start position:0% +form you begin to take it in and think +okay now why do I like + + align:start position:0% +okay now why do I like + + + align:start position:0% +okay now why do I like +it what am I going to do to that left + + align:start position:0% +it what am I going to do to that left + + + align:start position:0% +it what am I going to do to that left +side side the right side's cool right I + + align:start position:0% +side side the right side's cool right I + + + align:start position:0% +side side the right side's cool right I +looks good left side does not look good + + align:start position:0% +looks good left side does not look good + + + align:start position:0% +looks good left side does not look good +to + + align:start position:0% +to + + + align:start position:0% +to +me when you see something like that what + + align:start position:0% +me when you see something like that what + + + align:start position:0% +me when you see something like that what +is what do you think today's lecture has + + align:start position:0% +is what do you think today's lecture has + + + align:start position:0% +is what do you think today's lecture has +already said what to think what should I + + align:start position:0% +already said what to think what should I + + + align:start position:0% +already said what to think what should I +do to make that look + + align:start position:0% +do to make that look + + + align:start position:0% +do to make that look +better I should yep integrate by Parts + + align:start position:0% +better I should yep integrate by Parts + + + align:start position:0% +better I should yep integrate by Parts +if I integrate by Parts you see what I + + align:start position:0% +if I integrate by Parts you see what I + + + align:start position:0% +if I integrate by Parts you see what I +don't like about this about it as it is + + align:start position:0% +don't like about this about it as it is + + + align:start position:0% +don't like about this about it as it is +is two derivatives are hitting you + + align:start position:0% +is two derivatives are hitting you + + + align:start position:0% +is two derivatives are hitting you +and nobody and V is by itself and I want + + align:start position:0% +and nobody and V is by itself and I want + + + align:start position:0% +and nobody and V is by itself and I want +it to be symmetric so my I'm going to + + align:start position:0% +it to be symmetric so my I'm going to + + + align:start position:0% +it to be symmetric so my I'm going to +integrate this by Parts this is minus + + align:start position:0% +integrate this by Parts this is minus + + + align:start position:0% +integrate this by Parts this is minus +the derivative of something times times + + align:start position:0% +the derivative of something times times + + + align:start position:0% +the derivative of something times times +V and when I integrate by Parts I'm + + align:start position:0% +V and when I integrate by Parts I'm + + + align:start position:0% +V and when I integrate by Parts I'm +going to have it'll be an integral and + + align:start position:0% +going to have it'll be an integral and + + + align:start position:0% +going to have it'll be an integral and +what so can you integrate by parts now I + + align:start position:0% +what so can you integrate by parts now I + + + align:start position:0% +what so can you integrate by parts now I +mean this is + + align:start position:0% +mean this is + + + align:start position:0% +mean this is +like you probably haven't thought about + + align:start position:0% +like you probably haven't thought about + + + align:start position:0% +like you probably haven't thought about +integration by parts for a while just + + align:start position:0% +integration by parts for a while just + + + align:start position:0% +integration by parts for a while just +think of it as is taking the derivative + + align:start position:0% +think of it as is taking the derivative + + + align:start position:0% +think of it as is taking the derivative +off of this so it leaves that by + + align:start position:0% +off of this so it leaves that by + + + align:start position:0% +off of this so it leaves that by +itself and putting it + + align:start position:0% +itself and putting it + + + align:start position:0% +itself and putting it +onto V so it bring so it's DV + + align:start position:0% +onto V so it bring so it's DV + + + align:start position:0% +onto V so it bring so it's DV +DX and remembering the minus sign but we + + align:start position:0% +DX and remembering the minus sign but we + + + align:start position:0% +DX and remembering the minus sign but we +have a minus sign so now it's coming out + + align:start position:0% +have a minus sign so now it's coming out + + + align:start position:0% +have a minus sign so now it's coming out +plus that's the weak form can I can I + + align:start position:0% +plus that's the weak form can I can I + + + align:start position:0% +plus that's the weak form can I can I +put a circle around the weak + + align:start position:0% +put a circle around the weak + + + align:start position:0% +put a circle around the weak +form or not it wasn't exactly a circle + + align:start position:0% +form or not it wasn't exactly a circle + + + align:start position:0% +form or not it wasn't exactly a circle +okay but that's the weak form + + align:start position:0% +okay but that's the weak form + + + align:start position:0% +okay but that's the weak form +for every V this is I could give you a + + align:start position:0% +for every V this is I could give you a + + + align:start position:0% +for every V this is I could give you a +physical interpretation but I won't I + + align:start position:0% +physical interpretation but I won't I + + + align:start position:0% +physical interpretation but I won't I +won't uh do it just this + + align:start position:0% + + + + align:start position:0% + +minute this is this is going to hold for + + align:start position:0% +minute this is this is going to hold for + + + align:start position:0% +minute this is this is going to hold for +any for any + + align:start position:0% +any for any + + + align:start position:0% +any for any +V that's the weak + + align:start position:0% +V that's the weak + + + align:start position:0% +V that's the weak +form okay good + + align:start position:0% +form okay good + + + align:start position:0% +form okay good +now why do I want to why did I want to + + align:start position:0% +now why do I want to why did I want to + + + align:start position:0% +now why do I want to why did I want to +do that + + align:start position:0% +do that + + + align:start position:0% +do that +oh the person who + + align:start position:0% +oh the person who + + + align:start position:0% +oh the person who +reminds me about boundary conditions + + align:start position:0% +reminds me about boundary conditions + + + align:start position:0% +reminds me about boundary conditions +should remind me again that when I did + + align:start position:0% +should remind me again that when I did + + + align:start position:0% +should remind me again that when I did +this integration by parts there should + + align:start position:0% +this integration by parts there should + + + align:start position:0% +this integration by parts there should +been + + align:start position:0% +been + + + align:start position:0% +been +also uh what's what's the integrated + + align:start position:0% +also uh what's what's the integrated + + + align:start position:0% +also uh what's what's the integrated +part now that's that has to be evaluated + + align:start position:0% +part now that's that has to be evaluated + + + align:start position:0% +part now that's that has to be evaluated +at zero and + + align:start position:0% +at zero and + + + align:start position:0% +at zero and +one C so it's it's that times that right + + align:start position:0% +one C so it's it's that times that right + + + align:start position:0% +one C so it's it's that times that right +it's the C ofx D + + align:start position:0% +it's the C ofx D + + + align:start position:0% +it's the C ofx D +udx time V + + align:start position:0% + + + + align:start position:0% + +ofx uh maybe minus yeah you're right + + align:start position:0% +ofx uh maybe minus yeah you're right + + + align:start position:0% +ofx uh maybe minus yeah you're right +minus good what do I want this to come + + align:start position:0% +minus good what do I want this to come + + + align:start position:0% +minus good what do I want this to come +out zero of course I I don't want to + + align:start position:0% +out zero of course I I don't want to + + + align:start position:0% +out zero of course I I don't want to +think about this anymore all right so + + align:start position:0% +think about this anymore all right so + + + align:start position:0% +think about this anymore all right so +now I'm doing this free fix problem + + align:start position:0% +now I'm doing this free fix problem + + + align:start position:0% +now I'm doing this free fix problem +still so what's the deal on the free + + align:start position:0% +still so what's the deal on the free + + + align:start position:0% +still so what's the deal on the free +fixed problem Oh huh well let's + + align:start position:0% + + + + align:start position:0% + +see okay I got the two ends and I want + + align:start position:0% +see okay I got the two ends and I want + + + align:start position:0% +see okay I got the two ends and I want +them but I want them to be zero okay + + align:start position:0% +them but I want them to be zero okay + + + align:start position:0% +them but I want them to be zero okay +okay now at at the free + + align:start position:0% + + + + align:start position:0% + +end at the free end this had been at the + + align:start position:0% +end at the free end this had been at the + + + align:start position:0% +end at the free end this had been at the +free end I'm not controlling V I'm I + + align:start position:0% +free end I'm not controlling V I'm I + + + align:start position:0% +free end I'm not controlling V I'm I +wasn't controlling you and I'm not going + + align:start position:0% +wasn't controlling you and I'm not going + + + align:start position:0% +wasn't controlling you and I'm not going +to be controlling its friend + + align:start position:0% +to be controlling its friend + + + align:start position:0% +to be controlling its friend +V so this had to be had to be zero so + + align:start position:0% +V so this had to be had to be zero so + + + align:start position:0% +V so this had to be had to be zero so +this part will be zero at the free + + align:start position:0% +this part will be zero at the free + + + align:start position:0% +this part will be zero at the free +end that that boundary condition has + + align:start position:0% +end that that boundary condition has + + + align:start position:0% +end that that boundary condition has +just appeared Again Naturally I had to + + align:start position:0% +just appeared Again Naturally I had to + + + align:start position:0% +just appeared Again Naturally I had to +have it because I had no control over V + + align:start position:0% +have it because I had no control over V + + + align:start position:0% +have it because I had no control over V +and what about at the fixed end at the + + align:start position:0% +and what about at the fixed end at the + + + align:start position:0% +and what about at the fixed end at the +fixed end which is that uh yeah yeah + + align:start position:0% +fixed end which is that uh yeah yeah + + + align:start position:0% +fixed end which is that uh yeah yeah +this is at the free end now what's + + align:start position:0% +this is at the free end now what's + + + align:start position:0% +this is at the free end now what's +what's up at the fixed + + align:start position:0% +what's up at the fixed + + + align:start position:0% +what's up at the fixed +end the F what was the fixed end that's + + align:start position:0% +end the F what was the fixed end that's + + + align:start position:0% +end the F what was the fixed end that's +where U was + + align:start position:0% +where U was + + + align:start position:0% +where U was +Zero I'm going to make V also zero so + + align:start position:0% +Zero I'm going to make V also zero so + + + align:start position:0% +Zero I'm going to make V also zero so +there's when I said any v ofx i better + + align:start position:0% +there's when I said any v ofx i better + + + align:start position:0% +there's when I said any v ofx i better +put in with v equal Z at the fixed at at + + align:start position:0% +put in with v equal Z at the fixed at at + + + align:start position:0% +put in with v equal Z at the fixed at at +at at der lay points at fixed point at + + align:start position:0% +at at der lay points at fixed point at + + + align:start position:0% +at at der lay points at fixed point at +fixed + + align:start position:0% +fixed + + + align:start position:0% +fixed +M that I need + + align:start position:0% +M that I need + + + align:start position:0% +M that I need +that I need to know that V is zero at + + align:start position:0% +that I need to know that V is zero at + + + align:start position:0% +that I need to know that V is zero at +that at that end I need I had U equals + + align:start position:0% +that at that end I need I had U equals + + + align:start position:0% +that at that end I need I had U equals +zero here's why I here's why I'm I'm + + align:start position:0% +zero here's why I here's why I'm I'm + + + align:start position:0% +zero here's why I here's why I'm I'm +fine so I'm saying that anytime I have a + + align:start position:0% +fine so I'm saying that anytime I have a + + + align:start position:0% +fine so I'm saying that anytime I have a +derly condition a fixed condition that + + align:start position:0% +derly condition a fixed condition that + + + align:start position:0% +derly condition a fixed condition that +tells me you + + align:start position:0% +tells me you + + + align:start position:0% +tells me you +I think of v and you'll begin to think + + align:start position:0% +I think of v and you'll begin to think + + + align:start position:0% +I think of v and you'll begin to think +of v as a little movement away from you + + align:start position:0% +of v as a little movement away from you + + + align:start position:0% +of v as a little movement away from you +as a little movement V is you know U is + + align:start position:0% +as a little movement V is you know U is + + + align:start position:0% +as a little movement V is you know U is +some is some uh some uh is the solution + + align:start position:0% +some is some uh some uh is the solution + + + align:start position:0% +some is some uh some uh is the solution +now remember remind me this was free fix + + align:start position:0% +now remember remind me this was free fix + + + align:start position:0% +now remember remind me this was free fix +so it the the U might have been + + align:start position:0% +so it the the U might have been + + + align:start position:0% +so it the the U might have been +something like this right I I'll just + + align:start position:0% +something like this right I I'll just + + + align:start position:0% +something like this right I I'll just +draw that right that that's my U this + + align:start position:0% +draw that right that that's my U this + + + align:start position:0% +draw that right that that's my U this +guy was fixed right + + align:start position:0% +guy was fixed right + + + align:start position:0% +guy was fixed right +by + + align:start position:0% +by + + + align:start position:0% +by +U now I'm thinking of V's as the word v + + align:start position:0% +U now I'm thinking of V's as the word v + + + align:start position:0% +U now I'm thinking of V's as the word v +letter V is very fortunate because it + + align:start position:0% +letter V is very fortunate because it + + + align:start position:0% +letter V is very fortunate because it +stands for a virtual displacement a + + align:start position:0% +stands for a virtual displacement a + + + align:start position:0% +stands for a virtual displacement a +virtual displacement is a little + + align:start position:0% +virtual displacement is a little + + + align:start position:0% +virtual displacement is a little +displacement away from you but it has to + + align:start position:0% +displacement away from you but it has to + + + align:start position:0% +displacement away from you but it has to +satisfy the zero the fixed condition + + align:start position:0% +satisfy the zero the fixed condition + + + align:start position:0% +satisfy the zero the fixed condition +that you satisfi in other words the + + align:start position:0% +that you satisfi in other words the + + + align:start position:0% +that you satisfi in other words the +little virtual V can't move away from + + align:start position:0% +little virtual V can't move away from + + + align:start position:0% +little virtual V can't move away from +zero so I get I get this term is zero at + + align:start position:0% +zero so I get I get this term is zero at + + + align:start position:0% +zero so I get I get this term is zero at +the fix + + align:start position:0% + + + + align:start position:0% + +end okay so I've I that's the little + + align:start position:0% +end okay so I've I that's the little + + + align:start position:0% +end okay so I've I that's the little +five minute timeout to to check the + + align:start position:0% +five minute timeout to to check the + + + align:start position:0% +five minute timeout to to check the +boundary condition part the net result + + align:start position:0% +boundary condition part the net result + + + align:start position:0% +boundary condition part the net result +is that that term's gone and I've got + + align:start position:0% +is that that term's gone and I've got + + + align:start position:0% +is that that term's gone and I've got +the the um weak form as I want it okay + + align:start position:0% +the the um weak form as I want it okay + + + align:start position:0% +the the um weak form as I want it okay +three minutes to tell you to start to + + align:start position:0% +three minutes to tell you to start to + + + align:start position:0% +three minutes to tell you to start to +tell you the how to use the weak form + + align:start position:0% +tell you the how to use the weak form + + + align:start position:0% +tell you the how to use the weak form +okay so this is called gin's idea + + align:start position:0% +okay so this is called gin's idea + + + align:start position:0% +okay so this is called gin's idea +gurin method gurin + + align:start position:0% + + + + align:start position:0% + +method and it starts with the weak + + align:start position:0% + + + + align:start position:0% + +form okay okay so he's Russian we Russia + + align:start position:0% +form okay okay so he's Russian we Russia + + + align:start position:0% +form okay okay so he's Russian we Russia +gets in into the picture now we had + + align:start position:0% +gets in into the picture now we had + + + align:start position:0% +gets in into the picture now we had +France and Germany with the boundary + + align:start position:0% +France and Germany with the boundary + + + align:start position:0% +France and Germany with the boundary +conditions now we've got Russia with + + align:start position:0% +conditions now we've got Russia with + + + align:start position:0% +conditions now we've got Russia with +this fundamental principle of how to + + align:start position:0% +this fundamental principle of how to + + + align:start position:0% +this fundamental principle of how to +turn a continuous problem into a + + align:start position:0% +turn a continuous problem into a + + + align:start position:0% +turn a continuous problem into a +discrete problem that's what goin's idea + + align:start position:0% +discrete problem that's what goin's idea + + + align:start position:0% +discrete problem that's what goin's idea +does instead of a function unknown I + + align:start position:0% +does instead of a function unknown I + + + align:start position:0% +does instead of a function unknown I +want to have n unknowns I want to I want + + align:start position:0% +want to have n unknowns I want to I want + + + align:start position:0% +want to have n unknowns I want to I want +to get a discrete equation which will + + align:start position:0% +to get a discrete equation which will + + + align:start position:0% +to get a discrete equation which will +eventually be KU equal F so I'm going to + + align:start position:0% +eventually be KU equal F so I'm going to + + + align:start position:0% +eventually be KU equal F so I'm going to +get to an equation kual + + align:start position:0% +get to an equation kual + + + align:start position:0% +get to an equation kual +F but not by finite differences right I + + align:start position:0% +F but not by finite differences right I + + + align:start position:0% +F but not by finite differences right I +could but I'm not I'm doing it this weak + + align:start position:0% +could but I'm not I'm doing it this weak + + + align:start position:0% +could but I'm not I'm doing it this weak +gurkin finite element way okay so if I + + align:start position:0% +gurkin finite element way okay so if I + + + align:start position:0% +gurkin finite element way okay so if I +tell you the guran idea then then next + + align:start position:0% +tell you the guran idea then then next + + + align:start position:0% +tell you the guran idea then then next +time + + align:start position:0% +time + + + align:start position:0% +time +we bring in we have libraries of finite + + align:start position:0% +we bring in we have libraries of finite + + + align:start position:0% +we bring in we have libraries of finite +elements but you have to get the + + align:start position:0% +elements but you have to get the + + + align:start position:0% +elements but you have to get the +principle straight so it's goin's idea + + align:start position:0% +principle straight so it's goin's idea + + + align:start position:0% +principle straight so it's goin's idea +gin's idea was + + align:start position:0% +gin's idea was + + + align:start position:0% +gin's idea was +choose trial + + align:start position:0% + + + + align:start position:0% + +functions let me call them U1 no no I + + align:start position:0% +functions let me call them U1 no no I + + + align:start position:0% +functions let me call them U1 no no I +won't call them you what do I call + + align:start position:0% + + + + align:start position:0% + +them T oh my + + align:start position:0% + + + + align:start position:0% + +God have to get their names right + + align:start position:0% +God have to get their names right + + + align:start position:0% +God have to get their names right +cool um fee + + align:start position:0% +cool um fee + + + align:start position:0% +cool um fee +fee okay the Greeks get a shot here okay + + align:start position:0% +fee okay the Greeks get a shot here okay + + + align:start position:0% +fee okay the Greeks get a shot here okay +trial functions F1 of x up to v n + + align:start position:0% +trial functions F1 of x up to v n + + + align:start position:0% +trial functions F1 of x up to v n +ofx + + align:start position:0% +ofx + + + align:start position:0% +ofx +okay so that's that's a choice you make + + align:start position:0% +okay so that's that's a choice you make + + + align:start position:0% +okay so that's that's a choice you make +and you and you we have a free choice + + align:start position:0% +and you and you we have a free choice + + + align:start position:0% +and you and you we have a free choice +and it's a fundamental Choice through + + align:start position:0% +and it's a fundamental Choice through + + + align:start position:0% +and it's a fundamental Choice through +all of Applied math you choose some + + align:start position:0% +all of Applied math you choose some + + + align:start position:0% +all of Applied math you choose some +functions and if you choose them well + + align:start position:0% +functions and if you choose them well + + + align:start position:0% +functions and if you choose them well +you get a great method if you choose + + align:start position:0% +you get a great method if you choose + + + align:start position:0% +you get a great method if you choose +them badly you get a lousy method okay + + align:start position:0% +them badly you get a lousy method okay + + + align:start position:0% +them badly you get a lousy method okay +so you choose trial functions and now + + align:start position:0% +so you choose trial functions and now + + + align:start position:0% +so you choose trial functions and now +what's the idea going to be you're going + + align:start position:0% +what's the idea going to be you're going + + + align:start position:0% +what's the idea going to be you're going +to be you're + + align:start position:0% +to be you're + + + align:start position:0% +to be you're +approximate approximate U approximate + + align:start position:0% +approximate approximate U approximate + + + align:start position:0% +approximate approximate U approximate +solution will be some combination of + + align:start position:0% +solution will be some combination of + + + align:start position:0% +solution will be some combination of +them so combinations of those oh let me + + align:start position:0% +them so combinations of those oh let me + + + align:start position:0% +them so combinations of those oh let me +call the let me call the coefficients 's + + align:start position:0% +call the let me call the coefficients 's + + + align:start position:0% +call the let me call the coefficients 's +because those are the + + align:start position:0% +because those are the + + + align:start position:0% +because those are the +unknowns plus u n + + align:start position:0% +unknowns plus u n + + + align:start position:0% +unknowns plus u n +VN so those are the unknowns the N + + align:start position:0% +VN so those are the unknowns the N + + + align:start position:0% +VN so those are the unknowns the N +unknowns the N that's my yeah I'll I'll + + align:start position:0% +unknowns the N that's my yeah I'll I'll + + + align:start position:0% +unknowns the N that's my yeah I'll I'll +even yeah I'll even remove that for the + + align:start position:0% +even yeah I'll even remove that for the + + + align:start position:0% +even yeah I'll even remove that for the +moment well I leave it you see these are + + align:start position:0% +moment well I leave it you see these are + + + align:start position:0% +moment well I leave it you see these are +functions of + + align:start position:0% +functions of + + + align:start position:0% +functions of +X and these are + + align:start position:0% +X and these are + + + align:start position:0% +X and these are +numbers so our unknown our unknown our n + + align:start position:0% +numbers so our unknown our unknown our n + + + align:start position:0% +numbers so our unknown our unknown our n +unknown numbers are the coefficients to + + align:start position:0% +unknown numbers are the coefficients to + + + align:start position:0% +unknown numbers are the coefficients to +be decided of the functions we + + align:start position:0% +be decided of the functions we + + + align:start position:0% +be decided of the functions we +chose okay now I need n + + align:start position:0% +chose okay now I need n + + + align:start position:0% +chose okay now I need n +equations I've got n unknowns now + + align:start position:0% +equations I've got n unknowns now + + + align:start position:0% +equations I've got n unknowns now +they're the unknown coefficients of + + align:start position:0% +they're the unknown coefficients of + + + align:start position:0% +they're the unknown coefficients of +these functions I need n equations so I + + align:start position:0% +these functions I need n equations so I + + + align:start position:0% +these functions I need n equations so I +get n equations by choose + + align:start position:0% +get n equations by choose + + + align:start position:0% +get n equations by choose +test + + align:start position:0% +test + + + align:start position:0% +test +functions + + align:start position:0% +functions + + + align:start position:0% +functions +V1 + + align:start position:0% +V1 + + + align:start position:0% +V1 +V2 up to + + align:start position:0% +V2 up to + + + align:start position:0% +V2 up to +VN each V will give me an equation so + + align:start position:0% +VN each V will give me an equation so + + + align:start position:0% +VN each V will give me an equation so +I'll have n equations at the end I have + + align:start position:0% +I'll have n equations at the end I have + + + align:start position:0% +I'll have n equations at the end I have +n unknowns I'll have a square Matrix and + + align:start position:0% +n unknowns I'll have a square Matrix and + + + align:start position:0% +n unknowns I'll have a square Matrix and +that'll be and I'll write it as a it'll + + align:start position:0% +that'll be and I'll write it as a it'll + + + align:start position:0% +that'll be and I'll write it as a it'll +be a linear system I'll get to KU equal + + align:start position:0% +be a linear system I'll get to KU equal + + + align:start position:0% +be a linear system I'll get to KU equal +F but do you see how I'm getting there + + align:start position:0% +F but do you see how I'm getting there + + + align:start position:0% +F but do you see how I'm getting there +I'm getting there by using the weak form + + align:start position:0% +I'm getting there by using the weak form + + + align:start position:0% +I'm getting there by using the weak form +by using guren's idea of picking some + + align:start position:0% +by using guren's idea of picking some + + + align:start position:0% +by using guren's idea of picking some +trial functions and some test functions + + align:start position:0% +trial functions and some test functions + + + align:start position:0% +trial functions and some test functions +and putting them into the weak form so + + align:start position:0% +and putting them into the weak form so + + + align:start position:0% +and putting them into the weak form so +goin's idea is take these functions and + + align:start position:0% +goin's idea is take these functions and + + + align:start position:0% +goin's idea is take these functions and +these functions and apply the weak form + + align:start position:0% +these functions and apply the weak form + + + align:start position:0% +these functions and apply the weak form +just to those guys not to the real weak + + align:start position:0% +just to those guys not to the real weak + + + align:start position:0% +just to those guys not to the real weak +form the continuous weak form was for oh + + align:start position:0% +form the continuous weak form was for oh + + + align:start position:0% +form the continuous weak form was for oh +whole lot of + + align:start position:0% +whole lot of + + + align:start position:0% +whole lot of +V we'll get n equations by picking nvs + + align:start position:0% +V we'll get n equations by picking nvs + + + align:start position:0% +V we'll get n equations by picking nvs +then we'll get n unknowns by picking n + + align:start position:0% +then we'll get n unknowns by picking n + + + align:start position:0% +then we'll get n unknowns by picking n +fees and the point now so this method + + align:start position:0% +fees and the point now so this method + + + align:start position:0% +fees and the point now so this method +this idea was hundred years older than + + align:start position:0% +this idea was hundred years older than + + + align:start position:0% +this idea was hundred years older than +finite elements the finite element idea + + align:start position:0% +finite elements the finite element idea + + + align:start position:0% +finite elements the finite element idea +was a particular choice of these guys a + + align:start position:0% +was a particular choice of these guys a + + + align:start position:0% +was a particular choice of these guys a +particular choice of the fe's and the + + align:start position:0% +particular choice of the fe's and the + + + align:start position:0% +particular choice of the fe's and the +v's as simple + + align:start position:0% + + + + align:start position:0% + +pols and you might think well why didn't + + align:start position:0% +pols and you might think well why didn't + + + align:start position:0% +pols and you might think well why didn't +gurin try those first maybe he did but + + align:start position:0% +gurin try those first maybe he did but + + + align:start position:0% +gurin try those first maybe he did but +the PO the the key is that now with with + + align:start position:0% +the PO the the key is that now with with + + + align:start position:0% +the PO the the key is that now with with +uh the computing power we now have + + align:start position:0% +uh the computing power we now have + + + align:start position:0% +uh the computing power we now have +compared to gurin we can choose + + align:start position:0% +compared to gurin we can choose + + + align:start position:0% +compared to gurin we can choose +thousands of functions if we keep them + + align:start position:0% +thousands of functions if we keep them + + + align:start position:0% +thousands of functions if we keep them +simple so that that's really what's what + + align:start position:0% +simple so that that's really what's what + + + align:start position:0% +simple so that that's really what's what +what the finite element brought finite + + align:start position:0% +what the finite element brought finite + + + align:start position:0% +what the finite element brought finite +element method brought is keep the + + align:start position:0% +element method brought is keep the + + + align:start position:0% +element method brought is keep the +functions as simple pols and take many + + align:start position:0% +functions as simple pols and take many + + + align:start position:0% +functions as simple pols and take many +of them where gurkin who didn't have + + align:start position:0% +of them where gurkin who didn't have + + + align:start position:0% +of them where gurkin who didn't have +Matt lab or even a even a probably he + + align:start position:0% +Matt lab or even a even a probably he + + + align:start position:0% +Matt lab or even a even a probably he +didn't even have a desk computer he was + + align:start position:0% +didn't even have a desk computer he was + + + align:start position:0% +didn't even have a desk computer he was +pencil and paper he took one function or + + align:start position:0% +pencil and paper he took one function or + + + align:start position:0% +pencil and paper he took one function or +maybe two I mean like that took him a + + align:start position:0% +maybe two I mean like that took him a + + + align:start position:0% +maybe two I mean like that took him a +day so so now but we take thousands of + + align:start position:0% +day so so now but we take thousands of + + + align:start position:0% +day so so now but we take thousands of +functions simple functions and and we'll + + align:start position:0% +functions simple functions and and we'll + + + align:start position:0% +functions simple functions and and we'll +see on Friday the steps that get us to + + align:start position:0% +see on Friday the steps that get us to + + + align:start position:0% +see on Friday the steps that get us to +KU equal F so this is the prep for + + align:start position:0% +KU equal F so this is the prep for + + + align:start position:0% +KU equal F so this is the prep for +finite elements \ No newline at end of file diff --git a/WGDbIKtjmSs.txt b/WGDbIKtjmSs.txt new file mode 100644 index 0000000000000000000000000000000000000000..d12e0ef52cd20b6b4aa291fb3d65c01681975d9d --- /dev/null +++ b/WGDbIKtjmSs.txt @@ -0,0 +1,1993 @@ +OPERATOR: The following content +is provided under a + +Creative Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: So, if you remember, +just before the + +break, as long ago as it was, +we had looked at the problem + +of fitting curves to data. + +And the example we had seen, is +that it's often possible, + +in fact, usually possible, to +find a good fit to old values. + +What we looked at was, we looked +at a small number of + +points, we took a high degree +polynomial, sure enough, we + +got a great fit. + +The difficulty was, a great +fit to old values does not + +necessarily imply a good +fit to new values. + +And in general, that's +somewhat worrisome. + +So now I want to spend a little +bit of time I'm looking + +at some tools, that we can use +to better understand the + +notion of, when we have a +bunch of points, what + +do they look like? + +How does the variation work? + +This gets back to a concept that +we've used a number of + +times, which is a notion +of a distribution. + +Remember, the whole logic +behind our idea of using + +simulation, or polling, or any +kind of statistical technique, + +is the assumption that the +values we would draw were + +representative of the values +of the larger population. + +We're sampling some subset of +the population, and we're + +assuming that that sample is +representative of the greater + +population. + +We talked about several +different + +issues related to that. + +I now want to look at that a +little bit more formally. + +And we'll start with the very +old problem of rolling dice. + +I presume you've all +seen what a pair of + +dice look like, right? + +They've got the numbers 1 +through 6 on them, you roll + +them and something comes up. + +If you haven't seen it, if you +look at the very back, at the + +back page of the handout today, +you'll see a picture of + +a very old die. + +Some time from the fourth to +the second century BC. + +Looks remarkably like a modern +dice, except it's not made out + +of plastic, it's made +out of bones. + +And in fact, if you were +interested in the history of + +gambling, or if you happen to +play with dice, people do call + +them bones. + +And that just dates back to +the fact that the original + +ones were made that way. + +And in fact, what we'll see +is, that in the history of + +probability and statistics, an +awful lot of the math that we + +take for granted today, came +from people's attempts to + +understand various +games of chance. + +So, let's look at it. + +So we'll look at this program. + +You should have this in the +front of the handout. + +So I'm going to start +with a fair dice. + +That is to say, when you roll +it, it's equally probable that + +you get 1, 2, 3, 4, 5, or 6. + +And I'm going to throw a pair. + +You can see it's very simple. + +I'll take d 1, first die is +random dot choice from vals 1. + +d 2 will be random dot +choice from vals 2. + +So I'm going to pass it in two +sets of possible values, and + +randomly choose one or the +other, and then return them. + +And the way I'll conduct a +trial is, I'll take some + +number of throws, and two +different kinds of dice. + +Throws will be the empty +set, actually, yeah. + +And then I'll just do it. + +For i in range number of throws, +d 1, d 2 is equal to + +throw a pair, and then +I'll append it, and + +then I'll return it. + +Very simple, right? + +Could hardly imagine a simpler +little program. + +And then, we'll analyze it. + +And we're going to analyze it. + +Well, first let's analyze it one +way, and then we'll look + +at something slightly +different. + +I'm going to conduct some +number of trials + +with two fair die. + +Then I'm going to make a +histogram, because I happen to + +know that there are only +11 possible values, + +I'll make 11 bins. + +You may not have seen +this locution + +here, Pylab dot x ticks. + +That's telling it where to put +the markers on the x-axis, and + +what they should be. + +In this case 2 through 12, +and then I'll label it. + +So let's run this program. + +And here we see the distribution +of values. + +So we see that I get more 7s +than anything else, and fewer + +2s and 12s. + +Snake eyes and boxcars +to you gamblers. + +And it's a beautiful +distribution, in some sense. + +I ran it enough trials. + +This kind of distribution +is called normal. + +Also sometimes called +Gaussian, after the + +mathematician Gauss. + +Sometimes called the bell curve, +because in someone's + +imagination it looks +like a bell. + +We see these things +all the time. + +They're called normal, or +sometimes even natural, + +because it's probably the most +commonly observed probability + +distribution in nature. + +First documented, although I'm +sure not first seen, by + +deMoivre and Laplace +in the 1700s. + +And then in the 1800s, Gauss +used it to analyze + +astronomical data. + +And it got to be called, in +that case, the Gaussian + +distribution. + +So where do we see it occur? + +We see it occurring all +over the place. + +We certainly see it +rolling dice. + +We see it occur in things like +the distribution of heights. + +If we were to take the height of +all the students at MIT and + +plot the distribution, I would +be astonished if it didn't + +look more or less like that. + +It would be a normal +distribution. + +A lot of things in +the same height. + +Now presumably, we'd have to +round off to the nearest + +millimeter or something. + +And a few really tall people, +and a few really short people. + +It's just astonishing in nature +how often we look at + +these things. + +The graph looks exactly like +that, or similar to that. + +The shape is roughly that. + +The normal distribution can be +described, interestingly + +enough, with just two numbers. + +The mean and the standard +deviation. + +So if I give you those +two numbers, you + +can draw that curve. + +Now you might not be able to +label, you couldn't label the + +axes, because how would +you know how many + +trials I did, right? + +Whether I did 100, or 1,000 or a +million, but the shape would + +always be the same. + +And if I were to, instead of +doing, 100,000 throws of the + +dice, as I did here, I did a +million, the label on the + +y-axis would change, +but the shape would + +be absolutely identical. + +This is what's called a +stable distribution. + +As you change the scale, the +shape doesn't change. + +So the mean tells us where +it's centered, and the + +standard deviation, basically, +is a measure of statistical + +dispersion. + +It tells us how widely +spread the points of + +the data set are. + +If many points are going to be +very close to the mean, then + +the standard deviation is +what, big or small? + +Pardon? + +Small. + +If they're spread out, and it's +kind of a flat bell, then + +the standard deviation +will be large. + +And I'm sure you've all seen +standard deviations. + +We give exams, and we say here's +the mean, here's the + +standard deviation. + +And the notion is, that's trying +to tell you what the + +average score was, and how +spread out they are. + +Now as it happens, rarely do +we have exams that actually + +fall on a bell curve. + +Like this. + +So in a way, don't be deceived +by thinking that we're really + +giving you a good measure of the +dispersion, in the sense, + +that we would get with +the bell curve. + +So the standard deviation does +have a formal value, usually + +written sigma, and it's the +estimates of x squared minus + +the estimates of x, and then +I take all of this, the + +estimates of x, right, +squared. + +So I don't worry much about +this, but what I'm basically + +doing is, x is all of the +values I have. And I can + +square each of the values, and +then I subtract from that, the + +sum of the values, +squaring that. + +What's more important than this +formula, for most uses, + +is what people think of as the +-- why didn't I write it down + +-- this is interesting. + +There is a some number -- + +I see why, I did write +it down, it just + +got printed on two-sided. + +Is the Empirical Rule. + +And this applies for normal +distributions. + +So anyone know how much of the +data that you should expect to + +fall within one standard +deviation of the mean? + +68. + +So 68% within one, 95% of the +data falls within two, and + +almost all of the data +within three. + +These values are approximations, +by the way. + +So, this is, really 95% falls +within 1.96 standard + +deviations, it's not two. + +But this gives you a sense +of how spread out it is. + +And again, this applies only +for a normal distribution. + +If you compute the standard +deviation this way, and apply + +it to something other than a +normal distribution, there's + +no reason to expect that +Empirical Rule will hold. + +OK people with me on this? + +It's amazing to me how many +people in society talk about + +standard deviations +without actually + +knowing what they are. + +And there's another way to +look at the same data, or + +almost the same data. + +Since it's a random experiment, +it won't be + +exactly the same. + +So as before, we had the +distribution, and fortunately + +it looks pretty much +like the last one. + +We would've expected that. + +And I've now done something, +another way of looking at the + +same information, really, is, +I printed, I plotted, the + +probabilities of different +values. + +So we can see here that the +probability of getting a 7 is + +about 0.17 or something +like that. + +Now, since I threw 100,000 die, +it's not surprising that + +the probability of 0.17 +looks about the same + +as 17,000 over here. + +But it's just a different way +of looking at things. + +Right, had I thrown some +different number, it might + +have been harder to visualize +what the probability + +distribution looked like. + +But we often do talk +about that. + +How probable is a +certain value? + +People who design games of +chance, by the way, something + +I've been meaning to say. + +You'll notice down here there's +just, when we want to + +save these things, there's +this little icon that's a + +floppy disk, to indicate +store. + +And I thought maybe many of +you'd never seen a floppy + +disk, so I decided +to bring one in. + +You've seen the icons. + +And probably by the time most of +you got, any you ever had a + +machine with a quote +floppy drive? + +Did it actually flop the disk? + +No, they were pretty rigid, but +the old floppy disks were + +really floppy. + +Hence they got the name. + +And, you know it's kind of like +a giant size version. + +And it's amazing how people will +probably continue to talk + +about floppy disks as +long as they talk + +about dialing a telephone. + +And probably none of you've ever +actually dialed a phone, + +for that matter, just +pushed buttons . + +But they used to have dials +that you would twirl. + +Anyway, I just thought everyone +should at least see a + +floppy disk once. + +This is, by the way, a very good +way to get data security. + +There's probably no way in the +world to read the information + +on this disk anymore. + +All right, as I said people +who design games of chance + +understand these probabilities +very well. + +So I'm gonna now look at, show +how we can understand these + +things in some other ways +of popular example. + +A game of dice. + +Has anyone here ever played +the game called craps? + +Did you win or lose money? + +You won. + +All right, you beat the odds. + +Well, it's a very popular +game, and I'm going to + +explain it to you. + +As you will see, this is not +an endorsement of gambling, + +because one of the things you +will notice is, you are likely + +to lose money if you do this. + +So I tend not, I don't do it. + +All right, so how does +a game of craps work? + +You start by rolling two dice. + +If you get a 7 or an 11, the +roller, we'll call that the + +shooter, you win. + +If you get a 2, 3, or +a 12, you lose. + +I'm assuming here, you're +betting what's + +called the pass line. + +There are different ways to bet, +this is the most common + +way to bet, we'll just +deal with that. + +If it's not any of these, what +you get is, otherwise, the + +number becomes what's +called the point. + +Once you've got the point, you +keep rolling the dice until 1 + +of o things happens. + +You get a 7, in which case you +lose, or you get the point, in + +which case you win. + +So it's a pretty simple game. + +Very popular game. + +So I've implemented. + +So one of the interesting things +about this is, if you + +try and actually figure out +what the probabilities are + +using pencil and paper, +you can, but it gets + +a little bit involved. + +Gets involved because you have +to, all right, what are the + +odds of winning or losing +on the first throw? + +Well, you can compute those +pretty easily, and you can see + +that you'd actually win +more than you lose, + +on the first throw. + +But if you look at the +distribution of 7s and 11s and + +2s, 3s, and 12s, you add them +up, you'll see, well, this is + +more likely than this. + +But then you say, suppose +I don't get those. + +What's the likelihood of getting +each other possible + +point value, and then given that +point value, what's the + +likelihood of getting +that before a 7? + +And you can do it, but +it gets very tedious. + +So those of us who are +inclined to think + +computationally, and I hope by +now that's all of you as well + +as me, say well, instead of +doing the probabilities by + +hand, I'm just going to write +a little program. + +And it's a program that took me +maybe 10 minutes to write. + +You can see it's quite small, +I did it yesterday. + +So the first function here is +craps, it returns true if the + +shooter wins by betting +the pass line. + +And it's just does +what I said. + +Rolls them, if the total +is 1 or 11, it + +returns true, you win. + +If it's 2, 3, or 12, it returns +false, you lose. + +Otherwise the point +becomes the total. + +And then while true, I'll +just keep rolling. + +Until either, if the total gets +the point, I return true. + +Or if the total's equal +7, I return false. + +And that's it. + +So essentially I just took these +rules, typed them down, + +and I had my game. + +And then I'll simulate it will +some number of bets. + +Keeping track of the numbers +of wins and losses. + +Just by incrementing 1 or the +other, depending upon whether + +I return true or false. + +I'm going to, just to show what +we do, print the number + +of wins and losses. + +And then compute, how +does the house do? + +Not the gambler, but the person +who's running the game, + +the casino. + +Or in other circumstances, +other places. + +And then we'll see +how that goes. + +And I'll try it with +100,000 games. + +Now, this is more than 100,000 +rolls of the dice, right? + +Because I don't get a 7 +or 11, I keep rolling. + +So before I do it, I'll as the +easy question first. Who + +thinks the casino wins more +often than the player? + +Who thinks the player wins more +often than the casino? + +Well, very logical, casinos are +not in business of giving + +away money. + +So now the more interesting +question. + +How steep do you think the odds +are in the house's favor? + +Anyone want to guess? + +Actually pretty thin. + +Let's run it and see. + +So what we see is, the house +wins 50, in this case 50.424% + +of the time. + +Not a lot. + +On the other hand, if +people bet 100,000, + +the house wins 848. + +Now, 100,000 is actually +a small number. + +Let's get rid of these, should +have gotten rid of these + +figures, you don't need to +see them every time. + +We'll keep one figure, +just for fun. + +Let's try it again. + +Probably get a little +different answer. + +Considerable different, but +still, less than 51% of the + +time in this trial. + +But you can see that the house +is slowly but surely going to + +get rich playing this game. + +Now let's ask the other +interesting question. + +Just for fun, suppose +we want to cheat. + +Now, I realize none of you +would never do that. + +But let's consider using +a pair of loaded dice. + +So there's a long history, well +you can imagine when you + +looked at that old bone I showed +you, that it wasn't + +exactly fair. + +That some sides were a little +heavier than others, and in + +fact you didn't get, say, a +5 exactly 1/6 of the time. + +And therefore, if you were using +your own dice, instead + +of somebody else's, and you knew +what was most likely, you + +might do better. + +Well, the modern version of that +is, people do cheat by + +putting little weights in +dice, to just make tiny + +changes in the probability +of one number or + +another coming up. + +So let's do that. + +And let's first ask the +question, well, what would be + +a nice way to do that? + +It's very easy here. + +If we look at it, all I've +done is, I've changed the + +distribution of values, so +instead of here being 1, 2, 3, + +4, 5, and 6, it's 1, 2, +3, 4, 5, 5, and 6. + +I snuck in an extra 5 on +one of the two dice. + +So this has changed the odds of +rolling a 5 from 1 in 6 to + +roughly 3 in 12. + +Now 1/6, which is 2/12, vs. +3/12, it's not a big + +difference. + +And you can imagine, if you were +sitting there watching + +it, you wouldn't notice that 5 +was coming up a little bit + +more often than you expected. + +Normally. + +Close enough that you +wouldn't notice it. + +But let's see if, what +difference it makes? + +What difference do you think +it will make here? + +First of all, is it going +to be better or + +worse for the player? + +Who thinks better? + +Who thinks worse? + +Who thinks they haven't +a clue? + +All right, we have +an honest man. + +Where is Diogenes when +we we need him? + +The reward for honesty. + +I could reward you and wake +him up at the same time. + +It's good. + +All right, well, let's +see what happens. + +All right, so suddenly, the odds +have swung in favor of + +the player. + +This tiny little change has now +made it likely that the + +player win money, instead +of the house. + +So what's the point? + +The point is not, you should +go out and try and cheat + +casinos, because you'll probably +find an unpleasant + +consequence of that. + +The point is that, once I've +written this simulation, I can + +play thought experiments +in a very easy way. + +So-called what if games. + +What if we did this? + +What if we did that? + +And it's trivial to do those +kinds of things. + +And that's one of the reasons we +typically do try and write + +these simulations. + +So that we can experiment +with things. + +Are there any other experiments +people would like + +to perform while we're here? + +Any other sets of die you +might like to try? + +All right, someone give me a +suggestion of something that + +might work in the +house's favor. + +Suppose a casino wanted +to cheat. + +What do you think would +help them out? + +Yeah? + +STUDENT: Increase prevalence +of 1, instead of 5? + +PROFESSOR: All right, so let's +see if we increase the + +probability of 1, +what it does? + +Yep, clearly helped the +house out, didn't it? + +So that would be a good +thing for the house. + +Again, you know, three key +strokes and we get to try it. + +It's really a very nice kind +of thing to be able to do. + +OK, this works nicely. + +We'll get normal +distributions. + +We can look at some things. + +There are two other kinds +of distributions I + +want to talk about. + +We can get rid of this +distraction. + +As you can imagine, I played a +lot with these things, just + +cause it was fun +once I had it. + +You have these in +your handout. + +So the one on the upper right, +is the Gaussian, or normal, + +distribution we've been +talking about. + +As I said earlier, quite common, +we see it a lot. + +The upper left is what's called +a, and these, by the + +way, all of these distributions +are symmetric, + +just in this particular +picture. + +How do you spell symmetric, +one or two m's? + +I help here. + +That right? + +OK, thank you. + +And they're symmetric in the +sense that, if you take the + +mean, it looks the same on +both sides of the mean. + +Now in general, you can +have asymmetric + +distributions as well. + +But for simplicity, we'll here +look at symmetric ones. + +So we've seen the bell curve, +and then on the upper left is + +what's called the uniform. + +In a uniform distribution, each +value in the range is + +equally likely. + +So to characterize it, +you only need to give + +the range of values. + +I say the values range from +0 to 100, and it tells me + +everything I know about the +uniform distribution. + +Each value in that will occur +the same number of times. + +Have we seen a uniform +distribution? + +What have we seen that's +uniform here? + +Pardon? + +STUDENT: Playing dice. + +PROFESSOR: Playing dice. + +Exactly right. + +Each roll of the die +was equally likely. + +Between 1 and 6. + +So, we got a normal distribution +when I summed + +them, but if I gave you the +distribution of a single die, + +it would have been +uniform, right? + +So there's an interesting +lesson there. + +One die, the distribution was +uniform, but when I summed + +them, I ended up getting +a normal distribution. + +So where else do we see them? + +In principle, lottery winners +are uniformly distributed. + +Each number is equally +likely to come up. + +To a first approximation, +birthdays are uniformly + +distributed, things like that. + +But, in fact, they rarely +arise in nature. + +You'll hardly ever run a physics +experiment, or a + +biology experiment, or anything +like that, and come + +up with a uniform +distribution. + +Nor do they arise very often in +complex systems. So if you + +look at what happens in +financial markets, none of the + +interesting distributions +are uniform. + +You know, the prices of stocks, +for example, are + +clearly not uniformly +distributed. + +Up days and down days in the +stock market are not uniformly + +distributed. + +Winners of football games are +not uniformly distributed. + +People seem to like to use +them in games of chance, + +because they seem fair, but +mostly you see them only in + +invented things, rather +than real things. + +The third kind of distribution, +the one in the + +bottom, is the exponential +distribution. + +That's actually quite common +in the real world. + +It's often used, for example, +to model arrival times. + +If you want to model the +frequency at which, say, + +automobiles arrive, get on the +Mass Turnpike, you would find + +that the arrivals +are exponential. + +We see with an exponential is, +things fall off much more + +steeply around the mean than +with the normal distribution. + +All right, that make sense? + +What else is exponentially +distributed? + +Requests for web pages are +often exponentially + +distributed. + +The amount of traffic +at a website. + +How frequently they arrive. + +We'll see much more starting +next week, or maybe even + +starting Thursday, about +exponential distributions, as + +we go on with a final case study +that we'll be dealing + +with in the course. + +You can think of each of +these, by the way, as + +increasing order of +predictability. + +Uniform distribution means the +result is most unpredictable, + +it could be anything. + +A normal distribution says, +well, it's pretty predictable. + +Again, depending on the +standard deviation. + +If you guess the mean, you're +pretty close to right. + +The exponential is +very predictable. + +Most of the answers are +right around the mean. + +Now there are many other +distributions, there are + +Pareto distributions which +have fat tails, there are + +fractal distributions, there +are all sorts of things. + +We won't go into to +those details. + +Now, I hope you didn't find +this short excursion into + +statistics either too boring +or too confusing. + +The point was not to teach you +statistics, probability, we + +have multiple courses +to do that. + +But to give you some tools that +would help improve your + +intuition in thinking +about data. + +In closing, I want to give +a few words about + +the misuse of data. + +Since I think we misuse +data an awful lot. + +So, point number 0, as in the +most important, is beware of + +people who give you properties +of data, but not the data. + +We see that sort of thing +all the time. + +Where people come in, and they +say, OK, here it is, here's + +the mean value of the quiz, +and here's the standard + +deviation of the quiz, and that +just doesn't really tell + +you where you stand, +in some sense. + +Because it's probably not +normally distributed. + +You want to see the data. + +At the very least, if you see +the data, you can then say, + +yeah, it is normally +distributed, so the standard + +deviation is meaningful, +or not meaningful. + +So, whenever you can, +try and get, at + +least, to see the data. + +So that's 1, or 0. + +1 is, well, all right. + +I'm going to test your Latin. + +Cum hoc ergo propter hoc. + +All right. + +I need a Latin scholar +to translate this. + +Did not one of you take +Latin in high school? + +We have someone who did. + +Go ahead. + +STUDENT: I think it +means, with this, + +therefore, because of this. + +PROFESSOR: Exactly right. + +With this, therefore, +because of this. + +I'm glad that at least +one person + +has a classical education. + +I don't, by the way. + +Essentially what this is +telling us, is that + +correlation does not +imply causation. + +So sometimes two things +go together. + +They both go up, they +both go down. + +And people jump to the +conclusion that + +one causes the other. + +That there's a cause and +effect relationship. + +That is just not true. + +It's what's called a +logical fallacy. + +So we see some examples +of this. + +And you can get into +big trouble. + +So here's a very interesting +one. + +There was a very widely reported +epidemiological + +study, that's a medical study +where you get statistics about + +large populations. + +And it showed that women, who +are taking hormone replacement + +therapy, were found to have a +lower incidence of coronary + +heart disease than +women who didn't. + +This was a big study +of a lot of women. + +This led doctors to propose +that hormone replacement + +therapy for middle aged women +was protective against + +coronary heart disease. + +And in fact, in response to +this, a large number of + +medical societies recommended +this. + +And a large number of women +were given this therapy. + +Later, controlled trials showed +that in fact, hormone + +replacement therapy in women +caused a small and significant + +increase in coronary +heart disease. + +So they had taken the fact that +these were correlated, + +said one causes the other, made +a prescription, and it + +turned out to be +the wrong one. + +Now, how could this be? + +How could this be? + +It turned out that the women in +the original study who were + +taking the hormone replacement +therapy, tended to be from a + +higher socioeconomic group +than those who didn't. + +Because the therapy was not +covered by insurance, so the + +women who took it +were wealthy. + +Turns out wealthy people do a +lot of other things that are + +protective of their hearts. + +And, therefore, are in general +healthier than poor people. + +This is not a surprise. + +Rich people are healthier +than poor people. + +And so in fact, it was this +third variable that was + +actually the meaningful one. + +This is what is called in + +statistics, a lurking variable. + +Both of the things they were +looking at in this study, who + +took the therapy, and who had a +heart disease, each of those + +was correlated with the +lurking variable of + +socioeconomic position. + +And so, in effect, there +was no cause and effect + +relationship. + +And once they did another study, +in which the lurking + +variable was controlled, and +they looked at heart disease + +among rich women separately +from poor women, with this + +therapy, they discovered that +therapy was not good. + +It was, in fact, harmful. + +So this is a very important +moral to remember. + +When you look at correlations, +don't assume cause and effect. + +And don't assume that there +isn't a lurking variable that + +really is the dominant factor. + +So that's one statistical, a +second statistical worry. + +Number 2 is, beware of what's +called, non-response bias. + +Which is another fancy +way of saying, + +non-representative samples. + +No one doing a study beyond +the trivial can sample + +everybody or everything. + +And only mind readers can be +sure of what they've missed. + +Unless, of course, +people choose to + +miss things on purpose. + +Which you also see. + +And that brings me to +my next anecdote. + +A former professor at the +University of Nebraska, who + +later headed a group called The +Family Research Institute, + +which some of you may have heard +about, claimed that gay + +men have an average life +expectancy of 43 years. + +And they did a study full of +statistics showing that this + +was the case. + +And the key was, they calculated +the figure by + +checking gay newspapers for +obituaries and news about + +stories of death. + +So they went through the gay +newspapers, took a list of + +everybody whose obituary +appeared, how old they were + +when they died, took the +average, and said it was 43. + +Then they did a bunch of +statistics, with all sorts of + +tests, showing how, you know, +what the curves look like, the + +distributions, and +the significance. + +All the math was valid. + +The problem was, it was a very +unrepresentative sample. + +What was the most + +unrepresentative +thing about it? + +Somebody? + +STUDENT: Not all deaths +have obituaries. + +PROFESSOR: Well, that's +one thing. + +That's certainly true. + +But what else? + +Well, not all gay people +are dead, right? + +So if you're looking at +obituaries, you're in fact + +only getting -- + +I'm sure that's what you were +planning to say -- sorry. + +You're only getting the people +who are dead, so it's clearly + +going to make the number +look smaller, right? + +Furthermore, you're only getting +the ones that were + +reported in newspapers, the +newspapers are typically + +urban, rather than out in rural +areas, so it turns out, + +it's also biased against gays +who chose not come out of the + +closet, and therefore didn't +appear in these. + +Lots and lots of things +with the problems. + +Believe it or not, this +paper was published + +in a reputable journal. + +And someone checked all the +math, but missed the fact that + +all of that was irrelevant +because the sample was wrong. + +Data enhancement. + +It even sounds bad, right? + +You run an experiment, you get +your data, and you enhance it. + +It's kind of like when you ran +those physics experiments in + +high school, and you've got +answers that you knew didn't + +match the theory, so you +fudged the data? + +I know none of you would have +ever done that, but some + +people been known to do. + +That's not actually +what this means. + +What this means is, reading +more into the data than it + +actually implies. + +So well-meaning people are +often the guiltiest here. + +So here's another one +of my favorites. + +For example, there are people +who try to scare us into + +driving safely. + +Driving safely is +a good thing. + +By telling holiday deaths. + +So you'll read things like, +400 killed on the highways + +over long weekend. + +It sounds really bad, until +you observe the fact that + +roughly 400 people are killed +on any 3-day period. + +And in fact, it's no higher +on the holiday weekends. + +I'll bet you all thought +more people got + +killed on holiday weekends. + +Well, typically not. + +They just report how many died, +but they don't tell you + +the context, say, oh, by the +way, take any 3-day period. + +So the moral there is, you +really want to place the data + +in context. + +Data taken out of context +without comparison is usually + +meaningless. + +Another variance of this +is extrapolation. + +A commonly quoted statistic. + +Most auto accidents happen +within 10 miles of home. + +Anyone here heard +that statistic? + +It's true, but what +does it mean? + +Well, people tend to say it +means, it's dangerous to drive + +when you're near home. + +But in fact, most driving is +done within 10 miles of home. + +Furthermore, we don't actually +know where home is. + +Home is where the car is +supposedly garaged on the + +state registration forms. So, +data enhancements would + +suggest that I should register +my car in Alaska. + +And then I would never be +driving within 10 miles of + +home, and I would +be much safer. + +Well, it's probably +not a fact. + +So there are all sorts +of things on that. + +Well, I think I will come back +to this, because I have a + +couple more good stories which +I hate not to give you. + +So we'll come back on Thursday +and look at a couple of more + +things that can go wrong +with statistics. \ No newline at end of file diff --git a/Wn3QDv-Dt3M.txt b/Wn3QDv-Dt3M.txt new file mode 100644 index 0000000000000000000000000000000000000000..0033280eee1d9e9799db62258e9ce7af8e135bef --- /dev/null +++ b/Wn3QDv-Dt3M.txt @@ -0,0 +1,315 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu that's it + + align:start position:0% +ocw.mit.edu that's it + + + align:start position:0% +ocw.mit.edu that's it +I be there can you hear me yes okay be + + align:start position:0% +I be there can you hear me yes okay be + + + align:start position:0% +I be there can you hear me yes okay be +there uh + + align:start position:0% +there uh + + + align:start position:0% +there uh +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Applause] + + align:start position:0% + + + + align:start position:0% + +but you a good job and and and I think + + align:start position:0% +but you a good job and and and I think + + + align:start position:0% +but you a good job and and and I think +you enjoyed laste I think same process + + align:start position:0% +you enjoyed laste I think same process + + + align:start position:0% +you enjoyed laste I think same process +and I + + align:start position:0% +and I + + + align:start position:0% +and I +also to uh uh ask judges and see and and + + align:start position:0% +also to uh uh ask judges and see and and + + + align:start position:0% +also to uh uh ask judges and see and and +verify and everybody than coming and + + align:start position:0% +verify and everybody than coming and + + + align:start position:0% +verify and everybody than coming and +then being judges and I guess uh will + + align:start position:0% +then being judges and I guess uh will + + + align:start position:0% +then being judges and I guess uh will +coordinate uh with them get the + + align:start position:0% +coordinate uh with them get the + + + align:start position:0% +coordinate uh with them get the +information and and + + align:start position:0% +information and and + + + align:start position:0% +information and and +and what's going on there + + align:start position:0% +and what's going on there + + + align:start position:0% +and what's going on there +yeah okay good so I'm am hanging up and + + align:start position:0% +yeah okay good so I'm am hanging up and + + + align:start position:0% +yeah okay good so I'm am hanging up and +I have to run to my conference now okay + + align:start position:0% +I have to run to my conference now okay + + + align:start position:0% +I have to run to my conference now okay +bye + + align:start position:0% +bye + + + align:start position:0% +bye +bye okay so tomorrow uh we'll have class + + align:start position:0% +bye okay so tomorrow uh we'll have class + + + align:start position:0% +bye okay so tomorrow uh we'll have class +in the regular classroom + + align:start position:0% +in the regular classroom + + + align:start position:0% +in the regular classroom +34301 uh same time 10 to 12 uh there'll + + align:start position:0% +34301 uh same time 10 to 12 uh there'll + + + align:start position:0% +34301 uh same time 10 to 12 uh there'll +be course evaluations so your chance to + + align:start position:0% +be course evaluations so your chance to + + + align:start position:0% +be course evaluations so your chance to +tell us how you actually felt about the + + align:start position:0% +tell us how you actually felt about the + + + align:start position:0% +tell us how you actually felt about the +course and uh what you like and what you + + align:start position:0% +course and uh what you like and what you + + + align:start position:0% +course and uh what you like and what you +didn't like uh afterwards we'll have an + + align:start position:0% +didn't like uh afterwards we'll have an + + + align:start position:0% +didn't like uh afterwards we'll have an +award ceremony so for the winning team + + align:start position:0% +award ceremony so for the winning team + + + align:start position:0% +award ceremony so for the winning team +you will get some prizes and uh you'll + + align:start position:0% +you will get some prizes and uh you'll + + + align:start position:0% +you will get some prizes and uh you'll +uh get some cake and then uh that'll + + align:start position:0% +uh get some cake and then uh that'll + + + align:start position:0% +uh get some cake and then uh that'll +take us to around 11: 11:30 at which + + align:start position:0% +take us to around 11: 11:30 at which + + + align:start position:0% +take us to around 11: 11:30 at which +time we'll come back to start in the 7th + + align:start position:0% +time we'll come back to start in the 7th + + + align:start position:0% +time we'll come back to start in the 7th +Floor Lounge we'll have pizza and and + + align:start position:0% +Floor Lounge we'll have pizza and and + + + align:start position:0% +Floor Lounge we'll have pizza and and +more food for you guys to enjoy so + + align:start position:0% +more food for you guys to enjoy so + + + align:start position:0% +more food for you guys to enjoy so +thanks and see you tomorrow + + align:start position:0% +thanks and see you tomorrow + + + align:start position:0% +thanks and see you tomorrow +[Applause] \ No newline at end of file diff --git a/X1F6a1FWirM.txt b/X1F6a1FWirM.txt new file mode 100644 index 0000000000000000000000000000000000000000..30bf708db81ea2b8898a88c6cf76b5451a16c53c --- /dev/null +++ b/X1F6a1FWirM.txt @@ -0,0 +1,9992 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu it's going to be a strange + + align:start position:0% +ocw.mit.edu it's going to be a strange + + + align:start position:0% +ocw.mit.edu it's going to be a strange +in Rhythm not turning up here on Tuesday + + align:start position:0% +in Rhythm not turning up here on Tuesday + + + align:start position:0% +in Rhythm not turning up here on Tuesday +and Thursdays + + align:start position:0% +and Thursdays + + + align:start position:0% +and Thursdays +endlessly it's been a incredible + + align:start position:0% +endlessly it's been a incredible + + + align:start position:0% +endlessly it's been a incredible +Saga + + align:start position:0% + + + + align:start position:0% + +um you have a + + align:start position:0% +um you have a + + + align:start position:0% +um you have a +minute because Thursday will not be a + + align:start position:0% +minute because Thursday will not be a + + + align:start position:0% +minute because Thursday will not be a +good time for doing it I'd like to spend + + align:start position:0% +good time for doing it I'd like to spend + + + align:start position:0% +good time for doing it I'd like to spend +five minutes or 10 minutes with you + + align:start position:0% + + + + align:start position:0% + +uh I can't ask for advice as to how to + + align:start position:0% +uh I can't ask for advice as to how to + + + align:start position:0% +uh I can't ask for advice as to how to +do it + + align:start position:0% +do it + + + align:start position:0% +do it +better uh thank God I won't have to uh + + align:start position:0% +better uh thank God I won't have to uh + + + align:start position:0% +better uh thank God I won't have to uh +but I'd be interested in your + + align:start position:0% +but I'd be interested in your + + + align:start position:0% +but I'd be interested in your +general comments uh about uh what we try + + align:start position:0% +general comments uh about uh what we try + + + align:start position:0% +general comments uh about uh what we try +to do I'd like to pass it on + + align:start position:0% +to do I'd like to pass it on + + + align:start position:0% +to do I'd like to pass it on +to this is + + align:start position:0% +to this is + + + align:start position:0% +to this is +the 19 since 1956 this class is has been + + align:start position:0% +the 19 since 1956 this class is has been + + + align:start position:0% +the 19 since 1956 this class is has been +taught every year that's + + align:start position:0% +taught every year that's + + + align:start position:0% +taught every year that's +44 57 + + align:start position:0% + + + + align:start position:0% + +years after 157 years it should be + + align:start position:0% +years after 157 years it should be + + + align:start position:0% +years after 157 years it should be +retired which it is whether it will + + align:start position:0% +retired which it is whether it will + + + align:start position:0% +retired which it is whether it will +continue in any form or another is not + + align:start position:0% +continue in any form or another is not + + + align:start position:0% +continue in any form or another is not +up to me there's a rule thank god with + + align:start position:0% +up to me there's a rule thank god with + + + align:start position:0% +up to me there's a rule thank god with +it if you retire your successes are + + align:start position:0% + + + + align:start position:0% + +independent don't have to bear the + + align:start position:0% +independent don't have to bear the + + + align:start position:0% +independent don't have to bear the +burden of their prees + + align:start position:0% +burden of their prees + + + align:start position:0% +burden of their prees +unfortunately this class will be + + align:start position:0% +unfortunately this class will be + + + align:start position:0% +unfortunately this class will be +recorded for archival purposes so they + + align:start position:0% +recorded for archival purposes so they + + + align:start position:0% +recorded for archival purposes so they +won't be able to get rid of me that + + align:start position:0% +won't be able to get rid of me that + + + align:start position:0% +won't be able to get rid of me that +easily + + align:start position:0% + + + + align:start position:0% + +um um let's just spend a few minutes + + align:start position:0% +um um let's just spend a few minutes + + + align:start position:0% +um um let's just spend a few minutes +having a little discussion + + align:start position:0% +having a little discussion + + + align:start position:0% +having a little discussion +about this enormous problematic area + + align:start position:0% +about this enormous problematic area + + + align:start position:0% +about this enormous problematic area +dealing with the non-european + + align:start position:0% +dealing with the non-european + + + align:start position:0% +dealing with the non-european +non-american + + align:start position:0% +non-american + + + align:start position:0% +non-american +world and non selective Asian + + align:start position:0% + + + + align:start position:0% + +world it's called in some terms the + + align:start position:0% +world it's called in some terms the + + + align:start position:0% +world it's called in some terms the +developing world now the new name for it + + align:start position:0% +developing world now the new name for it + + + align:start position:0% +developing world now the new name for it +is the global + + align:start position:0% +is the global + + + align:start position:0% +is the global +South that is the term which has been + + align:start position:0% +South that is the term which has been + + + align:start position:0% +South that is the term which has been +appropriated by the newest attempt to + + align:start position:0% + + + + align:start position:0% + +galvaniz International and professional + + align:start position:0% +galvaniz International and professional + + + align:start position:0% +galvaniz International and professional +interest + + align:start position:0% +interest + + + align:start position:0% +interest +in a an apparently new way of doing + + align:start position:0% + + + + align:start position:0% + +things you must recall that I + + align:start position:0% +things you must recall that I + + + align:start position:0% +things you must recall that I +said that + + align:start position:0% +said that + + + align:start position:0% +said that +1950 was the first time a book in + + align:start position:0% +1950 was the first time a book in + + + align:start position:0% +1950 was the first time a book in +English and probably in any language + + align:start position:0% +English and probably in any language + + + align:start position:0% +English and probably in any language +appeared on the subject of the so-called + + align:start position:0% +appeared on the subject of the so-called + + + align:start position:0% +appeared on the subject of the so-called +world of international + + align:start position:0% +world of international + + + align:start position:0% +world of international +poverty this was not Fred Engles writing + + align:start position:0% +poverty this was not Fred Engles writing + + + align:start position:0% +poverty this was not Fred Engles writing +about man + + align:start position:0% +about man + + + align:start position:0% +about man +or it could be seen as equivalent but + + align:start position:0% +or it could be seen as equivalent but + + + align:start position:0% +or it could be seen as equivalent but +Charlie Abrams at MIT was a lawyer who + + align:start position:0% +Charlie Abrams at MIT was a lawyer who + + + align:start position:0% +Charlie Abrams at MIT was a lawyer who +had worked in India and decided to come + + align:start position:0% +had worked in India and decided to come + + + align:start position:0% +had worked in India and decided to come +here back here and write about it he was + + align:start position:0% +here back here and write about it he was + + + align:start position:0% +here back here and write about it he was +a New Yorker writing about the + + align:start position:0% +a New Yorker writing about the + + + align:start position:0% +a New Yorker writing about the +emerging problems of population growth + + align:start position:0% +emerging problems of population growth + + + align:start position:0% +emerging problems of population growth +and + + align:start position:0% + + + + align:start position:0% + +poverty It's + + align:start position:0% +poverty It's + + + align:start position:0% +poverty It's +Curious that when looking + + align:start position:0% +Curious that when looking + + + align:start position:0% +Curious that when looking +back on + + align:start position:0% +back on + + + align:start position:0% +back on +the on + + align:start position:0% +the on + + + align:start position:0% +the on +the situation in Manchester in a + + align:start position:0% + + + + align:start position:0% + +city when the young German could write + + align:start position:0% +city when the young German could write + + + align:start position:0% +city when the young German could write +about and + + align:start position:0% +about and + + + align:start position:0% +about and +analyze the industrial poverty that the + + align:start position:0% +analyze the industrial poverty that the + + + align:start position:0% +analyze the industrial poverty that the +sudden leap of + + align:start position:0% +sudden leap of + + + align:start position:0% +sudden leap of +economy had had taken in Great Britain + + align:start position:0% +economy had had taken in Great Britain + + + align:start position:0% +economy had had taken in Great Britain +only since + + align:start position:0% +only since + + + align:start position:0% +only since +some 80 years before if we count 1750 is + + align:start position:0% +some 80 years before if we count 1750 is + + + align:start position:0% +some 80 years before if we count 1750 is +the beginning + + align:start position:0% + + + + align:start position:0% + +date Engles and Marx were Engles + + align:start position:0% +date Engles and Marx were Engles + + + align:start position:0% +date Engles and Marx were Engles +particularly was + + align:start position:0% +particularly was + + + align:start position:0% +particularly was +dissatisfied with a pace of red + + align:start position:0% +dissatisfied with a pace of red + + + align:start position:0% +dissatisfied with a pace of red +recalibration in + + align:start position:0% +recalibration in + + + align:start position:0% +recalibration in +England he dismissed the moves of the + + align:start position:0% +England he dismissed the moves of the + + + align:start position:0% +England he dismissed the moves of the +chartist group + + align:start position:0% +chartist group + + + align:start position:0% +chartist group +as being + + align:start position:0% +as being + + + align:start position:0% +as being +ineffective the + + align:start position:0% + + + + align:start position:0% + +British move first through charity then + + align:start position:0% +British move first through charity then + + + align:start position:0% +British move first through charity then +through the state and the nation paying + + align:start position:0% +through the state and the nation paying + + + align:start position:0% +through the state and the nation paying +attention to so what is called social + + align:start position:0% +attention to so what is called social + + + align:start position:0% +attention to so what is called social +housing was + + align:start position:0% +housing was + + + align:start position:0% +housing was +definitive it was the first nation in + + align:start position:0% +definitive it was the first nation in + + + align:start position:0% +definitive it was the first nation in +the world to tackle this problem + + align:start position:0% +the world to tackle this problem + + + align:start position:0% +the world to tackle this problem +systematically not systematically + + align:start position:0% +systematically not systematically + + + align:start position:0% +systematically not systematically +partially but had Engles waited around + + align:start position:0% +partially but had Engles waited around + + + align:start position:0% +partially but had Engles waited around +in England until today he might have + + align:start position:0% +in England until today he might have + + + align:start position:0% +in England until today he might have +seen that the measures of success + + align:start position:0% +seen that the measures of success + + + align:start position:0% +seen that the measures of success +despite Maggie th's involvement in the + + align:start position:0% +despite Maggie th's involvement in the + + + align:start position:0% +despite Maggie th's involvement in the +interim + + align:start position:0% +interim + + + align:start position:0% +interim +um over a period one should keep on + + align:start position:0% +um over a period one should keep on + + + align:start position:0% +um over a period one should keep on +remembering the British as + + align:start position:0% +remembering the British as + + + align:start position:0% +remembering the British as +slow but + + align:start position:0% +slow but + + + align:start position:0% +slow but +determined uh I quoted sir Joseph Paxton + + align:start position:0% +determined uh I quoted sir Joseph Paxton + + + align:start position:0% +determined uh I quoted sir Joseph Paxton +in the builder of the Crystal Palace the + + align:start position:0% +in the builder of the Crystal Palace the + + + align:start position:0% +in the builder of the Crystal Palace the +The + + align:start position:0% +The + + + align:start position:0% +The +Gardener who said we do things by Common + + align:start position:0% +Gardener who said we do things by Common + + + align:start position:0% +Gardener who said we do things by Common +Sense and + + align:start position:0% +Sense and + + + align:start position:0% +Sense and +Technology almost everything was common + + align:start position:0% +Technology almost everything was common + + + align:start position:0% +Technology almost everything was common +sensical and even in regard + + align:start position:0% +sensical and even in regard + + + align:start position:0% +sensical and even in regard +to science + + align:start position:0% +to science + + + align:start position:0% +to science +and and the development of IM massive + + align:start position:0% +and and the development of IM massive + + + align:start position:0% +and and the development of IM massive +ways of technological innovation the + + align:start position:0% +ways of technological innovation the + + + align:start position:0% +ways of technological innovation the +world had never seen + + align:start position:0% +world had never seen + + + align:start position:0% +world had never seen +above all I remind + + align:start position:0% +above all I remind + + + align:start position:0% +above all I remind +you + + align:start position:0% +you + + + align:start position:0% +you +that what happened was the first + + align:start position:0% +that what happened was the first + + + align:start position:0% +that what happened was the first +destruction of the malthusian + + align:start position:0% +destruction of the malthusian + + + align:start position:0% +destruction of the malthusian +Trap which is + + align:start position:0% +Trap which is + + + align:start position:0% +Trap which is +fundamental you should as urbanist + + align:start position:0% +fundamental you should as urbanist + + + align:start position:0% +fundamental you should as urbanist +should remember as one of the key + + align:start position:0% +should remember as one of the key + + + align:start position:0% +should remember as one of the key +factors in human + + align:start position:0% + + + + align:start position:0% + +development in my little talk on Friday + + align:start position:0% +development in my little talk on Friday + + + align:start position:0% +development in my little talk on Friday +I'll start with + + align:start position:0% +I'll start with + + + align:start position:0% +I'll start with +I think the + + align:start position:0% +I think the + + + align:start position:0% +I think the +first and that's the increase in human + + align:start position:0% +first and that's the increase in human + + + align:start position:0% +first and that's the increase in human +brain size from 400 cubic cm to + + align:start position:0% +brain size from 400 cubic cm to + + + align:start position:0% +brain size from 400 cubic cm to +1450 and what caused + + align:start position:0% +1450 and what caused + + + align:start position:0% +1450 and what caused +that the malthusian Trap you will + + align:start position:0% +that the malthusian Trap you will + + + align:start position:0% +that the malthusian Trap you will +recall + + align:start position:0% +recall + + + align:start position:0% +recall +equated population growth with + + align:start position:0% +equated population growth with + + + align:start position:0% +equated population growth with +death a stable size of population was + + align:start position:0% +death a stable size of population was + + + align:start position:0% +death a stable size of population was +all that agricultural + + align:start position:0% +all that agricultural + + + align:start position:0% +all that agricultural +Innovation + + align:start position:0% + + + + align:start position:0% + +could Supply or could + + align:start position:0% +could Supply or could + + + align:start position:0% +could Supply or could +forall and the sudden capacity to + + align:start position:0% +forall and the sudden capacity to + + + align:start position:0% +forall and the sudden capacity to +unleash a population to move relatively + + align:start position:0% +unleash a population to move relatively + + + align:start position:0% +unleash a population to move relatively +freely uh was the Advent + + align:start position:0% +freely uh was the Advent + + + align:start position:0% +freely uh was the Advent +of the larger migration patterns I think + + align:start position:0% +of the larger migration patterns I think + + + align:start position:0% +of the larger migration patterns I think +that we see now where + + align:start position:0% + + + + align:start position:0% + +anyway London became the great largest + + align:start position:0% +anyway London became the great largest + + + align:start position:0% +anyway London became the great largest +city in the world in a very quick + + align:start position:0% +city in the world in a very quick + + + align:start position:0% +city in the world in a very quick +manner + + align:start position:0% +manner + + + align:start position:0% +manner +uh but we're not lecturing about London + + align:start position:0% +uh but we're not lecturing about London + + + align:start position:0% +uh but we're not lecturing about London +although it's tempting to recall London + + align:start position:0% +although it's tempting to recall London + + + align:start position:0% +although it's tempting to recall London +such a great + + align:start position:0% +such a great + + + align:start position:0% +such a great +story + + align:start position:0% +story + + + align:start position:0% +story +um Engles took to the + + align:start position:0% +um Engles took to the + + + align:start position:0% +um Engles took to the +road he and marks were in Paris in + + align:start position:0% +road he and marks were in Paris in + + + align:start position:0% +road he and marks were in Paris in +1848 and then Engles spread himself all + + align:start position:0% +1848 and then Engles spread himself all + + + align:start position:0% +1848 and then Engles spread himself all +over Europe nurturing evolving + + align:start position:0% +over Europe nurturing evolving + + + align:start position:0% +over Europe nurturing evolving +Marxism uh until eventually of course + + align:start position:0% +Marxism uh until eventually of course + + + align:start position:0% +Marxism uh until eventually of course +after his + + align:start position:0% + + + + align:start position:0% + +death Russia + + align:start position:0% +death Russia + + + align:start position:0% +death Russia +succeeded in attempting to transform the + + align:start position:0% +succeeded in attempting to transform the + + + align:start position:0% +succeeded in attempting to transform the +world + + align:start position:0% +world + + + align:start position:0% +world +world that transformation was built on + + align:start position:0% +world that transformation was built on + + + align:start position:0% +world that transformation was built on +the image of industrial + + align:start position:0% + + + + align:start position:0% + +poverty no + + align:start position:0% +poverty no + + + align:start position:0% +poverty no +advertisement I means the book + + align:start position:0% +advertisement I means the book + + + align:start position:0% +advertisement I means the book +sarod written by milutin the Russian + + align:start position:0% +sarod written by milutin the Russian + + + align:start position:0% +sarod written by milutin the Russian +architect bureaucrat starts off with a + + align:start position:0% +architect bureaucrat starts off with a + + + align:start position:0% +architect bureaucrat starts off with a +photograph of the industrial city smoke + + align:start position:0% +photograph of the industrial city smoke + + + align:start position:0% +photograph of the industrial city smoke +beling out of pipes work as + + align:start position:0% + + + + align:start position:0% + +disenfranchised I can't think of + + align:start position:0% +disenfranchised I can't think of + + + align:start position:0% +disenfranchised I can't think of +anything else that + + align:start position:0% +anything else that + + + align:start position:0% +anything else that +forced the publicity + + align:start position:0% + + + + align:start position:0% + +of the attempt to nationalize + + align:start position:0% + + + + align:start position:0% + +poverty the story of the + + align:start position:0% +poverty the story of the + + + align:start position:0% +poverty the story of the +so-call third world is + + align:start position:0% + + + + align:start position:0% + +different the battle 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+royalty 1870s + + + align:start position:0% +royalty 1870s +1860s went through various + + align:start position:0% +1860s went through various + + + align:start position:0% +1860s went through various +exercises uh including the Rabid the + + align:start position:0% +exercises uh including the Rabid the + + + align:start position:0% +exercises uh including the Rabid the +rampant period of Reds Vienna in the + + align:start position:0% +rampant period of Reds Vienna in the + + + align:start position:0% +rampant period of Reds Vienna in the +1920s after the 1418 War which produced + + align:start position:0% +1920s after the 1418 War which produced + + + align:start position:0% +1920s after the 1418 War which produced +Carl Marx + + align:start position:0% +Carl Marx + + + align:start position:0% +Carl Marx +off + + align:start position:0% +off + + + align:start position:0% +off +uh maor + + align:start position:0% +uh maor + + + align:start position:0% +uh maor +off it's interesting that the reaction + + align:start position:0% +off it's interesting that the reaction + + + align:start position:0% +off it's interesting that the reaction +of the major cities + + align:start position:0% +of the major cities + + + align:start position:0% +of the major cities +that we looked at the five major cities + + align:start position:0% +that we looked at the five major cities + + + align:start position:0% +that we looked at the five major cities +each produced a specific housing + + align:start position:0% +each produced a specific housing + + + align:start position:0% +each produced a specific housing +type London produced the residential + + align:start position:0% +type London produced the residential + + + align:start position:0% +type London produced the residential +Square Paris produced The Boulevard + + align:start position:0% +Square Paris produced The Boulevard + + + align:start position:0% +Square Paris produced The Boulevard +house the house man and Boulevard house + + align:start position:0% +house the house man and Boulevard house + + + align:start position:0% +house the house man and Boulevard house +Vienna produced the groupin in house the + + align:start position:0% +Vienna produced the groupin in house the + + + align:start position:0% +Vienna produced the groupin in house the +first large Palace likee condominium + + align:start position:0% +first large Palace likee condominium + + + align:start position:0% +first large Palace likee condominium +building and the + + align:start position:0% +building and the + + + align:start position:0% +building and the +H Barcelona produced the square block of + + align:start position:0% +H Barcelona produced the square block of + + + align:start position:0% +H Barcelona produced the square block of +and + + align:start position:0% +and + + + align:start position:0% +and +the so it's extraordinary that + + align:start position:0% +the so it's extraordinary that + + + align:start position:0% +the so it's extraordinary that +every major temp to reformulate the form + + align:start position:0% +every major temp to reformulate the form + + + align:start position:0% +every major temp to reformulate the form +of the city produces a new housing type + + align:start position:0% +of the city produces a new housing type + + + align:start position:0% +of the city produces a new housing type +in its in its + + align:start position:0% + + + + align:start position:0% + +wake Chicago I don't know what it + + align:start position:0% +wake Chicago I don't know what it + + + align:start position:0% +wake Chicago I don't know what it +did Chicago probably didn't produce a + + align:start position:0% +did Chicago probably didn't produce a + + + align:start position:0% +did Chicago probably didn't produce a +housing type + + align:start position:0% +housing type + + + align:start position:0% +housing type +uh the Genesis of the American Suburban + + align:start position:0% +uh the Genesis of the American Suburban + + + align:start position:0% +uh the Genesis of the American Suburban +house is + + align:start position:0% +house is + + + align:start position:0% +house is +old and starts with the + + align:start position:0% +old and starts with the + + + align:start position:0% +old and starts with the +British + + align:start position:0% + + + + align:start position:0% + +Conquest so come we switch back and then + + align:start position:0% +Conquest so come we switch back and then + + + align:start position:0% +Conquest so come we switch back and then +analogically to the condition of the of + + align:start position:0% +analogically to the condition of the of + + + align:start position:0% +analogically to the condition of the of +poverty in the developing world + + align:start position:0% + + + + align:start position:0% + +of all the demonstrations of + + align:start position:0% +of all the demonstrations of + + + align:start position:0% +of all the demonstrations of +international + + align:start position:0% +international + + + align:start position:0% +international +cooperation I argued that the Olympic + + align:start position:0% +cooperation I argued that the Olympic + + + align:start position:0% +cooperation I argued that the Olympic +Games stands out as the + + align:start position:0% +Games stands out as the + + + align:start position:0% +Games stands out as the +most + + align:start position:0% +most + + + align:start position:0% +most +regular and beneficient nobody objects + + align:start position:0% +regular and beneficient nobody objects + + + align:start position:0% +regular and beneficient nobody objects +to the Olympic + + align:start position:0% +to the Olympic + + + align:start position:0% +to the Olympic +Games uh they should have in 36 but they + + align:start position:0% +Games uh they should have in 36 but they + + + align:start position:0% +Games uh they should have in 36 but they +didn't certainly the Americans + + align:start position:0% +didn't certainly the Americans + + + align:start position:0% +didn't certainly the Americans +didn't uh + + align:start position:0% + + + + align:start position:0% + +the Olympic Games is been held in all of + + align:start position:0% +the Olympic Games is been held in all of + + + align:start position:0% +the Olympic Games is been held in all of +its years since + + align:start position:0% +its years since + + + align:start position:0% +its years since +1896 only once in a city in which the + + align:start position:0% +1896 only once in a city in which the + + + align:start position:0% +1896 only once in a city in which the +majority of people are poor that's + + align:start position:0% +majority of people are poor that's + + + align:start position:0% +majority of people are poor that's +Mexico it's + + align:start position:0% + + + + align:start position:0% + +1968 the funding of the Olympic Games is + + align:start position:0% +1968 the funding of the Olympic Games is + + + align:start position:0% +1968 the funding of the Olympic Games is +either in favor + + align:start position:0% + + + + align:start position:0% + +of National Economic gain advertising + + align:start position:0% +of National Economic gain advertising + + + align:start position:0% +of National Economic gain advertising +yourself on the international economic + + align:start position:0% +yourself on the international economic + + + align:start position:0% +yourself on the international economic +platform or at + + align:start position:0% +platform or at + + + align:start position:0% +platform or at +least gratifying a national impulse to + + align:start position:0% +least gratifying a national impulse to + + + align:start position:0% +least gratifying a national impulse to +be worldly and + + align:start position:0% +be worldly and + + + align:start position:0% +be worldly and +international uh and even more at best + + align:start position:0% +international uh and even more at best + + + align:start position:0% +international uh and even more at best +to satisfy perhaps a + + align:start position:0% +to satisfy perhaps a + + + align:start position:0% +to satisfy perhaps a +plung ambition in all of us to be part + + align:start position:0% +plung ambition in all of us to be part + + + align:start position:0% +plung ambition in all of us to be part +of a good + + align:start position:0% +of a good + + + align:start position:0% +of a good +World which is seldom available where + + align:start position:0% +World which is seldom available where + + + align:start position:0% +World which is seldom available where +people run in + + align:start position:0% +people run in + + + align:start position:0% +people run in +peace against each other as they did in + + align:start position:0% +peace against each other as they did in + + + align:start position:0% +peace against each other as they did in +1896 in + + align:start position:0% + + + + align:start position:0% + +Athens but the options for the + + align:start position:0% +Athens but the options for the + + + align:start position:0% +Athens but the options for the +developing world are few + + align:start position:0% +developing world are few + + + align:start position:0% +developing world are few +because of two meta + + align:start position:0% +because of two meta + + + align:start position:0% +because of two meta +conditions first of + + align:start position:0% + + + + align:start position:0% + +all the residue of + + align:start position:0% +all the residue of + + + align:start position:0% +all the residue of +colonialism and the mancipation of + + align:start position:0% +colonialism and the mancipation of + + + align:start position:0% +colonialism and the mancipation of +wealth from sources such as + + align:start position:0% +wealth from sources such as + + + align:start position:0% +wealth from sources such as +Mexico from sources such as India + + align:start position:0% +Mexico from sources such as India + + + align:start position:0% +Mexico from sources such as India +through the cotton + + align:start position:0% +through the cotton + + + align:start position:0% +through the cotton +trade + + align:start position:0% +trade + + + align:start position:0% +trade +from almost every African + + align:start position:0% + + + + align:start position:0% + +country gold and diamonds and uranium + + align:start position:0% +country gold and diamonds and uranium + + + align:start position:0% +country gold and diamonds and uranium +from South + + align:start position:0% +from South + + + align:start position:0% +from South +Africa + + align:start position:0% +Africa + + + align:start position:0% +Africa +um + + align:start position:0% +um + + + align:start position:0% +um +secondly particularly in Africa the + + align:start position:0% +secondly particularly in Africa the + + + align:start position:0% +secondly particularly in Africa the +incipient tradition of + + align:start position:0% +incipient tradition of + + + align:start position:0% +incipient tradition of +tribalism + + align:start position:0% +tribalism + + + align:start position:0% +tribalism +uh tribe tribes + + align:start position:0% +uh tribe tribes + + + align:start position:0% +uh tribe tribes +were the world was born in + + align:start position:0% + + + + align:start position:0% + +Africa the first + + align:start position:0% +Africa the first + + + align:start position:0% +Africa the first +species of Proto human was discovered a + + align:start position:0% +species of Proto human was discovered a + + + align:start position:0% +species of Proto human was discovered a +thousand miles from where I was + + align:start position:0% +thousand miles from where I was + + + align:start position:0% +thousand miles from where I was +born so I'm one of the + + align:start position:0% +born so I'm one of the + + + align:start position:0% +born so I'm one of the +ancestors + + align:start position:0% +ancestors + + + align:start position:0% +ancestors +theopus Africa + + align:start position:0% +theopus Africa + + + align:start position:0% +theopus Africa +gness that's 400 million years + + align:start position:0% + + + + align:start position:0% + +ago cities have only been going for + + align:start position:0% +ago cities have only been going for + + + align:start position:0% +ago cities have only been going for +20,000 what fraction of 400 million is + + align:start position:0% +20,000 what fraction of 400 million is + + + align:start position:0% +20,000 what fraction of 400 million is +20,000 it's a tiny + + align:start position:0% +20,000 it's a tiny + + + align:start position:0% +20,000 it's a tiny +percentage could somebody + + align:start position:0% +percentage could somebody + + + align:start position:0% +percentage could somebody +calculated 20,000 out of 400 + + align:start position:0% +calculated 20,000 out of 400 + + + align:start position:0% +calculated 20,000 out of 400 +million what percentage + + align:start position:0% + + + + align:start position:0% + +5% 5% + + align:start position:0% +5% 5% + + + align:start position:0% +5% 5% +5% + + align:start position:0% +5% + + + align:start position:0% +5% +yeah I conclude from that that we've not + + align:start position:0% +yeah I conclude from that that we've not + + + align:start position:0% +yeah I conclude from that that we've not +even started on sorting out + + align:start position:0% +even started on sorting out + + + align:start position:0% +even started on sorting out +urbanism we've got a long way to go that + + align:start position:0% +urbanism we've got a long way to go that + + + align:start position:0% +urbanism we've got a long way to go that +should satisfy all of you who young + + align:start position:0% +should satisfy all of you who young + + + align:start position:0% +should satisfy all of you who young +enough + + align:start position:0% +enough + + + align:start position:0% +enough +to rejoice in the + + align:start position:0% +to rejoice in the + + + align:start position:0% +to rejoice in the +finding + + align:start position:0% +finding + + + align:start position:0% +finding +uh + + align:start position:0% +uh + + + align:start position:0% +uh +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um tribalism + + align:start position:0% + + + + align:start position:0% + +he how much do you think that urbanism + + align:start position:0% +he how much do you think that urbanism + + + align:start position:0% +he how much do you think that urbanism +will attain a sort of maturity or + + align:start position:0% +will attain a sort of maturity or + + + align:start position:0% +will attain a sort of maturity or +homeostasis because of population rather + + align:start position:0% +homeostasis because of population rather + + + align:start position:0% +homeostasis because of population rather +than + + align:start position:0% +than + + + align:start position:0% +than +time population projection is is + + align:start position:0% +time population projection is is + + + align:start position:0% +time population projection is is +uncertain I'm going to give you read you + + align:start position:0% +uncertain I'm going to give you read you + + + align:start position:0% +uncertain I'm going to give you read you +a number of quotes from various sources + + align:start position:0% +a number of quotes from various sources + + + align:start position:0% +a number of quotes from various sources +about this + + align:start position:0% +about this + + + align:start position:0% +about this +phenomenon + + align:start position:0% +phenomenon + + + align:start position:0% +phenomenon +um the one + + align:start position:0% +um the one + + + align:start position:0% +um the one +that I find most + + align:start position:0% +that I find most + + + align:start position:0% +that I find most +dramatic touches on what you've just + + align:start position:0% + + + + align:start position:0% + +asked urbanization in developing + + align:start position:0% +asked urbanization in developing + + + align:start position:0% +asked urbanization in developing +countries may be the single greatest + + align:start position:0% +countries may be the single greatest + + + align:start position:0% +countries may be the single greatest +change in the + + align:start position:0% +change in the + + + align:start position:0% +change in the +century it is projected the developing + + align:start position:0% +century it is projected the developing + + + align:start position:0% +century it is projected the developing +countries will triple their builtup + + align:start position:0% +countries will triple their builtup + + + align:start position:0% +countries will triple their builtup +urban area being two between 2000 and + + align:start position:0% +urban area being two between 2000 and + + + align:start position:0% +urban area being two between 2000 and +203 from 200 ,000 Square kilm to 600,000 + + align:start position:0% +203 from 200 ,000 Square kilm to 600,000 + + + align:start position:0% +203 from 200 ,000 Square kilm to 600,000 +Square + + align:start position:0% +Square + + + align:start position:0% +Square +kilm these added 400 square kilm + + align:start position:0% +kilm these added 400 square kilm + + + align:start position:0% +kilm these added 400 square kilm +constructed in just 30 years equal the + + align:start position:0% +constructed in just 30 years equal the + + + align:start position:0% +constructed in just 30 years equal the +world's builtup urban area in + + align:start position:0% +world's builtup urban area in + + + align:start position:0% +world's builtup urban area in +2000 one could say humans are building a + + align:start position:0% +2000 one could say humans are building a + + + align:start position:0% +2000 one could say humans are building a +whole new world at about 10 times the + + align:start position:0% +whole new world at about 10 times the + + + align:start position:0% +whole new world at about 10 times the +speed in countries with severe resource + + align:start position:0% +speed in countries with severe resource + + + align:start position:0% +speed in countries with severe resource +constraints natural fiscal + + align:start position:0% +constraints natural fiscal + + + align:start position:0% +constraints natural fiscal +administrative and + + align:start position:0% +administrative and + + + align:start position:0% +administrative and +Technical now if this is + + align:start position:0% +Technical now if this is + + + align:start position:0% +Technical now if this is +correct it's + + align:start position:0% +correct it's + + + align:start position:0% +correct it's +impossible even China cannot build at + + align:start position:0% +impossible even China cannot build at + + + align:start position:0% +impossible even China cannot build at +this speed nor is does they have the + + align:start position:0% +this speed nor is does they have the + + + align:start position:0% +this speed nor is does they have the +developing World by its nature have all + + align:start position:0% +developing World by its nature have all + + + align:start position:0% +developing World by its nature have all +of the resources to do + + align:start position:0% + + + + align:start position:0% + +it slum population in the world is + + align:start position:0% +it slum population in the world is + + + align:start position:0% +it slum population in the world is +expected is now considered is now stated + + align:start position:0% +expected is now considered is now stated + + + align:start position:0% +expected is now considered is now stated +at about 1 billion people and is stated + + align:start position:0% +at about 1 billion people and is stated + + + align:start position:0% +at about 1 billion people and is stated +to double within the next 25 + + align:start position:0% + + + + align:start position:0% + +years let me + + align:start position:0% +years let me + + + align:start position:0% +years let me +just perhaps I should have gone through + + align:start position:0% +just perhaps I should have gone through + + + align:start position:0% +just perhaps I should have gone through +some of this material with you I always + + align:start position:0% +some of this material with you I always + + + align:start position:0% +some of this material with you I always +forget + + align:start position:0% + + + + align:start position:0% + +the world's largest cities is one of the + + align:start position:0% +the world's largest cities is one of the + + + align:start position:0% +the world's largest cities is one of the +indices + + align:start position:0% +indices + + + align:start position:0% +indices +of not very much other than population + + align:start position:0% +of not very much other than population + + + align:start position:0% +of not very much other than population +size New York was the largest city in + + align:start position:0% +size New York was the largest city in + + + align:start position:0% +size New York was the largest city in +the world in 1950 it's now sixth that's + + align:start position:0% +the world in 1950 it's now sixth that's + + + align:start position:0% +the world in 1950 it's now sixth that's +in the year + + align:start position:0% +in the year + + + align:start position:0% +in the year +2000 of course this is assuming that + + align:start position:0% +2000 of course this is assuming that + + + align:start position:0% +2000 of course this is assuming that +these measurements are + + align:start position:0% +these measurements are + + + align:start position:0% +these measurements are +constant what constitutes New York I + + align:start position:0% +constant what constitutes New York I + + + align:start position:0% +constant what constitutes New York I +don't know it's probably the standard + + align:start position:0% +don't know it's probably the standard + + + align:start position:0% +don't know it's probably the standard +metropolitan area I don't know that how + + align:start position:0% +metropolitan area I don't know that how + + + align:start position:0% +metropolitan area I don't know that how +that compares to + + align:start position:0% +that compares to + + + align:start position:0% +that compares to +Kolkata + + align:start position:0% +Kolkata + + + align:start position:0% +Kolkata +area but you can see the major European + + align:start position:0% +area but you can see the major European + + + align:start position:0% +area but you can see the major European +cities New York London Ryan + + align:start position:0% +cities New York London Ryan + + + align:start position:0% +cities New York London Ryan +Ru + + align:start position:0% + + + + align:start position:0% + +Paris + + align:start position:0% + + + + align:start position:0% + +Chicago have diminished in relative + + align:start position:0% +Chicago have diminished in relative + + + align:start position:0% +Chicago have diminished in relative +size as the growth of + + align:start position:0% +size as the growth of + + + align:start position:0% +size as the growth of +cities has taken place in Latin + + align:start position:0% +cities has taken place in Latin + + + align:start position:0% +cities has taken place in Latin +America Asia not yet significantly in + + align:start position:0% +America Asia not yet significantly in + + + align:start position:0% +America Asia not yet significantly in +Africa Cy very large + + align:start position:0% + + + + align:start position:0% + +cities the second two pages are just + + align:start position:0% +cities the second two pages are just + + + align:start position:0% +cities the second two pages are just +some cuttings from + + align:start position:0% + + + + align:start position:0% + +newspapers we saw johon + + align:start position:0% +newspapers we saw johon + + + align:start position:0% +newspapers we saw johon +Snow's 1854 discovery that Colo was + + align:start position:0% +Snow's 1854 discovery that Colo was + + + align:start position:0% +Snow's 1854 discovery that Colo was +water born and not my asmic + + align:start position:0% +water born and not my asmic + + + align:start position:0% +water born and not my asmic +in nature here you see Cola now being + + align:start position:0% +in nature here you see Cola now being + + + align:start position:0% +in nature here you see Cola now being +used as an index to + + align:start position:0% +used as an index to + + + align:start position:0% +used as an index to +determine 19th century conditions + + align:start position:0% +determine 19th century conditions + + + align:start position:0% +determine 19th century conditions +feeding on 19th century conditions color + + align:start position:0% +feeding on 19th century conditions color + + + align:start position:0% +feeding on 19th century conditions color +spreads in Latin + + align:start position:0% + + + + align:start position:0% + +America another phenomenon from this + + align:start position:0% +America another phenomenon from this + + + align:start position:0% +America another phenomenon from this +world a lovely Madness Argentina builds + + align:start position:0% +world a lovely Madness Argentina builds + + + align:start position:0% +world a lovely Madness Argentina builds +new capital in Patagonia they didn't + + align:start position:0% +new capital in Patagonia they didn't + + + align:start position:0% +new capital in Patagonia they didn't +build build the capital but they + + align:start position:0% +build build the capital but they + + + align:start position:0% +build build the capital but they +proposed building a new + + align:start position:0% +proposed building a new + + + align:start position:0% +proposed building a new +Capital One of + + align:start position:0% + + + + align:start position:0% + +the urbanistic outcomes + + align:start position:0% +the urbanistic outcomes + + + align:start position:0% +the urbanistic outcomes +of large population growth and + + align:start position:0% +of large population growth and + + + align:start position:0% +of large population growth and +Independence has been the notion that + + align:start position:0% +Independence has been the notion that + + + align:start position:0% +Independence has been the notion that +you need to + + align:start position:0% +you need to + + + align:start position:0% +you need to +establish your status through the + + align:start position:0% +establish your status through the + + + align:start position:0% +establish your status through the +building of a new + + align:start position:0% + + + + align:start position:0% + +capital these have become famous icons + + align:start position:0% +capital these have become famous icons + + + align:start position:0% +capital these have become famous icons +in the world + + align:start position:0% +in the world + + + align:start position:0% +in the world +Brazilia + + align:start position:0% + + + + align:start position:0% + +uh par + + align:start position:0% +uh par + + + align:start position:0% +uh par +L but less significantly chandigar in + + align:start position:0% +L but less significantly chandigar in + + + align:start position:0% +L but less significantly chandigar in +the Punjab after the division between + + align:start position:0% +the Punjab after the division between + + + align:start position:0% +the Punjab after the division between +Pakistan and India left the Punjab + + align:start position:0% +Pakistan and India left the Punjab + + + align:start position:0% +Pakistan and India left the Punjab +without a + + align:start position:0% +without a + + + align:start position:0% +without a +capital + + align:start position:0% +capital + + + align:start position:0% +capital +uh sorry + + align:start position:0% +uh sorry + + + align:start position:0% +uh sorry +Islam Islam Abad in Pakistan yes + + align:start position:0% +Islam Islam Abad in Pakistan yes + + + align:start position:0% +Islam Islam Abad in Pakistan yes +but the Indian part of what remains of + + align:start position:0% +but the Indian part of what remains of + + + align:start position:0% +but the Indian part of what remains of +the + + align:start position:0% + + + + align:start position:0% + +Punjab + + align:start position:0% +Punjab + + + align:start position:0% +Punjab +I did some work on chandigar with + + align:start position:0% +I did some work on chandigar with + + + align:start position:0% +I did some work on chandigar with +Charles + + align:start position:0% +Charles + + + align:start position:0% +Charles +Korea we published a piece in a book we + + align:start position:0% +Korea we published a piece in a book we + + + align:start position:0% +Korea we published a piece in a book we +edited on chandigar published in India + + align:start position:0% +edited on chandigar published in India + + + align:start position:0% +edited on chandigar published in India +in + + align:start position:0% +in + + + align:start position:0% +in +English + + align:start position:0% +English + + + align:start position:0% +English +um the story of chandigar is very much + + align:start position:0% +um the story of chandigar is very much + + + align:start position:0% +um the story of chandigar is very much +the story of trying to find an + + align:start position:0% +the story of trying to find an + + + align:start position:0% +the story of trying to find an +appropriate form for a post Colonial + + align:start position:0% +appropriate form for a post Colonial + + + align:start position:0% +appropriate form for a post Colonial +post native + + align:start position:0% + + + + align:start position:0% + +City Gandhi didn't leave any + + align:start position:0% +City Gandhi didn't leave any + + + align:start position:0% +City Gandhi didn't leave any +instructions on how to build cities + + align:start position:0% +instructions on how to build cities + + + align:start position:0% +instructions on how to build cities +neither did + + align:start position:0% +neither did + + + align:start position:0% +neither did +Marx the great minds of social + + align:start position:0% +Marx the great minds of social + + + align:start position:0% +Marx the great minds of social +change didn't take cities into account + + align:start position:0% +change didn't take cities into account + + + align:start position:0% +change didn't take cities into account +nor City were they be Bel laboring + + align:start position:0% +nor City were they be Bel laboring + + + align:start position:0% +nor City were they be Bel laboring +questions of architectural form they + + align:start position:0% +questions of architectural form they + + + align:start position:0% +questions of architectural form they +were too busy doing other + + align:start position:0% +were too busy doing other + + + align:start position:0% +were too busy doing other +things chandigar + + align:start position:0% + + + + align:start position:0% + +emerged as a complex + + align:start position:0% +emerged as a complex + + + align:start position:0% +emerged as a complex +mindset somewhere + + align:start position:0% +mindset somewhere + + + align:start position:0% +mindset somewhere +between Indian + + align:start position:0% +between Indian + + + align:start position:0% +between Indian +leaders imagining India to be on a + + align:start position:0% +leaders imagining India to be on a + + + align:start position:0% +leaders imagining India to be on a +progress transect + + align:start position:0% +progress transect + + + align:start position:0% +progress transect +towards + + align:start position:0% +towards + + + align:start position:0% +towards +modernism they after all were few Indian + + align:start position:0% +modernism they after all were few Indian + + + align:start position:0% +modernism they after all were few Indian +Architects old enough to be practicing + + align:start position:0% +Architects old enough to be practicing + + + align:start position:0% +Architects old enough to be practicing +significantly at the time they chose + + align:start position:0% +significantly at the time they chose + + + align:start position:0% +significantly at the time they chose +British + + align:start position:0% +British + + + align:start position:0% +British +architects who in turn said they weren't + + align:start position:0% +architects who in turn said they weren't + + + align:start position:0% +architects who in turn said they weren't +capable of doing the work and + + align:start position:0% +capable of doing the work and + + + align:start position:0% +capable of doing the work and +recommended French Architect by the name + + align:start position:0% +recommended French Architect by the name + + + align:start position:0% +recommended French Architect by the name +of + + align:start position:0% +of + + + align:start position:0% +of +lovier who came to India traveled around + + align:start position:0% +lovier who came to India traveled around + + + align:start position:0% +lovier who came to India traveled around +India and decided decided on a sectoral + + align:start position:0% +India and decided decided on a sectoral + + + align:start position:0% +India and decided decided on a sectoral +plan which he had played with in + + align:start position:0% +plan which he had played with in + + + align:start position:0% +plan which he had played with in +Bogata before coming to India without + + align:start position:0% +Bogata before coming to India without + + + align:start position:0% +Bogata before coming to India without +telling + + align:start position:0% +telling + + + align:start position:0% +telling +anybody uh and evolved a plan which is + + align:start position:0% +anybody uh and evolved a plan which is + + + align:start position:0% +anybody uh and evolved a plan which is +based on + + align:start position:0% +based on + + + align:start position:0% +based on +highway on series of five highways + + align:start position:0% +highway on series of five highways + + + align:start position:0% +highway on series of five highways +system although there were no cars in + + align:start position:0% +system although there were no cars in + + + align:start position:0% +system although there were no cars in +India at the + + align:start position:0% +India at the + + + align:start position:0% +India at the +time I checked on the car population of + + align:start position:0% +time I checked on the car population of + + + align:start position:0% +time I checked on the car population of +India in 1950 it was close to + + align:start position:0% +India in 1950 it was close to + + + align:start position:0% +India in 1950 it was close to +zero except + + align:start position:0% +zero except + + + align:start position:0% +zero except +for few thousand + + align:start position:0% +for few thousand + + + align:start position:0% +for few thousand +cars + + align:start position:0% + + + + align:start position:0% + +um shandar + + align:start position:0% + + + + align:start position:0% + +also didn't look into the future as far + + align:start position:0% + + + + align:start position:0% + +as how people would develop from a + + align:start position:0% +as how people would develop from a + + + align:start position:0% +as how people would develop from a +design mind + + align:start position:0% +design mind + + + align:start position:0% +design mind +Point + + align:start position:0% +Point + + + align:start position:0% +Point +uh first of all we have no way of + + align:start position:0% +uh first of all we have no way of + + + align:start position:0% +uh first of all we have no way of +dealing yet with immigration as a result + + align:start position:0% +dealing yet with immigration as a result + + + align:start position:0% +dealing yet with immigration as a result +of building an economic growth + + align:start position:0% + + + + align:start position:0% + +point there's an informal sector of + + align:start position:0% +point there's an informal sector of + + + align:start position:0% +point there's an informal sector of +chandigar both in chandigar and in the + + align:start position:0% +chandigar both in chandigar and in the + + + align:start position:0% +chandigar both in chandigar and in the +neighboring towns which are numers + + align:start position:0% +neighboring towns which are numers + + + align:start position:0% +neighboring towns which are numers +Shanda + + align:start position:0% +Shanda + + + align:start position:0% +Shanda +now land control + + align:start position:0% +now land control + + + align:start position:0% +now land control +is + + align:start position:0% + + + + align:start position:0% + +weak although the national government + + align:start position:0% +weak although the national government + + + align:start position:0% +weak although the national government +superintends over + + align:start position:0% +superintends over + + + align:start position:0% +superintends over +chandigar it sells land + + align:start position:0% +chandigar it sells land + + + align:start position:0% +chandigar it sells land +illegally north of the capital complex + + align:start position:0% +illegally north of the capital complex + + + align:start position:0% +illegally north of the capital complex +on in the path of the famous drawings of + + align:start position:0% +on in the path of the famous drawings of + + + align:start position:0% +on in the path of the famous drawings of +kusia and the imas in the + + align:start position:0% + + + + align:start position:0% + +distance I can go on at length about + + align:start position:0% +distance I can go on at length about + + + align:start position:0% +distance I can go on at length about +chandigar um + + align:start position:0% +chandigar um + + + align:start position:0% +chandigar um +the there was no attempt to look at the + + align:start position:0% +the there was no attempt to look at the + + + align:start position:0% +the there was no attempt to look at the +genius of Indian urbanism native Indian + + align:start position:0% +genius of Indian urbanism native Indian + + + align:start position:0% +genius of Indian urbanism native Indian +urbanism nobody looked at jaur and tried + + align:start position:0% +urbanism nobody looked at jaur and tried + + + align:start position:0% +urbanism nobody looked at jaur and tried +to make sense of + + align:start position:0% +to make sense of + + + align:start position:0% +to make sense of +jaur everything was to be in the gossip + + align:start position:0% +jaur everything was to be in the gossip + + + align:start position:0% +jaur everything was to be in the gossip +of modernism a modern + + align:start position:0% +of modernism a modern + + + align:start position:0% +of modernism a modern +project at least Lou Khan when he went + + align:start position:0% +project at least Lou Khan when he went + + + align:start position:0% +project at least Lou Khan when he went +to building Dhaka looked at the way + + align:start position:0% +to building Dhaka looked at the way + + + align:start position:0% +to building Dhaka looked at the way +Brick Layers laid bricks + + align:start position:0% +Brick Layers laid bricks + + + align:start position:0% +Brick Layers laid bricks +and built horizontal + + align:start position:0% +and built horizontal + + + align:start position:0% +and built horizontal +stripes in relation to the teres that + + align:start position:0% +stripes in relation to the teres that + + + align:start position:0% +stripes in relation to the teres that +were finished each + + align:start position:0% + + + + align:start position:0% + +day + + align:start position:0% +day + + + align:start position:0% +day +shanar + + align:start position:0% +shanar + + + align:start position:0% +shanar +uh is + + align:start position:0% +uh is + + + align:start position:0% +uh is +now a center which is historic in nature + + align:start position:0% +now a center which is historic in nature + + + align:start position:0% +now a center which is historic in nature +much like a Italian Hilltown and a + + align:start position:0% +much like a Italian Hilltown and a + + + align:start position:0% +much like a Italian Hilltown and a +periphery which is a chaotic + + align:start position:0% + + + + align:start position:0% + +apparently it's two cities + + align:start position:0% +apparently it's two cities + + + align:start position:0% +apparently it's two cities +the + + align:start position:0% +the + + + align:start position:0% +the +one envisioned by a single + + align:start position:0% +one envisioned by a single + + + align:start position:0% +one envisioned by a single +man and his + + align:start position:0% +man and his + + + align:start position:0% +man and his +cousin + + align:start position:0% +cousin + + + align:start position:0% +cousin +um the other built + + align:start position:0% +um the other built + + + align:start position:0% +um the other built +by the Free Will + + align:start position:0% +by the Free Will + + + align:start position:0% +by the Free Will +allowed K some of + + align:start position:0% +allowed K some of + + + align:start position:0% +allowed K some of +K's regulations still stand today they + + align:start position:0% +K's regulations still stand today they + + + align:start position:0% +K's regulations still stand today they +are meaningless in relation to a bicycle + + align:start position:0% +are meaningless in relation to a bicycle + + + align:start position:0% +are meaningless in relation to a bicycle +Shack + + align:start position:0% +Shack + + + align:start position:0% +Shack +on the + + align:start position:0% + + + + align:start position:0% + +periphery anyway that's so much for + + align:start position:0% +periphery anyway that's so much for + + + align:start position:0% +periphery anyway that's so much for +shandar shandar stand will stand as an + + align:start position:0% +shandar shandar stand will stand as an + + + align:start position:0% +shandar shandar stand will stand as an +emblem of + + align:start position:0% +emblem of + + + align:start position:0% +emblem of +India's attempts to calibrate + + align:start position:0% +India's attempts to calibrate + + + align:start position:0% +India's attempts to calibrate +itself and in that sense one should feel + + align:start position:0% +itself and in that sense one should feel + + + align:start position:0% +itself and in that sense one should feel +proud of it it could have been better a + + align:start position:0% +proud of it it could have been better a + + + align:start position:0% +proud of it it could have been better a +generation + + align:start position:0% +generation + + + align:start position:0% +generation +later some Indian Architects would have + + align:start position:0% +later some Indian Architects would have + + + align:start position:0% +later some Indian Architects would have +done the same thing + + align:start position:0% + + + + align:start position:0% + +thing there are buildings there that are + + align:start position:0% +thing there are buildings there that are + + + align:start position:0% +thing there are buildings there that are +going to stand for a long time the Law + + align:start position:0% +going to stand for a long time the Law + + + align:start position:0% +going to stand for a long time the Law +Courts for instance where is + + align:start position:0% +Courts for instance where is + + + align:start position:0% +Courts for instance where is +the governor's Palace was never + + align:start position:0% +the governor's Palace was never + + + align:start position:0% +the governor's Palace was never +built leaving + + align:start position:0% +built leaving + + + align:start position:0% +built leaving +the I getting into too much + + align:start position:0% +the I getting into too much + + + align:start position:0% +the I getting into too much +detail you know + + align:start position:0% +detail you know + + + align:start position:0% +detail you know +shandar or you should know it well + + align:start position:0% + + + + align:start position:0% + +the next page is a page of + + align:start position:0% +the next page is a page of + + + align:start position:0% +the next page is a page of +optimism from a Toronto + + align:start position:0% +optimism from a Toronto + + + align:start position:0% +optimism from a Toronto +newspaper arguing that things are going + + align:start position:0% +newspaper arguing that things are going + + + align:start position:0% +newspaper arguing that things are going +very well in the + + align:start position:0% + + + + align:start position:0% + +world sharing graphs of declining + + align:start position:0% +world sharing graphs of declining + + + align:start position:0% +world sharing graphs of declining +Warfare + + align:start position:0% + + + + align:start position:0% + +falling + + align:start position:0% + + + + align:start position:0% + +fertility not in the poorest countries + + align:start position:0% +fertility not in the poorest countries + + + align:start position:0% +fertility not in the poorest countries +but + + align:start position:0% +but + + + align:start position:0% +but +in inhabited countries Trends in life + + align:start position:0% +in inhabited countries Trends in life + + + align:start position:0% +in inhabited countries Trends in life +expectency Rising + + align:start position:0% + + + + align:start position:0% + +everywhere subsaharan Africa they SL + + align:start position:0% +everywhere subsaharan Africa they SL + + + align:start position:0% +everywhere subsaharan Africa they SL +under + + align:start position:0% + + + + align:start position:0% + +50 the environment has an enormous drop + + align:start position:0% +50 the environment has an enormous drop + + + align:start position:0% +50 the environment has an enormous drop +in the production of + + align:start position:0% + + + + align:start position:0% + +chlorocarbons at + + align:start position:0% +chlorocarbons at + + + align:start position:0% +chlorocarbons at +Bas the third + + align:start position:0% + + + + align:start position:0% + +world does be + + align:start position:0% +world does be + + + align:start position:0% +world does be +does + + align:start position:0% +does + + + align:start position:0% +does +does fairly + + align:start position:0% + + + + align:start position:0% + +well and so on + + align:start position:0% + + + + align:start position:0% + +next + + align:start position:0% +next + + + align:start position:0% +next +page gives a projected number of Slum + + align:start position:0% +page gives a projected number of Slum + + + align:start position:0% +page gives a projected number of Slum +dwellers in by + + align:start position:0% + + + + align:start position:0% + +region next page shows projections for + + align:start position:0% +region next page shows projections for + + + align:start position:0% +region next page shows projections for +world + + align:start position:0% +world + + + align:start position:0% +world +population population + + align:start position:0% + + + + align:start position:0% + +growth losing 25 + + align:start position:0% + + + + align:start position:0% + +5% in Eastern Europe as you go from east + + align:start position:0% +5% in Eastern Europe as you go from east + + + align:start position:0% +5% in Eastern Europe as you go from east +to west in Europe population + + align:start position:0% +to west in Europe population + + + align:start position:0% +to west in Europe population +growth loses drastically till the time + + align:start position:0% +growth loses drastically till the time + + + align:start position:0% +growth loses drastically till the time +you get to England where + + align:start position:0% +you get to England where + + + align:start position:0% +you get to England where +it'sit + + align:start position:0% +it'sit + + + align:start position:0% +it'sit +stable northern + + align:start position:0% +stable northern + + + align:start position:0% +stable northern +Europe Western Europe losing + + align:start position:0% +Europe Western Europe losing + + + align:start position:0% +Europe Western Europe losing +2% at the same time the major population + + align:start position:0% +2% at the same time the major population + + + align:start position:0% +2% at the same time the major population +grows + + align:start position:0% + + + + align:start position:0% + +uh in the United States plus + + align:start position:0% +uh in the United States plus + + + align:start position:0% +uh in the United States plus +33% this due to + + align:start position:0% +33% this due to + + + align:start position:0% +33% this due to +migration more than anything + + align:start position:0% + + + + align:start position:0% + +else the worst conditions are in Western + + align:start position:0% +else the worst conditions are in Western + + + align:start position:0% +else the worst conditions are in Western +Africa plus + + align:start position:0% +Africa plus + + + align:start position:0% +Africa plus +127% + + align:start position:0% +127% + + + align:start position:0% +127% +122% middle Africa Plus 175% + + align:start position:0% + + + + align:start position:0% + +South Central Asia plus + + align:start position:0% +South Central Asia plus + + + align:start position:0% +South Central Asia plus +55% Western Asia plus + + align:start position:0% + + + + align:start position:0% + +79% Japan minus + + align:start position:0% + + + + align:start position:0% + +177% people migrate to cities because + + align:start position:0% +177% people migrate to cities because + + + align:start position:0% +177% people migrate to cities because +there's a better chance in life than + + align:start position:0% +there's a better chance in life than + + + align:start position:0% +there's a better chance in life than +where they are they're not + + align:start position:0% +where they are they're not + + + align:start position:0% +where they are they're not +dumb the notion that people are animals + + align:start position:0% +dumb the notion that people are animals + + + align:start position:0% +dumb the notion that people are animals +and behave foolishly in going to cities + + align:start position:0% +and behave foolishly in going to cities + + + align:start position:0% +and behave foolishly in going to cities +is a foolish + + align:start position:0% +is a foolish + + + align:start position:0% +is a foolish +proposition the life Lottery is + + align:start position:0% +proposition the life Lottery is + + + align:start position:0% +proposition the life Lottery is +large in cities it's always been that + + align:start position:0% +large in cities it's always been that + + + align:start position:0% +large in cities it's always been that +way your daughter can go to school and + + align:start position:0% +way your daughter can go to school and + + + align:start position:0% +way your daughter can go to school and +marry a rich man it's unlikely to happen + + align:start position:0% +marry a rich man it's unlikely to happen + + + align:start position:0% +marry a rich man it's unlikely to happen +in a + + align:start position:0% +in a + + + align:start position:0% +in a +village there's a sanctity in numbers + + align:start position:0% +village there's a sanctity in numbers + + + align:start position:0% +village there's a sanctity in numbers +which you cannot + + align:start position:0% + + + + align:start position:0% + +deny number two + + align:start position:0% +deny number two + + + align:start position:0% +deny number two +staying in the rural areas is no + + align:start position:0% +staying in the rural areas is no + + + align:start position:0% +staying in the rural areas is no +blessing if only the rural areas is what + + align:start position:0% +blessing if only the rural areas is what + + + align:start position:0% +blessing if only the rural areas is what +our romantic vision of + + align:start position:0% +our romantic vision of + + + align:start position:0% +our romantic vision of +nature + + align:start position:0% +nature + + + align:start position:0% +nature +suggests beautiful + + align:start position:0% +suggests beautiful + + + align:start position:0% +suggests beautiful +landscape low inv involvement in work + + align:start position:0% +landscape low inv involvement in work + + + align:start position:0% +landscape low inv involvement in work +sitting on the porch drinking uh rum at + + align:start position:0% +sitting on the porch drinking uh rum at + + + align:start position:0% +sitting on the porch drinking uh rum at +sundown all images from the colonial + + align:start position:0% +sundown all images from the colonial + + + align:start position:0% +sundown all images from the colonial +tourist + + align:start position:0% +tourist + + + align:start position:0% +tourist +world uh + + align:start position:0% +world uh + + + align:start position:0% +world uh +I grew up in South Africa with Africans + + align:start position:0% +I grew up in South Africa with Africans + + + align:start position:0% +I grew up in South Africa with Africans +literature being filled with images of + + align:start position:0% +literature being filled with images of + + + align:start position:0% +literature being filled with images of +this kind Farmers sitting + + align:start position:0% +this kind Farmers sitting + + + align:start position:0% +this kind Farmers sitting +benighted on their porch whilst the + + align:start position:0% +benighted on their porch whilst the + + + align:start position:0% +benighted on their porch whilst the +black laborers slaved away in the + + align:start position:0% +black laborers slaved away in the + + + align:start position:0% +black laborers slaved away in the +distance and the young daughter who' + + align:start position:0% +distance and the young daughter who' + + + align:start position:0% +distance and the young daughter who' +gone to the city comes back with the + + align:start position:0% +gone to the city comes back with the + + + align:start position:0% +gone to the city comes back with the +illegitimate child and they all mourn + + align:start position:0% +illegitimate child and they all mourn + + + align:start position:0% +illegitimate child and they all mourn +the fact that the country is being going + + align:start position:0% +the fact that the country is being going + + + align:start position:0% +the fact that the country is being going +to dogs to the + + align:start position:0% + + + + align:start position:0% + +dogs there's no real much + + align:start position:0% + + + + align:start position:0% + +though even the + + align:start position:0% + + + + align:start position:0% + +Russians + + align:start position:0% +Russians + + + align:start position:0% +Russians +and many + + align:start position:0% +and many + + + align:start position:0% +and many +ideologies Sanctified the country as + + align:start position:0% +ideologies Sanctified the country as + + + align:start position:0% +ideologies Sanctified the country as +well as the city The Communist Manifesto + + align:start position:0% +well as the city The Communist Manifesto + + + align:start position:0% +well as the city The Communist Manifesto +says develop the country and the + + align:start position:0% +says develop the country and the + + + align:start position:0% +says develop the country and the +city the fact fact is that nobody's + + align:start position:0% +city the fact fact is that nobody's + + + align:start position:0% +city the fact fact is that nobody's +really effectively developed the + + align:start position:0% + + + + align:start position:0% + +country the United States is producing + + align:start position:0% +country the United States is producing + + + align:start position:0% +country the United States is producing +more food on 7% of the Agricultural + + align:start position:0% +more food on 7% of the Agricultural + + + align:start position:0% +more food on 7% of the Agricultural +population that it started + + align:start position:0% +population that it started + + + align:start position:0% +population that it started +with now that's not the correct + + align:start position:0% +with now that's not the correct + + + align:start position:0% +with now that's not the correct +statistic I haven't got the statistic in + + align:start position:0% +statistic I haven't got the statistic in + + + align:start position:0% +statistic I haven't got the statistic in +front of + + align:start position:0% +front of + + + align:start position:0% +front of +me excuse me but it's something like + + align:start position:0% +me excuse me but it's something like + + + align:start position:0% +me excuse me but it's something like +that in South Africa since apartate + + align:start position:0% +that in South Africa since apartate + + + align:start position:0% +that in South Africa since apartate +there's been enormous attempts + + align:start position:0% +there's been enormous attempts + + + align:start position:0% +there's been enormous attempts +to increase the amount of agricultural + + align:start position:0% +to increase the amount of agricultural + + + align:start position:0% +to increase the amount of agricultural +land owned by black people I think they + + align:start position:0% +land owned by black people I think they + + + align:start position:0% +land owned by black people I think they +still own less than + + align:start position:0% + + + + align:start position:0% + +20% brutal land reforms such as In by Mr + + align:start position:0% +20% brutal land reforms such as In by Mr + + + align:start position:0% +20% brutal land reforms such as In by Mr +mugabi in rishia or Zambia not rishia + + align:start position:0% +mugabi in rishia or Zambia not rishia + + + align:start position:0% +mugabi in rishia or Zambia not rishia +Zimbabwe uh has produced appalling + + align:start position:0% +Zimbabwe uh has produced appalling + + + align:start position:0% +Zimbabwe uh has produced appalling +economic + + align:start position:0% +economic + + + align:start position:0% +economic +results we haven't found a formula for + + align:start position:0% +results we haven't found a formula for + + + align:start position:0% +results we haven't found a formula for +making the land + + align:start position:0% +making the land + + + align:start position:0% +making the land +productive uh out of outside of heavy + + align:start position:0% +productive uh out of outside of heavy + + + align:start position:0% +productive uh out of outside of heavy +technology cor corporate manua + + align:start position:0% +technology cor corporate manua + + + align:start position:0% +technology cor corporate manua +production uh which the United States + + align:start position:0% +production uh which the United States + + + align:start position:0% +production uh which the United States +leads the world + + align:start position:0% + + + + align:start position:0% + +in + + align:start position:0% +in + + + align:start position:0% +in +there there + + align:start position:0% +there there + + + align:start position:0% +there there +are signs of migration from rural to + + align:start position:0% +are signs of migration from rural to + + + align:start position:0% +are signs of migration from rural to +city in India + + align:start position:0% +city in India + + + align:start position:0% +city in India +suggesting that + + align:start position:0% +suggesting that + + + align:start position:0% +suggesting that +people do both have part of their + + align:start position:0% +people do both have part of their + + + align:start position:0% +people do both have part of their +families in the country and work in the + + align:start position:0% +families in the country and work in the + + + align:start position:0% +families in the country and work in the +city and migrate selectively between + + align:start position:0% +city and migrate selectively between + + + align:start position:0% +city and migrate selectively between +them these are an intelligent form of + + align:start position:0% +them these are an intelligent form of + + + align:start position:0% +them these are an intelligent form of +migration uh but it's not very cons not + + align:start position:0% +migration uh but it's not very cons not + + + align:start position:0% +migration uh but it's not very cons not +yet considerably + + align:start position:0% +yet considerably + + + align:start position:0% +yet considerably +large U + + align:start position:0% +large U + + + align:start position:0% +large U +so where is the British by the enclosure + + align:start position:0% +so where is the British by the enclosure + + + align:start position:0% +so where is the British by the enclosure +of the Commons acts took land away from + + align:start position:0% +of the Commons acts took land away from + + + align:start position:0% +of the Commons acts took land away from +poor people forced them into cities + + align:start position:0% +poor people forced them into cities + + + align:start position:0% +poor people forced them into cities +today the process is that nobody's + + align:start position:0% +today the process is that nobody's + + + align:start position:0% +today the process is that nobody's +taking the land away from you except + + align:start position:0% +taking the land away from you except + + + align:start position:0% +taking the land away from you except +there's nothing to do on + + align:start position:0% + + + + align:start position:0% + +it + + align:start position:0% +it + + + align:start position:0% +it +migration is not a new + + align:start position:0% +migration is not a new + + + align:start position:0% +migration is not a new +phenomenon we started off as migrants he + + align:start position:0% +phenomenon we started off as migrants he + + + align:start position:0% +phenomenon we started off as migrants he +settled after 400 million + + align:start position:0% +settled after 400 million + + + align:start position:0% +settled after 400 million +years took a long time time to + + align:start position:0% + + + + align:start position:0% + +settle we've only settled for 20,000 + + align:start position:0% +settle we've only settled for 20,000 + + + align:start position:0% +settle we've only settled for 20,000 +years at + + align:start position:0% + + + + align:start position:0% + +best but the rural parts of the world + + align:start position:0% +best but the rural parts of the world + + + align:start position:0% +best but the rural parts of the world +are becoming more + + align:start position:0% +are becoming more + + + align:start position:0% +are becoming more +desolate L + + align:start position:0% +desolate L + + + align:start position:0% +desolate L +inhabited the problem with central + + align:start position:0% +inhabited the problem with central + + + align:start position:0% +inhabited the problem with central +Africa my and the highest migration + + align:start position:0% +Africa my and the highest migration + + + align:start position:0% +Africa my and the highest migration +rates is a combination of high fertility + + align:start position:0% +rates is a combination of high fertility + + + align:start position:0% +rates is a combination of high fertility +rates and urbanized + + align:start position:0% +rates and urbanized + + + align:start position:0% +rates and urbanized +ation you put the two together and you + + align:start position:0% +ation you put the two together and you + + + align:start position:0% +ation you put the two together and you +have a lethal + + align:start position:0% + + + + align:start position:0% + +combination aren there also factors of + + align:start position:0% +combination aren there also factors of + + + align:start position:0% +combination aren there also factors of +desertification desertification of of a + + align:start position:0% +desertification desertification of of a + + + align:start position:0% +desertification desertification of of a +lot of the + + align:start position:0% +lot of the + + + align:start position:0% +lot of the +Agricultural part + + align:start position:0% +Agricultural part + + + align:start position:0% +Agricultural part +of + + align:start position:0% +of + + + align:start position:0% +of +Depends you lose it depends where you + + align:start position:0% +Depends you lose it depends where you + + + align:start position:0% +Depends you lose it depends where you +are I mean in Israel in agricultural + + align:start position:0% +are I mean in Israel in agricultural + + + align:start position:0% +are I mean in Israel in agricultural +land is so valuable in Cuba cultural + + align:start position:0% +land is so valuable in Cuba cultural + + + align:start position:0% +land is so valuable in Cuba cultural +land is so valuable because the + + align:start position:0% +land is so valuable because the + + + align:start position:0% +land is so valuable because the +territory is so small in this country + + align:start position:0% +territory is so small in this country + + + align:start position:0% +territory is so small in this country +one flies over agricultural land + + align:start position:0% +one flies over agricultural land + + + align:start position:0% +one flies over agricultural land +endlessly and there's no pressure of + + align:start position:0% +endlessly and there's no pressure of + + + align:start position:0% +endlessly and there's no pressure of +densification the + + align:start position:0% +densification the + + + align:start position:0% +densification the +United sorry desert oh sorry I thought + + align:start position:0% +United sorry desert oh sorry I thought + + + align:start position:0% +United sorry desert oh sorry I thought +thought densification how is yes the + + align:start position:0% +thought densification how is yes the + + + align:start position:0% +thought densification how is yes the +enormous ecological + + align:start position:0% +enormous ecological + + + align:start position:0% +enormous ecological +problems uh untended land tends to get + + align:start position:0% +problems uh untended land tends to get + + + align:start position:0% +problems uh untended land tends to get +into no + + align:start position:0% +into no + + + align:start position:0% +into no +good when it's been tended + + align:start position:0% +good when it's been tended + + + align:start position:0% +good when it's been tended +already + + align:start position:0% +already + + + align:start position:0% +already +uh uh but ecologists know so much more + + align:start position:0% +uh uh but ecologists know so much more + + + align:start position:0% +uh uh but ecologists know so much more +about this + + align:start position:0% +about this + + + align:start position:0% +about this +now uh the knowledge of what to do about + + align:start position:0% +now uh the knowledge of what to do about + + + align:start position:0% +now uh the knowledge of what to do about +damned rivers and UND daming Rivers + + align:start position:0% +damned rivers and UND daming Rivers + + + align:start position:0% +damned rivers and UND daming Rivers +letting them throw + + align:start position:0% +letting them throw + + + align:start position:0% +letting them throw +freely uh is a major new ecological + + align:start position:0% +freely uh is a major new ecological + + + align:start position:0% +freely uh is a major new ecological +thrust + + align:start position:0% + + + + align:start position:0% + +um population growth is not + + align:start position:0% + + + + align:start position:0% + +how to + + align:start position:0% +how to + + + align:start position:0% +how to +be a good religious + + align:start position:0% +be a good religious + + + align:start position:0% +be a good religious +thing for the catholic's contraception + + align:start position:0% +thing for the catholic's contraception + + + align:start position:0% +thing for the catholic's contraception +is + + align:start position:0% +is + + + align:start position:0% +is +forbidden as it tries to convince the + + align:start position:0% +forbidden as it tries to convince the + + + align:start position:0% +forbidden as it tries to convince the +world that it has an Argentinian Pope + + align:start position:0% +world that it has an Argentinian Pope + + + align:start position:0% +world that it has an Argentinian Pope +who's a man who stood up against the + + align:start position:0% +who's a man who stood up against the + + + align:start position:0% +who's a man who stood up against the +military I'm not sure about that + + align:start position:0% +military I'm not sure about that + + + align:start position:0% +military I'm not sure about that +either uh but whether that's true or not + + align:start position:0% +either uh but whether that's true or not + + + align:start position:0% +either uh but whether that's true or not +uh modern man though he is he still + + align:start position:0% +uh modern man though he is he still + + + align:start position:0% +uh modern man though he is he still +believes in the sanctity of + + align:start position:0% +believes in the sanctity of + + + align:start position:0% +believes in the sanctity of +Life + + align:start position:0% + + + + align:start position:0% + +uh so new world must look to being able + + align:start position:0% +uh so new world must look to being able + + + align:start position:0% +uh so new world must look to being able +to cope with poverty at a mass + + align:start position:0% + + + + align:start position:0% + +scale urbaniza urbanized poverty not + + align:start position:0% +scale urbaniza urbanized poverty not + + + align:start position:0% +scale urbaniza urbanized poverty not +rural poverty although rural poverty + + align:start position:0% +rural poverty although rural poverty + + + align:start position:0% +rural poverty although rural poverty +will remain a + + align:start position:0% + + + + align:start position:0% + +phenomenon the people who + + align:start position:0% + + + + align:start position:0% + +will remain on the farm remain in small + + align:start position:0% +will remain on the farm remain in small + + + align:start position:0% +will remain on the farm remain in small +villages but they won't be a significant + + align:start position:0% +villages but they won't be a significant + + + align:start position:0% +villages but they won't be a significant +part of the + + align:start position:0% +part of the + + + align:start position:0% +part of the +population + + align:start position:0% + + + + align:start position:0% + +um that's the sad + + align:start position:0% +um that's the sad + + + align:start position:0% +um that's the sad +part I'm just going to read you a few + + align:start position:0% +part I'm just going to read you a few + + + align:start position:0% +part I'm just going to read you a few +figures + + align:start position:0% +figures + + + align:start position:0% +figures +from these + + align:start position:0% +from these + + + align:start position:0% +from these +texts the two + + align:start position:0% +texts the two + + + align:start position:0% +texts the two +Bas graphic texts + + align:start position:0% +Bas graphic texts + + + align:start position:0% +Bas graphic texts +are the exhibition book from the Koop + + align:start position:0% +are the exhibition book from the Koop + + + align:start position:0% +are the exhibition book from the Koop +Exhibition at the United Nation last + + align:start position:0% +Exhibition at the United Nation last + + + align:start position:0% +Exhibition at the United Nation last +year you should have seen the + + align:start position:0% +year you should have seen the + + + align:start position:0% +year you should have seen the +exhibition uh I had a little bit to do + + align:start position:0% +exhibition uh I had a little bit to do + + + align:start position:0% +exhibition uh I had a little bit to do +with + + align:start position:0% +with + + + align:start position:0% +with +it not saying so because I want to be + + align:start position:0% +it not saying so because I want to be + + + align:start position:0% +it not saying so because I want to be +proud and the Book of the + + align:start position:0% +proud and the Book of the + + + align:start position:0% +proud and the Book of the +Rockefeller foundation centy of the city + + align:start position:0% +Rockefeller foundation centy of the city + + + align:start position:0% +Rockefeller foundation centy of the city +both I refer to both of these in your + + align:start position:0% +both I refer to both of these in your + + + align:start position:0% +both I refer to both of these in your +reading they're the two best recent + + align:start position:0% +reading they're the two best recent + + + align:start position:0% +reading they're the two best recent +Publications I'm just going to quote + + align:start position:0% +Publications I'm just going to quote + + + align:start position:0% +Publications I'm just going to quote +here and there from + + align:start position:0% +here and there from + + + align:start position:0% +here and there from +them many of them are amped up about + + align:start position:0% + + + + align:start position:0% + +figures in a report on the future + + align:start position:0% +figures in a report on the future + + + align:start position:0% +figures in a report on the future +economy of India Goldman Sachs produc + + align:start position:0% +economy of India Goldman Sachs produc + + + align:start position:0% +economy of India Goldman Sachs produc +Pro s that city1 villages will continue + + align:start position:0% +Pro s that city1 villages will continue + + + align:start position:0% +Pro s that city1 villages will continue +to arrive in an Indian city every minute + + align:start position:0% +to arrive in an Indian city every minute + + + align:start position:0% +to arrive in an Indian city every minute +over the next 43 + + align:start position:0% +over the next 43 + + + align:start position:0% +over the next 43 +years 700 million people in + + align:start position:0% + + + + align:start position:0% + +all now how do you + + align:start position:0% +all now how do you + + + align:start position:0% +all now how do you +incubate 700 million people which is + + align:start position:0% +incubate 700 million people which is + + + align:start position:0% +incubate 700 million people which is +twice more than twice the population in + + align:start position:0% +twice more than twice the population in + + + align:start position:0% +twice more than twice the population in +the United States over 43 years we'll + + align:start position:0% +the United States over 43 years we'll + + + align:start position:0% +the United States over 43 years we'll +see I won't be around to + + align:start position:0% + + + + align:start position:0% + +Gerald k of Colombia + + align:start position:0% +Gerald k of Colombia + + + align:start position:0% +Gerald k of Colombia +University the world will have to build + + align:start position:0% +University the world will have to build + + + align:start position:0% +University the world will have to build +one city of 1 million people every 5 + + align:start position:0% +one city of 1 million people every 5 + + + align:start position:0% +one city of 1 million people every 5 +days for the next 42 + + align:start position:0% +days for the next 42 + + + align:start position:0% +days for the next 42 +years to accommodate the massive rural + + align:start position:0% +years to accommodate the massive rural + + + align:start position:0% +years to accommodate the massive rural +to City migration + + align:start position:0% + + + + align:start position:0% + +one city of 1 million every five days + + align:start position:0% +one city of 1 million every five days + + + align:start position:0% +one city of 1 million every five days +got a lot of work to + + align:start position:0% +got a lot of work to + + + align:start position:0% +got a lot of work to +do I'd be very happy in your pres + + align:start position:0% +do I'd be very happy in your pres + + + align:start position:0% +do I'd be very happy in your pres +profession you're going to be deluded + + align:start position:0% + + + + align:start position:0% + +by professional responsibilities + + align:start position:0% + + + + align:start position:0% + +now it goes on to talk about climate + + align:start position:0% +now it goes on to talk about climate + + + align:start position:0% +now it goes on to talk about climate +change 60% of the world cities are + + align:start position:0% +change 60% of the world cities are + + + align:start position:0% +change 60% of the world cities are +within walking distance of the + + align:start position:0% + + + + align:start position:0% + +sea the coastal provincial the coastal + + align:start position:0% +sea the coastal provincial the coastal + + + align:start position:0% +sea the coastal provincial the coastal +provinces of China experienced a net + + align:start position:0% +provinces of China experienced a net + + + align:start position:0% +provinces of China experienced a net +immigration of 17 million people in just + + align:start position:0% +immigration of 17 million people in just + + + align:start position:0% +immigration of 17 million people in just +the five years between 1995 and 2000 + + align:start position:0% +the five years between 1995 and 2000 + + + align:start position:0% +the five years between 1995 and 2000 +African half of these those cities + + align:start position:0% +African half of these those cities + + + align:start position:0% +African half of these those cities +including Lagos and they've shifted to + + align:start position:0% +including Lagos and they've shifted to + + + align:start position:0% +including Lagos and they've shifted to +Africa are in the low elevation coastal + + align:start position:0% +Africa are in the low elevation coastal + + + align:start position:0% +Africa are in the low elevation coastal +zone much of Mumbai India home to the + + align:start position:0% +zone much of Mumbai India home to the + + + align:start position:0% +zone much of Mumbai India home to the +largest slum settlement in the world is + + align:start position:0% +largest slum settlement in the world is + + + align:start position:0% +largest slum settlement in the world is +built essentially on + + align:start position:0% +built essentially on + + + align:start position:0% +built essentially on +landfill city is a t continuing Target + + align:start position:0% +landfill city is a t continuing Target + + + align:start position:0% +landfill city is a t continuing Target +for weather disasters + + align:start position:0% + + + + align:start position:0% + +we look in a minute at some few + + align:start position:0% + + + + align:start position:0% + +positives almost half the global + + align:start position:0% +positives almost half the global + + + align:start position:0% +positives almost half the global +population lives on less than $250 a + + align:start position:0% +population lives on less than $250 a + + + align:start position:0% +population lives on less than $250 a +day that is more than three billion + + align:start position:0% +day that is more than three billion + + + align:start position:0% +day that is more than three billion +people almost all in developing + + align:start position:0% +people almost all in developing + + + align:start position:0% +people almost all in developing +countries even more shocking the + + align:start position:0% +countries even more shocking the + + + align:start position:0% +countries even more shocking the +proportion of of people below the $250 + + align:start position:0% +proportion of of people below the $250 + + + align:start position:0% +proportion of of people below the $250 +per day poverty line has remained more + + align:start position:0% +per day poverty line has remained more + + + align:start position:0% +per day poverty line has remained more +or less constant between 1981 and + + align:start position:0% + + + + align:start position:0% + +2005 according to the World Bank the + + align:start position:0% +2005 according to the World Bank the + + + align:start position:0% +2005 according to the World Bank the +richest 20% of the world's population + + align:start position:0% +richest 20% of the world's population + + + align:start position:0% +richest 20% of the world's population +accounts for 76% of all consumption the + + align:start position:0% +accounts for 76% of all consumption the + + + align:start position:0% +accounts for 76% of all consumption the +bottom 40% accounts for only one 1.5% + + align:start position:0% + + + + align:start position:0% + +we want to look at I want you to look + + align:start position:0% +we want to look at I want you to look + + + align:start position:0% +we want to look at I want you to look +at some cases of + + align:start position:0% +at some cases of + + + align:start position:0% +at some cases of +optimism these are small + + align:start position:0% +optimism these are small + + + align:start position:0% +optimism these are small +situations which have improved through + + align:start position:0% +situations which have improved through + + + align:start position:0% +situations which have improved through +the ener of workers + + align:start position:0% +the ener of workers + + + align:start position:0% +the ener of workers +themselves before that this fits into + + align:start position:0% +themselves before that this fits into + + + align:start position:0% +themselves before that this fits into +the new paradigm which has emerged over + + align:start position:0% +the new paradigm which has emerged over + + + align:start position:0% +the new paradigm which has emerged over +the last few + + align:start position:0% +the last few + + + align:start position:0% +the last few +years in which theorists of developing + + align:start position:0% +years in which theorists of developing + + + align:start position:0% +years in which theorists of developing +countries and activists have + + align:start position:0% +countries and activists have + + + align:start position:0% +countries and activists have +argued that the only resource that + + align:start position:0% +argued that the only resource that + + + align:start position:0% +argued that the only resource that +people have is + + align:start position:0% +people have is + + + align:start position:0% +people have is +themselves that what we call Sweat + + align:start position:0% +themselves that what we call Sweat + + + align:start position:0% +themselves that what we call Sweat +Equity or human labor or + + align:start position:0% +Equity or human labor or + + + align:start position:0% +Equity or human labor or +human adapted human intelligence is all + + align:start position:0% +human adapted human intelligence is all + + + align:start position:0% +human adapted human intelligence is all +that people have so International + + align:start position:0% +that people have so International + + + align:start position:0% +that people have so International +Organization like slum dwellers + + align:start position:0% +Organization like slum dwellers + + + align:start position:0% +Organization like slum dwellers +International or the various Regional + + align:start position:0% +International or the various Regional + + + align:start position:0% +International or the various Regional +branches in India and in + + align:start position:0% +branches in India and in + + + align:start position:0% +branches in India and in +bang in Thailand and so + + align:start position:0% +bang in Thailand and so + + + align:start position:0% +bang in Thailand and so +on have the ambition to not sit around + + align:start position:0% +on have the ambition to not sit around + + + align:start position:0% +on have the ambition to not sit around +and wait for charity or benevolent + + align:start position:0% +and wait for charity or benevolent + + + align:start position:0% +and wait for charity or benevolent +dictatorship or any of other modalities + + align:start position:0% +dictatorship or any of other modalities + + + align:start position:0% +dictatorship or any of other modalities +but to harness to use their intelligence + + align:start position:0% +but to harness to use their intelligence + + + align:start position:0% +but to harness to use their intelligence +and + + align:start position:0% +and + + + align:start position:0% +and +their capacity as human beings to do + + align:start position:0% +their capacity as human beings to do + + + align:start position:0% +their capacity as human beings to do +something about it + + align:start position:0% + + + + align:start position:0% + +the problem with all of this yep can I + + align:start position:0% +the problem with all of this yep can I + + + align:start position:0% +the problem with all of this yep can I +read a + + align:start position:0% +read a + + + align:start position:0% +read a +quote sorry I can't hear um can I read a + + align:start position:0% +quote sorry I can't hear um can I read a + + + align:start position:0% +quote sorry I can't hear um can I read a +quote from one of the pap that I use for + + align:start position:0% +quote from one of the pap that I use for + + + align:start position:0% +quote from one of the pap that I use for +my paper yes please that is please + + align:start position:0% +my paper yes please that is please + + + align:start position:0% +my paper yes please that is please +somebody talk I'm tired of talking okay + + align:start position:0% +somebody talk I'm tired of talking okay + + + align:start position:0% +somebody talk I'm tired of talking okay +so it is in reference of the case of of + + align:start position:0% +so it is in reference of the case of of + + + align:start position:0% +so it is in reference of the case of of +the + + align:start position:0% +the + + + align:start position:0% +the +in South Africa in Cape Town K kich yeah + + align:start position:0% +in South Africa in Cape Town K kich yeah + + + align:start position:0% +in South Africa in Cape Town K kich yeah +K so uh this person who is the director + + align:start position:0% +K so uh this person who is the director + + + align:start position:0% +K so uh this person who is the director +of development services um Mr + + align:start position:0% +of development services um Mr + + + align:start position:0% +of development services um Mr +no talks in the conclusion of this paper + + align:start position:0% +no talks in the conclusion of this paper + + + align:start position:0% +no talks in the conclusion of this paper +about the people he says like talking in + + align:start position:0% +about the people he says like talking in + + + align:start position:0% +about the people he says like talking in +reference to yeah just read us the + + align:start position:0% +reference to yeah just read us the + + + align:start position:0% +reference to yeah just read us the +quote if we do not start immediately + + align:start position:0% +quote if we do not start immediately + + + align:start position:0% +quote if we do not start immediately +with meeting the local community's most + + align:start position:0% +with meeting the local community's most + + + align:start position:0% +with meeting the local community's most +urgent needs to lose our legitimacy as a + + align:start position:0% +urgent needs to lose our legitimacy as a + + + align:start position:0% +urgent needs to lose our legitimacy as a +public administration and if we do not + + align:start position:0% +public administration and if we do not + + + align:start position:0% +public administration and if we do not +do it in the most participatory way + + align:start position:0% +do it in the most participatory way + + + align:start position:0% +do it in the most participatory way +possible and this is the most important + + align:start position:0% +possible and this is the most important + + + align:start position:0% +possible and this is the most important +part we will waste the most important + + align:start position:0% +part we will waste the most important + + + align:start position:0% +part we will waste the most important +Capital we have the dedication of the + + align:start position:0% +Capital we have the dedication of the + + + align:start position:0% +Capital we have the dedication of the +people themselves and their will for + + align:start position:0% +people themselves and their will for + + + align:start position:0% +people themselves and their will for +change + + align:start position:0% +change + + + align:start position:0% +change +good I think one of the most impressive + + align:start position:0% +good I think one of the most impressive + + + align:start position:0% +good I think one of the most impressive +examples so far has been the + + align:start position:0% +examples so far has been the + + + align:start position:0% +examples so far has been the +300,000 person suburb of sou Paro 17 + + align:start position:0% +300,000 person suburb of sou Paro 17 + + + align:start position:0% +300,000 person suburb of sou Paro 17 +kilometers from the center of sa Pao + + align:start position:0% +kilometers from the center of sa Pao + + + align:start position:0% +kilometers from the center of sa Pao +called + + align:start position:0% + + + + align:start position:0% + +diadema fortunately they've published a + + align:start position:0% +diadema fortunately they've published a + + + align:start position:0% +diadema fortunately they've published a +book called diadema in the informal + + align:start position:0% +book called diadema in the informal + + + align:start position:0% +book called diadema in the informal +City I don't know I don't think the + + align:start position:0% +City I don't know I don't think the + + + align:start position:0% +City I don't know I don't think the +library has a copy of this + + align:start position:0% +library has a copy of this + + + align:start position:0% +library has a copy of this +book uh it's a case detailed case study + + align:start position:0% +book uh it's a case 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position:0% +decline all of this happens new housing +is built old housing is renewed people + + align:start position:0% +is built old housing is renewed people + + + align:start position:0% +is built old housing is renewed people +are part of a process + + align:start position:0% +are part of a process + + + align:start position:0% +are part of a process +which teaching in + + align:start position:0% +which teaching in + + + align:start position:0% +which teaching in +schools about crime + + align:start position:0% +schools about crime + + + align:start position:0% +schools about crime +guns are taken away at school I mean + + align:start position:0% +guns are taken away at school I mean + + + align:start position:0% +guns are taken away at school I mean +whole network of things happen which + + align:start position:0% +whole network of things happen which + + + align:start position:0% +whole network of things happen which +probably characterize a good town and + + align:start 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position:0% +modern world you've got to buy a house +your parents were too old to uneducated + + align:start position:0% +your parents were too old to uneducated + + + align:start position:0% +your parents were too old to uneducated +to in this kind of + + align:start position:0% +to in this kind of + + + align:start position:0% +to in this kind of +game where do you + + align:start position:0% +game where do you + + + align:start position:0% +game where do you +learn where is the social + + align:start position:0% +learn where is the social + + + align:start position:0% +learn where is the social +instruction this is in a middle class + + align:start position:0% + + + + align:start position:0% + +situation when my son bought an + + align:start position:0% +situation when my son bought an + + + align:start position:0% +situation when my son bought an +apartment in New York he was lucky to + + align:start position:0% +apartment in New York he was lucky to + + + align:start position:0% +apartment in New York he was lucky to +have a wife who was an + + align:start position:0% +have a wife who was an + + + align:start position:0% +have a wife who was an +accountant so he could stop remain being + + align:start position:0% +accountant so he could stop remain being + + + align:start position:0% +accountant so he could stop remain being +a theorist while his wife took care of + + align:start position:0% +a theorist while his wife took care of + + + align:start position:0% +a theorist while his wife took care of +all the financial stuff it's a wonderful + + align:start position:0% +all the financial stuff it's a wonderful + + + align:start position:0% +all the financial stuff it's a wonderful +combination but not many people luy to + + align:start position:0% +combination but not many people luy to + + + align:start position:0% +combination but not many people luy to +be very to + + align:start position:0% + + + + align:start position:0% + +accountant + + align:start position:0% + + + + align:start position:0% + +um so that piece deals with the + + align:start position:0% +um so that piece deals with the + + + align:start position:0% +um so that piece deals with the +enormous capacity for micro Finance to + + align:start position:0% +enormous capacity for micro Finance to + + + align:start position:0% +enormous capacity for micro Finance to +generate both a sense of + + align:start position:0% +generate both a sense of + + + align:start position:0% +generate both a sense of +trust it's it's analogous to the + + align:start position:0% +trust it's it's analogous to the + + + align:start position:0% +trust it's it's analogous to the +invention of the mortgage system in + + align:start position:0% +invention of the mortgage system in + + + align:start position:0% +invention of the mortgage system in +England in + + align:start position:0% +England in + + + align:start position:0% +England in +1830 the mortgage system took the + + align:start position:0% +1830 the mortgage system took the + + + align:start position:0% +1830 the mortgage system took the +business of borrowing money away from a + + align:start position:0% +business of borrowing money away from a + + + align:start position:0% +business of borrowing money away from a +crooked + + align:start position:0% +crooked + + + align:start position:0% +crooked +landowner person put it in the hands of + + align:start position:0% +landowner person put it in the hands of + + + align:start position:0% +landowner person put it in the hands of +a + + align:start position:0% +a + + + align:start position:0% +a +bank a bank May crook but it has to + + align:start position:0% +bank a bank May crook but it has to + + + align:start position:0% +bank a bank May crook but it has to +crook on a very much larger scale than + + align:start position:0% +crook on a very much larger scale than + + + align:start position:0% +crook on a very much larger scale than +you + + align:start position:0% +you + + + align:start position:0% +you +uh and uh the mortgage + + align:start position:0% +uh and uh the mortgage + + + align:start position:0% +uh and uh the mortgage +system in enable trust in the purchase + + align:start position:0% +system in enable trust in the purchase + + + align:start position:0% +system in enable trust in the purchase +of housing in a way that had never + + align:start position:0% +of housing in a way that had never + + + align:start position:0% +of housing in a way that had never +existed before you're always at the + + align:start position:0% +existed before you're always at the + + + align:start position:0% +existed before you're always at the +behest of your + + align:start position:0% + + + + align:start position:0% + +landlord you get the stories of + + align:start position:0% +landlord you get the stories of + + + align:start position:0% +landlord you get the stories of +La La travat in + + align:start position:0% +La La travat in + + + align:start position:0% +La La travat in +Paris artist living in the top floor of + + align:start position:0% +Paris artist living in the top floor of + + + align:start position:0% +Paris artist living in the top floor of +a houseman + + align:start position:0% +a houseman + + + align:start position:0% +a houseman +Boulevard hour and the knock on the door + + align:start position:0% +Boulevard hour and the knock on the door + + + align:start position:0% +Boulevard hour and the knock on the door +saying you haven't paid your rent for + + align:start position:0% +saying you haven't paid your rent for + + + align:start position:0% +saying you haven't paid your rent for +the last few months what are you going + + align:start position:0% +the last few months what are you going + + + align:start position:0% +the last few months what are you going +to do and you're starving of + + align:start position:0% + + + + align:start position:0% + +tuberculosis so that image is no longer + + align:start position:0% +tuberculosis so that image is no longer + + + align:start position:0% +tuberculosis so that image is no longer +present or not largely present in the + + align:start position:0% +present or not largely present in the + + + align:start position:0% +present or not largely present in the +mortgage system the micro Finance system + + align:start position:0% +mortgage system the micro Finance system + + + align:start position:0% +mortgage system the micro Finance system +is nous to the mortgage system in the + + align:start position:0% +is nous to the mortgage system in the + + + align:start position:0% +is nous to the mortgage system in the +building of trust 98% of the loans in + + align:start position:0% +building of trust 98% of the loans in + + + align:start position:0% +building of trust 98% of the loans in +gendered uh in India and micro Finance + + align:start position:0% +gendered uh in India and micro Finance + + + align:start position:0% +gendered uh in India and micro Finance +have been + + align:start position:0% + + + + align:start position:0% + +repaid which is an incredible statistic + + align:start position:0% +repaid which is an incredible statistic + + + align:start position:0% +repaid which is an incredible statistic +given the general condition of + + align:start position:0% +given the general condition of + + + align:start position:0% +given the general condition of +poverty and the law lawlessness + + align:start position:0% +poverty and the law lawlessness + + + align:start position:0% +poverty and the law lawlessness +lawlessness that it + + align:start position:0% + + + + align:start position:0% + +insinuate okay + + align:start position:0% + + + + align:start position:0% + +the trouble with seeing good things + + align:start position:0% + + + + align:start position:0% + +happen is that sometimes good things + + align:start position:0% +happen is that sometimes good things + + + align:start position:0% +happen is that sometimes good things +need to happen at a very large scale for + + align:start position:0% +need to happen at a very large scale for + + + align:start position:0% +need to happen at a very large scale for +them really to make a big + + align:start position:0% +them really to make a big + + + align:start position:0% +them really to make a big +impact scaling up diadema is + + align:start position:0% +impact scaling up diadema is + + + align:start position:0% +impact scaling up diadema is +difficult how do you get Tang diadema to + + align:start position:0% +difficult how do you get Tang diadema to + + + align:start position:0% +difficult how do you get Tang diadema to +occur in + + align:start position:0% +occur in + + + align:start position:0% +occur in +Tanzania + + align:start position:0% +Tanzania + + + align:start position:0% +Tanzania +when in the Congo + + align:start position:0% + + + + align:start position:0% + +in + + align:start position:0% + + + + align:start position:0% + +darur but at least they are small model + + align:start position:0% +darur but at least they are small model + + + align:start position:0% +darur but at least they are small model +now + + align:start position:0% + + + + align:start position:0% + +maybe we will not need massive + + align:start position:0% +maybe we will not need massive + + + align:start position:0% +maybe we will not need massive +International + + align:start position:0% +International + + + align:start position:0% +International +cooperation to generate new + + align:start position:0% +cooperation to generate new + + + align:start position:0% +cooperation to generate new +models I despair given the track rle + + align:start position:0% +models I despair given the track rle + + + align:start position:0% +models I despair given the track rle +sort + + align:start position:0% +sort + + + align:start position:0% +sort +of United League of Nations United + + align:start position:0% +of United League of Nations United + + + align:start position:0% +of United League of Nations United +Nations atomic + + align:start position:0% +Nations atomic + + + align:start position:0% +Nations atomic +energy and + + align:start position:0% +energy and + + + align:start position:0% +energy and +uh climate carbon control + + align:start position:0% + + + + align:start position:0% + +agreements as long as you ask the poor + + align:start position:0% + + + + align:start position:0% + +world to subdue the economic industrial + + align:start position:0% +world to subdue the economic industrial + + + align:start position:0% +world to subdue the economic industrial +activity on the grounds that they're + + align:start position:0% +activity on the grounds that they're + + + align:start position:0% +activity on the grounds that they're +contributing to climate + + align:start position:0% +contributing to climate + + + align:start position:0% +contributing to climate +change they rightfully can point to the + + align:start position:0% +change they rightfully can point to the + + + align:start position:0% +change they rightfully can point to the +United States having you built up its + + align:start position:0% +United States having you built up its + + + align:start position:0% +United States having you built up its +economy through smoke and + + align:start position:0% +economy through smoke and + + + align:start position:0% +economy through smoke and +railroads and uh now being the + + align:start position:0% + + + + align:start position:0% + +largest client + + align:start position:0% +largest client + + + align:start position:0% +largest client +for carbon production in the world comp + + align:start position:0% +for carbon production in the world comp + + + align:start position:0% +for carbon production in the world comp +complaining even the United States + + align:start position:0% +complaining even the United States + + + align:start position:0% +complaining even the United States +wouldn't sign the Kyoto agreement and + + align:start position:0% +wouldn't sign the Kyoto agreement and + + + align:start position:0% +wouldn't sign the Kyoto agreement and +Copenhagen got no + + align:start position:0% +Copenhagen got no + + + align:start position:0% +Copenhagen got no +further + + align:start position:0% + + + + align:start position:0% + +so I leave you + + align:start position:0% +so I leave you + + + align:start position:0% +so I leave you +with optimism and a kind of forboding + + align:start position:0% +with optimism and a kind of forboding + + + align:start position:0% +with optimism and a kind of forboding +the combination of climate change and + + align:start position:0% +the combination of climate change and + + + align:start position:0% +the combination of climate change and +poverty is a disastrous + + align:start position:0% +poverty is a disastrous + + + align:start position:0% +poverty is a disastrous +combination its effects + + align:start position:0% +combination its effects + + + align:start position:0% +combination its effects +will be particularly felt in waterborne + + align:start position:0% +will be particularly felt in waterborne + + + align:start position:0% +will be particularly felt in waterborne +cities like + + align:start position:0% +cities like + + + align:start position:0% +cities like +Dhaka in the imaya + + align:start position:0% +Dhaka in the imaya + + + align:start position:0% +Dhaka in the imaya +region because the imas depend control + + align:start position:0% +region because the imas depend control + + + align:start position:0% +region because the imas depend control +very much of the flood and drought + + align:start position:0% +very much of the flood and drought + + + align:start position:0% +very much of the flood and drought +Cycles in the areas it + + align:start position:0% + + + + align:start position:0% + +reaches wealth will be able to withstand + + align:start position:0% +reaches wealth will be able to withstand + + + align:start position:0% +reaches wealth will be able to withstand +climate + + align:start position:0% +climate + + + align:start position:0% +climate +change but by and + + align:start position:0% +change but by and + + + align:start position:0% +change but by and +large it'll modify + + align:start position:0% +large it'll modify + + + align:start position:0% +large it'll modify +Behavior + + align:start position:0% + + + + align:start position:0% + +but it will increase migration pressure + + align:start position:0% +but it will increase migration pressure + + + align:start position:0% +but it will increase migration pressure +on the United States and on Europe and + + align:start position:0% +on the United States and on Europe and + + + align:start position:0% +on the United States and on Europe and +on the established + + align:start position:0% +on the established + + + align:start position:0% +on the established +countries I don't think for the United + + align:start position:0% +countries I don't think for the United + + + align:start position:0% +countries I don't think for the United +States television could stand having + + align:start position:0% +States television could stand having + + + align:start position:0% +States television could stand having +children floating in + + align:start position:0% +children floating in + + + align:start position:0% +children floating in +water in Bangladesh without changing its + + align:start position:0% +water in Bangladesh without changing its + + + align:start position:0% +water in Bangladesh without changing its +migration + + align:start position:0% +migration + + + align:start position:0% +migration +attitudes migration + + align:start position:0% +attitudes migration + + + align:start position:0% +attitudes migration +is now under debate in this + + align:start position:0% +is now under debate in this + + + align:start position:0% +is now under debate in this +country as a migrant I'm myself of + + align:start position:0% +country as a migrant I'm myself of + + + align:start position:0% +country as a migrant I'm myself of +course I'm in favor of + + align:start position:0% + + + + align:start position:0% + +migration statistically we have built + + align:start position:0% +migration statistically we have built + + + align:start position:0% +migration statistically we have built +this + + align:start position:0% + + + + align:start position:0% + +country there are more foreign born + + align:start position:0% +country there are more foreign born + + + align:start position:0% +country there are more foreign born +professors and in the school than the + + align:start position:0% +professors and in the school than the + + + align:start position:0% +professors and in the school than the +are Americans I think I don't know + + align:start position:0% +are Americans I think I don't know + + + align:start position:0% +are Americans I think I don't know +there'll be one L + + align:start position:0% + + + + align:start position:0% + +soon + + align:start position:0% +soon + + + align:start position:0% +soon +um these are all trajectories for the + + align:start position:0% +um these are all trajectories for the + + + align:start position:0% +um these are all trajectories for the +long future but not so long it's already + + align:start position:0% +long future but not so long it's already + + + align:start position:0% +long future but not so long it's already +2013 some of these projections of + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +uh and there's no rest but except for + + align:start position:0% +uh and there's no rest but except for + + + align:start position:0% +uh and there's no rest but except for +the + + align:start position:0% +the + + + align:start position:0% +the +people who + + align:start position:0% + + + + align:start position:0% + +believe that science has no way of + + align:start position:0% +believe that science has no way of + + + align:start position:0% +believe that science has no way of +forecasting + + align:start position:0% +forecasting + + + align:start position:0% +forecasting +change anyway these are dull + + align:start position:0% + + + + align:start position:0% + +topics there's not much that you can go + + align:start position:0% +topics there's not much that you can go + + + align:start position:0% +topics there's not much that you can go +out and do about it except by yourself a + + align:start position:0% +out and do about it except by yourself a + + + align:start position:0% +out and do about it except by yourself a +hybrid car and eat + + align:start position:0% + + + + align:start position:0% + +green + + align:start position:0% +green + + + align:start position:0% +green +right the trouble with climate change + + align:start position:0% +right the trouble with climate change + + + align:start position:0% +right the trouble with climate change +it's too invisible + + align:start position:0% +it's too invisible + + + align:start position:0% +it's too invisible +it's not dramatic enough to stir the + + align:start position:0% +it's not dramatic enough to stir the + + + align:start position:0% +it's not dramatic enough to stir the +public + + align:start position:0% + + + + align:start position:0% + +conscience you think of the German + + align:start position:0% +conscience you think of the German + + + align:start position:0% +conscience you think of the German +Holocaust in 1936 when Berlin had the + + align:start position:0% +Holocaust in 1936 when Berlin had the + + + align:start position:0% +Holocaust in 1936 when Berlin had the +Olympic Games there were concentration + + align:start position:0% +Olympic Games there were concentration + + + align:start position:0% +Olympic Games there were concentration +camps within miles on the outskirts of + + align:start position:0% +camps within miles on the outskirts of + + + align:start position:0% +camps within miles on the outskirts of +of + + align:start position:0% +of + + + align:start position:0% +of +Berlin Avery brandage the leader of the + + align:start position:0% +Berlin Avery brandage the leader of the + + + align:start position:0% +Berlin Avery brandage the leader of the +American + + align:start position:0% +American + + + align:start position:0% +American +delegation castigated New York Jews in + + align:start position:0% +delegation castigated New York Jews in + + + align:start position:0% +delegation castigated New York Jews in +the New York Times for making a story of + + align:start position:0% + + + + align:start position:0% + +it the United States refused to take in + + align:start position:0% +it the United States refused to take in + + + align:start position:0% +it the United States refused to take in +a Bo of people from fleeing the + + align:start position:0% +a Bo of people from fleeing the + + + align:start position:0% +a Bo of people from fleeing the +Holocaust because they were they weren't + + align:start position:0% +Holocaust because they were they weren't + + + align:start position:0% +Holocaust because they were they weren't +legal citizens and so on and so + + align:start position:0% +legal citizens and so on and so + + + align:start position:0% +legal citizens and so on and so +on the demonstration of the Holocaust + + align:start position:0% +on the demonstration of the Holocaust + + + align:start position:0% +on the demonstration of the Holocaust +over 10 + + align:start position:0% +over 10 + + + align:start position:0% +over 10 +years of visibility + + align:start position:0% + + + + align:start position:0% + +was neglected by almost + + align:start position:0% + + + + align:start position:0% + +everybody I don't to have much trust in + + align:start position:0% +everybody I don't to have much trust in + + + align:start position:0% +everybody I don't to have much trust in +the Universal + + align:start position:0% +the Universal + + + align:start position:0% +the Universal +Consciousness the world doesn't have any + + align:start position:0% +Consciousness the world doesn't have any + + + align:start position:0% +Consciousness the world doesn't have any +conscience it only has selective + + align:start position:0% +conscience it only has selective + + + align:start position:0% +conscience it only has selective +Consciousness often in service of + + align:start position:0% +Consciousness often in service of + + + align:start position:0% +Consciousness often in service of +private good and National good the more + + align:start position:0% +private good and National good the more + + + align:start position:0% +private good and National good the more +Boston goes on about being strong the + + align:start position:0% +Boston goes on about being strong the + + + align:start position:0% +Boston goes on about being strong the +more I read kind of perverse + + align:start position:0% +more I read kind of perverse + + + align:start position:0% +more I read kind of perverse +nationalism creeping + + align:start position:0% +nationalism creeping + + + align:start position:0% +nationalism creeping +in again identifying yourself as able to + + align:start position:0% +in again identifying yourself as able to + + + align:start position:0% +in again identifying yourself as able to +be a Goliath + + align:start position:0% +be a Goliath + + + align:start position:0% +be a Goliath +withstanding the treachery of two young + + align:start position:0% + + + + align:start position:0% + +men anyway these are my personal + + align:start position:0% +men anyway these are my personal + + + align:start position:0% +men anyway these are my personal +positions + + align:start position:0% +positions + + + align:start position:0% +positions +U I don't know what you think about your + + align:start position:0% +U I don't know what you think about your + + + align:start position:0% +U I don't know what you think about your +future + + align:start position:0% + + + + align:start position:0% + +I grew up with the advantage of being a + + align:start position:0% +I grew up with the advantage of being a + + + align:start position:0% +I grew up with the advantage of being a +modernist and the world was very + + align:start position:0% +modernist and the world was very + + + align:start position:0% +modernist and the world was very +attractive only we could slay all of + + align:start position:0% +attractive only we could slay all of + + + align:start position:0% +attractive only we could slay all of +those 19th century + + align:start position:0% +those 19th century + + + align:start position:0% +those 19th century +Devils it's amazing to me to know that + + align:start position:0% +Devils it's amazing to me to know that + + + align:start position:0% +Devils it's amazing to me to know that +to + + align:start position:0% +to + + + align:start position:0% +to +think that I studied mod modern + + align:start position:0% +think that I studied mod modern + + + align:start position:0% +think that I studied mod modern +architectural history with secred Gideon + + align:start position:0% +architectural history with secred Gideon + + + align:start position:0% +architectural history with secred Gideon +at + + align:start position:0% +at + + + align:start position:0% +at +Harvard and Gideon in all of his + + align:start position:0% +Harvard and Gideon in all of his + + + align:start position:0% +Harvard and Gideon in all of his +teaching to us after all he wrote + + align:start position:0% +teaching to us after all he wrote + + + align:start position:0% +teaching to us after all he wrote +SpaceTime and + + align:start position:0% +SpaceTime and + + + align:start position:0% +SpaceTime and +architecture which was a big book at my + + align:start position:0% + + + + align:start position:0% + +day Gideon only referred to the terrible + + align:start position:0% +day Gideon only referred to the terrible + + + align:start position:0% +day Gideon only referred to the terrible +ruling Taste of the 19th century that it + + align:start position:0% +ruling Taste of the 19th century that it + + + align:start position:0% +ruling Taste of the 19th century that it +was producing architects of any + + align:start position:0% +was producing architects of any + + + align:start position:0% +was producing architects of any +consequence he never mentioned + + align:start position:0% +consequence he never mentioned + + + align:start position:0% +consequence he never mentioned +in anything to do with the + + align:start position:0% +in anything to do with the + + + align:start position:0% +in anything to do with the +city not in all of his evocation class + + align:start position:0% +city not in all of his evocation class + + + align:start position:0% +city not in all of his evocation class +after class of + + align:start position:0% + + + + align:start position:0% + +modernism it's sad or it's attractive + + align:start position:0% +modernism it's sad or it's attractive + + + align:start position:0% +modernism it's sad or it's attractive +that we've grown + + align:start position:0% + + + + align:start position:0% + +up at least I think we've grown + + align:start position:0% +up at least I think we've grown + + + align:start position:0% +up at least I think we've grown +up we're beginning to grow + + align:start position:0% +up we're beginning to grow + + + align:start position:0% +up we're beginning to grow +up we talk about architecture being + + align:start position:0% +up we talk about architecture being + + + align:start position:0% +up we talk about architecture being +Inseparable from urbanism now and yet we + + align:start position:0% +Inseparable from urbanism now and yet we + + + align:start position:0% +Inseparable from urbanism now and yet we +don't teach Urban + + align:start position:0% +don't teach Urban + + + align:start position:0% +don't teach Urban +at + + align:start position:0% +at + + + align:start position:0% +at +all this is the closest class you're + + align:start position:0% +all this is the closest class you're + + + align:start position:0% +all this is the closest class you're +going to get to dealing with urbanist + + align:start position:0% +going to get to dealing with urbanist + + + align:start position:0% +going to get to dealing with urbanist +and I know + + align:start position:0% +and I know + + + align:start position:0% +and I know +historian and uses sneaky me method to + + align:start position:0% +historian and uses sneaky me method to + + + align:start position:0% +historian and uses sneaky me method to +introduce + + align:start position:0% + + + + align:start position:0% + +history not being sure of the detailed + + align:start position:0% +history not being sure of the detailed + + + align:start position:0% +history not being sure of the detailed +facts + + align:start position:0% +facts + + + align:start position:0% +facts +myself I have to conjure + + align:start position:0% +myself I have to conjure + + + align:start position:0% +myself I have to conjure +up clever tricky ways of convincing + + align:start position:0% +up clever tricky ways of convincing + + + align:start position:0% +up clever tricky ways of convincing +you um there's no architectural + + align:start position:0% +you um there's no architectural + + + align:start position:0% +you um there's no architectural +curriculum in the world that doesn't + + align:start position:0% +curriculum in the world that doesn't + + + align:start position:0% +curriculum in the world that doesn't +require architectural history as a major + + align:start position:0% +require architectural history as a major + + + align:start position:0% +require architectural history as a major +element of its + + align:start position:0% + + + + align:start position:0% + +discourse there's no field in the + + align:start position:0% +discourse there's no field in the + + + align:start position:0% +discourse there's no field in the +Arts literature + + align:start position:0% +Arts literature + + + align:start position:0% +Arts literature +painting + + align:start position:0% +painting + + + align:start position:0% +painting +music it doesn't require an + + align:start position:0% +music it doesn't require an + + + align:start position:0% +music it doesn't require an +understanding of its predecessors + + align:start position:0% +understanding of its predecessors + + + align:start position:0% +understanding of its predecessors +you can't you can play the horn as much + + align:start position:0% +you can't you can play the horn as much + + + align:start position:0% +you can't you can play the horn as much +as you want to but you better know + + align:start position:0% +as you want to but you better know + + + align:start position:0% +as you want to but you better know +mide or at least one Symphony of msart + + align:start position:0% +mide or at least one Symphony of msart + + + align:start position:0% +mide or at least one Symphony of msart +in your + + align:start position:0% +in your + + + align:start position:0% +in your +exams you can be an architectural + + align:start position:0% +exams you can be an architectural + + + align:start position:0% +exams you can be an architectural +graduate with not knowing one city + + align:start position:0% +graduate with not knowing one city + + + align:start position:0% +graduate with not knowing one city +plan in + + align:start position:0% +plan in + + + align:start position:0% +plan in +history City plans are difficult to + + align:start position:0% +history City plans are difficult to + + + align:start position:0% +history City plans are difficult to +remember and I wouldn't want to be given + + align:start position:0% +remember and I wouldn't want to be given + + + align:start position:0% +remember and I wouldn't want to be given +an exam asking me to draw 10 City plans + + align:start position:0% +an exam asking me to draw 10 City plans + + + align:start position:0% +an exam asking me to draw 10 City plans +shandar is easy Manhattan is + + align:start position:0% +shandar is easy Manhattan is + + + align:start position:0% +shandar is easy Manhattan is +easy Once you + + align:start position:0% +easy Once you + + + align:start position:0% +easy Once you +depart + + align:start position:0% +depart + + + align:start position:0% +depart +anyway so go and + + align:start position:0% +anyway so go and + + + align:start position:0% +anyway so go and +uh finish your + + align:start position:0% +uh finish your + + + align:start position:0% +uh finish your +work have a great + + align:start position:0% +work have a great + + + align:start position:0% +work have a great +summer and uh I'll see you on Thursday + + align:start position:0% +summer and uh I'll see you on Thursday + + + align:start position:0% +summer and uh I'll see you on Thursday +if you have the + + align:start position:0% +if you have the + + + align:start position:0% +if you have the +time so much for the world + + align:start position:0% +time so much for the world + + + align:start position:0% +time so much for the world +of develop Ricardo what do you think is + + align:start position:0% +of develop Ricardo what do you think is + + + align:start position:0% +of develop Ricardo what do you think is +going to happen in + + align:start position:0% + + + + align:start position:0% + +Mexico now in relation to our general + + align:start position:0% +Mexico now in relation to our general + + + align:start position:0% +Mexico now in relation to our general +discussion this morning I think there's + + align:start position:0% +discussion this morning I think there's + + + align:start position:0% +discussion this morning I think there's +a there's a lot of discussion around + + align:start position:0% +a there's a lot of discussion around + + + align:start position:0% +a there's a lot of discussion around +Mexico City but I think that most people + + align:start position:0% +Mexico City but I think that most people + + + align:start position:0% +Mexico City but I think that most people +tend to neglect what's happening in the + + align:start position:0% +tend to neglect what's happening in the + + + align:start position:0% +tend to neglect what's happening in the +midsize cities in + + align:start position:0% +midsize cities in + + + align:start position:0% +midsize cities in +Mexico uh so not not not not necessarily + + align:start position:0% +Mexico uh so not not not not necessarily + + + align:start position:0% +Mexico uh so not not not not necessarily +places like + + align:start position:0% +places like + + + align:start position:0% +places like +monoa but actually places + + align:start position:0% + + + + align:start position:0% + +like which are part of the backb of + + align:start position:0% +like which are part of the backb of + + + align:start position:0% +like which are part of the backb of +where Mexican lives places like + + align:start position:0% +where Mexican lives places like + + + align:start position:0% +where Mexican lives places like +or + + align:start position:0% +or + + + align:start position:0% +or +and there fear that they're often + + align:start position:0% +and there fear that they're often + + + align:start position:0% +and there fear that they're often +thought of + + align:start position:0% +thought of + + + align:start position:0% +thought of +as basically an + + align:start position:0% + + + + align:start position:0% + +afterthought but you see cities there + + align:start position:0% +afterthought but you see cities there + + + align:start position:0% +afterthought but you see cities there +like U like Tijuana + + align:start position:0% +like U like Tijuana + + + align:start position:0% +like U like Tijuana +like who are really experimenting and + + align:start position:0% +like who are really experimenting and + + + align:start position:0% +like who are really experimenting and +pushing things forward for their + + align:start position:0% +pushing things forward for their + + + align:start position:0% +pushing things forward for their +population is very interesting not + + align:start position:0% +population is very interesting not + + + align:start position:0% +population is very interesting not +necessarily following the + + align:start position:0% + + + + align:start position:0% + +modelx is there any movement that that + + align:start position:0% +modelx is there any movement that that + + + align:start position:0% +modelx is there any movement that that +combines these + + align:start position:0% +combines these + + + align:start position:0% +combines these +efforts yeah yeah there are some + + align:start position:0% +efforts yeah yeah there are some + + + align:start position:0% +efforts yeah yeah there are some +programs okay there are some programs by + + align:start position:0% +programs okay there are some programs by + + + align:start position:0% +programs okay there are some programs by +the federal government uh + + align:start position:0% +the federal government uh + + + align:start position:0% +the federal government uh +called + + align:start position:0% +called + + + align:start position:0% +called +suain + + align:start position:0% +suain + + + align:start position:0% +suain +development uh and within each City uh + + align:start position:0% +development uh and within each City uh + + + align:start position:0% +development uh and within each City uh +there tends to be a local grassroot + + align:start position:0% +there tends to be a local grassroot + + + align:start position:0% +there tends to be a local grassroot +movements that are sort of pushing with + + align:start position:0% +movements that are sort of pushing with + + + align:start position:0% +movements that are sort of pushing with +thean + + align:start position:0% +thean + + + align:start position:0% +thean +development uh D it's easier if you just + + align:start position:0% +development uh D it's easier if you just + + + align:start position:0% +development uh D it's easier if you just +look at + + align:start position:0% +look at + + + align:start position:0% +look at +D it's holy sustainable Urban + + align:start position:0% +D it's holy sustainable Urban + + + align:start position:0% +D it's holy sustainable Urban +Development holy sustainable Urban + + align:start position:0% +Development holy sustainable Urban + + + align:start position:0% +Development holy sustainable Urban +Development + + align:start position:0% +Development + + + align:start position:0% +Development +yeah it's a it's a program from the + + align:start position:0% +yeah it's a it's a program from the + + + align:start position:0% +yeah it's a it's a program from the +federal government that finances housing + + align:start position:0% +federal government that finances housing + + + align:start position:0% +federal government that finances housing +because right now was driv about 950,000 + + align:start position:0% +because right now was driv about 950,000 + + + align:start position:0% +because right now was driv about 950,000 +a + + align:start position:0% +a + + + align:start position:0% +a +year so there is a lot + + align:start position:0% +year so there is a lot + + + align:start position:0% +year so there is a lot +there it's interesting times there I've + + align:start position:0% +there it's interesting times there I've + + + align:start position:0% +there it's interesting times there I've +in many places + + align:start position:0% + + + + align:start position:0% + +Amer + + align:start position:0% +Amer + + + align:start position:0% +Amer +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +well need hope + + align:start position:0% + + + + align:start position:0% + +this class was not to depress + + align:start position:0% +this class was not to depress + + + align:start position:0% +this class was not to depress +you I say this class was not designed to + + align:start position:0% +you I say this class was not designed to + + + align:start position:0% +you I say this class was not designed to +depress + + align:start position:0% +depress + + + align:start position:0% +depress +you on the contrary you could simply say + + align:start position:0% +you on the contrary you could simply say + + + align:start position:0% +you on the contrary you could simply say +over 10,000 years we' achieved more than + + align:start position:0% +over 10,000 years we' achieved more than + + + align:start position:0% +over 10,000 years we' achieved more than +400 million before + + align:start position:0% +400 million before + + + align:start position:0% +400 million before +us and there's many there many + + align:start position:0% + + + + align:start position:0% + +benefits that have come from heriz in + + align:start position:0% +benefits that have come from heriz in + + + align:start position:0% +benefits that have come from heriz in +our + + align:start position:0% + + + + align:start position:0% + +time maybe it'll continue but I + + align:start position:0% +time maybe it'll continue but I + + + align:start position:0% +time maybe it'll continue but I +hopefully less selectively than it's + + align:start position:0% +hopefully less selectively than it's + + + align:start position:0% +hopefully less selectively than it's +been up + + align:start position:0% +been up + + + align:start position:0% +been up +now there's + + align:start position:0% + + + + align:start position:0% + +no there's no + + align:start position:0% +no there's no + + + align:start position:0% +no there's no +law that asks you to be a social + + align:start position:0% +law that asks you to be a social + + + align:start position:0% +law that asks you to be a social +animal you can't drive into somebody + + align:start position:0% +animal you can't drive into somebody + + + align:start position:0% +animal you can't drive into somebody +else's G + + align:start position:0% +else's G + + + align:start position:0% +else's G +pardon and get away with + + align:start position:0% +pardon and get away with + + + align:start position:0% +pardon and get away with +it + + align:start position:0% +it + + + align:start position:0% +it +but there's nothing that requires you to + + align:start position:0% +but there's nothing that requires you to + + + align:start position:0% +but there's nothing that requires you to +see your own condition in the light of + + align:start position:0% +see your own condition in the light of + + + align:start position:0% +see your own condition in the light of +other people's less + + align:start position:0% +other people's less + + + align:start position:0% +other people's less +fortunate charity was invented by the + + align:start position:0% +fortunate charity was invented by the + + + align:start position:0% +fortunate charity was invented by the +British well charity has been with us + + align:start position:0% +British well charity has been with us + + + align:start position:0% +British well charity has been with us +forever + + align:start position:0% +forever + + + align:start position:0% +forever +but at the end of the 19th century + + align:start position:0% +but at the end of the 19th century + + + align:start position:0% +but at the end of the 19th century +charity was seen as the major + + align:start position:0% +charity was seen as the major + + + align:start position:0% +charity was seen as the major +involvement of + + align:start position:0% +involvement of + + + align:start position:0% +involvement of +wealth it still isy in this + + align:start position:0% +wealth it still isy in this + + + align:start position:0% +wealth it still isy in this +country I get upset every time I get a + + align:start position:0% +country I get upset every time I get a + + + align:start position:0% +country I get upset every time I get a +phone + + align:start position:0% +phone + + + align:start position:0% +phone +call asking me to donate something and + + align:start position:0% +call asking me to donate something and + + + align:start position:0% +call asking me to donate something and +trying to reconstruct my own + + align:start position:0% +trying to reconstruct my own + + + align:start position:0% +trying to reconstruct my own +ideology which is not in favor of + + align:start position:0% +ideology which is not in favor of + + + align:start position:0% +ideology which is not in favor of +Charity at all but charity being only a + + align:start position:0% +Charity at all but charity being only a + + + align:start position:0% +Charity at all but charity being only a +method of conceding the governments in + + align:start position:0% +method of conceding the governments in + + + align:start position:0% +method of conceding the governments in +in action + + align:start position:0% + + + + align:start position:0% + +there's + + align:start position:0% +there's + + + align:start position:0% +there's +no I don't know it's very + + align:start position:0% +no I don't know it's very + + + align:start position:0% +no I don't know it's very +complicated it's very fundamentally + + align:start position:0% +complicated it's very fundamentally + + + align:start position:0% +complicated it's very fundamentally +complicated as who as why why was I + + align:start position:0% +complicated as who as why why was I + + + align:start position:0% +complicated as who as why why was I +statistically + + align:start position:0% + + + + align:start position:0% + +born to have enough money to come and + + align:start position:0% +born to have enough money to come and + + + align:start position:0% +born to have enough money to come and +study here and then have enough energy + + align:start position:0% +study here and then have enough energy + + + align:start position:0% +study here and then have enough energy +to + + align:start position:0% +to + + + align:start position:0% +to +stay I never to answer that as opposed + + align:start position:0% +stay I never to answer that as opposed + + + align:start position:0% +stay I never to answer that as opposed +to a child growing up in the Congo + + align:start position:0% +to a child growing up in the Congo + + + align:start position:0% +to a child growing up in the Congo +today what statistical Writers Do I have + + align:start position:0% +today what statistical Writers Do I have + + + align:start position:0% +today what statistical Writers Do I have +over their child these are questions + + align:start position:0% +over their child these are questions + + + align:start position:0% +over their child these are questions +philosophers argued with they may be + + align:start position:0% + + + + align:start position:0% + +tedious but Marxism didn't solve the + + align:start position:0% +tedious but Marxism didn't solve the + + + align:start position:0% +tedious but Marxism didn't solve the +problem Marxism only introduced a new + + align:start position:0% +problem Marxism only introduced a new + + + align:start position:0% +problem Marxism only introduced a new +form of + + align:start position:0% +form of + + + align:start position:0% +form of +power despite all of the grassroot + + align:start position:0% +power despite all of the grassroot + + + align:start position:0% +power despite all of the grassroot +sentiments it uh + + align:start position:0% +sentiments it uh + + + align:start position:0% +sentiments it uh +didn't result in + + align:start position:0% +didn't result in + + + align:start position:0% +didn't result in +anything okay see you next week I'll see + + align:start position:0% +anything okay see you next week I'll see + + + align:start position:0% +anything okay see you next week I'll see +you later this week \ No newline at end of file diff --git a/XKeAd4xybjM.txt b/XKeAd4xybjM.txt new file mode 100644 index 0000000000000000000000000000000000000000..917045f8f21d871c0109ccc0b9fb977a137c4525 --- /dev/null +++ b/XKeAd4xybjM.txt @@ -0,0 +1,6080 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu so radioactive decay is kind + + align:start position:0% +ocw.mit.edu so radioactive decay is kind + + + align:start position:0% +ocw.mit.edu so radioactive decay is kind +of a classic example of A first order + + align:start position:0% +of a classic example of A first order + + + align:start position:0% +of a classic example of A first order +process so we are doing one little tiny + + align:start position:0% +process so we are doing one little tiny + + + align:start position:0% +process so we are doing one little tiny +section of the chapter on nuclear + + align:start position:0% +section of the chapter on nuclear + + + align:start position:0% +section of the chapter on nuclear +chemistry and we're doing that all today + + align:start position:0% +chemistry and we're doing that all today + + + align:start position:0% +chemistry and we're doing that all today +and so all we're really covering is uh + + align:start position:0% +and so all we're really covering is uh + + + align:start position:0% +and so all we're really covering is uh +problems associated with first order + + align:start position:0% +problems associated with first order + + + align:start position:0% +problems associated with first order +processes um so uh there's a this just + + align:start position:0% +processes um so uh there's a this just + + + align:start position:0% +processes um so uh there's a this just +just a small introduction to this idea + + align:start position:0% +just a small introduction to this idea + + + align:start position:0% +just a small introduction to this idea +all right so radioactive decay has a lot + + align:start position:0% +all right so radioactive decay has a lot + + + align:start position:0% +all right so radioactive decay has a lot +of applications there are medical + + align:start position:0% +of applications there are medical + + + align:start position:0% +of applications there are medical +applications including um Imaging organs + + align:start position:0% +applications including um Imaging organs + + + align:start position:0% +applications including um Imaging organs +and Bones uh including the heart and so + + align:start position:0% +and Bones uh including the heart and so + + + align:start position:0% +and Bones uh including the heart and so +there is compound that you already saw + + align:start position:0% +there is compound that you already saw + + + align:start position:0% +there is compound that you already saw +um called cardiolite and so we talked + + align:start position:0% +um called cardiolite and so we talked + + + align:start position:0% +um called cardiolite and so we talked +about this in transition metals because + + align:start position:0% +about this in transition metals because + + + align:start position:0% +about this in transition metals because +you have a transition metal and what is + + align:start position:0% +you have a transition metal and what is + + + align:start position:0% +you have a transition metal and what is +the uh geometry of this + + align:start position:0% +the uh geometry of this + + + align:start position:0% +the uh geometry of this +compound what octahedral and we have + + align:start position:0% +compound what octahedral and we have + + + align:start position:0% +compound what octahedral and we have +cyanide ligans which are what kind of + + align:start position:0% +cyanide ligans which are what kind of + + + align:start position:0% +cyanide ligans which are what kind of +field strength strong yeah so um this uh + + align:start position:0% +field strength strong yeah so um this uh + + + align:start position:0% +field strength strong yeah so um this uh +compound was designed in part by an MIT + + align:start position:0% +compound was designed in part by an MIT + + + align:start position:0% +compound was designed in part by an MIT +Professor um Alan Davidson you could go + + align:start position:0% +Professor um Alan Davidson you could go + + + align:start position:0% +Professor um Alan Davidson you could go +talk to him about this incredible + + align:start position:0% +talk to him about this incredible + + + align:start position:0% +talk to him about this incredible +Discovery and invention um it's used + + align:start position:0% +Discovery and invention um it's used + + + align:start position:0% +Discovery and invention um it's used +about 7 million times a year to image + + align:start position:0% +about 7 million times a year to image + + + align:start position:0% +about 7 million times a year to image +various organs um and has been for a + + align:start position:0% +various organs um and has been for a + + + align:start position:0% +various organs um and has been for a +very long time it's off patent now um + + align:start position:0% +very long time it's off patent now um + + + align:start position:0% +very long time it's off patent now um +but this this uh this patent made Alan + + align:start position:0% +but this this uh this patent made Alan + + + align:start position:0% +but this this uh this patent made Alan +Davidson MIT and MIT chemistry + + align:start position:0% +Davidson MIT and MIT chemistry + + + align:start position:0% +Davidson MIT and MIT chemistry +Department in enormous amount of money + + align:start position:0% +Department in enormous amount of money + + + align:start position:0% +Department in enormous amount of money +and so you could go talk to him about it + + align:start position:0% +and so you could go talk to him about it + + + align:start position:0% +and so you could go talk to him about it +except he's happily retired living in + + align:start position:0% +except he's happily retired living in + + + align:start position:0% +except he's happily retired living in +one of his homes um so uh so you can't + + align:start position:0% +one of his homes um so uh so you can't + + + align:start position:0% +one of his homes um so uh so you can't +really do that but anyway so this uses + + align:start position:0% +really do that but anyway so this uses + + + align:start position:0% +really do that but anyway so this uses +an isotope of TN which is metastable + + align:start position:0% +an isotope of TN which is metastable + + + align:start position:0% +an isotope of TN which is metastable +isotope um and so it's 99 it's an + + align:start position:0% +isotope um and so it's 99 it's an + + + align:start position:0% +isotope um and so it's 99 it's an +isotope um of uh the uh the normal 98 uh + + align:start position:0% +isotope um of uh the uh the normal 98 uh + + + align:start position:0% +isotope um of uh the uh the normal 98 uh +Atomic uh mass and so the next challenge + + align:start position:0% +Atomic uh mass and so the next challenge + + + align:start position:0% +Atomic uh mass and so the next challenge +they're always looking for the next + + align:start position:0% +they're always looking for the next + + + align:start position:0% +they're always looking for the next +great thing um the next great Imaging + + align:start position:0% +great thing um the next great Imaging + + + align:start position:0% +great thing um the next great Imaging +agent so that's this is still a very + + align:start position:0% +agent so that's this is still a very + + + align:start position:0% +agent so that's this is still a very +active area of research um and there's + + align:start position:0% +active area of research um and there's + + + align:start position:0% +active area of research um and there's +actually a talk just this week on campus + + align:start position:0% +actually a talk just this week on campus + + + align:start position:0% +actually a talk just this week on campus +about uh work in this area so this is + + align:start position:0% +about uh work in this area so this is + + + align:start position:0% +about uh work in this area so this is +transition metals combined with + + align:start position:0% +transition metals combined with + + + align:start position:0% +transition metals combined with +radioactivity so it's a two topics uh + + align:start position:0% +radioactivity so it's a two topics uh + + + align:start position:0% +radioactivity so it's a two topics uh +here in in the class so another of + + align:start position:0% +here in in the class so another of + + + align:start position:0% +here in in the class so another of +course important use is the potential of + + align:start position:0% +course important use is the potential of + + + align:start position:0% +course important use is the potential of +nuclear energy and the current use of + + align:start position:0% +nuclear energy and the current use of + + + align:start position:0% +nuclear energy and the current use of +nuclear energy this has many challenges + + align:start position:0% +nuclear energy this has many challenges + + + align:start position:0% +nuclear energy this has many challenges +and I don't want to go on record of what + + align:start position:0% +and I don't want to go on record of what + + + align:start position:0% +and I don't want to go on record of what +I think about nuclear energy I think + + align:start position:0% +I think about nuclear energy I think + + + align:start position:0% +I think about nuclear energy I think +it's a complicated problem um there are + + align:start position:0% +it's a complicated problem um there are + + + align:start position:0% +it's a complicated problem um there are +a lot of challenges but one I'd like to + + align:start position:0% +a lot of challenges but one I'd like to + + + align:start position:0% +a lot of challenges but one I'd like to +bring up because I think it's + + align:start position:0% +bring up because I think it's + + + align:start position:0% +bring up because I think it's +particularly um interesting to me is + + align:start position:0% +particularly um interesting to me is + + + align:start position:0% +particularly um interesting to me is +what to do with the waste and so um one + + align:start position:0% +what to do with the waste and so um one + + + align:start position:0% +what to do with the waste and so um one +uh story that I heard about actually + + align:start position:0% +uh story that I heard about actually + + + align:start position:0% +uh story that I heard about actually +there was a documentary made about this + + align:start position:0% +there was a documentary made about this + + + align:start position:0% +there was a documentary made about this +Finland is uh had this idea to create + + align:start position:0% +Finland is uh had this idea to create + + + align:start position:0% +Finland is uh had this idea to create +this threemile long tunnel and they + + align:start position:0% +this threemile long tunnel and they + + + align:start position:0% +this threemile long tunnel and they +wanted to store um 12,000 metric tons of + + align:start position:0% +wanted to store um 12,000 metric tons of + + + align:start position:0% +wanted to store um 12,000 metric tons of +nuclear waste and they wanted the + + align:start position:0% +nuclear waste and they wanted the + + + align:start position:0% +nuclear waste and they wanted the +containers to store it for a 100,000 + + align:start position:0% +containers to store it for a 100,000 + + + align:start position:0% +containers to store it for a 100,000 +years and this documentary asked a + + align:start position:0% +years and this documentary asked a + + + align:start position:0% +years and this documentary asked a +number of questions about this idea such + + align:start position:0% +number of questions about this idea such + + + align:start position:0% +number of questions about this idea such +as what kind of container do you use and + + align:start position:0% +as what kind of container do you use and + + + align:start position:0% +as what kind of container do you use and +how do you know the material you design + + align:start position:0% +how do you know the material you design + + + align:start position:0% +how do you know the material you design +your container is going to last 100,000 + + align:start position:0% +your container is going to last 100,000 + + + align:start position:0% +your container is going to last 100,000 +years um as experimental science we like + + align:start position:0% +years um as experimental science we like + + + align:start position:0% +years um as experimental science we like +to test how long things last but you + + align:start position:0% +to test how long things last but you + + + align:start position:0% +to test how long things last but you +can't really do this experiment um also + + align:start position:0% +can't really do this experiment um also + + + align:start position:0% +can't really do this experiment um also +kind of brought up the idea do you guard + + align:start position:0% +kind of brought up the idea do you guard + + + align:start position:0% +kind of brought up the idea do you guard +this facility for 100,000 years um + + align:start position:0% +this facility for 100,000 years um + + + align:start position:0% +this facility for 100,000 years um +because you can make bombs out of a lot + + align:start position:0% +because you can make bombs out of a lot + + + align:start position:0% +because you can make bombs out of a lot +of this uh radioactive waste so you kind + + align:start position:0% +of this uh radioactive waste so you kind + + + align:start position:0% +of this uh radioactive waste so you kind +of need to protect it um but uh maybe + + align:start position:0% +of need to protect it um but uh maybe + + + align:start position:0% +of need to protect it um but uh maybe +you should just bury it and then you + + align:start position:0% +you should just bury it and then you + + + align:start position:0% +you should just bury it and then you +know no one knows it's there so you + + align:start position:0% +know no one knows it's there so you + + + align:start position:0% +know no one knows it's there so you +don't have to guard it so they can't + + align:start position:0% +don't have to guard it so they can't + + + align:start position:0% +don't have to guard it so they can't +find it and use it but then what if + + align:start position:0% +find it and use it but then what if + + + align:start position:0% +find it and use it but then what if +someone stumbles apart it and releases + + align:start position:0% +someone stumbles apart it and releases + + + align:start position:0% +someone stumbles apart it and releases +all of this uh radioactivity so that + + align:start position:0% +all of this uh radioactivity so that + + + align:start position:0% +all of this uh radioactivity so that +would be bad so do you put warning signs + + align:start position:0% +would be bad so do you put warning signs + + + align:start position:0% +would be bad so do you put warning signs +for people who will be around 100,000 + + align:start position:0% +for people who will be around 100,000 + + + align:start position:0% +for people who will be around 100,000 +years from now saying hey don't go in + + align:start position:0% +years from now saying hey don't go in + + + align:start position:0% +years from now saying hey don't go in +here it looks like a pretty tunnel but + + align:start position:0% +here it looks like a pretty tunnel but + + + align:start position:0% +here it looks like a pretty tunnel but +hey um you know the half-life of the + + align:start position:0% +hey um you know the half-life of the + + + align:start position:0% +hey um you know the half-life of the +things stored here are 100,000 years so + + align:start position:0% +things stored here are 100,000 years so + + + align:start position:0% +things stored here are 100,000 years so +this is this is pretty radioactive still + + align:start position:0% +this is this is pretty radioactive still + + + align:start position:0% +this is this is pretty radioactive still +don't go inside and if you write this + + align:start position:0% +don't go inside and if you write this + + + align:start position:0% +don't go inside and if you write this +sign what language do you put it in so + + align:start position:0% +sign what language do you put it in so + + + align:start position:0% +sign what language do you put it in so +um the documentary pointed out that + + align:start position:0% +um the documentary pointed out that + + + align:start position:0% +um the documentary pointed out that +neanderthals um existed like 40 thou + + align:start position:0% +neanderthals um existed like 40 thou + + + align:start position:0% +neanderthals um existed like 40 thou +40,000 years ago so 100,000 years from + + align:start position:0% +40,000 years ago so 100,000 years from + + + align:start position:0% +40,000 years ago so 100,000 years from +now what's going to be going on how do + + align:start position:0% +now what's going to be going on how do + + + align:start position:0% +now what's going to be going on how do +you write a sign to people that long in + + align:start position:0% +you write a sign to people that long in + + + align:start position:0% +you write a sign to people that long in +the future anyway I just think that + + align:start position:0% +the future anyway I just think that + + + align:start position:0% +the future anyway I just think that +these are sort of interesting ideas and + + align:start position:0% +these are sort of interesting ideas and + + + align:start position:0% +these are sort of interesting ideas and +brings up the point that as scientists + + align:start position:0% +brings up the point that as scientists + + + align:start position:0% +brings up the point that as scientists +and Engineers we need to think not only + + align:start position:0% +and Engineers we need to think not only + + + align:start position:0% +and Engineers we need to think not only +about the science and engineering we're + + align:start position:0% +about the science and engineering we're + + + align:start position:0% +about the science and engineering we're +doing but the ramifications to society + + align:start position:0% +doing but the ramifications to society + + + align:start position:0% +doing but the ramifications to society +um and uh and sort of Sociology as well + + align:start position:0% +um and uh and sort of Sociology as well + + + align:start position:0% +um and uh and sort of Sociology as well +as politics involved in some of this + + align:start position:0% +as politics involved in some of this + + + align:start position:0% +as politics involved in some of this +this science so this is an interesting + + align:start position:0% +this science so this is an interesting + + + align:start position:0% +this science so this is an interesting +area for that intersection of the social + + align:start position:0% +area for that intersection of the social + + + align:start position:0% +area for that intersection of the social +sciences and the Natural Sciences and + + align:start position:0% +sciences and the Natural Sciences and + + + align:start position:0% +sciences and the Natural Sciences and +Engineering all right so radioactive + + align:start position:0% +Engineering all right so radioactive + + + align:start position:0% +Engineering all right so radioactive +decay definitely a useful thing + + align:start position:0% +decay definitely a useful thing + + + align:start position:0% +decay definitely a useful thing +dangerous and useful all at the same + + align:start position:0% +dangerous and useful all at the same + + + align:start position:0% +dangerous and useful all at the same +time oh look at that you know the + + align:start position:0% +time oh look at that you know the + + + align:start position:0% +time oh look at that you know the +clicker question is coming up at the + + align:start position:0% +clicker question is coming up at the + + + align:start position:0% +clicker question is coming up at the +bottom of the page okay we're not there + + align:start position:0% +bottom of the page okay we're not there + + + align:start position:0% +bottom of the page okay we're not there +yet it's okay we're not there yet all + + align:start position:0% +yet it's okay we're not there yet all + + + align:start position:0% +yet it's okay we're not there yet all +right um radio I just added that at the + + align:start position:0% +right um radio I just added that at the + + + align:start position:0% +right um radio I just added that at the +end and apparently didn't animate it + + align:start position:0% +end and apparently didn't animate it + + + align:start position:0% +end and apparently didn't animate it +well all right um so the decay of a + + align:start position:0% +well all right um so the decay of a + + + align:start position:0% +well all right um so the decay of a +nucleus is independent of how many + + align:start position:0% +nucleus is independent of how many + + + align:start position:0% +nucleus is independent of how many +nuclei are around it that's what makes + + align:start position:0% +nuclei are around it that's what makes + + + align:start position:0% +nuclei are around it that's what makes +it a first order process so because it's + + align:start position:0% +it a first order process so because it's + + + align:start position:0% +it a first order process so because it's +a first order process we can apply those + + align:start position:0% +a first order process we can apply those + + + align:start position:0% +a first order process we can apply those +first order integrated rate laws that we + + align:start position:0% +first order integrated rate laws that we + + + align:start position:0% +first order integrated rate laws that we +just dered so we had our rate law that + + align:start position:0% +just dered so we had our rate law that + + + align:start position:0% +just dered so we had our rate law that +the concentration of something a equals + + align:start position:0% +the concentration of something a equals + + + align:start position:0% +the concentration of something a equals +its original concentration to the e to + + align:start position:0% +its original concentration to the e to + + + align:start position:0% +its original concentration to the e to +the minus K which is our rate constant + + align:start position:0% +the minus K which is our rate constant + + + align:start position:0% +the minus K which is our rate constant +times time and also our Half-Life + + align:start position:0% +times time and also our Half-Life + + + align:start position:0% +times time and also our Half-Life +equation that we just + + align:start position:0% +equation that we just + + + align:start position:0% +equation that we just +used so instead of concentration of a + + align:start position:0% +used so instead of concentration of a + + + align:start position:0% +used so instead of concentration of a +though we're going to have a different + + align:start position:0% +though we're going to have a different + + + align:start position:0% +though we're going to have a different +thing to express of + + align:start position:0% +thing to express of + + + align:start position:0% +thing to express of +what we're interested in here which is n + + align:start position:0% +what we're interested in here which is n + + + align:start position:0% +what we're interested in here which is n +the number of + + align:start position:0% +the number of + + + align:start position:0% +the number of +nuclei so we can just write that same + + align:start position:0% +nuclei so we can just write that same + + + align:start position:0% +nuclei so we can just write that same +expression down but instead of + + align:start position:0% +expression down but instead of + + + align:start position:0% +expression down but instead of +concentration of a we're just going to + + align:start position:0% +concentration of a we're just going to + + + align:start position:0% +concentration of a we're just going to +use capital N so n the number of nuclei + + align:start position:0% +use capital N so n the number of nuclei + + + align:start position:0% +use capital N so n the number of nuclei +at some particular time equals how many + + align:start position:0% +at some particular time equals how many + + + align:start position:0% +at some particular time equals how many +nuclei were present originally times e + + align:start position:0% +nuclei were present originally times e + + + align:start position:0% +nuclei were present originally times e +to the minus K and here it is a rate + + align:start position:0% +to the minus K and here it is a rate + + + align:start position:0% +to the minus K and here it is a rate +constant still but it's a Decay constant + + align:start position:0% +constant still but it's a Decay constant + + + align:start position:0% +constant still but it's a Decay constant +in that the rate you're measuring is + + align:start position:0% +in that the rate you're measuring is + + + align:start position:0% +in that the rate you're measuring is +radioactive decay so it kind of has a + + align:start position:0% +radioactive decay so it kind of has a + + + align:start position:0% +radioactive decay so it kind of has a +special name although if you use rate + + align:start position:0% +special name although if you use rate + + + align:start position:0% +special name although if you use rate +constant for that it's that is what it + + align:start position:0% +constant for that it's that is what it + + + align:start position:0% +constant for that it's that is what it +is so that's okay T is still time and + + align:start position:0% +is so that's okay T is still time and + + + align:start position:0% +is so that's okay T is still time and +yes n um to the O is the original number + + align:start position:0% +yes n um to the O is the original number + + + align:start position:0% +yes n um to the O is the original number +of nuclei so we're just going to do a + + align:start position:0% +of nuclei so we're just going to do a + + + align:start position:0% +of nuclei so we're just going to do a +clicker question about how one goes + + align:start position:0% +clicker question about how one goes + + + align:start position:0% +clicker question about how one goes +about calculating the number of + + align:start position:0% + + + + align:start position:0% + +nuclei all right 10 more seconds + + align:start position:0% + + + + align:start position:0% + +all + + align:start position:0% +all + + + align:start position:0% +all +right so uh someone want to tell me for + + align:start position:0% +right so uh someone want to tell me for + + + align:start position:0% +right so uh someone want to tell me for +one of the Green Lantern + + align:start position:0% +one of the Green Lantern + + + align:start position:0% +one of the Green Lantern +t-shirts what is + + align:start position:0% +t-shirts what is + + + align:start position:0% +t-shirts what is +wrong with the other + + align:start position:0% +wrong with the other + + + align:start position:0% +wrong with the other +answers I I I think I saw your hand up + + align:start position:0% +answers I I I think I saw your hand up + + + align:start position:0% +answers I I I think I saw your hand up +first sorry + + align:start position:0% + + + + align:start position:0% + +folks let's see so uh answers one and + + align:start position:0% +folks let's see so uh answers one and + + + align:start position:0% +folks let's see so uh answers one and +two they have the wrong uh what was it + + align:start position:0% +two they have the wrong uh what was it + + + align:start position:0% +two they have the wrong uh what was it +the uh the the molar mass of uh Tech is + + align:start position:0% +the uh the the molar mass of uh Tech is + + + align:start position:0% +the uh the the molar mass of uh Tech is +that technum yeah uh and answer four + + align:start position:0% +that technum yeah uh and answer four + + + align:start position:0% +that technum yeah uh and answer four +does not multiply by avagadro's number + + align:start position:0% +does not multiply by avagadro's number + + + align:start position:0% +does not multiply by avagadro's number +so that's going to give you the number + + align:start position:0% +so that's going to give you the number + + + align:start position:0% +so that's going to give you the number +of moles of the particle right great job + + align:start position:0% +of moles of the particle right great job + + + align:start position:0% +of moles of the particle right great job +okay it's Thanksgiving I thought we + + align:start position:0% +okay it's Thanksgiving I thought we + + + align:start position:0% +okay it's Thanksgiving I thought we +needed a good prize today okay + + align:start position:0% +needed a good prize today okay + + + align:start position:0% +needed a good prize today okay +so right so one thing you also want to + + align:start position:0% +so right so one thing you also want to + + + align:start position:0% +so right so one thing you also want to +remember sort of your uh make sure that + + align:start position:0% +remember sort of your uh make sure that + + + align:start position:0% +remember sort of your uh make sure that +your units are good and it's really + + align:start position:0% +your units are good and it's really + + + align:start position:0% +your units are good and it's really +important in doing this you can take + + align:start position:0% +important in doing this you can take + + + align:start position:0% +important in doing this you can take +this back um to remember to + + align:start position:0% +this back um to remember to + + + align:start position:0% +this back um to remember to +use use the number that is here this + + align:start position:0% +use use the number that is here this + + + align:start position:0% +use use the number that is here this +atomic mass number not the one from the + + align:start position:0% +atomic mass number not the one from the + + + align:start position:0% +atomic mass number not the one from the +periodic table um in uh in calculating + + align:start position:0% +periodic table um in uh in calculating + + + align:start position:0% +periodic table um in uh in calculating +the problem oh actually the periodic + + align:start position:0% +the problem oh actually the periodic + + + align:start position:0% +the problem oh actually the periodic +table disappeared from that oh well okay + + align:start position:0% +table disappeared from that oh well okay + + + align:start position:0% +table disappeared from that oh well okay +so it's it's uh if you use the periodic + + align:start position:0% +so it's it's uh if you use the periodic + + + align:start position:0% +so it's it's uh if you use the periodic +table it's a close answer but sometimes + + align:start position:0% +table it's a close answer but sometimes + + + align:start position:0% +table it's a close answer but sometimes +sometimes it won't be so close um but + + align:start position:0% +sometimes it won't be so close um but + + + align:start position:0% +sometimes it won't be so close um but +remember when it tells you about the + + align:start position:0% +remember when it tells you about the + + + align:start position:0% +remember when it tells you about the +isotope it always has the um atomic mass + + align:start position:0% +isotope it always has the um atomic mass + + + align:start position:0% +isotope it always has the um atomic mass +that you should be using in the problem + + align:start position:0% +that you should be using in the problem + + + align:start position:0% +that you should be using in the problem +as part of the question so keep that in + + align:start position:0% +as part of the question so keep that in + + + align:start position:0% +as part of the question so keep that in +mind all right and yeah you definitely + + align:start position:0% +mind all right and yeah you definitely + + + align:start position:0% +mind all right and yeah you definitely +want to remember avagadro's number and + + align:start position:0% +want to remember avagadro's number and + + + align:start position:0% +want to remember avagadro's number and +the answers are such that it's hard to + + align:start position:0% +the answers are such that it's hard to + + + align:start position:0% +the answers are such that it's hard to +tell that you messed up with the + + align:start position:0% +tell that you messed up with the + + + align:start position:0% +tell that you messed up with the +wavelength it's really easy to tell you + + align:start position:0% +wavelength it's really easy to tell you + + + align:start position:0% +wavelength it's really easy to tell you +messed up if you didn't use avagadro's + + align:start position:0% +messed up if you didn't use avagadro's + + + align:start position:0% +messed up if you didn't use avagadro's +number because it doesn't make any sense + + align:start position:0% +number because it doesn't make any sense + + + align:start position:0% +number because it doesn't make any sense +with these it's a little harder all + + align:start position:0% +with these it's a little harder all + + + align:start position:0% +with these it's a little harder all +right so um remember to use the Isotopes + + align:start position:0% +right so um remember to use the Isotopes + + + align:start position:0% +right so um remember to use the Isotopes +atomic mass and also remember to use + + align:start position:0% +atomic mass and also remember to use + + + align:start position:0% +atomic mass and also remember to use +alagad number when doing this and then + + align:start position:0% +alagad number when doing this and then + + + align:start position:0% +alagad number when doing this and then +uh then you should be + + align:start position:0% +uh then you should be + + + align:start position:0% +uh then you should be +fine all right so this is really similar + + align:start position:0% +fine all right so this is really similar + + + align:start position:0% +fine all right so this is really similar +it's really similar depending on whether + + align:start position:0% +it's really similar depending on whether + + + align:start position:0% +it's really similar depending on whether +you're talking about chemical kinetics + + align:start position:0% +you're talking about chemical kinetics + + + align:start position:0% +you're talking about chemical kinetics +or nuclear kinetics um in doing these + + align:start position:0% +or nuclear kinetics um in doing these + + + align:start position:0% +or nuclear kinetics um in doing these +problems in terms of the + + align:start position:0% +problems in terms of the + + + align:start position:0% +problems in terms of the +equations um but + + align:start position:0% +equations um but + + + align:start position:0% +equations um but +uh in in chemical kinetics you're + + align:start position:0% +uh in in chemical kinetics you're + + + align:start position:0% +uh in in chemical kinetics you're +measuring the concentration whereas with + + align:start position:0% +measuring the concentration whereas with + + + align:start position:0% +measuring the concentration whereas with +nuclear kinetics you're measuring Decay + + align:start position:0% +nuclear kinetics you're measuring Decay + + + align:start position:0% +nuclear kinetics you're measuring Decay +event + + align:start position:0% +event + + + align:start position:0% +event +and so usually how do you measure Decay + + align:start position:0% +and so usually how do you measure Decay + + + align:start position:0% +and so usually how do you measure Decay +events and the most common way is here + + align:start position:0% +events and the most common way is here + + + align:start position:0% +events and the most common way is here +our uh Geer + + align:start position:0% +our uh Geer + + + align:start position:0% +our uh Geer +counter so just want to It's always + + align:start position:0% +counter so just want to It's always + + + align:start position:0% +counter so just want to It's always +important every once in a while at MIT + + align:start position:0% +important every once in a while at MIT + + + align:start position:0% +important every once in a while at MIT +to double check that uh the rooms that + + align:start position:0% +to double check that uh the rooms that + + + align:start position:0% +to double check that uh the rooms that +you're teaching in have not been + + align:start position:0% +you're teaching in have not been + + + align:start position:0% +you're teaching in have not been +contaminated by some wonderful + + align:start position:0% +contaminated by some wonderful + + + align:start position:0% +contaminated by some wonderful +experiments so so far we're good so here + + align:start position:0% +experiments so so far we're good so here + + + align:start position:0% +experiments so so far we're good so here +this uh is working you can hear the + + align:start position:0% +this uh is working you can hear the + + + align:start position:0% +this uh is working you can hear the +chips I think this is this is pretty + + align:start position:0% +chips I think this is this is pretty + + + align:start position:0% +chips I think this is this is pretty +good you don't have to be concerned + + align:start position:0% +good you don't have to be concerned + + + align:start position:0% +good you don't have to be concerned +about this there's always some + + align:start position:0% +about this there's always some + + + align:start position:0% +about this there's always some +background level it's fine so so um + + align:start position:0% +background level it's fine so so um + + + align:start position:0% +background level it's fine so so um +there are um gases in here that uh will + + align:start position:0% +there are um gases in here that uh will + + + align:start position:0% +there are um gases in here that uh will +get ionized by radiation which gives off + + align:start position:0% +get ionized by radiation which gives off + + + align:start position:0% +get ionized by radiation which gives off +then that's translated into that + + align:start position:0% +then that's translated into that + + + align:start position:0% +then that's translated into that +clicking noise so that's what has + + align:start position:0% +clicking noise so that's what has + + + align:start position:0% +clicking noise so that's what has +happening so it's measuring with our + + align:start position:0% +happening so it's measuring with our + + + align:start position:0% +happening so it's measuring with our +thing um whether there are any + + align:start position:0% +thing um whether there are any + + + align:start position:0% +thing um whether there are any +radioactive events going on and this is + + align:start position:0% +radioactive events going on and this is + + + align:start position:0% +radioactive events going on and this is +called a guer counter and we use x-rays + + align:start position:0% +called a guer counter and we use x-rays + + + align:start position:0% +called a guer counter and we use x-rays +in my lab so I went and uh and stole + + align:start position:0% +in my lab so I went and uh and stole + + + align:start position:0% +in my lab so I went and uh and stole +this from our x-ray facility before I + + align:start position:0% +this from our x-ray facility before I + + + align:start position:0% +this from our x-ray facility before I +came here luckily it's almost + + align:start position:0% +came here luckily it's almost + + + align:start position:0% +came here luckily it's almost +Thanksgiving so no one was collecting + + align:start position:0% +Thanksgiving so no one was collecting + + + align:start position:0% +Thanksgiving so no one was collecting +any data so no one will get in trouble + + align:start position:0% +any data so no one will get in trouble + + + align:start position:0% +any data so no one will get in trouble +for taking this right now um and Hans + + align:start position:0% +for taking this right now um and Hans + + + align:start position:0% +for taking this right now um and Hans +Gyer is the person who came up with this + + align:start position:0% +Gyer is the person who came up with this + + + align:start position:0% +Gyer is the person who came up with this +idea and this device does anyone + + align:start position:0% +idea and this device does anyone + + + align:start position:0% +idea and this device does anyone +remember where we heard that name before + + align:start position:0% +remember where we heard that name before + + + align:start position:0% +remember where we heard that name before +think back class + + align:start position:0% +think back class + + + align:start position:0% +think back class +two so he did that amazing uh gold foil + + align:start position:0% +two so he did that amazing uh gold foil + + + align:start position:0% +two so he did that amazing uh gold foil +experiment um and uh so our pingpong + + align:start position:0% +experiment um and uh so our pingpong + + + align:start position:0% +experiment um and uh so our pingpong +balls that we were throwing were + + align:start position:0% +balls that we were throwing were + + + align:start position:0% +balls that we were throwing were +duplicating the experiment that he did + + align:start position:0% +duplicating the experiment that he did + + + align:start position:0% +duplicating the experiment that he did +as a graduate student and luckily I + + align:start position:0% +as a graduate student and luckily I + + + align:start position:0% +as a graduate student and luckily I +think he was smart enough to realize + + align:start position:0% +think he was smart enough to realize + + + align:start position:0% +think he was smart enough to realize +that when you're working with he was + + align:start position:0% +that when you're working with he was + + + align:start position:0% +that when you're working with he was +working with a lot of radioactivity at + + align:start position:0% +working with a lot of radioactivity at + + + align:start position:0% +working with a lot of radioactivity at +that point they want should know exactly + + align:start position:0% +that point they want should know exactly + + + align:start position:0% +that point they want should know exactly +how much radioactivity you're working + + align:start position:0% +how much radioactivity you're working + + + align:start position:0% +how much radioactivity you're working +with and so uh you know these are very + + align:start position:0% +with and so uh you know these are very + + + align:start position:0% +with and so uh you know these are very +early day experiments and he came up + + align:start position:0% +early day experiments and he came up + + + align:start position:0% +early day experiments and he came up +with this device um that helped him know + + align:start position:0% +with this device um that helped him know + + + align:start position:0% +with this device um that helped him know +how safe he was and this is still you + + align:start position:0% +how safe he was and this is still you + + + align:start position:0% +how safe he was and this is still you +know the sort of the standard thing to + + align:start position:0% +know the sort of the standard thing to + + + align:start position:0% +know the sort of the standard thing to +have these around and double check that + + align:start position:0% +have these around and double check that + + + align:start position:0% +have these around and double check that +radio that there is no radiation leaks + + align:start position:0% +radio that there is no radiation leaks + + + align:start position:0% +radio that there is no radiation leaks +in places like that so the guer counter + + align:start position:0% +in places like that so the guer counter + + + align:start position:0% +in places like that so the guer counter +all right so uh also a couple of more uh + + align:start position:0% +all right so uh also a couple of more uh + + + align:start position:0% +all right so uh also a couple of more uh +terminology things + + align:start position:0% +terminology things + + + align:start position:0% +terminology things +Decay rate is also called activity or + + align:start position:0% +Decay rate is also called activity or + + + align:start position:0% +Decay rate is also called activity or +specific activity so you're talking + + align:start position:0% +specific activity so you're talking + + + align:start position:0% +specific activity so you're talking +about sort of how active your substance + + align:start position:0% +about sort of how active your substance + + + align:start position:0% +about sort of how active your substance +is that's really you know how how + + align:start position:0% +is that's really you know how how + + + align:start position:0% +is that's really you know how how +radioactive is it um and activity also + + align:start position:0% +radioactive is it um and activity also + + + align:start position:0% +radioactive is it um and activity also +has the letter A so we talking about the + + align:start position:0% +has the letter A so we talking about the + + + align:start position:0% +has the letter A so we talking about the +concentration of a and now we have a + + align:start position:0% +concentration of a and now we have a + + + align:start position:0% +concentration of a and now we have a +again there's a lot of A's in this unit + + align:start position:0% +again there's a lot of A's in this unit + + + align:start position:0% +again there's a lot of A's in this unit +um so that's the change now in the + + align:start position:0% +um so that's the change now in the + + + align:start position:0% +um so that's the change now in the +number of nuclei over time um that's the + + align:start position:0% +number of nuclei over time um that's the + + + align:start position:0% +number of nuclei over time um that's the +rate expression or the rate law K the + + align:start position:0% +rate expression or the rate law K the + + + align:start position:0% +rate expression or the rate law K the +Decay constant times the number of + + align:start position:0% +Decay constant times the number of + + + align:start position:0% +Decay constant times the number of +nuclei and because activity is + + align:start position:0% +nuclei and because activity is + + + align:start position:0% +nuclei and because activity is +proportional to the number of nuclei we + + align:start position:0% +proportional to the number of nuclei we + + + align:start position:0% +proportional to the number of nuclei we +can also take this expression that we + + align:start position:0% +can also take this expression that we + + + align:start position:0% +can also take this expression that we +had before that had the n's in it and + + align:start position:0% +had before that had the n's in it and + + + align:start position:0% +had before that had the n's in it and +rewrite it with a so now it's really + + align:start position:0% +rewrite it with a so now it's really + + + align:start position:0% +rewrite it with a so now it's really +just like that first order expression we + + align:start position:0% +just like that first order expression we + + + align:start position:0% +just like that first order expression we +had but without the concentration term + + align:start position:0% +had but without the concentration term + + + align:start position:0% +had but without the concentration term +um so we have the activity at some time + + align:start position:0% +um so we have the activity at some time + + + align:start position:0% +um so we have the activity at some time +equals the original activity of the + + align:start position:0% +equals the original activity of the + + + align:start position:0% +equals the original activity of the +material um times e to minus KT and all + + align:start position:0% +material um times e to minus KT and all + + + align:start position:0% +material um times e to minus KT and all +of these equations are going to be on + + align:start position:0% +of these equations are going to be on + + + align:start position:0% +of these equations are going to be on +your equation sheet um but you know if + + align:start position:0% +your equation sheet um but you know if + + + align:start position:0% +your equation sheet um but you know if +you mess up and use the wrong equation + + align:start position:0% +you mess up and use the wrong equation + + + align:start position:0% +you mess up and use the wrong equation +for this it doesn't matter as long as + + align:start position:0% +for this it doesn't matter as long as + + + align:start position:0% +for this it doesn't matter as long as +you're using the first order equation um + + align:start position:0% +you're using the first order equation um + + + align:start position:0% +you're using the first order equation um +whether it's concentration or activity + + align:start position:0% +whether it's concentration or activity + + + align:start position:0% +whether it's concentration or activity +it's the same idea that you can you can + + align:start position:0% +it's the same idea that you can you can + + + align:start position:0% +it's the same idea that you can you can +determine if you know the rate constant + + align:start position:0% +determine if you know the rate constant + + + align:start position:0% +determine if you know the rate constant +or the Decay constant how much material + + align:start position:0% +or the Decay constant how much material + + + align:start position:0% +or the Decay constant how much material +is left how much activity is left how + + align:start position:0% +is left how much activity is left how + + + align:start position:0% +is left how much activity is left how +many nuclei are left after a given + + align:start position:0% +many nuclei are left after a given + + + align:start position:0% +many nuclei are left after a given +amount of time all right so I know what + + align:start position:0% +amount of time all right so I know what + + + align:start position:0% +amount of time all right so I know what +you're all thinking now you're thinking + + align:start position:0% +you're all thinking now you're thinking + + + align:start position:0% +you're all thinking now you're thinking +this is is fantastic but what about the + + align:start position:0% +this is is fantastic but what about the + + + align:start position:0% +this is is fantastic but what about the +units um we must hear about the + + align:start position:0% +units um we must hear about the + + + align:start position:0% +units um we must hear about the +units so the SI units for uh for + + align:start position:0% +units so the SI units for uh for + + + align:start position:0% +units so the SI units for uh for +activity are the Beckel + + align:start position:0% +activity are the Beckel + + + align:start position:0% +activity are the Beckel +BQ and one Beckel is one radioactive + + align:start position:0% +BQ and one Beckel is one radioactive + + + align:start position:0% +BQ and one Beckel is one radioactive +disintegration per + + align:start position:0% +disintegration per + + + align:start position:0% +disintegration per +second and this is the newer unit the + + align:start position:0% +second and this is the newer unit the + + + align:start position:0% +second and this is the newer unit the +older unit was called a curee and + + align:start position:0% +older unit was called a curee and + + + align:start position:0% +older unit was called a curee and +sometimes you will still see this in the + + align:start position:0% +sometimes you will still see this in the + + + align:start position:0% +sometimes you will still see this in the +literature and a curee one curee was 3.7 + + align:start position:0% +literature and a curee one curee was 3.7 + + + align:start position:0% +literature and a curee one curee was 3.7 +* 10 10th disintegrations per second so + + align:start position:0% +* 10 10th disintegrations per second so + + + align:start position:0% +* 10 10th disintegrations per second so +was a much larger number than the + + align:start position:0% +was a much larger number than the + + + align:start position:0% +was a much larger number than the +current SI unit um so this was what one + + align:start position:0% +current SI unit um so this was what one + + + align:start position:0% +current SI unit um so this was what one +gram of a radium uh specific activity + + align:start position:0% +gram of a radium uh specific activity + + + align:start position:0% +gram of a radium uh specific activity +was so they Ed this big number but it's + + align:start position:0% +was so they Ed this big number but it's + + + align:start position:0% +was so they Ed this big number but it's +not was not really practical because you + + align:start position:0% +not was not really practical because you + + + align:start position:0% +not was not really practical because you +want to tell people like how much + + align:start position:0% +want to tell people like how much + + + align:start position:0% +want to tell people like how much +radiation would be safe for them to have + + align:start position:0% +radiation would be safe for them to have + + + align:start position:0% +radiation would be safe for them to have +in a year or something like that and you + + align:start position:0% +in a year or something like that and you + + + align:start position:0% +in a year or something like that and you +didn't want to use this this giant + + align:start position:0% +didn't want to use this this giant + + + align:start position:0% +didn't want to use this this giant +number for that so we've uh moved to + + align:start position:0% +number for that so we've uh moved to + + + align:start position:0% +number for that so we've uh moved to +here so anyone know or want to guess uh + + align:start position:0% +here so anyone know or want to guess uh + + + align:start position:0% +here so anyone know or want to guess uh +who uh who the older unit was uh named + + align:start position:0% +who uh who the older unit was uh named + + + align:start position:0% +who uh who the older unit was uh named +for of + + align:start position:0% +for of + + + align:start position:0% +for of +radioactivity one might think Marie cury + + align:start position:0% +radioactivity one might think Marie cury + + + align:start position:0% +radioactivity one might think Marie cury +but a lot of the uh evidence suggests it + + align:start position:0% +but a lot of the uh evidence suggests it + + + align:start position:0% +but a lot of the uh evidence suggests it +was actually her husband Pierre cury um + + align:start position:0% +was actually her husband Pierre cury um + + + align:start position:0% +was actually her husband Pierre cury um +who it was named after it's a bit + + align:start position:0% +who it was named after it's a bit + + + align:start position:0% +who it was named after it's a bit +controversial um but they both worked + + align:start position:0% +controversial um but they both worked + + + align:start position:0% +controversial um but they both worked +together and they worked with um HRI + + align:start position:0% +together and they worked with um HRI + + + align:start position:0% +together and they worked with um HRI +Beckel and they all won the 1903 Nobel + + align:start position:0% +Beckel and they all won the 1903 Nobel + + + align:start position:0% +Beckel and they all won the 1903 Nobel +Prize for discovering + + align:start position:0% +Prize for discovering + + + align:start position:0% +Prize for discovering +radioactivity 3 years later um Pierre C + + align:start position:0% +radioactivity 3 years later um Pierre C + + + align:start position:0% +radioactivity 3 years later um Pierre C +was killed crossing the street um he + + align:start position:0% +was killed crossing the street um he + + + align:start position:0% +was killed crossing the street um he +slipped when it was raining and a horse + + align:start position:0% +slipped when it was raining and a horse + + + align:start position:0% +slipped when it was raining and a horse +and wagon I guess ran over him and + + align:start position:0% +and wagon I guess ran over him and + + + align:start position:0% +and wagon I guess ran over him and +killed him so this is I think an example + + align:start position:0% +killed him so this is I think an example + + + align:start position:0% +killed him so this is I think an example +of you know someone who's so brilliant + + align:start position:0% +of you know someone who's so brilliant + + + align:start position:0% +of you know someone who's so brilliant +but you say they're so brilliant but do + + align:start position:0% +but you say they're so brilliant but do + + + align:start position:0% +but you say they're so brilliant but do +they look both ways before they cross + + align:start position:0% +they look both ways before they cross + + + align:start position:0% +they look both ways before they cross +the street so you are all very brilliant + + align:start position:0% +the street so you are all very brilliant + + + align:start position:0% +the street so you are all very brilliant +and I encourage you look both ways + + align:start position:0% +and I encourage you look both ways + + + align:start position:0% +and I encourage you look both ways +before you cross the street anyway so he + + align:start position:0% +before you cross the street anyway so he + + + align:start position:0% +before you cross the street anyway so he +he died and some of the stories are that + + align:start position:0% +he died and some of the stories are that + + + align:start position:0% +he died and some of the stories are that +they Nam the unit after him um as a + + align:start position:0% +they Nam the unit after him um as a + + + align:start position:0% +they Nam the unit after him um as a +tribute others say well it was really + + align:start position:0% +tribute others say well it was really + + + align:start position:0% +tribute others say well it was really +for both of them but in any case now + + align:start position:0% +for both of them but in any case now + + + align:start position:0% +for both of them but in any case now +it's named after the third person um hre + + align:start position:0% +it's named after the third person um hre + + + align:start position:0% +it's named after the third person um hre +Beckel okay so + + align:start position:0% +Beckel okay so + + + align:start position:0% +Beckel okay so +radioactivity um I'm going to tell you a + + align:start position:0% +radioactivity um I'm going to tell you a + + + align:start position:0% +radioactivity um I'm going to tell you a +little bit about + + align:start position:0% +little bit about + + + align:start position:0% +little bit about +radioactivity this chart is not in your + + align:start position:0% +radioactivity this chart is not in your + + + align:start position:0% +radioactivity this chart is not in your +handout because you're not responsible + + align:start position:0% +handout because you're not responsible + + + align:start position:0% +handout because you're not responsible +for knowing all this information so I + + align:start position:0% +for knowing all this information so I + + + align:start position:0% +for knowing all this information so I +just didn't put it in there um but you + + align:start position:0% +just didn't put it in there um but you + + + align:start position:0% +just didn't put it in there um but you +can look this up there's a couple of + + align:start position:0% +can look this up there's a couple of + + + align:start position:0% +can look this up there's a couple of +points I did make in your handout which + + align:start position:0% +points I did make in your handout which + + + align:start position:0% +points I did make in your handout which +is there are different types of + + align:start position:0% +is there are different types of + + + align:start position:0% +is there are different types of +radioactive of nuclear radiation we have + + align:start position:0% +radioactive of nuclear radiation we have + + + align:start position:0% +radioactive of nuclear radiation we have +Al um we have alpha particles alpha + + align:start position:0% +Al um we have alpha particles alpha + + + align:start position:0% +Al um we have alpha particles alpha +decay beta Decay gamma Decay some of + + align:start position:0% +decay beta Decay gamma Decay some of + + + align:start position:0% +decay beta Decay gamma Decay some of +those involve a mass change so like an + + align:start position:0% +those involve a mass change so like an + + + align:start position:0% +those involve a mass change so like an +alpha particle is the same as a helium 4 + + align:start position:0% +alpha particle is the same as a helium 4 + + + align:start position:0% +alpha particle is the same as a helium 4 +nucleus two protons two neutrons um beta + + align:start position:0% +nucleus two protons two neutrons um beta + + + align:start position:0% +nucleus two protons two neutrons um beta +Decay involves an electron gamma is a + + align:start position:0% +Decay involves an electron gamma is a + + + align:start position:0% +Decay involves an electron gamma is a +photon um so they're they're definitely + + align:start position:0% +photon um so they're they're definitely + + + align:start position:0% +photon um so they're they're definitely +different types some Mass change some + + align:start position:0% +different types some Mass change some + + + align:start position:0% +different types some Mass change some +not there also um really dramatic + + align:start position:0% +not there also um really dramatic + + + align:start position:0% +not there also um really dramatic +differences in Half-Life so again + + align:start position:0% +differences in Half-Life so again + + + align:start position:0% +differences in Half-Life so again +halflife depends in the material in + + align:start position:0% +halflife depends in the material in + + + align:start position:0% +halflife depends in the material in +question it depends on that decay + + align:start position:0% +question it depends on that decay + + + align:start position:0% +question it depends on that decay +constant that rate constant um and if we + + align:start position:0% +constant that rate constant um and if we + + + align:start position:0% +constant that rate constant um and if we +look at this table we can see things + + align:start position:0% +look at this table we can see things + + + align:start position:0% +look at this table we can see things +from + + align:start position:0% +from + + + align:start position:0% +from +milliseconds um and if we look at some + + align:start position:0% +milliseconds um and if we look at some + + + align:start position:0% +milliseconds um and if we look at some +of these D um is for day A is for year Y + + align:start position:0% +of these D um is for day A is for year Y + + + align:start position:0% +of these D um is for day A is for year Y +is also for year so sometimes you'll see + + align:start position:0% +is also for year so sometimes you'll see + + + align:start position:0% +is also for year so sometimes you'll see +y for year sometimes you'll see a I + + align:start position:0% +y for year sometimes you'll see a I + + + align:start position:0% +y for year sometimes you'll see a I +think most people guess that Y is for + + align:start position:0% +think most people guess that Y is for + + + align:start position:0% +think most people guess that Y is for +year that A is for year I don't really + + align:start position:0% +year that A is for year I don't really + + + align:start position:0% +year that A is for year I don't really +know um but anyway in this table it's a + + align:start position:0% +know um but anyway in this table it's a + + + align:start position:0% +know um but anyway in this table it's a +so if you see that don't be confused and + + align:start position:0% +so if you see that don't be confused and + + + align:start position:0% +so if you see that don't be confused and +GA that's Giga years so 10 10 to the 9th + + align:start position:0% +GA that's Giga years so 10 10 to the 9th + + + align:start position:0% +GA that's Giga years so 10 10 to the 9th +that's where the Finland uh 100,000 + + align:start position:0% +that's where the Finland uh 100,000 + + + align:start position:0% +that's where the Finland uh 100,000 +years comes from that we need to keep + + align:start position:0% +years comes from that we need to keep + + + align:start position:0% +years comes from that we need to keep +the stuff safe for a very very very very + + align:start position:0% +the stuff safe for a very very very very + + + align:start position:0% +the stuff safe for a very very very very +very very long amount of time for Giga + + align:start position:0% +very very long amount of time for Giga + + + align:start position:0% +very very long amount of time for Giga +years + + align:start position:0% +years + + + align:start position:0% +years +okay so in some Decay processes such as + + align:start position:0% +okay so in some Decay processes such as + + + align:start position:0% +okay so in some Decay processes such as +uranium 238 you have more than one type + + align:start position:0% +uranium 238 you have more than one type + + + align:start position:0% +uranium 238 you have more than one type +of uh nuclear radiation going on and it + + align:start position:0% +of uh nuclear radiation going on and it + + + align:start position:0% +of uh nuclear radiation going on and it +can involve a very long and complicated + + align:start position:0% +can involve a very long and complicated + + + align:start position:0% +can involve a very long and complicated +series of different + + align:start position:0% +series of different + + + align:start position:0% +series of different +events so here at MIT we spend most of + + align:start position:0% +events so here at MIT we spend most of + + + align:start position:0% +events so here at MIT we spend most of +our time talking about science and + + align:start position:0% +our time talking about science and + + + align:start position:0% +our time talking about science and +engineering but I feel like every once + + align:start position:0% +engineering but I feel like every once + + + align:start position:0% +engineering but I feel like every once +in a while we should throw in some + + align:start position:0% +in a while we should throw in some + + + align:start position:0% +in a while we should throw in some +poetry um into our science classes so + + align:start position:0% +poetry um into our science classes so + + + align:start position:0% +poetry um into our science classes so +once a year I like to read a chemistry + + align:start position:0% +once a year I like to read a chemistry + + + align:start position:0% +once a year I like to read a chemistry +poem to enrich our lives and today is + + align:start position:0% +poem to enrich our lives and today is + + + align:start position:0% +poem to enrich our lives and today is +that day in + + align:start position:0% +that day in + + + align:start position:0% +that day in +2014 and the poem I'm going to read to + + align:start position:0% +2014 and the poem I'm going to read to + + + align:start position:0% +2014 and the poem I'm going to read to +you is called the days of our half- + + align:start position:0% +you is called the days of our half- + + + align:start position:0% +you is called the days of our half- +lives and it is by Professor Mala radak + + align:start position:0% +lives and it is by Professor Mala radak + + + align:start position:0% +lives and it is by Professor Mala radak +Krishna she got her PhD here at MIT uh + + align:start position:0% +Krishna she got her PhD here at MIT uh + + + align:start position:0% +Krishna she got her PhD here at MIT uh +in the chemistry department and she + + align:start position:0% +in the chemistry department and she + + + align:start position:0% +in the chemistry department and she +wrote this book which she wanted me to + + align:start position:0% +wrote this book which she wanted me to + + + align:start position:0% +wrote this book which she wanted me to +point out is available on on Amazon if + + align:start position:0% +point out is available on on Amazon if + + + align:start position:0% +point out is available on on Amazon if +you're looking for a Christmas present + + align:start position:0% +you're looking for a Christmas present + + + align:start position:0% +you're looking for a Christmas present +for a very very geeky friend of yours um + + align:start position:0% +for a very very geeky friend of yours um + + + align:start position:0% +for a very very geeky friend of yours um +and so and it's illustrated by another + + align:start position:0% +and so and it's illustrated by another + + + align:start position:0% +and so and it's illustrated by another +MIT chemistry PhD Mar Riley who actually + + align:start position:0% +MIT chemistry PhD Mar Riley who actually + + + align:start position:0% +MIT chemistry PhD Mar Riley who actually +did the illustrations for the videos + + align:start position:0% +did the illustrations for the videos + + + align:start position:0% +did the illustrations for the videos +that I've been showing you in class so + + align:start position:0% +that I've been showing you in class so + + + align:start position:0% +that I've been showing you in class so +um I might chemist just really + + align:start position:0% +um I might chemist just really + + + align:start position:0% +um I might chemist just really +multi-talented individuals okay so I + + align:start position:0% +multi-talented individuals okay so I + + + align:start position:0% +multi-talented individuals okay so I +will read you this poem now and I as I + + align:start position:0% +will read you this poem now and I as I + + + align:start position:0% +will read you this poem now and I as I +read it to you I will point out what is + + align:start position:0% +read it to you I will point out what is + + + align:start position:0% +read it to you I will point out what is +happening in this uh decay process + + align:start position:0% +happening in this uh decay process + + + align:start position:0% +happening in this uh decay process +because all of mala's uh uh poetry is + + align:start position:0% +because all of mala's uh uh poetry is + + + align:start position:0% +because all of mala's uh uh poetry is +scientifically + + align:start position:0% +scientifically + + + align:start position:0% +scientifically +correct all + + align:start position:0% +correct all + + + align:start position:0% +correct all +right so Days of our half + + align:start position:0% + + + + align:start position:0% + +lives my dearest love I am writing you + + align:start position:0% +lives my dearest love I am writing you + + + align:start position:0% +lives my dearest love I am writing you +to tell you all that I've been through + + align:start position:0% +to tell you all that I've been through + + + align:start position:0% +to tell you all that I've been through +I've changed my whole identity but loved + + align:start position:0% +I've changed my whole identity but loved + + + align:start position:0% +I've changed my whole identity but loved +I can't pretend to be when I was uranium + + align:start position:0% +I can't pretend to be when I was uranium + + + align:start position:0% +I can't pretend to be when I was uranium + + align:start position:0% + + + align:start position:0% +you were on my case to start losing + + align:start position:0% +you were on my case to start losing + + + align:start position:0% +you were on my case to start losing +weight for five billion years I'd hoped + + align:start position:0% +weight for five billion years I'd hoped + + + align:start position:0% +weight for five billion years I'd hoped +and I'd prayed and finally I had an + + align:start position:0% +and I'd prayed and finally I had an + + + align:start position:0% +and I'd prayed and finally I had an +alpha + + align:start position:0% +alpha + + + align:start position:0% +alpha +decay two protons and two neutrons went + + align:start position:0% +decay two protons and two neutrons went + + + align:start position:0% +decay two protons and two neutrons went +right out the door and now I was thorium + + align:start position:0% +right out the door and now I was thorium + + + align:start position:0% +right out the door and now I was thorium +234 but my nucleus was still unfit for + + align:start position:0% +234 but my nucleus was still unfit for + + + align:start position:0% +234 but my nucleus was still unfit for +your eyes not positive enough for its + + align:start position:0% +your eyes not positive enough for its + + + align:start position:0% +your eyes not positive enough for its +large size but this time my halflife was + + align:start position:0% +large size but this time my halflife was + + + align:start position:0% +large size but this time my halflife was +not very long + + align:start position:0% +not very long + + + align:start position:0% +not very long +cuz my will to change was really quite + + align:start position:0% +cuz my will to change was really quite + + + align:start position:0% +cuz my will to change was really quite +strong it took just a month not even a + + align:start position:0% +strong it took just a month not even a + + + align:start position:0% +strong it took just a month not even a +millennium to Beta Decay into + + align:start position:0% +millennium to Beta Decay into + + + align:start position:0% +millennium to Beta Decay into +protactinium but still rejected me right + + align:start position:0% +protactinium but still rejected me right + + + align:start position:0% +protactinium but still rejected me right +off the bat + + align:start position:0% +off the bat + + + align:start position:0% +off the bat +protactinium who's heard of that so + + align:start position:0% +protactinium who's heard of that so + + + align:start position:0% +protactinium who's heard of that so +baited Decay I did once more to become + + align:start position:0% +baited Decay I did once more to become + + + align:start position:0% +baited Decay I did once more to become +uranium + + align:start position:0% + + + + align:start position:0% + +234 myself again but a new isotope you + + align:start position:0% +234 myself again but a new isotope you + + + align:start position:0% +234 myself again but a new isotope you +still weren't satisfied but I still had + + align:start position:0% +still weren't satisfied but I still had + + + align:start position:0% +still weren't satisfied but I still had +hope + + align:start position:0% +hope + + + align:start position:0% +hope +three Alpha decays T was hard but I + + align:start position:0% +three Alpha decays T was hard but I + + + align:start position:0% +three Alpha decays T was hard but I +stayed + + align:start position:0% +stayed + + + align:start position:0% +stayed +on through thorium then radium and then + + align:start position:0% +on through thorium then radium and then + + + align:start position:0% +on through thorium then radium and then +raid + + align:start position:0% +raid + + + align:start position:0% +raid +on I thought that I would finally please + + align:start position:0% +on I thought that I would finally please + + + align:start position:0% +on I thought that I would finally please +you my mask was a healthy + + align:start position:0% +you my mask was a healthy + + + align:start position:0% +you my mask was a healthy +222 but you said although I like your + + align:start position:0% +222 but you said although I like your + + + align:start position:0% +222 but you said although I like your +mass I don't want to be with a noble gas + + align:start position:0% + + + + align:start position:0% + +they dress so + + align:start position:0% + + + + align:start position:0% + +well you had a point though I wasn't + + align:start position:0% +well you had a point though I wasn't + + + align:start position:0% +well you had a point though I wasn't +reactive so in order to please you I + + align:start position:0% +reactive so in order to please you I + + + align:start position:0% +reactive so in order to please you I +stayed proactive a few days later I + + align:start position:0% +stayed proactive a few days later I + + + align:start position:0% +stayed proactive a few days later I +found you and said two more Alpha decays + + align:start position:0% +found you and said two more Alpha decays + + + align:start position:0% +found you and said two more Alpha decays +and + + align:start position:0% +and + + + align:start position:0% +and +now I am + + align:start position:0% +now I am + + + align:start position:0% +now I am +LED but you shook your head you were not + + align:start position:0% +LED but you shook your head you were not + + + align:start position:0% +LED but you shook your head you were not +too keen on my mass number of + + align:start position:0% +too keen on my mass number of + + + align:start position:0% +too keen on my mass number of +214 I had a bad experience with that + + align:start position:0% +214 I had a bad experience with that + + + align:start position:0% +214 I had a bad experience with that +Mass before and an unstable actine + + align:start position:0% +Mass before and an unstable actine + + + align:start position:0% +Mass before and an unstable actine +walked right out the + + align:start position:0% +walked right out the + + + align:start position:0% +walked right out the +door so in order to change I went away + + align:start position:0% +door so in order to change I went away + + + align:start position:0% +door so in order to change I went away +but all I could do was just baited Decay + + align:start position:0% +but all I could do was just baited Decay + + + align:start position:0% +but all I could do was just baited Decay +my hopes and my dreams started to go + + align:start position:0% +my hopes and my dreams started to go + + + align:start position:0% +my hopes and my dreams started to go +under cuz baited Decay does not change a + + align:start position:0% +under cuz baited Decay does not change a + + + align:start position:0% +under cuz baited Decay does not change a +mass + + align:start position:0% +mass + + + align:start position:0% +mass +number to + + align:start position:0% +number to + + + align:start position:0% +number to +bismuth and polonium I hoped and I + + align:start position:0% +bismuth and polonium I hoped and I + + + align:start position:0% +bismuth and polonium I hoped and I +beckoned my halflife was 164 + + align:start position:0% +beckoned my halflife was 164 + + + align:start position:0% +beckoned my halflife was 164 +microseconds and then finally I Alpha + + align:start position:0% +microseconds and then finally I Alpha + + + align:start position:0% +microseconds and then finally I Alpha +decayed and then I was led with a prew + + align:start position:0% +decayed and then I was led with a prew + + + align:start position:0% +decayed and then I was led with a prew +worthy mass of + + align:start position:0% + + + + align:start position:0% + +210 got to admit I was getting quite + + align:start position:0% +210 got to admit I was getting quite + + + align:start position:0% +210 got to admit I was getting quite +tired and my patience with you had + + align:start position:0% +tired and my patience with you had + + + align:start position:0% +tired and my patience with you had +nearly expired you were more demanding + + align:start position:0% +nearly expired you were more demanding + + + align:start position:0% +nearly expired you were more demanding +than any I dated and much of my energy + + align:start position:0% +than any I dated and much of my energy + + + align:start position:0% +than any I dated and much of my energy +had been + + align:start position:0% +had been + + + align:start position:0% +had been +liberated but you still weren't happy + + align:start position:0% +liberated but you still weren't happy + + + align:start position:0% +liberated but you still weren't happy +but you had a fix I really like the + + align:start position:0% +but you had a fix I really like the + + + align:start position:0% +but you had a fix I really like the +number + + align:start position:0% +number + + + align:start position:0% +number +206 so I waited for years until the day + + align:start position:0% +206 so I waited for years until the day + + + align:start position:0% +206 so I waited for years until the day +which began with another beta + + align:start position:0% +which began with another beta + + + align:start position:0% +which began with another beta +Decay and then one + + align:start position:0% +Decay and then one + + + align:start position:0% +Decay and then one +more and finally in the end I Alpha to + + align:start position:0% +more and finally in the end I Alpha to + + + align:start position:0% +more and finally in the end I Alpha to +Le 206 my friend to change any further I + + align:start position:0% +Le 206 my friend to change any further I + + + align:start position:0% +Le 206 my friend to change any further I +wouldn't be able no longer active but + + align:start position:0% +wouldn't be able no longer active but + + + align:start position:0% +wouldn't be able no longer active but +happily stable it took me a million + + align:start position:0% +happily stable it took me a million + + + align:start position:0% +happily stable it took me a million +years to do but look how I've changed + + align:start position:0% +years to do but look how I've changed + + + align:start position:0% +years to do but look how I've changed +and all just for + + align:start position:0% +and all just for + + + align:start position:0% +and all just for +you wait what did you say I've gotten so + + align:start position:0% +you wait what did you say I've gotten so + + + align:start position:0% +you wait what did you say I've gotten so +old that you'd rather be with a young + + align:start position:0% +old that you'd rather be with a young + + + align:start position:0% +old that you'd rather be with a young +lass of gold + + align:start position:0% +lass of gold + + + align:start position:0% +lass of gold +well I give up we're through my pumpkin + + align:start position:0% +well I give up we're through my pumpkin + + + align:start position:0% +well I give up we're through my pumpkin +shouldn't all my effort be counting for + + align:start position:0% +shouldn't all my effort be counting for + + + align:start position:0% +shouldn't all my effort be counting for +something well you won't be able to rule + + align:start position:0% +something well you won't be able to rule + + + align:start position:0% +something well you won't be able to rule +me anymore cuz I'm leaving you not for + + align:start position:0% +me anymore cuz I'm leaving you not for + + + align:start position:0% +me anymore cuz I'm leaving you not for +one Adam but + + align:start position:0% +one Adam but + + + align:start position:0% +one Adam but +four that's + + align:start position:0% +four that's + + + align:start position:0% +four that's +right while you were away + + align:start position:0% +right while you were away + + + align:start position:0% +right while you were away +diffusing I found some + + align:start position:0% +diffusing I found some + + + align:start position:0% +diffusing I found some +chlorines that I found quite + + align:start position:0% + + + + align:start position:0% + +amusing and we're going to form + + align:start position:0% +amusing and we're going to form + + + align:start position:0% +amusing and we're going to form +LED + + align:start position:0% +LED + + + align:start position:0% +LED +cl4 and you won't be hearing from me + + align:start position:0% +cl4 and you won't be hearing from me + + + align:start position:0% +cl4 and you won't be hearing from me +anymore see over the years I've grown + + align:start position:0% +anymore see over the years I've grown + + + align:start position:0% +anymore see over the years I've grown +quite wise I've learned that Love's + + align:start position:0% +quite wise I've learned that Love's + + + align:start position:0% +quite wise I've learned that Love's +about compromise you still have half of + + align:start position:0% +about compromise you still have half of + + + align:start position:0% +about compromise you still have half of +your half lives to live so go out there + + align:start position:0% +your half lives to live so go out there + + + align:start position:0% +your half lives to live so go out there +it's your turn to + + align:start position:0% +it's your turn to + + + align:start position:0% +it's your turn to +give thank + + align:start position:0% + + + + align:start position:0% + +you there's a whole book of them on + + align:start position:0% +you there's a whole book of them on + + + align:start position:0% +you there's a whole book of them on +Amazon + + align:start position:0% + + + + align:start position:0% + +okay so that is first + + align:start position:0% +okay so that is first + + + align:start position:0% +okay so that is first +order first order is pretty exciting it + + align:start position:0% +order first order is pretty exciting it + + + align:start position:0% +order first order is pretty exciting it +has nuclear Decay second order not quite + + align:start position:0% +has nuclear Decay second order not quite + + + align:start position:0% +has nuclear Decay second order not quite +as exciting but we should talk about it + + align:start position:0% +as exciting but we should talk about it + + + align:start position:0% +as exciting but we should talk about it +anyway all right so second order + + align:start position:0% +anyway all right so second order + + + align:start position:0% +anyway all right so second order +integrated rate + + align:start position:0% +integrated rate + + + align:start position:0% +integrated rate +laws we're not going to go through a + + align:start position:0% +laws we're not going to go through a + + + align:start position:0% +laws we're not going to go through a +derivation it's in your book but here is + + align:start position:0% +derivation it's in your book but here is + + + align:start position:0% +derivation it's in your book but here is +the equation if you do do the derivation + + align:start position:0% +the equation if you do do the derivation + + + align:start position:0% +the equation if you do do the derivation +so now we have one over the + + align:start position:0% +so now we have one over the + + + align:start position:0% +so now we have one over the +concentration of a at time t + + align:start position:0% +concentration of a at time t + + + align:start position:0% +concentration of a at time t +equals rate constant K * t plus 1 over + + align:start position:0% +equals rate constant K * t plus 1 over + + + align:start position:0% +equals rate constant K * t plus 1 over +the original concentration of + + align:start position:0% +the original concentration of + + + align:start position:0% +the original concentration of +a and we could plot this one over + + align:start position:0% +a and we could plot this one over + + + align:start position:0% +a and we could plot this one over +concentration of T versus time and if we + + align:start position:0% +concentration of T versus time and if we + + + align:start position:0% +concentration of T versus time and if we +did that you would have the opportunity + + align:start position:0% +did that you would have the opportunity + + + align:start position:0% +did that you would have the opportunity +for another clicker question + + align:start position:0% + + + + align:start position:0% + +all right 10 more + + align:start position:0% + + + + align:start position:0% + +seconds all right 90s yeah it's kind of + + align:start position:0% +seconds all right 90s yeah it's kind of + + + align:start position:0% +seconds all right 90s yeah it's kind of +hard to come up with clicker questions + + align:start position:0% +hard to come up with clicker questions + + + align:start position:0% +hard to come up with clicker questions +in this unit so uh but but it's fun for + + align:start position:0% +in this unit so uh but but it's fun for + + + align:start position:0% +in this unit so uh but but it's fun for +Thanksgiving we'll have lots of 90s okay + + align:start position:0% +Thanksgiving we'll have lots of 90s okay + + + align:start position:0% +Thanksgiving we'll have lots of 90s okay +um so right so we can just look and this + + align:start position:0% +um so right so we can just look and this + + + align:start position:0% +um so right so we can just look and this +is actually an expression for a straight + + align:start position:0% +is actually an expression for a straight + + + align:start position:0% +is actually an expression for a straight +line again so we're plotting on the Y + + align:start position:0% +line again so we're plotting on the Y + + + align:start position:0% +line again so we're plotting on the Y +AIS one over our concentration of a any + + align:start position:0% +AIS one over our concentration of a any + + + align:start position:0% +AIS one over our concentration of a any +at all the various different times um + + align:start position:0% +at all the various different times um + + + align:start position:0% +at all the various different times um +and versus time over here and so our + + align:start position:0% +and versus time over here and so our + + + align:start position:0% +and versus time over here and so our +intercept is going to be one over the + + align:start position:0% +intercept is going to be one over the + + + align:start position:0% +intercept is going to be one over the +initial concentration of a and our slope + + align:start position:0% +initial concentration of a and our slope + + + align:start position:0% +initial concentration of a and our slope +is going to be + + align:start position:0% +is going to be + + + align:start position:0% +is going to be +what K right so again you can measure + + align:start position:0% +what K right so again you can measure + + + align:start position:0% +what K right so again you can measure +your concentration as it changes with + + align:start position:0% +your concentration as it changes with + + + align:start position:0% +your concentration as it changes with +time how the concentration changes plot + + align:start position:0% +time how the concentration changes plot + + + align:start position:0% +time how the concentration changes plot +it and just determine your rate constant + + align:start position:0% +it and just determine your rate constant + + + align:start position:0% +it and just determine your rate constant +for that particular + + align:start position:0% +for that particular + + + align:start position:0% +for that particular +material all right + + align:start position:0% +material all right + + + align:start position:0% +material all right +so second order + + align:start position:0% +so second order + + + align:start position:0% +so second order +halflife we can do another derivation + + align:start position:0% +halflife we can do another derivation + + + align:start position:0% +halflife we can do another derivation +but um in this case I will just give you + + align:start position:0% +but um in this case I will just give you + + + align:start position:0% +but um in this case I will just give you +the equation so halflife equals 1 over K + + align:start position:0% +the equation so halflife equals 1 over K + + + align:start position:0% +the equation so halflife equals 1 over K +times your original concentration of a + + align:start position:0% +times your original concentration of a + + + align:start position:0% +times your original concentration of a +and so this is different from first + + align:start position:0% +and so this is different from first + + + align:start position:0% +and so this is different from first +order there is a concentration term in + + align:start position:0% +order there is a concentration term in + + + align:start position:0% +order there is a concentration term in +the equation so in for second order + + align:start position:0% +the equation so in for second order + + + align:start position:0% +the equation so in for second order +halflife it does depend on the starting + + align:start position:0% +halflife it does depend on the starting + + + align:start position:0% +halflife it does depend on the starting +concentration so that's really the big + + align:start position:0% +concentration so that's really the big + + + align:start position:0% +concentration so that's really the big +difference in first order it doesn't + + align:start position:0% +difference in first order it doesn't + + + align:start position:0% +difference in first order it doesn't +depend on the starting concentration + + align:start position:0% +depend on the starting concentration + + + align:start position:0% +depend on the starting concentration +just depends on the rate constant or the + + align:start position:0% +just depends on the rate constant or the + + + align:start position:0% +just depends on the rate constant or the +Decay constant which depends on the + + align:start position:0% +Decay constant which depends on the + + + align:start position:0% +Decay constant which depends on the +material in question with second order + + align:start position:0% +material in question with second order + + + align:start position:0% +material in question with second order +you do need to know how much you had + + align:start position:0% +you do need to know how much you had + + + align:start position:0% +you do need to know how much you had +originally so again how do you know if + + align:start position:0% +originally so again how do you know if + + + align:start position:0% +originally so again how do you know if +it's a first or a second order process + + align:start position:0% +it's a first or a second order process + + + align:start position:0% +it's a first or a second order process +and here it you really have to determine + + align:start position:0% +and here it you really have to determine + + + align:start position:0% +and here it you really have to determine +it experimentally so one thing you could + + align:start position:0% +it experimentally so one thing you could + + + align:start position:0% +it experimentally so one thing you could +do is measure how a changes over time + + align:start position:0% +do is measure how a changes over time + + + align:start position:0% +do is measure how a changes over time +and then plot your data using the + + align:start position:0% +and then plot your data using the + + + align:start position:0% +and then plot your data using the +equation for first order and you may see + + align:start position:0% +equation for first order and you may see + + + align:start position:0% +equation for first order and you may see +that uh yeah that does not form a + + align:start position:0% +that uh yeah that does not form a + + + align:start position:0% +that uh yeah that does not form a +straight line so when you're plotting + + align:start position:0% +straight line so when you're plotting + + + align:start position:0% +straight line so when you're plotting +with natural log of the concentration of + + align:start position:0% +with natural log of the concentration of + + + align:start position:0% +with natural log of the concentration of +a but then if you try plotting it one + + align:start position:0% +a but then if you try plotting it one + + + align:start position:0% +a but then if you try plotting it one +over the concentration of a may get a + + align:start position:0% +over the concentration of a may get a + + + align:start position:0% +over the concentration of a may get a +beautiful uh straight line with your + + align:start position:0% +beautiful uh straight line with your + + + align:start position:0% +beautiful uh straight line with your +data and so you'd say that's a second + + align:start position:0% +data and so you'd say that's a second + + + align:start position:0% +data and so you'd say that's a second +order process so again you're + + align:start position:0% +order process so again you're + + + align:start position:0% +order process so again you're +determining these things + + align:start position:0% +determining these things + + + align:start position:0% +determining these things +experimentally collecting data plotting + + align:start position:0% +experimentally collecting data plotting + + + align:start position:0% +experimentally collecting data plotting +the data determining rate constants + + align:start position:0% +the data determining rate constants + + + align:start position:0% +the data determining rate constants +determining the order of the reaction + + align:start position:0% +determining the order of the reaction + + + align:start position:0% +determining the order of the reaction +all right + + align:start position:0% +all right + + + align:start position:0% +all right +now this is very exciting what we're + + align:start position:0% +now this is very exciting what we're + + + align:start position:0% +now this is very exciting what we're +going to talk + + align:start position:0% +going to talk + + + align:start position:0% +going to talk +about is the relationship between rate + + align:start position:0% +about is the relationship between rate + + + align:start position:0% +about is the relationship between rate +constants and equilibrium constants so I + + align:start position:0% +constants and equilibrium constants so I + + + align:start position:0% +constants and equilibrium constants so I +love this I love when we come back to + + align:start position:0% +love this I love when we come back to + + + align:start position:0% +love this I love when we come back to +stuff that we've talked about before and + + align:start position:0% +stuff that we've talked about before and + + + align:start position:0% +stuff that we've talked about before and +see it in a slightly different way so at + + align:start position:0% +see it in a slightly different way so at + + + align:start position:0% +see it in a slightly different way so at +equilibrium we talked about how it's a + + align:start position:0% +equilibrium we talked about how it's a + + + align:start position:0% +equilibrium we talked about how it's a +dynamic process and you have the rate of + + align:start position:0% +dynamic process and you have the rate of + + + align:start position:0% +dynamic process and you have the rate of +the forward reaction equal the rate of + + align:start position:0% +the forward reaction equal the rate of + + + align:start position:0% +the forward reaction equal the rate of +the reverse reaction the reactions are + + align:start position:0% +the reverse reaction the reactions are + + + align:start position:0% +the reverse reaction the reactions are +still still going they haven't stopped + + align:start position:0% +still still going they haven't stopped + + + align:start position:0% +still still going they haven't stopped +but the rates are equal in both + + align:start position:0% +but the rates are equal in both + + + align:start position:0% +but the rates are equal in both +directions so we've talked about how to + + align:start position:0% +directions so we've talked about how to + + + align:start position:0% +directions so we've talked about how to +write an equilibrium constant for a + + align:start position:0% +write an equilibrium constant for a + + + align:start position:0% +write an equilibrium constant for a +reaction so if we have a reaction of a + + align:start position:0% +reaction so if we have a reaction of a + + + align:start position:0% +reaction so if we have a reaction of a +plus b going to C plus d we can write + + align:start position:0% +plus b going to C plus d we can write + + + align:start position:0% +plus b going to C plus d we can write +our equilibrium constant K and it's + + align:start position:0% +our equilibrium constant K and it's + + + align:start position:0% +our equilibrium constant K and it's +products over reactants unless one of + + align:start position:0% +products over reactants unless one of + + + align:start position:0% +products over reactants unless one of +our products of reactants is a solid or + + align:start position:0% +our products of reactants is a solid or + + + align:start position:0% +our products of reactants is a solid or +a very dilute solution it's the solvent + + align:start position:0% +a very dilute solution it's the solvent + + + align:start position:0% +a very dilute solution it's the solvent +and I heard from your Tas that in the + + align:start position:0% +and I heard from your Tas that in the + + + align:start position:0% +and I heard from your Tas that in the +last problem set some people had + + align:start position:0% +last problem set some people had + + + align:start position:0% +last problem set some people had +forgotten what goes into Q or k + + align:start position:0% +forgotten what goes into Q or k + + + align:start position:0% +forgotten what goes into Q or k +expression so that's good to review that + + align:start position:0% +expression so that's good to review that + + + align:start position:0% +expression so that's good to review that +for this next unit in exam four in the + + align:start position:0% +for this next unit in exam four in the + + + align:start position:0% +for this next unit in exam four in the +final um so products over + + align:start position:0% +final um so products over + + + align:start position:0% +final um so products over +reactants now + + align:start position:0% +reactants now + + + align:start position:0% +reactants now +suppose I tell you that it's a second + + align:start position:0% +suppose I tell you that it's a second + + + align:start position:0% +suppose I tell you that it's a second +order process and uh the rate of the + + align:start position:0% +order process and uh the rate of the + + + align:start position:0% +order process and uh the rate of the +forward reaction here A plus b we can + + align:start position:0% +forward reaction here A plus b we can + + + align:start position:0% +forward reaction here A plus b we can +write the rate law for that forward + + align:start position:0% +write the rate law for that forward + + + align:start position:0% +write the rate law for that forward +reaction being second order first order + + align:start position:0% +reaction being second order first order + + + align:start position:0% +reaction being second order first order +in a second or and first order in B so + + align:start position:0% +in a second or and first order in B so + + + align:start position:0% +in a second or and first order in B so +the rate constant for the forward + + align:start position:0% +the rate constant for the forward + + + align:start position:0% +the rate constant for the forward +direction is k1 and then times the + + align:start position:0% +direction is k1 and then times the + + + align:start position:0% +direction is k1 and then times the +concentration of a times the + + align:start position:0% +concentration of a times the + + + align:start position:0% +concentration of a times the +concentration of B for the reverse + + align:start position:0% +concentration of B for the reverse + + + align:start position:0% +concentration of B for the reverse +reaction the rate constant is K minus + + align:start position:0% +reaction the rate constant is K minus + + + align:start position:0% +reaction the rate constant is K minus +one and this is generally true in all + + align:start position:0% +one and this is generally true in all + + + align:start position:0% +one and this is generally true in all +the problems if it's the first step you + + align:start position:0% +the problems if it's the first step you + + + align:start position:0% +the problems if it's the first step you +have plus one K1 on the top K minus one + + align:start position:0% +have plus one K1 on the top K minus one + + + align:start position:0% +have plus one K1 on the top K minus one +on the bottom so we have K minus1 times + + align:start position:0% +on the bottom so we have K minus1 times + + + align:start position:0% +on the bottom so we have K minus1 times +the concentration of c and d so that's + + align:start position:0% +the concentration of c and d so that's + + + align:start position:0% +the concentration of c and d so that's +the backward + + align:start position:0% +the backward + + + align:start position:0% +the backward +Direction all right + + align:start position:0% +Direction all right + + + align:start position:0% +Direction all right +so at + + align:start position:0% +so at + + + align:start position:0% +so at +equilibrium these rates are equal we + + align:start position:0% +equilibrium these rates are equal we + + + align:start position:0% +equilibrium these rates are equal we +just talked about that we've seen that + + align:start position:0% +just talked about that we've seen that + + + align:start position:0% +just talked about that we've seen that +before the rate of the forward reaction + + align:start position:0% +before the rate of the forward reaction + + + align:start position:0% +before the rate of the forward reaction +so K1 * a * B is equal to K minus1 * C * + + align:start position:0% +so K1 * a * B is equal to K minus1 * C * + + + align:start position:0% +so K1 * a * B is equal to K minus1 * C * +D when you're at + + align:start position:0% +D when you're at + + + align:start position:0% +D when you're at +equilibrium so we can rearrange this + + align:start position:0% +equilibrium so we can rearrange this + + + align:start position:0% +equilibrium so we can rearrange this +equation now and say C and D over here + + align:start position:0% +equation now and say C and D over here + + + align:start position:0% +equation now and say C and D over here +over divide by A and B it's going to be + + align:start position:0% +over divide by A and B it's going to be + + + align:start position:0% +over divide by A and B it's going to be +equal to K1 over K + + align:start position:0% +equal to K1 over K + + + align:start position:0% +equal to K1 over K +minus1 and we also just saw that c * D + + align:start position:0% +minus1 and we also just saw that c * D + + + align:start position:0% +minus1 and we also just saw that c * D +over a * B was equal to + + align:start position:0% +over a * B was equal to + + + align:start position:0% +over a * B was equal to +K so therefore our equilibrium constant + + align:start position:0% +K so therefore our equilibrium constant + + + align:start position:0% +K so therefore our equilibrium constant +k equals K1 the rate constant for the + + align:start position:0% +k equals K1 the rate constant for the + + + align:start position:0% +k equals K1 the rate constant for the +forward Direction Over K minus one the + + align:start position:0% +forward Direction Over K minus one the + + + align:start position:0% +forward Direction Over K minus one the +rate constant for the reverse Direction + + align:start position:0% +rate constant for the reverse Direction + + + align:start position:0% +rate constant for the reverse Direction +so here we're relating equilibrium + + align:start position:0% +so here we're relating equilibrium + + + align:start position:0% +so here we're relating equilibrium +constants and rate + + align:start position:0% +constants and rate + + + align:start position:0% +constants and rate +constants so we thought a lot about + + align:start position:0% +constants so we thought a lot about + + + align:start position:0% +constants so we thought a lot about +what's true if you have a big + + align:start position:0% +what's true if you have a big + + + align:start position:0% +what's true if you have a big +equilibrium constant if you have a big + + align:start position:0% +equilibrium constant if you have a big + + + align:start position:0% +equilibrium constant if you have a big +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +constant if you have an equilibrium + + align:start position:0% +constant if you have an equilibrium + + + align:start position:0% +constant if you have an equilibrium +constant much greater than + + align:start position:0% +constant much greater than + + + align:start position:0% +constant much greater than +one what's the ratio to products and + + align:start position:0% +one what's the ratio to products and + + + align:start position:0% +one what's the ratio to products and +reactants at equilibrium there're more + + align:start position:0% +reactants at equilibrium there're more + + + align:start position:0% +reactants at equilibrium there're more +or less products at equilibrium than + + align:start position:0% +or less products at equilibrium than + + + align:start position:0% +or less products at equilibrium than +reactants more so we thought about that + + align:start position:0% +reactants more so we thought about that + + + align:start position:0% +reactants more so we thought about that +and now we can think about the + + align:start position:0% +and now we can think about the + + + align:start position:0% +and now we can think about the +relationship of the rate constants so if + + align:start position:0% +relationship of the rate constants so if + + + align:start position:0% +relationship of the rate constants so if +K is greater than one is k1 greater and + + align:start position:0% +K is greater than one is k1 greater and + + + align:start position:0% +K is greater than one is k1 greater and +less than k minus one + + align:start position:0% +less than k minus one + + + align:start position:0% +less than k minus one +greater and so that would then be the + + align:start position:0% +greater and so that would then be the + + + align:start position:0% +greater and so that would then be the +case where you have more products than + + align:start position:0% +case where you have more products than + + + align:start position:0% +case where you have more products than +reactants at equilibrium if K is less + + align:start position:0% +reactants at equilibrium if K is less + + + align:start position:0% +reactants at equilibrium if K is less +than one a case where there's more + + align:start position:0% +than one a case where there's more + + + align:start position:0% +than one a case where there's more +reactants than products at equilibrium + + align:start position:0% +reactants than products at equilibrium + + + align:start position:0% +reactants than products at equilibrium +then you have K1 is less than K minus + + align:start position:0% +then you have K1 is less than K minus + + + align:start position:0% +then you have K1 is less than K minus +one so again we can think about this in + + align:start position:0% +one so again we can think about this in + + + align:start position:0% +one so again we can think about this in +terms of thermodynamics we can also now + + align:start position:0% +terms of thermodynamics we can also now + + + align:start position:0% +terms of thermodynamics we can also now +think about it in terms of + + align:start position:0% +think about it in terms of + + + align:start position:0% +think about it in terms of +rates okay so one more thing that we + + align:start position:0% +rates okay so one more thing that we + + + align:start position:0% +rates okay so one more thing that we +need to uh cover before we end today and + + align:start position:0% +need to uh cover before we end today and + + + align:start position:0% +need to uh cover before we end today and +that is about elementary steps and + + align:start position:0% +that is about elementary steps and + + + align:start position:0% +that is about elementary steps and +molecularity which I just love saying + + align:start position:0% +molecularity which I just love saying + + + align:start position:0% +molecularity which I just love saying +that + + align:start position:0% +that + + + align:start position:0% +that +word so on Monday we're going to talk + + align:start position:0% +word so on Monday we're going to talk + + + align:start position:0% +word so on Monday we're going to talk +about mechanism of reactions most + + align:start position:0% +about mechanism of reactions most + + + align:start position:0% +about mechanism of reactions most +reactions do not occur in one step and + + align:start position:0% +reactions do not occur in one step and + + + align:start position:0% +reactions do not occur in one step and +we need to think about mechanisms I said + + align:start position:0% +we need to think about mechanisms I said + + + align:start position:0% +we need to think about mechanisms I said +it was Wednesday but it's actually + + align:start position:0% +it was Wednesday but it's actually + + + align:start position:0% +it was Wednesday but it's actually +Monday so it's coming up it's very + + align:start position:0% +Monday so it's coming up it's very + + + align:start position:0% +Monday so it's coming up it's very +exciting and we're going to talk a lot + + align:start position:0% +exciting and we're going to talk a lot + + + align:start position:0% +exciting and we're going to talk a lot +about elementary steps when we talk + + align:start position:0% +about elementary steps when we talk + + + align:start position:0% +about elementary steps when we talk +about mechanisms so an elementary um + + align:start position:0% +about mechanisms so an elementary um + + + align:start position:0% +about mechanisms so an elementary um +step is um one of the steps in the + + align:start position:0% +step is um one of the steps in the + + + align:start position:0% +step is um one of the steps in the +reaction so reactions usually don't + + align:start position:0% +reaction so reactions usually don't + + + align:start position:0% +reaction so reactions usually don't +occur in One Step they have many steps + + align:start position:0% +occur in One Step they have many steps + + + align:start position:0% +occur in One Step they have many steps +and each step is called an elementary + + align:start position:0% +and each step is called an elementary + + + align:start position:0% +and each step is called an elementary +reaction so we talked about last time + + align:start position:0% +reaction so we talked about last time + + + align:start position:0% +reaction so we talked about last time +that for the overall order of the + + align:start position:0% +that for the overall order of the + + + align:start position:0% +that for the overall order of the +reaction you can't just look at the + + align:start position:0% +reaction you can't just look at the + + + align:start position:0% +reaction you can't just look at the +stochiometry and say what the order of + + align:start position:0% +stochiometry and say what the order of + + + align:start position:0% +stochiometry and say what the order of +the reaction is so you can't predict it + + align:start position:0% +the reaction is so you can't predict it + + + align:start position:0% +the reaction is so you can't predict it +from stochiometry for an overall + + align:start position:0% +from stochiometry for an overall + + + align:start position:0% +from stochiometry for an overall +reaction but if it's an elementary + + align:start position:0% +reaction but if it's an elementary + + + align:start position:0% +reaction but if it's an elementary +reaction if it's a step that Elementary + + align:start position:0% +reaction if it's a step that Elementary + + + align:start position:0% +reaction if it's a step that Elementary +reaction is written exactly as it occurs + + align:start position:0% +reaction is written exactly as it occurs + + + align:start position:0% +reaction is written exactly as it occurs +so in that case the order and the rate + + align:start position:0% +so in that case the order and the rate + + + align:start position:0% +so in that case the order and the rate +law can be predicted so this is you + + align:start position:0% +law can be predicted so this is you + + + align:start position:0% +law can be predicted so this is you +breaking it down into sort of the + + align:start position:0% +breaking it down into sort of the + + + align:start position:0% +breaking it down into sort of the +smallest unit the smallest step this + + align:start position:0% +smallest unit the smallest step this + + + align:start position:0% +smallest unit the smallest step this +Elementary reaction so you can just look + + align:start position:0% +Elementary reaction so you can just look + + + align:start position:0% +Elementary reaction so you can just look +at the stochiometry for a single step + + align:start position:0% +at the stochiometry for a single step + + + align:start position:0% +at the stochiometry for a single step +for an elementary reaction and predict + + align:start position:0% +for an elementary reaction and predict + + + align:start position:0% +for an elementary reaction and predict +the order and the rate + + align:start position:0% +the order and the rate + + + align:start position:0% +the order and the rate +law so Elementary reactions occur + + align:start position:0% +law so Elementary reactions occur + + + align:start position:0% +law so Elementary reactions occur +exactly as written so that's what we're + + align:start position:0% +exactly as written so that's what we're + + + align:start position:0% +exactly as written so that's what we're +going to do on Monday we're going to + + align:start position:0% +going to do on Monday we're going to + + + align:start position:0% +going to do on Monday we're going to +break down our elementary our our + + align:start position:0% +break down our elementary our our + + + align:start position:0% +break down our elementary our our +mechanisms into Elementary steps write + + align:start position:0% +mechanisms into Elementary steps write + + + align:start position:0% +mechanisms into Elementary steps write +out the rate laws and then figure out um + + align:start position:0% +out the rate laws and then figure out um + + + align:start position:0% +out the rate laws and then figure out um +what kind of mechanism we might have all + + align:start position:0% +what kind of mechanism we might have all + + + align:start position:0% +what kind of mechanism we might have all +right so + + align:start position:0% +right so + + + align:start position:0% +right so +finally + + align:start position:0% +finally + + + align:start position:0% +finally +molecularity so molecularity is just the + + align:start position:0% +molecularity so molecularity is just the + + + align:start position:0% +molecularity so molecularity is just the +number of things that come together um + + align:start position:0% +number of things that come together um + + + align:start position:0% +number of things that come together um +to form a + + align:start position:0% +to form a + + + align:start position:0% +to form a +product and + + align:start position:0% +product and + + + align:start position:0% +product and +um here we have three names unimolecular + + align:start position:0% +um here we have three names unimolecular + + + align:start position:0% +um here we have three names unimolecular +bimolecular and + + align:start position:0% +bimolecular and + + + align:start position:0% +bimolecular and +termolecular unimolecular process what + + align:start position:0% +termolecular unimolecular process what + + + align:start position:0% +termolecular unimolecular process what +do you guess how many rea are coming + + align:start position:0% +do you guess how many rea are coming + + + align:start position:0% +do you guess how many rea are coming +together to form product + + align:start position:0% +together to form product + + + align:start position:0% +together to form product +one B molecular what do you guess two + + align:start position:0% +one B molecular what do you guess two + + + align:start position:0% +one B molecular what do you guess two +ter molecular is a little harder but + + align:start position:0% +ter molecular is a little harder but + + + align:start position:0% +ter molecular is a little harder but +just give it a whirl three yes so + + align:start position:0% +just give it a whirl three yes so + + + align:start position:0% +just give it a whirl three yes so +bimolecular is very + + align:start position:0% +bimolecular is very + + + align:start position:0% +bimolecular is very +common um + + align:start position:0% +common um + + + align:start position:0% +common um +so and termolecular is not so I have uh + + align:start position:0% +so and termolecular is not so I have uh + + + align:start position:0% +so and termolecular is not so I have uh +three uh three molecules to come + + align:start position:0% +three uh three molecules to come + + + align:start position:0% +three uh three molecules to come +together and if you try to think about + + align:start position:0% +together and if you try to think about + + + align:start position:0% +together and if you try to think about +how you get three things to come + + align:start position:0% +how you get three things to come + + + align:start position:0% +how you get three things to come +together all at the same time that's + + align:start position:0% +together all at the same time that's + + + align:start position:0% +together all at the same time that's +kind of rare usually when there three + + align:start position:0% +kind of rare usually when there three + + + align:start position:0% +kind of rare usually when there three +things reacting there multiple steps + + align:start position:0% +things reacting there multiple steps + + + align:start position:0% +things reacting there multiple steps +involved but two is good now finally + + align:start position:0% +involved but two is good now finally + + + align:start position:0% +involved but two is good now finally +we'll end with a clicker question um + + align:start position:0% +we'll end with a clicker question um + + + align:start position:0% +we'll end with a clicker question um +think about which of these would be + + align:start position:0% +think about which of these would be + + + align:start position:0% +think about which of these would be +examples of unimolecular + + align:start position:0% + + + + align:start position:0% + +processes 10 seconds + + align:start position:0% + + + + align:start position:0% + +yeah so it actually is one and two so uh + + align:start position:0% +yeah so it actually is one and two so uh + + + align:start position:0% +yeah so it actually is one and two so uh +most people got uh the two yes that's + + align:start position:0% +most people got uh the two yes that's + + + align:start position:0% +most people got uh the two yes that's +radioactive decay but the other you can + + align:start position:0% +radioactive decay but the other you can + + + align:start position:0% +radioactive decay but the other you can +have a decomposition so here we have + + align:start position:0% +have a decomposition so here we have + + + align:start position:0% +have a decomposition so here we have +decomposition into its elements is also + + align:start position:0% +decomposition into its elements is also + + + align:start position:0% +decomposition into its elements is also +uh A first order process all right Happy + + align:start position:0% +uh A first order process all right Happy + + + align:start position:0% +uh A first order process all right Happy +Thanksgiving everybody see you you next + + align:start position:0% +Thanksgiving everybody see you you next + + + align:start position:0% +Thanksgiving everybody see you you next +Monday \ No newline at end of file diff --git a/XaWCqLnjFZ8.txt b/XaWCqLnjFZ8.txt new file mode 100644 index 0000000000000000000000000000000000000000..4a57dfd291722350829a4f8d43cf1d3ef99c6854 --- /dev/null +++ b/XaWCqLnjFZ8.txt @@ -0,0 +1,2419 @@ +align:start position:0% + +very very happy. I actually transitions + + align:start position:0% +very very happy. I actually transitions + + + align:start position:0% +very very happy. I actually transitions +beautifully to Don Lassard's + + align:start position:0% +beautifully to Don Lassard's + + + align:start position:0% +beautifully to Don Lassard's +conversation on business models for + + align:start position:0% +conversation on business models for + + + align:start position:0% +conversation on business models for +deploying and how to get that upfront + + align:start position:0% +deploying and how to get that upfront + + + align:start position:0% +deploying and how to get that upfront +cost spread out. And uh Don, I I as I've + + align:start position:0% +cost spread out. And uh Don, I I as I've + + + align:start position:0% +cost spread out. And uh Don, I I as I've +done all all day, um you are much better + + align:start position:0% +done all all day, um you are much better + + + align:start position:0% +done all all day, um you are much better +off introducing yourself and all of your + + align:start position:0% +off introducing yourself and all of your + + + align:start position:0% +off introducing yourself and all of your +history than I I'll be brief on my + + align:start position:0% +history than I I'll be brief on my + + + align:start position:0% +history than I I'll be brief on my +history. I'm I'm Don Lassard. I'm an + + align:start position:0% +history. I'm I'm Don Lassard. I'm an + + + align:start position:0% +history. I'm I'm Don Lassard. I'm an +extinguished professor at MIT. + + align:start position:0% +extinguished professor at MIT. + + + align:start position:0% +extinguished professor at MIT. +51 years in the Sloan School. Uh my my + + align:start position:0% +51 years in the Sloan School. Uh my my + + + align:start position:0% +51 years in the Sloan School. Uh my my +claim to fame, I guess, here I I was one + + align:start position:0% +claim to fame, I guess, here I I was one + + + align:start position:0% +claim to fame, I guess, here I I was one +of the two faculty leaders on the energy + + align:start position:0% +of the two faculty leaders on the energy + + + align:start position:0% +of the two faculty leaders on the energy +minor that we built across all five + + align:start position:0% +minor that we built across all five + + + align:start position:0% +minor that we built across all five +schools, which was really really one of + + align:start position:0% +schools, which was really really one of + + + align:start position:0% +schools, which was really really one of +the most fun experiences at MIT. Uh I + + align:start position:0% +the most fun experiences at MIT. Uh I + + + align:start position:0% +the most fun experiences at MIT. Uh I +also once upon a time I taught finance + + align:start position:0% +also once upon a time I taught finance + + + align:start position:0% +also once upon a time I taught finance +and I came to realize this is largely + + align:start position:0% +and I came to realize this is largely + + + align:start position:0% +and I came to realize this is largely +about financial engineering. Not largely + + align:start position:0% +about financial engineering. Not largely + + + align:start position:0% +about financial engineering. Not largely +but financial engineering is + + align:start position:0% +but financial engineering is + + + align:start position:0% +but financial engineering is +overwhelmingly important here. Okay, I'm + + align:start position:0% +overwhelmingly important here. Okay, I'm + + + align:start position:0% +overwhelmingly important here. Okay, I'm +going to take just a little tiny slice + + align:start position:0% +going to take just a little tiny slice + + + align:start position:0% +going to take just a little tiny slice +of Nikki's presentation which is + + align:start position:0% +of Nikki's presentation which is + + + align:start position:0% +of Nikki's presentation which is +fantastic. Determining appropriate + + align:start position:0% +fantastic. Determining appropriate + + + align:start position:0% +fantastic. Determining appropriate +pricing that balances utility + + align:start position:0% +pricing that balances utility + + + align:start position:0% +pricing that balances utility +investments with customer usage. So to + + align:start position:0% +investments with customer usage. So to + + + align:start position:0% +investments with customer usage. So to +me that's the business model. All this + + align:start position:0% +me that's the business model. All this + + + align:start position:0% +me that's the business model. All this +other stuff is everything you need to do + + align:start position:0% +other stuff is everything you need to do + + + align:start position:0% +other stuff is everything you need to do +to get there. It's terribly even that + + align:start position:0% +to get there. It's terribly even that + + + align:start position:0% +to get there. It's terribly even that +piece is complicated enough. So, let's + + align:start position:0% +piece is complicated enough. So, let's + + + align:start position:0% +piece is complicated enough. So, let's +just focus on that one. Um, problem, + + align:start position:0% +just focus on that one. Um, problem, + + + align:start position:0% +just focus on that one. Um, problem, +right? High capital cost, but your + + align:start position:0% +right? High capital cost, but your + + + align:start position:0% +right? High capital cost, but your +all-in monthly cost has to come out + + align:start position:0% +all-in monthly cost has to come out + + + align:start position:0% +all-in monthly cost has to come out +about the same as the current all-in + + align:start position:0% +about the same as the current all-in + + + align:start position:0% +about the same as the current all-in +monthly cost of gas plus electricity. + + align:start position:0% +monthly cost of gas plus electricity. + + + align:start position:0% +monthly cost of gas plus electricity. +Otherwise, it's dead in the water. If + + align:start position:0% +Otherwise, it's dead in the water. If + + + align:start position:0% +Otherwise, it's dead in the water. If +you run current costs of geothermal, + + align:start position:0% +you run current costs of geothermal, + + + align:start position:0% +you run current costs of geothermal, +like your p even your second stage of + + align:start position:0% +like your p even your second stage of + + + align:start position:0% +like your p even your second stage of +your pilot through current utility + + align:start position:0% +your pilot through current utility + + + align:start position:0% +your pilot through current utility +models, it costs 2x at least. So it's + + align:start position:0% +models, it costs 2x at least. So it's + + + align:start position:0% +models, it costs 2x at least. So it's +two to three times as expensive as it + + align:start position:0% +two to three times as expensive as it + + + align:start position:0% +two to three times as expensive as it +needs to be to meet the cost right now. + + align:start position:0% +needs to be to meet the cost right now. + + + align:start position:0% +needs to be to meet the cost right now. +How do we get there? Well, this is my + + align:start position:0% +How do we get there? Well, this is my + + + align:start position:0% +How do we get there? Well, this is my +whole presentation. I have 17 more + + align:start position:0% +whole presentation. I have 17 more + + + align:start position:0% +whole presentation. I have 17 more +slides, but this is the whole + + align:start position:0% +slides, but this is the whole + + + align:start position:0% +slides, but this is the whole +presentation. + + align:start position:0% +presentation. + + + align:start position:0% +presentation. +Um, let's see. So, high capital costs. + + align:start position:0% +Um, let's see. So, high capital costs. + + + align:start position:0% +Um, let's see. So, high capital costs. +That's our issue. We are replacing ice + + align:start position:0% +That's our issue. We are replacing ice + + + align:start position:0% +That's our issue. We are replacing ice +boxes with refrigerators. + + align:start position:0% +boxes with refrigerators. + + + align:start position:0% +boxes with refrigerators. +We don't have to buy the ice every day, + + align:start position:0% +We don't have to buy the ice every day, + + + align:start position:0% +We don't have to buy the ice every day, +but the refrigerator costs a lot. And + + align:start position:0% +but the refrigerator costs a lot. And + + + align:start position:0% +but the refrigerator costs a lot. And +when I hear discussions of pricing, it + + align:start position:0% +when I hear discussions of pricing, it + + + align:start position:0% +when I hear discussions of pricing, it +seems to me we're still trying to price + + align:start position:0% +seems to me we're still trying to price + + + align:start position:0% +seems to me we're still trying to price +it. is if we're pricing ice whereas in + + align:start position:0% +it. is if we're pricing ice whereas in + + + align:start position:0% +it. is if we're pricing ice whereas in +fact we're renting a we're renting a + + align:start position:0% +fact we're renting a we're renting a + + + align:start position:0% +fact we're renting a we're renting a +refrigerator right so if you think of it + + align:start position:0% +refrigerator right so if you think of it + + + align:start position:0% +refrigerator right so if you think of it +as renting a refrigerator that's the + + align:start position:0% +as renting a refrigerator that's the + + + align:start position:0% +as renting a refrigerator that's the +analogy we want as opposed to we're + + align:start position:0% +analogy we want as opposed to we're + + + align:start position:0% +analogy we want as opposed to we're +buying ice uh so one-third bore holes + + align:start position:0% +buying ice uh so one-third bore holes + + + align:start position:0% +buying ice uh so one-third bore holes +one-ird system one-third customer and + + align:start position:0% +one-ird system one-third customer and + + + align:start position:0% +one-ird system one-third customer and +system and conversion I'd like I thought + + align:start position:0% +system and conversion I'd like I thought + + + align:start position:0% +system and conversion I'd like I thought +I'd corrected that how do we solve the + + align:start position:0% +I'd corrected that how do we solve the + + + align:start position:0% +I'd corrected that how do we solve the +problem is this is now 2x right we need + + align:start position:0% +problem is this is now 2x right we need + + + align:start position:0% +problem is this is now 2x right we need +to get monthly cost of the homeowner + + align:start position:0% +to get monthly cost of the homeowner + + + align:start position:0% +to get monthly cost of the homeowner +near current electrical and gas bill + + align:start position:0% +near current electrical and gas bill + + + align:start position:0% +near current electrical and gas bill +that's what we have to + + align:start position:0% +that's what we have to + + + align:start position:0% +that's what we have to +2x. How do we get there? Well, we got to + + align:start position:0% +2x. How do we get there? Well, we got to + + + align:start position:0% +2x. How do we get there? Well, we got to +reduce the capital cost. So, you got to + + align:start position:0% +reduce the capital cost. So, you got to + + + align:start position:0% +reduce the capital cost. So, you got to +work like crazy. The unions have to work + + align:start position:0% +work like crazy. The unions have to work + + + align:start position:0% +work like crazy. The unions have to work +like crazy. We have to get down a + + align:start position:0% +like crazy. We have to get down a + + + align:start position:0% +like crazy. We have to get down a +learning curve. We really have to do + + align:start position:0% +learning curve. We really have to do + + + align:start position:0% +learning curve. We really have to do +this, right? The capital cost must come + + align:start position:0% +this, right? The capital cost must come + + + align:start position:0% +this, right? The capital cost must come +down. + + align:start position:0% +down. + + + align:start position:0% +down. +We have to allocate. At the moment, + + align:start position:0% +We have to allocate. At the moment, + + + align:start position:0% +We have to allocate. At the moment, +we're overbuilding these systems. Loop + + align:start position:0% +we're overbuilding these systems. Loop + + + align:start position:0% +we're overbuilding these systems. Loop +one, 425 tons against 70 275 tons + + align:start position:0% +one, 425 tons against 70 275 tons + + + align:start position:0% +one, 425 tons against 70 275 tons +actually used, right? You overbuild the + + align:start position:0% +actually used, right? You overbuild the + + + align:start position:0% +actually used, right? You overbuild the +system or whatever the numbers are. + + align:start position:0% +system or whatever the numbers are. + + + align:start position:0% +system or whatever the numbers are. +Overbuild the system by a massive + + align:start position:0% +Overbuild the system by a massive + + + align:start position:0% +Overbuild the system by a massive +amount. Somehow or another the excess + + align:start position:0% +amount. Somehow or another the excess + + + align:start position:0% +amount. Somehow or another the excess +capacity has to get banked and the + + align:start position:0% +capacity has to get banked and the + + + align:start position:0% +capacity has to get banked and the +customers only have to get charged for + + align:start position:0% +customers only have to get charged for + + + align:start position:0% +customers only have to get charged for +the actual used capacity. Third, + + align:start position:0% +the actual used capacity. Third, + + + align:start position:0% +the actual used capacity. Third, +right, this is a lot of the discussion. + + align:start position:0% +right, this is a lot of the discussion. + + + align:start position:0% +right, this is a lot of the discussion. +How do we monetize some of these other + + align:start position:0% +How do we monetize some of these other + + + align:start position:0% +How do we monetize some of these other +benefits? How do we get a heat pump tax? + + align:start position:0% +benefits? How do we get a heat pump tax? + + + align:start position:0% +benefits? How do we get a heat pump tax? +How do we get an investment tax credit? + + align:start position:0% +How do we get an investment tax credit? + + + align:start position:0% +How do we get an investment tax credit? +How do we get some payment for the + + align:start position:0% +How do we get some payment for the + + + align:start position:0% +How do we get some payment for the +avoided utility investments? Those are + + align:start position:0% +avoided utility investments? Those are + + + align:start position:0% +avoided utility investments? Those are +huge. + + align:start position:0% +huge. + + + align:start position:0% +huge. +Monetize other benefits and apply. So + + align:start position:0% +Monetize other benefits and apply. So + + + align:start position:0% +Monetize other benefits and apply. So +and then the financial engineering part + + align:start position:0% +and then the financial engineering part + + + align:start position:0% +and then the financial engineering part +is how do we spread the recovery of the + + align:start position:0% +is how do we spread the recovery of the + + + align:start position:0% +is how do we spread the recovery of the +capital over 30 years in constant terms + + align:start position:0% +capital over 30 years in constant terms + + + align:start position:0% +capital over 30 years in constant terms +inflationadjusted terms real terms + + align:start position:0% +inflationadjusted terms real terms + + + align:start position:0% +inflationadjusted terms real terms +if we run it through the current utility + + align:start position:0% +if we run it through the current utility + + + align:start position:0% +if we run it through the current utility +model it looks like this in real terms + + align:start position:0% +model it looks like this in real terms + + + align:start position:0% +model it looks like this in real terms +it's big in the first year gets smaller + + align:start position:0% +it's big in the first year gets smaller + + + align:start position:0% +it's big in the first year gets smaller +over time it's twice as high as it ought + + align:start position:0% +over time it's twice as high as it ought + + + align:start position:0% +over time it's twice as high as it ought +to be because we're using we're not even + + align:start position:0% +to be because we're using we're not even + + + align:start position:0% +to be because we're using we're not even +using a nominal level payment mortgage + + align:start position:0% +using a nominal level payment mortgage + + + align:start position:0% +using a nominal level payment mortgage +we're using rate of return plus + + align:start position:0% +we're using rate of return plus + + + align:start position:0% +we're using rate of return plus +depreciation, right? + + align:start position:0% +depreciation, right? + + + align:start position:0% +depreciation, right? +Well, 30 years ago, we invented a level + + align:start position:0% +Well, 30 years ago, we invented a level + + + align:start position:0% +Well, 30 years ago, we invented a level +payment novel mortgage. How do we spread + + align:start position:0% +payment novel mortgage. How do we spread + + + align:start position:0% +payment novel mortgage. How do we spread +the cost of capital equally in real + + align:start position:0% +the cost of capital equally in real + + + align:start position:0% +the cost of capital equally in real +terms over time? If we could do all of + + align:start position:0% +terms over time? If we could do all of + + + align:start position:0% +terms over time? If we could do all of +those things, we'd be there. So, you do + + align:start position:0% +those things, we'd be there. So, you do + + + align:start position:0% +those things, we'd be there. So, you do +your job in getting the cost down, + + align:start position:0% +your job in getting the cost down, + + + align:start position:0% +your job in getting the cost down, +really build it neat. Uh we find a way + + align:start position:0% +really build it neat. Uh we find a way + + + align:start position:0% +really build it neat. Uh we find a way +to bring in some of the other grants and + + align:start position:0% +to bring in some of the other grants and + + + align:start position:0% +to bring in some of the other grants and +tax incentives. Uh we grab back some of + + align:start position:0% +tax incentives. Uh we grab back some of + + + align:start position:0% +tax incentives. Uh we grab back some of +the avoided costs out of the electrical + + align:start position:0% +the avoided costs out of the electrical + + + align:start position:0% +the avoided costs out of the electrical +system. Ideally, we get some carbon + + align:start position:0% +system. Ideally, we get some carbon + + + align:start position:0% +system. Ideally, we get some carbon +credits for the carbon saved and then we + + align:start position:0% +credits for the carbon saved and then we + + + align:start position:0% +credits for the carbon saved and then we +spread the capital cost evenly and then + + align:start position:0% +spread the capital cost evenly and then + + + align:start position:0% +spread the capital cost evenly and then +people say, "Gee, this is more + + align:start position:0% +people say, "Gee, this is more + + + align:start position:0% +people say, "Gee, this is more +economical + + align:start position:0% +economical + + + align:start position:0% +economical +than the existing system and it's better + + align:start position:0% +than the existing system and it's better + + + align:start position:0% +than the existing system and it's better +for our kids, it's better for our + + align:start position:0% +for our kids, it's better for our + + + align:start position:0% +for our kids, it's better for our +community, we avoid the heat islands, we + + align:start position:0% +community, we avoid the heat islands, we + + + align:start position:0% +community, we avoid the heat islands, we +avoid all the other stuff." So, we get + + align:start position:0% +avoid all the other stuff." So, we get + + + align:start position:0% +avoid all the other stuff." So, we get +all these other bennies for free in a + + align:start position:0% +all these other bennies for free in a + + + align:start position:0% +all these other bennies for free in a +sense. Okay. Uh learning curve. So, + + align:start position:0% +sense. Okay. Uh learning curve. So, + + + align:start position:0% +sense. Okay. Uh learning curve. So, +learning curve, right? + + align:start position:0% +learning curve, right? + + + align:start position:0% +learning curve, right? +There are learning curves out there. + + align:start position:0% +There are learning curves out there. + + + align:start position:0% +There are learning curves out there. +There's evidence out there. It looks + + align:start position:0% +There's evidence out there. It looks + + + align:start position:0% +There's evidence out there. It looks +like you've got 50% from one to two, but + + align:start position:0% +like you've got 50% from one to two, but + + + align:start position:0% +like you've got 50% from one to two, but +probably this is going to be an 11 or + + align:start position:0% +probably this is going to be an 11 or + + + align:start position:0% +probably this is going to be an 11 or +12% learning curve over time. Like a lot + + align:start position:0% +12% learning curve over time. Like a lot + + + align:start position:0% +12% learning curve over time. Like a lot +there's a lot of evidence on this. So to + + align:start position:0% +there's a lot of evidence on this. So to + + + align:start position:0% +there's a lot of evidence on this. So to +the ratebased folk, we'd say you got to + + align:start position:0% +the ratebased folk, we'd say you got to + + + align:start position:0% +the ratebased folk, we'd say you got to +be willing to eat some of it because + + align:start position:0% +be willing to eat some of it because + + + align:start position:0% +be willing to eat some of it because +you're investing against the learning + + align:start position:0% +you're investing against the learning + + + align:start position:0% +you're investing against the learning +curve and there's an investment in the + + align:start position:0% +curve and there's an investment in the + + + align:start position:0% +curve and there's an investment in the +learning curve. And so you can't load + + align:start position:0% +learning curve. And so you can't load + + + align:start position:0% +learning curve. And so you can't load +all of the current costs onto the + + align:start position:0% +all of the current costs onto the + + + align:start position:0% +all of the current costs onto the +current customers because part of the + + align:start position:0% +current customers because part of the + + + align:start position:0% +current customers because part of the +current cost is a public benefit of the + + align:start position:0% +current cost is a public benefit of the + + + align:start position:0% +current cost is a public benefit of the +learning curve that everyone else will + + align:start position:0% +learning curve that everyone else will + + + align:start position:0% +learning curve that everyone else will +gain. And so this has to be built into + + align:start position:0% +gain. And so this has to be built into + + + align:start position:0% +gain. And so this has to be built into +the thinking. Um + + align:start position:0% +the thinking. Um + + + align:start position:0% +the thinking. Um +excess capacity well let's allocate only + + align:start position:0% +excess capacity well let's allocate only + + + align:start position:0% +excess capacity well let's allocate only +the capacity used right and the excess + + align:start position:0% +the capacity used right and the excess + + + align:start position:0% +the capacity used right and the excess +capacity is banked. + + align:start position:0% +capacity is banked. + + + align:start position:0% +capacity is banked. +um mechanisms to monetize benefit. So, + + align:start position:0% +um mechanisms to monetize benefit. So, + + + align:start position:0% +um mechanisms to monetize benefit. So, +assignment of carbon tax or renewable + + align:start position:0% +assignment of carbon tax or renewable + + + align:start position:0% +assignment of carbon tax or renewable +energy, linkage of various incentive + + align:start position:0% +energy, linkage of various incentive + + + align:start position:0% +energy, linkage of various incentive +systems, assignment of voided cost + + align:start position:0% +systems, assignment of voided cost + + + align:start position:0% +systems, assignment of voided cost +credits. I mean, complicated, really + + align:start position:0% +credits. I mean, complicated, really + + + align:start position:0% +credits. I mean, complicated, really +complicated and hard to do, but we've + + align:start position:0% +complicated and hard to do, but we've + + + align:start position:0% +complicated and hard to do, but we've +got to get our act together and make + + align:start position:0% +got to get our act together and make + + + align:start position:0% +got to get our act together and make +this all in one place. + + align:start position:0% +this all in one place. + + + align:start position:0% +this all in one place. +Capital recovery model. And I don't + + align:start position:0% +Capital recovery model. And I don't + + + align:start position:0% +Capital recovery model. And I don't +expect everybody to follow this at uh + + align:start position:0% +expect everybody to follow this at uh + + + align:start position:0% +expect everybody to follow this at uh +3:30 in the afternoon. But if you take + + align:start position:0% +3:30 in the afternoon. But if you take + + + align:start position:0% +3:30 in the afternoon. But if you take +cost of capital times unavertised + + align:start position:0% +cost of capital times unavertised + + + align:start position:0% +cost of capital times unavertised +capital plus depreciation and you look + + align:start position:0% +capital plus depreciation and you look + + + align:start position:0% +capital plus depreciation and you look +at your annual charge, it starts on a + + align:start position:0% +at your annual charge, it starts on a + + + align:start position:0% +at your annual charge, it starts on a +50, you know, it starts high and it + + align:start position:0% +50, you know, it starts high and it + + + align:start position:0% +50, you know, it starts high and it +comes down over time. If you have a + + align:start position:0% +comes down over time. If you have a + + + align:start position:0% +comes down over time. If you have a +level nominal charge, right? It's like + + align:start position:0% +level nominal charge, right? It's like + + + align:start position:0% +level nominal charge, right? It's like +that. A level real charge would be + + align:start position:0% +that. A level real charge would be + + + align:start position:0% +that. A level real charge would be +rising over time with inflation. + + align:start position:0% +rising over time with inflation. + + + align:start position:0% +rising over time with inflation. +Short story. + + align:start position:0% +Short story. + + + align:start position:0% +Short story. +If you if you had a payment that looked + + align:start position:0% +If you if you had a payment that looked + + + align:start position:0% +If you if you had a payment that looked +like an index treasury + + align:start position:0% +like an index treasury + + + align:start position:0% +like an index treasury +and you could tell people that looks + + align:start position:0% +and you could tell people that looks + + + align:start position:0% +and you could tell people that looks +like social security because social + + align:start position:0% +like social security because social + + + align:start position:0% +like social security because social +security is indexed to inflation. + + align:start position:0% +security is indexed to inflation. + + + align:start position:0% +security is indexed to inflation. +If you have a payment that's indexed to + + align:start position:0% +If you have a payment that's indexed to + + + align:start position:0% +If you have a payment that's indexed to +social security, it can start at 1/ half + + align:start position:0% +social security, it can start at 1/ half + + + align:start position:0% +social security, it can start at 1/ half +the level of a fixed nominal payment and + + align:start position:0% +the level of a fixed nominal payment and + + + align:start position:0% +the level of a fixed nominal payment and +it will grow at social security over + + align:start position:0% +it will grow at social security over + + + align:start position:0% +it will grow at social security over +time and it will give the utility the + + align:start position:0% +time and it will give the utility the + + + align:start position:0% +time and it will give the utility the +rate of return that they're allowed full + + align:start position:0% +rate of return that they're allowed full + + + align:start position:0% +rate of return that they're allowed full +recovery of capital. + + align:start position:0% + + + + align:start position:0% + +It's fairly straightforward. Just have + + align:start position:0% +It's fairly straightforward. Just have + + + align:start position:0% +It's fairly straightforward. Just have +to do it. Okay. Uh so constant real + + align:start position:0% +to do it. Okay. Uh so constant real + + + align:start position:0% +to do it. Okay. Uh so constant real +capital recovery. There are ways to do + + align:start position:0% +capital recovery. There are ways to do + + + align:start position:0% +capital recovery. There are ways to do +this. Uh I wrote it up in 1975 for + + align:start position:0% +this. Uh I wrote it up in 1975 for + + + align:start position:0% +this. Uh I wrote it up in 1975 for +totally different reasons. Uh it's all + + align:start position:0% +totally different reasons. Uh it's all + + + align:start position:0% +totally different reasons. Uh it's all +in there. Okay. Now, alternative pricing + + align:start position:0% +in there. Okay. Now, alternative pricing + + + align:start position:0% +in there. Okay. Now, alternative pricing +models. Uh we could consumer purchase + + align:start position:0% +models. Uh we could consumer purchase + + + align:start position:0% +models. Uh we could consumer purchase +inhome uh and the utility supplies the + + align:start position:0% +inhome uh and the utility supplies the + + + align:start position:0% +inhome uh and the utility supplies the +common stuff or the utility supplies + + align:start position:0% +common stuff or the utility supplies + + + align:start position:0% +common stuff or the utility supplies +everything. Right? Those would be the + + align:start position:0% +everything. Right? Those would be the + + + align:start position:0% +everything. Right? Those would be the +two choices. And you could charge for + + align:start position:0% +two choices. And you could charge for + + + align:start position:0% +two choices. And you could charge for +thermal usage or you could charge for + + align:start position:0% +thermal usage or you could charge for + + + align:start position:0% +thermal usage or you could charge for +capacity. I personally like charging for + + align:start position:0% +capacity. I personally like charging for + + + align:start position:0% +capacity. I personally like charging for +capacity. I'm being told five minutes. I + + align:start position:0% +capacity. I'm being told five minutes. I + + + align:start position:0% +capacity. I'm being told five minutes. I +think thermal usage is a little bit like + + align:start position:0% +think thermal usage is a little bit like + + + align:start position:0% +think thermal usage is a little bit like +charging for ice in the ice box. I'd + + align:start position:0% +charging for ice in the ice box. I'd + + + align:start position:0% +charging for ice in the ice box. I'd +like capacities. These are fixed cost + + align:start position:0% +like capacities. These are fixed cost + + + align:start position:0% +like capacities. These are fixed cost +systems. You're largely talking about + + align:start position:0% +systems. You're largely talking about + + + align:start position:0% +systems. You're largely talking about +recovering capital costs. But one, two, + + align:start position:0% +recovering capital costs. But one, two, + + + align:start position:0% +recovering capital costs. But one, two, +or three or four. Okay. But now let's + + align:start position:0% +or three or four. Okay. But now let's + + + align:start position:0% +or three or four. Okay. But now let's +get simple pass forward. Stage one, + + align:start position:0% +get simple pass forward. Stage one, + + + align:start position:0% +get simple pass forward. Stage one, +pilot stage. Stage two, roll out stage. + + align:start position:0% +pilot stage. Stage two, roll out stage. + + + align:start position:0% +pilot stage. Stage two, roll out stage. +Stage three, steady state. In pilot + + align:start position:0% +Stage three, steady state. In pilot + + + align:start position:0% +Stage three, steady state. In pilot +stage, there are only very few systems. + + align:start position:0% +stage, there are only very few systems. + + + align:start position:0% +stage, there are only very few systems. +They're incomplete. There's no market + + align:start position:0% +They're incomplete. There's no market + + + align:start position:0% +They're incomplete. There's no market +for there's no thermal market and the + + align:start position:0% +for there's no thermal market and the + + + align:start position:0% +for there's no thermal market and the +vintage for the technical types the + + align:start position:0% +vintage for the technical types the + + + align:start position:0% +vintage for the technical types the +vintage of capital is too young. It's + + align:start position:0% +vintage of capital is too young. It's + + + align:start position:0% +vintage of capital is too young. It's +all new and so if you have standard rate + + align:start position:0% +all new and so if you have standard rate + + + align:start position:0% +all new and so if you have standard rate +recovery you're going to be recovering + + align:start position:0% +recovery you're going to be recovering + + + align:start position:0% +recovery you're going to be recovering +way too high rates. What would I do if I + + align:start position:0% +way too high rates. What would I do if I + + + align:start position:0% +way too high rates. What would I do if I +were in Jaime's position? I'd say in the + + align:start position:0% +were in Jaime's position? I'd say in the + + + align:start position:0% +were in Jaime's position? I'd say in the +short run we fix the cost equal to the + + align:start position:0% +short run we fix the cost equal to the + + + align:start position:0% +short run we fix the cost equal to the +current charge + + align:start position:0% +current charge + + + align:start position:0% +current charge +per unit of capacity period + + align:start position:0% +per unit of capacity period + + + align:start position:0% +per unit of capacity period +and we charge the customer with that + + align:start position:0% +and we charge the customer with that + + + align:start position:0% +and we charge the customer with that +amount and the difference 80% of the + + align:start position:0% +amount and the difference 80% of the + + + align:start position:0% +amount and the difference 80% of the +difference we stick on rate base + + align:start position:0% +difference we stick on rate base + + + align:start position:0% +difference we stick on rate base +20% of the difference we give to Nikki + + align:start position:0% +20% of the difference we give to Nikki + + + align:start position:0% +20% of the difference we give to Nikki +so she has an an incentive to bring the + + align:start position:0% +so she has an an incentive to bring the + + + align:start position:0% +so she has an an incentive to bring the +difference down right we say basically + + align:start position:0% +difference down right we say basically + + + align:start position:0% +difference down right we say basically +we're going to price it off current gas + + align:start position:0% +we're going to price it off current gas + + + align:start position:0% +we're going to price it off current gas +plus electricity + + align:start position:0% +plus electricity + + + align:start position:0% +plus electricity +and we're going to stick the rest of it + + align:start position:0% +and we're going to stick the rest of it + + + align:start position:0% +and we're going to stick the rest of it +the rate base for learning curve for + + align:start position:0% +the rate base for learning curve for + + + align:start position:0% +the rate base for learning curve for +learning for all of these other benefits + + align:start position:0% +learning for all of these other benefits + + + align:start position:0% +learning for all of these other benefits +in the first and you might to protect + + align:start position:0% +in the first and you might to protect + + + align:start position:0% +in the first and you might to protect +yourself you might say for up to 3% of + + align:start position:0% +yourself you might say for up to 3% of + + + align:start position:0% +yourself you might say for up to 3% of +the ext installed base or up to 5% of + + align:start position:0% +the ext installed base or up to 5% of + + + align:start position:0% +the ext installed base or up to 5% of +the installed base this is a learning + + align:start position:0% +the installed base this is a learning + + + align:start position:0% +the installed base this is a learning +investment just matches the old one + + align:start position:0% +investment just matches the old one + + + align:start position:0% +investment just matches the old one +roll out stage you're still going to + + align:start position:0% +roll out stage you're still going to + + + align:start position:0% +roll out stage you're still going to +have relatively few systems but you can + + align:start position:0% +have relatively few systems but you can + + + align:start position:0% +have relatively few systems but you can +you can do a cost of capital recovery on + + align:start position:0% +you can do a cost of capital recovery on + + + align:start position:0% +you can do a cost of capital recovery on +those systems as long as it's level and + + align:start position:0% +those systems as long as it's level and + + + align:start position:0% +those systems as long as it's level and +real as opposed to nominal and declining + + align:start position:0% +real as opposed to nominal and declining + + + align:start position:0% +real as opposed to nominal and declining +steady state, it doesn't matter because + + align:start position:0% +steady state, it doesn't matter because + + + align:start position:0% +steady state, it doesn't matter because +you're going to have investments of all + + align:start position:0% +you're going to have investments of all + + + align:start position:0% +you're going to have investments of all +vintages and it's going to look like the + + align:start position:0% +vintages and it's going to look like the + + + align:start position:0% +vintages and it's going to look like the +existing system and you could go back to + + align:start position:0% +existing system and you could go back to + + + align:start position:0% +existing system and you could go back to +the existing system if you wanted to. + + align:start position:0% +the existing system if you wanted to. + + + align:start position:0% +the existing system if you wanted to. +But by then, by then you would have + + align:start position:0% +But by then, by then you would have + + + align:start position:0% +But by then, by then you would have +devised a new system. And remember this + + align:start position:0% +devised a new system. And remember this + + + align:start position:0% +devised a new system. And remember this +is the problem for utilities in general. + + align:start position:0% +is the problem for utilities in general. + + + align:start position:0% +is the problem for utilities in general. +We're going from operating cost to + + align:start position:0% +We're going from operating cost to + + + align:start position:0% +We're going from operating cost to +capital costs. Renewables are capital + + align:start position:0% +capital costs. Renewables are capital + + + align:start position:0% +capital costs. Renewables are capital +costs. We're getting rid of fossil fuels + + align:start position:0% +costs. We're getting rid of fossil fuels + + + align:start position:0% +costs. We're getting rid of fossil fuels +which are operating costs. So this helps + + align:start position:0% +which are operating costs. So this helps + + + align:start position:0% +which are operating costs. So this helps +us actually move from a volumetric to a + + align:start position:0% +us actually move from a volumetric to a + + + align:start position:0% +us actually move from a volumetric to a +capacity charging system. Okay, I got + + align:start position:0% +capacity charging system. Okay, I got + + + align:start position:0% +capacity charging system. Okay, I got +one more two more minutes. Uh + + align:start position:0% +one more two more minutes. Uh + + + align:start position:0% +one more two more minutes. Uh +consideration for low-income lowwealth + + align:start position:0% +consideration for low-income lowwealth + + + align:start position:0% +consideration for low-income lowwealth +households. I think this would be a + + align:start position:0% +households. I think this would be a + + + align:start position:0% +households. I think this would be a +great area. Take the one-third that is + + align:start position:0% +great area. Take the one-third that is + + + align:start position:0% +great area. Take the one-third that is +the retrofit in the internal system. Get + + align:start position:0% +the retrofit in the internal system. Get + + + align:start position:0% +the retrofit in the internal system. Get +the Boston Foundation to work with you. + + align:start position:0% +the Boston Foundation to work with you. + + + align:start position:0% +the Boston Foundation to work with you. +Get them to buy down the cost of the + + align:start position:0% +Get them to buy down the cost of the + + + align:start position:0% +Get them to buy down the cost of the +household part for low-income + + align:start position:0% +household part for low-income + + + align:start position:0% +household part for low-income +households. + + align:start position:0% +households. + + + align:start position:0% +households. +Don't throw it at the utility. + + align:start position:0% +Don't throw it at the utility. + + + align:start position:0% +Don't throw it at the utility. +say twothirds of it is a standard rate + + align:start position:0% +say twothirds of it is a standard rate + + + align:start position:0% +say twothirds of it is a standard rate +and if you qualify low income we'll buy + + align:start position:0% +and if you qualify low income we'll buy + + + align:start position:0% +and if you qualify low income we'll buy +down the other third and that will help + + align:start position:0% +down the other third and that will help + + + align:start position:0% +down the other third and that will help +us get all of the 20 houses around the + + align:start position:0% +us get all of the 20 houses around the + + + align:start position:0% +us get all of the 20 houses around the +culdesac to convert. Uh then their + + align:start position:0% +culdesac to convert. Uh then their + + + align:start position:0% +culdesac to convert. Uh then their +appendices so that's it. Uh + + align:start position:0% + + + + align:start position:0% + +so thank you Don. So so Don is a + + align:start position:0% +so thank you Don. So so Don is a + + + align:start position:0% +so thank you Don. So so Don is a +neighbor and I went for a walk and I + + align:start position:0% +neighbor and I went for a walk and I + + + align:start position:0% +neighbor and I went for a walk and I +said well here's here's where we are + + align:start position:0% +said well here's here's where we are + + + align:start position:0% +said well here's here's where we are +with the cost. Can you figure out some + + align:start position:0% +with the cost. Can you figure out some + + + align:start position:0% +with the cost. Can you figure out some +solutions? So uh + + align:start position:0% +solutions? So uh + + + align:start position:0% +solutions? So uh +uh and I I just if you if you didn't + + align:start position:0% +uh and I I just if you if you didn't + + + align:start position:0% +uh and I I just if you if you didn't +catch that in in the delusion of + + align:start position:0% +catch that in in the delusion of + + + align:start position:0% +catch that in in the delusion of +information and ideas um he he's putting + + align:start position:0% +information and ideas um he he's putting + + + align:start position:0% +information and ideas um he he's putting +out a whole bunch of series of solutions + + align:start position:0% +out a whole bunch of series of solutions + + + align:start position:0% +out a whole bunch of series of solutions +to deal with the cost as it is today + + align:start position:0% +to deal with the cost as it is today + + + align:start position:0% +to deal with the cost as it is today +with the first projects. And one of the + + align:start position:0% +with the first projects. And one of the + + + align:start position:0% +with the first projects. And one of the +things I want to flag on that is that + + align:start position:0% +things I want to flag on that is that + + + align:start position:0% +things I want to flag on that is that +that cost today with these first + + align:start position:0% +that cost today with these first + + + align:start position:0% +that cost today with these first +projects includes the entire cost of the + + align:start position:0% +projects includes the entire cost of the + + + align:start position:0% +projects includes the entire cost of the +building transition which incidentally + + align:start position:0% +building transition which incidentally + + + align:start position:0% +building transition which incidentally +also includes all of the like challenges + + align:start position:0% +also includes all of the like challenges + + + align:start position:0% +also includes all of the like challenges +of our aging. I think someone said + + align:start position:0% +of our aging. I think someone said + + + align:start position:0% +of our aging. I think someone said +crappy buildings. Yeah, we we have + + align:start position:0% +crappy buildings. Yeah, we we have + + + align:start position:0% +crappy buildings. Yeah, we we have +crappy buildings here. Just saying it. + + align:start position:0% +crappy buildings here. Just saying it. + + + align:start position:0% +crappy buildings here. Just saying it. +and and all of those problems that are + + align:start position:0% +and and all of those problems that are + + + align:start position:0% +and and all of those problems that are +ne from a hundred years of neglect, the + + align:start position:0% +ne from a hundred years of neglect, the + + + align:start position:0% +ne from a hundred years of neglect, the +asbestos, the mold, the faulty wiring, + + align:start position:0% +asbestos, the mold, the faulty wiring, + + + align:start position:0% +asbestos, the mold, the faulty wiring, +the code violations, they are a part of + + align:start position:0% +the code violations, they are a part of + + + align:start position:0% +the code violations, they are a part of +the challenge of decarbonizing our + + align:start position:0% +the challenge of decarbonizing our + + + align:start position:0% +the challenge of decarbonizing our +buildings because you cross the + + align:start position:0% +buildings because you cross the + + + align:start position:0% +buildings because you cross the +threshold and you have to deal with + + align:start position:0% +threshold and you have to deal with + + + align:start position:0% +threshold and you have to deal with +them. And so that cost is baked into + + align:start position:0% +them. And so that cost is baked into + + + align:start position:0% +them. And so that cost is baked into +that total sum. Part of what Nikki was + + align:start position:0% +that total sum. Part of what Nikki was + + + align:start position:0% +that total sum. Part of what Nikki was +referring to as going into new build is + + align:start position:0% +referring to as going into new build is + + + align:start position:0% +referring to as going into new build is +you don't deal with that at all. And + + align:start position:0% +you don't deal with that at all. And + + + align:start position:0% +you don't deal with that at all. And +even today, those pipes and bore holes + + align:start position:0% +even today, those pipes and bore holes + + + align:start position:0% +even today, those pipes and bore holes +can actually balance out for the energy + + align:start position:0% +can actually balance out for the energy + + + align:start position:0% +can actually balance out for the energy +supply in a kind of more classic gas + + align:start position:0% +supply in a kind of more classic gas + + + align:start position:0% +supply in a kind of more classic gas +utility approach. So, the incredible + + align:start position:0% +utility approach. So, the incredible + + + align:start position:0% +utility approach. So, the incredible +news is that we might have tools to + + align:start position:0% +news is that we might have tools to + + + align:start position:0% +news is that we might have tools to +remove the cost of all of our building + + align:start position:0% +remove the cost of all of our building + + + align:start position:0% +remove the cost of all of our building +upgrades, which has all these other + + align:start position:0% +upgrades, which has all these other + + + align:start position:0% +upgrades, which has all these other +incredible benefits like health and + + align:start position:0% +incredible benefits like health and + + + align:start position:0% +incredible benefits like health and +well-being and comfort. Um, so I just I + + align:start position:0% +well-being and comfort. Um, so I just I + + + align:start position:0% +well-being and comfort. Um, so I just I +just wanted to clarify that distinction. \ No newline at end of file diff --git a/XaxjVRXonPg.txt b/XaxjVRXonPg.txt new file mode 100644 index 0000000000000000000000000000000000000000..a115db19b741264da167fac09f1a2449024f31ab --- /dev/null +++ b/XaxjVRXonPg.txt @@ -0,0 +1,1905 @@ +FEMALE SPEAKER: The following +content is provided under a + +creative commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation, or to view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: Hi. + +Today, we're going to generalize +our discussion of + +series to cover series of +functions rather than series + +of just constants. + +In other words, you'll notice +that, up until now, what we've + +been doing in our discussion of +series was have a bunch of + +fixed numbers and +then add them. + +You see, in the same way that +one starts with constants and + +ordinary arithmetic and then +starts talking about + +functions, the same thing occurs +here, that maybe we are + +now interested in a series +over a range of different + +values of 'x'. + +Now, rather than to talk +abstractly about this, I'd + +like to return to a topic that +we touched upon briefly much + +earlier in the course, and then +come back to that topic + +with far greater power +than we were able to + +exhibit up until now. + +And it's the idea of +approximating a function by + +polynomials. + +In other words, this question +of degree of contact. + +And again, rather than review +that abstractly, let's talk in + +terms of a picture. + +You see, today's lecture +is called polynomial + +approximations, and +the idea is this. + +Let's suppose we have the curve, +'y' equals 'f of x'. + +It's smooth. + +It passes through the origin. + +And we're told the following. + +We say, look, we're interested +in approximating this curve in + +a neighborhood of 'x' equals +0-- in other words, at this + +point here-- + +by various polynomials. + +Now, the simplest polynomial, +of course, is a constant. + +In other words, the question +is, how should we choose a + +straight line, 'y' equals a +constant, 'y' equals ''P sub + +0' of x'-- in other words, +a polynomial + +of degree 0, a constant-- + +if we want the best possible +horizontal line that + +approximates the curve at +this particular point? + +And I think you can see that +it's rather trivial at this + +case to say, OK, let's take +the horizontal line that + +passes through this point. + +See, any other horizontal line +misses this point altogether. + +OK, so far, so good. + +Then somebody says, now, look +it, if we remove the + +restriction that the line be +horizontal, what about any + +straight line? + +What straight line has the best +degree of contact with + +the curve at this particular +point? + +In other words, what first +degree polynomial has the + +highest degree of contact +over here? + +Now again, sparing +you the details-- + +because the details are +supplied in the text-- + +the polynomial there +is simply what? + +'f of 0' plus ''f prime +of 0' times 'x''. + +In other words, it's +a tangent line. + +The basic equation of a tangent +line is 'y' equals 'mx + +plus b', where 'm' is the slope, +which is 'f prime of + +0', and 'b' is the y-intercept, +which is + +'f of 0' over here. + +Now, the next question +comes up. + +What if we wanted a quadratic +polynomial, a second degree + +polynomial that fits the curve +even better, in other words, + +has a greater degree +of contact at + +this particular point? + +Let's label that 'y' equals ''P +sub 2' of x' to indicate a + +second degree polynomial. + +And to analyze what that +polynomial must look like, + +let's simply write down some +undetermined coefficients + +here, namely, let's let 'P2 of +x' be 'a0 plus 'a1x' plus 'a2 + +'x squared''. + +And the idea is to determine +what 'a0', 'a1', and 'a2' must + +look like if this polynomial is +to have a maximum degree of + +contact with the curve, +'y' equals 'f of x'. + +Now, what do you mean by maximum +degree of contact? + +Well, what you mean is you +want the function at 0 to + +equal the given function at 0. + +You want the first derivative +of 'P2' evaluated at 0 to + +equal the derivative of +'f' evaluated at 0. + +And you want the second +derivative of 'P2' evaluated + +at 0 equal to ''f double +prime' of 0'. + +Well, let's go through +this in slow motion. + +First of all, 'P2 of +0' is simply 'a0'. + +'P2 prime' is simply 'a1 plus '2 +a2 x'', and evaluating that + +when 'x' equals 0, we +just have 'a1'. + +So 'f of 0' must equal 'a0'. + +'a1' must equal 'f +prime of 0'. + +Now, what about the +second derivative? + +Notice that every time we +differentiate this polynomial, + +another term drops out. + +'a0' drops out the first time, +'a1' the second time. + +And when you've differentiated +this term twice, all you have + +left is '2 a2'. + +In other words, 'P2 +double prime' + +evaluated at 0 is '2 a2'. + +That must be 'f double +prime' of 0. + +Equating these two, 'a2' must +be the second derivative of + +'f' evaluated at 0 over 2. + +I inadvertently wrote in 2 +factorial here, which is the + +right answer, but I haven't led +up to that yet, so if you + +want to call this +2, that's fine. + +At any rate, here's +what I've shown. + +What I've shown is that, if +you want the polynomial of + +degree 2 that fits the curve the +best, in a neighborhood of + +0 comma 'f of 0', +this is how the + +coefficients must be chosen. + +And in fact, this situation +generalizes very nicely. + +You see, suppose you want the +n-th degree polynomial + +expression. + +Differentiate this 'n' times. + +You see, each time you +differentiate, one of these + +terms drops out. + +What happens to this term +as you differentiate it? + +The first time you differentiate +it, you bring + +down an 'n'. + +The next time you differentiate, +you bring down + +an 'n minus 1'. + +By the time you've +differentiated 'n' times, this + +is 'x to the 0', that's 1, 'a +sub n' is still here, and 'n' + +times 'n minus 1' times 'n minus +2', et cetera, is just + +what we call 'n factorial'. + +In other words, the n-th +derivative of ''P sub n' of x' + +is 'n factorial' times +'a sub n'. + +If you evaluate that at 0, +that's still 'n factorial' + +times 'a sub n'. + +That must also equal the n-th +derivative of the function + +evaluated at 0, by definition +of what you mean an n-th + +degree of contact. + +At any rate, that says that +the n-th coefficient, the + +coefficient of 'x to the n', +must be the n-th derivative of + +'f' evaluated at 0 over +'n factorial'. + +By the way, notice +what this says. + +And we'll come back to this +much more strongly later. + +It says that, for this +coefficient to exist, the n-th + +derivative of 'f' at +0 has to exist. + +In other words, if 'f' does +not possess its n-th + +derivative, this particular +equation doesn't make sense. + +And I'll show you what that +means in a little while. + +But at any rate, notice that +what we've now shown is that + +''P sub n' of x'-- + +if you want to use the +sigma notation-- + +can be written how? + +Well, it's the sum as 'k' goes +from 0 to 'n', the k-th + +derivative of 'f' evaluated at 0 +over 'k factorial', times 'x + +to the k-th' power. + +Which written out longhand +is simply what? + +'a0' plus 'a1x' plus ''a2 'x +squared'' over '2 factorial'' + +plus et cetera, the n-th +derivative of 'f' evaluated at + +0 over 'n factorial' +times 'x to the n'. + +And what we do is we let 'P of +x' denote the limit of ''P sub + +n' of x' as 'n' goes +to infinity. + +In other words, for a fixed +'x', we look at what the + +sequence converges to as 'n' +goes to infinity, and we + +denote that as a series. + +You see, what happens is 'x' is +a variable here, but if you + +replace 'x' by a specific +number, what's inside the + +summation sign becomes a +constant which depends only on + +'n', and we're back +to our study of + +ordinary series again. + +Now, what does 'P of x' +mean in this case? + +Going back to our diagram, it +means that, as we let n get + +bigger and bigger and we +determine more and more + +coefficients, we get what? + +Hopefully, what's a better fit +to the curve over here, that + +we get a greater degree of +contact every time we tack on + +the next term in the series. + +Now, because this may seem a +little bit abstract, let's + +illustrate this thing +numerically. + +Let's pick a specific example. + +And I'll pick an easy +one to compute. + +Let 'f of x' be 'e to the x'. + +After all, what could +be easier? + +Because the derivative of 'e to +the x' with respect to 'x' + +is just 'e to the x', so the +n-th derivative of 'e to the + +x' is always 'e to the x'. + +When 'x' is 0, 'e +to the 0' is 1. + +So the n-th derivative +of 'e to the x', + +evaluated at 0, is 1. + +If I divide that by 'n +factorial', I just get '1 over + +'n factorial''. + +In other words, the sequence +of polynomials that + +approximates 'e to the +x' is given by what? + +Summation ''x to the k' over +'k factorial'' as 'k' goes + +from '1 to n'. + +And again, what this +means is what? + +The first approximation is +the line, 'y' equals 1. + +The straight line approximation +for the highest + +degree of contact at +the origin is 'y' + +equals '1 plus x'. + +The best quadratic approximation +is 'y' equals '1 + +plus x plus ''x squared' +over 2'. + +The best cubic fit is when 'y' +is '1 plus x plus ''x squared' + +over 2', plus 'x cubed over +6'', 6 being 3 factorial. + +And we can continue on this way, +getting better fits as we + +add more and more terms. + +And again, I've spoken quite +rapidly, the reason being that + +this part is done superbly in +the textbook, complete with + +graphs, tables, and +what have you. + +Now, here's the question. + +The question is, look it, +we can compute 'Pn of x' + +for any given 'n'. + +And we intuitively get the +feeling that, as 'n' + +increases, 'Pn' hopefully will +look more like 'f of x'. + +In other words, what we would +like to do is to be able to + +compare, or better still, to +study 'f of x' by comparing it + +with the limit of 'Pn of x' +as 'n' goes to infinity. + +In other words, what we hope +will happen is that 'f of x' + +looks like ''P sub n' of x' +for large values of 'n'. + +Now, we don't know where this +is going to happen. + +In fact, the remainder of our +course now revolves about + +three questions. + +The three questions +are the following. + +First of all, does the limit, +'Pn of x' as 'n' approaches + +infinity, exist? + +In other words, does 'P of x' +exist in the first place? + +Does this limit always exists +for a given 'x'? + +Secondly, suppose the +limit does exist. + +How do we know it's going to +equal the given function, 'f + +of x', which it's trying +to approximate? + +In other words, how do we know +that we don't get an + +approximation which is nice near +the point of contact, but + +then, no matter how far out +we go beyond the point of + +contact, the approximation +doesn't become + +sufficiently good? + +See? + +And the third question that +comes up, assuming that the + +first have been answered, is +suppose the limit does exist-- + +in other words, suppose this +limit function, 'P of x', + +which is a limit of 'Pn of x' +as 'n' approaches infinity, + +does exist-- + +the question is, does 'P' +possess the polynomial + +properties that each piece +of 'n' possesses? + +In other words, the question +is, does the limit of a + +sequence of functions have the +same property that each of the + +members of the sequence has? + +For example, every polynomial +is continuous. + +The question, for example, that +might come up is, is the + +limit of a sequence of +continuous functions also + +continuous? + +Now, at first glance, it might +seem as if these are rather + +trivial to answer. + +Let me proceed next by showing +that the answer can be no to + +each of these three questions, +after which we'll then try to + +show when the answer +will be yes. + +The idea is this. + +Let me call these things +counter-examples, even though + +I don't know what better +word to use here. + +In other words, let me show +you an example where the + +answer to each of questions +one, two, and three + +happen to be false. + +For example, let 'f of x' +be '1 over '1 minus x''. + +As a review in taking +derivatives, 'f prime of x' + +would be '1 minus x' to the +minus 2 power, ''f double + +prime' of x' would be +2 times '1 minus x' + +to the minus 3 power. + +See, in other words, you bring +down the minus 2, but the + +derivative of what's inside with +respect to 'x' is minus. + +So a minus times +minus is plus. + +Similarly, the third derivative +of 'f of x' is 3 + +factorial, 2 times minus 3 times +minus 1, '1 minus x' to + +the minus fourth. + +And in general, the n-th +derivative of 'f', in this + +case, is 'n factorial' times +'1 minus x' to the what? + +Minus 'n minus 1'. + +In other words, notice that the +magnitude of the exponent + +is one greater than the number +we're taking the factorial of. + +At any rate, if I now compute +the n-th derivative of 'f' + +evaluated at 0, I just +get 'n factorial'. + +And if I divide 'n factorial' +by 'n factorial', I get 1. + +In other words, every one of +my coefficients of the + +approximating sequence of +polynomials is going to be 1. + +In other words, the +approximation for 'f of x', + +where 'f of x' is '1 over '1 +minus x'', is simply what? + +'Pn of x' is '1 plus x plus 'x +squared'', et cetera, plus et + +cetera, 'x to the n-th' power. + +Now, here's the interesting +point. + +This part is irrelevant. + +I just wanted to show you +something over here. + +Notice that 'f of 2' +is clearly minus 1. + +If I replace 'x' by 2 +over here, 1 over 1 + +minus 2 is minus 1. + +On the other hand, what I claim +is that the limit of a + +sequence, ''P sub n' of x', as +'n' goes to infinity doesn't + +even exist when 'x' is +2, because look what + +happens over here. + +When 'x' is 2, this is what? + +1 plus 2 plus 2 squared plus +et cetera '2 to the n'. + +That's 1 plus 2 plus 4 plus +8 plus 16, et cetera. + +And as I let 'n' go to infinity, +that sum increases + +without bound. + +In other words, here's an +example where the given limit + +didn't have to exist. + +In other words, the sequence +of polynomials does not + +converge at all at +'x' equals 2. + +So much for showing that +the answer to the first + +question can be no. + +As for the second question, +let's define a function as + +follows, to show you why +continuity is so important. + +Let 'f of x' be 'x squared' +if 'x' is less + +than or equal to 2. + +And let it be 4 if 'x' +is greater than 2. + +Now, if we compute the +derivatives of 'f' evaluated + +at 0, we find that what? +'f of 0' is 0. + +See, 'x squared' at 0 is 0. + +'2x' at 0 is 0. + +The second derivative here +is 2, so ''f double + +prime' of 0' is 2. + +And the third derivative and +higher, since this is only 'x + +squared', are identically 0. + +In other words, notice that the +second derivative of 'f' + +evaluated at 0 is 2. + +All other derivatives are 0. + +In other words, notice that +'Pn of x' is equal to 'x + +squared' when 'n' is +greater than 2. + +And that's a straightforward +computation. + +I will drill you on the homework +problems to show you + +how to get more facility. + +We're doing these things. + +But here's the key point. + +Let's look to see what the limit +of 'Pn of x' is as 'n' + +approaches infinity. + +Since 'Pn of x' is equal to 'x +squared' for all 'n', in + +particular, then, since this +doesn't depend on 'n', the + +limit off 'Pn of x' +as 'n' goes to + +infinity is just 'x squared'. + +What this says is this. + +Our function, 'f of x', +graphs like this. + +The sequence of polynomials-- + +which, by the way, converge +to the limit + +function, 'x squared'-- + +look what they do. + +They're just 'y' equals +'x squared'. + +In other words, somehow or +other, when we got to this + +sharp corner-- in other words, +notice that 'f of x' is not + +differentiable at this point-- + +our sequence of polynomials +blissfully went right on their + +merry way smoothly while +the function itself + +leveled off like this. + +In other words, the limit +function always exist, but as + +soon as 'x' is greater than 2, +in this example, the function, + +'P of x', no longer is +the same as 'f of x'. + +You see, 'P of x' is going up +like this, 'f of x' has just + +leveled off this way. + +There are even more glaring +examples, but I will leave + +those for the supplementary +notes to go + +into in more detail. + +But so far, we've seen what? + +That the answers to questions +one and two can be no. + +Let's now show that the +answer to question + +three can also be no. + +Let's define a sequence of +polynomials, ''P sub n' of x', + +to be 'x to the n', where the +domain of 'P sub n' is the + +interval from 0 to 1. + +What that means is something +like this. + +See, here's 0, 0. + +And I hope this reminds you of a +homework problem that we had + +very early in the course, but +that's irrelevant whether it + +does or not. + +'P1 of x' would look +like this. + +'P2 of x' would look +like this. + +'P3 of x' would look +like this. + +In other words, all of +these curves pass + +through 0, 0 and 1, 1. + +But as 'n' increases, +the degree of + +contact here gets better. + +At any rate, let's take a look +at the limit function. + +'P of x' is the limit of +''P sub n' of x' as + +'n' approaches infinity. + +'x to the n', as 'n' approaches +infinity, well, if + +'x' is less than 1 in magnitude, +'x to the n-th' + +approach is 0. + +On the other hand, if 'x' is +equal to 1, 1 to the n-th + +power is still 1 as 'n' +approaches infinity. + +Therefore, 'P of x' +would be what? + +It's 0 if 'x' is greater than or +equal to 0 but less than 1. + +And it's 1 if 'x' equals 1. + +Now, here's the key point. + +Observe that, since 'Pn of x' +is a polynomial, it's, in + +particular, continuous. + +In other words, each +'P sub n' is a + +continuous function, unbroken. + +On the other hand, look +at the limit function. + +It's 0 all the way up to 1. + +And that 1, the function +jumps to 1. + +In other words, graph-wise, +the thing looks like this. + +This is a graph, 'y' +equals 'P of x'. + +It's 0. + +All of a sudden, it jumps. + +Is the limit function, +therefore, continuous + +with 'x' equals 1. + +And the answer is no. + +There's a jump discontinuity +here. + +In other words, observe that +each 'P sub n' is continuous + +when 'x' equals 1. + +The limit function exists, +but it isn't continuous + +when 'x' equals 1. + +In other words, the properties +of a sequence of convergent + +functions do not have +to be inherited + +by the limit function. + +That shows, then, that the +answer to our three + +questions can be no. + +What we would like to do is +find out when and if the + +answer will be yes. + +What we shall do for the +remainder of today's lesson is + +answer the first +two questions. + +And this, by the way, is also +done very nicely in the text. + +The third question, for some +reason or other, is beyond the + +scope of the text. + +We will discuss this in our +future lectures, plus the + +supplementary notes. + +In fact, that the answer to +question number three will be + +the end of our course, when +we finally answer + +that particular question. + +But at any rate, what I'm saying +now is let's spend the + +remainder of today's lesson +in showing how to answer + +questions one and two in the +affirmative, and we'll save + +question three for the +remaining lectures. + +The first thing I'd like to +point out is the role of the + +ratio test and absolute +convergence. + +Namely, given the series +summation 'a n 'x to the n''-- + +And by the way, if you haven't +noticed this by now, it's + +rather conventional sometimes, +to save time, not to put the + +subscripts on here. + +But if it bothers you, I mean, +I could do things like this. + +It's just that to save time and +space, I sometimes will + +not put the subscripts +on here. + +But at any rate, let's just talk +about this for a moment. + +Notice that a series converges +as soon as it converges + +absolutely. + +The point is that, for a +positive series, I can use the + +ratio test or its equivalent. + +Namely, for example, what I can +do is to test summation + +absolute value, 'a n 'x to the +n'', for convergence by the + +ratio test, by the comparison +m by the + +integral test, et cetera. + +And what I'm saying is, if +that particular series + +converges, then the original +series, namely, the one + +without the absolute value +signs, converges absolutely + +for that same value of 'x'. + +Well, again, instead of talking +about that, let's look + +at a particular example. + +And it looks like I've scraped +the blackboard + +here a little bit. + +Let me just-- + +The first example is this. + +Let's suppose you look at +summation n goes from 0 to + +infinity, absolute value of +'x to the n-th' power. + +By the way, notice that this is +a geometric series with a + +ratio absolute value of 'x'. + +Consequently, the series +converges if and only if the + +absolute value of 'x' +is less than 1. + +By the way, let me make +a little aside here. + +Many people would tackle this +problem by the ratio test, as + +I hinted at over here. + +Namely, let the n-th term be +the absolute value of 'x to + +the n-th' power. + +Then the 'n plus first' term +would be the absolute value of + +'x to the 'n plus +first'' power. + +Then the ratio between these +two would be the absolute + +value of 'x'. + +Therefore, row, which is this +limit, would be the limit of + +the absolute value of 'x' +as 'n' goes to infinity. + +That's just equal to the +absolute value of 'x' itself. + +And for convergence, notice that +row must be less than 1, + +and that says what? + +The absolute value of 'x' must +be less than 1, just + +as we did over here. + +I simply would like to make a +little aside over here, and + +that is, if you use this +particular approach, that + +comes under the heading of +circular reasoning, because + +you may recall when we proved +the ratio test, we did it by + +comparing the series with the +geometric series, which meant + +that we already had +to know that the + +geometric series converged. + +And this is a geometric +series. + +But that's an aside which I just +wanted to mention to you + +in forms of circular +reasoning. + +The important point to +observe is what? + +That this series converges if +the absolute value of 'x' is + +less than 1. + +Consequently, that means that +the series without the + +absolute value sign converges, +in fact, absolutely, if the + +absolute value of 'x' +is less than 1. + +In other words, for this +particular series, '1 plus x + +plus 'x squared' plus 'x +cubed'', et cetera, that will + +converge to a finite limit +function if the absolute value + +of 'x' is less than 1. + +Let's look at another example. + +Suppose we look at the absolute +value of 'x to the + +n-th' power over +'n factorial'. + +If we look at this, the nth term +is the absolute value of + +'x to the n-th' over +'n factorial'. + +The 'n plus first' term, +therefore, is the absolute + +value of 'x to the 'n plus +1'', over ''n plus 1' + +factorial'. + +Therefore, the ratio between +the 'n plus first' term and + +the n-th term is the absolute +value of 'x' over 'n plus 1'. + +Rho is this particular limit. + +Well, the limit of the absolute +value of 'x' over 'n + +plus 1', as 'n' approaches +infinity-- + +and here's the key point. + +Notice that 'x' is a fixed but +finite number once we get + +started here. + +In other words, we pick +an 'x' and fixed it. + +That means that that +stays constant. + +But as 'n' goes to infinity, +the denominator increases + +without bound. + +That makes the limit +equal to 0. + +And 0 is obviously less than +1, regardless of what the + +value of 'x' happens +to be here. + +In other words, in this +particular case, this + +particular series converges for +all real values of 'x'. + +And we sometimes abbreviate that +by saying the absolute + +value of 'x' is less +than infinity. + +And therefore, the original +series, meaning the one + +without the absolute value sign, +would, in particular, + +converge also for +all real 'x'. + +The important point is that, in +general, given any series-- + +in other words, limit of a +sequence of polynomials of + +this particular type-- + +there always exists +a number 'M'. + +Now, 'M' may be as small as 0. + +It may be as large +as infinity. + +But there always exists an 'M', +such that the particular + +series will converge absolutely +if the magnitude of + +'x' is less than 'M', and +diverge if the magnitude of + +'x' is greater than 'M'. + +In other words, this particular +'M', which is + +called the radius of +convergence, governs the + +answer to the first question. + +In other words, it's this 'M', +which we often find by the + +ratio test, that determines +where the sequence of + +functions, ''P sub n' of x', for +what values of 'x', that + +will converge to 'P of x'. + +And again, I think this is kind +of difficult for you to + +see abstractly. + +The proof is done in the text. + +What I'd like to do is show +you pictorially what's + +happening over here. + +See, let's suppose we have +our series, summation + +'a n 'x to the n''. + +And we pick a particular value +of 'x', say 'x sub 1'. + +Now, the idea is this. + +If this particular series +converges-- + +and the proof is given in the +text, and I won't repeat it + +here because I want you to +see the overview here-- + +if this particular series +converges-- + +in other words, if the series +converges when 'x' is equal to + +'x sub 1'-- + +then it can be shown that it +converges absolutely for any + +'x' which is smaller in +magnitude then 'x sub 1'. + +In other words, the +gist is this. + +If I know that the series +converges over here, I can + +then draw this interval +surrounding 0, and conclude + +that the series converges +in this entire interval. + +Correspondingly, if this +particular series diverges-- + +and by the way, the whole proof +of this thing hinges on + +the comparison test, +essentially. + +See, if this thing diverges, +then certainly, if 'x' is + +larger than 'x1' in magnitude, +this will also diverge. + +In other words, once I know +that my series diverges at + +this particular value +of 'x1'.. + +of 'x', I know it diverges for +all values of 'x' which are + +greater in magnitude then 'x1', +which means, in terms of + +a picture, for everything +further away from 0, then 'x1' + +and minus 'x1'. + +In other words, if this +converges, this converges. + +In here, if this diverges, we +have divergence out here. + +Now, what does that mean? + +Let me show you again in terms +of a extended diagram. + +See, the idea goes something +like this. + +Given the series summation 'a n +'x to the n'', pick a number + +'x' equal to 'x1'. + +Suppose the series converges +at 'x1'. + +Then we know that it converges +every place in here, so + +there's no need to check +this any further. + +What we do next is we +pick a number, 'x2', + +outside of this interval. + +Say 'x2' is over here. + +Suppose, for the sake of +argument-- see, what we're + +saying is 'a n 'x 1 to the +n'' converges, so you + +just suppose this. + +That gives us this picture. + +Suppose 'a n 'x2 to +the n'' diverges. + +Then we know that the series +diverges for all + +larger values of 'x'. + +Now we know how the series +behaves exactly, except in the + +interval between +'x1' and 'x2'. + +So what we do next is what? + +We pick a number which +we'll call 'x3'. + +We then see whether this +converges or diverges. + +If it converges at 'x3', we +know that the radius of + +convergence extends all +the way between minus + +'x3' and plus 'x3'. + +If it diverges, we know that, +from 'x3' out and minus 'x3' + +out, the series diverges. + +In any event, each time we +perform this operation, we cut + +the remaining space down. + +And we can keep on +going this way. + +And you see what you're doing +then, is you're zeroing in on + +this number that we called +capital 'M' before. + +You see, it's just a series +of refinements. + +And by the way, the +formal proof of + +this looks very messy. + +And yet, when it's stripped of +all embellishment, that's + +exactly what the formal +proof says. + +Well, at any rate, I will +reinforce the rest of this + +between the text, the notes, +and the learning exercises. + +All I want to do now is talk +about the second question. + +In other words, we've now talked +about something called + +the radius of convergence, that +tells us when the series + +of functions converges to +the limit function. + +Now the question is, how can we +measure whether that limit + +function converges to the +original function that we're + +trying to approximate? + +In other words, how do we know +whether 'P of x' actually + +equals 'f of x'? + +And again, this is done +extremely well in the text. + +It's called Taylor's theorem +with remainder. + +The proof is given very, +very nicely. + +I think the hardest part is to +show what the thing means. + +You see, using integration +by parts repeatedly-- + +which is done in the text-- + +it follows that, if 'f' and +its first 'n plus 1' + +derivatives exist at 'x' equals +0, it turns out-- and + +this is why this is called +Taylor's theorem with + +remainder-- + +it turns out that 'f of x' can +be written as 'Pn of x' plus a + +remainder term-- ''r sub n' +of x'-- a remainder term. + +And then you see, +computationally, the text + +shows what that remainder +term looks like. + +It happens to be the integral +from 0 to 'x', ''x minus t' to + +the n-th' over 'n factorial', +'n plus first' derivative of + +'f of t', 'dt', from 't' equals +0 to 't' equals 'x'. + +This looks messy. + +It is messy. + +There's no need to hammer this +home in the lecture part of + +our course. + +What I prefer to do is to give +several learning exercises + +that will give you drill +in using this. + +But the point that I want you +to understand is that, since + +this is all done well in the +text, all I want you to do is + +to see where this +thing fits in. + +In other words, what the text +is showing is, look it, the + +difference between the +function which we're + +approximating at 0 comma 'f +of 0' by this sequence of + +polynomials, the difference +between that function and the + +nth member of that sequence +of polynomials is simply + +something called ''r sub n' of +x', where numerically ''r sub + +n' of x' looks like this. + +And the point is that, if you +now take the limit of this + +expression as 'n' goes to +infinity, remember, 'P of x' + +is this limit. + +Therefore, the only way that 'P +of x' can equal 'f of x' is + +if, for a given value of 'x', +this remainder goes to 0 as + +'n' goes to infinity. + +In other words, leaving the +computational details to the + +text, because it does it very +nicely, what we're saying is + +that the significance of +Taylor's remainder theorem is + +that, to find out where 'f of x' +and 'P of x' are identical, + +we simply-- + +and I say simply meaning +conceptually simply-- + +computationally, it might +be difficult. + +What we do computationally is +simply find all those values + +of 'x', for which ''r sub n' of +x' goes to 0 in the limit + +as 'n' goes to infinity. + +You see, what we've done is +we've now done two things. + +We've first shown when +the sequence of + +polynomials has a limit. + +And secondly, we've shown when +it does have a limit, when + +will it equal the given +function that + +it's trying to represent. + +The question that still remains +is, how do we know + +that the limit function has the +same properties as each + +member of the sequence? + +In fact, we've just given an +example where the limit + +function had different +properties. + +And the question is, under what +conditions can we be sure + +that certain nice results-- + +that we'd like to be true, +because they're true about + +each polynomial in +the sequence-- + +actually are true about +the limit function. + +In fact, that shall +be our topic for + +the next two lessons. + +And these next two lectures +should complete the course. + +At any rate, until next +time, goodbye. + +MALE SPEAKER: Funding for the +publication of this video was + +provided by the Gabriella and +Paul Rosenbaum Foundation. + +Help OCW continue to provide +free and open access to MIT + +courses by making a donation +at ocw.mit.edu/donate. \ No newline at end of file diff --git a/YBWv9EOX3pU.txt b/YBWv9EOX3pU.txt new file mode 100644 index 0000000000000000000000000000000000000000..d07e15a398a4b90dcbf7be196f3d8883e0c27fc8 --- /dev/null +++ b/YBWv9EOX3pU.txt @@ -0,0 +1,18259 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +so today at long long last we meet this + + align:start position:0% +so today at long long last we meet this + + + align:start position:0% +so today at long long last we meet this +fella uh named Albert Einstein we're + + align:start position:0% +fella uh named Albert Einstein we're + + + align:start position:0% +fella uh named Albert Einstein we're +going to talk a bit more about how he + + align:start position:0% +going to talk a bit more about how he + + + align:start position:0% +going to talk a bit more about how he +was approaching some of these questions + + align:start position:0% +was approaching some of these questions + + + align:start position:0% +was approaching some of these questions +uh in the early years of the 20th + + align:start position:0% +uh in the early years of the 20th + + + align:start position:0% +uh in the early years of the 20th +century oops + + align:start position:0% +century oops + + + align:start position:0% +century oops +so as usual today's class has three main + + align:start position:0% +so as usual today's class has three main + + + align:start position:0% +so as usual today's class has three main +parts we're going to look at Einstein + + align:start position:0% +parts we're going to look at Einstein + + + align:start position:0% +parts we're going to look at Einstein +leading up to this year of 1905 uh what + + align:start position:0% +leading up to this year of 1905 uh what + + + align:start position:0% +leading up to this year of 1905 uh what +were his early kind of educational + + align:start position:0% +were his early kind of educational + + + align:start position:0% +were his early kind of educational +experiences like how did he come to this + + align:start position:0% +experiences like how did he come to this + + + align:start position:0% +experiences like how did he come to this +question of the electronomics of moving + + align:start position:0% +question of the electronomics of moving + + + align:start position:0% +question of the electronomics of moving +bodies uh and what did he think was the + + align:start position:0% +bodies uh and what did he think was the + + + align:start position:0% +bodies uh and what did he think was the +most kind of compelling way to start + + align:start position:0% +most kind of compelling way to start + + + align:start position:0% +most kind of compelling way to start +addressing some of these questions for + + align:start position:0% +addressing some of these questions for + + + align:start position:0% +addressing some of these questions for +the middle part of today we'll talk + + align:start position:0% +the middle part of today we'll talk + + + align:start position:0% +the middle part of today we'll talk +about this this paper in particular the + + align:start position:0% +about this this paper in particular the + + + align:start position:0% +about this this paper in particular the +same this excerpt of the paper that you + + align:start position:0% +same this excerpt of the paper that you + + + align:start position:0% +same this excerpt of the paper that you +had in the reader um on the + + align:start position:0% +had in the reader um on the + + + align:start position:0% +had in the reader um on the +electronomically moving bodies what were + + align:start position:0% +electronomically moving bodies what were + + + align:start position:0% +electronomically moving bodies what were +some of the key ways in which Einstein + + align:start position:0% +some of the key ways in which Einstein + + + align:start position:0% +some of the key ways in which Einstein +was talking about what we would Now call + + align:start position:0% +was talking about what we would Now call + + + align:start position:0% +was talking about what we would Now call +the special theory of relativity and I + + align:start position:0% +the special theory of relativity and I + + + align:start position:0% +the special theory of relativity and I +had a little asterisk here to remind you + + align:start position:0% +had a little asterisk here to remind you + + + align:start position:0% +had a little asterisk here to remind you +for for this section for this class + + align:start position:0% +for for this section for this class + + + align:start position:0% +for for this section for this class +session + + align:start position:0% +session + + + align:start position:0% +session +I wrote up a little short set of extra + + align:start position:0% +I wrote up a little short set of extra + + + align:start position:0% +I wrote up a little short set of extra +notes not nearly so detailed as the + + align:start position:0% +notes not nearly so detailed as the + + + align:start position:0% +notes not nearly so detailed as the +previous set those are really just as a + + align:start position:0% +previous set those are really just as a + + + align:start position:0% +previous set those are really just as a +supplement for something I'm going to + + align:start position:0% +supplement for something I'm going to + + + align:start position:0% +supplement for something I'm going to +kind of probably not have much time to + + align:start position:0% +kind of probably not have much time to + + + align:start position:0% +kind of probably not have much time to +linger on in the class session itself + + align:start position:0% +linger on in the class session itself + + + align:start position:0% +linger on in the class session itself +today and that's a consequence of + + align:start position:0% +today and that's a consequence of + + + align:start position:0% +today and that's a consequence of +Einstein's work that he published in a + + align:start position:0% +Einstein's work that he published in a + + + align:start position:0% +Einstein's work that he published in a +separate follow-up article in which he + + align:start position:0% +separate follow-up article in which he + + + align:start position:0% +separate follow-up article in which he +derived this now rather famous relation + + align:start position:0% +derived this now rather famous relation + + + align:start position:0% +derived this now rather famous relation +that E equals MC squared so I'm going to + + align:start position:0% +that E equals MC squared so I'm going to + + + align:start position:0% +that E equals MC squared so I'm going to +kind of go through quickly today uh the + + align:start position:0% +kind of go through quickly today uh the + + + align:start position:0% +kind of go through quickly today uh the +nature of Einstein's argument that led + + align:start position:0% +nature of Einstein's argument that led + + + align:start position:0% +nature of Einstein's argument that led +him to that conclusion and then you have + + align:start position:0% +him to that conclusion and then you have + + + align:start position:0% +him to that conclusion and then you have +a couple pages I think it's only about + + align:start position:0% +a couple pages I think it's only about + + + align:start position:0% +a couple pages I think it's only about +five pages or so to read a little bit + + align:start position:0% +five pages or so to read a little bit + + + align:start position:0% +five pages or so to read a little bit +more detail about uh some of the ways + + align:start position:0% +more detail about uh some of the ways + + + align:start position:0% +more detail about uh some of the ways +that Einstein came about that conclusion + + align:start position:0% +that Einstein came about that conclusion + + + align:start position:0% +that Einstein came about that conclusion +so a little extra supplemental strictly + + align:start position:0% +so a little extra supplemental strictly + + + align:start position:0% +so a little extra supplemental strictly +optional as always but if you are + + align:start position:0% +optional as always but if you are + + + align:start position:0% +optional as always but if you are +curious about it there's some more + + align:start position:0% +curious about it there's some more + + + align:start position:0% +curious about it there's some more +materials there and then we'll we'll pan + + align:start position:0% +materials there and then we'll we'll pan + + + align:start position:0% +materials there and then we'll we'll pan +out again we'll kind of zoom out and try + + align:start position:0% +out again we'll kind of zoom out and try + + + align:start position:0% +out again we'll kind of zoom out and try +to make sense of why did Einstein + + align:start position:0% +to make sense of why did Einstein + + + align:start position:0% +to make sense of why did Einstein +approach these questions in the ways + + align:start position:0% +approach these questions in the ways + + + align:start position:0% +approach these questions in the ways +that he did what how can we think about + + align:start position:0% +that he did what how can we think about + + + align:start position:0% +that he did what how can we think about +what else Einstein was + + align:start position:0% +what else Einstein was + + + align:start position:0% +what else Einstein was +um thinking about was sort of immersed + + align:start position:0% +um thinking about was sort of immersed + + + align:start position:0% +um thinking about was sort of immersed +in what was going on in his life in his + + align:start position:0% +in what was going on in his life in his + + + align:start position:0% +in what was going on in his life in his +early professional career drawing in + + align:start position:0% +early professional career drawing in + + + align:start position:0% +early professional career drawing in +this case very heavily on that article + + align:start position:0% +this case very heavily on that article + + + align:start position:0% +this case very heavily on that article +by Peter Gallison on the reader to try + + align:start position:0% +by Peter Gallison on the reader to try + + + align:start position:0% +by Peter Gallison on the reader to try +to understand why Einstein approached as + + align:start position:0% +to understand why Einstein approached as + + + align:start position:0% +to understand why Einstein approached as +we'll see a very conventional question + + align:start position:0% +we'll see a very conventional question + + + align:start position:0% +we'll see a very conventional question +in rather unconventional ways that's our + + align:start position:0% +in rather unconventional ways that's our + + + align:start position:0% +in rather unconventional ways that's our +plan for today + + align:start position:0% +plan for today + + + align:start position:0% +plan for today +so let's jump in so remember what we're + + align:start position:0% +so let's jump in so remember what we're + + + align:start position:0% +so let's jump in so remember what we're +responding to what what's Einstein + + align:start position:0% +responding to what what's Einstein + + + align:start position:0% +responding to what what's Einstein +inheriting by the time he comes on the + + align:start position:0% +inheriting by the time he comes on the + + + align:start position:0% +inheriting by the time he comes on the +scene + + align:start position:0% +scene + + + align:start position:0% +scene +so we saw in the previous few lectures + + align:start position:0% +so we saw in the previous few lectures + + + align:start position:0% +so we saw in the previous few lectures +uh from last week the questions about + + align:start position:0% +uh from last week the questions about + + + align:start position:0% +uh from last week the questions about +the behavior the propagation of light + + align:start position:0% +the behavior the propagation of light + + + align:start position:0% +the behavior the propagation of light +waves in The Ether in that all pervasive + + align:start position:0% +waves in The Ether in that all pervasive + + + align:start position:0% +waves in The Ether in that all pervasive +kind of elastic medium called the light + + align:start position:0% +kind of elastic medium called the light + + + align:start position:0% +kind of elastic medium called the light +bearing or luminiferous ether those + + align:start position:0% +bearing or luminiferous ether those + + + align:start position:0% +bearing or luminiferous ether those +questions were really at the Forefront + + align:start position:0% +questions were really at the Forefront + + + align:start position:0% +questions were really at the Forefront +that was mainstream physics by the end + + align:start position:0% +that was mainstream physics by the end + + + align:start position:0% +that was mainstream physics by the end +of the 19th century + + align:start position:0% +of the 19th century + + + align:start position:0% +of the 19th century +and especially when we get to people + + align:start position:0% +and especially when we get to people + + + align:start position:0% +and especially when we get to people +like Hendrick Lorenz or Michaelson and + + align:start position:0% +like Hendrick Lorenz or Michaelson and + + + align:start position:0% +like Hendrick Lorenz or Michaelson and +Morley the topic that was often uh + + align:start position:0% +Morley the topic that was often uh + + + align:start position:0% +Morley the topic that was often uh +described was the electrodynamics of + + align:start position:0% +described was the electrodynamics of + + + align:start position:0% +described was the electrodynamics of +moving bodies the effort to generalize + + align:start position:0% +moving bodies the effort to generalize + + + align:start position:0% +moving bodies the effort to generalize +from James Clark Maxwell's work from the + + align:start position:0% +from James Clark Maxwell's work from the + + + align:start position:0% +from James Clark Maxwell's work from the +middle Decades of the 19th century in + + align:start position:0% +middle Decades of the 19th century in + + + align:start position:0% +middle Decades of the 19th century in +which Maxwell had worked out this really + + align:start position:0% +which Maxwell had worked out this really + + + align:start position:0% +which Maxwell had worked out this really +quite beautiful + + align:start position:0% +quite beautiful + + + align:start position:0% +quite beautiful +combination of electricity magnetism and + + align:start position:0% +combination of electricity magnetism and + + + align:start position:0% +combination of electricity magnetism and +Optics but he really was sort of + + align:start position:0% +Optics but he really was sort of + + + align:start position:0% +Optics but he really was sort of +treating uh light waves for the special + + align:start position:0% +treating uh light waves for the special + + + align:start position:0% +treating uh light waves for the special +case in which both the emitter and the + + align:start position:0% +case in which both the emitter and the + + + align:start position:0% +case in which both the emitter and the +receiver of those light waves were both + + align:start position:0% +receiver of those light waves were both + + + align:start position:0% +receiver of those light waves were both +at rest with respect to this + + align:start position:0% +at rest with respect to this + + + align:start position:0% +at rest with respect to this +light-bearing ether so the question then + + align:start position:0% +light-bearing ether so the question then + + + align:start position:0% +light-bearing ether so the question then +becomes what about moving bodies what if + + align:start position:0% +becomes what about moving bodies what if + + + align:start position:0% +becomes what about moving bodies what if +either the sender or the receiver of + + align:start position:0% +either the sender or the receiver of + + + align:start position:0% +either the sender or the receiver of +light or both were in motion with + + align:start position:0% +light or both were in motion with + + + align:start position:0% +light or both were in motion with +respect to each other and we expected + + align:start position:0% +respect to each other and we expected + + + align:start position:0% +respect to each other and we expected +ether that's the became known by this + + align:start position:0% +ether that's the became known by this + + + align:start position:0% +ether that's the became known by this +sort of Catchphrase the electronamics of + + align:start position:0% +sort of Catchphrase the electronamics of + + + align:start position:0% +sort of Catchphrase the electronamics of +moving bodies + + align:start position:0% +moving bodies + + + align:start position:0% +moving bodies +one of the key moments in that uh in + + align:start position:0% +one of the key moments in that uh in + + + align:start position:0% +one of the key moments in that uh in +that investigation that we saw from the + + align:start position:0% +that investigation that we saw from the + + + align:start position:0% +that investigation that we saw from the +1880s was performed by Albert Michelson + + align:start position:0% +1880s was performed by Albert Michelson + + + align:start position:0% +1880s was performed by Albert Michelson +and Edward Morley in what's now Case + + align:start position:0% +and Edward Morley in what's now Case + + + align:start position:0% +and Edward Morley in what's now Case +Western Reserve University in Cleveland + + align:start position:0% +Western Reserve University in Cleveland + + + align:start position:0% +Western Reserve University in Cleveland +uh in the United States so they use this + + align:start position:0% +uh in the United States so they use this + + + align:start position:0% +uh in the United States so they use this +enormous specially built interferometer + + align:start position:0% +enormous specially built interferometer + + + align:start position:0% +enormous specially built interferometer +of michelson's own design by the 1880s + + align:start position:0% +of michelson's own design by the 1880s + + + align:start position:0% +of michelson's own design by the 1880s +late 80s they were using an + + align:start position:0% +late 80s they were using an + + + align:start position:0% +late 80s they were using an +interferometer where each leg of this + + align:start position:0% +interferometer where each leg of this + + + align:start position:0% +interferometer where each leg of this +L-shaped instrument was 11 meters long + + align:start position:0% +L-shaped instrument was 11 meters long + + + align:start position:0% +L-shaped instrument was 11 meters long +that's about 34 feet on a side huge huge + + align:start position:0% +that's about 34 feet on a side huge huge + + + align:start position:0% +that's about 34 feet on a side huge huge +huge instrument + + align:start position:0% +huge instrument + + + align:start position:0% +huge instrument +that they designed and built expressly + + align:start position:0% +that they designed and built expressly + + + align:start position:0% +that they designed and built expressly +to try to measure changes in the + + align:start position:0% +to try to measure changes in the + + + align:start position:0% +to try to measure changes in the +behavior of light waves in particular in + + align:start position:0% +behavior of light waves in particular in + + + align:start position:0% +behavior of light waves in particular in +the relative speed with which waves + + align:start position:0% +the relative speed with which waves + + + align:start position:0% +the relative speed with which waves +would move through the ether depending + + align:start position:0% +would move through the ether depending + + + align:start position:0% +would move through the ether depending +on whether our own laboratory here on + + align:start position:0% +on whether our own laboratory here on + + + align:start position:0% +on whether our own laboratory here on +Earth was moving directly into the ether + + align:start position:0% +Earth was moving directly into the ether + + + align:start position:0% +Earth was moving directly into the ether +or some sort of perpendicular or the + + align:start position:0% +or some sort of perpendicular or the + + + align:start position:0% +or some sort of perpendicular or the +light Woods are moving perpendicular to + + align:start position:0% +light Woods are moving perpendicular to + + + align:start position:0% +light Woods are moving perpendicular to +the Earth's motion so would it be what + + align:start position:0% +the Earth's motion so would it be what + + + align:start position:0% +the Earth's motion so would it be what +we could think of as an ether headwind + + align:start position:0% +we could think of as an ether headwind + + + align:start position:0% +we could think of as an ether headwind +like if you're pedaling on your bicycle + + align:start position:0% +like if you're pedaling on your bicycle + + + align:start position:0% +like if you're pedaling on your bicycle +on an otherwise still day you'll feel + + align:start position:0% +on an otherwise still day you'll feel + + + align:start position:0% +on an otherwise still day you'll feel +the breeze on your face in the direction + + align:start position:0% +the breeze on your face in the direction + + + align:start position:0% +the breeze on your face in the direction +of your own motion + + align:start position:0% +of your own motion + + + align:start position:0% +of your own motion +and as we saw last time Michelson had + + align:start position:0% +and as we saw last time Michelson had + + + align:start position:0% +and as we saw last time Michelson had +reasoned there should be a similar + + align:start position:0% +reasoned there should be a similar + + + align:start position:0% +reasoned there should be a similar +effect for light waves because our whole + + align:start position:0% +effect for light waves because our whole + + + align:start position:0% +effect for light waves because our whole +laboratory on Earth was assuredly they + + align:start position:0% +laboratory on Earth was assuredly they + + + align:start position:0% +laboratory on Earth was assuredly they +were quite confident was moving through + + align:start position:0% +were quite confident was moving through + + + align:start position:0% +were quite confident was moving through +the ethers there should be some relative + + align:start position:0% +the ethers there should be some relative + + + align:start position:0% +the ethers there should be some relative +motion between uh the behavior of light + + align:start position:0% +motion between uh the behavior of light + + + align:start position:0% +motion between uh the behavior of light +waves as we measure them on Earth on an + + align:start position:0% +waves as we measure them on Earth on an + + + align:start position:0% +waves as we measure them on Earth on an +instrument like the interferometer and + + align:start position:0% +instrument like the interferometer and + + + align:start position:0% +instrument like the interferometer and +The all-pervasive Ether and as we saw we + + align:start position:0% +The all-pervasive Ether and as we saw we + + + align:start position:0% +The all-pervasive Ether and as we saw we +even read their brief paper + + align:start position:0% +even read their brief paper + + + align:start position:0% +even read their brief paper +despite some really Exquisite + + align:start position:0% +despite some really Exquisite + + + align:start position:0% +despite some really Exquisite +experimental design and sensitivity they + + align:start position:0% +experimental design and sensitivity they + + + align:start position:0% +experimental design and sensitivity they +never detected any clear evidence uh + + align:start position:0% +never detected any clear evidence uh + + + align:start position:0% +never detected any clear evidence uh +that would have been associated with uh + + align:start position:0% +that would have been associated with uh + + + align:start position:0% +that would have been associated with uh +the Earth's motion Through The Ether + + align:start position:0% +the Earth's motion Through The Ether + + + align:start position:0% +the Earth's motion Through The Ether +that was what became known as a null + + align:start position:0% +that was what became known as a null + + + align:start position:0% +that was what became known as a null +result the results were consistent with + + align:start position:0% +result the results were consistent with + + + align:start position:0% +result the results were consistent with +no change in relative speed no matter + + align:start position:0% +no change in relative speed no matter + + + align:start position:0% +no change in relative speed no matter +what direction those light beams were + + align:start position:0% +what direction those light beams were + + + align:start position:0% +what direction those light beams were +traveling and as we saw even though + + align:start position:0% +traveling and as we saw even though + + + align:start position:0% +traveling and as we saw even though +Michaelson won the Nobel Prize he was + + align:start position:0% +Michaelson won the Nobel Prize he was + + + align:start position:0% +Michaelson won the Nobel Prize he was +the first physicist based in the United + + align:start position:0% +the first physicist based in the United + + + align:start position:0% +the first physicist based in the United +States to win the Nobel Prize for + + align:start position:0% +States to win the Nobel Prize for + + + align:start position:0% +States to win the Nobel Prize for +physics he won in 1907 he died 20 years + + align:start position:0% +physics he won in 1907 he died 20 years + + + align:start position:0% +physics he won in 1907 he died 20 years +later still convinced that he had just + + align:start position:0% +later still convinced that he had just + + + align:start position:0% +later still convinced that he had just +messed up so that's you know sad for him + + align:start position:0% +messed up so that's you know sad for him + + + align:start position:0% +messed up so that's you know sad for him +and maybe we all suffer the same fate + + align:start position:0% +and maybe we all suffer the same fate + + + align:start position:0% +and maybe we all suffer the same fate +maybe we all win the Nobel Prize even if + + align:start position:0% +maybe we all win the Nobel Prize even if + + + align:start position:0% +maybe we all win the Nobel Prize even if +we're not satisfied with our work + + align:start position:0% +we're not satisfied with our work + + + align:start position:0% +we're not satisfied with our work +okay meanwhile some very leading very + + align:start position:0% +okay meanwhile some very leading very + + + align:start position:0% +okay meanwhile some very leading very +elite physicists back in Western Europe + + align:start position:0% +elite physicists back in Western Europe + + + align:start position:0% +elite physicists back in Western Europe +like Henry Lorenz were following + + align:start position:0% +like Henry Lorenz were following + + + align:start position:0% +like Henry Lorenz were following +Michaelson's and Morley's work quite + + align:start position:0% +Michaelson's and Morley's work quite + + + align:start position:0% +Michaelson's and Morley's work quite +carefully uh Lorenz was a mathematical + + align:start position:0% +carefully uh Lorenz was a mathematical + + + align:start position:0% +carefully uh Lorenz was a mathematical +physicist closer in spirit to James + + align:start position:0% +physicist closer in spirit to James + + + align:start position:0% +physicist closer in spirit to James +Clark Maxwell he wasn't building his own + + align:start position:0% +Clark Maxwell he wasn't building his own + + + align:start position:0% +Clark Maxwell he wasn't building his own +experiments but he was very attuned to + + align:start position:0% +experiments but he was very attuned to + + + align:start position:0% +experiments but he was very attuned to +what results Michaels and Morley and + + align:start position:0% +what results Michaels and Morley and + + + align:start position:0% +what results Michaels and Morley and +other experiments were finding and + + align:start position:0% +other experiments were finding and + + + align:start position:0% +other experiments were finding and +Lorenz finally introduces a way + + align:start position:0% +Lorenz finally introduces a way + + + align:start position:0% +Lorenz finally introduces a way +to accommodate this null result to + + align:start position:0% +to accommodate this null result to + + + align:start position:0% +to accommodate this null result to +explain + + align:start position:0% +explain + + + align:start position:0% +explain +why experiments like Michaels and + + align:start position:0% +why experiments like Michaels and + + + align:start position:0% +why experiments like Michaels and +Morales might indeed measure no offset + + align:start position:0% +Morales might indeed measure no offset + + + align:start position:0% +Morales might indeed measure no offset +no change in the relative speed and + + align:start position:0% +no change in the relative speed and + + + align:start position:0% +no change in the relative speed and +Lorenzo argument was because of Dynamics + + align:start position:0% +Lorenzo argument was because of Dynamics + + + align:start position:0% +Lorenzo argument was because of Dynamics +because the previous analyzes had + + align:start position:0% +because the previous analyzes had + + + align:start position:0% +because the previous analyzes had +dropped had missed one of the relevant + + align:start position:0% +dropped had missed one of the relevant + + + align:start position:0% +dropped had missed one of the relevant +forces in this case Lawrence argued that + + align:start position:0% +forces in this case Lawrence argued that + + + align:start position:0% +forces in this case Lawrence argued that +if the entire apparatus like everything + + align:start position:0% +if the entire apparatus like everything + + + align:start position:0% +if the entire apparatus like everything +else is immersed in this physical + + align:start position:0% +else is immersed in this physical + + + align:start position:0% +else is immersed in this physical +elastic medium of The Ether The Ether + + align:start position:0% +elastic medium of The Ether The Ether + + + align:start position:0% +elastic medium of The Ether The Ether +should exert a force on the material + + align:start position:0% +should exert a force on the material + + + align:start position:0% +should exert a force on the material +making up the arm of that instrument one + + align:start position:0% +making up the arm of that instrument one + + + align:start position:0% +making up the arm of that instrument one +of those L's one one edge of the L The + + align:start position:0% +of those L's one one edge of the L The + + + align:start position:0% +of those L's one one edge of the L The +Edge is moving directly into the ether + + align:start position:0% +Edge is moving directly into the ether + + + align:start position:0% +Edge is moving directly into the ether +wind that should be compressed or + + align:start position:0% +wind that should be compressed or + + + align:start position:0% +wind that should be compressed or +contracted because of a physical force a + + align:start position:0% +contracted because of a physical force a + + + align:start position:0% +contracted because of a physical force a +kind of resistive Force onto the + + align:start position:0% +kind of resistive Force onto the + + + align:start position:0% +kind of resistive Force onto the +interferometer itself uh the Irish + + align:start position:0% +interferometer itself uh the Irish + + + align:start position:0% +interferometer itself uh the Irish +mathematical physicist George Fitzgerald + + align:start position:0% +mathematical physicist George Fitzgerald + + + align:start position:0% +mathematical physicist George Fitzgerald +came up with a very similar argument + + align:start position:0% +came up with a very similar argument + + + align:start position:0% +came up with a very similar argument +right around the same time this was for + + align:start position:0% +right around the same time this was for + + + align:start position:0% +right around the same time this was for +some years known as the lorentz + + align:start position:0% +some years known as the lorentz + + + align:start position:0% +some years known as the lorentz +Fitzgerald's contraction or sometimes + + align:start position:0% +Fitzgerald's contraction or sometimes + + + align:start position:0% +Fitzgerald's contraction or sometimes +just as Lorenz contraction and the idea + + align:start position:0% +just as Lorenz contraction and the idea + + + align:start position:0% +just as Lorenz contraction and the idea +was that if there's a contraction by + + align:start position:0% +was that if there's a contraction by + + + align:start position:0% +was that if there's a contraction by +just such a an amount depending on the + + align:start position:0% +just such a an amount depending on the + + + align:start position:0% +just such a an amount depending on the +relative speed of the object Through The + + align:start position:0% +relative speed of the object Through The + + + align:start position:0% +relative speed of the object Through The +Ether V compared to the speed of light + + align:start position:0% +Ether V compared to the speed of light + + + align:start position:0% +Ether V compared to the speed of light +see + + align:start position:0% +see + + + align:start position:0% +see +if you cooked up the amount of + + align:start position:0% +if you cooked up the amount of + + + align:start position:0% +if you cooked up the amount of +contraction just right by that factory + + align:start position:0% +contraction just right by that factory + + + align:start position:0% +contraction just right by that factory +gamma that we encountered a few times + + align:start position:0% +gamma that we encountered a few times + + + align:start position:0% +gamma that we encountered a few times +then the um the expected offset in that + + align:start position:0% +then the um the expected offset in that + + + align:start position:0% +then the um the expected offset in that +race between the light waves traveling + + align:start position:0% +race between the light waves traveling + + + align:start position:0% +race between the light waves traveling +in the two different sides of the + + align:start position:0% +in the two different sides of the + + + align:start position:0% +in the two different sides of the +interferometer should exactly cancel the + + align:start position:0% +interferometer should exactly cancel the + + + align:start position:0% +interferometer should exactly cancel the +the Rays should be a tie after all one + + align:start position:0% +the Rays should be a tie after all one + + + align:start position:0% +the Rays should be a tie after all one +should actually expect a null result and + + align:start position:0% +should actually expect a null result and + + + align:start position:0% +should actually expect a null result and +all this came down from treating the + + align:start position:0% +all this came down from treating the + + + align:start position:0% +all this came down from treating the +electrodynamics of moving bodies by + + align:start position:0% +electrodynamics of moving bodies by + + + align:start position:0% +electrodynamics of moving bodies by +starting with the question of Dynamics + + align:start position:0% +starting with the question of Dynamics + + + align:start position:0% +starting with the question of Dynamics +are there all the forces at play rather + + align:start position:0% +are there all the forces at play rather + + + align:start position:0% +are there all the forces at play rather +than kinematics which is a study of the + + align:start position:0% +than kinematics which is a study of the + + + align:start position:0% +than kinematics which is a study of the +motion of objects through space and time + + align:start position:0% +motion of objects through space and time + + + align:start position:0% +motion of objects through space and time +so young Albert Einstein then it kind of + + align:start position:0% +so young Albert Einstein then it kind of + + + align:start position:0% +so young Albert Einstein then it kind of +inherits that set of questions it moves + + align:start position:0% +inherits that set of questions it moves + + + align:start position:0% +inherits that set of questions it moves +into that discussion a little bit later + + align:start position:0% +into that discussion a little bit later + + + align:start position:0% +into that discussion a little bit later +he was born in 1879 here's a rather + + align:start position:0% +he was born in 1879 here's a rather + + + align:start position:0% +he was born in 1879 here's a rather +adorable photo of young Einstein kind of + + align:start position:0% +adorable photo of young Einstein kind of + + + align:start position:0% +adorable photo of young Einstein kind of +Elementary School aged so he was born + + align:start position:0% +Elementary School aged so he was born + + + align:start position:0% +Elementary School aged so he was born +um sort of just before Michaelson and + + align:start position:0% +um sort of just before Michaelson and + + + align:start position:0% +um sort of just before Michaelson and +Morley actually began that series of + + align:start position:0% +Morley actually began that series of + + + align:start position:0% +Morley actually began that series of +experiments he was born after Maxwell's + + align:start position:0% +experiments he was born after Maxwell's + + + align:start position:0% +experiments he was born after Maxwell's +treatise + + align:start position:0% +treatise + + + align:start position:0% +treatise +before some of Hendrick Lorenzo's main + + align:start position:0% +before some of Hendrick Lorenzo's main + + + align:start position:0% +before some of Hendrick Lorenzo's main +work he was born in the in the town of + + align:start position:0% +work he was born in the in the town of + + + align:start position:0% +work he was born in the in the town of +om in what was then quite rural Germany + + align:start position:0% +om in what was then quite rural Germany + + + align:start position:0% +om in what was then quite rural Germany +not near any of the main city centers + + align:start position:0% +not near any of the main city centers + + + align:start position:0% +not near any of the main city centers +Einstein's main ambition when he was a + + align:start position:0% +Einstein's main ambition when he was a + + + align:start position:0% +Einstein's main ambition when he was a +young child was actually to join the + + align:start position:0% +young child was actually to join the + + + align:start position:0% +young child was actually to join the +business that his father and his uncle + + align:start position:0% +business that his father and his uncle + + + align:start position:0% +business that his father and his uncle +had created they were some of the first + + align:start position:0% +had created they were some of the first + + + align:start position:0% +had created they were some of the first +professional electrical engineers in + + align:start position:0% +professional electrical engineers in + + + align:start position:0% +professional electrical engineers in +these later Decades of the 19th century + + align:start position:0% +these later Decades of the 19th century + + + align:start position:0% +these later Decades of the 19th century +just like the kind of folks about whom + + align:start position:0% +just like the kind of folks about whom + + + align:start position:0% +just like the kind of folks about whom +Maxwell had written in England uh in the + + align:start position:0% +Maxwell had written in England uh in the + + + align:start position:0% +Maxwell had written in England uh in the +in the preface to his Treatise these + + align:start position:0% +in the preface to his Treatise these + + + align:start position:0% +in the preface to his Treatise these +so-called electricians that would soon + + align:start position:0% +so-called electricians that would soon + + + align:start position:0% +so-called electricians that would soon +be called electrical engineers + + align:start position:0% +be called electrical engineers + + + align:start position:0% +be called electrical engineers +so that's what I saw his own father did + + align:start position:0% +so that's what I saw his own father did + + + align:start position:0% +so that's what I saw his own father did +and his uncle they they formed a company + + align:start position:0% +and his uncle they they formed a company + + + align:start position:0% +and his uncle they they formed a company +together they were much better at + + align:start position:0% +together they were much better at + + + align:start position:0% +together they were much better at +engineering than a business the company + + align:start position:0% +engineering than a business the company + + + align:start position:0% +engineering than a business the company +went bankrupt multiple times they had to + + align:start position:0% +went bankrupt multiple times they had to + + + align:start position:0% +went bankrupt multiple times they had to +actually keep moving but they were + + align:start position:0% +actually keep moving but they were + + + align:start position:0% +actually keep moving but they were +working in this kind of exciting new + + align:start position:0% +working in this kind of exciting new + + + align:start position:0% +working in this kind of exciting new +area + + align:start position:0% +area + + + align:start position:0% +area +during the waves of things like + + align:start position:0% +during the waves of things like + + + align:start position:0% +during the waves of things like +wide-scale electrification the + + align:start position:0% +wide-scale electrification the + + + align:start position:0% +wide-scale electrification the +introduction of electric street lighting + + align:start position:0% +introduction of electric street lighting + + + align:start position:0% +introduction of electric street lighting +and more and more municipalities more + + align:start position:0% +and more and more municipalities more + + + align:start position:0% +and more and more municipalities more +and more ways in which electrification + + align:start position:0% +and more ways in which electrification + + + align:start position:0% +and more ways in which electrification +and therefore electrical gadgets were + + align:start position:0% +and therefore electrical gadgets were + + + align:start position:0% +and therefore electrical gadgets were +entering into quite common experience + + align:start position:0% +entering into quite common experience + + + align:start position:0% +entering into quite common experience +that's the world into which Einstein was + + align:start position:0% +that's the world into which Einstein was + + + align:start position:0% +that's the world into which Einstein was +literally born and that's what he wanted + + align:start position:0% +literally born and that's what he wanted + + + align:start position:0% +literally born and that's what he wanted +to work on + + align:start position:0% +to work on + + + align:start position:0% +to work on +turns out he dropped out of high school + + align:start position:0% +turns out he dropped out of high school + + + align:start position:0% +turns out he dropped out of high school +so he never got a high school diploma + + align:start position:0% +so he never got a high school diploma + + + align:start position:0% +so he never got a high school diploma +he developed a real a kind of allergy he + + align:start position:0% +he developed a real a kind of allergy he + + + align:start position:0% +he developed a real a kind of allergy he +got very frustrated with what he + + align:start position:0% +got very frustrated with what he + + + align:start position:0% +got very frustrated with what he +considered an overly kind of + + align:start position:0% +considered an overly kind of + + + align:start position:0% +considered an overly kind of +militaristic approach or a + + align:start position:0% +militaristic approach or a + + + align:start position:0% +militaristic approach or a +discipline-based approach uh in these + + align:start position:0% +discipline-based approach uh in these + + + align:start position:0% +discipline-based approach uh in these +kind of Prussian high schools so he + + align:start position:0% +kind of Prussian high schools so he + + + align:start position:0% +kind of Prussian high schools so he +ignored his teachers and got into + + align:start position:0% +ignored his teachers and got into + + + align:start position:0% +ignored his teachers and got into +trouble and finally just dropped out by + + align:start position:0% +trouble and finally just dropped out by + + + align:start position:0% +trouble and finally just dropped out by +all accounts his principal was just as + + align:start position:0% +all accounts his principal was just as + + + align:start position:0% +all accounts his principal was just as +happy to see him leave no one liked each + + align:start position:0% +happy to see him leave no one liked each + + + align:start position:0% +happy to see him leave no one liked each +other + + align:start position:0% +other + + + align:start position:0% +other +but he set his mind on entering this + + align:start position:0% +but he set his mind on entering this + + + align:start position:0% +but he set his mind on entering this +Elite Federal + + align:start position:0% +Elite Federal + + + align:start position:0% +Elite Federal +um Institute of Technology known as the + + align:start position:0% +um Institute of Technology known as the + + + align:start position:0% +um Institute of Technology known as the +ate heart eth that stands for the idea + + align:start position:0% +ate heart eth that stands for the idea + + + align:start position:0% +ate heart eth that stands for the idea +technician which is a phrase I never + + align:start position:0% +technician which is a phrase I never + + + align:start position:0% +technician which is a phrase I never +ever Tire of trying to pronounce we can + + align:start position:0% +ever Tire of trying to pronounce we can + + + align:start position:0% +ever Tire of trying to pronounce we can +just call it the eth this was basically + + align:start position:0% +just call it the eth this was basically + + + align:start position:0% +just call it the eth this was basically +like the MIT of Zurich + + align:start position:0% +like the MIT of Zurich + + + align:start position:0% +like the MIT of Zurich +although that's a bit unfair because eth + + align:start position:0% +although that's a bit unfair because eth + + + align:start position:0% +although that's a bit unfair because eth +actually predated uh the founding of our + + align:start position:0% +actually predated uh the founding of our + + + align:start position:0% +actually predated uh the founding of our +own MIT it was a place a lot like MIT it + + align:start position:0% +own MIT it was a place a lot like MIT it + + + align:start position:0% +own MIT it was a place a lot like MIT it +was a Polytechnic Polytechnic Institute + + align:start position:0% +was a Polytechnic Polytechnic Institute + + + align:start position:0% +was a Polytechnic Polytechnic Institute +with a real focus on science and + + align:start position:0% +with a real focus on science and + + + align:start position:0% +with a real focus on science and +engineering including these new areas + + align:start position:0% +engineering including these new areas + + + align:start position:0% +engineering including these new areas +like electrical engineering his main + + align:start position:0% +like electrical engineering his main + + + align:start position:0% +like electrical engineering his main +goal Einstein's goal was to was to even + + align:start position:0% +goal Einstein's goal was to was to even + + + align:start position:0% +goal Einstein's goal was to was to even +though he had no high school diploma and + + align:start position:0% +though he had no high school diploma and + + + align:start position:0% +though he had no high school diploma and +he dropped out he would take the special + + align:start position:0% +he dropped out he would take the special + + + align:start position:0% +he dropped out he would take the special +entrance exam for this one special place + + align:start position:0% +entrance exam for this one special place + + + align:start position:0% +entrance exam for this one special place +he most wanted to attend the eth or ate + + align:start position:0% +he most wanted to attend the eth or ate + + + align:start position:0% +he most wanted to attend the eth or ate +ha in Zurich Switzerland and then he + + align:start position:0% +ha in Zurich Switzerland and then he + + + align:start position:0% +ha in Zurich Switzerland and then he +could go in well he did take the exam he + + align:start position:0% +could go in well he did take the exam he + + + align:start position:0% +could go in well he did take the exam he +failed it because he kind of blew off + + align:start position:0% +failed it because he kind of blew off + + + align:start position:0% +failed it because he kind of blew off +the subjects that he didn't care about + + align:start position:0% +the subjects that he didn't care about + + + align:start position:0% +the subjects that he didn't care about +but the examiner for the physics and + + align:start position:0% +but the examiner for the physics and + + + align:start position:0% +but the examiner for the physics and +math sections a professor named Weber so + + align:start position:0% +math sections a professor named Weber so + + + align:start position:0% +math sections a professor named Weber so +enough promise in Einstein's portions of + + align:start position:0% +enough promise in Einstein's portions of + + + align:start position:0% +enough promise in Einstein's portions of +the entrance exam not on humanities not + + align:start position:0% +the entrance exam not on humanities not + + + align:start position:0% +the entrance exam not on humanities not +on languages not on History those he was + + align:start position:0% +on languages not on History those he was + + + align:start position:0% +on languages not on History those he was +quite terrible at at this time but for + + align:start position:0% +quite terrible at at this time but for + + + align:start position:0% +quite terrible at at this time but for +the physics and math portions he showed + + align:start position:0% +the physics and math portions he showed + + + align:start position:0% +the physics and math portions he showed +enough promise that he kind of pulled + + align:start position:0% +enough promise that he kind of pulled + + + align:start position:0% +enough promise that he kind of pulled +Young Einstein aside and said you failed + + align:start position:0% +Young Einstein aside and said you failed + + + align:start position:0% +Young Einstein aside and said you failed +you cannot come to the eth right now but + + align:start position:0% +you cannot come to the eth right now but + + + align:start position:0% +you cannot come to the eth right now but +if you go to a local school effectively + + align:start position:0% +if you go to a local school effectively + + + align:start position:0% +if you go to a local school effectively +a kind of local Community College a can + + align:start position:0% +a kind of local Community College a can + + + align:start position:0% +a kind of local Community College a can +total Regional kind of Community College + + align:start position:0% +total Regional kind of Community College + + + align:start position:0% +total Regional kind of Community College +nearby in Switzerland go there for a + + align:start position:0% +nearby in Switzerland go there for a + + + align:start position:0% +nearby in Switzerland go there for a +year work with some new teachers take + + align:start position:0% +year work with some new teachers take + + + align:start position:0% +year work with some new teachers take +our entrance exam again and that's what + + align:start position:0% +our entrance exam again and that's what + + + align:start position:0% +our entrance exam again and that's what +he did so he was admitted to his dream + + align:start position:0% +he did so he was admitted to his dream + + + align:start position:0% +he did so he was admitted to his dream +School the second time around they began + + align:start position:0% +School the second time around they began + + + align:start position:0% +School the second time around they began +studying in Zurich in the very late uh + + align:start position:0% +studying in Zurich in the very late uh + + + align:start position:0% +studying in Zurich in the very late uh +1800s + + align:start position:0% +1800s + + + align:start position:0% +1800s +once he worked so hard to get in + + align:start position:0% +once he worked so hard to get in + + + align:start position:0% +once he worked so hard to get in +including this extra year of just trying + + align:start position:0% +including this extra year of just trying + + + align:start position:0% +including this extra year of just trying +to take their engine exam he then + + align:start position:0% +to take their engine exam he then + + + align:start position:0% +to take their engine exam he then +proceeded to cut classes and read on his + + align:start position:0% +proceeded to cut classes and read on his + + + align:start position:0% +proceeded to cut classes and read on his +own this guy was I mean he was no + + align:start position:0% +own this guy was I mean he was no + + + align:start position:0% +own this guy was I mean he was no +Einstein he really just kept doing these + + align:start position:0% +Einstein he really just kept doing these + + + align:start position:0% +Einstein he really just kept doing these +stupid stupid things so even after + + align:start position:0% +stupid stupid things so even after + + + align:start position:0% +stupid stupid things so even after +working so hard to get into his dream + + align:start position:0% +working so hard to get into his dream + + + align:start position:0% +working so hard to get into his dream +University he basically cut his glasses + + align:start position:0% +University he basically cut his glasses + + + align:start position:0% +University he basically cut his glasses +or at least many of them any of the ones + + align:start position:0% +or at least many of them any of the ones + + + align:start position:0% +or at least many of them any of the ones +that he thought were not worth his time + + align:start position:0% +that he thought were not worth his time + + + align:start position:0% +that he thought were not worth his time +or for which he didn't really like the + + align:start position:0% +or for which he didn't really like the + + + align:start position:0% +or for which he didn't really like the +professors so he would read on his own + + align:start position:0% +professors so he would read on his own + + + align:start position:0% +professors so he would read on his own +the latest stuff is still pretty new + + align:start position:0% +the latest stuff is still pretty new + + + align:start position:0% +the latest stuff is still pretty new +stuff like Maxwell's Treatise on + + align:start position:0% +stuff like Maxwell's Treatise on + + + align:start position:0% +stuff like Maxwell's Treatise on +electricity magnetism like some of the + + align:start position:0% +electricity magnetism like some of the + + + align:start position:0% +electricity magnetism like some of the +very exciting work on statistical + + align:start position:0% +very exciting work on statistical + + + align:start position:0% +very exciting work on statistical +mechanics and the behavior of gases by + + align:start position:0% +mechanics and the behavior of gases by + + + align:start position:0% +mechanics and the behavior of gases by +people like Ludwig boltzmann and others + + align:start position:0% +people like Ludwig boltzmann and others + + + align:start position:0% +people like Ludwig boltzmann and others +he would read on his own + + align:start position:0% +he would read on his own + + + align:start position:0% +he would read on his own +now for some reason after cutting + + align:start position:0% +now for some reason after cutting + + + align:start position:0% +now for some reason after cutting +classes and letting his professors know + + align:start position:0% +classes and letting his professors know + + + align:start position:0% +classes and letting his professors know +how little he respected them he was not + + align:start position:0% +how little he respected them he was not + + + align:start position:0% +how little he respected them he was not +shy much like when he was in high school + + align:start position:0% +shy much like when he was in high school + + + align:start position:0% +shy much like when he was in high school +for some reason he couldn't get any good + + align:start position:0% +for some reason he couldn't get any good + + + align:start position:0% +for some reason he couldn't get any good +letters of recommendation upon + + align:start position:0% +letters of recommendation upon + + + align:start position:0% +letters of recommendation upon +graduating this this class is really + + align:start position:0% +graduating this this class is really + + + align:start position:0% +graduating this this class is really +full of good lessons for today so don't + + align:start position:0% +full of good lessons for today so don't + + + align:start position:0% +full of good lessons for today so don't +do the following don't annoy all of your + + align:start position:0% +do the following don't annoy all of your + + + align:start position:0% +do the following don't annoy all of your +professors so much that they all uh + + align:start position:0% +professors so much that they all uh + + + align:start position:0% +professors so much that they all uh +refuse to write you a strong + + align:start position:0% +refuse to write you a strong + + + align:start position:0% +refuse to write you a strong +recommendation + + align:start position:0% +recommendation + + + align:start position:0% +recommendation +so basically Einstein had a middling + + align:start position:0% +so basically Einstein had a middling + + + align:start position:0% +so basically Einstein had a middling +fairly mediocre grade point average + + align:start position:0% +fairly mediocre grade point average + + + align:start position:0% +fairly mediocre grade point average +because he kept cutting classes and + + align:start position:0% +because he kept cutting classes and + + + align:start position:0% +because he kept cutting classes and +ignoring stuff that wasn't interesting + + align:start position:0% +ignoring stuff that wasn't interesting + + + align:start position:0% +ignoring stuff that wasn't interesting +to him he was rude to the majority of + + align:start position:0% +to him he was rude to the majority of + + + align:start position:0% +to him he was rude to the majority of +his professors and for some reason + + align:start position:0% +his professors and for some reason + + + align:start position:0% +his professors and for some reason +couldn't get a job upon graduating he + + align:start position:0% +couldn't get a job upon graduating he + + + align:start position:0% +couldn't get a job upon graduating he +really couldn't figure this out the guy + + align:start position:0% +really couldn't figure this out the guy + + + align:start position:0% +really couldn't figure this out the guy +was kind of dumb for an Einstein + + align:start position:0% +was kind of dumb for an Einstein + + + align:start position:0% +was kind of dumb for an Einstein +in these young years so what happened + + align:start position:0% +in these young years so what happened + + + align:start position:0% +in these young years so what happened +was really in desperation with help from + + align:start position:0% +was really in desperation with help from + + + align:start position:0% +was really in desperation with help from +the father of one of his very close + + align:start position:0% +the father of one of his very close + + + align:start position:0% +the father of one of his very close +College friends uh the father of Marcel + + align:start position:0% +College friends uh the father of Marcel + + + align:start position:0% +College friends uh the father of Marcel +Grossman he was able to land an + + align:start position:0% +Grossman he was able to land an + + + align:start position:0% +Grossman he was able to land an +entry-level kind of civil service job in + + align:start position:0% +entry-level kind of civil service job in + + + align:start position:0% +entry-level kind of civil service job in +Barron Switzerland working in the local + + align:start position:0% +Barron Switzerland working in the local + + + align:start position:0% +Barron Switzerland working in the local +patent office he was hired as a patent + + align:start position:0% +patent office he was hired as a patent + + + align:start position:0% +patent office he was hired as a patent +officer third class there was no fourth + + align:start position:0% +officer third class there was no fourth + + + align:start position:0% +officer third class there was no fourth +class that was really the kind of + + align:start position:0% +class that was really the kind of + + + align:start position:0% +class that was really the kind of +entry-level position uh since he had a + + align:start position:0% +entry-level position uh since he had a + + + align:start position:0% +entry-level position uh since he had a +degree from a leading Technical + + align:start position:0% +degree from a leading Technical + + + align:start position:0% +degree from a leading Technical +Institute but was not otherwise highly + + align:start position:0% +Institute but was not otherwise highly + + + align:start position:0% +Institute but was not otherwise highly +recommended so even for Young Einstein + + align:start position:0% +recommended so even for Young Einstein + + + align:start position:0% +recommended so even for Young Einstein +it wasn't what he knew but who he knew + + align:start position:0% +it wasn't what he knew but who he knew + + + align:start position:0% +it wasn't what he knew but who he knew +he had to depend on his friends uh for + + align:start position:0% +he had to depend on his friends uh for + + + align:start position:0% +he had to depend on his friends uh for +help on the job market + + align:start position:0% +help on the job market + + + align:start position:0% +help on the job market +we also know quite well what happens + + align:start position:0% +we also know quite well what happens + + + align:start position:0% +we also know quite well what happens +next he fell in with some friends who + + align:start position:0% +next he fell in with some friends who + + + align:start position:0% +next he fell in with some friends who +were all around the same age all recent + + align:start position:0% +were all around the same age all recent + + + align:start position:0% +were all around the same age all recent +University graduates who are all living + + align:start position:0% +University graduates who are all living + + + align:start position:0% +University graduates who are all living +in Barron and they all had an interest + + align:start position:0% +in Barron and they all had an interest + + + align:start position:0% +in Barron and they all had an interest +in science uh this included uh young + + align:start position:0% +in science uh this included uh young + + + align:start position:0% +in science uh this included uh young +Maurice Sullivan uh Conrad Habib and + + align:start position:0% +Maurice Sullivan uh Conrad Habib and + + + align:start position:0% +Maurice Sullivan uh Conrad Habib and +then a recent graduate Albert Einstein + + align:start position:0% +then a recent graduate Albert Einstein + + + align:start position:0% +then a recent graduate Albert Einstein +they gave themselves the name the + + align:start position:0% +they gave themselves the name the + + + align:start position:0% +they gave themselves the name the +Olympia Academy because they were having + + align:start position:0% +Olympia Academy because they were having + + + align:start position:0% +Olympia Academy because they were having +fun that sounds like a like a triumphant + + align:start position:0% +fun that sounds like a like a triumphant + + + align:start position:0% +fun that sounds like a like a triumphant +um very prestigious uh Academy you know + + align:start position:0% +um very prestigious uh Academy you know + + + align:start position:0% +um very prestigious uh Academy you know +like Mount Olympus like the Greek + + align:start position:0% +like Mount Olympus like the Greek + + + align:start position:0% +like Mount Olympus like the Greek +Legends there's actually three recent + + align:start position:0% +Legends there's actually three recent + + + align:start position:0% +Legends there's actually three recent +college graduates meeting literally in + + align:start position:0% +college graduates meeting literally in + + + align:start position:0% +college graduates meeting literally in +the pub to drink a lot of beer and talk + + align:start position:0% +the pub to drink a lot of beer and talk + + + align:start position:0% +the pub to drink a lot of beer and talk +about philosophy but they figured they + + align:start position:0% +about philosophy but they figured they + + + align:start position:0% +about philosophy but they figured they +gave themselves an exalted name it would + + align:start position:0% +gave themselves an exalted name it would + + + align:start position:0% +gave themselves an exalted name it would +sound much more serious so the Olympic + + align:start position:0% +sound much more serious so the Olympic + + + align:start position:0% +sound much more serious so the Olympic +Academy was mostly those three folks + + align:start position:0% +Academy was mostly those three folks + + + align:start position:0% +Academy was mostly those three folks +reading on their own after hours after + + align:start position:0% +reading on their own after hours after + + + align:start position:0% +reading on their own after hours after +work + + align:start position:0% +work + + + align:start position:0% +work +and we even know quite a bit of what + + align:start position:0% +and we even know quite a bit of what + + + align:start position:0% +and we even know quite a bit of what +they were reading they wrote lots of + + align:start position:0% +they were reading they wrote lots of + + + align:start position:0% +they were reading they wrote lots of +letters to each other in between many of + + align:start position:0% +letters to each other in between many of + + + align:start position:0% +letters to each other in between many of +those letters have survived so we can + + align:start position:0% +those letters have survived so we can + + + align:start position:0% +those letters have survived so we can +reconstruct the kinds of questions and + + align:start position:0% +reconstruct the kinds of questions and + + + align:start position:0% +reconstruct the kinds of questions and +the kinds of materials of particular + + align:start position:0% +the kinds of materials of particular + + + align:start position:0% +the kinds of materials of particular +books that the Olympia Academy found + + align:start position:0% +books that the Olympia Academy found + + + align:start position:0% +books that the Olympia Academy found +really exciting one of the authors that + + align:start position:0% +really exciting one of the authors that + + + align:start position:0% +really exciting one of the authors that +they were especially excited about in + + align:start position:0% +they were especially excited about in + + + align:start position:0% +they were especially excited about in +the early years uh around 1900 was the + + align:start position:0% +the early years uh around 1900 was the + + + align:start position:0% +the early years uh around 1900 was the +Austrian polymath against ma here's an + + align:start position:0% +Austrian polymath against ma here's an + + + align:start position:0% +Austrian polymath against ma here's an +image of the English translation of one + + align:start position:0% +image of the English translation of one + + + align:start position:0% +image of the English translation of one +of his very influential books Mark was + + align:start position:0% +of his very influential books Mark was + + + align:start position:0% +of his very influential books Mark was +originally Austrian wrote his own books + + align:start position:0% +originally Austrian wrote his own books + + + align:start position:0% +originally Austrian wrote his own books +in German + + align:start position:0% +in German + + + align:start position:0% +in German +Einstein and his friends really just + + align:start position:0% +Einstein and his friends really just + + + align:start position:0% +Einstein and his friends really just +devoured these Mark was trained in + + align:start position:0% +devoured these Mark was trained in + + + align:start position:0% +devoured these Mark was trained in +mathematical physics in experimental + + align:start position:0% +mathematical physics in experimental + + + align:start position:0% +mathematical physics in experimental +physics we still talk about + + align:start position:0% +physics we still talk about + + + align:start position:0% +physics we still talk about +um uh mock numbers like for the speed of + + align:start position:0% +um uh mock numbers like for the speed of + + + align:start position:0% +um uh mock numbers like for the speed of +sound Mach 1 Mach 2 for jet planes and + + align:start position:0% +sound Mach 1 Mach 2 for jet planes and + + + align:start position:0% +sound Mach 1 Mach 2 for jet planes and +so on that's the same amounts Mark he + + align:start position:0% +so on that's the same amounts Mark he + + + align:start position:0% +so on that's the same amounts Mark he +later held a professorship in surgery + + align:start position:0% +later held a professorship in surgery + + + align:start position:0% +later held a professorship in surgery +and then finally in the history of + + align:start position:0% +and then finally in the history of + + + align:start position:0% +and then finally in the history of +philosophy of science Mark had quite a + + align:start position:0% +philosophy of science Mark had quite a + + + align:start position:0% +philosophy of science Mark had quite a +remarkable career so what he did in this + + align:start position:0% +remarkable career so what he did in this + + + align:start position:0% +remarkable career so what he did in this +series of books including the one which + + align:start position:0% +series of books including the one which + + + align:start position:0% +series of books including the one which +in English translations known as the + + align:start position:0% +in English translations known as the + + + align:start position:0% +in English translations known as the +science of mechanics which we know + + align:start position:0% +science of mechanics which we know + + + align:start position:0% +science of mechanics which we know +Einstein and his friends were really uh + + align:start position:0% +Einstein and his friends were really uh + + + align:start position:0% +Einstein and his friends were really uh +reading carefully + + align:start position:0% +reading carefully + + + align:start position:0% +reading carefully +Mark proposed this kind of scientific + + align:start position:0% +Mark proposed this kind of scientific + + + align:start position:0% +Mark proposed this kind of scientific +philosophy called positivism + + align:start position:0% +philosophy called positivism + + + align:start position:0% +philosophy called positivism +his argument was that only quantities + + align:start position:0% +his argument was that only quantities + + + align:start position:0% +his argument was that only quantities +that could be what he in his phrase + + align:start position:0% +that could be what he in his phrase + + + align:start position:0% +that could be what he in his phrase +could become objects of positive + + align:start position:0% +could become objects of positive + + + align:start position:0% +could become objects of positive +experience things we could literally + + align:start position:0% +experience things we could literally + + + align:start position:0% +experience things we could literally +touch and measure and and handle + + align:start position:0% +touch and measure and and handle + + + align:start position:0% +touch and measure and and handle +empirically and quantitatively only + + align:start position:0% +empirically and quantitatively only + + + align:start position:0% +empirically and quantitatively only +these objects of positive experience + + align:start position:0% +these objects of positive experience + + + align:start position:0% +these objects of positive experience +belonged in any proper scientific theory + + align:start position:0% +belonged in any proper scientific theory + + + align:start position:0% +belonged in any proper scientific theory +anything else Mark argued would lead to + + align:start position:0% +anything else Mark argued would lead to + + + align:start position:0% +anything else Mark argued would lead to +just sort of confusion and empty + + align:start position:0% +just sort of confusion and empty + + + align:start position:0% +just sort of confusion and empty +metaphysics which was his word for like + + align:start position:0% +metaphysics which was his word for like + + + align:start position:0% +metaphysics which was his word for like +bad bad stuff you'll just get yourself + + align:start position:0% +bad bad stuff you'll just get yourself + + + align:start position:0% +bad bad stuff you'll just get yourself +confused arguing about the equivalent of + + align:start position:0% +confused arguing about the equivalent of + + + align:start position:0% +confused arguing about the equivalent of +how many angels could dance on the head + + align:start position:0% +how many angels could dance on the head + + + align:start position:0% +how many angels could dance on the head +of a pin if you're not able to to + + align:start position:0% +of a pin if you're not able to to + + + align:start position:0% +of a pin if you're not able to to +actually subject those questions to uh + + align:start position:0% +actually subject those questions to uh + + + align:start position:0% +actually subject those questions to uh +to measurement or any kind of empirical + + align:start position:0% +to measurement or any kind of empirical + + + align:start position:0% +to measurement or any kind of empirical +input that became known as positivism + + align:start position:0% +input that became known as positivism + + + align:start position:0% +input that became known as positivism +and a lot of what mock did in this in + + align:start position:0% +and a lot of what mock did in this in + + + align:start position:0% +and a lot of what mock did in this in +this particular book very thick book The + + align:start position:0% +this particular book very thick book The + + + align:start position:0% +this particular book very thick book The +Science and mechanics was basically take + + align:start position:0% +Science and mechanics was basically take + + + align:start position:0% +Science and mechanics was basically take +Isaac Newton's work to tasks so mock + + align:start position:0% +Isaac Newton's work to tasks so mock + + + align:start position:0% +Isaac Newton's work to tasks so mock +laid out this entire program + + align:start position:0% +laid out this entire program + + + align:start position:0% +laid out this entire program +to basically say that Newtonian physics + + align:start position:0% +to basically say that Newtonian physics + + + align:start position:0% +to basically say that Newtonian physics +as successful as it was in Celestial + + align:start position:0% +as successful as it was in Celestial + + + align:start position:0% +as successful as it was in Celestial +mechanics and all kinds of applications + + align:start position:0% +mechanics and all kinds of applications + + + align:start position:0% +mechanics and all kinds of applications +it was riddled charged aerosmoc riddled + + align:start position:0% +it was riddled charged aerosmoc riddled + + + align:start position:0% +it was riddled charged aerosmoc riddled +with these sort of empty Notions that + + align:start position:0% +with these sort of empty Notions that + + + align:start position:0% +with these sort of empty Notions that +could never be subject to careful uh + + align:start position:0% +could never be subject to careful uh + + + align:start position:0% +could never be subject to careful uh +empirical measurements things like + + align:start position:0% +empirical measurements things like + + + align:start position:0% +empirical measurements things like +absolute space and absolute time so Mark + + align:start position:0% +absolute space and absolute time so Mark + + + align:start position:0% +absolute space and absolute time so Mark +says no matter the successes of Newton's + + align:start position:0% +says no matter the successes of Newton's + + + align:start position:0% +says no matter the successes of Newton's +physics it's riddled with these problems + + align:start position:0% +physics it's riddled with these problems + + + align:start position:0% +physics it's riddled with these problems +we should get rid of all these empty + + align:start position:0% +we should get rid of all these empty + + + align:start position:0% +we should get rid of all these empty +metaphysical Notions like absolute space + + align:start position:0% +metaphysical Notions like absolute space + + + align:start position:0% +metaphysical Notions like absolute space +and absolute time and this the Olympic + + align:start position:0% +and absolute time and this the Olympic + + + align:start position:0% +and absolute time and this the Olympic +Academy just ate this stuff up + + align:start position:0% +Academy just ate this stuff up + + + align:start position:0% +Academy just ate this stuff up +so Einstein we we know from + + align:start position:0% +so Einstein we we know from + + + align:start position:0% +so Einstein we we know from +contemporaneous uh letters and notes and + + align:start position:0% +contemporaneous uh letters and notes and + + + align:start position:0% +contemporaneous uh letters and notes and +so on was very directly inspired by + + align:start position:0% +so on was very directly inspired by + + + align:start position:0% +so on was very directly inspired by +Ernest Mock and he pursued this kind of + + align:start position:0% +Ernest Mock and he pursued this kind of + + + align:start position:0% +Ernest Mock and he pursued this kind of +critical reevaluation deciding we should + + align:start position:0% +critical reevaluation deciding we should + + + align:start position:0% +critical reevaluation deciding we should +begin with kinematics before even + + align:start position:0% +begin with kinematics before even + + + align:start position:0% +begin with kinematics before even +worrying about Dynamics remember + + align:start position:0% +worrying about Dynamics remember + + + align:start position:0% +worrying about Dynamics remember +kinematics is the study of bodies and + + align:start position:0% +kinematics is the study of bodies and + + + align:start position:0% +kinematics is the study of bodies and +motion through space and time things + + align:start position:0% +motion through space and time things + + + align:start position:0% +motion through space and time things +that at least in principle could be + + align:start position:0% +that at least in principle could be + + + align:start position:0% +that at least in principle could be +subject to observation and measurement + + align:start position:0% +subject to observation and measurement + + + align:start position:0% +subject to observation and measurement +so we better get that straight with this + + align:start position:0% +so we better get that straight with this + + + align:start position:0% +so we better get that straight with this +new critical Edge granted by ants mock + + align:start position:0% +new critical Edge granted by ants mock + + + align:start position:0% +new critical Edge granted by ants mock +before we even worry about things like + + align:start position:0% +before we even worry about things like + + + align:start position:0% +before we even worry about things like +the interplay of forces or the study of + + align:start position:0% +the interplay of forces or the study of + + + align:start position:0% +the interplay of forces or the study of +Dynamics + + align:start position:0% +Dynamics + + + align:start position:0% +Dynamics +so while he's working at the patent + + align:start position:0% +so while he's working at the patent + + + align:start position:0% +so while he's working at the patent +office he's still a patent officer third + + align:start position:0% +office he's still a patent officer third + + + align:start position:0% +office he's still a patent officer third +class meeting after hours with the + + align:start position:0% +class meeting after hours with the + + + align:start position:0% +class meeting after hours with the +Olympic Academy increasing neglecting + + align:start position:0% +Olympic Academy increasing neglecting + + + align:start position:0% +Olympic Academy increasing neglecting +his first wife and his young child uh + + align:start position:0% +his first wife and his young child uh + + + align:start position:0% +his first wife and his young child uh +basically blowing him off to go drink + + align:start position:0% +basically blowing him off to go drink + + + align:start position:0% +basically blowing him off to go drink +with his friends and talk about + + align:start position:0% +with his friends and talk about + + + align:start position:0% +with his friends and talk about +philosophy in the space of that time uh + + align:start position:0% +philosophy in the space of that time uh + + + align:start position:0% +philosophy in the space of that time uh +he submitted several papers to the + + align:start position:0% +he submitted several papers to the + + + align:start position:0% +he submitted several papers to the +leading Journal of physics really in + + align:start position:0% +leading Journal of physics really in + + + align:start position:0% +leading Journal of physics really in +certainly in in Europe or the North + + align:start position:0% +certainly in in Europe or the North + + + align:start position:0% +certainly in in Europe or the North +America at the time the aniline de + + align:start position:0% +America at the time the aniline de + + + align:start position:0% +America at the time the aniline de +physique at this point it was edited by + + align:start position:0% +physique at this point it was edited by + + + align:start position:0% +physique at this point it was edited by +Max Planck someone whose work will come + + align:start position:0% +Max Planck someone whose work will come + + + align:start position:0% +Max Planck someone whose work will come +to pretty soon in this class + + align:start position:0% +to pretty soon in this class + + + align:start position:0% +to pretty soon in this class +in 1905 Einstein hadroth is often called + + align:start position:0% +in 1905 Einstein hadroth is often called + + + align:start position:0% +in 1905 Einstein hadroth is often called +his miracle year or his honest mirabilis + + align:start position:0% +his miracle year or his honest mirabilis + + + align:start position:0% +his miracle year or his honest mirabilis +in Latin it turns out he actually it + + align:start position:0% +in Latin it turns out he actually it + + + align:start position:0% +in Latin it turns out he actually it +wasn't even a whole he was like a + + align:start position:0% +wasn't even a whole he was like a + + + align:start position:0% +wasn't even a whole he was like a +miracle two seasons he needed less than + + align:start position:0% +miracle two seasons he needed less than + + + align:start position:0% +miracle two seasons he needed less than +six months to introduce this entire body + + align:start position:0% +six months to introduce this entire body + + + align:start position:0% +six months to introduce this entire body +of work so here I'm showing just the + + align:start position:0% +of work so here I'm showing just the + + + align:start position:0% +of work so here I'm showing just the +dates at which these separate articles + + align:start position:0% +dates at which these separate articles + + + align:start position:0% +dates at which these separate articles +were received at the journal separate + + align:start position:0% +were received at the journal separate + + + align:start position:0% +were received at the journal separate +submissions that were clocked in at the + + align:start position:0% +submissions that were clocked in at the + + + align:start position:0% +submissions that were clocked in at the +Orlando physique and for now what we're + + align:start position:0% +Orlando physique and for now what we're + + + align:start position:0% +Orlando physique and for now what we're +going to do is focus on this third in + + align:start position:0% +going to do is focus on this third in + + + align:start position:0% +going to do is focus on this third in +his series which again today we refer to + + align:start position:0% +his series which again today we refer to + + + align:start position:0% +his series which again today we refer to +uh about by calling it the Special + + align:start position:0% +uh about by calling it the Special + + + align:start position:0% +uh about by calling it the Special +theory of relativity the actual article + + align:start position:0% +theory of relativity the actual article + + + align:start position:0% +theory of relativity the actual article +the first page it was shown here + + align:start position:0% +the first page it was shown here + + + align:start position:0% +the first page it was shown here +is entitled on the electromagnetics of + + align:start position:0% +is entitled on the electromagnetics of + + + align:start position:0% +is entitled on the electromagnetics of +moving bodies a title a phrase that by + + align:start position:0% +moving bodies a title a phrase that by + + + align:start position:0% +moving bodies a title a phrase that by +now sounds a conventional to us thanks + + align:start position:0% +now sounds a conventional to us thanks + + + align:start position:0% +now sounds a conventional to us thanks +to the last few lectures but especially + + align:start position:0% +to the last few lectures but especially + + + align:start position:0% +to the last few lectures but especially +to Einstein's readers back in the day + + align:start position:0% +to Einstein's readers back in the day + + + align:start position:0% +to Einstein's readers back in the day +that was exactly the topic on which + + align:start position:0% +that was exactly the topic on which + + + align:start position:0% +that was exactly the topic on which +leading figures like Hendrick Lawrence + + align:start position:0% +leading figures like Hendrick Lawrence + + + align:start position:0% +leading figures like Hendrick Lawrence +and George Fitzgerald and Michaelson and + + align:start position:0% +and George Fitzgerald and Michaelson and + + + align:start position:0% +and George Fitzgerald and Michaelson and +Morley and many many of their colleagues + + align:start position:0% +Morley and many many of their colleagues + + + align:start position:0% +Morley and many many of their colleagues +that's what they cared about and what + + align:start position:0% +that's what they cared about and what + + + align:start position:0% +that's what they cared about and what +they agreed was sort of front and center + + align:start position:0% +they agreed was sort of front and center + + + align:start position:0% +they agreed was sort of front and center +for Cutting Edge physics so Einstein's + + align:start position:0% +for Cutting Edge physics so Einstein's + + + align:start position:0% +for Cutting Edge physics so Einstein's +paper on the electrodomics and moving + + align:start position:0% +paper on the electrodomics and moving + + + align:start position:0% +paper on the electrodomics and moving +bodies has a conventional or + + align:start position:0% +bodies has a conventional or + + + align:start position:0% +bodies has a conventional or +recognizable title and yet as we'll talk + + align:start position:0% +recognizable title and yet as we'll talk + + + align:start position:0% +recognizable title and yet as we'll talk +about through much of today's class the + + align:start position:0% +about through much of today's class the + + + align:start position:0% +about through much of today's class the +rest of his approach to that + + align:start position:0% +rest of his approach to that + + + align:start position:0% +rest of his approach to that +conventional topic was anything but + + align:start position:0% +conventional topic was anything but + + + align:start position:0% +conventional topic was anything but +convention was quite unusual + + align:start position:0% +convention was quite unusual + + + align:start position:0% +convention was quite unusual +it didn't help his colleagues that the + + align:start position:0% +it didn't help his colleagues that the + + + align:start position:0% +it didn't help his colleagues that the +only real indication of where these + + align:start position:0% +only real indication of where these + + + align:start position:0% +only real indication of where these +unusual ideas came from was in the + + align:start position:0% +unusual ideas came from was in the + + + align:start position:0% +unusual ideas came from was in the +acknowledgments where he says in + + align:start position:0% +acknowledgments where he says in + + + align:start position:0% +acknowledgments where he says in +conclusion let me know that my friend + + align:start position:0% +conclusion let me know that my friend + + + align:start position:0% +conclusion let me know that my friend +and colleague Michelangelo besso stood + + align:start position:0% +and colleague Michelangelo besso stood + + + align:start position:0% +and colleague Michelangelo besso stood +fastly steadfastly stood by me in my + + align:start position:0% +fastly steadfastly stood by me in my + + + align:start position:0% +fastly steadfastly stood by me in my +work on the problem discussed here I've + + align:start position:0% +work on the problem discussed here I've + + + align:start position:0% +work on the problem discussed here I've +indebted to him for several valuable + + align:start position:0% +indebted to him for several valuable + + + align:start position:0% +indebted to him for several valuable +suggestions that didn't help clarify + + align:start position:0% +suggestions that didn't help clarify + + + align:start position:0% +suggestions that didn't help clarify +because besso was equally unknown it was + + align:start position:0% +because besso was equally unknown it was + + + align:start position:0% +because besso was equally unknown it was +another basically college friend of + + align:start position:0% +another basically college friend of + + + align:start position:0% +another basically college friend of +Einstein's another occasional member of + + align:start position:0% +Einstein's another occasional member of + + + align:start position:0% +Einstein's another occasional member of +that Olympia Academy so one totally + + align:start position:0% +that Olympia Academy so one totally + + + align:start position:0% +that Olympia Academy so one totally +unknown person is thanking another + + align:start position:0% +unknown person is thanking another + + + align:start position:0% +unknown person is thanking another +basically unknown person and otherwise + + align:start position:0% +basically unknown person and otherwise + + + align:start position:0% +basically unknown person and otherwise +his paper appears like it's you know + + align:start position:0% +his paper appears like it's you know + + + align:start position:0% +his paper appears like it's you know +from Mars + + align:start position:0% +from Mars + + + align:start position:0% +from Mars +they pause there ask if there any + + align:start position:0% +they pause there ask if there any + + + align:start position:0% +they pause there ask if there any +questions on that first part any + + align:start position:0% +questions on that first part any + + + align:start position:0% +questions on that first part any +questions so far + + align:start position:0% + + + + align:start position:0% + +yeah so in the paper itself that what I + + align:start position:0% +yeah so in the paper itself that what I + + + align:start position:0% +yeah so in the paper itself that what I +showed you is now on screen is the + + align:start position:0% +showed you is now on screen is the + + + align:start position:0% +showed you is now on screen is the +entirety of acknowledgments he only + + align:start position:0% +entirety of acknowledgments he only + + + align:start position:0% +entirety of acknowledgments he only +thanked besso by name and for some of + + align:start position:0% +thanked besso by name and for some of + + + align:start position:0% +thanked besso by name and for some of +the specific points in that paper it + + align:start position:0% +the specific points in that paper it + + + align:start position:0% +the specific points in that paper it +does seem from other letters that have + + align:start position:0% +does seem from other letters that have + + + align:start position:0% +does seem from other letters that have +survived and so on they discuss these + + align:start position:0% +survived and so on they discuss these + + + align:start position:0% +survived and so on they discuss these +things especially closely with besso he + + align:start position:0% +things especially closely with besso he + + + align:start position:0% +things especially closely with besso he +did not thank his his then wife Malay + + align:start position:0% +did not thank his his then wife Malay + + + align:start position:0% +did not thank his his then wife Malay +for marriage we can talk about that they + + align:start position:0% +for marriage we can talk about that they + + + align:start position:0% +for marriage we can talk about that they +had talked about some of the ideas some + + align:start position:0% +had talked about some of the ideas some + + + align:start position:0% +had talked about some of the ideas some +years earlier it's a continuing point of + + align:start position:0% +years earlier it's a continuing point of + + + align:start position:0% +years earlier it's a continuing point of +historical interest how much maleva had + + align:start position:0% +historical interest how much maleva had + + + align:start position:0% +historical interest how much maleva had +um talked about these specific ideas + + align:start position:0% +um talked about these specific ideas + + + align:start position:0% +um talked about these specific ideas +closer to 1905 it looks like not so much + + align:start position:0% +closer to 1905 it looks like not so much + + + align:start position:0% +closer to 1905 it looks like not so much +partly because she was um + + align:start position:0% +partly because she was um + + + align:start position:0% +partly because she was um +uh working uh in in her new new + + align:start position:0% +uh working uh in in her new new + + + align:start position:0% +uh working uh in in her new new +motherhood role in a very what was + + align:start position:0% +motherhood role in a very what was + + + align:start position:0% +motherhood role in a very what was +within a very traditional gendered role + + align:start position:0% +within a very traditional gendered role + + + align:start position:0% +within a very traditional gendered role +and not able to really keep up with her + + align:start position:0% +and not able to really keep up with her + + + align:start position:0% +and not able to really keep up with her +own physics and math studies so uh he + + align:start position:0% +own physics and math studies so uh he + + + align:start position:0% +own physics and math studies so uh he +was not thanking the Leva in the paper + + align:start position:0% +was not thanking the Leva in the paper + + + align:start position:0% +was not thanking the Leva in the paper +he did not think by name either um + + align:start position:0% +he did not think by name either um + + + align:start position:0% +he did not think by name either um +conrador or Maurice Sullivan although he + + align:start position:0% +conrador or Maurice Sullivan although he + + + align:start position:0% +conrador or Maurice Sullivan although he +was writing with them in fact he was + + align:start position:0% +was writing with them in fact he was + + + align:start position:0% +was writing with them in fact he was +talking with them in the letters more + + align:start position:0% +talking with them in the letters more + + + align:start position:0% +talking with them in the letters more +about some of those other papers that + + align:start position:0% +about some of those other papers that + + + align:start position:0% +about some of those other papers that +year at least from the letters that have + + align:start position:0% +year at least from the letters that have + + + align:start position:0% +year at least from the letters that have +survived in the actual printed paper the + + align:start position:0% +survived in the actual printed paper the + + + align:start position:0% +survived in the actual printed paper the +only person he thinks is this again + + align:start position:0% +only person he thinks is this again + + + align:start position:0% +only person he thinks is this again +largely unknown figure uh Michelle besso + + align:start position:0% +largely unknown figure uh Michelle besso + + + align:start position:0% +largely unknown figure uh Michelle besso +he also as you've seen even in the + + align:start position:0% +he also as you've seen even in the + + + align:start position:0% +he also as you've seen even in the +excerpt um that is in the reader for + + align:start position:0% +excerpt um that is in the reader for + + + align:start position:0% +excerpt um that is in the reader for +today he cites almost no other + + align:start position:0% +today he cites almost no other + + + align:start position:0% +today he cites almost no other +literature + + align:start position:0% +literature + + + align:start position:0% +literature +so we do know from some of the reading + + align:start position:0% +so we do know from some of the reading + + + align:start position:0% +so we do know from some of the reading +notes that have survived they were + + align:start position:0% +notes that have survived they were + + + align:start position:0% +notes that have survived they were +actually quite interested in work by + + align:start position:0% +actually quite interested in work by + + + align:start position:0% +actually quite interested in work by +people like Maxwell but also more recent + + align:start position:0% +people like Maxwell but also more recent + + + align:start position:0% +people like Maxwell but also more recent +work by people like Hendrick Lorenz + + align:start position:0% +work by people like Hendrick Lorenz + + + align:start position:0% +work by people like Hendrick Lorenz +um but he doesn't even cite Lorenzo's + + align:start position:0% +um but he doesn't even cite Lorenzo's + + + align:start position:0% +um but he doesn't even cite Lorenzo's +work uh in in the paper very very + + align:start position:0% +work uh in in the paper very very + + + align:start position:0% +work uh in in the paper very very +sparingly anyway so he's being very very + + align:start position:0% +sparingly anyway so he's being very very + + + align:start position:0% +sparingly anyway so he's being very very +we could say selective which is a nice + + align:start position:0% +we could say selective which is a nice + + + align:start position:0% +we could say selective which is a nice +way of saying he's being kind of a jerk + + align:start position:0% +way of saying he's being kind of a jerk + + + align:start position:0% +way of saying he's being kind of a jerk +frankly being incomplete at least in not + + align:start position:0% +frankly being incomplete at least in not + + + align:start position:0% +frankly being incomplete at least in not +citing his sources if he submitted that + + align:start position:0% +citing his sources if he submitted that + + + align:start position:0% +citing his sources if he submitted that +paper for our class he would not get a + + align:start position:0% +paper for our class he would not get a + + + align:start position:0% +paper for our class he would not get a +good grade you should cite your sources + + align:start position:0% +good grade you should cite your sources + + + align:start position:0% +good grade you should cite your sources +that's a reminder for everyone + + align:start position:0% +that's a reminder for everyone + + + align:start position:0% +that's a reminder for everyone +uh so he was in in the actual published + + align:start position:0% +uh so he was in in the actual published + + + align:start position:0% +uh so he was in in the actual published +version he was he was not sharing the + + align:start position:0% +version he was he was not sharing the + + + align:start position:0% +version he was he was not sharing the +love very broad it was very very limited + + align:start position:0% +love very broad it was very very limited + + + align:start position:0% +love very broad it was very very limited +acknowledgment of where this was coming + + align:start position:0% +acknowledgment of where this was coming + + + align:start position:0% +acknowledgment of where this was coming +from + + align:start position:0% +from + + + align:start position:0% +from +any other questions + + align:start position:0% + + + + align:start position:0% + +let's let's continue on let's see what + + align:start position:0% +let's let's continue on let's see what + + + align:start position:0% +let's let's continue on let's see what +else we can do now with with ISO once he + + align:start position:0% +else we can do now with with ISO once he + + + align:start position:0% +else we can do now with with ISO once he +actually does then move into the + + align:start position:0% +actually does then move into the + + + align:start position:0% +actually does then move into the +electronomics of moving bodies + + align:start position:0% +electronomics of moving bodies + + + align:start position:0% +electronomics of moving bodies +you can see the screen again I hope it's + + align:start position:0% +you can see the screen again I hope it's + + + align:start position:0% +you can see the screen again I hope it's +back on for everyone + + align:start position:0% +back on for everyone + + + align:start position:0% +back on for everyone +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so as you've seen the very opening + + align:start position:0% +so as you've seen the very opening + + + align:start position:0% +so as you've seen the very opening +paragraph begins with this kind of + + align:start position:0% +paragraph begins with this kind of + + + align:start position:0% +paragraph begins with this kind of +puzzling pronouncement puzzling at least + + align:start position:0% +puzzling pronouncement puzzling at least + + + align:start position:0% +puzzling pronouncement puzzling at least +to readers of the most prestigious + + align:start position:0% +to readers of the most prestigious + + + align:start position:0% +to readers of the most prestigious +physics journal uh in at least Western + + align:start position:0% +physics journal uh in at least Western + + + align:start position:0% +physics journal uh in at least Western +Europe and North America at the time + + align:start position:0% +Europe and North America at the time + + + align:start position:0% +Europe and North America at the time +he starts out by saying not that there + + align:start position:0% +he starts out by saying not that there + + + align:start position:0% +he starts out by saying not that there +is an error in Max's equations he + + align:start position:0% +is an error in Max's equations he + + + align:start position:0% +is an error in Max's equations he +doesn't say I found a missing factor of + + align:start position:0% +doesn't say I found a missing factor of + + + align:start position:0% +doesn't say I found a missing factor of +2 pi or missing you know minus sign he + + align:start position:0% +2 pi or missing you know minus sign he + + + align:start position:0% +2 pi or missing you know minus sign he +doesn't say I've conducted new high + + align:start position:0% +doesn't say I've conducted new high + + + align:start position:0% +doesn't say I've conducted new high +Precision experiments and I found you + + align:start position:0% +Precision experiments and I found you + + + align:start position:0% +Precision experiments and I found you +know a glitch or some empirical anomaly + + align:start position:0% +know a glitch or some empirical anomaly + + + align:start position:0% +know a glitch or some empirical anomaly +compared to previous experiments he + + align:start position:0% +compared to previous experiments he + + + align:start position:0% +compared to previous experiments he +starts out by saying there's an + + align:start position:0% +starts out by saying there's an + + + align:start position:0% +starts out by saying there's an +asymmetry in the explanation that is not + + align:start position:0% +asymmetry in the explanation that is not + + + align:start position:0% +asymmetry in the explanation that is not +present in the phenomena + + align:start position:0% +present in the phenomena + + + align:start position:0% +present in the phenomena +that's a pretty astonishing opening what + + align:start position:0% +that's a pretty astonishing opening what + + + align:start position:0% +that's a pretty astonishing opening what +is he referring to not some very + + align:start position:0% +is he referring to not some very + + + align:start position:0% +is he referring to not some very +complicated hard thing to calculate he's + + align:start position:0% +complicated hard thing to calculate he's + + + align:start position:0% +complicated hard thing to calculate he's +referring to something that turned out + + align:start position:0% +referring to something that turned out + + + align:start position:0% +referring to something that turned out +it turns it turns out to have been + + align:start position:0% +it turns it turns out to have been + + + align:start position:0% +it turns it turns out to have been +something like a school exercise that + + align:start position:0% +something like a school exercise that + + + align:start position:0% +something like a school exercise that +he'd encountered or very similar to what + + align:start position:0% +he'd encountered or very similar to what + + + align:start position:0% +he'd encountered or very similar to what +he encountered when he was a university + + align:start position:0% +he encountered when he was a university + + + align:start position:0% +he encountered when he was a university +student + + align:start position:0% +student + + + align:start position:0% +student +what if we take a simple bar magnet just + + align:start position:0% +what if we take a simple bar magnet just + + + align:start position:0% +what if we take a simple bar magnet just +a simple North and South Pole and a + + align:start position:0% +a simple North and South Pole and a + + + align:start position:0% +a simple North and South Pole and a +simple conducting coil that's connected + + align:start position:0% +simple conducting coil that's connected + + + align:start position:0% +simple conducting coil that's connected +to an ammeter we could measure if any + + align:start position:0% +to an ammeter we could measure if any + + + align:start position:0% +to an ammeter we could measure if any +electric current is flowing through that + + align:start position:0% +electric current is flowing through that + + + align:start position:0% +electric current is flowing through that +conducting coil + + align:start position:0% +conducting coil + + + align:start position:0% +conducting coil +what if the bar magnet and the coil are + + align:start position:0% +what if the bar magnet and the coil are + + + align:start position:0% +what if the bar magnet and the coil are +in some relative motion with respect to + + align:start position:0% +in some relative motion with respect to + + + align:start position:0% +in some relative motion with respect to +each other + + align:start position:0% +each other + + + align:start position:0% +each other +then it's a rather simple demonstration + + align:start position:0% +then it's a rather simple demonstration + + + align:start position:0% +then it's a rather simple demonstration +to find it's actually quite similar to + + align:start position:0% +to find it's actually quite similar to + + + align:start position:0% +to find it's actually quite similar to +what you know uh ursid had done in the + + align:start position:0% +what you know uh ursid had done in the + + + align:start position:0% +what you know uh ursid had done in the +1820s and then Faraday soon after that + + align:start position:0% +1820s and then Faraday soon after that + + + align:start position:0% +1820s and then Faraday soon after that +when the magnet and the coil are in + + align:start position:0% +when the magnet and the coil are in + + + align:start position:0% +when the magnet and the coil are in +relative motion a measurable electric + + align:start position:0% +relative motion a measurable electric + + + align:start position:0% +relative motion a measurable electric +current will be induced so the + + align:start position:0% +current will be induced so the + + + align:start position:0% +current will be induced so the +phenomenon is these two things moving + + align:start position:0% +phenomenon is these two things moving + + + align:start position:0% +phenomenon is these two things moving +with respect to each other current + + align:start position:0% +with respect to each other current + + + align:start position:0% +with respect to each other current +begins to flow where otherwise none had + + align:start position:0% +begins to flow where otherwise none had + + + align:start position:0% +begins to flow where otherwise none had +flowed before + + align:start position:0% +flowed before + + + align:start position:0% +flowed before +so physicists Einstein insists had given + + align:start position:0% +so physicists Einstein insists had given + + + align:start position:0% +so physicists Einstein insists had given +two completely different explanations + + align:start position:0% +two completely different explanations + + + align:start position:0% +two completely different explanations +for what he argued was only one single + + align:start position:0% +for what he argued was only one single + + + align:start position:0% +for what he argued was only one single +physical effect the physicist + + align:start position:0% +physical effect the physicist + + + align:start position:0% +physical effect the physicist +explanations to date had depended in + + align:start position:0% +explanations to date had depended in + + + align:start position:0% +explanations to date had depended in +Thailand which item was really moving so + + align:start position:0% +Thailand which item was really moving so + + + align:start position:0% +Thailand which item was really moving so +if you imagine there's a state of + + align:start position:0% +if you imagine there's a state of + + + align:start position:0% +if you imagine there's a state of +absolute rest then perhaps the bar + + align:start position:0% +absolute rest then perhaps the bar + + + align:start position:0% +absolute rest then perhaps the bar +magnet is really moving and the ammeter + + align:start position:0% +magnet is really moving and the ammeter + + + align:start position:0% +magnet is really moving and the ammeter +and the coil are really at rest and then + + align:start position:0% +and the coil are really at rest and then + + + align:start position:0% +and the coil are really at rest and then +you could analyze the system one way or + + align:start position:0% +you could analyze the system one way or + + + align:start position:0% +you could analyze the system one way or +the inverse this is the asymmetry in the + + align:start position:0% +the inverse this is the asymmetry in the + + + align:start position:0% +the inverse this is the asymmetry in the +explanation that Einstein says is not + + align:start position:0% +explanation that Einstein says is not + + + align:start position:0% +explanation that Einstein says is not +present in the phenomena let's take the + + align:start position:0% +present in the phenomena let's take the + + + align:start position:0% +present in the phenomena let's take the +first case let's imagine that the magnet + + align:start position:0% +first case let's imagine that the magnet + + + align:start position:0% +first case let's imagine that the magnet +is what's moving the bar mag is moving + + align:start position:0% +is what's moving the bar mag is moving + + + align:start position:0% +is what's moving the bar mag is moving +back and forth this is a faraday + + align:start position:0% +back and forth this is a faraday + + + align:start position:0% +back and forth this is a faraday +induction case from 18 20 21. we keep + + align:start position:0% +induction case from 18 20 21. we keep + + + align:start position:0% +induction case from 18 20 21. we keep +the electric coil perfectly at rest then + + align:start position:0% +the electric coil perfectly at rest then + + + align:start position:0% +the electric coil perfectly at rest then +using Maxwell's equations which we can + + align:start position:0% +using Maxwell's equations which we can + + + align:start position:0% +using Maxwell's equations which we can +read off from our t-shirt + + align:start position:0% +read off from our t-shirt + + + align:start position:0% +read off from our t-shirt +of which Einstein will do by this point + + align:start position:0% +of which Einstein will do by this point + + + align:start position:0% +of which Einstein will do by this point +there's going to be a changing magnetic + + align:start position:0% +there's going to be a changing magnetic + + + align:start position:0% +there's going to be a changing magnetic +field in this region of space where it + + align:start position:0% +field in this region of space where it + + + align:start position:0% +field in this region of space where it +was shaking removing that magnet back + + align:start position:0% +was shaking removing that magnet back + + + align:start position:0% +was shaking removing that magnet back +and forth so at any given location + + align:start position:0% +and forth so at any given location + + + align:start position:0% +and forth so at any given location +nearby the strength of the magnetic + + align:start position:0% +nearby the strength of the magnetic + + + align:start position:0% +nearby the strength of the magnetic +field and even the direction is a change + + align:start position:0% +field and even the direction is a change + + + align:start position:0% +field and even the direction is a change +in quantity over time so the variation + + align:start position:0% +in quantity over time so the variation + + + align:start position:0% +in quantity over time so the variation +in time is non-zero because we're + + align:start position:0% +in time is non-zero because we're + + + align:start position:0% +in time is non-zero because we're +actively moving them back + + align:start position:0% +actively moving them back + + + align:start position:0% +actively moving them back +from Maxwell's equations that will + + align:start position:0% +from Maxwell's equations that will + + + align:start position:0% +from Maxwell's equations that will +induce the set necessarily some electric + + align:start position:0% +induce the set necessarily some electric + + + align:start position:0% +induce the set necessarily some electric +field in that same region of space + + align:start position:0% +field in that same region of space + + + align:start position:0% +field in that same region of space +then we know that there's an electric + + align:start position:0% +then we know that there's an electric + + + align:start position:0% +then we know that there's an electric +field present in say around this area + + align:start position:0% +field present in say around this area + + + align:start position:0% +field present in say around this area +the electric field will exert a force on + + align:start position:0% +the electric field will exert a force on + + + align:start position:0% +the electric field will exert a force on +any little charged object that's within + + align:start position:0% +any little charged object that's within + + + align:start position:0% +any little charged object that's within +for example this conducting coil it will + + align:start position:0% +for example this conducting coil it will + + + align:start position:0% +for example this conducting coil it will +push the charges along the coil it will + + align:start position:0% +push the charges along the coil it will + + + align:start position:0% +push the charges along the coil it will +generate a current electric current was + + align:start position:0% +generate a current electric current was + + + align:start position:0% +generate a current electric current was +nothing but the motion of electric + + align:start position:0% +nothing but the motion of electric + + + align:start position:0% +nothing but the motion of electric +charges + + align:start position:0% +charges + + + align:start position:0% +charges +so the argument here would have been + + align:start position:0% +so the argument here would have been + + + align:start position:0% +so the argument here would have been +we're moving the magnet that makes a + + align:start position:0% +we're moving the magnet that makes a + + + align:start position:0% +we're moving the magnet that makes a +Time varying magnetic field from + + align:start position:0% +Time varying magnetic field from + + + align:start position:0% +Time varying magnetic field from +Maxwell's equations from this particular + + align:start position:0% +Maxwell's equations from this particular + + + align:start position:0% +Maxwell's equations from this particular +one of Max's equations a third one that + + align:start position:0% +one of Max's equations a third one that + + + align:start position:0% +one of Max's equations a third one that +induces an electric field that exerts a + + align:start position:0% +induces an electric field that exerts a + + + align:start position:0% +induces an electric field that exerts a +force that pushes charges along we + + align:start position:0% +force that pushes charges along we + + + align:start position:0% +force that pushes charges along we +measure current that's that's case one + + align:start position:0% +measure current that's that's case one + + + align:start position:0% +measure current that's that's case one +all right so it goes on to say what + + align:start position:0% +all right so it goes on to say what + + + align:start position:0% +all right so it goes on to say what +about the inverse this is one that + + align:start position:0% +about the inverse this is one that + + + align:start position:0% +about the inverse this is one that +actually um ersted it first found + + align:start position:0% +actually um ersted it first found + + + align:start position:0% +actually um ersted it first found +by accident what if the coil is moving + + align:start position:0% +by accident what if the coil is moving + + + align:start position:0% +by accident what if the coil is moving +but the magnets at rest well then we'd + + align:start position:0% +but the magnets at rest well then we'd + + + align:start position:0% +but the magnets at rest well then we'd +say there's a static magnetic field that + + align:start position:0% +say there's a static magnetic field that + + + align:start position:0% +say there's a static magnetic field that +nonetheless varies through space + + align:start position:0% +nonetheless varies through space + + + align:start position:0% +nonetheless varies through space +remember those kind of curving field + + align:start position:0% +remember those kind of curving field + + + align:start position:0% +remember those kind of curving field +lines the Faraday field lines around a + + align:start position:0% +lines the Faraday field lines around a + + + align:start position:0% +lines the Faraday field lines around a +bar magnet so there's some in + + align:start position:0% +bar magnet so there's some in + + + align:start position:0% +bar magnet so there's some in +homogeneity in space even though it's + + align:start position:0% +homogeneity in space even though it's + + + align:start position:0% +homogeneity in space even though it's +static it's stuck in time so this + + align:start position:0% +static it's stuck in time so this + + + align:start position:0% +static it's stuck in time so this +spatial curl is non-zero by Maxwell's + + align:start position:0% +spatial curl is non-zero by Maxwell's + + + align:start position:0% +spatial curl is non-zero by Maxwell's +fourth equation that will induce some + + align:start position:0% +fourth equation that will induce some + + + align:start position:0% +fourth equation that will induce some +electric current nearby and then uh you + + align:start position:0% +electric current nearby and then uh you + + + align:start position:0% +electric current nearby and then uh you +have this static electric field with + + align:start position:0% +have this static electric field with + + + align:start position:0% +have this static electric field with +charges moving around it so they have + + align:start position:0% +charges moving around it so they have + + + align:start position:0% +charges moving around it so they have +some velocity + + align:start position:0% +some velocity + + + align:start position:0% +some velocity +and the cross product of their velocity + + align:start position:0% +and the cross product of their velocity + + + align:start position:0% +and the cross product of their velocity +times the magnetic field will induce a + + align:start position:0% +times the magnetic field will induce a + + + align:start position:0% +times the magnetic field will induce a +force that will push the charges along + + align:start position:0% +force that will push the charges along + + + align:start position:0% +force that will push the charges along +we'll induce the current so Eisen argues + + align:start position:0% +we'll induce the current so Eisen argues + + + align:start position:0% +we'll induce the current so Eisen argues +that there's actually only one + + align:start position:0% +that there's actually only one + + + align:start position:0% +that there's actually only one +phenomenon when the magnet and coil are + + align:start position:0% +phenomenon when the magnet and coil are + + + align:start position:0% +phenomenon when the magnet and coil are +in relative motion you should measure a + + align:start position:0% +in relative motion you should measure a + + + align:start position:0% +in relative motion you should measure a +current and it can't matter he argues it + + align:start position:0% +current and it can't matter he argues it + + + align:start position:0% +current and it can't matter he argues it +shouldn't matter which one you say is + + align:start position:0% +shouldn't matter which one you say is + + + align:start position:0% +shouldn't matter which one you say is +really at rest or not he's he's + + align:start position:0% +really at rest or not he's he's + + + align:start position:0% +really at rest or not he's he's +borrowing that although not citing it + + align:start position:0% +borrowing that although not citing it + + + align:start position:0% +borrowing that although not citing it +he's barring that from Erin's mocks + + align:start position:0% +he's barring that from Erin's mocks + + + align:start position:0% +he's barring that from Erin's mocks +critique of Newton so you have one + + align:start position:0% +critique of Newton so you have one + + + align:start position:0% +critique of Newton so you have one +phenomenon that have been given two + + align:start position:0% +phenomenon that have been given two + + + align:start position:0% +phenomenon that have been given two +completely separate explanations and he + + align:start position:0% +completely separate explanations and he + + + align:start position:0% +completely separate explanations and he +says that's the asymmetry in the + + align:start position:0% +says that's the asymmetry in the + + + align:start position:0% +says that's the asymmetry in the +explanation there should only be one + + align:start position:0% +explanation there should only be one + + + align:start position:0% +explanation there should only be one +explanation there's some relative motion + + align:start position:0% +explanation there's some relative motion + + + align:start position:0% +explanation there's some relative motion +current is induced + + align:start position:0% + + + + align:start position:0% + +so that's the opening paragraph of this + + align:start position:0% +so that's the opening paragraph of this + + + align:start position:0% +so that's the opening paragraph of this +somewhat strange looking article a + + align:start position:0% +somewhat strange looking article a + + + align:start position:0% +somewhat strange looking article a +little while later just still on that + + align:start position:0% +little while later just still on that + + + align:start position:0% +little while later just still on that +first opening two pages + + align:start position:0% +first opening two pages + + + align:start position:0% +first opening two pages +he then introduces two postulates two + + align:start position:0% +he then introduces two postulates two + + + align:start position:0% +he then introduces two postulates two +axioms or conjectures he doesn't defend + + align:start position:0% +axioms or conjectures he doesn't defend + + + align:start position:0% +axioms or conjectures he doesn't defend +them he doesn't derive them he doesn't + + align:start position:0% +them he doesn't derive them he doesn't + + + align:start position:0% +them he doesn't derive them he doesn't +say I've tested them in the laboratory + + align:start position:0% +say I've tested them in the laboratory + + + align:start position:0% +say I've tested them in the laboratory +they hold up to within experimental + + align:start position:0% +they hold up to within experimental + + + align:start position:0% +they hold up to within experimental +error he says as you can see the + + align:start position:0% +error he says as you can see the + + + align:start position:0% +error he says as you can see the +quotation here on on the screen we're + + align:start position:0% +quotation here on on the screen we're + + + align:start position:0% +quotation here on on the screen we're +going to raise this conjecture to a + + align:start position:0% +going to raise this conjecture to a + + + align:start position:0% +going to raise this conjecture to a +postulate and basically see what follows + + align:start position:0% +postulate and basically see what follows + + + align:start position:0% +postulate and basically see what follows +from it the first one is that the laws + + align:start position:0% +from it the first one is that the laws + + + align:start position:0% +from it the first one is that the laws +of physics all the laws of physics must + + align:start position:0% +of physics all the laws of physics must + + + align:start position:0% +of physics all the laws of physics must +remain valid in any frame any a state of + + align:start position:0% +remain valid in any frame any a state of + + + align:start position:0% +remain valid in any frame any a state of +of observation that's moving at a + + align:start position:0% +of observation that's moving at a + + + align:start position:0% +of observation that's moving at a +constant speed these are would later be + + align:start position:0% +constant speed these are would later be + + + align:start position:0% +constant speed these are would later be +called inertial frames of reference + + align:start position:0% +called inertial frames of reference + + + align:start position:0% +called inertial frames of reference +meaning not accelerating it doesn't have + + align:start position:0% +meaning not accelerating it doesn't have + + + align:start position:0% +meaning not accelerating it doesn't have +to be at rest it can be moving at some + + align:start position:0% +to be at rest it can be moving at some + + + align:start position:0% +to be at rest it can be moving at some +constant speed as long as it doesn't + + align:start position:0% +constant speed as long as it doesn't + + + align:start position:0% +constant speed as long as it doesn't +speed up or slow down so no acceleration + + align:start position:0% +speed up or slow down so no acceleration + + + align:start position:0% +speed up or slow down so no acceleration +now that's just elevating + + align:start position:0% +now that's just elevating + + + align:start position:0% +now that's just elevating +um the the well-known relativity from + + align:start position:0% +um the the well-known relativity from + + + align:start position:0% +um the the well-known relativity from +Galileo going back to the early 1600s + + align:start position:0% +Galileo going back to the early 1600s + + + align:start position:0% +Galileo going back to the early 1600s +what have been called Galilean + + align:start position:0% +what have been called Galilean + + + align:start position:0% +what have been called Galilean +relativity applied to the laws of + + align:start position:0% +relativity applied to the laws of + + + align:start position:0% +relativity applied to the laws of +mechanics Galileo himself had argued and + + align:start position:0% +mechanics Galileo himself had argued and + + + align:start position:0% +mechanics Galileo himself had argued and +Newton agreed that the laws of mechanics + + align:start position:0% +Newton agreed that the laws of mechanics + + + align:start position:0% +Newton agreed that the laws of mechanics +should remain valid in any inertial + + align:start position:0% +should remain valid in any inertial + + + align:start position:0% +should remain valid in any inertial +frame of reference and all Einstein is + + align:start position:0% +frame of reference and all Einstein is + + + align:start position:0% +frame of reference and all Einstein is +doing here is he says he's raising it to + + align:start position:0% +doing here is he says he's raising it to + + + align:start position:0% +doing here is he says he's raising it to +a posture and extend it + + align:start position:0% +a posture and extend it + + + align:start position:0% +a posture and extend it +um to uh to all the laws of physics not + + align:start position:0% +um to uh to all the laws of physics not + + + align:start position:0% +um to uh to all the laws of physics not +just mechanics you see in this first + + align:start position:0% +just mechanics you see in this first + + + align:start position:0% +just mechanics you see in this first +part but electromagnetism objects even + + align:start position:0% +part but electromagnetism objects even + + + align:start position:0% +part but electromagnetism objects even +thermodynamics this is an extension of + + align:start position:0% +thermodynamics this is an extension of + + + align:start position:0% +thermodynamics this is an extension of +the Galilean relativity + + align:start position:0% +the Galilean relativity + + + align:start position:0% +the Galilean relativity +the second posture he says is only + + align:start position:0% +the second posture he says is only + + + align:start position:0% +the second posture he says is only +apparently irreconcilable with the first + + align:start position:0% +apparently irreconcilable with the first + + + align:start position:0% +apparently irreconcilable with the first +is that the speed of light will be + + align:start position:0% +is that the speed of light will be + + + align:start position:0% +is that the speed of light will be +constant independent of the motion of + + align:start position:0% +constant independent of the motion of + + + align:start position:0% +constant independent of the motion of +the source so any Observer no matter + + align:start position:0% +the source so any Observer no matter + + + align:start position:0% +the source so any Observer no matter +what their state of motion as long as + + align:start position:0% +what their state of motion as long as + + + align:start position:0% +what their state of motion as long as +they're in some inertial frame of + + align:start position:0% +they're in some inertial frame of + + + align:start position:0% +they're in some inertial frame of +reference we'll always measure light to + + align:start position:0% +reference we'll always measure light to + + + align:start position:0% +reference we'll always measure light to +be moving at the same speed C even if + + align:start position:0% +be moving at the same speed C even if + + + align:start position:0% +be moving at the same speed C even if +they're barreling down the road in the + + align:start position:0% +they're barreling down the road in the + + + align:start position:0% +they're barreling down the road in the +same direction as that light wave + + align:start position:0% +same direction as that light wave + + + align:start position:0% +same direction as that light wave +they'll measure that light wave moving + + align:start position:0% +they'll measure that light wave moving + + + align:start position:0% +they'll measure that light wave moving +away from them at that same speed c as + + align:start position:0% +away from them at that same speed c as + + + align:start position:0% +away from them at that same speed c as +if they were sitting at + + align:start position:0% +if they were sitting at + + + align:start position:0% +if they were sitting at +uh and he says only apparently + + align:start position:0% +uh and he says only apparently + + + align:start position:0% +uh and he says only apparently +irreconcilable with the first we'll see + + align:start position:0% +irreconcilable with the first we'll see + + + align:start position:0% +irreconcilable with the first we'll see +that in a moment he says if we adopt + + align:start position:0% +that in a moment he says if we adopt + + + align:start position:0% +that in a moment he says if we adopt +these two postulates again he hasn't + + align:start position:0% +these two postulates again he hasn't + + + align:start position:0% +these two postulates again he hasn't +proven them he hasn't really told us + + align:start position:0% +proven them he hasn't really told us + + + align:start position:0% +proven them he hasn't really told us +necessarily yet why we should buy any of + + align:start position:0% +necessarily yet why we should buy any of + + + align:start position:0% +necessarily yet why we should buy any of +this but if we adopt those two postures + + align:start position:0% +this but if we adopt those two postures + + + align:start position:0% +this but if we adopt those two postures +to start our argument then he says as + + align:start position:0% +to start our argument then he says as + + + align:start position:0% +to start our argument then he says as +you see later in that paragraph + + align:start position:0% +you see later in that paragraph + + + align:start position:0% +you see later in that paragraph +The luminiferous Ether will prove to be + + align:start position:0% +The luminiferous Ether will prove to be + + + align:start position:0% +The luminiferous Ether will prove to be +Superfluous it's amazing who refusation + + align:start position:0% +Superfluous it's amazing who refusation + + + align:start position:0% +Superfluous it's amazing who refusation +is the word in German he doesn't say + + align:start position:0% +is the word in German he doesn't say + + + align:start position:0% +is the word in German he doesn't say +he'll disprove The Ether he'll say it's + + align:start position:0% +he'll disprove The Ether he'll say it's + + + align:start position:0% +he'll disprove The Ether he'll say it's +just Irrelevant in one sentence on page + + align:start position:0% +just Irrelevant in one sentence on page + + + align:start position:0% +just Irrelevant in one sentence on page +two of an article by an unknown patent + + align:start position:0% +two of an article by an unknown patent + + + align:start position:0% +two of an article by an unknown patent +clerk he's basically not just said that + + align:start position:0% +clerk he's basically not just said that + + + align:start position:0% +clerk he's basically not just said that +people have misunderstood Maxwell's + + align:start position:0% +people have misunderstood Maxwell's + + + align:start position:0% +people have misunderstood Maxwell's +equations people for 100 years have been + + align:start position:0% +equations people for 100 years have been + + + align:start position:0% +equations people for 100 years have been +chasing an object that he says is merely + + align:start position:0% +chasing an object that he says is merely + + + align:start position:0% +chasing an object that he says is merely +irrelevant it is literally a red hair he + + align:start position:0% +irrelevant it is literally a red hair he + + + align:start position:0% +irrelevant it is literally a red hair he +argues it has been merely superfluous + + align:start position:0% +argues it has been merely superfluous + + + align:start position:0% +argues it has been merely superfluous +that is quite a strong opening to this + + align:start position:0% +that is quite a strong opening to this + + + align:start position:0% +that is quite a strong opening to this +paper + + align:start position:0% +paper + + + align:start position:0% +paper +now why did Einstein issues that second + + align:start position:0% +now why did Einstein issues that second + + + align:start position:0% +now why did Einstein issues that second +posture the one about the the constancy + + align:start position:0% +posture the one about the the constancy + + + align:start position:0% +posture the one about the the constancy +of the speed of light for any inertial + + align:start position:0% +of the speed of light for any inertial + + + align:start position:0% +of the speed of light for any inertial +Observer again he doesn't tell us why uh + + align:start position:0% +Observer again he doesn't tell us why uh + + + align:start position:0% +Observer again he doesn't tell us why uh +in this paper itself in the intervening + + align:start position:0% +in this paper itself in the intervening + + + align:start position:0% +in this paper itself in the intervening +uh more than 100 years uh other Scholars + + align:start position:0% +uh more than 100 years uh other Scholars + + + align:start position:0% +uh more than 100 years uh other Scholars +have been able to to fill in some of + + align:start position:0% +have been able to to fill in some of + + + align:start position:0% +have been able to to fill in some of +those pieces based on + + align:start position:0% +those pieces based on + + + align:start position:0% +those pieces based on +what at the time in unpublished uh notes + + align:start position:0% +what at the time in unpublished uh notes + + + align:start position:0% +what at the time in unpublished uh notes +and correspondence and reminiscences and + + align:start position:0% +and correspondence and reminiscences and + + + align:start position:0% +and correspondence and reminiscences and +so on so we now have a pretty good + + align:start position:0% +so on so we now have a pretty good + + + align:start position:0% +so on so we now have a pretty good +understanding of what Lena assigned to + + align:start position:0% +understanding of what Lena assigned to + + + align:start position:0% +understanding of what Lena assigned to +that strange sounding second posture and + + align:start position:0% +that strange sounding second posture and + + + align:start position:0% +that strange sounding second posture and +in fact it goes back to a thought + + align:start position:0% +in fact it goes back to a thought + + + align:start position:0% +in fact it goes back to a thought +experiment he'd had as a high school + + align:start position:0% +experiment he'd had as a high school + + + align:start position:0% +experiment he'd had as a high school +dropout at age 16. hey one of the things + + align:start position:0% +dropout at age 16. hey one of the things + + + align:start position:0% +dropout at age 16. hey one of the things +that literally kept him up at night was + + align:start position:0% +that literally kept him up at night was + + + align:start position:0% +that literally kept him up at night was +what would happen if you could catch up + + align:start position:0% +what would happen if you could catch up + + + align:start position:0% +what would happen if you could catch up +to a light wave so imagine being like a + + align:start position:0% +to a light wave so imagine being like a + + + align:start position:0% +to a light wave so imagine being like a +surfer here riding along a wave on the + + align:start position:0% +surfer here riding along a wave on the + + + align:start position:0% +surfer here riding along a wave on the +ocean if you're moving with that wave if + + align:start position:0% +ocean if you're moving with that wave if + + + align:start position:0% +ocean if you're moving with that wave if +you're surfing with at the same speed as + + align:start position:0% +you're surfing with at the same speed as + + + align:start position:0% +you're surfing with at the same speed as +that wave and you look up you chance to + + align:start position:0% +that wave and you look up you chance to + + + align:start position:0% +that wave and you look up you chance to +look up and see this wave Crest you know + + align:start position:0% +look up and see this wave Crest you know + + + align:start position:0% +look up and see this wave Crest you know +menacingly over your head at that moment + + align:start position:0% +menacingly over your head at that moment + + + align:start position:0% +menacingly over your head at that moment +the wave will appear Frozen in space + + align:start position:0% +the wave will appear Frozen in space + + + align:start position:0% +the wave will appear Frozen in space +you're moving at the same speed as the + + align:start position:0% +you're moving at the same speed as the + + + align:start position:0% +you're moving at the same speed as the +ocean wave so you and the wave move + + align:start position:0% +ocean wave so you and the wave move + + + align:start position:0% +ocean wave so you and the wave move +together toward the shore and it looks + + align:start position:0% +together toward the shore and it looks + + + align:start position:0% +together toward the shore and it looks +like you're you have a static wave + + align:start position:0% +like you're you have a static wave + + + align:start position:0% +like you're you have a static wave +configuration the wave has a Crest here + + align:start position:0% +configuration the wave has a Crest here + + + align:start position:0% +configuration the wave has a Crest here +a trough there and they're moving not + + align:start position:0% +a trough there and they're moving not + + + align:start position:0% +a trough there and they're moving not +they're not changing As you move + + align:start position:0% +they're not changing As you move + + + align:start position:0% +they're not changing As you move +together toward the shore + + align:start position:0% +together toward the shore + + + align:start position:0% +together toward the shore +now Einstein argued that should never be + + align:start position:0% +now Einstein argued that should never be + + + align:start position:0% +now Einstein argued that should never be +able to happen for a light wave he first + + align:start position:0% +able to happen for a light wave he first + + + align:start position:0% +able to happen for a light wave he first +just kind of intuited later he learned + + align:start position:0% +just kind of intuited later he learned + + + align:start position:0% +just kind of intuited later he learned +more at University when he studied some + + align:start position:0% +more at University when he studied some + + + align:start position:0% +more at University when he studied some +a little bit of Maxwell's equations he + + align:start position:0% +a little bit of Maxwell's equations he + + + align:start position:0% +a little bit of Maxwell's equations he +could fill this in in a bit more + + align:start position:0% +could fill this in in a bit more + + + align:start position:0% +could fill this in in a bit more +quantitative detail that with the power + + align:start position:0% +quantitative detail that with the power + + + align:start position:0% +quantitative detail that with the power +of Maxwell's equations if you're in a + + align:start position:0% +of Maxwell's equations if you're in a + + + align:start position:0% +of Maxwell's equations if you're in a +region of space away from charged matter + + align:start position:0% +region of space away from charged matter + + + align:start position:0% +region of space away from charged matter +with no electric currents flowing so if + + align:start position:0% +with no electric currents flowing so if + + + align:start position:0% +with no electric currents flowing so if +rho and J both vanish row and J + + align:start position:0% +rho and J both vanish row and J + + + align:start position:0% +rho and J both vanish row and J +then there's no way to use these + + align:start position:0% +then there's no way to use these + + + align:start position:0% +then there's no way to use these +equations + + align:start position:0% +equations + + + align:start position:0% +equations +Maxwell's equations to construct a + + align:start position:0% +Maxwell's equations to construct a + + + align:start position:0% +Maxwell's equations to construct a +static field configuration we have a + + align:start position:0% +static field configuration we have a + + + align:start position:0% +static field configuration we have a +fixed Frozen you know Crest here and + + align:start position:0% +fixed Frozen you know Crest here and + + + align:start position:0% +fixed Frozen you know Crest here and +trough there the electric and magnetic + + align:start position:0% +trough there the electric and magnetic + + + align:start position:0% +trough there the electric and magnetic +fields just don't behave that way if + + align:start position:0% +fields just don't behave that way if + + + align:start position:0% +fields just don't behave that way if +you're in a region that has no immediate + + align:start position:0% +you're in a region that has no immediate + + + align:start position:0% +you're in a region that has no immediate +sources so then if you could never see + + align:start position:0% +sources so then if you could never see + + + align:start position:0% +sources so then if you could never see +this Frozen static field configuration + + align:start position:0% +this Frozen static field configuration + + + align:start position:0% +this Frozen static field configuration +with a Crest that just stays stays um + + align:start position:0% +with a Crest that just stays stays um + + + align:start position:0% +with a Crest that just stays stays um +fixed like that + + align:start position:0% +fixed like that + + + align:start position:0% +fixed like that +then you'd better make sure no one could + + align:start position:0% +then you'd better make sure no one could + + + align:start position:0% +then you'd better make sure no one could +ever see that you better make sure no + + align:start position:0% +ever see that you better make sure no + + + align:start position:0% +ever see that you better make sure no +one could ever do like the surfer does + + align:start position:0% +one could ever do like the surfer does + + + align:start position:0% +one could ever do like the surfer does +and ride at the same speed as that light + + align:start position:0% +and ride at the same speed as that light + + + align:start position:0% +and ride at the same speed as that light +wave so he's really trying to avoid a + + align:start position:0% +wave so he's really trying to avoid a + + + align:start position:0% +wave so he's really trying to avoid a +reductio out of certain he's trying to + + align:start position:0% +reductio out of certain he's trying to + + + align:start position:0% +reductio out of certain he's trying to +avoid a contradiction + + align:start position:0% +avoid a contradiction + + + align:start position:0% +avoid a contradiction +how do you make sure no one ever would + + align:start position:0% +how do you make sure no one ever would + + + align:start position:0% +how do you make sure no one ever would +encounter this frozen field + + align:start position:0% +encounter this frozen field + + + align:start position:0% +encounter this frozen field +configuration which he argues is not at + + align:start position:0% +configuration which he argues is not at + + + align:start position:0% +configuration which he argues is not at +all consistent with the linear form of + + align:start position:0% +all consistent with the linear form of + + + align:start position:0% +all consistent with the linear form of +Max's equations make sure no one could + + align:start position:0% +Max's equations make sure no one could + + + align:start position:0% +Max's equations make sure no one could +ever catch up with a light wave if we + + align:start position:0% +ever catch up with a light wave if we + + + align:start position:0% +ever catch up with a light wave if we +could never surf at the same speed as a + + align:start position:0% +could never surf at the same speed as a + + + align:start position:0% +could never surf at the same speed as a +light wave we would never see this + + align:start position:0% +light wave we would never see this + + + align:start position:0% +light wave we would never see this +frozen field configuration with a height + + align:start position:0% +frozen field configuration with a height + + + align:start position:0% +frozen field configuration with a height +here and a trough there but otherwise + + align:start position:0% +here and a trough there but otherwise + + + align:start position:0% +here and a trough there but otherwise +static in time + + align:start position:0% +static in time + + + align:start position:0% +static in time +if we could never catch up the light + + align:start position:0% +if we could never catch up the light + + + align:start position:0% +if we could never catch up the light +wave we'll always see it traveling past + + align:start position:0% +wave we'll always see it traveling past + + + align:start position:0% +wave we'll always see it traveling past +us at the speed of light that was at + + align:start position:0% +us at the speed of light that was at + + + align:start position:0% +us at the speed of light that was at +least the intuition that he nursed over + + align:start position:0% +least the intuition that he nursed over + + + align:start position:0% +least the intuition that he nursed over +the course of 10 years between the age + + align:start position:0% +the course of 10 years between the age + + + align:start position:0% +the course of 10 years between the age +of 16 and 26. + + align:start position:0% + + + + align:start position:0% + +thank you Lucas by the way Julie that's + + align:start position:0% +thank you Lucas by the way Julie that's + + + align:start position:0% +thank you Lucas by the way Julie that's +a great question so I didn't want to + + align:start position:0% +a great question so I didn't want to + + + align:start position:0% +a great question so I didn't want to +spoil this because your first assignment + + align:start position:0% +spoil this because your first assignment + + + align:start position:0% +spoil this because your first assignment +as I'm sure you've seen is to imagine + + align:start position:0% +as I'm sure you've seen is to imagine + + + align:start position:0% +as I'm sure you've seen is to imagine +you're a referee for the journal + + align:start position:0% +you're a referee for the journal + + + align:start position:0% +you're a referee for the journal +reporting to the main editor box block + + align:start position:0% +reporting to the main editor box block + + + align:start position:0% +reporting to the main editor box block +that is still your assignment you still + + align:start position:0% +that is still your assignment you still + + + align:start position:0% +that is still your assignment you still +have to do that however the real answer + + align:start position:0% +have to do that however the real answer + + + align:start position:0% +have to do that however the real answer +as to why this paper uh was most likely + + align:start position:0% +as to why this paper uh was most likely + + + align:start position:0% +as to why this paper uh was most likely +published it was almost certainly never + + align:start position:0% +published it was almost certainly never + + + align:start position:0% +published it was almost certainly never +sent out for refereeing our modern idea + + align:start position:0% +sent out for refereeing our modern idea + + + align:start position:0% +sent out for refereeing our modern idea +that every single scientific paper + + align:start position:0% +that every single scientific paper + + + align:start position:0% +that every single scientific paper +should be subjected to peer review is + + align:start position:0% +should be subjected to peer review is + + + align:start position:0% +should be subjected to peer review is +quite recent in fact it only gets put in + + align:start position:0% +quite recent in fact it only gets put in + + + align:start position:0% +quite recent in fact it only gets put in +place with real uh regularity or + + align:start position:0% +place with real uh regularity or + + + align:start position:0% +place with real uh regularity or +standardization uh in the second half of + + align:start position:0% +standardization uh in the second half of + + + align:start position:0% +standardization uh in the second half of +the 20th century well after this time + + align:start position:0% +the 20th century well after this time + + + align:start position:0% +the 20th century well after this time +what was happening at many journals + + align:start position:0% +what was happening at many journals + + + align:start position:0% +what was happening at many journals +including the other than the physique + + align:start position:0% +including the other than the physique + + + align:start position:0% +including the other than the physique +including physical review here in the + + align:start position:0% +including physical review here in the + + + align:start position:0% +including physical review here in the +United States and many other leading + + align:start position:0% +United States and many other leading + + + align:start position:0% +United States and many other leading +journals at the time was that the first + + align:start position:0% +journals at the time was that the first + + + align:start position:0% +journals at the time was that the first +one or two submissions to a journal from + + align:start position:0% +one or two submissions to a journal from + + + align:start position:0% +one or two submissions to a journal from +an uh from a from an early author a new + + align:start position:0% +an uh from a from an early author a new + + + align:start position:0% +an uh from a from an early author a new +author those would often be very + + align:start position:0% +author those would often be very + + + align:start position:0% +author those would often be very +carefully scrutinized and reviewed they + + align:start position:0% +carefully scrutinized and reviewed they + + + align:start position:0% +carefully scrutinized and reviewed they +would be subject to purely peer-reviewed + + align:start position:0% +would be subject to purely peer-reviewed + + + align:start position:0% +would be subject to purely peer-reviewed +existed it just wasn't applied uniformly + + align:start position:0% +existed it just wasn't applied uniformly + + + align:start position:0% +existed it just wasn't applied uniformly +Einstein it turns out had published half + + align:start position:0% +Einstein it turns out had published half + + + align:start position:0% +Einstein it turns out had published half +a dozen or more articles in this journal + + align:start position:0% +a dozen or more articles in this journal + + + align:start position:0% +a dozen or more articles in this journal +before this time on frankly kind of + + align:start position:0% +before this time on frankly kind of + + + align:start position:0% +before this time on frankly kind of +minor topics minor even by by Einstein's + + align:start position:0% +minor topics minor even by by Einstein's + + + align:start position:0% +minor topics minor even by by Einstein's +own Reckoning he had published fairly + + align:start position:0% +own Reckoning he had published fairly + + + align:start position:0% +own Reckoning he had published fairly +conventional perfectly legitimate + + align:start position:0% +conventional perfectly legitimate + + + align:start position:0% +conventional perfectly legitimate +scientific articles in this journal so a + + align:start position:0% +scientific articles in this journal so a + + + align:start position:0% +scientific articles in this journal so a +few years Downstream from that like most + + align:start position:0% +few years Downstream from that like most + + + align:start position:0% +few years Downstream from that like most +other authors at the time his later + + align:start position:0% +other authors at the time his later + + + align:start position:0% +other authors at the time his later +Communications uh could be published + + align:start position:0% +Communications uh could be published + + + align:start position:0% +Communications uh could be published +kind of at the discretion of the editor + + align:start position:0% +kind of at the discretion of the editor + + + align:start position:0% +kind of at the discretion of the editor +without going through this rigorous + + align:start position:0% +without going through this rigorous + + + align:start position:0% +without going through this rigorous +refereeing process and by all likelihood + + align:start position:0% +refereeing process and by all likelihood + + + align:start position:0% +refereeing process and by all likelihood +uh Mark's block thought this was + + align:start position:0% +uh Mark's block thought this was + + + align:start position:0% +uh Mark's block thought this was +interesting enough it was on a timely + + align:start position:0% +interesting enough it was on a timely + + + align:start position:0% +interesting enough it was on a timely +topic because people were clearly + + align:start position:0% +topic because people were clearly + + + align:start position:0% +topic because people were clearly +concerned about the electronomics and + + align:start position:0% +concerned about the electronomics and + + + align:start position:0% +concerned about the electronomics and +moving bodies that it got into the + + align:start position:0% +moving bodies that it got into the + + + align:start position:0% +moving bodies that it got into the +journal without being subjected to the + + align:start position:0% +journal without being subjected to the + + + align:start position:0% +journal without being subjected to the +kind of scrutiny that Einstein's own + + align:start position:0% +kind of scrutiny that Einstein's own + + + align:start position:0% +kind of scrutiny that Einstein's own +first articles would have been or that + + align:start position:0% +first articles would have been or that + + + align:start position:0% +first articles would have been or that +any new Authors would have been you + + align:start position:0% +any new Authors would have been you + + + align:start position:0% +any new Authors would have been you +should ignore all that when you write + + align:start position:0% +should ignore all that when you write + + + align:start position:0% +should ignore all that when you write +your paper one pretend that this paper + + align:start position:0% +your paper one pretend that this paper + + + align:start position:0% +your paper one pretend that this paper +really is being subjected to careful and + + align:start position:0% +really is being subjected to careful and + + + align:start position:0% +really is being subjected to careful and +uh and uh you know thorough peer review + + align:start position:0% +uh and uh you know thorough peer review + + + align:start position:0% +uh and uh you know thorough peer review +the short answer historically is that + + align:start position:0% +the short answer historically is that + + + align:start position:0% +the short answer historically is that +this wasn't a special favorite Einstein + + align:start position:0% +this wasn't a special favorite Einstein + + + align:start position:0% +this wasn't a special favorite Einstein +the general policy was usually to + + align:start position:0% +the general policy was usually to + + + align:start position:0% +the general policy was usually to +basically let later articles by an + + align:start position:0% +basically let later articles by an + + + align:start position:0% +basically let later articles by an +established contributor get into the + + align:start position:0% +established contributor get into the + + + align:start position:0% +established contributor get into the +journal or much more um discretion to + + align:start position:0% +journal or much more um discretion to + + + align:start position:0% +journal or much more um discretion to +the to the to the editor + + align:start position:0% +the to the to the editor + + + align:start position:0% +the to the to the editor +a very good question any other questions + + align:start position:0% +a very good question any other questions + + + align:start position:0% +a very good question any other questions +of that + + align:start position:0% + + + + align:start position:0% + +yeah I mean so so he was known Enough by + + align:start position:0% +yeah I mean so so he was known Enough by + + + align:start position:0% +yeah I mean so so he was known Enough by +people like Max Planck to say let's let + + align:start position:0% +people like Max Planck to say let's let + + + align:start position:0% +people like Max Planck to say let's let +this Young Guy's next article come in + + align:start position:0% +this Young Guy's next article come in + + + align:start position:0% +this Young Guy's next article come in +right so he wasn't um this wasn't his + + align:start position:0% +right so he wasn't um this wasn't his + + + align:start position:0% +right so he wasn't um this wasn't his +first work ever + + align:start position:0% +first work ever + + + align:start position:0% +first work ever +on the other hand the other work that he + + align:start position:0% +on the other hand the other work that he + + + align:start position:0% +on the other hand the other work that he +published was you know kind of we might + + align:start position:0% +published was you know kind of we might + + + align:start position:0% +published was you know kind of we might +say work a day it was perfectly + + align:start position:0% +say work a day it was perfectly + + + align:start position:0% +say work a day it was perfectly +competent neither interesting nor + + align:start position:0% +competent neither interesting nor + + + align:start position:0% +competent neither interesting nor +Innovative by the standards of the day + + align:start position:0% +Innovative by the standards of the day + + + align:start position:0% +Innovative by the standards of the day +even by ISIS he was very harsh about his + + align:start position:0% +even by ISIS he was very harsh about his + + + align:start position:0% +even by ISIS he was very harsh about his +even his own earlier work so he had a + + align:start position:0% +even his own earlier work so he had a + + + align:start position:0% +even his own earlier work so he had a +small early paper trail he in the + + align:start position:0% +small early paper trail he in the + + + align:start position:0% +small early paper trail he in the +meantime had as I mentioned before had + + align:start position:0% +meantime had as I mentioned before had + + + align:start position:0% +meantime had as I mentioned before had +annoyed almost all of his superiors uh + + align:start position:0% +annoyed almost all of his superiors uh + + + align:start position:0% +annoyed almost all of his superiors uh +or or both at the patent office and when + + align:start position:0% +or or both at the patent office and when + + + align:start position:0% +or or both at the patent office and when +he was a university student + + align:start position:0% +he was a university student + + + align:start position:0% +he was a university student +he was by this point out of the + + align:start position:0% +he was by this point out of the + + + align:start position:0% +he was by this point out of the +mainstream he was not working in any of + + align:start position:0% +mainstream he was not working in any of + + + align:start position:0% +mainstream he was not working in any of +the uh kind of prestigious scientific + + align:start position:0% +the uh kind of prestigious scientific + + + align:start position:0% +the uh kind of prestigious scientific +research institutes he was not being + + align:start position:0% +research institutes he was not being + + + align:start position:0% +research institutes he was not being +invited to attend the usual scientific + + align:start position:0% +invited to attend the usual scientific + + + align:start position:0% +invited to attend the usual scientific +conferences he was by this point not + + align:start position:0% +conferences he was by this point not + + + align:start position:0% +conferences he was by this point not +well known he was a person who + + align:start position:0% +well known he was a person who + + + align:start position:0% +well known he was a person who +contributed the occasional article to + + align:start position:0% +contributed the occasional article to + + + align:start position:0% +contributed the occasional article to +otherwise very busy Journal + + align:start position:0% +otherwise very busy Journal + + + align:start position:0% +otherwise very busy Journal +and so he was you know he had the kind + + align:start position:0% +and so he was you know he had the kind + + + align:start position:0% +and so he was you know he had the kind +of bear credentials + + align:start position:0% +of bear credentials + + + align:start position:0% +of bear credentials +he had not yet by this point even + + align:start position:0% +he had not yet by this point even + + + align:start position:0% +he had not yet by this point even +finished his PhD in the early years uh + + align:start position:0% +finished his PhD in the early years uh + + + align:start position:0% +finished his PhD in the early years uh +he was you know a kind of competent + + align:start position:0% +he was you know a kind of competent + + + align:start position:0% +he was you know a kind of competent +recent graduate from a highly respected + + align:start position:0% +recent graduate from a highly respected + + + align:start position:0% +recent graduate from a highly respected +Technical Institute whether it was + + align:start position:0% +Technical Institute whether it was + + + align:start position:0% +Technical Institute whether it was +otherwise not considered kind of any + + align:start position:0% +otherwise not considered kind of any + + + align:start position:0% +otherwise not considered kind of any +great shakes well it's a good question + + align:start position:0% +great shakes well it's a good question + + + align:start position:0% +great shakes well it's a good question +uh D.A we'll come back to that actually + + align:start position:0% +uh D.A we'll come back to that actually + + + align:start position:0% +uh D.A we'll come back to that actually +in next lecture on Wednesday more of the + + align:start position:0% +in next lecture on Wednesday more of the + + + align:start position:0% +in next lecture on Wednesday more of the +reception of Einstein the person his + + align:start position:0% +reception of Einstein the person his + + + align:start position:0% +reception of Einstein the person his +career and also this work but the short + + align:start position:0% +career and also this work but the short + + + align:start position:0% +career and also this work but the short +answer was that it was um it was not + + align:start position:0% +answer was that it was um it was not + + + align:start position:0% +answer was that it was um it was not +standing out so I see Jade asked a good + + align:start position:0% +standing out so I see Jade asked a good + + + align:start position:0% +standing out so I see Jade asked a good +question how large was scientific + + align:start position:0% +question how large was scientific + + + align:start position:0% +question how large was scientific +Community this time very good + + align:start position:0% +Community this time very good + + + align:start position:0% +Community this time very good +so uh around 1900 a number of my + + align:start position:0% +so uh around 1900 a number of my + + + align:start position:0% +so uh around 1900 a number of my +colleagues did this famous census some + + align:start position:0% +colleagues did this famous census some + + + align:start position:0% +colleagues did this famous census some +years ago to in round numbers they're + + align:start position:0% +years ago to in round numbers they're + + + align:start position:0% +years ago to in round numbers they're +around 1 000 professional physicists in + + align:start position:0% +around 1 000 professional physicists in + + + align:start position:0% +around 1 000 professional physicists in +the world not just in Western Europe but + + align:start position:0% +the world not just in Western Europe but + + + align:start position:0% +the world not just in Western Europe but +including what could be reconstructed + + align:start position:0% +including what could be reconstructed + + + align:start position:0% +including what could be reconstructed +from Japan from parts of China from many + + align:start position:0% +from Japan from parts of China from many + + + align:start position:0% +from Japan from parts of China from many +many parts who were from India there + + align:start position:0% +many parts who were from India there + + + align:start position:0% +many parts who were from India there +were basically a thousand people whose + + align:start position:0% +were basically a thousand people whose + + + align:start position:0% +were basically a thousand people whose +day job whose actual profession was + + align:start position:0% +day job whose actual profession was + + + align:start position:0% +day job whose actual profession was +something like working physicists a + + align:start position:0% +something like working physicists a + + + align:start position:0% +something like working physicists a +thousand so Einstein was whether you + + align:start position:0% +thousand so Einstein was whether you + + + align:start position:0% +thousand so Einstein was whether you +count them in that thousand or not he + + align:start position:0% +count them in that thousand or not he + + + align:start position:0% +count them in that thousand or not he +wasn't really being paid as a working + + align:start position:0% +wasn't really being paid as a working + + + align:start position:0% +wasn't really being paid as a working +physicist uh he was one of you know on + + align:start position:0% +physicist uh he was one of you know on + + + align:start position:0% +physicist uh he was one of you know on +the order of a thousand or a few + + align:start position:0% +the order of a thousand or a few + + + align:start position:0% +the order of a thousand or a few +thousand who might be contributing at + + align:start position:0% +thousand who might be contributing at + + + align:start position:0% +thousand who might be contributing at +any given time to these leading journals + + align:start position:0% +any given time to these leading journals + + + align:start position:0% +any given time to these leading journals +like the analyst so it's not hundreds of + + align:start position:0% +like the analyst so it's not hundreds of + + + align:start position:0% +like the analyst so it's not hundreds of +thousands not a million people but it's + + align:start position:0% +thousands not a million people but it's + + + align:start position:0% +thousands not a million people but it's +not like there's only a dozen so it + + align:start position:0% +not like there's only a dozen so it + + + align:start position:0% +not like there's only a dozen so it +really was easy to like have a young + + align:start position:0% +really was easy to like have a young + + + align:start position:0% +really was easy to like have a young +person get a few competent articles in a + + align:start position:0% +person get a few competent articles in a + + + align:start position:0% +person get a few competent articles in a +journal but otherwise not stand out not + + align:start position:0% +journal but otherwise not stand out not + + + align:start position:0% +journal but otherwise not stand out not +really be noticed and that really seems + + align:start position:0% +really be noticed and that really seems + + + align:start position:0% +really be noticed and that really seems +to be where Iceland was in this point in + + align:start position:0% +to be where Iceland was in this point in + + + align:start position:0% +to be where Iceland was in this point in +his career it's an excellent question + + align:start position:0% + + + + align:start position:0% + +let me press on I want to get on to to + + align:start position:0% +let me press on I want to get on to to + + + align:start position:0% +let me press on I want to get on to to +um to what Einstein does in this paper + + align:start position:0% +um to what Einstein does in this paper + + + align:start position:0% +um to what Einstein does in this paper +we'll walk through these first few + + align:start position:0% +we'll walk through these first few + + + align:start position:0% +we'll walk through these first few +sections of uh of his paper from o5 so + + align:start position:0% +sections of uh of his paper from o5 so + + + align:start position:0% +sections of uh of his paper from o5 so +again he doesn't tell us he's inspired + + align:start position:0% +again he doesn't tell us he's inspired + + + align:start position:0% +again he doesn't tell us he's inspired +by Arizona it's quite clear from from + + align:start position:0% +by Arizona it's quite clear from from + + + align:start position:0% +by Arizona it's quite clear from from +some of his other uh unpublished + + align:start position:0% +some of his other uh unpublished + + + align:start position:0% +some of his other uh unpublished +materials of the time he wants to begin + + align:start position:0% +materials of the time he wants to begin + + + align:start position:0% +materials of the time he wants to begin +by rethinking kinematics the motion of + + align:start position:0% +by rethinking kinematics the motion of + + + align:start position:0% +by rethinking kinematics the motion of +objects you space and time not start + + align:start position:0% +objects you space and time not start + + + align:start position:0% +objects you space and time not start +with Dynamics what can we observe about + + align:start position:0% +with Dynamics what can we observe about + + + align:start position:0% +with Dynamics what can we observe about +how these things move and so he has + + align:start position:0% +how these things move and so he has + + + align:start position:0% +how these things move and so he has +these comments like this uh early again + + align:start position:0% +these comments like this uh early again + + + align:start position:0% +these comments like this uh early again +on either page two or page three quite + + align:start position:0% +on either page two or page three quite + + + align:start position:0% +on either page two or page three quite +early in the article + + align:start position:0% +early in the article + + + align:start position:0% +early in the article +if we wish to describe the motion of a + + align:start position:0% +if we wish to describe the motion of a + + + align:start position:0% +if we wish to describe the motion of a +material point we give the values of his + + align:start position:0% +material point we give the values of his + + + align:start position:0% +material point we give the values of his +coordinates as functions of the time + + align:start position:0% +coordinates as functions of the time + + + align:start position:0% +coordinates as functions of the time +this is like you know we we expect most + + align:start position:0% +this is like you know we we expect most + + + align:start position:0% +this is like you know we we expect most +high school students would have + + align:start position:0% +high school students would have + + + align:start position:0% +high school students would have +encountered how you use coordinates to + + align:start position:0% +encountered how you use coordinates to + + + align:start position:0% +encountered how you use coordinates to +describe the objects of motion the + + align:start position:0% +describe the objects of motion the + + + align:start position:0% +describe the objects of motion the +motion of mode of beauty the motion of + + align:start position:0% +motion of mode of beauty the motion of + + + align:start position:0% +motion of mode of beauty the motion of +objects + + align:start position:0% +objects + + + align:start position:0% +objects +he goes on now we must bear carefully + + align:start position:0% +he goes on now we must bear carefully + + + align:start position:0% +he goes on now we must bear carefully +mined for the mathematical script of + + align:start position:0% +mined for the mathematical script of + + + align:start position:0% +mined for the mathematical script of +this kind has no physical meaning that's + + align:start position:0% +this kind has no physical meaning that's + + + align:start position:0% +this kind has no physical meaning that's +very mocking + + align:start position:0% +very mocking + + + align:start position:0% +very mocking +unless we're quite clear as to what we + + align:start position:0% +unless we're quite clear as to what we + + + align:start position:0% +unless we're quite clear as to what we +will understand by time we have to take + + align:start position:0% +will understand by time we have to take + + + align:start position:0% +will understand by time we have to take +into account that all our judgments in + + align:start position:0% +into account that all our judgments in + + + align:start position:0% +into account that all our judgments in +which time plays a role are always + + align:start position:0% +which time plays a role are always + + + align:start position:0% +which time plays a role are always +judgments of simultaneous events if for + + align:start position:0% +judgments of simultaneous events if for + + + align:start position:0% +judgments of simultaneous events if for +instance I say that train arrives here + + align:start position:0% +instance I say that train arrives here + + + align:start position:0% +instance I say that train arrives here +at seven o'clock I mean something like + + align:start position:0% +at seven o'clock I mean something like + + + align:start position:0% +at seven o'clock I mean something like +this the pointing of a small hand on my + + align:start position:0% +this the pointing of a small hand on my + + + align:start position:0% +this the pointing of a small hand on my +watch to seven and the arrival of the + + align:start position:0% +watch to seven and the arrival of the + + + align:start position:0% +watch to seven and the arrival of the +train are simultaneous events this is in + + align:start position:0% +train are simultaneous events this is in + + + align:start position:0% +train are simultaneous events this is in +page two or three of one of the world's + + align:start position:0% +page two or three of one of the world's + + + align:start position:0% +page two or three of one of the world's +leading physics journals he's trying to + + align:start position:0% +leading physics journals he's trying to + + + align:start position:0% +leading physics journals he's trying to +explain how to use coordinates describe + + align:start position:0% +explain how to use coordinates describe + + + align:start position:0% +explain how to use coordinates describe +things like the passage of time it's + + align:start position:0% +things like the passage of time it's + + + align:start position:0% +things like the passage of time it's +unbelievable he was as you have probably + + align:start position:0% +unbelievable he was as you have probably + + + align:start position:0% +unbelievable he was as you have probably +noticed enamorative trains trains come + + align:start position:0% +noticed enamorative trains trains come + + + align:start position:0% +noticed enamorative trains trains come +up over and over again in his examples + + align:start position:0% +up over and over again in his examples + + + align:start position:0% +up over and over again in his examples +of this era + + align:start position:0% +of this era + + + align:start position:0% +of this era +so if there's no absolute time if we're + + align:start position:0% +so if there's no absolute time if we're + + + align:start position:0% +so if there's no absolute time if we're +going to be forced to think about what + + align:start position:0% +going to be forced to think about what + + + align:start position:0% +going to be forced to think about what +it comes to call the relativity of + + align:start position:0% +it comes to call the relativity of + + + align:start position:0% +it comes to call the relativity of +simultaneity how can we compare the + + align:start position:0% +simultaneity how can we compare the + + + align:start position:0% +simultaneity how can we compare the +times associated with different events + + align:start position:0% +times associated with different events + + + align:start position:0% +times associated with different events +he says well we can send light signals + + align:start position:0% +he says well we can send light signals + + + align:start position:0% +he says well we can send light signals +because at least if we buy that second + + align:start position:0% +because at least if we buy that second + + + align:start position:0% +because at least if we buy that second +postulate then every inertial Observer + + align:start position:0% +postulate then every inertial Observer + + + align:start position:0% +postulate then every inertial Observer +will agree on the speed at which light + + align:start position:0% +will agree on the speed at which light + + + align:start position:0% +will agree on the speed at which light +travels then we can use light signals as + + align:start position:0% +travels then we can use light signals as + + + align:start position:0% +travels then we can use light signals as +a kind of universal tool + + align:start position:0% +a kind of universal tool + + + align:start position:0% +a kind of universal tool +so imagine again this train scenario we + + align:start position:0% +so imagine again this train scenario we + + + align:start position:0% +so imagine again this train scenario we +have us standing here we're at position + + align:start position:0% +have us standing here we're at position + + + align:start position:0% +have us standing here we're at position +M on the train platform or the + + align:start position:0% +M on the train platform or the + + + align:start position:0% +M on the train platform or the +embankment watching this train go by at + + align:start position:0% +embankment watching this train go by at + + + align:start position:0% +embankment watching this train go by at +some constant speed + + align:start position:0% +some constant speed + + + align:start position:0% +some constant speed +as far as we're concerned but we stand + + align:start position:0% +as far as we're concerned but we stand + + + align:start position:0% +as far as we're concerned but we stand +here watching the train go by there were + + align:start position:0% +here watching the train go by there were + + + align:start position:0% +here watching the train go by there were +two assistants of ours two partners at + + align:start position:0% +two assistants of ours two partners at + + + align:start position:0% +two assistants of ours two partners at +standing at locations A and B + + align:start position:0% +standing at locations A and B + + + align:start position:0% +standing at locations A and B +and they both had lanterns in their + + align:start position:0% +and they both had lanterns in their + + + align:start position:0% +and they both had lanterns in their +hands and the question is did they turn + + align:start position:0% +hands and the question is did they turn + + + align:start position:0% +hands and the question is did they turn +on their lanterns simultaneously how + + align:start position:0% +on their lanterns simultaneously how + + + align:start position:0% +on their lanterns simultaneously how +could we tell if we know by prior + + align:start position:0% +could we tell if we know by prior + + + align:start position:0% +could we tell if we know by prior +measurement that we are equal distance + + align:start position:0% +measurement that we are equal distance + + + align:start position:0% +measurement that we are equal distance +from both A and B we're standing here + + align:start position:0% +from both A and B we're standing here + + + align:start position:0% +from both A and B we're standing here +we've measured out maybe ahead of time + + align:start position:0% +we've measured out maybe ahead of time + + + align:start position:0% +we've measured out maybe ahead of time +the sort of exact distance between each + + align:start position:0% +the sort of exact distance between each + + + align:start position:0% +the sort of exact distance between each +of our colleagues our partners we're in + + align:start position:0% +of our colleagues our partners we're in + + + align:start position:0% +of our colleagues our partners we're in +the middle + + align:start position:0% +the middle + + + align:start position:0% +the middle +if we then measure if we receive those + + align:start position:0% +if we then measure if we receive those + + + align:start position:0% +if we then measure if we receive those +light signals at the same time if they + + align:start position:0% +light signals at the same time if they + + + align:start position:0% +light signals at the same time if they +reach our nose at the same time as a + + align:start position:0% +reach our nose at the same time as a + + + align:start position:0% +reach our nose at the same time as a +small hand if our watch clicks to sevens + + align:start position:0% +small hand if our watch clicks to sevens + + + align:start position:0% +small hand if our watch clicks to sevens +like that we must conclude that the + + align:start position:0% +like that we must conclude that the + + + align:start position:0% +like that we must conclude that the +emission of that light happened + + align:start position:0% +emission of that light happened + + + align:start position:0% +emission of that light happened +simultaneously the event of turning of A + + align:start position:0% +simultaneously the event of turning of A + + + align:start position:0% +simultaneously the event of turning of A +and B turning on their lanterns must + + align:start position:0% +and B turning on their lanterns must + + + align:start position:0% +and B turning on their lanterns must +have occurred simultaneously because the + + align:start position:0% +have occurred simultaneously because the + + + align:start position:0% +have occurred simultaneously because the +light waves traveled the same distance + + align:start position:0% +light waves traveled the same distance + + + align:start position:0% +light waves traveled the same distance +the light waves couldn't have sped up or + + align:start position:0% +the light waves couldn't have sped up or + + + align:start position:0% +the light waves couldn't have sped up or +slowed down so they arrived at the same + + align:start position:0% +slowed down so they arrived at the same + + + align:start position:0% +slowed down so they arrived at the same +time they must have left at the same + + align:start position:0% +time they must have left at the same + + + align:start position:0% +time they must have left at the same +time the emissions must have been + + align:start position:0% +time the emissions must have been + + + align:start position:0% +time the emissions must have been +simultaneous + + align:start position:0% +simultaneous + + + align:start position:0% +simultaneous +what about our car our colleague who's + + align:start position:0% +what about our car our colleague who's + + + align:start position:0% +what about our car our colleague who's +riding at the midpoint of the train as + + align:start position:0% +riding at the midpoint of the train as + + + align:start position:0% +riding at the midpoint of the train as +the entire train rides past the train + + align:start position:0% +the entire train rides past the train + + + align:start position:0% +the entire train rides past the train +platform or the embankment at some + + align:start position:0% +platform or the embankment at some + + + align:start position:0% +platform or the embankment at some +constant speed the person's in the + + align:start position:0% +constant speed the person's in the + + + align:start position:0% +constant speed the person's in the +middle of the train so she knows she's + + align:start position:0% +middle of the train so she knows she's + + + align:start position:0% +middle of the train so she knows she's +equidistant from the people who are at + + align:start position:0% +equidistant from the people who are at + + + align:start position:0% +equidistant from the people who are at +the front of the back of the train at A + + align:start position:0% +the front of the back of the train at A + + + align:start position:0% +the front of the back of the train at A +and B + + align:start position:0% +and B + + + align:start position:0% +and B +she sees them both turn their lanterns + + align:start position:0% +she sees them both turn their lanterns + + + align:start position:0% +she sees them both turn their lanterns +on but she receives the light signal + + align:start position:0% +on but she receives the light signal + + + align:start position:0% +on but she receives the light signal +from person B first + + align:start position:0% +from person B first + + + align:start position:0% +from person B first +now she concludes that A and B did not + + align:start position:0% +now she concludes that A and B did not + + + align:start position:0% +now she concludes that A and B did not +turn their Lancers on simultaneously how + + align:start position:0% +turn their Lancers on simultaneously how + + + align:start position:0% +turn their Lancers on simultaneously how +could they have she's clearly + + align:start position:0% +could they have she's clearly + + + align:start position:0% +could they have she's clearly +equidistant between them she clearly + + align:start position:0% +equidistant between them she clearly + + + align:start position:0% +equidistant between them she clearly +receives a light from event B before the + + align:start position:0% +receives a light from event B before the + + + align:start position:0% +receives a light from event B before the +event the life of event a so clearly A + + align:start position:0% +event the life of event a so clearly A + + + align:start position:0% +event the life of event a so clearly A +and B could not have been uh emitted + + align:start position:0% +and B could not have been uh emitted + + + align:start position:0% +and B could not have been uh emitted +simultaneously + + align:start position:0% +simultaneously + + + align:start position:0% +simultaneously +now who's correct we might say we might + + align:start position:0% +now who's correct we might say we might + + + align:start position:0% +now who's correct we might say we might +stop her if he's no no no you're moving + + align:start position:0% +stop her if he's no no no you're moving + + + align:start position:0% +stop her if he's no no no you're moving +it doesn't work for you and she will + + align:start position:0% +it doesn't work for you and she will + + + align:start position:0% +it doesn't work for you and she will +justice as as uh as stubbornly stop her + + align:start position:0% +justice as as uh as stubbornly stop her + + + align:start position:0% +justice as as uh as stubbornly stop her +own feet and say according to Einstein's + + align:start position:0% +own feet and say according to Einstein's + + + align:start position:0% +own feet and say according to Einstein's +own posture number one the laws of + + align:start position:0% +own posture number one the laws of + + + align:start position:0% +own posture number one the laws of +physics are exactly as legitimate for + + align:start position:0% +physics are exactly as legitimate for + + + align:start position:0% +physics are exactly as legitimate for +her as they are for us she's moving in + + align:start position:0% +her as they are for us she's moving in + + + align:start position:0% +her as they are for us she's moving in +an inertial frame of reference she's + + align:start position:0% +an inertial frame of reference she's + + + align:start position:0% +an inertial frame of reference she's +moving in a constant speed all the laws + + align:start position:0% +moving in a constant speed all the laws + + + align:start position:0% +moving in a constant speed all the laws +of physics work for her she can draw all + + align:start position:0% +of physics work for her she can draw all + + + align:start position:0% +of physics work for her she can draw all +the same conclusions that we can she + + align:start position:0% +the same conclusions that we can she + + + align:start position:0% +the same conclusions that we can she +clearly was at the midpoint of A and B + + align:start position:0% +clearly was at the midpoint of A and B + + + align:start position:0% +clearly was at the midpoint of A and B +she clearly received life flash from V + + align:start position:0% +she clearly received life flash from V + + + align:start position:0% +she clearly received life flash from V +first + + align:start position:0% +first + + + align:start position:0% +first +this is what Einstein means by saying as + + align:start position:0% +this is what Einstein means by saying as + + + align:start position:0% +this is what Einstein means by saying as +he writes in the paper we can attribute + + align:start position:0% +he writes in the paper we can attribute + + + align:start position:0% +he writes in the paper we can attribute +no absolute meaning to the concept of + + align:start position:0% +no absolute meaning to the concept of + + + align:start position:0% +no absolute meaning to the concept of +simultaneity but rather that two events + + align:start position:0% +simultaneity but rather that two events + + + align:start position:0% +simultaneity but rather that two events +which examine from one coordinate system + + align:start position:0% +which examine from one coordinate system + + + align:start position:0% +which examine from one coordinate system +are simultaneous like us on the train + + align:start position:0% +are simultaneous like us on the train + + + align:start position:0% +are simultaneous like us on the train +platform can no longer be interpreted as + + align:start position:0% +platform can no longer be interpreted as + + + align:start position:0% +platform can no longer be interpreted as +simultaneous events when examined from a + + align:start position:0% +simultaneous events when examined from a + + + align:start position:0% +simultaneous events when examined from a +system which is in motion relative to + + align:start position:0% +system which is in motion relative to + + + align:start position:0% +system which is in motion relative to +that system remember nothing about + + align:start position:0% +that system remember nothing about + + + align:start position:0% +that system remember nothing about +forces not about her being knocked off + + align:start position:0% +forces not about her being knocked off + + + align:start position:0% +forces not about her being knocked off +course she's in a perfectly legitimate + + align:start position:0% +course she's in a perfectly legitimate + + + align:start position:0% +course she's in a perfectly legitimate +physical laboratory moving at a constant + + align:start position:0% +physical laboratory moving at a constant + + + align:start position:0% +physical laboratory moving at a constant +speed her conclusion is exactly as valid + + align:start position:0% +speed her conclusion is exactly as valid + + + align:start position:0% +speed her conclusion is exactly as valid +Einstein says as ours is therefore + + align:start position:0% +Einstein says as ours is therefore + + + align:start position:0% +Einstein says as ours is therefore +simultaneity is not shared across + + align:start position:0% +simultaneity is not shared across + + + align:start position:0% +simultaneity is not shared across +reference frames + + align:start position:0% +reference frames + + + align:start position:0% +reference frames +okay what do you do with that + + align:start position:0% +okay what do you do with that + + + align:start position:0% +okay what do you do with that +information + + align:start position:0% + + + + align:start position:0% + +this is what begins to lead + + align:start position:0% +this is what begins to lead + + + align:start position:0% +this is what begins to lead +to some new phenomena new at least for + + align:start position:0% +to some new phenomena new at least for + + + align:start position:0% +to some new phenomena new at least for +Einstein how do we measure the length of + + align:start position:0% +Einstein how do we measure the length of + + + align:start position:0% +Einstein how do we measure the length of +an object well as any good mocking kind + + align:start position:0% +an object well as any good mocking kind + + + align:start position:0% +an object well as any good mocking kind +of philosopher would say tell me exactly + + align:start position:0% +of philosopher would say tell me exactly + + + align:start position:0% +of philosopher would say tell me exactly +the empirical procedure to be followed + + align:start position:0% +the empirical procedure to be followed + + + align:start position:0% +the empirical procedure to be followed +well here's a good procedure at the same + + align:start position:0% +well here's a good procedure at the same + + + align:start position:0% +well here's a good procedure at the same +time + + align:start position:0% +time + + + align:start position:0% +time +measure the locations of the front and + + align:start position:0% +measure the locations of the front and + + + align:start position:0% +measure the locations of the front and +back of the object and then subtract + + align:start position:0% +back of the object and then subtract + + + align:start position:0% +back of the object and then subtract +take the difference at the same time + + align:start position:0% +take the difference at the same time + + + align:start position:0% +take the difference at the same time +so here's the train at rest in the + + align:start position:0% +so here's the train at rest in the + + + align:start position:0% +so here's the train at rest in the +station platform we're out on the train + + align:start position:0% +station platform we're out on the train + + + align:start position:0% +station platform we're out on the train +uh on the embankment we measure the + + align:start position:0% +uh on the embankment we measure the + + + align:start position:0% +uh on the embankment we measure the +front of the Train the back of the train + + align:start position:0% +front of the Train the back of the train + + + align:start position:0% +front of the Train the back of the train +take the difference we measure the + + align:start position:0% +take the difference we measure the + + + align:start position:0% +take the difference we measure the +length of the train to be length l + + align:start position:0% +length of the train to be length l + + + align:start position:0% +length of the train to be length l +what if we on the platform measure the + + align:start position:0% +what if we on the platform measure the + + + align:start position:0% +what if we on the platform measure the +length of the moving train as the train + + align:start position:0% +length of the moving train as the train + + + align:start position:0% +length of the moving train as the train +speed speeds passes at a constant speed + + align:start position:0% +speed speeds passes at a constant speed + + + align:start position:0% +speed speeds passes at a constant speed +V well at One Moment In Time + + align:start position:0% +V well at One Moment In Time + + + align:start position:0% +V well at One Moment In Time +simultaneously we measure the positions + + align:start position:0% +simultaneously we measure the positions + + + align:start position:0% +simultaneously we measure the positions +of the front and back of the train and + + align:start position:0% +of the front and back of the train and + + + align:start position:0% +of the front and back of the train and +we measure the train to be short we + + align:start position:0% +we measure the train to be short we + + + align:start position:0% +we measure the train to be short we +measure some length L Prime + + align:start position:0% +measure some length L Prime + + + align:start position:0% +measure some length L Prime +which is shorter than l in fact uh we'll + + align:start position:0% +which is shorter than l in fact uh we'll + + + align:start position:0% +which is shorter than l in fact uh we'll +see shorter by how much in a moment now + + align:start position:0% +see shorter by how much in a moment now + + + align:start position:0% +see shorter by how much in a moment now +the passenger on the train our colleague + + align:start position:0% +the passenger on the train our colleague + + + align:start position:0% +the passenger on the train our colleague +is sitting at that midpoint M Prime says + + align:start position:0% +is sitting at that midpoint M Prime says + + + align:start position:0% +is sitting at that midpoint M Prime says +no you messed up + + align:start position:0% +no you messed up + + + align:start position:0% +no you messed up +you got the wrong length because you + + align:start position:0% +you got the wrong length because you + + + align:start position:0% +you got the wrong length because you +messed up on simultaneity you first she + + align:start position:0% +messed up on simultaneity you first she + + + align:start position:0% +messed up on simultaneity you first she +accuses us we first measured the + + align:start position:0% +accuses us we first measured the + + + align:start position:0% +accuses us we first measured the +location of the front of the train + + align:start position:0% +location of the front of the train + + + align:start position:0% +location of the front of the train +waited for the train to slide by and + + align:start position:0% +waited for the train to slide by and + + + align:start position:0% +waited for the train to slide by and +later measure the position in the back + + align:start position:0% +later measure the position in the back + + + align:start position:0% +later measure the position in the back +of the train so of course our + + align:start position:0% +of the train so of course our + + + align:start position:0% +of the train so of course our +measurement was shorter than what should + + align:start position:0% +measurement was shorter than what should + + + align:start position:0% +measurement was shorter than what should +have been + + align:start position:0% +have been + + + align:start position:0% +have been +how does she know that we did them at + + align:start position:0% +how does she know that we did them at + + + align:start position:0% +how does she know that we did them at +different times because she asked her + + align:start position:0% +different times because she asked her + + + align:start position:0% +different times because she asked her +friends at the front and back of the + + align:start position:0% +friends at the front and back of the + + + align:start position:0% +friends at the front and back of the +train to release their lanterns she + + align:start position:0% +train to release their lanterns she + + + align:start position:0% +train to release their lanterns she +clearly got the light signal from V + + align:start position:0% +clearly got the light signal from V + + + align:start position:0% +clearly got the light signal from V +first so she knows we measured the front + + align:start position:0% +first so she knows we measured the front + + + align:start position:0% +first so she knows we measured the front +of the train at one moment and at some + + align:start position:0% +of the train at one moment and at some + + + align:start position:0% +of the train at one moment and at some +later time not simultaneously we measure + + align:start position:0% +later time not simultaneously we measure + + + align:start position:0% +later time not simultaneously we measure +the back of the train so of course we + + align:start position:0% +the back of the train so of course we + + + align:start position:0% +the back of the train so of course we +got the wrong answer because we messed + + align:start position:0% +got the wrong answer because we messed + + + align:start position:0% +got the wrong answer because we messed +up the measurement + + align:start position:0% +up the measurement + + + align:start position:0% +up the measurement +with only a little bit more work + + align:start position:0% +with only a little bit more work + + + align:start position:0% +with only a little bit more work +Einstein shows we can find out by how + + align:start position:0% +Einstein shows we can find out by how + + + align:start position:0% +Einstein shows we can find out by how +much these two measurements will + + align:start position:0% +much these two measurements will + + + align:start position:0% +much these two measurements will +disagree they disagree by exactly that + + align:start position:0% +disagree they disagree by exactly that + + + align:start position:0% +disagree they disagree by exactly that +factor gamma that we've now seen many + + align:start position:0% +factor gamma that we've now seen many + + + align:start position:0% +factor gamma that we've now seen many +many times that one over the square root + + align:start position:0% +many times that one over the square root + + + align:start position:0% +many times that one over the square root +of one minus the quantity of U over c + + align:start position:0% +of one minus the quantity of U over c + + + align:start position:0% +of one minus the quantity of U over c +squared + + align:start position:0% +squared + + + align:start position:0% +squared +just by taking into account kinematics + + align:start position:0% +just by taking into account kinematics + + + align:start position:0% +just by taking into account kinematics +how do we account for the motion of + + align:start position:0% +how do we account for the motion of + + + align:start position:0% +how do we account for the motion of +objects through space and time nothing + + align:start position:0% +objects through space and time nothing + + + align:start position:0% +objects through space and time nothing +about forces nothing about an ether + + align:start position:0% +about forces nothing about an ether + + + align:start position:0% +about forces nothing about an ether +Einstein arrives at exactly the same + + align:start position:0% +Einstein arrives at exactly the same + + + align:start position:0% +Einstein arrives at exactly the same +quantitative form as the Lorenz + + align:start position:0% +quantitative form as the Lorenz + + + align:start position:0% +quantitative form as the Lorenz +contraction because of our relativity of + + align:start position:0% +contraction because of our relativity of + + + align:start position:0% +contraction because of our relativity of +simultaneity not because of forces from + + align:start position:0% +simultaneity not because of forces from + + + align:start position:0% +simultaneity not because of forces from +The Ether + + align:start position:0% +The Ether + + + align:start position:0% +The Ether +so just to beat this dead horse to my + + align:start position:0% +so just to beat this dead horse to my + + + align:start position:0% +so just to beat this dead horse to my +side length contract can have nothing to + + align:start position:0% +side length contract can have nothing to + + + align:start position:0% +side length contract can have nothing to +do with forces or an ether it wasn't + + align:start position:0% +do with forces or an ether it wasn't + + + align:start position:0% +do with forces or an ether it wasn't +about Dynamics it was simply a + + align:start position:0% +about Dynamics it was simply a + + + align:start position:0% +about Dynamics it was simply a +consequence of kinematics once we take + + align:start position:0% +consequence of kinematics once we take + + + align:start position:0% +consequence of kinematics once we take +the time to understand how objects move + + align:start position:0% +the time to understand how objects move + + + align:start position:0% +the time to understand how objects move +through space and time and how we assign + + align:start position:0% +through space and time and how we assign + + + align:start position:0% +through space and time and how we assign +coordinates to that force-free motion + + align:start position:0% +coordinates to that force-free motion + + + align:start position:0% +coordinates to that force-free motion +he goes on the next uh step that he that + + align:start position:0% +he goes on the next uh step that he that + + + align:start position:0% +he goes on the next uh step that he that +he discusses is actually what comes to + + align:start position:0% +he discusses is actually what comes to + + + align:start position:0% +he discusses is actually what comes to +be known as time dilation how can we + + align:start position:0% +be known as time dilation how can we + + + align:start position:0% +be known as time dilation how can we +measure the duration between two events + + align:start position:0% +measure the duration between two events + + + align:start position:0% +measure the duration between two events +the time duration how long between how + + align:start position:0% +the time duration how long between how + + + align:start position:0% +the time duration how long between how +much time passes between two minutes + + align:start position:0% +much time passes between two minutes + + + align:start position:0% +much time passes between two minutes +well we can imagine building something + + align:start position:0% +well we can imagine building something + + + align:start position:0% +well we can imagine building something +called a light clock a thought + + align:start position:0% +called a light clock a thought + + + align:start position:0% +called a light clock a thought +experiment take two mirrors two + + align:start position:0% +experiment take two mirrors two + + + align:start position:0% +experiment take two mirrors two +reflecting mirrors and fix their + + align:start position:0% +reflecting mirrors and fix their + + + align:start position:0% +reflecting mirrors and fix their +relative height fix hold them in + + align:start position:0% +relative height fix hold them in + + + align:start position:0% +relative height fix hold them in +position so they have some height H + + align:start position:0% +position so they have some height H + + + align:start position:0% +position so they have some height H +between them + + align:start position:0% +between them + + + align:start position:0% +between them +and we'll tell the tick of a clock by + + align:start position:0% +and we'll tell the tick of a clock by + + + align:start position:0% +and we'll tell the tick of a clock by +bouncing a single light wave between + + align:start position:0% +bouncing a single light wave between + + + align:start position:0% +bouncing a single light wave between +them + + align:start position:0% +them + + + align:start position:0% +them +that's what sets our reference time + + align:start position:0% +that's what sets our reference time + + + align:start position:0% +that's what sets our reference time +between ticks and so the time between + + align:start position:0% +between ticks and so the time between + + + align:start position:0% +between ticks and so the time between +ticks when we're standing at rest with + + align:start position:0% +ticks when we're standing at rest with + + + align:start position:0% +ticks when we're standing at rest with +this clock + + align:start position:0% +this clock + + + align:start position:0% +this clock +is just the height between those mirrors + + align:start position:0% +is just the height between those mirrors + + + align:start position:0% +is just the height between those mirrors +divided by the speed with which the + + align:start position:0% +divided by the speed with which the + + + align:start position:0% +divided by the speed with which the +light hooks speed with which the light + + align:start position:0% +light hooks speed with which the light + + + align:start position:0% +light hooks speed with which the light +will travel so we have a fixed clock + + align:start position:0% +will travel so we have a fixed clock + + + align:start position:0% +will travel so we have a fixed clock +rate when we hold this clock at rest + + align:start position:0% +rate when we hold this clock at rest + + + align:start position:0% +rate when we hold this clock at rest +with respect to us it's given by the + + align:start position:0% +with respect to us it's given by the + + + align:start position:0% +with respect to us it's given by the +height and the speed of light + + align:start position:0% +height and the speed of light + + + align:start position:0% +height and the speed of light +what if our partner has an identical + + align:start position:0% +what if our partner has an identical + + + align:start position:0% +what if our partner has an identical +clock as she races past us on that + + align:start position:0% +clock as she races past us on that + + + align:start position:0% +clock as she races past us on that +moving train + + align:start position:0% +moving train + + + align:start position:0% +moving train +she's now moving on the train at a + + align:start position:0% +she's now moving on the train at a + + + align:start position:0% +she's now moving on the train at a +constant speed V how do we on the TR on + + align:start position:0% +constant speed V how do we on the TR on + + + align:start position:0% +constant speed V how do we on the TR on +the train platform watch the rate of her + + align:start position:0% +the train platform watch the rate of her + + + align:start position:0% +the train platform watch the rate of her +moving clock + + align:start position:0% +moving clock + + + align:start position:0% +moving clock +well we see this light wave travel this + + align:start position:0% +well we see this light wave travel this + + + align:start position:0% +well we see this light wave travel this +kind of Sawtooth pattern right uh it's + + align:start position:0% +kind of Sawtooth pattern right uh it's + + + align:start position:0% +kind of Sawtooth pattern right uh it's +emitted from the bottom mirror the + + align:start position:0% +emitted from the bottom mirror the + + + align:start position:0% +emitted from the bottom mirror the +entire assembly drifts to the right as + + align:start position:0% +entire assembly drifts to the right as + + + align:start position:0% +entire assembly drifts to the right as +the whole train moves by so by the time + + align:start position:0% +the whole train moves by so by the time + + + align:start position:0% +the whole train moves by so by the time +that light wave reaches the top mirror + + align:start position:0% +that light wave reaches the top mirror + + + align:start position:0% +that light wave reaches the top mirror +the entire assembly has moved it's moved + + align:start position:0% +the entire assembly has moved it's moved + + + align:start position:0% +the entire assembly has moved it's moved +some distance B + + align:start position:0% +some distance B + + + align:start position:0% +some distance B +likewise from the top to the bottom it + + align:start position:0% +likewise from the top to the bottom it + + + align:start position:0% +likewise from the top to the bottom it +moves another distance B and so on so + + align:start position:0% +moves another distance B and so on so + + + align:start position:0% +moves another distance B and so on so +we're watching their light beam in the + + align:start position:0% +we're watching their light beam in the + + + align:start position:0% +we're watching their light beam in the +moving light clock Trace out this + + align:start position:0% +moving light clock Trace out this + + + align:start position:0% +moving light clock Trace out this +Sawtooth pattern as opposed to moving + + align:start position:0% +Sawtooth pattern as opposed to moving + + + align:start position:0% +Sawtooth pattern as opposed to moving +with what for us would look like + + align:start position:0% +with what for us would look like + + + align:start position:0% +with what for us would look like +straight up and down + + align:start position:0% +straight up and down + + + align:start position:0% +straight up and down +so once again we can use this great + + align:start position:0% +so once again we can use this great + + + align:start position:0% +so once again we can use this great +invention of the Pythagorean theorem we + + align:start position:0% +invention of the Pythagorean theorem we + + + align:start position:0% +invention of the Pythagorean theorem we +have a beautiful right triangle we can + + align:start position:0% +have a beautiful right triangle we can + + + align:start position:0% +have a beautiful right triangle we can +relate the distance traveled as seen by + + align:start position:0% +relate the distance traveled as seen by + + + align:start position:0% +relate the distance traveled as seen by +us of the of the light beam in the + + align:start position:0% +us of the of the light beam in the + + + align:start position:0% +us of the of the light beam in the +moving clock that's his distance capital + + align:start position:0% +moving clock that's his distance capital + + + align:start position:0% +moving clock that's his distance capital +D + + align:start position:0% +D + + + align:start position:0% +D +we can relate the square of that + + align:start position:0% +we can relate the square of that + + + align:start position:0% +we can relate the square of that +distance to the sum of squares of the + + align:start position:0% +distance to the sum of squares of the + + + align:start position:0% +distance to the sum of squares of the +two sides as a right triangle to the + + align:start position:0% +two sides as a right triangle to the + + + align:start position:0% +two sides as a right triangle to the +drift distance while that light waves in + + align:start position:0% +drift distance while that light waves in + + + align:start position:0% +drift distance while that light waves in +motion entire clock drifts the distance + + align:start position:0% +motion entire clock drifts the distance + + + align:start position:0% +motion entire clock drifts the distance +b square that length plus the square of + + align:start position:0% +b square that length plus the square of + + + align:start position:0% +b square that length plus the square of +the height the height between mirrors + + align:start position:0% +the height the height between mirrors + + + align:start position:0% +the height the height between mirrors +okay well now we know much like when we + + align:start position:0% +okay well now we know much like when we + + + align:start position:0% +okay well now we know much like when we +talked about the swimmers in the race uh + + align:start position:0% +talked about the swimmers in the race uh + + + align:start position:0% +talked about the swimmers in the race uh +last time about the Michaelson Morley + + align:start position:0% +last time about the Michaelson Morley + + + align:start position:0% +last time about the Michaelson Morley +experiment we can fill in a bit more + + align:start position:0% +experiment we can fill in a bit more + + + align:start position:0% +experiment we can fill in a bit more +information we know that this distance + + align:start position:0% +information we know that this distance + + + align:start position:0% +information we know that this distance +capital D is the distance at which that + + align:start position:0% +capital D is the distance at which that + + + align:start position:0% +capital D is the distance at which that +lightweave light wave traveled that's + + align:start position:0% +lightweave light wave traveled that's + + + align:start position:0% +lightweave light wave traveled that's +this one and only constant C + + align:start position:0% +this one and only constant C + + + align:start position:0% +this one and only constant C +times how long it was in motion it was + + align:start position:0% +times how long it was in motion it was + + + align:start position:0% +times how long it was in motion it was +in transit from the bottom mirror to the + + align:start position:0% +in transit from the bottom mirror to the + + + align:start position:0% +in transit from the bottom mirror to the +top mirror some time delta T Prime + + align:start position:0% +top mirror some time delta T Prime + + + align:start position:0% +top mirror some time delta T Prime +that's our measurement of the duration + + align:start position:0% +that's our measurement of the duration + + + align:start position:0% +that's our measurement of the duration +of ticks of the moving clock that's our + + align:start position:0% +of ticks of the moving clock that's our + + + align:start position:0% +of ticks of the moving clock that's our +measurement of their clock rate so the + + align:start position:0% +measurement of their clock rate so the + + + align:start position:0% +measurement of their clock rate so the +distance it traveled sorry the distance + + align:start position:0% +distance it traveled sorry the distance + + + align:start position:0% +distance it traveled sorry the distance +it traveled is its speed times the + + align:start position:0% +it traveled is its speed times the + + + align:start position:0% +it traveled is its speed times the +duration it's in Flight okay likewise as + + align:start position:0% +duration it's in Flight okay likewise as + + + align:start position:0% +duration it's in Flight okay likewise as +drift distance is the speed at which the + + align:start position:0% +drift distance is the speed at which the + + + align:start position:0% +drift distance is the speed at which the +entire assembly is moving that's the + + align:start position:0% +entire assembly is moving that's the + + + align:start position:0% +entire assembly is moving that's the +capital V times that same duration how + + align:start position:0% +capital V times that same duration how + + + align:start position:0% +capital V times that same duration how +long between uh when the light waves at + + align:start position:0% +long between uh when the light waves at + + + align:start position:0% +long between uh when the light waves at +the bottom mirror and the top mirror + + align:start position:0% +the bottom mirror and the top mirror + + + align:start position:0% +the bottom mirror and the top mirror +okay and then we still have H squared on + + align:start position:0% +okay and then we still have H squared on + + + align:start position:0% +okay and then we still have H squared on +the and sorry gang + + align:start position:0% +the and sorry gang + + + align:start position:0% +the and sorry gang +well now we can fill in some other + + align:start position:0% +well now we can fill in some other + + + align:start position:0% +well now we can fill in some other +information we know what H squared is + + align:start position:0% +information we know what H squared is + + + align:start position:0% +information we know what H squared is +that's just related to our clock rate in + + align:start position:0% +that's just related to our clock rate in + + + align:start position:0% +that's just related to our clock rate in +our own reference frame age remember we + + align:start position:0% +our own reference frame age remember we + + + align:start position:0% +our own reference frame age remember we +can relate to uh to the the speed at + + align:start position:0% +can relate to uh to the the speed at + + + align:start position:0% +can relate to uh to the the speed at +which light is traveling times our tick + + align:start position:0% +which light is traveling times our tick + + + align:start position:0% +which light is traveling times our tick +rate on our clock and now it just takes + + align:start position:0% +rate on our clock and now it just takes + + + align:start position:0% +rate on our clock and now it just takes +that same amount of algebra just like in + + align:start position:0% +that same amount of algebra just like in + + + align:start position:0% +that same amount of algebra just like in +the Michaelson more experiment just like + + align:start position:0% +the Michaelson more experiment just like + + + align:start position:0% +the Michaelson more experiment just like +therefore in the lecture notes from from + + align:start position:0% +therefore in the lecture notes from from + + + align:start position:0% +therefore in the lecture notes from from +last week it takes very little work to + + align:start position:0% +last week it takes very little work to + + + align:start position:0% +last week it takes very little work to +derive a relationship between our + + align:start position:0% +derive a relationship between our + + + align:start position:0% +derive a relationship between our +measurement of the moving clocks tick + + align:start position:0% +measurement of the moving clocks tick + + + align:start position:0% +measurement of the moving clocks tick +rate and the our measurement of our own + + align:start position:0% +rate and the our measurement of our own + + + align:start position:0% +rate and the our measurement of our own +clocks tick rate and in fact remember + + align:start position:0% +clocks tick rate and in fact remember + + + align:start position:0% +clocks tick rate and in fact remember +that gamma is always larger than one if + + align:start position:0% +that gamma is always larger than one if + + + align:start position:0% +that gamma is always larger than one if +there's any relative speed we measure + + align:start position:0% +there's any relative speed we measure + + + align:start position:0% +there's any relative speed we measure +their clock to be running slowly the + + align:start position:0% +their clock to be running slowly the + + + align:start position:0% +their clock to be running slowly the +time between ticks on the moving clock + + align:start position:0% +time between ticks on the moving clock + + + align:start position:0% +time between ticks on the moving clock +will be slower than the time between + + align:start position:0% +will be slower than the time between + + + align:start position:0% +will be slower than the time between +ticks on our own clock that's at rest + + align:start position:0% +ticks on our own clock that's at rest + + + align:start position:0% +ticks on our own clock that's at rest +with respect to us not because there's a + + align:start position:0% +with respect to us not because there's a + + + align:start position:0% +with respect to us not because there's a +force not because of Any resistance from + + align:start position:0% +force not because of Any resistance from + + + align:start position:0% +force not because of Any resistance from +The Ether but simply because of + + align:start position:0% +The Ether but simply because of + + + align:start position:0% +The Ether but simply because of +kinematics + + align:start position:0% +kinematics + + + align:start position:0% +kinematics +this last part here will be especially + + align:start position:0% +this last part here will be especially + + + align:start position:0% +this last part here will be especially +um sketchy but here's why I invite you + + align:start position:0% +um sketchy but here's why I invite you + + + align:start position:0% +um sketchy but here's why I invite you +to look optional but you're invited to + + align:start position:0% +to look optional but you're invited to + + + align:start position:0% +to look optional but you're invited to +uh to look at the brief lecture notes on + + align:start position:0% +uh to look at the brief lecture notes on + + + align:start position:0% +uh to look at the brief lecture notes on +on the canvas side a few weeks later he + + align:start position:0% +on the canvas side a few weeks later he + + + align:start position:0% +on the canvas side a few weeks later he +submits this article the one we've been + + align:start position:0% +submits this article the one we've been + + + align:start position:0% +submits this article the one we've been +talking about the electronomically + + align:start position:0% +talking about the electronomically + + + align:start position:0% +talking about the electronomically +moving bodies he submits to the + + align:start position:0% +moving bodies he submits to the + + + align:start position:0% +moving bodies he submits to the +underlander Physique in June early June + + align:start position:0% +underlander Physique in June early June + + + align:start position:0% +underlander Physique in June early June +of 1905. he writes up a three-page + + align:start position:0% +of 1905. he writes up a three-page + + + align:start position:0% +of 1905. he writes up a three-page +follow-up that's probably that submitted + + align:start position:0% +follow-up that's probably that submitted + + + align:start position:0% +follow-up that's probably that submitted +the journal in September of 1905. he + + align:start position:0% +the journal in September of 1905. he + + + align:start position:0% +the journal in September of 1905. he +basically takes the summer and derives + + align:start position:0% +basically takes the summer and derives + + + align:start position:0% +basically takes the summer and derives +what is probably his best known equation + + align:start position:0% +what is probably his best known equation + + + align:start position:0% +what is probably his best known equation +ever which equals mc squared the nature + + align:start position:0% +ever which equals mc squared the nature + + + align:start position:0% +ever which equals mc squared the nature +of his original derivation goes like + + align:start position:0% +of his original derivation goes like + + + align:start position:0% +of his original derivation goes like +this and again some some the notes fill + + align:start position:0% +this and again some some the notes fill + + + align:start position:0% +this and again some some the notes fill +in some some of the some details of it + + align:start position:0% +in some some of the some details of it + + + align:start position:0% +in some some of the some details of it +but alternate derivation + + align:start position:0% +but alternate derivation + + + align:start position:0% +but alternate derivation +Einstein imagines a box a sealed box + + align:start position:0% +Einstein imagines a box a sealed box + + + align:start position:0% +Einstein imagines a box a sealed box +that's moving at some constant speed V + + align:start position:0% +that's moving at some constant speed V + + + align:start position:0% +that's moving at some constant speed V +just moving otherwise in isolation it's + + align:start position:0% +just moving otherwise in isolation it's + + + align:start position:0% +just moving otherwise in isolation it's +in constant speed + + align:start position:0% +in constant speed + + + align:start position:0% +in constant speed +in the middle of its journey two bursts + + align:start position:0% +in the middle of its journey two bursts + + + align:start position:0% +in the middle of its journey two bursts +of radiation of equal amounts of moving + + align:start position:0% +of radiation of equal amounts of moving + + + align:start position:0% +of radiation of equal amounts of moving +in opposite directions are emitted by + + align:start position:0% +in opposite directions are emitted by + + + align:start position:0% +in opposite directions are emitted by +that box + + align:start position:0% +that box + + + align:start position:0% +that box +so the Box emits the total amount of + + align:start position:0% +so the Box emits the total amount of + + + align:start position:0% +so the Box emits the total amount of +energy in the form of light waves + + align:start position:0% +energy in the form of light waves + + + align:start position:0% +energy in the form of light waves +radiation total energy e half the energy + + align:start position:0% +radiation total energy e half the energy + + + align:start position:0% +radiation total energy e half the energy +carried off in One Direction half in the + + align:start position:0% +carried off in One Direction half in the + + + align:start position:0% +carried off in One Direction half in the +other now because the momentum carried + + align:start position:0% +other now because the momentum carried + + + align:start position:0% +other now because the momentum carried +by that radiation is equal and opposite + + align:start position:0% +by that radiation is equal and opposite + + + align:start position:0% +by that radiation is equal and opposite +he argues it has no impact on the speed + + align:start position:0% +he argues it has no impact on the speed + + + align:start position:0% +he argues it has no impact on the speed +with which the box is moving right the + + align:start position:0% +with which the box is moving right the + + + align:start position:0% +with which the box is moving right the +momentum The Recoil from the emission in + + align:start position:0% +momentum The Recoil from the emission in + + + align:start position:0% +momentum The Recoil from the emission in +one side is exactly balanced by The + + align:start position:0% +one side is exactly balanced by The + + + align:start position:0% +one side is exactly balanced by The +Recoil from the emission and the other + + align:start position:0% +Recoil from the emission and the other + + + align:start position:0% +Recoil from the emission and the other +side so the boxes motion is unchanged + + align:start position:0% +side so the boxes motion is unchanged + + + align:start position:0% +side so the boxes motion is unchanged +even its velocity is unchanged even as + + align:start position:0% +even its velocity is unchanged even as + + + align:start position:0% +even its velocity is unchanged even as +it emits a total energy e in the form of + + align:start position:0% +it emits a total energy e in the form of + + + align:start position:0% +it emits a total energy e in the form of +radiation and then just keeps speeding + + align:start position:0% +radiation and then just keeps speeding + + + align:start position:0% +radiation and then just keeps speeding +along its way well Einstein argues again + + align:start position:0% +along its way well Einstein argues again + + + align:start position:0% +along its way well Einstein argues again +it only takes three pages in the journal + + align:start position:0% +it only takes three pages in the journal + + + align:start position:0% +it only takes three pages in the journal +that the kinetic energy of the Box must + + align:start position:0% +that the kinetic energy of the Box must + + + align:start position:0% +that the kinetic energy of the Box must +have changed we have to conserve total + + align:start position:0% +have changed we have to conserve total + + + align:start position:0% +have changed we have to conserve total +energy it has given up an energy e in + + align:start position:0% +energy it has given up an energy e in + + + align:start position:0% +energy it has given up an energy e in +the form of this radiation but its speed + + align:start position:0% +the form of this radiation but its speed + + + align:start position:0% +the form of this radiation but its speed +hasn't changed so what must have changed + + align:start position:0% +hasn't changed so what must have changed + + + align:start position:0% +hasn't changed so what must have changed +it's Mass if we imagine starting with + + align:start position:0% +it's Mass if we imagine starting with + + + align:start position:0% +it's Mass if we imagine starting with +the kinetic energy of the Box one-half + + align:start position:0% +the kinetic energy of the Box one-half + + + align:start position:0% +the kinetic energy of the Box one-half +MV squared he's convinced himself that V + + align:start position:0% +MV squared he's convinced himself that V + + + align:start position:0% +MV squared he's convinced himself that V +hasn't changed + + align:start position:0% +hasn't changed + + + align:start position:0% +hasn't changed +you have the kinetic energy of this of + + align:start position:0% +you have the kinetic energy of this of + + + align:start position:0% +you have the kinetic energy of this of +the Box must have been reduced by some + + align:start position:0% +the Box must have been reduced by some + + + align:start position:0% +the Box must have been reduced by some +amount e the only thing that could have + + align:start position:0% +amount e the only thing that could have + + + align:start position:0% +amount e the only thing that could have +changed was the mass of the box + + align:start position:0% +changed was the mass of the box + + + align:start position:0% +changed was the mass of the box +so he argues he actually has a brief + + align:start position:0% +so he argues he actually has a brief + + + align:start position:0% +so he argues he actually has a brief +calculation that some amount of mass of + + align:start position:0% +calculation that some amount of mass of + + + align:start position:0% +calculation that some amount of mass of +a box has been converted into the energy + + align:start position:0% +a box has been converted into the energy + + + align:start position:0% +a box has been converted into the energy +carried off by the radiation how much + + align:start position:0% +carried off by the radiation how much + + + align:start position:0% +carried off by the radiation how much +mass e divided by c squared and in fact + + align:start position:0% +mass e divided by c squared and in fact + + + align:start position:0% +mass e divided by c squared and in fact +if you do a little more work uh for uh + + align:start position:0% +if you do a little more work uh for uh + + + align:start position:0% +if you do a little more work uh for uh +for arbitrary speeds V that are not just + + align:start position:0% +for arbitrary speeds V that are not just + + + align:start position:0% +for arbitrary speeds V that are not just +small compared to the speed of light in + + align:start position:0% +small compared to the speed of light in + + + align:start position:0% +small compared to the speed of light in +fact the expression is gamma m c squared + + align:start position:0% +fact the expression is gamma m c squared + + + align:start position:0% +fact the expression is gamma m c squared +and again I go through that a little bit + + align:start position:0% +and again I go through that a little bit + + + align:start position:0% +and again I go through that a little bit +more detail in the lecture notes the + + align:start position:0% +more detail in the lecture notes the + + + align:start position:0% +more detail in the lecture notes the +point is this is the kind of three-page + + align:start position:0% +point is this is the kind of three-page + + + align:start position:0% +point is this is the kind of three-page +afterthought they submit to the + + align:start position:0% +afterthought they submit to the + + + align:start position:0% +afterthought they submit to the +underlying the Physique in September of + + align:start position:0% +underlying the Physique in September of + + + align:start position:0% +underlying the Physique in September of +1905 in the context of his work on the + + align:start position:0% +1905 in the context of his work on the + + + align:start position:0% +1905 in the context of his work on the +electronomics and moving bodies that he + + align:start position:0% +electronomics and moving bodies that he + + + align:start position:0% +electronomics and moving bodies that he +submitted in June let me pause here any + + align:start position:0% +submitted in June let me pause here any + + + align:start position:0% +submitted in June let me pause here any +questions on how Einstein's approaching + + align:start position:0% +questions on how Einstein's approaching + + + align:start position:0% +questions on how Einstein's approaching +this quite familiar question of um + + align:start position:0% +this quite familiar question of um + + + align:start position:0% +this quite familiar question of um +electronomics and moving bodies + + align:start position:0% + + + + align:start position:0% + +I see D.A asks in the chat + + align:start position:0% +I see D.A asks in the chat + + + align:start position:0% +I see D.A asks in the chat +the guy says early papers have improper + + align:start position:0% +the guy says early papers have improper + + + align:start position:0% +the guy says early papers have improper +citations well they had + + align:start position:0% +citations well they had + + + align:start position:0% +citations well they had +that's a good question I haven't rewrite + + align:start position:0% +that's a good question I haven't rewrite + + + align:start position:0% +that's a good question I haven't rewrite +his early papers in quite a long time he + + align:start position:0% +his early papers in quite a long time he + + + align:start position:0% +his early papers in quite a long time he +was never overly generous in these years + + align:start position:0% +was never overly generous in these years + + + align:start position:0% +was never overly generous in these years +he wasn't oversighted so that's true + + align:start position:0% +he wasn't oversighted so that's true + + + align:start position:0% +he wasn't oversighted so that's true +even from his articles from the very + + align:start position:0% +even from his articles from the very + + + align:start position:0% +even from his articles from the very +early uh 1900s + + align:start position:0% +early uh 1900s + + + align:start position:0% +early uh 1900s +I don't know that they were quite as + + align:start position:0% +I don't know that they were quite as + + + align:start position:0% +I don't know that they were quite as +bereft of relevant citations as as this + + align:start position:0% +bereft of relevant citations as as this + + + align:start position:0% +bereft of relevant citations as as this +nitro5 paper was + + align:start position:0% +nitro5 paper was + + + align:start position:0% +nitro5 paper was +in his early ones frankly were probably + + align:start position:0% +in his early ones frankly were probably + + + align:start position:0% +in his early ones frankly were probably +a little more + + align:start position:0% +a little more + + + align:start position:0% +a little more +conscientious because it was his first + + align:start position:0% +conscientious because it was his first + + + align:start position:0% +conscientious because it was his first +set of papers they were going to be he + + align:start position:0% +set of papers they were going to be he + + + align:start position:0% +set of papers they were going to be he +would have assumed they would have been + + align:start position:0% +would have assumed they would have been + + + align:start position:0% +would have assumed they would have been +subjected to more careful scrutiny and + + align:start position:0% +subjected to more careful scrutiny and + + + align:start position:0% +subjected to more careful scrutiny and +review uh so it wouldn't surprise me if + + align:start position:0% +review uh so it wouldn't surprise me if + + + align:start position:0% +review uh so it wouldn't surprise me if +he was a bit more conscientious inciting + + align:start position:0% +he was a bit more conscientious inciting + + + align:start position:0% +he was a bit more conscientious inciting +uh work but it's a good question we can + + align:start position:0% +uh work but it's a good question we can + + + align:start position:0% +uh work but it's a good question we can +look him up his papers are now easily + + align:start position:0% +look him up his papers are now easily + + + align:start position:0% +look him up his papers are now easily +available uh thanks to an international + + align:start position:0% +available uh thanks to an international + + + align:start position:0% +available uh thanks to an international +team of Scholars in something called the + + align:start position:0% +team of Scholars in something called the + + + align:start position:0% +team of Scholars in something called the +collected papers of Albert Einstein uh + + align:start position:0% +collected papers of Albert Einstein uh + + + align:start position:0% +collected papers of Albert Einstein uh +and so I don't know that's a good + + align:start position:0% +and so I don't know that's a good + + + align:start position:0% +and so I don't know that's a good +question I have to go back + + align:start position:0% +question I have to go back + + + align:start position:0% +question I have to go back +um how would you just got the advantage + + align:start position:0% +um how would you just got the advantage + + + align:start position:0% +um how would you just got the advantage +of History over the leading through the + + align:start position:0% +of History over the leading through the + + + align:start position:0% +of History over the leading through the +time silhou asks that's a great question + + align:start position:0% +time silhou asks that's a great question + + + align:start position:0% +time silhou asks that's a great question +so I'm going to actually pause on that + + align:start position:0% +so I'm going to actually pause on that + + + align:start position:0% +so I'm going to actually pause on that +because we're going to look a lot of + + align:start position:0% +because we're going to look a lot of + + + align:start position:0% +because we're going to look a lot of +that exact question uh in the in the + + align:start position:0% +that exact question uh in the in the + + + align:start position:0% +that exact question uh in the in the +next lecture so it's one thing for us to + + align:start position:0% +next lecture so it's one thing for us to + + + align:start position:0% +next lecture so it's one thing for us to +ask today do we think it's better or not + + align:start position:0% +ask today do we think it's better or not + + + align:start position:0% +ask today do we think it's better or not +as good + + align:start position:0% +as good + + + align:start position:0% +as good +and we can vote and so on have our have + + align:start position:0% +and we can vote and so on have our have + + + align:start position:0% +and we can vote and so on have our have +our our ideas about that I think it's a + + align:start position:0% +our our ideas about that I think it's a + + + align:start position:0% +our our ideas about that I think it's a +separate question I think it's more like + + align:start position:0% +separate question I think it's more like + + + align:start position:0% +separate question I think it's more like +what you're uh maybe what you're after + + align:start position:0% +what you're uh maybe what you're after + + + align:start position:0% +what you're uh maybe what you're after +how did experts at the time evaluate + + align:start position:0% +how did experts at the time evaluate + + + align:start position:0% +how did experts at the time evaluate +this work what did they think was novel + + align:start position:0% +this work what did they think was novel + + + align:start position:0% +this work what did they think was novel +about it did they care did they uh + + align:start position:0% +about it did they care did they uh + + + align:start position:0% +about it did they care did they uh +consider this an important Improvement + + align:start position:0% +consider this an important Improvement + + + align:start position:0% +consider this an important Improvement +and we'll look at that early reception + + align:start position:0% +and we'll look at that early reception + + + align:start position:0% +and we'll look at that early reception +uh really for the entire class next + + align:start position:0% +uh really for the entire class next + + + align:start position:0% +uh really for the entire class next +round + + align:start position:0% +round + + + align:start position:0% +round +Jade asks why was the mass energy + + align:start position:0% +Jade asks why was the mass energy + + + align:start position:0% +Jade asks why was the mass energy +equivalents included in the paper on + + align:start position:0% +equivalents included in the paper on + + + align:start position:0% +equivalents included in the paper on +electrons moving bodies oh good that's a + + align:start position:0% +electrons moving bodies oh good that's a + + + align:start position:0% +electrons moving bodies oh good that's a +good question Jane So Einstein came at + + align:start position:0% +good question Jane So Einstein came at + + + align:start position:0% +good question Jane So Einstein came at +that because he was still thinking about + + align:start position:0% +that because he was still thinking about + + + align:start position:0% +that because he was still thinking about +this motion of radiation the way that + + align:start position:0% +this motion of radiation the way that + + + align:start position:0% +this motion of radiation the way that +different observers would handle the + + align:start position:0% +different observers would handle the + + + align:start position:0% +different observers would handle the +question of the radiation of light + + align:start position:0% +question of the radiation of light + + + align:start position:0% +question of the radiation of light +this was light being emitted from a + + align:start position:0% +this was light being emitted from a + + + align:start position:0% +this was light being emitted from a +moving Source right this is us sitting + + align:start position:0% +moving Source right this is us sitting + + + align:start position:0% +moving Source right this is us sitting +at rest washing a box move past us at + + align:start position:0% +at rest washing a box move past us at + + + align:start position:0% +at rest washing a box move past us at +some constant speed emitting light that + + align:start position:0% +some constant speed emitting light that + + + align:start position:0% +some constant speed emitting light that +was in the in the rubric of the day that + + align:start position:0% +was in the in the rubric of the day that + + + align:start position:0% +was in the in the rubric of the day that +was an example of the electronomics of + + align:start position:0% +was an example of the electronomics of + + + align:start position:0% +was an example of the electronomics of +moving bodies the emission of + + align:start position:0% +moving bodies the emission of + + + align:start position:0% +moving bodies the emission of +electromagnetic radiation as seen from a + + align:start position:0% +electromagnetic radiation as seen from a + + + align:start position:0% +electromagnetic radiation as seen from a +reference frame different from our own + + align:start position:0% +reference frame different from our own + + + align:start position:0% +reference frame different from our own +so in that sense it fit within the + + align:start position:0% +so in that sense it fit within the + + + align:start position:0% +so in that sense it fit within the +rubric I said they made use of some + + align:start position:0% +rubric I said they made use of some + + + align:start position:0% +rubric I said they made use of some +particular relations he had derived in + + align:start position:0% +particular relations he had derived in + + + align:start position:0% +particular relations he had derived in +his longer paper on the electronomics + + align:start position:0% +his longer paper on the electronomics + + + align:start position:0% +his longer paper on the electronomics +and moving bodies but Verizon at first + + align:start position:0% +and moving bodies but Verizon at first + + + align:start position:0% +and moving bodies but Verizon at first +it really came from thinking about how a + + align:start position:0% +it really came from thinking about how a + + + align:start position:0% +it really came from thinking about how a +different observers observers in + + align:start position:0% +different observers observers in + + + align:start position:0% +different observers observers in +different states of motion characterize + + align:start position:0% +different states of motion characterize + + + align:start position:0% +different states of motion characterize +this radiation from a source that was + + align:start position:0% +this radiation from a source that was + + + align:start position:0% +this radiation from a source that was +either moving with respect to them or + + align:start position:0% +either moving with respect to them or + + + align:start position:0% +either moving with respect to them or +not he later comes to argue this is + + align:start position:0% +not he later comes to argue this is + + + align:start position:0% +not he later comes to argue this is +actually quite General it's not + + align:start position:0% +actually quite General it's not + + + align:start position:0% +actually quite General it's not +restricted to light waves or radiation + + align:start position:0% +restricted to light waves or radiation + + + align:start position:0% +restricted to light waves or radiation +at all but really even about + + align:start position:0% +at all but really even about + + + align:start position:0% +at all but really even about +electronomics he comes to see this as a + + align:start position:0% +electronomics he comes to see this as a + + + align:start position:0% +electronomics he comes to see this as a +very very general + + align:start position:0% +very very general + + + align:start position:0% +very very general +um uh relation but it comes to it + + align:start position:0% +um uh relation but it comes to it + + + align:start position:0% +um uh relation but it comes to it +originally from very directly from this + + align:start position:0% +originally from very directly from this + + + align:start position:0% +originally from very directly from this +work on electrodynamics and moving + + align:start position:0% +work on electrodynamics and moving + + + align:start position:0% +work on electrodynamics and moving +properties good question + + align:start position:0% +properties good question + + + align:start position:0% +properties good question +any other questions on that now we can + + align:start position:0% +any other questions on that now we can + + + align:start position:0% +any other questions on that now we can +turn to that to the last part for today + + align:start position:0% + + + + align:start position:0% + +so let's talk about Einstein and + + align:start position:0% +so let's talk about Einstein and + + + align:start position:0% +so let's talk about Einstein and +experiment and something like + + align:start position:0% +experiment and something like + + + align:start position:0% +experiment and something like +engineering practice + + align:start position:0% +engineering practice + + + align:start position:0% +engineering practice +for a long long time really from from + + align:start position:0% +for a long long time really from from + + + align:start position:0% +for a long long time really from from +early in the 20th century once + + align:start position:0% +early in the 20th century once + + + align:start position:0% +early in the 20th century once +Einstein's work did become known and + + align:start position:0% +Einstein's work did become known and + + + align:start position:0% +Einstein's work did become known and +celebrated and then scrutinized + + align:start position:0% + + + + align:start position:0% + +pardon me + + align:start position:0% +pardon me + + + align:start position:0% +pardon me +for a long time there was a a tradition + + align:start position:0% +for a long time there was a a tradition + + + align:start position:0% +for a long time there was a a tradition +by scientists by philosophers by + + align:start position:0% +by scientists by philosophers by + + + align:start position:0% +by scientists by philosophers by +historians by many kinds of Scholars + + align:start position:0% +historians by many kinds of Scholars + + + align:start position:0% +historians by many kinds of Scholars +a tradition of trying to read Einstein's + + align:start position:0% +a tradition of trying to read Einstein's + + + align:start position:0% +a tradition of trying to read Einstein's +paper from 1905 as some sort of direct + + align:start position:0% +paper from 1905 as some sort of direct + + + align:start position:0% +paper from 1905 as some sort of direct +response + + align:start position:0% +response + + + align:start position:0% +response +to to the null result of the Michelson + + align:start position:0% +to to the null result of the Michelson + + + align:start position:0% +to to the null result of the Michelson +experiment + + align:start position:0% +experiment + + + align:start position:0% +experiment +and so let's say the fact that Michaels + + align:start position:0% +and so let's say the fact that Michaels + + + align:start position:0% +and so let's say the fact that Michaels +and Marley could not find any + + align:start position:0% +and Marley could not find any + + + align:start position:0% +and Marley could not find any +measurable effects of our motion to The + + align:start position:0% +measurable effects of our motion to The + + + align:start position:0% +measurable effects of our motion to The +Ether must the argument had gone must + + align:start position:0% +Ether must the argument had gone must + + + align:start position:0% +Ether must the argument had gone must +have convinced Einstein to then get rid + + align:start position:0% +have convinced Einstein to then get rid + + + align:start position:0% +have convinced Einstein to then get rid +of The Ether because they've been + + align:start position:0% +of The Ether because they've been + + + align:start position:0% +of The Ether because they've been +somehow empirically disproven + + align:start position:0% +somehow empirically disproven + + + align:start position:0% +somehow empirically disproven +and that was really the kind of + + align:start position:0% +and that was really the kind of + + + align:start position:0% +and that was really the kind of +conventional way of trying to make sense + + align:start position:0% +conventional way of trying to make sense + + + align:start position:0% +conventional way of trying to make sense +of Einstein's own work on the + + align:start position:0% +of Einstein's own work on the + + + align:start position:0% +of Einstein's own work on the +electronomics of moving bodies + + align:start position:0% +electronomics of moving bodies + + + align:start position:0% +electronomics of moving bodies +there's a really quite amazing + + align:start position:0% +there's a really quite amazing + + + align:start position:0% +there's a really quite amazing +um critical review of that line of + + align:start position:0% +um critical review of that line of + + + align:start position:0% +um critical review of that line of +thought in this book uh by Gerald Holton + + align:start position:0% +thought in this book uh by Gerald Holton + + + align:start position:0% +thought in this book uh by Gerald Holton +Professor Holton is a retired uh + + align:start position:0% +Professor Holton is a retired uh + + + align:start position:0% +Professor Holton is a retired uh +professor at Harvard he was a member of + + align:start position:0% +professor at Harvard he was a member of + + + align:start position:0% +professor at Harvard he was a member of +both the physics department and the + + align:start position:0% +both the physics department and the + + + align:start position:0% +both the physics department and the +history science department and he wrote + + align:start position:0% +history science department and he wrote + + + align:start position:0% +history science department and he wrote +this really iconic quite lovely + + align:start position:0% +this really iconic quite lovely + + + align:start position:0% +this really iconic quite lovely +collection of essays it was first + + align:start position:0% +collection of essays it was first + + + align:start position:0% +collection of essays it was first +published uh through well the essays + + align:start position:0% +published uh through well the essays + + + align:start position:0% +published uh through well the essays +were published throughout the 1950s and + + align:start position:0% +were published throughout the 1950s and + + + align:start position:0% +were published throughout the 1950s and +60s the book pulled together in the + + align:start position:0% +60s the book pulled together in the + + + align:start position:0% +60s the book pulled together in the +early 70s still in print it's a lovely + + align:start position:0% +early 70s still in print it's a lovely + + + align:start position:0% +early 70s still in print it's a lovely +book + + align:start position:0% +book + + + align:start position:0% +book +and Halton argues I think really quite + + align:start position:0% +and Halton argues I think really quite + + + align:start position:0% +and Halton argues I think really quite +persuasively that this reading of + + align:start position:0% +persuasively that this reading of + + + align:start position:0% +persuasively that this reading of +Einstein as somehow responding + + align:start position:0% +Einstein as somehow responding + + + align:start position:0% +Einstein as somehow responding +consciously and directly to this + + align:start position:0% +consciously and directly to this + + + align:start position:0% +consciously and directly to this +Michaelson more the null result has + + align:start position:0% +Michaelson more the null result has + + + align:start position:0% +Michaelson more the null result has +almost no uh basis in fact in fact it's + + align:start position:0% +almost no uh basis in fact in fact it's + + + align:start position:0% +almost no uh basis in fact in fact it's +not clear whether Einstein even knew + + align:start position:0% +not clear whether Einstein even knew + + + align:start position:0% +not clear whether Einstein even knew +about the micro simulator results at the + + align:start position:0% +about the micro simulator results at the + + + align:start position:0% +about the micro simulator results at the +time if he did he seemed pretty + + align:start position:0% +time if he did he seemed pretty + + + align:start position:0% +time if he did he seemed pretty +unconcerned about them they did not seem + + align:start position:0% +unconcerned about them they did not seem + + + align:start position:0% +unconcerned about them they did not seem +to play any major role in his thinking + + align:start position:0% +to play any major role in his thinking + + + align:start position:0% +to play any major role in his thinking +that's an important distinction from + + align:start position:0% +that's an important distinction from + + + align:start position:0% +that's an important distinction from +people like Lorenz like George + + align:start position:0% +people like Lorenz like George + + + align:start position:0% +people like Lorenz like George +Fitzgerald or like others or we've + + align:start position:0% +Fitzgerald or like others or we've + + + align:start position:0% +Fitzgerald or like others or we've +mentioned + + align:start position:0% +mentioned + + + align:start position:0% +mentioned +plenty of people in Europe at the time + + align:start position:0% +plenty of people in Europe at the time + + + align:start position:0% +plenty of people in Europe at the time +were very concerned about the Michaelson + + align:start position:0% +were very concerned about the Michaelson + + + align:start position:0% +were very concerned about the Michaelson +Morley results Einstein seems not to + + align:start position:0% +Morley results Einstein seems not to + + + align:start position:0% +Morley results Einstein seems not to +have been one of them he might literally + + align:start position:0% +have been one of them he might literally + + + align:start position:0% +have been one of them he might literally +have not even heard about it yet or if + + align:start position:0% +have not even heard about it yet or if + + + align:start position:0% +have not even heard about it yet or if +he did he didn't pay much attention we + + align:start position:0% +he did he didn't pay much attention we + + + align:start position:0% +he did he didn't pay much attention we +get some textual evidence just by + + align:start position:0% +get some textual evidence just by + + + align:start position:0% +get some textual evidence just by +looking carefully at Einstein's paper + + align:start position:0% +looking carefully at Einstein's paper + + + align:start position:0% +looking carefully at Einstein's paper +itself this is again in the excerpt that + + align:start position:0% +itself this is again in the excerpt that + + + align:start position:0% +itself this is again in the excerpt that +you had for today + + align:start position:0% +you had for today + + + align:start position:0% +you had for today +right in the early early part of the + + align:start position:0% +right in the early early part of the + + + align:start position:0% +right in the early early part of the +paper he talks about what he calls + + align:start position:0% +paper he talks about what he calls + + + align:start position:0% +paper he talks about what he calls +unsuccessful attempts to discover any + + align:start position:0% +unsuccessful attempts to discover any + + + align:start position:0% +unsuccessful attempts to discover any +motion of the Earth relative to the + + align:start position:0% +motion of the Earth relative to the + + + align:start position:0% +motion of the Earth relative to the +light medium either they've all been + + align:start position:0% +light medium either they've all been + + + align:start position:0% +light medium either they've all been +unsuccessful + + align:start position:0% +unsuccessful + + + align:start position:0% +unsuccessful +and he's talking about quantity there + + align:start position:0% +and he's talking about quantity there + + + align:start position:0% +and he's talking about quantity there +the quantities of the first order say + + align:start position:0% +the quantities of the first order say + + + align:start position:0% +the quantities of the first order say +it's a quantity to to excuse me to the + + align:start position:0% +it's a quantity to to excuse me to the + + + align:start position:0% +it's a quantity to to excuse me to the +ratio V over C to the first Power one of + + align:start position:0% +ratio V over C to the first Power one of + + + align:start position:0% +ratio V over C to the first Power one of +the things that was so exciting to + + align:start position:0% +the things that was so exciting to + + + align:start position:0% +the things that was so exciting to +people about the Michaelson Memorial + + align:start position:0% +people about the Michaelson Memorial + + + align:start position:0% +people about the Michaelson Memorial +experiment was actually sensitive to + + align:start position:0% +experiment was actually sensitive to + + + align:start position:0% +experiment was actually sensitive to +quantities of the second order so + + align:start position:0% +quantities of the second order so + + + align:start position:0% +quantities of the second order so +Einstein is not only not citing a source + + align:start position:0% +Einstein is not only not citing a source + + + align:start position:0% +Einstein is not only not citing a source +it's telling us which particular + + align:start position:0% +it's telling us which particular + + + align:start position:0% +it's telling us which particular +experiments he had in mind which were + + align:start position:0% +experiments he had in mind which were + + + align:start position:0% +experiments he had in mind which were +these unsuccessful attempts to measure + + align:start position:0% +these unsuccessful attempts to measure + + + align:start position:0% +these unsuccessful attempts to measure +any motion the Earth relative to The + + align:start position:0% +any motion the Earth relative to The + + + align:start position:0% +any motion the Earth relative to The +Ether + + align:start position:0% +Ether + + + align:start position:0% +Ether +he's dismissing his entire class of + + align:start position:0% +he's dismissing his entire class of + + + align:start position:0% +he's dismissing his entire class of +first order experiments of which there + + align:start position:0% +first order experiments of which there + + + align:start position:0% +first order experiments of which there +were many fresnel aberration and so on + + align:start position:0% +were many fresnel aberration and so on + + + align:start position:0% +were many fresnel aberration and so on +he's not even talking about second order + + align:start position:0% +he's not even talking about second order + + + align:start position:0% +he's not even talking about second order +experiments let alone uh mentioning more + + align:start position:0% +experiments let alone uh mentioning more + + + align:start position:0% +experiments let alone uh mentioning more +specifically the Michaelson World + + align:start position:0% +specifically the Michaelson World + + + align:start position:0% +specifically the Michaelson World +experiment so Holton uh I think makes a + + align:start position:0% +experiment so Holton uh I think makes a + + + align:start position:0% +experiment so Holton uh I think makes a +pretty compelling argument that whatever + + align:start position:0% +pretty compelling argument that whatever + + + align:start position:0% +pretty compelling argument that whatever +Einstein was doing it was probably not + + align:start position:0% +Einstein was doing it was probably not + + + align:start position:0% +Einstein was doing it was probably not +responding in any kind of self-conscious + + align:start position:0% +responding in any kind of self-conscious + + + align:start position:0% +responding in any kind of self-conscious +careful direct way to the Michaelson + + align:start position:0% +careful direct way to the Michaelson + + + align:start position:0% +careful direct way to the Michaelson +Morely no result + + align:start position:0% +Morely no result + + + align:start position:0% +Morely no result +now that was sometimes taken by other + + align:start position:0% +now that was sometimes taken by other + + + align:start position:0% +now that was sometimes taken by other +people Downstream even from Professor + + align:start position:0% +people Downstream even from Professor + + + align:start position:0% +people Downstream even from Professor +holton's work to suggest that eiseng was + + align:start position:0% +holton's work to suggest that eiseng was + + + align:start position:0% +holton's work to suggest that eiseng was +somehow uninterested in experiments + + align:start position:0% +somehow uninterested in experiments + + + align:start position:0% +somehow uninterested in experiments +altogether and that seems like not + + align:start position:0% +altogether and that seems like not + + + align:start position:0% +altogether and that seems like not +correct either that's a kind of over + + align:start position:0% +correct either that's a kind of over + + + align:start position:0% +correct either that's a kind of over +interpretation of this question that's + + align:start position:0% +interpretation of this question that's + + + align:start position:0% +interpretation of this question that's +more specifically about Michaelson and + + align:start position:0% +more specifically about Michaelson and + + + align:start position:0% +more specifically about Michaelson and +Worley + + align:start position:0% +Worley + + + align:start position:0% +Worley +so so here's where this article by Peter + + align:start position:0% +so so here's where this article by Peter + + + align:start position:0% +so so here's where this article by Peter +gals and really drawn from from a from a + + align:start position:0% +gals and really drawn from from a from a + + + align:start position:0% +gals and really drawn from from a from a +really fascinating book that's why I + + align:start position:0% +really fascinating book that's why I + + + align:start position:0% +really fascinating book that's why I +think Allison's work can help put us + + align:start position:0% +think Allison's work can help put us + + + align:start position:0% +think Allison's work can help put us +back into Einstein's very specific world + + align:start position:0% +back into Einstein's very specific world + + + align:start position:0% +back into Einstein's very specific world +to his context to the things he really + + align:start position:0% +to his context to the things he really + + + align:start position:0% +to his context to the things he really +was concerned about and sometimes even + + align:start position:0% +was concerned about and sometimes even + + + align:start position:0% +was concerned about and sometimes even +quite obsessed about in the years and + + align:start position:0% +quite obsessed about in the years and + + + align:start position:0% +quite obsessed about in the years and +months and days and weeks leading up to + + align:start position:0% +months and days and weeks leading up to + + + align:start position:0% +months and days and weeks leading up to +his work on the electronomics of moving + + align:start position:0% +his work on the electronomics of moving + + + align:start position:0% +his work on the electronomics of moving +bodies and a lot of it has to do with + + align:start position:0% +bodies and a lot of it has to do with + + + align:start position:0% +bodies and a lot of it has to do with +things that we've already talked about + + align:start position:0% +things that we've already talked about + + + align:start position:0% +things that we've already talked about +things like train travel which he really + + align:start position:0% +things like train travel which he really + + + align:start position:0% +things like train travel which he really +really was enamored + + align:start position:0% +really was enamored + + + align:start position:0% +really was enamored +so until the late 19th century during + + align:start position:0% +so until the late 19th century during + + + align:start position:0% +so until the late 19th century during +Einstein's own childhood in fact + + align:start position:0% +Einstein's own childhood in fact + + + align:start position:0% +Einstein's own childhood in fact +there were no coordinated time zones we + + align:start position:0% +there were no coordinated time zones we + + + align:start position:0% +there were no coordinated time zones we +now know about time zones very well we + + align:start position:0% +now know about time zones very well we + + + align:start position:0% +now know about time zones very well we +have to navigate them carefully with + + align:start position:0% +have to navigate them carefully with + + + align:start position:0% +have to navigate them carefully with +these you know our asynchronous Zoom + + align:start position:0% +these you know our asynchronous Zoom + + + align:start position:0% +these you know our asynchronous Zoom +sessions and all the rest but even into + + align:start position:0% +sessions and all the rest but even into + + + align:start position:0% +sessions and all the rest but even into +Einstein's own childhood there were no + + align:start position:0% +Einstein's own childhood there were no + + + align:start position:0% +Einstein's own childhood there were no +coordinated time zones each Town kept + + align:start position:0% +coordinated time zones each Town kept + + + align:start position:0% +coordinated time zones each Town kept +its own local time based usually on a + + align:start position:0% +its own local time based usually on a + + + align:start position:0% +its own local time based usually on a +clock in its Town Square basically make + + align:start position:0% +clock in its Town Square basically make + + + align:start position:0% +clock in its Town Square basically make +sure an easily visible clock that + + align:start position:0% +sure an easily visible clock that + + + align:start position:0% +sure an easily visible clock that +everyone could sort of see and agree on + + align:start position:0% +everyone could sort of see and agree on + + + align:start position:0% +everyone could sort of see and agree on +that would set time and you set your + + align:start position:0% +that would set time and you set your + + + align:start position:0% +that would set time and you set your +watch based on the sort of highest Clock + + align:start position:0% +watch based on the sort of highest Clock + + + align:start position:0% +watch based on the sort of highest Clock +Tower in your town + + align:start position:0% +Tower in your town + + + align:start position:0% +Tower in your town +uh and so and there were these clock + + align:start position:0% +uh and so and there were these clock + + + align:start position:0% +uh and so and there were these clock +towers all over the place including of + + align:start position:0% +towers all over the place including of + + + align:start position:0% +towers all over the place including of +course the places like train stations or + + align:start position:0% +course the places like train stations or + + + align:start position:0% +course the places like train stations or +churches or other other tall buildings + + align:start position:0% +churches or other other tall buildings + + + align:start position:0% +churches or other other tall buildings +so and that wasn't true only in Europe + + align:start position:0% +so and that wasn't true only in Europe + + + align:start position:0% +so and that wasn't true only in Europe +that was also true in North America so + + align:start position:0% +that was also true in North America so + + + align:start position:0% +that was also true in North America so +for example in this time period + + align:start position:0% +for example in this time period + + + align:start position:0% +for example in this time period +passengers riding the train between + + align:start position:0% +passengers riding the train between + + + align:start position:0% +passengers riding the train between +Boston and New York City had to change + + align:start position:0% +Boston and New York City had to change + + + align:start position:0% +Boston and New York City had to change +their watches on average from about 37 + + align:start position:0% +their watches on average from about 37 + + + align:start position:0% +their watches on average from about 37 +minutes after the trip because the kind + + align:start position:0% +minutes after the trip because the kind + + + align:start position:0% +minutes after the trip because the kind +of there was no long distance + + align:start position:0% +of there was no long distance + + + align:start position:0% +of there was no long distance +coordination for clock uh for for for + + align:start position:0% +coordination for clock uh for for for + + + align:start position:0% +coordination for clock uh for for for +time so what we would have called 12 + + align:start position:0% +time so what we would have called 12 + + + align:start position:0% +time so what we would have called 12 +noon in Boston was off by on average + + align:start position:0% +noon in Boston was off by on average + + + align:start position:0% +noon in Boston was off by on average +more than half an hour compared to what + + align:start position:0% +more than half an hour compared to what + + + align:start position:0% +more than half an hour compared to what +would have been called noon in New York + + align:start position:0% +would have been called noon in New York + + + align:start position:0% +would have been called noon in New York +City and vice versa + + align:start position:0% +City and vice versa + + + align:start position:0% +City and vice versa +now that was true already starting you + + align:start position:0% +now that was true already starting you + + + align:start position:0% +now that was true already starting you +know from the earliest days of rail + + align:start position:0% +know from the earliest days of rail + + + align:start position:0% +know from the earliest days of rail +travel this became an especially + + align:start position:0% +travel this became an especially + + + align:start position:0% +travel this became an especially +pressing concern one that now had both + + align:start position:0% +pressing concern one that now had both + + + align:start position:0% +pressing concern one that now had both +commercial and soon military concerns + + align:start position:0% +commercial and soon military concerns + + + align:start position:0% +commercial and soon military concerns +for people like um uh General vanlanca + + align:start position:0% +for people like um uh General vanlanca + + + align:start position:0% +for people like um uh General vanlanca +uh in on the newly unified Germany you + + align:start position:0% +uh in on the newly unified Germany you + + + align:start position:0% +uh in on the newly unified Germany you +may remember we I mentioned briefly + + align:start position:0% +may remember we I mentioned briefly + + + align:start position:0% +may remember we I mentioned briefly +before uh Germany was actually a + + align:start position:0% +before uh Germany was actually a + + + align:start position:0% +before uh Germany was actually a +collection of separate kind of um + + align:start position:0% +collection of separate kind of um + + + align:start position:0% +collection of separate kind of um +there was no country of Germany it was a + + align:start position:0% +there was no country of Germany it was a + + + align:start position:0% +there was no country of Germany it was a +bunch of separate german-speaking lands + + align:start position:0% +bunch of separate german-speaking lands + + + align:start position:0% +bunch of separate german-speaking lands +until unified into a single country of + + align:start position:0% +until unified into a single country of + + + align:start position:0% +until unified into a single country of +Germany in 1871 right on the heels of + + align:start position:0% +Germany in 1871 right on the heels of + + + align:start position:0% +Germany in 1871 right on the heels of +its war with France in 1870. + + align:start position:0% +its war with France in 1870. + + + align:start position:0% +its war with France in 1870. +and as one of the leading military + + align:start position:0% +and as one of the leading military + + + align:start position:0% +and as one of the leading military +leaders from that uh it was elevated to + + align:start position:0% +leaders from that uh it was elevated to + + + align:start position:0% +leaders from that uh it was elevated to +accounts became a he was like knighted + + align:start position:0% +accounts became a he was like knighted + + + align:start position:0% +accounts became a he was like knighted +essentially count from malka is + + align:start position:0% +essentially count from malka is + + + align:start position:0% +essentially count from malka is +recounting why it was so important in + + align:start position:0% +recounting why it was so important in + + + align:start position:0% +recounting why it was so important in +this new system of a single unified + + align:start position:0% +this new system of a single unified + + + align:start position:0% +this new system of a single unified +Germany to pay closer attention to how + + align:start position:0% +Germany to pay closer attention to how + + + align:start position:0% +Germany to pay closer attention to how +we coordinate time and this is now take + + align:start position:0% +we coordinate time and this is now take + + + align:start position:0% +we coordinate time and this is now take +a quotation that I learned from Peter + + align:start position:0% +a quotation that I learned from Peter + + + align:start position:0% +a quotation that I learned from Peter +gauss's articles in your reading he says + + align:start position:0% +gauss's articles in your reading he says + + + align:start position:0% +gauss's articles in your reading he says +that Unity of time is indispensable for + + align:start position:0% +that Unity of time is indispensable for + + + align:start position:0% +that Unity of time is indispensable for +the satisfactory operating of Railways + + align:start position:0% +the satisfactory operating of Railways + + + align:start position:0% +the satisfactory operating of Railways +that's now universally recognized it's + + align:start position:0% +that's now universally recognized it's + + + align:start position:0% +that's now universally recognized it's +not disputed but my Gentleman Monahan we + + align:start position:0% +not disputed but my Gentleman Monahan we + + + align:start position:0% +not disputed but my Gentleman Monahan we +have in Germany five different units of + + align:start position:0% +have in Germany five different units of + + + align:start position:0% +have in Germany five different units of +time we have in Germany five zones with + + align:start position:0% +time we have in Germany five zones with + + + align:start position:0% +time we have in Germany five zones with +all the drawbacks and disadvantages + + align:start position:0% +all the drawbacks and disadvantages + + + align:start position:0% +all the drawbacks and disadvantages +which result there's no Nationwide + + align:start position:0% +which result there's no Nationwide + + + align:start position:0% +which result there's no Nationwide +coordination + + align:start position:0% +coordination + + + align:start position:0% +coordination +these have uh in those these we have in + + align:start position:0% +these have uh in those these we have in + + + align:start position:0% +these have uh in those these we have in +our own Fatherland besides those we + + align:start position:0% +our own Fatherland besides those we + + + align:start position:0% +our own Fatherland besides those we +dread to meet at the French and Russian + + align:start position:0% +dread to meet at the French and Russian + + + align:start position:0% +dread to meet at the French and Russian +board as we dread because those were + + align:start position:0% +board as we dread because those were + + + align:start position:0% +board as we dread because those were +sites of recent War this is I must say a + + align:start position:0% +sites of recent War this is I must say a + + + align:start position:0% +sites of recent War this is I must say a +ruin which has remained standing out of + + align:start position:0% +ruin which has remained standing out of + + + align:start position:0% +ruin which has remained standing out of +the one splintered condition of a + + align:start position:0% +the one splintered condition of a + + + align:start position:0% +the one splintered condition of a +Germany when it wasn't yet a unified + + align:start position:0% +Germany when it wasn't yet a unified + + + align:start position:0% +Germany when it wasn't yet a unified +country but which since we had become an + + align:start position:0% +country but which since we had become an + + + align:start position:0% +country but which since we had become an +Empire it is proper should be done away + + align:start position:0% +Empire it is proper should be done away + + + align:start position:0% +Empire it is proper should be done away +with we need to coordinate clocks at a + + align:start position:0% +with we need to coordinate clocks at a + + + align:start position:0% +with we need to coordinate clocks at a +distance and as I say this was + + align:start position:0% +distance and as I say this was + + + align:start position:0% +distance and as I say this was +especially relevant after the recent war + + align:start position:0% +especially relevant after the recent war + + + align:start position:0% +especially relevant after the recent war +with France that led to the unification + + align:start position:0% +with France that led to the unification + + + align:start position:0% +with France that led to the unification +of a single country of Germany this is + + align:start position:0% +of a single country of Germany this is + + + align:start position:0% +of a single country of Germany this is +all happening literally in Einstein's + + align:start position:0% +all happening literally in Einstein's + + + align:start position:0% +all happening literally in Einstein's +childhood remember Einstein was born in + + align:start position:0% +childhood remember Einstein was born in + + + align:start position:0% +childhood remember Einstein was born in +1879 the country into which he was born + + align:start position:0% +1879 the country into which he was born + + + align:start position:0% +1879 the country into which he was born +itself was actually quite new + + align:start position:0% +itself was actually quite new + + + align:start position:0% +itself was actually quite new +so one of the main ideas that a lot of + + align:start position:0% +so one of the main ideas that a lot of + + + align:start position:0% +so one of the main ideas that a lot of +Engineers and scientists were working on + + align:start position:0% +Engineers and scientists were working on + + + align:start position:0% +Engineers and scientists were working on +throughout Central Europe not just uh in + + align:start position:0% +throughout Central Europe not just uh in + + + align:start position:0% +throughout Central Europe not just uh in +Germany was to install what became known + + align:start position:0% +Germany was to install what became known + + + align:start position:0% +Germany was to install what became known +as mother clock's Mutual clock and to + + align:start position:0% +as mother clock's Mutual clock and to + + + align:start position:0% +as mother clock's Mutual clock and to +install them in central train stations + + align:start position:0% +install them in central train stations + + + align:start position:0% +install them in central train stations +connected to other Clocks by way of + + align:start position:0% +connected to other Clocks by way of + + + align:start position:0% +connected to other Clocks by way of +electromagnetic signals either Telegraph + + align:start position:0% +electromagnetic signals either Telegraph + + + align:start position:0% +electromagnetic signals either Telegraph +or increasingly radio waves this is what + + align:start position:0% +or increasingly radio waves this is what + + + align:start position:0% +or increasingly radio waves this is what +Peter gaussen wrote about in his really + + align:start position:0% +Peter gaussen wrote about in his really + + + align:start position:0% +Peter gaussen wrote about in his really +quite lovely book is science clocks + + align:start position:0% +quite lovely book is science clocks + + + align:start position:0% +quite lovely book is science clocks +progress maps and of course the reading + + align:start position:0% +progress maps and of course the reading + + + align:start position:0% +progress maps and of course the reading +we had today Peter's article is kind of + + align:start position:0% +we had today Peter's article is kind of + + + align:start position:0% +we had today Peter's article is kind of +draws on that larger body + + align:start position:0% +draws on that larger body + + + align:start position:0% +draws on that larger body +and so some of you may know the Eiffel + + align:start position:0% +and so some of you may know the Eiffel + + + align:start position:0% +and so some of you may know the Eiffel +Tower in Paris was under construction + + align:start position:0% +Tower in Paris was under construction + + + align:start position:0% +Tower in Paris was under construction +around 1910 one of the earliest uses for + + align:start position:0% +around 1910 one of the earliest uses for + + + align:start position:0% +around 1910 one of the earliest uses for +that was not only to draw American + + align:start position:0% +that was not only to draw American + + + align:start position:0% +that was not only to draw American +tourists that wasn't such a bad + + align:start position:0% +tourists that wasn't such a bad + + + align:start position:0% +tourists that wasn't such a bad +outcome either for the French but it was + + align:start position:0% +outcome either for the French but it was + + + align:start position:0% +outcome either for the French but it was +actually to serve as a transmitting + + align:start position:0% +actually to serve as a transmitting + + + align:start position:0% +actually to serve as a transmitting +tower for radio waves in part to + + align:start position:0% +tower for radio waves in part to + + + align:start position:0% +tower for radio waves in part to +transmit clock coordination signals it + + align:start position:0% +transmit clock coordination signals it + + + align:start position:0% +transmit clock coordination signals it +was one of the standardizing beacons to + + align:start position:0% +was one of the standardizing beacons to + + + align:start position:0% +was one of the standardizing beacons to +send out Standard time it is now 12 noon + + align:start position:0% +send out Standard time it is now 12 noon + + + align:start position:0% +send out Standard time it is now 12 noon +and beam that out by electromagnetic + + align:start position:0% +and beam that out by electromagnetic + + + align:start position:0% +and beam that out by electromagnetic +signal + + align:start position:0% +signal + + + align:start position:0% +signal +other uh municipalities we're laying + + align:start position:0% +other uh municipalities we're laying + + + align:start position:0% +other uh municipalities we're laying +Telegraph uh lines or stringing above + + align:start position:0% +Telegraph uh lines or stringing above + + + align:start position:0% +Telegraph uh lines or stringing above +ground Telegraph cable + + align:start position:0% +ground Telegraph cable + + + align:start position:0% +ground Telegraph cable +um to do the same thing to connect + + align:start position:0% +um to do the same thing to connect + + + align:start position:0% +um to do the same thing to connect +especially kind of main hubs on this now + + align:start position:0% +especially kind of main hubs on this now + + + align:start position:0% +especially kind of main hubs on this now +um uh Intercity rail system so they + + align:start position:0% +um uh Intercity rail system so they + + + align:start position:0% +um uh Intercity rail system so they +could coordinate trains uh clock signals + + align:start position:0% +could coordinate trains uh clock signals + + + align:start position:0% +could coordinate trains uh clock signals +even uh across the entire expanse of the + + align:start position:0% +even uh across the entire expanse of the + + + align:start position:0% +even uh across the entire expanse of the +continent + + align:start position:0% +continent + + + align:start position:0% +continent +uh and so every single part of these new + + align:start position:0% +uh and so every single part of these new + + + align:start position:0% +uh and so every single part of these new +systems uh were subject to patent claims + + align:start position:0% +systems uh were subject to patent claims + + + align:start position:0% +systems uh were subject to patent claims +this is exactly what isil was immersed + + align:start position:0% +this is exactly what isil was immersed + + + align:start position:0% +this is exactly what isil was immersed +in I was talking with some students + + align:start position:0% +in I was talking with some students + + + align:start position:0% +in I was talking with some students +before uh the class really began this + + align:start position:0% +before uh the class really began this + + + align:start position:0% +before uh the class really began this +afternoon + + align:start position:0% +afternoon + + + align:start position:0% +afternoon +it's really quite extraordinary Peter + + align:start position:0% +it's really quite extraordinary Peter + + + align:start position:0% +it's really quite extraordinary Peter +writes about this a bit in his book + + align:start position:0% +writes about this a bit in his book + + + align:start position:0% +writes about this a bit in his book +there was a rule at the baron patent + + align:start position:0% +there was a rule at the baron patent + + + align:start position:0% +there was a rule at the baron patent +office where Einstein was patented off + + align:start position:0% +office where Einstein was patented off + + + align:start position:0% +office where Einstein was patented off +as a third class uh that any records any + + align:start position:0% +as a third class uh that any records any + + + align:start position:0% +as a third class uh that any records any +unpublished records regarding the review + + align:start position:0% +unpublished records regarding the review + + + align:start position:0% +unpublished records regarding the review +of patent Applications had to be + + align:start position:0% +of patent Applications had to be + + + align:start position:0% +of patent Applications had to be +destroyed after some passenger time a + + align:start position:0% +destroyed after some passenger time a + + + align:start position:0% +destroyed after some passenger time a +couple decades and so they wound up + + align:start position:0% +couple decades and so they wound up + + + align:start position:0% +couple decades and so they wound up +destroying even the stuff that Einstein + + align:start position:0% +destroying even the stuff that Einstein + + + align:start position:0% +destroying even the stuff that Einstein +had served as a principal examiner on so + + align:start position:0% +had served as a principal examiner on so + + + align:start position:0% +had served as a principal examiner on so +we have very few Clues as to the very + + align:start position:0% +we have very few Clues as to the very + + + align:start position:0% +we have very few Clues as to the very +specific patents on which Einstein would + + align:start position:0% +specific patents on which Einstein would + + + align:start position:0% +specific patents on which Einstein would +have served as the lead examiner what we + + align:start position:0% +have served as the lead examiner what we + + + align:start position:0% +have served as the lead examiner what we +do know however what Peter makes Mary + + align:start position:0% +do know however what Peter makes Mary + + + align:start position:0% +do know however what Peter makes Mary +good use of in his study are the patents + + align:start position:0% +good use of in his study are the patents + + + align:start position:0% +good use of in his study are the patents +that were issued from that patent office + + align:start position:0% +that were issued from that patent office + + + align:start position:0% +that were issued from that patent office +in various years we also know that + + align:start position:0% +in various years we also know that + + + align:start position:0% +in various years we also know that +Einstein was working on the so-called + + align:start position:0% +Einstein was working on the so-called + + + align:start position:0% +Einstein was working on the so-called +Electro technical desk in particular so + + align:start position:0% +Electro technical desk in particular so + + + align:start position:0% +Electro technical desk in particular so +it's sort of all but unavoidable to + + align:start position:0% +it's sort of all but unavoidable to + + + align:start position:0% +it's sort of all but unavoidable to +conclude that Einstein was examining at + + align:start position:0% +conclude that Einstein was examining at + + + align:start position:0% +conclude that Einstein was examining at +least some of these gadgets along the + + align:start position:0% +least some of these gadgets along the + + + align:start position:0% +least some of these gadgets along the +way which exact was we don't know we do + + align:start position:0% +way which exact was we don't know we do + + + align:start position:0% +way which exact was we don't know we do +know from the volume of patents being + + align:start position:0% +know from the volume of patents being + + + align:start position:0% +know from the volume of patents being +applied for and the kinds of work being + + align:start position:0% +applied for and the kinds of work being + + + align:start position:0% +applied for and the kinds of work being +done + + align:start position:0% +done + + + align:start position:0% +done +that this was very much a a major + + align:start position:0% +that this was very much a a major + + + align:start position:0% +that this was very much a a major +concern at in the baron patent office as + + align:start position:0% +concern at in the baron patent office as + + + align:start position:0% +concern at in the baron patent office as +well as other parts of Europe Peter goes + + align:start position:0% +well as other parts of Europe Peter goes + + + align:start position:0% +well as other parts of Europe Peter goes +on this is my one of my favorite + + align:start position:0% +on this is my one of my favorite + + + align:start position:0% +on this is my one of my favorite +examples uh he he actually was able to + + align:start position:0% +examples uh he he actually was able to + + + align:start position:0% +examples uh he he actually was able to +reconstruct from Einstein's + + align:start position:0% +reconstruct from Einstein's + + + align:start position:0% +reconstruct from Einstein's +correspondence the walking path that + + align:start position:0% +correspondence the walking path that + + + align:start position:0% +correspondence the walking path that +Einstein would have taken between his + + align:start position:0% +Einstein would have taken between his + + + align:start position:0% +Einstein would have taken between his +apartment and Baron and his office at + + align:start position:0% +apartment and Baron and his office at + + + align:start position:0% +apartment and Baron and his office at +the patent office and here you see this + + align:start position:0% +the patent office and here you see this + + + align:start position:0% +the patent office and here you see this +map of all of the newly coordinated + + align:start position:0% +map of all of the newly coordinated + + + align:start position:0% +map of all of the newly coordinated +clocks literally dotting the line of the + + align:start position:0% +clocks literally dotting the line of the + + + align:start position:0% +clocks literally dotting the line of the +path along which Einstein would have + + align:start position:0% +path along which Einstein would have + + + align:start position:0% +path along which Einstein would have +walked they would have just recently + + align:start position:0% +walked they would have just recently + + + align:start position:0% +walked they would have just recently +been connected by these Telegraph and + + align:start position:0% +been connected by these Telegraph and + + + align:start position:0% +been connected by these Telegraph and +our radio signal methods to say that + + align:start position:0% +our radio signal methods to say that + + + align:start position:0% +our radio signal methods to say that +when you receive this electromagnetic + + align:start position:0% +when you receive this electromagnetic + + + align:start position:0% +when you receive this electromagnetic +signal that means it's 12 noon at the + + align:start position:0% +signal that means it's 12 noon at the + + + align:start position:0% +signal that means it's 12 noon at the +mother clock uh Implement an appropriate + + align:start position:0% +mother clock uh Implement an appropriate + + + align:start position:0% +mother clock uh Implement an appropriate +offset to take into account your + + align:start position:0% +offset to take into account your + + + align:start position:0% +offset to take into account your +distance from that mother clock and the + + align:start position:0% +distance from that mother clock and the + + + align:start position:0% +distance from that mother clock and the +speed of light so we know the nice I was + + align:start position:0% +speed of light so we know the nice I was + + + align:start position:0% +speed of light so we know the nice I was +literally immersed in these kinds of + + align:start position:0% +literally immersed in these kinds of + + + align:start position:0% +literally immersed in these kinds of +things even on his walk to work let + + align:start position:0% +things even on his walk to work let + + + align:start position:0% +things even on his walk to work let +alone at his patent desk + + align:start position:0% +alone at his patent desk + + + align:start position:0% +alone at his patent desk +so we come back to this very strange + + align:start position:0% +so we come back to this very strange + + + align:start position:0% +so we come back to this very strange +looking paper submitted to the + + align:start position:0% +looking paper submitted to the + + + align:start position:0% +looking paper submitted to the +underlying the physique uh in June of + + align:start position:0% +underlying the physique uh in June of + + + align:start position:0% +underlying the physique uh in June of +1905 on the electronomics and moving + + align:start position:0% +1905 on the electronomics and moving + + + align:start position:0% +1905 on the electronomics and moving +bodies again as I've mentioned many + + align:start position:0% +bodies again as I've mentioned many + + + align:start position:0% +bodies again as I've mentioned many +times the title sounds quite + + align:start position:0% +times the title sounds quite + + + align:start position:0% +times the title sounds quite +conventional the approach seems anything + + align:start position:0% +conventional the approach seems anything + + + align:start position:0% +conventional the approach seems anything +but conventional in terms of ordinary + + align:start position:0% +but conventional in terms of ordinary + + + align:start position:0% +but conventional in terms of ordinary +physics articles of the day of its of + + align:start position:0% +physics articles of the day of its of + + + align:start position:0% +physics articles of the day of its of +their own days let alone of our of our + + align:start position:0% +their own days let alone of our of our + + + align:start position:0% +their own days let alone of our of our +day today + + align:start position:0% +day today + + + align:start position:0% +day today +and yet if we think of this as the work + + align:start position:0% +and yet if we think of this as the work + + + align:start position:0% +and yet if we think of this as the work +of a patent clerk who's obsessed who's + + align:start position:0% +of a patent clerk who's obsessed who's + + + align:start position:0% +of a patent clerk who's obsessed who's +sort of enamored with this new + + align:start position:0% +sort of enamored with this new + + + align:start position:0% +sort of enamored with this new +technological stuff maybe begins to make + + align:start position:0% +technological stuff maybe begins to make + + + align:start position:0% +technological stuff maybe begins to make +a little more sense the lack of + + align:start position:0% +a little more sense the lack of + + + align:start position:0% +a little more sense the lack of +references might not only have been + + align:start position:0% +references might not only have been + + + align:start position:0% +references might not only have been +Einstein being lazy or uncharitable it + + align:start position:0% +Einstein being lazy or uncharitable it + + + align:start position:0% +Einstein being lazy or uncharitable it +also could be a way to emphasize + + align:start position:0% +also could be a way to emphasize + + + align:start position:0% +also could be a way to emphasize +priority and downplay precedence much + + align:start position:0% +priority and downplay precedence much + + + align:start position:0% +priority and downplay precedence much +like one would have to do uh to to get a + + align:start position:0% +like one would have to do uh to to get a + + + align:start position:0% +like one would have to do uh to to get a +patent I mean this is actually novel + + align:start position:0% +patent I mean this is actually novel + + + align:start position:0% +patent I mean this is actually novel +compared to what has done what was done + + align:start position:0% +compared to what has done what was done + + + align:start position:0% +compared to what has done what was done +before + + align:start position:0% +before + + + align:start position:0% +before +it was a very close focus on what we + + align:start position:0% +it was a very close focus on what we + + + align:start position:0% +it was a very close focus on what we +might call the operational details how + + align:start position:0% +might call the operational details how + + + align:start position:0% +might call the operational details how +would we really measure distances of + + align:start position:0% +would we really measure distances of + + + align:start position:0% +would we really measure distances of +space and time how would we actually + + align:start position:0% +space and time how would we actually + + + align:start position:0% +space and time how would we actually +coordinate our clocks if we're not uh + + align:start position:0% +coordinate our clocks if we're not uh + + + align:start position:0% +coordinate our clocks if we're not uh +right next to each other if we have some + + align:start position:0% +right next to each other if we have some + + + align:start position:0% +right next to each other if we have some +uh intervening state of motion how would + + align:start position:0% +uh intervening state of motion how would + + + align:start position:0% +uh intervening state of motion how would +you step by step establish things like + + align:start position:0% +you step by step establish things like + + + align:start position:0% +you step by step establish things like +clock coordination taking advantage of + + align:start position:0% +clock coordination taking advantage of + + + align:start position:0% +clock coordination taking advantage of +the exchange of electromagnetic signals + + align:start position:0% +the exchange of electromagnetic signals + + + align:start position:0% +the exchange of electromagnetic signals +it begins to look a bit more like a + + align:start position:0% +it begins to look a bit more like a + + + align:start position:0% +it begins to look a bit more like a +patent application and less like an + + align:start position:0% +patent application and less like an + + + align:start position:0% +patent application and less like an +exercise in mathematical physics of the + + align:start position:0% +exercise in mathematical physics of the + + + align:start position:0% +exercise in mathematical physics of the +sort that Hendrick Lorenz or others had + + align:start position:0% +sort that Hendrick Lorenz or others had + + + align:start position:0% +sort that Hendrick Lorenz or others had +done so that's what I that's the main + + align:start position:0% +done so that's what I that's the main + + + align:start position:0% +done so that's what I that's the main +takeaway uh that I keep in mind at least + + align:start position:0% +takeaway uh that I keep in mind at least + + + align:start position:0% +takeaway uh that I keep in mind at least +from Peter gallison's article and book + + align:start position:0% +from Peter gallison's article and book + + + align:start position:0% +from Peter gallison's article and book +and we can pause there + + align:start position:0% +and we can pause there + + + align:start position:0% +and we can pause there +and again I'll ask if there any + + align:start position:0% +and again I'll ask if there any + + + align:start position:0% +and again I'll ask if there any +questions + + align:start position:0% + + + + align:start position:0% + +so uh Babu Abba says I noticed the paper + + align:start position:0% +so uh Babu Abba says I noticed the paper + + + align:start position:0% +so uh Babu Abba says I noticed the paper +began with saying the Michael experience + + align:start position:0% +began with saying the Michael experience + + + align:start position:0% +began with saying the Michael experience +was a prerequisite uh that's certainly + + align:start position:0% +was a prerequisite uh that's certainly + + + align:start position:0% +was a prerequisite uh that's certainly +not by Einstein so it depends on which + + align:start position:0% +not by Einstein so it depends on which + + + align:start position:0% +not by Einstein so it depends on which +translation you're looking at it's true + + align:start position:0% +translation you're looking at it's true + + + align:start position:0% +translation you're looking at it's true +that later editors including Arnold + + align:start position:0% +that later editors including Arnold + + + align:start position:0% +that later editors including Arnold +Somerville who actually made the first + + align:start position:0% +Somerville who actually made the first + + + align:start position:0% +Somerville who actually made the first +trans one of the first translations + + align:start position:0% +trans one of the first translations + + + align:start position:0% +trans one of the first translations +or one of the first adaptations one of + + align:start position:0% +or one of the first adaptations one of + + + align:start position:0% +or one of the first adaptations one of +the first annotations many later editors + + align:start position:0% +the first annotations many later editors + + + align:start position:0% +the first annotations many later editors +have put stuff onto Einstein's paper and + + align:start position:0% +have put stuff onto Einstein's paper and + + + align:start position:0% +have put stuff onto Einstein's paper and +they're usually marked carefully with + + align:start position:0% +they're usually marked carefully with + + + align:start position:0% +they're usually marked carefully with +with footnotes in some of the uh + + align:start position:0% +with footnotes in some of the uh + + + align:start position:0% +with footnotes in some of the uh +translations it gets a little cluttered + + align:start position:0% +translations it gets a little cluttered + + + align:start position:0% +translations it gets a little cluttered +as to who put that footnote in so if + + align:start position:0% +as to who put that footnote in so if + + + align:start position:0% +as to who put that footnote in so if +you're a little careful so so Baba webel + + align:start position:0% +you're a little careful so so Baba webel + + + align:start position:0% +you're a little careful so so Baba webel +I I'm quite confident that whatever + + align:start position:0% +I I'm quite confident that whatever + + + align:start position:0% +I I'm quite confident that whatever +footnote you you have in mind was one of + + align:start position:0% +footnote you you have in mind was one of + + + align:start position:0% +footnote you you have in mind was one of +these later editions from a well-meaning + + align:start position:0% +these later editions from a well-meaning + + + align:start position:0% +these later editions from a well-meaning +editor or someone who thought they were + + align:start position:0% +editor or someone who thought they were + + + align:start position:0% +editor or someone who thought they were +helping to clarify but in fact was sort + + align:start position:0% +helping to clarify but in fact was sort + + + align:start position:0% +helping to clarify but in fact was sort +of falling into this what becomes now a + + align:start position:0% +of falling into this what becomes now a + + + align:start position:0% +of falling into this what becomes now a +kind of historical + + align:start position:0% +kind of historical + + + align:start position:0% +kind of historical +um trap so if we go back to the auto the + + align:start position:0% +um trap so if we go back to the auto the + + + align:start position:0% +um trap so if we go back to the auto the +physique itself or some of the more bare + + align:start position:0% +physique itself or some of the more bare + + + align:start position:0% +physique itself or some of the more bare +translations for example from the + + align:start position:0% +translations for example from the + + + align:start position:0% +translations for example from the +Einstein papers project the collected + + align:start position:0% +Einstein papers project the collected + + + align:start position:0% +Einstein papers project the collected +papers now but I'd sign them now the + + align:start position:0% +papers now but I'd sign them now the + + + align:start position:0% +papers now but I'd sign them now the +kind of industry Standard Version we can + + align:start position:0% +kind of industry Standard Version we can + + + align:start position:0% +kind of industry Standard Version we can +go very clearly what was exactly in + + align:start position:0% +go very clearly what was exactly in + + + align:start position:0% +go very clearly what was exactly in +Einstein's first published version and + + align:start position:0% +Einstein's first published version and + + + align:start position:0% +Einstein's first published version and +what was sort of added by later + + align:start position:0% +what was sort of added by later + + + align:start position:0% +what was sort of added by later +well-meaning but later editors + + align:start position:0% +well-meaning but later editors + + + align:start position:0% +well-meaning but later editors +uh so it's a good point thank you for + + align:start position:0% +uh so it's a good point thank you for + + + align:start position:0% +uh so it's a good point thank you for +raising Stanley asks + + align:start position:0% +raising Stanley asks + + + align:start position:0% +raising Stanley asks +um can we explain again why station + + align:start position:0% +um can we explain again why station + + + align:start position:0% +um can we explain again why station +Observer measures the length of moving + + align:start position:0% +Observer measures the length of moving + + + align:start position:0% +Observer measures the length of moving +trying to be smaller yeah very good + + align:start position:0% +trying to be smaller yeah very good + + + align:start position:0% +trying to be smaller yeah very good +because the different Notions + + align:start position:0% +because the different Notions + + + align:start position:0% +because the different Notions +simultaneously it's a great question + + align:start position:0% +simultaneously it's a great question + + + align:start position:0% +simultaneously it's a great question +Sammy uh it's worth sitting with this a + + align:start position:0% +Sammy uh it's worth sitting with this a + + + align:start position:0% +Sammy uh it's worth sitting with this a +little bit longer + + align:start position:0% + + + + align:start position:0% + +let me preview by saying we're going to + + align:start position:0% +let me preview by saying we're going to + + + align:start position:0% +let me preview by saying we're going to +come back to that in the in the in the + + align:start position:0% +come back to that in the in the in the + + + align:start position:0% +come back to that in the in the in the +next class session as well to consider + + align:start position:0% +next class session as well to consider + + + align:start position:0% +next class session as well to consider +not how Einstein himself made sense of + + align:start position:0% +not how Einstein himself made sense of + + + align:start position:0% +not how Einstein himself made sense of +that by how by how some later people + + align:start position:0% +that by how by how some later people + + + align:start position:0% +that by how by how some later people +wrestling with Einstein's work made + + align:start position:0% +wrestling with Einstein's work made + + + align:start position:0% +wrestling with Einstein's work made +sense of things like length contraction + + align:start position:0% +sense of things like length contraction + + + align:start position:0% +sense of things like length contraction +so this is not the last time we'll see + + align:start position:0% +so this is not the last time we'll see + + + align:start position:0% +so this is not the last time we'll see +it even even in this class + + align:start position:0% +it even even in this class + + + align:start position:0% +it even even in this class +but how did Einstein argue uh what did I + + align:start position:0% +but how did Einstein argue uh what did I + + + align:start position:0% +but how did Einstein argue uh what did I +argue was the origin of length + + align:start position:0% +argue was the origin of length + + + align:start position:0% +argue was the origin of length +contraction + + align:start position:0% +contraction + + + align:start position:0% +contraction +that was very clearly says the The Ether + + align:start position:0% +that was very clearly says the The Ether + + + align:start position:0% +that was very clearly says the The Ether +will be merely Superfluous he's going to + + align:start position:0% +will be merely Superfluous he's going to + + + align:start position:0% +will be merely Superfluous he's going to +not talk about a physical medium that's + + align:start position:0% +not talk about a physical medium that's + + + align:start position:0% +not talk about a physical medium that's +going to exert forces the way Lorenz did + + align:start position:0% +going to exert forces the way Lorenz did + + + align:start position:0% +going to exert forces the way Lorenz did +about that like squeezed beach ball + + align:start position:0% +about that like squeezed beach ball + + + align:start position:0% +about that like squeezed beach ball +for Einstein it's all about how we + + align:start position:0% +for Einstein it's all about how we + + + align:start position:0% +for Einstein it's all about how we +perform the measurement that kind of + + align:start position:0% +perform the measurement that kind of + + + align:start position:0% +perform the measurement that kind of +mock-like operation or how do you + + align:start position:0% +mock-like operation or how do you + + + align:start position:0% +mock-like operation or how do you +perform a measurement so he says here's + + align:start position:0% +perform a measurement so he says here's + + + align:start position:0% +perform a measurement so he says here's +how you perform a measurement of length + + align:start position:0% +how you perform a measurement of length + + + align:start position:0% +how you perform a measurement of length +or distance measure the front of the + + align:start position:0% +or distance measure the front of the + + + align:start position:0% +or distance measure the front of the +train and the back of the train at the + + align:start position:0% +train and the back of the train at the + + + align:start position:0% +train and the back of the train at the +same time and subtract take the + + align:start position:0% +same time and subtract take the + + + align:start position:0% +same time and subtract take the +difference + + align:start position:0% +difference + + + align:start position:0% +difference +so if we're at rest with respect to the + + align:start position:0% +so if we're at rest with respect to the + + + align:start position:0% +so if we're at rest with respect to the +object that's not very challenging the + + align:start position:0% +object that's not very challenging the + + + align:start position:0% +object that's not very challenging the +train is at rest in the station we can + + align:start position:0% +train is at rest in the station we can + + + align:start position:0% +train is at rest in the station we can +leisurely measure the front of the + + align:start position:0% +leisurely measure the front of the + + + align:start position:0% +leisurely measure the front of the +position the front mark it off on the + + align:start position:0% +position the front mark it off on the + + + align:start position:0% +position the front mark it off on the +train platform legally Mark the back we + + align:start position:0% +train platform legally Mark the back we + + + align:start position:0% +train platform legally Mark the back we +can then take the difference and say + + align:start position:0% +can then take the difference and say + + + align:start position:0% +can then take the difference and say +okay the train is you know 25 meters + + align:start position:0% +okay the train is you know 25 meters + + + align:start position:0% +okay the train is you know 25 meters +long or whatever the answer might be + + align:start position:0% +long or whatever the answer might be + + + align:start position:0% +long or whatever the answer might be +what happens when we try to measure the + + align:start position:0% +what happens when we try to measure the + + + align:start position:0% +what happens when we try to measure the +movement the length of the moving trade + + align:start position:0% +movement the length of the moving trade + + + align:start position:0% +movement the length of the moving trade +uh when we watched the moving train we + + align:start position:0% +uh when we watched the moving train we + + + align:start position:0% +uh when we watched the moving train we +should measure the front of the train + + align:start position:0% +should measure the front of the train + + + align:start position:0% +should measure the front of the train +and the rear of the train Mark Mark + + align:start position:0% +and the rear of the train Mark Mark + + + align:start position:0% +and the rear of the train Mark Mark +those positions at the same time and + + align:start position:0% +those positions at the same time and + + + align:start position:0% +those positions at the same time and +subtract the problem is based on this + + align:start position:0% +subtract the problem is based on this + + + align:start position:0% +subtract the problem is based on this +argument about the exchange light + + align:start position:0% +argument about the exchange light + + + align:start position:0% +argument about the exchange light +signals we no longer agree on what + + align:start position:0% +signals we no longer agree on what + + + align:start position:0% +signals we no longer agree on what +counts as at the same time as the + + align:start position:0% +counts as at the same time as the + + + align:start position:0% +counts as at the same time as the +Observer on the moving train does so the + + align:start position:0% +Observer on the moving train does so the + + + align:start position:0% +Observer on the moving train does so the +Observer on the moving train watches us + + align:start position:0% +Observer on the moving train watches us + + + align:start position:0% +Observer on the moving train watches us +do this and watches us do things at + + align:start position:0% +do this and watches us do things at + + + align:start position:0% +do this and watches us do things at +different times because of our relative + + align:start position:0% +different times because of our relative + + + align:start position:0% +different times because of our relative +states of motion + + align:start position:0% +states of motion + + + align:start position:0% +states of motion +so we think we've been very careful + + align:start position:0% +so we think we've been very careful + + + align:start position:0% +so we think we've been very careful +measuring at the same time the locations + + align:start position:0% +measuring at the same time the locations + + + align:start position:0% +measuring at the same time the locations +front and back and taking the difference + + align:start position:0% +front and back and taking the difference + + + align:start position:0% +front and back and taking the difference +our our partner on the train says you + + align:start position:0% +our our partner on the train says you + + + align:start position:0% +our our partner on the train says you +measure the first the front of the train + + align:start position:0% +measure the first the front of the train + + + align:start position:0% +measure the first the front of the train +first + + align:start position:0% +first + + + align:start position:0% +first +and then you waited some time went by + + align:start position:0% +and then you waited some time went by + + + align:start position:0% +and then you waited some time went by +during which the train is sliding past + + align:start position:0% +during which the train is sliding past + + + align:start position:0% +during which the train is sliding past +and then you mark the position of the + + align:start position:0% +and then you mark the position of the + + + align:start position:0% +and then you mark the position of the +rear so you might so it's like an unfair + + align:start position:0% +rear so you might so it's like an unfair + + + align:start position:0% +rear so you might so it's like an unfair +measurement they watch us Mark the front + + align:start position:0% +measurement they watch us Mark the front + + + align:start position:0% +measurement they watch us Mark the front +of the train wait a while and then Mark + + align:start position:0% +of the train wait a while and then Mark + + + align:start position:0% +of the train wait a while and then Mark +the rear of the train after the train + + align:start position:0% +the rear of the train after the train + + + align:start position:0% +the rear of the train after the train +has moved so along the direction of + + align:start position:0% +has moved so along the direction of + + + align:start position:0% +has moved so along the direction of +motion of course we measure a shorter + + align:start position:0% +motion of course we measure a shorter + + + align:start position:0% +motion of course we measure a shorter +distance because they argue we messed up + + align:start position:0% +distance because they argue we messed up + + + align:start position:0% +distance because they argue we messed up +on the timing + + align:start position:0% +on the timing + + + align:start position:0% +on the timing +now we could say no no you're wrong we + + align:start position:0% +now we could say no no you're wrong we + + + align:start position:0% +now we could say no no you're wrong we +did it right because you know this and + + align:start position:0% +did it right because you know this and + + + align:start position:0% +did it right because you know this and +that and say no no I'm right because I + + align:start position:0% +that and say no no I'm right because I + + + align:start position:0% +that and say no no I'm right because I +have these light signals they were + + align:start position:0% +have these light signals they were + + + align:start position:0% +have these light signals they were +exchanged from my partner's A and B + + align:start position:0% +exchanged from my partner's A and B + + + align:start position:0% +exchanged from my partner's A and B +who is stationed at the front and rear + + align:start position:0% +who is stationed at the front and rear + + + align:start position:0% +who is stationed at the front and rear +of the train and I got the light signal + + align:start position:0% +of the train and I got the light signal + + + align:start position:0% +of the train and I got the light signal +from the person at the front of the + + align:start position:0% +from the person at the front of the + + + align:start position:0% +from the person at the front of the +train before I got the light signal for + + align:start position:0% +train before I got the light signal for + + + align:start position:0% +train before I got the light signal for +the person the back of the train so you + + align:start position:0% +the person the back of the train so you + + + align:start position:0% +the person the back of the train so you +can't tell me you are a simultaneous you + + align:start position:0% +can't tell me you are a simultaneous you + + + align:start position:0% +can't tell me you are a simultaneous you +messed up you were lazy you were too + + align:start position:0% +messed up you were lazy you were too + + + align:start position:0% +messed up you were lazy you were too +slow right you messed up + + align:start position:0% +slow right you messed up + + + align:start position:0% +slow right you messed up +and we can't say I'm right you're on we + + align:start position:0% +and we can't say I'm right you're on we + + + align:start position:0% +and we can't say I'm right you're on we +can but she can say it with with equal + + align:start position:0% +can but she can say it with with equal + + + align:start position:0% +can but she can say it with with equal +confidence and equal fervor that's what + + align:start position:0% +confidence and equal fervor that's what + + + align:start position:0% +confidence and equal fervor that's what +what Einstein wanted to get at by by + + align:start position:0% +what Einstein wanted to get at by by + + + align:start position:0% +what Einstein wanted to get at by by +pairing those two starting postulates + + align:start position:0% +pairing those two starting postulates + + + align:start position:0% +pairing those two starting postulates +that all the laws of physics including + + align:start position:0% +that all the laws of physics including + + + align:start position:0% +that all the laws of physics including +all the laws of mechanics electricity + + align:start position:0% +all the laws of mechanics electricity + + + align:start position:0% +all the laws of mechanics electricity +magnetism Optics thermodynamics all the + + align:start position:0% +magnetism Optics thermodynamics all the + + + align:start position:0% +magnetism Optics thermodynamics all the +laws of physics hold just as valid for + + align:start position:0% +laws of physics hold just as valid for + + + align:start position:0% +laws of physics hold just as valid for +our partner on the moving trade if she's + + align:start position:0% +our partner on the moving trade if she's + + + align:start position:0% +our partner on the moving trade if she's +not speeding up or slowing down if it's + + align:start position:0% +not speeding up or slowing down if it's + + + align:start position:0% +not speeding up or slowing down if it's +an inertial motion + + align:start position:0% +an inertial motion + + + align:start position:0% +an inertial motion +they hold just as valid for her as they + + align:start position:0% +they hold just as valid for her as they + + + align:start position:0% +they hold just as valid for her as they +do for us so she can appeal to things + + align:start position:0% +do for us so she can appeal to things + + + align:start position:0% +do for us so she can appeal to things +like the behavior of light signals the + + align:start position:0% +like the behavior of light signals the + + + align:start position:0% +like the behavior of light signals the +behavior of her clocks on board and so + + align:start position:0% +behavior of her clocks on board and so + + + align:start position:0% +behavior of her clocks on board and so +on and she very clearly unambiguously + + align:start position:0% +on and she very clearly unambiguously + + + align:start position:0% +on and she very clearly unambiguously +receives a light signal from the front + + align:start position:0% +receives a light signal from the front + + + align:start position:0% +receives a light signal from the front +of the train first and later from the + + align:start position:0% +of the train first and later from the + + + align:start position:0% +of the train first and later from the +rear of the train so therefore if these + + align:start position:0% +rear of the train so therefore if these + + + align:start position:0% +rear of the train so therefore if these +light signals were emitted at the moment + + align:start position:0% +light signals were emitted at the moment + + + align:start position:0% +light signals were emitted at the moment +people tried to measure the front and + + align:start position:0% +people tried to measure the front and + + + align:start position:0% +people tried to measure the front and +back of the train she said well you + + align:start position:0% +back of the train she said well you + + + align:start position:0% +back of the train she said well you +messed up you didn't get the timing + + align:start position:0% +messed up you didn't get the timing + + + align:start position:0% +messed up you didn't get the timing +right because you measure the front of + + align:start position:0% +right because you measure the front of + + + align:start position:0% +right because you measure the front of +the train and then sometime later you + + align:start position:0% +the train and then sometime later you + + + align:start position:0% +the train and then sometime later you +measure the rear of the train and in the + + align:start position:0% +measure the rear of the train and in the + + + align:start position:0% +measure the rear of the train and in the +intervening moments the train slid in + + align:start position:0% +intervening moments the train slid in + + + align:start position:0% +intervening moments the train slid in +that direction of motion so you measured + + align:start position:0% +that direction of motion so you measured + + + align:start position:0% +that direction of motion so you measured +um the wrong location of the rear + + align:start position:0% +um the wrong location of the rear + + + align:start position:0% +um the wrong location of the rear +because you measured the rear of the + + align:start position:0% +because you measured the rear of the + + + align:start position:0% +because you measured the rear of the +train at the wrong time + + align:start position:0% +train at the wrong time + + + align:start position:0% +train at the wrong time +uh so again if that's still not super + + align:start position:0% +uh so again if that's still not super + + + align:start position:0% +uh so again if that's still not super +clear go over the you know the slides + + align:start position:0% +clear go over the you know the slides + + + align:start position:0% +clear go over the you know the slides +the picture might help a little bit I'd + + align:start position:0% +the picture might help a little bit I'd + + + align:start position:0% +the picture might help a little bit I'd +be glad to chat more um during office + + align:start position:0% +be glad to chat more um during office + + + align:start position:0% +be glad to chat more um during office +hours as well but we'll also come to + + align:start position:0% +hours as well but we'll also come to + + + align:start position:0% +hours as well but we'll also come to +that again on Wednesdays seeing it from + + align:start position:0% +that again on Wednesdays seeing it from + + + align:start position:0% +that again on Wednesdays seeing it from +still a different perspective so if it + + align:start position:0% +still a different perspective so if it + + + align:start position:0% +still a different perspective so if it +still doesn't doesn't quite sit right + + align:start position:0% +still doesn't doesn't quite sit right + + + align:start position:0% +still doesn't doesn't quite sit right +it's okay uh we'll get another crack at + + align:start position:0% +it's okay uh we'll get another crack at + + + align:start position:0% +it's okay uh we'll get another crack at +it on Wednesday + + align:start position:0% + + + + align:start position:0% + +great yeah but thank you a very very + + align:start position:0% +great yeah but thank you a very very + + + align:start position:0% +great yeah but thank you a very very +good observation so I think the way + + align:start position:0% +good observation so I think the way + + + align:start position:0% +good observation so I think the way +Einstein would have uh reconciled those + + align:start position:0% +Einstein would have uh reconciled those + + + align:start position:0% +Einstein would have uh reconciled those +two is saying and we can always + + align:start position:0% +two is saying and we can always + + + align:start position:0% +two is saying and we can always +establish a coordinate system + + align:start position:0% +establish a coordinate system + + + align:start position:0% +establish a coordinate system +we can always say this is my reference + + align:start position:0% +we can always say this is my reference + + + align:start position:0% +we can always say this is my reference +frame with respect to which I measure + + align:start position:0% +frame with respect to which I measure + + + align:start position:0% +frame with respect to which I measure +the passage of time I sign some + + align:start position:0% +the passage of time I sign some + + + align:start position:0% +the passage of time I sign some +coordinate T he even tells us how to + + align:start position:0% +coordinate T he even tells us how to + + + align:start position:0% +coordinate T he even tells us how to +measure the time of an event when the + + align:start position:0% +measure the time of an event when the + + + align:start position:0% +measure the time of an event when the +train pulls in and my watch says seven + + align:start position:0% +train pulls in and my watch says seven + + + align:start position:0% +train pulls in and my watch says seven +right so we can always in fact we have + + align:start position:0% +right so we can always in fact we have + + + align:start position:0% +right so we can always in fact we have +to always establish our own coordinate + + align:start position:0% +to always establish our own coordinate + + + align:start position:0% +to always establish our own coordinate +system that's especially convenient for + + align:start position:0% +system that's especially convenient for + + + align:start position:0% +system that's especially convenient for +us let's say at rest with respect to our + + align:start position:0% +us let's say at rest with respect to our + + + align:start position:0% +us let's say at rest with respect to our +own motion + + align:start position:0% +own motion + + + align:start position:0% +own motion +we can't appeal to any real any true + + align:start position:0% +we can't appeal to any real any true + + + align:start position:0% +we can't appeal to any real any true +coordination or any absolute criticism + + align:start position:0% +coordination or any absolute criticism + + + align:start position:0% +coordination or any absolute criticism +because he argues there is no such thing + + align:start position:0% +because he argues there is no such thing + + + align:start position:0% +because he argues there is no such thing +but we that doesn't stop us from from + + align:start position:0% +but we that doesn't stop us from from + + + align:start position:0% +but we that doesn't stop us from from +laying out our own Corners we have to do + + align:start position:0% +laying out our own Corners we have to do + + + align:start position:0% +laying out our own Corners we have to do +that in fact we have no choice but to + + align:start position:0% +that in fact we have no choice but to + + + align:start position:0% +that in fact we have no choice but to +set up our own coordinates because + + align:start position:0% +set up our own coordinates because + + + align:start position:0% +set up our own coordinates because +there's no absolute system to which we + + align:start position:0% +there's no absolute system to which we + + + align:start position:0% +there's no absolute system to which we +can appeal + + align:start position:0% +can appeal + + + align:start position:0% +can appeal +so he's arguing in in the case of the + + align:start position:0% +so he's arguing in in the case of the + + + align:start position:0% +so he's arguing in in the case of the +clock coordination that all these + + align:start position:0% +clock coordination that all these + + + align:start position:0% +clock coordination that all these +locations down the line + + align:start position:0% +locations down the line + + + align:start position:0% +locations down the line +the the baron train station wasn't + + align:start position:0% +the the baron train station wasn't + + + align:start position:0% +the the baron train station wasn't +picking up and moving with respect to + + align:start position:0% +picking up and moving with respect to + + + align:start position:0% +picking up and moving with respect to +the Zurich train station we should be + + align:start position:0% +the Zurich train station we should be + + + align:start position:0% +the Zurich train station we should be +able to apply one set of coordinates to + + align:start position:0% +able to apply one set of coordinates to + + + align:start position:0% +able to apply one set of coordinates to +all those things across space + + align:start position:0% +all those things across space + + + align:start position:0% +all those things across space +but how do we get our time coordinates + + align:start position:0% +but how do we get our time coordinates + + + align:start position:0% +but how do we get our time coordinates +to line up we have to do a little more + + align:start position:0% +to line up we have to do a little more + + + align:start position:0% +to line up we have to do a little more +work because they can't appeal to + + align:start position:0% +work because they can't appeal to + + + align:start position:0% +work because they can't appeal to +Absolute time any more than we can right + + align:start position:0% +Absolute time any more than we can right + + + align:start position:0% +Absolute time any more than we can right +so we have to therefore find a mechanism + + align:start position:0% +so we have to therefore find a mechanism + + + align:start position:0% +so we have to therefore find a mechanism +find an operation According to which we + + align:start position:0% +find an operation According to which we + + + align:start position:0% +find an operation According to which we +can line up our own coordinates we can + + align:start position:0% +can line up our own coordinates we can + + + align:start position:0% +can line up our own coordinates we can +get our coordinate systems to be in + + align:start position:0% +get our coordinate systems to be in + + + align:start position:0% +get our coordinate systems to be in +agreement or in alignment + + align:start position:0% +agreement or in alignment + + + align:start position:0% +agreement or in alignment +because we there's no absolute standard + + align:start position:0% +because we there's no absolute standard + + + align:start position:0% +because we there's no absolute standard +to which we can separately appeal how + + align:start position:0% +to which we can separately appeal how + + + align:start position:0% +to which we can separately appeal how +can we do that well we're all going to + + align:start position:0% +can we do that well we're all going to + + + align:start position:0% +can we do that well we're all going to +agree on the speed of light + + align:start position:0% +agree on the speed of light + + + align:start position:0% +agree on the speed of light +whether whether whether we're at rest + + align:start position:0% +whether whether whether we're at rest + + + align:start position:0% +whether whether whether we're at rest +with respect to each other or moving + + align:start position:0% +with respect to each other or moving + + + align:start position:0% +with respect to each other or moving +according to his second postulate light + + align:start position:0% +according to his second postulate light + + + align:start position:0% +according to his second postulate light +becomes this absolute kind of meter + + align:start position:0% +becomes this absolute kind of meter + + + align:start position:0% +becomes this absolute kind of meter +stick or you know measuring tool because + + align:start position:0% +stick or you know measuring tool because + + + align:start position:0% +stick or you know measuring tool because +we'll all agree on it that means + + align:start position:0% +we'll all agree on it that means + + + align:start position:0% +we'll all agree on it that means +that if we're using say radio waves from + + align:start position:0% +that if we're using say radio waves from + + + align:start position:0% +that if we're using say radio waves from +the Eiffel Tower to coordinate our + + align:start position:0% +the Eiffel Tower to coordinate our + + + align:start position:0% +the Eiffel Tower to coordinate our +clocks at a distance we know exactly how + + align:start position:0% +clocks at a distance we know exactly how + + + align:start position:0% +clocks at a distance we know exactly how +much time must have elapsed in our own + + align:start position:0% +much time must have elapsed in our own + + + align:start position:0% +much time must have elapsed in our own +coordinate system + + align:start position:0% +coordinate system + + + align:start position:0% +coordinate system +between when the Clock Struck 12 noon in + + align:start position:0% +between when the Clock Struck 12 noon in + + + align:start position:0% +between when the Clock Struck 12 noon in +Paris at the Eiffel Tower and that + + align:start position:0% +Paris at the Eiffel Tower and that + + + align:start position:0% +Paris at the Eiffel Tower and that +electromagnetic wave carried that signal + + align:start position:0% +electromagnetic wave carried that signal + + + align:start position:0% +electromagnetic wave carried that signal +it's 12 noon in Paris it's 12 noon in + + align:start position:0% +it's 12 noon in Paris it's 12 noon in + + + align:start position:0% +it's 12 noon in Paris it's 12 noon in +Paris it's 12 in Paris and then we + + align:start position:0% +Paris it's 12 in Paris and then we + + + align:start position:0% +Paris it's 12 in Paris and then we +received that signal sometime later + + align:start position:0% +received that signal sometime later + + + align:start position:0% +received that signal sometime later +we know exactly how long in our time + + align:start position:0% +we know exactly how long in our time + + + align:start position:0% +we know exactly how long in our time +units how long it's taken that signal to + + align:start position:0% +units how long it's taken that signal to + + + align:start position:0% +units how long it's taken that signal to +arrive because the light wave could only + + align:start position:0% +arrive because the light wave could only + + + align:start position:0% +arrive because the light wave could only +but have traveled at the speed of light + + align:start position:0% +but have traveled at the speed of light + + + align:start position:0% +but have traveled at the speed of light +so we can use this as a universalizing + + align:start position:0% +so we can use this as a universalizing + + + align:start position:0% +so we can use this as a universalizing +tool to coordinate our coordinate + + align:start position:0% +tool to coordinate our coordinate + + + align:start position:0% +tool to coordinate our coordinate +systems at a distance + + align:start position:0% +systems at a distance + + + align:start position:0% +systems at a distance +and then we can make sure that our clock + + align:start position:0% +and then we can make sure that our clock + + + align:start position:0% +and then we can make sure that our clock +is in the same reference frame as the + + align:start position:0% +is in the same reference frame as the + + + align:start position:0% +is in the same reference frame as the +Paris clock not by saying well I got the + + align:start position:0% +Paris clock not by saying well I got the + + + align:start position:0% +Paris clock not by saying well I got the +signal from Paris now I'll make my clock + + align:start position:0% +signal from Paris now I'll make my clock + + + align:start position:0% +signal from Paris now I'll make my clock +say 12 noon that wouldn't work by saying + + align:start position:0% +say 12 noon that wouldn't work by saying + + + align:start position:0% +say 12 noon that wouldn't work by saying +I got the signal from Paris I now know + + align:start position:0% +I got the signal from Paris I now know + + + align:start position:0% +I got the signal from Paris I now know +it's 12 noon plus the propagation time + + align:start position:0% +it's 12 noon plus the propagation time + + + align:start position:0% +it's 12 noon plus the propagation time +and I can calculate that without I can + + align:start position:0% +and I can calculate that without I can + + + align:start position:0% +and I can calculate that without I can +calculate that without worry because the + + align:start position:0% +calculate that without worry because the + + + align:start position:0% +calculate that without worry because the +propagation that signal is some + + align:start position:0% +propagation that signal is some + + + align:start position:0% +propagation that signal is some +Universal constant the propagation rate + + align:start position:0% +Universal constant the propagation rate + + + align:start position:0% +Universal constant the propagation rate +so if I have separately measured the + + align:start position:0% +so if I have separately measured the + + + align:start position:0% +so if I have separately measured the +distance between my you know house my + + align:start position:0% +distance between my you know house my + + + align:start position:0% +distance between my you know house my +train station and Paris or whatever the + + align:start position:0% +train station and Paris or whatever the + + + align:start position:0% +train station and Paris or whatever the +mother clock is referring to the Germans + + align:start position:0% +mother clock is referring to the Germans + + + align:start position:0% +mother clock is referring to the Germans +would never use Paris by the way that + + align:start position:0% +would never use Paris by the way that + + + align:start position:0% +would never use Paris by the way that +they would they would have hated that + + align:start position:0% +they would they would have hated that + + + align:start position:0% +they would they would have hated that +but whatever the mother clock is + + align:start position:0% +but whatever the mother clock is + + + align:start position:0% +but whatever the mother clock is +whatever standard we're using + + align:start position:0% +whatever standard we're using + + + align:start position:0% +whatever standard we're using +you can separately at your leisure + + align:start position:0% +you can separately at your leisure + + + align:start position:0% +you can separately at your leisure +measure your distance between them and + + align:start position:0% +measure your distance between them and + + + align:start position:0% +measure your distance between them and +then you'll know how long it will take + + align:start position:0% +then you'll know how long it will take + + + align:start position:0% +then you'll know how long it will take +for an electromagnetic wave to get from + + align:start position:0% +for an electromagnetic wave to get from + + + align:start position:0% +for an electromagnetic wave to get from +that mother clock signal to you it can't + + align:start position:0% +that mother clock signal to you it can't + + + align:start position:0% +that mother clock signal to you it can't +speed up or slow down because it's just + + align:start position:0% +speed up or slow down because it's just + + + align:start position:0% +speed up or slow down because it's just +speed of light right and so now you say + + align:start position:0% +speed of light right and so now you say + + + align:start position:0% +speed of light right and so now you say +I got the 12 o'clock signal from my + + align:start position:0% +I got the 12 o'clock signal from my + + + align:start position:0% +I got the 12 o'clock signal from my +relevant so-called mother clock I know + + align:start position:0% +relevant so-called mother clock I know + + + align:start position:0% +relevant so-called mother clock I know +set my clock automatically to do 12 plus + + align:start position:0% +set my clock automatically to do 12 plus + + + align:start position:0% +set my clock automatically to do 12 plus +appropriate offset and now I know my + + align:start position:0% +appropriate offset and now I know my + + + align:start position:0% +appropriate offset and now I know my +clocks are synchronized so if I had a + + align:start position:0% +clocks are synchronized so if I had a + + + align:start position:0% +clocks are synchronized so if I had a +partner standing between us midway + + align:start position:0% +partner standing between us midway + + + align:start position:0% +partner standing between us midway +between say Zurich and Paris or Zurich + + align:start position:0% +between say Zurich and Paris or Zurich + + + align:start position:0% +between say Zurich and Paris or Zurich +and baron whatever and we did a lantern + + align:start position:0% +and baron whatever and we did a lantern + + + align:start position:0% +and baron whatever and we did a lantern +trick we could confirm that our + + align:start position:0% +trick we could confirm that our + + + align:start position:0% +trick we could confirm that our +coordinates are now aligned how can we + + align:start position:0% +coordinates are now aligned how can we + + + align:start position:0% +coordinates are now aligned how can we +agree on the on the time coordinates at + + align:start position:0% +agree on the on the time coordinates at + + + align:start position:0% +agree on the on the time coordinates at +distant events trade light signals if I + + align:start position:0% +distant events trade light signals if I + + + align:start position:0% +distant events trade light signals if I +have a partner who's midway between you + + align:start position:0% +have a partner who's midway between you + + + align:start position:0% +have a partner who's midway between you +know me and the distant mother clock we + + align:start position:0% +know me and the distant mother clock we + + + align:start position:0% +know me and the distant mother clock we +can make sure we're still recorded we + + align:start position:0% +can make sure we're still recorded we + + + align:start position:0% +can make sure we're still recorded we +can do something like a calibration + + align:start position:0% +can do something like a calibration + + + align:start position:0% +can do something like a calibration +by doing another trick with light + + align:start position:0% +by doing another trick with light + + + align:start position:0% +by doing another trick with light +singles did the person in the middle + + align:start position:0% +singles did the person in the middle + + + align:start position:0% +singles did the person in the middle +receive the two lights at the same time + + align:start position:0% +receive the two lights at the same time + + + align:start position:0% +receive the two lights at the same time +if she was equidistant yes okay then our + + align:start position:0% +if she was equidistant yes okay then our + + + align:start position:0% +if she was equidistant yes okay then our +clocks indeed are synchronized so the + + align:start position:0% +clocks indeed are synchronized so the + + + align:start position:0% +clocks indeed are synchronized so the +idea is to is to take advantage of the + + align:start position:0% +idea is to is to take advantage of the + + + align:start position:0% +idea is to is to take advantage of the +universality of electromagnetic waves + + align:start position:0% +universality of electromagnetic waves + + + align:start position:0% +universality of electromagnetic waves +even if Baron is not literally flying + + align:start position:0% +even if Baron is not literally flying + + + align:start position:0% +even if Baron is not literally flying +past you know Berlin they're not in + + align:start position:0% +past you know Berlin they're not in + + + align:start position:0% +past you know Berlin they're not in +relative motion that way but they're + + align:start position:0% +relative motion that way but they're + + + align:start position:0% +relative motion that way but they're +still using a universal feature of + + align:start position:0% +still using a universal feature of + + + align:start position:0% +still using a universal feature of +electromagnetic magnetic waves and doing + + align:start position:0% +electromagnetic magnetic waves and doing + + + align:start position:0% +electromagnetic magnetic waves and doing +local coordination because it's all we + + align:start position:0% +local coordination because it's all we + + + align:start position:0% +local coordination because it's all we +can ever do + + align:start position:0% +can ever do + + + align:start position:0% +can ever do +because Einstein says there's no + + align:start position:0% +because Einstein says there's no + + + align:start position:0% +because Einstein says there's no +absolute standard to which we could + + align:start position:0% +absolute standard to which we could + + + align:start position:0% +absolute standard to which we could +otherwise appeal that that make a little + + align:start position:0% +otherwise appeal that that make a little + + + align:start position:0% +otherwise appeal that that make a little +more sense + + align:start position:0% +more sense + + + align:start position:0% +more sense +great thank you okay Bobby LaBelle says + + align:start position:0% +great thank you okay Bobby LaBelle says + + + align:start position:0% +great thank you okay Bobby LaBelle says +does anyone know why it's real life + + align:start position:0% +does anyone know why it's real life + + + align:start position:0% +does anyone know why it's real life +Wisconsin ah is it just a pasta + + align:start position:0% +Wisconsin ah is it just a pasta + + + align:start position:0% +Wisconsin ah is it just a pasta +that's a really deep and hard question + + align:start position:0% +that's a really deep and hard question + + + align:start position:0% +that's a really deep and hard question +about him so + + align:start position:0% +about him so + + + align:start position:0% +about him so +um + + align:start position:0% +um + + + align:start position:0% +um +Einstein made no effort to prove this or + + align:start position:0% +Einstein made no effort to prove this or + + + align:start position:0% +Einstein made no effort to prove this or +even justify he'd even tell us about his + + align:start position:0% +even justify he'd even tell us about his + + + align:start position:0% +even justify he'd even tell us about his +server idea it was a pretty cool idea I + + align:start position:0% +server idea it was a pretty cool idea I + + + align:start position:0% +server idea it was a pretty cool idea I +mean that that thought experiment was + + align:start position:0% +mean that that thought experiment was + + + align:start position:0% +mean that that thought experiment was +pretty awesome + + align:start position:0% +pretty awesome + + + align:start position:0% +pretty awesome +it's awesome for a 16 year old it's + + align:start position:0% +it's awesome for a 16 year old it's + + + align:start position:0% +it's awesome for a 16 year old it's +awesome for a 49 year old this is an + + align:start position:0% +awesome for a 49 year old this is an + + + align:start position:0% +awesome for a 49 year old this is an +awesome thought experiment he didn't + + align:start position:0% +awesome thought experiment he didn't + + + align:start position:0% +awesome thought experiment he didn't +even tell his readers that the dummy he + + align:start position:0% +even tell his readers that the dummy he + + + align:start position:0% +even tell his readers that the dummy he +could have at least put that in his + + align:start position:0% +could have at least put that in his + + + align:start position:0% +could have at least put that in his +paper he gives us no reason + + align:start position:0% +paper he gives us no reason + + + align:start position:0% +paper he gives us no reason +no reason no no compelling argument in + + align:start position:0% +no reason no no compelling argument in + + + align:start position:0% +no reason no no compelling argument in +this article to take on board that's + + align:start position:0% +this article to take on board that's + + + align:start position:0% +this article to take on board that's +very strange sounding posture about this + + align:start position:0% +very strange sounding posture about this + + + align:start position:0% +very strange sounding posture about this +the constancy the speed of light he has + + align:start position:0% +the constancy the speed of light he has + + + align:start position:0% +the constancy the speed of light he has +that very strange abbreviated paragraph + + align:start position:0% +that very strange abbreviated paragraph + + + align:start position:0% +that very strange abbreviated paragraph +I read out to you near the near the end + + align:start position:0% +I read out to you near the near the end + + + align:start position:0% +I read out to you near the near the end +of the class today about + + align:start position:0% +of the class today about + + + align:start position:0% +of the class today about +um the failure of efforts to measure a + + align:start position:0% +um the failure of efforts to measure a + + + align:start position:0% +um the failure of efforts to measure a +relative speed with respect um to a + + align:start position:0% +relative speed with respect um to a + + + align:start position:0% +relative speed with respect um to a +motion ether he doesn't tell us which + + align:start position:0% +motion ether he doesn't tell us which + + + align:start position:0% +motion ether he doesn't tell us which +experiments he almost certain doesn't + + align:start position:0% +experiments he almost certain doesn't + + + align:start position:0% +experiments he almost certain doesn't +mean Michael's Morley so there's some + + align:start position:0% +mean Michael's Morley so there's some + + + align:start position:0% +mean Michael's Morley so there's some +modest weak empirical evidence that + + align:start position:0% +modest weak empirical evidence that + + + align:start position:0% +modest weak empirical evidence that +seems to argue against that + + align:start position:0% +seems to argue against that + + + align:start position:0% +seems to argue against that +he's not giving us a hard proof in the + + align:start position:0% +he's not giving us a hard proof in the + + + align:start position:0% +he's not giving us a hard proof in the +years since then uh there have been + + align:start position:0% +years since then uh there have been + + + align:start position:0% +years since then uh there have been +more and more ideas built up going well + + align:start position:0% +more and more ideas built up going well + + + align:start position:0% +more and more ideas built up going well +beyond the original framework of + + align:start position:0% +beyond the original framework of + + + align:start position:0% +beyond the original framework of +Einstein's own work two words which we + + align:start position:0% +Einstein's own work two words which we + + + align:start position:0% +Einstein's own work two words which we +can we can appeal and we'll get a + + align:start position:0% +can we can appeal and we'll get a + + + align:start position:0% +can we can appeal and we'll get a +glimmer actually some of those first + + align:start position:0% +glimmer actually some of those first + + + align:start position:0% +glimmer actually some of those first +kinds of arguments in actually in + + align:start position:0% +kinds of arguments in actually in + + + align:start position:0% +kinds of arguments in actually in +Wednesday's class other kinds of + + align:start position:0% +Wednesday's class other kinds of + + + align:start position:0% +Wednesday's class other kinds of +symmetry arguments which were absolutely + + align:start position:0% +symmetry arguments which were absolutely + + + align:start position:0% +symmetry arguments which were absolutely +not the kind to which I signed appealed + + align:start position:0% +not the kind to which I signed appealed + + + align:start position:0% +not the kind to which I signed appealed +at the time + + align:start position:0% +at the time + + + align:start position:0% +at the time +that guarantees certain kinds of + + align:start position:0% +that guarantees certain kinds of + + + align:start position:0% +that guarantees certain kinds of +invariances certain kinds of geometrical + + align:start position:0% +invariances certain kinds of geometrical + + + align:start position:0% +invariances certain kinds of geometrical +properties that we'll look at quite + + align:start position:0% +properties that we'll look at quite + + + align:start position:0% +properties that we'll look at quite +squarely on Wednesday's class but in + + align:start position:0% +squarely on Wednesday's class but in + + + align:start position:0% +squarely on Wednesday's class but in +Einsteins on day it was it was frankly + + align:start position:0% +Einsteins on day it was it was frankly + + + align:start position:0% +Einsteins on day it was it was frankly +an Article of Faith that's what he calls + + align:start position:0% +an Article of Faith that's what he calls + + + align:start position:0% +an Article of Faith that's what he calls +it a posture + + align:start position:0% +it a posture + + + align:start position:0% +it a posture +uh and Stanley asks a follow-up of + + align:start position:0% +uh and Stanley asks a follow-up of + + + align:start position:0% +uh and Stanley asks a follow-up of +measuring the length of a moving train + + align:start position:0% +measuring the length of a moving train + + + align:start position:0% +measuring the length of a moving train +slicing a measure locations of front and + + align:start position:0% +slicing a measure locations of front and + + + align:start position:0% +slicing a measure locations of front and +back at the same time take the + + align:start position:0% +back at the same time take the + + + align:start position:0% +back at the same time take the +difference + + align:start position:0% +difference + + + align:start position:0% +difference +um but they at the same time is not well + + align:start position:0% +um but they at the same time is not well + + + align:start position:0% +um but they at the same time is not well +defined that's right exactly so saying + + align:start position:0% +defined that's right exactly so saying + + + align:start position:0% +defined that's right exactly so saying +that's exactly right so the idea is if + + align:start position:0% +that's exactly right so the idea is if + + + align:start position:0% +that's exactly right so the idea is if +our operation to measure debt length is + + align:start position:0% +our operation to measure debt length is + + + align:start position:0% +our operation to measure debt length is +measured front and back at the same time + + align:start position:0% +measured front and back at the same time + + + align:start position:0% +measured front and back at the same time +and we disagree about what counts at the + + align:start position:0% +and we disagree about what counts at the + + + align:start position:0% +and we disagree about what counts at the +same time and everything else flows from + + align:start position:0% +same time and everything else flows from + + + align:start position:0% +same time and everything else flows from +that argument side which is why it's um + + align:start position:0% +that argument side which is why it's um + + + align:start position:0% +that argument side which is why it's um +it's all about kinematics not not + + align:start position:0% +it's all about kinematics not not + + + align:start position:0% +it's all about kinematics not not +Dynamics frame it's all about how do we + + align:start position:0% +Dynamics frame it's all about how do we + + + align:start position:0% +Dynamics frame it's all about how do we +lay down coordinates with which to + + align:start position:0% +lay down coordinates with which to + + + align:start position:0% +lay down coordinates with which to +reckon the motion of objects you space + + align:start position:0% +reckon the motion of objects you space + + + align:start position:0% +reckon the motion of objects you space +in time so telling us do we need to make + + align:start position:0% +in time so telling us do we need to make + + + align:start position:0% +in time so telling us do we need to make +sure the measurement is taken are + + align:start position:0% +sure the measurement is taken are + + + align:start position:0% +sure the measurement is taken are +simultaneous yes that's right or rather + + align:start position:0% +simultaneous yes that's right or rather + + + align:start position:0% +simultaneous yes that's right or rather +it's to say our measurement of length + + align:start position:0% +it's to say our measurement of length + + + align:start position:0% +it's to say our measurement of length +will be relative to our reference frame + + align:start position:0% +will be relative to our reference frame + + + align:start position:0% +will be relative to our reference frame +it'll be totally correct in our own + + align:start position:0% +it'll be totally correct in our own + + + align:start position:0% +it'll be totally correct in our own +reference room according to our + + align:start position:0% +reference room according to our + + + align:start position:0% +reference room according to our +coordinates it just will no longer agree + + align:start position:0% +coordinates it just will no longer agree + + + align:start position:0% +coordinates it just will no longer agree +with someone's equally correct set of + + align:start position:0% +with someone's equally correct set of + + + align:start position:0% +with someone's equally correct set of +measurements in their own equally valid + + align:start position:0% +measurements in their own equally valid + + + align:start position:0% +measurements in their own equally valid +but moving reference frame that's what + + align:start position:0% +but moving reference frame that's what + + + align:start position:0% +but moving reference frame that's what +is pretty hard to get our heads around + + align:start position:0% +is pretty hard to get our heads around + + + align:start position:0% +is pretty hard to get our heads around +um Julian says you even need the second + + align:start position:0% +um Julian says you even need the second + + + align:start position:0% +um Julian says you even need the second +password if you are use the argument of + + align:start position:0% +password if you are use the argument of + + + align:start position:0% +password if you are use the argument of +the thought experiment good question + + align:start position:0% +the thought experiment good question + + + align:start position:0% +the thought experiment good question +Julia Einstein himself returned to this + + align:start position:0% +Julia Einstein himself returned to this + + + align:start position:0% +Julia Einstein himself returned to this +in later writings if we really really + + align:start position:0% +in later writings if we really really + + + align:start position:0% +in later writings if we really really +will actually come to this a bit later + + align:start position:0% +will actually come to this a bit later + + + align:start position:0% +will actually come to this a bit later +in Wednesday's question if we really + + align:start position:0% +in Wednesday's question if we really + + + align:start position:0% +in Wednesday's question if we really +take on board that Maxwell's equations + + align:start position:0% +take on board that Maxwell's equations + + + align:start position:0% +take on board that Maxwell's equations +should apply equally in every frame of + + align:start position:0% +should apply equally in every frame of + + + align:start position:0% +should apply equally in every frame of +reference then once you sort of know the + + align:start position:0% +reference then once you sort of know the + + + align:start position:0% +reference then once you sort of know the +answer once you're a post einsteinian + + align:start position:0% +answer once you're a post einsteinian + + + align:start position:0% +answer once you're a post einsteinian +you can go back and say oh Max equations + + align:start position:0% +you can go back and say oh Max equations + + + align:start position:0% +you can go back and say oh Max equations +are invariant with respect to the speed + + align:start position:0% +are invariant with respect to the speed + + + align:start position:0% +are invariant with respect to the speed +of light they predict it should be the + + align:start position:0% +of light they predict it should be the + + + align:start position:0% +of light they predict it should be the +same for all observers so maybe you just + + align:start position:0% +same for all observers so maybe you just + + + align:start position:0% +same for all observers so maybe you just +need posture one that kind of that's + + align:start position:0% +need posture one that kind of that's + + + align:start position:0% +need posture one that kind of that's +convincing if you already know the + + align:start position:0% +convincing if you already know the + + + align:start position:0% +convincing if you already know the +answer Einstein in 1905 didn't get there + + align:start position:0% +answer Einstein in 1905 didn't get there + + + align:start position:0% +answer Einstein in 1905 didn't get there +that way he wrestled with whether it was + + align:start position:0% +that way he wrestled with whether it was + + + align:start position:0% +that way he wrestled with whether it was +an auxiliary hypothesis later in his + + align:start position:0% +an auxiliary hypothesis later in his + + + align:start position:0% +an auxiliary hypothesis later in his +career it's a great question I'm going + + align:start position:0% +career it's a great question I'm going + + + align:start position:0% +career it's a great question I'm going +to pause there I know some folks will + + align:start position:0% +to pause there I know some folks will + + + align:start position:0% +to pause there I know some folks will +probably have to jump off for other + + align:start position:0% +probably have to jump off for other + + + align:start position:0% +probably have to jump off for other +classes great great questions + + align:start position:0% +classes great great questions + + + align:start position:0% +classes great great questions +um feel free to email me if you have + + align:start position:0% +um feel free to email me if you have + + + align:start position:0% +um feel free to email me if you have +other questions I'll have office hours + + align:start position:0% +other questions I'll have office hours + + + align:start position:0% +other questions I'll have office hours +um on Wednesday this week at 11 A.M + + align:start position:0% +um on Wednesday this week at 11 A.M + + + align:start position:0% +um on Wednesday this week at 11 A.M +Eastern feel free to pop in for that and + + align:start position:0% +Eastern feel free to pop in for that and + + + align:start position:0% +Eastern feel free to pop in for that and +we'll pick up the story then on + + align:start position:0% +we'll pick up the story then on + + + align:start position:0% +we'll pick up the story then on +Wednesday stay well everyone see you + + align:start position:0% +Wednesday stay well everyone see you + + + align:start position:0% +Wednesday stay well everyone see you +soon \ No newline at end of file diff --git a/YGpxOuDJdJw.txt b/YGpxOuDJdJw.txt new file mode 100644 index 0000000000000000000000000000000000000000..5f3aaa64170aa801431e76854105586723fc3878 --- /dev/null +++ b/YGpxOuDJdJw.txt @@ -0,0 +1,12675 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +so today we'll talk about constipation + + align:start position:0% +so today we'll talk about constipation + + + align:start position:0% +so today we'll talk about constipation +it's the first of the modeling modeling + + align:start position:0% +it's the first of the modeling modeling + + + align:start position:0% +it's the first of the modeling modeling +lectures we'll talk very briefly about + + align:start position:0% +lectures we'll talk very briefly about + + + align:start position:0% +lectures we'll talk very briefly about +the role that the different roles that + + align:start position:0% +the role that the different roles that + + + align:start position:0% +the role that the different roles that +customers have in in transit agencies + + align:start position:0% +customers have in in transit agencies + + + align:start position:0% +customers have in in transit agencies +and then we'll discuss three types of + + align:start position:0% +and then we'll discuss three types of + + + align:start position:0% +and then we'll discuss three types of +three categories of what are the roles + + align:start position:0% +three categories of what are the roles + + + align:start position:0% +three categories of what are the roles +why do we or how could it cost Maldives + + align:start position:0% +why do we or how could it cost Maldives + + + align:start position:0% +why do we or how could it cost Maldives +and start a custom model right it's a + + align:start position:0% +and start a custom model right it's a + + + align:start position:0% +and start a custom model right it's a +model mathematical model that takes some + + align:start position:0% +model mathematical model that takes some + + + align:start position:0% +model mathematical model that takes some +variables and predicts some cost for the + + align:start position:0% +variables and predicts some cost for the + + + align:start position:0% +variables and predicts some cost for the +agency could be operational cost it + + align:start position:0% +agency could be operational cost it + + + align:start position:0% +agency could be operational cost it +could be fixed cost so how could these + + align:start position:0% +could be fixed cost so how could these + + + align:start position:0% +could be fixed cost so how could these +be used the first role is predicting the + + align:start position:0% +be used the first role is predicting the + + + align:start position:0% +be used the first role is predicting the +cost change associated with a service + + align:start position:0% +cost change associated with a service + + + align:start position:0% +cost change associated with a service +change alright so this is a very + + align:start position:0% +change alright so this is a very + + + align:start position:0% +change alright so this is a very +traditional typical example so you might + + align:start position:0% +traditional typical example so you might + + + align:start position:0% +traditional typical example so you might +extend the routes as we're thinking + + align:start position:0% +extend the routes as we're thinking + + + align:start position:0% +extend the routes as we're thinking +about assignment ei extending it and you + + align:start position:0% +about assignment ei extending it and you + + + align:start position:0% +about assignment ei extending it and you +might wonder how much will that cost to + + align:start position:0% +might wonder how much will that cost to + + + align:start position:0% +might wonder how much will that cost to +operate right so you could use a cost + + align:start position:0% +operate right so you could use a cost + + + align:start position:0% +operate right so you could use a cost +model in that situation or maybe there's + + align:start position:0% +model in that situation or maybe there's + + + align:start position:0% +model in that situation or maybe there's +a wider increase in service + + align:start position:0% +a wider increase in service + + + align:start position:0% +a wider increase in service +maybe services being expanded from + + align:start position:0% +maybe services being expanded from + + + align:start position:0% +maybe services being expanded from +anything actually I'm running 24 hours + + align:start position:0% +anything actually I'm running 24 hours + + + align:start position:0% +anything actually I'm running 24 hours +how much would that cost so these are + + align:start position:0% +how much would that cost so these are + + + align:start position:0% +how much would that cost so these are +the kinds of questions service changes + + align:start position:0% +the kinds of questions service changes + + + align:start position:0% +the kinds of questions service changes +that you might want to have an idea of + + align:start position:0% +that you might want to have an idea of + + + align:start position:0% +that you might want to have an idea of +how much will that cost me so they are + + align:start position:0% +how much will that cost me so they are + + + align:start position:0% +how much will that cost me so they are +often concerned with marginal or + + align:start position:0% +often concerned with marginal or + + + align:start position:0% +often concerned with marginal or +incremental costs especially in this + + align:start position:0% +incremental costs especially in this + + + align:start position:0% +incremental costs especially in this +application so if you expand service to + + align:start position:0% +application so if you expand service to + + + align:start position:0% +application so if you expand service to +to cover all night for example you may + + align:start position:0% +to cover all night for example you may + + + align:start position:0% +to cover all night for example you may +not need that that changed may not + + align:start position:0% +not need that that changed may not + + + align:start position:0% +not need that that changed may not +trigger the need for a new bus + + align:start position:0% +trigger the need for a new bus + + + align:start position:0% +trigger the need for a new bus +maintenance facility or some large + + align:start position:0% +maintenance facility or some large + + + align:start position:0% +maintenance facility or some large +capital expenditure right so we're + + align:start position:0% +capital expenditure right so we're + + + align:start position:0% +capital expenditure right so we're +talking here about sort of incremental + + align:start position:0% +talking here about sort of incremental + + + align:start position:0% +talking here about sort of incremental +cost as I have buses whereas I have bus + + align:start position:0% +cost as I have buses whereas I have bus + + + align:start position:0% +cost as I have buses whereas I have bus +hours or as I add driver hours how much + + align:start position:0% +hours or as I add driver hours how much + + + align:start position:0% +hours or as I add driver hours how much +extra do I pay you have different + + align:start position:0% +extra do I pay you have different + + + align:start position:0% +extra do I pay you have different +results over different time periods this + + align:start position:0% +results over different time periods this + + + align:start position:0% +results over different time periods this +is important it doesn't cost the same to + + align:start position:0% +is important it doesn't cost the same to + + + align:start position:0% +is important it doesn't cost the same to +run service off-peak or at night as a US + + align:start position:0% +run service off-peak or at night as a US + + + align:start position:0% +run service off-peak or at night as a US +peak I'll talk more about that later in + + align:start position:0% +peak I'll talk more about that later in + + + align:start position:0% +peak I'll talk more about that later in +this lecture so but having that in mind + + align:start position:0% +this lecture so but having that in mind + + + align:start position:0% +this lecture so but having that in mind +and how + + align:start position:0% +and how + + + align:start position:0% +and how +a cost model Sun City design periods + + align:start position:0% +a cost model Sun City design periods + + + align:start position:0% +a cost model Sun City design periods +might be very important to get accurate + + align:start position:0% +might be very important to get accurate + + + align:start position:0% +might be very important to get accurate +estimates okay so these balls may also + + align:start position:0% +estimates okay so these balls may also + + + align:start position:0% +estimates okay so these balls may also +be used for routine performance + + align:start position:0% +be used for routine performance + + + align:start position:0% +be used for routine performance +monitoring and service poll teachers you + + align:start position:0% +monitoring and service poll teachers you + + + align:start position:0% +monitoring and service poll teachers you +might remember from the short-term + + align:start position:0% +might remember from the short-term + + + align:start position:0% +might remember from the short-term +funding lectures that there are some + + align:start position:0% +funding lectures that there are some + + + align:start position:0% +funding lectures that there are some +processes where every bus route might be + + align:start position:0% +processes where every bus route might be + + + align:start position:0% +processes where every bus route might be +reviewed and you might decide that you + + align:start position:0% +reviewed and you might decide that you + + + align:start position:0% +reviewed and you might decide that you +need to add service based on its + + align:start position:0% +need to add service based on its + + + align:start position:0% +need to add service based on its +performance or you might decide that a + + align:start position:0% +performance or you might decide that a + + + align:start position:0% +performance or you might decide that a +bus or isn't meeting the requirements to + + align:start position:0% +bus or isn't meeting the requirements to + + + align:start position:0% +bus or isn't meeting the requirements to +be financially sustainable so you are + + align:start position:0% +be financially sustainable so you are + + + align:start position:0% +be financially sustainable so you are +considering removing dropping servers on + + align:start position:0% +considering removing dropping servers on + + + align:start position:0% +considering removing dropping servers on +how much will you save by doing that all + + align:start position:0% +how much will you save by doing that all + + + align:start position:0% +how much will you save by doing that all +those are applications of okay the + + align:start position:0% +those are applications of okay the + + + align:start position:0% +those are applications of okay the +second point here is that you can + + align:start position:0% +second point here is that you can + + + align:start position:0% +second point here is that you can +predict the cross chains associated with + + align:start position:0% +predict the cross chains associated with + + + align:start position:0% +predict the cross chains associated with +the change in production and process now + + align:start position:0% +the change in production and process now + + + align:start position:0% +the change in production and process now +we're not talking so much service but + + align:start position:0% +we're not talking so much service but + + + align:start position:0% +we're not talking so much service but +we're thinking of what happens is you + + align:start position:0% +we're thinking of what happens is you + + + align:start position:0% +we're thinking of what happens is you +know labor agreements that does not + + align:start position:0% +know labor agreements that does not + + + align:start position:0% +know labor agreements that does not +allow part-timers and now we've + + align:start position:0% +allow part-timers and now we've + + + align:start position:0% +allow part-timers and now we've +negotiated the ability to hire + + align:start position:0% +negotiated the ability to hire + + + align:start position:0% +negotiated the ability to hire +part-timers what is the cost structure + + align:start position:0% +part-timers what is the cost structure + + + align:start position:0% +part-timers what is the cost structure +what about if I want to contract out + + align:start position:0% +what about if I want to contract out + + + align:start position:0% +what about if I want to contract out +meat that's work I'm doing that right + + align:start position:0% +meat that's work I'm doing that right + + + align:start position:0% +meat that's work I'm doing that right +now in-house and now maybe for a portion + + align:start position:0% +now in-house and now maybe for a portion + + + align:start position:0% +now in-house and now maybe for a portion +or for all of it we are looking at + + align:start position:0% +or for all of it we are looking at + + + align:start position:0% +or for all of it we are looking at +public-private partnerships to contract + + align:start position:0% +public-private partnerships to contract + + + align:start position:0% +public-private partnerships to contract +up making this work or conflicting out + + align:start position:0% +up making this work or conflicting out + + + align:start position:0% +up making this work or conflicting out +suburban bustards with low ridership and + + align:start position:0% +suburban bustards with low ridership and + + + align:start position:0% +suburban bustards with low ridership and +they're kind of on the outskirts you + + align:start position:0% +they're kind of on the outskirts you + + + align:start position:0% +they're kind of on the outskirts you +want to drop service but maybe you don't + + align:start position:0% +want to drop service but maybe you don't + + + align:start position:0% +want to drop service but maybe you don't +need big 40-foot buses and you can run + + align:start position:0% +need big 40-foot buses and you can run + + + align:start position:0% +need big 40-foot buses and you can run +them with smaller buses quickly contract + + align:start position:0% +them with smaller buses quickly contract + + + align:start position:0% +them with smaller buses quickly contract +those out what will that do the cost new + + align:start position:0% +those out what will that do the cost new + + + align:start position:0% +those out what will that do the cost new +fare technology the VTA who's who's here + + align:start position:0% +fare technology the VTA who's who's here + + + align:start position:0% +fare technology the VTA who's who's here +a long time ago we had tokens here and + + align:start position:0% +a long time ago we had tokens here and + + + align:start position:0% +a long time ago we had tokens here and +we move to the Charlie part and now the + + align:start position:0% +we move to the Charlie part and now the + + + align:start position:0% +we move to the Charlie part and now the +NPT is thinking about the next + + align:start position:0% +NPT is thinking about the next + + + align:start position:0% +NPT is thinking about the next +generation of fare collection for the + + align:start position:0% +generation of fare collection for the + + + align:start position:0% +generation of fare collection for the +for Boston so cuz I remember her + + align:start position:0% +for Boston so cuz I remember her + + + align:start position:0% +for Boston so cuz I remember her +and Wilson for their betoken stuff so I + + align:start position:0% +and Wilson for their betoken stuff so I + + + align:start position:0% +and Wilson for their betoken stuff so I +think the last station was second + + align:start position:0% +think the last station was second + + + align:start position:0% +think the last station was second +etc yes so anytime something like this + + align:start position:0% +etc yes so anytime something like this + + + align:start position:0% +etc yes so anytime something like this +happens there's a change in costs + + align:start position:0% +happens there's a change in costs + + + align:start position:0% +happens there's a change in costs +registration costs and the recovery of + + align:start position:0% +registration costs and the recovery of + + + align:start position:0% +registration costs and the recovery of +the fare recovery ratio might change so + + align:start position:0% +the fare recovery ratio might change so + + + align:start position:0% +the fare recovery ratio might change so +can we model that can we use cost models + + align:start position:0% +can we model that can we use cost models + + + align:start position:0% +can we model that can we use cost models +to predict those changes in cost or in + + align:start position:0% +to predict those changes in cost or in + + + align:start position:0% +to predict those changes in cost or in +okay then another sort of third and very + + align:start position:0% +okay then another sort of third and very + + + align:start position:0% +okay then another sort of third and very +important allegation not so much in + + align:start position:0% +important allegation not so much in + + + align:start position:0% +important allegation not so much in +Boston right now but certainly in other + + align:start position:0% +Boston right now but certainly in other + + + align:start position:0% +Boston right now but certainly in other +jurisdictions + + align:start position:0% +jurisdictions + + + align:start position:0% +jurisdictions +it's the allocation of subsidy required + + align:start position:0% +it's the allocation of subsidy required + + + align:start position:0% +it's the allocation of subsidy required +by jurisdiction so if you look at for + + align:start position:0% +by jurisdiction so if you look at for + + + align:start position:0% +by jurisdiction so if you look at for +example the wall model and there are + + align:start position:0% +example the wall model and there are + + + align:start position:0% +example the wall model and there are +different districts and they all have to + + align:start position:0% +different districts and they all have to + + + align:start position:0% +different districts and they all have to +pay for service right so there are many + + align:start position:0% +pay for service right so there are many + + + align:start position:0% +pay for service right so there are many +examples of this and over the states and + + align:start position:0% +examples of this and over the states and + + + align:start position:0% +examples of this and over the states and +also internationally where different + + align:start position:0% +also internationally where different + + + align:start position:0% +also internationally where different +jurisdictions are essentially partnering + + align:start position:0% +jurisdictions are essentially partnering + + + align:start position:0% +jurisdictions are essentially partnering +to to subsidize public transportation + + align:start position:0% +to to subsidize public transportation + + + align:start position:0% +to to subsidize public transportation +service and we know what the total cost + + align:start position:0% +service and we know what the total cost + + + align:start position:0% +service and we know what the total cost +of operation is so how much is fair that + + align:start position:0% +of operation is so how much is fair that + + + align:start position:0% +of operation is so how much is fair that +each jurisdiction pay according to size + + align:start position:0% +each jurisdiction pay according to size + + + align:start position:0% +each jurisdiction pay according to size +according to how many people often it's + + align:start position:0% +according to how many people often it's + + + align:start position:0% +according to how many people often it's +according to how many people ride from + + align:start position:0% +according to how many people ride from + + + align:start position:0% +according to how many people ride from +those jurisdictions so see you might you + + align:start position:0% +those jurisdictions so see you might you + + + align:start position:0% +those jurisdictions so see you might you +might have a data collection to figure + + align:start position:0% +might have a data collection to figure + + + align:start position:0% +might have a data collection to figure +out how many people are taking buses + + align:start position:0% +out how many people are taking buses + + + align:start position:0% +out how many people are taking buses +from each of the jurisdictions and then + + align:start position:0% +from each of the jurisdictions and then + + + align:start position:0% +from each of the jurisdictions and then +you need to allocate a cost allocation + + align:start position:0% +you need to allocate a cost allocation + + + align:start position:0% +you need to allocate a cost allocation +model to take all the costs including + + align:start position:0% +model to take all the costs including + + + align:start position:0% +model to take all the costs including +the things that are sort of more obvious + + align:start position:0% +the things that are sort of more obvious + + + align:start position:0% +the things that are sort of more obvious +like the bus hours that operate in those + + align:start position:0% +like the bus hours that operate in those + + + align:start position:0% +like the bus hours that operate in those +jurisdictions but also things that are + + align:start position:0% +jurisdictions but also things that are + + + align:start position:0% +jurisdictions but also things that are +not directly connected to the + + align:start position:0% +not directly connected to the + + + align:start position:0% +not directly connected to the +jurisdictions such as administration + + align:start position:0% +jurisdictions such as administration + + + align:start position:0% +jurisdictions such as administration +costs and facility maintenance and so + + align:start position:0% +costs and facility maintenance and so + + + align:start position:0% +costs and facility maintenance and so +all of that needs to be allocated to a + + align:start position:0% +all of that needs to be allocated to a + + + align:start position:0% +all of that needs to be allocated to a +jurisdiction so that the costs can be + + align:start position:0% +jurisdiction so that the costs can be + + + align:start position:0% +jurisdiction so that the costs can be +evenly or fairly split and doing that + + align:start position:0% +evenly or fairly split and doing that + + + align:start position:0% +evenly or fairly split and doing that +right is critical often even for the + + align:start position:0% +right is critical often even for the + + + align:start position:0% +right is critical often even for the +decision to participate or not in this + + align:start position:0% +decision to participate or not in this + + + align:start position:0% +decision to participate or not in this +program Virginia you see yeah very new + + align:start position:0% +program Virginia you see yeah very new + + + align:start position:0% +program Virginia you see yeah very new +yorky in New York Port Authority of New + + align:start position:0% +yorky in New York Port Authority of New + + + align:start position:0% +yorky in New York Port Authority of New +Jersey you know do you also need like + + align:start position:0% +Jersey you know do you also need like + + + align:start position:0% +Jersey you know do you also need like +there are many examples of different + + align:start position:0% +there are many examples of different + + + align:start position:0% +there are many examples of different +structures of how different + + align:start position:0% +structures of how different + + + align:start position:0% +structures of how different +jurisdictions come together to provide + + align:start position:0% +jurisdictions come together to provide + + + align:start position:0% +jurisdictions come together to provide +service so in some cases you have many + + align:start position:0% +service so in some cases you have many + + + align:start position:0% +service so in some cases you have many +different operators and more commonly + + align:start position:0% +different operators and more commonly + + + align:start position:0% +different operators and more commonly +and in the west of the u.s. many + + align:start position:0% +and in the west of the u.s. many + + + align:start position:0% +and in the west of the u.s. many +different operators all providing + + align:start position:0% +different operators all providing + + + align:start position:0% +different operators all providing +service somehow in other cases you have + + align:start position:0% +service somehow in other cases you have + + + align:start position:0% +service somehow in other cases you have +one major operator but funded by + + align:start position:0% +one major operator but funded by + + + align:start position:0% +one major operator but funded by +different jurisdictions all right so you + + align:start position:0% +different jurisdictions all right so you + + + align:start position:0% +different jurisdictions all right so you +might remember we've only talked about + + align:start position:0% +might remember we've only talked about + + + align:start position:0% +might remember we've only talked about +mobile capacities and costs that + + align:start position:0% +mobile capacities and costs that + + + align:start position:0% +mobile capacities and costs that +especially in the u.s. though in North + + align:start position:0% +especially in the u.s. though in North + + + align:start position:0% +especially in the u.s. though in North +America costs are divided into capital + + align:start position:0% +America costs are divided into capital + + + align:start position:0% +America costs are divided into capital +expenditures and operations expenditures + + align:start position:0% +expenditures and operations expenditures + + + align:start position:0% +expenditures and operations expenditures +so capital costs have to do with the + + align:start position:0% +so capital costs have to do with the + + + align:start position:0% +so capital costs have to do with the +purchase of vehicles or a lot midlife + + align:start position:0% +purchase of vehicles or a lot midlife + + + align:start position:0% +purchase of vehicles or a lot midlife +remodel vehicles heavy maintenance the + + align:start position:0% +remodel vehicles heavy maintenance the + + + align:start position:0% +remodel vehicles heavy maintenance the +fixed facility construction so + + align:start position:0% +fixed facility construction so + + + align:start position:0% +fixed facility construction so +construction or major repairs of tracks + + align:start position:0% +construction or major repairs of tracks + + + align:start position:0% +construction or major repairs of tracks +garage stations bus stops and then other + + align:start position:0% +garage stations bus stops and then other + + + align:start position:0% +garage stations bus stops and then other +long-term physical assets so + + align:start position:0% +long-term physical assets so + + + align:start position:0% +long-term physical assets so +administration building and then there's + + align:start position:0% +administration building and then there's + + + align:start position:0% +administration building and then there's +operating costs so those have to do with + + align:start position:0% +operating costs so those have to do with + + + align:start position:0% +operating costs so those have to do with +that they're more proportional to how + + align:start position:0% +that they're more proportional to how + + + align:start position:0% +that they're more proportional to how +much service you output so labor wages + + align:start position:0% +much service you output so labor wages + + + align:start position:0% +much service you output so labor wages +and benefits materials and supplies + + align:start position:0% +and benefits materials and supplies + + + align:start position:0% +and benefits materials and supplies +materials includes fuel right and tires + + align:start position:0% +materials includes fuel right and tires + + + align:start position:0% +materials includes fuel right and tires +and electricity to run the power Metro + + align:start position:0% +and electricity to run the power Metro + + + align:start position:0% +and electricity to run the power Metro +then there's agency administration and + + align:start position:0% +then there's agency administration and + + + align:start position:0% +then there's agency administration and +other kinds of expenses of this nature + + align:start position:0% +other kinds of expenses of this nature + + + align:start position:0% +other kinds of expenses of this nature +right so it's important to keep those + + align:start position:0% +right so it's important to keep those + + + align:start position:0% +right so it's important to keep those +two in mind because the costs models + + align:start position:0% +two in mind because the costs models + + + align:start position:0% +two in mind because the costs models +that we specified should take this into + + align:start position:0% +that we specified should take this into + + + align:start position:0% +that we specified should take this into +consideration and be able to allocate + + align:start position:0% +consideration and be able to allocate + + + align:start position:0% +consideration and be able to allocate +the capital and operating expenses + + align:start position:0% +the capital and operating expenses + + + align:start position:0% +the capital and operating expenses +separately all right so there are three + + align:start position:0% +separately all right so there are three + + + align:start position:0% +separately all right so there are three +types of cost models that we're gonna + + align:start position:0% +types of cost models that we're gonna + + + align:start position:0% +types of cost models that we're gonna +discuss first is a fully allocated + + align:start position:0% +discuss first is a fully allocated + + + align:start position:0% +discuss first is a fully allocated +council factor of all it's the simplest + + align:start position:0% +council factor of all it's the simplest + + + align:start position:0% +council factor of all it's the simplest +of the ones we'll discuss one of the + + align:start position:0% +of the ones we'll discuss one of the + + + align:start position:0% +of the ones we'll discuss one of the +problems with that model is that it + + align:start position:0% +problems with that model is that it + + + align:start position:0% +problems with that model is that it +allocates all the costs to some + + align:start position:0% +allocates all the costs to some + + + align:start position:0% +allocates all the costs to some +categories and it's not sensitive to + + align:start position:0% +categories and it's not sensitive to + + + align:start position:0% +categories and it's not sensitive to +time periods as I said earlier + + align:start position:0% +time periods as I said earlier + + + align:start position:0% +time periods as I said earlier +some costs vary a lot by time period so + + align:start position:0% +some costs vary a lot by time period so + + + align:start position:0% +some costs vary a lot by time period so +the second model essentially is a + + align:start position:0% +the second model essentially is a + + + align:start position:0% +the second model essentially is a +variation or an extension of the first + + align:start position:0% +variation or an extension of the first + + + align:start position:0% +variation or an extension of the first +one where we do take some specific costs + + align:start position:0% +one where we do take some specific costs + + + align:start position:0% +one where we do take some specific costs +that are very sensitive to time and and + + align:start position:0% +that are very sensitive to time and and + + + align:start position:0% +that are very sensitive to time and and +capture that those offences over time + + align:start position:0% +capture that those offences over time + + + align:start position:0% +capture that those offences over time +and then we'll talk about incremental + + align:start position:0% +and then we'll talk about incremental + + + align:start position:0% +and then we'll talk about incremental +fixed variable customers we're doing + + align:start position:0% +fixed variable customers we're doing + + + align:start position:0% +fixed variable customers we're doing +examples of all of these a certain worth + + align:start position:0% +examples of all of these a certain worth + + + align:start position:0% +examples of all of these a certain worth +the first one the fully allocated cost + + align:start position:0% +the first one the fully allocated cost + + + align:start position:0% +the first one the fully allocated cost +effective also here's what you do you + + align:start position:0% +effective also here's what you do you + + + align:start position:0% +effective also here's what you do you +select some causal factors right so + + align:start position:0% +select some causal factors right so + + + align:start position:0% +select some causal factors right so +these are not necessarily may be causal + + align:start position:0% +these are not necessarily may be causal + + + align:start position:0% +these are not necessarily may be causal +factors not the best term but that's + + align:start position:0% +factors not the best term but that's + + + align:start position:0% +factors not the best term but that's +what this models class is called I would + + align:start position:0% +what this models class is called I would + + + align:start position:0% +what this models class is called I would +say these are explanatory variables more + + align:start position:0% +say these are explanatory variables more + + + align:start position:0% +say these are explanatory variables more +more than causal factors they don't have + + align:start position:0% +more than causal factors they don't have + + + align:start position:0% +more than causal factors they don't have +to cause the cost directly but they are + + align:start position:0% +to cause the cost directly but they are + + + align:start position:0% +to cause the cost directly but they are +useless explanatory variables of a model + + align:start position:0% +useless explanatory variables of a model + + + align:start position:0% +useless explanatory variables of a model +of cost right so then you assign each + + align:start position:0% +of cost right so then you assign each + + + align:start position:0% +of cost right so then you assign each +expense type to each of the factors so + + align:start position:0% +expense type to each of the factors so + + + align:start position:0% +expense type to each of the factors so +for example operator wages and benefits + + align:start position:0% +for example operator wages and benefits + + + align:start position:0% +for example operator wages and benefits +where would that go if you were thinking + + align:start position:0% +where would that go if you were thinking + + + align:start position:0% +where would that go if you were thinking +of three kinds of explanatory variables + + align:start position:0% +of three kinds of explanatory variables + + + align:start position:0% +of three kinds of explanatory variables +vehicle hours being one vehicle miles + + align:start position:0% +vehicle hours being one vehicle miles + + + align:start position:0% +vehicle hours being one vehicle miles +would be being the second one peak + + align:start position:0% +would be being the second one peak + + + align:start position:0% +would be being the second one peak +vehicles being the third and you're + + align:start position:0% +vehicles being the third and you're + + + align:start position:0% +vehicles being the third and you're +going to say every cost you incur to one + + align:start position:0% +going to say every cost you incur to one + + + align:start position:0% +going to say every cost you incur to one +of those three then operator ways and + + align:start position:0% +of those three then operator ways and + + + align:start position:0% +of those three then operator ways and +benefits are more appropriately assigned + + align:start position:0% +benefits are more appropriately assigned + + + align:start position:0% +benefits are more appropriately assigned +to vehicle hours right because you pay + + align:start position:0% +to vehicle hours right because you pay + + + align:start position:0% +to vehicle hours right because you pay +each drivers by the hour so this is the + + align:start position:0% +each drivers by the hour so this is the + + + align:start position:0% +each drivers by the hour so this is the +one that it relates to most closely fuel + + align:start position:0% +one that it relates to most closely fuel + + + align:start position:0% +one that it relates to most closely fuel +so fuel may be a combination of evil + + align:start position:0% +so fuel may be a combination of evil + + + align:start position:0% +so fuel may be a combination of evil +hours and evil miles or if you have to + + align:start position:0% +hours and evil miles or if you have to + + + align:start position:0% +hours and evil miles or if you have to +assign them to one then the evil miles + + align:start position:0% +assign them to one then the evil miles + + + align:start position:0% +assign them to one then the evil miles +you think of the fuel mileage of + + align:start position:0% +you think of the fuel mileage of + + + align:start position:0% +you think of the fuel mileage of +vehicles right so that's the one that + + align:start position:0% +vehicles right so that's the one that + + + align:start position:0% +vehicles right so that's the one that +most closely relates vehicle miles to + + align:start position:0% +most closely relates vehicle miles to + + + align:start position:0% +most closely relates vehicle miles to +feel and then administration + + align:start position:0% +feel and then administration + + + align:start position:0% +feel and then administration +well administration you might want to + + align:start position:0% +well administration you might want to + + + align:start position:0% +well administration you might want to +assign it to big vehicles because big + + align:start position:0% +assign it to big vehicles because big + + + align:start position:0% +assign it to big vehicles because big +vehicles is a proxy for how big is this + + align:start position:0% +vehicles is a proxy for how big is this + + + align:start position:0% +vehicles is a proxy for how big is this +agency and the bigger that agency the + + align:start position:0% +agency and the bigger that agency the + + + align:start position:0% +agency and the bigger that agency the +bigger the administration costs right so + + align:start position:0% +bigger the administration costs right so + + + align:start position:0% +bigger the administration costs right so +it's one way of assigning these things + + align:start position:0% +it's one way of assigning these things + + + align:start position:0% +it's one way of assigning these things +so this is an example right + + align:start position:0% +so this is an example right + + + align:start position:0% +so this is an example right +after you do all those assignments you + + align:start position:0% +after you do all those assignments you + + + align:start position:0% +after you do all those assignments you +calculate the average costs for each of + + align:start position:0% +calculate the average costs for each of + + + align:start position:0% +calculate the average costs for each of +the + + align:start position:0% +the + + + align:start position:0% +the +so you have for example the cost of the + + align:start position:0% +so you have for example the cost of the + + + align:start position:0% +so you have for example the cost of the +signs the vehicle hours so I have a + + align:start position:0% +signs the vehicle hours so I have a + + + align:start position:0% +signs the vehicle hours so I have a +total number of people hours and you + + align:start position:0% +total number of people hours and you + + + align:start position:0% +total number of people hours and you +have those unit costs and then the + + align:start position:0% +have those unit costs and then the + + + align:start position:0% +have those unit costs and then the +customer was simply each of those unit + + align:start position:0% +customer was simply each of those unit + + + align:start position:0% +customer was simply each of those unit +costs the lighter or multiplied by the + + align:start position:0% +costs the lighter or multiplied by the + + + align:start position:0% +costs the lighter or multiplied by the +three expire variable so you write so + + align:start position:0% +three expire variable so you write so + + + align:start position:0% +three expire variable so you write so +you multiply your unit vehicle our cost + + align:start position:0% +you multiply your unit vehicle our cost + + + align:start position:0% +you multiply your unit vehicle our cost +way number people hours your you know + + align:start position:0% +way number people hours your you know + + + align:start position:0% +way number people hours your you know +people miles cost by people miles and + + align:start position:0% +people miles cost by people miles and + + + align:start position:0% +people miles cost by people miles and +your a unit be vehicles cosplay vehicles + + align:start position:0% +your a unit be vehicles cosplay vehicles + + + align:start position:0% +your a unit be vehicles cosplay vehicles +and that is the total cost of the agency + + align:start position:0% + + + + align:start position:0% + +categories to say the cost to sign the + + align:start position:0% +categories to say the cost to sign the + + + align:start position:0% +categories to say the cost to sign the +vehicle hours are as yes so that's one + + align:start position:0% +vehicle hours are as yes so that's one + + + align:start position:0% +vehicle hours are as yes so that's one +of the that's one of the characteristics + + align:start position:0% +of the that's one of the characteristics + + + align:start position:0% +of the that's one of the characteristics +and perhaps weaknesses of this kind of + + align:start position:0% +and perhaps weaknesses of this kind of + + + align:start position:0% +and perhaps weaknesses of this kind of +model that requires judgment of the + + align:start position:0% +model that requires judgment of the + + + align:start position:0% +model that requires judgment of the +person to assign to first to generate + + align:start position:0% +person to assign to first to generate + + + align:start position:0% +person to assign to first to generate +these classes and these explanatory + + align:start position:0% +these classes and these explanatory + + + align:start position:0% +these classes and these explanatory +variables and second to assign them to + + align:start position:0% +variables and second to assign them to + + + align:start position:0% +variables and second to assign them to +each cost class or each account in a + + align:start position:0% +each cost class or each account in a + + + align:start position:0% +each cost class or each account in a +letter to each of these explanatory + + align:start position:0% +letter to each of these explanatory + + + align:start position:0% +letter to each of these explanatory +variables so but these ones are are used + + align:start position:0% +variables so but these ones are are used + + + align:start position:0% +variables so but these ones are are used +in the industry so so okay so if you + + align:start position:0% +in the industry so so okay so if you + + + align:start position:0% +in the industry so so okay so if you +plug in the number of evil hours and + + align:start position:0% +plug in the number of evil hours and + + + align:start position:0% +plug in the number of evil hours and +equal miles and P vehicles that you use + + align:start position:0% +equal miles and P vehicles that you use + + + align:start position:0% +equal miles and P vehicles that you use +to estimate this model then you're just + + align:start position:0% +to estimate this model then you're just + + + align:start position:0% +to estimate this model then you're just +going to get the total cost of + + align:start position:0% +going to get the total cost of + + + align:start position:0% +going to get the total cost of +operations or of our total combined cost + + align:start position:0% +operations or of our total combined cost + + + align:start position:0% +operations or of our total combined cost +if on the same period that these data + + align:start position:0% +if on the same period that these data + + + align:start position:0% +if on the same period that these data +came from but more interesting if you + + align:start position:0% +came from but more interesting if you + + + align:start position:0% +came from but more interesting if you +are considering expanding service and + + align:start position:0% +are considering expanding service and + + + align:start position:0% +are considering expanding service and +that will increase the end of our + + align:start position:0% +that will increase the end of our + + + align:start position:0% +that will increase the end of our +vehicle miles and P vehicles then this + + align:start position:0% +vehicle miles and P vehicles then this + + + align:start position:0% +vehicle miles and P vehicles then this +model will work in some ways to forecast + + align:start position:0% +model will work in some ways to forecast + + + align:start position:0% +model will work in some ways to forecast +what the total cost will be after you + + align:start position:0% +what the total cost will be after you + + + align:start position:0% +what the total cost will be after you +grow your agency right so this is + + align:start position:0% + + + + align:start position:0% + +shouldn't be because right you want to + + align:start position:0% +shouldn't be because right you want to + + + align:start position:0% +shouldn't be because right you want to +see all the kinds of expenses so I think + + align:start position:0% +see all the kinds of expenses so I think + + + align:start position:0% +see all the kinds of expenses so I think +a year make sense fit of fiscal year + + align:start position:0% +a year make sense fit of fiscal year + + + align:start position:0% +a year make sense fit of fiscal year +right because you'll have to put on a + + align:start position:0% +right because you'll have to put on a + + + align:start position:0% +right because you'll have to put on a +state out of state + + align:start position:0% +state out of state + + + align:start position:0% +state out of state +you don't count them on that fiscal year + + align:start position:0% +you don't count them on that fiscal year + + + align:start position:0% +you don't count them on that fiscal year +basis + + align:start position:0% +basis + + + align:start position:0% +basis +okay so here's an example from 1996 of + + align:start position:0% +okay so here's an example from 1996 of + + + align:start position:0% +okay so here's an example from 1996 of +plus and the MBTA so we have those three + + align:start position:0% +plus and the MBTA so we have those three + + + align:start position:0% +plus and the MBTA so we have those three +variables that we talked about leave our + + align:start position:0% +variables that we talked about leave our + + + align:start position:0% +variables that we talked about leave our +people miles antique vehicles we divide + + align:start position:0% +people miles antique vehicles we divide + + + align:start position:0% +people miles antique vehicles we divide +each of those into variable or fixed so + + align:start position:0% +each of those into variable or fixed so + + + align:start position:0% +each of those into variable or fixed so +some of the expenses are considered + + align:start position:0% +some of the expenses are considered + + + align:start position:0% +some of the expenses are considered +variable because they sort of scale up + + align:start position:0% +variable because they sort of scale up + + + align:start position:0% +variable because they sort of scale up +more linearly as you increase number of + + align:start position:0% +more linearly as you increase number of + + + align:start position:0% +more linearly as you increase number of +evil hours and others are more fixed + + align:start position:0% +evil hours and others are more fixed + + + align:start position:0% +evil hours and others are more fixed +expenses you wouldn't expect to get + + align:start position:0% +expenses you wouldn't expect to get + + + align:start position:0% +expenses you wouldn't expect to get +extra fixed costs by adding a few buses + + align:start position:0% +extra fixed costs by adding a few buses + + + align:start position:0% +extra fixed costs by adding a few buses +right so one example of that is if you + + align:start position:0% +right so one example of that is if you + + + align:start position:0% +right so one example of that is if you +yeah if you get 10 more buses for a new + + align:start position:0% +yeah if you get 10 more buses for a new + + + align:start position:0% +yeah if you get 10 more buses for a new +bus route you don't need a new + + align:start position:0% +bus route you don't need a new + + + align:start position:0% +bus route you don't need a new +maintenance facility right so your + + align:start position:0% +maintenance facility right so your + + + align:start position:0% +maintenance facility right so your +maintenance facility might be a + + align:start position:0% +maintenance facility might be a + + + align:start position:0% +maintenance facility might be a +considered a fixed expense and you might + + align:start position:0% +considered a fixed expense and you might + + + align:start position:0% +considered a fixed expense and you might +want a variable cost model to predict + + align:start position:0% +want a variable cost model to predict + + + align:start position:0% +want a variable cost model to predict +the changes of that small change or that + + align:start position:0% +the changes of that small change or that + + + align:start position:0% +the changes of that small change or that +marginal change so that's why we divide + + align:start position:0% +marginal change so that's why we divide + + + align:start position:0% +marginal change so that's why we divide +things into fixed and variable the total + + align:start position:0% +things into fixed and variable the total + + + align:start position:0% +things into fixed and variable the total +cost to be allocated is one hundred and + + align:start position:0% +cost to be allocated is one hundred and + + + align:start position:0% +cost to be allocated is one hundred and +seventy three point six million and will + + align:start position:0% +seventy three point six million and will + + + align:start position:0% +seventy three point six million and will +be divided over these six categories the + + align:start position:0% +be divided over these six categories the + + + align:start position:0% +be divided over these six categories the +three variables and they're fixed and + + align:start position:0% +three variables and they're fixed and + + + align:start position:0% +three variables and they're fixed and +variable + + align:start position:0% +variable + + + align:start position:0% +variable +variance here we have the percentages of + + align:start position:0% +variance here we have the percentages of + + + align:start position:0% +variance here we have the percentages of +each and the unit costs so now water + + align:start position:0% +each and the unit costs so now water + + + align:start position:0% +each and the unit costs so now water +pumping cost models followings approach + + align:start position:0% +pumping cost models followings approach + + + align:start position:0% +pumping cost models followings approach +us a first and simple one very + + align:start position:0% +us a first and simple one very + + + align:start position:0% +us a first and simple one very +traditional model is the first one + + align:start position:0% +traditional model is the first one + + + align:start position:0% +traditional model is the first one +listed here so 39.82 which is the total + + align:start position:0% +listed here so 39.82 which is the total + + + align:start position:0% +listed here so 39.82 which is the total +unit cost of rubbing vehicle hours it's + + align:start position:0% +unit cost of rubbing vehicle hours it's + + + align:start position:0% +unit cost of rubbing vehicle hours it's +a solid 30 7.39 2.69 times the number + + align:start position:0% +a solid 30 7.39 2.69 times the number + + + align:start position:0% +a solid 30 7.39 2.69 times the number +for any day of hours and then 280 41 + + align:start position:0% +for any day of hours and then 280 41 + + + align:start position:0% +for any day of hours and then 280 41 +which is the sum of 2.27 at zero point + + align:start position:0% +which is the sum of 2.27 at zero point + + + align:start position:0% +which is the sum of 2.27 at zero point +fourteen times from your yellow miles + + align:start position:0% +fourteen times from your yellow miles + + + align:start position:0% +fourteen times from your yellow miles +times some factor and that factor + + align:start position:0% +times some factor and that factor + + + align:start position:0% +times some factor and that factor +essentially here we have we're not we're + + align:start position:0% +essentially here we have we're not we're + + + align:start position:0% +essentially here we have we're not we're +not considered we're not capturing the + + align:start position:0% +not considered we're not capturing the + + + align:start position:0% +not considered we're not capturing the +difference between fixed and variable + + align:start position:0% +difference between fixed and variable + + + align:start position:0% +difference between fixed and variable +costs right so that's why we add them up + + align:start position:0% +costs right so that's why we add them up + + + align:start position:0% +costs right so that's why we add them up +here 39 + + align:start position:0% +here 39 + + + align:start position:0% +here 39 +2.41 the other characteristic of this + + align:start position:0% +2.41 the other characteristic of this + + + align:start position:0% +2.41 the other characteristic of this +model is that it does not take vehicles + + align:start position:0% +model is that it does not take vehicles + + + align:start position:0% +model is that it does not take vehicles +as an explanatory variable right so we + + align:start position:0% +as an explanatory variable right so we + + + align:start position:0% +as an explanatory variable right so we +address that with this adjustment factor + + align:start position:0% +address that with this adjustment factor + + + align:start position:0% +address that with this adjustment factor +if you take the total cost which is + + align:start position:0% +if you take the total cost which is + + + align:start position:0% +if you take the total cost which is +honor and seventy three point six and + + align:start position:0% +honor and seventy three point six and + + + align:start position:0% +honor and seventy three point six and +you divided by the sum this sum of the + + align:start position:0% +you divided by the sum this sum of the + + + align:start position:0% +you divided by the sum this sum of the +unit costs for row any vehicle hours and + + align:start position:0% +unit costs for row any vehicle hours and + + + align:start position:0% +unit costs for row any vehicle hours and +revenue vehicle miles you get one point + + align:start position:0% +revenue vehicle miles you get one point + + + align:start position:0% +revenue vehicle miles you get one point +two six so any questions and you've + + align:start position:0% +two six so any questions and you've + + + align:start position:0% +two six so any questions and you've +invited by the total of the total number + + align:start position:0% +invited by the total of the total number + + + align:start position:0% +invited by the total of the total number +of unit costs that you are capturing + + align:start position:0% +of unit costs that you are capturing + + + align:start position:0% +of unit costs that you are capturing +with explanatory variables which is + + align:start position:0% +with explanatory variables which is + + + align:start position:0% +with explanatory variables which is +[Music] + + align:start position:0% + + + + align:start position:0% + +right so we're dividing the total by the + + align:start position:0% +right so we're dividing the total by the + + + align:start position:0% +right so we're dividing the total by the +amount that we did capture and then okay + + align:start position:0% +amount that we did capture and then okay + + + align:start position:0% +amount that we did capture and then okay +the factors of so this is a very simple + + align:start position:0% +the factors of so this is a very simple + + + align:start position:0% +the factors of so this is a very simple +model of a full annual cost for the + + align:start position:0% +model of a full annual cost for the + + + align:start position:0% +model of a full annual cost for the +agency yeah we're looking at the fiscal + + align:start position:0% +agency yeah we're looking at the fiscal + + + align:start position:0% +agency yeah we're looking at the fiscal +year and it's sensitive to two variables + + align:start position:0% +year and it's sensitive to two variables + + + align:start position:0% +year and it's sensitive to two variables +it's not sunset it's a time period and + + align:start position:0% +it's not sunset it's a time period and + + + align:start position:0% +it's not sunset it's a time period and +it's mixing and fixed and variable costs + + align:start position:0% +it's mixing and fixed and variable costs + + + align:start position:0% +it's mixing and fixed and variable costs +so this model may not be the best one + + align:start position:0% +so this model may not be the best one + + + align:start position:0% +so this model may not be the best one +for some applications + + align:start position:0% +for some applications + + + align:start position:0% +for some applications +I just what's the intuition behind using + + align:start position:0% +I just what's the intuition behind using + + + align:start position:0% +I just what's the intuition behind using +vehicle hours it's something that you + + align:start position:0% +vehicle hours it's something that you + + + align:start position:0% +vehicle hours it's something that you +think I see is always measure + + align:start position:0% +think I see is always measure + + + align:start position:0% +think I see is always measure +reporter so it's something that there's + + align:start position:0% +reporter so it's something that there's + + + align:start position:0% +reporter so it's something that there's +already a data collection effort for it + + align:start position:0% +already a data collection effort for it + + + align:start position:0% +already a data collection effort for it +but if you think about especially its + + align:start position:0% +but if you think about especially its + + + align:start position:0% +but if you think about especially its +tradition obligations without automatic + + align:start position:0% +tradition obligations without automatic + + + align:start position:0% +tradition obligations without automatic +data function there's an effort to + + align:start position:0% +data function there's an effort to + + + align:start position:0% +data function there's an effort to +measure anything you deliver all right + + align:start position:0% +measure anything you deliver all right + + + align:start position:0% +measure anything you deliver all right +collect how much output you produce and + + align:start position:0% +collect how much output you produce and + + + align:start position:0% +collect how much output you produce and +so you already have that it's something + + align:start position:0% +so you already have that it's something + + + align:start position:0% +so you already have that it's something +that then you can use and it relates to + + align:start position:0% +that then you can use and it relates to + + + align:start position:0% +that then you can use and it relates to +service right so it's lutely to service + + align:start position:0% +service right so it's lutely to service + + + align:start position:0% +service right so it's lutely to service +output so if you want to these are + + align:start position:0% +output so if you want to these are + + + align:start position:0% +output so if you want to these are +variables that are also going to be + + align:start position:0% +variables that are also going to be + + + align:start position:0% +variables that are also going to be +found in any service planning proposal + + align:start position:0% +found in any service planning proposal + + + align:start position:0% +found in any service planning proposal +in some way or another if you increase + + align:start position:0% +in some way or another if you increase + + + align:start position:0% +in some way or another if you increase +if you extend routes than that increases + + align:start position:0% +if you extend routes than that increases + + + align:start position:0% +if you extend routes than that increases +both of these right I guess my my other + + align:start position:0% +both of these right I guess my my other + + + align:start position:0% +both of these right I guess my my other +question was like what's the intuition + + align:start position:0% +question was like what's the intuition + + + align:start position:0% +question was like what's the intuition +behind vehicle hours being more + + align:start position:0% +behind vehicle hours being more + + + align:start position:0% +behind vehicle hours being more +expressively more expensive in vehicle + + align:start position:0% +expressively more expensive in vehicle + + + align:start position:0% +expressively more expensive in vehicle +miles the events on how you assign each + + align:start position:0% +miles the events on how you assign each + + + align:start position:0% +miles the events on how you assign each +of these cost categories - yeah + + align:start position:0% +of these cost categories - yeah + + + align:start position:0% +of these cost categories - yeah +right so it's not that like operating a + + align:start position:0% +right so it's not that like operating a + + + align:start position:0% +right so it's not that like operating a +bus well I mean in this case wages are + + align:start position:0% +bus well I mean in this case wages are + + + align:start position:0% +bus well I mean in this case wages are +Prince wages and benefits or principal + + align:start position:0% +Prince wages and benefits or principal + + + align:start position:0% +Prince wages and benefits or principal +one of the key yeah one of the key costs + + align:start position:0% +one of the key yeah one of the key costs + + + align:start position:0% +one of the key yeah one of the key costs +for the agency and that's being + + align:start position:0% +for the agency and that's being + + + align:start position:0% +for the agency and that's being +reflected entirely in vehicle hours and + + align:start position:0% +reflected entirely in vehicle hours and + + + align:start position:0% +reflected entirely in vehicle hours and +potentially fuel is a second one and + + align:start position:0% +potentially fuel is a second one and + + + align:start position:0% +potentially fuel is a second one and +that is at least partially covered by + + align:start position:0% +that is at least partially covered by + + + align:start position:0% +that is at least partially covered by +rotating vehicle hours it could be I'm + + align:start position:0% +rotating vehicle hours it could be I'm + + + align:start position:0% +rotating vehicle hours it could be I'm +not sure in this model if it is I + + align:start position:0% +not sure in this model if it is I + + + align:start position:0% +not sure in this model if it is I +suspect that everything was assigned to + + align:start position:0% +suspect that everything was assigned to + + + align:start position:0% +suspect that everything was assigned to +be able - but but it could be so yeah + + align:start position:0% +be able - but but it could be so yeah + + + align:start position:0% +be able - but but it could be so yeah +vehicle hours is the proxy for more + + align:start position:0% +vehicle hours is the proxy for more + + + align:start position:0% +vehicle hours is the proxy for more +things and more costs are being assigned + + align:start position:0% +things and more costs are being assigned + + + align:start position:0% +things and more costs are being assigned +to that variable you know I can use some + + align:start position:0% +to that variable you know I can use some + + + align:start position:0% +to that variable you know I can use some +examples of variable and fixed costs + + align:start position:0% + + + + align:start position:0% + +yeah we'll actually see more of those + + align:start position:0% +yeah we'll actually see more of those + + + align:start position:0% +yeah we'll actually see more of those +but you know variable cost fuel is + + align:start position:0% +but you know variable cost fuel is + + + align:start position:0% +but you know variable cost fuel is +variable right because you as you drive + + align:start position:0% +variable right because you as you drive + + + align:start position:0% +variable right because you as you drive +more you consume more and if you all of + + align:start position:0% +more you consume more and if you all of + + + align:start position:0% +more you consume more and if you all of +a sudden operate the service then you'll + + align:start position:0% +a sudden operate the service then you'll + + + align:start position:0% +a sudden operate the service then you'll +see that drop immediately a fixed cost + + align:start position:0% +see that drop immediately a fixed cost + + + align:start position:0% +see that drop immediately a fixed cost +could be + + align:start position:0% +could be + + + align:start position:0% +could be +the administration costs or for let's + + align:start position:0% +the administration costs or for let's + + + align:start position:0% +the administration costs or for let's +say your service planning team right + + align:start position:0% +say your service planning team right + + + align:start position:0% +say your service planning team right +so you've hired people and if you drop + + align:start position:0% +so you've hired people and if you drop + + + align:start position:0% +so you've hired people and if you drop +service a little bit you're not + + align:start position:0% +service a little bit you're not + + + align:start position:0% +service a little bit you're not +necessarily going to fire people or if + + align:start position:0% +necessarily going to fire people or if + + + align:start position:0% +necessarily going to fire people or if +you expound service you're not + + align:start position:0% +you expound service you're not + + + align:start position:0% +you expound service you're not +necessarily going to hire a bunch of + + align:start position:0% +necessarily going to hire a bunch of + + + align:start position:0% +necessarily going to hire a bunch of +people or you may not need new offices + + align:start position:0% +people or you may not need new offices + + + align:start position:0% +people or you may not need new offices +for them so all those things are more + + align:start position:0% +for them so all those things are more + + + align:start position:0% +for them so all those things are more +fixed Thanks okay okay second model so + + align:start position:0% +fixed Thanks okay okay second model so + + + align:start position:0% +fixed Thanks okay okay second model so +here we have the same first part of the + + align:start position:0% +here we have the same first part of the + + + align:start position:0% +here we have the same first part of the +model but now instead of using the + + align:start position:0% +model but now instead of using the + + + align:start position:0% +model but now instead of using the +adjustment factor we directly take the + + align:start position:0% +adjustment factor we directly take the + + + align:start position:0% +adjustment factor we directly take the +unit cost of peak vehicles and add it in + + align:start position:0% +unit cost of peak vehicles and add it in + + + align:start position:0% +unit cost of peak vehicles and add it in +so now we have a model as sensitive to + + align:start position:0% +so now we have a model as sensitive to + + + align:start position:0% +so now we have a model as sensitive to +peak vehicles as well okay and we don't + + align:start position:0% +peak vehicles as well okay and we don't + + + align:start position:0% +peak vehicles as well okay and we don't +need the adjustment because all of the + + align:start position:0% +need the adjustment because all of the + + + align:start position:0% +need the adjustment because all of the +things that have been assigned to these + + align:start position:0% +things that have been assigned to these + + + align:start position:0% +things that have been assigned to these +vehicles are are it's being directly + + align:start position:0% +vehicles are are it's being directly + + + align:start position:0% +vehicles are are it's being directly +related to the vehicles that's a simple + + align:start position:0% +related to the vehicles that's a simple + + + align:start position:0% +related to the vehicles that's a simple +variation and here we have a variable + + align:start position:0% +variation and here we have a variable + + + align:start position:0% +variation and here we have a variable +annual cost model so these first two + + align:start position:0% +annual cost model so these first two + + + align:start position:0% +annual cost model so these first two +have all of the costs fixed and variable + + align:start position:0% +have all of the costs fixed and variable + + + align:start position:0% +have all of the costs fixed and variable +but for some applications you're only + + align:start position:0% +but for some applications you're only + + + align:start position:0% +but for some applications you're only +interested in variable angle cost and + + align:start position:0% +interested in variable angle cost and + + + align:start position:0% +interested in variable angle cost and +I've given the example of minor + + align:start position:0% +I've given the example of minor + + + align:start position:0% +I've given the example of minor +expansion at service where you add a + + align:start position:0% +expansion at service where you add a + + + align:start position:0% +expansion at service where you add a +little bit of service or remove a little + + align:start position:0% +little bit of service or remove a little + + + align:start position:0% +little bit of service or remove a little +bit of service and you wouldn't expect + + align:start position:0% +bit of service and you wouldn't expect + + + align:start position:0% +bit of service and you wouldn't expect +to imperfect cost as a result so here we + + align:start position:0% +to imperfect cost as a result so here we + + + align:start position:0% +to imperfect cost as a result so here we +then only consider the unit costs of the + + align:start position:0% +then only consider the unit costs of the + + + align:start position:0% +then only consider the unit costs of the +variable portion of any vehicle hours + + align:start position:0% +variable portion of any vehicle hours + + + align:start position:0% +variable portion of any vehicle hours +which is 37 point 13 and 2.27 for + + align:start position:0% +which is 37 point 13 and 2.27 for + + + align:start position:0% +which is 37 point 13 and 2.27 for +revenue vehicle miles yeah any questions + + align:start position:0% +revenue vehicle miles yeah any questions + + + align:start position:0% +revenue vehicle miles yeah any questions +on these okay as I mentioned before one + + align:start position:0% +on these okay as I mentioned before one + + + align:start position:0% +on these okay as I mentioned before one +of the key witnesses of these walls so + + align:start position:0% +of the key witnesses of these walls so + + + align:start position:0% +of the key witnesses of these walls so +they're not sensitive to time periods + + align:start position:0% +they're not sensitive to time periods + + + align:start position:0% +they're not sensitive to time periods +right so it's much more expensive to + + align:start position:0% +right so it's much more expensive to + + + align:start position:0% +right so it's much more expensive to +operate service on the deep than it is + + align:start position:0% +operate service on the deep than it is + + + align:start position:0% +operate service on the deep than it is +off-peak if you were to use say that I + + align:start position:0% +off-peak if you were to use say that I + + + align:start position:0% +off-peak if you were to use say that I +rely on cost model for the streets 1778 + + align:start position:0% +rely on cost model for the streets 1778 + + + align:start position:0% +rely on cost model for the streets 1778 +and now we want to expand it to go to + + align:start position:0% +and now we want to expand it to go to + + + align:start position:0% +and now we want to expand it to go to +Kendall or Lechmere somewhere else and + + align:start position:0% +Kendall or Lechmere somewhere else and + + + align:start position:0% +Kendall or Lechmere somewhere else and +you have a greater number for many of + + align:start position:0% +you have a greater number for many of + + + align:start position:0% +you have a greater number for many of +you about hours having a vehicle miles + + align:start position:0% +you about hours having a vehicle miles + + + align:start position:0% +you about hours having a vehicle miles +if you maybe a few expenses + + align:start position:0% +if you maybe a few expenses + + + align:start position:0% +if you maybe a few expenses +proportionally throughout the peak + + align:start position:0% +proportionally throughout the peak + + + align:start position:0% +proportionally throughout the peak +you're fine but if you only expand + + align:start position:0% +you're fine but if you only expand + + + align:start position:0% +you're fine but if you only expand +certain the peak or do it + + align:start position:0% +certain the peak or do it + + + align:start position:0% +certain the peak or do it +disproportionately peak off-peak then + + align:start position:0% +disproportionately peak off-peak then + + + align:start position:0% +disproportionately peak off-peak then +this model will not capture those + + align:start position:0% +this model will not capture those + + + align:start position:0% +this model will not capture those +differences very well and for that we + + align:start position:0% +differences very well and for that we + + + align:start position:0% +differences very well and for that we +need a temporal variation which is our + + align:start position:0% +need a temporal variation which is our + + + align:start position:0% +need a temporal variation which is our +master ticket but but why why wouldn't + + align:start position:0% +master ticket but but why why wouldn't + + + align:start position:0% +master ticket but but why why wouldn't +you capture it because suppose I add + + align:start position:0% +you capture it because suppose I add + + + align:start position:0% +you capture it because suppose I add +service suppose I had a bus on the beach + + align:start position:0% +service suppose I had a bus on the beach + + + align:start position:0% +service suppose I had a bus on the beach +so now peak vehicles that gets impacted + + align:start position:0% +so now peak vehicles that gets impacted + + + align:start position:0% +so now peak vehicles that gets impacted +and suppose I take a few and I and they + + align:start position:0% +and suppose I take a few and I and they + + + align:start position:0% +and suppose I take a few and I and they +say okay there's fuel fuel affects + + align:start position:0% +say okay there's fuel fuel affects + + + align:start position:0% +say okay there's fuel fuel affects +revenue miles but also it affects + + align:start position:0% +revenue miles but also it affects + + + align:start position:0% +revenue miles but also it affects +revenue America put fuel in twice both + + align:start position:0% +revenue America put fuel in twice both + + + align:start position:0% +revenue America put fuel in twice both +in India hours and - now I can also take + + align:start position:0% +in India hours and - now I can also take + + + align:start position:0% +in India hours and - now I can also take +into account the fact that you know the + + align:start position:0% +into account the fact that you know the + + + align:start position:0% +into account the fact that you know the +bus is sitting in traffic and burning + + align:start position:0% +bus is sitting in traffic and burning + + + align:start position:0% +bus is sitting in traffic and burning +fuel and also but but I'm taking that + + align:start position:0% +fuel and also but but I'm taking that + + + align:start position:0% +fuel and also but but I'm taking that +into account so so why is this model + + align:start position:0% +into account so so why is this model + + + align:start position:0% +into account so so why is this model +necessarily Charlotte that's it goes + + align:start position:0% +necessarily Charlotte that's it goes + + + align:start position:0% +necessarily Charlotte that's it goes +back to the questions why why does this + + align:start position:0% +back to the questions why why does this + + + align:start position:0% +back to the questions why why does this +model not adequately capture peak versus + + align:start position:0% +model not adequately capture peak versus + + + align:start position:0% +model not adequately capture peak versus +off-peak cost so it goes back to this + + align:start position:0% +off-peak cost so it goes back to this + + + align:start position:0% +off-peak cost so it goes back to this +calculating average costs by factor + + align:start position:0% +calculating average costs by factor + + + align:start position:0% +calculating average costs by factor +right so these are averages containing + + align:start position:0% +right so these are averages containing + + + align:start position:0% +right so these are averages containing +averages of all the vehicles at all + + align:start position:0% +averages of all the vehicles at all + + + align:start position:0% +averages of all the vehicles at all +times of day and dividing by explaining + + align:start position:0% +times of day and dividing by explaining + + + align:start position:0% +times of day and dividing by explaining +them with an explanatory variable that + + align:start position:0% +them with an explanatory variable that + + + align:start position:0% +them with an explanatory variable that +is not necessarily what's directly + + align:start position:0% +is not necessarily what's directly + + + align:start position:0% +is not necessarily what's directly +crossing it right so especially driver + + align:start position:0% +crossing it right so especially driver + + + align:start position:0% +crossing it right so especially driver +costs are going to vary a lot by sort of + + align:start position:0% +costs are going to vary a lot by sort of + + + align:start position:0% +costs are going to vary a lot by sort of +feed off peak and we're taking an + + align:start position:0% +feed off peak and we're taking an + + + align:start position:0% +feed off peak and we're taking an +average so if you increase service + + align:start position:0% +average so if you increase service + + + align:start position:0% +average so if you increase service +proportionally you're fine but the unit + + align:start position:0% +proportionally you're fine but the unit + + + align:start position:0% +proportionally you're fine but the unit +cost is not reflecting the difference + + align:start position:0% +cost is not reflecting the difference + + + align:start position:0% +cost is not reflecting the difference +between peak and off-peak so what's the + + align:start position:0% +between peak and off-peak so what's the + + + align:start position:0% +between peak and off-peak so what's the +unit cost itself is more than though + + align:start position:0% +unit cost itself is more than though + + + align:start position:0% +unit cost itself is more than though +more than the independent variable that + + align:start position:0% +more than the independent variable that + + + align:start position:0% +more than the independent variable that +you put in which is what you're saying + + align:start position:0% +you put in which is what you're saying + + + align:start position:0% +you put in which is what you're saying +you're saying I can measure the + + align:start position:0% +you're saying I can measure the + + + align:start position:0% +you're saying I can measure the +independent variable precisely so I can + + align:start position:0% +independent variable precisely so I can + + + align:start position:0% +independent variable precisely so I can +plug it in you know well but your factor + + align:start position:0% +plug it in you know well but your factor + + + align:start position:0% +plug it in you know well but your factor +is not really them I think so the + + align:start position:0% +is not really them I think so the + + + align:start position:0% +is not really them I think so the +approach of this model which is an + + align:start position:0% +approach of this model which is an + + + align:start position:0% +approach of this model which is an +extension of the first one is to do + + align:start position:0% +extension of the first one is to do + + + align:start position:0% +extension of the first one is to do +everything that we did except for driver + + align:start position:0% +everything that we did except for driver + + + align:start position:0% +everything that we did except for driver +costs because these costs are very cents + + align:start position:0% +costs because these costs are very cents + + + align:start position:0% +costs because these costs are very cents +the time of day and for for those costs + + align:start position:0% +the time of day and for for those costs + + + align:start position:0% +the time of day and for for those costs +for crew costs we take the day we + + align:start position:0% +for crew costs we take the day we + + + align:start position:0% +for crew costs we take the day we +divided it to 30-minute periods and then + + align:start position:0% +divided it to 30-minute periods and then + + + align:start position:0% +divided it to 30-minute periods and then +we look at all runs now a run is what a + + align:start position:0% +we look at all runs now a run is what a + + + align:start position:0% +we look at all runs now a run is what a +driver does in a day right that's their + + align:start position:0% +driver does in a day right that's their + + + align:start position:0% +driver does in a day right that's their +their shift right it's a sequence of + + align:start position:0% +their shift right it's a sequence of + + + align:start position:0% +their shift right it's a sequence of +trips that are being operated by single + + align:start position:0% +trips that are being operated by single + + + align:start position:0% +trips that are being operated by single +driver and we look at all runs and all + + align:start position:0% +driver and we look at all runs and all + + + align:start position:0% +driver and we look at all runs and all +periods and for each period a run that + + align:start position:0% +periods and for each period a run that + + + align:start position:0% +periods and for each period a run that +is at least this house at least fifteen + + align:start position:0% +is at least this house at least fifteen + + + align:start position:0% +is at least this house at least fifteen +minutes in that period gets included in + + align:start position:0% +minutes in that period gets included in + + + align:start position:0% +minutes in that period gets included in +that period right and then we compute + + align:start position:0% +that period right and then we compute + + + align:start position:0% +that period right and then we compute +the average pay-for-view hour by + + align:start position:0% +the average pay-for-view hour by + + + align:start position:0% +the average pay-for-view hour by +dividing the daily pay by the number of + + align:start position:0% +dividing the daily pay by the number of + + + align:start position:0% +dividing the daily pay by the number of +vehicle hours over all runs in that + + align:start position:0% +vehicle hours over all runs in that + + + align:start position:0% +vehicle hours over all runs in that +period so each of these runs is going to + + align:start position:0% +period so each of these runs is going to + + + align:start position:0% +period so each of these runs is going to +have a different cost some runs are + + align:start position:0% +have a different cost some runs are + + + align:start position:0% +have a different cost some runs are +gonna operate more in the peak and + + align:start position:0% +gonna operate more in the peak and + + + align:start position:0% +gonna operate more in the peak and +they're gonna have more overtime for + + align:start position:0% +they're gonna have more overtime for + + + align:start position:0% +they're gonna have more overtime for +example or more spreaded penalties and + + align:start position:0% +example or more spreaded penalties and + + + align:start position:0% +example or more spreaded penalties and +we'll talk about those now and so those + + align:start position:0% +we'll talk about those now and so those + + + align:start position:0% +we'll talk about those now and so those +runs will be more expensive other runs + + align:start position:0% +runs will be more expensive other runs + + + align:start position:0% +runs will be more expensive other runs +that are straight are going to be less + + align:start position:0% +that are straight are going to be less + + + align:start position:0% +that are straight are going to be less +expensive and you can calculate an + + align:start position:0% +expensive and you can calculate an + + + align:start position:0% +expensive and you can calculate an +average for each 30 or 15-minute period + + align:start position:0% +average for each 30 or 15-minute period + + + align:start position:0% +average for each 30 or 15-minute period +so now we have an average again but it's + + align:start position:0% +so now we have an average again but it's + + + align:start position:0% +so now we have an average again but it's +by time of day for a small bucket of + + align:start position:0% +by time of day for a small bucket of + + + align:start position:0% +by time of day for a small bucket of +time and then for each of those we find + + align:start position:0% +time and then for each of those we find + + + align:start position:0% +time and then for each of those we find +the minimum the average of the maximum + + align:start position:0% +the minimum the average of the maximum + + + align:start position:0% +the minimum the average of the maximum +so we're not only going to look at + + align:start position:0% +so we're not only going to look at + + + align:start position:0% +so we're not only going to look at +average is where you'll also look at the + + align:start position:0% +average is where you'll also look at the + + + align:start position:0% +average is where you'll also look at the +distribution of costs along each period + + align:start position:0% +distribution of costs along each period + + + align:start position:0% +distribution of costs along each period +and this is just an equation for average + + align:start position:0% +and this is just an equation for average + + + align:start position:0% +and this is just an equation for average +so what we have here is the sum over all + + align:start position:0% +so what we have here is the sum over all + + + align:start position:0% +so what we have here is the sum over all +runs in a specific period this is the + + align:start position:0% +runs in a specific period this is the + + + align:start position:0% +runs in a specific period this is the +wage the total pay for that room divided + + align:start position:0% +wage the total pay for that room divided + + + align:start position:0% +wage the total pay for that room divided +by the number of hours + + align:start position:0% +by the number of hours + + + align:start position:0% +by the number of hours +so we compute the average okay if we + + align:start position:0% +so we compute the average okay if we + + + align:start position:0% +so we compute the average okay if we +look at the driver requirements for the + + align:start position:0% +look at the driver requirements for the + + + align:start position:0% +look at the driver requirements for the +MBTA back in 1983 30 1980 this is what + + align:start position:0% +MBTA back in 1983 30 1980 this is what + + + align:start position:0% +MBTA back in 1983 30 1980 this is what +we get so many more drivers are required + + align:start position:0% +we get so many more drivers are required + + + align:start position:0% +we get so many more drivers are required +in the a.m. peak and the PMP then are + + align:start position:0% +in the a.m. peak and the PMP then are + + + align:start position:0% +in the a.m. peak and the PMP then are +required off-peak or early + + align:start position:0% +required off-peak or early + + + align:start position:0% +required off-peak or early +the morning or late in the afternoon and + + align:start position:0% +the morning or late in the afternoon and + + + align:start position:0% +the morning or late in the afternoon and +evening + + align:start position:0% +evening + + + align:start position:0% +evening +why is that we've talked up a little bit + + align:start position:0% +why is that we've talked up a little bit + + + align:start position:0% +why is that we've talked up a little bit +about it already + + align:start position:0% +about it already + + + align:start position:0% +about it already +so you you provide more service why do + + align:start position:0% +so you you provide more service why do + + + align:start position:0% +so you you provide more service why do +you need to provide more service because + + align:start position:0% +you need to provide more service because + + + align:start position:0% +you need to provide more service because +more there's more demand for it right so + + align:start position:0% +more there's more demand for it right so + + + align:start position:0% +more there's more demand for it right so +if you provide the same level of service + + align:start position:0% +if you provide the same level of service + + + align:start position:0% +if you provide the same level of service +your buses would be too crowded and you + + align:start position:0% +your buses would be too crowded and you + + + align:start position:0% +your buses would be too crowded and you +would not deliver enough capacity what + + align:start position:0% +would not deliver enough capacity what + + + align:start position:0% +would not deliver enough capacity what +else they're also in traffic so buses + + align:start position:0% +else they're also in traffic so buses + + + align:start position:0% +else they're also in traffic so buses +are so in every trip that you run it + + align:start position:0% +are so in every trip that you run it + + + align:start position:0% +are so in every trip that you run it +takes longer great and stuck in traffic + + align:start position:0% +takes longer great and stuck in traffic + + + align:start position:0% +takes longer great and stuck in traffic +and well time for longer right so okay + + align:start position:0% +and well time for longer right so okay + + + align:start position:0% +and well time for longer right so okay +so if you need more if you need to + + align:start position:0% +so if you need more if you need to + + + align:start position:0% +so if you need more if you need to +provide more frequent service and each + + align:start position:0% +provide more frequent service and each + + + align:start position:0% +provide more frequent service and each +run that you do which trip that we run + + align:start position:0% +run that you do which trip that we run + + + align:start position:0% +run that you do which trip that we run +is slower then that means that you have + + align:start position:0% +is slower then that means that you have + + + align:start position:0% +is slower then that means that you have +a greater cycle time and a greater + + align:start position:0% +a greater cycle time and a greater + + + align:start position:0% +a greater cycle time and a greater +frequency and therefore a greater + + align:start position:0% +frequency and therefore a greater + + + align:start position:0% +frequency and therefore a greater +vehicle requirement from your first time + + align:start position:0% +vehicle requirement from your first time + + + align:start position:0% +vehicle requirement from your first time +right + + align:start position:0% +right + + + align:start position:0% +right +so and of course you need drivers the + + align:start position:0% +so and of course you need drivers the + + + align:start position:0% +so and of course you need drivers the +driverless vehicles so your driver + + align:start position:0% +driverless vehicles so your driver + + + align:start position:0% +driverless vehicles so your driver +requirements also goes up great so + + align:start position:0% +requirements also goes up great so + + + align:start position:0% +requirements also goes up great so +what's wrong with the time what's + + align:start position:0% +what's wrong with the time what's + + + align:start position:0% +what's wrong with the time what's +inconvenient about the timing of the + + align:start position:0% +inconvenient about the timing of the + + + align:start position:0% +inconvenient about the timing of the +peaks they are eight hours apart how + + align:start position:0% +peaks they are eight hours apart how + + + align:start position:0% +peaks they are eight hours apart how +long your shifts the bidding it always + + align:start position:0% +long your shifts the bidding it always + + + align:start position:0% +long your shifts the bidding it always +want rate so if we hire someone to start + + align:start position:0% +want rate so if we hire someone to start + + + align:start position:0% +want rate so if we hire someone to start +their shift at 6 a.m. they can't cover + + align:start position:0% +their shift at 6 a.m. they can't cover + + + align:start position:0% +their shift at 6 a.m. they can't cover +the pnt they only are the antique okay + + align:start position:0% +the pnt they only are the antique okay + + + align:start position:0% +the pnt they only are the antique okay +so what do we do if what one option is + + align:start position:0% +so what do we do if what one option is + + + align:start position:0% +so what do we do if what one option is +to hire part-timers so use full-time + + align:start position:0% +to hire part-timers so use full-time + + + align:start position:0% +to hire part-timers so use full-time +employees for the base and then hire + + align:start position:0% +employees for the base and then hire + + + align:start position:0% +employees for the base and then hire +part-timers for the peaks that's the + + align:start position:0% +part-timers for the peaks that's the + + + align:start position:0% +part-timers for the peaks that's the +least expensive and most efficient + + align:start position:0% +least expensive and most efficient + + + align:start position:0% +least expensive and most efficient +options but unions don't like it because + + align:start position:0% +options but unions don't like it because + + + align:start position:0% +options but unions don't like it because +if you have a high percentage of + + align:start position:0% +if you have a high percentage of + + + align:start position:0% +if you have a high percentage of +part-time drivers it's not to the + + align:start position:0% +part-time drivers it's not to the + + + align:start position:0% +part-time drivers it's not to the +benefit of their unions and police if + + align:start position:0% +benefit of their unions and police if + + + align:start position:0% +benefit of their unions and police if +you don't allow Proclaimers or a cap + + align:start position:0% +you don't allow Proclaimers or a cap + + + align:start position:0% +you don't allow Proclaimers or a cap +they allow in some part-timers then the + + align:start position:0% +they allow in some part-timers then the + + + align:start position:0% +they allow in some part-timers then the +agency is required to hire full-time + + align:start position:0% +agency is required to hire full-time + + + align:start position:0% +agency is required to hire full-time +employees to cover the a.m. and the p.m. + + align:start position:0% +employees to cover the a.m. and the p.m. + + + align:start position:0% +employees to cover the a.m. and the p.m. +peak and if you only do that then that's + + align:start position:0% +peak and if you only do that then that's + + + align:start position:0% +peak and if you only do that then that's +terribly inefficient because you're + + align:start position:0% +terribly inefficient because you're + + + align:start position:0% +terribly inefficient because you're +hiring for eight hours and you can only + + align:start position:0% +hiring for eight hours and you can only + + + align:start position:0% +hiring for eight hours and you can only +operate two or three that's all that you + + align:start position:0% +operate two or three that's all that you + + + align:start position:0% +operate two or three that's all that you +need a driver for but there is + + align:start position:0% +need a driver for but there is + + + align:start position:0% +need a driver for but there is +some arrangement you can actually have + + align:start position:0% +some arrangement you can actually have + + + align:start position:0% +some arrangement you can actually have +shifts that have a break in the middle + + align:start position:0% +shifts that have a break in the middle + + + align:start position:0% +shifts that have a break in the middle +of the day and these are called spread + + align:start position:0% +of the day and these are called spread + + + align:start position:0% +of the day and these are called spread +shifts right so these some of these + + align:start position:0% +shifts right so these some of these + + + align:start position:0% +shifts right so these some of these +shifts operated for two or three hours + + align:start position:0% +shifts operated for two or three hours + + + align:start position:0% +shifts operated for two or three hours +in the morning have a long break during + + align:start position:0% +in the morning have a long break during + + + align:start position:0% +in the morning have a long break during +the day and operate for two or three + + align:start position:0% +the day and operate for two or three + + + align:start position:0% +the day and operate for two or three +hours in the afternoon and often these + + align:start position:0% +hours in the afternoon and often these + + + align:start position:0% +hours in the afternoon and often these +shifts are paid spread penalty so in + + align:start position:0% +shifts are paid spread penalty so in + + + align:start position:0% +shifts are paid spread penalty so in +this example what we have in white here + + align:start position:0% +this example what we have in white here + + + align:start position:0% +this example what we have in white here +are shifts that lasts between ten hours + + align:start position:0% +are shifts that lasts between ten hours + + + align:start position:0% +are shifts that lasts between ten hours +and the eleven hours so the spread is + + align:start position:0% +and the eleven hours so the spread is + + + align:start position:0% +and the eleven hours so the spread is +the difference between the checkout time + + align:start position:0% +the difference between the checkout time + + + align:start position:0% +the difference between the checkout time +and the check-in time right and shifts + + align:start position:0% +and the check-in time right and shifts + + + align:start position:0% +and the check-in time right and shifts +in white here + + align:start position:0% +in white here + + + align:start position:0% +in white here +have a spread between ten and eleven + + align:start position:0% +have a spread between ten and eleven + + + align:start position:0% +have a spread between ten and eleven +hours those drivers are paid a fifty + + align:start position:0% +hours those drivers are paid a fifty + + + align:start position:0% +hours those drivers are paid a fifty +percent premium for any hours above + + align:start position:0% +percent premium for any hours above + + + align:start position:0% +percent premium for any hours above +eight hours okay so and then there are + + align:start position:0% +eight hours okay so and then there are + + + align:start position:0% +eight hours okay so and then there are +these other shifts that are between + + align:start position:0% +these other shifts that are between + + + align:start position:0% +these other shifts that are between +eleven and thirteen hours so we love + + align:start position:0% +eleven and thirteen hours so we love + + + align:start position:0% +eleven and thirteen hours so we love +that twelve + + align:start position:0% +that twelve + + + align:start position:0% +that twelve +when dark gray and twelve thirteen + + align:start position:0% +when dark gray and twelve thirteen + + + align:start position:0% +when dark gray and twelve thirteen +shaded diagonally these shifts are paid + + align:start position:0% +shaded diagonally these shifts are paid + + + align:start position:0% +shaded diagonally these shifts are paid +under percent so they're paid double for + + align:start position:0% +under percent so they're paid double for + + + align:start position:0% +under percent so they're paid double for +any hours in excess of the I guess in + + align:start position:0% +any hours in excess of the I guess in + + + align:start position:0% +any hours in excess of the I guess in +excess of 11 in this case right so + + align:start position:0% +excess of 11 in this case right so + + + align:start position:0% +excess of 11 in this case right so +that's going to drive the costs up right + + align:start position:0% +that's going to drive the costs up right + + + align:start position:0% +that's going to drive the costs up right +because if you look at the total pay for + + align:start position:0% +because if you look at the total pay for + + + align:start position:0% +because if you look at the total pay for +that shift over the day then the unit + + align:start position:0% +that shift over the day then the unit + + + align:start position:0% +that shift over the day then the unit +paid for per hour for that for each of + + align:start position:0% +paid for per hour for that for each of + + + align:start position:0% +paid for per hour for that for each of +those drivers is higher right and if you + + align:start position:0% +those drivers is higher right and if you + + + align:start position:0% +those drivers is higher right and if you +look at any time slice of the day Peaks + + align:start position:0% +look at any time slice of the day Peaks + + + align:start position:0% +look at any time slice of the day Peaks +are going to have many more of those + + align:start position:0% +are going to have many more of those + + + align:start position:0% +are going to have many more of those +riders than off-peak right so the + + align:start position:0% +riders than off-peak right so the + + + align:start position:0% +riders than off-peak right so the +average our personal drivers on any + + align:start position:0% +average our personal drivers on any + + + align:start position:0% +average our personal drivers on any +bucket of time there's 30 minutes white + + align:start position:0% +bucket of time there's 30 minutes white + + + align:start position:0% +bucket of time there's 30 minutes white +is gonna be cutter so could you explain + + align:start position:0% +is gonna be cutter so could you explain + + + align:start position:0% +is gonna be cutter so could you explain +me for like let's say I'm a driver that + + align:start position:0% +me for like let's say I'm a driver that + + + align:start position:0% +me for like let's say I'm a driver that +runs the shifts with 12 hours less than + + align:start position:0% +runs the shifts with 12 hours less than + + + align:start position:0% +runs the shifts with 12 hours less than +spread 13 hours about the bottom one so + + align:start position:0% +spread 13 hours about the bottom one so + + + align:start position:0% +spread 13 hours about the bottom one so +what they're driving the peatones yeah + + align:start position:0% +what they're driving the peatones yeah + + + align:start position:0% +what they're driving the peatones yeah +when like when would I work and then + + align:start position:0% +when like when would I work and then + + + align:start position:0% +when like when would I work and then +what hours do I get that's on the same + + align:start position:0% +what hours do I get that's on the same + + + align:start position:0% +what hours do I get that's on the same +way for the next slide so so here we + + align:start position:0% +way for the next slide so so here we + + + align:start position:0% +way for the next slide so so here we +have a + + align:start position:0% +have a + + + align:start position:0% +have a +the runs by a driver you can see the if + + align:start position:0% +the runs by a driver you can see the if + + + align:start position:0% +the runs by a driver you can see the if +you draw a line here this is 8 a.m. + + align:start position:0% +you draw a line here this is 8 a.m. + + + align:start position:0% +you draw a line here this is 8 a.m. +so an peak and then this is 5 p.m. right + + align:start position:0% +so an peak and then this is 5 p.m. right + + + align:start position:0% +so an peak and then this is 5 p.m. right +around here so you see that if if you + + align:start position:0% +around here so you see that if if you + + + align:start position:0% +around here so you see that if if you +draw a line between 8 & 5 p.m. + + align:start position:0% +draw a line between 8 & 5 p.m. + + + align:start position:0% +draw a line between 8 & 5 p.m. +these are the shifts that start during + + align:start position:0% +these are the shifts that start during + + + align:start position:0% +these are the shifts that start during +the a.m. peak right and those shifts + + align:start position:0% +the a.m. peak right and those shifts + + + align:start position:0% +the a.m. peak right and those shifts +have the biggest spreads so any one of + + align:start position:0% +have the biggest spreads so any one of + + + align:start position:0% +have the biggest spreads so any one of +these rows is an example of one run and + + align:start position:0% +these rows is an example of one run and + + + align:start position:0% +these rows is an example of one run and +you could be one of these drivers so if + + align:start position:0% +you could be one of these drivers so if + + + align:start position:0% +you could be one of these drivers so if +you have this day you check-in at 6:30 + + align:start position:0% +you have this day you check-in at 6:30 + + + align:start position:0% +you have this day you check-in at 6:30 +yeah you have a pretty long break during + + align:start position:0% +yeah you have a pretty long break during + + + align:start position:0% +yeah you have a pretty long break during +the day and you check out at 8 at 6 p.m. + + align:start position:0% +the day and you check out at 8 at 6 p.m. + + + align:start position:0% +the day and you check out at 8 at 6 p.m. +so you do an hour and you could have + + align:start position:0% +so you do an hour and you could have + + + align:start position:0% +so you do an hour and you could have +longer ones too there are will be some + + align:start position:0% +longer ones too there are will be some + + + align:start position:0% +longer ones too there are will be some +rules that prevent excessively long ones + + align:start position:0% +rules that prevent excessively long ones + + + align:start position:0% +rules that prevent excessively long ones +when you were staying on you get 50% + + align:start position:0% +when you were staying on you get 50% + + + align:start position:0% +when you were staying on you get 50% +more is that bus driver doing it + + align:start position:0% +more is that bus driver doing it + + + align:start position:0% +more is that bus driver doing it +ok 50% more Freddy only the hours that + + align:start position:0% +ok 50% more Freddy only the hours that + + + align:start position:0% +ok 50% more Freddy only the hours that +are working yes yes and that will vary + + align:start position:0% +are working yes yes and that will vary + + + align:start position:0% +are working yes yes and that will vary +by agreement so you are paid the spread + + align:start position:0% +by agreement so you are paid the spread + + + align:start position:0% +by agreement so you are paid the spread +penalty and you are paid there are a + + align:start position:0% +penalty and you are paid there are a + + + align:start position:0% +penalty and you are paid there are a +bunch of rules like no matter how many + + align:start position:0% +bunch of rules like no matter how many + + + align:start position:0% +bunch of rules like no matter how many +hours are they if you + + align:start position:0% +hours are they if you + + + align:start position:0% +hours are they if you +therefore swing pay bonus so if you + + align:start position:0% +therefore swing pay bonus so if you + + + align:start position:0% +therefore swing pay bonus so if you +stuck your day somewhere different than + + align:start position:0% +stuck your day somewhere different than + + + align:start position:0% +stuck your day somewhere different than +you end the day then you have to pay the + + align:start position:0% +you end the day then you have to pay the + + + align:start position:0% +you end the day then you have to pay the +person I think 30 minutes extra for + + align:start position:0% +person I think 30 minutes extra for + + + align:start position:0% +person I think 30 minutes extra for +further driving time or whatever you + + align:start position:0% +further driving time or whatever you + + + align:start position:0% +further driving time or whatever you +know for getting to the other location + + align:start position:0% +know for getting to the other location + + + align:start position:0% +know for getting to the other location +where you potentially left your car so + + align:start position:0% +where you potentially left your car so + + + align:start position:0% +where you potentially left your car so +there are compensations for all these + + align:start position:0% +there are compensations for all these + + + align:start position:0% +there are compensations for all these +things and the point here in this cost + + align:start position:0% +things and the point here in this cost + + + align:start position:0% +things and the point here in this cost +modeling lecture is that these drivers + + align:start position:0% +modeling lecture is that these drivers + + + align:start position:0% +modeling lecture is that these drivers +will spread with large spreads cost more + + align:start position:0% +will spread with large spreads cost more + + + align:start position:0% +will spread with large spreads cost more +right so we want to build a cost model + + align:start position:0% +right so we want to build a cost model + + + align:start position:0% +right so we want to build a cost model +that recognizes those differences + + align:start position:0% +that recognizes those differences + + + align:start position:0% +that recognizes those differences +especially with regards to driver hours + + align:start position:0% +especially with regards to driver hours + + + align:start position:0% +especially with regards to driver hours +so we expend service and requiring more + + align:start position:0% +so we expend service and requiring more + + + align:start position:0% +so we expend service and requiring more +driver hours more in the people in the + + align:start position:0% +driver hours more in the people in the + + + align:start position:0% +driver hours more in the people in the +off-peak then we need to account for + + align:start position:0% +off-peak then we need to account for + + + align:start position:0% +off-peak then we need to account for +those differences here's a graph of my + + align:start position:0% +those differences here's a graph of my + + + align:start position:0% +those differences here's a graph of my +time of day of the wage cost per + + align:start position:0% +time of day of the wage cost per + + + align:start position:0% +time of day of the wage cost per +platform hour + + align:start position:0% +platform hour + + + align:start position:0% +platform hour +just by our / the base pay rate so + + align:start position:0% +just by our / the base pay rate so + + + align:start position:0% +just by our / the base pay rate so +off-peak you see that the average is + + align:start position:0% +off-peak you see that the average is + + + align:start position:0% +off-peak you see that the average is +very close to one right but if you if + + align:start position:0% +very close to one right but if you if + + + align:start position:0% +very close to one right but if you if +you go to the peak then you're paying an + + align:start position:0% +you go to the peak then you're paying an + + + align:start position:0% +you go to the peak then you're paying an +average of say 25% higher because some + + align:start position:0% +average of say 25% higher because some + + + align:start position:0% +average of say 25% higher because some +of the drivers are straight shifts but + + align:start position:0% +of the drivers are straight shifts but + + + align:start position:0% +of the drivers are straight shifts but +there's a mix of drivers that are spread + + align:start position:0% +there's a mix of drivers that are spread + + + align:start position:0% +there's a mix of drivers that are spread +large spread and being paid some spread + + align:start position:0% +large spread and being paid some spread + + + align:start position:0% +large spread and being paid some spread +penalty so that drives the costs up okay + + align:start position:0% +penalty so that drives the costs up okay + + + align:start position:0% +penalty so that drives the costs up okay +here's an exercise to solidify this + + align:start position:0% +here's an exercise to solidify this + + + align:start position:0% +here's an exercise to solidify this +concept before that we got a question + + align:start position:0% +concept before that we got a question + + + align:start position:0% +concept before that we got a question +come on but I'm praised a night + + align:start position:0% +come on but I'm praised a night + + + align:start position:0% +come on but I'm praised a night +I mean that someone starts working at + + align:start position:0% +I mean that someone starts working at + + + align:start position:0% +I mean that someone starts working at +night and drive some trains and they and + + align:start position:0% +night and drive some trains and they and + + + align:start position:0% +night and drive some trains and they and +after that day we stop work so for + + align:start position:0% +after that day we stop work so for + + + align:start position:0% +after that day we stop work so for +safety reasons a lot of labor agreements + + align:start position:0% +safety reasons a lot of labor agreements + + + align:start position:0% +safety reasons a lot of labor agreements +required and any work rules require a + + align:start position:0% +required and any work rules require a + + + align:start position:0% +required and any work rules require a +minimum amount of break between the end + + align:start position:0% +minimum amount of break between the end + + + align:start position:0% +minimum amount of break between the end +of the run and will start the next time + + align:start position:0% +of the run and will start the next time + + + align:start position:0% +of the run and will start the next time +yeah be 12 hours or 50 so you know where + + align:start position:0% +yeah be 12 hours or 50 so you know where + + + align:start position:0% +yeah be 12 hours or 50 so you know where +that person sleeps us up to them I + + align:start position:0% +that person sleeps us up to them I + + + align:start position:0% +that person sleeps us up to them I +suppose most of them go home but you + + align:start position:0% +suppose most of them go home but you + + + align:start position:0% +suppose most of them go home but you +normally the rules won't allow you to + + align:start position:0% +normally the rules won't allow you to + + + align:start position:0% +normally the rules won't allow you to +have a run if you end service at 5:00 + + align:start position:0% +have a run if you end service at 5:00 + + + align:start position:0% +have a run if you end service at 5:00 +you won't be able to check in at 8:00 + + align:start position:0% +you won't be able to check in at 8:00 + + + align:start position:0% +you won't be able to check in at 8:00 +again if you live full day the end 5:00 + + align:start position:0% +again if you live full day the end 5:00 + + + align:start position:0% +again if you live full day the end 5:00 +a.m. you're probably not going to be + + align:start position:0% +a.m. you're probably not going to be + + + align:start position:0% +a.m. you're probably not going to be +allowed to start the next full day at 8 + + align:start position:0% +allowed to start the next full day at 8 + + + align:start position:0% +allowed to start the next full day at 8 +a.m. because that's not a long enough + + align:start position:0% +a.m. because that's not a long enough + + + align:start position:0% +a.m. because that's not a long enough +break I know the unsafe right yeah yeah + + align:start position:0% +break I know the unsafe right yeah yeah + + + align:start position:0% +break I know the unsafe right yeah yeah +Japan it is very common to have some + + align:start position:0% +Japan it is very common to have some + + + align:start position:0% +Japan it is very common to have some +place to provide and also enable us to + + align:start position:0% +place to provide and also enable us to + + + align:start position:0% +place to provide and also enable us to +run very late night that's I didn't know + + align:start position:0% + + + + align:start position:0% + +once a week shifts but no one continued + + align:start position:0% +once a week shifts but no one continued + + + align:start position:0% +once a week shifts but no one continued +work so you would just live at work you + + align:start position:0% +work so you would just live at work you + + + align:start position:0% +work so you would just live at work you +know cultural differences Chicago which + + align:start position:0% +know cultural differences Chicago which + + + align:start position:0% +know cultural differences Chicago which +runs overnight service there's so few + + align:start position:0% +runs overnight service there's so few + + + align:start position:0% +runs overnight service there's so few +enough shifts that basically everything + + align:start position:0% +enough shifts that basically everything + + + align:start position:0% +enough shifts that basically everything +that's alright is a straight shift yeah + + align:start position:0% +that's alright is a straight shift yeah + + + align:start position:0% +that's alright is a straight shift yeah +I think when you bid for an overnight + + align:start position:0% +I think when you bid for an overnight + + + align:start position:0% +I think when you bid for an overnight +shift you basically get all overnight + + align:start position:0% +shift you basically get all overnight + + + align:start position:0% +shift you basically get all overnight +shifts so you keep on serve that rhythms + + align:start position:0% +shifts so you keep on serve that rhythms + + + align:start position:0% +shifts so you keep on serve that rhythms +yes overnight today so yeah and and + + align:start position:0% +yes overnight today so yeah and and + + + align:start position:0% +yes overnight today so yeah and and +there are some operators that really + + align:start position:0% +there are some operators that really + + + align:start position:0% +there are some operators that really +like the overnight shift here cos it + + align:start position:0% +like the overnight shift here cos it + + + align:start position:0% +like the overnight shift here cos it +provides you know they can care for kids + + align:start position:0% +provides you know they can care for kids + + + align:start position:0% +provides you know they can care for kids +during the day or just personally they + + align:start position:0% +during the day or just personally they + + + align:start position:0% +during the day or just personally they +also get a premium there are usually + + align:start position:0% +also get a premium there are usually + + + align:start position:0% +also get a premium there are usually +premiums for running on holidays or + + align:start position:0% +premiums for running on holidays or + + + align:start position:0% +premiums for running on holidays or +running late at night so the least + + align:start position:0% +running late at night so the least + + + align:start position:0% +running late at night so the least +desirable bronze might have an extra + + align:start position:0% +desirable bronze might have an extra + + + align:start position:0% +desirable bronze might have an extra +premium associated to compensate for the + + align:start position:0% +premium associated to compensate for the + + + align:start position:0% +premium associated to compensate for the +inconvenience or the undecidability + + align:start position:0% +inconvenience or the undecidability + + + align:start position:0% +inconvenience or the undecidability +they're all great so we have we have an + + align:start position:0% +they're all great so we have we have an + + + align:start position:0% +they're all great so we have we have an +example here where we we've done this + + align:start position:0% +example here where we we've done this + + + align:start position:0% +example here where we we've done this +exercise and we've looked at all periods + + align:start position:0% +exercise and we've looked at all periods + + + align:start position:0% +exercise and we've looked at all periods +with a minimum the average and the + + align:start position:0% +with a minimum the average and the + + + align:start position:0% +with a minimum the average and the +maximum unit costs for drivers so crew + + align:start position:0% +maximum unit costs for drivers so crew + + + align:start position:0% +maximum unit costs for drivers so crew +for peak of peak and the combination of + + align:start position:0% +for peak of peak and the combination of + + + align:start position:0% +for peak of peak and the combination of +peak and off-peak and we have six + + align:start position:0% +peak and off-peak and we have six + + + align:start position:0% +peak and off-peak and we have six +different scenarios and we want to + + align:start position:0% +different scenarios and we want to + + + align:start position:0% +different scenarios and we want to +choose the unit cost for each of these + + align:start position:0% +choose the unit cost for each of these + + + align:start position:0% +choose the unit cost for each of these +right so let's go one day one so what + + align:start position:0% +right so let's go one day one so what + + + align:start position:0% +right so let's go one day one so what +happens if we want to increase the peak + + align:start position:0% +happens if we want to increase the peak + + + align:start position:0% +happens if we want to increase the peak +and off-peak service proportionally + + align:start position:0% +and off-peak service proportionally + + + align:start position:0% +and off-peak service proportionally +which unit cost from this matrix would + + align:start position:0% +which unit cost from this matrix would + + + align:start position:0% +which unit cost from this matrix would +you use what so we're hearing combined + + align:start position:0% +you use what so we're hearing combined + + + align:start position:0% +you use what so we're hearing combined +agreement yeah and from combined but you + + align:start position:0% +agreement yeah and from combined but you + + + align:start position:0% +agreement yeah and from combined but you +take minimum average or maximum + + align:start position:0% +take minimum average or maximum + + + align:start position:0% +take minimum average or maximum +average combined yeah okay and why is + + align:start position:0% +average combined yeah okay and why is + + + align:start position:0% +average combined yeah okay and why is +that it's because it's proportional + + align:start position:0% +that it's because it's proportional + + + align:start position:0% +that it's because it's proportional +right on both ends and we don't actually + + align:start position:0% +right on both ends and we don't actually + + + align:start position:0% +right on both ends and we don't actually +need the temporal variation for this so + + align:start position:0% +need the temporal variation for this so + + + align:start position:0% +need the temporal variation for this so +what if it's a proportional decrease + + align:start position:0% +what if it's a proportional decrease + + + align:start position:0% +what if it's a proportional decrease +would we use the same one some people + + align:start position:0% +would we use the same one some people + + + align:start position:0% +would we use the same one some people +are saying the same ones you're saying + + align:start position:0% +are saying the same ones you're saying + + + align:start position:0% +are saying the same ones you're saying +minimum what's your idea for minimum + + align:start position:0% + + + + align:start position:0% + +okay so if it's deep it would be for the + + align:start position:0% +okay so if it's deep it would be for the + + + align:start position:0% +okay so if it's deep it would be for the +peak hours its off-peak hours but but + + align:start position:0% +peak hours its off-peak hours but but + + + align:start position:0% +peak hours its off-peak hours but but +memories like within the hour + + align:start position:0% +memories like within the hour + + + align:start position:0% +memories like within the hour +then there are some drivers that are + + align:start position:0% +then there are some drivers that are + + + align:start position:0% +then there are some drivers that are +paying more on average because some of + + align:start position:0% +paying more on average because some of + + + align:start position:0% +paying more on average because some of +them are have spreadability some others + + align:start position:0% +them are have spreadability some others + + + align:start position:0% +them are have spreadability some others +don't so even the peaks are straight + + align:start position:0% +don't so even the peaks are straight + + + align:start position:0% +don't so even the peaks are straight +shifts and those are questions I guess + + align:start position:0% +shifts and those are questions I guess + + + align:start position:0% +shifts and those are questions I guess +wouldn't you want to use like if we're + + align:start position:0% +wouldn't you want to use like if we're + + + align:start position:0% +wouldn't you want to use like if we're +gonna add to the peak what is it a bad + + align:start position:0% +gonna add to the peak what is it a bad + + + align:start position:0% +gonna add to the peak what is it a bad +assumption to assume that it's more + + align:start position:0% +assumption to assume that it's more + + + align:start position:0% +assumption to assume that it's more +expensive we're getting to that so the + + align:start position:0% +expensive we're getting to that so the + + + align:start position:0% +expensive we're getting to that so the +third one is increases and the idea is + + align:start position:0% +third one is increases and the idea is + + + align:start position:0% +third one is increases and the idea is +that if you increase things + + align:start position:0% +that if you increase things + + + align:start position:0% +that if you increase things +proportionally then you're gonna have + + align:start position:0% +proportionally then you're gonna have + + + align:start position:0% +proportionally then you're gonna have +the same mix that you have now but a + + align:start position:0% +the same mix that you have now but a + + + align:start position:0% +the same mix that you have now but a +little more each so right if you if you + + align:start position:0% +little more each so right if you if you + + + align:start position:0% +little more each so right if you if you +add service both peak and off-peak and + + align:start position:0% +add service both peak and off-peak and + + + align:start position:0% +add service both peak and off-peak and +proportion which means that if there is + + align:start position:0% +proportion which means that if there is + + + align:start position:0% +proportion which means that if there is +twice as much peak service then you're + + align:start position:0% +twice as much peak service then you're + + + align:start position:0% +twice as much peak service then you're +gonna have twice much more peak service + + align:start position:0% +gonna have twice much more peak service + + + align:start position:0% +gonna have twice much more peak service +then then you're gonna have the same + + align:start position:0% +then then you're gonna have the same + + + align:start position:0% +then then you're gonna have the same +distribution of spread penalties and + + align:start position:0% +distribution of spread penalties and + + + align:start position:0% +distribution of spread penalties and +therefore the same average costs so but + + align:start position:0% +therefore the same average costs so but + + + align:start position:0% +therefore the same average costs so but +now we go to the next question or just + + align:start position:0% +now we go to the next question or just + + + align:start position:0% +now we go to the next question or just +increases in peak period services only + + align:start position:0% +increases in peak period services only + + + align:start position:0% +increases in peak period services only +which of these would you use back we're + + align:start position:0% +which of these would you use back we're + + + align:start position:0% +which of these would you use back we're +hearing Max and peak yeah all right so + + align:start position:0% +hearing Max and peak yeah all right so + + + align:start position:0% +hearing Max and peak yeah all right so +basically if we're increasing the peak + + align:start position:0% +basically if we're increasing the peak + + + align:start position:0% +basically if we're increasing the peak +period only yeah we're gonna have to do + + align:start position:0% +period only yeah we're gonna have to do + + + align:start position:0% +period only yeah we're gonna have to do +more of these spread ships $45 right + + align:start position:0% +more of these spread ships $45 right + + + align:start position:0% +more of these spread ships $45 right +maximum peak what if it's a decrease in + + align:start position:0% +maximum peak what if it's a decrease in + + + align:start position:0% +maximum peak what if it's a decrease in +peak period service so now we're coming + + align:start position:0% +peak period service so now we're coming + + + align:start position:0% +peak period service so now we're coming +back here and we're only taking the top + + align:start position:0% +back here and we're only taking the top + + + align:start position:0% +back here and we're only taking the top +of the top oh we're not doing anything + + align:start position:0% +of the top oh we're not doing anything + + + align:start position:0% +of the top oh we're not doing anything +to the same 45 going down right okay + + align:start position:0% +to the same 45 going down right okay + + + align:start position:0% +to the same 45 going down right okay +great okay + + align:start position:0% +great okay + + + align:start position:0% +great okay +increases in off-peak period services on + + align:start position:0% +increases in off-peak period services on + + + align:start position:0% +increases in off-peak period services on +me so now we're leaving the peak where + + align:start position:0% +me so now we're leaving the peak where + + + align:start position:0% +me so now we're leaving the peak where +it is and we're decreasing service off + + align:start position:0% +it is and we're decreasing service off + + + align:start position:0% +it is and we're decreasing service off +Pete so here and maybe decreasing so + + align:start position:0% +Pete so here and maybe decreasing so + + + align:start position:0% +Pete so here and maybe decreasing so +decreasing + + align:start position:0% + + + + align:start position:0% + +okay that's actually the high end of + + align:start position:0% +okay that's actually the high end of + + + align:start position:0% +okay that's actually the high end of +what it could be so off of the cells + + align:start position:0% +what it could be so off of the cells + + + align:start position:0% +what it could be so off of the cells +here yes that's the one + + align:start position:0% + + + + align:start position:0% + +but it could actually be closer to zero + + align:start position:0% +but it could actually be closer to zero + + + align:start position:0% +but it could actually be closer to zero +if you're depending on the cost + + align:start position:0% +if you're depending on the cost + + + align:start position:0% +if you're depending on the cost +structure and the specialties you will + + align:start position:0% +structure and the specialties you will + + + align:start position:0% +structure and the specialties you will +be able to convert some of the drivers + + align:start position:0% +be able to convert some of the drivers + + + align:start position:0% +be able to convert some of the drivers +that are peak to spread to non spread + + align:start position:0% +that are peak to spread to non spread + + + align:start position:0% +that are peak to spread to non spread +shifts so you'll get straight shifts + + align:start position:0% +shifts so you'll get straight shifts + + + align:start position:0% +shifts so you'll get straight shifts +from these drivers and that mentally + + align:start position:0% +from these drivers and that mentally + + + align:start position:0% +from these drivers and that mentally +compensates so much that it's a free + + align:start position:0% +compensates so much that it's a free + + + align:start position:0% +compensates so much that it's a free +conversion so what about + + align:start position:0% + + + + align:start position:0% + +decreases end of the period + + align:start position:0% + + + + align:start position:0% + +so now we are actually decreasing topic + + align:start position:0% +so now we are actually decreasing topic + + + align:start position:0% +so now we are actually decreasing topic +so what two things happen there's only a + + align:start position:0% +so what two things happen there's only a + + + align:start position:0% +so what two things happen there's only a +few services or straight runs right + + align:start position:0% +few services or straight runs right + + + align:start position:0% +few services or straight runs right +they're not spread so if you remove + + align:start position:0% +they're not spread so if you remove + + + align:start position:0% +they're not spread so if you remove +those but keep the people operation the + + align:start position:0% +those but keep the people operation the + + + align:start position:0% +those but keep the people operation the +same then for any of those that you + + align:start position:0% +same then for any of those that you + + + align:start position:0% +same then for any of those that you +remove you have to add in the most + + align:start position:0% +remove you have to add in the most + + + align:start position:0% +remove you have to add in the most +expensive ones okay so what was the net + + align:start position:0% +expensive ones okay so what was the net + + + align:start position:0% +expensive ones okay so what was the net +effect it's been there's probably gonna + + align:start position:0% +effect it's been there's probably gonna + + + align:start position:0% +effect it's been there's probably gonna +be close to zero okay because because of + + align:start position:0% +be close to zero okay because because of + + + align:start position:0% +be close to zero okay because because of +this effect okay we can expend again + + align:start position:0% +this effect okay we can expend again + + + align:start position:0% +this effect okay we can expend again +this depends on the specific costs for + + align:start position:0% +this depends on the specific costs for + + + align:start position:0% +this depends on the specific costs for +the idea so if you only decrease + + align:start position:0% +the idea so if you only decrease + + + align:start position:0% +the idea so if you only decrease +off-peak services then you have to + + align:start position:0% +off-peak services then you have to + + + align:start position:0% +off-peak services then you have to +remove fields straight runs and not pay + + align:start position:0% +remove fields straight runs and not pay + + + align:start position:0% +remove fields straight runs and not pay +them the full day but you have to then + + align:start position:0% +them the full day but you have to then + + + align:start position:0% +them the full day but you have to then +get it you have to convert some of the + + align:start position:0% +get it you have to convert some of the + + + align:start position:0% +get it you have to convert some of the +existing spread rounds to go straight to + + align:start position:0% +existing spread rounds to go straight to + + + align:start position:0% +existing spread rounds to go straight to +from straight to your spread it by the + + align:start position:0% +from straight to your spread it by the + + + align:start position:0% +from straight to your spread it by the +net cost is your other because you even + + align:start position:0% +net cost is your other because you even + + + align:start position:0% +net cost is your other because you even +though you're reducing the number of + + align:start position:0% +though you're reducing the number of + + + align:start position:0% +though you're reducing the number of +driver hours you will increase the + + align:start position:0% +driver hours you will increase the + + + align:start position:0% +driver hours you will increase the +proportion of the most expensive ones + + align:start position:0% +proportion of the most expensive ones + + + align:start position:0% +proportion of the most expensive ones +only in the peak so you might not wind + + align:start position:0% +only in the peak so you might not wind + + + align:start position:0% +only in the peak so you might not wind +up saving anybody exactly where would + + align:start position:0% +up saving anybody exactly where would + + + align:start position:0% +up saving anybody exactly where would +you put it in the matrix well it's not + + align:start position:0% +you put it in the matrix well it's not + + + align:start position:0% +you put it in the matrix well it's not +in the matrix okay but if anything you + + align:start position:0% +in the matrix okay but if anything you + + + align:start position:0% +in the matrix okay but if anything you +would look at off-peak minimum but it's + + align:start position:0% +would look at off-peak minimum but it's + + + align:start position:0% +would look at off-peak minimum but it's +gonna be in the range of 0 to 30 and + + align:start position:0% +gonna be in the range of 0 to 30 and + + + align:start position:0% +gonna be in the range of 0 to 30 and +again I'm depending on the specific + + align:start position:0% +again I'm depending on the specific + + + align:start position:0% +again I'm depending on the specific +numbers it could even be that you have + + align:start position:0% +numbers it could even be that you have + + + align:start position:0% +numbers it could even be that you have +to pay more or it was gonna be like the + + align:start position:0% +to pay more or it was gonna be like the + + + align:start position:0% +to pay more or it was gonna be like the +octave minimum and that peanuts yeah it + + align:start position:0% +octave minimum and that peanuts yeah it + + + align:start position:0% +octave minimum and that peanuts yeah it +could be that's a good idea + + align:start position:0% +could be that's a good idea + + + align:start position:0% +could be that's a good idea +so but again it depends on the specifics + + align:start position:0% +so but again it depends on the specifics + + + align:start position:0% +so but again it depends on the specifics +and this is a cost small isn't so + + align:start position:0% +and this is a cost small isn't so + + + align:start position:0% +and this is a cost small isn't so +precise because you're not actually + + align:start position:0% +precise because you're not actually + + + align:start position:0% +precise because you're not actually +increasing peak service layer + + align:start position:0% +increasing peak service layer + + + align:start position:0% +increasing peak service layer +proportionally + + align:start position:0% +proportionally + + + align:start position:0% +proportionally +it's not proportionally we're just + + align:start position:0% +it's not proportionally we're just + + + align:start position:0% +it's not proportionally we're just +decreasing but then is proportionately + + align:start position:0% +decreasing but then is proportionately + + + align:start position:0% +decreasing but then is proportionately +more alright so that was good + + align:start position:0% +more alright so that was good + + + align:start position:0% +more alright so that was good +there's a mistake in the slide please + + align:start position:0% +there's a mistake in the slide please + + + align:start position:0% +there's a mistake in the slide please +fix it it's us here see page 8 it should + + align:start position:0% +fix it it's us here see page 8 it should + + + align:start position:0% +fix it it's us here see page 8 it should +be see page 6 so okay so from page 6 the + + align:start position:0% +be see page 6 so okay so from page 6 the + + + align:start position:0% +be see page 6 so okay so from page 6 the +total fixed cost to be out here is forty + + align:start position:0% +total fixed cost to be out here is forty + + + align:start position:0% +total fixed cost to be out here is forty +four point six million and that is the + + align:start position:0% +four point six million and that is the + + + align:start position:0% +four point six million and that is the +sum of we want to allocate a fixed cost + + align:start position:0% +sum of we want to allocate a fixed cost + + + align:start position:0% +sum of we want to allocate a fixed cost +so that is the sum of all the fixed + + align:start position:0% +so that is the sum of all the fixed + + + align:start position:0% +so that is the sum of all the fixed +costs that appear on page six five point + + align:start position:0% +costs that appear on page six five point + + + align:start position:0% +costs that appear on page six five point +seven three and thirty five point nine + + align:start position:0% +seven three and thirty five point nine + + + align:start position:0% +seven three and thirty five point nine +that's up to forty four point six and + + align:start position:0% +that's up to forty four point six and + + + align:start position:0% +that's up to forty four point six and +now we have here number of buses + + align:start position:0% +now we have here number of buses + + + align:start position:0% +now we have here number of buses +operating on the peak on the base on the + + align:start position:0% +operating on the peak on the base on the + + + align:start position:0% +operating on the peak on the base on the +evening Saturday and Sunday the number + + align:start position:0% +evening Saturday and Sunday the number + + + align:start position:0% +evening Saturday and Sunday the number +of hours so beat out four point five six + + align:start position:0% +of hours so beat out four point five six + + + align:start position:0% +of hours so beat out four point five six +base hours for evening hours for a total + + align:start position:0% +base hours for evening hours for a total + + + align:start position:0% +base hours for evening hours for a total +of fourteen point five hours per week + + align:start position:0% +of fourteen point five hours per week + + + align:start position:0% +of fourteen point five hours per week +day 12 hours operating Saturday 12 hours + + align:start position:0% +day 12 hours operating Saturday 12 hours + + + align:start position:0% +day 12 hours operating Saturday 12 hours +operating Sunday and the objective of + + align:start position:0% +operating Sunday and the objective of + + + align:start position:0% +operating Sunday and the objective of +this model is to take the fixed costs + + align:start position:0% +this model is to take the fixed costs + + + align:start position:0% +this model is to take the fixed costs +incurred by the agency and allocate them + + align:start position:0% +incurred by the agency and allocate them + + + align:start position:0% +incurred by the agency and allocate them +to vehicle hours right so let's say that + + align:start position:0% +to vehicle hours right so let's say that + + + align:start position:0% +to vehicle hours right so let's say that +we have to do this allocation we can + + align:start position:0% +we have to do this allocation we can + + + align:start position:0% +we have to do this allocation we can +start with one way of looking at this is + + align:start position:0% +start with one way of looking at this is + + + align:start position:0% +start with one way of looking at this is +these evening buses 200-250 evening + + align:start position:0% +these evening buses 200-250 evening + + + align:start position:0% +these evening buses 200-250 evening +buses are also operating in the base and + + align:start position:0% +buses are also operating in the base and + + + align:start position:0% +buses are also operating in the base and +then the peak right then there's an + + align:start position:0% +then the peak right then there's an + + + align:start position:0% +then the peak right then there's an +additional 125 buses that are operating + + align:start position:0% +additional 125 buses that are operating + + + align:start position:0% +additional 125 buses that are operating +only in the base and in at Saturdays + + align:start position:0% +only in the base and in at Saturdays + + + align:start position:0% +only in the base and in at Saturdays +during Saturday's right and then there's + + align:start position:0% +during Saturday's right and then there's + + + align:start position:0% +during Saturday's right and then there's +an additional 400 buses that are + + align:start position:0% +an additional 400 buses that are + + + align:start position:0% +an additional 400 buses that are +operating only in the peak during the + + align:start position:0% +operating only in the peak during the + + + align:start position:0% +operating only in the peak during the +weekday okay so let's allocate costs to + + align:start position:0% +weekday okay so let's allocate costs to + + + align:start position:0% +weekday okay so let's allocate costs to +the 250 the additional 125 and the + + align:start position:0% +the 250 the additional 125 and the + + + align:start position:0% +the 250 the additional 125 and the +additional 400 + + align:start position:0% +additional 400 + + + align:start position:0% +additional 400 +according to how long they operate and + + align:start position:0% +according to how long they operate and + + + align:start position:0% +according to how long they operate and +how much it costs based on the unit + + align:start position:0% +how much it costs based on the unit + + + align:start position:0% +how much it costs based on the unit +costs that we calculate in this example + + align:start position:0% +costs that we calculate in this example + + + align:start position:0% +costs that we calculate in this example +so we start with a 250 buses + + align:start position:0% +so we start with a 250 buses + + + align:start position:0% +so we start with a 250 buses +all time periods what's the share of + + align:start position:0% +all time periods what's the share of + + + align:start position:0% +all time periods what's the share of +fixed costs to be allocated to them it's + + align:start position:0% +fixed costs to be allocated to them it's + + + align:start position:0% +fixed costs to be allocated to them it's +32 percent it's 250 buses divided by the + + align:start position:0% +32 percent it's 250 buses divided by the + + + align:start position:0% +32 percent it's 250 buses divided by the +total number of buses which is 775 + + align:start position:0% +total number of buses which is 775 + + + align:start position:0% +total number of buses which is 775 +that's 32% 32% of the total cost is 14 + + align:start position:0% +that's 32% 32% of the total cost is 14 + + + align:start position:0% +that's 32% 32% of the total cost is 14 +point 4 million that's how much money we + + align:start position:0% +point 4 million that's how much money we + + + align:start position:0% +point 4 million that's how much money we +want to allocate to these to these buses + + align:start position:0% +want to allocate to these to these buses + + + align:start position:0% +want to allocate to these to these buses +and how many bus hours are created in + + align:start position:0% +and how many bus hours are created in + + + align:start position:0% +and how many bus hours are created in +the whole year well there's 250 buses + + align:start position:0% +the whole year well there's 250 buses + + + align:start position:0% +the whole year well there's 250 buses +and we want to add up the hours operated + + align:start position:0% +and we want to add up the hours operated + + + align:start position:0% +and we want to add up the hours operated +during weekdays during Saturday's and + + align:start position:0% +during weekdays during Saturday's and + + + align:start position:0% +during weekdays during Saturday's and +drink some of these for the whole week + + align:start position:0% +drink some of these for the whole week + + + align:start position:0% +drink some of these for the whole week +so there are roughly 250 weekdays in a + + align:start position:0% +so there are roughly 250 weekdays in a + + + align:start position:0% +so there are roughly 250 weekdays in a +year + + align:start position:0% +year + + + align:start position:0% +year +58 Saturdays and 57 some days up to 365 + + align:start position:0% +58 Saturdays and 57 some days up to 365 + + + align:start position:0% +58 Saturdays and 57 some days up to 365 +days and there are 14.5 hours during the + + align:start position:0% +days and there are 14.5 hours during the + + + align:start position:0% +days and there are 14.5 hours during the +weekday and 12 on the weekends so we + + align:start position:0% +weekday and 12 on the weekends so we + + + align:start position:0% +weekday and 12 on the weekends so we +have those up we multiply by the number + + align:start position:0% +have those up we multiply by the number + + + align:start position:0% +have those up we multiply by the number +of buses and we get 1 point to 1.25 + + align:start position:0% +of buses and we get 1 point to 1.25 + + + align:start position:0% +of buses and we get 1 point to 1.25 +million + + align:start position:0% +million + + + align:start position:0% +million +bus hours for the whole year ok and we + + align:start position:0% +bus hours for the whole year ok and we + + + align:start position:0% +bus hours for the whole year ok and we +divide the 14 point four million dollars + + align:start position:0% +divide the 14 point four million dollars + + + align:start position:0% +divide the 14 point four million dollars +by 1.25 million bus hours we get an + + align:start position:0% +by 1.25 million bus hours we get an + + + align:start position:0% +by 1.25 million bus hours we get an +average cost per bus hour of 11 dollars + + align:start position:0% +average cost per bus hour of 11 dollars + + + align:start position:0% +average cost per bus hour of 11 dollars +upfront and that's the base which is the + + align:start position:0% +upfront and that's the base which is the + + + align:start position:0% +upfront and that's the base which is the +only thing that applies in the evening + + align:start position:0% +only thing that applies in the evening + + + align:start position:0% +only thing that applies in the evening +and some breaks and this a portion of + + align:start position:0% +and some breaks and this a portion of + + + align:start position:0% +and some breaks and this a portion of +what applies in Saturday weekday days + + align:start position:0% +what applies in Saturday weekday days + + + align:start position:0% +what applies in Saturday weekday days +and peak but only a portion so now let's + + align:start position:0% +and peak but only a portion so now let's + + + align:start position:0% +and peak but only a portion so now let's +move to the next 125 buses operating on + + align:start position:0% +move to the next 125 buses operating on + + + align:start position:0% +move to the next 125 buses operating on +all time periods except Sundays and + + align:start position:0% +all time periods except Sundays and + + + align:start position:0% +all time periods except Sundays and +weekday evenings so how much money we + + align:start position:0% +weekday evenings so how much money we + + + align:start position:0% +weekday evenings so how much money we +have to allocate the 40 4.6 million + + align:start position:0% +have to allocate the 40 4.6 million + + + align:start position:0% +have to allocate the 40 4.6 million +total divided by the additional 125 + + align:start position:0% +total divided by the additional 125 + + + align:start position:0% +total divided by the additional 125 +buses divided by the total of our buses + + align:start position:0% +buses divided by the total of our buses + + + align:start position:0% +buses divided by the total of our buses +that's 7.2 million dollars how many + + align:start position:0% +that's 7.2 million dollars how many + + + align:start position:0% +that's 7.2 million dollars how many +total loss hours are operated by those + + align:start position:0% +total loss hours are operated by those + + + align:start position:0% +total loss hours are operated by those +25 busses well it's a 10.5 hours + + align:start position:0% +25 busses well it's a 10.5 hours + + + align:start position:0% +25 busses well it's a 10.5 hours +excluding the evening during the + + align:start position:0% +excluding the evening during the + + + align:start position:0% +excluding the evening during the +weekdays thanks to 250 weekdays plus the + + align:start position:0% +weekdays thanks to 250 weekdays plus the + + + align:start position:0% +weekdays thanks to 250 weekdays plus the +12 hours on Saturdays times the 58 + + align:start position:0% +12 hours on Saturdays times the 58 + + + align:start position:0% +12 hours on Saturdays times the 58 +Saturdays so that's point 42 million + + align:start position:0% +Saturdays so that's point 42 million + + + align:start position:0% +Saturdays so that's point 42 million +plus hours and some point two divided by + + align:start position:0% +plus hours and some point two divided by + + + align:start position:0% +plus hours and some point two divided by +point 42 is $17.49 + + align:start position:0% +point 42 is $17.49 + + + align:start position:0% +point 42 is $17.49 +cost per part we follow okay now let's + + align:start position:0% +cost per part we follow okay now let's + + + align:start position:0% +cost per part we follow okay now let's +do the peak that's the most expensive + + align:start position:0% +do the peak that's the most expensive + + + align:start position:0% +do the peak that's the most expensive +part so how much do we have to allocate + + align:start position:0% +part so how much do we have to allocate + + + align:start position:0% +part so how much do we have to allocate +it's 23 million how do we get to us + + align:start position:0% +it's 23 million how do we get to us + + + align:start position:0% +it's 23 million how do we get to us +forty four point six total times four + + align:start position:0% +forty four point six total times four + + + align:start position:0% +forty four point six total times four +hundred divided by seven seventy five + + align:start position:0% +hundred divided by seven seventy five + + + align:start position:0% +hundred divided by seven seventy five +and how many annual bus hours do we need + + align:start position:0% +and how many annual bus hours do we need + + + align:start position:0% +and how many annual bus hours do we need +to do we operate you're in the peak it's + + align:start position:0% +to do we operate you're in the peak it's + + + align:start position:0% +to do we operate you're in the peak it's +four hundred additional buses only in + + align:start position:0% +four hundred additional buses only in + + + align:start position:0% +four hundred additional buses only in +the peak times 4.5 hours of the beep + + align:start position:0% +the peak times 4.5 hours of the beep + + + align:start position:0% +the peak times 4.5 hours of the beep +times 250 weekdays and that's a point + + align:start position:0% +times 250 weekdays and that's a point + + + align:start position:0% +times 250 weekdays and that's a point +forty five million hours and twenty + + align:start position:0% +forty five million hours and twenty + + + align:start position:0% +forty five million hours and twenty +three million by point forty five is + + align:start position:0% +three million by point forty five is + + + align:start position:0% +three million by point forty five is +fifty one dollars and 11 cents average + + align:start position:0% +fifty one dollars and 11 cents average + + + align:start position:0% +fifty one dollars and 11 cents average +cost per bus hour or per people's hour + + align:start position:0% +cost per bus hour or per people's hour + + + align:start position:0% +cost per bus hour or per people's hour +in this case okay so we know enough unit + + align:start position:0% +in this case okay so we know enough unit + + + align:start position:0% +in this case okay so we know enough unit +costs for peak the base for the evenings + + align:start position:0% +costs for peak the base for the evenings + + + align:start position:0% +costs for peak the base for the evenings +and Sundays operation which is three so + + align:start position:0% +and Sundays operation which is three so + + + align:start position:0% +and Sundays operation which is three so +the variable vehicle cost was thirty + + align:start position:0% +the variable vehicle cost was thirty + + + align:start position:0% +the variable vehicle cost was thirty +seven point thirteen we got calculated + + align:start position:0% +seven point thirteen we got calculated + + + align:start position:0% +seven point thirteen we got calculated +that from the previous model that you + + align:start position:0% +that from the previous model that you + + + align:start position:0% +that from the previous model that you +can find in page six and now we can + + align:start position:0% +can find in page six and now we can + + + align:start position:0% +can find in page six and now we can +adjust the these costs by its time + + align:start position:0% + + + + align:start position:0% + +periods so for some day evening service + + align:start position:0% +periods so for some day evening service + + + align:start position:0% +periods so for some day evening service +we will increase the thirty seven + + align:start position:0% +we will increase the thirty seven + + + align:start position:0% +we will increase the thirty seven +dollars and thirteen cents by eleven + + align:start position:0% +dollars and thirteen cents by eleven + + + align:start position:0% +dollars and thirteen cents by eleven +dollars and fifty two for Saturday and + + align:start position:0% +dollars and fifty two for Saturday and + + + align:start position:0% +dollars and fifty two for Saturday and +weekday service we want to increase the + + align:start position:0% +weekday service we want to increase the + + + align:start position:0% +weekday service we want to increase the +cost the base class of 37 13 by 13 + + align:start position:0% +cost the base class of 37 13 by 13 + + + align:start position:0% +cost the base class of 37 13 by 13 +dollars ninety seven and four we they + + align:start position:0% +dollars ninety seven and four we they + + + align:start position:0% +dollars ninety seven and four we they +keep we want to increase it by thirty + + align:start position:0% +keep we want to increase it by thirty + + + align:start position:0% +keep we want to increase it by thirty +two hours and 86 cents and notice that + + align:start position:0% +two hours and 86 cents and notice that + + + align:start position:0% +two hours and 86 cents and notice that +when we look at Saturday and weekday we + + align:start position:0% +when we look at Saturday and weekday we + + + align:start position:0% +when we look at Saturday and weekday we +have to combine two unit costs that + + align:start position:0% +have to combine two unit costs that + + + align:start position:0% +have to combine two unit costs that +because we have a portion of Saturday + + align:start position:0% +because we have a portion of Saturday + + + align:start position:0% +because we have a portion of Saturday +and weekday pacers is from the first + + align:start position:0% +and weekday pacers is from the first + + + align:start position:0% +and weekday pacers is from the first +three hundred and seventy-five buses and + + align:start position:0% +three hundred and seventy-five buses and + + + align:start position:0% +three hundred and seventy-five buses and +the portion of it is from the additional + + align:start position:0% +the portion of it is from the additional + + + align:start position:0% +the portion of it is from the additional +more expensive hundred twenty-five + + align:start position:0% +more expensive hundred twenty-five + + + align:start position:0% +more expensive hundred twenty-five +possible and when we do peak the same + + align:start position:0% +possible and when we do peak the same + + + align:start position:0% +possible and when we do peak the same +thing applies so we start with the two + + align:start position:0% +thing applies so we start with the two + + + align:start position:0% +thing applies so we start with the two +hundred fifty base buses 1152 then we + + align:start position:0% +hundred fifty base buses 1152 then we + + + align:start position:0% +hundred fifty base buses 1152 then we +have + + align:start position:0% +have + + + align:start position:0% +have +25 at 17,000 14 cents and then we have + + align:start position:0% +25 at 17,000 14 cents and then we have + + + align:start position:0% +25 at 17,000 14 cents and then we have +the peak of the peak losses which are + + align:start position:0% +the peak of the peak losses which are + + + align:start position:0% +the peak of the peak losses which are +four hundred times the unit cost for + + align:start position:0% +four hundred times the unit cost for + + + align:start position:0% +four hundred times the unit cost for +those buses which is much higher and + + align:start position:0% +those buses which is much higher and + + + align:start position:0% +those buses which is much higher and +that's the total cost the total unit + + align:start position:0% +that's the total cost the total unit + + + align:start position:0% +that's the total cost the total unit +cost for a weekday pieces okay questions + + align:start position:0% +cost for a weekday pieces okay questions + + + align:start position:0% +cost for a weekday pieces okay questions +on this you have a question you can this + + align:start position:0% +on this you have a question you can this + + + align:start position:0% +on this you have a question you can this +is all sort of written here and all the + + align:start position:0% +is all sort of written here and all the + + + align:start position:0% +is all sort of written here and all the +numbers are copied from previous slides + + align:start position:0% +numbers are copied from previous slides + + + align:start position:0% +numbers are copied from previous slides +so you should be able to follow this on + + align:start position:0% +so you should be able to follow this on + + + align:start position:0% +so you should be able to follow this on +your own if you're a little lost but if + + align:start position:0% +your own if you're a little lost but if + + + align:start position:0% +your own if you're a little lost but if +not come see me after class and we can + + align:start position:0% +not come see me after class and we can + + + align:start position:0% +not come see me after class and we can +talk about it okay so now let's compare + + align:start position:0% +talk about it okay so now let's compare + + + align:start position:0% +talk about it okay so now let's compare +the models we started out with a very + + align:start position:0% +the models we started out with a very + + + align:start position:0% +the models we started out with a very +traditional symbol all the first one we + + align:start position:0% +traditional symbol all the first one we + + + align:start position:0% +traditional symbol all the first one we +gave which was full annual cost and it + + align:start position:0% +gave which was full annual cost and it + + + align:start position:0% +gave which was full annual cost and it +had this factor which accounted for the + + align:start position:0% +had this factor which accounted for the + + + align:start position:0% +had this factor which accounted for the +fact that we weren't including the peak + + align:start position:0% +fact that we weren't including the peak + + + align:start position:0% +fact that we weren't including the peak +vehicle the costs associated with Pete + + align:start position:0% +vehicle the costs associated with Pete + + + align:start position:0% +vehicle the costs associated with Pete +vehicles so that was the first example + + align:start position:0% +vehicles so that was the first example + + + align:start position:0% +vehicles so that was the first example +we also had in that page a variable cost + + align:start position:0% +we also had in that page a variable cost + + + align:start position:0% +we also had in that page a variable cost +model which only accounts for variable + + align:start position:0% +model which only accounts for variable + + + align:start position:0% +model which only accounts for variable +costs so it excludes fixed costs and now + + align:start position:0% +costs so it excludes fixed costs and now + + + align:start position:0% +costs so it excludes fixed costs and now +we can look up the peak period model and + + align:start position:0% +we can look up the peak period model and + + + align:start position:0% +we can look up the peak period model and +off-peak period model so we make an + + align:start position:0% +off-peak period model so we make an + + + align:start position:0% +off-peak period model so we make an +adjustment to the first model which to + + align:start position:0% +adjustment to the first model which to + + + align:start position:0% +adjustment to the first model which to +this variable cost model with the unit + + align:start position:0% +this variable cost model with the unit + + + align:start position:0% +this variable cost model with the unit +cost that we just calculated so if we + + align:start position:0% +cost that we just calculated so if we + + + align:start position:0% +cost that we just calculated so if we +take the 37 point $13 of rubbing in vivo + + align:start position:0% +take the 37 point $13 of rubbing in vivo + + + align:start position:0% +take the 37 point $13 of rubbing in vivo +ours that was in our initial variable + + align:start position:0% +ours that was in our initial variable + + + align:start position:0% +ours that was in our initial variable +customer and we add the unit cost for + + align:start position:0% +customer and we add the unit cost for + + + align:start position:0% +customer and we add the unit cost for +peak revenue hours which is 32 and 32 + + align:start position:0% +peak revenue hours which is 32 and 32 + + + align:start position:0% +peak revenue hours which is 32 and 32 +dollars and 86 cents from right here so + + align:start position:0% +dollars and 86 cents from right here so + + + align:start position:0% +dollars and 86 cents from right here so +that's the weekday service unit cost we + + align:start position:0% +that's the weekday service unit cost we + + + align:start position:0% +that's the weekday service unit cost we +get $69.99 + + align:start position:0% +get $69.99 + + + align:start position:0% +get $69.99 +so we now that becomes our unit cost and + + align:start position:0% +so we now that becomes our unit cost and + + + align:start position:0% +so we now that becomes our unit cost and +we have the 2.41 2.41 + + align:start position:0% +we have the 2.41 2.41 + + + align:start position:0% +we have the 2.41 2.41 +i mean ii here + + align:start position:0% +i mean ii here + + + align:start position:0% +i mean ii here +that comes from page six directly I + + align:start position:0% +that comes from page six directly I + + + align:start position:0% +that comes from page six directly I +believe yes so that's the combination of + + align:start position:0% +believe yes so that's the combination of + + + align:start position:0% +believe yes so that's the combination of +2.27 and point forty because we're not + + align:start position:0% +2.27 and point forty because we're not + + + align:start position:0% +2.27 and point forty because we're not +be we're not counting the temporal + + align:start position:0% +be we're not counting the temporal + + + align:start position:0% +be we're not counting the temporal +difference on people or revenue be able + + align:start position:0% +difference on people or revenue be able + + + align:start position:0% +difference on people or revenue be able +max we're only doing for any vehicle + + align:start position:0% +max we're only doing for any vehicle + + + align:start position:0% +max we're only doing for any vehicle +ours right it's for driver cost and + + align:start position:0% +ours right it's for driver cost and + + + align:start position:0% +ours right it's for driver cost and +Driver cost were associated with our + + align:start position:0% +Driver cost were associated with our + + + align:start position:0% +Driver cost were associated with our +Ataman rights so that stays the same so + + align:start position:0% +Ataman rights so that stays the same so + + + align:start position:0% +Ataman rights so that stays the same so +this is our to a full annual peak cost + + align:start position:0% +this is our to a full annual peak cost + + + align:start position:0% +this is our to a full annual peak cost +no and if we want to increase people + + align:start position:0% +no and if we want to increase people + + + align:start position:0% +no and if we want to increase people +only service we use a small not the + + align:start position:0% +only service we use a small not the + + + align:start position:0% +only service we use a small not the +other one and it'll reflect more + + align:start position:0% +other one and it'll reflect more + + + align:start position:0% +other one and it'll reflect more +faithfully what the costs will be we can + + align:start position:0% +faithfully what the costs will be we can + + + align:start position:0% +faithfully what the costs will be we can +do the same with both pictures so we + + align:start position:0% +do the same with both pictures so we + + + align:start position:0% +do the same with both pictures so we +take the thirty seven dollars and + + align:start position:0% +take the thirty seven dollars and + + + align:start position:0% +take the thirty seven dollars and +thirteen cents and we can add the + + align:start position:0% +thirteen cents and we can add the + + + align:start position:0% +thirteen cents and we can add the +combination of the portion of it that is + + align:start position:0% +combination of the portion of it that is + + + align:start position:0% +combination of the portion of it that is +1152 and the portion of it that is $13 + + align:start position:0% +1152 and the portion of it that is $13 + + + align:start position:0% +1152 and the portion of it that is $13 +ninety-seven cents let's do so for off + + align:start position:0% +ninety-seven cents let's do so for off + + + align:start position:0% +ninety-seven cents let's do so for off +period model we start out with the base + + align:start position:0% +period model we start out with the base + + + align:start position:0% +period model we start out with the base +cost of thirty seven dollars and that's + + align:start position:0% +cost of thirty seven dollars and that's + + + align:start position:0% +cost of thirty seven dollars and that's +going to apply only for the fraction of + + align:start position:0% +going to apply only for the fraction of + + + align:start position:0% +going to apply only for the fraction of +off-peak hours that are sort of Sunday + + align:start position:0% +off-peak hours that are sort of Sunday + + + align:start position:0% +off-peak hours that are sort of Sunday +and weekday evening right so this is + + align:start position:0% +and weekday evening right so this is + + + align:start position:0% +and weekday evening right so this is +some day an evening service only right + + align:start position:0% +some day an evening service only right + + + align:start position:0% +some day an evening service only right +so the question is how many Sunday and + + align:start position:0% +so the question is how many Sunday and + + + align:start position:0% +so the question is how many Sunday and +evening service hours are there in a + + align:start position:0% +evening service hours are there in a + + + align:start position:0% +evening service hours are there in a +year well + + align:start position:0% +year well + + + align:start position:0% +year well +it's the proportions this one right here + + align:start position:0% +it's the proportions this one right here + + + align:start position:0% +it's the proportions this one right here +1684 / 3000 o calculate that - in a + + align:start position:0% +1684 / 3000 o calculate that - in a + + + align:start position:0% +1684 / 3000 o calculate that - in a +second we also want to add the other + + align:start position:0% +second we also want to add the other + + + align:start position:0% +second we also want to add the other +cost which is thirteen dollars and 97 + + align:start position:0% +cost which is thirteen dollars and 97 + + + align:start position:0% +cost which is thirteen dollars and 97 +cents and the proportion is okay so + + align:start position:0% +cents and the proportion is okay so + + + align:start position:0% +cents and the proportion is okay so +where do we get sixteen eighty four and + + align:start position:0% +where do we get sixteen eighty four and + + + align:start position:0% +where do we get sixteen eighty four and +will need six from it's similar to + + align:start position:0% +will need six from it's similar to + + + align:start position:0% +will need six from it's similar to +before right we just count how many + + align:start position:0% +before right we just count how many + + + align:start position:0% +before right we just count how many +hours that are so so let's just do it + + align:start position:0% +hours that are so so let's just do it + + + align:start position:0% +hours that are so so let's just do it +quickly here for the record so let's + + align:start position:0% +quickly here for the record so let's + + + align:start position:0% +quickly here for the record so let's +just compute the bottom one actually and + + align:start position:0% +just compute the bottom one actually and + + + align:start position:0% +just compute the bottom one actually and +you'll get the idea for the others + + align:start position:0% +you'll get the idea for the others + + + align:start position:0% +you'll get the idea for the others +because to do all off peak hours so we + + align:start position:0% +because to do all off peak hours so we + + + align:start position:0% +because to do all off peak hours so we +have ten hours ten off the hours and the + + align:start position:0% +have ten hours ten off the hours and the + + + align:start position:0% +have ten hours ten off the hours and the +weekday times 250 weekdays for a year + + align:start position:0% +weekday times 250 weekdays for a year + + + align:start position:0% +weekday times 250 weekdays for a year +plus so this is we things plus twelve + + align:start position:0% +plus so this is we things plus twelve + + + align:start position:0% +plus so this is we things plus twelve +hours on Saturdays and we said there are + + align:start position:0% +hours on Saturdays and we said there are + + + align:start position:0% +hours on Saturdays and we said there are +some 58 Saturdays per year plus twelve + + align:start position:0% +some 58 Saturdays per year plus twelve + + + align:start position:0% +some 58 Saturdays per year plus twelve +hours on Sundays I said 57 Sundays + + align:start position:0% +hours on Sundays I said 57 Sundays + + + align:start position:0% +hours on Sundays I said 57 Sundays +oh yeah and that comes out to 3,800 + + align:start position:0% + + + + align:start position:0% + +hours and you can select combinations of + + align:start position:0% +hours and you can select combinations of + + + align:start position:0% +hours and you can select combinations of +these to get the 1684 and at 196 right + + align:start position:0% +these to get the 1684 and at 196 right + + + align:start position:0% +these to get the 1684 and at 196 right +so yes exactly so that's okay + + align:start position:0% +so yes exactly so that's okay + + + align:start position:0% +so yes exactly so that's okay +so the people follow this allocation + + align:start position:0% +so the people follow this allocation + + + align:start position:0% +so the people follow this allocation +example so we're doing is taking + + align:start position:0% +example so we're doing is taking + + + align:start position:0% +example so we're doing is taking +dividing the day in two periods some + + align:start position:0% +dividing the day in two periods some + + + align:start position:0% +dividing the day in two periods some +periods we recognize are more expensive + + align:start position:0% +periods we recognize are more expensive + + + align:start position:0% +periods we recognize are more expensive +than others to run we take the now we + + align:start position:0% +than others to run we take the now we + + + align:start position:0% +than others to run we take the now we +have fixed costs that we ought to + + align:start position:0% +have fixed costs that we ought to + + + align:start position:0% +have fixed costs that we ought to +allocate them across periods and I won't + + align:start position:0% +allocate them across periods and I won't + + + align:start position:0% +allocate them across periods and I won't +go get more cost to the peak exacts that + + align:start position:0% +go get more cost to the peak exacts that + + + align:start position:0% +go get more cost to the peak exacts that +sort of costs more so we then use these + + align:start position:0% +sort of costs more so we then use these + + + align:start position:0% +sort of costs more so we then use these +unit costs to endow and we count how + + align:start position:0% +unit costs to endow and we count how + + + align:start position:0% +unit costs to endow and we count how +many hours we've provided off p.m. + + align:start position:0% +many hours we've provided off p.m. + + + align:start position:0% +many hours we've provided off p.m. +during the peak and we do things and + + align:start position:0% +during the peak and we do things and + + + align:start position:0% +during the peak and we do things and +proportions eventually these are not the + + align:start position:0% +proportions eventually these are not the + + + align:start position:0% +proportions eventually these are not the +only Gospels that you can come up with + + align:start position:0% +only Gospels that you can come up with + + + align:start position:0% +only Gospels that you can come up with +they are not the only ways of allocating + + align:start position:0% +they are not the only ways of allocating + + + align:start position:0% +they are not the only ways of allocating +costs but they provide an example of how + + align:start position:0% +costs but they provide an example of how + + + align:start position:0% +costs but they provide an example of how +you can go about allocating cost + + align:start position:0% +you can go about allocating cost + + + align:start position:0% +you can go about allocating cost +allocating costs bizarre science is also + + align:start position:0% +allocating costs bizarre science is also + + + align:start position:0% +allocating costs bizarre science is also +an art and you encounter it in agencies + + align:start position:0% +an art and you encounter it in agencies + + + align:start position:0% +an art and you encounter it in agencies +because you have these huge budgets and + + align:start position:0% +because you have these huge budgets and + + + align:start position:0% +because you have these huge budgets and +huge expenditures and many projects + + align:start position:0% +huge expenditures and many projects + + + align:start position:0% +huge expenditures and many projects +require you to outlook to a portion or + + align:start position:0% +require you to outlook to a portion or + + + align:start position:0% +require you to outlook to a portion or +allocate costs and if you want to have a + + align:start position:0% +allocate costs and if you want to have a + + + align:start position:0% +allocate costs and if you want to have a +cost model he has to do it because your + + align:start position:0% +cost model he has to do it because your + + + align:start position:0% +cost model he has to do it because your +cost model should your flat + + align:start position:0% + + + + align:start position:0% + +okay the last the third and last type of + + align:start position:0% +okay the last the third and last type of + + + align:start position:0% +okay the last the third and last type of +is the incremental fixed variable all so + + align:start position:0% +is the incremental fixed variable all so + + + align:start position:0% +is the incremental fixed variable all so +here it's somewhat similar to the ones + + align:start position:0% +here it's somewhat similar to the ones + + + align:start position:0% +here it's somewhat similar to the ones +that we saw before but now we classified + + align:start position:0% +that we saw before but now we classified + + + align:start position:0% +that we saw before but now we classified +costs as being variable semi variable + + align:start position:0% +costs as being variable semi variable + + + align:start position:0% +costs as being variable semi variable +and six so we have a little more + + align:start position:0% + + + + align:start position:0% + +precision a little more precision in + + align:start position:0% +precision a little more precision in + + + align:start position:0% +precision a little more precision in +what we consider fixed or variable we + + align:start position:0% +what we consider fixed or variable we + + + align:start position:0% +what we consider fixed or variable we +also have the same explanatory variables + + align:start position:0% +also have the same explanatory variables + + + align:start position:0% +also have the same explanatory variables +that we had before so vehicle hours + + align:start position:0% +that we had before so vehicle hours + + + align:start position:0% +that we had before so vehicle hours +people miles MP vehicles so now the + + align:start position:0% +people miles MP vehicles so now the + + + align:start position:0% +people miles MP vehicles so now the +combination these are certain nine + + align:start position:0% +combination these are certain nine + + + align:start position:0% +combination these are certain nine +different explanatory variables and we + + align:start position:0% +different explanatory variables and we + + + align:start position:0% +different explanatory variables and we +do the same things we have done before + + align:start position:0% +do the same things we have done before + + + align:start position:0% +do the same things we have done before +we go we have a schedule of expenses + + align:start position:0% +we go we have a schedule of expenses + + + align:start position:0% +we go we have a schedule of expenses +these are accounts so crew ages people + + align:start position:0% +these are accounts so crew ages people + + + align:start position:0% +these are accounts so crew ages people +servicing fuel tires insurance traffic + + align:start position:0% +servicing fuel tires insurance traffic + + + align:start position:0% +servicing fuel tires insurance traffic +stop + + align:start position:0% +stop + + + align:start position:0% +stop +things like publicity and rents and + + align:start position:0% +things like publicity and rents and + + + align:start position:0% +things like publicity and rents and +building maintenance everything is + + align:start position:0% +building maintenance everything is + + + align:start position:0% +building maintenance everything is +included so all your budget is going to + + align:start position:0% +included so all your budget is going to + + + align:start position:0% +included so all your budget is going to +fall into some category is divided among + + align:start position:0% +fall into some category is divided among + + + align:start position:0% +fall into some category is divided among +these categories so now you decide for + + align:start position:0% +these categories so now you decide for + + + align:start position:0% +these categories so now you decide for +each of these which ones which which of + + align:start position:0% +each of these which ones which which of + + + align:start position:0% +each of these which ones which which of +these three resources apply and which + + align:start position:0% +these three resources apply and which + + + align:start position:0% +these three resources apply and which +cost type you consider this to be so for + + align:start position:0% +cost type you consider this to be so for + + + align:start position:0% +cost type you consider this to be so for +example your wages + + align:start position:0% +example your wages + + + align:start position:0% +example your wages +let's associate that with bus hours as + + align:start position:0% +let's associate that with bus hours as + + + align:start position:0% +let's associate that with bus hours as +we did before and that's fully variable + + align:start position:0% +we did before and that's fully variable + + + align:start position:0% +we did before and that's fully variable +right so that should we should feel + + align:start position:0% +right so that should we should feel + + + align:start position:0% +right so that should we should feel +comfortable with things like building + + align:start position:0% +comfortable with things like building + + + align:start position:0% +comfortable with things like building +utilities that shouldn't be variable + + align:start position:0% +utilities that shouldn't be variable + + + align:start position:0% +utilities that shouldn't be variable +right so that's a fixed cost and we'll + + align:start position:0% +right so that's a fixed cost and we'll + + + align:start position:0% +right so that's a fixed cost and we'll +so sit up with P buses because people + + align:start position:0% +so sit up with P buses because people + + + align:start position:0% +so sit up with P buses because people +assists the one that we say it is a good + + align:start position:0% +assists the one that we say it is a good + + + align:start position:0% +assists the one that we say it is a good +proxy for how big the agency is so P + + align:start position:0% +proxy for how big the agency is so P + + + align:start position:0% +proxy for how big the agency is so P +buses is again like agency size if you + + align:start position:0% +buses is again like agency size if you + + + align:start position:0% +buses is again like agency size if you +will okay + + align:start position:0% +will okay + + + align:start position:0% +will okay +so then there are things in the middle + + align:start position:0% +so then there are things in the middle + + + align:start position:0% +so then there are things in the middle +so publicity well so many variable + + align:start position:0% +so publicity well so many variable + + + align:start position:0% +so publicity well so many variable +because if you to leave somewhat you + + align:start position:0% +because if you to leave somewhat you + + + align:start position:0% +because if you to leave somewhat you +increase service there's gonna be some + + align:start position:0% +increase service there's gonna be some + + + align:start position:0% +increase service there's gonna be some +amount of additional policy there's not + + align:start position:0% +amount of additional policy there's not + + + align:start position:0% +amount of additional policy there's not +gonna be necessarily a linear proportion + + align:start position:0% +gonna be necessarily a linear proportion + + + align:start position:0% +gonna be necessarily a linear proportion +increase with I'll see you know we have + + align:start position:0% +increase with I'll see you know we have + + + align:start position:0% +increase with I'll see you know we have +one more bus then you have that much + + align:start position:0% +one more bus then you have that much + + + align:start position:0% +one more bus then you have that much +more marketing more publicity expense + + align:start position:0% +more marketing more publicity expense + + + align:start position:0% +more marketing more publicity expense +you have some of those expenses + + align:start position:0% +you have some of those expenses + + + align:start position:0% +you have some of those expenses +are having an office and staffs of some + + align:start position:0% +are having an office and staffs of some + + + align:start position:0% +are having an office and staffs of some +salaries portions fixed but them there's + + align:start position:0% +salaries portions fixed but them there's + + + align:start position:0% +salaries portions fixed but them there's +extra space that we have to cover on + + align:start position:0% +extra space that we have to cover on + + + align:start position:0% +extra space that we have to cover on +each additional bus so that part is + + align:start position:0% +each additional bus so that part is + + + align:start position:0% +each additional bus so that part is +variable so now we have a sunny variable + + align:start position:0% +variable so now we have a sunny variable + + + align:start position:0% +variable so now we have a sunny variable +cost and you can associate that in this + + align:start position:0% +cost and you can associate that in this + + + align:start position:0% +cost and you can associate that in this +case with peak buses because for each + + align:start position:0% +case with peak buses because for each + + + align:start position:0% +case with peak buses because for each +beep bus you have them that's how many + + align:start position:0% +beep bus you have them that's how many + + + align:start position:0% +beep bus you have them that's how many +buses you have to plaster without right + + align:start position:0% +buses you have to plaster without right + + + align:start position:0% +buses you have to plaster without right +that gives you an example so you can go + + align:start position:0% +that gives you an example so you can go + + + align:start position:0% +that gives you an example so you can go +through each of these again this + + align:start position:0% +through each of these again this + + + align:start position:0% +through each of these again this +requires judgment and therefore each + + align:start position:0% +requires judgment and therefore each + + + align:start position:0% +requires judgment and therefore each +person might do it slightly differently + + align:start position:0% +person might do it slightly differently + + + align:start position:0% +person might do it slightly differently +but you you use the schedule and you + + align:start position:0% +but you you use the schedule and you + + + align:start position:0% +but you you use the schedule and you +then build your you calculate your unit + + align:start position:0% +then build your you calculate your unit + + + align:start position:0% +then build your you calculate your unit +costs much like we did with your + + align:start position:0% +costs much like we did with your + + + align:start position:0% +costs much like we did with your +examples and you then apply it all so + + align:start position:0% +examples and you then apply it all so + + + align:start position:0% +examples and you then apply it all so +but now we have more precision so if you + + align:start position:0% +but now we have more precision so if you + + + align:start position:0% +but now we have more precision so if you +if you have some some kind of new + + align:start position:0% +if you have some some kind of new + + + align:start position:0% +if you have some some kind of new +expense or you the site are gonna save + + align:start position:0% +expense or you the site are gonna save + + + align:start position:0% +expense or you the site are gonna save +some money somehow then you decide what + + align:start position:0% +some money somehow then you decide what + + + align:start position:0% +some money somehow then you decide what +how am I going to spend less or spend + + align:start position:0% +how am I going to spend less or spend + + + align:start position:0% +how am I going to spend less or spend +more would that be a variable semi + + align:start position:0% +more would that be a variable semi + + + align:start position:0% +more would that be a variable semi +variable or fixed cost with that what I + + align:start position:0% +variable or fixed cost with that what I + + + align:start position:0% +variable or fixed cost with that what I +associate that with people I would + + align:start position:0% +associate that with people I would + + + align:start position:0% +associate that with people I would +people miles or peak vehicles and then + + align:start position:0% +people miles or peak vehicles and then + + + align:start position:0% +people miles or peak vehicles and then +you use that unit cost to bring the + + align:start position:0% +you use that unit cost to bring the + + + align:start position:0% +you use that unit cost to bring the +total cost up we're down from the agency + + align:start position:0% +total cost up we're down from the agency + + + align:start position:0% +total cost up we're down from the agency +and you can even more detailed models + + align:start position:0% +and you can even more detailed models + + + align:start position:0% +and you can even more detailed models +you could just go buy expense category + + align:start position:0% +you could just go buy expense category + + + align:start position:0% +you could just go buy expense category +and do your engineering style sort of + + align:start position:0% +and do your engineering style sort of + + + align:start position:0% +and do your engineering style sort of +budget if you want to really calculate + + align:start position:0% +budget if you want to really calculate + + + align:start position:0% +budget if you want to really calculate +exactly how much cost you'll save or + + align:start position:0% +exactly how much cost you'll save or + + + align:start position:0% +exactly how much cost you'll save or +exactly how much extra cost you'll incur + + align:start position:0% +exactly how much extra cost you'll incur + + + align:start position:0% +exactly how much extra cost you'll incur +but these cuffs models are applied more + + align:start position:0% +but these cuffs models are applied more + + + align:start position:0% +but these cuffs models are applied more +a little more a little more bluntly in + + align:start position:0% +a little more a little more bluntly in + + + align:start position:0% +a little more a little more bluntly in +projects where you are evaluating + + align:start position:0% +projects where you are evaluating + + + align:start position:0% +projects where you are evaluating +especially at an early stage what it + + align:start position:0% +especially at an early stage what it + + + align:start position:0% +especially at an early stage what it +would cost and you have different + + align:start position:0% +would cost and you have different + + + align:start position:0% +would cost and you have different +scenarios and you want to quickly know + + align:start position:0% +scenarios and you want to quickly know + + + align:start position:0% +scenarios and you want to quickly know +how much it would cost + + align:start position:0% +how much it would cost + + + align:start position:0% +how much it would cost +alright so questions you have the + + align:start position:0% +alright so questions you have the + + + align:start position:0% +alright so questions you have the +proportion of yeah so you use + + align:start position:0% +proportion of yeah so you use + + + align:start position:0% +proportion of yeah so you use +essentially your lumping things a little + + align:start position:0% +essentially your lumping things a little + + + align:start position:0% +essentially your lumping things a little +less + + align:start position:0% +less + + + align:start position:0% +less +you have more variable so your unit + + align:start position:0% +you have more variable so your unit + + + align:start position:0% +you have more variable so your unit +costs or more precise yes and I think + + align:start position:0% +costs or more precise yes and I think + + + align:start position:0% +costs or more precise yes and I think +the ability to move to more + + align:start position:0% +the ability to move to more + + + align:start position:0% +the ability to move to more +sophisticated models is sort of + + align:start position:0% +sophisticated models is sort of + + + align:start position:0% +sophisticated models is sort of +increasing now that everything is + + align:start position:0% +increasing now that everything is + + + align:start position:0% +increasing now that everything is +computer-based + + align:start position:0% + + + + align:start position:0% + +back in slide 11 you said it's possible + + align:start position:0% +back in slide 11 you said it's possible + + + align:start position:0% +back in slide 11 you said it's possible +that reducing driver hours periods + + align:start position:0% +that reducing driver hours periods + + + align:start position:0% +that reducing driver hours periods +I have no factor could even he actually + + align:start position:0% +I have no factor could even he actually + + + align:start position:0% +I have no factor could even he actually +increased costs couldn't well yeah it + + align:start position:0% +increased costs couldn't well yeah it + + + align:start position:0% +increased costs couldn't well yeah it +shouldn't because it shouldn't increase + + align:start position:0% +shouldn't because it shouldn't increase + + + align:start position:0% +shouldn't because it shouldn't increase +costs ask this Eric is it ever the case + + align:start position:0% +costs ask this Eric is it ever the case + + + align:start position:0% +costs ask this Eric is it ever the case +that off-peak service for this really + + align:start position:0% +that off-peak service for this really + + + align:start position:0% +that off-peak service for this really +low demand exists simply for the + + align:start position:0% +low demand exists simply for the + + + align:start position:0% +low demand exists simply for the +convenience of scheduling shifts rather + + align:start position:0% +convenience of scheduling shifts rather + + + align:start position:0% +convenience of scheduling shifts rather +than needy + + align:start position:0% + + + + align:start position:0% + +potentially but because driver costs are + + align:start position:0% +potentially but because driver costs are + + + align:start position:0% +potentially but because driver costs are +not the only cost of operating service + + align:start position:0% +not the only cost of operating service + + + align:start position:0% +not the only cost of operating service +you would then also agree to spend extra + + align:start position:0% +you would then also agree to spend extra + + + align:start position:0% +you would then also agree to spend extra +fuel and extra maintenance cost and that + + align:start position:0% +fuel and extra maintenance cost and that + + + align:start position:0% +fuel and extra maintenance cost and that +is also a significant portion so you + + align:start position:0% +is also a significant portion so you + + + align:start position:0% +is also a significant portion so you +don't it's not just free where it's only + + align:start position:0% +don't it's not just free where it's only + + + align:start position:0% +don't it's not just free where it's only +only this part might be free no the + + align:start position:0% +only this part might be free no the + + + align:start position:0% +only this part might be free no the +whole thing so but yeah I think yeah if + + align:start position:0% +whole thing so but yeah I think yeah if + + + align:start position:0% +whole thing so but yeah I think yeah if +you find yourself in a situation where + + align:start position:0% +you find yourself in a situation where + + + align:start position:0% +you find yourself in a situation where +you're you your labor agreement requires + + align:start position:0% +you're you your labor agreement requires + + + align:start position:0% +you're you your labor agreement requires +you to have maybe there's a cap on how + + align:start position:0% +you to have maybe there's a cap on how + + + align:start position:0% +you to have maybe there's a cap on how +much spread you can have so you have all + + align:start position:0% +much spread you can have so you have all + + + align:start position:0% +much spread you can have so you have all +these straight runs and they're only + + align:start position:0% +these straight runs and they're only + + + align:start position:0% +these straight runs and they're only +working for four hours and then you say + + align:start position:0% +working for four hours and then you say + + + align:start position:0% +working for four hours and then you say +well you know let's add service and + + align:start position:0% +well you know let's add service and + + + align:start position:0% +well you know let's add service and +let's make a piece or off-peak service + + align:start position:0% +let's make a piece or off-peak service + + + align:start position:0% +let's make a piece or off-peak service +very good so yeah I could hop in this + + align:start position:0% +very good so yeah I could hop in this + + + align:start position:0% +very good so yeah I could hop in this +but I saw the management decision + + align:start position:0% +but I saw the management decision + + + align:start position:0% +but I saw the management decision +that's not something + + align:start position:0% + + + + align:start position:0% + +yes so in this example we only have + + align:start position:0% +yes so in this example we only have + + + align:start position:0% +yes so in this example we only have +three well we have - pirate or variables + + align:start position:0% +three well we have - pirate or variables + + + align:start position:0% +three well we have - pirate or variables +which are the combination of the three + + align:start position:0% +which are the combination of the three + + + align:start position:0% +which are the combination of the three +resource variables and the three cross + + align:start position:0% +resource variables and the three cross + + + align:start position:0% +resource variables and the three cross +types for them if you go back to the + + align:start position:0% +types for them if you go back to the + + + align:start position:0% +types for them if you go back to the +first example in each lecture we have + + align:start position:0% +first example in each lecture we have + + + align:start position:0% +first example in each lecture we have +three explanatory variables both powers + + align:start position:0% +three explanatory variables both powers + + + align:start position:0% +three explanatory variables both powers +of smiles and people losses and we have + + align:start position:0% +of smiles and people losses and we have + + + align:start position:0% +of smiles and people losses and we have +to assign everything to one of these + + align:start position:0% +to assign everything to one of these + + + align:start position:0% +to assign everything to one of these +three so of those three peak buses is + + align:start position:0% +three so of those three peak buses is + + + align:start position:0% +three so of those three peak buses is +something that most closely relates to + + align:start position:0% +something that most closely relates to + + + align:start position:0% +something that most closely relates to +how large your agency is right much more + + align:start position:0% +how large your agency is right much more + + + align:start position:0% +how large your agency is right much more +so than bus hours or bus months and if + + align:start position:0% +so than bus hours or bus months and if + + + align:start position:0% +so than bus hours or bus months and if +you had other variables then maybe they + + align:start position:0% +you had other variables then maybe they + + + align:start position:0% +you had other variables then maybe they +also be even closer to agency size but + + align:start position:0% +also be even closer to agency size but + + + align:start position:0% +also be even closer to agency size but +in this example we only have these + + align:start position:0% +in this example we only have these + + + align:start position:0% +in this example we only have these +things yeah and what why people's as + + align:start position:0% +things yeah and what why people's as + + + align:start position:0% +things yeah and what why people's as +well because if you have more buses you + + align:start position:0% +well because if you have more buses you + + + align:start position:0% +well because if you have more buses you +know they're your parking garage for + + align:start position:0% +know they're your parking garage for + + + align:start position:0% +know they're your parking garage for +them you need air refueling a + + align:start position:0% +them you need air refueling a + + + align:start position:0% +them you need air refueling a +maintenance facility you might need more + + align:start position:0% +maintenance facility you might need more + + + align:start position:0% +maintenance facility you might need more +mechanics and more right so the main + + align:start position:0% +mechanics and more right so the main + + + align:start position:0% +mechanics and more right so the main +costs that are mostly fixed scale up + + align:start position:0% +costs that are mostly fixed scale up + + + align:start position:0% +costs that are mostly fixed scale up +with how many vehicles on your garage + + align:start position:0% +with how many vehicles on your garage + + + align:start position:0% +with how many vehicles on your garage +and how many garages you have and all + + align:start position:0% +and how many garages you have and all + + + align:start position:0% +and how many garages you have and all +this thing's another detail which with + + align:start position:0% +this thing's another detail which with + + + align:start position:0% +this thing's another detail which with +regards to variable and fixed + + align:start position:0% +regards to variable and fixed + + + align:start position:0% +regards to variable and fixed +so again if you if you have to incur an + + align:start position:0% +so again if you if you have to incur an + + + align:start position:0% +so again if you if you have to incur an +expense that is more marginal then you + + align:start position:0% +expense that is more marginal then you + + + align:start position:0% +expense that is more marginal then you +might want to give a variable cost of + + align:start position:0% +might want to give a variable cost of + + + align:start position:0% +might want to give a variable cost of +all because you may not need another + + align:start position:0% +all because you may not need another + + + align:start position:0% +all because you may not need another +garage for example for a few extra buses + + align:start position:0% +garage for example for a few extra buses + + + align:start position:0% +garage for example for a few extra buses +but at some point you do incur on you + + align:start position:0% +but at some point you do incur on you + + + align:start position:0% +but at some point you do incur on you +reach an investment threshold where well + + align:start position:0% +reach an investment threshold where well + + + align:start position:0% +reach an investment threshold where well +now you've you've crossed the line and + + align:start position:0% +now you've you've crossed the line and + + + align:start position:0% +now you've you've crossed the line and +you do not even as a master facility and + + align:start position:0% +you do not even as a master facility and + + + align:start position:0% +you do not even as a master facility and +you have to hire people to run the + + align:start position:0% +you have to hire people to run the + + + align:start position:0% +you have to hire people to run the +facility and that's gonna be that's + + align:start position:0% +facility and that's gonna be that's + + + align:start position:0% +facility and that's gonna be that's +going to include your based cost so that + + align:start position:0% +going to include your based cost so that + + + align:start position:0% +going to include your based cost so that +happens in lonely fashion rather than + + align:start position:0% +happens in lonely fashion rather than + + + align:start position:0% +happens in lonely fashion rather than +variable and scaling opportunity we have + + align:start position:0% +variable and scaling opportunity we have + + + align:start position:0% +variable and scaling opportunity we have +another show in ten minutes and maybe it + + align:start position:0% +another show in ten minutes and maybe it + + + align:start position:0% +another show in ten minutes and maybe it +would be a good opportunity to discuss + + align:start position:0% +would be a good opportunity to discuss + + + align:start position:0% +would be a good opportunity to discuss +the first assignment which I have not + + align:start position:0% +the first assignment which I have not + + + align:start position:0% +the first assignment which I have not +finished grading I'm sorry + + align:start position:0% +finished grading I'm sorry + + + align:start position:0% +finished grading I'm sorry +I hope to you soon but we might as well + + align:start position:0% +I hope to you soon but we might as well + + + align:start position:0% +I hope to you soon but we might as well +go over it and discuss the solution okay + + align:start position:0% + + + + align:start position:0% + +back in your plea you had had some + + align:start position:0% +back in your plea you had had some + + + align:start position:0% +back in your plea you had had some +sample data right in a spreadsheet you + + align:start position:0% +sample data right in a spreadsheet you + + + align:start position:0% +sample data right in a spreadsheet you +have to calculate the first question was + + align:start position:0% +have to calculate the first question was + + + align:start position:0% +have to calculate the first question was +calculate statistics my direction so + + align:start position:0% +calculate statistics my direction so + + + align:start position:0% +calculate statistics my direction so +this this is a spreadsheet time of day + + align:start position:0% +this this is a spreadsheet time of day + + + align:start position:0% +this this is a spreadsheet time of day +in running time given to you I like to + + align:start position:0% +in running time given to you I like to + + + align:start position:0% +in running time given to you I like to +use the indirect function I don't know + + align:start position:0% +use the indirect function I don't know + + + align:start position:0% +use the indirect function I don't know +what people know it or not but it's + + align:start position:0% +what people know it or not but it's + + + align:start position:0% +what people know it or not but it's +convenient so if you type the range name + + align:start position:0% +convenient so if you type the range name + + + align:start position:0% +convenient so if you type the range name +and cell then you can compete things as + + align:start position:0% +and cell then you can compete things as + + + align:start position:0% +and cell then you can compete things as +a function of that range name and that's + + align:start position:0% +a function of that range name and that's + + + align:start position:0% +a function of that range name and that's +very convenient so I selected the range + + align:start position:0% +very convenient so I selected the range + + + align:start position:0% +very convenient so I selected the range +b2 to be 751 and that corresponds to all + + align:start position:0% +b2 to be 751 and that corresponds to all + + + align:start position:0% +b2 to be 751 and that corresponds to all +the data on this right all the data off + + align:start position:0% +the data on this right all the data off + + + align:start position:0% +the data on this right all the data off +this first sheet so and then I do the + + align:start position:0% +this first sheet so and then I do the + + + align:start position:0% +this first sheet so and then I do the +same for Direction 2 so therefore when I + + align:start position:0% +same for Direction 2 so therefore when I + + + align:start position:0% +same for Direction 2 so therefore when I +go to mean I say equals average and + + align:start position:0% +go to mean I say equals average and + + + align:start position:0% +go to mean I say equals average and +directive before and I'm pointing the + + align:start position:0% +directive before and I'm pointing the + + + align:start position:0% +directive before and I'm pointing the +mean to the range which is a variable + + align:start position:0% +mean to the range which is a variable + + + align:start position:0% +mean to the range which is a variable +itself that's very neat so you can do up + + align:start position:0% +itself that's very neat so you can do up + + + align:start position:0% +itself that's very neat so you can do up +for average median in max and for some + + align:start position:0% +for average median in max and for some + + + align:start position:0% +for average median in max and for some +time and then filled to the right + + align:start position:0% +time and then filled to the right + + + align:start position:0% +time and then filled to the right +because you have a different a different + + align:start position:0% +because you have a different a different + + + align:start position:0% +because you have a different a different +range here so it'll reflect that it's a + + align:start position:0% +range here so it'll reflect that it's a + + + align:start position:0% +range here so it'll reflect that it's a +little trick so these are the statistics + + align:start position:0% +little trick so these are the statistics + + + align:start position:0% +little trick so these are the statistics +this was very straightforward then + + align:start position:0% +this was very straightforward then + + + align:start position:0% +this was very straightforward then +question 4 starts getting more + + align:start position:0% +question 4 starts getting more + + + align:start position:0% +question 4 starts getting more +transportation itself this requires some + + align:start position:0% +transportation itself this requires some + + + align:start position:0% +transportation itself this requires some +judgment so we're saying what's the + + align:start position:0% +judgment so we're saying what's the + + + align:start position:0% +judgment so we're saying what's the +running time what's the recovery time + + align:start position:0% +running time what's the recovery time + + + align:start position:0% +running time what's the recovery time +what's the half cycle time what's the + + align:start position:0% +what's the half cycle time what's the + + + align:start position:0% +what's the half cycle time what's the +cycle time so running time should be + + align:start position:0% +cycle time so running time should be + + + align:start position:0% +cycle time so running time should be +something that happens typically because + + align:start position:0% +something that happens typically because + + + align:start position:0% +something that happens typically because +this is what you publish on your + + align:start position:0% +this is what you publish on your + + + align:start position:0% +this is what you publish on your +schedules is what's gonna go on your + + align:start position:0% +schedules is what's gonna go on your + + + align:start position:0% +schedules is what's gonna go on your +journey planner right so people need to + + align:start position:0% +journey planner right so people need to + + + align:start position:0% +journey planner right so people need to +know what to expect + + align:start position:0% +know what to expect + + + align:start position:0% +know what to expect +and therefore running time should be + + align:start position:0% +and therefore running time should be + + + align:start position:0% +and therefore running time should be +based on the average or the media those + + align:start position:0% +based on the average or the media those + + + align:start position:0% +based on the average or the media those +are the two of these statistics they + + align:start position:0% +are the two of these statistics they + + + align:start position:0% +are the two of these statistics they +computed before these should be the + + align:start position:0% +computed before these should be the + + + align:start position:0% +computed before these should be the +little tool you use I usually prefer the + + align:start position:0% +little tool you use I usually prefer the + + + align:start position:0% +little tool you use I usually prefer the +medium because the average is affected + + align:start position:0% +medium because the average is affected + + + align:start position:0% +medium because the average is affected +by outliers and by heavy sort of tails + + align:start position:0% +by outliers and by heavy sort of tails + + + align:start position:0% +by outliers and by heavy sort of tails +on the right quite a bit so I usually go + + align:start position:0% +on the right quite a bit so I usually go + + + align:start position:0% +on the right quite a bit so I usually go +for the medium or the 50th percentile + + align:start position:0% +for the medium or the 50th percentile + + + align:start position:0% +for the medium or the 50th percentile +right + + align:start position:0% +right + + + align:start position:0% +right +recovery time so what is the recovery + + align:start position:0% +recovery time so what is the recovery + + + align:start position:0% +recovery time so what is the recovery +thing for for making up well first of + + align:start position:0% +thing for for making up well first of + + + align:start position:0% +thing for for making up well first of +all so the drivers and then second of + + align:start position:0% +all so the drivers and then second of + + + align:start position:0% +all so the drivers and then second of +all to make up for problems in the + + align:start position:0% +all to make up for problems in the + + + align:start position:0% +all to make up for problems in the +schedule so let's say I'm just riding + + align:start position:0% +schedule so let's say I'm just riding + + + align:start position:0% +schedule so let's say I'm just riding +out on this bus route and it takes me + + align:start position:0% +out on this bus route and it takes me + + + align:start position:0% +out on this bus route and it takes me +longer we can characterize it as a + + align:start position:0% +longer we can characterize it as a + + + align:start position:0% +longer we can characterize it as a +problem of scale so the schedule is of + + align:start position:0% +problem of scale so the schedule is of + + + align:start position:0% +problem of scale so the schedule is of +the deterministic decision about how + + align:start position:0% +the deterministic decision about how + + + align:start position:0% +the deterministic decision about how +long it will take you and the reality is + + align:start position:0% +long it will take you and the reality is + + + align:start position:0% +long it will take you and the reality is +that running things of stochastic + + align:start position:0% +that running things of stochastic + + + align:start position:0% +that running things of stochastic +variable it varies from 0 so you want to + + align:start position:0% +variable it varies from 0 so you want to + + + align:start position:0% +variable it varies from 0 so you want to +say you want to make a claim about what + + align:start position:0% +say you want to make a claim about what + + + align:start position:0% +say you want to make a claim about what +the typical running pain is but then you + + align:start position:0% +the typical running pain is but then you + + + align:start position:0% +the typical running pain is but then you +have to have some recovery time to + + align:start position:0% +have to have some recovery time to + + + align:start position:0% +have to have some recovery time to +account for anything later than that and + + align:start position:0% +account for anything later than that and + + + align:start position:0% +account for anything later than that and +you recognize it's a way of recognizing + + align:start position:0% +you recognize it's a way of recognizing + + + align:start position:0% +you recognize it's a way of recognizing +that these running times are stochastic + + align:start position:0% +that these running times are stochastic + + + align:start position:0% +that these running times are stochastic +so the half cycle time is how much time + + align:start position:0% +so the half cycle time is how much time + + + align:start position:0% +so the half cycle time is how much time +you budget for the run including those + + align:start position:0% +you budget for the run including those + + + align:start position:0% +you budget for the run including those +late ones right + + align:start position:0% +late ones right + + + align:start position:0% +late ones right +so I subbed up to a high percentile the + + align:start position:0% +so I subbed up to a high percentile the + + + align:start position:0% +so I subbed up to a high percentile the +95th in this is the reading was + + align:start position:0% +95th in this is the reading was + + + align:start position:0% +95th in this is the reading was +suggesting that you could use 15% times + + align:start position:0% +suggesting that you could use 15% times + + + align:start position:0% +suggesting that you could use 15% times +average or things like that when you + + align:start position:0% +average or things like that when you + + + align:start position:0% +average or things like that when you +have data then you should use the data + + align:start position:0% +have data then you should use the data + + + align:start position:0% +have data then you should use the data +right so the technique of taking an + + align:start position:0% +right so the technique of taking an + + + align:start position:0% +right so the technique of taking an +average and multiplying it by percentage + + align:start position:0% +average and multiplying it by percentage + + + align:start position:0% +average and multiplying it by percentage +is what industry typically does when you + + align:start position:0% +is what industry typically does when you + + + align:start position:0% +is what industry typically does when you +don't have automatically collected data + + align:start position:0% +don't have automatically collected data + + + align:start position:0% +don't have automatically collected data +when you essentially send someone out to + + align:start position:0% +when you essentially send someone out to + + + align:start position:0% +when you essentially send someone out to +drive behind the bus or to do or a write + + align:start position:0% +drive behind the bus or to do or a write + + + align:start position:0% +drive behind the bus or to do or a write +checker to collect data on the bus and + + align:start position:0% +checker to collect data on the bus and + + + align:start position:0% +checker to collect data on the bus and +you do five or six maybe ten trips you + + align:start position:0% +you do five or six maybe ten trips you + + + align:start position:0% +you do five or six maybe ten trips you +get an average and that's not enough to + + align:start position:0% +get an average and that's not enough to + + + align:start position:0% +get an average and that's not enough to +estimate your + + align:start position:0% +estimate your + + + align:start position:0% +estimate your +for high percentiles because he probably + + align:start position:0% +for high percentiles because he probably + + + align:start position:0% +for high percentiles because he probably +didn't see the hyper Sun file and those + + align:start position:0% +didn't see the hyper Sun file and those + + + align:start position:0% +didn't see the hyper Sun file and those +only ten trips so therefore you have to + + align:start position:0% +only ten trips so therefore you have to + + + align:start position:0% +only ten trips so therefore you have to +Lyons different method and then you + + align:start position:0% +Lyons different method and then you + + + align:start position:0% +Lyons different method and then you +could multiply it by percentage but if + + align:start position:0% +could multiply it by percentage but if + + + align:start position:0% +could multiply it by percentage but if +you have data then you should use of + + align:start position:0% +you have data then you should use of + + + align:start position:0% +you have data then you should use of +data and 10% 15% 20% whatever you use + + align:start position:0% +data and 10% 15% 20% whatever you use + + + align:start position:0% +data and 10% 15% 20% whatever you use +might not be adequate for the specific + + align:start position:0% +might not be adequate for the specific + + + align:start position:0% +might not be adequate for the specific +bus route so because he updated you can + + align:start position:0% +bus route so because he updated you can + + + align:start position:0% +bus route so because he updated you can +actually measure how variable it is and + + align:start position:0% +actually measure how variable it is and + + + align:start position:0% +actually measure how variable it is and +therefore high percentiles a better + + align:start position:0% +therefore high percentiles a better + + + align:start position:0% +therefore high percentiles a better +choice 95 is one in 20 right so if you + + align:start position:0% +choice 95 is one in 20 right so if you + + + align:start position:0% +choice 95 is one in 20 right so if you +think of there being 20 week days in a + + align:start position:0% +think of there being 20 week days in a + + + align:start position:0% +think of there being 20 week days in a +month + + align:start position:0% +month + + + align:start position:0% +month +then you're saying well about if for + + align:start position:0% +then you're saying well about if for + + + align:start position:0% +then you're saying well about if for +that for the 8 o´clock trip I expect it + + align:start position:0% +that for the 8 o´clock trip I expect it + + + align:start position:0% +that for the 8 o´clock trip I expect it +to be late about once in a month it's + + align:start position:0% +to be late about once in a month it's + + + align:start position:0% +to be late about once in a month it's +too early to start at Lee experience it + + align:start position:0% +too early to start at Lee experience it + + + align:start position:0% +too early to start at Lee experience it +was for there to be an ongoing effects + + align:start position:0% +was for there to be an ongoing effects + + + align:start position:0% +was for there to be an ongoing effects +on the next trip essentially and for + + align:start position:0% +on the next trip essentially and for + + + align:start position:0% +on the next trip essentially and for +every other time of the month I expected + + align:start position:0% +every other time of the month I expected + + + align:start position:0% +every other time of the month I expected +it to run smoothly so that's why maybe + + align:start position:0% +it to run smoothly so that's why maybe + + + align:start position:0% +it to run smoothly so that's why maybe +500 typical choice here lower numbers of + + align:start position:0% +500 typical choice here lower numbers of + + + align:start position:0% +500 typical choice here lower numbers of +percentiles are common especially a + + align:start position:0% +percentiles are common especially a + + + align:start position:0% +percentiles are common especially a +high-frequency service 1985 question + + align:start position:0% +high-frequency service 1985 question + + + align:start position:0% +high-frequency service 1985 question +back yeah so how do you use the recovery + + align:start position:0% +back yeah so how do you use the recovery + + + align:start position:0% +back yeah so how do you use the recovery +you said so the half cycle exactly the + + align:start position:0% +you said so the half cycle exactly the + + + align:start position:0% +you said so the half cycle exactly the +half cycle is 95 and recovery times of + + align:start position:0% +half cycle is 95 and recovery times of + + + align:start position:0% +half cycle is 95 and recovery times of +difference between the half cycle and + + align:start position:0% +difference between the half cycle and + + + align:start position:0% +difference between the half cycle and +the typical so on your journey planner + + align:start position:0% +the typical so on your journey planner + + + align:start position:0% +the typical so on your journey planner +you only put the writing time but then + + align:start position:0% +you only put the writing time but then + + + align:start position:0% +you only put the writing time but then +between trips you have the time and then + + align:start position:0% +between trips you have the time and then + + + align:start position:0% +between trips you have the time and then +the cycle thing is the sum of both half + + align:start position:0% +the cycle thing is the sum of both half + + + align:start position:0% +the cycle thing is the sum of both half +cycle times right so that's pretty + + align:start position:0% +cycle times right so that's pretty + + + align:start position:0% +cycle times right so that's pretty +straightforward questions 5 was how many + + align:start position:0% +straightforward questions 5 was how many + + + align:start position:0% +straightforward questions 5 was how many +needles that you need to operate this + + align:start position:0% +needles that you need to operate this + + + align:start position:0% +needles that you need to operate this +and there's an equation which is maybe + + align:start position:0% +and there's an equation which is maybe + + + align:start position:0% +and there's an equation which is maybe +the most important equation in the whole + + align:start position:0% +the most important equation in the whole + + + align:start position:0% +the most important equation in the whole +course number of vehicles equals cycle + + align:start position:0% +course number of vehicles equals cycle + + + align:start position:0% +course number of vehicles equals cycle +time divided by that way and you need to + + align:start position:0% +time divided by that way and you need to + + + align:start position:0% +time divided by that way and you need to +round up so cycle time is 84 minutes the + + align:start position:0% +round up so cycle time is 84 minutes the + + + align:start position:0% +round up so cycle time is 84 minutes the +headway we said was 10 minutes so that's + + align:start position:0% +headway we said was 10 minutes so that's + + + align:start position:0% +headway we said was 10 minutes so that's +84 the weight of a tent a point for + + align:start position:0% +84 the weight of a tent a point for + + + align:start position:0% +84 the weight of a tent a point for +round up that's nine vehicles + + align:start position:0% +round up that's nine vehicles + + + align:start position:0% +round up that's nine vehicles +well through question 6 asks you to plot + + align:start position:0% +well through question 6 asks you to plot + + + align:start position:0% +well through question 6 asks you to plot +the times + + align:start position:0% + + + + align:start position:0% + +hopefully you label your axes and did + + align:start position:0% +hopefully you label your axes and did + + + align:start position:0% +hopefully you label your axes and did +everything you know like you should + + align:start position:0% +everything you know like you should + + + align:start position:0% +everything you know like you should +so here's time of day and here's running + + align:start position:0% +so here's time of day and here's running + + + align:start position:0% +so here's time of day and here's running +times and direction in one running times + + align:start position:0% +times and direction in one running times + + + align:start position:0% +times and direction in one running times +in Direction 2 and we identify that not + + align:start position:0% +in Direction 2 and we identify that not + + + align:start position:0% +in Direction 2 and we identify that not +all these running times come from the + + align:start position:0% +all these running times come from the + + + align:start position:0% +all these running times come from the +same operating environment we can see + + align:start position:0% +same operating environment we can see + + + align:start position:0% +same operating environment we can see +that there are some peeps and some of + + align:start position:0% +that there are some peeps and some of + + + align:start position:0% +that there are some peeps and some of +these and everything wrong because we + + align:start position:0% +these and everything wrong because we + + + align:start position:0% +these and everything wrong because we +mixed up all the data and we shouldn't + + align:start position:0% +mixed up all the data and we shouldn't + + + align:start position:0% +mixed up all the data and we shouldn't +have right so so the question was what + + align:start position:0% +have right so so the question was what + + + align:start position:0% +have right so so the question was what +are these periods so AMD going from 7:00 + + align:start position:0% +are these periods so AMD going from 7:00 + + + align:start position:0% +are these periods so AMD going from 7:00 +to 9:00 midday from 9 to 16 and p.m. + + align:start position:0% +to 9:00 midday from 9 to 16 and p.m. + + + align:start position:0% +to 9:00 midday from 9 to 16 and p.m. +from 16 to 8 a 24-hour format and now we + + align:start position:0% +from 16 to 8 a 24-hour format and now we + + + align:start position:0% +from 16 to 8 a 24-hour format and now we +have to redo all the work we have to + + align:start position:0% +have to redo all the work we have to + + + align:start position:0% +have to redo all the work we have to +compute the same statistics I just + + align:start position:0% +compute the same statistics I just + + + align:start position:0% +compute the same statistics I just +changed the ranges and copy the formulas + + align:start position:0% +changed the ranges and copy the formulas + + + align:start position:0% +changed the ranges and copy the formulas +from below and the filter right and we + + align:start position:0% +from below and the filter right and we + + + align:start position:0% +from below and the filter right and we +have all those statistics that's great + + align:start position:0% +have all those statistics that's great + + + align:start position:0% +have all those statistics that's great +we repeat the competition and we get + + align:start position:0% +we repeat the competition and we get + + + align:start position:0% +we repeat the competition and we get +people requirement late period now so we + + align:start position:0% +people requirement late period now so we + + + align:start position:0% +people requirement late period now so we +have we still need 90 vehicles in the + + align:start position:0% +have we still need 90 vehicles in the + + + align:start position:0% +have we still need 90 vehicles in the +a.m. and p.m. Peaks but it turns out + + align:start position:0% +a.m. and p.m. Peaks but it turns out + + + align:start position:0% +a.m. and p.m. Peaks but it turns out +that we only need seven in the race + + align:start position:0% +that we only need seven in the race + + + align:start position:0% +that we only need seven in the race +between Peaks so that's great + + align:start position:0% +between Peaks so that's great + + + align:start position:0% +between Peaks so that's great +what's the cycle time the cycle time + + align:start position:0% +what's the cycle time the cycle time + + + align:start position:0% +what's the cycle time the cycle time +once you've calculated you can flip this + + align:start position:0% +once you've calculated you can flip this + + + align:start position:0% +once you've calculated you can flip this +equation I could have an entire lecture + + align:start position:0% +equation I could have an entire lecture + + + align:start position:0% +equation I could have an entire lecture +on this equation well believe yeah I + + align:start position:0% +on this equation well believe yeah I + + + align:start position:0% +on this equation well believe yeah I +guess it's you can flip it around and + + align:start position:0% +guess it's you can flip it around and + + + align:start position:0% +guess it's you can flip it around and +there's many ways of interpreting + + align:start position:0% +there's many ways of interpreting + + + align:start position:0% +there's many ways of interpreting +situation but if you solve for C cycle + + align:start position:0% +situation but if you solve for C cycle + + + align:start position:0% +situation but if you solve for C cycle +time equals number of vehicles things + + align:start position:0% +time equals number of vehicles things + + + align:start position:0% +time equals number of vehicles things +that way right now you don't round any + + align:start position:0% +that way right now you don't round any + + + align:start position:0% +that way right now you don't round any +direction so once you've decided what n + + align:start position:0% +direction so once you've decided what n + + + align:start position:0% +direction so once you've decided what n +is then you solve this efficient for C + + align:start position:0% +is then you solve this efficient for C + + + align:start position:0% +is then you solve this efficient for C +and revise your cycle time because he + + align:start position:0% +and revise your cycle time because he + + + align:start position:0% +and revise your cycle time because he +rolled it up your cycle time will come + + align:start position:0% +rolled it up your cycle time will come + + + align:start position:0% +rolled it up your cycle time will come +and therefore your recovery time is up + + align:start position:0% +and therefore your recovery time is up + + + align:start position:0% +and therefore your recovery time is up +so right so the cycle the revised cycle + + align:start position:0% +so right so the cycle the revised cycle + + + align:start position:0% +so right so the cycle the revised cycle +time is 90 minutes am Fe M Peaks 17 + + align:start position:0% +time is 90 minutes am Fe M Peaks 17 + + + align:start position:0% +time is 90 minutes am Fe M Peaks 17 +units off-peak and the recovery times + + align:start position:0% +units off-peak and the recovery times + + + align:start position:0% +units off-peak and the recovery times +the difference between the typical + + align:start position:0% +the difference between the typical + + + align:start position:0% +the difference between the typical +running time the cycle time + + align:start position:0% +running time the cycle time + + + align:start position:0% +running time the cycle time +so then I asked what is you have done + + align:start position:0% +so then I asked what is you have done + + + align:start position:0% +so then I asked what is you have done +the mistake of using although they + + align:start position:0% +the mistake of using although they + + + align:start position:0% +the mistake of using although they +didn't bind that means that you're fine + + align:start position:0% +didn't bind that means that you're fine + + + align:start position:0% +didn't bind that means that you're fine +and AM and PM Peaks but it would be + + align:start position:0% +and AM and PM Peaks but it would be + + + align:start position:0% +and AM and PM Peaks but it would be +excessively provisioning resources and + + align:start position:0% +excessively provisioning resources and + + + align:start position:0% +excessively provisioning resources and +the off-peak so your cycle time was 90 + + align:start position:0% +the off-peak so your cycle time was 90 + + + align:start position:0% +the off-peak so your cycle time was 90 +because he said it was nine vehicles and + + align:start position:0% +because he said it was nine vehicles and + + + align:start position:0% +because he said it was nine vehicles and +that recovery time would be thirty + + align:start position:0% +that recovery time would be thirty + + + align:start position:0% +that recovery time would be thirty +minutes and a half which would be + + align:start position:0% +minutes and a half which would be + + + align:start position:0% +minutes and a half which would be +excessive right so yeah yeah I prefer + + align:start position:0% +excessive right so yeah yeah I prefer + + + align:start position:0% +excessive right so yeah yeah I prefer +the hidden medians a better choice but + + align:start position:0% +the hidden medians a better choice but + + + align:start position:0% +the hidden medians a better choice but +it's both are fine yeah especially if + + align:start position:0% +it's both are fine yeah especially if + + + align:start position:0% +it's both are fine yeah especially if +you remove outliers from the from the + + align:start position:0% +you remove outliers from the from the + + + align:start position:0% +you remove outliers from the from the +average and this day I didn't have + + align:start position:0% +average and this day I didn't have + + + align:start position:0% +average and this day I didn't have +outliers as you can see on the graphs + + align:start position:0% +outliers as you can see on the graphs + + + align:start position:0% +outliers as you can see on the graphs +it's very suspiciously clean and very + + align:start position:0% +it's very suspiciously clean and very + + + align:start position:0% +it's very suspiciously clean and very +precise places where the period be + + align:start position:0% +precise places where the period be + + + align:start position:0% +precise places where the period be +incident but they don't go get for the + + align:start position:0% +incident but they don't go get for the + + + align:start position:0% +incident but they don't go get for the +assignment three does not look like that + + align:start position:0% +assignment three does not look like that + + + align:start position:0% +assignment three does not look like that +so alright question nine said now we + + align:start position:0% +so alright question nine said now we + + + align:start position:0% +so alright question nine said now we +might end up this bus route runs in a + + align:start position:0% +might end up this bus route runs in a + + + align:start position:0% +might end up this bus route runs in a +loop it only has one turn and I provide + + align:start position:0% +loop it only has one turn and I provide + + + align:start position:0% +loop it only has one turn and I provide +the we have data here for that combined + + align:start position:0% +the we have data here for that combined + + + align:start position:0% +the we have data here for that combined +operation of running in down that down + + align:start position:0% +operation of running in down that down + + + align:start position:0% +operation of running in down that down +and coming back so what is the we said + + align:start position:0% +and coming back so what is the we said + + + align:start position:0% +and coming back so what is the we said +we have a headway of seven minutes and + + align:start position:0% +we have a headway of seven minutes and + + + align:start position:0% +we have a headway of seven minutes and +we are running with a fleet size of ten + + align:start position:0% +we are running with a fleet size of ten + + + align:start position:0% +we are running with a fleet size of ten +vehicles how reliable is this service so + + align:start position:0% +vehicles how reliable is this service so + + + align:start position:0% +vehicles how reliable is this service so +we can compute from the headway and + + align:start position:0% +we can compute from the headway and + + + align:start position:0% +we can compute from the headway and +fleet size the cycle time using this + + align:start position:0% +fleet size the cycle time using this + + + align:start position:0% +fleet size the cycle time using this +equation right here and we have some + + align:start position:0% +equation right here and we have some + + + align:start position:0% +equation right here and we have some +peanuts and what we want to do then is + + align:start position:0% +peanuts and what we want to do then is + + + align:start position:0% +peanuts and what we want to do then is +from all these observations you can + + align:start position:0% +from all these observations you can + + + align:start position:0% +from all these observations you can +think of this as some sort of + + align:start position:0% +think of this as some sort of + + + align:start position:0% +think of this as some sort of +probability distribution right so we + + align:start position:0% +probability distribution right so we + + + align:start position:0% +probability distribution right so we +have we have some distribution running + + align:start position:0% +have we have some distribution running + + + align:start position:0% +have we have some distribution running +time this is probability density and + + align:start position:0% +time this is probability density and + + + align:start position:0% +time this is probability density and +this is right + + align:start position:0% + + + + align:start position:0% + +and we said the cycle time 70 so some + + align:start position:0% +and we said the cycle time 70 so some + + + align:start position:0% +and we said the cycle time 70 so some +people fall somewhere around here turns + + align:start position:0% +people fall somewhere around here turns + + + align:start position:0% +people fall somewhere around here turns +out if you if you look it up and that's + + align:start position:0% +out if you if you look it up and that's + + + align:start position:0% +out if you if you look it up and that's +very close to 50% so I the way I + + align:start position:0% +very close to 50% so I the way I + + + align:start position:0% +very close to 50% so I the way I +computed it I use the spreadsheets Solar + + align:start position:0% +computed it I use the spreadsheets Solar + + + align:start position:0% +computed it I use the spreadsheets Solar +will see the different names right + + align:start position:0% +will see the different names right + + + align:start position:0% +will see the different names right +so I said calculate the percentile of + + align:start position:0% +so I said calculate the percentile of + + + align:start position:0% +so I said calculate the percentile of +whatever percentile I give you here + + align:start position:0% +whatever percentile I give you here + + + align:start position:0% +whatever percentile I give you here +right so initially I said to I don't + + align:start position:0% +right so initially I said to I don't + + + align:start position:0% +right so initially I said to I don't +know maybe I set it to 95 right and it + + align:start position:0% +know maybe I set it to 95 right and it + + + align:start position:0% +know maybe I set it to 95 right and it +gave me look for some tile this + + align:start position:0% +gave me look for some tile this + + + align:start position:0% +gave me look for some tile this +percentile is running on the a.m. peak + + align:start position:0% +percentile is running on the a.m. peak + + + align:start position:0% +percentile is running on the a.m. peak +data or whatever is I'm she's 40 tonight + + align:start position:0% +data or whatever is I'm she's 40 tonight + + + align:start position:0% +data or whatever is I'm she's 40 tonight +and then I said change that percentile + + align:start position:0% +and then I said change that percentile + + + align:start position:0% +and then I said change that percentile +such that the cell equals 70 and it + + align:start position:0% +such that the cell equals 70 and it + + + align:start position:0% +such that the cell equals 70 and it +solved it and Keith 476 okay so it's not + + align:start position:0% +solved it and Keith 476 okay so it's not + + + align:start position:0% +solved it and Keith 476 okay so it's not +reliable you know that's the probability + + align:start position:0% +reliable you know that's the probability + + + align:start position:0% +reliable you know that's the probability +that you can run in 70 minutes or less + + align:start position:0% +that you can run in 70 minutes or less + + + align:start position:0% +that you can run in 70 minutes or less +and therefore you don't costly lace on + + align:start position:0% +and therefore you don't costly lace on + + + align:start position:0% +and therefore you don't costly lace on +the next trip you're gonna be okay + + align:start position:0% +the next trip you're gonna be okay + + + align:start position:0% +the next trip you're gonna be okay +sorry not not reliable thing okay so + + align:start position:0% +sorry not not reliable thing okay so + + + align:start position:0% +sorry not not reliable thing okay so +question then is the challenge question + + align:start position:0% +question then is the challenge question + + + align:start position:0% +question then is the challenge question +and yeah now we have two terminals so + + align:start position:0% +and yeah now we have two terminals so + + + align:start position:0% +and yeah now we have two terminals so +now you have recovery + + align:start position:0% +now you have recovery + + + align:start position:0% +now you have recovery +I'm started a you go this way you reach + + align:start position:0% +I'm started a you go this way you reach + + + align:start position:0% +I'm started a you go this way you reach +B you do recovery there and then you run + + align:start position:0% +B you do recovery there and then you run + + + align:start position:0% +B you do recovery there and then you run +back so you have recovery here and here + + align:start position:0% +back so you have recovery here and here + + + align:start position:0% +back so you have recovery here and here +and we're asking about turns here are + + align:start position:0% +and we're asking about turns here are + + + align:start position:0% +and we're asking about turns here are +saying what's the probability with the + + align:start position:0% +saying what's the probability with the + + + align:start position:0% +saying what's the probability with the +same situation of seven minute halfway + + align:start position:0% +same situation of seven minute halfway + + + align:start position:0% +same situation of seven minute halfway +and fleet six of ten that this trip can + + align:start position:0% +and fleet six of ten that this trip can + + + align:start position:0% +and fleet six of ten that this trip can +be parked on time right so for that the + + align:start position:0% +be parked on time right so for that the + + + align:start position:0% +be parked on time right so for that the +different approaches for this how many + + align:start position:0% +different approaches for this how many + + + align:start position:0% +different approaches for this how many +of you to try the question and how many + + align:start position:0% +of you to try the question and how many + + + align:start position:0% +of you to try the question and how many +of you think they solves the question + + align:start position:0% + + + + align:start position:0% + +I think so so it's actually not that + + align:start position:0% +I think so so it's actually not that + + + align:start position:0% +I think so so it's actually not that +difficult you you can essentially what + + align:start position:0% +difficult you you can essentially what + + + align:start position:0% +difficult you you can essentially what +you have is a situation where you have + + align:start position:0% +you have is a situation where you have + + + align:start position:0% +you have is a situation where you have +different cases right so if you run here + + align:start position:0% +different cases right so if you run here + + + align:start position:0% +different cases right so if you run here +and you reach Terminal B early before + + align:start position:0% +and you reach Terminal B early before + + + align:start position:0% +and you reach Terminal B early before +you your half cycle things completed + + align:start position:0% +you your half cycle things completed + + + align:start position:0% +you your half cycle things completed +then you recover a beat until you reach + + align:start position:0% +then you recover a beat until you reach + + + align:start position:0% +then you recover a beat until you reach +your house cycle time right and in that + + align:start position:0% +your house cycle time right and in that + + + align:start position:0% +your house cycle time right and in that +case the only thing that matters is the + + align:start position:0% +case the only thing that matters is the + + + align:start position:0% +case the only thing that matters is the +right I'm coming back but there is a + + align:start position:0% +right I'm coming back but there is a + + + align:start position:0% +right I'm coming back but there is a +case where you run here and late and you + + align:start position:0% +case where you run here and late and you + + + align:start position:0% +case where you run here and late and you +depart immediately from the D so for + + align:start position:0% +depart immediately from the D so for + + + align:start position:0% +depart immediately from the D so for +those cases you have to compute the + + align:start position:0% +those cases you have to compute the + + + align:start position:0% +those cases you have to compute the +probability that the combination of + + align:start position:0% +probability that the combination of + + + align:start position:0% +probability that the combination of +running this way and that way is less + + align:start position:0% +running this way and that way is less + + + align:start position:0% +running this way and that way is less +than 70 so you have those two cases one + + align:start position:0% +than 70 so you have those two cases one + + + align:start position:0% +than 70 so you have those two cases one +way of doing that is to take all the + + align:start position:0% +way of doing that is to take all the + + + align:start position:0% +way of doing that is to take all the +running times that apply I think I think + + align:start position:0% +running times that apply I think I think + + + align:start position:0% +running times that apply I think I think +this Saturday in peak so Direction one + + align:start position:0% +this Saturday in peak so Direction one + + + align:start position:0% +this Saturday in peak so Direction one +is on column a to this direction + + align:start position:0% +is on column a to this direction + + + align:start position:0% +is on column a to this direction +two is on Row one so I done the + + align:start position:0% +two is on Row one so I done the + + + align:start position:0% +two is on Row one so I done the +transpose and put it on row and then for + + align:start position:0% +transpose and put it on row and then for + + + align:start position:0% +transpose and put it on row and then for +each of these cells we can compute the + + align:start position:0% +each of these cells we can compute the + + + align:start position:0% +each of these cells we can compute the +combat the combined running time so + + align:start position:0% +combat the combined running time so + + + align:start position:0% +combat the combined running time so +notice that for the first one we're + + align:start position:0% +notice that for the first one we're + + + align:start position:0% +notice that for the first one we're +saying max of 35 which is the half cycle + + align:start position:0% +saying max of 35 which is the half cycle + + + align:start position:0% +saying max of 35 which is the half cycle +time I decided here arbitrarily to split + + align:start position:0% +time I decided here arbitrarily to split + + + align:start position:0% +time I decided here arbitrarily to split +the whole cycle time of 70 minutes in + + align:start position:0% +the whole cycle time of 70 minutes in + + + align:start position:0% +the whole cycle time of 70 minutes in +half so I'm saying the half cycle for + + align:start position:0% +half so I'm saying the half cycle for + + + align:start position:0% +half so I'm saying the half cycle for +the first run is 35 minutes and so the + + align:start position:0% +the first run is 35 minutes and so the + + + align:start position:0% +the first run is 35 minutes and so the +time of departure from B is gonna be the + + align:start position:0% +time of departure from B is gonna be the + + + align:start position:0% +time of departure from B is gonna be the +maximum of 35 for cases where it was + + align:start position:0% +maximum of 35 for cases where it was + + + align:start position:0% +maximum of 35 for cases where it was +faster than 35 or the running time if it + + align:start position:0% +faster than 35 or the running time if it + + + align:start position:0% +faster than 35 or the running time if it +was a longer than 35 and then we have + + align:start position:0% +was a longer than 35 and then we have + + + align:start position:0% +was a longer than 35 and then we have +the running time in the refrain + + align:start position:0% +the running time in the refrain + + + align:start position:0% +the running time in the refrain +direction so we combined these two + + align:start position:0% +direction so we combined these two + + + align:start position:0% +direction so we combined these two +distributions that's called the + + align:start position:0% +distributions that's called the + + + align:start position:0% +distributions that's called the +convolution by adding all these up and + + align:start position:0% +convolution by adding all these up and + + + align:start position:0% +convolution by adding all these up and +all of these are possibilities right all + + align:start position:0% +all of these are possibilities right all + + + align:start position:0% +all of these are possibilities right all +the combinations of these observations + + align:start position:0% +the combinations of these observations + + + align:start position:0% +the combinations of these observations +are possibilities and then we repeat the + + align:start position:0% +are possibilities and then we repeat the + + + align:start position:0% +are possibilities and then we repeat the +same thing so we say let's assume this + + align:start position:0% +same thing so we say let's assume this + + + align:start position:0% +same thing so we say let's assume this +is 50% and let's calculate the + + align:start position:0% +is 50% and let's calculate the + + + align:start position:0% +is 50% and let's calculate the +percentile on all the + + align:start position:0% +percentile on all the + + + align:start position:0% +percentile on all the +and matrix and ask the spreadsheet to + + align:start position:0% +and matrix and ask the spreadsheet to + + + align:start position:0% +and matrix and ask the spreadsheet to +provide a result for the percentile that + + align:start position:0% +provide a result for the percentile that + + + align:start position:0% +provide a result for the percentile that +gives you a 70 and the answer is 4 1 + + align:start position:0% + + + + align:start position:0% + +then there was an another question which + + align:start position:0% +then there was an another question which + + + align:start position:0% +then there was an another question which +is very important it's not a number but + + align:start position:0% +is very important it's not a number but + + + align:start position:0% +is very important it's not a number but +it said there's this person who is + + align:start position:0% +it said there's this person who is + + + align:start position:0% +it said there's this person who is +watching these be able to recover the + + align:start position:0% +watching these be able to recover the + + + align:start position:0% +watching these be able to recover the +terminal and this person is annoying the + + align:start position:0% +terminal and this person is annoying the + + + align:start position:0% +terminal and this person is annoying the +service is not frequent enough these + + align:start position:0% +service is not frequent enough these + + + align:start position:0% +service is not frequent enough these +drivers are wasting time or they're + + align:start position:0% +drivers are wasting time or they're + + + align:start position:0% +drivers are wasting time or they're +sitting there and already and that + + align:start position:0% +sitting there and already and that + + + align:start position:0% +sitting there and already and that +person proposes you should run these + + align:start position:0% +person proposes you should run these + + + align:start position:0% +person proposes you should run these +sort of this person activists and + + align:start position:0% +sort of this person activists and + + + align:start position:0% +sort of this person activists and +they've gotten on the bus and they've + + align:start position:0% +they've gotten on the bus and they've + + + align:start position:0% +they've gotten on the bus and they've +measured the average time and they say + + align:start position:0% +measured the average time and they say + + + align:start position:0% +measured the average time and they say +you can run this much faster you don't + + align:start position:0% +you can run this much faster you don't + + + align:start position:0% +you can run this much faster you don't +have to wait there budgeting for so much + + align:start position:0% +have to wait there budgeting for so much + + + align:start position:0% +have to wait there budgeting for so much +time so you should run this an average + + align:start position:0% +time so you should run this an average + + + align:start position:0% +time so you should run this an average +with average running times and it's your + + align:start position:0% +with average running times and it's your + + + align:start position:0% +with average running times and it's your +turn to sort of argue back so hopefully + + align:start position:0% +turn to sort of argue back so hopefully + + + align:start position:0% +turn to sort of argue back so hopefully +you said no recovery time is important + + align:start position:0% +you said no recovery time is important + + + align:start position:0% +you said no recovery time is important +he don't have recovery time the main + + align:start position:0% +he don't have recovery time the main + + + align:start position:0% +he don't have recovery time the main +trips will have will be will start late + + align:start position:0% +trips will have will be will start late + + + align:start position:0% +trips will have will be will start late +and you're trying to take your bus based + + align:start position:0% +and you're trying to take your bus based + + + align:start position:0% +and you're trying to take your bus based +on schedule then it'll never be there on + + align:start position:0% +on schedule then it'll never be there on + + + align:start position:0% +on schedule then it'll never be there on +time ok that would be double mean that + + align:start position:0% +time ok that would be double mean that + + + align:start position:0% +time ok that would be double mean that +you have to wait a lot longer and it + + align:start position:0% +you have to wait a lot longer and it + + + align:start position:0% +you have to wait a lot longer and it +will be very annoying for everyone so + + align:start position:0% +will be very annoying for everyone so + + + align:start position:0% +will be very annoying for everyone so +that's it for assignment one I hope you + + align:start position:0% +that's it for assignment one I hope you + + + align:start position:0% +that's it for assignment one I hope you +understood all of this if you have + + align:start position:0% +understood all of this if you have + + + align:start position:0% +understood all of this if you have +questions let me know I will read it and + + align:start position:0% +questions let me know I will read it and + + + align:start position:0% +questions let me know I will read it and +have it back to you as soon as possible \ No newline at end of file diff --git a/YZ5pOgY5hEE.txt b/YZ5pOgY5hEE.txt new file mode 100644 index 0000000000000000000000000000000000000000..b5bcbed53d74313f1d503e04808d21e4cf9aba96 --- /dev/null +++ b/YZ5pOgY5hEE.txt @@ -0,0 +1,14379 @@ +align:start position:0% + +hi everyone we're gonna started now so + + align:start position:0% +hi everyone we're gonna started now so + + + align:start position:0% +hi everyone we're gonna started now so +this week's lecture is really picking up + + align:start position:0% +this week's lecture is really picking up + + + align:start position:0% +this week's lecture is really picking up +where last weeks left off right remember + + align:start position:0% +where last weeks left off right remember + + + align:start position:0% +where last weeks left off right remember +we spent last week talking about tall + + align:start position:0% +we spent last week talking about tall + + + align:start position:0% +we spent last week talking about tall +building friends and I told you how for + + align:start position:0% +building friends and I told you how for + + + align:start position:0% +building friends and I told you how for +last week we're just gonna focus on a + + align:start position:0% +last week we're just gonna focus on a + + + align:start position:0% +last week we're just gonna focus on a +one time step setting well as we know + + align:start position:0% +one time step setting well as we know + + + align:start position:0% +one time step setting well as we know +lots of medicine has to do with multiple + + align:start position:0% +lots of medicine has to do with multiple + + + align:start position:0% +lots of medicine has to do with multiple +sequential decisions across time and + + align:start position:0% +sequential decisions across time and + + + align:start position:0% +sequential decisions across time and +that'll be the focus of this whole + + align:start position:0% +that'll be the focus of this whole + + + align:start position:0% +that'll be the focus of this whole +week's worth of discussions and as I + + align:start position:0% +week's worth of discussions and as I + + + align:start position:0% +week's worth of discussions and as I +thought about ruling what should I teach + + align:start position:0% +thought about ruling what should I teach + + + align:start position:0% +thought about ruling what should I teach +in this lecture I realized that the + + align:start position:0% +in this lecture I realized that the + + + align:start position:0% +in this lecture I realized that the +person who knew the most about the topic + + align:start position:0% +person who knew the most about the topic + + + align:start position:0% +person who knew the most about the topic +was in fact a postdoctoral researcher in + + align:start position:0% +was in fact a postdoctoral researcher in + + + align:start position:0% +was in fact a postdoctoral researcher in +my lab most when that's not bacon you + + align:start position:0% +my lab most when that's not bacon you + + + align:start position:0% +my lab most when that's not bacon you +know I'll take I'll take that I'll take + + align:start position:0% +know I'll take I'll take that I'll take + + + align:start position:0% +know I'll take I'll take that I'll take +that it's very fair it's very and this + + align:start position:0% +that it's very fair it's very and this + + + align:start position:0% +that it's very fair it's very and this +is Frederick Johansen he'll be a + + align:start position:0% +is Frederick Johansen he'll be a + + + align:start position:0% +is Frederick Johansen he'll be a +professor in Chalmers and Sweden + + align:start position:0% +professor in Chalmers and Sweden + + + align:start position:0% +professor in Chalmers and Sweden +starting in September anyway thank you + + align:start position:0% +starting in September anyway thank you + + + align:start position:0% +starting in September anyway thank you +so much David that's very generous + + align:start position:0% +so much David that's very generous + + + align:start position:0% +so much David that's very generous +yeah so as David mentioned last time we + + align:start position:0% +yeah so as David mentioned last time we + + + align:start position:0% +yeah so as David mentioned last time we +looked at a lot at causal effects and + + align:start position:0% +looked at a lot at causal effects and + + + align:start position:0% +looked at a lot at causal effects and +that's where we will start this + + align:start position:0% +that's where we will start this + + + align:start position:0% +that's where we will start this +discussion too so I'll just start with + + align:start position:0% +discussion too so I'll just start with + + + align:start position:0% +discussion too so I'll just start with +this reminder here we we essentially + + align:start position:0% +this reminder here we we essentially + + + align:start position:0% +this reminder here we we essentially +introduced four quantities last time or + + align:start position:0% +introduced four quantities last time or + + + align:start position:0% +introduced four quantities last time or +the last two lectures so first I know we + + align:start position:0% +the last two lectures so first I know we + + + align:start position:0% +the last two lectures so first I know we +had two potential outcomes which + + align:start position:0% +had two potential outcomes which + + + align:start position:0% +had two potential outcomes which +represented the outcomes that we would + + align:start position:0% +represented the outcomes that we would + + + align:start position:0% +represented the outcomes that we would +see of some treatment choice under the + + align:start position:0% +see of some treatment choice under the + + + align:start position:0% +see of some treatment choice under the +various choices or the two different + + align:start position:0% +various choices or the two different + + + align:start position:0% +various choices or the two different +choices one is zero and we had two + + align:start position:0% +choices one is zero and we had two + + + align:start position:0% +choices one is zero and we had two +covariates over start we had a + + align:start position:0% +covariates over start we had a + + + align:start position:0% +covariates over start we had a +covariates sudoko variate axe and a + + align:start position:0% +covariates sudoko variate axe and a + + + align:start position:0% +covariates sudoko variate axe and a +treatment t and we were interested in + + align:start position:0% +treatment t and we were interested in + + + align:start position:0% +treatment t and we were interested in +essentially what is the effect of this + + align:start position:0% +essentially what is the effect of this + + + align:start position:0% +essentially what is the effect of this +treatment T on the outcome Y given the + + align:start position:0% +treatment T on the outcome Y given the + + + align:start position:0% +treatment T on the outcome Y given the +covariates X and the effect that we + + align:start position:0% +covariates X and the effect that we + + + align:start position:0% +covariates X and the effect that we +focused on that time was the conditional + + align:start position:0% +focused on that time was the conditional + + + align:start position:0% +focused on that time was the conditional +average treatment effect which is + + align:start position:0% +average treatment effect which is + + + align:start position:0% +average treatment effect which is +exactly the difference between these + + align:start position:0% +exactly the difference between these + + + align:start position:0% +exactly the difference between these +potential outcomes conditioned on the + + align:start position:0% +potential outcomes conditioned on the + + + align:start position:0% +potential outcomes conditioned on the +features so the whole last week was + + align:start position:0% +features so the whole last week was + + + align:start position:0% +features so the whole last week was +about trying to identify this quantity + + align:start position:0% +about trying to identify this quantity + + + align:start position:0% +about trying to identify this quantity +using various methods and the question + + align:start position:0% +using various methods and the question + + + align:start position:0% +using various methods and the question +that didn't come up so much or one + + align:start position:0% +that didn't come up so much or one + + + align:start position:0% +that didn't come up so much or one +question that didn't come up too much is + + align:start position:0% +question that didn't come up too much is + + + align:start position:0% +question that didn't come up too much is +how do we use this quantity we might be + + align:start position:0% +how do we use this quantity we might be + + + align:start position:0% +how do we use this quantity we might be +interested in it just in terms of of its + + align:start position:0% +interested in it just in terms of of its + + + align:start position:0% +interested in it just in terms of of its +absolute magnitude how + + align:start position:0% +absolute magnitude how + + + align:start position:0% +absolute magnitude how +but we might also be interested in + + align:start position:0% +but we might also be interested in + + + align:start position:0% +but we might also be interested in +designing a policy for how to treat our + + align:start position:0% +designing a policy for how to treat our + + + align:start position:0% +designing a policy for how to treat our +patients based on this quantity so today + + align:start position:0% +patients based on this quantity so today + + + align:start position:0% +patients based on this quantity so today +we will focus on policies and what I + + align:start position:0% +we will focus on policies and what I + + + align:start position:0% +we will focus on policies and what I +mean by that specifically is something + + align:start position:0% +mean by that specifically is something + + + align:start position:0% +mean by that specifically is something +that takes into account what we know + + align:start position:0% +that takes into account what we know + + + align:start position:0% +that takes into account what we know +about a patient and produces a choice or + + align:start position:0% +about a patient and produces a choice or + + + align:start position:0% +about a patient and produces a choice or +inaction as an output typically we'll + + align:start position:0% +inaction as an output typically we'll + + + align:start position:0% +inaction as an output typically we'll +think of policies as depending on + + align:start position:0% +think of policies as depending on + + + align:start position:0% +think of policies as depending on +medical history perhaps which treatments + + align:start position:0% +medical history perhaps which treatments + + + align:start position:0% +medical history perhaps which treatments +they have received previously what state + + align:start position:0% +they have received previously what state + + + align:start position:0% +they have received previously what state +is the patient currently n but we can + + align:start position:0% +is the patient currently n but we can + + + align:start position:0% +is the patient currently n but we can +also base it's purely on this number + + align:start position:0% +also base it's purely on this number + + + align:start position:0% +also base it's purely on this number +that we produce last time the + + align:start position:0% +that we produce last time the + + + align:start position:0% +that we produce last time the +conditional average treatment effect and + + align:start position:0% +conditional average treatment effect and + + + align:start position:0% +conditional average treatment effect and +one very or natural policy is to say PI + + align:start position:0% +one very or natural policy is to say PI + + + align:start position:0% +one very or natural policy is to say PI +of X is equal to the indicator function + + align:start position:0% +of X is equal to the indicator function + + + align:start position:0% +of X is equal to the indicator function +representing if the state is positive so + + align:start position:0% +representing if the state is positive so + + + align:start position:0% +representing if the state is positive so +if the effect is positive we treat the + + align:start position:0% +if the effect is positive we treat the + + + align:start position:0% +if the effect is positive we treat the +patient if the effect is negative we + + align:start position:0% +patient if the effect is negative we + + + align:start position:0% +patient if the effect is negative we +don't and of course positive will be + + align:start position:0% +don't and of course positive will be + + + align:start position:0% +don't and of course positive will be +relative to the the usefulness of the + + align:start position:0% +relative to the the usefulness of the + + + align:start position:0% +relative to the the usefulness of the +outcome being high but yeah this is a + + align:start position:0% +outcome being high but yeah this is a + + + align:start position:0% +outcome being high but yeah this is a +very natural policy to consider however + + align:start position:0% +very natural policy to consider however + + + align:start position:0% +very natural policy to consider however +we can also think about much more + + align:start position:0% +we can also think about much more + + + align:start position:0% +we can also think about much more +complicated policies that that are not + + align:start position:0% +complicated policies that that are not + + + align:start position:0% +complicated policies that that are not +just based on this this number the + + align:start position:0% +just based on this this number the + + + align:start position:0% +just based on this this number the +quality of the outcome we can think + + align:start position:0% +quality of the outcome we can think + + + align:start position:0% +quality of the outcome we can think +about policies are taking into account + + align:start position:0% +about policies are taking into account + + + align:start position:0% +about policies are taking into account +legislation or cost of medication or + + align:start position:0% +legislation or cost of medication or + + + align:start position:0% +legislation or cost of medication or +side effects we're not going to do that + + align:start position:0% +side effects we're not going to do that + + + align:start position:0% +side effects we're not going to do that +today but that's something that you can + + align:start position:0% +today but that's something that you can + + + align:start position:0% +today but that's something that you can +keep in mind as we discuss these things + + align:start position:0% + + + + align:start position:0% + +so David mentioned we should now move + + align:start position:0% +so David mentioned we should now move + + + align:start position:0% +so David mentioned we should now move +from the one-step setting where we have + + align:start position:0% +from the one-step setting where we have + + + align:start position:0% +from the one-step setting where we have +a single treatment acting at a single + + align:start position:0% +a single treatment acting at a single + + + align:start position:0% +a single treatment acting at a single +time and we only have to take into + + align:start position:0% +time and we only have to take into + + + align:start position:0% +time and we only have to take into +account the state of a patient at once + + align:start position:0% +account the state of a patient at once + + + align:start position:0% +account the state of a patient at once +basically and we will move from that to + + align:start position:0% +basically and we will move from that to + + + align:start position:0% +basically and we will move from that to +the sequential setting and my first + + align:start position:0% +the sequential setting and my first + + + align:start position:0% +the sequential setting and my first +example of such a setting is sepsis + + align:start position:0% +example of such a setting is sepsis + + + align:start position:0% +example of such a setting is sepsis +management so sepsis is a complication + + align:start position:0% +management so sepsis is a complication + + + align:start position:0% +management so sepsis is a complication +of an infection which can have very + + align:start position:0% +of an infection which can have very + + + align:start position:0% +of an infection which can have very +disastrous consequences it can lead to + + align:start position:0% +disastrous consequences it can lead to + + + align:start position:0% +disastrous consequences it can lead to +organ failure and ultimately death and + + align:start position:0% +organ failure and ultimately death and + + + align:start position:0% +organ failure and ultimately death and +it's actually one of the leading causes + + align:start position:0% +it's actually one of the leading causes + + + align:start position:0% +it's actually one of the leading causes +of deaths in the ICU so it's of course + + align:start position:0% +of deaths in the ICU so it's of course + + + align:start position:0% +of deaths in the ICU so it's of course +important that we can manage and treat + + align:start position:0% +important that we can manage and treat + + + align:start position:0% +important that we can manage and treat +this condition when you start treating + + align:start position:0% +this condition when you start treating + + + align:start position:0% +this condition when you start treating +stuff just the primary target the first + + align:start position:0% +stuff just the primary target the first + + + align:start position:0% +stuff just the primary target the first +thing is you should think about fixing + + align:start position:0% +thing is you should think about fixing + + + align:start position:0% +thing is you should think about fixing +its the infection itself if we don't + + align:start position:0% +its the infection itself if we don't + + + align:start position:0% +its the infection itself if we don't +treat the infection things are going to + + align:start position:0% +treat the infection things are going to + + + align:start position:0% +treat the infection things are going to +keep being bad but even if you figure + + align:start position:0% +keep being bad but even if you figure + + + align:start position:0% +keep being bad but even if you figure +out the right antibiotic to treat the + + align:start position:0% +out the right antibiotic to treat the + + + align:start position:0% +out the right antibiotic to treat the +infection + + align:start position:0% +infection + + + align:start position:0% +infection +it's the source of the septic shock of + + align:start position:0% +it's the source of the septic shock of + + + align:start position:0% +it's the source of the septic shock of +the septic inflammation there are a lot + + align:start position:0% +the septic inflammation there are a lot + + + align:start position:0% +the septic inflammation there are a lot +of different conditions that we need to + + align:start position:0% +of different conditions that we need to + + + align:start position:0% +of different conditions that we need to +manage because this the infection itself + + align:start position:0% +manage because this the infection itself + + + align:start position:0% +manage because this the infection itself +can lead to fever breathing difficulty + + align:start position:0% +can lead to fever breathing difficulty + + + align:start position:0% +can lead to fever breathing difficulty +slow heart s or low blood pressure high + + align:start position:0% +slow heart s or low blood pressure high + + + align:start position:0% +slow heart s or low blood pressure high +heart rate all these kinds of things + + align:start position:0% +heart rate all these kinds of things + + + align:start position:0% +heart rate all these kinds of things +that are symptoms but not the causing + + align:start position:0% +that are symptoms but not the causing + + + align:start position:0% +that are symptoms but not the causing +themselves but we still have to manage + + align:start position:0% +themselves but we still have to manage + + + align:start position:0% +themselves but we still have to manage +them somehow so that the patient + + align:start position:0% +them somehow so that the patient + + + align:start position:0% +them somehow so that the patient +survives and is comfortable so when I + + align:start position:0% +survives and is comfortable so when I + + + align:start position:0% +survives and is comfortable so when I +say sepsis management I I'm talking + + align:start position:0% +say sepsis management I I'm talking + + + align:start position:0% +say sepsis management I I'm talking +about managing such quantities over time + + align:start position:0% +about managing such quantities over time + + + align:start position:0% +about managing such quantities over time +over a patient stay in the in the + + align:start position:0% +over a patient stay in the in the + + + align:start position:0% +over a patient stay in the in the +hospital so last time again just to + + align:start position:0% +hospital so last time again just to + + + align:start position:0% +hospital so last time again just to +really hammer this in we talked about + + align:start position:0% +really hammer this in we talked about + + + align:start position:0% +really hammer this in we talked about +potential outcomes and the choice of a + + align:start position:0% +potential outcomes and the choice of a + + + align:start position:0% +potential outcomes and the choice of a +single treatment so we can think about + + align:start position:0% +single treatment so we can think about + + + align:start position:0% +single treatment so we can think about +this in the septic setting as a patient + + align:start position:0% +this in the septic setting as a patient + + + align:start position:0% +this in the septic setting as a patient +coming in or a patient already being in + + align:start position:0% +coming in or a patient already being in + + + align:start position:0% +coming in or a patient already being in +the hospital assumably and it's + + align:start position:0% +the hospital assumably and it's + + + align:start position:0% +the hospital assumably and it's +presenting with breathing difficulties + + align:start position:0% +presenting with breathing difficulties + + + align:start position:0% +presenting with breathing difficulties +so that means that their blood oxygen + + align:start position:0% +so that means that their blood oxygen + + + align:start position:0% +so that means that their blood oxygen +will be low because they can't breathe + + align:start position:0% +will be low because they can't breathe + + + align:start position:0% +will be low because they can't breathe +on their own and we might want to put + + align:start position:0% +on their own and we might want to put + + + align:start position:0% +on their own and we might want to put +them on mechanical ventilation so that + + align:start position:0% +them on mechanical ventilation so that + + + align:start position:0% +them on mechanical ventilation so that +we can ensure that they get sufficient + + align:start position:0% +we can ensure that they get sufficient + + + align:start position:0% +we can ensure that they get sufficient +oxygen we can view this as a single + + align:start position:0% +oxygen we can view this as a single + + + align:start position:0% +oxygen we can view this as a single +choice should we put the the the patient + + align:start position:0% +choice should we put the the the patient + + + align:start position:0% +choice should we put the the the patient +on mechanical ventilation or not but + + align:start position:0% +on mechanical ventilation or not but + + + align:start position:0% +on mechanical ventilation or not but +what we need to take into account here + + align:start position:0% +what we need to take into account here + + + align:start position:0% +what we need to take into account here +is what will happen after we make that + + align:start position:0% +is what will happen after we make that + + + align:start position:0% +is what will happen after we make that +choice well what would be the side + + align:start position:0% +choice well what would be the side + + + align:start position:0% +choice well what would be the side +effects of this choice going further + + align:start position:0% +effects of this choice going further + + + align:start position:0% +effects of this choice going further +because we want to make sure that the + + align:start position:0% +because we want to make sure that the + + + align:start position:0% +because we want to make sure that the +patient is comfortable and in good + + align:start position:0% +patient is comfortable and in good + + + align:start position:0% +patient is comfortable and in good +health throughout their stay so today we + + align:start position:0% +health throughout their stay so today we + + + align:start position:0% +health throughout their stay so today we +will move towards sequential decision + + align:start position:0% +will move towards sequential decision + + + align:start position:0% +will move towards sequential decision +making and in particular what I alluded + + align:start position:0% +making and in particular what I alluded + + + align:start position:0% +making and in particular what I alluded +to just now is that decisions made in + + align:start position:0% +to just now is that decisions made in + + + align:start position:0% +to just now is that decisions made in +sequence may have the property that + + align:start position:0% +sequence may have the property that + + + align:start position:0% +sequence may have the property that +choice is early on rule out certain + + align:start position:0% +choice is early on rule out certain + + + align:start position:0% +choice is early on rule out certain +choices later and we'll see an example + + align:start position:0% +choices later and we'll see an example + + + align:start position:0% +choices later and we'll see an example +of that very very soon and in particular + + align:start position:0% +of that very very soon and in particular + + + align:start position:0% +of that very very soon and in particular +we'll be interested in coming up with a + + align:start position:0% +we'll be interested in coming up with a + + + align:start position:0% +we'll be interested in coming up with a +policy for making decisions repeatedly + + align:start position:0% +policy for making decisions repeatedly + + + align:start position:0% +policy for making decisions repeatedly +that optimizes a given outcome something + + align:start position:0% +that optimizes a given outcome something + + + align:start position:0% +that optimizes a given outcome something +that we care about + + align:start position:0% +that we care about + + + align:start position:0% +that we care about +it could be optimizes the or reduce + + align:start position:0% +it could be optimizes the or reduce + + + align:start position:0% +it could be optimizes the or reduce +minimize the risk of death it could be a + + align:start position:0% +minimize the risk of death it could be a + + + align:start position:0% +minimize the risk of death it could be a +reward that says that the vitals of the + + align:start position:0% +reward that says that the vitals of the + + + align:start position:0% +reward that says that the vitals of the +patients are in the right range you + + align:start position:0% +patients are in the right range you + + + align:start position:0% +patients are in the right range you +might want off to my stat but + + align:start position:0% +might want off to my stat but + + + align:start position:0% +might want off to my stat but +essentially think about it now as as + + align:start position:0% +essentially think about it now as as + + + align:start position:0% +essentially think about it now as as +having this this choice of administering + + align:start position:0% +having this this choice of administering + + + align:start position:0% +having this this choice of administering +a medication or an intervention at any + + align:start position:0% +a medication or an intervention at any + + + align:start position:0% +a medication or an intervention at any +time T + + align:start position:0% +time T + + + align:start position:0% +time T +and having the best policy for doing + + align:start position:0% +and having the best policy for doing + + + align:start position:0% +and having the best policy for doing +some okay I'm gonna skip that one okay + + align:start position:0% +some okay I'm gonna skip that one okay + + + align:start position:0% +some okay I'm gonna skip that one okay +so I mentioned already one potential + + align:start position:0% +so I mentioned already one potential + + + align:start position:0% +so I mentioned already one potential +choice that we might want to make in the + + align:start position:0% +choice that we might want to make in the + + + align:start position:0% +choice that we might want to make in the +management of a septic patient which is + + align:start position:0% +management of a septic patient which is + + + align:start position:0% +management of a septic patient which is +to put them on mechanical ventilation + + align:start position:0% +to put them on mechanical ventilation + + + align:start position:0% +to put them on mechanical ventilation +because they can't breathe on their own + + align:start position:0% +because they can't breathe on their own + + + align:start position:0% +because they can't breathe on their own +a side effect of doing so is that they + + align:start position:0% +a side effect of doing so is that they + + + align:start position:0% +a side effect of doing so is that they +might be my suffer discomfort from + + align:start position:0% +might be my suffer discomfort from + + + align:start position:0% +might be my suffer discomfort from +having from being intubated and well the + + align:start position:0% +having from being intubated and well the + + + align:start position:0% +having from being intubated and well the +procedure is not painless is not without + + align:start position:0% +procedure is not painless is not without + + + align:start position:0% +procedure is not painless is not without +discomfort so something that you might + + align:start position:0% +discomfort so something that you might + + + align:start position:0% +discomfort so something that you might +have to do putting them on mechanical + + align:start position:0% +have to do putting them on mechanical + + + align:start position:0% +have to do putting them on mechanical +ventilation is to sedate the patient so + + align:start position:0% +ventilation is to sedate the patient so + + + align:start position:0% +ventilation is to sedate the patient so +this is a sort of an action that is + + align:start position:0% +this is a sort of an action that is + + + align:start position:0% +this is a sort of an action that is +informed by the previous action because + + align:start position:0% +informed by the previous action because + + + align:start position:0% +informed by the previous action because +if we didn't put the patient on + + align:start position:0% +if we didn't put the patient on + + + align:start position:0% +if we didn't put the patient on +mechanical ventilation maybe we wouldn't + + align:start position:0% +mechanical ventilation maybe we wouldn't + + + align:start position:0% +mechanical ventilation maybe we wouldn't +consider them for sedation when we + + align:start position:0% +consider them for sedation when we + + + align:start position:0% +consider them for sedation when we +sedate a patient we run the risk of + + align:start position:0% +sedate a patient we run the risk of + + + align:start position:0% +sedate a patient we run the risk of +lowering their blood pressure so we + + align:start position:0% +lowering their blood pressure so we + + + align:start position:0% +lowering their blood pressure so we +might need to manage that too so if + + align:start position:0% +might need to manage that too so if + + + align:start position:0% +might need to manage that too so if +their blood pressure gets too low maybe + + align:start position:0% +their blood pressure gets too low maybe + + + align:start position:0% +their blood pressure gets too low maybe +we need to administer vasopressors which + + align:start position:0% +we need to administer vasopressors which + + + align:start position:0% +we need to administer vasopressors which +artificially raise the blood pressure or + + align:start position:0% +artificially raise the blood pressure or + + + align:start position:0% +artificially raise the blood pressure or +fluids or anything else that that takes + + align:start position:0% +fluids or anything else that that takes + + + align:start position:0% +fluids or anything else that that takes +care of this issue so just just think of + + align:start position:0% +care of this issue so just just think of + + + align:start position:0% +care of this issue so just just think of +this as an example of choices cascading + + align:start position:0% +this as an example of choices cascading + + + align:start position:0% +this as an example of choices cascading +in terms of their consequences as we + + align:start position:0% +in terms of their consequences as we + + + align:start position:0% +in terms of their consequences as we +roll forward in time ultimately we will + + align:start position:0% +roll forward in time ultimately we will + + + align:start position:0% +roll forward in time ultimately we will +face the end of the the patient's stay + + align:start position:0% +face the end of the the patient's stay + + + align:start position:0% +face the end of the the patient's stay +and hopefully we managed the patient in + + align:start position:0% +and hopefully we managed the patient in + + + align:start position:0% +and hopefully we managed the patient in +a successful way so that their the + + align:start position:0% +a successful way so that their the + + + align:start position:0% +a successful way so that their the +response or their their outcome is a + + align:start position:0% +response or their their outcome is a + + + align:start position:0% +response or their their outcome is a +good one what I what I'm illustrating + + align:start position:0% +good one what I what I'm illustrating + + + align:start position:0% +good one what I what I'm illustrating +here is that for any one patient in our + + align:start position:0% +here is that for any one patient in our + + + align:start position:0% +here is that for any one patient in our +hospitals or in the healthcare system we + + align:start position:0% +hospitals or in the healthcare system we + + + align:start position:0% +hospitals or in the healthcare system we +will only observe one trajectory through + + align:start position:0% +will only observe one trajectory through + + + align:start position:0% +will only observe one trajectory through +these options so I will show this type + + align:start position:0% +these options so I will show this type + + + align:start position:0% +these options so I will show this type +of illustration many many times but I + + align:start position:0% +of illustration many many times but I + + + align:start position:0% +of illustration many many times but I +hope you can the you can realize the the + + align:start position:0% +hope you can the you can realize the the + + + align:start position:0% +hope you can the you can realize the the +the scope of the decision space here + + align:start position:0% +the scope of the decision space here + + + align:start position:0% +the scope of the decision space here +essentially at any point we can choose a + + align:start position:0% +essentially at any point we can choose a + + + align:start position:0% +essentially at any point we can choose a +different action and usually the number + + align:start position:0% +different action and usually the number + + + align:start position:0% +different action and usually the number +of decisions that we make in a in a ICU + + align:start position:0% +of decisions that we make in a in a ICU + + + align:start position:0% +of decisions that we make in a in a ICU +setting for example is much larger than + + align:start position:0% +setting for example is much larger than + + + align:start position:0% +setting for example is much larger than +we could ever test in in a randomized + + align:start position:0% +we could ever test in in a randomized + + + align:start position:0% +we could ever test in in a randomized +trial think of all of these different + + align:start position:0% +trial think of all of these different + + + align:start position:0% +trial think of all of these different +trajectories as being different + + align:start position:0% +trajectories as being different + + + align:start position:0% +trajectories as being different +alarms in a randomized control trial + + align:start position:0% +alarms in a randomized control trial + + + align:start position:0% +alarms in a randomized control trial +that you want + + align:start position:0% +that you want + + + align:start position:0% +that you want +compare the effects or the outcomes of + + align:start position:0% +compare the effects or the outcomes of + + + align:start position:0% +compare the effects or the outcomes of +its infeasible to run such a trial + + align:start position:0% +its infeasible to run such a trial + + + align:start position:0% +its infeasible to run such a trial +typically so one of the big reasons that + + align:start position:0% +typically so one of the big reasons that + + + align:start position:0% +typically so one of the big reasons that +we were talking about reinforcement + + align:start position:0% +we were talking about reinforcement + + + align:start position:0% +we were talking about reinforcement +learning today and talking about + + align:start position:0% +learning today and talking about + + + align:start position:0% +learning today and talking about +learning policies rather than causal + + align:start position:0% +learning policies rather than causal + + + align:start position:0% +learning policies rather than causal +effects in the setup that we did last + + align:start position:0% +effects in the setup that we did last + + + align:start position:0% +effects in the setup that we did last +week is because the space of possible + + align:start position:0% +week is because the space of possible + + + align:start position:0% +week is because the space of possible +action trajectories is so large so said + + align:start position:0% +action trajectories is so large so said + + + align:start position:0% +action trajectories is so large so said +having said that we now turn to trying + + align:start position:0% +having said that we now turn to trying + + + align:start position:0% +having said that we now turn to trying +to find essentially the policy that + + align:start position:0% +to find essentially the policy that + + + align:start position:0% +to find essentially the policy that +picks this orange path here that leads + + align:start position:0% +picks this orange path here that leads + + + align:start position:0% +picks this orange path here that leads +to a good outcome and to to reason about + + align:start position:0% +to a good outcome and to to reason about + + + align:start position:0% +to a good outcome and to to reason about +such a thing we need to also reason + + align:start position:0% +such a thing we need to also reason + + + align:start position:0% +such a thing we need to also reason +about what is a good outcome what is a + + align:start position:0% +about what is a good outcome what is a + + + align:start position:0% +about what is a good outcome what is a +good reward for for our agent as it + + align:start position:0% +good reward for for our agent as it + + + align:start position:0% +good reward for for our agent as it +proceeds through time and it makes + + align:start position:0% +proceeds through time and it makes + + + align:start position:0% +proceeds through time and it makes +choices some policies that we that we + + align:start position:0% +choices some policies that we that we + + + align:start position:0% +choices some policies that we that we +produce as machine or this might not be + + align:start position:0% +produce as machine or this might not be + + + align:start position:0% +produce as machine or this might not be +appropriate for a healthcare setting and + + align:start position:0% +appropriate for a healthcare setting and + + + align:start position:0% +appropriate for a healthcare setting and +like we had to have to somehow restrict + + align:start position:0% +like we had to have to somehow restrict + + + align:start position:0% +like we had to have to somehow restrict +ourself to something that's realistic I + + align:start position:0% +ourself to something that's realistic I + + + align:start position:0% +ourself to something that's realistic I +won't focus very much in this today it's + + align:start position:0% +won't focus very much in this today it's + + + align:start position:0% +won't focus very much in this today it's +something that will come up in the + + align:start position:0% +something that will come up in the + + + align:start position:0% +something that will come up in the +discussion tomorrow hopefully and also + + align:start position:0% +discussion tomorrow hopefully and also + + + align:start position:0% +discussion tomorrow hopefully and also +the the notion of evaluating something + + align:start position:0% +the the notion of evaluating something + + + align:start position:0% +the the notion of evaluating something +for for use in the healthcare system + + align:start position:0% +for for use in the healthcare system + + + align:start position:0% +for for use in the healthcare system +will also be talked about tomorrow + + align:start position:0% +will also be talked about tomorrow + + + align:start position:0% +will also be talked about tomorrow +Thursday sorry Thursday next time okay + + align:start position:0% +Thursday sorry Thursday next time okay + + + align:start position:0% +Thursday sorry Thursday next time okay +so I'll start by just briefly mentioning + + align:start position:0% +so I'll start by just briefly mentioning + + + align:start position:0% +so I'll start by just briefly mentioning +some success stories and these are not + + align:start position:0% +some success stories and these are not + + + align:start position:0% +some success stories and these are not +from the healthcare setting as you can + + align:start position:0% +from the healthcare setting as you can + + + align:start position:0% +from the healthcare setting as you can +guess from the pictures how many have + + align:start position:0% +guess from the pictures how many have + + + align:start position:0% +guess from the pictures how many have +seen some of these pictures okay great + + align:start position:0% +seen some of these pictures okay great + + + align:start position:0% +seen some of these pictures okay great +great almost everyone yeah so these are + + align:start position:0% +great almost everyone yeah so these are + + + align:start position:0% +great almost everyone yeah so these are +from from various video games almost all + + align:start position:0% +from from various video games almost all + + + align:start position:0% +from from various video games almost all +of them well games anyhow and these are + + align:start position:0% +of them well games anyhow and these are + + + align:start position:0% +of them well games anyhow and these are +these are good examples of when + + align:start position:0% +these are good examples of when + + + align:start position:0% +these are good examples of when +reinforcement learning works essentially + + align:start position:0% +reinforcement learning works essentially + + + align:start position:0% +reinforcement learning works essentially +that's why I use this in this in this + + align:start position:0% +that's why I use this in this in this + + + align:start position:0% +that's why I use this in this in this +slide here because essentially it's very + + align:start position:0% +slide here because essentially it's very + + + align:start position:0% +slide here because essentially it's very +hard to argue that the computer or the + + align:start position:0% +hard to argue that the computer or the + + + align:start position:0% +hard to argue that the computer or the +the program that eventually beat Lisa + + align:start position:0% +the program that eventually beat Lisa + + + align:start position:0% +the program that eventually beat Lisa +dole I think it's in this picture but + + align:start position:0% +dole I think it's in this picture but + + + align:start position:0% +dole I think it's in this picture but +also later go champions essentially in + + align:start position:0% +also later go champions essentially in + + + align:start position:0% +also later go champions essentially in +the alphago picture in the top left it's + + align:start position:0% +the alphago picture in the top left it's + + + align:start position:0% +the alphago picture in the top left it's +hard to argue that they're not doing a + + align:start position:0% +hard to argue that they're not doing a + + + align:start position:0% +hard to argue that they're not doing a +good job because they clearly beat + + align:start position:0% +good job because they clearly beat + + + align:start position:0% +good job because they clearly beat +humans here + + align:start position:0% +humans here + + + align:start position:0% +humans here +but one of the one of the things I want + + align:start position:0% +but one of the one of the things I want + + + align:start position:0% +but one of the one of the things I want +you to keep in mind is throughout this + + align:start position:0% +you to keep in mind is throughout this + + + align:start position:0% +you to keep in mind is throughout this +talk is what is different between these + + align:start position:0% +talk is what is different between these + + + align:start position:0% +talk is what is different between these +kinds of scenarios and we'll come back + + align:start position:0% +kinds of scenarios and we'll come back + + + align:start position:0% +kinds of scenarios and we'll come back +to that later + + align:start position:0% +to that later + + + align:start position:0% +to that later +and what is what is different to to the + + align:start position:0% +and what is what is different to to the + + + align:start position:0% +and what is what is different to to the +healthcare setting essentially so I just + + align:start position:0% +healthcare setting essentially so I just + + + align:start position:0% +healthcare setting essentially so I just +simply added another exemplar that's why + + align:start position:0% +simply added another exemplar that's why + + + align:start position:0% +simply added another exemplar that's why +I recognized so there was a reasonably + + align:start position:0% +I recognized so there was a reasonably + + + align:start position:0% +I recognized so there was a reasonably +one that's a little bit closer to my + + align:start position:0% +one that's a little bit closer to my + + + align:start position:0% +one that's a little bit closer to my +heart which is Alvis star the play + + align:start position:0% +heart which is Alvis star the play + + + align:start position:0% +heart which is Alvis star the play +Starcraft I like Starcraft so you know + + align:start position:0% +Starcraft I like Starcraft so you know + + + align:start position:0% +Starcraft I like Starcraft so you know +it should be on the slide anyway let's + + align:start position:0% +it should be on the slide anyway let's + + + align:start position:0% +it should be on the slide anyway let's +move on + + align:start position:0% +move on + + + align:start position:0% +move on +broadly speaking these can be summarized + + align:start position:0% +broadly speaking these can be summarized + + + align:start position:0% +broadly speaking these can be summarized +in the following picture what goes all + + align:start position:0% +in the following picture what goes all + + + align:start position:0% +in the following picture what goes all +into those systems there's a lot more + + align:start position:0% +into those systems there's a lot more + + + align:start position:0% +into those systems there's a lot more +nuance when it comes to something like + + align:start position:0% +nuance when it comes to something like + + + align:start position:0% +nuance when it comes to something like +go but for the purpose of this class we + + align:start position:0% +go but for the purpose of this class we + + + align:start position:0% +go but for the purpose of this class we +will summarize them with a slide so + + align:start position:0% +will summarize them with a slide so + + + align:start position:0% +will summarize them with a slide so +essentially one of the three quantities + + align:start position:0% +essentially one of the three quantities + + + align:start position:0% +essentially one of the three quantities +that matters for a reinforcement + + align:start position:0% +that matters for a reinforcement + + + align:start position:0% +that matters for a reinforcement +learning is this state of the + + align:start position:0% +learning is this state of the + + + align:start position:0% +learning is this state of the +environment the state of the game the + + align:start position:0% +environment the state of the game the + + + align:start position:0% +environment the state of the game the +state of the patient the state of the + + align:start position:0% +state of the patient the state of the + + + align:start position:0% +state of the patient the state of the +thing that we want to optimize + + align:start position:0% +thing that we want to optimize + + + align:start position:0% +thing that we want to optimize +essentially so in this case I've chosen + + align:start position:0% +essentially so in this case I've chosen + + + align:start position:0% +essentially so in this case I've chosen +tic-tac-toe here we have a state which + + align:start position:0% +tic-tac-toe here we have a state which + + + align:start position:0% +tic-tac-toe here we have a state which +represents the current positions of the + + align:start position:0% +represents the current positions of the + + + align:start position:0% +represents the current positions of the +of the circles and crosses and given + + align:start position:0% +of the circles and crosses and given + + + align:start position:0% +of the circles and crosses and given +that that state of the game my job as a + + align:start position:0% +that that state of the game my job as a + + + align:start position:0% +that that state of the game my job as a +player is to choose one of the possible + + align:start position:0% +player is to choose one of the possible + + + align:start position:0% +player is to choose one of the possible +or yeah the possible actions one of the + + align:start position:0% +or yeah the possible actions one of the + + + align:start position:0% +or yeah the possible actions one of the +three squares to put my cross in so I'm + + align:start position:0% +three squares to put my cross in so I'm + + + align:start position:0% +three squares to put my cross in so I'm +the blue player here and I can consider + + align:start position:0% +the blue player here and I can consider + + + align:start position:0% +the blue player here and I can consider +these five is it choices for where to + + align:start position:0% +these five is it choices for where to + + + align:start position:0% +these five is it choices for where to +put my next cross and each of those will + + align:start position:0% +put my next cross and each of those will + + + align:start position:0% +put my next cross and each of those will +lead me to a new state of the game if I + + align:start position:0% +lead me to a new state of the game if I + + + align:start position:0% +lead me to a new state of the game if I +put my my cross over here that means + + align:start position:0% +put my my cross over here that means + + + align:start position:0% +put my my cross over here that means +that I mean now in this box and I have a + + align:start position:0% +that I mean now in this box and I have a + + + align:start position:0% +that I mean now in this box and I have a +new set of actions available to me for + + align:start position:0% +new set of actions available to me for + + + align:start position:0% +new set of actions available to me for +the next round depending on what the red + + align:start position:0% +the next round depending on what the red + + + align:start position:0% +the next round depending on what the red +player does so we have the state we have + + align:start position:0% +player does so we have the state we have + + + align:start position:0% +player does so we have the state we have +the actions and we have the next status + + align:start position:0% +the actions and we have the next status + + + align:start position:0% +the actions and we have the next status +and so we have a trajectory or a + + align:start position:0% +and so we have a trajectory or a + + + align:start position:0% +and so we have a trajectory or a +transition of states and the last + + align:start position:0% +transition of states and the last + + + align:start position:0% +transition of states and the last +quantity that we need is the notion of a + + align:start position:0% +quantity that we need is the notion of a + + + align:start position:0% +quantity that we need is the notion of a +reward that's very important for + + align:start position:0% +reward that's very important for + + + align:start position:0% +reward that's very important for +reinforcement learning because that's + + align:start position:0% +reinforcement learning because that's + + + align:start position:0% +reinforcement learning because that's +what's drive the learning itself we + + align:start position:0% +what's drive the learning itself we + + + align:start position:0% +what's drive the learning itself we +strive to optimize the reward or the + + align:start position:0% +strive to optimize the reward or the + + + align:start position:0% +strive to optimize the reward or the +outcome of something so if we look at + + align:start position:0% +outcome of something so if we look at + + + align:start position:0% +outcome of something so if we look at +the action to the farthest right here + + align:start position:0% +the action to the farthest right here + + + align:start position:0% +the action to the farthest right here +essentially I left myself open to an + + align:start position:0% +essentially I left myself open to an + + + align:start position:0% +essentially I left myself open to an +attack by the red player here because I + + align:start position:0% +attack by the red player here because I + + + align:start position:0% +attack by the red player here because I +didn't put my cross there which means + + align:start position:0% +didn't put my cross there which means + + + align:start position:0% +didn't put my cross there which means +that probably if the red player is + + align:start position:0% +that probably if the red player is + + + align:start position:0% +that probably if the red player is +decent he will put his circle here and I + + align:start position:0% +decent he will put his circle here and I + + + align:start position:0% +decent he will put his circle here and I +will incur a loss + + align:start position:0% +will incur a loss + + + align:start position:0% +will incur a loss +so my reward will be negative if we take + + align:start position:0% +so my reward will be negative if we take + + + align:start position:0% +so my reward will be negative if we take +positivity be good and this is something + + align:start position:0% +positivity be good and this is something + + + align:start position:0% +positivity be good and this is something +that I can learn from going forward + + align:start position:0% +that I can learn from going forward + + + align:start position:0% +that I can learn from going forward +essentially what I want to avoid is + + align:start position:0% +essentially what I want to avoid is + + + align:start position:0% +essentially what I want to avoid is +ending up in the state that's shown in + + align:start position:0% +ending up in the state that's shown in + + + align:start position:0% +ending up in the state that's shown in +the bottom right here this is the the + + align:start position:0% +the bottom right here this is the the + + + align:start position:0% +the bottom right here this is the the +basic idea of reinforcement learning for + + align:start position:0% +basic idea of reinforcement learning for + + + align:start position:0% +basic idea of reinforcement learning for +for videogames and for anything else + + align:start position:0% +for videogames and for anything else + + + align:start position:0% +for videogames and for anything else +so if we take this board analogy or this + + align:start position:0% +so if we take this board analogy or this + + + align:start position:0% +so if we take this board analogy or this +example and and move to the healthcare + + align:start position:0% +example and and move to the healthcare + + + align:start position:0% +example and and move to the healthcare +setting we can think of the state of a + + align:start position:0% +setting we can think of the state of a + + + align:start position:0% +setting we can think of the state of a +patient ask the game board or the state + + align:start position:0% +patient ask the game board or the state + + + align:start position:0% +patient ask the game board or the state +of the game we will always call this s T + + align:start position:0% +of the game we will always call this s T + + + align:start position:0% +of the game we will always call this s T +in this talk the treatments that we + + align:start position:0% +in this talk the treatments that we + + + align:start position:0% +in this talk the treatments that we +prescribe or interventions will be a T + + align:start position:0% +prescribe or interventions will be a T + + + align:start position:0% +prescribe or interventions will be a T +and these are like the actions in the + + align:start position:0% +and these are like the actions in the + + + align:start position:0% +and these are like the actions in the +game obviously the outcomes of a patient + + align:start position:0% +game obviously the outcomes of a patient + + + align:start position:0% +game obviously the outcomes of a patient +could be mortality could be managing + + align:start position:0% +could be mortality could be managing + + + align:start position:0% +could be mortality could be managing +vitals will be just like the rewards in + + align:start position:0% +vitals will be just like the rewards in + + + align:start position:0% +vitals will be just like the rewards in +the game having lost or won and then I + + align:start position:0% +the game having lost or won and then I + + + align:start position:0% +the game having lost or won and then I +put the end here what could possibly go + + align:start position:0% +put the end here what could possibly go + + + align:start position:0% +put the end here what could possibly go +wrong well as I alluded to before + + align:start position:0% +wrong well as I alluded to before + + + align:start position:0% +wrong well as I alluded to before +healthcare is not a game in the same + + align:start position:0% +healthcare is not a game in the same + + + align:start position:0% +healthcare is not a game in the same +sense that a video game is a game but + + align:start position:0% +sense that a video game is a game but + + + align:start position:0% +sense that a video game is a game but +they share a lot of mathematical + + align:start position:0% +they share a lot of mathematical + + + align:start position:0% +they share a lot of mathematical +structure so that's why I make the + + align:start position:0% +structure so that's why I make the + + + align:start position:0% +structure so that's why I make the +analogy here these quantities here si + + align:start position:0% +analogy here these quantities here si + + + align:start position:0% +analogy here these quantities here si +and R will form something called a + + align:start position:0% +and R will form something called a + + + align:start position:0% +and R will form something called a +decision process and that's what we'll + + align:start position:0% +decision process and that's what we'll + + + align:start position:0% +decision process and that's what we'll +talk about next this is the outline for + + align:start position:0% +talk about next this is the outline for + + + align:start position:0% +talk about next this is the outline for +today and Thursday I won't get to this + + align:start position:0% +today and Thursday I won't get to this + + + align:start position:0% +today and Thursday I won't get to this +today but these are the topics were + + align:start position:0% +today but these are the topics were + + + align:start position:0% +today but these are the topics were +considering so a decision process is + + align:start position:0% +considering so a decision process is + + + align:start position:0% +considering so a decision process is +essentially the the world that describes + + align:start position:0% +essentially the the world that describes + + + align:start position:0% +essentially the the world that describes +the data that we access or the the world + + align:start position:0% +the data that we access or the the world + + + align:start position:0% +the data that we access or the the world +that we were managing our agent in and + + align:start position:0% +that we were managing our agent in and + + + align:start position:0% +that we were managing our agent in and +it's often very often if you've ever + + align:start position:0% +it's often very often if you've ever + + + align:start position:0% +it's often very often if you've ever +seen reinforcement learning taught is + + align:start position:0% +seen reinforcement learning taught is + + + align:start position:0% +seen reinforcement learning taught is +you have seen this picture in some form + + align:start position:0% +you have seen this picture in some form + + + align:start position:0% +you have seen this picture in some form +usually sometimes there's some mouse and + + align:start position:0% +usually sometimes there's some mouse and + + + align:start position:0% +usually sometimes there's some mouse and +some cheese and there's other things + + align:start position:0% +some cheese and there's other things + + + align:start position:0% +some cheese and there's other things +going on but you know what I'm talking + + align:start position:0% +going on but you know what I'm talking + + + align:start position:0% +going on but you know what I'm talking +about + + align:start position:0% +about + + + align:start position:0% +about +and but there are the same basic + + align:start position:0% +and but there are the same basic + + + align:start position:0% +and but there are the same basic +components so there's the concept of an + + align:start position:0% +components so there's the concept of an + + + align:start position:0% +components so there's the concept of an +agent let's think doctor for now that + + align:start position:0% +agent let's think doctor for now that + + + align:start position:0% +agent let's think doctor for now that +takes actions repeatedly over time so + + align:start position:0% +takes actions repeatedly over time so + + + align:start position:0% +takes actions repeatedly over time so +this T here indicates an index of time + + align:start position:0% +this T here indicates an index of time + + + align:start position:0% +this T here indicates an index of time +and we see that essentially increasing + + align:start position:0% +and we see that essentially increasing + + + align:start position:0% +and we see that essentially increasing +as we spin around this wheel here we + + align:start position:0% +as we spin around this wheel here we + + + align:start position:0% +as we spin around this wheel here we +move forward in time so an agent takes + + align:start position:0% +move forward in time so an agent takes + + + align:start position:0% +move forward in time so an agent takes +an action and at any time point receives + + align:start position:0% +an action and at any time point receives + + + align:start position:0% +an action and at any time point receives +an award reward for that action and that + + align:start position:0% +an award reward for that action and that + + + align:start position:0% +an award reward for that action and that +would + + align:start position:0% +would + + + align:start position:0% +would +as I said before the environment is + + align:start position:0% +as I said before the environment is + + + align:start position:0% +as I said before the environment is +responsible for giving that reward so + + align:start position:0% +responsible for giving that reward so + + + align:start position:0% +responsible for giving that reward so +for example if I'm the doctor I'm the + + align:start position:0% +for example if I'm the doctor I'm the + + + align:start position:0% +for example if I'm the doctor I'm the +agent I make an action or an + + align:start position:0% +agent I make an action or an + + + align:start position:0% +agent I make an action or an +intervention to my patient the patient + + align:start position:0% +intervention to my patient the patient + + + align:start position:0% +intervention to my patient the patient +will be the environment and essential + + align:start position:0% +will be the environment and essential + + + align:start position:0% +will be the environment and essential +response to does not respond to my + + align:start position:0% +response to does not respond to my + + + align:start position:0% +response to does not respond to my +intervention + + align:start position:0% +intervention + + + align:start position:0% +intervention +the state here is the state of the + + align:start position:0% +the state here is the state of the + + + align:start position:0% +the state here is the state of the +patient as I mentioned before for + + align:start position:0% +patient as I mentioned before for + + + align:start position:0% +patient as I mentioned before for +example but it might also be a state of + + align:start position:0% +example but it might also be a state of + + + align:start position:0% +example but it might also be a state of +more broadly than the patient like the + + align:start position:0% +more broadly than the patient like the + + + align:start position:0% +more broadly than the patient like the +the the the settings of the Machine that + + align:start position:0% +the the the settings of the Machine that + + + align:start position:0% +the the the settings of the Machine that +they're attached to or the the + + align:start position:0% +they're attached to or the the + + + align:start position:0% +they're attached to or the the +availability of certain drugs in the + + align:start position:0% +availability of certain drugs in the + + + align:start position:0% +availability of certain drugs in the +hospital or something like that so we + + align:start position:0% +hospital or something like that so we + + + align:start position:0% +hospital or something like that so we +can think a little bit more broadly in a + + align:start position:0% +can think a little bit more broadly in a + + + align:start position:0% +can think a little bit more broadly in a +patient - I said partially observed here + + align:start position:0% +patient - I said partially observed here + + + align:start position:0% +patient - I said partially observed here +in that I might not actually know + + align:start position:0% +in that I might not actually know + + + align:start position:0% +in that I might not actually know +everything about the patient that's + + align:start position:0% +everything about the patient that's + + + align:start position:0% +everything about the patient that's +relevant to me and we will come back a + + align:start position:0% +relevant to me and we will come back a + + + align:start position:0% +relevant to me and we will come back a +little bit later to that so there are + + align:start position:0% +little bit later to that so there are + + + align:start position:0% +little bit later to that so there are +two different formulations that are very + + align:start position:0% +two different formulations that are very + + + align:start position:0% +two different formulations that are very +close to each other which is when you + + align:start position:0% +close to each other which is when you + + + align:start position:0% +close to each other which is when you +know everything about s and which when + + align:start position:0% +know everything about s and which when + + + align:start position:0% +know everything about s and which when +you don't well for the longest part of + + align:start position:0% +you don't well for the longest part of + + + align:start position:0% +you don't well for the longest part of +this talk focus on where I know + + align:start position:0% +this talk focus on where I know + + + align:start position:0% +this talk focus on where I know +everything that is irrelevant about the + + align:start position:0% +everything that is irrelevant about the + + + align:start position:0% +everything that is irrelevant about the +environment okay to make this all a bit + + align:start position:0% +environment okay to make this all a bit + + + align:start position:0% +environment okay to make this all a bit +more concrete I'll return to the picture + + align:start position:0% +more concrete I'll return to the picture + + + align:start position:0% +more concrete I'll return to the picture +that I showed you before but now put it + + align:start position:0% +that I showed you before but now put it + + + align:start position:0% +that I showed you before but now put it +in context of the paper that you read + + align:start position:0% +in context of the paper that you read + + + align:start position:0% +in context of the paper that you read +right was that the compulsory one the + + align:start position:0% +right was that the compulsory one the + + + align:start position:0% +right was that the compulsory one the +mechanical ventilation okay great so in + + align:start position:0% +mechanical ventilation okay great so in + + + align:start position:0% +mechanical ventilation okay great so in +this case they had an interesting reward + + align:start position:0% +this case they had an interesting reward + + + align:start position:0% +this case they had an interesting reward +structure essentially the thing that + + align:start position:0% +structure essentially the thing that + + + align:start position:0% +structure essentially the thing that +they were trying to optimize was a + + align:start position:0% +they were trying to optimize was a + + + align:start position:0% +they were trying to optimize was a +reward related to the vitals of the + + align:start position:0% +reward related to the vitals of the + + + align:start position:0% +reward related to the vitals of the +patient but also to whether they were + + align:start position:0% +patient but also to whether they were + + + align:start position:0% +patient but also to whether they were +kept on mechanical ventilation or not + + align:start position:0% +kept on mechanical ventilation or not + + + align:start position:0% +kept on mechanical ventilation or not +and the idea of this paper is that you + + align:start position:0% +and the idea of this paper is that you + + + align:start position:0% +and the idea of this paper is that you +don't want to keep a patient + + align:start position:0% +don't want to keep a patient + + + align:start position:0% +don't want to keep a patient +unnecessarily on mechanical ventilation + + align:start position:0% +unnecessarily on mechanical ventilation + + + align:start position:0% +unnecessarily on mechanical ventilation +because it has the sight aspects that we + + align:start position:0% +because it has the sight aspects that we + + + align:start position:0% +because it has the sight aspects that we +talked about before so at any time a + + align:start position:0% +talked about before so at any time a + + + align:start position:0% +talked about before so at any time a +point in time since we can think about + + align:start position:0% +point in time since we can think about + + + align:start position:0% +point in time since we can think about +taking a patient on or off and also + + align:start position:0% +taking a patient on or off and also + + + align:start position:0% +taking a patient on or off and also +dealing with the sedatives that are + + align:start position:0% +dealing with the sedatives that are + + + align:start position:0% +dealing with the sedatives that are +prescribed to them so in this example + + align:start position:0% +prescribed to them so in this example + + + align:start position:0% +prescribed to them so in this example +the state that they consider in this in + + align:start position:0% +the state that they consider in this in + + + align:start position:0% +the state that they consider in this in +this application included the + + align:start position:0% +this application included the + + + align:start position:0% +this application included the +demographic information of the patient + + align:start position:0% +demographic information of the patient + + + align:start position:0% +demographic information of the patient +it doesn't really change over time their + + align:start position:0% +it doesn't really change over time their + + + align:start position:0% +it doesn't really change over time their +physiological measurements ventilator + + align:start position:0% +physiological measurements ventilator + + + align:start position:0% +physiological measurements ventilator +settings control consciousness level the + + align:start position:0% +settings control consciousness level the + + + align:start position:0% +settings control consciousness level the +dosages of the sedatives they use which + + align:start position:0% +dosages of the sedatives they use which + + + align:start position:0% +dosages of the sedatives they use which +could be + + align:start position:0% +could be + + + align:start position:0% +could be +an action I suppose and a number of + + align:start position:0% +an action I suppose and a number of + + + align:start position:0% +an action I suppose and a number of +other things and these are the values + + align:start position:0% +other things and these are the values + + + align:start position:0% +other things and these are the values +that we have to keep track on of moving + + align:start position:0% +that we have to keep track on of moving + + + align:start position:0% +that we have to keep track on of moving +forward in time the actions concretely + + align:start position:0% +forward in time the actions concretely + + + align:start position:0% +forward in time the actions concretely +included whether to intubate or extubate + + align:start position:0% +included whether to intubate or extubate + + + align:start position:0% +included whether to intubate or extubate +the patient as well as the administer + + align:start position:0% +the patient as well as the administer + + + align:start position:0% +the patient as well as the administer +and dosing the sedatives so this is + + align:start position:0% +and dosing the sedatives so this is + + + align:start position:0% +and dosing the sedatives so this is +again an example of a so-called decision + + align:start position:0% +again an example of a so-called decision + + + align:start position:0% +again an example of a so-called decision +process and essentially the the process + + align:start position:0% +process and essentially the the process + + + align:start position:0% +process and essentially the the process +is the distribution of these quantities + + align:start position:0% +is the distribution of these quantities + + + align:start position:0% +is the distribution of these quantities +that have been talking about over time + + align:start position:0% +that have been talking about over time + + + align:start position:0% +that have been talking about over time +so we have the states the actions and + + align:start position:0% +so we have the states the actions and + + + align:start position:0% +so we have the states the actions and +the rewards they all traverse or they + + align:start position:0% +the rewards they all traverse or they + + + align:start position:0% +the rewards they all traverse or they +all evolve over time and the the loss of + + align:start position:0% +all evolve over time and the the loss of + + + align:start position:0% +all evolve over time and the the loss of +how that happens is the decision process + + align:start position:0% +how that happens is the decision process + + + align:start position:0% +how that happens is the decision process +I mentioned before that we will be + + align:start position:0% +I mentioned before that we will be + + + align:start position:0% +I mentioned before that we will be +talking about policies today and + + align:start position:0% +talking about policies today and + + + align:start position:0% +talking about policies today and +typically there's a distinction between + + align:start position:0% +typically there's a distinction between + + + align:start position:0% +typically there's a distinction between +what is called a behavior policy and a + + align:start position:0% +what is called a behavior policy and a + + + align:start position:0% +what is called a behavior policy and a +target policy or there are different + + align:start position:0% +target policy or there are different + + + align:start position:0% +target policy or there are different +words for this essentially the thing + + align:start position:0% +words for this essentially the thing + + + align:start position:0% +words for this essentially the thing +that we observe is usually called a + + align:start position:0% +that we observe is usually called a + + + align:start position:0% +that we observe is usually called a +behavior policy by that I mean if we go + + align:start position:0% +behavior policy by that I mean if we go + + + align:start position:0% +behavior policy by that I mean if we go +to a hospital and watch what's what's + + align:start position:0% +to a hospital and watch what's what's + + + align:start position:0% +to a hospital and watch what's what's +happening there at the moment that will + + align:start position:0% +happening there at the moment that will + + + align:start position:0% +happening there at the moment that will +be the behavior policy and I will denote + + align:start position:0% +be the behavior policy and I will denote + + + align:start position:0% +be the behavior policy and I will denote +that mu so that is what we have to learn + + align:start position:0% +that mu so that is what we have to learn + + + align:start position:0% +that mu so that is what we have to learn +from essentially so decision processes + + align:start position:0% +from essentially so decision processes + + + align:start position:0% +from essentially so decision processes +so far are incredibly general I haven't + + align:start position:0% +so far are incredibly general I haven't + + + align:start position:0% +so far are incredibly general I haven't +said anything about what this + + align:start position:0% +said anything about what this + + + align:start position:0% +said anything about what this +distribution is like but the the + + align:start position:0% +distribution is like but the the + + + align:start position:0% +distribution is like but the the +absolutely dominant restriction that + + align:start position:0% +absolutely dominant restriction that + + + align:start position:0% +absolutely dominant restriction that +people make when they study the system + + align:start position:0% +people make when they study the system + + + align:start position:0% +people make when they study the system +processes is to look at and mark of + + align:start position:0% +processes is to look at and mark of + + + align:start position:0% +processes is to look at and mark of +decision processes and these have a + + align:start position:0% +decision processes and these have a + + + align:start position:0% +decision processes and these have a +specific conditional independence + + align:start position:0% +specific conditional independence + + + align:start position:0% +specific conditional independence +structure that I will illustrate in the + + align:start position:0% +structure that I will illustrate in the + + + align:start position:0% +structure that I will illustrate in the +next slide but I'll just define it + + align:start position:0% +next slide but I'll just define it + + + align:start position:0% +next slide but I'll just define it +mathematically here it says essentially + + align:start position:0% +mathematically here it says essentially + + + align:start position:0% +mathematically here it says essentially +that all of the quantities that we care + + align:start position:0% +that all of the quantities that we care + + + align:start position:0% +that all of the quantities that we care +about the states I guess that should say + + align:start position:0% +about the states I guess that should say + + + align:start position:0% +about the states I guess that should say +state reports in the actions only depend + + align:start position:0% +state reports in the actions only depend + + + align:start position:0% +state reports in the actions only depend +on the most most recent state in action + + align:start position:0% +on the most most recent state in action + + + align:start position:0% +on the most most recent state in action +so if we want to or if we observe an + + align:start position:0% +so if we want to or if we observe an + + + align:start position:0% +so if we want to or if we observe an +action taken by a doctor in the hospital + + align:start position:0% +action taken by a doctor in the hospital + + + align:start position:0% +action taken by a doctor in the hospital +for example to make a mark of assumption + + align:start position:0% +for example to make a mark of assumption + + + align:start position:0% +for example to make a mark of assumption +would would say that this doctor did not + + align:start position:0% +would would say that this doctor did not + + + align:start position:0% +would would say that this doctor did not +look at anything that happened earlier + + align:start position:0% +look at anything that happened earlier + + + align:start position:0% +look at anything that happened earlier +in time or any other information than + + align:start position:0% +in time or any other information than + + + align:start position:0% +in time or any other information than +what is in the state variable that we + + align:start position:0% +what is in the state variable that we + + + align:start position:0% +what is in the state variable that we +observe at that time that is the + + align:start position:0% +observe at that time that is the + + + align:start position:0% +observe at that time that is the +assumption that we make yeah + + align:start position:0% +assumption that we make yeah + + + align:start position:0% +assumption that we make yeah +like the consumption you can make for a + + align:start position:0% +like the consumption you can make for a + + + align:start position:0% +like the consumption you can make for a +healthcare because yet you don't measure + + align:start position:0% +healthcare because yet you don't measure + + + align:start position:0% +healthcare because yet you don't measure +you don't have access to the real estate + + align:start position:0% +you don't have access to the real estate + + + align:start position:0% +you don't have access to the real estate +but only about what's measured about + + align:start position:0% +but only about what's measured about + + + align:start position:0% +but only about what's measured about +your state in healthcare it's a very + + align:start position:0% +your state in healthcare it's a very + + + align:start position:0% +your state in healthcare it's a very +good question so the nice thing in terms + + align:start position:0% +good question so the nice thing in terms + + + align:start position:0% +good question so the nice thing in terms +of inferring causal quantities is that + + align:start position:0% +of inferring causal quantities is that + + + align:start position:0% +of inferring causal quantities is that +we only need the things that we're used + + align:start position:0% +we only need the things that we're used + + + align:start position:0% +we only need the things that we're used +to make the decision in the first place + + align:start position:0% +to make the decision in the first place + + + align:start position:0% +to make the decision in the first place +so the doctor can only act on such + + align:start position:0% +so the doctor can only act on such + + + align:start position:0% +so the doctor can only act on such +information - unless we don't record + + align:start position:0% +information - unless we don't record + + + align:start position:0% +information - unless we don't record +everything that the doctor knows which + + align:start position:0% +everything that the doctor knows which + + + align:start position:0% +everything that the doctor knows which +is also the case so it's it's something + + align:start position:0% +is also the case so it's it's something + + + align:start position:0% +is also the case so it's it's something +that we have to worry about for sure + + align:start position:0% +that we have to worry about for sure + + + align:start position:0% +that we have to worry about for sure +yeah another another way to to lose + + align:start position:0% +yeah another another way to to lose + + + align:start position:0% +yeah another another way to to lose +information as I mentioned that is + + align:start position:0% +information as I mentioned that is + + + align:start position:0% +information as I mentioned that is +relevant for this is if we we look to to + + align:start position:0% +relevant for this is if we we look to to + + + align:start position:0% +relevant for this is if we we look to to +like to tune what's the opposite of far + + align:start position:0% +like to tune what's the opposite of far + + + align:start position:0% +like to tune what's the opposite of far +to knee our back in time essentially so + + align:start position:0% +to knee our back in time essentially so + + + align:start position:0% +to knee our back in time essentially so +we don't look at the entire history of + + align:start position:0% +we don't look at the entire history of + + + align:start position:0% +we don't look at the entire history of +the patient and when I say St here it + + align:start position:0% +the patient and when I say St here it + + + align:start position:0% +the patient and when I say St here it +doesn't have to be they instill the + + align:start position:0% +doesn't have to be they instill the + + + align:start position:0% +doesn't have to be they instill the +instantaneous like a snapshot of a + + align:start position:0% +instantaneous like a snapshot of a + + + align:start position:0% +instantaneous like a snapshot of a +patient we can also include history + + align:start position:0% +patient we can also include history + + + align:start position:0% +patient we can also include history +there again we'll come back to that a + + align:start position:0% +there again we'll come back to that a + + + align:start position:0% +there again we'll come back to that a +little later + + align:start position:0% +little later + + + align:start position:0% +little later +yeah okay so the Markham assumption + + align:start position:0% +yeah okay so the Markham assumption + + + align:start position:0% +yeah okay so the Markham assumption +essentially looks like this or this is + + align:start position:0% +essentially looks like this or this is + + + align:start position:0% +essentially looks like this or this is +how I will illustrate anyway we have a + + align:start position:0% +how I will illustrate anyway we have a + + + align:start position:0% +how I will illustrate anyway we have a +sequence of states here that evolve over + + align:start position:0% +sequence of states here that evolve over + + + align:start position:0% +sequence of states here that evolve over +time I'm not allowing myself to put some + + align:start position:0% +time I'm not allowing myself to put some + + + align:start position:0% +time I'm not allowing myself to put some +dots here because I don't want to draw + + align:start position:0% +dots here because I don't want to draw + + + align:start position:0% +dots here because I don't want to draw +forever and but essentially you can + + align:start position:0% +forever and but essentially you can + + + align:start position:0% +forever and but essentially you can +think of this pattern repeating where + + align:start position:0% +think of this pattern repeating where + + + align:start position:0% +think of this pattern repeating where +the previous state goes into the next + + align:start position:0% +the previous state goes into the next + + + align:start position:0% +the previous state goes into the next +state the action goes into the next + + align:start position:0% +state the action goes into the next + + + align:start position:0% +state the action goes into the next +stage and the action and state goes into + + align:start position:0% +stage and the action and state goes into + + + align:start position:0% +stage and the action and state goes into +the reward this is the world that we + + align:start position:0% +the reward this is the world that we + + + align:start position:0% +the reward this is the world that we +will live in for this lecture something + + align:start position:0% +will live in for this lecture something + + + align:start position:0% +will live in for this lecture something +that's not allowed under the mark of + + align:start position:0% +that's not allowed under the mark of + + + align:start position:0% +that's not allowed under the mark of +assumption is an edge like this which + + align:start position:0% +assumption is an edge like this which + + + align:start position:0% +assumption is an edge like this which +says that the an action in the early + + align:start position:0% +says that the an action in the early + + + align:start position:0% +says that the an action in the early +time in places' an action at a later + + align:start position:0% +time in places' an action at a later + + + align:start position:0% +time in places' an action at a later +time + + align:start position:0% +time + + + align:start position:0% +time +and specifically it can't do so without + + align:start position:0% +and specifically it can't do so without + + + align:start position:0% +and specifically it can't do so without +casting through estates for example it + + align:start position:0% +casting through estates for example it + + + align:start position:0% +casting through estates for example it +very well can have an influence on 80 by + + align:start position:0% +very well can have an influence on 80 by + + + align:start position:0% +very well can have an influence on 80 by +this trajectory here but not directly + + align:start position:0% +this trajectory here but not directly + + + align:start position:0% +this trajectory here but not directly +that's the amount Markov assumption in + + align:start position:0% +that's the amount Markov assumption in + + + align:start position:0% +that's the amount Markov assumption in +this case so you can see that there's if + + align:start position:0% +this case so you can see that there's if + + + align:start position:0% +this case so you can see that there's if +I were to draw the graph of all the + + align:start position:0% +I were to draw the graph of all the + + + align:start position:0% +I were to draw the graph of all the +different measurements + + align:start position:0% +different measurements + + + align:start position:0% +different measurements +we that we see and during a stay + + align:start position:0% +we that we see and during a stay + + + align:start position:0% +we that we see and during a stay +essentially you could there are a lot of + + align:start position:0% +essentially you could there are a lot of + + + align:start position:0% +essentially you could there are a lot of +errors that I could have had in this + + align:start position:0% +errors that I could have had in this + + + align:start position:0% +errors that I could have had in this +picture that I don't have so it may seem + + align:start position:0% +picture that I don't have so it may seem + + + align:start position:0% +picture that I don't have so it may seem +that the Markham assumption is a very + + align:start position:0% +that the Markham assumption is a very + + + align:start position:0% +that the Markham assumption is a very +very strong one but one way to ensure + + align:start position:0% +very strong one but one way to ensure + + + align:start position:0% +very strong one but one way to ensure +that the Markov assumption is more + + align:start position:0% +that the Markov assumption is more + + + align:start position:0% +that the Markov assumption is more +likely is to include more things in your + + align:start position:0% +likely is to include more things in your + + + align:start position:0% +likely is to include more things in your +state including some reason of the + + align:start position:0% +state including some reason of the + + + align:start position:0% +state including some reason of the +history etc but I mentioned before an + + align:start position:0% +history etc but I mentioned before an + + + align:start position:0% +history etc but I mentioned before an +even stronger restriction of decision + + align:start position:0% +even stronger restriction of decision + + + align:start position:0% +even stronger restriction of decision +processes is to assume that the states + + align:start position:0% +processes is to assume that the states + + + align:start position:0% +processes is to assume that the states +over time are themselves independent so + + align:start position:0% +over time are themselves independent so + + + align:start position:0% +over time are themselves independent so +this goes by different names sometimes + + align:start position:0% +this goes by different names sometimes + + + align:start position:0% +this goes by different names sometimes +under the name contextual bandits but + + align:start position:0% +under the name contextual bandits but + + + align:start position:0% +under the name contextual bandits but +the bandits part of that itself is not + + align:start position:0% +the bandits part of that itself is not + + + align:start position:0% +the bandits part of that itself is not +so relevant here so let's not go into + + align:start position:0% +so relevant here so let's not go into + + + align:start position:0% +so relevant here so let's not go into +that name for too much but essentially + + align:start position:0% +that name for too much but essentially + + + align:start position:0% +that name for too much but essentially +what we can say is here then the the + + align:start position:0% +what we can say is here then the the + + + align:start position:0% +what we can say is here then the the +state at that later time point is not + + align:start position:0% +state at that later time point is not + + + align:start position:0% +state at that later time point is not +influenced directly by the state at the + + align:start position:0% +influenced directly by the state at the + + + align:start position:0% +influenced directly by the state at the +previous time point nor the action at a + + align:start position:0% +previous time point nor the action at a + + + align:start position:0% +previous time point nor the action at a +previous time point so if you've if you + + align:start position:0% +previous time point so if you've if you + + + align:start position:0% +previous time point so if you've if you +remember what we did last week this + + align:start position:0% +remember what we did last week this + + + align:start position:0% +remember what we did last week this +looks like basically T repetitions of + + align:start position:0% +looks like basically T repetitions of + + + align:start position:0% +looks like basically T repetitions of +the very simple graph that we had for + + align:start position:0% +the very simple graph that we had for + + + align:start position:0% +the very simple graph that we had for +estimating potential outcomes and that + + align:start position:0% +estimating potential outcomes and that + + + align:start position:0% +estimating potential outcomes and that +is indeed mathematically equivalent if + + align:start position:0% +is indeed mathematically equivalent if + + + align:start position:0% +is indeed mathematically equivalent if +we assume that this s here represents + + align:start position:0% +we assume that this s here represents + + + align:start position:0% +we assume that this s here represents +the state of a patient and all patients + + align:start position:0% +the state of a patient and all patients + + + align:start position:0% +the state of a patient and all patients +are drawn from some some process + + align:start position:0% +are drawn from some some process + + + align:start position:0% +are drawn from some some process +essentially so that s 0 1 etc from up to + + align:start position:0% +essentially so that s 0 1 etc from up to + + + align:start position:0% +essentially so that s 0 1 etc from up to +s T are all iid draws of the same + + align:start position:0% +s T are all iid draws of the same + + + align:start position:0% +s T are all iid draws of the same +distribution then we have essentially + + align:start position:0% +distribution then we have essentially + + + align:start position:0% +distribution then we have essentially +the model for T different patients + + align:start position:0% +the model for T different patients + + + align:start position:0% +the model for T different patients +without a single time step or single + + align:start position:0% +without a single time step or single + + + align:start position:0% +without a single time step or single +single action instead of them being + + align:start position:0% +single action instead of them being + + + align:start position:0% +single action instead of them being +dependent in some way so we can see that + + align:start position:0% +dependent in some way so we can see that + + + align:start position:0% +dependent in some way so we can see that +by by going backwards through my slides + + align:start position:0% +by by going backwards through my slides + + + align:start position:0% +by by going backwards through my slides +this is essentially what we had last + + align:start position:0% +this is essentially what we had last + + + align:start position:0% +this is essentially what we had last +week and we just have to add more arrows + + align:start position:0% +week and we just have to add more arrows + + + align:start position:0% +week and we just have to add more arrows +to get to whatever we have this week + + align:start position:0% +to get to whatever we have this week + + + align:start position:0% +to get to whatever we have this week +which indicates that last week was a + + align:start position:0% +which indicates that last week was a + + + align:start position:0% +which indicates that last week was a +special case of this just as David said + + align:start position:0% +special case of this just as David said + + + align:start position:0% +special case of this just as David said +before it also hints at the + + align:start position:0% +before it also hints at the + + + align:start position:0% +before it also hints at the +reinforcement learning probably more + + align:start position:0% +reinforcement learning probably more + + + align:start position:0% +reinforcement learning probably more +complicated than the potential outcomes + + align:start position:0% +complicated than the potential outcomes + + + align:start position:0% +complicated than the potential outcomes +problem and we'll see more examples of + + align:start position:0% +problem and we'll see more examples of + + + align:start position:0% +problem and we'll see more examples of +that later but like with causal effect + + align:start position:0% +that later but like with causal effect + + + align:start position:0% +that later but like with causal effect +estimation that we did last week we're + + align:start position:0% +estimation that we did last week we're + + + align:start position:0% +estimation that we did last week we're +interested in the influences of + + align:start position:0% +interested in the influences of + + + align:start position:0% +interested in the influences of +just a few variables essentially so last + + align:start position:0% +just a few variables essentially so last + + + align:start position:0% +just a few variables essentially so last +time we study the effect of a single + + align:start position:0% +time we study the effect of a single + + + align:start position:0% +time we study the effect of a single +treatment choice and in this case we + + align:start position:0% +treatment choice and in this case we + + + align:start position:0% +treatment choice and in this case we +will study the influence of these + + align:start position:0% +will study the influence of these + + + align:start position:0% +will study the influence of these +various actions that we take along the + + align:start position:0% +various actions that we take along the + + + align:start position:0% +various actions that we take along the +way that will be the goal and it could + + align:start position:0% +way that will be the goal and it could + + + align:start position:0% +way that will be the goal and it could +be either through an immediate effect on + + align:start position:0% +be either through an immediate effect on + + + align:start position:0% +be either through an immediate effect on +the the immediate reward or it can be + + align:start position:0% +the the immediate reward or it can be + + + align:start position:0% +the the immediate reward or it can be +through the impact that an action has on + + align:start position:0% +through the impact that an action has on + + + align:start position:0% +through the impact that an action has on +the state trajectory itself so okay I + + align:start position:0% +the state trajectory itself so okay I + + + align:start position:0% +the state trajectory itself so okay I +told you the about the world now that we + + align:start position:0% +told you the about the world now that we + + + align:start position:0% +told you the about the world now that we +live in we have these essays and ours + + align:start position:0% +live in we have these essays and ours + + + align:start position:0% +live in we have these essays and ours +and I haven't told you so much about the + + align:start position:0% +and I haven't told you so much about the + + + align:start position:0% +and I haven't told you so much about the +the goal that we're trying to solve or + + align:start position:0% +the goal that we're trying to solve or + + + align:start position:0% +the goal that we're trying to solve or +the the problem that we're trying to + + align:start position:0% +the the problem that we're trying to + + + align:start position:0% +the the problem that we're trying to +solve most RL or reinforcement learning + + align:start position:0% +solve most RL or reinforcement learning + + + align:start position:0% +solve most RL or reinforcement learning +is aimed at optimizing the value of a + + align:start position:0% +is aimed at optimizing the value of a + + + align:start position:0% +is aimed at optimizing the value of a +policy or finding a policy that has a + + align:start position:0% +policy or finding a policy that has a + + + align:start position:0% +policy or finding a policy that has a +good return a good sum of rewards there + + align:start position:0% +good return a good sum of rewards there + + + align:start position:0% +good return a good sum of rewards there +are many names for this but essentially + + align:start position:0% +are many names for this but essentially + + + align:start position:0% +are many names for this but essentially +a policy that does well the notion of + + align:start position:0% +a policy that does well the notion of + + + align:start position:0% +a policy that does well the notion of +well that we will be using in this + + align:start position:0% +well that we will be using in this + + + align:start position:0% +well that we will be using in this +lecture is that of a return so the + + align:start position:0% +lecture is that of a return so the + + + align:start position:0% +lecture is that of a return so the +return at a time step T following the + + align:start position:0% +return at a time step T following the + + + align:start position:0% +return at a time step T following the +policy PI that I had before is the sum + + align:start position:0% +policy PI that I had before is the sum + + + align:start position:0% +policy PI that I had before is the sum +of the future rewards that we see if we + + align:start position:0% +of the future rewards that we see if we + + + align:start position:0% +of the future rewards that we see if we +were to act according to that policy so + + align:start position:0% +were to act according to that policy so + + + align:start position:0% +were to act according to that policy so +essentially I stop now I ask ok how if I + + align:start position:0% +essentially I stop now I ask ok how if I + + + align:start position:0% +essentially I stop now I ask ok how if I +keep on doing the same as I've done + + align:start position:0% +keep on doing the same as I've done + + + align:start position:0% +keep on doing the same as I've done +through my whole life maybe that was a + + align:start position:0% +through my whole life maybe that was a + + + align:start position:0% +through my whole life maybe that was a +good policy I don't know + + align:start position:0% +good policy I don't know + + + align:start position:0% +good policy I don't know +and keep going until the end of time + + align:start position:0% +and keep going until the end of time + + + align:start position:0% +and keep going until the end of time +what is that how well will I do what is + + align:start position:0% +what is that how well will I do what is + + + align:start position:0% +what is that how well will I do what is +the sum of those rewards that I get + + align:start position:0% +the sum of those rewards that I get + + + align:start position:0% +the sum of those rewards that I get +essentially that's the return the value + + align:start position:0% +essentially that's the return the value + + + align:start position:0% +essentially that's the return the value +is the expectation of such things so if + + align:start position:0% +is the expectation of such things so if + + + align:start position:0% +is the expectation of such things so if +if I'm not the only person but there's + + align:start position:0% +if I'm not the only person but there's + + + align:start position:0% +if I'm not the only person but there's +the whole population of us the + + align:start position:0% +the whole population of us the + + + align:start position:0% +the whole population of us the +expectation over that population is the + + align:start position:0% +expectation over that population is the + + + align:start position:0% +expectation over that population is the +value of the policy so if we take + + align:start position:0% +value of the policy so if we take + + + align:start position:0% +value of the policy so if we take +patients as a better analogy than my + + align:start position:0% +patients as a better analogy than my + + + align:start position:0% +patients as a better analogy than my +life may be what the expectation is over + + align:start position:0% +life may be what the expectation is over + + + align:start position:0% +life may be what the expectation is over +patients if we act on every patient in + + align:start position:0% +patients if we act on every patient in + + + align:start position:0% +patients if we act on every patient in +our population the same way according to + + align:start position:0% +our population the same way according to + + + align:start position:0% +our population the same way according to +the same policy that is what is the + + align:start position:0% +the same policy that is what is the + + + align:start position:0% +the same policy that is what is the +expected return over those patients so + + align:start position:0% +expected return over those patients so + + + align:start position:0% +expected return over those patients so +as an example I drew a few trajectories + + align:start position:0% +as an example I drew a few trajectories + + + align:start position:0% +as an example I drew a few trajectories +again because I like drawing and we can + + align:start position:0% +again because I like drawing and we can + + + align:start position:0% +again because I like drawing and we can +think about three different patients + + align:start position:0% +think about three different patients + + + align:start position:0% +think about three different patients +here they start in different states and + + align:start position:0% +here they start in different states and + + + align:start position:0% +here they start in different states and +they will have different + + align:start position:0% +they will have different + + + align:start position:0% +they will have different +action trajectories as a result so we're + + align:start position:0% +action trajectories as a result so we're + + + align:start position:0% +action trajectories as a result so we're +treating them with the same policy let's + + align:start position:0% +treating them with the same policy let's + + + align:start position:0% +treating them with the same policy let's +call it pi but because they're in + + align:start position:0% +call it pi but because they're in + + + align:start position:0% +call it pi but because they're in +different states they will have + + align:start position:0% +different states they will have + + + align:start position:0% +different states they will have +different actions at different at the + + align:start position:0% +different actions at different at the + + + align:start position:0% +different actions at different at the +same times so here we take a action we + + align:start position:0% +same times so here we take a action we + + + align:start position:0% +same times so here we take a action we +go down here we take a selection we go + + align:start position:0% +go down here we take a selection we go + + + align:start position:0% +go down here we take a selection we go +down that's what that means here the + + align:start position:0% +down that's what that means here the + + + align:start position:0% +down that's what that means here the +specifics of this is not so important + + align:start position:0% +specifics of this is not so important + + + align:start position:0% +specifics of this is not so important +that's why what I want you to pay + + align:start position:0% +that's why what I want you to pay + + + align:start position:0% +that's why what I want you to pay +attention to is that after each at each + + align:start position:0% +attention to is that after each at each + + + align:start position:0% +attention to is that after each at each +action we get our reward and at the end + + align:start position:0% +action we get our reward and at the end + + + align:start position:0% +action we get our reward and at the end +we can sum those up and that's our + + align:start position:0% +we can sum those up and that's our + + + align:start position:0% +we can sum those up and that's our +return + + align:start position:0% +return + + + align:start position:0% +return +so each patient has one set of one value + + align:start position:0% +so each patient has one set of one value + + + align:start position:0% +so each patient has one set of one value +for their own trajectory and the value + + align:start position:0% +for their own trajectory and the value + + + align:start position:0% +for their own trajectory and the value +of the policy is then the average value + + align:start position:0% +of the policy is then the average value + + + align:start position:0% +of the policy is then the average value +of such trajectories okay so that is + + align:start position:0% +of such trajectories okay so that is + + + align:start position:0% +of such trajectories okay so that is +what we're trying to optimize we have + + align:start position:0% +what we're trying to optimize we have + + + align:start position:0% +what we're trying to optimize we have +now a notion of good and we want to find + + align:start position:0% +now a notion of good and we want to find + + + align:start position:0% +now a notion of good and we want to find +a PI such that V PI up there is good + + align:start position:0% +a PI such that V PI up there is good + + + align:start position:0% +a PI such that V PI up there is good +that's the goal all right so I think + + align:start position:0% +that's the goal all right so I think + + + align:start position:0% +that's the goal all right so I think +it's time for for a bit of an example + + align:start position:0% +it's time for for a bit of an example + + + align:start position:0% +it's time for for a bit of an example +here I want you to play along in a + + align:start position:0% +here I want you to play along in a + + + align:start position:0% +here I want you to play along in a +second + + align:start position:0% +second + + + align:start position:0% +second +you're gonna you're going to solve this + + align:start position:0% +you're gonna you're going to solve this + + + align:start position:0% +you're gonna you're going to solve this +problem it's not a hard one so I think + + align:start position:0% +problem it's not a hard one so I think + + + align:start position:0% +problem it's not a hard one so I think +you'll manage I think I think you'll be + + align:start position:0% +you'll manage I think I think you'll be + + + align:start position:0% +you'll manage I think I think you'll be +fine but this is now on yet another + + align:start position:0% +fine but this is now on yet another + + + align:start position:0% +fine but this is now on yet another +example of a world to be in this is the + + align:start position:0% +example of a world to be in this is the + + + align:start position:0% +example of a world to be in this is the +robot in a room and I've stolen this + + align:start position:0% +robot in a room and I've stolen this + + + align:start position:0% +robot in a room and I've stolen this +slide from David who stole it from Peter + + align:start position:0% +slide from David who stole it from Peter + + + align:start position:0% +slide from David who stole it from Peter +boudic I am yeah + + align:start position:0% +boudic I am yeah + + + align:start position:0% +boudic I am yeah +and yeah so credits to him all right the + + align:start position:0% +and yeah so credits to him all right the + + + align:start position:0% +and yeah so credits to him all right the +rules of this world says the following + + align:start position:0% +rules of this world says the following + + + align:start position:0% +rules of this world says the following +if you tell the robot who is traversing + + align:start position:0% +if you tell the robot who is traversing + + + align:start position:0% +if you tell the robot who is traversing +this the set of tiles here if you tell + + align:start position:0% +this the set of tiles here if you tell + + + align:start position:0% +this the set of tiles here if you tell +the robot to go up there's a chance he + + align:start position:0% +the robot to go up there's a chance he + + + align:start position:0% +the robot to go up there's a chance he +doesn't go up but go somewhere else so + + align:start position:0% +doesn't go up but go somewhere else so + + + align:start position:0% +doesn't go up but go somewhere else so +we have stochastic transitions + + align:start position:0% +we have stochastic transitions + + + align:start position:0% +we have stochastic transitions +essentially if I say up it goes up with + + align:start position:0% +essentially if I say up it goes up with + + + align:start position:0% +essentially if I say up it goes up with +point a probability and somewhere else + + align:start position:0% +point a probability and somewhere else + + + align:start position:0% +point a probability and somewhere else +with uniform probability say so point + + align:start position:0% +with uniform probability say so point + + + align:start position:0% +with uniform probability say so point +eight up and then point to this the only + + align:start position:0% +eight up and then point to this the only + + + align:start position:0% +eight up and then point to this the only +possible direction to go in if you start + + align:start position:0% +possible direction to go in if you start + + + align:start position:0% +possible direction to go in if you start +here so point two in that way okay + + align:start position:0% +here so point two in that way okay + + + align:start position:0% +here so point two in that way okay +there's a chance you've moved in the + + align:start position:0% +there's a chance you've moved in the + + + align:start position:0% +there's a chance you've moved in the +wrong direction what I'm trying to + + align:start position:0% +wrong direction what I'm trying to + + + align:start position:0% +wrong direction what I'm trying to +illustrate you know there's no chance + + align:start position:0% +illustrate you know there's no chance + + + align:start position:0% +illustrate you know there's no chance +that they're going in the opposite + + align:start position:0% +that they're going in the opposite + + + align:start position:0% +that they're going in the opposite +direction say so if I say right here it + + align:start position:0% +direction say so if I say right here it + + + align:start position:0% +direction say so if I say right here it +can't go that way + + align:start position:0% +can't go that way + + + align:start position:0% +can't go that way +right + + align:start position:0% + + + + align:start position:0% + +their rewards in this game is +1 in the + + align:start position:0% +their rewards in this game is +1 in the + + + align:start position:0% +their rewards in this game is +1 in the +green box up there and -1 in the box + + align:start position:0% +green box up there and -1 in the box + + + align:start position:0% +green box up there and -1 in the box +here and these are also terminal states + + align:start position:0% +here and these are also terminal states + + + align:start position:0% +here and these are also terminal states +so I haven't told you what that is but + + align:start position:0% +so I haven't told you what that is but + + + align:start position:0% +so I haven't told you what that is but +is essentially a state in which the game + + align:start position:0% +is essentially a state in which the game + + + align:start position:0% +is essentially a state in which the game +ends so once you get to either plus 1 or + + align:start position:0% +ends so once you get to either plus 1 or + + + align:start position:0% +ends so once you get to either plus 1 or +minus 1 the game is over for each step + + align:start position:0% +minus 1 the game is over for each step + + + align:start position:0% +minus 1 the game is over for each step +that the robot takes it incurs 0.04 + + align:start position:0% +that the robot takes it incurs 0.04 + + + align:start position:0% +that the robot takes it incurs 0.04 +negative reward so that says essentially + + align:start position:0% +negative reward so that says essentially + + + align:start position:0% +negative reward so that says essentially +that if you keep going for a long time + + align:start position:0% +that if you keep going for a long time + + + align:start position:0% +that if you keep going for a long time +your reward would be bad your value of + + align:start position:0% +your reward would be bad your value of + + + align:start position:0% +your reward would be bad your value of +the value of the policy will be bad so + + align:start position:0% +the value of the policy will be bad so + + + align:start position:0% +the value of the policy will be bad so +you want to be efficient so basically + + align:start position:0% +you want to be efficient so basically + + + align:start position:0% +you want to be efficient so basically +you can you can figure out you want to + + align:start position:0% +you can you can figure out you want to + + + align:start position:0% +you can you can figure out you want to +get to the green thing that's one part + + align:start position:0% +get to the green thing that's one part + + + align:start position:0% +get to the green thing that's one part +of it but you also want to do it quickly + + align:start position:0% +of it but you also want to do it quickly + + + align:start position:0% +of it but you also want to do it quickly +so what I want you to do now is to + + align:start position:0% +so what I want you to do now is to + + + align:start position:0% +so what I want you to do now is to +essentially figure out what is the best + + align:start position:0% +essentially figure out what is the best + + + align:start position:0% +essentially figure out what is the best +policy + + align:start position:0% +policy + + + align:start position:0% +policy +mm in terms of in which way I should the + + align:start position:0% +mm in terms of in which way I should the + + + align:start position:0% +mm in terms of in which way I should the +arrows point in each of these different + + align:start position:0% +arrows point in each of these different + + + align:start position:0% +arrows point in each of these different +boxes fill in the question mark with an + + align:start position:0% +boxes fill in the question mark with an + + + align:start position:0% +boxes fill in the question mark with an +arrow pointing in some direction we know + + align:start position:0% +arrow pointing in some direction we know + + + align:start position:0% +arrow pointing in some direction we know +that transitions will be stochastic so + + align:start position:0% +that transitions will be stochastic so + + + align:start position:0% +that transitions will be stochastic so +you might need to take that into account + + align:start position:0% +you might need to take that into account + + + align:start position:0% +you might need to take that into account +but essentially figure out how do I have + + align:start position:0% +but essentially figure out how do I have + + + align:start position:0% +but essentially figure out how do I have +a policy that gives me the biggest + + align:start position:0% +a policy that gives me the biggest + + + align:start position:0% +a policy that gives me the biggest +expected reward and I'll ask you in a + + align:start position:0% +expected reward and I'll ask you in a + + + align:start position:0% +expected reward and I'll ask you in a +few minutes if one of you is brave + + align:start position:0% +few minutes if one of you is brave + + + align:start position:0% +few minutes if one of you is brave +enough to put it on the board or + + align:start position:0% +enough to put it on the board or + + + align:start position:0% +enough to put it on the board or +something + + align:start position:0% +something + + + align:start position:0% +something +ok there's no discount + + align:start position:0% + + + + align:start position:0% + +it's accursed so I had a question which + + align:start position:0% +it's accursed so I had a question which + + + align:start position:0% +it's accursed so I had a question which +what is the action space and essentially + + align:start position:0% +what is the action space and essentially + + + align:start position:0% +what is the action space and essentially +the action space is always up down left + + align:start position:0% +the action space is always up down left + + + align:start position:0% +the action space is always up down left +or right depending on if there's a wall + + align:start position:0% +or right depending on if there's a wall + + + align:start position:0% +or right depending on if there's a wall +or not so you can't you can't go right + + align:start position:0% +or not so you can't you can't go right + + + align:start position:0% +or not so you can't you can't go right +here for example you can't go left you + + align:start position:0% +here for example you can't go left you + + + align:start position:0% +here for example you can't go left you +exactly yeah good point so each each box + + align:start position:0% +exactly yeah good point so each each box + + + align:start position:0% +exactly yeah good point so each each box +at the end when you're done should + + align:start position:0% +at the end when you're done should + + + align:start position:0% +at the end when you're done should +contain an arrow pointing in some + + align:start position:0% +contain an arrow pointing in some + + + align:start position:0% +contain an arrow pointing in some +direction all right I think we'll we'll + + align:start position:0% +direction all right I think we'll we'll + + + align:start position:0% +direction all right I think we'll we'll +see if anybody has solved this problem + + align:start position:0% +see if anybody has solved this problem + + + align:start position:0% +see if anybody has solved this problem +now who thinks they have solved it + + align:start position:0% +now who thinks they have solved it + + + align:start position:0% +now who thinks they have solved it +Gretchen would you would you like to + + align:start position:0% +Gretchen would you would you like to + + + align:start position:0% +Gretchen would you would you like to +share your solution yes + + align:start position:0% +share your solution yes + + + align:start position:0% +share your solution yes +yeah sake it's going to go up first okay + + align:start position:0% +yeah sake it's going to go up first okay + + + align:start position:0% +yeah sake it's going to go up first okay +I'm gonna try and look at this oh sorry + + align:start position:0% +I'm gonna try and look at this oh sorry + + + align:start position:0% +I'm gonna try and look at this oh sorry +about that okay you're saying up here + + align:start position:0% +about that okay you're saying up here + + + align:start position:0% +about that okay you're saying up here +yeah okay yes okay okay + + align:start position:0% +yeah okay yes okay okay + + + align:start position:0% +yeah okay yes okay okay +and then okay so what about these ones + + align:start position:0% + + + + align:start position:0% + +this is also part of the policy by the + + align:start position:0% +this is also part of the policy by the + + + align:start position:0% +this is also part of the policy by the +way oh so this usually means something + + align:start position:0% +way oh so this usually means something + + + align:start position:0% +way oh so this usually means something +else we'll get to that later + + align:start position:0% +else we'll get to that later + + + align:start position:0% +else we'll get to that later +but there is a reward for for just + + align:start position:0% +but there is a reward for for just + + + align:start position:0% +but there is a reward for for just +taking any step so it's yeah if you move + + align:start position:0% +taking any step so it's yeah if you move + + + align:start position:0% +taking any step so it's yeah if you move +into a space that is not terminal you + + align:start position:0% +into a space that is not terminal you + + + align:start position:0% +into a space that is not terminal you +incurred that negative reward exactly + + align:start position:0% +incurred that negative reward exactly + + + align:start position:0% +incurred that negative reward exactly +right long- + + align:start position:0% +right long- + + + align:start position:0% +right long- +if we had this there's some chance I'd + + align:start position:0% +if we had this there's some chance I'd + + + align:start position:0% +if we had this there's some chance I'd +never get out about there's very little + + align:start position:0% +never get out about there's very little + + + align:start position:0% +never get out about there's very little +chance of negative gap but it's a very + + align:start position:0% +chance of negative gap but it's a very + + + align:start position:0% +chance of negative gap but it's a very +bad policy because you keep moving back + + align:start position:0% +bad policy because you keep moving back + + + align:start position:0% +bad policy because you keep moving back +and forth alright + + align:start position:0% +and forth alright + + + align:start position:0% +and forth alright +we had an arm somewhere what should I do + + align:start position:0% +we had an arm somewhere what should I do + + + align:start position:0% +we had an arm somewhere what should I do +here huh you could take a vote okay here + + align:start position:0% +here huh you could take a vote okay here + + + align:start position:0% +here huh you could take a vote okay here +things right really everything's left + + align:start position:0% + + + + align:start position:0% + +remember so this is the well good yeah + + align:start position:0% +remember so this is the well good yeah + + + align:start position:0% +remember so this is the well good yeah +so this is the part that we already + + align:start position:0% +so this is the part that we already + + + align:start position:0% +so this is the part that we already +determined if we had deterministic + + align:start position:0% +determined if we had deterministic + + + align:start position:0% +determined if we had deterministic +transitions this would be great okay + + align:start position:0% +transitions this would be great okay + + + align:start position:0% +transitions this would be great okay +because we don't have to think about the + + align:start position:0% +because we don't have to think about the + + + align:start position:0% +because we don't have to think about the +other ones this is what Peter put on the + + align:start position:0% +other ones this is what Peter put on the + + + align:start position:0% +other ones this is what Peter put on the +slide so I'm gonna have to disagree with + + align:start position:0% +slide so I'm gonna have to disagree with + + + align:start position:0% +slide so I'm gonna have to disagree with +the with the vote there actually and it + + align:start position:0% +the with the vote there actually and it + + + align:start position:0% +the with the vote there actually and it +it depends actually heavily on the minus + + align:start position:0% +it depends actually heavily on the minus + + + align:start position:0% +it depends actually heavily on the minus +0.04 so if you increase that by a little + + align:start position:0% +0.04 so if you increase that by a little + + + align:start position:0% +0.04 so if you increase that by a little +bit you might want to go that way + + align:start position:0% +bit you might want to go that way + + + align:start position:0% +bit you might want to go that way +instead or if you decrease it remember + + align:start position:0% +instead or if you decrease it remember + + + align:start position:0% +instead or if you decrease it remember +decrease exactly and if you increase it + + align:start position:0% +decrease exactly and if you increase it + + + align:start position:0% +decrease exactly and if you increase it +you might get something else it might + + align:start position:0% +you might get something else it might + + + align:start position:0% +you might get something else it might +actually be good to terminate so those + + align:start position:0% +actually be good to terminate so those + + + align:start position:0% +actually be good to terminate so those +details matters a little bit but I think + + align:start position:0% +details matters a little bit but I think + + + align:start position:0% +details matters a little bit but I think +you got the + + align:start position:0% +you got the + + + align:start position:0% +you got the +idea and especially I like that you + + align:start position:0% +idea and especially I like that you + + + align:start position:0% +idea and especially I like that you +commented that you want to stay away + + align:start position:0% +commented that you want to stay away + + + align:start position:0% +commented that you want to stay away +from the red one because if you look at + + align:start position:0% +from the red one because if you look at + + + align:start position:0% +from the red one because if you look at +these different paths you go up there + + align:start position:0% +these different paths you go up there + + + align:start position:0% +these different paths you go up there +and there they have the same number of + + align:start position:0% +and there they have the same number of + + + align:start position:0% +and there they have the same number of +states but there's less chance you end + + align:start position:0% +states but there's less chance you end + + + align:start position:0% +states but there's less chance you end +up in the red box if you take the the + + align:start position:0% +up in the red box if you take the the + + + align:start position:0% +up in the red box if you take the the +upper route great so we have an example + + align:start position:0% +upper route great so we have an example + + + align:start position:0% +upper route great so we have an example +of a policy and we have an example of a + + align:start position:0% +of a policy and we have an example of a + + + align:start position:0% +of a policy and we have an example of a +decision process and things are working + + align:start position:0% +decision process and things are working + + + align:start position:0% +decision process and things are working +out so far but how do we do this I mean + + align:start position:0% +out so far but how do we do this I mean + + + align:start position:0% +out so far but how do we do this I mean +as far as the class goes this was a + + align:start position:0% +as far as the class goes this was a + + + align:start position:0% +as far as the class goes this was a +black box experiment I don't know + + align:start position:0% +black box experiment I don't know + + + align:start position:0% +black box experiment I don't know +anything about how you figured that out + + align:start position:0% +anything about how you figured that out + + + align:start position:0% +anything about how you figured that out +so reinforcement learning is about that + + align:start position:0% +so reinforcement learning is about that + + + align:start position:0% +so reinforcement learning is about that +music enforcement learning is to try and + + align:start position:0% +music enforcement learning is to try and + + + align:start position:0% +music enforcement learning is to try and +come up with a policy in a sort of + + align:start position:0% +come up with a policy in a sort of + + + align:start position:0% +come up with a policy in a sort of +rigorous way hopefully ideally so that + + align:start position:0% +rigorous way hopefully ideally so that + + + align:start position:0% +rigorous way hopefully ideally so that +would be the next topic here up until + + align:start position:0% +would be the next topic here up until + + + align:start position:0% +would be the next topic here up until +this point are any questions study + + align:start position:0% +this point are any questions study + + + align:start position:0% +this point are any questions study +you've been dying to ask but haven't + + align:start position:0% + + + + align:start position:0% + +interesting I guess it depends a little + + align:start position:0% +interesting I guess it depends a little + + + align:start position:0% +interesting I guess it depends a little +bit on how it manifests in that if it + + align:start position:0% +bit on how it manifests in that if it + + + align:start position:0% +bit on how it manifests in that if it +also influenced your previous like your + + align:start position:0% +also influenced your previous like your + + + align:start position:0% +also influenced your previous like your +most recent action maybe you'll you have + + align:start position:0% +most recent action maybe you'll you have + + + align:start position:0% +most recent action maybe you'll you have +an observation of that already in some + + align:start position:0% +an observation of that already in some + + + align:start position:0% +an observation of that already in some +sense it will it's a very broad question + + align:start position:0% +sense it will it's a very broad question + + + align:start position:0% +sense it will it's a very broad question +how do what effect will they have did + + align:start position:0% +how do what effect will they have did + + + align:start position:0% +how do what effect will they have did +you have something specific in mind + + align:start position:0% + + + + align:start position:0% + +interesting + + align:start position:0% +interesting + + + align:start position:0% +interesting +so I guess my response there is that the + + align:start position:0% +so I guess my response there is that the + + + align:start position:0% +so I guess my response there is that the +the the the action didn't really depend + + align:start position:0% +the the the action didn't really depend + + + align:start position:0% +the the the action didn't really depend +on the choice of action before because + + align:start position:0% +on the choice of action before because + + + align:start position:0% +on the choice of action before because +the policy remained the same you can + + align:start position:0% +the policy remained the same you can + + + align:start position:0% +the policy remained the same you can +have it you could have a bias towards an + + align:start position:0% +have it you could have a bias towards an + + + align:start position:0% +have it you could have a bias towards an +action without that being dependent on + + align:start position:0% +action without that being dependent on + + + align:start position:0% +action without that being dependent on +what you gave as action before if you + + align:start position:0% +what you gave as action before if you + + + align:start position:0% +what you gave as action before if you +know what I mean say that it's a my + + align:start position:0% +know what I mean say that it's a my + + + align:start position:0% +know what I mean say that it's a my +probability of giving action one is one + + align:start position:0% +probability of giving action one is one + + + align:start position:0% +probability of giving action one is one +then it doesn't matter that I gave it in + + align:start position:0% +then it doesn't matter that I gave it in + + + align:start position:0% +then it doesn't matter that I gave it in +the past but policy is still the same so + + align:start position:0% +the past but policy is still the same so + + + align:start position:0% +the past but policy is still the same so +not necessarily it could have other + + align:start position:0% +not necessarily it could have other + + + align:start position:0% +not necessarily it could have other +consequences that we we might we have + + align:start position:0% +consequences that we we might we have + + + align:start position:0% +consequences that we we might we have +reason to come back to that question + + align:start position:0% +reason to come back to that question + + + align:start position:0% +reason to come back to that question +later yeah yep + + align:start position:0% +later yeah yep + + + align:start position:0% +later yeah yep +practically I would think that a doctor + + align:start position:0% +practically I would think that a doctor + + + align:start position:0% +practically I would think that a doctor +would want to be consistent and so you + + align:start position:0% +would want to be consistent and so you + + + align:start position:0% +would want to be consistent and so you +wouldn't for example want to put + + align:start position:0% +wouldn't for example want to put + + + align:start position:0% +wouldn't for example want to put +somebody on a ventilator and completely + + align:start position:0% +somebody on a ventilator and completely + + + align:start position:0% +somebody on a ventilator and completely +yeah I think it's a great example and + + align:start position:0% +yeah I think it's a great example and + + + align:start position:0% +yeah I think it's a great example and +what what you would hope is that the the + + align:start position:0% +what what you would hope is that the the + + + align:start position:0% +what what you would hope is that the the +state variable in that case includes + + align:start position:0% +state variable in that case includes + + + align:start position:0% +state variable in that case includes +some notion of treatment history but + + align:start position:0% +some notion of treatment history but + + + align:start position:0% +some notion of treatment history but +that's what you what's your job is then + + align:start position:0% +that's what you what's your job is then + + + align:start position:0% +that's what you what's your job is then +yeah so that's why state can be somewhat + + align:start position:0% +yeah so that's why state can be somewhat + + + align:start position:0% +yeah so that's why state can be somewhat +misleading as a term at least for me I + + align:start position:0% +misleading as a term at least for me I + + + align:start position:0% +misleading as a term at least for me I +don't know I'm not American so or + + align:start position:0% +don't know I'm not American so or + + + align:start position:0% +don't know I'm not American so or +english-speaking but but but but yeah I + + align:start position:0% +english-speaking but but but but yeah I + + + align:start position:0% +english-speaking but but but but yeah I +think of it as two instantaneous + + align:start position:0% +think of it as two instantaneous + + + align:start position:0% +think of it as two instantaneous +sometimes so we'll move into + + align:start position:0% +sometimes so we'll move into + + + align:start position:0% +sometimes so we'll move into +reinforcement learning now and what I + + align:start position:0% +reinforcement learning now and what I + + + align:start position:0% +reinforcement learning now and what I +had you do on the last slide well I + + align:start position:0% +had you do on the last slide well I + + + align:start position:0% +had you do on the last slide well I +don't know which method you use but most + + align:start position:0% +don't know which method you use but most + + + align:start position:0% +don't know which method you use but most +likely the middle one there are three + + align:start position:0% +likely the middle one there are three + + + align:start position:0% +likely the middle one there are three +very common paradigms for reinforcement + + align:start position:0% +very common paradigms for reinforcement + + + align:start position:0% +very common paradigms for reinforcement +learning and they are essentially + + align:start position:0% +learning and they are essentially + + + align:start position:0% +learning and they are essentially +divided by what they focus on modeling + + align:start position:0% +divided by what they focus on modeling + + + align:start position:0% +divided by what they focus on modeling +unsurprisingly model based RL focused on + + align:start position:0% +unsurprisingly model based RL focused on + + + align:start position:0% +unsurprisingly model based RL focused on +well it has some sort of model in it at + + align:start position:0% +well it has some sort of model in it at + + + align:start position:0% +well it has some sort of model in it at +least and the model that they did what + + align:start position:0% +least and the model that they did what + + + align:start position:0% +least and the model that they did what +do you mean by model in this case is a + + align:start position:0% +do you mean by model in this case is a + + + align:start position:0% +do you mean by model in this case is a +model of the transitions so what state + + align:start position:0% +model of the transitions so what state + + + align:start position:0% +model of the transitions so what state +will I end up in given the action in the + + align:start position:0% +will I end up in given the action in the + + + align:start position:0% +will I end up in given the action in the +state I'm in at the moment so model + + align:start position:0% +state I'm in at the moment so model + + + align:start position:0% +state I'm in at the moment so model +based RL tries to essentially create a + + align:start position:0% +based RL tries to essentially create a + + + align:start position:0% +based RL tries to essentially create a +model for the environment or of the + + align:start position:0% +model for the environment or of the + + + align:start position:0% +model for the environment or of the +environment and there are many well + + align:start position:0% +environment and there are many well + + + align:start position:0% +environment and there are many well +there are several examples of model + + align:start position:0% +there are several examples of model + + + align:start position:0% +there are several examples of model +based RL one of them is G computation + + align:start position:0% +based RL one of them is G computation + + + align:start position:0% +based RL one of them is G computation +which comes out of the statistic + + align:start position:0% +which comes out of the statistic + + + align:start position:0% +which comes out of the statistic +literature if you like an MD piece or + + align:start position:0% +literature if you like an MD piece or + + + align:start position:0% +literature if you like an MD piece or +essentially that's the MD piece that's + + align:start position:0% +essentially that's the MD piece that's + + + align:start position:0% +essentially that's the MD piece that's +remarkable decision process which is + + align:start position:0% +remarkable decision process which is + + + align:start position:0% +remarkable decision process which is +essentially trying to estimate the whole + + align:start position:0% +essentially trying to estimate the whole + + + align:start position:0% +essentially trying to estimate the whole +distribution that we talked about before + + align:start position:0% +distribution that we talked about before + + + align:start position:0% +distribution that we talked about before +the there are various ups and downsides + + align:start position:0% +the there are various ups and downsides + + + align:start position:0% +the there are various ups and downsides +of this we won't have time to go into + + align:start position:0% +of this we won't have time to go into + + + align:start position:0% +of this we won't have time to go into +all of these paradigms today we will + + align:start position:0% +all of these paradigms today we will + + + align:start position:0% +all of these paradigms today we will +actually focus only on value-based RL + + align:start position:0% +actually focus only on value-based RL + + + align:start position:0% +actually focus only on value-based RL +today but yeah you can ask me offline if + + align:start position:0% +today but yeah you can ask me offline if + + + align:start position:0% +today but yeah you can ask me offline if +you're interested in model-based RL the + + align:start position:0% +you're interested in model-based RL the + + + align:start position:0% +you're interested in model-based RL the +rightmost one here is policy based RL + + align:start position:0% +rightmost one here is policy based RL + + + align:start position:0% +rightmost one here is policy based RL +where you essentially focus only on + + align:start position:0% +where you essentially focus only on + + + align:start position:0% +where you essentially focus only on +modeling the policy that the was acted + + align:start position:0% +modeling the policy that the was acted + + + align:start position:0% +modeling the policy that the was acted +or you act + + align:start position:0% +or you act + + + align:start position:0% +or you act +that was used in the data that you + + align:start position:0% +that was used in the data that you + + + align:start position:0% +that was used in the data that you +observed and the policy that your that + + align:start position:0% +observed and the policy that your that + + + align:start position:0% +observed and the policy that your that +you want to essentially arrive at so + + align:start position:0% +you want to essentially arrive at so + + + align:start position:0% +you want to essentially arrive at so +you're optimizing a policy and you're + + align:start position:0% +you're optimizing a policy and you're + + + align:start position:0% +you're optimizing a policy and you're +estimating a policy that was used in the + + align:start position:0% +estimating a policy that was used in the + + + align:start position:0% +estimating a policy that was used in the +past and the metal one focuses on either + + align:start position:0% +past and the metal one focuses on either + + + align:start position:0% +past and the metal one focuses on either +of those and focus on only estimating + + align:start position:0% +of those and focus on only estimating + + + align:start position:0% +of those and focus on only estimating +the return that was the G or the the + + align:start position:0% +the return that was the G or the the + + + align:start position:0% +the return that was the G or the the +reward function as a function of your + + align:start position:0% +reward function as a function of your + + + align:start position:0% +reward function as a function of your +actions and States and it's kind of + + align:start position:0% +actions and States and it's kind of + + + align:start position:0% +actions and States and it's kind of +interesting to me that you can kind of + + align:start position:0% +interesting to me that you can kind of + + + align:start position:0% +interesting to me that you can kind of +pick any of the variables a s and R and + + align:start position:0% +pick any of the variables a s and R and + + + align:start position:0% +pick any of the variables a s and R and +model those and you can arrive at + + align:start position:0% +model those and you can arrive at + + + align:start position:0% +model those and you can arrive at +something reasonable in reinforcement + + align:start position:0% +something reasonable in reinforcement + + + align:start position:0% +something reasonable in reinforcement +learning this one is particularly + + align:start position:0% +learning this one is particularly + + + align:start position:0% +learning this one is particularly +interesting because it doesn't even look + + align:start position:0% +interesting because it doesn't even look + + + align:start position:0% +interesting because it doesn't even look +at yeah it doesn't try to understand how + + align:start position:0% +at yeah it doesn't try to understand how + + + align:start position:0% +at yeah it doesn't try to understand how +do you arrive at a certain return based + + align:start position:0% +do you arrive at a certain return based + + + align:start position:0% +do you arrive at a certain return based +on the actions in the States is just + + align:start position:0% +on the actions in the States is just + + + align:start position:0% +on the actions in the States is just +optimize the policy directly and it has + + align:start position:0% +optimize the policy directly and it has + + + align:start position:0% +optimize the policy directly and it has +some obvious well not obvious but it has + + align:start position:0% +some obvious well not obvious but it has + + + align:start position:0% +some obvious well not obvious but it has +some downsides not doing that so okay + + align:start position:0% +some downsides not doing that so okay + + + align:start position:0% +some downsides not doing that so okay +anyway we're going to focus on value + + align:start position:0% +anyway we're going to focus on value + + + align:start position:0% +anyway we're going to focus on value +base RL and the very very dominant + + align:start position:0% +base RL and the very very dominant + + + align:start position:0% +base RL and the very very dominant +instantiation of value base RL is + + align:start position:0% +instantiation of value base RL is + + + align:start position:0% +instantiation of value base RL is +q-learning I'm sure you've heard of it + + align:start position:0% +q-learning I'm sure you've heard of it + + + align:start position:0% +q-learning I'm sure you've heard of it +it was a drill it is what drove the + + align:start position:0% +it was a drill it is what drove the + + + align:start position:0% +it was a drill it is what drove the +success stories that I showed before the + + align:start position:0% +success stories that I showed before the + + + align:start position:0% +success stories that I showed before the +the goal and the Starcraft and + + align:start position:0% +the goal and the Starcraft and + + + align:start position:0% +the goal and the Starcraft and +everything G estimation is another + + align:start position:0% +everything G estimation is another + + + align:start position:0% +everything G estimation is another +example of this which again is coming + + align:start position:0% +example of this which again is coming + + + align:start position:0% +example of this which again is coming +from the statistic literature but we'll + + align:start position:0% +from the statistic literature but we'll + + + align:start position:0% +from the statistic literature but we'll +focus on q-learning today so Q learning + + align:start position:0% +focus on q-learning today so Q learning + + + align:start position:0% +focus on q-learning today so Q learning +is an example of dynamic programming in + + align:start position:0% +is an example of dynamic programming in + + + align:start position:0% +is an example of dynamic programming in +some sense that's how it's usually + + align:start position:0% +some sense that's how it's usually + + + align:start position:0% +some sense that's how it's usually +explained and I just wanted to check how + + align:start position:0% +explained and I just wanted to check how + + + align:start position:0% +explained and I just wanted to check how +many I've heard the phrase dynamic + + align:start position:0% +many I've heard the phrase dynamic + + + align:start position:0% +many I've heard the phrase dynamic +programming before okay great so I think + + align:start position:0% +programming before okay great so I think + + + align:start position:0% +programming before okay great so I think +that I won't go into details of dynamic + + align:start position:0% +that I won't go into details of dynamic + + + align:start position:0% +that I won't go into details of dynamic +program in general but the general idea + + align:start position:0% +program in general but the general idea + + + align:start position:0% +program in general but the general idea +is is one of recursion that you in in + + align:start position:0% +is is one of recursion that you in in + + + align:start position:0% +is is one of recursion that you in in +this case you know something about what + + align:start position:0% +this case you know something about what + + + align:start position:0% +this case you know something about what +is what is a good terminal state and + + align:start position:0% +is what is a good terminal state and + + + align:start position:0% +is what is a good terminal state and +then you want to figure out how to get + + align:start position:0% +then you want to figure out how to get + + + align:start position:0% +then you want to figure out how to get +there and what how to get to the state + + align:start position:0% +there and what how to get to the state + + + align:start position:0% +there and what how to get to the state +before that and the state before that + + align:start position:0% +before that and the state before that + + + align:start position:0% +before that and the state before that +and so on that is the recursion that we + + align:start position:0% +and so on that is the recursion that we + + + align:start position:0% +and so on that is the recursion that we +will be talking about so and inst with + + align:start position:0% +will be talking about so and inst with + + + align:start position:0% +will be talking about so and inst with +the end state that is the best here it's + + align:start position:0% +the end state that is the best here it's + + + align:start position:0% +the end state that is the best here it's +fairly obvious that it's the plus one + + align:start position:0% +fairly obvious that it's the plus one + + + align:start position:0% +fairly obvious that it's the plus one +here and the best way or the only way to + + align:start position:0% +here and the best way or the only way to + + + align:start position:0% +here and the best way or the only way to +get there is by by stopping here first + + align:start position:0% +get there is by by stopping here first + + + align:start position:0% +get there is by by stopping here first +because you can't move from here since + + align:start position:0% +because you can't move from here since + + + align:start position:0% +because you can't move from here since +it's a terminal State so your only your + + align:start position:0% +it's a terminal State so your only your + + + align:start position:0% +it's a terminal State so your only your +only bet is that one and then we can ask + + align:start position:0% +only bet is that one and then we can ask + + + align:start position:0% +only bet is that one and then we can ask +what is the best way to get to three one + + align:start position:0% +what is the best way to get to three one + + + align:start position:0% +what is the best way to get to three one +how do we get to the state before the + + align:start position:0% +how do we get to the state before the + + + align:start position:0% +how do we get to the state before the +best date well we can say that + + align:start position:0% +best date well we can say that + + + align:start position:0% +best date well we can say that +one way is to get from go from here and + + align:start position:0% +one way is to get from go from here and + + + align:start position:0% +one way is to get from go from here and +one way from here and as we got from the + + align:start position:0% +one way from here and as we got from the + + + align:start position:0% +one way from here and as we got from the +audience before this is a slightly worse + + align:start position:0% +audience before this is a slightly worse + + + align:start position:0% +audience before this is a slightly worse +way to get there than from there because + + align:start position:0% +way to get there than from there because + + + align:start position:0% +way to get there than from there because +here we have an possibility of ending up + + align:start position:0% +here we have an possibility of ending up + + + align:start position:0% +here we have an possibility of ending up +in minus one so then we recurse further + + align:start position:0% +in minus one so then we recurse further + + + align:start position:0% +in minus one so then we recurse further +and essentially we end up with something + + align:start position:0% +and essentially we end up with something + + + align:start position:0% +and essentially we end up with something +like this that says like the try to + + align:start position:0% +like this that says like the try to + + + align:start position:0% +like this that says like the try to +illustrate here is that the green boxes + + align:start position:0% +illustrate here is that the green boxes + + + align:start position:0% +illustrate here is that the green boxes +hope you can I'm sorry for any + + align:start position:0% +hope you can I'm sorry for any + + + align:start position:0% +hope you can I'm sorry for any +colorblind members of the audience + + align:start position:0% +colorblind members of the audience + + + align:start position:0% +colorblind members of the audience +because this was a poor choice of mine + + align:start position:0% +because this was a poor choice of mine + + + align:start position:0% +because this was a poor choice of mine +anyway this bottom side here is mostly + + align:start position:0% +anyway this bottom side here is mostly + + + align:start position:0% +anyway this bottom side here is mostly +red and this is mostly green and you can + + align:start position:0% +red and this is mostly green and you can + + + align:start position:0% +red and this is mostly green and you can +follow the green color here essentially + + align:start position:0% +follow the green color here essentially + + + align:start position:0% +follow the green color here essentially +to get to the best end state and what I + + align:start position:0% +to get to the best end state and what I + + + align:start position:0% +to get to the best end state and what I +used here too to color this in is this + + align:start position:0% +used here too to color this in is this + + + align:start position:0% +used here too to color this in is this +idea of knowing how good is status + + align:start position:0% +idea of knowing how good is status + + + align:start position:0% +idea of knowing how good is status +depending on how good the state after + + align:start position:0% +depending on how good the state after + + + align:start position:0% +depending on how good the state after +that status so I knew that +1 is a good + + align:start position:0% +that status so I knew that +1 is a good + + + align:start position:0% +that status so I knew that +1 is a good +end State over there and that led me to + + align:start position:0% +end State over there and that led me to + + + align:start position:0% +end State over there and that led me to +to recurse backwards essentially so the + + align:start position:0% +to recurse backwards essentially so the + + + align:start position:0% +to recurse backwards essentially so the +question then is how do we get how do we + + align:start position:0% +question then is how do we get how do we + + + align:start position:0% +question then is how do we get how do we +know that that state over there is a + + align:start position:0% +know that that state over there is a + + + align:start position:0% +know that that state over there is a +good one + + align:start position:0% +good one + + + align:start position:0% +good one +when we have it visualized in front of + + align:start position:0% +when we have it visualized in front of + + + align:start position:0% +when we have it visualized in front of +us it's very easy to see and it's very + + align:start position:0% +us it's very easy to see and it's very + + + align:start position:0% +us it's very easy to see and it's very +easy because we know that +1 is a + + align:start position:0% +easy because we know that +1 is a + + + align:start position:0% +easy because we know that +1 is a +terminal state here it ends there so + + align:start position:0% +terminal state here it ends there so + + + align:start position:0% +terminal state here it ends there so +that's the only those are the only sort + + align:start position:0% +that's the only those are the only sort + + + align:start position:0% +that's the only those are the only sort +of states we need to consider in this + + align:start position:0% +of states we need to consider in this + + + align:start position:0% +of states we need to consider in this +case but more in general how do we learn + + align:start position:0% +case but more in general how do we learn + + + align:start position:0% +case but more in general how do we learn +what is the value of a state that will + + align:start position:0% +what is the value of a state that will + + + align:start position:0% +what is the value of a state that will +be the purpose of Q learning ok after if + + align:start position:0% +be the purpose of Q learning ok after if + + + align:start position:0% +be the purpose of Q learning ok after if +we have an idea of what is a good state + + align:start position:0% +we have an idea of what is a good state + + + align:start position:0% +we have an idea of what is a good state +we can always sort of do that recursion + + align:start position:0% +we can always sort of do that recursion + + + align:start position:0% +we can always sort of do that recursion +that I explained very briefly you find a + + align:start position:0% +that I explained very briefly you find a + + + align:start position:0% +that I explained very briefly you find a +state that has two high value and you + + align:start position:0% +state that has two high value and you + + + align:start position:0% +state that has two high value and you +figure out how to get there ok so we're + + align:start position:0% +figure out how to get there ok so we're + + + align:start position:0% +figure out how to get there ok so we're +going to have to define now what is what + + align:start position:0% +going to have to define now what is what + + + align:start position:0% +going to have to define now what is what +I mean by value I've used that word a + + align:start position:0% +I mean by value I've used that word a + + + align:start position:0% +I mean by value I've used that word a +few different times I say recall here + + align:start position:0% +few different times I say recall here + + + align:start position:0% +few different times I say recall here +but I don't know if I actually had it on + + align:start position:0% +but I don't know if I actually had it on + + + align:start position:0% +but I don't know if I actually had it on +a slide before so let's just say this is + + align:start position:0% +a slide before so let's just say this is + + + align:start position:0% +a slide before so let's just say this is +the definition of value that we will be + + align:start position:0% +the definition of value that we will be + + + align:start position:0% +the definition of value that we will be +working with so the value is I think I + + align:start position:0% +working with so the value is I think I + + + align:start position:0% +working with so the value is I think I +had it looks like before actually this + + align:start position:0% +had it looks like before actually this + + + align:start position:0% +had it looks like before actually this +is the expected return remember this G + + align:start position:0% +is the expected return remember this G + + + align:start position:0% +is the expected return remember this G +here was the sum of rewards going into + + align:start position:0% +here was the sum of rewards going into + + + align:start position:0% +here was the sum of rewards going into +the future starting at time T + + align:start position:0% +the future starting at time T + + + align:start position:0% +the future starting at time T +and the value then of this state is the + + align:start position:0% +and the value then of this state is the + + + align:start position:0% +and the value then of this state is the +expectation of such returns so before I + + align:start position:0% +expectation of such returns so before I + + + align:start position:0% +expectation of such returns so before I +said that the value of a policy was the + + align:start position:0% +said that the value of a policy was the + + + align:start position:0% +said that the value of a policy was the +expectation of returns period and the + + align:start position:0% +expectation of returns period and the + + + align:start position:0% +expectation of returns period and the +value the value of a States and the + + align:start position:0% +value the value of a States and the + + + align:start position:0% +value the value of a States and the +policy is the value of such returns + + align:start position:0% +policy is the value of such returns + + + align:start position:0% +policy is the value of such returns +starting in a certain state we can + + align:start position:0% +starting in a certain state we can + + + align:start position:0% +starting in a certain state we can +stratify this further if you like and + + align:start position:0% +stratify this further if you like and + + + align:start position:0% +stratify this further if you like and +say that the value of a state action + + align:start position:0% +say that the value of a state action + + + align:start position:0% +say that the value of a state action +pair is the expected return starting in + + align:start position:0% +pair is the expected return starting in + + + align:start position:0% +pair is the expected return starting in +a certain state and taking an action a + + align:start position:0% +a certain state and taking an action a + + + align:start position:0% +a certain state and taking an action a +and after that following the policy PI + + align:start position:0% +and after that following the policy PI + + + align:start position:0% +and after that following the policy PI +this would be the the sort of this + + align:start position:0% +this would be the the sort of this + + + align:start position:0% +this would be the the sort of this +circle Q value of the state action pair + + align:start position:0% +circle Q value of the state action pair + + + align:start position:0% +circle Q value of the state action pair +s a okay and this is where Q learning + + align:start position:0% +s a okay and this is where Q learning + + + align:start position:0% +s a okay and this is where Q learning +gets its name so Q learning attempts to + + align:start position:0% +gets its name so Q learning attempts to + + + align:start position:0% +gets its name so Q learning attempts to +estimate the Q function the expected + + align:start position:0% +estimate the Q function the expected + + + align:start position:0% +estimate the Q function the expected +return starting in a state s and taking + + align:start position:0% +return starting in a state s and taking + + + align:start position:0% +return starting in a state s and taking +action a from data and it does so the Q + + align:start position:0% +action a from data and it does so the Q + + + align:start position:0% +action a from data and it does so the Q +learning is also associated with a + + align:start position:0% +learning is also associated with a + + + align:start position:0% +learning is also associated with a +deterministic policy so the policy and + + align:start position:0% +deterministic policy so the policy and + + + align:start position:0% +deterministic policy so the policy and +the Q function go together in this + + align:start position:0% +the Q function go together in this + + + align:start position:0% +the Q function go together in this +specific way if we have a Q function Q + + align:start position:0% +specific way if we have a Q function Q + + + align:start position:0% +specific way if we have a Q function Q +that tries to estimate the value of a + + align:start position:0% +that tries to estimate the value of a + + + align:start position:0% +that tries to estimate the value of a +policy pie the pie itself is the arc max + + align:start position:0% +policy pie the pie itself is the arc max + + + align:start position:0% +policy pie the pie itself is the arc max +according to that Q it sounds a little + + align:start position:0% +according to that Q it sounds a little + + + align:start position:0% +according to that Q it sounds a little +recursive but hopefully it will be okay + + align:start position:0% +recursive but hopefully it will be okay + + + align:start position:0% +recursive but hopefully it will be okay +it may be it's more obviously if we look + + align:start position:0% +it may be it's more obviously if we look + + + align:start position:0% +it may be it's more obviously if we look +here so Q I said before what's the value + + align:start position:0% +here so Q I said before what's the value + + + align:start position:0% +here so Q I said before what's the value +of starting and s taking action a and + + align:start position:0% +of starting and s taking action a and + + + align:start position:0% +of starting and s taking action a and +then following policy PI okay this is + + align:start position:0% +then following policy PI okay this is + + + align:start position:0% +then following policy PI okay this is +defined by the the the the decision + + align:start position:0% +defined by the the the the decision + + + align:start position:0% +defined by the the the the decision +process itself the best PI the best + + align:start position:0% +process itself the best PI the best + + + align:start position:0% +process itself the best PI the best +policy is the one that has the highest Q + + align:start position:0% +policy is the one that has the highest Q + + + align:start position:0% +policy is the one that has the highest Q +and this is what we call a Q star okay + + align:start position:0% +and this is what we call a Q star okay + + + align:start position:0% +and this is what we call a Q star okay +this is it well that it's not what we + + align:start position:0% +this is it well that it's not what we + + + align:start position:0% +this is it well that it's not what we +call Q so this will cook little Q star Q + + align:start position:0% +call Q so this will cook little Q star Q + + + align:start position:0% +call Q so this will cook little Q star Q +star the best estimate of this is + + align:start position:0% +star the best estimate of this is + + + align:start position:0% +star the best estimate of this is +obviously the thing itself so if you can + + align:start position:0% +obviously the thing itself so if you can + + + align:start position:0% +obviously the thing itself so if you can +find a good function that assigns a + + align:start position:0% +find a good function that assigns a + + + align:start position:0% +find a good function that assigns a +value to a state action pair the best + + align:start position:0% +value to a state action pair the best + + + align:start position:0% +value to a state action pair the best +such function you can get is the one + + align:start position:0% +such function you can get is the one + + + align:start position:0% +such function you can get is the one +that has that is equal to a little Q + + align:start position:0% +that has that is equal to a little Q + + + align:start position:0% +that has that is equal to a little Q +star I hope that wasn't too confusing + + align:start position:0% +star I hope that wasn't too confusing + + + align:start position:0% +star I hope that wasn't too confusing +I'll show on the next slide right that + + align:start position:0% +I'll show on the next slide right that + + + align:start position:0% +I'll show on the next slide right that +might be reasonable + + align:start position:0% +might be reasonable + + + align:start position:0% +might be reasonable +so cue learning is based on a general + + align:start position:0% +so cue learning is based on a general + + + align:start position:0% +so cue learning is based on a general +idea from dynamic programming which is + + align:start position:0% +idea from dynamic programming which is + + + align:start position:0% +idea from dynamic programming which is +the so-called bellman equation there we + + align:start position:0% +the so-called bellman equation there we + + + align:start position:0% +the so-called bellman equation there we +go so bellman optimality says that if + + align:start position:0% +go so bellman optimality says that if + + + align:start position:0% +go so bellman optimality says that if +this is an association of bellman + + align:start position:0% +this is an association of bellman + + + align:start position:0% +this is an association of bellman +optimality which says that the the best + + align:start position:0% +optimality which says that the the best + + + align:start position:0% +optimality which says that the the best +the Q star the best state action value + + align:start position:0% +the Q star the best state action value + + + align:start position:0% +the Q star the best state action value +function has the property that it is + + align:start position:0% +function has the property that it is + + + align:start position:0% +function has the property that it is +equal to the immediate reward of taking + + align:start position:0% +equal to the immediate reward of taking + + + align:start position:0% +equal to the immediate reward of taking +action and state s plus this which is + + align:start position:0% +action and state s plus this which is + + + align:start position:0% +action and state s plus this which is +the maximum Q value for the next state + + align:start position:0% +the maximum Q value for the next state + + + align:start position:0% +the maximum Q value for the next state +so we're going to stare at this for a + + align:start position:0% +so we're going to stare at this for a + + + align:start position:0% +so we're going to stare at this for a +bit because it's something to digest + + align:start position:0% +bit because it's something to digest + + + align:start position:0% +bit because it's something to digest +that I think little bit here to digest + + align:start position:0% +that I think little bit here to digest + + + align:start position:0% +that I think little bit here to digest +remember Q star assigns the value to any + + align:start position:0% +remember Q star assigns the value to any + + + align:start position:0% +remember Q star assigns the value to any +state action pair so we have Q star here + + align:start position:0% +state action pair so we have Q star here + + + align:start position:0% +state action pair so we have Q star here +we have Q star here this thing here is + + align:start position:0% +we have Q star here this thing here is + + + align:start position:0% +we have Q star here this thing here is +supposed to represent the value going + + align:start position:0% +supposed to represent the value going + + + align:start position:0% +supposed to represent the value going +forward in time after I've made this + + align:start position:0% +forward in time after I've made this + + + align:start position:0% +forward in time after I've made this +choice action a in state s so if I have + + align:start position:0% +choice action a in state s so if I have + + + align:start position:0% +choice action a in state s so if I have +a good idea of how good it is to take + + align:start position:0% +a good idea of how good it is to take + + + align:start position:0% +a good idea of how good it is to take +action in state s it should both + + align:start position:0% +action in state s it should both + + + align:start position:0% +action in state s it should both +incorporate the immediate rewards that I + + align:start position:0% +incorporate the immediate rewards that I + + + align:start position:0% +incorporate the immediate rewards that I +guess that's our T and how good that + + align:start position:0% +guess that's our T and how good that + + + align:start position:0% +guess that's our T and how good that +choice was going forward so think about + + align:start position:0% +choice was going forward so think about + + + align:start position:0% +choice was going forward so think about +mechanical ventilation as I said before + + align:start position:0% +mechanical ventilation as I said before + + + align:start position:0% +mechanical ventilation as I said before +if we put a patient on mechanical + + align:start position:0% +if we put a patient on mechanical + + + align:start position:0% +if we put a patient on mechanical +ventilation we have to do a bunch of + + align:start position:0% +ventilation we have to do a bunch of + + + align:start position:0% +ventilation we have to do a bunch of +other things after that if none of those + + align:start position:0% +other things after that if none of those + + + align:start position:0% +other things after that if none of those +other things lead to a good outcome this + + align:start position:0% +other things lead to a good outcome this + + + align:start position:0% +other things lead to a good outcome this +part will be low even if the immediate + + align:start position:0% +part will be low even if the immediate + + + align:start position:0% +part will be low even if the immediate +return is good so for the optimal Q star + + align:start position:0% +return is good so for the optimal Q star + + + align:start position:0% +return is good so for the optimal Q star +this this quantity wholes we know that + + align:start position:0% +this this quantity wholes we know that + + + align:start position:0% +this this quantity wholes we know that +we can prove that okay + + align:start position:0% +we can prove that okay + + + align:start position:0% +we can prove that okay +so the question is how do we find this + + align:start position:0% +so the question is how do we find this + + + align:start position:0% +so the question is how do we find this +thing how we find Q star because Q star + + align:start position:0% +thing how we find Q star because Q star + + + align:start position:0% +thing how we find Q star because Q star +is not only the thing that gives you the + + align:start position:0% +is not only the thing that gives you the + + + align:start position:0% +is not only the thing that gives you the +optimal policy + + align:start position:0% +optimal policy + + + align:start position:0% +optimal policy +it also satisfied this equality this is + + align:start position:0% +it also satisfied this equality this is + + + align:start position:0% +it also satisfied this equality this is +not true for every Q function but it's + + align:start position:0% +not true for every Q function but it's + + + align:start position:0% +not true for every Q function but it's +true for the optimal one questions this + + align:start position:0% +true for the optimal one questions this + + + align:start position:0% +true for the optimal one questions this +is uh yeah if you haven't seen this + + align:start position:0% +is uh yeah if you haven't seen this + + + align:start position:0% +is uh yeah if you haven't seen this +before it might be a little tough to + + align:start position:0% +before it might be a little tough to + + + align:start position:0% +before it might be a little tough to +digest it's the notation clear + + align:start position:0% +digest it's the notation clear + + + align:start position:0% +digest it's the notation clear +essentially here you have the the state + + align:start position:0% +essentially here you have the the state + + + align:start position:0% +essentially here you have the the state +that you arriving at the next time a + + align:start position:0% +that you arriving at the next time a + + + align:start position:0% +that you arriving at the next time a +prime is the parameter of this here or + + align:start position:0% +prime is the parameter of this here or + + + align:start position:0% +prime is the parameter of this here or +the argument to this you're taking the + + align:start position:0% +the argument to this you're taking the + + + align:start position:0% +the argument to this you're taking the +best possible Q + + align:start position:0% +best possible Q + + + align:start position:0% +best possible Q +star value in the state that you arrived + + align:start position:0% +star value in the state that you arrived + + + align:start position:0% +star value in the state that you arrived +at after yeah good example you have in + + align:start position:0% +at after yeah good example you have in + + + align:start position:0% +at after yeah good example you have in +the board yes + + align:start position:0% +the board yes + + + align:start position:0% +the board yes +actually I might do a full example of Q + + align:start position:0% +actually I might do a full example of Q + + + align:start position:0% +actually I might do a full example of Q +learning in a second yes I will I'll get + + align:start position:0% +learning in a second yes I will I'll get + + + align:start position:0% +learning in a second yes I will I'll get +to that a gentleman okay + + align:start position:0% + + + + align:start position:0% + +yeah I was debating where the do they + + align:start position:0% +yeah I was debating where the do they + + + align:start position:0% +yeah I was debating where the do they +might take some time but it could be + + align:start position:0% +might take some time but it could be + + + align:start position:0% +might take some time but it could be +useful so where are we + + align:start position:0% +useful so where are we + + + align:start position:0% +useful so where are we +yes okay so what I showed you before the + + align:start position:0% +yes okay so what I showed you before the + + + align:start position:0% +yes okay so what I showed you before the +bellman inequality we know that this + + align:start position:0% +bellman inequality we know that this + + + align:start position:0% +bellman inequality we know that this +holds for the optimal thing and if + + align:start position:0% +holds for the optimal thing and if + + + align:start position:0% +holds for the optimal thing and if +there's a equality that is true at an + + align:start position:0% +there's a equality that is true at an + + + align:start position:0% +there's a equality that is true at an +optimum one general idea in optimization + + align:start position:0% +optimum one general idea in optimization + + + align:start position:0% +optimum one general idea in optimization +is this a so-called fixed point + + align:start position:0% +is this a so-called fixed point + + + align:start position:0% +is this a so-called fixed point +iteration that you can do to arrive + + align:start position:0% +iteration that you can do to arrive + + + align:start position:0% +iteration that you can do to arrive +there and that's essentially what we + + align:start position:0% +there and that's essentially what we + + + align:start position:0% +there and that's essentially what we +will do to get to a good Q yeah so a + + align:start position:0% +will do to get to a good Q yeah so a + + + align:start position:0% +will do to get to a good Q yeah so a +nice thing about Q learning is that if + + align:start position:0% +nice thing about Q learning is that if + + + align:start position:0% +nice thing about Q learning is that if +you're states and action spaces are + + align:start position:0% +you're states and action spaces are + + + align:start position:0% +you're states and action spaces are +small and discreet you can represent the + + align:start position:0% +small and discreet you can represent the + + + align:start position:0% +small and discreet you can represent the +Q function as a table so all you have to + + align:start position:0% +Q function as a table so all you have to + + + align:start position:0% +Q function as a table so all you have to +keep track of is how good is the the the + + align:start position:0% +keep track of is how good is the the the + + + align:start position:0% +keep track of is how good is the the the +a certain action in a certain state or + + align:start position:0% +a certain action in a certain state or + + + align:start position:0% +a certain action in a certain state or +all actions in whole states rather so + + align:start position:0% +all actions in whole states rather so + + + align:start position:0% +all actions in whole states rather so +that's what we did here this is a table + + align:start position:0% +that's what we did here this is a table + + + align:start position:0% +that's what we did here this is a table +I've essentially + + align:start position:0% +I've essentially + + + align:start position:0% +I've essentially +I've described to you the policy here + + align:start position:0% +I've described to you the policy here + + + align:start position:0% +I've described to you the policy here +but what we'll do next is to to describe + + align:start position:0% +but what we'll do next is to to describe + + + align:start position:0% +but what we'll do next is to to describe +the value of each action so you can + + align:start position:0% +the value of each action so you can + + + align:start position:0% +the value of each action so you can +think of it a value of taking the right + + align:start position:0% +think of it a value of taking the right + + + align:start position:0% +think of it a value of taking the right +one bottom top and left essentially + + align:start position:0% +one bottom top and left essentially + + + align:start position:0% +one bottom top and left essentially +those will be the values that we need to + + align:start position:0% +those will be the values that we need to + + + align:start position:0% +those will be the values that we need to +consider and so what Q learning can do + + align:start position:0% +consider and so what Q learning can do + + + align:start position:0% +consider and so what Q learning can do +with the screech States is to + + align:start position:0% +with the screech States is to + + + align:start position:0% +with the screech States is to +essentially start from somewhere start + + align:start position:0% +essentially start from somewhere start + + + align:start position:0% +essentially start from somewhere start +from some idea of what Q is it could be + + align:start position:0% +from some idea of what Q is it could be + + + align:start position:0% +from some idea of what Q is it could be +random could be zero and then repeat the + + align:start position:0% +random could be zero and then repeat the + + + align:start position:0% +random could be zero and then repeat the +following fixed point iteration where + + align:start position:0% +following fixed point iteration where + + + align:start position:0% +following fixed point iteration where +you update your former idea of what Q + + align:start position:0% +you update your former idea of what Q + + + align:start position:0% +you update your former idea of what Q +should be when its current value plus + + align:start position:0% +should be when its current value plus + + + align:start position:0% +should be when its current value plus +some essentially a mixture of the + + align:start position:0% +some essentially a mixture of the + + + align:start position:0% +some essentially a mixture of the +immediate reward for taking action 80 in + + align:start position:0% +immediate reward for taking action 80 in + + + align:start position:0% +immediate reward for taking action 80 in +that state and the future reward as + + align:start position:0% +that state and the future reward as + + + align:start position:0% +that state and the future reward as +judged by your current estimate of the Q + + align:start position:0% +judged by your current estimate of the Q + + + align:start position:0% +judged by your current estimate of the Q +function some will do that now in + + align:start position:0% +function some will do that now in + + + align:start position:0% +function some will do that now in +practice yeah this + + align:start position:0% +practice yeah this + + + align:start position:0% +practice yeah this +the probabilities are like the game so + + align:start position:0% +the probabilities are like the game so + + + align:start position:0% +the probabilities are like the game so +they're not used here actually a value + + align:start position:0% +they're not used here actually a value + + + align:start position:0% +they're not used here actually a value +based RL I didn't say that explicitly + + align:start position:0% +based RL I didn't say that explicitly + + + align:start position:0% +based RL I didn't say that explicitly +but they don't rely on knowing the + + align:start position:0% +but they don't rely on knowing the + + + align:start position:0% +but they don't rely on knowing the +transition probabilities what you might + + align:start position:0% +transition probabilities what you might + + + align:start position:0% +transition probabilities what you might +ask is where do we get the s and the ACE + + align:start position:0% +ask is where do we get the s and the ACE + + + align:start position:0% +ask is where do we get the s and the ACE +and they're ours from and we'll get to + + align:start position:0% +and they're ours from and we'll get to + + + align:start position:0% +and they're ours from and we'll get to +that how do we estimate these we'll get + + align:start position:0% +that how do we estimate these we'll get + + + align:start position:0% +that how do we estimate these we'll get +to that later + + align:start position:0% +to that later + + + align:start position:0% +to that later +good question um okay I'm gonna throw a + + align:start position:0% +good question um okay I'm gonna throw a + + + align:start position:0% +good question um okay I'm gonna throw a +very messy slide at you here you go a + + align:start position:0% +very messy slide at you here you go a + + + align:start position:0% +very messy slide at you here you go a +lot of numbers so what I done now here + + align:start position:0% +lot of numbers so what I done now here + + + align:start position:0% +lot of numbers so what I done now here +is some more exhaustive version of what + + align:start position:0% +is some more exhaustive version of what + + + align:start position:0% +is some more exhaustive version of what +I put on the board for each little + + align:start position:0% +I put on the board for each little + + + align:start position:0% +I put on the board for each little +triangle here it represents the Q value + + align:start position:0% +triangle here it represents the Q value + + + align:start position:0% +triangle here it represents the Q value +for the state action pair so this + + align:start position:0% +for the state action pair so this + + + align:start position:0% +for the state action pair so this +triangle is again for the action right + + align:start position:0% +triangle is again for the action right + + + align:start position:0% +triangle is again for the action right +if you're in this state okay so what + + align:start position:0% +if you're in this state okay so what + + + align:start position:0% +if you're in this state okay so what +I've put on the first slide here is the + + align:start position:0% +I've put on the first slide here is the + + + align:start position:0% +I've put on the first slide here is the +immediate reward of each action so we + + align:start position:0% +immediate reward of each action so we + + + align:start position:0% +immediate reward of each action so we +know that any step will cost us cost us + + align:start position:0% +know that any step will cost us cost us + + + align:start position:0% +know that any step will cost us cost us +minus 0.04 so that's why there's a lot + + align:start position:0% +minus 0.04 so that's why there's a lot + + + align:start position:0% +minus 0.04 so that's why there's a lot +of those here these white boxes here are + + align:start position:0% +of those here these white boxes here are + + + align:start position:0% +of those here these white boxes here are +not possible actions okay up here you + + align:start position:0% +not possible actions okay up here you + + + align:start position:0% +not possible actions okay up here you +have a point nine six because it's one + + align:start position:0% +have a point nine six because it's one + + + align:start position:0% +have a point nine six because it's one +which is the immediate reward of going + + align:start position:0% +which is the immediate reward of going + + + align:start position:0% +which is the immediate reward of going +right here minus point oh four these two + + align:start position:0% +right here minus point oh four these two + + + align:start position:0% +right here minus point oh four these two +are minus one point oh four for the same + + align:start position:0% +are minus one point oh four for the same + + + align:start position:0% +are minus one point oh four for the same +reason but because we arrived in minus + + align:start position:0% +reason but because we arrived in minus + + + align:start position:0% +reason but because we arrived in minus +one okay so that's the first step and + + align:start position:0% +one okay so that's the first step and + + + align:start position:0% +one okay so that's the first step and +the second step done we initialized Q's + + align:start position:0% +the second step done we initialized Q's + + + align:start position:0% +the second step done we initialized Q's +to be zero and then we picked these two + + align:start position:0% +to be zero and then we picked these two + + + align:start position:0% +to be zero and then we picked these two +parameters of the problem alpha and + + align:start position:0% +parameters of the problem alpha and + + + align:start position:0% +parameters of the problem alpha and +gamma to be one and then we did the + + align:start position:0% +gamma to be one and then we did the + + + align:start position:0% +gamma to be one and then we did the +first iteration of Q learning where we + + align:start position:0% +first iteration of Q learning where we + + + align:start position:0% +first iteration of Q learning where we +set the Q to be at the old version of Q + + align:start position:0% +set the Q to be at the old version of Q + + + align:start position:0% +set the Q to be at the old version of Q +which was zero plus alpha times this + + align:start position:0% +which was zero plus alpha times this + + + align:start position:0% +which was zero plus alpha times this +this thing here so Q is zero that means + + align:start position:0% +this thing here so Q is zero that means + + + align:start position:0% +this thing here so Q is zero that means +that this is also zero so the only thing + + align:start position:0% +that this is also zero so the only thing + + + align:start position:0% +that this is also zero so the only thing +we need to look at is this thing here + + align:start position:0% +we need to look at is this thing here + + + align:start position:0% +we need to look at is this thing here +this also is 0 because the Q's for all + + align:start position:0% +this also is 0 because the Q's for all + + + align:start position:0% +this also is 0 because the Q's for all +states were 0 so the only thing we're + + align:start position:0% +states were 0 so the only thing we're + + + align:start position:0% +states were 0 so the only thing we're +not with this are and that's what + + align:start position:0% +not with this are and that's what + + + align:start position:0% +not with this are and that's what +populated this table here okay + + align:start position:0% + + + + align:start position:0% + +next time step where I'm doing cooling + + align:start position:0% +next time step where I'm doing cooling + + + align:start position:0% +next time step where I'm doing cooling +now in a way where I update all the + + align:start position:0% +now in a way where I update all the + + + align:start position:0% +now in a way where I update all the +states at once all the station action + + align:start position:0% +states at once all the station action + + + align:start position:0% +states at once all the station action +pairs at once how can I do that well it + + align:start position:0% +pairs at once how can I do that well it + + + align:start position:0% +pairs at once how can I do that well it +depends on the question I got there + + align:start position:0% +depends on the question I got there + + + align:start position:0% +depends on the question I got there +essentially what data do I observe or + + align:start position:0% +essentially what data do I observe or + + + align:start position:0% +essentially what data do I observe or +how do I get to know the rewards of the + + align:start position:0% +how do I get to know the rewards of the + + + align:start position:0% +how do I get to know the rewards of the +SNA pairs and we'll come back to that so + + align:start position:0% +SNA pairs and we'll come back to that so + + + align:start position:0% +SNA pairs and we'll come back to that so +in the next step I have to update + + align:start position:0% +in the next step I have to update + + + align:start position:0% +in the next step I have to update +everything again so it's a previous Q + + align:start position:0% +everything again so it's a previous Q + + + align:start position:0% +everything again so it's a previous Q +value which was minus 0.04 for a lot of + + align:start position:0% +value which was minus 0.04 for a lot of + + + align:start position:0% +value which was minus 0.04 for a lot of +things then plus the immediate reward + + align:start position:0% +things then plus the immediate reward + + + align:start position:0% +things then plus the immediate reward +which was this RT and I have to keep + + align:start position:0% +which was this RT and I have to keep + + + align:start position:0% +which was this RT and I have to keep +going so that the the dominant thing for + + align:start position:0% +going so that the the dominant thing for + + + align:start position:0% +going so that the the dominant thing for +the table this time was that the best q + + align:start position:0% +the table this time was that the best q + + + align:start position:0% +the table this time was that the best q +value for for almost all of these boxes + + align:start position:0% +value for for almost all of these boxes + + + align:start position:0% +value for for almost all of these boxes +was minus 0.04 so essentially I will add + + align:start position:0% +was minus 0.04 so essentially I will add + + + align:start position:0% +was minus 0.04 so essentially I will add +the immediate reward plus that almost + + align:start position:0% +the immediate reward plus that almost + + + align:start position:0% +the immediate reward plus that almost +everywhere what is interesting though is + + align:start position:0% +everywhere what is interesting though is + + + align:start position:0% +everywhere what is interesting though is +that here the best q value was 0.96 and + + align:start position:0% +that here the best q value was 0.96 and + + + align:start position:0% +that here the best q value was 0.96 and +it will remain remains so that means + + align:start position:0% +it will remain remains so that means + + + align:start position:0% +it will remain remains so that means +that the best Q value for the adjacent + + align:start position:0% +that the best Q value for the adjacent + + + align:start position:0% +that the best Q value for the adjacent +states would look at this max here and + + align:start position:0% +states would look at this max here and + + + align:start position:0% +states would look at this max here and +get 0.96 out okay and then add the + + align:start position:0% +get 0.96 out okay and then add the + + + align:start position:0% +get 0.96 out okay and then add the +immediate rewards so this thing here + + align:start position:0% +immediate rewards so this thing here + + + align:start position:0% +immediate rewards so this thing here +getting to here gives me point 96 minus + + align:start position:0% +getting to here gives me point 96 minus + + + align:start position:0% +getting to here gives me point 96 minus +0.04 for the immediate reward and now we + + align:start position:0% +0.04 for the immediate reward and now we + + + align:start position:0% +0.04 for the immediate reward and now we +can sort of figure out what will happen + + align:start position:0% +can sort of figure out what will happen + + + align:start position:0% +can sort of figure out what will happen +next this this these values would sort + + align:start position:0% +next this this these values would sort + + + align:start position:0% +next this this these values would sort +of spread out as you go further away + + align:start position:0% +of spread out as you go further away + + + align:start position:0% +of spread out as you go further away +from the further away from the +1 I + + align:start position:0% +from the further away from the +1 I + + + align:start position:0% +from the further away from the +1 I +don't think we should go through all of + + align:start position:0% +don't think we should go through all of + + + align:start position:0% +don't think we should go through all of +this but you get a sense for extent + + align:start position:0% +this but you get a sense for extent + + + align:start position:0% +this but you get a sense for extent +essentially how information is moved + + align:start position:0% +essentially how information is moved + + + align:start position:0% +essentially how information is moved +from the +1 and away and I'm sure that's + + align:start position:0% +from the +1 and away and I'm sure that's + + + align:start position:0% +from the +1 and away and I'm sure that's +sort of how you solved it yourself in + + align:start position:0% +sort of how you solved it yourself in + + + align:start position:0% +sort of how you solved it yourself in +your head but this this makes it clear + + align:start position:0% +your head but this this makes it clear + + + align:start position:0% +your head but this this makes it clear +why you can do that even if you don't + + align:start position:0% +why you can do that even if you don't + + + align:start position:0% +why you can do that even if you don't +know where the terminal states are or + + align:start position:0% +know where the terminal states are or + + + align:start position:0% +know where the terminal states are or +where the best where the value of these + + align:start position:0% +where the best where the value of these + + + align:start position:0% +where the best where the value of these +state action pairs are yep this + + align:start position:0% +state action pairs are yep this + + + align:start position:0% +state action pairs are yep this +calculation assumed + + align:start position:0% +calculation assumed + + + align:start position:0% +calculation assumed +you want to move in a certain direction + + align:start position:0% +you want to move in a certain direction + + + align:start position:0% +you want to move in a certain direction +yes sorry thanks for reminding me that's + + align:start position:0% +yes sorry thanks for reminding me that's + + + align:start position:0% +yes sorry thanks for reminding me that's +your Lebanon slide yes thank you yeah + + align:start position:0% +your Lebanon slide yes thank you yeah + + + align:start position:0% +your Lebanon slide yes thank you yeah +I'm gonna I'm gonna skip the rest of + + align:start position:0% +I'm gonna I'm gonna skip the rest of + + + align:start position:0% +I'm gonna I'm gonna skip the rest of +this I hope you forgive me we can talk + + align:start position:0% +this I hope you forgive me we can talk + + + align:start position:0% +this I hope you forgive me we can talk +more about it later but one of the one + + align:start position:0% +more about it later but one of the one + + + align:start position:0% +more about it later but one of the one +of the things that is thanks for + + align:start position:0% +of the things that is thanks for + + + align:start position:0% +of the things that is thanks for +reminding me Pete there that one of the + + align:start position:0% +reminding me Pete there that one of the + + + align:start position:0% +reminding me Pete there that one of the +things I exported here was that I + + align:start position:0% +things I exported here was that I + + + align:start position:0% +things I exported here was that I +assumed deterministic transitions + + align:start position:0% +assumed deterministic transitions + + + align:start position:0% +assumed deterministic transitions +another thing that I relied very heavily + + align:start position:0% +another thing that I relied very heavily + + + align:start position:0% +another thing that I relied very heavily +on here is that I can represent this q + + align:start position:0% +on here is that I can represent this q + + + align:start position:0% +on here is that I can represent this q +function as a table like I drew all + + align:start position:0% +function as a table like I drew all + + + align:start position:0% +function as a table like I drew all +these boxes and I fill the numbers in + + align:start position:0% +these boxes and I fill the numbers in + + + align:start position:0% +these boxes and I fill the numbers in +that's easy enough but what if I have + + align:start position:0% +that's easy enough but what if I have + + + align:start position:0% +that's easy enough but what if I have +thousands of states and thousands of + + align:start position:0% +thousands of states and thousands of + + + align:start position:0% +thousands of states and thousands of +actions that's a large table and not + + align:start position:0% +actions that's a large table and not + + + align:start position:0% +actions that's a large table and not +only is that a large table for me to + + align:start position:0% +only is that a large table for me to + + + align:start position:0% +only is that a large table for me to +keep in memory it's also very bad for me + + align:start position:0% +keep in memory it's also very bad for me + + + align:start position:0% +keep in memory it's also very bad for me +statistically if I want to observe + + align:start position:0% +statistically if I want to observe + + + align:start position:0% +statistically if I want to observe +anything about a state action pair I + + align:start position:0% +anything about a state action pair I + + + align:start position:0% +anything about a state action pair I +have to do that action in that state and + + align:start position:0% +have to do that action in that state and + + + align:start position:0% +have to do that action in that state and +if you think about treating patients in + + align:start position:0% +if you think about treating patients in + + + align:start position:0% +if you think about treating patients in +a hospital you're not going to try + + align:start position:0% +a hospital you're not going to try + + + align:start position:0% +a hospital you're not going to try +everything in every stage usually you're + + align:start position:0% +everything in every stage usually you're + + + align:start position:0% +everything in every stage usually you're +also not going to have infinite number + + align:start position:0% +also not going to have infinite number + + + align:start position:0% +also not going to have infinite number +of numbers of patients so how do you how + + align:start position:0% +of numbers of patients so how do you how + + + align:start position:0% +of numbers of patients so how do you how +do you figure out what is the immediate + + align:start position:0% +do you figure out what is the immediate + + + align:start position:0% +do you figure out what is the immediate +reward of taking a certain state action + + align:start position:0% +reward of taking a certain state action + + + align:start position:0% +reward of taking a certain state action +in a certain state and this is where + + align:start position:0% +in a certain state and this is where + + + align:start position:0% +in a certain state and this is where +function approximation comes in + + align:start position:0% +function approximation comes in + + + align:start position:0% +function approximation comes in +essentially if you can't represent your + + align:start position:0% +essentially if you can't represent your + + + align:start position:0% +essentially if you can't represent your +data as a table either for statistical + + align:start position:0% +data as a table either for statistical + + + align:start position:0% +data as a table either for statistical +reasons or for well memory reasons let's + + align:start position:0% +reasons or for well memory reasons let's + + + align:start position:0% +reasons or for well memory reasons let's +say you might want to approximate the Q + + align:start position:0% +say you might want to approximate the Q + + + align:start position:0% +say you might want to approximate the Q +function with with a parametric function + + align:start position:0% +function with with a parametric function + + + align:start position:0% +function with with a parametric function +or with a number matching function and + + align:start position:0% +or with a number matching function and + + + align:start position:0% +or with a number matching function and +this is exactly what we can do so we can + + align:start position:0% +this is exactly what we can do so we can + + + align:start position:0% +this is exactly what we can do so we can +draw now an analogy to what we did last + + align:start position:0% +draw now an analogy to what we did last + + + align:start position:0% +draw now an analogy to what we did last +week I'm gonna come back to this but + + align:start position:0% +week I'm gonna come back to this but + + + align:start position:0% +week I'm gonna come back to this but +essentially instead of of doing this + + align:start position:0% +essentially instead of of doing this + + + align:start position:0% +essentially instead of of doing this +fixed point iteration that we did before + + align:start position:0% +fixed point iteration that we did before + + + align:start position:0% +fixed point iteration that we did before +we will try and look for a function Q + + align:start position:0% +we will try and look for a function Q + + + align:start position:0% +we will try and look for a function Q +theta that is equal to R plus gamma max + + align:start position:0% +theta that is equal to R plus gamma max + + + align:start position:0% +theta that is equal to R plus gamma max +max Q and this is the the remember + + align:start position:0% +max Q and this is the the remember + + + align:start position:0% +max Q and this is the the remember +before we had the bellmen inequality we + + align:start position:0% +before we had the bellmen inequality we + + + align:start position:0% +before we had the bellmen inequality we +said that Q star si is equal to R si + + align:start position:0% +said that Q star si is equal to R si + + + align:start position:0% +said that Q star si is equal to R si +let's say plus gamma max max a prime + + align:start position:0% + + + + align:start position:0% + +you Jesus + + align:start position:0% +you Jesus + + + align:start position:0% +you Jesus +please start s prime a prime where s + + align:start position:0% +please start s prime a prime where s + + + align:start position:0% +please start s prime a prime where s +prime is the state we get to after + + align:start position:0% +prime is the state we get to after + + + align:start position:0% +prime is the state we get to after +taking X in a in state s so the only + + align:start position:0% +taking X in a in state s so the only + + + align:start position:0% +taking X in a in state s so the only +thing I've done here is to take this + + align:start position:0% +thing I've done here is to take this + + + align:start position:0% +thing I've done here is to take this +equality and make it instead a loss + + align:start position:0% +equality and make it instead a loss + + + align:start position:0% +equality and make it instead a loss +function on the violation of this + + align:start position:0% +function on the violation of this + + + align:start position:0% +function on the violation of this +equality so by minimizing this quantity + + align:start position:0% +equality so by minimizing this quantity + + + align:start position:0% +equality so by minimizing this quantity +I will find something that has + + align:start position:0% +I will find something that has + + + align:start position:0% +I will find something that has +approximately the bellmen equality that + + align:start position:0% +approximately the bellmen equality that + + + align:start position:0% +approximately the bellmen equality that +we talked about before this is the idea + + align:start position:0% +we talked about before this is the idea + + + align:start position:0% +we talked about before this is the idea +of fitted q-learning where you + + align:start position:0% +of fitted q-learning where you + + + align:start position:0% +of fitted q-learning where you +substitute the the tabular + + align:start position:0% +substitute the the tabular + + + align:start position:0% +substitute the the tabular +representation where they with a + + align:start position:0% +representation where they with a + + + align:start position:0% +representation where they with a +function approximation essentially so + + align:start position:0% +function approximation essentially so + + + align:start position:0% +function approximation essentially so +just to make this a bit more concrete we + + align:start position:0% +just to make this a bit more concrete we + + + align:start position:0% +just to make this a bit more concrete we +can think about the case where we have + + align:start position:0% +can think about the case where we have + + + align:start position:0% +can think about the case where we have +only a single step there's only a single + + align:start position:0% +only a single step there's only a single + + + align:start position:0% +only a single step there's only a single +action to make which means that there is + + align:start position:0% +action to make which means that there is + + + align:start position:0% +action to make which means that there is +no future part of this equation here + + align:start position:0% +no future part of this equation here + + + align:start position:0% +no future part of this equation here +this part goes away because there's only + + align:start position:0% +this part goes away because there's only + + + align:start position:0% +this part goes away because there's only +one one stage in our trajectory so we + + align:start position:0% +one one stage in our trajectory so we + + + align:start position:0% +one one stage in our trajectory so we +have only the immediate reward and we + + align:start position:0% +have only the immediate reward and we + + + align:start position:0% +have only the immediate reward and we +have only the Q function now this is + + align:start position:0% +have only the Q function now this is + + + align:start position:0% +have only the Q function now this is +exactly a regression like equation in + + align:start position:0% +exactly a regression like equation in + + + align:start position:0% +exactly a regression like equation in +the way that you've seen it when + + align:start position:0% +the way that you've seen it when + + + align:start position:0% +the way that you've seen it when +estimating potential outcomes RT here + + align:start position:0% +estimating potential outcomes RT here + + + align:start position:0% +estimating potential outcomes RT here +represents the sorry the the the outcome + + align:start position:0% +represents the sorry the the the outcome + + + align:start position:0% +represents the sorry the the the outcome +of doing action a in state s and Q here + + align:start position:0% +of doing action a in state s and Q here + + + align:start position:0% +of doing action a in state s and Q here +will be our estimate of this RT so if if + + align:start position:0% +will be our estimate of this RT so if if + + + align:start position:0% +will be our estimate of this RT so if if +we only again I've said this before if + + align:start position:0% +we only again I've said this before if + + + align:start position:0% +we only again I've said this before if +we have a single time point in our inner + + align:start position:0% +we have a single time point in our inner + + + align:start position:0% +we have a single time point in our inner +process that the problem reduces to + + align:start position:0% +process that the problem reduces to + + + align:start position:0% +process that the problem reduces to +estimating potential outcomes just the + + align:start position:0% +estimating potential outcomes just the + + + align:start position:0% +estimating potential outcomes just the +way as the way we saw it last time we + + align:start position:0% +way as the way we saw it last time we + + + align:start position:0% +way as the way we saw it last time we +have curves that correspond to the + + align:start position:0% +have curves that correspond to the + + + align:start position:0% +have curves that correspond to the +different the outcomes under different + + align:start position:0% +different the outcomes under different + + + align:start position:0% +different the outcomes under different +actions and we can do regression + + align:start position:0% +actions and we can do regression + + + align:start position:0% +actions and we can do regression +adjustment trying to find an F such that + + align:start position:0% +adjustment trying to find an F such that + + + align:start position:0% +adjustment trying to find an F such that +this quantity is small so that we can + + align:start position:0% +this quantity is small so that we can + + + align:start position:0% +this quantity is small so that we can +model each different potential outcomes + + align:start position:0% +model each different potential outcomes + + + align:start position:0% +model each different potential outcomes +and that's exactly what happens with the + + align:start position:0% +and that's exactly what happens with the + + + align:start position:0% +and that's exactly what happens with the +fit acute iteration if you have a single + + align:start position:0% +fit acute iteration if you have a single + + + align:start position:0% +fit acute iteration if you have a single +time step two so to make it even more + + align:start position:0% +time step two so to make it even more + + + align:start position:0% +time step two so to make it even more +concrete we can say that this there's + + align:start position:0% +concrete we can say that this there's + + + align:start position:0% +concrete we can say that this there's +some some target value G hat which + + align:start position:0% +some some target value G hat which + + + align:start position:0% +some some target value G hat which +represents the immediate reward in the + + align:start position:0% +represents the immediate reward in the + + + align:start position:0% +represents the immediate reward in the +future rewards that is the + + align:start position:0% +future rewards that is the + + + align:start position:0% +future rewards that is the +target of our regression and we're + + align:start position:0% +target of our regression and we're + + + align:start position:0% +target of our regression and we're +fitting some function to that value okay + + align:start position:0% + + + + align:start position:0% + +so the question we got before was how do + + align:start position:0% +so the question we got before was how do + + + align:start position:0% +so the question we got before was how do +i how do I make use of or how do I know + + align:start position:0% +i how do I make use of or how do I know + + + align:start position:0% +i how do I make use of or how do I know +the transition matrix well how do I get + + align:start position:0% +the transition matrix well how do I get + + + align:start position:0% +the transition matrix well how do I get +like any information about this thing + + align:start position:0% +like any information about this thing + + + align:start position:0% +like any information about this thing +okay I say here on the sly that okay we + + align:start position:0% +okay I say here on the sly that okay we + + + align:start position:0% +okay I say here on the sly that okay we +have some target that's our plus future + + align:start position:0% +have some target that's our plus future + + + align:start position:0% +have some target that's our plus future +Q values we have some prediction we have + + align:start position:0% +Q values we have some prediction we have + + + align:start position:0% +Q values we have some prediction we have +an expectation over transitions here but + + align:start position:0% +an expectation over transitions here but + + + align:start position:0% +an expectation over transitions here but +how do I evaluate this thing the + + align:start position:0% +how do I evaluate this thing the + + + align:start position:0% +how do I evaluate this thing the +transitions I have to get from somewhere + + align:start position:0% +transitions I have to get from somewhere + + + align:start position:0% +transitions I have to get from somewhere +right and another way to say that is + + align:start position:0% +right and another way to say that is + + + align:start position:0% +right and another way to say that is +what are the inputs in the outputs of + + align:start position:0% +what are the inputs in the outputs of + + + align:start position:0% +what are the inputs in the outputs of +our regression because in in when we + + align:start position:0% +our regression because in in when we + + + align:start position:0% +our regression because in in when we +estimate potential outcomes we have a + + align:start position:0% +estimate potential outcomes we have a + + + align:start position:0% +estimate potential outcomes we have a +very clear idea of this we know that Y + + align:start position:0% +very clear idea of this we know that Y + + + align:start position:0% +very clear idea of this we know that Y +is the outcome itself is a target and + + align:start position:0% +is the outcome itself is a target and + + + align:start position:0% +is the outcome itself is a target and +the the input is the you know the + + align:start position:0% +the the input is the you know the + + + align:start position:0% +the the input is the you know the +covariance X okay but here we have a + + align:start position:0% +covariance X okay but here we have a + + + align:start position:0% +covariance X okay but here we have a +sort of moving torii because this Y or + + align:start position:0% +sort of moving torii because this Y or + + + align:start position:0% +sort of moving torii because this Y or +this Q hat it has to come from somewhere + + align:start position:0% +this Q hat it has to come from somewhere + + + align:start position:0% +this Q hat it has to come from somewhere +- this is something that we estimate as + + align:start position:0% +- this is something that we estimate as + + + align:start position:0% +- this is something that we estimate as +well so usually what happens is that we + + align:start position:0% +well so usually what happens is that we + + + align:start position:0% +well so usually what happens is that we +we alternate between updating this + + align:start position:0% +we alternate between updating this + + + align:start position:0% +we alternate between updating this +target Q and Q theta so essentially we + + align:start position:0% +target Q and Q theta so essentially we + + + align:start position:0% +target Q and Q theta so essentially we +copy Q theta to become our new Q hat we + + align:start position:0% +copy Q theta to become our new Q hat we + + + align:start position:0% +copy Q theta to become our new Q hat we +we iterate this somehow but I still + + align:start position:0% +we iterate this somehow but I still + + + align:start position:0% +we iterate this somehow but I still +haven't told you how do you evaluate + + align:start position:0% +haven't told you how do you evaluate + + + align:start position:0% +haven't told you how do you evaluate +this expectation so usually in RL there + + align:start position:0% +this expectation so usually in RL there + + + align:start position:0% +this expectation so usually in RL there +are a few different ways to do this and + + align:start position:0% + + + + align:start position:0% + +either depending on where you come from + + align:start position:0% +either depending on where you come from + + + align:start position:0% +either depending on where you come from +essentially these are different or these + + align:start position:0% +essentially these are different or these + + + align:start position:0% +essentially these are different or these +are varying ly viable so if we look back + + align:start position:0% +are varying ly viable so if we look back + + + align:start position:0% +are varying ly viable so if we look back +at this this thing here it relies on + + align:start position:0% +at this this thing here it relies on + + + align:start position:0% +at this this thing here it relies on +having tuples of transitions the states + + align:start position:0% +having tuples of transitions the states + + + align:start position:0% +having tuples of transitions the states +the action the next state and the reward + + align:start position:0% +the action the next state and the reward + + + align:start position:0% +the action the next state and the reward +that I got so I have to somehow observe + + align:start position:0% +that I got so I have to somehow observe + + + align:start position:0% +that I got so I have to somehow observe +those and I can obtain them in various + + align:start position:0% +those and I can obtain them in various + + + align:start position:0% +those and I can obtain them in various +ways a very common one when it comes to + + align:start position:0% +ways a very common one when it comes to + + + align:start position:0% +ways a very common one when it comes to +learning to play video games for example + + align:start position:0% +learning to play video games for example + + + align:start position:0% +learning to play video games for example +I said you do something called on policy + + align:start position:0% +I said you do something called on policy + + + align:start position:0% +I said you do something called on policy +exploration that means that you observe + + align:start position:0% +exploration that means that you observe + + + align:start position:0% +exploration that means that you observe +data from the policy that you're + + align:start position:0% +data from the policy that you're + + + align:start position:0% +data from the policy that you're +currently optimizing you just play the + + align:start position:0% +currently optimizing you just play the + + + align:start position:0% +currently optimizing you just play the +game according to the policy that you + + align:start position:0% +game according to the policy that you + + + align:start position:0% +game according to the policy that you +have at the moment and the analogy in + + align:start position:0% +have at the moment and the analogy in + + + align:start position:0% +have at the moment and the analogy in +healthcare would be that you you have + + align:start position:0% +healthcare would be that you you have + + + align:start position:0% +healthcare would be that you you have +some idea of how how to treat patients + + align:start position:0% +some idea of how how to treat patients + + + align:start position:0% +some idea of how how to treat patients +and you just do that and see what + + align:start position:0% +and you just do that and see what + + + align:start position:0% +and you just do that and see what +happens + + align:start position:0% +happens + + + align:start position:0% +happens +that could be problematic especially if + + align:start position:0% +that could be problematic especially if + + + align:start position:0% +that could be problematic especially if +you got that policy like if you randomly + + align:start position:0% +you got that policy like if you randomly + + + align:start position:0% +you got that policy like if you randomly +initialized it or if you got it for some + + align:start position:0% +initialized it or if you got it for some + + + align:start position:0% +initialized it or if you got it for some +somewhere very suboptimal right a + + align:start position:0% +somewhere very suboptimal right a + + + align:start position:0% +somewhere very suboptimal right a +different thing that we more perhaps + + align:start position:0% +different thing that we more perhaps + + + align:start position:0% +different thing that we more perhaps +comfortable with in healthcare in + + align:start position:0% +comfortable with in healthcare in + + + align:start position:0% +comfortable with in healthcare in +restricted setting is the idea of a + + align:start position:0% +restricted setting is the idea of a + + + align:start position:0% +restricted setting is the idea of a +randomized trial where instead of trying + + align:start position:0% +randomized trial where instead of trying + + + align:start position:0% +randomized trial where instead of trying +out some policy in that you're currently + + align:start position:0% +out some policy in that you're currently + + + align:start position:0% +out some policy in that you're currently +learning you decide on a population + + align:start position:0% +learning you decide on a population + + + align:start position:0% +learning you decide on a population +where it's okay to flip a coin + + align:start position:0% +where it's okay to flip a coin + + + align:start position:0% +where it's okay to flip a coin +essentially where between different + + align:start position:0% +essentially where between different + + + align:start position:0% +essentially where between different +actions that you have the difference + + align:start position:0% +actions that you have the difference + + + align:start position:0% +actions that you have the difference +here between the difference between the + + align:start position:0% +here between the difference between the + + + align:start position:0% +here between the difference between the +sequential setting and the one-step + + align:start position:0% +sequential setting and the one-step + + + align:start position:0% +sequential setting and the one-step +setting is that now you have to + + align:start position:0% +setting is that now you have to + + + align:start position:0% +setting is that now you have to +randomize a sequence of actions which is + + align:start position:0% +randomize a sequence of actions which is + + + align:start position:0% +randomize a sequence of actions which is +a little bit unlike the the clinical + + align:start position:0% +a little bit unlike the the clinical + + + align:start position:0% +a little bit unlike the the clinical +trial that you have seen before I think + + align:start position:0% +trial that you have seen before I think + + + align:start position:0% +trial that you have seen before I think +the last one which is the the most study + + align:start position:0% +the last one which is the the most study + + + align:start position:0% +the last one which is the the most study +one when it comes to practice I would + + align:start position:0% +one when it comes to practice I would + + + align:start position:0% +one when it comes to practice I would +say is off policy where is the one that + + align:start position:0% +say is off policy where is the one that + + + align:start position:0% +say is off policy where is the one that +we talked about rather today this week + + align:start position:0% +we talked about rather today this week + + + align:start position:0% +we talked about rather today this week +is off policy evaluation or or learning + + align:start position:0% +is off policy evaluation or or learning + + + align:start position:0% +is off policy evaluation or or learning +in which case you you you observe + + align:start position:0% +in which case you you you observe + + + align:start position:0% +in which case you you you observe +healthcare records for example you + + align:start position:0% +healthcare records for example you + + + align:start position:0% +healthcare records for example you +observe registry so you observe some + + align:start position:0% +observe registry so you observe some + + + align:start position:0% +observe registry so you observe some +data from the healthcare system where + + align:start position:0% +data from the healthcare system where + + + align:start position:0% +data from the healthcare system where +patients have already been treated and + + align:start position:0% +patients have already been treated and + + + align:start position:0% +patients have already been treated and +you try to extract a good policy based + + align:start position:0% +you try to extract a good policy based + + + align:start position:0% +you try to extract a good policy based +on that information so that means that + + align:start position:0% +on that information so that means that + + + align:start position:0% +on that information so that means that +you see these transitions between a + + align:start position:0% +you see these transitions between a + + + align:start position:0% +you see these transitions between a +state and action in the next state and + + align:start position:0% +state and action in the next state and + + + align:start position:0% +state and action in the next state and +the reward you see that based on what + + align:start position:0% +the reward you see that based on what + + + align:start position:0% +the reward you see that based on what +happened in the past and you have to + + align:start position:0% +happened in the past and you have to + + + align:start position:0% +happened in the past and you have to +figure out a pattern there that helps + + align:start position:0% +figure out a pattern there that helps + + + align:start position:0% +figure out a pattern there that helps +you come up with a good action or a good + + align:start position:0% +you come up with a good action or a good + + + align:start position:0% +you come up with a good action or a good +policy so we'll focus on that one for + + align:start position:0% +policy so we'll focus on that one for + + + align:start position:0% +policy so we'll focus on that one for +now and I'll just end the last part of + + align:start position:0% +now and I'll just end the last part of + + + align:start position:0% +now and I'll just end the last part of +this talk will be about how we can + + align:start position:0% +this talk will be about how we can + + + align:start position:0% +this talk will be about how we can +essentially what we had to be careful + + align:start position:0% +essentially what we had to be careful + + + align:start position:0% +essentially what we had to be careful +with when we learn with off policy data + + align:start position:0% +with when we learn with off policy data + + + align:start position:0% +with when we learn with off policy data +and the question is up until this point + + align:start position:0% + + + + align:start position:0% + +yep + + align:start position:0% + + + + align:start position:0% + +sorry violence that has to be met my + + align:start position:0% +sorry violence that has to be met my + + + align:start position:0% +sorry violence that has to be met my +answer + + align:start position:0% + + + + align:start position:0% + +yeah I'll get to that on the next set of + + align:start position:0% +yeah I'll get to that on the next set of + + + align:start position:0% +yeah I'll get to that on the next set of +five I get to that in the next two + + align:start position:0% +five I get to that in the next two + + + align:start position:0% +five I get to that in the next two +slides yeah thank you any other + + align:start position:0% +slides yeah thank you any other + + + align:start position:0% +slides yeah thank you any other +questions about the queue learning part + + align:start position:0% +questions about the queue learning part + + + align:start position:0% +questions about the queue learning part +a colleague of mine Rahul he said or + + align:start position:0% +a colleague of mine Rahul he said or + + + align:start position:0% +a colleague of mine Rahul he said or +maybe it was he just paraphrased it from + + align:start position:0% +maybe it was he just paraphrased it from + + + align:start position:0% +maybe it was he just paraphrased it from +someone else but essentially you have to + + align:start position:0% +someone else but essentially you have to + + + align:start position:0% +someone else but essentially you have to +see RL ten times before you get it or + + align:start position:0% +see RL ten times before you get it or + + + align:start position:0% +see RL ten times before you get it or +something to that effect I had the same + + align:start position:0% +something to that effect I had the same + + + align:start position:0% +something to that effect I had the same +experience so hopefully you have + + align:start position:0% +experience so hopefully you have + + + align:start position:0% +experience so hopefully you have +questions for me after but what yeah + + align:start position:0% +questions for me after but what yeah + + + align:start position:0% +questions for me after but what yeah +exactly + + align:start position:0% +exactly + + + align:start position:0% +exactly +but but I think what you should take + + align:start position:0% +but but I think what you should take + + + align:start position:0% +but but I think what you should take +from the the last two sections if not + + align:start position:0% +from the the last two sections if not + + + align:start position:0% +from the the last two sections if not +how to do Q learning in detail because I + + align:start position:0% +how to do Q learning in detail because I + + + align:start position:0% +how to do Q learning in detail because I +lost over a lot of things you should + + align:start position:0% +lost over a lot of things you should + + + align:start position:0% +lost over a lot of things you should +take into it take with you the idea of + + align:start position:0% +take into it take with you the idea of + + + align:start position:0% +take into it take with you the idea of +dynamic programming and figuring out how + + align:start position:0% +dynamic programming and figuring out how + + + align:start position:0% +dynamic programming and figuring out how +can I learn about what's good early on + + align:start position:0% +can I learn about what's good early on + + + align:start position:0% +can I learn about what's good early on +in my process from what's good late and + + align:start position:0% +in my process from what's good late and + + + align:start position:0% +in my process from what's good late and +the idea of moving to Ward's the good + + align:start position:0% +the idea of moving to Ward's the good + + + align:start position:0% +the idea of moving to Ward's the good +state and not just arriving there + + align:start position:0% +state and not just arriving there + + + align:start position:0% +state and not just arriving there +immediately and there are many ways to + + align:start position:0% +immediately and there are many ways to + + + align:start position:0% +immediately and there are many ways to +to think about that okay well moving to + + align:start position:0% +to think about that okay well moving to + + + align:start position:0% +to think about that okay well moving to +off policy learning and again the setup + + align:start position:0% +off policy learning and again the setup + + + align:start position:0% +off policy learning and again the setup +here is that we we receive trajectories + + align:start position:0% +here is that we we receive trajectories + + + align:start position:0% +here is that we we receive trajectories +of patient states actions and rewards + + align:start position:0% +of patient states actions and rewards + + + align:start position:0% +of patient states actions and rewards +from some source we don't know what this + + align:start position:0% +from some source we don't know what this + + + align:start position:0% +from some source we don't know what this +source is necessarily I will we probably + + align:start position:0% +source is necessarily I will we probably + + + align:start position:0% +source is necessarily I will we probably +know what the source is but we don't + + align:start position:0% +know what the source is but we don't + + + align:start position:0% +know what the source is but we don't +know how these actions were performed ie + + align:start position:0% +know how these actions were performed ie + + + align:start position:0% +know how these actions were performed ie +we don't know what the policy was that + + align:start position:0% +we don't know what the policy was that + + + align:start position:0% +we don't know what the policy was that +generated these trajectories and this is + + align:start position:0% +generated these trajectories and this is + + + align:start position:0% +generated these trajectories and this is +the same set up as in when you estimated + + align:start position:0% +the same set up as in when you estimated + + + align:start position:0% +the same set up as in when you estimated +causal effects last week to a large + + align:start position:0% +causal effects last week to a large + + + align:start position:0% +causal effects last week to a large +extent we say that the actions are drawn + + align:start position:0% +extent we say that the actions are drawn + + + align:start position:0% +extent we say that the actions are drawn +again according to some behavior policy + + align:start position:0% +again according to some behavior policy + + + align:start position:0% +again according to some behavior policy +unknown to us but we want to figure out + + align:start position:0% +unknown to us but we want to figure out + + + align:start position:0% +unknown to us but we want to figure out +what is the value of a new policy PI so + + align:start position:0% +what is the value of a new policy PI so + + + align:start position:0% +what is the value of a new policy PI so +when I want to show you very early on I + + align:start position:0% +when I want to show you very early on I + + + align:start position:0% +when I want to show you very early on I +wish I had that slide again but + + align:start position:0% +wish I had that slide again but + + + align:start position:0% +wish I had that slide again but +essentially a bunch of patient + + align:start position:0% +essentially a bunch of patient + + + align:start position:0% +essentially a bunch of patient +trajectories and some returned patient + + align:start position:0% +trajectories and some returned patient + + + align:start position:0% +trajectories and some returned patient +trajectory some returned the average of + + align:start position:0% +trajectory some returned the average of + + + align:start position:0% +trajectory some returned the average of +those that's called the value if we have + + align:start position:0% +those that's called the value if we have + + + align:start position:0% +those that's called the value if we have +trajectories according to a certain + + align:start position:0% +trajectories according to a certain + + + align:start position:0% +trajectories according to a certain +policy that is the value of that policy + + align:start position:0% +policy that is the value of that policy + + + align:start position:0% +policy that is the value of that policy +the average of these things but when we + + align:start position:0% +the average of these things but when we + + + align:start position:0% +the average of these things but when we +have trajectories according to one + + align:start position:0% +have trajectories according to one + + + align:start position:0% +have trajectories according to one +policy and want to figure out the value + + align:start position:0% +policy and want to figure out the value + + + align:start position:0% +policy and want to figure out the value +of another one that's the same problem + + align:start position:0% +of another one that's the same problem + + + align:start position:0% +of another one that's the same problem +as the Coverity justman problem that you + + align:start position:0% +as the Coverity justman problem that you + + + align:start position:0% +as the Coverity justman problem that you +had last week essentially or what the + + align:start position:0% +had last week essentially or what the + + + align:start position:0% +had last week essentially or what the +compounding problem essentially like the + + align:start position:0% +compounding problem essentially like the + + + align:start position:0% +compounding problem essentially like the +the the the trajectories that we draw + + align:start position:0% +the the the trajectories that we draw + + + align:start position:0% +the the the trajectories that we draw +our biased according to the policy of + + align:start position:0% +our biased according to the policy of + + + align:start position:0% +our biased according to the policy of +the clinician + + align:start position:0% +the clinician + + + align:start position:0% +the clinician +that created them and we want to figure + + align:start position:0% +that created them and we want to figure + + + align:start position:0% +that created them and we want to figure +out the value of a different policy so + + align:start position:0% +out the value of a different policy so + + + align:start position:0% +out the value of a different policy so +it's the same as the confounding problem + + align:start position:0% +it's the same as the confounding problem + + + align:start position:0% +it's the same as the confounding problem +from the last time and because it is the + + align:start position:0% +from the last time and because it is the + + + align:start position:0% +from the last time and because it is the +same as the confounding from problems + + align:start position:0% +same as the confounding from problems + + + align:start position:0% +same as the confounding from problems +from last time we know that this is at + + align:start position:0% +from last time we know that this is at + + + align:start position:0% +from last time we know that this is at +least as hard as doing that we have + + align:start position:0% +least as hard as doing that we have + + + align:start position:0% +least as hard as doing that we have +confounding I already alluded to a + + align:start position:0% +confounding I already alluded to a + + + align:start position:0% +confounding I already alluded to a +various issues when you mentioned + + align:start position:0% +various issues when you mentioned + + + align:start position:0% +various issues when you mentioned +overlap or positivity as well and in + + align:start position:0% +overlap or positivity as well and in + + + align:start position:0% +overlap or positivity as well and in +fact we need to make the same + + align:start position:0% +fact we need to make the same + + + align:start position:0% +fact we need to make the same +assumptions but even stronger + + align:start position:0% +assumptions but even stronger + + + align:start position:0% +assumptions but even stronger +assumptions for this to be possible + + align:start position:0% + + + + align:start position:0% + +these are sufficient conditions so under + + align:start position:0% +these are sufficient conditions so under + + + align:start position:0% +these are sufficient conditions so under +very certain circumstances you don't + + align:start position:0% +very certain circumstances you don't + + + align:start position:0% +very certain circumstances you don't +need them but in the general case well I + + align:start position:0% +need them but in the general case well I + + + align:start position:0% +need them but in the general case well I +should say these are fairly general + + align:start position:0% +should say these are fairly general + + + align:start position:0% +should say these are fairly general +assumptions that are still strict that's + + align:start position:0% +assumptions that are still strict that's + + + align:start position:0% +assumptions that are still strict that's +how I should put it so last time we + + align:start position:0% +how I should put it so last time we + + + align:start position:0% +how I should put it so last time we +looked at something called strong ignore + + align:start position:0% +looked at something called strong ignore + + + align:start position:0% +looked at something called strong ignore +ability I realized the text is pretty + + align:start position:0% +ability I realized the text is pretty + + + align:start position:0% +ability I realized the text is pretty +small here can you see in the back is + + align:start position:0% +small here can you see in the back is + + + align:start position:0% +small here can you see in the back is +that okay okay great so strong ignore + + align:start position:0% +that okay okay great so strong ignore + + + align:start position:0% +that okay okay great so strong ignore +ability said that the potential outcomes + + align:start position:0% +ability said that the potential outcomes + + + align:start position:0% +ability said that the potential outcomes +y0 and y1 are conditionally independent + + align:start position:0% +y0 and y1 are conditionally independent + + + align:start position:0% +y0 and y1 are conditionally independent +of the treatment t given the set of + + align:start position:0% +of the treatment t given the set of + + + align:start position:0% +of the treatment t given the set of +variables x or the variable x and that's + + align:start position:0% +variables x or the variable x and that's + + + align:start position:0% +variables x or the variable x and that's +saying that it doesn't matter if we know + + align:start position:0% +saying that it doesn't matter if we know + + + align:start position:0% +saying that it doesn't matter if we know +what treatment was given we can figure + + align:start position:0% +what treatment was given we can figure + + + align:start position:0% +what treatment was given we can figure +out just based on X what would happen + + align:start position:0% +out just based on X what would happen + + + align:start position:0% +out just based on X what would happen +under either treatment arm where we to + + align:start position:0% +under either treatment arm where we to + + + align:start position:0% +under either treatment arm where we to +treat this patient with with T equals + + align:start position:0% +treat this patient with with T equals + + + align:start position:0% +treat this patient with with T equals +zero T was one we had an idea of or an + + align:start position:0% +zero T was one we had an idea of or an + + + align:start position:0% +zero T was one we had an idea of or an +assumption of overlap which says that + + align:start position:0% +assumption of overlap which says that + + + align:start position:0% +assumption of overlap which says that +any treatment could be observed in any + + align:start position:0% +any treatment could be observed in any + + + align:start position:0% +any treatment could be observed in any +state or any context X and yeah but + + align:start position:0% +state or any context X and yeah but + + + align:start position:0% +state or any context X and yeah but +that's what that means + + align:start position:0% +that's what that means + + + align:start position:0% +that's what that means +and that is only to to ensure that we + + align:start position:0% +and that is only to to ensure that we + + + align:start position:0% +and that is only to to ensure that we +can estimate at least a conditional + + align:start position:0% +can estimate at least a conditional + + + align:start position:0% +can estimate at least a conditional +average treatment effect at X and if we + + align:start position:0% +average treatment effect at X and if we + + + align:start position:0% +average treatment effect at X and if we +want to estimate the average treatment + + align:start position:0% +want to estimate the average treatment + + + align:start position:0% +want to estimate the average treatment +effect in a population we would need to + + align:start position:0% +effect in a population we would need to + + + align:start position:0% +effect in a population we would need to +know that we need to have that for every + + align:start position:0% +know that we need to have that for every + + + align:start position:0% +know that we need to have that for every +X in a population so what happens in the + + align:start position:0% +X in a population so what happens in the + + + align:start position:0% +X in a population so what happens in the +sequential case is that we need even + + align:start position:0% +sequential case is that we need even + + + align:start position:0% +sequential case is that we need even +stronger assumptions there's some + + align:start position:0% +stronger assumptions there's some + + + align:start position:0% +stronger assumptions there's some +notation I haven't introduced here and + + align:start position:0% +notation I haven't introduced here and + + + align:start position:0% +notation I haven't introduced here and +apologize for that but there's a bar + + align:start position:0% +apologize for that but there's a bar + + + align:start position:0% +apologize for that but there's a bar +here over the these asses and A's I + + align:start position:0% +here over the these asses and A's I + + + align:start position:0% +here over the these asses and A's I +don't know if you can see it that + + align:start position:0% +don't know if you can see it that + + + align:start position:0% +don't know if you can see it that +usually indicates in this literature + + align:start position:0% +usually indicates in this literature + + + align:start position:0% +usually indicates in this literature +that you're looking at the sequence up + + align:start position:0% +that you're looking at the sequence up + + + align:start position:0% +that you're looking at the sequence up +to the index here so all the states up + + align:start position:0% +to the index here so all the states up + + + align:start position:0% +to the index here so all the states up +until t have observed and all the + + align:start position:0% +until t have observed and all the + + + align:start position:0% +until t have observed and all the +actions up until t minus 1 maybe this + + align:start position:0% +actions up until t minus 1 maybe this + + + align:start position:0% +actions up until t minus 1 maybe this +should yeah exactly happened + + align:start position:0% +should yeah exactly happened + + + align:start position:0% +should yeah exactly happened +- one so in order for the the best + + align:start position:0% +- one so in order for the the best + + + align:start position:0% +- one so in order for the the best +policy to be identifiable or the value + + align:start position:0% +policy to be identifiable or the value + + + align:start position:0% +policy to be identifiable or the value +of a policy to be identifiable we need + + align:start position:0% +of a policy to be identifiable we need + + + align:start position:0% +of a policy to be identifiable we need +this strong condition so the the return + + align:start position:0% +this strong condition so the the return + + + align:start position:0% +this strong condition so the the return +of a policy is independent of the + + align:start position:0% +of a policy is independent of the + + + align:start position:0% +of a policy is independent of the +current action given everything that + + align:start position:0% +current action given everything that + + + align:start position:0% +current action given everything that +happened in the past this is not this is + + align:start position:0% +happened in the past this is not this is + + + align:start position:0% +happened in the past this is not this is +weaker than the mark of assumption to be + + align:start position:0% +weaker than the mark of assumption to be + + + align:start position:0% +weaker than the mark of assumption to be +clear because there we said that + + align:start position:0% +clear because there we said that + + + align:start position:0% +clear because there we said that +anything that happens in the future is + + align:start position:0% +anything that happens in the future is + + + align:start position:0% +anything that happens in the future is +conditionally independent given the + + align:start position:0% +conditionally independent given the + + + align:start position:0% +conditionally independent given the +current state so this is weaker because + + align:start position:0% +current state so this is weaker because + + + align:start position:0% +current state so this is weaker because +we we now just need to observe something + + align:start position:0% +we we now just need to observe something + + + align:start position:0% +we we now just need to observe something +in the history we need to observe all + + align:start position:0% +in the history we need to observe all + + + align:start position:0% +in the history we need to observe all +the compounds in the history in some + + align:start position:0% +the compounds in the history in some + + + align:start position:0% +the compounds in the history in some +sense we don't need to summarize them in + + align:start position:0% +sense we don't need to summarize them in + + + align:start position:0% +sense we don't need to summarize them in +s and we'll get back to this on the next + + align:start position:0% +s and we'll get back to this on the next + + + align:start position:0% +s and we'll get back to this on the next +slide positivity is the real difficult + + align:start position:0% +slide positivity is the real difficult + + + align:start position:0% +slide positivity is the real difficult +one though because what we're saying is + + align:start position:0% +one though because what we're saying is + + + align:start position:0% +one though because what we're saying is +that at any point in the trajectory any + + align:start position:0% +that at any point in the trajectory any + + + align:start position:0% +that at any point in the trajectory any +action should be possible in order for + + align:start position:0% +action should be possible in order for + + + align:start position:0% +action should be possible in order for +us to figure if - in order for us to + + align:start position:0% +us to figure if - in order for us to + + + align:start position:0% +us to figure if - in order for us to +estimate the value of any possible + + align:start position:0% +estimate the value of any possible + + + align:start position:0% +estimate the value of any possible +policy and that we know that that's not + + align:start position:0% +policy and that we know that that's not + + + align:start position:0% +policy and that we know that that's not +going to be true in practice we're not + + align:start position:0% +going to be true in practice we're not + + + align:start position:0% +going to be true in practice we're not +going to consider every possible action + + align:start position:0% +going to consider every possible action + + + align:start position:0% +going to consider every possible action +at every different every possible point + + align:start position:0% +at every different every possible point + + + align:start position:0% +at every different every possible point +for in the health care setting there's + + align:start position:0% +for in the health care setting there's + + + align:start position:0% +for in the health care setting there's +just no way so what that tells us is + + align:start position:0% +just no way so what that tells us is + + + align:start position:0% +just no way so what that tells us is +that we should we can't estimate the + + align:start position:0% +that we should we can't estimate the + + + align:start position:0% +that we should we can't estimate the +value of every possible policy we can + + align:start position:0% +value of every possible policy we can + + + align:start position:0% +value of every possible policy we can +only estimate the value of policies that + + align:start position:0% +only estimate the value of policies that + + + align:start position:0% +only estimate the value of policies that +are consistent with the with the with + + align:start position:0% +are consistent with the with the with + + + align:start position:0% +are consistent with the with the with +the support that we do have if we never + + align:start position:0% +the support that we do have if we never + + + align:start position:0% +the support that we do have if we never +see action for at time 3 there's no way + + align:start position:0% +see action for at time 3 there's no way + + + align:start position:0% +see action for at time 3 there's no way +we can learn about a policy that does + + align:start position:0% +we can learn about a policy that does + + + align:start position:0% +we can learn about a policy that does +that that takes action for at time 3 + + align:start position:0% +that that takes action for at time 3 + + + align:start position:0% +that that takes action for at time 3 +that's what I'm trying to say so in some + + align:start position:0% +that's what I'm trying to say so in some + + + align:start position:0% +that's what I'm trying to say so in some +sense this is yeah it's stronger just + + align:start position:0% +sense this is yeah it's stronger just + + + align:start position:0% +sense this is yeah it's stronger just +because of how sequential settings work + + align:start position:0% +because of how sequential settings work + + + align:start position:0% +because of how sequential settings work +it's more about the application demand + + align:start position:0% +it's more about the application demand + + + align:start position:0% +it's more about the application demand +than anything I would say in the next + + align:start position:0% +than anything I would say in the next + + + align:start position:0% +than anything I would say in the next +set of slides we'll focus on a + + align:start position:0% +set of slides we'll focus on a + + + align:start position:0% +set of slides we'll focus on a +sequential randomization or sequential + + align:start position:0% +sequential randomization or sequential + + + align:start position:0% +sequential randomization or sequential +ignore ability is sometimes called and + + align:start position:0% +ignore ability is sometimes called and + + + align:start position:0% +ignore ability is sometimes called and +tomorrow we'll talk a little bit about + + align:start position:0% +tomorrow we'll talk a little bit about + + + align:start position:0% +tomorrow we'll talk a little bit about +the statistics involved in or resulting + + align:start position:0% +the statistics involved in or resulting + + + align:start position:0% +the statistics involved in or resulting +from the positivity assumption and and + + align:start position:0% +from the positivity assumption and and + + + align:start position:0% +from the positivity assumption and and +and things like importance meeting + + align:start position:0% +and things like importance meeting + + + align:start position:0% +and things like importance meeting +etcetera did I say tomorrow I meant + + align:start position:0% +etcetera did I say tomorrow I meant + + + align:start position:0% +etcetera did I say tomorrow I meant +Thursday + + align:start position:0% +Thursday + + + align:start position:0% +Thursday +okay so last recap on the potential + + align:start position:0% +okay so last recap on the potential + + + align:start position:0% +okay so last recap on the potential +outcome story this is a slide I'm not + + align:start position:0% +outcome story this is a slide I'm not + + + align:start position:0% +outcome story this is a slide I'm not +sure if you showed this one but it's + + align:start position:0% +sure if you showed this one but it's + + + align:start position:0% +sure if you showed this one but it's +someone that we use that in a lot of + + align:start position:0% +someone that we use that in a lot of + + + align:start position:0% +someone that we use that in a lot of +and it's again just serves to illustrate + + align:start position:0% +and it's again just serves to illustrate + + + align:start position:0% +and it's again just serves to illustrate +the idea of a one time step decision so + + align:start position:0% +the idea of a one time step decision so + + + align:start position:0% +the idea of a one time step decision so +we have here Anna a patient comes in she + + align:start position:0% +we have here Anna a patient comes in she + + + align:start position:0% +we have here Anna a patient comes in she +has high blood blood sugar and some + + align:start position:0% +has high blood blood sugar and some + + + align:start position:0% +has high blood blood sugar and some +other properties and we're debating + + align:start position:0% +other properties and we're debating + + + align:start position:0% +other properties and we're debating +whether to give her a medication a or B + + align:start position:0% +whether to give her a medication a or B + + + align:start position:0% +whether to give her a medication a or B +and to do that we want to figure out + + align:start position:0% +and to do that we want to figure out + + + align:start position:0% +and to do that we want to figure out +what would be her blood sugar under this + + align:start position:0% +what would be her blood sugar under this + + + align:start position:0% +what would be her blood sugar under this +different choices a few months down the + + align:start position:0% +different choices a few months down the + + + align:start position:0% +different choices a few months down the +line so I'm just gonna I'm just using + + align:start position:0% +line so I'm just gonna I'm just using + + + align:start position:0% +line so I'm just gonna I'm just using +this here to introduce you to the + + align:start position:0% +this here to introduce you to the + + + align:start position:0% +this here to introduce you to the +patient Anna and we're going to talk + + align:start position:0% +patient Anna and we're going to talk + + + align:start position:0% +patient Anna and we're going to talk +about a little bit more so treating Anna + + align:start position:0% +about a little bit more so treating Anna + + + align:start position:0% +about a little bit more so treating Anna +once we can represent as this causal + + align:start position:0% +once we can represent as this causal + + + align:start position:0% +once we can represent as this causal +graph that you've seen a lot of times + + align:start position:0% +graph that you've seen a lot of times + + + align:start position:0% +graph that you've seen a lot of times +now we had some treatment a we have some + + align:start position:0% +now we had some treatment a we have some + + + align:start position:0% +now we had some treatment a we have some +state s and some outcome + + align:start position:0% +state s and some outcome + + + align:start position:0% +state s and some outcome +r we want to figure out the effect of + + align:start position:0% +r we want to figure out the effect of + + + align:start position:0% +r we want to figure out the effect of +this a on the alkmaar ignore ability in + + align:start position:0% +this a on the alkmaar ignore ability in + + + align:start position:0% +this a on the alkmaar ignore ability in +this case just says that the potential + + align:start position:0% +this case just says that the potential + + + align:start position:0% +this case just says that the potential +outcomes of under each action a is + + align:start position:0% +outcomes of under each action a is + + + align:start position:0% +outcomes of under each action a is +conditional independent of a given s and + + align:start position:0% +conditional independent of a given s and + + + align:start position:0% +conditional independent of a given s and +so we know that the ignore ability is + + align:start position:0% +so we know that the ignore ability is + + + align:start position:0% +so we know that the ignore ability is +the it's a sufficient inability and + + align:start position:0% +the it's a sufficient inability and + + + align:start position:0% +the it's a sufficient inability and +overlap is sufficient conditions for + + align:start position:0% +overlap is sufficient conditions for + + + align:start position:0% +overlap is sufficient conditions for +identification of this effect but what + + align:start position:0% +identification of this effect but what + + + align:start position:0% +identification of this effect but what +happens now if we add another time point + + align:start position:0% +happens now if we add another time point + + + align:start position:0% +happens now if we add another time point +okay so in this case if I have no extra + + align:start position:0% +okay so in this case if I have no extra + + + align:start position:0% +okay so in this case if I have no extra +arrows here I just have completely + + align:start position:0% +arrows here I just have completely + + + align:start position:0% +arrows here I just have completely +independent time points ignore ability + + align:start position:0% +independent time points ignore ability + + + align:start position:0% +independent time points ignore ability +clearly still holds there's no links + + align:start position:0% +clearly still holds there's no links + + + align:start position:0% +clearly still holds there's no links +going from a to R there's no from s to + + align:start position:0% +going from a to R there's no from s to + + + align:start position:0% +going from a to R there's no from s to +or etc so ignore ability is still fine + + align:start position:0% +or etc so ignore ability is still fine + + + align:start position:0% +or etc so ignore ability is still fine +okay if I if I somehow you know choose + + align:start position:0% +okay if I if I somehow you know choose + + + align:start position:0% +okay if I if I somehow you know choose +or if Anna's health status in the future + + align:start position:0% +or if Anna's health status in the future + + + align:start position:0% +or if Anna's health status in the future +depends on the actions that I take now + + align:start position:0% +depends on the actions that I take now + + + align:start position:0% +depends on the actions that I take now +here then then I have to take the + + align:start position:0% +here then then I have to take the + + + align:start position:0% +here then then I have to take the +situation is a little bit different so + + align:start position:0% +situation is a little bit different so + + + align:start position:0% +situation is a little bit different so +this is now not in the completely + + align:start position:0% +this is now not in the completely + + + align:start position:0% +this is now not in the completely +independent actions that I make with the + + align:start position:0% +independent actions that I make with the + + + align:start position:0% +independent actions that I make with the +actions here influence the state in the + + align:start position:0% +actions here influence the state in the + + + align:start position:0% +actions here influence the state in the +future so we've seen this this is again + + align:start position:0% +future so we've seen this this is again + + + align:start position:0% +future so we've seen this this is again +this is a mark of decision process that + + align:start position:0% +this is a mark of decision process that + + + align:start position:0% +this is a mark of decision process that +you've seen before and this is very + + align:start position:0% +you've seen before and this is very + + + align:start position:0% +you've seen before and this is very +likely this is very likely in practice + + align:start position:0% +likely this is very likely in practice + + + align:start position:0% +likely this is very likely in practice +also if Anna for example is diabetic as + + align:start position:0% +also if Anna for example is diabetic as + + + align:start position:0% +also if Anna for example is diabetic as +we saw in the example that I mentioned + + align:start position:0% +we saw in the example that I mentioned + + + align:start position:0% +we saw in the example that I mentioned +it's likely that she will remain so so + + align:start position:0% +it's likely that she will remain so so + + + align:start position:0% +it's likely that she will remain so so +these previous state will influence the + + align:start position:0% +these previous state will influence the + + + align:start position:0% +these previous state will influence the +future state these things seem very + + align:start position:0% +future state these things seem very + + + align:start position:0% +future state these things seem very +reasonable right but now I'm trying to + + align:start position:0% +reasonable right but now I'm trying to + + + align:start position:0% +reasonable right but now I'm trying to +argue + + align:start position:0% +argue + + + align:start position:0% +argue +about the sequential ignore ability + + align:start position:0% +about the sequential ignore ability + + + align:start position:0% +about the sequential ignore ability +assumption how can we break that how can + + align:start position:0% +assumption how can we break that how can + + + align:start position:0% +assumption how can we break that how can +we break ignore ability when it comes to + + align:start position:0% +we break ignore ability when it comes to + + + align:start position:0% +we break ignore ability when it comes to +the sequential setting well if you have + + align:start position:0% +the sequential setting well if you have + + + align:start position:0% +the sequential setting well if you have +if you have an action here so the + + align:start position:0% +if you have an action here so the + + + align:start position:0% +if you have an action here so the +outcome at a later point depends on an + + align:start position:0% +outcome at a later point depends on an + + + align:start position:0% +outcome at a later point depends on an +earlier choice that might certainly be + + align:start position:0% +earlier choice that might certainly be + + + align:start position:0% +earlier choice that might certainly be +the case because we could have a delayed + + align:start position:0% +the case because we could have a delayed + + + align:start position:0% +the case because we could have a delayed +effect of something so if we measure say + + align:start position:0% +effect of something so if we measure say + + + align:start position:0% +effect of something so if we measure say +a lab value and which could be in in the + + align:start position:0% +a lab value and which could be in in the + + + align:start position:0% +a lab value and which could be in in the +right range or not it would could very + + align:start position:0% +right range or not it would could very + + + align:start position:0% +right range or not it would could very +well depend on medication we gave a long + + align:start position:0% +well depend on medication we gave a long + + + align:start position:0% +well depend on medication we gave a long +time ago okay + + align:start position:0% +time ago okay + + + align:start position:0% +time ago okay +and it's also likely that the reward + + align:start position:0% +and it's also likely that the reward + + + align:start position:0% +and it's also likely that the reward +could be depend on a state which is much + + align:start position:0% +could be depend on a state which is much + + + align:start position:0% +could be depend on a state which is much +earlier depending on what we include in + + align:start position:0% +earlier depending on what we include in + + + align:start position:0% +earlier depending on what we include in +that state variable okay we already have + + align:start position:0% +that state variable okay we already have + + + align:start position:0% +that state variable okay we already have +an example I think from the audience on + + align:start position:0% +an example I think from the audience on + + + align:start position:0% +an example I think from the audience on +that so actually ignore ability should + + align:start position:0% +that so actually ignore ability should + + + align:start position:0% +that so actually ignore ability should +have a big red cross over it because it + + align:start position:0% +have a big red cross over it because it + + + align:start position:0% +have a big red cross over it because it +doesn't hold there and it's luckily on + + align:start position:0% +doesn't hold there and it's luckily on + + + align:start position:0% +doesn't hold there and it's luckily on +the next slide because they're even more + + align:start position:0% +the next slide because they're even more + + + align:start position:0% +the next slide because they're even more +errors that we can have conceivably in + + align:start position:0% +errors that we can have conceivably in + + + align:start position:0% +errors that we can have conceivably in +the medical setting right so + + align:start position:0% +the medical setting right so + + + align:start position:0% +the medical setting right so +oh yeah the example that we got from + + align:start position:0% +oh yeah the example that we got from + + + align:start position:0% +oh yeah the example that we got from +people for words essentially that if + + align:start position:0% +people for words essentially that if + + + align:start position:0% +people for words essentially that if +we've tried an action previously we + + align:start position:0% +we've tried an action previously we + + + align:start position:0% +we've tried an action previously we +might not want to try it again or like + + align:start position:0% +might not want to try it again or like + + + align:start position:0% +might not want to try it again or like +if we knew that something worked + + align:start position:0% +if we knew that something worked + + + align:start position:0% +if we knew that something worked +previously we might want to do it again + + align:start position:0% +previously we might want to do it again + + + align:start position:0% +previously we might want to do it again +so if we had a good reward here we might + + align:start position:0% +so if we had a good reward here we might + + + align:start position:0% +so if we had a good reward here we might +want to do the same thing twice and this + + align:start position:0% +want to do the same thing twice and this + + + align:start position:0% +want to do the same thing twice and this +arrow here says that if if we know that + + align:start position:0% +arrow here says that if if we know that + + + align:start position:0% +arrow here says that if if we know that +a patient had a symptom earlier on we + + align:start position:0% +a patient had a symptom earlier on we + + + align:start position:0% +a patient had a symptom earlier on we +might want to base our actions on it + + align:start position:0% +might want to base our actions on it + + + align:start position:0% +might want to base our actions on it +later or even Noah the patient was had + + align:start position:0% +later or even Noah the patient was had + + + align:start position:0% +later or even Noah the patient was had +an allergic reaction at some point for + + align:start position:0% +an allergic reaction at some point for + + + align:start position:0% +an allergic reaction at some point for +example we might not want to use that + + align:start position:0% +example we might not want to use that + + + align:start position:0% +example we might not want to use that +medication at a later time + + align:start position:0% + + + + align:start position:0% + +exactly exactly so this depends on what + + align:start position:0% +exactly exactly so this depends on what + + + align:start position:0% +exactly exactly so this depends on what +you put in the snake so this is this is + + align:start position:0% +you put in the snake so this is this is + + + align:start position:0% +you put in the snake so this is this is +the like this is an example where I + + align:start position:0% +the like this is an example where I + + + align:start position:0% +the like this is an example where I +introduced these arrows to show that if + + align:start position:0% +introduced these arrows to show that if + + + align:start position:0% +introduced these arrows to show that if +I haven't got that information here then + + align:start position:0% +I haven't got that information here then + + + align:start position:0% +I haven't got that information here then +I introduce this dependence okay so if I + + align:start position:0% +I introduce this dependence okay so if I + + + align:start position:0% +I introduce this dependence okay so if I +if I don't have the information about + + align:start position:0% +if I don't have the information about + + + align:start position:0% +if I don't have the information about +what was it a allergic reaction or some + + align:start position:0% +what was it a allergic reaction or some + + + align:start position:0% +what was it a allergic reaction or some +symptom before in here then I'm then I + + align:start position:0% +symptom before in here then I'm then I + + + align:start position:0% +symptom before in here then I'm then I +have to do something else right so + + align:start position:0% +have to do something else right so + + + align:start position:0% +have to do something else right so +exactly that is the point if I can + + align:start position:0% +exactly that is the point if I can + + + align:start position:0% +exactly that is the point if I can +summarize history in some good way if I + + align:start position:0% +summarize history in some good way if I + + + align:start position:0% +summarize history in some good way if I +can compress all of these for valuable + + align:start position:0% +can compress all of these for valuable + + + align:start position:0% +can compress all of these for valuable +of a variables sorry + + align:start position:0% +of a variables sorry + + + align:start position:0% +of a variables sorry +into some some variable age standing for + + align:start position:0% +into some some variable age standing for + + + align:start position:0% +into some some variable age standing for +the history then I have you know + + align:start position:0% +the history then I have you know + + + align:start position:0% +the history then I have you know +with respect to that history hmm + + align:start position:0% +with respect to that history hmm + + + align:start position:0% +with respect to that history hmm +the problem with that the problem I mean + + align:start position:0% +the problem with that the problem I mean + + + align:start position:0% +the problem with that the problem I mean +this is this is your solution and it + + align:start position:0% +this is this is your solution and it + + + align:start position:0% +this is this is your solution and it +introduces a new problem because history + + align:start position:0% +introduces a new problem because history + + + align:start position:0% +introduces a new problem because history +is usually a really large thing usually + + align:start position:0% +is usually a really large thing usually + + + align:start position:0% +is usually a really large thing usually +I mean we know that history grows with + + align:start position:0% +I mean we know that history grows with + + + align:start position:0% +I mean we know that history grows with +time obviously but usually we don't know + + align:start position:0% +time obviously but usually we don't know + + + align:start position:0% +time obviously but usually we don't know +serve patience for the same number of + + align:start position:0% +serve patience for the same number of + + + align:start position:0% +serve patience for the same number of +time points so how do we represent that + + align:start position:0% +time points so how do we represent that + + + align:start position:0% +time points so how do we represent that +in for a program how do we represent + + align:start position:0% +in for a program how do we represent + + + align:start position:0% +in for a program how do we represent +that your learning algorithm that's + + align:start position:0% +that your learning algorithm that's + + + align:start position:0% +that your learning algorithm that's +something we have to deal with and you + + align:start position:0% +something we have to deal with and you + + + align:start position:0% +something we have to deal with and you +can you can pad a history with zeros etc + + align:start position:0% +can you can pad a history with zeros etc + + + align:start position:0% +can you can pad a history with zeros etc +but if you keep every time step and + + align:start position:0% +but if you keep every time step and + + + align:start position:0% +but if you keep every time step and +repeat every variable in every time step + + align:start position:0% +repeat every variable in every time step + + + align:start position:0% +repeat every variable in every time step +you get a very large object right that + + align:start position:0% +you get a very large object right that + + + align:start position:0% +you get a very large object right that +might introduce statistical problems + + align:start position:0% +might introduce statistical problems + + + align:start position:0% +might introduce statistical problems +because now you have much more variance + + align:start position:0% +because now you have much more variance + + + align:start position:0% +because now you have much more variance +if you have new variables etc so one + + align:start position:0% +if you have new variables etc so one + + + align:start position:0% +if you have new variables etc so one +thing that people do is that they look + + align:start position:0% +thing that people do is that they look + + + align:start position:0% +thing that people do is that they look +some amount of time backwards so instead + + align:start position:0% +some amount of time backwards so instead + + + align:start position:0% +some amount of time backwards so instead +of just looking at one time step back + + align:start position:0% +of just looking at one time step back + + + align:start position:0% +of just looking at one time step back +you now look at the length K window and + + align:start position:0% +you now look at the length K window and + + + align:start position:0% +you now look at the length K window and +your state essentially grows by by a + + align:start position:0% +your state essentially grows by by a + + + align:start position:0% +your state essentially grows by by a +factor K and another alternative is to + + align:start position:0% +factor K and another alternative is to + + + align:start position:0% +factor K and another alternative is to +try and learn a summary function learn + + align:start position:0% +try and learn a summary function learn + + + align:start position:0% +try and learn a summary function learn +some function that is relevant for + + align:start position:0% +some function that is relevant for + + + align:start position:0% +some function that is relevant for +predicting the outcome that takes all of + + align:start position:0% +predicting the outcome that takes all of + + + align:start position:0% +predicting the outcome that takes all of +the history into account and but has a + + align:start position:0% +the history into account and but has a + + + align:start position:0% +the history into account and but has a +smaller representation than just T times + + align:start position:0% +smaller representation than just T times + + + align:start position:0% +smaller representation than just T times +the variables that you have but this is + + align:start position:0% +the variables that you have but this is + + + align:start position:0% +the variables that you have but this is +something that needs needs to happen + + align:start position:0% +something that needs needs to happen + + + align:start position:0% +something that needs needs to happen +usually if you work with any most + + align:start position:0% +usually if you work with any most + + + align:start position:0% +usually if you work with any most +healthcare data in practice you have to + + align:start position:0% +healthcare data in practice you have to + + + align:start position:0% +healthcare data in practice you have to +make choices about this I just want to + + align:start position:0% +make choices about this I just want to + + + align:start position:0% +make choices about this I just want to +stress that that's something you really + + align:start position:0% +stress that that's something you really + + + align:start position:0% +stress that that's something you really +can't avoid okay + + align:start position:0% +can't avoid okay + + + align:start position:0% +can't avoid okay +the last point I want to make is that + + align:start position:0% +the last point I want to make is that + + + align:start position:0% +the last point I want to make is that +unobserved confounding is also a problem + + align:start position:0% +unobserved confounding is also a problem + + + align:start position:0% +unobserved confounding is also a problem +that is not avoidable just due to + + align:start position:0% +that is not avoidable just due to + + + align:start position:0% +that is not avoidable just due to +summarizing history we can introduce new + + align:start position:0% +summarizing history we can introduce new + + + align:start position:0% +summarizing history we can introduce new +confounding that is a problem if we + + align:start position:0% +confounding that is a problem if we + + + align:start position:0% +confounding that is a problem if we +don't summarize history well but we can + + align:start position:0% +don't summarize history well but we can + + + align:start position:0% +don't summarize history well but we can +also have unobserved confounders just + + align:start position:0% +also have unobserved confounders just + + + align:start position:0% +also have unobserved confounders just +like we can in the one-step setting so + + align:start position:0% +like we can in the one-step setting so + + + align:start position:0% +like we can in the one-step setting so +one case is the the one example is if we + + align:start position:0% +one case is the the one example is if we + + + align:start position:0% +one case is the the one example is if we +have an unobserved confounder for in the + + align:start position:0% +have an unobserved confounder for in the + + + align:start position:0% +have an unobserved confounder for in the +same way as we did before it impacts + + align:start position:0% +same way as we did before it impacts + + + align:start position:0% +same way as we did before it impacts +both the immediate or the action at time + + align:start position:0% +both the immediate or the action at time + + + align:start position:0% +both the immediate or the action at time +one and the reward at time one but of + + align:start position:0% +one and the reward at time one but of + + + align:start position:0% +one and the reward at time one but of +course now we're in the sequential + + align:start position:0% +course now we're in the sequential + + + align:start position:0% +course now we're in the sequential +setting the compounding structure could + + align:start position:0% +setting the compounding structure could + + + align:start position:0% +setting the compounding structure could +be much more complicated we could have a + + align:start position:0% +be much more complicated we could have a + + + align:start position:0% +be much more complicated we could have a +confounder that influences an early + + align:start position:0% +confounder that influences an early + + + align:start position:0% +confounder that influences an early +action and a late reward so it might be + + align:start position:0% +action and a late reward so it might be + + + align:start position:0% +action and a late reward so it might be +a little harder for us to characterize + + align:start position:0% +a little harder for us to characterize + + + align:start position:0% +a little harder for us to characterize +what is the set of potential confounders + + align:start position:0% +what is the set of potential confounders + + + align:start position:0% +what is the set of potential confounders +I just wanted to point that out and do + + align:start position:0% +I just wanted to point that out and do + + + align:start position:0% +I just wanted to point that out and do +it + + align:start position:0% +it + + + align:start position:0% +it +reinforce that this is only harder than + + align:start position:0% +reinforce that this is only harder than + + + align:start position:0% +reinforce that this is only harder than +the one subsetting so we're wrapping up + + align:start position:0% +the one subsetting so we're wrapping up + + + align:start position:0% +the one subsetting so we're wrapping up +now I just want to end on a point about + + align:start position:0% +now I just want to end on a point about + + + align:start position:0% +now I just want to end on a point about +the the games that we looked at before + + align:start position:0% +the the games that we looked at before + + + align:start position:0% +the the games that we looked at before +one of the big reasons that they the + + align:start position:0% +one of the big reasons that they the + + + align:start position:0% +one of the big reasons that they the +these algorithms were so successful in + + align:start position:0% +these algorithms were so successful in + + + align:start position:0% +these algorithms were so successful in +playing games was that we have full + + align:start position:0% +playing games was that we have full + + + align:start position:0% +playing games was that we have full +observability in these settings we know + + align:start position:0% +observability in these settings we know + + + align:start position:0% +observability in these settings we know +everything from the from the game board + + align:start position:0% +everything from the from the game board + + + align:start position:0% +everything from the from the game board +itself when it comes to go at least and + + align:start position:0% +itself when it comes to go at least and + + + align:start position:0% +itself when it comes to go at least and +we can debate that with it when it comes + + align:start position:0% +we can debate that with it when it comes + + + align:start position:0% +we can debate that with it when it comes +to the video games but but in go we have + + align:start position:0% +to the video games but but in go we have + + + align:start position:0% +to the video games but but in go we have +complete observability of the board + + align:start position:0% +complete observability of the board + + + align:start position:0% +complete observability of the board +everything we need to know for an + + align:start position:0% +everything we need to know for an + + + align:start position:0% +everything we need to know for an +optimal decision is there at any time + + align:start position:0% +optimal decision is there at any time + + + align:start position:0% +optimal decision is there at any time +point so not only not only can we + + align:start position:0% +point so not only not only can we + + + align:start position:0% +point so not only not only can we +observe it through the history but in + + align:start position:0% +observe it through the history but in + + + align:start position:0% +observe it through the history but in +the case of go you don't even need to + + align:start position:0% +the case of go you don't even need to + + + align:start position:0% +the case of go you don't even need to +look at history week we certainly have + + align:start position:0% +look at history week we certainly have + + + align:start position:0% +look at history week we certainly have +more come to mark of dynamics with + + align:start position:0% +more come to mark of dynamics with + + + align:start position:0% +more come to mark of dynamics with +respect to the board itself you don't + + align:start position:0% +respect to the board itself you don't + + + align:start position:0% +respect to the board itself you don't +ever have to remember what what wasn't + + align:start position:0% +ever have to remember what what wasn't + + + align:start position:0% +ever have to remember what what wasn't +move earlier on unless you want to read + + align:start position:0% +move earlier on unless you want to read + + + align:start position:0% +move earlier on unless you want to read +into your opponent I suppose but that's + + align:start position:0% +into your opponent I suppose but that's + + + align:start position:0% +into your opponent I suppose but that's +a game theoretic sort of notion we're + + align:start position:0% +a game theoretic sort of notion we're + + + align:start position:0% +a game theoretic sort of notion we're +not going to get into here but more + + align:start position:0% +not going to get into here but more + + + align:start position:0% +not going to get into here but more +importantly we can explore the dynamics + + align:start position:0% +importantly we can explore the dynamics + + + align:start position:0% +importantly we can explore the dynamics +of these systems almost limitlessly just + + align:start position:0% +of these systems almost limitlessly just + + + align:start position:0% +of these systems almost limitlessly just +by simulation and self play and that's + + align:start position:0% +by simulation and self play and that's + + + align:start position:0% +by simulation and self play and that's +true regardless if you have follow-ups + + align:start position:0% +true regardless if you have follow-ups + + + align:start position:0% +true regardless if you have follow-ups +of ability or not like in StarCraft you + + align:start position:0% +of ability or not like in StarCraft you + + + align:start position:0% +of ability or not like in StarCraft you +might not have full of serve ability but + + align:start position:0% +might not have full of serve ability but + + + align:start position:0% +might not have full of serve ability but +you can try your things out endlessly + + align:start position:0% +you can try your things out endlessly + + + align:start position:0% +you can try your things out endlessly +and contrast up with having I don't know + + align:start position:0% +and contrast up with having I don't know + + + align:start position:0% +and contrast up with having I don't know +700 patients with rheumatoid arthritis + + align:start position:0% +700 patients with rheumatoid arthritis + + + align:start position:0% +700 patients with rheumatoid arthritis +or something like that those are the + + align:start position:0% +or something like that those are the + + + align:start position:0% +or something like that those are the +samples you have you're not going to get + + align:start position:0% +samples you have you're not going to get + + + align:start position:0% +samples you have you're not going to get +new ones so that is like this is an + + align:start position:0% +new ones so that is like this is an + + + align:start position:0% +new ones so that is like this is an +amazing obstacle for us to overcome if + + align:start position:0% +amazing obstacle for us to overcome if + + + align:start position:0% +amazing obstacle for us to overcome if +we want to do this in a good way the + + align:start position:0% +we want to do this in a good way the + + + align:start position:0% +we want to do this in a good way the +current all our albums are really really + + align:start position:0% +current all our albums are really really + + + align:start position:0% +current all our albums are really really +inefficient with the data that they use + + align:start position:0% +inefficient with the data that they use + + + align:start position:0% +inefficient with the data that they use +and that's why this limitless + + align:start position:0% +and that's why this limitless + + + align:start position:0% +and that's why this limitless +exploration where simulation has been so + + align:start position:0% +exploration where simulation has been so + + + align:start position:0% +exploration where simulation has been so +important for these games and that's + + align:start position:0% +important for these games and that's + + + align:start position:0% +important for these games and that's +also why the games are the success + + align:start position:0% +also why the games are the success + + + align:start position:0% +also why the games are the success +stories of this a last point is that + + align:start position:0% +stories of this a last point is that + + + align:start position:0% +stories of this a last point is that +typically for these settings that I put + + align:start position:0% +typically for these settings that I put + + + align:start position:0% +typically for these settings that I put +here we have we have no noise + + align:start position:0% +here we have we have no noise + + + align:start position:0% +here we have we have no noise +essentially we get perfect observations + + align:start position:0% +essentially we get perfect observations + + + align:start position:0% +essentially we get perfect observations +of actions and states and outcomes and + + align:start position:0% +of actions and states and outcomes and + + + align:start position:0% +of actions and states and outcomes and +everything like that and that's really + + align:start position:0% +everything like that and that's really + + + align:start position:0% +everything like that and that's really +true in any real world application all + + align:start position:0% +true in any real world application all + + + align:start position:0% +true in any real world application all +right I'm gonna wrap up tomorrow + + align:start position:0% +right I'm gonna wrap up tomorrow + + + align:start position:0% +right I'm gonna wrap up tomorrow +nope Thursday David is going to talk + + align:start position:0% +nope Thursday David is going to talk + + + align:start position:0% +nope Thursday David is going to talk +about more explicitly if we want to do + + align:start position:0% +about more explicitly if we want to do + + + align:start position:0% +about more explicitly if we want to do +this properly in health care what's + + align:start position:0% +this properly in health care what's + + + align:start position:0% +this properly in health care what's +going to happen we're gonna have a great + + align:start position:0% +going to happen we're gonna have a great + + + align:start position:0% +going to happen we're gonna have a great +discussion I'm sure as well so don't + + align:start position:0% +discussion I'm sure as well so don't + + + align:start position:0% +discussion I'm sure as well so don't +mind this slide it's Thursday alright + + align:start position:0% +mind this slide it's Thursday alright + + + align:start position:0% +mind this slide it's Thursday alright +thanks a lot + + align:start position:0% +thanks a lot + + + align:start position:0% +thanks a lot +[Applause] \ No newline at end of file diff --git a/Y_Ac6KiQ1t0.txt b/Y_Ac6KiQ1t0.txt new file mode 100644 index 0000000000000000000000000000000000000000..7ac58795d289cae05db77b3ba7c6652e4f98d8a0 --- /dev/null +++ b/Y_Ac6KiQ1t0.txt @@ -0,0 +1,6939 @@ +align:start position:0% + +okay guys uh we're almost ready + + align:start position:0% + + + + align:start position:0% + +to make this make this lecture + + align:start position:0% +to make this make this lecture + + + align:start position:0% +to make this make this lecture +Immortal + + align:start position:0% +Immortal + + + align:start position:0% +Immortal +okay are we on all right this is an + + align:start position:0% +okay are we on all right this is an + + + align:start position:0% +okay are we on all right this is an +important lecture it's about + + align:start position:0% +important lecture it's about + + + align:start position:0% +important lecture it's about +projection and and uh let me start by + + align:start position:0% +projection and and uh let me start by + + + align:start position:0% +projection and and uh let me start by +just projecting a vector B down on a + + align:start position:0% +just projecting a vector B down on a + + + align:start position:0% +just projecting a vector B down on a +vector a so just to so you see what the + + align:start position:0% +vector a so just to so you see what the + + + align:start position:0% +vector a so just to so you see what the +geometry looks like in when I'm in in + + align:start position:0% +geometry looks like in when I'm in in + + + align:start position:0% +geometry looks like in when I'm in in +just two Dimensions I'd like to find the + + align:start position:0% +just two Dimensions I'd like to find the + + + align:start position:0% +just two Dimensions I'd like to find the +point along this + + align:start position:0% +point along this + + + align:start position:0% +point along this +line so that that line through a is a + + align:start position:0% +line so that that line through a is a + + + align:start position:0% +line so that that line through a is a +one-dimensional Subspace so I'm starting + + align:start position:0% +one-dimensional Subspace so I'm starting + + + align:start position:0% +one-dimensional Subspace so I'm starting +with one dimension I'd like to find the + + align:start position:0% +with one dimension I'd like to find the + + + align:start position:0% +with one dimension I'd like to find the +point on that line closest to B + + align:start position:0% +point on that line closest to B + + + align:start position:0% +point on that line closest to B +can I just take that problem first and + + align:start position:0% +can I just take that problem first and + + + align:start position:0% +can I just take that problem first and +then I'll explain why I want to do it + + align:start position:0% +then I'll explain why I want to do it + + + align:start position:0% +then I'll explain why I want to do it +and why I want to project on other + + align:start position:0% +and why I want to project on other + + + align:start position:0% +and why I want to project on other +subspaces so where where is the point + + align:start position:0% +subspaces so where where is the point + + + align:start position:0% +subspaces so where where is the point +closest to B that's on that line it's + + align:start position:0% +closest to B that's on that line it's + + + align:start position:0% +closest to B that's on that line it's +somewhere there and let me connect + + align:start position:0% + + + + align:start position:0% + +that and and what's the whole point of + + align:start position:0% +that and and what's the whole point of + + + align:start position:0% +that and and what's the whole point of +my picture now what what's the where + + align:start position:0% +my picture now what what's the where + + + align:start position:0% +my picture now what what's the where +does orthogonality come into this + + align:start position:0% +does orthogonality come into this + + + align:start position:0% +does orthogonality come into this +picture + + align:start position:0% +picture + + + align:start position:0% +picture +the whole point is that this this best + + align:start position:0% +the whole point is that this this best + + + align:start position:0% +the whole point is that this this best +point that's the projection + + align:start position:0% +point that's the projection + + + align:start position:0% +point that's the projection +P of B onto the + + align:start position:0% +P of B onto the + + + align:start position:0% +P of B onto the +line uh where is + + align:start position:0% +line uh where is + + + align:start position:0% +line uh where is +orthogonality it's the fact that that's + + align:start position:0% +orthogonality it's the fact that that's + + + align:start position:0% +orthogonality it's the fact that that's +a right angle that this the error this + + align:start position:0% +a right angle that this the error this + + + align:start position:0% +a right angle that this the error this +is like how much I'm Wrong by this is + + align:start position:0% +is like how much I'm Wrong by this is + + + align:start position:0% +is like how much I'm Wrong by this is +the difference between B and P the whole + + align:start position:0% +the difference between B and P the whole + + + align:start position:0% +the difference between B and P the whole +point is that that that that's + + align:start position:0% +point is that that that that's + + + align:start position:0% +point is that that that that's +perpendicular to a that's got to give us + + align:start position:0% +perpendicular to a that's got to give us + + + align:start position:0% +perpendicular to a that's got to give us +the equation that's got to tell us + + align:start position:0% +the equation that's got to tell us + + + align:start position:0% +the equation that's got to tell us +that's that's the one fact we know + + align:start position:0% +that's that's the one fact we know + + + align:start position:0% +that's that's the one fact we know +that's got to tell us where that + + align:start position:0% +that's got to tell us where that + + + align:start position:0% +that's got to tell us where that +projection is let me also say look I + + align:start position:0% +projection is let me also say look I + + + align:start position:0% +projection is let me also say look I +I've drawn a triangle there so if we + + align:start position:0% +I've drawn a triangle there so if we + + + align:start position:0% +I've drawn a triangle there so if we +were doing trigonometry we would do like + + align:start position:0% +were doing trigonometry we would do like + + + align:start position:0% +were doing trigonometry we would do like +we would have angles Theta and distances + + align:start position:0% +we would have angles Theta and distances + + + align:start position:0% +we would have angles Theta and distances +that would involve sin Theta and cos + + align:start position:0% +that would involve sin Theta and cos + + + align:start position:0% +that would involve sin Theta and cos +Theta that leads to lousy formulas + + align:start position:0% +Theta that leads to lousy formulas + + + align:start position:0% +Theta that leads to lousy formulas +compared to linear algebra the the the + + align:start position:0% +compared to linear algebra the the the + + + align:start position:0% +compared to linear algebra the the the +formula that we want comes out nicely + + align:start position:0% +formula that we want comes out nicely + + + align:start position:0% +formula that we want comes out nicely +and what's the what do we know we know + + align:start position:0% +and what's the what do we know we know + + + align:start position:0% +and what's the what do we know we know +that P this projection is some multiple + + align:start position:0% +that P this projection is some multiple + + + align:start position:0% +that P this projection is some multiple +of a right it's on that line so we know + + align:start position:0% +of a right it's on that line so we know + + + align:start position:0% +of a right it's on that line so we know +it's it's in that one-dimensional + + align:start position:0% +it's it's in that one-dimensional + + + align:start position:0% +it's it's in that one-dimensional +Subspace it's some multiple let me call + + align:start position:0% +Subspace it's some multiple let me call + + + align:start position:0% +Subspace it's some multiple let me call +that multiple X of a so really it's that + + align:start position:0% +that multiple X of a so really it's that + + + align:start position:0% +that multiple X of a so really it's that +number X I'd like to + + align:start position:0% +number X I'd like to + + + align:start position:0% +number X I'd like to +find so th this is going to be simple in + + align:start position:0% +find so th this is going to be simple in + + + align:start position:0% +find so th this is going to be simple in +1D so let's just carry it through and + + align:start position:0% +1D so let's just carry it through and + + + align:start position:0% +1D so let's just carry it through and +then see how it goes in high dimension + + align:start position:0% +then see how it goes in high dimension + + + align:start position:0% +then see how it goes in high dimension +okay the key fact is so the the key the + + align:start position:0% +okay the key fact is so the the key the + + + align:start position:0% +okay the key fact is so the the key the +key to everything is that perpendicular + + align:start position:0% +key to everything is that perpendicular + + + align:start position:0% +key to everything is that perpendicular +the fact that that a is perpendicular to + + align:start position:0% +the fact that that a is perpendicular to + + + align:start position:0% +the fact that that a is perpendicular to +a is perpendicular to + + align:start position:0% +a is perpendicular to + + + align:start position:0% +a is perpendicular to +e which is B minus a x x a I don't care + + align:start position:0% +e which is B minus a x x a I don't care + + + align:start position:0% +e which is B minus a x x a I don't care +if that's x a that that equals + + align:start position:0% +if that's x a that that equals + + + align:start position:0% +if that's x a that that equals +zero you see that as the central + + align:start position:0% +zero you see that as the central + + + align:start position:0% +zero you see that as the central +equation that's saying that this + + align:start position:0% +equation that's saying that this + + + align:start position:0% +equation that's saying that this +a is perpendicular to this correction + + align:start position:0% +a is perpendicular to this correction + + + align:start position:0% +a is perpendicular to this correction +that's going to tell us what x is let me + + align:start position:0% +that's going to tell us what x is let me + + + align:start position:0% +that's going to tell us what x is let me +just raise the board and simplify that + + align:start position:0% +just raise the board and simplify that + + + align:start position:0% +just raise the board and simplify that +and out will come X + + align:start position:0% +and out will come X + + + align:start position:0% +and out will come X +okay so if I simplify that uh let's see + + align:start position:0% +okay so if I simplify that uh let's see + + + align:start position:0% +okay so if I simplify that uh let's see +I'll move one to to one term to one side + + align:start position:0% +I'll move one to to one term to one side + + + align:start position:0% +I'll move one to to one term to one side +the other term will be on the other side + + align:start position:0% +the other term will be on the other side + + + align:start position:0% +the other term will be on the other side +it looks to me like x * a transpose + + align:start position:0% +it looks to me like x * a transpose + + + align:start position:0% +it looks to me like x * a transpose +a is equal to a transpose + + align:start position:0% + + + + align:start position:0% + +B right I have a transpose B is one one + + align:start position:0% +B right I have a transpose B is one one + + + align:start position:0% +B right I have a transpose B is one one +term a transpose a is the other so right + + align:start position:0% +term a transpose a is the other so right + + + align:start position:0% +term a transpose a is the other so right +away here's my a transpose a but it it's + + align:start position:0% +away here's my a transpose a but it it's + + + align:start position:0% +away here's my a transpose a but it it's +just a number now and I divide by it and + + align:start position:0% +just a number now and I divide by it and + + + align:start position:0% +just a number now and I divide by it and +I get the answer X is a transpose B over + + align:start position:0% +I get the answer X is a transpose B over + + + align:start position:0% +I get the answer X is a transpose B over +a transpose + + align:start position:0% + + + + align:start position:0% + +A and P the projection I wanted is + + align:start position:0% +A and P the projection I wanted is + + + align:start position:0% +A and P the projection I wanted is +that's the that's the right multiple + + align:start position:0% +that's the that's the right multiple + + + align:start position:0% +that's the that's the right multiple +that's got a cosine Theta built in but + + align:start position:0% +that's got a cosine Theta built in but + + + align:start position:0% +that's got a cosine Theta built in but +we don't need to look at Angles we've + + align:start position:0% +we don't need to look at Angles we've + + + align:start position:0% +we don't need to look at Angles we've +just got vectors here and the projection + + align:start position:0% +just got vectors here and the projection + + + align:start position:0% +just got vectors here and the projection +is p + + align:start position:0% +is p + + + align:start position:0% +is p +is + + align:start position:0% +is + + + align:start position:0% +is +a times that + + align:start position:0% +a times that + + + align:start position:0% +a times that +X or x times that a but I I'm really + + align:start position:0% +X or x times that a but I I'm really + + + align:start position:0% +X or x times that a but I I'm really +going to eventually I'm going to want + + align:start position:0% +going to eventually I'm going to want + + + align:start position:0% +going to eventually I'm going to want +that X coming on the right hand side so + + align:start position:0% +that X coming on the right hand side so + + + align:start position:0% +that X coming on the right hand side so +you see that I've + + align:start position:0% +you see that I've + + + align:start position:0% +you see that I've +got two of the three formulas + + align:start position:0% +got two of the three formulas + + + align:start position:0% +got two of the three formulas +already right here I've got the the the + + align:start position:0% +already right here I've got the the the + + + align:start position:0% +already right here I've got the the the +equation that's the equation that that + + align:start position:0% +equation that's the equation that that + + + align:start position:0% +equation that's the equation that that +that that leads me to the answer here's + + align:start position:0% +that that leads me to the answer here's + + + align:start position:0% +that that leads me to the answer here's +here's the answer for x and here's the + + align:start position:0% +here's the answer for x and here's the + + + align:start position:0% +here's the answer for x and here's the +projection okay can I do add just one + + align:start position:0% +projection okay can I do add just one + + + align:start position:0% +projection okay can I do add just one +more thing to this onedimensional + + align:start position:0% +more thing to this onedimensional + + + align:start position:0% +more thing to this onedimensional +problem one more like lift it up into + + align:start position:0% +problem one more like lift it up into + + + align:start position:0% +problem one more like lift it up into +linear algebra into + + align:start position:0% + + + + align:start position:0% + +matrices here's the last thing I want to + + align:start position:0% +matrices here's the last thing I want to + + + align:start position:0% +matrices here's the last thing I want to +do with but don't forget those formulas + + align:start position:0% +do with but don't forget those formulas + + + align:start position:0% +do with but don't forget those formulas +a transpose B over a transpose + + align:start position:0% +a transpose B over a transpose + + + align:start position:0% +a transpose B over a transpose +a actually let's look at that for a + + align:start position:0% +a actually let's look at that for a + + + align:start position:0% +a actually let's look at that for a +moment first uh um + + align:start position:0% + + + + align:start position:0% + +suppose uh and and and a well then I + + align:start position:0% +suppose uh and and and a well then I + + + align:start position:0% +suppose uh and and and a well then I +I'll let me I'll let me take this next + + align:start position:0% +I'll let me I'll let me take this next + + + align:start position:0% +I'll let me I'll let me take this next +step so p is a * X so can I write that + + align:start position:0% +step so p is a * X so can I write that + + + align:start position:0% +step so p is a * X so can I write that +then p is a * this neat number a + + align:start position:0% +then p is a * this neat number a + + + align:start position:0% +then p is a * this neat number a +transpose B over a transpose + + align:start position:0% + + + + align:start position:0% + +a that's our + + align:start position:0% +a that's our + + + align:start position:0% +a that's our +projection can I ask a couple of + + align:start position:0% +projection can I ask a couple of + + + align:start position:0% +projection can I ask a couple of +questions about it just while we look + + align:start position:0% +questions about it just while we look + + + align:start position:0% +questions about it just while we look +get that digest that formula + + align:start position:0% +get that digest that formula + + + align:start position:0% +get that digest that formula +suppose B is doubled suppose I change B + + align:start position:0% +suppose B is doubled suppose I change B + + + align:start position:0% +suppose B is doubled suppose I change B +to + + align:start position:0% +to + + + align:start position:0% +to +2B what happens to the + + align:start position:0% + + + + align:start position:0% + +projection so suppose I instead of that + + align:start position:0% +projection so suppose I instead of that + + + align:start position:0% +projection so suppose I instead of that +Vector B that I drew on the board make + + align:start position:0% +Vector B that I drew on the board make + + + align:start position:0% +Vector B that I drew on the board make +it 2 B twice as long what's what's the + + align:start position:0% +it 2 B twice as long what's what's the + + + align:start position:0% +it 2 B twice as long what's what's the +projection + + align:start position:0% +projection + + + align:start position:0% +projection +now it's double to right it's going to + + align:start position:0% +now it's double to right it's going to + + + align:start position:0% +now it's double to right it's going to +be twice as far if B goes twice as far + + align:start position:0% +be twice as far if B goes twice as far + + + align:start position:0% +be twice as far if B goes twice as far +the projection will go twice as far and + + align:start position:0% +the projection will go twice as far and + + + align:start position:0% +the projection will go twice as far and +you see it there if I put in an extra + + align:start position:0% +you see it there if I put in an extra + + + align:start position:0% +you see it there if I put in an extra +Factor two then then P's got that factor + + align:start position:0% +Factor two then then P's got that factor + + + align:start position:0% +Factor two then then P's got that factor +too now what about if I double + + align:start position:0% +too now what about if I double + + + align:start position:0% +too now what about if I double +A what if I double the vector a that I'm + + align:start position:0% +A what if I double the vector a that I'm + + + align:start position:0% +A what if I double the vector a that I'm +projecting + + align:start position:0% +projecting + + + align:start position:0% +projecting +onto what what + + align:start position:0% +onto what what + + + align:start position:0% +onto what what +changes no the projection doesn't change + + align:start position:0% +changes no the projection doesn't change + + + align:start position:0% +changes no the projection doesn't change +at all right CU I'm just the line didn't + + align:start position:0% +at all right CU I'm just the line didn't + + + align:start position:0% +at all right CU I'm just the line didn't +change if I double a or I take minus a + + align:start position:0% +change if I double a or I take minus a + + + align:start position:0% +change if I double a or I take minus a +it's still that same line the projection + + align:start position:0% +it's still that same line the projection + + + align:start position:0% +it's still that same line the projection +still in the same place and of course if + + align:start position:0% +still in the same place and of course if + + + align:start position:0% +still in the same place and of course if +I double A I get a four up up above and + + align:start position:0% +I double A I get a four up up above and + + + align:start position:0% +I double A I get a four up up above and +I get a four extra four below they + + align:start position:0% +I get a four extra four below they + + + align:start position:0% +I get a four extra four below they +cancel out and the projection is the + + align:start position:0% +cancel out and the projection is the + + + align:start position:0% +cancel out and the projection is the +same okay so + + align:start position:0% +same okay so + + + align:start position:0% +same okay so +really this I want to look at + + align:start position:0% +really this I want to look at + + + align:start position:0% +really this I want to look at +this + + align:start position:0% +this + + + align:start position:0% +this +as the projection is there's a matrix + + align:start position:0% +as the projection is there's a matrix + + + align:start position:0% +as the projection is there's a matrix +here the projection is being + + align:start position:0% +here the projection is being + + + align:start position:0% +here the projection is being +is carried out by some Matrix that I'm + + align:start position:0% +is carried out by some Matrix that I'm + + + align:start position:0% +is carried out by some Matrix that I'm +going to call the projection Matrix and + + align:start position:0% +going to call the projection Matrix and + + + align:start position:0% +going to call the projection Matrix and +in other words the projection is some + + align:start position:0% +in other words the projection is some + + + align:start position:0% +in other words the projection is some +Matrix that acts on this guy B and + + align:start position:0% +Matrix that acts on this guy B and + + + align:start position:0% +Matrix that acts on this guy B and +produces the projection the + + align:start position:0% +produces the projection the + + + align:start position:0% +produces the projection the +projection + + align:start position:0% +projection + + + align:start position:0% +projection +p is the projection Matrix acting on + + align:start position:0% +p is the projection Matrix acting on + + + align:start position:0% +p is the projection Matrix acting on +whatever the input is the input is B the + + align:start position:0% +whatever the input is the input is B the + + + align:start position:0% +whatever the input is the input is B the +projection Matrix is p okay actually you + + align:start position:0% +projection Matrix is p okay actually you + + + align:start position:0% +projection Matrix is p okay actually you +can tell me right away what this + + align:start position:0% +can tell me right away what this + + + align:start position:0% +can tell me right away what this +projection Matrix is so this is a + + align:start position:0% +projection Matrix is so this is a + + + align:start position:0% +projection Matrix is so this is a +pretty interesting + + align:start position:0% +pretty interesting + + + align:start position:0% +pretty interesting +Matrix what Matrix is multiplying B I'm + + align:start position:0% +Matrix what Matrix is multiplying B I'm + + + align:start position:0% +Matrix what Matrix is multiplying B I'm +just just from my formula I see what p + + align:start position:0% +just just from my formula I see what p + + + align:start position:0% +just just from my formula I see what p +is p this projection + + align:start position:0% + + + + align:start position:0% + +Matrix + + align:start position:0% +Matrix + + + align:start position:0% +Matrix +is what is it I see a a transpose + + align:start position:0% +is what is it I see a a transpose + + + align:start position:0% +is what is it I see a a transpose +above and I see a transpose a below + + align:start position:0% + + + + align:start position:0% + +and those don't cancel that's not + + align:start position:0% +and those don't cancel that's not + + + align:start position:0% +and those don't cancel that's not +one right that's a matrix because down + + align:start position:0% +one right that's a matrix because down + + + align:start position:0% +one right that's a matrix because down +here the a transpose a that's just a + + align:start position:0% +here the a transpose a that's just a + + + align:start position:0% +here the a transpose a that's just a +number a transpose a that's the length + + align:start position:0% +number a transpose a that's the length + + + align:start position:0% +number a transpose a that's the length +of a squ and up above is a column time a + + align:start position:0% +of a squ and up above is a column time a + + + align:start position:0% +of a squ and up above is a column time a +row column time a row is a matrix so + + align:start position:0% +row column time a row is a matrix so + + + align:start position:0% +row column time a row is a matrix so +this is a full scale n byn Matrix if I + + align:start position:0% +this is a full scale n byn Matrix if I + + + align:start position:0% +this is a full scale n byn Matrix if I +if I'm in N + + align:start position:0% +if I'm in N + + + align:start position:0% +if I'm in N +Dimension and it's kind of an + + align:start position:0% +Dimension and it's kind of an + + + align:start position:0% +Dimension and it's kind of an +interesting one and it's the one which + + align:start position:0% +interesting one and it's the one which + + + align:start position:0% +interesting one and it's the one which +If I multiply by B then I get this you + + align:start position:0% +If I multiply by B then I get this you + + + align:start position:0% +If I multiply by B then I get this you +see once again I'm putting parentheses + + align:start position:0% +see once again I'm putting parentheses + + + align:start position:0% +see once again I'm putting parentheses +in different places I'm putting the + + align:start position:0% +in different places I'm putting the + + + align:start position:0% +in different places I'm putting the +parentheses like + + align:start position:0% +parentheses like + + + align:start position:0% +parentheses like +there I'm saying okay that's really the + + align:start position:0% +there I'm saying okay that's really the + + + align:start position:0% +there I'm saying okay that's really the +Matrix that produces + + align:start position:0% +Matrix that produces + + + align:start position:0% +Matrix that produces +this + + align:start position:0% +this + + + align:start position:0% +this +projection okay now tell me + + align:start position:0% +projection okay now tell me + + + align:start position:0% +projection okay now tell me +all right what are the properties of + + align:start position:0% +all right what are the properties of + + + align:start position:0% +all right what are the properties of +that + + align:start position:0% +that + + + align:start position:0% +that +Matrix I'm just using letters here A and + + align:start position:0% +Matrix I'm just using letters here A and + + + align:start position:0% +Matrix I'm just using letters here A and +B I could put in numbers but I think + + align:start position:0% +B I could put in numbers but I think + + + align:start position:0% +B I could put in numbers but I think +it's for once it's clearer with letters + + align:start position:0% +it's for once it's clearer with letters + + + align:start position:0% +it's for once it's clearer with letters +because all formulas are simple a + + align:start position:0% +because all formulas are simple a + + + align:start position:0% +because all formulas are simple a +transpose B over a transpose a that's + + align:start position:0% +transpose B over a transpose a that's + + + align:start position:0% +transpose B over a transpose a that's +the number that multiplies the A and + + align:start position:0% +the number that multiplies the A and + + + align:start position:0% +the number that multiplies the A and +then I see wait a minute there's a + + align:start position:0% +then I see wait a minute there's a + + + align:start position:0% +then I see wait a minute there's a +matrix here and what's the rank of that + + align:start position:0% +matrix here and what's the rank of that + + + align:start position:0% +matrix here and what's the rank of that +matrix by the + + align:start position:0% +matrix by the + + + align:start position:0% +matrix by the +way what what's the rank of that Matrix + + align:start position:0% +way what what's the rank of that Matrix + + + align:start position:0% +way what what's the rank of that Matrix +yeah let me let me just ask you about + + align:start position:0% +yeah let me let me just ask you about + + + align:start position:0% +yeah let me let me just ask you about +that Matrix which looks a little strange + + align:start position:0% +that Matrix which looks a little strange + + + align:start position:0% +that Matrix which looks a little strange +a a transpose over this number but + + align:start position:0% + + + + align:start position:0% + +uh well I could ask you it's column + + align:start position:0% +uh well I could ask you it's column + + + align:start position:0% +uh well I could ask you it's column +space yeah let me ask you it's column + + align:start position:0% +space yeah let me ask you it's column + + + align:start position:0% +space yeah let me ask you it's column +space so what's the column space of a + + align:start position:0% +space so what's the column space of a + + + align:start position:0% +space so what's the column space of a +matrix it's it's if you multiply that + + align:start position:0% +matrix it's it's if you multiply that + + + align:start position:0% +matrix it's it's if you multiply that +matrix by anything you always get in the + + align:start position:0% +matrix by anything you always get in the + + + align:start position:0% +matrix by anything you always get in the +column space right + + align:start position:0% +column space right + + + align:start position:0% +column space right +the column space of a matrix + + align:start position:0% +the column space of a matrix + + + align:start position:0% +the column space of a matrix +is when you multiply any vector by that + + align:start position:0% +is when you multiply any vector by that + + + align:start position:0% +is when you multiply any vector by that +Matrix any Vector + + align:start position:0% +Matrix any Vector + + + align:start position:0% +Matrix any Vector +B by The Matrix you always land in the + + align:start position:0% +B by The Matrix you always land in the + + + align:start position:0% +B by The Matrix you always land in the +column space that's that's what column + + align:start position:0% +column space that's that's what column + + + align:start position:0% +column space that's that's what column +spaces + + align:start position:0% +spaces + + + align:start position:0% +spaces +were now what space do we always land in + + align:start position:0% +were now what space do we always land in + + + align:start position:0% +were now what space do we always land in +what's the column space of what's the + + align:start position:0% +what's the column space of what's the + + + align:start position:0% +what's the column space of what's the +result when I multiply this any Vector B + + align:start position:0% +result when I multiply this any Vector B + + + align:start position:0% +result when I multiply this any Vector B +by my Matrix + + align:start position:0% +by my Matrix + + + align:start position:0% +by my Matrix +so I have P * + + align:start position:0% +so I have P * + + + align:start position:0% +so I have P * +B where am + + align:start position:0% +B where am + + + align:start position:0% +B where am +I I'm on that line right the column + + align:start position:0% +I I'm on that line right the column + + + align:start position:0% +I I'm on that line right the column +space so here are facts about this + + align:start position:0% +space so here are facts about this + + + align:start position:0% +space so here are facts about this +Matrix the column space of + + align:start position:0% +Matrix the column space of + + + align:start position:0% +Matrix the column space of +P of this projection Matrix is the line + + align:start position:0% +P of this projection Matrix is the line + + + align:start position:0% +P of this projection Matrix is the line +through + + align:start position:0% + + + + align:start position:0% + +a and the rank of this + + align:start position:0% +a and the rank of this + + + align:start position:0% +a and the rank of this +Matrix is + + align:start position:0% + + + + align:start position:0% + +you can all say it at + + align:start position:0% +you can all say it at + + + align:start position:0% +you can all say it at +once one right the rank is one this is a + + align:start position:0% +once one right the rank is one this is a + + + align:start position:0% +once one right the rank is one this is a +rank one Matrix actually it's exactly + + align:start position:0% +rank one Matrix actually it's exactly + + + align:start position:0% +rank one Matrix actually it's exactly +the form that we we're familiar with + + align:start position:0% +the form that we we're familiar with + + + align:start position:0% +the form that we we're familiar with +with rank one Matrix M with a rank one + + align:start position:0% +with rank one Matrix M with a rank one + + + align:start position:0% +with rank one Matrix M with a rank one +Matrix a column times a row that's a + + align:start position:0% +Matrix a column times a row that's a + + + align:start position:0% +Matrix a column times a row that's a +rank one Matrix that column is + + align:start position:0% +rank one Matrix that column is + + + align:start position:0% +rank one Matrix that column is +the is the basis for the column + + align:start position:0% +the is the basis for the column + + + align:start position:0% +the is the basis for the column +space just one dimension okay + + align:start position:0% +space just one dimension okay + + + align:start position:0% +space just one dimension okay +so I know that much about the Matrix but + + align:start position:0% +so I know that much about the Matrix but + + + align:start position:0% +so I know that much about the Matrix but +now there are two more facts about the + + align:start position:0% +now there are two more facts about the + + + align:start position:0% +now there are two more facts about the +Matrix that that I want to that I want + + align:start position:0% +Matrix that that I want to that I want + + + align:start position:0% +Matrix that that I want to that I want +to + + align:start position:0% +to + + + align:start position:0% +to +notice is first of all is the Matrix + + align:start position:0% +notice is first of all is the Matrix + + + align:start position:0% +notice is first of all is the Matrix +symmetric that's a natural question for + + align:start position:0% +symmetric that's a natural question for + + + align:start position:0% +symmetric that's a natural question for +matrices and the answer is yes if I take + + align:start position:0% +matrices and the answer is yes if I take + + + align:start position:0% +matrices and the answer is yes if I take +the transpose of this there's a number + + align:start position:0% +the transpose of this there's a number + + + align:start position:0% +the transpose of this there's a number +down there the transpose of a a + + align:start position:0% +down there the transpose of a a + + + align:start position:0% +down there the transpose of a a +transpose is a a transpose so p is + + align:start position:0% +transpose is a a transpose so p is + + + align:start position:0% +transpose is a a transpose so p is +symmetric ppose equals P so this is a + + align:start position:0% +symmetric ppose equals P so this is a + + + align:start position:0% +symmetric ppose equals P so this is a +key property that the projection Matrix + + align:start position:0% +key property that the projection Matrix + + + align:start position:0% +key property that the projection Matrix +is + + align:start position:0% +is + + + align:start position:0% +is +symmetric one more property now and this + + align:start position:0% +symmetric one more property now and this + + + align:start position:0% +symmetric one more property now and this +is the real + + align:start position:0% +is the real + + + align:start position:0% +is the real +one what happens if I do the projection + + align:start position:0% +one what happens if I do the projection + + + align:start position:0% +one what happens if I do the projection +twice so I'm looking up looking for + + align:start position:0% +twice so I'm looking up looking for + + + align:start position:0% +twice so I'm looking up looking for +something some information about + + align:start position:0% +something some information about + + + align:start position:0% +something some information about +p² but just give me in terms of that + + align:start position:0% +p² but just give me in terms of that + + + align:start position:0% +p² but just give me in terms of that +picture in terms of my picture + + align:start position:0% +picture in terms of my picture + + + align:start position:0% +picture in terms of my picture +I take any Vector + + align:start position:0% +I take any Vector + + + align:start position:0% +I take any Vector +B I multiply it by my projection Matrix + + align:start position:0% +B I multiply it by my projection Matrix + + + align:start position:0% +B I multiply it by my projection Matrix +and that puts me there so this is + + align:start position:0% +and that puts me there so this is + + + align:start position:0% +and that puts me there so this is +PB and now I project + + align:start position:0% +PB and now I project + + + align:start position:0% +PB and now I project +again what happens now what happens when + + align:start position:0% +again what happens now what happens when + + + align:start position:0% +again what happens now what happens when +I apply the projection Matrix a second + + align:start position:0% +I apply the projection Matrix a second + + + align:start position:0% +I apply the projection Matrix a second +time to this so I'm applying it once + + align:start position:0% +time to this so I'm applying it once + + + align:start position:0% +time to this so I'm applying it once +brings me here and the second time + + align:start position:0% +brings me here and the second time + + + align:start position:0% +brings me here and the second time +brings me + + align:start position:0% +brings me + + + align:start position:0% +brings me +I stay put right the projection for a + + align:start position:0% +I stay put right the projection for a + + + align:start position:0% +I stay put right the projection for a +point on this line the projection is + + align:start position:0% +point on this line the projection is + + + align:start position:0% +point on this line the projection is +right where it is the projection is the + + align:start position:0% +right where it is the projection is the + + + align:start position:0% +right where it is the projection is the +same point so that means that if I + + align:start position:0% +same point so that means that if I + + + align:start position:0% +same point so that means that if I +project + + align:start position:0% +project + + + align:start position:0% +project +twice I get the same answer as I did in + + align:start position:0% +twice I get the same answer as I did in + + + align:start position:0% +twice I get the same answer as I did in +the first projection so those are the + + align:start position:0% +the first projection so those are the + + + align:start position:0% +the first projection so those are the +two properties that tell me I'm looking + + align:start position:0% +two properties that tell me I'm looking + + + align:start position:0% +two properties that tell me I'm looking +at a projection Matrix + + align:start position:0% +at a projection Matrix + + + align:start position:0% +at a projection Matrix +it's + + align:start position:0% +it's + + + align:start position:0% +it's +symmetric and its square is itself + + align:start position:0% +symmetric and its square is itself + + + align:start position:0% +symmetric and its square is itself +because if I project the second time + + align:start position:0% +because if I project the second time + + + align:start position:0% +because if I project the second time +it's the same result as the first + + align:start position:0% +it's the same result as the first + + + align:start position:0% +it's the same result as the first +projection okay so that's uh and and + + align:start position:0% +projection okay so that's uh and and + + + align:start position:0% +projection okay so that's uh and and +then here's the exact formula when I + + align:start position:0% +then here's the exact formula when I + + + align:start position:0% +then here's the exact formula when I +know what I'm projecting onto that line + + align:start position:0% +know what I'm projecting onto that line + + + align:start position:0% +know what I'm projecting onto that line +to a then I know what p is so do you see + + align:start position:0% +to a then I know what p is so do you see + + + align:start position:0% +to a then I know what p is so do you see +that I have all the pieces here for + + align:start position:0% +that I have all the pieces here for + + + align:start position:0% +that I have all the pieces here for +projection on a line + + align:start position:0% + + + + align:start position:0% + +now and those please remember those so + + align:start position:0% +now and those please remember those so + + + align:start position:0% +now and those please remember those so +there are three formulas to remember the + + align:start position:0% +there are three formulas to remember the + + + align:start position:0% +there are three formulas to remember the +formula for x the formula for p which is + + align:start position:0% +formula for x the formula for p which is + + + align:start position:0% +formula for x the formula for p which is +just ax and then the formula for capital + + align:start position:0% +just ax and then the formula for capital + + + align:start position:0% +just ax and then the formula for capital +P which is the + + align:start position:0% +P which is the + + + align:start position:0% +P which is the +Matrix good good okay now I want to move + + align:start position:0% +Matrix good good okay now I want to move + + + align:start position:0% +Matrix good good okay now I want to move +to more + + align:start position:0% +to more + + + align:start position:0% +to more +Dimensions so we're going to have three + + align:start position:0% +Dimensions so we're going to have three + + + align:start position:0% +Dimensions so we're going to have three +formulas again but you'll have + + align:start position:0% +formulas again but you'll have + + + align:start position:0% +formulas again but you'll have +to they they'll be a little different + + align:start position:0% +to they they'll be a little different + + + align:start position:0% +to they they'll be a little different +because we won't have a single line but + + align:start position:0% +because we won't have a single line but + + + align:start position:0% +because we won't have a single line but +uh a plane or threedimensional or a n + + align:start position:0% +uh a plane or threedimensional or a n + + + align:start position:0% +uh a plane or threedimensional or a n +dimensional + + align:start position:0% +dimensional + + + align:start position:0% +dimensional +Subs okay so so now I'm move to the next + + align:start position:0% + + + + align:start position:0% + +question maybe I maybe I'll say first + + align:start position:0% + + + + align:start position:0% + +let me say first why I want this + + align:start position:0% +let me say first why I want this + + + align:start position:0% +let me say first why I want this +projection and then we'll figure out + + align:start position:0% +projection and then we'll figure out + + + align:start position:0% +projection and then we'll figure out +what it is we'll go completely in + + align:start position:0% +what it is we'll go completely in + + + align:start position:0% +what it is we'll go completely in +parallel there and then we'll use it + + align:start position:0% +parallel there and then we'll use it + + + align:start position:0% +parallel there and then we'll use it +okay why do I want this projection well + + align:start position:0% +okay why do I want this projection well + + + align:start position:0% +okay why do I want this projection well +so why why + + align:start position:0% + + + + align:start position:0% + +project it's + + align:start position:0% +project it's + + + align:start position:0% +project it's +because I'm as as I mentioned last time + + align:start position:0% +because I'm as as I mentioned last time + + + align:start position:0% +because I'm as as I mentioned last time +this new chapter deals with + + align:start position:0% + + + + align:start position:0% + +equations axal + + align:start position:0% + + + + align:start position:0% + +B may + + align:start position:0% +B may + + + align:start position:0% +B may +have no + + align:start position:0% + + + + align:start position:0% + +solution so that that's that's really my + + align:start position:0% +solution so that that's that's really my + + + align:start position:0% +solution so that that's that's really my +problem that I'm I'm given a a bunch of + + align:start position:0% +problem that I'm I'm given a a bunch of + + + align:start position:0% +problem that I'm I'm given a a bunch of +equations probably too many + + align:start position:0% +equations probably too many + + + align:start position:0% +equations probably too many +equations more equations than + + align:start position:0% +equations more equations than + + + align:start position:0% +equations more equations than +unknowns and I can't solve + + align:start position:0% +unknowns and I can't solve + + + align:start position:0% +unknowns and I can't solve +them okay so what do I do I solve the + + align:start position:0% +them okay so what do I do I solve the + + + align:start position:0% +them okay so what do I do I solve the +closest problem that I can solve and + + align:start position:0% +closest problem that I can solve and + + + align:start position:0% +closest problem that I can solve and +what's the closest one well ax will + + align:start position:0% +what's the closest one well ax will + + + align:start position:0% +what's the closest one well ax will +always be in the column space of a + + align:start position:0% +always be in the column space of a + + + align:start position:0% +always be in the column space of a +that's my problem my problem is ax has + + align:start position:0% +that's my problem my problem is ax has + + + align:start position:0% +that's my problem my problem is ax has +to be in the column space and B is + + align:start position:0% +to be in the column space and B is + + + align:start position:0% +to be in the column space and B is +probably not in the + + align:start position:0% +probably not in the + + + align:start position:0% +probably not in the +col so I change + + align:start position:0% +col so I change + + + align:start position:0% +col so I change +B to + + align:start position:0% +B to + + + align:start position:0% +B to +what I choose the closest Vector in the + + align:start position:0% +what I choose the closest Vector in the + + + align:start position:0% +what I choose the closest Vector in the +column + + align:start position:0% +column + + + align:start position:0% +column +space so I'll + + align:start position:0% + + + + align:start position:0% + +solve ax = P + + align:start position:0% +solve ax = P + + + align:start position:0% +solve ax = P +instead that that one I can do where p + + align:start position:0% +instead that that one I can do where p + + + align:start position:0% +instead that that one I can do where p +is this is the + + align:start position:0% +is this is the + + + align:start position:0% +is this is the +projection of B + + align:start position:0% +projection of B + + + align:start position:0% +projection of B +onto the column + + align:start position:0% +onto the column + + + align:start position:0% +onto the column +space that's why I want to be able to do + + align:start position:0% +space that's why I want to be able to do + + + align:start position:0% +space that's why I want to be able to do +this because I I have to find a solution + + align:start position:0% +this because I I have to find a solution + + + align:start position:0% +this because I I have to find a solution +here and I'm going to put a little hat + + align:start position:0% +here and I'm going to put a little hat + + + align:start position:0% +here and I'm going to put a little hat +there to indicate that it's not the X + + align:start position:0% +there to indicate that it's not the X + + + align:start position:0% +there to indicate that it's not the X +it's not the x that doesn't + + align:start position:0% +it's not the x that doesn't + + + align:start position:0% +it's not the x that doesn't +exist it's the X hat that's best + + align:start position:0% +exist it's the X hat that's best + + + align:start position:0% +exist it's the X hat that's best +possible so if so I must be able to + + align:start position:0% +possible so if so I must be able to + + + align:start position:0% +possible so if so I must be able to +figure out what's the good projection + + align:start position:0% +figure out what's the good projection + + + align:start position:0% +figure out what's the good projection +there what's the good right hand side + + align:start position:0% +there what's the good right hand side + + + align:start position:0% +there what's the good right hand side +that is in the column space that's as + + align:start position:0% +that is in the column space that's as + + + align:start position:0% +that is in the column space that's as +close as possible to be and then I'm + + align:start position:0% +close as possible to be and then I'm + + + align:start position:0% +close as possible to be and then I'm +then I know what to do okay so now I've + + align:start position:0% +then I know what to do okay so now I've + + + align:start position:0% +then I know what to do okay so now I've +got that problem so so that's that's why + + align:start position:0% +got that problem so so that's that's why + + + align:start position:0% +got that problem so so that's that's why +I have the problem again but now let me + + align:start position:0% +I have the problem again but now let me + + + align:start position:0% +I have the problem again but now let me +say I'm in three + + align:start position:0% +say I'm in three + + + align:start position:0% +say I'm in three +dimensions so I have a + + align:start position:0% +dimensions so I have a + + + align:start position:0% +dimensions so I have a +plane maybe for example + + align:start position:0% +plane maybe for example + + + align:start position:0% +plane maybe for example +and I have a vector B that's not in the + + align:start position:0% + + + + align:start position:0% + +plane and I want to Project + + align:start position:0% +plane and I want to Project + + + align:start position:0% +plane and I want to Project +B down into the + + align:start position:0% + + + + align:start position:0% + +plan + + align:start position:0% +plan + + + align:start position:0% +plan +okay so there's my question how do I + + align:start position:0% +okay so there's my question how do I + + + align:start position:0% +okay so there's my question how do I +project a vector and I'm I'm really what + + align:start position:0% +project a vector and I'm I'm really what + + + align:start position:0% +project a vector and I'm I'm really what +I'm looking for is a nice + + align:start position:0% +I'm looking for is a nice + + + align:start position:0% +I'm looking for is a nice +formula and I'm counting on linear + + align:start position:0% +formula and I'm counting on linear + + + align:start position:0% +formula and I'm counting on linear +algebra to just come out right a nice + + align:start position:0% +algebra to just come out right a nice + + + align:start position:0% +algebra to just come out right a nice +formula + + align:start position:0% +formula + + + align:start position:0% +formula +for the projection of of B into the + + align:start position:0% +for the projection of of B into the + + + align:start position:0% +for the projection of of B into the +plane the nearest point so this again a + + align:start position:0% +plane the nearest point so this again a + + + align:start position:0% +plane the nearest point so this again a +right angle is going to be + + align:start position:0% +right angle is going to be + + + align:start position:0% +right angle is going to be +crucial okay now so what's first of all + + align:start position:0% +crucial okay now so what's first of all + + + align:start position:0% +crucial okay now so what's first of all +I've got to say what is that plane to + + align:start position:0% +I've got to say what is that plane to + + + align:start position:0% +I've got to say what is that plane to +get a formula I have to tell you what + + align:start position:0% +get a formula I have to tell you what + + + align:start position:0% +get a formula I have to tell you what +the plane is how am I going to tell you + + align:start position:0% +the plane is how am I going to tell you + + + align:start position:0% +the plane is how am I going to tell you +a plane I'll tell you a a basis for the + + align:start position:0% +a plane I'll tell you a a basis for the + + + align:start position:0% +a plane I'll tell you a a basis for the +plane I'll tell you two vectors + + align:start position:0% +plane I'll tell you two vectors + + + align:start position:0% +plane I'll tell you two vectors +A1 and A2 that that give you a basis for + + align:start position:0% +A1 and A2 that that give you a basis for + + + align:start position:0% +A1 and A2 that that give you a basis for +the flame so let let say say there's an + + align:start position:0% +the flame so let let say say there's an + + + align:start position:0% +the flame so let let say say there's an +A1 and here's a a vector + + align:start position:0% +A1 and here's a a vector + + + align:start position:0% +A1 and here's a a vector +A2 they don't have to be + + align:start position:0% +A2 they don't have to be + + + align:start position:0% +A2 they don't have to be +perpendicular but they better be + + align:start position:0% +perpendicular but they better be + + + align:start position:0% +perpendicular but they better be +independent because then that tells me + + align:start position:0% +independent because then that tells me + + + align:start position:0% +independent because then that tells me +the plane the plane is the it's the + + align:start position:0% +the plane the plane is the it's the + + + align:start position:0% +the plane the plane is the it's the +plane + + align:start position:0% + + + + align:start position:0% + +of A1 and A2 + + align:start position:0% + + + + align:start position:0% + +and actually going back to my to this to + + align:start position:0% +and actually going back to my to this to + + + align:start position:0% +and actually going back to my to this to +this connection this plane is a column + + align:start position:0% +this connection this plane is a column + + + align:start position:0% +this connection this plane is a column +space it's the it's the column + + align:start position:0% + + + + align:start position:0% + +space + + align:start position:0% +space + + + align:start position:0% +space +of what + + align:start position:0% +of what + + + align:start position:0% +of what +Matrix what what Matrix so how do I + + align:start position:0% +Matrix what what Matrix so how do I + + + align:start position:0% +Matrix what what Matrix so how do I +connect the two + + align:start position:0% +connect the two + + + align:start position:0% +connect the two +questions I'm trying I'm I'm thinking + + align:start position:0% +questions I'm trying I'm I'm thinking + + + align:start position:0% +questions I'm trying I'm I'm thinking +how how do I project onto a + + align:start position:0% +how how do I project onto a + + + align:start position:0% +how how do I project onto a +plane and I want to get a matrix in + + align:start position:0% +plane and I want to get a matrix in + + + align:start position:0% +plane and I want to get a matrix in +here everything's cleaner if I write it + + align:start position:0% +here everything's cleaner if I write it + + + align:start position:0% +here everything's cleaner if I write it +in terms of a matrix so what + + align:start position:0% +in terms of a matrix so what + + + align:start position:0% +in terms of a matrix so what +Matrix has these has that column space + + align:start position:0% +Matrix has these has that column space + + + align:start position:0% +Matrix has these has that column space +well of course it's just the Matrix that + + align:start position:0% +well of course it's just the Matrix that + + + align:start position:0% +well of course it's just the Matrix that +has A1 in the First Column and A2 in the + + align:start position:0% +has A1 in the First Column and A2 in the + + + align:start position:0% +has A1 in the First Column and A2 in the +second + + align:start position:0% +second + + + align:start position:0% +second +column right just just let's be sure + + align:start position:0% +column right just just let's be sure + + + align:start position:0% +column right just just let's be sure +we've got the the question before we get + + align:start position:0% +we've got the the question before we get + + + align:start position:0% +we've got the the question before we get +to + + align:start position:0% +to + + + align:start position:0% +to +answer so I'm looking + + align:start position:0% +answer so I'm looking + + + align:start position:0% +answer so I'm looking +for again I'm given a matrix a with two + + align:start position:0% +for again I'm given a matrix a with two + + + align:start position:0% +for again I'm given a matrix a with two +columns and really I'm ready once I get + + align:start position:0% +columns and really I'm ready once I get + + + align:start position:0% +columns and really I'm ready once I get +to two I'm ready for n so it could be + + align:start position:0% +to two I'm ready for n so it could be + + + align:start position:0% +to two I'm ready for n so it could be +two columns it could be n columns I'll + + align:start position:0% +two columns it could be n columns I'll + + + align:start position:0% +two columns it could be n columns I'll +write the answer in terms of the Matrix + + align:start position:0% +write the answer in terms of the Matrix + + + align:start position:0% +write the answer in terms of the Matrix +a and the point will be those two + + align:start position:0% +a and the point will be those two + + + align:start position:0% +a and the point will be those two +columns describe the plane they describe + + align:start position:0% +columns describe the plane they describe + + + align:start position:0% +columns describe the plane they describe +the column space and I want to + + align:start position:0% +the column space and I want to + + + align:start position:0% +the column space and I want to +project okay and I'm given a vector B + + align:start position:0% +project okay and I'm given a vector B + + + align:start position:0% +project okay and I'm given a vector B +that's probably not in the column space + + align:start position:0% +that's probably not in the column space + + + align:start position:0% +that's probably not in the column space +of course if B is in the column space my + + align:start position:0% +of course if B is in the column space my + + + align:start position:0% +of course if B is in the column space my +projection is simple it's just + + align:start position:0% +projection is simple it's just + + + align:start position:0% +projection is simple it's just +B but most likely I have an error E this + + align:start position:0% +B but most likely I have an error E this + + + align:start position:0% +B but most likely I have an error E this +B minus P + + align:start position:0% +B minus P + + + align:start position:0% +B minus P +part which is probably not zero okay but + + align:start position:0% +part which is probably not zero okay but + + + align:start position:0% +part which is probably not zero okay but +the beauty is that I know + + align:start position:0% +the beauty is that I know + + + align:start position:0% +the beauty is that I know +the from + + align:start position:0% +the from + + + align:start position:0% +the from +geometry or I could get it from calculus + + align:start position:0% +geometry or I could get it from calculus + + + align:start position:0% +geometry or I could get it from calculus +or I could get it from linear algebra + + align:start position:0% +or I could get it from linear algebra + + + align:start position:0% +or I could get it from linear algebra +that that this this Vector this this is + + align:start position:0% +that that this this Vector this this is + + + align:start position:0% +that that this this Vector this this is +the part of B that's that's + + align:start position:0% +the part of B that's that's + + + align:start position:0% +the part of B that's that's +perpendicular to the + + align:start position:0% +perpendicular to the + + + align:start position:0% +perpendicular to the +plane that that e is perpendicular is + + align:start position:0% +plane that that e is perpendicular is + + + align:start position:0% +plane that that e is perpendicular is +perpendicular to the + + align:start position:0% +perpendicular to the + + + align:start position:0% +perpendicular to the +plane you're you're intuition is saying + + align:start position:0% +plane you're you're intuition is saying + + + align:start position:0% +plane you're you're intuition is saying +that that's the crucial fact that that + + align:start position:0% +that that's the crucial fact that that + + + align:start position:0% +that that's the crucial fact that that +that's that that's going to give us the + + align:start position:0% +that's that that's going to give us the + + + align:start position:0% +that's that that's going to give us the +answer okay so let me that's the problem + + align:start position:0% +answer okay so let me that's the problem + + + align:start position:0% +answer okay so let me that's the problem +now for the + + align:start position:0% + + + + align:start position:0% + +answer so so this is a lecture that's + + align:start position:0% +answer so so this is a lecture that's + + + align:start position:0% +answer so so this is a lecture that's +really like moving + + align:start position:0% +really like moving + + + align:start position:0% +really like moving +along because uh I'm just popping that + + align:start position:0% +along because uh I'm just popping that + + + align:start position:0% +along because uh I'm just popping that +problem up there and asking you what + + align:start position:0% +problem up there and asking you what + + + align:start position:0% +problem up there and asking you what +combination now yeah so what is P what + + align:start position:0% +combination now yeah so what is P what + + + align:start position:0% +combination now yeah so what is P what +is this projection P this is projection + + align:start position:0% +is this projection P this is projection + + + align:start position:0% +is this projection P this is projection +p is some multiple + + align:start position:0% +p is some multiple + + + align:start position:0% +p is some multiple +of + + align:start position:0% + + + + align:start position:0% + +these bases guys right some multiple of + + align:start position:0% +these bases guys right some multiple of + + + align:start position:0% +these bases guys right some multiple of +the + + align:start position:0% +the + + + align:start position:0% +the +columns but I don't like writing out X1 + + align:start position:0% +columns but I don't like writing out X1 + + + align:start position:0% +columns but I don't like writing out X1 +A1 Plus X2 A2 I would rather write that + + align:start position:0% +A1 Plus X2 A2 I would rather write that + + + align:start position:0% +A1 Plus X2 A2 I would rather write that +as a + + align:start position:0% +as a + + + align:start position:0% +as a +x well actually I should put if I'm + + align:start position:0% +x well actually I should put if I'm + + + align:start position:0% +x well actually I should put if I'm +really doing everything right I should + + align:start position:0% +really doing everything right I should + + + align:start position:0% +really doing everything right I should +put a little hat on it to remember that + + align:start position:0% +put a little hat on it to remember that + + + align:start position:0% +put a little hat on it to remember that +that that this x that those are the + + align:start position:0% +that that this x that those are the + + + align:start position:0% +that that this x that those are the +numbers and I could have put a hat way + + align:start position:0% +numbers and I could have put a hat way + + + align:start position:0% +numbers and I could have put a hat way +back + + align:start position:0% +back + + + align:start position:0% +back +there is right so this is this is the + + align:start position:0% +there is right so this is this is the + + + align:start position:0% +there is right so this is this is the +projection p p is + + align:start position:0% +projection p p is + + + align:start position:0% +projection p p is +axar and I'm looking for + + align:start position:0% +axar and I'm looking for + + + align:start position:0% +axar and I'm looking for +xar so that's what I want an + + align:start position:0% + + + + align:start position:0% + +equation so so so now I've got hold of + + align:start position:0% +equation so so so now I've got hold of + + + align:start position:0% +equation so so so now I've got hold of +the problem the problem is find the + + align:start position:0% +the problem the problem is find the + + + align:start position:0% +the problem the problem is find the +right combination of the columns so + + align:start position:0% +right combination of the columns so + + + align:start position:0% +right combination of the columns so +that the error Vector is perpendicular + + align:start position:0% +that the error Vector is perpendicular + + + align:start position:0% +that the error Vector is perpendicular +to the + + align:start position:0% +to the + + + align:start position:0% +to the +plane now let me turn that into an + + align:start position:0% +plane now let me turn that into an + + + align:start position:0% +plane now let me turn that into an +equation so what so I'll raise the board + + align:start position:0% +equation so what so I'll raise the board + + + align:start position:0% +equation so what so I'll raise the board +and just turn that turn what we've just + + align:start position:0% +and just turn that turn what we've just + + + align:start position:0% +and just turn that turn what we've just +done into an + + align:start position:0% + + + + align:start position:0% + +equation so let me I'll I'll write again + + align:start position:0% +equation so let me I'll I'll write again + + + align:start position:0% +equation so let me I'll I'll write again +the main point the projection is a XB X + + align:start position:0% +the main point the projection is a XB X + + + align:start position:0% +the main point the projection is a XB X +hat and our problem is find X + + align:start position:0% + + + + align:start position:0% + +hat and the key + + align:start position:0% +hat and the key + + + align:start position:0% +hat and the key +is + + align:start position:0% +is + + + align:start position:0% +is +that B minus ax + + align:start position:0% +that B minus ax + + + align:start position:0% +that B minus ax +hat that's the error this is the E is + + align:start position:0% +hat that's the error this is the E is + + + align:start position:0% +hat that's the error this is the E is +perpendicular + + align:start position:0% + + + + align:start position:0% + +to the + + align:start position:0% + + + + align:start position:0% + +plane that's got to give + + align:start position:0% +plane that's got to give + + + align:start position:0% +plane that's got to give +me well what am I looking for I'm + + align:start position:0% +me well what am I looking for I'm + + + align:start position:0% +me well what am I looking for I'm +looking for two equations now because + + align:start position:0% +looking for two equations now because + + + align:start position:0% +looking for two equations now because +I've got an X1 and an + + align:start position:0% + + + + align:start position:0% + +X2 and I'll get two equations because so + + align:start position:0% +X2 and I'll get two equations because so + + + align:start position:0% +X2 and I'll get two equations because so +this thing e is perpendicular to the + + align:start position:0% + + + + align:start position:0% + +plane so what does that mean I guess it + + align:start position:0% +plane so what does that mean I guess it + + + align:start position:0% +plane so what does that mean I guess it +means it's perpendic I to A1 and also to + + align:start position:0% +means it's perpendic I to A1 and also to + + + align:start position:0% +means it's perpendic I to A1 and also to +A2 right those are two vectors in the + + align:start position:0% +A2 right those are two vectors in the + + + align:start position:0% +A2 right those are two vectors in the +plane and the things that are + + align:start position:0% +plane and the things that are + + + align:start position:0% +plane and the things that are +perpendicular to the plane are + + align:start position:0% +perpendicular to the plane are + + + align:start position:0% +perpendicular to the plane are +perpendicular to A1 and A2 let me just + + align:start position:0% +perpendicular to A1 and A2 let me just + + + align:start position:0% +perpendicular to A1 and A2 let me just +repeat this this guy then is + + align:start position:0% +repeat this this guy then is + + + align:start position:0% +repeat this this guy then is +perpendicular to the plane so it's + + align:start position:0% +perpendicular to the plane so it's + + + align:start position:0% +perpendicular to the plane so it's +perpendicular to that vector and that + + align:start position:0% +perpendicular to that vector and that + + + align:start position:0% +perpendicular to that vector and that +Vector not it's not it's perpendicular + + align:start position:0% +Vector not it's not it's perpendicular + + + align:start position:0% +Vector not it's not it's perpendicular +to that of course but it's so it's + + align:start position:0% +to that of course but it's so it's + + + align:start position:0% +to that of course but it's so it's +perpendicular to everything in the plane + + align:start position:0% +perpendicular to everything in the plane + + + align:start position:0% +perpendicular to everything in the plane +and the plane is really told me by A1 + + align:start position:0% +and the plane is really told me by A1 + + + align:start position:0% +and the plane is really told me by A1 +and A2 so really I have the equations A1 + + align:start position:0% +and A2 so really I have the equations A1 + + + align:start position:0% +and A2 so really I have the equations A1 +transpose b - + + align:start position:0% +transpose b - + + + align:start position:0% +transpose b - +ax is zero and also A2 + + align:start position:0% +ax is zero and also A2 + + + align:start position:0% +ax is zero and also A2 +transpose B minus + + align:start position:0% +transpose B minus + + + align:start position:0% +transpose B minus +ax is + + align:start position:0% + + + + align:start position:0% + +zero those are my two + + align:start position:0% + + + + align:start position:0% + +equ but + + align:start position:0% +equ but + + + align:start position:0% +equ but +I want those in Matrix + + align:start position:0% +I want those in Matrix + + + align:start position:0% +I want those in Matrix +form I want to put those two equations + + align:start position:0% +form I want to put those two equations + + + align:start position:0% +form I want to put those two equations +together as a matrix equation and it's + + align:start position:0% +together as a matrix equation and it's + + + align:start position:0% +together as a matrix equation and it's +just comes out right look at the Matrix + + align:start position:0% +just comes out right look at the Matrix + + + align:start position:0% +just comes out right look at the Matrix +a + + align:start position:0% +a + + + align:start position:0% +a +transpose put A1 A1 transposes its first + + align:start position:0% +transpose put A1 A1 transposes its first + + + align:start position:0% +transpose put A1 A1 transposes its first +row A2 transposes its second row that + + align:start position:0% +row A2 transposes its second row that + + + align:start position:0% +row A2 transposes its second row that +multiplies this B minus + + align:start position:0% + + + + align:start position:0% + +ax and gives me the zero and the zero + + align:start position:0% + + + + align:start position:0% + +um you see that I'm just this is one way + + align:start position:0% +um you see that I'm just this is one way + + + align:start position:0% +um you see that I'm just this is one way +to to to come up with this equation so + + align:start position:0% +to to to come up with this equation so + + + align:start position:0% +to to to come up with this equation so +the equation I'm coming up with is a + + align:start position:0% +the equation I'm coming up with is a + + + align:start position:0% +the equation I'm coming up with is a +transpose b - a + + align:start position:0% +transpose b - a + + + align:start position:0% +transpose b - a +x is + + align:start position:0% + + + + align:start position:0% + +zero + + align:start position:0% +zero + + + align:start position:0% +zero +okay that's my equation + + align:start position:0% +okay that's my equation + + + align:start position:0% +okay that's my equation +all right now I I want to stop for a + + align:start position:0% +all right now I I want to stop for a + + + align:start position:0% +all right now I I want to stop for a +moment before I solve it and just think + + align:start position:0% +moment before I solve it and just think + + + align:start position:0% +moment before I solve it and just think +about it first of all do you see that + + align:start position:0% +about it first of all do you see that + + + align:start position:0% +about it first of all do you see that +that + + align:start position:0% +that + + + align:start position:0% +that +equation back in the very first problem + + align:start position:0% +equation back in the very first problem + + + align:start position:0% +equation back in the very first problem +I solv on a line what was what was + + align:start position:0% +I solv on a line what was what was + + + align:start position:0% +I solv on a line what was what was +uh on a line the The Matrix a only had + + align:start position:0% +uh on a line the The Matrix a only had + + + align:start position:0% +uh on a line the The Matrix a only had +one column it was just little + + align:start position:0% +one column it was just little + + + align:start position:0% +one column it was just little +a so in the first problem I solved + + align:start position:0% +a so in the first problem I solved + + + align:start position:0% +a so in the first problem I solved +projecting on a line this for for + + align:start position:0% +projecting on a line this for for + + + align:start position:0% +projecting on a line this for for +Capital a you just change that to little + + align:start position:0% +Capital a you just change that to little + + + align:start position:0% +Capital a you just change that to little +a and you have the same equation that we + + align:start position:0% +a and you have the same equation that we + + + align:start position:0% +a and you have the same equation that we +solved + + align:start position:0% +solved + + + align:start position:0% +solved +before a transpose eals + + align:start position:0% +before a transpose eals + + + align:start position:0% +before a transpose eals +Z okay now a second thing second + + align:start position:0% +Z okay now a second thing second + + + align:start position:0% +Z okay now a second thing second +comment I would like to since I know + + align:start position:0% +comment I would like to since I know + + + align:start position:0% +comment I would like to since I know +about these four + + align:start position:0% +about these four + + + align:start position:0% +about these four +subspaces I would like to get them into + + align:start position:0% +subspaces I would like to get them into + + + align:start position:0% +subspaces I would like to get them into +this picture + + align:start position:0% + + + + align:start position:0% + +so let me ask the + + align:start position:0% +so let me ask the + + + align:start position:0% +so let me ask the +question what Subspace is this thing + + align:start position:0% +question what Subspace is this thing + + + align:start position:0% +question what Subspace is this thing +in which of the four subspaces is that + + align:start position:0% +in which of the four subspaces is that + + + align:start position:0% +in which of the four subspaces is that +error Vector e this is this is nothing + + align:start position:0% +error Vector e this is this is nothing + + + align:start position:0% +error Vector e this is this is nothing +but e this is this Sky coming down the + + align:start position:0% +but e this is this Sky coming down the + + + align:start position:0% +but e this is this Sky coming down the +in in down perpendicular to the plane + + align:start position:0% +in in down perpendicular to the plane + + + align:start position:0% +in in down perpendicular to the plane +what Subspace is e + + align:start position:0% +what Subspace is e + + + align:start position:0% +what Subspace is e +in from this equation + + align:start position:0% + + + + align:start position:0% + +well the equation is saying a transpose + + align:start position:0% +well the equation is saying a transpose + + + align:start position:0% +well the equation is saying a transpose +e is zero so I'm learning here that e is + + align:start position:0% +e is zero so I'm learning here that e is + + + align:start position:0% +e is zero so I'm learning here that e is +in the null space of a + + align:start position:0% + + + + align:start position:0% + +transpose right that's my equation and + + align:start position:0% +transpose right that's my equation and + + + align:start position:0% +transpose right that's my equation and +now I just want to see hey of course + + align:start position:0% +now I just want to see hey of course + + + align:start position:0% +now I just want to see hey of course +that that was right + + align:start position:0% +that that was right + + + align:start position:0% +that that was right +because things that are in the null + + align:start position:0% +because things that are in the null + + + align:start position:0% +because things that are in the null +space of a + + align:start position:0% +space of a + + + align:start position:0% +space of a +transpose what do we know about the null + + align:start position:0% +transpose what do we know about the null + + + align:start position:0% +transpose what do we know about the null +space of a + + align:start position:0% + + + + align:start position:0% + +transpose so the last lecture gave us + + align:start position:0% +transpose so the last lecture gave us + + + align:start position:0% +transpose so the last lecture gave us +the sort of the geometry of these + + align:start position:0% +the sort of the geometry of these + + + align:start position:0% +the sort of the geometry of these +subspaces and the orthogonality of them + + align:start position:0% +subspaces and the orthogonality of them + + + align:start position:0% +subspaces and the orthogonality of them +and do you remember what it was what on + + align:start position:0% +and do you remember what it was what on + + + align:start position:0% +and do you remember what it was what on +the on the on the right side of our big + + align:start position:0% +the on the on the right side of our big + + + align:start position:0% +the on the on the right side of our big +figure we always have the null space of + + align:start position:0% +figure we always have the null space of + + + align:start position:0% +figure we always have the null space of +a transpose and + + align:start position:0% +a transpose and + + + align:start position:0% +a transpose and +the column space of a and their + + align:start position:0% +the column space of a and their + + + align:start position:0% +the column space of a and their +orthogon so e in the null space of a + + align:start position:0% +orthogon so e in the null space of a + + + align:start position:0% +orthogon so e in the null space of a +transpose is saying e is perpendicular + + align:start position:0% +transpose is saying e is perpendicular + + + align:start position:0% +transpose is saying e is perpendicular +to the column space of + + align:start position:0% +to the column space of + + + align:start position:0% +to the column space of +a + + align:start position:0% + + + + align:start position:0% + +yes like I I just feel okay the damn + + align:start position:0% +yes like I I just feel okay the damn + + + align:start position:0% +yes like I I just feel okay the damn +thing came out right uh the equation for + + align:start position:0% +thing came out right uh the equation for + + + align:start position:0% +thing came out right uh the equation for +the the equation that I struggled to + + align:start position:0% +the the equation that I struggled to + + + align:start position:0% +the the equation that I struggled to +find for e + + align:start position:0% +find for e + + + align:start position:0% +find for e +really + + align:start position:0% +really + + + align:start position:0% +really +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +said what I wanted that the the the + + align:start position:0% +said what I wanted that the the the + + + align:start position:0% +said what I wanted that the the the +error E is perpendicular to the coln + + align:start position:0% +error E is perpendicular to the coln + + + align:start position:0% +error E is perpendicular to the coln +space of a just right and from our four + + align:start position:0% +space of a just right and from our four + + + align:start position:0% +space of a just right and from our four +fundamental subspaces we knew that that + + align:start position:0% +fundamental subspaces we knew that that + + + align:start position:0% +fundamental subspaces we knew that that +is the same as that to say e is in the + + align:start position:0% +is the same as that to say e is in the + + + align:start position:0% +is the same as that to say e is in the +null space of a transpose says e is + + align:start position:0% +null space of a transpose says e is + + + align:start position:0% +null space of a transpose says e is +perpendicular to the column space okay + + align:start position:0% +perpendicular to the column space okay + + + align:start position:0% +perpendicular to the column space okay +so we got this equation now let's just + + align:start position:0% +so we got this equation now let's just + + + align:start position:0% +so we got this equation now let's just +solve it all right let me just rewrite + + align:start position:0% +solve it all right let me just rewrite + + + align:start position:0% +solve it all right let me just rewrite +it as a transpose a + + align:start position:0% +it as a transpose a + + + align:start position:0% +it as a transpose a +x equal a transpose B that's our + + align:start position:0% +x equal a transpose B that's our + + + align:start position:0% +x equal a transpose B that's our +equation that gives us + + align:start position:0% + + + + align:start position:0% + +X and oh I allow me to keep remembering + + align:start position:0% +X and oh I allow me to keep remembering + + + align:start position:0% +X and oh I allow me to keep remembering +the one-dimensional case the + + align:start position:0% +the one-dimensional case the + + + align:start position:0% +the one-dimensional case the +one-dimensional + + align:start position:0% +one-dimensional + + + align:start position:0% +one-dimensional +case this was little a so this was just + + align:start position:0% +case this was little a so this was just + + + align:start position:0% +case this was little a so this was just +a number little a little a transpose a + + align:start position:0% +a number little a little a transpose a + + + align:start position:0% +a number little a little a transpose a +transpose a was just a vector row times + + align:start position:0% +transpose a was just a vector row times + + + align:start position:0% +transpose a was just a vector row times +a column a number and this was a number + + align:start position:0% +a column a number and this was a number + + + align:start position:0% +a column a number and this was a number +and X was the ratio of those numbers but + + align:start position:0% +and X was the ratio of those numbers but + + + align:start position:0% +and X was the ratio of those numbers but +now we've got + + align:start position:0% +now we've got + + + align:start position:0% +now we've got +matrices this this one is n byn a + + align:start position:0% +matrices this this one is n byn a + + + align:start position:0% +matrices this this one is n byn a +transpose a is an N byn Matrix okay so + + align:start position:0% +transpose a is an N byn Matrix okay so + + + align:start position:0% +transpose a is an N byn Matrix okay so +can I move to + + align:start position:0% +can I move to + + + align:start position:0% +can I move to +the next board for the + + align:start position:0% + + + + align:start position:0% + +solution okay there this is the the the + + align:start position:0% +solution okay there this is the the the + + + align:start position:0% +solution okay there this is the the the +key + + align:start position:0% +key + + + align:start position:0% +key +equation now I'm ready for the formulas + + align:start position:0% +equation now I'm ready for the formulas + + + align:start position:0% +equation now I'm ready for the formulas +that we have to remember what's X + + align:start position:0% +that we have to remember what's X + + + align:start position:0% +that we have to remember what's X +hat what's the + + align:start position:0% +hat what's the + + + align:start position:0% +hat what's the +projection what's the projection Matrix + + align:start position:0% +projection what's the projection Matrix + + + align:start position:0% +projection what's the projection Matrix +those are my three questions that we + + align:start position:0% +those are my three questions that we + + + align:start position:0% +those are my three questions that we +answered in the 1D case and now we're + + align:start position:0% +answered in the 1D case and now we're + + + align:start position:0% +answered in the 1D case and now we're +ready for in the N dimensional case so + + align:start position:0% +ready for in the N dimensional case so + + + align:start position:0% +ready for in the N dimensional case so +what is X hat well what can I say + + align:start position:0% +what is X hat well what can I say + + + align:start position:0% +what is X hat well what can I say +but a transpose a inverse + + align:start position:0% + + + + align:start position:0% + +a transpose + + align:start position:0% +a transpose + + + align:start position:0% +a transpose +B okay that's the solution to to our + + align:start position:0% + + + + align:start position:0% + +equation what's the projection that's + + align:start position:0% +equation what's the projection that's + + + align:start position:0% +equation what's the projection that's +more interesting what's the + + align:start position:0% +more interesting what's the + + + align:start position:0% +more interesting what's the +projection the projection + + align:start position:0% + + + + align:start position:0% + +is a xat that's how X hat got into the + + align:start position:0% +is a xat that's how X hat got into the + + + align:start position:0% +is a xat that's how X hat got into the +picture in the first place X hat was + + align:start position:0% +picture in the first place X hat was + + + align:start position:0% +picture in the first place X hat was +the was the combination of column and I + + align:start position:0% +the was the combination of column and I + + + align:start position:0% +the was the combination of column and I +had to look for those numbers and now I + + align:start position:0% +had to look for those numbers and now I + + + align:start position:0% +had to look for those numbers and now I +found them was the combination of The + + align:start position:0% +found them was the combination of The + + + align:start position:0% +found them was the combination of The +Columns of a that gave me the projection + + align:start position:0% +Columns of a that gave me the projection + + + align:start position:0% +Columns of a that gave me the projection +okay so now I know what this guy is so + + align:start position:0% +okay so now I know what this guy is so + + + align:start position:0% +okay so now I know what this guy is so +it's just I multiply by a a a transpose + + align:start position:0% +it's just I multiply by a a a transpose + + + align:start position:0% +it's just I multiply by a a a transpose +a inverse a transpose + + align:start position:0% + + + + align:start position:0% + +B that's looking a little messy but it's + + align:start position:0% +B that's looking a little messy but it's + + + align:start position:0% +B that's looking a little messy but it's +uh not + + align:start position:0% + + + + align:start position:0% + +bad that that combination is is our like + + align:start position:0% +bad that that combination is is our like + + + align:start position:0% +bad that that combination is is our like +magic combination this is the thing + + align:start position:0% +magic combination this is the thing + + + align:start position:0% +magic combination this is the thing +which is which Ed which was which is + + align:start position:0% +which is which Ed which was which is + + + align:start position:0% +which is which Ed which was which is +like uh what's it like what was it in + + align:start position:0% +like uh what's it like what was it in + + + align:start position:0% +like uh what's it like what was it in +one + + align:start position:0% +one + + + align:start position:0% +one +dimension what was that we had this we + + align:start position:0% +dimension what was that we had this we + + + align:start position:0% +dimension what was that we had this we +must have had this thing way back at the + + align:start position:0% +must have had this thing way back at the + + + align:start position:0% +must have had this thing way back at the +beginning of the + + align:start position:0% +beginning of the + + + align:start position:0% +beginning of the +lecture what did we oh then a was just a + + align:start position:0% +lecture what did we oh then a was just a + + + align:start position:0% +lecture what did we oh then a was just a +column so it was little a little a + + align:start position:0% +column so it was little a little a + + + align:start position:0% +column so it was little a little a +transpose over a transpose a right + + align:start position:0% +transpose over a transpose a right + + + align:start position:0% +transpose over a transpose a right +that's what it was in + + align:start position:0% + + + + align:start position:0% + +1D you see what's happened in more + + align:start position:0% +1D you see what's happened in more + + + align:start position:0% +1D you see what's happened in more +Dimensions I I'm not allowed to just + + align:start position:0% +Dimensions I I'm not allowed to just + + + align:start position:0% +Dimensions I I'm not allowed to just +divide because because I don't have a + + align:start position:0% +divide because because I don't have a + + + align:start position:0% +divide because because I don't have a +number I have to put inverse because I + + align:start position:0% +number I have to put inverse because I + + + align:start position:0% +number I have to put inverse because I +have an N byn + + align:start position:0% +have an N byn + + + align:start position:0% +have an N byn +Matrix but same formula + + align:start position:0% + + + + align:start position:0% + +and now tell me what's the projection + + align:start position:0% +and now tell me what's the projection + + + align:start position:0% +and now tell me what's the projection +Matrix what + + align:start position:0% +Matrix what + + + align:start position:0% +Matrix what +Matrix is multiplying B to give the + + align:start position:0% + + + + align:start position:0% + +projection right there just there it I + + align:start position:0% +projection right there just there it I + + + align:start position:0% +projection right there just there it I +even I even already underlined it by + + align:start position:0% +even I even already underlined it by + + + align:start position:0% +even I even already underlined it by +action the projection + + align:start position:0% + + + + align:start position:0% + +Matrix which I use capital P is this + + align:start position:0% +Matrix which I use capital P is this + + + align:start position:0% +Matrix which I use capital P is this +it's it's that thing so I write it again + + align:start position:0% +it's it's that thing so I write it again + + + align:start position:0% +it's it's that thing so I write it again +a * + + align:start position:0% +a * + + + align:start position:0% +a * +a transpose a inverse * + + align:start position:0% + + + + align:start position:0% + +aose + + align:start position:0% +aose + + + align:start position:0% +aose +now if you bear with me I'll think + + align:start position:0% +now if you bear with me I'll think + + + align:start position:0% +now if you bear with me I'll think +about what I what I what have I done + + align:start position:0% +about what I what I what have I done + + + align:start position:0% +about what I what I what have I done +here I've got this + + align:start position:0% +here I've got this + + + align:start position:0% +here I've got this +formula now the first thing that occurs + + align:start position:0% +formula now the first thing that occurs + + + align:start position:0% +formula now the first thing that occurs +to me is + + align:start position:0% + + + + align:start position:0% + +is something bad look um why don't I + + align:start position:0% +is something bad look um why don't I + + + align:start position:0% +is something bad look um why don't I +just you know here's a product of two + + align:start position:0% +just you know here's a product of two + + + align:start position:0% +just you know here's a product of two +matrices and I want its + + align:start position:0% +matrices and I want its + + + align:start position:0% +matrices and I want its +inverse why don't I just use the formula + + align:start position:0% +inverse why don't I just use the formula + + + align:start position:0% +inverse why don't I just use the formula +I know for the inverse of a product and + + align:start position:0% +I know for the inverse of a product and + + + align:start position:0% +I know for the inverse of a product and +say okay that's a inverse time a + + align:start position:0% +say okay that's a inverse time a + + + align:start position:0% +say okay that's a inverse time a +transpose + + align:start position:0% + + + + align:start position:0% + +inverse what will happen if I do + + align:start position:0% +inverse what will happen if I do + + + align:start position:0% +inverse what will happen if I do +that what will happen if I if I say hey + + align:start position:0% +that what will happen if I if I say hey + + + align:start position:0% +that what will happen if I if I say hey +this is a inverse * a transpose inverse + + align:start position:0% +this is a inverse * a transpose inverse + + + align:start position:0% +this is a inverse * a transpose inverse +then shall I do + + align:start position:0% +then shall I do + + + align:start position:0% +then shall I do +it it's going to go on videotape if I do + + align:start position:0% +it it's going to go on videotape if I do + + + align:start position:0% +it it's going to go on videotape if I do +it and I don't all right I'll put it + + align:start position:0% +it and I don't all right I'll put it + + + align:start position:0% +it and I don't all right I'll put it +there but just like don't take the + + align:start position:0% +there but just like don't take the + + + align:start position:0% +there but just like don't take the +videotape quite so carefully okay so if + + align:start position:0% +videotape quite so carefully okay so if + + + align:start position:0% +videotape quite so carefully okay so if +I if I put that thing it would be a a + + align:start position:0% +I if I put that thing it would be a a + + + align:start position:0% +I if I put that thing it would be a a +inverse a transpose inverse a + + align:start position:0% +inverse a transpose inverse a + + + align:start position:0% +inverse a transpose inverse a +transpose and what's that + + align:start position:0% +transpose and what's that + + + align:start position:0% +transpose and what's that +that's the + + align:start position:0% + + + + align:start position:0% + +identity but what's going + + align:start position:0% +identity but what's going + + + align:start position:0% +identity but what's going +on so right you see my question is + + align:start position:0% +on so right you see my question is + + + align:start position:0% +on so right you see my question is +somehow I did I did something wrong that + + align:start position:0% +somehow I did I did something wrong that + + + align:start position:0% +somehow I did I did something wrong that +wasn't allowed and and and why is + + align:start position:0% +wasn't allowed and and and why is + + + align:start position:0% +wasn't allowed and and and why is +that because a is not a square Matrix a + + align:start position:0% +that because a is not a square Matrix a + + + align:start position:0% +that because a is not a square Matrix a +is not a square Matrix it doesn't have + + align:start position:0% +is not a square Matrix it doesn't have + + + align:start position:0% +is not a square Matrix it doesn't have +an inverse + + align:start position:0% +an inverse + + + align:start position:0% +an inverse +so so I have to leave it that way this + + align:start position:0% +so so I have to leave it that way this + + + align:start position:0% +so so I have to leave it that way this +is not okay if if a was a square + + align:start position:0% +is not okay if if a was a square + + + align:start position:0% +is not okay if if a was a square +invertible Matrix then then I couldn't + + align:start position:0% + + + + align:start position:0% + +complain yeah I I'll think let me think + + align:start position:0% +complain yeah I I'll think let me think + + + align:start position:0% +complain yeah I I'll think let me think +about that case but but my main case the + + align:start position:0% +about that case but but my main case the + + + align:start position:0% +about that case but but my main case the +whole reason I'm doing all this is that + + align:start position:0% +whole reason I'm doing all this is that + + + align:start position:0% +whole reason I'm doing all this is that +a is this Matrix that + + align:start position:0% +a is this Matrix that + + + align:start position:0% +a is this Matrix that +has X too many rows it's just got a + + align:start position:0% +has X too many rows it's just got a + + + align:start position:0% +has X too many rows it's just got a +couple of columns like A1 and A2 + + align:start position:0% +couple of columns like A1 and A2 + + + align:start position:0% +couple of columns like A1 and A2 +but lots of rows not square and if it's + + align:start position:0% +but lots of rows not square and if it's + + + align:start position:0% +but lots of rows not square and if it's +not Square this a transpose a is square + + align:start position:0% +not Square this a transpose a is square + + + align:start position:0% +not Square this a transpose a is square +but I can't pull it apart like this so I + + align:start position:0% +but I can't pull it apart like this so I + + + align:start position:0% +but I can't pull it apart like this so I +I I'm not allowed to to do this pull + + align:start position:0% +I I'm not allowed to to do this pull + + + align:start position:0% +I I'm not allowed to to do this pull +apart except if a was Square now if a is + + align:start position:0% +apart except if a was Square now if a is + + + align:start position:0% +apart except if a was Square now if a is +square what's what's going on if a is a + + align:start position:0% +square what's what's going on if a is a + + + align:start position:0% +square what's what's going on if a is a +square Matrix a nice Square in + + align:start position:0% +square Matrix a nice Square in + + + align:start position:0% +square Matrix a nice Square in +invertible + + align:start position:0% + + + + align:start position:0% + +matx what's up with that what's what's + + align:start position:0% +matx what's up with that what's what's + + + align:start position:0% +matx what's up with that what's what's +with that case so this is + + align:start position:0% +with that case so this is + + + align:start position:0% +with that case so this is +all the formula ought to work then too + + align:start position:0% +all the formula ought to work then too + + + align:start position:0% +all the formula ought to work then too +if a is a nice Square invertible Matrix + + align:start position:0% +if a is a nice Square invertible Matrix + + + align:start position:0% +if a is a nice Square invertible Matrix +what's its column space so it's a nice n + + align:start position:0% +what's its column space so it's a nice n + + + align:start position:0% +what's its column space so it's a nice n +byn invertible everything great Matrix + + align:start position:0% +byn invertible everything great Matrix + + + align:start position:0% +byn invertible everything great Matrix +what's its column + + align:start position:0% +what's its column + + + align:start position:0% +what's its column +space the whole of + + align:start position:0% +space the whole of + + + align:start position:0% +space the whole of +RN so what's the projection Matrix if + + align:start position:0% +RN so what's the projection Matrix if + + + align:start position:0% +RN so what's the projection Matrix if +I'm projecting under the whole + + align:start position:0% +I'm projecting under the whole + + + align:start position:0% +I'm projecting under the whole +Space it's the identity right if I'm + + align:start position:0% +Space it's the identity right if I'm + + + align:start position:0% +Space it's the identity right if I'm +projecting + + align:start position:0% +projecting + + + align:start position:0% +projecting +B on the whole Space not just onto a + + align:start position:0% +B on the whole Space not just onto a + + + align:start position:0% +B on the whole Space not just onto a +plane but onto all of 3D then B is + + align:start position:0% +plane but onto all of 3D then B is + + + align:start position:0% +plane but onto all of 3D then B is +already in the column space the + + align:start position:0% +already in the column space the + + + align:start position:0% +already in the column space the +projection is the identity and this is + + align:start position:0% +projection is the identity and this is + + + align:start position:0% +projection is the identity and this is +gives me the correct formula p is R but + + align:start position:0% +gives me the correct formula p is R but + + + align:start position:0% +gives me the correct formula p is R but +if I'm projecting on a Subspace then I + + align:start position:0% +if I'm projecting on a Subspace then I + + + align:start position:0% +if I'm projecting on a Subspace then I +can't split those apart and I have to + + align:start position:0% +can't split those apart and I have to + + + align:start position:0% +can't split those apart and I have to +stay with that formula + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and what can I say so so I remember this + + align:start position:0% +and what can I say so so I remember this + + + align:start position:0% +and what can I say so so I remember this +formula for 1D and that's what it looks + + align:start position:0% +formula for 1D and that's what it looks + + + align:start position:0% +formula for 1D and that's what it looks +like in nend + + align:start position:0% +like in nend + + + align:start position:0% +like in nend +dimension and what are the properties + + align:start position:0% +dimension and what are the properties + + + align:start position:0% +dimension and what are the properties +that I expected for any projection + + align:start position:0% +that I expected for any projection + + + align:start position:0% +that I expected for any projection +Matrix and I still expect for this one + + align:start position:0% +Matrix and I still expect for this one + + + align:start position:0% +Matrix and I still expect for this one +that Matrix should be symmetric and it + + align:start position:0% +that Matrix should be symmetric and it + + + align:start position:0% +that Matrix should be symmetric and it +is p transposes + + align:start position:0% +is p transposes + + + align:start position:0% +is p transposes +p because if I transpose this this guy + + align:start position:0% +p because if I transpose this this guy + + + align:start position:0% +p because if I transpose this this guy +symmetric + + align:start position:0% +symmetric + + + align:start position:0% +symmetric +and it's inverse of symmetric and if I + + align:start position:0% +and it's inverse of symmetric and if I + + + align:start position:0% +and it's inverse of symmetric and if I +transpose this one when I transpose it + + align:start position:0% +transpose this one when I transpose it + + + align:start position:0% +transpose this one when I transpose it +will pop up there become a the a + + align:start position:0% +will pop up there become a the a + + + align:start position:0% +will pop up there become a the a +transpose will pop up here and I'm back + + align:start position:0% +transpose will pop up here and I'm back + + + align:start position:0% +transpose will pop up here and I'm back +to P + + align:start position:0% +to P + + + align:start position:0% +to P +again and do we dare try the other + + align:start position:0% +again and do we dare try the other + + + align:start position:0% +again and do we dare try the other +property which is + + align:start position:0% +property which is + + + align:start position:0% +property which is +p² = + + align:start position:0% + + + + align:start position:0% + +p it it's got to be right + + align:start position:0% + + + + align:start position:0% + +cuz we know geometrically that the first + + align:start position:0% +cuz we know geometrically that the first + + + align:start position:0% +cuz we know geometrically that the first +projection pops us onto the column space + + align:start position:0% +projection pops us onto the column space + + + align:start position:0% +projection pops us onto the column space +and the second one leaves us where we + + align:start position:0% +and the second one leaves us where we + + + align:start position:0% +and the second one leaves us where we +are so I expect that if I multiply by + + align:start position:0% +are so I expect that if I multiply by + + + align:start position:0% +are so I expect that if I multiply by +and let me do it if I multiply by + + align:start position:0% +and let me do it if I multiply by + + + align:start position:0% +and let me do it if I multiply by +another P so there's another a another a + + align:start position:0% +another P so there's another a another a + + + align:start position:0% +another P so there's another a another a +transpose + + align:start position:0% +transpose + + + align:start position:0% +transpose +a inverse + + align:start position:0% +a inverse + + + align:start position:0% +a inverse +a + + align:start position:0% +a + + + align:start position:0% +a +transpose can you + + align:start position:0% +transpose can you + + + align:start position:0% +transpose can you +God eight A's in a row is like OB scene + + align:start position:0% +God eight A's in a row is like OB scene + + + align:start position:0% +God eight A's in a row is like OB scene +but uh uh do you see that it + + align:start position:0% +but uh uh do you see that it + + + align:start position:0% +but uh uh do you see that it +works so I'm squaring that so what do I + + align:start position:0% +works so I'm squaring that so what do I + + + align:start position:0% +works so I'm squaring that so what do I +do how do I see that multiplication + + align:start position:0% +do how do I see that multiplication + + + align:start position:0% +do how do I see that multiplication +well yeah I just want to put parentheses + + align:start position:0% +well yeah I just want to put parentheses + + + align:start position:0% +well yeah I just want to put parentheses +in good places so I see what's happening + + align:start position:0% +in good places so I see what's happening + + + align:start position:0% +in good places so I see what's happening +yeah here's an a transpose a sitting + + align:start position:0% +yeah here's an a transpose a sitting + + + align:start position:0% +yeah here's an a transpose a sitting +together so when that a transpose a + + align:start position:0% +together so when that a transpose a + + + align:start position:0% +together so when that a transpose a +multiplies its inverse all that stuff go + + align:start position:0% +multiplies its inverse all that stuff go + + + align:start position:0% +multiplies its inverse all that stuff go +right and leaves just the a transpose at + + align:start position:0% +right and leaves just the a transpose at + + + align:start position:0% +right and leaves just the a transpose at +the end which is just what we + + align:start position:0% +the end which is just what we + + + align:start position:0% +the end which is just what we +want so P ^2 equals P so sure enough + + align:start position:0% +want so P ^2 equals P so sure enough + + + align:start position:0% +want so P ^2 equals P so sure enough +those two properties hold okay that's + + align:start position:0% +those two properties hold okay that's + + + align:start position:0% +those two properties hold okay that's +that okay we really have got now all the + + align:start position:0% +that okay we really have got now all the + + + align:start position:0% +that okay we really have got now all the +formulas X hat the projection p and the + + align:start position:0% +formulas X hat the projection p and the + + + align:start position:0% +formulas X hat the projection p and the +projection Matrix Capital C and now my + + align:start position:0% +projection Matrix Capital C and now my + + + align:start position:0% +projection Matrix Capital C and now my +job is to use + + align:start position:0% +job is to use + + + align:start position:0% +job is to use +okay so when would + + align:start position:0% +okay so when would + + + align:start position:0% +okay so when would +I when would I uh have a bunch of + + align:start position:0% +I when would I uh have a bunch of + + + align:start position:0% +I when would I uh have a bunch of +equations too many equations and yet I + + align:start position:0% +equations too many equations and yet I + + + align:start position:0% +equations too many equations and yet I +want the best answer and the the + + align:start position:0% +want the best answer and the the + + + align:start position:0% +want the best answer and the the +most important example the most common + + align:start position:0% +most important example the most common + + + align:start position:0% +most important example the most common +example is if I have + + align:start position:0% +example is if I have + + + align:start position:0% +example is if I have +points here's the here's the + + align:start position:0% +points here's the here's the + + + align:start position:0% +points here's the here's the +application these squares + + align:start position:0% + + + + align:start position:0% + +fitting by a + + align:start position:0% + + + + align:start position:0% + +lot okay so I I'll start this + + align:start position:0% +lot okay so I I'll start this + + + align:start position:0% +lot okay so I I'll start this +application today and there's more in it + + align:start position:0% +application today and there's more in it + + + align:start position:0% +application today and there's more in it +than uh I can do in this same lecture so + + align:start position:0% +than uh I can do in this same lecture so + + + align:start position:0% +than uh I can do in this same lecture so +that'll give me a chance to recap the + + align:start position:0% +that'll give me a chance to recap the + + + align:start position:0% +that'll give me a chance to recap the +formulas and there they are and and + + align:start position:0% +formulas and there they are and and + + + align:start position:0% +formulas and there they are and and +recap the idea so let me let me start + + align:start position:0% +recap the idea so let me let me start + + + align:start position:0% +recap the idea so let me let me start +the problem uh + + align:start position:0% +the problem uh + + + align:start position:0% +the problem uh +today I'm + + align:start position:0% +today I'm + + + align:start position:0% +today I'm +given a bunch of data + + align:start position:0% +given a bunch of data + + + align:start position:0% +given a bunch of data +points and they lie close to a line but + + align:start position:0% +points and they lie close to a line but + + + align:start position:0% +points and they lie close to a line but +not on a line let me take this say at + + align:start position:0% +not on a line let me take this say at + + + align:start position:0% +not on a line let me take this say at +tal to 1 2 and + + align:start position:0% +tal to 1 2 and + + + align:start position:0% +tal to 1 2 and +3 I have + + align:start position:0% +3 I have + + + align:start position:0% +3 I have +one and two and two again so my data + + align:start position:0% +one and two and two again so my data + + + align:start position:0% +one and two and two again so my data +points are are this is the like the time + + align:start position:0% +points are are this is the like the time + + + align:start position:0% +points are are this is the like the time +Direction and this is like well let me + + align:start position:0% +Direction and this is like well let me + + + align:start position:0% +Direction and this is like well let me +call that b or Y or something I'm given + + align:start position:0% +call that b or Y or something I'm given + + + align:start position:0% +call that b or Y or something I'm given +these three + + align:start position:0% +these three + + + align:start position:0% +these three +points and I want + + align:start position:0% +points and I want + + + align:start position:0% +points and I want +to fit them by a line by the best + + align:start position:0% +to fit them by a line by the best + + + align:start position:0% +to fit them by a line by the best +straight line so the problem is fit the + + align:start position:0% +straight line so the problem is fit the + + + align:start position:0% +straight line so the problem is fit the +points uh + + align:start position:0% +points uh + + + align:start position:0% +points uh +one one is the first point the second + + align:start position:0% +one one is the first point the second + + + align:start position:0% +one one is the first point the second +point is T = + + align:start position:0% +point is T = + + + align:start position:0% +point is T = +2 b = 1 and the third point is T = 3 Bal + + align:start position:0% + + + + align:start position:0% + +2 so those are my three point tal sorry + + align:start position:0% +2 so those are my three point tal sorry + + + align:start position:0% +2 so those are my three point tal sorry +that's + + align:start position:0% +that's + + + align:start position:0% +that's +two + + align:start position:0% +two + + + align:start position:0% +two +yeah okay so this is the0 1 one this is + + align:start position:0% +yeah okay so this is the0 1 one this is + + + align:start position:0% +yeah okay so this is the0 1 one this is +the 22 and that's the 32 and of course + + align:start position:0% +the 22 and that's the 32 and of course + + + align:start position:0% +the 22 and that's the 32 and of course +there isn't a line that goes through + + align:start position:0% +there isn't a line that goes through + + + align:start position:0% +there isn't a line that goes through +so I'm looking for the best line I'm + + align:start position:0% +so I'm looking for the best line I'm + + + align:start position:0% +so I'm looking for the best line I'm +looking for a line that probably goes + + align:start position:0% +looking for a line that probably goes + + + align:start position:0% +looking for a line that probably goes +somewhere you think it goes somewhere + + align:start position:0% +somewhere you think it goes somewhere + + + align:start position:0% +somewhere you think it goes somewhere +like + + align:start position:0% +like + + + align:start position:0% +like +that I'm look I didn't mean to make it + + align:start position:0% +that I'm look I didn't mean to make it + + + align:start position:0% +that I'm look I didn't mean to make it +go through that point it won't it'll + + align:start position:0% +go through that point it won't it'll + + + align:start position:0% +go through that point it won't it'll +kind of it'll it'll go between so the + + align:start position:0% +kind of it'll it'll go between so the + + + align:start position:0% +kind of it'll it'll go between so the +error there and the error there and the + + align:start position:0% +error there and the error there and the + + + align:start position:0% +error there and the error there and the +error there + + align:start position:0% +error there + + + align:start position:0% +error there +are as small as I can get + + align:start position:0% +are as small as I can get + + + align:start position:0% +are as small as I can get +them okay what I'd like to do is + + align:start position:0% +them okay what I'd like to do is + + + align:start position:0% +them okay what I'd like to do is +find the Matrix a because once I found + + align:start position:0% +find the Matrix a because once I found + + + align:start position:0% +find the Matrix a because once I found +the Matrix a the formulas take + + align:start position:0% +the Matrix a the formulas take + + + align:start position:0% +the Matrix a the formulas take +over so what I I'm looking for this line + + align:start position:0% +over so what I I'm looking for this line + + + align:start position:0% +over so what I I'm looking for this line +B is C + + + align:start position:0% + + + + align:start position:0% + +DT so this is in the homework that I + + align:start position:0% +DT so this is in the homework that I + + + align:start position:0% +DT so this is in the homework that I +sent out for today find the best line so + + align:start position:0% +sent out for today find the best line so + + + align:start position:0% +sent out for today find the best line so +I'm looking for these numbers C and + + align:start position:0% +I'm looking for these numbers C and + + + align:start position:0% +I'm looking for these numbers C and +D that tell me the + + align:start position:0% +D that tell me the + + + align:start position:0% +D that tell me the +line and I want them to be as close to + + align:start position:0% +line and I want them to be as close to + + + align:start position:0% +line and I want them to be as close to +going through those three points as I + + align:start position:0% +going through those three points as I + + + align:start position:0% +going through those three points as I +can get I can't get exactly so there are + + align:start position:0% +can get I can't get exactly so there are + + + align:start position:0% +can get I can't get exactly so there are +three equations to go through the three + + align:start position:0% +three equations to go through the three + + + align:start position:0% +three equations to go through the three +points it would it will go exactly + + align:start position:0% +points it would it will go exactly + + + align:start position:0% +points it would it will go exactly +through that + + align:start position:0% +through that + + + align:start position:0% +through that +point if let's see that first point has + + align:start position:0% +point if let's see that first point has + + + align:start position:0% +point if let's see that first point has +tal to 1 so that would say C + d = 1 + + align:start position:0% +tal to 1 so that would say C + d = 1 + + + align:start position:0% +tal to 1 so that would say C + d = 1 +this is the 1 + + align:start position:0% +this is the 1 + + + align:start position:0% +this is the 1 +one the second Point T is + + align:start position:0% +one the second Point T is + + + align:start position:0% +one the second Point T is +2 so C + 2D should come out to equal + + align:start position:0% +2 so C + 2D should come out to equal + + + align:start position:0% +2 so C + 2D should come out to equal +two but I also want to get the third + + align:start position:0% +two but I also want to get the third + + + align:start position:0% +two but I also want to get the third +equation in and that that third equation + + align:start position:0% +equation in and that that third equation + + + align:start position:0% +equation in and that that third equation +T is 3 so C + + + align:start position:0% +T is 3 so C + + + + align:start position:0% +T is 3 so C + +3D equal only + + align:start position:0% + + + + align:start position:0% + +2 that that's the key is to write down + + align:start position:0% +2 that that's the key is to write down + + + align:start position:0% +2 that that's the key is to write down +what equations we would like to solve + + align:start position:0% +what equations we would like to solve + + + align:start position:0% +what equations we would like to solve +but can't reason we if we could solve + + align:start position:0% +but can't reason we if we could solve + + + align:start position:0% +but can't reason we if we could solve +them that would mean that we could put a + + align:start position:0% +them that would mean that we could put a + + + align:start position:0% +them that would mean that we could put a +line through all three points + + align:start position:0% +line through all three points + + + align:start position:0% +line through all three points +and of course if these numbers one 2 two + + align:start position:0% +and of course if these numbers one 2 two + + + align:start position:0% +and of course if these numbers one 2 two +were different we could do + + align:start position:0% +were different we could do + + + align:start position:0% +were different we could do +it but with those numbers 1 two two we + + align:start position:0% +it but with those numbers 1 two two we + + + align:start position:0% +it but with those numbers 1 two two we +can't so what is our equation + + align:start position:0% +can't so what is our equation + + + align:start position:0% +can't so what is our equation +axal axal B that we can't + + align:start position:0% +axal axal B that we can't + + + align:start position:0% +axal axal B that we can't +solve I I I want I just want to say + + align:start position:0% +solve I I I want I just want to say + + + align:start position:0% +solve I I I want I just want to say +what's the Matrix here what's the + + align:start position:0% +what's the Matrix here what's the + + + align:start position:0% +what's the Matrix here what's the +unknown X and what's the right hand side + + align:start position:0% +unknown X and what's the right hand side + + + align:start position:0% +unknown X and what's the right hand side +so this is the Matrix is + + align:start position:0% +so this is the Matrix is + + + align:start position:0% +so this is the Matrix is +111 1 2 + + align:start position:0% + + + + align:start position:0% + +3 the unknown is c and + + align:start position:0% +3 the unknown is c and + + + align:start position:0% +3 the unknown is c and +d and the right hand side is 1 + + align:start position:0% + + + + align:start position:0% + +two2 right I've just taken my equations + + align:start position:0% +two2 right I've just taken my equations + + + align:start position:0% +two2 right I've just taken my equations +and I've said what is ax and what is b + + align:start position:0% + + + + align:start position:0% + +then there's no solution this is the + + align:start position:0% +then there's no solution this is the + + + align:start position:0% +then there's no solution this is the +typical case where I have three + + align:start position:0% +typical case where I have three + + + align:start position:0% +typical case where I have three +equations two unknowns no solution but + + align:start position:0% +equations two unknowns no solution but + + + align:start position:0% +equations two unknowns no solution but +I'm still looking for the best + + align:start position:0% +I'm still looking for the best + + + align:start position:0% +I'm still looking for the best +solution and the best solution + + align:start position:0% +solution and the best solution + + + align:start position:0% +solution and the best solution +is taken is is to solve not this + + align:start position:0% +is taken is is to solve not this + + + align:start position:0% +is taken is is to solve not this +equation axal B which has which has no + + align:start position:0% +equation axal B which has which has no + + + align:start position:0% +equation axal B which has which has no +solution but the equation that does have + + align:start position:0% +solution but the equation that does have + + + align:start position:0% +solution but the equation that does have +a solution solution which + + align:start position:0% +a solution solution which + + + align:start position:0% +a solution solution which +was this one so that's the equation to + + align:start position:0% +was this one so that's the equation to + + + align:start position:0% +was this one so that's the equation to +solve that's the central equation of the + + align:start position:0% +solve that's the central equation of the + + + align:start position:0% +solve that's the central equation of the +subject I can't solve axal B but + + align:start position:0% +subject I can't solve axal B but + + + align:start position:0% +subject I can't solve axal B but +magically when I multiply both sides by + + align:start position:0% +magically when I multiply both sides by + + + align:start position:0% +magically when I multiply both sides by +a + + align:start position:0% +a + + + align:start position:0% +a +transpose I get an equation that I can + + align:start position:0% +transpose I get an equation that I can + + + align:start position:0% +transpose I get an equation that I can +solve and its solution gives me X the + + align:start position:0% +solve and its solution gives me X the + + + align:start position:0% +solve and its solution gives me X the +best X the best projection and I + + align:start position:0% +best X the best projection and I + + + align:start position:0% +best X the best projection and I +discover what's the Matrix that's behind + + align:start position:0% +discover what's the Matrix that's behind + + + align:start position:0% +discover what's the Matrix that's behind +it + + align:start position:0% +it + + + align:start position:0% +it +okay so next time I'll complete an + + align:start position:0% +okay so next time I'll complete an + + + align:start position:0% +okay so next time I'll complete an +example numerical example today was all + + align:start position:0% +example numerical example today was all + + + align:start position:0% +example numerical example today was all +letter numbers next time thank \ No newline at end of file diff --git a/Z1iXHd349bo.txt b/Z1iXHd349bo.txt new file mode 100644 index 0000000000000000000000000000000000000000..306b26ce2f495f7b33a5671bde0d1257aa93199c --- /dev/null +++ b/Z1iXHd349bo.txt @@ -0,0 +1,4674 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or to view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +SHAWN COLE: Great. + +It's a real pleasure to be +here and thank you for + +listening to me. + +This is perhaps the capstone +lecture of the course or at + +least the last lecture +of the course. + +And I'm going to try to pick +up right where Michael left + +off talking about intention +to treat and moving on to + +treatment of the treated. + +But with any luck, they'll be +some time at the end where we + +can have more general +discussions or questions if + +people are still interested +about particular topics or + +have questions. + +And I'll stay after class +to talk to people. + +And I think you have my +email on the slides. + +So feel free to get in touch +with me at any time. + +We've got this great project. + +We want to evaluate +it or write JPAL. + +So what are we going +to do today? + +Look at some challenges to +randomized evaluations. + +So these problems. + +So basically, when people don't +do what you assign them + +to do because you can't +control them. + +You can control undergraduates +in a lab, but in the real + +world it's a lot harder. + +Then we're going to talk about +sort of how do you choose + +which effects to report +in your study? + +So you've got your study, you +did a bunch of household + +surveying, what do you +want to report? + +How credible are your results? + +Then we'll spend some time +talking about external + +validity, which is sort of the +question, OK, I have a study + +that I think is internally +valid. + +We did the randomization +correctly and the results we + +think are legitimate. + +But how much can that tell +us about the greater + +world around us? + +And finally, we'll conclude +by talking about cost + +effectiveness. + +Which, as economists, is +very important to us. + +So we may have a program that's +effective, but how do + +we compare whether we should +spend our precious aid or + +budget dollars on that +particular program as composed + +to a host of other programs? + +And so I usually teach at HBS +in the case method, which is + +very different than a lecture +format because it's basically + +the students always talking +and me refereeing. + +I'm not going to do that +today, but I'm very + +comfortable with interruptions, +or questions, + +or requests for clarification, +et cetera. + +And I think we all stay more +engaged if there's more + +discussion. + +And so that's super valuable. + +So that's the outline +for today. + +And the slides up here are going +to differ a little bit + +from the slides that you have +printed out because there was + +some last minute optimization +and re-coordination. + +So the basic problem, which I +think Michael talked about, is + +that individuals are allocated +to treatment groups and they + +don't receive treatment, or +individuals are allocated to + +the assignment group, +but somehow + +managed to get treatment. + +So you talked about students +didn't show up at school, so + +they didn't get the treatment +on the treatment day. + +Or the program said you can't +give this program, you can't + +give de-worming medicine to +girls over the age of 13 + +because of health reasons. + +They may be pregnant and we +don't know how the de-worming + +medicine affects pregnancy. + +So what do you do? + +You came up with the solution +of estimating the program + +effect, ITT. + +Which is to use the original +assignment. + +So we have our baseline survey, +our baseline list of + +schools or people and we flipped +our coins or run our + +[UNINTELLIGIBLE] code +to randomize. + +So then it would just evaluate +them no matter what actually + +happened and them. + +We count them in the treatment +group or we count them in the + +control group. + +And that gives us our intention +to treat estimate. + +And so the interpretation of +that is, what was the average + +effect on an individual in the +treated population relative to + +an individual in the comparison +population? + +And you've already covered +this with Michael? + +This is just a review. + +So is this the right +number to look for? + +Well, if you're thinking about +putting in a de-worming + +program, you have to realize +that people aren't going to be + +at school when the government +shows up to administer the + +de-worming program to +all their students. + +And that's that. + +So maybe we can just pause for +a second and think about some + +programs that if you're +an [? IPARA ?] + +you think you're going to be +involved with, or if you're + +involved in an NGO, the type +of program you're running. + +And maybe a few people can +volunteer what the intent to + +treat estimate might look like +in their evaluation and + +whether it's something +they care about. + +Put this into practice. + +I should be comfortable with +long pregnant pauses as well. + +Any examples? + +Excellent. + +AUDIENCE: So one of the projects +that we're working on + +is looking at the impact of +financial education in low + +income communities +in New York City. + +Obviously we're trying to +measure the impact that + +financial education has, but +we're working specifically + +with a certain NGO to implement +that education. + +Whatever estimate we get that's +the intention to treat + +will just be measuring the +impact of the program. + +SHAWN COLE: And so what are the +compliance problems you + +anticipate there? + +AUDIENCE: Maybe people not +showing up for classes or not + +following through on whatever +they're asked + +to do in the education. + +SHAWN COLE: Or people in the +control group could get on the + +internet and download the +government's financial + +literacy program and study +very industriously + +themselves and learn. + +The intention to treat will tell +you what the program does + +and you could imagine that if +only 15% of the people turn up + +for your meetings, you're going +to have a pretty small + +difference between the treatment +group and the + +comparison group. + +That'll be an accurate measure +of the program, but that's not + +going to tell us much about +how important financial + +literacy is in making +financial decisions. + +So if maybe your outcome +variable is what interest rate + +do people borrow at, or do they +pay their credit cards + +back on time, you might +not find much effect. + +From that we can't conclude +that financial education + +doesn't affect credit card +repayment behavior. + +We just have to conclude that +this particular program we + +delivered wasn't +very effective. + +So that's an example. + +Any other examples? + +The point is hopefully +pretty clear. + +Great. + +So I don't know if you went +through these calculations. + +Yeah, OK. + +It's absolutely simple. + +You just take the average in +this one, average in this one, + +and it's the difference. + +So it's not rocket science. + +So it relates to the actual +program and it gives us an + +estimate of the program's +impact. + +I guess the second method we're +going to talk about, + +which you talked about in your +learning groups this morning + +too, is treatment +on the treated. + +And maybe you could motivate +this by telling the joke about + +the econometricians or + +statisticians who went hunting. + +Have you heard this? + +So the first one aims at a deer +and shoots and misses 10 + +meters to the left. + +And the second one aims at +the deer and misses 10 + +meters to the right. + +And the third one says, +yes, we got it. + +So the intention to treat is +giving us the average program + +effect, but maybe we care more +about what's the effect of + +knowing financial literacy? + +What's the effect of actually +changing people's + +understanding of financial +literacy? + +And that's where the treatment +on the treated estimate can + +provide some assistance. + +So again, we went back to the +worming example which you + +talked about. + +And so we have 76% of the +people in the treatment + +schools got some treatment +in the first round. + +And in the next round +it was 72%. + +So that's actually nowhere +near 100%. + +One-fifth of the students +are not getting + +their de-worming medicine. + +And some students in the +comparison group received + +treatment also. + +So for example, I think when you +were testing the children + +and you found that they had +worms in the comparison group, + +the sort of medical protocol +required you + +to give them treatment. + +So what would you do if you +wanted to know the effect of + +medicine on the children +who took the medicine? + +And so you can't just compare +children who took the medicine + +with children who didn't +take the medicine. + +That leads to all the same +selection problems we had in + +the first few days of class +where the people who decided + +not to come to school that day +or weren't able to make it to + +school that day are different +than the people who did. + +And the people in the comparison +group who went out + +to the pharmacy and bought the +de-worming medicine are going + +to be different than the +people who didn't. + +So what we do in this case is +something really quite simple + +and it's at the foundation of +the entire field of modern + +empirical research. + +But we won't go into all the +details, we'll just talk about + +this treatment on the treated +estimator, or ToT. + +And so what you don't do is just +take the change of the + +people who were treated and the +change of the people who + +were not treated and +compare them. + +That would be just silly because +people who are treated + +are different than the people +who are not treated. + +So I think conceptually, this +is actually a really simple + +thing that we're doing. + +So I don't want to get bogged +down or confused in the math. + +But in the ideal experiment, in +the treatment group 100% of + +the people are treated. + +In the comparison group, 0% +of the people are treated. + +And then the average difference +is just the average + +treatment effect. + +But in real life when we do our +experiments, we very often + +have leakage across groups. + +So the treatment control +difference is not 1, 100% in + +the treatment group treated +and 0% in the + +control group treated. + +But it's smaller. + +The formal econometric +phrase for this is + +instrumental variables. + +We instrument the probability of +treatment with the original + +assignment and this will rescale +the difference in + +means to give us a better +estimate of what the effect of + +the treatment on the people +who were treated is. + +So this is a simple example. + +And it turns out it gets +more complicated. + +We're not going to go into +all the nuances. + +But just suppose for simplicity +that children who + +get the treatment have a weight +gain of A, irrespective + +of whether they're in +the treatment or + +in the control school. + +And children who get no +treatment have a weight gain + +of B. Again, in both schools. + +And we want to know A minus B, +the difference between getting + +treated and not getting +treated. + +This is the math. + +And maybe it looks complicated, + +but it's really not. + +I think if we work through the +Excel worksheet explaining + +what we're doing and then go +back to the math, it'll become + +pretty clear. + +Imagine we run this experiment +with pupils in School 1 and + +pupils in School 2. + +We intended to treat everybody +in School 1. + +We intended for everybody +in School 2 to be + +in the control group. + +Unfortunately, we were only able +to treat 6 out of the 10 + +people in this group and 2 out +of the 10 people in this group + +managed to get treatment +somehow. + +The formula sort of guides us +through what we need to do and + +then we can talk about the +intuition between what it is. + +Is there a heroic soul who's +willing to try and just talk + +through the math +and figure out? + +A non-heroic soul? + +Cold call. + +So, Will, let's start out +with the easy stuff. + +So the formula we want is the +average in the treatment group + +minus the average in the control +group divided by the + +probability of treatment in the +treatment group minus the + +probability of treatment +in the control group. + +OK, so how do we calculate +all of these things? + +AUDIENCE: So first you want to +look at the change in the + +treatment group. + +So you average out the observed +change in weight for + +the treatment group. + +SHAWN COLE: Great. + +OK, so that's three. + +AUDIENCE: You do the same +calculation for the control + +group looking at the average +change in weight. + +You take the difference between +those two numbers and + +that's the numerator of +the proper fraction. + +SHAWN COLE: OK, so +that's yt minus-- + +OK. + +AUDIENCE: And then to do the +second half of the calculation + +you've got the denominator. + +Compare the rate of compliance +in the treatment group to the + +rate of compliance in +the control group. + +So the percentage in the +treatment group that actually + +complied would be 0.6. + +SHAWN COLE: 1, 2, 3, 4, 5, 6. + +Awesome. + +OK. + +AUDIENCE: And for the control +group, it would be + +the 2 out of 10. + +So the rate that received +the treatment. + +So 0.6 minus 0.2. + +SHAWN COLE: 0.6 minus 0.2. + +OK. + +And now? + +AUDIENCE: Just divide +the top and bottom. + +SHAWN COLE: OK, so +that's the math. + +See if we got it right. + +Yes, we got it right. + +Excellent. + +So what's the intuition behind +what we're doing here? + +AUDIENCE: You're sort of doing +a weighted average. + +SHAWN COLE: OK, we're certainly +taking the two + +averages and we're taking +the difference of them. + +And what do you mean +by weighting? + +AUDIENCE: You're weighting +them by the degree of + +compliance. + +SHAWN COLE: So if the difference +in compliance-- + +keeping the top term the +same, so suppose + +that this is still-- + +AUDIENCE: If compliance were +really horrible you'd end up + +with no effect. + +It could swap the difference +between the + +control and the treatment. + +SHAWN COLE: OK, so let's take +the mental exercise, keeping + +this yt minus yc the +same at 2.1. + +If the compliance in the +treatment group goes down from + +0.6 to 0.3, what's going to +happen to the ToT effect? + +Is it going to go up or down? + +AUDIENCE: Up. + +SHAWN COLE: Why? + +AUDIENCE: +[UNINTELLIGIBLE PHRASE] + +The people that you were +targeting are not receiving + +the treatment. + +So in a sense, the effect that +you are trying to describe is + +not what we would expect would +happen because some of these + +people did not comply with what +you were expecting from + +the beginning. + +AUDIENCE: It could go either +up or down depending on the + +second parameter. + +SHAWN COLE: OK, so what I want +to do is I want to say there + +are four parameters here. + +There's the average in +the treatment group. + +There's the average in +the control group. + +There's the probability of +treatment in the treatment + +group and the probability +of treatment + +in the control group. + +If this goes down, what's the +ToT estimate going to do? + +It's going to go? + +AUDIENCE: Increase. + +SHAWN COLE: Why? + +AUDIENCE: Because you previously +underestimated the + +effect because not that many +people received the treatment. + +SHAWN COLE: So mathematically, +if we're making the + +denominator smaller, the size of +the fraction has to go up. + +That's just a law +of mathematics. + +But the intuition, what I'm +looking for is the intuition. + +So what's going on? + +So suppose I first tell you +that this difference is 3. + +Can you guys not see +these numbers here? + +AUDIENCE: No. + +SHAWN COLE: That's excellent. + +OK, so let me use a blackboard, +I think this'll be + +a little bit helpful. + +AUDIENCE: So were you asking +just basically that because + +not everybody is being +treated it's + +diluting the overall result? + +SHAWN COLE: Explain this. + +Give us the sort of intuition. + +I said that this treatment group +has an average of 3 and + +the control group has an +average of 0.1 I think. + +No 0.9. + +And first I told you that the +probability of treatment + +conditional on being in the +treatment group is 0.6. + +But now I tell you actually +it's much lower. + +It's only 0.3. + +So we know from the math +that it's going to + +be higher, but why? + +What's the intuition? + +Why does it have to be higher? + +AUDIENCE: Because the gap in +outcomes is actually caused by + +fewer people. + +Meaning that for those two +people it must have been a + +really big gap to balance out +the average to still be a lot + +higher when everyone else +in the treated group + +actually got zeros. + +SHAWN COLE: Yeah, absolutely. + +So we've got some difference +in observed outcomes. + +And that has to be caused by the +fact that there were more + +people in the treatment group +treated than in the control + +group who were treated. + +So if there were a whole lot +of people in the treatment + +group treated, then this rate +difference could be just that + +the average score is two higher +for each person in the + +treatment group, if +everybody in the + +treatment group were treated. + +But if only three people in +the treatment group were + +treated, to raise the average +from 0.9 to 3, you have to + +have a really big effect +on those three people. + +So that's all the treatment on +the treated estimator is + +doing, is it's rescaling this +observed effect to account for + +the fact that the difference +is not 1 here. + +If we had perfect compliance, +if this were 1 and this were + +0, then the denominator of the +fraction would just be 1. + +This would look just like the +intention to treat and the + +intention to treat and the +treatment on the treated + +estimators would be the same. + +But if we have imperfect +compliance, then we can scale + +up the effect to account for +the fact that all of the + +change has to be due to the fact +that a smaller number of + +people were getting +the treatment. + +AUDIENCE: Now you can only do +this because you believe there + +is no systematic difference for +why people were treated or + +not in between these +two groups? + +SHAWN COLE: Right. + +So there's some technical +assumptions on how you + +interpret these effects. + +But if we agree that the effect +is basically a constant + +effect, so our literacy program +has the same effect on + +everybody, then this +is perfectly fine. + +And we can do this because +we randomly assigned the + +treatment in the control group +so ex ante the two + +groups are the same. + +Will? + +AUDIENCE: So why do you not have +to worry that the people + +in the treatment group who +actually comply are the more + +motivated batch of the +treatment group? + +SHAWN COLE: Right. + +That is a concern and it's +covered in the papers, which + +I'll get to at the end. + +Basically, the sort of +aggressive intuition is that + +this tends to measure the +effect on people who are + +affected by the program. + +But in general, this is a +pretty good way of just + +scaling up your program effects +to account for the + +possibility of noncompliance. + +So moving back to-- + +sure. + +AUDIENCE: Did you answer +his question? + +SHAWN COLE: Why do we have +to worry about it? + +AUDIENCE: Yeah. + +It seemed like it's +a serious problem. + +AUDIENCE: It started random, but +then people who actually + +got treated, if they were +treated because they were + +systematically different +then it's no longer-- + +your control group is no longer +a good representation + +of the [UNINTELLIGIBLE]. + +SHAWN COLE: Right. + +There are technical assumptions +about monotonicity + +and independence that I sort of +would rather not go into. + +But if you'll at least just +grant that there's a constant + +treatment effect, then I think +we're fine and by scaling up + +the impact to account for the +non-compliers, we'll be OK. + +AUDIENCE: Is the idea-- sorry +not to belabor the point. + +But is the idea that this method +will get the correct + +magnitude of the treatment on +those who are treated in this + +study, but you can't necessarily +extrapolate that + +to say, that would have +been the same + +treatment on the treated. + +Would you be able to force these +other people who might + +be different in some +way to get treated. + +SHAWN COLE: Right. + +This will tell you the correct +magnitude of the people who + +because they were treated, +get the treatment. + +So that's again, a relevant +parameter when you're running + +a program that causes people +to take the treatment, you + +have the effect. + +If on the other hand you're the +government and you have + +some ability to compel +compliance, then you might not + +get effect. + +So you may worry about this. + +Some people have done studies to +try and sort of see how big + +a problem this is. + +And one example I can cite is +some studies on educational + +literature. + +So in the US people have looked +at mandatory school + +attendance laws that say in some +states you can drop out + +of school at the age of 16 and +in some states you can drop + +out of school at +the age of 15. + +And so changes in these +laws induce some + +people to stay in longer. + +But probably nobody here would +have been affected by one of + +these mandatory schooling laws +because we were all planning + +to go on to college anyway. + +And so people have compared +estimates in the US with those + +in the UK where the mandatory +schooling law were very + +binding and they found that +the point estimates were + +pretty similar. + +So that's an example of where +it can be reasonable. + +But this is something that you +have to treat with a little + +bit of caution. + +So there are other challenges +with this. + +To get the ToT, we need to +know the probability of + +treatment conditional being +on the treatment and the + +probability of being treated +condition on being in the + +control group. + +So why might these +be hard to get? + +AUDIENCE: I actually +had a question. + +I don't know if it's +directly related. + +Does this work if the +probability that you're + +treated in both the treatment +and control turn out to be + +equal or is there probability +that-- + +SHAWN COLE: Great question. + +So you're anticipating a slide +three slides from now. + +So let's go there and +then we'll come + +back to my other problem. + +But this is the equation. + +So what happens if the +probability of treatment and + +the treatment in the control +group is the same? + +AUDIENCE: Mathematically +you have problems. + +SHAWN COLE: Mathematically +you're dividing something by 0 + +and you're going to get infinity +or negative infinity. + +So yeah, that's not +successful. + +I mean, another way of +putting that is that + +your experiment failed. + +You randomly assigned treatment +and you assumed that + +your program, a financial +literacy education program, + +de-worming medicine, is going +to deliver a product. + +But if, in fact, it doesn't +change the probability of + +treatment at all, then +your program failed. + +It's sort of like if I +were to sit here and + +working with an [? MFI, ?] + +send them an email and say, +I'm assigning these 50 + +villages to treatment and these +50 villages to control. + +And then the email gets lost and +they don't do any sort of + +treatment or control. + +And then they send me the +data back a year later + +and I do the analysis. + +Well, I'm going to find that +there's no difference in + +probability of treatment between +the two groups and I + +won't have anything interesting +to say. + +So that's definitely +one problem. + +The experiment doesn't work +unless the treatment induces a + +change in probability of +treatment between the + +treatment in the comparison +groups. + +So that's one problem. + +There's a second problem with +this estimation since we're on + +this slide, which is perhaps, +slightly more technical. + +But if the difference between +the treatment and the + +comparison group is small. + +So say it's 10% of the treatment +group are treated + +and none of the comparison +group is treated. + +Then we're estimating the mean +of all of the treated people + +minus the mean of all the +control people and dividing by + +0.1, which is the same thing +as multiplying by 10. + +So if there's a little bit of +noise in these measures, then + +instead of-- + +suppose the true mean +is 3, but you + +happened to measure 3.1. + +Then that noise is going +to be blown up by a + +factor of 10 as well. + +So the estimate is going to be +much less precise when the + +difference in treatment between +the treatment and the + +comparison group is low. + +And as you said, if it gets +to 0, you're in a pickle. + +AUDIENCE: That's a pretty +extreme problem. + +It means I had a treatment +group and + +only 10% of the people. + +SHAWN COLE: Sure. + +That's true, but it's not +implausible that you'd want to + +run that type of experiment. + +So if you think of-- + +I don't know the exact numbers +on the flu encouragement + +design papers. + +To try and understand how +effective a flu shot is, you + +can send out letters to a bunch +of people and some of + +the people-- the control group, +you just send a letter + +saying, just for your +information, the influenza + +season is coming. + +Please wash your hands a lot. + +The treatment group you send a +letter saying that information + +plus we're offering free flu +shots down at the clinic, why + +don't you come down? + +And you may only get +a 10% response + +rate from that letter. + +But in that case, the treatment +is very cheap. + +It's just $0.32, or whatever +a stamp cost these days. + +So you could do a study +with 100,000 people. + +Then you would estimate both of +these things very precisely + +because you'd have 50,000 people +in the treatment group, + +50,000 people in the +control group. + +And you'd have these numbers and +so you could come up with + +an estimate. + +It's not like we should give up +on an experiment that has a + +low probability of treatment, +it's just if we think we're + +going to be there we want +to do our power + +calculations carefully. + +And I think you would have +seen when you did your-- + +did your power calculations +include noncompliance? + +OK, so if you start adjusting +the power calculations for + +noncompliance, you see that you +need larger sample sizes. + +And so that's an important +lesson as well. + +Sticking with that +flu example. + +Why might this be hard? + +When we sent out these letters +to all these people either + +encouraging them to wash their +hands or encouraging them to + +get flu shots. + +AUDIENCE: We have +to observe both. + +Whether there's treatment in +your control in particular, + +that could be really +hard to do. + +SHAWN COLE: So maybe if you're +directing them to your flu + +clinic, you're going sort of +observe everybody you send a + +letter who comes in +for a flu shot. + +And maybe they're employees of +Blue Cross Blue Shield or + +something and you hope you'll +get a good estimate. + +But what about this, you've got +50,000 people you've sent + +letters to in the +control group. + +What can you do? + +Do you have to phone up all +50,000 people and try and-- + +AUDIENCE: And say, oh, by +the way, did you happen + +to get a flu shot. + +SHAWN COLE: Exactly. + +So do we need to make 50,000 +telephone calls + +to solve this problem? + +AUDIENCE: Randomly sample. + +SHAWN COLE: Randomly sample? + +So pick 500, even 1,000, +or who knows? + +Maybe even 200 people, 300 +people will give you a pretty + +good estimate of what this is. + +You just need to make sure that +it is a randomly selected + +sample and you're not just +asking all of the people in + +this particular clinic. + +We're getting a little +bit out of order. + +I've gone through the math, but +PowerPoint wouldn't let + +you see it. + +But at least suffice it to say +Will talked us through it. + +It's not a lot of fancy +econometrics we're doing here. + +This is called the Wald estimate +if you've taken + +econometrics. + +But it's a very simple +method for coming up. + +So there's some problems or +there's some areas where this + +could be a problem. + +And Will hinted at one. + +We can mention a +couple others. + +So how might this treatment on +the treatment design fail, + +let's say, in the +letters example, + +the influenza example? + +So we're sending out +a bunch of letters. + +So suppose the treatment group +is you send out a bunch of + +letters saying, it's flu season, +come get a flu shot. + +And the control group is you +don't send out any letters. + +And so what happens? + +Suppose you get 50% +compliance. + +So treated and the +control group, + +compliance means flu shot. + +You get 50%. + +Let's make it easy, in the +control group you get 0%. + +You do a sample and just +nobody gets a flu shot. + +Maybe this is in a developing +country where people don't + +tend to think about flu shots. + +And suppose you get the flu +rate to be 10% here. + +We could say this +is in Mexico. + +And 15% here. + +Do I have my math right? + +Yeah. + +So what would the treatment on +the treated estimate here be? + +AUDIENCE: 20%? + +SHAWN COLE: So what's +the formula? + +AUDIENCE: 10 minus 15. + +Divided by 0.5. + +SHAWN COLE: Minus 0. + +So it's minus 10. + +So giving the flu shot to a +population will reduce the + +incidence of flu by 10 +percentage points. + +So what's an example of how this +experiment could fail, or + +how this number could +not be correct? + +AUDIENCE: By reminding people to +get a flu shot, you remind + +them that the flu is out there +and they might do other things + +besides get a flu shot. + +SHAWN COLE: Absolutely. + +So now they wash their hands, or +they don't go out in public + +places, or they wear masks. + +And so you think that you're +reducing the flu a lot by + +these flu shots. + +But maybe in fact, washing +your hands is a lot more + +important than-- + +in fact, I think it probably +is-- washing your hands off + +and is a lot more important +than getting a flu shot. + +And that's what's giving +you the effect. + +So if you're scaling up this +impact in the treatment on the + +treated to give yourself credit +for the fact that 50% + +of the people didn't +get a flu shot. + +If instead they're actually +washing their hands a lot, + +then this won't be the +correct estimate of + +treatment on the treated. + +Is that reasonably clear? + +AUDIENCE: I have a question. + +Will it be a good estimate of +the impact of that specific + +intervention on the treated? + +So instead of measuring the +impact of the flu shot, you're + +measuring the impact of +reminding people about flu + +shots and giving them +access to free ones? + +SHAWN COLE: So would you want +to scale that up or not? + +Which estimate would you +want to take there? + +AUDIENCE: Depends on what +you're interested in. + +SHAWN COLE: So suppose we're +interested in, what's the + +impact of sending a letter +to somebody and + +offering them a flu shot? + +Is the correct estimate 5 +percentage points or 10 + +percentage points? + +AUDIENCE: 5. + +SHAWN COLE: Why? + +AUDIENCE: Then your intent +to treat is maybe more + +interesting because you want +to take into account that + +people change their behavior and +their compliance rates are + +[UNINTELLIGIBLE]. + +SHAWN COLE: Right. + +So then we're really interested +in the package of + +effects that sending a letter +causes, which includes + +sometimes getting a +shot, more likely. + +But also washing your hands +or being more careful. + +So the intent to treat-- + +and as we say, so if you have +this situation, you should + +only use intent to treat. + +And intent to treat is very +interesting and it tells us + +the effect of sending out +a letter, but it doesn't + +necessarily tell us the effect +of the flu shot. + +Anybody have any examples from +their own programs or + +projected projects where they're +concerned about this? + +Maybe you guys can be at least +sure to work this in on your + +presentations tomorrow. + +What about when you have +spillovers or externalities? + +So I think Michael talked +about spillovers and + +externalities this morning. + +But he might not have +integrated that with + +intention to treat. + +Is that a correct + +characterization of his lecture? + +Excellent. + +How could we go wrong-- let's +stick to something I know + +well-- with the Balsakhi +Program. + +In the Balsakhi Program, +we have + +treatment and control schools. + +And sort of the compliance is +20% in the treatment schools + +and 0% in the control schools. + +And the change in test +scores is, let's + +say, 1 standard deviation. + +No, that's going to +be way to high. + +0.2 standard deviations +here and 0 + +standard deviations here. + +So quickly, as a review, how do +we get the ITT estimator? + +This is what we call +a chip shot at HBS. + +But since we're not awarding +points for participation there + +aren't a lot of golfers +out there. + +AUDIENCE: Intention to treat? + +It's just 0.2. + +SHAWN COLE: OK and how +did you get that? + +You just saw it? + +AUDIENCE: You just +subtract it. + +You don't have to do anything. + +SHAWN COLE: So it's 0.2. + +AUDIENCE: Minus 0. + +SHAWN COLE: Minus 0. + +Over? + +AUDIENCE: Wait, are +you saying-- + +SHAWN COLE: Oh, sorry. + +Intent to treat. + +Yeah, exactly. + +Yeah, you're right. + +Sorry, my bad. + +So the intent to treat is 0.2. + +And what's the treatment +on the treated? + +AUDIENCE: 0.2 minus 0. + +SHAWN COLE: Great. + +AUDIENCE: Over 0.2 minus 0. + +SHAWN COLE: This is confusing. + +This is the standard deviations +in test score and + +this is the percentage +compliance. + +And so what's that +going to give us? + +AUDIENCE: 1. + +SHAWN COLE: 1. + +So wow, that's a spectacularly +effective program. + +I was very proud to be +associated with it. + +It raised test scores by +1 standard deviation. + +Which if you know the education +literature, is a + +pretty big impact. + +What might we be concerned +about in this case? + +So what did the Balsakhi +Program do? + +Refresh ourselves. + +It takes 20% of the students, +pulls them out of the + +classroom during the +regular class, and + +sends them to a tutor. + +And these are the kids who are +often in the back of the + +class, the teacher's not paying +attention to them + +because they're only teaching +to the top of the class. + +Maybe they're making +trouble, throwing + +things around, et cetera. + +What could go wrong? + +AUDIENCE: You're attributing the +fact to just taking this + +class to just those students +in particular. + +Whereas you're taking them out +of the class, so you're making + +the class that you left +behind smaller. + +So there's effects-- + +SHAWN COLE: Right, so how does +making the class that you left + +behind smaller matter? + +AUDIENCE: Usually it's easier +to learn in a smaller group. + +SHAWN COLE: That's why we teach +a JPAL maximum class + +size of 15 or 20. + +We hope that small classes +are more effective. + +And there's also a tracking +argument that maybe now the + +teacher can focus really on the +homogeneous group rather + +than having to teach to multiple +levels, et cetera. + +So there are all these other +reasons to think that it may + +be the case that they're going +to be some spillovers. + +So how would you explain in +words to a policymaker why + +you're not sure that 1 is +the right effective + +treatment on treated? + +This is particular for the IPA +folks who will have to be + +doing this to earn +their paychecks. + +But anybody is welcome. + +AUDIENCE: There were sidebar +benefits to the control group. + +SHAWN COLE: Right. + +Well, not the control group. + +AUDIENCE: I mean to the-- + +SHAWN COLE: Untreated students +in the treatment group. + +So we were attributing all of +this test gain to sending + +these kids out to class. + +But in fact, there could've +been some test gain in the + +other groups. + +In the extreme, I suppose you +could imagine that there's no + +performance gain for the +children who go out to the + +Balsakhis, but getting those +misbehaving children out of + +the class causes everybody else +to learn so much more + +effectively that it raises +the test score. + +So the program still has an +effect, but the way it has an + +effect is by getting +the misbehaving + +children out of the class. + +Now it turns out that that's +not the case that there are + +sort of some interesting ways +to try and tease out how big + +the spillovers were. + +And I encourage you to read +the paper if you're + +interested. + +And it turns out that there's +not really any evidence of + +spillovers, so it really does +seem like the effect happened + +through the Balsakhi Program. + +But it's definitely something we +want to be aware about when + +we're doing our analysis. + +OK, so we've already +talked about this. + +If you have partial +compliance, your + +power may be affected. + +So the intention to treat is +often appropriate for program + +evaluations. + +It's simple to calculate. + +It's easy to explain. + +If you do this program, you'll +get a mean change in your + +outcome of 0.3, 0.4, 0.5. + +There are a lot of +advantages to it. + +But sometimes you may be +interested as well on the + +program itself. + +And as we said, it measures the +treatment effect for those + +who take the treatment because +they're assigned to it. + +If you have people who +will never ever + +ever take the treatment. + +If you tried to run a randomized +evaluation on + +Christian scientists who refuse +medical treatment and + +you assign them free medical +care, you're not going to find + +any effect. + +But we can find the effect of +the treatment on people who + +take the treatment when +they're offered it. + +And so when you're doing the +design of your experiment, + +it's important to think through +these issues and think + +at the end of the day, at the +end of the study, in two years + +time when we've collected all +the data and analyzed it, what + +sort of results are we +going to report? + +How are we going +to report them? + +And how are we going to explain +them to other folks? + +So that is intention to treat +and treatment on the treated. + +And let's move briefly to the +choice of outcomes and + +covariates. + +We always look forward to your +feedback from the course. + +But in my view, the course might +benefit from a little + +bit more focus on some of the +practical aspects of doing an + +evaluation. + +So for example, survey design +and determining what outcomes. + +Although maybe many of you are +already familiar with that. + +So often when you do these +randomized evaluations, you do + +like a household survey or you +have administrative data on + +the individual and you have 100 +or you have 150 variables + +about them. + +So you go into the field with +a 20 page survey and you sit + +and you ask, how many +cows do you have? + +How many goats do you have? + +How much land do you have? + +What was your monthly income? + +Are your children going +to school, et cetera. + +And so if you imagine an outcome +like microfinance, + +which we hope causes people to +be more productive and engaged + +and boosts household income, +arguably boosts women's + +empowerment, et cetera. + +There are sort of a lot of +things that could plausibly + +happen because you offer +people microfinance. + +But from a statistical side, +this offers some challenges. + +So what's the problem when +you're interested in how + +microfinance affects 40 +different outcomes. + +So education, consumption, +feelings of empowerment, + +number of hours worked. + +You know, you can come up with a +lot of plausible things that + +you think microfinance +would affect. + +AUDIENCE: At a 0.5 level too, +those will come out + +significant having +40 even though-- + +SHAWN COLE: Right. + +So for people who haven't done +hypothesis testing, hypothesis + +testing, which is what we use +to analyze data says, how + +likely is it that the difference +between the + +treatment and the control +group is because of the + +program or simply because +of random chance? + +And so you can look at the +distribution of outcomes in + +the treatment group and the +control group and observe + +their means and their variances +and the number of + +observations, and you can come +up with a rule that says it's + +very, very unlikely. + +Only 1 in 100 times would this +thing have happened because of + +random chance. + +The standard that tends to be +used in economics and the + +medical literature is this +5% p value, which + +is 1 out of 20 times. + +But if you're looking at 40 +outcomes, then on average, 2 + +of them are going to be +statistically significant just + +out of random chance. + +So if I were to just randomly +divide this group, this class + +into two groups, and started +looking at things like US born + +or foreign born, or Yankees fan +or Red Sox fan, or what + +have you, it wouldn't be too +hard to eventually find + +something that were +statistically significantly + +different between +the two groups. + +This is a challenge. + +There are a few ways to deal + +effectively with this challenge. + +So this isn't a particularly +difficult challenge. + +So what the medical literature +does in which, I think, we're + +sort of slowly moving towards +in social sciences, is you + +have to stay in advance where +you expect to find effects. + +So if you're going to the FDA +to test the efficacy of a + +drug, when you apply for the +phase III evaluation you have + +to say, I think this is +going to cure Shawn's + +male pattern baldness. + +And I think that this is going +to result in a more charming + +personality. + +And then you find Shawn and all +of his brothers and you + +run the experiment. + +And then if the outcome turns +out that the treatment group + +is now never get sick, simply +immune from all diseases. + +In the past year, nobody in the +treatment group got sick, + +you can't then go out and market +that drug as something + +that cures diseases because +that wasn't your stated + +hypothesis test ahead of time. + +So oftentimes, we have a +lot of guidance on what + +hypotheses to test. + +So if we're doing a financial +literacy program, we expect + +that to effect financial +outcomes and not employment + +and not divorce rates. + +Although you could +tell a story that + +eventually gets you there. + +But when you're reporting your +results to the world then, + +what you want to do is report +the results on all the + +measured outcomes, +even the ones for + +which you find no effect. + +So then, anybody who takes the +study can look and say, OK, + +they're saying that their +program has a great effect on + +income and children's schooling +and health. + +But they tested 200 things, so +I'm a little bit skeptical. + +Or but they only tested 6 things +and half of them were + +large statistically significant +impact, so I + +really believe that study. + +Maybe it's a little unfortunate +the last class of + +the course is about sort of +challenges with randomized + +evaluations because I should +just take a sidebar to + +emphasize that these problems +we're talking about are not + +unique to randomized +evaluations. + +Any evaluation you +run these risks. + +So if it's just sort of the +standard, what we like to + +think of as a pretty bad +evaluation where you just find + +some treatment people and find +some associated comparison + +people and do a survey, you're +going to run into this exact + +same problem. + +So don't take many of these as +a criticism as randomized + +evaluation, but just take +them as good science. + +What to do for good science. + +And there are other things you +can do which is to adjust your + +standard errors. + +So we have a very simple way of + +calculating standard errors. + +But if you're testing multiple +hypotheses, then you can + +actually statistically take that +into account and come up + +with sort of corrected +or bounds on + +your standard errors. + +And those are described in the +literature that I'm going to + +refer to you at the end +of the talk as well. + +AUDIENCE: What about taking half +your data and mining it? + +SHAWN COLE: And throwing +the rest away? + +AUDIENCE: No, I mine +half of my data. + +I just figure out what really +matters and that's how I + +generate my hypothesis. + +SHAWN COLE: That sounds +reasonable to me. + +AUDIENCE: I better have had +a big enough sample. + +SHAWN COLE: Yeah, you better +have had a big enough sample. + +I think sort of that +intuition is-- + +data mining is problematic, but +it is useful when you run + +a study to report all of your +results because if there are + +some surprising things there, we +don't know whether they're + +there because of chance +or because the + +program had that effect. + +But that gives us sort of a +view on what to do when we + +test again. + +So if we're going to try this +microfinance program out in + +some other country or some other +area of the country, we + +said it had this surprising +effect on girl's empowerment. + +So now let's make that one of +our key outcomes and let's + +test it again. + +So I think that sounds +pretty reasonable. + +There's a pretty advanced, +developed statistical + +literature on hypothesis testing +and how you develop + +hypotheses. + +But that sounds not unreasonable +to me. + +Other thoughts? + +So another possibility is +heterogeneous treatment + +effects, which is what +we often look for. + +So you might think that the +financial literacy program is + +more effective with women than +men because women started out + +with lower levels of initial +financial literacy, or you + +might think that the de-worming +medication is more + +effective for children who live +near the river because + +then they play outside more +often, or something like that. + +And so it's very tempting to +run your regressions for + +different subgroups. + +But again, there's this risk +that you're data mining. + +Suppose I wanted to show that +I randomly assigned you this + +group into a treatment +and control group. + +And I wanted to show that +Yankees and Red Sox + +preferences were significantly +different in the two groups. + +I could probably cut the data +in different ways and + +eventually find some subset of +you for whom the treatment and + +the control variables were +actually different. + +And so you want to be aware +of that possibility. + +And again, like the FDA drug +trial way to avoid this is + +just to announce in advance +which subgroups you expect + +this product to be more or less +effective for and make + +sure you have a sufficient +sample size to test + +statistical significance +within those subgroups. + +Again, as a service to all the +consumers of your studies, + +report the results on +all the subgroups. + +Even the subgroups for whom the +program's not effective. + +So there's another +problem that-- + +did we talk about clustering in +groups, data in the power + +calculations? + +OK, so that is sort of the bane +of statistical analysis. + +Or as we liked to say when I was +a graduate student, sort + +of people used to not really +appreciate the importance of + +these grouped errors. + +It was much easier to write a +paper back then because you + +found lots of statistically +significant results. + +And once you start using +this cluster + +adjustment, it's a lot harder. + +Now only 5% of results are +statistically significant. + +So we whined that if only we +had graduated five years + +earlier, it would have +been much easier to + +get our thesis done. + +But we here don't care about +getting the thesis done. + +We here care about finding out +the truth and measuring the + +potential for cluster in +standard errors, or clustering + +common shocks from the +group is very strong. + +You can often get estimates of +the correlation within groups + +using survey data that +you already have. + +That will inform your +power calculations. + +But when you're doing your +analysis, you need to adjust + +your statistical results +for this clustering. + +And in particular, you run into +problems when your groups + +are very small. + +So if you're thinking, I want +to do an evaluation where I + +had 15 treatment villages +and 15 control villages. + +Well, it's very likely that +outcomes are going to be + +correlated within +that village. + +And then, all of a sudden, you +only have 30 clusters. + +And even the statistical +technique isn't great for + +sample sizes that +are that small. + +You have to use other +statistical techniques, which + +are sort of valid, but +less powerful. + +So we won't go into the +randomization inference. + +Again, it's mentioned in this +paper I was talking about. + +You should be aware of this and +I think the most important + +time to think about this is +when you're designing your + +evaluation, to make sure you +get enough clusters. + +And if you can, it's almost +always preferable to randomize + +by individual than group. + +Because randomizing by group +requires typically, much + +larger sample sizes. + +AUDIENCE: Can you just say one +more thing or give us a + +reference on what you meant by +other statistical techniques + +that are valid, but +not as powerful? + +SHAWN COLE: Sure. + +Let me just skip to this. + +This should be on your +slide package. + +The ultimate slide is additional +resources. + +And so there's a paper called +"Using Randomization in + +Development Economics Research: +A Toolkit, by + +Esther, Rachel, and Michael. + +And this goes through everything +we've talked about + +this week in pretty careful +detail, works out the math, + +and gives you references +to what you need. + +So it's in there. + +Josh Angrist, who's on the +faculty here, has a very good + +book called "Mostly Harmless +Econometrics." But it's + +designed for academics. + +It's not really a textbook. + +But it goes through these things +in very, very, very + +good detail and it's +fun to read. + +But specifically, the +technique is called + +randomization inference. + +It was developed by Fisher. + +And what you do is +you basically-- + +so you have your treatment and +your control group and your + +mean between the treatment and +the mean in the control and + +you test the statistical +significance. + +And then what you do is you +just randomly reassign + +everybody to either treatment or +control, regardless of what + +they actually did, and see if +there's a difference between + +the treatment and +control group. + +And if you do that a hundred +times, you can sort of get a + +sense for how often you find +statistically significant + +differences or not. + +It's related to bootstrapping. + +That's a reasonable method, but +the problem with that is + +the statistical power's +not very good. + +So you need a larger sample. + +And then once you have a larger +sample, then you don't + +need to worry about it because +you can cluster. + +So another question that's +maybe a little bit more + +technical is when you're doing +your analysis, your regression + +analysis, is what covariates +do you want to control for? + +So we're looking at the effect +of financial literacy + +education on credit +card repayment. + +When we do our statistical +analysis, do we want to + +control for the age of the +person, for their gender, for + +their initial measured +level of financial + +literacy, et cetera. + +Now the beauty of randomization +is that it + +doesn't matter. + +Even if you don't have data on +any of these covariates, as + +long as the program was +initially randomly assigned + +and the sample size is large +enough, then you'll be OK. + +But what the controls can do is +that they can help you get + +a more precise estimate. + +So if a lot of people's credit +card repayment behavior is + +explained by whether they ate a +cookie as a child or not and + +you happen to have that +particular data for people who + +have been reading The New +Yorker, then you can soak up + +some of the variation +and come up with a + +more precise estimate. + +Or you can control for +age, or control for + +income, or other things. + +So it's often desirable to +have additional controls. + +But what you don't want to do is +control for a variable that + +might have been affected by +the treatment itself. + +So if you're looking at the +effect of microfinance on + +women's empowerment, so that's +the goal of your study. + +And then you would say, well, +women who have higher levels + +of income report higher levels +of feeling empowered. + +So that's an important + +determinant of feeling empowered. + +We should include that +in our control + +when we do our analysis. + +But if it turns out that +microfinance increased income + +and increased control, then we +might conclude that there's no + +effect because we're attributing +the effect to the + +differences in income. + +Is that clear? + +A lot of these are fairly +nuanced issues and it's often + +worth consulting an academic +or often a PhD student are + +eager to work on projects +like this as well. + +Just as a rule, it's important +to report the raw differences + +and the regression +adjusted results. + +I think we advance a very strong +view that randomized + +evaluation is a very credible +method of evaluation. + +But even still, there are always +ways to tweak or twist + +things a little bit to try and +get the results you want. + +So you could have a survey with +a hundred people or a + +hundred outcomes and only +report seven of them. + +That might make your program +look better than it is. + +So these rules we're proposing +are ways to give people an + +honest and a thorough +view of the + +effectiveness of your program. + +So another rule is that when +you're reporting your + +regression results, you should +include the results with the + +covariates, as well as the +results without the + +covariates. + +So now let's talk about threats +to external validity. + +So we spent a lot of time so +far talking about internal + +validity, which is +sort of was the + +treatment randomly assigned? + +Did enough people in the +treatment group comply that + +you have a difference +between the + +treatment and control group? + +But it's not sufficient to know +that we've learned a lot + +from a randomized evaluation. + +So there's some threats that +just doing the evaluation + +itself may have some impact +above and beyond the program. + +And so these are called +Hawthorne and Henry effects. + +And maybe we'll go back to the +audience for some examples of + +a Hawthorne effect. + +So a Hawthorne effect is when +the treatment group behavior + +changes because of +the experiment. + +What's an example of that? + +Anybody familiar with the +original Hawthorne study? + +AUDIENCE: Was is the lights +being dimmed or different + +levels of lights and workers +felt like they were getting + +attention paid to them +no matter what the + +light level was at? + +It's just that there was +something going on and so + +their productivity was higher. + +SHAWN COLE: I actually don't +remember the study. + +Can I just try and +rephrase that? + +You can tell me whether +I'm right. + +So the experiment was to try and +figure out how the level + +of lighting in a factory +affects productivity? + +I suppose. + +And so they said we're going to +raise the level of lighting + +in this sort of select, maybe +even randomly selected. + +We randomly select 50 out of 100 +of our work groups and we + +roll in an extra light. + +And they're like, oh +great, management + +really cares about us. + +They're including us +in this survey. + +They're giving us extra light. + +We're going to work +extra hard. + +And so you find a higher +output from that group. + +Alternatively, if you had said, +maybe people are getting + +distracted by having +too much light. + +So management picked these 50 +groups, went in and unscrewed + +some light bulbs. + +They're working in sort +of a dim area, they'd + +be like, oh, wow. + +Management really cares +about our well being. + +Now we focus on the natural +light and we're going to work + +really hard. + +So just the act of sort of being +in the treatment causes + +your behavior to change. + +And so what's wrong with that? + +I mean we're trying to measure +the effect of treatment. + +If the effect of treatment +is to increase + +productivity, fine. + +AUDIENCE: Maybe you can not +make a generalization to a + +population that doesn't have +change that behavior because + +doesn't get the treatment +already. + +AUDIENCE: You run around +changing the light levels at + +different factories and you +don't get the effect because + +the real treatment was people +running around and testing and + +observing and measuring +the change in light. + +SHAWN COLE: Right. + +And saying, we're really glad +you're part of this study. + +It's very important. + +AUDIENCE: Which was +really what got + +people to work harder. + +SHAWN COLE: Right. + +You might be able to generalize +that if we decided + +to run this study in every +factory in our firm, then we + +might get similar results +in different factories. + +But probably, within a few +months, people would sort of + +just catch on that this is +just kind of wacky, and + +what's going on? + +It wouldn't really be the +effect of the program. + +Any other examples from your +programs of Hawthorne effects? + +Or things you might +be worried about? + +AUDIENCE: It seems like a lot +of behavior situations, + +there's a threat to this. + +Especially if you have some in +developing country context + +where you have foreigners coming +in or people from the + +capitol coming in. + +Especially if it's something +that-- again, with a behavior + +change where OK, I know I'm +supposed to be washing my + +hands with soap. + +I normally don't, but I know +that the white people get + +really happy when I do it and +they're coming in to evaluate. + +So I'm going to go ahead-- + +SHAWN COLE: Right. + +So if you show up from abroad +and put posters encouraging + +people to wash their hands, +people may pay more + +attention to that. + +What does that validate +or not invalidate? + +So suppose we did this and we +found that the effect was it + +reduces reported incidence +of diarrhea by 15%. + +AUDIENCE: If you then don't +still have white people coming + +into the village, then the same +effect might not happen. + +SHAWN COLE: Right. + +So I guess it's a little bit +nuanced because we should + +distinguish between the program +generalizability, + +which is the program could be +white people come into the + +village, and Hawthorne effects, +which is because I + +know I'm in the treatment group +in the study, I'm going + +to act differently. + +So what's another example of +really, a Hawthorne effect? + +I'm sympathetic to yours as a +Hawthorne effect, but I want + +to really sort of nail it. + +AUDIENCE: There's one for hand +washing where every week + +people go into the villages +and then tell them the + +importance of hand washing as +a way to prevent malaria. + +And every time they ask them, +did you wash hands? + +Do you wash hands? + +But that's not sustainable on +a long-term basis because-- + +and at the same time, you're +distributing free soap. + +So how do you separate +everything? + +SHAWN COLE: I would say again, +that's the program. + +And so we would say if we scaled +that program up to all + +of the country, we'd be fine. + +If we go in every week and +tell people to wash their + +hands and distribute +soap, that's fine. + +AUDIENCE: So sometimes on +sexual behavior studies, + +you'll find that a treatment +group that is encouraged to + +adopt condoms, or something. + +And then in the post-measurement +period, they + +know what the intervention +is about. + +And so if you ask them, what has +your sexual behavior been + +in the last week, they're much +more likely to say that + +they've been using condoms. + +Or change their partnering +habits or these other sorts of + +things that have nothing +to do with-- + +SHAWN COLE: Right. + +So the effect of being in the +treatment group and knowing + +that you're getting this +treatment might change how you + +answer the survey questions, +even if you + +didn't behave that way. + +Any other? + +AUDIENCE: For the Hawthorne +effect? + +SHAWN COLE: So it's certainly +a problem with your survey. + +AUDIENCE: It might change +other aspects of their + +behavior other than condom use +that would be simply because + +they know that you're looking. + +SHAWN COLE: So I mean I would've +said something like I + +know that they really care about +me and so because I'm + +part of this MIT Poverty Action +Lab Study, it must be + +really important +that I do this. + +But if you were to generalize +the program, not as part of a + +study, then people would react +to it differently. + +The other side of the coin is +the John Henry effect, which + +is people in the comparison +group behave differently. + +What are examples of that? + +AUDIENCE: The village in the +control group is resentful to + +the politician who they +perceived as determining who + +got treatment status and so +they don't try as hard on + +whatever's being measured. + +Or they intentionally turn in +a poor performance as a sign + +of protest. + +SHAWN COLE: Right. + +They're like, why am I in the +control group of this study. + +I wanted to be in the +treatment group. + +I'm not going to use fertilizer +because I know this + +study's about fertilizer +or something. + +Other thoughts? + +AUDIENCE: You could +do the opposite. + +I could say, oh, those guys, +they got the treatment. + +But I don't need that. + +I can do just as well, +so I'm going to-- + +SHAWN COLE: I'm going to pull +myself by my bootstraps. + +AUDIENCE: [UNINTELLIGIBLE] going +to start studying and + +double up and I'll show them. + +SHAWN COLE: That's an +interesting problem, is we + +don't really know which way +these effects go ex ante. + +The Hawthorne or John Henry +effects could be positive or + +could be negative and could +be a challenge for the + +evaluation. + +So how do you sort of try +and address this to + +resolve these problems? + +AUDIENCE: It'd be hard +to do statistically. + +AUDIENCE: This could be +dangerous I suppose. + +But if you try to make the +people in the control group, + +for instance, feel special +in some other way. + +But in a way that you can say +is not related to anything + +you're measuring from +the treatment. + +SHAWN COLE: Right. + +So we're doing a financial +literacy evaluation where + +we're showing financial +literacy videos to the + +treatment group. + +In the control group we're +bringing them in and we're + +showing them films about health +or something that we + +don't think will have any effect +on financial literacy, + +but lots of the things +are the same. + +In the medical literature they +do often double blind studies, + +where you don't even know +whether you're in the + +treatment group or the +control group. + +So you can't get despondent for +being in the control group + +because you don't know +you're there. + +Sometimes these are sort of +inevitable and you can't get + +around them, but you should +think about them carefully and + +try to minimize the risk. + +So another problem with +evaluations is sort of + +behavioral responses +to evaluations. + +So we assign some schools to +treatment schools and some + +schools to comparison schools. + +And the people in the comparison +school say, oh. + +So we give textbooks to +the treatment school. + +So lots of people +say, hey, this + +school's got new textbooks. + +I'm going to go to +this school. + +And so that increases +the class size. + +So the textbooks may benefit +the test score, but the + +increased class size offsets +that and you find no effect of + +textbooks because +the behavioral + +responses undid this. + +Whereas if you were to do it +throughout the country and + +give every school new textbooks, +then there'd be no + +transferring around because +there'd be no reason to change + +schools because your school +would have free + +textbooks as well. + +So that's sort of another. + +AUDIENCE: I just wanted to go +back to your question about + +how to minimize the Hawthorne +and John Henry effect. + +We're doing an impact study, +impact evaluation on + +microfinance product +in Mexico. + +We try not to talk +about the study. + +The people at the top know that +they're implementing this + +study, but the participants +don't know + +anything about the study. + +And it's very kind of hush +hush, basically to try to + +avoid changing behavior. + +And obviously that's not +always possible. + +But to the extent that it is, +people don't have to know that + +they're part of a study. + +SHAWN COLE: I'm sure everybody +here who's lived in the US has + +participated in a study +sponsored by a credit card + +company that does randomized +evaluations to figure out how + +to get people to sign up +for their credit cards. + +So they randomly send some +people 10 point font on the + +outside letter, some people +12 point font + +on the outside letter. + +Some people 16 point font +on the outside letter. + +And they keep track of who +responds and they figure out + +that this is the right +font size. + +And then they say, what +color should it be? + +This is the right color. + +What should the teaser +interest rate be? + +And so lots of firms do this +without you even knowing it. + +And then you won't get any John +Henry or John Hawthorne + +effects because people won't +even know they're in + +experiments. + +Sometimes there are sort of +consent issues that you need + +people's informed consent that +preclude that from happening. + +There's some issues that we were +touching on before, sort + +of the generalizability +of results. + +So can the program be +replicated on a + +large national scale? + +So we're going in and giving +free soap to these villages, + +but it would get expensive to +give free soap to every + +village in the country. + +The study sample, is +it representative? + +So what's a problem you +might run into here? + +AUDIENCE: If for logistical +reasons, you're only doing it + +in one state in a country and +it's randomized within the + +state, but then there's just +a different culture in the + +state, or there's a really +strong history or traditions + +in the state that then are not +generalizable up to the + +country as a whole. + +SHAWN COLE: A problem you often +run into is NGOs will, I + +think for reasonable reasons +say, OK, let's do this study + +at out best bank branch or +at our best district. + +Because doing a study +is pretty hard. + +You have to have treatment and +you have to have control and + +keep track of who's +in which group. + +And so these people have been +with us for five years and + +they can do the study +really well. + +And so you do the study and you +find some nice effect, but + +that is the effect of putting +your best people into the + +program and you only +have 20 of them. + +And now when you try to scale +it up to 500 villages, you + +just don't have that level of +human capital to implement the + +same quality of program +elsewhere. + +So sensitivity of results. + +This is sort of important, but +may be second order important. + +The state of the art and the +sciences, we're still looking + +for things that work +and work well. + +So we're not as worried about +figuring out if we give the + +de-worming tablet every month +versus every three weeks, + +which one is more effective. + +I mean that's a useful important +question and it + +probably deserves a study. + +But it's hard enough to get the +big picture studies done + +to then move onto the +sensitivity of the results. + +That said, sometimes there are +often interesting economic + +questions you have. + +So you want to know whether +microfinance has an impact on + +people's wealth. + +But you might also care about +the interest rate. + +And so for microfinance to be +sustainable, the interest rate + +has to be high. + +But for it to generate a lot of +income for the borrowers, + +the interest rate +has to be low. + +So you could try your program +at different interest rates + +and see whether you find the +same effect at different + +interest rates. + +That would be very +interesting. + +So there's often a trade-off +between internal + +and external validity. + +In my experience, I think it's +probably reasonable to focus + +on the first pass on the +internal validity. + +Because the advantage of picking +your best branch or + +picking your good people to get +the study done and done + +well and have a large treatment +effect is that we + +were sure we know what +we're measuring. + +It's often hard to measure +effects in the real world. + +It's not as if the hundred +people in this room are the + +first people to think +we should do + +something to reduce poverty. + +It's a difficult and +thorny problem. + +And so if we can throw sort of +our best program and show that + +our best program is effective, +then we can sort of work on + +expanding and testing our +second best program. + +Statistical power is often +stronger if you have a very + +homogeneous sample. + +So if you can randomize in a set +of twins or something like + +that, you have very good +statistical power. + +But twins might not be +representative of the general + +population. + +And then, of course, the +study location is + +almost never random. + +In Indonesia we did manage to do +a nationally representative + +randomized evaluation of a +financial literacy program, + +but that was just because the +world bank was doing a + +nationally representative survey +and we persuaded them + +to tack the experiment +on at the end. + +But otherwise it's almost always +prohibitively expensive + +to travel around to hundreds +of locations. + +But at the end of the day, +you do care a lot + +about external validity. + +You want to know that before +you throw a lot of money at + +the program, can you get +the same effect when + +you scale it up? + +And is this program effective +for large populations? + +So in the last 5 or 10 minutes, +we'll talk a little + +bit about cost effectiveness. + +So you've done your program, +you've done your evaluation, + +you've got the efficacy. + +You know how much it costs +to deliver the program. + +Now how do you decide which +program to pursue? + +I guess the important thing +in this is pretty obvious. + +It's just finding a metric that +you can use to compare + +different programs. + +So in educational programs +we often look at years of + +schooling as an output. + +Having an extra teacher causes +people to stay in school + +longer, but extra teachers +are expensive. + +You can figure out how much +it costs per child year of + +schooling you create. + +In health programs, they have +something called a disability + +adjusted life year, which I'm +sure some of you know a lot + +better than I do. + +But it's basically an unimpaired +year of life with + +no disability counts as one. + +If your legs are immobile, +then maybe + +it'd be 0.6 or something. + +And it sort of gets adjusted +down to figure out which + +health interventions are more +or less cost effective. + +Or you could do cost +per death averted. + +I think the interesting takeaway +here is that doing + +these types of comparisons can +sometimes lead to pretty + +surprising results. + +So we know how to get people in +school by reducing the cost + +of education, so the PROGRESA +program in Mexico made + +conditional cash transfers +to students' parents + +who attended school. + +Providing free uniforms +increases attendance. + +Providing school meals +increases attendance. + +We've looked at incentives +to increase learning. + +But we've also looked at +the de-worming case. + +If you'd said five years ago +to educational people who + +specialize in education in +developing countries, what do + +you think a very high impact +intervention would be? + +I think very few people would +have suggested de-worming. + +But if you do the math, you can +figure out that an extra + +teacher will induce let's say +one year of additional + +schooling, but costs +$55 per pupil. + +So the cost per additional year +of schooling is here for + +extra teacher. + +Iron supplements here. + +School meals here. + +Deworming here. + +So it's just tremendously cost +effective to provide this + +de-worming medicine +as a means of + +increasing years of education. + +Much cheaper than scholarships +for girls, et cetera, or + +school uniforms. + +And you could do this +calculation not just for + +education, you could say, there +are a lot of things that + +we care about. + +We care about health outcomes, +human capital investment, + +externalities. + +And so an interesting thing +that came out of the + +de-worming study was that if you +did the old studies that + +didn't take into account the +externalities and just sort of + +treated some people in a school +but not other people in + +a school, it didn't look like +a very good intervention. + +Because the kids would keep +reinfecting each other even + +though they'd just been treated, +and so it wasn't that + +cost effective. + +But once you did the school +level randomization and took + +into account for the +externalities, then the + +program turned out to look very, +very cheap as a way of + +providing education. + +It's also an incredibly +effective way of improving + +health outcomes, de-worming. + +And much more effective, for +example, than treating + +schistosomiasis. + +You can do even more +calculations. + +You can say OK, so we know that +the deworming medicine is + +going to increase years +of education by 0.2. + +Well, what's 0.2 years +of education worth? + +There are economists who have +done estimates of the returns + +to schooling in Kenya. + +They say if you get an extra +year of schooling, you're + +going to get 7% more income +throughout your life. + +And then so you've got +40 years of life + +at 7% higher income. + +You can take the present value +of that stream of additional + +wage payments and you can see +that, wow, by investing only + +$0.49, we're going to generate +$20 more in wages at net + +present value, on average. + +And so if you have a tax rate +of 10%, that's clearly a + +profitable intervention +for the government if + +it's patient enough. + +Because it'll take in $2 in net +present value in taxes at + +a cost of only $0.49 +of delivering. + +Of course, there may +not be any taxes on + +informal labor in Kenya. + +So I think this is an example we +like to cite first, because + +Michael helped prepare this +particular lecture the first + +time around and is fond +of that paper. + +But second, I think it's a very +nice example of a program + +that has a really big +macro effect. + +So basically, it's been adopted +nationwide in Uganda, + +and they're expanding +it a lot in Kenya. + +It's been tried in India and +many other countries have + +realized that this is a + +tremendously effective program. + +And the ability to have this +randomized evaluation, there's + +very credible evidence that +said, we had these treatment + +groups, these control groups. + +We followed people for three +years and the reason why our + +results are so different than +the other results that you + +were citing as a reason not to +provide de-worming is because + +of these externalities. + +And we can show you why these +externalities matter. + +The credibility of that study +really helped to transform + +policy and literally save +thousands, tens of + +thousands of lives. + +Maybe more. + +Other examples. + +PROGRESA, which some of you +might be familiar with. + +It's actually the government of +Mexico decided to integrate + +a bunch of randomized +evaluations into its social + +welfare programs. + +That methodology and the results +of what's been shown + +effective in that program have +been adopted throughout Latin + +America and elsewhere. + +And Ben Olken, whom you saw +earlier, did some experiments + +on threat of audits in Indonesia +for corruption. + +And the government of Indonesia +is increasing the + +probability of audits as a way +of fighting corruption in the + +nation's fourth most +populous country. + +So I think the conclusion is +that these evaluations, which + +take a lot of time and +take a lot of effort, + +let's not kid ourselves. + +If you sign up for one +of these, it's + +going to be a big affair. + +But it can have a tremendous +impact. + +It's very important to know from +your own perspective how + +effective your program +is, but you can + +influence policy a lot. + +So I'm just going to conclude +with two things. + +One is this mention of the +additional resources, which + +should be on the JPAL website. + +This is a book you have +to buy for $60. + +Only buy this if you're +already familiar with + +econometrics. + +But they're both great +treatments of the material + +we've covered this week. + +And I believe JPAL is in the +process of developing a + +practitioner's guide as well. + +This is a much more +technical guide + +that's full of equations. + +But hopefully, as you've seen +throughout the last week, + +we've tried to explain things +in ways that are accessible + +that you can explain to people +who haven't taken econometrics + +and that will hopefully be +coming out pretty soon. + +And so if I were just to at +least take two seconds to give + +my perspective, I'm young but +I've done a few of these. + +It's probably helpful when +you're doing one of these + +evaluations to engage +in academics. + +If you're thinking of doing +a study, you just + +send an email to JPAL. + +They'll send it out to their +network of 15 or 20 people and + +I don't know what the +response rate is. + +But I think there's a lot of +interest in doing these + +experiments. + +IPA is another organization +that does this. + +But there's some subtle nuanced +issues that require + +careful thinking through. + +Or you could just call me up +and say, we're going to be + +doing this study. + +We're spending a lot of money +on it, can we just talk + +through these issues with you? + +I'd be perfectly happy +to do that. + +And then, one thought. + +Just a few thoughts +on keeping your + +evaluation costs effective. + +And maybe even think about this +when you're proposing + +your program tomorrow, is that +randomizing at the individual + +level where possible and +appropriate is a tremendously + +useful way to keep costs down. + +Because their statistical power +is so much higher, so to + +detect any given effect size you +can do it with many fewer + +observations. + +Another way to save a lot +of money is to use + +administrative data. + +So if you can get people to give +you access in New York to + +their checking accounts and +credit card statements, and + +get those reported, at a +low cost to you, the + +administrative data is often of +very high quality and can + +be collected for little money. + +And then the third trick is +sort of using lotteries to + +ensure high compliance. + +So if you sort of announce +that you've got this new + +program and you let everybody +who's interested apply, and + +then you sort of randomly select +60 and have 60 as a + +control group, then the +compliance is going to be + +pretty high in the +treatment group. + +That Wald estimator, the +difference between these two + +things, is going to +be pretty high. + +So we're at 2:25, which at MIT +is the end of the class. + +And I guess the end of the +course, at least from the + +lecturing side. + +So thank you very much and I +will be around here to answer + +questions for the next +15 minutes if people + +would like to talk. \ No newline at end of file diff --git a/Z7ftUJAx-1E.txt b/Z7ftUJAx-1E.txt new file mode 100644 index 0000000000000000000000000000000000000000..4462d42b5404964e6d4bbca853d6b3a910b5e37a --- /dev/null +++ b/Z7ftUJAx-1E.txt @@ -0,0 +1,1601 @@ +PROFESSOR: Since z, that's +straight up. + +And that is going to provide +for you a cell that has the + +shape of a square prism. + +This would be a1. + +This would be a2. + +And this would be a3-- + +I'm sorry, this would be c. + +And if you took the choice for +the third translation as 1/2 + +half of a1 plus 1/2 of a2 plus +some amount z up above the + +base of the cell, and then +redefined a T3 prime that + +would be equal to-- + +sorry. + +What am I doing here? + +Yeah. + +This is right. + +1/2 of a1 1/2 of a2, +and z straight up. + +Define a T3 prime as 2T3 +minus a1 minus a2. + +And that will define for you, +again, a cell in the shape of + +a square prism with a1 and a2. + +And now the translation that +went up directly over the + +center of the base +of the net below. + +Twice that minus a2 minus a1 +brings you back to a third + +translation T3 prime that's +normal to the base. + +So both cells have +the same shape. + +This is a primitive. + +This is a body-centered +tetragonal lattice. + +And the symbol that's used to +represent the body-centered + +lattice is I. One of the few +cases, again, where one has to + +be bilingual. + +The German word for +body-centered is + +innenzentriert. + +So there's Schoenflies +at work again. + +So primitive body-centered +represented by I. + +And that brings us to one final +case, and that is the + +plane groups that have +a hexagonal shape. + +And here we have a funny +situation in that the same + +choices of the third translation +do not work for + +all of the plane groups. + +If you have a base +to the cell-- + +and again, the two edges +of that net are + +identical by symmetry-- + +if it has a three-fold axis in +it and nothing else, than + +there are two choices. + +You can either have T3 be equal +to 0a1 plus 0a2 and an + +amount z straight up. + +And that will give you a cell +that is a primitive cell. + +This would be a1. + +This would be a2. + +And just as we did for +tetragonal, we'd call the + +third axis c, This will work +for a three-fold axis. + +So there is a space group P3. + +This will also work for all +of the other groups. + +So there's P3M1 and a P31M. + +And a P6 will work. + +And a P6mm will work. + +So look it here. + +We've got five additional space +groups in addition to + +the lattice type. + +This is the primitive +hexagonal lattice. + +For a three-fold axis, we +have another choice. + +We could pick T3 so that it +took the origin three-fold + +axis and put it directly +over this one. + +Looks as though you could have +a different distinct lattice + +if you move the origin lattice +point over the three-fold axis + +that sits at a location +1/3, 2/3. + +This one is at 2/3, 1/3. + +Let me demonstrate, I think +convincingly and clearly, that + +those two choices are exactly +the same thing. + +And the way that I can show that +is, once again, to draw + +this net a1, a2. + +And suppose I pick the part of +the offset of T3 that is + +within the plane of the net as +going from this lattice point + +to this one here. + +Then if I go twice that +translation T3, that's gonna + +put me directly over this +three-fold axis. + +And if I go three translations +T3, I'll be directly over the + +lattice point on the +ground floor. + +So putting the original lattice +point over this + +three-fold axis or this +three-fold axis is exactly the + +same thing. + +And I can change one into the +other just by flipping this + +thing 180 degrees. + +So it's obviously +the same choice. + +This description of T3, if I +define the direction of c now + +as 3T3 defined in this fashion, +minus a1 minus a2, is + +gonna be a funny situation. + +It's gonna be a peculiar sort of +double body-centered cell. + +Of course, along the long +diagonal of the hexagonal + +cell, I'll have one lattice +point that's 1/3 of the way + +along that long diagonal, and +another interior lattice point + +that's 2/3 of the way along +that long diagonal. + +OK. + +This double body-centered cell, +so to speak, actually + +can be redefined in terms of +a primitive cell, not a + +primitive cell that is this +particular description of a + +primitive hexagonal lattice. + +This is not a primitive +hexagonal lattice. + +But suppose I go from this +interior lattice point along + +the long diagonal of the +cell to this location + +and call that a1. + +Remember that there is a +three-fold axis sneaking down + +through the center of this +triangle, goes through the + +lattice point, and comes +out the center of + +the triangle below. + +If I go up to this lattice point +and up to this lattice + +point, I have three translations +that are + +straddling the three-fold +axis. + +And that three-fold axis rotates +one into the other. + +So this new definition of +a cell that is in fact + +primitive a1, a2-- + +and they're all equivalent +by symmetry. + +I always get in trouble when +I try to draw it, but that + +actually defines a cell +with a shape that + +we've not seen before. + +That is a cell that has the +shape of a rhombohedron. + +And as I say, I always get in +trouble when I try to draw it. + +It's got three translations +like this and three + +translations skewed by 60 +degree sitting on top. + +Everybody can see that's a +rhombohedron, can't you? + +Say yes. + +Be nice. + +So this is another primitive +cell that's a choice for this + +triple cell. + +And this consequently gives +its name to this lattice. + +This is called a rhombohedral +lattice, regardless of whether + +you pick the primitive cell in +the shape of the rhombohedron + +or this peculiar double +body-centered cell. + +So this is a rhombohedral +lattice. + +And this is represented in a +space group symbol by the + +letter R, standing +for rhombohedral. + +So just the three-fold axis +with this choice of + +translations, that would +be space group R3. + +AUDIENCE: [INAUDIBLE]? + +PROFESSOR: Yeah. + +a1 like this. a2 like this. a3, +I'm taking a right-handed + +system, comes from the centered +lattice point. + +So let me draw it +in projection. + +It's easier to see. + +Here's the outline of +the hexagonal net. + +Here's the three-fold axis. + +And I've taken a1 coming +up like this. + +I've taken a2 coming up out +of the board like this. + +And I've taken a3 coming +out like this. + +OK. + +So these are the three edges +of the rhombohedron. + +Notice that I cannot have that +lattice with a lot of the + +hexagonal plane groups. + +I cannot do it for +six-fold axis. + +Because a six-fold axis-- + +P6 and P6MM have a six-fold axis +here and three-fold axes + +in the middle of the cell. + +So I cannot have a rhombohedral +lattice for P6 or + +P6<M. The primitive hexagonal +lattice is the + +only thing that works. + +And then we have this curious +situation with the two + +alternative settings of point +group 3M in a hexagonal net, + +P3M1 and P31M. + +For P3M1, I have symmetry 3M +at both the origin lattice + +point and in the center of +these two triangles. + +So for P3M1, in addition to a +three-fold axis, I could put + +in 3M1, stack up plane +group P3M1. + +But I cannot do this for 31M. + +That's impossible. + +Because if you look at P31M, +there is symmetry 3M at the + +origin and only symmetry 3 in +the center of the triangles. + +So if I try to pick this as a +third translation for plane + +group P31M, I'm taking symmetry +3M and plopping it + +down on top of symmetry 3, and +that wrecks the plane group. + +So for the rhombohedral +lattice, I can + +only have 3M1 or P3. + +P6 has a six-fold axis at the +origin lattice point. + +The two centers of the triangles +are three-fold axes. + +So primitive for the six-fold +axis, either P6 or P6MM, is + +the only choice. + +So if anybody's counting-- +and I wasn't-- + +we've got 11 lattices so far. + +And the only ones that we +haven't been able to get by + +simple stacking of the plane +groups are the systems that + +you all know as your +favorites. + +The cubic or isometric stems +for the fact that the + +translations are identical +in all three directions. + +Let me quickly dispose of +those by starting with a + +four-fold axis coming out of one +face of a tetragonal cell + +and saying now if this is a +cubic symmetry, I have a + +three-fold access that comes +out, sort of, in the direction + +of a body diagonal. + +But this three-fold axis is +gonna rotate that four-fold + +access to this direction +and to this direction. + +We've seen that if I look down +along the diagonal of a + +equally axed tetragonal prism, +the three-fold axis takes this + +face, rotates it into this +face, and rotates + +it into this face. + +So I have to have a four-fold +axis coming out of every one + +of the faces. + +And having that arrangement of +four-fold axes means that not + +only will the two translations +be identical in the base of + +the cell, as is the case for +tetragonal, but if I put in + +that three-fold axis as an +extender, all three edges of + +the cell have to be identical +by symmetry. + +So I can do this for a primitive +tetragonal lattice. + +And that's gonna give me a +primitive isometric lattice. + +I can do this for a + +body-centered tetragonal lattice. + +So that would be indicated by +the symbol I. So it's a + +body-centered cubic lattice. + +And if you add up everything +we've done to this point, + +there are 13 space lattices, +a very unlucky number. + +And as you all know, +there are 14. + +We've missed one. + +So what have we not done? + +We stacked up all the plane +groups in all possible ways. + +We've taken the four-fold axes +out of the face normals, all + +three face normals of +a tetragonal cell. + +And that forced it to become +a cubic lattice. + +What have we done wrong? + +Actually, we can get the +fourteenth space lattice by a + +little bit of sleight of hand +that is not obvious. + +Let's say that this is the base +of a tetragonal lattice + +that we used as the parent +for our cubic lattice. + +Let me change that primitive +square in the base of the + +tetragonal cell and change it +into a centered square. + +There'd be no reason for doing +that for a plane group. + +But let me notice now that if +this is the direction of a + +four-fold axis, rather than +having the three-fold axis + +come out of this direction +relative to this super double + +square, I can make the +three-fold axis come out in + +this direction. + +Ah-ha. + +So what I have now is a cell +that is centered, has a center + +in the base and has translations +that are + +perpendicular to the +base like this. + +And if this is the direction of +the four-fold axis and this + +is the direction of the +three-fold axis, that + +three-fold axis is going to put +a centered lattice point + +on the remaining faces +of the cube. + +So it's only if I notice I can +make a double square base to + +the cell again, put the +three-fold axis of a cubic + +symmetry along the direction +of the body diagonal, I + +generate lattice points in the +middle of the other faces as + +well, and this gives me the +lattice known as F, the + +face-centered cubic lattice. + +And the edges of the cell here +are all identical, equivalent + +by symmetry. + +So they're labeled a1, a2, a3. + +Have you ever seen a lattice +constant for a + +cubic crystal a0? + +Has anybody ever seen that? + +A lot of people do it. + +And if you see that notation in +a publication, you will be + +entitled to sneer +at it knowingly. + +It's logical, three, +two, one, zero. + +By extrapolation, if you've +got an a3, an a2, a1, you + +gotta have an a0, right? + +Well, not necessarily. + +That sort of algebra +doesn't apply to + +labeling of cell edges. + +It comes from a curious +historic precedent. + +Come back, again, to the fact +that for literally more than + +100 years, people developed +symmetry theory and had a + +pretty good idea that crystals +were based on packing of + +units, molecules, whatever they +were, that were on the + +nodes of a lattice. + +But they couldn't measure the +size and shape of the lattice. + +And that was the brilliance of +the famous experiment by Max + +von Laue because that, in one +fell swoop, show that the + +mysterious radiation x-rays +were just electromagnetic + +radiation of a very +short wavelength. + +And that's what he really +gained notoriety for. + +But at the same time, he proved +for the first time, + +unequivocally, that crystals +were based on a lattice. + +And that was the other side +of his double-edged + +accomplishment. + +Up until that time, people +learned about crystals by + +studying the morphology and +measuring the angles between + +crystal faces and recording +different faces on a crystal. + +I mean, I can just see one of +these old guys working a + +little bit before his wife made +him come down and sit for + +supper because it was +getting cold. + +And he'd let out +a, whoop, huh? + +A 13 27 face. + +What the hey. + +It's a new face on potassium +tartrate, something like that. + +This was the way these guys +got their jollies. + +And on the basis of the angles +between faces, as I said on + +several occasions, they could +determine a ratio of axes, a + +ratio of a to b to c, if their +assignment of indices to faces + +were correct. + +And how did you know? + +Well, along came x-rays, a and +you could measure for sure. + +So what people started doing +to distinguish a to b to c + +ratios determined from crystal +morphology, they put the zeros + +on it to indicate real values +from diffraction. + +And when little people came +afterwards and they didn't + +realize the reason for doing +that-- nobody's done this for + +over 100 years because everybody +determines lattice + +constants using diffraction-- + +but some people have +seen these zeros. + +So they say, I'm not doing +proper notation. + +And you know how furious +crystallographers get if you + +don't use proper notation. + +So let me write a0 +as the lattice + +constant of my cubic crystal. + +You see this commonly. + +And there's been no need +for it for 100 years. + +So anyway, that's the origin +of the subscript zero. + +There are a lot of dumb things +that take place among normally + +rational people. + +I said a moment ago-- +and I crossed my + +fingers when I said it-- + +that c is the label that is +assigned to the unique axis, + +the axis that is unique +because of symmetry. + +Sometimes you see monoclinic +crystals, which have a + +two-fold axis and/or a mirror +plane perpendicular to the + +two-fold axis, labelled with +this as b, this is a, and this + +as c, and the angle between +them-- that's the general + +obtuse angle-- + +as beta. + +There is a story behind +this lapse of + +standardness in notation. + +How do people decide on what +proper notation is? + +Well, there is an organization +called the International Union + +of Crystallography, which +is the equivalent of the + +International Union of Pure and +Applied Physics and the + +International Union of Pure +and Applied Chemistry. + +And they meet every +three years. + +And there are special +commissions for people who + +like to fight and argue out +conventions and nomenclature. + +And this is such a silly +abomination that there was a + +move made when they came out +with their new edition of + +international tables to change +this and do it the way you do + +for all of the other crystal +systems, namely a, b with + +gamma between them, and c coming +out this way as the + +direction of the +two-fold axis. + +And this would be the +mirror plane. + +And that would put this in +accord with tetragonal and + +hexagonal and everything else. + +And it was logical and seemed +the right thing to do. + +So how do people decide +on nomenclature? + +This is something that people +fight with with more passion + +than anything else in science. + +So you make a proposal. + +The proposal goes to the +national committees of + +crystallography in countries +over the world. + +They discuss it. + +They fight about it. + +They vote on it. + +Then it comes back to the +International Union. + +And finally, if everybody seems +agreed, they present it + +at the next meeting of the +International Union Of + +crystallography for a vote. + +And that's exactly what happened +with the proposal to + +standardized notation. + +This took place maybe, I don't +know, in the 1950s. + +Everybody was in favor. + +The discussion proceeded +rationally. + +Then this little guy jumps up +in the front row, short of + +stature, balding of head, with +a very piercing nasal voice. + +And he gets up and he enters +into this diatribe. + +b-axis unique was good +enough for Curie. + +b-axis unique was good +enough for Mauguin. + +B-axis unique was-- and all +the names were French. + +Actually, he wasn't French. + +He was Belgian. + +So he went on and on and on. + +And he so cowed this group of +300 rational delegates, that + +they didn't cave in entirely. + +What they did was they entered +every entry for monoclinic + +crystals in the international +tables twice, once with this + +set of labels, once with +this set of labels. + +And to indicate that this was +the preferred notation, this + +is labeled the first setting. + +And to indicate second-class +citizenship no matter what + +Curie, Mauguin, Bravais, and all +of these other guys felt, + +this was called the +second setting. + +And I'm not kidding. + +I'll bring in a copy of the +international tables for x-ray + +crystallography. + +Every entry for a monoclinic +crystals is in there twice. + +AUDIENCE: And no one in the past +50 years has tried to get + +rid of the second set? + +PROFESSOR: No. + +Actually, the reason is +it is expensive to + +revise these tables. + +And I brought in on the first +day, you don't remember, my + +copy of international tables +for x-ray crystallography, + +which is about this +big and cost $100. + +And then the new version +which is twice as large + +dimensionally, four times as +heavy in terms of weight, and + +I think about eight times +as expensive in + +terms of actual cost. + +So you don't do this casually. + +If there's something actually +new comes out, you make a + +little supplement that +people can stick + +in the pages somewhere. + +AUDIENCE: Don't they still have + +PDFs nowadays or something? + +PROFESSOR: The last volume came +out before PDF, before + +very intensive use of computers +for such data. + +The journals now are +all done online. + +You submit papers online and +they're archived online as + +well in addition to hard copy. + +But that's something that was +before the time of the + +publication of the last +set of volumes. + +Well, I am almost done with +talking about lattices. + +But I have a thought question. + +You've all heard of this castle +in Ireland that has + +this famous rock in the side +of the castle called the + +blarney stone? + +And you, to get the gift of gab, +have to lean over this + +rather dangerous wall and +somebody holds your ankles and + +you go down and you kiss +the blarney stone. + +And that gives you supposedly +the gift of gab. + +But kissing is a dangerous +occupation. + +You've all heard about kissing +disease mononucleosis? + +And with all those people +smooching the blarney stone, + +I've always been afraid the +blarney stone might + +come down with mono. + +And if the blarney stone became +ill in this session, + +would it have to be + +transferred to the Mono Clinic? + +I don't know. + +All right. + +Here in all their glory are +the 14 space lattices, or + +Bravais lattices as they're +finally called. + +The labels a, b, c, et cetera, +are not on them, but the c + +axis is vertical. + +You'll see that the hexagonal +rhombohedral lattice is shown + +referred to hexagonal axes. + +In the international tables, +you will find all the + +information both referred to +rhombohedral lattices and to + +the triple hexagonal +cell as well. + +Now, into these lattices one +should drop those of the 32 + +point groups that the lattices +can accommodate. + +That's gonna be a lot +of additions. + +Besides that, there is the +option of having the symmetry + +elements of the point group +not intersect at a common + +point, but interleave them as we +did, for example, with the + +glide planes in P2GG, and +in some of the other + +two-dimensional plane +groups as well. + +Then we would do what we also +did in two dimensions, take + +the mirror planes and replace +them by glide + +planes, one or the both. + +And you might think that we +really have an enormous amount + +of work to do. + +We haven't considered any +symmetry combinations that + +involve a horizontal +mirror plane. + +For example, we look at what +symmetry 2 requires and we + +found the primitive monoclinic +lattice, and the side-centered + +monoclinic lattice, and the + +body-centered monoclinic lattice. + +So there's more than one lattice +type into which we can + +drop a given point group. + +But what would you have if +you had a mirror plane + +perpendicular to the +two-fold axis? + +What kind of lattice +will that require? + +OK. + +Let me, in one masterful swoop, +convince you that we + +have done almost the better +part of the work. + +Let us ask what does inversion +require of a lattice? + +What does the symmetry of +inversion, which didn't appear + +in any of the plane groups at +all because that's inherently + +a three-dimensional point +group operation? + +Well, think about it. + +All inversion says is that, if, +hey, there's a translation + +that goes up this way, there +should be another translation + +minus T in the opposite +direction. + +And any lattice whatsoever can +make that claim and satisfy + +that requirement. + +So let me now just quickly say +that if we have derived the + +lattice types, and by +implication the space groups + +as well, for a two-fold axis, +for a four-fold axis, for a + +six-fold axis, and so on, we +have automatically satisfied + +the requirements for any point +group that results when you + +add inversion to a two-fold +axis, when you add inversion + +to a four-fold axis, or add +inversion to a six-fold axis. + +So it turns out that the +requirements of a six-fold + +axis, which gave us the +primitive hexagonal lattice, + +are also met by 6 over M. The +requirements of a four-fold + +axis, which gave us the lattices +primitive tetragonal + +and body-centered tetragonal, +are also satisfied for 4 over + +M. + +So, any one of the +point groups that + +differs from the 11-- + +from the 10 two-dimensional +symmetries-- + +namely 1, 2, 3, 4, 6, M, +2MM, 3M, 4MM, and 6MM-- + +any symmetry that you get by +adding inversion to those + +two-dimensional point groups is +automatically going to be + +happy in the space lattices +that we've + +derived to this point. + +So we have done an enormous +fraction of the work that's + +required to derive space +lattices, and the + +space groups as well. + +So there is not too much +more to be done. + +And what I will do for probably +the next meeting is + +to derive a few of the space +groups for the lower + +symmetries which are not too +complicated, just to show you + +how the game plays out. + +And then I will mention a little +bit about the special + +idiosyncrasies of the +orthorhombic brick-shaped + +cells where there is nothing +more distinct about one + +direction and the other. + +All the inter-axial angles +are 90 degrees. + +The translations are general. + +So there are peculiarities in +notation there that are unique + +to the orthorhombic system. + +And then I want to spend, +perhaps, one class talking a + +little bit about crystal +chemistry. + +Have any of you had a class in +solid state chemistry or + +crystal chemistry? + +OK. + +One. + +One of the main uses of space +group theory is the + +description of crystal +structures. + +So I think I might, as a minor +digression, take an hour to + +talk about packing and some of +the concepts used to describe + +the close-packed structures and +ionic structures and give + +you a problem that ask you, as +I already did, to generate a + +structure, simple-minded +two-dimensional structure, and + +do some interpretation of it. + +So, I think this will be worth +saying a little bit about just + +so that one of the main +applications of symmetry + +theory does not escape without +any discussion at all. + +We will, after about two more +lectures, have a complete + +change of direction and start +talking about properties of + +crystals and how these +properties are impacted by the + +fact that crystals +have symmetry. + +So we're gonna use some of our +results in symmetry, but not + +all that much, but develop +remarkable mileage in + +predicting anisotropy in +crystals just on the basis of + +the symmetry which that crystal +possesses, that + +certain physical properties as +a function of direction are + +weird surfaces that have lumps +and noses and bulges in them. + +And certain properties have this +anisotropy universally, + +regardless of the chemistry or +composition of the crystal. + +Given the symmetry of the +crystal, the anisotropy has to + +be in this fashion. + +We'll be able to show that some +properties simply cannot + +exist, period, regardless of +composition and structure in + +materials that have certain +symmetries. + +So that'll be the direction +we take off in. + +I mentioned at the beginning of +the term-- you've probably + +forgotten-- + +there is a lovely book on +tensors and physical + +properties by a gentleman named +J. F. Nye, N-Y-E. And + +the title of the book +is Physical + +Properties of Crystals. + +This is a nice place to go +for further reading. + +We will go through roughly +half of Nye's book with a + +little more emphasis on the +consequences of symmetry than + +what he does. + +But if you want to do some extra +reading, I asked the + +Coop to stock this book. + +But I suggest that you not +rush out and buy it. + +It's available in paperback, +which means it's cheap, but + +only relatively so. + +There's no such thing as +a cheap technical book, + +paperbacked or not, +these days. + +It's also on reserve +in the library. + +So, see if you need +the extra help. + +See if you would like to +do some reading in Nye. + +And make sure you want to before +you go out and put your + +money down at the Coop. + +The last part of Nye +is an elegant, + +beautiful part of the book. + +It deals with the thermodynamic +relations + +between different properties. + +And it's a unique treatment +that is developed by Nye. + +We won't do any of that, but +it's a nice thing to have. + +So don't rush out and +spend your money. + +But if you want additional +reading and just going to the + +reserved book collection is not +enough, then Nye is not at + +all a bad copy of +a book to have. + +I think most of you have +probably seen Nye, not the + +book but the man. + +How many of you have seen the +famous Bragg bubble raft movie + +on disk locations, where he +floats sheets of bundles and + +sheers them and you see his +dislocation go zipping across? + +At one stage in that movie, +there's an assistant who + +tiptoes, trying to be +unobtrusive, across the + +background. + +But the camera catches him +scurrying behind Bragg. + +That's Nye. + +So if you've seen the +movie, you've seen + +what Nye looks like. + +OK. + +I'll call it quits +there for today. + +And we'll see you next +week on Tuesday. \ No newline at end of file diff --git a/Z8oMbOj9IWM.txt b/Z8oMbOj9IWM.txt new file mode 100644 index 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position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT open courseware + + align:start position:0% +of MIT courses visit MIT open courseware + + + align:start position:0% +of MIT courses visit MIT open courseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay welcome to uh + + align:start position:0% +ocw.mit.edu okay welcome to uh + + + align:start position:0% +ocw.mit.edu okay welcome to uh +underactuated robotics I'm glad you're + + align:start position:0% +underactuated robotics I'm glad you're + + + align:start position:0% +underactuated robotics I'm glad you're +all here can I get a quick show of hands + + align:start position:0% +all here can I get a quick show of hands + + + align:start position:0% +all here can I get a quick show of hands +actually who who considers themselves + + align:start position:0% +actually who who considers themselves + + + align:start position:0% +actually who who considers themselves +hardcore robotics + + align:start position:0% +hardcore robotics + + + align:start position:0% +hardcore robotics +types don't be shy it's a good thing to + + align:start position:0% +types don't be shy it's a good thing to + + + align:start position:0% +types don't be shy it's a good thing to +do who's who's sort of here to see what + + align:start position:0% +do who's who's sort of here to see what + + + align:start position:0% +do who's who's sort of here to see what +this is all + + align:start position:0% + + + + align:start position:0% + +about okay good good um so so I've + + align:start position:0% +about okay good good um so so I've + + + align:start position:0% +about okay good good um so so I've +taught the course twice before um this + + align:start position:0% +taught the course twice before um this + + + align:start position:0% +taught the course twice before um this +is the first time that it's a it's a tqe + + align:start position:0% +is the first time that it's a it's a tqe + + + align:start position:0% +is the first time that it's a it's a tqe +course for area 2 so I'm hoping to + + align:start position:0% +course for area 2 so I'm hoping to + + + align:start position:0% +course for area 2 so I'm hoping to +excite a slightly more General audience + + align:start position:0% +excite a slightly more General audience + + + align:start position:0% +excite a slightly more General audience +and uh your responsibility then is to to + + align:start position:0% +and uh your responsibility then is to to + + + align:start position:0% +and uh your responsibility then is to to +ask me questions if I say things that I + + align:start position:0% +ask me questions if I say things that I + + + align:start position:0% +ask me questions if I say things that I +if I assume prior now knowled that that + + align:start position:0% +if I assume prior now knowled that that + + + align:start position:0% +if I assume prior now knowled that that +people don't have and uh and make sure + + align:start position:0% +people don't have and uh and make sure + + + align:start position:0% +people don't have and uh and make sure +that that everything is coming + + align:start position:0% +that that everything is coming + + + align:start position:0% +that that everything is coming +across the only real PRX that I assume + + align:start position:0% +across the only real PRX that I assume + + + align:start position:0% +across the only real PRX that I assume +for the + + align:start position:0% + + + + align:start position:0% + +course are basically some comfort with + + align:start position:0% +course are basically some comfort with + + + align:start position:0% +course are basically some comfort with +uh differential equations and and + + align:start position:0% +uh differential equations and and + + + align:start position:0% +uh differential equations and and +ordinary differential equations + + align:start position:0% + + + + align:start position:0% + +Odes I assume some comfort with linear + + align:start position:0% +Odes I assume some comfort with linear + + + align:start position:0% +Odes I assume some comfort with linear +algebra + + align:start position:0% + + + + align:start position:0% + +and we use a lot of mat lab so it helps + + align:start position:0% +and we use a lot of mat lab so it helps + + + align:start position:0% +and we use a lot of mat lab so it helps +if you know Matt + + align:start position:0% + + + + align:start position:0% + +lab what I don't assume is that you're + + align:start position:0% +lab what I don't assume is that you're + + + align:start position:0% +lab what I don't assume is that you're +sort of you've I mean it's great if you + + align:start position:0% +sort of you've I mean it's great if you + + + align:start position:0% +sort of you've I mean it's great if you +have taken U previous robotics courses + + align:start position:0% +have taken U previous robotics courses + + + align:start position:0% +have taken U previous robotics courses +that's certainly a good thing but um I'm + + align:start position:0% +that's certainly a good thing but um I'm + + + align:start position:0% +that's certainly a good thing but um I'm +not going to assume everybody knows how + + align:start position:0% +not going to assume everybody knows how + + + align:start position:0% +not going to assume everybody knows how +to crank out the kinematics or dynamics + + align:start position:0% +to crank out the kinematics or dynamics + + + align:start position:0% +to crank out the kinematics or dynamics +of um rigid body manipulators and things + + align:start position:0% +of um rigid body manipulators and things + + + align:start position:0% +of um rigid body manipulators and things +like like that so hopefully if You' got + + align:start position:0% +like like that so hopefully if You' got + + + align:start position:0% +like like that so hopefully if You' got +a a background in here then everything + + align:start position:0% +a a background in here then everything + + + align:start position:0% +a a background in here then everything +else should follow and the the course is + + align:start position:0% +else should follow and the the course is + + + align:start position:0% +else should follow and the the course is +got a set of course notes that will be + + align:start position:0% +got a set of course notes that will be + + + align:start position:0% +got a set of course notes that will be +published um on the website just after + + align:start position:0% +published um on the website just after + + + align:start position:0% +published um on the website just after +the lectures and uh they should be + + align:start position:0% +the lectures and uh they should be + + + align:start position:0% +the lectures and uh they should be +pretty much uh contain what you need to + + align:start position:0% +pretty much uh contain what you need to + + + align:start position:0% +pretty much uh contain what you need to +know or at least have links to the + + align:start position:0% +know or at least have links to the + + + align:start position:0% +know or at least have links to the +things you need to + + align:start position:0% +things you need to + + + align:start position:0% +things you need to +know okay + + align:start position:0% + + + + align:start position:0% + +so today is uh the + + align:start position:0% + + + + align:start position:0% + +warmup I want to start with some + + align:start position:0% +warmup I want to start with some + + + align:start position:0% +warmup I want to start with some +motivation I want to make sure everybody + + align:start position:0% +motivation I want to make sure everybody + + + align:start position:0% +motivation I want to make sure everybody +leaves understanding the title of the + + align:start position:0% +leaves understanding the title of the + + + align:start position:0% +leaves understanding the title of the +course if nothing else so I want to tell + + align:start position:0% +course if nothing else so I want to tell + + + align:start position:0% +course if nothing else so I want to tell +you some some motivation why I think + + align:start position:0% +you some some motivation why I think + + + align:start position:0% +you some some motivation why I think +underactuated robotics is um such an + + align:start position:0% +underactuated robotics is um such an + + + align:start position:0% +underactuated robotics is um such an +important topic in + + align:start position:0% +important topic in + + + align:start position:0% +important topic in +robotics I'm going to give you some some + + align:start position:0% +robotics I'm going to give you some some + + + align:start position:0% +robotics I'm going to give you some some +basic + + align:start position:0% +basic + + + align:start position:0% +basic +definitions including the definition of + + align:start position:0% + + + + align:start position:0% + +underactuated I'm going to go through an + + align:start position:0% +underactuated I'm going to go through an + + + align:start position:0% +underactuated I'm going to go through an +example with um working out um the + + align:start position:0% +example with um working out um the + + + align:start position:0% +example with um working out um the +equations of motion for a simple system + + align:start position:0% +equations of motion for a simple system + + + align:start position:0% +equations of motion for a simple system +to sort of a review + + align:start position:0% +to sort of a review + + + align:start position:0% +to sort of a review +of of + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +Dynamics and then I'm going to tell you + + align:start position:0% +Dynamics and then I'm going to tell you + + + align:start position:0% +Dynamics and then I'm going to tell you +quickly um you know in the last minutes + + align:start position:0% +quickly um you know in the last minutes + + + align:start position:0% +quickly um you know in the last minutes +everything else you're going to learn in + + align:start position:0% +everything else you're going to learn in + + + align:start position:0% +everything else you're going to learn in +the course + + align:start position:0% + + + + align:start position:0% + +right and then we'll go through that + + align:start position:0% +right and then we'll go through that + + + align:start position:0% +right and then we'll go through that +more slowly in the next 25 + + align:start position:0% +more slowly in the next 25 + + + align:start position:0% +more slowly in the next 25 +lectures okay so let me actually start + + align:start position:0% +lectures okay so let me actually start + + + align:start position:0% +lectures okay so let me actually start +with some some motivation that involves + + align:start position:0% +with some some motivation that involves + + + align:start position:0% +with some some motivation that involves +plugging in this + + align:start position:0% + + + + align:start position:0% + +guy okay how many people have seen azimo + + align:start position:0% +guy okay how many people have seen azimo + + + align:start position:0% +guy okay how many people have seen azimo +before good see um okay so azimo let's + + align:start position:0% +before good see um okay so azimo let's + + + align:start position:0% +before good see um okay so azimo let's +let's watch the little promotional video + + align:start position:0% +let's watch the little promotional video + + + align:start position:0% +let's watch the little promotional video +for Honda's + + align:start position:0% +for Honda's + + + align:start position:0% +for Honda's +azimo azimo is um this is a few years + + align:start position:0% +azimo azimo is um this is a few years + + + align:start position:0% +azimo azimo is um this is a few years +old now but aimo absolutely is sort of + + align:start position:0% +old now but aimo absolutely is sort of + + + align:start position:0% +old now but aimo absolutely is sort of +the Pinnacle of Robotics engineering + + align:start position:0% +the Pinnacle of Robotics engineering + + + align:start position:0% +the Pinnacle of Robotics engineering +over the last uh 20 years I'd say even + + align:start position:0% +over the last uh 20 years I'd say even + + + align:start position:0% +over the last uh 20 years I'd say even +so so Honda turns out without telling + + align:start position:0% +so so Honda turns out without telling + + + align:start position:0% +so so Honda turns out without telling +anybody was working on walking robots + + align:start position:0% +anybody was working on walking robots + + + align:start position:0% +anybody was working on walking robots +for about from the early 80s till they + + align:start position:0% +for about from the early 80s till they + + + align:start position:0% +for about from the early 80s till they +announced to the world in 1997 that + + align:start position:0% +announced to the world in 1997 that + + + align:start position:0% +announced to the world in 1997 that +they'd start building these walking + + align:start position:0% +they'd start building these walking + + + align:start position:0% +they'd start building these walking +robots and they started putting on these + + align:start position:0% +robots and they started putting on these + + + align:start position:0% +robots and they started putting on these +shows where they kick soccer balls and + + align:start position:0% +shows where they kick soccer balls and + + + align:start position:0% +shows where they kick soccer balls and +walk upstairs it's absolutely absolutely + + align:start position:0% +walk upstairs it's absolutely absolutely + + + align:start position:0% +walk upstairs it's absolutely absolutely +amazing I mean this is this is it this + + align:start position:0% +amazing I mean this is this is it this + + + align:start position:0% +amazing I mean this is this is it this +is what we've been waiting for in + + align:start position:0% +is what we've been waiting for in + + + align:start position:0% +is what we've been waiting for in +robotics for a very long time this is a + + align:start position:0% +robotics for a very long time this is a + + + align:start position:0% +robotics for a very long time this is a +humanoid robot absolutely um doing + + align:start position:0% +humanoid robot absolutely um doing + + + align:start position:0% +humanoid robot absolutely um doing +fantastic things it's a Marvel of + + align:start position:0% +fantastic things it's a Marvel of + + + align:start position:0% +fantastic things it's a Marvel of +engineering the um the Precision the + + align:start position:0% +engineering the um the Precision the + + + align:start position:0% +engineering the um the Precision the +amount of computation going on in there + + align:start position:0% +amount of computation going on in there + + + align:start position:0% +amount of computation going on in there +it's just it's something we've been + + align:start position:0% +it's just it's something we've been + + + align:start position:0% +it's just it's something we've been +waiting a long time for okay but let's + + align:start position:0% +waiting a long time for okay but let's + + + align:start position:0% +waiting a long time for okay but let's +watch it again and be a little more + + align:start position:0% +watch it again and be a little more + + + align:start position:0% +watch it again and be a little more +critical this time so what's wrong with + + align:start position:0% +critical this time so what's wrong with + + + align:start position:0% +critical this time so what's wrong with +Asa when it's walking okay it looks a + + align:start position:0% +Asa when it's walking okay it looks a + + + align:start position:0% +Asa when it's walking okay it looks a +little stiff right it looks kind of like + + align:start position:0% +little stiff right it looks kind of like + + + align:start position:0% +little stiff right it looks kind of like +a guy in a space suit if you look + + align:start position:0% +a guy in a space suit if you look + + + align:start position:0% +a guy in a space suit if you look +carefully you'll notice that it's always + + align:start position:0% +carefully you'll notice that it's always + + + align:start position:0% +carefully you'll notice that it's always +got one foot flat on the ground + + align:start position:0% +got one foot flat on the ground + + + align:start position:0% +got one foot flat on the ground +that doesn't look quite right okay we + + align:start position:0% +that doesn't look quite right okay we + + + align:start position:0% +that doesn't look quite right okay we +we'll forgive the goalie uh he's not + + align:start position:0% +we'll forgive the goalie uh he's not + + + align:start position:0% +we'll forgive the goalie uh he's not +he's work in progress I guess but the + + align:start position:0% +he's work in progress I guess but the + + + align:start position:0% +he's work in progress I guess but the +whole thing just looks a little bit um + + align:start position:0% +whole thing just looks a little bit um + + + align:start position:0% +whole thing just looks a little bit um +like a machine that's let me say not + + align:start position:0% +like a machine that's let me say not + + + align:start position:0% +like a machine that's let me say not +comfortable with its own Dynamics it's + + align:start position:0% +comfortable with its own Dynamics it's + + + align:start position:0% +comfortable with its own Dynamics it's +taking a very conservative approach the + + align:start position:0% +taking a very conservative approach the + + + align:start position:0% +taking a very conservative approach the +fact that it can go upstairs is really + + align:start position:0% +fact that it can go upstairs is really + + + align:start position:0% +fact that it can go upstairs is really +remarkable it does have to know exactly + + align:start position:0% +remarkable it does have to know exactly + + + align:start position:0% +remarkable it does have to know exactly +where those stairs are and the geometry + + align:start position:0% +where those stairs are and the geometry + + + align:start position:0% +where those stairs are and the geometry +of the stairs but you see it's taking a + + align:start position:0% +of the stairs but you see it's taking a + + + align:start position:0% +of the stairs but you see it's taking a +very very conservative approach to + + align:start position:0% +very very conservative approach to + + + align:start position:0% +very very conservative approach to +walking it's always walking with its + + align:start position:0% +walking it's always walking with its + + + align:start position:0% +walking it's always walking with its +knees bent its feet flat on the ground + + align:start position:0% +knees bent its feet flat on the ground + + + align:start position:0% +knees bent its feet flat on the ground +and has this sort of rigid you know + + align:start position:0% +and has this sort of rigid you know + + + align:start position:0% +and has this sort of rigid you know +astronaut walk to it okay why is that + + align:start position:0% +astronaut walk to it okay why is that + + + align:start position:0% +astronaut walk to it okay why is that +bad um it's bad because it it requires a + + align:start position:0% +bad um it's bad because it it requires a + + + align:start position:0% +bad um it's bad because it it requires a +lot of energy first of all so just to + + align:start position:0% +lot of energy first of all so just to + + + align:start position:0% +lot of energy first of all so just to +imagine walking around with your knees + + align:start position:0% +imagine walking around with your knees + + + align:start position:0% +imagine walking around with your knees +bent right all the time it turns out + + align:start position:0% +bent right all the time it turns out + + + align:start position:0% +bent right all the time it turns out +asmo uses 20 times as much energy if you + + align:start position:0% +asmo uses 20 times as much energy if you + + + align:start position:0% +asmo uses 20 times as much energy if you +scale out mass and everything um as a + + align:start position:0% +scale out mass and everything um as a + + + align:start position:0% +scale out mass and everything um as a +human does when it walks 20 times and + + align:start position:0% +human does when it walks 20 times and + + + align:start position:0% +human does when it walks 20 times and +that makes a practical difference + + align:start position:0% +that makes a practical difference + + + align:start position:0% +that makes a practical difference +because the batteries it's got in its + + align:start position:0% +because the batteries it's got in its + + + align:start position:0% +because the batteries it's got in its +belly uh only last 26 minutes right and + + align:start position:0% +belly uh only last 26 minutes right and + + + align:start position:0% +belly uh only last 26 minutes right and +it's a lot of batteries okay um it + + align:start position:0% +it's a lot of batteries okay um it + + + align:start position:0% +it's a lot of batteries okay um it +matters because it's walking because of + + align:start position:0% +matters because it's walking because of + + + align:start position:0% +matters because it's walking because of +this very conservative approach to + + align:start position:0% +this very conservative approach to + + + align:start position:0% +this very conservative approach to +walking it's walking a lot slower than + + align:start position:0% +walking it's walking a lot slower than + + + align:start position:0% +walking it's walking a lot slower than +you and you or I would okay they + + align:start position:0% +you and you or I would okay they + + + align:start position:0% +you and you or I would okay they +actually have top running sort of speeds + + align:start position:0% +actually have top running sort of speeds + + + align:start position:0% +actually have top running sort of speeds +of of aimo there are six um kilometers + + align:start position:0% +of of aimo there are six um kilometers + + + align:start position:0% +of of aimo there are six um kilometers +an hour um but that's a little bit below + + align:start position:0% +an hour um but that's a little bit below + + + align:start position:0% +an hour um but that's a little bit below +where you or I would sort of comfortably + + align:start position:0% +where you or I would sort of comfortably + + + align:start position:0% +where you or I would sort of comfortably +transition from walking to running if we + + align:start position:0% +transition from walking to running if we + + + align:start position:0% +transition from walking to running if we +were just going down the street so it's + + align:start position:0% +were just going down the street so it's + + + align:start position:0% +were just going down the street so it's +considerably slower uh than a human when + + align:start position:0% +considerably slower uh than a human when + + + align:start position:0% +considerably slower uh than a human when +it runs and although there's some really + + align:start position:0% +it runs and although there's some really + + + align:start position:0% +it runs and although there's some really +amazing videos of sort of walking on + + align:start position:0% +amazing videos of sort of walking on + + + align:start position:0% +amazing videos of sort of walking on +stairs and things like that the videos + + align:start position:0% +stairs and things like that the videos + + + align:start position:0% +stairs and things like that the videos +you won't see are the ones of it sort of + + align:start position:0% +you won't see are the ones of it sort of + + + align:start position:0% +you won't see are the ones of it sort of +walking on terrain it doesn't know + + align:start position:0% +walking on terrain it doesn't know + + + align:start position:0% +walking on terrain it doesn't know +everything about or even uneven terrain + + align:start position:0% +everything about or even uneven terrain + + + align:start position:0% +everything about or even uneven terrain +it doesn't do uneven terrain + + align:start position:0% +it doesn't do uneven terrain + + + align:start position:0% +it doesn't do uneven terrain +particularly + + align:start position:0% +particularly + + + align:start position:0% +particularly +well okay so in some ways Asimo is the + + align:start position:0% +well okay so in some ways Asimo is the + + + align:start position:0% +well okay so in some ways Asimo is the +very natural progression of what robotic + + align:start position:0% +very natural progression of what robotic + + + align:start position:0% +very natural progression of what robotic +arm technology which started in factory + + align:start position:0% +arm technology which started in factory + + + align:start position:0% +arm technology which started in factory +room floors sort of matured into a + + align:start position:0% +room floors sort of matured into a + + + align:start position:0% +room floors sort of matured into a +walking robot okay it's a very high gain + + align:start position:0% +walking robot okay it's a very high gain + + + align:start position:0% +walking robot okay it's a very high gain +we'll talk a lot what that means it's a + + align:start position:0% +we'll talk a lot what that means it's a + + + align:start position:0% +we'll talk a lot what that means it's a +very high gain um system it's using a + + align:start position:0% +very high gain um system it's using a + + + align:start position:0% +very high gain um system it's using a +lot of energy and and feedback in order + + align:start position:0% +lot of energy and and feedback in order + + + align:start position:0% +lot of energy and and feedback in order +to try to rigidly follow some trajectory + + align:start position:0% +to try to rigidly follow some trajectory + + + align:start position:0% +to try to rigidly follow some trajectory +that it's thought a lot about okay and + + align:start position:0% +that it's thought a lot about okay and + + + align:start position:0% +that it's thought a lot about okay and +it's doing that in a very conservative + + align:start position:0% +it's doing that in a very conservative + + + align:start position:0% +it's doing that in a very conservative +regime feet flat on the ground knees + + align:start position:0% +regime feet flat on the ground knees + + + align:start position:0% +regime feet flat on the ground knees +bent + + align:start position:0% +bent + + + align:start position:0% +bent +okay so there's a different approach to + + align:start position:0% +okay so there's a different approach to + + + align:start position:0% +okay so there's a different approach to +walking out + + align:start position:0% +walking out + + + align:start position:0% +walking out +there um this one was built by Cornell + + align:start position:0% +there um this one was built by Cornell + + + align:start position:0% +there um this one was built by Cornell +it's called a passive Dynamic Walker + + align:start position:0% +it's called a passive Dynamic Walker + + + align:start position:0% +it's called a passive Dynamic Walker +okay it's almost not a robot whatsoever + + align:start position:0% +okay it's almost not a robot whatsoever + + + align:start position:0% +okay it's almost not a robot whatsoever +it's a it's a of sticks and hinges with + + align:start position:0% +it's a it's a of sticks and hinges with + + + align:start position:0% +it's a it's a of sticks and hinges with +ball bearings at the joints but if you + + align:start position:0% +ball bearings at the joints but if you + + + align:start position:0% +ball bearings at the joints but if you +put this thing on a small ramp going + + align:start position:0% +put this thing on a small ramp going + + + align:start position:0% +put this thing on a small ramp going +down and give it a little + + align:start position:0% +down and give it a little + + + align:start position:0% +down and give it a little +push look what it can + + align:start position:0% +push look what it can + + + align:start position:0% +push look what it can +do right that's just falling down a ramp + + align:start position:0% +do right that's just falling down a ramp + + + align:start position:0% +do right that's just falling down a ramp +completely passive machine powered only + + align:start position:0% +completely passive machine powered only + + + align:start position:0% +completely passive machine powered only +by gravity okay so these passive Walkers + + align:start position:0% +by gravity okay so these passive Walkers + + + align:start position:0% +by gravity okay so these passive Walkers +are sort of a fantastic demo I mean I + + align:start position:0% +are sort of a fantastic demo I mean I + + + align:start position:0% +are sort of a fantastic demo I mean I +just it's unbelievable that they could + + align:start position:0% +just it's unbelievable that they could + + + align:start position:0% +just it's unbelievable that they could +they can build these things that that + + align:start position:0% +they can build these things that that + + + align:start position:0% +they can build these things that that +walk it's a glorified Slinky but it's + + align:start position:0% +walk it's a glorified Slinky but it's + + + align:start position:0% +walk it's a glorified Slinky but it's +it's walking like you and me right + + align:start position:0% +it's walking like you and me right + + + align:start position:0% +it's walking like you and me right +probably more so most people would say + + align:start position:0% +probably more so most people would say + + + align:start position:0% +probably more so most people would say +that looks a little bit more like The + + align:start position:0% +that looks a little bit more like The + + + align:start position:0% +that looks a little bit more like The +Way We Walk than azimo does but what's + + align:start position:0% +Way We Walk than azimo does but what's + + + align:start position:0% +Way We Walk than azimo does but what's +really amazing about it is it says that + + align:start position:0% +really amazing about it is it says that + + + align:start position:0% +really amazing about it is it says that +this really conservative High Gain feet + + align:start position:0% +this really conservative High Gain feet + + + align:start position:0% +this really conservative High Gain feet +on the flat flat on the ground uh + + align:start position:0% +on the flat flat on the ground uh + + + align:start position:0% +on the flat flat on the ground uh +approach to walking it's certainly not a + + align:start position:0% +approach to walking it's certainly not a + + + align:start position:0% +approach to walking it's certainly not a +necessary one okay and it suggests that + + align:start position:0% +necessary one okay and it suggests that + + + align:start position:0% +necessary one okay and it suggests that +if you really want to do some energy + + align:start position:0% +if you really want to do some energy + + + align:start position:0% +if you really want to do some energy +efficient walking maybe even more robust + + align:start position:0% +efficient walking maybe even more robust + + + align:start position:0% +efficient walking maybe even more robust +walking then um then what you need to do + + align:start position:0% +walking then um then what you need to do + + + align:start position:0% +walking then um then what you need to do +is not cancel out your Dynamics with + + align:start position:0% +is not cancel out your Dynamics with + + + align:start position:0% +is not cancel out your Dynamics with +with High Gain feedback and follow some + + align:start position:0% +with High Gain feedback and follow some + + + align:start position:0% +with High Gain feedback and follow some +trajectory you need to think a lot about + + align:start position:0% +trajectory you need to think a lot about + + + align:start position:0% +trajectory you need to think a lot about +the Dynamics of your robot okay so this + + align:start position:0% +the Dynamics of your robot okay so this + + + align:start position:0% +the Dynamics of your robot okay so this +is just the Dynamics of the robot doing + + align:start position:0% +is just the Dynamics of the robot doing + + + align:start position:0% +is just the Dynamics of the robot doing +all the work no control system no + + align:start position:0% +all the work no control system no + + + align:start position:0% +all the work no control system no +computers + + align:start position:0% +computers + + + align:start position:0% +computers +nothing okay so that's a story in + + align:start position:0% +nothing okay so that's a story in + + + align:start position:0% +nothing okay so that's a story in +Walking about why maybe Dynamics matter + + align:start position:0% +Walking about why maybe Dynamics matter + + + align:start position:0% +Walking about why maybe Dynamics matter +a lot and and we should really start by + + align:start position:0% +a lot and and we should really start by + + + align:start position:0% +a lot and and we should really start by +understanding the Dynamics before we do + + align:start position:0% +understanding the Dynamics before we do + + + align:start position:0% +understanding the Dynamics before we do +a whole bunch of sort of robotic arm + + align:start position:0% +a whole bunch of sort of robotic arm + + + align:start position:0% +a whole bunch of sort of robotic arm +control it's actually true in a lot of + + align:start position:0% +control it's actually true in a lot of + + + align:start position:0% +control it's actually true in a lot of +different fields my other favorite story + + align:start position:0% +different fields my other favorite story + + + align:start position:0% +different fields my other favorite story +these days is is um flying things okay + + align:start position:0% +these days is is um flying things okay + + + align:start position:0% +these days is is um flying things okay +so if you look at um if you look at + + align:start position:0% +so if you look at um if you look at + + + align:start position:0% +so if you look at um if you look at +state-of-the-art military aircraft um + + align:start position:0% +state-of-the-art military aircraft um + + + align:start position:0% +state-of-the-art military aircraft um +this is a an F14 landing on an aircraft + + align:start position:0% +this is a an F14 landing on an aircraft + + + align:start position:0% +this is a an F14 landing on an aircraft +carrier okay um even in the the sort of + + align:start position:0% +carrier okay um even in the the sort of + + + align:start position:0% +carrier okay um even in the the sort of +the most highly engineered Control + + align:start position:0% +the most highly engineered Control + + + align:start position:0% +the most highly engineered Control +Systems we have it tends to be that that + + align:start position:0% +Systems we have it tends to be that that + + + align:start position:0% +Systems we have it tends to be that that +aircraft stay in a very very + + align:start position:0% +aircraft stay in a very very + + + align:start position:0% +aircraft stay in a very very +conservative flight onel envelope the + + align:start position:0% +conservative flight onel envelope the + + + align:start position:0% +conservative flight onel envelope the +same way that azimo stays with its feet + + align:start position:0% +same way that azimo stays with its feet + + + align:start position:0% +same way that azimo stays with its feet +flat on the ground and does this this + + align:start position:0% +flat on the ground and does this this + + + align:start position:0% +flat on the ground and does this this +really stiff control uh the airplane + + align:start position:0% +really stiff control uh the airplane + + + align:start position:0% +really stiff control uh the airplane +stays at a very low angle relative to + + align:start position:0% +stays at a very low angle relative to + + + align:start position:0% +stays at a very low angle relative to +the oncoming flow and uses High Gain + + align:start position:0% +the oncoming flow and uses High Gain + + + align:start position:0% +the oncoming flow and uses High Gain +Control in order to stabilize it so + + align:start position:0% +Control in order to stabilize it so + + + align:start position:0% +Control in order to stabilize it so +fighter jets you might you might know + + align:start position:0% +fighter jets you might you might know + + + align:start position:0% +fighter jets you might you might know +the P fighter jets are tend to be um + + align:start position:0% +the P fighter jets are tend to be um + + + align:start position:0% +the P fighter jets are tend to be um +passively unstable and control systems + + align:start position:0% +passively unstable and control systems + + + align:start position:0% +passively unstable and control systems +are doing amazing things to make these + + align:start position:0% +are doing amazing things to make these + + + align:start position:0% +are doing amazing things to make these +guys work but they're not doing some + + align:start position:0% +guys work but they're not doing some + + + align:start position:0% +guys work but they're not doing some +basic things that that you could see + + align:start position:0% +basic things that that you could see + + + align:start position:0% +basic things that that you could see +every time you look out your window + + align:start position:0% +every time you look out your window + + + align:start position:0% +every time you look out your window +right so here's a a cardinal uh doing + + align:start position:0% +right so here's a a cardinal uh doing + + + align:start position:0% +right so here's a a cardinal uh doing +sort of the same thing you know landing + + align:start position:0% +sort of the same thing you know landing + + + align:start position:0% +sort of the same thing you know landing +on an aircraft carrier landing on a + + align:start position:0% +on an aircraft carrier landing on a + + + align:start position:0% +on an aircraft carrier landing on a +branch about the same thing okay but + + align:start position:0% +branch about the same thing okay but + + + align:start position:0% +branch about the same thing okay but +unlike the the airplane the Cardinal's + + align:start position:0% +unlike the the airplane the Cardinal's + + + align:start position:0% +unlike the the airplane the Cardinal's +got his wings spread out way out to here + + align:start position:0% +got his wings spread out way out to here + + + align:start position:0% +got his wings spread out way out to here +right um and what that means if you if + + align:start position:0% +right um and what that means if you if + + + align:start position:0% +right um and what that means if you if +you know anything about aerodynamics + + align:start position:0% +you know anything about aerodynamics + + + align:start position:0% +you know anything about aerodynamics +okay if you take your if you take a wing + + align:start position:0% +okay if you take your if you take a wing + + + align:start position:0% +okay if you take your if you take a wing +and the air flow is moving this way and + + align:start position:0% +and the air flow is moving this way and + + + align:start position:0% +and the air flow is moving this way and +you have it at a low angle relative to + + align:start position:0% +you have it at a low angle relative to + + + align:start position:0% +you have it at a low angle relative to +the oncoming flow then you have a very + + align:start position:0% +the oncoming flow then you have a very + + + align:start position:0% +the oncoming flow then you have a very +simple um attached flow on the back of + + align:start position:0% +simple um attached flow on the back of + + + align:start position:0% +simple um attached flow on the back of +the Wings okay and it turns out that + + align:start position:0% +the Wings okay and it turns out that + + + align:start position:0% +the Wings okay and it turns out that +sort of linear control and linear models + + align:start position:0% +sort of linear control and linear models + + + align:start position:0% +sort of linear control and linear models +of the Dynamics work pretty well in that + + align:start position:0% +of the Dynamics work pretty well in that + + + align:start position:0% +of the Dynamics work pretty well in that +regime if you go up to a small angle of + + align:start position:0% +regime if you go up to a small angle of + + + align:start position:0% +regime if you go up to a small angle of +attack kind of like this this the + + align:start position:0% +attack kind of like this this the + + + align:start position:0% +attack kind of like this this the +fighter Jet's doing then the air can + + align:start position:0% +fighter Jet's doing then the air can + + + align:start position:0% +fighter Jet's doing then the air can +sort of bend around the wing everything + + align:start position:0% +sort of bend around the wing everything + + + align:start position:0% +sort of bend around the wing everything +still stays attached they say to the + + align:start position:0% +still stays attached they say to the + + + align:start position:0% +still stays attached they say to the +wing and uh and you can still do sort of + + align:start position:0% +wing and uh and you can still do sort of + + + align:start position:0% +wing and uh and you can still do sort of +linear control ideas okay but if you go + + align:start position:0% +linear control ideas okay but if you go + + + align:start position:0% +linear control ideas okay but if you go +up and stall your wings out that's + + align:start position:0% +up and stall your wings out that's + + + align:start position:0% +up and stall your wings out that's +what's Happening Here you if you go up + + align:start position:0% +what's Happening Here you if you go up + + + align:start position:0% +what's Happening Here you if you go up +to a higher angle of attack right the + + align:start position:0% +to a higher angle of attack right the + + + align:start position:0% +to a higher angle of attack right the +air sort of can no longer uh bend around + + align:start position:0% +air sort of can no longer uh bend around + + + align:start position:0% +air sort of can no longer uh bend around +the wing fast enough something more + + align:start position:0% +the wing fast enough something more + + + align:start position:0% +the wing fast enough something more +dramatic happens you get a big vortex in + + align:start position:0% +dramatic happens you get a big vortex in + + + align:start position:0% +dramatic happens you get a big vortex in +this picture and what happens is the + + align:start position:0% +this picture and what happens is the + + + align:start position:0% +this picture and what happens is the +flow gets much more unsteady it starts + + align:start position:0% +flow gets much more unsteady it starts + + + align:start position:0% +flow gets much more unsteady it starts +shedding vortices and you you start + + align:start position:0% +shedding vortices and you you start + + + align:start position:0% +shedding vortices and you you start +stalling your wing okay now in these + + align:start position:0% +stalling your wing okay now in these + + + align:start position:0% +stalling your wing okay now in these +regimes so far the Dynamics have proven + + align:start position:0% +regimes so far the Dynamics have proven + + + align:start position:0% +regimes so far the Dynamics have proven +very very complicated to even understand + + align:start position:0% +very very complicated to even understand + + + align:start position:0% +very very complicated to even understand +to even model okay and harder + + align:start position:0% +to even model okay and harder + + + align:start position:0% +to even model okay and harder +considerably harder to + + align:start position:0% +considerably harder to + + + align:start position:0% +considerably harder to +control the bird's doing it every day of + + align:start position:0% +control the bird's doing it every day of + + + align:start position:0% +control the bird's doing it every day of +the week somehow we don't know exactly + + align:start position:0% +the week somehow we don't know exactly + + + align:start position:0% +the week somehow we don't know exactly +how but he does it all the time right + + align:start position:0% +how but he does it all the time right + + + align:start position:0% +how but he does it all the time right +and he does it with Gusty environments + + align:start position:0% +and he does it with Gusty environments + + + align:start position:0% +and he does it with Gusty environments +he does it when the branch is moving + + align:start position:0% +he does it when the branch is moving + + + align:start position:0% +he does it when the branch is moving +right he probably misses every once in a + + align:start position:0% +right he probably misses every once in a + + + align:start position:0% +right he probably misses every once in a +while but he's doing a pretty darn good + + align:start position:0% +while but he's doing a pretty darn good + + + align:start position:0% +while but he's doing a pretty darn good +job okay um there's a reason why he does + + align:start position:0% +job okay um there's a reason why he does + + + align:start position:0% +job okay um there's a reason why he does +it too right it's not just to show off + + align:start position:0% +it too right it's not just to show off + + + align:start position:0% +it too right it's not just to show off +or something but uh if you are willing + + align:start position:0% +or something but uh if you are willing + + + align:start position:0% +or something but uh if you are willing +to go into this more complicated flight + + align:start position:0% +to go into this more complicated flight + + + align:start position:0% +to go into this more complicated flight +regime by stalling your wings and and if + + align:start position:0% +regime by stalling your wings and and if + + + align:start position:0% +regime by stalling your wings and and if +your goal is stopping then actually you + + align:start position:0% +your goal is stopping then actually you + + + align:start position:0% +your goal is stopping then actually you +get a huge benefit by going up to that + + align:start position:0% +get a huge benefit by going up to that + + + align:start position:0% +get a huge benefit by going up to that +high angle of attack not only do you get + + align:start position:0% +high angle of attack not only do you get + + + align:start position:0% +high angle of attack not only do you get +more drag just because you have more + + align:start position:0% +more drag just because you have more + + + align:start position:0% +more drag just because you have more +surface area exposed to the flow but + + align:start position:0% +surface area exposed to the flow but + + + align:start position:0% +surface area exposed to the flow but +when you start getting Separation on the + + align:start position:0% +when you start getting Separation on the + + + align:start position:0% +when you start getting Separation on the +back of your wing you leave a pocket of + + align:start position:0% +back of your wing you leave a pocket of + + + align:start position:0% +back of your wing you leave a pocket of +low pressure behind the the the the wing + + align:start position:0% +low pressure behind the the the the wing + + + align:start position:0% +low pressure behind the the the the wing +the air can't quite come in and fill in + + align:start position:0% +the air can't quite come in and fill in + + + align:start position:0% +the air can't quite come in and fill in +the the the space right behind the wing + + align:start position:0% +the the the space right behind the wing + + + align:start position:0% +the the the space right behind the wing +and that acts like an air Brak it's + + align:start position:0% +and that acts like an air Brak it's + + + align:start position:0% +and that acts like an air Brak it's +called pressure drag okay so the birds + + align:start position:0% +called pressure drag okay so the birds + + + align:start position:0% +called pressure drag okay so the birds +the planes are coming into this + + align:start position:0% +the planes are coming into this + + + align:start position:0% +the planes are coming into this +conservative approach in order to + + align:start position:0% +conservative approach in order to + + + align:start position:0% +conservative approach in order to +maintain Control Authority + + align:start position:0% +maintain Control Authority + + + align:start position:0% +maintain Control Authority +the birds are going hitting the brakes + + align:start position:0% +the birds are going hitting the brakes + + + align:start position:0% +the birds are going hitting the brakes +hitting the air brakes and coming to + + align:start position:0% +hitting the air brakes and coming to + + + align:start position:0% +hitting the air brakes and coming to +still somehow doing enough control to + + align:start position:0% +still somehow doing enough control to + + + align:start position:0% +still somehow doing enough control to +hit that perch which is kinematically + + align:start position:0% +hit that perch which is kinematically + + + align:start position:0% +hit that perch which is kinematically +more difficult than I think than even a + + align:start position:0% +more difficult than I think than even a + + + align:start position:0% +more difficult than I think than even a +hitting an aircraft + + align:start position:0% +hitting an aircraft + + + align:start position:0% +hitting an aircraft +carrier all right so so we've been in my + + align:start position:0% +carrier all right so so we've been in my + + + align:start position:0% +carrier all right so so we've been in my +group we've been working on trying to + + align:start position:0% +group we've been working on trying to + + + align:start position:0% +group we've been working on trying to +make um planes do that kind of thing so + + align:start position:0% +make um planes do that kind of thing so + + + align:start position:0% +make um planes do that kind of thing so +this is our airplane that comes in and + + align:start position:0% +this is our airplane that comes in and + + + align:start position:0% +this is our airplane that comes in and +tries to execute a very high angle of + + align:start position:0% +tries to execute a very high angle of + + + align:start position:0% +tries to execute a very high angle of +attack maneuver in order to land on a + + align:start position:0% +attack maneuver in order to land on a + + + align:start position:0% +attack maneuver in order to land on a +perch it's a slow motion shot up + + align:start position:0% +perch it's a slow motion shot up + + + align:start position:0% +perch it's a slow motion shot up +slowed down so you can see what + + align:start position:0% + + + + align:start position:0% + +happens okay and actually just to + + align:start position:0% +happens okay and actually just to + + + align:start position:0% +happens okay and actually just to +convince you that the flow is + + align:start position:0% +convince you that the flow is + + + align:start position:0% +convince you that the flow is +complicated this isn't our best flow + + align:start position:0% +complicated this isn't our best flow + + + align:start position:0% +complicated this isn't our best flow +visualization but it shows you what's + + align:start position:0% +visualization but it shows you what's + + + align:start position:0% +visualization but it shows you what's +what's going on here the the air flow as + + align:start position:0% +what's going on here the the air flow as + + + align:start position:0% +what's going on here the the air flow as +it comes in this is now that same plane + + align:start position:0% +it comes in this is now that same plane + + + align:start position:0% +it comes in this is now that same plane +with with we're meting smoke from the + + align:start position:0% +with with we're meting smoke from the + + + align:start position:0% +with with we're meting smoke from the +the the front of the wing the Leading + + align:start position:0% +the the front of the wing the Leading + + + align:start position:0% +the the front of the wing the Leading +Edge of the wing and it comes in at a + + align:start position:0% +Edge of the wing and it comes in at a + + + align:start position:0% +Edge of the wing and it comes in at a +low angle of attack and you can see the + + align:start position:0% +low angle of attack and you can see the + + + align:start position:0% +low angle of attack and you can see the +air is mostly it's actually it's + + align:start position:0% +air is mostly it's actually it's + + + align:start position:0% +air is mostly it's actually it's +actually already stalled because it's a + + align:start position:0% +actually already stalled because it's a + + + align:start position:0% +actually already stalled because it's a +flat plate but the air is sort of on top + + align:start position:0% +flat plate but the air is sort of on top + + + align:start position:0% +flat plate but the air is sort of on top +of the wing in the same way I showed you + + align:start position:0% +of the wing in the same way I showed you + + + align:start position:0% +of the wing in the same way I showed you +in that that picture um and as you go up + + align:start position:0% +in that that picture um and as you go up + + + align:start position:0% +in that that picture um and as you go up +to a high angle of attack uh you get + + align:start position:0% +to a high angle of attack uh you get + + + align:start position:0% +to a high angle of attack uh you get +this big tip Vortex that rolls over + + align:start position:0% +this big tip Vortex that rolls over + + + align:start position:0% +this big tip Vortex that rolls over +everything gets a lot more + + align:start position:0% + + + + align:start position:0% + +complicated okay so the point I'm trying + + align:start position:0% +complicated okay so the point I'm trying + + + align:start position:0% +complicated okay so the point I'm trying +to make with these two examples are + + align:start position:0% +to make with these two examples are + + + align:start position:0% +to make with these two examples are +first of + + align:start position:0% +first of + + + align:start position:0% +first of +all robots today are just really really + + align:start position:0% +all robots today are just really really + + + align:start position:0% +all robots today are just really really +conservative dynamically they're very + + align:start position:0% +conservative dynamically they're very + + + align:start position:0% +conservative dynamically they're very +very conservative they're operating just + + align:start position:0% +very conservative they're operating just + + + align:start position:0% +very conservative they're operating just +a fraction of the the level of + + align:start position:0% +a fraction of the the level of + + + align:start position:0% +a fraction of the the level of +performance that they should already + + align:start position:0% +performance that they should already + + + align:start position:0% +performance that they should already +expect given the same U mechanical + + align:start position:0% +expect given the same U mechanical + + + align:start position:0% +expect given the same U mechanical +design right with the same mechanical + + align:start position:0% +design right with the same mechanical + + + align:start position:0% +design right with the same mechanical +design as simple little plane but better + + align:start position:0% +design as simple little plane but better + + + align:start position:0% +design as simple little plane but better +control we can start doing things that + + align:start position:0% +control we can start doing things that + + + align:start position:0% +control we can start doing things that +look more like birds right and the + + align:start position:0% +look more like birds right and the + + + align:start position:0% +look more like birds right and the +second point that I'm going to make uh + + align:start position:0% +second point that I'm going to make uh + + + align:start position:0% +second point that I'm going to make uh +more formally in a minute is that the + + align:start position:0% +more formally in a minute is that the + + + align:start position:0% +more formally in a minute is that the +underactuated systems underactuated + + align:start position:0% +underactuated systems underactuated + + + align:start position:0% +underactuated systems underactuated +robotics is essentially the the art the + + align:start position:0% +robotics is essentially the the art the + + + align:start position:0% +robotics is essentially the the art the +science of trying to build machines + + align:start position:0% +science of trying to build machines + + + align:start position:0% +science of trying to build machines +which use their Dynamics more cleverly + + align:start position:0% +which use their Dynamics more cleverly + + + align:start position:0% +which use their Dynamics more cleverly +instead of trying to to build Control + + align:start position:0% +instead of trying to to build Control + + + align:start position:0% +instead of trying to to build Control +Systems which which use actuation motor + + align:start position:0% +Systems which which use actuation motor + + + align:start position:0% +Systems which which use actuation motor +output in order to override the Dynamics + + align:start position:0% +output in order to override the Dynamics + + + align:start position:0% +output in order to override the Dynamics +we're going to we're going to to do an + + align:start position:0% +we're going to we're going to to do an + + + align:start position:0% +we're going to we're going to to do an +underactuated system that just pushes + + align:start position:0% +underactuated system that just pushes + + + align:start position:0% +underactuated system that just pushes +and pulls the natural Dynamics tries to + + align:start position:0% +and pulls the natural Dynamics tries to + + + align:start position:0% +and pulls the natural Dynamics tries to +do these more exciting Dynamic + + align:start position:0% +do these more exciting Dynamic + + + align:start position:0% +do these more exciting Dynamic +things as a consequence we need to do + + align:start position:0% +things as a consequence we need to do + + + align:start position:0% +things as a consequence we need to do +smarter control okay this is a computer + + align:start position:0% +smarter control okay this is a computer + + + align:start position:0% +smarter control okay this is a computer +science course so so what have I said + + align:start position:0% +science course so so what have I said + + + align:start position:0% +science course so so what have I said +anything to do with computer science yet + + align:start position:0% +anything to do with computer science yet + + + align:start position:0% +anything to do with computer science yet +I believe that there's new techniques + + align:start position:0% +I believe that there's new techniques + + + align:start position:0% +I believe that there's new techniques +from computer science machine learning + + align:start position:0% +from computer science machine learning + + + align:start position:0% +from computer science machine learning +motion planning that are basically + + align:start position:0% +motion planning that are basically + + + align:start position:0% +motion planning that are basically +changing the game it's allowing us to + + align:start position:0% +changing the game it's allowing us to + + + align:start position:0% +changing the game it's allowing us to +solve some of these control problems + + align:start position:0% +solve some of these control problems + + + align:start position:0% +solve some of these control problems +that haven't been solved + + align:start position:0% +that haven't been solved + + + align:start position:0% +that haven't been solved +before okay um um just to just + + align:start position:0% +before okay um um just to just + + + align:start position:0% +before okay um um just to just +to throw a few more cool examples out so + + align:start position:0% +to throw a few more cool examples out so + + + align:start position:0% +to throw a few more cool examples out so +so if we're willing to do more clever + + align:start position:0% +so if we're willing to do more clever + + + align:start position:0% +so if we're willing to do more clever +things with our Dynamics then there's + + align:start position:0% +things with our Dynamics then there's + + + align:start position:0% +things with our Dynamics then there's +just countless things that we can do so + + align:start position:0% +just countless things that we can do so + + + align:start position:0% +just countless things that we can do so +um if you just think of if you just care + + align:start position:0% +um if you just think of if you just care + + + align:start position:0% +um if you just think of if you just care +about efficiency this is an albatross + + align:start position:0% +about efficiency this is an albatross + + + align:start position:0% +about efficiency this is an albatross +this is a Wandering Albatross okay um if + + align:start position:0% +this is a Wandering Albatross okay um if + + + align:start position:0% +this is a Wandering Albatross okay um if +you just measure the the energy in some + + align:start position:0% +you just measure the the energy in some + + + align:start position:0% +you just measure the the energy in some +some metabolic estimate of the energy it + + align:start position:0% +some metabolic estimate of the energy it + + + align:start position:0% +some metabolic estimate of the energy it +it consumes uh versus the distance it + + align:start position:0% +it consumes uh versus the distance it + + + align:start position:0% +it consumes uh versus the distance it +travels then it's about the same as a + + align:start position:0% +travels then it's about the same as a + + + align:start position:0% +travels then it's about the same as a +747 which is actually kind of cool + + align:start position:0% +747 which is actually kind of cool + + + align:start position:0% +747 which is actually kind of cool +because it's they're quite different + + align:start position:0% +because it's they're quite different + + + align:start position:0% +because it's they're quite different +sizes but if you do some dimensionless + + align:start position:0% +sizes but if you do some dimensionless + + + align:start position:0% +sizes but if you do some dimensionless +cost of transport it actually works out + + align:start position:0% +cost of transport it actually works out + + + align:start position:0% +cost of transport it actually works out +to be almost the same efficiency as a + + align:start position:0% +to be almost the same efficiency as a + + + align:start position:0% +to be almost the same efficiency as a +747 so maybe we haven't gained anything + + align:start position:0% +747 so maybe we haven't gained anything + + + align:start position:0% +747 so maybe we haven't gained anything +but it turns out if you if you look more + + align:start position:0% +but it turns out if you if you look more + + + align:start position:0% +but it turns out if you if you look more +carefully the albatross uses the same + + align:start position:0% +carefully the albatross uses the same + + + align:start position:0% +carefully the albatross uses the same +amount of energy when it's sitting on + + align:start position:0% +amount of energy when it's sitting on + + + align:start position:0% +amount of energy when it's sitting on +the beach as it does when it's uh flying + + align:start position:0% +the beach as it does when it's uh flying + + + align:start position:0% +the beach as it does when it's uh flying +across the ocean so this guy can fly for + + align:start position:0% +across the ocean so this guy can fly for + + + align:start position:0% +across the ocean so this guy can fly for +hours days without ever flapping its + + align:start position:0% +hours days without ever flapping its + + + align:start position:0% +hours days without ever flapping its +wings okay they take the go across the + + align:start position:0% +wings okay they take the go across the + + + align:start position:0% +wings okay they take the go across the +entire ocean that way right into the + + align:start position:0% +entire ocean that way right into the + + + align:start position:0% +entire ocean that way right into the +wind out of the Wind name it because + + align:start position:0% +wind out of the Wind name it because + + + align:start position:0% +wind out of the Wind name it because +they're sitting there and they're just + + align:start position:0% +they're sitting there and they're just + + + align:start position:0% +they're sitting there and they're just +riding on um gradients over the due to + + align:start position:0% +riding on um gradients over the due to + + + align:start position:0% +riding on um gradients over the due to +the wind over the ocean okay so so the + + align:start position:0% +the wind over the ocean okay so so the + + + align:start position:0% +the wind over the ocean okay so so the +energetic cost of this guy's + + align:start position:0% +energetic cost of this guy's + + + align:start position:0% +energetic cost of this guy's +experiencing is just digestion and + + align:start position:0% +experiencing is just digestion and + + + align:start position:0% +experiencing is just digestion and +things like that it's he's actually not + + align:start position:0% +things like that it's he's actually not + + + align:start position:0% +things like that it's he's actually not +doing hardly any mechanical work in + + align:start position:0% +doing hardly any mechanical work in + + + align:start position:0% +doing hardly any mechanical work in +order to fly across the + + align:start position:0% +order to fly across the + + + align:start position:0% +order to fly across the +ocean okay if you care about + + align:start position:0% +ocean okay if you care about + + + align:start position:0% +ocean okay if you care about +maneuverability you know so Falcons have + + align:start position:0% +maneuverability you know so Falcons have + + + align:start position:0% +maneuverability you know so Falcons have +been recently clocked at diving at 240 + + align:start position:0% +been recently clocked at diving at 240 + + + align:start position:0% +been recently clocked at diving at 240 +miles an hour this one is pulling out of + + align:start position:0% +miles an hour this one is pulling out of + + + align:start position:0% +miles an hour this one is pulling out of +that 240 M hour dive to catch a sparrow + + align:start position:0% +that 240 M hour dive to catch a sparrow + + + align:start position:0% +that 240 M hour dive to catch a sparrow +right + + align:start position:0% +right + + + align:start position:0% +right +that's pretty good I mean planes in + + align:start position:0% +that's pretty good I mean planes in + + + align:start position:0% +that's pretty good I mean planes in +terms of she sheer speed planes are + + align:start position:0% +terms of she sheer speed planes are + + + align:start position:0% +terms of she sheer speed planes are +going to win every day of the week but + + align:start position:0% +going to win every day of the week but + + + align:start position:0% +going to win every day of the week but +if you look at some sort of + + align:start position:0% +if you look at some sort of + + + align:start position:0% +if you look at some sort of +dimensionless um aspect of + + align:start position:0% +dimensionless um aspect of + + + align:start position:0% +dimensionless um aspect of +maneuverability then then birds are + + align:start position:0% +maneuverability then then birds are + + + align:start position:0% +maneuverability then then birds are +still the masters of the sky okay bats + + align:start position:0% +still the masters of the sky okay bats + + + align:start position:0% +still the masters of the sky okay bats +can actually been be flying full speed + + align:start position:0% +can actually been be flying full speed + + + align:start position:0% +can actually been be flying full speed +this way in two flaps which turns out to + + align:start position:0% +this way in two flaps which turns out to + + + align:start position:0% +this way in two flaps which turns out to +be just over just under half of the + + align:start position:0% +be just over just under half of the + + + align:start position:0% +be just over just under half of the +wingspan they can be flying full speed + + align:start position:0% +wingspan they can be flying full speed + + + align:start position:0% +wingspan they can be flying full speed +the other way right two to five flaps + + align:start position:0% +the other way right two to five flaps + + + align:start position:0% +the other way right two to five flaps +these guys at Browner have been + + align:start position:0% +these guys at Browner have been + + + align:start position:0% +these guys at Browner have been +recording this + + align:start position:0% +recording this + + + align:start position:0% +recording this +okay they can obviously bats bats are + + align:start position:0% +okay they can obviously bats bats are + + + align:start position:0% +okay they can obviously bats bats are +actually some of the most maneuverable + + align:start position:0% +actually some of the most maneuverable + + + align:start position:0% +actually some of the most maneuverable +they can fly at high speeds through + + align:start position:0% +they can fly at high speeds through + + + align:start position:0% +they can fly at high speeds through +thick rainforest they can fly in caves + + align:start position:0% +thick rainforest they can fly in caves + + + align:start position:0% +thick rainforest they can fly in caves +with a thousand other bats on top of + + align:start position:0% +with a thousand other bats on top of + + + align:start position:0% +with a thousand other bats on top of +them at least that's what I get out of + + align:start position:0% +them at least that's what I get out of + + + align:start position:0% +them at least that's what I get out of +the movies + + align:start position:0% +the movies + + + align:start position:0% +the movies +right and they're doing all these just + + align:start position:0% +right and they're doing all these just + + + align:start position:0% +right and they're doing all these just +incredibly Dynamic things in ways that + + align:start position:0% +incredibly Dynamic things in ways that + + + align:start position:0% +incredibly Dynamic things in ways that +our control systems can't even come + + align:start position:0% +our control systems can't even come + + + align:start position:0% +our control systems can't even come +close to right + + align:start position:0% + + + + align:start position:0% + +now and this is one of my favorite + + align:start position:0% +now and this is one of my favorite + + + align:start position:0% +now and this is one of my favorite +videos of all time um if you again the + + align:start position:0% +videos of all time um if you again the + + + align:start position:0% +videos of all time um if you again the +story about efficiency this is a fish + + align:start position:0% +story about efficiency this is a fish + + + align:start position:0% +story about efficiency this is a fish +now not a not a bird but um it's almost + + align:start position:0% +now not a not a bird but um it's almost + + + align:start position:0% +now not a not a bird but um it's almost +the same thing they're both operating in + + align:start position:0% +the same thing they're both operating in + + + align:start position:0% +the same thing they're both operating in +a fluid these this is a rainbow trout + + align:start position:0% +a fluid these this is a rainbow trout + + + align:start position:0% +a fluid these this is a rainbow trout +okay so the rainbow trout um are the + + align:start position:0% +okay so the rainbow trout um are the + + + align:start position:0% +okay so the rainbow trout um are the +fish that swim up stream at Mating + + align:start position:0% +fish that swim up stream at Mating + + + align:start position:0% +fish that swim up stream at Mating +Season okay so so every year they make + + align:start position:0% +Season okay so so every year they make + + + align:start position:0% +Season okay so so every year they make +their their March up the streams um it + + align:start position:0% +their their March up the streams um it + + + align:start position:0% +their their March up the streams um it +turns out if you watch these rainbow + + align:start position:0% +turns out if you watch these rainbow + + + align:start position:0% +turns out if you watch these rainbow +trout they tend to hang out behind rocks + + align:start position:0% +trout they tend to hang out behind rocks + + + align:start position:0% +trout they tend to hang out behind rocks +okay someone thought maybe that's it + + align:start position:0% +okay someone thought maybe that's it + + + align:start position:0% +okay someone thought maybe that's it +seems like it's tiring work going + + align:start position:0% +seems like it's tiring work going + + + align:start position:0% +seems like it's tiring work going +Upstream maybe there's something clever + + align:start position:0% +Upstream maybe there's something clever + + + align:start position:0% +Upstream maybe there's something clever +going on when they're hanging out behind + + align:start position:0% +going on when they're hanging out behind + + + align:start position:0% +going on when they're hanging out behind +these rocks um so what they did is they + + align:start position:0% +these rocks um so what they did is they + + + align:start position:0% +these rocks um so what they did is they +took that rainbow out they put it in a + + align:start position:0% +took that rainbow out they put it in a + + + align:start position:0% +took that rainbow out they put it in a +water tunnel okay and you're looking at + + align:start position:0% +water tunnel okay and you're looking at + + + align:start position:0% +water tunnel okay and you're looking at +a view from above of the fish swimming + + align:start position:0% +a view from above of the fish swimming + + + align:start position:0% +a view from above of the fish swimming +in the water tunnel this is George L + + align:start position:0% +in the water tunnel this is George L + + + align:start position:0% +in the water tunnel this is George L +lud's Lab at Harvard and that's what it + + align:start position:0% +lud's Lab at Harvard and that's what it + + + align:start position:0% +lud's Lab at Harvard and that's what it +looks like when it's just swimming in + + align:start position:0% +looks like when it's just swimming in + + + align:start position:0% +looks like when it's just swimming in +sort of Open Water okay if you take that + + align:start position:0% +sort of Open Water okay if you take that + + + align:start position:0% +sort of Open Water okay if you take that +same fish put it in the water tunnel but + + align:start position:0% +same fish put it in the water tunnel but + + + align:start position:0% +same fish put it in the water tunnel but +put a rock in front of it now if you've + + align:start position:0% +put a rock in front of it now if you've + + + align:start position:0% +put a rock in front of it now if you've +looked at rocks in a in in a river uh + + align:start position:0% +looked at rocks in a in in a river uh + + + align:start position:0% +looked at rocks in a in in a river uh +behind a rock you'll get some swirling + + align:start position:0% +behind a rock you'll get some swirling + + + align:start position:0% +behind a rock you'll get some swirling +vortices some + + align:start position:0% +vortices some + + + align:start position:0% +vortices some +edies okay um the fish behind the rock + + align:start position:0% +edies okay um the fish behind the rock + + + align:start position:0% +edies okay um the fish behind the rock +just completely changes the kin matics + + align:start position:0% +just completely changes the kin matics + + + align:start position:0% +just completely changes the kin matics +of its + + align:start position:0% +of its + + + align:start position:0% +of its +gate okay so that's suggestive that + + align:start position:0% +gate okay so that's suggestive that + + + align:start position:0% +gate okay so that's suggestive that +there's something clever going on here + + align:start position:0% +there's something clever going on here + + + align:start position:0% +there's something clever going on here +but here's the this is the Clincher here + + align:start position:0% +but here's the this is the Clincher here + + + align:start position:0% +but here's the this is the Clincher here +the Dynamics matter if you're a fish + + align:start position:0% +the Dynamics matter if you're a fish + + + align:start position:0% +the Dynamics matter if you're a fish +okay this is now a dead + + align:start position:0% +okay this is now a dead + + + align:start position:0% +okay this is now a dead +fish right it's a dead fish there's a + + align:start position:0% +fish right it's a dead fish there's a + + + align:start position:0% +fish right it's a dead fish there's a +piece of string making sure it doesn't + + align:start position:0% +piece of string making sure it doesn't + + + align:start position:0% +piece of string making sure it doesn't +go back and get caught in the the the + + align:start position:0% +go back and get caught in the the the + + + align:start position:0% +go back and get caught in the the the +grates that would be messy okay but it's + + align:start position:0% +grates that would be messy okay but it's + + + align:start position:0% +grates that would be messy okay but it's +it's slack if it if it if it's as it's + + align:start position:0% +it's slack if it if it if it's as it's + + + align:start position:0% +it's slack if it if it if it's as it's +moving around you'll see what when the + + align:start position:0% +moving around you'll see what when the + + + align:start position:0% +moving around you'll see what when the +the the string is catching this is our + + align:start position:0% +the the string is catching this is our + + + align:start position:0% +the the string is catching this is our +Rock now it's a half cylinder the + + align:start position:0% +Rock now it's a half cylinder the + + + align:start position:0% +Rock now it's a half cylinder the +water's going this way there's going to + + align:start position:0% +water's going this way there's going to + + + align:start position:0% +water's going this way there's going to +be swirling vortices off the back of + + align:start position:0% +be swirling vortices off the back of + + + align:start position:0% +be swirling vortices off the back of +that rock let's see what happens if you + + align:start position:0% +that rock let's see what happens if you + + + align:start position:0% +that rock let's see what happens if you +put a dead fish behind the uh behind the + + align:start position:0% +put a dead fish behind the uh behind the + + + align:start position:0% +put a dead fish behind the uh behind the +rock okay so the vortices are knocking + + align:start position:0% +rock okay so the vortices are knocking + + + align:start position:0% +rock okay so the vortices are knocking +the fish around that's not too + + align:start position:0% +the fish around that's not too + + + align:start position:0% +the fish around that's not too +surprising what's really + + align:start position:0% +surprising what's really + + + align:start position:0% +surprising what's really +cool is when the dead fish start + + align:start position:0% +cool is when the dead fish start + + + align:start position:0% +cool is when the dead fish start +swimming Upstream + + align:start position:0% +swimming Upstream + + + align:start position:0% +swimming Upstream +right that's pretty good so the water's + + align:start position:0% +right that's pretty good so the water's + + + align:start position:0% +right that's pretty good so the water's +going that way and the fish just went + + align:start position:0% +going that way and the fish just went + + + align:start position:0% +going that way and the fish just went +that way okay um and it's dead + + align:start position:0% +that way okay um and it's dead + + + align:start position:0% +that way okay um and it's dead +so so Dynamics matter if you're a fish + + align:start position:0% + + + + align:start position:0% + +and um if you care about + + align:start position:0% +and um if you care about + + + align:start position:0% +and um if you care about +birds mechanically we're capable now of + + align:start position:0% +birds mechanically we're capable now of + + + align:start position:0% +birds mechanically we're capable now of +building robotic Birds this is our best + + align:start position:0% +building robotic Birds this is our best + + + align:start position:0% +building robotic Birds this is our best +copy of a hobby + + align:start position:0% +copy of a hobby + + + align:start position:0% +copy of a hobby +ornithopter um but we can build birds + + align:start position:0% +ornithopter um but we can build birds + + + align:start position:0% +ornithopter um but we can build birds +that that fly around with with Derek at + + align:start position:0% +that that fly around with with Derek at + + + align:start position:0% +that that fly around with with Derek at +the + + align:start position:0% +the + + + align:start position:0% +the +controls but if you ask me how to + + align:start position:0% +controls but if you ask me how to + + + align:start position:0% +controls but if you ask me how to +control this bird to make it do you know + + align:start position:0% +control this bird to make it do you know + + + align:start position:0% +control this bird to make it do you know +land on a perch pull energy out of the + + align:start position:0% +land on a perch pull energy out of the + + + align:start position:0% +land on a perch pull energy out of the +air we haven't got a clue right we're + + align:start position:0% +air we haven't got a clue right we're + + + align:start position:0% +air we haven't got a clue right we're +working on it we haven't got a clue yeah + + align:start position:0% +working on it we haven't got a clue yeah + + + align:start position:0% +working on it we haven't got a clue yeah +that hit a tree and D dere + + align:start position:0% + + + + align:start position:0% + +covered we've got our first um the first + + align:start position:0% +covered we've got our first um the first + + + align:start position:0% +covered we've got our first um the first +flight of our big 2 meter wingspan auton + + align:start position:0% +flight of our big 2 meter wingspan auton + + + align:start position:0% +flight of our big 2 meter wingspan auton +this is an autonomous flight you can + + align:start position:0% +this is an autonomous flight you can + + + align:start position:0% +this is an autonomous flight you can +tell it's autonomous because it flies + + align:start position:0% +tell it's autonomous because it flies + + + align:start position:0% +tell it's autonomous because it flies +straight until it about runs into the + + align:start position:0% +straight until it about runs into the + + + align:start position:0% +straight until it about runs into the +building and then we hit the brakes and + + align:start position:0% +building and then we hit the brakes and + + + align:start position:0% +building and then we hit the brakes and +it has to go and hit the trash can but + + align:start position:0% +it has to go and hit the trash can but + + + align:start position:0% +it has to go and hit the trash can but +um mechanically we're close to where we + + align:start position:0% +um mechanically we're close to where we + + + align:start position:0% +um mechanically we're close to where we +want to be uh to to replicate some of + + align:start position:0% +want to be uh to to replicate some of + + + align:start position:0% +want to be uh to to replicate some of +Nature's machines I we got a long way to + + align:start position:0% +Nature's machines I we got a long way to + + + align:start position:0% +Nature's machines I we got a long way to +go but but really we're at the point + + align:start position:0% +go but but really we're at the point + + + align:start position:0% +go but but really we're at the point +where we have to figure out how to take + + align:start position:0% +where we have to figure out how to take + + + align:start position:0% +where we have to figure out how to take +these magnificent dynamical machines and + + align:start position:0% +these magnificent dynamical machines and + + + align:start position:0% +these magnificent dynamical machines and +control them and that's what the course + + align:start position:0% +control them and that's what the course + + + align:start position:0% +control them and that's what the course +is about + + align:start position:0% + + + + align:start position:0% + +okay okay so let's get a a little bit + + align:start position:0% +okay okay so let's get a a little bit + + + align:start position:0% +okay okay so let's get a a little bit +more um careful in in uh what I mean by + + align:start position:0% +more um careful in in uh what I mean by + + + align:start position:0% +more um careful in in uh what I mean by +underactuated system so we we give you + + align:start position:0% +underactuated system so we we give you + + + align:start position:0% +underactuated system so we we give you +some motivation we're going to try to + + align:start position:0% +some motivation we're going to try to + + + align:start position:0% +some motivation we're going to try to +make robots that that run like humans + + align:start position:0% +make robots that that run like humans + + + align:start position:0% +make robots that that run like humans +run like gazel right swim like dead fish + + align:start position:0% +run like gazel right swim like dead fish + + + align:start position:0% +run like gazel right swim like dead fish +and uh and fly like that that Falcon + + align:start position:0% +and uh and fly like that that Falcon + + + align:start position:0% +and uh and fly like that that Falcon +that that comes down so um not a tall + + align:start position:0% +that that comes down so um not a tall + + + align:start position:0% +that that comes down so um not a tall +order at all right um so in order to + + align:start position:0% +order at all right um so in order to + + + align:start position:0% +order at all right um so in order to +start doing that let's start by just uh + + align:start position:0% +start doing that let's start by just uh + + + align:start position:0% +start doing that let's start by just uh +defining what it means to be + + align:start position:0% +defining what it means to be + + + align:start position:0% +defining what it means to be +underactuated okay + + align:start position:0% +underactuated okay + + + align:start position:0% +underactuated okay +let me ground things in uh in an + + align:start position:0% +let me ground things in uh in an + + + align:start position:0% +let me ground things in uh in an +example let's take a um a two-link + + align:start position:0% +example let's take a um a two-link + + + align:start position:0% +example let's take a um a two-link +robotic + + align:start position:0% + + + + align:start position:0% + +arm okay I'm going + + align:start position:0% +arm okay I'm going + + + align:start position:0% +arm okay I'm going +to um describe the state of this system + + align:start position:0% +to um describe the state of this system + + + align:start position:0% +to um describe the state of this system +with Theta 1 and a relative angle here + + align:start position:0% +with Theta 1 and a relative angle here + + + align:start position:0% +with Theta 1 and a relative angle here +Theta + + align:start position:0% + + + + align:start position:0% + +2 you know let me quickly draw that sort + + align:start position:0% +2 you know let me quickly draw that sort + + + align:start position:0% +2 you know let me quickly draw that sort +of twice as + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +big we'll parameterize it here with the + + align:start position:0% +big we'll parameterize it here with the + + + align:start position:0% +big we'll parameterize it here with the +that'll be L1 the length this will be L2 + + align:start position:0% + + + + align:start position:0% + +here so we'll call this Mass one Mass 2 + + align:start position:0% +here so we'll call this Mass one Mass 2 + + + align:start position:0% +here so we'll call this Mass one Mass 2 +so we'll assume it's a a massless rod + + align:start position:0% +so we'll assume it's a a massless rod + + + align:start position:0% +so we'll assume it's a a massless rod +with a point mass at the end just to + + align:start position:0% +with a point mass at the end just to + + + align:start position:0% +with a point mass at the end just to +keep the equations a little cleaner for + + align:start position:0% +keep the equations a little cleaner for + + + align:start position:0% +keep the equations a little cleaner for +today okay and it's got two angles that + + align:start position:0% +today okay and it's got two angles that + + + align:start position:0% +today okay and it's got two angles that +I care about and there's a couple + + align:start position:0% +I care about and there's a couple + + + align:start position:0% +I care about and there's a couple +lengths at + + align:start position:0% +lengths at + + + align:start position:0% +lengths at +play + + align:start position:0% +play + + + align:start position:0% +play +so throughout the class I'm going to use + + align:start position:0% +so throughout the class I'm going to use + + + align:start position:0% +so throughout the class I'm going to use +uh the convention that Q + + align:start position:0% +uh the convention that Q + + + align:start position:0% +uh the convention that Q +is a a vector of the sort of joint + + align:start position:0% +is a a vector of the sort of joint + + + align:start position:0% +is a a vector of the sort of joint +angles or the the the coordinates of the + + align:start position:0% +angles or the the the coordinates of the + + + align:start position:0% +angles or the the the coordinates of the +robot in this case it's going to be + + align:start position:0% +robot in this case it's going to be + + + align:start position:0% +robot in this case it's going to be +Theta 1 and Theta + + align:start position:0% + + + + align:start position:0% + +2 okay if I have Motors on the robot + + align:start position:0% +2 okay if I have Motors on the robot + + + align:start position:0% +2 okay if I have Motors on the robot +let's say I can apply a torque here + + align:start position:0% +let's say I can apply a torque here + + + align:start position:0% +let's say I can apply a torque here +because I have a motor at the elbow + + align:start position:0% +because I have a motor at the elbow + + + align:start position:0% +because I have a motor at the elbow +maybe a torque here so I'll call this + + align:start position:0% +maybe a torque here so I'll call this + + + align:start position:0% +maybe a torque here so I'll call this +torque one this torque + + align:start position:0% +torque one this torque + + + align:start position:0% +torque one this torque +2 I'm going to call that U + + align:start position:0% +2 I'm going to call that U + + + align:start position:0% +2 I'm going to call that U +a vector U there's all the inputs to the + + align:start position:0% +a vector U there's all the inputs to the + + + align:start position:0% +a vector U there's all the inputs to the +system so this is the + + align:start position:0% +system so this is the + + + align:start position:0% +system so this is the +um joint + + align:start position:0% + + + + align:start position:0% + +coordinates these are the control + + align:start position:0% + + + + align:start position:0% + +inputs okay so it turns out if you want + + align:start position:0% +inputs okay so it turns out if you want + + + align:start position:0% +inputs okay so it turns out if you want +to write out the dynamics of this system + + align:start position:0% +to write out the dynamics of this system + + + align:start position:0% +to write out the dynamics of this system +if you want to be able to say simulate + + align:start position:0% +if you want to be able to say simulate + + + align:start position:0% +if you want to be able to say simulate +the um the way that this pendulum moves + + align:start position:0% +the um the way that this pendulum moves + + + align:start position:0% +the um the way that this pendulum moves +well most of the robots we care about in + + align:start position:0% +well most of the robots we care about in + + + align:start position:0% +well most of the robots we care about in +this class are are second order right so + + align:start position:0% +this class are are second order right so + + + align:start position:0% +this class are are second order right so +so everything's based on their + + align:start position:0% +so everything's based on their + + + align:start position:0% +so everything's based on their +mechanical system so we've got FAL ma + + align:start position:0% +mechanical system so we've got FAL ma + + + align:start position:0% +mechanical system so we've got FAL ma +governing + + align:start position:0% +governing + + + align:start position:0% +governing +everything in this case um a is going to + + align:start position:0% +everything in this case um a is going to + + + align:start position:0% +everything in this case um a is going to +be the D the second derivative of Q + + align:start position:0% +be the D the second derivative of Q + + + align:start position:0% +be the D the second derivative of Q +right so what I really have + + align:start position:0% +right so what I really have + + + align:start position:0% +right so what I really have +I'm G I should also say that Q dot is + + align:start position:0% +I'm G I should also say that Q dot is + + + align:start position:0% +I'm G I should also say that Q dot is +going to be the joint + + align:start position:0% + + + + align:start position:0% + +velocities and Q double dot is the joint + + align:start position:0% + + + + align:start position:0% + +accelerations + + align:start position:0% +accelerations + + + align:start position:0% +accelerations +so if I want to write describe the + + align:start position:0% +so if I want to write describe the + + + align:start position:0% +so if I want to write describe the +motion of these systems of these of this + + align:start position:0% +motion of these systems of these of this + + + align:start position:0% +motion of these systems of these of this +kind of a robot then what I need is to + + align:start position:0% +kind of a robot then what I need is to + + + align:start position:0% +kind of a robot then what I need is to +find um an equation that tells me the + + align:start position:0% +find um an equation that tells me the + + + align:start position:0% +find um an equation that tells me the +acceleration of that system based on the + + align:start position:0% +acceleration of that system based on the + + + align:start position:0% +acceleration of that system based on the +current uh position velocity of the + + align:start position:0% +current uh position velocity of the + + + align:start position:0% +current uh position velocity of the +robot and the current control + + align:start position:0% +robot and the current control + + + align:start position:0% +robot and the current control +inputs okay if we're living in second + + align:start position:0% +inputs okay if we're living in second + + + align:start position:0% +inputs okay if we're living in second +order um mechanical systems + + align:start position:0% +order um mechanical systems + + + align:start position:0% +order um mechanical systems +world then that means I'm I'm looking + + align:start position:0% +world then that means I'm I'm looking + + + align:start position:0% +world then that means I'm I'm looking +for for a governing equation equations + + align:start position:0% +for for a governing equation equations + + + align:start position:0% +for for a governing equation equations +of motion of the form f is some + + align:start position:0% +of motion of the form f is some + + + align:start position:0% +of motion of the form f is some +nonlinear function of q q do U + + align:start position:0% +nonlinear function of q q do U + + + align:start position:0% +nonlinear function of q q do U +potentially time too if there's a if + + align:start position:0% +potentially time too if there's a if + + + align:start position:0% +potentially time too if there's a if +it's a Time varying Dynamics if + + align:start position:0% +it's a Time varying Dynamics if + + + align:start position:0% +it's a Time varying Dynamics if +there's something else going on clocked + + align:start position:0% +there's something else going on clocked + + + align:start position:0% +there's something else going on clocked +by + + align:start position:0% + + + + align:start position:0% + +time okay so so basically the entire + + align:start position:0% +time okay so so basically the entire + + + align:start position:0% +time okay so so basically the entire +class we're going to be looking at + + align:start position:0% +class we're going to be looking at + + + align:start position:0% +class we're going to be looking at +second order systems governed by some + + align:start position:0% +second order systems governed by some + + + align:start position:0% +second order systems governed by some +nonlinear equations like + + align:start position:0% +nonlinear equations like + + + align:start position:0% +nonlinear equations like +that it turns out that actually most of + + align:start position:0% +that it turns out that actually most of + + + align:start position:0% +that it turns out that actually most of +the robots we care about there's even a + + align:start position:0% +the robots we care about there's even a + + + align:start position:0% +the robots we care about there's even a +simpler + + align:start position:0% +simpler + + + align:start position:0% +simpler +form um turns out we + + align:start position:0% +form um turns out we + + + align:start position:0% +form um turns out we +can almost always find it's not always + + align:start position:0% +can almost always find it's not always + + + align:start position:0% +can almost always find it's not always +but uh for Many Robots we find + + align:start position:0% +but uh for Many Robots we find + + + align:start position:0% +but uh for Many Robots we find +that the equations of motion are + + align:start position:0% +that the equations of motion are + + + align:start position:0% +that the equations of motion are +actually linear in + + align:start position:0% +actually linear in + + + align:start position:0% +actually linear in +U okay if I'm going to put in um torqus + + align:start position:0% +U okay if I'm going to put in um torqus + + + align:start position:0% +U okay if I'm going to put in um torqus +or something to my robot then it turns + + align:start position:0% +or something to my robot then it turns + + + align:start position:0% +or something to my robot then it turns +out that the way that the Torx effect + + align:start position:0% +out that the way that the Torx effect + + + align:start position:0% +out that the way that the Torx effect +accelerations is is is linear in the + + align:start position:0% +accelerations is is is linear in the + + + align:start position:0% +accelerations is is is linear in the +input so let me write a second form + + align:start position:0% +input so let me write a second form + + + align:start position:0% +input so let me write a second form +which takes advantage of that + + align:start position:0% + + + + align:start position:0% + +observation + + align:start position:0% + + + + align:start position:0% + +okay so it's just I've I've said almost + + align:start position:0% +okay so it's just I've I've said almost + + + align:start position:0% +okay so it's just I've I've said almost +nothing here this is I'm just saying + + align:start position:0% +nothing here this is I'm just saying + + + align:start position:0% +nothing here this is I'm just saying +there's some nonlinear terms that depend + + align:start position:0% +there's some nonlinear terms that depend + + + align:start position:0% +there's some nonlinear terms that depend +on the current state and velocity and + + align:start position:0% +on the current state and velocity and + + + align:start position:0% +on the current state and velocity and +time there's some other nonlinear terms + + align:start position:0% +time there's some other nonlinear terms + + + align:start position:0% +time there's some other nonlinear terms +that get multiplied by U but the only + + align:start position:0% +that get multiplied by U but the only + + + align:start position:0% +that get multiplied by U but the only +Power in this is that I'm saying that + + align:start position:0% +Power in this is that I'm saying that + + + align:start position:0% +Power in this is that I'm saying that +the the whole thing is linear in you and + + align:start position:0% +the the whole thing is linear in you and + + + align:start position:0% +the the whole thing is linear in you and +that turns out to be I'll convince you + + align:start position:0% +that turns out to be I'll convince you + + + align:start position:0% +that turns out to be I'll convince you +as we go forward that that's + + align:start position:0% + + + + align:start position:0% + +true okay so here's our we're + + align:start position:0% +true okay so here's our we're + + + align:start position:0% +true okay so here's our we're +finally grounding everything here let me + + align:start position:0% +finally grounding everything here let me + + + align:start position:0% +finally grounding everything here let me +tell you what fully actuated + + align:start position:0% + + + + align:start position:0% + +means + + align:start position:0% + + + + align:start position:0% + +just think about what this equation is + + align:start position:0% +just think about what this equation is + + + align:start position:0% +just think about what this equation is +too so Q is a vector qou dot is also a + + align:start position:0% +too so Q is a vector qou dot is also a + + + align:start position:0% +too so Q is a vector qou dot is also a +vector in this case Q is a 2x1 vector Q + + align:start position:0% +vector in this case Q is a 2x1 vector Q + + + align:start position:0% +vector in this case Q is a 2x1 vector Q +dot then is also a 2x1 vector right Q + + align:start position:0% +dot then is also a 2x1 vector right Q + + + align:start position:0% +dot then is also a 2x1 vector right Q +double dot is also a 2x1 vector so this + + align:start position:0% +double dot is also a 2x1 vector so this + + + align:start position:0% +double dot is also a 2x1 vector so this +is a vector equation of a 2x1 vector in + + align:start position:0% +is a vector equation of a 2x1 vector in + + + align:start position:0% +is a vector equation of a 2x1 vector in +this case this is some Vector 2 by one + + align:start position:0% +this case this is some Vector 2 by one + + + align:start position:0% +this case this is some Vector 2 by one +vector this is in my case I I had also + + align:start position:0% +vector this is in my case I I had also + + + align:start position:0% +vector this is in my case I I had also +two control inputs so this is also a 2 + + align:start position:0% +two control inputs so this is also a 2 + + + align:start position:0% +two control inputs so this is also a 2 +by1 Vector which means what do this + + align:start position:0% +by1 Vector which means what do this + + + align:start position:0% +by1 Vector which means what do this +thing got to be that's got to be a 2 by + + align:start position:0% +thing got to be that's got to be a 2 by + + + align:start position:0% +thing got to be that's got to be a 2 by +two Matrix in that example + + align:start position:0% + + + + align:start position:0% + +right what + + align:start position:0% +right what + + + align:start position:0% +right what +matters what makes life dramatically + + align:start position:0% +matters what makes life dramatically + + + align:start position:0% +matters what makes life dramatically +easier and what most robots today have + + align:start position:0% +easier and what most robots today have + + + align:start position:0% +easier and what most robots today have +really assumed is that they assume that + + align:start position:0% +really assumed is that they assume that + + + align:start position:0% +really assumed is that they assume that +F2 is full + + align:start position:0% +F2 is full + + + align:start position:0% +F2 is full +rank okay so so a robot is fully + + align:start position:0% +rank okay so so a robot is fully + + + align:start position:0% +rank okay so so a robot is fully +actuated a robot of this form is fully + + align:start position:0% +actuated a robot of this form is fully + + + align:start position:0% +actuated a robot of this form is fully +actuated + + align:start position:0% +actuated + + + align:start position:0% +actuated +if the + + align:start position:0% +if the + + + align:start position:0% +if the +rank of + + align:start position:0% +rank of + + + align:start position:0% +rank of +F2 q q do in + + align:start position:0% +F2 q q do in + + + align:start position:0% +F2 q q do in +time is equal I'll write the dimension + + align:start position:0% +time is equal I'll write the dimension + + + align:start position:0% +time is equal I'll write the dimension +of Q here it's full + + align:start position:0% + + + + align:start position:0% + +rank okay why does that matter what does + + align:start position:0% +rank okay why does that matter what does + + + align:start position:0% +rank okay why does that matter what does +that mean first + + align:start position:0% + + + + align:start position:0% + +what it means is + + align:start position:0% +what it means is + + + align:start position:0% +what it means is +that um if I know F1 and + + align:start position:0% +that um if I know F1 and + + + align:start position:0% +that um if I know F1 and +F2 then I can use + + align:start position:0% +F2 then I can use + + + align:start position:0% +F2 then I can use +you to do anything I want to Q double + + align:start position:0% +you to do anything I want to Q double + + + align:start position:0% +you to do anything I want to Q double +dot okay I'll show you that I could say + + align:start position:0% +dot okay I'll show you that I could say + + + align:start position:0% +dot okay I'll show you that I could say +that right now pretty explicitly okay so + + align:start position:0% +that right now pretty explicitly okay so + + + align:start position:0% +that right now pretty explicitly okay so +let's say I know exactly what F1 and F2 + + align:start position:0% +let's say I know exactly what F1 and F2 + + + align:start position:0% +let's say I know exactly what F1 and F2 +are right let's say I choose a control + + align:start position:0% +are right let's say I choose a control + + + align:start position:0% +are right let's say I choose a control +law I want to choose U um as some + + align:start position:0% +law I want to choose U um as some + + + align:start position:0% +law I want to choose U um as some +function I'll just call it Pi of q q Dot + + align:start position:0% +function I'll just call it Pi of q q Dot + + + align:start position:0% +function I'll just call it Pi of q q Dot +and time right so I want to come up with + + align:start position:0% +and time right so I want to come up with + + + align:start position:0% +and time right so I want to come up with +a controller which looks at my positions + + align:start position:0% +a controller which looks at my positions + + + align:start position:0% +a controller which looks at my positions +my velocities what time it is and comes + + align:start position:0% +my velocities what time it is and comes + + + align:start position:0% +my velocities what time it is and comes +up with a a torque let's say I + + align:start position:0% +up with a a torque let's say I + + + align:start position:0% +up with a a torque let's say I +did + + align:start position:0% +did + + + align:start position:0% +did +um + + align:start position:0% +um + + + align:start position:0% +um +F2 inverse q q Dot and time + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +times + + align:start position:0% +times + + + align:start position:0% +times +F1 q q + + align:start position:0% +F1 q q + + + align:start position:0% +F1 q q +do + + align:start position:0% +do + + + align:start position:0% +do +time plus I don't know some other + + align:start position:0% +time plus I don't know some other + + + align:start position:0% +time plus I don't know some other +controlling but I Want U Prime let's + + align:start position:0% +controlling but I Want U Prime let's + + + align:start position:0% +controlling but I Want U Prime let's +call + + align:start position:0% + + + + align:start position:0% + +it so if the rank of F2 if it's full + + align:start position:0% +it so if the rank of F2 if it's full + + + align:start position:0% +it so if the rank of F2 if it's full +rank if it's got the same rank is the + + align:start position:0% +rank if it's got the same rank is the + + + align:start position:0% +rank if it's got the same rank is the +dimension of Q then that means that this + + align:start position:0% +dimension of Q then that means that this + + + align:start position:0% +dimension of Q then that means that this +F2 inverse + + align:start position:0% +F2 inverse + + + align:start position:0% +F2 inverse +exists right and I think that if you + + align:start position:0% +exists right and I think that if you + + + align:start position:0% +exists right and I think that if you +plug this in for you right there what + + align:start position:0% +plug this in for you right there what + + + align:start position:0% +plug this in for you right there what +you're going to see is that this cancels + + align:start position:0% +you're going to see is that this cancels + + + align:start position:0% +you're going to see is that this cancels +out this right if I did it right then + + align:start position:0% +out this right if I did it right then + + + align:start position:0% +out this right if I did it right then +and this cancels out + + align:start position:0% +and this cancels out + + + align:start position:0% +and this cancels out +this and what I'm left with is a simple + + align:start position:0% +this and what I'm left with is a simple + + + align:start position:0% +this and what I'm left with is a simple +system + + align:start position:0% +system + + + align:start position:0% +system +now Q do equal U + + align:start position:0% +now Q do equal U + + + align:start position:0% +now Q do equal U +Prime + + align:start position:0% + + + + align:start position:0% + +where do you where do you want Q + + align:start position:0% +where do you where do you want Q + + + align:start position:0% +where do you where do you want Q +do this is um this is U Prime so just + + align:start position:0% +do this is um this is U Prime so just + + + align:start position:0% +do this is um this is U Prime so just +some other U so what what I'm trying to + + align:start position:0% +some other U so what what I'm trying to + + + align:start position:0% +some other U so what what I'm trying to +do is is now say that I'm going to + + align:start position:0% +do is is now say that I'm going to + + + align:start position:0% +do is is now say that I'm going to +change the effectively change the the + + align:start position:0% +change the effectively change the the + + + align:start position:0% +change the effectively change the the +equations of motion of my system into + + align:start position:0% +equations of motion of my system into + + + align:start position:0% +equations of motion of my system into +this U + + align:start position:0% +this U + + + align:start position:0% +this U +Prime okay you could I might have called + + align:start position:0% +Prime okay you could I might have called + + + align:start position:0% +Prime okay you could I might have called +that maybe q. desired or something like + + align:start position:0% +that maybe q. desired or something like + + + align:start position:0% +that maybe q. desired or something like +that that would be fine + + align:start position:0% +that that would be fine + + + align:start position:0% +that that would be fine +too okay so what did we just do we did a + + align:start position:0% +too okay so what did we just do we did a + + + align:start position:0% +too okay so what did we just do we did a +trick called feedback + + align:start position:0% + + + + align:start position:0% + +linearization okay I took what was + + align:start position:0% +linearization okay I took what was + + + align:start position:0% +linearization okay I took what was +potentially a very complicated nonlinear + + align:start position:0% +potentially a very complicated nonlinear + + + align:start position:0% +potentially a very complicated nonlinear +equations of + + align:start position:0% +equations of + + + align:start position:0% +equations of +motion and because I could + + align:start position:0% +motion and because I could + + + align:start position:0% +motion and because I could +using my control input command every qou + + align:start position:0% +using my control input command every qou + + + align:start position:0% +using my control input command every qou +dot I can essentially effectively + + align:start position:0% +dot I can essentially effectively + + + align:start position:0% +dot I can essentially effectively +replace the equations of + + align:start position:0% +replace the equations of + + + align:start position:0% +replace the equations of +motion with a simpler equations this is + + align:start position:0% +motion with a simpler equations this is + + + align:start position:0% +motion with a simpler equations this is +actually a trivially simple equations + + align:start position:0% +actually a trivially simple equations + + + align:start position:0% +actually a trivially simple equations +this is a for those of you that know + + align:start position:0% +this is a for those of you that know + + + align:start position:0% +this is a for those of you that know +this is which would be a a series of of + + align:start position:0% +this is which would be a a series of of + + + align:start position:0% +this is which would be a a series of of +single input single output systems the + + align:start position:0% +single input single output systems the + + + align:start position:0% +single input single output systems the +they're they're decoupled right so q. + + align:start position:0% +they're they're decoupled right so q. + + + align:start position:0% +they're they're decoupled right so q. +one is is equal to the first element of + + align:start position:0% +one is is equal to the first element of + + + align:start position:0% +one is is equal to the first element of +this it's just two + + align:start position:0% +this it's just two + + + align:start position:0% +this it's just two +vectors + + align:start position:0% + + + + align:start position:0% + +so that just looks like a trick I'm + + align:start position:0% +so that just looks like a trick I'm + + + align:start position:0% +so that just looks like a trick I'm +going to ground it in a in a in some in + + align:start position:0% +going to ground it in a in a in some in + + + align:start position:0% +going to ground it in a in a in some in +an example in a second + + align:start position:0% + + + + align:start position:0% + +here but first let's let's finish + + align:start position:0% +here but first let's let's finish + + + align:start position:0% +here but first let's let's finish +defining what underactuated means so + + align:start position:0% +defining what underactuated means so + + + align:start position:0% +defining what underactuated means so +what is underactuated going to + + align:start position:0% +what is underactuated going to + + + align:start position:0% +what is underactuated going to +mean if the F Matrix is inal that's + + align:start position:0% +mean if the F Matrix is inal that's + + + align:start position:0% +mean if the F Matrix is inal that's +right + + align:start position:0% + + + + align:start position:0% + +good + + align:start position:0% + + + + align:start position:0% + +okay yeah it's under a system of that + + align:start position:0% +okay yeah it's under a system of that + + + align:start position:0% +okay yeah it's under a system of that +form is underactuated if um the + + align:start position:0% +form is underactuated if um the + + + align:start position:0% +form is underactuated if um the +rank of + + align:start position:0% +rank of + + + align:start position:0% +rank of +F2 q q Dot and + + align:start position:0% +F2 q q Dot and + + + align:start position:0% +F2 q q Dot and +time is less than the dimension of + + align:start position:0% + + + + align:start position:0% + +Q in words what underactuated + + align:start position:0% + + + + align:start position:0% + +means a system is + + align:start position:0% + + + + align:start position:0% + +underactuated if the + + align:start position:0% +underactuated if the + + + align:start position:0% +underactuated if the +control input cannot + + align:start position:0% +control input cannot + + + align:start position:0% +control input cannot +accelerate the system in every direction + + align:start position:0% +accelerate the system in every direction + + + align:start position:0% +accelerate the system in every direction +okay that's what that's what this + + align:start position:0% +okay that's what that's what this + + + align:start position:0% +okay that's what that's what this +equation says if the + + align:start position:0% +equation says if the + + + align:start position:0% +equation says if the +control + + align:start position:0% +control + + + align:start position:0% +control +input + + align:start position:0% + + + + align:start position:0% + +U + + align:start position:0% + + + + align:start position:0% + +cannot + + align:start position:0% + + + + align:start position:0% + +produce + + align:start position:0% + + + + align:start position:0% + +okay that's just what the equation said + + align:start position:0% +okay that's just what the equation said + + + align:start position:0% +okay that's just what the equation said +you could imagine if the uh um if the + + align:start position:0% +you could imagine if the uh um if the + + + align:start position:0% +you could imagine if the uh um if the +form of the equations wasn't linear in U + + align:start position:0% +form of the equations wasn't linear in U + + + align:start position:0% +form of the equations wasn't linear in U +then we'd have to adapt our um this rank + + align:start position:0% +then we'd have to adapt our um this rank + + + align:start position:0% +then we'd have to adapt our um this rank +condition to to do this but this I think + + align:start position:0% +condition to to do this but this I think + + + align:start position:0% +condition to to do this but this I think +for today is a is a very good working + + align:start position:0% +for today is a is a very good working + + + align:start position:0% +for today is a is a very good working +definition of of underactuated and we'll + + align:start position:0% +definition of of underactuated and we'll + + + align:start position:0% +definition of of underactuated and we'll +we'll improve it as we go through the + + align:start position:0% +we'll improve it as we go through the + + + align:start position:0% +we'll improve it as we go through the +class there's a couple things to note + + align:start position:0% +class there's a couple things to note + + + align:start position:0% +class there's a couple things to note +about it first of all as I've defined it + + align:start position:0% +about it first of all as I've defined it + + + align:start position:0% +about it first of all as I've defined it +here whether you're underactuated or not + + align:start position:0% +here whether you're underactuated or not + + + align:start position:0% +here whether you're underactuated or not +actually depends on your state right so + + align:start position:0% +actually depends on your state right so + + + align:start position:0% +actually depends on your state right so +you could call say that that a robot was + + align:start position:0% +you could call say that that a robot was + + + align:start position:0% +you could call say that that a robot was +was fully actuated in some states and + + align:start position:0% +was fully actuated in some states and + + + align:start position:0% +was fully actuated in some states and +underactuated in other states now why + + align:start position:0% +underactuated in other states now why + + + align:start position:0% +underactuated in other states now why +would that happen maybe you're maybe + + align:start position:0% +would that happen maybe you're maybe + + + align:start position:0% +would that happen maybe you're maybe +there's a a torque limit or there's an + + align:start position:0% +there's a a torque limit or there's an + + + align:start position:0% +there's a a torque limit or there's an +obstacle or something like this that + + align:start position:0% +obstacle or something like this that + + + align:start position:0% +obstacle or something like this that +that prevents you from producing + + align:start position:0% +that prevents you from producing + + + align:start position:0% +that prevents you from producing +accelerations when you're in some + + align:start position:0% +accelerations when you're in some + + + align:start position:0% +accelerations when you're in some +configurations okay + + align:start position:0% +configurations okay + + + align:start position:0% +configurations okay +intuitively um what's happening in + + align:start position:0% +intuitively um what's happening in + + + align:start position:0% +intuitively um what's happening in +azimo is that it's trying to stay in + + align:start position:0% +azimo is that it's trying to stay in + + + align:start position:0% +azimo is that it's trying to stay in +this very conservative regime because + + align:start position:0% +this very conservative regime because + + + align:start position:0% +this very conservative regime because +then it can those are the states where + + align:start position:0% +then it can those are the states where + + + align:start position:0% +then it can those are the states where +it can act like it's fully actuated and + + align:start position:0% +it can act like it's fully actuated and + + + align:start position:0% +it can act like it's fully actuated and +if it was running like you or me then + + align:start position:0% +if it was running like you or me then + + + align:start position:0% +if it was running like you or me then +it's + + align:start position:0% +it's + + + align:start position:0% +it's +underactuated but what I want to try to + + align:start position:0% +underactuated but what I want to try to + + + align:start position:0% +underactuated but what I want to try to +impress on you is that um this dichotomy + + align:start position:0% +impress on you is that um this dichotomy + + + align:start position:0% +impress on you is that um this dichotomy +between fully actuated and underactuated + + align:start position:0% +between fully actuated and underactuated + + + align:start position:0% +between fully actuated and underactuated +systems it's it's pervasive I mean it's + + align:start position:0% +systems it's it's pervasive I mean it's + + + align:start position:0% +systems it's it's pervasive I mean it's +so robotics for the last uh 30 some + + align:start position:0% +so robotics for the last uh 30 some + + + align:start position:0% +so robotics for the last uh 30 some +easily years has almost um completely + + align:start position:0% +easily years has almost um completely + + + align:start position:0% +easily years has almost um completely +made this this assumption that F2 is is + + align:start position:0% +made this this assumption that F2 is is + + + align:start position:0% +made this this assumption that F2 is is +um full rank when designing controllers + + align:start position:0% +um full rank when designing controllers + + + align:start position:0% +um full rank when designing controllers +if you learn about adaptive control all + + align:start position:0% +if you learn about adaptive control all + + + align:start position:0% +if you learn about adaptive control all +these manipulator control ideas computat + + align:start position:0% +these manipulator control ideas computat + + + align:start position:0% +these manipulator control ideas computat +toric methods all these things you're + + align:start position:0% +toric methods all these things you're + + + align:start position:0% +toric methods all these things you're +implicitly making this assumption that + + align:start position:0% +implicitly making this assumption that + + + align:start position:0% +implicitly making this assumption that +you can produce arbitrary + + align:start position:0% +you can produce arbitrary + + + align:start position:0% +you can produce arbitrary +um + + align:start position:0% +um + + + align:start position:0% +um +torqus you can use you can use arbitrary + + align:start position:0% +torqus you can use you can use arbitrary + + + align:start position:0% +torqus you can use you can use arbitrary +control effort to produce arbitrary + + align:start position:0% +control effort to produce arbitrary + + + align:start position:0% +control effort to produce arbitrary +accelerations what that does that's why + + align:start position:0% +accelerations what that does that's why + + + align:start position:0% +accelerations what that does that's why +all these proofs exist for adaptive + + align:start position:0% +all these proofs exist for adaptive + + + align:start position:0% +all these proofs exist for adaptive +control and the like because you can you + + align:start position:0% +control and the like because you can you + + + align:start position:0% +control and the like because you can you +can then effectively turn your system + + align:start position:0% +can then effectively turn your system + + + align:start position:0% +can then effectively turn your system +into a linear system that we know how to + + align:start position:0% +into a linear system that we know how to + + + align:start position:0% +into a linear system that we know how to +think + + align:start position:0% +think + + + align:start position:0% +think +about and the reason the dichotomy is so + + align:start position:0% +about and the reason the dichotomy is so + + + align:start position:0% +about and the reason the dichotomy is so +strong is because what happens if you're + + align:start position:0% +strong is because what happens if you're + + + align:start position:0% +strong is because what happens if you're +a control designer and you don't have + + align:start position:0% +a control designer and you don't have + + + align:start position:0% +a control designer and you don't have +the ability to take your nonlinear + + align:start position:0% +the ability to take your nonlinear + + + align:start position:0% +the ability to take your nonlinear +system and turn it into a linear system + + align:start position:0% +system and turn it into a linear system + + + align:start position:0% +system and turn it into a linear system +is that you have no choice but to start + + align:start position:0% +is that you have no choice but to start + + + align:start position:0% +is that you have no choice but to start +reasoning about the nonlinear dynamics + + align:start position:0% +reasoning about the nonlinear dynamics + + + align:start position:0% +reasoning about the nonlinear dynamics +of your + + align:start position:0% +of your + + + align:start position:0% +of your +system reasoning about the long-term + + align:start position:0% +system reasoning about the long-term + + + align:start position:0% +system reasoning about the long-term +nonlinear dynamics of the + + align:start position:0% +nonlinear dynamics of the + + + align:start position:0% +nonlinear dynamics of the +system + + align:start position:0% +system + + + align:start position:0% +system +okay and analytics break down pretty + + align:start position:0% +okay and analytics break down pretty + + + align:start position:0% +okay and analytics break down pretty +quick but computers can help Okay that's + + align:start position:0% +quick but computers can help Okay that's + + + align:start position:0% +quick but computers can help Okay that's +why we're revisiting this kind of idea + + align:start position:0% +why we're revisiting this kind of idea + + + align:start position:0% +why we're revisiting this kind of idea +so factory room robotic arms tend to be + + align:start position:0% +so factory room robotic arms tend to be + + + align:start position:0% +so factory room robotic arms tend to be +fully actuated except for very + + align:start position:0% +fully actuated except for very + + + align:start position:0% +fully actuated except for very +exceptional cases um walking robots and + + align:start position:0% +exceptional cases um walking robots and + + + align:start position:0% +exceptional cases um walking robots and +things like that as we'll see are + + align:start position:0% +things like that as we'll see are + + + align:start position:0% +things like that as we'll see are +underactuated so so let's do that that + + align:start position:0% + + + + align:start position:0% + +example absolutely I'm going to finish + + align:start position:0% +example absolutely I'm going to finish + + + align:start position:0% +example absolutely I'm going to finish +making that argument but but absolutely + + align:start position:0% +making that argument but but absolutely + + + align:start position:0% +making that argument but but absolutely +that's exactly what I'm saying the + + align:start position:0% +that's exactly what I'm saying the + + + align:start position:0% +that's exactly what I'm saying the +question was am I implying that um that + + align:start position:0% +question was am I implying that um that + + + align:start position:0% +question was am I implying that um that +we need to do underactuated robotics to + + align:start position:0% +we need to do underactuated robotics to + + + align:start position:0% +we need to do underactuated robotics to +have agile robots yeah I would even say + + align:start position:0% +have agile robots yeah I would even say + + + align:start position:0% +have agile robots yeah I would even say +that I'm implying I'm a little biased + + align:start position:0% +that I'm implying I'm a little biased + + + align:start position:0% +that I'm implying I'm a little biased +but I'm implying that every interesting + + align:start position:0% +but I'm implying that every interesting + + + align:start position:0% +but I'm implying that every interesting +problem in robotics is interesting + + align:start position:0% +problem in robotics is interesting + + + align:start position:0% +problem in robotics is interesting +because it's + + align:start position:0% +because it's + + + align:start position:0% +because it's +underactuated if you think about the + + align:start position:0% +underactuated if you think about the + + + align:start position:0% +underactuated if you think about the +problems that are unsolved in robotics + + align:start position:0% +problems that are unsolved in robotics + + + align:start position:0% +problems that are unsolved in robotics +maybe manipulation walking cool flying + + align:start position:0% +maybe manipulation walking cool flying + + + align:start position:0% +maybe manipulation walking cool flying +things if you look closely if you if the + + align:start position:0% +things if you look closely if you if the + + + align:start position:0% +things if you look closely if you if the +control problem is considered unsolved + + align:start position:0% +control problem is considered unsolved + + + align:start position:0% +control problem is considered unsolved +uh it's probably underactuated okay the + + align:start position:0% +uh it's probably underactuated okay the + + + align:start position:0% +uh it's probably underactuated okay the +things we know how to do really well you + + align:start position:0% +things we know how to do really well you + + + align:start position:0% +things we know how to do really well you +know picking and placing Parts in a on a + + align:start position:0% +know picking and placing Parts in a on a + + + align:start position:0% +know picking and placing Parts in a on a +factory room floor it's fully actuated + + align:start position:0% +factory room floor it's fully actuated + + + align:start position:0% +factory room floor it's fully actuated +okay now manipulation is hard for many + + align:start position:0% +okay now manipulation is hard for many + + + align:start position:0% +okay now manipulation is hard for many +other reasons you have to find the thing + + align:start position:0% +other reasons you have to find the thing + + + align:start position:0% +other reasons you have to find the thing +you're manipulating you have to think + + align:start position:0% +you're manipulating you have to think + + + align:start position:0% +you're manipulating you have to think +about it but uh but there's something + + align:start position:0% +about it but uh but there's something + + + align:start position:0% +about it but uh but there's something +fundamental in robotics research that + + align:start position:0% +fundamental in robotics research that + + + align:start position:0% +fundamental in robotics research that +happens if your system suddenly if you + + align:start position:0% +happens if your system suddenly if you + + + align:start position:0% +happens if your system suddenly if you +don't have complete Control Authority + + align:start position:0% +don't have complete Control Authority + + + align:start position:0% +don't have complete Control Authority +and it all the interesting problems that + + align:start position:0% +and it all the interesting problems that + + + align:start position:0% +and it all the interesting problems that +are left seem to be + + align:start position:0% + + + + align:start position:0% + +underactuated okay so instead of talking + + align:start position:0% +underactuated okay so instead of talking + + + align:start position:0% +underactuated okay so instead of talking +about abstract FS let's make it specific + + align:start position:0% +about abstract FS let's make it specific + + + align:start position:0% +about abstract FS let's make it specific +okay um let's write the equations of + + align:start position:0% +okay um let's write the equations of + + + align:start position:0% +okay um let's write the equations of +motion for our two-link robotic + + align:start position:0% +motion for our two-link robotic + + + align:start position:0% +motion for our two-link robotic +arm um so I I I'll how many people have + + align:start position:0% +arm um so I I I'll how many people have + + + align:start position:0% +arm um so I I I'll how many people have +seen lran + + align:start position:0% +seen lran + + + align:start position:0% +seen lran +mechanics cool um so the the class isn't + + align:start position:0% +mechanics cool um so the the class isn't + + + align:start position:0% +mechanics cool um so the the class isn't +going to depend on it I'm going to do it + + align:start position:0% +going to depend on it I'm going to do it + + + align:start position:0% +going to depend on it I'm going to do it +once quickly and it's in the notes um if + + align:start position:0% +once quickly and it's in the notes um if + + + align:start position:0% +once quickly and it's in the notes um if +you haven't seen Loni mechanics it's a + + align:start position:0% +you haven't seen Loni mechanics it's a + + + align:start position:0% +you haven't seen Loni mechanics it's a +good thing to know um and it's in the + + align:start position:0% +good thing to know um and it's in the + + + align:start position:0% +good thing to know um and it's in the +appendix of the course notes it'll be + + align:start position:0% +appendix of the course notes it'll be + + + align:start position:0% +appendix of the course notes it'll be +posted um but I want you to see it once + + align:start position:0% +posted um but I want you to see it once + + + align:start position:0% +posted um but I want you to see it once +to just see see that there is is + + align:start position:0% +to just see see that there is is + + + align:start position:0% +to just see see that there is is +actually if what you care about first is + + align:start position:0% +actually if what you care about first is + + + align:start position:0% +actually if what you care about first is +just coming up with the equations of + + align:start position:0% +just coming up with the equations of + + + align:start position:0% +just coming up with the equations of +motion then there's actually a fairly um + + align:start position:0% +motion then there's actually a fairly um + + + align:start position:0% +motion then there's actually a fairly um +procedural way to do that for for even + + align:start position:0% +procedural way to do that for for even + + + align:start position:0% +procedural way to do that for for even +pretty complicated systems so let's do + + align:start position:0% +pretty complicated systems so let's do + + + align:start position:0% +pretty complicated systems so let's do +it for this not very complicated system + + align:start position:0% +it for this not very complicated system + + + align:start position:0% +it for this not very complicated system +um okay so let me let me do that um in + + align:start position:0% +um okay so let me let me do that um in + + + align:start position:0% +um okay so let me let me do that um in +pieces so let's say um this is mass one + + align:start position:0% +pieces so let's say um this is mass one + + + align:start position:0% +pieces so let's say um this is mass one +um let's say that I it's at position + + align:start position:0% +um let's say that I it's at position + + + align:start position:0% +um let's say that I it's at position +X1 okay if I if I call this sort of X1 + + align:start position:0% +X1 okay if I if I call this sort of X1 + + + align:start position:0% +X1 okay if I if I call this sort of X1 +and X2 + + align:start position:0% +and X2 + + + align:start position:0% +and X2 +X and Y that make some coordinate system + + align:start position:0% +X and Y that make some coordinate system + + + align:start position:0% +X and Y that make some coordinate system +there let's call let's say that the the + + align:start position:0% +there let's call let's say that the the + + + align:start position:0% +there let's call let's say that the the +mass here is at X1 and the mass 2 is at + + align:start position:0% +mass here is at X1 and the mass 2 is at + + + align:start position:0% +mass here is at X1 and the mass 2 is at +X2 so the first thing to do is just to + + align:start position:0% +X2 so the first thing to do is just to + + + align:start position:0% +X2 so the first thing to do is just to +think about um the kinematics of the + + align:start position:0% + + + + align:start position:0% + +robot and in this case they're pretty + + align:start position:0% +robot and in this case they're pretty + + + align:start position:0% +robot and in this case they're pretty +simple so as I've written it + + align:start position:0% +simple so as I've written it + + + align:start position:0% +simple so as I've written it +X1 is what is it the the X position in + + align:start position:0% +X1 is what is it the the X position in + + + align:start position:0% +X1 is what is it the the X position in +X1 here is L + + align:start position:0% +X1 here is L + + + align:start position:0% +X1 here is L +Time s or cosine + + align:start position:0% + + + + align:start position:0% + +s of theta + + align:start position:0% +s of theta + + + align:start position:0% +s of theta +1 okay and the other one is + + align:start position:0% +1 okay and the other one is + + + align:start position:0% +1 okay and the other one is +L1 + + align:start position:0% +L1 + + + align:start position:0% +L1 +cosine Theta + + align:start position:0% +cosine Theta + + + align:start position:0% +cosine Theta +1 now we're going to all get bored real + + align:start position:0% +1 now we're going to all get bored real + + + align:start position:0% +1 now we're going to all get bored real +quick if I don't adopt a short hand so + + align:start position:0% +quick if I don't adopt a short hand so + + + align:start position:0% +quick if I don't adopt a short hand so +let me just call that L1 S1 so that'll + + align:start position:0% +let me just call that L1 S1 so that'll + + + align:start position:0% +let me just call that L1 S1 so that'll +be Shand for S of theta 1 okay and this + + align:start position:0% +be Shand for S of theta 1 okay and this + + + align:start position:0% +be Shand for S of theta 1 okay and this +will be L1 cosine + + align:start position:0% + + + + align:start position:0% + +1 okay if I want to do the um kinematics + + align:start position:0% +1 okay if I want to do the um kinematics + + + align:start position:0% +1 okay if I want to do the um kinematics +of X2 here um that's going to depend on + + align:start position:0% +of X2 here um that's going to depend on + + + align:start position:0% +of X2 here um that's going to depend on +Theta 2 it's actually also going to + + align:start position:0% +Theta 2 it's actually also going to + + + align:start position:0% +Theta 2 it's actually also going to +depend on Theta 1 because I've got this + + align:start position:0% +depend on Theta 1 because I've got this + + + align:start position:0% +depend on Theta 1 because I've got this +in a relative frame that Theta 2 is + + align:start position:0% +in a relative frame that Theta 2 is + + + align:start position:0% +in a relative frame that Theta 2 is +relative to the first link so it turns + + align:start position:0% +relative to the first link so it turns + + + align:start position:0% +relative to the first link so it turns +out the the kinematics of X2 we can + + align:start position:0% +out the the kinematics of X2 we can + + + align:start position:0% +out the the kinematics of X2 we can +actually start with just X1 it's the + + align:start position:0% +actually start with just X1 it's the + + + align:start position:0% +actually start with just X1 it's the +position of X1 plus another Vector which + + align:start position:0% +position of X1 plus another Vector which + + + align:start position:0% +position of X1 plus another Vector which +is um L2 s of theta 1 + Theta + + align:start position:0% +is um L2 s of theta 1 + Theta + + + align:start position:0% +is um L2 s of theta 1 + Theta +2 if you work it out that's the the + + align:start position:0% +2 if you work it out that's the the + + + align:start position:0% +2 if you work it out that's the the +right + + align:start position:0% +right + + + align:start position:0% +right +thing + + align:start position:0% +thing + + + align:start position:0% +thing +cosine Theta 1 + Theta + + align:start position:0% +cosine Theta 1 + Theta + + + align:start position:0% +cosine Theta 1 + Theta +2 which I'll Shand as X1 + + align:start position:0% +2 which I'll Shand as X1 + + + align:start position:0% +2 which I'll Shand as X1 ++ L2 S1 + + + align:start position:0% ++ L2 S1 + + + + align:start position:0% ++ L2 S1 + +2ga L2 C1 + + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +[Music] + + align:start position:0% + + + + align:start position:0% + +2 okay so the derivatives aren't too bad + + align:start position:0% +2 okay so the derivatives aren't too bad + + + align:start position:0% +2 okay so the derivatives aren't too bad +I can do those Let's uh let's see say if + + align:start position:0% +I can do those Let's uh let's see say if + + + align:start position:0% +I can do those Let's uh let's see say if +I want the rate of change of X1 that's + + align:start position:0% +I want the rate of change of X1 that's + + + align:start position:0% +I want the rate of change of X1 that's +going to now intuitively that's going to + + align:start position:0% +going to now intuitively that's going to + + + align:start position:0% +going to now intuitively that's going to +start depending on the + + align:start position:0% +start depending on the + + + align:start position:0% +start depending on the +um on the joint velocities right so how + + align:start position:0% +um on the joint velocities right so how + + + align:start position:0% +um on the joint velocities right so how +does that work out the time derivative + + align:start position:0% +does that work out the time derivative + + + align:start position:0% +does that work out the time derivative +of X1 is going to + + align:start position:0% +of X1 is going to + + + align:start position:0% +of X1 is going to +be L1 + + align:start position:0% +be L1 + + + align:start position:0% +be L1 +cosine um Theta 1 * Theta 1 dot + + align:start position:0% +cosine um Theta 1 * Theta 1 dot + + + align:start position:0% +cosine um Theta 1 * Theta 1 dot +right and then L1 sin Theta 1 * Theta 1 + + align:start position:0% + + + + align:start position:0% + +Dot and X2 dot it's going to be X1 dot + + align:start position:0% +Dot and X2 dot it's going to be X1 dot + + + align:start position:0% +Dot and X2 dot it's going to be X1 dot +plus um + + align:start position:0% +plus um + + + align:start position:0% +plus um +L2 C1 + 2 * Theta 1 dot plus Theta 2 + + align:start position:0% + + + + align:start position:0% + +Dot and L2 s 1 + 2 Theta 1. + + align:start position:0% +Dot and L2 s 1 + 2 Theta 1. + + + align:start position:0% +Dot and L2 s 1 + 2 Theta 1. +plus Theta 2 + + align:start position:0% + + + + align:start position:0% + +dot okay so we we now we solve the + + align:start position:0% +dot okay so we we now we solve the + + + align:start position:0% +dot okay so we we now we solve the +kinematics of the + + align:start position:0% +kinematics of the + + + align:start position:0% +kinematics of the +machine to write the + + align:start position:0% + + + + align:start position:0% + +Dynamics lran + + align:start position:0% + + + + align:start position:0% + +style we need to think about the energy + + align:start position:0% +style we need to think about the energy + + + align:start position:0% +style we need to think about the energy +of the system so let's call T the total + + align:start position:0% +of the system so let's call T the total + + + align:start position:0% +of the system so let's call T the total +kinetic energy + + align:start position:0% + + + + align:start position:0% + +and in this case it's pretty simple + + align:start position:0% +and in this case it's pretty simple + + + align:start position:0% +and in this case it's pretty simple +that's this is why I went with Point + + align:start position:0% +that's this is why I went with Point + + + align:start position:0% +that's this is why I went with Point +masses okay it's 1 12 mv^ + + align:start position:0% +masses okay it's 1 12 mv^ + + + align:start position:0% +masses okay it's 1 12 mv^ +2 right which in Vector form looks like + + align:start position:0% +2 right which in Vector form looks like + + + align:start position:0% +2 right which in Vector form looks like +12 um X1 dot transpose M1 X1 Dot + + align:start position:0% +12 um X1 dot transpose M1 X1 Dot + + + align:start position:0% +12 um X1 dot transpose M1 X1 Dot +plus 12 X2 dot + + align:start position:0% +plus 12 X2 dot + + + align:start position:0% +plus 12 X2 dot +transpose M2 X2 + + align:start position:0% +transpose M2 X2 + + + align:start position:0% +transpose M2 X2 +[Music] + + align:start position:0% + + + + align:start position:0% + +do okay and then we're going to define + + align:start position:0% +do okay and then we're going to define + + + align:start position:0% +do okay and then we're going to define +the total potential + + align:start position:0% + + + + align:start position:0% + +energy as U + + align:start position:0% + + + + align:start position:0% + +and this it's just mg times the position + + align:start position:0% +and this it's just mg times the position + + + align:start position:0% +and this it's just mg times the position +the vertical position of the thing so + + align:start position:0% +the vertical position of the thing so + + + align:start position:0% +the vertical position of the thing so +it's just Mass 1 time + + align:start position:0% +it's just Mass 1 time + + + align:start position:0% +it's just Mass 1 time +gravity + + align:start position:0% +gravity + + + align:start position:0% +gravity +times um I'll call + + align:start position:0% +times um I'll call + + + align:start position:0% +times um I'll call +it um I guess I'll just call it + + align:start position:0% +it um I guess I'll just call it + + + align:start position:0% +it um I guess I'll just call it +y1 which which is the the second element + + align:start position:0% +y1 which which is the the second element + + + align:start position:0% +y1 which which is the the second element +of + + align:start position:0% +of + + + align:start position:0% +of +that why don't even not introduce a new + + align:start position:0% +that why don't even not introduce a new + + + align:start position:0% +that why don't even not introduce a new +symbol we'll just do L1 + + align:start position:0% + + + + align:start position:0% + +C1 + + align:start position:0% +C1 + + + align:start position:0% +C1 +negative and this is minus M2 G um + + align:start position:0% +negative and this is minus M2 G um + + + align:start position:0% +negative and this is minus M2 G um +Y2 which is L1 + + align:start position:0% +Y2 which is L1 + + + align:start position:0% +Y2 which is L1 +C1 + + align:start position:0% + + + + align:start position:0% + +plus + + align:start position:0% +plus + + + align:start position:0% +plus +L2 C1 + + + align:start position:0% +L2 C1 + + + + align:start position:0% +L2 C1 + +2 sorry for going into the corner okay + + align:start position:0% +2 sorry for going into the corner okay + + + align:start position:0% +2 sorry for going into the corner okay +but you can all write the um + + align:start position:0% + + + + align:start position:0% + +the the kinetic and potential energy of + + align:start position:0% +the the kinetic and potential energy of + + + align:start position:0% +the the kinetic and potential energy of +the + + align:start position:0% +the + + + align:start position:0% +the +system okay so lran um derivations of + + align:start position:0% +system okay so lran um derivations of + + + align:start position:0% +system okay so lran um derivations of +the equations of motion just + + align:start position:0% +the equations of motion just + + + align:start position:0% +the equations of motion just +uses this lran which is the the + + align:start position:0% +uses this lran which is the the + + + align:start position:0% +uses this lran which is the the +difference in the kinetic minus + + align:start position:0% +difference in the kinetic minus + + + align:start position:0% +difference in the kinetic minus +potential and now we I think a very good + + align:start position:0% +potential and now we I think a very good + + + align:start position:0% +potential and now we I think a very good +exercise is to understand the the reason + + align:start position:0% +exercise is to understand the the reason + + + align:start position:0% +exercise is to understand the the reason +why this works but for our class we can + + align:start position:0% +why this works but for our class we can + + + align:start position:0% +why this works but for our class we can +actually just use it as a as a crank + + align:start position:0% +actually just use it as a as a crank + + + align:start position:0% +actually just use it as a as a crank +that we can turn if if we write this out + + align:start position:0% +that we can turn if if we write this out + + + align:start position:0% +that we can turn if if we write this out +um and then you do some simple math on + + align:start position:0% + + + + align:start position:0% + +it where this is called a generalized + + align:start position:0% + + + + align:start position:0% + +Force + + align:start position:0% +Force + + + align:start position:0% +Force +then it turns out if you plug these in + + align:start position:0% +then it turns out if you plug these in + + + align:start position:0% +then it turns out if you plug these in +to this equation turn your Calculus + + align:start position:0% +to this equation turn your Calculus + + + align:start position:0% +to this equation turn your Calculus +crank then you end up with the equations + + align:start position:0% +crank then you end up with the equations + + + align:start position:0% +crank then you end up with the equations +of motion you end up with two equations + + align:start position:0% +of motion you end up with two equations + + + align:start position:0% +of motion you end up with two equations +that have the form + + align:start position:0% + + + + align:start position:0% + +um they give you some equations in terms + + align:start position:0% +um they give you some equations in terms + + + align:start position:0% +um they give you some equations in terms +of F Q Q do Q dble dot + + align:start position:0% +of F Q Q do Q dble dot + + + align:start position:0% +of F Q Q do Q dble dot +um is some function of q and and this is + + align:start position:0% +um is some function of q and and this is + + + align:start position:0% +um is some function of q and and this is +actually where the U's come in so in the + + align:start position:0% +actually where the U's come in so in the + + + align:start position:0% +actually where the U's come in so in the +simplest form it comes up like + + align:start position:0% + + + + align:start position:0% + +this and with a little work let me call + + align:start position:0% +this and with a little work let me call + + + align:start position:0% +this and with a little work let me call +that F lran so it's not the same f with + + align:start position:0% +that F lran so it's not the same f with + + + align:start position:0% +that F lran so it's not the same f with +a little work you can separate out the Q + + align:start position:0% +a little work you can separate out the Q + + + align:start position:0% +a little work you can separate out the Q +double dots and get it + + align:start position:0% +double dots and get it + + + align:start position:0% +double dots and get it +to um the vector equations we were + + align:start position:0% +to um the vector equations we were + + + align:start position:0% +to um the vector equations we were +talking about + + align:start position:0% + + + + align:start position:0% + +before okay if you take those equations + + align:start position:0% +before okay if you take those equations + + + align:start position:0% +before okay if you take those equations +that you get and you pop them into mat + + align:start position:0% +that you get and you pop them into mat + + + align:start position:0% +that you get and you pop them into mat +lab + + align:start position:0% + + + + align:start position:0% + +then it's pretty + + align:start position:0% +then it's pretty + + + align:start position:0% +then it's pretty +simple to uh start simulating the + + align:start position:0% +simple to uh start simulating the + + + align:start position:0% +simple to uh start simulating the +equations of motion + + align:start position:0% +equations of motion + + + align:start position:0% +equations of motion +of the two link arm this is with zero + + align:start position:0% +of the two link arm this is with zero + + + align:start position:0% +of the two link arm this is with zero +control input so this is just what + + align:start position:0% +control input so this is just what + + + align:start position:0% +control input so this is just what +happens if you take some um two-link arm + + align:start position:0% +happens if you take some um two-link arm + + + align:start position:0% +happens if you take some um two-link arm +apply no torque let it go then you + + align:start position:0% +apply no torque let it go then you + + + align:start position:0% +apply no torque let it go then you +get this now I put some damping in there + + align:start position:0% +get this now I put some damping in there + + + align:start position:0% +get this now I put some damping in there +extra so we didn't have a demonstration + + align:start position:0% +extra so we didn't have a demonstration + + + align:start position:0% +extra so we didn't have a demonstration +of Chaos + + align:start position:0% +of Chaos + + + align:start position:0% +of Chaos +but + + align:start position:0% + + + + align:start position:0% + +uh there's a pretty procedural way to go + + align:start position:0% +uh there's a pretty procedural way to go + + + align:start position:0% +uh there's a pretty procedural way to go +from very simple kinematics doing some + + align:start position:0% +from very simple kinematics doing some + + + align:start position:0% +from very simple kinematics doing some +pretty um simple energy calculations and + + align:start position:0% +pretty um simple energy calculations and + + + align:start position:0% +pretty um simple energy calculations and +getting yourself to a simulation of even + + align:start position:0% +getting yourself to a simulation of even + + + align:start position:0% +getting yourself to a simulation of even +very complicated um mechanical systems + + align:start position:0% +very complicated um mechanical systems + + + align:start position:0% +very complicated um mechanical systems +okay so the for Dynamics we understand + + align:start position:0% +okay so the for Dynamics we understand + + + align:start position:0% +okay so the for Dynamics we understand +now it turns out there's actually very + + align:start position:0% +now it turns out there's actually very + + + align:start position:0% +now it turns out there's actually very +good algorithms for this too if you have + + align:start position:0% +good algorithms for this too if you have + + + align:start position:0% +good algorithms for this too if you have +a 100 link robot you certainly wouldn't + + align:start position:0% +a 100 link robot you certainly wouldn't + + + align:start position:0% +a 100 link robot you certainly wouldn't +want to go turn the crank by hand but + + align:start position:0% +want to go turn the crank by hand but + + + align:start position:0% +want to go turn the crank by hand but +you can um download good software + + align:start position:0% +you can um download good software + + + align:start position:0% +you can um download good software +packages that write recursive versions + + align:start position:0% +packages that write recursive versions + + + align:start position:0% +packages that write recursive versions +of this algorithm that that have very + + align:start position:0% +of this algorithm that that have very + + + align:start position:0% +of this algorithm that that have very +efficient computation of those + + align:start position:0% +efficient computation of those + + + align:start position:0% +efficient computation of those +Dynamics + + align:start position:0% +Dynamics + + + align:start position:0% +Dynamics +okay now let's start thinking about what + + align:start position:0% +okay now let's start thinking about what + + + align:start position:0% +okay now let's start thinking about what +it means to have control in that + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +system + + align:start position:0% + + + + align:start position:0% + +turns out if you do enough of these + + align:start position:0% +turns out if you do enough of these + + + align:start position:0% +turns out if you do enough of these +equations if you punch in enough + + align:start position:0% +equations if you punch in enough + + + align:start position:0% +equations if you punch in enough +different robotic arms and walking + + align:start position:0% +different robotic arms and walking + + + align:start position:0% +different robotic arms and walking +robots or whatever oh done yeah maybe is + + align:start position:0% +robots or whatever oh done yeah maybe is + + + align:start position:0% +robots or whatever oh done yeah maybe is +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +okay good + + align:start position:0% + + + + align:start position:0% + +catch + + align:start position:0% + + + + align:start position:0% + +um okay so if you start punching these + + align:start position:0% +um okay so if you start punching these + + + align:start position:0% +um okay so if you start punching these +equations enough then then you start + + align:start position:0% +equations enough then then you start + + + align:start position:0% +equations enough then then you start +noticing a pattern turns out even very + + align:start position:0% +noticing a pattern turns out even very + + + align:start position:0% +noticing a pattern turns out even very +complicated uh robotic arms tend to have + + align:start position:0% +complicated uh robotic arms tend to have + + + align:start position:0% +complicated uh robotic arms tend to have +equations that fall into this stereotype + + align:start position:0% + + + + align:start position:0% + +form + + align:start position:0% + + + + align:start position:0% + +okay this is almost just fals ma this + + align:start position:0% +okay this is almost just fals ma this + + + align:start position:0% +okay this is almost just fals ma this +is the mass Matrix The inertial + + align:start position:0% + + + + align:start position:0% + +Matrix + + align:start position:0% +Matrix + + + align:start position:0% +Matrix +the C + + align:start position:0% +the C + + + align:start position:0% +the C +here is the + + align:start position:0% +here is the + + + align:start position:0% +here is the +uh coriolis + + align:start position:0% + + + + align:start position:0% + +terms the G here is the gravitational + + align:start position:0% +terms the G here is the gravitational + + + align:start position:0% +terms the G here is the gravitational +terms potential + + align:start position:0% + + + + align:start position:0% + +terms and then this is the torque + + align:start position:0% + + + + align:start position:0% + +these are called the manipulator + + align:start position:0% +these are called the manipulator + + + align:start position:0% +these are called the manipulator +equations we're going to revisit them + + align:start position:0% +equations we're going to revisit them + + + align:start position:0% +equations we're going to revisit them +you don't have to have complete + + align:start position:0% +you don't have to have complete + + + align:start position:0% +you don't have to have complete +intuition about them right now but what + + align:start position:0% +intuition about them right now but what + + + align:start position:0% +intuition about them right now but what +I want you to + + align:start position:0% + + + + align:start position:0% + +understand is that if you take the lran + + align:start position:0% +understand is that if you take the lran + + + align:start position:0% +understand is that if you take the lran +Dynamics on some rigid body + + align:start position:0% +Dynamics on some rigid body + + + align:start position:0% +Dynamics on some rigid body +manipulator then you're going to get + + align:start position:0% +manipulator then you're going to get + + + align:start position:0% +manipulator then you're going to get +something out in a form that looks like + + align:start position:0% +something out in a form that looks like + + + align:start position:0% +something out in a form that looks like +this now this is actually a pretty + + align:start position:0% +this now this is actually a pretty + + + align:start position:0% +this now this is actually a pretty +powerful equation it tells you that you + + align:start position:0% +powerful equation it tells you that you + + + align:start position:0% +powerful equation it tells you that you +know tells you a lot of things so + + align:start position:0% +know tells you a lot of things so + + + align:start position:0% +know tells you a lot of things so +there's a a q double dot term that's + + align:start position:0% +there's a a q double dot term that's + + + align:start position:0% +there's a a q double dot term that's +multiplied linearly by something that + + align:start position:0% +multiplied linearly by something that + + + align:start position:0% +multiplied linearly by something that +only depends on Q okay so by leaving out + + align:start position:0% +only depends on Q okay so by leaving out + + + align:start position:0% +only depends on Q okay so by leaving out +Q dot here I've already strengthened my + + align:start position:0% +Q dot here I've already strengthened my + + + align:start position:0% +Q dot here I've already strengthened my +form by putting qou dot in linear here + + align:start position:0% +form by putting qou dot in linear here + + + align:start position:0% +form by putting qou dot in linear here +so not arbitrary equations don't fit + + align:start position:0% +so not arbitrary equations don't fit + + + align:start position:0% +so not arbitrary equations don't fit +this this is a pretty special set of + + align:start position:0% +this this is a pretty special set of + + + align:start position:0% +this this is a pretty special set of +equations there's some terms that depend + + align:start position:0% +equations there's some terms that depend + + + align:start position:0% +equations there's some terms that depend +on Q Dot and then there's some potential + + align:start position:0% +on Q Dot and then there's some potential + + + align:start position:0% +on Q Dot and then there's some potential +terms which only depend on + + align:start position:0% +terms which only depend on + + + align:start position:0% +terms which only depend on +Q and then we have our joint torque kind + + align:start position:0% +Q and then we have our joint torque kind + + + align:start position:0% +Q and then we have our joint torque kind +of things over here okay and in fact + + align:start position:0% +of things over here okay and in fact + + + align:start position:0% +of things over here okay and in fact +there's actually a lot of well-known + + align:start position:0% +there's actually a lot of well-known + + + align:start position:0% +there's actually a lot of well-known +structure in these equations so it turns + + align:start position:0% +structure in these equations so it turns + + + align:start position:0% +structure in these equations so it turns +out I could have written the energy of + + align:start position:0% +out I could have written the energy of + + + align:start position:0% +out I could have written the energy of +the system as 1/2 um q. + + align:start position:0% +the system as 1/2 um q. + + + align:start position:0% +the system as 1/2 um q. +transpose HQ Q dot this inertial + + align:start position:0% +transpose HQ Q dot this inertial + + + align:start position:0% +transpose HQ Q dot this inertial +Matrix analogous to Mass + + align:start position:0% +Matrix analogous to Mass + + + align:start position:0% +Matrix analogous to Mass +is related to the kinetic energy of the + + align:start position:0% + + + + align:start position:0% + +system and what that means actually just + + align:start position:0% +system and what that means actually just + + + align:start position:0% +system and what that means actually just +by thinking of it this way um we + + align:start position:0% +by thinking of it this way um we + + + align:start position:0% +by thinking of it this way um we +actually it's well known that H is + + align:start position:0% +actually it's well known that H is + + + align:start position:0% +actually it's well known that H is +positive definite it's uniformly + + align:start position:0% +positive definite it's uniformly + + + align:start position:0% +positive definite it's uniformly +positive definite okay you can't have a + + align:start position:0% +positive definite okay you can't have a + + + align:start position:0% +positive definite okay you can't have a +negative energy NE negative kinetic + + align:start position:0% +negative energy NE negative kinetic + + + align:start position:0% +negative energy NE negative kinetic +energy and that manifests itself that + + align:start position:0% +energy and that manifests itself that + + + align:start position:0% +energy and that manifests itself that +that this Matrix H which appears all the + + align:start position:0% +that this Matrix H which appears all the + + + align:start position:0% +that this Matrix H which appears all the +time turns out to be um equivalent + + align:start position:0% +time turns out to be um equivalent + + + align:start position:0% +time turns out to be um equivalent +to its transpose it's symmetric and it's + + align:start position:0% +to its transpose it's symmetric and it's + + + align:start position:0% +to its transpose it's symmetric and it's +positive + + align:start position:0% + + + + align:start position:0% + +definite that's shorthand for positive + + align:start position:0% +definite that's shorthand for positive + + + align:start position:0% +definite that's shorthand for positive +definite right it's a matrix greater + + align:start position:0% +definite right it's a matrix greater + + + align:start position:0% +definite right it's a matrix greater +than + + align:start position:0% + + + + align:start position:0% + +zero and in fact if you if you look + + align:start position:0% +zero and in fact if you if you look + + + align:start position:0% +zero and in fact if you if you look +at the uh equations I punched in for the + + align:start position:0% + + + + align:start position:0% + +uh the robotic arm it's exactly just a + + align:start position:0% +uh the robotic arm it's exactly just a + + + align:start position:0% +uh the robotic arm it's exactly just a +matter of computing h c g and B which + + align:start position:0% + + + + align:start position:0% + +is the Matrix that Maps your control + + align:start position:0% +is the Matrix that Maps your control + + + align:start position:0% +is the Matrix that Maps your control +inputs into joint + + align:start position:0% + + + + align:start position:0% + +torqus + + align:start position:0% +torqus + + + align:start position:0% +torqus +so H is a ntial matrix C is coris G is + + align:start position:0% +so H is a ntial matrix C is coris G is + + + align:start position:0% +so H is a ntial matrix C is coris G is +gravity I think B was just cuz people + + align:start position:0% +gravity I think B was just cuz people + + + align:start position:0% +gravity I think B was just cuz people +were running out of letters I don't know + + align:start position:0% +were running out of letters I don't know + + + align:start position:0% +were running out of letters I don't know +I don't know a reason to call it B but + + align:start position:0% +I don't know a reason to call it B but + + + align:start position:0% +I don't know a reason to call it B but +in general b could be a function of Q + + align:start position:0% +in general b could be a function of Q + + + align:start position:0% +in general b could be a function of Q +maybe but it's just some mapping between + + align:start position:0% +maybe but it's just some mapping between + + + align:start position:0% +maybe but it's just some mapping between +your control inputs and the torqux that + + align:start position:0% +your control inputs and the torqux that + + + align:start position:0% +your control inputs and the torqux that +you want to + + align:start position:0% + + + + align:start position:0% + +get okay so um so knowing that I've I've + + align:start position:0% +get okay so um so knowing that I've I've + + + align:start position:0% +get okay so um so knowing that I've I've +take taken my simple + + align:start position:0% +take taken my simple + + + align:start position:0% +take taken my simple +manipulator I found equations a motion + + align:start position:0% +manipulator I found equations a motion + + + align:start position:0% +manipulator I found equations a motion +to take this form um if I have uh torqux + + align:start position:0% +to take this form um if I have uh torqux + + + align:start position:0% +to take this form um if I have uh torqux +to give torqus at both the um elbow and + + align:start position:0% +to give torqus at both the um elbow and + + + align:start position:0% +to give torqus at both the um elbow and +the + + align:start position:0% +the + + + align:start position:0% +the +shoulder then it turns out for that + + align:start position:0% + + + + align:start position:0% + +example H and C and G all just come from + + align:start position:0% +example H and C and G all just come from + + + align:start position:0% +example H and C and G all just come from +lran and + + align:start position:0% +lran and + + + align:start position:0% +lran and +B what's B going to be in that example + + align:start position:0% + + + + align:start position:0% + +what size is it going to be + + align:start position:0% + + + + align:start position:0% + +first 2 by + + align:start position:0% + + + + align:start position:0% + +two and if I'm assuming that my control + + align:start position:0% +two and if I'm assuming that my control + + + align:start position:0% +two and if I'm assuming that my control +inputs are exactly um uh the Torx Then I + + align:start position:0% +inputs are exactly um uh the Torx Then I + + + align:start position:0% +inputs are exactly um uh the Torx Then I +then B is just the identity Matrix 2 X2 + + align:start position:0% +then B is just the identity Matrix 2 X2 + + + align:start position:0% +then B is just the identity Matrix 2 X2 +identity + + align:start position:0% + + + + align:start position:0% + +Matrix okay is the system fully + + align:start position:0% +Matrix okay is the system fully + + + align:start position:0% +Matrix okay is the system fully +actuated yes why is it fully actuated + + align:start position:0% +actuated yes why is it fully actuated + + + align:start position:0% +actuated yes why is it fully actuated +the r Matrix is two okay but there's one + + align:start position:0% +the r Matrix is two okay but there's one + + + align:start position:0% +the r Matrix is two okay but there's one +other term that there's one other part + + align:start position:0% +other term that there's one other part + + + align:start position:0% +other term that there's one other part +of that + + align:start position:0% +of that + + + align:start position:0% +of that +statement that's equal the + + align:start position:0% +statement that's equal the + + + align:start position:0% +statement that's equal the +dimension but but I need to I need to + + align:start position:0% +dimension but but I need to I need to + + + align:start position:0% +dimension but but I need to I need to +get the mapping from Q dot to + + align:start position:0% +get the mapping from Q dot to + + + align:start position:0% +get the mapping from Q dot to +U yeah because the inertial matrices are + + align:start position:0% +U yeah because the inertial matrices are + + + align:start position:0% +U yeah because the inertial matrices are +always also positive definite right that + + align:start position:0% +always also positive definite right that + + + align:start position:0% +always also positive definite right that +if I actually write + + align:start position:0% +if I actually write + + + align:start position:0% +if I actually write +out Q dot for these systems I get an H + + align:start position:0% +out Q dot for these systems I get an H + + + align:start position:0% +out Q dot for these systems I get an H +inverse Q times all that stuff right + + align:start position:0% +inverse Q times all that stuff right + + + align:start position:0% +inverse Q times all that stuff right +BQ U minus C well leave the Q dot minus + + align:start position:0% +BQ U minus C well leave the Q dot minus + + + align:start position:0% +BQ U minus C well leave the Q dot minus +G + + align:start position:0% + + + + align:start position:0% + +okay and we know H inverse exists I told + + align:start position:0% +okay and we know H inverse exists I told + + + align:start position:0% +okay and we know H inverse exists I told +you it's positive definite so as long as + + align:start position:0% +you it's positive definite so as long as + + + align:start position:0% +you it's positive definite so as long as +this thing is full rank which as you + + align:start position:0% +this thing is full rank which as you + + + align:start position:0% +this thing is full rank which as you +said it is then that system is fully + + align:start position:0% + + + + align:start position:0% + +actuated okay that means I can do + + align:start position:0% +actuated okay that means I can do + + + align:start position:0% +actuated okay that means I can do +anything I want to that system what + + align:start position:0% +anything I want to that system what + + + align:start position:0% +anything I want to that system what +should we do to that system what should + + align:start position:0% +should we do to that system what should + + + align:start position:0% +should we do to that system what should +we do let's + + align:start position:0% +we do let's + + + align:start position:0% +we do let's +uh let's replace the Dynamics with + + align:start position:0% +uh let's replace the Dynamics with + + + align:start position:0% +uh let's replace the Dynamics with +something else okay what can't do + + align:start position:0% +something else okay what can't do + + + align:start position:0% +something else okay what can't do +anything it's going to have to be um two + + align:start position:0% +anything it's going to have to be um two + + + align:start position:0% +anything it's going to have to be um two +variables or less the system I want to + + align:start position:0% +variables or less the system I want to + + + align:start position:0% +variables or less the system I want to +simulate right I can't make it simulate + + align:start position:0% +simulate right I can't make it simulate + + + align:start position:0% +simulate right I can't make it simulate +a whip if I've only got two but I can + + align:start position:0% +a whip if I've only got two but I can + + + align:start position:0% +a whip if I've only got two but I can +make it simulate any sort of + + align:start position:0% +make it simulate any sort of + + + align:start position:0% +make it simulate any sort of +two-dimensional second order + + align:start position:0% +two-dimensional second order + + + align:start position:0% +two-dimensional second order +system okay how about um how about we + + align:start position:0% +system okay how about um how about we + + + align:start position:0% +system okay how about um how about we +take our two-link pendulum and make it + + align:start position:0% +take our two-link pendulum and make it + + + align:start position:0% +take our two-link pendulum and make it +act like a on link P pendulum that's a + + align:start position:0% +act like a on link P pendulum that's a + + + align:start position:0% +act like a on link P pendulum that's a +simple enough thing to do okay so what + + align:start position:0% +simple enough thing to do okay so what + + + align:start position:0% +simple enough thing to do okay so what +I'd do is I'd find the equations of + + align:start position:0% +I'd do is I'd find the equations of + + + align:start position:0% +I'd do is I'd find the equations of +motion for the one link + + align:start position:0% +motion for the one link + + + align:start position:0% +motion for the one link +pendulum and I'd just do my feedback + + align:start position:0% +pendulum and I'd just do my feedback + + + align:start position:0% +pendulum and I'd just do my feedback +linearization trick I'd cancel it out + + align:start position:0% +linearization trick I'd cancel it out + + + align:start position:0% +linearization trick I'd cancel it out +and I'd replace um the Dynamics with the + + align:start position:0% +and I'd replace um the Dynamics with the + + + align:start position:0% +and I'd replace um the Dynamics with the +onelink pendulum + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +all right so if you can see this + + align:start position:0% +all right so if you can see this + + + align:start position:0% +all right so if you can see this +the um it's just a matter of saying U is + + align:start position:0% +the um it's just a matter of saying U is + + + align:start position:0% +the um it's just a matter of saying U is +C * + + align:start position:0% +C * + + + align:start position:0% +C * +x + + align:start position:0% + + + + align:start position:0% + +dot in my in my mat lab code and in + + align:start position:0% +dot in my in my mat lab code and in + + + align:start position:0% +dot in my in my mat lab code and in +lecture I I I'll use x to mean um Q the + + align:start position:0% +lecture I I I'll use x to mean um Q the + + + align:start position:0% +lecture I I I'll use x to mean um Q the +combination of Q and Q + + align:start position:0% + + + + align:start position:0% + +dot okay + + align:start position:0% + + + + align:start position:0% + +I can just do my exact feedback + + align:start position:0% +I can just do my exact feedback + + + align:start position:0% +I can just do my exact feedback +linearization trick c u is C plus + + align:start position:0% +linearization trick c u is C plus + + + align:start position:0% +linearization trick c u is C plus +G um let's see if I can make this show + + align:start position:0% +G um let's see if I can make this show + + + align:start position:0% +G um let's see if I can make this show +up a little + + align:start position:0% + + + + align:start position:0% + +better and there's the equations of a + + align:start position:0% +better and there's the equations of a + + + align:start position:0% +better and there's the equations of a +simple pendulum with a little + + align:start position:0% +simple pendulum with a little + + + align:start position:0% +simple pendulum with a little +damping okay my control + + align:start position:0% +damping okay my control + + + align:start position:0% +damping okay my control +system if I + + align:start position:0% +system if I + + + align:start position:0% +system if I +say lecture one I think I put under + + align:start position:0% +say lecture one I think I put under + + + align:start position:0% +say lecture one I think I put under +simple + + align:start position:0% +simple + + + align:start position:0% +simple +pend then suddenly my two- link pendulum + + align:start position:0% +pend then suddenly my two- link pendulum + + + align:start position:0% +pend then suddenly my two- link pendulum +the Dynamics of my two- link pendulum + + align:start position:0% +the Dynamics of my two- link pendulum + + + align:start position:0% +the Dynamics of my two- link pendulum +I'm simulating those entire Dynamics + + align:start position:0% +I'm simulating those entire Dynamics + + + align:start position:0% +I'm simulating those entire Dynamics +work out to be dynamics of my one link + + align:start position:0% +work out to be dynamics of my one link + + + align:start position:0% +work out to be dynamics of my one link +pendulum okay so maybe not a useful + + align:start position:0% +pendulum okay so maybe not a useful + + + align:start position:0% +pendulum okay so maybe not a useful +trick if I really wanted a onelink + + align:start position:0% +trick if I really wanted a onelink + + + align:start position:0% +trick if I really wanted a onelink +pendulum I could have done a one link + + align:start position:0% +pendulum I could have done a one link + + + align:start position:0% +pendulum I could have done a one link +pendulum let's say I want to do + + align:start position:0% +pendulum let's say I want to do + + + align:start position:0% +pendulum let's say I want to do +something more clever maybe um let's + + align:start position:0% +something more clever maybe um let's + + + align:start position:0% +something more clever maybe um let's +invert gravity right let's just let's + + align:start position:0% +invert gravity right let's just let's + + + align:start position:0% +invert gravity right let's just let's +take my inverted pendulum problem and + + align:start position:0% +take my inverted pendulum problem and + + + align:start position:0% +take my inverted pendulum problem and +make it work by just replacing the + + align:start position:0% +make it work by just replacing the + + + align:start position:0% +make it work by just replacing the +Dynamics of my pendulum with an upside + + align:start position:0% +Dynamics of my pendulum with an upside + + + align:start position:0% +Dynamics of my pendulum with an upside +down pendulum right so maybe if I if I + + align:start position:0% +down pendulum right so maybe if I if I + + + align:start position:0% +down pendulum right so maybe if I if I +want to just get the pendulum to the top + + align:start position:0% +want to just get the pendulum to the top + + + align:start position:0% +want to just get the pendulum to the top +let's just make it act like an upside + + align:start position:0% +let's just make it act like an upside + + + align:start position:0% +let's just make it act like an upside +down pendulum okay so we can do that + + align:start position:0% + + + + align:start position:0% + +too + + align:start position:0% + + + + align:start position:0% + +right when I say it the way I'm saying + + align:start position:0% +right when I say it the way I'm saying + + + align:start position:0% +right when I say it the way I'm saying +it I hope it sounds sort of like you + + align:start position:0% +it I hope it sounds sort of like you + + + align:start position:0% +it I hope it sounds sort of like you +know of course if the system's feedback + + align:start position:0% +know of course if the system's feedback + + + align:start position:0% +know of course if the system's feedback +linearizable you can do whatever you + + align:start position:0% +linearizable you can do whatever you + + + align:start position:0% +linearizable you can do whatever you +want you know it's easy it's not worth + + align:start position:0% +want you know it's easy it's not worth + + + align:start position:0% +want you know it's easy it's not worth +thinking about these kind of things + + align:start position:0% +thinking about these kind of things + + + align:start position:0% +thinking about these kind of things +right I mean that's what I'm trying to + + align:start position:0% +right I mean that's what I'm trying to + + + align:start position:0% +right I mean that's what I'm trying to +communicate but but almost every cool + + align:start position:0% +communicate but but almost every cool + + + align:start position:0% +communicate but but almost every cool +robot that + + align:start position:0% +robot that + + + align:start position:0% +robot that +works you know works because of these + + align:start position:0% +works you know works because of these + + + align:start position:0% +works you know works because of these +kind of tricks right they're hidden + + align:start position:0% +kind of tricks right they're hidden + + + align:start position:0% +kind of tricks right they're hidden +they're but they're there right the + + align:start position:0% +they're but they're there right the + + + align:start position:0% +they're but they're there right the +reason a lot of the the the reason + + align:start position:0% +reason a lot of the the the reason + + + align:start position:0% +reason a lot of the the the reason +robotic arms work as well as they do is + + align:start position:0% +robotic arms work as well as they do is + + + align:start position:0% +robotic arms work as well as they do is +because you can do this okay now there's + + align:start position:0% +because you can do this okay now there's + + + align:start position:0% +because you can do this okay now there's +limits right you can only do this if you + + align:start position:0% +limits right you can only do this if you + + + align:start position:0% +limits right you can only do this if you +have unlimited + + align:start position:0% +have unlimited + + + align:start position:0% +have unlimited +torque right in practice a lot of + + align:start position:0% +torque right in practice a lot of + + + align:start position:0% +torque right in practice a lot of +robotic arms have almost unlimited + + align:start position:0% +robotic arms have almost unlimited + + + align:start position:0% +robotic arms have almost unlimited +torque to give right you got big + + align:start position:0% +torque to give right you got big + + + align:start position:0% +torque to give right you got big +gearboxes right + + align:start position:0% +gearboxes right + + + align:start position:0% +gearboxes right +uh you'd be surprised how how pervasive + + align:start position:0% +uh you'd be surprised how how pervasive + + + align:start position:0% +uh you'd be surprised how how pervasive +this idea is okay + + align:start position:0% +this idea is okay + + + align:start position:0% +this idea is okay +so um what this class is about is what + + align:start position:0% +so um what this class is about is what + + + align:start position:0% +so um what this class is about is what +happens if you can't do + + align:start position:0% + + + + align:start position:0% + +that all right so let's take our our two + + align:start position:0% +that all right so let's take our our two + + + align:start position:0% +that all right so let's take our our two +link arm how are we going to break it + + align:start position:0% +link arm how are we going to break it + + + align:start position:0% +link arm how are we going to break it +how are we going to make it so we can't + + align:start position:0% +how are we going to make it so we can't + + + align:start position:0% +how are we going to make it so we can't +do that + + align:start position:0% +do that + + + align:start position:0% +do that +anymore what's a more interesting + + align:start position:0% +anymore what's a more interesting + + + align:start position:0% +anymore what's a more interesting +problem M get get rid of a motor let's + + align:start position:0% +problem M get get rid of a motor let's + + + align:start position:0% +problem M get get rid of a motor let's +let's get rid of you know let's get rid + + align:start position:0% +let's get rid of you know let's get rid + + + align:start position:0% +let's get rid of you know let's get rid +of the shoulder motor that seems like an + + align:start position:0% +of the shoulder motor that seems like an + + + align:start position:0% +of the shoulder motor that seems like an +important one let's see what happens if + + align:start position:0% +important one let's see what happens if + + + align:start position:0% +important one let's see what happens if +we take rid of that right out of there + + align:start position:0% +we take rid of that right out of there + + + align:start position:0% +we take rid of that right out of there +okay so the equations of motion actually + + align:start position:0% +okay so the equations of motion actually + + + align:start position:0% +okay so the equations of motion actually +stay exactly the same except for now um + + align:start position:0% +stay exactly the same except for now um + + + align:start position:0% +stay exactly the same except for now um +B of Q is going to have to be smaller If + + align:start position:0% +B of Q is going to have to be smaller If + + + align:start position:0% +B of Q is going to have to be smaller If +U is now + + align:start position:0% + + + + align:start position:0% + +um If U is now just onedimensional + + align:start position:0% +um If U is now just onedimensional + + + align:start position:0% +um If U is now just onedimensional +right I got a single control + + align:start position:0% +right I got a single control + + + align:start position:0% +right I got a single control +input then B of Q + + align:start position:0% +input then B of Q + + + align:start position:0% +input then B of Q +is just going to be what + + align:start position:0% + + + + align:start position:0% + +size it's going to be uh it's got to get + + align:start position:0% +size it's going to be uh it's got to get + + + align:start position:0% +size it's going to be uh it's got to get +to a two-dimensional thing so it's going + + align:start position:0% +to a two-dimensional thing so it's going + + + align:start position:0% +to a two-dimensional thing so it's going +to be a 2X + + align:start position:0% +to be a 2X + + + align:start position:0% +to be a 2X +one + + align:start position:0% +one + + + align:start position:0% +one +right and let's say if I as I drew it + + align:start position:0% +right and let's say if I as I drew it + + + align:start position:0% +right and let's say if I as I drew it +that 2x1 it's going to have nothing to + + align:start position:0% +that 2x1 it's going to have nothing to + + + align:start position:0% +that 2x1 it's going to have nothing to +do to the shoulder motor if I assume the + + align:start position:0% +do to the shoulder motor if I assume the + + + align:start position:0% +do to the shoulder motor if I assume the +the first one is the the shoulder and + + align:start position:0% +the first one is the the shoulder and + + + align:start position:0% +the first one is the the shoulder and +it's going to have direct control of the + + align:start position:0% +it's going to have direct control of the + + + align:start position:0% +it's going to have direct control of the +elbow + + align:start position:0% + + + + align:start position:0% + +okay sudden that's it's a whole + + align:start position:0% +okay sudden that's it's a whole + + + align:start position:0% +okay sudden that's it's a whole +different game okay turns out you can + + align:start position:0% +different game okay turns out you can + + + align:start position:0% +different game okay turns out you can +still solve that problem I wasn't + + align:start position:0% +still solve that problem I wasn't + + + align:start position:0% +still solve that problem I wasn't +thinking of showing this but let + + align:start position:0% + + + + align:start position:0% + +me preview something to come quickly + + align:start position:0% + + + + align:start position:0% + +here this is exactly that that system + + align:start position:0% +here this is exactly that that system + + + align:start position:0% +here this is exactly that that system +it's a system we're going to talk about + + align:start position:0% +it's a system we're going to talk about + + + align:start position:0% +it's a system we're going to talk about +it's called the acrobot it's got inertia + + align:start position:0% +it's called the acrobot it's got inertia + + + align:start position:0% +it's called the acrobot it's got inertia +in the links instead of the the mass and + + align:start position:0% +in the links instead of the the mass and + + + align:start position:0% +in the links instead of the the mass and +if you take these computer science + + align:start position:0% +if you take these computer science + + + align:start position:0% +if you take these computer science +techniques I'm going to tell you about + + align:start position:0% +techniques I'm going to tell you about + + + align:start position:0% +techniques I'm going to tell you about +um then you can for instance find a + + align:start position:0% +um then you can for instance find a + + + align:start position:0% +um then you can for instance find a +solution for the torque at the elbow to + + align:start position:0% +solution for the torque at the elbow to + + + align:start position:0% +solution for the torque at the elbow to +try to make this thing go to the top + + align:start position:0% +try to make this thing go to the top + + + align:start position:0% +try to make this thing go to the top +okay if you think about it it's actually + + align:start position:0% +okay if you think about it it's actually + + + align:start position:0% +okay if you think about it it's actually +it's called the acrobot because it's + + align:start position:0% +it's called the acrobot because it's + + + align:start position:0% +it's called the acrobot because it's +like an acrobat on the high bar right + + align:start position:0% +like an acrobat on the high bar right + + + align:start position:0% +like an acrobat on the high bar right +where you don't have you know you can + + align:start position:0% +where you don't have you know you can + + + align:start position:0% +where you don't have you know you can +only give a little bit of torque at the + + align:start position:0% +only give a little bit of torque at the + + + align:start position:0% +only give a little bit of torque at the +wrist you can do a lot with your waist + + align:start position:0% +wrist you can do a lot with your waist + + + align:start position:0% +wrist you can do a lot with your waist +potentially with your so this if you do + + align:start position:0% +potentially with your so this if you do + + + align:start position:0% +potentially with your so this if you do +it a clever job you can actually pump up + + align:start position:0% +it a clever job you can actually pump up + + + align:start position:0% +it a clever job you can actually pump up +energy and swing up and get to the top + + align:start position:0% +energy and swing up and get to the top + + + align:start position:0% +energy and swing up and get to the top +okay but that's a lot harder problem + + align:start position:0% +okay but that's a lot harder problem + + + align:start position:0% +okay but that's a lot harder problem +right I can't write that down in a a + + align:start position:0% +right I can't write that down in a a + + + align:start position:0% +right I can't write that down in a a +single uh board here at 72 Point + + align:start position:0% +single uh board here at 72 Point + + + align:start position:0% +single uh board here at 72 Point +font but we're going to do that in in + + align:start position:0% +font but we're going to do that in in + + + align:start position:0% +font but we're going to do that in in +very very soon okay so + + align:start position:0% +very very soon okay so + + + align:start position:0% +very very soon okay so +um so I I hope you sort of know what + + align:start position:0% +um so I I hope you sort of know what + + + align:start position:0% +um so I I hope you sort of know what +underactuated means now + + align:start position:0% +underactuated means now + + + align:start position:0% +underactuated means now +um why would I care about a system + + align:start position:0% +um why would I care about a system + + + align:start position:0% +um why would I care about a system +that's missing its shoulder + + align:start position:0% +that's missing its shoulder + + + align:start position:0% +that's missing its shoulder +motor that seems pretty arbitrary if I'm + + align:start position:0% +motor that seems pretty arbitrary if I'm + + + align:start position:0% +motor that seems pretty arbitrary if I'm +building a robot I might as well order + + align:start position:0% +building a robot I might as well order + + + align:start position:0% +building a robot I might as well order +enough Motors to put them everywhere + + align:start position:0% +enough Motors to put them everywhere + + + align:start position:0% +enough Motors to put them everywhere +right turns out if you care about + + align:start position:0% +right turns out if you care about + + + align:start position:0% +right turns out if you care about +walking robots um the simplest one of + + align:start position:0% +walking robots um the simplest one of + + + align:start position:0% +walking robots um the simplest one of +the simplest models of a walking robot + + align:start position:0% +the simplest models of a walking robot + + + align:start position:0% +the simplest models of a walking robot +it's called the compass gate robot it's + + align:start position:0% +it's called the compass gate robot it's + + + align:start position:0% +it's called the compass gate robot it's +got a mass at the hip it's got two legs + + align:start position:0% +got a mass at the hip it's got two legs + + + align:start position:0% +got a mass at the hip it's got two legs +um we can even assume it's got a pin + + align:start position:0% +um we can even assume it's got a pin + + + align:start position:0% +um we can even assume it's got a pin +joint here that's the connection to the + + align:start position:0% +joint here that's the connection to the + + + align:start position:0% +joint here that's the connection to the +that's the foot on the ground um and + + align:start position:0% +that's the foot on the ground um and + + + align:start position:0% +that's the foot on the ground um and +it's got a torque to give here at the + + align:start position:0% +it's got a torque to give here at the + + + align:start position:0% +it's got a torque to give here at the +hip but it can't apply torque to the + + align:start position:0% +hip but it can't apply torque to the + + + align:start position:0% +hip but it can't apply torque to the +ground it's not because it's not an + + align:start position:0% +ground it's not because it's not an + + + align:start position:0% +ground it's not because it's not an +artificial if I had a foot + + align:start position:0% +artificial if I had a foot + + + align:start position:0% +artificial if I had a foot +then then suddenly my toe somewhere + + align:start position:0% +then then suddenly my toe somewhere + + + align:start position:0% +then then suddenly my toe somewhere +somewhere you're not bolted to the + + align:start position:0% +somewhere you're not bolted to the + + + align:start position:0% +somewhere you're not bolted to the +ground right so you've got a bunch of + + align:start position:0% +ground right so you've got a bunch of + + + align:start position:0% +ground right so you've got a bunch of +interesting links and you can control + + align:start position:0% +interesting links and you can control + + + align:start position:0% +interesting links and you can control +your your um you can you can apply + + align:start position:0% +your your um you can you can apply + + + align:start position:0% +your your um you can you can apply +torque between your links but the place + + align:start position:0% +torque between your links but the place + + + align:start position:0% +torque between your links but the place +where you might want it the most your + + align:start position:0% +where you might want it the most your + + + align:start position:0% +where you might want it the most your +shoulder motor your elbow motor whatever + + align:start position:0% +shoulder motor your elbow motor whatever + + + align:start position:0% +shoulder motor your elbow motor whatever +it is the place that connects you to the + + align:start position:0% +it is the place that connects you to the + + + align:start position:0% +it is the place that connects you to the +ground you don't have a a motor and you + + align:start position:0% +ground you don't have a a motor and you + + + align:start position:0% +ground you don't have a a motor and you +can't have a motor unless you're willing + + align:start position:0% +can't have a motor unless you're willing + + + align:start position:0% +can't have a motor unless you're willing +to stick yourself to the ground suction + + align:start position:0% +to stick yourself to the ground suction + + + align:start position:0% +to stick yourself to the ground suction +cups are a viable thing for walking + + align:start position:0% +cups are a viable thing for walking + + + align:start position:0% +cups are a viable thing for walking +robots I guess but + + align:start position:0% +robots I guess but + + + align:start position:0% +robots I guess but +um the more interesting problem is how + + align:start position:0% +um the more interesting problem is how + + + align:start position:0% +um the more interesting problem is how +do you do control if you don't have to + + align:start position:0% +do you do control if you don't have to + + + align:start position:0% +do you do control if you don't have to +be stuck to the ground okay so that two + + align:start position:0% +be stuck to the ground okay so that two + + + align:start position:0% +be stuck to the ground okay so that two +link uh simple Point Mass thing is + + align:start position:0% +link uh simple Point Mass thing is + + + align:start position:0% +link uh simple Point Mass thing is +actually exactly the Dynamics of the + + align:start position:0% +actually exactly the Dynamics of the + + + align:start position:0% +actually exactly the Dynamics of the +compass gate Walker that we'll talk + + align:start position:0% +compass gate Walker that we'll talk + + + align:start position:0% +compass gate Walker that we'll talk +about um fairly soon okay so I've got no + + align:start position:0% +about um fairly soon okay so I've got no + + + align:start position:0% +about um fairly soon okay so I've got no +torque here torque equals zero there + + align:start position:0% +torque here torque equals zero there + + + align:start position:0% +torque here torque equals zero there +okay every walking robot is + + align:start position:0% +okay every walking robot is + + + align:start position:0% +okay every walking robot is +underactuated um the same thing's true + + align:start position:0% +underactuated um the same thing's true + + + align:start position:0% +underactuated um the same thing's true +if if if I'm a u if I'm a you know a + + align:start position:0% +if if if I'm a u if I'm a you know a + + + align:start position:0% +if if if I'm a u if I'm a you know a +humanoid I'm trying to control all of my + + align:start position:0% +humanoid I'm trying to control all of my + + + align:start position:0% +humanoid I'm trying to control all of my +state variabl that's the question right + + align:start position:0% +state variabl that's the question right + + + align:start position:0% +state variabl that's the question right +can I do I have enough um Motors to to + + align:start position:0% +can I do I have enough um Motors to to + + + align:start position:0% +can I do I have enough um Motors to to +instantaneously affect every state + + align:start position:0% +instantaneously affect every state + + + align:start position:0% +instantaneously affect every state +variable that's the + + align:start position:0% +variable that's the + + + align:start position:0% +variable that's the +question um if you count the number of + + align:start position:0% +question um if you count the number of + + + align:start position:0% +question um if you count the number of +motors on me right it's a lot I know + + align:start position:0% +motors on me right it's a lot I know + + + align:start position:0% +motors on me right it's a lot I know +they might not be as strong as they used + + align:start position:0% +they might not be as strong as they used + + + align:start position:0% +they might not be as strong as they used +to be but they're they're there there's + + align:start position:0% +to be but they're they're there there's + + + align:start position:0% +to be but they're they're there there's +a lot of of them um if you count the + + align:start position:0% +a lot of of them um if you count the + + + align:start position:0% +a lot of of them um if you count the +number of degrees of freedom that's hard + + align:start position:0% +number of degrees of freedom that's hard + + + align:start position:0% +number of degrees of freedom that's hard +too but no matter what you count your + + align:start position:0% +too but no matter what you count your + + + align:start position:0% +too but no matter what you count your +tally adds up to if I + + align:start position:0% +tally adds up to if I + + + align:start position:0% +tally adds up to if I +jump uh when I'm up in the air I'm not + + align:start position:0% +jump uh when I'm up in the air I'm not + + + align:start position:0% +jump uh when I'm up in the air I'm not +going to do that for you but uh when I'm + + align:start position:0% +going to do that for you but uh when I'm + + + align:start position:0% +going to do that for you but uh when I'm +up in the air none of those Motors no + + align:start position:0% +up in the air none of those Motors no + + + align:start position:0% +up in the air none of those Motors no +matter what I do I can do something with + + align:start position:0% +matter what I do I can do something with + + + align:start position:0% +matter what I do I can do something with +my arms whatever ignoring aerodynamic + + align:start position:0% +my arms whatever ignoring aerodynamic + + + align:start position:0% +my arms whatever ignoring aerodynamic +forces none of those Motors are going to + + align:start position:0% +forces none of those Motors are going to + + + align:start position:0% +forces none of those Motors are going to +change the trajectory of my center of + + align:start position:0% +change the trajectory of my center of + + + align:start position:0% +change the trajectory of my center of +mass right there's nothing I can do to + + align:start position:0% +mass right there's nothing I can do to + + + align:start position:0% +mass right there's nothing I can do to +change the trajectory of my center of + + align:start position:0% +change the trajectory of my center of + + + align:start position:0% +change the trajectory of my center of +mass I can move relative to my center of + + align:start position:0% +mass I can move relative to my center of + + + align:start position:0% +mass I can move relative to my center of +mass change my angular momentum I cons + + align:start position:0% +mass change my angular momentum I cons + + + align:start position:0% +mass change my angular momentum I cons +my but I can I can move things around um + + align:start position:0% +my but I can I can move things around um + + + align:start position:0% +my but I can I can move things around um +but nothing I can do is going to move my + + align:start position:0% +but nothing I can do is going to move my + + + align:start position:0% +but nothing I can do is going to move my +center of mass right a walking robot a + + align:start position:0% +center of mass right a walking robot a + + + align:start position:0% +center of mass right a walking robot a +jumping robot for sure is underactuated + + align:start position:0% +jumping robot for sure is underactuated + + + align:start position:0% +jumping robot for sure is underactuated +okay a flying machine is underactuated + + align:start position:0% +okay a flying machine is underactuated + + + align:start position:0% +okay a flying machine is underactuated +okay you I mean fighter jets are a good + + align:start position:0% +okay you I mean fighter jets are a good + + + align:start position:0% +okay you I mean fighter jets are a good +example you can go that way pretty well + + align:start position:0% +example you can go that way pretty well + + + align:start position:0% +example you can go that way pretty well +you know they don't go backwards so well + + align:start position:0% +you know they don't go backwards so well + + + align:start position:0% +you know they don't go backwards so well +for instance right right they don't go + + align:start position:0% +for instance right right they don't go + + + align:start position:0% +for instance right right they don't go +directly up so well although I could + + align:start position:0% +directly up so well although I could + + + align:start position:0% +directly up so well although I could +show you videos of that kind of thing um + + align:start position:0% +show you videos of that kind of thing um + + + align:start position:0% +show you videos of that kind of thing um +right Birds you name it these systems + + align:start position:0% +right Birds you name it these systems + + + align:start position:0% +right Birds you name it these systems +tend to have control variables that that + + align:start position:0% +tend to have control variables that that + + + align:start position:0% +tend to have control variables that that +are not you're not in complete control + + align:start position:0% +are not you're not in complete control + + + align:start position:0% +are not you're not in complete control +of manipulation if I'm throwing this + + align:start position:0% +of manipulation if I'm throwing this + + + align:start position:0% +of manipulation if I'm throwing this +chalk around I don't have complete + + align:start position:0% +chalk around I don't have complete + + + align:start position:0% +chalk around I don't have complete +control of that chalk okay if I if I + + align:start position:0% +control of that chalk okay if I if I + + + align:start position:0% +control of that chalk okay if I if I +form a force closure with it then you + + align:start position:0% +form a force closure with it then you + + + align:start position:0% +form a force closure with it then you +could maybe start thinking I'm a I'm I'm + + align:start position:0% +could maybe start thinking I'm a I'm I'm + + + align:start position:0% +could maybe start thinking I'm a I'm I'm +a fully actuated system I can move this + + align:start position:0% +a fully actuated system I can move this + + + align:start position:0% +a fully actuated system I can move this +this thing around that's fine but I + + align:start position:0% +this thing around that's fine but I + + + align:start position:0% +this thing around that's fine but I +think the interesting part of + + align:start position:0% +think the interesting part of + + + align:start position:0% +think the interesting part of +manipulation is before you get that + + align:start position:0% +manipulation is before you get that + + + align:start position:0% +manipulation is before you get that +Force + + align:start position:0% +Force + + + align:start position:0% +Force +closure okay so every interesting + + align:start position:0% +closure okay so every interesting + + + align:start position:0% +closure okay so every interesting +problem in robotics is + + align:start position:0% +problem in robotics is + + + align:start position:0% +problem in robotics is +underactuated um + + align:start position:0% +underactuated um + + + align:start position:0% +underactuated um +I'm going to um give a quick um sketch + + align:start position:0% +I'm going to um give a quick um sketch + + + align:start position:0% +I'm going to um give a quick um sketch +of what the rest of the term has for you + + align:start position:0% +of what the rest of the term has for you + + + align:start position:0% +of what the rest of the term has for you +and then we're actually I'm going to try + + align:start position:0% +and then we're actually I'm going to try + + + align:start position:0% +and then we're actually I'm going to try +we're going to try something new um on + + align:start position:0% +we're going to try something new um on + + + align:start position:0% +we're going to try something new um on +the website so the website's going to + + align:start position:0% +the website so the website's going to + + + align:start position:0% +the website so the website's going to +contain everything after today it's + + align:start position:0% +contain everything after today it's + + + align:start position:0% +contain everything after today it's +we're a paper lless existence um the + + align:start position:0% +we're a paper lless existence um the + + + align:start position:0% +we're a paper lless existence um the +website will have your problem sets + + align:start position:0% +website will have your problem sets + + + align:start position:0% +website will have your problem sets +it'll have the lecture notes you can + + align:start position:0% +it'll have the lecture notes you can + + + align:start position:0% +it'll have the lecture notes you can +submit your problem sets on the website + + align:start position:0% +submit your problem sets on the website + + + align:start position:0% +submit your problem sets on the website +okay we're also going to try a new thing + + align:start position:0% +okay we're also going to try a new thing + + + align:start position:0% +okay we're also going to try a new thing +when I post the PDFs of the problem set + + align:start position:0% +when I post the PDFs of the problem set + + + align:start position:0% +when I post the PDFs of the problem set +um you'll be able to download them and + + align:start position:0% +um you'll be able to download them and + + + align:start position:0% +um you'll be able to download them and +print them out if you like um but you'll + + align:start position:0% +print them out if you like um but you'll + + + align:start position:0% +print them out if you like um but you'll +also be able to to to uh use this sort + + align:start position:0% +also be able to to to uh use this sort + + + align:start position:0% +also be able to to to uh use this sort +of interactive PDF viewer where people + + align:start position:0% +of interactive PDF viewer where people + + + align:start position:0% +of interactive PDF viewer where people +instead of having a forum or something + + align:start position:0% +instead of having a forum or something + + + align:start position:0% +instead of having a forum or something +on the on the website you could you + + align:start position:0% +on the on the website you could you + + + align:start position:0% +on the on the website you could you +could go right into the PDF and Mark say + + align:start position:0% +could go right into the PDF and Mark say + + + align:start position:0% +could go right into the PDF and Mark say +I don't understand what this means um + + align:start position:0% +I don't understand what this means um + + + align:start position:0% +I don't understand what this means um +you can choose whether it's Anonymous + + align:start position:0% +you can choose whether it's Anonymous + + + align:start position:0% +you can choose whether it's Anonymous +you can choose whether it's everybody + + align:start position:0% +you can choose whether it's everybody + + + align:start position:0% +you can choose whether it's everybody +knows who said it you can choose if it's + + align:start position:0% +knows who said it you can choose if it's + + + align:start position:0% +knows who said it you can choose if it's +just private um s just a minute we just + + align:start position:0% +just private um s just a minute we just + + + align:start position:0% +just private um s just a minute we just +s show so it's a demo of that um we'll + + align:start position:0% +s show so it's a demo of that um we'll + + + align:start position:0% +s show so it's a demo of that um we'll +see if it works and and uh it might be a + + align:start position:0% +see if it works and and uh it might be a + + + align:start position:0% +see if it works and and uh it might be a +cool way to to uh uh communicate outside + + align:start position:0% +cool way to to uh uh communicate outside + + + align:start position:0% +cool way to to uh uh communicate outside +of the the + + align:start position:0% +of the the + + + align:start position:0% +of the the +room but let me tell you let me forecast + + align:start position:0% +room but let me tell you let me forecast + + + align:start position:0% +room but let me tell you let me forecast +um what's what's coming here okay I + + align:start position:0% +um what's what's coming here okay I + + + align:start position:0% +um what's what's coming here okay I +haven't actually told you why this is a + + align:start position:0% +haven't actually told you why this is a + + + align:start position:0% +haven't actually told you why this is a +computer science class yet so I can't + + align:start position:0% +computer science class yet so I can't + + + align:start position:0% +computer science class yet so I can't +can't let you leave without that here's + + align:start position:0% +can't let you leave without that here's + + + align:start position:0% +can't let you leave without that here's +roughly what we're doing okay on on + + align:start position:0% +roughly what we're doing okay on on + + + align:start position:0% +roughly what we're doing okay on on +Thursday um we're going to talk about + + align:start position:0% +Thursday um we're going to talk about + + + align:start position:0% +Thursday um we're going to talk about +the simple pendulum right so I just we + + align:start position:0% +the simple pendulum right so I just we + + + align:start position:0% +the simple pendulum right so I just we +talked about a two link pendulum just + + align:start position:0% +talked about a two link pendulum just + + + align:start position:0% +talked about a two link pendulum just +now we're going to take a step backwards + + align:start position:0% +now we're going to take a step backwards + + + align:start position:0% +now we're going to take a step backwards +on Thursday we're going to talk about + + align:start position:0% +on Thursday we're going to talk about + + + align:start position:0% +on Thursday we're going to talk about +the Dynamics of a simple pendulum but + + align:start position:0% +the Dynamics of a simple pendulum but + + + align:start position:0% +the Dynamics of a simple pendulum but +we're going to talk about everything + + align:start position:0% +we're going to talk about everything + + + align:start position:0% +we're going to talk about everything +there is to know about the simple + + align:start position:0% +there is to know about the simple + + + align:start position:0% +there is to know about the simple +pendulum and we're going to really think + + align:start position:0% +pendulum and we're going to really think + + + align:start position:0% +pendulum and we're going to really think +about the nonlinear Dynamics and how to + + align:start position:0% +about the nonlinear Dynamics and how to + + + align:start position:0% +about the nonlinear Dynamics and how to +think about about that okay and then + + align:start position:0% +think about about that okay and then + + + align:start position:0% +think about about that okay and then +we're going to think about how to + + align:start position:0% +we're going to think about how to + + + align:start position:0% +we're going to think about how to +control that simple pendulum but as we + + align:start position:0% +control that simple pendulum but as we + + + align:start position:0% +control that simple pendulum but as we +go in the class we're going to get to + + align:start position:0% +go in the class we're going to get to + + + align:start position:0% +go in the class we're going to get to +more and more interesting systems okay + + align:start position:0% +more and more interesting systems okay + + + align:start position:0% +more and more interesting systems okay +um we're going to get to uh a cart pole + + align:start position:0% +um we're going to get to uh a cart pole + + + align:start position:0% +um we're going to get to uh a cart pole +system these are some of the model + + align:start position:0% +system these are some of the model + + + align:start position:0% +system these are some of the model +systems in uh um underactuated robotics + + align:start position:0% +systems in uh um underactuated robotics + + + align:start position:0% +systems in uh um underactuated robotics +we're going to get to the acrobot system + + align:start position:0% +we're going to get to the acrobot system + + + align:start position:0% +we're going to get to the acrobot system +I just showed you a two-link thing with + + align:start position:0% +I just showed you a two-link thing with + + + align:start position:0% +I just showed you a two-link thing with +a torque here and no torque there this + + align:start position:0% +a torque here and no torque there this + + + align:start position:0% +a torque here and no torque there this +one has a force here we're going to + + align:start position:0% +one has a force here we're going to + + + align:start position:0% +one has a force here we're going to +think about sort of the toy systems for + + align:start position:0% +think about sort of the toy systems for + + + align:start position:0% +think about sort of the toy systems for +underactuated robotics + + align:start position:0% +underactuated robotics + + + align:start position:0% +underactuated robotics +and then we're going to start + + align:start position:0% +and then we're going to start + + + align:start position:0% +and then we're going to start +splintering into + + align:start position:0% +splintering into + + + align:start position:0% +splintering into +um into different uh domains if we care + + align:start position:0% +um into different uh domains if we care + + + align:start position:0% +um into different uh domains if we care +about walking then we can start thinking + + align:start position:0% +about walking then we can start thinking + + + align:start position:0% +about walking then we can start thinking +about these sort of compass gate type + + align:start position:0% +about these sort of compass gate type + + + align:start position:0% +about these sort of compass gate type +robots and I'll we'll talk about more + + align:start position:0% +robots and I'll we'll talk about more + + + align:start position:0% +robots and I'll we'll talk about more +complicated robots and the key + + align:start position:0% +complicated robots and the key + + + align:start position:0% +complicated robots and the key +difference between here and here is just + + align:start position:0% +difference between here and here is just + + + align:start position:0% +difference between here and here is just +we added a few um extra degrees of + + align:start position:0% +we added a few um extra degrees of + + + align:start position:0% +we added a few um extra degrees of +freedom here to here the the + + align:start position:0% +freedom here to here the the + + + align:start position:0% +freedom here to here the the +dimensionality of walking robots isn't + + align:start position:0% +dimensionality of walking robots isn't + + + align:start position:0% +dimensionality of walking robots isn't +actually necessarily that high but what + + align:start position:0% +actually necessarily that high but what + + + align:start position:0% +actually necessarily that high but what +happens is you have to think about + + align:start position:0% +happens is you have to think about + + + align:start position:0% +happens is you have to think about +systems with impacts + + align:start position:0% + + + + align:start position:0% + +and you have to think about limit Cycles + + align:start position:0% +and you have to think about limit Cycles + + + align:start position:0% +and you have to think about limit Cycles +we'll we'll develop some of those + + align:start position:0% + + + + align:start position:0% + +tool okay and then we're going to think + + align:start position:0% +tool okay and then we're going to think + + + align:start position:0% +tool okay and then we're going to think +about how do you get away from these toy + + align:start position:0% +about how do you get away from these toy + + + align:start position:0% +about how do you get away from these toy +systems by making higher dimensional + + align:start position:0% +systems by making higher dimensional + + + align:start position:0% +systems by making higher dimensional +systems and it can sort of come from + + align:start position:0% +systems and it can sort of come from + + + align:start position:0% +systems and it can sort of come from +walking to we'll we'll have for instance + + align:start position:0% +walking to we'll we'll have for instance + + + align:start position:0% +walking to we'll we'll have for instance +you know multi-link + + align:start position:0% +you know multi-link + + + align:start position:0% +you know multi-link +robots Okay and think about how to + + align:start position:0% +robots Okay and think about how to + + + align:start position:0% +robots Okay and think about how to +control the higher dimensional systems + + align:start position:0% +control the higher dimensional systems + + + align:start position:0% +control the higher dimensional systems +more + + align:start position:0% +more + + + align:start position:0% +more +degrees of freedom d + + align:start position:0% +degrees of freedom d + + + align:start position:0% +degrees of freedom d +fs + + align:start position:0% +fs + + + align:start position:0% +fs +okay then we're going to think about + + align:start position:0% +okay then we're going to think about + + + align:start position:0% +okay then we're going to think about +what happens if I take these model + + align:start position:0% +what happens if I take these model + + + align:start position:0% +what happens if I take these model +systems and add some um uncertainty or + + align:start position:0% + + + + align:start position:0% + +stochasticity and so a toy example for + + align:start position:0% +stochasticity and so a toy example for + + + align:start position:0% +stochasticity and so a toy example for +that might be a walking robot walking on + + align:start position:0% +that might be a walking robot walking on + + + align:start position:0% +that might be a walking robot walking on +rough terrain let's + + align:start position:0% + + + + align:start position:0% + +say okay and then we're going to think + + align:start position:0% +say okay and then we're going to think + + + align:start position:0% +say okay and then we're going to think +about how to take these model systems + + align:start position:0% +about how to take these model systems + + + align:start position:0% +about how to take these model systems +and what happens if we don't know the + + align:start position:0% +and what happens if we don't know the + + + align:start position:0% +and what happens if we don't know the +model okay + + align:start position:0% + + + + align:start position:0% + +um and that's certainly the case if you + + align:start position:0% +um and that's certainly the case if you + + + align:start position:0% +um and that's certainly the case if you +got a A little perching airplane for + + align:start position:0% +got a A little perching airplane for + + + align:start position:0% +got a A little perching airplane for +instance or a a little robotic bird I + + align:start position:0% +instance or a a little robotic bird I + + + align:start position:0% +instance or a a little robotic bird I +have a two-year-old daughter and I've + + align:start position:0% +have a two-year-old daughter and I've + + + align:start position:0% +have a two-year-old daughter and I've +started being asked to cartoon + + align:start position:0% +started being asked to cartoon + + + align:start position:0% +started being asked to cartoon +everything I I say so um I'll subject + + align:start position:0% +everything I I say so um I'll subject + + + align:start position:0% +everything I I say so um I'll subject +you to some very bad but sort of quick + + align:start position:0% +you to some very bad but sort of quick + + + align:start position:0% +you to some very bad but sort of quick +cartoons + + align:start position:0% +cartoons + + + align:start position:0% +cartoons +um okay so that's the systems we're + + align:start position:0% +um okay so that's the systems we're + + + align:start position:0% +um okay so that's the systems we're +going to think about and the reasons + + align:start position:0% +going to think about and the reasons + + + align:start position:0% +going to think about and the reasons +that they're interesting turns out we're + + align:start position:0% +that they're interesting turns out we're + + + align:start position:0% +that they're interesting turns out we're +going to take a very computational + + align:start position:0% +going to take a very computational + + + align:start position:0% +going to take a very computational +approach to them okay so in this system + + align:start position:0% +approach to them okay so in this system + + + align:start position:0% +approach to them okay so in this system +we're going to start introducing optimal + + align:start position:0% + + + + align:start position:0% + +control we're going to say let's say I + + align:start position:0% +control we're going to say let's say I + + + align:start position:0% +control we're going to say let's say I +want to get the pendulum to the top but + + align:start position:0% +want to get the pendulum to the top but + + + align:start position:0% +want to get the pendulum to the top but +I want to do it for instance by + + align:start position:0% +I want to do it for instance by + + + align:start position:0% +I want to do it for instance by +minimizing energy or minimizing the time + + align:start position:0% +minimizing energy or minimizing the time + + + align:start position:0% +minimizing energy or minimizing the time +I get there so we're going to talk about + + align:start position:0% +I get there so we're going to talk about + + + align:start position:0% +I get there so we're going to talk about +optimal + + align:start position:0% + + + + align:start position:0% + +control and as much as we can we're + + align:start position:0% +control and as much as we can we're + + + align:start position:0% +control and as much as we can we're +going to talk about analytical optimal + + align:start position:0% + + + + align:start position:0% + +control but pretty quick we're going to + + align:start position:0% +control but pretty quick we're going to + + + align:start position:0% +control but pretty quick we're going to +run out of things we can do analytically + + align:start position:0% +run out of things we can do analytically + + + align:start position:0% +run out of things we can do analytically +and we're going to start looking at + + align:start position:0% +and we're going to start looking at + + + align:start position:0% +and we're going to start looking at +numerical optimal control computer + + align:start position:0% +numerical optimal control computer + + + align:start position:0% +numerical optimal control computer +science again + + align:start position:0% +science again + + + align:start position:0% +science again +um based on dynamic + + align:start position:0% + + + + align:start position:0% + +programming okay and that's going to get + + align:start position:0% +programming okay and that's going to get + + + align:start position:0% +programming okay and that's going to get +us + + align:start position:0% + + + + align:start position:0% + +somewhere when we start taking these + + align:start position:0% +somewhere when we start taking these + + + align:start position:0% +somewhere when we start taking these +slightly more interesting systems like + + align:start position:0% +slightly more interesting systems like + + + align:start position:0% +slightly more interesting systems like +this we're going to have to develop some + + align:start position:0% +this we're going to have to develop some + + + align:start position:0% +this we're going to have to develop some +some better + + align:start position:0% +some better + + + align:start position:0% +some better +tools + + align:start position:0% +tools + + + align:start position:0% +tools +we're going to do um numerical optimal + + align:start position:0% + + + + align:start position:0% + +control with something called policy + + align:start position:0% + + + + align:start position:0% + +search which is a combination of tools + + align:start position:0% +search which is a combination of tools + + + align:start position:0% +search which is a combination of tools +from reinforcement learning machine + + align:start position:0% +from reinforcement learning machine + + + align:start position:0% +from reinforcement learning machine +learning and numerical + + align:start position:0% + + + + align:start position:0% + +optimization okay + + align:start position:0% +optimization okay + + + align:start position:0% +optimization okay +we'll be able to do some of our impact + + align:start position:0% +we'll be able to do some of our impact + + + align:start position:0% +we'll be able to do some of our impact +modeling with that too I + + align:start position:0% +modeling with that too I + + + align:start position:0% +modeling with that too I +guess when we start getting into higher + + align:start position:0% +guess when we start getting into higher + + + align:start position:0% +guess when we start getting into higher +and higher dimensional systems we're + + align:start position:0% +and higher dimensional systems we're + + + align:start position:0% +and higher dimensional systems we're +going to have to give up on the + + align:start position:0% +going to have to give up on the + + + align:start position:0% +going to have to give up on the +opportunity to completely solve an + + align:start position:0% +opportunity to completely solve an + + + align:start position:0% +opportunity to completely solve an +optimal control problem numerically or + + align:start position:0% +optimal control problem numerically or + + + align:start position:0% +optimal control problem numerically or +analytically and we're going to start + + align:start position:0% +analytically and we're going to start + + + align:start position:0% +analytically and we're going to start +talking about approximate policy search + + align:start position:0% +talking about approximate policy search + + + align:start position:0% +talking about approximate policy search +and motion planning + + align:start position:0% +and motion planning + + + align:start position:0% +and motion planning +okay and I'm drawing it like this + + align:start position:0% +okay and I'm drawing it like this + + + align:start position:0% +okay and I'm drawing it like this +because I want you to see the that we're + + align:start position:0% +because I want you to see the that we're + + + align:start position:0% +because I want you to see the that we're +taking a very spiral course through the + + align:start position:0% +taking a very spiral course through the + + + align:start position:0% +taking a very spiral course through the +class we're going to develop tools that + + align:start position:0% +class we're going to develop tools that + + + align:start position:0% +class we're going to develop tools that +every time I develop a new tool we're + + align:start position:0% +every time I develop a new tool we're + + + align:start position:0% +every time I develop a new tool we're +going to make sure we understand what + + align:start position:0% +going to make sure we understand what + + + align:start position:0% +going to make sure we understand what +the heck they do to the pendulum the + + align:start position:0% +the heck they do to the pendulum the + + + align:start position:0% +the heck they do to the pendulum the +cart pole and things like that and work + + align:start position:0% +cart pole and things like that and work + + + align:start position:0% +cart pole and things like that and work +back up so we're going to cover motion + + align:start position:0% +back up so we're going to cover motion + + + align:start position:0% +back up so we're going to cover motion +planning if you know um randomized + + align:start position:0% +planning if you know um randomized + + + align:start position:0% +planning if you know um randomized +motion planning rrts feedback motion + + align:start position:0% +motion planning rrts feedback motion + + + align:start position:0% +motion planning rrts feedback motion +planning you're going to see that + + align:start position:0% + + + + align:start position:0% + +here okay and then when you get into the + + align:start position:0% +here okay and then when you get into the + + + align:start position:0% +here okay and then when you get into the +the really good stuff here when you got + + align:start position:0% +the really good stuff here when you got + + + align:start position:0% +the really good stuff here when you got +uncertainty stochasticity and unknown + + align:start position:0% +uncertainty stochasticity and unknown + + + align:start position:0% +uncertainty stochasticity and unknown +models that we're going to have to get + + align:start position:0% +models that we're going to have to get + + + align:start position:0% +models that we're going to have to get +into pure machine learning approaches + + align:start position:0% +into pure machine learning approaches + + + align:start position:0% +into pure machine learning approaches +some cases + + align:start position:0% +some cases + + + align:start position:0% +some cases +um that looks just like my yellow + + align:start position:0% + + + + align:start position:0% + +but control based on reinforcement + + align:start position:0% +but control based on reinforcement + + + align:start position:0% +but control based on reinforcement +learning for instance and that's how + + align:start position:0% +learning for instance and that's how + + + align:start position:0% +learning for instance and that's how +we're going to address some of these + + align:start position:0% +we're going to address some of these + + + align:start position:0% +we're going to address some of these +systems that are more + + align:start position:0% +systems that are more + + + align:start position:0% +systems that are more +complicated still + + align:start position:0% + + + + align:start position:0% + +okay so we're going to root everything + + align:start position:0% +okay so we're going to root everything + + + align:start position:0% +okay so we're going to root everything +in mechanical systems because that's + + align:start position:0% +in mechanical systems because that's + + + align:start position:0% +in mechanical systems because that's +what I care about I want things to move + + align:start position:0% +what I care about I want things to move + + + align:start position:0% +what I care about I want things to move +um but we're going to do it in a pretty + + align:start position:0% +um but we're going to do it in a pretty + + + align:start position:0% +um but we're going to do it in a pretty +computer sciency way okay because I + + align:start position:0% +computer sciency way okay because I + + + align:start position:0% +computer sciency way okay because I +think the computer scientists have + + align:start position:0% +think the computer scientists have + + + align:start position:0% +think the computer scientists have +turned a corner and are going to solve + + align:start position:0% +turned a corner and are going to solve + + + align:start position:0% +turned a corner and are going to solve +all these problems \ No newline at end of file diff --git a/ZEmvTidO7k4.txt b/ZEmvTidO7k4.txt new file mode 100644 index 0000000000000000000000000000000000000000..f82ba8bec24a1c0507af19c4c29d34705d6ac154 --- /dev/null +++ b/ZEmvTidO7k4.txt @@ -0,0 +1,3117 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: Good +afternoon, everybody. + +Let me just remind +you where we are. + +We're describing +interaction between + +the electromagnetic +field and atoms. + +And we had formulated +an exact approach + +using the time evolution +operators and diagrams. + +And well, I think +we understood what + +it means when atoms in +the ground state emit + +photons which are virtually +absorbed and all that. + +So we figured out what is +really inside this formalism + +and what are the processes. + +What we want to continue +discussing today + +is one problem which you +often have such approaches. + +And this is the +problem of resonance. + +If you have a +perturbative treatment, + +even if you carry +to infinite order, + +you have, formally, +divergences if you + +have resonant interaction. + +Because the ground +state and the photon + +has exactly the same energy +as the excited state. + +And that means if you write +down the perturbative expansion, + +you have a 0 in the denominator. + +You have a divergence. + +And I reminded you that +in a phenomenological way, + +you've seen that this +problem can be "fixed" + +by adding an imaginary +part to the energy level + +just saying, well, +the excited state + +couples by spontaneous emission +to the radiation field. + +And the level has [INAUDIBLE]. + +Well, but you know, sometimes +putting an imaginary part + +into Schrodinger's +equation means + +it's no longer unitary +time evolution. + +It has its problem. + +But anyway, we want to +now look deeper into it. + +I want to show you +what are the tools + +to treat those infinity +source divergences + +in a consistent and +a systematic way. + +And one hint how we have to +do it comes by simply taking + +this energy denominator and +expanding it in gamma, simply + +a Taylor expansion in gamma. + +And then, we realize +gamma is often + +calculated in second +order Fermi's golden rule. + +But since you have +here all orders n, + +that tells us that +doing something here + +probably means infinite orders +in a perturbation series. + +And that's what I want +to show you today. + +I want to show you that I +can go beyond this result. + +But I can reproduce +this result by going + +to infinite order in +perturbation theory. + +And it means to sum up an +infinite number of diagrams. + +Who of you have +actually seen those kind + +of diagrammatic +tricks and summation? + +A few, OK. + +So it's maybe nice +to see it again. + +But for those who +haven't seen it, + +welcome to the +magic of diagrams. + +I learned it from +those examples. + +And I really like it. + +It's a very elegant way +to combine equations + +with graphical manipulations. + +So that's our agenda for at +least the first part of today. + +And OK, we want to +understand the time + +evolution of this system. + +Our tool is a time +evolution operator. + +And at the end of +the class on Monday, + +I told you, well, +let's simplify things. + +Let's get rid of those +temporal integrations + +and multiple integrals by simply +doing a Fourier transform. + +Because a Fourier +transform turns an integral + +or convolution into a product. + +And so therefore, we introduced +the Fourier transform, + +or the Laplace transform, of +the time evolution operator. + +And this iterative equation +where we get the nth order + +by plugging the n +minus first order + +on the right hand side, +this iterative equation + +turns now into a simpler +algebraic iterative + +equation for the +Fourier transform. + +So this is now the starting +point for our discussion today. + +We want to calculate the Fourier +transform of the time evolution + +operator to infinite orders. + +So let me-- well, of course, +any questions before I continue? + +So unfortunately, [INAUDIBLE]. + +We should copy this equation. + +Because we need it. + +So OK, we want to +take this equation. + +And now we want to iterate it. + +So the resolving G +in 0's order is G0. + +Now plug G0 into the right +hand side of the equation, + +and you get the first +order, which is G0VG0. + +Now plug that into the end +of the iterative equation, + +and you get the second +order, G0VG0VG0. + +I think you've got the idea. + +It's almost like a +geometric series-- + +well, a geometric +series with operators. + +But this is already +sort of a hint. + +A geometric series can be summed +up to infinity rather easy. + +So we have to introduce +now the eigenfunctions + +of the unperturbed operator. + +So these are, let's say, the +ground state, excited state, + +next excited state of +your favorite atom. + +And they have +eigenenergies Ek-- nope. + +So if you are now expressing +the equation above in the basis + +kl-- so in other words, +this is an operator, + +and we want to know +the matrix element + +between eigenfunctions k and l. + +The other thing we +need is that G0. + +Remember the Fourier +transform-- and I + +gave you sort a mini +derivation here-- is just 1 + +over energy minus H. And if you +apply that now to the operator + +G0, so G0 is nothing +like-- is given by that. + +So therefore, if you +write now this equation + +as matrix elements, +the first part, the G0, + +gives us 1 minus +1 over Z minus Ek. + +And since we are diagonal +in H0, it's delta kl. + +And well, now you +see the structure + +if you sum over +intermediate states, + +or if you introduce +intermediate states. + +So this is how we +have to write it. + +So this is just writing +it down in basis function + +of the unperturbed operator H0. + +But now we can formulate the +problem we are encountering + +and we want to solve. + +Namely, we have the +problem with one state. + +Our problem is the +excited state b. + +And we have a +resonant excitation + +from the count state a. + +So this is a discrete eigenstate +of the unperturbed Hamiltonian + +with energy Eb. + +And therefore, we have terms, +and actually divergent terms, + +which are 1 over Z minus Eb. + +And just to make +the connection, this + +is sort of the description that +book Z is in the complex plane + +and can have imaginary values. + +Sometimes, scattering +and evolution equations + +are better formulated when you +do it in the complex plane. + +It doesn't really +matter for us here. + +Just remember, Z is the energy. + +And it is the initial energy. + +And the initial +energy is if it's + +a ground state and a resonant +photon, we have a problem. + +Because the denominator is 0. + +So in other words, for +resonant excitation, + +we are interested +in the case that Z + +is on the order of +this close to Eb. + +OK, so what we +want to do now is-- + +and this is the basic idea. + +By looking at this +formally, exact calculation, + +we say the difficult parts are +those where we have this energy + +denominator, which vanishes. + +The other parts are simple. + +They don't have any divergences. + +They are not resonant and such. + +So what we want to do +is now, in some way, + +we want to sort of +give special treatment, + +factor out the +problematic terms. + +And the rest is easy. + +And for the easy part, +which has no divergence, + +we can make any kind +of approximation + +we want without +altering the physics. + +But the resonant part, this +needs special attention. + +Because if I treat it +literally in those expressions, + +they don't make +sense mathematically. + +Because they cause infinities. + +I could continue to do it +completely algebraically. + +But because I think it's +just beautiful method, + +I want to look at this equation +and write it down in symbols. + +So we want to arrive at a +diagrammatic representation + +for this matrix element +of the resolvent Gbb. + +And I use symbols where the +circle means the interaction. + +The straight line stands for +the term which is problematic, + +which has resonant-- the +resonant interaction has + +the divergent denominator. + +And then, I'll use a dashed +line for all other terms, + +all other intermediate +states, where i is not b, + +and therefore there +is not a problem. + +It's not resonant. + +We don't have a divergence. + +So I'm just sort of-- you +see the structure of the sum. + +We sort of propagate here. + +We make a transition +from l to k. + +And then, we propagate here. + +So in this kind of order, +you start in this state, + +you have a vertex, you go to the +other state, you have a vertex, + +you go to the next +state, you have a vertex. + +This is how the system works. + +This is sort of what quantum +mechanics does for you. + +And what we're going to do is, +this is an algebraic equation. + +And now we want to order +them in the following way. + +We want to figure out +which of those expressions + +include this problematic term +exactly twice or three times + +or four times. + +So we regroup those infinite +sums, these algebraic terms, + +in such a way that +we say, OK, which + +one has the occurrence of +this once, twice, three times, + +four times? + +So we regroup the terms, and +then we see what we can do. + +Now, I've picked the +matrix element Gbb. + +So that means over +here and over here + +we start out in the state b. + +So if I write down +all terms which + +contain this +resonant term twice, + +well, we start with +a resonant term. + +And we have to end +with a resonant term, + +because we have +the matrix element + +Gbb, which I'm focusing now on. + +And so there can be one vertex. + +We can start with this term. + +And now we can do +something else in between. + +But we are not allowed to +go back to the state b. + +Because we are only +looking at terms + +where the solid +line appears twice. + +So therefore, this can only be +a dashed line, another state. + +We can go through two vertices. + +But it can only include +dashed lines in between. + +So let me use another +symbol for it. + +So we start with that state. + +We end with a state b. + +But in between, we can sort +of once, twice, three times + +go through other +intermediate states. + +But we never are allowed to +create another divergence. + +And this infinite +sum over all other + +states-- I don't know +how to calculate it yet. + +But I'll just call +it a square box. + +So in other words, what is +sort of in lowest order, + +the operator V, with these +other infinity terms, + +I symbolize that kind of much +more complicated vertex, which + +includes an infinite sum, by +a square and not by a circle. + +So diagrammatically-- +feel free to write it down + +mathematically. + +It's obvious how to do it. + +The square box is the circle +plus all terms like this. + +Let's go back to equations. + +We call this the +function Rb of Z. + +And what I've shown +in diagrams above + +is nothing else than the +circle Vbb, the matrix element + +of the interaction. + +But now we have +sums where we're not + +allowed to go through +the resonant state. + +We have to go from b to +an intermediate state. + +We propagate in the +intermediate state. + +And then, we have to go back. + +And it's clear how to +go to higher terms. + +So we've just defined +this function R + +by focusing on two occurrences +of the straight line. + +Well, let's look at +higher order terms. + +What happens when Z minus +Eb, the divergent term, + +comes to the power n? + +Well, we just dealt +with n equals 2. + +Let's now look at n equals 3. + +Colin. + +AUDIENCE: I'm trying +to find the definition. + +Is the box a T-matrix +or the S-matrix? + +What's the definition +of the [INAUDIBLE]. + +The S is-- + +PROFESSOR: No, the +T-matrix is actually + +the matrix, the relevant matrix, +of the time evolution operator. + +And if you factor out the delta +function for the energy shell, + +you get the S-matrix. + +But we're not talking about a +time evolution operator here. + +We're talking about +the Fourier transform. + +And we're looking at +the resolvent, which + +is the function G. And now, +we've introduced a function R. + +I actually tried to +look up-- I wanted + +to use the correct +word in class. + +I couldn't find the name. + +In the book, it's just +called the function R. + +So it is the function R. +And the function R turns out + +to be the kernel of the +resolvent G. But none of it + +is the S-matrix and T-matrix. + +It is related. + +Because if you do the inverse +Fourier transform from G, + +we go back to U. +And then, we have, + +I would say, the T-matrix. + +AUDIENCE: This is +the self energy? + +PROFESSOR: We will find that R +has a real and imaginary part. + +One is a self energy, +and the other one + +is a decay rate, has +an imaginary part. + +But the real part will +be the self energy. + +Yes, we connect a +lot of passwords + +you may have heard +here and there. + +OK, the question is, do +we have to now define + +pentagons and hexagons? + +Do we have to find +more and more symbols + +for more and more +complicated sums? + +But the nice thing is no. + +Because n equals 3 means we +have to start in state b. + +We have to stand in state b. + +And one time in +the time evolution, + +we can go through state b. + +And now, between that, we +can go from here to there + +with any combination +of states you want. + +But one thing is not allowed-- +to involve the state b. + +Because we are focusing on three +occurrences of the state b. + +And everything else +other than the state b + +has already a symbol. + +It is the square symbol. + +So this is the exact +representation for n equals 3. + +And the contribution +to the resolvent + +G, the Fourier transform of +the time evolution operator, + +is-- well, we have factored out +three occurrences of the state + +b. + +And then, we have three +occurrences of the state b. + +We need two square boxes. + +But the square box +has already a name + +and an algebraic definition. + +So this is nothing +else than-- I think + +it's called the +kernel Rb squared. + +OK, I've shown you n equals 2. + +I've shown you n equals 3. + +I assume it's now absolutely +clear how to continue. + +It just involves +more and more power. + +So the lowest order is that. + +And whenever we ask +what happens when + +we allow more appearances of +the state b, for each of them, + +we obtain another square box. + +So by looking at the +terms which are bothersome + +and regrouping +the infinite terms + +according to one occurrence, +two occurrence, three + +occurrence of this +divergent denominator, + +we have now found an exact +expression for Gb of Z. + +And since this is now +an algebraic equation + +with a geometric series, +we can write it exactly + +as this minus Rb of Z. + +Well, like with +every exact result, + +you have to ask, what +is the use for it? + +Because we started +out with U, which + +we couldn't calculate +with Fourier transform. + +We had G, which we +couldn't calculate. + +And now we've expressed G in +R, which of course we cannot + +calculate exactly. + +But there is an importance. + +We have made progress for +the following reasons. + +Namely, the first is that +those resonant terms, which + +appears in the time evolution +whenever the system goes back + +to the state b, is now +fully accounted for. + +We have sort of factored +those terms out. + +We've given them +special treatment. + +And therefore, and this is the +main result, the exposition + +which now is the non-trivial +expression, the function + +of the kernel, has +no divergences. + +And therefore, because there +is no critical part to it, + +rather simple +approximations can be made + +and lead to physically +meaningful results. + +That's an idea you may +see often in physics. + +You have a theory whether +it's something complicated, + +non-perturbative divergence. + +But you just rewrite the +theory, transform the equations + +in such a way that +structure of the equations + +now accounts for the +physics behind it. + +And the part which has +to be calculated now + +can be calculated with +crude approximation. + +And you still get the +correct physics out of it. + +The structure of the equation +accounts for the physics. + +And the numerical part +has become very harmless. + +But what it does is even if +you do now a lowest order + +approximation to +the function R, even + +those very simple +approximations correspond + +to an infinite number of terms +in the original expansion. + +Or in other words, the message +is, you have an expression. + +And if you do a perturbative +expansion-- well, + +maybe you should do some form +of perturbative expansion + +not to the whole expression. + +You should do it +to some denominator + +or to some part of +the denominator. + +Because then, the +perturbative expansion + +involves no divergent +terms and can be performed. + +So therefore, we are +now in a position + +to make approximations +to the function R. + +And the simplest +approximation which we can do + +is we can just try to +see if we can get away + +with very low order. + +It's maybe not getting +into any divergences here. + +And let me call this +now the triangle. + +So the circle was the +naked interaction. + +The square would be +the exact function + +if you sum up those +interactions to all orders. + +And the triangle is now, +well, the step in between. + +We hope to get away +with a triangle. + +So that would mean +the following, + +that the exact formulation +involved-- let me get black-- + +had a propagator. + +The state b has to go +through multiple squares. + +This is how it propagates. + +This would be the exact +result after the resummation + +we have done. + +And an approximate result +is now that the squares + +are replaced by triangles. + +So that's pretty neat. + +But the importance comes now +when I pull things together, + +I want to show you +what we have exactly + +done for treating an +atom in the excited state + +and for treating +light scattering. + +So in other words, +that's our result. + +We have derived it. + +I just go now and apply to +an excited atomic state. + +So the state we +are interested in + +is the atomic state +b and no photons. + +And the property +of the atomic state + +is obtained when we know +the function Gb of Z. + +Just to tell you what it means, +this is the time evolution + +operator when we +Fourier transform, + +an inverse Fourier or Laplace +transform, which is a contour + +integral in the complex plane, +a generalization of the Fourier + +transform. + +This would take us then +to the time evolution + +for the atom in state b. + +So this is now the diagram +matrix element of the T-matrix. + +And this is the matrix element +between state B0B0 and the time + +evolution operator. + +So we are calculating, +of course, + +the Fourier transform of the +time evolution of the state + +b by the Fourier transform +through the resolvent G. + +And all the work we have +done with our diagrams + +means instead of +calculating G, we + +are calculating the +kernel of Z. And if you + +use the lowest second +order approach, then + +diagrammatically-- just give me +one second, photon was emitted. + +Yeah, sorry, so the +process we have considered + +is that we go to second order. + +We can go through an +intermediate state, + +can say, absorbing it and +meeting a virtual photon. + +That's what two vertices mean. + +At the first vertex, +the photon appears. + +At the second vertex, +the photon disappears. + +So that means now that we, +with this approximation, + +approximate Gb of Z, the Fourier +transform, the resolvents, + +in the following way. + +We let b just propagate, +which is problematic + +because this has divergences. + +But we are allowing +now the state b + +to go through +intermediate states a. + +And remember, since this +appears in the denominator, that + +means for G, just make +a Taylor expansion in R, + +that it has this +process to all orders. + +So that propagator, the +sort of propagation G, + +involves now all +possibilities that we + +have to end up in state b again. + +But we can go through +intermediate states + +a or a prime as +often as we want. + +Or actually, we +have summed it up. + +Our results contain those +processes to infinite order. + +So the question is, +what have we neglected? + +I mean, that looks like a lot. + +We allow the state b to emit +a photon, go to another state. + +It's reabsorbed and such. + +So the question is +now, what is neglected? + +So what we neglect +is actually a lot. + +In this lowest order +approximation for the function + +R, we approximated +R by second order. + +We have only two vertices. + +So what we neglect +are all processes + +where we have not +just two vertices + +and one intermediate +states, where + +we have several intermediate +states between two + +occurrences of the state B0. + +Or diagrammatically, +what we have neglected + +is-- let me just +give you an example. + +So what we have neglected +is we have to always start + +with a state b, and we +have to end with a state b. + +But now the idea +was that-- one, two, + +let me just go +through four vertices. + +The approximation +we have done-- you + +have to sort of look through +that maybe after the lecture + +and see that that's +what we've really done, + +but trust me-- is that when the +system goes away from the state + +b into an intermediate +state a, at + +the next vertex it has to +go back to the state b. + +So what we have not +included is processes + +where we go through states +a, a prime, a double prime, + +and then eventually we +go back to the state a. + +Or we have not included +processes where we scatter, + +absorb. + +This is a state a. + +But then, we don't go back to b. + +We go to a prime. + +Then, we scatter again. + +Here we are in state +a double prime. + +And then, we are back in b. + +So in other words, we have said +whenever something happens, + +and we go away from +state b, the next vertex + +has to go back to state b. + +This is the nature of the +lowest order approximation. + +We have included +to infinite order + +all processes where the +state b emits a photon, + +reabsorbs it, emits +and reabsorbs it. + +But the system cannot go sort +of two steps away from the state + +b. + +It's only one step, +and then go back. + +This is the nature +of the approximation. + +OK, so our result +for this kernel, + +which describes the state b, +is we have-- just go back, + +let you see it again. + +I'm writing now for you down +the equation for the triangle, + +which is an interaction +V, an intermediate state, + +and another interaction V, which +is nothing else than Fermi's + +golden rule where we-- well, +with a little twist-- have + +the initial state. + +The dipole interaction or +the [? p.a ?] interaction + +takes us to an +intermediate state + +with a photon with [INAUDIBLE] +and polarization epsilon. + +We propagate in the +intermediate state Ea. + +And now we have to go back. + +But we have to go back with +the same matrix element. + +So therefore the matrix +element is squared. + +And we have a double sum. + +We sum over all possible +states of the photon. + +And we can sum over all +intermediate atomic states. + +Yes, so this is +what we have done. + +This expression has in general +a real part and imaginary part. + +It's a function of +the initial energy E. + +And it has an imaginary part. + +Yes, let me now +interpret it in two ways. + +But before I do that, +are there any questions? + +Yes. + +AUDIENCE: Just +mathematically, how do you + +get an imaginary +part out of this? + +It's all real +components, because we + +have magnitude squared +divided by, presumably, + +the energies real and so on. + +PROFESSOR: OK, this +is now something + +to do that we have +resonant terms. + +And what we often do is we +add an infinitesimal eta, + +and then let eta go to 0. + +And it's the same if you +have the function 1 over x. + +And look at a real part +and imaginary part. + +It needs a little bit +of correct treatment + +of functions in +the complex plane. + +Let me actually write it down. + +Then it becomes clear. + +But yes, thanks +for the question. + +So I always said, we +do a Fourier transform, + +but it's a Laplace transform. + +We do a Fourier +transform at real energy. + +But if you do an +integration along when + +you do the Fourier +transform, you + +have to integrate over omega. + +But the function we integrate, +the time evolution operator, + +has poles in omega. + +So we can't just +Fourier transform. + +Because we go right +through the poles. + +But what we can do is we can add +an imaginary part plus or minus + +eta. + +And we can just go +around the poles. + +And then, it becomes +mathematically meaningful. + +And what we're doing here +is-- but I'm not really + +explaining it +mathematically-- we + +have played those tricks here. + +But I hope it becomes +clear if I say + +what the real and +imaginary parts are. + +So the real part is +this matrix element + +squared, but double sum. + +But what we use is the +principle part of it, + +which is well defined in the +theory of complex functions. + +And it's divergent, but you +take a certain symmetric + +limiting procedure. + +So you have to +interpret that as-- you + +have to introduce a limiting +procedure to make sure + +that the divergence cancels out. + +And the imaginary part, value of +the imaginary part of something + +which diverges-- and if you +treat the eta correctly, + +let the eta go to 0, you will +realize that the imaginary part + +turns into a delta function. + +So what we get is +2pi over H bar matrix + +element squared times +the delta function. + +So that's something +which you have seen. + +So the imaginary part gets +us Fermi's golden rule. + +And the real part has +actually-- remember + +when we discussed +the AC Stark shift. + +The AC Stark shift has a 1 +over [INAUDIBLE] dependence. + +And you recognize that here. + +So this is actually nothing +else than the AC Stark + +shift not due to a laser beam, +but due to one photon per mode. + +Because we started with an +atom in an excited state. + +It can emit a +photon in any mode. + +And this photon is now +creating an AC Stark shift. + +And this is mathematically +the expression. + +And such AC Stark shifts +which appear as self energies, + +as energy shifts created +by the state, this + +is nothing else than +the famous Lamb shift. + +So that's what we get out here. + +I have already-- +do I in this sum? + +What we have here is +we have this function R + +in the real and imaginary part, +which depends on the energy E. + +But remember, we worked so +hard with diagrams to make sure + +that the triangle-- first the +square, and then the triangle, + +and this is what +we calculate here-- + +has no resonant structure +at the energy Eb. + +So therefore, we can neglect +the energy dependence of that + +and simply replace the +argument E by the energy + +we are interested in, +namely energies close to Eb. + +So in other words, when we had +the function, the resolvent Gb + +of Z, all the dependence on +energy came from this kernel. + +But this kernel is now +so well-behaved, there + +are no resonant terms, that +we can neglect its energy + +dependence. + +This actually has a name +which we will encounter later + +when we discuss master equation +and optical Bloch equations. + +So this replace, neglect +E and set, or replace + +the dependence by E, +by taking the value + +at Eb, this corresponds to +the Markov approximation. + +The Markov approximation +often means + +that some relaxation time +or some response of a system + +is replaced by delta function. + +Well, we've done the same here. + +Because if you replace some +temporal response function + +by a delta function, that +means the Fourier transform + +becomes constant. + +And by neglecting the +energy dependence, + +we are now saying everything +is constant as a function + +of energy. + +And that means in +the temporal domain + +that we have a delta function. + +I don't want to go further here. + +But when we talk about +the master equation, + +we will also make a +Markov approximation + +later on, but then in +the temporal domain. + +And the two are equivalent here. + +So what we've got +now is we found + +a solution for the Fourier +transform of the time evolution + +operator, which initially +had a divergence at energy b. + +And this was the +problem we are facing. + +But by now, calculating +the function R, + +we have a correction, which +is a radiative shift, which + +comes from the real part. + +And we obtained, as +promised, the imaginary part, + +which we can approximate +by Fermi's golden rule. + +If we now Fourier transform back +and obtain the time evolution + +of this state, it no longer +evolves with the energy Eb. + +It has a shifted energy +by this self energy. + +And this is called +the radiative shift. + +But in addition, because +of the imaginary part, + +it has now an exponential decay. + +And you should now-- well, this +is what we may have expected. + +But there are two +things you should learn. + +The first thing is that +the exponential decay + +would be different if we had not +made the Markov approximation. + +If we had kept a dependence of +this imaginary part on energy, + +the Fourier transform +would not have simply + +given us an exponential. + +So therefore, the +exponential decay + +involves an approximation +that the R function + +has no energy dependence. + +And you would say, well, +is that really possible? + +If you have an +atom, and it decays, + +or you have the atom in state +b, at very, very short times + +you need Fourier +transform elements + +of large amounts of energy. + +So maybe for the first +femtosecond for the time + +evolution of an excited +state, you need whatever, + +a whole X-ray +spectrum of energies. + +And it's obvious that the +properties of this expression + +where you sum over +all states, something + +will happen when you go +past the normal excitation + +energy or the ionization +energy of the atom. + +So what you can +immediately read form here + +is that exponential decay +is a simple approximation. + +It works very well. + +But at very early times, +it will break down. + +Because then, the energy +dependence matters. + +But the longer you wait-- if +you wait a few nanoseconds, + +the Fourier transform, the +relevant part of the Fourier + +transform, is only a small +energy or frequency interval + +around the resonance energy. + +And then, the density of +states of your photon field + +is pretty much +constant around here. + +And then, this +approximation is excellent. + +So I hope what you have +learned from the treatment + +is number one, where the +exponential decay comes from. + +Of course you knew that +from coupling to all modes, + +but that the approximation +which leads to exponential decay + +would also involve +the density of states + +and the density of +modes is constant, + +which is excellent +for certain times + +but which is of course +violated at early times. + +And finally, if we hadn't +done the infinite summation + +of diagrams, if we had done +a perturbative expansion, + +we would have never +obtained exponential decay. + +We would have obtained +some polynominal decay. + +Questions about that? + +Yes. + +AUDIENCE: What is the +polynominal decay? + +PROFESSOR: Some power law. + +1 minus the time-- +as far as I know, + +it would just +involve powers of n. + +If you do lowest order +perturbation theory, + +instead of getting +an exponential decay, + +you would just get +a linear slope. + +That's perturbation theory. + +And if you fix it, I think +you get quadratic terms. + +So it's the sum of power loss. + +Of course, an +exponential function + +has a Taylor expansion, +which is an infinite sum + +of polynominal terms. + +And therefore, we need infinite +order to get the exponential. + +So it's not really +profound what I'm saying. + +It's pretty much an exponential +function is non-perturbative. + +Other questions? + +So let me wrap up this chapter. + +What we have discussed +here is-- I haven't really + +discussed resonant scattering. + +I've now focused +on the function Gb. + +I focused on what +happens to the state b. + +But this is-- and this is +what I want to show you now-- + +the only element we need to +discuss resonant scattering. + +So when we have an atom +in the ground state, + +and a photon comes along, and +it takes the atom to the excited + +state b, then we go +back to the same state-- + +could be also another state-- +by emitting a photon k + +prime epsilon prime. + +And the relevant matrix element +of the time evolution operator, + +which is the T-matrix, involves +now the matrix element, + +the initial energy minus +the intermediate energy. + +And the critical +part is really-- + +you can do it mathematically. + +I just show it +here as a summary. + +The critical part is really +the propagation of the state + +b, which is problematic. + +But we have now learned, +and it transfers exactly + +to the light scattering +problem, that we + +have to include now radiative +shifts and an imaginary part + +for the decay to +the time evolution. + +And that means that this diagram +here for light scattering + +has been-- we have +added other terms to it. + +And the other terms +are, of course, + +that when we scatter light of +an excited state like this, + +the excited state can sort of +emit photons and reabsorb them. + +And it can do that to-- +so we go to that state. + +It can do that to +infinite order. + +So in other words, +for any problem now + +which involves +the excited state, + +we replace the 0's order +propagation of the state b. + +And mathematically, it means +we replace this function + +by the resolvent, which +we have calculated + +by doing an approximation +to the kernel R. Questions? + +AUDIENCE: Question, [INAUDIBLE]? + +PROFESSOR: Pardon? + +AUDIENCE: Is this [INAUDIBLE]? + +PROFESSOR: Yeah, +OK, what happens + +is if you're off-resonant, +you don't have a problem. + +This extra term delta and +gamma, the radiative shift + +and the line widths +only matter when + +the black term is close to 0. + +If you have a large +detuning delta here, + +then the small shift in the +line widths don't matter. + +So everything we have +done by correcting + +the naked propagation +of the state + +b by the correct propagation +with this infinite emission + +and reabsorption +of virtual photons, + +this is only needed if +the denominator is 0. + +And then, we have to figure +out what else happens. + +And what else +happens is obtained + +in higher order with this +non-perturbative treatment. + +Other questions? + +OK, 20 minutes left. + +So we now change gears. + +We move onto the +optical Bloch equation. + +But let me give you one summary +on this chapter of diagrams. + +Until maybe 10, 15 +years ago here at MIT, + +we were not teaching that. + +And I felt often in +discussion with students + +that a little bit more of a +complete picture behind atom + +photon processes is needed. + +What I summarized could of +course cover a whole semester + +course in QED and how +to do calculation. + +And if you're interested +in mathematical rigor, + +the green book, +Atom-Photon Interactions, + +is pretty rigorous and +still very physical. + +But on the other +hand, many of you + +experimentalists, +I think you should + +have sort of this picture +behind it, what really happens, + +what kind of emission +processes are + +responsible for which effect. + +And at least this +is sort of for me + +a take-home message which +I hope you can enjoy even + +without mathematical rigor, +that the fact that the excited + +state has [INAUDIBLE] really +comes from an infinite number + +of absorption, of emission +and reabsorption processes. + +So you should maybe +think about when + +you take an atom to +the excited state + +that the excited state does more +than just absorb the photon, + +the atom is excited, +and then it emits. + +The real nature of +this state is that it + +couples to many, many modes. + +It emits photons +and reabsorbs them. + +And you can often neglect +that in the simple description + +of your experiment. + +But if you take certain +expressions seriously, + +they would have divergences. + +And that's what we discussed +without this infinite number + +of processes which happen. + +Of course, yes, the whole +other regime which I should + +mention-- and this is +when you can completely + +neglect the coupling +to many modes. + +If you do Rabi oscillation +with resonant interaction, + +you don't need all that. + +Because then, you're really +looking at discrete states. + +So it really also depends +what you want to describe. + +If you do cavity +QED with an atom, + +you have the +Jaynes-Cummings model. + +And you have an exact solution. + +Then you have a +similar mode problem. + +But here we have +discussed what happens + +if you want to scatter +light in free space. + +And then, you have to deal with +the divergence of the excited + +state. + +OK, the next chapter is called +Derivation of the Optical Bloch + +Equation. + +And yes, what we really need +for a number of phenomenon + +in AMO physics for laser +cooling, light forces, and much + +more are the optical +Bloch equations. + +But what I try in this +chapter-- to give you + +sort of the fundamental +story, the profound story, + +the fundamental insight behind +the optical Bloch equations. + +Because what the optical Bloch +equations are is the following. + +We want to describe +a quantum system. + +But the quantum system is +coupled to the environment. + +And that means we +have dissipation. + +And this is something +which is not easily dealt + +with in simple quantum physics. + +Because a simply quantum +system undergoes unitary time + +evolution described +by a Hamiltonian. + +And unitary time evolution does +not allow entropy to increase, + +does not allow energies +to be exchanged. + +So a lot of things which +happen in our experiments + +and in daily life come because +the system we are looking at, + +it follows +Schrodinger's equation. + +But it is coupled to +a much bigger system. + +And so in this +section, what I want + +to address at the most +fundamental limit is, what + +is the step where we go +from reversible equation, + +unitary time evolution, to +something which is called + +relaxation, which +is dissipative, + +where entropy is increased? + +And the step, of course, +is we go from pure states + +to statistical operators. + +We describe the big system. + +But then, we focus +on the small system. + +And I want to show you, +first with a simple example, + +but next week in +more generality, + +how this completely +changes the nature + +of the description +of the small system. + +A small system which +I just described + +by Schrodinger's equation, +now follows the density matrix + +equation, has relaxation, the +entropy increases, and such. + +So to maybe set the stage, +one of the simplest systems + +we can imagine is the +Jaynes-Cummings model, + +that we have an atom +in a cavity interacting + +with one mode of +the radiation field. + +And in this cause in part +one, we've dealt with it + +and looked at vacuum Robi +oscillation and a few really + +neat things. + +But what happens is that the +system is an open quantum + +system. + +You can have +spontaneous emission. + +And if your mirrors are +not 100.00% reflectivity, + +some light leaks out. + +So in other words, we have +coupling to the environment. + +Of course, we can say +we simply describe it. + +We have our atoms, +maybe the one mode + +plus the one mode of the +electromagnetic field. + +And then, we have +the environment, + +which may consist of photons +which are leaking out + +and photons which are +spontaneously emitted. + +So this is our system. + +And of course, if you write +down the total Hamiltonian + +and do the time +evolution, something + +will come out which, +in general, is + +very complicated, +very entangled. + +The atom is entangled. + +The atom moving to +the left side is + +entangled with a photon which +was emitted to the right side. + +And the recall of the +photons push the atom. + +So you have to know, to keep +track of all the photons, which + +have been scattered in +the lifetime of an atom. + +So you can do that. + +And you do that by +propagating the system + +with its total Hamiltonian. + +But often, what +we do is we simply + +put the photons in a trash can. + +We trash them. + +We're not interested in +what the photons are doing. + +We're not keeping track of them. + +Actually, they hit the +wall of our vacuum chamber, + +and we couldn't even +keep track of them. + +The vacuum chamber has +taken care of them. + +So all that we are +interested in-- how do we now + +describe the atomic system? + +What, after the time +evolution, is now + +the density matrix +of the system? + +Of course, if we use +the full description, + +we know the initial +state of the environment. + +We know the initial +state or our system. + +We propagate it exactly with +the correct time evolution, + +we get everything. + +And then, we could reduce +by doing a partial trace. + +We could reduce the description. + +What is now the +probabilistic description + +for density matrix of the atom? + +But this is rather complicated. + +What we want to do is we want +to do it as a derivation. + +But in the end, we want to +have a formulation which simply + +tells us, what is +the atomic density + +matrix as a function of the +initial atomic density matrix? + +So in other words, all that +happens with the environment-- + +that there's initial state, +that it gets entangled, + +and then we neglect maybe not +keeping track of the photons-- + +we're not interested +in all of that. + +We really want to focus on +what happens to the atom. + +How does an initial +state of the atom + +propagate into a final state? + +And this is done by +optical Bloch equations. + +This is done by the +master equation. + +So the master +equation, you can see, + +focuses on the relevant part +of the system, maybe just + +a single atom. + +And we can neglect +the million photons + +which have been emitted. + +But those million +photons which have + +been emitted into +the environment, + +they change, of course. + +They change this density +matrix of the atom. + +And if you find a description, +the master equation + +is including with extra terms +what those photons have done. + +Maybe this sounds very abstract. + +But in the end, you will +find that maybe photons which + +emitted produce some damping. + +Or if you put atoms in +molasses, the atomic motion + +comes to a standstill. + +So in other words, +we want to develop + +a systematic approximation +scheme for the master equation + +whether effect of all these +many, many degrees of freedom + +can maybe be simply expressed +by a few damping terms. + +So that's the idea. + +So yes, you know already one +example of a master equation. + +And these are Einstein's +rate equations, + +which we have discussed in +the first part of the course. + +If you have a two +level system which + +is coupled to the +radiation field, + +then we obtained +equations that the rate + +of change of the +ground state population + +is related to the +excited state population + +through spontaneous emission +described by the Einstein e + +coefficient. + +And if you have a +spectral density + +of the electromagnetic field, +it causes stimulated emission. + +And it causes absorption +described by the Einstein b + +coefficient. + +And you have a similar +equation for the excited state. + +So this is clearly the +semi-classical limit + +of what we want to accomplish. + +But we want to know more. + +We really want to +know not just, what + +is the rate equation +for the atom? + +We want to know, you can +see, the wave function. + +Well, wave function slash +statistical operator-- + +the statistical +operator contains + +all information of +the wave function. + +And if the wave function +is a pure state, + +it has a certain +statistical operator. + +And we can find the pure state. + +So that's what we want to do. + +But sort of just +genetically, we really + +want to find the full +quantum time evolution. + +And now I just want +to express that. + +We have to be careful. + +The time evolution +as a Hamiltonian, + +if you now bring +in the environment, + +cannot be simply included +by adding an imaginary term. + +This here violates the +unitary time evolution. + +In other words, when we find +an equation for the quantum + +system, how it evolves, +it's not that everything + +you think which +phenomenologically works will + +work. + +It has to be consistent with +the loss of quantum physics. + +In other words, when we find an +equation for the statistical-- + +if you find an equation which +describes the atomic system, + +it will be a requirement +that a density matrix + +turns into a density matrix. + +So certain structure +has to be obeyed. + +And that is actually +extremely restrictive. + +And our derivation of +the master equation + +will actually show what +kind of operators applied + +to the atomic density +matrix are consistent, are + +quantum mechanically consistent. + +This is actually +something-- well, + +we're not doing a lot of +equations or work today, + +so let me rather be +a little bit chatty. + +This is actually something which +is the frontier of our field, + +both in theory in ion traps +and with neutral atoms, + +that we have some evolution +of an atomic system + +by coupling it to +the environment. + +Well, the usual environment +you can think of + +is just taking photons away. + +It gives us a damping +term of the excited state. + +But now you can +ask the question, + +can you construct +an environment which + +has some degrees of freedom +with laser fields, RF + +fields, and such? + +You call it the environment, +and this environment + +does something really fancy. + +And the system +comes in equilibrium + +with the environment. + +But could you engineer +the environment + +that the system comes +into equilibrium + +with the environment, and +it is in a fancy super fluid + +or fancy entangled state? + +So can you engineer the +environment in such a way + +that it does something +really fancy to your system? + +Well, you can dream of it. + +But you dreams are restricted +by the mathematical structure + +of all possible master +equations in the world. + +Because the environment +cannot do everything for you. + +The environment +can only do for you + +what can come out of all +possible Hamiltonians. + +And the fact that +the total system + +evolves in a unitary way +with the total Hamiltonian + +of the system, this +is really restricting. + +This operator sort of stands for +all possible master equations. + +It's restricting +the master equation + +for your atomic density matrix. + +There was just-- I +think was it this year + +or last year-- a nice +science and nature paper + +by [INAUDIBLE] where +they engineered + +the environment around +ions in an ion trap. + +And that stabilized +the ion in the state, + +which was an unusual state, +not what the normal environment + +would have done. + +So anyway, what +I will be telling + +you is also sort of +relevant to understand + +this sort of frontier +in our field which + +is called environment +engineering. + +OK, density matrix-- +good, five more minutes. + +So what we have is +we have a system. + +And we have this environment. + +And what we are exchanging +with the environment + +is both energy, +but also entropy. + +And so when we transfer +energy or heat, + +there is a corresponding +change in energy. + +And it's a general property +of all quantum systems. + +It's a consequence of the +fluctuation dissipation + +principle, the fluctuation +dissipation theorem, + +that you cannot have any form +of relaxation without noise. + +So for instance, when we +discuss optical molasses-- + +we do that in a few weeks, where +the atomic motion is damped-- + +well, you have a damping term. + +It seems it brings some +motion through friction + +to a standstill. + +But we know by +general principles + +that damping is not +possible without noise. + +So when somebody sells you a +wonderful damping scheme which + +damps the motion, you +should always ask, + +but there must be noise. + +What is the ultimate noise? + +And it's fundamental +that it is there. + +So therefore, our derivation +of the master equation + +will also display +that, that we do not + +get any form of damping without +at least the fundamental + +quantum noise. + +So what we need is we need +a description of the quantum + +noise, which comes from +coupling to the environment. + +The tool which we use for +that is the density matrix. + +I assume everybody here is +familiar with the density + +matrix. + +The atomic lecture +notes on the wiki + +have a small tutorial +on the density matrix + +if you want to freshen up your +knowledge about density matrix, + +maybe read about it. + +I don't want to +cover it in class. + +The one thing we need, and +I just want to remind you, + +is for all density matrices, +you can always unravel it. + +The density matrix +can be written + +as a probabilistic +sum over states. + +This will actually +play a major role. + +We will make certain +models for damping. + +And it's really beautiful. + +On Monday, I will give you +the beam splitter model + +for the optical Bloch equation. + +I really like it. + +Because it's a +microscopic model. + +And it shows you a lot of +fundamental principles. + +But the important +part is whenever + +we have a way to construct +a density matrix by saying, + +we have certain +quantum states k, + +and we just add them +up probabilistically, + +this kind of microscopic +interpretation of the density + +matrix is called unravelling. + +It's sort of writing it +as a specific diagonal sum + +over states. + +But those unravellings +are not unique. + +They describe one possibility. + +But there are other +possibilities. + +And the one example +which I can give you + +is that if you have a +density matrix like this, + +you can write the density +matrix as this form suggests, + +as a probabilistic sum of +being in the state 0, 0, + +or in the state 1, 1 with +probability 1/4 and 3/4. + +But you can also write it as +being with equal probability + +in two states a and b +where the states a and b + +are superpositions +of state 0 and 1. + +And you can see by inspection +that this will do the trick. + +So we'll talk a lot about +unravelling of the density + +matrix. + +That's why I want +to say up front, + +that the same density +matrix can be thought + +of as being created by +different processes. + +But this actually makes +it even more powerful. + +Because we have a unified +description, or even + +an identical description, +for different microscopic + +processes. + +OK, any last questions? + +Well then, let's enjoy the open +house with incoming graduate + +students, and I'll +see you on Monday. \ No newline at end of file diff --git a/ZEsk64C0fJg.txt b/ZEsk64C0fJg.txt new file mode 100644 index 0000000000000000000000000000000000000000..029b20159c23729c2301d8a65782720220279c10 --- /dev/null +++ b/ZEsk64C0fJg.txt @@ -0,0 +1,1619 @@ +align:start position:0% + +trees are about the most basic data + + align:start position:0% +trees are about the most basic data + + + align:start position:0% +trees are about the most basic data +structure uh that you're ever going to + + align:start position:0% +structure uh that you're ever going to + + + align:start position:0% +structure uh that you're ever going to +come across they're they pervade + + align:start position:0% +come across they're they pervade + + + align:start position:0% +come across they're they pervade +computer science and other subjects so + + align:start position:0% +computer science and other subjects so + + + align:start position:0% +computer science and other subjects so +let's talk about them and the simplest + + align:start position:0% +let's talk about them and the simplest + + + align:start position:0% +let's talk about them and the simplest +definition of a tree is that a tree is a + + align:start position:0% +definition of a tree is that a tree is a + + + align:start position:0% +definition of a tree is that a tree is a +connected graph with no Cycles in this + + align:start position:0% +connected graph with no Cycles in this + + + align:start position:0% +connected graph with no Cycles in this +setting we're talking about simple + + align:start position:0% +setting we're talking about simple + + + align:start position:0% +setting we're talking about simple +graphs and trees with undirected edges + + align:start position:0% +graphs and trees with undirected edges + + + align:start position:0% +graphs and trees with undirected edges +um well in order to make sense out that + + align:start position:0% +um well in order to make sense out that + + + align:start position:0% +um well in order to make sense out that +we better have a definition of a cycle + + align:start position:0% +we better have a definition of a cycle + + + align:start position:0% +we better have a definition of a cycle +there's a picture of a typical tree um + + align:start position:0% +there's a picture of a typical tree um + + + align:start position:0% +there's a picture of a typical tree um +but to be precise what's a cycle in a + + align:start position:0% +but to be precise what's a cycle in a + + + align:start position:0% +but to be precise what's a cycle in a +simple graph well it's a closed walk of + + align:start position:0% +simple graph well it's a closed walk of + + + align:start position:0% +simple graph well it's a closed walk of +length greater than two that doesn't + + align:start position:0% +length greater than two that doesn't + + + align:start position:0% +length greater than two that doesn't +cross itself so the not Crossing itself + + align:start position:0% +cross itself so the not Crossing itself + + + align:start position:0% +cross itself so the not Crossing itself +is the standard definition of a cycle + + align:start position:0% +is the standard definition of a cycle + + + align:start position:0% +is the standard definition of a cycle +that we were using in a directed graph + + align:start position:0% +that we were using in a directed graph + + + align:start position:0% +that we were using in a directed graph +it simply means that it's a path uh + + align:start position:0% +it simply means that it's a path uh + + + align:start position:0% +it simply means that it's a path uh +except that the beginning and end vertex + + align:start position:0% +except that the beginning and end vertex + + + align:start position:0% +except that the beginning and end vertex +are the same so it looks like um you + + align:start position:0% +are the same so it looks like um you + + + align:start position:0% +are the same so it looks like um you +start someplace at V and then you go + + align:start position:0% +start someplace at V and then you go + + + align:start position:0% +start someplace at V and then you go +around to a and to W and it's all + + align:start position:0% +around to a and to W and it's all + + + align:start position:0% +around to a and to W and it's all +distinct vertices as you go around in + + align:start position:0% +distinct vertices as you go around in + + + align:start position:0% +distinct vertices as you go around in +this path except that the path ends with + + align:start position:0% +this path except that the path ends with + + + align:start position:0% +this path except that the path ends with +it starts at V which is what keeps it + + align:start position:0% +it starts at V which is what keeps it + + + align:start position:0% +it starts at V which is what keeps it +from being a path and makes it a cycle + + align:start position:0% +from being a path and makes it a cycle + + + align:start position:0% +from being a path and makes it a cycle +now the length greater than two is what + + align:start position:0% +now the length greater than two is what + + + align:start position:0% +now the length greater than two is what +is the difference between the definition + + align:start position:0% +is the difference between the definition + + + align:start position:0% +is the difference between the definition +of cycle between simple graphs and uh + + align:start position:0% +of cycle between simple graphs and uh + + + align:start position:0% +of cycle between simple graphs and uh +directed graphs in a directed graph it's + + align:start position:0% +directed graphs in a directed graph it's + + + align:start position:0% +directed graphs in a directed graph it's +perfectly possible to have a self-loop + + align:start position:0% +perfectly possible to have a self-loop + + + align:start position:0% +perfectly possible to have a self-loop +of length one that is an interesting and + + align:start position:0% +of length one that is an interesting and + + + align:start position:0% +of length one that is an interesting and +important kind of cycle to have but we + + align:start position:0% +important kind of cycle to have but we + + + align:start position:0% +important kind of cycle to have but we +forbid them in simple graphs because + + align:start position:0% +forbid them in simple graphs because + + + align:start position:0% +forbid them in simple graphs because +there's no way to avoid having a cycle + + align:start position:0% +there's no way to avoid having a cycle + + + align:start position:0% +there's no way to avoid having a cycle +of length too because you always have + + align:start position:0% +of length too because you always have + + + align:start position:0% +of length too because you always have +the ability to go back and forth across + + align:start position:0% +the ability to go back and forth across + + + align:start position:0% +the ability to go back and forth across +an edge that's not interesting and so we + + align:start position:0% +an edge that's not interesting and so we + + + align:start position:0% +an edge that's not interesting and so we +don't consider that to be a cycle uh a + + align:start position:0% +don't consider that to be a cycle uh a + + + align:start position:0% +don't consider that to be a cycle uh a +cycle then has to be of length greater + + align:start position:0% +cycle then has to be of length greater + + + align:start position:0% +cycle then has to be of length greater +than two it also rules out the cycle of + + align:start position:0% +than two it also rules out the cycle of + + + align:start position:0% +than two it also rules out the cycle of +length zero which you get by taking a a + + align:start position:0% +length zero which you get by taking a a + + + align:start position:0% +length zero which you get by taking a a +Vertex all by itself okay with that + + align:start position:0% +Vertex all by itself okay with that + + + align:start position:0% +Vertex all by itself okay with that +technical definition we now know what a + + align:start position:0% +technical definition we now know what a + + + align:start position:0% +technical definition we now know what a +cycle is in the simple graph and we + + align:start position:0% +cycle is in the simple graph and we + + + align:start position:0% +cycle is in the simple graph and we +understand the definition of tree um + + align:start position:0% +understand the definition of tree um + + + align:start position:0% +understand the definition of tree um +here are some more pictures of trees + + align:start position:0% +here are some more pictures of trees + + + align:start position:0% +here are some more pictures of trees +simple graphs with no + + align:start position:0% +simple graphs with no + + + align:start position:0% +simple graphs with no +Cycles now they really come up all the + + align:start position:0% +Cycles now they really come up all the + + + align:start position:0% +Cycles now they really come up all the +time and why is that well there're Are + + align:start position:0% +time and why is that well there're Are + + + align:start position:0% +time and why is that well there're Are +Family trees which you may be familiar + + align:start position:0% +Family trees which you may be familiar + + + align:start position:0% +Family trees which you may be familiar +with where you're uh drawing a a a + + align:start position:0% +with where you're uh drawing a a a + + + align:start position:0% +with where you're uh drawing a a a +picture of the descendants of a given + + align:start position:0% +picture of the descendants of a given + + + align:start position:0% +picture of the descendants of a given +person and they keep branching out in a + + align:start position:0% +person and they keep branching out in a + + + align:start position:0% +person and they keep branching out in a +in a tree structure as traditionally + + align:start position:0% +in a tree structure as traditionally + + + align:start position:0% +in a tree structure as traditionally +displayed um uh there are search trees + + align:start position:0% +displayed um uh there are search trees + + + align:start position:0% +displayed um uh there are search trees +which come up over time in computer + + align:start position:0% +which come up over time in computer + + + align:start position:0% +which come up over time in computer +science where you branch on the answer + + align:start position:0% +science where you branch on the answer + + + align:start position:0% +science where you branch on the answer +to some question which tells you which + + align:start position:0% +to some question which tells you which + + + align:start position:0% +to some question which tells you which +way to search next uh there are game + + align:start position:0% +way to search next uh there are game + + + align:start position:0% +way to search next uh there are game +trees which we've already discussed in + + align:start position:0% +trees which we've already discussed in + + + align:start position:0% +trees which we've already discussed in +this class which are used to define + + align:start position:0% +this class which are used to define + + + align:start position:0% +this class which are used to define +games and strategies there are parse + + align:start position:0% +games and strategies there are parse + + + align:start position:0% +games and strategies there are parse +trees that come up uh in uh uh in + + align:start position:0% +trees that come up uh in uh uh in + + + align:start position:0% +trees that come up uh in uh uh in +compiler technology and in language + + align:start position:0% +compiler technology and in language + + + align:start position:0% +compiler technology and in language +Theory and then there are spanning trees + + align:start position:0% +Theory and then there are spanning trees + + + align:start position:0% +Theory and then there are spanning trees +which we're going to be talking about + + align:start position:0% +which we're going to be talking about + + + align:start position:0% +which we're going to be talking about +some + + align:start position:0% +some + + + align:start position:0% +some +today uh now there in addition to these + + align:start position:0% +today uh now there in addition to these + + + align:start position:0% +today uh now there in addition to these +places where trees come up there are a + + align:start position:0% +places where trees come up there are a + + + align:start position:0% +places where trees come up there are a +lot of different kinds of trees there's + + align:start position:0% +lot of different kinds of trees there's + + + align:start position:0% +lot of different kinds of trees there's +rooted trees where there's some + + align:start position:0% +rooted trees where there's some + + + align:start position:0% +rooted trees where there's some +designated vertex called the root and + + align:start position:0% +designated vertex called the root and + + + align:start position:0% +designated vertex called the root and +you think of of of getting to all the + + align:start position:0% +you think of of of getting to all the + + + align:start position:0% +you think of of of getting to all the +other vertices from the root uh there + + align:start position:0% +other vertices from the root uh there + + + align:start position:0% +other vertices from the root uh there +are ordered trees where when you're at a + + align:start position:0% +are ordered trees where when you're at a + + + align:start position:0% +are ordered trees where when you're at a +given vertex uh there's a distinct order + + align:start position:0% +given vertex uh there's a distinct order + + + align:start position:0% +given vertex uh there's a distinct order +in which you are uh going to be uh in + + align:start position:0% +in which you are uh going to be uh in + + + align:start position:0% +in which you are uh going to be uh in +which the exit edges from a Vertex are + + align:start position:0% +which the exit edges from a Vertex are + + + align:start position:0% +which the exit edges from a Vertex are +there's a first one and the second one + + align:start position:0% +there's a first one and the second one + + + align:start position:0% +there's a first one and the second one +and the third one or a left one and the + + align:start position:0% +and the third one or a left one and the + + + align:start position:0% +and the third one or a left one and the +next leftmost and so on so that there's + + align:start position:0% +next leftmost and so on so that there's + + + align:start position:0% +next leftmost and so on so that there's +an order in which you can choose to + + align:start position:0% +an order in which you can choose to + + + align:start position:0% +an order in which you can choose to +leave the vertex um there are binary + + align:start position:0% +leave the vertex um there are binary + + + align:start position:0% +leave the vertex um there are binary +trees in which uh each vertex has sort + + align:start position:0% +trees in which uh each vertex has sort + + + align:start position:0% +trees in which uh each vertex has sort +of two ways out exactly um or no ways + + align:start position:0% +of two ways out exactly um or no ways + + + align:start position:0% +of two ways out exactly um or no ways +out if it's a so-called leaf and then + + align:start position:0% +out if it's a so-called leaf and then + + + align:start position:0% +out if it's a so-called leaf and then +there are complete trees uh whose + + align:start position:0% +there are complete trees uh whose + + + align:start position:0% +there are complete trees uh whose +definition I'll uh is not important to + + align:start position:0% +definition I'll uh is not important to + + + align:start position:0% +definition I'll uh is not important to +us because we're not going to consider + + align:start position:0% +us because we're not going to consider + + + align:start position:0% +us because we're not going to consider +any of these there's also by the way + + align:start position:0% +any of these there's also by the way + + + align:start position:0% +any of these there's also by the way +directed trees in which um uh edges are + + align:start position:0% +directed trees in which um uh edges are + + + align:start position:0% +directed trees in which um uh edges are +uh have a direction as in uh a Digraph + + align:start position:0% +uh have a direction as in uh a Digraph + + + align:start position:0% +uh have a direction as in uh a Digraph +tree but we're not considering any of + + align:start position:0% +tree but we're not considering any of + + + align:start position:0% +tree but we're not considering any of +these we're going to focus on so-called + + align:start position:0% +these we're going to focus on so-called + + + align:start position:0% +these we're going to focus on so-called +pure trees which are unordered unrooted + + align:start position:0% +pure trees which are unordered unrooted + + + align:start position:0% +pure trees which are unordered unrooted +undirected and that's what we're talking + + align:start position:0% +undirected and that's what we're talking + + + align:start position:0% +undirected and that's what we're talking +about so let's examine some more + + align:start position:0% +about so let's examine some more + + + align:start position:0% +about so let's examine some more +properties of trees and equivalent + + align:start position:0% +properties of trees and equivalent + + + align:start position:0% +properties of trees and equivalent +definitions of trees it's will be + + align:start position:0% +definitions of trees it's will be + + + align:start position:0% +definitions of trees it's will be +important for theoretical reasons and + + align:start position:0% +important for theoretical reasons and + + + align:start position:0% +important for theoretical reasons and +convenience to know lots of different + + align:start position:0% +convenience to know lots of different + + + align:start position:0% +convenience to know lots of different +characterizations of trees so we've + + align:start position:0% +characterizations of trees so we've + + + align:start position:0% +characterizations of trees so we've +starting off with definition which says + + align:start position:0% +starting off with definition which says + + + align:start position:0% +starting off with definition which says +it's a uh uh a connected simple graph + + align:start position:0% +it's a uh uh a connected simple graph + + + align:start position:0% +it's a uh uh a connected simple graph +with no Cycles but there's other ways to + + align:start position:0% +with no Cycles but there's other ways to + + + align:start position:0% +with no Cycles but there's other ways to +characterize it so an edge in a simple + + align:start position:0% +characterize it so an edge in a simple + + + align:start position:0% +characterize it so an edge in a simple +graph is called a cut Edge if when you + + align:start position:0% +graph is called a cut Edge if when you + + + align:start position:0% +graph is called a cut Edge if when you +remove it from the graph two vertices + + align:start position:0% +remove it from the graph two vertices + + + align:start position:0% +remove it from the graph two vertices +that used to be connected that is used + + align:start position:0% +that used to be connected that is used + + + align:start position:0% +that used to be connected that is used +to have a path between them cease to + + align:start position:0% +to have a path between them cease to + + + align:start position:0% +to have a path between them cease to +have a path between them so here's a + + align:start position:0% +have a path between them so here's a + + + align:start position:0% +have a path between them so here's a +simple graph illustration and that edge + + align:start position:0% +simple graph illustration and that edge + + + align:start position:0% +simple graph illustration and that edge +e is a cut Edge because if I delete it + + align:start position:0% +e is a cut Edge because if I delete it + + + align:start position:0% +e is a cut Edge because if I delete it +then uh there are now two components + + align:start position:0% +then uh there are now two components + + + align:start position:0% +then uh there are now two components +there used to be two vertices uh + + align:start position:0% +there used to be two vertices uh + + + align:start position:0% +there used to be two vertices uh +actually any of the vertices here used + + align:start position:0% +actually any of the vertices here used + + + align:start position:0% +actually any of the vertices here used +to be connected to any of the vertices + + align:start position:0% +to be connected to any of the vertices + + + align:start position:0% +to be connected to any of the vertices +there via that edge but once I've + + align:start position:0% +there via that edge but once I've + + + align:start position:0% +there via that edge but once I've +deleted that edge all of those vertices + + align:start position:0% +deleted that edge all of those vertices + + + align:start position:0% +deleted that edge all of those vertices +here and there that used to be connected + + align:start position:0% +here and there that used to be connected + + + align:start position:0% +here and there that used to be connected +no longer are so that makes e a cut Edge + + align:start position:0% +no longer are so that makes e a cut Edge + + + align:start position:0% +no longer are so that makes e a cut Edge +um f is not a cut Edge because even if I + + align:start position:0% +um f is not a cut Edge because even if I + + + align:start position:0% +um f is not a cut Edge because even if I +delete Edge uh F there is in fact still + + align:start position:0% +delete Edge uh F there is in fact still + + + align:start position:0% +delete Edge uh F there is in fact still +a path from every vertex to every other + + align:start position:0% +a path from every vertex to every other + + + align:start position:0% +a path from every vertex to every other +vertex here so that f is not + + align:start position:0% +vertex here so that f is not + + + align:start position:0% +vertex here so that f is not +disconnecting + + align:start position:0% +disconnecting + + + align:start position:0% +disconnecting +anything um + + align:start position:0% +anything um + + + align:start position:0% +anything um +and as I say it's still connected after + + align:start position:0% +and as I say it's still connected after + + + align:start position:0% +and as I say it's still connected after +you delete it so now we get a simple way + + align:start position:0% +you delete it so now we get a simple way + + + align:start position:0% +you delete it so now we get a simple way +to characterize trees in terms of cut + + align:start position:0% +to characterize trees in terms of cut + + + align:start position:0% +to characterize trees in terms of cut +edges um because an edge is not a cut + + align:start position:0% +edges um because an edge is not a cut + + + align:start position:0% +edges um because an edge is not a cut +Edge if and only if it's on a cycle if + + align:start position:0% +Edge if and only if it's on a cycle if + + + align:start position:0% +Edge if and only if it's on a cycle if +you think about that if it's on a cycle + + align:start position:0% +you think about that if it's on a cycle + + + align:start position:0% +you think about that if it's on a cycle +and you cut an edge out of a cycle then + + align:start position:0% +and you cut an edge out of a cycle then + + + align:start position:0% +and you cut an edge out of a cycle then +everything on the cycle is still + + align:start position:0% +everything on the cycle is still + + + align:start position:0% +everything on the cycle is still +connected by going the other way around + + align:start position:0% +connected by going the other way around + + + align:start position:0% +connected by going the other way around +the cycle that doesn't use that edge uh + + align:start position:0% +the cycle that doesn't use that edge uh + + + align:start position:0% +the cycle that doesn't use that edge uh +and uh if it's not on a cycle then in + + align:start position:0% +and uh if it's not on a cycle then in + + + align:start position:0% +and uh if it's not on a cycle then in +fact you can think through that deleting + + align:start position:0% +fact you can think through that deleting + + + align:start position:0% +fact you can think through that deleting +it means that uh + + align:start position:0% +it means that uh + + + align:start position:0% +it means that uh +there's not going to be two paths + + align:start position:0% +there's not going to be two paths + + + align:start position:0% +there's not going to be two paths +between two things at its at its end + + align:start position:0% +between two things at its at its end + + + align:start position:0% +between two things at its at its end +points and so it will separate + + align:start position:0% +points and so it will separate + + + align:start position:0% +points and so it will separate +them okay um so another way then to + + align:start position:0% +them okay um so another way then to + + + align:start position:0% +them okay um so another way then to +define a tree is to say a tree is a + + align:start position:0% +define a tree is to say a tree is a + + + align:start position:0% +define a tree is to say a tree is a +connected graph where every Edge is a + + align:start position:0% +connected graph where every Edge is a + + + align:start position:0% +connected graph where every Edge is a +cut Edge that is as soon as you cut any + + align:start position:0% +cut Edge that is as soon as you cut any + + + align:start position:0% +cut Edge that is as soon as you cut any +Edge out of a tree it stops being + + align:start position:0% +Edge out of a tree it stops being + + + align:start position:0% +Edge out of a tree it stops being +connected uh that yields another way to + + align:start position:0% +connected uh that yields another way to + + + align:start position:0% +connected uh that yields another way to +say that something is a tree a a tree is + + align:start position:0% +say that something is a tree a a tree is + + + align:start position:0% +say that something is a tree a a tree is +a simple graph that is connected and is + + align:start position:0% +a simple graph that is connected and is + + + align:start position:0% +a simple graph that is connected and is +Edge minimal which again means that if + + align:start position:0% +Edge minimal which again means that if + + + align:start position:0% +Edge minimal which again means that if +you remove any Edge it stops having that + + align:start position:0% +you remove any Edge it stops having that + + + align:start position:0% +you remove any Edge it stops having that +property of being connected so it's an + + align:start position:0% +property of being connected so it's an + + + align:start position:0% +property of being connected so it's an +edge minimal connected graph that's kind + + align:start position:0% +edge minimal connected graph that's kind + + + align:start position:0% +edge minimal connected graph that's kind +of the reason why trees are so important + + align:start position:0% +of the reason why trees are so important + + + align:start position:0% +of the reason why trees are so important +because if you're trying to figure out a + + align:start position:0% +because if you're trying to figure out a + + + align:start position:0% +because if you're trying to figure out a +way to get a whole bunch of things a + + align:start position:0% +way to get a whole bunch of things a + + + align:start position:0% +way to get a whole bunch of things a +whole bunch of vertices connected a tree + + align:start position:0% +whole bunch of vertices connected a tree + + + align:start position:0% +whole bunch of vertices connected a tree +is going to have the minimum number of + + align:start position:0% +is going to have the minimum number of + + + align:start position:0% +is going to have the minimum number of +edges that are sufficient to get them + + align:start position:0% +edges that are sufficient to get them + + + align:start position:0% +edges that are sufficient to get them +all connected if you think about uh + + align:start position:0% +all connected if you think about uh + + + align:start position:0% +all connected if you think about uh +different uh nodes in a network that + + align:start position:0% +different uh nodes in a network that + + + align:start position:0% +different uh nodes in a network that +need to communicate with each other and + + align:start position:0% +need to communicate with each other and + + + align:start position:0% +need to communicate with each other and +you want to know how many direct + + align:start position:0% +you want to know how many direct + + + align:start position:0% +you want to know how many direct +connections do there have to be between + + align:start position:0% +connections do there have to be between + + + align:start position:0% +connections do there have to be between +uh these communication centers in order + + align:start position:0% +uh these communication centers in order + + + align:start position:0% +uh these communication centers in order +for everybody to talk to everybody else + + align:start position:0% +for everybody to talk to everybody else + + + align:start position:0% +for everybody to talk to everybody else +the answer is it's got to be a tree on N + + align:start position:0% +the answer is it's got to be a tree on N + + + align:start position:0% +the answer is it's got to be a tree on N +vertices and a tree on N vertices is + + align:start position:0% +vertices and a tree on N vertices is + + + align:start position:0% +vertices and a tree on N vertices is +going to have exactly n minus one edges + + align:start position:0% +going to have exactly n minus one edges + + + align:start position:0% +going to have exactly n minus one edges +so that gives you still another + + align:start position:0% +so that gives you still another + + + align:start position:0% +so that gives you still another +equivalent definition of a tree a tree + + align:start position:0% +equivalent definition of a tree a tree + + + align:start position:0% +equivalent definition of a tree a tree +is a connected graph that has n vertices + + align:start position:0% +is a connected graph that has n vertices + + + align:start position:0% +is a connected graph that has n vertices +and N minus one + + align:start position:0% +and N minus one + + + align:start position:0% +and N minus one +edges um a a kind of dual way to think + + align:start position:0% +edges um a a kind of dual way to think + + + align:start position:0% +edges um a a kind of dual way to think +about it is that uh a tree is an ayylic + + align:start position:0% +about it is that uh a tree is an ayylic + + + align:start position:0% +about it is that uh a tree is an ayylic +graph that has as many edges as it + + align:start position:0% +graph that has as many edges as it + + + align:start position:0% +graph that has as many edges as it +possibly could without having any Cycles + + align:start position:0% +possibly could without having any Cycles + + + align:start position:0% +possibly could without having any Cycles +so typically uh an ayylic graph might + + align:start position:0% +so typically uh an ayylic graph might + + + align:start position:0% +so typically uh an ayylic graph might +not be connected but as long as it's not + + align:start position:0% +not be connected but as long as it's not + + + align:start position:0% +not be connected but as long as it's not +connected you can keep adding edges that + + align:start position:0% +connected you can keep adding edges that + + + align:start position:0% +connected you can keep adding edges that +will connect things up without creating + + align:start position:0% +will connect things up without creating + + + align:start position:0% +will connect things up without creating +Cycles but the minute you get a tree so + + align:start position:0% +Cycles but the minute you get a tree so + + + align:start position:0% +Cycles but the minute you get a tree so +that everything's connected you can't + + align:start position:0% +that everything's connected you can't + + + align:start position:0% +that everything's connected you can't +add add another Edge so an edge Min an + + align:start position:0% +add add another Edge so an edge Min an + + + align:start position:0% +add add another Edge so an edge Min an +edge maximal acyclic graph is still + + align:start position:0% +edge maximal acyclic graph is still + + + align:start position:0% +edge maximal acyclic graph is still +another way to characterize trees and + + align:start position:0% +another way to characterize trees and + + + align:start position:0% +another way to characterize trees and +maybe the most useful way uh is to say + + align:start position:0% +maybe the most useful way uh is to say + + + align:start position:0% +maybe the most useful way uh is to say +that a graph in which there is a unique + + align:start position:0% +that a graph in which there is a unique + + + align:start position:0% +that a graph in which there is a unique +path between any two vertices is a tree + + align:start position:0% +path between any two vertices is a tree + + + align:start position:0% +path between any two vertices is a tree +so of course if there's a unique path in + + align:start position:0% +so of course if there's a unique path in + + + align:start position:0% +so of course if there's a unique path in +particular is a path so all the vertices + + align:start position:0% +particular is a path so all the vertices + + + align:start position:0% +particular is a path so all the vertices +have to be connected but what makes it a + + align:start position:0% +have to be connected but what makes it a + + + align:start position:0% +have to be connected but what makes it a +tree is that there aren't two different + + align:start position:0% +tree is that there aren't two different + + + align:start position:0% +tree is that there aren't two different +ways to connect between two vertices + + align:start position:0% +ways to connect between two vertices + + + align:start position:0% +ways to connect between two vertices +because as soon as they were there would + + align:start position:0% +because as soon as they were there would + + + align:start position:0% +because as soon as they were there would +be a cycle and those are some of the + + align:start position:0% +be a cycle and those are some of the + + + align:start position:0% +be a cycle and those are some of the +basic ways that trees can be formulated + + align:start position:0% +basic ways that trees can be formulated + + + align:start position:0% +basic ways that trees can be formulated +equivalently and in fact there's lots + + align:start position:0% +equivalently and in fact there's lots + + + align:start position:0% +equivalently and in fact there's lots +more but this is enough for today \ No newline at end of file diff --git a/ZLnj2cnCPGE.txt b/ZLnj2cnCPGE.txt new file mode 100644 index 0000000000000000000000000000000000000000..ad24182d443b1be3cf8e5fd59dc9189895077f1c --- /dev/null +++ b/ZLnj2cnCPGE.txt @@ -0,0 +1,11944 @@ +align:start position:0% + +externalities + + align:start position:0% +externalities + + + align:start position:0% +externalities +so so far in the class we once again + + align:start position:0% +so so far in the class we once again + + + align:start position:0% +so so far in the class we once again +remember the big picture we started with + + align:start position:0% +remember the big picture we started with + + + align:start position:0% +remember the big picture we started with +the first fundamental theorem of welfare + + align:start position:0% +the first fundamental theorem of welfare + + + align:start position:0% +the first fundamental theorem of welfare +economics which is that the + + align:start position:0% +economics which is that the + + + align:start position:0% +economics which is that the +competitive market will maximize total + + align:start position:0% +competitive market will maximize total + + + align:start position:0% +competitive market will maximize total +social welfare + + align:start position:0% +social welfare + + + align:start position:0% +social welfare +then we said that will not be true under + + align:start position:0% +then we said that will not be true under + + + align:start position:0% +then we said that will not be true under +conditions of market failure remember + + align:start position:0% +conditions of market failure remember + + + align:start position:0% +conditions of market failure remember +market failure doesn't mean market + + align:start position:0% +market failure doesn't mean market + + + align:start position:0% +market failure doesn't mean market +collapse + + align:start position:0% +collapse + + + align:start position:0% +collapse +it means that when there are barriers to + + align:start position:0% +it means that when there are barriers to + + + align:start position:0% +it means that when there are barriers to +the market achieving + + align:start position:0% +the market achieving + + + align:start position:0% +the market achieving +this first best outcome okay one barrier + + align:start position:0% +this first best outcome okay one barrier + + + align:start position:0% +this first best outcome okay one barrier +is imperfect competition + + align:start position:0% +is imperfect competition + + + align:start position:0% +is imperfect competition +one barrier was imperfect information + + align:start position:0% +one barrier was imperfect information + + + align:start position:0% +one barrier was imperfect information +a third barrier to uh + + align:start position:0% +a third barrier to uh + + + align:start position:0% +a third barrier to uh +to welfare maximization or a third + + align:start position:0% +to welfare maximization or a third + + + align:start position:0% +to welfare maximization or a third +source of market failure + + align:start position:0% +source of market failure + + + align:start position:0% +source of market failure +is externalities okay that's the third + + align:start position:0% +is externalities okay that's the third + + + align:start position:0% +is externalities okay that's the third +source of market value we're going to + + align:start position:0% +source of market value we're going to + + + align:start position:0% +source of market value we're going to +talk about that today + + align:start position:0% +talk about that today + + + align:start position:0% +talk about that today +and what is an extra now we'll be very + + align:start position:0% +and what is an extra now we'll be very + + + align:start position:0% +and what is an extra now we'll be very +clear about the definition + + align:start position:0% +clear about the definition + + + align:start position:0% +clear about the definition +an externality occurs + + align:start position:0% +an externality occurs + + + align:start position:0% +an externality occurs +whenever one party's actions makes + + align:start position:0% +whenever one party's actions makes + + + align:start position:0% +whenever one party's actions makes +another party + + align:start position:0% +another party + + + align:start position:0% +another party +better or worse off okay + + align:start position:0% +better or worse off okay + + + align:start position:0% +better or worse off okay +let's do it look at any person whether + + align:start position:0% +let's do it look at any person whether + + + align:start position:0% +let's do it look at any person whether +my actions make you + + align:start position:0% +my actions make you + + + align:start position:0% +my actions make you +better or worse off but i don't bear the + + align:start position:0% +better or worse off but i don't bear the + + + align:start position:0% +better or worse off but i don't bear the +consequences of that + + align:start position:0% +consequences of that + + + align:start position:0% +consequences of that +so when my actions make you better or + + align:start position:0% +so when my actions make you better or + + + align:start position:0% +so when my actions make you better or +worse off + + align:start position:0% +worse off + + + align:start position:0% +worse off +but i don't bear the consequences then + + align:start position:0% +but i don't bear the consequences then + + + align:start position:0% +but i don't bear the consequences then +there's an externality + + align:start position:0% +there's an externality + + + align:start position:0% +there's an externality +okay so let's talk about that + + align:start position:0% +okay so let's talk about that + + + align:start position:0% +okay so let's talk about that +in the context let's start with the + + align:start position:0% +in the context let's start with the + + + align:start position:0% +in the context let's start with the +classic example of externalities + + align:start position:0% +classic example of externalities + + + align:start position:0% +classic example of externalities +which is a negative production + + align:start position:0% +which is a negative production + + + align:start position:0% +which is a negative production +externality + + align:start position:0% + + + + align:start position:0% + +a negative production externality + + align:start position:0% +a negative production externality + + + align:start position:0% +a negative production externality +okay the class example + + align:start position:0% +okay the class example + + + align:start position:0% +okay the class example +is you've got a river on that river is a + + align:start position:0% +is you've got a river on that river is a + + + align:start position:0% +is you've got a river on that river is a +steel plant + + align:start position:0% +steel plant + + + align:start position:0% +steel plant +that steel plant produces steel okay + + align:start position:0% +that steel plant produces steel okay + + + align:start position:0% +that steel plant produces steel okay +but as a byproduct of that production it + + align:start position:0% +but as a byproduct of that production it + + + align:start position:0% +but as a byproduct of that production it +dumps sludge into the river + + align:start position:0% +dumps sludge into the river + + + align:start position:0% +dumps sludge into the river +okay you guys remember the lorax it's + + align:start position:0% +okay you guys remember the lorax it's + + + align:start position:0% +okay you guys remember the lorax it's +basically lorax okay + + align:start position:0% +basically lorax okay + + + align:start position:0% +basically lorax okay +so basically the steel plant dumps + + align:start position:0% +so basically the steel plant dumps + + + align:start position:0% +so basically the steel plant dumps +sludge into the river + + align:start position:0% +sludge into the river + + + align:start position:0% +sludge into the river +okay that sludge floats down the river + + align:start position:0% +okay that sludge floats down the river + + + align:start position:0% +okay that sludge floats down the river +and kills the fish + + align:start position:0% +and kills the fish + + + align:start position:0% +and kills the fish +those killed fish mean that fishermen + + align:start position:0% +those killed fish mean that fishermen + + + align:start position:0% +those killed fish mean that fishermen +cannot make as much money + + align:start position:0% +cannot make as much money + + + align:start position:0% +cannot make as much money +fishing on the river okay + + align:start position:0% +fishing on the river okay + + + align:start position:0% +fishing on the river okay +so basically there's sludge coming out + + align:start position:0% +so basically there's sludge coming out + + + align:start position:0% +so basically there's sludge coming out +of the factory + + align:start position:0% +of the factory + + + align:start position:0% +of the factory +okay and + + align:start position:0% +okay and + + + align:start position:0% +okay and +that sludge we're gonna make the + + align:start position:0% +that sludge we're gonna make the + + + align:start position:0% +that sludge we're gonna make the +assumptions directly proportional to + + align:start position:0% +assumptions directly proportional to + + + align:start position:0% +assumptions directly proportional to +production of steel + + align:start position:0% +production of steel + + + align:start position:0% +production of steel +so we say for every unit of steel + + align:start position:0% +so we say for every unit of steel + + + align:start position:0% +so we say for every unit of steel +produced there's one unit of sludge that + + align:start position:0% +produced there's one unit of sludge that + + + align:start position:0% +produced there's one unit of sludge that +emits from the factory + + align:start position:0% +emits from the factory + + + align:start position:0% +emits from the factory +okay just make this model easy so every + + align:start position:0% +okay just make this model easy so every + + + align:start position:0% +okay just make this model easy so every +unit of steel there's one unit of sludge + + align:start position:0% +unit of steel there's one unit of sludge + + + align:start position:0% +unit of steel there's one unit of sludge +that sludge floats down the river and + + align:start position:0% +that sludge floats down the river and + + + align:start position:0% +that sludge floats down the river and +kills the fish unfortunately there are + + align:start position:0% +kills the fish unfortunately there are + + + align:start position:0% +kills the fish unfortunately there are +fishermen + + align:start position:0% +fishermen + + + align:start position:0% +fishermen +down this river who are trying to catch + + align:start position:0% +down this river who are trying to catch + + + align:start position:0% +down this river who are trying to catch +fish and that hurts their livelihood + + align:start position:0% +fish and that hurts their livelihood + + + align:start position:0% +fish and that hurts their livelihood +okay so this is a classic example + + align:start position:0% +okay so this is a classic example + + + align:start position:0% +okay so this is a classic example +of loading by an externality because the + + align:start position:0% +of loading by an externality because the + + + align:start position:0% +of loading by an externality because the +steel plant's behavior + + align:start position:0% +steel plant's behavior + + + align:start position:0% +steel plant's behavior +is imposing a cost on the fishermen + + align:start position:0% +is imposing a cost on the fishermen + + + align:start position:0% +is imposing a cost on the fishermen +their sludge is the most caused the + + align:start position:0% +their sludge is the most caused the + + + align:start position:0% +their sludge is the most caused the +fisherman but the steel plant doesn't + + align:start position:0% +fisherman but the steel plant doesn't + + + align:start position:0% +fisherman but the steel plant doesn't +bear any consequence of that they just + + align:start position:0% +bear any consequence of that they just + + + align:start position:0% +bear any consequence of that they just +dump the sludge and forget about it + + align:start position:0% +dump the sludge and forget about it + + + align:start position:0% +dump the sludge and forget about it +okay so that's mean by negative it's a + + align:start position:0% +okay so that's mean by negative it's a + + + align:start position:0% +okay so that's mean by negative it's a +negative externality because my actions + + align:start position:0% +negative externality because my actions + + + align:start position:0% +negative externality because my actions +are hurting you + + align:start position:0% +are hurting you + + + align:start position:0% +are hurting you +the steel plants actually are hurting + + align:start position:0% +the steel plants actually are hurting + + + align:start position:0% +the steel plants actually are hurting +the fishermen it's a production + + align:start position:0% +the fishermen it's a production + + + align:start position:0% +the fishermen it's a production +externality because it comes out of the + + align:start position:0% +externality because it comes out of the + + + align:start position:0% +externality because it comes out of the +production process + + align:start position:0% +production process + + + align:start position:0% +production process +in this case for steel so that's mean by + + align:start position:0% +in this case for steel so that's mean by + + + align:start position:0% +in this case for steel so that's mean by +negative + + align:start position:0% +negative + + + align:start position:0% +negative +production externality it means that + + align:start position:0% +production externality it means that + + + align:start position:0% +production externality it means that +when + + align:start position:0% +when + + + align:start position:0% +when +one party's production adversely affects + + align:start position:0% +one party's production adversely affects + + + align:start position:0% +one party's production adversely affects +another party + + align:start position:0% +another party + + + align:start position:0% +another party +but the party doing the production + + align:start position:0% +but the party doing the production + + + align:start position:0% +but the party doing the production +doesn't bear any consequences of that + + align:start position:0% +doesn't bear any consequences of that + + + align:start position:0% +doesn't bear any consequences of that +then that's a negative production + + align:start position:0% +then that's a negative production + + + align:start position:0% +then that's a negative production +externality so what effect does that + + align:start position:0% +externality so what effect does that + + + align:start position:0% +externality so what effect does that +have let's go to figure 22 1 + + align:start position:0% +have let's go to figure 22 1 + + + align:start position:0% +have let's go to figure 22 1 +and talk rapidly about how we think + + align:start position:0% +and talk rapidly about how we think + + + align:start position:0% +and talk rapidly about how we think +about production externalities + + align:start position:0% +about production externalities + + + align:start position:0% +about production externalities +okay this is the market for steel + + align:start position:0% +okay this is the market for steel + + + align:start position:0% +okay this is the market for steel +if you're 21 is the market for steel the + + align:start position:0% +if you're 21 is the market for steel the + + + align:start position:0% +if you're 21 is the market for steel the +quantity of steel on the x-axis the + + align:start position:0% +quantity of steel on the x-axis the + + + align:start position:0% +quantity of steel on the x-axis the +price is still in the y-axis + + align:start position:0% +price is still in the y-axis + + + align:start position:0% +price is still in the y-axis +okay the market is initially in + + align:start position:0% +okay the market is initially in + + + align:start position:0% +okay the market is initially in +equilibrium point a + + align:start position:0% +equilibrium point a + + + align:start position:0% +equilibrium point a +that is where demand which is the + + align:start position:0% +that is where demand which is the + + + align:start position:0% +that is where demand which is the +downward sloping blue line equals supply + + align:start position:0% +downward sloping blue line equals supply + + + align:start position:0% +downward sloping blue line equals supply +which is the upward sloping blue line + + align:start position:0% +which is the upward sloping blue line + + + align:start position:0% +which is the upward sloping blue line +now as we said in a perfectly + + align:start position:0% +now as we said in a perfectly + + + align:start position:0% +now as we said in a perfectly +competitive market + + align:start position:0% +competitive market + + + align:start position:0% +competitive market +demand represents the marginal + + align:start position:0% +demand represents the marginal + + + align:start position:0% +demand represents the marginal +willingness to pay + + align:start position:0% +willingness to pay + + + align:start position:0% +willingness to pay +for the good which is equal to the + + align:start position:0% +for the good which is equal to the + + + align:start position:0% +for the good which is equal to the +marginal benefit that consumers get from + + align:start position:0% +marginal benefit that consumers get from + + + align:start position:0% +marginal benefit that consumers get from +consuming the good + + align:start position:0% +consuming the good + + + align:start position:0% +consuming the good +okay the marginal benefit of consuming + + align:start position:0% +okay the marginal benefit of consuming + + + align:start position:0% +okay the marginal benefit of consuming +the good is the marginal willingness to + + align:start position:0% +the good is the marginal willingness to + + + align:start position:0% +the good is the marginal willingness to +pay + + align:start position:0% +pay + + + align:start position:0% +pay +and that's what's represented by the + + align:start position:0% +and that's what's represented by the + + + align:start position:0% +and that's what's represented by the +demand curve okay + + align:start position:0% +demand curve okay + + + align:start position:0% +demand curve okay +we're not going to touch that here we're + + align:start position:0% +we're not going to touch that here we're + + + align:start position:0% +we're not going to touch that here we're +going to leave that alone + + align:start position:0% +going to leave that alone + + + align:start position:0% +going to leave that alone +okay the supply curve is the firm's + + align:start position:0% +okay the supply curve is the firm's + + + align:start position:0% +okay the supply curve is the firm's +marginal willing supply which is their + + align:start position:0% +marginal willing supply which is their + + + align:start position:0% +marginal willing supply which is their +marginal cost + + align:start position:0% +marginal cost + + + align:start position:0% +marginal cost +okay so in the perfectly competitive + + align:start position:0% +okay so in the perfectly competitive + + + align:start position:0% +okay so in the perfectly competitive +market where marginal benefit + + align:start position:0% +market where marginal benefit + + + align:start position:0% +market where marginal benefit +equals marginal cost we get equilibrium + + align:start position:0% +equals marginal cost we get equilibrium + + + align:start position:0% +equals marginal cost we get equilibrium +and that yields the welfare maximizing + + align:start position:0% +and that yields the welfare maximizing + + + align:start position:0% +and that yields the welfare maximizing +outcome the market succeeds it does not + + align:start position:0% +outcome the market succeeds it does not + + + align:start position:0% +outcome the market succeeds it does not +fail + + align:start position:0% +fail + + + align:start position:0% +fail +okay the difference now is we're now + + align:start position:0% +okay the difference now is we're now + + + align:start position:0% +okay the difference now is we're now +going to drive a wedge + + align:start position:0% +going to drive a wedge + + + align:start position:0% +going to drive a wedge +between privately perceived benefits + + align:start position:0% +between privately perceived benefits + + + align:start position:0% +between privately perceived benefits +and social benefits so for the + + align:start position:0% +and social benefits so for the + + + align:start position:0% +and social benefits so for the +consumption of steel with the demand + + align:start position:0% +consumption of steel with the demand + + + align:start position:0% +consumption of steel with the demand +curve + + align:start position:0% +curve + + + align:start position:0% +curve +we're going to say the benefit to + + align:start position:0% +we're going to say the benefit to + + + align:start position:0% +we're going to say the benefit to +individuals is the benefit to society + + align:start position:0% +individuals is the benefit to society + + + align:start position:0% +individuals is the benefit to society +they're one in the same that's what + + align:start position:0% +they're one in the same that's what + + + align:start position:0% +they're one in the same that's what +we've assumed all course + + align:start position:0% +we've assumed all course + + + align:start position:0% +we've assumed all course +but for the supply of steel we're going + + align:start position:0% +but for the supply of steel we're going + + + align:start position:0% +but for the supply of steel we're going +to say wait a second the benefit to + + align:start position:0% +to say wait a second the benefit to + + + align:start position:0% +to say wait a second the benefit to +society + + align:start position:0% +society + + + align:start position:0% +society +is different than a benefit to the steel + + align:start position:0% +is different than a benefit to the steel + + + align:start position:0% +is different than a benefit to the steel +producers or i'm sorry the cost to + + align:start position:0% +producers or i'm sorry the cost to + + + align:start position:0% +producers or i'm sorry the cost to +society + + align:start position:0% +society + + + align:start position:0% +society +is different than the cost of steel + + align:start position:0% +is different than the cost of steel + + + align:start position:0% +is different than the cost of steel +producers the cost steel producers + + align:start position:0% +producers the cost steel producers + + + align:start position:0% +producers the cost steel producers +which is their private marginal cost is + + align:start position:0% +which is their private marginal cost is + + + align:start position:0% +which is their private marginal cost is +supply curve + + align:start position:0% +supply curve + + + align:start position:0% +supply curve +but the social marginal cost + + align:start position:0% +but the social marginal cost + + + align:start position:0% +but the social marginal cost +is adds the damage they're doing to the + + align:start position:0% +is adds the damage they're doing to the + + + align:start position:0% +is adds the damage they're doing to the +fishermen + + align:start position:0% +fishermen + + + align:start position:0% +fishermen +that is society encompasses all the + + align:start position:0% +that is society encompasses all the + + + align:start position:0% +that is society encompasses all the +actors in society + + align:start position:0% +actors in society + + + align:start position:0% +actors in society +it encompasses both the steel plant and + + align:start position:0% +it encompasses both the steel plant and + + + align:start position:0% +it encompasses both the steel plant and +the fishermen + + align:start position:0% +the fishermen + + + align:start position:0% +the fishermen +so the co marginal cost society is the + + align:start position:0% +so the co marginal cost society is the + + + align:start position:0% +so the co marginal cost society is the +cost of producing the steel + + align:start position:0% +cost of producing the steel + + + align:start position:0% +cost of producing the steel +plus the marginal damage + + align:start position:0% +plus the marginal damage + + + align:start position:0% +plus the marginal damage +being done to the fishermen so social + + align:start position:0% +being done to the fishermen so social + + + align:start position:0% +being done to the fishermen so social +marginal cost + + align:start position:0% +marginal cost + + + align:start position:0% +marginal cost +equals private marginal cost plus + + align:start position:0% +equals private marginal cost plus + + + align:start position:0% +equals private marginal cost plus +marginal damage + + align:start position:0% +marginal damage + + + align:start position:0% +marginal damage +social marginal cost that goes private + + align:start position:0% +social marginal cost that goes private + + + align:start position:0% +social marginal cost that goes private +marginal cost plus the marginal damage + + align:start position:0% +marginal cost plus the marginal damage + + + align:start position:0% +marginal cost plus the marginal damage +and we see that as the red line + + align:start position:0% + + + + align:start position:0% + +okay what that means from a + + align:start position:0% +okay what that means from a + + + align:start position:0% +okay what that means from a +welfare perspective what we care about + + align:start position:0% +welfare perspective what we care about + + + align:start position:0% +welfare perspective what we care about +is social marginal benefits and costs + + align:start position:0% +is social marginal benefits and costs + + + align:start position:0% +is social marginal benefits and costs +not private marginal benefits and costs + + align:start position:0% +not private marginal benefits and costs + + + align:start position:0% +not private marginal benefits and costs +so what that means is the social optimum + + align:start position:0% +so what that means is the social optimum + + + align:start position:0% +so what that means is the social optimum +the welfare maximizing optim is actually + + align:start position:0% +the welfare maximizing optim is actually + + + align:start position:0% +the welfare maximizing optim is actually +at point c + + align:start position:0% +at point c + + + align:start position:0% +at point c +point c is the left maximizing optim + + align:start position:0% +point c is the left maximizing optim + + + align:start position:0% +point c is the left maximizing optim +where the social marginal cost + + align:start position:0% +where the social marginal cost + + + align:start position:0% +where the social marginal cost +equals the social marginal benefit + + align:start position:0% + + + + align:start position:0% + +okay and therefore we over + + align:start position:0% +okay and therefore we over + + + align:start position:0% +okay and therefore we over +produce what's happening + + align:start position:0% +produce what's happening + + + align:start position:0% +produce what's happening +is the steel company not considering the + + align:start position:0% +is the steel company not considering the + + + align:start position:0% +is the steel company not considering the +damage they're doing through production + + align:start position:0% +damage they're doing through production + + + align:start position:0% +damage they're doing through production +the fishermen + + align:start position:0% +the fishermen + + + align:start position:0% +the fishermen +produces too much the steel company + + align:start position:0% +produces too much the steel company + + + align:start position:0% +produces too much the steel company +produces at the point where private + + align:start position:0% +produces at the point where private + + + align:start position:0% +produces at the point where private +marginal cost + + align:start position:0% +marginal cost + + + align:start position:0% +marginal cost +equals private marginal benefit which in + + align:start position:0% +equals private marginal benefit which in + + + align:start position:0% +equals private marginal benefit which in +our case equals social marginal benefit + + align:start position:0% +our case equals social marginal benefit + + + align:start position:0% +our case equals social marginal benefit +okay that's the that's the private + + align:start position:0% +okay that's the that's the private + + + align:start position:0% +okay that's the that's the private +market decision + + align:start position:0% +market decision + + + align:start position:0% +market decision +but in fact it should be producing at + + align:start position:0% +but in fact it should be producing at + + + align:start position:0% +but in fact it should be producing at +the point + + align:start position:0% +the point + + + align:start position:0% +the point +where social marginal cost equals + + align:start position:0% +where social marginal cost equals + + + align:start position:0% +where social marginal cost equals +private marginal benefit + + align:start position:0% +private marginal benefit + + + align:start position:0% +private marginal benefit +private marginal but equals social + + align:start position:0% +private marginal but equals social + + + align:start position:0% +private marginal but equals social +marginal benefit okay + + align:start position:0% +marginal benefit okay + + + align:start position:0% +marginal benefit okay +and the point of so where social margin + + align:start position:0% +and the point of so where social margin + + + align:start position:0% +and the point of so where social margin +costs equal social marginal benefit is + + align:start position:0% +costs equal social marginal benefit is + + + align:start position:0% +costs equal social marginal benefit is +lower production why because + + align:start position:0% +lower production why because + + + align:start position:0% +lower production why because +lower production avoids that reduces the + + align:start position:0% +lower production avoids that reduces the + + + align:start position:0% +lower production avoids that reduces the +damage being done to the fishermen down + + align:start position:0% +damage being done to the fishermen down + + + align:start position:0% +damage being done to the fishermen down +the river + + align:start position:0% +the river + + + align:start position:0% +the river +okay so the optimum from society's + + align:start position:0% +okay so the optimum from society's + + + align:start position:0% +okay so the optimum from society's +perspective + + align:start position:0% +perspective + + + align:start position:0% +perspective +is point c in other words there is a + + align:start position:0% +is point c in other words there is a + + + align:start position:0% +is point c in other words there is a +market failure the private market + + align:start position:0% +market failure the private market + + + align:start position:0% +market failure the private market +is not delivering the welfare maximizing + + align:start position:0% +is not delivering the welfare maximizing + + + align:start position:0% +is not delivering the welfare maximizing +outcome + + align:start position:0% +outcome + + + align:start position:0% +outcome +and we could see that creates a + + align:start position:0% +and we could see that creates a + + + align:start position:0% +and we could see that creates a +deadweight loss + + align:start position:0% +deadweight loss + + + align:start position:0% +deadweight loss +the deadweight loss is the units that + + align:start position:0% +the deadweight loss is the units that + + + align:start position:0% +the deadweight loss is the units that +are traded + + align:start position:0% +are traded + + + align:start position:0% +are traded +that are socially inefficient why + + align:start position:0% +that are socially inefficient why + + + align:start position:0% +that are socially inefficient why +they're socially inefficient they're + + align:start position:0% +they're socially inefficient they're + + + align:start position:0% +they're socially inefficient they're +privately efficient + + align:start position:0% +privately efficient + + + align:start position:0% +privately efficient +they're using q2 and q1 before we + + align:start position:0% +they're using q2 and q1 before we + + + align:start position:0% +they're using q2 and q1 before we +introduce externalities we'd say well + + align:start position:0% +introduce externalities we'd say well + + + align:start position:0% +introduce externalities we'd say well +it's a shame if they don't get produced + + align:start position:0% +it's a shame if they don't get produced + + + align:start position:0% +it's a shame if they don't get produced +right + + align:start position:0% +right + + + align:start position:0% +right +if you ignore sales would say the + + align:start position:0% +if you ignore sales would say the + + + align:start position:0% +if you ignore sales would say the +institute q2 and q1 well they have a + + align:start position:0% +institute q2 and q1 well they have a + + + align:start position:0% +institute q2 and q1 well they have a +benefit higher than their cost + + align:start position:0% +benefit higher than their cost + + + align:start position:0% +benefit higher than their cost +so they should get produced but actually + + align:start position:0% +so they should get produced but actually + + + align:start position:0% +so they should get produced but actually +in the world of accidentalities their + + align:start position:0% +in the world of accidentalities their + + + align:start position:0% +in the world of accidentalities their +benefit is + + align:start position:0% +benefit is + + + align:start position:0% +benefit is +lower than their cost because their cost + + align:start position:0% +lower than their cost because their cost + + + align:start position:0% +lower than their cost because their cost +incorporates the damage done to the fish + + align:start position:0% +incorporates the damage done to the fish + + + align:start position:0% +incorporates the damage done to the fish +so there's a deadweight loss critically + + align:start position:0% +so there's a deadweight loss critically + + + align:start position:0% +so there's a deadweight loss critically +i don't know how to draw these + + align:start position:0% +i don't know how to draw these + + + align:start position:0% +i don't know how to draw these +deadweight loss triangles remember + + align:start position:0% +deadweight loss triangles remember + + + align:start position:0% +deadweight loss triangles remember +deadweight loss triangles always point + + align:start position:0% +deadweight loss triangles always point + + + align:start position:0% +deadweight loss triangles always point +to the optimum the deadweight loss + + align:start position:0% +to the optimum the deadweight loss + + + align:start position:0% +to the optimum the deadweight loss +triangle is the area abc + + align:start position:0% +triangle is the area abc + + + align:start position:0% +triangle is the area abc +okay it's drawn its units that are sold + + align:start position:0% +okay it's drawn its units that are sold + + + align:start position:0% +okay it's drawn its units that are sold +where the social marginal cost exceeds + + align:start position:0% +where the social marginal cost exceeds + + + align:start position:0% +where the social marginal cost exceeds +the social marginal benefit + + align:start position:0% +the social marginal benefit + + + align:start position:0% +the social marginal benefit +and that's that deadweight loss triangle + + align:start position:0% +and that's that deadweight loss triangle + + + align:start position:0% +and that's that deadweight loss triangle +so there's an inefficiency + + align:start position:0% +so there's an inefficiency + + + align:start position:0% +so there's an inefficiency +arising from the fact the private actors + + align:start position:0% +arising from the fact the private actors + + + align:start position:0% +arising from the fact the private actors +do not account for the social + + align:start position:0% +do not account for the social + + + align:start position:0% +do not account for the social +implications of their actions okay + + align:start position:0% +implications of their actions okay + + + align:start position:0% +implications of their actions okay +questions about that so + + align:start position:0% +questions about that so + + + align:start position:0% +questions about that so +we have a classic example perhaps the + + align:start position:0% +we have a classic example perhaps the + + + align:start position:0% +we have a classic example perhaps the +classic example in all of economics + + align:start position:0% +classic example in all of economics + + + align:start position:0% +classic example in all of economics +of a market failure the classic example + + align:start position:0% +of a market failure the classic example + + + align:start position:0% +of a market failure the classic example +is a market failure happens + + align:start position:0% +is a market failure happens + + + align:start position:0% +is a market failure happens +when the social implications of your + + align:start position:0% +when the social implications of your + + + align:start position:0% +when the social implications of your +actions + + align:start position:0% +actions + + + align:start position:0% +actions +okay uh are different than the private + + align:start position:0% +okay uh are different than the private + + + align:start position:0% +okay uh are different than the private +implications + + align:start position:0% +implications + + + align:start position:0% +implications +since people maximize their own private + + align:start position:0% +since people maximize their own private + + + align:start position:0% +since people maximize their own private +well-being that's what adam smith sort + + align:start position:0% +well-being that's what adam smith sort + + + align:start position:0% +well-being that's what adam smith sort +of taught us + + align:start position:0% +of taught us + + + align:start position:0% +of taught us +the notion of the invisible hand is that + + align:start position:0% +the notion of the invisible hand is that + + + align:start position:0% +the notion of the invisible hand is that +the market acting in its own interests + + align:start position:0% +the market acting in its own interests + + + align:start position:0% +the market acting in its own interests +will deliver the best outcomes for + + align:start position:0% +will deliver the best outcomes for + + + align:start position:0% +will deliver the best outcomes for +society we're saying no that's not true + + align:start position:0% +society we're saying no that's not true + + + align:start position:0% +society we're saying no that's not true +if the market is own interest has + + align:start position:0% +if the market is own interest has + + + align:start position:0% +if the market is own interest has +implications for other parties + + align:start position:0% +implications for other parties + + + align:start position:0% +implications for other parties +that are not accounted for + + align:start position:0% + + + + align:start position:0% + +okay now + + align:start position:0% +okay now + + + align:start position:0% +okay now +externalities don't have to just be on + + align:start position:0% +externalities don't have to just be on + + + align:start position:0% +externalities don't have to just be on +the + + align:start position:0% +the + + + align:start position:0% +the +uh production side we can also have + + align:start position:0% +uh production side we can also have + + + align:start position:0% +uh production side we can also have +negative consumption + + align:start position:0% +negative consumption + + + align:start position:0% +negative consumption +externalities + + align:start position:0% + + + + align:start position:0% + +that would be a case where my literally + + align:start position:0% +that would be a case where my literally + + + align:start position:0% +that would be a case where my literally +consuming a good + + align:start position:0% +consuming a good + + + align:start position:0% +consuming a good +makes you worse off + + align:start position:0% +makes you worse off + + + align:start position:0% +makes you worse off +my consuming a good makes you worse off + + align:start position:0% +my consuming a good makes you worse off + + + align:start position:0% +my consuming a good makes you worse off +okay so let me start with a simple + + align:start position:0% +okay so let me start with a simple + + + align:start position:0% +okay so let me start with a simple +question + + align:start position:0% +question + + + align:start position:0% +question +let's start with a perfectly competitive + + align:start position:0% +let's start with a perfectly competitive + + + align:start position:0% +let's start with a perfectly competitive +market + + align:start position:0% +market + + + align:start position:0% +market +if i consume a good i raise demand for + + align:start position:0% +if i consume a good i raise demand for + + + align:start position:0% +if i consume a good i raise demand for +that good + + align:start position:0% +that good + + + align:start position:0% +that good +that raises the price is that an + + align:start position:0% +that raises the price is that an + + + align:start position:0% +that raises the price is that an +externality + + align:start position:0% +externality + + + align:start position:0% +externality +in a perfectly competitive market it's + + align:start position:0% +in a perfectly competitive market it's + + + align:start position:0% +in a perfectly competitive market it's +not why isn't that an externality + + align:start position:0% +not why isn't that an externality + + + align:start position:0% +not why isn't that an externality +if i consume the if i want to consume + + align:start position:0% +if i consume the if i want to consume + + + align:start position:0% +if i consume the if i want to consume +the good the price goes up everyone pays + + align:start position:0% +the good the price goes up everyone pays + + + align:start position:0% +the good the price goes up everyone pays +a higher price + + align:start position:0% +a higher price + + + align:start position:0% +a higher price +why is that not an externality yeah + + align:start position:0% +why is that not an externality yeah + + + align:start position:0% +why is that not an externality yeah +because you also bear the costs and + + align:start position:0% +because you also bear the costs and + + + align:start position:0% +because you also bear the costs and +accidentally only occurs when you don't + + align:start position:0% +accidentally only occurs when you don't + + + align:start position:0% +accidentally only occurs when you don't +bear the cost of your actions + + align:start position:0% +bear the cost of your actions + + + align:start position:0% +bear the cost of your actions +when you want a car and therefore the + + align:start position:0% +when you want a car and therefore the + + + align:start position:0% +when you want a car and therefore the +price of cars goes up + + align:start position:0% +price of cars goes up + + + align:start position:0% +price of cars goes up +you pay that higher price accidentally + + align:start position:0% +you pay that higher price accidentally + + + align:start position:0% +you pay that higher price accidentally +only occur when you don't bear the + + align:start position:0% +only occur when you don't bear the + + + align:start position:0% +only occur when you don't bear the +consequences + + align:start position:0% +consequences + + + align:start position:0% +consequences +so in general could some checklists + + align:start position:0% +so in general could some checklists + + + align:start position:0% +so in general could some checklists +don't happen through causing higher + + align:start position:0% +don't happen through causing higher + + + align:start position:0% +don't happen through causing higher +prices + + align:start position:0% +prices + + + align:start position:0% +prices +because substitutionalities happen more + + align:start position:0% +because substitutionalities happen more + + + align:start position:0% +because substitutionalities happen more +directly when my consumption affects you + + align:start position:0% +directly when my consumption affects you + + + align:start position:0% +directly when my consumption affects you +so the best example this would be + + align:start position:0% +so the best example this would be + + + align:start position:0% +so the best example this would be +smoking + + align:start position:0% +smoking + + + align:start position:0% +smoking +okay when i smoke it affects you + + align:start position:0% +okay when i smoke it affects you + + + align:start position:0% +okay when i smoke it affects you +it affects you a number of ways most + + align:start position:0% +it affects you a number of ways most + + + align:start position:0% +it affects you a number of ways most +directly if i smoke in this classroom + + align:start position:0% +directly if i smoke in this classroom + + + align:start position:0% +directly if i smoke in this classroom +you get secondhand smoke and you get ill + + align:start position:0% +you get secondhand smoke and you get ill + + + align:start position:0% +you get secondhand smoke and you get ill +as a result + + align:start position:0% +as a result + + + align:start position:0% +as a result +but that's not all it affects you + + align:start position:0% +but that's not all it affects you + + + align:start position:0% +but that's not all it affects you +because + + align:start position:0% +because + + + align:start position:0% +because +if i smoke and i get sick + + align:start position:0% +if i smoke and i get sick + + + align:start position:0% +if i smoke and i get sick +and my health care costs go up + + align:start position:0% +and my health care costs go up + + + align:start position:0% +and my health care costs go up +then while i work at mit all my fellow + + align:start position:0% +then while i work at mit all my fellow + + + align:start position:0% +then while i work at mit all my fellow +mit employees bear those costs because + + align:start position:0% +mit employees bear those costs because + + + align:start position:0% +mit employees bear those costs because +we all share health insurance + + align:start position:0% +we all share health insurance + + + align:start position:0% +we all share health insurance +and when i retire all society bears + + align:start position:0% +and when i retire all society bears + + + align:start position:0% +and when i retire all society bears +those costs because those costs are paid + + align:start position:0% +those costs because those costs are paid + + + align:start position:0% +those costs because those costs are paid +for by the medicare program + + align:start position:0% +for by the medicare program + + + align:start position:0% +for by the medicare program +which is financed by taxation + + align:start position:0% +which is financed by taxation + + + align:start position:0% +which is financed by taxation +so my health care costs are an + + align:start position:0% +so my health care costs are an + + + align:start position:0% +so my health care costs are an +externality secondhand smoke's an + + align:start position:0% +externality secondhand smoke's an + + + align:start position:0% +externality secondhand smoke's an +externality + + align:start position:0% +externality + + + align:start position:0% +externality +what are some other exodus from smoking + + align:start position:0% +what are some other exodus from smoking + + + align:start position:0% +what are some other exodus from smoking +what are other externalities that can + + align:start position:0% +what are other externalities that can + + + align:start position:0% +what are other externalities that can +then occur can occur from smoking yeah + + align:start position:0% +then occur can occur from smoking yeah + + + align:start position:0% +then occur can occur from smoking yeah +environmental damage from the production + + align:start position:0% +environmental damage from the production + + + align:start position:0% +environmental damage from the production +well that would be a production + + align:start position:0% +well that would be a production + + + align:start position:0% +well that would be a production +externality + + align:start position:0% +externality + + + align:start position:0% +externality +okay we're gonna leave that alone for + + align:start position:0% +okay we're gonna leave that alone for + + + align:start position:0% +okay we're gonna leave that alone for +now i'm just talking about from + + align:start position:0% +now i'm just talking about from + + + align:start position:0% +now i'm just talking about from +consuming cigarettes + + align:start position:0% +consuming cigarettes + + + align:start position:0% +consuming cigarettes +from consuming cigarettes what else what + + align:start position:0% +from consuming cigarettes what else what + + + align:start position:0% +from consuming cigarettes what else what +other damage comes so i make you i + + align:start position:0% +other damage comes so i make you i + + + align:start position:0% +other damage comes so i make you i +make you sick through secondhand smoke i + + align:start position:0% +make you sick through secondhand smoke i + + + align:start position:0% +make you sick through secondhand smoke i +might raise health care costs + + align:start position:0% +might raise health care costs + + + align:start position:0% +might raise health care costs +i might raise health care costs okay + + align:start position:0% +i might raise health care costs okay + + + align:start position:0% +i might raise health care costs okay +what else do their externality what else + + align:start position:0% +what else do their externality what else + + + align:start position:0% +what else do their externality what else +does smoking + + align:start position:0% +does smoking + + + align:start position:0% +does smoking +do + + align:start position:0% + + + + align:start position:0% + +well turns out there are 100 000 this is + + align:start position:0% +well turns out there are 100 000 this is + + + align:start position:0% +well turns out there are 100 000 this is +a number which i triple check + + align:start position:0% +a number which i triple check + + + align:start position:0% +a number which i triple check +because i still can't believe it 100 000 + + align:start position:0% +because i still can't believe it 100 000 + + + align:start position:0% +because i still can't believe it 100 000 +people + + align:start position:0% +people + + + align:start position:0% +people +every single year die in fires caused by + + align:start position:0% +every single year die in fires caused by + + + align:start position:0% +every single year die in fires caused by +smokers + + align:start position:0% +smokers + + + align:start position:0% +smokers +not in the u.s worldwide which is a + + align:start position:0% +not in the u.s worldwide which is a + + + align:start position:0% +not in the u.s worldwide which is a +crazy number but if you think about + + align:start position:0% +crazy number but if you think about + + + align:start position:0% +crazy number but if you think about +how tightly plaque slums are in + + align:start position:0% +how tightly plaque slums are in + + + align:start position:0% +how tightly plaque slums are in +developing countries + + align:start position:0% +developing countries + + + align:start position:0% +developing countries +one person falling asleep with their + + align:start position:0% +one person falling asleep with their + + + align:start position:0% +one person falling asleep with their +cigarette burning can kill thousands of + + align:start position:0% +cigarette burning can kill thousands of + + + align:start position:0% +cigarette burning can kill thousands of +people + + align:start position:0% +people + + + align:start position:0% +people +okay that is an externality because my + + align:start position:0% +okay that is an externality because my + + + align:start position:0% +okay that is an externality because my +action + + align:start position:0% +action + + + align:start position:0% +action +to smoke has killed you okay i'm clearly + + align:start position:0% +to smoke has killed you okay i'm clearly + + + align:start position:0% +to smoke has killed you okay i'm clearly +not going to compensate you for that + + align:start position:0% +not going to compensate you for that + + + align:start position:0% +not going to compensate you for that +so that's another externality okay + + align:start position:0% +so that's another externality okay + + + align:start position:0% +so that's another externality okay +what about the fact that smokers are + + align:start position:0% +what about the fact that smokers are + + + align:start position:0% +what about the fact that smokers are +less productive at work + + align:start position:0% +less productive at work + + + align:start position:0% +less productive at work +they have to take more smoke breaks they + + align:start position:0% +they have to take more smoke breaks they + + + align:start position:0% +they have to take more smoke breaks they +might get sick more often + + align:start position:0% +might get sick more often + + + align:start position:0% +might get sick more often +is that an externality or not + + align:start position:0% +is that an externality or not + + + align:start position:0% +is that an externality or not +the fact that smokers are less + + align:start position:0% +the fact that smokers are less + + + align:start position:0% +the fact that smokers are less +productive at work is that external or + + align:start position:0% +productive at work is that external or + + + align:start position:0% +productive at work is that external or +not + + align:start position:0% +not + + + align:start position:0% +not +why or why not yeah not necessarily + + align:start position:0% +why or why not yeah not necessarily + + + align:start position:0% +why or why not yeah not necessarily +because if they're less productive they + + align:start position:0% +because if they're less productive they + + + align:start position:0% +because if they're less productive they +might do less work and get paid less + + align:start position:0% +might do less work and get paid less + + + align:start position:0% +might do less work and get paid less +exactly it's not an externality if + + align:start position:0% +exactly it's not an externality if + + + align:start position:0% +exactly it's not an externality if +they're paid less + + align:start position:0% +they're paid less + + + align:start position:0% +they're paid less +this is the key thing okay which is only + + align:start position:0% +this is the key thing okay which is only + + + align:start position:0% +this is the key thing okay which is only +excellent if you don't bear the + + align:start position:0% +excellent if you don't bear the + + + align:start position:0% +excellent if you don't bear the +consequences smokers are less productive + + align:start position:0% +consequences smokers are less productive + + + align:start position:0% +consequences smokers are less productive +at work + + align:start position:0% +at work + + + align:start position:0% +at work +and they get paid less as a result by + + align:start position:0% +and they get paid less as a result by + + + align:start position:0% +and they get paid less as a result by +exactly the same amount they're less + + align:start position:0% +exactly the same amount they're less + + + align:start position:0% +exactly the same amount they're less +productive + + align:start position:0% +productive + + + align:start position:0% +productive +there's no externality but if their wage + + align:start position:0% +there's no externality but if their wage + + + align:start position:0% +there's no externality but if their wage +doesn't fully adjust + + align:start position:0% +doesn't fully adjust + + + align:start position:0% +doesn't fully adjust +and therefore the law of productivity + + align:start position:0% +and therefore the law of productivity + + + align:start position:0% +and therefore the law of productivity +affects everybody else in the firm or + + align:start position:0% +affects everybody else in the firm or + + + align:start position:0% +affects everybody else in the firm or +the firm's profits that is an + + align:start position:0% +the firm's profits that is an + + + align:start position:0% +the firm's profits that is an +externality + + align:start position:0% +externality + + + align:start position:0% +externality +okay so this is the deep aspect of + + align:start position:0% +okay so this is the deep aspect of + + + align:start position:0% +okay so this is the deep aspect of +externalities you have to think about + + align:start position:0% +externalities you have to think about + + + align:start position:0% +externalities you have to think about +whether + + align:start position:0% +whether + + + align:start position:0% +whether +people are compensating for it okay + + align:start position:0% +people are compensating for it okay + + + align:start position:0% +people are compensating for it okay +you have to think about that okay most + + align:start position:0% +you have to think about that okay most + + + align:start position:0% +you have to think about that okay most +importantly + + align:start position:0% +importantly + + + align:start position:0% +importantly +the fact i kill myself + + align:start position:0% +the fact i kill myself + + + align:start position:0% +the fact i kill myself +by smoking is not an externality + + align:start position:0% +by smoking is not an externality + + + align:start position:0% +by smoking is not an externality +okay smokers die seven years earlier on + + align:start position:0% +okay smokers die seven years earlier on + + + align:start position:0% +okay smokers die seven years earlier on +average + + align:start position:0% +average + + + align:start position:0% +average +roughly speaking every cigarette you + + align:start position:0% +roughly speaking every cigarette you + + + align:start position:0% +roughly speaking every cigarette you +smoke lowers your life by seven minutes + + align:start position:0% +smoke lowers your life by seven minutes + + + align:start position:0% +smoke lowers your life by seven minutes +it's pretty linear okay + + align:start position:0% +it's pretty linear okay + + + align:start position:0% +it's pretty linear okay +but you know what if i sit by myself on + + align:start position:0% +but you know what if i sit by myself on + + + align:start position:0% +but you know what if i sit by myself on +a rock in the middle of nowhere and + + align:start position:0% +a rock in the middle of nowhere and + + + align:start position:0% +a rock in the middle of nowhere and +smoke till i die + + align:start position:0% +smoke till i die + + + align:start position:0% +smoke till i die +no problem + + align:start position:0% + + + + align:start position:0% + +because in that case the social + + align:start position:0% +because in that case the social + + + align:start position:0% +because in that case the social +implications are the private + + align:start position:0% +implications are the private + + + align:start position:0% +implications are the private +implications + + align:start position:0% +implications + + + align:start position:0% +implications +i've made my privately optimal decision + + align:start position:0% +i've made my privately optimal decision + + + align:start position:0% +i've made my privately optimal decision +and there's no effect on anybody else so + + align:start position:0% +and there's no effect on anybody else so + + + align:start position:0% +and there's no effect on anybody else so +it's also socially optimal + + align:start position:0% +it's also socially optimal + + + align:start position:0% +it's also socially optimal +there's only externality if we have one + + align:start position:0% +there's only externality if we have one + + + align:start position:0% +there's only externality if we have one +of these mechanisms like if and smoking + + align:start position:0% +of these mechanisms like if and smoking + + + align:start position:0% +of these mechanisms like if and smoking +i'm in the woods and i started firing + + align:start position:0% +i'm in the woods and i started firing + + + align:start position:0% +i'm in the woods and i started firing +the fire + + align:start position:0% +the fire + + + align:start position:0% +the fire +company has to come that's an + + align:start position:0% +company has to come that's an + + + align:start position:0% +company has to come that's an +externality but as long as i just sit by + + align:start position:0% +externality but as long as i just sit by + + + align:start position:0% +externality but as long as i just sit by +myself and i don't i don't bother + + align:start position:0% +myself and i don't i don't bother + + + align:start position:0% +myself and i don't i don't bother +anybody + + align:start position:0% +anybody + + + align:start position:0% +anybody +smoke till i die there's no + + align:start position:0% +smoke till i die there's no + + + align:start position:0% +smoke till i die there's no +externalities okay + + align:start position:0% +externalities okay + + + align:start position:0% +externalities okay +so exercises come through the effects on + + align:start position:0% +so exercises come through the effects on + + + align:start position:0% +so exercises come through the effects on +others so let's think about + + align:start position:0% +others so let's think about + + + align:start position:0% +others so let's think about +the externals of smoking let's think + + align:start position:0% +the externals of smoking let's think + + + align:start position:0% +the externals of smoking let's think +about a negative consumption externality + + align:start position:0% +about a negative consumption externality + + + align:start position:0% +about a negative consumption externality +okay here we have the market for + + align:start position:0% +okay here we have the market for + + + align:start position:0% +okay here we have the market for +cigarettes + + align:start position:0% +cigarettes + + + align:start position:0% +cigarettes +on the x-axis we have the num i'm sorry + + align:start position:0% +on the x-axis we have the num i'm sorry + + + align:start position:0% +on the x-axis we have the num i'm sorry +figured 22-2 + + align:start position:0% +figured 22-2 + + + align:start position:0% +figured 22-2 +on the x-axis we have the number of + + align:start position:0% +on the x-axis we have the number of + + + align:start position:0% +on the x-axis we have the number of +cigarettes quantity cigarettes + + align:start position:0% +cigarettes quantity cigarettes + + + align:start position:0% +cigarettes quantity cigarettes +consumed on the y-axis we have the price + + align:start position:0% +consumed on the y-axis we have the price + + + align:start position:0% +consumed on the y-axis we have the price +of cigarettes per pack + + align:start position:0% +of cigarettes per pack + + + align:start position:0% +of cigarettes per pack +we have initial equilibria point a which + + align:start position:0% +we have initial equilibria point a which + + + align:start position:0% +we have initial equilibria point a which +is where + + align:start position:0% +is where + + + align:start position:0% +is where +the private marginal benefit + + align:start position:0% +the private marginal benefit + + + align:start position:0% +the private marginal benefit +equals the private marginal cost here + + align:start position:0% +equals the private marginal cost here + + + align:start position:0% +equals the private marginal cost here +we're going to assume there's no + + align:start position:0% +we're going to assume there's no + + + align:start position:0% +we're going to assume there's no +externalities from producing tobacco + + align:start position:0% +externalities from producing tobacco + + + align:start position:0% +externalities from producing tobacco +let's assume there's no sludge produced + + align:start position:0% +let's assume there's no sludge produced + + + align:start position:0% +let's assume there's no sludge produced +whatever + + align:start position:0% +whatever + + + align:start position:0% +whatever +that's a separate issue okay there may + + align:start position:0% +that's a separate issue okay there may + + + align:start position:0% +that's a separate issue okay there may +be production externalities too we + + align:start position:0% +be production externalities too we + + + align:start position:0% +be production externalities too we +covered those you already know how to + + align:start position:0% +covered those you already know how to + + + align:start position:0% +covered those you already know how to +think about those + + align:start position:0% +think about those + + + align:start position:0% +think about those +here but here let's assume there aren't + + align:start position:0% +here but here let's assume there aren't + + + align:start position:0% +here but here let's assume there aren't +any let's assume the social marginal + + align:start position:0% +any let's assume the social marginal + + + align:start position:0% +any let's assume the social marginal +cost equals a private marginal cost no + + align:start position:0% +cost equals a private marginal cost no + + + align:start position:0% +cost equals a private marginal cost no +production externalities + + align:start position:0% +production externalities + + + align:start position:0% +production externalities +but there is a consumption externality + + align:start position:0% +but there is a consumption externality + + + align:start position:0% +but there is a consumption externality +every cigarette i smoke is bad for + + align:start position:0% +every cigarette i smoke is bad for + + + align:start position:0% +every cigarette i smoke is bad for +society + + align:start position:0% +society + + + align:start position:0% +society +what that means is the social marginal + + align:start position:0% +what that means is the social marginal + + + align:start position:0% +what that means is the social marginal +benefit is below the private marginal + + align:start position:0% +benefit is below the private marginal + + + align:start position:0% +benefit is below the private marginal +benefit + + align:start position:0% +benefit + + + align:start position:0% +benefit +the social marginal benefit is the + + align:start position:0% +the social marginal benefit is the + + + align:start position:0% +the social marginal benefit is the +private marginal benefit minus marginal + + align:start position:0% +private marginal benefit minus marginal + + + align:start position:0% +private marginal benefit minus marginal +the marginal damage i'm doing md's the + + align:start position:0% +the marginal damage i'm doing md's the + + + align:start position:0% +the marginal damage i'm doing md's the +marginal damage + + align:start position:0% +marginal damage + + + align:start position:0% +marginal damage +the marginal damage i'm doing that's + + align:start position:0% +the marginal damage i'm doing that's + + + align:start position:0% +the marginal damage i'm doing that's +estimated to be about + + align:start position:0% +estimated to be about + + + align:start position:0% +estimated to be about +absent secondhand smoke the damage for + + align:start position:0% +absent secondhand smoke the damage for + + + align:start position:0% +absent secondhand smoke the damage for +smoking is about 50 cents a pack + + align:start position:0% +smoking is about 50 cents a pack + + + align:start position:0% +smoking is about 50 cents a pack +the second hand smoke part is really + + align:start position:0% +the second hand smoke part is really + + + align:start position:0% +the second hand smoke part is really +hard uh + + align:start position:0% +hard uh + + + align:start position:0% +hard uh +uh and the estimates are anywhere from + + align:start position:0% +uh and the estimates are anywhere from + + + align:start position:0% +uh and the estimates are anywhere from +one cent to two dollars per pack + + align:start position:0% +one cent to two dollars per pack + + + align:start position:0% +one cent to two dollars per pack +so that's hard to know how big that is + + align:start position:0% +so that's hard to know how big that is + + + align:start position:0% +so that's hard to know how big that is +okay but + + align:start position:0% +okay but + + + align:start position:0% +okay but +certainly um uh we have we have + + align:start position:0% +certainly um uh we have we have + + + align:start position:0% +certainly um uh we have we have +this negative consumption externality + + align:start position:0% +this negative consumption externality + + + align:start position:0% +this negative consumption externality +which is that basically + + align:start position:0% +which is that basically + + + align:start position:0% +which is that basically +um the every pack of cigarettes i smoke + + align:start position:0% +um the every pack of cigarettes i smoke + + + align:start position:0% +um the every pack of cigarettes i smoke +is worth at least 50 cents less to + + align:start position:0% +is worth at least 50 cents less to + + + align:start position:0% +is worth at least 50 cents less to +society than it's worth to me + + align:start position:0% +society than it's worth to me + + + align:start position:0% +society than it's worth to me +because i'm have these external effects + + align:start position:0% +because i'm have these external effects + + + align:start position:0% +because i'm have these external effects +in society and perhaps a lot + + align:start position:0% +in society and perhaps a lot + + + align:start position:0% +in society and perhaps a lot +more than that as a result i should + + align:start position:0% +more than that as a result i should + + + align:start position:0% +more than that as a result i should +smoke i choose to smoke at point a + + align:start position:0% +smoke i choose to smoke at point a + + + align:start position:0% +smoke i choose to smoke at point a +but the social optimum is point c so + + align:start position:0% +but the social optimum is point c so + + + align:start position:0% +but the social optimum is point c so +once again i've created a deadweight + + align:start position:0% +once again i've created a deadweight + + + align:start position:0% +once again i've created a deadweight +loss once again i'm over + + align:start position:0% +loss once again i'm over + + + align:start position:0% +loss once again i'm over +consuming there's over consumption here + + align:start position:0% +consuming there's over consumption here + + + align:start position:0% +consuming there's over consumption here +just like there's over production seals + + align:start position:0% +just like there's over production seals + + + align:start position:0% +just like there's over production seals +over consumption + + align:start position:0% +over consumption + + + align:start position:0% +over consumption +and a dead weight loss because they're + + align:start position:0% +and a dead weight loss because they're + + + align:start position:0% +and a dead weight loss because they're +units that are privately optimal to + + align:start position:0% +units that are privately optimal to + + + align:start position:0% +units that are privately optimal to +consume + + align:start position:0% +consume + + + align:start position:0% +consume +but not socially optimal + + align:start position:0% + + + + align:start position:0% + +okay now um + + align:start position:0% + + + + align:start position:0% + +externalities this is kind of a fun + + align:start position:0% +externalities this is kind of a fun + + + align:start position:0% +externalities this is kind of a fun +topic because it is interesting i talked + + align:start position:0% +topic because it is interesting i talked + + + align:start position:0% +topic because it is interesting i talked +so let's talk for a second about + + align:start position:0% +so let's talk for a second about + + + align:start position:0% +so let's talk for a second about +secondhand smoke and whether that's + + align:start position:0% +secondhand smoke and whether that's + + + align:start position:0% +secondhand smoke and whether that's +actual externality + + align:start position:0% +actual externality + + + align:start position:0% +actual externality +so almost all the damage taken at smoke + + align:start position:0% +so almost all the damage taken at smoke + + + align:start position:0% +so almost all the damage taken at smoke +is not done by smoking in a crowd it's + + align:start position:0% +is not done by smoking in a crowd it's + + + align:start position:0% +is not done by smoking in a crowd it's +done to family members + + align:start position:0% +done to family members + + + align:start position:0% +done to family members +almost all the damage taken in smoke is + + align:start position:0% +almost all the damage taken in smoke is + + + align:start position:0% +almost all the damage taken in smoke is +done to family members mostly it's that + + align:start position:0% +done to family members mostly it's that + + + align:start position:0% +done to family members mostly it's that +you make your family members sick by + + align:start position:0% +you make your family members sick by + + + align:start position:0% +you make your family members sick by +smoking + + align:start position:0% +smoking + + + align:start position:0% +smoking +is that an externality when or when is + + align:start position:0% +is that an externality when or when is + + + align:start position:0% +is that an externality when or when is +it not an extra under what conditions + + align:start position:0% +it not an extra under what conditions + + + align:start position:0% +it not an extra under what conditions +might it not be an externality + + align:start position:0% +might it not be an externality + + + align:start position:0% +might it not be an externality +yeah well i guess it wouldn't be an + + align:start position:0% +yeah well i guess it wouldn't be an + + + align:start position:0% +yeah well i guess it wouldn't be an +externality if like let's say you die + + align:start position:0% +externality if like let's say you die + + + align:start position:0% +externality if like let's say you die +and then the consequences of them + + align:start position:0% +and then the consequences of them + + + align:start position:0% +and then the consequences of them +getting sick doesn't affect you at all + + align:start position:0% +getting sick doesn't affect you at all + + + align:start position:0% +getting sick doesn't affect you at all +or well obviously no no no no that would + + align:start position:0% +or well obviously no no no no that would + + + align:start position:0% +or well obviously no no no no that would +be okay so what under what conditions + + align:start position:0% +be okay so what under what conditions + + + align:start position:0% +be okay so what under what conditions +under what conditions would it not be + + align:start position:0% +under what conditions would it not be + + + align:start position:0% +under what conditions would it not be +externally when so + + align:start position:0% +externally when so + + + align:start position:0% +externally when so +yeah if you're like if your family gets + + align:start position:0% +yeah if you're like if your family gets + + + align:start position:0% +yeah if you're like if your family gets +sick + + align:start position:0% +sick + + + align:start position:0% +sick +yeah if i care about my family in + + align:start position:0% +yeah if i care about my family in + + + align:start position:0% +yeah if i care about my family in +particular if i maximize + + align:start position:0% +particular if i maximize + + + align:start position:0% +particular if i maximize +family utility that's not an externality + + align:start position:0% +family utility that's not an externality + + + align:start position:0% +family utility that's not an externality +if my if i maximize not my usually my + + align:start position:0% +if my if i maximize not my usually my + + + align:start position:0% +if my if i maximize not my usually my +family's utility + + align:start position:0% +family's utility + + + align:start position:0% +family's utility +then i will essentially internalize + + align:start position:0% +then i will essentially internalize + + + align:start position:0% +then i will essentially internalize +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +internalize the externality + + align:start position:0% + + + + align:start position:0% + +just like a lower wage means that i bear + + align:start position:0% +just like a lower wage means that i bear + + + align:start position:0% +just like a lower wage means that i bear +the consequences for being a less + + align:start position:0% +the consequences for being a less + + + align:start position:0% +the consequences for being a less +productive worker + + align:start position:0% +productive worker + + + align:start position:0% +productive worker +okay if i care about my whole family's + + align:start position:0% +okay if i care about my whole family's + + + align:start position:0% +okay if i care about my whole family's +happiness + + align:start position:0% +happiness + + + align:start position:0% +happiness +and i make my kids sick by smoking + + align:start position:0% +and i make my kids sick by smoking + + + align:start position:0% +and i make my kids sick by smoking +then my smoking decision will actually + + align:start position:0% +then my smoking decision will actually + + + align:start position:0% +then my smoking decision will actually +reflect the total consequences for my + + align:start position:0% +reflect the total consequences for my + + + align:start position:0% +reflect the total consequences for my +family + + align:start position:0% +family + + + align:start position:0% +family +i will smoke only if thoughtful for my + + align:start position:0% +i will smoke only if thoughtful for my + + + align:start position:0% +i will smoke only if thoughtful for my +family for me to do so it doesn't mean i + + align:start position:0% +family for me to do so it doesn't mean i + + + align:start position:0% +family for me to do so it doesn't mean i +won't smoke + + align:start position:0% +won't smoke + + + align:start position:0% +won't smoke +it just means i must i'll have to enjoy + + align:start position:0% +it just means i must i'll have to enjoy + + + align:start position:0% +it just means i must i'll have to enjoy +it enough that it's worth + + align:start position:0% +it enough that it's worth + + + align:start position:0% +it enough that it's worth +making my kids sick okay it doesn't mean + + align:start position:0% +making my kids sick okay it doesn't mean + + + align:start position:0% +making my kids sick okay it doesn't mean +that's an + + align:start position:0% +that's an + + + align:start position:0% +that's an +incorrect decision because after all the + + align:start position:0% +incorrect decision because after all the + + + align:start position:0% +incorrect decision because after all the +odds are you know make your kids that + + align:start position:0% +odds are you know make your kids that + + + align:start position:0% +odds are you know make your kids that +sick and + + align:start position:0% +sick and + + + align:start position:0% +sick and +you know you might like smoking a lot + + align:start position:0% +you know you might like smoking a lot + + + align:start position:0% +you know you might like smoking a lot +okay it's just that + + align:start position:0% +okay it's just that + + + align:start position:0% +okay it's just that +you will internalize the external + + align:start position:0% +you will internalize the external + + + align:start position:0% +you will internalize the external +because you only smoke to the extent + + align:start position:0% +because you only smoke to the extent + + + align:start position:0% +because you only smoke to the extent +that it is optimal for the whole family + + align:start position:0% +that it is optimal for the whole family + + + align:start position:0% +that it is optimal for the whole family +so it's not necessarily an externality + + align:start position:0% +so it's not necessarily an externality + + + align:start position:0% +so it's not necessarily an externality +okay so we'd like actually to test + + align:start position:0% +okay so we'd like actually to test + + + align:start position:0% +okay so we'd like actually to test +whether it's an external there's + + align:start position:0% +whether it's an external there's + + + align:start position:0% +whether it's an external there's +actually a clever test of this + + align:start position:0% +actually a clever test of this + + + align:start position:0% +actually a clever test of this +which is there's a test of whether + + align:start position:0% +which is there's a test of whether + + + align:start position:0% +which is there's a test of whether +people maximize family utility + + align:start position:0% +people maximize family utility + + + align:start position:0% +people maximize family utility +which is if people maximize family + + align:start position:0% +which is if people maximize family + + + align:start position:0% +which is if people maximize family +utility + + align:start position:0% +utility + + + align:start position:0% +utility +what would be the implications of giving + + align:start position:0% +what would be the implications of giving + + + align:start position:0% +what would be the implications of giving +a father a dollar versus giving a mother + + align:start position:0% +a father a dollar versus giving a mother + + + align:start position:0% +a father a dollar versus giving a mother +a dollar + + align:start position:0% +a dollar + + + align:start position:0% +a dollar +if both the father and the mother are + + align:start position:0% +if both the father and the mother are + + + align:start position:0% +if both the father and the mother are +maximizing a family utility function + + align:start position:0% +maximizing a family utility function + + + align:start position:0% +maximizing a family utility function +the same family utility function then + + align:start position:0% +the same family utility function then + + + align:start position:0% +the same family utility function then +should it matter whether i give a dollar + + align:start position:0% +should it matter whether i give a dollar + + + align:start position:0% +should it matter whether i give a dollar +to a father a dollar to a mother + + align:start position:0% +to a father a dollar to a mother + + + align:start position:0% +to a father a dollar to a mother +no it shouldn't because it's a dollar to + + align:start position:0% +no it shouldn't because it's a dollar to + + + align:start position:0% +no it shouldn't because it's a dollar to +the family we're maximizing family + + align:start position:0% +the family we're maximizing family + + + align:start position:0% +the family we're maximizing family +utilities up to a family budget + + align:start position:0% +utilities up to a family budget + + + align:start position:0% +utilities up to a family budget +constraint + + align:start position:0% +constraint + + + align:start position:0% +constraint +it shouldn't matter who gets the dollar + + align:start position:0% +it shouldn't matter who gets the dollar + + + align:start position:0% +it shouldn't matter who gets the dollar +so one test of family utility + + align:start position:0% +so one test of family utility + + + align:start position:0% +so one test of family utility +maximization is + + align:start position:0% +maximization is + + + align:start position:0% +maximization is +does it matter who gets the money and it + + align:start position:0% +does it matter who gets the money and it + + + align:start position:0% +does it matter who gets the money and it +turns out it does a lot + + align:start position:0% +turns out it does a lot + + + align:start position:0% +turns out it does a lot +okay so there's a great test of this + + align:start position:0% +okay so there's a great test of this + + + align:start position:0% +okay so there's a great test of this +they um + + align:start position:0% +they um + + + align:start position:0% +they um +in the uk these have a tax system + + align:start position:0% +in the uk these have a tax system + + + align:start position:0% +in the uk these have a tax system +where essentially uh the way there was a + + align:start position:0% +where essentially uh the way there was a + + + align:start position:0% +where essentially uh the way there was a +credit they gave for every kid + + align:start position:0% +credit they gave for every kid + + + align:start position:0% +credit they gave for every kid +and the way the credit worked is there'd + + align:start position:0% +and the way the credit worked is there'd + + + align:start position:0% +and the way the credit worked is there'd +be a check sent home + + align:start position:0% +be a check sent home + + + align:start position:0% +be a check sent home +okay then they changed it so instead + + align:start position:0% +okay then they changed it so instead + + + align:start position:0% +okay then they changed it so instead +they said well instead of sending a + + align:start position:0% +they said well instead of sending a + + + align:start position:0% +they said well instead of sending a +check home we're just going to add it + + align:start position:0% +check home we're just going to add it + + + align:start position:0% +check home we're just going to add it +into pay into wages + + align:start position:0% +into pay into wages + + + align:start position:0% +into pay into wages +so instead of getting a check sent home + + align:start position:0% +so instead of getting a check sent home + + + align:start position:0% +so instead of getting a check sent home +we're just going to raise your wages + + align:start position:0% +we're just going to raise your wages + + + align:start position:0% +we're just going to raise your wages +well it had no effect on family budgets + + align:start position:0% +well it had no effect on family budgets + + + align:start position:0% +well it had no effect on family budgets +they literally just changed it the + + align:start position:0% +they literally just changed it the + + + align:start position:0% +they literally just changed it the +difference was + + align:start position:0% +difference was + + + align:start position:0% +difference was +back in this in the 70s men worked and + + align:start position:0% +back in this in the 70s men worked and + + + align:start position:0% +back in this in the 70s men worked and +women didn't + + align:start position:0% +women didn't + + + align:start position:0% +women didn't +so when the check came home women + + align:start position:0% +so when the check came home women + + + align:start position:0% +so when the check came home women +controlled it + + align:start position:0% +controlled it + + + align:start position:0% +controlled it +but was in wages men controlled it so if + + align:start position:0% +but was in wages men controlled it so if + + + align:start position:0% +but was in wages men controlled it so if +there's family utility maximization it + + align:start position:0% +there's family utility maximization it + + + align:start position:0% +there's family utility maximization it +shouldn't matter + + align:start position:0% +shouldn't matter + + + align:start position:0% +shouldn't matter +but it turned out as soon as they + + align:start position:0% +but it turned out as soon as they + + + align:start position:0% +but it turned out as soon as they +changed the way they paid it spending on + + align:start position:0% +changed the way they paid it spending on + + + align:start position:0% +changed the way they paid it spending on +kids went down and spending on drugs and + + align:start position:0% +kids went down and spending on drugs and + + + align:start position:0% +kids went down and spending on drugs and +alcohol went up + + align:start position:0% +alcohol went up + + + align:start position:0% +alcohol went up +because basically guys don't care about + + align:start position:0% +because basically guys don't care about + + + align:start position:0% +because basically guys don't care about +kids as much as women do sorry guys + + align:start position:0% +kids as much as women do sorry guys + + + align:start position:0% +kids as much as women do sorry guys +it's just i don't know i don't know what + + align:start position:0% +it's just i don't know i don't know what + + + align:start position:0% +it's just i don't know i don't know what +the evolutionary biology is at least in + + align:start position:0% +the evolutionary biology is at least in + + + align:start position:0% +the evolutionary biology is at least in +the 70s they didn't + + align:start position:0% +the 70s they didn't + + + align:start position:0% +the 70s they didn't +so that's sort of a rejection of family + + align:start position:0% +so that's sort of a rejection of family + + + align:start position:0% +so that's sort of a rejection of family +utility maximization who had the dollars + + align:start position:0% +utility maximization who had the dollars + + + align:start position:0% +utility maximization who had the dollars +actually mattered it's kind of a neat + + align:start position:0% +actually mattered it's kind of a neat + + + align:start position:0% +actually mattered it's kind of a neat +study + + align:start position:0% +study + + + align:start position:0% +study +for how you think about these about + + align:start position:0% +for how you think about these about + + + align:start position:0% +for how you think about these about +these theories so it suggests that + + align:start position:0% +these theories so it suggests that + + + align:start position:0% +these theories so it suggests that +secondhand smoke probably people don't + + align:start position:0% +secondhand smoke probably people don't + + + align:start position:0% +secondhand smoke probably people don't +perfectly maximize family chills there + + align:start position:0% +perfectly maximize family chills there + + + align:start position:0% +perfectly maximize family chills there +probably are some externalities + + align:start position:0% +probably are some externalities + + + align:start position:0% +probably are some externalities +okay so that's uh so that's a negative + + align:start position:0% +okay so that's uh so that's a negative + + + align:start position:0% +okay so that's uh so that's a negative +consumption externality + + align:start position:0% +consumption externality + + + align:start position:0% +consumption externality +there can also of course be positive + + align:start position:0% +there can also of course be positive + + + align:start position:0% +there can also of course be positive +externalities + + align:start position:0% +externalities + + + align:start position:0% +externalities +so let's talk about a positive + + align:start position:0% +so let's talk about a positive + + + align:start position:0% +so let's talk about a positive +consumption externally + + align:start position:0% + + + + align:start position:0% + +let's talk about my neighbor i don't get + + align:start position:0% +let's talk about my neighbor i don't get + + + align:start position:0% +let's talk about my neighbor i don't get +along with my neighbor + + align:start position:0% +along with my neighbor + + + align:start position:0% +along with my neighbor +okay um and partly it's because my + + align:start position:0% +okay um and partly it's because my + + + align:start position:0% +okay um and partly it's because my +neighbor + + align:start position:0% +neighbor + + + align:start position:0% +neighbor +has a habit of starting big projects and + + align:start position:0% +has a habit of starting big projects and + + + align:start position:0% +has a habit of starting big projects and +leaving them half done + + align:start position:0% +leaving them half done + + + align:start position:0% +leaving them half done +and about 25 years ago 20 years ago he + + align:start position:0% +and about 25 years ago 20 years ago he + + + align:start position:0% +and about 25 years ago 20 years ago he +started a big project to landscape his + + align:start position:0% +started a big project to landscape his + + + align:start position:0% +started a big project to landscape his +yard + + align:start position:0% +yard + + + align:start position:0% +yard +created these huge mounds of dirt that i + + align:start position:0% +created these huge mounds of dirt that i + + + align:start position:0% +created these huge mounds of dirt that i +look at directly from my kitchen and + + align:start position:0% +look at directly from my kitchen and + + + align:start position:0% +look at directly from my kitchen and +then stopped + + align:start position:0% +then stopped + + + align:start position:0% +then stopped +so for 20 years i've had to stare at + + align:start position:0% +so for 20 years i've had to stare at + + + align:start position:0% +so for 20 years i've had to stare at +huge amounts of dirt + + align:start position:0% +huge amounts of dirt + + + align:start position:0% +huge amounts of dirt +okay now um + + align:start position:0% +okay now um + + + align:start position:0% +okay now um +let's think about my neighbor's decision + + align:start position:0% +let's think about my neighbor's decision + + + align:start position:0% +let's think about my neighbor's decision +to go and get rid of those piles of dirt + + align:start position:0% +to go and get rid of those piles of dirt + + + align:start position:0% +to go and get rid of those piles of dirt +let's say that that would cost one + + align:start position:0% +let's say that that would cost one + + + align:start position:0% +let's say that that would cost one +thousand dollars + + align:start position:0% +thousand dollars + + + align:start position:0% +thousand dollars +so the cost is a thousand dollars + + align:start position:0% +so the cost is a thousand dollars + + + align:start position:0% +so the cost is a thousand dollars +okay and let's say the benefit to my + + align:start position:0% +okay and let's say the benefit to my + + + align:start position:0% +okay and let's say the benefit to my +neighbor + + align:start position:0% +neighbor + + + align:start position:0% +neighbor +from doing so is clearly less than a + + align:start position:0% +from doing so is clearly less than a + + + align:start position:0% +from doing so is clearly less than a +thousand dollars we would have done it + + align:start position:0% +thousand dollars we would have done it + + + align:start position:0% +thousand dollars we would have done it +let's say it's 800 so that's why he + + align:start position:0% +let's say it's 800 so that's why he + + + align:start position:0% +let's say it's 800 so that's why he +leaves those piles of dirt + + align:start position:0% +leaves those piles of dirt + + + align:start position:0% +leaves those piles of dirt +because the cost is a thousand dollars + + align:start position:0% +because the cost is a thousand dollars + + + align:start position:0% +because the cost is a thousand dollars +to remove them it's only worth injured + + align:start position:0% +to remove them it's only worth injured + + + align:start position:0% +to remove them it's only worth injured +to him + + align:start position:0% +to him + + + align:start position:0% +to him +but what he's not accounting for is if + + align:start position:0% +but what he's not accounting for is if + + + align:start position:0% +but what he's not accounting for is if +he removed them + + align:start position:0% +he removed them + + + align:start position:0% +he removed them +there'd be positive benefit to me + + align:start position:0% +there'd be positive benefit to me + + + align:start position:0% +there'd be positive benefit to me +of another 300 + + align:start position:0% + + + + align:start position:0% + +so actually the total social benefit of + + align:start position:0% +so actually the total social benefit of + + + align:start position:0% +so actually the total social benefit of +removing the dirt piles + + align:start position:0% +removing the dirt piles + + + align:start position:0% +removing the dirt piles +is higher than the social cost from a + + align:start position:0% +is higher than the social cost from a + + + align:start position:0% +is higher than the social cost from a +social perspective he should do it + + align:start position:0% +social perspective he should do it + + + align:start position:0% +social perspective he should do it +but he doesn't because privately it's + + align:start position:0% +but he doesn't because privately it's + + + align:start position:0% +but he doesn't because privately it's +not optimal to do so + + align:start position:0% +not optimal to do so + + + align:start position:0% +not optimal to do so +okay so that is a positive + + align:start position:0% +okay so that is a positive + + + align:start position:0% +okay so that is a positive +consumption externality yeah does this + + align:start position:0% +consumption externality yeah does this + + + align:start position:0% +consumption externality yeah does this +mean you'd be willing to pay him like + + align:start position:0% +mean you'd be willing to pay him like + + + align:start position:0% +mean you'd be willing to pay him like + + align:start position:0% + + + align:start position:0% +to do it well this leads to a very deep + + align:start position:0% +to do it well this leads to a very deep + + + align:start position:0% +to do it well this leads to a very deep +question + + align:start position:0% +question + + + align:start position:0% +question +which is can't all externality simply be + + align:start position:0% +which is can't all externality simply be + + + align:start position:0% +which is can't all externality simply be +internalized let's take this example + + align:start position:0% +internalized let's take this example + + + align:start position:0% +internalized let's take this example +why can't i just go over an offer to pay + + align:start position:0% +why can't i just go over an offer to pay + + + align:start position:0% +why can't i just go over an offer to pay +him + + align:start position:0% +him + + + align:start position:0% +him +okay well and in fact with any example + + align:start position:0% +okay well and in fact with any example + + + align:start position:0% +okay well and in fact with any example +we can do that why can't the fisherman + + align:start position:0% +we can do that why can't the fisherman + + + align:start position:0% +we can do that why can't the fisherman +just go pay the steel plant + + align:start position:0% +just go pay the steel plant + + + align:start position:0% +just go pay the steel plant +okay why can't you pay me not to smoke + + align:start position:0% +okay why can't you pay me not to smoke + + + align:start position:0% +okay why can't you pay me not to smoke +in class + + align:start position:0% +in class + + + align:start position:0% +in class +okay indeed with any of these + + align:start position:0% +okay indeed with any of these + + + align:start position:0% +okay indeed with any of these +externalities the question why can't + + align:start position:0% +externalities the question why can't + + + align:start position:0% +externalities the question why can't +they all be internalized + + align:start position:0% +they all be internalized + + + align:start position:0% +they all be internalized +and indeed there's a school of thought + + align:start position:0% +and indeed there's a school of thought + + + align:start position:0% +and indeed there's a school of thought +which suggests that exercises aren't + + align:start position:0% +which suggests that exercises aren't + + + align:start position:0% +which suggests that exercises aren't +real a problem they can all just be + + align:start position:0% +real a problem they can all just be + + + align:start position:0% +real a problem they can all just be +internalized + + align:start position:0% +internalized + + + align:start position:0% +internalized +but of course that's totally wrong okay + + align:start position:0% +but of course that's totally wrong okay + + + align:start position:0% +but of course that's totally wrong okay +let's start with a hard example + + align:start position:0% +let's start with a hard example + + + align:start position:0% +let's start with a hard example +let's talk about the biggest + + align:start position:0% +let's talk about the biggest + + + align:start position:0% +let's talk about the biggest +environmental + + align:start position:0% +environmental + + + align:start position:0% +environmental +externality which is global warming okay + + align:start position:0% +externality which is global warming okay + + + align:start position:0% +externality which is global warming okay +with global warming okay every tangle + + align:start position:0% +with global warming okay every tangle + + + align:start position:0% +with global warming okay every tangle +time you drive + + align:start position:0% +time you drive + + + align:start position:0% +time you drive +you are bringing people of bangladesh + + align:start position:0% +you are bringing people of bangladesh + + + align:start position:0% +you are bringing people of bangladesh +that much closer to being underwater + + align:start position:0% +that much closer to being underwater + + + align:start position:0% +that much closer to being underwater +how could you possibly negotiate that + + align:start position:0% +how could you possibly negotiate that + + + align:start position:0% +how could you possibly negotiate that +how could you possibly negotiate where + + align:start position:0% +how could you possibly negotiate where + + + align:start position:0% +how could you possibly negotiate where +the people of bangladesh would come and + + align:start position:0% +the people of bangladesh would come and + + + align:start position:0% +the people of bangladesh would come and +say we'll drive a little bit less so i + + align:start position:0% +say we'll drive a little bit less so i + + + align:start position:0% +say we'll drive a little bit less so i +don't go underwater + + align:start position:0% +don't go underwater + + + align:start position:0% +don't go underwater +okay that's not happening okay but even + + align:start position:0% +okay that's not happening okay but even + + + align:start position:0% +okay that's not happening okay but even +with these simple cases think about this + + align:start position:0% +with these simple cases think about this + + + align:start position:0% +with these simple cases think about this +why can't i just go to my neighbor and + + align:start position:0% +why can't i just go to my neighbor and + + + align:start position:0% +why can't i just go to my neighbor and +offer 200 bucks + + align:start position:0% +offer 200 bucks + + + align:start position:0% +offer 200 bucks +there's three problems first problem is + + align:start position:0% +there's three problems first problem is + + + align:start position:0% +there's three problems first problem is +there's uh the fact that + + align:start position:0% +there's uh the fact that + + + align:start position:0% +there's uh the fact that +i don't really know what his costs are + + align:start position:0% +i don't really know what his costs are + + + align:start position:0% +i don't really know what his costs are +and what his benefits are + + align:start position:0% +and what his benefits are + + + align:start position:0% +and what his benefits are +and that i might i don't want to offer + + align:start position:0% +and that i might i don't want to offer + + + align:start position:0% +and that i might i don't want to offer +more than i have to to get him do it + + align:start position:0% +more than i have to to get him do it + + + align:start position:0% +more than i have to to get him do it +okay the second problem is he don't know + + align:start position:0% +okay the second problem is he don't know + + + align:start position:0% +okay the second problem is he don't know +how it doesn't know how i feel so it's + + align:start position:0% +how it doesn't know how i feel so it's + + + align:start position:0% +how it doesn't know how i feel so it's +an information asymmetry + + align:start position:0% +an information asymmetry + + + align:start position:0% +an information asymmetry +which makes negotiations hard the third + + align:start position:0% +which makes negotiations hard the third + + + align:start position:0% +which makes negotiations hard the third +problem too which is it'd just be deeply + + align:start position:0% +problem too which is it'd just be deeply + + + align:start position:0% +problem too which is it'd just be deeply +weird to do that + + align:start position:0% +weird to do that + + + align:start position:0% +weird to do that +right i mean it's just not how society + + align:start position:0% +right i mean it's just not how society + + + align:start position:0% +right i mean it's just not how society +works you think about a class case of an + + align:start position:0% +works you think about a class case of an + + + align:start position:0% +works you think about a class case of an +external you probably all run into + + align:start position:0% +external you probably all run into + + + align:start position:0% +external you probably all run into +with your neighbor playing their music + + align:start position:0% +with your neighbor playing their music + + + align:start position:0% +with your neighbor playing their music +too loud + + align:start position:0% +too loud + + + align:start position:0% +too loud +okay if your neighbor plays their music + + align:start position:0% +okay if your neighbor plays their music + + + align:start position:0% +okay if your neighbor plays their music +too loud that is an externality + + align:start position:0% +too loud that is an externality + + + align:start position:0% +too loud that is an externality +on you okay now in principle + + align:start position:0% +on you okay now in principle + + + align:start position:0% +on you okay now in principle +you go to your neighbor and say well + + align:start position:0% +you go to your neighbor and say well + + + align:start position:0% +you go to your neighbor and say well +look i'm studying for a test + + align:start position:0% +look i'm studying for a test + + + align:start position:0% +look i'm studying for a test +this test will raise my grade by 10 + + align:start position:0% +this test will raise my grade by 10 + + + align:start position:0% +this test will raise my grade by 10 +points a higher grade + + align:start position:0% +points a higher grade + + + align:start position:0% +points a higher grade +in this class will raise my earnings by + + align:start position:0% +in this class will raise my earnings by + + + align:start position:0% +in this class will raise my earnings by +a thousand dollars + + align:start position:0% +a thousand dollars + + + align:start position:0% +a thousand dollars +so i'm willing to pay you 83 to stop + + align:start position:0% +so i'm willing to pay you 83 to stop + + + align:start position:0% +so i'm willing to pay you 83 to stop +playing music + + align:start position:0% +playing music + + + align:start position:0% +playing music +because i've calculated my lifetime + + align:start position:0% +because i've calculated my lifetime + + + align:start position:0% +because i've calculated my lifetime +earning effect you're playing the music + + align:start position:0% +earning effect you're playing the music + + + align:start position:0% +earning effect you're playing the music +okay even at mit okay that'd be sort of + + align:start position:0% +okay even at mit okay that'd be sort of + + + align:start position:0% +okay even at mit okay that'd be sort of +deeply weird to do + + align:start position:0% +deeply weird to do + + + align:start position:0% +deeply weird to do +so what do you do you either shut up + + align:start position:0% +so what do you do you either shut up + + + align:start position:0% +so what do you do you either shut up +about it you go yell at them + + align:start position:0% +about it you go yell at them + + + align:start position:0% +about it you go yell at them +okay but yelling induces is an honestly + + align:start position:0% +okay but yelling induces is an honestly + + + align:start position:0% +okay but yelling induces is an honestly +efficient way to resolve it because + + align:start position:0% +efficient way to resolve it because + + + align:start position:0% +efficient way to resolve it because +maybe they really want to play the music + + align:start position:0% +maybe they really want to play the music + + + align:start position:0% +maybe they really want to play the music +the efficient thing would be if it's + + align:start position:0% +the efficient thing would be if it's + + + align:start position:0% +the efficient thing would be if it's +worth more than eight three dollars then + + align:start position:0% +worth more than eight three dollars then + + + align:start position:0% +worth more than eight three dollars then +to play the music they should get to pay + + align:start position:0% +to play the music they should get to pay + + + align:start position:0% +to play the music they should get to pay +it and just pay you 83 + + align:start position:0% +it and just pay you 83 + + + align:start position:0% +it and just pay you 83 +but in fact that doesn't work so in fact + + align:start position:0% +but in fact that doesn't work so in fact + + + align:start position:0% +but in fact that doesn't work so in fact +private solutions these problems simply + + align:start position:0% +private solutions these problems simply + + + align:start position:0% +private solutions these problems simply +do not work + + align:start position:0% +do not work + + + align:start position:0% +do not work +okay it's just hard to figure out how + + align:start position:0% +okay it's just hard to figure out how + + + align:start position:0% +okay it's just hard to figure out how +you can really get people privately + + align:start position:0% +you can really get people privately + + + align:start position:0% +you can really get people privately +to internalize uh these um + + align:start position:0% +to internalize uh these um + + + align:start position:0% +to internalize uh these um +uh these externalities okay because + + align:start position:0% +uh these externalities okay because + + + align:start position:0% +uh these externalities okay because +negotiation is difficult because there's + + align:start position:0% +negotiation is difficult because there's + + + align:start position:0% +negotiation is difficult because there's +just socially awkward + + align:start position:0% +just socially awkward + + + align:start position:0% +just socially awkward +there is a famous apocryphal story told + + align:start position:0% +there is a famous apocryphal story told + + + align:start position:0% +there is a famous apocryphal story told +of a famous economist + + align:start position:0% +of a famous economist + + + align:start position:0% +of a famous economist +who was on a flight want to get work + + align:start position:0% +who was on a flight want to get work + + + align:start position:0% +who was on a flight want to get work +done and couldn't because the person + + align:start position:0% +done and couldn't because the person + + + align:start position:0% +done and couldn't because the person +actually wouldn't stop talking + + align:start position:0% +actually wouldn't stop talking + + + align:start position:0% +actually wouldn't stop talking +so they actually offered them 10 bucks + + align:start position:0% +so they actually offered them 10 bucks + + + align:start position:0% +so they actually offered them 10 bucks +to shut up uh i don't believe that + + align:start position:0% +to shut up uh i don't believe that + + + align:start position:0% +to shut up uh i don't believe that +actually happened but + + align:start position:0% +actually happened but + + + align:start position:0% +actually happened but +you know makes for a good story okay so + + align:start position:0% +you know makes for a good story okay so + + + align:start position:0% +you know makes for a good story okay so +that's a positive consumption externally + + align:start position:0% +that's a positive consumption externally + + + align:start position:0% +that's a positive consumption externally +finally we have positive production + + align:start position:0% +finally we have positive production + + + align:start position:0% +finally we have positive production +externalities + + align:start position:0% + + + + align:start position:0% + +the classic example positive production + + align:start position:0% +the classic example positive production + + + align:start position:0% +the classic example positive production +externality + + align:start position:0% +externality + + + align:start position:0% +externality +is um r d by private firms + + align:start position:0% +is um r d by private firms + + + align:start position:0% +is um r d by private firms +okay when a firm does research and + + align:start position:0% +okay when a firm does research and + + + align:start position:0% +okay when a firm does research and +development + + align:start position:0% +development + + + align:start position:0% +development +they don't just create learning for + + align:start position:0% +they don't just create learning for + + + align:start position:0% +they don't just create learning for +themselves they create learning that + + align:start position:0% +themselves they create learning that + + + align:start position:0% +themselves they create learning that +might benefit other firms as well okay + + align:start position:0% +might benefit other firms as well okay + + + align:start position:0% +might benefit other firms as well okay +and indeed the best economic estimates + + align:start position:0% +and indeed the best economic estimates + + + align:start position:0% +and indeed the best economic estimates +suggest that the social returns to a + + align:start position:0% +suggest that the social returns to a + + + align:start position:0% +suggest that the social returns to a +dollar of r d + + align:start position:0% +dollar of r d + + + align:start position:0% +dollar of r d +are two and a half times the private + + align:start position:0% +are two and a half times the private + + + align:start position:0% +are two and a half times the private +returns that every dollar of r d a firm + + align:start position:0% +returns that every dollar of r d a firm + + + align:start position:0% +returns that every dollar of r d a firm +does + + align:start position:0% +does + + + align:start position:0% +does +benefits society by two and a half times + + align:start position:0% +benefits society by two and a half times + + + align:start position:0% +benefits society by two and a half times +how much it benefits the firm + + align:start position:0% +how much it benefits the firm + + + align:start position:0% +how much it benefits the firm +and as a result firms under invest in r + + align:start position:0% +and as a result firms under invest in r + + + align:start position:0% +and as a result firms under invest in r +d + + align:start position:0% +d + + + align:start position:0% +d +okay as well firms under invest in r d + + align:start position:0% +okay as well firms under invest in r d + + + align:start position:0% +okay as well firms under invest in r d +okay uh and they are and that's leading + + align:start position:0% +okay uh and they are and that's leading + + + align:start position:0% +okay uh and they are and that's leading +them + + align:start position:0% +them + + + align:start position:0% +them +to uh that's leading to too little r d + + align:start position:0% +to uh that's leading to too little r d + + + align:start position:0% +to uh that's leading to too little r d +being done in society that affects all + + align:start position:0% +being done in society that affects all + + + align:start position:0% +being done in society that affects all +of us because that affects growth + + align:start position:0% +of us because that affects growth + + + align:start position:0% +of us because that affects growth +that's what my new book jumps starting + + align:start position:0% +that's what my new book jumps starting + + + align:start position:0% +that's what my new book jumps starting +america is all about is about why we + + align:start position:0% +america is all about is about why we + + + align:start position:0% +america is all about is about why we +need the government to come in + + align:start position:0% +need the government to come in + + + align:start position:0% +need the government to come in +and invest more in our because firms + + align:start position:0% +and invest more in our because firms + + + align:start position:0% +and invest more in our because firms +under invest okay essentially firms + + align:start position:0% +under invest okay essentially firms + + + align:start position:0% +under invest okay essentially firms +don't account for the spillovers + + align:start position:0% +don't account for the spillovers + + + align:start position:0% +don't account for the spillovers +that their investments have on others so + + align:start position:0% +that their investments have on others so + + + align:start position:0% +that their investments have on others so +a great example used in the book + + align:start position:0% +a great example used in the book + + + align:start position:0% +a great example used in the book +is the example of when two drug + + align:start position:0% +is the example of when two drug + + + align:start position:0% +is the example of when two drug +companies were racing to invent statins + + align:start position:0% +companies were racing to invent statins + + + align:start position:0% +companies were racing to invent statins +you guys are too young to know about + + align:start position:0% +you guys are too young to know about + + + align:start position:0% +you guys are too young to know about +statins but statins are basically a + + align:start position:0% +statins but statins are basically a + + + align:start position:0% +statins but statins are basically a +cholesterol lowering drug that's a + + align:start position:0% +cholesterol lowering drug that's a + + + align:start position:0% +cholesterol lowering drug that's a +miracle it saves hundreds of thousands + + align:start position:0% +miracle it saves hundreds of thousands + + + align:start position:0% +miracle it saves hundreds of thousands +of lives every year that says about 200 + + align:start position:0% +of lives every year that says about 200 + + + align:start position:0% +of lives every year that says about 200 +000 lives a year are saved by people + + align:start position:0% +000 lives a year are saved by people + + + align:start position:0% +000 lives a year are saved by people +lowering the cholesterol for being on + + align:start position:0% +lowering the cholesterol for being on + + + align:start position:0% +lowering the cholesterol for being on +statins + + align:start position:0% +statins + + + align:start position:0% +statins +statins are being invented in the early + + align:start position:0% +statins are being invented in the early + + + align:start position:0% +statins are being invented in the early +1980s by two rival drug companies + + align:start position:0% +1980s by two rival drug companies + + + align:start position:0% +1980s by two rival drug companies +merck in the us and senko in japan they + + align:start position:0% +merck in the us and senko in japan they + + + align:start position:0% +merck in the us and senko in japan they +were racing developed these statins + + align:start position:0% +were racing developed these statins + + + align:start position:0% +were racing developed these statins +and then thank you suddenly stopped and + + align:start position:0% +and then thank you suddenly stopped and + + + align:start position:0% +and then thank you suddenly stopped and +merck found out to the great finance + + align:start position:0% +merck found out to the great finance + + + align:start position:0% +merck found out to the great finance +because some dogs got sick + + align:start position:0% +because some dogs got sick + + + align:start position:0% +because some dogs got sick +in drug truck in the animal trials and + + align:start position:0% +in drug truck in the animal trials and + + + align:start position:0% +in drug truck in the animal trials and +so merc went to thank you and said hey + + align:start position:0% +so merc went to thank you and said hey + + + align:start position:0% +so merc went to thank you and said hey +where's the dog what's going on say he + + align:start position:0% +where's the dog what's going on say he + + + align:start position:0% +where's the dog what's going on say he +said we're not going to tell you + + align:start position:0% +said we're not going to tell you + + + align:start position:0% +said we're not going to tell you +you're our competitor so murk offered to + + align:start position:0% +you're our competitor so murk offered to + + + align:start position:0% +you're our competitor so murk offered to +pay the money they offered to partner + + align:start position:0% +pay the money they offered to partner + + + align:start position:0% +pay the money they offered to partner +sake you said no way + + align:start position:0% +sake you said no way + + + align:start position:0% +sake you said no way +this is private r d we don't want to + + align:start position:0% +this is private r d we don't want to + + + align:start position:0% +this is private r d we don't want to +share it with you so merc stopped too + + align:start position:0% +share it with you so merc stopped too + + + align:start position:0% +share it with you so merc stopped too +five years later some academics got + + align:start position:0% +five years later some academics got + + + align:start position:0% +five years later some academics got +permission to run trials on statins + + align:start position:0% +permission to run trials on statins + + + align:start position:0% +permission to run trials on statins +turns out that what happened the dogs + + align:start position:0% +turns out that what happened the dogs + + + align:start position:0% +turns out that what happened the dogs +had nothing to do with the drug + + align:start position:0% +had nothing to do with the drug + + + align:start position:0% +had nothing to do with the drug +they were fine it's totally safe and + + align:start position:0% +they were fine it's totally safe and + + + align:start position:0% +they were fine it's totally safe and +statins were invented + + align:start position:0% +statins were invented + + + align:start position:0% +statins were invented +and save on 200 000 lives a year but + + align:start position:0% +and save on 200 000 lives a year but + + + align:start position:0% +and save on 200 000 lives a year but +five years after they should have + + align:start position:0% +five years after they should have + + + align:start position:0% +five years after they should have +literally one million people died okay + + align:start position:0% +literally one million people died okay + + + align:start position:0% +literally one million people died okay +because there was they could not benefit + + align:start position:0% +because there was they could not benefit + + + align:start position:0% +because there was they could not benefit +from the spillovers of r d knowledge + + align:start position:0% +from the spillovers of r d knowledge + + + align:start position:0% +from the spillovers of r d knowledge +okay this is an example and by under + + align:start position:0% +okay this is an example and by under + + + align:start position:0% +okay this is an example and by under +investment in r d + + align:start position:0% +investment in r d + + + align:start position:0% +investment in r d +okay so we have x analysis to be + + align:start position:0% +okay so we have x analysis to be + + + align:start position:0% +okay so we have x analysis to be +negative or positive the q production + + align:start position:0% +negative or positive the q production + + + align:start position:0% +negative or positive the q production +side or consumption side + + align:start position:0% +side or consumption side + + + align:start position:0% +side or consumption side +questions about that yeah so regardless + + align:start position:0% +questions about that yeah so regardless + + + align:start position:0% +questions about that yeah so regardless +if they're negative or positive + + align:start position:0% +if they're negative or positive + + + align:start position:0% +if they're negative or positive +externalities still create that weight + + align:start position:0% +externalities still create that weight + + + align:start position:0% +externalities still create that weight +loss yes we're also negative or positive + + align:start position:0% +loss yes we're also negative or positive + + + align:start position:0% +loss yes we're also negative or positive +everybody says + + align:start position:0% +everybody says + + + align:start position:0% +everybody says +still create deadweight loss because if + + align:start position:0% +still create deadweight loss because if + + + align:start position:0% +still create deadweight loss because if +they're positive i should um + + align:start position:0% +they're positive i should um + + + align:start position:0% +they're positive i should um +um jason just send me a note next year + + align:start position:0% +um jason just send me a note next year + + + align:start position:0% +um jason just send me a note next year +next year we should have in the handout + + align:start position:0% +next year we should have in the handout + + + align:start position:0% +next year we should have in the handout +a positive + + align:start position:0% +a positive + + + align:start position:0% +a positive +threat well i'll just do it here i can + + align:start position:0% +threat well i'll just do it here i can + + + align:start position:0% +threat well i'll just do it here i can +i'm i'm not i'm capable of drawing graph + + align:start position:0% +i'm i'm not i'm capable of drawing graph + + + align:start position:0% +i'm i'm not i'm capable of drawing graph +so let's say about r and d okay here's + + align:start position:0% +so let's say about r and d okay here's + + + align:start position:0% +so let's say about r and d okay here's +the quantity of r d + + align:start position:0% +the quantity of r d + + + align:start position:0% +the quantity of r d +okay here's the cost of r d the price of + + align:start position:0% +okay here's the cost of r d the price of + + + align:start position:0% +okay here's the cost of r d the price of +r d + + align:start position:0% +r d + + + align:start position:0% +r d +so basically and here's the the um + + align:start position:0% +so basically and here's the the um + + + align:start position:0% +so basically and here's the the um +here's the uh so here's going to be the + + align:start position:0% +here's the uh so here's going to be the + + + align:start position:0% +here's the uh so here's going to be the +demand for r d + + align:start position:0% +demand for r d + + + align:start position:0% +demand for r d +okay here's good demand which is private + + align:start position:0% +okay here's good demand which is private + + + align:start position:0% +okay here's good demand which is private +marginal benefit + + align:start position:0% +marginal benefit + + + align:start position:0% +marginal benefit +and here's the uh here's the supply + + align:start position:0% +and here's the uh here's the supply + + + align:start position:0% +and here's the uh here's the supply +which is the private marginal cost okay + + align:start position:0% +which is the private marginal cost okay + + + align:start position:0% +which is the private marginal cost okay +and let's just say that there's no + + align:start position:0% +and let's just say that there's no + + + align:start position:0% +and let's just say that there's no +excellence from actually th + + align:start position:0% +excellence from actually th + + + align:start position:0% +excellence from actually th +this is a consumption exercise this is + + align:start position:0% +this is a consumption exercise this is + + + align:start position:0% +this is a consumption exercise this is +this is a production externality + + align:start position:0% +this is a production externality + + + align:start position:0% +this is a production externality +so basically the point is that when a + + align:start position:0% +so basically the point is that when a + + + align:start position:0% +so basically the point is that when a +firm does r d + + align:start position:0% +firm does r d + + + align:start position:0% +firm does r d +they do until the benefits to the firm + + align:start position:0% +they do until the benefits to the firm + + + align:start position:0% +they do until the benefits to the firm +okay + + align:start position:0% +okay + + + align:start position:0% +okay +equal the cost to the firm so they do an + + align:start position:0% +equal the cost to the firm so they do an + + + align:start position:0% +equal the cost to the firm so they do an +optimal they do an amount of r d + + align:start position:0% +optimal they do an amount of r d + + + align:start position:0% +optimal they do an amount of r d +of uh you know q1 + + align:start position:0% +of uh you know q1 + + + align:start position:0% +of uh you know q1 +okay at a price of p1 now but what + + align:start position:0% +okay at a price of p1 now but what + + + align:start position:0% +okay at a price of p1 now but what +they're missing + + align:start position:0% +they're missing + + + align:start position:0% +they're missing +is that in fact what they're missing is + + align:start position:0% +is that in fact what they're missing is + + + align:start position:0% +is that in fact what they're missing is +that the cost + + align:start position:0% +that the cost + + + align:start position:0% +that the cost +to them are actually well below + + align:start position:0% +to them are actually well below + + + align:start position:0% +to them are actually well below +uh well below what it truly cost because + + align:start position:0% +uh well below what it truly cost because + + + align:start position:0% +uh well below what it truly cost because +they are benefiting others by doing it + + align:start position:0% +they are benefiting others by doing it + + + align:start position:0% +they are benefiting others by doing it +okay so the supply curve the pri + + align:start position:0% +okay so the supply curve the pri + + + align:start position:0% +okay so the supply curve the pri +the the true social supply curve is down + + align:start position:0% +the the true social supply curve is down + + + align:start position:0% +the the true social supply curve is down +here the social marginal cost + + align:start position:0% +here the social marginal cost + + + align:start position:0% +here the social marginal cost +is the private marginal cost minus the + + align:start position:0% +is the private marginal cost minus the + + + align:start position:0% +is the private marginal cost minus the +social benefits + + align:start position:0% + + + + align:start position:0% + +that we get from doing that r d so as a + + align:start position:0% +that we get from doing that r d so as a + + + align:start position:0% +that we get from doing that r d so as a +result + + align:start position:0% +result + + + align:start position:0% +result +they should be doing q2 r d but they're + + align:start position:0% +they should be doing q2 r d but they're + + + align:start position:0% +they should be doing q2 r d but they're +not + + align:start position:0% +not + + + align:start position:0% +not +they're doing too little r d and that's + + align:start position:0% +they're doing too little r d and that's + + + align:start position:0% +they're doing too little r d and that's +making a deadweight loss + + align:start position:0% +making a deadweight loss + + + align:start position:0% +making a deadweight loss +the deadweight loss remember is with + + align:start position:0% +the deadweight loss remember is with + + + align:start position:0% +the deadweight loss remember is with +reference to the optimal point + + align:start position:0% +reference to the optimal point + + + align:start position:0% +reference to the optimal point +this is the deadweight loss this + + align:start position:0% +this is the deadweight loss this + + + align:start position:0% +this is the deadweight loss this +deadweight loss from under producing + + align:start position:0% +deadweight loss from under producing + + + align:start position:0% +deadweight loss from under producing +um r d the difference between uh + + align:start position:0% +um r d the difference between uh + + + align:start position:0% +um r d the difference between uh +no i'm sorry i got that wrong this is + + align:start position:0% +no i'm sorry i got that wrong this is + + + align:start position:0% +no i'm sorry i got that wrong this is +always triangle's always confusing i got + + align:start position:0% +always triangle's always confusing i got + + + align:start position:0% +always triangle's always confusing i got +that wrong + + align:start position:0% +that wrong + + + align:start position:0% +that wrong +okay it's the difference between the + + align:start position:0% +okay it's the difference between the + + + align:start position:0% +okay it's the difference between the +social marginal cost between the social + + align:start position:0% +social marginal cost between the social + + + align:start position:0% +social marginal cost between the social +marginal cost + + align:start position:0% +marginal cost + + + align:start position:0% +marginal cost +and the private marginal benefit so + + align:start position:0% +and the private marginal benefit so + + + align:start position:0% +and the private marginal benefit so +basically + + align:start position:0% +basically + + + align:start position:0% +basically +let me think about this for one second + + align:start position:0% +let me think about this for one second + + + align:start position:0% +let me think about this for one second +it's always a little bit hard to do so + + align:start position:0% +it's always a little bit hard to do so + + + align:start position:0% +it's always a little bit hard to do so +basically their units + + align:start position:0% +basically their units + + + align:start position:0% +basically their units +they their units they under produce so + + align:start position:0% +they their units they under produce so + + + align:start position:0% +they their units they under produce so +essentially + + align:start position:0% +essentially + + + align:start position:0% +essentially +what they're they should be producing + + align:start position:0% +what they're they should be producing + + + align:start position:0% +what they're they should be producing +this many units + + align:start position:0% +this many units + + + align:start position:0% +this many units +yeah between the with the private margin + + align:start position:0% +yeah between the with the private margin + + + align:start position:0% +yeah between the with the private margin +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +it says i hit it right that's the + + align:start position:0% +it says i hit it right that's the + + + align:start position:0% +it says i hit it right that's the +deadweight loss + + align:start position:0% +deadweight loss + + + align:start position:0% +deadweight loss +okay yeah so basically what you have is + + align:start position:0% +okay yeah so basically what you have is + + + align:start position:0% +okay yeah so basically what you have is +you're going to have + + align:start position:0% +you're going to have + + + align:start position:0% +you're going to have +under production of r d just like you + + align:start position:0% +under production of r d just like you + + + align:start position:0% +under production of r d just like you +had over production of steel + + align:start position:0% +had over production of steel + + + align:start position:0% +had over production of steel +okay yeah uh why would the social + + align:start position:0% +okay yeah uh why would the social + + + align:start position:0% +okay yeah uh why would the social +marginal costs go down + + align:start position:0% +marginal costs go down + + + align:start position:0% +marginal costs go down +marginal benefit because this the + + align:start position:0% +marginal benefit because this the + + + align:start position:0% +marginal benefit because this the +marginal benefit is + + align:start position:0% +marginal benefit is + + + align:start position:0% +marginal benefit is +what's the marginal benefit of another + + align:start position:0% +what's the marginal benefit of another + + + align:start position:0% +what's the marginal benefit of another +dollar of r d + + align:start position:0% +dollar of r d + + + align:start position:0% +dollar of r d +that's that's basically that's + + align:start position:0% +that's that's basically that's + + + align:start position:0% +that's that's basically that's +essentially what's the knowledge created + + align:start position:0% +essentially what's the knowledge created + + + align:start position:0% +essentially what's the knowledge created +okay you could you could view this + + align:start position:0% +okay you could you could view this + + + align:start position:0% +okay you could you could view this +either way but the idea here is + + align:start position:0% +either way but the idea here is + + + align:start position:0% +either way but the idea here is +i'm producing r d i'm not consuming r d + + align:start position:0% +i'm producing r d i'm not consuming r d + + + align:start position:0% +i'm producing r d i'm not consuming r d +this is the benefit of consuming r + + align:start position:0% +this is the benefit of consuming r + + + align:start position:0% +this is the benefit of consuming r +d this is sort of the benefit side of + + align:start position:0% +d this is sort of the benefit side of + + + align:start position:0% +d this is sort of the benefit side of +consuming that r d this is the use so + + align:start position:0% +consuming that r d this is the use so + + + align:start position:0% +consuming that r d this is the use so +you think it was lowering the cost of + + align:start position:0% +you think it was lowering the cost of + + + align:start position:0% +you think it was lowering the cost of +producing the r d + + align:start position:0% +producing the r d + + + align:start position:0% +producing the r d +is sort of the way we think about it + + align:start position:0% +is sort of the way we think about it + + + align:start position:0% +is sort of the way we think about it +okay but the main thing is not + + align:start position:0% +okay but the main thing is not + + + align:start position:0% +okay but the main thing is not +is not yeah so is the the marginal + + align:start position:0% +is not yeah so is the the marginal + + + align:start position:0% +is not yeah so is the the marginal +change between the + + align:start position:0% +change between the + + + align:start position:0% +change between the +social curve and the private curve is + + align:start position:0% +social curve and the private curve is + + + align:start position:0% +social curve and the private curve is +that + + align:start position:0% +that + + + align:start position:0% +that +linear or as it grows that that's a + + align:start position:0% +linear or as it grows that that's a + + + align:start position:0% +linear or as it grows that that's a +great question i'm always making it + + align:start position:0% +great question i'm always making it + + + align:start position:0% +great question i'm always making it +i'm making a constant i'm assuming + + align:start position:0% +i'm making a constant i'm assuming + + + align:start position:0% +i'm making a constant i'm assuming +marginal damage marginal damage or + + align:start position:0% +marginal damage marginal damage or + + + align:start position:0% +marginal damage marginal damage or +marginal benefits are constant + + align:start position:0% +marginal benefits are constant + + + align:start position:0% +marginal benefits are constant +mathematically whichever triangle you + + align:start position:0% +mathematically whichever triangle you + + + align:start position:0% +mathematically whichever triangle you +choose is the same + + align:start position:0% +choose is the same + + + align:start position:0% +choose is the same +yeah exactly because because i'm making + + align:start position:0% +yeah exactly because because i'm making + + + align:start position:0% +yeah exactly because because i'm making +constant in fact you could imagine it + + align:start position:0% +constant in fact you could imagine it + + + align:start position:0% +constant in fact you could imagine it +could be growing or shrinking + + align:start position:0% +could be growing or shrinking + + + align:start position:0% +could be growing or shrinking +okay now with this in mind + + align:start position:0% +okay now with this in mind + + + align:start position:0% +okay now with this in mind +and realizing the private sector can't + + align:start position:0% +and realizing the private sector can't + + + align:start position:0% +and realizing the private sector can't +solve this for the reasons we talked + + align:start position:0% +solve this for the reasons we talked + + + align:start position:0% +solve this for the reasons we talked +about + + align:start position:0% +about + + + align:start position:0% +about +let's talk about the role let's talk + + align:start position:0% +let's talk about the role let's talk + + + align:start position:0% +let's talk about the role let's talk +about + + align:start position:0% +about + + + align:start position:0% +about +the role of government government + + align:start position:0% +the role of government government + + + align:start position:0% +the role of government government +solutions + + align:start position:0% + + + + align:start position:0% + +so once again remember the basic logic + + align:start position:0% +so once again remember the basic logic + + + align:start position:0% +so once again remember the basic logic +of this class + + align:start position:0% +of this class + + + align:start position:0% +of this class +which is that um the basic lodge of the + + align:start position:0% +which is that um the basic lodge of the + + + align:start position:0% +which is that um the basic lodge of the +class + + align:start position:0% +class + + + align:start position:0% +class +which is that um if uh + + align:start position:0% +which is that um if uh + + + align:start position:0% +which is that um if uh +the ethos of the class is that the + + align:start position:0% +the ethos of the class is that the + + + align:start position:0% +the ethos of the class is that the +market knows best + + align:start position:0% +market knows best + + + align:start position:0% +market knows best +unless there's a market failure if + + align:start position:0% +unless there's a market failure if + + + align:start position:0% +unless there's a market failure if +there's a market failure the private + + align:start position:0% +there's a market failure the private + + + align:start position:0% +there's a market failure the private +market will deliver deadweight loss + + align:start position:0% +market will deliver deadweight loss + + + align:start position:0% +market will deliver deadweight loss +now we have to ask can the government + + align:start position:0% +now we have to ask can the government + + + align:start position:0% +now we have to ask can the government +actually make it better remember we + + align:start position:0% +actually make it better remember we + + + align:start position:0% +actually make it better remember we +talked about monopoly regulation the + + align:start position:0% +talked about monopoly regulation the + + + align:start position:0% +talked about monopoly regulation the +government may or may not make it better + + align:start position:0% +government may or may not make it better + + + align:start position:0% +government may or may not make it better +okay infrared information asymmetries + + align:start position:0% +okay infrared information asymmetries + + + align:start position:0% +okay infrared information asymmetries +that may or may not make it better same + + align:start position:0% +that may or may not make it better same + + + align:start position:0% +that may or may not make it better same +thing with externalities the government + + align:start position:0% +thing with externalities the government + + + align:start position:0% +thing with externalities the government +may not make it better so let's say how + + align:start position:0% +may not make it better so let's say how + + + align:start position:0% +may not make it better so let's say how +the government in theory + + align:start position:0% +the government in theory + + + align:start position:0% +the government in theory +could make it better okay well there's + + align:start position:0% +could make it better okay well there's + + + align:start position:0% +could make it better okay well there's +two ways the government could make it + + align:start position:0% +two ways the government could make it + + + align:start position:0% +two ways the government could make it +better + + align:start position:0% +better + + + align:start position:0% +better +one way is by regulation so go back to + + align:start position:0% +one way is by regulation so go back to + + + align:start position:0% +one way is by regulation so go back to +figure um + + align:start position:0% +figure um + + + align:start position:0% +figure um +22-1 okay + + align:start position:0% +22-1 okay + + + align:start position:0% +22-1 okay +the government could literally regulate + + align:start position:0% +the government could literally regulate + + + align:start position:0% +the government could literally regulate +and could say look + + align:start position:0% +and could say look + + + align:start position:0% +and could say look +we know the optimal level of steel to be + + align:start position:0% +we know the optimal level of steel to be + + + align:start position:0% +we know the optimal level of steel to be +produced as q2 + + align:start position:0% +produced as q2 + + + align:start position:0% +produced as q2 +we're just going to tell you you produce + + align:start position:0% +we're just going to tell you you produce + + + align:start position:0% +we're just going to tell you you produce +q2 that's it + + align:start position:0% +q2 that's it + + + align:start position:0% +q2 that's it +problem solved okay we just say hey + + align:start position:0% +problem solved okay we just say hey + + + align:start position:0% +problem solved okay we just say hey +steel plant + + align:start position:0% +steel plant + + + align:start position:0% +steel plant +we know that optim's q2 you produce q2 + + align:start position:0% +we know that optim's q2 you produce q2 + + + align:start position:0% +we know that optim's q2 you produce q2 +problem solved + + align:start position:0% +problem solved + + + align:start position:0% +problem solved +the problem with that is that requires + + align:start position:0% +the problem with that is that requires + + + align:start position:0% +the problem with that is that requires +the government to know quite a lot + + align:start position:0% +the government to know quite a lot + + + align:start position:0% +the government to know quite a lot +the government needs to know both the + + align:start position:0% +the government needs to know both the + + + align:start position:0% +the government needs to know both the +supply and the demand curves + + align:start position:0% +supply and the demand curves + + + align:start position:0% +supply and the demand curves +to figure out where q2 is and what they + + align:start position:0% +to figure out where q2 is and what they + + + align:start position:0% +to figure out where q2 is and what they +should regulate + + align:start position:0% +should regulate + + + align:start position:0% +should regulate +let's say all the government knows is + + align:start position:0% +let's say all the government knows is + + + align:start position:0% +let's say all the government knows is +the damage being done and let's say the + + align:start position:0% +the damage being done and let's say the + + + align:start position:0% +the damage being done and let's say the +damage is linear they can approximate as + + align:start position:0% +damage is linear they can approximate as + + + align:start position:0% +damage is linear they can approximate as +linear + + align:start position:0% +linear + + + align:start position:0% +linear +then there's a much easier solution + + align:start position:0% +then there's a much easier solution + + + align:start position:0% +then there's a much easier solution +which is a corrective tax + + align:start position:0% +which is a corrective tax + + + align:start position:0% +which is a corrective tax +what if the government came in and said + + align:start position:0% +what if the government came in and said + + + align:start position:0% +what if the government came in and said +look i don't know where demand and + + align:start position:0% +look i don't know where demand and + + + align:start position:0% +look i don't know where demand and +supply curves are + + align:start position:0% +supply curves are + + + align:start position:0% +supply curves are +i don't really know it's really hard to + + align:start position:0% +i don't really know it's really hard to + + + align:start position:0% +i don't really know it's really hard to +figure it out all i know is that + + align:start position:0% +figure it out all i know is that + + + align:start position:0% +figure it out all i know is that +for every unit of steel you produce + + align:start position:0% +for every unit of steel you produce + + + align:start position:0% +for every unit of steel you produce +which is you know sludge you're killing + + align:start position:0% +which is you know sludge you're killing + + + align:start position:0% +which is you know sludge you're killing +a hundred dollars worth of fish that's + + align:start position:0% +a hundred dollars worth of fish that's + + + align:start position:0% +a hundred dollars worth of fish that's +what i know that i can study + + align:start position:0% +what i know that i can study + + + align:start position:0% +what i know that i can study +environmentally + + align:start position:0% +environmentally + + + align:start position:0% +environmentally +okay what if i simply tax the steel + + align:start position:0% +okay what if i simply tax the steel + + + align:start position:0% +okay what if i simply tax the steel +plant + + align:start position:0% +plant + + + align:start position:0% +plant +by a hundred dollars for every unit of + + align:start position:0% +by a hundred dollars for every unit of + + + align:start position:0% +by a hundred dollars for every unit of +steel they produced that if i imposed a + + align:start position:0% +steel they produced that if i imposed a + + + align:start position:0% +steel they produced that if i imposed a +tax + + align:start position:0% +tax + + + align:start position:0% +tax +on the steel plant + + align:start position:0% + + + + align:start position:0% + +one unit of steel is one unit of sludge + + align:start position:0% +one unit of steel is one unit of sludge + + + align:start position:0% +one unit of steel is one unit of sludge +in this example so i'm going to tax + + align:start position:0% +in this example so i'm going to tax + + + align:start position:0% +in this example so i'm going to tax +every unit of steel they produce + + align:start position:0% +every unit of steel they produce + + + align:start position:0% +every unit of steel they produce +which is which which is the sales + + align:start position:0% +which is which which is the sales + + + align:start position:0% +which is which which is the sales +pricing wanting you to sludge + + align:start position:0% +pricing wanting you to sludge + + + align:start position:0% +pricing wanting you to sludge +okay what if i impose that tax well + + align:start position:0% +okay what if i impose that tax well + + + align:start position:0% +okay what if i impose that tax well +let's look at figure 22 + + align:start position:0% +let's look at figure 22 + + + align:start position:0% +let's look at figure 22 +3. what does that do to the firm's + + align:start position:0% +3. what does that do to the firm's + + + align:start position:0% +3. what does that do to the firm's +decision + + align:start position:0% +decision + + + align:start position:0% +decision +okay well before the government came in + + align:start position:0% +okay well before the government came in + + + align:start position:0% +okay well before the government came in +the firm was producing at point a + + align:start position:0% +the firm was producing at point a + + + align:start position:0% +the firm was producing at point a +where their private margin cost equal + + align:start position:0% +where their private margin cost equal + + + align:start position:0% +where their private margin cost equal +the private marginal benefits which is + + align:start position:0% +the private marginal benefits which is + + + align:start position:0% +the private marginal benefits which is +the social marginal benefit + + align:start position:0% +the social marginal benefit + + + align:start position:0% +the social marginal benefit +now the government comes in and levies a + + align:start position:0% +now the government comes in and levies a + + + align:start position:0% +now the government comes in and levies a +tax + + align:start position:0% +tax + + + align:start position:0% +tax +it levies a tax of exactly md the + + align:start position:0% +it levies a tax of exactly md the + + + align:start position:0% +it levies a tax of exactly md the +marginal damage + + align:start position:0% +marginal damage + + + align:start position:0% +marginal damage +what does it do it shifts their private + + align:start position:0% +what does it do it shifts their private + + + align:start position:0% +what does it do it shifts their private +marginal cost curve + + align:start position:0% +marginal cost curve + + + align:start position:0% +marginal cost curve +to the social marginal cost curve it has + + align:start position:0% +to the social marginal cost curve it has + + + align:start position:0% +to the social marginal cost curve it has +caused the firm to internalize the + + align:start position:0% +caused the firm to internalize the + + + align:start position:0% +caused the firm to internalize the +externality + + align:start position:0% +externality + + + align:start position:0% +externality +because now the firm is paying an amount + + align:start position:0% +because now the firm is paying an amount + + + align:start position:0% +because now the firm is paying an amount +exactly equal to the damage they're + + align:start position:0% +exactly equal to the damage they're + + + align:start position:0% +exactly equal to the damage they're +doing to society + + align:start position:0% +doing to society + + + align:start position:0% +doing to society +so a corrective tax can cause the firm + + align:start position:0% +so a corrective tax can cause the firm + + + align:start position:0% +so a corrective tax can cause the firm +to internalize the externality + + align:start position:0% +to internalize the externality + + + align:start position:0% +to internalize the externality +correct attacks cause the firm to + + align:start position:0% +correct attacks cause the firm to + + + align:start position:0% +correct attacks cause the firm to +internalize the externality + + align:start position:0% +internalize the externality + + + align:start position:0% +internalize the externality +okay essentially corrective tax by the + + align:start position:0% +okay essentially corrective tax by the + + + align:start position:0% +okay essentially corrective tax by the +government + + align:start position:0% +government + + + align:start position:0% +government +can get us to the right answer because + + align:start position:0% +can get us to the right answer because + + + align:start position:0% +can get us to the right answer because +it gets firms do the right thing + + align:start position:0% +it gets firms do the right thing + + + align:start position:0% +it gets firms do the right thing +okay gets firms to pay attention to + + align:start position:0% +okay gets firms to pay attention to + + + align:start position:0% +okay gets firms to pay attention to +social costs not just + + align:start position:0% +social costs not just + + + align:start position:0% +social costs not just +the uh not just the private costs + + align:start position:0% +the uh not just the private costs + + + align:start position:0% +the uh not just the private costs +okay similarly the same thing with a + + align:start position:0% +okay similarly the same thing with a + + + align:start position:0% +okay similarly the same thing with a +positive externality + + align:start position:0% +positive externality + + + align:start position:0% +positive externality +what could the government do with a + + align:start position:0% +what could the government do with a + + + align:start position:0% +what could the government do with a +positive externality + + align:start position:0% +positive externality + + + align:start position:0% +positive externality +yeah it could subsidize by exact so + + align:start position:0% +yeah it could subsidize by exact so + + + align:start position:0% +yeah it could subsidize by exact so +imagine i knew exactly how much + + align:start position:0% +imagine i knew exactly how much + + + align:start position:0% +imagine i knew exactly how much +social benefit there was per unit of r d + + align:start position:0% +social benefit there was per unit of r d + + + align:start position:0% +social benefit there was per unit of r d +if i subsidized the firm doing r + + align:start position:0% +if i subsidized the firm doing r + + + align:start position:0% +if i subsidized the firm doing r +d then i would lower their costs right + + align:start position:0% +d then i would lower their costs right + + + align:start position:0% +d then i would lower their costs right +if i offered them a subsidy of this + + align:start position:0% +if i offered them a subsidy of this + + + align:start position:0% +if i offered them a subsidy of this +amount + + align:start position:0% +amount + + + align:start position:0% +amount +their cost curve would shift down + + align:start position:0% +their cost curve would shift down + + + align:start position:0% +their cost curve would shift down +although the costs are indeed we get to + + align:start position:0% +although the costs are indeed we get to + + + align:start position:0% +although the costs are indeed we get to +the right point + + align:start position:0% +the right point + + + align:start position:0% +the right point +so a corrective tax of the amount of + + align:start position:0% +so a corrective tax of the amount of + + + align:start position:0% +so a corrective tax of the amount of +damage + + align:start position:0% +damage + + + align:start position:0% +damage +gets firms to internalize the + + align:start position:0% +gets firms to internalize the + + + align:start position:0% +gets firms to internalize the +externality a corrective + + align:start position:0% +externality a corrective + + + align:start position:0% +externality a corrective +subsidy of that amount gets firms to + + align:start position:0% +subsidy of that amount gets firms to + + + align:start position:0% +subsidy of that amount gets firms to +internalize the externality + + align:start position:0% +internalize the externality + + + align:start position:0% +internalize the externality +or individuals to exercise the + + align:start position:0% +or individuals to exercise the + + + align:start position:0% +or individuals to exercise the +internality + + align:start position:0% +internality + + + align:start position:0% +internality +and we can get to the optimal outcome by + + align:start position:0% +and we can get to the optimal outcome by + + + align:start position:0% +and we can get to the optimal outcome by +the government imposing a corrective tax + + align:start position:0% +the government imposing a corrective tax + + + align:start position:0% +the government imposing a corrective tax +or subsidy of the right amount + + align:start position:0% +or subsidy of the right amount + + + align:start position:0% +or subsidy of the right amount +now we can of course also get there with + + align:start position:0% +now we can of course also get there with + + + align:start position:0% +now we can of course also get there with +regulation it's just a lot harder + + align:start position:0% +regulation it's just a lot harder + + + align:start position:0% +regulation it's just a lot harder +okay questions about that + + align:start position:0% +okay questions about that + + + align:start position:0% +okay questions about that +okay this is our first example + + align:start position:0% +okay this is our first example + + + align:start position:0% +okay this is our first example +of good taxes okay taxes have been bad + + align:start position:0% +of good taxes okay taxes have been bad + + + align:start position:0% +of good taxes okay taxes have been bad +throughout this course the role of taxes + + align:start position:0% +throughout this course the role of taxes + + + align:start position:0% +throughout this course the role of taxes +has been + + align:start position:0% +has been + + + align:start position:0% +has been +has been distortion to the economy we + + align:start position:0% +has been distortion to the economy we + + + align:start position:0% +has been distortion to the economy we +haven't talked about a lot we'll talk + + align:start position:0% +haven't talked about a lot we'll talk + + + align:start position:0% +haven't talked about a lot we'll talk +about it more in a couple lectures + + align:start position:0% +about it more in a couple lectures + + + align:start position:0% +about it more in a couple lectures +they've been distortion entered the + + align:start position:0% +they've been distortion entered the + + + align:start position:0% +they've been distortion entered the +economy this is saying no + + align:start position:0% +economy this is saying no + + + align:start position:0% +economy this is saying no +a tax can actually play a positive role + + align:start position:0% +a tax can actually play a positive role + + + align:start position:0% +a tax can actually play a positive role +because a tax can correct + + align:start position:0% +because a tax can correct + + + align:start position:0% +because a tax can correct +a market failure now as always if the + + align:start position:0% +a market failure now as always if the + + + align:start position:0% +a market failure now as always if the +tax is said incorrectly it could make + + align:start position:0% +tax is said incorrectly it could make + + + align:start position:0% +tax is said incorrectly it could make +things worse + + align:start position:0% +things worse + + + align:start position:0% +things worse +okay if said a tax that was five times + + align:start position:0% +okay if said a tax that was five times + + + align:start position:0% +okay if said a tax that was five times +the marginal damage you'd make things + + align:start position:0% +the marginal damage you'd make things + + + align:start position:0% +the marginal damage you'd make things +worse + + align:start position:0% +worse + + + align:start position:0% +worse +but if you said it correctly it can make + + align:start position:0% +but if you said it correctly it can make + + + align:start position:0% +but if you said it correctly it can make +things better we're offering the + + align:start position:0% +things better we're offering the + + + align:start position:0% +things better we're offering the +potential + + align:start position:0% +potential + + + align:start position:0% +potential +for government intervention to make + + align:start position:0% +for government intervention to make + + + align:start position:0% +for government intervention to make +things better here questions about that + + align:start position:0% +things better here questions about that + + + align:start position:0% +things better here questions about that +okay so what do we have we have a + + align:start position:0% +okay so what do we have we have a + + + align:start position:0% +okay so what do we have we have a +situation where the private market is + + align:start position:0% +situation where the private market is + + + align:start position:0% +situation where the private market is +not delivering + + align:start position:0% +not delivering + + + align:start position:0% +not delivering +the optimal outcome the prime minister + + align:start position:0% +the optimal outcome the prime minister + + + align:start position:0% +the optimal outcome the prime minister +of the optimal outcome + + align:start position:0% +of the optimal outcome + + + align:start position:0% +of the optimal outcome +where it seems hard to think of private + + align:start position:0% +where it seems hard to think of private + + + align:start position:0% +where it seems hard to think of private +solutions + + align:start position:0% +solutions + + + align:start position:0% +solutions +but where a government solution is + + align:start position:0% +but where a government solution is + + + align:start position:0% +but where a government solution is +through regulation or easier corrective + + align:start position:0% +through regulation or easier corrective + + + align:start position:0% +through regulation or easier corrective +taxation + + align:start position:0% +taxation + + + align:start position:0% +taxation +can get us to the optimal outcome so now + + align:start position:0% +can get us to the optimal outcome so now + + + align:start position:0% +can get us to the optimal outcome so now +let's ask how does this actually work in + + align:start position:0% +let's ask how does this actually work in + + + align:start position:0% +let's ask how does this actually work in +practice + + align:start position:0% + + + + align:start position:0% + +and let's talk about two examples let's + + align:start position:0% +and let's talk about two examples let's + + + align:start position:0% +and let's talk about two examples let's +talk about environmental externalities + + align:start position:0% +talk about environmental externalities + + + align:start position:0% +talk about environmental externalities +and health externalities + + align:start position:0% +and health externalities + + + align:start position:0% +and health externalities +start with environmental externals and + + align:start position:0% +start with environmental externals and + + + align:start position:0% +start with environmental externals and +of course the most important + + align:start position:0% +of course the most important + + + align:start position:0% +of course the most important +is global warming okay uh + + align:start position:0% +is global warming okay uh + + + align:start position:0% +is global warming okay uh +currently the amount of carbon dioxide + + align:start position:0% +currently the amount of carbon dioxide + + + align:start position:0% +currently the amount of carbon dioxide +the atmosphere is at its highest level + + align:start position:0% +the atmosphere is at its highest level + + + align:start position:0% +the atmosphere is at its highest level +in 400 + + align:start position:0% +in 400 + + + align:start position:0% +in 400 +000 years uh + + align:start position:0% +000 years uh + + + align:start position:0% +000 years uh +basically every year becomes the hottest + + align:start position:0% +basically every year becomes the hottest + + + align:start position:0% +basically every year becomes the hottest +year on record almost linearly almost + + align:start position:0% +year on record almost linearly almost + + + align:start position:0% +year on record almost linearly almost +monotonically every year is the hottest + + align:start position:0% +monotonically every year is the hottest + + + align:start position:0% +monotonically every year is the hottest +year on record + + align:start position:0% +year on record + + + align:start position:0% +year on record +we're heating up scientists predict uh + + align:start position:0% +we're heating up scientists predict uh + + + align:start position:0% +we're heating up scientists predict uh +that it's possible + + align:start position:0% +that it's possible + + + align:start position:0% +that it's possible +the central prediction is that + + align:start position:0% +the central prediction is that + + + align:start position:0% +the central prediction is that +temperatures will rise by more than two + + align:start position:0% +temperatures will rise by more than two + + + align:start position:0% +temperatures will rise by more than two +degrees fahrenheit by the end of the + + align:start position:0% +degrees fahrenheit by the end of the + + + align:start position:0% +degrees fahrenheit by the end of the +uh but i'm sorry by more than two + + align:start position:0% +uh but i'm sorry by more than two + + + align:start position:0% +uh but i'm sorry by more than two +degrees celsius by the end of the + + align:start position:0% +degrees celsius by the end of the + + + align:start position:0% +degrees celsius by the end of the +of the um of the century but it could be + + align:start position:0% +of the um of the century but it could be + + + align:start position:0% +of the um of the century but it could be +more than that + + align:start position:0% +more than that + + + align:start position:0% +more than that +there's actually currently the best + + align:start position:0% +there's actually currently the best + + + align:start position:0% +there's actually currently the best +estimate is that + + align:start position:0% +estimate is that + + + align:start position:0% +estimate is that +there's there's a all there's as much as + + align:start position:0% +there's there's a all there's as much as + + + align:start position:0% +there's there's a all there's as much as +a 10 + + align:start position:0% +a 10 + + + align:start position:0% +a 10 +chance that temperatures go up by 10 + + align:start position:0% +chance that temperatures go up by 10 + + + align:start position:0% +chance that temperatures go up by 10 +degrees by the end of the century which + + align:start position:0% +degrees by the end of the century which + + + align:start position:0% +degrees by the end of the century which +would end human life + + align:start position:0% +would end human life + + + align:start position:0% +would end human life +basically in most of the world okay + + align:start position:0% +basically in most of the world okay + + + align:start position:0% +basically in most of the world okay +there's a non-trivial chance + + align:start position:0% +there's a non-trivial chance + + + align:start position:0% +there's a non-trivial chance +we're all gone by 200. not my problem + + align:start position:0% +we're all gone by 200. not my problem + + + align:start position:0% +we're all gone by 200. not my problem +largely not your problem + + align:start position:0% +largely not your problem + + + align:start position:0% +largely not your problem +certainly your kid's problem okay okay + + align:start position:0% +certainly your kid's problem okay okay + + + align:start position:0% +certainly your kid's problem okay okay +by and large we are basically uh we are + + align:start position:0% +by and large we are basically uh we are + + + align:start position:0% +by and large we are basically uh we are +basically + + align:start position:0% +basically + + + align:start position:0% +basically +we have a we know for sure there's gonna + + align:start position:0% +we have a we know for sure there's gonna + + + align:start position:0% +we have a we know for sure there's gonna +be negative implications + + align:start position:0% +be negative implications + + + align:start position:0% +be negative implications +basically we are essentially unless + + align:start position:0% +basically we are essentially unless + + + align:start position:0% +basically we are essentially unless +unless there's a radical new + + align:start position:0% +unless there's a radical new + + + align:start position:0% +unless there's a radical new +technology invented bangladesh is gone + + align:start position:0% +technology invented bangladesh is gone + + + align:start position:0% +technology invented bangladesh is gone +it's over for bangladesh + + align:start position:0% +it's over for bangladesh + + + align:start position:0% +it's over for bangladesh +cape cod is gone much of florida is gone + + align:start position:0% +cape cod is gone much of florida is gone + + + align:start position:0% +cape cod is gone much of florida is gone +that's already happening + + align:start position:0% +that's already happening + + + align:start position:0% +that's already happening +okay at this point the question is can + + align:start position:0% +okay at this point the question is can + + + align:start position:0% +okay at this point the question is can +we actually stop + + align:start position:0% +we actually stop + + + align:start position:0% +we actually stop +the entire east and west coast and much + + align:start position:0% +the entire east and west coast and much + + + align:start position:0% +the entire east and west coast and much +of the south from disappearing as well + + align:start position:0% +of the south from disappearing as well + + + align:start position:0% +of the south from disappearing as well +and many other countries in the world + + align:start position:0% +and many other countries in the world + + + align:start position:0% +and many other countries in the world +from disappearing + + align:start position:0% +from disappearing + + + align:start position:0% +from disappearing +okay that's the sort of decision we have + + align:start position:0% +okay that's the sort of decision we have + + + align:start position:0% +okay that's the sort of decision we have +to make now + + align:start position:0% +to make now + + + align:start position:0% +to make now +okay so basically this is a classic + + align:start position:0% +okay so basically this is a classic + + + align:start position:0% +okay so basically this is a classic +negative externality because + + align:start position:0% +negative externality because + + + align:start position:0% +negative externality because +that negative situation you were not + + align:start position:0% +that negative situation you were not + + + align:start position:0% +that negative situation you were not +thinking about that when you filled up + + align:start position:0% +thinking about that when you filled up + + + align:start position:0% +thinking about that when you filled up +your car last time + + align:start position:0% +your car last time + + + align:start position:0% +your car last time +you're not thinking about the fact the + + align:start position:0% +you're not thinking about the fact the + + + align:start position:0% +you're not thinking about the fact the +fossil fuels you're emitting are + + align:start position:0% +fossil fuels you're emitting are + + + align:start position:0% +fossil fuels you're emitting are +contributing to that + + align:start position:0% +contributing to that + + + align:start position:0% +contributing to that +okay it's a classic negative externality + + align:start position:0% +okay it's a classic negative externality + + + align:start position:0% +okay it's a classic negative externality +so what can the government do well the + + align:start position:0% +so what can the government do well the + + + align:start position:0% +so what can the government do well the +natural solution would be corrective + + align:start position:0% +natural solution would be corrective + + + align:start position:0% +natural solution would be corrective +taxation + + align:start position:0% +taxation + + + align:start position:0% +taxation +the natural solution would be to have a + + align:start position:0% +the natural solution would be to have a + + + align:start position:0% +the natural solution would be to have a +carbon tax + + align:start position:0% +carbon tax + + + align:start position:0% +carbon tax +to literally say this is the amount we + + align:start position:0% +to literally say this is the amount we + + + align:start position:0% +to literally say this is the amount we +actually have a pretty good sense from + + align:start position:0% +actually have a pretty good sense from + + + align:start position:0% +actually have a pretty good sense from +from engineering models what the cost of + + align:start position:0% +from engineering models what the cost of + + + align:start position:0% +from engineering models what the cost of +carbon is what the marginal cost of + + align:start position:0% +carbon is what the marginal cost of + + + align:start position:0% +carbon is what the marginal cost of +carbon is + + align:start position:0% +carbon is + + + align:start position:0% +carbon is +okay and we could literally impose a tax + + align:start position:0% +okay and we could literally impose a tax + + + align:start position:0% +okay and we could literally impose a tax +on the use of carbon of that amount + + align:start position:0% +on the use of carbon of that amount + + + align:start position:0% +on the use of carbon of that amount +i think it would amount to something i + + align:start position:0% +i think it would amount to something i + + + align:start position:0% +i think it would amount to something i +don't know the numbers these days it's + + align:start position:0% +don't know the numbers these days it's + + + align:start position:0% +don't know the numbers these days it's +something like between 25 and 50 cents a + + align:start position:0% +something like between 25 and 50 cents a + + + align:start position:0% +something like between 25 and 50 cents a +gallon of gas + + align:start position:0% +gallon of gas + + + align:start position:0% +gallon of gas +so it's a lot but it's not we've seen + + align:start position:0% +so it's a lot but it's not we've seen + + + align:start position:0% +so it's a lot but it's not we've seen +gas prices in the last year go up and + + align:start position:0% +gas prices in the last year go up and + + + align:start position:0% +gas prices in the last year go up and +down by that much + + align:start position:0% +down by that much + + + align:start position:0% +down by that much +okay that's not an outrageous amount + + align:start position:0% +okay that's not an outrageous amount + + + align:start position:0% +okay that's not an outrageous amount +okay + + align:start position:0% +okay + + + align:start position:0% +okay +in europe they already have gasoline + + align:start position:0% +in europe they already have gasoline + + + align:start position:0% +in europe they already have gasoline +taxes well above that level + + align:start position:0% +taxes well above that level + + + align:start position:0% +taxes well above that level +okay so corrective taxation in principle + + align:start position:0% +okay so corrective taxation in principle + + + align:start position:0% +okay so corrective taxation in principle +could be the answer we could literally + + align:start position:0% +could be the answer we could literally + + + align:start position:0% +could be the answer we could literally +just use engineering models to compute + + align:start position:0% +just use engineering models to compute + + + align:start position:0% +just use engineering models to compute +the cost social cost of carbon + + align:start position:0% +the cost social cost of carbon + + + align:start position:0% +the cost social cost of carbon +we could put a tax on it and then at + + align:start position:0% +we could put a tax on it and then at + + + align:start position:0% +we could put a tax on it and then at +least we would + + align:start position:0% +least we would + + + align:start position:0% +least we would +stop global warming going forward you + + align:start position:0% +stop global warming going forward you + + + align:start position:0% +stop global warming going forward you +know bangladesh may be gone + + align:start position:0% +know bangladesh may be gone + + + align:start position:0% +know bangladesh may be gone +but we can maybe save a lot of the rest + + align:start position:0% +but we can maybe save a lot of the rest + + + align:start position:0% +but we can maybe save a lot of the rest +of the world okay + + align:start position:0% +of the world okay + + + align:start position:0% +of the world okay +so that's um that's in theory in + + align:start position:0% +so that's um that's in theory in + + + align:start position:0% +so that's um that's in theory in +practice + + align:start position:0% +practice + + + align:start position:0% +practice +in 1994 bill clinton proposed a three + + align:start position:0% +in 1994 bill clinton proposed a three + + + align:start position:0% +in 1994 bill clinton proposed a three +cent gas tax + + align:start position:0% +cent gas tax + + + align:start position:0% +cent gas tax +and lost congress okay in practice + + align:start position:0% +and lost congress okay in practice + + + align:start position:0% +and lost congress okay in practice +people don't like gas taxes uh it's very + + align:start position:0% +people don't like gas taxes uh it's very + + + align:start position:0% +people don't like gas taxes uh it's very +hard politically in the u.s and other + + align:start position:0% +hard politically in the u.s and other + + + align:start position:0% +hard politically in the u.s and other +places + + align:start position:0% +places + + + align:start position:0% +places +and that is why the world has turned to + + align:start position:0% +and that is why the world has turned to + + + align:start position:0% +and that is why the world has turned to +a different approach + + align:start position:0% +a different approach + + + align:start position:0% +a different approach +which is quantity regulation which is + + align:start position:0% +which is quantity regulation which is + + + align:start position:0% +which is quantity regulation which is +say look + + align:start position:0% +say look + + + align:start position:0% +say look +in practice we should have a global + + align:start position:0% +in practice we should have a global + + + align:start position:0% +in practice we should have a global +carbon tax + + align:start position:0% +carbon tax + + + align:start position:0% +carbon tax +in theories of global heart attacks in + + align:start position:0% +in theories of global heart attacks in + + + align:start position:0% +in theories of global heart attacks in +practice that's hard that's why we have + + align:start position:0% +practice that's hard that's why we have + + + align:start position:0% +practice that's hard that's why we have +uh negotiations that's why we try to + + align:start position:0% +uh negotiations that's why we try to + + + align:start position:0% +uh negotiations that's why we try to +have a global negotiation + + align:start position:0% +have a global negotiation + + + align:start position:0% +have a global negotiation +to try to get a global cap on carbon + + align:start position:0% +to try to get a global cap on carbon + + + align:start position:0% +to try to get a global cap on carbon +emissions actually have a quantity + + align:start position:0% +emissions actually have a quantity + + + align:start position:0% +emissions actually have a quantity +regulation + + align:start position:0% +regulation + + + align:start position:0% +regulation +okay to actually have a quantity + + align:start position:0% +okay to actually have a quantity + + + align:start position:0% +okay to actually have a quantity +regulation uh we started this the first + + align:start position:0% +regulation uh we started this the first + + + align:start position:0% +regulation uh we started this the first +true global negotiation was in kyoto + + align:start position:0% +true global negotiation was in kyoto + + + align:start position:0% +true global negotiation was in kyoto +japan + + align:start position:0% +japan + + + align:start position:0% +japan +in december 1997 + + align:start position:0% +in december 1997 + + + align:start position:0% +in december 1997 +i was fortunate enough to be there for + + align:start position:0% +i was fortunate enough to be there for + + + align:start position:0% +i was fortunate enough to be there for +that negotiation i was in the clinton + + align:start position:0% +that negotiation i was in the clinton + + + align:start position:0% +that negotiation i was in the clinton +administration at the time + + align:start position:0% +administration at the time + + + align:start position:0% +administration at the time +and um uh we got to uh go over and do + + align:start position:0% +and um uh we got to uh go over and do + + + align:start position:0% +and um uh we got to uh go over and do +that negotiation was actually pretty + + align:start position:0% +that negotiation was actually pretty + + + align:start position:0% +that negotiation was actually pretty +neat because + + align:start position:0% +neat because + + + align:start position:0% +neat because +they decided i was going the last minute + + align:start position:0% +they decided i was going the last minute + + + align:start position:0% +they decided i was going the last minute +and the only plane left to go on was air + + align:start position:0% +and the only plane left to go on was air + + + align:start position:0% +and the only plane left to go on was air +force two + + align:start position:0% +force two + + + align:start position:0% +force two +so i had to fly over the vice president + + align:start position:0% +so i had to fly over the vice president + + + align:start position:0% +so i had to fly over the vice president +on air force two which was pretty cool + + align:start position:0% +on air force two which was pretty cool + + + align:start position:0% +on air force two which was pretty cool +super cool they have really nice seats + + align:start position:0% +super cool they have really nice seats + + + align:start position:0% +super cool they have really nice seats +and stuff and so i sat down on the phone + + align:start position:0% +and stuff and so i sat down on the phone + + + align:start position:0% +and stuff and so i sat down on the phone +next to me rang + + align:start position:0% +next to me rang + + + align:start position:0% +next to me rang +i was like i think i was like hello like + + align:start position:0% +i was like i think i was like hello like + + + align:start position:0% +i was like i think i was like hello like +hey john i'm like oh my god + + align:start position:0% +hey john i'm like oh my god + + + align:start position:0% +hey john i'm like oh my god +it was i'm calling from japan but like + + align:start position:0% +it was i'm calling from japan but like + + + align:start position:0% +it was i'm calling from japan but like +getting a personal phone call and + + align:start position:0% +getting a personal phone call and + + + align:start position:0% +getting a personal phone call and +playing was super cool + + align:start position:0% +playing was super cool + + + align:start position:0% +playing was super cool +um so anyway so went over to kyoto i + + align:start position:0% +um so anyway so went over to kyoto i + + + align:start position:0% +um so anyway so went over to kyoto i +learned how these negotiations work + + align:start position:0% +learned how these negotiations work + + + align:start position:0% +learned how these negotiations work +which is uh over + + align:start position:0% +which is uh over + + + align:start position:0% +which is uh over +five days i slept four hours um they in + + align:start position:0% +five days i slept four hours um they in + + + align:start position:0% +five days i slept four hours um they in +japan they sell + + align:start position:0% +japan they sell + + + align:start position:0% +japan they sell +um they sold the time this coffee and + + align:start position:0% +um they sold the time this coffee and + + + align:start position:0% +um they sold the time this coffee and +cans so you just chug these cans of + + align:start position:0% +cans so you just chug these cans of + + + align:start position:0% +cans so you just chug these cans of +coffee all the time + + align:start position:0% +coffee all the time + + + align:start position:0% +coffee all the time +and stay awake and basically everyone's + + align:start position:0% +and stay awake and basically everyone's + + + align:start position:0% +and stay awake and basically everyone's +so tired by the angel's degree just to + + align:start position:0% +so tired by the angel's degree just to + + + align:start position:0% +so tired by the angel's degree just to +kind of get out get it done + + align:start position:0% +kind of get out get it done + + + align:start position:0% +kind of get out get it done +and that's the way the negotiations work + + align:start position:0% +and that's the way the negotiations work + + + align:start position:0% +and that's the way the negotiations work +um so we agreed + + align:start position:0% +um so we agreed + + + align:start position:0% +um so we agreed +to the kyoto global warming treaty which + + align:start position:0% +to the kyoto global warming treaty which + + + align:start position:0% +to the kyoto global warming treaty which +would have lowered emissions + + align:start position:0% +would have lowered emissions + + + align:start position:0% +would have lowered emissions +worldwide but the u.s did not sign on + + align:start position:0% +worldwide but the u.s did not sign on + + + align:start position:0% +worldwide but the u.s did not sign on +the u.s + + align:start position:0% +the u.s + + + align:start position:0% +the u.s +refused to sign on there's been + + align:start position:0% +refused to sign on there's been + + + align:start position:0% +refused to sign on there's been +continuing negotiations most recently we + + align:start position:0% +continuing negotiations most recently we + + + align:start position:0% +continuing negotiations most recently we +know about the paris round of + + align:start position:0% +know about the paris round of + + + align:start position:0% +know about the paris round of +negotiations + + align:start position:0% +negotiations + + + align:start position:0% +negotiations +which us did sign on to but the current + + align:start position:0% +which us did sign on to but the current + + + align:start position:0% +which us did sign on to but the current +administration has pulled this back out + + align:start position:0% +administration has pulled this back out + + + align:start position:0% +administration has pulled this back out +of + + align:start position:0% +of + + + align:start position:0% +of +so we have a problem which is that + + align:start position:0% +so we have a problem which is that + + + align:start position:0% +so we have a problem which is that +basically we're heading to this + + align:start position:0% +basically we're heading to this + + + align:start position:0% +basically we're heading to this +environmental + + align:start position:0% +environmental + + + align:start position:0% +environmental +environmental catastrophe and the world + + align:start position:0% +environmental catastrophe and the world + + + align:start position:0% +environmental catastrophe and the world +can't agree on + + align:start position:0% +can't agree on + + + align:start position:0% +can't agree on +um actions to take uh and + + align:start position:0% +um actions to take uh and + + + align:start position:0% +um actions to take uh and +you know uh it's not it's not really a + + align:start position:0% +you know uh it's not it's not really a + + + align:start position:0% +you know uh it's not it's not really a +choice + + align:start position:0% +choice + + + align:start position:0% +choice +and we have to do something uh or or + + align:start position:0% +and we have to do something uh or or + + + align:start position:0% +and we have to do something uh or or +we'll or our grandkids will all be under + + align:start position:0% +we'll or our grandkids will all be under + + + align:start position:0% +we'll or our grandkids will all be under +water + + align:start position:0% +water + + + align:start position:0% +water +or great cancer cancers will all be + + align:start position:0% +or great cancer cancers will all be + + + align:start position:0% +or great cancer cancers will all be +under water we have to do something + + align:start position:0% +under water we have to do something + + + align:start position:0% +under water we have to do something +um the optimistics case that will do + + align:start position:0% +um the optimistics case that will do + + + align:start position:0% +um the optimistics case that will do +something comes from the + + align:start position:0% +something comes from the + + + align:start position:0% +something comes from the +example of what's called + + align:start position:0% +example of what's called + + + align:start position:0% +example of what's called +chlorofluorocarbons when i was a kid + + align:start position:0% +chlorofluorocarbons when i was a kid + + + align:start position:0% +chlorofluorocarbons when i was a kid +many many products were made what's + + align:start position:0% +many many products were made what's + + + align:start position:0% +many many products were made what's +called chlorofluorocarbons they were in + + align:start position:0% +called chlorofluorocarbons they were in + + + align:start position:0% +called chlorofluorocarbons they were in +refrigerators + + align:start position:0% +refrigerators + + + align:start position:0% +refrigerators +they were in aerosol sprays etc + + align:start position:0% +they were in aerosol sprays etc + + + align:start position:0% +they were in aerosol sprays etc +scientists realized they were actually + + align:start position:0% +scientists realized they were actually + + + align:start position:0% +scientists realized they were actually +damaging the ozone layer which protects + + align:start position:0% +damaging the ozone layer which protects + + + align:start position:0% +damaging the ozone layer which protects +us from ultraviolet rays from the sun + + align:start position:0% +us from ultraviolet rays from the sun + + + align:start position:0% +us from ultraviolet rays from the sun +and we were like yeah whatever much like + + align:start position:0% +and we were like yeah whatever much like + + + align:start position:0% +and we were like yeah whatever much like +they are with global warming now yeah + + align:start position:0% +they are with global warming now yeah + + + align:start position:0% +they are with global warming now yeah +whatever but then + + align:start position:0% +whatever but then + + + align:start position:0% +whatever but then +a hole opened up in the ozone + + align:start position:0% +a hole opened up in the ozone + + + align:start position:0% +a hole opened up in the ozone +layer like literally it's like oh my god + + align:start position:0% +layer like literally it's like oh my god + + + align:start position:0% +layer like literally it's like oh my god +there's a hole in the ozone layer and + + align:start position:0% +there's a hole in the ozone layer and + + + align:start position:0% +there's a hole in the ozone layer and +180 countries got together almost + + align:start position:0% +180 countries got together almost + + + align:start position:0% +180 countries got together almost +overnight and banned chlorofluorocarbons + + align:start position:0% +overnight and banned chlorofluorocarbons + + + align:start position:0% +overnight and banned chlorofluorocarbons +like literally almost overnight they + + align:start position:0% +like literally almost overnight they + + + align:start position:0% +like literally almost overnight they +were gone it was amazing + + align:start position:0% +were gone it was amazing + + + align:start position:0% +were gone it was amazing +international cooperation of terrific + + align:start position:0% +international cooperation of terrific + + + align:start position:0% +international cooperation of terrific +international cooperation to take an + + align:start position:0% +international cooperation to take an + + + align:start position:0% +international cooperation to take an +environmental catastron and deal with it + + align:start position:0% +environmental catastron and deal with it + + + align:start position:0% +environmental catastron and deal with it +the problem is global warming doesn't + + align:start position:0% +the problem is global warming doesn't + + + align:start position:0% +the problem is global warming doesn't +quite work that way okay by the time + + align:start position:0% +quite work that way okay by the time + + + align:start position:0% +quite work that way okay by the time +we say oh my god bangladesh is + + align:start position:0% +we say oh my god bangladesh is + + + align:start position:0% +we say oh my god bangladesh is +underwater it's too late + + align:start position:0% +underwater it's too late + + + align:start position:0% +underwater it's too late +so the question is sort of how do we get + + align:start position:0% +so the question is sort of how do we get + + + align:start position:0% +so the question is sort of how do we get +politicians and the public interested in + + align:start position:0% +politicians and the public interested in + + + align:start position:0% +politicians and the public interested in +taking something on + + align:start position:0% +taking something on + + + align:start position:0% +taking something on +we don't have the symbol like a hole in + + align:start position:0% +we don't have the symbol like a hole in + + + align:start position:0% +we don't have the symbol like a hole in +ozone layer to actually + + align:start position:0% +ozone layer to actually + + + align:start position:0% +ozone layer to actually +represent the damage that's being done + + align:start position:0% +represent the damage that's being done + + + align:start position:0% +represent the damage that's being done +and that is the challenge of facing + + align:start position:0% +and that is the challenge of facing + + + align:start position:0% +and that is the challenge of facing +something like global warming but we + + align:start position:0% +something like global warming but we + + + align:start position:0% +something like global warming but we +have to take it on + + align:start position:0% +have to take it on + + + align:start position:0% +have to take it on +okay so that's environmental + + align:start position:0% +okay so that's environmental + + + align:start position:0% +okay so that's environmental +externalities the other big type of + + align:start position:0% +externalities the other big type of + + + align:start position:0% +externalities the other big type of +externalities are health externalities + + align:start position:0% + + + + align:start position:0% + +our health externalities i talked about + + align:start position:0% +our health externalities i talked about + + + align:start position:0% +our health externalities i talked about +smoking but indeed there are huge + + align:start position:0% +smoking but indeed there are huge + + + align:start position:0% +smoking but indeed there are huge +externalities levied by a bunch of + + align:start position:0% +externalities levied by a bunch of + + + align:start position:0% +externalities levied by a bunch of +activities that we do that impact our + + align:start position:0% +activities that we do that impact our + + + align:start position:0% +activities that we do that impact our +health + + align:start position:0% +health + + + align:start position:0% +health +so for example drinking drunk driving + + align:start position:0% +so for example drinking drunk driving + + + align:start position:0% +so for example drinking drunk driving +causes 13 000 deaths per year + + align:start position:0% +causes 13 000 deaths per year + + + align:start position:0% +causes 13 000 deaths per year +13 000 deaths per year okay to put a put + + align:start position:0% +13 000 deaths per year okay to put a put + + + align:start position:0% +13 000 deaths per year okay to put a put +to put a sort of blunt face on it four + + align:start position:0% +to put a sort of blunt face on it four + + + align:start position:0% +to put a sort of blunt face on it four +911s every year + + align:start position:0% +911s every year + + + align:start position:0% +911s every year +from drunk driving okay plus 400 + + align:start position:0% +from drunk driving okay plus 400 + + + align:start position:0% +from drunk driving okay plus 400 +000 injuries every year for people + + align:start position:0% +000 injuries every year for people + + + align:start position:0% +000 injuries every year for people +driving drunk + + align:start position:0% +driving drunk + + + align:start position:0% +driving drunk +um consuming gasoline global warming + + align:start position:0% +um consuming gasoline global warming + + + align:start position:0% +um consuming gasoline global warming +okay is a huge externalities um perhaps + + align:start position:0% +okay is a huge externalities um perhaps + + + align:start position:0% +okay is a huge externalities um perhaps +one of the biggest + + align:start position:0% +one of the biggest + + + align:start position:0% +one of the biggest +exercises facing us the biggest social + + align:start position:0% +exercises facing us the biggest social + + + align:start position:0% +exercises facing us the biggest social +externality is obesity + + align:start position:0% +externality is obesity + + + align:start position:0% +externality is obesity +okay obesity causes a lot of illnesses + + align:start position:0% +okay obesity causes a lot of illnesses + + + align:start position:0% +okay obesity causes a lot of illnesses +uh that cost a lot of money um + + align:start position:0% +uh that cost a lot of money um + + + align:start position:0% +uh that cost a lot of money um +projections are that children born in + + align:start position:0% +projections are that children born in + + + align:start position:0% +projections are that children born in +the year 2000 so about about your kid + + align:start position:0% +the year 2000 so about about your kid + + + align:start position:0% +the year 2000 so about about your kid +about your generation um one-third of + + align:start position:0% +about your generation um one-third of + + + align:start position:0% +about your generation um one-third of +them will get diabetes before they die + + align:start position:0% +them will get diabetes before they die + + + align:start position:0% +them will get diabetes before they die +okay based on current weight projections + + align:start position:0% +okay based on current weight projections + + + align:start position:0% +okay based on current weight projections +now as you notice looking around this + + align:start position:0% +now as you notice looking around this + + + align:start position:0% +now as you notice looking around this +room + + align:start position:0% +room + + + align:start position:0% +room +that's not a problem of the elite east + + align:start position:0% +that's not a problem of the elite east + + + align:start position:0% +that's not a problem of the elite east +coast people okay + + align:start position:0% +coast people okay + + + align:start position:0% +coast people okay +it's not a problem it's a problem the + + align:start position:0% +it's not a problem it's a problem the + + + align:start position:0% +it's not a problem it's a problem the +less educated it's problem concentrated + + align:start position:0% +less educated it's problem concentrated + + + align:start position:0% +less educated it's problem concentrated +more in the south + + align:start position:0% +more in the south + + + align:start position:0% +more in the south +okay but nonetheless it's if you look at + + align:start position:0% +okay but nonetheless it's if you look at + + + align:start position:0% +okay but nonetheless it's if you look at +a number of southern states the obesity + + align:start position:0% +a number of southern states the obesity + + + align:start position:0% +a number of southern states the obesity +rate is above 35 percent + + align:start position:0% +rate is above 35 percent + + + align:start position:0% +rate is above 35 percent +literally more than one in three people + + align:start position:0% +literally more than one in three people + + + align:start position:0% +literally more than one in three people +in the state are obese + + align:start position:0% +in the state are obese + + + align:start position:0% +in the state are obese +okay this is a huge problem and it's + + align:start position:0% +okay this is a huge problem and it's + + + align:start position:0% +okay this is a huge problem and it's +going to cause huge + + align:start position:0% +going to cause huge + + + align:start position:0% +going to cause huge +social if that's huge social + + align:start position:0% +social if that's huge social + + + align:start position:0% +social if that's huge social +consequences for our country the + + align:start position:0% +consequences for our country the + + + align:start position:0% +consequences for our country the +question is what do we do about these + + align:start position:0% +question is what do we do about these + + + align:start position:0% +question is what do we do about these +what are the things like smoking and + + align:start position:0% +what are the things like smoking and + + + align:start position:0% +what are the things like smoking and +drinking + + align:start position:0% +drinking + + + align:start position:0% +drinking +and obesity and there's essentially um + + align:start position:0% +and obesity and there's essentially um + + + align:start position:0% +and obesity and there's essentially um +there's essentially uh four answers + + align:start position:0% +there's essentially uh four answers + + + align:start position:0% +there's essentially uh four answers +the first is information + + align:start position:0% +the first is information + + + align:start position:0% +the first is information +can we just inform people about the + + align:start position:0% +can we just inform people about the + + + align:start position:0% +can we just inform people about the +damages and indeed this has been shown + + align:start position:0% +damages and indeed this has been shown + + + align:start position:0% +damages and indeed this has been shown +to work + + align:start position:0% +to work + + + align:start position:0% +to work +with smoking okay we knew smoking was + + align:start position:0% +with smoking okay we knew smoking was + + + align:start position:0% +with smoking okay we knew smoking was +bad for you about + + align:start position:0% +bad for you about + + + align:start position:0% +bad for you about +in 1954 okay but we only really got + + align:start position:0% +in 1954 okay but we only really got + + + align:start position:0% +in 1954 okay but we only really got +through to people + + align:start position:0% +through to people + + + align:start position:0% +through to people +starting really in the 1970s and 80s but + + align:start position:0% +starting really in the 1970s and 80s but + + + align:start position:0% +starting really in the 1970s and 80s but +it's had enormous effect + + align:start position:0% +it's had enormous effect + + + align:start position:0% +it's had enormous effect +smoking's fallen incredibly in the u.s + + align:start position:0% +smoking's fallen incredibly in the u.s + + + align:start position:0% +smoking's fallen incredibly in the u.s +to that information but here's the + + align:start position:0% +to that information but here's the + + + align:start position:0% +to that information but here's the +interesting thing + + align:start position:0% +interesting thing + + + align:start position:0% +interesting thing +okay smoking rates smoking used to be 50 + + align:start position:0% +okay smoking rates smoking used to be 50 + + + align:start position:0% +okay smoking rates smoking used to be 50 +percent + + align:start position:0% +percent + + + align:start position:0% +percent +in the entire every adult the fifth year + + align:start position:0% +in the entire every adult the fifth year + + + align:start position:0% +in the entire every adult the fifth year +out smoke didn't matter race gender + + align:start position:0% +out smoke didn't matter race gender + + + align:start position:0% +out smoke didn't matter race gender +class whatever + + align:start position:0% +class whatever + + + align:start position:0% +class whatever +now smoking essentially down to zero + + align:start position:0% +now smoking essentially down to zero + + + align:start position:0% +now smoking essentially down to zero +among the well-educated and still about + + align:start position:0% +among the well-educated and still about + + + align:start position:0% +among the well-educated and still about +twenty percent + + align:start position:0% +twenty percent + + + align:start position:0% +twenty percent +unless educated so information works + + align:start position:0% +unless educated so information works + + + align:start position:0% +unless educated so information works +but only works in a very uh inequitable + + align:start position:0% +but only works in a very uh inequitable + + + align:start position:0% +but only works in a very uh inequitable +way + + align:start position:0% +way + + + align:start position:0% +way +okay so information is one solution the + + align:start position:0% +okay so information is one solution the + + + align:start position:0% +okay so information is one solution the +second solution + + align:start position:0% +second solution + + + align:start position:0% +second solution +is taxation + + align:start position:0% + + + + align:start position:0% + +and indeed this has been shown to work + + align:start position:0% +and indeed this has been shown to work + + + align:start position:0% +and indeed this has been shown to work +for cigarettes once again + + align:start position:0% +for cigarettes once again + + + align:start position:0% +for cigarettes once again +smoking is price sensitive the + + align:start position:0% +smoking is price sensitive the + + + align:start position:0% +smoking is price sensitive the +elasticity of smoke with respect to the + + align:start position:0% +elasticity of smoke with respect to the + + + align:start position:0% +elasticity of smoke with respect to the +price is about minus 0.4 + + align:start position:0% +price is about minus 0.4 + + + align:start position:0% +price is about minus 0.4 +about every 10 you raise the price of + + align:start position:0% +about every 10 you raise the price of + + + align:start position:0% +about every 10 you raise the price of +cigarettes there's about four percent + + align:start position:0% +cigarettes there's about four percent + + + align:start position:0% +cigarettes there's about four percent +less smoking + + align:start position:0% +less smoking + + + align:start position:0% +less smoking +it works in particular youth smoking + + align:start position:0% +it works in particular youth smoking + + + align:start position:0% +it works in particular youth smoking +is very price sensitive use are very + + align:start position:0% +is very price sensitive use are very + + + align:start position:0% +is very price sensitive use are very +priceless because you + + align:start position:0% +priceless because you + + + align:start position:0% +priceless because you +have less money so they're very price + + align:start position:0% +have less money so they're very price + + + align:start position:0% +have less money so they're very price +sensitive + + align:start position:0% +sensitive + + + align:start position:0% +sensitive +so you so so it actually works um + + align:start position:0% +so you so so it actually works um + + + align:start position:0% +so you so so it actually works um +but that's sort of the easy case tax + + align:start position:0% +but that's sort of the easy case tax + + + align:start position:0% +but that's sort of the easy case tax +cigarettes is easy because every + + align:start position:0% +cigarettes is easy because every + + + align:start position:0% +cigarettes is easy because every +cigarette's bad for you + + align:start position:0% +cigarette's bad for you + + + align:start position:0% +cigarette's bad for you +taxing alcohol is trickier because after + + align:start position:0% +taxing alcohol is trickier because after + + + align:start position:0% +taxing alcohol is trickier because after +almost the damage is done by a tiny + + align:start position:0% +almost the damage is done by a tiny + + + align:start position:0% +almost the damage is done by a tiny +share of drinkers + + align:start position:0% +share of drinkers + + + align:start position:0% +share of drinkers +most of us will consume alcohol + + align:start position:0% +most of us will consume alcohol + + + align:start position:0% +most of us will consume alcohol +responsibly most of our lives + + align:start position:0% +responsibly most of our lives + + + align:start position:0% +responsibly most of our lives +and not cause any external damage okay + + align:start position:0% +and not cause any external damage okay + + + align:start position:0% +and not cause any external damage okay +but most of the damage is done by tiny + + align:start position:0% +but most of the damage is done by tiny + + + align:start position:0% +but most of the damage is done by tiny +shared drinking so taxes is trickier + + align:start position:0% +shared drinking so taxes is trickier + + + align:start position:0% +shared drinking so taxes is trickier +if i approach the big resident alcohol + + align:start position:0% +if i approach the big resident alcohol + + + align:start position:0% +if i approach the big resident alcohol +taxes you'll say wait a second i'm a + + align:start position:0% +taxes you'll say wait a second i'm a + + + align:start position:0% +taxes you'll say wait a second i'm a +responsible drinker why are you taxing + + align:start position:0% +responsible drinker why are you taxing + + + align:start position:0% +responsible drinker why are you taxing +why you taxing me so that's a little bit + + align:start position:0% +why you taxing me so that's a little bit + + + align:start position:0% +why you taxing me so that's a little bit +trickier not to mention obesity taxing + + align:start position:0% +trickier not to mention obesity taxing + + + align:start position:0% +trickier not to mention obesity taxing +food is maybe the trickiest of all + + align:start position:0% +food is maybe the trickiest of all + + + align:start position:0% +food is maybe the trickiest of all +okay so taxes are trickier you could + + align:start position:0% +okay so taxes are trickier you could + + + align:start position:0% +okay so taxes are trickier you could +maybe try + + align:start position:0% +maybe try + + + align:start position:0% +maybe try +an alternative thing you could do as + + align:start position:0% +an alternative thing you could do as + + + align:start position:0% +an alternative thing you could do as +penalties so instead of taxing alcohol + + align:start position:0% +penalties so instead of taxing alcohol + + + align:start position:0% +penalties so instead of taxing alcohol +we could just steep in the penalties for + + align:start position:0% +we could just steep in the penalties for + + + align:start position:0% +we could just steep in the penalties for +drunk driving + + align:start position:0% +drunk driving + + + align:start position:0% +drunk driving +you know if you killed a few drunk + + align:start position:0% +you know if you killed a few drunk + + + align:start position:0% +you know if you killed a few drunk +drivers it'd be less drunk driving + + align:start position:0% +drivers it'd be less drunk driving + + + align:start position:0% +drivers it'd be less drunk driving +okay but the problem is that's a pretty + + align:start position:0% +okay but the problem is that's a pretty + + + align:start position:0% +okay but the problem is that's a pretty +extreme penalty and what if you got it + + align:start position:0% +extreme penalty and what if you got it + + + align:start position:0% +extreme penalty and what if you got it +wrong you feel kind of bad about killing + + align:start position:0% +wrong you feel kind of bad about killing + + + align:start position:0% +wrong you feel kind of bad about killing +someone + + align:start position:0% +someone + + + align:start position:0% +someone +because the breathalyzer didn't work + + align:start position:0% +because the breathalyzer didn't work + + + align:start position:0% +because the breathalyzer didn't work +there was a series of articles actually + + align:start position:0% +there was a series of articles actually + + + align:start position:0% +there was a series of articles actually +new york times about how terrible + + align:start position:0% +new york times about how terrible + + + align:start position:0% +new york times about how terrible +breathalyzers are + + align:start position:0% +breathalyzers are + + + align:start position:0% +breathalyzers are +and how inaccurate they are okay so + + align:start position:0% +and how inaccurate they are okay so + + + align:start position:0% +and how inaccurate they are okay so +problem with penalties is we can't + + align:start position:0% +problem with penalties is we can't + + + align:start position:0% +problem with penalties is we can't +enforce them perfectly + + align:start position:0% +enforce them perfectly + + + align:start position:0% +enforce them perfectly +okay so that's the third solution the + + align:start position:0% +okay so that's the third solution the + + + align:start position:0% +okay so that's the third solution the +final solution the one that's really + + align:start position:0% +final solution the one that's really + + + align:start position:0% +final solution the one that's really +most discussed right now + + align:start position:0% +most discussed right now + + + align:start position:0% +most discussed right now +is illegality what if we just made these + + align:start position:0% +is illegality what if we just made these + + + align:start position:0% +is illegality what if we just made these +things illegal and this comes to + + align:start position:0% +things illegal and this comes to + + + align:start position:0% +things illegal and this comes to +the discussion of marijuana should + + align:start position:0% +the discussion of marijuana should + + + align:start position:0% +the discussion of marijuana should +marijuana be legal + + align:start position:0% +marijuana be legal + + + align:start position:0% +marijuana be legal +okay well illegality is an extreme form + + align:start position:0% +okay well illegality is an extreme form + + + align:start position:0% +okay well illegality is an extreme form +of lowering externalities now obviously + + align:start position:0% +of lowering externalities now obviously + + + align:start position:0% +of lowering externalities now obviously +when pot's illegal people still smoke + + align:start position:0% +when pot's illegal people still smoke + + + align:start position:0% +when pot's illegal people still smoke +pot + + align:start position:0% +pot + + + align:start position:0% +pot +but it's still true when you make it + + align:start position:0% +but it's still true when you make it + + + align:start position:0% +but it's still true when you make it +legal it's consumed at much higher + + align:start position:0% +legal it's consumed at much higher + + + align:start position:0% +legal it's consumed at much higher +levels + + align:start position:0% +levels + + + align:start position:0% +levels +okay legality does matter so for example + + align:start position:0% +okay legality does matter so for example + + + align:start position:0% +okay legality does matter so for example +you've done studies + + align:start position:0% +you've done studies + + + align:start position:0% +you've done studies +yes people under 21 drink but literally + + align:start position:0% +yes people under 21 drink but literally + + + align:start position:0% +yes people under 21 drink but literally +to look at people the day after the 21st + + align:start position:0% +to look at people the day after the 21st + + + align:start position:0% +to look at people the day after the 21st +birthday they drink much more than the + + align:start position:0% +birthday they drink much more than the + + + align:start position:0% +birthday they drink much more than the +day before their 21st not on the 21st + + align:start position:0% +day before their 21st not on the 21st + + + align:start position:0% +day before their 21st not on the 21st +birthday that's the party we ignore that + + align:start position:0% +birthday that's the party we ignore that + + + align:start position:0% +birthday that's the party we ignore that +but the day after the 21st birthday and + + align:start position:0% +but the day after the 21st birthday and + + + align:start position:0% +but the day after the 21st birthday and +thereafter they're drinking at much + + align:start position:0% +thereafter they're drinking at much + + + align:start position:0% +thereafter they're drinking at much +higher levels than before + + align:start position:0% +higher levels than before + + + align:start position:0% +higher levels than before +legality matters okay it's also true the + + align:start position:0% +legality matters okay it's also true the + + + align:start position:0% +legality matters okay it's also true the +day after 21st birthday people are much + + align:start position:0% +day after 21st birthday people are much + + + align:start position:0% +day after 21st birthday people are much +more likely to die in a drunk driving + + align:start position:0% +more likely to die in a drunk driving + + + align:start position:0% +more likely to die in a drunk driving +accident than the day before their 21st + + align:start position:0% +accident than the day before their 21st + + + align:start position:0% +accident than the day before their 21st +birthday + + align:start position:0% +birthday + + + align:start position:0% +birthday +okay so legality matters so the point is + + align:start position:0% +okay so legality matters so the point is + + + align:start position:0% +okay so legality matters so the point is +we have a whole series of tools + + align:start position:0% +we have a whole series of tools + + + align:start position:0% +we have a whole series of tools +to think about this and the question is + + align:start position:0% +to think about this and the question is + + + align:start position:0% +to think about this and the question is +how should we combine and use them + + align:start position:0% +how should we combine and use them + + + align:start position:0% +how should we combine and use them +and the answer is take 1441 + + align:start position:0% +and the answer is take 1441 + + + align:start position:0% +and the answer is take 1441 +and i'll teach you all about it but we + + align:start position:0% +and i'll teach you all about it but we + + + align:start position:0% +and i'll teach you all about it but we +don't have any more time here + + align:start position:0% +don't have any more time here + + + align:start position:0% +don't have any more time here +this just raises the issues to think + + align:start position:0% +this just raises the issues to think + + + align:start position:0% +this just raises the issues to think +about with externalities it's an + + align:start position:0% +about with externalities it's an + + + align:start position:0% +about with externalities it's an +important topic to think about i realize + + align:start position:0% +important topic to think about i realize + + + align:start position:0% +important topic to think about i realize +it's a lot to cover in one lecture + + align:start position:0% +it's a lot to cover in one lecture + + + align:start position:0% +it's a lot to cover in one lecture +i just want to sort of give you a taste + + align:start position:0% +i just want to sort of give you a taste + + + align:start position:0% +i just want to sort of give you a taste +for how economists think about analyzing + + align:start position:0% +for how economists think about analyzing + + + align:start position:0% +for how economists think about analyzing +this kind of market failure + + align:start position:0% +this kind of market failure + + + align:start position:0% +this kind of market failure +you \ No newline at end of file diff --git a/ZOBgPxmXeVM.txt b/ZOBgPxmXeVM.txt new file mode 100644 index 0000000000000000000000000000000000000000..eda983b73ba773e614172d826d9e3c008e574578 --- /dev/null +++ b/ZOBgPxmXeVM.txt @@ -0,0 +1,7088 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu all right so this is lecture + + align:start position:0% +ocw.mit.edu all right so this is lecture + + + align:start position:0% +ocw.mit.edu all right so this is lecture +15 it's the last topic today and Friday + + align:start position:0% +15 it's the last topic today and Friday + + + align:start position:0% +15 it's the last topic today and Friday +lectures 15 and 16 trusses within the + + align:start position:0% +lectures 15 and 16 trusses within the + + + align:start position:0% +lectures 15 and 16 trusses within the +chapter 2 the last topic we'll do for + + align:start position:0% +chapter 2 the last topic we'll do for + + + align:start position:0% +chapter 2 the last topic we'll do for +discreet uh systems and it's a lot of + + align:start position:0% +discreet uh systems and it's a lot of + + + align:start position:0% +discreet uh systems and it's a lot of +fun yeah uh I wanted to say a few words + + align:start position:0% +fun yeah uh I wanted to say a few words + + + align:start position:0% +fun yeah uh I wanted to say a few words +first about last night's exam um several + + align:start position:0% +first about last night's exam um several + + + align:start position:0% +first about last night's exam um several +words first uh o overall I'm sure it's + + align:start position:0% +words first uh o overall I'm sure it's + + + align:start position:0% +words first uh o overall I'm sure it's +going to be fine the rise is grading the + + align:start position:0% +going to be fine the rise is grading the + + + align:start position:0% +going to be fine the rise is grading the +first two problems he'll pass them to + + align:start position:0% +first two problems he'll pass them to + + + align:start position:0% +first two problems he'll pass them to +Peter for the next two and I'll get them + + align:start position:0% +Peter for the next two and I'll get them + + + align:start position:0% +Peter for the next two and I'll get them +back I I pretty sure it'd be next week + + align:start position:0% +back I I pretty sure it'd be next week + + + align:start position:0% +back I I pretty sure it'd be next week +um I felt it was a fair exam except I I + + align:start position:0% +um I felt it was a fair exam except I I + + + align:start position:0% +um I felt it was a fair exam except I I +I should have done a better job in uh + + align:start position:0% +I should have done a better job in uh + + + align:start position:0% +I should have done a better job in uh +connecting in in in helping you with the + + align:start position:0% +connecting in in in helping you with the + + + align:start position:0% +connecting in in in helping you with the +Matrix a especially in in problem one I + + align:start position:0% +Matrix a especially in in problem one I + + + align:start position:0% +Matrix a especially in in problem one I +I'm glad that hint was there the the the + + align:start position:0% +I'm glad that hint was there the the the + + + align:start position:0% +I'm glad that hint was there the the the +Matrix a not that that goes with free + + align:start position:0% +Matrix a not that that goes with free + + + align:start position:0% +Matrix a not that that goes with free +free to + + align:start position:0% +free to + + + align:start position:0% +free to +uh sort of say what what kind of Matrix + + align:start position:0% +uh sort of say what what kind of Matrix + + + align:start position:0% +uh sort of say what what kind of Matrix +to be looking for and I thought I'd just + + align:start position:0% +to be looking for and I thought I'd just + + + align:start position:0% +to be looking for and I thought I'd just +repeat uh make that make the connections + + align:start position:0% +repeat uh make that make the connections + + + align:start position:0% +repeat uh make that make the connections +that I uh should have made uh uh earlier + + align:start position:0% +that I uh should have made uh uh earlier + + + align:start position:0% +that I uh should have made uh uh earlier +uh so just just so we all see the the + + align:start position:0% +uh so just just so we all see the the + + + align:start position:0% +uh so just just so we all see the the +the point about + + align:start position:0% +the point about + + + align:start position:0% +the point about +these these A's and the a not and the a + + align:start position:0% +these these A's and the a not and the a + + + align:start position:0% +these these A's and the a not and the a +transpose A's so if I take for that aot + + align:start position:0% +transpose A's so if I take for that aot + + + align:start position:0% +transpose A's so if I take for that aot +the free free one everybody sees that + + align:start position:0% +the free free one everybody sees that + + + align:start position:0% +the free free one everybody sees that +this is and this connects of course with + + align:start position:0% +this is and this connects of course with + + + align:start position:0% +this is and this connects of course with +our graphs our graph is just this simple + + align:start position:0% +our graphs our graph is just this simple + + + align:start position:0% +our graphs our graph is just this simple +graph with uh well actually is it how + + align:start position:0% +graph with uh well actually is it how + + + align:start position:0% +graph with uh well actually is it how +many is it five nodes I guess there are + + align:start position:0% +many is it five nodes I guess there are + + + align:start position:0% +many is it five nodes I guess there are +five so because there's a because as it + + align:start position:0% +five so because there's a because as it + + + align:start position:0% +five so because there's a because as it +stands I have 1 2 3 4 five columns I've + + align:start position:0% +stands I have 1 2 3 4 five columns I've + + + align:start position:0% +stands I have 1 2 3 4 five columns I've +got five U's + + align:start position:0% +got five U's + + + align:start position:0% +got five U's +u0o down U1 down to u4 + + align:start position:0% + + + + align:start position:0% + +and if I take a transpose a that that + + align:start position:0% +and if I take a transpose a that that + + + align:start position:0% +and if I take a transpose a that that +would be the free free Matrix what size + + align:start position:0% +would be the free free Matrix what size + + + align:start position:0% +would be the free free Matrix what size +would it be and what Matrix would it be + + align:start position:0% +would it be and what Matrix would it be + + + align:start position:0% +would it be and what Matrix would it be +just if if I if we do that + + align:start position:0% +just if if I if we do that + + + align:start position:0% +just if if I if we do that +multiplication what this is a first + + align:start position:0% +multiplication what this is a first + + + align:start position:0% +multiplication what this is a first +difference Matrix when I do a not + + align:start position:0% +difference Matrix when I do a not + + + align:start position:0% +difference Matrix when I do a not +transpose a not I'll get one of our + + align:start position:0% +transpose a not I'll get one of our + + + align:start position:0% +transpose a not I'll get one of our +second difference matrices so it'll be + + align:start position:0% +second difference matrices so it'll be + + + align:start position:0% +second difference matrices so it'll be +one of our special ones which special + + align:start position:0% +one of our special ones which special + + + align:start position:0% +one of our special ones which special +ones which special one would it be B + + align:start position:0% +ones which special one would it be B + + + align:start position:0% +ones which special one would it be B +it'll be the Matrix B that has both ends + + align:start position:0% +it'll be the Matrix B that has both ends + + + align:start position:0% +it'll be the Matrix B that has both ends +free and what size will it be I guess + + align:start position:0% +free and what size will it be I guess + + + align:start position:0% +free and what size will it be I guess +it'll be + + align:start position:0% +it'll be + + + align:start position:0% +it'll be +5x5 because because I'm + + align:start position:0% +5x5 because because I'm + + + align:start position:0% +5x5 because because I'm +taking uh is that no yeah that that's + + align:start position:0% +taking uh is that no yeah that that's + + + align:start position:0% +taking uh is that no yeah that that's +right that would be 5x 4 * a KN which is + + align:start position:0% +right that would be 5x 4 * a KN which is + + + align:start position:0% +right that would be 5x 4 * a KN which is +4x5 so it'll be five the 5x5 Matrix B + + align:start position:0% +4x5 so it'll be five the 5x5 Matrix B + + + align:start position:0% +4x5 so it'll be five the 5x5 Matrix B +can I call it B5 okay so that's that was + + align:start position:0% +can I call it B5 okay so that's that was + + + align:start position:0% +can I call it B5 okay so that's that was +there as a hint + + align:start position:0% +there as a hint + + + align:start position:0% +there as a hint +the that isn't the correct Matrix for + + align:start position:0% +the that isn't the correct Matrix for + + + align:start position:0% +the that isn't the correct Matrix for +problem one because problem one was + + align:start position:0% +problem one because problem one was + + + align:start position:0% +problem one because problem one was +fixed fixed let's get there in two steps + + align:start position:0% +fixed fixed let's get there in two steps + + + align:start position:0% +fixed fixed let's get there in two steps +suppose it's fixed free so suppose I uh + + align:start position:0% +suppose it's fixed free so suppose I uh + + + align:start position:0% +suppose it's fixed free so suppose I uh +make you not equal zero so I ground the + + align:start position:0% +make you not equal zero so I ground the + + + align:start position:0% +make you not equal zero so I ground the +top note I support the top note oh no + + align:start position:0% +top note I support the top note oh no + + + align:start position:0% +top note I support the top note oh no +shall I do you not yeah I'll do you not + + align:start position:0% +shall I do you not yeah I'll do you not + + + align:start position:0% +shall I do you not yeah I'll do you not +so that not that would knock out this + + align:start position:0% +so that not that would knock out this + + + align:start position:0% +so that not that would knock out this +one if I say you not if if I fix you not + + align:start position:0% +one if I say you not if if I fix you not + + + align:start position:0% +one if I say you not if if I fix you not +say at zero or whatever now I've got uh + + align:start position:0% +say at zero or whatever now I've got uh + + + align:start position:0% +say at zero or whatever now I've got uh +the next a I won't call it a KN + + align:start position:0% +the next a I won't call it a KN + + + align:start position:0% +the next a I won't call it a KN +anymore now 4x4 what Matrix now if I do + + align:start position:0% +anymore now 4x4 what Matrix now if I do + + + align:start position:0% +anymore now 4x4 what Matrix now if I do +a transpose a what which of our special + + align:start position:0% +a transpose a what which of our special + + + align:start position:0% +a transpose a what which of our special +matrices am I going to get T it'll be T + + align:start position:0% +matrices am I going to get T it'll be T + + + align:start position:0% +matrices am I going to get T it'll be T +it'll be the one that has the first uh + + align:start position:0% +it'll be the one that has the first uh + + + align:start position:0% +it'll be the one that has the first uh +the first the one one entry will only be + + align:start position:0% +the first the one one entry will only be + + + align:start position:0% +the first the one one entry will only be +one so when I that'll be the fixed free + + align:start position:0% +one so when I that'll be the fixed free + + + align:start position:0% +one so when I that'll be the fixed free +Matrix it'll be of what size four now + + align:start position:0% +Matrix it'll be of what size four now + + + align:start position:0% +Matrix it'll be of what size four now +I've only got four unknowns U1 to u4 + + align:start position:0% +I've only got four unknowns U1 to u4 + + + align:start position:0% +I've only got four unknowns U1 to u4 +okay that still is not what problem one + + align:start position:0% +okay that still is not what problem one + + + align:start position:0% +okay that still is not what problem one +is problem one was fixed fixed so as I + + align:start position:0% +is problem one was fixed fixed so as I + + + align:start position:0% +is problem one was fixed fixed so as I +did in the review that would knock out + + align:start position:0% +did in the review that would knock out + + + align:start position:0% +did in the review that would knock out +both of these columns so this now is the + + align:start position:0% +both of these columns so this now is the + + + align:start position:0% +both of these columns so this now is the +Matrix that I was looking for in problem + + align:start position:0% +Matrix that I was looking for in problem + + + align:start position:0% +Matrix that I was looking for in problem +one and I wish I had made these steps uh + + align:start position:0% +one and I wish I had made these steps uh + + + align:start position:0% +one and I wish I had made these steps uh +you know emphasized these steps in + + align:start position:0% +you know emphasized these steps in + + + align:start position:0% +you know emphasized these steps in +advance I apologize okay so what fix + + align:start position:0% +advance I apologize okay so what fix + + + align:start position:0% +advance I apologize okay so what fix +fixed if without the C part in + + align:start position:0% +fixed if without the C part in + + + align:start position:0% +fixed if without the C part in +it uh just focusing on the a what what + + align:start position:0% +it uh just focusing on the a what what + + + align:start position:0% +it uh just focusing on the a what what +fix fix Matrix would I get which one of + + align:start position:0% +fix fix Matrix would I get which one of + + + align:start position:0% +fix fix Matrix would I get which one of +our guys would it be K of size three and + + align:start position:0% +our guys would it be K of size three and + + + align:start position:0% +our guys would it be K of size three and +while we're at + + align:start position:0% +while we're at + + + align:start position:0% +while we're at +it what would be the + + align:start position:0% +it what would be the + + + align:start position:0% +it what would be the +story how would I get one of these + + align:start position:0% +story how would I get one of these + + + align:start position:0% +story how would I get one of these +circular ones which we haven't which is + + align:start position:0% +circular ones which we haven't which is + + + align:start position:0% +circular ones which we haven't which is +sort of on our special list for fora + + align:start position:0% +sort of on our special list for fora + + + align:start position:0% +sort of on our special list for fora +it's the really special guy uh so a + + align:start position:0% +it's the really special guy uh so a + + + align:start position:0% +it's the really special guy uh so a +circular one I'm going to make a I'm + + align:start position:0% +circular one I'm going to make a I'm + + + align:start position:0% +circular one I'm going to make a I'm +going to connect u4 back to + + align:start position:0% + + + + align:start position:0% + +u0o so I'm going to put these guys back + + align:start position:0% +u0o so I'm going to put these guys back + + + align:start position:0% +u0o so I'm going to put these guys back +in and what else would change if u4 was + + align:start position:0% +in and what else would change if u4 was + + + align:start position:0% +in and what else would change if u4 was +connected back to U now I'm aiming for + + align:start position:0% +connected back to U now I'm aiming for + + + align:start position:0% +connected back to U now I'm aiming for +this circulent what what Matrix a a is + + align:start position:0% +this circulent what what Matrix a a is + + + align:start position:0% +this circulent what what Matrix a a is +going to give me the circulent so + + align:start position:0% +going to give me the circulent so + + + align:start position:0% +going to give me the circulent so +again these guys are the a transpose a + + align:start position:0% +again these guys are the a transpose a + + + align:start position:0% +again these guys are the a transpose a +this over here was the A and over here + + align:start position:0% +this over here was the A and over here + + + align:start position:0% +this over here was the A and over here +is the a transpose a and now I want to + + align:start position:0% +is the a transpose a and now I want to + + + align:start position:0% +is the a transpose a and now I want to +make I want to fix a and then I want to + + align:start position:0% +make I want to fix a and then I want to + + + align:start position:0% +make I want to fix a and then I want to +see the a transpose a so if suppose I + + align:start position:0% +see the a transpose a so if suppose I + + + align:start position:0% +see the a transpose a so if suppose I +give you that graph then oops I should + + align:start position:0% +give you that graph then oops I should + + + align:start position:0% +give you that graph then oops I should +have well uh just shall I just to keep + + align:start position:0% +have well uh just shall I just to keep + + + align:start position:0% +have well uh just shall I just to keep +this well no let me let me do it right + + align:start position:0% +this well no let me let me do it right + + + align:start position:0% +this well no let me let me do it right +connect the whole + + align:start position:0% +connect the whole + + + align:start position:0% +connect the whole +the whole guy so so number the fifth + + align:start position:0% +the whole guy so so number the fifth + + + align:start position:0% +the whole guy so so number the fifth +node coming back to the + + align:start position:0% +node coming back to the + + + align:start position:0% +node coming back to the +first so that's my circle of nodes it's + + align:start position:0% +first so that's my circle of nodes it's + + + align:start position:0% +first so that's my circle of nodes it's +a simple graph what what's the a for + + align:start position:0% +a simple graph what what's the a for + + + align:start position:0% +a simple graph what what's the a for +what's the a circulent now just just + + align:start position:0% +what's the a circulent now just just + + + align:start position:0% +what's the a circulent now just just +this is so this is this would be the a + + align:start position:0% +this is so this is this would be the a + + + align:start position:0% +this is so this is this would be the a +for the for the circulent + + align:start position:0% +for the for the circulent + + + align:start position:0% +for the for the circulent +case so it's it's got that back in that + + align:start position:0% +case so it's it's got that back in that + + + align:start position:0% +case so it's it's got that back in that +shouldn't be erased that shouldn't be be + + align:start position:0% +shouldn't be erased that shouldn't be be + + + align:start position:0% +shouldn't be erased that shouldn't be be +erased and what else has it + + align:start position:0% + + + + align:start position:0% + +got what what if I ask you for the + + align:start position:0% +got what what if I ask you for the + + + align:start position:0% +got what what if I ask you for the +incidence Matrix now I'm in section 24 + + align:start position:0% +incidence Matrix now I'm in section 24 + + + align:start position:0% +incidence Matrix now I'm in section 24 +like I've given you a graph or you can + + align:start position:0% +like I've given you a graph or you can + + + align:start position:0% +like I've given you a graph or you can +think of masses and springs in a circle + + align:start position:0% +think of masses and springs in a circle + + + align:start position:0% +think of masses and springs in a circle +uh so I've got five masses five Springs + + align:start position:0% +uh so I've got five masses five Springs + + + align:start position:0% +uh so I've got five masses five Springs +what what's my Matrix a + + align:start position:0% +what what's my Matrix a + + + align:start position:0% +what what's my Matrix a +missing it needs another another row + + align:start position:0% +missing it needs another another row + + + align:start position:0% +missing it needs another another row +it's got another we just has put in + + align:start position:0% +it's got another we just has put in + + + align:start position:0% +it's got another we just has put in +another Edge it needs another row that + + align:start position:0% +another Edge it needs another row that + + + align:start position:0% +another Edge it needs another row that +row that edge went from the last node + + align:start position:0% +row that edge went from the last node + + + align:start position:0% +row that edge went from the last node +back to the first node + + align:start position:0% +back to the first node + + + align:start position:0% +back to the first node +so so we've got a a a fifth row so you + + align:start position:0% +so so we've got a a a fifth row so you + + + align:start position:0% +so so we've got a a a fifth row so you +see now it really is circulent this I + + align:start position:0% +see now it really is circulent this I + + + align:start position:0% +see now it really is circulent this I +would call this one also I'd call that a + + align:start position:0% +would call this one also I'd call that a + + + align:start position:0% +would call this one also I'd call that a +circulent matrix the + + align:start position:0% +circulent matrix the + + + align:start position:0% +circulent matrix the +diagonals are complete are there are + + align:start position:0% +diagonals are complete are there are + + + align:start position:0% +diagonals are complete are there are +constant that that that's what I would + + align:start position:0% +constant that that that's what I would + + + align:start position:0% +constant that that that's what I would +what I and Matt lab and everybody else + + align:start position:0% +what I and Matt lab and everybody else + + + align:start position:0% +what I and Matt lab and everybody else +would call a tuplets matrix and the + + align:start position:0% +would call a tuplets matrix and the + + + align:start position:0% +would call a tuplets matrix and the +command tuplets could create this uh + + align:start position:0% +command tuplets could create this uh + + + align:start position:0% +command tuplets could create this uh +that diagonal is constant that diagonal + + align:start position:0% +that diagonal is constant that diagonal + + + align:start position:0% +that diagonal is constant that diagonal +is constant other diagonals are constant + + align:start position:0% +is constant other diagonals are constant + + + align:start position:0% +is constant other diagonals are constant +but more than that what what's + + align:start position:0% +but more than that what what's + + + align:start position:0% +but more than that what what's +additional here in the circulent which + + align:start position:0% +additional here in the circulent which + + + align:start position:0% +additional here in the circulent which +is the thing that makes forier happy the + + align:start position:0% +is the thing that makes forier happy the + + + align:start position:0% +is the thing that makes forier happy the +diagonal circles + + align:start position:0% +diagonal circles + + + align:start position:0% +diagonal circles +around that diagonal is only got four + + align:start position:0% +around that diagonal is only got four + + + align:start position:0% +around that diagonal is only got four +entries in it but it circles around sort + + align:start position:0% +entries in it but it circles around sort + + + align:start position:0% +entries in it but it circles around sort +of periodically to the fifth it's fifth + + align:start position:0% +of periodically to the fifth it's fifth + + + align:start position:0% +of periodically to the fifth it's fifth +entry so that's more than templets it's + + align:start position:0% +entry so that's more than templets it's + + + align:start position:0% +entry so that's more than templets it's +circulent because it's it's coming + + align:start position:0% +circulent because it's it's coming + + + align:start position:0% +circulent because it's it's coming +around again this we'll see in the in + + align:start position:0% +around again this we'll see in the in + + + align:start position:0% +around again this we'll see in the in +the discrete fora transform it's really + + align:start position:0% +the discrete fora transform it's really + + + align:start position:0% +the discrete fora transform it's really +all good stuff and now now there's my a + + align:start position:0% +all good stuff and now now there's my a + + + align:start position:0% +all good stuff and now now there's my a +circulent and what would be my a + + align:start position:0% +circulent and what would be my a + + + align:start position:0% +circulent and what would be my a +transpose circulent a circulent what + + align:start position:0% +transpose circulent a circulent what + + + align:start position:0% +transpose circulent a circulent what +would be a transpose a say if I take + + align:start position:0% +would be a transpose a say if I take + + + align:start position:0% +would be a transpose a say if I take +that 5x5 + + align:start position:0% +that 5x5 + + + align:start position:0% +that 5x5 +Matrix + + align:start position:0% +Matrix + + + align:start position:0% +Matrix +C finally I've created so I've already + + align:start position:0% +C finally I've created so I've already + + + align:start position:0% +C finally I've created so I've already +got B I've got T I've got K all those + + align:start position:0% +got B I've got T I've got K all those + + + align:start position:0% +got B I've got T I've got K all those +three special guys and now the a + + align:start position:0% +three special guys and now the a + + + align:start position:0% +three special guys and now the a +transpose a for this circulent so that's + + align:start position:0% +transpose a for this circulent so that's + + + align:start position:0% +transpose a for this circulent so that's +a first difference Matrix for a periodic + + align:start position:0% +a first difference Matrix for a periodic + + + align:start position:0% +a first difference Matrix for a periodic +problem and a transpose a will be a + + align:start position:0% +problem and a transpose a will be a + + + align:start position:0% +problem and a transpose a will be a +second difference Matrix for a periodic + + align:start position:0% +second difference Matrix for a periodic + + + align:start position:0% +second difference Matrix for a periodic +problem C5 I guess it'll be five + + align:start position:0% +problem C5 I guess it'll be five + + + align:start position:0% +problem C5 I guess it'll be five +okay I hope that brings together what I + + align:start position:0% +okay I hope that brings together what I + + + align:start position:0% +okay I hope that brings together what I +if I was on the ball I would have + + align:start position:0% +if I was on the ball I would have + + + align:start position:0% +if I was on the ball I would have +brought it together before the quiz let + + align:start position:0% +brought it together before the quiz let + + + align:start position:0% +brought it together before the quiz let +me let me can I just say a few words + + align:start position:0% +me let me can I just say a few words + + + align:start position:0% +me let me can I just say a few words +about the quiz and + + align:start position:0% +about the quiz and + + + align:start position:0% +about the quiz and +grades uh they come out + + align:start position:0% +grades uh they come out + + + align:start position:0% +grades uh they come out +fine really they do I've been doing this + + align:start position:0% +fine really they do I've been doing this + + + align:start position:0% +fine really they do I've been doing this +a long time and uh just you know like + + align:start position:0% +a long time and uh just you know like + + + align:start position:0% +a long time and uh just you know like +enjoy October don't don't uh don't I I'm + + align:start position:0% +enjoy October don't don't uh don't I I'm + + + align:start position:0% +enjoy October don't don't uh don't I I'm +sorry to give you any exam at all but + + align:start position:0% +sorry to give you any exam at all but + + + align:start position:0% +sorry to give you any exam at all but +it's uh you know it's it's a chance for + + align:start position:0% +it's uh you know it's it's a chance for + + + align:start position:0% +it's uh you know it's it's a chance for +you to show yeah I'm working on this + + align:start position:0% +you to show yeah I'm working on this + + + align:start position:0% +you to show yeah I'm working on this +stuff I'm learning it everybody do learn + + align:start position:0% +stuff I'm learning it everybody do learn + + + align:start position:0% +stuff I'm learning it everybody do learn +it first time I don't learn it first + + align:start position:0% +it first time I don't learn it first + + + align:start position:0% +it first time I don't learn it first +time every time I teach the course I + + align:start position:0% +time every time I teach the course I + + + align:start position:0% +time every time I teach the course I +learn something more and uh if if you're + + align:start position:0% +learn something more and uh if if you're + + + align:start position:0% +learn something more and uh if if you're +learning from this course then then I'm + + align:start position:0% +learning from this course then then I'm + + + align:start position:0% +learning from this course then then I'm +totally happy and I I and I believe + + align:start position:0% +totally happy and I I and I believe + + + align:start position:0% +totally happy and I I and I believe +that's a case so I am entirely happy and + + align:start position:0% +that's a case so I am entirely happy and + + + align:start position:0% +that's a case so I am entirely happy and +I hope the quiz you know some some + + align:start position:0% +I hope the quiz you know some some + + + align:start position:0% +I hope the quiz you know some some +points of it + + align:start position:0% +points of it + + + align:start position:0% +points of it +were uh I wish I'd prepared better but + + align:start position:0% +were uh I wish I'd prepared better but + + + align:start position:0% +were uh I wish I'd prepared better but +uh I I I feel pretty good about it I + + align:start position:0% +uh I I I feel pretty good about it I + + + align:start position:0% +uh I I I feel pretty good about it I +feel good about it let me just say yeah + + align:start position:0% +feel good about it let me just say yeah + + + align:start position:0% +feel good about it let me just say yeah +yeah so and I'm happy to have any + + align:start position:0% +yeah so and I'm happy to have any + + + align:start position:0% +yeah so and I'm happy to have any +comments email or or in + + align:start position:0% +comments email or or in + + + align:start position:0% +comments email or or in +person but allow me to go forward with + + align:start position:0% +person but allow me to go forward with + + + align:start position:0% +person but allow me to go forward with +trusses however I'm ready always for for + + align:start position:0% +trusses however I'm ready always for for + + + align:start position:0% +trusses however I'm ready always for for +a comment yeah okay okay anyway enjoy + + align:start position:0% +a comment yeah okay okay anyway enjoy + + + align:start position:0% +a comment yeah okay okay anyway enjoy +trusses enjoy life yeah right okay and + + align:start position:0% +trusses enjoy life yeah right okay and + + + align:start position:0% +trusses enjoy life yeah right okay and +and now this should have been in the + + align:start position:0% +and now this should have been in the + + + align:start position:0% +and now this should have been in the +book this page so if I if it wasn't too + + align:start position:0% +book this page so if I if it wasn't too + + + align:start position:0% +book this page so if I if it wasn't too +late I would like paste it in because + + align:start position:0% +late I would like paste it in because + + + align:start position:0% +late I would like paste it in because +that this connects a transpose a to a + + align:start position:0% +that this connects a transpose a to a + + + align:start position:0% +that this connects a transpose a to a +special matrices in the way I had in my + + align:start position:0% +special matrices in the way I had in my + + + align:start position:0% +special matrices in the way I had in my +mind but I didn't put it on the board + + align:start position:0% +mind but I didn't put it on the board + + + align:start position:0% +mind but I didn't put it on the board +until just now right okay so I'll cover + + align:start position:0% +until just now right okay so I'll cover + + + align:start position:0% +until just now right okay so I'll cover +that + + align:start position:0% +that + + + align:start position:0% +that +up and ready to go with + + align:start position:0% +up and ready to go with + + + align:start position:0% +up and ready to go with +trusses + + align:start position:0% +trusses + + + align:start position:0% +trusses +okay so trust is we want to know what's + + align:start position:0% +okay so trust is we want to know what's + + + align:start position:0% +okay so trust is we want to know what's +the you know what's up we want to get + + align:start position:0% +the you know what's up we want to get + + + align:start position:0% +the you know what's up we want to get +the setup right once once we get the set + + align:start position:0% +the setup right once once we get the set + + + align:start position:0% +the setup right once once we get the set +up we'll know uh What + + align:start position:0% +up we'll know uh What + + + align:start position:0% +up we'll know uh What +uh what we're looking for okay so H + + align:start position:0% +uh what we're looking for okay so H + + + align:start position:0% +uh what we're looking for okay so H +trust is a bunch of elastic + + align:start position:0% +trust is a bunch of elastic + + + align:start position:0% +trust is a bunch of elastic +bars at with pin joints connecting them + + align:start position:0% +bars at with pin joints connecting them + + + align:start position:0% +bars at with pin joints connecting them +now what do I mean by a pin joint I mean + + align:start position:0% +now what do I mean by a pin joint I mean + + + align:start position:0% +now what do I mean by a pin joint I mean +that the the bar can + + align:start position:0% +that the the bar can + + + align:start position:0% +that the the bar can +bars + + align:start position:0% +bars + + + align:start position:0% +bars +can stretching the bars takes Force + + align:start position:0% +can stretching the bars takes Force + + + align:start position:0% +can stretching the bars takes Force +turning around the pin joint doesn't + + align:start position:0% +turning around the pin joint doesn't + + + align:start position:0% +turning around the pin joint doesn't +take Force so so the pin just lets them + + align:start position:0% +take Force so so the pin just lets them + + + align:start position:0% +take Force so so the pin just lets them +lets them turn + + align:start position:0% +lets them turn + + + align:start position:0% +lets them turn +but but uh so we'll have forces in those + + align:start position:0% +but but uh so we'll have forces in those + + + align:start position:0% +but but uh so we'll have forces in those +bars so it's like masses and + + align:start position:0% +bars so it's like masses and + + + align:start position:0% +bars so it's like masses and +springs exactly like masses and springs + + align:start position:0% +springs exactly like masses and springs + + + align:start position:0% +springs exactly like masses and springs +but yet the we have a two D problem so + + align:start position:0% +but yet the we have a two D problem so + + + align:start position:0% +but yet the we have a two D problem so +it's a two-dimensional problem with + + align:start position:0% +it's a two-dimensional problem with + + + align:start position:0% +it's a two-dimensional problem with +masses and springs and we could + + align:start position:0% +masses and springs and we could + + + align:start position:0% +masses and springs and we could +certainly have a 3D trust but 2D is the + + align:start position:0% +certainly have a 3D trust but 2D is the + + + align:start position:0% +certainly have a 3D trust but 2D is the +makes all the important points and then + + align:start position:0% +makes all the important points and then + + + align:start position:0% +makes all the important points and then +I can count the bars 1 2 3 4 + + align:start position:0% +I can count the bars 1 2 3 4 + + + align:start position:0% +I can count the bars 1 2 3 4 +five and I can count the nodes happen to + + align:start position:0% +five and I can count the nodes happen to + + + align:start position:0% +five and I can count the nodes happen to +be five here but now comes the moment I + + align:start position:0% +be five here but now comes the moment I + + + align:start position:0% +be five here but now comes the moment I +have to tell you what are the unknowns + + align:start position:0% +have to tell you what are the unknowns + + + align:start position:0% +have to tell you what are the unknowns +what are the use because of course you + + align:start position:0% +what are the use because of course you + + + align:start position:0% +what are the use because of course you +know that I'm going to go from use to e + + align:start position:0% +know that I'm going to go from use to e + + + align:start position:0% +know that I'm going to go from use to e +to + + align:start position:0% +to + + + align:start position:0% +to +W's to forces F and you know that a + + align:start position:0% +W's to forces F and you know that a + + + align:start position:0% +W's to forces F and you know that a +matrix a is going to do that a matrix C + + align:start position:0% +matrix a is going to do that a matrix C + + + align:start position:0% +matrix a is going to do that a matrix C +is going to do that a matrix a transpose + + align:start position:0% +is going to do that a matrix a transpose + + + align:start position:0% +is going to do that a matrix a transpose +is going to do that you're all ready you + + align:start position:0% +is going to do that you're all ready you + + + align:start position:0% +is going to do that you're all ready you +just we need to know what's the setup + + align:start position:0% +just we need to know what's the setup + + + align:start position:0% +just we need to know what's the setup +what are these matrices okay and how + + align:start position:0% +what are these matrices okay and how + + + align:start position:0% +what are these matrices okay and how +many so let me explain the setup + + align:start position:0% +many so let me explain the setup + + + align:start position:0% +many so let me explain the setup +typical uh node node one + + align:start position:0% +typical uh node node one + + + align:start position:0% +typical uh node node one +we have forces in these bars so that one + + align:start position:0% +we have forces in these bars so that one + + + align:start position:0% +we have forces in these bars so that one +node one could have a force it it we're + + align:start position:0% +node one could have a force it it we're + + + align:start position:0% +node one could have a force it it we're +in the plane so we have a horizontal + + align:start position:0% +in the plane so we have a horizontal + + + align:start position:0% +in the plane so we have a horizontal +force and a vertical Force together that + + align:start position:0% +force and a vertical Force together that + + + align:start position:0% +force and a vertical Force together that +would give a force allow produces a + + align:start position:0% +would give a force allow produces a + + + align:start position:0% +would give a force allow produces a +force in any direction whatever so this + + align:start position:0% +force in any direction whatever so this + + + align:start position:0% +force in any direction whatever so this +is the key point that there's a + + align:start position:0% +is the key point that there's a + + + align:start position:0% +is the key point that there's a +horizontal Force F horizontal one + + align:start position:0% +horizontal Force F horizontal one + + + align:start position:0% +horizontal Force F horizontal one +the one being the force on node one but + + align:start position:0% +the one being the force on node one but + + + align:start position:0% +the one being the force on node one but +there's also a vertical + + align:start position:0% +there's also a vertical + + + align:start position:0% +there's also a vertical +Force and and let me take horizontal to + + align:start position:0% +Force and and let me take horizontal to + + + align:start position:0% +Force and and let me take horizontal to +the right positive to the right vertical + + align:start position:0% +the right positive to the right vertical + + + align:start position:0% +the right positive to the right vertical +positive upwards just to have a + + align:start position:0% +positive upwards just to have a + + + align:start position:0% +positive upwards just to have a +convention so how many FS have I + + align:start position:0% +convention so how many FS have I + + + align:start position:0% +convention so how many FS have I +got well with f the point is I now have + + align:start position:0% +got well with f the point is I now have + + + align:start position:0% +got well with f the point is I now have +two per node that's that's the + + align:start position:0% +two per node that's that's the + + + align:start position:0% +two per node that's that's the +difference I have two per node two + + align:start position:0% +difference I have two per node two + + + align:start position:0% +difference I have two per node two +forces and I have two displacements per + + align:start position:0% +forces and I have two displacements per + + + align:start position:0% +forces and I have two displacements per +node because the that Point under there + + align:start position:0% +node because the that Point under there + + + align:start position:0% +node because the that Point under there +will be more forces some may be pulling + + align:start position:0% +will be more forces some may be pulling + + + align:start position:0% +will be more forces some may be pulling +this way + + align:start position:0% +this way + + + align:start position:0% +this way +whatever under the maybe let's look at + + align:start position:0% +whatever under the maybe let's look at + + + align:start position:0% +whatever under the maybe let's look at +node two so node two could have a couple + + align:start position:0% +node two so node two could have a couple + + + align:start position:0% +node two so node two could have a couple +of forces on it fh2 and fv2 and it moves + + align:start position:0% +of forces on it fh2 and fv2 and it moves + + + align:start position:0% +of forces on it fh2 and fv2 and it moves +like the other nodes uh so let me now + + align:start position:0% +like the other nodes uh so let me now + + + align:start position:0% +like the other nodes uh so let me now +I'm introducing the unknowns U is the + + align:start position:0% +I'm introducing the unknowns U is the + + + align:start position:0% +I'm introducing the unknowns U is the +movement U again horizontal and again + + align:start position:0% +movement U again horizontal and again + + + align:start position:0% +movement U again horizontal and again +now we're talking about node two and it + + align:start position:0% +now we're talking about node two and it + + + align:start position:0% +now we're talking about node two and it +moves up or or doesn't or moves down but + + align:start position:0% +moves up or or doesn't or moves down but + + + align:start position:0% +moves up or or doesn't or moves down but +that that's an unknown u a displacement + + align:start position:0% +that that's an unknown u a displacement + + + align:start position:0% +that that's an unknown u a displacement +a vertical displacement of node two do + + align:start position:0% +a vertical displacement of node two do + + + align:start position:0% +a vertical displacement of node two do +you see the + + align:start position:0% +you see the + + + align:start position:0% +you see the +setup two forces per node two + + align:start position:0% +setup two forces per node two + + + align:start position:0% +setup two forces per node two +displacements per node so that is some + + align:start position:0% +displacements per node so that is some + + + align:start position:0% +displacements per node so that is some +so that's like like the number of + + align:start position:0% +so that's like like the number of + + + align:start position:0% +so that's like like the number of +unknowns is is like + + align:start position:0% +unknowns is is like + + + align:start position:0% +unknowns is is like +doubled like doubled and that produces + + align:start position:0% +doubled like doubled and that produces + + + align:start position:0% +doubled like doubled and that produces +an interesting situation uh I've marked + + align:start position:0% +an interesting situation uh I've marked + + + align:start position:0% +an interesting situation uh I've marked +supports + + align:start position:0% +supports + + + align:start position:0% +supports +here so let me just let's just speak + + align:start position:0% +here so let me just let's just speak + + + align:start position:0% +here so let me just let's just speak +about supports so what's happening at + + align:start position:0% +about supports so what's happening at + + + align:start position:0% +about supports so what's happening at +the supports at the + + align:start position:0% +the supports at the + + + align:start position:0% +the supports at the +support uh there's no movement that's + + align:start position:0% +support uh there's no movement that's + + + align:start position:0% +support uh there's no movement that's +that's a it's a the whole that that + + align:start position:0% +that's a it's a the whole that that + + + align:start position:0% +that's a it's a the whole that that +point is pinned so this this is telling + + align:start position:0% +point is pinned so this this is telling + + + align:start position:0% +point is pinned so this this is telling +me that U horizontal 5 is zero and U + + align:start position:0% +me that U horizontal 5 is zero and U + + + align:start position:0% +me that U horizontal 5 is zero and U +vertical oh sorry that was + + align:start position:0% +vertical oh sorry that was + + + align:start position:0% +vertical oh sorry that was +four and it'll be the same for five U + + align:start position:0% +four and it'll be the same for five U + + + align:start position:0% +four and it'll be the same for five U +vertical five is zero it's like + + align:start position:0% +vertical five is zero it's like + + + align:start position:0% +vertical five is zero it's like +grounding a node in the electrical case + + align:start position:0% +grounding a node in the electrical case + + + align:start position:0% +grounding a node in the electrical case +we we all we just see this pattern over + + align:start position:0% +we we all we just see this pattern over + + + align:start position:0% +we we all we just see this pattern over +and over and we want to see okay what + + align:start position:0% +and over and we want to see okay what + + + align:start position:0% +and over and we want to see okay what +does it look like for trusses so here's + + align:start position:0% +does it look like for trusses so here's + + + align:start position:0% +does it look like for trusses so here's +a support that fixes those so those are + + align:start position:0% +a support that fixes those so those are + + + align:start position:0% +a support that fixes those so those are +not unknowns and similarly they're not + + align:start position:0% +not unknowns and similarly they're not + + + align:start position:0% +not unknowns and similarly they're not +unknowns there whoops I'm still saying + + align:start position:0% +unknowns there whoops I'm still saying + + + align:start position:0% +unknowns there whoops I'm still saying +five and I mean four so so + + align:start position:0% +five and I mean four so so + + + align:start position:0% +five and I mean four so so +so those are boundary conditions end + + align:start position:0% +so those are boundary conditions end + + + align:start position:0% +so those are boundary conditions end +conditions whatever and similarly here + + align:start position:0% +conditions whatever and similarly here + + + align:start position:0% +conditions whatever and similarly here +so how many unknowns are there you if + + align:start position:0% +so how many unknowns are there you if + + + align:start position:0% +so how many unknowns are there you if +you now look at this + + align:start position:0% +you now look at this + + + align:start position:0% +you now look at this +picture how many unknown displacements + + align:start position:0% +picture how many unknown displacements + + + align:start position:0% +picture how many unknown displacements +are there in this trust six six right + + align:start position:0% +are there in this trust six six right + + + align:start position:0% +are there in this trust six six right +two here two here two here and none + + align:start position:0% +two here two here two here and none + + + align:start position:0% +two here two here two here and none +there so the number of actual unknowns + + align:start position:0% +there so the number of actual unknowns + + + align:start position:0% +there so the number of actual unknowns +is + + align:start position:0% +is + + + align:start position:0% +is +six we could I would my idea would be + + align:start position:0% +six we could I would my idea would be + + + align:start position:0% +six we could I would my idea would be +that it's twice the number of + + align:start position:0% +that it's twice the number of + + + align:start position:0% +that it's twice the number of +nodes minus the number of fixed things + + align:start position:0% +nodes minus the number of fixed things + + + align:start position:0% +nodes minus the number of fixed things +reaction whatever that are would be four + + align:start position:0% +reaction whatever that are would be four + + + align:start position:0% +reaction whatever that are would be four +in this case I've got two ground two + + align:start position:0% +in this case I've got two ground two + + + align:start position:0% +in this case I've got two ground two +fixed here and two fixed here so this + + align:start position:0% +fixed here and two fixed here so this + + + align:start position:0% +fixed here and two fixed here so this +would be 2 * 5 10 possible displacements + + align:start position:0% +would be 2 * 5 10 possible displacements + + + align:start position:0% +would be 2 * 5 10 possible displacements +but R counts the number of fixed displac + + align:start position:0% +but R counts the number of fixed displac + + + align:start position:0% +but R counts the number of fixed displac +ments four and leaves us with six okay + + align:start position:0% +ments four and leaves us with six okay + + + align:start position:0% +ments four and leaves us with six okay +okay so my Matrix a will now be it's + + align:start position:0% +okay so my Matrix a will now be it's + + + align:start position:0% +okay so my Matrix a will now be it's +always M by n my Matrix a will be 5 by + + align:start position:0% +always M by n my Matrix a will be 5 by + + + align:start position:0% +always M by n my Matrix a will be 5 by + + align:start position:0% + + + align:start position:0% +okay okay now you're going to ask what + + align:start position:0% +okay okay now you're going to ask what + + + align:start position:0% +okay okay now you're going to ask what +is that + + align:start position:0% +is that + + + align:start position:0% +is that +Matrix but let me hold that off for a + + align:start position:0% +Matrix but let me hold that off for a + + + align:start position:0% +Matrix but let me hold that off for a +little + + align:start position:0% +little + + + align:start position:0% +little +moment I wanted you to see its shape + + align:start position:0% +moment I wanted you to see its shape + + + align:start position:0% +moment I wanted you to see its shape +first so you could now do this for for a + + align:start position:0% +first so you could now do this for for a + + + align:start position:0% +first so you could now do this for for a +large trust right + + align:start position:0% +large trust right + + + align:start position:0% +large trust right +two you count the bars and you could + + align:start position:0% +two you count the bars and you could + + + align:start position:0% +two you count the bars and you could +count the nodes and then you could count + + align:start position:0% +count the nodes and then you could count + + + align:start position:0% +count the nodes and then you could count +the unknown displacements U so u u has + + align:start position:0% +the unknown displacements U so u u has + + + align:start position:0% +the unknown displacements U so u u has +uh so this is there are six U's six U's + + align:start position:0% +uh so this is there are six U's six U's + + + align:start position:0% +uh so this is there are six U's six U's +here and there are five + + align:start position:0% +here and there are five + + + align:start position:0% +here and there are five +E's and there are five bar forces and + + align:start position:0% +E's and there are five bar forces and + + + align:start position:0% +E's and there are five bar forces and +there's + + align:start position:0% + + + + align:start position:0% + +six equilibrium balance for balances 66 + + align:start position:0% +six equilibrium balance for balances 66 + + + align:start position:0% +six equilibrium balance for balances 66 +for the node count for the unknowns + + align:start position:0% +for the node count for the unknowns + + + align:start position:0% +for the node count for the unknowns +count 55 for the bars count okay + + align:start position:0% +count 55 for the bars count okay + + + align:start position:0% +count 55 for the bars count okay +now Point here's a point about this + + align:start position:0% +now Point here's a point about this + + + align:start position:0% +now Point here's a point about this +particular + + align:start position:0% +particular + + + align:start position:0% +particular +trust it's not safe to get on it right + + align:start position:0% +trust it's not safe to get on it right + + + align:start position:0% +trust it's not safe to get on it right +that's that's and I want to say why is + + align:start position:0% +that's that's and I want to say why is + + + align:start position:0% +that's that's and I want to say why is +it not safe so this is a this is a + + align:start position:0% +it not safe so this is a this is a + + + align:start position:0% +it not safe so this is a this is a +feature that comes into the trust + + align:start position:0% +feature that comes into the trust + + + align:start position:0% +feature that comes into the trust +question that makes it a little new and + + align:start position:0% +question that makes it a little new and + + + align:start position:0% +question that makes it a little new and +more interesting the + + align:start position:0% +more interesting the + + + align:start position:0% +more interesting the +little twist compared to the previous + + align:start position:0% +little twist compared to the previous + + + align:start position:0% +little twist compared to the previous +examples + + align:start position:0% +examples + + + align:start position:0% +examples +this that bar that truss you know I + + align:start position:0% +this that bar that truss you know I + + + align:start position:0% +this that bar that truss you know I +wouldn't stand on it now why not okay + + align:start position:0% +wouldn't stand on it now why not okay + + + align:start position:0% +wouldn't stand on it now why not okay +well purely for linear algebra reasons + + align:start position:0% +well purely for linear algebra reasons + + + align:start position:0% +well purely for linear algebra reasons +right of course uh The Matrix a is 5X 6 + + align:start position:0% +right of course uh The Matrix a is 5X 6 + + + align:start position:0% +right of course uh The Matrix a is 5X 6 +so now what do we know about a matrix + + align:start position:0% +so now what do we know about a matrix + + + align:start position:0% +so now what do we know about a matrix +that's 5x6 so a is + + align:start position:0% +that's 5x6 so a is + + + align:start position:0% +that's 5x6 so a is +5x6 five rows as always for the M six + + align:start position:0% +5x6 five rows as always for the M six + + + align:start position:0% +5x6 five rows as always for the M six +columns because now we have six unknowns + + align:start position:0% +columns because now we have six unknowns + + + align:start position:0% +columns because now we have six unknowns +and what what do I know about any 5x6 + + align:start position:0% +and what what do I know about any 5x6 + + + align:start position:0% +and what what do I know about any 5x6 +Matrix there I'm I want to ask about the + + align:start position:0% +Matrix there I'm I want to ask about the + + + align:start position:0% +Matrix there I'm I want to ask about the +equation Au U equals + + align:start position:0% +equation Au U equals + + + align:start position:0% +equation Au U equals +z so I want to ask about it in linear + + align:start position:0% +z so I want to ask about it in linear + + + align:start position:0% +z so I want to ask about it in linear +algebra language and then I want to ask + + align:start position:0% +algebra language and then I want to ask + + + align:start position:0% +algebra language and then I want to ask +about it in physical language and the + + align:start position:0% +about it in physical language and the + + + align:start position:0% +about it in physical language and the +beauty is the the thing that makes truss + + align:start position:0% +beauty is the the thing that makes truss + + + align:start position:0% +beauty is the the thing that makes truss +is sort of fun is these matrices a get + + align:start position:0% +is sort of fun is these matrices a get + + + align:start position:0% +is sort of fun is these matrices a get +pretty big fast because if I put when I + + align:start position:0% +pretty big fast because if I put when I + + + align:start position:0% +pretty big fast because if I put when I +put a few more nodes on the the book has + + align:start position:0% +put a few more nodes on the the book has + + + align:start position:0% +put a few more nodes on the the book has +a picture of a sort of + + align:start position:0% +a picture of a sort of + + + align:start position:0% +a picture of a sort of +Treehouse uh then a is is growing and I + + align:start position:0% +Treehouse uh then a is is growing and I + + + align:start position:0% +Treehouse uh then a is is growing and I +don't all the time write down the Matrix + + align:start position:0% +don't all the time write down the Matrix + + + align:start position:0% +don't all the time write down the Matrix +a I haven't written it down here what + + align:start position:0% +a I haven't written it down here what + + + align:start position:0% +a I haven't written it down here what +I've written down is just its size + + align:start position:0% +I've written down is just its size + + + align:start position:0% +I've written down is just its size +because that's enough to tell us + + align:start position:0% +because that's enough to tell us + + + align:start position:0% +because that's enough to tell us +something about this set of equations Au + + align:start position:0% +something about this set of equations Au + + + align:start position:0% +something about this set of equations Au +equals z what's the story on Au equals z + + align:start position:0% +equals z what's the story on Au equals z + + + align:start position:0% +equals z what's the story on Au equals z +well of course it has the solution U + + align:start position:0% +well of course it has the solution U + + + align:start position:0% +well of course it has the solution U +equals z nothing moving you know if if I + + align:start position:0% +equals z nothing moving you know if if I + + + align:start position:0% +equals z nothing moving you know if if I +have no displacement if the U's are all + + align:start position:0% +have no displacement if the U's are all + + + align:start position:0% +have no displacement if the U's are all +zero then I have no stretching the E are + + align:start position:0% +zero then I have no stretching the E are + + + align:start position:0% +zero then I have no stretching the E are +stretching elongation as before the how + + align:start position:0% +stretching elongation as before the how + + + align:start position:0% +stretching elongation as before the how +far does the bar stretch okay so if I + + align:start position:0% +far does the bar stretch okay so if I + + + align:start position:0% +far does the bar stretch okay so if I +have zero U's and zero e but what other + + align:start position:0% +have zero U's and zero e but what other + + + align:start position:0% +have zero U's and zero e but what other +possibility am I going to have + + align:start position:0% + + + + align:start position:0% + +here I'm going to have probably one + + align:start position:0% +here I'm going to have probably one + + + align:start position:0% +here I'm going to have probably one +solution to this system that isn't zero + + align:start position:0% +solution to this system that isn't zero + + + align:start position:0% +solution to this system that isn't zero +I'm probably going to have one set of + + align:start position:0% +I'm probably going to have one set of + + + align:start position:0% +I'm probably going to have one set of +displacements U yeah look look what's + + align:start position:0% +displacements U yeah look look what's + + + align:start position:0% +displacements U yeah look look what's +happening here this this is au is the + + align:start position:0% +happening here this this is au is the + + + align:start position:0% +happening here this this is au is the +E so I'm going to have this I'm going to + + align:start position:0% +E so I'm going to have this I'm going to + + + align:start position:0% +E so I'm going to have this I'm going to +have at least one and and probably in + + align:start position:0% +have at least one and and probably in + + + align:start position:0% +have at least one and and probably in +this case it will be one there will be + + align:start position:0% +this case it will be one there will be + + + align:start position:0% +this case it will be one there will be +one uh it the the neat word for it is is + + align:start position:0% +one uh it the the neat word for it is is + + + align:start position:0% +one uh it the the neat word for it is is +a mechanism + + align:start position:0% + + + + align:start position:0% + +and what does that mean a mechanism is a + + align:start position:0% +and what does that mean a mechanism is a + + + align:start position:0% +and what does that mean a mechanism is a +solution to Au equals z so that a + + align:start position:0% +solution to Au equals z so that a + + + align:start position:0% +solution to Au equals z so that a +mechanism is a is a movement of the bar + + align:start position:0% +mechanism is a is a movement of the bar + + + align:start position:0% +mechanism is a is a movement of the bar +so it's going to be nonzero the bars are + + align:start position:0% +so it's going to be nonzero the bars are + + + align:start position:0% +so it's going to be nonzero the bars are +going to move a little I mean sorry the + + align:start position:0% +going to move a little I mean sorry the + + + align:start position:0% +going to move a little I mean sorry the +nodes are going to move a little the + + align:start position:0% +nodes are going to move a little the + + + align:start position:0% +nodes are going to move a little the +nodes will move a little + + align:start position:0% +nodes will move a little + + + align:start position:0% +nodes will move a little +bit in this U because it isn't zero but + + align:start position:0% +bit in this U because it isn't zero but + + + align:start position:0% +bit in this U because it isn't zero but +the bars won't + + align:start position:0% +the bars won't + + + align:start position:0% +the bars won't +stretch so that's the that tells us + + align:start position:0% +stretch so that's the that tells us + + + align:start position:0% +stretch so that's the that tells us +we've got uh instability here that of + + align:start position:0% +we've got uh instability here that of + + + align:start position:0% +we've got uh instability here that of +course that always this any if there's a + + align:start position:0% +course that always this any if there's a + + + align:start position:0% +course that always this any if there's a +solution to that that's always telling + + align:start position:0% +solution to that that's always telling + + + align:start position:0% +solution to that that's always telling +us that a transpose a is singular so let + + align:start position:0% +us that a transpose a is singular so let + + + align:start position:0% +us that a transpose a is singular so let +me just put that a transpose a or a + + align:start position:0% +me just put that a transpose a or a + + + align:start position:0% +me just put that a transpose a or a +transpose CA C couldn't save it will be + + align:start position:0% +transpose CA C couldn't save it will be + + + align:start position:0% +transpose CA C couldn't save it will be +singular it it's like our free free + + align:start position:0% +singular it it's like our free free + + + align:start position:0% +singular it it's like our free free +thing in being singular but the picture + + align:start position:0% +thing in being singular but the picture + + + align:start position:0% +thing in being singular but the picture +doesn't look free free does it it it's + + align:start position:0% +doesn't look free free does it it it's + + + align:start position:0% +doesn't look free free does it it it's +got supports in here just uh not good + + align:start position:0% +got supports in here just uh not good + + + align:start position:0% +got supports in here just uh not good +enough and I believe that if you look at + + align:start position:0% +enough and I believe that if you look at + + + align:start position:0% +enough and I believe that if you look at +this + + align:start position:0% +this + + + align:start position:0% +this +truss you could describe you could tell + + align:start position:0% +truss you could describe you could tell + + + align:start position:0% +truss you could describe you could tell +me and you could draw a movement of that + + align:start position:0% +me and you could draw a movement of that + + + align:start position:0% +me and you could draw a movement of that +truss in + + align:start position:0% +truss in + + + align:start position:0% +truss in +which the there is displacement but no + + align:start position:0% +which the there is displacement but no + + + align:start position:0% +which the there is displacement but no +stretching let let me ask you how to + + align:start position:0% +stretching let let me ask you how to + + + align:start position:0% +stretching let let me ask you how to +draw that so the so and I + + align:start position:0% +draw that so the so and I + + + align:start position:0% +draw that so the so and I +believe everybody understood why was + + align:start position:0% +believe everybody understood why was + + + align:start position:0% +believe everybody understood why was +there a solution it was because we have + + align:start position:0% +there a solution it was because we have + + + align:start position:0% +there a solution it was because we have +six unknowns and we only have five + + align:start position:0% +six unknowns and we only have five + + + align:start position:0% +six unknowns and we only have five +equations so so this is five equations + + align:start position:0% +equations so so this is five equations + + + align:start position:0% +equations so so this is five equations +anytime you have five equations with a + + align:start position:0% +anytime you have five equations with a + + + align:start position:0% +anytime you have five equations with a +zero on the right hand side so five + + align:start position:0% +zero on the right hand side so five + + + align:start position:0% +zero on the right hand side so five +homogeneous equations whatever you want + + align:start position:0% +homogeneous equations whatever you want + + + align:start position:0% +homogeneous equations whatever you want +to say when it's zero on the right and + + align:start position:0% +to say when it's zero on the right and + + + align:start position:0% +to say when it's zero on the right and +six unknowns six + + align:start position:0% +six unknowns six + + + align:start position:0% +six unknowns six +U's then you're going to have solution + + align:start position:0% +U's then you're going to have solution + + + align:start position:0% +U's then you're going to have solution +you couldn't it you can't help it you've + + align:start position:0% +you couldn't it you can't help it you've + + + align:start position:0% +you couldn't it you can't help it you've +got + + align:start position:0% +got + + + align:start position:0% +got +that many degrees of freedom you've only + + align:start position:0% +that many degrees of freedom you've only + + + align:start position:0% +that many degrees of freedom you've only +got that many constraints there's going + + align:start position:0% +got that many constraints there's going + + + align:start position:0% +got that many constraints there's going +to be solution okay tell me how to draw + + align:start position:0% +to be solution okay tell me how to draw + + + align:start position:0% +to be solution okay tell me how to draw +that let me put in the trust + + align:start position:0% +that let me put in the trust + + + align:start position:0% +that let me put in the trust +now what's the solution that so this is + + align:start position:0% +now what's the solution that so this is + + + align:start position:0% +now what's the solution that so this is +the the the fun part in a in a spe in a + + align:start position:0% +the the the fun part in a in a spe in a + + + align:start position:0% +the the the fun part in a in a spe in a +particular example at the start what is + + align:start position:0% +particular example at the start what is + + + align:start position:0% +particular example at the start what is +the how could that + + align:start position:0% + + + + align:start position:0% + +move without uh + + align:start position:0% +move without uh + + + align:start position:0% +move without uh +yeah without stretching + + align:start position:0% + + + + align:start position:0% + +bars um let me + + align:start position:0% +bars um let me + + + align:start position:0% +bars um let me +see oh yeah what could + + align:start position:0% +see oh yeah what could + + + align:start position:0% +see oh yeah what could +happen yeah what what do you mean now + + align:start position:0% +happen yeah what what do you mean now + + + align:start position:0% +happen yeah what what do you mean now +what who's going to move + + align:start position:0% +what who's going to move + + + align:start position:0% +what who's going to move +where what what's the movement here I + + align:start position:0% +where what what's the movement here I + + + align:start position:0% +where what what's the movement here I +and I want to draw it over there so + + align:start position:0% +and I want to draw it over there so + + + align:start position:0% +and I want to draw it over there so +often you give the answer by drawing as + + align:start position:0% +often you give the answer by drawing as + + + align:start position:0% +often you give the answer by drawing as +well as by telling me the six unknown + + align:start position:0% +well as by telling me the six unknown + + + align:start position:0% +well as by telling me the six unknown +use so so what can happen at this + + align:start position:0% + + + + align:start position:0% + +thing so you're going to say the trust + + align:start position:0% +thing so you're going to say the trust + + + align:start position:0% +thing so you're going to say the trust +could these + + align:start position:0% +could these + + + align:start position:0% +could these +These Bars could turn a + + align:start position:0% +These Bars could turn a + + + align:start position:0% +These Bars could turn a +little and you notice that word a little + + align:start position:0% +little and you notice that word a little + + + align:start position:0% +little and you notice that word a little +we're talking small displacement small + + align:start position:0% +we're talking small displacement small + + + align:start position:0% +we're talking small displacement small +stretches all the time here you you I'll + + align:start position:0% +stretches all the time here you you I'll + + + align:start position:0% +stretches all the time here you you I'll +see I'll show you why why you know we're + + align:start position:0% +see I'll show you why why you know we're + + + align:start position:0% +see I'll show you why why you know we're +always making that linearity assumption + + align:start position:0% +always making that linearity assumption + + + align:start position:0% +always making that linearity assumption +so we're just or small assumption okay + + align:start position:0% +so we're just or small assumption okay + + + align:start position:0% +so we're just or small assumption okay +those move a little and what is the what + + align:start position:0% +those move a little and what is the what + + + align:start position:0% +those move a little and what is the what +happens to that triangle at the + + align:start position:0% +happens to that triangle at the + + + align:start position:0% +happens to that triangle at the +top sort of just moves along right so + + align:start position:0% +top sort of just moves along right so + + + align:start position:0% +top sort of just moves along right so +that the the picture you would draw + + align:start position:0% +that the the picture you would draw + + + align:start position:0% +that the the picture you would draw +would be that you + + align:start position:0% +would be that you + + + align:start position:0% +would be that you +started you started + + align:start position:0% +started you started + + + align:start position:0% +started you started +there and it moved along a little I I'll + + align:start position:0% +there and it moved along a little I I'll + + + align:start position:0% +there and it moved along a little I I'll +make it a larger displacement than I + + align:start position:0% +make it a larger displacement than I + + + align:start position:0% +make it a larger displacement than I +really have in mind the these guys of + + align:start position:0% +really have in mind the these guys of + + + align:start position:0% +really have in mind the these guys of +course are here so they come they come + + align:start position:0% +course are here so they come they come + + + align:start position:0% +course are here so they come they come +out and the rest of the trust the top of + + align:start position:0% +out and the rest of the trust the top of + + + align:start position:0% +out and the rest of the trust the top of +the trust just kind of goes with it goes + + align:start position:0% +the trust just kind of goes with it goes + + + align:start position:0% +the trust just kind of goes with it goes +with the flow is that that that would be + + align:start position:0% +with the flow is that that that would be + + + align:start position:0% +with the flow is that that that would be +the answer that I would be looking for + + align:start position:0% +the answer that I would be looking for + + + align:start position:0% +the answer that I would be looking for +for uh to draw the mechanism that would + + align:start position:0% +for uh to draw the mechanism that would + + + align:start position:0% +for uh to draw the mechanism that would +show it and if I wanted to write down + + align:start position:0% +show it and if I wanted to write down + + + align:start position:0% +show it and if I wanted to write down +the U that goes with + + align:start position:0% +the U that goes with + + + align:start position:0% +the U that goes with +it what would it be let me again number + + align:start position:0% +it what would it be let me again number + + + align:start position:0% +it what would it be let me again number +these guys this is one two and this is + + align:start position:0% +these guys this is one two and this is + + + align:start position:0% +these guys this is one two and this is +three so what's going + + align:start position:0% +three so what's going + + + align:start position:0% +three so what's going +on what are the displacements of nodes + + align:start position:0% +on what are the displacements of nodes + + + align:start position:0% +on what are the displacements of nodes +one two and three and the I'll always + + align:start position:0% +one two and three and the I'll always + + + align:start position:0% +one two and three and the I'll always +write + + align:start position:0% +write + + + align:start position:0% +write +U1 horizontal before vertical can we + + align:start position:0% +U1 horizontal before vertical can we + + + align:start position:0% +U1 horizontal before vertical can we +make an agreement so I want to know + + align:start position:0% +make an agreement so I want to know + + + align:start position:0% +make an agreement so I want to know +about the horizontal movement then the + + align:start position:0% +about the horizontal movement then the + + + align:start position:0% +about the horizontal movement then the +vertical movement of node one then node + + align:start position:0% +vertical movement of node one then node + + + align:start position:0% +vertical movement of node one then node +two then node three so I'll have six + + align:start position:0% +two then node three so I'll have six + + + align:start position:0% +two then node three so I'll have six +numbers there and what what could I put + + align:start position:0% +numbers there and what what could I put + + + align:start position:0% +numbers there and what what could I put +in for those six numbers so the + + align:start position:0% +in for those six numbers so the + + + align:start position:0% +in for those six numbers so the +horizontal let me suppose that that + + align:start position:0% +horizontal let me suppose that that + + + align:start position:0% +horizontal let me suppose that that +first guy I'll I'll put a + + align:start position:0% +first guy I'll I'll put a + + + align:start position:0% +first guy I'll I'll put a +one really that's a bigger number than I + + align:start position:0% +one really that's a bigger number than I + + + align:start position:0% +one really that's a bigger number than I +should put but it's a convenient number + + align:start position:0% +should put but it's a convenient number + + + align:start position:0% +should put but it's a convenient number +so I'll just take it to be one even + + align:start position:0% +so I'll just take it to be one even + + + align:start position:0% +so I'll just take it to be one even +though I really have in mind let's say + + align:start position:0% +though I really have in mind let's say + + + align:start position:0% +though I really have in mind let's say +that's one angstrom or one one tiny + + align:start position:0% +that's one angstrom or one one tiny + + + align:start position:0% +that's one angstrom or one one tiny +little person okay okay so what is ah + + align:start position:0% +little person okay okay so what is ah + + + align:start position:0% +little person okay okay so what is ah +what what about the + + align:start position:0% +what what about the + + + align:start position:0% +what what about the +rest what's what's uh the + + align:start position:0% +rest what's what's uh the + + + align:start position:0% +rest what's what's uh the +vertical oh yeah this is a key Point + + align:start position:0% +vertical oh yeah this is a key Point + + + align:start position:0% +vertical oh yeah this is a key Point +here + + align:start position:0% +here + + + align:start position:0% +here +what's the vertical movement that this + + align:start position:0% +what's the vertical movement that this + + + align:start position:0% +what's the vertical movement that this +movement to me is + + align:start position:0% +movement to me is + + + align:start position:0% +movement to me is +horizontal I'm going to say that the + + align:start position:0% +horizontal I'm going to say that the + + + align:start position:0% +horizontal I'm going to say that the +vertical movement is + + align:start position:0% +vertical movement is + + + align:start position:0% +vertical movement is +zero of node one just moves over and + + align:start position:0% +zero of node one just moves over and + + + align:start position:0% +zero of node one just moves over and +node two does the same and node three + + align:start position:0% +node two does the same and node three + + + align:start position:0% +node two does the same and node three +does the same so that's my solution one + + align:start position:0% +does the same so that's my solution one + + + align:start position:0% +does the same so that's my solution one +Z One 0 one 0er that that's a simple + + align:start position:0% +Z One 0 one 0er that that's a simple + + + align:start position:0% +Z One 0 one 0er that that's a simple +movement a simple set of + + align:start position:0% +movement a simple set of + + + align:start position:0% +movement a simple set of +displacements thing moves to the right + + align:start position:0% +displacements thing moves to the right + + + align:start position:0% +displacements thing moves to the right +and + + align:start position:0% +and + + + align:start position:0% +and +um and with I I have not written down + + align:start position:0% +um and with I I have not written down + + + align:start position:0% +um and with I I have not written down +the Matrix a but probably won't even do + + align:start position:0% +the Matrix a but probably won't even do + + + align:start position:0% +the Matrix a but probably won't even do +it until next time uh but you'll see + + align:start position:0% +it until next time uh but you'll see + + + align:start position:0% +it until next time uh but you'll see +that when we do the Matrix a for this + + align:start position:0% +that when we do the Matrix a for this + + + align:start position:0% +that when we do the Matrix a for this +particular trust will have this + + align:start position:0% +particular trust will have this + + + align:start position:0% +particular trust will have this +particular U as a as a mechanism as a in + + align:start position:0% +particular U as a as a mechanism as a in + + + align:start position:0% +particular U as a as a mechanism as a in +linear algebra U is in the null space of + + align:start position:0% +linear algebra U is in the null space of + + + align:start position:0% +linear algebra U is in the null space of +a Au U is zero that's all that means + + align:start position:0% +a Au U is zero that's all that means + + + align:start position:0% +a Au U is zero that's all that means +okay you you see more or less what's + + align:start position:0% +okay you you see more or less what's + + + align:start position:0% +okay you you see more or less what's +up but now there's one little thing that + + align:start position:0% +up but now there's one little thing that + + + align:start position:0% +up but now there's one little thing that +may be bothering + + align:start position:0% +may be bothering + + + align:start position:0% +may be bothering +you which is + + align:start position:0% +you which is + + + align:start position:0% +you which is +what if I come back to the 0000 Z there + + align:start position:0% +what if I come back to the 0000 Z there + + + align:start position:0% +what if I come back to the 0000 Z there +you you could correctly say wait a + + align:start position:0% +you you could correctly say wait a + + + align:start position:0% +you you could correctly say wait a +minute those bars if those bars didn't + + align:start position:0% +minute those bars if those bars didn't + + + align:start position:0% +minute those bars if those bars didn't +stretch if they just rotated as you told + + align:start position:0% +stretch if they just rotated as you told + + + align:start position:0% +stretch if they just rotated as you told +me to do + + align:start position:0% +me to do + + + align:start position:0% +me to do +then this was across it was mostly + + align:start position:0% +then this was across it was mostly + + + align:start position:0% +then this was across it was mostly +across but a little bit down + + align:start position:0% +across but a little bit down + + + align:start position:0% +across but a little bit down +right and I'm saying no I'm saying zero + + align:start position:0% +right and I'm saying no I'm saying zero + + + align:start position:0% +right and I'm saying no I'm saying zero +okay so H how how do I get away with + + align:start position:0% +okay so H how how do I get away with + + + align:start position:0% +okay so H how how do I get away with +that + + align:start position:0% +that + + + align:start position:0% +that +right okay so I'm saying in 18085 it's a + + align:start position:0% +right okay so I'm saying in 18085 it's a + + + align:start position:0% +right okay so I'm saying in 18085 it's a +zero right okay and why all right so + + align:start position:0% +zero right okay and why all right so + + + align:start position:0% +zero right okay and why all right so +that so this is like a little timeout uh + + align:start position:0% +that so this is like a little timeout uh + + + align:start position:0% +that so this is like a little timeout uh +just to just to focus in on let me focus + + align:start position:0% +just to just to focus in on let me focus + + + align:start position:0% +just to just to focus in on let me focus +in on node two so here's the guy here's + + align:start position:0% +in on node two so here's the guy here's + + + align:start position:0% +in on node two so here's the guy here's +the bottom node four that's so it it + + align:start position:0% +the bottom node four that's so it it + + + align:start position:0% +the bottom node four that's so it it +used to be vertical up to this was node + + align:start position:0% +used to be vertical up to this was node + + + align:start position:0% +used to be vertical up to this was node +two and this was number four and then it + + align:start position:0% +two and this was number four and then it + + + align:start position:0% +two and this was number four and then it +rotated a little to there to this + + align:start position:0% +rotated a little to there to this + + + align:start position:0% +rotated a little to there to this +position so it went this angle if this + + align:start position:0% +position so it went this angle if this + + + align:start position:0% +position so it went this angle if this +angle was let's say + + align:start position:0% + + + + align:start position:0% + +Theta then what is this what is that + + align:start position:0% +Theta then what is this what is that + + + align:start position:0% +Theta then what is this what is that +actual position so this let's say this + + align:start position:0% +actual position so this let's say this + + + align:start position:0% +actual position so this let's say this +was let's say the bar had length one + + align:start position:0% +was let's say the bar had length one + + + align:start position:0% +was let's say the bar had length one +this is the origin 0 0 this is the the + + align:start position:0% +this is the origin 0 0 this is the the + + + align:start position:0% +this is the origin 0 0 this is the the +01 above it okay and + + align:start position:0% +01 above it okay and + + + align:start position:0% +01 above it okay and +now that's before it moved then it moved + + align:start position:0% +now that's before it moved then it moved + + + align:start position:0% +now that's before it moved then it moved +a little bit moved it moved to an angle + + align:start position:0% +a little bit moved it moved to an angle + + + align:start position:0% +a little bit moved it moved to an angle +Theta what's the position of that bar of + + align:start position:0% +Theta what's the position of that bar of + + + align:start position:0% +Theta what's the position of that bar of +that of that node what's the the new + + align:start position:0% +that of that node what's the the new + + + align:start position:0% +that of that node what's the the new +position of the node and then we we'll + + align:start position:0% +position of the node and then we we'll + + + align:start position:0% +position of the node and then we we'll +look at the difference and we'll see the + + align:start position:0% +look at the difference and we'll see the + + + align:start position:0% +look at the difference and we'll see the +movement U the displacement so what is + + align:start position:0% +movement U the displacement so what is + + + align:start position:0% +movement U the displacement so what is +the what is the uh how far did it + + align:start position:0% +the what is the uh how far did it + + + align:start position:0% +the what is the uh how far did it +move is it what's the what's the x + + align:start position:0% +move is it what's the what's the x + + + align:start position:0% +move is it what's the what's the x +coordinate how how far did it go across + + align:start position:0% +coordinate how how far did it go across + + + align:start position:0% +coordinate how how far did it go across +let me if I put in that line you'll + + align:start position:0% +let me if I put in that line you'll + + + align:start position:0% +let me if I put in that line you'll +you'll know so the the movement across + + align:start position:0% +you'll know so the the movement across + + + align:start position:0% +you'll know so the the movement across +was sin Theta good sin + + align:start position:0% +was sin Theta good sin + + + align:start position:0% +was sin Theta good sin +Theta and the movement + + align:start position:0% +Theta and the movement + + + align:start position:0% +Theta and the movement +down well I guess yeah yeah so let let's + + align:start position:0% +down well I guess yeah yeah so let let's + + + align:start position:0% +down well I guess yeah yeah so let let's +that's find its position and then we'll + + align:start position:0% +that's find its position and then we'll + + + align:start position:0% +that's find its position and then we'll +take the difference so so what's the + + align:start position:0% +take the difference so so what's the + + + align:start position:0% +take the difference so so what's the +what's the + + align:start position:0% +what's the + + + align:start position:0% +what's the +vertical uh new position for that + + align:start position:0% +vertical uh new position for that + + + align:start position:0% +vertical uh new position for that +guy it's I guess it's yeah it moved by + + align:start position:0% +guy it's I guess it's yeah it moved by + + + align:start position:0% +guy it's I guess it's yeah it moved by +it moved by it moved + + align:start position:0% +it moved by it moved + + + align:start position:0% +it moved by it moved +across by sin + + align:start position:0% +across by sin + + + align:start position:0% +across by sin +Theta and down + + align:start position:0% + + + + align:start position:0% + +by 1 - cosine Theta it it are you agreed + + align:start position:0% +by 1 - cosine Theta it it are you agreed + + + align:start position:0% +by 1 - cosine Theta it it are you agreed +with that because here's cosine Theta + + align:start position:0% +with that because here's cosine Theta + + + align:start position:0% +with that because here's cosine Theta +right + + align:start position:0% +right + + + align:start position:0% +right +there + + align:start position:0% +there + + + align:start position:0% +there +and and here's the little bit it moved + + align:start position:0% +and and here's the little bit it moved + + + align:start position:0% +and and here's the little bit it moved +down okay so that now we've these are + + align:start position:0% +down okay so that now we've these are + + + align:start position:0% +down okay so that now we've these are +exactly correct yeah this is in the + + align:start position:0% +exactly correct yeah this is in the + + + align:start position:0% +exactly correct yeah this is in the +position sin Theta cos Theta and the + + align:start position:0% +position sin Theta cos Theta and the + + + align:start position:0% +position sin Theta cos Theta and the +difference was the 1 minus cos Theta + + align:start position:0% +difference was the 1 minus cos Theta + + + align:start position:0% +difference was the 1 minus cos Theta +okay now so now here comes the key Point + + align:start position:0% +okay now so now here comes the key Point + + + align:start position:0% +okay now so now here comes the key Point +approximately sin Theta is approx + + align:start position:0% +approximately sin Theta is approx + + + align:start position:0% +approximately sin Theta is approx +imately if Theta is small and now here + + align:start position:0% +imately if Theta is small and now here + + + align:start position:0% +imately if Theta is small and now here +comes the smallness sin Theta is + + align:start position:0% +comes the smallness sin Theta is + + + align:start position:0% +comes the smallness sin Theta is +approximately sin Theta is approximately + + align:start position:0% +approximately sin Theta is approximately + + + align:start position:0% +approximately sin Theta is approximately +Theta and 1 minus cosine Theta is + + align:start position:0% +Theta and 1 minus cosine Theta is + + + align:start position:0% +Theta and 1 minus cosine Theta is +approximately what now this is the + + align:start position:0% +approximately what now this is the + + + align:start position:0% +approximately what now this is the +important point the the it's + + align:start position:0% +important point the the it's + + + align:start position:0% +important point the the it's +a what is what is so Theta is like the + + align:start position:0% +a what is what is so Theta is like the + + + align:start position:0% +a what is what is so Theta is like the +first term if if I expand the I mean the + + align:start position:0% +first term if if I expand the I mean the + + + align:start position:0% +first term if if I expand the I mean the +exact term would be Theta minus Theta + + align:start position:0% +exact term would be Theta minus Theta + + + align:start position:0% +exact term would be Theta minus Theta +cubed over six do do do dot but I'm only + + align:start position:0% +cubed over six do do do dot but I'm only + + + align:start position:0% +cubed over six do do do dot but I'm only +keeping that that term and 1us cosine + + align:start position:0% +keeping that that term and 1us cosine + + + align:start position:0% +keeping that that term and 1us cosine +Theta now what what's the what's the + + align:start position:0% +Theta now what what's the what's the + + + align:start position:0% +Theta now what what's the what's the +formula for cos Theta this is like worth + + align:start position:0% +formula for cos Theta this is like worth + + + align:start position:0% +formula for cos Theta this is like worth +just it's a one because of course cosine + + align:start position:0% +just it's a one because of course cosine + + + align:start position:0% +just it's a one because of course cosine +of 0 is 1 and then you subtract what + + align:start position:0% +of 0 is 1 and then you subtract what + + + align:start position:0% +of 0 is 1 and then you subtract what +Theta 2 over 2 and so + + align:start position:0% +Theta 2 over 2 and so + + + align:start position:0% +Theta 2 over 2 and so +on and then plus Theta 4 over 24 + + align:start position:0% +on and then plus Theta 4 over 24 + + + align:start position:0% +on and then plus Theta 4 over 24 +whatever okay so the ones cancel as we + + align:start position:0% +whatever okay so the ones cancel as we + + + align:start position:0% +whatever okay so the ones cancel as we +expect and I'm getting Theta 2/ + + align:start position:0% +expect and I'm getting Theta 2/ + + + align:start position:0% +expect and I'm getting Theta 2/ +2 and the and and this yeah so here was + + align:start position:0% +2 and the and and this yeah so here was + + + align:start position:0% +2 and the and and this yeah so here was +Theta to the first Power Theta Cub was + + align:start position:0% +Theta to the first Power Theta Cub was + + + align:start position:0% +Theta to the first Power Theta Cub was +we didn't care and we don't care about + + align:start position:0% +we didn't care and we don't care about + + + align:start position:0% +we didn't care and we don't care about +Theta squar so that's that's why it's + + align:start position:0% +Theta squar so that's that's why it's + + + align:start position:0% +Theta squar so that's that's why it's +zero because it's a second order + + align:start position:0% +zero because it's a second order + + + align:start position:0% +zero because it's a second order +movement right it's it's it's a if if + + align:start position:0% +movement right it's it's it's a if if + + + align:start position:0% +movement right it's it's it's a if if +Theta is small as I'm going to assume + + align:start position:0% +Theta is small as I'm going to assume + + + align:start position:0% +Theta is small as I'm going to assume +small displacements Theta + + align:start position:0% +small displacements Theta + + + align:start position:0% +small displacements Theta +squar would would if I allowed Theta squ + + align:start position:0% +squar would would if I allowed Theta squ + + + align:start position:0% +squar would would if I allowed Theta squ +and cos Theta in here I'd have a + + align:start position:0% +and cos Theta in here I'd have a + + + align:start position:0% +and cos Theta in here I'd have a +nonlinear + + align:start position:0% +nonlinear + + + align:start position:0% +nonlinear +problem and I don't want that and I + + align:start position:0% +problem and I don't want that and I + + + align:start position:0% +problem and I don't want that and I +don't need it I mean finite elements + + align:start position:0% +don't need it I mean finite elements + + + align:start position:0% +don't need it I mean finite elements +structures Bridges + + align:start position:0% +structures Bridges + + + align:start position:0% +structures Bridges +whatever you your first hope and + + align:start position:0% +whatever you your first hope and + + + align:start position:0% +whatever you your first hope and +expectation and calculation is small + + align:start position:0% +expectation and calculation is small + + + align:start position:0% +expectation and calculation is small +Theta linear problem + + align:start position:0% +Theta linear problem + + + align:start position:0% +Theta linear problem +so to a linear person Theta squ is zero + + align:start position:0% +so to a linear person Theta squ is zero + + + align:start position:0% +so to a linear person Theta squ is zero +that's that that's why this that's why + + align:start position:0% +that's that that's why this that's why + + + align:start position:0% +that's that that's why this that's why +those guys are zero okay so that's a + + align:start position:0% +those guys are zero okay so that's a + + + align:start position:0% +those guys are zero okay so that's a +assumption we'll often see will so it + + align:start position:0% +assumption we'll often see will so it + + + align:start position:0% +assumption we'll often see will so it +kind of was if you yeah there there are + + align:start position:0% +kind of was if you yeah there there are + + + align:start position:0% +kind of was if you yeah there there are +two kinds of + + align:start position:0% +two kinds of + + + align:start position:0% +two kinds of +nonlinearity in in uh structures in + + align:start position:0% +nonlinearity in in uh structures in + + + align:start position:0% +nonlinearity in in uh structures in +elasticity one is the one would be to + + align:start position:0% +elasticity one is the one would be to + + + align:start position:0% +elasticity one is the one would be to +allow this geometric nonlinearity + + align:start position:0% +allow this geometric nonlinearity + + + align:start position:0% +allow this geometric nonlinearity +theta's large displacements Theta large + + align:start position:0% +theta's large displacements Theta large + + + align:start position:0% +theta's large displacements Theta large +enough so that you you can't neglect + + align:start position:0% +enough so that you you can't neglect + + + align:start position:0% +enough so that you you can't neglect +Theta squar that's a tough one if you + + align:start position:0% +Theta squar that's a tough one if you + + + align:start position:0% +Theta squar that's a tough one if you +allow geometric nonlinearity in as some + + align:start position:0% +allow geometric nonlinearity in as some + + + align:start position:0% +allow geometric nonlinearity in as some +as finite element codes have to do you + + align:start position:0% +as finite element codes have to do you + + + align:start position:0% +as finite element codes have to do you +know if you like Abacus is a code that + + align:start position:0% +know if you like Abacus is a code that + + + align:start position:0% +know if you like Abacus is a code that +does major finite element calculations + + align:start position:0% +does major finite element calculations + + + align:start position:0% +does major finite element calculations +nonlinear ones I mean they at the + + align:start position:0% +nonlinear ones I mean they at the + + + align:start position:0% +nonlinear ones I mean they at the +beginning they were studying what + + align:start position:0% +beginning they were studying what + + + align:start position:0% +beginning they were studying what +happens what are the stresses on cables + + align:start position:0% +happens what are the stresses on cables + + + align:start position:0% +happens what are the stresses on cables +under the Atlantic I mean it's th those + + align:start position:0% +under the Atlantic I mean it's th those + + + align:start position:0% +under the Atlantic I mean it's th those +are fascinating problems or I mentioned + + align:start position:0% +are fascinating problems or I mentioned + + + align:start position:0% +are fascinating problems or I mentioned +car crashes I mean car crashes the + + align:start position:0% +car crashes I mean car crashes the + + + align:start position:0% +car crashes I mean car crashes the +geometry changes you have big + + align:start position:0% +geometry changes you have big + + + align:start position:0% +geometry changes you have big +displacements but we're talking here + + align:start position:0% +displacements but we're talking here + + + align:start position:0% +displacements but we're talking here +about the linear small displacement case + + align:start position:0% +about the linear small displacement case + + + align:start position:0% +about the linear small displacement case +Okay so that's that we + + align:start position:0% +Okay so that's that we + + + align:start position:0% +Okay so that's that we +will don't forget that part that that + + align:start position:0% +will don't forget that part that that + + + align:start position:0% +will don't forget that part that that +uh when the trust gets more complicated + + align:start position:0% +uh when the trust gets more complicated + + + align:start position:0% +uh when the trust gets more complicated +the principle stays the same that uh + + align:start position:0% +the principle stays the same that uh + + + align:start position:0% +the principle stays the same that uh +that we distinguish between the thetas + + align:start position:0% +that we distinguish between the thetas + + + align:start position:0% +that we distinguish between the thetas +that matter and the Theta squares that + + align:start position:0% +that matter and the Theta squares that + + + align:start position:0% +that matter and the Theta squares that +don't + + align:start position:0% +don't + + + align:start position:0% +don't +okay so now + + align:start position:0% +okay so now + + + align:start position:0% +okay so now +what now I guess I'm ready to give you + + align:start position:0% +what now I guess I'm ready to give you + + + align:start position:0% +what now I guess I'm ready to give you +to complete this picture a little more + + align:start position:0% +to complete this picture a little more + + + align:start position:0% +to complete this picture a little more +okay so let me so we've understood + + align:start position:0% +okay so let me so we've understood + + + align:start position:0% +okay so let me so we've understood +what's the idea of a mechanism oh how + + align:start position:0% +what's the idea of a mechanism oh how + + + align:start position:0% +what's the idea of a mechanism oh how +how could I prevent a + + align:start position:0% +how could I prevent a + + + align:start position:0% +how could I prevent a +mechanism how if if in other words if if + + align:start position:0% +mechanism how if if in other words if if + + + align:start position:0% +mechanism how if if in other words if if +I stood on this + + align:start position:0% +I stood on this + + + align:start position:0% +I stood on this +truss the + + align:start position:0% +truss the + + + align:start position:0% +truss the +slightest W bit of wind would crash it + + align:start position:0% +slightest W bit of wind would crash it + + + align:start position:0% +slightest W bit of wind would crash it +down right I mean so so so that's + + align:start position:0% +down right I mean so so so that's + + + align:start position:0% +down right I mean so so so that's +unstable that's an unstable + + align:start position:0% +unstable that's an unstable + + + align:start position:0% +unstable that's an unstable +trust uh how could I make it + + align:start position:0% +trust uh how could I make it + + + align:start position:0% +trust uh how could I make it +stable I mean if you were designing this + + align:start position:0% +stable I mean if you were designing this + + + align:start position:0% +stable I mean if you were designing this +thing what would you do at another Edge + + align:start position:0% +thing what would you do at another Edge + + + align:start position:0% +thing what would you do at another Edge +you'd stick in another bar maybe stick + + align:start position:0% +you'd stick in another bar maybe stick + + + align:start position:0% +you'd stick in another bar maybe stick +in a bar + + align:start position:0% +in a bar + + + align:start position:0% +in a bar +there what would happen + + align:start position:0% +there what would happen + + + align:start position:0% +there what would happen +now would it now be stable you that's + + align:start position:0% +now would it now be stable you that's + + + align:start position:0% +now would it now be stable you that's +You' have to answer that question you + + align:start position:0% +You' have to answer that question you + + + align:start position:0% +You' have to answer that question you +couldn't just put in bars you know + + align:start position:0% +couldn't just put in bars you know + + + align:start position:0% +couldn't just put in bars you know +whatever you you want to put bars that + + align:start position:0% +whatever you you want to put bars that + + + align:start position:0% +whatever you you want to put bars that +do the job okay now how many bars we've + + align:start position:0% +do the job okay now how many bars we've + + + align:start position:0% +do the job okay now how many bars we've +now got six bars so m is now up to six + + align:start position:0% +now got six bars so m is now up to six + + + align:start position:0% +now got six bars so m is now up to six +The Matrix a is 6x6 now whatever that + + align:start position:0% +The Matrix a is 6x6 now whatever that + + + align:start position:0% +The Matrix a is 6x6 now whatever that +Matrix may be we have six bars six + + align:start position:0% +Matrix may be we have six bars six + + + align:start position:0% +Matrix may be we have six bars six +displacements we can hope that we now + + align:start position:0% +displacements we can hope that we now + + + align:start position:0% +displacements we can hope that we now +have a 6x6 well we do have a 6x6 Matrix + + align:start position:0% +have a 6x6 well we do have a 6x6 Matrix + + + align:start position:0% +have a 6x6 well we do have a 6x6 Matrix +whatever it looks like and we can hope + + align:start position:0% +whatever it looks like and we can hope + + + align:start position:0% +whatever it looks like and we can hope +that it's not singular + + align:start position:0% +that it's not singular + + + align:start position:0% +that it's not singular +we can hope it's invertible we can hope + + align:start position:0% +we can hope it's invertible we can hope + + + align:start position:0% +we can hope it's invertible we can hope +that that mechanism is killed and you + + align:start position:0% +that that mechanism is killed and you + + + align:start position:0% +that that mechanism is killed and you +see it is killed the 6x6 this this that + + align:start position:0% +see it is killed the 6x6 this this that + + + align:start position:0% +see it is killed the 6x6 this this that +trust is now stable no no mechanism + + align:start position:0% +trust is now stable no no mechanism + + + align:start position:0% +trust is now stable no no mechanism +there right that that's I mean you again + + align:start position:0% +there right that that's I mean you again + + + align:start position:0% +there right that that's I mean you again +I haven't written down the Matrix + + align:start position:0% +I haven't written down the Matrix + + + align:start position:0% +I haven't written down the Matrix +but I'm I'm really calling for + + align:start position:0% +but I'm I'm really calling for + + + align:start position:0% +but I'm I'm really calling for +engineering intuition here that that + + align:start position:0% +engineering intuition here that that + + + align:start position:0% +engineering intuition here that that +this trust is now stable and of course I + + align:start position:0% +this trust is now stable and of course I + + + align:start position:0% +this trust is now stable and of course I +can make it even more stable by adding a + + align:start position:0% +can make it even more stable by adding a + + + align:start position:0% +can make it even more stable by adding a +seventh Edge the seventh bar so when it + + align:start position:0% +seventh Edge the seventh bar so when it + + + align:start position:0% +seventh Edge the seventh bar so when it +was six I had Square matrices a + + align:start position:0% +was six I had Square matrices a + + + align:start position:0% +was six I had Square matrices a +transpose and then C and then a would + + align:start position:0% +transpose and then C and then a would + + + align:start position:0% +transpose and then C and then a would +have been Square now I've got seven + + align:start position:0% +have been Square now I've got seven + + + align:start position:0% +have been Square now I've got seven +bars and uh so i' put now I put in a + + align:start position:0% +bars and uh so i' put now I put in a + + + align:start position:0% +bars and uh so i' put now I put in a +seventh guy m is now up to + + align:start position:0% +seventh guy m is now up to + + + align:start position:0% +seventh guy m is now up to +S my Matrix a would now be 7 + + align:start position:0% + + + + align:start position:0% + +by6 and there won't be any solution + + align:start position:0% +by6 and there won't be any solution + + + align:start position:0% +by6 and there won't be any solution +mechanism will be + + align:start position:0% +mechanism will be + + + align:start position:0% +mechanism will be +gone because I've now got uh what seven + + align:start position:0% +gone because I've now got uh what seven + + + align:start position:0% +gone because I've now got uh what seven +equations and still so same six Ed so we + + align:start position:0% +equations and still so same six Ed so we + + + align:start position:0% +equations and still so same six Ed so we +begin to get a feel of is are there + + align:start position:0% +begin to get a feel of is are there + + + align:start position:0% +begin to get a feel of is are there +Solutions not what I want to what I'm + + align:start position:0% +Solutions not what I want to what I'm + + + align:start position:0% +Solutions not what I want to what I'm +saying + + align:start position:0% +saying + + + align:start position:0% +saying +is I can't tell just from the count that + + align:start position:0% +is I can't tell just from the count that + + + align:start position:0% +is I can't tell just from the count that +that a is not singular I I could have a + + align:start position:0% +that a is not singular I I could have a + + + align:start position:0% +that a is not singular I I could have a +lot of bars and still be + + align:start position:0% +lot of bars and still be + + + align:start position:0% +lot of bars and still be +unstable invent a trust for me just just + + align:start position:0% +unstable invent a trust for me just just + + + align:start position:0% +unstable invent a trust for me just just +cuz how could I how could you invent a + + align:start position:0% +cuz how could I how could you invent a + + + align:start position:0% +cuz how could I how could you invent a +trust rust that had maybe it has seven + + align:start position:0% +trust rust that had maybe it has seven + + + align:start position:0% +trust rust that had maybe it has seven +bars with those seven bars those + + align:start position:0% +bars with those seven bars those + + + align:start position:0% +bars with those seven bars those +diagonal guys that did it that that made + + align:start position:0% +diagonal guys that did it that that made + + + align:start position:0% +diagonal guys that did it that that made +it stable our I tells us that before we + + align:start position:0% +it stable our I tells us that before we + + + align:start position:0% +it stable our I tells us that before we +do any linear algebra tell me a a 7 by a + + align:start position:0% +do any linear algebra tell me a a 7 by a + + + align:start position:0% +do any linear algebra tell me a a 7 by a +thing well yeah okay so here would be + + align:start position:0% +thing well yeah okay so here would be + + + align:start position:0% +thing well yeah okay so here would be +shall we support both both of these let + + align:start position:0% +shall we support both both of these let + + + align:start position:0% +shall we support both both of these let +me I'll start out the same okay + + align:start position:0% +me I'll start out the same okay + + + align:start position:0% +me I'll start out the same okay +now yeah what how could I let's see I I + + align:start position:0% +now yeah what how could I let's see I I + + + align:start position:0% +now yeah what how could I let's see I I +haven't prepared how could I get a whole + + align:start position:0% +haven't prepared how could I get a whole + + + align:start position:0% +haven't prepared how could I get a whole +lot of bars yeah I I I might not get + + align:start position:0% +lot of bars yeah I I I might not get + + + align:start position:0% +lot of bars yeah I I I might not get +seven by six exactly but H how could I + + align:start position:0% +seven by six exactly but H how could I + + + align:start position:0% +seven by six exactly but H how could I +have plenty of bars and still + + align:start position:0% + + + + align:start position:0% + +unstable well I could add in suppose I + + align:start position:0% +unstable well I could add in suppose I + + + align:start position:0% +unstable well I could add in suppose I +do this oh yeah th this is already + + align:start position:0% +do this oh yeah th this is already + + + align:start position:0% +do this oh yeah th this is already +that's a good example that's that's not + + align:start position:0% +that's a good example that's that's not + + + align:start position:0% +that's a good example that's that's not +stable right okay every let's let's + + align:start position:0% +stable right okay every let's let's + + + align:start position:0% +stable right okay every let's let's +practice with that one that's just my + + align:start position:0% +practice with that one that's just my + + + align:start position:0% +practice with that one that's just my +idea and the and problems in the book + + align:start position:0% +idea and the and problems in the book + + + align:start position:0% +idea and the and problems in the book +just ask you to practice with things + + align:start position:0% +just ask you to practice with things + + + align:start position:0% +just ask you to practice with things +like that tell me the count first what + + align:start position:0% +like that tell me the count first what + + + align:start position:0% +like that tell me the count first what +is M the number of + + align:start position:0% +is M the number of + + + align:start position:0% +is M the number of +bars six what is n the number of + + align:start position:0% +bars six what is n the number of + + + align:start position:0% +bars six what is n the number of +unknowns little n the number of unknowns + + align:start position:0% +unknowns little n the number of unknowns + + + align:start position:0% +unknowns little n the number of unknowns +what's what's my shape of my Matrix here + + align:start position:0% +what's what's my shape of my Matrix here + + + align:start position:0% +what's what's my shape of my Matrix here +a is it's got six bars and how many + + align:start position:0% +a is it's got six bars and how many + + + align:start position:0% +a is it's got six bars and how many +unknowns eight eight right two here two + + align:start position:0% +unknowns eight eight right two here two + + + align:start position:0% +unknowns eight eight right two here two +two two none here 6 by eight okay and + + align:start position:0% +two two none here 6 by eight okay and + + + align:start position:0% +two two none here 6 by eight okay and +how many mechanisms am I now + + align:start position:0% +how many mechanisms am I now + + + align:start position:0% +how many mechanisms am I now +expecting probably two probably two the + + align:start position:0% +expecting probably two probably two the + + + align:start position:0% +expecting probably two probably two the +there will be two independent mechanisms + + align:start position:0% +there will be two independent mechanisms + + + align:start position:0% +there will be two independent mechanisms +here uh can you tell me what they look + + align:start position:0% +here uh can you tell me what they look + + + align:start position:0% +here uh can you tell me what they look +like draw them what would they look like + + align:start position:0% +like draw them what would they look like + + + align:start position:0% +like draw them what would they look like +how what would be two different things + + align:start position:0% +how what would be two different things + + + align:start position:0% +how what would be two different things +that could happen could go wrong with + + align:start position:0% +that could happen could go wrong with + + + align:start position:0% +that could happen could go wrong with +that + + align:start position:0% +that + + + align:start position:0% +that +Truss + + align:start position:0% + + + + align:start position:0% + +you see it right this this could turn as + + align:start position:0% +you see it right this this could turn as + + + align:start position:0% +you see it right this this could turn as +in our example with the top part moving + + align:start position:0% +in our example with the top part moving + + + align:start position:0% +in our example with the top part moving +with it or a second one possibility + + align:start position:0% +with it or a second one possibility + + + align:start position:0% +with it or a second one possibility +would be the top part goes and the + + align:start position:0% +would be the top part goes and the + + + align:start position:0% +would be the top part goes and the +bottom part stays or any + + align:start position:0% +bottom part stays or any + + + align:start position:0% +bottom part stays or any +combination so the whole thing could go + + align:start position:0% +combination so the whole thing could go + + + align:start position:0% +combination so the whole thing could go +like that that would be one but that + + align:start position:0% +like that that would be one but that + + + align:start position:0% +like that that would be one but that +wouldn't be the only one of course so in + + align:start position:0% +wouldn't be the only one of course so in + + + align:start position:0% +wouldn't be the only one of course so in +other words we have a twood dimension + + align:start position:0% +other words we have a twood dimension + + + align:start position:0% +other words we have a twood dimension +space of mechanisms and you could give + + align:start position:0% +space of mechanisms and you could give + + + align:start position:0% +space of mechanisms and you could give +me two different and there aren't there + + align:start position:0% +me two different and there aren't there + + + align:start position:0% +me two different and there aren't there +are not two there are not just two guys + + align:start position:0% +are not two there are not just two guys + + + align:start position:0% +are not two there are not just two guys +all their combinations are there so this + + align:start position:0% +all their combinations are there so this + + + align:start position:0% +all their combinations are there so this +would have two + + align:start position:0% +would have two + + + align:start position:0% +would have two +mechanisms two + + align:start position:0% +mechanisms two + + + align:start position:0% +mechanisms two +mechanisms and I could put in bars of + + align:start position:0% +mechanisms and I could put in bars of + + + align:start position:0% +mechanisms and I could put in bars of +course that would try to save it well I + + align:start position:0% +course that would try to save it well I + + + align:start position:0% +course that would try to save it well I +could how many bars what's the minimum + + align:start position:0% +could how many bars what's the minimum + + + align:start position:0% +could how many bars what's the minimum +number of bars I absolutely need to to + + align:start position:0% +number of bars I absolutely need to to + + + align:start position:0% +number of bars I absolutely need to to +make this thing stable again two well + + align:start position:0% +make this thing stable again two well + + + align:start position:0% +make this thing stable again two well +now suppose I put in these two + + align:start position:0% + + + + align:start position:0% + +bars right I've got enough bars I've got + + align:start position:0% +bars right I've got enough bars I've got + + + align:start position:0% +bars right I've got enough bars I've got +an 8 by8 Matrix but I haven't saved it + + align:start position:0% +an 8 by8 Matrix but I haven't saved it + + + align:start position:0% +an 8 by8 Matrix but I haven't saved it +right because it still has that + + align:start position:0% +right because it still has that + + + align:start position:0% +right because it still has that +mechanism so so you you can't assume + + align:start position:0% +mechanism so so you you can't assume + + + align:start position:0% +mechanism so so you you can't assume +that because the count is right you've + + align:start position:0% +that because the count is right you've + + + align:start position:0% +that because the count is right you've +you've avoided mechanisms because in + + align:start position:0% +you've avoided mechanisms because in + + + align:start position:0% +you've avoided mechanisms because in +that example you haven't okay so that + + align:start position:0% +that example you haven't okay so that + + + align:start position:0% +that example you haven't okay so that +would be a case of square 8 by8 but um + + align:start position:0% +would be a case of square 8 by8 but um + + + align:start position:0% +would be a case of square 8 by8 but um +but not not good The Matrix still has so + + align:start position:0% +but not not good The Matrix still has so + + + align:start position:0% +but not not good The Matrix still has so +as soon as I see there's a solution to + + align:start position:0% +as soon as I see there's a solution to + + + align:start position:0% +as soon as I see there's a solution to +Au equals z I know that a transpose a + + align:start position:0% +Au equals z I know that a transpose a + + + align:start position:0% +Au equals z I know that a transpose a +will be singular and unstable okay uh + + align:start position:0% +will be singular and unstable okay uh + + + align:start position:0% +will be singular and unstable okay uh +before I go to the framework let's just + + align:start position:0% +before I go to the framework let's just + + + align:start position:0% +before I go to the framework let's just +do one more thing suppose I take + + align:start position:0% +do one more thing suppose I take + + + align:start position:0% +do one more thing suppose I take +away the + + align:start position:0% + + + + align:start position:0% + +supports all + + align:start position:0% +supports all + + + align:start position:0% +supports all +right I'll put in let me put in some + + align:start position:0% +right I'll put in let me put in some + + + align:start position:0% +right I'll put in let me put in some +bars s though I'll put in some + + align:start position:0% +bars s though I'll put in some + + + align:start position:0% +bars s though I'll put in some +bars okay plenty of + + align:start position:0% +bars okay plenty of + + + align:start position:0% +bars okay plenty of +bars want another one okay how many bars + + align:start position:0% +bars want another one okay how many bars + + + align:start position:0% +bars want another one okay how many bars +have I got lots right okay now the + + align:start position:0% +have I got lots right okay now the + + + align:start position:0% +have I got lots right okay now the +Matrix a what do you what do you think + + align:start position:0% +Matrix a what do you what do you think + + + align:start position:0% +Matrix a what do you what do you think +about this are there Solutions you + + align:start position:0% +about this are there Solutions you + + + align:start position:0% +about this are there Solutions you +haven't even seen The Matrix a of course + + align:start position:0% +haven't even seen The Matrix a of course + + + align:start position:0% +haven't even seen The Matrix a of course +but you've seen the trust that's what + + align:start position:0% +but you've seen the trust that's what + + + align:start position:0% +but you've seen the trust that's what +matters how many solutions are there + + align:start position:0% +matters how many solutions are there + + + align:start position:0% +matters how many solutions are there +solutions to Au equals z are there way + + align:start position:0% +solutions to Au equals z are there way + + + align:start position:0% +solutions to Au equals z are there way +that this trust could move without + + align:start position:0% +that this trust could move without + + + align:start position:0% +that this trust could move without +stretching are there ways that this + + align:start position:0% +stretching are there ways that this + + + align:start position:0% +stretching are there ways that this +trust could move without stretching and + + align:start position:0% +trust could move without stretching and + + + align:start position:0% +trust could move without stretching and +what are they and how many are there and + + align:start position:0% +what are they and how many are there and + + + align:start position:0% +what are they and how many are there and +and what what name should we use okay + + align:start position:0% +and what what name should we use okay + + + align:start position:0% +and what what name should we use okay +what are they how how could that move + + align:start position:0% +what are they how how could that move + + + align:start position:0% +what are they how how could that move +without + + align:start position:0% +without + + + align:start position:0% +without +stretching well it's got no supports at + + align:start position:0% +stretching well it's got no supports at + + + align:start position:0% +stretching well it's got no supports at +all it's just free out there in space so + + align:start position:0% +all it's just free out there in space so + + + align:start position:0% +all it's just free out there in space so +it could move how many ways could it + + align:start position:0% +it could move how many ways could it + + + align:start position:0% +it could move how many ways could it +move three it could move everybody could + + align:start position:0% +move three it could move everybody could + + + align:start position:0% +move three it could move everybody could +move this way all all ones on the + + align:start position:0% +move this way all all ones on the + + + align:start position:0% +move this way all all ones on the +horizontal guys everybody could move + + align:start position:0% +horizontal guys everybody could move + + + align:start position:0% +horizontal guys everybody could move +this way all six ones on the vertical + + align:start position:0% +this way all six ones on the vertical + + + align:start position:0% +this way all six ones on the vertical +guys there'll be 12 uh unknowns here and + + align:start position:0% +guys there'll be 12 uh unknowns here and + + + align:start position:0% +guys there'll be 12 uh unknowns here and +it could also rotate what would be the + + align:start position:0% +it could also rotate what would be the + + + align:start position:0% +it could also rotate what would be the +rotation I'm not talking about this + + align:start position:0% +rotation I'm not talking about this + + + align:start position:0% +rotation I'm not talking about this +rotation this could not happen What + + align:start position:0% +rotation this could not happen What + + + align:start position:0% +rotation this could not happen What +could happen What rotation could happen + + align:start position:0% +could happen What rotation could happen + + + align:start position:0% +could happen What rotation could happen +here for this so there are there's a + + align:start position:0% +here for this so there are there's a + + + align:start position:0% +here for this so there are there's a +third rigid motion translation trans + + align:start position:0% +third rigid motion translation trans + + + align:start position:0% +third rigid motion translation trans +transation and rotation around well take + + align:start position:0% +transation and rotation around well take + + + align:start position:0% +transation and rotation around well take +this + + align:start position:0% +this + + + align:start position:0% +this +one as an example the whole thing could + + align:start position:0% +one as an example the whole thing could + + + align:start position:0% +one as an example the whole thing could +swing around this that would be a motion + + align:start position:0% +swing around this that would be a motion + + + align:start position:0% +swing around this that would be a motion +well now you're going to say well why + + align:start position:0% +well now you're going to say well why + + + align:start position:0% +well now you're going to say well why +didn't I swing it around that one and of + + align:start position:0% +didn't I swing it around that one and of + + + align:start position:0% +didn't I swing it around that one and of +course it could but what would be the + + align:start position:0% +course it could but what would be the + + + align:start position:0% +course it could but what would be the +deal it would have to be I would I'll + + align:start position:0% +deal it would have to be I would I'll + + + align:start position:0% +deal it would have to be I would I'll +only have three rigid there are only + + align:start position:0% +only have three rigid there are only + + + align:start position:0% +only have three rigid there are only +three rigid + + align:start position:0% +three rigid + + + align:start position:0% +three rigid +motions right up and around so if you + + align:start position:0% +motions right up and around so if you + + + align:start position:0% +motions right up and around so if you +give me another one like around this one + + align:start position:0% +give me another one like around this one + + + align:start position:0% +give me another one like around this one +then somehow it had to be a combination + + align:start position:0% +then somehow it had to be a combination + + + align:start position:0% +then somehow it had to be a combination +of those I don't even want to think what + + align:start position:0% +of those I don't even want to think what + + + align:start position:0% +of those I don't even want to think what +combination it is but there are three + + align:start position:0% +combination it is but there are three + + + align:start position:0% +combination it is but there are three +rigid motions so I I sort of distinguish + + align:start position:0% +rigid motions so I I sort of distinguish + + + align:start position:0% +rigid motions so I I sort of distinguish +mechanisms this word mechanism so that's + + align:start position:0% +mechanisms this word mechanism so that's + + + align:start position:0% +mechanisms this word mechanism so that's +where the the trust + + align:start position:0% +where the the trust + + + align:start position:0% +where the the trust +deforms in these and rigid motions so + + align:start position:0% +deforms in these and rigid motions so + + + align:start position:0% +deforms in these and rigid motions so +I'll say Plus possibly plus rigid + + align:start position:0% +I'll say Plus possibly plus rigid + + + align:start position:0% +I'll say Plus possibly plus rigid +motions and rigid motions would be uh + + align:start position:0% +motions and rigid motions would be uh + + + align:start position:0% +motions and rigid motions would be uh +non + + align:start position:0% +non + + + align:start position:0% +non +uh the the you know there's no it's not + + align:start position:0% +uh the the you know there's no it's not + + + align:start position:0% +uh the the you know there's no it's not +it doesn't deform internally the whole + + align:start position:0% +it doesn't deform internally the whole + + + align:start position:0% +it doesn't deform internally the whole +thing + + align:start position:0% +thing + + + align:start position:0% +thing +moves and this is of course what we get + + align:start position:0% +moves and this is of course what we get + + + align:start position:0% +moves and this is of course what we get +in the case of not enough supports and + + align:start position:0% +in the case of not enough supports and + + + align:start position:0% +in the case of not enough supports and +this is what we get in the case of not + + align:start position:0% +this is what we get in the case of not + + + align:start position:0% +this is what we get in the case of not +enough bars yeah so there those maybe + + align:start position:0% +enough bars yeah so there those maybe + + + align:start position:0% +enough bars yeah so there those maybe +it's worth separating those two in in + + align:start position:0% +it's worth separating those two in in + + + align:start position:0% +it's worth separating those two in in +the examples we do we usually put in + + align:start position:0% +the examples we do we usually put in + + + align:start position:0% +the examples we do we usually put in +enough supports to to kill the rigid + + align:start position:0% +enough supports to to kill the rigid + + + align:start position:0% +enough supports to to kill the rigid +motions and then the question will be + + align:start position:0% +motions and then the question will be + + + align:start position:0% +motions and then the question will be +are there some mechanisms okay now I + + align:start position:0% +are there some mechanisms okay now I + + + align:start position:0% +are there some mechanisms okay now I +have to say start by on on what this is + + align:start position:0% +have to say start by on on what this is + + + align:start position:0% +have to say start by on on what this is +uh well it be just a very quick start so + + align:start position:0% +uh well it be just a very quick start so + + + align:start position:0% +uh well it be just a very quick start so +that what I'll do at the beginning of + + align:start position:0% +that what I'll do at the beginning of + + + align:start position:0% +that what I'll do at the beginning of +Friday so Friday's the other lecture on + + align:start position:0% +Friday so Friday's the other lecture on + + + align:start position:0% +Friday so Friday's the other lecture on +this topic and then the the homework + + align:start position:0% +this topic and then the the homework + + + align:start position:0% +this topic and then the the homework +will ask you to do some trusses in this + + align:start position:0% +will ask you to do some trusses in this + + + align:start position:0% +will ask you to do some trusses in this +uh section it's probably section 2 + + align:start position:0% +uh section it's probably section 2 + + + align:start position:0% +uh section it's probably section 2 +Something + + align:start position:0% +Something + + + align:start position:0% +Something +2 s maybe + + align:start position:0% +2 s maybe + + + align:start position:0% +2 s maybe +uh um yeah what's the Matrix C last + + align:start position:0% +uh um yeah what's the Matrix C last + + + align:start position:0% +uh um yeah what's the Matrix C last +second question what's the Matrix C what + + align:start position:0% +second question what's the Matrix C what + + + align:start position:0% +second question what's the Matrix C what +size is it what size is the Matrix C for + + align:start position:0% +size is it what size is the Matrix C for + + + align:start position:0% +size is it what size is the Matrix C for +our original problem our or or + + align:start position:0% +our original problem our or or + + + align:start position:0% +our original problem our or or +no what size is C is C + + align:start position:0% +no what size is C is C + + + align:start position:0% +no what size is C is C +involving if I know and if I know these + + align:start position:0% +involving if I know and if I know these + + + align:start position:0% +involving if I know and if I know these +numbers what size is + + align:start position:0% +numbers what size is + + + align:start position:0% +numbers what size is +C 5 by five M by m right C is that + + align:start position:0% +C 5 by five M by m right C is that + + + align:start position:0% +C 5 by five M by m right C is that +diagonal + + align:start position:0% +diagonal + + + align:start position:0% +diagonal +matrix one entry for each Bar C is just + + align:start position:0% +matrix one entry for each Bar C is just + + + align:start position:0% +matrix one entry for each Bar C is just +C has a C1 C2 C3 and and and this this W + + align:start position:0% +C has a C1 C2 C3 and and and this this W + + + align:start position:0% +C has a C1 C2 C3 and and and this this W +equals CE is just hooks law in each + + align:start position:0% +equals CE is just hooks law in each + + + align:start position:0% +equals CE is just hooks law in each +bar so simple it it it's it's gets there + + align:start position:0% +bar so simple it it it's it's gets there + + + align:start position:0% +bar so simple it it it's it's gets there +in the middle just the way that c in the + + align:start position:0% +in the middle just the way that c in the + + + align:start position:0% +in the middle just the way that c in the +first exam problem popped in and other + + align:start position:0% +first exam problem popped in and other + + + align:start position:0% +first exam problem popped in and other +C's that that that gets there in the + + align:start position:0% +C's that that that gets there in the + + + align:start position:0% +C's that that that gets there in the +middle uh but it's very extremely simple + + align:start position:0% +middle uh but it's very extremely simple + + + align:start position:0% +middle uh but it's very extremely simple +okay so the real tension is on a as + + align:start position:0% +okay so the real tension is on a as + + + align:start position:0% +okay so the real tension is on a as +usual and that will come Friday morning \ No newline at end of file diff --git a/ZqF-7bjnzCU.txt b/ZqF-7bjnzCU.txt new file mode 100644 index 0000000000000000000000000000000000000000..5e7dc7b8ae7bc6483d3fcc242fb009ddf7ec4047 --- /dev/null +++ b/ZqF-7bjnzCU.txt @@ -0,0 +1,11851 @@ +align:start position:0% + +these i'm going to record two lectures + + align:start position:0% +these i'm going to record two lectures + + + align:start position:0% +these i'm going to record two lectures +today + + align:start position:0% +today + + + align:start position:0% +today +these are the final two lectures i will + + align:start position:0% +these are the final two lectures i will + + + align:start position:0% +these are the final two lectures i will +be recording for eight nine sixty two + + align:start position:0% +be recording for eight nine sixty two + + + align:start position:0% +be recording for eight nine sixty two +these are actually the uh i actually + + align:start position:0% +these are actually the uh i actually + + + align:start position:0% +these are actually the uh i actually +have notes on an additional two lectures + + align:start position:0% +have notes on an additional two lectures + + + align:start position:0% +have notes on an additional two lectures +um i have notes for an additional two + + align:start position:0% +um i have notes for an additional two + + + align:start position:0% +um i have notes for an additional two +lectures + + align:start position:0% +lectures + + + align:start position:0% +lectures +but those additional two lectures + + align:start position:0% +but those additional two lectures + + + align:start position:0% +but those additional two lectures +are somewhat advanced material it's sort + + align:start position:0% +are somewhat advanced material it's sort + + + align:start position:0% +are somewhat advanced material it's sort +of + + align:start position:0% +of + + + align:start position:0% +of +fun to go over them in the last week of + + align:start position:0% +fun to go over them in the last week of + + + align:start position:0% +fun to go over them in the last week of +the course for certain students it can + + align:start position:0% +the course for certain students it can + + + align:start position:0% +the course for certain students it can +be a great introduction to some of the + + align:start position:0% +be a great introduction to some of the + + + align:start position:0% +be a great introduction to some of the +most important topics in modern research + + align:start position:0% +most important topics in modern research + + + align:start position:0% +most important topics in modern research +but i am not going to come into campus + + align:start position:0% +but i am not going to come into campus + + + align:start position:0% +but i am not going to come into campus +and present those lectures okay given + + align:start position:0% +and present those lectures okay given + + + align:start position:0% +and present those lectures okay given +everything that's going on right now + + align:start position:0% +everything that's going on right now + + + align:start position:0% +everything that's going on right now +to be blunt they're kind of bonus + + align:start position:0% +to be blunt they're kind of bonus + + + align:start position:0% +to be blunt they're kind of bonus +material and + + align:start position:0% +material and + + + align:start position:0% +material and +uh this isn't the time this is not the + + align:start position:0% +uh this isn't the time this is not the + + + align:start position:0% +uh this isn't the time this is not the +semester for us to go through our + + align:start position:0% +semester for us to go through our + + + align:start position:0% +semester for us to go through our +bonuses + + align:start position:0% +bonuses + + + align:start position:0% +bonuses +i will make those notes available + + align:start position:0% +i will make those notes available + + + align:start position:0% +i will make those notes available +i will be happy to discuss them in a + + align:start position:0% +i will be happy to discuss them in a + + + align:start position:0% +i will be happy to discuss them in a +saner moment with any student who is + + align:start position:0% +saner moment with any student who is + + + align:start position:0% +saner moment with any student who is +interested in them + + align:start position:0% +interested in them + + + align:start position:0% +interested in them +but this semester let's just focus on + + align:start position:0% +but this semester let's just focus on + + + align:start position:0% +but this semester let's just focus on +the core material + + align:start position:0% +the core material + + + align:start position:0% +the core material +so that brings us to the topic of what + + align:start position:0% +so that brings us to the topic of what + + + align:start position:0% +so that brings us to the topic of what +we are studying today + + align:start position:0% +we are studying today + + + align:start position:0% +we are studying today +while i correct my handwriting so if i + + align:start position:0% +while i correct my handwriting so if i + + + align:start position:0% +while i correct my handwriting so if i +can do a recap of what we discussed last + + align:start position:0% +can do a recap of what we discussed last + + + align:start position:0% +can do a recap of what we discussed last +time + + align:start position:0% +time + + + align:start position:0% +time +we took a look at a space-time that is + + align:start position:0% +we took a look at a space-time that is + + + align:start position:0% +we took a look at a space-time that is +it has this schwarzschild solution uh + + align:start position:0% +it has this schwarzschild solution uh + + + align:start position:0% +it has this schwarzschild solution uh +written in the + + align:start position:0% +written in the + + + align:start position:0% +written in the +shield coordinates everywhere okay we in + + align:start position:0% +shield coordinates everywhere okay we in + + + align:start position:0% +shield coordinates everywhere okay we in +our previous lecture + + align:start position:0% +our previous lecture + + + align:start position:0% +our previous lecture +we looked at a space time that was uh + + align:start position:0% +we looked at a space time that was uh + + + align:start position:0% +we looked at a space time that was uh +that described a + + align:start position:0% +that described a + + + align:start position:0% +that described a +fluid body a spherically symmetric fluid + + align:start position:0% +fluid body a spherically symmetric fluid + + + align:start position:0% +fluid body a spherically symmetric fluid +body + + align:start position:0% +body + + + align:start position:0% +body +uh and it had a surface this was the + + align:start position:0% +uh and it had a surface this was the + + + align:start position:0% +uh and it had a surface this was the +solution that we used for its exterior + + align:start position:0% +solution that we used for its exterior + + + align:start position:0% +solution that we used for its exterior +this ends up describing + + align:start position:0% +this ends up describing + + + align:start position:0% +this ends up describing +a solution of uh that has + + align:start position:0% +a solution of uh that has + + + align:start position:0% +a solution of uh that has +zero stress energy tensor so it + + align:start position:0% +zero stress energy tensor so it + + + align:start position:0% +zero stress energy tensor so it +describes a vacuum situation + + align:start position:0% +describes a vacuum situation + + + align:start position:0% +describes a vacuum situation +okay so if i imagine a space time that + + align:start position:0% +okay so if i imagine a space time that + + + align:start position:0% +okay so if i imagine a space time that +looks like this + + align:start position:0% +looks like this + + + align:start position:0% +looks like this +everywhere well what i end up finding is + + align:start position:0% +everywhere well what i end up finding is + + + align:start position:0% +everywhere well what i end up finding is +that this + + align:start position:0% +that this + + + align:start position:0% +that this +is a vacuum solution it has t mu nu + + align:start position:0% +is a vacuum solution it has t mu nu + + + align:start position:0% +is a vacuum solution it has t mu nu +equals zero + + align:start position:0% +equals zero + + + align:start position:0% +equals zero +everywhere however it also has a mass + + align:start position:0% +everywhere however it also has a mass + + + align:start position:0% +everywhere however it also has a mass +m so this is a vacuum solution with mass + + align:start position:0% +m so this is a vacuum solution with mass + + + align:start position:0% +m so this is a vacuum solution with mass +which + + align:start position:0% +which + + + align:start position:0% +which +is well that's weird um + + align:start position:0% +is well that's weird um + + + align:start position:0% +is well that's weird um +we examined some of its curvature + + align:start position:0% +we examined some of its curvature + + + align:start position:0% +we examined some of its curvature +properties and we found that at r + + align:start position:0% +properties and we found that at r + + + align:start position:0% +properties and we found that at r +equals zero there is a tidal singularity + + align:start position:0% +equals zero there is a tidal singularity + + + align:start position:0% +equals zero there is a tidal singularity +okay an invariant quantity that we + + align:start position:0% +okay an invariant quantity that we + + + align:start position:0% +okay an invariant quantity that we +constructed from the title tensors + + align:start position:0% +constructed from the title tensors + + + align:start position:0% +constructed from the title tensors +blows up at r equals zero + + align:start position:0% +blows up at r equals zero + + + align:start position:0% +blows up at r equals zero +r equals 2g m looks a little bit funny + + align:start position:0% +r equals 2g m looks a little bit funny + + + align:start position:0% +r equals 2g m looks a little bit funny +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +it turns out tides are well behaved + + align:start position:0% +it turns out tides are well behaved + + + align:start position:0% +it turns out tides are well behaved +there okay there's nothing pathological + + align:start position:0% +there okay there's nothing pathological + + + align:start position:0% +there okay there's nothing pathological +in the space time there + + align:start position:0% +in the space time there + + + align:start position:0% +in the space time there +but there's a chord in singularity our + + align:start position:0% +but there's a chord in singularity our + + + align:start position:0% +but there's a chord in singularity our +coordinate t is behaving oddly + + align:start position:0% +coordinate t is behaving oddly + + + align:start position:0% +coordinate t is behaving oddly +and where we left things last time is i + + align:start position:0% +and where we left things last time is i + + + align:start position:0% +and where we left things last time is i +did a little diagnosis of this by + + align:start position:0% +did a little diagnosis of this by + + + align:start position:0% +did a little diagnosis of this by +imagining a body that falls + + align:start position:0% +imagining a body that falls + + + align:start position:0% +imagining a body that falls +into it falls in the space time from + + align:start position:0% +into it falls in the space time from + + + align:start position:0% +into it falls in the space time from +some starting radius + + align:start position:0% +some starting radius + + + align:start position:0% +some starting radius +and i looked at the motion of this thing + + align:start position:0% +and i looked at the motion of this thing + + + align:start position:0% +and i looked at the motion of this thing +as a function of time + + align:start position:0% +as a function of time + + + align:start position:0% +as a function of time +what we find is that if we look at the + + align:start position:0% +what we find is that if we look at the + + + align:start position:0% +what we find is that if we look at the +motion of this thing as a function of + + align:start position:0% +motion of this thing as a function of + + + align:start position:0% +motion of this thing as a function of +the proper time of that in falling body + + align:start position:0% +the proper time of that in falling body + + + align:start position:0% +the proper time of that in falling body +it crosses 2gm in finite proper time + + align:start position:0% +it crosses 2gm in finite proper time + + + align:start position:0% +it crosses 2gm in finite proper time +and shortly afterwards again in finite + + align:start position:0% +and shortly afterwards again in finite + + + align:start position:0% +and shortly afterwards again in finite +proper time + + align:start position:0% +proper time + + + align:start position:0% +proper time +it reaches the r equals zero title + + align:start position:0% +it reaches the r equals zero title + + + align:start position:0% +it reaches the r equals zero title +singularity if i look at that same + + align:start position:0% +singularity if i look at that same + + + align:start position:0% +singularity if i look at that same +motion + + align:start position:0% +motion + + + align:start position:0% +motion +as a function of of the coordinate time + + align:start position:0% +as a function of of the coordinate time + + + align:start position:0% +as a function of of the coordinate time +t + + align:start position:0% +t + + + align:start position:0% +t +it never even reaches never even reaches + + align:start position:0% +it never even reaches never even reaches + + + align:start position:0% +it never even reaches never even reaches +r equals two gm + + align:start position:0% +r equals two gm + + + align:start position:0% +r equals two gm +okay we found the solution which you can + + align:start position:0% +okay we found the solution which you can + + + align:start position:0% +okay we found the solution which you can +see in notes that i've put online and + + align:start position:0% +see in notes that i've put online and + + + align:start position:0% +see in notes that i've put online and +that are presented + + align:start position:0% +that are presented + + + align:start position:0% +that are presented +in the uh the previous lecture uh but we + + align:start position:0% +in the uh the previous lecture uh but we + + + align:start position:0% +in the uh the previous lecture uh but we +found a solution in which it just + + align:start position:0% +found a solution in which it just + + + align:start position:0% +found a solution in which it just +asymptotically approaches + + align:start position:0% +asymptotically approaches + + + align:start position:0% +asymptotically approaches +r equals 2g m only reaching that + + align:start position:0% +r equals 2g m only reaching that + + + align:start position:0% +r equals 2g m only reaching that +that radius in the t goes to infinity + + align:start position:0% +that radius in the t goes to infinity + + + align:start position:0% +that radius in the t goes to infinity +limit + + align:start position:0% +limit + + + align:start position:0% +limit +there are two starkly different pictures + + align:start position:0% +there are two starkly different pictures + + + align:start position:0% +there are two starkly different pictures +of the kinematics of this end falling + + align:start position:0% +of the kinematics of this end falling + + + align:start position:0% +of the kinematics of this end falling +body + + align:start position:0% +body + + + align:start position:0% +body +so the question is what is going on here + + align:start position:0% +so the question is what is going on here + + + align:start position:0% +so the question is what is going on here +and as food for thought i reminded us + + align:start position:0% +and as food for thought i reminded us + + + align:start position:0% +and as food for thought i reminded us +that uh these coordinates if we sort of + + align:start position:0% +that uh these coordinates if we sort of + + + align:start position:0% +that uh these coordinates if we sort of +look at the way that space line behaves + + align:start position:0% +look at the way that space line behaves + + + align:start position:0% +look at the way that space line behaves +for a very very very large m + + align:start position:0% +for a very very very large m + + + align:start position:0% +for a very very very large m +it should be very very very large r not + + align:start position:0% +it should be very very very large r not + + + align:start position:0% +it should be very very very large r not +m but for very large + + align:start position:0% +m but for very large + + + align:start position:0% +m but for very large +r are much much greater than 2 gm this + + align:start position:0% +r are much much greater than 2 gm this + + + align:start position:0% +r are much much greater than 2 gm this +turns into the line element of flat + + align:start position:0% +turns into the line element of flat + + + align:start position:0% +turns into the line element of flat +space time + + align:start position:0% +space time + + + align:start position:0% +space time +flat space time is what we use in + + align:start position:0% +flat space time is what we use in + + + align:start position:0% +flat space time is what we use in +special relativity and our time + + align:start position:0% +special relativity and our time + + + align:start position:0% +special relativity and our time +coordinate there is designed using this + + align:start position:0% +coordinate there is designed using this + + + align:start position:0% +coordinate there is designed using this +einstein synchronization behavior + + align:start position:0% +einstein synchronization behavior + + + align:start position:0% +einstein synchronization behavior +this einstein synchronization procedure + + align:start position:0% +this einstein synchronization procedure + + + align:start position:0% +this einstein synchronization procedure +excuse me which means that + + align:start position:0% +excuse me which means that + + + align:start position:0% +excuse me which means that +the properties of light as it propagates + + align:start position:0% +the properties of light as it propagates + + + align:start position:0% +the properties of light as it propagates +through space-time + + align:start position:0% +through space-time + + + align:start position:0% +through space-time +are built into the coordinate system + + align:start position:0% +are built into the coordinate system + + + align:start position:0% +are built into the coordinate system +so that suggests what we might want to + + align:start position:0% +so that suggests what we might want to + + + align:start position:0% +so that suggests what we might want to +start doing in order to try to get some + + align:start position:0% +start doing in order to try to get some + + + align:start position:0% +start doing in order to try to get some +insight as to what is going on with this + + align:start position:0% +insight as to what is going on with this + + + align:start position:0% +insight as to what is going on with this +weirdos + + align:start position:0% +weirdos + + + align:start position:0% +weirdos +this weird coordinate this weird space + + align:start position:0% +this weird coordinate this weird space + + + align:start position:0% +this weird coordinate this weird space +time is to + + align:start position:0% +time is to + + + align:start position:0% +time is to +think about light as it propagates in + + align:start position:0% +think about light as it propagates in + + + align:start position:0% +think about light as it propagates in +the space think about what happens to + + align:start position:0% +the space think about what happens to + + + align:start position:0% +the space think about what happens to +radiation + + align:start position:0% +radiation + + + align:start position:0% +radiation +as it propagates + + align:start position:0% + + + + align:start position:0% + +so let's imagine + + align:start position:0% + + + + align:start position:0% + +as the body falls + + align:start position:0% + + + + align:start position:0% + +that it emits a radial pulse + + align:start position:0% + + + + align:start position:0% + +with a frequency as measured + + align:start position:0% +with a frequency as measured + + + align:start position:0% +with a frequency as measured +according to the in falling let's say + + align:start position:0% +according to the in falling let's say + + + align:start position:0% +according to the in falling let's say +there's an observer who's falling in + + align:start position:0% +there's an observer who's falling in + + + align:start position:0% +there's an observer who's falling in +it's got a little radio transmitter + + align:start position:0% +it's got a little radio transmitter + + + align:start position:0% +it's got a little radio transmitter +that's beaming this message out + + align:start position:0% +that's beaming this message out + + + align:start position:0% +that's beaming this message out +and according to that that observer this + + align:start position:0% +and according to that that observer this + + + align:start position:0% +and according to that that observer this +thing is emitted with a frequent the the + + align:start position:0% +thing is emitted with a frequent the the + + + align:start position:0% +thing is emitted with a frequent the the +pulse has a frequency + + align:start position:0% +pulse has a frequency + + + align:start position:0% +pulse has a frequency +omega + + align:start position:0% + + + + align:start position:0% + +very far away + + align:start position:0% +very far away + + + align:start position:0% +very far away +we can describe the momentum + + align:start position:0% +we can describe the momentum + + + align:start position:0% +we can describe the momentum +of this radial pulse + + align:start position:0% + + + + align:start position:0% + +like so i imagine the thing is + + align:start position:0% +like so i imagine the thing is + + + align:start position:0% +like so i imagine the thing is +propagating out uh + + align:start position:0% +propagating out uh + + + align:start position:0% +propagating out uh +radially and very very far away + + align:start position:0% +radially and very very far away + + + align:start position:0% +radially and very very far away +where the space time is approximately + + align:start position:0% +where the space time is approximately + + + align:start position:0% +where the space time is approximately +flat + + align:start position:0% +flat + + + align:start position:0% +flat +it's simply the four velocity there give + + align:start position:0% +it's simply the four velocity there give + + + align:start position:0% +it's simply the four velocity there give +me the four momentum + + align:start position:0% +me the four momentum + + + align:start position:0% +me the four momentum +that describes a uh null judaism moving + + align:start position:0% +that describes a uh null judaism moving + + + align:start position:0% +that describes a uh null judaism moving +the radial direction + + align:start position:0% +the radial direction + + + align:start position:0% +the radial direction +okay minus sign here because with the + + align:start position:0% +okay minus sign here because with the + + + align:start position:0% +okay minus sign here because with the +index in the upstairs position in this + + align:start position:0% +index in the upstairs position in this + + + align:start position:0% +index in the upstairs position in this +asymptotically + + align:start position:0% +asymptotically + + + align:start position:0% +asymptotically +flat region that would be the energy so + + align:start position:0% +flat region that would be the energy so + + + align:start position:0% +flat region that would be the energy so +a couple of facts to bear in mind + + align:start position:0% + + + + align:start position:0% + +the energy measured + + align:start position:0% + + + + align:start position:0% + +by an observer with four velocity u + + align:start position:0% + + + + align:start position:0% + +is given by let's call it e sub u + + align:start position:0% +is given by let's call it e sub u + + + align:start position:0% +is given by let's call it e sub u +the energy measured by observer u + + align:start position:0% +the energy measured by observer u + + + align:start position:0% +the energy measured by observer u +this is minus p dot u + + align:start position:0% + + + + align:start position:0% + +we developed this in special relativity + + align:start position:0% +we developed this in special relativity + + + align:start position:0% +we developed this in special relativity +um but remember the way that we use the + + align:start position:0% +um but remember the way that we use the + + + align:start position:0% +um but remember the way that we use the +equivalence principle we're going to use + + align:start position:0% +equivalence principle we're going to use + + + align:start position:0% +equivalence principle we're going to use +the einstein equivalence principle + + align:start position:0% +the einstein equivalence principle + + + align:start position:0% +the einstein equivalence principle +and any law that holds in a freely + + align:start position:0% +and any law that holds in a freely + + + align:start position:0% +and any law that holds in a freely +falling frame if i can write it in a + + align:start position:0% +falling frame if i can write it in a + + + align:start position:0% +falling frame if i can write it in a +tensorial way that works in that freely + + align:start position:0% +tensorial way that works in that freely + + + align:start position:0% +tensorial way that works in that freely +following frame it works in any frame + + align:start position:0% +following frame it works in any frame + + + align:start position:0% +following frame it works in any frame +so this tensorial statement holds true + + align:start position:0% +so this tensorial statement holds true + + + align:start position:0% +so this tensorial statement holds true +even though we are now working + + align:start position:0% +even though we are now working + + + align:start position:0% +even though we are now working +in the space time that is distinctly + + align:start position:0% +in the space time that is distinctly + + + align:start position:0% +in the space time that is distinctly +different from special relativity + + align:start position:0% +different from special relativity + + + align:start position:0% +different from special relativity +we also know that in a + + align:start position:0% +we also know that in a + + + align:start position:0% +we also know that in a +time independent space time + + align:start position:0% + + + + align:start position:0% + +the downstairs t component + + align:start position:0% +the downstairs t component + + + align:start position:0% +the downstairs t component +of four momentum is constant + + align:start position:0% + + + + align:start position:0% + +so what this basically means is if + + align:start position:0% +so what this basically means is if + + + align:start position:0% +so what this basically means is if +um + + align:start position:0% +um + + + align:start position:0% +um +if i think about this radial pulse with + + align:start position:0% +if i think about this radial pulse with + + + align:start position:0% +if i think about this radial pulse with +its lights propagating out through the + + align:start position:0% +its lights propagating out through the + + + align:start position:0% +its lights propagating out through the +space time + + align:start position:0% +space time + + + align:start position:0% +space time +the value p0 associated with this + + align:start position:0% +the value p0 associated with this + + + align:start position:0% +the value p0 associated with this +thing's four momentum it's the same + + align:start position:0% +thing's four momentum it's the same + + + align:start position:0% +thing's four momentum it's the same +everywhere along its trajectory + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +so let's consider + + align:start position:0% + + + + align:start position:0% + +a static observer sitting in the short + + align:start position:0% +a static observer sitting in the short + + + align:start position:0% +a static observer sitting in the short +shield space time + + align:start position:0% +shield space time + + + align:start position:0% +shield space time +okay i'm going to require + + align:start position:0% + + + + align:start position:0% + +g alpha beta u alpha u beta to be equal + + align:start position:0% +g alpha beta u alpha u beta to be equal + + + align:start position:0% +g alpha beta u alpha u beta to be equal +to -1 + + align:start position:0% +to -1 + + + align:start position:0% +to -1 +and i will require that this have some + + align:start position:0% +and i will require that this have some + + + align:start position:0% +and i will require that this have some +time-like piece but this observer is + + align:start position:0% +time-like piece but this observer is + + + align:start position:0% +time-like piece but this observer is +static + + align:start position:0% +static + + + align:start position:0% +static +so their spatial components or their + + align:start position:0% +so their spatial components or their + + + align:start position:0% +so their spatial components or their +four velocity are equal to zero + + align:start position:0% +four velocity are equal to zero + + + align:start position:0% +four velocity are equal to zero +looks like by the way just pause one + + align:start position:0% +looks like by the way just pause one + + + align:start position:0% +looks like by the way just pause one +moment here i'm gonna looks like the + + align:start position:0% +moment here i'm gonna looks like the + + + align:start position:0% +moment here i'm gonna looks like the +projector is on because of + + align:start position:0% + + + + align:start position:0% + +i should probably just leave it as is + + align:start position:0% +i should probably just leave it as is + + + align:start position:0% +i should probably just leave it as is +all right i'm not gonna worry about that + + align:start position:0% +all right i'm not gonna worry about that + + + align:start position:0% +all right i'm not gonna worry about that +just leave that as it is sorry let's go + + align:start position:0% +just leave that as it is sorry let's go + + + align:start position:0% +just leave that as it is sorry let's go +back to what i'm talking about here so i + + align:start position:0% +back to what i'm talking about here so i + + + align:start position:0% +back to what i'm talking about here so i +have a static observer so an observer + + align:start position:0% +have a static observer so an observer + + + align:start position:0% +have a static observer so an observer +who is + + align:start position:0% +who is + + + align:start position:0% +who is +not moving in space they're only moving + + align:start position:0% +not moving in space they're only moving + + + align:start position:0% +not moving in space they're only moving +through time + + align:start position:0% +through time + + + align:start position:0% +through time +and i need to normalize their four + + align:start position:0% +and i need to normalize their four + + + align:start position:0% +and i need to normalize their four +velocity okay + + align:start position:0% +velocity okay + + + align:start position:0% +velocity okay +bear in mind this is not a freely + + align:start position:0% +bear in mind this is not a freely + + + align:start position:0% +bear in mind this is not a freely +flowing observer okay this is an + + align:start position:0% +flowing observer okay this is an + + + align:start position:0% +flowing observer okay this is an +observer who + + align:start position:0% +observer who + + + align:start position:0% +observer who +must be accelerated in some sense there + + align:start position:0% +must be accelerated in some sense there + + + align:start position:0% +must be accelerated in some sense there +must be some kind of a mechanism + + align:start position:0% +must be some kind of a mechanism + + + align:start position:0% +must be some kind of a mechanism +that is allowing this observer to hover + + align:start position:0% +that is allowing this observer to hover + + + align:start position:0% +that is allowing this observer to hover +at the fixed location and space time + + align:start position:0% +at the fixed location and space time + + + align:start position:0% +at the fixed location and space time +that where they are at + + align:start position:0% +that where they are at + + + align:start position:0% +that where they are at +so when i put these two constraints + + align:start position:0% +so when i put these two constraints + + + align:start position:0% +so when i put these two constraints +together + + align:start position:0% +together + + + align:start position:0% +together +and i tie it into that space time + + align:start position:0% + + + + align:start position:0% + +what i find is that the timeline + + align:start position:0% +what i find is that the timeline + + + align:start position:0% +what i find is that the timeline +component + + align:start position:0% + + + + align:start position:0% + +is one square root of one minus two g m + + align:start position:0% +is one square root of one minus two g m + + + align:start position:0% +is one square root of one minus two g m +over r + + align:start position:0% + + + + align:start position:0% + +so let's compare + + align:start position:0% + + + + align:start position:0% + +the energy that is emitted at radius + + align:start position:0% +the energy that is emitted at radius + + + align:start position:0% +the energy that is emitted at radius +r to the energy that is absorbed at some + + align:start position:0% +r to the energy that is absorbed at some + + + align:start position:0% +r to the energy that is absorbed at some +radius big r + + align:start position:0% + + + + align:start position:0% + +so i'm going to imagine + + align:start position:0% + + + + align:start position:0% + +and so reason i formulate in this way + + align:start position:0% +and so reason i formulate in this way + + + align:start position:0% +and so reason i formulate in this way +what i want to do now is + + align:start position:0% +what i want to do now is + + + align:start position:0% +what i want to do now is +ask myself well what is the + + align:start position:0% +ask myself well what is the + + + align:start position:0% +ask myself well what is the +energy that an observer at little r + + align:start position:0% +energy that an observer at little r + + + align:start position:0% +energy that an observer at little r +would measure here + + align:start position:0% + + + + align:start position:0% + +what is the energy that is observed by + + align:start position:0% +what is the energy that is observed by + + + align:start position:0% +what is the energy that is observed by +the person + + align:start position:0% +the person + + + align:start position:0% +the person +at radius capital r + + align:start position:0% + + + + align:start position:0% + +and now we know if i imagine that these + + align:start position:0% +and now we know if i imagine that these + + + align:start position:0% +and now we know if i imagine that these +are both being measured by + + align:start position:0% +are both being measured by + + + align:start position:0% +are both being measured by +static observers + + align:start position:0% + + + + align:start position:0% + +because p sub t p sub zero or p sub t + + align:start position:0% +because p sub t p sub zero or p sub t + + + align:start position:0% +because p sub t p sub zero or p sub t +because it is a constant as the light + + align:start position:0% +because it is a constant as the light + + + align:start position:0% +because it is a constant as the light +propagates out + + align:start position:0% + + + + align:start position:0% + +i can take the ratio of these two + + align:start position:0% +i can take the ratio of these two + + + align:start position:0% +i can take the ratio of these two +and the energy + + align:start position:0% +and the energy + + + align:start position:0% +and the energy +observed at capital r versus the energy + + align:start position:0% +observed at capital r versus the energy + + + align:start position:0% +observed at capital r versus the energy +emitted at little r + + align:start position:0% + + + + align:start position:0% + +hang on a second + + align:start position:0% + + + + align:start position:0% + +as i was looking over my notes there was + + align:start position:0% +as i was looking over my notes there was + + + align:start position:0% +as i was looking over my notes there was +a result that made no sense + + align:start position:0% + + + + align:start position:0% + +that's because i had a typo + + align:start position:0% +that's because i had a typo + + + align:start position:0% +that's because i had a typo +so if those are you following along the + + align:start position:0% +so if those are you following along the + + + align:start position:0% +so if those are you following along the +four velocity component should have been + + align:start position:0% +four velocity component should have been + + + align:start position:0% +four velocity component should have been +a one over the square root of that + + align:start position:0% +a one over the square root of that + + + align:start position:0% +a one over the square root of that +quantity i had earlier + + align:start position:0% +quantity i had earlier + + + align:start position:0% +quantity i had earlier +suddenly what i'm about to write down + + align:start position:0% +suddenly what i'm about to write down + + + align:start position:0% +suddenly what i'm about to write down +makes a lot more sense + + align:start position:0% +makes a lot more sense + + + align:start position:0% +makes a lot more sense +so this becomes + + align:start position:0% + + + + align:start position:0% + +let's imagine that the observer is so + + align:start position:0% +let's imagine that the observer is so + + + align:start position:0% +let's imagine that the observer is so +far away that they are effectively + + align:start position:0% +far away that they are effectively + + + align:start position:0% +far away that they are effectively +uh infinite infinitely far away so the + + align:start position:0% +uh infinite infinitely far away so the + + + align:start position:0% +uh infinite infinitely far away so the +question i'm asking + + align:start position:0% +question i'm asking + + + align:start position:0% +question i'm asking +is if i imagine that the light pulse + + align:start position:0% +is if i imagine that the light pulse + + + align:start position:0% +is if i imagine that the light pulse +is emitted at some radius little r + + align:start position:0% +is emitted at some radius little r + + + align:start position:0% +is emitted at some radius little r +what would a very distant observer + + align:start position:0% +what would a very distant observer + + + align:start position:0% +what would a very distant observer +measure the energy of that pulse to be + + align:start position:0% +measure the energy of that pulse to be + + + align:start position:0% +measure the energy of that pulse to be +okay so my light bulbs are radial pulse + + align:start position:0% +okay so my light bulbs are radial pulse + + + align:start position:0% +okay so my light bulbs are radial pulse +is emitted at some finite radius + + align:start position:0% +is emitted at some finite radius + + + align:start position:0% +is emitted at some finite radius +and we'll call e infinity the value that + + align:start position:0% +and we'll call e infinity the value that + + + align:start position:0% +and we'll call e infinity the value that +is measured by a very distant observer + + align:start position:0% + + + + align:start position:0% + +this becomes square root 1 minus 2 gm + + align:start position:0% +this becomes square root 1 minus 2 gm + + + align:start position:0% +this becomes square root 1 minus 2 gm +over r + + align:start position:0% + + + + align:start position:0% + +notice that the energy no matter how + + align:start position:0% +notice that the energy no matter how + + + align:start position:0% +notice that the energy no matter how +energetic the light is when you emit it + + align:start position:0% +energetic the light is when you emit it + + + align:start position:0% +energetic the light is when you emit it +i describe that as being + + align:start position:0% +i describe that as being + + + align:start position:0% +i describe that as being +a radio pulse but it could be a laser + + align:start position:0% +a radio pulse but it could be a laser + + + align:start position:0% +a radio pulse but it could be a laser +pointer + + align:start position:0% +pointer + + + align:start position:0% +pointer +it could be ultraviolet it could be a + + align:start position:0% +it could be ultraviolet it could be a + + + align:start position:0% +it could be ultraviolet it could be a +gamma ray you know you could just + + align:start position:0% +gamma ray you know you could just + + + align:start position:0% +gamma ray you know you could just +honk whatever massively powerful source + + align:start position:0% +honk whatever massively powerful source + + + align:start position:0% +honk whatever massively powerful source +of photons you want you're pointing it + + align:start position:0% +of photons you want you're pointing it + + + align:start position:0% +of photons you want you're pointing it +out + + align:start position:0% +out + + + align:start position:0% +out +uh in the radial direction and hoping + + align:start position:0% +uh in the radial direction and hoping + + + align:start position:0% +uh in the radial direction and hoping +that your distant friend can measure it + + align:start position:0% +that your distant friend can measure it + + + align:start position:0% +that your distant friend can measure it +no matter what energy you emit as you + + align:start position:0% +no matter what energy you emit as you + + + align:start position:0% +no matter what energy you emit as you +are falling in + + align:start position:0% +are falling in + + + align:start position:0% +are falling in +as you approach r equals 2 gm + + align:start position:0% +as you approach r equals 2 gm + + + align:start position:0% +as you approach r equals 2 gm +the amount of energy in that beam that + + align:start position:0% +the amount of energy in that beam that + + + align:start position:0% +the amount of energy in that beam that +reaches + + align:start position:0% +reaches + + + align:start position:0% +reaches +a distant observer goes to zero + + align:start position:0% + + + + align:start position:0% + +no matter how energetic my pulse of + + align:start position:0% +no matter how energetic my pulse of + + + align:start position:0% +no matter how energetic my pulse of +light + + align:start position:0% + + + + align:start position:0% + +no energy reaches distant observers + + align:start position:0% + + + + align:start position:0% + +as the emitter + + align:start position:0% + + + + align:start position:0% + +approaches r equals 2g m + + align:start position:0% +approaches r equals 2g m + + + align:start position:0% +approaches r equals 2g m +in a similar way imagine that as you are + + align:start position:0% +in a similar way imagine that as you are + + + align:start position:0% +in a similar way imagine that as you are +falling in and you've got this little + + align:start position:0% +falling in and you've got this little + + + align:start position:0% +falling in and you've got this little +beacon + + align:start position:0% +beacon + + + align:start position:0% +beacon +that you're sending messages out to your + + align:start position:0% +that you're sending messages out to your + + + align:start position:0% +that you're sending messages out to your +distant friends + + align:start position:0% + + + + align:start position:0% + +imagine you send them out with a with + + align:start position:0% +imagine you send them out with a with + + + align:start position:0% +imagine you send them out with a with +pulses that are separated by + + align:start position:0% +pulses that are separated by + + + align:start position:0% +pulses that are separated by +delta t + + align:start position:0% + + + + align:start position:0% + +so the person in the falling frame turns + + align:start position:0% +so the person in the falling frame turns + + + align:start position:0% +so the person in the falling frame turns +his beacon on for a moment + + align:start position:0% +his beacon on for a moment + + + align:start position:0% +his beacon on for a moment +every delta let's say delta t is every + + align:start position:0% +every delta let's say delta t is every + + + align:start position:0% +every delta let's say delta t is every +second + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +the interval between pulses as measured + + align:start position:0% +the interval between pulses as measured + + + align:start position:0% +the interval between pulses as measured +far away + + align:start position:0% +far away + + + align:start position:0% +far away +one can show using a similar kind of + + align:start position:0% + + + + align:start position:0% + +calculation + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +you pick up a factor of 1 over square + + align:start position:0% +you pick up a factor of 1 over square + + + align:start position:0% +you pick up a factor of 1 over square +root 1 minus + + align:start position:0% +root 1 minus + + + align:start position:0% +root 1 minus +2 gm over r this + + align:start position:0% +2 gm over r this + + + align:start position:0% +2 gm over r this +goes to infinity + + align:start position:0% + + + + align:start position:0% + +is our goes to 2g m + + align:start position:0% +is our goes to 2g m + + + align:start position:0% +is our goes to 2g m +[Applause] + + align:start position:0% + + + + align:start position:0% + +so remember the time coordinate was + + align:start position:0% +so remember the time coordinate was + + + align:start position:0% +so remember the time coordinate was +originally defined + + align:start position:0% +originally defined + + + align:start position:0% +originally defined +by imagining that i can synchronize all + + align:start position:0% +by imagining that i can synchronize all + + + align:start position:0% +by imagining that i can synchronize all +of my clocks using + + align:start position:0% +of my clocks using + + + align:start position:0% +of my clocks using +light pulses that are bouncing around + + align:start position:0% +light pulses that are bouncing around + + + align:start position:0% +light pulses that are bouncing around +but we can kind of see here + + align:start position:0% +but we can kind of see here + + + align:start position:0% +but we can kind of see here +is that light pulses that are emitted + + align:start position:0% +is that light pulses that are emitted + + + align:start position:0% +is that light pulses that are emitted +in the vicinity of r equals 2 gm they're + + align:start position:0% +in the vicinity of r equals 2 gm they're + + + align:start position:0% +in the vicinity of r equals 2 gm they're +kind of going to hell + + align:start position:0% +kind of going to hell + + + align:start position:0% +kind of going to hell +okay so if i imagine let's just say for + + align:start position:0% +okay so if i imagine let's just say for + + + align:start position:0% +okay so if i imagine let's just say for +the sake of argument i'm using a green + + align:start position:0% +the sake of argument i'm using a green + + + align:start position:0% +the sake of argument i'm using a green +laser pointer + + align:start position:0% +laser pointer + + + align:start position:0% +laser pointer +as the thing that i use for my einstein + + align:start position:0% +as the thing that i use for my einstein + + + align:start position:0% +as the thing that i use for my einstein +synchronization procedure + + align:start position:0% +synchronization procedure + + + align:start position:0% +synchronization procedure +um and you know suppose that i actually + + align:start position:0% +um and you know suppose that i actually + + + align:start position:0% +um and you know suppose that i actually +tell i communicate what time is on the + + align:start position:0% +tell i communicate what time is on the + + + align:start position:0% +tell i communicate what time is on the +clock by a modulation of the signal + + align:start position:0% +clock by a modulation of the signal + + + align:start position:0% +clock by a modulation of the signal +so suppose that i modulate it by putting + + align:start position:0% +so suppose that i modulate it by putting + + + align:start position:0% +so suppose that i modulate it by putting +you know little little spacings on it + + align:start position:0% +you know little little spacings on it + + + align:start position:0% +you know little little spacings on it +that tend to be about a second long + + align:start position:0% +that tend to be about a second long + + + align:start position:0% +that tend to be about a second long +let's just say that it's like a + + align:start position:0% +let's just say that it's like a + + + align:start position:0% +let's just say that it's like a +microsecond long so i can really pack + + align:start position:0% +microsecond long so i can really pack + + + align:start position:0% +microsecond long so i can really pack +some information into that + + align:start position:0% +some information into that + + + align:start position:0% +some information into that +well the laser pointers that are + + align:start position:0% +well the laser pointers that are + + + align:start position:0% +well the laser pointers that are +emitting from r + + align:start position:0% +emitting from r + + + align:start position:0% +emitting from r +equals two gm + + align:start position:0% + + + + align:start position:0% + +their signal infinitely red shifts away + + align:start position:0% +their signal infinitely red shifts away + + + align:start position:0% +their signal infinitely red shifts away +they lose all their energy so they're + + align:start position:0% +they lose all their energy so they're + + + align:start position:0% +they lose all their energy so they're +not green if they're really close to it + + align:start position:0% +not green if they're really close to it + + + align:start position:0% +not green if they're really close to it +maybe they'll be red when they get to + + align:start position:0% +maybe they'll be red when they get to + + + align:start position:0% +maybe they'll be red when they get to +the next thing instead of + + align:start position:0% +the next thing instead of + + + align:start position:0% +the next thing instead of +being a pulse every uh microsecond every + + align:start position:0% +being a pulse every uh microsecond every + + + align:start position:0% +being a pulse every uh microsecond every +two microseconds and the closer we get + + align:start position:0% +two microseconds and the closer we get + + + align:start position:0% +two microseconds and the closer we get +to it + + align:start position:0% +to it + + + align:start position:0% +to it +uh the more redshifted it becomes and + + align:start position:0% +uh the more redshifted it becomes and + + + align:start position:0% +uh the more redshifted it becomes and +the more extended the interval between + + align:start position:0% +the more extended the interval between + + + align:start position:0% +the more extended the interval between +pulses becomes + + align:start position:0% + + + + align:start position:0% + +i'm going to post to the 8962 website + + align:start position:0% +i'm going to post to the 8962 website + + + align:start position:0% +i'm going to post to the 8962 website +a set of notes that sort of cleans up + + align:start position:0% +a set of notes that sort of cleans up + + + align:start position:0% +a set of notes that sort of cleans up +this calculation a little bit just goes + + align:start position:0% +this calculation a little bit just goes + + + align:start position:0% +this calculation a little bit just goes +through this in a little bit more detail + + align:start position:0% +through this in a little bit more detail + + + align:start position:0% +through this in a little bit more detail +it was something i wrote in the spring + + align:start position:0% +it was something i wrote in the spring + + + align:start position:0% +it was something i wrote in the spring +2019 semester in response to a good + + align:start position:0% +2019 semester in response to a good + + + align:start position:0% +2019 semester in response to a good +question that a student had asked me + + align:start position:0% +question that a student had asked me + + + align:start position:0% +question that a student had asked me +about this + + align:start position:0% +about this + + + align:start position:0% +about this +i think they do a nice job of just going + + align:start position:0% +i think they do a nice job of just going + + + align:start position:0% +i think they do a nice job of just going +over this calculation and they give a + + align:start position:0% +over this calculation and they give a + + + align:start position:0% +over this calculation and they give a +couple of examples the way this is + + align:start position:0% +couple of examples the way this is + + + align:start position:0% +couple of examples the way this is +behaving + + align:start position:0% +behaving + + + align:start position:0% +behaving +the key thing which i want to emphasize + + align:start position:0% +the key thing which i want to emphasize + + + align:start position:0% +the key thing which i want to emphasize +is that + + align:start position:0% +is that + + + align:start position:0% +is that +as r goes to 2g m + + align:start position:0% + + + + align:start position:0% + +what we see is that uh + + align:start position:0% +what we see is that uh + + + align:start position:0% +what we see is that uh +well let's just put it this way in fact + + align:start position:0% +well let's just put it this way in fact + + + align:start position:0% +well let's just put it this way in fact +let's remove the word as the surface + + align:start position:0% + + + + align:start position:0% + +r equals two gm corresponds to + + align:start position:0% +r equals two gm corresponds to + + + align:start position:0% +r equals two gm corresponds to +infinite redshift + + align:start position:0% + + + + align:start position:0% + +okay we've talked already a little bit + + align:start position:0% +okay we've talked already a little bit + + + align:start position:0% +okay we've talked already a little bit +about if i have light + + align:start position:0% +about if i have light + + + align:start position:0% +about if i have light +climbing out of a gravitational field + + align:start position:0% +climbing out of a gravitational field + + + align:start position:0% +climbing out of a gravitational field +the light gets a little bit redder as it + + align:start position:0% +the light gets a little bit redder as it + + + align:start position:0% +the light gets a little bit redder as it +climbs out + + align:start position:0% +climbs out + + + align:start position:0% +climbs out +well at this particular surface the + + align:start position:0% +well at this particular surface the + + + align:start position:0% +well at this particular surface the +sphere of + + align:start position:0% +sphere of + + + align:start position:0% +sphere of +radius 2g m in this space on if you can + + align:start position:0% +radius 2g m in this space on if you can + + + align:start position:0% +radius 2g m in this space on if you can +get down to there + + align:start position:0% +get down to there + + + align:start position:0% +get down to there +that red ship and becomes infinite all + + align:start position:0% +that red ship and becomes infinite all + + + align:start position:0% +that red ship and becomes infinite all +of the energy is drained out of it as it + + align:start position:0% +of the energy is drained out of it as it + + + align:start position:0% +of the energy is drained out of it as it +climbs out + + align:start position:0% +climbs out + + + align:start position:0% +climbs out +so what this basically tells us is that + + align:start position:0% +so what this basically tells us is that + + + align:start position:0% +so what this basically tells us is that +this surface + + align:start position:0% +this surface + + + align:start position:0% +this surface +breaks the einstein synchronization + + align:start position:0% +breaks the einstein synchronization + + + align:start position:0% +breaks the einstein synchronization +procedure and it renders that time + + align:start position:0% +procedure and it renders that time + + + align:start position:0% +procedure and it renders that time +coordinate + + align:start position:0% +coordinate + + + align:start position:0% +coordinate +bad at least if we are concerned about + + align:start position:0% +bad at least if we are concerned about + + + align:start position:0% +bad at least if we are concerned about +understanding things right at this + + align:start position:0% + + + + align:start position:0% + +surface + + align:start position:0% + + + + align:start position:0% + +okay as long as we're standing where as + + align:start position:0% +okay as long as we're standing where as + + + align:start position:0% +okay as long as we're standing where as +long as we're concerned uh concerned + + align:start position:0% +long as we're concerned uh concerned + + + align:start position:0% +long as we're concerned uh concerned +with the exterior of this surface + + align:start position:0% +with the exterior of this surface + + + align:start position:0% +with the exterior of this surface +that's not a problem okay everything + + align:start position:0% +that's not a problem okay everything + + + align:start position:0% +that's not a problem okay everything +works fine as long as we move away from + + align:start position:0% +works fine as long as we move away from + + + align:start position:0% +works fine as long as we move away from +this coordinate singularity sort of in + + align:start position:0% +this coordinate singularity sort of in + + + align:start position:0% +this coordinate singularity sort of in +the same way + + align:start position:0% +the same way + + + align:start position:0% +the same way +that many of the pathologies associated + + align:start position:0% +that many of the pathologies associated + + + align:start position:0% +that many of the pathologies associated +with the spherical coordinate system + + align:start position:0% +with the spherical coordinate system + + + align:start position:0% +with the spherical coordinate system +near the north and south pole they're + + align:start position:0% +near the north and south pole they're + + + align:start position:0% +near the north and south pole they're +fine as long as you're not trying to do + + align:start position:0% +fine as long as you're not trying to do + + + align:start position:0% +fine as long as you're not trying to do +things like measure + + align:start position:0% +things like measure + + + align:start position:0% +things like measure +uh the um the the the latitude angle + + align:start position:0% +uh the um the the the latitude angle + + + align:start position:0% +uh the um the the the latitude angle +excuse me the longitude angle + + align:start position:0% +excuse me the longitude angle + + + align:start position:0% +excuse me the longitude angle +corresponds to the north pole it's + + align:start position:0% +corresponds to the north pole it's + + + align:start position:0% +corresponds to the north pole it's +not even well defined okay in the same + + align:start position:0% +not even well defined okay in the same + + + align:start position:0% +not even well defined okay in the same +way this is basically telling us that + + align:start position:0% +way this is basically telling us that + + + align:start position:0% +way this is basically telling us that +the coordinate t in which we wrote down + + align:start position:0% +the coordinate t in which we wrote down + + + align:start position:0% +the coordinate t in which we wrote down +this space time + + align:start position:0% +this space time + + + align:start position:0% +this space time +isn't really well defined at r equals 2 + + align:start position:0% +isn't really well defined at r equals 2 + + + align:start position:0% +isn't really well defined at r equals 2 +gm + + align:start position:0% +gm + + + align:start position:0% +gm +so + + align:start position:0% + + + + align:start position:0% + +what we need to do if we want to try to + + align:start position:0% +what we need to do if we want to try to + + + align:start position:0% +what we need to do if we want to try to +get some hey i'm over here camera + + align:start position:0% +get some hey i'm over here camera + + + align:start position:0% +get some hey i'm over here camera +if we want to try to get a little bit of + + align:start position:0% +if we want to try to get a little bit of + + + align:start position:0% +if we want to try to get a little bit of +insight as to what is going on here + + align:start position:0% +insight as to what is going on here + + + align:start position:0% +insight as to what is going on here +we need a better time coordinate + + align:start position:0% + + + + align:start position:0% + +so i'm going to talk about a couple and + + align:start position:0% +so i'm going to talk about a couple and + + + align:start position:0% +so i'm going to talk about a couple and +the way that we're going to formulate + + align:start position:0% +the way that we're going to formulate + + + align:start position:0% +the way that we're going to formulate +these + + align:start position:0% +these + + + align:start position:0% +these +is all the pathologies are revealed when + + align:start position:0% +is all the pathologies are revealed when + + + align:start position:0% +is all the pathologies are revealed when +we look at + + align:start position:0% +we look at + + + align:start position:0% +we look at +behavior of light propagating in the + + align:start position:0% +behavior of light propagating in the + + + align:start position:0% +behavior of light propagating in the +space time so let's play around with + + align:start position:0% +space time so let's play around with + + + align:start position:0% +space time so let's play around with +light let's look at null geodesics in + + align:start position:0% +light let's look at null geodesics in + + + align:start position:0% +light let's look at null geodesics in +this space time + + align:start position:0% +this space time + + + align:start position:0% +this space time +so to begin with let's stick for just + + align:start position:0% +so to begin with let's stick for just + + + align:start position:0% +so to begin with let's stick for just +the next couple moments with the + + align:start position:0% +the next couple moments with the + + + align:start position:0% +the next couple moments with the +original schwarzschild coordinates + + align:start position:0% + + + + align:start position:0% + +okay so i'm going to look at null + + align:start position:0% +okay so i'm going to look at null + + + align:start position:0% +okay so i'm going to look at null +judaism so i'm going to set + + align:start position:0% +judaism so i'm going to set + + + align:start position:0% +judaism so i'm going to set +0 and i'm going to ask myself how does + + align:start position:0% +0 and i'm going to ask myself how does + + + align:start position:0% +0 and i'm going to ask myself how does +it move to an interval of dt + + align:start position:0% +it move to an interval of dt + + + align:start position:0% +it move to an interval of dt +and an interval of dr + + align:start position:0% + + + + align:start position:0% + +okay so we can solve this + + align:start position:0% +okay so we can solve this + + + align:start position:0% +okay so we can solve this +to find how if an object is moving on a + + align:start position:0% +to find how if an object is moving on a + + + align:start position:0% +to find how if an object is moving on a +radial knull judaism + + align:start position:0% +radial knull judaism + + + align:start position:0% +radial knull judaism +how do dt and dr behave how does dtdr + + align:start position:0% +how do dt and dr behave how does dtdr + + + align:start position:0% +how do dt and dr behave how does dtdr +behave put it that way + + align:start position:0% + + + + align:start position:0% + +okay so we can solve that's what my dtdr + + align:start position:0% +okay so we can solve that's what my dtdr + + + align:start position:0% +okay so we can solve that's what my dtdr +looks like uh + + align:start position:0% +looks like uh + + + align:start position:0% +looks like uh +plus the plus sign corresponds to a + + align:start position:0% +plus the plus sign corresponds to a + + + align:start position:0% +plus the plus sign corresponds to a +solution that is moving the outward in + + align:start position:0% +solution that is moving the outward in + + + align:start position:0% +solution that is moving the outward in +all direction + + align:start position:0% +all direction + + + align:start position:0% +all direction +a minus sign is an inward directed null + + align:start position:0% +a minus sign is an inward directed null + + + align:start position:0% +a minus sign is an inward directed null +judaism + + align:start position:0% +judaism + + + align:start position:0% +judaism +these define we consider to be the + + align:start position:0% +these define we consider to be the + + + align:start position:0% +these define we consider to be the +opening angle so dtdr + + align:start position:0% + + + + align:start position:0% + +defines the opening angle of a light + + align:start position:0% + + + + align:start position:0% + +cone + + align:start position:0% +cone + + + align:start position:0% +cone +so if we go uh to very very very large r + + align:start position:0% + + + + align:start position:0% + +okay we get d t d r equals one + + align:start position:0% + + + + align:start position:0% + +and this corresponds in the units in + + align:start position:0% +and this corresponds in the units in + + + align:start position:0% +and this corresponds in the units in +which c equals one + + align:start position:0% +which c equals one + + + align:start position:0% +which c equals one +to light moving on a 45 degree angle in + + align:start position:0% +to light moving on a 45 degree angle in + + + align:start position:0% +to light moving on a 45 degree angle in +this uh in a space time diagram + + align:start position:0% +this uh in a space time diagram + + + align:start position:0% +this uh in a space time diagram +this is familiar behavior from special + + align:start position:0% + + + + align:start position:0% + +relativity + + align:start position:0% +relativity + + + align:start position:0% +relativity +um but as r goes to 2g m + + align:start position:0% +um but as r goes to 2g m + + + align:start position:0% +um but as r goes to 2g m +we see + + align:start position:0% + + + + align:start position:0% + +the tdr going to zero let's make a + + align:start position:0% +the tdr going to zero let's make a + + + align:start position:0% +the tdr going to zero let's make a +sketch and see what sort of dtdr + + align:start position:0% +sketch and see what sort of dtdr + + + align:start position:0% +sketch and see what sort of dtdr +what the the the tangent to a null + + align:start position:0% +what the the the tangent to a null + + + align:start position:0% +what the the the tangent to a null +judaist looks like in the tr + + align:start position:0% +judaist looks like in the tr + + + align:start position:0% +judaist looks like in the tr +plane uh as a function of radius + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so this little dash here means i'm sort + + align:start position:0% +so this little dash here means i'm sort + + + align:start position:0% +so this little dash here means i'm sort +of imagining + + align:start position:0% +of imagining + + + align:start position:0% +of imagining +that i'm going to stretch my r axis so + + align:start position:0% +that i'm going to stretch my r axis so + + + align:start position:0% +that i'm going to stretch my r axis so +that out here + + align:start position:0% +that out here + + + align:start position:0% +that out here +you're in the asymptotically flat region + + align:start position:0% +you're in the asymptotically flat region + + + align:start position:0% +you're in the asymptotically flat region +where things look like + + align:start position:0% +where things look like + + + align:start position:0% +where things look like +special relativity + + align:start position:0% + + + + align:start position:0% + +so here we are out in this + + align:start position:0% +so here we are out in this + + + align:start position:0% +so here we are out in this +asymptotically flat region + + align:start position:0% +asymptotically flat region + + + align:start position:0% +asymptotically flat region +my outward going light ray goes off at + + align:start position:0% +my outward going light ray goes off at + + + align:start position:0% +my outward going light ray goes off at +45 degree angle in the rt plane + + align:start position:0% +45 degree angle in the rt plane + + + align:start position:0% +45 degree angle in the rt plane +m1 goes and 45 degree angle pointing + + align:start position:0% +m1 goes and 45 degree angle pointing + + + align:start position:0% +m1 goes and 45 degree angle pointing +inside + + align:start position:0% +inside + + + align:start position:0% +inside +down here in the stronger field it's + + align:start position:0% +down here in the stronger field it's + + + align:start position:0% +down here in the stronger field it's +gonna be a little bit steeper than us + + align:start position:0% +gonna be a little bit steeper than us + + + align:start position:0% +gonna be a little bit steeper than us +okay and so the opening angle of my + + align:start position:0% +okay and so the opening angle of my + + + align:start position:0% +okay and so the opening angle of my +light cone + + align:start position:0% + + + + align:start position:0% + +is closing up + + align:start position:0% +is closing up + + + align:start position:0% +is closing up +here it will have closed up + + align:start position:0% +here it will have closed up + + + align:start position:0% +here it will have closed up +a lot more + + align:start position:0% + + + + align:start position:0% + +here it's closed up practically all the + + align:start position:0% +here it's closed up practically all the + + + align:start position:0% +here it's closed up practically all the +way and as i approach r equals 2 gm + + align:start position:0% +way and as i approach r equals 2 gm + + + align:start position:0% +way and as i approach r equals 2 gm +both the inward and the outward + + align:start position:0% +both the inward and the outward + + + align:start position:0% +both the inward and the outward +direction in these coordinates + + align:start position:0% +direction in these coordinates + + + align:start position:0% +direction in these coordinates +go parallel to 2gm + + align:start position:0% +go parallel to 2gm + + + align:start position:0% +go parallel to 2gm +so you can see the collapse of the light + + align:start position:0% +so you can see the collapse of the light + + + align:start position:0% +so you can see the collapse of the light +cone + + align:start position:0% +cone + + + align:start position:0% +cone +in these coordinates + + align:start position:0% + + + + align:start position:0% + +as you approach this coordinate + + align:start position:0% +as you approach this coordinate + + + align:start position:0% +as you approach this coordinate +singularity so we need a healthier + + align:start position:0% +singularity so we need a healthier + + + align:start position:0% +singularity so we need a healthier +coordinate system + + align:start position:0% +coordinate system + + + align:start position:0% +coordinate system +one thing that we can do is we can move + + align:start position:0% +one thing that we can do is we can move + + + align:start position:0% +one thing that we can do is we can move +the pathology + + align:start position:0% +the pathology + + + align:start position:0% +the pathology +out of our time coordinate and into our + + align:start position:0% +out of our time coordinate and into our + + + align:start position:0% +out of our time coordinate and into our +radial coordinate with the following + + align:start position:0% + + + + align:start position:0% + +definition + + align:start position:0% + + + + align:start position:0% + +suppose you choose + + align:start position:0% + + + + align:start position:0% + +a radial coordinate r star such that dt + + align:start position:0% +a radial coordinate r star such that dt + + + align:start position:0% +a radial coordinate r star such that dt +equals plus or minus dr star everywhere + + align:start position:0% +equals plus or minus dr star everywhere + + + align:start position:0% +equals plus or minus dr star everywhere +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so in if i replace my horizontal axis + + align:start position:0% +so in if i replace my horizontal axis + + + align:start position:0% +so in if i replace my horizontal axis +with pardon me + + align:start position:0% +with pardon me + + + align:start position:0% +with pardon me +if i replace my horizontal axis with the + + align:start position:0% +if i replace my horizontal axis with the + + + align:start position:0% +if i replace my horizontal axis with the +r star + + align:start position:0% +r star + + + align:start position:0% +r star +this will be 45 degree angles everywhere + + align:start position:0% +this will be 45 degree angles everywhere + + + align:start position:0% +this will be 45 degree angles everywhere +okay but to make this work + + align:start position:0% + + + + align:start position:0% + +what you find is our star + + align:start position:0% + + + + align:start position:0% + +must look like this what you basically + + align:start position:0% +must look like this what you basically + + + align:start position:0% +must look like this what you basically +see + + align:start position:0% +see + + + align:start position:0% +see +is that this coordinate system takes r + + align:start position:0% +is that this coordinate system takes r + + + align:start position:0% +is that this coordinate system takes r +equals 2g + + align:start position:0% +equals 2g + + + align:start position:0% +equals 2g +m and it moves it to r star equals + + align:start position:0% +m and it moves it to r star equals + + + align:start position:0% +m and it moves it to r star equals +minus infinity + + align:start position:0% + + + + align:start position:0% + +so the way that this coordinate + + align:start position:0% +so the way that this coordinate + + + align:start position:0% +so the way that this coordinate +representation that this different + + align:start position:0% +representation that this different + + + align:start position:0% +representation that this different +radial coordinate makes + + align:start position:0% +radial coordinate makes + + + align:start position:0% +radial coordinate makes +the um the way that this makes + + align:start position:0% +the um the way that this makes + + + align:start position:0% +the um the way that this makes +the the the light cones always have 45 + + align:start position:0% +the the the light cones always have 45 + + + align:start position:0% +the the the light cones always have 45 +degrees + + align:start position:0% +degrees + + + align:start position:0% +degrees +open really nine degrees opening makes + + align:start position:0% +open really nine degrees opening makes + + + align:start position:0% +open really nine degrees opening makes +the light rays always go off at 45 + + align:start position:0% +the light rays always go off at 45 + + + align:start position:0% +the light rays always go off at 45 +degree angles + + align:start position:0% +degree angles + + + align:start position:0% +degree angles +is by essentially constantly stretching + + align:start position:0% +is by essentially constantly stretching + + + align:start position:0% +is by essentially constantly stretching +the radial axis so that this guy just + + align:start position:0% +the radial axis so that this guy just + + + align:start position:0% +the radial axis so that this guy just +gets stretched out so that it's opening + + align:start position:0% +gets stretched out so that it's opening + + + align:start position:0% +gets stretched out so that it's opening +at 90 degrees this guy is stretched a + + align:start position:0% +at 90 degrees this guy is stretched a + + + align:start position:0% +at 90 degrees this guy is stretched a +little bit less this guy stretched a + + align:start position:0% +little bit less this guy stretched a + + + align:start position:0% +little bit less this guy stretched a +little bit less + + align:start position:0% +little bit less + + + align:start position:0% +little bit less +basically not stretched when you're + + align:start position:0% +basically not stretched when you're + + + align:start position:0% +basically not stretched when you're +really far away but as you approach + + align:start position:0% +really far away but as you approach + + + align:start position:0% +really far away but as you approach +r equals 2g m you're infinitely + + align:start position:0% +r equals 2g m you're infinitely + + + align:start position:0% +r equals 2g m you're infinitely +stretching in these coordinates + + align:start position:0% +stretching in these coordinates + + + align:start position:0% +stretching in these coordinates +okay these are known + + align:start position:0% + + + + align:start position:0% + +as + + align:start position:0% +as + + + align:start position:0% +as +tortoise coordinates + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +basically because you start walking + + align:start position:0% +basically because you start walking + + + align:start position:0% +basically because you start walking +taking ever slower and slower steps + + align:start position:0% +taking ever slower and slower steps + + + align:start position:0% +taking ever slower and slower steps +um even steps if you imagine you're + + align:start position:0% +um even steps if you imagine you're + + + align:start position:0% +um even steps if you imagine you're +stepping evenly in + + align:start position:0% +stepping evenly in + + + align:start position:0% +stepping evenly in +r star you're taking ever smaller and + + align:start position:0% +r star you're taking ever smaller and + + + align:start position:0% +r star you're taking ever smaller and +smaller steps in + + align:start position:0% +smaller steps in + + + align:start position:0% +smaller steps in +r as you approach the + + align:start position:0% +r as you approach the + + + align:start position:0% +r as you approach the +infinite redshift surface + + align:start position:0% + + + + align:start position:0% + +so with that tortoise coordinate defined + + align:start position:0% +so with that tortoise coordinate defined + + + align:start position:0% +so with that tortoise coordinate defined +you then you use that as an intermediary + + align:start position:0% +you then you use that as an intermediary + + + align:start position:0% +you then you use that as an intermediary +to define + + align:start position:0% +to define + + + align:start position:0% +to define +a couple of new coordinates for your + + align:start position:0% +a couple of new coordinates for your + + + align:start position:0% +a couple of new coordinates for your +space time that are adapted to radiation + + align:start position:0% +space time that are adapted to radiation + + + align:start position:0% +space time that are adapted to radiation +so we're going to define v + + align:start position:0% +so we're going to define v + + + align:start position:0% +so we're going to define v +to be t plus r + + align:start position:0% +to be t plus r + + + align:start position:0% +to be t plus r +star r star and the + + align:start position:0% +star r star and the + + + align:start position:0% +star r star and the +importance of this is that this is a + + align:start position:0% +importance of this is that this is a + + + align:start position:0% +importance of this is that this is a +coordinate that's not hard to convince + + align:start position:0% +coordinate that's not hard to convince + + + align:start position:0% +coordinate that's not hard to convince +yourself + + align:start position:0% +yourself + + + align:start position:0% +yourself +this is constant on an in-going + + align:start position:0% +this is constant on an in-going + + + align:start position:0% +this is constant on an in-going +radial null ray + + align:start position:0% + + + + align:start position:0% + +i'm going to define a coordinate u to be + + align:start position:0% +i'm going to define a coordinate u to be + + + align:start position:0% +i'm going to define a coordinate u to be +t minus r star and this is constant + + align:start position:0% + + + + align:start position:0% + +on outgoing + + align:start position:0% + + + + align:start position:0% + +radial null rays + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so this basically means that if i'm + + align:start position:0% +so this basically means that if i'm + + + align:start position:0% +so this basically means that if i'm +working in this coordinate system + + align:start position:0% +working in this coordinate system + + + align:start position:0% +working in this coordinate system +r star uh if i want to know the behavior + + align:start position:0% +r star uh if i want to know the behavior + + + align:start position:0% +r star uh if i want to know the behavior +of this guy + + align:start position:0% +of this guy + + + align:start position:0% +of this guy +um well an outgoing radial null ray you + + align:start position:0% +um well an outgoing radial null ray you + + + align:start position:0% +um well an outgoing radial null ray you +just might say ah that's the null ray + + align:start position:0% +just might say ah that's the null ray + + + align:start position:0% +just might say ah that's the null ray +that has u + + align:start position:0% +that has u + + + align:start position:0% +that has u +equals 17. okay and that will then pick + + align:start position:0% +equals 17. okay and that will then pick + + + align:start position:0% +equals 17. okay and that will then pick +out an entire fam basically a you know a + + align:start position:0% +out an entire fam basically a you know a + + + align:start position:0% +out an entire fam basically a you know a +whole sequence of events along which + + align:start position:0% +whole sequence of events along which + + + align:start position:0% +whole sequence of events along which +that null ray + + align:start position:0% +that null ray + + + align:start position:0% +that null ray +uh has propagated + + align:start position:0% + + + + align:start position:0% + +um and uh you know as you can see it + + align:start position:0% +um and uh you know as you can see it + + + align:start position:0% +um and uh you know as you can see it +vastly simplifies how we describe it + + align:start position:0% +vastly simplifies how we describe it + + + align:start position:0% +vastly simplifies how we describe it +so once once you've + + align:start position:0% +so once once you've + + + align:start position:0% +so once once you've +defined these two coordinates you can + + align:start position:0% +defined these two coordinates you can + + + align:start position:0% +defined these two coordinates you can +rewrite the schwarzschild space time in + + align:start position:0% +rewrite the schwarzschild space time in + + + align:start position:0% +rewrite the schwarzschild space time in +terms of them + + align:start position:0% +terms of them + + + align:start position:0% +terms of them +it is generally best to choose + + align:start position:0% +it is generally best to choose + + + align:start position:0% +it is generally best to choose +so we're going to take this another step + + align:start position:0% +so we're going to take this another step + + + align:start position:0% +so we're going to take this another step +in just a moment but we'll start you + + align:start position:0% +in just a moment but we'll start you + + + align:start position:0% +in just a moment but we'll start you +choose + + align:start position:0% +choose + + + align:start position:0% +choose +either v or u and you replace the short + + align:start position:0% +either v or u and you replace the short + + + align:start position:0% +either v or u and you replace the short +shield time + + align:start position:0% + + + + align:start position:0% + +so let's replace uh + + align:start position:0% +so let's replace uh + + + align:start position:0% +so let's replace uh +let's let's let's use v to replace time + + align:start position:0% + + + + align:start position:0% + +so when you go and you look at what your + + align:start position:0% +so when you go and you look at what your + + + align:start position:0% +so when you go and you look at what your +new coordinate system looks like + + align:start position:0% +new coordinate system looks like + + + align:start position:0% +new coordinate system looks like +and remember the way you do this is it's + + align:start position:0% +and remember the way you do this is it's + + + align:start position:0% +and remember the way you do this is it's +the usual thing you're going to + + align:start position:0% +the usual thing you're going to + + + align:start position:0% +the usual thing you're going to +make your your matrix of partial + + align:start position:0% +make your your matrix of partial + + + align:start position:0% +make your your matrix of partial +derivatives between your old coordinate + + align:start position:0% +derivatives between your old coordinate + + + align:start position:0% +derivatives between your old coordinate +system so + + align:start position:0% +system so + + + align:start position:0% +system so +your old coordinates are t + + align:start position:0% +your old coordinates are t + + + align:start position:0% +your old coordinates are t +r theta and phi and then they go over to + + align:start position:0% +r theta and phi and then they go over to + + + align:start position:0% +r theta and phi and then they go over to +v + + align:start position:0% +v + + + align:start position:0% +v +r theta and phi + + align:start position:0% +r theta and phi + + + align:start position:0% +r theta and phi +okay + + align:start position:0% + + + + align:start position:0% + +um so you make your matrix of partial + + align:start position:0% +um so you make your matrix of partial + + + align:start position:0% +um so you make your matrix of partial +derivatives describing this + + align:start position:0% +derivatives describing this + + + align:start position:0% +derivatives describing this +and here's what you find when you change + + align:start position:0% +and here's what you find when you change + + + align:start position:0% +and here's what you find when you change +to the metric in the new representation + + align:start position:0% + + + + align:start position:0% + +notice there's no dr squared term at all + + align:start position:0% +notice there's no dr squared term at all + + + align:start position:0% +notice there's no dr squared term at all +okay + + align:start position:0% +okay + + + align:start position:0% +okay +we do still see something that's you + + align:start position:0% +we do still see something that's you + + + align:start position:0% +we do still see something that's you +know at least a coordinate singularity + + align:start position:0% +know at least a coordinate singularity + + + align:start position:0% +know at least a coordinate singularity +at + + align:start position:0% +at + + + align:start position:0% +at +r equals 2g m we haven't quite gotten + + align:start position:0% +r equals 2g m we haven't quite gotten + + + align:start position:0% +r equals 2g m we haven't quite gotten +rid of it entirely here but we've + + align:start position:0% +rid of it entirely here but we've + + + align:start position:0% +rid of it entirely here but we've +definitely + + align:start position:0% +definitely + + + align:start position:0% +definitely +modified uh the strength of this + + align:start position:0% +modified uh the strength of this + + + align:start position:0% +modified uh the strength of this +you know the impact of this coordinate + + align:start position:0% +you know the impact of this coordinate + + + align:start position:0% +you know the impact of this coordinate +singularity so in this coordinate system + + align:start position:0% +singularity so in this coordinate system + + + align:start position:0% +singularity so in this coordinate system +you can then so set ds squared equal to + + align:start position:0% +you can then so set ds squared equal to + + + align:start position:0% +you can then so set ds squared equal to +zero + + align:start position:0% +zero + + + align:start position:0% +zero +and you find two solutions describing + + align:start position:0% +and you find two solutions describing + + + align:start position:0% +and you find two solutions describing +radial null curves + + align:start position:0% + + + + align:start position:0% + +so dvd r equals zero + + align:start position:0% +so dvd r equals zero + + + align:start position:0% +so dvd r equals zero +for ingoing + + align:start position:0% + + + + align:start position:0% + +and that you know by definition these + + align:start position:0% +and that you know by definition these + + + align:start position:0% +and that you know by definition these +things are constant on an in-goaling + + align:start position:0% +things are constant on an in-goaling + + + align:start position:0% +things are constant on an in-goaling +radial null ray and so as you move along + + align:start position:0% +radial null ray and so as you move along + + + align:start position:0% +radial null ray and so as you move along +it v + + align:start position:0% +it v + + + align:start position:0% +it v +remains constant + + align:start position:0% + + + + align:start position:0% + +okay and you get something a little bit + + align:start position:0% +okay and you get something a little bit + + + align:start position:0% +okay and you get something a little bit +more complicated for the outgoing one + + align:start position:0% + + + + align:start position:0% + +let's redraw this using my new + + align:start position:0% +let's redraw this using my new + + + align:start position:0% +let's redraw this using my new +coordinates + + align:start position:0% +coordinates + + + align:start position:0% +coordinates +okay + + align:start position:0% + + + + align:start position:0% + +so i'm going to leave my horizontal axis + + align:start position:0% +so i'm going to leave my horizontal axis + + + align:start position:0% +so i'm going to leave my horizontal axis +as r but i'm going to make my time axis + + align:start position:0% +as r but i'm going to make my time axis + + + align:start position:0% +as r but i'm going to make my time axis +be v + + align:start position:0% + + + + align:start position:0% + +so out here + + align:start position:0% + + + + align:start position:0% + +here's my ingoing null ray + + align:start position:0% + + + + align:start position:0% + +and here's my let's make that a little + + align:start position:0% +and here's my let's make that a little + + + align:start position:0% +and here's my let's make that a little +closer to 45 degrees + + align:start position:0% +closer to 45 degrees + + + align:start position:0% +closer to 45 degrees +here's my alkaline already okay as i + + align:start position:0% +here's my alkaline already okay as i + + + align:start position:0% +here's my alkaline already okay as i +move in + + align:start position:0% +move in + + + align:start position:0% +move in +to smaller and smaller values of r + + align:start position:0% +to smaller and smaller values of r + + + align:start position:0% +to smaller and smaller values of r +notice in the limit as r goes to 2 gm + + align:start position:0% +notice in the limit as r goes to 2 gm + + + align:start position:0% +notice in the limit as r goes to 2 gm +the slope becomes infinite okay so this + + align:start position:0% +the slope becomes infinite okay so this + + + align:start position:0% +the slope becomes infinite okay so this +thing gets steeper + + align:start position:0% +thing gets steeper + + + align:start position:0% +thing gets steeper +this one keeps pointing in so this guy + + align:start position:0% +this one keeps pointing in so this guy + + + align:start position:0% +this one keeps pointing in so this guy +gets steeper + + align:start position:0% + + + + align:start position:0% + +steeper right here + + align:start position:0% +steeper right here + + + align:start position:0% +steeper right here +it lies pointing exactly straight up + + align:start position:0% +it lies pointing exactly straight up + + + align:start position:0% +it lies pointing exactly straight up +what's kind of cool is that in these + + align:start position:0% +what's kind of cool is that in these + + + align:start position:0% +what's kind of cool is that in these +coordinates i can actually look at what + + align:start position:0% +coordinates i can actually look at what + + + align:start position:0% +coordinates i can actually look at what +it looks like inside this thing + + align:start position:0% +it looks like inside this thing + + + align:start position:0% +it looks like inside this thing +and so inside this guy tips over and + + align:start position:0% +and so inside this guy tips over and + + + align:start position:0% +and so inside this guy tips over and +gets a negative slope + + align:start position:0% +gets a negative slope + + + align:start position:0% +gets a negative slope +looks like this + + align:start position:0% + + + + align:start position:0% + +now bear in mind these two things they + + align:start position:0% +now bear in mind these two things they + + + align:start position:0% +now bear in mind these two things they +denote the null rays + + align:start position:0% +denote the null rays + + + align:start position:0% +denote the null rays +all radial time-like + + align:start position:0% + + + + align:start position:0% + +trajectories + + align:start position:0% +trajectories + + + align:start position:0% +trajectories +and indeed all time light trajectories + + align:start position:0% +and indeed all time light trajectories + + + align:start position:0% +and indeed all time light trajectories +not just + + align:start position:0% +not just + + + align:start position:0% +not just +the radial ones all time-like + + align:start position:0% +the radial ones all time-like + + + align:start position:0% +the radial ones all time-like +trajectories + + align:start position:0% +trajectories + + + align:start position:0% +trajectories +must follow a world line + + align:start position:0% + + + + align:start position:0% + +that is bounded by these two sides + + align:start position:0% + + + + align:start position:0% + +okay so if i'm out here everything + + align:start position:0% +okay so if i'm out here everything + + + align:start position:0% +okay so if i'm out here everything +in here describes trajectories that a + + align:start position:0% +in here describes trajectories that a + + + align:start position:0% +in here describes trajectories that a +time-like observer can follow + + align:start position:0% +time-like observer can follow + + + align:start position:0% +time-like observer can follow +everything in here describes trajectory + + align:start position:0% +everything in here describes trajectory + + + align:start position:0% +everything in here describes trajectory +a time-like observer can follow + + align:start position:0% +a time-like observer can follow + + + align:start position:0% +a time-like observer can follow +everything in here everything in here + + align:start position:0% + + + + align:start position:0% + +notice when i'm at this one here + + align:start position:0% +notice when i'm at this one here + + + align:start position:0% +notice when i'm at this one here +right at r equals 2 gm every allowed + + align:start position:0% +right at r equals 2 gm every allowed + + + align:start position:0% +right at r equals 2 gm every allowed +time-like trajectory points + + align:start position:0% +time-like trajectory points + + + align:start position:0% +time-like trajectory points +towards r equals zero + + align:start position:0% +towards r equals zero + + + align:start position:0% +towards r equals zero +okay at best i can imagine + + align:start position:0% +okay at best i can imagine + + + align:start position:0% +okay at best i can imagine +an observer who's very close to the + + align:start position:0% +an observer who's very close to the + + + align:start position:0% +an observer who's very close to the +speed of light who sort of skims along + + align:start position:0% +speed of light who sort of skims along + + + align:start position:0% +speed of light who sort of skims along +inside of this thing + + align:start position:0% +inside of this thing + + + align:start position:0% +inside of this thing +but they are time like so they will have + + align:start position:0% +but they are time like so they will have + + + align:start position:0% +but they are time like so they will have +a little bit of a slope + + align:start position:0% +a little bit of a slope + + + align:start position:0% +a little bit of a slope +that points them inward + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% + + + + align:start position:0% + +okay as you move inside articles two gem + + align:start position:0% +okay as you move inside articles two gem + + + align:start position:0% +okay as you move inside articles two gem +it's even more so okay you can't even + + align:start position:0% +it's even more so okay you can't even + + + align:start position:0% +it's even more so okay you can't even +sort of go parallel to the articles to + + align:start position:0% +sort of go parallel to the articles to + + + align:start position:0% +sort of go parallel to the articles to +gm line they all point towards this + + align:start position:0% +gm line they all point towards this + + + align:start position:0% +gm line they all point towards this +thing + + align:start position:0% +thing + + + align:start position:0% +thing +all future trajectory once you get to r + + align:start position:0% +all future trajectory once you get to r + + + align:start position:0% +all future trajectory once you get to r +equals two gm + + align:start position:0% +equals two gm + + + align:start position:0% +equals two gm +all trajectories as they move to the + + align:start position:0% +all trajectories as they move to the + + + align:start position:0% +all trajectories as they move to the +future must + + align:start position:0% +future must + + + align:start position:0% +future must +move to smaller radius + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +what this tells us in particular + + align:start position:0% +what this tells us in particular + + + align:start position:0% +what this tells us in particular +is that once you have reached + + align:start position:0% +is that once you have reached + + + align:start position:0% +is that once you have reached +r equals 2 gm + + align:start position:0% +r equals 2 gm + + + align:start position:0% +r equals 2 gm +you are never coming back + + align:start position:0% + + + + align:start position:0% + +all allowed trajectories everything that + + align:start position:0% +all allowed trajectories everything that + + + align:start position:0% +all allowed trajectories everything that +is permissible by the laws of physics + + align:start position:0% +is permissible by the laws of physics + + + align:start position:0% +is permissible by the laws of physics +moves along a trajectory that points + + align:start position:0% +moves along a trajectory that points + + + align:start position:0% +moves along a trajectory that points +towards r equals zero once you hit that + + align:start position:0% +towards r equals zero once you hit that + + + align:start position:0% +towards r equals zero once you hit that +r equals two g m line + + align:start position:0% +r equals two g m line + + + align:start position:0% +r equals two g m line +because of this this surface r + + align:start position:0% +because of this this surface r + + + align:start position:0% +because of this this surface r +this uh surface of infinite redshift is + + align:start position:0% +this uh surface of infinite redshift is + + + align:start position:0% +this uh surface of infinite redshift is +given the name + + align:start position:0% + + + + align:start position:0% + +let me come back to the point i was + + align:start position:0% +let me come back to the point i was + + + align:start position:0% +let me come back to the point i was +making so the surface r equals 2gm + + align:start position:0% +making so the surface r equals 2gm + + + align:start position:0% +making so the surface r equals 2gm +nothing that crosses it is ever going to + + align:start position:0% +nothing that crosses it is ever going to + + + align:start position:0% +nothing that crosses it is ever going to +come back + + align:start position:0% +come back + + + align:start position:0% +come back +this surface of infinite redshift + + align:start position:0% + + + + align:start position:0% + +we call an event horizon + + align:start position:0% + + + + align:start position:0% + +okay um no events + + align:start position:0% +okay um no events + + + align:start position:0% +okay um no events +that are on the other side of r equals 2 + + align:start position:0% +that are on the other side of r equals 2 + + + align:start position:0% +that are on the other side of r equals 2 +gm + + align:start position:0% +gm + + + align:start position:0% +gm +can have any causal influence on events + + align:start position:0% +can have any causal influence on events + + + align:start position:0% +can have any causal influence on events +on the outside + + align:start position:0% + + + + align:start position:0% + +if you have a space time with an event + + align:start position:0% +if you have a space time with an event + + + align:start position:0% +if you have a space time with an event +horizon like this and this one that we + + align:start position:0% +horizon like this and this one that we + + + align:start position:0% +horizon like this and this one that we +are talking about right here i'm going + + align:start position:0% +are talking about right here i'm going + + + align:start position:0% +are talking about right here i'm going +to talk at the end of my + + align:start position:0% +to talk at the end of my + + + align:start position:0% +to talk at the end of my +my final lecture that i record uh about + + align:start position:0% +my final lecture that i record uh about + + + align:start position:0% +my final lecture that i record uh about +maybe i'm actually going to do it in + + align:start position:0% +maybe i'm actually going to do it in + + + align:start position:0% +maybe i'm actually going to do it in +this one yeah i am so at the end of this + + align:start position:0% +this one yeah i am so at the end of this + + + align:start position:0% +this one yeah i am so at the end of this +lecture that i'm recording i'm going to + + align:start position:0% +lecture that i'm recording i'm going to + + + align:start position:0% +lecture that i'm recording i'm going to +go over a couple of other space times + + align:start position:0% +go over a couple of other space times + + + align:start position:0% +go over a couple of other space times +that have this structure + + align:start position:0% +that have this structure + + + align:start position:0% +that have this structure +such space times are called + + align:start position:0% + + + + align:start position:0% + +wait for it + + align:start position:0% + + + + align:start position:0% + +such space times are called black + + align:start position:0% + + + + align:start position:0% + +holes they are black + + align:start position:0% +holes they are black + + + align:start position:0% +holes they are black +because light cannot get out of them and + + align:start position:0% +because light cannot get out of them and + + + align:start position:0% +because light cannot get out of them and +they're holes + + align:start position:0% +they're holes + + + align:start position:0% +they're holes +because you just jump into them and you + + align:start position:0% +because you just jump into them and you + + + align:start position:0% +because you just jump into them and you +ain't never coming out + + align:start position:0% +ain't never coming out + + + align:start position:0% +ain't never coming out +so let me pause for just one moment i + + align:start position:0% +so let me pause for just one moment i + + + align:start position:0% +so let me pause for just one moment i +want to send a quick note to the odl + + align:start position:0% +want to send a quick note to the odl + + + align:start position:0% +want to send a quick note to the odl +person who + + align:start position:0% +person who + + + align:start position:0% +person who +is helping me out here + + align:start position:0% +is helping me out here + + + align:start position:0% +is helping me out here +i just want to let her know that this + + align:start position:0% +i just want to let her know that this + + + align:start position:0% +i just want to let her know that this +lecture may run a tiny bit long + + align:start position:0% + + + + align:start position:0% + +since i spent a moment chatting with a + + align:start position:0% +since i spent a moment chatting with a + + + align:start position:0% +since i spent a moment chatting with a +police officer who checked in on me + + align:start position:0% + + + + align:start position:0% + +okay if you're watching elaine hi um + + align:start position:0% +okay if you're watching elaine hi um + + + align:start position:0% +okay if you're watching elaine hi um +so i just sent you a quick note letting + + align:start position:0% +so i just sent you a quick note letting + + + align:start position:0% +so i just sent you a quick note letting +you know that uh + + align:start position:0% +you know that uh + + + align:start position:0% +you know that uh +i'm likely to run a little bit long all + + align:start position:0% +i'm likely to run a little bit long all + + + align:start position:0% +i'm likely to run a little bit long all +right let's get back to the two black + + align:start position:0% +right let's get back to the two black + + + align:start position:0% +right let's get back to the two black +holes + + align:start position:0% +holes + + + align:start position:0% +holes +so to sort of + + align:start position:0% +so to sort of + + + align:start position:0% +so to sort of +call out some of the structure of this + + align:start position:0% +call out some of the structure of this + + + align:start position:0% +call out some of the structure of this +space time + + align:start position:0% +space time + + + align:start position:0% +space time +i want to spend just a few minutes + + align:start position:0% +i want to spend just a few minutes + + + align:start position:0% +i want to spend just a few minutes +talking about a + + align:start position:0% +talking about a + + + align:start position:0% +talking about a +one final coordinate transformation + + align:start position:0% +one final coordinate transformation + + + align:start position:0% +one final coordinate transformation +that is very useful but looks really + + align:start position:0% +that is very useful but looks really + + + align:start position:0% +that is very useful but looks really +weird + + align:start position:0% +weird + + + align:start position:0% +weird +so just bear with me as i go through + + align:start position:0% +so just bear with me as i go through + + + align:start position:0% +so just bear with me as i go through +this + + align:start position:0% +this + + + align:start position:0% +this +a very useful but unquestionably + + align:start position:0% +a very useful but unquestionably + + + align:start position:0% +a very useful but unquestionably +somewhat + + align:start position:0% +somewhat + + + align:start position:0% +somewhat +obtuse coordinate transformation + + align:start position:0% + + + + align:start position:0% + +what i'm going to do is put i'm going to + + align:start position:0% +what i'm going to do is put i'm going to + + + align:start position:0% +what i'm going to do is put i'm going to +define a coordinate v + + align:start position:0% +define a coordinate v + + + align:start position:0% +define a coordinate v +prime + + align:start position:0% + + + + align:start position:0% + +this is given by taking the exponential + + align:start position:0% +this is given by taking the exponential + + + align:start position:0% +this is given by taking the exponential +of the tortoise coordinate + + align:start position:0% +of the tortoise coordinate + + + align:start position:0% +of the tortoise coordinate +v excuse me the in-going coordinate + + align:start position:0% +v excuse me the in-going coordinate + + + align:start position:0% +v excuse me the in-going coordinate +time v normalized to 4g m + + align:start position:0% +time v normalized to 4g m + + + align:start position:0% +time v normalized to 4g m +u prime will be the exponent of u + + align:start position:0% + + + + align:start position:0% + +time that works well for the outgoing + + align:start position:0% +time that works well for the outgoing + + + align:start position:0% +time that works well for the outgoing +coordinate system divided by + + align:start position:0% +coordinate system divided by + + + align:start position:0% +coordinate system divided by +4g m i'm then going to define + + align:start position:0% +4g m i'm then going to define + + + align:start position:0% +4g m i'm then going to define +capital t to be + + align:start position:0% +capital t to be + + + align:start position:0% +capital t to be +one half v prime + + align:start position:0% +one half v prime + + + align:start position:0% +one half v prime +plus u prime capital r + + align:start position:0% +plus u prime capital r + + + align:start position:0% +plus u prime capital r +to be one half v prime minus u prime + + align:start position:0% +to be one half v prime minus u prime + + + align:start position:0% +to be one half v prime minus u prime +it's then simple to show + + align:start position:0% +it's then simple to show + + + align:start position:0% +it's then simple to show +where simple is professor speak for + + align:start position:0% +where simple is professor speak for + + + align:start position:0% +where simple is professor speak for +a student could probably do it in an + + align:start position:0% +a student could probably do it in an + + + align:start position:0% +a student could probably do it in an +hour or so sort of + + align:start position:0% +hour or so sort of + + + align:start position:0% +hour or so sort of +tedious but straightforward just hooking + + align:start position:0% +tedious but straightforward just hooking + + + align:start position:0% +tedious but straightforward just hooking +together lots of definitions and + + align:start position:0% +together lots of definitions and + + + align:start position:0% +together lots of definitions and +slogging through a couple of + + align:start position:0% + + + + align:start position:0% + +identities + + align:start position:0% +identities + + + align:start position:0% +identities +it's simple to show that + + align:start position:0% +it's simple to show that + + + align:start position:0% +it's simple to show that +capital t relates to + + align:start position:0% +capital t relates to + + + align:start position:0% +capital t relates to +short shield time t and short shield + + align:start position:0% +short shield time t and short shield + + + align:start position:0% +short shield time t and short shield +radius r + + align:start position:0% +radius r + + + align:start position:0% +radius r +like so there's two branches + + align:start position:0% + + + + align:start position:0% + +okay so this is how one relates + + align:start position:0% +okay so this is how one relates + + + align:start position:0% +okay so this is how one relates +capital t and capital r to short shield + + align:start position:0% +capital t and capital r to short shield + + + align:start position:0% +capital t and capital r to short shield +t and short shield r + + align:start position:0% +t and short shield r + + + align:start position:0% +t and short shield r +in the region + + align:start position:0% + + + + align:start position:0% + +r greater than or equal to two g m + + align:start position:0% + + + + align:start position:0% + +you find a somewhat different solution + + align:start position:0% + + + + align:start position:0% + +oh + + align:start position:0% + + + + align:start position:0% + +in the region are less than two gm + + align:start position:0% +in the region are less than two gm + + + align:start position:0% +in the region are less than two gm +so if you're looking at this and kind of + + align:start position:0% +so if you're looking at this and kind of + + + align:start position:0% +so if you're looking at this and kind of +going what the hell are you talking + + align:start position:0% +going what the hell are you talking + + + align:start position:0% +going what the hell are you talking +about here + + align:start position:0% +about here + + + align:start position:0% +about here +that's fine + + align:start position:0% + + + + align:start position:0% + +let me just write down two more + + align:start position:0% + + + + align:start position:0% + +relationships + + align:start position:0% +relationships + + + align:start position:0% +relationships +and then i'll describe what this is good + + align:start position:0% + + + + align:start position:0% + +for + + align:start position:0% + + + + align:start position:0% + +so a particularly clean inversion + + align:start position:0% + + + + align:start position:0% + +between + + align:start position:0% + + + + align:start position:0% + +tr + + align:start position:0% + + + + align:start position:0% + +and the original short shield tr + + align:start position:0% + + + + align:start position:0% + +both the + + align:start position:0% +both the + + + align:start position:0% +both the +r greater than 2 gm and r less than 2 gm + + align:start position:0% +r greater than 2 gm and r less than 2 gm + + + align:start position:0% +r greater than 2 gm and r less than 2 gm +branches can be subsumed into this + + align:start position:0% + + + + align:start position:0% + +okay and you find + + align:start position:0% +okay and you find + + + align:start position:0% +okay and you find +t over r + + align:start position:0% +t over r + + + align:start position:0% +t over r +looks like the hyperbolic tangent + + align:start position:0% + + + + align:start position:0% + +t over four g m when you're in the + + align:start position:0% +t over four g m when you're in the + + + align:start position:0% +t over four g m when you're in the +exterior + + align:start position:0% + + + + align:start position:0% + +and the hyperbolic cotangent + + align:start position:0% + + + + align:start position:0% + +in the interior + + align:start position:0% +in the interior + + + align:start position:0% +in the interior +so these rather bizarre looking + + align:start position:0% +so these rather bizarre looking + + + align:start position:0% +so these rather bizarre looking +coordinates + + align:start position:0% +coordinates + + + align:start position:0% +coordinates +these are known as + + align:start position:0% + + + + align:start position:0% + +kruskal + + align:start position:0% +kruskal + + + align:start position:0% +kruskal +chicago's coordinates + + align:start position:0% + + + + align:start position:0% + +just leave that down like so + + align:start position:0% + + + + align:start position:0% + +so when one goes into this i'm not going + + align:start position:0% +so when one goes into this i'm not going + + + align:start position:0% +so when one goes into this i'm not going +to deny this is a bizarre looking + + align:start position:0% +to deny this is a bizarre looking + + + align:start position:0% +to deny this is a bizarre looking +coordinate system okay but it's got + + align:start position:0% +coordinate system okay but it's got + + + align:start position:0% +coordinate system okay but it's got +several features that uh make it + + align:start position:0% +several features that uh make it + + + align:start position:0% +several features that uh make it +very useful for understanding what is + + align:start position:0% +very useful for understanding what is + + + align:start position:0% +very useful for understanding what is +going on + + align:start position:0% +going on + + + align:start position:0% +going on +physically in the space time + + align:start position:0% + + + + align:start position:0% + +so first if you rewrite your metric in + + align:start position:0% +so first if you rewrite your metric in + + + align:start position:0% +so first if you rewrite your metric in +terms of capital t + + align:start position:0% +terms of capital t + + + align:start position:0% +terms of capital t +and capital r what you get + + align:start position:0% + + + + align:start position:0% + +is a form that has no singularities it's + + align:start position:0% +is a form that has no singularities it's + + + align:start position:0% +is a form that has no singularities it's +well behaved + + align:start position:0% +well behaved + + + align:start position:0% +well behaved +everywhere except that r equals zero + + align:start position:0% + + + + align:start position:0% + +so you get a you do get a singularity + + align:start position:0% +so you get a you do get a singularity + + + align:start position:0% +so you get a you do get a singularity +there things blow up as + + align:start position:0% +there things blow up as + + + align:start position:0% +there things blow up as +r goes to zero + + align:start position:0% + + + + align:start position:0% + +there's no other coordinate pathologies + + align:start position:0% + + + + align:start position:0% + +and then you get sort of an angular + + align:start position:0% +and then you get sort of an angular + + + align:start position:0% +and then you get sort of an angular +sector it's actually cleanest in terms + + align:start position:0% +sector it's actually cleanest in terms + + + align:start position:0% +sector it's actually cleanest in terms +of the schwarzschild radius r so we'll + + align:start position:0% +of the schwarzschild radius r so we'll + + + align:start position:0% +of the schwarzschild radius r so we'll +leave it in terms of that + + align:start position:0% +leave it in terms of that + + + align:start position:0% +leave it in terms of that +one thing which is nice is notice that + + align:start position:0% +one thing which is nice is notice that + + + align:start position:0% +one thing which is nice is notice that +radial + + align:start position:0% +radial + + + align:start position:0% +radial +geodesics radial excuse me radial null + + align:start position:0% +geodesics radial excuse me radial null + + + align:start position:0% +geodesics radial excuse me radial null +judaism + + align:start position:0% + + + + align:start position:0% + +they simply obey + + align:start position:0% + + + + align:start position:0% + +dt equals plus or minus dr everywhere + + align:start position:0% +dt equals plus or minus dr everywhere + + + align:start position:0% +dt equals plus or minus dr everywhere +okay the only place where you run into a + + align:start position:0% +okay the only place where you run into a + + + align:start position:0% +okay the only place where you run into a +little bit of problem is + + align:start position:0% +little bit of problem is + + + align:start position:0% +little bit of problem is +as r goes to zero + + align:start position:0% +as r goes to zero + + + align:start position:0% +as r goes to zero +and uh that's special okay so i got that + + align:start position:0% +and uh that's special okay so i got that + + + align:start position:0% +and uh that's special okay so i got that +just by setting + + align:start position:0% +just by setting + + + align:start position:0% +just by setting +dx squared equals zero it's radial so my + + align:start position:0% +dx squared equals zero it's radial so my + + + align:start position:0% +dx squared equals zero it's radial so my +d omega goes to zero + + align:start position:0% +d omega goes to zero + + + align:start position:0% +d omega goes to zero +and then just dt equals plus or minus + + align:start position:0% +and then just dt equals plus or minus + + + align:start position:0% +and then just dt equals plus or minus +dr so that's really nice okay and we're + + align:start position:0% +dr so that's really nice okay and we're + + + align:start position:0% +dr so that's really nice okay and we're +i'm going to make a sketch in just a + + align:start position:0% +i'm going to make a sketch in just a + + + align:start position:0% +i'm going to make a sketch in just a +moment + + align:start position:0% +moment + + + align:start position:0% +moment +and the fact that i know light always + + align:start position:0% +and the fact that i know light always + + + align:start position:0% +and the fact that i know light always +moves along + + align:start position:0% +moves along + + + align:start position:0% +moves along +45 degree lines in this coordinate + + align:start position:0% +45 degree lines in this coordinate + + + align:start position:0% +45 degree lines in this coordinate +system is going to help me to understand + + align:start position:0% +system is going to help me to understand + + + align:start position:0% +system is going to help me to understand +the causal structure + + align:start position:0% +the causal structure + + + align:start position:0% +the causal structure +of this space time + + align:start position:0% + + + + align:start position:0% + +the causal structure is what i mean by + + align:start position:0% +the causal structure is what i mean by + + + align:start position:0% +the causal structure is what i mean by +which events can + + align:start position:0% +which events can + + + align:start position:0% +which events can +influence other events + + align:start position:0% +influence other events + + + align:start position:0% +influence other events +what can exert a causal influence on + + align:start position:0% +what can exert a causal influence on + + + align:start position:0% +what can exert a causal influence on +what + + align:start position:0% + + + + align:start position:0% + +so as i move on i'm going to make a + + align:start position:0% +so as i move on i'm going to make a + + + align:start position:0% +so as i move on i'm going to make a +sketch in just a moment + + align:start position:0% +sketch in just a moment + + + align:start position:0% +sketch in just a moment +i want to highlight a couple of + + align:start position:0% +i want to highlight a couple of + + + align:start position:0% +i want to highlight a couple of +behaviors + + align:start position:0% +behaviors + + + align:start position:0% +behaviors +that we see that are really sort of + + align:start position:0% +that we see that are really sort of + + + align:start position:0% +that we see that are really sort of +called out in + + align:start position:0% +called out in + + + align:start position:0% +called out in +uh this mapping between the two + + align:start position:0% +uh this mapping between the two + + + align:start position:0% +uh this mapping between the two +coordinate systems + + align:start position:0% + + + + align:start position:0% + +so notice that a surface + + align:start position:0% + + + + align:start position:0% + +of constant short shield radius constant + + align:start position:0% +of constant short shield radius constant + + + align:start position:0% +of constant short shield radius constant +r + + align:start position:0% + + + + align:start position:0% + +forms a hyperbola + + align:start position:0% + + + + align:start position:0% + +in the kruskal shakira's coordinates + + align:start position:0% + + + + align:start position:0% + +okay um notice + + align:start position:0% +okay um notice + + + align:start position:0% +okay um notice +that lines excuse me surfaces of + + align:start position:0% +that lines excuse me surfaces of + + + align:start position:0% +that lines excuse me surfaces of +constant time + + align:start position:0% +constant time + + + align:start position:0% +constant time +they form lines in that they form lines + + align:start position:0% +they form lines in that they form lines + + + align:start position:0% +they form lines in that they form lines +of slope t over r equal to some constant + + align:start position:0% + + + + align:start position:0% + +so they are lines with + + align:start position:0% + + + + align:start position:0% + +t over r equaling + + align:start position:0% +t over r equaling + + + align:start position:0% +t over r equaling +on the exterior let's just focus on the + + align:start position:0% +on the exterior let's just focus on the + + + align:start position:0% +on the exterior let's just focus on the +exterior they have a slope + + align:start position:0% +exterior they have a slope + + + align:start position:0% +exterior they have a slope +that's given by the tangent excuse me + + align:start position:0% +that's given by the tangent excuse me + + + align:start position:0% +that's given by the tangent excuse me +the hyperbolic tangent of t over four gm + + align:start position:0% + + + + align:start position:0% + +okay on the interior replaced with + + align:start position:0% +okay on the interior replaced with + + + align:start position:0% +okay on the interior replaced with +cotangent + + align:start position:0% +cotangent + + + align:start position:0% +cotangent +hyperbolic cotangent + + align:start position:0% + + + + align:start position:0% + +the last thing which i'd like to note + + align:start position:0% +the last thing which i'd like to note + + + align:start position:0% +the last thing which i'd like to note +before i make a sketch here + + align:start position:0% +before i make a sketch here + + + align:start position:0% +before i make a sketch here +is let's look at this special surface of + + align:start position:0% +is let's look at this special surface of + + + align:start position:0% +is let's look at this special surface of +infinite redshift + + align:start position:0% +infinite redshift + + + align:start position:0% +infinite redshift +this event horizon + + align:start position:0% + + + + align:start position:0% + +so if i plug in + + align:start position:0% + + + + align:start position:0% + +r equals 2gm + + align:start position:0% + + + + align:start position:0% + +plug this in over here i get t squared + + align:start position:0% +plug this in over here i get t squared + + + align:start position:0% +plug this in over here i get t squared +minus r squared equals + + align:start position:0% +minus r squared equals + + + align:start position:0% +minus r squared equals +zero this is the asymptotic limit of + + align:start position:0% +zero this is the asymptotic limit of + + + align:start position:0% +zero this is the asymptotic limit of +those hyperbole they just become + + align:start position:0% +those hyperbole they just become + + + align:start position:0% +those hyperbole they just become +lines + + align:start position:0% + + + + align:start position:0% + +t equals plus or minus r so + + align:start position:0% +t equals plus or minus r so + + + align:start position:0% +t equals plus or minus r so +the event horizon in this coordinate + + align:start position:0% +the event horizon in this coordinate + + + align:start position:0% +the event horizon in this coordinate +representation is just going to be a + + align:start position:0% +representation is just going to be a + + + align:start position:0% +representation is just going to be a +pair of lines + + align:start position:0% +pair of lines + + + align:start position:0% +pair of lines +uh crossing in the origin of these + + align:start position:0% +uh crossing in the origin of these + + + align:start position:0% +uh crossing in the origin of these +coordinate systems + + align:start position:0% +coordinate systems + + + align:start position:0% +coordinate systems +okay play our 45 degree lines crossing + + align:start position:0% +okay play our 45 degree lines crossing + + + align:start position:0% +okay play our 45 degree lines crossing +the origin of this coordinate system + + align:start position:0% +the origin of this coordinate system + + + align:start position:0% +the origin of this coordinate system +notice also that t + + align:start position:0% +notice also that t + + + align:start position:0% +notice also that t +equals plus or minus r this corresponds + + align:start position:0% +equals plus or minus r this corresponds + + + align:start position:0% +equals plus or minus r this corresponds +to short shield t going to + + align:start position:0% +to short shield t going to + + + align:start position:0% +to short shield t going to +plus or minus infinity okay so this + + align:start position:0% +plus or minus infinity okay so this + + + align:start position:0% +plus or minus infinity okay so this +indeed is a weird singular limit + + align:start position:0% +indeed is a weird singular limit + + + align:start position:0% +indeed is a weird singular limit +of the time coordinate of the short + + align:start position:0% +of the time coordinate of the short + + + align:start position:0% +of the time coordinate of the short +shield time coordinate + + align:start position:0% +shield time coordinate + + + align:start position:0% +shield time coordinate +so i have you can find much prettier + + align:start position:0% +so i have you can find much prettier + + + align:start position:0% +so i have you can find much prettier +versions + + align:start position:0% +versions + + + align:start position:0% +versions +of this figure than the one i'm about to + + align:start position:0% +of this figure than the one i'm about to + + + align:start position:0% +of this figure than the one i'm about to +attempt to sketch + + align:start position:0% +attempt to sketch + + + align:start position:0% +attempt to sketch +let's see what i can do with this so + + align:start position:0% + + + + align:start position:0% + +horizontal will be the kruskal shakira's + + align:start position:0% +horizontal will be the kruskal shakira's + + + align:start position:0% +horizontal will be the kruskal shakira's +coordinate r vertical will be the + + align:start position:0% +coordinate r vertical will be the + + + align:start position:0% +coordinate r vertical will be the +coordinate + + align:start position:0% +coordinate + + + align:start position:0% +coordinate +t + + align:start position:0% + + + + align:start position:0% + +here is the event horizon + + align:start position:0% +here is the event horizon + + + align:start position:0% +here is the event horizon +r equals t or + + align:start position:0% +r equals t or + + + align:start position:0% +r equals t or +r equals little r equals 2 gm + + align:start position:0% +r equals little r equals 2 gm + + + align:start position:0% +r equals little r equals 2 gm +some different surface + + align:start position:0% + + + + align:start position:0% + +of r equal to some constant value + + align:start position:0% +of r equal to some constant value + + + align:start position:0% +of r equal to some constant value +greater than + + align:start position:0% +greater than + + + align:start position:0% +greater than +2g m will live on a hyperbola like so + + align:start position:0% + + + + align:start position:0% + +some value of r equals constant but less + + align:start position:0% +some value of r equals constant but less + + + align:start position:0% +some value of r equals constant but less +than 2 gm + + align:start position:0% +than 2 gm + + + align:start position:0% +than 2 gm +lies on a hyperbola like so + + align:start position:0% + + + + align:start position:0% + +in particular there is one special + + align:start position:0% +in particular there is one special + + + align:start position:0% +in particular there is one special +hyperbola corresponding to r + + align:start position:0% +hyperbola corresponding to r + + + align:start position:0% +hyperbola corresponding to r +equals zero + + align:start position:0% + + + + align:start position:0% + +and this + + align:start position:0% + + + + align:start position:0% + +this is where my artistry is going to + + align:start position:0% +this is where my artistry is going to + + + align:start position:0% +this is where my artistry is going to +truly fail me + + align:start position:0% +truly fail me + + + align:start position:0% +truly fail me +this is an infinite title singularity + + align:start position:0% +this is an infinite title singularity + + + align:start position:0% +this is an infinite title singularity +okay now the thing which is particularly + + align:start position:0% +okay now the thing which is particularly + + + align:start position:0% +okay now the thing which is particularly +useful + + align:start position:0% +useful + + + align:start position:0% +useful +about this on this particular coordinate + + align:start position:0% +about this on this particular coordinate + + + align:start position:0% +about this on this particular coordinate +system is remember + + align:start position:0% +system is remember + + + align:start position:0% +system is remember +light always moves in the capital r + + align:start position:0% +light always moves in the capital r + + + align:start position:0% +light always moves in the capital r +capital t coordinates it always moves on + + align:start position:0% +capital t coordinates it always moves on + + + align:start position:0% +capital t coordinates it always moves on +lines + + align:start position:0% +lines + + + align:start position:0% +lines +that go dt equals plus or minus dr + + align:start position:0% +that go dt equals plus or minus dr + + + align:start position:0% +that go dt equals plus or minus dr +and so what you can see is that if i + + align:start position:0% +and so what you can see is that if i + + + align:start position:0% +and so what you can see is that if i +imagine i start + + align:start position:0% +imagine i start + + + align:start position:0% +imagine i start +here and i send out a little light pulse + + align:start position:0% +here and i send out a little light pulse + + + align:start position:0% +here and i send out a little light pulse +okay a radially outgoing light pulse + + align:start position:0% + + + + align:start position:0% + +it'll always go away and uh + + align:start position:0% +it'll always go away and uh + + + align:start position:0% +it'll always go away and uh +you know go to larger and larger values + + align:start position:0% +you know go to larger and larger values + + + align:start position:0% +you know go to larger and larger values +of r + + align:start position:0% +of r + + + align:start position:0% +of r +just sort of you know constantly moves + + align:start position:0% +just sort of you know constantly moves + + + align:start position:0% +just sort of you know constantly moves +along this particular + + align:start position:0% +along this particular + + + align:start position:0% +along this particular +trajectory let me write out again what + + align:start position:0% +trajectory let me write out again what + + + align:start position:0% +trajectory let me write out again what +i'm doing here + + align:start position:0% +i'm doing here + + + align:start position:0% +i'm doing here +so a radial outgoing + + align:start position:0% +so a radial outgoing + + + align:start position:0% +so a radial outgoing +light ray + + align:start position:0% + + + + align:start position:0% + +it will follow dt equals dr + + align:start position:0% +it will follow dt equals dr + + + align:start position:0% +it will follow dt equals dr +but notice this line goes parallel to + + align:start position:0% +but notice this line goes parallel to + + + align:start position:0% +but notice this line goes parallel to +the event horizon + + align:start position:0% +the event horizon + + + align:start position:0% +the event horizon +if i am on the inside of this guy and i + + align:start position:0% +if i am on the inside of this guy and i + + + align:start position:0% +if i am on the inside of this guy and i +try to make a light pulse that goes + + align:start position:0% +try to make a light pulse that goes + + + align:start position:0% +try to make a light pulse that goes +outside points in the radial direction + + align:start position:0% +outside points in the radial direction + + + align:start position:0% +outside points in the radial direction +all it does is in these coordinates it + + align:start position:0% +all it does is in these coordinates it + + + align:start position:0% +all it does is in these coordinates it +moves parallel to the event horizon + + align:start position:0% +moves parallel to the event horizon + + + align:start position:0% +moves parallel to the event horizon +it can never cross it and in fact + + align:start position:0% +it can never cross it and in fact + + + align:start position:0% +it can never cross it and in fact +because this is a hyperbola + + align:start position:0% +because this is a hyperbola + + + align:start position:0% +because this is a hyperbola +one finds that even though you have + + align:start position:0% +one finds that even though you have + + + align:start position:0% +one finds that even though you have +tried to make this guy + + align:start position:0% +tried to make this guy + + + align:start position:0% +tried to make this guy +as outgoing as outgoing can be it will + + align:start position:0% +as outgoing as outgoing can be it will + + + align:start position:0% +as outgoing as outgoing can be it will +eventually + + align:start position:0% +eventually + + + align:start position:0% +eventually +intersect the r equals zero + + align:start position:0% +intersect the r equals zero + + + align:start position:0% +intersect the r equals zero +title singularity + + align:start position:0% + + + + align:start position:0% + +since i cannot have any event here + + align:start position:0% +since i cannot have any event here + + + align:start position:0% +since i cannot have any event here +that communicates with any event on the + + align:start position:0% +that communicates with any event on the + + + align:start position:0% +that communicates with any event on the +other side of this + + align:start position:0% +other side of this + + + align:start position:0% +other side of this +this region + + align:start position:0% + + + + align:start position:0% + +everything at + + align:start position:0% +everything at + + + align:start position:0% +everything at +r less than 2m + + align:start position:0% +r less than 2m + + + align:start position:0% +r less than 2m +less than 2 gm + + align:start position:0% +less than 2 gm + + + align:start position:0% +less than 2 gm +these will be causally disconnected + + align:start position:0% + + + + align:start position:0% + +not casually pardon me + + align:start position:0% + + + + align:start position:0% + +they are causally disconnected from the + + align:start position:0% +they are causally disconnected from the + + + align:start position:0% +they are causally disconnected from the +world + + align:start position:0% + + + + align:start position:0% + +that lies outside of rh2 gm + + align:start position:0% + + + + align:start position:0% + +so in my notes and in carol's textbook + + align:start position:0% +so in my notes and in carol's textbook + + + align:start position:0% +so in my notes and in carol's textbook +there's another coordinate system that + + align:start position:0% +there's another coordinate system that + + + align:start position:0% +there's another coordinate system that +you can do + + align:start position:0% +you can do + + + align:start position:0% +you can do +which essentially takes points that are + + align:start position:0% +which essentially takes points that are + + + align:start position:0% +which essentially takes points that are +infinitely far away and brings them into + + align:start position:0% +infinitely far away and brings them into + + + align:start position:0% +infinitely far away and brings them into +a finite coordinate + + align:start position:0% +a finite coordinate + + + align:start position:0% +a finite coordinate +uh location um and those + + align:start position:0% +uh location um and those + + + align:start position:0% +uh location um and those +that that final thing is what's known as + + align:start position:0% +that that final thing is what's known as + + + align:start position:0% +that that final thing is what's known as +append it's puts in what are called + + align:start position:0% +append it's puts in what are called + + + align:start position:0% +append it's puts in what are called +penrose coordinates and allows you to + + align:start position:0% +penrose coordinates and allows you to + + + align:start position:0% +penrose coordinates and allows you to +make what's called the penrose diagram + + align:start position:0% +make what's called the penrose diagram + + + align:start position:0% +make what's called the penrose diagram +uh which displays in a very simple way + + align:start position:0% +uh which displays in a very simple way + + + align:start position:0% +uh which displays in a very simple way +how different events are either + + align:start position:0% +how different events are either + + + align:start position:0% +how different events are either +causally connected or causally + + align:start position:0% +causally connected or causally + + + align:start position:0% +causally connected or causally +disconnected from the others + + align:start position:0% +disconnected from the others + + + align:start position:0% +disconnected from the others +fairly advanced stuff not important but + + align:start position:0% +fairly advanced stuff not important but + + + align:start position:0% +fairly advanced stuff not important but +many of you may find it interesting + + align:start position:0% +many of you may find it interesting + + + align:start position:0% +many of you may find it interesting +happy to talk further once we all have + + align:start position:0% +happy to talk further once we all have + + + align:start position:0% +happy to talk further once we all have +the bandwidth to have those kinds of + + align:start position:0% +the bandwidth to have those kinds of + + + align:start position:0% +the bandwidth to have those kinds of +conversations + + align:start position:0% +conversations + + + align:start position:0% +conversations +[Applause] + + align:start position:0% + + + + align:start position:0% + +so let me summarize + + align:start position:0% + + + + align:start position:0% + +so the summary is that this space time + + align:start position:0% +so the summary is that this space time + + + align:start position:0% +so the summary is that this space time +so we + + align:start position:0% +so we + + + align:start position:0% +so we +earlier we were looking at the space + + align:start position:0% +earlier we were looking at the space + + + align:start position:0% +earlier we were looking at the space +time of a spherically symmetric + + align:start position:0% +time of a spherically symmetric + + + align:start position:0% +time of a spherically symmetric +fluid object uh we found a particularly + + align:start position:0% +fluid object uh we found a particularly + + + align:start position:0% +fluid object uh we found a particularly +clean form for the exterior of that + + align:start position:0% +clean form for the exterior of that + + + align:start position:0% +clean form for the exterior of that +object where it was a vacuum solution + + align:start position:0% + + + + align:start position:0% + +if we imagine a space time that has this + + align:start position:0% +if we imagine a space time that has this + + + align:start position:0% +if we imagine a space time that has this +everywhere then we get + + align:start position:0% + + + + align:start position:0% + +this solution that we call a black hole + + align:start position:0% +this solution that we call a black hole + + + align:start position:0% +this solution that we call a black hole +okay so i emphasize this is vacuum + + align:start position:0% +okay so i emphasize this is vacuum + + + align:start position:0% +okay so i emphasize this is vacuum +everywhere but + + align:start position:0% +everywhere but + + + align:start position:0% +everywhere but +sort of the the analysis kind of goes to + + align:start position:0% +sort of the the analysis kind of goes to + + + align:start position:0% +sort of the the analysis kind of goes to +hell at r equals zero so there's some + + align:start position:0% +hell at r equals zero so there's some + + + align:start position:0% +hell at r equals zero so there's some +singular field equations there trying to + + align:start position:0% +singular field equations there trying to + + + align:start position:0% +singular field equations there trying to +describe the stress energy + + align:start position:0% +describe the stress energy + + + align:start position:0% +describe the stress energy +its behavior as you approach there uh + + align:start position:0% +its behavior as you approach there uh + + + align:start position:0% +its behavior as you approach there uh +let's just say we're not quite sure + + align:start position:0% +let's just say we're not quite sure + + + align:start position:0% +let's just say we're not quite sure +what's going on + + align:start position:0% + + + + align:start position:0% + +in this coordinate system we see + + align:start position:0% +in this coordinate system we see + + + align:start position:0% +in this coordinate system we see +weird things happening as we approach + + align:start position:0% +weird things happening as we approach + + + align:start position:0% +weird things happening as we approach +equals 2g m this is simply a coordinate + + align:start position:0% +equals 2g m this is simply a coordinate + + + align:start position:0% +equals 2g m this is simply a coordinate +singularity there's really nothing going + + align:start position:0% +singularity there's really nothing going + + + align:start position:0% +singularity there's really nothing going +bad with the + + align:start position:0% +bad with the + + + align:start position:0% +bad with the +physics here but our attempt to use + + align:start position:0% +physics here but our attempt to use + + + align:start position:0% +physics here but our attempt to use +a time coordinate that's based on + + align:start position:0% +a time coordinate that's based on + + + align:start position:0% +a time coordinate that's based on +essentially the way light moves in empty + + align:start position:0% +essentially the way light moves in empty + + + align:start position:0% +essentially the way light moves in empty +space it's failing in this region + + align:start position:0% +space it's failing in this region + + + align:start position:0% +space it's failing in this region +and all of this lecture is about + + align:start position:0% +and all of this lecture is about + + + align:start position:0% +and all of this lecture is about +uncovering this and seeing that + + align:start position:0% +uncovering this and seeing that + + + align:start position:0% +uncovering this and seeing that +in fact this is a surface of infinite + + align:start position:0% +in fact this is a surface of infinite + + + align:start position:0% +in fact this is a surface of infinite +redshift + + align:start position:0% +redshift + + + align:start position:0% +redshift +uh beyond which things cannot + + align:start position:0% +uh beyond which things cannot + + + align:start position:0% +uh beyond which things cannot +communicate + + align:start position:0% +communicate + + + align:start position:0% +communicate +so + + align:start position:0% + + + + align:start position:0% + +this is one of the big discoveries that + + align:start position:0% +this is one of the big discoveries that + + + align:start position:0% +this is one of the big discoveries that +came out of general relativity + + align:start position:0% +came out of general relativity + + + align:start position:0% +came out of general relativity +okay this creature we call the black + + align:start position:0% +okay this creature we call the black + + + align:start position:0% +okay this creature we call the black +hole + + align:start position:0% +hole + + + align:start position:0% +hole +it is not the only solution in the + + align:start position:0% +it is not the only solution in the + + + align:start position:0% +it is not the only solution in the +einstein field equations that we call a + + align:start position:0% +einstein field equations that we call a + + + align:start position:0% +einstein field equations that we call a +black hole + + align:start position:0% +black hole + + + align:start position:0% +black hole +let me talk briefly about two others + + align:start position:0% + + + + align:start position:0% + +so another one has a space time that + + align:start position:0% +so another one has a space time that + + + align:start position:0% +so another one has a space time that +looks like this + + align:start position:0% + + + + align:start position:0% + +okay so where'd this come from well + + align:start position:0% +okay so where'd this come from well + + + align:start position:0% +okay so where'd this come from well +suppose i bung this through the einstein + + align:start position:0% +suppose i bung this through the einstein + + + align:start position:0% +suppose i bung this through the einstein +field equations + + align:start position:0% +field equations + + + align:start position:0% +field equations +what i find is that it comes from + + align:start position:0% +what i find is that it comes from + + + align:start position:0% +what i find is that it comes from +a non-zero stress energy tensor in fact + + align:start position:0% +a non-zero stress energy tensor in fact + + + align:start position:0% +a non-zero stress energy tensor in fact +it's a stress energy tensor + + align:start position:0% +it's a stress energy tensor + + + align:start position:0% +it's a stress energy tensor +it looks like this + + align:start position:0% + + + + align:start position:0% + +this is the stress energy tensor of a + + align:start position:0% +this is the stress energy tensor of a + + + align:start position:0% +this is the stress energy tensor of a +coulomb + + align:start position:0% +coulomb + + + align:start position:0% +coulomb +electric field with total charge q + + align:start position:0% + + + + align:start position:0% + +this represents a charged black hole + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +whoops uh + + align:start position:0% +whoops uh + + + align:start position:0% +whoops uh +this turns out if you analyze this thing + + align:start position:0% +this turns out if you analyze this thing + + + align:start position:0% +this turns out if you analyze this thing +carefully you find + + align:start position:0% +carefully you find + + + align:start position:0% +carefully you find +it has an event horizon + + align:start position:0% +it has an event horizon + + + align:start position:0% +it has an event horizon +it turns out to be located at g + + align:start position:0% + + + + align:start position:0% + +there's a quantity that involves square + + align:start position:0% +there's a quantity that involves square + + + align:start position:0% +there's a quantity that involves square +root of m squared minus q squared + + align:start position:0% +root of m squared minus q squared + + + align:start position:0% +root of m squared minus q squared +now if q these are in don't even ask me + + align:start position:0% +now if q these are in don't even ask me + + + align:start position:0% +now if q these are in don't even ask me +what the units are that this is being + + align:start position:0% +what the units are that this is being + + + align:start position:0% +what the units are that this is being +measured in + + align:start position:0% +measured in + + + align:start position:0% +measured in +they're pretty goofy units but if in + + align:start position:0% +they're pretty goofy units but if in + + + align:start position:0% +they're pretty goofy units but if in +these units + + align:start position:0% +these units + + + align:start position:0% +these units +q the magnitude of q is greater than m + + align:start position:0% +q the magnitude of q is greater than m + + + align:start position:0% +q the magnitude of q is greater than m +there's no horizon there is still + + align:start position:0% +there's no horizon there is still + + + align:start position:0% +there's no horizon there is still +however + + align:start position:0% +however + + + align:start position:0% +however +an infinite title singularity at r + + align:start position:0% +an infinite title singularity at r + + + align:start position:0% +an infinite title singularity at r +equals zero + + align:start position:0% +equals zero + + + align:start position:0% +equals zero +so such a solution would give us what is + + align:start position:0% +so such a solution would give us what is + + + align:start position:0% +so such a solution would give us what is +known as a naked singularity + + align:start position:0% +known as a naked singularity + + + align:start position:0% +known as a naked singularity +um i have a few few comments and i have + + align:start position:0% +um i have a few few comments and i have + + + align:start position:0% +um i have a few few comments and i have +a couple notes on these but they're not + + align:start position:0% +a couple notes on these but they're not + + + align:start position:0% +a couple notes on these but they're not +as important as + + align:start position:0% +as important as + + + align:start position:0% +as important as +other things i'd like to talk about you + + align:start position:0% +other things i'd like to talk about you + + + align:start position:0% +other things i'd like to talk about you +might wonder where does that + + align:start position:0% +might wonder where does that + + + align:start position:0% +might wonder where does that +r horizon actually come from okay that + + align:start position:0% +r horizon actually come from okay that + + + align:start position:0% +r horizon actually come from okay that +is what you get when you find the root + + align:start position:0% +is what you get when you find the root + + + align:start position:0% +is what you get when you find the root +where you look for the place where + + align:start position:0% +where you look for the place where + + + align:start position:0% +where you look for the place where +the metric function vanishes okay notice + + align:start position:0% +the metric function vanishes okay notice + + + align:start position:0% +the metric function vanishes okay notice +there's only one metric function that + + align:start position:0% +there's only one metric function that + + + align:start position:0% +there's only one metric function that +appears in there 1 minus 2 gm over r + + align:start position:0% +appears in there 1 minus 2 gm over r + + + align:start position:0% +appears in there 1 minus 2 gm over r +plus q squared over r squared so in + + align:start position:0% +plus q squared over r squared so in + + + align:start position:0% +plus q squared over r squared so in +general + + align:start position:0% +general + + + align:start position:0% +general +if you have what's known as a stationary + + align:start position:0% +if you have what's known as a stationary + + + align:start position:0% +if you have what's known as a stationary +space time + + align:start position:0% +space time + + + align:start position:0% +space time +you can find coordinates such that + + align:start position:0% +you can find coordinates such that + + + align:start position:0% +you can find coordinates such that +surfaces of constant r are + + align:start position:0% +surfaces of constant r are + + + align:start position:0% +surfaces of constant r are +space-like surfaces + + align:start position:0% +space-like surfaces + + + align:start position:0% +space-like surfaces +if you look for the place where a + + align:start position:0% +if you look for the place where a + + + align:start position:0% +if you look for the place where a +surface of constant r + + align:start position:0% +surface of constant r + + + align:start position:0% +surface of constant r +makes a transition from being a + + align:start position:0% +makes a transition from being a + + + align:start position:0% +makes a transition from being a +space-like surface + + align:start position:0% +space-like surface + + + align:start position:0% +space-like surface +to being a null surface + + align:start position:0% +to being a null surface + + + align:start position:0% +to being a null surface +that tells you that you have located + + align:start position:0% +that tells you that you have located + + + align:start position:0% +that tells you that you have located +that tells you that you have located + + align:start position:0% +that tells you that you have located + + + align:start position:0% +that tells you that you have located +a an event horizon + + align:start position:0% + + + + align:start position:0% + +okay this is discussed in a little bit + + align:start position:0% +okay this is discussed in a little bit + + + align:start position:0% +okay this is discussed in a little bit +more detail in my notes there's also + + align:start position:0% +more detail in my notes there's also + + + align:start position:0% +more detail in my notes there's also +some very nice discussion + + align:start position:0% +some very nice discussion + + + align:start position:0% +some very nice discussion +in carol's textbook what it boils down + + align:start position:0% +in carol's textbook what it boils down + + + align:start position:0% +in carol's textbook what it boils down +to + + align:start position:0% +to + + + align:start position:0% +to +is that if you can find a radial + + align:start position:0% +is that if you can find a radial + + + align:start position:0% +is that if you can find a radial +coordinate that allows you to do this + + align:start position:0% +coordinate that allows you to do this + + + align:start position:0% +coordinate that allows you to do this +then the condition g upstairs r upstairs + + align:start position:0% +then the condition g upstairs r upstairs + + + align:start position:0% +then the condition g upstairs r upstairs +r + + align:start position:0% +r + + + align:start position:0% +r +equals zero defines your event horizon + + align:start position:0% +equals zero defines your event horizon + + + align:start position:0% +equals zero defines your event horizon +okay + + align:start position:0% +okay + + + align:start position:0% +okay +just so happens that it's also equal to + + align:start position:0% +just so happens that it's also equal to + + + align:start position:0% +just so happens that it's also equal to +g downstairs t + + align:start position:0% +g downstairs t + + + align:start position:0% +g downstairs t +downstairs t equals zero in this case + + align:start position:0% +downstairs t equals zero in this case + + + align:start position:0% +downstairs t equals zero in this case +and in the schwarzschild case + + align:start position:0% +and in the schwarzschild case + + + align:start position:0% +and in the schwarzschild case +but it's not like that for all black + + align:start position:0% +but it's not like that for all black + + + align:start position:0% +but it's not like that for all black +holes that you can write down + + align:start position:0% +holes that you can write down + + + align:start position:0% +holes that you can write down +in particular let me write down the + + align:start position:0% +in particular let me write down the + + + align:start position:0% +in particular let me write down the +final black hole space time + + align:start position:0% +final black hole space time + + + align:start position:0% +final black hole space time +i want to discuss in this lecture + + align:start position:0% + + + + align:start position:0% + +this one's going to take a minute so + + align:start position:0% +this one's going to take a minute so + + + align:start position:0% +this one's going to take a minute so +bear with me + + align:start position:0% + + + + align:start position:0% + +you + + align:start position:0% + + + + align:start position:0% + +okay so in this space time + + align:start position:0% +okay so in this space time + + + align:start position:0% +okay so in this space time +the symbol delta i've written here this + + align:start position:0% +the symbol delta i've written here this + + + align:start position:0% +the symbol delta i've written here this +is r squared minus + + align:start position:0% +is r squared minus + + + align:start position:0% +is r squared minus +2 gm r plus a squared + + align:start position:0% +2 gm r plus a squared + + + align:start position:0% +2 gm r plus a squared +rho squared is r squared plus + + align:start position:0% +rho squared is r squared plus + + + align:start position:0% +rho squared is r squared plus +a squared + + align:start position:0% + + + + align:start position:0% + +cosine of squared of theta + + align:start position:0% + + + + align:start position:0% + +this thing turns out if you uh + + align:start position:0% +this thing turns out if you uh + + + align:start position:0% +this thing turns out if you uh +compute the inverse metric components + + align:start position:0% +compute the inverse metric components + + + align:start position:0% +compute the inverse metric components +you find that g upstairs are + + align:start position:0% +you find that g upstairs are + + + align:start position:0% +you find that g upstairs are +upstairs r is proportional to delta and + + align:start position:0% +upstairs r is proportional to delta and + + + align:start position:0% +upstairs r is proportional to delta and +so there's a horizon + + align:start position:0% + + + + align:start position:0% + +where delta equals zero + + align:start position:0% + + + + align:start position:0% + +ah sorry + + align:start position:0% + + + + align:start position:0% + +that turns out to be located a race that + + align:start position:0% +that turns out to be located a race that + + + align:start position:0% +that turns out to be located a race that +looks like this + + align:start position:0% + + + + align:start position:0% + +this represents + + align:start position:0% +this represents + + + align:start position:0% +this represents +the space time of a spinning black hole + + align:start position:0% +the space time of a spinning black hole + + + align:start position:0% +the space time of a spinning black hole +it was discovered by roy kerr + + align:start position:0% + + + + align:start position:0% + +a mathematician from new zealand + + align:start position:0% + + + + align:start position:0% + +i think this was actually a big part of + + align:start position:0% +i think this was actually a big part of + + + align:start position:0% +i think this was actually a big part of +his phd work + + align:start position:0% + + + + align:start position:0% + +so it is known as a cur + + align:start position:0% +so it is known as a cur + + + align:start position:0% +so it is known as a cur +black hole the parameter a + + align:start position:0% + + + + align:start position:0% + +is related to the angular momentum the + + align:start position:0% +is related to the angular momentum the + + + align:start position:0% +is related to the angular momentum the +spin angular momentum of the black hole + + align:start position:0% +spin angular momentum of the black hole + + + align:start position:0% +spin angular momentum of the black hole +in the units that we measure these + + align:start position:0% +in the units that we measure these + + + align:start position:0% +in the units that we measure these +normalized to the mass + + align:start position:0% + + + + align:start position:0% + +so notice that in order for this to + + align:start position:0% +so notice that in order for this to + + + align:start position:0% +so notice that in order for this to +actually + + align:start position:0% +actually + + + align:start position:0% +actually +have a horizon + + align:start position:0% + + + + align:start position:0% + +you need that a to be less than or equal + + align:start position:0% +you need that a to be less than or equal + + + align:start position:0% +you need that a to be less than or equal +to + + align:start position:0% +to + + + align:start position:0% +to +gm if it saturates that bound + + align:start position:0% +gm if it saturates that bound + + + align:start position:0% +gm if it saturates that bound +then you get what's known as a maximal + + align:start position:0% +then you get what's known as a maximal + + + align:start position:0% +then you get what's known as a maximal +black hole + + align:start position:0% +black hole + + + align:start position:0% +black hole +so it has a couple of noteworthy + + align:start position:0% +so it has a couple of noteworthy + + + align:start position:0% +so it has a couple of noteworthy +features + + align:start position:0% + + + + align:start position:0% + +first it is not spherically + + align:start position:0% +first it is not spherically + + + align:start position:0% +first it is not spherically +symmetric + + align:start position:0% + + + + align:start position:0% + +okay if it were spherically symmetric we + + align:start position:0% +okay if it were spherically symmetric we + + + align:start position:0% +okay if it were spherically symmetric we +could write + + align:start position:0% +could write + + + align:start position:0% +could write +the d theta squared d phi squared piece + + align:start position:0% +the d theta squared d phi squared piece + + + align:start position:0% +the d theta squared d phi squared piece +we could find + + align:start position:0% +we could find + + + align:start position:0% +we could find +some radial coordinate such that + + align:start position:0% + + + + align:start position:0% + +there was some simple radius such that + + align:start position:0% + + + + align:start position:0% + +g theta theta was simply sine squared + + align:start position:0% +g theta theta was simply sine squared + + + align:start position:0% +g theta theta was simply sine squared +g theta theta this is the condition that + + align:start position:0% +g theta theta this is the condition that + + + align:start position:0% +g theta theta this is the condition that +defines spherical symmetry + + align:start position:0% +defines spherical symmetry + + + align:start position:0% +defines spherical symmetry +and uh there is no radial coordinates no + + align:start position:0% +and uh there is no radial coordinates no + + + align:start position:0% +and uh there is no radial coordinates no +angle independent radial coordinate that + + align:start position:0% +angle independent radial coordinate that + + + align:start position:0% +angle independent radial coordinate that +allows you to do that notice also that + + align:start position:0% +allows you to do that notice also that + + + align:start position:0% +allows you to do that notice also that +there is a connection + + align:start position:0% + + + + align:start position:0% + +in this coordinate system between t and + + align:start position:0% +in this coordinate system between t and + + + align:start position:0% +in this coordinate system between t and +phi + + align:start position:0% + + + + align:start position:0% + +gt phi is equal to -2 + + align:start position:0% + + + + align:start position:0% + +gm a r + + align:start position:0% + + + + align:start position:0% + +sine squared theta over r squared + + align:start position:0% +sine squared theta over r squared + + + align:start position:0% +sine squared theta over r squared +y minus two and not minus four well + + align:start position:0% +y minus two and not minus four well + + + align:start position:0% +y minus two and not minus four well +remember what i have there + + align:start position:0% +remember what i have there + + + align:start position:0% +remember what i have there +is g t phi d t d phi plus + + align:start position:0% +is g t phi d t d phi plus + + + align:start position:0% +is g t phi d t d phi plus +g phi t d v d t + + align:start position:0% +g phi t d v d t + + + align:start position:0% +g phi t d v d t +one can show that this term + + align:start position:0% +one can show that this term + + + align:start position:0% +one can show that this term +um it reflects the kind of physics in + + align:start position:0% +um it reflects the kind of physics in + + + align:start position:0% +um it reflects the kind of physics in +which + + align:start position:0% +which + + + align:start position:0% +which +the spin of the black hole introduces + + align:start position:0% +the spin of the black hole introduces + + + align:start position:0% +the spin of the black hole introduces +a spinning almost magnetic-like element + + align:start position:0% +a spinning almost magnetic-like element + + + align:start position:0% +a spinning almost magnetic-like element +to gravitation + + align:start position:0% +to gravitation + + + align:start position:0% +to gravitation +if you guys do the homework assignment + + align:start position:0% +if you guys do the homework assignment + + + align:start position:0% +if you guys do the homework assignment +i've assigned in which you compute + + align:start position:0% + + + + align:start position:0% + +the linearized effect on a space time of + + align:start position:0% +the linearized effect on a space time of + + + align:start position:0% +the linearized effect on a space time of +a spinning body + + align:start position:0% +a spinning body + + + align:start position:0% +a spinning body +you'll get a flavor of this okay this + + align:start position:0% +you'll get a flavor of this okay this + + + align:start position:0% +you'll get a flavor of this okay this +ends up giving you a + + align:start position:0% +ends up giving you a + + + align:start position:0% +ends up giving you a +that that calculation gives you a + + align:start position:0% +that that calculation gives you a + + + align:start position:0% +that that calculation gives you a +similar term in the space time + + align:start position:0% +similar term in the space time + + + align:start position:0% +similar term in the space time +uh which further analysis shows leads to + + align:start position:0% +uh which further analysis shows leads to + + + align:start position:0% +uh which further analysis shows leads to +bodies + + align:start position:0% +bodies + + + align:start position:0% +bodies +essentially what you find is that if you + + align:start position:0% +essentially what you find is that if you + + + align:start position:0% +essentially what you find is that if you +have an orbit + + align:start position:0% +have an orbit + + + align:start position:0% +have an orbit +that goes in the same sense as the body + + align:start position:0% +that goes in the same sense as the body + + + align:start position:0% +that goes in the same sense as the body +spin versus an orbit that goes in the + + align:start position:0% +spin versus an orbit that goes in the + + + align:start position:0% +spin versus an orbit that goes in the +opposite sense of the body spin + + align:start position:0% +opposite sense of the body spin + + + align:start position:0% +opposite sense of the body spin +there's a splitting in the orbit's + + align:start position:0% +there's a splitting in the orbit's + + + align:start position:0% +there's a splitting in the orbit's +properties due to that + + align:start position:0% +properties due to that + + + align:start position:0% +properties due to that +okay so it breaks the symmetry between + + align:start position:0% +okay so it breaks the symmetry between + + + align:start position:0% +okay so it breaks the symmetry between +what we call a pro-grade orbit + + align:start position:0% +what we call a pro-grade orbit + + + align:start position:0% +what we call a pro-grade orbit +and a retrograde orbit + + align:start position:0% +and a retrograde orbit + + + align:start position:0% +and a retrograde orbit +this is one of the most important + + align:start position:0% +this is one of the most important + + + align:start position:0% +this is one of the most important +solutions + + align:start position:0% +solutions + + + align:start position:0% +solutions +uh that we know of in general relativity + + align:start position:0% +uh that we know of in general relativity + + + align:start position:0% +uh that we know of in general relativity +because of result that i'm going to + + align:start position:0% +because of result that i'm going to + + + align:start position:0% +because of result that i'm going to +discuss now + + align:start position:0% +discuss now + + + align:start position:0% +discuss now +oh first of all i should mention that in + + align:start position:0% +oh first of all i should mention that in + + + align:start position:0% +oh first of all i should mention that in +fact you can combine + + align:start position:0% +fact you can combine + + + align:start position:0% +fact you can combine +charge with spin + + align:start position:0% + + + + align:start position:0% + +i'm not going to write down the result + + align:start position:0% +i'm not going to write down the result + + + align:start position:0% +i'm not going to write down the result +because it's + + align:start position:0% +because it's + + + align:start position:0% +because it's +just kind of messy but it does exist in + + align:start position:0% +just kind of messy but it does exist in + + + align:start position:0% +just kind of messy but it does exist in +closed form + + align:start position:0% + + + + align:start position:0% + +if you're interested in this read about + + align:start position:0% +if you're interested in this read about + + + align:start position:0% +if you're interested in this read about +what is called the + + align:start position:0% +what is called the + + + align:start position:0% +what is called the +kerr newman solution + + align:start position:0% + + + + align:start position:0% + +so we have your keeping score we have + + align:start position:0% +so we have your keeping score we have + + + align:start position:0% +so we have your keeping score we have +the spherically symmetric + + align:start position:0% +the spherically symmetric + + + align:start position:0% +the spherically symmetric +black hole which only has a mass you + + align:start position:0% +black hole which only has a mass you + + + align:start position:0% +black hole which only has a mass you +have the + + align:start position:0% +have the + + + align:start position:0% +have the +charge black hole whose name i forgot to + + align:start position:0% +charge black hole whose name i forgot to + + + align:start position:0% +charge black hole whose name i forgot to +list + + align:start position:0% +list + + + align:start position:0% +list +sorry about that this guy is known as + + align:start position:0% + + + + align:start position:0% + +the reisner + + align:start position:0% +the reisner + + + align:start position:0% +the reisner +reisner + + align:start position:0% + + + + align:start position:0% + +nordstrom black hole + + align:start position:0% +nordstrom black hole + + + align:start position:0% +nordstrom black hole +one of those o's i believe is supposed + + align:start position:0% +one of those o's i believe is supposed + + + align:start position:0% +one of those o's i believe is supposed +to have a stroke through it those who + + align:start position:0% +to have a stroke through it those who + + + align:start position:0% +to have a stroke through it those who +speak scandinavian languages + + align:start position:0% +speak scandinavian languages + + + align:start position:0% +speak scandinavian languages +can probably spell it and pronounce it + + align:start position:0% +can probably spell it and pronounce it + + + align:start position:0% +can probably spell it and pronounce it +better than i can + + align:start position:0% +better than i can + + + align:start position:0% +better than i can +so we have schwartshield which is only + + align:start position:0% +so we have schwartshield which is only + + + align:start position:0% +so we have schwartshield which is only +mass reisner nordstrom + + align:start position:0% +mass reisner nordstrom + + + align:start position:0% +mass reisner nordstrom +which is mass and charge ker which is + + align:start position:0% +which is mass and charge ker which is + + + align:start position:0% +which is mass and charge ker which is +mass and spin + + align:start position:0% +mass and spin + + + align:start position:0% +mass and spin +and car newman which is mass spin and + + align:start position:0% +and car newman which is mass spin and + + + align:start position:0% +and car newman which is mass spin and +charge you might start thinking all + + align:start position:0% +charge you might start thinking all + + + align:start position:0% +charge you might start thinking all +right well + + align:start position:0% +right well + + + align:start position:0% +right well +does this keep going do i have a + + align:start position:0% +does this keep going do i have a + + + align:start position:0% +does this keep going do i have a +solution for a black hole that's got + + align:start position:0% +solution for a black hole that's got + + + align:start position:0% +solution for a black hole that's got +you know + + align:start position:0% + + + + align:start position:0% + +northern hemisphere bigger than the + + align:start position:0% +northern hemisphere bigger than the + + + align:start position:0% +northern hemisphere bigger than the +southern hemisphere do i have to + + align:start position:0% +southern hemisphere do i have to + + + align:start position:0% +southern hemisphere do i have to +you know every time you think about + + align:start position:0% +you know every time you think about + + + align:start position:0% +you know every time you think about +adding a bit of extra schmutz to this + + align:start position:0% +adding a bit of extra schmutz to this + + + align:start position:0% +adding a bit of extra schmutz to this +thing + + align:start position:0% +thing + + + align:start position:0% +thing +do i need another solution well let me + + align:start position:0% +do i need another solution well let me + + + align:start position:0% +do i need another solution well let me +describe + + align:start position:0% +describe + + + align:start position:0% +describe +a remarkable theorem + + align:start position:0% + + + + align:start position:0% + +the only + + align:start position:0% + + + + align:start position:0% + +stationary + + align:start position:0% +stationary + + + align:start position:0% +stationary +space times + + align:start position:0% + + + + align:start position:0% + +in three plus one dimensions + + align:start position:0% + + + + align:start position:0% + +with event horizons + + align:start position:0% + + + + align:start position:0% + +are the kern newman black holes + + align:start position:0% + + + + align:start position:0% + +completely parameterized by mass + + align:start position:0% + + + + align:start position:0% + +spin and + + align:start position:0% +spin and + + + align:start position:0% +spin and +charge if you take that + + align:start position:0% +charge if you take that + + + align:start position:0% +charge if you take that +uh if you take your current urban solute + + align:start position:0% +uh if you take your current urban solute + + + align:start position:0% +uh if you take your current urban solute +current newman solution you set charge + + align:start position:0% +current newman solution you set charge + + + align:start position:0% +current newman solution you set charge +to zero you get ker + + align:start position:0% +to zero you get ker + + + align:start position:0% +to zero you get ker +if you take cur and you set spin to zero + + align:start position:0% +if you take cur and you set spin to zero + + + align:start position:0% +if you take cur and you set spin to zero +you get short shield + + align:start position:0% +you get short shield + + + align:start position:0% +you get short shield +so the current newman solution gives me + + align:start position:0% +so the current newman solution gives me + + + align:start position:0% +so the current newman solution gives me +something that includes these other ones + + align:start position:0% +something that includes these other ones + + + align:start position:0% +something that includes these other ones +as sort of a subset + + align:start position:0% +as sort of a subset + + + align:start position:0% +as sort of a subset +and what this theorem states is that the + + align:start position:0% +and what this theorem states is that the + + + align:start position:0% +and what this theorem states is that the +only so stationary + + align:start position:0% +only so stationary + + + align:start position:0% +only so stationary +means time independent + + align:start position:0% + + + + align:start position:0% + +so in other words the only space times + + align:start position:0% +so in other words the only space times + + + align:start position:0% +so in other words the only space times +that + + align:start position:0% +that + + + align:start position:0% +that +are not dynamically but that have event + + align:start position:0% +are not dynamically but that have event + + + align:start position:0% +are not dynamically but that have event +horizons + + align:start position:0% +horizons + + + align:start position:0% +horizons +at least with three space and one time + + align:start position:0% +at least with three space and one time + + + align:start position:0% +at least with three space and one time +dimension + + align:start position:0% +dimension + + + align:start position:0% +dimension +are the current newman black holes once + + align:start position:0% +are the current newman black holes once + + + align:start position:0% +are the current newman black holes once +you know these you have characterized + + align:start position:0% +you know these you have characterized + + + align:start position:0% +you know these you have characterized +all black holes you can care about and + + align:start position:0% +all black holes you can care about and + + + align:start position:0% +all black holes you can care about and +in fact + + align:start position:0% +in fact + + + align:start position:0% +in fact +in any astrophysical context + + align:start position:0% +in any astrophysical context + + + align:start position:0% +in any astrophysical context +any object any macroscopic object with + + align:start position:0% +any object any macroscopic object with + + + align:start position:0% +any object any macroscopic object with +charge + + align:start position:0% +charge + + + align:start position:0% +charge +is rapidly neutralized by ambient plasma + + align:start position:0% +is rapidly neutralized by ambient plasma + + + align:start position:0% +is rapidly neutralized by ambient plasma +that just sort of fills all of space + + align:start position:0% +that just sort of fills all of space + + + align:start position:0% +that just sort of fills all of space +and so this curve solution + + align:start position:0% +and so this curve solution + + + align:start position:0% +and so this curve solution +in fact gives an exact mathematical + + align:start position:0% +in fact gives an exact mathematical + + + align:start position:0% +in fact gives an exact mathematical +description + + align:start position:0% +description + + + align:start position:0% +description +to every black hole that we observe in + + align:start position:0% +to every black hole that we observe in + + + align:start position:0% +to every black hole that we observe in +the universe + + align:start position:0% +the universe + + + align:start position:0% +the universe +that is an amazing statement okay + + align:start position:0% +that is an amazing statement okay + + + align:start position:0% +that is an amazing statement okay +of course as a physicist you want to + + align:start position:0% +of course as a physicist you want to + + + align:start position:0% +of course as a physicist you want to +test this uh + + align:start position:0% +test this uh + + + align:start position:0% +test this uh +and this in fact is much of what my + + align:start position:0% +and this in fact is much of what my + + + align:start position:0% +and this in fact is much of what my +research and research of many of my + + align:start position:0% +research and research of many of my + + + align:start position:0% +research and research of many of my +colleagues is about can we actually + + align:start position:0% +colleagues is about can we actually + + + align:start position:0% +colleagues is about can we actually +formulate tests of this care hypothesis + + align:start position:0% +formulate tests of this care hypothesis + + + align:start position:0% +formulate tests of this care hypothesis +and many of us have spent our careers + + align:start position:0% +and many of us have spent our careers + + + align:start position:0% +and many of us have spent our careers +coming up with such things suffice it to + + align:start position:0% +coming up with such things suffice it to + + + align:start position:0% +coming up with such things suffice it to +say + + align:start position:0% +say + + + align:start position:0% +say +in the roughly negative five minutes i + + align:start position:0% +in the roughly negative five minutes i + + + align:start position:0% +in the roughly negative five minutes i +have left in this lecture + + align:start position:0% +have left in this lecture + + + align:start position:0% +have left in this lecture +that the current metric has survived + + align:start position:0% +that the current metric has survived + + + align:start position:0% +that the current metric has survived +every test that we have thrown at it + + align:start position:0% +every test that we have thrown at it + + + align:start position:0% +every test that we have thrown at it +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +so this is a this metric like i said + + align:start position:0% +so this is a this metric like i said + + + align:start position:0% +so this is a this metric like i said +was essentially derived by the + + align:start position:0% +was essentially derived by the + + + align:start position:0% +was essentially derived by the +mathematician roy kerr as his phd thesis + + align:start position:0% +mathematician roy kerr as his phd thesis + + + align:start position:0% +mathematician roy kerr as his phd thesis +and uh it has really earned him a place + + align:start position:0% +and uh it has really earned him a place + + + align:start position:0% +and uh it has really earned him a place +in physicist valhalla + + align:start position:0% + + + + align:start position:0% + +let me just conclude this lecture by + + align:start position:0% +let me just conclude this lecture by + + + align:start position:0% +let me just conclude this lecture by +making one comment here + + align:start position:0% + + + + align:start position:0% + +an important word in this theorem yeah + + align:start position:0% +an important word in this theorem yeah + + + align:start position:0% +an important word in this theorem yeah +an important word in this theorem + + align:start position:0% +an important word in this theorem + + + align:start position:0% +an important word in this theorem +is a statement that the only stationary + + align:start position:0% +is a statement that the only stationary + + + align:start position:0% +is a statement that the only stationary +space times are the current newman ones + + align:start position:0% +space times are the current newman ones + + + align:start position:0% +space times are the current newman ones +stationary space times the vent horizon + + align:start position:0% +stationary space times the vent horizon + + + align:start position:0% +stationary space times the vent horizon +so the current new and black holes + + align:start position:0% +so the current new and black holes + + + align:start position:0% +so the current new and black holes +what this means is that when + + align:start position:0% +what this means is that when + + + align:start position:0% +what this means is that when +a black hole forms + + align:start position:0% +a black hole forms + + + align:start position:0% +a black hole forms +it may be dynamical it may not + + align:start position:0% +it may be dynamical it may not + + + align:start position:0% +it may be dynamical it may not +yet be stationary + + align:start position:0% +yet be stationary + + + align:start position:0% +yet be stationary +and so the way that this theorem + + align:start position:0% +and so the way that this theorem + + + align:start position:0% +and so the way that this theorem +which is known as the no hair theorem + + align:start position:0% + + + + align:start position:0% + +the way that it is enforced + + align:start position:0% +the way that it is enforced + + + align:start position:0% +the way that it is enforced +is that imagine i have some kind of an + + align:start position:0% +is that imagine i have some kind of an + + + align:start position:0% +is that imagine i have some kind of an +object + + align:start position:0% +object + + + align:start position:0% +object +that due to physics that you know we + + align:start position:0% +that due to physics that you know we + + + align:start position:0% +that due to physics that you know we +don't have time to go into here + + align:start position:0% +don't have time to go into here + + + align:start position:0% +don't have time to go into here +imagine that this thing uh it its + + align:start position:0% +imagine that this thing uh it its + + + align:start position:0% +imagine that this thing uh it its +physics changes in such a way that it + + align:start position:0% +physics changes in such a way that it + + + align:start position:0% +physics changes in such a way that it +can no longer + + align:start position:0% +can no longer + + + align:start position:0% +can no longer +its fluid can no longer support its own + + align:start position:0% +its fluid can no longer support its own + + + align:start position:0% +its fluid can no longer support its own +mass against gravity + + align:start position:0% + + + + align:start position:0% + +and it collapses to a black hole okay + + align:start position:0% +and it collapses to a black hole okay + + + align:start position:0% +and it collapses to a black hole okay +initially this could be a huge + + align:start position:0% +initially this could be a huge + + + align:start position:0% +initially this could be a huge +complicated + + align:start position:0% +complicated + + + align:start position:0% +complicated +mess + + align:start position:0% + + + + align:start position:0% + +could have a massive mass charge spin + + align:start position:0% + + + + align:start position:0% + +magnetic fields who knows + + align:start position:0% + + + + align:start position:0% + +the no hair theorem guarantees that + + align:start position:0% +the no hair theorem guarantees that + + + align:start position:0% +the no hair theorem guarantees that +after + + align:start position:0% +after + + + align:start position:0% +after +some period of time it will be totally + + align:start position:0% +some period of time it will be totally + + + align:start position:0% +some period of time it will be totally +characterized by three numbers the mass + + align:start position:0% +characterized by three numbers the mass + + + align:start position:0% +characterized by three numbers the mass +the spin parameter a and the charge q + + align:start position:0% +the spin parameter a and the charge q + + + align:start position:0% +the spin parameter a and the charge q +what goes on is that during the collapse + + align:start position:0% +what goes on is that during the collapse + + + align:start position:0% +what goes on is that during the collapse +process + + align:start position:0% + + + + align:start position:0% + +radiation is generated + + align:start position:0% + + + + align:start position:0% + +what this radiation does is it it + + align:start position:0% +what this radiation does is it it + + + align:start position:0% +what this radiation does is it it +carries away + + align:start position:0% +carries away + + + align:start position:0% +carries away +gravitational waves carries away + + align:start position:0% +gravitational waves carries away + + + align:start position:0% +gravitational waves carries away +electromagnetic waves + + align:start position:0% +electromagnetic waves + + + align:start position:0% +electromagnetic waves +some of this is actually absorbed by + + align:start position:0% +some of this is actually absorbed by + + + align:start position:0% +some of this is actually absorbed by +this black hole + + align:start position:0% +this black hole + + + align:start position:0% +this black hole +and it does so in such a way that it + + align:start position:0% +and it does so in such a way that it + + + align:start position:0% +and it does so in such a way that it +precisely cancels out everything in the + + align:start position:0% +precisely cancels out everything in the + + + align:start position:0% +precisely cancels out everything in the +space time that + + align:start position:0% +space time that + + + align:start position:0% +space time that +does not fit the kern newman form + + align:start position:0% +does not fit the kern newman form + + + align:start position:0% +does not fit the kern newman form +you wind up so in you know this is one + + align:start position:0% +you wind up so in you know this is one + + + align:start position:0% +you wind up so in you know this is one +of these things where + + align:start position:0% + + + + align:start position:0% + +we really can only probe this either + + align:start position:0% +we really can only probe this either + + + align:start position:0% +we really can only probe this either +with observations + + align:start position:0% +with observations + + + align:start position:0% +with observations +um that sort of look at things like + + align:start position:0% +um that sort of look at things like + + + align:start position:0% +um that sort of look at things like +black holes + + align:start position:0% +black holes + + + align:start position:0% +black holes +and compact bodies colliding and forming + + align:start position:0% +and compact bodies colliding and forming + + + align:start position:0% +and compact bodies colliding and forming +black holes + + align:start position:0% +black holes + + + align:start position:0% +black holes +and looking at what the end state looks + + align:start position:0% +and looking at what the end state looks + + + align:start position:0% +and looking at what the end state looks +like or we can do this with numerical + + align:start position:0% +like or we can do this with numerical + + + align:start position:0% +like or we can do this with numerical +experiments where we + + align:start position:0% +experiments where we + + + align:start position:0% +experiments where we +simulate very complicated collapsing or + + align:start position:0% +simulate very complicated collapsing or + + + align:start position:0% +simulate very complicated collapsing or +colliding objects on a supercomputer + + align:start position:0% +colliding objects on a supercomputer + + + align:start position:0% +colliding objects on a supercomputer +and look at what the end result is what + + align:start position:0% +and look at what the end result is what + + + align:start position:0% +and look at what the end result is what +we always find + + align:start position:0% +we always find + + + align:start position:0% +we always find +is that the complex radiation that is + + align:start position:0% +is that the complex radiation that is + + + align:start position:0% +is that the complex radiation that is +generated + + align:start position:0% +generated + + + align:start position:0% +generated +in the collapse and the collision + + align:start position:0% +in the collapse and the collision + + + align:start position:0% +in the collapse and the collision +process always + + align:start position:0% +process always + + + align:start position:0% +process always +shaves away every bit of structure + + align:start position:0% +shaves away every bit of structure + + + align:start position:0% +shaves away every bit of structure +except for exactly what is left + + align:start position:0% +except for exactly what is left + + + align:start position:0% +except for exactly what is left +to leave it in the current newman form + + align:start position:0% +to leave it in the current newman form + + + align:start position:0% +to leave it in the current newman form +at the end really when we do these + + align:start position:0% +at the end really when we do these + + + align:start position:0% +at the end really when we do these +calculations we generally wind up with a + + align:start position:0% +calculations we generally wind up with a + + + align:start position:0% +calculations we generally wind up with a +curve black hole because we tend to + + align:start position:0% +curve black hole because we tend to + + + align:start position:0% +curve black hole because we tend to +study astrophysical problems that are + + align:start position:0% +study astrophysical problems that are + + + align:start position:0% +study astrophysical problems that are +electrically neutral + + align:start position:0% +electrically neutral + + + align:start position:0% +electrically neutral +so this is a result that is sometimes + + align:start position:0% +so this is a result that is sometimes + + + align:start position:0% +so this is a result that is sometimes +called + + align:start position:0% +called + + + align:start position:0% +called +price's theorem + + align:start position:0% + + + + align:start position:0% + +based on sort of uh foundational um + + align:start position:0% +based on sort of uh foundational um + + + align:start position:0% +based on sort of uh foundational um +calculations that were done by my friend + + align:start position:0% +calculations that were done by my friend + + + align:start position:0% +calculations that were done by my friend +richard price he did much of this right + + align:start position:0% +richard price he did much of this right + + + align:start position:0% +richard price he did much of this right +around the time i was born + + align:start position:0% +around the time i was born + + + align:start position:0% +around the time i was born +um uh in the days of being a a phd + + align:start position:0% +um uh in the days of being a a phd + + + align:start position:0% +um uh in the days of being a a phd +student and + + align:start position:0% +student and + + + align:start position:0% +student and +looking at the behavior of highly + + align:start position:0% +looking at the behavior of highly + + + align:start position:0% +looking at the behavior of highly +distorted black holes and seeing + + align:start position:0% +distorted black holes and seeing + + + align:start position:0% +distorted black holes and seeing +how the no hair theorem is you know if + + align:start position:0% +how the no hair theorem is you know if + + + align:start position:0% +how the no hair theorem is you know if +you can you can imagine making a space + + align:start position:0% +you can you can imagine making a space + + + align:start position:0% +you can you can imagine making a space +time that contains what should be a + + align:start position:0% +time that contains what should be a + + + align:start position:0% +time that contains what should be a +black hole but you somehow distort it + + align:start position:0% +black hole but you somehow distort it + + + align:start position:0% +black hole but you somehow distort it +and what you find + + align:start position:0% +and what you find + + + align:start position:0% +and what you find +is it becomes dynamical and it vibrates + + align:start position:0% +is it becomes dynamical and it vibrates + + + align:start position:0% +is it becomes dynamical and it vibrates +in such a way as to get rid of that + + align:start position:0% +in such a way as to get rid of that + + + align:start position:0% +in such a way as to get rid of that +distortion and you leave behind + + align:start position:0% +distortion and you leave behind + + + align:start position:0% +distortion and you leave behind +something that is precisely ker + + align:start position:0% +something that is precisely ker + + + align:start position:0% +something that is precisely ker +or kern newman if you have charge + + align:start position:0% +or kern newman if you have charge + + + align:start position:0% +or kern newman if you have charge +price's theorem is a semi-facetious + + align:start position:0% +price's theorem is a semi-facetious + + + align:start position:0% +price's theorem is a semi-facetious +statement that tells me + + align:start position:0% +statement that tells me + + + align:start position:0% +statement that tells me +everything in the space-time that can be + + align:start position:0% +everything in the space-time that can be + + + align:start position:0% +everything in the space-time that can be +rated + + align:start position:0% +rated + + + align:start position:0% +rated +is radiated in other words any bit of + + align:start position:0% +is radiated in other words any bit of + + + align:start position:0% +is radiated in other words any bit of +structure + + align:start position:0% + + + + align:start position:0% + +any bit of structure in the space-time + + align:start position:0% +any bit of structure in the space-time + + + align:start position:0% +any bit of structure in the space-time +that does not comport with the current + + align:start position:0% +that does not comport with the current + + + align:start position:0% +that does not comport with the current +newman solution + + align:start position:0% +newman solution + + + align:start position:0% +newman solution +radiates away and only cur newman is + + align:start position:0% +radiates away and only cur newman is + + + align:start position:0% +radiates away and only cur newman is +left + + align:start position:0% +left + + + align:start position:0% +left +so that concludes this lecture uh my + + align:start position:0% +so that concludes this lecture uh my + + + align:start position:0% +so that concludes this lecture uh my +final lecture which i will record in + + align:start position:0% +final lecture which i will record in + + + align:start position:0% +final lecture which i will record in +about + + align:start position:0% +about + + + align:start position:0% +about +15 minutes is one in which + + align:start position:0% +15 minutes is one in which + + + align:start position:0% +15 minutes is one in which +we are going to look at one of the ways + + align:start position:0% +we are going to look at one of the ways + + + align:start position:0% +we are going to look at one of the ways +in which we test this space + + align:start position:0% +in which we test this space + + + align:start position:0% +in which we test this space +time which is by studying the behavior + + align:start position:0% +time which is by studying the behavior + + + align:start position:0% +time which is by studying the behavior +of + + align:start position:0% +of + + + align:start position:0% +of +orbits going around a black hole so i + + align:start position:0% +orbits going around a black hole so i + + + align:start position:0% +orbits going around a black hole so i +will stop here \ No newline at end of file diff --git a/ZvL88xqYSak.txt b/ZvL88xqYSak.txt new file mode 100644 index 0000000000000000000000000000000000000000..8426c3ab727008c2c3c1b7c73d7a649865cd6d37 --- /dev/null +++ b/ZvL88xqYSak.txt @@ -0,0 +1,427 @@ +align:start position:0% + +hi I'm Gilbert Strang I'm a math + + align:start position:0% +hi I'm Gilbert Strang I'm a math + + + align:start position:0% +hi I'm Gilbert Strang I'm a math +professor at + + align:start position:0% +professor at + + + align:start position:0% +professor at +MIT and I'm cleave Mohler I'm one of the + + align:start position:0% +MIT and I'm cleave Mohler I'm one of the + + + align:start position:0% +MIT and I'm cleave Mohler I'm one of the +founders of math works and I am chief + + align:start position:0% +founders of math works and I am chief + + + align:start position:0% +founders of math works and I am chief +mathematician Gil and I have made a + + align:start position:0% +mathematician Gil and I have made a + + + align:start position:0% +mathematician Gil and I have made a +video series about uh ordinary + + align:start position:0% +video series about uh ordinary + + + align:start position:0% +video series about uh ordinary +differential + + align:start position:0% +differential + + + align:start position:0% +differential +equations uh this developed really from + + align:start position:0% +equations uh this developed really from + + + align:start position:0% +equations uh this developed really from +uh my experience of the linear algebra + + align:start position:0% +uh my experience of the linear algebra + + + align:start position:0% +uh my experience of the linear algebra +class uh it videotape it's shown on open + + align:start position:0% +class uh it videotape it's shown on open + + + align:start position:0% +class uh it videotape it's shown on open +courseware and it was my first uh time + + align:start position:0% +courseware and it was my first uh time + + + align:start position:0% +courseware and it was my first uh time +to discover that millions of people were + + align:start position:0% +to discover that millions of people were + + + align:start position:0% +to discover that millions of people were +learning watching it and + + align:start position:0% +learning watching it and + + + align:start position:0% +learning watching it and +uh it just seemed possible to tackle the + + align:start position:0% +uh it just seemed possible to tackle the + + + align:start position:0% +uh it just seemed possible to tackle the +other major undergraduate course after + + align:start position:0% +other major undergraduate course after + + + align:start position:0% +other major undergraduate course after +calculus the other lead into engineering + + align:start position:0% +calculus the other lead into engineering + + + align:start position:0% +calculus the other lead into engineering +and science uh differential equations + + align:start position:0% +and science uh differential equations + + + align:start position:0% +and science uh differential equations +with the two sides of the formulas and + + align:start position:0% +with the two sides of the formulas and + + + align:start position:0% +with the two sides of the formulas and +the computations this is not only for + + align:start position:0% +the computations this is not only for + + + align:start position:0% +the computations this is not only for +students uh that are currently in school + + align:start position:0% +students uh that are currently in school + + + align:start position:0% +students uh that are currently in school +after calculus but it's also for + + align:start position:0% +after calculus but it's also for + + + align:start position:0% +after calculus but it's also for +lifelong Learners people who want to + + align:start position:0% +lifelong Learners people who want to + + + align:start position:0% +lifelong Learners people who want to +come back to this + + align:start position:0% +come back to this + + + align:start position:0% +come back to this +material maybe after years out of school + + align:start position:0% +material maybe after years out of school + + + align:start position:0% +material maybe after years out of school +we want to F uh help people who uh are + + align:start position:0% +we want to F uh help people who uh are + + + align:start position:0% +we want to F uh help people who uh are +using mat lab to solve differential + + align:start position:0% +using mat lab to solve differential + + + align:start position:0% +using mat lab to solve differential +equations uh to + + align:start position:0% +equations uh to + + + align:start position:0% +equations uh to +uh understand the mat lab OD Suite to + + align:start position:0% +uh understand the mat lab OD Suite to + + + align:start position:0% +uh understand the mat lab OD Suite to +turn the black boxes into gray boxes + + align:start position:0% +turn the black boxes into gray boxes + + + align:start position:0% +turn the black boxes into gray boxes +where you have some understanding the + + align:start position:0% +where you have some understanding the + + + align:start position:0% +where you have some understanding the +mathematics that underlies them really + + align:start position:0% +mathematics that underlies them really + + + align:start position:0% +mathematics that underlies them really +differential equations is the expression + + align:start position:0% +differential equations is the expression + + + align:start position:0% +differential equations is the expression +the mathematical expression of change so + + align:start position:0% +the mathematical expression of change so + + + align:start position:0% +the mathematical expression of change so +engineering Finance + + align:start position:0% +engineering Finance + + + align:start position:0% +engineering Finance +economics uh life sciences medical + + align:start position:0% +economics uh life sciences medical + + + align:start position:0% +economics uh life sciences medical +Sciences where you're seeing things + + align:start position:0% +Sciences where you're seeing things + + + align:start position:0% +Sciences where you're seeing things +change over + + align:start position:0% +change over + + + align:start position:0% +change over +time uh those are modeled by + + align:start position:0% +time uh those are modeled by + + + align:start position:0% +time uh those are modeled by +differential equations so we want to + + align:start position:0% +differential equations so we want to + + + align:start position:0% +differential equations so we want to +understand what do Solutions look like + + align:start position:0% +understand what do Solutions look like + + + align:start position:0% +understand what do Solutions look like +for formulas and what do they look like + + align:start position:0% +for formulas and what do they look like + + + align:start position:0% +for formulas and what do they look like +for numbers for actual + + align:start position:0% +for numbers for actual + + + align:start position:0% +for numbers for actual +quantities Gillan Matrix guys our + + align:start position:0% +quantities Gillan Matrix guys our + + + align:start position:0% +quantities Gillan Matrix guys our +professional lives have been involved + + align:start position:0% +professional lives have been involved + + + align:start position:0% +professional lives have been involved +with matrices and mat lab started life + + align:start position:0% +with matrices and mat lab started life + + + align:start position:0% +with matrices and mat lab started life +as Matrix laboratory here we are doing + + align:start position:0% +as Matrix laboratory here we are doing + + + align:start position:0% +as Matrix laboratory here we are doing +differential equations why is that + + align:start position:0% +differential equations why is that + + + align:start position:0% +differential equations why is that +that's because matrices are fundamental + + align:start position:0% +that's because matrices are fundamental + + + align:start position:0% +that's because matrices are fundamental +in understanding modern differential + + align:start position:0% +in understanding modern differential + + + align:start position:0% +in understanding modern differential +equations systems of + + align:start position:0% +equations systems of + + + align:start position:0% +equations systems of +ordinary differential equations are the + + align:start position:0% +ordinary differential equations are the + + + align:start position:0% +ordinary differential equations are the +key to understanding uh modern + + align:start position:0% +key to understanding uh modern + + + align:start position:0% +key to understanding uh modern +applications of differential + + align:start position:0% +applications of differential + + + align:start position:0% +applications of differential +equations we hope you enjoy it \ No newline at end of file diff --git a/_8TPfNfgH0I.txt b/_8TPfNfgH0I.txt new file mode 100644 index 0000000000000000000000000000000000000000..a67b340b09fdbd259ae48ad343af9b75998dd617 --- /dev/null +++ b/_8TPfNfgH0I.txt @@ -0,0 +1,3243 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a creative commons license your support + + align:start position:0% +a creative commons license your support + + + align:start position:0% +a creative commons license your support +will help mit opencourseware continue to + + align:start position:0% +will help mit opencourseware continue to + + + align:start position:0% +will help mit opencourseware continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of mit courses + + align:start position:0% +materials from hundreds of mit courses + + + align:start position:0% +materials from hundreds of mit courses +visit mit opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +so uh + + align:start position:0% +so uh + + + align:start position:0% +so uh +hi everybody my name is xiaopo and we + + align:start position:0% +hi everybody my name is xiaopo and we + + + align:start position:0% +hi everybody my name is xiaopo and we +are going to present on light + + align:start position:0% +are going to present on light + + + align:start position:0% +are going to present on light +propagation in south westland modulated + + align:start position:0% +propagation in south westland modulated + + + align:start position:0% +propagation in south westland modulated +media so + + align:start position:0% + + + + align:start position:0% + +this is the outline of our presentation + + align:start position:0% +this is the outline of our presentation + + + align:start position:0% +this is the outline of our presentation +i will first + + align:start position:0% +i will first + + + align:start position:0% +i will first +show you some of the basic concept and + + align:start position:0% +show you some of the basic concept and + + + align:start position:0% +show you some of the basic concept and +carpet will present some of the + + align:start position:0% +carpet will present some of the + + + align:start position:0% +carpet will present some of the +some our simulation results + + align:start position:0% +some our simulation results + + + align:start position:0% +some our simulation results +so we'll start with photonic crystal and + + align:start position:0% +so we'll start with photonic crystal and + + + align:start position:0% +so we'll start with photonic crystal and +basically photonic crystal are + + align:start position:0% +basically photonic crystal are + + + align:start position:0% +basically photonic crystal are +artificial medius with purely index + + align:start position:0% +artificial medius with purely index + + + align:start position:0% +artificial medius with purely index +contrast and + + align:start position:0% +contrast and + + + align:start position:0% +contrast and +the periodicity and the spacing will + + align:start position:0% +the periodicity and the spacing will + + + align:start position:0% +the periodicity and the spacing will +determine the relevant light frequency + + align:start position:0% +determine the relevant light frequency + + + align:start position:0% +determine the relevant light frequency +and because of this photonic crystal uh + + align:start position:0% +and because of this photonic crystal uh + + + align:start position:0% +and because of this photonic crystal uh +we can actually manipulate the light in + + align:start position:0% +we can actually manipulate the light in + + + align:start position:0% +we can actually manipulate the light in +many many interesting way that we will + + align:start position:0% +many many interesting way that we will + + + align:start position:0% +many many interesting way that we will +show you uh later in the presentation + + align:start position:0% +show you uh later in the presentation + + + align:start position:0% +show you uh later in the presentation +so to + + align:start position:0% +so to + + + align:start position:0% +so to +to understand the light propagation in + + align:start position:0% +to understand the light propagation in + + + align:start position:0% +to understand the light propagation in +photonic crystal we have to + + align:start position:0% +photonic crystal we have to + + + align:start position:0% +photonic crystal we have to +come back to this maxwell equation which + + align:start position:0% +come back to this maxwell equation which + + + align:start position:0% +come back to this maxwell equation which +describes the light propagation + + align:start position:0% +describes the light propagation + + + align:start position:0% +describes the light propagation +in dielectric media + + align:start position:0% +in dielectric media + + + align:start position:0% +in dielectric media +and if we expand if we express the field + + align:start position:0% +and if we expand if we express the field + + + align:start position:0% +and if we expand if we express the field +in + + align:start position:0% +in + + + align:start position:0% +in +a set of + + align:start position:0% +a set of + + + align:start position:0% +a set of +harmonic modes we can actually reduce + + align:start position:0% +harmonic modes we can actually reduce + + + align:start position:0% +harmonic modes we can actually reduce +the equation to a + + align:start position:0% +the equation to a + + + align:start position:0% +the equation to a +eigen value problem with hermitian + + align:start position:0% +eigen value problem with hermitian + + + align:start position:0% +eigen value problem with hermitian +operator + + align:start position:0% + + + + align:start position:0% + +and some of the important properties of + + align:start position:0% +and some of the important properties of + + + align:start position:0% +and some of the important properties of +these harmonic modes are omega square is + + align:start position:0% +these harmonic modes are omega square is + + + align:start position:0% +these harmonic modes are omega square is +real and positive + + align:start position:0% +real and positive + + + align:start position:0% +real and positive +and + + align:start position:0% +and + + + align:start position:0% +and +they are orthogonal and + + align:start position:0% +they are orthogonal and + + + align:start position:0% +they are orthogonal and +also there are scale and variance means + + align:start position:0% +also there are scale and variance means + + + align:start position:0% +also there are scale and variance means +that + + align:start position:0% +that + + + align:start position:0% +that +one result one solution in one scale can + + align:start position:0% +one result one solution in one scale can + + + align:start position:0% +one result one solution in one scale can +be + + align:start position:0% +be + + + align:start position:0% +be +can be fit to other solutions in other + + align:start position:0% +can be fit to other solutions in other + + + align:start position:0% +can be fit to other solutions in other +scales as well + + align:start position:0% +scales as well + + + align:start position:0% +scales as well +and also in periodic + + align:start position:0% +and also in periodic + + + align:start position:0% +and also in periodic +dielectric medium we know that it must + + align:start position:0% +dielectric medium we know that it must + + + align:start position:0% +dielectric medium we know that it must +satisfy the + + align:start position:0% +satisfy the + + + align:start position:0% +satisfy the +blood condition also so + + align:start position:0% +blood condition also so + + + align:start position:0% +blood condition also so +it means that + + align:start position:0% +it means that + + + align:start position:0% +it means that +we can choose the computational domain + + align:start position:0% +we can choose the computational domain + + + align:start position:0% +we can choose the computational domain +in one unit cell of the + + align:start position:0% +in one unit cell of the + + + align:start position:0% +in one unit cell of the +infinite + + align:start position:0% +infinite + + + align:start position:0% +infinite +large crystal and you can just do the + + align:start position:0% +large crystal and you can just do the + + + align:start position:0% +large crystal and you can just do the +computation models in finding a cell and + + align:start position:0% +computation models in finding a cell and + + + align:start position:0% +computation models in finding a cell and +we can understand the whole + + align:start position:0% +we can understand the whole + + + align:start position:0% +we can understand the whole +crystal + + align:start position:0% +crystal + + + align:start position:0% +crystal +and basically uh we'll use fdtd in our + + align:start position:0% +and basically uh we'll use fdtd in our + + + align:start position:0% +and basically uh we'll use fdtd in our +uh + + align:start position:0% +uh + + + align:start position:0% +uh +this project and basically is means + + align:start position:0% +this project and basically is means + + + align:start position:0% +this project and basically is means +finite difference time domain method and + + align:start position:0% +finite difference time domain method and + + + align:start position:0% +finite difference time domain method and +it's widely used in + + align:start position:0% +it's widely used in + + + align:start position:0% +it's widely used in +computational models to understand the + + align:start position:0% +computational models to understand the + + + align:start position:0% +computational models to understand the +interaction of the electromagnetic + + align:start position:0% +interaction of the electromagnetic + + + align:start position:0% +interaction of the electromagnetic +uh electromagnetic wave in the + + align:start position:0% +uh electromagnetic wave in the + + + align:start position:0% +uh electromagnetic wave in the +dielectric medium and one of the good + + align:start position:0% +dielectric medium and one of the good + + + align:start position:0% +dielectric medium and one of the good +things about this method is it can + + align:start position:0% +things about this method is it can + + + align:start position:0% +things about this method is it can +it can compute the response of a linear + + align:start position:0% +it can compute the response of a linear + + + align:start position:0% +it can compute the response of a linear +system + + align:start position:0% +system + + + align:start position:0% +system +at many frequencies with a + + align:start position:0% +at many frequencies with a + + + align:start position:0% +at many frequencies with a +single combination and basically we just + + align:start position:0% +single combination and basically we just + + + align:start position:0% +single combination and basically we just +by using four transform the response of + + align:start position:0% +by using four transform the response of + + + align:start position:0% +by using four transform the response of +a single pulse + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +this is uh the approach we use for the + + align:start position:0% +this is uh the approach we use for the + + + align:start position:0% +this is uh the approach we use for the +fdtd basically we try to discretize the + + align:start position:0% +fdtd basically we try to discretize the + + + align:start position:0% +fdtd basically we try to discretize the +maxwell equation and + + align:start position:0% + + + + align:start position:0% + +in some boundary condition and we just + + align:start position:0% +in some boundary condition and we just + + + align:start position:0% +in some boundary condition and we just +time matching the field to obtain the + + align:start position:0% +time matching the field to obtain the + + + align:start position:0% +time matching the field to obtain the +time response + + align:start position:0% + + + + align:start position:0% + +this showed some of the equations and + + align:start position:0% +this showed some of the equations and + + + align:start position:0% +this showed some of the equations and +also the discretized maxwell curve + + align:start position:0% +also the discretized maxwell curve + + + align:start position:0% +also the discretized maxwell curve +equation and this + + align:start position:0% + + + + align:start position:0% + +this actually uh + + align:start position:0% +this actually uh + + + align:start position:0% +this actually uh +is + + align:start position:0% +is + + + align:start position:0% +is +uh one way we discretize + + align:start position:0% +uh one way we discretize + + + align:start position:0% +uh one way we discretize +the maxwell equation and basically the + + align:start position:0% +the maxwell equation and basically the + + + align:start position:0% +the maxwell equation and basically the +the field are separated in uh + + align:start position:0% +the field are separated in uh + + + align:start position:0% +the field are separated in uh +temporarily temporal domain in half + + align:start position:0% +temporarily temporal domain in half + + + align:start position:0% +temporarily temporal domain in half +half of the time stack and as well as + + align:start position:0% +half of the time stack and as well as + + + align:start position:0% +half of the time stack and as well as +in the special domain they are separated + + align:start position:0% +in the special domain they are separated + + + align:start position:0% +in the special domain they are separated +in half grip cell so the center + + align:start position:0% +in half grip cell so the center + + + align:start position:0% +in half grip cell so the center +difference + + align:start position:0% +difference + + + align:start position:0% +difference +uh in both time and space domain is are + + align:start position:0% +uh in both time and space domain is are + + + align:start position:0% +uh in both time and space domain is are +used to approximate the + + align:start position:0% +used to approximate the + + + align:start position:0% +used to approximate the +electromagnetic wave in the grid in each + + align:start position:0% +electromagnetic wave in the grid in each + + + align:start position:0% +electromagnetic wave in the grid in each +grid + + align:start position:0% + + + + align:start position:0% + +yeah there are paths to carpets for our + + align:start position:0% +yeah there are paths to carpets for our + + + align:start position:0% +yeah there are paths to carpets for our +simulation result + + align:start position:0% + + + + align:start position:0% + +thanks travel now in this part i will uh + + align:start position:0% +thanks travel now in this part i will uh + + + align:start position:0% +thanks travel now in this part i will uh +explain you so uh + + align:start position:0% +explain you so uh + + + align:start position:0% +explain you so uh +i will give you some of the simulation + + align:start position:0% +i will give you some of the simulation + + + align:start position:0% +i will give you some of the simulation +result and using this simulation result + + align:start position:0% +result and using this simulation result + + + align:start position:0% +result and using this simulation result +i will try to explain why photonic + + align:start position:0% +i will try to explain why photonic + + + align:start position:0% +i will try to explain why photonic +crystal are quite useful and what type + + align:start position:0% +crystal are quite useful and what type + + + align:start position:0% +crystal are quite useful and what type +of property they have + + align:start position:0% +of property they have + + + align:start position:0% +of property they have +and uh + + align:start position:0% + + + + align:start position:0% + +basically uh how we can apply them in a + + align:start position:0% +basically uh how we can apply them in a + + + align:start position:0% +basically uh how we can apply them in a +real life application + + align:start position:0% +real life application + + + align:start position:0% +real life application +so for this uh study we have considered + + align:start position:0% +so for this uh study we have considered + + + align:start position:0% +so for this uh study we have considered +this type of uh + + align:start position:0% + + + + align:start position:0% + +rod structure where we have a circular + + align:start position:0% +rod structure where we have a circular + + + align:start position:0% +rod structure where we have a circular +rod of aluminum uh which are placed at + + align:start position:0% +rod of aluminum uh which are placed at + + + align:start position:0% +rod of aluminum uh which are placed at +the + + align:start position:0% +the + + + align:start position:0% +the +constant distance + + align:start position:0% +constant distance + + + align:start position:0% +constant distance +uh + + align:start position:0% +uh + + + align:start position:0% +uh +they have constant spacing so we can uh + + align:start position:0% +they have constant spacing so we can uh + + + align:start position:0% +they have constant spacing so we can uh +while simulating we can just consider + + align:start position:0% +while simulating we can just consider + + + align:start position:0% +while simulating we can just consider +that a top view means a cross section + + align:start position:0% +that a top view means a cross section + + + align:start position:0% +that a top view means a cross section +along the uh + + align:start position:0% +along the uh + + + align:start position:0% +along the uh +one cross section and we can study their + + align:start position:0% +one cross section and we can study their + + + align:start position:0% +one cross section and we can study their +property + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +for the uh fdtd simulation we have used + + align:start position:0% +for the uh fdtd simulation we have used + + + align:start position:0% +for the uh fdtd simulation we have used +a limited software which is a demo + + align:start position:0% +a limited software which is a demo + + + align:start position:0% +a limited software which is a demo +version of that limiting software + + align:start position:0% +version of that limiting software + + + align:start position:0% +version of that limiting software +so in that simulation software we have + + align:start position:0% +so in that simulation software we have + + + align:start position:0% +so in that simulation software we have +applied + + align:start position:0% +applied + + + align:start position:0% +applied +means basically uh we apply a short + + align:start position:0% +means basically uh we apply a short + + + align:start position:0% +means basically uh we apply a short +short pulse so basically which + + align:start position:0% +short pulse so basically which + + + align:start position:0% +short pulse so basically which +corresponds to a combination of many uh + + align:start position:0% +corresponds to a combination of many uh + + + align:start position:0% +corresponds to a combination of many uh +various frequencies + + align:start position:0% +various frequencies + + + align:start position:0% +various frequencies +so + + align:start position:0% +so + + + align:start position:0% +so +we apply that + + align:start position:0% +we apply that + + + align:start position:0% +we apply that +short pulse to our structure + + align:start position:0% +short pulse to our structure + + + align:start position:0% +short pulse to our structure +and + + align:start position:0% +and + + + align:start position:0% +and +we + + align:start position:0% +we + + + align:start position:0% +we +time step the simulation so basically we + + align:start position:0% +time step the simulation so basically we + + + align:start position:0% +time step the simulation so basically we +calculate its uh time time response + + align:start position:0% +calculate its uh time time response + + + align:start position:0% +calculate its uh time time response +so ah after the time from that time + + align:start position:0% +so ah after the time from that time + + + align:start position:0% +so ah after the time from that time +response we uh uh do the fourier + + align:start position:0% +response we uh uh do the fourier + + + align:start position:0% +response we uh uh do the fourier +transform and uh + + align:start position:0% +transform and uh + + + align:start position:0% +transform and uh +get its frequency response now as the uh + + align:start position:0% +get its frequency response now as the uh + + + align:start position:0% +get its frequency response now as the uh +this uh structure is a + + align:start position:0% +this uh structure is a + + + align:start position:0% +this uh structure is a +it is a finite structure and uh we + + align:start position:0% +it is a finite structure and uh we + + + align:start position:0% +it is a finite structure and uh we +assume that our uh photonic crystal is + + align:start position:0% +assume that our uh photonic crystal is + + + align:start position:0% +assume that our uh photonic crystal is +infinite uh + + align:start position:0% +infinite uh + + + align:start position:0% +infinite uh +in dimension we need to uh bound over + + align:start position:0% +in dimension we need to uh bound over + + + align:start position:0% +in dimension we need to uh bound over +the uh this structure using a perfectly + + align:start position:0% +the uh this structure using a perfectly + + + align:start position:0% +the uh this structure using a perfectly +matched layer + + align:start position:0% +matched layer + + + align:start position:0% +matched layer +uh basically what perfectly match layer + + align:start position:0% +uh basically what perfectly match layer + + + align:start position:0% +uh basically what perfectly match layer +does is ah it absorbs the light + + align:start position:0% +does is ah it absorbs the light + + + align:start position:0% +does is ah it absorbs the light +uh in a such a way that there is no + + align:start position:0% +uh in a such a way that there is no + + + align:start position:0% +uh in a such a way that there is no +reflection at the boundary + + align:start position:0% +reflection at the boundary + + + align:start position:0% +reflection at the boundary +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +uh in this simulation we can see that uh + + align:start position:0% +uh in this simulation we can see that uh + + + align:start position:0% +uh in this simulation we can see that uh +at one particular frequency uh + + align:start position:0% +at one particular frequency uh + + + align:start position:0% +at one particular frequency uh +near this frequency + + align:start position:0% +near this frequency + + + align:start position:0% +near this frequency +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh we can see uh + + align:start position:0% +uh we can see uh + + + align:start position:0% +uh we can see uh +that uh + + align:start position:0% +that uh + + + align:start position:0% +that uh +there is a uh propagation of the light + + align:start position:0% +there is a uh propagation of the light + + + align:start position:0% +there is a uh propagation of the light +means we can see the field distribution + + align:start position:0% +means we can see the field distribution + + + align:start position:0% +means we can see the field distribution +along the whole photonic crystal + + align:start position:0% +along the whole photonic crystal + + + align:start position:0% +along the whole photonic crystal +and + + align:start position:0% +and + + + align:start position:0% +and +in this region uh there is no field + + align:start position:0% +in this region uh there is no field + + + align:start position:0% +in this region uh there is no field +propagation + + align:start position:0% +propagation + + + align:start position:0% +propagation +in the photonic crystal + + align:start position:0% +in the photonic crystal + + + align:start position:0% +in the photonic crystal +so + + align:start position:0% +so + + + align:start position:0% +so +okay basically we will show you some + + align:start position:0% +okay basically we will show you some + + + align:start position:0% +okay basically we will show you some +video + + align:start position:0% +video + + + align:start position:0% +video +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so this is the time domain behavior + + align:start position:0% +so this is the time domain behavior + + + align:start position:0% +so this is the time domain behavior +so here we can see that that + + align:start position:0% +so here we can see that that + + + align:start position:0% +so here we can see that that +incident pulse is a plane wave ah along + + align:start position:0% +incident pulse is a plane wave ah along + + + align:start position:0% +incident pulse is a plane wave ah along +the y direction + + align:start position:0% +the y direction + + + align:start position:0% +the y direction +so + + align:start position:0% +so + + + align:start position:0% +so +uh + + align:start position:0% +uh + + + align:start position:0% +uh +at this particular frequency we can see + + align:start position:0% +at this particular frequency we can see + + + align:start position:0% +at this particular frequency we can see +that pulses uh + + align:start position:0% +that pulses uh + + + align:start position:0% +that pulses uh +uh that + + align:start position:0% +uh that + + + align:start position:0% +uh that +electromagnetic wave is is uh able to + + align:start position:0% +electromagnetic wave is is uh able to + + + align:start position:0% +electromagnetic wave is is uh able to +propagate through the crystal now uh + + align:start position:0% +propagate through the crystal now uh + + + align:start position:0% +propagate through the crystal now uh +this is uh quite surprising thing that + + align:start position:0% +this is uh quite surprising thing that + + + align:start position:0% +this is uh quite surprising thing that +even though the dimension uh spacing + + align:start position:0% +even though the dimension uh spacing + + + align:start position:0% +even though the dimension uh spacing +between the two crystals which act as a + + align:start position:0% +between the two crystals which act as a + + + align:start position:0% +between the two crystals which act as a +scatterer is a much + + align:start position:0% +scatterer is a much + + + align:start position:0% +scatterer is a much +quite less than lambda so there are + + align:start position:0% +quite less than lambda so there are + + + align:start position:0% +quite less than lambda so there are +multiple scattered even though we are + + align:start position:0% +multiple scattered even though we are + + + align:start position:0% +multiple scattered even though we are +getting a quite good wave propagation + + align:start position:0% +getting a quite good wave propagation + + + align:start position:0% +getting a quite good wave propagation +and + + align:start position:0% +and + + + align:start position:0% +and +in this case + + align:start position:0% + + + + align:start position:0% + +we can see that um + + align:start position:0% +we can see that um + + + align:start position:0% +we can see that um +it act + + align:start position:0% +it act + + + align:start position:0% +it act +it is + + align:start position:0% +it is + + + align:start position:0% +it is +not allowing it doesn't allow that wave + + align:start position:0% +not allowing it doesn't allow that wave + + + align:start position:0% +not allowing it doesn't allow that wave +to propagate through the crystal so + + align:start position:0% +to propagate through the crystal so + + + align:start position:0% +to propagate through the crystal so +basically it acts as a mirror + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +the next thing comes is that when we + + align:start position:0% +the next thing comes is that when we + + + align:start position:0% +the next thing comes is that when we +have to design a photonic crystal we + + align:start position:0% +have to design a photonic crystal we + + + align:start position:0% +have to design a photonic crystal we +have to understand like at what + + align:start position:0% +have to understand like at what + + + align:start position:0% +have to understand like at what +frequency uh + + align:start position:0% +frequency uh + + + align:start position:0% +frequency uh +uh how it will behave + + align:start position:0% +uh how it will behave + + + align:start position:0% +uh how it will behave +so that + + align:start position:0% +so that + + + align:start position:0% +so that +behavior can we can understand by using + + align:start position:0% +behavior can we can understand by using + + + align:start position:0% +behavior can we can understand by using +a dispersion diagram + + align:start position:0% +a dispersion diagram + + + align:start position:0% +a dispersion diagram +uh this dispersion diagram we calculated + + align:start position:0% +uh this dispersion diagram we calculated + + + align:start position:0% +uh this dispersion diagram we calculated +using this same numerical software + + align:start position:0% +using this same numerical software + + + align:start position:0% +using this same numerical software +so to calculate this dispersion diagram + + align:start position:0% +so to calculate this dispersion diagram + + + align:start position:0% +so to calculate this dispersion diagram +we just consider a single + + align:start position:0% +we just consider a single + + + align:start position:0% +we just consider a single +unit of that photonic crystal which is a + + align:start position:0% +unit of that photonic crystal which is a + + + align:start position:0% +unit of that photonic crystal which is a +and uh beyond that uh + + align:start position:0% +and uh beyond that uh + + + align:start position:0% +and uh beyond that uh +unit the field will be + + align:start position:0% +unit the field will be + + + align:start position:0% +unit the field will be +uh means the field will be pure periodic + + align:start position:0% +uh means the field will be pure periodic + + + align:start position:0% +uh means the field will be pure periodic +so we can bound that + + align:start position:0% +so we can bound that + + + align:start position:0% +so we can bound that +so we can bound that uh + + align:start position:0% +so we can bound that uh + + + align:start position:0% +so we can bound that uh +structure using a + + align:start position:0% +structure using a + + + align:start position:0% +structure using a +block boundary condition so basically + + align:start position:0% +block boundary condition so basically + + + align:start position:0% +block boundary condition so basically +block boundary condition will specify + + align:start position:0% +block boundary condition will specify + + + align:start position:0% +block boundary condition will specify +that what mode we are + + align:start position:0% +that what mode we are + + + align:start position:0% +that what mode we are +interested to + + align:start position:0% +interested to + + + align:start position:0% +interested to +excite in the structure + + align:start position:0% +excite in the structure + + + align:start position:0% +excite in the structure +so + + align:start position:0% +so + + + align:start position:0% +so +we use that block boundary condition and + + align:start position:0% +we use that block boundary condition and + + + align:start position:0% +we use that block boundary condition and +we excite the + + align:start position:0% +we excite the + + + align:start position:0% +we excite the +uh + + align:start position:0% +uh + + + align:start position:0% +uh +field using a dipole source so + + align:start position:0% +field using a dipole source so + + + align:start position:0% +field using a dipole source so +and we calculate + + align:start position:0% +and we calculate + + + align:start position:0% +and we calculate +that field + + align:start position:0% +that field + + + align:start position:0% +that field +a temporal response using the various + + align:start position:0% +a temporal response using the various + + + align:start position:0% +a temporal response using the various +monitors inside the structure + + align:start position:0% +monitors inside the structure + + + align:start position:0% +monitors inside the structure +and using the fourier transform we can + + align:start position:0% +and using the fourier transform we can + + + align:start position:0% +and using the fourier transform we can +see that what frequency can exist in + + align:start position:0% +see that what frequency can exist in + + + align:start position:0% +see that what frequency can exist in +this structure at for a given mode + + align:start position:0% +this structure at for a given mode + + + align:start position:0% +this structure at for a given mode +so basically it will give us the idea + + align:start position:0% +so basically it will give us the idea + + + align:start position:0% +so basically it will give us the idea +about + + align:start position:0% +about + + + align:start position:0% +about +the behavior of the given photonic + + align:start position:0% +the behavior of the given photonic + + + align:start position:0% +the behavior of the given photonic +crystal + + align:start position:0% +crystal + + + align:start position:0% +crystal +now uh + + align:start position:0% +now uh + + + align:start position:0% +now uh +we may as uh + + align:start position:0% +we may as uh + + + align:start position:0% +we may as uh +there may be uh another thing is like uh + + align:start position:0% +there may be uh another thing is like uh + + + align:start position:0% +there may be uh another thing is like uh +what are the possible values of uh that + + align:start position:0% +what are the possible values of uh that + + + align:start position:0% +what are the possible values of uh that +wave vector that we have to take + + align:start position:0% +wave vector that we have to take + + + align:start position:0% +wave vector that we have to take +means uh like in real uh uh real wave + + align:start position:0% +means uh like in real uh uh real wave + + + align:start position:0% +means uh like in real uh uh real wave +propagation like in air we can have + + align:start position:0% +propagation like in air we can have + + + align:start position:0% +propagation like in air we can have +infinite number of k values and for + + align:start position:0% +infinite number of k values and for + + + align:start position:0% +infinite number of k values and for +infinite yeah but in this case we can + + align:start position:0% +infinite yeah but in this case we can + + + align:start position:0% +infinite yeah but in this case we can +see that our uh use from block uh + + align:start position:0% +see that our uh use from block uh + + + align:start position:0% +see that our uh use from block uh +theorem we can say that our response has + + align:start position:0% +theorem we can say that our response has + + + align:start position:0% +theorem we can say that our response has +this type of format and if we take uh + + align:start position:0% +this type of format and if we take uh + + + align:start position:0% +this type of format and if we take uh +some value k + + align:start position:0% +some value k + + + align:start position:0% +some value k +which is a + + align:start position:0% +which is a + + + align:start position:0% +which is a +uh + + align:start position:0% +uh + + + align:start position:0% +uh +which which has this type of form + + align:start position:0% +which which has this type of form + + + align:start position:0% +which which has this type of form +so basically this ko and k will have + + align:start position:0% +so basically this ko and k will have + + + align:start position:0% +so basically this ko and k will have +similar mode profile and when we have + + align:start position:0% +similar mode profile and when we have + + + align:start position:0% +similar mode profile and when we have +similar mode profile we will get the + + align:start position:0% +similar mode profile we will get the + + + align:start position:0% +similar mode profile we will get the +similar + + align:start position:0% +similar + + + align:start position:0% +similar +same frequency values + + align:start position:0% +same frequency values + + + align:start position:0% +same frequency values +for that mode + + align:start position:0% +for that mode + + + align:start position:0% +for that mode +so + + align:start position:0% +so + + + align:start position:0% +so +uh + + align:start position:0% +uh + + + align:start position:0% +uh +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so + + align:start position:0% +so + + + align:start position:0% +so +uh so basically uh we can reduce uh we + + align:start position:0% +uh so basically uh we can reduce uh we + + + align:start position:0% +uh so basically uh we can reduce uh we +can uh + + align:start position:0% +can uh + + + align:start position:0% +can uh +limit over the values of k and we can + + align:start position:0% +limit over the values of k and we can + + + align:start position:0% +limit over the values of k and we can +calculate that means we can get this + + align:start position:0% +calculate that means we can get this + + + align:start position:0% +calculate that means we can get this +value of k from this dillonium zone + + align:start position:0% +value of k from this dillonium zone + + + align:start position:0% +value of k from this dillonium zone +so for different type of crystal we have + + align:start position:0% +so for different type of crystal we have + + + align:start position:0% +so for different type of crystal we have +we can have + + align:start position:0% +we can have + + + align:start position:0% +we can have +different millonium zone + + align:start position:0% + + + + align:start position:0% + +uh now + + align:start position:0% +uh now + + + align:start position:0% +uh now +uh yeah + + align:start position:0% +uh yeah + + + align:start position:0% +uh yeah +now in the previous case uh + + align:start position:0% +now in the previous case uh + + + align:start position:0% +now in the previous case uh +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh + + align:start position:0% +uh + + + align:start position:0% +uh +we showed you that uh at one at certain + + align:start position:0% +we showed you that uh at one at certain + + + align:start position:0% +we showed you that uh at one at certain +frequency we uh we will not get the + + align:start position:0% +frequency we uh we will not get the + + + align:start position:0% +frequency we uh we will not get the +propagation of wave it will act as a + + align:start position:0% +propagation of wave it will act as a + + + align:start position:0% +propagation of wave it will act as a +mirror but uh the + + align:start position:0% +mirror but uh the + + + align:start position:0% +mirror but uh the +uh + + align:start position:0% +uh + + + align:start position:0% +uh +now if we introduce some uh type of + + align:start position:0% +now if we introduce some uh type of + + + align:start position:0% +now if we introduce some uh type of +defect in that photonic crystal we can + + align:start position:0% +defect in that photonic crystal we can + + + align:start position:0% +defect in that photonic crystal we can +allow the light to propagate through + + align:start position:0% +allow the light to propagate through + + + align:start position:0% +allow the light to propagate through +that uh + + align:start position:0% +that uh + + + align:start position:0% +that uh +structure like in this case uh we change + + align:start position:0% +structure like in this case uh we change + + + align:start position:0% +structure like in this case uh we change +the + + align:start position:0% +the + + + align:start position:0% +the +radius of the + + align:start position:0% +radius of the + + + align:start position:0% +radius of the +uh certain uh + + align:start position:0% +uh certain uh + + + align:start position:0% +uh certain uh +diameter of the roads in one particular + + align:start position:0% +diameter of the roads in one particular + + + align:start position:0% +diameter of the roads in one particular +uh + + align:start position:0% +uh + + + align:start position:0% +uh +location like in this case we created a + + align:start position:0% +location like in this case we created a + + + align:start position:0% +location like in this case we created a +line defect in that photonic crystal and + + align:start position:0% +line defect in that photonic crystal and + + + align:start position:0% +line defect in that photonic crystal and +we will see that how this structure will + + align:start position:0% +we will see that how this structure will + + + align:start position:0% +we will see that how this structure will +behave + + align:start position:0% + + + + align:start position:0% + +so using this fdtd simulation we can see + + align:start position:0% +so using this fdtd simulation we can see + + + align:start position:0% +so using this fdtd simulation we can see +that uh + + align:start position:0% +that uh + + + align:start position:0% +that uh +initially it wasn't able to uh allow + + align:start position:0% +initially it wasn't able to uh allow + + + align:start position:0% +initially it wasn't able to uh allow +means it didn't allow the wave + + align:start position:0% +means it didn't allow the wave + + + align:start position:0% +means it didn't allow the wave +propagation but when where we have this + + align:start position:0% +propagation but when where we have this + + + align:start position:0% +propagation but when where we have this +defect it is allowing means it allows + + align:start position:0% +defect it is allowing means it allows + + + align:start position:0% +defect it is allowing means it allows +the light to propagate and it acts as a + + align:start position:0% +the light to propagate and it acts as a + + + align:start position:0% +the light to propagate and it acts as a +waveguide + + align:start position:0% +waveguide + + + align:start position:0% +waveguide +so basically uh + + align:start position:0% +so basically uh + + + align:start position:0% +so basically uh +when we have uh + + align:start position:0% +when we have uh + + + align:start position:0% +when we have uh +when we apply a uh frequency which is in + + align:start position:0% +when we apply a uh frequency which is in + + + align:start position:0% +when we apply a uh frequency which is in +the bandfast region and we introduce a + + align:start position:0% +the bandfast region and we introduce a + + + align:start position:0% +the bandfast region and we introduce a +defect in a certain way we can control + + align:start position:0% +defect in a certain way we can control + + + align:start position:0% +defect in a certain way we can control +the uh + + align:start position:0% +the uh + + + align:start position:0% +the uh +propagation of light and in that way we + + align:start position:0% +propagation of light and in that way we + + + align:start position:0% +propagation of light and in that way we +can control + + align:start position:0% +can control + + + align:start position:0% +can control +the flow of light + + align:start position:0% +the flow of light + + + align:start position:0% +the flow of light +and the second example which we + + align:start position:0% +and the second example which we + + + align:start position:0% +and the second example which we +simulated is + + align:start position:0% +simulated is + + + align:start position:0% +simulated is +from the paper uh in which they + + align:start position:0% +from the paper uh in which they + + + align:start position:0% +from the paper uh in which they +use a + + align:start position:0% +use a + + + align:start position:0% +use a +photonic crystal to focus on light and + + align:start position:0% +photonic crystal to focus on light and + + + align:start position:0% +photonic crystal to focus on light and +they are using it as a green lens + + align:start position:0% +they are using it as a green lens + + + align:start position:0% +they are using it as a green lens +so + + align:start position:0% +so + + + align:start position:0% +so +to use them as as a green lens + + align:start position:0% +to use them as as a green lens + + + align:start position:0% +to use them as as a green lens +uh + + align:start position:0% +uh + + + align:start position:0% +uh +basically they use a specially modulated + + align:start position:0% +basically they use a specially modulated + + + align:start position:0% +basically they use a specially modulated +spacing of a + + align:start position:0% +spacing of a + + + align:start position:0% +spacing of a +same material which is a aluminum + + align:start position:0% +same material which is a aluminum + + + align:start position:0% +same material which is a aluminum +and in the center as in this figure you + + align:start position:0% +and in the center as in this figure you + + + align:start position:0% +and in the center as in this figure you +can see that in the center the spacing + + align:start position:0% +can see that in the center the spacing + + + align:start position:0% +can see that in the center the spacing +between the rod is + + align:start position:0% +between the rod is + + + align:start position:0% +between the rod is +low + + align:start position:0% +low + + + align:start position:0% +low +and as we go + + align:start position:0% +and as we go + + + align:start position:0% +and as we go +away from the center we are increasing + + align:start position:0% +away from the center we are increasing + + + align:start position:0% +away from the center we are increasing +the spacing + + align:start position:0% +the spacing + + + align:start position:0% +the spacing +and + + align:start position:0% + + + + align:start position:0% + +yeah so in this simulation also we + + align:start position:0% +yeah so in this simulation also we + + + align:start position:0% +yeah so in this simulation also we +use a + + align:start position:0% + + + + align:start position:0% + +broad pulse + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +at some point + + align:start position:0% +at some point + + + align:start position:0% +at some point +a certain frequency range we can see + + align:start position:0% +a certain frequency range we can see + + + align:start position:0% +a certain frequency range we can see +that + + align:start position:0% +that + + + align:start position:0% +that +we are applying the pulse + + align:start position:0% + + + + align:start position:0% + +at the + + align:start position:0% +at the + + + align:start position:0% +at the +this side and as it passes through the + + align:start position:0% +this side and as it passes through the + + + align:start position:0% +this side and as it passes through the +photonic crystal it is reduces the size + + align:start position:0% +photonic crystal it is reduces the size + + + align:start position:0% +photonic crystal it is reduces the size +of the + + align:start position:0% +of the + + + align:start position:0% +of the +it reduces the size of the beam and we + + align:start position:0% +it reduces the size of the beam and we + + + align:start position:0% +it reduces the size of the beam and we +can get a focusing effect as shown in + + align:start position:0% +can get a focusing effect as shown in + + + align:start position:0% +can get a focusing effect as shown in +this + + align:start position:0% +this + + + align:start position:0% +this +simulation result + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +now + + align:start position:0% +now + + + align:start position:0% +now +again coming back to this fdd uh + + align:start position:0% +again coming back to this fdd uh + + + align:start position:0% +again coming back to this fdd uh +basically what fdtd uh + + align:start position:0% +basically what fdtd uh + + + align:start position:0% +basically what fdtd uh +does is it discretizes the equation + + align:start position:0% +does is it discretizes the equation + + + align:start position:0% +does is it discretizes the equation +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +uh + + align:start position:0% +uh + + + align:start position:0% +uh +that discrete + + align:start position:0% +that discrete + + + align:start position:0% +that discrete +can + + align:start position:0% +can + + + align:start position:0% +can +write that + + align:start position:0% +write that + + + align:start position:0% +write that +in the electric form and uh + + align:start position:0% +in the electric form and uh + + + align:start position:0% +in the electric form and uh +if we know the initial condition we can + + align:start position:0% +if we know the initial condition we can + + + align:start position:0% +if we know the initial condition we can +do the time st time marching and we can + + align:start position:0% +do the time st time marching and we can + + + align:start position:0% +do the time st time marching and we can +find the solution in the space and as + + align:start position:0% +find the solution in the space and as + + + align:start position:0% +find the solution in the space and as +well as + + align:start position:0% +well as + + + align:start position:0% +well as +for all the time for example we can + + align:start position:0% +for all the time for example we can + + + align:start position:0% +for all the time for example we can +consider this bundy example with simple + + align:start position:0% +consider this bundy example with simple + + + align:start position:0% +consider this bundy example with simple +wave propagation equation + + align:start position:0% +wave propagation equation + + + align:start position:0% +wave propagation equation +so if we use a tail summation we can + + align:start position:0% +so if we use a tail summation we can + + + align:start position:0% +so if we use a tail summation we can +represent + + align:start position:0% +represent + + + align:start position:0% +represent +differentiation in our difference + + align:start position:0% +differentiation in our difference + + + align:start position:0% +differentiation in our difference +equation form + + align:start position:0% +equation form + + + align:start position:0% +equation form +and for difference equation form we can + + align:start position:0% +and for difference equation form we can + + + align:start position:0% +and for difference equation form we can +say that we can + + align:start position:0% +say that we can + + + align:start position:0% +say that we can +get the next time uh field value using + + align:start position:0% +get the next time uh field value using + + + align:start position:0% +get the next time uh field value using +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh + + align:start position:0% +uh + + + align:start position:0% +uh +all the values available at one time + + align:start position:0% +all the values available at one time + + + align:start position:0% +all the values available at one time +step + + align:start position:0% +step + + + align:start position:0% +step +before so + + align:start position:0% +before so + + + align:start position:0% +before so +basically the example shows uh using on + + align:start position:0% +basically the example shows uh using on + + + align:start position:0% +basically the example shows uh using on +the example how we calculated how the + + align:start position:0% +the example how we calculated how the + + + align:start position:0% +the example how we calculated how the +wave propagates with her time + + align:start position:0% + + + + align:start position:0% + +and this uh yield lattice which is used + + align:start position:0% +and this uh yield lattice which is used + + + align:start position:0% +and this uh yield lattice which is used +for that electromagnetic calculation + + align:start position:0% + + + + align:start position:0% + +yeah so in summary we can say that + + align:start position:0% +yeah so in summary we can say that + + + align:start position:0% +yeah so in summary we can say that +photonic crystal have various + + align:start position:0% +photonic crystal have various + + + align:start position:0% +photonic crystal have various +interesting properties and that can be + + align:start position:0% +interesting properties and that can be + + + align:start position:0% +interesting properties and that can be +used to control the + + align:start position:0% +used to control the + + + align:start position:0% +used to control the +behave light at + + align:start position:0% +behave light at + + + align:start position:0% +behave light at +micro nanoscale and this + + align:start position:0% +micro nanoscale and this + + + align:start position:0% +micro nanoscale and this +characterization requires a use of + + align:start position:0% +characterization requires a use of + + + align:start position:0% +characterization requires a use of +numerical techniques such as fdtd + + align:start position:0% +numerical techniques such as fdtd + + + align:start position:0% +numerical techniques such as fdtd +and + + align:start position:0% +and + + + align:start position:0% +and +we are thankful to satoshi who is our + + align:start position:0% +we are thankful to satoshi who is our + + + align:start position:0% +we are thankful to satoshi who is our +mentor for this project + + align:start position:0% +mentor for this project + + + align:start position:0% +mentor for this project +big question \ No newline at end of file diff --git a/_WV4JlBOQro.txt b/_WV4JlBOQro.txt new file mode 100644 index 0000000000000000000000000000000000000000..3221e674c5081ff2a03cc7fe6015c11aa54b4ed3 --- /dev/null +++ b/_WV4JlBOQro.txt @@ -0,0 +1,2321 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +[MUSIC PLAYING] + +PROFESSOR: In discussing the +sampling theorem, we saw that + +for a band limited signal, +which is sampled at a + +frequency that is at least twice +the highest frequency, + +we can implement exact +reconstruction of the original + +signal by low pass filtering an +impulse train, whose areas + +are identical to the +sample values. + +Well essentially, this low +pass filtering operation + +provides for us an interpolation +in between the + +sampled values. + +In other words, the output of a +low pass filter, in fact, is + +a continuous curve, which fits +between the sampled values + +some continuous function. + +Now, I'm sure that many of you +are familiar with other kinds + +of interpolation that we could +potentially provide in between + +sampled values. + +And in fact, in today's lecture +what I would like to + +do is first of all developed +the interpretation of the + +reconstruction as an +interpolation process and then + +also see how this exact +interpolation, using a low + +pass filter, relates to other +kinds of interpolation, such + +as linear interpolation +that you may + +already be familiar with. + +Well to begin, let's again +review what the overall system + +is for exact sampling +and reconstruction. + +And so let me remind you that +the overall system for + +sampling and desampling, or +reconstruction, is as I + +indicate here. + +The sampling process consists +of multiplying + +by an impulse train. + +And then the reconstruction +process corresponds to + +processing that impulse train +with a low pass filter. + +So if the spectrum of the +original signal is what I + +indicate in this diagram, then +after sampling with an impulse + +train, that spectrum +is replicated. + +And this replicated spectrum +for reconstruction is then + +processed through a +low pass filter. + +And so, in fact, if this +frequency response is an ideal + +low pass filter, as I indicate +on the diagram below, then + +multiplying the spectrum of +the sample signal by this + +extracts for us just the +portion of the spectrum + +centered around the origin. + +And what we're left with, +then, is the spectrum, + +finally, of the reconstructed +signal, which for the case of + +an ideal low pass filter is +exactly equal to the spectrum + +of the original signal. + +Now, that is the frequency +domain picture of the sampling + +and reconstruction. + +Let's also look at, basically, +the same process. + +But let's examine it now +in the time domain. + +Well in the time domain, what we +have is our original signal + +multiplied by an +impulse train. + +And this then is the sample +signal, or the impulse train + +whose areas are equal to +the sample values. + +And because of the fact that +this is an impulse train, in + +fact, we can take this term +inside the summation. + +And of course, what counts +about x of t in this + +expression is just as values +at the sampling instance, + +which are displaced in time by +capital T. And so what we can + +equivalently write is the +expression for the impulse + +train samples, or impulse train +of samples, as I've + +indicated here. + +Simply an impulse train, whose +areas are the sampled values. + +Now, in the reconstruction we +process that impulse train + +with a low pass filter. + +That's the basic notion +of the reconstruction. + +And so in the time domain, the +reconstructed signal is + +related to the impulse train +of samples through a + +convolution with the filter +impulse response. + +And carrying out this +convolution, since this is + +just a train of pulses, in +effect, what happens in this + +convolution is that this +impulse response gets + +reproduced at each of the +locations of the impulses in x + +of p of t with the +appropriate area. + +And finally, then, in the time +domain, the reconstructed + +signal is simply a linear +combination of shifted + +versions of the impulse response +with amplitudes, + +which are the sample values. + +And so this expression, in +fact then, is our basic + +reconstruction expression +in the time domain. + +Well in terms of a diagram, we +can think of the original + +waveform as I've shown here. + +And the red arrows denote the +sampled wave form, or the + +train of impulses, whose +amplitudes are the sampled + +values of the original +continuous time signal. + +And then, I've shown here what +might be a typical impulse + +response, particularly typical +in the case where we're + +talking about reconstruction +with an ideal low pass filter. + +Now, what happens in the +reconstruction is that the + +convolution of these impulses +with this impulse response + +means that in the +reconstruction, we superimpose + +one of these impulse +responses-- + +whatever the filter impulse +response happens to be-- + +at each of these +time instance. + +And in doing that, then +those are added up. + +And that gives us the total +reconstructed signal. + +Of course, for the case in which +the filter is an ideal + +low pass filter, then what we +know is that in that case, the + +impulse response is of the +form of a sync function. + +But generally, we may want to +consider other kinds of + +impulse responses. + +And so in fact, the +interpolating impulse response + +may have and will have, as this +discussion goes along, + +some different shapes. + +Now what I'd like to do is +illustrate, or demonstrate, + +this process of effectively +doing the interpolation by + +replacing each of the impulses +by an appropriate + +interpolating impulse response +and adding these up. + +And I'd like to do this +with a computer + +movie that we generated. + +And what you'll see in the +computer movie is, + +essentially, an original +wave form, which is + +a continuous curve. + +And then below that in the movie +is a train of samples. + +And then below that will be +the reconstructed signal. + +And the reconstruction will be +carried out by showing the + +location of the impulse response +as it moves along in + +the wave form. + +And then the reconstructed curve +is simply the summation + +of those as that impulse +response moves along. + +So what you'll see then is an +impulse response like this-- + +for the particular case of an +ideal low pass filter for the + +reconstruction-- + +placed successively at the +locations of these impulses. + +And that is the convolution +process. + +And below that then will be +the summation of these. + +And the summation of those +will then be the + +reconstructed signal. + +So let's take a look at, first +of all that reconstruction + +where the impulse response +corresponds to the impulse + +response of an ideal +low pass filter. + +Shown here, first, is the +continuous time signal, which + +we want to sample and then +reconstruct using band limited + +interpolation, or equivalently, +ideal low pass + +filtering on the +set of samples. + +So the first step then +is to sample this + +continuous time signal. + +And we see here now the +set of samples. + +And superimposed on the samples +are the original + +continuous time signal to focus +on the fact that those + +are samples of the top curve. + +Let's now remove the continuous +time envelope of + +the samples. + +And it's this set of samples +that we then want to use for + +the reconstruction. + +The reconstruction process, +interpreted as interpolation, + +consists of replacing +each sample with a + +sine x over x function. + +And so let's first consider +the sample at t equals 0. + +And here is the interpolating +sine x over x function + +associated with that sample. + +Now, the more general process +then is to place a sine x over + +x function at the time location +of each sample and + +superimpose those. + +Let's begin that process at the +left-hand set of samples. + +And in the bottom curve, we'll +build up the reconstruction as + +those sine x over x functions +are added together. + +So we begin with the +left-hand sample. + +And we see there the sine x over +x function on the bottom + +curve is the first step +in the reconstruction. + +We now have the sine x over x +function associated with the + +second sample. + +Let's add that in. + +Now we move on to the +third sample. + +And that sine x over x +function is added in. + +Continuing on, the next sample +generates a sine x over x + +function, which is superimposed +on the result + +that we've accumulated so far. + +And now let's just speed +up the process. + +We'll move on to the +fifth sample. + +Add that in. + +The sixth sample, add that in. + +And continue on through +the set of samples. + +And keep in mind the fact that, +basically, what we're + +doing explicitly here is the +convolution of the impulse + +train with a sine x +over x function. + +And because the set of samples +that we started with were + +samples of an exactly band +limited function, what we are + +reconstructing exactly is the +original continuous time + +signal that we have +on the top trace. + +OK, so that then kind of gives +you the picture of doing + +interpolation by replacing +the impulses by + +a continuous curve. + +And that's the way we're fitting +a continuous curve to + +the original impulse train. + +And let me stress that this +reconstruction process-- + +by putting the impulses +through a filter-- + +follows this relationship +whether or not this impulse + +response, in fact, corresponds +to an ideal low pass filter. + +What this expression always says +is that reconstructing + +this way corresponds to +replacing the impulses by a + +shifted impulse response with +an amplitude that is an + +amplitude corresponding +to the sample value. + +Now the kind of reconstruction +that we've just talked about, + +and the ideal reconstruction, +is often referred to as band + +limited interpolation because +we're interpolating in between + +the samples by making the +assumption that the signal is + +band limited and using the +impulse response for an ideal + +low pass filter, which has a cut +off frequency consistent + +with the assumed bandwidth +for the signal. + +So if we look here, for example, +at the impulse train, + +then in the demonstration that +you just saw, we built up the + +reconstructed curve by replacing +each of these + +impulses with the +sync function. + +And the sum of those built up +the reconstructed curve. + +Well, there are lots of other +kinds of interpolation that + +are perhaps maybe not as exact +but often easier to implement. + +And what I'd like to +do is focus our + +attention on two of these. + +The first that I want to mention +is what's referred to + +as the zero order hold, where +in effect, we do the + +interpolation in between these +sample values by simply + +holding the sample value until +the next sampling instant. + +And the reconstruction that we +end up, in that case, will + +look something like this. + +It's a staircase, or box car, +kind of function where we've + +simply held the sample value +until the next sampling + +instant and then replaced by +that value, held it until the + +next sampling instant, +et cetera. + +Now that's one kind +of interpolation. + +Another kind of very common +interpolation is what's + +referred to as linear +interpolation, where we simply + +fit a straight line between +the sampled values. + +And in that case, the type of +reconstruction that we would + +get would look something like I +indicate here, where we take + +a sample value, and the +following sample value, and + +simply fit an interpolated curve +between them, which is a + +straight line. + +Now interestingly, in fact, both +the zero order hold and + +the linear interpolation, which +is often referred to as + +a first order hold, can also +be either implemented or + +interpreted, both implemented +and interpreted, in the + +context of the equation that +we just developed. + +In particular, the processing +of the impulse train of + +samples by a linear time +invariant filter. + +Specifically, if we consider +a system where the impulse + +response is a rectangular +function, then in fact, if we + +processed the train of samples +through a filter with this + +impulse response, exactly the +reconstruction that we would + +get is what I've shown here. + +Alternatively, if we chose an +impulse response which was a + +triangular impulse response, +then what in effect happens is + +that each of these impulses +activates this triangle. + +And when we add up those +triangles at successive + +locations, in fact, what we +generate is this linear + +interpolation. + +So what this says, in fact, is +that either a zero order hold, + +which holds the value, or +linear interpolation can + +likewise be interpreted as a +process of convulving the + +impulse train of samples +with an appropriate + +filter impulse response. + +Well, what I'd like to do is +demonstrate, as we did with + +the band limited interpolation +or the sync interpolation as + +it's sometimes called-- +interpolating with + +a sine x over x-- + +let me now show the process. + +First of all, where we have +a zero order hold as + +corresponding to this +impulse response. + +In which case, we'll see +basically the same process as + +we saw in the computer generated +movie previously. + +But now, rather than a sync +function replacing each of + +these impulses, we'll have +a rectangular function. + +That will generate then our +approximation, which is a zero + +order hold. + +And following that, we'll do +exactly the same thing with + +the same wave form, using +a first order hold or a + +triangular impulse response. + +In which case, what we'll see +again is that as the triangle + +moves along here, and we build +up the running sum or the + +convolution, then we'll, in +fact, fit the original curve + +with a linear curve. + +So now let's again look at that, +remembering that at the + +top we'll see the original +continuous curve, exactly the + +one that we had before. + +Below it, the set of samples +together with the impulse + +response moving along. + +And then finally below that, +the accumulation of those + +impulse responses, or +equivalently the convolution, + +or equivalently the +reconstruction. + +So we have the same continuous +time signal that we use + +previously with band limited +interpolation. + +And in this case now, we want to +sample and then interpolate + +first with a zero order +hold and then with + +a first order hold. + +So the first step then +is to sample the + +continuous time signal. + +And we show here the set +of samples, once again, + +superimposed on which we have +the continuous time signal, + +which of course is exactly +the same curve as + +we have in the top. + +Well, let's remove that envelope +so that we focus + +attention on the samples that +we're using to interpolate. + +And the interpolation process +consists of replacing each + +sample by a rectangular signal, +whose amplitude is + +equal to the sample size. + +So let's put one, first of all, +at t equals 0 associated + +with that sample. + +And that then would be the +interpolating rectangle + +associated with the sample +at t equals 0. + +Now to build up the +interpolation, what we'll have + +is one of those at each +sample time, and + +those are added together. + +We'll start that process, +as we did before, at the + +left-hand end of the set of +samples and build the + +interpolating signal +on the bottom. + +So with the left-hand sample, +we have first the rectangle + +associated with that. + +That's shown now on +the bottom curve. + +We now have an interpolating +rectangle with a second sample + +that gets added into +the bottom curve. + +Similarly, an interpolating +rectangle with the zero order + +hold with the third sample. + +We add that into the +bottom curve. + +And as we proceed, we're +building a staircase + +approximation. + +On to the next sample, that gets +added in as we see there. + +And now let's speed +up the process. + +And we'll see the staircase +approximation building up. + +And notice in this case, as in +the previous case, that what + +we're basically watching +dynamically is the convolution + +of the impulse train of samples +with the impulse + +response of the interpolating +filter, which in this + +particular case is just +a rectangular pulse. + +And so this staircase +approximation that we're + +generating is the zero order +hold interpolation between the + +samples of the band limited +signal, which is at the top. + +Now let's do the same thing +with a first order hold. + +So in this case, we want to +interpolate using a triangular + +impulse response rather then +the sine x over x, or + +rectangular impulse responses +that we showed previously. + +So first, let's say with the +sample at t equals 0, we would + +replace that with a triangular +interpolating function. + +And more generally, each impulse +or sample is replaced + +with a triangular interpolating +function of a + +height equal to the +sample type. + +And these are superimposed +to generate the linear + +interpolation. + +We'll begin this process with +the leftmost sample. + +And we'll build the +superposition below in the + +bottom curve. + +So here is the interpolating +triangle for + +the leftmost sample. + +And now it's reproduced below. + +With the second sample, we +have an interpolating + +triangle, which is added +into the bottom curve. + +And now on to the +third sample. + +And again, that interpolating +triangle will be added on to + +the curve that we've +developed so far. + +And now onto the next sample. + +We add that in. + +Then we'll speed +up the process. + +And as we proceed through, we +are building, basically, a + +linear interpolation in between +the sample points, + +essentially corresponding to-- + +if one wants to think +of it this way-- + +connecting the dots. + +And what you're watching, once +again, is essentially the + +convolution process convulving +the impulse train with the + +impulse response of the +interpolating filter. + +And what we're generating, +then, is a linear + +approximation to the band +limited continuous time curve + +at the top. + +OK, so what we have then is +several other kinds of + +interpolation, which fit within +the same context as + +exact band limited +interpolation. + +One being interpolation in the +time domain with an impulse + +response, which is +a rectangle. + +The second being interpolation +in the time domain with an + +impulse response, which +is a triangle. + +And in fact, it's interesting +to also look at the + +relationship between that and +band limited interpolation. + +Look at it, specifically, +in the frequency domain. + +Well, in the frequency domain, +what we know, of course, is + +that for exact interpolation, +what we want as our + +interpolating filter is an +ideal low pass filter. + +Now keep in mind, by the way, +that an ideal low pass filter + +is an abstraction, as I've +stressed several + +times in the past. + +An ideal low pass filter is a +non-causal filter and, in + +fact, infinite extent, which is +one of the reasons why in + +any case we would use some +approximation to it. + +But here, what we have is the +exact interpolating filter. + +And that corresponds to an +ideal low pass filter. + +If, instead, we carried out the +interpolating using the + +zero order hold, the zero order +hold has a rectangular + +impulse response. + +And that means in the frequency +domain, its + +frequency response is of the +form of a sync function, or + +sine x over x. + +And so this, in fact, when we're +doing the reconstruction + +with a zero order hold, is the +associated frequency response. + +Now notice that it does some + +approximate low pass filtering. + +But of course, it permits +significant energy outside the + +past band of the filter. + +Well, instead of the zero order +hold, if we used the + +first order hold corresponding +to the triangular impulse + +response, in that case then in +the frequency domain, the + +associated frequency response +would be the Fourier transform + +of the triangle. + +And the Fourier transform of a +triangle is a sine squared x + +over x squared kind +of function. + +And so in that case, what we +would have for the frequency + +response, associated with the +first order hold, is a + +frequency response +as I show here. + +And the fact that there's +somewhat more attenuation + +outside the past band of the +ideal filter is what suggests, + +in fact, that the first order +hold, or linear interpolation, + +gives us a somewhat smoother +approximation to the original + +signal than the zero +order hold does. + +And so, in fact, just to compare +these two, we can see + +that here is the ideal filter. + +Here is the zero order hold, +corresponding to generating a + +box car kind of reconstruction. + +And here is the first order +hold, corresponding to a + +linear interpolation. + +Now in fact, in many sampling +systems, in any sampling + +system really, we need to use +some approximation to the low + +pass filter. + +And very often, in fact, what +is done in many sampling + +systems, is to first use just +the zero order hold, and then + +follow the zero order +hold with some + +additional low pass filtering. + +Well, to illustrate some of +these ideas and the notion of + +doing a reconstruction with a +zero order hold or first order + +hold and then in fact adding +to that some additional low + +pass filtering, what I'd like +to do is demonstrate, or + +illustrate, sampling and +interpolation in the context + +of some images. + +An image, of course, is a +two-dimensional signal. + +The independent variables +are spatial + +variables not time variables. + +And of course, we can sample +in both of the spatial + +dimensions, both in x and y. + +And what I've chosen as a +possibly appropriate choice + +for an image is, again, +our friend and + +colleague J.B.J. Fourier. + +So let's begin with the original +image, which we then + +want to sample and +reconstruct. + +And the sampling is done by +effectively multiplying by a + +pulse both horizontally +and vertically. + +The sample picture is then +the next one that I show. + +And as you can see, this +corresponds, in effect, to + +extracting small brightness +elements out of + +the original image. + +In fact, let's look in +a little closer. + +And what you can see, +essentially, is that what we + +have, of course, are not +impulses spatially but small + +spatial pillars that implement +the sampling for us. + +OK, now going back to the +original sample picture, we + +know that a picture can be +reconstructed by low pass + +filtering from the samples. + +And in fact, we can do that +optically in this case by + +simply defocusing the camera. + +And when we do that, what +happens is that we smear out + +the picture, or effectively +convulve the impulses with the + +point spread function of +the optical system. + +And this then is not too +bad a reconstruction. + +So that's an approximate +reconstruction. + +And focusing back now +what we have again + +is the sample picture. + +Now these images are, in fact, +taken off a computer display. + +And a common procedure in +computer generated or + +displayed images is in fact the +use of a zero order hold. + +And if the sampling rate is +high enough, then that + +actually works reasonably +well. + +So now let's look at the result +of applying a zero + +order hold to the sample image +that I just showed. + +The zero order hold corresponds +to replacing the + +impulses by rectangles. + +And you can see that what that +generates is a mosaic effect, + +as you would expect. + +And in fact, let's go in a +little closer and emphasize + +the mosaic effect. + +You can see that, essentially, +where there were impulses + +previously, there are now +rectangles with those + +brightness values. + +A very common procedure with +computer generated images is + +to first do a zero order hold, +as we've done here, and then + +follow that with some additional +low pass filtering. + +And fact, we can do that low +pass filtering now again by + +defocusing the camera. + +And you can begin to see that +with the zero order hold plus + +the low pass filtering, the + +reconstruction is not that bad. + +Well, let's go back to +the full image with + +the zero order hold. + +And again, now the effect of +low pass filtering will be + +somewhat better. + +And let's defocus again here. + +And you can begin to see that +this is a reasonable + +reconstruction. + +With the mosaic, in fact, with +this back in focus, you can + +apply your own low pass +filtering to it either by + +squinting, or if you have the +right or wrong kind of + +eyeglasses, either taking them +off or putting them on. + +Now, in addition to the zero +order hold, we can, of course, + +apply a first order hold. + +And that would correspond to +replacing the impulses, + +instead of with rectangles as +we have here, replacing them + +with triangles. + +And so now let's take a look at +the result of a first order + +hold applied to the +original samples. + +And you can see now that the +reconstruction is somewhat + +smoother because of the fact +that we're using an impulse + +response that's somewhat +smoother or a corresponding + +frequency response that +has a sharper cut off. + +I emphasize again that this is +a somewhat low pass filtered + +version of the original because +we have under sampled + +somewhat spatially to bring out +the point that I want to + +illustrate. + +OK, to emphasize these effects +even more, what I'd like to do + +is go through, basically, +the same sequence again. + +But in this case, what we'll +do is double the sample + +spacing both horizontal +and vertically. + +This of course, means that +we'll be even more highly + +under sampled than in the ones +I previously showed. + +And so the result of the +reconstructions with some low + +pass filtering will be a much +more low pass filtered image. + +So we now have the +sampled picture. + +But I've now under sampled +considerably more. + +And you can see the effect +of the sampling. + +And if we now apply a zero order +hold to this picture, we + +will again get a mosaic. + +And let's look at that. + +And that mosaic, of +course, looks even + +blockier than the original. + +And again, it emphasizes the +fact that the zero order hold + +simply corresponds to filling +in squares, or replacing the + +impulses, by squares, with the + +corresponding brightness values. + +Finally, if we, instead of a +zero order hold, use a first + +order hold, corresponding to two +dimensional triangles in + +place of these original +blocks. + +What we get is the next image. + +And that, again, is a smoother +reconstruction consistent with + +the fact that the triangles +are smoother than the + +rectangles. + +Again, I emphasize that this +looks so highly low pass + +filtered because of the fact +that we've under sampled so + +severely to essentially +emphasize the effect. + +As I mentioned, the images that +we just looked at were + +taken from a computer, although +of course the + +original images were continuous +time images or more + +specifically, continuous +space. + +That is the independent +variable + +is a spatial variable. + +Now, computer processing of +signals, pictures, speech, or + +whatever the signals are is +very important and useful + +because it offers a lot +of flexibility. + +And in fact, the kinds of things +that I showed with + +these pictures would have been +very hard to do without, in + +fact, doing computer +processing. + +Well, in computer processing +of any kind of signal, + +basically what's required is +that we do the processing in + +the context of discrete time +signals and discrete time + +processing because of the +fact that a computer + +is run off a clock. + +And essentially, things happen +in the computer as a sequence + +of numbers and as a sequence +of events. + +Well, it turns out that the +sampling theorem, in fact, as + +I've indicated previously, +provides us with a very nice + +mechanism for converting our +continuous time signals into + +discrete time signals. + +For example, for computer +processing or, in fact, if + +it's not a computer for some +other kind of discrete time or + +perhaps digital processing. + +Well, the basic idea, as I've +indicated previously, is to + +carry out discrete time +processing of continuous time + +signals by first converting the +continuous time signal to + +a discrete time signal, carry +out the appropriate discrete + +time processing of the discrete +time signal, and then + +after we're done with that +processing, converting from + +the discrete time sequence +back to a continuous time + +signal, corresponding to the +output that we have here. + +Well in the remainder of this +lecture, what I'd like to + +analyze is the first step in +that process, namely the + +conversion from a continuous +time signal to a discrete time + +signal and understand how the +two relate both in the time + +domain and in the frequency +domain. + +And in the next lecture, we'll +be analyzing and demonstrating + +the overall system, including +some intermediate processing. + +So the first step in the process +is the conversion from + +a continuous time signal to +a discrete time signal. + +And that can be thought of as +a process that involves two + +steps, although in practical +terms it may not be + +implemented specifically +as these two steps. + +The two steps are to first +convert from the continuous + +time, or continuous time +continuous signal, to an + +impulse train through a sampling +process and then to + +convert that impulse train to +a discrete time sequence. + +And the discrete time sequence +x of n is simply then a + +sequence of values which are the +samples of the continuous + +time signal. + +And as we'll see as we walk +through this, basically the + +step of going from the impulse +train to the sequence + +corresponds principally to a +relabeling step where we pick + +off the impulse values and use +those as the sequence values + +for the discrete time signal. + +So what I'd like to do as a +first step in understanding + +this process is to analyze +it in particular with our + +attention focused on trying +to understand what the + +relationship is in the frequency +domain between the + +discrete time Fourier transform +of the sequence, + +discrete time signal, and the +continuous time Fourier + +transform of the original +unsampled, and then the + +sampled signal. + +So let's go through that. + +And in particular, what we have +is a process where the + +continuous time signal is, +of course, modulated or + +multiplied by an +impulse train. + +And that gives us, +then, another + +continuous time signal. + +We're still in the continuous +time domain. + +It gives us another continuous +time signal, which is an + +impulse train. + +And in fact, we've gone +through this analysis + +previously. + +And what we have is this +multiplication or taking this + +term inside the summation and +recognizing that the impulse + +train is simply an impulse +train with areas of the + +impulses, which are +the samples of the + +continuous time function. + +We can then carry out +the analysis in + +the frequency domain. + +Now in the time domain, we have +a multiplication process. + +So in the frequency domain, we +have a convolution of the + +Fourier transform of the +continuous time signal, the + +original signal, and the Fourier +transform of the + +impulse train, which is itself +an impulse train. + +So in the frequency domain then, +the Fourier transform of + +the sampled signal, which is +an impulse train, is the + +convolution of the Fourier +transform of the sampling + +function P of t and the Fourier +transform of the + +sampled signal. + +Since the sampling signal is a +periodic impulse train, its + +Fourier transform is +an impulse train. + +And consequently, carrying out +this convolution in effect + +says that this Fourier +transform simply gets + +replicated at each of the +locations of these impulses. + +And finally, what we end up +with then is a Fourier + +transform after the sampling +process, which is the original + +Fourier transform of the +continuous signal but added to + +itself shifted by integer +multiples of + +the sampling frequency. + +And so this is the basic +equation then that tells us in + +the frequency domain what +happens through the first part + +of this two step process. + +Now I emphasize that it's +a two step process. + +The first process is sampling, +where we're still essentially + +in the continuous time world. + +The next step is essentially a +relabeling process, where we + +convert that impulse train +simply to a sequence. + +So let's look at +the next step. + +The next step is to take the +impulse train and convert it + +through a process +to a sequence. + +And the sequence values are +simply then samples of the + +original continuous signal. + +And so now we can +analyze this. + +And what we want to relate is +the discrete time Fourier + +transform of this and the +continuous time Fourier + +transform of this, or in fact, +the continuous time Fourier + +transform of x of C of T. + +OK, we have the impulse train. + +And it's Fourier transform we +can get by simply evaluating + +the Fourier transform. + +And since the Fourier +transform of this-- + +since this corresponds +to an impulse train-- + +the Fourier transform, by the +time we change some sums and + +integrals, will then have this +impulse replaced by the + +Fourier transform of the shifted +impulse, which is this + +exponential factor. + +So this expression is the +Fourier transform of the + +impulse train, the continuous +time Fourier transform. + +And alternatively, we can look +at the Fourier transform of + +the sequence. + +And this, of course, +is a discrete + +time Fourier transform. + +So we have the continuous time +Fourier transform of the + +impulse train, we have the +discrete Fourier transform of + +the sequence. + +And now we want to look at +how those two relate. + +Well, it pretty much falls out +of just comparing these two + +summations. + +In particular, this term and +this term are identical. + +That's just a relabeling of what +the sequence values are. + +And notice that when we compare +these exponential + +factors, they're identical as +long as we associate capital + +omega with little omega times +capital T. In other words, if + +we were to replace here capital +omega by little omega + +times capital T, and replace x +of n by x of c of nt, then + +this expression would be +identical to this expression. + +So in fact, these two are equal +with a relabeling, or + +with a transformation, between +small omega and capital omega. + +And so in fact, the relationship +that we have is + +that the discrete time Fourier +transform of the sequence of + +samples is equal to the +continuous time Fourier + +transform of the impulse train +of samples where we associate + +the continuous time frequency +variable and the discrete time + +frequency variable through +a frequency scaling as I + +indicate here. + +Or said another way, the +discrete time spectrum is the + +continuous time spectrum of the +samples with small omega + +replaced by capital +omega divided by + +capital T. All right. + +So we have then this +two step process. + +The first step is taking the +continuous time signal, + +sampling it with an +impulse train. + +In the frequency domain, that +corresponds to replicating the + +Fourier transform +of the original + +continuous time signal. + +The second step is relabeling +that, in effect turning it + +into a sequence. + +And what that does in the +frequency domain is provide us + +with a rescaling of the +frequency axis, or as we'll + +see a frequency normalization, +which is associated with the + +corresponding time + +normalization in the time domain. + +Well, let's look at those +statements a little more + +specifically. + +What I show here +is the original + +continuous time signal. + +And then below it is +the sampled signal. + +And these two are signals in +the continuous time domain. + +Now, what is the conversion +from this + +impulse train to a sequence? + +Well, it's simply taking these +impulse areas, or these sample + +values, and relabeling them, in +effect as I show below, as + +sequence values. + +And essentially, I'm now +replacing the impulse by the + +designation of a +sequence value. + +That's one step. + +But the other important step to +focus on is that whereas in + +the impulse train, these +impulses are spaced by integer + +multiples of the sampling +period capital T. In the + +sequence, of course, because +of the way that we label + +sequences, these are always +spaced by simply integer + +multiples of one. + +So in effect, you could say that +the step in going from + +here to here corresponds to +normalizing out in the time + +domain the sampling +period capital T. + +To stress that another way, if +the sampling period were + +doubled so that in this picture, +the spacing stretched + +out by a factor of two. + +Nevertheless, for the discrete +time signal, the spacing would + +remain as one. + +And essentially, it's the +envelope of those sequence + +values that would then get +compressed in time. + +So you can think of the step +in going from the impulse + +train to the samples as, +essentially, a time + +normalization. + +Now let's look at this in +the frequency domain. + +In the frequency domain, what +we have is the Fourier + +transform of our original +continuous signal. + +After sampling with an impulse +train, this spectrum retains + +its shape but is replicated at +integer multiples of the + +sampling frequency 2 pi over +capital T, as I indicate here. + +Now, we know that a discrete +time spectrum must be periodic + +in frequency with a +period of 2 pi. + +Here, we have the periodicity. + +But it's not periodic with +a period of 2 pi. + +It's periodic with a period, +which is equal to + +the sampling frequency. + +However, in converting from the +samples to the sequence + +values, we go through +another step. + +What's the other step? + +The other step is a time +normalization, where we take + +the impulses, which are spaced +by the sampling period. + +And we rescale that, essentially +in the time + +domain, to a spacing +which is unity. + +So we're dividing out in the +time domain by a factor, which + +is equal to the sampling +period. + +Well, dividing out in the time +domain by capital T would + +correspond to multiplying in +the frequency domain the + +frequency axis by capital T. +And indeed, what happens is + +that in going from the impulse +train to the sequence values, + +we now rescale this axis so +that, in fact, the axis gets + +stretched by capital T. And +the frequency, which + +corresponded to 2 pi over +capital T, now gets + +renormalized to 2 pi. + +So just looking at this again, +and perhaps with the overall + +picture, in the time domain, +we've gone from a continuous + +curve to samples, relabeled +those, and in effect + +implemented a time +normalization. + +Corresponding in the frequency +domain, we have replicated the + +spectrum through the initial +sampling process and then + +rescaled the frequency axis +so that, in fact, now this + +periodicity corresponds to a +periodicity here, which is 2 + +pi, and here, which is the +sampling frequency. + +So very often, in fact-- +and we'll be + +doing this next time-- + +when you think of continuous +time signals, which have been + +converted to discrete time +signals, when you look at the + +discrete time frequency axis, +the frequency 2 pi is + +associated with the sampling +frequency as it was applied to + +the original continuous +time signal. + +Now as I indicated, what we'll +want to go on to from here is + +an understanding of what +happens when we take a + +continuous time signal, convert +it to a discrete time + +signal as I've just gone +through, do some discrete time + +processing with a linear time +invariant system, and then + +carry that back into the +continuous time world. + +That is a procedure that we'll +go through, and analyze, and + +in fact, illustrate in some +detail next time. + +In preparation for that, what I +would be eager to encourage + +you to do using the study guide +and in reviewing this + +lecture, is to begin the next +lecture with a careful and + +thorough understanding +of the arguments that + +I've just gone through. + +In particular, understanding the +process that's involved in + +going from a continuous time +signal through sampling to a + +discrete time signal. + +And what that means in the +frequency domain in terms of + +taking the original spectrum, +replicating it because of the + +sampling process, and then +rescaling that so that the + +periodicity gets rescaled so +that it's periodic with a + +period of 2 pi. + +So we'll continue with that next +time, focusing now on the + +subsequent steps in +the processing. + +Thank you. \ No newline at end of file diff --git a/_ZG2U_lfc1Q.txt b/_ZG2U_lfc1Q.txt new file mode 100644 index 0000000000000000000000000000000000000000..a61e0594db78fe957ef543cb1e93d826d3451a15 --- /dev/null +++ b/_ZG2U_lfc1Q.txt @@ -0,0 +1,4987 @@ +align:start position:0% + +hi uh the topic of this video is SC + + align:start position:0% +hi uh the topic of this video is SC + + + align:start position:0% +hi uh the topic of this video is SC +triple product uh that is a very + + align:start position:0% +triple product uh that is a very + + + align:start position:0% +triple product uh that is a very +important topic for J uh I'll probably + + align:start position:0% +important topic for J uh I'll probably + + + align:start position:0% +important topic for J uh I'll probably +say this is the most important topic for + + align:start position:0% +say this is the most important topic for + + + align:start position:0% +say this is the most important topic for +J more than cross product more than dot + + align:start position:0% +J more than cross product more than dot + + + align:start position:0% +J more than cross product more than dot +product because this combines both cross + + align:start position:0% +product because this combines both cross + + + align:start position:0% +product because this combines both cross +product and do product uh there are a + + align:start position:0% +product and do product uh there are a + + + align:start position:0% +product and do product uh there are a +lot of questions which come in J just + + align:start position:0% +lot of questions which come in J just + + + align:start position:0% +lot of questions which come in J just +based on scaler triple product uh it is + + align:start position:0% +based on scaler triple product uh it is + + + align:start position:0% +based on scaler triple product uh it is +a very very important concept uh and I + + align:start position:0% +a very very important concept uh and I + + + align:start position:0% +a very very important concept uh and I +hope that this video will be able to + + align:start position:0% +hope that this video will be able to + + + align:start position:0% +hope that this video will be able to +give you a very very good example of + + align:start position:0% +give you a very very good example of + + + align:start position:0% +give you a very very good example of +basic understanding of skillable + + align:start position:0% +basic understanding of skillable + + + align:start position:0% +basic understanding of skillable +product uh the idea behind this video + + align:start position:0% +product uh the idea behind this video + + + align:start position:0% +product uh the idea behind this video +would be to First introduce scal triple + + align:start position:0% +would be to First introduce scal triple + + + align:start position:0% +would be to First introduce scal triple +product to you and then do a few + + align:start position:0% +product to you and then do a few + + + align:start position:0% +product to you and then do a few +problems on uh on this topic after that + + align:start position:0% +problems on uh on this topic after that + + + align:start position:0% +problems on uh on this topic after that +there will be also a followup video in + + align:start position:0% +there will be also a followup video in + + + align:start position:0% +there will be also a followup video in +which we'll go over more examples of + + align:start position:0% +which we'll go over more examples of + + + align:start position:0% +which we'll go over more examples of +scal triple product okay uh so what is a + + align:start position:0% +scal triple product okay uh so what is a + + + align:start position:0% +scal triple product okay uh so what is a +scal triple product till now we have + + align:start position:0% +scal triple product till now we have + + + align:start position:0% +scal triple product till now we have +done dot product which was a dob uh then + + align:start position:0% +done dot product which was a dob uh then + + + align:start position:0% +done dot product which was a dob uh then +we have done cross product which is a + + align:start position:0% +we have done cross product which is a + + + align:start position:0% +we have done cross product which is a +cross B now this ISS a scalar triple + + align:start position:0% +cross B now this ISS a scalar triple + + + align:start position:0% +cross B now this ISS a scalar triple +product so the name suggests triple + + align:start position:0% +product so the name suggests triple + + + align:start position:0% +product so the name suggests triple +means there are three quantities Vector + + align:start position:0% +means there are three quantities Vector + + + align:start position:0% +means there are three quantities Vector +a vector B Vector C and it is scalar + + align:start position:0% +a vector B Vector C and it is scalar + + + align:start position:0% +a vector B Vector C and it is scalar +product like dot product was a scalar + + align:start position:0% +product like dot product was a scalar + + + align:start position:0% +product like dot product was a scalar +product similarly this is also a scalar + + align:start position:0% +product similarly this is also a scalar + + + align:start position:0% +product similarly this is also a scalar +product but it is a scalar triple + + align:start position:0% +product but it is a scalar triple + + + align:start position:0% +product but it is a scalar triple +product so there will be three Vector + + align:start position:0% +product so there will be three Vector + + + align:start position:0% +product so there will be three Vector +quantities a b and c and the output + + align:start position:0% +quantities a b and c and the output + + + align:start position:0% +quantities a b and c and the output +would be a scalar okay so let us first + + align:start position:0% +would be a scalar okay so let us first + + + align:start position:0% +would be a scalar okay so let us first +discuss how we can get a scalar quantity + + align:start position:0% +discuss how we can get a scalar quantity + + + align:start position:0% +discuss how we can get a scalar quantity +out of three vectors so let us say we + + align:start position:0% +out of three vectors so let us say we + + + align:start position:0% +out of three vectors so let us say we +have Vector + + align:start position:0% +have Vector + + + align:start position:0% +have Vector +a and we have Vector + + align:start position:0% +a and we have Vector + + + align:start position:0% +a and we have Vector +B and we have Vector + + align:start position:0% +B and we have Vector + + + align:start position:0% +B and we have Vector +C + + align:start position:0% +C + + + align:start position:0% +C +now how can I get a scalar quantity out + + align:start position:0% +now how can I get a scalar quantity out + + + align:start position:0% +now how can I get a scalar quantity out +of this can I do a do B + + align:start position:0% +of this can I do a do B + + + align:start position:0% +of this can I do a do B +do + + align:start position:0% +do + + + align:start position:0% +do +c so this would mean that and let me put + + align:start position:0% +c so this would mean that and let me put + + + align:start position:0% +c so this would mean that and let me put +brackets here if I do this then this + + align:start position:0% +brackets here if I do this then this + + + align:start position:0% +brackets here if I do this then this +would mean a do B is a scalar quantity + + align:start position:0% +would mean a do B is a scalar quantity + + + align:start position:0% +would mean a do B is a scalar quantity +then I cannot dot it with C okay so this + + align:start position:0% +then I cannot dot it with C okay so this + + + align:start position:0% +then I cannot dot it with C okay so this +is not + + align:start position:0% +is not + + + align:start position:0% +is not +possible can I + + align:start position:0% +possible can I + + + align:start position:0% +possible can I +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +do a cross + + align:start position:0% +do a cross + + + align:start position:0% +do a cross +B Cross of + + align:start position:0% + + + + align:start position:0% + +C this would mean that there is it this + + align:start position:0% +C this would mean that there is it this + + + align:start position:0% +C this would mean that there is it this +is a vector quantity and then I'm taking + + align:start position:0% +is a vector quantity and then I'm taking + + + align:start position:0% +is a vector quantity and then I'm taking +a vector cross another Vector that will + + align:start position:0% +a vector cross another Vector that will + + + align:start position:0% +a vector cross another Vector that will +give me a vector output this unit is + + align:start position:0% +give me a vector output this unit is + + + align:start position:0% +give me a vector output this unit is +this operation is not possible this + + align:start position:0% +this operation is not possible this + + + align:start position:0% +this operation is not possible this +would give me a vector + + align:start position:0% +would give me a vector + + + align:start position:0% +would give me a vector +output but we want a scalar output so + + align:start position:0% +output but we want a scalar output so + + + align:start position:0% +output but we want a scalar output so +this is also not possible we will also + + align:start position:0% +this is also not possible we will also + + + align:start position:0% +this is also not possible we will also +be discussing what kind of product is + + align:start position:0% +be discussing what kind of product is + + + align:start position:0% +be discussing what kind of product is +this but that is a part of the next + + align:start position:0% +this but that is a part of the next + + + align:start position:0% +this but that is a part of the next +video but this will give me a vector + + align:start position:0% +video but this will give me a vector + + + align:start position:0% +video but this will give me a vector +output so this is not good for + + align:start position:0% +output so this is not good for + + + align:start position:0% +output so this is not good for +us however can we do something like this + + align:start position:0% +us however can we do something like this + + + align:start position:0% +us however can we do something like this +A cross B do c + + align:start position:0% +A cross B do c + + + align:start position:0% +A cross B do c +this is a vector then dotted with a + + align:start position:0% +this is a vector then dotted with a + + + align:start position:0% +this is a vector then dotted with a +vector and this gives a scalar + + align:start position:0% +vector and this gives a scalar + + + align:start position:0% +vector and this gives a scalar +output this is a + + align:start position:0% +output this is a + + + align:start position:0% +output this is a +correct okay so this is what we want to + + align:start position:0% +correct okay so this is what we want to + + + align:start position:0% +correct okay so this is what we want to +know so scalar triple product is defined + + align:start position:0% + + + + align:start position:0% + +as a cross B + + align:start position:0% +as a cross B + + + align:start position:0% +as a cross B +doted with C okay so what does this mean + + align:start position:0% +doted with C okay so what does this mean + + + align:start position:0% +doted with C okay so what does this mean +what does this mean this means that if I + + align:start position:0% +what does this mean this means that if I + + + align:start position:0% +what does this mean this means that if I +know I know what + + align:start position:0% + + + + align:start position:0% + +is and this is dotted with + + align:start position:0% + + + + align:start position:0% + +right so how can we then get the answer + + align:start position:0% +right so how can we then get the answer + + + align:start position:0% +right so how can we then get the answer +if you basically do this the expansion + + align:start position:0% +if you basically do this the expansion + + + align:start position:0% +if you basically do this the expansion +would be something like + + align:start position:0% + + + + align:start position:0% + +this you can imagine that basically you + + align:start position:0% +this you can imagine that basically you + + + align:start position:0% +this you can imagine that basically you +have you will find I component and then + + align:start position:0% +have you will find I component and then + + + align:start position:0% +have you will find I component and then +multiply all of that with CX so rather + + align:start position:0% +multiply all of that with CX so rather + + + align:start position:0% +multiply all of that with CX so rather +than doing I JK separately you can just + + align:start position:0% +than doing I JK separately you can just + + + align:start position:0% +than doing I JK separately you can just +put CX Cy CZ in the determinant at the + + align:start position:0% + + + + align:start position:0% + +top okay this is an important property + + align:start position:0% +top okay this is an important property + + + align:start position:0% +top okay this is an important property +here which I've written + + align:start position:0% +here which I've written + + + align:start position:0% +here which I've written +[Music] + + align:start position:0% + + + + align:start position:0% + +down okay + + align:start position:0% + + + + align:start position:0% + +now okay you have you're first dot a + + align:start position:0% +now okay you have you're first dot a + + + align:start position:0% +now okay you have you're first dot a +dotting A cross B with a cross B do c + + align:start position:0% +dotting A cross B with a cross B do c + + + align:start position:0% +dotting A cross B with a cross B do c +now can you see something else also + + align:start position:0% +now can you see something else also + + + align:start position:0% +now can you see something else also +which might or might not be that obvious + + align:start position:0% +which might or might not be that obvious + + + align:start position:0% +which might or might not be that obvious +basically we know + + align:start position:0% + + + + align:start position:0% + +that we + + align:start position:0% + + + + align:start position:0% + +know that A cross B + + align:start position:0% + + + + align:start position:0% + +dotted with C is equal to C + + align:start position:0% +dotted with C is equal to C + + + align:start position:0% +dotted with C is equal to C +dot A cross + + align:start position:0% +dot A cross + + + align:start position:0% +dot A cross +B right so A cross B do c is equal to C + + align:start position:0% +B right so A cross B do c is equal to C + + + align:start position:0% +B right so A cross B do c is equal to C +cross a dob we know that because this is + + align:start position:0% +cross a dob we know that because this is + + + align:start position:0% +cross a dob we know that because this is +a DOT product this is a vector so you + + align:start position:0% +a DOT product this is a vector so you + + + align:start position:0% +a DOT product this is a vector so you +just took the this let us say this let + + align:start position:0% +just took the this let us say this let + + + align:start position:0% +just took the this let us say this let +us call this + + align:start position:0% +us call this + + + align:start position:0% +us call this +Vector + + align:start position:0% +Vector + + + align:start position:0% +Vector +D then D do c is equal to C do d right + + align:start position:0% +D then D do c is equal to C do d right + + + align:start position:0% +D then D do c is equal to C do d right +so all you all you're saying is a cross + + align:start position:0% +so all you all you're saying is a cross + + + align:start position:0% +so all you all you're saying is a cross +B do c is equal to C Cross C C do a + + align:start position:0% +B do c is equal to C Cross C C do a + + + align:start position:0% +B do c is equal to C Cross C C do a +cross B we know this okay also there are + + align:start position:0% +cross B we know this okay also there are + + + align:start position:0% +cross B we know this okay also there are +some properties of determinant which + + align:start position:0% +some properties of determinant which + + + align:start position:0% +some properties of determinant which +basically means that you can flip two + + align:start position:0% +basically means that you can flip two + + + align:start position:0% +basically means that you can flip two +determinants uh and then the answer + + align:start position:0% +determinants uh and then the answer + + + align:start position:0% +determinants uh and then the answer +would become a negative that and if you + + align:start position:0% +would become a negative that and if you + + + align:start position:0% +would become a negative that and if you +flip twice then the answer would remain + + align:start position:0% +flip twice then the answer would remain + + + align:start position:0% +flip twice then the answer would remain +the same so if you think if I flip a and + + align:start position:0% +the same so if you think if I flip a and + + + align:start position:0% +the same so if you think if I flip a and +C then a will come to the top and c will + + align:start position:0% +C then a will come to the top and c will + + + align:start position:0% +C then a will come to the top and c will +come to the bottom then if I F Flip Flip + + align:start position:0% +come to the bottom then if I F Flip Flip + + + align:start position:0% +come to the bottom then if I F Flip Flip +uh A and B then B will come to the + + align:start position:0% +uh A and B then B will come to the + + + align:start position:0% +uh A and B then B will come to the +middle and B and sorry so we'll first + + align:start position:0% +middle and B and sorry so we'll first + + + align:start position:0% +middle and B and sorry so we'll first +flip a and C and then flip B and C so it + + align:start position:0% +flip a and C and then flip B and C so it + + + align:start position:0% +flip a and C and then flip B and C so it +will become a b c in other + + align:start position:0% +will become a b c in other + + + align:start position:0% +will become a b c in other +words A cross + + align:start position:0% + + + + align:start position:0% + +B dotted with C can also + + align:start position:0% +B dotted with C can also + + + align:start position:0% +B dotted with C can also +be ax a y a + + align:start position:0% +be ax a y a + + + align:start position:0% +be ax a y a +z BX b y + + align:start position:0% +z BX b y + + + align:start position:0% +z BX b y +bz CX Cy + + align:start position:0% +bz CX Cy + + + align:start position:0% +bz CX Cy +CZ and this I have done by flipping row + + align:start position:0% +CZ and this I have done by flipping row + + + align:start position:0% +CZ and this I have done by flipping row +twice flip + + align:start position:0% + + + + align:start position:0% + +in + + align:start position:0% + + + + align:start position:0% + +C and + + align:start position:0% + + + + align:start position:0% + +AO and + + align:start position:0% + + + + align:start position:0% + +then B row and c + + align:start position:0% + + + + align:start position:0% + +row you'll get this however if you think + + align:start position:0% +row you'll get this however if you think + + + align:start position:0% +row you'll get this however if you think +about this here whatever was in the dot + + align:start position:0% +about this here whatever was in the dot + + + align:start position:0% +about this here whatever was in the dot +came at the top now if I want to + + align:start position:0% +came at the top now if I want to + + + align:start position:0% +came at the top now if I want to +write this down now I can write this + + align:start position:0% +write this down now I can write this + + + align:start position:0% +write this down now I can write this +also as a + + align:start position:0% + + + + align:start position:0% + +dot b Cross + + align:start position:0% +dot b Cross + + + align:start position:0% +dot b Cross +C okay a do B cross + + align:start position:0% +C okay a do B cross + + + align:start position:0% +C okay a do B cross +a so what was what what I have what I + + align:start position:0% +a so what was what what I have what I + + + align:start position:0% +a so what was what what I have what I +have done here what I'm saying is + + align:start position:0% +have done here what I'm saying is + + + align:start position:0% +have done here what I'm saying is +whatever was in the dot came at the top + + align:start position:0% +whatever was in the dot came at the top + + + align:start position:0% +whatever was in the dot came at the top +row so whatever was in the dot came at + + align:start position:0% +row so whatever was in the dot came at + + + align:start position:0% +row so whatever was in the dot came at +the top row the single Vector came at + + align:start position:0% +the top row the single Vector came at + + + align:start position:0% +the top row the single Vector came at +the top row now I written this down so A + + align:start position:0% +the top row now I written this down so A + + + align:start position:0% +the top row now I written this down so A +cross B do c is equal to a do B Cross + + align:start position:0% +cross B do c is equal to a do B Cross + + + align:start position:0% +cross B do c is equal to a do B Cross +C and this is a super important property + + align:start position:0% +C and this is a super important property + + + align:start position:0% +C and this is a super important property +like A A cross B do c equal to a b Cross + + align:start position:0% +like A A cross B do c equal to a b Cross + + + align:start position:0% +like A A cross B do c equal to a b Cross +C in other words you can flip the sign + + align:start position:0% +C in other words you can flip the sign + + + align:start position:0% +C in other words you can flip the sign +of a and b so the first property that we + + align:start position:0% +of a and b so the first property that we + + + align:start position:0% +of a and b so the first property that we +have discussed was + + align:start position:0% +have discussed was + + + align:start position:0% +have discussed was +this okay and the second property that I + + align:start position:0% +this okay and the second property that I + + + align:start position:0% +this okay and the second property that I +want to discuss is that I want to + + align:start position:0% +want to discuss is that I want to + + + align:start position:0% +want to discuss is that I want to +highlight is this a cross A cross B do c + + align:start position:0% +highlight is this a cross A cross B do c + + + align:start position:0% +highlight is this a cross A cross B do c +is equal to a b Cross + + align:start position:0% +is equal to a b Cross + + + align:start position:0% +is equal to a b Cross +C third property + + align:start position:0% +C third property + + + align:start position:0% +C third property +so a cross a do B Cross + + align:start position:0% +so a cross a do B Cross + + + align:start position:0% +so a cross a do B Cross +C is equal to a DOT A cross B + + align:start position:0% +C is equal to a DOT A cross B + + + align:start position:0% +C is equal to a DOT A cross B +dot C and sometimes this is written as a + + align:start position:0% +dot C and sometimes this is written as a + + + align:start position:0% +dot C and sometimes this is written as a +b + + align:start position:0% +b + + + align:start position:0% +b +c + + align:start position:0% +c + + + align:start position:0% +c +okay sometimes this is written as a a b + + align:start position:0% +okay sometimes this is written as a a b + + + align:start position:0% +okay sometimes this is written as a a b +c because Dot and cross doesn't matter + + align:start position:0% +c because Dot and cross doesn't matter + + + align:start position:0% +c because Dot and cross doesn't matter +it doesn't matter you are taking dot + + align:start position:0% +it doesn't matter you are taking dot + + + align:start position:0% +it doesn't matter you are taking dot +here or cross here it will always come + + align:start position:0% +here or cross here it will always come + + + align:start position:0% +here or cross here it will always come +out to be fine it will always be the + + align:start position:0% +out to be fine it will always be the + + + align:start position:0% +out to be fine it will always be the +same okay so I hope that this is making + + align:start position:0% +same okay so I hope that this is making + + + align:start position:0% +same okay so I hope that this is making +sense that we first said this is a + + align:start position:0% +sense that we first said this is a + + + align:start position:0% +sense that we first said this is a +determinant then we flipped the rows so + + align:start position:0% +determinant then we flipped the rows so + + + align:start position:0% +determinant then we flipped the rows so +that the value Remains the Same and then + + align:start position:0% +that the value Remains the Same and then + + + align:start position:0% +that the value Remains the Same and then +because the top row was a DOT do alone + + align:start position:0% +because the top row was a DOT do alone + + + align:start position:0% +because the top row was a DOT do alone +Vector then we said a do B Cross C so A + + align:start position:0% +Vector then we said a do B Cross C so A + + + align:start position:0% +Vector then we said a do B Cross C so A +cross B do c is same as a b Cross + + align:start position:0% +cross B do c is same as a b Cross + + + align:start position:0% +cross B do c is same as a b Cross +C okay uh and we also know that A cross + + align:start position:0% +C okay uh and we also know that A cross + + + align:start position:0% +C okay uh and we also know that A cross +B do c is equal to C cross and we also + + align:start position:0% +B do c is equal to C cross and we also + + + align:start position:0% +B do c is equal to C cross and we also +know that know that this is the same as + + align:start position:0% +know that know that this is the same as + + + align:start position:0% +know that know that this is the same as +because this is a cross B do c so we can + + align:start position:0% +because this is a cross B do c so we can + + + align:start position:0% +because this is a cross B do c so we can +also write this as C do a cross + + align:start position:0% +also write this as C do a cross + + + align:start position:0% +also write this as C do a cross +B right so we can + + align:start position:0% +B right so we can + + + align:start position:0% +B right so we can +r c cross a. B + + align:start position:0% + + + + align:start position:0% + +right this can also be written or this + + align:start position:0% +right this can also be written or this + + + align:start position:0% +right this can also be written or this +this can also be + + align:start position:0% + + + + align:start position:0% + +cab because now we are taking the + + align:start position:0% +cab because now we are taking the + + + align:start position:0% +cab because now we are taking the +associative property of dot similarly + + align:start position:0% +associative property of dot similarly + + + align:start position:0% +associative property of dot similarly +now I can write this + + align:start position:0% +now I can write this + + + align:start position:0% +now I can write this +as B do c cross + + align:start position:0% +as B do c cross + + + align:start position:0% +as B do c cross +a I'm taking the property of I'm + + align:start position:0% +a I'm taking the property of I'm + + + align:start position:0% +a I'm taking the property of I'm +flipping Dots here again and equal + + align:start position:0% +flipping Dots here again and equal + + + align:start position:0% +flipping Dots here again and equal +to + + align:start position:0% +to + + + align:start position:0% +to +uh now I'm changing writing this as B + + align:start position:0% +uh now I'm changing writing this as B + + + align:start position:0% +uh now I'm changing writing this as B +Cross C do a changing Dot and cross and + + align:start position:0% +Cross C do a changing Dot and cross and + + + align:start position:0% +Cross C do a changing Dot and cross and +this is b c + + align:start position:0% + + + + align:start position:0% + +a okay this is a very very important + + align:start position:0% +a okay this is a very very important + + + align:start position:0% +a okay this is a very very important +property what what I'm trying what I'm + + align:start position:0% +property what what I'm trying what I'm + + + align:start position:0% +property what what I'm trying what I'm +trying to say here is a cross B do c so + + align:start position:0% +trying to say here is a cross B do c so + + + align:start position:0% +trying to say here is a cross B do c so +I hope this makes sense you can change + + align:start position:0% +I hope this makes sense you can change + + + align:start position:0% +I hope this makes sense you can change +Dot and cross one thing and then it this + + align:start position:0% +Dot and cross one thing and then it this + + + align:start position:0% +Dot and cross one thing and then it this +seems to be a cyclic property the cyclic + + align:start position:0% +seems to be a cyclic property the cyclic + + + align:start position:0% +seems to be a cyclic property the cyclic +property says that a should go to + + align:start position:0% +property says that a should go to + + + align:start position:0% +property says that a should go to +B and then B should go to C and then see + + align:start position:0% +B and then B should go to C and then see + + + align:start position:0% +B and then B should go to C and then see +it should go to + + align:start position:0% +it should go to + + + align:start position:0% +it should go to +a so what is happening is a b c a b and + + align:start position:0% +a so what is happening is a b c a b and + + + align:start position:0% +a so what is happening is a b c a b and +then C so you can always think cyclic AB + + align:start position:0% +then C so you can always think cyclic AB + + + align:start position:0% +then C so you can always think cyclic AB +BC so the the cycle is always + + align:start position:0% +BC so the the cycle is always + + + align:start position:0% +BC so the the cycle is always +ABC and that is that means if as long as + + align:start position:0% +ABC and that is that means if as long as + + + align:start position:0% +ABC and that is that means if as long as +you have AB BC written in the correct + + align:start position:0% +you have AB BC written in the correct + + + align:start position:0% +you have AB BC written in the correct +cycle then the value Remains the Same in + + align:start position:0% +cycle then the value Remains the Same in + + + align:start position:0% +cycle then the value Remains the Same in +other + + align:start position:0% +other + + + align:start position:0% +other +words a b + + align:start position:0% +words a b + + + align:start position:0% +words a b +c is equal to C + + align:start position:0% +c is equal to C + + + align:start position:0% +c is equal to C +AB is equal to + + align:start position:0% +AB is equal to + + + align:start position:0% +AB is equal to +BCA and I I just want to highlight one + + align:start position:0% +BCA and I I just want to highlight one + + + align:start position:0% +BCA and I I just want to highlight one +thing and after that that this is equal + + align:start position:0% + + + + align:start position:0% + +to minus of + + align:start position:0% +to minus of + + + align:start position:0% +to minus of +ACB so if you FP two things so rather so + + align:start position:0% +ACB so if you FP two things so rather so + + + align:start position:0% +ACB so if you FP two things so rather so +the cycle has broken now it is not ABC + + align:start position:0% +the cycle has broken now it is not ABC + + + align:start position:0% +the cycle has broken now it is not ABC +it is ACB so you have broken the cycle + + align:start position:0% +it is ACB so you have broken the cycle + + + align:start position:0% +it is ACB so you have broken the cycle +and you have reversed the cycle so + + align:start position:0% +and you have reversed the cycle so + + + align:start position:0% +and you have reversed the cycle so +rather than ABC you're not going ACB so + + align:start position:0% +rather than ABC you're not going ACB so + + + align:start position:0% +rather than ABC you're not going ACB so +that's why you have a negative sign and + + align:start position:0% +that's why you have a negative sign and + + + align:start position:0% +that's why you have a negative sign and +you can check that that if you flip just + + align:start position:0% +you can check that that if you flip just + + + align:start position:0% +you can check that that if you flip just +two rows just B and C only one row if + + align:start position:0% +two rows just B and C only one row if + + + align:start position:0% +two rows just B and C only one row if +you like if you exchange one time then + + align:start position:0% +you like if you exchange one time then + + + align:start position:0% +you like if you exchange one time then +the is a negative sign in front of the + + align:start position:0% +the is a negative sign in front of the + + + align:start position:0% +the is a negative sign in front of the +determinant so that is why there is a + + align:start position:0% +determinant so that is why there is a + + + align:start position:0% +determinant so that is why there is a +negative sign here and now here you can + + align:start position:0% +negative sign here and now here you can + + + align:start position:0% +negative sign here and now here you can +again make the cycle that this is equal + + align:start position:0% +again make the cycle that this is equal + + + align:start position:0% +again make the cycle that this is equal +to minus + + align:start position:0% +to minus + + + align:start position:0% +to minus +BAC again the cycle is now ACB not ABC + + align:start position:0% +BAC again the cycle is now ACB not ABC + + + align:start position:0% +BAC again the cycle is now ACB not ABC +and is equal to + + align:start position:0% +and is equal to + + + align:start position:0% +and is equal to +minus CB a okay so this is a very very + + align:start position:0% +minus CB a okay so this is a very very + + + align:start position:0% +minus CB a okay so this is a very very +important property I hope that you are + + align:start position:0% +important property I hope that you are + + + align:start position:0% +important property I hope that you are +able to Now understand what we are doing + + align:start position:0% +able to Now understand what we are doing + + + align:start position:0% +able to Now understand what we are doing +so we discuss a lot of things very + + align:start position:0% +so we discuss a lot of things very + + + align:start position:0% +so we discuss a lot of things very +quickly one thing that this is a scalar + + align:start position:0% +quickly one thing that this is a scalar + + + align:start position:0% +quickly one thing that this is a scalar +product a cross b. C is a scalar product + + align:start position:0% +product a cross b. C is a scalar product + + + align:start position:0% +product a cross b. C is a scalar product +a because A cross B is a vector and then + + align:start position:0% +a because A cross B is a vector and then + + + align:start position:0% +a because A cross B is a vector and then +you're dotting it with + + align:start position:0% +you're dotting it with + + + align:start position:0% +you're dotting it with +c and + + align:start position:0% +c and + + + align:start position:0% +c and +then uh the second thing we discussed + + align:start position:0% +then uh the second thing we discussed + + + align:start position:0% +then uh the second thing we discussed +was you can flip the sign of Dot and + + align:start position:0% +was you can flip the sign of Dot and + + + align:start position:0% +was you can flip the sign of Dot and +cross that is because whenever when + + align:start position:0% +cross that is because whenever when + + + align:start position:0% +cross that is because whenever when +through the determinant property I + + align:start position:0% +through the determinant property I + + + align:start position:0% +through the determinant property I +showed that when you flip twice you can + + align:start position:0% +showed that when you flip twice you can + + + align:start position:0% +showed that when you flip twice you can +basically see that a cross b. C is equal + + align:start position:0% +basically see that a cross b. C is equal + + + align:start position:0% +basically see that a cross b. C is equal +to a b Cross C in the third property you + + align:start position:0% +to a b Cross C in the third property you + + + align:start position:0% +to a b Cross C in the third property you +said there is a cyclic property of the + + align:start position:0% +said there is a cyclic property of the + + + align:start position:0% +said there is a cyclic property of the +whole system and that we saw by + + align:start position:0% +whole system and that we saw by + + + align:start position:0% +whole system and that we saw by +exchanging the dot and cross that uh + + align:start position:0% +exchanging the dot and cross that uh + + + align:start position:0% +exchanging the dot and cross that uh +sorry by exchanging like using the + + align:start position:0% +sorry by exchanging like using the + + + align:start position:0% +sorry by exchanging like using the +property of dot product that a cross b. + + align:start position:0% +property of dot product that a cross b. + + + align:start position:0% +property of dot product that a cross b. +C is equal to c. A cross + + align:start position:0% +C is equal to c. A cross + + + align:start position:0% +C is equal to c. A cross +B so there are a lot of things here so a + + align:start position:0% +B so there are a lot of things here so a + + + align:start position:0% +B so there are a lot of things here so a +you should take some time to just digest + + align:start position:0% +you should take some time to just digest + + + align:start position:0% +you should take some time to just digest +these things because these things will + + align:start position:0% +these things because these things will + + + align:start position:0% +these things because these things will +be used in and out and they're very very + + align:start position:0% +be used in and out and they're very very + + + align:start position:0% +be used in and out and they're very very +important for the chapter of vectors so + + align:start position:0% +important for the chapter of vectors so + + + align:start position:0% +important for the chapter of vectors so +please please take your time to + + align:start position:0% +please please take your time to + + + align:start position:0% +please please take your time to +understand these things just very slowly + + align:start position:0% +understand these things just very slowly + + + align:start position:0% +understand these things just very slowly +go through like writing these equations + + align:start position:0% +go through like writing these equations + + + align:start position:0% +go through like writing these equations +and then you should be able to + + align:start position:0% +and then you should be able to + + + align:start position:0% +and then you should be able to +understand this I don't think this is a + + align:start position:0% +understand this I don't think this is a + + + align:start position:0% +understand this I don't think this is a +very very difficult concept to grasp but + + align:start position:0% +very very difficult concept to grasp but + + + align:start position:0% +very very difficult concept to grasp but +once you have but for once you have to + + align:start position:0% +once you have but for once you have to + + + align:start position:0% +once you have but for once you have to +really understand it + + align:start position:0% +really understand it + + + align:start position:0% +really understand it +okay so two things you can exchange the + + align:start position:0% +okay so two things you can exchange the + + + align:start position:0% +okay so two things you can exchange the +sign of Dot and cross and there's a + + align:start position:0% +sign of Dot and cross and there's a + + + align:start position:0% +sign of Dot and cross and there's a +cyclic property and for a. B Cross C you + + align:start position:0% +cyclic property and for a. B Cross C you + + + align:start position:0% +cyclic property and for a. B Cross C you +can just use a determinant okay you can + + align:start position:0% +can just use a determinant okay you can + + + align:start position:0% +can just use a determinant okay you can +use a + + align:start position:0% +use a + + + align:start position:0% +use a +determinant now the next thing that I + + align:start position:0% +determinant now the next thing that I + + + align:start position:0% +determinant now the next thing that I +want to discuss like all uh other + + align:start position:0% +want to discuss like all uh other + + + align:start position:0% +want to discuss like all uh other +products is the physical + + align:start position:0% + + + + align:start position:0% + +significance is the physical + + align:start position:0% +significance is the physical + + + align:start position:0% +significance is the physical +significance and + + align:start position:0% + + + + align:start position:0% + +what the what is the physical + + align:start position:0% +what the what is the physical + + + align:start position:0% +what the what is the physical +significance of A cross B do c + + align:start position:0% + + + + align:start position:0% + +so what we basically we have to + + align:start position:0% +so what we basically we have to + + + align:start position:0% +so what we basically we have to +realize is that this condition a do B + + align:start position:0% +realize is that this condition a do B + + + align:start position:0% +realize is that this condition a do B +Cross C if this is zero + + align:start position:0% + + + + align:start position:0% + +then then a b c are + + align:start position:0% +then then a b c are + + + align:start position:0% +then then a b c are +coplanar are Cooper + + align:start position:0% + + + + align:start position:0% + +and I want to prove so I've written the + + align:start position:0% +and I want to prove so I've written the + + + align:start position:0% +and I want to prove so I've written the +so this is the first part of the + + align:start position:0% + + + + align:start position:0% + +significance and I want to stress on + + align:start position:0% +significance and I want to stress on + + + align:start position:0% +significance and I want to stress on +this quite a lot because this is + + align:start position:0% +this quite a lot because this is + + + align:start position:0% +this quite a lot because this is +something which you will use again a lot + + align:start position:0% +something which you will use again a lot + + + align:start position:0% +something which you will use again a lot +in questions so what does this mean how + + align:start position:0% +in questions so what does this mean how + + + align:start position:0% +in questions so what does this mean how +what does this mean so let us say you + + align:start position:0% +what does this mean so let us say you + + + align:start position:0% +what does this mean so let us say you +have two Vector + + align:start position:0% +have two Vector + + + align:start position:0% +have two Vector +B and + + align:start position:0% +B and + + + align:start position:0% +B and +C B and C here then B Cross C so two + + align:start position:0% +C B and C here then B Cross C so two + + + align:start position:0% +C B and C here then B Cross C so two +vectors are always cop linear okay so if + + align:start position:0% +vectors are always cop linear okay so if + + + align:start position:0% +vectors are always cop linear okay so if +you have two vectors like this let us + + align:start position:0% +you have two vectors like this let us + + + align:start position:0% +you have two vectors like this let us +say you have two vectors like this then + + align:start position:0% +say you have two vectors like this then + + + align:start position:0% +say you have two vectors like this then +you can always pass a plane through them + + align:start position:0% +you can always pass a plane through them + + + align:start position:0% +you can always pass a plane through them +right you can always pass a plane + + align:start position:0% +right you can always pass a plane + + + align:start position:0% +right you can always pass a plane +through these two vectors so B and C are + + align:start position:0% +through these two vectors so B and C are + + + align:start position:0% +through these two vectors so B and C are +vectors two vectors and then you you + + align:start position:0% +vectors two vectors and then you you + + + align:start position:0% +vectors two vectors and then you you +have pass a plane through them then + + align:start position:0% +have pass a plane through them then + + + align:start position:0% +have pass a plane through them then +there is a perpendicular Vector B Cross + + align:start position:0% +there is a perpendicular Vector B Cross + + + align:start position:0% +there is a perpendicular Vector B Cross +C is a vector perpendicular to both B + + align:start position:0% +C is a vector perpendicular to both B + + + align:start position:0% +C is a vector perpendicular to both B +and C this is something we have + + align:start position:0% +and C this is something we have + + + align:start position:0% +and C this is something we have +discussed in cross product so if you are + + align:start position:0% +discussed in cross product so if you are + + + align:start position:0% +discussed in cross product so if you are +not if you cannot recall it please go + + align:start position:0% +not if you cannot recall it please go + + + align:start position:0% +not if you cannot recall it please go +and check back the notes on cross + + align:start position:0% +and check back the notes on cross + + + align:start position:0% +and check back the notes on cross +product and whenever there is B Cross C + + align:start position:0% +product and whenever there is B Cross C + + + align:start position:0% +product and whenever there is B Cross C +the vector which is let's say n is + + align:start position:0% +the vector which is let's say n is + + + align:start position:0% +the vector which is let's say n is +perpendicular to both B and C now what + + align:start position:0% +perpendicular to both B and C now what + + + align:start position:0% +perpendicular to both B and C now what +we are seeing is + + align:start position:0% +we are seeing is + + + align:start position:0% +we are seeing is +that this n Vector is perpendicular to + + align:start position:0% +that this n Vector is perpendicular to + + + align:start position:0% +that this n Vector is perpendicular to +the plane of B and C now a do n because + + align:start position:0% +the plane of B and C now a do n because + + + align:start position:0% +the plane of B and C now a do n because +B Cross C is n because B Cross C here we + + align:start position:0% +B Cross C is n because B Cross C here we + + + align:start position:0% +B Cross C is n because B Cross C here we +are saying let say B Cross C is n a do n + + align:start position:0% +are saying let say B Cross C is n a do n + + + align:start position:0% +are saying let say B Cross C is n a do n +is + + align:start position:0% +is + + + align:start position:0% +is +Zer a do n is z what does this mean that + + align:start position:0% +Zer a do n is z what does this mean that + + + align:start position:0% +Zer a do n is z what does this mean that +A and N are perpendicular now so if a + + align:start position:0% +A and N are perpendicular now so if a + + + align:start position:0% +A and N are perpendicular now so if a +and N are perpendicular to now then a + + align:start position:0% +and N are perpendicular to now then a + + + align:start position:0% +and N are perpendicular to now then a +has to line in the plate a has to lie in + + align:start position:0% +has to line in the plate a has to lie in + + + align:start position:0% +has to line in the plate a has to lie in +the plane of B and C so this means that + + align:start position:0% +the plane of B and C so this means that + + + align:start position:0% +the plane of B and C so this means that +a has to lie in the plane of B and C + + align:start position:0% +a has to lie in the plane of B and C + + + align:start position:0% +a has to lie in the plane of B and C +C or a b c are co-planar and what does + + align:start position:0% +C or a b c are co-planar and what does + + + align:start position:0% +C or a b c are co-planar and what does +coplanar mean Cooper means that if there + + align:start position:0% +coplanar mean Cooper means that if there + + + align:start position:0% +coplanar mean Cooper means that if there +are three vectors you can pass a plane + + align:start position:0% +are three vectors you can pass a plane + + + align:start position:0% +are three vectors you can pass a plane +through them okay so two vectors you can + + align:start position:0% +through them okay so two vectors you can + + + align:start position:0% +through them okay so two vectors you can +always pass a plane through them but if + + align:start position:0% +always pass a plane through them but if + + + align:start position:0% +always pass a plane through them but if +there are three vectors let's say there + + align:start position:0% +there are three vectors let's say there + + + align:start position:0% +there are three vectors let's say there +are two vectors like this and one vector + + align:start position:0% +are two vectors like this and one vector + + + align:start position:0% +are two vectors like this and one vector +one vector like like this you cannot + + align:start position:0% +one vector like like this you cannot + + + align:start position:0% +one vector like like this you cannot +pass a plane through them only two + + align:start position:0% +pass a plane through them only two + + + align:start position:0% +pass a plane through them only two +vectors you can pass a plane but if + + align:start position:0% +vectors you can pass a plane but if + + + align:start position:0% +vectors you can pass a plane but if +there are three vectors you can not + + align:start position:0% +there are three vectors you can not + + + align:start position:0% +there are three vectors you can not +always pass a plane through them and + + align:start position:0% +always pass a plane through them and + + + align:start position:0% +always pass a plane through them and +when can you pass a plane through them + + align:start position:0% +when can you pass a plane through them + + + align:start position:0% +when can you pass a plane through them +whenever a do B cross c0 or the scale + + align:start position:0% +whenever a do B cross c0 or the scale + + + align:start position:0% +whenever a do B cross c0 or the scale +triple product is zero and how are we + + align:start position:0% +triple product is zero and how are we + + + align:start position:0% +triple product is zero and how are we +explaining this we are saying that b + + align:start position:0% +explaining this we are saying that b + + + align:start position:0% +explaining this we are saying that b +Cross C is a PL is a vector which is + + align:start position:0% +Cross C is a PL is a vector which is + + + align:start position:0% +Cross C is a PL is a vector which is +perpendicular to both B and C or the is + + align:start position:0% +perpendicular to both B and C or the is + + + align:start position:0% +perpendicular to both B and C or the is +perpendicular to the plane of B and C + + align:start position:0% +perpendicular to the plane of B and C + + + align:start position:0% +perpendicular to the plane of B and C +and when a do n is zero that means A and + + align:start position:0% +and when a do n is zero that means A and + + + align:start position:0% +and when a do n is zero that means A and +B Cross C are perpendicular because dot + + align:start position:0% +B Cross C are perpendicular because dot + + + align:start position:0% +B Cross C are perpendicular because dot +product is zero when our two vectors are + + align:start position:0% +product is zero when our two vectors are + + + align:start position:0% +product is zero when our two vectors are +perpendicular so that forces a has to + + align:start position:0% +perpendicular so that forces a has to + + + align:start position:0% +perpendicular so that forces a has to +line in the plane of B and C okay this + + align:start position:0% +line in the plane of B and C okay this + + + align:start position:0% +line in the plane of B and C okay this +is very very important and I mean you + + align:start position:0% +is very very important and I mean you + + + align:start position:0% +is very very important and I mean you +just have to just remember this that + + align:start position:0% +just have to just remember this that + + + align:start position:0% +just have to just remember this that +whenever you see that two vectors are + + align:start position:0% +whenever you see that two vectors are + + + align:start position:0% +whenever you see that two vectors are +coplanar just + + align:start position:0% +coplanar just + + + align:start position:0% +coplanar just +very uh you should remember that the + + align:start position:0% +very uh you should remember that the + + + align:start position:0% +very uh you should remember that the +scalar T product is zero also you should + + align:start position:0% +scalar T product is zero also you should + + + align:start position:0% +scalar T product is zero also you should +remember this that coplanarity also + + align:start position:0% + + + + align:start position:0% + +means coplanarity also + + align:start position:0% + + + + align:start position:0% + +means that you can + + align:start position:0% + + + + align:start position:0% + +represent the third Vector as a linear + + align:start position:0% +represent the third Vector as a linear + + + align:start position:0% +represent the third Vector as a linear +combination of the first two vectors + + align:start position:0% +combination of the first two vectors + + + align:start position:0% +combination of the first two vectors +that is also a way to understand Co + + align:start position:0% +that is also a way to understand Co + + + align:start position:0% +that is also a way to understand Co +planarity what is co planarity so when + + align:start position:0% +planarity what is co planarity so when + + + align:start position:0% +planarity what is co planarity so when +will this happen when can you represent + + align:start position:0% +will this happen when can you represent + + + align:start position:0% +will this happen when can you represent +a vector as two two some uh linear + + align:start position:0% +a vector as two two some uh linear + + + align:start position:0% +a vector as two two some uh linear +combination of A and B so let us say + + align:start position:0% +combination of A and B so let us say + + + align:start position:0% +combination of A and B so let us say +there is a and + + align:start position:0% +there is a and + + + align:start position:0% +there is a and +b and there is a plane which passes + + align:start position:0% +b and there is a plane which passes + + + align:start position:0% +b and there is a plane which passes +through them then you're saying that you + + align:start position:0% +through them then you're saying that you + + + align:start position:0% +through them then you're saying that you +are stretching one vector or doing + + align:start position:0% +are stretching one vector or doing + + + align:start position:0% +are stretching one vector or doing +something to the like stretch l and m + + align:start position:0% +something to the like stretch l and m + + + align:start position:0% +something to the like stretch l and m +like could be anything any in uh any + + align:start position:0% +like could be anything any in uh any + + + align:start position:0% +like could be anything any in uh any +real values let is say you made one + + align:start position:0% +real values let is say you made one + + + align:start position:0% +real values let is say you made one +vector half another Vector double and + + align:start position:0% +vector half another Vector double and + + + align:start position:0% +vector half another Vector double and +then now you're adding them so you will + + align:start position:0% +then now you're adding them so you will + + + align:start position:0% +then now you're adding them so you will +basically be completing some sort of + + align:start position:0% +basically be completing some sort of + + + align:start position:0% +basically be completing some sort of +some sort of addition and addition + + align:start position:0% +some sort of addition and addition + + + align:start position:0% +some sort of addition and addition +forces you to not leave that plane so + + align:start position:0% +forces you to not leave that plane so + + + align:start position:0% +forces you to not leave that plane so +that is why that these three things are + + align:start position:0% +that is why that these three things are + + + align:start position:0% +that is why that these three things are +copal and you can also imagine if you + + align:start position:0% +copal and you can also imagine if you + + + align:start position:0% +copal and you can also imagine if you +have if I put uh C is equal to L A Plus + + align:start position:0% +have if I put uh C is equal to L A Plus + + + align:start position:0% +have if I put uh C is equal to L A Plus +MB here right uh L A Plus MB here C here + + align:start position:0% +MB here right uh L A Plus MB here C here + + + align:start position:0% +MB here right uh L A Plus MB here C here +as L A Plus MB then if I take Cross of B + + align:start position:0% +as L A Plus MB then if I take Cross of B + + + align:start position:0% +as L A Plus MB then if I take Cross of B +with B it will become + + align:start position:0% +with B it will become + + + align:start position:0% +with B it will become +zero right uh and then it will basically + + align:start position:0% +zero right uh and then it will basically + + + align:start position:0% +zero right uh and then it will basically +become a do B cross a right a do B cross + + align:start position:0% +become a do B cross a right a do B cross + + + align:start position:0% +become a do B cross a right a do B cross +a and then you can flip Dot and cross + + align:start position:0% +a and then you can flip Dot and cross + + + align:start position:0% +a and then you can flip Dot and cross +Dot and cross and it'll become uh a + + align:start position:0% +Dot and cross and it'll become uh a + + + align:start position:0% +Dot and cross and it'll become uh a +cross a do B and Dot Cross of a with a + + align:start position:0% +cross a do B and Dot Cross of a with a + + + align:start position:0% +cross a do B and Dot Cross of a with a +will also be zero I mean you can check + + align:start position:0% +will also be zero I mean you can check + + + align:start position:0% +will also be zero I mean you can check +you can just put it back here and check + + align:start position:0% +you can just put it back here and check + + + align:start position:0% +you can just put it back here and check +yourself that this will always come out + + align:start position:0% +yourself that this will always come out + + + align:start position:0% +yourself that this will always come out +to be zero so coity also you can also + + align:start position:0% +to be zero so coity also you can also + + + align:start position:0% +to be zero so coity also you can also +understand that City means that one + + align:start position:0% +understand that City means that one + + + align:start position:0% +understand that City means that one +vector can be written as a linear + + align:start position:0% +vector can be written as a linear + + + align:start position:0% +vector can be written as a linear +combination of the other two vectors and + + align:start position:0% +combination of the other two vectors and + + + align:start position:0% +combination of the other two vectors and +that ABC is the scal table product ABC + + align:start position:0% +that ABC is the scal table product ABC + + + align:start position:0% +that ABC is the scal table product ABC +is + + align:start position:0% +is + + + align:start position:0% +is +zero so I hope that uh this is sort of + + align:start position:0% +zero so I hope that uh this is sort of + + + align:start position:0% +zero so I hope that uh this is sort of +giving some insight to you what does + + align:start position:0% +giving some insight to you what does + + + align:start position:0% +giving some insight to you what does +scalar product mean so dot product was + + align:start position:0% +scalar product mean so dot product was + + + align:start position:0% +scalar product mean so dot product was +the projection uh of Vector on the other + + align:start position:0% +the projection uh of Vector on the other + + + align:start position:0% +the projection uh of Vector on the other +cross product was a vector perpendicular + + align:start position:0% +cross product was a vector perpendicular + + + align:start position:0% +cross product was a vector perpendicular +to the both the vectors and scalar dble + + align:start position:0% +to the both the vectors and scalar dble + + + align:start position:0% +to the both the vectors and scalar dble +product equal to zero means a condition + + align:start position:0% +product equal to zero means a condition + + + align:start position:0% +product equal to zero means a condition +for City + + align:start position:0% +for City + + + align:start position:0% +for City +okay second thing that I just want you + + align:start position:0% +okay second thing that I just want you + + + align:start position:0% +okay second thing that I just want you +to learn as a formula that is more like + + align:start position:0% +to learn as a formula that is more like + + + align:start position:0% +to learn as a formula that is more like +a formula that if there is a parallel + + align:start position:0% +a formula that if there is a parallel + + + align:start position:0% +a formula that if there is a parallel +pipid what is a parallel pipid is like + + align:start position:0% + + + + align:start position:0% + +a it's like a rectangle but rather than + + align:start position:0% +a it's like a rectangle but rather than + + + align:start position:0% +a it's like a rectangle but rather than +having perpendicular + + align:start position:0% +having perpendicular + + + align:start position:0% +having perpendicular +sides uh + + align:start position:0% + + + + align:start position:0% + +it is + + align:start position:0% +it is + + + align:start position:0% +it is +just parallel so it's like a 3D + + align:start position:0% +just parallel so it's like a 3D + + + align:start position:0% +just parallel so it's like a 3D +parallelogram okay 3D + + align:start position:0% +parallelogram okay 3D + + + align:start position:0% +parallelogram okay 3D +parallelogram and the volume of uh + + align:start position:0% +parallelogram and the volume of uh + + + align:start position:0% +parallelogram and the volume of uh +volume of parall + + align:start position:0% + + + + align:start position:0% + +pipid is + + align:start position:0% +pipid is + + + align:start position:0% +pipid is +ABC if the three sides are a vector B + + align:start position:0% +ABC if the three sides are a vector B + + + align:start position:0% +ABC if the three sides are a vector B +Vector C Vector then the volume of + + align:start position:0% +Vector C Vector then the volume of + + + align:start position:0% +Vector C Vector then the volume of +parallel is a BC there there are a lot + + align:start position:0% +parallel is a BC there there are a lot + + + align:start position:0% +parallel is a BC there there are a lot +of proofs for this I don't think you + + align:start position:0% +of proofs for this I don't think you + + + align:start position:0% +of proofs for this I don't think you +need to really understand the proofs so + + align:start position:0% +need to really understand the proofs so + + + align:start position:0% +need to really understand the proofs so +this is like a vector is this entire + + align:start position:0% +this is like a vector is this entire + + + align:start position:0% +this is like a vector is this entire +side C Vector is this entire side B + + align:start position:0% +side C Vector is this entire side B + + + align:start position:0% +side C Vector is this entire side B +Vector is this entire side then the + + align:start position:0% +Vector is this entire side then the + + + align:start position:0% +Vector is this entire side then the +volume of parallel paper is + + align:start position:0% +volume of parallel paper is + + + align:start position:0% +volume of parallel paper is +ABC + + align:start position:0% +ABC + + + align:start position:0% +ABC +okay and + + align:start position:0% +okay and + + + align:start position:0% +okay and +uh if there's a tetrahedron + + align:start position:0% + + + + align:start position:0% + +if there's a + + align:start position:0% + + + + align:start position:0% + +tetrahedron so I'm just + + align:start position:0% + + + + align:start position:0% + +trite with these sides a b c then Tetra + + align:start position:0% +trite with these sides a b c then Tetra + + + align:start position:0% +trite with these sides a b c then Tetra +hrin would be ABC by + + align:start position:0% +hrin would be ABC by + + + align:start position:0% +hrin would be ABC by +6 okay + + align:start position:0% + + + + align:start position:0% + +so I mean if it's a little bit unclear + + align:start position:0% +so I mean if it's a little bit unclear + + + align:start position:0% +so I mean if it's a little bit unclear +to you just do not worry too much about + + align:start position:0% +to you just do not worry too much about + + + align:start position:0% +to you just do not worry too much about +this just uh go back and look at some + + align:start position:0% +this just uh go back and look at some + + + align:start position:0% +this just uh go back and look at some +images of tetrad parallel pipid and just + + align:start position:0% +images of tetrad parallel pipid and just + + + align:start position:0% +images of tetrad parallel pipid and just +remember that the side whenever sides + + align:start position:0% +remember that the side whenever sides + + + align:start position:0% +remember that the side whenever sides +are a b and c then the volume of + + align:start position:0% +are a b and c then the volume of + + + align:start position:0% +are a b and c then the volume of +parallel PID is a BC and volume of + + align:start position:0% +parallel PID is a BC and volume of + + + align:start position:0% +parallel PID is a BC and volume of +tetradon is ABC by 6 okay so we have + + align:start position:0% +tetradon is ABC by 6 okay so we have + + + align:start position:0% +tetradon is ABC by 6 okay so we have +discussed again now let us recap + + align:start position:0% +discussed again now let us recap + + + align:start position:0% +discussed again now let us recap +whatever we have discussed so this this + + align:start position:0% +whatever we have discussed so this this + + + align:start position:0% +whatever we have discussed so this this +ends the property discussion + + align:start position:0% +ends the property discussion + + + align:start position:0% +ends the property discussion +of uh property discussion of uh the SC + + align:start position:0% +of uh property discussion of uh the SC + + + align:start position:0% +of uh property discussion of uh the SC +triple product + + align:start position:0% +triple product + + + align:start position:0% +triple product +and what we have discussed is if a do B + + align:start position:0% +and what we have discussed is if a do B + + + align:start position:0% +and what we have discussed is if a do B +Cross C we can write it as a + + align:start position:0% +Cross C we can write it as a + + + align:start position:0% +Cross C we can write it as a +determinant okay uh then we + + align:start position:0% +determinant okay uh then we + + + align:start position:0% +determinant okay uh then we +also also learned that you can flip Dot + + align:start position:0% +also also learned that you can flip Dot + + + align:start position:0% +also also learned that you can flip Dot +and cross and that is I showed that by + + align:start position:0% +and cross and that is I showed that by + + + align:start position:0% +and cross and that is I showed that by +if you flip to twice uh scale + + align:start position:0% +if you flip to twice uh scale + + + align:start position:0% +if you flip to twice uh scale +determinant twice then you can get the + + align:start position:0% +determinant twice then you can get the + + + align:start position:0% +determinant twice then you can get the +same sign and hence a CR b equal a b CR + + align:start position:0% +same sign and hence a CR b equal a b CR + + + align:start position:0% +same sign and hence a CR b equal a b CR +C then we learn about the cyclic + + align:start position:0% +C then we learn about the cyclic + + + align:start position:0% +C then we learn about the cyclic +property of ABC and that there will be + + align:start position:0% +property of ABC and that there will be + + + align:start position:0% +property of ABC and that there will be +minus sign whenever the cycle is broken + + align:start position:0% +minus sign whenever the cycle is broken + + + align:start position:0% +minus sign whenever the cycle is broken +or becomes reversed and then we + + align:start position:0% +or becomes reversed and then we + + + align:start position:0% +or becomes reversed and then we +discussed two things about physical sign + + align:start position:0% +discussed two things about physical sign + + + align:start position:0% +discussed two things about physical sign +significance condition for coplanarity + + align:start position:0% +significance condition for coplanarity + + + align:start position:0% +significance condition for coplanarity +means that one vector is a linear + + align:start position:0% +means that one vector is a linear + + + align:start position:0% +means that one vector is a linear +combination of the other two vectors and + + align:start position:0% +combination of the other two vectors and + + + align:start position:0% +combination of the other two vectors and +that is also expressed in terms of a b + + align:start position:0% +that is also expressed in terms of a b + + + align:start position:0% +that is also expressed in terms of a b +Cross C equal to Z because B Cross C is + + align:start position:0% +Cross C equal to Z because B Cross C is + + + align:start position:0% +Cross C equal to Z because B Cross C is +a vector perpendicular to the plane of B + + align:start position:0% +a vector perpendicular to the plane of B + + + align:start position:0% +a vector perpendicular to the plane of B +and C and if a DOT that a do n is zero + + align:start position:0% +and C and if a DOT that a do n is zero + + + align:start position:0% +and C and if a DOT that a do n is zero +that means a has to lie in the plane of + + align:start position:0% +that means a has to lie in the plane of + + + align:start position:0% +that means a has to lie in the plane of +B and C and finally if ABC are sides of + + align:start position:0% +B and C and finally if ABC are sides of + + + align:start position:0% +B and C and finally if ABC are sides of +parall and tetraden then the Vol volume + + align:start position:0% +parall and tetraden then the Vol volume + + + align:start position:0% +parall and tetraden then the Vol volume +is ABC and ABC by 6 okay so these are + + align:start position:0% +is ABC and ABC by 6 okay so these are + + + align:start position:0% +is ABC and ABC by 6 okay so these are +the properties that we have discussed + + align:start position:0% +the properties that we have discussed + + + align:start position:0% +the properties that we have discussed +please remember them learn them they + + align:start position:0% +please remember them learn them they + + + align:start position:0% +please remember them learn them they +should be on fingertips whenever you see + + align:start position:0% +should be on fingertips whenever you see + + + align:start position:0% +should be on fingertips whenever you see +them + + align:start position:0% +them + + + align:start position:0% +them +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now let us try to let us try to do + + align:start position:0% +so now let us try to let us try to do + + + align:start position:0% +so now let us try to let us try to do +some very quick problems uh small + + align:start position:0% +some very quick problems uh small + + + align:start position:0% +some very quick problems uh small +problems and the problems + + align:start position:0% +problems and the problems + + + align:start position:0% +problems and the problems +are first + + align:start position:0% +are first + + + align:start position:0% +are first +problem so let + + align:start position:0% +problem so let + + + align:start position:0% +problem so let +me create some clear demarcation so the + + align:start position:0% +me create some clear demarcation so the + + + align:start position:0% +me create some clear demarcation so the +problem first problem + + align:start position:0% +problem first problem + + + align:start position:0% +problem first problem +is if AB BC + + align:start position:0% + + + + align:start position:0% + +R if ABC + + align:start position:0% +R if ABC + + + align:start position:0% +R if ABC +are co- + + align:start position:0% + + + + align:start position:0% + +planer if ABC are + + align:start position:0% + + + + align:start position:0% + +Cooper what is the value + + align:start position:0% + + + + align:start position:0% + +of what is the value + + align:start position:0% +of what is the value + + + align:start position:0% +of what is the value +of 2 A minus B + + align:start position:0% + + + + align:start position:0% + +2 B- + + align:start position:0% + + + + align:start position:0% + +C and 2 c - + + align:start position:0% +C and 2 c - + + + align:start position:0% +C and 2 c - +A + + align:start position:0% +A + + + align:start position:0% +A +okay so they have we have been told that + + align:start position:0% +okay so they have we have been told that + + + align:start position:0% +okay so they have we have been told that +there are three vectors A B C which are + + align:start position:0% +there are three vectors A B C which are + + + align:start position:0% +there are three vectors A B C which are +co-planar and then we have been asked to + + align:start position:0% +co-planar and then we have been asked to + + + align:start position:0% +co-planar and then we have been asked to +find the what the value of some scal + + align:start position:0% +find the what the value of some scal + + + align:start position:0% +find the what the value of some scal +triple product of linear combination of + + align:start position:0% +triple product of linear combination of + + + align:start position:0% +triple product of linear combination of +A and B and C so there is one way to + + align:start position:0% +A and B and C so there is one way to + + + align:start position:0% +A and B and C so there is one way to +solve this problem is that you take the + + align:start position:0% +solve this problem is that you take the + + + align:start position:0% +solve this problem is that you take the +cross of this so I mean you can just + + align:start position:0% +cross of this so I mean you can just + + + align:start position:0% +cross of this so I mean you can just +start taking cross and then taking Dot + + align:start position:0% +start taking cross and then taking Dot + + + align:start position:0% +start taking cross and then taking Dot +and then trying to find something in + + align:start position:0% +and then trying to find something in + + + align:start position:0% +and then trying to find something in +terms of a b and c but my point here is + + align:start position:0% +terms of a b and c but my point here is + + + align:start position:0% +terms of a b and c but my point here is +really to make you understand what what + + align:start position:0% +really to make you understand what what + + + align:start position:0% +really to make you understand what what +this means so think think about three + + align:start position:0% +this means so think think about three + + + align:start position:0% +this means so think think about three +vectors think about three vectors let's + + align:start position:0% +vectors think about three vectors let's + + + align:start position:0% +vectors think about three vectors let's +say a b and c and they're co-planar and + + align:start position:0% +say a b and c and they're co-planar and + + + align:start position:0% +say a b and c and they're co-planar and +they're co-planar so if you have uh two + + align:start position:0% +they're co-planar so if you have uh two + + + align:start position:0% +they're co-planar so if you have uh two +vectors like this and you have the third + + align:start position:0% +vectors like this and you have the third + + + align:start position:0% +vectors like this and you have the third +Vector like this they they're in a plane + + align:start position:0% +Vector like this they they're in a plane + + + align:start position:0% +Vector like this they they're in a plane +now what you doing is you just taking a + + align:start position:0% +now what you doing is you just taking a + + + align:start position:0% +now what you doing is you just taking a +linear combination of these three + + align:start position:0% +linear combination of these three + + + align:start position:0% +linear combination of these three +vectors can you ever go out of the plane + + align:start position:0% +vectors can you ever go out of the plane + + + align:start position:0% +vectors can you ever go out of the plane +can you ever create a vector which is + + align:start position:0% +can you ever create a vector which is + + + align:start position:0% +can you ever create a vector which is +out of the plane so for instance if C is + + align:start position:0% +out of the plane so for instance if C is + + + align:start position:0% +out of the plane so for instance if C is +La a plus MB because ABC Are CL planer + + align:start position:0% +La a plus MB because ABC Are CL planer + + + align:start position:0% +La a plus MB because ABC Are CL planer +that means L A Plus + + align:start position:0% +that means L A Plus + + + align:start position:0% +that means L A Plus +MB then 2 A minus B is a linear + + align:start position:0% +MB then 2 A minus B is a linear + + + align:start position:0% +MB then 2 A minus B is a linear +combination of a and b 2 B minus C + + align:start position:0% +combination of a and b 2 B minus C + + + align:start position:0% +combination of a and b 2 B minus C +because C is L A Plus MB is also a + + align:start position:0% +because C is L A Plus MB is also a + + + align:start position:0% +because C is L A Plus MB is also a +linear combination of A and B and 2 C + + align:start position:0% +linear combination of A and B and 2 C + + + align:start position:0% +linear combination of A and B and 2 C +minus a is also a linear combination of + + align:start position:0% +minus a is also a linear combination of + + + align:start position:0% +minus a is also a linear combination of +A and B so even all these three vectors + + align:start position:0% +A and B so even all these three vectors + + + align:start position:0% +A and B so even all these three vectors +are just linear combination of A and B + + align:start position:0% +are just linear combination of A and B + + + align:start position:0% +are just linear combination of A and B +so that means that they are in the same + + align:start position:0% +so that means that they are in the same + + + align:start position:0% +so that means that they are in the same +plane so you don't even need to do + + align:start position:0% +plane so you don't even need to do + + + align:start position:0% +plane so you don't even need to do +anything you don't even even have to + + align:start position:0% +anything you don't even even have to + + + align:start position:0% +anything you don't even even have to +calculate you can just directly write + + align:start position:0% +calculate you can just directly write + + + align:start position:0% +calculate you can just directly write +that this is equal to zero because if a + + align:start position:0% +that this is equal to zero because if a + + + align:start position:0% +that this is equal to zero because if a +BC are co-planar then any linear + + align:start position:0% +BC are co-planar then any linear + + + align:start position:0% +BC are co-planar then any linear +combination of these vectors would also + + align:start position:0% +combination of these vectors would also + + + align:start position:0% +combination of these vectors would also +lie in the same plane so these three + + align:start position:0% +lie in the same plane so these three + + + align:start position:0% +lie in the same plane so these three +vectors are just in the same plane so + + align:start position:0% +vectors are just in the same plane so + + + align:start position:0% +vectors are just in the same plane so +you don't even need to worry about it + + align:start position:0% +you don't even need to worry about it + + + align:start position:0% +you don't even need to worry about it +you just have to understand okay these + + align:start position:0% +you just have to understand okay these + + + align:start position:0% +you just have to understand okay these +three vectors are coplanar so any linear + + align:start position:0% +three vectors are coplanar so any linear + + + align:start position:0% +three vectors are coplanar so any linear +combination of them has to be coplanar + + align:start position:0% +combination of them has to be coplanar + + + align:start position:0% +combination of them has to be coplanar +so that means this is zero which is a + + align:start position:0% +so that means this is zero which is a + + + align:start position:0% +so that means this is zero which is a +condition of scal triple product so I + + align:start position:0% +condition of scal triple product so I + + + align:start position:0% +condition of scal triple product so I +can bet that a lot of students here will + + align:start position:0% +can bet that a lot of students here will + + + align:start position:0% +can bet that a lot of students here will +try to solve this problem + + align:start position:0% +try to solve this problem + + + align:start position:0% +try to solve this problem +they will they will start with ABC is + + align:start position:0% +they will they will start with ABC is + + + align:start position:0% +they will they will start with ABC is +zero and then they will expand this + + align:start position:0% +zero and then they will expand this + + + align:start position:0% +zero and then they will expand this +using taking a cross here and a DOT here + + align:start position:0% +using taking a cross here and a DOT here + + + align:start position:0% +using taking a cross here and a DOT here +and then opening up the brackets and + + align:start position:0% +and then opening up the brackets and + + + align:start position:0% +and then opening up the brackets and +then trying to solve it somehow but you + + align:start position:0% +then trying to solve it somehow but you + + + align:start position:0% +then trying to solve it somehow but you +don't even have to you just have to + + align:start position:0% +don't even have to you just have to + + + align:start position:0% +don't even have to you just have to +understand that coplanarity means that + + align:start position:0% +understand that coplanarity means that + + + align:start position:0% +understand that coplanarity means that +the three three vectors are in the same + + align:start position:0% +the three three vectors are in the same + + + align:start position:0% +the three three vectors are in the same +plane or they can be expressed a linear + + align:start position:0% +plane or they can be expressed a linear + + + align:start position:0% +plane or they can be expressed a linear +combination of each other and any Vector + + align:start position:0% +combination of each other and any Vector + + + align:start position:0% +combination of each other and any Vector +will also lie in the same plane okay so + + align:start position:0% +will also lie in the same plane okay so + + + align:start position:0% +will also lie in the same plane okay so +I hope that this gives you some insight + + align:start position:0% +I hope that this gives you some insight + + + align:start position:0% +I hope that this gives you some insight +about scalar triple + + align:start position:0% + + + + align:start position:0% + +okay the second problem that I want to + + align:start position:0% +okay the second problem that I want to + + + align:start position:0% +okay the second problem that I want to +do is + + align:start position:0% +do is + + + align:start position:0% +do is +that what is the value of + + align:start position:0% + + + + align:start position:0% + +Lambda + + align:start position:0% +Lambda + + + align:start position:0% +Lambda +Lambda such + + align:start position:0% + + + + align:start position:0% + +that Lambda + + align:start position:0% + + + + align:start position:0% + +i+ J + K + + align:start position:0% + + + + align:start position:0% + +comma I + + align:start position:0% +comma I + + + align:start position:0% +comma I ++ 2 Lambda J + K + + align:start position:0% + + + + align:start position:0% + +cap and I + J + + align:start position:0% +cap and I + J + + + align:start position:0% +cap and I + J ++ are + + align:start position:0% + + + + align:start position:0% + +coer okay so what is the value of Lambda + + align:start position:0% +coer okay so what is the value of Lambda + + + align:start position:0% +coer okay so what is the value of Lambda +such that these three vectors are co- + + align:start position:0% +such that these three vectors are co- + + + align:start position:0% +such that these three vectors are co- +planer the question is begging you would + + align:start position:0% +planer the question is begging you would + + + align:start position:0% +planer the question is begging you would +say remember the condition of + + align:start position:0% +say remember the condition of + + + align:start position:0% +say remember the condition of +coplanarity the condition of coplanarity + + align:start position:0% +coplanarity the condition of coplanarity + + + align:start position:0% +coplanarity the condition of coplanarity +is a b cross c0 that's it so what how + + align:start position:0% +is a b cross c0 that's it so what how + + + align:start position:0% +is a b cross c0 that's it so what how +can you write a b Cross C is that we + + align:start position:0% +can you write a b Cross C is that we + + + align:start position:0% +can you write a b Cross C is that we +have discussed it is a determinant so + + align:start position:0% +have discussed it is a determinant so + + + align:start position:0% +have discussed it is a determinant so +let us call this a vector B vector and C + + align:start position:0% +let us call this a vector B vector and C + + + align:start position:0% +let us call this a vector B vector and C +Vector then a do B Cross + + align:start position:0% +Vector then a do B Cross + + + align:start position:0% +Vector then a do B Cross +C is equal + + align:start position:0% +C is equal + + + align:start position:0% +C is equal +to Lambda so just take the coefficients + + align:start position:0% +to Lambda so just take the coefficients + + + align:start position:0% +to Lambda so just take the coefficients +Lambda 1 1 + + align:start position:0% +Lambda 1 1 + + + align:start position:0% +Lambda 1 1 +1 2 + + align:start position:0% + + + + align:start position:0% + +Lambda + + align:start position:0% +Lambda + + + align:start position:0% +Lambda +1 and 11 one + + align:start position:0% + + + + align:start position:0% + +one and you have to + + align:start position:0% +one and you have to + + + align:start position:0% +one and you have to +make this equal to zero + + align:start position:0% +make this equal to zero + + + align:start position:0% +make this equal to zero +okay and if you you should be now I hope + + align:start position:0% +okay and if you you should be now I hope + + + align:start position:0% +okay and if you you should be now I hope +with time it will be become you become + + align:start position:0% +with time it will be become you become + + + align:start position:0% +with time it will be become you become +very quick with uh + + align:start position:0% +very quick with uh + + + align:start position:0% +very quick with uh +taking uh opening up determinants uh and + + align:start position:0% +taking uh opening up determinants uh and + + + align:start position:0% +taking uh opening up determinants uh and +if you open up the determinant you will + + align:start position:0% +if you open up the determinant you will + + + align:start position:0% +if you open up the determinant you will +actually find that this is 2 Lambda + + align:start position:0% +actually find that this is 2 Lambda + + + align:start position:0% +actually find that this is 2 Lambda +squ - 3 Lambda + 1 = 0 you can check + + align:start position:0% +squ - 3 Lambda + 1 = 0 you can check + + + align:start position:0% +squ - 3 Lambda + 1 = 0 you can check +that this is what it comes out and that + + align:start position:0% +that this is what it comes out and that + + + align:start position:0% +that this is what it comes out and that +would give you the + + align:start position:0% +would give you the + + + align:start position:0% +would give you the +answer at Lambda equal to + + align:start position:0% +answer at Lambda equal to + + + align:start position:0% +answer at Lambda equal to +1 comma + + align:start position:0% +1 comma + + + align:start position:0% +1 comma +half so this again in an objective type + + align:start position:0% +half so this again in an objective type + + + align:start position:0% +half so this again in an objective type +problem this could be a multiple choice + + align:start position:0% +problem this could be a multiple choice + + + align:start position:0% +problem this could be a multiple choice +problem and can we check can we check + + align:start position:0% +problem and can we check can we check + + + align:start position:0% +problem and can we check can we check +the answer if we what does Lambda equal + + align:start position:0% +the answer if we what does Lambda equal + + + align:start position:0% +the answer if we what does Lambda equal +to 1 mean + + align:start position:0% +to 1 mean + + + align:start position:0% +to 1 mean +so what does Lambda equal to 1 and half + + align:start position:0% +so what does Lambda equal to 1 and half + + + align:start position:0% +so what does Lambda equal to 1 and half +mean here okay so if Lambda is equal to + + align:start position:0% +mean here okay so if Lambda is equal to + + + align:start position:0% +mean here okay so if Lambda is equal to +1 then this becomes I + J + K and this + + align:start position:0% +1 then this becomes I + J + K and this + + + align:start position:0% +1 then this becomes I + J + K and this +becomes I + J plus K so they're the same + + align:start position:0% +becomes I + J plus K so they're the same + + + align:start position:0% +becomes I + J plus K so they're the same +Vector so if they're the same Vector + + align:start position:0% +Vector so if they're the same Vector + + + align:start position:0% +Vector so if they're the same Vector +then that means that their cross will + + align:start position:0% +then that means that their cross will + + + align:start position:0% +then that means that their cross will +always be zero so if they're the same + + align:start position:0% +always be zero so if they're the same + + + align:start position:0% +always be zero so if they're the same +Vector then basically this becomes two + + align:start position:0% +Vector then basically this becomes two + + + align:start position:0% +Vector then basically this becomes two +vectors which can which can always uh + + align:start position:0% +vectors which can which can always uh + + + align:start position:0% +vectors which can which can always uh +which will obviously be CL planer so + + align:start position:0% +which will obviously be CL planer so + + + align:start position:0% +which will obviously be CL planer so +rather than three vectors if the two + + align:start position:0% +rather than three vectors if the two + + + align:start position:0% +rather than three vectors if the two +vectors are same basically you are + + align:start position:0% +vectors are same basically you are + + + align:start position:0% +vectors are same basically you are +saying that there are only two vectors + + align:start position:0% +saying that there are only two vectors + + + align:start position:0% +saying that there are only two vectors +which are always copar if Lambda is half + + align:start position:0% +which are always copar if Lambda is half + + + align:start position:0% +which are always copar if Lambda is half +then this becomes I plus J plus K so and + + align:start position:0% +then this becomes I plus J plus K so and + + + align:start position:0% +then this becomes I plus J plus K so and +then these two become same so again they + + align:start position:0% +then these two become same so again they + + + align:start position:0% +then these two become same so again they +become two vectors and they're always + + align:start position:0% +become two vectors and they're always + + + align:start position:0% +become two vectors and they're always +Cooper okay so I hope that with this you + + align:start position:0% +Cooper okay so I hope that with this you + + + align:start position:0% +Cooper okay so I hope that with this you +are able to physically also understand + + align:start position:0% +are able to physically also understand + + + align:start position:0% +are able to physically also understand +the meaning of scal triple product so in + + align:start position:0% +the meaning of scal triple product so in + + + align:start position:0% +the meaning of scal triple product so in +this video we covered very important + + align:start position:0% +this video we covered very important + + + align:start position:0% +this video we covered very important +topic of scaler triple product we + + align:start position:0% +topic of scaler triple product we + + + align:start position:0% +topic of scaler triple product we +discussed its properties we discussed + + align:start position:0% +discussed its properties we discussed + + + align:start position:0% +discussed its properties we discussed +four properties and then we did two + + align:start position:0% +four properties and then we did two + + + align:start position:0% +four properties and then we did two +examples to understand what is the + + align:start position:0% +examples to understand what is the + + + align:start position:0% +examples to understand what is the +meaning of scalar Dev product and how to + + align:start position:0% +meaning of scalar Dev product and how to + + + align:start position:0% +meaning of scalar Dev product and how to +apply it in the next video we'll be + + align:start position:0% +apply it in the next video we'll be + + + align:start position:0% +apply it in the next video we'll be +discussing vector triple product uh and + + align:start position:0% +discussing vector triple product uh and + + + align:start position:0% +discussing vector triple product uh and +I hope you enjoyed this video please + + align:start position:0% +I hope you enjoyed this video please + + + align:start position:0% +I hope you enjoyed this video please +check out the next video thank you \ No newline at end of file diff --git a/_jKHejk45Sg.txt b/_jKHejk45Sg.txt new file mode 100644 index 0000000000000000000000000000000000000000..a055ba2eb53bc0bf1feb650f3606bd2cf0a5fdfe --- /dev/null +++ b/_jKHejk45Sg.txt @@ -0,0 +1,9411 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free to make a donation or to view + + align:start position:0% +for free to make a donation or to view + + + align:start position:0% +for free to make a donation or to view +additional materials from hundreds of + + align:start position:0% +additional materials from hundreds of + + + align:start position:0% +additional materials from hundreds of +MIT courses visit MIT opencourseware at + + align:start position:0% +MIT courses visit MIT opencourseware at + + + align:start position:0% +MIT courses visit MIT opencourseware at +ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +there's some comments from the grader + + align:start position:0% +there's some comments from the grader + + + align:start position:0% +there's some comments from the grader +who look at your homeworks so a couple + + align:start position:0% +who look at your homeworks so a couple + + + align:start position:0% +who look at your homeworks so a couple +of a couple of points to remember that + + align:start position:0% +of a couple of points to remember that + + + align:start position:0% +of a couple of points to remember that +they seem to be sort of pervasive in + + align:start position:0% +they seem to be sort of pervasive in + + + align:start position:0% +they seem to be sort of pervasive in +several homeworks one is that one will + + align:start position:0% +several homeworks one is that one will + + + align:start position:0% +several homeworks one is that one will +do Snell's law we have to apply + + align:start position:0% +do Snell's law we have to apply + + + align:start position:0% +do Snell's law we have to apply +the rule their own goals like n sine + + align:start position:0% +the rule their own goals like n sine + + + align:start position:0% +the rule their own goals like n sine +theta equals and prime sine theta Prime + + align:start position:0% +theta equals and prime sine theta Prime + + + align:start position:0% +theta equals and prime sine theta Prime +right so remember that theta prime is + + align:start position:0% +right so remember that theta prime is + + + align:start position:0% +right so remember that theta prime is +measured with respect to the normal to + + align:start position:0% +measured with respect to the normal to + + + align:start position:0% +measured with respect to the normal to +the interface so if this line is the + + align:start position:0% +the interface so if this line is the + + + align:start position:0% +the interface so if this line is the +interface I have for example air and + + align:start position:0% +interface I have for example air and + + + align:start position:0% +interface I have for example air and +glass here oh + + align:start position:0% + + + + align:start position:0% + +I + + align:start position:0% +I + + + align:start position:0% +I +think my hand is confusing maybe I + + align:start position:0% +think my hand is confusing maybe I + + + align:start position:0% +think my hand is confusing maybe I +should turn off the coffee + + align:start position:0% + + + + align:start position:0% + +okay so if this is the interface aring + + align:start position:0% +okay so if this is the interface aring + + + align:start position:0% +okay so if this is the interface aring +glass yeah I think my hand was + + align:start position:0% +glass yeah I think my hand was + + + align:start position:0% +glass yeah I think my hand was +professional + + align:start position:0% +professional + + + align:start position:0% +professional +okay and + + align:start position:0% +okay and + + + align:start position:0% +okay and +there a is incident for example like + + align:start position:0% +there a is incident for example like + + + align:start position:0% +there a is incident for example like +this + + align:start position:0% +this + + + align:start position:0% +this +then we apply Snell's law with respect + + align:start position:0% +then we apply Snell's law with respect + + + align:start position:0% +then we apply Snell's law with respect +to the normal so this is the angle theta + + align:start position:0% +to the normal so this is the angle theta + + + align:start position:0% +to the normal so this is the angle theta +naught this one out here not the other + + align:start position:0% +naught this one out here not the other + + + align:start position:0% +naught this one out here not the other +way around but this one and of course + + align:start position:0% +way around but this one and of course + + + align:start position:0% +way around but this one and of course +the same goes to the other side of the + + align:start position:0% +the same goes to the other side of the + + + align:start position:0% +the same goes to the other side of the +whoops the other side of the interface + + align:start position:0% +whoops the other side of the interface + + + align:start position:0% +whoops the other side of the interface +that I would go in kind of like this + + align:start position:0% +that I would go in kind of like this + + + align:start position:0% +that I would go in kind of like this +that would be set a prime okay so that + + align:start position:0% +that would be set a prime okay so that + + + align:start position:0% +that would be set a prime okay so that +was one one comment from the homeworks + + align:start position:0% + + + + align:start position:0% + +the other comment is about PIR the IR + + align:start position:0% +the other comment is about PIR the IR + + + align:start position:0% +the other comment is about PIR the IR +actually happens for all angle of + + align:start position:0% +actually happens for all angle of + + + align:start position:0% +actually happens for all angle of +incidence that are larger than the + + align:start position:0% +incidence that are larger than the + + + align:start position:0% +incidence that are larger than the +critical angle there seem to be some + + align:start position:0% +critical angle there seem to be some + + + align:start position:0% +critical angle there seem to be some +confusion that somehow dar happens only + + align:start position:0% +confusion that somehow dar happens only + + + align:start position:0% +confusion that somehow dar happens only +at the critical angle that is not true + + align:start position:0% +at the critical angle that is not true + + + align:start position:0% +at the critical angle that is not true +in fact strictly speaking at exactly the + + align:start position:0% +in fact strictly speaking at exactly the + + + align:start position:0% +in fact strictly speaking at exactly the +critical angle TIR does not happen what + + align:start position:0% +critical angle TIR does not happen what + + + align:start position:0% +critical angle TIR does not happen what +does happen is this surface wave that I + + align:start position:0% +does happen is this surface wave that I + + + align:start position:0% +does happen is this surface wave that I +mentioned in the note but for all angles + + align:start position:0% +mentioned in the note but for all angles + + + align:start position:0% +mentioned in the note but for all angles +that are + + align:start position:0% +that are + + + align:start position:0% +that are +greater than the critical angle this is + + align:start position:0% +greater than the critical angle this is + + + align:start position:0% +greater than the critical angle this is +when we have the TIR + + align:start position:0% +when we have the TIR + + + align:start position:0% +when we have the TIR +addition for all those angles from + + align:start position:0% +addition for all those angles from + + + align:start position:0% +addition for all those angles from +critical all the way to whatever it is + + align:start position:0% +critical all the way to whatever it is + + + align:start position:0% +critical all the way to whatever it is +90 90 degrees I suppose + + align:start position:0% + + + + align:start position:0% + +the third comment and actually this is + + align:start position:0% +the third comment and actually this is + + + align:start position:0% +the third comment and actually this is +the last one + + align:start position:0% +the last one + + + align:start position:0% +the last one +the third comment is about the speed of + + align:start position:0% +the third comment is about the speed of + + + align:start position:0% +the third comment is about the speed of +light + + align:start position:0% +light + + + align:start position:0% +light +some of you and actually this is also in + + align:start position:0% +some of you and actually this is also in + + + align:start position:0% +some of you and actually this is also in +relation to the swimmer problem + + align:start position:0% +relation to the swimmer problem + + + align:start position:0% +relation to the swimmer problem +there was some confusion where the speed + + align:start position:0% +there was some confusion where the speed + + + align:start position:0% +there was some confusion where the speed +of light is proportional to ending to + + align:start position:0% +of light is proportional to ending to + + + align:start position:0% +of light is proportional to ending to +the index of refraction or inversely + + align:start position:0% +the index of refraction or inversely + + + align:start position:0% +the index of refraction or inversely +proportional it is in fact inversely + + align:start position:0% +proportional it is in fact inversely + + + align:start position:0% +proportional it is in fact inversely +proportional the speed of light goes + + align:start position:0% +proportional the speed of light goes + + + align:start position:0% +proportional the speed of light goes +like C / n + + align:start position:0% +like C / n + + + align:start position:0% +like C / n +okay where n is the index of refraction + + align:start position:0% +okay where n is the index of refraction + + + align:start position:0% +okay where n is the index of refraction +and I don't have the same mnemonic for + + align:start position:0% +and I don't have the same mnemonic for + + + align:start position:0% +and I don't have the same mnemonic for +this but but + + align:start position:0% +this but but + + + align:start position:0% +this but but +one way to remember it is that C the + + align:start position:0% +one way to remember it is that C the + + + align:start position:0% +one way to remember it is that C the +speed of light is value is the highest + + align:start position:0% +speed of light is value is the highest + + + align:start position:0% +speed of light is value is the highest +speed that anything can have so + + align:start position:0% +speed that anything can have so + + + align:start position:0% +speed that anything can have so +therefore when light enters the material + + align:start position:0% +therefore when light enters the material + + + align:start position:0% +therefore when light enters the material +can only go slower + + align:start position:0% +can only go slower + + + align:start position:0% +can only go slower +so so then the index of refraction tells + + align:start position:0% +so so then the index of refraction tells + + + align:start position:0% +so so then the index of refraction tells +you the amount by which the speed of + + align:start position:0% +you the amount by which the speed of + + + align:start position:0% +you the amount by which the speed of +light becomes slower in a given and + + align:start position:0% +light becomes slower in a given and + + + align:start position:0% +light becomes slower in a given and +given dielectric + + align:start position:0% +given dielectric + + + align:start position:0% +given dielectric +okay so these are these are some + + align:start position:0% +okay so these are these are some + + + align:start position:0% +okay so these are these are some +things that are useful to keep in mind + + align:start position:0% +things that are useful to keep in mind + + + align:start position:0% +things that are useful to keep in mind +as we move forward + + align:start position:0% + + + + align:start position:0% + +okay these are two dots don't mean + + align:start position:0% +okay these are two dots don't mean + + + align:start position:0% +okay these are two dots don't mean +anything it's just the ink from the + + align:start position:0% +anything it's just the ink from the + + + align:start position:0% +anything it's just the ink from the +market that penetrated the piece of + + align:start position:0% +market that penetrated the piece of + + + align:start position:0% +market that penetrated the piece of +paper so please ignore them + + align:start position:0% +paper so please ignore them + + + align:start position:0% +paper so please ignore them +okay so last time the topic was + + align:start position:0% +okay so last time the topic was + + + align:start position:0% +okay so last time the topic was +composite optical elements so we started + + align:start position:0% +composite optical elements so we started + + + align:start position:0% +composite optical elements so we started +with an example of two lenses + + align:start position:0% +with an example of two lenses + + + align:start position:0% +with an example of two lenses +two thin lenses that were in tandem and + + align:start position:0% +two thin lenses that were in tandem and + + + align:start position:0% +two thin lenses that were in tandem and +we did the imaging condition + + align:start position:0% +we did the imaging condition + + + align:start position:0% +we did the imaging condition +magnification and all those beautiful + + align:start position:0% +magnification and all those beautiful + + + align:start position:0% +magnification and all those beautiful +things with it and then we also looked + + align:start position:0% +things with it and then we also looked + + + align:start position:0% +things with it and then we also looked +at the thin lens I'm sorry at the thick + + align:start position:0% +at the thin lens I'm sorry at the thick + + + align:start position:0% +at the thin lens I'm sorry at the thick +lens where the thickness is defined as + + align:start position:0% +lens where the thickness is defined as + + + align:start position:0% +lens where the thickness is defined as +you recall it is defined relative to the + + align:start position:0% +you recall it is defined relative to the + + + align:start position:0% +you recall it is defined relative to the +paraxial approximation if the distance + + align:start position:0% +paraxial approximation if the distance + + + align:start position:0% +paraxial approximation if the distance +between the two curved surfaces exceeds + + align:start position:0% +between the two curved surfaces exceeds + + + align:start position:0% +between the two curved surfaces exceeds +the + + align:start position:0% +the + + + align:start position:0% +the +cosine theta whatever it is that the + + align:start position:0% +cosine theta whatever it is that the + + + align:start position:0% +cosine theta whatever it is that the +paraxial approximation + + align:start position:0% +paraxial approximation + + + align:start position:0% +paraxial approximation +limits for the for the negligible + + align:start position:0% +limits for the for the negligible + + + align:start position:0% +limits for the for the negligible +distance then we call the lens thick and + + align:start position:0% +distance then we call the lens thick and + + + align:start position:0% +distance then we call the lens thick and +we saw that + + align:start position:0% +we saw that + + + align:start position:0% +we saw that +there is some differences for example + + align:start position:0% +there is some differences for example + + + align:start position:0% +there is some differences for example +the focal length is a little bit + + align:start position:0% +the focal length is a little bit + + + align:start position:0% +the focal length is a little bit +different the formula than it is for the + + align:start position:0% +different the formula than it is for the + + + align:start position:0% +different the formula than it is for the +case of the thin lens but the primary + + align:start position:0% +case of the thin lens but the primary + + + align:start position:0% +case of the thin lens but the primary +reason why we did it is because I wanted + + align:start position:0% +reason why we did it is because I wanted + + + align:start position:0% +reason why we did it is because I wanted +to define this concept of principle + + align:start position:0% +to define this concept of principle + + + align:start position:0% +to define this concept of principle +planes so the principle planes + + align:start position:0% +planes so the principle planes + + + align:start position:0% +planes so the principle planes +are moved slowly so the camera can + + align:start position:0% +are moved slowly so the camera can + + + align:start position:0% +are moved slowly so the camera can +follow me so the principle planes are + + align:start position:0% +follow me so the principle planes are + + + align:start position:0% +follow me so the principle planes are +basically look the locations where the + + align:start position:0% +basically look the locations where the + + + align:start position:0% +basically look the locations where the +Rays bend at once so in a thick optical + + align:start position:0% +Rays bend at once so in a thick optical + + + align:start position:0% +Rays bend at once so in a thick optical +element whether it is a thick land so it + + align:start position:0% +element whether it is a thick land so it + + + align:start position:0% +element whether it is a thick land so it +is a composite of several lenses in + + align:start position:0% +is a composite of several lenses in + + + align:start position:0% +is a composite of several lenses in +tandem as you can imagine the Rays will + + align:start position:0% +tandem as you can imagine the Rays will + + + align:start position:0% +tandem as you can imagine the Rays will +Bend several times they may Bend up down + + align:start position:0% +Bend several times they may Bend up down + + + align:start position:0% +Bend several times they may Bend up down +straight and so on and so forth but the + + align:start position:0% +straight and so on and so forth but the + + + align:start position:0% +straight and so on and so forth but the +idea is that if you take parallel ray + + align:start position:0% +idea is that if you take parallel ray + + + align:start position:0% +idea is that if you take parallel ray +from infinity after however many times + + align:start position:0% +from infinity after however many times + + + align:start position:0% +from infinity after however many times +it bends in this case it bends twice + + align:start position:0% +it bends in this case it bends twice + + + align:start position:0% +it bends in this case it bends twice +once here and once here eventually it + + align:start position:0% +once here and once here eventually it + + + align:start position:0% +once here and once here eventually it +comes out at the final propagation and + + align:start position:0% +comes out at the final propagation and + + + align:start position:0% +comes out at the final propagation and +so the principal plane is the plane that + + align:start position:0% +so the principal plane is the plane that + + + align:start position:0% +so the principal plane is the plane that +you obtain if you extend the incoming + + align:start position:0% +you obtain if you extend the incoming + + + align:start position:0% +you obtain if you extend the incoming +ray you extend the outgoing ray and you + + align:start position:0% +ray you extend the outgoing ray and you + + + align:start position:0% +ray you extend the outgoing ray and you +find where they meet that is the + + align:start position:0% +find where they meet that is the + + + align:start position:0% +find where they meet that is the +principal plane in fact in general it is + + align:start position:0% +principal plane in fact in general it is + + + align:start position:0% +principal plane in fact in general it is +a principal surface if you really do the + + align:start position:0% +a principal surface if you really do the + + + align:start position:0% +a principal surface if you really do the +geometry right it is not a plane it + + align:start position:0% +geometry right it is not a plane it + + + align:start position:0% +geometry right it is not a plane it +turns out to be a curved surface but + + align:start position:0% +turns out to be a curved surface but + + + align:start position:0% +turns out to be a curved surface but +within the paraxial approximation it is + + align:start position:0% +within the paraxial approximation it is + + + align:start position:0% +within the paraxial approximation it is +a plane so that's why we refer it with + + align:start position:0% +a plane so that's why we refer it with + + + align:start position:0% +a plane so that's why we refer it with +sometimes as a principal plane or the + + align:start position:0% +sometimes as a principal plane or the + + + align:start position:0% +sometimes as a principal plane or the +principal surface I + + align:start position:0% +principal surface I + + + align:start position:0% +principal surface I +kind of try to stick to the term + + align:start position:0% +kind of try to stick to the term + + + align:start position:0% +kind of try to stick to the term +principal plane in the note and then + + align:start position:0% +principal plane in the note and then + + + align:start position:0% +principal plane in the note and then +relative to the principal plane as we + + align:start position:0% +relative to the principal plane as we + + + align:start position:0% +relative to the principal plane as we +did last time you can define the various + + align:start position:0% +did last time you can define the various + + + align:start position:0% +did last time you can define the various +quantities the effective focal length is + + align:start position:0% +quantities the effective focal length is + + + align:start position:0% +quantities the effective focal length is +simply the distance from that principal + + align:start position:0% +simply the distance from that principal + + + align:start position:0% +simply the distance from that principal +plane to the focal point so basically as + + align:start position:0% +plane to the focal point so basically as + + + align:start position:0% +plane to the focal point so basically as +far as a laser that are coming from the + + align:start position:0% +far as a laser that are coming from the + + + align:start position:0% +far as a laser that are coming from the +left are concerned the principal plane + + align:start position:0% +left are concerned the principal plane + + + align:start position:0% +left are concerned the principal plane +is acting like a thin lens right because + + align:start position:0% +is acting like a thin lens right because + + + align:start position:0% +is acting like a thin lens right because +the + + align:start position:0% +the + + + align:start position:0% +the +is acting like a thin lens with the + + align:start position:0% +is acting like a thin lens with the + + + align:start position:0% +is acting like a thin lens with the +focal length equal to the effective + + align:start position:0% +focal length equal to the effective + + + align:start position:0% +focal length equal to the effective +focal length of the composite okay + + align:start position:0% +focal length of the composite okay + + + align:start position:0% +focal length of the composite okay +because this is the Ray coming from + + align:start position:0% +because this is the Ray coming from + + + align:start position:0% +because this is the Ray coming from +infinity and when it comes out it is as + + align:start position:0% +infinity and when it comes out it is as + + + align:start position:0% +infinity and when it comes out it is as +if I had put a thin lens in this + + align:start position:0% +if I had put a thin lens in this + + + align:start position:0% +if I had put a thin lens in this +particular location the + + align:start position:0% +particular location the + + + align:start position:0% +particular location the +opposite is true for + + align:start position:0% +opposite is true for + + + align:start position:0% +opposite is true for +images at infinity so if you take away + + align:start position:0% +images at infinity so if you take away + + + align:start position:0% +images at infinity so if you take away +from this point here it actually goes to + + align:start position:0% +from this point here it actually goes to + + + align:start position:0% +from this point here it actually goes to +the first principal plane and then takes + + align:start position:0% +the first principal plane and then takes + + + align:start position:0% +the first principal plane and then takes +off to infinity now of course again this + + align:start position:0% +off to infinity now of course again this + + + align:start position:0% +off to infinity now of course again this +is what I get when I take the incoming + + align:start position:0% +is what I get when I take the incoming + + + align:start position:0% +is what I get when I take the incoming +ray and the outgoing ray and I find + + align:start position:0% +ray and the outgoing ray and I find + + + align:start position:0% +ray and the outgoing ray and I find +where they meet in general this Ray also + + align:start position:0% +where they meet in general this Ray also + + + align:start position:0% +where they meet in general this Ray also +suffers multiple refraction but if I + + align:start position:0% +suffers multiple refraction but if I + + + align:start position:0% +suffers multiple refraction but if I +take the first one and the very last one + + align:start position:0% +take the first one and the very last one + + + align:start position:0% +take the first one and the very last one +and then I can have a thin lens at the + + align:start position:0% +and then I can have a thin lens at the + + + align:start position:0% +and then I can have a thin lens at the +first principal plane so this is the + + align:start position:0% +first principal plane so this is the + + + align:start position:0% +first principal plane so this is the +this is the idea and we can see the + + align:start position:0% +this is the idea and we can see the + + + align:start position:0% +this is the idea and we can see the +reason why they are convenient when we + + align:start position:0% +reason why they are convenient when we + + + align:start position:0% +reason why they are convenient when we +do the imaging condition for the day for + + align:start position:0% +do the imaging condition for the day for + + + align:start position:0% +do the imaging condition for the day for +the composite optical element so will + + align:start position:0% +the composite optical element so will + + + align:start position:0% +the composite optical element so will +not do this against a back went through + + align:start position:0% +not do this against a back went through + + + align:start position:0% +not do this against a back went through +it in great detail last time but you can + + align:start position:0% +it in great detail last time but you can + + + align:start position:0% +it in great detail last time but you can +see that basically if you know the + + align:start position:0% +see that basically if you know the + + + align:start position:0% +see that basically if you know the +principal planes then we don't have to + + align:start position:0% +principal planes then we don't have to + + + align:start position:0% +principal planes then we don't have to +worry about the rest of the physical + + align:start position:0% +worry about the rest of the physical + + + align:start position:0% +worry about the rest of the physical +system anymore because we can discover + + align:start position:0% +system anymore because we can discover + + + align:start position:0% +system anymore because we can discover +things like imaging condition + + align:start position:0% +things like imaging condition + + + align:start position:0% +things like imaging condition +magnification and so on and so forth + + align:start position:0% +magnification and so on and so forth + + + align:start position:0% +magnification and so on and so forth +simply by applying the rules that we + + align:start position:0% +simply by applying the rules that we + + + align:start position:0% +simply by applying the rules that we +learned in the case of the thin lens so + + align:start position:0% +learned in the case of the thin lens so + + + align:start position:0% +learned in the case of the thin lens so +for example in this case if in order to + + align:start position:0% +for example in this case if in order to + + + align:start position:0% +for example in this case if in order to +find the image I take a ray that is + + align:start position:0% +find the image I take a ray that is + + + align:start position:0% +find the image I take a ray that is +horizontal therefore it could have come + + align:start position:0% +horizontal therefore it could have come + + + align:start position:0% +horizontal therefore it could have come +from infinity I drag it all the way to + + align:start position:0% +from infinity I drag it all the way to + + + align:start position:0% +from infinity I drag it all the way to +the second principal plane then I know + + align:start position:0% +the second principal plane then I know + + + align:start position:0% +the second principal plane then I know +it has to go through the focus okay and + + align:start position:0% +it has to go through the focus okay and + + + align:start position:0% +it has to go through the focus okay and +then I extend it further then I take + + align:start position:0% +then I extend it further then I take + + + align:start position:0% +then I extend it further then I take +another one that goes for the first + + align:start position:0% +another one that goes for the first + + + align:start position:0% +another one that goes for the first +focus then I know that the first + + align:start position:0% +focus then I know that the first + + + align:start position:0% +focus then I know that the first +principle plane this ray will have to + + align:start position:0% +principle plane this ray will have to + + + align:start position:0% +principle plane this ray will have to +become horizontal and again take off + + align:start position:0% +become horizontal and again take off + + + align:start position:0% +become horizontal and again take off +towards infinity + + align:start position:0% +towards infinity + + + align:start position:0% +towards infinity +so therefore this ray goes like this and + + align:start position:0% +so therefore this ray goes like this and + + + align:start position:0% +so therefore this ray goes like this and +then where they meet is actually the + + align:start position:0% +then where they meet is actually the + + + align:start position:0% +then where they meet is actually the +location of the image so this is the + + align:start position:0% +location of the image so this is the + + + align:start position:0% +location of the image so this is the +ideal and then all the rest of the + + align:start position:0% +ideal and then all the rest of the + + + align:start position:0% +ideal and then all the rest of the +formulas about the imaging distances the + + align:start position:0% +formulas about the imaging distances the + + + align:start position:0% +formulas about the imaging distances the +magnifications lateral angular and so on + + align:start position:0% +magnifications lateral angular and so on + + + align:start position:0% +magnifications lateral angular and so on +and so forth they all fall out from the + + align:start position:0% +and so forth they all fall out from the + + + align:start position:0% +and so forth they all fall out from the +similar triangles in this diagram just + + align:start position:0% +similar triangles in this diagram just + + + align:start position:0% +similar triangles in this diagram just +in the same way we did them for the + + align:start position:0% +in the same way we did them for the + + + align:start position:0% +in the same way we did them for the +Finland except now we have this sort of + + align:start position:0% +Finland except now we have this sort of + + + align:start position:0% +Finland except now we have this sort of +additional space between the two + + align:start position:0% +additional space between the two + + + align:start position:0% +additional space between the two +principal planes so you have to be + + align:start position:0% +principal planes so you have to be + + + align:start position:0% +principal planes so you have to be +careful when we deal with the Ray that + + align:start position:0% +careful when we deal with the Ray that + + + align:start position:0% +careful when we deal with the Ray that +is coming horizontal at the input it has + + align:start position:0% +is coming horizontal at the input it has + + + align:start position:0% +is coming horizontal at the input it has +to bend at the second principal plane + + align:start position:0% +to bend at the second principal plane + + + align:start position:0% +to bend at the second principal plane +and when we take the Ray that goes + + align:start position:0% +and when we take the Ray that goes + + + align:start position:0% +and when we take the Ray that goes +through the first focal point and comes + + align:start position:0% +through the first focal point and comes + + + align:start position:0% +through the first focal point and comes +out horizontal that one has to go + + align:start position:0% +out horizontal that one has to go + + + align:start position:0% +out horizontal that one has to go +through the first principal plane and + + align:start position:0% +through the first principal plane and + + + align:start position:0% +through the first principal plane and +the reason I'm emphasizing this is + + align:start position:0% +the reason I'm emphasizing this is + + + align:start position:0% +the reason I'm emphasizing this is +because + + align:start position:0% +because + + + align:start position:0% +because +this is the generic edge were the first + + align:start position:0% +this is the generic edge were the first + + + align:start position:0% +this is the generic edge were the first +principal plane is to the left the + + align:start position:0% +principal plane is to the left the + + + align:start position:0% +principal plane is to the left the +second is to the right but there is + + align:start position:0% +second is to the right but there is + + + align:start position:0% +second is to the right but there is +optical systems where they may actually + + align:start position:0% +optical systems where they may actually + + + align:start position:0% +optical systems where they may actually +be swapped you may have the second + + align:start position:0% +be swapped you may have the second + + + align:start position:0% +be swapped you may have the second +principal plane to the left of the first + + align:start position:0% +principal plane to the left of the first + + + align:start position:0% +principal plane to the left of the first +principal plane there is no rule that + + align:start position:0% +principal plane there is no rule that + + + align:start position:0% +principal plane there is no rule that +forbids that that can happen so that's + + align:start position:0% +forbids that that can happen so that's + + + align:start position:0% +forbids that that can happen so that's +fine we still have to apply the same + + align:start position:0% +fine we still have to apply the same + + + align:start position:0% +fine we still have to apply the same +rule but we have to be careful where we + + align:start position:0% +rule but we have to be careful where we + + + align:start position:0% +rule but we have to be careful where we +bend the Ray so one of the homeworks you + + align:start position:0% +bend the Ray so one of the homeworks you + + + align:start position:0% +bend the Ray so one of the homeworks you +will see the homework that we posted + + align:start position:0% +will see the homework that we posted + + + align:start position:0% +will see the homework that we posted +today and they're due actually next week + + align:start position:0% +today and they're due actually next week + + + align:start position:0% +today and they're due actually next week +you will see that this happens in one of + + align:start position:0% +you will see that this happens in one of + + + align:start position:0% +you will see that this happens in one of +the optical systems that will give you + + align:start position:0% +the optical systems that will give you + + + align:start position:0% +the optical systems that will give you +their the second principal plane is + + align:start position:0% +their the second principal plane is + + + align:start position:0% +their the second principal plane is +actually to the left so I'll let you + + align:start position:0% +actually to the left so I'll let you + + + align:start position:0% +actually to the left so I'll let you +work that out by yourself but but keep + + align:start position:0% +work that out by yourself but but keep + + + align:start position:0% +work that out by yourself but but keep +that in mind always identify which + + align:start position:0% +that in mind always identify which + + + align:start position:0% +that in mind always identify which +principal plane you are using for any + + align:start position:0% +principal plane you are using for any + + + align:start position:0% +principal plane you are using for any +given imaging condition + + align:start position:0% +given imaging condition + + + align:start position:0% +given imaging condition +okay + + align:start position:0% +okay + + + align:start position:0% +okay +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +any questions + + align:start position:0% +any questions + + + align:start position:0% +any questions +about all of this + + align:start position:0% + + + + align:start position:0% + +and someone say at least good morning so + + align:start position:0% +and someone say at least good morning so + + + align:start position:0% +and someone say at least good morning so +now if our sound has been restored + + align:start position:0% +now if our sound has been restored + + + align:start position:0% +now if our sound has been restored +hello hello can you hear us + + align:start position:0% +hello hello can you hear us + + + align:start position:0% +hello hello can you hear us +okay there nobody wants to say good + + align:start position:0% +okay there nobody wants to say good + + + align:start position:0% +okay there nobody wants to say good +night no there's no sound against + + align:start position:0% +night no there's no sound against + + + align:start position:0% +night no there's no sound against +okay I'll keep going and hopefully + + align:start position:0% +okay I'll keep going and hopefully + + + align:start position:0% +okay I'll keep going and hopefully +sometime at some point we'll have sound + + align:start position:0% +sometime at some point we'll have sound + + + align:start position:0% +sometime at some point we'll have sound +or at some time you'll wake up enough to + + align:start position:0% +or at some time you'll wake up enough to + + + align:start position:0% +or at some time you'll wake up enough to +be willing to say good morning + + align:start position:0% + + + + align:start position:0% + +okay so today we will deal with a topic + + align:start position:0% +okay so today we will deal with a topic + + + align:start position:0% +okay so today we will deal with a topic +called stops and apertures and + + align:start position:0% +called stops and apertures and + + + align:start position:0% +called stops and apertures and +basically we'll spend the rest of the + + align:start position:0% +basically we'll spend the rest of the + + + align:start position:0% +basically we'll spend the rest of the +hour + + align:start position:0% +hour + + + align:start position:0% +hour +learning the meaning of all these terms + + align:start position:0% +learning the meaning of all these terms + + + align:start position:0% +learning the meaning of all these terms +so quite a few of them aperture pupil + + align:start position:0% +so quite a few of them aperture pupil + + + align:start position:0% +so quite a few of them aperture pupil +entrance/exit popular then who have + + align:start position:0% +entrance/exit popular then who have + + + align:start position:0% +entrance/exit popular then who have +filled stopped window entrance and exit + + align:start position:0% +filled stopped window entrance and exit + + + align:start position:0% +filled stopped window entrance and exit +and so on so we'll spend some time + + align:start position:0% +and so on so we'll spend some time + + + align:start position:0% +and so on so we'll spend some time +learning what these things are and why + + align:start position:0% +learning what these things are and why + + + align:start position:0% +learning what these things are and why +they're useful in an optical system + + align:start position:0% +they're useful in an optical system + + + align:start position:0% +they're useful in an optical system +so start from the first one they happen + + align:start position:0% +so start from the first one they happen + + + align:start position:0% +so start from the first one they happen +to stop the aperture stop has to do with + + align:start position:0% +to stop the aperture stop has to do with + + + align:start position:0% +to stop the aperture stop has to do with +the fact that any optical instrument in + + align:start position:0% +the fact that any optical instrument in + + + align:start position:0% +the fact that any optical instrument in +practice has a finite size and therefore + + align:start position:0% +practice has a finite size and therefore + + + align:start position:0% +practice has a finite size and therefore +okay let me back up so the instrument + + align:start position:0% +okay let me back up so the instrument + + + align:start position:0% +okay let me back up so the instrument +has a finite size but a point source as + + align:start position:0% +has a finite size but a point source as + + + align:start position:0% +has a finite size but a point source as +we learned it actually at least an ideal + + align:start position:0% +we learned it actually at least an ideal + + + align:start position:0% +we learned it actually at least an ideal +source it emits kind of isotropically + + align:start position:0% +source it emits kind of isotropically + + + align:start position:0% +source it emits kind of isotropically +all the way for pi steady steady ins + + align:start position:0% +all the way for pi steady steady ins + + + align:start position:0% +all the way for pi steady steady ins +around the location of the point source + + align:start position:0% +around the location of the point source + + + align:start position:0% +around the location of the point source +so + + align:start position:0% +so + + + align:start position:0% +so +what this means then is that the optical + + align:start position:0% +what this means then is that the optical + + + align:start position:0% +what this means then is that the optical +instrument can only capture a fraction + + align:start position:0% +instrument can only capture a fraction + + + align:start position:0% +instrument can only capture a fraction +of the light that this that any given + + align:start position:0% +of the light that this that any given + + + align:start position:0% +of the light that this that any given +point source is emitting so the aperture + + align:start position:0% +point source is emitting so the aperture + + + align:start position:0% +point source is emitting so the aperture +actually helps us quantify how much is + + align:start position:0% +actually helps us quantify how much is + + + align:start position:0% +actually helps us quantify how much is +the light that an optical instrument can + + align:start position:0% +the light that an optical instrument can + + + align:start position:0% +the light that an optical instrument can +admit given the location of a point + + align:start position:0% +admit given the location of a point + + + align:start position:0% +admit given the location of a point +source so it is defined actually with + + align:start position:0% +source so it is defined actually with + + + align:start position:0% +source so it is defined actually with +respect to a point source that is + + align:start position:0% +respect to a point source that is + + + align:start position:0% +respect to a point source that is +located at the optical axis that is at + + align:start position:0% +located at the optical axis that is at + + + align:start position:0% +located at the optical axis that is at +the center where all the optics are + + align:start position:0% +the center where all the optics are + + + align:start position:0% +the center where all the optics are +rotationally symmetric about and there + + align:start position:0% +rotationally symmetric about and there + + + align:start position:0% +rotationally symmetric about and there +is two concepts here one is the physical + + align:start position:0% +is two concepts here one is the physical + + + align:start position:0% +is two concepts here one is the physical +stop so the physical stop is you can + + align:start position:0% +stop so the physical stop is you can + + + align:start position:0% +stop so the physical stop is you can +think of it as the rim of the optics the + + align:start position:0% +think of it as the rim of the optics the + + + align:start position:0% +think of it as the rim of the optics the +the physical limit the Y on which the + + align:start position:0% +the physical limit the Y on which the + + + align:start position:0% +the physical limit the Y on which the +rays that are coming from the source + + align:start position:0% +rays that are coming from the source + + + align:start position:0% +rays that are coming from the source +they miss the optical elements in the + + align:start position:0% +they miss the optical elements in the + + + align:start position:0% +they miss the optical elements in the +system those of you who have cameras + + align:start position:0% +system those of you who have cameras + + + align:start position:0% +system those of you who have cameras +you're also familiar with the with + + align:start position:0% +you're also familiar with the with + + + align:start position:0% +you're also familiar with the with +physical stops that in relatively + + align:start position:0% +physical stops that in relatively + + + align:start position:0% +physical stops that in relatively +complicated optical systems for example + + align:start position:0% +complicated optical systems for example + + + align:start position:0% +complicated optical systems for example +the lens that goes with the camera + + align:start position:0% +the lens that goes with the camera + + + align:start position:0% +the lens that goes with the camera +inside there is a little hole that is + + align:start position:0% +inside there is a little hole that is + + + align:start position:0% +inside there is a little hole that is +very often adjustable depending on the + + align:start position:0% +very often adjustable depending on the + + + align:start position:0% +very often adjustable depending on the +light level and so on this hole nowadays + + align:start position:0% +light level and so on this hole nowadays + + + align:start position:0% +light level and so on this hole nowadays +automatically in the old days with + + align:start position:0% +automatically in the old days with + + + align:start position:0% +automatically in the old days with +photographers having manual control you + + align:start position:0% +photographers having manual control you + + + align:start position:0% +photographers having manual control you +could actually open and close that + + align:start position:0% +could actually open and close that + + + align:start position:0% +could actually open and close that +opening to admit more or less light this + + align:start position:0% +opening to admit more or less light this + + + align:start position:0% +opening to admit more or less light this +is called the aperture stop in the we + + align:start position:0% +is called the aperture stop in the we + + + align:start position:0% +is called the aperture stop in the we +also are familiar with something else + + align:start position:0% +also are familiar with something else + + + align:start position:0% +also are familiar with something else +the pupil of our eyes if you look at + + align:start position:0% +the pupil of our eyes if you look at + + + align:start position:0% +the pupil of our eyes if you look at +someone's eyes there is a little hole + + align:start position:0% +someone's eyes there is a little hole + + + align:start position:0% +someone's eyes there is a little hole +and if you look in a bright environment + + align:start position:0% +and if you look in a bright environment + + + align:start position:0% +and if you look in a bright environment +this hole is relatively small if you + + align:start position:0% +this hole is relatively small if you + + + align:start position:0% +this hole is relatively small if you +move to a dark environment our eyes have + + align:start position:0% +move to a dark environment our eyes have + + + align:start position:0% +move to a dark environment our eyes have +a mechanism that kind of measures the + + align:start position:0% +a mechanism that kind of measures the + + + align:start position:0% +a mechanism that kind of measures the +ambient light and opens up or close down + + align:start position:0% +ambient light and opens up or close down + + + align:start position:0% +ambient light and opens up or close down +the pupil so this is the aperture stop + + align:start position:0% +the pupil so this is the aperture stop + + + align:start position:0% +the pupil so this is the aperture stop +for the optical system of our high + + align:start position:0% +for the optical system of our high + + + align:start position:0% +for the optical system of our high +so the Apple to stop then is the + + align:start position:0% +so the Apple to stop then is the + + + align:start position:0% +so the Apple to stop then is the +physical element that limits the + + align:start position:0% +physical element that limits the + + + align:start position:0% +physical element that limits the +acceptance of the light rays okay so in + + align:start position:0% +acceptance of the light rays okay so in + + + align:start position:0% +acceptance of the light rays okay so in +this case the Apple to stop you can + + align:start position:0% +this case the Apple to stop you can + + + align:start position:0% +this case the Apple to stop you can +think of this this sort of black thick + + align:start position:0% +think of this this sort of black thick + + + align:start position:0% +think of this this sort of black thick +line here you can think of it as a + + align:start position:0% +line here you can think of it as a + + + align:start position:0% +line here you can think of it as a +physical for example a metal plate with + + align:start position:0% +physical for example a metal plate with + + + align:start position:0% +physical for example a metal plate with +a hole in the center so that hole would + + align:start position:0% +a hole in the center so that hole would + + + align:start position:0% +a hole in the center so that hole would +be the actual Apple to stop in this + + align:start position:0% +be the actual Apple to stop in this + + + align:start position:0% +be the actual Apple to stop in this +particular instrument + + align:start position:0% +particular instrument + + + align:start position:0% +particular instrument +the numerical aperture is a + + align:start position:0% +the numerical aperture is a + + + align:start position:0% +the numerical aperture is a +mathematical quantity it is the angle + + align:start position:0% +mathematical quantity it is the angle + + + align:start position:0% +mathematical quantity it is the angle +subtended + + align:start position:0% +subtended + + + align:start position:0% +subtended +from the point source to the rim of the + + align:start position:0% +from the point source to the rim of the + + + align:start position:0% +from the point source to the rim of the +physical aperture stop + + align:start position:0% +physical aperture stop + + + align:start position:0% +physical aperture stop +and I was a little bit sloppy when I + + align:start position:0% +and I was a little bit sloppy when I + + + align:start position:0% +and I was a little bit sloppy when I +called the angle it is not the actual + + align:start position:0% +called the angle it is not the actual + + + align:start position:0% +called the angle it is not the actual +definition is the sine of that angle + + align:start position:0% +definition is the sine of that angle + + + align:start position:0% +definition is the sine of that angle +multiplied by the index of refraction + + align:start position:0% +multiplied by the index of refraction + + + align:start position:0% +multiplied by the index of refraction +now we've already seen since Niles law + + align:start position:0% +now we've already seen since Niles law + + + align:start position:0% +now we've already seen since Niles law +several times you can guess immediately + + align:start position:0% +several times you can guess immediately + + + align:start position:0% +several times you can guess immediately +the reason people define the numerical + + align:start position:0% +the reason people define the numerical + + + align:start position:0% +the reason people define the numerical +aperture this way is solid this quantity + + align:start position:0% +aperture this way is solid this quantity + + + align:start position:0% +aperture this way is solid this quantity +is concerned when you go through a flat + + align:start position:0% +is concerned when you go through a flat + + + align:start position:0% +is concerned when you go through a flat +refractive interfaces so that is very + + align:start position:0% +refractive interfaces so that is very + + + align:start position:0% +refractive interfaces so that is very +convenient because well as we'll see + + align:start position:0% +convenient because well as we'll see + + + align:start position:0% +convenient because well as we'll see +later the numerical aperture is a very + + align:start position:0% +later the numerical aperture is a very + + + align:start position:0% +later the numerical aperture is a very +important + + align:start position:0% +important + + + align:start position:0% +important +quantity in characterize in an optical + + align:start position:0% +quantity in characterize in an optical + + + align:start position:0% +quantity in characterize in an optical +system so therefore by sticking the + + align:start position:0% +system so therefore by sticking the + + + align:start position:0% +system so therefore by sticking the +index of refraction in this definition + + align:start position:0% +index of refraction in this definition + + + align:start position:0% +index of refraction in this definition +here who make sure that the numerical + + align:start position:0% +here who make sure that the numerical + + + align:start position:0% +here who make sure that the numerical +aperture is preserved as Ray's go + + align:start position:0% +aperture is preserved as Ray's go + + + align:start position:0% +aperture is preserved as Ray's go +through various elements in the system + + align:start position:0% +through various elements in the system + + + align:start position:0% +through various elements in the system +at least the elements without power + + align:start position:0% +at least the elements without power + + + align:start position:0% +at least the elements without power +without optical power that is as they go + + align:start position:0% +without optical power that is as they go + + + align:start position:0% +without optical power that is as they go +through flat interfaces so that is + + align:start position:0% +through flat interfaces so that is + + + align:start position:0% +through flat interfaces so that is +definition now of course in many optical + + align:start position:0% +definition now of course in many optical + + + align:start position:0% +definition now of course in many optical +systems the index where the object lives + + align:start position:0% +systems the index where the object lives + + + align:start position:0% +systems the index where the object lives +is air so therefore n is 1 and also in + + align:start position:0% +is air so therefore n is 1 and also in + + + align:start position:0% +is air so therefore n is 1 and also in +this class at least we deal with the + + align:start position:0% +this class at least we deal with the + + + align:start position:0% +this class at least we deal with the +paraxial approximation where the sine of + + align:start position:0% +paraxial approximation where the sine of + + + align:start position:0% +paraxial approximation where the sine of +the angle is approximately equal to the + + align:start position:0% +the angle is approximately equal to the + + + align:start position:0% +the angle is approximately equal to the +angle itself so therefore indeed the + + align:start position:0% +angle itself so therefore indeed the + + + align:start position:0% +angle itself so therefore indeed the +numerical aperture is approximately + + align:start position:0% +numerical aperture is approximately + + + align:start position:0% +numerical aperture is approximately +involved equal to the angle itself + + align:start position:0% +involved equal to the angle itself + + + align:start position:0% +involved equal to the angle itself +however as you have seen from the + + align:start position:0% +however as you have seen from the + + + align:start position:0% +however as you have seen from the +homework if you already studied in many + + align:start position:0% +homework if you already studied in many + + + align:start position:0% +homework if you already studied in many +optical systems the object lives in + + align:start position:0% +optical systems the object lives in + + + align:start position:0% +optical systems the object lives in +space of refractive index different than + + align:start position:0% +space of refractive index different than + + + align:start position:0% +space of refractive index different than +one for example in immersion microscopy + + align:start position:0% +one for example in immersion microscopy + + + align:start position:0% +one for example in immersion microscopy +we put a droplet of oil we drop with + + align:start position:0% +we put a droplet of oil we drop with + + + align:start position:0% +we put a droplet of oil we drop with +rapid ablative oil on top of the sample + + align:start position:0% +rapid ablative oil on top of the sample + + + align:start position:0% +rapid ablative oil on top of the sample +then we stick the objective so that + + align:start position:0% +then we stick the objective so that + + + align:start position:0% +then we stick the objective so that +there is oil in this space here between + + align:start position:0% +there is oil in this space here between + + + align:start position:0% +there is oil in this space here between +the sample of the objective well in that + + align:start position:0% +the sample of the objective well in that + + + align:start position:0% +the sample of the objective well in that +case we really should include the index + + align:start position:0% +case we really should include the index + + + align:start position:0% +case we really should include the index +of refraction in the definition of the + + align:start position:0% +of refraction in the definition of the + + + align:start position:0% +of refraction in the definition of the +optic of the numerical aperture + + align:start position:0% +optic of the numerical aperture + + + align:start position:0% +optic of the numerical aperture +so of course you cannot speak yet but I + + align:start position:0% +so of course you cannot speak yet but I + + + align:start position:0% +so of course you cannot speak yet but I +do want to ask a question myself now + + align:start position:0% +do want to ask a question myself now + + + align:start position:0% +do want to ask a question myself now +and if you can answer oh well those of + + align:start position:0% +and if you can answer oh well those of + + + align:start position:0% +and if you can answer oh well those of +you can answer easily those of you in + + align:start position:0% +you can answer easily those of you in + + + align:start position:0% +you can answer easily those of you in +Boston if you want answer just please + + align:start position:0% +Boston if you want answer just please + + + align:start position:0% +Boston if you want answer just please +wave and and we'll figure out how to do + + align:start position:0% +wave and and we'll figure out how to do + + + align:start position:0% +wave and and we'll figure out how to do +it but the question I wanted to ask what + + align:start position:0% +it but the question I wanted to ask what + + + align:start position:0% +it but the question I wanted to ask what +do you think the value of the numerical + + align:start position:0% +do you think the value of the numerical + + + align:start position:0% +do you think the value of the numerical +aperture is is it smaller than one + + align:start position:0% +aperture is is it smaller than one + + + align:start position:0% +aperture is is it smaller than one +bigger than one what is it + + align:start position:0% +bigger than one what is it + + + align:start position:0% +bigger than one what is it +do this if you think that the numerical + + align:start position:0% +do this if you think that the numerical + + + align:start position:0% +do this if you think that the numerical +aperture is bigger than one do this if + + align:start position:0% +aperture is bigger than one do this if + + + align:start position:0% +aperture is bigger than one do this if +you think that the numerical aperture is + + align:start position:0% +you think that the numerical aperture is + + + align:start position:0% +you think that the numerical aperture is +always less than one + + align:start position:0% +always less than one + + + align:start position:0% +always less than one +what's the verdict + + align:start position:0% + + + + align:start position:0% + +always less than 1 + + align:start position:0% +always less than 1 + + + align:start position:0% +always less than 1 +okay anybody who thinks the opposite + + align:start position:0% +okay anybody who thinks the opposite + + + align:start position:0% +okay anybody who thinks the opposite +that the numerical aperture can be + + align:start position:0% +that the numerical aperture can be + + + align:start position:0% +that the numerical aperture can be +bigger than 1 + + align:start position:0% + + + + align:start position:0% + +this is really strange I feel like + + align:start position:0% +this is really strange I feel like + + + align:start position:0% +this is really strange I feel like +working as ported to a different century + + align:start position:0% +working as ported to a different century + + + align:start position:0% +working as ported to a different century +now + + align:start position:0% + + + + align:start position:0% + +ok so actually + + align:start position:0% +ok so actually + + + align:start position:0% +ok so actually +in principle and in fact people do it I + + align:start position:0% +in principle and in fact people do it I + + + align:start position:0% +in principle and in fact people do it I +can construct an optical instrument with + + align:start position:0% +can construct an optical instrument with + + + align:start position:0% +can construct an optical instrument with +a relatively large acceptance angle for + + align:start position:0% +a relatively large acceptance angle for + + + align:start position:0% +a relatively large acceptance angle for +example theta may be as high as 75 + + align:start position:0% +example theta may be as high as 75 + + + align:start position:0% +example theta may be as high as 75 +degrees 80 degrees it is not uncommon in + + align:start position:0% +degrees 80 degrees it is not uncommon in + + + align:start position:0% +degrees 80 degrees it is not uncommon in +high-end microscope objective objective + + align:start position:0% +high-end microscope objective objective + + + align:start position:0% +high-end microscope objective objective +lenses to have a very high acceptance + + align:start position:0% +lenses to have a very high acceptance + + + align:start position:0% +lenses to have a very high acceptance +angle + + align:start position:0% +angle + + + align:start position:0% +angle +of course this would violate the + + align:start position:0% +of course this would violate the + + + align:start position:0% +of course this would violate the +paraxial approximation but that is no + + align:start position:0% +paraxial approximation but that is no + + + align:start position:0% +paraxial approximation but that is no +problem you know the fact that the + + align:start position:0% +problem you know the fact that the + + + align:start position:0% +problem you know the fact that the +instrument is non production actually + + align:start position:0% +instrument is non production actually + + + align:start position:0% +instrument is non production actually +does not make it an invalid instrument + + align:start position:0% +does not make it an invalid instrument + + + align:start position:0% +does not make it an invalid instrument +so it's fine all it means is that our + + align:start position:0% +so it's fine all it means is that our + + + align:start position:0% +so it's fine all it means is that our +simple theory here does not apply and we + + align:start position:0% +simple theory here does not apply and we + + + align:start position:0% +simple theory here does not apply and we +have to be more sophisticated with the + + align:start position:0% +have to be more sophisticated with the + + + align:start position:0% +have to be more sophisticated with the +analysis but we can have a large + + align:start position:0% +analysis but we can have a large + + + align:start position:0% +analysis but we can have a large +acceptance angle for example so in that + + align:start position:0% +acceptance angle for example so in that + + + align:start position:0% +acceptance angle for example so in that +case the sine of this angle may be close + + align:start position:0% +case the sine of this angle may be close + + + align:start position:0% +case the sine of this angle may be close +to one maybe 0.9 or point 95 and also in + + align:start position:0% +to one maybe 0.9 or point 95 and also in + + + align:start position:0% +to one maybe 0.9 or point 95 and also in +addition remember that we can use + + align:start position:0% +addition remember that we can use + + + align:start position:0% +addition remember that we can use +immersion so we can put the object in + + align:start position:0% +immersion so we can put the object in + + + align:start position:0% +immersion so we can put the object in +liquid of index of refraction for + + align:start position:0% +liquid of index of refraction for + + + align:start position:0% +liquid of index of refraction for +example if it is water that would be 1.3 + + align:start position:0% +example if it is water that would be 1.3 + + + align:start position:0% +example if it is water that would be 1.3 +if it is one of the emulsion oils that + + align:start position:0% +if it is one of the emulsion oils that + + + align:start position:0% +if it is one of the emulsion oils that +we'll use in microscopy what is the + + align:start position:0% +we'll use in microscopy what is the + + + align:start position:0% +we'll use in microscopy what is the +index typically 1.4 1.0 + + align:start position:0% +index typically 1.4 1.0 + + + align:start position:0% +index typically 1.4 1.0 +just the same as glass + + align:start position:0% + + + + align:start position:0% + +okay so even higher than 4 for immersion + + align:start position:0% +okay so even higher than 4 for immersion + + + align:start position:0% +okay so even higher than 4 for immersion +instruments 1.5 for 5 1 4 I'm sorry 1 + + align:start position:0% +instruments 1.5 for 5 1 4 I'm sorry 1 + + + align:start position:0% +instruments 1.5 for 5 1 4 I'm sorry 1 +point 5 1 4 and + + align:start position:0% +point 5 1 4 and + + + align:start position:0% +point 5 1 4 and +so in that case if I do one point five + + align:start position:0% +so in that case if I do one point five + + + align:start position:0% +so in that case if I do one point five +one four times point 9 of course it will + + align:start position:0% +one four times point 9 of course it will + + + align:start position:0% +one four times point 9 of course it will +be bigger than 1 + + align:start position:0% + + + + align:start position:0% + +I + + align:start position:0% +I + + + align:start position:0% +I +don't know what it is but it would be + + align:start position:0% +don't know what it is but it would be + + + align:start position:0% +don't know what it is but it would be +definitely bigger than one so actually I + + align:start position:0% +definitely bigger than one so actually I + + + align:start position:0% +definitely bigger than one so actually I +can have a numerical aperture that is + + align:start position:0% +can have a numerical aperture that is + + + align:start position:0% +can have a numerical aperture that is +bigger than one that is a kind of a + + align:start position:0% +bigger than one that is a kind of a + + + align:start position:0% +bigger than one that is a kind of a +useful point to remember + + align:start position:0% +useful point to remember + + + align:start position:0% +useful point to remember +related to the notes or the numerical + + align:start position:0% +related to the notes or the numerical + + + align:start position:0% +related to the notes or the numerical +aperture is used very commonly in + + align:start position:0% +aperture is used very commonly in + + + align:start position:0% +aperture is used very commonly in +microscopy when we characterize + + align:start position:0% +microscopy when we characterize + + + align:start position:0% +microscopy when we characterize +objective lenses typically we + + align:start position:0% +objective lenses typically we + + + align:start position:0% +objective lenses typically we +characterize them by their numerical + + align:start position:0% +characterize them by their numerical + + + align:start position:0% +characterize them by their numerical +aperture + + align:start position:0% +aperture + + + align:start position:0% +aperture +in photography especially people prefer + + align:start position:0% +in photography especially people prefer + + + align:start position:0% +in photography especially people prefer +to use an alternate quantity known as + + align:start position:0% +to use an alternate quantity known as + + + align:start position:0% +to use an alternate quantity known as +the F number so the F number is kind of + + align:start position:0% +the F number so the F number is kind of + + + align:start position:0% +the F number so the F number is kind of +the inverse of the numerical aperture + + align:start position:0% +the inverse of the numerical aperture + + + align:start position:0% +the inverse of the numerical aperture +times a factor of 1/2 which always + + align:start position:0% +times a factor of 1/2 which always + + + align:start position:0% +times a factor of 1/2 which always +confuses the hell out of me but but + + align:start position:0% +confuses the hell out of me but but + + + align:start position:0% +confuses the hell out of me but but +anyway the F number it is written like + + align:start position:0% +anyway the F number it is written like + + + align:start position:0% +anyway the F number it is written like +this and people replace the hash symbol + + align:start position:0% +this and people replace the hash symbol + + + align:start position:0% +this and people replace the hash symbol +with the actual number for example if + + align:start position:0% +with the actual number for example if + + + align:start position:0% +with the actual number for example if +you look at at the lens of a camera it + + align:start position:0% +you look at at the lens of a camera it + + + align:start position:0% +you look at at the lens of a camera it +might same thing it may something like f + + align:start position:0% +might same thing it may something like f + + + align:start position:0% +might same thing it may something like f +/ 8 this means that the F number of this + + align:start position:0% +/ 8 this means that the F number of this + + + align:start position:0% +/ 8 this means that the F number of this +camera lens is 8 so the rule of thumb is + + align:start position:0% +camera lens is 8 so the rule of thumb is + + + align:start position:0% +camera lens is 8 so the rule of thumb is +what does your money go when you pay + + align:start position:0% +what does your money go when you pay + + + align:start position:0% +what does your money go when you pay +money for a very good quality microscope + + align:start position:0% +money for a very good quality microscope + + + align:start position:0% +money for a very good quality microscope +objective one of others that cost + + align:start position:0% +objective one of others that cost + + + align:start position:0% +objective one of others that cost +$10,000 or so typically you pay in a + + align:start position:0% +$10,000 or so typically you pay in a + + + align:start position:0% +$10,000 or so typically you pay in a +microscope objective you pay for a large + + align:start position:0% +microscope objective you pay for a large + + + align:start position:0% +microscope objective you pay for a large +numerical aperture when you walk into a + + align:start position:0% +numerical aperture when you walk into a + + + align:start position:0% +numerical aperture when you walk into a +store and you buy a high-end expensive + + align:start position:0% +store and you buy a high-end expensive + + + align:start position:0% +store and you buy a high-end expensive +camera lens one of those Nikon or or a + + align:start position:0% +camera lens one of those Nikon or or a + + + align:start position:0% +camera lens one of those Nikon or or a +Zeiss really expensive multi-element + + align:start position:0% +Zeiss really expensive multi-element + + + align:start position:0% +Zeiss really expensive multi-element +lenses that look about as big as you + + align:start position:0% +lenses that look about as big as you + + + align:start position:0% +lenses that look about as big as you +know as my computer here what you pay + + align:start position:0% +know as my computer here what you pay + + + align:start position:0% +know as my computer here what you pay +there is for a really low F number ok so + + align:start position:0% +there is for a really low F number ok so + + + align:start position:0% +there is for a really low F number ok so +generally large numerical aperture is + + align:start position:0% +generally large numerical aperture is + + + align:start position:0% +generally large numerical aperture is +good or equivalently low F number is + + align:start position:0% +good or equivalently low F number is + + + align:start position:0% +good or equivalently low F number is +good provided you can afford it of + + align:start position:0% +good provided you can afford it of + + + align:start position:0% +good provided you can afford it of +course + + align:start position:0% +course + + + align:start position:0% +course +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so the moment the way we defined it so + + align:start position:0% +so the moment the way we defined it so + + + align:start position:0% +so the moment the way we defined it so +far the numerical aperture it seems to + + align:start position:0% +far the numerical aperture it seems to + + + align:start position:0% +far the numerical aperture it seems to +be related only to the energy acceptance + + align:start position:0% +be related only to the energy acceptance + + + align:start position:0% +be related only to the energy acceptance +of the optical system that is how much + + align:start position:0% +of the optical system that is how much + + + align:start position:0% +of the optical system that is how much +how many watts of optical power the + + align:start position:0% +how many watts of optical power the + + + align:start position:0% +how many watts of optical power the +optical system admit so these are of + + align:start position:0% +optical system admit so these are of + + + align:start position:0% +optical system admit so these are of +course important but you might wonder + + align:start position:0% +course important but you might wonder + + + align:start position:0% +course important but you might wonder +why am I making such a big deal in white + + align:start position:0% +why am I making such a big deal in white + + + align:start position:0% +why am I making such a big deal in white +pull pay so much money for high na well + + align:start position:0% +pull pay so much money for high na well + + + align:start position:0% +pull pay so much money for high na well +again the energy acceptance as you can + + align:start position:0% +again the energy acceptance as you can + + + align:start position:0% +again the energy acceptance as you can +imagine is incredibly important because + + align:start position:0% +imagine is incredibly important because + + + align:start position:0% +imagine is incredibly important because +it will determine how many useful + + align:start position:0% +it will determine how many useful + + + align:start position:0% +it will determine how many useful +photons from the object you admit into + + align:start position:0% +photons from the object you admit into + + + align:start position:0% +photons from the object you admit into +your system for imaging purposes but as + + align:start position:0% +your system for imaging purposes but as + + + align:start position:0% +your system for imaging purposes but as +we will learn later + + align:start position:0% +we will learn later + + + align:start position:0% +we will learn later +the numerical aperture also defines the + + align:start position:0% +the numerical aperture also defines the + + + align:start position:0% +the numerical aperture also defines the +resolution of an optical system and + + align:start position:0% +resolution of an optical system and + + + align:start position:0% +resolution of an optical system and +right now you probably know from + + align:start position:0% +right now you probably know from + + + align:start position:0% +right now you probably know from +everyday life what resolution means + + align:start position:0% +everyday life what resolution means + + + align:start position:0% +everyday life what resolution means +people talk about resolution in their + + align:start position:0% +people talk about resolution in their + + + align:start position:0% +people talk about resolution in their +camera and your television and so on and + + align:start position:0% +camera and your television and so on and + + + align:start position:0% +camera and your television and so on and +so forth we will do a precise definition + + align:start position:0% +so forth we will do a precise definition + + + align:start position:0% +so forth we will do a precise definition +of resolution later about a month from + + align:start position:0% +of resolution later about a month from + + + align:start position:0% +of resolution later about a month from +now will define it very precisely and + + align:start position:0% +now will define it very precisely and + + + align:start position:0% +now will define it very precisely and +we'll see why and how it is related to + + align:start position:0% +we'll see why and how it is related to + + + align:start position:0% +we'll see why and how it is related to +this numerical aperture quantity but + + align:start position:0% +this numerical aperture quantity but + + + align:start position:0% +this numerical aperture quantity but +again the rule is that the lie that the + + align:start position:0% +again the rule is that the lie that the + + + align:start position:0% +again the rule is that the lie that the +largest the numerical aperture or + + align:start position:0% +largest the numerical aperture or + + + align:start position:0% +largest the numerical aperture or +equivalently the smaller the f-number + + align:start position:0% +equivalently the smaller the f-number + + + align:start position:0% +equivalently the smaller the f-number +the better the resolution of an optical + + align:start position:0% +the better the resolution of an optical + + + align:start position:0% +the better the resolution of an optical +system so we will see this can come up + + align:start position:0% +system so we will see this can come up + + + align:start position:0% +system so we will see this can come up +again and again + + align:start position:0% +again and again + + + align:start position:0% +again and again +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +that's the basic definition that we that + + align:start position:0% +that's the basic definition that we that + + + align:start position:0% +that's the basic definition that we that +we use now related to this concept of a + + align:start position:0% +we use now related to this concept of a + + + align:start position:0% +we use now related to this concept of a +per to stop a numerical aperture then is + + align:start position:0% +per to stop a numerical aperture then is + + + align:start position:0% +per to stop a numerical aperture then is +to sort of derivative definitions and + + align:start position:0% +to sort of derivative definitions and + + + align:start position:0% +to sort of derivative definitions and +these are called the pupils the entrance + + align:start position:0% +these are called the pupils the entrance + + + align:start position:0% +these are called the pupils the entrance +and exit pupils so in order to define + + align:start position:0% +and exit pupils so in order to define + + + align:start position:0% +and exit pupils so in order to define +those I kind of need a multi element + + align:start position:0% +those I kind of need a multi element + + + align:start position:0% +those I kind of need a multi element +optical system so a sort of concocted + + align:start position:0% +optical system so a sort of concocted + + + align:start position:0% +optical system so a sort of concocted +one over there I just made it up this is + + align:start position:0% +one over there I just made it up this is + + + align:start position:0% +one over there I just made it up this is +not nothing in particular I just stuck + + align:start position:0% +not nothing in particular I just stuck + + + align:start position:0% +not nothing in particular I just stuck +some lenses in tandem and I put an apple + + align:start position:0% +some lenses in tandem and I put an apple + + + align:start position:0% +some lenses in tandem and I put an apple +to stop somewhere in the middle okay so + + align:start position:0% +to stop somewhere in the middle okay so + + + align:start position:0% +to stop somewhere in the middle okay so +think of this again as the physical + + align:start position:0% +think of this again as the physical + + + align:start position:0% +think of this again as the physical +element a hole that I put in there + + align:start position:0% +element a hole that I put in there + + + align:start position:0% +element a hole that I put in there +so the reason we need this additional + + align:start position:0% +so the reason we need this additional + + + align:start position:0% +so the reason we need this additional +definitions of the pupils is that if the + + align:start position:0% +definitions of the pupils is that if the + + + align:start position:0% +definitions of the pupils is that if the +aperture stop is varied inside an + + align:start position:0% +aperture stop is varied inside an + + + align:start position:0% +aperture stop is varied inside an +optical instrument as it happens for + + align:start position:0% +optical instrument as it happens for + + + align:start position:0% +optical instrument as it happens for +example in your camera lens if you look + + align:start position:0% +example in your camera lens if you look + + + align:start position:0% +example in your camera lens if you look +at your photographic camera that you + + align:start position:0% +at your photographic camera that you + + + align:start position:0% +at your photographic camera that you +have at home you will see that the + + align:start position:0% +have at home you will see that the + + + align:start position:0% +have at home you will see that the +aperture is buried inside a relatively + + align:start position:0% +aperture is buried inside a relatively + + + align:start position:0% +aperture is buried inside a relatively +large lens barrel if you have a + + align:start position:0% +large lens barrel if you have a + + + align:start position:0% +large lens barrel if you have a +sophisticated camera + + align:start position:0% +sophisticated camera + + + align:start position:0% +sophisticated camera +the aperture is a physical element + + align:start position:0% +the aperture is a physical element + + + align:start position:0% +the aperture is a physical element +the whole length so if you look at the + + align:start position:0% +the whole length so if you look at the + + + align:start position:0% +the whole length so if you look at the +at your lens from there from the one + + align:start position:0% +at your lens from there from the one + + + align:start position:0% +at your lens from there from the one +side that looks towards the object or + + align:start position:0% +side that looks towards the object or + + + align:start position:0% +side that looks towards the object or +from the opposite side that looks + + align:start position:0% +from the opposite side that looks + + + align:start position:0% +from the opposite side that looks +towards the words the CCD you will see + + align:start position:0% +towards the words the CCD you will see + + + align:start position:0% +towards the words the CCD you will see +an opportunity but you will not see the + + align:start position:0% +an opportunity but you will not see the + + + align:start position:0% +an opportunity but you will not see the +aperture itself you will see the image + + align:start position:0% +aperture itself you will see the image + + + align:start position:0% +aperture itself you will see the image +of that aperture stop through the + + align:start position:0% +of that aperture stop through the + + + align:start position:0% +of that aperture stop through the +elements that precede or succeeded so + + align:start position:0% +elements that precede or succeeded so + + + align:start position:0% +elements that precede or succeeded so +because of that people have defined this + + align:start position:0% +because of that people have defined this + + + align:start position:0% +because of that people have defined this +concept of the entrance and exit pupil + + align:start position:0% +concept of the entrance and exit pupil + + + align:start position:0% +concept of the entrance and exit pupil +so the entrance pupil is what you get if + + align:start position:0% +so the entrance pupil is what you get if + + + align:start position:0% +so the entrance pupil is what you get if +you take this aperture stop and now you + + align:start position:0% +you take this aperture stop and now you + + + align:start position:0% +you take this aperture stop and now you +treat it as an object in the imaging + + align:start position:0% +treat it as an object in the imaging + + + align:start position:0% +treat it as an object in the imaging +system and you imagine through the + + align:start position:0% +system and you imagine through the + + + align:start position:0% +system and you imagine through the +proceeding optical elements now here + + align:start position:0% +proceeding optical elements now here + + + align:start position:0% +proceeding optical elements now here +have committed a mortal violation I + + align:start position:0% +have committed a mortal violation I + + + align:start position:0% +have committed a mortal violation I +emerged from right to left we said last + + align:start position:0% +emerged from right to left we said last + + + align:start position:0% +emerged from right to left we said last +time that every time we will write down + + align:start position:0% +time that every time we will write down + + + align:start position:0% +time that every time we will write down +an optical system the light is assumed + + align:start position:0% +an optical system the light is assumed + + + align:start position:0% +an optical system the light is assumed +to go from all the ways from left to + + align:start position:0% +to go from all the ways from left to + + + align:start position:0% +to go from all the ways from left to +right + + align:start position:0% +right + + + align:start position:0% +right +so here this is an exception when we + + align:start position:0% +so here this is an exception when we + + + align:start position:0% +so here this is an exception when we +deal with a pursue stops we actually + + align:start position:0% +deal with a pursue stops we actually + + + align:start position:0% +deal with a pursue stops we actually +image from right to left right because + + align:start position:0% +image from right to left right because + + + align:start position:0% +image from right to left right because +we really need to look at this as the + + align:start position:0% +we really need to look at this as the + + + align:start position:0% +we really need to look at this as the +object and image it through the optical + + align:start position:0% +object and image it through the optical + + + align:start position:0% +object and image it through the optical +elements that precede it so if we do + + align:start position:0% +elements that precede it so if we do + + + align:start position:0% +elements that precede it so if we do +that then we get the entrance pupil so + + align:start position:0% +that then we get the entrance pupil so + + + align:start position:0% +that then we get the entrance pupil so +in this case + + align:start position:0% +in this case + + + align:start position:0% +in this case +it would look something like this so + + align:start position:0% +it would look something like this so + + + align:start position:0% +it would look something like this so +this is now not a physical physical + + align:start position:0% +this is now not a physical physical + + + align:start position:0% +this is now not a physical physical +component anymore it is the image of the + + align:start position:0% +component anymore it is the image of the + + + align:start position:0% +component anymore it is the image of the +physical component that was inside the + + align:start position:0% +physical component that was inside the + + + align:start position:0% +physical component that was inside the +system and we imaged it through the + + align:start position:0% +system and we imaged it through the + + + align:start position:0% +system and we imaged it through the +elements that preceded it in that + + align:start position:0% +elements that preceded it in that + + + align:start position:0% +elements that preceded it in that +optical system okay similarly we can + + align:start position:0% +optical system okay similarly we can + + + align:start position:0% +optical system okay similarly we can +define the exit pupil if we image the + + align:start position:0% +define the exit pupil if we image the + + + align:start position:0% +define the exit pupil if we image the +physical apples to stop through the + + align:start position:0% +physical apples to stop through the + + + align:start position:0% +physical apples to stop through the +elements that succeeded okay so the two + + align:start position:0% +elements that succeeded okay so the two + + + align:start position:0% +elements that succeeded okay so the two +definitions are kind of conjugate + + align:start position:0% +definitions are kind of conjugate + + + align:start position:0% +definitions are kind of conjugate +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now with respect to this + + align:start position:0% +now with respect to this + + + align:start position:0% +now with respect to this +to this entrance exit pupil egg entrance + + align:start position:0% +to this entrance exit pupil egg entrance + + + align:start position:0% +to this entrance exit pupil egg entrance +exit pupils and aperture stops this is a + + align:start position:0% +exit pupils and aperture stops this is a + + + align:start position:0% +exit pupils and aperture stops this is a +mouthful who can define two significant + + align:start position:0% +mouthful who can define two significant + + + align:start position:0% +mouthful who can define two significant +rays that come up in the design of + + align:start position:0% +rays that come up in the design of + + + align:start position:0% +rays that come up in the design of +optical systems all the time and we'll + + align:start position:0% +optical systems all the time and we'll + + + align:start position:0% +optical systems all the time and we'll +see why + + align:start position:0% +see why + + + align:start position:0% +see why +the first one is called the chief ray + + align:start position:0% +the first one is called the chief ray + + + align:start position:0% +the first one is called the chief ray +and the chief ray is defined as the Ray + + align:start position:0% +and the chief ray is defined as the Ray + + + align:start position:0% +and the chief ray is defined as the Ray +that goes through the center of the + + align:start position:0% +that goes through the center of the + + + align:start position:0% +that goes through the center of the +upper to stop the physical aperture stop + + align:start position:0% +upper to stop the physical aperture stop + + + align:start position:0% +upper to stop the physical aperture stop +okay + + align:start position:0% + + + + align:start position:0% + +so that's one the other is called the + + align:start position:0% +so that's one the other is called the + + + align:start position:0% +so that's one the other is called the +marginal ray and it is the Ray that goes + + align:start position:0% +marginal ray and it is the Ray that goes + + + align:start position:0% +marginal ray and it is the Ray that goes +through the rim of the physical aperture + + align:start position:0% +through the rim of the physical aperture + + + align:start position:0% +through the rim of the physical aperture +stop that is the Ray that just clears + + align:start position:0% +stop that is the Ray that just clears + + + align:start position:0% +stop that is the Ray that just clears +the aperture if you take the next ray + + align:start position:0% +the aperture if you take the next ray + + + align:start position:0% +the aperture if you take the next ray +that would propagate at a slightly + + align:start position:0% +that would propagate at a slightly + + + align:start position:0% +that would propagate at a slightly +higher angle with respect to this one + + align:start position:0% +higher angle with respect to this one + + + align:start position:0% +higher angle with respect to this one +this leg would actually hit the physical + + align:start position:0% +this leg would actually hit the physical + + + align:start position:0% +this leg would actually hit the physical +block that is located at the aperture + + align:start position:0% +block that is located at the aperture + + + align:start position:0% +block that is located at the aperture +plane and would miss so this last ray + + align:start position:0% +plane and would miss so this last ray + + + align:start position:0% +plane and would miss so this last ray +just before the upper two stop + + align:start position:0% +just before the upper two stop + + + align:start position:0% +just before the upper two stop +blocks the rest of the light this is + + align:start position:0% +blocks the rest of the light this is + + + align:start position:0% +blocks the rest of the light this is +called the marginal ray + + align:start position:0% +called the marginal ray + + + align:start position:0% +called the marginal ray +so you can already see the importance of + + align:start position:0% +so you can already see the importance of + + + align:start position:0% +so you can already see the importance of +this because the marginal a kind of + + align:start position:0% +this because the marginal a kind of + + + align:start position:0% +this because the marginal a kind of +defines again the angle of acceptance of + + align:start position:0% +defines again the angle of acceptance of + + + align:start position:0% +defines again the angle of acceptance of +the optical system except this time + + align:start position:0% +the optical system except this time + + + align:start position:0% +the optical system except this time +notice that I've done this for an + + align:start position:0% +notice that I've done this for an + + + align:start position:0% +notice that I've done this for an +off-axis object point recall that the + + align:start position:0% +off-axis object point recall that the + + + align:start position:0% +off-axis object point recall that the +numerical aperture the way I define it + + align:start position:0% +numerical aperture the way I define it + + + align:start position:0% +numerical aperture the way I define it +before it was still the angle of + + align:start position:0% +before it was still the angle of + + + align:start position:0% +before it was still the angle of +acceptance but for an own axis object + + align:start position:0% +acceptance but for an own axis object + + + align:start position:0% +acceptance but for an own axis object +point here and the marginal in the Chi + + align:start position:0% +point here and the marginal in the Chi + + + align:start position:0% +point here and the marginal in the Chi +phrase I can define them for any point I + + align:start position:0% +phrase I can define them for any point I + + + align:start position:0% +phrase I can define them for any point I +like okay any point I like in the other + + align:start position:0% +like okay any point I like in the other + + + align:start position:0% +like okay any point I like in the other +it is in the object space + + align:start position:0% +it is in the object space + + + align:start position:0% +it is in the object space +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and + + align:start position:0% +and + + + align:start position:0% +and +this statement is sort of okay I already + + align:start position:0% +this statement is sort of okay I already + + + align:start position:0% +this statement is sort of okay I already +decided that they defined that vis Ray's + + align:start position:0% +decided that they defined that vis Ray's + + + align:start position:0% +decided that they defined that vis Ray's +helped us define the angle of acceptance + + align:start position:0% +helped us define the angle of acceptance + + + align:start position:0% +helped us define the angle of acceptance +now before I show the next slide and + + align:start position:0% + + + + align:start position:0% + +since they're + + align:start position:0% +since they're + + + align:start position:0% +since they're +these today is this too + + align:start position:0% +these today is this too + + + align:start position:0% +these today is this too +important race what do you think they + + align:start position:0% +important race what do you think they + + + align:start position:0% +important race what do you think they +might go with respect to the entrance + + align:start position:0% +might go with respect to the entrance + + + align:start position:0% +might go with respect to the entrance +and exit pupils by definition they go + + align:start position:0% +and exit pupils by definition they go + + + align:start position:0% +and exit pupils by definition they go +through the center and edge of the apple + + align:start position:0% +through the center and edge of the apple + + + align:start position:0% +through the center and edge of the apple +to stop respectively the chief and + + align:start position:0% +to stop respectively the chief and + + + align:start position:0% +to stop respectively the chief and +marginal ray so therefore with respect + + align:start position:0% +marginal ray so therefore with respect + + + align:start position:0% +marginal ray so therefore with respect +to the entrance and exit pupils what do + + align:start position:0% +to the entrance and exit pupils what do + + + align:start position:0% +to the entrance and exit pupils what do +you think the rays would pass + + align:start position:0% + + + + align:start position:0% + +so the answer is that they should pass + + align:start position:0% +so the answer is that they should pass + + + align:start position:0% +so the answer is that they should pass +through the center and edge respectively + + align:start position:0% +through the center and edge respectively + + + align:start position:0% +through the center and edge respectively +as well because the entrance and exit + + align:start position:0% +as well because the entrance and exit + + + align:start position:0% +as well because the entrance and exit +pupils are images of the aperture stop + + align:start position:0% +pupils are images of the aperture stop + + + align:start position:0% +pupils are images of the aperture stop +so for example if the chief area goes to + + align:start position:0% +so for example if the chief area goes to + + + align:start position:0% +so for example if the chief area goes to +the center of the aperture stop then you + + align:start position:0% +the center of the aperture stop then you + + + align:start position:0% +the center of the aperture stop then you +should also go through the center of the + + align:start position:0% +should also go through the center of the + + + align:start position:0% +should also go through the center of the +entrance and exit pupils because these + + align:start position:0% +entrance and exit pupils because these + + + align:start position:0% +entrance and exit pupils because these +are images of the aperture stop through + + align:start position:0% +are images of the aperture stop through + + + align:start position:0% +are images of the aperture stop through +the preceding and succeeding element and + + align:start position:0% +the preceding and succeeding element and + + + align:start position:0% +the preceding and succeeding element and +similarly the marginal ray hits the rim + + align:start position:0% +similarly the marginal ray hits the rim + + + align:start position:0% +similarly the marginal ray hits the rim +of the Apple to stop therefore it should + + align:start position:0% +of the Apple to stop therefore it should + + + align:start position:0% +of the Apple to stop therefore it should +also hit the rim of a of the act of the + + align:start position:0% +also hit the rim of a of the act of the + + + align:start position:0% +also hit the rim of a of the act of the +entrance and exit pupils respectively + + align:start position:0% +entrance and exit pupils respectively + + + align:start position:0% +entrance and exit pupils respectively +now for the marginal rate there could be + + align:start position:0% +now for the marginal rate there could be + + + align:start position:0% +now for the marginal rate there could be +magnifications involved so for example + + align:start position:0% +magnifications involved so for example + + + align:start position:0% +magnifications involved so for example +the distance from the optical axis to + + align:start position:0% +the distance from the optical axis to + + + align:start position:0% +the distance from the optical axis to +the rim it may be different in the upper + + align:start position:0% +the rim it may be different in the upper + + + align:start position:0% +the rim it may be different in the upper +to stop plane then it is for example in + + align:start position:0% +to stop plane then it is for example in + + + align:start position:0% +to stop plane then it is for example in +the entrance pupil plane and that is + + align:start position:0% +the entrance pupil plane and that is + + + align:start position:0% +the entrance pupil plane and that is +because in this case the optical system + + align:start position:0% +because in this case the optical system + + + align:start position:0% +because in this case the optical system +has magnified the upper to stop so the + + align:start position:0% +has magnified the upper to stop so the + + + align:start position:0% +has magnified the upper to stop so the +entrance pupil in this case is bigger + + align:start position:0% +entrance pupil in this case is bigger + + + align:start position:0% +entrance pupil in this case is bigger +than the physical stop itself so + + align:start position:0% +than the physical stop itself so + + + align:start position:0% +than the physical stop itself so +therefore the marginal a it hits the + + align:start position:0% +therefore the marginal a it hits the + + + align:start position:0% +therefore the marginal a it hits the +optical axis at a different location and + + align:start position:0% +optical axis at a different location and + + + align:start position:0% +optical axis at a different location and +also as you can see there's an inversion + + align:start position:0% +also as you can see there's an inversion + + + align:start position:0% +also as you can see there's an inversion +it hits at the bottom at the Apple to + + align:start position:0% +it hits at the bottom at the Apple to + + + align:start position:0% +it hits at the bottom at the Apple to +stop and then it hits at the top at the + + align:start position:0% +stop and then it hits at the top at the + + + align:start position:0% +stop and then it hits at the top at the +entrance pupil this is fine but what I + + align:start position:0% +entrance pupil this is fine but what I + + + align:start position:0% +entrance pupil this is fine but what I +because of the way optical systems + + align:start position:0% +because of the way optical systems + + + align:start position:0% +because of the way optical systems +behave they can produce inversions and + + align:start position:0% +behave they can produce inversions and + + + align:start position:0% +behave they can produce inversions and +magnification and as we have seen but + + align:start position:0% +magnification and as we have seen but + + + align:start position:0% +magnification and as we have seen but +what I want to emphasize is that they go + + align:start position:0% +what I want to emphasize is that they go + + + align:start position:0% +what I want to emphasize is that they go +through the limb + + align:start position:0% +through the limb + + + align:start position:0% +through the limb +because of that property that that the + + align:start position:0% +because of that property that that the + + + align:start position:0% +because of that property that that the +aperture is imaged at the entrance and + + align:start position:0% +aperture is imaged at the entrance and + + + align:start position:0% +aperture is imaged at the entrance and +exit pupils respectively + + align:start position:0% +exit pupils respectively + + + align:start position:0% +exit pupils respectively +okay and of course the two eyes will + + align:start position:0% +okay and of course the two eyes will + + + align:start position:0% +okay and of course the two eyes will +also meet again at the corresponding + + align:start position:0% +also meet again at the corresponding + + + align:start position:0% +also meet again at the corresponding +image point at the image plane right + + align:start position:0% +image point at the image plane right + + + align:start position:0% +image point at the image plane right +because the today is emanated from the + + align:start position:0% +because the today is emanated from the + + + align:start position:0% +because the today is emanated from the +object if the imaging system is good + + align:start position:0% +object if the imaging system is good + + + align:start position:0% +object if the imaging system is good +that is if it does form an image + + align:start position:0% +that is if it does form an image + + + align:start position:0% +that is if it does form an image +properly and we don't have some kind of + + align:start position:0% +properly and we don't have some kind of + + + align:start position:0% +properly and we don't have some kind of +a weird defocus or some other kind of + + align:start position:0% +a weird defocus or some other kind of + + + align:start position:0% +a weird defocus or some other kind of +inconvenience then the Torah is should + + align:start position:0% +inconvenience then the Torah is should + + + align:start position:0% +inconvenience then the Torah is should +better meet again at the image point + + align:start position:0% +better meet again at the image point + + + align:start position:0% +better meet again at the image point +right because + + align:start position:0% +right because + + + align:start position:0% +right because +the entire spherical ray bundle that + + align:start position:0% +the entire spherical ray bundle that + + + align:start position:0% +the entire spherical ray bundle that +emanated here that diverged here it also + + align:start position:0% +emanated here that diverged here it also + + + align:start position:0% +emanated here that diverged here it also +converge by the time it arrives here so + + align:start position:0% +converge by the time it arrives here so + + + align:start position:0% +converge by the time it arrives here so +therefore these two rays are just + + align:start position:0% +therefore these two rays are just + + + align:start position:0% +therefore these two rays are just +members of this spherical lab bundle so + + align:start position:0% +members of this spherical lab bundle so + + + align:start position:0% +members of this spherical lab bundle so +they will meet again at the object point + + align:start position:0% +they will meet again at the object point + + + align:start position:0% +they will meet again at the object point +okay so + + align:start position:0% + + + + align:start position:0% + +any questions I know this frustrating + + align:start position:0% +any questions I know this frustrating + + + align:start position:0% +any questions I know this frustrating +even if you have a question you cannot + + align:start position:0% +even if you have a question you cannot + + + align:start position:0% +even if you have a question you cannot +speak your mind but any questions can + + align:start position:0% +speak your mind but any questions can + + + align:start position:0% +speak your mind but any questions can +you just wave at least so I know to save + + align:start position:0% +you just wave at least so I know to save + + + align:start position:0% +you just wave at least so I know to save +time later who answer the question + + align:start position:0% + + + + align:start position:0% + +so how do you define the distance + + align:start position:0% +so how do you define the distance + + + align:start position:0% +so how do you define the distance +between the + + align:start position:0% +between the + + + align:start position:0% +between the +scan here we + + align:start position:0% +scan here we + + + align:start position:0% +scan here we +move on with a slightly different + + align:start position:0% +move on with a slightly different + + + align:start position:0% +move on with a slightly different +concept and then we'll come back to this + + align:start position:0% +concept and then we'll come back to this + + + align:start position:0% +concept and then we'll come back to this +topic again + + align:start position:0% +topic again + + + align:start position:0% +topic again +so the next topic is a different kind of + + align:start position:0% +so the next topic is a different kind of + + + align:start position:0% +so the next topic is a different kind of +stop called the field stop + + align:start position:0% +stop called the field stop + + + align:start position:0% +stop called the field stop +to remember the definition of chief ray + + align:start position:0% +to remember the definition of chief ray + + + align:start position:0% +to remember the definition of chief ray +we said that the chief ray is a ray that + + align:start position:0% +we said that the chief ray is a ray that + + + align:start position:0% +we said that the chief ray is a ray that +goes through the center of the pupil + + align:start position:0% +goes through the center of the pupil + + + align:start position:0% +goes through the center of the pupil +I mean the entrance pupil the aperture + + align:start position:0% +I mean the entrance pupil the aperture + + + align:start position:0% +I mean the entrance pupil the aperture +controls okay so here is a chief ray + + align:start position:0% +controls okay so here is a chief ray + + + align:start position:0% +controls okay so here is a chief ray +from a tunnel object and here is a chief + + align:start position:0% +from a tunnel object and here is a chief + + + align:start position:0% +from a tunnel object and here is a chief +ray from a short object + + align:start position:0% + + + + align:start position:0% + +the bother the chief rays they will go + + align:start position:0% +the bother the chief rays they will go + + + align:start position:0% +the bother the chief rays they will go +through the center of the Apple to stop + + align:start position:0% +through the center of the Apple to stop + + + align:start position:0% +through the center of the Apple to stop +by definition and of course they will + + align:start position:0% +by definition and of course they will + + + align:start position:0% +by definition and of course they will +also go through the center of the + + align:start position:0% +also go through the center of the + + + align:start position:0% +also go through the center of the +entrance pupil the entrance pupil used + + align:start position:0% +entrance pupil the entrance pupil used + + + align:start position:0% +entrance pupil the entrance pupil used +to be here if you remember I'm not + + align:start position:0% +to be here if you remember I'm not + + + align:start position:0% +to be here if you remember I'm not +drawing it anymore because I don't want + + align:start position:0% +drawing it anymore because I don't want + + + align:start position:0% +drawing it anymore because I don't want +to clutter this diagram but it used to + + align:start position:0% +to clutter this diagram but it used to + + + align:start position:0% +to clutter this diagram but it used to +be here so the Torah is they meet at + + align:start position:0% +be here so the Torah is they meet at + + + align:start position:0% +be here so the Torah is they meet at +this point because there are the images + + align:start position:0% +this point because there are the images + + + align:start position:0% +this point because there are the images +of the aperture however these layers + + align:start position:0% +of the aperture however these layers + + + align:start position:0% +of the aperture however these layers +will go off access at other points of + + align:start position:0% +will go off access at other points of + + + align:start position:0% +will go off access at other points of +the optical system and there will be + + align:start position:0% +the optical system and there will be + + + align:start position:0% +the optical system and there will be +some point in the optical system where + + align:start position:0% +some point in the optical system where + + + align:start position:0% +some point in the optical system where +one of these guys may get cut this + + align:start position:0% +one of these guys may get cut this + + + align:start position:0% +one of these guys may get cut this +element is the optical system that + + align:start position:0% +element is the optical system that + + + align:start position:0% +element is the optical system that +limits the chief rays okay that element + + align:start position:0% +limits the chief rays okay that element + + + align:start position:0% +limits the chief rays okay that element +is called the field stop and + + align:start position:0% +is called the field stop and + + + align:start position:0% +is called the field stop and +the physical significance of the field + + align:start position:0% +the physical significance of the field + + + align:start position:0% +the physical significance of the field +stop is actually very important and even + + align:start position:0% +stop is actually very important and even + + + align:start position:0% +stop is actually very important and even +more intuitive than the Apple to stop + + align:start position:0% +more intuitive than the Apple to stop + + + align:start position:0% +more intuitive than the Apple to stop +the field stop is what defines the field + + align:start position:0% +the field stop is what defines the field + + + align:start position:0% +the field stop is what defines the field +of view another field of view has a + + align:start position:0% +of view another field of view has a + + + align:start position:0% +of view another field of view has a +formal definition it is this angle here + + align:start position:0% +formal definition it is this angle here + + + align:start position:0% +formal definition it is this angle here +that they do but even in colloquial + + align:start position:0% +that they do but even in colloquial + + + align:start position:0% +that they do but even in colloquial +language when we say the field of view + + align:start position:0% +language when we say the field of view + + + align:start position:0% +language when we say the field of view +we know exactly what we mean in a moment + + align:start position:0% +we know exactly what we mean in a moment + + + align:start position:0% +we know exactly what we mean in a moment +the field of view is basically the size + + align:start position:0% +the field of view is basically the size + + + align:start position:0% +the field of view is basically the size +that can be visible at and outside the + + align:start position:0% +that can be visible at and outside the + + + align:start position:0% +that can be visible at and outside the +field of view the image is not form so + + align:start position:0% +field of view the image is not form so + + + align:start position:0% +field of view the image is not form so +an example is if I look at you well + + align:start position:0% +an example is if I look at you well + + + align:start position:0% +an example is if I look at you well +actually this is great because I look at + + align:start position:0% +actually this is great because I look at + + + align:start position:0% +actually this is great because I look at +you through a camera right and the way + + align:start position:0% +you through a camera right and the way + + + align:start position:0% +you through a camera right and the way +the camera is pointed right now I can + + align:start position:0% +the camera is pointed right now I can + + + align:start position:0% +the camera is pointed right now I can +only see the central row of desks out in + + align:start position:0% +only see the central row of desks out in + + + align:start position:0% +only see the central row of desks out in +Cambridge but I cannot see those of you + + align:start position:0% +Cambridge but I cannot see those of you + + + align:start position:0% +Cambridge but I cannot see those of you +who are seated on the left the right so + + align:start position:0% +who are seated on the left the right so + + + align:start position:0% +who are seated on the left the right so +you might be picking your nose for + + align:start position:0% +you might be picking your nose for + + + align:start position:0% +you might be picking your nose for +example and I would not be able to see + + align:start position:0% +example and I would not be able to see + + + align:start position:0% +example and I would not be able to see +it and that's because you are outside my + + align:start position:0% +it and that's because you are outside my + + + align:start position:0% +it and that's because you are outside my +field of view + + align:start position:0% + + + + align:start position:0% + +thank you for the control for telling + + align:start position:0% +thank you for the control for telling + + + align:start position:0% +thank you for the control for telling +the camera now what is happening my + + align:start position:0% +the camera now what is happening my + + + align:start position:0% +the camera now what is happening my +field of view is shifting okay so the + + align:start position:0% +field of view is shifting okay so the + + + align:start position:0% +field of view is shifting okay so the +field stop in this case is actually the + + align:start position:0% +field stop in this case is actually the + + + align:start position:0% +field stop in this case is actually the +dye the electronic dye that captures the + + align:start position:0% +dye the electronic dye that captures the + + + align:start position:0% +dye the electronic dye that captures the +image electronically on your side then + + align:start position:0% +image electronically on your side then + + + align:start position:0% +image electronically on your side then +transmits it to us here in Singapore + + align:start position:0% +transmits it to us here in Singapore + + + align:start position:0% +transmits it to us here in Singapore +this is the physical field store that + + align:start position:0% +this is the physical field store that + + + align:start position:0% +this is the physical field store that +limits how many of you I can see it can + + align:start position:0% +limits how many of you I can see it can + + + align:start position:0% +limits how many of you I can see it can +at any given instance so the field stop + + align:start position:0% +at any given instance so the field stop + + + align:start position:0% +at any given instance so the field stop +is is + + align:start position:0% +is is + + + align:start position:0% +is is +second to the numerical aperture and the + + align:start position:0% +second to the numerical aperture and the + + + align:start position:0% +second to the numerical aperture and the +aperture stop is another very important + + align:start position:0% +aperture stop is another very important + + + align:start position:0% +aperture stop is another very important +quality it tells us how big is the size + + align:start position:0% +quality it tells us how big is the size + + + align:start position:0% +quality it tells us how big is the size +of an object that we can see okay so if + + align:start position:0% +of an object that we can see okay so if + + + align:start position:0% +of an object that we can see okay so if +you look for example at a telescope if + + align:start position:0% +you look for example at a telescope if + + + align:start position:0% +you look for example at a telescope if +you look at the night sky through a + + align:start position:0% +you look at the night sky through a + + + align:start position:0% +you look at the night sky through a +telescope the field of view is there + + align:start position:0% +telescope the field of view is there + + + align:start position:0% +telescope the field of view is there +basically how many stars can fit what + + align:start position:0% +basically how many stars can fit what + + + align:start position:0% +basically how many stars can fit what +portion of the sky you can fit within + + align:start position:0% +portion of the sky you can fit within + + + align:start position:0% +portion of the sky you can fit within +your image when you look through the + + align:start position:0% +your image when you look through the + + + align:start position:0% +your image when you look through the +telescope when you look to a microscope + + align:start position:0% +telescope when you look to a microscope + + + align:start position:0% +telescope when you look to a microscope +similarly the size of the specimen that + + align:start position:0% +similarly the size of the specimen that + + + align:start position:0% +similarly the size of the specimen that +you can observe in the microscope that + + align:start position:0% +you can observe in the microscope that + + + align:start position:0% +you can observe in the microscope that +would be the field of view now + + align:start position:0% +would be the field of view now + + + align:start position:0% +would be the field of view now +intuitively we would like to define the + + align:start position:0% +intuitively we would like to define the + + + align:start position:0% +intuitively we would like to define the +field of view in physical size in meters + + align:start position:0% +field of view in physical size in meters + + + align:start position:0% +field of view in physical size in meters +or millimeters or microns or whatever + + align:start position:0% +or millimeters or microns or whatever + + + align:start position:0% +or millimeters or microns or whatever +the case might be for issues that will + + align:start position:0% +the case might be for issues that will + + + align:start position:0% +the case might be for issues that will +become apparent a little bit later we + + align:start position:0% +become apparent a little bit later we + + + align:start position:0% +become apparent a little bit later we +prefer to define the field of view as an + + align:start position:0% +prefer to define the field of view as an + + + align:start position:0% +prefer to define the field of view as an +angle actually the angle subtended + + align:start position:0% +angle actually the angle subtended + + + align:start position:0% +angle actually the angle subtended +towards the object and you can guess I + + align:start position:0% +towards the object and you can guess I + + + align:start position:0% +towards the object and you can guess I +don't even have to make the word you can + + align:start position:0% +don't even have to make the word you can + + + align:start position:0% +don't even have to make the word you can +guess why we define angry instead of + + align:start position:0% +guess why we define angry instead of + + + align:start position:0% +guess why we define angry instead of +physical side that is because very often + + align:start position:0% +physical side that is because very often + + + align:start position:0% +physical side that is because very often +optical optical systems has have + + align:start position:0% +optical optical systems has have + + + align:start position:0% +optical optical systems has have +variable magnification so with the same + + align:start position:0% +variable magnification so with the same + + + align:start position:0% +variable magnification so with the same +optical system might move a lens and + + align:start position:0% +optical system might move a lens and + + + align:start position:0% +optical system might move a lens and +then the object would move but the field + + align:start position:0% +then the object would move but the field + + + align:start position:0% +then the object would move but the field +of view might not change okay so if I + + align:start position:0% +of view might not change okay so if I + + + align:start position:0% +of view might not change okay so if I +define it as a size and I move it here + + align:start position:0% +define it as a size and I move it here + + + align:start position:0% +define it as a size and I move it here +then the size would be bigger right + + align:start position:0% +then the size would be bigger right + + + align:start position:0% +then the size would be bigger right +whereas the angle generally is preserved + + align:start position:0% +whereas the angle generally is preserved + + + align:start position:0% +whereas the angle generally is preserved +so that's why we define the field of + + align:start position:0% +so that's why we define the field of + + + align:start position:0% +so that's why we define the field of +view as an angle in radians or degrees + + align:start position:0% +view as an angle in radians or degrees + + + align:start position:0% +view as an angle in radians or degrees +instead of instead of physical distances + + align:start position:0% +instead of instead of physical distances + + + align:start position:0% +instead of instead of physical distances +the meaning of the field stop + + align:start position:0% +the meaning of the field stop + + + align:start position:0% +the meaning of the field stop +and similarly to the entrance and exit + + align:start position:0% +and similarly to the entrance and exit + + + align:start position:0% +and similarly to the entrance and exit +pupils that we saw for the Apple to stop + + align:start position:0% +pupils that we saw for the Apple to stop + + + align:start position:0% +pupils that we saw for the Apple to stop +we can define equivalent quantities for + + align:start position:0% +we can define equivalent quantities for + + + align:start position:0% +we can define equivalent quantities for +the field stop but we'll call them + + align:start position:0% +the field stop but we'll call them + + + align:start position:0% +the field stop but we'll call them +windows + + align:start position:0% +windows + + + align:start position:0% +windows +so if we image the field stop through + + align:start position:0% +so if we image the field stop through + + + align:start position:0% +so if we image the field stop through +the proceeding elements we get what is + + align:start position:0% +the proceeding elements we get what is + + + align:start position:0% +the proceeding elements we get what is +called the entrance window if we image + + align:start position:0% +called the entrance window if we image + + + align:start position:0% +called the entrance window if we image +it through the succeed in elements we + + align:start position:0% +it through the succeed in elements we + + + align:start position:0% +it through the succeed in elements we +get what is called the exit window and + + align:start position:0% +get what is called the exit window and + + + align:start position:0% +get what is called the exit window and +generally in an optical system these + + align:start position:0% +generally in an optical system these + + + align:start position:0% +generally in an optical system these +windows they should coincide with your + + align:start position:0% +windows they should coincide with your + + + align:start position:0% +windows they should coincide with your +object and image planes respectively so + + align:start position:0% +object and image planes respectively so + + + align:start position:0% +object and image planes respectively so +the entrance windows should coincide + + align:start position:0% +the entrance windows should coincide + + + align:start position:0% +the entrance windows should coincide +with the object plane the exit window + + align:start position:0% +with the object plane the exit window + + + align:start position:0% +with the object plane the exit window +should coincide with the image plane if + + align:start position:0% +should coincide with the image plane if + + + align:start position:0% +should coincide with the image plane if +that's not the case there's something + + align:start position:0% +that's not the case there's something + + + align:start position:0% +that's not the case there's something +wrong with the optical system it can + + align:start position:0% +wrong with the optical system it can + + + align:start position:0% +wrong with the optical system it can +happen it is not impossible but there's + + align:start position:0% +happen it is not impossible but there's + + + align:start position:0% +happen it is not impossible but there's +something wrong with the optical system + + align:start position:0% +something wrong with the optical system + + + align:start position:0% +something wrong with the optical system +ok so now that we did that let's put all + + align:start position:0% +ok so now that we did that let's put all + + + align:start position:0% +ok so now that we did that let's put all +these definitions together + + align:start position:0% +these definitions together + + + align:start position:0% +these definitions together +this is another confusing diagram but it + + align:start position:0% +this is another confusing diagram but it + + + align:start position:0% +this is another confusing diagram but it +solves everything it solves that safe + + align:start position:0% +solves everything it solves that safe + + + align:start position:0% +solves everything it solves that safe +and marginal rays it solve the two + + align:start position:0% +and marginal rays it solve the two + + + align:start position:0% +and marginal rays it solve the two +physical stops the upper two stopped in + + align:start position:0% +physical stops the upper two stopped in + + + align:start position:0% +physical stops the upper two stopped in +the field stop and then it solves their + + align:start position:0% +the field stop and then it solves their + + + align:start position:0% +the field stop and then it solves their +images with respect to the preceding and + + align:start position:0% +images with respect to the preceding and + + + align:start position:0% +images with respect to the preceding and +succeeding elements that are called the + + align:start position:0% +succeeding elements that are called the + + + align:start position:0% +succeeding elements that are called the +entrance and exit pupil and windows + + align:start position:0% +entrance and exit pupil and windows + + + align:start position:0% +entrance and exit pupil and windows +respectively I realize this is a bunch + + align:start position:0% +respectively I realize this is a bunch + + + align:start position:0% +respectively I realize this is a bunch +of terms that I threw at you at once + + align:start position:0% +of terms that I threw at you at once + + + align:start position:0% +of terms that I threw at you at once +so so treat this as an information + + align:start position:0% +so so treat this as an information + + + align:start position:0% +so so treat this as an information +session then go back and make sure you + + align:start position:0% +session then go back and make sure you + + + align:start position:0% +session then go back and make sure you +read them again from the north and from + + align:start position:0% +read them again from the north and from + + + align:start position:0% +read them again from the north and from +the book so you make sure they sort of + + align:start position:0% +the book so you make sure they sort of + + + align:start position:0% +the book so you make sure they sort of +solidify in your mind + + align:start position:0% +solidify in your mind + + + align:start position:0% +solidify in your mind +but this diagram actually spent a lot of + + align:start position:0% +but this diagram actually spent a lot of + + + align:start position:0% +but this diagram actually spent a lot of +time making this diagram because I + + align:start position:0% +time making this diagram because I + + + align:start position:0% +time making this diagram because I +actually drew it by hand instead of + + align:start position:0% +actually drew it by hand instead of + + + align:start position:0% +actually drew it by hand instead of +using an optical software I do it by + + align:start position:0% +using an optical software I do it by + + + align:start position:0% +using an optical software I do it by +hand so took me a lot of time to make it + + align:start position:0% +hand so took me a lot of time to make it + + + align:start position:0% +hand so took me a lot of time to make it +accurate but to the best that I can I + + align:start position:0% +accurate but to the best that I can I + + + align:start position:0% +accurate but to the best that I can I +tried it split the hardware except for + + align:start position:0% +tried it split the hardware except for + + + align:start position:0% +tried it split the hardware except for +this lens here this less doesn't look + + align:start position:0% +this lens here this less doesn't look + + + align:start position:0% +this lens here this less doesn't look +very good it's a negative lens it should + + align:start position:0% +very good it's a negative lens it should + + + align:start position:0% +very good it's a negative lens it should +have sort of developed this way bangle + + align:start position:0% +have sort of developed this way bangle + + + align:start position:0% +have sort of developed this way bangle +even more if I had done this properly + + align:start position:0% +even more if I had done this properly + + + align:start position:0% +even more if I had done this properly +this would then become monster so I + + align:start position:0% +this would then become monster so I + + + align:start position:0% +this would then become monster so I +didn't do it but anyway but you can see + + align:start position:0% +didn't do it but anyway but you can see + + + align:start position:0% +didn't do it but anyway but you can see +how it works + + align:start position:0% +how it works + + + align:start position:0% +how it works +here's the chief reg let's stretch it + + align:start position:0% +here's the chief reg let's stretch it + + + align:start position:0% +here's the chief reg let's stretch it +through the system + + align:start position:0% +through the system + + + align:start position:0% +through the system +so here's the chief ray it goes to the + + align:start position:0% +so here's the chief ray it goes to the + + + align:start position:0% +so here's the chief ray it goes to the +center of the entrance pupil + + align:start position:0% +center of the entrance pupil + + + align:start position:0% +center of the entrance pupil +then it goes through the edge of the + + align:start position:0% +then it goes through the edge of the + + + align:start position:0% +then it goes through the edge of the +field stop so that means that I chose + + align:start position:0% +field stop so that means that I chose + + + align:start position:0% +field stop so that means that I chose +that see fray the propagates at an angle + + align:start position:0% +that see fray the propagates at an angle + + + align:start position:0% +that see fray the propagates at an angle +equal to what equal to the field of view + + align:start position:0% +equal to what equal to the field of view + + + align:start position:0% +equal to what equal to the field of view +right because this is the last chief + + align:start position:0% +right because this is the last chief + + + align:start position:0% +right because this is the last chief +Frey admitted through a system if I put + + align:start position:0% +Frey admitted through a system if I put + + + align:start position:0% +Frey admitted through a system if I put +them chief ray at a bigger angle that is + + align:start position:0% +them chief ray at a bigger angle that is + + + align:start position:0% +them chief ray at a bigger angle that is +a taller object it would miss the field + + align:start position:0% +a taller object it would miss the field + + + align:start position:0% +a taller object it would miss the field +stop okay then the same chief lyric goes + + align:start position:0% +stop okay then the same chief lyric goes + + + align:start position:0% +stop okay then the same chief lyric goes +on it goes through a center of the Apple + + align:start position:0% +on it goes through a center of the Apple + + + align:start position:0% +on it goes through a center of the Apple +to stop again then again through the + + align:start position:0% +to stop again then again through the + + + align:start position:0% +to stop again then again through the +center of the exit pupil and finally hit + + align:start position:0% +center of the exit pupil and finally hit + + + align:start position:0% +center of the exit pupil and finally hit +the edge of the exit window which is + + align:start position:0% +the edge of the exit window which is + + + align:start position:0% +the edge of the exit window which is +also the tip of the image okay that's + + align:start position:0% +also the tip of the image okay that's + + + align:start position:0% +also the tip of the image okay that's +the chief Rendon let's go through the + + align:start position:0% +the chief Rendon let's go through the + + + align:start position:0% +the chief Rendon let's go through the +marginal Ray + + align:start position:0% +marginal Ray + + + align:start position:0% +marginal Ray +the marginal ray will hit the rim of the + + align:start position:0% +the marginal ray will hit the rim of the + + + align:start position:0% +the marginal ray will hit the rim of the +entrance pupil then we'll hit the limb + + align:start position:0% +entrance pupil then we'll hit the limb + + + align:start position:0% +entrance pupil then we'll hit the limb +of the field stop again why I'll give + + align:start position:0% +of the field stop again why I'll give + + + align:start position:0% +of the field stop again why I'll give +you 30 seconds to think about it why + + align:start position:0% +you 30 seconds to think about it why + + + align:start position:0% +you 30 seconds to think about it why +does the marginal they hit the rim of + + align:start position:0% +does the marginal they hit the rim of + + + align:start position:0% +does the marginal they hit the rim of +the field stop again + + align:start position:0% + + + + align:start position:0% + +my computer has actually timer so I can + + align:start position:0% +my computer has actually timer so I can + + + align:start position:0% +my computer has actually timer so I can +count seconds very precise oh + + align:start position:0% + + + + align:start position:0% + +there is not this so you can even speak + + align:start position:0% +there is not this so you can even speak + + + align:start position:0% +there is not this so you can even speak +your mind no + + align:start position:0% + + + + align:start position:0% + +thanks by the way for taking thanks + + align:start position:0% +thanks by the way for taking thanks + + + align:start position:0% +thanks by the way for taking thanks +control + + align:start position:0% + + + + align:start position:0% + +anybody why does the marginal they also + + align:start position:0% +anybody why does the marginal they also + + + align:start position:0% +anybody why does the marginal they also +go through the rim the edge of the field + + align:start position:0% +go through the rim the edge of the field + + + align:start position:0% +go through the rim the edge of the field +stop + + align:start position:0% + + + + align:start position:0% + +because + + align:start position:0% +because + + + align:start position:0% +because +the entrance window is an image of the + + align:start position:0% +the entrance window is an image of the + + + align:start position:0% +the entrance window is an image of the +field stop or I guess the other way + + align:start position:0% +field stop or I guess the other way + + + align:start position:0% +field stop or I guess the other way +around so the marginal rate is I me age + + align:start position:0% +around so the marginal rate is I me age + + + align:start position:0% +around so the marginal rate is I me age +the interest window setting beyond the + + align:start position:0% +the interest window setting beyond the + + + align:start position:0% +the interest window setting beyond the +edge of the field stop also + + align:start position:0% +edge of the field stop also + + + align:start position:0% +edge of the field stop also +these two planes are images of each + + align:start position:0% +these two planes are images of each + + + align:start position:0% +these two planes are images of each +other so since the marginal rain meets + + align:start position:0% +other so since the marginal rain meets + + + align:start position:0% +other so since the marginal rain meets +the chief ray here then it should also + + align:start position:0% +the chief ray here then it should also + + + align:start position:0% +the chief ray here then it should also +meet that safe ray here again + + align:start position:0% +meet that safe ray here again + + + align:start position:0% +meet that safe ray here again +another way to put it is that this is + + align:start position:0% +another way to put it is that this is + + + align:start position:0% +another way to put it is that this is +actually an intermediate image plane for + + align:start position:0% +actually an intermediate image plane for + + + align:start position:0% +actually an intermediate image plane for +this particular optical system okay so + + align:start position:0% +this particular optical system okay so + + + align:start position:0% +this particular optical system okay so +then in other words you would see an + + align:start position:0% +then in other words you would see an + + + align:start position:0% +then in other words you would see an +image of the object itself here if you + + align:start position:0% +image of the object itself here if you + + + align:start position:0% +image of the object itself here if you +were to stick your high okay then the + + align:start position:0% +were to stick your high okay then the + + + align:start position:0% +were to stick your high okay then the +margin leg will go again now goes again + + align:start position:0% +margin leg will go again now goes again + + + align:start position:0% +margin leg will go again now goes again +through the edge of the upper to stop + + align:start position:0% +through the edge of the upper to stop + + + align:start position:0% +through the edge of the upper to stop +again and that is of course because it + + align:start position:0% +again and that is of course because it + + + align:start position:0% +again and that is of course because it +went through the edge of the pupil and + + align:start position:0% +went through the edge of the pupil and + + + align:start position:0% +went through the edge of the pupil and +since the pupil of the upper to stop our + + align:start position:0% +since the pupil of the upper to stop our + + + align:start position:0% +since the pupil of the upper to stop our +images of each other then it has to go + + align:start position:0% +images of each other then it has to go + + + align:start position:0% +images of each other then it has to go +through the edge again okay now we'll + + align:start position:0% +through the edge again okay now we'll + + + align:start position:0% +through the edge again okay now we'll +become repetitive it will hit again + + align:start position:0% +become repetitive it will hit again + + + align:start position:0% +become repetitive it will hit again +varying of the exit pupil for the same + + align:start position:0% +varying of the exit pupil for the same + + + align:start position:0% +varying of the exit pupil for the same +reason and then finally it would hit the + + align:start position:0% +reason and then finally it would hit the + + + align:start position:0% +reason and then finally it would hit the +edge of the exit window because the exit + + align:start position:0% +edge of the exit window because the exit + + + align:start position:0% +edge of the exit window because the exit +window is an image of the field stop so + + align:start position:0% +window is an image of the field stop so + + + align:start position:0% +window is an image of the field stop so +these multiple imaging + + align:start position:0% +these multiple imaging + + + align:start position:0% +these multiple imaging +requirements they sort of make this all + + align:start position:0% +requirements they sort of make this all + + + align:start position:0% +requirements they sort of make this all +makes sense ray but but this is how the + + align:start position:0% +makes sense ray but but this is how the + + + align:start position:0% +makes sense ray but but this is how the +world + + align:start position:0% +world + + + align:start position:0% +world +the marginal ray as the name suggests + + align:start position:0% +the marginal ray as the name suggests + + + align:start position:0% +the marginal ray as the name suggests +hits the rims of everything the Apple to + + align:start position:0% +hits the rims of everything the Apple to + + + align:start position:0% +hits the rims of everything the Apple to +stop the pupils the windows and all that + + align:start position:0% +stop the pupils the windows and all that + + + align:start position:0% +stop the pupils the windows and all that +the chief ray it goes through the center + + align:start position:0% +the chief ray it goes through the center + + + align:start position:0% +the chief ray it goes through the center +of the pupils and runs an exit and the + + align:start position:0% +of the pupils and runs an exit and the + + + align:start position:0% +of the pupils and runs an exit and the +Apple to stop and hits the edges the + + align:start position:0% +Apple to stop and hits the edges the + + + align:start position:0% +Apple to stop and hits the edges the +rims of the field stop and the + + align:start position:0% +rims of the field stop and the + + + align:start position:0% +rims of the field stop and the +Associated entrance and exit window + + align:start position:0% +Associated entrance and exit window + + + align:start position:0% +Associated entrance and exit window +and + + align:start position:0% +and + + + align:start position:0% +and +finally another to have everything + + align:start position:0% +finally another to have everything + + + align:start position:0% +finally another to have everything +together here is again the Tiffany the + + align:start position:0% +together here is again the Tiffany the + + + align:start position:0% +together here is again the Tiffany the +definition of the field of view it is + + align:start position:0% +definition of the field of view it is + + + align:start position:0% +definition of the field of view it is +the ante between the last two she fries + + align:start position:0% +the ante between the last two she fries + + + align:start position:0% +the ante between the last two she fries +admitted by the system last - meaning + + align:start position:0% +admitted by the system last - meaning + + + align:start position:0% +admitted by the system last - meaning +that it is the last - that the field + + align:start position:0% +that it is the last - that the field + + + align:start position:0% +that it is the last - that the field +stop with admit and + + align:start position:0% +stop with admit and + + + align:start position:0% +stop with admit and +the numerical aperture is the angle + + align:start position:0% +the numerical aperture is the angle + + + align:start position:0% +the numerical aperture is the angle +between the two marginal rays that + + align:start position:0% +between the two marginal rays that + + + align:start position:0% +between the two marginal rays that +depart from the center of the from the + + align:start position:0% +depart from the center of the from the + + + align:start position:0% +depart from the center of the from the +center of the window that is from the + + align:start position:0% +center of the window that is from the + + + align:start position:0% +center of the window that is from the +optical axis itself okay we do not + + align:start position:0% +optical axis itself okay we do not + + + align:start position:0% +optical axis itself okay we do not +define the numerical aperture from + + align:start position:0% +define the numerical aperture from + + + align:start position:0% +define the numerical aperture from +from off axis points the reason is that + + align:start position:0% +from off axis points the reason is that + + + align:start position:0% +from off axis points the reason is that +in poorly designed optical systems + + align:start position:0% +in poorly designed optical systems + + + align:start position:0% +in poorly designed optical systems +let me say in an ideal optical system + + align:start position:0% +let me say in an ideal optical system + + + align:start position:0% +let me say in an ideal optical system +the numerical aperture should be equal + + align:start position:0% +the numerical aperture should be equal + + + align:start position:0% +the numerical aperture should be equal +no matter where you are within the field + + align:start position:0% +no matter where you are within the field + + + align:start position:0% +no matter where you are within the field +of view the numerical aperture should be + + align:start position:0% +of view the numerical aperture should be + + + align:start position:0% +of view the numerical aperture should be +the same in practice that is very + + align:start position:0% +the same in practice that is very + + + align:start position:0% +the same in practice that is very +difficult to do and if you do a + + align:start position:0% +difficult to do and if you do a + + + align:start position:0% +difficult to do and if you do a +particularly pull a particularly poor + + align:start position:0% +particularly pull a particularly poor + + + align:start position:0% +particularly pull a particularly poor +job as a designer the numerical aperture + + align:start position:0% +job as a designer the numerical aperture + + + align:start position:0% +job as a designer the numerical aperture +can decrease drastically + + align:start position:0% + + + + align:start position:0% + +when you go of access here in fact in + + align:start position:0% +when you go of access here in fact in + + + align:start position:0% +when you go of access here in fact in +the next example that I will show this + + align:start position:0% +the next example that I will show this + + + align:start position:0% +the next example that I will show this +will happen the numerical aperture + + align:start position:0% +will happen the numerical aperture + + + align:start position:0% +will happen the numerical aperture +become drastically smaller as you go off + + align:start position:0% +become drastically smaller as you go off + + + align:start position:0% +become drastically smaller as you go off +axis that is very that is called + + align:start position:0% +axis that is very that is called + + + align:start position:0% +axis that is very that is called +vignetting it is one of those French + + align:start position:0% +vignetting it is one of those French + + + align:start position:0% +vignetting it is one of those French +words that have crept in optics and is + + align:start position:0% +words that have crept in optics and is + + + align:start position:0% +words that have crept in optics and is +difficult to pronounce you will see it + + align:start position:0% +difficult to pronounce you will see it + + + align:start position:0% +difficult to pronounce you will see it +written in a second I will just add it + + align:start position:0% +written in a second I will just add it + + + align:start position:0% +written in a second I will just add it +down here vignette in it is very + + align:start position:0% +down here vignette in it is very + + + align:start position:0% +down here vignette in it is very +annoying because if you have vignette in + + align:start position:0% +annoying because if you have vignette in + + + align:start position:0% +annoying because if you have vignette in +an optical system then the edges of the + + align:start position:0% +an optical system then the edges of the + + + align:start position:0% +an optical system then the edges of the +image they appear darker remember the + + align:start position:0% +image they appear darker remember the + + + align:start position:0% +image they appear darker remember the +numerical aperture is the amount of + + align:start position:0% +numerical aperture is the amount of + + + align:start position:0% +numerical aperture is the amount of +light that the optical system admits + + align:start position:0% +light that the optical system admits + + + align:start position:0% +light that the optical system admits +well if I admit more light in the center + + align:start position:0% +well if I admit more light in the center + + + align:start position:0% +well if I admit more light in the center +I have a larger numerical aperture in + + align:start position:0% +I have a larger numerical aperture in + + + align:start position:0% +I have a larger numerical aperture in +the center and the America numerical + + align:start position:0% +the center and the America numerical + + + align:start position:0% +the center and the America numerical +aperture decreases as a goal of axis it + + align:start position:0% +aperture decreases as a goal of axis it + + + align:start position:0% +aperture decreases as a goal of axis it +means that the edges of the image will + + align:start position:0% +means that the edges of the image will + + + align:start position:0% +means that the edges of the image will +be darker right it will be dimmer and + + align:start position:0% +be darker right it will be dimmer and + + + align:start position:0% +be darker right it will be dimmer and +that is of course very undesirable and + + align:start position:0% +that is of course very undesirable and + + + align:start position:0% +that is of course very undesirable and +generally when we design microscopes + + align:start position:0% +generally when we design microscopes + + + align:start position:0% +generally when we design microscopes +telescopes and such we try to make sure + + align:start position:0% +telescopes and such we try to make sure + + + align:start position:0% +telescopes and such we try to make sure +that this will not happen + + align:start position:0% +that this will not happen + + + align:start position:0% +that this will not happen +but anyway because this could happen + + align:start position:0% +but anyway because this could happen + + + align:start position:0% +but anyway because this could happen +that's why the numerical aperture is + + align:start position:0% +that's why the numerical aperture is + + + align:start position:0% +that's why the numerical aperture is +defined at the center or on axis so that + + align:start position:0% +defined at the center or on axis so that + + + align:start position:0% +defined at the center or on axis so that +it has an unambiguous definition okay + + align:start position:0% + + + + align:start position:0% + +so having said that let's look now at an + + align:start position:0% +so having said that let's look now at an + + + align:start position:0% +so having said that let's look now at an +example that will actually reveal this + + align:start position:0% +example that will actually reveal this + + + align:start position:0% +example that will actually reveal this +vignette and phenomenon in addition to + + align:start position:0% +vignette and phenomenon in addition to + + + align:start position:0% +vignette and phenomenon in addition to +other things so this example is + + align:start position:0% +other things so this example is + + + align:start position:0% +other things so this example is +very simple it is a just a single thin + + align:start position:0% +very simple it is a just a single thin + + + align:start position:0% +very simple it is a just a single thin +lens and then in front of the thin lens + + align:start position:0% +lens and then in front of the thin lens + + + align:start position:0% +lens and then in front of the thin lens +were recruited with put + + align:start position:0% +were recruited with put + + + align:start position:0% +were recruited with put +an aperture stop + + align:start position:0% +an aperture stop + + + align:start position:0% +an aperture stop +and you can think of it actually this is + + align:start position:0% +and you can think of it actually this is + + + align:start position:0% +and you can think of it actually this is +a very simplified model of the eye of + + align:start position:0% +a very simplified model of the eye of + + + align:start position:0% +a very simplified model of the eye of +the human eye who have a lens in front + + align:start position:0% +the human eye who have a lens in front + + + align:start position:0% +the human eye who have a lens in front +of it in the human eye we'll call it the + + align:start position:0% +of it in the human eye we'll call it the + + + align:start position:0% +of it in the human eye we'll call it the +pupil leg of course in the human eye in + + align:start position:0% +pupil leg of course in the human eye in + + + align:start position:0% +pupil leg of course in the human eye in +actuality also has an additional lens in + + align:start position:0% +actuality also has an additional lens in + + + align:start position:0% +actuality also has an additional lens in +front of the pupil called the cornea but + + align:start position:0% +front of the pupil called the cornea but + + + align:start position:0% +front of the pupil called the cornea but +anyway so that's why this is perhaps not + + align:start position:0% +anyway so that's why this is perhaps not + + + align:start position:0% +anyway so that's why this is perhaps not +an ideal model but but anyway that's the + + align:start position:0% +an ideal model but but anyway that's the + + + align:start position:0% +an ideal model but but anyway that's the +example that chose to do and in addition + + align:start position:0% +example that chose to do and in addition + + + align:start position:0% +example that chose to do and in addition +it has a field stop which is located at + + align:start position:0% +it has a field stop which is located at + + + align:start position:0% +it has a field stop which is located at +the image plane now generally if you see + + align:start position:0% +the image plane now generally if you see + + + align:start position:0% +the image plane now generally if you see +a stop at the image plane this is a good + + align:start position:0% +a stop at the image plane this is a good + + + align:start position:0% +a stop at the image plane this is a good +candidate to be the field top right + + align:start position:0% +candidate to be the field top right + + + align:start position:0% +candidate to be the field top right +because clearly if I image anything + + align:start position:0% +because clearly if I image anything + + + align:start position:0% +because clearly if I image anything +outside this opening this is what + + align:start position:0% +outside this opening this is what + + + align:start position:0% +outside this opening this is what +aperture means by the way literally + + align:start position:0% +aperture means by the way literally + + + align:start position:0% +aperture means by the way literally +aperture means opening so if I need + + align:start position:0% +aperture means opening so if I need + + + align:start position:0% +aperture means opening so if I need +image anything outside this opening then + + align:start position:0% +image anything outside this opening then + + + align:start position:0% +image anything outside this opening then +it will hit the block and therefore it + + align:start position:0% +it will hit the block and therefore it + + + align:start position:0% +it will hit the block and therefore it +will not damage so therefore this is + + align:start position:0% +will not damage so therefore this is + + + align:start position:0% +will not damage so therefore this is +very clearly the field so physically the + + align:start position:0% +very clearly the field so physically the + + + align:start position:0% +very clearly the field so physically the +field stop is for example as I mentioned + + align:start position:0% +field stop is for example as I mentioned + + + align:start position:0% +field stop is for example as I mentioned +earlier it is the size of the chip that + + align:start position:0% +earlier it is the size of the chip that + + + align:start position:0% +earlier it is the size of the chip that +registers the digital image right this + + align:start position:0% +registers the digital image right this + + + align:start position:0% +registers the digital image right this +is a very simple instance of a field + + align:start position:0% +is a very simple instance of a field + + + align:start position:0% +is a very simple instance of a field +stop in old-fashioned cameras that used + + align:start position:0% +stop in old-fashioned cameras that used + + + align:start position:0% +stop in old-fashioned cameras that used +film when the field stop would be in + + align:start position:0% +film when the field stop would be in + + + align:start position:0% +film when the field stop would be in +that case the film itself read wherever + + align:start position:0% +that case the film itself read wherever + + + align:start position:0% +that case the film itself read wherever +the film is chemically active this is + + align:start position:0% +the film is chemically active this is + + + align:start position:0% +the film is chemically active this is +where you record the image outside it + + align:start position:0% +where you record the image outside it + + + align:start position:0% +where you record the image outside it +just lost whatever is imaged outside + + align:start position:0% +just lost whatever is imaged outside + + + align:start position:0% +just lost whatever is imaged outside +that area is lost + + align:start position:0% +that area is lost + + + align:start position:0% +that area is lost +okay so this case it is pretty clear who + + align:start position:0% +okay so this case it is pretty clear who + + + align:start position:0% +okay so this case it is pretty clear who +is the aperture and who is the field + + align:start position:0% +is the aperture and who is the field + + + align:start position:0% +is the aperture and who is the field +stop so you can see very clearly that if + + align:start position:0% +stop so you can see very clearly that if + + + align:start position:0% +stop so you can see very clearly that if +you take an object point at the on the + + align:start position:0% +you take an object point at the on the + + + align:start position:0% +you take an object point at the on the +axis then the + + align:start position:0% +axis then the + + + align:start position:0% +axis then the +physical aperture here will block the + + align:start position:0% +physical aperture here will block the + + + align:start position:0% +physical aperture here will block the +angle of acceptance from this particular + + align:start position:0% +angle of acceptance from this particular + + + align:start position:0% +angle of acceptance from this particular +point and therefore this is the Apple to + + align:start position:0% +point and therefore this is the Apple to + + + align:start position:0% +point and therefore this is the Apple to +stop and also because there is no + + align:start position:0% +stop and also because there is no + + + align:start position:0% +stop and also because there is no +elements to the left this is also the + + align:start position:0% +elements to the left this is also the + + + align:start position:0% +elements to the left this is also the +entrance pupil right if there is no + + align:start position:0% +entrance pupil right if there is no + + + align:start position:0% +entrance pupil right if there is no +elements to image it through the + + align:start position:0% +elements to image it through the + + + align:start position:0% +elements to image it through the +aperture stop will also be + + align:start position:0% +aperture stop will also be + + + align:start position:0% +aperture stop will also be +simultaneously the entrance pupil what + + align:start position:0% +simultaneously the entrance pupil what + + + align:start position:0% +simultaneously the entrance pupil what +means that if you look at them as an + + align:start position:0% +means that if you look at them as an + + + align:start position:0% +means that if you look at them as an +instrument you will actually see the + + align:start position:0% +instrument you will actually see the + + + align:start position:0% +instrument you will actually see the +pupil itself before you AC anything else + + align:start position:0% +pupil itself before you AC anything else + + + align:start position:0% +pupil itself before you AC anything else +and so that's why the two things are + + align:start position:0% +and so that's why the two things are + + + align:start position:0% +and so that's why the two things are +actually coincident in this case what + + align:start position:0% +actually coincident in this case what + + + align:start position:0% +actually coincident in this case what +about the exit pupil well the exit pupil + + align:start position:0% +about the exit pupil well the exit pupil + + + align:start position:0% +about the exit pupil well the exit pupil +is what I will see on this side if I + + align:start position:0% +is what I will see on this side if I + + + align:start position:0% +is what I will see on this side if I +image this element through the + + align:start position:0% +image this element through the + + + align:start position:0% +image this element through the +succeeding elements so the succeeding + + align:start position:0% +succeeding elements so the succeeding + + + align:start position:0% +succeeding elements so the succeeding +element is this lens here so what will I + + align:start position:0% +element is this lens here so what will I + + + align:start position:0% +element is this lens here so what will I +see if I'm at this through the lens well + + align:start position:0% +see if I'm at this through the lens well + + + align:start position:0% +see if I'm at this through the lens well +this element now forget about the actual + + align:start position:0% +this element now forget about the actual + + + align:start position:0% +this element now forget about the actual +object of the system one will question + + align:start position:0% +object of the system one will question + + + align:start position:0% +object of the system one will question +when we ask what are the entrance exit + + align:start position:0% +when we ask what are the entrance exit + + + align:start position:0% +when we ask what are the entrance exit +pupils this is now our object we are + + align:start position:0% +pupils this is now our object we are + + + align:start position:0% +pupils this is now our object we are +trying to see where this would be imaged + + align:start position:0% +trying to see where this would be imaged + + + align:start position:0% +trying to see where this would be imaged +through the optical system and we notice + + align:start position:0% +through the optical system and we notice + + + align:start position:0% +through the optical system and we notice +that this is between the focal point and + + align:start position:0% +that this is between the focal point and + + + align:start position:0% +that this is between the focal point and +the lens okay here's the focal point + + align:start position:0% +the lens okay here's the focal point + + + align:start position:0% +the lens okay here's the focal point +here's the lens this is in between + + align:start position:0% +here's the lens this is in between + + + align:start position:0% +here's the lens this is in between +therefore this will form a virtual image + + align:start position:0% +therefore this will form a virtual image + + + align:start position:0% +therefore this will form a virtual image +so the exit pupil would be somewhere out + + align:start position:0% +so the exit pupil would be somewhere out + + + align:start position:0% +so the exit pupil would be somewhere out +here it would be actually to the left of + + align:start position:0% +here it would be actually to the left of + + + align:start position:0% +here it would be actually to the left of +the lens that is not surprising all it + + align:start position:0% +the lens that is not surprising all it + + + align:start position:0% +the lens that is not surprising all it +means that if I go here and look at the + + align:start position:0% +means that if I go here and look at the + + + align:start position:0% +means that if I go here and look at the +optical instrument this way what we will + + align:start position:0% +optical instrument this way what we will + + + align:start position:0% +optical instrument this way what we will +see I will see a virtual image of the + + align:start position:0% +see I will see a virtual image of the + + + align:start position:0% +see I will see a virtual image of the +pupil very similar to the virtual images + + align:start position:0% +pupil very similar to the virtual images + + + align:start position:0% +pupil very similar to the virtual images +that you saw last time in the demo in + + align:start position:0% +that you saw last time in the demo in + + + align:start position:0% +that you saw last time in the demo in +the class when Pat brought the magnifier + + align:start position:0% +the class when Pat brought the magnifier + + + align:start position:0% +the class when Pat brought the magnifier +objective okay so that's that's the exit + + align:start position:0% +objective okay so that's that's the exit + + + align:start position:0% +objective okay so that's that's the exit +pupil over here and what about the + + align:start position:0% +pupil over here and what about the + + + align:start position:0% +pupil over here and what about the +marginal in-chief range well here is the + + align:start position:0% +marginal in-chief range well here is the + + + align:start position:0% +marginal in-chief range well here is the +here they are here's the marginal ray + + align:start position:0% +here they are here's the marginal ray + + + align:start position:0% +here they are here's the marginal ray +here the chief ray the chief ray by + + align:start position:0% +here the chief ray the chief ray by + + + align:start position:0% +here the chief ray the chief ray by +definition has to go through the center + + align:start position:0% +definition has to go through the center + + + align:start position:0% +definition has to go through the center +of the Apple to stop so that that is + + align:start position:0% +of the Apple to stop so that that is + + + align:start position:0% +of the Apple to stop so that that is +indeed the marginal marginal ray hits + + align:start position:0% +indeed the marginal marginal ray hits + + + align:start position:0% +indeed the marginal marginal ray hits +the rim and + + align:start position:0% +the rim and + + + align:start position:0% +the rim and +what about the field of view where the + + align:start position:0% +what about the field of view where the + + + align:start position:0% +what about the field of view where the +field of view will be defined by the + + align:start position:0% +field of view will be defined by the + + + align:start position:0% +field of view will be defined by the +pupil AB so it would be defined by the + + align:start position:0% +pupil AB so it would be defined by the + + + align:start position:0% +pupil AB so it would be defined by the +field stop now notice that the field + + align:start position:0% +field stop now notice that the field + + + align:start position:0% +field stop now notice that the field +stop is also the exit window because + + align:start position:0% +stop is also the exit window because + + + align:start position:0% +stop is also the exit window because +there's no optical element to its right + + align:start position:0% +there's no optical element to its right + + + align:start position:0% +there's no optical element to its right +so therefore that is the exit window the + + align:start position:0% +so therefore that is the exit window the + + + align:start position:0% +so therefore that is the exit window the +entrance window is at the object plane + + align:start position:0% +entrance window is at the object plane + + + align:start position:0% +entrance window is at the object plane +right since this is the object plane + + align:start position:0% +right since this is the object plane + + + align:start position:0% +right since this is the object plane +this is the image plane + + align:start position:0% +this is the image plane + + + align:start position:0% +this is the image plane +satisfy an emergent condition that is if + + align:start position:0% +satisfy an emergent condition that is if + + + align:start position:0% +satisfy an emergent condition that is if +you image the field stop through the + + align:start position:0% +you image the field stop through the + + + align:start position:0% +you image the field stop through the +proceeding optical elements you will + + align:start position:0% +proceeding optical elements you will + + + align:start position:0% +proceeding optical elements you will +arrive here so that's the entrance + + align:start position:0% +arrive here so that's the entrance + + + align:start position:0% +arrive here so that's the entrance +window and + + align:start position:0% +window and + + + align:start position:0% +window and +of course the field of view is defined + + align:start position:0% +of course the field of view is defined + + + align:start position:0% +of course the field of view is defined +by the tutsi phrase that just clear the + + align:start position:0% +by the tutsi phrase that just clear the + + + align:start position:0% +by the tutsi phrase that just clear the +field stop so here they are and the + + align:start position:0% +field stop so here they are and the + + + align:start position:0% +field stop so here they are and the +angle between the two is the field of + + align:start position:0% +angle between the two is the field of + + + align:start position:0% +angle between the two is the field of +view by the way there isn't one + + align:start position:0% +view by the way there isn't one + + + align:start position:0% +view by the way there isn't one +ambiguity in the literature some people + + align:start position:0% +ambiguity in the literature some people + + + align:start position:0% +ambiguity in the literature some people +define the field of view as the full + + align:start position:0% +define the field of view as the full + + + align:start position:0% +define the field of view as the full +angry some people define it as the half + + align:start position:0% +angry some people define it as the half + + + align:start position:0% +angry some people define it as the half +angry it's a matter of taste how you + + align:start position:0% +angry it's a matter of taste how you + + + align:start position:0% +angry it's a matter of taste how you +want to define it but just make sure you + + align:start position:0% +want to define it but just make sure you + + + align:start position:0% +want to define it but just make sure you +you tell people what you really mean if + + align:start position:0% +you tell people what you really mean if + + + align:start position:0% +you tell people what you really mean if +you really bring the full thing you know + + align:start position:0% +you really bring the full thing you know + + + align:start position:0% +you really bring the full thing you know +okay + + align:start position:0% + + + + align:start position:0% + +okay and + + align:start position:0% + + + + align:start position:0% + +oh + + align:start position:0% + + + + align:start position:0% + +yes nevermind and in this case I + + align:start position:0% +yes nevermind and in this case I + + + align:start position:0% +yes nevermind and in this case I +actually worked out the math I will not + + align:start position:0% +actually worked out the math I will not + + + align:start position:0% +actually worked out the math I will not +go through it here I will let you do it + + align:start position:0% +go through it here I will let you do it + + + align:start position:0% +go through it here I will let you do it +by yourself if I put some symbols for + + align:start position:0% +by yourself if I put some symbols for + + + align:start position:0% +by yourself if I put some symbols for +example if I call the + + align:start position:0% +example if I call the + + + align:start position:0% +example if I call the +the size of the aperture stop I call it + + align:start position:0% +the size of the aperture stop I call it + + + align:start position:0% +the size of the aperture stop I call it +a + + align:start position:0% +a + + + align:start position:0% +a +the size of the field stop I call it W + + align:start position:0% +the size of the field stop I call it W + + + align:start position:0% +the size of the field stop I call it W +prime then have distance Z between the + + align:start position:0% +prime then have distance Z between the + + + align:start position:0% +prime then have distance Z between the +upper to stop at the lens distance s + + align:start position:0% +upper to stop at the lens distance s + + + align:start position:0% +upper to stop at the lens distance s +prime between the lens and the field + + align:start position:0% +prime between the lens and the field + + + align:start position:0% +prime between the lens and the field +stop and + + align:start position:0% + + + + align:start position:0% + +then this calculation shows you where + + align:start position:0% +then this calculation shows you where + + + align:start position:0% +then this calculation shows you where +how you find the + + align:start position:0% +how you find the + + + align:start position:0% +how you find the +the other elements of the system for + + align:start position:0% +the other elements of the system for + + + align:start position:0% +the other elements of the system for +example when it comes to the entrance + + align:start position:0% +example when it comes to the entrance + + + align:start position:0% +example when it comes to the entrance +pupil what should you do well for the + + align:start position:0% +pupil what should you do well for the + + + align:start position:0% +pupil what should you do well for the +entrance pupil we have to consider this + + align:start position:0% +entrance pupil we have to consider this + + + align:start position:0% +entrance pupil we have to consider this +optical system + + align:start position:0% +optical system + + + align:start position:0% +optical system +is that aperture stop then have distance + + align:start position:0% +is that aperture stop then have distance + + + align:start position:0% +is that aperture stop then have distance +Z then have the lens and + + align:start position:0% +Z then have the lens and + + + align:start position:0% +Z then have the lens and +then if well I'm sorry the entrance + + align:start position:0% +then if well I'm sorry the entrance + + + align:start position:0% +then if well I'm sorry the entrance +pupil is the I should have said the exit + + align:start position:0% +pupil is the I should have said the exit + + + align:start position:0% +pupil is the I should have said the exit +pupil so where is the exit pupil will + + align:start position:0% +pupil so where is the exit pupil will + + + align:start position:0% +pupil so where is the exit pupil will +have to image this up or to stop through + + align:start position:0% +have to image this up or to stop through + + + align:start position:0% +have to image this up or to stop through +the system so how do we image it well + + align:start position:0% +the system so how do we image it well + + + align:start position:0% +the system so how do we image it well +let's say that the exit pupil $0.08 is + + align:start position:0% +let's say that the exit pupil $0.08 is + + + align:start position:0% +let's say that the exit pupil $0.08 is +at some distance Z prime to the right of + + align:start position:0% +at some distance Z prime to the right of + + + align:start position:0% +at some distance Z prime to the right of +the lens well how do we find the prime + + align:start position:0% +the lens well how do we find the prime + + + align:start position:0% +the lens well how do we find the prime +we apply the imaging condition 1 over Z + + align:start position:0% +we apply the imaging condition 1 over Z + + + align:start position:0% +we apply the imaging condition 1 over Z +plus 1 over Z prime equals 1 over F we + + align:start position:0% +plus 1 over Z prime equals 1 over F we + + + align:start position:0% +plus 1 over Z prime equals 1 over F we +can solve that 1 over Z prime equals 1 + + align:start position:0% +can solve that 1 over Z prime equals 1 + + + align:start position:0% +can solve that 1 over Z prime equals 1 +over F minus 1 over Z this is also known + + align:start position:0% +over F minus 1 over Z this is also known + + + align:start position:0% +over F minus 1 over Z this is also known +as Z minus F over F times Z or Z prime + + align:start position:0% +as Z minus F over F times Z or Z prime + + + align:start position:0% +as Z minus F over F times Z or Z prime +equals F times Z over Z minus F now I + + align:start position:0% +equals F times Z over Z minus F now I + + + align:start position:0% +equals F times Z over Z minus F now I +said that the + + align:start position:0% +said that the + + + align:start position:0% +said that the +the Apple to stop is wheel in between + + align:start position:0% +the Apple to stop is wheel in between + + + align:start position:0% +the Apple to stop is wheel in between +the focal point and the lens that means + + align:start position:0% +the focal point and the lens that means + + + align:start position:0% +the focal point and the lens that means +that Z + + align:start position:0% + + + + align:start position:0% + +is less than F in this case therefore + + align:start position:0% +is less than F in this case therefore + + + align:start position:0% +is less than F in this case therefore +this quantity since Z is less than F + + align:start position:0% +this quantity since Z is less than F + + + align:start position:0% +this quantity since Z is less than F +this quantity turn out to be negative if + + align:start position:0% +this quantity turn out to be negative if + + + align:start position:0% +this quantity turn out to be negative if +it is negative it means that my + + align:start position:0% +it is negative it means that my + + + align:start position:0% +it is negative it means that my +assumption before that the exit pupil is + + align:start position:0% +assumption before that the exit pupil is + + + align:start position:0% +assumption before that the exit pupil is +to the right was incorrect + + align:start position:0% +to the right was incorrect + + + align:start position:0% +to the right was incorrect +my assumption would have been correct if + + align:start position:0% +my assumption would have been correct if + + + align:start position:0% +my assumption would have been correct if +Z prime had turn out to be a positive + + align:start position:0% +Z prime had turn out to be a positive + + + align:start position:0% +Z prime had turn out to be a positive +quantity since this is turning out to be + + align:start position:0% +quantity since this is turning out to be + + + align:start position:0% +quantity since this is turning out to be +negative here it means that the actual + + align:start position:0% +negative here it means that the actual + + + align:start position:0% +negative here it means that the actual +exit pupil is to the right I'm sorry it + + align:start position:0% +exit pupil is to the right I'm sorry it + + + align:start position:0% +exit pupil is to the right I'm sorry it +is to the left opposite from my + + align:start position:0% +is to the left opposite from my + + + align:start position:0% +is to the left opposite from my +assumption so therefore the exit pupil + + align:start position:0% +assumption so therefore the exit pupil + + + align:start position:0% +assumption so therefore the exit pupil +is over here as I already said as I + + align:start position:0% +is over here as I already said as I + + + align:start position:0% +is over here as I already said as I +already said before and + + align:start position:0% +already said before and + + + align:start position:0% +already said before and +better this result these are these are + + align:start position:0% +better this result these are these are + + + align:start position:0% +better this result these are these are +all the quantities here you can see the + + align:start position:0% +all the quantities here you can see the + + + align:start position:0% +all the quantities here you can see the +marginal way from the field edge the + + align:start position:0% +marginal way from the field edge the + + + align:start position:0% +marginal way from the field edge the +marginal way from one axis the chief ray + + align:start position:0% +marginal way from one axis the chief ray + + + align:start position:0% +marginal way from one axis the chief ray +and so on and so forth and the last + + align:start position:0% +and so on and so forth and the last + + + align:start position:0% +and so on and so forth and the last +comment here I did not really prove it + + align:start position:0% +comment here I did not really prove it + + + align:start position:0% +comment here I did not really prove it +mathematically you can do it if you like + + align:start position:0% +mathematically you can do it if you like + + + align:start position:0% +mathematically you can do it if you like +it's a little bit of a more involved + + align:start position:0% +it's a little bit of a more involved + + + align:start position:0% +it's a little bit of a more involved +calculation but even visually here you + + align:start position:0% +calculation but even visually here you + + + align:start position:0% +calculation but even visually here you +can see that the angle between marginal + + align:start position:0% +can see that the angle between marginal + + + align:start position:0% +can see that the angle between marginal +rays on axis is even in my handwritten + + align:start position:0% +rays on axis is even in my handwritten + + + align:start position:0% +rays on axis is even in my handwritten +diagram here it is visibly larger than + + align:start position:0% +diagram here it is visibly larger than + + + align:start position:0% +diagram here it is visibly larger than +the angle between the two marginal rays + + align:start position:0% +the angle between the two marginal rays + + + align:start position:0% +the angle between the two marginal rays +of axis this means that this particular + + align:start position:0% +of axis this means that this particular + + + align:start position:0% +of axis this means that this particular +system here is subject to vignetting + + align:start position:0% +system here is subject to vignetting + + + align:start position:0% +system here is subject to vignetting +that I mentioned earlier does the term + + align:start position:0% +that I mentioned earlier does the term + + + align:start position:0% +that I mentioned earlier does the term +here vignette in which means it is not a + + align:start position:0% +here vignette in which means it is not a + + + align:start position:0% +here vignette in which means it is not a +very good way very well designed optical + + align:start position:0% +very good way very well designed optical + + + align:start position:0% +very good way very well designed optical +system in sophisticated optical system + + align:start position:0% +system in sophisticated optical system + + + align:start position:0% +system in sophisticated optical system +today's rules that we follow in order to + + align:start position:0% +today's rules that we follow in order to + + + align:start position:0% +today's rules that we follow in order to +avoid vignetting when I described the + + align:start position:0% +avoid vignetting when I described the + + + align:start position:0% +avoid vignetting when I described the +microscope + + align:start position:0% +microscope + + + align:start position:0% +microscope +next week I mean no nothing should it + + align:start position:0% +next week I mean no nothing should it + + + align:start position:0% +next week I mean no nothing should it +mean next Wednesday in today's from + + align:start position:0% +mean next Wednesday in today's from + + + align:start position:0% +mean next Wednesday in today's from +today I will show you how my microscopes + + align:start position:0% +today I will show you how my microscopes + + + align:start position:0% +today I will show you how my microscopes +are designed in order to avoid vignette + + align:start position:0% +are designed in order to avoid vignette + + + align:start position:0% +are designed in order to avoid vignette +in' + + align:start position:0% +in' + + + align:start position:0% +in' +and that's it i've already gone two + + align:start position:0% +and that's it i've already gone two + + + align:start position:0% +and that's it i've already gone two +minutes over time I think we conclude + + align:start position:0% +minutes over time I think we conclude + + + align:start position:0% +minutes over time I think we conclude +unless there's any question that someone + + align:start position:0% +unless there's any question that someone + + + align:start position:0% +unless there's any question that someone +asked not whether some \ No newline at end of file diff --git a/_ly5LmLte50.txt b/_ly5LmLte50.txt new file mode 100644 index 0000000000000000000000000000000000000000..e068e7d0b54a4cf287587446c595ce8d187ffc07 --- /dev/null +++ b/_ly5LmLte50.txt @@ -0,0 +1,3479 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: All right, so +this brief reminder here + +is about the basic requirements +in this course, which + +are that we have +two written reports. + +And that's the main thing I want +to remind you of, one in vision + +and one in audition. + +And I presume all of you +have the syllabus that + +was a hand out. + +And in that syllabus-- +and if you don't have it, + +we can provide you, of +course, with a copy. + +And on the second +page of the syllabus, + +it says written +report, vision part, + +and this report is one that is +based on an article published + +many years ago, which is +very influential article back + +in 1967 about the so-called +accessory optic system. + +And what I would like you to +do is to read that article + +but then proceed +through the internet + +to see what have become +the most recent discoveries + +about the so-called +accessory optic system. + +And that's what your +report needs to be about. + +You can be reasonably +summary about it + +so that you don't need +to write 50 pages. + +But you know, you can +write this whole thing up + +in four or five pages, +taking into account + +as I've said what +has been discovered + +since those days about the +so-called accessory optic + +system. + +The reason I thought this would +be a good assignment because it + +will give you a good historical +sense of how knowledge has + +expanded, in this +case, since the 1960s, + +in uncovering yet +another attribute + +that you have in the +visual system that + +starts with a specialized +set of cells in the retina + +and then proceeds through +a special series of steps + +until it connects with +the ocular motor system. + +So anyway, that's the task. + +And that will consist +of 10% of the report, + +of your total grade. + +And the same thing is +10% also for addition. + +Then the midterm exam +is going to consist + +of 25% of your exams. + +And the final exam is a total +55, a which 15 is vision + +and 40 is audition. + +So if you add them all up, +you have an equal distribution + +in percentages for +vision and for audition. + +So that then is +the basic layout. + +And so what I would like +you to start thinking about + +is how you're going to +put this report together. + +I was hoping that perhaps you +could get it done by midterm. + +But I don't have a hard +and fast rule about that. + +As long as you get it in before +the final exam, that's fine. + +But it may make +life easier if you + +can start working on that while +we are talking about vision, + +rather than waiting +until we are covering + +the auditory system +in the course. + +Does anybody have any questions +about this basic layout? + +OK. + +All right, now +today we are going + +to talk about form perception. + +Let me say one more thing, +that next time as you have it + +on the syllabus, we are going +to be covering illusions. + +I think that'll be fun. + +You'll see all kinds of +interesting illusions + +and some inferences +as to what we + +think about how those +illusions come about by virtue + +of the fact that there are +all sorts of interesting rules + +and facts about how the +visual system works. + +And then during the second +half over the next lecture, + +this is this coming +Wednesday, we + +are going to talk about +visual prosthesis. + +All right, so that +in essence what is we + +are going to cover next time. + +So now let's get back to today. + +We are going to talk +about form perception. + +This is a topic that, +even at this stage, + +we still only have +rather limited knowledge + +about how the brain is +capable of carrying out + +the perception of form. + +And we are going to look at +some inferences and some ideas + +about it. + +And I will also provide you with +a brief historical background. + +Because this has been a +topic of tremendous interest + +for people for centuries, +trying to understand just + +how we are capable of seeing +forms, shapes, patterns. + +All right, so the +first influential idea + +that emerged about this +is called structuralism. + +And this idea actually took +place in the late 19th century. + +And one of the prime proponents +was a fellow called Titchener. + +And they had, in trying to come +to grips with how we do this, + +had a rather basic +idea, much like building + +a house with bricks. + +The idea was that +perception is an aggregate + +of simple elements. + +We just have a whole bunch of +elements that you put together. + +And that generates a +more complex precept, OK. + +The problem with this approach, +well, the first problem + +was that they began +to do experiments. + +And they asked subjects +to try to divorce + +a personal impression of +anything they looked at. + +But to sort of +physically describe it. + +So for example, if you +looked at an apple, + +how do you have the +idea that it's an apple? + +And so they said, well, +it has say, four colors. + +And so the person would +list four colors and said + +would have several shades. + +And put all those +together, add them all up, + +and that equals apple. + +Well, that was the idea then. + +And when they did +this systematically, + +and the thing became +almost ridiculous. + +Because they came up +with more than 40,000 + +elementary sensations, +thinking that somehow you + +puts these elementary +sensations together, + +40,000 of them, +and that gives us + +a sense of an apple, +or banana, or whatever. + +Now as soon as this sort +of became well known, + +a lot of opposition arose. + +And one of the most +famous ones then + +was the opposition +that was brought + +about by Gestalt psychologists. + +And the first consideration that +I want to sort of bring up here + +is a rather simple picture. + +Here's a picture +everybody looks at that. + +OK, what did you see there? + +You saw a car, right? + +Now if you look at it, +I mean this is actually + +a picture of a car, +all right, but it's + +interrupted by all these +vertical bars here. + +And yet we're able to +infer that it's a car. + +And so the question comes +up, how do you do this? + +I mean, you can't simply +just add up a bunch of bricks + +and say it's a car. + +Because there's all +this interruption. + +And most things that +we see in the world, + +we see in a +discontinuous fashion. + +And as a result of this, +the Gestalt psychologists, + +which happened sort +of in the 1920s, + +began to think about +this whole problem + +in a very different way. + +And they made a +tremendous influence. + +And they came up +with these new ideas + +of how we create the +perception of form. + +The founder of the +Gestalt psychology + +is a fellow called +Max Wertheimer. + +So now, you can look this +up in Wikipedia, by the way, + +if you look at +them more closely, + +they came up with a few basic +principles of organization. + +And they call this grouping. + +They argue that in the brain, +somehow we group things up. + +And one of the things we group +has to do with proximity. + +Another one has to +do with similarity, + +another one with common motion, +another one with closure, + +and another one with +figure-ground perception. + +This last one I'm going to talk +about at the end of today's + +presentation. + +But now I'm going to give you +an example of these top two. + +All right, so the most +important conclusion + +that they had come to which was +very much against structuralism + +is that the whole +that you see is + +different from the +sum of its parts. + +Somehow, there is +an active process + +that creates our ability to +see something that is not + +evidenced from its +individual parts. + +Now here is an example of +what these principles are. + +Grouping by proximity, so +here we have a bunch of dots. + +And if you'll put them +closer together vertically, + +you see a bunch of +vertical lines essentially. + +And if you put them closer +together horizontally, + +you see a bunch +of vertical lines, + +horizontal lines, +vertical lines. + +Yeah? + +So we group things +due to proximity. + +Another reason we group +things is shown here, + +is we group things according to +shape, or similarity of shape, + +I should really say. + +And here what we +have, you can readily + +see a group of nine disks here, +and a group of nine triangles. + +And if they're not all +the same as down here, + +then you have much more +difficulty grouping it. + +So there's a strong tendency +that we group things together + +that are similar. + +So these are some +general principles + +of how we organize +our visual percepts. + +So now we can look at some +more of these examples. + +In doing this, we +are now going to try + +to be able to say a bit +more about the brain itself. + +And in doing so, it's evident +that the three major theories + +that try to deal with how +the brain does it, according + +to the first of +these, form perception + +is accomplished by neurons +that respond selectively + +to line segments of +different orientations. + +Now that theory, +obviously, is the outgrowth + +of what we talked about when it +was discovered that in V1, we + +have orientation +selected neurons. + +And this orientation +selectivity is something + +that you see in +several progressively + +higher visual areas, as if +everything in the world out + +there was broken down into +oriented line segments, which + +are then somehow put together +according to there orientation + +to enable us to see shapes. + +So that's one theory. + +Another theory is that form +perception is accomplished + +by spatial mapping of the visual +scene onto the visual cortex. + +And I will elaborate +on each of these. + +And the third theory is one that +form perception is accomplished + +by virtue of Fourier analysis. + +So let us first then +turn to form perception, + +supposedly based on breaking +down the visual scene + +into oriented line segments. + +Now, one of the big +problems with this + +is that when you look +at a famous art work + +that you see in every day +in the Wall Street Journal, + +there is an artist who +created this originally. + +And he created faces +like this using only dots + +and varied the spatial +frequency of the dots, + +as you can see here. + +This happens to be a +person called Larry Poons. + +I'm sure none of you +have heard of him. + +But here was one of the +pictures many years ago + +in the Wall Street Journal. + +And even today, as I say, you +can see faces created this way. + +And you can readily +recognize them, + +even though there are no +oriented line segments here. + +And in fact, if you sort +of squint up and you three + +quarter ways close your +eyes, so you can't even + +see the dots anymore, +you can still + +make out that face +very, very clearly. + +That's because the spatial +frequency effect here + +is very important, +and the degree + +of shading, meaning that +this involves rather low + +spatial frequency +analyses, rather than + +the analysis of particular +orientations of line segments. + +Now this particular +analysis has its counterpart + +in the observation that +many of you have seen. + +When you look at a person's +face on television, + +and they want to +prevent you from being + +able to see that face because +it's confidential or something, + +what do they do? + +Anybody remember? + +What you do is +you put up a bunch + +of squares of different +spatial frequencies. + +And each square is comprised +of the mean illumination + +level of the actual face. + +If you do that, this high +frequency information + +is something that +interferes with your ability + +to analyze face. + +So to give you an example +of this, I'm sure all of you + +have seen this, but +mainly I show you this. + +Here we have this example. + +How many of you can tell +who these people are here? + +I guess nobody can, right? + +Now then what we +can do is we can + +increase the frequency of these. + +Here it is. + +And it's still very +difficult to tell. + +And now I'm going to show +you the actual photograph. + +And what I'm curious about is +how many of these two people + +you actually know. + +I can tell you +right away, they're + +extremely famous +actors and actresses. + +Who recognizes these people? + +How many of you recognize? + +Let me see your hand. + +Only a few people recognize it. + +That's how quickly time goes by. + +These were the most central, +most exciting, best known + +people in the movies. + +And this is Humphrey +Bogart, Ingrid Bergman. + +OK, so these are these +two very famous people + +whose faces were obstructed +by this and by this using + +these high contrast edges +that obscure your ability + +to smoothly analyze faces. + +So that then suggests that this +idea that we extensively use + +oriented line segments +to analyze faces at least + +is an insufficient +explanation of how + +the brain processes shapes. + +Now another idea is so-called +topographic mapping. + +This idea I'm sure +you can already + +reject on the basis +of what I told you + +about how the visual +system is laid out. + +But now I'm going +to belabor that + +so that you can +follow it closely. + +Here we have a +runner, of course. + +And here we have a monkey brain +to make it easy to understand. + +And the idea here there is +that this image, once it + +was discovered that the +visual field is laid out + +topographically in +the visual cortex, + +the idea was that what +happens is somehow, + +and I may be am unfair +to poke fun of it, + +but the idea is +that the mind can + +look at the creation of this +image on the cortical surface + +there. + +And thereby, it can identify. + +OK, it's almost +like a photograph, + +looking at a photograph. + +In this case the mind looks at +the photograph, so to speak, + +on the cortical surface. + +So they thought at +the time is that this + +is what you have there, OK. + +That's the imprint +of this image. + +And indeed, you say, +oh my goodness, that's + +just like that. + +Therefore, I can recognize that +person, and so on and so on. + +Well, I mean that's a cute idea. + +But then when you +take into account + +this has been discovered +subsequently to these ideas, + +that the topographic +layout in the visual cortex + +is actually not one to one +because of the magnification + +factor. + +So let's look at +that in some detail. + +Here is an actual reconstruction +of the monkey area V1 here. + +And here is the visual field. + +And we are going to +put these red arrows + +in the contralateral hemifield. + +Now remember what +I told you before, + +that if you look at +the visual scene, + +you can imagine your eyes +being vertically cut in half. + +And you have a nasal +and temporal hemiretina. + +And the one which is +contralateral hemifield + +crosses over and gets into +this half of the brain. + +And this one crosses +over to that half. + +So now if you do this and +take the magnification factor + +into account, you +look at these arrows, + +which are all +identical in size, OK. + +There are one, two, three, +four, five, six, seven of them. + +What you can see here +is the actual impression + +on the cortical +surface of the neurons + +that are being activated +by this look like this, + +nothing like those arrows there. + +And in fact, the central +arrow is much bigger + +because of the huge +magnification factor. + +Now this is already +creates a major problem + +in trying to believe in +that particular theory, + +the topographic mapping theory. + +But now, if instead, +you put those arrows + +halfway across each of +the hemispheres like that, + +then whatever is on +this side goes here. + +Whatever is on this +side goes there. + +And this is the impression +that is created. + +And my goodness, you +create that impression. + +And you say to yourself, my god. + +If that's the case, +how come I can + +see seven straight +arrows of equal size + +when this is the impression that +is being created in the brain? + +So therefore, obviously, they +are not using a topographic map + +to analyze the +visual scene at all. + +Now this can be driven +home even further. + +Let me make another point here. + +Here we have a monkey visual +cortex again from the rear. + +Here is the visual +field laid out. + +And if here we put in a bunch +of dots in a circular fashion, + +this is the activation there. + +Now you say, oh, that's not bad. + +That looks like a circle. + +But then if you put it along +the midline, half and half, + +then this is the +actual activation. + +But you still see a circle, +even though the activation, + +in terms of the topography, +is nothing like a circle. + +So that indeed created a +much, much greater degree + +of skepticism +among investigators + +to try to understand +how we process shape. + +Now let me make one +other point here, + +which is a wonderful +story, which + +I think will be good +for you to remember. + +That's called the +Giotto story, which + +says that when Pope +Benedict, that was + +in the 12th century, +or the 13th century, + +he set out to have the walls +of the great cathedral of Saint + +Peter in Rome redecorated. + +And so he sent out a +bunch of messengers + +to various artists +in Italy and asked + +them to provide some +of their best work + +so he could evaluate +it and could + +pick one guy to actually +do the redecoration. + +Well, one of these messengers +went to Ambrogio Bondone Giotto + +and asked him, he was +a well known artist, + +and asked him to provide +a painting of his, + +a drawing of his. + +And Giotto said, +oh, my goodness. + +I just don't have +anything around. + +But I tell you what I'll do. + +He took out a red pen and +drew a perfect circle, OK. + +And so the messenger +took this to the pope. + +And the pope said, my god. + +I can't believe how +incredible this is. + +And so Giotto got the +job of redecorating + +the cathedral of Saint Peter. + +To this day, there is +this expression in Italy, + +in Tuscany in Italy, which +says the round O of Giotto, OK. + +So this is the +round O of Giotto, + +which somehow, in a sense, +denotes perfection, perfection + +in sight and in perfection +in your ability of execution + +in terms of a +drawing, for example. + +All right, now to highlight +this even further, + +let me point out +this to you here. + +What we have here is a bunch of +imperfect circles, one of which + +is perfect. + +So if you keep +looking around, you + +should be able to +spot which one it is. + +And you should tell me what +letter denotes that circle. + +Which one is a perfect circle? + +AUDIENCE: C. + +PROFESSOR: Very good, all right. + +So we are incredibly good. + +There's a slight difference +here, OK, or even slight + +difference here. + +And yet, we can see this +very slight difference. + +And we can tell what +a perfect circle is. + +I mean, that's incredible +given how the impressions are + +made by those circles +on the visual cortex. + +So that is an +incredible puzzle of how + +we are capable of doing this. + +And I'm afraid, +even to this day, + +we don't have a really good +answer of how this happens. + +OK, now the third theory +that has become actually + +probably right now, one of +the most successful ones, + +it claims that you +analyze the visual scene + +by taking into account the +spatial frequencies that + +are impinging on the retina, OK. + +This was created by Fergus +Campbell and John Robson, + +very influential. + +And they pointed out, first of +all, that a very interesting + +finding, which I think +I've mentioned once + +before, that if you vary the +spatial frequency [? both, ?] + +as well as the contrast, we +have this sensitivity function + +like this. + +I did show you a picture +of it the last time. + +And then, furthermore, +what they had shown + +is that you can create all +kinds of complex precepts + +by varying the gratings. + +Make them simple gratings, +compound gratings, + +and compound gratings +with much lower contrast. + +And this is simple different +spatial frequencies. + +These are compound. + +And these, as I've said, are +lower spatial frequencies. + +So then if you again +squint, then you + +will see something +much smoother. + +So they actually carried out a +detailed mathematical analysis + +using Fourier analysis. + +And what they did +was quite remarkable. + +They would down break +down a visual scene, + +like a photograph of New +York with all the skylights, + +OK, skyscrapers. + +And then they would convert +that using Fourier analysis. + +And they could recreate +the visual scene + +with a high degree of +accuracy using that procedure. + +Now if indeed the +visual system uses this, + +you have a number of basic +logical requirements. + +And those basic logical, +let me come back to that, + +the basic logical +requirements are + +that you need spatial +frequency analysis. + +And I've shown you that already +when we talked about V1, + +that neurons there are +spatial frequency selective. + +Secondly, that there +are contrast selective, + +which you know already. + +And of course, the +orientation selective, + +and they can tell +you about phase. + +As long as you have +these four attributes, + +you can perform a +detailed Fourier analysis + +to reconstruct the visual scene. + +So now to stress +this even further, + +they did a series of +experiments, in which they + +asked a question, +is it true that you + +have a particular spatial +frequency analysis, + +that you can manipulate that? + +And so they did an +experiment, which + +called a frequency-specific +adaptation experiment. + +They would present to +a subject this display + +and have the subject look at +this for a couple of minutes + +without having to fixate. + +And then they would +look at each of those. + +And they found that this, which +is the same spatial frequency, + +they had difficulty seeing +because of this adaptation. + +And so then they did a +series of careful studies + +and carried out this +analysis and showed + +that you could get any +kind of spatial frequency + +to lose your sensitivity +for it if you + +had been pre-exposed to it. + +So that's what that looked like. + +And by doing this +systematically, + +they came up with +the idea that what + +you have in the visual cortex +is a series of channels + +that are spatial +frequency-selective. + +And I showed you +we talked about V1, + +that indeed, there are neurons +there that are selected + +to particular +spatial frequencies. + +And they proposed that you have +a series of channels like this, + +OK, that peak at different +spatial frequencies. + +And by activating +them selectively, + +you can reconstruct +virtually anything out + +in the visual scene +using Fourier analysis. + +Now OK, I think that then is +the essence of that theory. + +And I can tell you that some +people avidly believe in it. + +And there are some people +who are highly skeptical. + +I'm not sure where I stand +at this stage about that. + +But now, people began +to study our shape, + +the ability to see shapes by +recording various visual areas. + +And I want to tell you next +about some studies that + +had been done primarily +in Japan looking + +at inferotemporal cortex, +which is [INAUDIBLE] already + +mentioned that to be involved +in the analysis of shapes + +and in particular, in the +analysis of faces as well. + +So what these +investigators did is + +they would record to +individual neurons + +in inferotemporal cortex. + +And when they did that, they +would present various stimuli + +to see how those +cells responded. + +And they found, they +claimed to find, + +that there was some +incredible specificity + +in inferotemporal +cortex for shapes. + +And so what they did, +here's an example. + +Here, we have the neurons' +responses, histograms. + +And on top, above it, we +have the particular shape + +that was presented repeatedly. + +So this particular cell +responded vigorously to this, + +but very poorly to that, +and so on down the line. + +But you can see +that it responded + +to several different shapes, +quite well to this one, + +reasonably well to that one, +so a whole range of them. + +So it wasn't like this +particular neuron responded + +only to one particular shape. + +But that idea that +you have neurons + +which are specific +for certain shapes + +did take on a lot of attraction +on part of investigators. + +And some of them +indeed thought that you + +have these neurons +which are selective + +to individual elements +in the visual scene. + +And those subsequently +the critics refer to + +as your having +grandmother cells. + +Somewhere in the +brain there's a cell + +that represents your +grandmother, all right. + +Now that idea was +disabuse subsequently. + +But it took very stronghold +in many investigators' minds. + +And here's another +example of yet + +another inferotemporal +neurons, in this case again + +for various shapes, showing +that this shape was, + +elicited a lot of responses, +as well as did this. + +The rest of them didn't +respond, didn't elicit as much + +of a response. + +So these kinds of +experiments then, + +they tried to systematize. + +And they came up with an idea +which, at least to my mind, + +borders on the absurd, +which is shown here. + +Here is a section of +inferotemporal cortex. + +And they argue that +they are columns there, + +and that these columns +represent different percepts. + +So here we have a +bunch of percepts + +that process the monkey. + +This is a monkey, of course, +that process monkey faces. + +And by inference, +therefore, there + +must be some areas in +inferotemporal cortex + +that process human +faces in humans. + +And then others process +different aspects + +of the visual scene. + +Now the big problem, technical +problem, with this approach + +is that when you record +from individual neurons, + +all right, typically +in these experiments, + +you can study a single neuron +for a fairly limited time, + +not like for months on end, just +maybe a few hours or something. + +And so because of +that, you can only + +present a limited number +of visual stimuli. + +Now there are millions of +visual stimuli out there. + +And so to really establish how +specific this particular neuron + +is, they say well, these are +the only shapes it's showing us. + +What if you use the +cross, or who knows, + +many, many other +things, something + +that is three dimensional? + +How would these cells respond? + +And so these cells respond +to different degrees, + +to hundreds and hundreds and +hundreds of different stimuli. + +And the real fact then is +that anytime a stimulus + +appears out there, you're +activating tens of thousands + +of neurons, maybe even +more, in the visual system. + +And each of those +neurons, especially + +in inferotemporal cortex, +responds to different degrees + +to the different stimuli. + +It is the compendium of these +many, many neurons firing + +into different degrees +to different stimuli + +that gives you sort of an +overall computational ability + +to say what that stimulus is. + +Now to be able to analyze +that, it is that complicated, + +that really takes +a lot of effort. + +Now some people are +now trying to do this. + +And the way you +try to do this is + +that you're recording +from hundreds and hundreds + +of neurons with +multiple electrodes, + +present various scenes. + +And you see how these neurons +respond as an aggregate, + +so that you can determine +whether or not there is indeed + +the potential for some +sort of computation + +that takes place in +gaining the impression + +of a particular individual face. + +Now one of the very +important facts + +here is, of course, that as you +look around the visual scene, + +let's imagine you're +looking at a face. + +You're looking at +a face head on. + +You're looking at a +face in a profile. + +You're looking at a face tilted. + +You're looking at a face close. + +You're looking at a face far. + +And it's still +all the same face. + +And yet the +impressions that face + +makes on the visual +system, in the retina, + +in the geniculate, in the visual +cortex, varies a great deal. + +And yet we can come +up with constancy, + +which is sort of a +higher level process. + +And I'll come to +that in short order. + +All right, so now, +therefore, we need + +to start to talk about what we +call intermediate level vision. + +What is intermediate +level vision? + +So far, we've talked +almost exclusively + +about basic visual capacities, +color, brightness, pattern, + +texture, motion, +depth, the very, + +just the very basic types. + +But now when we talk about +intermediate visual capacities, + +we talk about constancy. + +One example of +constancy, of course, + +is that the face that +you're looking at, + +whether it's profile, or head +on, or near, or far, it's + +still the same face. + +So we get constancy out of it. + +Then there's an +important necessity + +to be able to select +various aspects out + +of the visual scene, to be +able to select if you recognize + +things, to induce +transposition and variance, + +and to be able to +make comparisons, + +and also lastly, to be able to +say where things are in space. + +So those are these +intermediate capacities. + +And we'll talk a little +bit about them next. + +All right, so here's an +example of constancy. + +What we have here +is a bunch of words + +for doubt in different +sizes, and orientations, + +and some handwritten, and so on. + +And yet all of them say +the same thing, doubt. + +We extract that, OK. + +Now to make this +even more difficult, + +I'm going to tell you that +there's one of these words here + +which is not doubt +and see who can + +find the word that is not doubt. + +Everybody find it yet? + +OK, right there, not +doubt but doubts. + +And so we are able to +extract the difference + +in this kind of +visual scene, even + +though it is incredibly subtle. + +And yet, we are also able +to say that this doubt, + +and this doubt, and this +doubt are all the same, + +even though they're different +size or different in print. + +We can extract from +that the common element. + +So this is an +incredible capacity + +on part of the visual system. + +And of course, the big question +comes up, how is this achieved? + +And at this stage, we only +have very preliminary answers + +to that. + +OK, so now I want to show you a +couple other cute things here. + +This is another famous +artist, Hirschfeld, + +He is no longer with +us, unfortunately. + +He published hundreds +of these little cartoons + +in The New Yorker, all right. + +Now, you see his named +here, Hirschfeld. + +What do you see at +the end of his name? + +What's that-- what is this? + +What, that? + +Huh? + +A number three. + +Why does it say +Hirschfeld three? + +His name isn't Hirschfeld three. + +And then if you've +seen several of these, + +how many of you have +seen these before? + +Oh, you missed out on +something very good. + +At least look it up sometimes +again on the internet. + +Just type in Hirschfeld. + +And some of these will come up. + +So he says three. + +And some of his +pictures may have one. + +Some of his pictures may +have five or six at the end. + +And you say, well, +what on earth is that? + +Anybody know? + +Yes. + +AUDIENCE: Doesn't he have other +names hidden in the images? + +So maybe that's the [INAUDIBLE]. + +PROFESSOR: Ah ha, +you're thinking well. + +OK, that's getting there. + +OK, so he's telling us +something that there + +are three of in this picture. + +That's what he's telling us. + +OK. + +So what is the three of +that he has in this picture? + +Ah ha, anybody want +to come up with? + +It + +AUDIENCE: The line orientation? + +PROFESSOR: Huh? + +AUDIENCE: Like the +orientation of the line? + +PROFESSOR: Orientation? + +No. + +Mhm. + +OK, I'll give you a clue. + +Hirschfeld had a daughter-- + +AUDIENCE: Nina. + +PROFESSOR: Who he was very +fond-- hey, fantastic, Nina. + +OK. + +So had a daughter, Nina. + +And he decided in his display +to put her name up there. + +And now he said three, +that he put her name up + +there three times. + +Now who can find +all three of them? + +AUDIENCE: [INAUDIBLE] +the arm [INAUDIBLE]. + +PROFESSOR: OK, here's one. + +Here is another one. + +OK, and here is the +third one, in the arms. + +And so if you, that's one of +the fun things you can do. + +Back when he was +doing this actively, + +every time he had a +cartoon like this, + +I would spend some time trying +to see where were the Ninas. + +[LAUGHTER] + +So that I think is +quite remarkable + +and further highlights +the complexities + +and the remarkability +of our visual system. + +OK, so now, I'm showing +you yet another picture. + +In this case again, +you have to be + +knowledgeable about something. + +Does anybody know who this is? + +Oh, all right. + +Well, let me see if +I make it smaller. + +Can you see that now? + +Who is that? + +OK, that's Voltaire. + +All right. + +Now Voltaire, 18th century, is +a guy who had outdone all of us. + +And he had written 2,000 books. + +Can you believe that? + +The guy had written 2,000 books. + +But that's not the +prime point here. + +Most of us who know a +little bit about history + +immediately recognize him +as, oh yeah, that's Voltaire. + +But then if you go back here and +you look at this more closely, + +and so what I'm going +to do here is just + +to tell you what a +remarkable artist. + +The guy who did this +is Salvador Dali. + +This, by the way, +is his wife, OK. + +And so what I'm +going to do here, + +I'm going to blow up the +center portion of this figure. + +There it is. + +Can you see this? + +This is two faces, two nuns. + +And this is their outfit. + +So there's nothing there +that is really Voltaire. + +But he's such a +remarkable artist + +that he could create Voltaire +by playing around with this, OK. + +So let me go back to +the display again. + +OK, so this is Salvador Dali. + +And certainly, it's an +artist who is remarkable. + +He has many paintings +in which this kind + +of a double confusing thing, +playing on your ability to see. + +So because of that, +for people like me + +who's interested in +how we see things, + +certainly I'm very +intrigued by his artwork. + +And you may enjoy looking +that up again on the internet. + +OK, so now I'm going to tell you +yet another interesting aspect + +of art involved in this. + +And this one has to do with a +book, a very clever book that + +was written by David Hockney. + +Has anybody ever heard of him? + +I'm not surprised since +he's not that well known. + +But the book he wrote is +called Secret Knowledge. + +Now what was that all about? + +Well, he analyzed how artists +created paintings way, + +way, way back when and +in subsequent years + +up to the present. + +And now I'm going to show +you some of his pictures + +and give you a sense of +what this is all about. + +Here is a picture, OK, by +Masolino da Panicale in 1425. + +This was a typical kind +of picture back then. + +Artists had a very +poor sense of how + +to create depth +perception in a painting. + +That was before they came +up with vanishing point. + +And so this kind of looks flat +and fairly expressionless. + +This was in 1425. + +And then Hockney noticed +that just five years later, + +another artist came +up with a picture, + +just five years later, that +looks almost like a photograph. + +And he said, what on +earth has happened? + +And that's why the book is +called the Secret Knowledge. + +So what happened? + +Anybody know? + +Ah, all right. + +Well, let me tell +you what happened. + +What happened is that at +that time, in the 1400s, + +they came up with the lens, OK. + +And so they created a device +called the camera obscura. + +Does anybody know what +the camera obscura is? + +It's essentially very +similar to a camera, OK. + +So here we have it. + +Here's a camera obscura. + +And what they did, +these artists, + +they would create a building. + +So it will be dark inside. + +And then they would +put the lens here. + +And they would put +some object out here + +that they wanted to +make a painting of. + +And that would be reflected +onto a piece of canvas here. + +Of course, it would +be upside down, right? + +And then they would paint it. + +And so once it was painted, +they could turn it around + +and finish it and sell it. + +Now, the reason they did this, +the prime reason they did this, + +is because it was much +much, much quicker + +to create a portrait, +for example, + +by using this procedure than +to actually look at a person + +and paint them on the +canvas while looking at it. + +OK. + +So that was done. + +And of course, this was +sort of a no, no thing. + +And because of that, +it was kept secret. + +All these artists who did this, +and some very famous artists + +did so, were very careful +never to disclose to the public + +that they did this +kind of thing. + +Because it was conceived to be +kind of a cheating thing, OK. + +So what happened then was +that all these paintings were + +created. + +And here's an example +by van Eyck in 1436. + +Again, this looks much +like a photograph. + +But some other thing +is a bit distorted. + +So Hockney undertook a +careful, detailed analysis + +of how we could tell +whether a painting was + +a real painting or one that +used the camera obscura method. + +And that's also a real +painting in a sense, + +but a painting using the +camera obscura method. + +And he came up with +a series of criteria + +which are listed in the book. + +But I'm only going to +deal with one of them. + +OK, so here is an example. + +This is in 1597. + +This is by Caravaggio, OK. + +And what is notable +about this person? + +Well, to Hockney, +what was notable + +is that this person +is holding the wine + +glass in his left hand. + +Yeah? + +And he said, huh. + +That's curious. + +And then he looked at a whole +bunch of other paintings. + +And he had one in +which there were + +three people on the painting. + +And all three of them +were left handed. + +Yeah. + +And he said, my god, +that is really curious. + +And he said, well, +let me analyze + +what happens when you +do this kind of stuff + +with the camera obscura method. + +So here's the example of this. + +This is the original +image, he claims, + +meaning the person is right +handed, is not left handed. + +Then you put this +person through the lens + +and put him up here +upside down like that, OK. + +He's painted on the +canvas like that. + +And then what you do is you +rotate this 180 degrees. + +And when you do +that, lo and behold, + +the person becomes left hand. + +And to make this clear, +I added the F here. + +So this is a normal +F. This is what + +is projected onto the canvas. + +And this is when you +rotate it 180 degrees. + +So you reverse the left +according to Hockney, + +reverse the image. + +And so it was a dead giveaway +that most of the people who + +appeared left handed in his +paintings, in these paintings, + +I should say, not +just Caravaggio, + +but several other people, +used the camera obscura method + +for creating the painting. + +All right, so that +is the process. + +And then I want to show you +one more example of this. + +OK, this is a very famous +painting also, all right. + +This is the so-called marriage +of Giovanni Arnolfini. + +And this by van Eyck, again +1493, way, way, way, way, way, + +way back then. + +Now this is a famous painting. + +Now there's one +interesting thing + +first of all I +want to point out. + +You see this here? + +That's proof that +in those days they + +had come up with the lens, yeah. + +Now what is wrong +with this picture? + +This guy who is about +to marry this woman + +is holding her +with his left hand. + +I mean, that's unacceptable. + +You're supposed to hold it +with the right hand, yeah. + +Now the reason he's holding +it with the left hand + +is because the artist, van +Eyck, used the camera, according + +to Hockney, used the camera +obscura method to take this, + +to paint this picture, OK. + +And then he rotated +180 degrees and became, + +he became left +handed as a result. + +Now if instead of having +done that, you would go back, + +you don't have to go back. + +Go back to here, and +let's go back to this. + +If you take this guy here +and you create the picture. + +But then instead of rotating +it, if you could flip it, + +then you would, he will +remain right handed. + +But of course, we can't do +that because it's on a canvas. + +It's not on a transparency. + +So that then is the +interesting story of artwork + +that was created using +the camera obscura + +system that further +the highlights + +the amazing interestingly +complicated manner + +in which we can analyze the +visual scene for shapes. + +All right, now another factor +that is in a similar vein + +has to do with the +recognition of faces. + +Lots of experiments have +been done, including several + +in our department here, +that has recognized + +that, unfortunate use of +terms, recognition, recognize, + +became aware of the fact that +facial recognition depends + +very heavily on seeing +faces right side up. + +When faces are upside down, +you have great difficulty + +telling who is who, OK. + +So let's do that. + +Here are a bunch of faces. + +And I bet you can you +can tell this one, right? + +Who is it? + +And who is this? + +Very good. + +And those two you don't know. + +The problem is that I am +going to flip this over now. + +And you still don't +know who those two are. + +OK, so this one +is Norbert Wiener. + +Now all of you know +about Norbert Wiener. + +He is one of the great +geniuses of our time. + +He came up with +the digital code. + +He used to be a +professor at MIT. + +And this here is Chuck Vest. + +Anybody recognize him? + +Chuck Vest was a +president of MIT for what? + +For eight years, I believe, +maybe more, 12 years? + +I forget. + +And he has sunk into +obscurity, even though he + +was incredibly visible +for many, many years. + +If I had shown this to you +say eight or 10 years ago, + +you would immediately +recognize him. + +Because he, at that time, +was a president at MIT. + +So that then is an +interesting fact + +that even though we are capable +of using intermediate level + +vision in a very +sophisticated way, + +it does not seem to work that +well for upside down faces. + +You guys did pretty +good with those. + +But it takes a while. + +If I had flashed that +on in a tachistoscope, + +you wouldn't have had a vague +idea of who those people were. + +But once it's on for a while +and you can analyze it, + +you can eventually tell +even an upside down face. + +OK, now in the same vein +as we are talking about, + +our ability to process shapes +based on contours and whatnot, + +one of the interesting set of +experiments people had done + +is to look at what is +called subjective contours. + +And so let me give you a +couple of examples of that. + +Here's an example. + +Almost instantly, here +you can see a disk. + +And here you can +see a square rotated + +45 degrees, a +diamond if you will. + +But if you analyze +this carefully, + +you can see that about +80% of this border + +here is not a border. + +There's no border here. + +There's no border here, +here, here, here, here. + +And yet we can see a square. + +So there's some strange ability +in part of the visual system + +to complete inferred borders. + +All right, I'll come back +to that in just a minute. + +Now another example +of this is shown here. + +Can you make out +what it says here? + +If you look a little bit, +you should be able to see. + +What is it? + +Visual system, very good. + +It was difficult to see. + +But as soon as I +turn this into color, + +you have no trouble at all. + +And that highlights +another important reason + +why color vision is so +useful and has evolved. + +Because it enables +us to see borders, + +where under certain conditions +and lighting conditions, + +borders would not be visible +on the black and white. + +OK, so now that's another +interesting example, + +has to do with further +subjective contours. + +And here's an example of +one with a high contrast, + +where you can +readily see a cube. + +Does everybody see a cube there? + +All right, but if you look +here, it's next to impossible + +to see that. + +Because here the +stimuli are isoluminant. + +So here you eliminated +contrast, which + +is a very important +aspect of being + +able to analyze the visual +scene in various ways, + +including three dimensions. + +All right, so now here's a +very interesting discovery that + +was made by recording +an area, V2. + +The recordings were +then made to see + +whether those neurons +perceive subjective contours. + +So here's a receptive field. + +And you take this bar and move +it back and forth across it. + +And you can see it gives +a vigorous response. + +Now you do the same thing. + +But you don't, here you have +only a subjective contour. + +And then you move this +back and forth across. + +Somehow the information is +added up from other areas, + +so that this cell +responds, not that well, + +but responds reasonably well +to the subjective contour. + +So it's said that in +V2, you can carry out + +some of these higher +level processes that + +enables you to +complete figures even + +when they are +incomplete like that. + +OK, here's another +example of that. + +This is even more dramatic. + +In this case, we take this +bar back and forth across. + +That's a vigorous response. + +And then you do the same thing. + +You create a bar here simply +by these continuous horizontal + +bars. + +And still, the cell +responds quite well, + +as if it were +seeing an edge here. + +So we have this kind of +completion in area V2. + +So this is sort +of an initial hint + +then that already +in area V2, you + +begin to process +higher level events, + +among which is the +fact that you can + +complete incomplete contours. + +All right, so now, the next +thing we're going to turn to, + +we're going to ask +the question, when + +we deal with these +so-called intermediate level + +visual capacities, what +happens when you take out + +such areas as V4 and +MT to your ability + +to see these intermediate +visual capacities? + +So let me describe +to you some of these, + +how one would do +experiments like this. + +First of all, +monkeys are trained. + +This is done with monkeys, of +course, because we can't just + +take a human and remove V4 MT. + +And so what you do here is you +first present a fixation spot. + +Once the monkey fixates, +you present a shape, + +in this case a square. + +And then you present a whole +bunch of other ones, only one + +of which is the same +as the original. + +And the monkey has to +make a [INAUDIBLE] there + +to be rewarded. + +So he has to be able to +detect identity, which + +is an intermediate +visual capacity. + +So that's what this is like. + +And so then what +you can do here is + +to vary the amount +of information + +you can provide, again by +reducing the amount of contour + +information that +you can provide. + +You can do this in several ways. + +First of all, before we do that, +I'll come to that in a second, + +let's just see, how +does the monkey do + +when you do those very similar +shapes I just have shown you + +after you take out area V4? + +What you find here is that the +monkey initially, after you + +take out the area V4, can't +even do the regular task, which + +is this one, right? + +So this is identical to +this one in this case. + +And when you do that, he does +very poorly to begin with + +and then gradually, +over many, many days, + +improves a great deal. + +Then if you put a new figure +in, then it takes a while for it + +to learn that, all right. + +Now then, what you +can do, now I come + +to this business of +having these same figures. + +But you can vary +them now, so that you + +have to do a transposition to +do an intermediate visual task. + +In this case, what you do +is that you vary the size. + +In this case, it's +identical just like it was. + +In this case, you see that +this is smaller than this. + +But you say, oh, I have +to go find the circle. + +I'm not looking for identity. + +I'm looking for something +that's the same looking. + +And here we have +even bigger case. + +This is a triangle. + +And so the monkey +makes a [INAUDIBLE] + +to that one here to this one. + +So that has to do a +test position in size. + +Another thing you can +do that we talked about, + +you can vary the amount +of contour information + +by doing this kind of occlusion. + +And the degree of +occlusion you can + +vary by varying the spatial +frequency of the display. + +And lastly, you can also +decrease or increase the amount + +of contour information +that you provide. + +Now if you do with this, you get +a huge effect after V4 lesion. + +This was the normal condition +with the varied object size. + +This is the occlusion. + +And here is the varied +contour information. + +You can see that there is +quite a dramatic loss, not + +a total, but quite a notable +loss, in the monkey's ability + +to perform this task. + +And this is also reflected +in the huge increase + +in the latencies with which the +monkey can perform the task. + +So area V4 seems to +play an important role + +in these intermediate +visual capacities. + +And I come to some more examples +of that in just a minute. + +Now, yet another +important factor + +in analyzing the +visual scene occurs + +when it is our task +to find something + +out there that is +less noticeable. + +Remember, we talked a little +bit about using camouflage, + +in which case, you have to find +something lesser to survive. + +Now in this case, +what we can do here, + +do a similar +experiment in a monkey. + +On the left side, +the target, the one + +the monkey's supposed to select, +has a much higher contrast + +than the distractors. + +And you can vary the +degree of difference, + +but always the target is +brighter than the others, + +so that it stands out. + +But then, you must +be equally able, + +whether you're an +animal or a human, + +to be able to pull +out something that's + +lesser in the visuals field. + +And you have to +be able to do this + +if you are going to survive +in your environment. + +Now here then, the task is to +go to this lesser stimulus, + +because it's the odd stimulus. + +So what you're extracting +is the odd stimulus. + +Here it's easy to extract, and +here it's difficult to extract. + +And so now the question is what +happens in the visual cortex? + +What area plays a role in this? + +And so it was +discovered that area V4 + +is very important for this. + +And let me explain +this to you then. + +You do an experiment in +which you remove area V4 + +and see what happens. + +And here what we have is +when the star gets brighter, + +you vary the +luminance difference. + +And you can see there's a mild +deficit with the V4 lesion, + +highly significant +but still fairly mild. + +On the other hand, when +you make it dimmer, + +the monkey is practically +staying at the probability. + +He cannot do the task at all. + +So somehow, V4 plays +a very important role + +in being able to ferret +out some subtle things + +in the environment, +lesser things. + +All right, so this +then brings us + +to yet another way +of analyzing this. + +We can, in this case, +go to the larger target, + +in this case to +the smaller target. + +And you can recognize yourself +that this is certainly + +easier than that. + +But a normal monkey can do +both of these quite well, + +shown here. + +This is the normal +monkey's performance, + +the target larger, here +the target smaller. + +He does extremely well. + +But with a V4 lesion when +the target is smaller, + +it's totally devastated, so +as if area V4 were involved + +in the analysis of subtle +things, things which are lesser + +then, rather than +being reflex like + +and going to the brightest, +biggest thing in the world. + +OK, so that then indeed +highlights the fact + +that we have some +of these areas, + +including V4 and of +course, therefore MT, + +that involved in these much more +subtle types of visual analyses + +that we need to perform. + +Now capitalizing on these +kinds of subtle things + +that we are capable of doing, +artists, in addition to + +the ones that I've +shown you before, also + +created all kinds of percepts, I +should say paintings, sketches, + +precepts, that cause +confusion by playing around + +with these factors. + +One of these here is a very well +known audience called Escher. + +This was so near the +end of the 19th century. + +And here what we +have is this is sort + +of a figure-ground confusion. + +Here what we have is a bunch +of birds that fly to the right, + +and also a bunch of birds +that fly to the left. + +And so it's confusing. + +It's alternating. + +You don't know +which one is which. + +And it has to do with a +very, very clever creation + +of figure-ground confusions. + +And actually, next time +we talk about illusions, + +I will bring in some more of +these kinds of curious effects. + +And then here's another one. + +And it's very hard for you to +tell are the stairs going up? + +Are they going down? + +What's going on? + +It's the same kind of +play with the paintings + +to create confusion +in your perceptions. + +And then here is +yet another one, + +where you don't know +is water running up, + +or is the water +running down here? + +That's again an +interesting confusion + +that Escher has created. + +All right, so that +then is the essence + +of what I wanted to +cover today to highlight + +the fact that our +ability to extract shape + +information in the world +is absolutely incredible. + +And it has triggered +not only experiments + +to try to understand +that by scientists, + +but it has created a +tremendous amount of artwork + +that played with these +because it was so enjoyable. + +And certainly, the several +paintings that I have shown you + +must have given you +a pretty good sense + +of how artists capitalize on +these limitations in ability + +to extract intermediate +and high level vision + +capacities from +the visual scene. + +All right, so to summarize +them, first of all, + +I mentioned three +major theories that + +have to do with form processing. + +The one, the orientation +of line segments. + +And I pointed out to you +that that theory is not + +particularly powerful. + +And then the one, the +topographic theory, + +which turned out to be +bordering on the ridiculous. + +And finally, Fourier +analysis, which + +seems to have a lot of +power, even though it also + +has created a lot of skeptics. + +All right, then I pointed +out to that are the V2, V4, + +and inferotemporal cortex, +play important roles + +in intermediate vision, these +intermediate visual capacities + +we talked about in detail. + +Then I pointed out to +you also that in V2, it + +was discovered that there +are some neurons that + +respond to subjective contours, +indicating that already in area + +V2, we can perform these +incredibly higher level + +abilities to extract +information when + +it is unclear in +the visual scene. + +Then I pointed out to +you that recognition + +of objects transformed +in the various ways + +is compromised by V4 and +inferotemporal lesions. + +And V4 lesions also +produce major deficits + +in learning and selecting +lesser stimuli, which + +is a very important +attribute for us + +to be able not the respond +in reflex-like fashion + +to what is most +obvious out there, + +but to be able to +extract the subtle things + +from the visual scene. + +Some inferotemporal neurons +are selective for objects + +including faces. + +But most respond to a variety +of objects whose recognition is + +based on the +differential activity + +of a great many neurons. + +OK, so that then brings me +to the last point, which + +is how we process and deal +with ambiguities in perception, + +unfortunately still +remains a mystery. + +And so there's a lot of space +here for new investigators + +to come up with exciting, +interesting new findings + +about how the brain performs +these kinds of subtle analyses + +of the visual scene. + +OK, I think I'll leave +this until next time. + +I'll talk about this next time. + +OK, does anybody +have any questions? + +All right, I hope that you +can take a little bit of time + +out, look at some of these +artists on the internet, + +and look at Hirschfeld and the +Ninas that I had shown you. \ No newline at end of file diff --git a/_vA3IT2KZs0.txt b/_vA3IT2KZs0.txt new file mode 100644 index 0000000000000000000000000000000000000000..d7cabf5932a9e50878ae1ee7fd220a529568e1d4 --- /dev/null +++ b/_vA3IT2KZs0.txt @@ -0,0 +1,1883 @@ +align:start position:0% + +well i + + align:start position:0% +well i + + + align:start position:0% +well i +i i gotta show you the spider because um + + align:start position:0% +i i gotta show you the spider because um + + + align:start position:0% +i i gotta show you the spider because um +and if you're interested professor + + align:start position:0% +and if you're interested professor + + + align:start position:0% +and if you're interested professor +bueller + + align:start position:0% +bueller + + + align:start position:0% +bueller +does some wonderful work on spider silk + + align:start position:0% +does some wonderful work on spider silk + + + align:start position:0% +does some wonderful work on spider silk +because i think this is a + + align:start position:0% +because i think this is a + + + align:start position:0% +because i think this is a +a great example of something that nature + + align:start position:0% +a great example of something that nature + + + align:start position:0% +a great example of something that nature +can do + + align:start position:0% +can do + + + align:start position:0% +can do +that that gives us a sense of how far + + align:start position:0% +that that gives us a sense of how far + + + align:start position:0% +that that gives us a sense of how far +away we are + + align:start position:0% +away we are + + + align:start position:0% +away we are +like i said we're very proud of this + + align:start position:0% +like i said we're very proud of this + + + align:start position:0% +like i said we're very proud of this +and we want to do more right and so we + + align:start position:0% +and we want to do more right and so we + + + align:start position:0% +and we want to do more right and so we +take our two + + align:start position:0% +take our two + + + align:start position:0% +take our two +mers and we mix them together and we + + align:start position:0% +mers and we mix them together and we + + + align:start position:0% +mers and we mix them together and we +make branches maybe we're going to try + + align:start position:0% +make branches maybe we're going to try + + + align:start position:0% +make branches maybe we're going to try +to add a third + + align:start position:0% +to add a third + + + align:start position:0% +to add a third +meanwhile nature has had a lot more + + align:start position:0% +meanwhile nature has had a lot more + + + align:start position:0% +meanwhile nature has had a lot more +flexibility and a lot more time + + align:start position:0% +flexibility and a lot more time + + + align:start position:0% +flexibility and a lot more time +what can it do well here's spider silk + + align:start position:0% +what can it do well here's spider silk + + + align:start position:0% +what can it do well here's spider silk +now + + align:start position:0% +now + + + align:start position:0% +now +this is a spider spider is is an + + align:start position:0% +this is a spider spider is is an + + + align:start position:0% +this is a spider spider is is an +incredible + + align:start position:0% +incredible + + + align:start position:0% +incredible +polymer synthesis machine it's an + + align:start position:0% +polymer synthesis machine it's an + + + align:start position:0% +polymer synthesis machine it's an +incredible polymer synthesis machine + + align:start position:0% +incredible polymer synthesis machine + + + align:start position:0% +incredible polymer synthesis machine +and here it is weaving a web and i love + + align:start position:0% +and here it is weaving a web and i love + + + align:start position:0% +and here it is weaving a web and i love +this because i think it's so cool + + align:start position:0% +this because i think it's so cool + + + align:start position:0% +this because i think it's so cool +okay there's music i guess i forgot + + align:start position:0% +okay there's music i guess i forgot + + + align:start position:0% +okay there's music i guess i forgot +about that + + align:start position:0% +about that + + + align:start position:0% +about that +and there it is now watch out of here + + align:start position:0% +and there it is now watch out of here + + + align:start position:0% +and there it is now watch out of here +this is the this is the + + align:start position:0% +this is the this is the + + + align:start position:0% +this is the this is the +front back of the spider there's there's + + align:start position:0% +front back of the spider there's there's + + + align:start position:0% +front back of the spider there's there's +there it is right there it's making + + align:start position:0% +there it is right there it's making + + + align:start position:0% +there it is right there it's making +protein + + align:start position:0% +protein + + + align:start position:0% +protein +that's called spider silk right but + + align:start position:0% +that's called spider silk right but + + + align:start position:0% +that's called spider silk right but +these are proteins these are polymers + + align:start position:0% +these are proteins these are polymers + + + align:start position:0% +these are proteins these are polymers +it is doing condensation polymerization + + align:start position:0% +it is doing condensation polymerization + + + align:start position:0% +it is doing condensation polymerization +right there + + align:start position:0% +right there + + + align:start position:0% +right there +and and then there's all sorts of + + align:start position:0% +and and then there's all sorts of + + + align:start position:0% +and and then there's all sorts of +structural stuff that it does right it's + + align:start position:0% +structural stuff that it does right it's + + + align:start position:0% +structural stuff that it does right it's +got a specialized hook it knows how to + + align:start position:0% +got a specialized hook it knows how to + + + align:start position:0% +got a specialized hook it knows how to +step it creates look at that there's a + + align:start position:0% +step it creates look at that there's a + + + align:start position:0% +step it creates look at that there's a +branch place where it knows to put it + + align:start position:0% +branch place where it knows to put it + + + align:start position:0% +branch place where it knows to put it +right it's already created the glue um + + align:start position:0% +right it's already created the glue um + + + align:start position:0% +right it's already created the glue um +but it and so it not only is it putting + + align:start position:0% +but it and so it not only is it putting + + + align:start position:0% +but it and so it not only is it putting +this spider silk out there + + align:start position:0% +this spider silk out there + + + align:start position:0% +this spider silk out there +but it can put other types of polymer + + align:start position:0% +but it can put other types of polymer + + + align:start position:0% +but it can put other types of polymer +depending on what it needs does it need + + align:start position:0% +depending on what it needs does it need + + + align:start position:0% +depending on what it needs does it need +something really sticky less sticky + + align:start position:0% +something really sticky less sticky + + + align:start position:0% +something really sticky less sticky +right and so there it is weaving its web + + align:start position:0% +right and so there it is weaving its web + + + align:start position:0% +right and so there it is weaving its web +and it's generating + + align:start position:0% +and it's generating + + + align:start position:0% +and it's generating +this polymer on the fly right it's doing + + align:start position:0% +this polymer on the fly right it's doing + + + align:start position:0% +this polymer on the fly right it's doing +condensation polymerization + + align:start position:0% +condensation polymerization + + + align:start position:0% +condensation polymerization +now a couple properties about spider + + align:start position:0% +now a couple properties about spider + + + align:start position:0% +now a couple properties about spider +silk okay + + align:start position:0% +silk okay + + + align:start position:0% +silk okay +so here we go let's see so spider silk + + align:start position:0% +so here we go let's see so spider silk + + + align:start position:0% +so here we go let's see so spider silk +this is this is just one + + align:start position:0% +this is this is just one + + + align:start position:0% +this is this is just one +example of what nature can do it's five + + align:start position:0% +example of what nature can do it's five + + + align:start position:0% +example of what nature can do it's five +times stronger than steel + + align:start position:0% +times stronger than steel + + + align:start position:0% +times stronger than steel +[Music] + + align:start position:0% + + + + align:start position:0% + +remember the chart mechanical strength + + align:start position:0% +remember the chart mechanical strength + + + align:start position:0% +remember the chart mechanical strength +chart nothing nothing was stronger than + + align:start position:0% +chart nothing nothing was stronger than + + + align:start position:0% +chart nothing nothing was stronger than +seal spider silk is five times stronger + + align:start position:0% +seal spider silk is five times stronger + + + align:start position:0% +seal spider silk is five times stronger +just to give you a sense the the example + + align:start position:0% +just to give you a sense the the example + + + align:start position:0% +just to give you a sense the the example +i i found that i like + + align:start position:0% +i i found that i like + + + align:start position:0% +i i found that i like +if if um if you had a spider silk that + + align:start position:0% +if if um if you had a spider silk that + + + align:start position:0% +if if um if you had a spider silk that +was a pencil width + + align:start position:0% +was a pencil width + + + align:start position:0% +was a pencil width +and you made a strand it would stop a + + align:start position:0% +and you made a strand it would stop a + + + align:start position:0% +and you made a strand it would stop a +boeing 747 in midair + + align:start position:0% +boeing 747 in midair + + + align:start position:0% +boeing 747 in midair +that's how strong it is oh it keeps + + align:start position:0% +that's how strong it is oh it keeps + + + align:start position:0% +that's how strong it is oh it keeps +keep strengths here's another thing + + align:start position:0% +keep strengths here's another thing + + + align:start position:0% +keep strengths here's another thing +keeps + + align:start position:0% +keeps + + + align:start position:0% +keeps +strength + + align:start position:0% + + + + align:start position:0% + +below 40 degrees c + + align:start position:0% +below 40 degrees c + + + align:start position:0% +below 40 degrees c +we can't do that just take a take a + + align:start position:0% +we can't do that just take a take a + + + align:start position:0% +we can't do that just take a take a +rubber ball and and put it at that low + + align:start position:0% +rubber ball and and put it at that low + + + align:start position:0% +rubber ball and and put it at that low +of a temperature and try to bounce it + + align:start position:0% +of a temperature and try to bounce it + + + align:start position:0% +of a temperature and try to bounce it +it's going to shatter + + align:start position:0% +it's going to shatter + + + align:start position:0% +it's going to shatter +right no spider cell can keep that + + align:start position:0% +right no spider cell can keep that + + + align:start position:0% +right no spider cell can keep that +strength and not break + + align:start position:0% +strength and not break + + + align:start position:0% +strength and not break +it's elastic so it's got + + align:start position:0% +it's elastic so it's got + + + align:start position:0% +it's elastic so it's got +throughout all of this it's got an + + align:start position:0% +throughout all of this it's got an + + + align:start position:0% +throughout all of this it's got an +elastic property of + + align:start position:0% +elastic property of + + + align:start position:0% +elastic property of +4x so it can be stretched to four times + + align:start position:0% +4x so it can be stretched to four times + + + align:start position:0% +4x so it can be stretched to four times +its original strength + + align:start position:0% +its original strength + + + align:start position:0% +its original strength +right okay compare that with nitrile + + align:start position:0% +right okay compare that with nitrile + + + align:start position:0% +right okay compare that with nitrile +nitrile rubber could also go to very + + align:start position:0% +nitrile rubber could also go to very + + + align:start position:0% +nitrile rubber could also go to very +very high + + align:start position:0% +very high + + + align:start position:0% +very high +uh elastic you know elongation right so + + align:start position:0% +uh elastic you know elongation right so + + + align:start position:0% +uh elastic you know elongation right so +if you go back to nitrile right here it + + align:start position:0% +if you go back to nitrile right here it + + + align:start position:0% +if you go back to nitrile right here it +is in the table + + align:start position:0% +is in the table + + + align:start position:0% +is in the table +we're very happy with this but this only + + align:start position:0% +we're very happy with this but this only + + + align:start position:0% +we're very happy with this but this only +had two monomers to play with + + align:start position:0% +had two monomers to play with + + + align:start position:0% +had two monomers to play with +right we played with two monomers and we + + align:start position:0% +right we played with two monomers and we + + + align:start position:0% +right we played with two monomers and we +got to here and look at the sacrifice + + align:start position:0% +got to here and look at the sacrifice + + + align:start position:0% +got to here and look at the sacrifice +in the strength look at how much we had + + align:start position:0% +in the strength look at how much we had + + + align:start position:0% +in the strength look at how much we had +to sacrifice strength + + align:start position:0% +to sacrifice strength + + + align:start position:0% +to sacrifice strength +spiders don't have to do that here's the + + align:start position:0% +spiders don't have to do that here's the + + + align:start position:0% +spiders don't have to do that here's the +last one + + align:start position:0% + + + + align:start position:0% + +fully recycles now + + align:start position:0% +fully recycles now + + + align:start position:0% +fully recycles now +the thing is that this is actually + + align:start position:0% +the thing is that this is actually + + + align:start position:0% +the thing is that this is actually +kind of incredible right spider webs get + + align:start position:0% +kind of incredible right spider webs get + + + align:start position:0% +kind of incredible right spider webs get +dusty spider webs get dusty they lose + + align:start position:0% +dusty spider webs get dusty they lose + + + align:start position:0% +dusty spider webs get dusty they lose +their stickiness + + align:start position:0% +their stickiness + + + align:start position:0% +their stickiness +so many spiders know this and just + + align:start position:0% +so many spiders know this and just + + + align:start position:0% +so many spiders know this and just +simply + + align:start position:0% +simply + + + align:start position:0% +simply +have to weave a new web every day but + + align:start position:0% +have to weave a new web every day but + + + align:start position:0% +have to weave a new web every day but +they don't leave the old web there they + + align:start position:0% +they don't leave the old web there they + + + align:start position:0% +they don't leave the old web there they +actually eat it + + align:start position:0% +actually eat it + + + align:start position:0% +actually eat it +and they fully recycle it fully + + align:start position:0% +and they fully recycle it fully + + + align:start position:0% +and they fully recycle it fully +right they eat the web fully recycle it + + align:start position:0% +right they eat the web fully recycle it + + + align:start position:0% +right they eat the web fully recycle it +process it + + align:start position:0% +process it + + + align:start position:0% +process it +have this condensation polymerization + + align:start position:0% +have this condensation polymerization + + + align:start position:0% +have this condensation polymerization +work + + align:start position:0% +work + + + align:start position:0% +work +and make a new one the next day right + + align:start position:0% +and make a new one the next day right + + + align:start position:0% +and make a new one the next day right +so we don't come close to this spider we + + align:start position:0% +so we don't come close to this spider we + + + align:start position:0% +so we don't come close to this spider we +don't even come + + align:start position:0% +don't even come + + + align:start position:0% +don't even come +anywhere near it right in terms of where + + align:start position:0% +anywhere near it right in terms of where + + + align:start position:0% +anywhere near it right in terms of where +we are + + align:start position:0% +we are + + + align:start position:0% +we are +even though i gave you all this + + align:start position:0% +even though i gave you all this + + + align:start position:0% +even though i gave you all this +wonderful things that we're doing with + + align:start position:0% +wonderful things that we're doing with + + + align:start position:0% +wonderful things that we're doing with +engineering + + align:start position:0% +engineering + + + align:start position:0% +engineering +we still have so far that we could go if + + align:start position:0% +we still have so far that we could go if + + + align:start position:0% +we still have so far that we could go if +we could just figure out how nature + + align:start position:0% +we could just figure out how nature + + + align:start position:0% +we could just figure out how nature +works + + align:start position:0% +works + + + align:start position:0% +works +okay and this gets me to what we do + + align:start position:0% +okay and this gets me to what we do + + + align:start position:0% +okay and this gets me to what we do +and so i've got my why this matters now + + align:start position:0% +and so i've got my why this matters now + + + align:start position:0% +and so i've got my why this matters now +and um so spider eats its web + + align:start position:0% +and um so spider eats its web + + + align:start position:0% +and um so spider eats its web +fully recycles it spins the new web the + + align:start position:0% +fully recycles it spins the new web the + + + align:start position:0% +fully recycles it spins the new web the +next day here's what we do with our + + align:start position:0% +next day here's what we do with our + + + align:start position:0% +next day here's what we do with our +uh our our polymers + + align:start position:0% +uh our our polymers + + + align:start position:0% +uh our our polymers +um i already talked about the oceans + + align:start position:0% +um i already talked about the oceans + + + align:start position:0% +um i already talked about the oceans +here's what we do on land this is a tire + + align:start position:0% +here's what we do on land this is a tire + + + align:start position:0% +here's what we do on land this is a tire +these are tires + + align:start position:0% +these are tires + + + align:start position:0% +these are tires +and tires are very difficult to recycle + + align:start position:0% +and tires are very difficult to recycle + + + align:start position:0% +and tires are very difficult to recycle +why because + + align:start position:0% +why because + + + align:start position:0% +why because +you they're they're too vulcanized + + align:start position:0% +you they're they're too vulcanized + + + align:start position:0% +you they're they're too vulcanized +they've got too much crosslink remember + + align:start position:0% +they've got too much crosslink remember + + + align:start position:0% +they've got too much crosslink remember +if the crosslink density + + align:start position:0% +if the crosslink density + + + align:start position:0% +if the crosslink density +is too strong which you need to make a + + align:start position:0% +is too strong which you need to make a + + + align:start position:0% +is too strong which you need to make a +tire + + align:start position:0% +tire + + + align:start position:0% +tire +then um then you can't recycle it in + + align:start position:0% +then um then you can't recycle it in + + + align:start position:0% +then um then you can't recycle it in +fact what happens is and + + align:start position:0% +fact what happens is and + + + align:start position:0% +fact what happens is and +here's a there's a tire mound here's + + align:start position:0% +here's a there's a tire mound here's + + + align:start position:0% +here's a there's a tire mound here's +here it is from a satellite picture + + align:start position:0% +here it is from a satellite picture + + + align:start position:0% +here it is from a satellite picture +those are tires + + align:start position:0% +those are tires + + + align:start position:0% +those are tires +those are tire mounts here's what + + align:start position:0% +those are tire mounts here's what + + + align:start position:0% +those are tire mounts here's what +happens when one catches fire here's + + align:start position:0% +happens when one catches fire here's + + + align:start position:0% +happens when one catches fire here's +what happens when many catch fire + + align:start position:0% +what happens when many catch fire + + + align:start position:0% +what happens when many catch fire +right it's actually very hard fire to + + align:start position:0% +right it's actually very hard fire to + + + align:start position:0% +right it's actually very hard fire to +control + + align:start position:0% +control + + + align:start position:0% +control +once they catch um and but we don't we + + align:start position:0% +once they catch um and but we don't we + + + align:start position:0% +once they catch um and but we don't we +don't really know how to recycle them + + align:start position:0% +don't really know how to recycle them + + + align:start position:0% +don't really know how to recycle them +well yet what can we do + + align:start position:0% + + + + align:start position:0% + +on the science and engineering side you + + align:start position:0% +on the science and engineering side you + + + align:start position:0% +on the science and engineering side you +know the fact of the matter is there's a + + align:start position:0% +know the fact of the matter is there's a + + + align:start position:0% +know the fact of the matter is there's a +lot of work to do but there are + + align:start position:0% +lot of work to do but there are + + + align:start position:0% +lot of work to do but there are +promising directions so i wanted to + + align:start position:0% +promising directions so i wanted to + + + align:start position:0% +promising directions so i wanted to +leave you + + align:start position:0% +leave you + + + align:start position:0% +leave you +with a little bit of that and and i'm + + align:start position:0% +with a little bit of that and and i'm + + + align:start position:0% +with a little bit of that and and i'm +not going to go into great detail just + + align:start position:0% +not going to go into great detail just + + + align:start position:0% +not going to go into great detail just +want to show you and there's references + + align:start position:0% +want to show you and there's references + + + align:start position:0% +want to show you and there's references +here you can look at + + align:start position:0% +here you can look at + + + align:start position:0% +here you can look at +this was published a couple of years ago + + align:start position:0% +this was published a couple of years ago + + + align:start position:0% +this was published a couple of years ago +in nature one direction + + align:start position:0% +in nature one direction + + + align:start position:0% +in nature one direction +is in is in self-healing polymers this + + align:start position:0% +is in is in self-healing polymers this + + + align:start position:0% +is in is in self-healing polymers this +is a very exciting direction + + align:start position:0% +is a very exciting direction + + + align:start position:0% +is a very exciting direction +what can we do we can we can go away + + align:start position:0% +what can we do we can we can go away + + + align:start position:0% +what can we do we can we can go away +from this whole single-use idea and make + + align:start position:0% +from this whole single-use idea and make + + + align:start position:0% +from this whole single-use idea and make +stuff last longer + + align:start position:0% +stuff last longer + + + align:start position:0% +stuff last longer +right so that would be beneficial maybe + + align:start position:0% +right so that would be beneficial maybe + + + align:start position:0% +right so that would be beneficial maybe +not if it winds up in the ocean + + align:start position:0% +not if it winds up in the ocean + + + align:start position:0% +not if it winds up in the ocean +but in terms of just how how long we can + + align:start position:0% +but in terms of just how how long we can + + + align:start position:0% +but in terms of just how how long we can +use these materials + + align:start position:0% +use these materials + + + align:start position:0% +use these materials +um so one direction is well you got + + align:start position:0% +um so one direction is well you got + + + align:start position:0% +um so one direction is well you got +these these polymer networks and you + + align:start position:0% +these these polymer networks and you + + + align:start position:0% +these these polymer networks and you +incorporate little gels little beads in + + align:start position:0% +incorporate little gels little beads in + + + align:start position:0% +incorporate little gels little beads in +here + + align:start position:0% +here + + + align:start position:0% +here +but the beads don't open up until + + align:start position:0% +but the beads don't open up until + + + align:start position:0% +but the beads don't open up until +a crack comes along so they're sensitive + + align:start position:0% +a crack comes along so they're sensitive + + + align:start position:0% +a crack comes along so they're sensitive +to a crack and when they feel a crack in + + align:start position:0% +to a crack and when they feel a crack in + + + align:start position:0% +to a crack and when they feel a crack in +the material + + align:start position:0% +the material + + + align:start position:0% +the material +they open up and they pour a healing + + align:start position:0% +they open up and they pour a healing + + + align:start position:0% +they open up and they pour a healing +liquid + + align:start position:0% +liquid + + + align:start position:0% +liquid +that then solidifies that's a + + align:start position:0% +that then solidifies that's a + + + align:start position:0% +that then solidifies that's a +self-healing kind of approach you can do + + align:start position:0% +self-healing kind of approach you can do + + + align:start position:0% +self-healing kind of approach you can do +that at different scales all the way + + align:start position:0% +that at different scales all the way + + + align:start position:0% +that at different scales all the way +down to the strand + + align:start position:0% +down to the strand + + + align:start position:0% +down to the strand +you can do that larger scales and here's + + align:start position:0% +you can do that larger scales and here's + + + align:start position:0% +you can do that larger scales and here's +a whole system + + align:start position:0% +a whole system + + + align:start position:0% +a whole system +where there's actually this healing + + align:start position:0% +where there's actually this healing + + + align:start position:0% +where there's actually this healing +material being flow flowed through a + + align:start position:0% +material being flow flowed through a + + + align:start position:0% +material being flow flowed through a +polymer structure + + align:start position:0% +polymer structure + + + align:start position:0% +polymer structure +just like arteries in our body again + + align:start position:0% +just like arteries in our body again + + + align:start position:0% +just like arteries in our body again +always there to try to heal the material + + align:start position:0% +always there to try to heal the material + + + align:start position:0% +always there to try to heal the material +right + + align:start position:0% +right + + + align:start position:0% +right +another direction is in fully recovering + + align:start position:0% +another direction is in fully recovering + + + align:start position:0% +another direction is in fully recovering +and + + align:start position:0% +and + + + align:start position:0% +and +again i don't want to go into full + + align:start position:0% +again i don't want to go into full + + + align:start position:0% +again i don't want to go into full +detail here you can look up some of the + + align:start position:0% +detail here you can look up some of the + + + align:start position:0% +detail here you can look up some of the +stuff that this was published last year + + align:start position:0% +stuff that this was published last year + + + align:start position:0% +stuff that this was published last year +can we take the polymer and chemically + + align:start position:0% +can we take the polymer and chemically + + + align:start position:0% +can we take the polymer and chemically +decompose it all the way back to the + + align:start position:0% +decompose it all the way back to the + + + align:start position:0% +decompose it all the way back to the +monomer + + align:start position:0% +monomer + + + align:start position:0% +monomer +can we go back to where we started can + + align:start position:0% +can we go back to where we started can + + + align:start position:0% +can we go back to where we started can +we do what the spider does + + align:start position:0% +we do what the spider does + + + align:start position:0% +we do what the spider does +right the answer is no not today + + align:start position:0% +right the answer is no not today + + + align:start position:0% +right the answer is no not today +but if we could that would open up + + align:start position:0% +but if we could that would open up + + + align:start position:0% +but if we could that would open up +a whole lot of doors for recycling + + align:start position:0% +a whole lot of doors for recycling + + + align:start position:0% +a whole lot of doors for recycling +that are closed today can we do this in + + align:start position:0% +that are closed today can we do this in + + + align:start position:0% +that are closed today can we do this in +a way that is + + align:start position:0% +a way that is + + + align:start position:0% +a way that is +efficient right and and then + + align:start position:0% +efficient right and and then + + + align:start position:0% +efficient right and and then +the another direction of work that i + + align:start position:0% +the another direction of work that i + + + align:start position:0% +the another direction of work that i +think is very important + + align:start position:0% +think is very important + + + align:start position:0% +think is very important +is in making thermosets so heavily + + align:start position:0% +is in making thermosets so heavily + + + align:start position:0% +is in making thermosets so heavily +cross-linked so you get all the hardness + + align:start position:0% +cross-linked so you get all the hardness + + + align:start position:0% +cross-linked so you get all the hardness +and all the properties you need of the + + align:start position:0% +and all the properties you need of the + + + align:start position:0% +and all the properties you need of the +polymer + + align:start position:0% +polymer + + + align:start position:0% +polymer +that's heavily crosslinked but easily + + align:start position:0% +that's heavily crosslinked but easily + + + align:start position:0% +that's heavily crosslinked but easily +breakable in the crosslink and there is + + align:start position:0% +breakable in the crosslink and there is + + + align:start position:0% +breakable in the crosslink and there is +good work going on in this direction + + align:start position:0% +good work going on in this direction + + + align:start position:0% +good work going on in this direction +can we make degradable thermosets + + align:start position:0% +can we make degradable thermosets + + + align:start position:0% +can we make degradable thermosets +that's another really important + + align:start position:0% +that's another really important + + + align:start position:0% +that's another really important +direction and last + + align:start position:0% +direction and last + + + align:start position:0% +direction and last +we should be encouraging people if you + + align:start position:0% +we should be encouraging people if you + + + align:start position:0% +we should be encouraging people if you +can't do any of this + + align:start position:0% +can't do any of this + + + align:start position:0% +can't do any of this +at least take the polymer out of the + + align:start position:0% +at least take the polymer out of the + + + align:start position:0% +at least take the polymer out of the +landfill and make something with it and + + align:start position:0% +landfill and make something with it and + + + align:start position:0% +landfill and make something with it and +there are projects you can look at here + + align:start position:0% +there are projects you can look at here + + + align:start position:0% +there are projects you can look at here +waste management + + align:start position:0% +waste management + + + align:start position:0% +waste management +journal and in making bricks out of + + align:start position:0% +journal and in making bricks out of + + + align:start position:0% +journal and in making bricks out of +polymers incorporating them into + + align:start position:0% +polymers incorporating them into + + + align:start position:0% +polymers incorporating them into +construction materials + + align:start position:0% +construction materials + + + align:start position:0% +construction materials +right these are important directions and + + align:start position:0% +right these are important directions and + + + align:start position:0% +right these are important directions and +we need a lot more + + align:start position:0% +we need a lot more + + + align:start position:0% +we need a lot more +hopefully in the very near term + + align:start position:0% +hopefully in the very near term + + + align:start position:0% +hopefully in the very near term +you \ No newline at end of file diff --git a/a3_1OFrNMXw.txt b/a3_1OFrNMXw.txt new file mode 100644 index 0000000000000000000000000000000000000000..0c6f3d745365544b0e3feaf7755b90601b286d51 --- /dev/null +++ b/a3_1OFrNMXw.txt @@ -0,0 +1,7755 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +so let's talk about reacting gas + + align:start position:0% +so let's talk about reacting gas + + + align:start position:0% +so let's talk about reacting gas +equilibrium we started setting this up + + align:start position:0% +equilibrium we started setting this up + + + align:start position:0% +equilibrium we started setting this up +last time and now we're going to derive + + align:start position:0% +last time and now we're going to derive + + + align:start position:0% +last time and now we're going to derive +the key equation + + align:start position:0% + + + + align:start position:0% + +so we're going to equilibrate + + align:start position:0% +so we're going to equilibrate + + + align:start position:0% +so we're going to equilibrate +it's really hard to say the word + + align:start position:0% +it's really hard to say the word + + + align:start position:0% +it's really hard to say the word +equilibrate while writing the word + + align:start position:0% +equilibrate while writing the word + + + align:start position:0% +equilibrate while writing the word +equilibrium I've somehow got that right + + align:start position:0% +equilibrium I've somehow got that right + + + align:start position:0% +equilibrium I've somehow got that right +gas phase reaction at equilibrium at + + align:start position:0% +gas phase reaction at equilibrium at + + + align:start position:0% +gas phase reaction at equilibrium at +fixed + + align:start position:0% +fixed + + + align:start position:0% +fixed +t + + align:start position:0% +t + + + align:start position:0% +t +and P + + align:start position:0% +and P + + + align:start position:0% +and P +so we mix gases and we let them react if + + align:start position:0% +so we mix gases and we let them react if + + + align:start position:0% +so we mix gases and we let them react if +we're going to do this in general terms + + align:start position:0% +we're going to do this in general terms + + + align:start position:0% +we're going to do this in general terms +reaction a plus b + + align:start position:0% +reaction a plus b + + + align:start position:0% +reaction a plus b +goes to 2C + + align:start position:0% +goes to 2C + + + align:start position:0% +goes to 2C +and of course everything we're going to + + align:start position:0% +and of course everything we're going to + + + align:start position:0% +and of course everything we're going to +do is is General it doesn't have to be + + align:start position:0% +do is is General it doesn't have to be + + + align:start position:0% +do is is General it doesn't have to be +for a reaction of this form + + align:start position:0% +for a reaction of this form + + + align:start position:0% +for a reaction of this form +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so we know that the condition of + + align:start position:0% +so we know that the condition of + + + align:start position:0% +so we know that the condition of +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +at fixed temperature and pressure is + + align:start position:0% +at fixed temperature and pressure is + + + align:start position:0% +at fixed temperature and pressure is +that the Gibbs energy is at an extrema + + align:start position:0% +that the Gibbs energy is at an extrema + + + align:start position:0% +that the Gibbs energy is at an extrema +and so we care about its differential + + align:start position:0% +and so we care about its differential + + + align:start position:0% +and so we care about its differential +so let's + + align:start position:0% +so let's + + + align:start position:0% +so let's +use what we know + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +okay so here we have the total + + align:start position:0% +okay so here we have the total + + + align:start position:0% +okay so here we have the total +differential of the given strategy for + + align:start position:0% +differential of the given strategy for + + + align:start position:0% +differential of the given strategy for +changes of temperature change the + + align:start position:0% +changes of temperature change the + + + align:start position:0% +changes of temperature change the +pressure and changes of mold number + + align:start position:0% +pressure and changes of mold number + + + align:start position:0% +pressure and changes of mold number +and again the independent variables for + + align:start position:0% +and again the independent variables for + + + align:start position:0% +and again the independent variables for +Gibbs are temperature pressure and mole + + align:start position:0% +Gibbs are temperature pressure and mole + + + align:start position:0% +Gibbs are temperature pressure and mole +number you can see that right here in + + align:start position:0% +number you can see that right here in + + + align:start position:0% +number you can see that right here in +the differential form and why do we + + align:start position:0% +the differential form and why do we + + + align:start position:0% +the differential form and why do we +choose that that free energy why do we + + align:start position:0% +choose that that free energy why do we + + + align:start position:0% +choose that that free energy why do we +choose Gibbs why is this convenient + + align:start position:0% +choose Gibbs why is this convenient + + + align:start position:0% +choose Gibbs why is this convenient +because we can ignore two-thirds of the + + align:start position:0% +because we can ignore two-thirds of the + + + align:start position:0% +because we can ignore two-thirds of the +right hand side of the equation for + + align:start position:0% +right hand side of the equation for + + + align:start position:0% +right hand side of the equation for +fixed temperature and pressure + + align:start position:0% +fixed temperature and pressure + + + align:start position:0% +fixed temperature and pressure +right those are fixed fixed and stubborn + + align:start position:0% +right those are fixed fixed and stubborn + + + align:start position:0% +right those are fixed fixed and stubborn +and independent or like synonymous and + + align:start position:0% +and independent or like synonymous and + + + align:start position:0% +and independent or like synonymous and +thermal right if they're independent + + align:start position:0% +thermal right if they're independent + + + align:start position:0% +thermal right if they're independent +that means they can be stubborn and not + + align:start position:0% +that means they can be stubborn and not + + + align:start position:0% +that means they can be stubborn and not +move so those go to zero and we care + + align:start position:0% +move so those go to zero and we care + + + align:start position:0% +move so those go to zero and we care +only about this term + + align:start position:0% + + + + align:start position:0% + +so we're going to be spending the the + + align:start position:0% +so we're going to be spending the the + + + align:start position:0% +so we're going to be spending the the +lecture analyzing + + align:start position:0% +lecture analyzing + + + align:start position:0% +lecture analyzing +that term + + align:start position:0% +that term + + + align:start position:0% +that term +and so equilibrium + + align:start position:0% + + + + align:start position:0% + +is determined by + + align:start position:0% + + + + align:start position:0% + +the chem potentials + + align:start position:0% + + + + align:start position:0% + +mu I + + align:start position:0% + + + + align:start position:0% + +and the mole numbers + + align:start position:0% + + + + align:start position:0% + +so that's going to be it + + align:start position:0% +so that's going to be it + + + align:start position:0% +so that's going to be it +our entropy and our volume are not going + + align:start position:0% +our entropy and our volume are not going + + + align:start position:0% +our entropy and our volume are not going +to be explicitly part of this + + align:start position:0% + + + + align:start position:0% + +oh + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +so at equilibrium + + align:start position:0% + + + + align:start position:0% + +d g equals + + align:start position:0% + + + + align:start position:0% + +now that's the equilibrium expression + + align:start position:0% +now that's the equilibrium expression + + + align:start position:0% +now that's the equilibrium expression +so um + + align:start position:0% + + + + align:start position:0% + +all that + + align:start position:0% + + + + align:start position:0% + +how many + + align:start position:0% +how many + + + align:start position:0% +how many +independent variables are they + + align:start position:0% +independent variables are they + + + align:start position:0% +independent variables are they +in this case + + align:start position:0% + + + + align:start position:0% + +I'll remind you we have a general + + align:start position:0% +I'll remind you we have a general + + + align:start position:0% +I'll remind you we have a general +reaction a plus b + + align:start position:0% +reaction a plus b + + + align:start position:0% +reaction a plus b +goes to 2C that's a reaction + + align:start position:0% +goes to 2C that's a reaction + + + align:start position:0% +goes to 2C that's a reaction +um + + align:start position:0% +um + + + align:start position:0% +um +let me break that down a little bit + + align:start position:0% +let me break that down a little bit + + + align:start position:0% +let me break that down a little bit +somebody tell me what other components + + align:start position:0% + + + + align:start position:0% + +let's list the components + + align:start position:0% + + + + align:start position:0% + +now those are the eye labels components + + align:start position:0% +now those are the eye labels components + + + align:start position:0% +now those are the eye labels components +I what are the what are the components + + align:start position:0% +I what are the what are the components + + + align:start position:0% +I what are the what are the components +in the system + + align:start position:0% + + + + align:start position:0% + +components are a b and c right so this + + align:start position:0% +components are a b and c right so this + + + align:start position:0% +components are a b and c right so this +label + + align:start position:0% +label + + + align:start position:0% +label +runs over a b and c okay + + align:start position:0% +runs over a b and c okay + + + align:start position:0% +runs over a b and c okay +so we have three mole numbers and of a + + align:start position:0% +so we have three mole numbers and of a + + + align:start position:0% +so we have three mole numbers and of a +and if B and N of C + + align:start position:0% +and if B and N of C + + + align:start position:0% +and if B and N of C +how many independent variables we have + + align:start position:0% + + + + align:start position:0% + +this is um carried from the previous + + align:start position:0% +this is um carried from the previous + + + align:start position:0% +this is um carried from the previous +lecture like five + + align:start position:0% + + + + align:start position:0% + +five + + align:start position:0% +five + + + align:start position:0% +five +um Can how do you get five + + align:start position:0% +um Can how do you get five + + + align:start position:0% +um Can how do you get five +number of components and then two + + align:start position:0% +number of components and then two + + + align:start position:0% +number of components and then two +independent variables for thermodynamics + + align:start position:0% +independent variables for thermodynamics + + + align:start position:0% +independent variables for thermodynamics +so + + align:start position:0% +so + + + align:start position:0% +so +um I see you're you're taking the + + align:start position:0% +um I see you're you're taking the + + + align:start position:0% +um I see you're you're taking the +numbers three and two but you're adding + + align:start position:0% +numbers three and two but you're adding + + + align:start position:0% +numbers three and two but you're adding +them and then you should be subtracting + + align:start position:0% +them and then you should be subtracting + + + align:start position:0% +them and then you should be subtracting +them + + align:start position:0% +them + + + align:start position:0% +them +uh and the reason is the following + + align:start position:0% +uh and the reason is the following + + + align:start position:0% +uh and the reason is the following +we have three components + + align:start position:0% + + + + align:start position:0% + +we have + + align:start position:0% +we have + + + align:start position:0% +we have +three + + align:start position:0% +three + + + align:start position:0% +three +ni's right + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% +but + + + align:start position:0% +but +reaction balance + + align:start position:0% + + + + align:start position:0% + +means + + align:start position:0% + + + + align:start position:0% + +there's + + align:start position:0% +there's + + + align:start position:0% +there's +only one + + align:start position:0% +only one + + + align:start position:0% +only one +degree of freedom + + align:start position:0% + + + + align:start position:0% + +how do we know that + + align:start position:0% +how do we know that + + + align:start position:0% +how do we know that +because + + align:start position:0% +because + + + align:start position:0% +because +we have + + align:start position:0% +we have + + + align:start position:0% +we have +two + + align:start position:0% +two + + + align:start position:0% +two +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +constraints + + align:start position:0% +constraints + + + align:start position:0% +constraints +what are they + + align:start position:0% +what are they + + + align:start position:0% +what are they +the N of a over a nu of a + + align:start position:0% +the N of a over a nu of a + + + align:start position:0% +the N of a over a nu of a +equals DN of B remember this from the + + align:start position:0% +equals DN of B remember this from the + + + align:start position:0% +equals DN of B remember this from the +last time the new b equals the N of C + + align:start position:0% +last time the new b equals the N of C + + + align:start position:0% +last time the new b equals the N of C +over Nu of C + + align:start position:0% +over Nu of C + + + align:start position:0% +over Nu of C +there's two + + align:start position:0% +there's two + + + align:start position:0% +there's two +independent equations in here you can + + align:start position:0% +independent equations in here you can + + + align:start position:0% +independent equations in here you can +count the equal signs there are two + + align:start position:0% +count the equal signs there are two + + + align:start position:0% +count the equal signs there are two +equal signs so we have three components + + align:start position:0% +equal signs so we have three components + + + align:start position:0% +equal signs so we have three components +but two constraints which means there's + + align:start position:0% +but two constraints which means there's + + + align:start position:0% +but two constraints which means there's +only one degree of freedom + + align:start position:0% + + + + align:start position:0% + +and we introduced this reaction extent + + align:start position:0% + + + + align:start position:0% + +equals dxc + + align:start position:0% +equals dxc + + + align:start position:0% +equals dxc +you don't have to use C to answer any + + align:start position:0% +you don't have to use C to answer any + + + align:start position:0% +you don't have to use C to answer any +problem you're going to find in this + + align:start position:0% +problem you're going to find in this + + + align:start position:0% +problem you're going to find in this +class but it is a nice general form okay + + align:start position:0% +class but it is a nice general form okay + + + align:start position:0% +class but it is a nice general form okay +so we have + + align:start position:0% +so we have + + + align:start position:0% +so we have +for one reaction + + align:start position:0% + + + + align:start position:0% + +univariant it could be called we have + + align:start position:0% +univariant it could be called we have + + + align:start position:0% +univariant it could be called we have +only one degree of + + align:start position:0% + + + + align:start position:0% + +all right so now we're going to solve uh + + align:start position:0% +all right so now we're going to solve uh + + + align:start position:0% +all right so now we're going to solve uh +the reaction + + align:start position:0% +the reaction + + + align:start position:0% +the reaction +equilibrium condition + + align:start position:0% +equilibrium condition + + + align:start position:0% +equilibrium condition +by applying those constraints so apply + + align:start position:0% +by applying those constraints so apply + + + align:start position:0% +by applying those constraints so apply +constraints + + align:start position:0% + + + + align:start position:0% + +and here + + align:start position:0% + + + + align:start position:0% + +I'm going to arbitrarily choose the + + align:start position:0% +I'm going to arbitrarily choose the + + + align:start position:0% +I'm going to arbitrarily choose the +product mole number as the independent + + align:start position:0% +product mole number as the independent + + + align:start position:0% +product mole number as the independent +variable + + align:start position:0% + + + + align:start position:0% + +so let's see we have d n of a + + align:start position:0% +so let's see we have d n of a + + + align:start position:0% +so let's see we have d n of a +equals Nu of a over Nu of C + + align:start position:0% +equals Nu of a over Nu of C + + + align:start position:0% +equals Nu of a over Nu of C +e n of C + + align:start position:0% +e n of C + + + align:start position:0% +e n of C +equals minus one half + + align:start position:0% +equals minus one half + + + align:start position:0% +equals minus one half +d n of C + + align:start position:0% +d n of C + + + align:start position:0% +d n of C +d n of b equals new B over new C + + align:start position:0% +d n of b equals new B over new C + + + align:start position:0% +d n of b equals new B over new C +d n of C equals + + align:start position:0% +d n of C equals + + + align:start position:0% +d n of C equals +minus one half the N of C + + align:start position:0% +minus one half the N of C + + + align:start position:0% +minus one half the N of C +again this this sort of makes sense a + + align:start position:0% +again this this sort of makes sense a + + + align:start position:0% +again this this sort of makes sense a +plus b going to C for every mole of C + + align:start position:0% +plus b going to C for every mole of C + + + align:start position:0% +plus b going to C for every mole of C +that's created + + align:start position:0% +that's created + + + align:start position:0% +that's created +there + + align:start position:0% +there + + + align:start position:0% +there +2C I apologize + + align:start position:0% +2C I apologize + + + align:start position:0% +2C I apologize +for every two moles of C that are + + align:start position:0% +for every two moles of C that are + + + align:start position:0% +for every two moles of C that are +created there's one mole of a and one + + align:start position:0% +created there's one mole of a and one + + + align:start position:0% +created there's one mole of a and one +mole of B that are destroyed so it works + + align:start position:0% +mole of B that are destroyed so it works + + + align:start position:0% +mole of B that are destroyed so it works +out right for every + + align:start position:0% + + + + align:start position:0% + +two moles of c are created you destroy + + align:start position:0% +two moles of c are created you destroy + + + align:start position:0% +two moles of c are created you destroy +one each mole of A and B okay + + align:start position:0% +one each mole of A and B okay + + + align:start position:0% +one each mole of A and B okay +um so what I'm going to do is I'm going + + align:start position:0% +um so what I'm going to do is I'm going + + + align:start position:0% +um so what I'm going to do is I'm going +to plug these into my expression for DG + + align:start position:0% + + + + align:start position:0% + +DG equals again repeating from the + + align:start position:0% +DG equals again repeating from the + + + align:start position:0% +DG equals again repeating from the +previous + + align:start position:0% +previous + + + align:start position:0% +previous +board mu of i d n of I and now I'm going + + align:start position:0% +board mu of i d n of I and now I'm going + + + align:start position:0% +board mu of i d n of I and now I'm going +to eliminate DNA V A and DN of B and + + align:start position:0% +to eliminate DNA V A and DN of B and + + + align:start position:0% +to eliminate DNA V A and DN of B and +write everything in terms of the NFC and + + align:start position:0% +write everything in terms of the NFC and + + + align:start position:0% +write everything in terms of the NFC and +you get the following + + align:start position:0% +you get the following + + + align:start position:0% +you get the following +U of A + + align:start position:0% +U of A + + + align:start position:0% +U of A +new of a over new C + + align:start position:0% +new of a over new C + + + align:start position:0% +new of a over new C +Plus + + align:start position:0% +Plus + + + align:start position:0% +Plus +mu of B + + align:start position:0% +mu of B + + + align:start position:0% +mu of B +Nu of B over a new of C plus mu of C + + align:start position:0% + + + + align:start position:0% + +and here is + + align:start position:0% +and here is + + + align:start position:0% +and here is +my equilibrium conditions + + align:start position:0% + + + + align:start position:0% + +okay now this should have a certain kind + + align:start position:0% +okay now this should have a certain kind + + + align:start position:0% +okay now this should have a certain kind +of + + align:start position:0% +of + + + align:start position:0% +of +similarity to what we did with the case + + align:start position:0% +similarity to what we did with the case + + + align:start position:0% +similarity to what we did with the case +of unitary systems when we can when we + + align:start position:0% +of unitary systems when we can when we + + + align:start position:0% +of unitary systems when we can when we +derive the equilibrium condition for two + + align:start position:0% +derive the equilibrium condition for two + + + align:start position:0% +derive the equilibrium condition for two +phase coexistence + + align:start position:0% +phase coexistence + + + align:start position:0% +phase coexistence +we had a chemical we had an entropy I + + align:start position:0% +we had a chemical we had an entropy I + + + align:start position:0% +we had a chemical we had an entropy I +think in that case on the left hand side + + align:start position:0% +think in that case on the left hand side + + + align:start position:0% +think in that case on the left hand side +and we needed it to be + + align:start position:0% +and we needed it to be + + + align:start position:0% +and we needed it to be +at an extrema or optimized that is its + + align:start position:0% +at an extrema or optimized that is its + + + align:start position:0% +at an extrema or optimized that is its +differential being zero + + align:start position:0% + + + + align:start position:0% + +right so + + align:start position:0% +right so + + + align:start position:0% +right so +um we have one independent variable here + + align:start position:0% +um we have one independent variable here + + + align:start position:0% +um we have one independent variable here +DN of C + + align:start position:0% + + + + align:start position:0% + +write down some points here + + align:start position:0% +write down some points here + + + align:start position:0% +write down some points here +d n c is unconstrained + + align:start position:0% + + + + align:start position:0% + +it's unconstrained + + align:start position:0% +it's unconstrained + + + align:start position:0% +it's unconstrained +can't + + align:start position:0% + + + + align:start position:0% + +we can't assume that this is zero why is + + align:start position:0% +we can't assume that this is zero why is + + + align:start position:0% +we can't assume that this is zero why is +that + + align:start position:0% +that + + + align:start position:0% +that +why can't we assume that's zero + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +we call this an unconstrained + + align:start position:0% + + + + align:start position:0% + +internal variable + + align:start position:0% + + + + align:start position:0% + +why is it unconstrained + + align:start position:0% +why is it unconstrained + + + align:start position:0% +why is it unconstrained +because even a equilibrium the reaction + + align:start position:0% +because even a equilibrium the reaction + + + align:start position:0% +because even a equilibrium the reaction +doesn't stop + + align:start position:0% +doesn't stop + + + align:start position:0% +doesn't stop +right + + align:start position:0% +right + + + align:start position:0% +right +so we can constrain pressure we have + + align:start position:0% +so we can constrain pressure we have + + + align:start position:0% +so we can constrain pressure we have +pressure gauges and pressure regulators + + align:start position:0% +pressure gauges and pressure regulators + + + align:start position:0% +pressure gauges and pressure regulators +right those exist you can buy them we + + align:start position:0% +right those exist you can buy them we + + + align:start position:0% +right those exist you can buy them we +can constrain temperature we have + + align:start position:0% +can constrain temperature we have + + + align:start position:0% +can constrain temperature we have +thermostats right those exist you can + + align:start position:0% +thermostats right those exist you can + + + align:start position:0% +thermostats right those exist you can +buy them and you can think of different + + align:start position:0% +buy them and you can think of different + + + align:start position:0% +buy them and you can think of different +experimental setups to constrain the + + align:start position:0% +experimental setups to constrain the + + + align:start position:0% +experimental setups to constrain the +temperature and constrain the pressure + + align:start position:0% +temperature and constrain the pressure + + + align:start position:0% +temperature and constrain the pressure +however I want you to think of a box of + + align:start position:0% +however I want you to think of a box of + + + align:start position:0% +however I want you to think of a box of +gas and you have molecules of a b and c + + align:start position:0% +gas and you have molecules of a b and c + + + align:start position:0% +gas and you have molecules of a b and c +and they're zooming around in here + + align:start position:0% +and they're zooming around in here + + + align:start position:0% +and they're zooming around in here +and this reaction can take place right + + align:start position:0% +and this reaction can take place right + + + align:start position:0% +and this reaction can take place right +you can't stop it + + align:start position:0% +you can't stop it + + + align:start position:0% +you can't stop it +so even at equilibrium this is going to + + align:start position:0% +so even at equilibrium this is going to + + + align:start position:0% +so even at equilibrium this is going to +fluctuate the reaction is going to run a + + align:start position:0% +fluctuate the reaction is going to run a + + + align:start position:0% +fluctuate the reaction is going to run a +little to the right the left and if + + align:start position:0% +little to the right the left and if + + + align:start position:0% +little to the right the left and if +you're away from equilibrium the + + align:start position:0% +you're away from equilibrium the + + + align:start position:0% +you're away from equilibrium the +reaction will definitely either run to + + align:start position:0% +reaction will definitely either run to + + + align:start position:0% +reaction will definitely either run to +the right or to the left right depending + + align:start position:0% +the right or to the left right depending + + + align:start position:0% +the right or to the left right depending +that's the meaning of unconstrained you + + align:start position:0% +that's the meaning of unconstrained you + + + align:start position:0% +that's the meaning of unconstrained you +can't fix it right you can't go in there + + align:start position:0% +can't fix it right you can't go in there + + + align:start position:0% +can't fix it right you can't go in there +with your Atomic tweezers and stop the + + align:start position:0% +with your Atomic tweezers and stop the + + + align:start position:0% +with your Atomic tweezers and stop the +atoms from reacting + + align:start position:0% +atoms from reacting + + + align:start position:0% +atoms from reacting +that's an important concept so if we + + align:start position:0% +that's an important concept so if we + + + align:start position:0% +that's an important concept so if we +have + + align:start position:0% +have + + + align:start position:0% +have +um and this is rather like the case in + + align:start position:0% +um and this is rather like the case in + + + align:start position:0% +um and this is rather like the case in +unary + + align:start position:0% +unary + + + align:start position:0% +unary +um two-phase system when we had a phase + + align:start position:0% +um two-phase system when we had a phase + + + align:start position:0% +um two-phase system when we had a phase +boundary and we couldn't stop the phase + + align:start position:0% +boundary and we couldn't stop the phase + + + align:start position:0% +boundary and we couldn't stop the phase +boundary from fluctuating right we + + align:start position:0% +boundary from fluctuating right we + + + align:start position:0% +boundary from fluctuating right we +couldn't stop a little bit of solid from + + align:start position:0% +couldn't stop a little bit of solid from + + + align:start position:0% +couldn't stop a little bit of solid from +evaporating for instance or a little bit + + align:start position:0% +evaporating for instance or a little bit + + + align:start position:0% +evaporating for instance or a little bit +of gas from condensing that would be an + + align:start position:0% +of gas from condensing that would be an + + + align:start position:0% +of gas from condensing that would be an +equivalent example the math worked out + + align:start position:0% +equivalent example the math worked out + + + align:start position:0% +equivalent example the math worked out +in a very similar way so if we need this + + align:start position:0% +in a very similar way so if we need this + + + align:start position:0% +in a very similar way so if we need this +expression to be zero and this in + + align:start position:0% +expression to be zero and this in + + + align:start position:0% +expression to be zero and this in +general is non-zero how do we enforce + + align:start position:0% +general is non-zero how do we enforce + + + align:start position:0% +general is non-zero how do we enforce +equilibrium + + align:start position:0% + + + + align:start position:0% + +so you have to assume that the + + align:start position:0% +so you have to assume that the + + + align:start position:0% +so you have to assume that the +coefficient is zero then since + + align:start position:0% +coefficient is zero then since + + + align:start position:0% +coefficient is zero then since +coefficients thank you I didn't say you + + align:start position:0% +coefficients thank you I didn't say you + + + align:start position:0% +coefficients thank you I didn't say you +said that but that's exactly right if + + align:start position:0% +said that but that's exactly right if + + + align:start position:0% +said that but that's exactly right if +you have a function you're optimizing it + + align:start position:0% +you have a function you're optimizing it + + + align:start position:0% +you have a function you're optimizing it +here I draw for maximum same thing for a + + align:start position:0% +here I draw for maximum same thing for a + + + align:start position:0% +here I draw for maximum same thing for a +minimum + + align:start position:0% +minimum + + + align:start position:0% +minimum +how do you enforce the condition of + + align:start position:0% +how do you enforce the condition of + + + align:start position:0% +how do you enforce the condition of +being optimized you make the slope zero + + align:start position:0% +being optimized you make the slope zero + + + align:start position:0% +being optimized you make the slope zero +right + + align:start position:0% +right + + + align:start position:0% +right +that's what we're doing here + + align:start position:0% + + + + align:start position:0% + +coefficient + + align:start position:0% + + + + align:start position:0% + +the coefficient + + align:start position:0% +the coefficient + + + align:start position:0% +the coefficient +d g + + align:start position:0% +d g + + + align:start position:0% +d g +NC + + align:start position:0% +NC + + + align:start position:0% +NC +must + + align:start position:0% +must + + + align:start position:0% +must +be zero + + align:start position:0% +be zero + + + align:start position:0% +be zero +at equilibrium + + align:start position:0% +at equilibrium + + + align:start position:0% +at equilibrium +that becomes the equilibrium condition + + align:start position:0% + + + + align:start position:0% + +thank you + + align:start position:0% +thank you + + + align:start position:0% +thank you +right so there's some calculus in here + + align:start position:0% +right so there's some calculus in here + + + align:start position:0% +right so there's some calculus in here +there's some you know in this case one + + align:start position:0% +there's some you know in this case one + + + align:start position:0% +there's some you know in this case one +dimensional function optimization in + + align:start position:0% +dimensional function optimization in + + + align:start position:0% +dimensional function optimization in +here that's calculus and then there's + + align:start position:0% +here that's calculus and then there's + + + align:start position:0% +here that's calculus and then there's +also some some science right you have to + + align:start position:0% +also some some science right you have to + + + align:start position:0% +also some some science right you have to +recognize that this reaction is going to + + align:start position:0% +recognize that this reaction is going to + + + align:start position:0% +recognize that this reaction is going to +happen you're not going to stop it and + + align:start position:0% +happen you're not going to stop it and + + + align:start position:0% +happen you're not going to stop it and +so um if DNC can't be enforced to be + + align:start position:0% +so um if DNC can't be enforced to be + + + align:start position:0% +so um if DNC can't be enforced to be +zero then you've got to call this thing + + align:start position:0% +zero then you've got to call this thing + + + align:start position:0% +zero then you've got to call this thing +equals to zero the equilibrium condition + + align:start position:0% +equals to zero the equilibrium condition + + + align:start position:0% +equals to zero the equilibrium condition +so there's a lot in here there's a lot + + align:start position:0% +so there's a lot in here there's a lot + + + align:start position:0% +so there's a lot in here there's a lot +to unpack + + align:start position:0% +to unpack + + + align:start position:0% +to unpack +all right so um + + align:start position:0% +all right so um + + + align:start position:0% +all right so um +all right now unfortunately we have + + align:start position:0% +all right now unfortunately we have + + + align:start position:0% +all right now unfortunately we have +expression to those chemical potentials + + align:start position:0% +expression to those chemical potentials + + + align:start position:0% +expression to those chemical potentials +so we're going to substitute + + align:start position:0% +so we're going to substitute + + + align:start position:0% +so we're going to substitute +substitute + + align:start position:0% +substitute + + + align:start position:0% +substitute +ideal gas + + align:start position:0% + + + + align:start position:0% + +mixture + + align:start position:0% + + + + align:start position:0% + +expressions + + align:start position:0% +expressions + + + align:start position:0% +expressions +this is from last time + + align:start position:0% +this is from last time + + + align:start position:0% +this is from last time +for the MU eyes we have expressions for + + align:start position:0% +for the MU eyes we have expressions for + + + align:start position:0% +for the MU eyes we have expressions for +the Miu eyes from last time + + align:start position:0% +the Miu eyes from last time + + + align:start position:0% +the Miu eyes from last time +so I'm going to substitute those in + + align:start position:0% +so I'm going to substitute those in + + + align:start position:0% +so I'm going to substitute those in +and I get the following d g equals + + align:start position:0% +and I get the following d g equals + + + align:start position:0% +and I get the following d g equals +mu a naught that is + + align:start position:0% +mu a naught that is + + + align:start position:0% +mu a naught that is +component a and it's reference State + + align:start position:0% +component a and it's reference State + + + align:start position:0% +component a and it's reference State +pure at one atmosphere plus RT natural + + align:start position:0% +pure at one atmosphere plus RT natural + + + align:start position:0% +pure at one atmosphere plus RT natural +log + + align:start position:0% +log + + + align:start position:0% +log +partial pressure of a + + align:start position:0% +partial pressure of a + + + align:start position:0% +partial pressure of a +over standard pressure + + align:start position:0% + + + + align:start position:0% + +this quantity times mu a over mu C + + align:start position:0% + + + + align:start position:0% + +Plus + + align:start position:0% +Plus + + + align:start position:0% +Plus +u b naught plus RT natural log partial + + align:start position:0% +u b naught plus RT natural log partial + + + align:start position:0% +u b naught plus RT natural log partial +pressure V over standard pressure + + align:start position:0% + + + + align:start position:0% + +new B over Nu C + + align:start position:0% + + + + align:start position:0% + +plus mu C naught + + align:start position:0% +plus mu C naught + + + align:start position:0% +plus mu C naught +plus RT natural log pressure C over + + align:start position:0% +plus RT natural log pressure C over + + + align:start position:0% +plus RT natural log pressure C over +standard pressure + + align:start position:0% + + + + align:start position:0% + +this whole thing + + align:start position:0% + + + + align:start position:0% + +times d n of C equals + + align:start position:0% +times d n of C equals + + + align:start position:0% +times d n of C equals +zero + + align:start position:0% + + + + align:start position:0% + +and as a reminder mu I have not + + align:start position:0% +and as a reminder mu I have not + + + align:start position:0% +and as a reminder mu I have not +equals the reference or standard + + align:start position:0% + + + + align:start position:0% + +standard + + align:start position:0% +standard + + + align:start position:0% +standard +chem potential + + align:start position:0% + + + + align:start position:0% + +of + + align:start position:0% +of + + + align:start position:0% +of +component a + + align:start position:0% + + + + align:start position:0% + +and I should say component I + + align:start position:0% +and I should say component I + + + align:start position:0% +and I should say component I +at pressure + + align:start position:0% + + + + align:start position:0% + +peanut + + align:start position:0% + + + + align:start position:0% + +and temp + + align:start position:0% +and temp + + + align:start position:0% +and temp +t + + align:start position:0% +t + + + align:start position:0% +t +and for p naught we almost always choose + + align:start position:0% +and for p naught we almost always choose + + + align:start position:0% +and for p naught we almost always choose +one atmosphere + + align:start position:0% + + + + align:start position:0% + +okay so we substitute now we're going to + + align:start position:0% +okay so we substitute now we're going to + + + align:start position:0% +okay so we substitute now we're going to +collect terms + + align:start position:0% + + + + align:start position:0% + +collect terms + + align:start position:0% + + + + align:start position:0% + +and multiply through + + align:start position:0% + + + + align:start position:0% + +by new C I'm going to get the following + + align:start position:0% +by new C I'm going to get the following + + + align:start position:0% +by new C I'm going to get the following +new of a mu + + align:start position:0% +new of a mu + + + align:start position:0% +new of a mu +a naught + + align:start position:0% + + + + align:start position:0% + +plus Nu of B + + align:start position:0% +plus Nu of B + + + align:start position:0% +plus Nu of B +mu B not + + align:start position:0% + + + + align:start position:0% + +plus mu of c u c not + + align:start position:0% +plus mu of c u c not + + + align:start position:0% +plus mu of c u c not +group these + + align:start position:0% +group these + + + align:start position:0% +group these +plus RT + + align:start position:0% +plus RT + + + align:start position:0% +plus RT +natural log + + align:start position:0% +natural log + + + align:start position:0% +natural log +P of a over P naught + + align:start position:0% + + + + align:start position:0% + +to the power Nu a + + align:start position:0% +to the power Nu a + + + align:start position:0% +to the power Nu a +P of B over P naught + + align:start position:0% +P of B over P naught + + + align:start position:0% +P of B over P naught +to Tower Group B + + align:start position:0% +to Tower Group B + + + align:start position:0% +to Tower Group B +over C over P naught + + align:start position:0% +over C over P naught + + + align:start position:0% +over C over P naught +to the power U of C equals zero + + align:start position:0% +to the power U of C equals zero + + + align:start position:0% +to the power U of C equals zero +just just manipulating the thing which + + align:start position:0% +just just manipulating the thing which + + + align:start position:0% +just just manipulating the thing which +we wrote down previously + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +we're going to continue to + + align:start position:0% +we're going to continue to + + + align:start position:0% +we're going to continue to +simplify this we're going to define + + align:start position:0% +simplify this we're going to define + + + align:start position:0% +simplify this we're going to define +something + + align:start position:0% +something + + + align:start position:0% +something +to find Delta G naught + + align:start position:0% +to find Delta G naught + + + align:start position:0% +to find Delta G naught +equals this thing in parentheses + + align:start position:0% + + + + align:start position:0% + +equals the sum + + align:start position:0% +equals the sum + + + align:start position:0% +equals the sum +over I of the new of I + + align:start position:0% +over I of the new of I + + + align:start position:0% +over I of the new of I +times the reference potentials + + align:start position:0% +times the reference potentials + + + align:start position:0% +times the reference potentials +why does that make sense to Define it + + align:start position:0% +why does that make sense to Define it + + + align:start position:0% +why does that make sense to Define it +that way in this case it's the following + + align:start position:0% +that way in this case it's the following + + + align:start position:0% +that way in this case it's the following +2 mu of C naught minus mu of a naught + + align:start position:0% +2 mu of C naught minus mu of a naught + + + align:start position:0% +2 mu of C naught minus mu of a naught +minus mu of B not + + align:start position:0% +minus mu of B not + + + align:start position:0% +minus mu of B not +recalling again what our reaction is + + align:start position:0% +recalling again what our reaction is + + + align:start position:0% +recalling again what our reaction is +it's a plus b going to 2C + + align:start position:0% + + + + align:start position:0% + +so what is this thing + + align:start position:0% + + + + align:start position:0% + +it's the free energy + + align:start position:0% + + + + align:start position:0% + +change + + align:start position:0% + + + + align:start position:0% + +of the reaction + + align:start position:0% + + + + align:start position:0% + +when all components + + align:start position:0% + + + + align:start position:0% + +are in + + align:start position:0% +are in + + + align:start position:0% +are in +their standard state + + align:start position:0% + + + + align:start position:0% + +so for instance if you take if we assume + + align:start position:0% +so for instance if you take if we assume + + + align:start position:0% +so for instance if you take if we assume +that our standard pressure is one + + align:start position:0% +that our standard pressure is one + + + align:start position:0% +that our standard pressure is one +atmosphere if we take one atmosphere of + + align:start position:0% +atmosphere if we take one atmosphere of + + + align:start position:0% +atmosphere if we take one atmosphere of +a and you react it with one atmosphere + + align:start position:0% +a and you react it with one atmosphere + + + align:start position:0% +a and you react it with one atmosphere +of B + + align:start position:0% +of B + + + align:start position:0% +of B +and you produce + + align:start position:0% +and you produce + + + align:start position:0% +and you produce +um + + align:start position:0% +um + + + align:start position:0% +um +C where C is also one atmosphere + + align:start position:0% +C where C is also one atmosphere + + + align:start position:0% +C where C is also one atmosphere +the change in Gibbs free energy is just + + align:start position:0% +the change in Gibbs free energy is just + + + align:start position:0% +the change in Gibbs free energy is just +Delta G naught + + align:start position:0% + + + + align:start position:0% + +and that doesn't have to ever correspond + + align:start position:0% +and that doesn't have to ever correspond + + + align:start position:0% +and that doesn't have to ever correspond +to a physically + + align:start position:0% +to a physically + + + align:start position:0% +to a physically +practical reaction + + align:start position:0% +practical reaction + + + align:start position:0% +practical reaction +right you might not ever realize that + + align:start position:0% +right you might not ever realize that + + + align:start position:0% +right you might not ever realize that +particular reaction in the lab + + align:start position:0% +particular reaction in the lab + + + align:start position:0% +particular reaction in the lab +but Thermo is all about State functions + + align:start position:0% +but Thermo is all about State functions + + + align:start position:0% +but Thermo is all about State functions +and reference data and we're picking + + align:start position:0% +and reference data and we're picking + + + align:start position:0% +and reference data and we're picking +convenient reference data and you can + + align:start position:0% +convenient reference data and you can + + + align:start position:0% +convenient reference data and you can +imagine that reaction even if you don't + + align:start position:0% +imagine that reaction even if you don't + + + align:start position:0% +imagine that reaction even if you don't +carry it out that is what atmosphere of + + align:start position:0% +carry it out that is what atmosphere of + + + align:start position:0% +carry it out that is what atmosphere of +a one atmosphere B and one atmosphere of + + align:start position:0% +a one atmosphere B and one atmosphere of + + + align:start position:0% +a one atmosphere B and one atmosphere of +C at equilibrium + + align:start position:0% +C at equilibrium + + + align:start position:0% +C at equilibrium +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +um you will find the Delta Gene uh one + + align:start position:0% +um you will find the Delta Gene uh one + + + align:start position:0% +um you will find the Delta Gene uh one +second sorry you will find these Delta G + + align:start position:0% +second sorry you will find these Delta G + + + align:start position:0% +second sorry you will find these Delta G +naughts in in + + align:start position:0% +naughts in in + + + align:start position:0% +naughts in in +databases and that's the sort of thing + + align:start position:0% +databases and that's the sort of thing + + + align:start position:0% +databases and that's the sort of thing +you're going to find if you if you're + + align:start position:0% +you're going to find if you if you're + + + align:start position:0% +you're going to find if you if you're +trying to engineer something and you + + align:start position:0% +trying to engineer something and you + + + align:start position:0% +trying to engineer something and you +need to design a reactor + + align:start position:0% +need to design a reactor + + + align:start position:0% +need to design a reactor +um you're going to be looking at these + + align:start position:0% +um you're going to be looking at these + + + align:start position:0% +um you're going to be looking at these +Delta G not and going forward from there + + align:start position:0% + + + + align:start position:0% + +uh yeah sorry I just had a quick + + align:start position:0% +uh yeah sorry I just had a quick + + + align:start position:0% +uh yeah sorry I just had a quick +question is uh + + align:start position:0% +question is uh + + + align:start position:0% +question is uh +are all those partial pressures + + align:start position:0% +are all those partial pressures + + + align:start position:0% +are all those partial pressures +um in the natural log + + align:start position:0% + + + + align:start position:0% + +they make that really explicit + + align:start position:0% + + + + align:start position:0% + +does that help + + align:start position:0% + + + + align:start position:0% + +yeah thanks yeah and that that just + + align:start position:0% +yeah thanks yeah and that that just + + + align:start position:0% +yeah thanks yeah and that that just +comes from the properties of natural + + align:start position:0% +comes from the properties of natural + + + align:start position:0% +comes from the properties of natural +logs you know + + align:start position:0% + + + + align:start position:0% + +natural log X + + align:start position:0% +natural log X + + + align:start position:0% +natural log X +plus natural log y equals natural log X + + align:start position:0% +plus natural log y equals natural log X + + + align:start position:0% +plus natural log y equals natural log X +Y + + align:start position:0% +Y + + + align:start position:0% +Y +so we just apply that sum product rule + + align:start position:0% +so we just apply that sum product rule + + + align:start position:0% +so we just apply that sum product rule +uh three you know multiple times + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% +foreign + + + align:start position:0% +foreign +continue simplifying we're simplifying + + align:start position:0% + + + + align:start position:0% + +I realized that we're all in pond with + + align:start position:0% +I realized that we're all in pond with + + + align:start position:0% +I realized that we're all in pond with +my kids over the weekend I think that + + align:start position:0% +my kids over the weekend I think that + + + align:start position:0% +my kids over the weekend I think that +was the road we said sort of above all + + align:start position:0% +was the road we said sort of above all + + + align:start position:0% +was the road we said sort of above all +simplified + + align:start position:0% +simplified + + + align:start position:0% +simplified +it's like he was describing what someone + + align:start position:0% +it's like he was describing what someone + + + align:start position:0% +it's like he was describing what someone +should do in Mathematica + + align:start position:0% + + + + align:start position:0% + +so we're going to Define this thing + + align:start position:0% +so we're going to Define this thing + + + align:start position:0% +so we're going to Define this thing +called the equilibrium constant which + + align:start position:0% +called the equilibrium constant which + + + align:start position:0% +called the equilibrium constant which +some of you may have encountered + + align:start position:0% +some of you may have encountered + + + align:start position:0% +some of you may have encountered +um in other classes but here we've + + align:start position:0% +um in other classes but here we've + + + align:start position:0% +um in other classes but here we've +derived at K of P equals + + align:start position:0% +derived at K of P equals + + + align:start position:0% +derived at K of P equals +product operator + + align:start position:0% + + + + align:start position:0% + +over components P of I + + align:start position:0% + + + + align:start position:0% + +partial pressure + + align:start position:0% +partial pressure + + + align:start position:0% +partial pressure +normalized to standard pressure to the + + align:start position:0% +normalized to standard pressure to the + + + align:start position:0% +normalized to standard pressure to the +power of Nu of I so that is the + + align:start position:0% +power of Nu of I so that is the + + + align:start position:0% +power of Nu of I so that is the +equilibrium constant in terms of the + + align:start position:0% +equilibrium constant in terms of the + + + align:start position:0% +equilibrium constant in terms of the +pressures that's case of P + + align:start position:0% + + + + align:start position:0% + +okay so that's kind of a big deal + + align:start position:0% +okay so that's kind of a big deal + + + align:start position:0% +okay so that's kind of a big deal +because it shows up in in all over the + + align:start position:0% +because it shows up in in all over the + + + align:start position:0% +because it shows up in in all over the +place + + align:start position:0% +place + + + align:start position:0% +place +including in some introductory chemistry + + align:start position:0% +including in some introductory chemistry + + + align:start position:0% +including in some introductory chemistry +classes + + align:start position:0% +classes + + + align:start position:0% +classes +all right we're going to further + + align:start position:0% +all right we're going to further + + + align:start position:0% +all right we're going to further +simplify + + align:start position:0% + + + + align:start position:0% + +simplify + + align:start position:0% + + + + align:start position:0% + +by assuming + + align:start position:0% +by assuming + + + align:start position:0% +by assuming +that + + align:start position:0% +that + + + align:start position:0% +that +total + + align:start position:0% +total + + + align:start position:0% +total +pressure + + align:start position:0% + + + + align:start position:0% + +we're simplifying here so the total + + align:start position:0% +we're simplifying here so the total + + + align:start position:0% +we're simplifying here so the total +pressure is the reference pressure + + align:start position:0% + + + + align:start position:0% + +so that + + align:start position:0% +so that + + + align:start position:0% +so that +P of I over P naught equals x of I + + align:start position:0% +P of I over P naught equals x of I + + + align:start position:0% +P of I over P naught equals x of I +making that even simpler again using + + align:start position:0% +making that even simpler again using + + + align:start position:0% +making that even simpler again using +Dalton's rule + + align:start position:0% +Dalton's rule + + + align:start position:0% +Dalton's rule +and if we make that simplification + + align:start position:0% +and if we make that simplification + + + align:start position:0% +and if we make that simplification +we get + + align:start position:0% +we get + + + align:start position:0% +we get +a cleaner expression + + align:start position:0% + + + + align:start position:0% + +for the equilibrium constant which is + + align:start position:0% +for the equilibrium constant which is + + + align:start position:0% +for the equilibrium constant which is +the one that we're going to use most + + align:start position:0% +the one that we're going to use most + + + align:start position:0% +the one that we're going to use most +often in this class + + align:start position:0% + + + + align:start position:0% + +and for this reaction again for the + + align:start position:0% +and for this reaction again for the + + + align:start position:0% +and for this reaction again for the +reaction of a plus b going to two c + + align:start position:0% +reaction of a plus b going to two c + + + align:start position:0% +reaction of a plus b going to two c +this equilibrium constant is the mole + + align:start position:0% +this equilibrium constant is the mole + + + align:start position:0% +this equilibrium constant is the mole +fraction of c squared + + align:start position:0% +fraction of c squared + + + align:start position:0% +fraction of c squared +over the mole fraction of a the mole + + align:start position:0% +over the mole fraction of a the mole + + + align:start position:0% +over the mole fraction of a the mole +fraction of B + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% +so um + + + align:start position:0% +so um +foreign + + align:start position:0% + + + + align:start position:0% + +ification and then I'm going to stop and + + align:start position:0% +ification and then I'm going to stop and + + + align:start position:0% +ification and then I'm going to stop and +ask for questions we're going to collect + + align:start position:0% +ask for questions we're going to collect + + + align:start position:0% +ask for questions we're going to collect +terms + + align:start position:0% + + + + align:start position:0% + +to write + + align:start position:0% +to write + + + align:start position:0% +to write +concise + + align:start position:0% + + + + align:start position:0% + +expression + + align:start position:0% + + + + align:start position:0% + +for reaction + + align:start position:0% + + + + align:start position:0% + +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +constant + + align:start position:0% +constant + + + align:start position:0% +constant +and this is the sort of expression that + + align:start position:0% +and this is the sort of expression that + + + align:start position:0% +and this is the sort of expression that +you may have been given + + align:start position:0% +you may have been given + + + align:start position:0% +you may have been given +in a chemistry class or you might find + + align:start position:0% +in a chemistry class or you might find + + + align:start position:0% +in a chemistry class or you might find +in Wikipedia + + align:start position:0% + + + + align:start position:0% + +or k p equals e + + align:start position:0% +or k p equals e + + + align:start position:0% +or k p equals e +minus Delta G naught over r t + + align:start position:0% +minus Delta G naught over r t + + + align:start position:0% +minus Delta G naught over r t +okay so this is our our final answer + + align:start position:0% +okay so this is our our final answer + + + align:start position:0% +okay so this is our our final answer +this is what we're going to + + align:start position:0% +this is what we're going to + + + align:start position:0% +this is what we're going to +this is what's going to be useful for + + align:start position:0% +this is what's going to be useful for + + + align:start position:0% +this is what's going to be useful for +you right after this class + + align:start position:0% + + + + align:start position:0% + +when you're analyzing reacting gas + + align:start position:0% +when you're analyzing reacting gas + + + align:start position:0% +when you're analyzing reacting gas +systems but now you've seen it derived + + align:start position:0% +systems but now you've seen it derived + + + align:start position:0% +systems but now you've seen it derived +and you know where it comes from + + align:start position:0% +and you know where it comes from + + + align:start position:0% +and you know where it comes from +um I want to pause now + + align:start position:0% +um I want to pause now + + + align:start position:0% +um I want to pause now +um I went through that basically uh with + + align:start position:0% +um I went through that basically uh with + + + align:start position:0% +um I went through that basically uh with +that interruption or hardly without + + align:start position:0% +that interruption or hardly without + + + align:start position:0% +that interruption or hardly without +interruption so I want to pause and take + + align:start position:0% +interruption so I want to pause and take + + + align:start position:0% +interruption so I want to pause and take +questions + + align:start position:0% +questions + + + align:start position:0% +questions +um + + align:start position:0% +um + + + align:start position:0% +um +it wasn't fun I saw a great + + align:start position:0% +it wasn't fun I saw a great + + + align:start position:0% +it wasn't fun I saw a great +demonstration of thermal there was one + + align:start position:0% +demonstration of thermal there was one + + + align:start position:0% +demonstration of thermal there was one +person out on the eyes this is on + + align:start position:0% +person out on the eyes this is on + + + align:start position:0% +person out on the eyes this is on +Saturday I mean it was warm and one + + align:start position:0% +Saturday I mean it was warm and one + + + align:start position:0% +Saturday I mean it was warm and one +person was out on the ice and everyone + + align:start position:0% +person was out on the ice and everyone + + + align:start position:0% +person was out on the ice and everyone +who wasn't on the ice was watching this + + align:start position:0% +who wasn't on the ice was watching this + + + align:start position:0% +who wasn't on the ice was watching this +person and the ice was um was it was + + align:start position:0% +person and the ice was um was it was + + + align:start position:0% +person and the ice was um was it was +sunny + + align:start position:0% +sunny + + + align:start position:0% +sunny +and uh they fell through + + align:start position:0% +and uh they fell through + + + align:start position:0% +and uh they fell through +so it was thorough in action I saw + + align:start position:0% +so it was thorough in action I saw + + + align:start position:0% +so it was thorough in action I saw +someone fall through the eyes they were + + align:start position:0% +someone fall through the eyes they were + + + align:start position:0% +someone fall through the eyes they were +fine I think everybody were laughing at + + align:start position:0% +fine I think everybody were laughing at + + + align:start position:0% +fine I think everybody were laughing at +them it wasn't very deep where they were + + align:start position:0% +them it wasn't very deep where they were + + + align:start position:0% +them it wasn't very deep where they were +and uh they struggled back onto the show + + align:start position:0% +and uh they struggled back onto the show + + + align:start position:0% +and uh they struggled back onto the show +with their friends and I'm sure we're + + align:start position:0% +with their friends and I'm sure we're + + + align:start position:0% +with their friends and I'm sure we're +laughing for the rest of the day so + + align:start position:0% +laughing for the rest of the day so + + + align:start position:0% +laughing for the rest of the day so +there's thermodynamics in action at + + align:start position:0% +there's thermodynamics in action at + + + align:start position:0% +there's thermodynamics in action at +Walden Pond + + align:start position:0% +Walden Pond + + + align:start position:0% +Walden Pond +I don't have a picture to share with you + + align:start position:0% +I don't have a picture to share with you + + + align:start position:0% +I don't have a picture to share with you +though all right questions + + align:start position:0% +though all right questions + + + align:start position:0% +though all right questions +um on how we got this because we're + + align:start position:0% +um on how we got this because we're + + + align:start position:0% +um on how we got this because we're +going to be using this a lot + + align:start position:0% + + + + align:start position:0% + +yeah I have a question about the mole + + align:start position:0% +yeah I have a question about the mole + + + align:start position:0% +yeah I have a question about the mole +fractions + + align:start position:0% + + + + align:start position:0% + +from are they the mole fractions that + + align:start position:0% +from are they the mole fractions that + + + align:start position:0% +from are they the mole fractions that +the components find themselves in our + + align:start position:0% +the components find themselves in our + + + align:start position:0% +the components find themselves in our +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +um right so uh first of all let me + + align:start position:0% +um right so uh first of all let me + + + align:start position:0% +um right so uh first of all let me +answer your question in two parts + + align:start position:0% +answer your question in two parts + + + align:start position:0% +answer your question in two parts +thank you + + align:start position:0% + + + + align:start position:0% + +first off this is Dalton's role right + + align:start position:0% +first off this is Dalton's role right + + + align:start position:0% +first off this is Dalton's role right +it's the definition of partial pressure + + align:start position:0% +it's the definition of partial pressure + + + align:start position:0% +it's the definition of partial pressure +is almost right so that's double control + + align:start position:0% +is almost right so that's double control + + + align:start position:0% +is almost right so that's double control +um what uh + + align:start position:0% +um what uh + + + align:start position:0% +um what uh +what mole fractions are we talking about + + align:start position:0% +what mole fractions are we talking about + + + align:start position:0% +what mole fractions are we talking about +here right that's a great that's a great + + align:start position:0% +here right that's a great that's a great + + + align:start position:0% +here right that's a great that's a great +point + + align:start position:0% +point + + + align:start position:0% +point +so + + align:start position:0% +so + + + align:start position:0% +so +um we're not going to do this a whole + + align:start position:0% +um we're not going to do this a whole + + + align:start position:0% +um we're not going to do this a whole +bunch in this class but you're set up to + + align:start position:0% +bunch in this class but you're set up to + + + align:start position:0% +bunch in this class but you're set up to +do this + + align:start position:0% +do this + + + align:start position:0% +do this +um + + align:start position:0% + + + + align:start position:0% + +let's imagine non-equilibrium + + align:start position:0% +let's imagine non-equilibrium + + + align:start position:0% +let's imagine non-equilibrium +and equilibrium + + align:start position:0% +and equilibrium + + + align:start position:0% +and equilibrium +not equilibrium there's something called + + align:start position:0% +not equilibrium there's something called + + + align:start position:0% +not equilibrium there's something called +sometimes it's written as reaction + + align:start position:0% +sometimes it's written as reaction + + + align:start position:0% +sometimes it's written as reaction +quotient sometimes it's written as + + align:start position:0% +quotient sometimes it's written as + + + align:start position:0% +quotient sometimes it's written as +reaction constant it has different forms + + align:start position:0% +reaction constant it has different forms + + + align:start position:0% +reaction constant it has different forms +but it's written it's the exact same + + align:start position:0% +but it's written it's the exact same + + + align:start position:0% +but it's written it's the exact same +thing + + align:start position:0% + + + + align:start position:0% + +as a reaction constant + + align:start position:0% +as a reaction constant + + + align:start position:0% +as a reaction constant +but in general + + align:start position:0% +but in general + + + align:start position:0% +but in general +in general it's not equal + + align:start position:0% + + + + align:start position:0% + +to its equilibrium value + + align:start position:0% + + + + align:start position:0% + +in general it's not equal to its + + align:start position:0% +in general it's not equal to its + + + align:start position:0% +in general it's not equal to its +equilibrium value + + align:start position:0% +equilibrium value + + + align:start position:0% +equilibrium value +so let's see + + align:start position:0% +so let's see + + + align:start position:0% +so let's see +what that means + + align:start position:0% +what that means + + + align:start position:0% +what that means +uh + + align:start position:0% +uh + + + align:start position:0% +uh +say + + align:start position:0% +say + + + align:start position:0% +say +that Q is greater + + align:start position:0% +that Q is greater + + + align:start position:0% +that Q is greater +than K sub p + + align:start position:0% + + + + align:start position:0% + +right so the numerator is too large or + + align:start position:0% +right so the numerator is too large or + + + align:start position:0% +right so the numerator is too large or +the denominator is + + align:start position:0% +the denominator is + + + align:start position:0% +the denominator is +too small relative to equilibrium right + + align:start position:0% + + + + align:start position:0% + +so if the numerator is too large or the + + align:start position:0% +so if the numerator is too large or the + + + align:start position:0% +so if the numerator is too large or the +denominator is too small relative to + + align:start position:0% +denominator is too small relative to + + + align:start position:0% +denominator is too small relative to +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +what direction will the reaction run + + align:start position:0% +what direction will the reaction run + + + align:start position:0% +what direction will the reaction run +and we can answer the question thinking + + align:start position:0% +and we can answer the question thinking + + + align:start position:0% +and we can answer the question thinking +specifically about this case + + align:start position:0% + + + + align:start position:0% + +would it go to the left towards the + + align:start position:0% +would it go to the left towards the + + + align:start position:0% +would it go to the left towards the +reactants + + align:start position:0% +reactants + + + align:start position:0% +reactants +right let's look at this if this thing + + align:start position:0% +right let's look at this if this thing + + + align:start position:0% +right let's look at this if this thing +is too big relative to equilibrium that + + align:start position:0% +is too big relative to equilibrium that + + + align:start position:0% +is too big relative to equilibrium that +means there's too much C or is not + + align:start position:0% +means there's too much C or is not + + + align:start position:0% +means there's too much C or is not +enough a times B + + align:start position:0% +enough a times B + + + align:start position:0% +enough a times B +sorry I was really messy though that's X + + align:start position:0% +sorry I was really messy though that's X + + + align:start position:0% +sorry I was really messy though that's X +of a so what that's telling you is that + + align:start position:0% +of a so what that's telling you is that + + + align:start position:0% +of a so what that's telling you is that +you're out of equilibrium and your + + align:start position:0% +you're out of equilibrium and your + + + align:start position:0% +you're out of equilibrium and your +battery equilibrium to the right + + align:start position:0% +battery equilibrium to the right + + + align:start position:0% +battery equilibrium to the right +and the reaction will run spontaneously + + align:start position:0% +and the reaction will run spontaneously + + + align:start position:0% +and the reaction will run spontaneously +to the left + + align:start position:0% +to the left + + + align:start position:0% +to the left +and the math works out you will find in + + align:start position:0% +and the math works out you will find in + + + align:start position:0% +and the math works out you will find in +this situation that running to the left + + align:start position:0% +this situation that running to the left + + + align:start position:0% +this situation that running to the left +decreases the Gibbs free energy + + align:start position:0% +decreases the Gibbs free energy + + + align:start position:0% +decreases the Gibbs free energy +in other words + + align:start position:0% +in other words + + + align:start position:0% +in other words +d + + align:start position:0% +d + + + align:start position:0% +d +G + + align:start position:0% + + + + align:start position:0% + +M of C + + align:start position:0% +M of C + + + align:start position:0% +M of C +what's our situation here let me try to + + align:start position:0% +what's our situation here let me try to + + + align:start position:0% +what's our situation here let me try to +let me try to draw that we have this is + + align:start position:0% +let me try to draw that we have this is + + + align:start position:0% +let me try to draw that we have this is +a situation where gives free energy + + align:start position:0% +a situation where gives free energy + + + align:start position:0% +a situation where gives free energy +versus n of C you want to run to the + + align:start position:0% +versus n of C you want to run to the + + + align:start position:0% +versus n of C you want to run to the +left to decrease skip so you have a + + align:start position:0% +left to decrease skip so you have a + + + align:start position:0% +left to decrease skip so you have a +curve like that right you run to the + + align:start position:0% +curve like that right you run to the + + + align:start position:0% +curve like that right you run to the +left to decrease skips the math will all + + align:start position:0% +left to decrease skips the math will all + + + align:start position:0% +left to decrease skips the math will all +work out I know I'm being qualitative + + align:start position:0% +work out I know I'm being qualitative + + + align:start position:0% +work out I know I'm being qualitative +here DG dnfc + + align:start position:0% +here DG dnfc + + + align:start position:0% +here DG dnfc +is greater than zero positive slope and + + align:start position:0% +is greater than zero positive slope and + + + align:start position:0% +is greater than zero positive slope and +so it's telling you the reaction we run + + align:start position:0% +so it's telling you the reaction we run + + + align:start position:0% +so it's telling you the reaction we run +to the left + + align:start position:0% +to the left + + + align:start position:0% +to the left +and um + + align:start position:0% +and um + + + align:start position:0% +and um +the difference between the reaction + + align:start position:0% +the difference between the reaction + + + align:start position:0% +the difference between the reaction +quotient and the equilibrium constant + + align:start position:0% +quotient and the equilibrium constant + + + align:start position:0% +quotient and the equilibrium constant +that can be called reaction Affinity or + + align:start position:0% +that can be called reaction Affinity or + + + align:start position:0% +that can be called reaction Affinity or +driving force and there's all sorts of + + align:start position:0% +driving force and there's all sorts of + + + align:start position:0% +driving force and there's all sorts of +analyzes of this and it has and it + + align:start position:0% +analyzes of this and it has and it + + + align:start position:0% +analyzes of this and it has and it +couples to rate and there's a lot of + + align:start position:0% +couples to rate and there's a lot of + + + align:start position:0% +couples to rate and there's a lot of +Engineering in here right you want to + + align:start position:0% +Engineering in here right you want to + + + align:start position:0% +Engineering in here right you want to +figure out if you want to design a + + align:start position:0% +figure out if you want to design a + + + align:start position:0% +figure out if you want to design a +reactor how far away from equilibrium + + align:start position:0% +reactor how far away from equilibrium + + + align:start position:0% +reactor how far away from equilibrium +should you design it to be stuff like + + align:start position:0% +should you design it to be stuff like + + + align:start position:0% +should you design it to be stuff like +that + + align:start position:0% +that + + + align:start position:0% +that +on the contrary right let's say Q is + + align:start position:0% +on the contrary right let's say Q is + + + align:start position:0% +on the contrary right let's say Q is +less than K of p i mean it's going to be + + align:start position:0% +less than K of p i mean it's going to be + + + align:start position:0% +less than K of p i mean it's going to be +the opposite this is a case where + + align:start position:0% +the opposite this is a case where + + + align:start position:0% +the opposite this is a case where +there's not enough numerator there's too + + align:start position:0% +there's not enough numerator there's too + + + align:start position:0% +there's not enough numerator there's too +much denominator right the quotient is + + align:start position:0% +much denominator right the quotient is + + + align:start position:0% +much denominator right the quotient is +small smaller than equilibrium + + align:start position:0% +small smaller than equilibrium + + + align:start position:0% +small smaller than equilibrium +so this is the case + + align:start position:0% +so this is the case + + + align:start position:0% +so this is the case +where + + align:start position:0% +where + + + align:start position:0% +where +you're going to decrease Gibbs energy by + + align:start position:0% +you're going to decrease Gibbs energy by + + + align:start position:0% +you're going to decrease Gibbs energy by +going to the right + + align:start position:0% + + + + align:start position:0% + +d g + + align:start position:0% +d g + + + align:start position:0% +d g +d n of C less than zero and the reaction + + align:start position:0% +d n of C less than zero and the reaction + + + align:start position:0% +d n of C less than zero and the reaction +will drive to the right + + align:start position:0% +will drive to the right + + + align:start position:0% +will drive to the right +at equilibrium + + align:start position:0% +at equilibrium + + + align:start position:0% +at equilibrium +right + + align:start position:0% +right + + + align:start position:0% +right +um at equilibrium + + align:start position:0% + + + + align:start position:0% + +n of c g + + align:start position:0% +n of c g + + + align:start position:0% +n of c g +right you're right there where the good + + align:start position:0% +right you're right there where the good + + + align:start position:0% +right you're right there where the good +free energy is minimize + + align:start position:0% +free energy is minimize + + + align:start position:0% +free energy is minimize +so you can write down this expression + + align:start position:0% +so you can write down this expression + + + align:start position:0% +so you can write down this expression +out of equilibrium right and you might + + align:start position:0% +out of equilibrium right and you might + + + align:start position:0% +out of equilibrium right and you might +and compare this to this expression + + align:start position:0% +and compare this to this expression + + + align:start position:0% +and compare this to this expression +which you get from the thermodynamics of + + align:start position:0% +which you get from the thermodynamics of + + + align:start position:0% +which you get from the thermodynamics of +the reaction and determine whether your + + align:start position:0% +the reaction and determine whether your + + + align:start position:0% +the reaction and determine whether your +reaction will run spontaneously to the + + align:start position:0% +reaction will run spontaneously to the + + + align:start position:0% +reaction will run spontaneously to the +right or to the left or is it or is it + + align:start position:0% +right or to the left or is it or is it + + + align:start position:0% +right or to the left or is it or is it +actually at equilibrium + + align:start position:0% + + + + align:start position:0% + +did that help answer your question I'm + + align:start position:0% +did that help answer your question I'm + + + align:start position:0% +did that help answer your question I'm +not sure + + align:start position:0% +not sure + + + align:start position:0% +not sure +uh yeah that made sense thank you so you + + align:start position:0% +uh yeah that made sense thank you so you + + + align:start position:0% +uh yeah that made sense thank you so you +can basically you can evaluate this + + align:start position:0% +can basically you can evaluate this + + + align:start position:0% +can basically you can evaluate this +instantaneously whether or not it's + + align:start position:0% +instantaneously whether or not it's + + + align:start position:0% +instantaneously whether or not it's +equilibrium to 10 depends right but you + + align:start position:0% +equilibrium to 10 depends right but you + + + align:start position:0% +equilibrium to 10 depends right but you +can always sort of write that thing down + + align:start position:0% +can always sort of write that thing down + + + align:start position:0% +can always sort of write that thing down +um and again we're not doing really we + + align:start position:0% +um and again we're not doing really we + + + align:start position:0% +um and again we're not doing really we +don't really have the time + + align:start position:0% +don't really have the time + + + align:start position:0% +don't really have the time +in this class to talk about a bunch + + align:start position:0% +in this class to talk about a bunch + + + align:start position:0% +in this class to talk about a bunch +about out of equilibrium reactions and + + align:start position:0% +about out of equilibrium reactions and + + + align:start position:0% +about out of equilibrium reactions and +talk about rates and affinities and + + align:start position:0% +talk about rates and affinities and + + + align:start position:0% +talk about rates and affinities and +stuff but but um that will come later uh + + align:start position:0% +stuff but but um that will come later uh + + + align:start position:0% +stuff but but um that will come later uh +um + + align:start position:0% +um + + + align:start position:0% +um +in course three and other courses right + + align:start position:0% +in course three and other courses right + + + align:start position:0% +in course three and other courses right +and so you're sort of well set up + + align:start position:0% +and so you're sort of well set up + + + align:start position:0% +and so you're sort of well set up +because you because because we + + align:start position:0% +because you because because we + + + align:start position:0% +because you because because we +understand equilibrium we can start + + align:start position:0% +understand equilibrium we can start + + + align:start position:0% +understand equilibrium we can start +analyzing you know out of equilibrium + + align:start position:0% +analyzing you know out of equilibrium + + + align:start position:0% +analyzing you know out of equilibrium +situations + + align:start position:0% +situations + + + align:start position:0% +situations +and non-equilibrium thermos is exists + + align:start position:0% +and non-equilibrium thermos is exists + + + align:start position:0% +and non-equilibrium thermos is exists +it's a fascinating topic I think um and + + align:start position:0% +it's a fascinating topic I think um and + + + align:start position:0% +it's a fascinating topic I think um and +I teach it as part of the advanced + + align:start position:0% +I teach it as part of the advanced + + + align:start position:0% +I teach it as part of the advanced +Thermo class but we have no time for it + + align:start position:0% +Thermo class but we have no time for it + + + align:start position:0% +Thermo class but we have no time for it +here + + align:start position:0% + + + + align:start position:0% + +other questions + + align:start position:0% + + + + align:start position:0% + +I'd like to make sure that people this + + align:start position:0% +I'd like to make sure that people this + + + align:start position:0% +I'd like to make sure that people this +is um a point from last lecture but I'd + + align:start position:0% +is um a point from last lecture but I'd + + + align:start position:0% +is um a point from last lecture but I'd +like to make people sure that people + + align:start position:0% +like to make people sure that people + + + align:start position:0% +like to make people sure that people +understand how we get this numerative + + align:start position:0% +understand how we get this numerative + + + align:start position:0% +understand how we get this numerative +denominator thing out of this expression + + align:start position:0% +denominator thing out of this expression + + + align:start position:0% +denominator thing out of this expression +remember the reaction coefficients are + + align:start position:0% +remember the reaction coefficients are + + + align:start position:0% +remember the reaction coefficients are +positive + + align:start position:0% +positive + + + align:start position:0% +positive +for products and negative for reactants + + align:start position:0% +for products and negative for reactants + + + align:start position:0% +for products and negative for reactants +so products end up with a positive power + + align:start position:0% +so products end up with a positive power + + + align:start position:0% +so products end up with a positive power +and reactants end up + + align:start position:0% +and reactants end up + + + align:start position:0% +and reactants end up +in the basement here with with a + + align:start position:0% +in the basement here with with a + + + align:start position:0% +in the basement here with with a +negative power so + + align:start position:0% +negative power so + + + align:start position:0% +negative power so +um you know often if you've seen this + + align:start position:0% +um you know often if you've seen this + + + align:start position:0% +um you know often if you've seen this +before let's say an introductory + + align:start position:0% +before let's say an introductory + + + align:start position:0% +before let's say an introductory +chemistry you're probably told just to + + align:start position:0% +chemistry you're probably told just to + + + align:start position:0% +chemistry you're probably told just to +put products on the top and reactants on + + align:start position:0% +put products on the top and reactants on + + + align:start position:0% +put products on the top and reactants on +the bottom + + align:start position:0% +the bottom + + + align:start position:0% +the bottom +well this is this is where that comes + + align:start position:0% +well this is this is where that comes + + + align:start position:0% +well this is this is where that comes +from so + + align:start position:0% +from so + + + align:start position:0% +from so +it's good to know it comes from + + align:start position:0% +it's good to know it comes from + + + align:start position:0% +it's good to know it comes from +somewhere + + align:start position:0% +somewhere + + + align:start position:0% +somewhere +maybe everyone understood that I don't + + align:start position:0% +maybe everyone understood that I don't + + + align:start position:0% +maybe everyone understood that I don't +know but + + align:start position:0% +know but + + + align:start position:0% +know but +worth mentioning + + align:start position:0% + + + + align:start position:0% + +so on the pset you're asked to evaluate + + align:start position:0% +so on the pset you're asked to evaluate + + + align:start position:0% +so on the pset you're asked to evaluate +the equilibrium condition for a couple + + align:start position:0% +the equilibrium condition for a couple + + + align:start position:0% +the equilibrium condition for a couple +of reactions + + align:start position:0% +of reactions + + + align:start position:0% +of reactions +and that often boils down to finding the + + align:start position:0% +and that often boils down to finding the + + + align:start position:0% +and that often boils down to finding the +Delta G's + + align:start position:0% +Delta G's + + + align:start position:0% +Delta G's +so I want to make this really explicit + + align:start position:0% +so I want to make this really explicit + + + align:start position:0% +so I want to make this really explicit +here before moving on + + align:start position:0% +here before moving on + + + align:start position:0% +here before moving on +Delta G's + + align:start position:0% + + + + align:start position:0% + +Delta G naught equals g naught products + + align:start position:0% +Delta G naught equals g naught products + + + align:start position:0% +Delta G naught equals g naught products +minus GI reactants + + align:start position:0% + + + + align:start position:0% + +right so that's right G not products + + align:start position:0% +right so that's right G not products + + + align:start position:0% +right so that's right G not products +at some temperature + + align:start position:0% +at some temperature + + + align:start position:0% +at some temperature +let's say T2 + + align:start position:0% +let's say T2 + + + align:start position:0% +let's say T2 +equals + + align:start position:0% +equals + + + align:start position:0% +equals +G naught products + + align:start position:0% +G naught products + + + align:start position:0% +G naught products +at T1 plus some intervals and we've done + + align:start position:0% +at T1 plus some intervals and we've done + + + align:start position:0% +at T1 plus some intervals and we've done +those integrals already we know how to + + align:start position:0% +those integrals already we know how to + + + align:start position:0% +those integrals already we know how to +do those integrals for instance you + + align:start position:0% +do those integrals for instance you + + + align:start position:0% +do those integrals for instance you +integrate entropy or temperature or + + align:start position:0% +integrate entropy or temperature or + + + align:start position:0% +integrate entropy or temperature or +something like that + + align:start position:0% + + + + align:start position:0% + +G not reactants + + align:start position:0% +G not reactants + + + align:start position:0% +G not reactants +at some temperature 2 equals g naught + + align:start position:0% +at some temperature 2 equals g naught + + + align:start position:0% +at some temperature 2 equals g naught +reactants at some temperature one plus + + align:start position:0% +reactants at some temperature one plus + + + align:start position:0% +reactants at some temperature one plus +integrals + + align:start position:0% + + + + align:start position:0% + +so we're seeing that Delta G naught at + + align:start position:0% +so we're seeing that Delta G naught at + + + align:start position:0% +so we're seeing that Delta G naught at +some T2 equals Delta G naught at some T1 + + align:start position:0% +some T2 equals Delta G naught at some T1 + + + align:start position:0% +some T2 equals Delta G naught at some T1 +plus integrals + + align:start position:0% + + + + align:start position:0% + +and these + + align:start position:0% + + + + align:start position:0% + +these depend on the heat capacity + + align:start position:0% +these depend on the heat capacity + + + align:start position:0% +these depend on the heat capacity +differences + + align:start position:0% +differences + + + align:start position:0% +differences +so I'm doing this at a very high level + + align:start position:0% +so I'm doing this at a very high level + + + align:start position:0% +so I'm doing this at a very high level +and quickly here + + align:start position:0% +and quickly here + + + align:start position:0% +and quickly here +um because I want to highlight the + + align:start position:0% +um because I want to highlight the + + + align:start position:0% +um because I want to highlight the +similarity to the case of the unary + + align:start position:0% +similarity to the case of the unary + + + align:start position:0% +similarity to the case of the unary +Transformations we had + + align:start position:0% +Transformations we had + + + align:start position:0% +Transformations we had +um in unary systems we had + + align:start position:0% +um in unary systems we had + + + align:start position:0% +um in unary systems we had +Transformations between phases + + align:start position:0% +Transformations between phases + + + align:start position:0% +Transformations between phases +and we can analyze things like the + + align:start position:0% +and we can analyze things like the + + + align:start position:0% +and we can analyze things like the +change of Gibbs free energy or any other + + align:start position:0% +change of Gibbs free energy or any other + + + align:start position:0% +change of Gibbs free energy or any other +state function change of H or change of + + align:start position:0% +state function change of H or change of + + + align:start position:0% +state function change of H or change of +s + + align:start position:0% +s + + + align:start position:0% +s +across that transformation + + align:start position:0% +across that transformation + + + align:start position:0% +across that transformation +and we could calculate the temperature + + align:start position:0% +and we could calculate the temperature + + + align:start position:0% +and we could calculate the temperature +dependence of that by integrating things + + align:start position:0% +dependence of that by integrating things + + + align:start position:0% +dependence of that by integrating things +that depended on heat capacity + + align:start position:0% +that depended on heat capacity + + + align:start position:0% +that depended on heat capacity +differences + + align:start position:0% +differences + + + align:start position:0% +differences +it's all formally the same right now + + align:start position:0% +it's all formally the same right now + + + align:start position:0% +it's all formally the same right now +we're having a transformation from + + align:start position:0% +we're having a transformation from + + + align:start position:0% +we're having a transformation from +reactants to products + + align:start position:0% +reactants to products + + + align:start position:0% +reactants to products +the Delta G naught is important that + + align:start position:0% +the Delta G naught is important that + + + align:start position:0% +the Delta G naught is important that +helps us determine equilibrium condition + + align:start position:0% +helps us determine equilibrium condition + + + align:start position:0% +helps us determine equilibrium condition +and in general it's temperature + + align:start position:0% +and in general it's temperature + + + align:start position:0% +and in general it's temperature +dependent + + align:start position:0% + + + + align:start position:0% + +and you're going to find things like + + align:start position:0% +and you're going to find things like + + + align:start position:0% +and you're going to find things like +Delta G naughts or their equivalents + + align:start position:0% +Delta G naughts or their equivalents + + + align:start position:0% +Delta G naughts or their equivalents +tabulated at standard temperatures and + + align:start position:0% +tabulated at standard temperatures and + + + align:start position:0% +tabulated at standard temperatures and +databases and you might be asked to + + align:start position:0% +databases and you might be asked to + + + align:start position:0% +databases and you might be asked to +calculate reaction balance at some other + + align:start position:0% +calculate reaction balance at some other + + + align:start position:0% +calculate reaction balance at some other +temperature + + align:start position:0% +temperature + + + align:start position:0% +temperature +and to do that you're going to need the + + align:start position:0% +and to do that you're going to need the + + + align:start position:0% +and to do that you're going to need the +CPS and the Delta CPS so formally it's + + align:start position:0% +CPS and the Delta CPS so formally it's + + + align:start position:0% +CPS and the Delta CPS so formally it's +very similar to the unit case + + align:start position:0% +very similar to the unit case + + + align:start position:0% +very similar to the unit case +I want to highlight that + + align:start position:0% + + + + align:start position:0% + +all right and if a sorry if the problem + + align:start position:0% +all right and if a sorry if the problem + + + align:start position:0% +all right and if a sorry if the problem +is just happening at standard + + align:start position:0% +is just happening at standard + + + align:start position:0% +is just happening at standard +temperature can you then just use the + + align:start position:0% +temperature can you then just use the + + + align:start position:0% +temperature can you then just use the +standard Gibbs values and I guess you + + align:start position:0% +standard Gibbs values and I guess you + + + align:start position:0% +standard Gibbs values and I guess you +wouldn't need to integrate in that case + + align:start position:0% +wouldn't need to integrate in that case + + + align:start position:0% +wouldn't need to integrate in that case +yes indeed yep H not for elements + + align:start position:0% + + + + align:start position:0% + +at standard temperature and pressure is + + align:start position:0% +at standard temperature and pressure is + + + align:start position:0% +at standard temperature and pressure is +defined as zero + + align:start position:0% +defined as zero + + + align:start position:0% +defined as zero +s naught for elements at standard + + align:start position:0% +s naught for elements at standard + + + align:start position:0% +s naught for elements at standard +temperature and pressure is a number + + align:start position:0% +temperature and pressure is a number + + + align:start position:0% +temperature and pressure is a number +often in the back of the off + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +Delta H naught Delta s naught Delta G + + align:start position:0% +Delta H naught Delta s naught Delta G + + + align:start position:0% +Delta H naught Delta s naught Delta G +not for compounds + + align:start position:0% +not for compounds + + + align:start position:0% +not for compounds +those are numbers often found in the + + align:start position:0% +those are numbers often found in the + + + align:start position:0% +those are numbers often found in the +back of the off for common reactions + + align:start position:0% +back of the off for common reactions + + + align:start position:0% +back of the off for common reactions +that's right and so if you're a standard + + align:start position:0% +that's right and so if you're a standard + + + align:start position:0% +that's right and so if you're a standard +temperature and pressure you normally + + align:start position:0% +temperature and pressure you normally + + + align:start position:0% +temperature and pressure you normally +have everything you need even in + + align:start position:0% +have everything you need even in + + + align:start position:0% +have everything you need even in +Wikipedia + + align:start position:0% +Wikipedia + + + align:start position:0% +Wikipedia +for standard reactions + + align:start position:0% +for standard reactions + + + align:start position:0% +for standard reactions +and um + + align:start position:0% +and um + + + align:start position:0% +and um +you know I mean we're analyzing like + + align:start position:0% +you know I mean we're analyzing like + + + align:start position:0% +you know I mean we're analyzing like +ammonia in this you know so it's very + + align:start position:0% +ammonia in this you know so it's very + + + align:start position:0% +ammonia in this you know so it's very +common substances uh easy to find the + + align:start position:0% +common substances uh easy to find the + + + align:start position:0% +common substances uh easy to find the +data + + align:start position:0% + + + + align:start position:0% + +thank you for that + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +let me move on + + align:start position:0% +let me move on + + + align:start position:0% +let me move on +risk of repeating myself notes + + align:start position:0% +risk of repeating myself notes + + + align:start position:0% +risk of repeating myself notes +on reaction equilibrium + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +a negative + + align:start position:0% + + + + align:start position:0% + +a negative Delta G naught + + align:start position:0% + + + + align:start position:0% + +drives reaction + + align:start position:0% +drives reaction + + + align:start position:0% +drives reaction +to the right + + align:start position:0% + + + + align:start position:0% + +that's sort of a straightforward point + + align:start position:0% +that's sort of a straightforward point + + + align:start position:0% +that's sort of a straightforward point +adding + + align:start position:0% +adding + + + align:start position:0% +adding +more + + align:start position:0% +more + + + align:start position:0% +more +of a given component + + align:start position:0% + + + + align:start position:0% + +shift reaction balance + + align:start position:0% + + + + align:start position:0% + +it shifts the reaction balance to + + align:start position:0% +it shifts the reaction balance to + + + align:start position:0% +it shifts the reaction balance to +maintain equilibrium + + align:start position:0% +maintain equilibrium + + + align:start position:0% +maintain equilibrium +that's for the shot to the a again + + align:start position:0% + + + + align:start position:0% + +any change + + align:start position:0% + + + + align:start position:0% + +in the status quo + + align:start position:0% + + + + align:start position:0% + +prompts + + align:start position:0% + + + + align:start position:0% + +and opposing + + align:start position:0% + + + + align:start position:0% + +reaction + + align:start position:0% +reaction + + + align:start position:0% +reaction +in the responding system + + align:start position:0% + + + + align:start position:0% + +and I'll one more thing + + align:start position:0% +and I'll one more thing + + + align:start position:0% +and I'll one more thing +four three + + align:start position:0% +four three + + + align:start position:0% +four three +or more + + align:start position:0% +or more + + + align:start position:0% +or more +components + + align:start position:0% + + + + align:start position:0% + +there's no unique + + align:start position:0% +there's no unique + + + align:start position:0% +there's no unique +equilogram condition + + align:start position:0% + + + + align:start position:0% + +so let's analyze again this case + + align:start position:0% +so let's analyze again this case + + + align:start position:0% +so let's analyze again this case +X of c squared x of a x of B + + align:start position:0% +X of c squared x of a x of B + + + align:start position:0% +X of c squared x of a x of B +and this equals + + align:start position:0% + + + + align:start position:0% + +okay so this thing here is just a number + + align:start position:0% +okay so this thing here is just a number + + + align:start position:0% +okay so this thing here is just a number +let's say at a given temperature + + align:start position:0% + + + + align:start position:0% + +it's a number + + align:start position:0% + + + + align:start position:0% + +and we have + + align:start position:0% + + + + align:start position:0% + +three variables + + align:start position:0% +three variables + + + align:start position:0% +three variables +we know that X of a plus X of B plus X + + align:start position:0% +we know that X of a plus X of B plus X + + + align:start position:0% +we know that X of a plus X of B plus X +of C equals one + + align:start position:0% +of C equals one + + + align:start position:0% +of C equals one +by definition right they're mole + + align:start position:0% +by definition right they're mole + + + align:start position:0% +by definition right they're mole +fractions + + align:start position:0% + + + + align:start position:0% + +we still have one degree of freedom + + align:start position:0% +we still have one degree of freedom + + + align:start position:0% +we still have one degree of freedom +at equilibrium + + align:start position:0% +at equilibrium + + + align:start position:0% +at equilibrium +so there's an infinite number of of + + align:start position:0% +so there's an infinite number of of + + + align:start position:0% +so there's an infinite number of of +compositions that would satisfy + + align:start position:0% +compositions that would satisfy + + + align:start position:0% +compositions that would satisfy +equilibrium here + + align:start position:0% + + + + align:start position:0% + +you can play with the method if you want + + align:start position:0% +you can play with the method if you want + + + align:start position:0% +you can play with the method if you want +to parameterize you know + + align:start position:0% +to parameterize you know + + + align:start position:0% +to parameterize you know +fix you can fix X of c and then + + align:start position:0% +fix you can fix X of c and then + + + align:start position:0% +fix you can fix X of c and then +calculate X of a as a function of X and + + align:start position:0% +calculate X of a as a function of X and + + + align:start position:0% +calculate X of a as a function of X and +B here if you like + + align:start position:0% +B here if you like + + + align:start position:0% +B here if you like +um you know there's lots of ways to sort + + align:start position:0% +um you know there's lots of ways to sort + + + align:start position:0% +um you know there's lots of ways to sort +of slice this but basically + + align:start position:0% +of slice this but basically + + + align:start position:0% +of slice this but basically +um + + align:start position:0% +um + + + align:start position:0% +um +you know you could you could shift your + + align:start position:0% +you know you could you could shift your + + + align:start position:0% +you know you could you could shift your +equilibrium balance so how does that + + align:start position:0% +equilibrium balance so how does that + + + align:start position:0% +equilibrium balance so how does that +work + + align:start position:0% +work + + + align:start position:0% +work +let's see how this works with the shots + + align:start position:0% +let's see how this works with the shots + + + align:start position:0% +let's see how this works with the shots +of the a let's say you're at equilibrium + + align:start position:0% +of the a let's say you're at equilibrium + + + align:start position:0% +of the a let's say you're at equilibrium +let's say you're at equilibrium and you + + align:start position:0% +let's say you're at equilibrium and you + + + align:start position:0% +let's say you're at equilibrium and you +add a little bit of more X and B you + + align:start position:0% +add a little bit of more X and B you + + + align:start position:0% +add a little bit of more X and B you +inject a little bit more component B + + align:start position:0% +inject a little bit more component B + + + align:start position:0% +inject a little bit more component B +into your system + + align:start position:0% +into your system + + + align:start position:0% +into your system +so + + align:start position:0% +so + + + align:start position:0% +so +the + + align:start position:0% +the + + + align:start position:0% +the +denominator ticked up a little bit + + align:start position:0% + + + + align:start position:0% + +how's the reaction going to respond + + align:start position:0% + + + + align:start position:0% + +how's the reaction going to respond we + + align:start position:0% +how's the reaction going to respond we + + + align:start position:0% +how's the reaction going to respond we +just add a little bit more of B + + align:start position:0% +just add a little bit more of B + + + align:start position:0% +just add a little bit more of B +we kicked it out of equilibrium how the + + align:start position:0% +we kicked it out of equilibrium how the + + + align:start position:0% +we kicked it out of equilibrium how the +reaction respond + + align:start position:0% +reaction respond + + + align:start position:0% +reaction respond +it'll slow to the right to make more c + + align:start position:0% +it'll slow to the right to make more c + + + align:start position:0% +it'll slow to the right to make more c +yeah it's going to Swerve to the right + + align:start position:0% +yeah it's going to Swerve to the right + + + align:start position:0% +yeah it's going to Swerve to the right +to try to counteract that change and + + align:start position:0% +to try to counteract that change and + + + align:start position:0% +to try to counteract that change and +bring this expression back to + + align:start position:0% +bring this expression back to + + + align:start position:0% +bring this expression back to +equilibrium so you add more B the + + align:start position:0% +equilibrium so you add more B the + + + align:start position:0% +equilibrium so you add more B the +reaction shifts to the right likewise if + + align:start position:0% +reaction shifts to the right likewise if + + + align:start position:0% +reaction shifts to the right likewise if +you add more C the reaction will shift + + align:start position:0% +you add more C the reaction will shift + + + align:start position:0% +you add more C the reaction will shift +to the left if you take away some a the + + align:start position:0% +to the left if you take away some a the + + + align:start position:0% +to the left if you take away some a the +reaction will shift to the left and so + + align:start position:0% +reaction will shift to the left and so + + + align:start position:0% +reaction will shift to the left and so +forth and so on you cannot get away from + + align:start position:0% +forth and so on you cannot get away from + + + align:start position:0% +forth and so on you cannot get away from +the shot of the a it's always going to + + align:start position:0% +the shot of the a it's always going to + + + align:start position:0% +the shot of the a it's always going to +be there trying to restore equilibrium + + align:start position:0% + + + + align:start position:0% + +it's in the math I know it Bears + + align:start position:0% +it's in the math I know it Bears + + + align:start position:0% +it's in the math I know it Bears +pointing out from time to time + + align:start position:0% +pointing out from time to time + + + align:start position:0% +pointing out from time to time +all right + + align:start position:0% +all right + + + align:start position:0% +all right +let's talk about temperature dependence + + align:start position:0% +let's talk about temperature dependence + + + align:start position:0% +let's talk about temperature dependence +this gets to one of the problems in the + + align:start position:0% +this gets to one of the problems in the + + + align:start position:0% +this gets to one of the problems in the +homework + + align:start position:0% + + + + align:start position:0% + +temperature dependence + + align:start position:0% + + + + align:start position:0% + +of reaction + + align:start position:0% + + + + align:start position:0% + +equilibrium + + align:start position:0% + + + + align:start position:0% + +now I'm just going to do some math here + + align:start position:0% +now I'm just going to do some math here + + + align:start position:0% +now I'm just going to do some math here +and we'll talk about the meaning let's + + align:start position:0% +and we'll talk about the meaning let's + + + align:start position:0% +and we'll talk about the meaning let's +calculate the partial with temperature + + align:start position:0% +calculate the partial with temperature + + + align:start position:0% +calculate the partial with temperature +at fixed pressure + + align:start position:0% +at fixed pressure + + + align:start position:0% +at fixed pressure +of reaction balance + + align:start position:0% +of reaction balance + + + align:start position:0% +of reaction balance +and I'll do log of kfp because the math + + align:start position:0% +and I'll do log of kfp because the math + + + align:start position:0% +and I'll do log of kfp because the math +is easier this way this is D DT + + align:start position:0% +is easier this way this is D DT + + + align:start position:0% +is easier this way this is D DT +at fixed pressure + + align:start position:0% +at fixed pressure + + + align:start position:0% +at fixed pressure +of minus Delta G naught over RT + + align:start position:0% + + + + align:start position:0% + +okay and by Chain rule this equals Delta + + align:start position:0% +okay and by Chain rule this equals Delta + + + align:start position:0% +okay and by Chain rule this equals Delta +H naught over r t squared + + align:start position:0% +H naught over r t squared + + + align:start position:0% +H naught over r t squared +minus 1 over RT + + align:start position:0% +minus 1 over RT + + + align:start position:0% +minus 1 over RT +D Delta H naught + + align:start position:0% +D Delta H naught + + + align:start position:0% +D Delta H naught +DT + + align:start position:0% +DT + + + align:start position:0% +DT +and fixed pressure + + align:start position:0% +and fixed pressure + + + align:start position:0% +and fixed pressure +plus 1 over r + + align:start position:0% +plus 1 over r + + + align:start position:0% +plus 1 over r +D Delta s naught DT + + align:start position:0% +D Delta s naught DT + + + align:start position:0% +D Delta s naught DT +if expression so that's just the chain + + align:start position:0% +if expression so that's just the chain + + + align:start position:0% +if expression so that's just the chain +rule + + align:start position:0% +rule + + + align:start position:0% +rule +D Delta H naught + + align:start position:0% +D Delta H naught + + + align:start position:0% +D Delta H naught +over DT at fixed pressure + + align:start position:0% +over DT at fixed pressure + + + align:start position:0% +over DT at fixed pressure +equals Delta CP again coming back to + + align:start position:0% +equals Delta CP again coming back to + + + align:start position:0% +equals Delta CP again coming back to +transformation quantities + + align:start position:0% +transformation quantities + + + align:start position:0% +transformation quantities +and D Delta s naught DT + + align:start position:0% +and D Delta s naught DT + + + align:start position:0% +and D Delta s naught DT +at fixed pressure + + align:start position:0% +at fixed pressure + + + align:start position:0% +at fixed pressure +equals Delta c p over t + + align:start position:0% +equals Delta c p over t + + + align:start position:0% +equals Delta c p over t +relying on this a lot and you might you + + align:start position:0% +relying on this a lot and you might you + + + align:start position:0% +relying on this a lot and you might you +might want to remind yourself of this + + align:start position:0% +might want to remind yourself of this + + + align:start position:0% +might want to remind yourself of this +you might want to show this just in the + + align:start position:0% +you might want to show this just in the + + + align:start position:0% +you might want to show this just in the +minutes after class it's um + + align:start position:0% + + + + align:start position:0% + +you can go back to when we introduce + + align:start position:0% +you can go back to when we introduce + + + align:start position:0% +you can go back to when we introduce +these potentials so using these + + align:start position:0% +these potentials so using these + + + align:start position:0% +these potentials so using these +Expressions we find D + + align:start position:0% +Expressions we find D + + + align:start position:0% +Expressions we find D +log of K of P + + align:start position:0% +log of K of P + + + align:start position:0% +log of K of P +DT + + align:start position:0% +DT + + + align:start position:0% +DT +at fixed pressure + + align:start position:0% +at fixed pressure + + + align:start position:0% +at fixed pressure +equals + + align:start position:0% +equals + + + align:start position:0% +equals +Delta H naught over r t squared + + align:start position:0% +Delta H naught over r t squared + + + align:start position:0% +Delta H naught over r t squared +and this has a name + + align:start position:0% +and this has a name + + + align:start position:0% +and this has a name +this is called the vent off + + align:start position:0% +this is called the vent off + + + align:start position:0% +this is called the vent off +equation + + align:start position:0% + + + + align:start position:0% + +um okay you're going to use a form of + + align:start position:0% +um okay you're going to use a form of + + + align:start position:0% +um okay you're going to use a form of +this in + + align:start position:0% +this in + + + align:start position:0% +this in +the homework + + align:start position:0% +the homework + + + align:start position:0% +the homework +because you are ex you are implicitly + + align:start position:0% +because you are ex you are implicitly + + + align:start position:0% +because you are ex you are implicitly +asked to calculate how the reaction + + align:start position:0% +asked to calculate how the reaction + + + align:start position:0% +asked to calculate how the reaction +balance changes with temperature + + align:start position:0% + + + + align:start position:0% + +let's see how this works out let's see + + align:start position:0% +let's see how this works out let's see + + + align:start position:0% +let's see how this works out let's see +how the math works so for example let's + + align:start position:0% +how the math works so for example let's + + + align:start position:0% +how the math works so for example let's +consider an endothermic reaction + + align:start position:0% + + + + align:start position:0% + +endothermic + + align:start position:0% +endothermic + + + align:start position:0% +endothermic +reaction + + align:start position:0% +reaction + + + align:start position:0% +reaction +Q + + align:start position:0% +Q + + + align:start position:0% +Q +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and Delta H naught are greater than zero + + align:start position:0% +and Delta H naught are greater than zero + + + align:start position:0% +and Delta H naught are greater than zero +right that's an endothermic reaction for + + align:start position:0% +right that's an endothermic reaction for + + + align:start position:0% +right that's an endothermic reaction for +example that's the cold pack + + align:start position:0% +example that's the cold pack + + + align:start position:0% +example that's the cold pack +right + + align:start position:0% +right + + + align:start position:0% +right +sorry instant cold pack + + align:start position:0% +sorry instant cold pack + + + align:start position:0% +sorry instant cold pack +Delta H equals reversible Heat + + align:start position:0% +Delta H equals reversible Heat + + + align:start position:0% +Delta H equals reversible Heat +for the reaction + + align:start position:0% +for the reaction + + + align:start position:0% +for the reaction +Delta H greater than zero means D log k + + align:start position:0% +Delta H greater than zero means D log k + + + align:start position:0% +Delta H greater than zero means D log k +p DT pressure + + align:start position:0% +p DT pressure + + + align:start position:0% +p DT pressure +is greater than zero + + align:start position:0% +is greater than zero + + + align:start position:0% +is greater than zero +what does that mean + + align:start position:0% + + + + align:start position:0% + +reaction + + align:start position:0% +reaction + + + align:start position:0% +reaction +moves to the + + align:start position:0% + + + + align:start position:0% + +right or left with increasing + + align:start position:0% +right or left with increasing + + + align:start position:0% +right or left with increasing +temperature + + align:start position:0% + + + + align:start position:0% + +with increasing temperature do I move to + + align:start position:0% +with increasing temperature do I move to + + + align:start position:0% +with increasing temperature do I move to +the right or the left if this condition + + align:start position:0% +the right or the left if this condition + + + align:start position:0% +the right or the left if this condition +is true + + align:start position:0% + + + + align:start position:0% + +to the right move to the right right K + + align:start position:0% +to the right move to the right right K + + + align:start position:0% +to the right move to the right right K +of p is product over reactants so if kfp + + align:start position:0% +of p is product over reactants so if kfp + + + align:start position:0% +of p is product over reactants so if kfp +is increasing if this slope is positive + + align:start position:0% +is increasing if this slope is positive + + + align:start position:0% +is increasing if this slope is positive +that means I'm moving + + align:start position:0% +that means I'm moving + + + align:start position:0% +that means I'm moving +to the right + + align:start position:0% +to the right + + + align:start position:0% +to the right +reaction moves to the right + + align:start position:0% + + + + align:start position:0% + +with increasing temperature + + align:start position:0% +with increasing temperature + + + align:start position:0% +with increasing temperature +what does that mean the system + + align:start position:0% + + + + align:start position:0% + +tries + + align:start position:0% +tries + + + align:start position:0% +tries +right it doesn't actually know what it's + + align:start position:0% +right it doesn't actually know what it's + + + align:start position:0% +right it doesn't actually know what it's +doing + + align:start position:0% +doing + + + align:start position:0% +doing +to oppose + + align:start position:0% + + + + align:start position:0% + +the temp rise + + align:start position:0% + + + + align:start position:0% + +by taking up heat + + align:start position:0% + + + + align:start position:0% + +in an endothermic reaction + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% +foreign + + + align:start position:0% +foreign +if you try to raise the temperature it's + + align:start position:0% +if you try to raise the temperature it's + + + align:start position:0% +if you try to raise the temperature it's +going cold pack on you + + align:start position:0% +going cold pack on you + + + align:start position:0% +going cold pack on you +that's what the half says + + align:start position:0% + + + + align:start position:0% + +you cannot get away + + align:start position:0% + + + + align:start position:0% + +from the shot to the A + + align:start position:0% + + + + align:start position:0% + +and the light the uh Converse of course + + align:start position:0% +and the light the uh Converse of course + + + align:start position:0% +and the light the uh Converse of course +is going to happen for an exothermic + + align:start position:0% +is going to happen for an exothermic + + + align:start position:0% +is going to happen for an exothermic +reaction let me ask you + + align:start position:0% +reaction let me ask you + + + align:start position:0% +reaction let me ask you +um + + align:start position:0% +um + + + align:start position:0% +um +if I just rip that wrote that backwards + + align:start position:0% +if I just rip that wrote that backwards + + + align:start position:0% +if I just rip that wrote that backwards +right products I just flip it make + + align:start position:0% +right products I just flip it make + + + align:start position:0% +right products I just flip it make +product reactants reactants products + + align:start position:0% +product reactants reactants products + + + align:start position:0% +product reactants reactants products +everything I just said would be + + align:start position:0% + + + + align:start position:0% + +have it sine flipped and it works out + + align:start position:0% +have it sine flipped and it works out + + + align:start position:0% +have it sine flipped and it works out +because nature doesn't know how I wrote + + align:start position:0% +because nature doesn't know how I wrote + + + align:start position:0% +because nature doesn't know how I wrote +this and she doesn't care how I wrote + + align:start position:0% +this and she doesn't care how I wrote + + + align:start position:0% +this and she doesn't care how I wrote +this right it doesn't know what the + + align:start position:0% +this right it doesn't know what the + + + align:start position:0% +this right it doesn't know what the +difference between products and + + align:start position:0% +difference between products and + + + align:start position:0% +difference between products and +reactants are + + align:start position:0% +reactants are + + + align:start position:0% +reactants are +so + + align:start position:0% +so + + + align:start position:0% +so +an exothermic reaction + + align:start position:0% +an exothermic reaction + + + align:start position:0% +an exothermic reaction +moves to the left with increasing temp + + align:start position:0% +moves to the left with increasing temp + + + align:start position:0% +moves to the left with increasing temp +right okay \ No newline at end of file diff --git a/a4krZtUkzMM.txt b/a4krZtUkzMM.txt new file mode 100644 index 0000000000000000000000000000000000000000..a5a0f737dd3e8749d2ac5e51bd78bc49a07ae2e1 --- /dev/null +++ b/a4krZtUkzMM.txt @@ -0,0 +1,9235 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu well this is one of my + + align:start position:0% +ocw.mit.edu well this is one of my + + + align:start position:0% +ocw.mit.edu well this is one of my +favorite lectures and I could easily + + align:start position:0% +favorite lectures and I could easily + + + align:start position:0% +favorite lectures and I could easily +lecture on this subject for a couple of + + align:start position:0% +lecture on this subject for a couple of + + + align:start position:0% +lecture on this subject for a couple of +weeks and I'm going to do it all in one + + align:start position:0% +weeks and I'm going to do it all in one + + + align:start position:0% +weeks and I'm going to do it all in one +day because it is atoms and uh uh I + + align:start position:0% +day because it is atoms and uh uh I + + + align:start position:0% +day because it is atoms and uh uh I +think that it takes us a little beyond + + align:start position:0% +think that it takes us a little beyond + + + align:start position:0% +think that it takes us a little beyond +what is the appropriate level of this + + align:start position:0% +what is the appropriate level of this + + + align:start position:0% +what is the appropriate level of this +course we want to be able to + + align:start position:0% +course we want to be able to + + + align:start position:0% +course we want to be able to +build some kind of a model that + + align:start position:0% +build some kind of a model that + + + align:start position:0% +build some kind of a model that +describes what we can see in the + + align:start position:0% +describes what we can see in the + + + align:start position:0% +describes what we can see in the +spectrum of many electron atoms and this + + align:start position:0% +spectrum of many electron atoms and this + + + align:start position:0% +spectrum of many electron atoms and this +will teach + + align:start position:0% +will teach + + + align:start position:0% +will teach +us uh useful things about how do we + + align:start position:0% +us uh useful things about how do we + + + align:start position:0% +us uh useful things about how do we +model the Spectre of many electron + + align:start position:0% +model the Spectre of many electron + + + align:start position:0% +model the Spectre of many electron +molecules which in some ways are easier + + align:start position:0% +molecules which in some ways are easier + + + align:start position:0% +molecules which in some ways are easier +than many electron + + align:start position:0% +than many electron + + + align:start position:0% +than many electron +atoms + + align:start position:0% +atoms + + + align:start position:0% +atoms +um + + align:start position:0% +um + + + align:start position:0% +um +so the way we + + align:start position:0% +so the way we + + + align:start position:0% +so the way we +first uh motivate the problem is + + align:start position:0% +first uh motivate the problem is + + + align:start position:0% +first uh motivate the problem is +for one + + align:start position:0% +for one + + + align:start position:0% +for one +electron atoms and these are there are + + align:start position:0% +electron atoms and these are there are + + + align:start position:0% +electron atoms and these are there are +two kinds of one electron atoms the + + align:start position:0% +two kinds of one electron atoms the + + + align:start position:0% +two kinds of one electron atoms the +really one electron atoms which are all + + align:start position:0% +really one electron atoms which are all + + + align:start position:0% +really one electron atoms which are all +like hydrogen and don't have any + + align:start position:0% +like hydrogen and don't have any + + + align:start position:0% +like hydrogen and don't have any +complexity + + align:start position:0% +complexity + + + align:start position:0% +complexity +uh then there's alkal + + align:start position:0% + + + + align:start position:0% + +like where there's one electron outside + + align:start position:0% +like where there's one electron outside + + + align:start position:0% +like where there's one electron outside +of closed shells and then we we split + + align:start position:0% +of closed shells and then we we split + + + align:start position:0% +of closed shells and then we we split +the degeneracy say of uh 3s 3p + + align:start position:0% +the degeneracy say of uh 3s 3p + + + align:start position:0% +the degeneracy say of uh 3s 3p +3D they're no longer + + align:start position:0% +3D they're no longer + + + align:start position:0% +3D they're no longer +degenerate uh but we still have + + align:start position:0% +degenerate uh but we still have + + + align:start position:0% +degenerate uh but we still have +something that's really important and + + align:start position:0% +something that's really important and + + + align:start position:0% +something that's really important and +that + + align:start position:0% +that + + + align:start position:0% +that +is one orbital + + align:start position:0% + + + + align:start position:0% + +one + + align:start position:0% + + + + align:start position:0% + +state and + + align:start position:0% +state and + + + align:start position:0% +state and +so because of that it's really trivial + + align:start position:0% +so because of that it's really trivial + + + align:start position:0% +so because of that it's really trivial +seeing the periodic table in alkal like + + align:start position:0% +seeing the periodic table in alkal like + + + align:start position:0% +seeing the periodic table in alkal like +Spectra you can ask well let's suppose + + align:start position:0% +Spectra you can ask well let's suppose + + + align:start position:0% +Spectra you can ask well let's suppose +we have pottassium + + align:start position:0% +we have pottassium + + + align:start position:0% +we have pottassium +calcium plus or pottassium uh what's + + align:start position:0% +calcium plus or pottassium uh what's + + + align:start position:0% +calcium plus or pottassium uh what's +below + + align:start position:0% + + + + align:start position:0% + +potassium ridum I was going to say + + align:start position:0% +potassium ridum I was going to say + + + align:start position:0% +potassium ridum I was going to say +cesium but it's rubidium okay + + align:start position:0% +cesium but it's rubidium okay + + + align:start position:0% +cesium but it's rubidium okay +so what can we guess about the energy + + align:start position:0% +so what can we guess about the energy + + + align:start position:0% +so what can we guess about the energy +levels for first going potassium + + align:start position:0% +levels for first going potassium + + + align:start position:0% +levels for first going potassium +calcium is it potassium or is it sodium + + align:start position:0% +calcium is it potassium or is it sodium + + + align:start position:0% +calcium is it potassium or is it sodium +before + + align:start position:0% +before + + + align:start position:0% +before +calcium calcium before calcium yes it is + + align:start position:0% +calcium calcium before calcium yes it is + + + align:start position:0% +calcium calcium before calcium yes it is +okay I just I'm just just just checking + + align:start position:0% +okay I just I'm just just just checking + + + align:start position:0% +okay I just I'm just just just checking +if we got chemist in here or + + align:start position:0% +if we got chemist in here or + + + align:start position:0% +if we got chemist in here or +not okay so here what we're doing is + + align:start position:0% +not okay so here what we're doing is + + + align:start position:0% +not okay so here what we're doing is +we're looking at the energy level + + align:start position:0% +we're looking at the energy level + + + align:start position:0% +we're looking at the energy level +structure of potassium a neutral + + align:start position:0% +structure of potassium a neutral + + + align:start position:0% +structure of potassium a neutral +molecule uh atom and calcium ion we know + + align:start position:0% +molecule uh atom and calcium ion we know + + + align:start position:0% +molecule uh atom and calcium ion we know +that the only thing that changes when we + + align:start position:0% +that the only thing that changes when we + + + align:start position:0% +that the only thing that changes when we +go from potassium to calcium is that the + + align:start position:0% +go from potassium to calcium is that the + + + align:start position:0% +go from potassium to calcium is that the +charge on the nucleus + + align:start position:0% +charge on the nucleus + + + align:start position:0% +charge on the nucleus +increases so that means we expect that + + align:start position:0% +increases so that means we expect that + + + align:start position:0% +increases so that means we expect that +the energy levels will get farther + + align:start position:0% + + + + align:start position:0% + +apart uh so that's pretty + + align:start position:0% +apart uh so that's pretty + + + align:start position:0% +apart uh so that's pretty +easy and we can do much more sophis at + + align:start position:0% +easy and we can do much more sophis at + + + align:start position:0% +easy and we can do much more sophis at +things already in freshman chemistry + + align:start position:0% +things already in freshman chemistry + + + align:start position:0% +things already in freshman chemistry +pottassium to ridium well what's + + align:start position:0% +pottassium to ridium well what's + + + align:start position:0% +pottassium to ridium well what's +happened here well the charge on the + + align:start position:0% +happened here well the charge on the + + + align:start position:0% +happened here well the charge on the +nucleus has increased a whole bunch but + + align:start position:0% +nucleus has increased a whole bunch but + + + align:start position:0% +nucleus has increased a whole bunch but +we filled the shell and all of the + + align:start position:0% +we filled the shell and all of the + + + align:start position:0% +we filled the shell and all of the +electrons that went into that F filled + + align:start position:0% +electrons that went into that F filled + + + align:start position:0% +electrons that went into that F filled +shell are pretty + + align:start position:0% +shell are pretty + + + align:start position:0% +shell are pretty +compact uh and so they Shield pretty + + align:start position:0% +compact uh and so they Shield pretty + + + align:start position:0% +compact uh and so they Shield pretty +well and so uh we have to decide will + + align:start position:0% +well and so uh we have to decide will + + + align:start position:0% +well and so uh we have to decide will +the first excited state of + + align:start position:0% +the first excited state of + + + align:start position:0% +the first excited state of +Rubidium be at higher or lower energy + + align:start position:0% +Rubidium be at higher or lower energy + + + align:start position:0% +Rubidium be at higher or lower energy +than that for + + align:start position:0% +than that for + + + align:start position:0% +than that for +potassium why do we is that a hard + + align:start position:0% +potassium why do we is that a hard + + + align:start position:0% +potassium why do we is that a hard +Choice well because the energy levels go + + align:start position:0% +Choice well because the energy levels go + + + align:start position:0% +Choice well because the energy levels go +as Z + + align:start position:0% +as Z + + + align:start position:0% +as Z +effective squared over n star + + align:start position:0% +effective squared over n star + + + align:start position:0% +effective squared over n star +squared so n has + + align:start position:0% +squared so n has + + + align:start position:0% +squared so n has +increased when you go from potassium to + + align:start position:0% +increased when you go from potassium to + + + align:start position:0% +increased when you go from potassium to +rubidium n star is probably going to + + align:start position:0% +rubidium n star is probably going to + + + align:start position:0% +rubidium n star is probably going to +increase pretty much the same way that n + + align:start position:0% +increase pretty much the same way that n + + + align:start position:0% +increase pretty much the same way that n +did and Z effective is going to increase + + align:start position:0% +did and Z effective is going to increase + + + align:start position:0% +did and Z effective is going to increase +and so the these are going up together + + align:start position:0% +and so the these are going up together + + + align:start position:0% +and so the these are going up together +and who wins well you you calibrate + + align:start position:0% +and who wins well you you calibrate + + + align:start position:0% +and who wins well you you calibrate +yourself and once you've calibrated + + align:start position:0% +yourself and once you've calibrated + + + align:start position:0% +yourself and once you've calibrated +yourself once going down a column you + + align:start position:0% +yourself once going down a column you + + + align:start position:0% +yourself once going down a column you +pretty much know that the energy the the + + align:start position:0% +pretty much know that the energy the the + + + align:start position:0% +pretty much know that the energy the the +first excited state tends to move down a + + align:start position:0% +first excited state tends to move down a + + + align:start position:0% +first excited state tends to move down a +little + + align:start position:0% +little + + + align:start position:0% +little +bit that's a harder decision than the + + align:start position:0% +bit that's a harder decision than the + + + align:start position:0% +bit that's a harder decision than the +first excited States moving up a lot as + + align:start position:0% +first excited States moving up a lot as + + + align:start position:0% +first excited States moving up a lot as +you follow an ISO electronic rather than + + align:start position:0% +you follow an ISO electronic rather than + + + align:start position:0% +you follow an ISO electronic rather than +an isov veence sequence but that's it + + align:start position:0% +an isov veence sequence but that's it + + + align:start position:0% +an isov veence sequence but that's it +that's all there is if there were only + + align:start position:0% +that's all there is if there were only + + + align:start position:0% +that's all there is if there were only +one orbital one + + align:start position:0% +one orbital one + + + align:start position:0% +one orbital one +state is is it clear that um going from + + align:start position:0% +state is is it clear that um going from + + + align:start position:0% +state is is it clear that um going from +potassium to ridium is a similar thing + + align:start position:0% +potassium to ridium is a similar thing + + + align:start position:0% +potassium to ridium is a similar thing +from going from calcium plus to strum + + align:start position:0% +from going from calcium plus to strum + + + align:start position:0% +from going from calcium plus to strum +plus yes why why why is + + align:start position:0% +plus yes why why why is + + + align:start position:0% +plus yes why why why is +it absolutely clear that at some + + align:start position:0% +it absolutely clear that at some + + + align:start position:0% +it absolutely clear that at some +point inar could dominate over that they + + align:start position:0% +point inar could dominate over that they + + + align:start position:0% +point inar could dominate over that they +that they could switch if you just make + + align:start position:0% +that they could switch if you just make + + + align:start position:0% +that they could switch if you just make +and start okay what what you would do is + + align:start position:0% +and start okay what what you would do is + + + align:start position:0% +and start okay what what you would do is +You' build a model you'd say okay as we + + align:start position:0% +You' build a model you'd say okay as we + + + align:start position:0% +You' build a model you'd say okay as we +fill a + + align:start position:0% +fill a + + + align:start position:0% +fill a +shell uh the charge on the nucleus has + + align:start position:0% +shell uh the charge on the nucleus has + + + align:start position:0% +shell uh the charge on the nucleus has +gone up and the shielding due to the fil + + align:start position:0% +gone up and the shielding due to the fil + + + align:start position:0% +gone up and the shielding due to the fil +you know each electron gets a certain + + align:start position:0% +you know each electron gets a certain + + + align:start position:0% +you know each electron gets a certain +fractional shielding and so you can + + align:start position:0% +fractional shielding and so you can + + + align:start position:0% +fractional shielding and so you can +build a model that ought to uh fit + + align:start position:0% +build a model that ought to uh fit + + + align:start position:0% +build a model that ought to uh fit +essentially all of the isoelectronic + + align:start position:0% +essentially all of the isoelectronic + + + align:start position:0% +essentially all of the isoelectronic +molecules so you could do potassium + + align:start position:0% +molecules so you could do potassium + + + align:start position:0% +molecules so you could do potassium +calcium plus uh Scandium 2+ Etc as you + + align:start position:0% +calcium plus uh Scandium 2+ Etc as you + + + align:start position:0% +calcium plus uh Scandium 2+ Etc as you +go across and you'd build a simple model + + align:start position:0% +go across and you'd build a simple model + + + align:start position:0% +go across and you'd build a simple model +and you'd have also want to describe so + + align:start position:0% +and you'd have also want to describe so + + + align:start position:0% +and you'd have also want to describe so +if anybody's outlier you say that's + + align:start position:0% +if anybody's outlier you say that's + + + align:start position:0% +if anybody's outlier you say that's +either interesting or + + align:start position:0% + + + + align:start position:0% + +wrong the ideas are you know we have + + align:start position:0% +wrong the ideas are you know we have + + + align:start position:0% +wrong the ideas are you know we have +orbitals and they are shielded by all of + + align:start position:0% +orbitals and they are shielded by all of + + + align:start position:0% +orbitals and they are shielded by all of +the filled orbitals and we're only + + align:start position:0% +the filled orbitals and we're only + + + align:start position:0% +the filled orbitals and we're only +putting one electron in an open shell + + align:start position:0% +putting one electron in an open shell + + + align:start position:0% +putting one electron in an open shell +and as a result we have really simple + + align:start position:0% +and as a result we have really simple + + + align:start position:0% +and as a result we have really simple +stuff unfortunately for atoms and + + align:start position:0% +stuff unfortunately for atoms and + + + align:start position:0% +stuff unfortunately for atoms and +molecules the world does not consist of + + align:start position:0% +molecules the world does not consist of + + + align:start position:0% +molecules the world does not consist of +one electron systems it's many electron + + align:start position:0% +one electron systems it's many electron + + + align:start position:0% +one electron systems it's many electron +systems and we somehow have to deal with + + align:start position:0% +systems and we somehow have to deal with + + + align:start position:0% +systems and we somehow have to deal with +that and so the the framework of this + + align:start position:0% +that and so the the framework of this + + + align:start position:0% +that and so the the framework of this +lecture is to show how do we build an + + align:start position:0% +lecture is to show how do we build an + + + align:start position:0% +lecture is to show how do we build an +effective + + align:start position:0% +effective + + + align:start position:0% +effective +hamiltonian which describes the + + align:start position:0% +hamiltonian which describes the + + + align:start position:0% +hamiltonian which describes the +electronic structure of many electron + + align:start position:0% +electronic structure of many electron + + + align:start position:0% +electronic structure of many electron +atoms and these provide us with guidance + + align:start position:0% +atoms and these provide us with guidance + + + align:start position:0% +atoms and these provide us with guidance +for what we are going to experience when + + align:start position:0% +for what we are going to experience when + + + align:start position:0% +for what we are going to experience when +we build effective hamiltonians for the + + align:start position:0% +we build effective hamiltonians for the + + + align:start position:0% +we build effective hamiltonians for the +electronic structure of molec + + align:start position:0% +electronic structure of molec + + + align:start position:0% +electronic structure of molec +ules and electr effective hamiltonians + + align:start position:0% +ules and electr effective hamiltonians + + + align:start position:0% +ules and electr effective hamiltonians +in + + align:start position:0% + + + + align:start position:0% + +general okay because the problem is + + align:start position:0% +general okay because the problem is + + + align:start position:0% +general okay because the problem is +calcium + + align:start position:0% +calcium + + + align:start position:0% +calcium +neutral has an electronic structure + + align:start position:0% +neutral has an electronic structure + + + align:start position:0% +neutral has an electronic structure +where the we know that the lowest + + align:start position:0% +where the we know that the lowest + + + align:start position:0% +where the we know that the lowest +electronic configuration is two + + align:start position:0% +electronic configuration is two + + + align:start position:0% +electronic configuration is two +electrons in s + + align:start position:0% + + + + align:start position:0% + +orbitals and then it has 4S + + align:start position:0% +orbitals and then it has 4S + + + align:start position:0% +orbitals and then it has 4S +uh 4 + + align:start position:0% +uh 4 + + + align:start position:0% +uh 4 +p and uh uh then + + align:start position:0% +p and uh uh then + + + align:start position:0% +p and uh uh then +uh there might be a higher you there are + + align:start position:0% +uh there might be a higher you there are + + + align:start position:0% +uh there might be a higher you there are +going to be higher configurations this + + align:start position:0% +going to be higher configurations this + + + align:start position:0% +going to be higher configurations this +is easy this just H gives rise to a + + align:start position:0% +is easy this just H gives rise to a + + + align:start position:0% +is easy this just H gives rise to a +singlet s State this gives rise to a + + align:start position:0% +singlet s State this gives rise to a + + + align:start position:0% +singlet s State this gives rise to a +singlet P State and a triplet P State + + align:start position:0% +singlet P State and a triplet P State + + + align:start position:0% +singlet P State and a triplet P State +how do I know that well that's the + + align:start position:0% +how do I know that well that's the + + + align:start position:0% +how do I know that well that's the +subject of this lecture but uh the + + align:start position:0% +subject of this lecture but uh the + + + align:start position:0% +subject of this lecture but uh the +lowly instead of one orbital one state + + align:start position:0% +lowly instead of one orbital one state + + + align:start position:0% +lowly instead of one orbital one state +we get a configuration several + + align:start position:0% +we get a configuration several + + + align:start position:0% +we get a configuration several +States and suppose we go to Scandium + + align:start position:0% +States and suppose we go to Scandium + + + align:start position:0% +States and suppose we go to Scandium +well then uh we might have uh 4S d^2 or + + align:start position:0% +well then uh we might have uh 4S d^2 or + + + align:start position:0% +well then uh we might have uh 4S d^2 or +3d2 or something like that and let me + + align:start position:0% +3d2 or something like that and let me + + + align:start position:0% +3d2 or something like that and let me +tell you d squ d squ gives rise to uh + + align:start position:0% +tell you d squ d squ gives rise to uh + + + align:start position:0% +tell you d squ d squ gives rise to uh +singlet G triplet F singlet D triplet P + + align:start position:0% +singlet G triplet F singlet D triplet P + + + align:start position:0% +singlet G triplet F singlet D triplet P +and siget S so it gives rise to all of + + align:start position:0% +and siget S so it gives rise to all of + + + align:start position:0% +and siget S so it gives rise to all of +these states and each of these states + + align:start position:0% +these states and each of these states + + + align:start position:0% +these states and each of these states +has spin uh spin + + align:start position:0% +has spin uh spin + + + align:start position:0% +has spin uh spin +components so what do we + + align:start position:0% +components so what do we + + + align:start position:0% +components so what do we +do how do we what why where where is + + align:start position:0% +do how do we what why where where is + + + align:start position:0% +do how do we what why where where is +periodicity how do we begin to + + align:start position:0% +periodicity how do we begin to + + + align:start position:0% +periodicity how do we begin to +understand how to make comparisons + + align:start position:0% +understand how to make comparisons + + + align:start position:0% +understand how to make comparisons +between calcium and Scandium when we + + align:start position:0% +between calcium and Scandium when we + + + align:start position:0% +between calcium and Scandium when we +don't even know what the metric is we + + align:start position:0% +don't even know what the metric is we + + + align:start position:0% +don't even know what the metric is we +don't know what to look at what do we + + align:start position:0% +don't know what to look at what do we + + + align:start position:0% +don't know what to look at what do we +get you know when there's many states + + align:start position:0% +get you know when there's many states + + + align:start position:0% +get you know when there's many states +coming from a + + align:start position:0% +coming from a + + + align:start position:0% +coming from a +configuration how do we decide how to + + align:start position:0% +configuration how do we decide how to + + + align:start position:0% +configuration how do we decide how to +impose periodicity on + + align:start position:0% +impose periodicity on + + + align:start position:0% +impose periodicity on +what so we need a model where the + + align:start position:0% +what so we need a model where the + + + align:start position:0% +what so we need a model where the +parameters in the model are + + align:start position:0% +parameters in the model are + + + align:start position:0% +parameters in the model are +interpretable have the periodicity that + + align:start position:0% +interpretable have the periodicity that + + + align:start position:0% +interpretable have the periodicity that +we can understand based on shielding and + + align:start position:0% +we can understand based on shielding and + + + align:start position:0% +we can understand based on shielding and +you know Trends and sizes and this model + + align:start position:0% +you know Trends and sizes and this model + + + align:start position:0% +you know Trends and sizes and this model +wants to be both qualitative and + + align:start position:0% + + + + align:start position:0% + +quantitative now this is really + + align:start position:0% +quantitative now this is really + + + align:start position:0% +quantitative now this is really +important and uh uh you know you know as + + align:start position:0% +important and uh uh you know you know as + + + align:start position:0% +important and uh uh you know you know as +soon as you start looking at tables of + + align:start position:0% +soon as you start looking at tables of + + + align:start position:0% +soon as you start looking at tables of +atomic energy levels you + + align:start position:0% +atomic energy levels you + + + align:start position:0% +atomic energy levels you +say this is really + + align:start position:0% +say this is really + + + align:start position:0% +say this is really +awful this is you know how could anybody + + align:start position:0% +awful this is you know how could anybody + + + align:start position:0% +awful this is you know how could anybody +make any sense out of this yes maybe I + + align:start position:0% +make any sense out of this yes maybe I + + + align:start position:0% +make any sense out of this yes maybe I +could assign the Spectrum but is it + + align:start position:0% +could assign the Spectrum but is it + + + align:start position:0% +could assign the Spectrum but is it +interesting is there anything that I can + + align:start position:0% +interesting is there anything that I can + + + align:start position:0% +interesting is there anything that I can +uh glean from these + + align:start position:0% + + + + align:start position:0% + +patterns well you know one thing you + + align:start position:0% +patterns well you know one thing you + + + align:start position:0% +patterns well you know one thing you +might do is say okay I can probably + + align:start position:0% +might do is say okay I can probably + + + align:start position:0% +might do is say okay I can probably +develop some rules they're called hun + + align:start position:0% +develop some rules they're called hun + + + align:start position:0% +develop some rules they're called hun +rules which once I write down a + + align:start position:0% +rules which once I write down a + + + align:start position:0% +rules which once I write down a +configuration I can write what are the + + align:start position:0% +configuration I can write what are the + + + align:start position:0% +configuration I can write what are the +ls terms that's what they're called that + + align:start position:0% +ls terms that's what they're called that + + + align:start position:0% +ls terms that's what they're called that +arise from that configuration and of + + align:start position:0% +arise from that configuration and of + + + align:start position:0% +arise from that configuration and of +those which one is the + + align:start position:0% +those which one is the + + + align:start position:0% +those which one is the +lowest and of those uh of the lowest one + + align:start position:0% +lowest and of those uh of the lowest one + + + align:start position:0% +lowest and of those uh of the lowest one +which J is the lowest so those are the + + align:start position:0% +which J is the lowest so those are the + + + align:start position:0% +which J is the lowest so those are the +Hun's three rules and so you could say + + align:start position:0% +Hun's three rules and so you could say + + + align:start position:0% +Hun's three rules and so you could say +well I'm going to try to impose + + align:start position:0% +well I'm going to try to impose + + + align:start position:0% +well I'm going to try to impose +periodicity by just deciding what's the + + align:start position:0% +periodicity by just deciding what's the + + + align:start position:0% +periodicity by just deciding what's the +lowest energy lsj energy level of a + + align:start position:0% +lowest energy lsj energy level of a + + + align:start position:0% +lowest energy lsj energy level of a +configuration well that wouldn't get you + + align:start position:0% +configuration well that wouldn't get you + + + align:start position:0% +configuration well that wouldn't get you +very + + align:start position:0% +very + + + align:start position:0% +very +far because sometimes the uh the lsj + + align:start position:0% +far because sometimes the uh the lsj + + + align:start position:0% +far because sometimes the uh the lsj +terms are very widely spread and then + + align:start position:0% +terms are very widely spread and then + + + align:start position:0% +terms are very widely spread and then +the next one they're not so widely + + align:start position:0% +the next one they're not so widely + + + align:start position:0% +the next one they're not so widely +spread the the it might be sensible to + + align:start position:0% +spread the the it might be sensible to + + + align:start position:0% +spread the the it might be sensible to +say okay I've got a configuration let's + + align:start position:0% +say okay I've got a configuration let's + + + align:start position:0% +say okay I've got a configuration let's +let's calculate the degeneracy weighted + + align:start position:0% +let's calculate the degeneracy weighted + + + align:start position:0% +let's calculate the degeneracy weighted +average energy of the + + align:start position:0% +average energy of the + + + align:start position:0% +average energy of the +configuration but that requires knowing + + align:start position:0% +configuration but that requires knowing + + + align:start position:0% +configuration but that requires knowing +a lot and often all states of a + + align:start position:0% +a lot and often all states of a + + + align:start position:0% +a lot and often all states of a +configuration aren't observable so + + align:start position:0% +configuration aren't observable so + + + align:start position:0% +configuration aren't observable so +that's not a good thing either so what + + align:start position:0% +that's not a good thing either so what + + + align:start position:0% +that's not a good thing either so what +we need is a way of describing the + + align:start position:0% +we need is a way of describing the + + + align:start position:0% +we need is a way of describing the +states of something that's just a little + + align:start position:0% +states of something that's just a little + + + align:start position:0% +states of something that's just a little +bit complicated in terms of + + align:start position:0% +bit complicated in terms of + + + align:start position:0% +bit complicated in terms of +parameters which we can + + align:start position:0% +parameters which we can + + + align:start position:0% +parameters which we can +understand and this is why I love this + + align:start position:0% +understand and this is why I love this + + + align:start position:0% +understand and this is why I love this +lecture or this topic but you know I + + align:start position:0% +lecture or this topic but you know I + + + align:start position:0% +lecture or this topic but you know I +can't do justice to it because you know + + align:start position:0% +can't do justice to it because you know + + + align:start position:0% +can't do justice to it because you know +if I I did you would probably all need + + align:start position:0% +if I I did you would probably all need + + + align:start position:0% +if I I did you would probably all need +to spend a week at + + align:start position:0% + + + + align:start position:0% + +McLean's all right so let me give sort + + align:start position:0% +McLean's all right so let me give sort + + + align:start position:0% +McLean's all right so let me give sort +of an outline of of what we + + align:start position:0% + + + + align:start position:0% + +do we take an atom and we would we would + + align:start position:0% +do we take an atom and we would we would + + + align:start position:0% +do we take an atom and we would we would +do the same thing for a molecule I just + + align:start position:0% +do the same thing for a molecule I just + + + align:start position:0% +do the same thing for a molecule I just +haven't taught that to you yet we start + + align:start position:0% +haven't taught that to you yet we start + + + align:start position:0% +haven't taught that to you yet we start +we know what the atom is and we write + + align:start position:0% +we know what the atom is and we write + + + align:start position:0% +we know what the atom is and we write +the + + align:start position:0% +the + + + align:start position:0% +the +list + + align:start position:0% +list + + + align:start position:0% +list +of orbital + + align:start position:0% + + + + align:start position:0% + +occupancies we know how to do that from + + align:start position:0% +occupancies we know how to do that from + + + align:start position:0% +occupancies we know how to do that from +freshman chemistry we know alal and so + + align:start position:0% +freshman chemistry we know alal and so + + + align:start position:0% +freshman chemistry we know alal and so +you know we we can pretty much guess the + + align:start position:0% +you know we we can pretty much guess the + + + align:start position:0% +you know we we can pretty much guess the +orbital occupancies of the lowest lying + + align:start position:0% +orbital occupancies of the lowest lying + + + align:start position:0% +orbital occupancies of the lowest lying +state of any atom and that's called the + + align:start position:0% +state of any atom and that's called the + + + align:start position:0% +state of any atom and that's called the +electronic + + align:start position:0% + + + + align:start position:0% + +configuration and you could also uh + + align:start position:0% +configuration and you could also uh + + + align:start position:0% +configuration and you could also uh +write + + align:start position:0% +write + + + align:start position:0% +write +configurations that are likely to be + + align:start position:0% +configurations that are likely to be + + + align:start position:0% +configurations that are likely to be +excited but relatively low-lying + + align:start position:0% +excited but relatively low-lying + + + align:start position:0% +excited but relatively low-lying +and you're going to want to do that + + align:start position:0% +and you're going to want to do that + + + align:start position:0% +and you're going to want to do that +anyway because if you're going to be + + align:start position:0% +anyway because if you're going to be + + + align:start position:0% +anyway because if you're going to be +observing a spectrum you're going to be + + align:start position:0% +observing a spectrum you're going to be + + + align:start position:0% +observing a spectrum you're going to be +observing transitions between states + + align:start position:0% +observing transitions between states + + + align:start position:0% +observing transitions between states +belonging to two different + + align:start position:0% +belonging to two different + + + align:start position:0% +belonging to two different +configurations and so you're going to + + align:start position:0% +configurations and so you're going to + + + align:start position:0% +configurations and so you're going to +have to somehow use freshman chemistry + + align:start position:0% +have to somehow use freshman chemistry + + + align:start position:0% +have to somehow use freshman chemistry +ideas to say okay we have this + + align:start position:0% +ideas to say okay we have this + + + align:start position:0% +ideas to say okay we have this +configuration and this configuration and + + align:start position:0% +configuration and this configuration and + + + align:start position:0% +configuration and this configuration and +this one and this one that's probably + + align:start position:0% +this one and this one that's probably + + + align:start position:0% +this one and this one that's probably +enough to figure out what's going on + + align:start position:0% +enough to figure out what's going on + + + align:start position:0% +enough to figure out what's going on +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +okay once you have that you want to know + + align:start position:0% +okay once you have that you want to know + + + align:start position:0% +okay once you have that you want to know +what LS + + align:start position:0% +what LS + + + align:start position:0% +what LS +terms + + align:start position:0% +terms + + + align:start position:0% +terms +arise and this is this is a topic that + + align:start position:0% +arise and this is this is a topic that + + + align:start position:0% +arise and this is this is a topic that +is usually taught in an inorganic + + align:start position:0% +is usually taught in an inorganic + + + align:start position:0% +is usually taught in an inorganic +chemistry course and it's taught in a + + align:start position:0% +chemistry course and it's taught in a + + + align:start position:0% +chemistry course and it's taught in a +very obscure way it says this is what + + align:start position:0% +very obscure way it says this is what + + + align:start position:0% +very obscure way it says this is what +you do why you do it well I can't tell + + align:start position:0% +you do why you do it well I can't tell + + + align:start position:0% +you do why you do it well I can't tell +you that because that's too much such an + + align:start position:0% +you that because that's too much such an + + + align:start position:0% +you that because that's too much such an +Advan topic but I'm going to test you on + + align:start position:0% +Advan topic but I'm going to test you on + + + align:start position:0% +Advan topic but I'm going to test you on +it and you're going to have to learn + + align:start position:0% +it and you're going to have to learn + + + align:start position:0% +it and you're going to have to learn +this method of mlms + + align:start position:0% + + + + align:start position:0% + +boxes and that bookkeeping method which + + align:start position:0% +boxes and that bookkeeping method which + + + align:start position:0% +boxes and that bookkeeping method which +maybe some most of you have seen but not + + align:start position:0% +maybe some most of you have seen but not + + + align:start position:0% +maybe some most of you have seen but not +everybody that it used to be always + + align:start position:0% +everybody that it used to be always + + + align:start position:0% +everybody that it used to be always +taught even in quantum mechanics courses + + align:start position:0% +taught even in quantum mechanics courses + + + align:start position:0% +taught even in quantum mechanics courses +but you know that uh 30 years ago it's + + align:start position:0% +but you know that uh 30 years ago it's + + + align:start position:0% +but you know that uh 30 years ago it's +dropped out of quantum mechanics and was + + align:start position:0% +dropped out of quantum mechanics and was + + + align:start position:0% +dropped out of quantum mechanics and was +left in inorganic I don't know what + + align:start position:0% +left in inorganic I don't know what + + + align:start position:0% +left in inorganic I don't know what +you've seen that in in organic right y + + align:start position:0% +you've seen that in in organic right y + + + align:start position:0% +you've seen that in in organic right y +yeah and probably everybody has uh so + + align:start position:0% +yeah and probably everybody has uh so + + + align:start position:0% +yeah and probably everybody has uh so +what is this well what's going on here + + align:start position:0% +what is this well what's going on here + + + align:start position:0% +what is this well what's going on here +ml is the IG value associated with the + + align:start position:0% +ml is the IG value associated with the + + + align:start position:0% +ml is the IG value associated with the +operator LZ and Ms is the IG value + + align:start position:0% +operator LZ and Ms is the IG value + + + align:start position:0% +operator LZ and Ms is the IG value +associated with the operator + + align:start position:0% +associated with the operator + + + align:start position:0% +associated with the operator +SZ and + + align:start position:0% +SZ and + + + align:start position:0% +SZ and +u l s + + align:start position:0% +u l s + + + align:start position:0% +u l s +LZ s s + + align:start position:0% +LZ s s + + + align:start position:0% +LZ s s +SZ are a mutually commuting set of + + align:start position:0% +SZ are a mutually commuting set of + + + align:start position:0% +SZ are a mutually commuting set of +operators which also commute with the uh + + align:start position:0% +operators which also commute with the uh + + + align:start position:0% +operators which also commute with the uh +electronic hamiltonian but not the spin + + align:start position:0% +electronic hamiltonian but not the spin + + + align:start position:0% +electronic hamiltonian but not the spin +orbit + + align:start position:0% + + + + align:start position:0% + +hamiltonian so that means that we can + + align:start position:0% +hamiltonian so that means that we can + + + align:start position:0% +hamiltonian so that means that we can +write basis functions of the electronic + + align:start position:0% +write basis functions of the electronic + + + align:start position:0% +write basis functions of the electronic +hamiltonian uh that are expressed in + + align:start position:0% +hamiltonian uh that are expressed in + + + align:start position:0% +hamiltonian uh that are expressed in +terms of the quantum numbers associated + + align:start position:0% +terms of the quantum numbers associated + + + align:start position:0% +terms of the quantum numbers associated +with the igen values of these operators + + align:start position:0% +with the igen values of these operators + + + align:start position:0% +with the igen values of these operators +that the we can label + + align:start position:0% +that the we can label + + + align:start position:0% +that the we can label +things and so what we're doing is we're + + align:start position:0% +things and so what we're doing is we're + + + align:start position:0% +things and so what we're doing is we're +somehow discovering some good quantum + + align:start position:0% +somehow discovering some good quantum + + + align:start position:0% +somehow discovering some good quantum +numbers ml Ms L and S they're good + + align:start position:0% +numbers ml Ms L and S they're good + + + align:start position:0% +numbers ml Ms L and S they're good +enough excluding spin orbit uh that we + + align:start position:0% +enough excluding spin orbit uh that we + + + align:start position:0% +enough excluding spin orbit uh that we +can uh simplify the electronic + + align:start position:0% +can uh simplify the electronic + + + align:start position:0% +can uh simplify the electronic +hamiltonian and we know that little M + + align:start position:0% +hamiltonian and we know that little M + + + align:start position:0% +hamiltonian and we know that little M +subel and Little M subs and little L + + align:start position:0% +subel and Little M subs and little L + + + align:start position:0% +subel and Little M subs and little L +those are not good quantum numbers of + + align:start position:0% +those are not good quantum numbers of + + + align:start position:0% +those are not good quantum numbers of +the electronic + + align:start position:0% +the electronic + + + align:start position:0% +the electronic +hamiltonian because of our friend 1 over + + align:start position:0% +hamiltonian because of our friend 1 over + + + align:start position:0% +hamiltonian because of our friend 1 over +r j the inter electronic + + align:start position:0% + + + + align:start position:0% + +repulsive and + + align:start position:0% + + + + align:start position:0% + +uh I could say a lot about this but I + + align:start position:0% +uh I could say a lot about this but I + + + align:start position:0% +uh I could say a lot about this but I +think I shouldn't because I I think I + + align:start position:0% +think I shouldn't because I I think I + + + align:start position:0% +think I shouldn't because I I think I +want to give you the big + + align:start position:0% +want to give you the big + + + align:start position:0% +want to give you the big +picture uh but you know this is you've + + align:start position:0% +picture uh but you know this is you've + + + align:start position:0% +picture uh but you know this is you've +got me here you know if you want to ask + + align:start position:0% +got me here you know if you want to ask + + + align:start position:0% +got me here you know if you want to ask +questions I really know more more than + + align:start position:0% +questions I really know more more than + + + align:start position:0% +questions I really know more more than +probably anybody at MIT about atomic + + align:start position:0% +probably anybody at MIT about atomic + + + align:start position:0% +probably anybody at MIT about atomic +structure and how you reduce that to uh + + align:start position:0% +structure and how you reduce that to uh + + + align:start position:0% +structure and how you reduce that to uh +many electron uh to to uh effective + + align:start position:0% +many electron uh to to uh effective + + + align:start position:0% +many electron uh to to uh effective +hamiltonians it's just not taught + + align:start position:0% +hamiltonians it's just not taught + + + align:start position:0% +hamiltonians it's just not taught +anymore + + align:start position:0% +anymore + + + align:start position:0% +anymore +um okay + + align:start position:0% + + + + align:start position:0% + +so if + + align:start position:0% +so if + + + align:start position:0% +so if +we look at the the possible values of M + + align:start position:0% +we look at the the possible values of M + + + align:start position:0% +we look at the the possible values of M +sub l and m sub + + align:start position:0% +sub l and m sub + + + align:start position:0% +sub l and m sub +L is the sum over + + align:start position:0% +L is the sum over + + + align:start position:0% +L is the sum over +electrons of Little M + + align:start position:0% + + + + align:start position:0% + +subel and so if I say we have a + + align:start position:0% +subel and so if I say we have a + + + align:start position:0% +subel and so if I say we have a +configuration D + + align:start position:0% +configuration D + + + align:start position:0% +configuration D +Squared well D can have m + + align:start position:0% +Squared well D can have m + + + align:start position:0% +Squared well D can have m +subel 2 1 0 -1 -2 these are the possible + + align:start position:0% +subel 2 1 0 -1 -2 these are the possible + + + align:start position:0% +subel 2 1 0 -1 -2 these are the possible +values of M sub + + align:start position:0% +values of M sub + + + align:start position:0% +values of M sub +l and m + + align:start position:0% +l and m + + + align:start position:0% +l and m +Subs can have values plus a half and + + align:start position:0% +Subs can have values plus a half and + + + align:start position:0% +Subs can have values plus a half and +minus a half and + + align:start position:0% + + + + align:start position:0% + +so these 10 + + align:start position:0% +so these 10 + + + align:start position:0% +so these 10 +symbols correspond to labels of spin + + align:start position:0% +symbols correspond to labels of spin + + + align:start position:0% +symbols correspond to labels of spin +orbitals which are basis functions which + + align:start position:0% +orbitals which are basis functions which + + + align:start position:0% +orbitals which are basis functions which +are are our basis + + align:start position:0% +are are our basis + + + align:start position:0% +are are our basis +functions so everything is going to be + + align:start position:0% +functions so everything is going to be + + + align:start position:0% +functions so everything is going to be +expressed in terms + + align:start position:0% + + + + align:start position:0% + +of States involving two of these at a + + align:start position:0% +of States involving two of these at a + + + align:start position:0% +of States involving two of these at a +time because we say it's + + align:start position:0% +time because we say it's + + + align:start position:0% +time because we say it's +d^2 so we have to pick two of + + align:start position:0% +d^2 so we have to pick two of + + + align:start position:0% +d^2 so we have to pick two of +these and if you pick two of these you + + align:start position:0% +these and if you pick two of these you + + + align:start position:0% +these and if you pick two of these you +immediately Know M subel capital M subel + + align:start position:0% +immediately Know M subel capital M subel + + + align:start position:0% +immediately Know M subel capital M subel +the total number the total projection of + + align:start position:0% +the total number the total projection of + + + align:start position:0% +the total number the total projection of +the + + align:start position:0% +the + + + align:start position:0% +the +orbital angular momentum on Z and M subs + + align:start position:0% +orbital angular momentum on Z and M subs + + + align:start position:0% +orbital angular momentum on Z and M subs +any2 and so that says well why don't we + + align:start position:0% +any2 and so that says well why don't we + + + align:start position:0% +any2 and so that says well why don't we +do that then why don't we just somehow + + align:start position:0% +do that then why don't we just somehow + + + align:start position:0% +do that then why don't we just somehow +pick the various possible combinations + + align:start position:0% +pick the various possible combinations + + + align:start position:0% +pick the various possible combinations +of these and we know okay we got 10 of + + align:start position:0% +of these and we know okay we got 10 of + + + align:start position:0% +of these and we know okay we got 10 of +these and how many combinations can + + align:start position:0% +these and how many combinations can + + + align:start position:0% +these and how many combinations can +there be well there's 10 * 9 over 2 + + align:start position:0% +there be well there's 10 * 9 over 2 + + + align:start position:0% +there be well there's 10 * 9 over 2 +because of the Exclusion + + align:start position:0% +because of the Exclusion + + + align:start position:0% +because of the Exclusion +Principle we don't know what the you + + align:start position:0% +Principle we don't know what the you + + + align:start position:0% +Principle we don't know what the you +know in inorganic chemistry when this is + + align:start position:0% +know in inorganic chemistry when this is + + + align:start position:0% +know in inorganic chemistry when this is +taught the Exclusion Principle is + + align:start position:0% +taught the Exclusion Principle is + + + align:start position:0% +taught the Exclusion Principle is +basically said you can't put two + + align:start position:0% +basically said you can't put two + + + align:start position:0% +basically said you can't put two +electrons into the same spin orbital + + align:start position:0% +electrons into the same spin orbital + + + align:start position:0% +electrons into the same spin orbital +that's + + align:start position:0% +that's + + + align:start position:0% +that's +it but there's something deeper behind + + align:start position:0% +it but there's something deeper behind + + + align:start position:0% +it but there's something deeper behind +that but anyway you know how to + + align:start position:0% +that but anyway you know how to + + + align:start position:0% +that but anyway you know how to +calculate the degeneracy 10 choices + + align:start position:0% +calculate the degeneracy 10 choices + + + align:start position:0% +calculate the degeneracy 10 choices +one's used up now nine choices didn't + + align:start position:0% +one's used up now nine choices didn't + + + align:start position:0% +one's used up now nine choices didn't +matter which order you filled it so 45 + + align:start position:0% +matter which order you filled it so 45 + + + align:start position:0% +matter which order you filled it so 45 +there are 45 possible mels and ms's so + + align:start position:0% +there are 45 possible mels and ms's so + + + align:start position:0% +there are 45 possible mels and ms's so +we we do this silly game of uh m L + + align:start position:0% +we we do this silly game of uh m L + + + align:start position:0% +we we do this silly game of uh m L +Ms + + align:start position:0% +Ms + + + align:start position:0% +Ms +and we could be really anal about it and + + align:start position:0% +and we could be really anal about it and + + + align:start position:0% +and we could be really anal about it and +go from the maximum possible value of + + align:start position:0% +go from the maximum possible value of + + + align:start position:0% +go from the maximum possible value of +mvl which is four down to the minimum + + align:start position:0% +mvl which is four down to the minimum + + + align:start position:0% +mvl which is four down to the minimum +possible value which is minus 4 and M of + + align:start position:0% +possible value which is minus 4 and M of + + + align:start position:0% +possible value which is minus 4 and M of +s from 1 to minus1 and there would be 45 + + align:start position:0% +s from 1 to minus1 and there would be 45 + + + align:start position:0% +s from 1 to minus1 and there would be 45 +boxes to fill in but we all you know + + align:start position:0% +boxes to fill in but we all you know + + + align:start position:0% +boxes to fill in but we all you know +we're told don't do that just take one + + align:start position:0% +we're told don't do that just take one + + + align:start position:0% +we're told don't do that just take one +of the you know take the uh this subset + + align:start position:0% +of the you know take the uh this subset + + + align:start position:0% +of the you know take the uh this subset +4 3 2 1 zero and fill out that corner of + + align:start position:0% +4 3 2 1 zero and fill out that corner of + + + align:start position:0% +4 3 2 1 zero and fill out that corner of +the table that's going to be enough and + + align:start position:0% +the table that's going to be enough and + + + align:start position:0% +the table that's going to be enough and +then there's there ensues the magic + + align:start position:0% +then there's there ensues the magic + + + align:start position:0% +then there's there ensues the magic +Crossing out of + + align:start position:0% +Crossing out of + + + align:start position:0% +Crossing out of +boxes and from that you do you determine + + align:start position:0% +boxes and from that you do you determine + + + align:start position:0% +boxes and from that you do you determine +the allowed values of mvl and M ofs and + + align:start position:0% +the allowed values of mvl and M ofs and + + + align:start position:0% +the allowed values of mvl and M ofs and +I just can't believe that this has been + + align:start position:0% +I just can't believe that this has been + + + align:start position:0% +I just can't believe that this has been +taught to almost every chemist for hund + + align:start position:0% +taught to almost every chemist for hund + + + align:start position:0% +taught to almost every chemist for hund +100 years and you know nobody + + align:start position:0% +100 years and you know nobody + + + align:start position:0% +100 years and you know nobody +understands what this + + align:start position:0% +understands what this + + + align:start position:0% +understands what this +is and I hope that when we're done you + + align:start position:0% +is and I hope that when we're done you + + + align:start position:0% +is and I hope that when we're done you +will understand + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +because L2 LZ s s SZ commute with the + + align:start position:0% +because L2 LZ s s SZ commute with the + + + align:start position:0% +because L2 LZ s s SZ commute with the +hamiltonian the electronic + + align:start position:0% +hamiltonian the electronic + + + align:start position:0% +hamiltonian the electronic +hamiltonian it says that there are going + + align:start position:0% +hamiltonian it says that there are going + + + align:start position:0% +hamiltonian it says that there are going +to be States labeled by these the + + align:start position:0% +to be States labeled by these the + + + align:start position:0% +to be States labeled by these the +quantum numbers associated with them and + + align:start position:0% +quantum numbers associated with them and + + + align:start position:0% +quantum numbers associated with them and +if we're entitled to have a particular + + align:start position:0% +if we're entitled to have a particular + + + align:start position:0% +if we're entitled to have a particular +value of L ands then there are going to + + align:start position:0% +value of L ands then there are going to + + + align:start position:0% +value of L ands then there are going to +be 2 L + 1 * 2 s + + + align:start position:0% +be 2 L + 1 * 2 s + + + + align:start position:0% +be 2 L + 1 * 2 s + +1 States associated with you're going to + + align:start position:0% +1 States associated with you're going to + + + align:start position:0% +1 States associated with you're going to +get the full LS term not a part of it + + align:start position:0% +get the full LS term not a part of it + + + align:start position:0% +get the full LS term not a part of it +that's a little harder for me to + + align:start position:0% +that's a little harder for me to + + + align:start position:0% +that's a little harder for me to + around but it's true you're + + align:start position:0% + around but it's true you're + + + align:start position:0% + around but it's true you're +entitled to get them all and that's why + + align:start position:0% +entitled to get them all and that's why + + + align:start position:0% +entitled to get them all and that's why +this method of boxes + + align:start position:0% +this method of boxes + + + align:start position:0% +this method of boxes +works but it's you know it's a lot of + + align:start position:0% +works but it's you know it's a lot of + + + align:start position:0% +works but it's you know it's a lot of +work for very little because you really + + align:start position:0% +work for very little because you really + + + align:start position:0% +work for very little because you really +do want to know what possible LS terms + + align:start position:0% +do want to know what possible LS terms + + + align:start position:0% +do want to know what possible LS terms +arise but you could also look them up in + + align:start position:0% +arise but you could also look them up in + + + align:start position:0% +arise but you could also look them up in +condent shortly or Tink them or some + + align:start position:0% +condent shortly or Tink them or some + + + align:start position:0% +condent shortly or Tink them or some +some book and after a little bit of + + align:start position:0% +some book and after a little bit of + + + align:start position:0% +some book and after a little bit of +looking at this you can get the idea + + align:start position:0% +looking at this you can get the idea + + + align:start position:0% +looking at this you can get the idea +that as long as you have no more than + + align:start position:0% +that as long as you have no more than + + + align:start position:0% +that as long as you have no more than +three electrons or three holes in a + + align:start position:0% +three electrons or three holes in a + + + align:start position:0% +three electrons or three holes in a +particular shell you can figure it all + + align:start position:0% +particular shell you can figure it all + + + align:start position:0% +particular shell you can figure it all +out and if there's electrons in + + align:start position:0% +out and if there's electrons in + + + align:start position:0% +out and if there's electrons in +different + + align:start position:0% +different + + + align:start position:0% +different +L's that makes it easy iier rather than + + align:start position:0% +L's that makes it easy iier rather than + + + align:start position:0% +L's that makes it easy iier rather than +harder so it's not a big deal you could + + align:start position:0% +harder so it's not a big deal you could + + + align:start position:0% +harder so it's not a big deal you could +probably learn that better than uh this + + align:start position:0% +probably learn that better than uh this + + + align:start position:0% +probably learn that better than uh this +method of boxes which is something that + + align:start position:0% +method of boxes which is something that + + + align:start position:0% +method of boxes which is something that +occupies space in your brain that could + + align:start position:0% +occupies space in your brain that could + + + align:start position:0% +occupies space in your brain that could +be used for other things um okay so we + + align:start position:0% +be used for other things um okay so we + + + align:start position:0% +be used for other things um okay so we +have this method of boxes and we find + + align:start position:0% +have this method of boxes and we find + + + align:start position:0% +have this method of boxes and we find +out what the L's and S is for molecules + + align:start position:0% +out what the L's and S is for molecules + + + align:start position:0% +out what the L's and S is for molecules +you have to do the same sort of thing + + align:start position:0% +you have to do the same sort of thing + + + align:start position:0% +you have to do the same sort of thing +but the worst case you have for a + + align:start position:0% +but the worst case you have for a + + + align:start position:0% +but the worst case you have for a +molecule is an orbital that can have + + align:start position:0% +molecule is an orbital that can have + + + align:start position:0% +molecule is an orbital that can have +four electrons in it Pi orbitals or + + align:start position:0% +four electrons in it Pi orbitals or + + + align:start position:0% +four electrons in it Pi orbitals or +Delta + + align:start position:0% +Delta + + + align:start position:0% +Delta +orbitals and so and since holes are + + align:start position:0% +orbitals and so and since holes are + + + align:start position:0% +orbitals and so and since holes are +equivalent to electrons the worst case + + align:start position:0% +equivalent to electrons the worst case + + + align:start position:0% +equivalent to electrons the worst case +you'd ever encounter would be Delta + + align:start position:0% +you'd ever encounter would be Delta + + + align:start position:0% +you'd ever encounter would be Delta +squar or pi^ squar and that's easy so + + align:start position:0% +squar or pi^ squar and that's easy so + + + align:start position:0% +squar or pi^ squar and that's easy so +the you know the stuff we do with atoms + + align:start position:0% +the you know the stuff we do with atoms + + + align:start position:0% +the you know the stuff we do with atoms +is a lot harder than what we do for + + align:start position:0% +is a lot harder than what we do for + + + align:start position:0% +is a lot harder than what we do for +molecules and so there are just a few + + align:start position:0% +molecules and so there are just a few + + + align:start position:0% +molecules and so there are just a few +things you need to remember and you've + + align:start position:0% +things you need to remember and you've + + + align:start position:0% +things you need to remember and you've +got this completely + + align:start position:0% +got this completely + + + align:start position:0% +got this completely +knocked Okay so so we can work out for a + + align:start position:0% +knocked Okay so so we can work out for a + + + align:start position:0% +knocked Okay so so we can work out for a +particular configuration what are the ls + + align:start position:0% +particular configuration what are the ls + + + align:start position:0% +particular configuration what are the ls +terms and then our job really begins not + + align:start position:0% +terms and then our job really begins not + + + align:start position:0% +terms and then our job really begins not +ends as it does in inorganic chemistry + + align:start position:0% +ends as it does in inorganic chemistry + + + align:start position:0% +ends as it does in inorganic chemistry +in in inorganic chemistry you do this + + align:start position:0% +in in inorganic chemistry you do this + + + align:start position:0% +in in inorganic chemistry you do this +and you say okay which is the lowest one + + align:start position:0% +and you say okay which is the lowest one + + + align:start position:0% +and you say okay which is the lowest one +and now we'll stick it into an + + align:start position:0% +and now we'll stick it into an + + + align:start position:0% +and now we'll stick it into an +octahedral or a + + align:start position:0% +octahedral or a + + + align:start position:0% +octahedral or a +tetrahedral environment and that'll + + align:start position:0% +tetrahedral environment and that'll + + + align:start position:0% +tetrahedral environment and that'll +split according to ligan field Theory + + align:start position:0% +split according to ligan field Theory + + + align:start position:0% +split according to ligan field Theory +and that tells us the electronic + + align:start position:0% +and that tells us the electronic + + + align:start position:0% +and that tells us the electronic +structure that we care about so all this + + align:start position:0% +structure that we care about so all this + + + align:start position:0% +structure that we care about so all this +work to determine a few low-lying States + + align:start position:0% +work to determine a few low-lying States + + + align:start position:0% +work to determine a few low-lying States +and okay but we don't do that we're + + align:start position:0% +and okay but we don't do that we're + + + align:start position:0% +and okay but we don't do that we're +we're not going to put this in + + align:start position:0% +we're not going to put this in + + + align:start position:0% +we're not going to put this in +a a lattice or anything like that we're + + align:start position:0% +a a lattice or anything like that we're + + + align:start position:0% +a a lattice or anything like that we're +it's in the gas phase okay and we would + + align:start position:0% +it's in the gas phase okay and we would + + + align:start position:0% +it's in the gas phase okay and we would +like to be able to describe all of the + + align:start position:0% +like to be able to describe all of the + + + align:start position:0% +like to be able to describe all of the +energy levels of the states that come + + align:start position:0% +energy levels of the states that come + + + align:start position:0% +energy levels of the states that come +from a particular + + align:start position:0% + + + + align:start position:0% + +configuration + + align:start position:0% +configuration + + + align:start position:0% +configuration +so the method of boxes tells us which LS + + align:start position:0% +so the method of boxes tells us which LS + + + align:start position:0% +so the method of boxes tells us which LS +States but what we really want is how to + + align:start position:0% +States but what we really want is how to + + + align:start position:0% +States but what we really want is how to +write things + + align:start position:0% + + + + align:start position:0% + +like + + align:start position:0% +like + + + align:start position:0% +like +this as some kind of linear combination + + align:start position:0% +this as some kind of linear combination + + + align:start position:0% +this as some kind of linear combination +of the terms that are in the + + align:start position:0% +of the terms that are in the + + + align:start position:0% +of the terms that are in the +boxes the pairs of spin + + align:start position:0% +boxes the pairs of spin + + + align:start position:0% +boxes the pairs of spin +orbitals now we get the Exclusion + + align:start position:0% +orbitals now we get the Exclusion + + + align:start position:0% +orbitals now we get the Exclusion +Principle the poly principle uh says + + align:start position:0% +Principle the poly principle uh says + + + align:start position:0% +Principle the poly principle uh says +that the wave function is antisymmetric + + align:start position:0% +that the wave function is antisymmetric + + + align:start position:0% +that the wave function is antisymmetric +with respect to permutation of any two + + align:start position:0% +with respect to permutation of any two + + + align:start position:0% +with respect to permutation of any two +electrons because electrons are fans + + align:start position:0% +electrons because electrons are fans + + + align:start position:0% +electrons because electrons are fans +this other thing is just a special case + + align:start position:0% +this other thing is just a special case + + + align:start position:0% +this other thing is just a special case +of it and so how can we possibly write a + + align:start position:0% +of it and so how can we possibly write a + + + align:start position:0% +of it and so how can we possibly write a +wave function which is antisymmetric + + align:start position:0% +wave function which is antisymmetric + + + align:start position:0% +wave function which is antisymmetric +with respect to all pairs of electrons + + align:start position:0% +with respect to all pairs of electrons + + + align:start position:0% +with respect to all pairs of electrons +and the answer is stupid write a + + align:start position:0% +and the answer is stupid write a + + + align:start position:0% +and the answer is stupid write a +determinant because you per you know + + align:start position:0% +determinant because you per you know + + + align:start position:0% +determinant because you per you know +permute the rows and Columns of a + + align:start position:0% +permute the rows and Columns of a + + + align:start position:0% +permute the rows and Columns of a +terminant and changes sign that's what + + align:start position:0% +terminant and changes sign that's what + + + align:start position:0% +terminant and changes sign that's what +we mean by anti-symmetric and so we get + + align:start position:0% +we mean by anti-symmetric and so we get + + + align:start position:0% +we mean by anti-symmetric and so we get +what are called Slater + + align:start position:0% + + + + align:start position:0% + +determinants and if I'm not mistaken + + align:start position:0% +determinants and if I'm not mistaken + + + align:start position:0% +determinants and if I'm not mistaken +this room was probably Slater + + align:start position:0% +this room was probably Slater + + + align:start position:0% +this room was probably Slater +office a long time ago he was an MIT + + align:start position:0% +office a long time ago he was an MIT + + + align:start position:0% +office a long time ago he was an MIT +faculty member and he did hang out in + + align:start position:0% +faculty member and he did hang out in + + + align:start position:0% +faculty member and he did hang out in +these parts it could have been his + + align:start position:0% +these parts it could have been his + + + align:start position:0% +these parts it could have been his +office and uh um but anyway A Slater + + align:start position:0% +office and uh um but anyway A Slater + + + align:start position:0% +office and uh um but anyway A Slater +determined so A Slater determin is just + + align:start position:0% +determined so A Slater determin is just + + + align:start position:0% +determined so A Slater determin is just +an anti- symmetrized collection of spin + + align:start position:0% +an anti- symmetrized collection of spin + + + align:start position:0% +an anti- symmetrized collection of spin +orbitals and we label it uh if it were P + + align:start position:0% +orbitals and we label it uh if it were P + + + align:start position:0% +orbitals and we label it uh if it were P +squ we we would label it say one uh uh + + align:start position:0% +squ we we would label it say one uh uh + + + align:start position:0% +squ we we would label it say one uh uh +one bar + + align:start position:0% + + + + align:start position:0% + +so that would be M sub L of 1 M sub L of + + align:start position:0% +so that would be M sub L of 1 M sub L of + + + align:start position:0% +so that would be M sub L of 1 M sub L of +1 M subs of a half M subs of minus a + + align:start position:0% +1 M subs of a half M subs of minus a + + + align:start position:0% +1 M subs of a half M subs of minus a +half so that's + + align:start position:0% +half so that's + + + align:start position:0% +half so that's +ml2 Ms = + + align:start position:0% +ml2 Ms = + + + align:start position:0% +ml2 Ms = +Z so that's a Slater determinant and so + + align:start position:0% +Z so that's a Slater determinant and so + + + align:start position:0% +Z so that's a Slater determinant and so +that's a basis + + align:start position:0% +that's a basis + + + align:start position:0% +that's a basis +function and we would like to find what + + align:start position:0% +function and we would like to find what + + + align:start position:0% +function and we would like to find what +linear combination of these guys makes + + align:start position:0% +linear combination of these guys makes + + + align:start position:0% +linear combination of these guys makes +these guys cuz these are much more + + align:start position:0% +these guys cuz these are much more + + + align:start position:0% +these guys cuz these are much more +useful than + + align:start position:0% +useful than + + + align:start position:0% +useful than +these however these are are really + + align:start position:0% +these however these are are really + + + align:start position:0% +these however these are are really +useful for evaluating Matrix elements of + + align:start position:0% +useful for evaluating Matrix elements of + + + align:start position:0% +useful for evaluating Matrix elements of +operators but these are useful for + + align:start position:0% +operators but these are useful for + + + align:start position:0% +operators but these are useful for +applying symmetry now before I get too + + align:start position:0% +applying symmetry now before I get too + + + align:start position:0% +applying symmetry now before I get too +far gone there's this wonderful book + + align:start position:0% +far gone there's this wonderful book + + + align:start position:0% +far gone there's this wonderful book +group Theory and quantum mechanics by + + align:start position:0% +group Theory and quantum mechanics by + + + align:start position:0% +group Theory and quantum mechanics by +Michael + + align:start position:0% +Michael + + + align:start position:0% +Michael +tinum and there's uh Pages 154 to + + align:start position:0% +tinum and there's uh Pages 154 to + + + align:start position:0% +tinum and there's uh Pages 154 to +188 gives you all of the algebra that I + + align:start position:0% +188 gives you all of the algebra that I + + + align:start position:0% +188 gives you all of the algebra that I +would develop in the four or five + + align:start position:0% +would develop in the four or five + + + align:start position:0% +would develop in the four or five +lectures on this subject and it's really + + align:start position:0% +lectures on this subject and it's really + + + align:start position:0% +lectures on this subject and it's really +beautiful it's hard + + align:start position:0% +beautiful it's hard + + + align:start position:0% +beautiful it's hard +but it's not as hard as some other uh uh + + align:start position:0% +but it's not as hard as some other uh uh + + + align:start position:0% +but it's not as hard as some other uh uh +presentations of it and this is a + + align:start position:0% +presentations of it and this is a + + + align:start position:0% +presentations of it and this is a +wonderful old book uh which uh I learned + + align:start position:0% +wonderful old book uh which uh I learned + + + align:start position:0% +wonderful old book uh which uh I learned +Quant mechanics + + align:start position:0% + + + + align:start position:0% + +from okay + + align:start position:0% +from okay + + + align:start position:0% +from okay +so we want to find the correct linear + + align:start position:0% +so we want to find the correct linear + + + align:start position:0% +so we want to find the correct linear +combination of these guys that makes + + align:start position:0% +combination of these guys that makes + + + align:start position:0% +combination of these guys that makes +these guys + + align:start position:0% +these guys + + + align:start position:0% +these guys +I'm not going to tell you how to do + + align:start position:0% +I'm not going to tell you how to do + + + align:start position:0% +I'm not going to tell you how to do +that uh you you don't really want me to + + align:start position:0% +that uh you you don't really want me to + + + align:start position:0% +that uh you you don't really want me to +tell you how I do it because there are + + align:start position:0% +tell you how I do it because there are + + + align:start position:0% +tell you how I do it because there are +powerful methods involving angular + + align:start position:0% +powerful methods involving angular + + + align:start position:0% +powerful methods involving angular +momentum coupling coefficients 36 njs + + align:start position:0% +momentum coupling coefficients 36 njs + + + align:start position:0% +momentum coupling coefficients 36 njs +which is the way you do it especially if + + align:start position:0% +which is the way you do it especially if + + + align:start position:0% +which is the way you do it especially if +you were going to use a computer program + + align:start position:0% +you were going to use a computer program + + + align:start position:0% +you were going to use a computer program +and there's create there's raising and + + align:start position:0% +and there's create there's raising and + + + align:start position:0% +and there's create there's raising and +lowering operators which is the way I do + + align:start position:0% +lowering operators which is the way I do + + + align:start position:0% +lowering operators which is the way I do +it which is had been a nightmare of + + align:start position:0% +it which is had been a nightmare of + + + align:start position:0% +it which is had been a nightmare of +first year graduate student taking my + + align:start position:0% +first year graduate student taking my + + + align:start position:0% +first year graduate student taking my +quantum mechanics class for 25 years + + align:start position:0% +quantum mechanics class for 25 years + + + align:start position:0% +quantum mechanics class for 25 years +until I was kicked out of the course no + + align:start position:0% +until I was kicked out of the course no + + + align:start position:0% +until I was kicked out of the course no +longer allowed to teach that course + + align:start position:0% +longer allowed to teach that course + + + align:start position:0% +longer allowed to teach that course +probably because of the way I do all + + align:start position:0% +probably because of the way I do all + + + align:start position:0% +probably because of the way I do all +this Atomic physics okay + + align:start position:0% + + + + align:start position:0% + +so so once we can find a way to write + + align:start position:0% +so so once we can find a way to write + + + align:start position:0% +so so once we can find a way to write +these things as linear combination of + + align:start position:0% +these things as linear combination of + + + align:start position:0% +these things as linear combination of +these + + align:start position:0% +these + + + align:start position:0% +these +things then we are in a position to + + align:start position:0% +things then we are in a position to + + + align:start position:0% +things then we are in a position to +evaluate matri elements of the terms + + align:start position:0% +evaluate matri elements of the terms + + + align:start position:0% +evaluate matri elements of the terms +that that make up the hamiltonian so the + + align:start position:0% +that that make up the hamiltonian so the + + + align:start position:0% +that that make up the hamiltonian so the +hamiltonian + + align:start position:0% +hamiltonian + + + align:start position:0% +hamiltonian +involves uh the + + align:start position:0% +involves uh the + + + align:start position:0% +involves uh the +um uh oh let's just call it this this + + align:start position:0% +um uh oh let's just call it this this + + + align:start position:0% +um uh oh let's just call it this this +and this so this is you know some sort + + align:start position:0% +and this so this is you know some sort + + + align:start position:0% +and this so this is you know some sort +of orbital energies it's kind of a a + + align:start position:0% +of orbital energies it's kind of a a + + + align:start position:0% +of orbital energies it's kind of a a +hary fock thing that decides what the + + align:start position:0% +hary fock thing that decides what the + + + align:start position:0% +hary fock thing that decides what the +energies of each orbital will be + + align:start position:0% +energies of each orbital will be + + + align:start position:0% +energies of each orbital will be +depending on what the states of the + + align:start position:0% +depending on what the states of the + + + align:start position:0% +depending on what the states of the +other electron + + align:start position:0% +other electron + + + align:start position:0% +other electron +are so so we could we could say okay + + align:start position:0% +are so so we could we could say okay + + + align:start position:0% +are so so we could we could say okay +that is expressed in terms of orbital + + align:start position:0% +that is expressed in terms of orbital + + + align:start position:0% +that is expressed in terms of orbital +energies and maybe there's some hidden + + align:start position:0% +energies and maybe there's some hidden + + + align:start position:0% +energies and maybe there's some hidden +complexity because the energy of an + + align:start position:0% +complexity because the energy of an + + + align:start position:0% +complexity because the energy of an +orbital depends on what other what other + + align:start position:0% +orbital depends on what other what other + + + align:start position:0% +orbital depends on what other what other +orbitals are occupied because we know + + align:start position:0% +orbitals are occupied because we know + + + align:start position:0% +orbitals are occupied because we know +about shielding so we have to be a + + align:start position:0% +about shielding so we have to be a + + + align:start position:0% +about shielding so we have to be a +little bit you + + align:start position:0% +little bit you + + + align:start position:0% +little bit you +know complicated about this but so we + + align:start position:0% +know complicated about this but so we + + + align:start position:0% +know complicated about this but so we +have orbital energies and this is the + + align:start position:0% +have orbital energies and this is the + + + align:start position:0% +have orbital energies and this is the +inter electron IC + + align:start position:0% +inter electron IC + + + align:start position:0% +inter electron IC +repulsion and this is expressed in terms + + align:start position:0% +repulsion and this is expressed in terms + + + align:start position:0% +repulsion and this is expressed in terms +of what are called Slater Condon or uh + + align:start position:0% +of what are called Slater Condon or uh + + + align:start position:0% +of what are called Slater Condon or uh +Kum and + + align:start position:0% +Kum and + + + align:start position:0% +Kum and +exchange integrals these are these are + + align:start position:0% +exchange integrals these are these are + + + align:start position:0% +exchange integrals these are these are +one electron these are two electron + + align:start position:0% +one electron these are two electron + + + align:start position:0% +one electron these are two electron +operators this is a one electron + + align:start position:0% +operators this is a one electron + + + align:start position:0% +operators this is a one electron +operator that's easy Matrix elements of + + align:start position:0% +operator that's easy Matrix elements of + + + align:start position:0% +operator that's easy Matrix elements of +two electron operators is why this + + align:start position:0% +two electron operators is why this + + + align:start position:0% +two electron operators is why this +lecture takes this topic takes four or + + align:start position:0% +lecture takes this topic takes four or + + + align:start position:0% +lecture takes this topic takes four or +five lectures + + align:start position:0% +five lectures + + + align:start position:0% +five lectures +but it's a very valuable thing to know + + align:start position:0% +but it's a very valuable thing to know + + + align:start position:0% +but it's a very valuable thing to know +how to evaluate Matrix elements of one + + align:start position:0% +how to evaluate Matrix elements of one + + + align:start position:0% +how to evaluate Matrix elements of one +and two electron operators in a Slater + + align:start position:0% +and two electron operators in a Slater + + + align:start position:0% +and two electron operators in a Slater +determin basis it's neat it simplifies + + align:start position:0% +determin basis it's neat it simplifies + + + align:start position:0% +determin basis it's neat it simplifies +things and + + align:start position:0% +things and + + + align:start position:0% +things and +uh I recommend it but I'm not going to + + align:start position:0% +uh I recommend it but I'm not going to + + + align:start position:0% +uh I recommend it but I'm not going to +teach it to you because that that would + + align:start position:0% +teach it to you because that that would + + + align:start position:0% +teach it to you because that that would +really be taking advantage of your + + align:start position:0% +really be taking advantage of your + + + align:start position:0% +really be taking advantage of your +credulity and then there's the spin + + align:start position:0% +credulity and then there's the spin + + + align:start position:0% +credulity and then there's the spin +orbit which is expressed as you some + + align:start position:0% +orbit which is expressed as you some + + + align:start position:0% +orbit which is expressed as you some +sort of a an + + align:start position:0% + + + + align:start position:0% + +operator and + + align:start position:0% +operator and + + + align:start position:0% +operator and +so this is a one electron operator it's + + align:start position:0% +so this is a one electron operator it's + + + align:start position:0% +so this is a one electron operator it's +a sum over the individual electrons or + + align:start position:0% +a sum over the individual electrons or + + + align:start position:0% +a sum over the individual electrons or +orbitals L L.S well you know what to do + + align:start position:0% +orbitals L L.S well you know what to do + + + align:start position:0% +orbitals L L.S well you know what to do +with L.S in a basis set in which you've + + align:start position:0% +with L.S in a basis set in which you've + + + align:start position:0% +with L.S in a basis set in which you've +specified M subel and M subs or L and S + + align:start position:0% +specified M subel and M subs or L and S + + + align:start position:0% +specified M subel and M subs or L and S +and + + align:start position:0% +and + + + align:start position:0% +and +J so this operator is pretty easy and + + align:start position:0% +J so this operator is pretty easy and + + + align:start position:0% +J so this operator is pretty easy and +uh okay and so these are the three + + align:start position:0% +uh okay and so these are the three + + + align:start position:0% +uh okay and so these are the three +things that you need in order to uh + + align:start position:0% +things that you need in order to uh + + + align:start position:0% +things that you need in order to uh +describe the energy levels and + + align:start position:0% +describe the energy levels and + + + align:start position:0% +describe the energy levels and +so + + align:start position:0% +so + + + align:start position:0% +so +this this this + + align:start position:0% +this this this + + + align:start position:0% +this this this +and Zeta NL is where the periodicity + + align:start position:0% +and Zeta NL is where the periodicity + + + align:start position:0% +and Zeta NL is where the periodicity +is your ideas for how do properties of + + align:start position:0% +is your ideas for how do properties of + + + align:start position:0% +is your ideas for how do properties of +atoms vary as you go across the table + + align:start position:0% +atoms vary as you go across the table + + + align:start position:0% +atoms vary as you go across the table +it's all written into + + align:start position:0% +it's all written into + + + align:start position:0% +it's all written into +these + + align:start position:0% +these + + + align:start position:0% +these +parameters if you look at a a table of + + align:start position:0% +parameters if you look at a a table of + + + align:start position:0% +parameters if you look at a a table of +uh values of orbital energies the + + align:start position:0% +uh values of orbital energies the + + + align:start position:0% +uh values of orbital energies the +interelectronic repulsion kolum integral + + align:start position:0% +interelectronic repulsion kolum integral + + + align:start position:0% +interelectronic repulsion kolum integral +and exchange integral the spin orbit + + align:start position:0% +and exchange integral the spin orbit + + + align:start position:0% +and exchange integral the spin orbit +they all can be understood in a simple + + align:start position:0% +they all can be understood in a simple + + + align:start position:0% +they all can be understood in a simple +uh framework and that means you could + + align:start position:0% +uh framework and that means you could + + + align:start position:0% +uh framework and that means you could +also represent all of the electronic + + align:start position:0% +also represent all of the electronic + + + align:start position:0% +also represent all of the electronic +states of all atoms in uh by doing some + + align:start position:0% +states of all atoms in uh by doing some + + + align:start position:0% +states of all atoms in uh by doing some +kind of a squares fit to some data + + align:start position:0% +kind of a squares fit to some data + + + align:start position:0% +kind of a squares fit to some data +fitting these parameters and then you + + align:start position:0% +fitting these parameters and then you + + + align:start position:0% +fitting these parameters and then you +generate everything and this is actually + + align:start position:0% +generate everything and this is actually + + + align:start position:0% +generate everything and this is actually +quite wonderful because not only does + + align:start position:0% +quite wonderful because not only does + + + align:start position:0% +quite wonderful because not only does +this present the + + align:start position:0% +this present the + + + align:start position:0% +this present the +periodicity it also enables you to + + align:start position:0% +periodicity it also enables you to + + + align:start position:0% +periodicity it also enables you to +calculate everything that you could + + align:start position:0% +calculate everything that you could + + + align:start position:0% +calculate everything that you could +possibly + + align:start position:0% +possibly + + + align:start position:0% +possibly +observe transition relative intensities + + align:start position:0% +observe transition relative intensities + + + align:start position:0% +observe transition relative intensities +patterns of energy levels uh it it + + align:start position:0% +patterns of energy levels uh it it + + + align:start position:0% +patterns of energy levels uh it it +enables you to do wonderful things but + + align:start position:0% +enables you to do wonderful things but + + + align:start position:0% +enables you to do wonderful things but +the important thing is + + align:start position:0% +the important thing is + + + align:start position:0% +the important thing is +what we learned in freshman chemistry + + align:start position:0% +what we learned in freshman chemistry + + + align:start position:0% +what we learned in freshman chemistry +about the periodic table is all written + + align:start position:0% +about the periodic table is all written + + + align:start position:0% +about the periodic table is all written +in these + + align:start position:0% +in these + + + align:start position:0% +in these +parameters and you can understand them + + align:start position:0% +parameters and you can understand them + + + align:start position:0% +parameters and you can understand them +and I consider that to be really + + align:start position:0% +and I consider that to be really + + + align:start position:0% +and I consider that to be really +beautiful but I'm + + align:start position:0% + + + + align:start position:0% + +strange okay so now let's go to page + + align:start position:0% +strange okay so now let's go to page + + + align:start position:0% +strange okay so now let's go to page +four of the + + align:start position:0% + + + + align:start position:0% + +notes and + + align:start position:0% +notes and + + + align:start position:0% +notes and +uh um + + align:start position:0% + + + + align:start position:0% + +I'm just going to talk you through a lot + + align:start position:0% +I'm just going to talk you through a lot + + + align:start position:0% +I'm just going to talk you through a lot +of the qualitative stuff yes if you have + + align:start position:0% +of the qualitative stuff yes if you have + + + align:start position:0% +of the qualitative stuff yes if you have +one more copy of the notes can I have um + + align:start position:0% +one more copy of the notes can I have um + + + align:start position:0% +one more copy of the notes can I have um +if you don't have there you go okay + + align:start position:0% + + + + align:start position:0% + +okay all right so on page + + align:start position:0% +okay all right so on page + + + align:start position:0% +okay all right so on page +four + + align:start position:0% +four + + + align:start position:0% +four +um there is a little table of the states + + align:start position:0% +um there is a little table of the states + + + align:start position:0% +um there is a little table of the states +that arise from the various number of + + align:start position:0% +that arise from the various number of + + + align:start position:0% +that arise from the various number of +electrons in D orbitals + + align:start position:0% +electrons in D orbitals + + + align:start position:0% +electrons in D orbitals +it's really simple for S it's really + + align:start position:0% +it's really simple for S it's really + + + align:start position:0% +it's really simple for S it's really +simple for p it's pretty simple for D + + align:start position:0% +simple for p it's pretty simple for D + + + align:start position:0% +simple for p it's pretty simple for D +until you get to three four and five D + + align:start position:0% + + + + align:start position:0% + +electrons there is this + + align:start position:0% +electrons there is this + + + align:start position:0% +electrons there is this +wonderful thing that + + align:start position:0% +wonderful thing that + + + align:start position:0% +wonderful thing that +electrons and + + align:start position:0% +electrons and + + + align:start position:0% +electrons and +holes as far as this algebra is + + align:start position:0% +holes as far as this algebra is + + + align:start position:0% +holes as far as this algebra is +concerned are the same and so if you + + align:start position:0% +concerned are the same and so if you + + + align:start position:0% +concerned are the same and so if you +work out D2 D1 you have d if you work + + align:start position:0% +work out D2 D1 you have d if you work + + + align:start position:0% +work out D2 D1 you have d if you work +out d^2 you have d8 and so on and the + + align:start position:0% +out d^2 you have d8 and so on and the + + + align:start position:0% +out d^2 you have d8 and so on and the +only thing that's different is the sign + + align:start position:0% +only thing that's different is the sign + + + align:start position:0% +only thing that's different is the sign +of the spin orbit constant or the sign + + align:start position:0% +of the spin orbit constant or the sign + + + align:start position:0% +of the spin orbit constant or the sign +of the spin orbit when you've done stuff + + align:start position:0% +of the spin orbit when you've done stuff + + + align:start position:0% +of the spin orbit when you've done stuff +and there are other things about + + align:start position:0% +and there are other things about + + + align:start position:0% +and there are other things about +half-filled shells and half filled + + align:start position:0% +half-filled shells and half filled + + + align:start position:0% +half-filled shells and half filled +subshells that appear when you start + + align:start position:0% +subshells that appear when you start + + + align:start position:0% +subshells that appear when you start +doing Lian field theory on these + + align:start position:0% +doing Lian field theory on these + + + align:start position:0% +doing Lian field theory on these +things there's so what you see is + + align:start position:0% +things there's so what you see is + + + align:start position:0% +things there's so what you see is +there's 10 of these there's 45 of these + + align:start position:0% +there's 10 of these there's 45 of these + + + align:start position:0% +there's 10 of these there's 45 of these +there's 120 of D cubed 210 of D4 and 224 + + align:start position:0% +there's 120 of D cubed 210 of D4 and 224 + + + align:start position:0% +there's 120 of D cubed 210 of D4 and 224 +of D5 why would you care well it gets + + align:start position:0% +of D5 why would you care well it gets + + + align:start position:0% +of D5 why would you care well it gets +complicated and wait till you get to F + + align:start position:0% +complicated and wait till you get to F + + + align:start position:0% +complicated and wait till you get to F +because you can always get up get up to + + align:start position:0% +because you can always get up get up to + + + align:start position:0% +because you can always get up get up to +F7 and you could calculate what F does + + align:start position:0% +F7 and you could calculate what F does + + + align:start position:0% +F7 and you could calculate what F does +it's terrible it's just + + align:start position:0% +it's terrible it's just + + + align:start position:0% +it's terrible it's just +frightening um okay so there are lots of + + align:start position:0% +frightening um okay so there are lots of + + + align:start position:0% +frightening um okay so there are lots of +States but then there's rules + + align:start position:0% +States but then there's rules + + + align:start position:0% +States but then there's rules +for + + align:start position:0% +for + + + align:start position:0% +for +um what is lowest + + align:start position:0% + + + + align:start position:0% + +and since most spectroscopies bottom up + + align:start position:0% +and since most spectroscopies bottom up + + + align:start position:0% +and since most spectroscopies bottom up +we do care about what is the lowest + + align:start position:0% +we do care about what is the lowest + + + align:start position:0% +we do care about what is the lowest +state of each + + align:start position:0% + + + + align:start position:0% + +configuration and there are three hun + + align:start position:0% +configuration and there are three hun + + + align:start position:0% +configuration and there are three hun +rules that tell you what is the lowest + + align:start position:0% +rules that tell you what is the lowest + + + align:start position:0% +rules that tell you what is the lowest +state of each configuration and they + + align:start position:0% +state of each configuration and they + + + align:start position:0% +state of each configuration and they +tell you nothing more than what is the + + align:start position:0% +tell you nothing more than what is the + + + align:start position:0% +tell you nothing more than what is the +lowest state of each configuration they + + align:start position:0% +lowest state of each configuration they + + + align:start position:0% +lowest state of each configuration they +don't tell you anything about the order + + align:start position:0% +don't tell you anything about the order + + + align:start position:0% +don't tell you anything about the order +of the states other than what's lowest + + align:start position:0% +of the states other than what's lowest + + + align:start position:0% +of the states other than what's lowest +and and there are many people and many + + align:start position:0% +and and there are many people and many + + + align:start position:0% +and and there are many people and many +textbooks who have that + + align:start position:0% +textbooks who have that + + + align:start position:0% +textbooks who have that +wrong and so what is lowest maximum spin + + align:start position:0% +wrong and so what is lowest maximum spin + + + align:start position:0% +wrong and so what is lowest maximum spin +of those the one that's lowest is + + align:start position:0% +of those the one that's lowest is + + + align:start position:0% +of those the one that's lowest is +maximum + + align:start position:0% +maximum + + + align:start position:0% +maximum +L that's one State Maximum L maximum s + + align:start position:0% +L that's one State Maximum L maximum s + + + align:start position:0% +L that's one State Maximum L maximum s +nothing about the ordering of + + align:start position:0% +nothing about the ordering of + + + align:start position:0% +nothing about the ordering of +States if you don't have the maximum L + + align:start position:0% +States if you don't have the maximum L + + + align:start position:0% +States if you don't have the maximum L +and maximum s well then the maximum s + + align:start position:0% +and maximum s well then the maximum s + + + align:start position:0% +and maximum s well then the maximum s +but a different L well that might be + + align:start position:0% +but a different L well that might be + + + align:start position:0% +but a different L well that might be +low-lying it might not it doesn't tell + + align:start position:0% +low-lying it might not it doesn't tell + + + align:start position:0% +low-lying it might not it doesn't tell +Mr hun doesn't tell you anything about + + align:start position:0% +Mr hun doesn't tell you anything about + + + align:start position:0% +Mr hun doesn't tell you anything about +that and I can derive you know where + + align:start position:0% +that and I can derive you know where + + + align:start position:0% +that and I can derive you know where +these come from and of then you have + + align:start position:0% +these come from and of then you have + + + align:start position:0% +these come from and of then you have +maximum L maximum s which J is the + + align:start position:0% +maximum L maximum s which J is the + + + align:start position:0% +maximum L maximum s which J is the +lowest and if you have a less than half + + align:start position:0% +lowest and if you have a less than half + + + align:start position:0% +lowest and if you have a less than half +fied shell the lowest possible J is + + align:start position:0% +fied shell the lowest possible J is + + + align:start position:0% +fied shell the lowest possible J is +lowest in energy and if you have a more + + align:start position:0% +lowest in energy and if you have a more + + + align:start position:0% +lowest in energy and if you have a more +than half fied shell the highest + + align:start position:0% +than half fied shell the highest + + + align:start position:0% +than half fied shell the highest +possible J is lowest in energy and if + + align:start position:0% +possible J is lowest in energy and if + + + align:start position:0% +possible J is lowest in energy and if +you have a half filled shell there isn't + + align:start position:0% +you have a half filled shell there isn't + + + align:start position:0% +you have a half filled shell there isn't +any spin orbit splitting + + align:start position:0% +any spin orbit splitting + + + align:start position:0% +any spin orbit splitting +so that's a little bit beyond the Huns + + align:start position:0% +so that's a little bit beyond the Huns + + + align:start position:0% +so that's a little bit beyond the Huns +rules so there are three Huns rules and + + align:start position:0% +rules so there are three Huns rules and + + + align:start position:0% +rules so there are three Huns rules and +they tell you what is the lowest state + + align:start position:0% +they tell you what is the lowest state + + + align:start position:0% +they tell you what is the lowest state +of a configuration so that's going to + + align:start position:0% +of a configuration so that's going to + + + align:start position:0% +of a configuration so that's going to +tell you what's the ground + + align:start position:0% +tell you what's the ground + + + align:start position:0% +tell you what's the ground +state and it's probably going to tell + + align:start position:0% +state and it's probably going to tell + + + align:start position:0% +state and it's probably going to tell +you what are the allowed transitions to + + align:start position:0% +you what are the allowed transitions to + + + align:start position:0% +you what are the allowed transitions to +the lowest state of each configuration + + align:start position:0% +the lowest state of each configuration + + + align:start position:0% +the lowest state of each configuration +that would enable you to begin to know + + align:start position:0% +that would enable you to begin to know + + + align:start position:0% +that would enable you to begin to know +the electronic structure of the molecule + + align:start position:0% +the electronic structure of the molecule + + + align:start position:0% +the electronic structure of the molecule +so it's really important Huns + + align:start position:0% +so it's really important Huns + + + align:start position:0% +so it's really important Huns +rules okay + + align:start position:0% +rules okay + + + align:start position:0% +rules okay +so um + + align:start position:0% + + + + align:start position:0% + +we know how to represent all of the + + align:start position:0% +we know how to represent all of the + + + align:start position:0% +we know how to represent all of the +states of all of the lowline + + align:start position:0% +states of all of the lowline + + + align:start position:0% +states of all of the lowline +configuration in terms of these orbital + + align:start position:0% +configuration in terms of these orbital + + + align:start position:0% +configuration in terms of these orbital +energies the uh Kum and exchange + + align:start position:0% +energies the uh Kum and exchange + + + align:start position:0% +energies the uh Kum and exchange +integrals to electron and the spin + + align:start position:0% +integrals to electron and the spin + + + align:start position:0% +integrals to electron and the spin +orbit and so we need to write an + + align:start position:0% +orbit and so we need to write an + + + align:start position:0% +orbit and so we need to write an +effective hamiltonian now that will + + align:start position:0% +effective hamiltonian now that will + + + align:start position:0% +effective hamiltonian now that will +generate the actual energy levels and + + align:start position:0% +generate the actual energy levels and + + + align:start position:0% +generate the actual energy levels and +ion + + align:start position:0% +ion + + + align:start position:0% +ion +vectors that will be what we encounter + + align:start position:0% +vectors that will be what we encounter + + + align:start position:0% +vectors that will be what we encounter +in the Spectrum so in the Spectrum we + + align:start position:0% +in the Spectrum so in the Spectrum we + + + align:start position:0% +in the Spectrum so in the Spectrum we +see energy levels and we work backwards + + align:start position:0% +see energy levels and we work backwards + + + align:start position:0% +see energy levels and we work backwards +to get these things but if we haven't + + align:start position:0% +to get these things but if we haven't + + + align:start position:0% +to get these things but if we haven't +recorded a spectrum we use periodicity + + align:start position:0% +recorded a spectrum we use periodicity + + + align:start position:0% +recorded a spectrum we use periodicity +to make good guesses of these things and + + align:start position:0% +to make good guesses of these things and + + + align:start position:0% +to make good guesses of these things and +then we uh we attempt to make sense of + + align:start position:0% +then we uh we attempt to make sense of + + + align:start position:0% +then we uh we attempt to make sense of +what we're going to observe in the + + align:start position:0% +what we're going to observe in the + + + align:start position:0% +what we're going to observe in the +Spectrum and since you know I'm a + + align:start position:0% +Spectrum and since you know I'm a + + + align:start position:0% +Spectrum and since you know I'm a +professor I don't uh + + align:start position:0% +professor I don't uh + + + align:start position:0% +professor I don't uh +um I don't encounter the + + align:start position:0% +um I don't encounter the + + + align:start position:0% +um I don't encounter the +Spectra I encounter other people's + + align:start position:0% +Spectra I encounter other people's + + + align:start position:0% +Spectra I encounter other people's +analyses of the Spectra and then make + + align:start position:0% +analyses of the Spectra and then make + + + align:start position:0% +analyses of the Spectra and then make +comments on whether they're right or not + + align:start position:0% +comments on whether they're right or not + + + align:start position:0% +comments on whether they're right or not +but I don't analyze Spectra I really am + + align:start position:0% +but I don't analyze Spectra I really am + + + align:start position:0% +but I don't analyze Spectra I really am +interested in the hamiltonian that + + align:start position:0% +interested in the hamiltonian that + + + align:start position:0% +interested in the hamiltonian that +represents + + align:start position:0% +represents + + + align:start position:0% +represents +them nice work if you can get it okay + + align:start position:0% +them nice work if you can get it okay + + + align:start position:0% +them nice work if you can get it okay +so uh on page + + align:start position:0% +so uh on page + + + align:start position:0% +so uh on page +five it's illustrating periodicity in a + + align:start position:0% +five it's illustrating periodicity in a + + + align:start position:0% +five it's illustrating periodicity in a +beautiful and subtle way this is a a + + align:start position:0% +beautiful and subtle way this is a a + + + align:start position:0% +beautiful and subtle way this is a a +figure from tinum there's a similar + + align:start position:0% +figure from tinum there's a similar + + + align:start position:0% +figure from tinum there's a similar +figure in count in shortly + + align:start position:0% +figure in count in shortly + + + align:start position:0% +figure in count in shortly +and so this is X the + + align:start position:0% +and so this is X the + + + align:start position:0% +and so this is X the +number of the + + align:start position:0% + + + + align:start position:0% + +electrons and this is the spin orbit + + align:start position:0% +electrons and this is the spin orbit + + + align:start position:0% +electrons and this is the spin orbit +there's two different things plotted + + align:start position:0% +there's two different things plotted + + + align:start position:0% +there's two different things plotted +here one plotted here is something + + align:start position:0% +here one plotted here is something + + + align:start position:0% +here one plotted here is something +that's going up like that and another + + align:start position:0% +that's going up like that and another + + + align:start position:0% +that's going up like that and another +thing that's plotted here is something + + align:start position:0% +thing that's plotted here is something + + + align:start position:0% +thing that's plotted here is something +that's small crosses through zero and + + align:start position:0% +that's small crosses through zero and + + + align:start position:0% +that's small crosses through zero and +gets large + + align:start position:0% +gets large + + + align:start position:0% +gets large +five this is the one electron spin orbit + + align:start position:0% +five this is the one electron spin orbit + + + align:start position:0% +five this is the one electron spin orbit +parameter which has to increase + + align:start position:0% +parameter which has to increase + + + align:start position:0% +parameter which has to increase +monotonically as because it goes as Z to + + align:start position:0% +monotonically as because it goes as Z to + + + align:start position:0% +monotonically as because it goes as Z to +the 4th as you make the charge on the + + align:start position:0% +the 4th as you make the charge on the + + + align:start position:0% +the 4th as you make the charge on the +nucleus larger the electron the next + + align:start position:0% +nucleus larger the electron the next + + + align:start position:0% +nucleus larger the electron the next +electron always sees a larger Z + + align:start position:0% +electron always sees a larger Z + + + align:start position:0% +electron always sees a larger Z +effective because the previous electron + + align:start position:0% +effective because the previous electron + + + align:start position:0% +effective because the previous electron +didn't Shield perfectly so you get that + + align:start position:0% +didn't Shield perfectly so you get that + + + align:start position:0% +didn't Shield perfectly so you get that +and this is what you expect and it's + + align:start position:0% +and this is what you expect and it's + + + align:start position:0% +and this is what you expect and it's +beautiful and it's + + align:start position:0% +beautiful and it's + + + align:start position:0% +beautiful and it's +monotonic this is kind of ugly because + + align:start position:0% +monotonic this is kind of ugly because + + + align:start position:0% +monotonic this is kind of ugly because +it changes sign and it's got a lot of + + align:start position:0% +it changes sign and it's got a lot of + + + align:start position:0% +it changes sign and it's got a lot of +curvature this is the spin orbit + + align:start position:0% +curvature this is the spin orbit + + + align:start position:0% +curvature this is the spin orbit +constant associated with the lowest + + align:start position:0% +constant associated with the lowest + + + align:start position:0% +constant associated with the lowest +energy LS + + align:start position:0% +energy LS + + + align:start position:0% +energy LS +term and uh uh + + align:start position:0% +term and uh uh + + + align:start position:0% +term and uh uh +so the lowest energy LS term of a + + align:start position:0% +so the lowest energy LS term of a + + + align:start position:0% +so the lowest energy LS term of a +particular + + align:start position:0% +particular + + + align:start position:0% +particular +configuration uh varies in a peculiar + + align:start position:0% +configuration uh varies in a peculiar + + + align:start position:0% +configuration uh varies in a peculiar +way as you add electrons and when you + + align:start position:0% +way as you add electrons and when you + + + align:start position:0% +way as you add electrons and when you +get past half it changes sign and so + + align:start position:0% +get past half it changes sign and so + + + align:start position:0% +get past half it changes sign and so +this sign Chang is the kind of thing + + align:start position:0% +this sign Chang is the kind of thing + + + align:start position:0% +this sign Chang is the kind of thing +that you'd really not like you know if + + align:start position:0% +that you'd really not like you know if + + + align:start position:0% +that you'd really not like you know if +you're having a a a model because most + + align:start position:0% +you're having a a a model because most + + + align:start position:0% +you're having a a a model because most +models like to be monotonic and so this + + align:start position:0% +models like to be monotonic and so this + + + align:start position:0% +models like to be monotonic and so this +is already concealing the the hidden + + align:start position:0% +is already concealing the the hidden + + + align:start position:0% +is already concealing the the hidden +beauty of this period periodic trend you + + align:start position:0% +beauty of this period periodic trend you + + + align:start position:0% +beauty of this period periodic trend you +can capture it but anyway this is when + + align:start position:0% +can capture it but anyway this is when + + + align:start position:0% +can capture it but anyway this is when +you look at either the spin orbit + + align:start position:0% +you look at either the spin orbit + + + align:start position:0% +you look at either the spin orbit +coupling constant of the D electron or + + align:start position:0% +coupling constant of the D electron or + + + align:start position:0% +coupling constant of the D electron or +the spin orbit coupling constant of an + + align:start position:0% +the spin orbit coupling constant of an + + + align:start position:0% +the spin orbit coupling constant of an +LS term they're different things you get + + align:start position:0% +LS term they're different things you get + + + align:start position:0% +LS term they're different things you get +these two different regular + + align:start position:0% +these two different regular + + + align:start position:0% +these two different regular +curves okay now we're going to go to + + align:start position:0% +curves okay now we're going to go to + + + align:start position:0% +curves okay now we're going to go to +page seven where the uh rubber hits the + + align:start position:0% + + + + align:start position:0% + +road + + align:start position:0% +road + + + align:start position:0% +road +okay when you are dealing with Slater + + align:start position:0% + + + + align:start position:0% + +determinants and you want to evaluate + + align:start position:0% +determinants and you want to evaluate + + + align:start position:0% +determinants and you want to evaluate +Matrix elements of one and two electron + + align:start position:0% +Matrix elements of one and two electron + + + align:start position:0% +Matrix elements of one and two electron +operators there's an algebra that you + + align:start position:0% +operators there's an algebra that you + + + align:start position:0% +operators there's an algebra that you +have to learn how to do the algebra is a + + align:start position:0% +have to learn how to do the algebra is a + + + align:start position:0% +have to learn how to do the algebra is a +little bit complicated and and I don't + + align:start position:0% +little bit complicated and and I don't + + + align:start position:0% +little bit complicated and and I don't +want to teach it to you but uh so you do + + align:start position:0% +want to teach it to you but uh so you do + + + align:start position:0% +want to teach it to you but uh so you do +this algebra and the interelectronic + + align:start position:0% +this algebra and the interelectronic + + + align:start position:0% +this algebra and the interelectronic +repulsion H uh effective hamiltonian for + + align:start position:0% +repulsion H uh effective hamiltonian for + + + align:start position:0% +repulsion H uh effective hamiltonian for +uh p^ + + align:start position:0% +uh p^ + + + align:start position:0% +uh p^ +s can be written in terms of the fs and + + align:start position:0% +s can be written in terms of the fs and + + + align:start position:0% +s can be written in terms of the fs and +G's uh it turns out you never get any + + align:start position:0% +G's uh it turns out you never get any + + + align:start position:0% +G's uh it turns out you never get any +G's if you have two identical electrons + + align:start position:0% +G's if you have two identical electrons + + + align:start position:0% +G's if you have two identical electrons +you only get G's if you have say an S + + align:start position:0% +you only get G's if you have say an S + + + align:start position:0% +you only get G's if you have say an S +and A P P or p and a d so there's no G's + + align:start position:0% +and A P P or p and a d so there's no G's + + + align:start position:0% +and A P P or p and a d so there's no G's +in this Matrix on the top of page seven + + align:start position:0% +in this Matrix on the top of page seven + + + align:start position:0% +in this Matrix on the top of page seven +it's just expressed in terms + + align:start position:0% +it's just expressed in terms + + + align:start position:0% +it's just expressed in terms +of + + align:start position:0% +of + + + align:start position:0% +of +F0 and + + align:start position:0% +F0 and + + + align:start position:0% +F0 and +FS2 okay what's this this is um + + align:start position:0% + + + + align:start position:0% + +um if if the electrons are P electrons + + align:start position:0% +um if if the electrons are P electrons + + + align:start position:0% +um if if the electrons are P electrons +the maximum index you can have is 2 * 1 + + align:start position:0% +the maximum index you can have is 2 * 1 + + + align:start position:0% +the maximum index you can have is 2 * 1 +2 * l so if you had F electrons you'd + + align:start position:0% +2 * l so if you had F electrons you'd + + + align:start position:0% +2 * l so if you had F electrons you'd +have F0 F2 F4 and + + align:start position:0% + + + + align:start position:0% + +F6 okay so but since it's only P you + + align:start position:0% +F6 okay so but since it's only P you + + + align:start position:0% +F6 okay so but since it's only P you +have F0 and F2 and so what you end up + + align:start position:0% +have F0 and F2 and so what you end up + + + align:start position:0% +have F0 and F2 and so what you end up +is you write down Matrix elements of the + + align:start position:0% +is you write down Matrix elements of the + + + align:start position:0% +is you write down Matrix elements of the +uh Slater determinants and you discover + + align:start position:0% +uh Slater determinants and you discover + + + align:start position:0% +uh Slater determinants and you discover +that + + align:start position:0% +that + + + align:start position:0% +that +uh this guy is + + align:start position:0% +uh this guy is + + + align:start position:0% +uh this guy is +diagonal and you discover that uh let's + + align:start position:0% +diagonal and you discover that uh let's + + + align:start position:0% +diagonal and you discover that uh let's +just + + align:start position:0% + + + + align:start position:0% + +write these are the ls states that you + + align:start position:0% +write these are the ls states that you + + + align:start position:0% +write these are the ls states that you +can have for p^ S and this is a 1x one + + align:start position:0% +can have for p^ S and this is a 1x one + + + align:start position:0% +can have for p^ S and this is a 1x one +this is a 1x one and this is a + + align:start position:0% +this is a 1x one and this is a + + + align:start position:0% +this is a 1x one and this is a +3X3 and so there's a number that goes + + align:start position:0% +3X3 and so there's a number that goes + + + align:start position:0% +3X3 and so there's a number that goes +here a different number that goes here a + + align:start position:0% +here a different number that goes here a + + + align:start position:0% +here a different number that goes here a +third number that goes in all three + + align:start position:0% +third number that goes in all three + + + align:start position:0% +third number that goes in all three +places + + align:start position:0% + + + + align:start position:0% + +here so the electronic + + align:start position:0% +here so the electronic + + + align:start position:0% +here so the electronic +structure is uh determined by the inter + + align:start position:0% +structure is uh determined by the inter + + + align:start position:0% +structure is uh determined by the inter +electronic repulsion and we have a state + + align:start position:0% +electronic repulsion and we have a state + + + align:start position:0% +electronic repulsion and we have a state +an energy for the single s State for the + + align:start position:0% +an energy for the single s State for the + + + align:start position:0% +an energy for the single s State for the +singlet D State and for the triplet P + + align:start position:0% +singlet D State and for the triplet P + + + align:start position:0% +singlet D State and for the triplet P +State and we get that by just evaluating + + align:start position:0% +State and we get that by just evaluating + + + align:start position:0% +State and we get that by just evaluating +Matrix elements of 1 / + + align:start position:0% +Matrix elements of 1 / + + + align:start position:0% +Matrix elements of 1 / +R12 in this Slater determinantal basis + + align:start position:0% +R12 in this Slater determinantal basis + + + align:start position:0% +R12 in this Slater determinantal basis +learning the algebra to do that and if + + align:start position:0% +learning the algebra to do that and if + + + align:start position:0% +learning the algebra to do that and if +you're a theorist you'll learn that uh + + align:start position:0% +you're a theorist you'll learn that uh + + + align:start position:0% +you're a theorist you'll learn that uh +and uh uh if you look at tinum you can + + align:start position:0% +and uh uh if you look at tinum you can + + + align:start position:0% +and uh uh if you look at tinum you can +learn it and some of you already know it + + align:start position:0% +learn it and some of you already know it + + + align:start position:0% +learn it and some of you already know it +okay so this + + align:start position:0% +okay so this + + + align:start position:0% +okay so this +hamiltonian is fully + + align:start position:0% +hamiltonian is fully + + + align:start position:0% +hamiltonian is fully +diagonal and you say oh hooray I don't + + align:start position:0% +diagonal and you say oh hooray I don't + + + align:start position:0% +diagonal and you say oh hooray I don't +have to do any work with a diagonal + + align:start position:0% +have to do any work with a diagonal + + + align:start position:0% +have to do any work with a diagonal +matrix + + align:start position:0% +matrix + + + align:start position:0% +matrix +unfortunately you almost always have to + + align:start position:0% +unfortunately you almost always have to + + + align:start position:0% +unfortunately you almost always have to +deal with spin orbit and the spin orbit + + align:start position:0% +deal with spin orbit and the spin orbit + + + align:start position:0% +deal with spin orbit and the spin orbit +Matrix is not diagonal in one in the + + align:start position:0% +Matrix is not diagonal in one in the + + + align:start position:0% +Matrix is not diagonal in one in the +usual basis so spin + + align:start position:0% + + + + align:start position:0% + +orbit so the spin orbit operator has the + + align:start position:0% +orbit so the spin orbit operator has the + + + align:start position:0% +orbit so the spin orbit operator has the +form Zeta uh l i + + align:start position:0% + + + + align:start position:0% + +SI and you can prove that that is a + + align:start position:0% +SI and you can prove that that is a + + + align:start position:0% +SI and you can prove that that is a +scalar operator with respect to Big + + align:start position:0% + + + + align:start position:0% + +J and because that's a scalar operator + + align:start position:0% +J and because that's a scalar operator + + + align:start position:0% +J and because that's a scalar operator +with respect to Big J it has only Delta + + align:start position:0% +with respect to Big J it has only Delta + + + align:start position:0% +with respect to Big J it has only Delta +J equals zero Matrix + + align:start position:0% +J equals zero Matrix + + + align:start position:0% +J equals zero Matrix +elements and the Matrix elements are + + align:start position:0% +elements and the Matrix elements are + + + align:start position:0% +elements and the Matrix elements are +independent of M sub J + + align:start position:0% + + + + align:start position:0% + +so we + + align:start position:0% +so we + + + align:start position:0% +so we +can uh use + + align:start position:0% +can uh use + + + align:start position:0% +can uh use +this to + + align:start position:0% +this to + + + align:start position:0% +this to +simplify the spin orbit Matrix element + + align:start position:0% +simplify the spin orbit Matrix element + + + align:start position:0% +simplify the spin orbit Matrix element +Matrix if we write it in either the + + align:start position:0% +Matrix if we write it in either the + + + align:start position:0% +Matrix if we write it in either the +lsj + + align:start position:0% +lsj + + + align:start position:0% +lsj +MJ + + align:start position:0% +MJ + + + align:start position:0% +MJ +or J1 J2 J MJ basis + + align:start position:0% + + + + align:start position:0% + +okay so this is the basis we like + + align:start position:0% +okay so this is the basis we like + + + align:start position:0% +okay so this is the basis we like +because that's the one that's one of the + + align:start position:0% +because that's the one that's one of the + + + align:start position:0% +because that's the one that's one of the +ones we used for + + align:start position:0% +ones we used for + + + align:start position:0% +ones we used for +this this is a little bit problematic + + align:start position:0% +this this is a little bit problematic + + + align:start position:0% +this this is a little bit problematic +because we have to do some we have to do + + align:start position:0% +because we have to do some we have to do + + + align:start position:0% +because we have to do some we have to do +a transformation from this angular + + align:start position:0% +a transformation from this angular + + + align:start position:0% +a transformation from this angular +momentum function to this one in order + + align:start position:0% +momentum function to this one in order + + + align:start position:0% +momentum function to this one in order +to use this for spin orbit and now why + + align:start position:0% +to use this for spin orbit and now why + + + align:start position:0% +to use this for spin orbit and now why +would we care about that well it's + + align:start position:0% +would we care about that well it's + + + align:start position:0% +would we care about that well it's +because spin orbit it's a one electron + + align:start position:0% +because spin orbit it's a one electron + + + align:start position:0% +because spin orbit it's a one electron +operator it's diagonal in J1 it's + + align:start position:0% +operator it's diagonal in J1 it's + + + align:start position:0% +operator it's diagonal in J1 it's +diagonal in J2 it's diagonal in J and so + + align:start position:0% +diagonal in J2 it's diagonal in J and so + + + align:start position:0% +diagonal in J2 it's diagonal in J and so +if we use this basis set spin orbit is + + align:start position:0% +if we use this basis set spin orbit is + + + align:start position:0% +if we use this basis set spin orbit is +fully + + align:start position:0% +fully + + + align:start position:0% +fully +diagonal but this is + + align:start position:0% +diagonal but this is + + + align:start position:0% +diagonal but this is +not if we go to that basis set we spoil + + align:start position:0% +not if we go to that basis set we spoil + + + align:start position:0% +not if we go to that basis set we spoil +the diagonal nature of this if we work + + align:start position:0% +the diagonal nature of this if we work + + + align:start position:0% +the diagonal nature of this if we work +in this basis we don't have any trouble + + align:start position:0% +in this basis we don't have any trouble + + + align:start position:0% +in this basis we don't have any trouble +writing down the Matrix but it's not + + align:start position:0% + + + + align:start position:0% + +diagonal so uh at the top of page seven + + align:start position:0% +diagonal so uh at the top of page seven + + + align:start position:0% +diagonal so uh at the top of page seven +what time is it am I done am I out of + + align:start position:0% +what time is it am I done am I out of + + + align:start position:0% +what time is it am I done am I out of +time 548 oh I got enough time to talk + + align:start position:0% +time 548 oh I got enough time to talk + + + align:start position:0% +time 548 oh I got enough time to talk +for another 10 minutes or so okay so at + + align:start position:0% +for another 10 minutes or so okay so at + + + align:start position:0% +for another 10 minutes or so okay so at +top of page seven you have the spin orb + + align:start position:0% +top of page seven you have the spin orb + + + align:start position:0% +top of page seven you have the spin orb +at hamiltonian and it's it's a bunch of + + align:start position:0% +at hamiltonian and it's it's a bunch of + + + align:start position:0% +at hamiltonian and it's it's a bunch of +2 by tws because you notice that there's + + align:start position:0% +2 by tws because you notice that there's + + + align:start position:0% +2 by tws because you notice that there's +two Jal 2s and there's two J equals z + + align:start position:0% +two Jal 2s and there's two J equals z + + + align:start position:0% +two Jal 2s and there's two J equals z +and one J equal 1 so we have a 2X two + + align:start position:0% +and one J equal 1 so we have a 2X two + + + align:start position:0% +and one J equal 1 so we have a 2X two +for J equal 2 a 2x2 for J Z and a 1x one + + align:start position:0% +for J equal 2 a 2x2 for J Z and a 1x one + + + align:start position:0% +for J equal 2 a 2x2 for J Z and a 1x one +for J equal + + align:start position:0% + + + + align:start position:0% + +1 and uh so if we take the spin orbit + + align:start position:0% +1 and uh so if we take the spin orbit + + + align:start position:0% +1 and uh so if we take the spin orbit +and Inter electronic repulsion matrices + + align:start position:0% +and Inter electronic repulsion matrices + + + align:start position:0% +and Inter electronic repulsion matrices +and combine + + align:start position:0% +and combine + + + align:start position:0% +and combine +them uh we'll get a 2X two a 1 by one + + align:start position:0% +them uh we'll get a 2X two a 1 by one + + + align:start position:0% +them uh we'll get a 2X two a 1 by one +and a 2X + + align:start position:0% +and a 2X + + + align:start position:0% +and a 2X +two and nobody has trouble dealing with + + align:start position:0% +two and nobody has trouble dealing with + + + align:start position:0% +two and nobody has trouble dealing with +a 2X two Matrix we know how to + + align:start position:0% +a 2X two Matrix we know how to + + + align:start position:0% +a 2X two Matrix we know how to +diagonalize it + + align:start position:0% +diagonalize it + + + align:start position:0% +diagonalize it +now in case you have forgotten + + align:start position:0% + + + + align:start position:0% + +if you have a 2X two + + align:start position:0% + + + + align:start position:0% + +Matrix has this + + align:start position:0% +Matrix has this + + + align:start position:0% +Matrix has this +form + + align:start position:0% +form + + + align:start position:0% +form +and it's always useful to replace it by + + align:start position:0% +and it's always useful to replace it by + + + align:start position:0% +and it's always useful to replace it by +uh um + + align:start position:0% +uh um + + + align:start position:0% +uh um +e e bar 0 0 + + align:start position:0% +e e bar 0 0 + + + align:start position:0% +e e bar 0 0 +plus uh Delta / 2us Delta / 2 v + + align:start position:0% +plus uh Delta / 2us Delta / 2 v + + + align:start position:0% +plus uh Delta / 2us Delta / 2 v +v because this is diagonal that's just + + align:start position:0% +v because this is diagonal that's just + + + align:start position:0% +v because this is diagonal that's just +taking out the center of gravity and + + align:start position:0% +taking out the center of gravity and + + + align:start position:0% +taking out the center of gravity and +this has a secular equation that is so + + align:start position:0% +this has a secular equation that is so + + + align:start position:0% +this has a secular equation that is so +simple the energy levels of this are + + align:start position:0% +simple the energy levels of this are + + + align:start position:0% +simple the energy levels of this are +just the square root of Delta s over 4 + + + align:start position:0% +just the square root of Delta s over 4 + + + + align:start position:0% +just the square root of Delta s over 4 + +V ^2 sare root plus plus or minus + + align:start position:0% +V ^2 sare root plus plus or minus + + + align:start position:0% +V ^2 sare root plus plus or minus +so this is you know you as soon as you + + align:start position:0% +so this is you know you as soon as you + + + align:start position:0% +so this is you know you as soon as you +have a 2X two you know you're going to + + align:start position:0% +have a 2X two you know you're going to + + + align:start position:0% +have a 2X two you know you're going to +be able to get to this and then the + + align:start position:0% +be able to get to this and then the + + + align:start position:0% +be able to get to this and then the +problem is solved so all of + + align:start position:0% +problem is solved so all of + + + align:start position:0% +problem is solved so all of +these uh these matrices can be then + + align:start position:0% +these uh these matrices can be then + + + align:start position:0% +these uh these matrices can be then +written as uh so you can find the igen + + align:start position:0% +written as uh so you can find the igen + + + align:start position:0% +written as uh so you can find the igen +values you can find the igen vectors + + align:start position:0% +values you can find the igen vectors + + + align:start position:0% +values you can find the igen vectors +you've got + + align:start position:0% + + + + align:start position:0% + +everything are you all with me on + + align:start position:0% +everything are you all with me on + + + align:start position:0% +everything are you all with me on +this okay + + align:start position:0% +this okay + + + align:start position:0% +this okay +now I think the last main point I want + + align:start position:0% +now I think the last main point I want + + + align:start position:0% +now I think the last main point I want +to make + + align:start position:0% +to make + + + align:start position:0% +to make +is we have two basis sets one in which + + align:start position:0% +is we have two basis sets one in which + + + align:start position:0% +is we have two basis sets one in which +the spin orbit is diagonal and the other + + align:start position:0% +the spin orbit is diagonal and the other + + + align:start position:0% +the spin orbit is diagonal and the other +in which the + + align:start position:0% +in which the + + + align:start position:0% +in which the +electronic term is diagonal and that's a + + align:start position:0% +electronic term is diagonal and that's a + + + align:start position:0% +electronic term is diagonal and that's a +uh that's typical of what you encounter + + align:start position:0% +uh that's typical of what you encounter + + + align:start position:0% +uh that's typical of what you encounter +when you do effective hamiltonians you + + align:start position:0% +when you do effective hamiltonians you + + + align:start position:0% +when you do effective hamiltonians you +generally have two two physical + + align:start position:0% +generally have two two physical + + + align:start position:0% +generally have two two physical +effects + + align:start position:0% +effects + + + align:start position:0% +effects +one + + align:start position:0% +one + + + align:start position:0% +one +uh and they oppose each each other in + + align:start position:0% +uh and they oppose each each other in + + + align:start position:0% +uh and they oppose each each other in +the sense that one likes a particular + + align:start position:0% +the sense that one likes a particular + + + align:start position:0% +the sense that one likes a particular +representation the other likes the + + align:start position:0% +representation the other likes the + + + align:start position:0% +representation the other likes the +different + + align:start position:0% +different + + + align:start position:0% +different +representation in representation number + + align:start position:0% +representation in representation number + + + align:start position:0% +representation in representation number +one one operator is diagonal and the + + align:start position:0% +one one operator is diagonal and the + + + align:start position:0% +one one operator is diagonal and the +other is off diagonal in the other in + + align:start position:0% +other is off diagonal in the other in + + + align:start position:0% +other is off diagonal in the other in +the other representation it's the other + + align:start position:0% +the other representation it's the other + + + align:start position:0% +the other representation it's the other +way + + align:start position:0% +way + + + align:start position:0% +way +around you know it's like you + + align:start position:0% +around you know it's like you + + + align:start position:0% +around you know it's like you +know an incompatible relationship + + align:start position:0% +know an incompatible relationship + + + align:start position:0% +know an incompatible relationship +leading to a divorce no matter what you + + align:start position:0% +leading to a divorce no matter what you + + + align:start position:0% +leading to a divorce no matter what you +do you can have Ian values but you can't + + align:start position:0% +do you can have Ian values but you can't + + + align:start position:0% +do you can have Ian values but you can't +have simple representation so uh and it + + align:start position:0% +have simple representation so uh and it + + + align:start position:0% +have simple representation so uh and it +always happens that there is a term that + + align:start position:0% +always happens that there is a term that + + + align:start position:0% +always happens that there is a term that +uh one term always opposes another and + + align:start position:0% +uh one term always opposes another and + + + align:start position:0% +uh one term always opposes another and +sometimes you play favorites you say I I + + align:start position:0% +sometimes you play favorites you say I I + + + align:start position:0% +sometimes you play favorites you say I I +like spin orbit and so I'm always going + + align:start position:0% +like spin orbit and so I'm always going + + + align:start position:0% +like spin orbit and so I'm always going +to choose the spin orbit diagonal and + + align:start position:0% +to choose the spin orbit diagonal and + + + align:start position:0% +to choose the spin orbit diagonal and +sometimes that's good and sometimes + + align:start position:0% +sometimes that's good and sometimes + + + align:start position:0% +sometimes that's good and sometimes +that's bad and so this nice figure that + + align:start position:0% +that's bad and so this nice figure that + + + align:start position:0% +that's bad and so this nice figure that +I work so hard over the years on page + + align:start position:0% +I work so hard over the years on page + + + align:start position:0% +I work so hard over the years on page +eight uh this illustrates the + + align:start position:0% +eight uh this illustrates the + + + align:start position:0% +eight uh this illustrates the +qualitative energy level structure for + + align:start position:0% +qualitative energy level structure for + + + align:start position:0% +qualitative energy level structure for +p^2 uh in The Zeta equals + + align:start position:0% +p^2 uh in The Zeta equals + + + align:start position:0% +p^2 uh in The Zeta equals +z F2 not equal to zero limit and here is + + align:start position:0% +z F2 not equal to zero limit and here is + + + align:start position:0% +z F2 not equal to zero limit and here is +in the uh F2 equals z Zeta equals not + + align:start position:0% +in the uh F2 equals z Zeta equals not + + + align:start position:0% +in the uh F2 equals z Zeta equals not +equal to zero + + align:start position:0% +equal to zero + + + align:start position:0% +equal to zero +limit and so what I did is I I energy + + align:start position:0% +limit and so what I did is I I energy + + + align:start position:0% +limit and so what I did is I I energy +levels uh and then I normalize by + + align:start position:0% +levels uh and then I normalize by + + + align:start position:0% +levels uh and then I normalize by +dividing uh by the extreme you know the + + align:start position:0% +dividing uh by the extreme you know the + + + align:start position:0% +dividing uh by the extreme you know the +energy difference between the top and + + align:start position:0% +energy difference between the top and + + + align:start position:0% +energy difference between the top and +the bottom so that they could be put on + + align:start position:0% +the bottom so that they could be put on + + + align:start position:0% +the bottom so that they could be put on +to the exact same scale so you see in + + align:start position:0% +to the exact same scale so you see in + + + align:start position:0% +to the exact same scale so you see in +one case we have a pattern of three + + align:start position:0% +one case we have a pattern of three + + + align:start position:0% +one case we have a pattern of three +degenerate one and one and over here we + + align:start position:0% +degenerate one and one and over here we + + + align:start position:0% +degenerate one and one and over here we +have a pattern of + + align:start position:0% +have a pattern of + + + align:start position:0% +have a pattern of +two two and + + align:start position:0% +two two and + + + align:start position:0% +two two and +one this is the ls this is the uh uh the + + align:start position:0% +one this is the ls this is the uh uh the + + + align:start position:0% +one this is the ls this is the uh uh the +LS s limit where spin orbit is not + + align:start position:0% +LS s limit where spin orbit is not + + + align:start position:0% +LS s limit where spin orbit is not +important and this is the JJ limit where + + align:start position:0% +important and this is the JJ limit where + + + align:start position:0% +important and this is the JJ limit where +spin orbit is so important that the + + align:start position:0% +spin orbit is so important that the + + + align:start position:0% +spin orbit is so important that the +inter electronic repulsion is not + + align:start position:0% +inter electronic repulsion is not + + + align:start position:0% +inter electronic repulsion is not +important you rarely get to this limit + + align:start position:0% +important you rarely get to this limit + + + align:start position:0% +important you rarely get to this limit +except when you get into the very bottom + + align:start position:0% +except when you get into the very bottom + + + align:start position:0% +except when you get into the very bottom +of the periodic table where spin orbit + + align:start position:0% +of the periodic table where spin orbit + + + align:start position:0% +of the periodic table where spin orbit +is Big compared to inter electronic + + align:start position:0% +is Big compared to inter electronic + + + align:start position:0% +is Big compared to inter electronic +repulsion and that's partly because spin + + align:start position:0% +repulsion and that's partly because spin + + + align:start position:0% +repulsion and that's partly because spin +orbit is big and partly because the + + align:start position:0% +orbit is big and partly because the + + + align:start position:0% +orbit is big and partly because the +orbitals have gotten so large that they + + align:start position:0% +orbitals have gotten so large that they + + + align:start position:0% +orbitals have gotten so large that they +don't repel each other anymore + + align:start position:0% +don't repel each other anymore + + + align:start position:0% +don't repel each other anymore +more so uh but these are two very + + align:start position:0% +more so uh but these are two very + + + align:start position:0% +more so uh but these are two very +different patterns and you're sort of + + align:start position:0% +different patterns and you're sort of + + + align:start position:0% +different patterns and you're sort of +alert for uh these in the spectrum that + + align:start position:0% +alert for uh these in the spectrum that + + + align:start position:0% +alert for uh these in the spectrum that +tells you what are going to be the good + + align:start position:0% +tells you what are going to be the good + + + align:start position:0% +tells you what are going to be the good +quantum numbers it tells you something + + align:start position:0% +quantum numbers it tells you something + + + align:start position:0% +quantum numbers it tells you something +about relative intensi it tells you what + + align:start position:0% +about relative intensi it tells you what + + + align:start position:0% +about relative intensi it tells you what +pattern what what part of the pattern do + + align:start position:0% +pattern what what part of the pattern do + + + align:start position:0% +pattern what what part of the pattern do +you need to see to figure out what + + align:start position:0% +you need to see to figure out what + + + align:start position:0% +you need to see to figure out what +states you're + + align:start position:0% +states you're + + + align:start position:0% +states you're +in the next lecture is going to be an + + align:start position:0% +in the next lecture is going to be an + + + align:start position:0% +in the next lecture is going to be an +elementary lecture on how do we assign + + align:start position:0% +elementary lecture on how do we assign + + + align:start position:0% +elementary lecture on how do we assign +atomic spectrum never will you find + + align:start position:0% +atomic spectrum never will you find + + + align:start position:0% +atomic spectrum never will you find +anything in any textbook except in + + align:start position:0% +anything in any textbook except in + + + align:start position:0% +anything in any textbook except in +herzberg's little book on Atomic Spectra + + align:start position:0% +herzberg's little book on Atomic Spectra + + + align:start position:0% +herzberg's little book on Atomic Spectra +where it describes how do we assign a + + align:start position:0% +where it describes how do we assign a + + + align:start position:0% +where it describes how do we assign a +spectrum and so it you know it's + + align:start position:0% +spectrum and so it you know it's + + + align:start position:0% +spectrum and so it you know it's +something you have to do and so I will + + align:start position:0% +something you have to do and so I will + + + align:start position:0% +something you have to do and so I will +talk about but I use these kinds of + + align:start position:0% +talk about but I use these kinds of + + + align:start position:0% +talk about but I use these kinds of +patterns as well as some simpler ideas + + align:start position:0% +patterns as well as some simpler ideas + + + align:start position:0% +patterns as well as some simpler ideas +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +so uh is there any connection between + + align:start position:0% +so uh is there any connection between + + + align:start position:0% +so uh is there any connection between +the energy splittings that you wrote + + align:start position:0% +the energy splittings that you wrote + + + align:start position:0% +the energy splittings that you wrote +here like success to 9 F2 and what page + + align:start position:0% +here like success to 9 F2 and what page + + + align:start position:0% +here like success to 9 F2 and what page +are we on uh this page eight yes is + + align:start position:0% +are we on uh this page eight yes is + + + align:start position:0% +are we on uh this page eight yes is +there any connection in the The Zeta + + align:start position:0% +there any connection in the The Zeta + + + align:start position:0% +there any connection in the The Zeta +equals 0 and The Zeta do not equal Z + + align:start position:0% +equals 0 and The Zeta do not equal Z + + + align:start position:0% +equals 0 and The Zeta do not equal Z +Limit between the energy splittings of + + align:start position:0% +Limit between the energy splittings of + + + align:start position:0% +Limit between the energy splittings of +the course + + align:start position:0% +the course + + + align:start position:0% +the course +structure well if I've chosen the two + + align:start position:0% +structure well if I've chosen the two + + + align:start position:0% +structure well if I've chosen the two +limits the two limits that are perfectly + + align:start position:0% +limits the two limits that are perfectly + + + align:start position:0% +limits the two limits that are perfectly +in one + + align:start position:0% +in one + + + align:start position:0% +in one +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um for the same you know I've chosen it + + align:start position:0% +um for the same you know I've chosen it + + + align:start position:0% +um for the same you know I've chosen it +for uh for p squ right and and so uh + + align:start position:0% +for uh for p squ right and and so uh + + + align:start position:0% +for uh for p squ right and and so uh +these + + align:start position:0% +these + + + align:start position:0% +these +patterns uh there can't be any + + align:start position:0% +patterns uh there can't be any + + + align:start position:0% +patterns uh there can't be any +resemblance between the two patterns + + align:start position:0% +resemblance between the two patterns + + + align:start position:0% +resemblance between the two patterns +because they're determined by two + + align:start position:0% +because they're determined by two + + + align:start position:0% +because they're determined by two +completely different yeah right and but + + align:start position:0% +completely different yeah right and but + + + align:start position:0% +completely different yeah right and but +what you can see is on the next page I I + + align:start position:0% +what you can see is on the next page I I + + + align:start position:0% +what you can see is on the next page I I +describe the energy level patterns in + + align:start position:0% +describe the energy level patterns in + + + align:start position:0% +describe the energy level patterns in +the extreme limits and for two real + + align:start position:0% +the extreme limits and for two real + + + align:start position:0% +the extreme limits and for two real +atoms in between those limits and so you + + align:start position:0% +atoms in between those limits and so you + + + align:start position:0% +atoms in between those limits and so you +can see how uh you as you go from the + + align:start position:0% +can see how uh you as you go from the + + + align:start position:0% +can see how uh you as you go from the +spin orbit is zero to the spin orbit of + + align:start position:0% +spin orbit is zero to the spin orbit of + + + align:start position:0% +spin orbit is zero to the spin orbit of +small limit the pattern is still + + align:start position:0% +small limit the pattern is still + + + align:start position:0% +small limit the pattern is still +clear you just split the spin or the + + align:start position:0% +clear you just split the spin or the + + + align:start position:0% +clear you just split the spin or the +triplet P state which is the lowest + + align:start position:0% +triplet P state which is the lowest + + + align:start position:0% +triplet P state which is the lowest +State because of HS rules and then as we + + align:start position:0% +State because of HS rules and then as we + + + align:start position:0% +State because of HS rules and then as we +go up in spin orbit coupling strength + + align:start position:0% +go up in spin orbit coupling strength + + + align:start position:0% +go up in spin orbit coupling strength +and down in in electronic repulsion we + + align:start position:0% +and down in in electronic repulsion we + + + align:start position:0% +and down in in electronic repulsion we +see that the uh the J equals Zer levels + + align:start position:0% +see that the uh the J equals Zer levels + + + align:start position:0% +see that the uh the J equals Zer levels +repel the Daylights out of each other + + align:start position:0% +repel the Daylights out of each other + + + align:start position:0% +repel the Daylights out of each other +and the J equal two levels also try to + + align:start position:0% +and the J equal two levels also try to + + + align:start position:0% +and the J equal two levels also try to +repel and eventually you end up with + + align:start position:0% +repel and eventually you end up with + + + align:start position:0% +repel and eventually you end up with +this pattern where now you have the JJ + + align:start position:0% +this pattern where now you have the JJ + + + align:start position:0% +this pattern where now you have the JJ +limit where all it matters is the two J + + align:start position:0% +limit where all it matters is the two J + + + align:start position:0% +limit where all it matters is the two J +values of the two + + align:start position:0% +values of the two + + + align:start position:0% +values of the two +electrons uh and it doesn't matter that + + align:start position:0% +electrons uh and it doesn't matter that + + + align:start position:0% +electrons uh and it doesn't matter that +three Hales plus three halves can make + + align:start position:0% +three Hales plus three halves can make + + + align:start position:0% +three Hales plus three halves can make +either zero or + + align:start position:0% +either zero or + + + align:start position:0% +either zero or +three that's + + align:start position:0% + + + + align:start position:0% + +interesting well they can make zero or + + align:start position:0% +interesting well they can make zero or + + + align:start position:0% +interesting well they can make zero or +two because of the uh it's true it's not + + align:start position:0% +two because of the uh it's true it's not + + + align:start position:0% +two because of the uh it's true it's not +a mistake it was a mistake here you + + align:start position:0% +a mistake it was a mistake here you + + + align:start position:0% +a mistake it was a mistake here you +know there on the previous page I + + align:start position:0% +know there on the previous page I + + + align:start position:0% +know there on the previous page I +explained how the Exclusion Principle + + align:start position:0% +explained how the Exclusion Principle + + + align:start position:0% +explained how the Exclusion Principle +knocks out something but anyway so you + + align:start position:0% +knocks out something but anyway so you + + + align:start position:0% +knocks out something but anyway so you +you get a pattern of two two and one and + + align:start position:0% +you get a pattern of two two and one and + + + align:start position:0% +you get a pattern of two two and one and +it just has to do with the spin orbit + + align:start position:0% +it just has to do with the spin orbit + + + align:start position:0% +it just has to do with the spin orbit +not changing J for individual electrons + + align:start position:0% +not changing J for individual electrons + + + align:start position:0% +not changing J for individual electrons +but it will + + align:start position:0% +but it will + + + align:start position:0% +but it will +change um it will change L and s but not + + align:start position:0% +change um it will change L and s but not + + + align:start position:0% +change um it will change L and s but not +J for the overall so and you can write + + align:start position:0% +J for the overall so and you can write + + + align:start position:0% +J for the overall so and you can write +as you can always do in effective + + align:start position:0% +as you can always do in effective + + + align:start position:0% +as you can always do in effective +hamiltonian land you can write the + + align:start position:0% +hamiltonian land you can write the + + + align:start position:0% +hamiltonian land you can write the +effective hamiltonian either the + + align:start position:0% +effective hamiltonian either the + + + align:start position:0% +effective hamiltonian either the +lsj or the JJJ limit I don't know you + + align:start position:0% +lsj or the JJJ limit I don't know you + + + align:start position:0% +lsj or the JJJ limit I don't know you +know the English language is defective + + align:start position:0% +know the English language is defective + + + align:start position:0% +know the English language is defective +there's no different tone for o + + align:start position:0% +there's no different tone for o + + + align:start position:0% +there's no different tone for o +uppercase and lowercase letters so JJJ + + align:start position:0% +uppercase and lowercase letters so JJJ + + + align:start position:0% +uppercase and lowercase letters so JJJ +sounds really stupid but it's really + + align:start position:0% +sounds really stupid but it's really + + + align:start position:0% +sounds really stupid but it's really +referred to as JJ as opposed to JJJ but + + align:start position:0% +referred to as JJ as opposed to JJJ but + + + align:start position:0% +referred to as JJ as opposed to JJJ but +anyway that's all I have to say I think + + align:start position:0% +anyway that's all I have to say I think + + + align:start position:0% +anyway that's all I have to say I think +uh and I do have a + + align:start position:0% +uh and I do have a + + + align:start position:0% +uh and I do have a +suggestion this is not required however + + align:start position:0% +suggestion this is not required however + + + align:start position:0% +suggestion this is not required however +I do recommend that you go through the + + align:start position:0% +I do recommend that you go through the + + + align:start position:0% +I do recommend that you go through the +algebra uh that's on pages 5 through 11 + + align:start position:0% +algebra uh that's on pages 5 through 11 + + + align:start position:0% +algebra uh that's on pages 5 through 11 +for p squ to do D Squared and all of the + + align:start position:0% +for p squ to do D Squared and all of the + + + align:start position:0% +for p squ to do D Squared and all of the +critical + + align:start position:0% +critical + + + align:start position:0% +critical +stuff uh you will be able to find in + + align:start position:0% +stuff uh you will be able to find in + + + align:start position:0% +stuff uh you will be able to find in +Condon shortly or tinum it's it's in the + + align:start position:0% +Condon shortly or tinum it's it's in the + + + align:start position:0% +Condon shortly or tinum it's it's in the +you know it's this is not an assignment + + align:start position:0% +you know it's this is not an assignment + + + align:start position:0% +you know it's this is not an assignment +I do recommend it if you're going to + + align:start position:0% +I do recommend it if you're going to + + + align:start position:0% +I do recommend it if you're going to +learn this material uh it's a good idea + + align:start position:0% +learn this material uh it's a good idea + + + align:start position:0% +learn this material uh it's a good idea +but it's not as important as some of the + + align:start position:0% +but it's not as important as some of the + + + align:start position:0% +but it's not as important as some of the +other stuff that I will + + align:start position:0% +other stuff that I will + + + align:start position:0% +other stuff that I will +uh deal + + align:start position:0% + + + + align:start position:0% + +with + + align:start position:0% +with + + + align:start position:0% +with +okay you missed noa's + + align:start position:0% +okay you missed noa's + + + align:start position:0% +okay you missed noa's +lecture you had to listen to me I don't + + align:start position:0% +lecture you had to listen to me I don't + + + align:start position:0% +lecture you had to listen to me I don't +know whether whether that's a plus or a + + align:start position:0% +know whether whether that's a plus or a + + + align:start position:0% +know whether whether that's a plus or a +minus but anyway see you on Wednesday + + align:start position:0% +minus but anyway see you on Wednesday + + + align:start position:0% +minus but anyway see you on Wednesday +can I ask a question + + align:start position:0% +can I ask a question + + + align:start position:0% +can I ask a question +sure + + align:start position:0% +sure + + + align:start position:0% +sure +um put back before the first thing you + + align:start position:0% +um put back before the first thing you + + + align:start position:0% +um put back before the first thing you +do is you list the orbital + + align:start position:0% +do is you list the orbital + + + align:start position:0% +do is you list the orbital +configurations yes and then you + + align:start position:0% +configurations yes and then you + + + align:start position:0% +configurations yes and then you +calculate these okay um freshman + + align:start position:0% +calculate these okay um freshman + + + align:start position:0% +calculate these okay um freshman +chemistry ideas get most of the orbital + + align:start position:0% +chemistry ideas get most of the orbital + + + align:start position:0% +chemistry ideas get most of the orbital +configurations right for atoms but maybe + + align:start position:0% +configurations right for atoms but maybe + + + align:start position:0% +configurations right for atoms but maybe +not technum or some other weird + + align:start position:0% +not technum or some other weird + + + align:start position:0% +not technum or some other weird +transition metals for m ules it can also + + align:start position:0% +transition metals for m ules it can also + + + align:start position:0% +transition metals for m ules it can also +be occasionally difficult right and so + + align:start position:0% +be occasionally difficult right and so + + + align:start position:0% +be occasionally difficult right and so +of course we can also I mean we also + + align:start position:0% +of course we can also I mean we also + + + align:start position:0% +of course we can also I mean we also +know cuz we have books and and other + + align:start position:0% +know cuz we have books and and other + + + align:start position:0% +know cuz we have books and and other +people have done experiments and they're + + align:start position:0% +people have done experiments and they're + + + align:start position:0% +people have done experiments and they're +not more sistic is what they really are + + align:start position:0% +not more sistic is what they really are + + + align:start position:0% +not more sistic is what they really are +well usually what happens is when you do + + align:start position:0% +well usually what happens is when you do + + + align:start position:0% +well usually what happens is when you do +these sorts of + + align:start position:0% +these sorts of + + + align:start position:0% +these sorts of +things you know the + + align:start position:0% +things you know the + + + align:start position:0% +things you know the +trends and so there are you like your + + align:start position:0% +trends and so there are you like your + + + align:start position:0% +trends and so there are you like your +friend they're known unknowns and + + align:start position:0% +friend they're known unknowns and + + + align:start position:0% +friend they're known unknowns and +unknown unknowns well uh + + align:start position:0% +unknown unknowns well uh + + + align:start position:0% +unknown unknowns well uh +the when you have two things pointing in + + align:start position:0% +the when you have two things pointing in + + + align:start position:0% +the when you have two things pointing in +the same + + align:start position:0% +the same + + + align:start position:0% +the same +direction it's always easy to make a + + align:start position:0% +direction it's always easy to make a + + + align:start position:0% +direction it's always easy to make a +deduction when they're pointing in + + align:start position:0% +deduction when they're pointing in + + + align:start position:0% +deduction when they're pointing in +different directions it's much more + + align:start position:0% +different directions it's much more + + + align:start position:0% +different directions it's much more +subtle you need to actually calculate + + align:start position:0% +subtle you need to actually calculate + + + align:start position:0% +subtle you need to actually calculate +num sometimes you have to calculate but + + align:start position:0% +num sometimes you have to calculate but + + + align:start position:0% +num sometimes you have to calculate but +usually you can say well there this is + + align:start position:0% +usually you can say well there this is + + + align:start position:0% +usually you can say well there this is +interesting because there's a delicate + + align:start position:0% +interesting because there's a delicate + + + align:start position:0% +interesting because there's a delicate +balance between these two + + align:start position:0% +balance between these two + + + align:start position:0% +balance between these two +symmetries and if we look at a series of + + align:start position:0% +symmetries and if we look at a series of + + + align:start position:0% +symmetries and if we look at a series of +isoelectronic molecul ules it might + + align:start position:0% +isoelectronic molecul ules it might + + + align:start position:0% +isoelectronic molecul ules it might +switch as it does actually for The + + align:start position:0% +switch as it does actually for The + + + align:start position:0% +switch as it does actually for The +Alkali + + align:start position:0% +Alkali + + + align:start position:0% +Alkali +oxides The Alkali + + align:start position:0% +oxides The Alkali + + + align:start position:0% +oxides The Alkali +monoxides uh you would naively predict + + align:start position:0% +monoxides uh you would naively predict + + + align:start position:0% +monoxides uh you would naively predict +that there is well there's a doublet pi + + align:start position:0% +that there is well there's a doublet pi + + + align:start position:0% +that there is well there's a doublet pi +and a doublet Sigma State and their + + align:start position:0% +and a doublet Sigma State and their + + + align:start position:0% +and a doublet Sigma State and their +relative order is is uh CH reverses as + + align:start position:0% +relative order is is uh CH reverses as + + + align:start position:0% +relative order is is uh CH reverses as +you go up the periodic table because + + align:start position:0% +you go up the periodic table because + + + align:start position:0% +you go up the periodic table because +there is an overlap repulsion effect and + + align:start position:0% +there is an overlap repulsion effect and + + + align:start position:0% +there is an overlap repulsion effect and +a quadripole effect and they go in + + align:start position:0% +a quadripole effect and they go in + + + align:start position:0% +a quadripole effect and they go in +opposite + + align:start position:0% +opposite + + + align:start position:0% +opposite +directions and so you can understand it + + align:start position:0% +directions and so you can understand it + + + align:start position:0% +directions and so you can understand it +but usually when you know you have + + align:start position:0% +but usually when you know you have + + + align:start position:0% +but usually when you know you have +opposite effects you have to find some + + align:start position:0% +opposite effects you have to find some + + + align:start position:0% +opposite effects you have to find some +reason for deciding which one's going to + + align:start position:0% +reason for deciding which one's going to + + + align:start position:0% +reason for deciding which one's going to +win but very often you know that they're + + align:start position:0% +win but very often you know that they're + + + align:start position:0% +win but very often you know that they're +both going in the same direction \ No newline at end of file diff --git a/aDAsbWBTlvI.txt b/aDAsbWBTlvI.txt new file mode 100644 index 0000000000000000000000000000000000000000..858b1f52edf5008d91e2fc6e66f7eae822a5871a --- /dev/null +++ b/aDAsbWBTlvI.txt @@ -0,0 +1,147 @@ +align:start position:0% + +so the development of speaking and + + align:start position:0% +so the development of speaking and + + + align:start position:0% +so the development of speaking and +listening requires interactions with + + align:start position:0% +listening requires interactions with + + + align:start position:0% +listening requires interactions with +somebody else + + align:start position:0% +somebody else + + + align:start position:0% +somebody else +so that has to be done in classroom + + align:start position:0% +so that has to be done in classroom + + + align:start position:0% +so that has to be done in classroom +because there are not so many Japanese + + align:start position:0% +because there are not so many Japanese + + + align:start position:0% +because there are not so many Japanese +people on campus at MIT so classroom + + align:start position:0% +people on campus at MIT so classroom + + + align:start position:0% +people on campus at MIT so classroom +activities really focus on the + + align:start position:0% +activities really focus on the + + + align:start position:0% +activities really focus on the +development of listening and speaking + + align:start position:0% +development of listening and speaking + + + align:start position:0% +development of listening and speaking +whereas reading and writing students can + + align:start position:0% +whereas reading and writing students can + + + align:start position:0% +whereas reading and writing students can +do them like outside class and then in + + align:start position:0% +do them like outside class and then in + + + align:start position:0% +do them like outside class and then in +particular our textbook has so called + + align:start position:0% +particular our textbook has so called + + + align:start position:0% +particular our textbook has so called +workbook and then they can do writing + + align:start position:0% +workbook and then they can do writing + + + align:start position:0% +workbook and then they can do writing +practice by themselves in fact we do we + + align:start position:0% +practice by themselves in fact we do we + + + align:start position:0% +practice by themselves in fact we do we +provide assignment and so that they can + + align:start position:0% +provide assignment and so that they can + + + align:start position:0% +provide assignment and so that they can +just you know practice writing at home + + align:start position:0% +just you know practice writing at home + + + align:start position:0% +just you know practice writing at home +for reading we have our textbook has + + align:start position:0% +for reading we have our textbook has + + + align:start position:0% +for reading we have our textbook has +reading section for each lesson and we + + align:start position:0% +reading section for each lesson and we + + + align:start position:0% +reading section for each lesson and we +conduct we provide reading session one + + align:start position:0% +conduct we provide reading session one + + + align:start position:0% +conduct we provide reading session one +day for each lesson in class \ No newline at end of file diff --git a/aY7d_-INloc.txt b/aY7d_-INloc.txt new file mode 100644 index 0000000000000000000000000000000000000000..68d2cbaa86b9ace4a7a99bbecda88aae9466f9ff --- /dev/null +++ b/aY7d_-INloc.txt @@ -0,0 +1,2643 @@ +align:start position:0% + +right so + + align:start position:0% +right so + + + align:start position:0% +right so +it's about this particular plant here + + align:start position:0% +it's about this particular plant here + + + align:start position:0% +it's about this particular plant here +uh which is a desalination plant i + + align:start position:0% +uh which is a desalination plant i + + + align:start position:0% +uh which is a desalination plant i +prefer to call it de-salting because uh + + align:start position:0% +prefer to call it de-salting because uh + + + align:start position:0% +prefer to call it de-salting because uh +salination implies that you're actually + + align:start position:0% +salination implies that you're actually + + + align:start position:0% +salination implies that you're actually +going to the effort of putting salt in + + align:start position:0% +going to the effort of putting salt in + + + align:start position:0% +going to the effort of putting salt in +the water which you don't have to + + align:start position:0% +the water which you don't have to + + + align:start position:0% +the water which you don't have to +so it is + + align:start position:0% +so it is + + + align:start position:0% +so it is +a huge plant it's one of the largest + + align:start position:0% +a huge plant it's one of the largest + + + align:start position:0% +a huge plant it's one of the largest +desolding desalination plants in the + + align:start position:0% +desolding desalination plants in the + + + align:start position:0% +desolding desalination plants in the +world and it was built in victoria which + + align:start position:0% +world and it was built in victoria which + + + align:start position:0% +world and it was built in victoria which +is a + + align:start position:0% +is a + + + align:start position:0% +is a +southern state of um australia whose + + align:start position:0% +southern state of um australia whose + + + align:start position:0% +southern state of um australia whose +capital is melbourne + + align:start position:0% +capital is melbourne + + + align:start position:0% +capital is melbourne +and + + align:start position:0% +and + + + align:start position:0% +and +um + + align:start position:0% + + + + align:start position:0% + +it has it is a mega plant + + align:start position:0% +it has it is a mega plant + + + align:start position:0% +it has it is a mega plant +it has a hundred capacity of 150 billion + + align:start position:0% +it has a hundred capacity of 150 billion + + + align:start position:0% +it has a hundred capacity of 150 billion +liters or the a year + + align:start position:0% +liters or the a year + + + align:start position:0% +liters or the a year +and interestingly it was built in three + + align:start position:0% +and interestingly it was built in three + + + align:start position:0% +and interestingly it was built in three +modules + + align:start position:0% +modules + + + align:start position:0% +modules +uh so that the modules here are 50 + + align:start position:0% +uh so that the modules here are 50 + + + align:start position:0% +uh so that the modules here are 50 +billion a year + + align:start position:0% +billion a year + + + align:start position:0% +billion a year +and um + + align:start position:0% +and um + + + align:start position:0% +and um +but they were built all at once + + align:start position:0% +but they were built all at once + + + align:start position:0% +but they were built all at once +the capital cost was three and a half + + align:start position:0% +the capital cost was three and a half + + + align:start position:0% +the capital cost was three and a half +billion aussie dollars + + align:start position:0% +billion aussie dollars + + + align:start position:0% +billion aussie dollars +which is something around + + align:start position:0% +which is something around + + + align:start position:0% +which is something around +two and a half billion us dollars it's a + + align:start position:0% +two and a half billion us dollars it's a + + + align:start position:0% +two and a half billion us dollars it's a +big project + + align:start position:0% +big project + + + align:start position:0% +big project +started in 2009 um + + align:start position:0% +started in 2009 um + + + align:start position:0% +started in 2009 um +completed in 2012 and + + align:start position:0% +completed in 2012 and + + + align:start position:0% +completed in 2012 and +uh it was what they call a + + align:start position:0% +uh it was what they call a + + + align:start position:0% +uh it was what they call a +public-private partnership that is it + + align:start position:0% +public-private partnership that is it + + + align:start position:0% +public-private partnership that is it +was built by private investors who + + align:start position:0% +was built by private investors who + + + align:start position:0% +was built by private investors who +fronted up the capital + + align:start position:0% +fronted up the capital + + + align:start position:0% +fronted up the capital +and it's designed to guarantee supply + + align:start position:0% +and it's designed to guarantee supply + + + align:start position:0% +and it's designed to guarantee supply +through uh 2039 as it was built with a + + align:start position:0% +through uh 2039 as it was built with a + + + align:start position:0% +through uh 2039 as it was built with a +30-year forecast in mind so this is an + + align:start position:0% +30-year forecast in mind so this is an + + + align:start position:0% +30-year forecast in mind so this is an +example of a massive investment initial + + align:start position:0% +example of a massive investment initial + + + align:start position:0% +example of a massive investment initial +investment to be maximum forecast over + + align:start position:0% +investment to be maximum forecast over + + + align:start position:0% +investment to be maximum forecast over +30 years + + align:start position:0% +30 years + + + align:start position:0% +30 years +maximum forecast driven by two things + + align:start position:0% +maximum forecast driven by two things + + + align:start position:0% +maximum forecast driven by two things +uh generally one is + + align:start position:0% +uh generally one is + + + align:start position:0% +uh generally one is +by the increasing population of + + align:start position:0% +by the increasing population of + + + align:start position:0% +by the increasing population of +melbourne itself as a + + align:start position:0% +melbourne itself as a + + + align:start position:0% +melbourne itself as a +really a very attractive and interesting + + align:start position:0% +really a very attractive and interesting + + + align:start position:0% +really a very attractive and interesting +city + + align:start position:0% +city + + + align:start position:0% +city +all very lively i'd recommend a visit to + + align:start position:0% +all very lively i'd recommend a visit to + + + align:start position:0% +all very lively i'd recommend a visit to +anyone i worked on the airports there + + align:start position:0% +anyone i worked on the airports there + + + align:start position:0% +anyone i worked on the airports there +and uh also because of + + align:start position:0% +and uh also because of + + + align:start position:0% +and uh also because of +increasing effect of climate change + + align:start position:0% +increasing effect of climate change + + + align:start position:0% +increasing effect of climate change +leading to + + align:start position:0% +leading to + + + align:start position:0% +leading to +plausible uh in increased uh + + align:start position:0% +plausible uh in increased uh + + + align:start position:0% +plausible uh in increased uh +periods of drought and low water in the + + align:start position:0% +periods of drought and low water in the + + + align:start position:0% +periods of drought and low water in the +reservoirs so a 30-year forecast now + + align:start position:0% +reservoirs so a 30-year forecast now + + + align:start position:0% +reservoirs so a 30-year forecast now +here's the let's think about the + + align:start position:0% +here's the let's think about the + + + align:start position:0% +here's the let's think about the +economics + + align:start position:0% +economics + + + align:start position:0% +economics +about this + + align:start position:0% +about this + + + align:start position:0% +about this +so the first so what happens is they + + align:start position:0% +so the first so what happens is they + + + align:start position:0% +so the first so what happens is they +build the plant and they keep it on tap + + align:start position:0% +build the plant and they keep it on tap + + + align:start position:0% +build the plant and they keep it on tap +they maintain it but they don't deliver + + align:start position:0% +they maintain it but they don't deliver + + + align:start position:0% +they maintain it but they don't deliver +any water until the + + align:start position:0% +any water until the + + + align:start position:0% +any water until the +water authorities of the state of + + align:start position:0% +water authorities of the state of + + + align:start position:0% +water authorities of the state of +victoria + + align:start position:0% +victoria + + + align:start position:0% +victoria +and a water board they have there + + align:start position:0% +and a water board they have there + + + align:start position:0% +and a water board they have there +ask for some + + align:start position:0% +ask for some + + + align:start position:0% +ask for some +so + + align:start position:0% +so + + + align:start position:0% +so +in 2016 as four years after the opening + + align:start position:0% +in 2016 as four years after the opening + + + align:start position:0% +in 2016 as four years after the opening +they placed an order for 50 billion + + align:start position:0% +they placed an order for 50 billion + + + align:start position:0% +they placed an order for 50 billion +leaders that is one-third of the + + align:start position:0% +leaders that is one-third of the + + + align:start position:0% +leaders that is one-third of the +capacity + + align:start position:0% +capacity + + + align:start position:0% +capacity +uh two years later they put in an order + + align:start position:0% +uh two years later they put in an order + + + align:start position:0% +uh two years later they put in an order +for + + align:start position:0% +for + + + align:start position:0% +for +less than 50 billion + + align:start position:0% +less than 50 billion + + + align:start position:0% +less than 50 billion +and just this year that is + + align:start position:0% +and just this year that is + + + align:start position:0% +and just this year that is +uh starting uh in april but basically + + align:start position:0% +uh starting uh in april but basically + + + align:start position:0% +uh starting uh in april but basically +into + + align:start position:0% +into + + + align:start position:0% +into +um the season the summer season which is + + align:start position:0% +um the season the summer season which is + + + align:start position:0% +um the season the summer season which is +what we think of fall summer + + align:start position:0% +what we think of fall summer + + + align:start position:0% +what we think of fall summer +fall winter and spring + + align:start position:0% +fall winter and spring + + + align:start position:0% +fall winter and spring +um + + align:start position:0% +um + + + align:start position:0% +um +they wanted 50 more billion so here what + + align:start position:0% +they wanted 50 more billion so here what + + + align:start position:0% +they wanted 50 more billion so here what +you have + + align:start position:0% +you have + + + align:start position:0% +you have +is a huge investment + + align:start position:0% +is a huge investment + + + align:start position:0% +is a huge investment +in + + align:start position:0% +in + + + align:start position:0% +in +that for the first that is so nothing + + align:start position:0% +that for the first that is so nothing + + + align:start position:0% +that for the first that is so nothing +there's no return on the first three + + align:start position:0% +there's no return on the first three + + + align:start position:0% +there's no return on the first three +years because it's under construction + + align:start position:0% +years because it's under construction + + + align:start position:0% +years because it's under construction +then for the next four years nothing + + align:start position:0% +then for the next four years nothing + + + align:start position:0% +then for the next four years nothing +happens + + align:start position:0% +happens + + + align:start position:0% +happens +the first order + + align:start position:0% +the first order + + + align:start position:0% +the first order +is for + + align:start position:0% +is for + + + align:start position:0% +is for +one-third of the total capacity + + align:start position:0% +one-third of the total capacity + + + align:start position:0% +one-third of the total capacity +the next two orders are for at least + + align:start position:0% +the next two orders are for at least + + + align:start position:0% +the next two orders are for at least +one-third the capacity but we haven't + + align:start position:0% +one-third the capacity but we haven't + + + align:start position:0% +one-third the capacity but we haven't +gotten anywhere near the full capacity + + align:start position:0% +gotten anywhere near the full capacity + + + align:start position:0% +gotten anywhere near the full capacity +so it posed the question + + align:start position:0% +so it posed the question + + + align:start position:0% +so it posed the question +uh should they have phased the modules + + align:start position:0% +uh should they have phased the modules + + + align:start position:0% +uh should they have phased the modules +over time i mean + + align:start position:0% +over time i mean + + + align:start position:0% +over time i mean +so far + + align:start position:0% +so far + + + align:start position:0% +so far +only two-thirds the capex has been uh + + align:start position:0% +only two-thirds the capex has been uh + + + align:start position:0% +only two-thirds the capex has been uh +has not been needed for a decade roughly + + align:start position:0% +has not been needed for a decade roughly + + + align:start position:0% +has not been needed for a decade roughly +speaking + + align:start position:0% +speaking + + + align:start position:0% +speaking +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +what do you think what are your + + align:start position:0% +what do you think what are your + + + align:start position:0% +what do you think what are your +reactions to this + + align:start position:0% +reactions to this + + + align:start position:0% +reactions to this +now they could say well a crisis could + + align:start position:0% +now they could say well a crisis could + + + align:start position:0% +now they could say well a crisis could +occur any time etc etc but um + + align:start position:0% +occur any time etc etc but um + + + align:start position:0% +occur any time etc etc but um +uh what do you think + + align:start position:0% +uh what do you think + + + align:start position:0% +uh what do you think +any thoughts or comments about this + + align:start position:0% +any thoughts or comments about this + + + align:start position:0% +any thoughts or comments about this +okay elias go ahead + + align:start position:0% +okay elias go ahead + + + align:start position:0% +okay elias go ahead +oh + + align:start position:0% +oh + + + align:start position:0% +oh +it's not a question i was just going to + + align:start position:0% +it's not a question i was just going to + + + align:start position:0% +it's not a question i was just going to +say that that's an example of the + + align:start position:0% +say that that's an example of the + + + align:start position:0% +say that that's an example of the +forecast it's always wrong + + align:start position:0% +forecast it's always wrong + + + align:start position:0% +forecast it's always wrong +well i don't know if the forecast was + + align:start position:0% +well i don't know if the forecast was + + + align:start position:0% +well i don't know if the forecast was +wrong + + align:start position:0% +wrong + + + align:start position:0% +wrong +um because it was the the forecast + + align:start position:0% +um because it was the the forecast + + + align:start position:0% +um because it was the the forecast +wasn't timed it sort of said they + + align:start position:0% +wasn't timed it sort of said they + + + align:start position:0% +wasn't timed it sort of said they +basically forecast a maximum possible + + align:start position:0% +basically forecast a maximum possible + + + align:start position:0% +basically forecast a maximum possible +demand and we don't know if that was + + align:start position:0% +demand and we don't know if that was + + + align:start position:0% +demand and we don't know if that was +wrong + + align:start position:0% +wrong + + + align:start position:0% +wrong +but + + align:start position:0% +but + + + align:start position:0% +but +it um + + align:start position:0% +it um + + + align:start position:0% +it um +uh we you know it's uncertain uh so they + + align:start position:0% +uh we you know it's uncertain uh so they + + + align:start position:0% +uh we you know it's uncertain uh so they +knew it was uncertain but the + + align:start position:0% +knew it was uncertain but the + + + align:start position:0% +knew it was uncertain but the +implications might have been well if + + align:start position:0% +implications might have been well if + + + align:start position:0% +implications might have been well if +it's going to go up by + + align:start position:0% +it's going to go up by + + + align:start position:0% +it's going to go up by +uh to a need 150 over all that time + + align:start position:0% +uh to a need 150 over all that time + + + align:start position:0% +uh to a need 150 over all that time +maybe they should have + + align:start position:0% +maybe they should have + + + align:start position:0% +maybe they should have +done it incrementally i mean the + + align:start position:0% +done it incrementally i mean the + + + align:start position:0% +done it incrementally i mean the +forecast might be right they might need + + align:start position:0% +forecast might be right they might need + + + align:start position:0% +forecast might be right they might need +a + + align:start position:0% +a + + + align:start position:0% +a +as much as the maximum at some time so + + align:start position:0% +as much as the maximum at some time so + + + align:start position:0% +as much as the maximum at some time so +hard to say + + align:start position:0% +hard to say + + + align:start position:0% +hard to say +i mean + + align:start position:0% +i mean + + + align:start position:0% +i mean +just like uh fire escapes uh or + + align:start position:0% +just like uh fire escapes uh or + + + align:start position:0% +just like uh fire escapes uh or +emergency exits from a building they may + + align:start position:0% +emergency exits from a building they may + + + align:start position:0% +emergency exits from a building they may +never be used doesn't mean it wasn't a + + align:start position:0% +never be used doesn't mean it wasn't a + + + align:start position:0% +never be used doesn't mean it wasn't a +good idea so having extra capacity don't + + align:start position:0% +good idea so having extra capacity don't + + + align:start position:0% +good idea so having extra capacity don't +use is not necessarily bad + + align:start position:0% +use is not necessarily bad + + + align:start position:0% +use is not necessarily bad +um but there's money involved in this + + align:start position:0% +um but there's money involved in this + + + align:start position:0% +um but there's money involved in this +and the other ways that deal with low + + align:start position:0% +and the other ways that deal with low + + + align:start position:0% +and the other ways that deal with low +water levels uh having a desalting plant + + align:start position:0% +water levels uh having a desalting plant + + + align:start position:0% +water levels uh having a desalting plant +is uh + + align:start position:0% +is uh + + + align:start position:0% +is uh +is a pretty special thing um there's + + align:start position:0% +is a pretty special thing um there's + + + align:start position:0% +is a pretty special thing um there's +water rationing and other kind of things + + align:start position:0% +water rationing and other kind of things + + + align:start position:0% +water rationing and other kind of things +so + + align:start position:0% +so + + + align:start position:0% +so +it's an issue is this was this + + align:start position:0% +it's an issue is this was this + + + align:start position:0% +it's an issue is this was this +a good investment is is the question i'm + + align:start position:0% +a good investment is is the question i'm + + + align:start position:0% +a good investment is is the question i'm +throwing out there + + align:start position:0% +throwing out there + + + align:start position:0% +throwing out there +joshua go ahead + + align:start position:0% +joshua go ahead + + + align:start position:0% +joshua go ahead +good morning professor so are you saying + + align:start position:0% +good morning professor so are you saying + + + align:start position:0% +good morning professor so are you saying +that they have capacity for 96 billion + + align:start position:0% +that they have capacity for 96 billion + + + align:start position:0% +that they have capacity for 96 billion +liters but they're only really using + + align:start position:0% +liters but they're only really using + + + align:start position:0% +liters but they're only really using +uh 50 billion liters + + align:start position:0% +uh 50 billion liters + + + align:start position:0% +uh 50 billion liters +i said they had capacity + + align:start position:0% +i said they had capacity + + + align:start position:0% +i said they had capacity +450 billion + + align:start position:0% +450 billion + + + align:start position:0% +450 billion +oh after construction this year in 2020 + + align:start position:0% +oh after construction this year in 2020 + + + align:start position:0% +oh after construction this year in 2020 +the capacity was all built as i + + align:start position:0% +the capacity was all built as i + + + align:start position:0% +the capacity was all built as i +as you can see on the slide now that was + + align:start position:0% +as you can see on the slide now that was + + + align:start position:0% +as you can see on the slide now that was +opened in 2012. for the first four years + + align:start position:0% +opened in 2012. for the first four years + + + align:start position:0% +opened in 2012. for the first four years +this thing didn't do a thing + + align:start position:0% +this thing didn't do a thing + + + align:start position:0% +this thing didn't do a thing +uh that's not necessarily bad i mean i + + align:start position:0% +uh that's not necessarily bad i mean i + + + align:start position:0% +uh that's not necessarily bad i mean i +have life insurance and i haven't died + + align:start position:0% +have life insurance and i haven't died + + + align:start position:0% +have life insurance and i haven't died +yet so i'm pretty happy about that but + + align:start position:0% +yet so i'm pretty happy about that but + + + align:start position:0% +yet so i'm pretty happy about that but +um + + align:start position:0% +um + + + align:start position:0% +um +still it was a very large uh + + align:start position:0% +still it was a very large uh + + + align:start position:0% +still it was a very large uh +and for the first decade just depending + + align:start position:0% +and for the first decade just depending + + + align:start position:0% +and for the first decade just depending +on when you start but uh they ha that is + + align:start position:0% +on when you start but uh they ha that is + + + align:start position:0% +on when you start but uh they ha that is +until 2020 they've only used up to + + align:start position:0% +until 2020 they've only used up to + + + align:start position:0% +until 2020 they've only used up to +one third of it which happens to be one + + align:start position:0% +one third of it which happens to be one + + + align:start position:0% +one third of it which happens to be one +of the just one of their modules + + align:start position:0% +of the just one of their modules + + + align:start position:0% +of the just one of their modules +capacity + + align:start position:0% +capacity + + + align:start position:0% +capacity +um are we talking the same language or + + align:start position:0% +um are we talking the same language or + + + align:start position:0% +um are we talking the same language or +are i + + align:start position:0% +are i + + + align:start position:0% +are i +we are i i thought it was uh + + align:start position:0% +we are i i thought it was uh + + + align:start position:0% +we are i i thought it was uh +construction and they built it and but + + align:start position:0% +construction and they built it and but + + + align:start position:0% +construction and they built it and but +they still only had a need for 50 uh 50 + + align:start position:0% +they still only had a need for 50 uh 50 + + + align:start position:0% +they still only had a need for 50 uh 50 +billion liters but i i would agree i + + align:start position:0% +billion liters but i i would agree i + + + align:start position:0% +billion liters but i i would agree i +think that they probably overshot and + + align:start position:0% +think that they probably overshot and + + + align:start position:0% +think that they probably overshot and +could have uh + + align:start position:0% +could have uh + + + align:start position:0% +could have uh +built incrementally and saved + + align:start position:0% +built incrementally and saved + + + align:start position:0% +built incrementally and saved +considerable amount of money uh at least + + align:start position:0% +considerable amount of money uh at least + + + align:start position:0% +considerable amount of money uh at least +in terms of net present value terms yes + + align:start position:0% +in terms of net present value terms yes + + + align:start position:0% +in terms of net present value terms yes +that's the that's what i'm uh thinking + + align:start position:0% +that's the that's what i'm uh thinking + + + align:start position:0% +that's the that's what i'm uh thinking +of now it turns out that the investors + + align:start position:0% +of now it turns out that the investors + + + align:start position:0% +of now it turns out that the investors +aren't having a hard time because + + align:start position:0% +aren't having a hard time because + + + align:start position:0% +aren't having a hard time because +um + + align:start position:0% +um + + + align:start position:0% +um +they're getting paid + + align:start position:0% +they're getting paid + + + align:start position:0% +they're getting paid +um the city is paying for them so um + + align:start position:0% +um the city is paying for them so um + + + align:start position:0% +um the city is paying for them so um +because they + + align:start position:0% +because they + + + align:start position:0% +because they +i've invested all that money in uh it's + + align:start position:0% +i've invested all that money in uh it's + + + align:start position:0% +i've invested all that money in uh it's +also possible they'll never use the + + align:start position:0% +also possible they'll never use the + + + align:start position:0% +also possible they'll never use the +water so they had a deal where the city + + align:start position:0% +water so they had a deal where the city + + + align:start position:0% +water so they had a deal where the city +actually pays them about 600 million a + + align:start position:0% +actually pays them about 600 million a + + + align:start position:0% +actually pays them about 600 million a +year just to keep the plant alive and to + + align:start position:0% +year just to keep the plant alive and to + + + align:start position:0% +year just to keep the plant alive and to +pay for the interest and the + + align:start position:0% +pay for the interest and the + + + align:start position:0% +pay for the interest and the +depreciations and so forth so + + align:start position:0% +depreciations and so forth so + + + align:start position:0% +depreciations and so forth so +the investors haven't heard but if it's + + align:start position:0% +the investors haven't heard but if it's + + + align:start position:0% +the investors haven't heard but if it's +too much construction it means that this + + align:start position:0% +too much construction it means that this + + + align:start position:0% +too much construction it means that this +uh the city of melbourne and the state + + align:start position:0% +uh the city of melbourne and the state + + + align:start position:0% +uh the city of melbourne and the state +of victoria have overpaid so too much is + + align:start position:0% +of victoria have overpaid so too much is + + + align:start position:0% +of victoria have overpaid so too much is +investment but the private investors i + + align:start position:0% +investment but the private investors i + + + align:start position:0% +investment but the private investors i +think are doing fine + + align:start position:0% +think are doing fine + + + align:start position:0% +think are doing fine +um + + align:start position:0% +um + + + align:start position:0% +um +other comments did you say well in drop + + align:start position:0% +other comments did you say well in drop + + + align:start position:0% +other comments did you say well in drop +yeah there are quite a few uh ali next + + align:start position:0% +yeah there are quite a few uh ali next + + + align:start position:0% +yeah there are quite a few uh ali next +professor so um yeah i was uh thinking + + align:start position:0% +professor so um yeah i was uh thinking + + + align:start position:0% +professor so um yeah i was uh thinking +of the um the trade-off between + + align:start position:0% +of the um the trade-off between + + + align:start position:0% +of the um the trade-off between +uh first + + align:start position:0% +uh first + + + align:start position:0% +uh first +uh building the flexibility + + align:start position:0% +uh building the flexibility + + + align:start position:0% +uh building the flexibility +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and then the exponent that is um + + align:start position:0% +and then the exponent that is um + + + align:start position:0% +and then the exponent that is um +are variable for the + + align:start position:0% +are variable for the + + + align:start position:0% +are variable for the +economies of scale + + align:start position:0% +economies of scale + + + align:start position:0% +economies of scale +so + + align:start position:0% +so + + + align:start position:0% +so +about just the economics but then as you + + align:start position:0% +about just the economics but then as you + + + align:start position:0% +about just the economics but then as you +said there is a + + align:start position:0% +said there is a + + + align:start position:0% +said there is a +sometimes for big infrastructure we're + + align:start position:0% +sometimes for big infrastructure we're + + + align:start position:0% +sometimes for big infrastructure we're +being paid for just having the capacity + + align:start position:0% +being paid for just having the capacity + + + align:start position:0% +being paid for just having the capacity +yeah so + + align:start position:0% +yeah so + + + align:start position:0% +yeah so +and but also there can be + + align:start position:0% +and but also there can be + + + align:start position:0% +and but also there can be +uh political reasons behind it etc so + + align:start position:0% +uh political reasons behind it etc so + + + align:start position:0% +uh political reasons behind it etc so +this is way beyond the the economics + + align:start position:0% +this is way beyond the the economics + + + align:start position:0% +this is way beyond the the economics +well that's right i mean + + align:start position:0% +well that's right i mean + + + align:start position:0% +well that's right i mean +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the + + align:start position:0% +the + + + align:start position:0% +the +people who at the drought when they + + align:start position:0% +people who at the drought when they + + + align:start position:0% +people who at the drought when they +ordered this about 15 years ago + + align:start position:0% +ordered this about 15 years ago + + + align:start position:0% +ordered this about 15 years ago +uh the local + + align:start position:0% +uh the local + + + align:start position:0% +uh the local +um + + align:start position:0% +um + + + align:start position:0% +um +minister + + align:start position:0% +minister + + + align:start position:0% +minister +um the leader of the state uh which saw + + align:start position:0% +um the leader of the state uh which saw + + + align:start position:0% +um the leader of the state uh which saw +this is a good thing he was being very + + align:start position:0% +this is a good thing he was being very + + + align:start position:0% +this is a good thing he was being very +uh prudent and uh + + align:start position:0% +uh prudent and uh + + + align:start position:0% +uh prudent and uh +there was jobs and a lot of people were + + align:start position:0% +there was jobs and a lot of people were + + + align:start position:0% +there was jobs and a lot of people were +happy about it the press + + align:start position:0% +happy about it the press + + + align:start position:0% +happy about it the press +until about uh 2014 + + align:start position:0% +until about uh 2014 + + + align:start position:0% +until about uh 2014 +was + + align:start position:0% +was + + + align:start position:0% +was +very against because there was this huge + + align:start position:0% +very against because there was this huge + + + align:start position:0% +very against because there was this huge +investment i mean for + + align:start position:0% +investment i mean for + + + align:start position:0% +investment i mean for +um + + align:start position:0% +um + + + align:start position:0% +um +a relatively small area this is a huge + + align:start position:0% +a relatively small area this is a huge + + + align:start position:0% +a relatively small area this is a huge +amount of money and it was absolutely in + + align:start position:0% +amount of money and it was absolutely in + + + align:start position:0% +amount of money and it was absolutely in +mothballs or it was just maintained kept + + align:start position:0% +mothballs or it was just maintained kept + + + align:start position:0% +mothballs or it was just maintained kept +alive at uh at a cost of over 600 + + align:start position:0% +alive at uh at a cost of over 600 + + + align:start position:0% +alive at uh at a cost of over 600 +million dollars a year paid by the + + align:start position:0% +million dollars a year paid by the + + + align:start position:0% +million dollars a year paid by the +citizens of uh melbourne and victoria uh + + align:start position:0% +citizens of uh melbourne and victoria uh + + + align:start position:0% +citizens of uh melbourne and victoria uh +for this so they were less happy with + + align:start position:0% +for this so they were less happy with + + + align:start position:0% +for this so they were less happy with +that + + align:start position:0% +that + + + align:start position:0% +that +um + + align:start position:0% +um + + + align:start position:0% +um +yeah i'm i don't i can't give you the + + align:start position:0% +yeah i'm i don't i can't give you the + + + align:start position:0% +yeah i'm i don't i can't give you the +more of the details but i'm just posing + + align:start position:0% +more of the details but i'm just posing + + + align:start position:0% +more of the details but i'm just posing +the question here is + + align:start position:0% +the question here is + + + align:start position:0% +the question here is +and what's remarkable about this case + + align:start position:0% +and what's remarkable about this case + + + align:start position:0% +and what's remarkable about this case +from my perspective is that in fact the + + align:start position:0% +from my perspective is that in fact the + + + align:start position:0% +from my perspective is that in fact the +modules of 60 50 billion uh were + + align:start position:0% +modules of 60 50 billion uh were + + + align:start position:0% +modules of 60 50 billion uh were +part of the design these were so some of + + align:start position:0% +part of the design these were so some of + + + align:start position:0% +part of the design these were so some of +the most massive uh desalting + + align:start position:0% +the most massive uh desalting + + + align:start position:0% +the most massive uh desalting +plants available at the time so + + align:start position:0% +plants available at the time so + + + align:start position:0% +plants available at the time so +um they felt they were already pushing + + align:start position:0% +um they felt they were already pushing + + + align:start position:0% +um they felt they were already pushing +the capacity for the it's a reverse + + align:start position:0% +the capacity for the it's a reverse + + + align:start position:0% +the capacity for the it's a reverse +osmosis + + align:start position:0% +osmosis + + + align:start position:0% +osmosis +approach + + align:start position:0% +approach + + + align:start position:0% +approach +um + + align:start position:0% +um + + + align:start position:0% +um +so you could + + align:start position:0% +so you could + + + align:start position:0% +so you could +easily think that maybe building a 100 + + align:start position:0% +easily think that maybe building a 100 + + + align:start position:0% +easily think that maybe building a 100 +billion capacity + + align:start position:0% +billion capacity + + + align:start position:0% +billion capacity +in the first phase might be good and + + align:start position:0% +in the first phase might be good and + + + align:start position:0% +in the first phase might be good and +then if you really were getting more + + align:start position:0% +then if you really were getting more + + + align:start position:0% +then if you really were getting more +increase and more demands for it maybe + + align:start position:0% +increase and more demands for it maybe + + + align:start position:0% +increase and more demands for it maybe +you have another module later on so + + align:start position:0% +you have another module later on so + + + align:start position:0% +you have another module later on so +that's the question i wish to have put + + align:start position:0% +that's the question i wish to have put + + + align:start position:0% +that's the question i wish to have put +out the table i think i'll take one more + + align:start position:0% +out the table i think i'll take one more + + + align:start position:0% +out the table i think i'll take one more +question then we'll go to our to the + + align:start position:0% +question then we'll go to our to the + + + align:start position:0% +question then we'll go to our to the +presentation + + align:start position:0% +presentation + + + align:start position:0% +presentation +uh jeff next jeff go ahead this is the + + align:start position:0% +uh jeff next jeff go ahead this is the + + + align:start position:0% +uh jeff next jeff go ahead this is the +last one um i'm glad to talk about it uh + + align:start position:0% +last one um i'm glad to talk about it uh + + + align:start position:0% +last one um i'm glad to talk about it uh +later on but uh for now jeff go ahead + + align:start position:0% +later on but uh for now jeff go ahead + + + align:start position:0% +later on but uh for now jeff go ahead +yeah i just have kind of two thoughts + + align:start position:0% +yeah i just have kind of two thoughts + + + align:start position:0% +yeah i just have kind of two thoughts +one is i've been thinking about this + + align:start position:0% +one is i've been thinking about this + + + align:start position:0% +one is i've been thinking about this +previously too with like how + + align:start position:0% +previously too with like how + + + align:start position:0% +previously too with like how +and i don't know how it works in the + + align:start position:0% +and i don't know how it works in the + + + align:start position:0% +and i don't know how it works in the +australian government but the federal + + align:start position:0% +australian government but the federal + + + align:start position:0% +australian government but the federal +contracting + + align:start position:0% +contracting + + + align:start position:0% +contracting +process is so + + align:start position:0% +process is so + + + align:start position:0% +process is so +long and tedious that + + align:start position:0% +long and tedious that + + + align:start position:0% +long and tedious that +i feel like building flexibility to you + + align:start position:0% +i feel like building flexibility to you + + + align:start position:0% +i feel like building flexibility to you +know + + align:start position:0% +know + + + align:start position:0% +know +um + + align:start position:0% +um + + + align:start position:0% +um +add on to a project later on might be + + align:start position:0% +add on to a project later on might be + + + align:start position:0% +add on to a project later on might be +kind of a preventative measure and just + + align:start position:0% +kind of a preventative measure and just + + + align:start position:0% +kind of a preventative measure and just +building the capacity all up front makes + + align:start position:0% +building the capacity all up front makes + + + align:start position:0% +building the capacity all up front makes +more sense + + align:start position:0% +more sense + + + align:start position:0% +more sense +and the second is if they built the big + + align:start position:0% +and the second is if they built the big + + + align:start position:0% +and the second is if they built the big +capacity it could have + + align:start position:0% +capacity it could have + + + align:start position:0% +capacity it could have +been dependent on how the environmental + + align:start position:0% +been dependent on how the environmental + + + align:start position:0% +been dependent on how the environmental +factors were then you know a drought in + + align:start position:0% +factors were then you know a drought in + + + align:start position:0% +factors were then you know a drought in +2008 or whenever + + align:start position:0% +2008 or whenever + + + align:start position:0% +2008 or whenever +yeah well + + align:start position:0% +yeah well + + + align:start position:0% +yeah well +part of uh i have a number of former + + align:start position:0% +part of uh i have a number of former + + + align:start position:0% +part of uh i have a number of former +students working in the government + + align:start position:0% +students working in the government + + + align:start position:0% +students working in the government +particularly in the military for + + align:start position:0% +particularly in the military for + + + align:start position:0% +particularly in the military for +procurement and part of their design is + + align:start position:0% +procurement and part of their design is + + + align:start position:0% +procurement and part of their design is +is so right now one of our students uh + + align:start position:0% +is so right now one of our students uh + + + align:start position:0% +is so right now one of our students uh +uh jason bartolome uh who's running a + + align:start position:0% +uh jason bartolome uh who's running a + + + align:start position:0% +uh jason bartolome uh who's running a +huge missile + + align:start position:0% +huge missile + + + align:start position:0% +huge missile +project + + align:start position:0% +project + + + align:start position:0% +project +uh utah + + align:start position:0% +uh utah + + + align:start position:0% +uh utah +is basically setting up the whole + + align:start position:0% +is basically setting up the whole + + + align:start position:0% +is basically setting up the whole +program + + align:start position:0% +program + + + align:start position:0% +program +uh for with the + + align:start position:0% +uh for with the + + + align:start position:0% +uh for with the +uh having the bidders right at the start + + align:start position:0% +uh having the bidders right at the start + + + align:start position:0% +uh having the bidders right at the start +bid on the project in terms of + + align:start position:0% +bid on the project in terms of + + + align:start position:0% +bid on the project in terms of +demonstrating their flexibility so + + align:start position:0% +demonstrating their flexibility so + + + align:start position:0% +demonstrating their flexibility so +they're baking it into it rather than + + align:start position:0% +they're baking it into it rather than + + + align:start position:0% +they're baking it into it rather than +coming at a re rethinking the + + align:start position:0% +coming at a re rethinking the + + + align:start position:0% +coming at a re rethinking the +procurement process in five or ten years + + align:start position:0% +procurement process in five or ten years + + + align:start position:0% +procurement process in five or ten years +of making that a condition from the + + align:start position:0% +of making that a condition from the + + + align:start position:0% +of making that a condition from the +start and i think that's that's an + + align:start position:0% +start and i think that's that's an + + + align:start position:0% +start and i think that's that's an +important part of having the flexibility + + align:start position:0% +important part of having the flexibility + + + align:start position:0% +important part of having the flexibility +is that just you bake it into and + + align:start position:0% +is that just you bake it into and + + + align:start position:0% +is that just you bake it into and +for those who are taking the full + + align:start position:0% +for those who are taking the full + + + align:start position:0% +for those who are taking the full +semester course that will be one of the + + align:start position:0% +semester course that will be one of the + + + align:start position:0% +semester course that will be one of the +issues we all deal with how do you go + + align:start position:0% +issues we all deal with how do you go + + + align:start position:0% +issues we all deal with how do you go +from having a good idea to implementing + + align:start position:0% +from having a good idea to implementing + + + align:start position:0% +from having a good idea to implementing +it properly + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/akWLXjbYHK4.txt b/akWLXjbYHK4.txt new file mode 100644 index 0000000000000000000000000000000000000000..ed30a68cb70ccee728f063935f54a72d89c1e900 --- /dev/null +++ b/akWLXjbYHK4.txt @@ -0,0 +1,8227 @@ +align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +oh + + align:start position:0% +oh + + + align:start position:0% +oh +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +hi today I'd like to continue the + + align:start position:0% +hi today I'd like to continue the + + + align:start position:0% +hi today I'd like to continue the +discussion that we started last time + + align:start position:0% +discussion that we started last time + + + align:start position:0% +discussion that we started last time +looking at how we evaluate the stability + + align:start position:0% +looking at how we evaluate the stability + + + align:start position:0% +looking at how we evaluate the stability +of a feedback system based on frequency + + align:start position:0% +of a feedback system based on frequency + + + align:start position:0% +of a feedback system based on frequency +domain Concepts and then extend that + + align:start position:0% +domain Concepts and then extend that + + + align:start position:0% +domain Concepts and then extend that +development to one of the major issues + + align:start position:0% +development to one of the major issues + + + align:start position:0% +development to one of the major issues +of our subject in particular particular + + align:start position:0% +of our subject in particular particular + + + align:start position:0% +of our subject in particular particular +compensation how do we modify a system + + align:start position:0% +compensation how do we modify a system + + + align:start position:0% +compensation how do we modify a system +in order to hopefully improve its + + align:start position:0% + + + + align:start position:0% + +performance as an illustration of how we + + align:start position:0% +performance as an illustration of how we + + + align:start position:0% +performance as an illustration of how we +might determine relative stability for a + + align:start position:0% +might determine relative stability for a + + + align:start position:0% +might determine relative stability for a +feedback system let's consider a system + + align:start position:0% +feedback system let's consider a system + + + align:start position:0% +feedback system let's consider a system +where we've already performed the + + align:start position:0% +where we've already performed the + + + align:start position:0% +where we've already performed the +Nyquist test and found out that that the + + align:start position:0% +Nyquist test and found out that that the + + + align:start position:0% +Nyquist test and found out that that the +system is in fact stable we've chosen a + + align:start position:0% +system is in fact stable we've chosen a + + + align:start position:0% +system is in fact stable we've chosen a +two-pole system for an illustration and + + align:start position:0% +two-pole system for an illustration and + + + align:start position:0% +two-pole system for an illustration and +we know that any negative feed back + + align:start position:0% +we know that any negative feed back + + + align:start position:0% +we know that any negative feed back +system which has two poles in its Loop + + align:start position:0% +system which has two poles in its Loop + + + align:start position:0% +system which has two poles in its Loop +transmission with both poles in the left + + align:start position:0% +transmission with both poles in the left + + + align:start position:0% +transmission with both poles in the left +half of the S plane will in fact be + + align:start position:0% +half of the S plane will in fact be + + + align:start position:0% +half of the S plane will in fact be +stable we in an absolute sense we've + + align:start position:0% +stable we in an absolute sense we've + + + align:start position:0% +stable we in an absolute sense we've +looked at at that situation before so we + + align:start position:0% +looked at at that situation before so we + + + align:start position:0% +looked at at that situation before so we +know either by a nist test which we + + align:start position:0% +know either by a nist test which we + + + align:start position:0% +know either by a nist test which we +could do fairly easily for this system + + align:start position:0% +could do fairly easily for this system + + + align:start position:0% +could do fairly easily for this system +or by any of the other experience that + + align:start position:0% +or by any of the other experience that + + + align:start position:0% +or by any of the other experience that +we've had that this system will in fact + + align:start position:0% +we've had that this system will in fact + + + align:start position:0% +we've had that this system will in fact +be stable in an absolute sense and we'd + + align:start position:0% +be stable in an absolute sense and we'd + + + align:start position:0% +be stable in an absolute sense and we'd +like to look at at the absolute + + align:start position:0% +like to look at at the absolute + + + align:start position:0% +like to look at at the absolute +stability of this system using the + + align:start position:0% +stability of this system using the + + + align:start position:0% +stability of this system using the +Nickels chart as our Aid to evaluating + + align:start position:0% +Nickels chart as our Aid to evaluating + + + align:start position:0% +Nickels chart as our Aid to evaluating +absolute stability or Rel I'm sorry + + align:start position:0% +absolute stability or Rel I'm sorry + + + align:start position:0% +absolute stability or Rel I'm sorry +relative + + align:start position:0% +relative + + + align:start position:0% +relative +stability well in order to do that we go + + align:start position:0% +stability well in order to do that we go + + + align:start position:0% +stability well in order to do that we go +ahead and focus on the corner of the + + align:start position:0% +ahead and focus on the corner of the + + + align:start position:0% +ahead and focus on the corner of the +nickel's chart that's of most interest + + align:start position:0% +nickel's chart that's of most interest + + + align:start position:0% +nickel's chart that's of most interest +to us in particular the part that lies + + align:start position:0% +to us in particular the part that lies + + + align:start position:0% +to us in particular the part that lies +near a magnitude of the loop + + align:start position:0% +near a magnitude of the loop + + + align:start position:0% +near a magnitude of the loop +transmission of one and an angle of the + + align:start position:0% +transmission of one and an angle of the + + + align:start position:0% +transmission of one and an angle of the +loop transmission of minus + + align:start position:0% +loop transmission of minus + + + align:start position:0% +loop transmission of minus +180° so we focus on this corner of the + + align:start position:0% +180° so we focus on this corner of the + + + align:start position:0% +180° so we focus on this corner of the +Nickels + + align:start position:0% +Nickels + + + align:start position:0% +Nickels +chart and what we can do is plot our + + align:start position:0% +chart and what we can do is plot our + + + align:start position:0% +chart and what we can do is plot our +Loop transmission or actually the + + align:start position:0% +Loop transmission or actually the + + + align:start position:0% +Loop transmission or actually the +negative of the loop transmission the AF + + align:start position:0% +negative of the loop transmission the AF + + + align:start position:0% +negative of the loop transmission the AF +product uh on the gain phase coordinates + + align:start position:0% +product uh on the gain phase coordinates + + + align:start position:0% +product uh on the gain phase coordinates +these are the background coordinates for + + align:start position:0% +these are the background coordinates for + + + align:start position:0% +these are the background coordinates for +the Nickels + + align:start position:0% +the Nickels + + + align:start position:0% +the Nickels +chart and what I've shown here is + + align:start position:0% +chart and what I've shown here is + + + align:start position:0% +chart and what I've shown here is +precisely that construction for three + + align:start position:0% +precisely that construction for three + + + align:start position:0% +precisely that construction for three +different values of a KN we have a two- + + align:start position:0% +different values of a KN we have a two- + + + align:start position:0% +different values of a KN we have a two- +pole system as you recall from the + + align:start position:0% +pole system as you recall from the + + + align:start position:0% +pole system as you recall from the +material on the Blackboard with a single + + align:start position:0% +material on the Blackboard with a single + + + align:start position:0% +material on the Blackboard with a single +pole on the negative real axis at s + + align:start position:0% +pole on the negative real axis at s + + + align:start position:0% +pole on the negative real axis at s +equal minus1 another pole at s equal uh + + align:start position:0% +equal minus1 another pole at s equal uh + + + align:start position:0% +equal minus1 another pole at s equal uh +minus 10 and so we have a two- pole + + align:start position:0% +minus 10 and so we have a two- pole + + + align:start position:0% +minus 10 and so we have a two- pole +system and what I've done is plot that + + align:start position:0% +system and what I've done is plot that + + + align:start position:0% +system and what I've done is plot that +transfer function for three different + + align:start position:0% +transfer function for three different + + + align:start position:0% +transfer function for three different +values of a knot here's the curve that + + align:start position:0% +values of a knot here's the curve that + + + align:start position:0% +values of a knot here's the curve that +results for an a knot of + + align:start position:0% +results for an a knot of + + + align:start position:0% +results for an a knot of +8.5 here's the curve that results for an + + align:start position:0% +8.5 here's the curve that results for an + + + align:start position:0% +8.5 here's the curve that results for an +a knot of 22 the middle curve and here's + + align:start position:0% +a knot of 22 the middle curve and here's + + + align:start position:0% +a knot of 22 the middle curve and here's +the curve that results for an aot of + + align:start position:0% +the curve that results for an aot of + + + align:start position:0% +the curve that results for an aot of +50 these curves of course are are simply + + align:start position:0% +50 these curves of course are are simply + + + align:start position:0% +50 these curves of course are are simply +or effectively the left hand and part of + + align:start position:0% +or effectively the left hand and part of + + + align:start position:0% +or effectively the left hand and part of +the Nyquist construction if we had the + + align:start position:0% +the Nyquist construction if we had the + + + align:start position:0% +the Nyquist construction if we had the +entire gain phase plane running out to 0 + + align:start position:0% +entire gain phase plane running out to 0 + + + align:start position:0% +entire gain phase plane running out to 0 +degrees here and did our Nyquist + + align:start position:0% +degrees here and did our Nyquist + + + align:start position:0% +degrees here and did our Nyquist +construction we'd have a curve that did + + align:start position:0% +construction we'd have a curve that did + + + align:start position:0% +construction we'd have a curve that did +something like so reached minus 180° ASM + + align:start position:0% +something like so reached minus 180° ASM + + + align:start position:0% +something like so reached minus 180° ASM +totically the Contour would close this + + align:start position:0% +totically the Contour would close this + + + align:start position:0% +totically the Contour would close this +way and so forth so what we have is is + + align:start position:0% +way and so forth so what we have is is + + + align:start position:0% +way and so forth so what we have is is +simply the leftand portion or a piece of + + align:start position:0% +simply the leftand portion or a piece of + + + align:start position:0% +simply the leftand portion or a piece of +the leftand portion of the Nyquist + + align:start position:0% +the leftand portion of the Nyquist + + + align:start position:0% +the leftand portion of the Nyquist +construction when we do a gain phase + + align:start position:0% +construction when we do a gain phase + + + align:start position:0% +construction when we do a gain phase +plot of the AF product + + align:start position:0% +plot of the AF product + + + align:start position:0% +plot of the AF product +Omega is a parameter along these curves + + align:start position:0% +Omega is a parameter along these curves + + + align:start position:0% +Omega is a parameter along these curves +here we have for example on the a equal + + align:start position:0% +here we have for example on the a equal + + + align:start position:0% +here we have for example on the a equal +8.5 curve uh Omega equal 2 Omega equal 5 + + align:start position:0% +8.5 curve uh Omega equal 2 Omega equal 5 + + + align:start position:0% +8.5 curve uh Omega equal 2 Omega equal 5 +Omega equal 10 uh here on the AAL 22 + + align:start position:0% +Omega equal 10 uh here on the AAL 22 + + + align:start position:0% +Omega equal 10 uh here on the AAL 22 +curve Omega equal 2 Omega equal 5 and so + + align:start position:0% +curve Omega equal 2 Omega equal 5 and so + + + align:start position:0% +curve Omega equal 2 Omega equal 5 and so +forth so Omega is a parameter along this + + align:start position:0% +forth so Omega is a parameter along this + + + align:start position:0% +forth so Omega is a parameter along this +curve in the gain phase plane and what + + align:start position:0% +curve in the gain phase plane and what + + + align:start position:0% +curve in the gain phase plane and what +we're able to do then is determine the + + align:start position:0% +we're able to do then is determine the + + + align:start position:0% +we're able to do then is determine the +Clos Loop gain of our system by simply + + align:start position:0% +Clos Loop gain of our system by simply + + + align:start position:0% +Clos Loop gain of our system by simply +going ahead and looking at the magnitude + + align:start position:0% +going ahead and looking at the magnitude + + + align:start position:0% +going ahead and looking at the magnitude +of G over 1 plus G in these coordinates + + align:start position:0% +of G over 1 plus G in these coordinates + + + align:start position:0% +of G over 1 plus G in these coordinates +uh and if we cared to the angle for + + align:start position:0% +uh and if we cared to the angle for + + + align:start position:0% +uh and if we cared to the angle for +various values of Omega and a specific + + align:start position:0% +various values of Omega and a specific + + + align:start position:0% +various values of Omega and a specific +value of a and we can see how that works + + align:start position:0% +value of a and we can see how that works + + + align:start position:0% +value of a and we can see how that works +for example uh if we look at the AF + + align:start position:0% +for example uh if we look at the AF + + + align:start position:0% +for example uh if we look at the AF +product that corresponds to an a knot of + + align:start position:0% +product that corresponds to an a knot of + + + align:start position:0% +product that corresponds to an a knot of +8.5 we find out that uh at sufficiently + + align:start position:0% +8.5 we find out that uh at sufficiently + + + align:start position:0% +8.5 we find out that uh at sufficiently +low frequencies back near Omega equals z + + align:start position:0% +low frequencies back near Omega equals z + + + align:start position:0% +low frequencies back near Omega equals z +this curve eventually levels out at + + align:start position:0% +this curve eventually levels out at + + + align:start position:0% +this curve eventually levels out at +at 0 degrees and and a magnitude of + + align:start position:0% +at 0 degrees and and a magnitude of + + + align:start position:0% +at 0 degrees and and a magnitude of +about a closed loop magnitude of about + + align:start position:0% +about a closed loop magnitude of about + + + align:start position:0% +about a closed loop magnitude of about +0.9 we can get that either by analytic + + align:start position:0% +0.9 we can get that either by analytic + + + align:start position:0% +0.9 we can get that either by analytic +manipulations or look at the complete + + align:start position:0% +manipulations or look at the complete + + + align:start position:0% +manipulations or look at the complete +chart we find out that the low frequency + + align:start position:0% +chart we find out that the low frequency + + + align:start position:0% +chart we find out that the low frequency +magnitude for this system with a f equal + + align:start position:0% +magnitude for this system with a f equal + + + align:start position:0% +magnitude for this system with a f equal +to or a equal to 8.5 the low frequency + + align:start position:0% +to or a equal to 8.5 the low frequency + + + align:start position:0% +to or a equal to 8.5 the low frequency +closed loop magnitude would be about + + align:start position:0% +closed loop magnitude would be about + + + align:start position:0% +closed loop magnitude would be about +0.9 as frequency increases here's aega + + align:start position:0% +0.9 as frequency increases here's aega + + + align:start position:0% +0.9 as frequency increases here's aega +equals 2 Omega equals 5 we begin to + + align:start position:0% +equals 2 Omega equals 5 we begin to + + + align:start position:0% +equals 2 Omega equals 5 we begin to +climb up in magnitude here we touch a + + align:start position:0% +climb up in magnitude here we touch a + + + align:start position:0% +climb up in magnitude here we touch a +contour that's about a magnitude of one + + align:start position:0% +contour that's about a magnitude of one + + + align:start position:0% +contour that's about a magnitude of one +G over 1 + G equal 1 so here's that + + align:start position:0% +G over 1 + G equal 1 so here's that + + + align:start position:0% +G over 1 + G equal 1 so here's that +contour and we just about touch that + + align:start position:0% +contour and we just about touch that + + + align:start position:0% +contour and we just about touch that +somewhere on the order of Omega equals 5 + + align:start position:0% +somewhere on the order of Omega equals 5 + + + align:start position:0% +somewhere on the order of Omega equals 5 +somewhere in here the curve gets a + + align:start position:0% +somewhere in here the curve gets a + + + align:start position:0% +somewhere in here the curve gets a +little bit busy but somewhere in here at + + align:start position:0% +little bit busy but somewhere in here at + + + align:start position:0% +little bit busy but somewhere in here at +Omega equal 5 we hit a closed loop + + align:start position:0% +Omega equal 5 we hit a closed loop + + + align:start position:0% +Omega equal 5 we hit a closed loop +magnitude of about 1 and then begin to + + align:start position:0% +magnitude of about 1 and then begin to + + + align:start position:0% +magnitude of about 1 and then begin to +drop off to lower closed loop magnitudes + + align:start position:0% +drop off to lower closed loop magnitudes + + + align:start position:0% +drop off to lower closed loop magnitudes +here we're back down to uh 085 for + + align:start position:0% +here we're back down to uh 085 for + + + align:start position:0% +here we're back down to uh 085 for +example and eventually we get to a + + align:start position:0% +example and eventually we get to a + + + align:start position:0% +example and eventually we get to a +magnitude of about 7 at Omega equals 10 + + align:start position:0% +magnitude of about 7 at Omega equals 10 + + + align:start position:0% +magnitude of about 7 at Omega equals 10 +and if we keep track of things beyond + + align:start position:0% +and if we keep track of things beyond + + + align:start position:0% +and if we keep track of things beyond +that the closed loop magnitude drops off + + align:start position:0% +that the closed loop magnitude drops off + + + align:start position:0% +that the closed loop magnitude drops off +roughly as one over frequency squared uh + + align:start position:0% +roughly as one over frequency squared uh + + + align:start position:0% +roughly as one over frequency squared uh +since in this region for higher values + + align:start position:0% +since in this region for higher values + + + align:start position:0% +since in this region for higher values +of Omega the system is basically per + + align:start position:0% +of Omega the system is basically per + + + align:start position:0% +of Omega the system is basically per +behaving in an open loop fashion the + + align:start position:0% +behaving in an open loop fashion the + + + align:start position:0% +behaving in an open loop fashion the +magnitude of the loop transmission is + + align:start position:0% +magnitude of the loop transmission is + + + align:start position:0% +magnitude of the loop transmission is +small compared to one and the closed + + align:start position:0% +small compared to one and the closed + + + align:start position:0% +small compared to one and the closed +loop gain then is just about equal to + + align:start position:0% +loop gain then is just about equal to + + + align:start position:0% +loop gain then is just about equal to +the forward path gain so we can plot the + + align:start position:0% +the forward path gain so we can plot the + + + align:start position:0% +the forward path gain so we can plot the +closed loop response of the system for + + align:start position:0% +closed loop response of the system for + + + align:start position:0% +closed loop response of the system for +that case and we've done that here uh we + + align:start position:0% +that case and we've done that here uh we + + + align:start position:0% +that case and we've done that here uh we +start out this would be about + + align:start position:0% +start out this would be about + + + align:start position:0% +start out this would be about +0.9 the magnitude Peaks up just a little + + align:start position:0% +0.9 the magnitude Peaks up just a little + + + align:start position:0% +0.9 the magnitude Peaks up just a little +bit uh reaches a magnitude of about one + + align:start position:0% +bit uh reaches a magnitude of about one + + + align:start position:0% +bit uh reaches a magnitude of about one +as we saw from the nickels construction + + align:start position:0% +as we saw from the nickels construction + + + align:start position:0% +as we saw from the nickels construction +drops off to 7007 or 7 and we said that + + align:start position:0% +drops off to 7007 or 7 and we said that + + + align:start position:0% +drops off to 7007 or 7 and we said that +that occurs at a frequency of about 10 + + align:start position:0% +that occurs at a frequency of about 10 + + + align:start position:0% +that occurs at a frequency of about 10 +so on our Omega axis we'd find out for + + align:start position:0% +so on our Omega axis we'd find out for + + + align:start position:0% +so on our Omega axis we'd find out for +this particular system we had a + + align:start position:0% +this particular system we had a + + + align:start position:0% +this particular system we had a +magnitude of 7 uh at a frequency of 10 + + align:start position:0% +magnitude of 7 uh at a frequency of 10 + + + align:start position:0% +magnitude of 7 uh at a frequency of 10 +so we're able to determine a good bit + + align:start position:0% +so we're able to determine a good bit + + + align:start position:0% +so we're able to determine a good bit +from this kind of construction we are + + align:start position:0% +from this kind of construction we are + + + align:start position:0% +from this kind of construction we are +able to determine for example the + + align:start position:0% +able to determine for example the + + + align:start position:0% +able to determine for example the +so-called half power frequency of the + + align:start position:0% +so-called half power frequency of the + + + align:start position:0% +so-called half power frequency of the +closed loop system + + align:start position:0% +closed loop system + + + align:start position:0% +closed loop system +we're also able to get a very good + + align:start position:0% +we're also able to get a very good + + + align:start position:0% +we're also able to get a very good +indication of relative stability here we + + align:start position:0% +indication of relative stability here we + + + align:start position:0% +indication of relative stability here we +have very little peaking for a f equals + + align:start position:0% +have very little peaking for a f equals + + + align:start position:0% +have very little peaking for a f equals +8.5 and we conclude that's a fairly + + align:start position:0% +8.5 and we conclude that's a fairly + + + align:start position:0% +8.5 and we conclude that's a fairly +stable system that's a very very well- + + align:start position:0% +stable system that's a very very well- + + + align:start position:0% +stable system that's a very very well- +behaved system in fact let's look at + + align:start position:0% +behaved system in fact let's look at + + + align:start position:0% +behaved system in fact let's look at +what happens for an aot of of 22 this + + align:start position:0% +what happens for an aot of of 22 this + + + align:start position:0% +what happens for an aot of of 22 this +Construction in the on the Nickels + + align:start position:0% +Construction in the on the Nickels + + + align:start position:0% +Construction in the on the Nickels +chart uh here again if we went through + + align:start position:0% +chart uh here again if we went through + + + align:start position:0% +chart uh here again if we went through +the numbers we'd find out that at very + + align:start position:0% +the numbers we'd find out that at very + + + align:start position:0% +the numbers we'd find out that at very +low frequencies the closed loop magnit + + align:start position:0% +low frequencies the closed loop magnit + + + align:start position:0% +low frequencies the closed loop magnit +itude was actually about + + align:start position:0% +itude was actually about + + + align:start position:0% +itude was actually about +.95 it' be 22 over 23 which is about + + align:start position:0% +.95 it' be 22 over 23 which is about + + + align:start position:0% +.95 it' be 22 over 23 which is about +.95 um as we go to higher frequencies we + + align:start position:0% +.95 um as we go to higher frequencies we + + + align:start position:0% +.95 um as we go to higher frequencies we +begin to get some peaking here uh at + + align:start position:0% +begin to get some peaking here uh at + + + align:start position:0% +begin to get some peaking here uh at +Omega equals 5 we're on a contour + + align:start position:0% +Omega equals 5 we're on a contour + + + align:start position:0% +Omega equals 5 we're on a contour +magnitude of G over 1 plus G of 1.05 so + + align:start position:0% +magnitude of G over 1 plus G of 1.05 so + + + align:start position:0% +magnitude of G over 1 plus G of 1.05 so +we're beginning to Peak up a little bit + + align:start position:0% +we're beginning to Peak up a little bit + + + align:start position:0% +we're beginning to Peak up a little bit +at Omega equals + + align:start position:0% +at Omega equals + + + align:start position:0% +at Omega equals +10 here on on our construction we have a + + align:start position:0% +10 here on on our construction we have a + + + align:start position:0% +10 here on on our construction we have a +magnitude of 1.3 three and for AAL 22 we + + align:start position:0% +magnitude of 1.3 three and for AAL 22 we + + + align:start position:0% +magnitude of 1.3 three and for AAL 22 we +reach a maximum magnitude our closest + + align:start position:0% +reach a maximum magnitude our closest + + + align:start position:0% +reach a maximum magnitude our closest +proximity in a nickel chart sents to the + + align:start position:0% +proximity in a nickel chart sents to the + + + align:start position:0% +proximity in a nickel chart sents to the +minus one point we reach a maximum + + align:start position:0% +minus one point we reach a maximum + + + align:start position:0% +minus one point we reach a maximum +magnitude of + + align:start position:0% +magnitude of + + + align:start position:0% +magnitude of +1.4 at Omega is a little bit above 10 + + align:start position:0% +1.4 at Omega is a little bit above 10 + + + align:start position:0% +1.4 at Omega is a little bit above 10 +here's Omega equal 10 here's Omega + + align:start position:0% +here's Omega equal 10 here's Omega + + + align:start position:0% +here's Omega equal 10 here's Omega +equals 20 here's the highest point we + + align:start position:0% +equals 20 here's the highest point we + + + align:start position:0% +equals 20 here's the highest point we +reach on the Nickels chart a magnitude + + align:start position:0% +reach on the Nickels chart a magnitude + + + align:start position:0% +reach on the Nickels chart a magnitude +of + + align:start position:0% +of + + + align:start position:0% +of +1.4 and so that's the maximum closed + + align:start position:0% +1.4 and so that's the maximum closed + + + align:start position:0% +1.4 and so that's the maximum closed +loop magnitude we get uh we've dropped + + align:start position:0% +loop magnitude we get uh we've dropped + + + align:start position:0% +loop magnitude we get uh we've dropped +off to a magnitude of 7 by approximately + + align:start position:0% +off to a magnitude of 7 by approximately + + + align:start position:0% +off to a magnitude of 7 by approximately +Omega equals 20 so we're able to draw + + align:start position:0% +Omega equals 20 so we're able to draw + + + align:start position:0% +Omega equals 20 so we're able to draw +the closed loop response for that system + + align:start position:0% +the closed loop response for that system + + + align:start position:0% +the closed loop response for that system +using the information that we've gained + + align:start position:0% +using the information that we've gained + + + align:start position:0% +using the information that we've gained +from the Nickels chart uh here we start + + align:start position:0% +from the Nickels chart uh here we start + + + align:start position:0% +from the Nickels chart uh here we start +out at about + + align:start position:0% +out at about + + + align:start position:0% +out at about +.95 we Peak up to a maximum value of + + align:start position:0% +.95 we Peak up to a maximum value of + + + align:start position:0% +.95 we Peak up to a maximum value of +about 1.4 for this particular value of a + + align:start position:0% +about 1.4 for this particular value of a + + + align:start position:0% +about 1.4 for this particular value of a +f KN or a this is the curve that + + align:start position:0% +f KN or a this is the curve that + + + align:start position:0% +f KN or a this is the curve that +corresponds to a equals 22 + + align:start position:0% +corresponds to a equals 22 + + + align:start position:0% +corresponds to a equals 22 +and the 707 frequency when we're down to + + align:start position:0% +and the 707 frequency when we're down to + + + align:start position:0% +and the 707 frequency when we're down to +uh about 1 over theare < TK of two of + + align:start position:0% +uh about 1 over theare < TK of two of + + + align:start position:0% +uh about 1 over theare < TK of two of +the low frequency gain occurs in this + + align:start position:0% +the low frequency gain occurs in this + + + align:start position:0% +the low frequency gain occurs in this +system at about + + align:start position:0% +system at about + + + align:start position:0% +system at about +20 radians per second this point is + + align:start position:0% +20 radians per second this point is + + + align:start position:0% +20 radians per second this point is +about 20 radians per + + align:start position:0% +about 20 radians per + + + align:start position:0% +about 20 radians per +second as we go to progressively larger + + align:start position:0% +second as we go to progressively larger + + + align:start position:0% +second as we go to progressively larger +values for a KN the system again becomes + + align:start position:0% +values for a KN the system again becomes + + + align:start position:0% +values for a KN the system again becomes +progressively less stable the relative + + align:start position:0% +progressively less stable the relative + + + align:start position:0% +progressively less stable the relative +stability of the system drops and that + + align:start position:0% +stability of the system drops and that + + + align:start position:0% +stability of the system drops and that +corresponds very nicely to what we've + + align:start position:0% +corresponds very nicely to what we've + + + align:start position:0% +corresponds very nicely to what we've +seen for example in a root Locus + + align:start position:0% +seen for example in a root Locus + + + align:start position:0% +seen for example in a root Locus +development where where we saw that as + + align:start position:0% +development where where we saw that as + + + align:start position:0% +development where where we saw that as +we increase a KN in a two pole system + + align:start position:0% +we increase a KN in a two pole system + + + align:start position:0% +we increase a KN in a two pole system +the dapping ratio of the complex + + align:start position:0% +the dapping ratio of the complex + + + align:start position:0% +the dapping ratio of the complex +conjugate the dominant pole pair the + + align:start position:0% +conjugate the dominant pole pair the + + + align:start position:0% +conjugate the dominant pole pair the +only complex conjugate pole pair for for + + align:start position:0% +only complex conjugate pole pair for for + + + align:start position:0% +only complex conjugate pole pair for for +that two two- pole system gets + + align:start position:0% +that two two- pole system gets + + + align:start position:0% +that two two- pole system gets +progressively smaller and so we'd expect + + align:start position:0% +progressively smaller and so we'd expect + + + align:start position:0% +progressively smaller and so we'd expect +this behavior that the system becomes + + align:start position:0% +this behavior that the system becomes + + + align:start position:0% +this behavior that the system becomes +progressively less stable for larger + + align:start position:0% +progressively less stable for larger + + + align:start position:0% +progressively less stable for larger +values of a KN in the two pole system + + align:start position:0% +values of a KN in the two pole system + + + align:start position:0% +values of a KN in the two pole system +and our nickels construction confirms + + align:start position:0% +and our nickels construction confirms + + + align:start position:0% +and our nickels construction confirms +that let's look for one final value of a + + align:start position:0% +that let's look for one final value of a + + + align:start position:0% +that let's look for one final value of a +knot in particular an a KN of 50 here's + + align:start position:0% +knot in particular an a KN of 50 here's + + + align:start position:0% +knot in particular an a KN of 50 here's +the nickels chart construction that + + align:start position:0% +the nickels chart construction that + + + align:start position:0% +the nickels chart construction that +corresponds to that situation uh again + + align:start position:0% +corresponds to that situation uh again + + + align:start position:0% +corresponds to that situation uh again +we would start out actually at at a + + align:start position:0% +we would start out actually at at a + + + align:start position:0% +we would start out actually at at a +value of G over 1 plus G of about + + align:start position:0% +value of G over 1 plus G of about + + + align:start position:0% +value of G over 1 plus G of about +.98 for Omega equals z uh we'd have a + + align:start position:0% +.98 for Omega equals z uh we'd have a + + + align:start position:0% +.98 for Omega equals z uh we'd have a +value of 50 over + + align:start position:0% +value of 50 over + + + align:start position:0% +value of 50 over +51 about about + + align:start position:0% +51 about about + + + align:start position:0% +51 about about +98 here at Omega equals 2 we'd be up to + + align:start position:0% +98 here at Omega equals 2 we'd be up to + + + align:start position:0% +98 here at Omega equals 2 we'd be up to +099 uh at Omega equals 5 we'd be up to + + align:start position:0% +099 uh at Omega equals 5 we'd be up to + + + align:start position:0% +099 uh at Omega equals 5 we'd be up to +1.02 we intersect that curve on the + + align:start position:0% +1.02 we intersect that curve on the + + + align:start position:0% +1.02 we intersect that curve on the +Nickels chart at Omega equals 10 we're + + align:start position:0% +Nickels chart at Omega equals 10 we're + + + align:start position:0% +Nickels chart at Omega equals 10 we're +up to + + align:start position:0% +up to + + + align:start position:0% +up to +1.2 at Omega equals 20 we hit our Peak + + align:start position:0% +1.2 at Omega equals 20 we hit our Peak + + + align:start position:0% +1.2 at Omega equals 20 we hit our Peak +response the peak Clos Loop response and + + align:start position:0% +response the peak Clos Loop response and + + + align:start position:0% +response the peak Clos Loop response and +the magnitude is just about two so we + + align:start position:0% +the magnitude is just about two so we + + + align:start position:0% +the magnitude is just about two so we +hit a maximum resonant Peak with a + + align:start position:0% +hit a maximum resonant Peak with a + + + align:start position:0% +hit a maximum resonant Peak with a +magnitude of two at Omega equals about + + align:start position:0% +magnitude of two at Omega equals about + + + align:start position:0% +magnitude of two at Omega equals about +20 and then we're down to 7 by somewhere + + align:start position:0% +20 and then we're down to 7 by somewhere + + + align:start position:0% +20 and then we're down to 7 by somewhere +below Omega equals 50 here's Omega equal + + align:start position:0% +below Omega equals 50 here's Omega equal + + + align:start position:0% +below Omega equals 50 here's Omega equal +50 here's Omega equal 20 here's the 7 + + align:start position:0% +50 here's Omega equal 20 here's the 7 + + + align:start position:0% +50 here's Omega equal 20 here's the 7 +curve value for G over 1 + G so we hit + + align:start position:0% +curve value for G over 1 + G so we hit + + + align:start position:0% +curve value for G over 1 + G so we hit +that at Omega equal 40 or 45 something + + align:start position:0% +that at Omega equal 40 or 45 something + + + align:start position:0% +that at Omega equal 40 or 45 something +like that and again we can draw that + + align:start position:0% +like that and again we can draw that + + + align:start position:0% +like that and again we can draw that +construction or determine the + + align:start position:0% +construction or determine the + + + align:start position:0% +construction or determine the +corresponding closed loop gain for U + + align:start position:0% +corresponding closed loop gain for U + + + align:start position:0% +corresponding closed loop gain for U +that value of of a KN in particular an a + + align:start position:0% +that value of of a KN in particular an a + + + align:start position:0% +that value of of a KN in particular an a +knot of 50 we'd find that the peak + + align:start position:0% +knot of 50 we'd find that the peak + + + align:start position:0% +knot of 50 we'd find that the peak +magnitude is about two as we've seen + + align:start position:0% +magnitude is about two as we've seen + + + align:start position:0% +magnitude is about two as we've seen +from the Nickels chart and that the uh + + align:start position:0% +from the Nickels chart and that the uh + + + align:start position:0% +from the Nickels chart and that the uh +707 frequency is about 40 or 45 radians + + align:start position:0% +707 frequency is about 40 or 45 radians + + + align:start position:0% +707 frequency is about 40 or 45 radians +per second somewhere in + + align:start position:0% +per second somewhere in + + + align:start position:0% +per second somewhere in +here so we can quite quickly with the + + align:start position:0% +here so we can quite quickly with the + + + align:start position:0% +here so we can quite quickly with the +aid of the Nickels chart determine the + + align:start position:0% +aid of the Nickels chart determine the + + + align:start position:0% +aid of the Nickels chart determine the +closed loop transfer function of the + + align:start position:0% +closed loop transfer function of the + + + align:start position:0% +closed loop transfer function of the +system and of course get a very graphic + + align:start position:0% +system and of course get a very graphic + + + align:start position:0% +system and of course get a very graphic +indication of the deteriorating + + align:start position:0% +indication of the deteriorating + + + align:start position:0% +indication of the deteriorating +stability as we go to larger and larger + + align:start position:0% +stability as we go to larger and larger + + + align:start position:0% +stability as we go to larger and larger +values for a + + align:start position:0% +values for a + + + align:start position:0% +values for a +KN well that sort of a construction is + + align:start position:0% +KN well that sort of a construction is + + + align:start position:0% +KN well that sort of a construction is +is fairly easily done although in + + align:start position:0% +is fairly easily done although in + + + align:start position:0% +is fairly easily done although in +reality we normally don't even have to + + align:start position:0% +reality we normally don't even have to + + + align:start position:0% +reality we normally don't even have to +do that much work in order to get a good + + align:start position:0% +do that much work in order to get a good + + + align:start position:0% +do that much work in order to get a good +indication of relative stability via + + align:start position:0% +indication of relative stability via + + + align:start position:0% +indication of relative stability via +frequency domain + + align:start position:0% +frequency domain + + + align:start position:0% +frequency domain +techniques and in particular it it + + align:start position:0% +techniques and in particular it it + + + align:start position:0% +techniques and in particular it it +happens that the closed loop response of + + align:start position:0% +happens that the closed loop response of + + + align:start position:0% +happens that the closed loop response of +the system is very nicely characterized + + align:start position:0% +the system is very nicely characterized + + + align:start position:0% +the system is very nicely characterized +by several parameters relating to the + + align:start position:0% +by several parameters relating to the + + + align:start position:0% +by several parameters relating to the +loop transmission or the AF product and + + align:start position:0% +loop transmission or the AF product and + + + align:start position:0% +loop transmission or the AF product and +I'd like to define those and then see + + align:start position:0% +I'd like to define those and then see + + + align:start position:0% +I'd like to define those and then see +how we use + + align:start position:0% +how we use + + + align:start position:0% +how we use +them here we have what might be a sort + + align:start position:0% +them here we have what might be a sort + + + align:start position:0% +them here we have what might be a sort +of typical AF product bod plot uh we're + + align:start position:0% +of typical AF product bod plot uh we're + + + align:start position:0% +of typical AF product bod plot uh we're +run running of course on a common + + align:start position:0% +run running of course on a common + + + align:start position:0% +run running of course on a common +frequency scale here so + + align:start position:0% +frequency scale here so + + + align:start position:0% +frequency scale here so +Omega goes in this direction these are + + align:start position:0% +Omega goes in this direction these are + + + align:start position:0% +Omega goes in this direction these are +the usual bod plot coordinates a + + align:start position:0% +the usual bod plot coordinates a + + + align:start position:0% +the usual bod plot coordinates a +logarithmic axis for frequency a + + align:start position:0% +logarithmic axis for frequency a + + + align:start position:0% +logarithmic axis for frequency a +logarithmic axis for magnitude here's a + + align:start position:0% +logarithmic axis for magnitude here's a + + + align:start position:0% +logarithmic axis for magnitude here's a +magnitude of the AF product equal to one + + align:start position:0% +magnitude of the AF product equal to one + + + align:start position:0% +magnitude of the AF product equal to one +we're evaluating AF of J Omega and we'd + + align:start position:0% +we're evaluating AF of J Omega and we'd + + + align:start position:0% +we're evaluating AF of J Omega and we'd +have logarithmic spacing here 10 100 a + + align:start position:0% +have logarithmic spacing here 10 100 a + + + align:start position:0% +have logarithmic spacing here 10 100 a +th000 or whatever and similarly uh on + + align:start position:0% +th000 or whatever and similarly uh on + + + align:start position:0% +th000 or whatever and similarly uh on +the same common frequency scale we plot + + align:start position:0% +the same common frequency scale we plot + + + align:start position:0% +the same common frequency scale we plot +the angle associated with the AF product + + align:start position:0% +the angle associated with the AF product + + + align:start position:0% +the angle associated with the AF product +uh possibly going from 0 deg to- 180° + + align:start position:0% +uh possibly going from 0 deg to- 180° + + + align:start position:0% +uh possibly going from 0 deg to- 180° +and then beyond so here we have the + + align:start position:0% +and then beyond so here we have the + + + align:start position:0% +and then beyond so here we have the +usual bod plot presentation for uh a an + + align:start position:0% +usual bod plot presentation for uh a an + + + align:start position:0% +usual bod plot presentation for uh a an +AF transfer function and let's define a + + align:start position:0% +AF transfer function and let's define a + + + align:start position:0% +AF transfer function and let's define a +couple of quantities one of these is the + + align:start position:0% +couple of quantities one of these is the + + + align:start position:0% +couple of quantities one of these is the +crossover frequency Omega C and that's + + align:start position:0% +crossover frequency Omega C and that's + + + align:start position:0% +crossover frequency Omega C and that's +simply the frequency where the magnitude + + align:start position:0% +simply the frequency where the magnitude + + + align:start position:0% +simply the frequency where the magnitude +of the loop + + align:start position:0% +of the loop + + + align:start position:0% +of the loop +transmission goes to + + align:start position:0% +transmission goes to + + + align:start position:0% +transmission goes to +one I'd also then like to define the + + align:start position:0% +one I'd also then like to define the + + + align:start position:0% +one I'd also then like to define the +phase margin of the system and to + + align:start position:0% +phase margin of the system and to + + + align:start position:0% +phase margin of the system and to +determine the phase margin assuming we + + align:start position:0% +determine the phase margin assuming we + + + align:start position:0% +determine the phase margin assuming we +have a stable system incidentally for + + align:start position:0% +have a stable system incidentally for + + + align:start position:0% +have a stable system incidentally for +any of this we really have to go back + + align:start position:0% +any of this we really have to go back + + + align:start position:0% +any of this we really have to go back +and and check via Nyquist test whether + + align:start position:0% +and and check via Nyquist test whether + + + align:start position:0% +and and check via Nyquist test whether +the system is stable or not but we very + + align:start position:0% +the system is stable or not but we very + + + align:start position:0% +the system is stable or not but we very +rapidly learn to recognize familiar + + align:start position:0% +rapidly learn to recognize familiar + + + align:start position:0% +rapidly learn to recognize familiar +patterns and if we have sort of a a + + align:start position:0% +patterns and if we have sort of a a + + + align:start position:0% +patterns and if we have sort of a a +well- behaved maybe typical common kind + + align:start position:0% +well- behaved maybe typical common kind + + + align:start position:0% +well- behaved maybe typical common kind +of a system uh where the magnitude is + + align:start position:0% +of a system uh where the magnitude is + + + align:start position:0% +of a system uh where the magnitude is +sort of a monotonic decreasing function + + align:start position:0% +sort of a monotonic decreasing function + + + align:start position:0% +sort of a monotonic decreasing function +of frequency uh the angle starts out + + align:start position:0% +of frequency uh the angle starts out + + + align:start position:0% +of frequency uh the angle starts out +possibly close to 0 degrees or in the + + align:start position:0% +possibly close to 0 degrees or in the + + + align:start position:0% +possibly close to 0 degrees or in the +case where our Loop transmission + + align:start position:0% +case where our Loop transmission + + + align:start position:0% +case where our Loop transmission +includes an integration which is a + + align:start position:0% +includes an integration which is a + + + align:start position:0% +includes an integration which is a +fairly common case in mechanical systems + + align:start position:0% +fairly common case in mechanical systems + + + align:start position:0% +fairly common case in mechanical systems +uh the angle of the AF product would + + align:start position:0% +uh the angle of the AF product would + + + align:start position:0% +uh the angle of the AF product would +start at minus 90° uh and then again + + align:start position:0% +start at minus 90° uh and then again + + + align:start position:0% +start at minus 90° uh and then again +drops off and goes through minus 180° + + align:start position:0% +drops off and goes through minus 180° + + + align:start position:0% +drops off and goes through minus 180° +only once it doesn't wiggle back and + + align:start position:0% +only once it doesn't wiggle back and + + + align:start position:0% +only once it doesn't wiggle back and +forth around the minus 180 degree line + + align:start position:0% +forth around the minus 180 degree line + + + align:start position:0% +forth around the minus 180 degree line +if we have this sort of a uh well- + + align:start position:0% +if we have this sort of a uh well- + + + align:start position:0% +if we have this sort of a uh well- +behaved kind of a system then in fact uh + + align:start position:0% +behaved kind of a system then in fact uh + + + align:start position:0% +behaved kind of a system then in fact uh +the Nyquist test simplifies greatly and + + align:start position:0% +the Nyquist test simplifies greatly and + + + align:start position:0% +the Nyquist test simplifies greatly and +we can convince ourselves that providing + + align:start position:0% +we can convince ourselves that providing + + + align:start position:0% +we can convince ourselves that providing +the angle has not yet reached minus + + align:start position:0% +the angle has not yet reached minus + + + align:start position:0% +the angle has not yet reached minus +180° when the magnitude has gotten down + + align:start position:0% +180° when the magnitude has gotten down + + + align:start position:0% +180° when the magnitude has gotten down +to one the system will be stable and so + + align:start position:0% +to one the system will be stable and so + + + align:start position:0% +to one the system will be stable and so +here we've shown that situation the + + align:start position:0% +here we've shown that situation the + + + align:start position:0% +here we've shown that situation the +magnitude of the AF product is one uh + + align:start position:0% +magnitude of the AF product is one uh + + + align:start position:0% +magnitude of the AF product is one uh +the angle is somewhat more positive than + + align:start position:0% +the angle is somewhat more positive than + + + align:start position:0% +the angle is somewhat more positive than +minus 180 de and for this sort of a + + align:start position:0% +minus 180 de and for this sort of a + + + align:start position:0% +minus 180 de and for this sort of a +simple well- behaved system why that + + align:start position:0% +simple well- behaved system why that + + + align:start position:0% +simple well- behaved system why that +guarantees stability if we conducted the + + align:start position:0% +guarantees stability if we conducted the + + + align:start position:0% +guarantees stability if we conducted the +Nyquist test once we've convinced + + align:start position:0% +Nyquist test once we've convinced + + + align:start position:0% +Nyquist test once we've convinced +ourselves the system is stable we can + + align:start position:0% +ourselves the system is stable we can + + + align:start position:0% +ourselves the system is stable we can +look at the crossover frequency in other + + align:start position:0% +look at the crossover frequency in other + + + align:start position:0% +look at the crossover frequency in other +words look at the frequency where the + + align:start position:0% +words look at the frequency where the + + + align:start position:0% +words look at the frequency where the +magnitude of the AF product is one and + + align:start position:0% +magnitude of the AF product is one and + + + align:start position:0% +magnitude of the AF product is one and +this distance is the phase + + align:start position:0% + + + + align:start position:0% + +margin in other words the phase margin + + align:start position:0% +margin in other words the phase margin + + + align:start position:0% +margin in other words the phase margin +represents the difference between the + + align:start position:0% +represents the difference between the + + + align:start position:0% +represents the difference between the +angle of the AF product at the crossover + + align:start position:0% +angle of the AF product at the crossover + + + align:start position:0% +angle of the AF product at the crossover +frequency and minus + + align:start position:0% +frequency and minus + + + align:start position:0% +frequency and minus +180° in some sense it's a measure of the + + align:start position:0% +180° in some sense it's a measure of the + + + align:start position:0% +180° in some sense it's a measure of the +amount of additional negative phase + + align:start position:0% +amount of additional negative phase + + + align:start position:0% +amount of additional negative phase +shift we could add to to the loop + + align:start position:0% +shift we could add to to the loop + + + align:start position:0% +shift we could add to to the loop +transmission before the system became + + align:start position:0% +transmission before the system became + + + align:start position:0% +transmission before the system became +unstable if we could somehow reach in + + align:start position:0% +unstable if we could somehow reach in + + + align:start position:0% +unstable if we could somehow reach in +and add negative phase shift to the + + align:start position:0% +and add negative phase shift to the + + + align:start position:0% +and add negative phase shift to the +system if we added this much of negative + + align:start position:0% +system if we added this much of negative + + + align:start position:0% +system if we added this much of negative +fa negative phase shift to the system + + align:start position:0% +fa negative phase shift to the system + + + align:start position:0% +fa negative phase shift to the system +why the angle of AF would be minus 180 + + align:start position:0% +why the angle of AF would be minus 180 + + + align:start position:0% +why the angle of AF would be minus 180 +deg at the frequency where its magnitude + + align:start position:0% +deg at the frequency where its magnitude + + + align:start position:0% +deg at the frequency where its magnitude +is one and that would give us uh a minus + + align:start position:0% +is one and that would give us uh a minus + + + align:start position:0% +is one and that would give us uh a minus +one or a a pole on the imaginary axis a + + align:start position:0% +one or a a pole on the imaginary axis a + + + align:start position:0% +one or a a pole on the imaginary axis a +closed loop pole on the imaginary axis + + align:start position:0% +closed loop pole on the imaginary axis + + + align:start position:0% +closed loop pole on the imaginary axis +the system would be + + align:start position:0% +the system would be + + + align:start position:0% +the system would be +unstable uh the final quantity that we'd + + align:start position:0% +unstable uh the final quantity that we'd + + + align:start position:0% +unstable uh the final quantity that we'd +like to Define is a quantity called the + + align:start position:0% +like to Define is a quantity called the + + + align:start position:0% +like to Define is a quantity called the +gain margin uh and in particular the + + align:start position:0% +gain margin uh and in particular the + + + align:start position:0% +gain margin uh and in particular the +gain margin is the amount of additional + + align:start position:0% +gain margin is the amount of additional + + + align:start position:0% +gain margin is the amount of additional +gain we could provide to the system + + align:start position:0% +gain we could provide to the system + + + align:start position:0% +gain we could provide to the system +assuming we kept the angle fixed before + + align:start position:0% +assuming we kept the angle fixed before + + + align:start position:0% +assuming we kept the angle fixed before +we incurred instability so in this + + align:start position:0% +we incurred instability so in this + + + align:start position:0% +we incurred instability so in this +picture it's the amount we could push up + + align:start position:0% +picture it's the amount we could push up + + + align:start position:0% +picture it's the amount we could push up +the AF curve before the system became un + + align:start position:0% +the AF curve before the system became un + + + align:start position:0% +the AF curve before the system became un +stable and to do that we could look at + + align:start position:0% +stable and to do that we could look at + + + align:start position:0% +stable and to do that we could look at +the point where the the frequency where + + align:start position:0% +the point where the the frequency where + + + align:start position:0% +the point where the the frequency where +the angle went through- + + align:start position:0% +the angle went through- + + + align:start position:0% +the angle went through- +180° if we P pushed the magnitude curve + + align:start position:0% +180° if we P pushed the magnitude curve + + + align:start position:0% +180° if we P pushed the magnitude curve +up by this much we'd have a magnitude of + + align:start position:0% +up by this much we'd have a magnitude of + + + align:start position:0% +up by this much we'd have a magnitude of +one when the angle of the AF product was + + align:start position:0% +one when the angle of the AF product was + + + align:start position:0% +one when the angle of the AF product was +minus 180° that again would be the + + align:start position:0% +minus 180° that again would be the + + + align:start position:0% +minus 180° that again would be the +borderline case between stability and + + align:start position:0% +borderline case between stability and + + + align:start position:0% +borderline case between stability and +instability and so this distance + + align:start position:0% +instability and so this distance + + + align:start position:0% +instability and so this distance +reflects the gain margin of the + + align:start position:0% +reflects the gain margin of the + + + align:start position:0% +reflects the gain margin of the +system we can look at those same + + align:start position:0% +system we can look at those same + + + align:start position:0% +system we can look at those same +quantities in a gain phase plot if we + + align:start position:0% +quantities in a gain phase plot if we + + + align:start position:0% +quantities in a gain phase plot if we +care to we frequently do use gain phase + + align:start position:0% +care to we frequently do use gain phase + + + align:start position:0% +care to we frequently do use gain phase +plots for nickels constructions and so + + align:start position:0% +plots for nickels constructions and so + + + align:start position:0% +plots for nickels constructions and so +forth incidentally drawing a gain phase + + align:start position:0% +forth incidentally drawing a gain phase + + + align:start position:0% +forth incidentally drawing a gain phase +plot is a little bit more cumbersome + + align:start position:0% +plot is a little bit more cumbersome + + + align:start position:0% +plot is a little bit more cumbersome +than drawing a a bod plot mainly because + + align:start position:0% +than drawing a a bod plot mainly because + + + align:start position:0% +than drawing a a bod plot mainly because +we can make ASM totic approximations and + + align:start position:0% +we can make ASM totic approximations and + + + align:start position:0% +we can make ASM totic approximations and +and particularly to the magnitude + + align:start position:0% +and particularly to the magnitude + + + align:start position:0% +and particularly to the magnitude +portion of a of a b plot get a very very + + align:start position:0% +portion of a of a b plot get a very very + + + align:start position:0% +portion of a of a b plot get a very very +good approximation as a series of + + align:start position:0% +good approximation as a series of + + + align:start position:0% +good approximation as a series of +straight line segments where we just + + align:start position:0% +straight line segments where we just + + + align:start position:0% +straight line segments where we just +sort of round in a little bit where two + + align:start position:0% +sort of round in a little bit where two + + + align:start position:0% +sort of round in a little bit where two +straight lines segments + + align:start position:0% +straight lines segments + + + align:start position:0% +straight lines segments +intersect uh drawing a gain phase plot + + align:start position:0% +intersect uh drawing a gain phase plot + + + align:start position:0% +intersect uh drawing a gain phase plot +is a little bit more difficult possibly + + align:start position:0% +is a little bit more difficult possibly + + + align:start position:0% +is a little bit more difficult possibly +the easiest way to develop a gain phase + + align:start position:0% +the easiest way to develop a gain phase + + + align:start position:0% +the easiest way to develop a gain phase +plot is to simply draw the B plot first + + align:start position:0% +plot is to simply draw the B plot first + + + align:start position:0% +plot is to simply draw the B plot first +and then transfer values of magnitude + + align:start position:0% +and then transfer values of magnitude + + + align:start position:0% +and then transfer values of magnitude +and angle that corespond to a given + + align:start position:0% +and angle that corespond to a given + + + align:start position:0% +and angle that corespond to a given +frequency so here we have such a gain + + align:start position:0% +frequency so here we have such a gain + + + align:start position:0% +frequency so here we have such a gain +phase plot uh let's assume that + + align:start position:0% +phase plot uh let's assume that + + + align:start position:0% +phase plot uh let's assume that +increasing Omega runs along this + + align:start position:0% +increasing Omega runs along this + + + align:start position:0% +increasing Omega runs along this +direction uh which would be the case + + align:start position:0% +direction uh which would be the case + + + align:start position:0% +direction uh which would be the case +corresponding to the B plot that we've + + align:start position:0% +corresponding to the B plot that we've + + + align:start position:0% +corresponding to the B plot that we've +shown as Omega increases the magnitude + + align:start position:0% +shown as Omega increases the magnitude + + + align:start position:0% +shown as Omega increases the magnitude +goes down the angle goes more negative + + align:start position:0% +goes down the angle goes more negative + + + align:start position:0% +goes down the angle goes more negative +the curve goes in this direction the + + align:start position:0% +the curve goes in this direction the + + + align:start position:0% +the curve goes in this direction the +gain phase curve goes in this direction + + align:start position:0% +gain phase curve goes in this direction + + + align:start position:0% +gain phase curve goes in this direction +in these coordinates we get the + + align:start position:0% +in these coordinates we get the + + + align:start position:0% +in these coordinates we get the +crossover frequency Omega c as by + + align:start position:0% +crossover frequency Omega c as by + + + align:start position:0% +crossover frequency Omega c as by +looking at the parameter Omega along the + + align:start position:0% +looking at the parameter Omega along the + + + align:start position:0% +looking at the parameter Omega along the +curve so here is the frequency Omega c + + align:start position:0% +curve so here is the frequency Omega c + + + align:start position:0% +curve so here is the frequency Omega c +as Omega runs along the + + align:start position:0% +as Omega runs along the + + + align:start position:0% +as Omega runs along the +curve the dist distance betweenus + + align:start position:0% +curve the dist distance betweenus + + + align:start position:0% +curve the dist distance betweenus +180° and the actual angle of AF at Omega + + align:start position:0% +180° and the actual angle of AF at Omega + + + align:start position:0% +180° and the actual angle of AF at Omega +C is the phase margin of the system so + + align:start position:0% +C is the phase margin of the system so + + + align:start position:0% +C is the phase margin of the system so +that's this + + align:start position:0% + + + + align:start position:0% + +distance and the uh gain margin is + + align:start position:0% +distance and the uh gain margin is + + + align:start position:0% +distance and the uh gain margin is +effectively this distance in other words + + align:start position:0% +effectively this distance in other words + + + align:start position:0% +effectively this distance in other words +we could push up the magnitude curve or + + align:start position:0% +we could push up the magnitude curve or + + + align:start position:0% +we could push up the magnitude curve or +the gain phase curve by this amount + + align:start position:0% +the gain phase curve by this amount + + + align:start position:0% +the gain phase curve by this amount +before we incurred instability and so + + align:start position:0% +before we incurred instability and so + + + align:start position:0% +before we incurred instability and so +this then is the gain margin or that + + align:start position:0% +this then is the gain margin or that + + + align:start position:0% +this then is the gain margin or that +ratio the ratio of this gain into one is + + align:start position:0% +ratio the ratio of this gain into one is + + + align:start position:0% +ratio the ratio of this gain into one is +the gain margin of the system so again + + align:start position:0% +the gain margin of the system so again + + + align:start position:0% +the gain margin of the system so again +we can Define the quantities phase + + align:start position:0% +we can Define the quantities phase + + + align:start position:0% +we can Define the quantities phase +margin gain margin and crossover + + align:start position:0% +margin gain margin and crossover + + + align:start position:0% +margin gain margin and crossover +frequency uh in either a bod plot + + align:start position:0% +frequency uh in either a bod plot + + + align:start position:0% +frequency uh in either a bod plot +presentation or a gain phase + + align:start position:0% +presentation or a gain phase + + + align:start position:0% +presentation or a gain phase +presentation now the the value of these + + align:start position:0% +presentation now the the value of these + + + align:start position:0% +presentation now the the value of these +quantities uh is that they very very + + align:start position:0% +quantities uh is that they very very + + + align:start position:0% +quantities uh is that they very very +accurate + + align:start position:0% +accurate + + + align:start position:0% +accurate +predict important features of the closed + + align:start position:0% +predict important features of the closed + + + align:start position:0% +predict important features of the closed +loop response of the system if we assume + + align:start position:0% +loop response of the system if we assume + + + align:start position:0% +loop response of the system if we assume +we have a topology with a frequency + + align:start position:0% +we have a topology with a frequency + + + align:start position:0% +we have a topology with a frequency +independent feedback path the one we've + + align:start position:0% +independent feedback path the one we've + + + align:start position:0% +independent feedback path the one we've +been looking at in the Nickels + + align:start position:0% +been looking at in the Nickels + + + align:start position:0% +been looking at in the Nickels +construction we can then get a a very + + align:start position:0% +construction we can then get a a very + + + align:start position:0% +construction we can then get a a very +good indication of important parameters + + align:start position:0% +good indication of important parameters + + + align:start position:0% +good indication of important parameters +of the system by looking simply at these + + align:start position:0% +of the system by looking simply at these + + + align:start position:0% +of the system by looking simply at these +quantities in general the speed of + + align:start position:0% +quantities in general the speed of + + + align:start position:0% +quantities in general the speed of +response of the system scales directly + + align:start position:0% +response of the system scales directly + + + align:start position:0% +response of the system scales directly +with crossover frequency assuming we can + + align:start position:0% +with crossover frequency assuming we can + + + align:start position:0% +with crossover frequency assuming we can +maintain equivalent values of gain + + align:start position:0% +maintain equivalent values of gain + + + align:start position:0% +maintain equivalent values of gain +margin and phase margin for two systems + + align:start position:0% +margin and phase margin for two systems + + + align:start position:0% +margin and phase margin for two systems +that have different crossover + + align:start position:0% +that have different crossover + + + align:start position:0% +that have different crossover +frequencies any measure of the Dynamics + + align:start position:0% +frequencies any measure of the Dynamics + + + align:start position:0% +frequencies any measure of the Dynamics +of those systems the half power + + align:start position:0% +of those systems the half power + + + align:start position:0% +of those systems the half power +frequency the rise time and response to + + align:start position:0% +frequency the rise time and response to + + + align:start position:0% +frequency the rise time and response to +a step any of those sorts of measures of + + align:start position:0% +a step any of those sorts of measures of + + + align:start position:0% +a step any of those sorts of measures of +speed of response will scale directly + + align:start position:0% +speed of response will scale directly + + + align:start position:0% +speed of response will scale directly +with crossover frequency a higher + + align:start position:0% +with crossover frequency a higher + + + align:start position:0% +with crossover frequency a higher +crossover frequency of course + + align:start position:0% +crossover frequency of course + + + align:start position:0% +crossover frequency of course +corresponding to a wider bandwidth + + align:start position:0% +corresponding to a wider bandwidth + + + align:start position:0% +corresponding to a wider bandwidth +system a faster rise time + + align:start position:0% +system a faster rise time + + + align:start position:0% +system a faster rise time +system uh gain margin is is kind of an + + align:start position:0% +system uh gain margin is is kind of an + + + align:start position:0% +system uh gain margin is is kind of an +override kind of a thing not much + + align:start position:0% +override kind of a thing not much + + + align:start position:0% +override kind of a thing not much +happens uh to deteriorate system + + align:start position:0% +happens uh to deteriorate system + + + align:start position:0% +happens uh to deteriorate system +performance until we get down to gain + + align:start position:0% +performance until we get down to gain + + + align:start position:0% +performance until we get down to gain +margins that become sort of too small + + align:start position:0% +margins that become sort of too small + + + align:start position:0% +margins that become sort of too small +and what's too small well if you have a + + align:start position:0% +and what's too small well if you have a + + + align:start position:0% +and what's too small well if you have a +gain margin of three or more possibly or + + align:start position:0% +gain margin of three or more possibly or + + + align:start position:0% +gain margin of three or more possibly or +or maybe a little bit more than that why + + align:start position:0% +or maybe a little bit more than that why + + + align:start position:0% +or maybe a little bit more than that why +it turns out that the gain margin has + + align:start position:0% +it turns out that the gain margin has + + + align:start position:0% +it turns out that the gain margin has +relatively little influence on the + + align:start position:0% +relatively little influence on the + + + align:start position:0% +relatively little influence on the +relative stability of the system it does + + align:start position:0% +relative stability of the system it does + + + align:start position:0% +relative stability of the system it does +give you a measure of of how much margin + + align:start position:0% +give you a measure of of how much margin + + + align:start position:0% +give you a measure of of how much margin +you have how tolerant or intolerant you + + align:start position:0% +you have how tolerant or intolerant you + + + align:start position:0% +you have how tolerant or intolerant you +are uh to changes in various system + + align:start position:0% +are uh to changes in various system + + + align:start position:0% +are uh to changes in various system +parameters how sensitive you are to + + align:start position:0% +parameters how sensitive you are to + + + align:start position:0% +parameters how sensitive you are to +changes in certain quantities that + + align:start position:0% +changes in certain quantities that + + + align:start position:0% +changes in certain quantities that +affect the loop transmission magnitude + + align:start position:0% +affect the loop transmission magnitude + + + align:start position:0% +affect the loop transmission magnitude +for example if we had a gain margin of + + align:start position:0% +for example if we had a gain margin of + + + align:start position:0% +for example if we had a gain margin of +three then increasing the loop + + align:start position:0% +three then increasing the loop + + + align:start position:0% +three then increasing the loop +transmission magnitude by a factor of + + align:start position:0% +transmission magnitude by a factor of + + + align:start position:0% +transmission magnitude by a factor of +three would cause the system to become + + align:start position:0% +three would cause the system to become + + + align:start position:0% +three would cause the system to become +unstable but if we have a gain margin of + + align:start position:0% +unstable but if we have a gain margin of + + + align:start position:0% +unstable but if we have a gain margin of +three and are sure we'll maintain it it + + align:start position:0% +three and are sure we'll maintain it it + + + align:start position:0% +three and are sure we'll maintain it it +has relatively little influence on the + + align:start position:0% +has relatively little influence on the + + + align:start position:0% +has relatively little influence on the +stability uh the relative stability of + + align:start position:0% +stability uh the relative stability of + + + align:start position:0% +stability uh the relative stability of +the system the big indicator of relative + + align:start position:0% +the system the big indicator of relative + + + align:start position:0% +the system the big indicator of relative +stability is the phase margin and in + + align:start position:0% +stability is the phase margin and in + + + align:start position:0% +stability is the phase margin and in +fact there is a very good + + align:start position:0% +fact there is a very good + + + align:start position:0% +fact there is a very good +relationship uh between phase margin and + + align:start position:0% +relationship uh between phase margin and + + + align:start position:0% +relationship uh between phase margin and +a quantity that we might Define as m + + align:start position:0% +a quantity that we might Define as m + + + align:start position:0% +a quantity that we might Define as m +subp m subp is a frequency do domain + + align:start position:0% +subp m subp is a frequency do domain + + + align:start position:0% +subp m subp is a frequency do domain +concept and in fact the MP is the ratio + + align:start position:0% +concept and in fact the MP is the ratio + + + align:start position:0% +concept and in fact the MP is the ratio +of the maximum resonant Peak that we get + + align:start position:0% +of the maximum resonant Peak that we get + + + align:start position:0% +of the maximum resonant Peak that we get +for a system in our standard form with + + align:start position:0% +for a system in our standard form with + + + align:start position:0% +for a system in our standard form with +unity feedback the maximum Peak we get + + align:start position:0% +unity feedback the maximum Peak we get + + + align:start position:0% +unity feedback the maximum Peak we get +uh divided by the low frequency + + align:start position:0% +uh divided by the low frequency + + + align:start position:0% +uh divided by the low frequency +magnitude of the closed loop gain in the + + align:start position:0% +magnitude of the closed loop gain in the + + + align:start position:0% +magnitude of the closed loop gain in the +case that we worked out on the Nickels + + align:start position:0% +case that we worked out on the Nickels + + + align:start position:0% +case that we worked out on the Nickels +chart a little bit earlier for all three + + align:start position:0% +chart a little bit earlier for all three + + + align:start position:0% +chart a little bit earlier for all three +of our systems we had very nearly uh a + + align:start position:0% +of our systems we had very nearly uh a + + + align:start position:0% +of our systems we had very nearly uh a +magnitude of the closed loop gain of one + + align:start position:0% +magnitude of the closed loop gain of one + + + align:start position:0% +magnitude of the closed loop gain of one +at sufficiently low frequencies and so + + align:start position:0% +at sufficiently low frequencies and so + + + align:start position:0% +at sufficiently low frequencies and so +the peak values here very re very nearly + + align:start position:0% +the peak values here very re very nearly + + + align:start position:0% +the peak values here very re very nearly +reflect mCP uh for the case where a FN + + align:start position:0% +reflect mCP uh for the case where a FN + + + align:start position:0% +reflect mCP uh for the case where a FN +was 22 we have an MP of about + + align:start position:0% +was 22 we have an MP of about + + + align:start position:0% +was 22 we have an MP of about +1.4 for a case where where the a f KN + + align:start position:0% +1.4 for a case where where the a f KN + + + align:start position:0% +1.4 for a case where where the a f KN +product is 50 uh we have about two for + + align:start position:0% +product is 50 uh we have about two for + + + align:start position:0% +product is 50 uh we have about two for +the maximum magnitude of the resonant + + align:start position:0% +the maximum magnitude of the resonant + + + align:start position:0% +the maximum magnitude of the resonant +Peak and we get a very very good + + align:start position:0% +Peak and we get a very very good + + + align:start position:0% +Peak and we get a very very good +indication of relative stabil ility by + + align:start position:0% +indication of relative stabil ility by + + + align:start position:0% +indication of relative stabil ility by +focusing simply on MP we can design our + + align:start position:0% +focusing simply on MP we can design our + + + align:start position:0% +focusing simply on MP we can design our +systems when we go to do it really using + + align:start position:0% +systems when we go to do it really using + + + align:start position:0% +systems when we go to do it really using +that as our principal indicator of + + align:start position:0% +that as our principal indicator of + + + align:start position:0% +that as our principal indicator of +relative + + align:start position:0% +relative + + + align:start position:0% +relative +stability there's a very good empirical + + align:start position:0% +stability there's a very good empirical + + + align:start position:0% +stability there's a very good empirical +relationship between MP and the phase + + align:start position:0% +relationship between MP and the phase + + + align:start position:0% +relationship between MP and the phase +margin and that's simply that mCP is + + align:start position:0% +margin and that's simply that mCP is + + + align:start position:0% +margin and that's simply that mCP is +about equal to one over s of the phase + + align:start position:0% +about equal to one over s of the phase + + + align:start position:0% +about equal to one over s of the phase +margin that's not a a mathematically + + align:start position:0% +margin that's not a a mathematically + + + align:start position:0% +margin that's not a a mathematically +exact relationship but just a + + align:start position:0% +exact relationship but just a + + + align:start position:0% +exact relationship but just a +relationship that empirically exists for + + align:start position:0% +relationship that empirically exists for + + + align:start position:0% +relationship that empirically exists for +most systems of interest and we can at + + align:start position:0% +most systems of interest and we can at + + + align:start position:0% +most systems of interest and we can at +least offer a plausibility argument for + + align:start position:0% +least offer a plausibility argument for + + + align:start position:0% +least offer a plausibility argument for +why that relationship might hold or + + align:start position:0% +why that relationship might hold or + + + align:start position:0% +why that relationship might hold or +might be a good + + align:start position:0% +might be a good + + + align:start position:0% +might be a good +approximation as + + align:start position:0% + + + + align:start position:0% + +follows here uh We've shown a much + + align:start position:0% +follows here uh We've shown a much + + + align:start position:0% +follows here uh We've shown a much +simplified Nyquist chart + + align:start position:0% +simplified Nyquist chart + + + align:start position:0% +simplified Nyquist chart +um and eliminated a lot of the uh + + align:start position:0% +um and eliminated a lot of the uh + + + align:start position:0% +um and eliminated a lot of the uh +additional Contours that confuse the + + align:start position:0% +additional Contours that confuse the + + + align:start position:0% +additional Contours that confuse the +issue and we focused once again on the + + align:start position:0% +issue and we focused once again on the + + + align:start position:0% +issue and we focused once again on the +the magnitude equals 1 angle equals + + align:start position:0% +the magnitude equals 1 angle equals + + + align:start position:0% +the magnitude equals 1 angle equals +minus 180° region of the + + align:start position:0% +minus 180° region of the + + + align:start position:0% +minus 180° region of the +Nickels + + align:start position:0% +Nickels + + + align:start position:0% +Nickels +chart and what I've assumed is that + + align:start position:0% +chart and what I've assumed is that + + + align:start position:0% +chart and what I've assumed is that +there's a straight line + + align:start position:0% +there's a straight line + + + align:start position:0% +there's a straight line +relationship in this vicinity at least + + align:start position:0% +relationship in this vicinity at least + + + align:start position:0% +relationship in this vicinity at least +uh between the magnitude and angle of + + align:start position:0% +uh between the magnitude and angle of + + + align:start position:0% +uh between the magnitude and angle of +the AF product so here are several + + align:start position:0% +the AF product so here are several + + + align:start position:0% +the AF product so here are several +possible AF products with different + + align:start position:0% +possible AF products with different + + + align:start position:0% +possible AF products with different +slopes in the gain phase plan + + align:start position:0% +slopes in the gain phase plan + + + align:start position:0% +slopes in the gain phase plan +and what I'll assume is that or we'll do + + align:start position:0% +and what I'll assume is that or we'll do + + + align:start position:0% +and what I'll assume is that or we'll do +the construction such that all of these + + align:start position:0% +the construction such that all of these + + + align:start position:0% +the construction such that all of these +systems all of these AF products have + + align:start position:0% +systems all of these AF products have + + + align:start position:0% +systems all of these AF products have +phase margins of + + align:start position:0% +phase margins of + + + align:start position:0% +phase margins of +45° that says that they all go through + + align:start position:0% +45° that says that they all go through + + + align:start position:0% +45° that says that they all go through +the point magnitude of AF equals 1 angle + + align:start position:0% +the point magnitude of AF equals 1 angle + + + align:start position:0% +the point magnitude of AF equals 1 angle +of AF equals - + + align:start position:0% +of AF equals - + + + align:start position:0% +of AF equals - +135° this distance then is 45° we have a + + align:start position:0% +135° this distance then is 45° we have a + + + align:start position:0% +135° this distance then is 45° we have a +a phase margin correspondingly of 45° so + + align:start position:0% +a phase margin correspondingly of 45° so + + + align:start position:0% +a phase margin correspondingly of 45° so +all the curves are constructed to go + + align:start position:0% +all the curves are constructed to go + + + align:start position:0% +all the curves are constructed to go +through this point magnitude equals 1 + + align:start position:0% +through this point magnitude equals 1 + + + align:start position:0% +through this point magnitude equals 1 +angle equals - + + align:start position:0% +angle equals - + + + align:start position:0% +angle equals - +135° and we simply have different slopes + + align:start position:0% +135° and we simply have different slopes + + + align:start position:0% +135° and we simply have different slopes +or approximating different kinds of AF + + align:start position:0% +or approximating different kinds of AF + + + align:start position:0% +or approximating different kinds of AF +products all with the same phase margin + + align:start position:0% +products all with the same phase margin + + + align:start position:0% +products all with the same phase margin +and we can now begin to look at the MP + + align:start position:0% +and we can now begin to look at the MP + + + align:start position:0% +and we can now begin to look at the MP +the maximum value of the closed loop + + align:start position:0% +the maximum value of the closed loop + + + align:start position:0% +the maximum value of the closed loop +response that we get for those various + + align:start position:0% +response that we get for those various + + + align:start position:0% +response that we get for those various +curves and if for example we look at + + align:start position:0% +curves and if for example we look at + + + align:start position:0% +curves and if for example we look at +this curve here we're up to a closed + + align:start position:0% +this curve here we're up to a closed + + + align:start position:0% +this curve here we're up to a closed +loop magnitude of 1.2 here we're up to a + + align:start position:0% +loop magnitude of 1.2 here we're up to a + + + align:start position:0% +loop magnitude of 1.2 here we're up to a +closed loop mag magnitude of + + align:start position:0% +closed loop mag magnitude of + + + align:start position:0% +closed loop mag magnitude of +1.3 uh and we get to our MP our maximum + + align:start position:0% +1.3 uh and we get to our MP our maximum + + + align:start position:0% +1.3 uh and we get to our MP our maximum +value for the closed loop magnitude + + align:start position:0% +value for the closed loop magnitude + + + align:start position:0% +value for the closed loop magnitude +somewhere in here somewhere between the + + align:start position:0% +somewhere in here somewhere between the + + + align:start position:0% +somewhere in here somewhere between the +1.4 and the 1.3 curve maybe + + align:start position:0% +1.4 and the 1.3 curve maybe + + + align:start position:0% +1.4 and the 1.3 curve maybe +1.35 we have a little greater slope like + + align:start position:0% +1.35 we have a little greater slope like + + + align:start position:0% +1.35 we have a little greater slope like +so for our assumed AF product again with + + align:start position:0% +so for our assumed AF product again with + + + align:start position:0% +so for our assumed AF product again with +a phase margin of + + align:start position:0% +a phase margin of + + + align:start position:0% +a phase margin of +45° why let's see here we have a a + + align:start position:0% +45° why let's see here we have a a + + + align:start position:0% +45° why let's see here we have a a +closed loop response a magnitude of 1.2 + + align:start position:0% +closed loop response a magnitude of 1.2 + + + align:start position:0% +closed loop response a magnitude of 1.2 +here we're up to + + align:start position:0% +here we're up to + + + align:start position:0% +here we're up to +1.3 and that's the maximum MP for this + + align:start position:0% +1.3 and that's the maximum MP for this + + + align:start position:0% +1.3 and that's the maximum MP for this +particular curve MP is is 1.3 we have a + + align:start position:0% +particular curve MP is is 1.3 we have a + + + align:start position:0% +particular curve MP is is 1.3 we have a +little greater + + align:start position:0% +little greater + + + align:start position:0% +little greater +slope uh and Chase things through we + + align:start position:0% +slope uh and Chase things through we + + + align:start position:0% +slope uh and Chase things through we +find out that the MP that results is + + align:start position:0% +find out that the MP that results is + + + align:start position:0% +find out that the MP that results is +about + + align:start position:0% +about + + + align:start position:0% +about +1.4 however uh if we have an even + + align:start position:0% +1.4 however uh if we have an even + + + align:start position:0% +1.4 however uh if we have an even +flatter curve we can get to MPS higher + + align:start position:0% +flatter curve we can get to MPS higher + + + align:start position:0% +flatter curve we can get to MPS higher +than 1.4 for example if we had a curve + + align:start position:0% +than 1.4 for example if we had a curve + + + align:start position:0% +than 1.4 for example if we had a curve +like this we'd get up to about 1 .7 for + + align:start position:0% +like this we'd get up to about 1 .7 for + + + align:start position:0% +like this we'd get up to about 1 .7 for +an MP but those result in in + + align:start position:0% +an MP but those result in in + + + align:start position:0% +an MP but those result in in +progressively smaller values of gain + + align:start position:0% +progressively smaller values of gain + + + align:start position:0% +progressively smaller values of gain +margin for example this distance here's + + align:start position:0% +margin for example this distance here's + + + align:start position:0% +margin for example this distance here's +the magnitude one point and here is our + + align:start position:0% +the magnitude one point and here is our + + + align:start position:0% +the magnitude one point and here is our +uh curve going through minus 180 degrees + + align:start position:0% +uh curve going through minus 180 degrees + + + align:start position:0% +uh curve going through minus 180 degrees +that distance happens to correspond to a + + align:start position:0% +that distance happens to correspond to a + + + align:start position:0% +that distance happens to correspond to a +gain margin of + + align:start position:0% +gain margin of + + + align:start position:0% +gain margin of +2.2 for the system that has an MP of + + align:start position:0% +2.2 for the system that has an MP of + + + align:start position:0% +2.2 for the system that has an MP of +1.5 larger values of MP require + + align:start position:0% +1.5 larger values of MP require + + + align:start position:0% +1.5 larger values of MP require +correspondingly smaller values of G gain + + align:start position:0% +correspondingly smaller values of G gain + + + align:start position:0% +correspondingly smaller values of G gain +margin as I indicated before if we have + + align:start position:0% +margin as I indicated before if we have + + + align:start position:0% +margin as I indicated before if we have +enough gain margin where enough is + + align:start position:0% +enough gain margin where enough is + + + align:start position:0% +enough gain margin where enough is +possibly three then in fact this + + align:start position:0% +possibly three then in fact this + + + align:start position:0% +possibly three then in fact this +approximation is a very very good + + align:start position:0% + + + + align:start position:0% + +one uh we can do this same sort of + + align:start position:0% +one uh we can do this same sort of + + + align:start position:0% +one uh we can do this same sort of +construction the same kind of + + align:start position:0% +construction the same kind of + + + align:start position:0% +construction the same kind of +construction that I've just done + + align:start position:0% +construction that I've just done + + + align:start position:0% +construction that I've just done +choosing different values for phase + + align:start position:0% +choosing different values for phase + + + align:start position:0% +choosing different values for phase +margin we might try it for 30 degrees + + align:start position:0% +margin we might try it for 30 degrees + + + align:start position:0% +margin we might try it for 30 degrees +and for 60 degrees and so on and when we + + align:start position:0% +and for 60 degrees and so on and when we + + + align:start position:0% +and for 60 degrees and so on and when we +do that uh and sort of experim or + + align:start position:0% +do that uh and sort of experim or + + + align:start position:0% +do that uh and sort of experim or +empirically fit resultant data points we + + align:start position:0% +empirically fit resultant data points we + + + align:start position:0% +empirically fit resultant data points we +find that that this approximation is a + + align:start position:0% +find that that this approximation is a + + + align:start position:0% +find that that this approximation is a +good one it happens that the ease of + + align:start position:0% +good one it happens that the ease of + + + align:start position:0% +good one it happens that the ease of +doing this sort of thing is + + align:start position:0% +doing this sort of thing is + + + align:start position:0% +doing this sort of thing is +so it's such a simple construction to do + + align:start position:0% +so it's such a simple construction to do + + + align:start position:0% +so it's such a simple construction to do +where we can quickly and rapidly draw a + + align:start position:0% +where we can quickly and rapidly draw a + + + align:start position:0% +where we can quickly and rapidly draw a +bod plot we can go ahead and from the + + align:start position:0% +bod plot we can go ahead and from the + + + align:start position:0% +bod plot we can go ahead and from the +Bodi plot determine first of all uh is + + align:start position:0% +Bodi plot determine first of all uh is + + + align:start position:0% +Bodi plot determine first of all uh is +the system stable we can translate a bod + + align:start position:0% +the system stable we can translate a bod + + + align:start position:0% +the system stable we can translate a bod +plot into Nyquist coordinates and + + align:start position:0% +plot into Nyquist coordinates and + + + align:start position:0% +plot into Nyquist coordinates and +determine rapidly if the system is + + align:start position:0% +determine rapidly if the system is + + + align:start position:0% +determine rapidly if the system is +stable we're then able to go ahead and + + align:start position:0% +stable we're then able to go ahead and + + + align:start position:0% +stable we're then able to go ahead and +and and from the bod plot evaluate the + + align:start position:0% +and and from the bod plot evaluate the + + + align:start position:0% +and and from the bod plot evaluate the +crossover frequency very rapidly we're + + align:start position:0% +crossover frequency very rapidly we're + + + align:start position:0% +crossover frequency very rapidly we're +able to determine the gain margin and + + align:start position:0% +able to determine the gain margin and + + + align:start position:0% +able to determine the gain margin and +see if it's quote enough and then we're + + align:start position:0% +see if it's quote enough and then we're + + + align:start position:0% +see if it's quote enough and then we're +able to find the phase margin of our + + align:start position:0% +able to find the phase margin of our + + + align:start position:0% +able to find the phase margin of our +system and that those constructions are + + align:start position:0% +system and that those constructions are + + + align:start position:0% +system and that those constructions are +very rapid and give us remarkably good + + align:start position:0% +very rapid and give us remarkably good + + + align:start position:0% +very rapid and give us remarkably good +results when we ask about the + + align:start position:0% +results when we ask about the + + + align:start position:0% +results when we ask about the +performance of a feedback system once we + + align:start position:0% +performance of a feedback system once we + + + align:start position:0% +performance of a feedback system once we +know the phase margin and the crossover + + align:start position:0% +know the phase margin and the crossover + + + align:start position:0% +know the phase margin and the crossover +frequency we can make excellent + + align:start position:0% +frequency we can make excellent + + + align:start position:0% +frequency we can make excellent +predictions about the closed loop + + align:start position:0% +predictions about the closed loop + + + align:start position:0% +predictions about the closed loop +response of the system and because it's + + align:start position:0% +response of the system and because it's + + + align:start position:0% +response of the system and because it's +so easy to do I think almost all of the + + align:start position:0% +so easy to do I think almost all of the + + + align:start position:0% +so easy to do I think almost all of the +numerical work that one does with + + align:start position:0% +numerical work that one does with + + + align:start position:0% +numerical work that one does with +feedback systems really is based on + + align:start position:0% +feedback systems really is based on + + + align:start position:0% +feedback systems really is based on +these kinds of frequency domain Concepts + + align:start position:0% +these kinds of frequency domain Concepts + + + align:start position:0% +these kinds of frequency domain Concepts +we may use root Locus as an aid to + + align:start position:0% +we may use root Locus as an aid to + + + align:start position:0% +we may use root Locus as an aid to +quickly seeing what's going on in the + + align:start position:0% +quickly seeing what's going on in the + + + align:start position:0% +quickly seeing what's going on in the +system and what might happen if we + + align:start position:0% +system and what might happen if we + + + align:start position:0% +system and what might happen if we +change to zero location or what might + + align:start position:0% +change to zero location or what might + + + align:start position:0% +change to zero location or what might +happen if we change the location of a + + align:start position:0% +happen if we change the location of a + + + align:start position:0% +happen if we change the location of a +pole and that sort of thing we can use + + align:start position:0% +pole and that sort of thing we can use + + + align:start position:0% +pole and that sort of thing we can use +root Locus Concepts to explore those + + align:start position:0% +root Locus Concepts to explore those + + + align:start position:0% +root Locus Concepts to explore those +issues very quickly but when we want to + + align:start position:0% +issues very quickly but when we want to + + + align:start position:0% +issues very quickly but when we want to +get numerical results when we'd like to + + align:start position:0% +get numerical results when we'd like to + + + align:start position:0% +get numerical results when we'd like to +go ahead and and determine uh the + + align:start position:0% +go ahead and and determine uh the + + + align:start position:0% +go ahead and and determine uh the +correct value for certain system + + align:start position:0% +correct value for certain system + + + align:start position:0% +correct value for certain system +parameters we almost invariably do that + + align:start position:0% +parameters we almost invariably do that + + + align:start position:0% +parameters we almost invariably do that +using bod plot frequency domain kinds of + + align:start position:0% +using bod plot frequency domain kinds of + + + align:start position:0% +using bod plot frequency domain kinds of +techniques I'd now like to introduce the + + align:start position:0% +techniques I'd now like to introduce the + + + align:start position:0% +techniques I'd now like to introduce the +idea of + + align:start position:0% +idea of + + + align:start position:0% +idea of +compensation compensation uh simply in + + align:start position:0% +compensation compensation uh simply in + + + align:start position:0% +compensation compensation uh simply in +indicates that we're interested in + + align:start position:0% +indicates that we're interested in + + + align:start position:0% +indicates that we're interested in +modifying a feedback system hopefully in + + align:start position:0% +modifying a feedback system hopefully in + + + align:start position:0% +modifying a feedback system hopefully in +order to improve its + + align:start position:0% +order to improve its + + + align:start position:0% +order to improve its +performance uh when we put together a + + align:start position:0% +performance uh when we put together a + + + align:start position:0% +performance uh when we put together a +feedback system why as we might imagine + + align:start position:0% +feedback system why as we might imagine + + + align:start position:0% +feedback system why as we might imagine +what usually happens is we find out that + + align:start position:0% +what usually happens is we find out that + + + align:start position:0% +what usually happens is we find out that +we can't get the desired values of + + align:start position:0% +we can't get the desired values of + + + align:start position:0% +we can't get the desired values of +desensitivity or the desired values of + + align:start position:0% +desensitivity or the desired values of + + + align:start position:0% +desensitivity or the desired values of +speed of response uh without paying a + + align:start position:0% +speed of response uh without paying a + + + align:start position:0% +speed of response uh without paying a +stability penalty that we're unwilling + + align:start position:0% +stability penalty that we're unwilling + + + align:start position:0% +stability penalty that we're unwilling +to to pay and so the question is what + + align:start position:0% +to to pay and so the question is what + + + align:start position:0% +to to pay and so the question is what +can we do in order to modify the system + + align:start position:0% +can we do in order to modify the system + + + align:start position:0% +can we do in order to modify the system +to improve its performance that process + + align:start position:0% +to improve its performance that process + + + align:start position:0% +to improve its performance that process +of modification is known as + + align:start position:0% +of modification is known as + + + align:start position:0% +of modification is known as +compensation and what we do is is look + + align:start position:0% +compensation and what we do is is look + + + align:start position:0% +compensation and what we do is is look +for certain figures of Merit or + + align:start position:0% +for certain figures of Merit or + + + align:start position:0% +for certain figures of Merit or +indicators of system performance that + + align:start position:0% +indicators of system performance that + + + align:start position:0% +indicators of system performance that +guide us in this design + + align:start position:0% +guide us in this design + + + align:start position:0% +guide us in this design +process well what might be good + + align:start position:0% +process well what might be good + + + align:start position:0% +process well what might be good +indicators of of system performance in + + align:start position:0% +indicators of of system performance in + + + align:start position:0% +indicators of of system performance in +particular the relative stability of a + + align:start position:0% +particular the relative stability of a + + + align:start position:0% +particular the relative stability of a +feedback system it's very hard to to + + align:start position:0% +feedback system it's very hard to to + + + align:start position:0% +feedback system it's very hard to to +make uh sweeping General statements in + + align:start position:0% +make uh sweeping General statements in + + + align:start position:0% +make uh sweeping General statements in +that so much depends on the particular + + align:start position:0% +that so much depends on the particular + + + align:start position:0% +that so much depends on the particular +application for example if you're + + align:start position:0% +application for example if you're + + + align:start position:0% +application for example if you're +designing an aircraft Landing system the + + align:start position:0% +designing an aircraft Landing system the + + + align:start position:0% +designing an aircraft Landing system the +thing you want to avoid is any + + align:start position:0% +thing you want to avoid is any + + + align:start position:0% +thing you want to avoid is any +undershoot and so here we have a a very + + align:start position:0% +undershoot and so here we have a a very + + + align:start position:0% +undershoot and so here we have a a very +very conservative kind of requirement + + align:start position:0% +very conservative kind of requirement + + + align:start position:0% +very conservative kind of requirement +where we have to make sure that the the + + align:start position:0% +where we have to make sure that the the + + + align:start position:0% +where we have to make sure that the the +aircraft doesn't undershoot that's the + + align:start position:0% +aircraft doesn't undershoot that's the + + + align:start position:0% +aircraft doesn't undershoot that's the +the bad condition in an aircraft Landing + + align:start position:0% +the bad condition in an aircraft Landing + + + align:start position:0% +the bad condition in an aircraft Landing +system uh furthermore the degree to + + align:start position:0% +system uh furthermore the degree to + + + align:start position:0% +system uh furthermore the degree to +which we're willing to approach + + align:start position:0% +which we're willing to approach + + + align:start position:0% +which we're willing to approach +instability if you will the the the + + align:start position:0% +instability if you will the the the + + + align:start position:0% +instability if you will the the the +proximity we're willing to come to to a + + align:start position:0% +proximity we're willing to come to to a + + + align:start position:0% +proximity we're willing to come to to a +system that's unstable depends in part + + align:start position:0% +system that's unstable depends in part + + + align:start position:0% +system that's unstable depends in part +on on how how sure we are of the + + align:start position:0% +on on how how sure we are of the + + + align:start position:0% +on on how how sure we are of the +parameters and the fact will they remain + + align:start position:0% +parameters and the fact will they remain + + + align:start position:0% +parameters and the fact will they remain +fixed or is a system that's uh has a a + + align:start position:0% +fixed or is a system that's uh has a a + + + align:start position:0% +fixed or is a system that's uh has a a +minor stability problem today will it + + align:start position:0% +minor stability problem today will it + + + align:start position:0% +minor stability problem today will it +get worse as time goes on because of + + align:start position:0% +get worse as time goes on because of + + + align:start position:0% +get worse as time goes on because of +some unfortunate change in parameters so + + align:start position:0% +some unfortunate change in parameters so + + + align:start position:0% +some unfortunate change in parameters so +we really have to have a good feeling + + align:start position:0% +we really have to have a good feeling + + + align:start position:0% +we really have to have a good feeling +for the the actual details of the system + + align:start position:0% +for the the actual details of the system + + + align:start position:0% +for the the actual details of the system +when we go through this process but as + + align:start position:0% +when we go through this process but as + + + align:start position:0% +when we go through this process but as +sort of General guidelines we find of + + align:start position:0% +sort of General guidelines we find of + + + align:start position:0% +sort of General guidelines we find of +course that as we compr romis stability + + align:start position:0% +course that as we compr romis stability + + + align:start position:0% +course that as we compr romis stability +as we go to a relatively less stable + + align:start position:0% +as we go to a relatively less stable + + + align:start position:0% +as we go to a relatively less stable +system the advantages we gain in in + + align:start position:0% +system the advantages we gain in in + + + align:start position:0% +system the advantages we gain in in +exchange for that are generally a higher + + align:start position:0% +exchange for that are generally a higher + + + align:start position:0% +exchange for that are generally a higher +crossover frequency if we have a a sort + + align:start position:0% +crossover frequency if we have a a sort + + + align:start position:0% +crossover frequency if we have a a sort +of typical AF plot like this where the + + align:start position:0% +of typical AF plot like this where the + + + align:start position:0% +of typical AF plot like this where the +magnitude drops down monotonically the + + align:start position:0% +magnitude drops down monotonically the + + + align:start position:0% +magnitude drops down monotonically the +angle again is a a function at least in + + align:start position:0% +angle again is a a function at least in + + + align:start position:0% +angle again is a a function at least in +the vicinity of the crossover frequency + + align:start position:0% +the vicinity of the crossover frequency + + + align:start position:0% +the vicinity of the crossover frequency +that's a monotonic decreasing function + + align:start position:0% +that's a monotonic decreasing function + + + align:start position:0% +that's a monotonic decreasing function +uh now we find out that as we might for + + align:start position:0% +uh now we find out that as we might for + + + align:start position:0% +uh now we find out that as we might for +example increase the AF product + + align:start position:0% +example increase the AF product + + + align:start position:0% +example increase the AF product +crossover moves out the system gets + + align:start position:0% +crossover moves out the system gets + + + align:start position:0% +crossover moves out the system gets +faster because we've increased the AF + + align:start position:0% +faster because we've increased the AF + + + align:start position:0% +faster because we've increased the AF +product we get greater desensitivity but + + align:start position:0% +product we get greater desensitivity but + + + align:start position:0% +product we get greater desensitivity but +unfortunately the price we pay is one of + + align:start position:0% +unfortunately the price we pay is one of + + + align:start position:0% +unfortunately the price we pay is one of +reduced phase Marg consequently reduced + + align:start position:0% +reduced phase Marg consequently reduced + + + align:start position:0% +reduced phase Marg consequently reduced +stability so there's almost always that + + align:start position:0% +stability so there's almost always that + + + align:start position:0% +stability so there's almost always that +tradeoff where uh higher values of of + + align:start position:0% +tradeoff where uh higher values of of + + + align:start position:0% +tradeoff where uh higher values of of +crossover frequency and and greater + + align:start position:0% +crossover frequency and and greater + + + align:start position:0% +crossover frequency and and greater +amounts of desensitivity invariably lead + + align:start position:0% +amounts of desensitivity invariably lead + + + align:start position:0% +amounts of desensitivity invariably lead +to uh smaller phase margins consequently + + align:start position:0% +to uh smaller phase margins consequently + + + align:start position:0% +to uh smaller phase margins consequently +less relative stability but if we look + + align:start position:0% +less relative stability but if we look + + + align:start position:0% +less relative stability but if we look +at at some of the indicators of relative + + align:start position:0% +at at some of the indicators of relative + + + align:start position:0% +at at some of the indicators of relative +stability we find out that for many + + align:start position:0% +stability we find out that for many + + + align:start position:0% +stability we find out that for many +systems of Interest anyway we achieve + + align:start position:0% +systems of Interest anyway we achieve + + + align:start position:0% +systems of Interest anyway we achieve +satisfactory compromises between speed + + align:start position:0% +satisfactory compromises between speed + + + align:start position:0% +satisfactory compromises between speed +of response and relative stability if we + + align:start position:0% +of response and relative stability if we + + + align:start position:0% +of response and relative stability if we +look either for overshoots in response + + align:start position:0% +look either for overshoots in response + + + align:start position:0% +look either for overshoots in response +to a step that are possibly 10 to 50% of + + align:start position:0% +to a step that are possibly 10 to 50% of + + + align:start position:0% +to a step that are possibly 10 to 50% of +the amplitude of the step this is a Time + + align:start position:0% +the amplitude of the step this is a Time + + + align:start position:0% +the amplitude of the step this is a Time +domain measure and we've earlier looked + + align:start position:0% +domain measure and we've earlier looked + + + align:start position:0% +domain measure and we've earlier looked +at step responses for systems if we + + align:start position:0% +at step responses for systems if we + + + align:start position:0% +at step responses for systems if we +Define the peak overshoot uh as the + + align:start position:0% +Define the peak overshoot uh as the + + + align:start position:0% +Define the peak overshoot uh as the +percentage overshoot from final value + + align:start position:0% +percentage overshoot from final value + + + align:start position:0% +percentage overshoot from final value +for the step uh typically uh systems are + + align:start position:0% +for the step uh typically uh systems are + + + align:start position:0% +for the step uh typically uh systems are +designed for peak overshoots of possibly + + align:start position:0% +designed for peak overshoots of possibly + + + align:start position:0% +designed for peak overshoots of possibly +10 to + + align:start position:0% +10 to + + + align:start position:0% +10 to +50% uh we might if we look at the + + align:start position:0% +50% uh we might if we look at the + + + align:start position:0% +50% uh we might if we look at the +corresponding frequency domain + + align:start position:0% +corresponding frequency domain + + + align:start position:0% +corresponding frequency domain +evaluations of stability MP the amount + + align:start position:0% +evaluations of stability MP the amount + + + align:start position:0% +evaluations of stability MP the amount +of resonant Peak that we have in the + + align:start position:0% +of resonant Peak that we have in the + + + align:start position:0% +of resonant Peak that we have in the +closed loop frequency response again uh + + align:start position:0% +closed loop frequency response again uh + + + align:start position:0% +closed loop frequency response again uh +people oftimes look for M MPS or + + align:start position:0% +people oftimes look for M MPS or + + + align:start position:0% +people oftimes look for M MPS or +designed for MPS somewhere between one + + align:start position:0% +designed for MPS somewhere between one + + + align:start position:0% +designed for MPS somewhere between one +and two or uh maybe a little bit greater + + align:start position:0% +and two or uh maybe a little bit greater + + + align:start position:0% +and two or uh maybe a little bit greater +than one one may be an overly + + align:start position:0% +than one one may be an overly + + + align:start position:0% +than one one may be an overly +conservative value of MP we may have + + align:start position:0% +conservative value of MP we may have + + + align:start position:0% +conservative value of MP we may have +compromised speed of response too much + + align:start position:0% +compromised speed of response too much + + + align:start position:0% +compromised speed of response too much +for stability in that case and if we use + + align:start position:0% +for stability in that case and if we use + + + align:start position:0% +for stability in that case and if we use +as our indicator of relative stability + + align:start position:0% +as our indicator of relative stability + + + align:start position:0% +as our indicator of relative stability +the damping ratio associated with a + + align:start position:0% +the damping ratio associated with a + + + align:start position:0% +the damping ratio associated with a +dominant closed loop pole pair again + + align:start position:0% +dominant closed loop pole pair again + + + align:start position:0% +dominant closed loop pole pair again +people uh are oftentimes generally happy + + align:start position:0% +people uh are oftentimes generally happy + + + align:start position:0% +people uh are oftentimes generally happy +with systems that have damping ratio + + align:start position:0% +with systems that have damping ratio + + + align:start position:0% +with systems that have damping ratio +somewhere between 3 and and 7 for the + + align:start position:0% +somewhere between 3 and and 7 for the + + + align:start position:0% +somewhere between 3 and and 7 for the +dominant pole + + align:start position:0% +dominant pole + + + align:start position:0% +dominant pole +pair what control do we have over these + + align:start position:0% +pair what control do we have over these + + + align:start position:0% +pair what control do we have over these +parameters what kind of changes can we + + align:start position:0% +parameters what kind of changes can we + + + align:start position:0% +parameters what kind of changes can we +make to a system uh in order to modif y + + align:start position:0% +make to a system uh in order to modif y + + + align:start position:0% +make to a system uh in order to modif y +these parameters and at the same time + + align:start position:0% +these parameters and at the same time + + + align:start position:0% +these parameters and at the same time +change crossover frequency and and and + + align:start position:0% +change crossover frequency and and and + + + align:start position:0% +change crossover frequency and and and +so forth well of course again we're very + + align:start position:0% +so forth well of course again we're very + + + align:start position:0% +so forth well of course again we're very +much uh dependent on the precise details + + align:start position:0% +much uh dependent on the precise details + + + align:start position:0% +much uh dependent on the precise details +of the system and I'm I'm sure that as + + align:start position:0% +of the system and I'm I'm sure that as + + + align:start position:0% +of the system and I'm I'm sure that as +we go along we'll see many examples of + + align:start position:0% +we go along we'll see many examples of + + + align:start position:0% +we go along we'll see many examples of +this we'll have a number of + + align:start position:0% +this we'll have a number of + + + align:start position:0% +this we'll have a number of +demonstrations later in the program in + + align:start position:0% +demonstrations later in the program in + + + align:start position:0% +demonstrations later in the program in +in the course and we'll see how the the + + align:start position:0% +in the course and we'll see how the the + + + align:start position:0% +in the course and we'll see how the the +or the constraints that that affect us + + align:start position:0% +or the constraints that that affect us + + + align:start position:0% +or the constraints that that affect us +when we look at actual physical systems + + align:start position:0% +when we look at actual physical systems + + + align:start position:0% +when we look at actual physical systems +but let's uh consider one possible + + align:start position:0% +but let's uh consider one possible + + + align:start position:0% +but let's uh consider one possible +modification a very simple one in + + align:start position:0% +modification a very simple one in + + + align:start position:0% +modification a very simple one in +particular changing the AF or a fnot + + align:start position:0% +particular changing the AF or a fnot + + + align:start position:0% +particular changing the AF or a fnot +product we've already looked at that in + + align:start position:0% +product we've already looked at that in + + + align:start position:0% +product we've already looked at that in +the earlier example today when we did + + align:start position:0% +the earlier example today when we did + + + align:start position:0% +the earlier example today when we did +the Nickels chart construction we found + + align:start position:0% +the Nickels chart construction we found + + + align:start position:0% +the Nickels chart construction we found +out in a very direct way how changes in + + align:start position:0% +out in a very direct way how changes in + + + align:start position:0% +out in a very direct way how changes in +that case in a not affected MP for the + + align:start position:0% +that case in a not affected MP for the + + + align:start position:0% +that case in a not affected MP for the +system what we assumed in doing that + + align:start position:0% +system what we assumed in doing that + + + align:start position:0% +system what we assumed in doing that +construction was that we were able to + + align:start position:0% +construction was that we were able to + + + align:start position:0% +construction was that we were able to +change a KN change the magnitude of the + + align:start position:0% +change a KN change the magnitude of the + + + align:start position:0% +change a KN change the magnitude of the +loop transmission without making any + + align:start position:0% +loop transmission without making any + + + align:start position:0% +loop transmission without making any +change in the angle associated with the + + align:start position:0% +change in the angle associated with the + + + align:start position:0% +change in the angle associated with the +a F product and that is realistic in + + align:start position:0% +a F product and that is realistic in + + + align:start position:0% +a F product and that is realistic in +some cases but not always for example if + + align:start position:0% +some cases but not always for example if + + + align:start position:0% +some cases but not always for example if +we have a Servo mechanism a mechanical + + align:start position:0% +we have a Servo mechanism a mechanical + + + align:start position:0% +we have a Servo mechanism a mechanical +feedback system where + + align:start position:0% +feedback system where + + + align:start position:0% +feedback system where +the frequencies Associated the critical + + align:start position:0% +the frequencies Associated the critical + + + align:start position:0% +the frequencies Associated the critical +frequencies associated with many of the + + align:start position:0% +frequencies associated with many of the + + + align:start position:0% +frequencies associated with many of the +elements in the loop are quite low + + align:start position:0% +elements in the loop are quite low + + + align:start position:0% +elements in the loop are quite low +corresponding to Mechanical frequencies + + align:start position:0% +corresponding to Mechanical frequencies + + + align:start position:0% +corresponding to Mechanical frequencies +a few Hertz in many cases we're + + align:start position:0% +a few Hertz in many cases we're + + + align:start position:0% +a few Hertz in many cases we're +generally able to change the loop + + align:start position:0% +generally able to change the loop + + + align:start position:0% +generally able to change the loop +transmission magnitude it will + + align:start position:0% +transmission magnitude it will + + + align:start position:0% +transmission magnitude it will +electronically if the signal exists in + + align:start position:0% +electronically if the signal exists in + + + align:start position:0% +electronically if the signal exists in +electrical form at some point we can put + + align:start position:0% +electrical form at some point we can put + + + align:start position:0% +electrical form at some point we can put +in an amplify wi that has a bandwidth so + + align:start position:0% +in an amplify wi that has a bandwidth so + + + align:start position:0% +in an amplify wi that has a bandwidth so +far in excess of the mechanical + + align:start position:0% +far in excess of the mechanical + + + align:start position:0% +far in excess of the mechanical +bandwidths that we don't modify we don't + + align:start position:0% +bandwidths that we don't modify we don't + + + align:start position:0% +bandwidths that we don't modify we don't +add any additional poles uh we don't add + + align:start position:0% +add any additional poles uh we don't add + + + align:start position:0% +add any additional poles uh we don't add +any we don't change the phase + + align:start position:0% +any we don't change the phase + + + align:start position:0% +any we don't change the phase +characteristics of loop transmission + + align:start position:0% +characteristics of loop transmission + + + align:start position:0% +characteristics of loop transmission +we're able to Simply modify the + + align:start position:0% +we're able to Simply modify the + + + align:start position:0% +we're able to Simply modify the +magnitude characteristics and we can + + align:start position:0% +magnitude characteristics and we can + + + align:start position:0% +magnitude characteristics and we can +either increase the magnitude or + + align:start position:0% +either increase the magnitude or + + + align:start position:0% +either increase the magnitude or +decrease the magnitude with relatively + + align:start position:0% +decrease the magnitude with relatively + + + align:start position:0% +decrease the magnitude with relatively +little trouble however if we for example + + align:start position:0% +little trouble however if we for example + + + align:start position:0% +little trouble however if we for example +consider an operational amplifier and + + align:start position:0% +consider an operational amplifier and + + + align:start position:0% +consider an operational amplifier and +partic in particular a very fast + + align:start position:0% +partic in particular a very fast + + + align:start position:0% +partic in particular a very fast +operational amplifier maybe an amplifier + + align:start position:0% +operational amplifier maybe an amplifier + + + align:start position:0% +operational amplifier maybe an amplifier +that has 100 mahz Unity gain frequency + + align:start position:0% +that has 100 mahz Unity gain frequency + + + align:start position:0% +that has 100 mahz Unity gain frequency +and such kinds of operational amplifiers + + align:start position:0% +and such kinds of operational amplifiers + + + align:start position:0% +and such kinds of operational amplifiers +exist uh then if we want to increase the + + align:start position:0% +exist uh then if we want to increase the + + + align:start position:0% +exist uh then if we want to increase the +loop transmission magnetude basically we + + align:start position:0% +loop transmission magnetude basically we + + + align:start position:0% +loop transmission magnetude basically we +have to add another stage and that may + + align:start position:0% +have to add another stage and that may + + + align:start position:0% +have to add another stage and that may +be very very difficult to do without + + align:start position:0% +be very very difficult to do without + + + align:start position:0% +be very very difficult to do without +dramatically changing the the nature of + + align:start position:0% +dramatically changing the the nature of + + + align:start position:0% +dramatically changing the the nature of +the phase curve so in that case we have + + align:start position:0% +the phase curve so in that case we have + + + align:start position:0% +the phase curve so in that case we have +relatively less freedom on on the + + align:start position:0% +relatively less freedom on on the + + + align:start position:0% +relatively less freedom on on the +manipulations we're able to do with the + + align:start position:0% +manipulations we're able to do with the + + + align:start position:0% +manipulations we're able to do with the +a f product because changing the a f + + align:start position:0% +a f product because changing the a f + + + align:start position:0% +a f product because changing the a f +product affects something + + align:start position:0% +product affects something + + + align:start position:0% +product affects something +else let's however look at one case + + align:start position:0% +else let's however look at one case + + + align:start position:0% +else let's however look at one case +involving an amplifier an oper + + align:start position:0% +involving an amplifier an oper + + + align:start position:0% +involving an amplifier an oper +operational amplifier where we are able + + align:start position:0% +operational amplifier where we are able + + + align:start position:0% +operational amplifier where we are able +to modify the a fnot product in + + align:start position:0% +to modify the a fnot product in + + + align:start position:0% +to modify the a fnot product in +particular we're able to lower it at + + align:start position:0% +particular we're able to lower it at + + + align:start position:0% +particular we're able to lower it at +least without modifying + + align:start position:0% +least without modifying + + + align:start position:0% +least without modifying +the angle associated with the AF + + align:start position:0% +the angle associated with the AF + + + align:start position:0% +the angle associated with the AF +product and let's look at the + + align:start position:0% +product and let's look at the + + + align:start position:0% +product and let's look at the +configuration that I've shown in + + align:start position:0% +configuration that I've shown in + + + align:start position:0% +configuration that I've shown in +particular we have a non-inverting + + align:start position:0% +particular we have a non-inverting + + + align:start position:0% +particular we have a non-inverting +operational amplifier configuration the + + align:start position:0% +operational amplifier configuration the + + + align:start position:0% +operational amplifier configuration the +input applied to the non-inverting input + + align:start position:0% +input applied to the non-inverting input + + + align:start position:0% +input applied to the non-inverting input +terminal of the operational amplifier + + align:start position:0% +terminal of the operational amplifier + + + align:start position:0% +terminal of the operational amplifier +and then feedback from the output + + align:start position:0% +and then feedback from the output + + + align:start position:0% +and then feedback from the output +through a resistive attenuator + + align:start position:0% +through a resistive attenuator + + + align:start position:0% +through a resistive attenuator +uh to the inverting input terminal of + + align:start position:0% +uh to the inverting input terminal of + + + align:start position:0% +uh to the inverting input terminal of +the amplifier and we've looked at this + + align:start position:0% +the amplifier and we've looked at this + + + align:start position:0% +the amplifier and we've looked at this +case earlier and we found out that + + align:start position:0% +case earlier and we found out that + + + align:start position:0% +case earlier and we found out that +providing we can ignore loading that the + + align:start position:0% +providing we can ignore loading that the + + + align:start position:0% +providing we can ignore loading that the +input of the amplifier applies to the + + align:start position:0% +input of the amplifier applies to the + + + align:start position:0% +input of the amplifier applies to the +feedback Network and loading that the + + align:start position:0% +feedback Network and loading that the + + + align:start position:0% +feedback Network and loading that the +feedback Network applies to the output + + align:start position:0% +feedback Network applies to the output + + + align:start position:0% +feedback Network applies to the output +of the amplifier we get a very nice + + align:start position:0% +of the amplifier we get a very nice + + + align:start position:0% +of the amplifier we get a very nice +physical correspondence between this + + align:start position:0% +physical correspondence between this + + + align:start position:0% +physical correspondence between this +topology and the corresponding block + + align:start position:0% +topology and the corresponding block + + + align:start position:0% +topology and the corresponding block +diagram uh an input we subtract from + + align:start position:0% +diagram uh an input we subtract from + + + align:start position:0% +diagram uh an input we subtract from +that input a fraction of the out output + + align:start position:0% +that input a fraction of the out output + + + align:start position:0% +that input a fraction of the out output +voltage in particular a fraction that's + + align:start position:0% +voltage in particular a fraction that's + + + align:start position:0% +voltage in particular a fraction that's +dependent on the ratio R1 over R1 + R2 + + align:start position:0% +dependent on the ratio R1 over R1 + R2 + + + align:start position:0% +dependent on the ratio R1 over R1 + R2 +simply the attenuation ratio of this + + align:start position:0% +simply the attenuation ratio of this + + + align:start position:0% +simply the attenuation ratio of this +network uh the difference between those + + align:start position:0% +network uh the difference between those + + + align:start position:0% +network uh the difference between those +two voltages the signal right here is + + align:start position:0% +two voltages the signal right here is + + + align:start position:0% +two voltages the signal right here is +the differential signal applied to the + + align:start position:0% +the differential signal applied to the + + + align:start position:0% +the differential signal applied to the +input of the operational amplifier that + + align:start position:0% +input of the operational amplifier that + + + align:start position:0% +input of the operational amplifier that +gets scaled by an amount a of s to + + align:start position:0% +gets scaled by an amount a of s to + + + align:start position:0% +gets scaled by an amount a of s to +generate the output voltage so we get a + + align:start position:0% +generate the output voltage so we get a + + + align:start position:0% +generate the output voltage so we get a +very very nice correspondence between + + align:start position:0% +very very nice correspondence between + + + align:start position:0% +very very nice correspondence between +the physical embodiment and the block + + align:start position:0% +the physical embodiment and the block + + + align:start position:0% +the physical embodiment and the block +diagram + + align:start position:0% +diagram + + + align:start position:0% +diagram +now suppose we build up one of these and + + align:start position:0% +now suppose we build up one of these and + + + align:start position:0% +now suppose we build up one of these and +what we find is that the system is not + + align:start position:0% +what we find is that the system is not + + + align:start position:0% +what we find is that the system is not +acceptably stable we suspect that the + + align:start position:0% +acceptably stable we suspect that the + + + align:start position:0% +acceptably stable we suspect that the +loop transmission magnitude is too large + + align:start position:0% +loop transmission magnitude is too large + + + align:start position:0% +loop transmission magnitude is too large +and we either have either the systems + + align:start position:0% +and we either have either the systems + + + align:start position:0% +and we either have either the systems +absolutely unstable or we have too large + + align:start position:0% +absolutely unstable or we have too large + + + align:start position:0% +absolutely unstable or we have too large +an MP or the damping ratio of the + + align:start position:0% +an MP or the damping ratio of the + + + align:start position:0% +an MP or the damping ratio of the +dominant pole pair is too small or + + align:start position:0% +dominant pole pair is too small or + + + align:start position:0% +dominant pole pair is too small or +somehow we've gotten an indication that + + align:start position:0% +somehow we've gotten an indication that + + + align:start position:0% +somehow we've gotten an indication that +the system is is not acceptably stable + + align:start position:0% +the system is is not acceptably stable + + + align:start position:0% +the system is is not acceptably stable +how can we lower the loop Loop + + align:start position:0% +how can we lower the loop Loop + + + align:start position:0% +how can we lower the loop Loop +transmission magnitude we might believe + + align:start position:0% +transmission magnitude we might believe + + + align:start position:0% +transmission magnitude we might believe +that we have this kind of a picture + + align:start position:0% +that we have this kind of a picture + + + align:start position:0% +that we have this kind of a picture +associated with the loop transmission + + align:start position:0% +associated with the loop transmission + + + align:start position:0% +associated with the loop transmission +again sort of very frequently occurring + + align:start position:0% +again sort of very frequently occurring + + + align:start position:0% +again sort of very frequently occurring +well- behaved one where the magnitude + + align:start position:0% +well- behaved one where the magnitude + + + align:start position:0% +well- behaved one where the magnitude +drops off with increasing frequency the + + align:start position:0% +drops off with increasing frequency the + + + align:start position:0% +drops off with increasing frequency the +angle drops off and in that situation we + + align:start position:0% +angle drops off and in that situation we + + + align:start position:0% +angle drops off and in that situation we +increase phase margin as we lower + + align:start position:0% +increase phase margin as we lower + + + align:start position:0% +increase phase margin as we lower +crossover frequency if we can attenuate + + align:start position:0% +crossover frequency if we can attenuate + + + align:start position:0% +crossover frequency if we can attenuate +the AF product without changing the + + align:start position:0% +the AF product without changing the + + + align:start position:0% +the AF product without changing the +angle characteristics we get increasing + + align:start position:0% +angle characteristics we get increasing + + + align:start position:0% +angle characteristics we get increasing +values of phase margin as we push this + + align:start position:0% +values of phase margin as we push this + + + align:start position:0% +values of phase margin as we push this +curve + + align:start position:0% +curve + + + align:start position:0% +curve +down the difficulty is that there's an + + align:start position:0% +down the difficulty is that there's an + + + align:start position:0% +down the difficulty is that there's an +interdependence between the ideal closed + + align:start position:0% +interdependence between the ideal closed + + + align:start position:0% +interdependence between the ideal closed +loop gain which is simply the reciprocal + + align:start position:0% +loop gain which is simply the reciprocal + + + align:start position:0% +loop gain which is simply the reciprocal +of the + + align:start position:0% +of the + + + align:start position:0% +of the +feedback transfer function uh in + + align:start position:0% +feedback transfer function uh in + + + align:start position:0% +feedback transfer function uh in +particular R1 + R2 over R1 that's the + + align:start position:0% +particular R1 + R2 over R1 that's the + + + align:start position:0% +particular R1 + R2 over R1 that's the +ideal closed loop + + align:start position:0% +ideal closed loop + + + align:start position:0% +ideal closed loop +gain and the loop transmission the + + align:start position:0% +gain and the loop transmission the + + + align:start position:0% +gain and the loop transmission the +negative of the loop transmission for + + align:start position:0% +negative of the loop transmission for + + + align:start position:0% +negative of the loop transmission for +this system is simply a of s * R1 / R1 + + + align:start position:0% +this system is simply a of s * R1 / R1 + + + + align:start position:0% +this system is simply a of s * R1 / R1 + +R2 and uh it seems seems that we we we + + align:start position:0% +R2 and uh it seems seems that we we we + + + align:start position:0% +R2 and uh it seems seems that we we we +have a problem because we have to choose + + align:start position:0% +have a problem because we have to choose + + + align:start position:0% +have a problem because we have to choose +the ratio R1 over R1 + R2 on the basis + + align:start position:0% +the ratio R1 over R1 + R2 on the basis + + + align:start position:0% +the ratio R1 over R1 + R2 on the basis +of the ideal closed loop gain but once + + align:start position:0% +of the ideal closed loop gain but once + + + align:start position:0% +of the ideal closed loop gain but once +we once we make that choice we've pinned + + align:start position:0% +we once we make that choice we've pinned + + + align:start position:0% +we once we make that choice we've pinned +the value of the loop transmission well + + align:start position:0% +the value of the loop transmission well + + + align:start position:0% +the value of the loop transmission well +the way out of this problem or this + + align:start position:0% +the way out of this problem or this + + + align:start position:0% +the way out of this problem or this +interdependence is to add one more + + align:start position:0% +interdependence is to add one more + + + align:start position:0% +interdependence is to add one more +component suppose we put in a resistor + + align:start position:0% +component suppose we put in a resistor + + + align:start position:0% +component suppose we put in a resistor +between the + + align:start position:0% +between the + + + align:start position:0% +between the +inputs + + align:start position:0% + + + + align:start position:0% + +R if we do that that we can remodel the + + align:start position:0% +R if we do that that we can remodel the + + + align:start position:0% +R if we do that that we can remodel the +system as + + align:start position:0% +system as + + + align:start position:0% +system as +follows uh we have our input applied to + + align:start position:0% +follows uh we have our input applied to + + + align:start position:0% +follows uh we have our input applied to +the non-inverting input of the amplifier + + align:start position:0% +the non-inverting input of the amplifier + + + align:start position:0% +the non-inverting input of the amplifier +that corresponds directly we have the + + align:start position:0% +that corresponds directly we have the + + + align:start position:0% +that corresponds directly we have the +resistor R between the non-inverting and + + align:start position:0% +resistor R between the non-inverting and + + + align:start position:0% +resistor R between the non-inverting and +the inverting input terminals let's + + align:start position:0% +the inverting input terminals let's + + + align:start position:0% +the inverting input terminals let's +define the voltage between those two + + align:start position:0% +define the voltage between those two + + + align:start position:0% +define the voltage between those two +terminals as VCB and then I'd like to + + align:start position:0% +terminals as VCB and then I'd like to + + + align:start position:0% +terminals as VCB and then I'd like to +change my representation of the feedback + + align:start position:0% +change my representation of the feedback + + + align:start position:0% +change my representation of the feedback +Network a little bit to make a Fant + + align:start position:0% +Network a little bit to make a Fant + + + align:start position:0% +Network a little bit to make a Fant +equivalent for it and in order to do + + align:start position:0% +equivalent for it and in order to do + + + align:start position:0% +equivalent for it and in order to do +that we get a thant equivalent generator + + align:start position:0% +that we get a thant equivalent generator + + + align:start position:0% +that we get a thant equivalent generator +that's simply a scaled function of the + + align:start position:0% +that's simply a scaled function of the + + + align:start position:0% +that's simply a scaled function of the +output voltage in particular R1 over R1 + + align:start position:0% +output voltage in particular R1 over R1 + + + align:start position:0% +output voltage in particular R1 over R1 +plus R2 * V out let's define that + + align:start position:0% +plus R2 * V out let's define that + + + align:start position:0% +plus R2 * V out let's define that +voltage as + + align:start position:0% +voltage as + + + align:start position:0% +voltage as +VA in parallel or with an output + + align:start position:0% +VA in parallel or with an output + + + align:start position:0% +VA in parallel or with an output +resistance that's the parallel + + align:start position:0% +resistance that's the parallel + + + align:start position:0% +resistance that's the parallel +combination of the r1r2 network so all + + align:start position:0% +combination of the r1r2 network so all + + + align:start position:0% +combination of the r1r2 network so all +I've done is make a theant equivalent + + align:start position:0% +I've done is make a theant equivalent + + + align:start position:0% +I've done is make a theant equivalent +for for this point looking back into the + + align:start position:0% +for for this point looking back into the + + + align:start position:0% +for for this point looking back into the +network at this point when we do that we + + align:start position:0% +network at this point when we do that we + + + align:start position:0% +network at this point when we do that we +see V out scaled by the R1 over R1 Plus + + align:start position:0% +see V out scaled by the R1 over R1 Plus + + + align:start position:0% +see V out scaled by the R1 over R1 Plus +R2 ratio and the th thant equivalent + + align:start position:0% +R2 ratio and the th thant equivalent + + + align:start position:0% +R2 ratio and the th thant equivalent +output resistance of that generator is + + align:start position:0% +output resistance of that generator is + + + align:start position:0% +output resistance of that generator is +R1 in parallel with R2 so we've remodled + + align:start position:0% +R1 in parallel with R2 so we've remodled + + + align:start position:0% +R1 in parallel with R2 so we've remodled +that way once we do that we can get our + + align:start position:0% +that way once we do that we can get our + + + align:start position:0% +that way once we do that we can get our +block diagram quite directly uh what we + + align:start position:0% +block diagram quite directly uh what we + + + align:start position:0% +block diagram quite directly uh what we +find out is that this voltage ve which + + align:start position:0% +find out is that this voltage ve which + + + align:start position:0% +find out is that this voltage ve which +is the voltage we're sort of trying to + + align:start position:0% +is the voltage we're sort of trying to + + + align:start position:0% +is the voltage we're sort of trying to +generate at this point in the block + + align:start position:0% +generate at this point in the block + + + align:start position:0% +generate at this point in the block +diagram uh we can consider the + + align:start position:0% +diagram uh we can consider the + + + align:start position:0% +diagram uh we can consider the +superposition of of two parts uh we get + + align:start position:0% +superposition of of two parts uh we get + + + align:start position:0% +superposition of of two parts uh we get +the contribution that exists or when + + align:start position:0% +the contribution that exists or when + + + align:start position:0% +the contribution that exists or when +this generator is is zero but VI is + + align:start position:0% +this generator is is zero but VI is + + + align:start position:0% +this generator is is zero but VI is +present that's simply VI * R over r + r + + align:start position:0% +present that's simply VI * R over r + r + + + align:start position:0% +present that's simply VI * R over r + r +Prime so that's this path plus we get + + align:start position:0% +Prime so that's this path plus we get + + + align:start position:0% +Prime so that's this path plus we get +the contribution that's present when + + align:start position:0% +the contribution that's present when + + + align:start position:0% +the contribution that's present when +this generator is active but this one is + + align:start position:0% +this generator is active but this one is + + + align:start position:0% +this generator is active but this one is +zero that comes in with a minus sign a + + align:start position:0% +zero that comes in with a minus sign a + + + align:start position:0% +zero that comes in with a minus sign a +positive voltage on this generator gives + + align:start position:0% +positive voltage on this generator gives + + + align:start position:0% +positive voltage on this generator gives +us a negative contribution to ve and the + + align:start position:0% +us a negative contribution to ve and the + + + align:start position:0% +us a negative contribution to ve and the +amount is simply + + align:start position:0% +amount is simply + + + align:start position:0% +amount is simply +VA times again the attenuation ratio R + + align:start position:0% +VA times again the attenuation ratio R + + + align:start position:0% +VA times again the attenuation ratio R +over r + r Prime so this voltage in our + + align:start position:0% +over r + r Prime so this voltage in our + + + align:start position:0% +over r + r Prime so this voltage in our +block diagram would be VA we would scale + + align:start position:0% +block diagram would be VA we would scale + + + align:start position:0% +block diagram would be VA we would scale +VA by an amount R over R plus r Prime + + align:start position:0% +VA by an amount R over R plus r Prime + + + align:start position:0% +VA by an amount R over R plus r Prime +and subtract it from this voltage the + + align:start position:0% +and subtract it from this voltage the + + + align:start position:0% +and subtract it from this voltage the +result would be + + align:start position:0% +result would be + + + align:start position:0% +result would be +ve similarly VA is simply the output + + align:start position:0% +ve similarly VA is simply the output + + + align:start position:0% +ve similarly VA is simply the output +voltage scaled by the ratio R1 over R1 + + + align:start position:0% +voltage scaled by the ratio R1 over R1 + + + + align:start position:0% +voltage scaled by the ratio R1 over R1 + +R2 that's how we Define VA over here so + + align:start position:0% +R2 that's how we Define VA over here so + + + align:start position:0% +R2 that's how we Define VA over here so +we get that corresponding block diagram + + align:start position:0% +we get that corresponding block diagram + + + align:start position:0% +we get that corresponding block diagram +what we're then able to do is do a a + + align:start position:0% +what we're then able to do is do a a + + + align:start position:0% +what we're then able to do is do a a +little bit of block diagram manipulation + + align:start position:0% +little bit of block diagram manipulation + + + align:start position:0% +little bit of block diagram manipulation +and if you remember uh in this + + align:start position:0% +and if you remember uh in this + + + align:start position:0% +and if you remember uh in this +particular situation where we have the + + align:start position:0% +particular situation where we have the + + + align:start position:0% +particular situation where we have the +same factor R over r + r Prime on both + + align:start position:0% +same factor R over r + r Prime on both + + + align:start position:0% +same factor R over r + r Prime on both +inputs to a summing point we're able to + + align:start position:0% +inputs to a summing point we're able to + + + align:start position:0% +inputs to a summing point we're able to +slide that quantity past the summing + + align:start position:0% +slide that quantity past the summing + + + align:start position:0% +slide that quantity past the summing +point when we do that we get rid + + align:start position:0% +point when we do that we get rid + + + align:start position:0% +point when we do that we get rid +of these two + + align:start position:0% + + + + align:start position:0% + +blocks + + align:start position:0% + + + + align:start position:0% + +and we slide that attenuation ratio past + + align:start position:0% +and we slide that attenuation ratio past + + + align:start position:0% +and we slide that attenuation ratio past +the summing point so we gain a block in + + align:start position:0% + + + + align:start position:0% + +here and the block that we gain is + + align:start position:0% +here and the block that we gain is + + + align:start position:0% +here and the block that we gain is +simply the attenuation ratio + + align:start position:0% +simply the attenuation ratio + + + align:start position:0% +simply the attenuation ratio +R over r + r + + align:start position:0% +R over r + r + + + align:start position:0% +R over r + r +Prime now what we see is we've have + + align:start position:0% +Prime now what we see is we've have + + + align:start position:0% +Prime now what we see is we've have +broken the interdependence between ideal + + align:start position:0% +broken the interdependence between ideal + + + align:start position:0% +broken the interdependence between ideal +closed loop gain and loop transmission + + align:start position:0% +closed loop gain and loop transmission + + + align:start position:0% +closed loop gain and loop transmission +magnitude because the ideal closed loop + + align:start position:0% +magnitude because the ideal closed loop + + + align:start position:0% +magnitude because the ideal closed loop +gain for this system assuming large + + align:start position:0% +gain for this system assuming large + + + align:start position:0% +gain for this system assuming large +enough Loop transmission magnitude is + + align:start position:0% +enough Loop transmission magnitude is + + + align:start position:0% +enough Loop transmission magnitude is +simply the reciprocal of the feedback + + align:start position:0% +simply the reciprocal of the feedback + + + align:start position:0% +simply the reciprocal of the feedback +path in particular R1 plus R2 divided by + + align:start position:0% +path in particular R1 plus R2 divided by + + + align:start position:0% +path in particular R1 plus R2 divided by +R1 so we haven't changed the ideal + + align:start position:0% +R1 so we haven't changed the ideal + + + align:start position:0% +R1 so we haven't changed the ideal +closed loop gain however the loop + + align:start position:0% +closed loop gain however the loop + + + align:start position:0% +closed loop gain however the loop +transmission now for this system picks + + align:start position:0% +transmission now for this system picks + + + align:start position:0% +transmission now for this system picks +up an additional term term Let's see we + + align:start position:0% +up an additional term term Let's see we + + + align:start position:0% +up an additional term term Let's see we +have a of s we have R1 / R1 + R2 but we + + align:start position:0% +have a of s we have R1 / R1 + R2 but we + + + align:start position:0% +have a of s we have R1 / R1 + R2 but we +have an additional attenuation Factor R + + align:start position:0% +have an additional attenuation Factor R + + + align:start position:0% +have an additional attenuation Factor R +over r + r + + align:start position:0% +over r + r + + + align:start position:0% +over r + r +Prime and so what we're able to do is + + align:start position:0% +Prime and so what we're able to do is + + + align:start position:0% +Prime and so what we're able to do is +modify the loop transmission magnitude + + align:start position:0% +modify the loop transmission magnitude + + + align:start position:0% +modify the loop transmission magnitude +or at least lower it without making + + align:start position:0% +or at least lower it without making + + + align:start position:0% +or at least lower it without making +corresponding changes in the ideal + + align:start position:0% +corresponding changes in the ideal + + + align:start position:0% +corresponding changes in the ideal +closed loop gain and so if we had a + + align:start position:0% +closed loop gain and so if we had a + + + align:start position:0% +closed loop gain and so if we had a +system where we found that the system + + align:start position:0% +system where we found that the system + + + align:start position:0% +system where we found that the system +was inadequately stable uh this sort of + + align:start position:0% +was inadequately stable uh this sort of + + + align:start position:0% +was inadequately stable uh this sort of +a system for whatever ideal closed loop + + align:start position:0% +a system for whatever ideal closed loop + + + align:start position:0% +a system for whatever ideal closed loop +gain we wanted we'd be able to improve + + align:start position:0% +gain we wanted we'd be able to improve + + + align:start position:0% +gain we wanted we'd be able to improve +the stability by adding this this one + + align:start position:0% +the stability by adding this this one + + + align:start position:0% +the stability by adding this this one +resistor this is actually a fairly + + align:start position:0% +resistor this is actually a fairly + + + align:start position:0% +resistor this is actually a fairly +frequently done what we find out is that + + align:start position:0% +frequently done what we find out is that + + + align:start position:0% +frequently done what we find out is that +there are certain operational amplifiers + + align:start position:0% +there are certain operational amplifiers + + + align:start position:0% +there are certain operational amplifiers +sold for example that are not guaranteed + + align:start position:0% +sold for example that are not guaranteed + + + align:start position:0% +sold for example that are not guaranteed +to be Unity gain stable in other words + + align:start position:0% +to be Unity gain stable in other words + + + align:start position:0% +to be Unity gain stable in other words +if we wrap feedback from the output of + + align:start position:0% +if we wrap feedback from the output of + + + align:start position:0% +if we wrap feedback from the output of +the amplifier back to its input just put + + align:start position:0% +the amplifier back to its input just put + + + align:start position:0% +the amplifier back to its input just put +a wire from the output back to the + + align:start position:0% +a wire from the output back to the + + + align:start position:0% +a wire from the output back to the +inverting input th such amplifiers are + + align:start position:0% +inverting input th such amplifiers are + + + align:start position:0% +inverting input th such amplifiers are +not guaranteed to be stable if they are + + align:start position:0% +not guaranteed to be stable if they are + + + align:start position:0% +not guaranteed to be stable if they are +stable under those conditions sort of we + + align:start position:0% +stable under those conditions sort of we + + + align:start position:0% +stable under those conditions sort of we +speak of them as being Unity gain stable + + align:start position:0% +speak of them as being Unity gain stable + + + align:start position:0% +speak of them as being Unity gain stable +what we really mean is that they're + + align:start position:0% +what we really mean is that they're + + + align:start position:0% +what we really mean is that they're +stable in a loop that has an F equal to + + align:start position:0% +stable in a loop that has an F equal to + + + align:start position:0% +stable in a loop that has an F equal to +one well uh suppose we'd like to take + + align:start position:0% +one well uh suppose we'd like to take + + + align:start position:0% +one well uh suppose we'd like to take +such an amplifier and run it at a closed + + align:start position:0% +such an amplifier and run it at a closed + + + align:start position:0% +such an amplifier and run it at a closed +loop non-inverting gain of two for + + align:start position:0% +loop non-inverting gain of two for + + + align:start position:0% +loop non-inverting gain of two for +example uh but the manufacturer only + + align:start position:0% +example uh but the manufacturer only + + + align:start position:0% +example uh but the manufacturer only +guarantees stability if if f is less + + align:start position:0% +guarantees stability if if f is less + + + align:start position:0% +guarantees stability if if f is less +than 1/5 in other words if we attenuate + + align:start position:0% +than 1/5 in other words if we attenuate + + + align:start position:0% +than 1/5 in other words if we attenuate +the signals fed back by a factor of more + + align:start position:0% +the signals fed back by a factor of more + + + align:start position:0% +the signals fed back by a factor of more +than five uh we can use this sort of of + + align:start position:0% +than five uh we can use this sort of of + + + align:start position:0% +than five uh we can use this sort of of +approach in order to attenuate the + + align:start position:0% +approach in order to attenuate the + + + align:start position:0% +approach in order to attenuate the +feedback the signal fed back to the + + align:start position:0% +feedback the signal fed back to the + + + align:start position:0% +feedback the signal fed back to the +amplifier lower the loop transmission + + align:start position:0% +amplifier lower the loop transmission + + + align:start position:0% +amplifier lower the loop transmission +magnitude so that the amplifier + + align:start position:0% +magnitude so that the amplifier + + + align:start position:0% +magnitude so that the amplifier +configuration becomes stable say there + + align:start position:0% +configuration becomes stable say there + + + align:start position:0% +configuration becomes stable say there +are commercially available amplifiers + + align:start position:0% +are commercially available amplifiers + + + align:start position:0% +are commercially available amplifiers +that are are intended to run that way + + align:start position:0% +that are are intended to run that way + + + align:start position:0% +that are are intended to run that way +you gain certain advantages in the + + align:start position:0% +you gain certain advantages in the + + + align:start position:0% +you gain certain advantages in the +design of the amplifier if you design it + + align:start position:0% +design of the amplifier if you design it + + + align:start position:0% +design of the amplifier if you design it +other than than + + align:start position:0% +other than than + + + align:start position:0% +other than than +for stability with direct feedback and + + align:start position:0% +for stability with direct feedback and + + + align:start position:0% +for stability with direct feedback and +when that happens if you want to run the + + align:start position:0% +when that happens if you want to run the + + + align:start position:0% +when that happens if you want to run the +amplifier Lo closed loop gains this sort + + align:start position:0% +amplifier Lo closed loop gains this sort + + + align:start position:0% +amplifier Lo closed loop gains this sort +of approach allows you to maintain + + align:start position:0% + + + + align:start position:0% + +stability the modification of of the + + align:start position:0% +stability the modification of of the + + + align:start position:0% +stability the modification of of the +loop transmission magnitude uh assumed + + align:start position:0% +loop transmission magnitude uh assumed + + + align:start position:0% +loop transmission magnitude uh assumed +to be done without changing the angle + + align:start position:0% +to be done without changing the angle + + + align:start position:0% +to be done without changing the angle +associated with the AF product is only + + align:start position:0% +associated with the AF product is only + + + align:start position:0% +associated with the AF product is only +one of the ways we can modify a system + + align:start position:0% +one of the ways we can modify a system + + + align:start position:0% +one of the ways we can modify a system +in order to compensate it in order to + + align:start position:0% +in order to compensate it in order to + + + align:start position:0% +in order to compensate it in order to +hopefully improve its performance next + + align:start position:0% +hopefully improve its performance next + + + align:start position:0% +hopefully improve its performance next +time we'll look at several other options + + align:start position:0% +time we'll look at several other options + + + align:start position:0% +time we'll look at several other options +for improving the performance of + + align:start position:0% +for improving the performance of + + + align:start position:0% +for improving the performance of +feedback systems or compensating such + + align:start position:0% +feedback systems or compensating such + + + align:start position:0% +feedback systems or compensating such +systems + + align:start position:0% +systems + + + align:start position:0% +systems +thank + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/alnDYYwAs74.txt b/alnDYYwAs74.txt new file mode 100644 index 0000000000000000000000000000000000000000..2ebd36dcd5036ddaa02405fe8712526f000b363c --- /dev/null +++ b/alnDYYwAs74.txt @@ -0,0 +1,1723 @@ +align:start position:0% + +I think collectively I did not hear like + + align:start position:0% +I think collectively I did not hear like + + + align:start position:0% +I think collectively I did not hear like +they're not here the full-fledged + + align:start position:0% +they're not here the full-fledged + + + align:start position:0% +they're not here the full-fledged +justification of the cautionary + + align:start position:0% +justification of the cautionary + + + align:start position:0% +justification of the cautionary +principle and I think that focusing on + + align:start position:0% +principle and I think that focusing on + + + align:start position:0% +principle and I think that focusing on +the fact that its application would be + + align:start position:0% +the fact that its application would be + + + align:start position:0% +the fact that its application would be +the greatest good for the greatest + + align:start position:0% +the greatest good for the greatest + + + align:start position:0% +the greatest good for the greatest +number of people is probably a + + align:start position:0% +number of people is probably a + + + align:start position:0% +number of people is probably a +manifestly wrong because I think there + + align:start position:0% +manifestly wrong because I think there + + + align:start position:0% +manifestly wrong because I think there +plenty of instances where being + + align:start position:0% +plenty of instances where being + + + align:start position:0% +plenty of instances where being +precautionary means that you you look + + align:start position:0% +precautionary means that you you look + + + align:start position:0% +precautionary means that you you look +out for subgroups or sub effects which + + align:start position:0% +out for subgroups or sub effects which + + + align:start position:0% +out for subgroups or sub effects which +in fact are very unlikely in a world of + + align:start position:0% +in fact are very unlikely in a world of + + + align:start position:0% +in fact are very unlikely in a world of +certainty one can argue the utilitarian + + align:start position:0% +certainty one can argue the utilitarian + + + align:start position:0% +certainty one can argue the utilitarian +ethics applies it is you up if you ban a + + align:start position:0% +ethics applies it is you up if you ban a + + + align:start position:0% +ethics applies it is you up if you ban a +chemical you're going to have a certain + + align:start position:0% +chemical you're going to have a certain + + + align:start position:0% +chemical you're going to have a certain +cost then you're going to have a certain + + align:start position:0% +cost then you're going to have a certain + + + align:start position:0% +cost then you're going to have a certain +benefit as soon as the cost becomes + + align:start position:0% +benefit as soon as the cost becomes + + + align:start position:0% +benefit as soon as the cost becomes +uncertain or the benefit becomes + + align:start position:0% +uncertain or the benefit becomes + + + align:start position:0% +uncertain or the benefit becomes +uncertain which is related to risk + + align:start position:0% +uncertain which is related to risk + + + align:start position:0% +uncertain which is related to risk +necessity because the benefit of + + align:start position:0% +necessity because the benefit of + + + align:start position:0% +necessity because the benefit of +controlling the chemical is derived from + + align:start position:0% +controlling the chemical is derived from + + + align:start position:0% +controlling the chemical is derived from +doing some sort of risk assessment we + + align:start position:0% +doing some sort of risk assessment we + + + align:start position:0% +doing some sort of risk assessment we +has high uncertainty service but it's + + align:start position:0% +has high uncertainty service but it's + + + align:start position:0% +has high uncertainty service but it's +not the only thing that is in + + align:start position:0% +not the only thing that is in + + + align:start position:0% +not the only thing that is in +certainties costs have uncertainties too + + align:start position:0% +certainties costs have uncertainties too + + + align:start position:0% +certainties costs have uncertainties too +so as soon as you depart from a well + + align:start position:0% +so as soon as you depart from a well + + + align:start position:0% +so as soon as you depart from a well +defined benefit and a well defined cost + + align:start position:0% +defined benefit and a well defined cost + + + align:start position:0% +defined benefit and a well defined cost +utilitarian ethics is no longer + + align:start position:0% +utilitarian ethics is no longer + + + align:start position:0% +utilitarian ethics is no longer +important because what's important is + + align:start position:0% +important because what's important is + + + align:start position:0% +important because what's important is +what how you value the mistakes that you + + align:start position:0% +what how you value the mistakes that you + + + align:start position:0% +what how you value the mistakes that you +could make a type 1 error comes when you + + align:start position:0% +could make a type 1 error comes when you + + + align:start position:0% +could make a type 1 error comes when you +fail to regulate something and it later + + align:start position:0% +fail to regulate something and it later + + + align:start position:0% +fail to regulate something and it later +turns up to be worse than you thought or + + align:start position:0% +turns up to be worse than you thought or + + + align:start position:0% +turns up to be worse than you thought or +at the tails of the distribution and + + align:start position:0% +at the tails of the distribution and + + + align:start position:0% +at the tails of the distribution and +what you're thinking a type 2 error is + + align:start position:0% +what you're thinking a type 2 error is + + + align:start position:0% +what you're thinking a type 2 error is +where you regulate and things turn out + + align:start position:0% +where you regulate and things turn out + + + align:start position:0% +where you regulate and things turn out +to be not as bad as you thought and + + align:start position:0% +to be not as bad as you thought and + + + align:start position:0% +to be not as bad as you thought and +impose a higher cost upon but there's a + + align:start position:0% +impose a higher cost upon but there's a + + + align:start position:0% +impose a higher cost upon but there's a +type 3 error which is you're working in + + align:start position:0% +type 3 error which is you're working in + + + align:start position:0% +type 3 error which is you're working in +the world + + align:start position:0% +the world + + + align:start position:0% +the world +and I think that's what you already + + align:start position:0% +and I think that's what you already + + + align:start position:0% +and I think that's what you already +missed the point is that when you + + align:start position:0% +missed the point is that when you + + + align:start position:0% +missed the point is that when you +abandon chemical you don't just that + + align:start position:0% +abandon chemical you don't just that + + + align:start position:0% +abandon chemical you don't just that +isn't all that happens what happens is + + align:start position:0% +isn't all that happens what happens is + + + align:start position:0% +isn't all that happens what happens is +you you end up coming face-to-face with + + align:start position:0% +you you end up coming face-to-face with + + + align:start position:0% +you you end up coming face-to-face with +a substitute with an alternative + + align:start position:0% +a substitute with an alternative + + + align:start position:0% +a substitute with an alternative +technology with alternative ways to meet + + align:start position:0% +technology with alternative ways to meet + + + align:start position:0% +technology with alternative ways to meet +the public needs and so a straight + + align:start position:0% +the public needs and so a straight + + + align:start position:0% +the public needs and so a straight +cost-benefit analysis even with + + align:start position:0% +cost-benefit analysis even with + + + align:start position:0% +cost-benefit analysis even with +uncertainty unless it includes the + + align:start position:0% +uncertainty unless it includes the + + + align:start position:0% +uncertainty unless it includes the +alternatives that you have is not a + + align:start position:0% +alternatives that you have is not a + + + align:start position:0% +alternatives that you have is not a +complete analysis and you can make + + align:start position:0% +complete analysis and you can make + + + align:start position:0% +complete analysis and you can make +anything look good depending upon how + + align:start position:0% +anything look good depending upon how + + + align:start position:0% +anything look good depending upon how +you value your life or value the + + align:start position:0% +you value your life or value the + + + align:start position:0% +you value your life or value the +environment and so the precautionary + + align:start position:0% +environment and so the precautionary + + + align:start position:0% +environment and so the precautionary +principle even properly which is which + + align:start position:0% +principle even properly which is which + + + align:start position:0% +principle even properly which is which +applies when you have great + + align:start position:0% +applies when you have great + + + align:start position:0% +applies when you have great +uncertainties ask ask the question what + + align:start position:0% +uncertainties ask ask the question what + + + align:start position:0% +uncertainties ask ask the question what +are the alternatives to the action that + + align:start position:0% +are the alternatives to the action that + + + align:start position:0% +are the alternatives to the action that +you've decided to promote and you know + + align:start position:0% +you've decided to promote and you know + + + align:start position:0% +you've decided to promote and you know +their alternatives are there substitutes + + align:start position:0% +their alternatives are there substitutes + + + align:start position:0% +their alternatives are there substitutes +I'll give you one more one more common + + align:start position:0% +I'll give you one more one more common + + + align:start position:0% +I'll give you one more one more common +in that I know the work of Cass Sunstein + + align:start position:0% +in that I know the work of Cass Sunstein + + + align:start position:0% +in that I know the work of Cass Sunstein +well you know I graduated from moines + + align:start position:0% +well you know I graduated from moines + + + align:start position:0% +well you know I graduated from moines +same law school I think he is a poor + + align:start position:0% +same law school I think he is a poor + + + align:start position:0% +same law school I think he is a poor +scholar because I think he doesn't + + align:start position:0% +scholar because I think he doesn't + + + align:start position:0% +scholar because I think he doesn't +understand + + align:start position:0% +understand + + + align:start position:0% +understand +you heard it here really understand what + + align:start position:0% +you heard it here really understand what + + + align:start position:0% +you heard it here really understand what +this whole issue is about there's never + + align:start position:0% +this whole issue is about there's never + + + align:start position:0% +this whole issue is about there's never +that's never really understood it for + + align:start position:0% +that's never really understood it for + + + align:start position:0% +that's never really understood it for +example I mean people say well suppose + + align:start position:0% +example I mean people say well suppose + + + align:start position:0% +example I mean people say well suppose +you bought you you regulate my own + + align:start position:0% +you bought you you regulate my own + + + align:start position:0% +you bought you you regulate my own +chloride you put worker controls on + + align:start position:0% +chloride you put worker controls on + + + align:start position:0% +chloride you put worker controls on +vinyl chloride and the workers now are a + + align:start position:0% +vinyl chloride and the workers now are a + + + align:start position:0% +vinyl chloride and the workers now are a +smaller salary because the vinyl + + align:start position:0% +smaller salary because the vinyl + + + align:start position:0% +smaller salary because the vinyl +chloride leaves you can't afford to pay + + align:start position:0% +chloride leaves you can't afford to pay + + + align:start position:0% +chloride leaves you can't afford to pay +them so what do they do they quit their + + align:start position:0% +them so what do they do they quit their + + + align:start position:0% +them so what do they do they quit their +health clubs they buy less lean damn + + align:start position:0% +health clubs they buy less lean damn + + + align:start position:0% +health clubs they buy less lean damn +burger and the health impact is argued + + align:start position:0% +burger and the health impact is argued + + + align:start position:0% +burger and the health impact is argued +by keep my son state is worse than if + + align:start position:0% +by keep my son state is worse than if + + + align:start position:0% +by keep my son state is worse than if +you regulated the hazard because you + + align:start position:0% +you regulated the hazard because you + + + align:start position:0% +you regulated the hazard because you +made the workers poor and they eat fatty + + align:start position:0% +made the workers poor and they eat fatty + + + align:start position:0% +made the workers poor and they eat fatty +hamburger and don't exercise but that + + align:start position:0% +hamburger and don't exercise but that + + + align:start position:0% +hamburger and don't exercise but that +doesn't take into account the fact that + + align:start position:0% +doesn't take into account the fact that + + + align:start position:0% +doesn't take into account the fact that +when you regulate vinyl chloride what + + align:start position:0% +when you regulate vinyl chloride what + + + align:start position:0% +when you regulate vinyl chloride what +replaces it let's say is polyethylene so + + align:start position:0% +replaces it let's say is polyethylene so + + + align:start position:0% +replaces it let's say is polyethylene so +those industries increase production + + align:start position:0% +those industries increase production + + + align:start position:0% +those industries increase production +increase the wages of their workers who + + align:start position:0% +increase the wages of their workers who + + + align:start position:0% +increase the wages of their workers who +don't join enough clubs and neatly in a + + align:start position:0% +don't join enough clubs and neatly in a + + + align:start position:0% +don't join enough clubs and neatly in a +burger know if you're really going to + + align:start position:0% +burger know if you're really going to + + + align:start position:0% +burger know if you're really going to +take this capitalist to the extreme you + + align:start position:0% +take this capitalist to the extreme you + + + align:start position:0% +take this capitalist to the extreme you +can see how ridiculous it is + + align:start position:0% +can see how ridiculous it is + + + align:start position:0% +can see how ridiculous it is +because you you can't really determine + + align:start position:0% +because you you can't really determine + + + align:start position:0% +because you you can't really determine +but what you can determine what + + align:start position:0% +but what you can determine what + + + align:start position:0% +but what you can determine what +regulation is shows when it's stringent + + align:start position:0% +regulation is shows when it's stringent + + + align:start position:0% +regulation is shows when it's stringent +we don't make marginal changes in + + align:start position:0% +we don't make marginal changes in + + + align:start position:0% +we don't make marginal changes in +production you make serious shifts in + + align:start position:0% +production you make serious shifts in + + + align:start position:0% +production you make serious shifts in +the nature of industrial policy and you + + align:start position:0% +the nature of industrial policy and you + + + align:start position:0% +the nature of industrial policy and you +shift to non chemical affinities for + + align:start position:0% +shift to non chemical affinities for + + + align:start position:0% +shift to non chemical affinities for +example the banning of CFCs didn't just + + align:start position:0% +example the banning of CFCs didn't just + + + align:start position:0% +example the banning of CFCs didn't just +supply one inhale it which was slightly + + align:start position:0% +supply one inhale it which was slightly + + + align:start position:0% +supply one inhale it which was slightly +better the people started to use + + align:start position:0% +better the people started to use + + + align:start position:0% +better the people started to use +pumpkins do some less product then + + align:start position:0% +pumpkins do some less product then + + + align:start position:0% +pumpkins do some less product then +that's too bad for the producer but you + + align:start position:0% +that's too bad for the producer but you + + + align:start position:0% +that's too bad for the producer but you +don't need an inhaler to deliver the + + align:start position:0% +don't need an inhaler to deliver the + + + align:start position:0% +don't need an inhaler to deliver the +ultimate are those things so what it is + + align:start position:0% +ultimate are those things so what it is + + + align:start position:0% +ultimate are those things so what it is +narrowly defined you work on the wrong + + align:start position:0% +narrowly defined you work on the wrong + + + align:start position:0% +narrowly defined you work on the wrong +problem and you ignore how you feel + + align:start position:0% +problem and you ignore how you feel + + + align:start position:0% +problem and you ignore how you feel +about air of voyages that's + + align:start position:0% + + + + align:start position:0% + +like be like the article said I'm going + + align:start position:0% +like be like the article said I'm going + + + align:start position:0% +like be like the article said I'm going +with that action you know they take the + + align:start position:0% +with that action you know they take the + + + align:start position:0% +with that action you know they take the +global one in the situation you know + + align:start position:0% +global one in the situation you know + + + align:start position:0% +global one in the situation you know +this middle ground I think is a fiction + + align:start position:0% +this middle ground I think is a fiction + + + align:start position:0% +this middle ground I think is a fiction +we either have to regard the probability + + align:start position:0% +we either have to regard the probability + + + align:start position:0% +we either have to regard the probability +of serious global index as as within the + + align:start position:0% +of serious global index as as within the + + + align:start position:0% +of serious global index as as within the +realm of possibility or you don't + + align:start position:0% +realm of possibility or you don't + + + align:start position:0% +realm of possibility or you don't +and and you even people who don't aren't + + align:start position:0% +and and you even people who don't aren't + + + align:start position:0% +and and you even people who don't aren't +certain about the science but you ask + + align:start position:0% +certain about the science but you ask + + + align:start position:0% +certain about the science but you ask +them the question should we plan for + + align:start position:0% +them the question should we plan for + + + align:start position:0% +them the question should we plan for +rising sea level should we plan for + + align:start position:0% +rising sea level should we plan for + + + align:start position:0% +rising sea level should we plan for +floods and drafts would be a bad thing + + align:start position:0% +floods and drafts would be a bad thing + + + align:start position:0% +floods and drafts would be a bad thing +to do and the answer in there becomes no + + align:start position:0% +to do and the answer in there becomes no + + + align:start position:0% +to do and the answer in there becomes no +it should be a good thing to do and if + + align:start position:0% +it should be a good thing to do and if + + + align:start position:0% +it should be a good thing to do and if +you have if you act in a timely fashion + + align:start position:0% +you have if you act in a timely fashion + + + align:start position:0% +you have if you act in a timely fashion +even if you try out to be wrong you have + + align:start position:0% +even if you try out to be wrong you have + + + align:start position:0% +even if you try out to be wrong you have +imagine what would happen if you turned + + align:start position:0% +imagine what would happen if you turned + + + align:start position:0% +imagine what would happen if you turned +out to be right but you're not to have + + align:start position:0% +out to be right but you're not to have + + + align:start position:0% +out to be right but you're not to have +the coastal cities disappear in + + align:start position:0% +the coastal cities disappear in + + + align:start position:0% +the coastal cities disappear in +Indonesia I think the + + align:start position:0% +Indonesia I think the + + + align:start position:0% +Indonesia I think the +Prussian principle has been criticized + + align:start position:0% +Prussian principle has been criticized + + + align:start position:0% +Prussian principle has been criticized +by people who have an economic horse dog + + align:start position:0% +by people who have an economic horse dog + + + align:start position:0% +by people who have an economic horse dog +in that fight that it's too expensive + + align:start position:0% +in that fight that it's too expensive + + + align:start position:0% +in that fight that it's too expensive +and their particular industry will + + align:start position:0% +and their particular industry will + + + align:start position:0% +and their particular industry will +disappear but the alternative is they + + align:start position:0% +disappear but the alternative is they + + + align:start position:0% +disappear but the alternative is they +have generally other people bear the + + align:start position:0% +have generally other people bear the + + + align:start position:0% +have generally other people bear the +cost + + align:start position:0% +cost + + + align:start position:0% +cost +so who bears the cost and who eats the + + align:start position:0% +so who bears the cost and who eats the + + + align:start position:0% +so who bears the cost and who eats the +benefit of the decided policy is very + + align:start position:0% +benefit of the decided policy is very + + + align:start position:0% +benefit of the decided policy is very +important and the distributional effects + + align:start position:0% +important and the distributional effects + + + align:start position:0% +important and the distributional effects +of going one way or the other are really + + align:start position:0% +of going one way or the other are really + + + align:start position:0% +of going one way or the other are really +serious I mean if you decide to put a + + align:start position:0% +serious I mean if you decide to put a + + + align:start position:0% +serious I mean if you decide to put a +carbon tax on oil let me tell you the + + align:start position:0% +carbon tax on oil let me tell you the + + + align:start position:0% +carbon tax on oil let me tell you the +petroleum industry will survive + + align:start position:0% +petroleum industry will survive + + + align:start position:0% +petroleum industry will survive +petroleum industry if you don't put a + + align:start position:0% +petroleum industry if you don't put a + + + align:start position:0% +petroleum industry if you don't put a +carbon tax on the form it's not clear + + align:start position:0% +carbon tax on the form it's not clear + + + align:start position:0% +carbon tax on the form it's not clear +that the planet will survive so you have + + align:start position:0% +that the planet will survive so you have + + + align:start position:0% +that the planet will survive so you have +to ask whose ox is being gored how + + align:start position:0% +to ask whose ox is being gored how + + + align:start position:0% +to ask whose ox is being gored how +certain are we that you are producing an + + align:start position:0% +certain are we that you are producing an + + + align:start position:0% +certain are we that you are producing an +irreducible effect on these people and + + align:start position:0% +irreducible effect on these people and + + + align:start position:0% +irreducible effect on these people and +do you want to keep your options open so + + align:start position:0% +do you want to keep your options open so + + + align:start position:0% +do you want to keep your options open so +I reject the fact that what you're + + align:start position:0% +I reject the fact that what you're + + + align:start position:0% +I reject the fact that what you're +trying to do + + align:start position:0% +trying to do + + + align:start position:0% +trying to do +find a middle ground I finally but I + + align:start position:0% +find a middle ground I finally but I + + + align:start position:0% +find a middle ground I finally but I +want to turn the dials over the last + + align:start position:0% +want to turn the dials over the last + + + align:start position:0% +want to turn the dials over the last +note one more tick beyond what and + + align:start position:0% +note one more tick beyond what and + + + align:start position:0% +note one more tick beyond what and +they've just said I believe that take + + align:start position:0% +they've just said I believe that take + + + align:start position:0% +they've just said I believe that take +the climate change example that if you + + align:start position:0% +the climate change example that if you + + + align:start position:0% +the climate change example that if you +say let's take this seriously because it + + align:start position:0% +say let's take this seriously because it + + + align:start position:0% +say let's take this seriously because it +might happen that a whole series of + + align:start position:0% +might happen that a whole series of + + + align:start position:0% +might happen that a whole series of +second and third-order decisions can get + + align:start position:0% +second and third-order decisions can get + + + align:start position:0% +second and third-order decisions can get +made then in fact wouldn't get made + + align:start position:0% +made then in fact wouldn't get made + + + align:start position:0% +made then in fact wouldn't get made +otherwise it's related to the point + + align:start position:0% +otherwise it's related to the point + + + align:start position:0% +otherwise it's related to the point +you're making first and that that would + + align:start position:0% +you're making first and that that would + + + align:start position:0% +you're making first and that that would +create all kinds of benefits because + + align:start position:0% +create all kinds of benefits because + + + align:start position:0% +create all kinds of benefits because +people don't do it and create this + + align:start position:0% +people don't do it and create this + + + align:start position:0% +people don't do it and create this +benefits they'll do it to create + + align:start position:0% +benefits they'll do it to create + + + align:start position:0% +benefits they'll do it to create +benefits but they never would have + + align:start position:0% +benefits but they never would have + + + align:start position:0% +benefits but they never would have +searched they never would have tried the + + align:start position:0% +searched they never would have tried the + + + align:start position:0% +searched they never would have tried the +never would have looked there so when we + + align:start position:0% +never would have looked there so when we + + + align:start position:0% +never would have looked there so when we +talk to communities are taking various + + align:start position:0% +talk to communities are taking various + + + align:start position:0% +talk to communities are taking various +moves to manage potential climate risks + + align:start position:0% +moves to manage potential climate risks + + + align:start position:0% +moves to manage potential climate risks +we say and once you do it in a way that + + align:start position:0% +we say and once you do it in a way that + + + align:start position:0% +we say and once you do it in a way that +creates all kinds of other second and + + align:start position:0% +creates all kinds of other second and + + + align:start position:0% +creates all kinds of other second and +third-order benefits now instead of just + + align:start position:0% +third-order benefits now instead of just + + + align:start position:0% +third-order benefits now instead of just +looking at what the costs are and + + align:start position:0% +looking at what the costs are and + + + align:start position:0% +looking at what the costs are and +arguing it the long term benefits + + align:start position:0% +arguing it the long term benefits + + + align:start position:0% +arguing it the long term benefits +outweigh the short term costs my + + align:start position:0% +outweigh the short term costs my + + + align:start position:0% +outweigh the short term costs my +argument is once you try to do something + + align:start position:0% +argument is once you try to do something + + + align:start position:0% +argument is once you try to do something +that deals with those risks and creates + + align:start position:0% +that deals with those risks and creates + + + align:start position:0% +that deals with those risks and creates +all kinds of short-term benefits and + + align:start position:0% +all kinds of short-term benefits and + + + align:start position:0% +all kinds of short-term benefits and +that becomes a design consideration in + + align:start position:0% +that becomes a design consideration in + + + align:start position:0% +that becomes a design consideration in +formulating the policy and if you can't + + align:start position:0% +formulating the policy and if you can't + + + align:start position:0% +formulating the policy and if you can't +do it you can't do it but I would argue + + align:start position:0% +do it you can't do it but I would argue + + + align:start position:0% +do it you can't do it but I would argue +that the problem with the precautionary + + align:start position:0% +that the problem with the precautionary + + + align:start position:0% +that the problem with the precautionary +principle is it doesn't four it doesn't + + align:start position:0% +principle is it doesn't four it doesn't + + + align:start position:0% +principle is it doesn't four it doesn't +link to and let's look at ways of using + + align:start position:0% +link to and let's look at ways of using + + + align:start position:0% +link to and let's look at ways of using +this period that we're not going to do + + align:start position:0% +this period that we're not going to do + + + align:start position:0% +this period that we're not going to do +something that I told you the story + + align:start position:0% +something that I told you the story + + + align:start position:0% +something that I told you the story +about the central Arctic and the + + align:start position:0% +about the central Arctic and the + + + align:start position:0% +about the central Arctic and the +Fisheries question you can use a period + + align:start position:0% +Fisheries question you can use a period + + + align:start position:0% +Fisheries question you can use a period +of time to do more scientific + + align:start position:0% +of time to do more scientific + + + align:start position:0% +of time to do more scientific +investigation that might in fact lead us + + align:start position:0% +investigation that might in fact lead us + + + align:start position:0% +investigation that might in fact lead us +to understand better ways of using those + + align:start position:0% +to understand better ways of using those + + + align:start position:0% +to understand better ways of using those +resources to suppose - oh my god we're + + align:start position:0% +resources to suppose - oh my god we're + + + align:start position:0% +resources to suppose - oh my god we're +scared a bad thing could happen they + + align:start position:0% +scared a bad thing could happen they + + + align:start position:0% +scared a bad thing could happen they +might only be a 1% chance but oh my god + + align:start position:0% +might only be a 1% chance but oh my god + + + align:start position:0% +might only be a 1% chance but oh my god +if it happens horrible horrible things + + align:start position:0% +if it happens horrible horrible things + + + align:start position:0% +if it happens horrible horrible things +will affect us in the future + + align:start position:0% +will affect us in the future + + + align:start position:0% +will affect us in the future +so let's not do it yeah but the + + align:start position:0% +so let's not do it yeah but the + + + align:start position:0% +so let's not do it yeah but the +principle has been linked to + + align:start position:0% +principle has been linked to + + + align:start position:0% +principle has been linked to +alternatives analysis now nobody doesn't + + align:start position:0% +alternatives analysis now nobody doesn't + + + align:start position:0% +alternatives analysis now nobody doesn't +ask what our killer is and by the way + + align:start position:0% +ask what our killer is and by the way + + + align:start position:0% +ask what our killer is and by the way +big failure Bush and Cheney decided + + align:start position:0% +big failure Bush and Cheney decided + + + align:start position:0% +big failure Bush and Cheney decided +we're going to get Saddam before you get + + align:start position:0% +we're going to get Saddam before you get + + + align:start position:0% +we're going to get Saddam before you get +us he was operating under precautionary + + align:start position:0% +us he was operating under precautionary + + + align:start position:0% +us he was operating under precautionary +principle look what the application of + + align:start position:0% +principle look what the application of + + + align:start position:0% +principle look what the application of +that requirement + + align:start position:0% +that requirement + + + align:start position:0% +that requirement +brought us but if you if you only say + + align:start position:0% +brought us but if you if you only say + + + align:start position:0% +brought us but if you if you only say +let's look at alternatives that's not + + align:start position:0% +let's look at alternatives that's not + + + align:start position:0% +let's look at alternatives that's not +the same as let's search for alternative + + align:start position:0% +the same as let's search for alternative + + + align:start position:0% +the same as let's search for alternative +right that both reduce the risk and + + align:start position:0% +right that both reduce the risk and + + + align:start position:0% +right that both reduce the risk and +creative writing social term and let's + + align:start position:0% +creative writing social term and let's + + + align:start position:0% +creative writing social term and let's +be clear about trying to distribute the + + align:start position:0% +be clear about trying to distribute the + + + align:start position:0% +be clear about trying to distribute the +benefits of those alternatives and it + + align:start position:0% +benefits of those alternatives and it + + + align:start position:0% +benefits of those alternatives and it +progresses way you could add that too + + align:start position:0% +progresses way you could add that too + + + align:start position:0% +progresses way you could add that too +right anyway \ No newline at end of file diff --git a/ayIgWaBE0aw.txt b/ayIgWaBE0aw.txt new file mode 100644 index 0000000000000000000000000000000000000000..7c5a8c83f0715a2240da28748fb384d94ef4b566 --- /dev/null +++ b/ayIgWaBE0aw.txt @@ -0,0 +1,971 @@ +align:start position:0% + +so we're going to return to our + + align:start position:0% +so we're going to return to our + + + align:start position:0% +so we're going to return to our +one-dimensional elastic collision with + + align:start position:0% +one-dimensional elastic collision with + + + align:start position:0% +one-dimensional elastic collision with +no external forces so we have object one + + align:start position:0% +no external forces so we have object one + + + align:start position:0% +no external forces so we have object one +moving with velocity V one initial and + + align:start position:0% +moving with velocity V one initial and + + + align:start position:0% +moving with velocity V one initial and +object to maybe it's moving this way + + align:start position:0% +object to maybe it's moving this way + + + align:start position:0% +object to maybe it's moving this way +with the two initial I hat again on a + + align:start position:0% +with the two initial I hat again on a + + + align:start position:0% +with the two initial I hat again on a +frictionless surface and we'll call that + + align:start position:0% +frictionless surface and we'll call that + + + align:start position:0% +frictionless surface and we'll call that +our initial state and here you can + + align:start position:0% +our initial state and here you can + + + align:start position:0% +our initial state and here you can +imagine we're going to use a ground + + align:start position:0% +imagine we're going to use a ground + + + align:start position:0% +imagine we're going to use a ground +reference frame so both objects are + + align:start position:0% +reference frame so both objects are + + + align:start position:0% +reference frame so both objects are +moving and our final state has object + + align:start position:0% +moving and our final state has object + + + align:start position:0% +moving and our final state has object +one well we don't know again which way + + align:start position:0% +one well we don't know again which way + + + align:start position:0% +one well we don't know again which way +it's going we can just say it bounced + + align:start position:0% +it's going we can just say it bounced + + + align:start position:0% +it's going we can just say it bounced +back and object two also bounced back + + align:start position:0% +back and object two also bounced back + + + align:start position:0% +back and object two also bounced back +but the goal of our problem of course is + + align:start position:0% +but the goal of our problem of course is + + + align:start position:0% +but the goal of our problem of course is +to determine these vectors and by + + align:start position:0% +to determine these vectors and by + + + align:start position:0% +to determine these vectors and by +knowing the vectors we know which way + + align:start position:0% +knowing the vectors we know which way + + + align:start position:0% +knowing the vectors we know which way +they go now because energy and momentum + + align:start position:0% +they go now because energy and momentum + + + align:start position:0% +they go now because energy and momentum +are constant let's write down our two + + align:start position:0% +are constant let's write down our two + + + align:start position:0% +are constant let's write down our two +equations and I'm going to write them + + align:start position:0% +equations and I'm going to write them + + + align:start position:0% +equations and I'm going to write them +down again in terms of components so we + + align:start position:0% +down again in terms of components so we + + + align:start position:0% +down again in terms of components so we +have one-half m1 v1 X initial squared + + align:start position:0% +have one-half m1 v1 X initial squared + + + align:start position:0% +have one-half m1 v1 X initial squared +plus one-half m2 v2 X initial squared + + align:start position:0% +plus one-half m2 v2 X initial squared + + + align:start position:0% +plus one-half m2 v2 X initial squared +equals one-half m1 v1 X final squared + + align:start position:0% +equals one-half m1 v1 X final squared + + + align:start position:0% +equals one-half m1 v1 X final squared +plus one-half m2 v2 X final squared now + + align:start position:0% +plus one-half m2 v2 X final squared now + + + align:start position:0% +plus one-half m2 v2 X final squared now +we're going to do some algebraic + + align:start position:0% +we're going to do some algebraic + + + align:start position:0% +we're going to do some algebraic +manipulations here so the first thing + + align:start position:0% +manipulations here so the first thing + + + align:start position:0% +manipulations here so the first thing +I'm going to do is just eliminate these + + align:start position:0% +I'm going to do is just eliminate these + + + align:start position:0% +I'm going to do is just eliminate these +halves because it's not necessary and I + + align:start position:0% +halves because it's not necessary and I + + + align:start position:0% +halves because it's not necessary and I +don't want to rewrite this equation and + + align:start position:0% +don't want to rewrite this equation and + + + align:start position:0% +don't want to rewrite this equation and +this is our constant fact that our + + align:start position:0% +this is our constant fact that our + + + align:start position:0% +this is our constant fact that our +energy is constant and now our condition + + align:start position:0% +energy is constant and now our condition + + + align:start position:0% +energy is constant and now our condition +that momentum is constant we'll write + + align:start position:0% +that momentum is constant we'll write + + + align:start position:0% +that momentum is constant we'll write +this now I'm going to leave a little + + align:start position:0% +this now I'm going to leave a little + + + align:start position:0% +this now I'm going to leave a little +space here intentionally and our + + align:start position:0% +space here intentionally and our + + + align:start position:0% +space here intentionally and our +condition that momentum is constant is + + align:start position:0% +condition that momentum is constant is + + + align:start position:0% +condition that momentum is constant is +m1 the X initial plus m2 v2 X initial + + align:start position:0% +m1 the X initial plus m2 v2 X initial + + + align:start position:0% +m1 the X initial plus m2 v2 X initial +equals m1 the 1x final plus m2 v2 X + + align:start position:0% +equals m1 the 1x final plus m2 v2 X + + + align:start position:0% +equals m1 the 1x final plus m2 v2 X +final now this energy equation can be + + align:start position:0% +final now this energy equation can be + + + align:start position:0% +final now this energy equation can be +factored in by bringing all the m1 terms + + align:start position:0% +factored in by bringing all the m1 terms + + + align:start position:0% +factored in by bringing all the m1 terms +to one side + + align:start position:0% +to one side + + + align:start position:0% +to one side +- turns to the other side so when I + + align:start position:0% +- turns to the other side so when I + + + align:start position:0% +- turns to the other side so when I +write that I'll need a little room I + + align:start position:0% +write that I'll need a little room I + + + align:start position:0% +write that I'll need a little room I +have M 1 V 1 X initial squared minus V 1 + + align:start position:0% +have M 1 V 1 X initial squared minus V 1 + + + align:start position:0% +have M 1 V 1 X initial squared minus V 1 +X final square and that's equal to M to + + align:start position:0% +X final square and that's equal to M to + + + align:start position:0% +X final square and that's equal to M to +be 2x final squared minus V 2 X initial + + align:start position:0% +be 2x final squared minus V 2 X initial + + + align:start position:0% +be 2x final squared minus V 2 X initial +squared so I've just brought those terms + + align:start position:0% +squared so I've just brought those terms + + + align:start position:0% +squared so I've just brought those terms +over the other side now likewise I'll do + + align:start position:0% +over the other side now likewise I'll do + + + align:start position:0% +over the other side now likewise I'll do +the same thing down here I have M 1 V 1 + + align:start position:0% +the same thing down here I have M 1 V 1 + + + align:start position:0% +the same thing down here I have M 1 V 1 +X initial minus V 1 X final and that's + + align:start position:0% +X initial minus V 1 X final and that's + + + align:start position:0% +X initial minus V 1 X final and that's +equal to M 2 V 2 X final minus V 2 X + + align:start position:0% +equal to M 2 V 2 X final minus V 2 X + + + align:start position:0% +equal to M 2 V 2 X final minus V 2 X +initial now here comes the algebraic + + align:start position:0% +initial now here comes the algebraic + + + align:start position:0% +initial now here comes the algebraic +trick in which I'm going to linearize + + align:start position:0% +trick in which I'm going to linearize + + + align:start position:0% +trick in which I'm going to linearize +these systems this is a squared minus B + + align:start position:0% +these systems this is a squared minus B + + + align:start position:0% +these systems this is a squared minus B +squared which factors into a plus B + + align:start position:0% +squared which factors into a plus B + + + align:start position:0% +squared which factors into a plus B +times a minus B so let's give ourselves + + align:start position:0% +times a minus B so let's give ourselves + + + align:start position:0% +times a minus B so let's give ourselves +a little room and one you want X initial + + align:start position:0% +a little room and one you want X initial + + + align:start position:0% +a little room and one you want X initial +plus let's put the minus sign first + + align:start position:0% + + + + align:start position:0% + +minus b 1x final times V 1 X initial + + align:start position:0% +minus b 1x final times V 1 X initial + + + align:start position:0% +minus b 1x final times V 1 X initial +plus V 1 X final factored that term we + + align:start position:0% +plus V 1 X final factored that term we + + + align:start position:0% +plus V 1 X final factored that term we +have the same factoring on the other + + align:start position:0% +have the same factoring on the other + + + align:start position:0% +have the same factoring on the other +side so it's just identical the 2x final + + align:start position:0% +side so it's just identical the 2x final + + + align:start position:0% +side so it's just identical the 2x final +minus V 2 X initial times the 2x final + + align:start position:0% +minus V 2 X initial times the 2x final + + + align:start position:0% +minus V 2 X initial times the 2x final +plus B 2 X initial now let's call this + + align:start position:0% +plus B 2 X initial now let's call this + + + align:start position:0% +plus B 2 X initial now let's call this +equation 1 a and our momentum factored + + align:start position:0% +equation 1 a and our momentum factored + + + align:start position:0% +equation 1 a and our momentum factored +as 2a + + align:start position:0% +as 2a + + + align:start position:0% +as 2a +now if you notice the momentum piece is + + align:start position:0% +now if you notice the momentum piece is + + + align:start position:0% +now if you notice the momentum piece is +appearing exactly there and exactly here + + align:start position:0% +appearing exactly there and exactly here + + + align:start position:0% +appearing exactly there and exactly here +so when I divide 1 a by 2a and I'll just + + align:start position:0% +so when I divide 1 a by 2a and I'll just + + + align:start position:0% +so when I divide 1 a by 2a and I'll just +symbolically represent that then these + + align:start position:0% +symbolically represent that then these + + + align:start position:0% +symbolically represent that then these +two pieces cancel and that leads to just + + align:start position:0% +two pieces cancel and that leads to just + + + align:start position:0% +two pieces cancel and that leads to just +this term equal to that term and the + + align:start position:0% +this term equal to that term and the + + + align:start position:0% +this term equal to that term and the +significance as you'll see when I write + + align:start position:0% +significance as you'll see when I write + + + align:start position:0% +significance as you'll see when I write +it out 1/2 x 1x final equals V 2x final + + align:start position:0% +it out 1/2 x 1x final equals V 2x final + + + align:start position:0% +it out 1/2 x 1x final equals V 2x final +v2x initial I've solved the quad I've + + align:start position:0% +v2x initial I've solved the quad I've + + + align:start position:0% +v2x initial I've solved the quad I've +eliminated the square terms linearized + + align:start position:0% +eliminated the square terms linearized + + + align:start position:0% +eliminated the square terms linearized +the system now I still want to write + + align:start position:0% +the system now I still want to write + + + align:start position:0% +the system now I still want to write +this equation in another way another + + align:start position:0% +this equation in another way another + + + align:start position:0% +this equation in another way another +important point to notice is that this + + align:start position:0% +important point to notice is that this + + + align:start position:0% +important point to notice is that this +equation is independent of mass now what + + align:start position:0% +equation is independent of mass now what + + + align:start position:0% +equation is independent of mass now what +I want to do is write this in terms of + + align:start position:0% +I want to do is write this in terms of + + + align:start position:0% +I want to do is write this in terms of +those concepts of relative velocity we + + align:start position:0% +those concepts of relative velocity we + + + align:start position:0% +those concepts of relative velocity we +had remember just to motivate this the + + align:start position:0% +had remember just to motivate this the + + + align:start position:0% +had remember just to motivate this the +relative by definition was v1 minus v2 + + align:start position:0% +relative by definition was v1 minus v2 + + + align:start position:0% +relative by definition was v1 minus v2 +so let's write this in terms of the + + align:start position:0% +so let's write this in terms of the + + + align:start position:0% +so let's write this in terms of the +initial and the final so in order to do + + align:start position:0% +initial and the final so in order to do + + + align:start position:0% +initial and the final so in order to do +that we have to bring this initial term + + align:start position:0% +that we have to bring this initial term + + + align:start position:0% +that we have to bring this initial term +over to here and this final term over to + + align:start position:0% +over to here and this final term over to + + + align:start position:0% +over to here and this final term over to +there and so this equation which will + + align:start position:0% +there and so this equation which will + + + align:start position:0% +there and so this equation which will +give it a number three and now we'll + + align:start position:0% +give it a number three and now we'll + + + align:start position:0% +give it a number three and now we'll +modify that by calling it 3a we have v1 + + align:start position:0% +modify that by calling it 3a we have v1 + + + align:start position:0% +modify that by calling it 3a we have v1 +X initial minus b2 X initial now notice + + align:start position:0% +X initial minus b2 X initial now notice + + + align:start position:0% +X initial minus b2 X initial now notice +the sign I'm going to want to keep the + + align:start position:0% +the sign I'm going to want to keep the + + + align:start position:0% +the sign I'm going to want to keep the +order of one and two so I have to put a + + align:start position:0% +order of one and two so I have to put a + + + align:start position:0% +order of one and two so I have to put a +minus sign + + align:start position:0% +minus sign + + + align:start position:0% +minus sign +v1 X final minus the 2x final + + align:start position:0% + + + + align:start position:0% + +and when written this way this is the + + align:start position:0% +and when written this way this is the + + + align:start position:0% +and when written this way this is the +font this is the initial component of + + align:start position:0% +font this is the initial component of + + + align:start position:0% +font this is the initial component of +the relative velocity and in there is + + align:start position:0% +the relative velocity and in there is + + + align:start position:0% +the relative velocity and in there is +the final component of relative velocity + + align:start position:0% +the final component of relative velocity + + + align:start position:0% +the final component of relative velocity +so by combining these two equations I + + align:start position:0% +so by combining these two equations I + + + align:start position:0% +so by combining these two equations I +have this remarkable result that the + + align:start position:0% +have this remarkable result that the + + + align:start position:0% +have this remarkable result that the +relative initial is minus the relative + + align:start position:0% +relative initial is minus the relative + + + align:start position:0% +relative initial is minus the relative +final and this condition is a very + + align:start position:0% +final and this condition is a very + + + align:start position:0% +final and this condition is a very +powerful tool for simply analyzing one + + align:start position:0% +powerful tool for simply analyzing one + + + align:start position:0% +powerful tool for simply analyzing one +dimensional elastic inelastic collisions + + align:start position:0% +dimensional elastic inelastic collisions + + + align:start position:0% +dimensional elastic inelastic collisions +I'd like to even give this a name I like + + align:start position:0% +I'd like to even give this a name I like + + + align:start position:0% +I'd like to even give this a name I like +to call it the energy momentum equation + + align:start position:0% +to call it the energy momentum equation + + + align:start position:0% +to call it the energy momentum equation +now there's a lot of significant things + + align:start position:0% +now there's a lot of significant things + + + align:start position:0% +now there's a lot of significant things +about this so let's just think about it + + align:start position:0% +about this so let's just think about it + + + align:start position:0% +about this so let's just think about it +for a moment we have that V relative + + align:start position:0% +for a moment we have that V relative + + + align:start position:0% +for a moment we have that V relative +initial in magnitude is equal to the + + align:start position:0% +initial in magnitude is equal to the + + + align:start position:0% +initial in magnitude is equal to the +relative final and so right away this + + align:start position:0% +relative final and so right away this + + + align:start position:0% +relative final and so right away this +gives us some insight into any collision + + align:start position:0% +gives us some insight into any collision + + + align:start position:0% +gives us some insight into any collision +we can see whether a collision if we + + align:start position:0% +we can see whether a collision if we + + + align:start position:0% +we can see whether a collision if we +know what the relative initial velocity + + align:start position:0% +know what the relative initial velocity + + + align:start position:0% +know what the relative initial velocity +is we know that the final relative + + align:start position:0% +is we know that the final relative + + + align:start position:0% +is we know that the final relative +velocity has the same magnitude but + + align:start position:0% +velocity has the same magnitude but + + + align:start position:0% +velocity has the same magnitude but +simply switches direction and that's a + + align:start position:0% +simply switches direction and that's a + + + align:start position:0% +simply switches direction and that's a +powerful tool in which to analyze + + align:start position:0% +powerful tool in which to analyze + + + align:start position:0% +powerful tool in which to analyze +collisions without doing a lot of + + align:start position:0% +collisions without doing a lot of + + + align:start position:0% +collisions without doing a lot of +algebra \ No newline at end of file diff --git a/bH4L4Nv_PeA.txt b/bH4L4Nv_PeA.txt new file mode 100644 index 0000000000000000000000000000000000000000..74a066f091c6348ae148574aeacb03531856e0a5 --- /dev/null +++ b/bH4L4Nv_PeA.txt @@ -0,0 +1,459 @@ +align:start position:0% + +lint it's a um online tool so um many + + align:start position:0% +lint it's a um online tool so um many + + + align:start position:0% +lint it's a um online tool so um many +teachers use it you can record your + + align:start position:0% +teachers use it you can record your + + + align:start position:0% +teachers use it you can record your +voice you can ask student to record + + align:start position:0% +voice you can ask student to record + + + align:start position:0% +voice you can ask student to record +their voice you can assign the speaking + + align:start position:0% +their voice you can assign the speaking + + + align:start position:0% +their voice you can assign the speaking +uh lessons on assignment on that that's + + align:start position:0% +uh lessons on assignment on that that's + + + align:start position:0% +uh lessons on assignment on that that's +very uh convenient because everybody has + + align:start position:0% +very uh convenient because everybody has + + + align:start position:0% +very uh convenient because everybody has +a computer and you don't need to go to + + align:start position:0% +a computer and you don't need to go to + + + align:start position:0% +a computer and you don't need to go to +the uh lab anymore so um the tool link + + align:start position:0% +the uh lab anymore so um the tool link + + + align:start position:0% +the uh lab anymore so um the tool link +is is created by two MIT students so + + align:start position:0% +is is created by two MIT students so + + + align:start position:0% +is is created by two MIT students so +when they started um they want us to + + align:start position:0% +when they started um they want us to + + + align:start position:0% +when they started um they want us to +participate as a guinea pig so it was + + align:start position:0% +participate as a guinea pig so it was + + + align:start position:0% +participate as a guinea pig so it was +fun what I use for this class because I + + align:start position:0% +fun what I use for this class because I + + + align:start position:0% +fun what I use for this class because I +discover I usually think in our class is + + align:start position:0% +discover I usually think in our class is + + + align:start position:0% +discover I usually think in our class is +the time to speak I don't like to spend + + align:start position:0% +the time to speak I don't like to spend + + + align:start position:0% +the time to speak I don't like to spend +a lot of time explaining things or teach + + align:start position:0% +a lot of time explaining things or teach + + + align:start position:0% +a lot of time explaining things or teach +them how to pronounce words because they + + align:start position:0% +them how to pronounce words because they + + + align:start position:0% +them how to pronounce words because they +they know the alphabet part the Ping + + align:start position:0% +they know the alphabet part the Ping + + + align:start position:0% +they know the alphabet part the Ping +part already um so I like them to do + + align:start position:0% +part already um so I like them to do + + + align:start position:0% +part already um so I like them to do +this mechanic works at home and in class + + align:start position:0% +this mechanic works at home and in class + + + align:start position:0% +this mechanic works at home and in class +they're well prepared and then we talk + + align:start position:0% +they're well prepared and then we talk + + + align:start position:0% +they're well prepared and then we talk +about this + + align:start position:0% +about this + + + align:start position:0% +about this +lesson and uh uh and I realized that + + align:start position:0% +lesson and uh uh and I realized that + + + align:start position:0% +lesson and uh uh and I realized that +giving them a quiz of this content is + + align:start position:0% +giving them a quiz of this content is + + + align:start position:0% +giving them a quiz of this content is +not enough because I realized students + + align:start position:0% +not enough because I realized students + + + align:start position:0% +not enough because I realized students +study they do so they want to do well in + + align:start position:0% +study they do so they want to do well in + + + align:start position:0% +study they do so they want to do well in +their quiz so they read the text + + align:start position:0% +their quiz so they read the text + + + align:start position:0% +their quiz so they read the text +silently at home so they might know what + + align:start position:0% +silently at home so they might know what + + + align:start position:0% +silently at home so they might know what +it means they don't know how to + + align:start position:0% +it means they don't know how to + + + align:start position:0% +it means they don't know how to +pronounce it so how do I fix it because + + align:start position:0% +pronounce it so how do I fix it because + + + align:start position:0% +pronounce it so how do I fix it because +I used to spend time to ask everybody to + + align:start position:0% +I used to spend time to ask everybody to + + + align:start position:0% +I used to spend time to ask everybody to +read one line of the class I I encounter + + align:start position:0% +read one line of the class I I encounter + + + align:start position:0% +read one line of the class I I encounter +this problem the kids just they can + + align:start position:0% +this problem the kids just they can + + + align:start position:0% +this problem the kids just they can +translate the sentence they cannot say + + align:start position:0% +translate the sentence they cannot say + + + align:start position:0% +translate the sentence they cannot say +the vocabulary in Chinese when they read + + align:start position:0% +the vocabulary in Chinese when they read + + + align:start position:0% +the vocabulary in Chinese when they read +it they say I know that word but I don't + + align:start position:0% +it they say I know that word but I don't + + + align:start position:0% +it they say I know that word but I don't +know how to pronounce it so I that's it + + align:start position:0% +know how to pronounce it so I that's it + + + align:start position:0% +know how to pronounce it so I that's it +dawned on me that you know they did + + align:start position:0% +dawned on me that you know they did + + + align:start position:0% +dawned on me that you know they did +prepare but they not reading out loud at + + align:start position:0% +prepare but they not reading out loud at + + + align:start position:0% +prepare but they not reading out loud at +home so they don't know how to pronounce + + align:start position:0% +home so they don't know how to pronounce + + + align:start position:0% +home so they don't know how to pronounce +the words if you don't know you don't + + align:start position:0% +the words if you don't know you don't + + + align:start position:0% +the words if you don't know you don't +know how to pronounce it you're not + + align:start position:0% +know how to pronounce it you're not + + + align:start position:0% +know how to pronounce it you're not +learning it so so I created this I + + align:start position:0% +learning it so so I created this I + + + align:start position:0% +learning it so so I created this I +didn't create a link I I add the actual + + align:start position:0% +didn't create a link I I add the actual + + + align:start position:0% +didn't create a link I I add the actual +assignment every new lesson I asked them + + align:start position:0% +assignment every new lesson I asked them + + + align:start position:0% +assignment every new lesson I asked them +to read the textbook a recorded voice on + + align:start position:0% +to read the textbook a recorded voice on + + + align:start position:0% +to read the textbook a recorded voice on +the link link this uh web tool and send + + align:start position:0% +the link link this uh web tool and send + + + align:start position:0% +the link link this uh web tool and send +it to me well I can cheat + + align:start position:0% +it to me well I can cheat + + + align:start position:0% +it to me well I can cheat +so I found out that many student want to + + align:start position:0% +so I found out that many student want to + + + align:start position:0% +so I found out that many student want to +have a perfect recording so they they + + align:start position:0% +have a perfect recording so they they + + + align:start position:0% +have a perfect recording so they they +will read 10 times before they record it + + align:start position:0% +will read 10 times before they record it + + + align:start position:0% +will read 10 times before they record it +which is great because they basically + + align:start position:0% +which is great because they basically + + + align:start position:0% +which is great because they basically +memorize the text and they know every + + align:start position:0% +memorize the text and they know every + + + align:start position:0% +memorize the text and they know every +words how to pronounce it that's my goal + + align:start position:0% +words how to pronounce it that's my goal + + + align:start position:0% +words how to pronounce it that's my goal +so that's how I use I find it I don't + + align:start position:0% +so that's how I use I find it I don't + + + align:start position:0% +so that's how I use I find it I don't +need to spend more time to check do you + + align:start position:0% +need to spend more time to check do you + + + align:start position:0% +need to spend more time to check do you +know how to pronounce this words anymore + + align:start position:0% +know how to pronounce this words anymore + + + align:start position:0% +know how to pronounce this words anymore +because they have to do it yeah so + + align:start position:0% +because they have to do it yeah so + + + align:start position:0% +because they have to do it yeah so +that's how I use it \ No newline at end of file diff --git a/bJvv5SckGeA.txt b/bJvv5SckGeA.txt new file mode 100644 index 0000000000000000000000000000000000000000..e15cd21d9ec4b7728206e10be9a8cbcfb75b0711 --- /dev/null +++ b/bJvv5SckGeA.txt @@ -0,0 +1,9437 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu so last time we started to + + align:start position:0% +ocw.mit.edu so last time we started to + + + align:start position:0% +ocw.mit.edu so last time we started to +think about sampling + + align:start position:0% +think about sampling + + + align:start position:0% +think about sampling +and that's what I want to finish up + + align:start position:0% +and that's what I want to finish up + + + align:start position:0% +and that's what I want to finish up +today the I think sampling is a very + + align:start position:0% +today the I think sampling is a very + + + align:start position:0% +today the I think sampling is a very +important issue it's one of the + + align:start position:0% +important issue it's one of the + + + align:start position:0% +important issue it's one of the +strengths of this course because we can + + align:start position:0% +strengths of this course because we can + + + align:start position:0% +strengths of this course because we can +think about on equal footing the way + + align:start position:0% +think about on equal footing the way + + + align:start position:0% +think about on equal footing the way +signals work in a CT system or in a DT + + align:start position:0% +signals work in a CT system or in a DT + + + align:start position:0% +signals work in a CT system or in a DT +system when the signals are CT when the + + align:start position:0% +system when the signals are CT when the + + + align:start position:0% +system when the signals are CT when the +signals are DT and in specifically when + + align:start position:0% +signals are DT and in specifically when + + + align:start position:0% +signals are DT and in specifically when +you convert between them converting + + align:start position:0% +you convert between them converting + + + align:start position:0% +you convert between them converting +between them like we saw last + + align:start position:0% +between them like we saw last + + + align:start position:0% +between them like we saw last +time we're that's a very important + + align:start position:0% +time we're that's a very important + + + align:start position:0% +time we're that's a very important +process because many of the kinds of + + align:start position:0% +process because many of the kinds of + + + align:start position:0% +process because many of the kinds of +signals that we want to think about + + align:start position:0% +signals that we want to think about + + + align:start position:0% +signals that we want to think about +occur in in physical have a physical + + align:start position:0% +occur in in physical have a physical + + + align:start position:0% +occur in in physical have a physical +origin where they are naturally + + align:start position:0% +origin where they are naturally + + + align:start position:0% +origin where they are naturally +continuous time or continuous space + + align:start position:0% +continuous time or continuous space + + + align:start position:0% +continuous time or continuous space +kinds of signals but we would like to + + align:start position:0% +kinds of signals but we would like to + + + align:start position:0% +kinds of signals but we would like to +use inexpensive digital electronics in + + align:start position:0% +use inexpensive digital electronics in + + + align:start position:0% +use inexpensive digital electronics in +order to process them so it's important + + align:start position:0% +order to process them so it's important + + + align:start position:0% +order to process them so it's important +to understand how we can take a CT + + align:start position:0% +to understand how we can take a CT + + + align:start position:0% +to understand how we can take a CT +signal and represent the information + + align:start position:0% +signal and represent the information + + + align:start position:0% +signal and represent the information +that's + + align:start position:0% +that's + + + align:start position:0% +that's +there in a DT + + align:start position:0% +there in a DT + + + align:start position:0% +there in a DT +Manner and it's completely + + align:start position:0% +Manner and it's completely + + + align:start position:0% +Manner and it's completely +remarkable that you can even do that + + align:start position:0% +remarkable that you can even do that + + + align:start position:0% +remarkable that you can even do that +right CT signals are in some + + align:start position:0% +right CT signals are in some + + + align:start position:0% +right CT signals are in some +arbitrarily more complicated than DT + + align:start position:0% +arbitrarily more complicated than DT + + + align:start position:0% +arbitrarily more complicated than DT +signals DT signals only exist at integer + + align:start position:0% +signals DT signals only exist at integer + + + align:start position:0% +signals DT signals only exist at integer +multiples of time at integer values of + + align:start position:0% +multiples of time at integer values of + + + align:start position:0% +multiples of time at integer values of +time CT signals in principle can do + + align:start position:0% +time CT signals in principle can do + + + align:start position:0% +time CT signals in principle can do +anything between two consecutive samples + + align:start position:0% +anything between two consecutive samples + + + align:start position:0% +anything between two consecutive samples +of a DT signal so in some sense they're + + align:start position:0% +of a DT signal so in some sense they're + + + align:start position:0% +of a DT signal so in some sense they're +arbitrarily more complicated so it's + + align:start position:0% +arbitrarily more complicated so it's + + + align:start position:0% +arbitrarily more complicated so it's +kind of remarkable at + + align:start position:0% +kind of remarkable at + + + align:start position:0% +kind of remarkable at +all that we can talk meaningfully about + + align:start position:0% +all that we can talk meaningfully about + + + align:start position:0% +all that we can talk meaningfully about +how you can represent the information + + align:start position:0% +how you can represent the information + + + align:start position:0% +how you can represent the information +that's in a CT system with a DT + + align:start position:0% +that's in a CT system with a DT + + + align:start position:0% +that's in a CT system with a DT +equivalent system and the point point is + + align:start position:0% +equivalent system and the point point is + + + align:start position:0% +equivalent system and the point point is +and the reason we're doing it now in + + align:start position:0% +and the reason we're doing it now in + + + align:start position:0% +and the reason we're doing it now in +this part of the course is that by + + align:start position:0% +this part of the course is that by + + + align:start position:0% +this part of the course is that by +thinking about 48 transforms + + align:start position:0% +thinking about 48 transforms + + + align:start position:0% +thinking about 48 transforms +everything's very simple something that + + align:start position:0% +everything's very simple something that + + + align:start position:0% +everything's very simple something that +could be conceptually quite complicated + + align:start position:0% +could be conceptually quite complicated + + + align:start position:0% +could be conceptually quite complicated +is in fact extremely simple to think + + align:start position:0% +is in fact extremely simple to think + + + align:start position:0% +is in fact extremely simple to think +about so last time we saw that the way + + align:start position:0% +about so last time we saw that the way + + + align:start position:0% +about so last time we saw that the way +to think about the signal if you want to + + align:start position:0% +to think about the signal if you want to + + + align:start position:0% +to think about the signal if you want to +sample it if you want to convert a CT + + align:start position:0% +sample it if you want to convert a CT + + + align:start position:0% +sample it if you want to convert a CT +signal to a DC signal the way to think + + align:start position:0% +signal to a DC signal the way to think + + + align:start position:0% +signal to a DC signal the way to think +about it is to think about the 4A + + align:start position:0% +about it is to think about the 4A + + + align:start position:0% +about it is to think about the 4A +transform so then uh the example that we + + align:start position:0% +transform so then uh the example that we + + + align:start position:0% +transform so then uh the example that we +talked about last time you think about + + align:start position:0% +talked about last time you think about + + + align:start position:0% +talked about last time you think about +uh a CT signal X oft you think about its + + align:start position:0% +uh a CT signal X oft you think about its + + + align:start position:0% +uh a CT signal X oft you think about its +samples taken uniformly in + + align:start position:0% +samples taken uniformly in + + + align:start position:0% +samples taken uniformly in +time and then in order to think about + + align:start position:0% +time and then in order to think about + + + align:start position:0% +time and then in order to think about +the information and whether or not + + align:start position:0% +the information and whether or not + + + align:start position:0% +the information and whether or not +you've captured it all the question is + + align:start position:0% +you've captured it all the question is + + + align:start position:0% +you've captured it all the question is +can you + + align:start position:0% +can you + + + align:start position:0% +can you +reconstruct the original thing that you + + align:start position:0% +reconstruct the original thing that you + + + align:start position:0% +reconstruct the original thing that you +started with from the samples + + align:start position:0% +started with from the samples + + + align:start position:0% +started with from the samples +only okay well in general no so what + + align:start position:0% +only okay well in general no so what + + + align:start position:0% +only okay well in general no so what +we're really asking is what are the + + align:start position:0% +we're really asking is what are the + + + align:start position:0% +we're really asking is what are the +rules what are the conditions under + + align:start position:0% +rules what are the conditions under + + + align:start position:0% +rules what are the conditions under +which you can do that and are they + + align:start position:0% +which you can do that and are they + + + align:start position:0% +which you can do that and are they +useful conditions or not so the first + + align:start position:0% +useful conditions or not so the first + + + align:start position:0% +useful conditions or not so the first +way you can think about taking the + + align:start position:0% +way you can think about taking the + + + align:start position:0% +way you can think about taking the +samples and turning them back into a + + align:start position:0% +samples and turning them back into a + + + align:start position:0% +samples and turning them back into a +continuous time signal is something that + + align:start position:0% +continuous time signal is something that + + + align:start position:0% +continuous time signal is something that +we called impulse + + align:start position:0% +we called impulse + + + align:start position:0% +we called impulse +reconstruction in impulse reconstruction + + align:start position:0% +reconstruction in impulse reconstruction + + + align:start position:0% +reconstruction in impulse reconstruction +we substitute for every sample an + + align:start position:0% +we substitute for every sample an + + + align:start position:0% +we substitute for every sample an +Impulse appropriately located in time + + align:start position:0% +Impulse appropriately located in time + + + align:start position:0% +Impulse appropriately located in time +and appropriately scaled in amplitude + + align:start position:0% +and appropriately scaled in amplitude + + + align:start position:0% +and appropriately scaled in amplitude +the appropriate scale in amplitude is + + align:start position:0% +the appropriate scale in amplitude is + + + align:start position:0% +the appropriate scale in amplitude is +that you take the samples and you wait + + align:start position:0% +that you take the samples and you wait + + + align:start position:0% +that you take the samples and you wait +the impulses you wait the impulse at the + + align:start position:0% +the impulses you wait the impulse at the + + + align:start position:0% +the impulses you wait the impulse at the +nth time integ at the nth time step by + + align:start position:0% +nth time integ at the nth time step by + + + align:start position:0% +nth time integ at the nth time step by +the + + align:start position:0% +the + + + align:start position:0% +the +um sample value for time + + align:start position:0% +um sample value for time + + + align:start position:0% +um sample value for time +n and you put the nth one at time NT and + + align:start position:0% +n and you put the nth one at time NT and + + + align:start position:0% +n and you put the nth one at time NT and +cap T So impulse reconstruction really + + align:start position:0% +cap T So impulse reconstruction really + + + align:start position:0% +cap T So impulse reconstruction really +easy take all the samples that you got + + align:start position:0% +easy take all the samples that you got + + + align:start position:0% +easy take all the samples that you got +by uniform + + align:start position:0% +by uniform + + + align:start position:0% +by uniform +sampling substitute for every sample one + + align:start position:0% +sampling substitute for every sample one + + + align:start position:0% +sampling substitute for every sample one +impulse appropriately timed + + align:start position:0% +impulse appropriately timed + + + align:start position:0% +impulse appropriately timed +appropriately + + align:start position:0% +appropriately + + + align:start position:0% +appropriately +weighted okay that's great it's + + align:start position:0% +weighted okay that's great it's + + + align:start position:0% +weighted okay that's great it's +especially nice because there's a simple + + align:start position:0% +especially nice because there's a simple + + + align:start position:0% +especially nice because there's a simple +4A representation for that process + + align:start position:0% +4A representation for that process + + + align:start position:0% +4A representation for that process +that process if we think about just + + align:start position:0% +that process if we think about just + + + align:start position:0% +that process if we think about just +taking X of T and turning it into this + + align:start position:0% +taking X of T and turning it into this + + + align:start position:0% +taking X of T and turning it into this +impulse + + align:start position:0% + + + + align:start position:0% + +reconstruction that impulse + + align:start position:0% +reconstruction that impulse + + + align:start position:0% +reconstruction that impulse +reconstruction is precisely the same as + + align:start position:0% +reconstruction is precisely the same as + + + align:start position:0% +reconstruction is precisely the same as +if I had multiplied the original signal + + align:start position:0% +if I had multiplied the original signal + + + align:start position:0% +if I had multiplied the original signal +X of + + align:start position:0% +X of + + + align:start position:0% +X of +T by an Impulse train impuls is + + align:start position:0% +T by an Impulse train impuls is + + + align:start position:0% +T by an Impulse train impuls is +separated by capital T unit height so + + align:start position:0% +separated by capital T unit height so + + + align:start position:0% +separated by capital T unit height so +that means the transformation can be + + align:start position:0% +that means the transformation can be + + + align:start position:0% +that means the transformation can be +thought of in terms of fora transforms + + align:start position:0% +thought of in terms of fora transforms + + + align:start position:0% +thought of in terms of fora transforms +as the convolution of the original + + align:start position:0% +as the convolution of the original + + + align:start position:0% +as the convolution of the original +Spectrum the the the original 48 + + align:start position:0% +Spectrum the the the original 48 + + + align:start position:0% +Spectrum the the the original 48 +transform with the 4A transform of + + align:start position:0% +transform with the 4A transform of + + + align:start position:0% +transform with the 4A transform of +impulse train which is just another + + align:start position:0% +impulse train which is just another + + + align:start position:0% +impulse train which is just another +impulse + + align:start position:0% +impulse + + + align:start position:0% +impulse +train so the rule is you can do the you + + align:start position:0% +train so the rule is you can do the you + + + align:start position:0% +train so the rule is you can do the you +can represent all the information in the + + align:start position:0% +can represent all the information in the + + + align:start position:0% +can represent all the information in the +signal if the signal started out being + + align:start position:0% +signal if the signal started out being + + + align:start position:0% +signal if the signal started out being +band + + align:start position:0% +band + + + align:start position:0% +band +limited okay if the signal had a region + + align:start position:0% +limited okay if the signal had a region + + + align:start position:0% +limited okay if the signal had a region +of frequency over which it is nonzero + + align:start position:0% +of frequency over which it is nonzero + + + align:start position:0% +of frequency over which it is nonzero +and for the rest of frequency the signal + + align:start position:0% +and for the rest of frequency the signal + + + align:start position:0% +and for the rest of frequency the signal +is zero then when you do the aliasing + + align:start position:0% +is zero then when you do the aliasing + + + align:start position:0% +is zero then when you do the aliasing +you can arrange to the period so that + + align:start position:0% +you can arrange to the period so that + + + align:start position:0% +you can arrange to the period so that +the aliased copy uh so that the U + + align:start position:0% +the aliased copy uh so that the U + + + align:start position:0% +the aliased copy uh so that the U +convolved copies don't overlap with each + + align:start position:0% +convolved copies don't overlap with each + + + align:start position:0% +convolved copies don't overlap with each +other okay so that was a simple way of + + align:start position:0% +other okay so that was a simple way of + + + align:start position:0% +other okay so that was a simple way of +thinking about can you how much + + align:start position:0% +thinking about can you how much + + + align:start position:0% +thinking about can you how much +information was in the samples by + + align:start position:0% +information was in the samples by + + + align:start position:0% +information was in the samples by +thinking about the impulse + + align:start position:0% +thinking about the impulse + + + align:start position:0% +thinking about the impulse +reconstruction of course the signal that + + align:start position:0% +reconstruction of course the signal that + + + align:start position:0% +reconstruction of course the signal that +we reconstruct by this convolution + + align:start position:0% +we reconstruct by this convolution + + + align:start position:0% +we reconstruct by this convolution +process has multiple copies of the same + + align:start position:0% +process has multiple copies of the same + + + align:start position:0% +process has multiple copies of the same +frequency content so we don't like that + + align:start position:0% +frequency content so we don't like that + + + align:start position:0% +frequency content so we don't like that +so you can throw away those extra copies + + align:start position:0% +so you can throw away those extra copies + + + align:start position:0% +so you can throw away those extra copies +by doing a low pass filtering operation + + align:start position:0% +by doing a low pass filtering operation + + + align:start position:0% +by doing a low pass filtering operation +and we call that reconstruction the XR + + align:start position:0% +and we call that reconstruction the XR + + + align:start position:0% +and we call that reconstruction the XR +we call that the band limited + + align:start position:0% +we call that the band limited + + + align:start position:0% +we call that the band limited +reconstruction it's like the impulse + + align:start position:0% +reconstruction it's like the impulse + + + align:start position:0% +reconstruction it's like the impulse +reconstruction except that it's band + + align:start position:0% +reconstruction except that it's band + + + align:start position:0% +reconstruction except that it's band +limited okay so we think of two ways of + + align:start position:0% +limited okay so we think of two ways of + + + align:start position:0% +limited okay so we think of two ways of +doing the Reconstruction from the + + align:start position:0% +doing the Reconstruction from the + + + align:start position:0% +doing the Reconstruction from the +samples the impulse reconstruction the + + align:start position:0% +samples the impulse reconstruction the + + + align:start position:0% +samples the impulse reconstruction the +band limited reconstruction and the key + + align:start position:0% +band limited reconstruction and the key + + + align:start position:0% +band limited reconstruction and the key +is the sampling theorem the sampling + + align:start position:0% +is the sampling theorem the sampling + + + align:start position:0% +is the sampling theorem the sampling +theorem says that if the original + + align:start position:0% +theorem says that if the original + + + align:start position:0% +theorem says that if the original +signal had nonf frequency uh non-zero + + align:start position:0% +signal had nonf frequency uh non-zero + + + align:start position:0% +signal had nonf frequency uh non-zero +frequency content own over only some + + align:start position:0% +frequency content own over only some + + + align:start position:0% +frequency content own over only some +particular range of frequencies you can + + align:start position:0% +particular range of frequencies you can + + + align:start position:0% +particular range of frequencies you can +sample fast enough so that you can + + align:start position:0% +sample fast enough so that you can + + + align:start position:0% +sample fast enough so that you can +represent all the information that's in + + align:start position:0% +represent all the information that's in + + + align:start position:0% +represent all the information that's in +the continuous time signal with the + + align:start position:0% +the continuous time signal with the + + + align:start position:0% +the continuous time signal with the +samples okay is that all clear the point + + align:start position:0% +samples okay is that all clear the point + + + align:start position:0% +samples okay is that all clear the point +is we're trying to represent the + + align:start position:0% +is we're trying to represent the + + + align:start position:0% +is we're trying to represent the +information in a CT signal using + + align:start position:0% +information in a CT signal using + + + align:start position:0% +information in a CT signal using +DT and that the 48 transform is a very + + align:start position:0% +DT and that the 48 transform is a very + + + align:start position:0% +DT and that the 48 transform is a very +way to visualize when and when when you + + align:start position:0% +way to visualize when and when when you + + + align:start position:0% +way to visualize when and when when you +can do that and when you cannot do that + + align:start position:0% +can do that and when you cannot do that + + + align:start position:0% +can do that and when you cannot do that +you still rep you still end up in a + + align:start position:0% +you still rep you still end up in a + + + align:start position:0% +you still rep you still end up in a +physical system perhaps generating + + align:start position:0% +physical system perhaps generating + + + align:start position:0% +physical system perhaps generating +signals whose frequency content falls + + align:start position:0% +signals whose frequency content falls + + + align:start position:0% +signals whose frequency content falls +out of that range we saw an illustration + + align:start position:0% +out of that range we saw an illustration + + + align:start position:0% +out of that range we saw an illustration +of that last time but you can so for + + align:start position:0% +of that last time but you can so for + + + align:start position:0% +of that last time but you can so for +example if you were to try to represent + + align:start position:0% +example if you were to try to represent + + + align:start position:0% +example if you were to try to represent +a signal with this + + align:start position:0% +a signal with this + + + align:start position:0% +a signal with this +transform using a sampling period T so + + align:start position:0% +transform using a sampling period T so + + + align:start position:0% +transform using a sampling period T so +that the uh impulses in frequency were + + align:start position:0% +that the uh impulses in frequency were + + + align:start position:0% +that the uh impulses in frequency were +separated by 2 pi/ T which happened to + + align:start position:0% +separated by 2 pi/ T which happened to + + + align:start position:0% +separated by 2 pi/ T which happened to +be less than twice this + + align:start position:0% +be less than twice this + + + align:start position:0% +be less than twice this +distance + + align:start position:0% +distance + + + align:start position:0% +distance +then it would + + align:start position:0% +then it would + + + align:start position:0% +then it would +Alias that's bad so we would typically + + align:start position:0% +Alias that's bad so we would typically + + + align:start position:0% +Alias that's bad so we would typically +also include an anti-aliasing + + align:start position:0% +also include an anti-aliasing + + + align:start position:0% +also include an anti-aliasing +filter pre-filter the signal from + + align:start position:0% +filter pre-filter the signal from + + + align:start position:0% +filter pre-filter the signal from +physics get rid of the parts that you + + align:start position:0% +physics get rid of the parts that you + + + align:start position:0% +physics get rid of the parts that you +know are going to be a problem when you + + align:start position:0% +know are going to be a problem when you + + + align:start position:0% +know are going to be a problem when you +try to + + align:start position:0% +try to + + + align:start position:0% +try to +sample then go ahead and do the regular + + align:start position:0% +sample then go ahead and do the regular + + + align:start position:0% +sample then go ahead and do the regular +uh sampling the regular uniform sampling + + align:start position:0% +uh sampling the regular uniform sampling + + + align:start position:0% +uh sampling the regular uniform sampling +the regular band limited + + align:start position:0% +the regular band limited + + + align:start position:0% +the regular band limited +reconstruction and the signal that you + + align:start position:0% +reconstruction and the signal that you + + + align:start position:0% +reconstruction and the signal that you +reconstruct won't be an identical copy + + align:start position:0% +reconstruct won't be an identical copy + + + align:start position:0% +reconstruct won't be an identical copy +but it will be as close as you can given + + align:start position:0% +but it will be as close as you can given + + + align:start position:0% +but it will be as close as you can given +the sampling + + align:start position:0% +the sampling + + + align:start position:0% +the sampling +theorem okay so that's what we did last + + align:start position:0% +theorem okay so that's what we did last + + + align:start position:0% +theorem okay so that's what we did last +time what I want to do today is think + + align:start position:0% +time what I want to do today is think + + + align:start position:0% +time what I want to do today is think +about some other issues that come up + + align:start position:0% +about some other issues that come up + + + align:start position:0% +about some other issues that come up +when you try to represent a continuous + + align:start position:0% +when you try to represent a continuous + + + align:start position:0% +when you try to represent a continuous +signal in a discrete domain so in + + align:start position:0% +signal in a discrete domain so in + + + align:start position:0% +signal in a discrete domain so in +addition to thinking about discretizing + + align:start position:0% +addition to thinking about discretizing + + + align:start position:0% +addition to thinking about discretizing +time we also have to think about + + align:start position:0% +time we also have to think about + + + align:start position:0% +time we also have to think about +discretizing + + align:start position:0% +discretizing + + + align:start position:0% +discretizing +amplitude because if we want to + + align:start position:0% +amplitude because if we want to + + + align:start position:0% +amplitude because if we want to +represent a signal by bits uh so we have + + align:start position:0% +represent a signal by bits uh so we have + + + align:start position:0% +represent a signal by bits uh so we have +to represent not only the time but also + + align:start position:0% +to represent not only the time but also + + + align:start position:0% +to represent not only the time but also +the amplitude in bits I'll talk about + + align:start position:0% +the amplitude in bits I'll talk about + + + align:start position:0% +the amplitude in bits I'll talk about +several different kinds of schemes for + + align:start position:0% +several different kinds of schemes for + + + align:start position:0% +several different kinds of schemes for +that in the simplest kinds of schemes + + align:start position:0% +that in the simplest kinds of schemes + + + align:start position:0% +that in the simplest kinds of schemes +the code for the representation and + + align:start position:0% +the code for the representation and + + + align:start position:0% +the code for the representation and +amplitude is separately derived from the + + align:start position:0% +amplitude is separately derived from the + + + align:start position:0% +amplitude is separately derived from the +code for the representation in time so + + align:start position:0% +code for the representation in time so + + + align:start position:0% +code for the representation in time so +we can think of it as two boxes a + + align:start position:0% +we can think of it as two boxes a + + + align:start position:0% +we can think of it as two boxes a +sampling box following followed by a + + align:start position:0% +sampling box following followed by a + + + align:start position:0% +sampling box following followed by a +quantization + + align:start position:0% +quantization + + + align:start position:0% +quantization +box the first box the sampling box takes + + align:start position:0% +box the first box the sampling box takes + + + align:start position:0% +box the first box the sampling box takes +the CT signal of time and turns it into + + align:start position:0% +the CT signal of time and turns it into + + + align:start position:0% +the CT signal of time and turns it into +a DT signal the second box takes the + + align:start position:0% +a DT signal the second box takes the + + + align:start position:0% +a DT signal the second box takes the +samples which have a continuous domain + + align:start position:0% +samples which have a continuous domain + + + align:start position:0% +samples which have a continuous domain +and turn them into samples from a finite + + align:start position:0% +and turn them into samples from a finite + + + align:start position:0% +and turn them into samples from a finite +domain from a discret + + align:start position:0% +domain from a discret + + + align:start position:0% +domain from a discret +domain + + align:start position:0% +domain + + + align:start position:0% +domain +okay so if you're doing that kind of a + + align:start position:0% +okay so if you're doing that kind of a + + + align:start position:0% +okay so if you're doing that kind of a +quantization + + align:start position:0% +quantization + + + align:start position:0% +quantization +scheme then the thing you have to think + + align:start position:0% +scheme then the thing you have to think + + + align:start position:0% +scheme then the thing you have to think +about is how many bits you're willing to + + align:start position:0% +about is how many bits you're willing to + + + align:start position:0% +about is how many bits you're willing to +use to represent each sample I mean this + + align:start position:0% +use to represent each sample I mean this + + + align:start position:0% +use to represent each sample I mean this +is the simplest kind of a scheme that + + align:start position:0% +is the simplest kind of a scheme that + + + align:start position:0% +is the simplest kind of a scheme that +you could use there's much more + + align:start position:0% +you could use there's much more + + + align:start position:0% +you could use there's much more +complicated schemes by the end of the + + align:start position:0% +complicated schemes by the end of the + + + align:start position:0% +complicated schemes by the end of the +hour I'll tell you about a scheme that + + align:start position:0% +hour I'll tell you about a scheme that + + + align:start position:0% +hour I'll tell you about a scheme that +is uh much more efficient than this + + align:start position:0% +is uh much more efficient than this + + + align:start position:0% +is uh much more efficient than this +but this is kind of the base level this + + align:start position:0% +but this is kind of the base level this + + + align:start position:0% +but this is kind of the base level this +is where you would start so if you + + align:start position:0% +is where you would start so if you + + + align:start position:0% +is where you would start so if you +wanted to represent an amplitude in a + + align:start position:0% +wanted to represent an amplitude in a + + + align:start position:0% +wanted to represent an amplitude in a +discrete representation one way you + + align:start position:0% +discrete representation one way you + + + align:start position:0% +discrete representation one way you +could do about it one way you could + + align:start position:0% +could do about it one way you could + + + align:start position:0% +could do about it one way you could +think about it is to think about the map + + align:start position:0% +think about it is to think about the map + + + align:start position:0% +think about it is to think about the map +between the + + align:start position:0% +between the + + + align:start position:0% +between the +continuous values that the sample could + + align:start position:0% +continuous values that the sample could + + + align:start position:0% +continuous values that the sample could +uh + + align:start position:0% +uh + + + align:start position:0% +uh +acquire and map it to a discrete output + + align:start position:0% +acquire and map it to a discrete output + + + align:start position:0% +acquire and map it to a discrete output +set so for example if you were using a + + align:start position:0% +set so for example if you were using a + + + align:start position:0% +set so for example if you were using a +two bit if you were using two bits per + + align:start position:0% +two bit if you were using two bits per + + + align:start position:0% +two bit if you were using two bits per +sample then + + align:start position:0% +sample then + + + align:start position:0% +sample then +you might represent any voltage between + + align:start position:0% +you might represent any voltage between + + + align:start position:0% +you might represent any voltage between +minus a half and a half by some code + + align:start position:0% +minus a half and a half by some code + + + align:start position:0% +minus a half and a half by some code +01 any voltage that's in the range half + + align:start position:0% +01 any voltage that's in the range half + + + align:start position:0% +01 any voltage that's in the range half +to one as the code one Z and any voltage + + align:start position:0% +to one as the code one Z and any voltage + + + align:start position:0% +to one as the code one Z and any voltage +in the range minus one to minus a half + + align:start position:0% +in the range minus one to minus a half + + + align:start position:0% +in the range minus one to minus a half +as Z 0 that would be a way of taking a + + align:start position:0% +as Z 0 that would be a way of taking a + + + align:start position:0% +as Z 0 that would be a way of taking a +continuous range of possible amplitudes + + align:start position:0% +continuous range of possible amplitudes + + + align:start position:0% +continuous range of possible amplitudes +and turning it into a discrete number um + + align:start position:0% +and turning it into a discrete number um + + + align:start position:0% +and turning it into a discrete number um +using just two + + align:start position:0% +using just two + + + align:start position:0% +using just two +bits obviously if you use more bits you + + align:start position:0% +bits obviously if you use more bits you + + + align:start position:0% +bits obviously if you use more bits you +can get greater precision what's showed + + align:start position:0% +can get greater precision what's showed + + + align:start position:0% +can get greater precision what's showed +below here is what if my signal was a + + align:start position:0% +below here is what if my signal was a + + + align:start position:0% +below here is what if my signal was a +function of time looked like the red + + align:start position:0% +function of time looked like the red + + + align:start position:0% +function of time looked like the red +waveform my discrete representation + + align:start position:0% +waveform my discrete representation + + + align:start position:0% +waveform my discrete representation +might look like the blue waveform right + + align:start position:0% +might look like the blue waveform right + + + align:start position:0% +might look like the blue waveform right +if I'm imagining that I only have two + + align:start position:0% +if I'm imagining that I only have two + + + align:start position:0% +if I'm imagining that I only have two +bits then I only have three possible + + align:start position:0% +bits then I only have three possible + + + align:start position:0% +bits then I only have three possible +symmetric um outputs so that might be + + align:start position:0% +symmetric um outputs so that might be + + + align:start position:0% +symmetric um outputs so that might be +represented by the blue and the + + align:start position:0% +represented by the blue and the + + + align:start position:0% +represented by the blue and the +difference between the red and the blue + + align:start position:0% +difference between the red and the blue + + + align:start position:0% +difference between the red and the blue +is showed in the green and as you can + + align:start position:0% +is showed in the green and as you can + + + align:start position:0% +is showed in the green and as you can +see as you go to more bits you obviously + + align:start position:0% +see as you go to more bits you obviously + + + align:start position:0% +see as you go to more bits you obviously +get errors the green signal is it's + + align:start position:0% +get errors the green signal is it's + + + align:start position:0% +get errors the green signal is it's +getting smaller right so the key thing + + align:start position:0% +getting smaller right so the key thing + + + align:start position:0% +getting smaller right so the key thing +then is how many bits do you + + align:start position:0% +then is how many bits do you + + + align:start position:0% +then is how many bits do you +need for the thing that you're trying to + + align:start position:0% +need for the thing that you're trying to + + + align:start position:0% +need for the thing that you're trying to +represent so I like hearing right so + + align:start position:0% +represent so I like hearing right so + + + align:start position:0% +represent so I like hearing right so +I'll illustrate the number of bits by + + align:start position:0% +I'll illustrate the number of bits by + + + align:start position:0% +I'll illustrate the number of bits by +thinking about sound you can hear sounds + + align:start position:0% +thinking about sound you can hear sounds + + + align:start position:0% +thinking about sound you can hear sounds +that range in amplitude over a range of + + align:start position:0% +that range in amplitude over a range of + + + align:start position:0% +that range in amplitude over a range of +about a million to + + align:start position:0% +about a million to + + + align:start position:0% +about a million to +one so if you were to put put a a person + + align:start position:0% +one so if you were to put put a a person + + + align:start position:0% +one so if you were to put put a a person +with good ears not me one of you if you + + align:start position:0% +with good ears not me one of you if you + + + align:start position:0% +with good ears not me one of you if you +were to put one of you into a quiet room + + align:start position:0% +were to put one of you into a quiet room + + + align:start position:0% +were to put one of you into a quiet room +and let you sit there until you adapted + + align:start position:0% +and let you sit there until you adapted + + + align:start position:0% +and let you sit there until you adapted +and then played the faintest sound that + + align:start position:0% +and then played the faintest sound that + + + align:start position:0% +and then played the faintest sound that +you could possibly + + align:start position:0% +you could possibly + + + align:start position:0% +you could possibly +hear then uh uh multiply by 10 multiply + + align:start position:0% +hear then uh uh multiply by 10 multiply + + + align:start position:0% +hear then uh uh multiply by 10 multiply +by 10 multiply by 10 you could make it a + + align:start position:0% +by 10 multiply by 10 you could make it a + + + align:start position:0% +by 10 multiply by 10 you could make it a +million + + align:start position:0% +million + + + align:start position:0% +million +times uh more intense in pressure you + + align:start position:0% +times uh more intense in pressure you + + + align:start position:0% +times uh more intense in pressure you +could amplify the pressure by a million + + align:start position:0% +could amplify the pressure by a million + + + align:start position:0% +could amplify the pressure by a million +before it would start to hurt wouldn't + + align:start position:0% +before it would start to hurt wouldn't + + + align:start position:0% +before it would start to hurt wouldn't +damage yet you'd have to go to about oh + + align:start position:0% +damage yet you'd have to go to about oh + + + align:start position:0% +damage yet you'd have to go to about oh +8 million and then it would start to + + align:start position:0% +8 million and then it would start to + + + align:start position:0% +8 million and then it would start to +damage uh but you could do about a + + align:start position:0% +damage uh but you could do about a + + + align:start position:0% +damage uh but you could do about a +million to one over the range from just + + align:start position:0% +million to one over the range from just + + + align:start position:0% +million to one over the range from just +barely audible to starts to + + align:start position:0% +barely audible to starts to + + + align:start position:0% +barely audible to starts to +hurt so how many bits would it take to + + align:start position:0% +hurt so how many bits would it take to + + + align:start position:0% +hurt so how many bits would it take to +do that + + align:start position:0% + + + + align:start position:0% + +range + + align:start position:0% + + + + align:start position:0% + +so how many minutes would it take raise + + align:start position:0% +so how many minutes would it take raise + + + align:start position:0% +so how many minutes would it take raise +your hands show me a number of fingers + + align:start position:0% +your hands show me a number of fingers + + + align:start position:0% +your hands show me a number of fingers +how many bits would it take to represent + + align:start position:0% +how many bits would it take to represent + + + align:start position:0% +how many bits would it take to represent +a million to + + align:start position:0% +a million to + + + align:start position:0% +a million to +one okay 100% I think it's 100% so um + + align:start position:0% +one okay 100% I think it's 100% so um + + + align:start position:0% +one okay 100% I think it's 100% so um +easy question so if you use one bit you + + align:start position:0% +easy question so if you use one bit you + + + align:start position:0% +easy question so if you use one bit you +can represent two levels + + align:start position:0% +can represent two levels + + + align:start position:0% +can represent two levels +if you use two bits you can do four 8 16 + + align:start position:0% +if you use two bits you can do four 8 16 + + + align:start position:0% +if you use two bits you can do four 8 16 +32 by the time you get to 10 bits you're + + align:start position:0% +32 by the time you get to 10 bits you're + + + align:start position:0% +32 by the time you get to 10 bits you're +up to 1024 by the time you're up to 20 + + align:start position:0% +up to 1024 by the time you're up to 20 + + + align:start position:0% +up to 1024 by the time you're up to 20 +bits you're up to 1024 squared so 20 + + align:start position:0% +bits you're up to 1024 squared so 20 + + + align:start position:0% +bits you're up to 1024 squared so 20 +bits okay 20 bits ought to do + + align:start position:0% +bits okay 20 bits ought to do + + + align:start position:0% +bits okay 20 bits ought to do +it and in fact 20 bits uh if you were to + + align:start position:0% +it and in fact 20 bits uh if you were to + + + align:start position:0% +it and in fact 20 bits uh if you were to +buy a high-end audio system it would be + + align:start position:0% +buy a high-end audio system it would be + + + align:start position:0% +buy a high-end audio system it would be +24 bits there are people who claim you + + align:start position:0% +24 bits there are people who claim you + + + align:start position:0% +24 bits there are people who claim you +need 32 I think they're kind of crazy + + align:start position:0% +need 32 I think they're kind of crazy + + + align:start position:0% +need 32 I think they're kind of crazy +but a high-end audio system would would + + align:start position:0% +but a high-end audio system would would + + + align:start position:0% +but a high-end audio system would would +be a 24-bit system now if you were to + + align:start position:0% +be a 24-bit system now if you were to + + + align:start position:0% +be a 24-bit system now if you were to +listen to sort of CD quality CDs are + + align:start position:0% +listen to sort of CD quality CDs are + + + align:start position:0% +listen to sort of CD quality CDs are +16bits okay so there are people even me + + align:start position:0% +16bits okay so there are people even me + + + align:start position:0% +16bits okay so there are people even me +who claim that they can tell the + + align:start position:0% +who claim that they can tell the + + + align:start position:0% +who claim that they can tell the +difference between a concert and a CD + + align:start position:0% +difference between a concert and a CD + + + align:start position:0% +difference between a concert and a CD +representation of a concert okay so so + + align:start position:0% +representation of a concert okay so so + + + align:start position:0% +representation of a concert okay so so +there might be some limitations of + + align:start position:0% +there might be some limitations of + + + align:start position:0% +there might be some limitations of +representing audio with 16 bits but what + + align:start position:0% +representing audio with 16 bits but what + + + align:start position:0% +representing audio with 16 bits but what +I'll show you is a demo where I've + + align:start position:0% +I'll show you is a demo where I've + + + align:start position:0% +I'll show you is a demo where I've +showed the same piece of music at 16 + + align:start position:0% +showed the same piece of music at 16 + + + align:start position:0% +showed the same piece of music at 16 +bits 8 Bits 6 bits four bits two bits + + align:start position:0% +bits 8 Bits 6 bits four bits two bits + + + align:start position:0% +bits 8 Bits 6 bits four bits two bits +and one bit per sample so that you get + + align:start position:0% +and one bit per sample so that you get + + + align:start position:0% +and one bit per sample so that you get +the idea of what a quantization error + + align:start position:0% +the idea of what a quantization error + + + align:start position:0% +the idea of what a quantization error +sounds like + + align:start position:0% + + + + align:start position:0% + +yes it's the distribution right there's + + align:start position:0% +yes it's the distribution right there's + + + align:start position:0% +yes it's the distribution right there's +lots of things that are different and + + align:start position:0% +lots of things that are different and + + + align:start position:0% +lots of things that are different and +you're raising a very good point you + + align:start position:0% +you're raising a very good point you + + + align:start position:0% +you're raising a very good point you +certainly don't get the spatial aspects + + align:start position:0% +certainly don't get the spatial aspects + + + align:start position:0% +certainly don't get the spatial aspects +of a + + align:start position:0% +of a + + + align:start position:0% +of a +concert right we try to fake you out + + align:start position:0% +concert right we try to fake you out + + + align:start position:0% +concert right we try to fake you out +right we put false cues in so the violin + + align:start position:0% +right we put false cues in so the violin + + + align:start position:0% +right we put false cues in so the violin +sounds like it's on the right side right + + align:start position:0% +sounds like it's on the right side right + + + align:start position:0% +sounds like it's on the right side right +but those are all fake usually well + + align:start position:0% +but those are all fake usually well + + + align:start position:0% +but those are all fake usually well +they're not completely fake so um and we + + align:start position:0% +they're not completely fake so um and we + + + align:start position:0% +they're not completely fake so um and we +have stereo and we have 5 + one um yeah + + align:start position:0% +have stereo and we have 5 + one um yeah + + + align:start position:0% +have stereo and we have 5 + one um yeah +so we have lots of different + + align:start position:0% +so we have lots of different + + + align:start position:0% +so we have lots of different +representations but if you were to + + align:start position:0% +representations but if you were to + + + align:start position:0% +representations but if you were to +imagine listening in a concert + + align:start position:0% +imagine listening in a concert + + + align:start position:0% +imagine listening in a concert +monoral so plug your ear clamp your head + + align:start position:0% +monoral so plug your ear clamp your head + + + align:start position:0% +monoral so plug your ear clamp your head +so you can't turn and compare that to + + align:start position:0% +so you can't turn and compare that to + + + align:start position:0% +so you can't turn and compare that to +listening with a mono + + align:start position:0% +listening with a mono + + + align:start position:0% +listening with a mono +headphone that's what I'm talking about + + align:start position:0% +headphone that's what I'm talking about + + + align:start position:0% +headphone that's what I'm talking about +so if you didn't get spatial cues and + + align:start position:0% +so if you didn't get spatial cues and + + + align:start position:0% +so if you didn't get spatial cues and +things like + + align:start position:0% +things like + + + align:start position:0% +things like +that okay so the qu so the issue then is + + align:start position:0% +that okay so the qu so the issue then is + + + align:start position:0% +that okay so the qu so the issue then is +to to listen to different levels of + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +quantization + + align:start position:0% +quantization + + + align:start position:0% +quantization +[Music] + + align:start position:0% + + + + align:start position:0% + +so it's actually kind of amazing right + + align:start position:0% +so it's actually kind of amazing right + + + align:start position:0% +so it's actually kind of amazing right +you can you can sort of tell what the + + align:start position:0% +you can you can sort of tell what the + + + align:start position:0% +you can you can sort of tell what the +piece is the whole way down how many of + + align:start position:0% +piece is the whole way down how many of + + + align:start position:0% +piece is the whole way down how many of +you could tell the difference between 16 + + align:start position:0% +you could tell the difference between 16 + + + align:start position:0% +you could tell the difference between 16 +and + + align:start position:0% + + + + align:start position:0% + +eight how many of you could tell that + + align:start position:0% +eight how many of you could tell that + + + align:start position:0% +eight how many of you could tell that +difference between eight and + + align:start position:0% +difference between eight and + + + align:start position:0% +difference between eight and +six how many could you tell how many of + + align:start position:0% +six how many could you tell how many of + + + align:start position:0% +six how many could you tell how many of +you could tell any difference whatever + + align:start position:0% +you could tell any difference whatever + + + align:start position:0% +you could tell any difference whatever +just joking what's the s what's the + + align:start position:0% +just joking what's the s what's the + + + align:start position:0% +just joking what's the s what's the +difference in the sound + + align:start position:0% +difference in the sound + + + align:start position:0% +difference in the sound +quality what's the effect of + + align:start position:0% +quality what's the effect of + + + align:start position:0% +quality what's the effect of +quantizing kind of + + align:start position:0% +quantizing kind of + + + align:start position:0% +quantizing kind of +fuzzy uh so could you simulate the fuzzy + + align:start position:0% +fuzzy uh so could you simulate the fuzzy + + + align:start position:0% +fuzzy uh so could you simulate the fuzzy +sound what would you do if you wanted to + + align:start position:0% +sound what would you do if you wanted to + + + align:start position:0% +sound what would you do if you wanted to +sort of simulate the fuzzy + + align:start position:0% +sort of simulate the fuzzy + + + align:start position:0% +sort of simulate the fuzzy +sound besides of course quantizing which + + align:start position:0% +sound besides of course quantizing which + + + align:start position:0% +sound besides of course quantizing which +would be a perfect simulation but uh + + align:start position:0% + + + + align:start position:0% + +noise it kind of sounds + + align:start position:0% +noise it kind of sounds + + + align:start position:0% +noise it kind of sounds +hissy right it sounds kind of noisy and + + align:start position:0% +hissy right it sounds kind of noisy and + + + align:start position:0% +hissy right it sounds kind of noisy and +that's kind of the point so + + align:start position:0% +that's kind of the point so + + + align:start position:0% +that's kind of the point so +um and that's an important issue because + + align:start position:0% +um and that's an important issue because + + + align:start position:0% +um and that's an important issue because +it affects how much music you can put on + + align:start position:0% +it affects how much music you can put on + + + align:start position:0% +it affects how much music you can put on +any given medium so for example in a CD + + align:start position:0% +any given medium so for example in a CD + + + align:start position:0% +any given medium so for example in a CD +CDs are 16 bits per sample two channels + + align:start position:0% +CDs are 16 bits per sample two channels + + + align:start position:0% +CDs are 16 bits per sample two channels +44.1 kilos samples per second um 60 + + align:start position:0% +44.1 kilos samples per second um 60 + + + align:start position:0% +44.1 kilos samples per second um 60 +seconds per minute 74 minutes is a + + align:start position:0% +seconds per minute 74 minutes is a + + + align:start position:0% +seconds per minute 74 minutes is a +typical recording time for a CD + + align:start position:0% +typical recording time for a CD + + + align:start position:0% +typical recording time for a CD +uh so you end up with about a gigabyte + + align:start position:0% +uh so you end up with about a gigabyte + + + align:start position:0% +uh so you end up with about a gigabyte +and that's what you can put on one of + + align:start position:0% +and that's what you can put on one of + + + align:start position:0% +and that's what you can put on one of +those little plastic + + align:start position:0% +those little plastic + + + align:start position:0% +those little plastic +things if you were willing to live with + + align:start position:0% +things if you were willing to live with + + + align:start position:0% +things if you were willing to live with +8bit instead of + + align:start position:0% +8bit instead of + + + align:start position:0% +8bit instead of +16bit you could obviously put on 148 + + align:start position:0% +16bit you could obviously put on 148 + + + align:start position:0% +16bit you could obviously put on 148 +minutes right so people don't take these + + align:start position:0% +minutes right so people don't take these + + + align:start position:0% +minutes right so people don't take these +don't make these decisions lightly right + + align:start position:0% +don't make these decisions lightly right + + + align:start position:0% +don't make these decisions lightly right +yeah it's how many people do you make + + align:start position:0% +yeah it's how many people do you make + + + align:start position:0% +yeah it's how many people do you make +Angry for one reason or the other right + + align:start position:0% +Angry for one reason or the other right + + + align:start position:0% +Angry for one reason or the other right +you can make them angry because they + + align:start position:0% +you can make them angry because they + + + align:start position:0% +you can make them angry because they +don't get much music or you can make + + align:start position:0% +don't get much music or you can make + + + align:start position:0% +don't get much music or you can make +them angry because they don't get high + + align:start position:0% +them angry because they don't get high + + + align:start position:0% +them angry because they don't get high +quality right uh so you get to sort of + + align:start position:0% +quality right uh so you get to sort of + + + align:start position:0% +quality right uh so you get to sort of +trade off the kind of people who hate + + align:start position:0% +trade off the kind of people who hate + + + align:start position:0% +trade off the kind of people who hate +you so but that's the kind of idea right + + align:start position:0% +you so but that's the kind of idea right + + + align:start position:0% +you so but that's the kind of idea right +so if you have a piece of plastic on + + align:start position:0% +so if you have a piece of plastic on + + + align:start position:0% +so if you have a piece of plastic on +which you can put uh one + + align:start position:0% +which you can put uh one + + + align:start position:0% +which you can put uh one +gigabyte you have to think about how + + align:start position:0% +gigabyte you have to think about how + + + align:start position:0% +gigabyte you have to think about how +you're going to represent + + align:start position:0% +you're going to represent + + + align:start position:0% +you're going to represent +it and it matters how frequently you + + align:start position:0% +it and it matters how frequently you + + + align:start position:0% +it and it matters how frequently you +sample and also with what quantization + + align:start position:0% +sample and also with what quantization + + + align:start position:0% +sample and also with what quantization +you um represent each sample same sort + + align:start position:0% +you um represent each sample same sort + + + align:start position:0% +you um represent each sample same sort +of thing happens for pictures here's a + + align:start position:0% +of thing happens for pictures here's a + + + align:start position:0% +of thing happens for pictures here's a +relatively highquality + + align:start position:0% +relatively highquality + + + align:start position:0% +relatively highquality +picture uh where it's sample it's 280 x + + align:start position:0% +picture uh where it's sample it's 280 x + + + align:start position:0% +picture uh where it's sample it's 280 x +280 uh pixels and it's an 8 bit + + align:start position:0% +280 uh pixels and it's an 8 bit + + + align:start position:0% +280 uh pixels and it's an 8 bit +representation in amplitude the point's + + align:start position:0% +representation in amplitude the point's + + + align:start position:0% +representation in amplitude the point's +just that the kinds of things that + + align:start position:0% +just that the kinds of things that + + + align:start position:0% +just that the kinds of things that +happen when you quantize a picture are + + align:start position:0% +happen when you quantize a picture are + + + align:start position:0% +happen when you quantize a picture are +very similar to the same sorts of things + + align:start position:0% +very similar to the same sorts of things + + + align:start position:0% +very similar to the same sorts of things +that happen when you quantized audio so + + align:start position:0% +that happen when you quantized audio so + + + align:start position:0% +that happen when you quantized audio so +if we take this picture and compare it + + align:start position:0% +if we take this picture and compare it + + + align:start position:0% +if we take this picture and compare it +to substitute for each pixel a quantized + + align:start position:0% +to substitute for each pixel a quantized + + + align:start position:0% +to substitute for each pixel a quantized +version of the amplitud + + align:start position:0% +version of the amplitud + + + align:start position:0% +version of the amplitud +quantize here to 8 Bits And here to + + align:start position:0% +quantize here to 8 Bits And here to + + + align:start position:0% +quantize here to 8 Bits And here to +seven + + align:start position:0% +seven + + + align:start position:0% +seven +bits okay you might be able to see the + + align:start position:0% +bits okay you might be able to see the + + + align:start position:0% +bits okay you might be able to see the +difference if I come up really close I + + align:start position:0% +difference if I come up really close I + + + align:start position:0% +difference if I come up really close I +can certainly see quantization + + align:start position:0% +can certainly see quantization + + + align:start position:0% +can certainly see quantization +effects if I drop the right one to + + align:start position:0% +effects if I drop the right one to + + + align:start position:0% +effects if I drop the right one to +six + + align:start position:0% +six + + + align:start position:0% +six +five + + align:start position:0% +five + + + align:start position:0% +five + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + + align:start position:0% + +two one + + align:start position:0% +two one + + + align:start position:0% +two one +okay so the so here's eight bits and + + align:start position:0% +okay so the so here's eight bits and + + + align:start position:0% +okay so the so here's eight bits and +four bits remember that when we thought + + align:start position:0% +four bits remember that when we thought + + + align:start position:0% +four bits remember that when we thought +about the audio example it sounded fuzzy + + align:start position:0% +about the audio example it sounded fuzzy + + + align:start position:0% +about the audio example it sounded fuzzy +it sounded + + align:start position:0% +it sounded + + + align:start position:0% +it sounded +hissy what's the effect of quantizing + + align:start position:0% +hissy what's the effect of quantizing + + + align:start position:0% +hissy what's the effect of quantizing +here + + align:start position:0% + + + + align:start position:0% + +yeah sharp and cont say + + align:start position:0% +yeah sharp and cont say + + + align:start position:0% +yeah sharp and cont say +again well there's certainly a problem + + align:start position:0% +again well there's certainly a problem + + + align:start position:0% +again well there's certainly a problem +so both of these pictures have high + + align:start position:0% +so both of these pictures have high + + + align:start position:0% +so both of these pictures have high +contrast right how would I see contrast + + align:start position:0% +contrast right how would I see contrast + + + align:start position:0% +contrast right how would I see contrast +in the pictures + + align:start position:0% +in the pictures + + + align:start position:0% +in the pictures +right contrast refers to having big + + align:start position:0% +right contrast refers to having big + + + align:start position:0% +right contrast refers to having big +Steps step changes in brightness so like + + align:start position:0% +Steps step changes in brightness so like + + + align:start position:0% +Steps step changes in brightness so like +I might see a high contrast between this + + align:start position:0% +I might see a high contrast between this + + + align:start position:0% +I might see a high contrast between this +petal and that leaf right and and I + + align:start position:0% +petal and that leaf right and and I + + + align:start position:0% +petal and that leaf right and and I +still have a a high contrast at the + + align:start position:0% +still have a a high contrast at the + + + align:start position:0% +still have a a high contrast at the +analogous place over here so there is + + align:start position:0% +analogous place over here so there is + + + align:start position:0% +analogous place over here so there is +some contrast + + align:start position:0% +some contrast + + + align:start position:0% +some contrast +effects a little more subtly the + + align:start position:0% +effects a little more subtly the + + + align:start position:0% +effects a little more subtly the +contrast affects how well you see the + + align:start position:0% +contrast affects how well you see the + + + align:start position:0% +contrast affects how well you see the +quantization so if I changed the picture + + align:start position:0% +quantization so if I changed the picture + + + align:start position:0% +quantization so if I changed the picture +to have different amounts of contrast I + + align:start position:0% +to have different amounts of contrast I + + + align:start position:0% +to have different amounts of contrast I +could affect whether whether you could + + align:start position:0% +could affect whether whether you could + + + align:start position:0% +could affect whether whether you could +see the + + align:start position:0% +see the + + + align:start position:0% +see the +quantization uh well or + + align:start position:0% +quantization uh well or + + + align:start position:0% +quantization uh well or +poorly what so in audio the effect of + + align:start position:0% +poorly what so in audio the effect of + + + align:start position:0% +poorly what so in audio the effect of +quantizing as I quantized more and more + + align:start position:0% +quantizing as I quantized more and more + + + align:start position:0% +quantizing as I quantized more and more +and more I caused more and more hiss in + + align:start position:0% +and more I caused more and more hiss in + + + align:start position:0% +and more I caused more and more hiss in +the background what's the effect here + + align:start position:0% +the background what's the effect here + + + align:start position:0% +the background what's the effect here +what's the effect of quantitizing + + align:start position:0% +what's the effect of quantitizing + + + align:start position:0% +what's the effect of quantitizing +out I have fewer + + align:start position:0% + + + + align:start position:0% + +Grays absolutely could you give me sort + + align:start position:0% +Grays absolutely could you give me sort + + + align:start position:0% +Grays absolutely could you give me sort +of a qu qualitative assessment of the + + align:start position:0% +of a qu qualitative assessment of the + + + align:start position:0% +of a qu qualitative assessment of the +kinds of errors that you see here + + align:start position:0% +kinds of errors that you see here + + + align:start position:0% +kinds of errors that you see here +compared to the kinds of errors that you + + align:start position:0% +compared to the kinds of errors that you + + + align:start position:0% +compared to the kinds of errors that you +don't see there yeah there's banding why + + align:start position:0% +don't see there yeah there's banding why + + + align:start position:0% +don't see there yeah there's banding why +would there be banding nobody said the + + align:start position:0% +would there be banding nobody said the + + + align:start position:0% +would there be banding nobody said the +audio sounded like it was banded right + + align:start position:0% +audio sounded like it was banded right + + + align:start position:0% +audio sounded like it was banded right +that we just don't hear that way right + + align:start position:0% +that we just don't hear that way right + + + align:start position:0% +that we just don't hear that way right +what even though we're doing a similar + + align:start position:0% +what even though we're doing a similar + + + align:start position:0% +what even though we're doing a similar +process why do we see banding in + + align:start position:0% +process why do we see banding in + + + align:start position:0% +process why do we see banding in +pictures what's the what's causing the + + align:start position:0% +pictures what's the what's causing the + + + align:start position:0% +pictures what's the what's causing the +banding + + align:start position:0% + + + + align:start position:0% + +yeah yeah exactly so the pixels that are + + align:start position:0% +yeah yeah exactly so the pixels that are + + + align:start position:0% +yeah yeah exactly so the pixels that are +nearby so take the pixels here which + + align:start position:0% +nearby so take the pixels here which + + + align:start position:0% +nearby so take the pixels here which +came from pixels over here they have + + align:start position:0% +came from pixels over here they have + + + align:start position:0% +came from pixels over here they have +nearly the same gray value but the + + align:start position:0% +nearly the same gray value but the + + + align:start position:0% +nearly the same gray value but the +quantizer is making up its mind in a in + + align:start position:0% +quantizer is making up its mind in a in + + + align:start position:0% +quantizer is making up its mind in a in +a very precise um at a very precise + + align:start position:0% +a very precise um at a very precise + + + align:start position:0% +a very precise um at a very precise +level it's deciding oh you're between + + align:start position:0% +level it's deciding oh you're between + + + align:start position:0% +level it's deciding oh you're between +these two levels turn into this number + + align:start position:0% +these two levels turn into this number + + + align:start position:0% +these two levels turn into this number +if you're between these two levels turn + + align:start position:0% +if you're between these two levels turn + + + align:start position:0% +if you're between these two levels turn +into this other number so you get the + + align:start position:0% +into this other number so you get the + + + align:start position:0% +into this other number so you get the +bands because there's correlations in + + align:start position:0% +bands because there's correlations in + + + align:start position:0% +bands because there's correlations in +the brightnesses of pixels that are + + align:start position:0% +the brightnesses of pixels that are + + + align:start position:0% +the brightnesses of pixels that are +nearby right so you get this banding + + align:start position:0% +nearby right so you get this banding + + + align:start position:0% +nearby right so you get this banding +thing that can be objectionable whenever + + align:start position:0% +thing that can be objectionable whenever + + + align:start position:0% +thing that can be objectionable whenever +the quantization is not sufficient + + align:start position:0% +the quantization is not sufficient + + + align:start position:0% +the quantization is not sufficient +okay so one way you can reduce that is + + align:start position:0% +okay so one way you can reduce that is + + + align:start position:0% +okay so one way you can reduce that is +called + + align:start position:0% +called + + + align:start position:0% +called +dithering dithering means add noise + + align:start position:0% +dithering dithering means add noise + + + align:start position:0% +dithering dithering means add noise +that's kind of weird so I want to get + + align:start position:0% +that's kind of weird so I want to get + + + align:start position:0% +that's kind of weird so I want to get +rid of the Bands so what do I do I take + + align:start position:0% +rid of the Bands so what do I do I take + + + align:start position:0% +rid of the Bands so what do I do I take +every + + align:start position:0% +every + + + align:start position:0% +every +pixel and before I quantize it I add + + align:start position:0% +pixel and before I quantize it I add + + + align:start position:0% +pixel and before I quantize it I add +noise to it then even if the pixel came + + align:start position:0% +noise to it then even if the pixel came + + + align:start position:0% +noise to it then even if the pixel came +from a region that were nearly the same + + align:start position:0% +from a region that were nearly the same + + + align:start position:0% +from a region that were nearly the same +U amplitude to start with each + + align:start position:0% +U amplitude to start with each + + + align:start position:0% +U amplitude to start with each +individual pixel gets a different amount + + align:start position:0% +individual pixel gets a different amount + + + align:start position:0% +individual pixel gets a different amount +of noise so they quantize + + align:start position:0% +of noise so they quantize + + + align:start position:0% +of noise so they quantize +differently right and if I choose my + + align:start position:0% +differently right and if I choose my + + + align:start position:0% +differently right and if I choose my +noise in a clever way I could choose my + + align:start position:0% +noise in a clever way I could choose my + + + align:start position:0% +noise in a clever way I could choose my +noise to be plus or minus one Quantum so + + align:start position:0% +noise to be plus or minus one Quantum so + + + align:start position:0% +noise to be plus or minus one Quantum so +I could choose a random number generator + + align:start position:0% +I could choose a random number generator + + + align:start position:0% +I could choose a random number generator +that gave me numbers that were evenly + + align:start position:0% +that gave me numbers that were evenly + + + align:start position:0% +that gave me numbers that were evenly +distributed over the range minus one2 + + align:start position:0% +distributed over the range minus one2 + + + align:start position:0% +distributed over the range minus one2 +Quantum to plus 1 Quantum and if I do + + align:start position:0% +Quantum to plus 1 Quantum and if I do + + + align:start position:0% +Quantum to plus 1 Quantum and if I do +that then I can generate a picture that + + align:start position:0% +that then I can generate a picture that + + + align:start position:0% +that then I can generate a picture that +is quantized but was dithered before it + + align:start position:0% +is quantized but was dithered before it + + + align:start position:0% +is quantized but was dithered before it +was quantized okay so the two pictures + + align:start position:0% +was quantized okay so the two pictures + + + align:start position:0% +was quantized okay so the two pictures +are both quantized at the level of seven + + align:start position:0% +are both quantized at the level of seven + + + align:start position:0% +are both quantized at the level of seven +bits but the one on the right had + + align:start position:0% +bits but the one on the right had + + + align:start position:0% +bits but the one on the right had +thether added to it first so I'm adding + + align:start position:0% +thether added to it first so I'm adding + + + align:start position:0% +thether added to it first so I'm adding +noise before I do the quantization and + + align:start position:0% +noise before I do the quantization and + + + align:start position:0% +noise before I do the quantization and +you can't see too much it's seven six + + align:start position:0% +you can't see too much it's seven six + + + align:start position:0% +you can't see too much it's seven six + + align:start position:0% + + + align:start position:0% + + align:start position:0% + + + + align:start position:0% + +three okay so what's the difference + + align:start position:0% +three okay so what's the difference + + + align:start position:0% +three okay so what's the difference +between the two well over here I had + + align:start position:0% +between the two well over here I had + + + align:start position:0% +between the two well over here I had +these + + align:start position:0% +these + + + align:start position:0% +these +bands because the amplitudes were such + + align:start position:0% +bands because the amplitudes were such + + + align:start position:0% +bands because the amplitudes were such +that they all got converted into the + + align:start position:0% +that they all got converted into the + + + align:start position:0% +that they all got converted into the +same output the bands have disappeared + + align:start position:0% +same output the bands have disappeared + + + align:start position:0% +same output the bands have disappeared +over there + + align:start position:0% +over there + + + align:start position:0% +over there +right + + align:start position:0% +right + + + align:start position:0% +right +to even one the bands have disappeared + + align:start position:0% +to even one the bands have disappeared + + + align:start position:0% +to even one the bands have disappeared +right but that's obviously not a good + + align:start position:0% +right but that's obviously not a good + + + align:start position:0% +right but that's obviously not a good +solution so what's wrong with with + + align:start position:0% + + + + align:start position:0% + +dither noisy yeah I'm kind of going back + + align:start position:0% +dither noisy yeah I'm kind of going back + + + align:start position:0% +dither noisy yeah I'm kind of going back +to the his thing right now I've taken a + + align:start position:0% +to the his thing right now I've taken a + + + align:start position:0% +to the his thing right now I've taken a +picture that had had bands and I've + + align:start position:0% +picture that had had bands and I've + + + align:start position:0% +picture that had had bands and I've +turned it into a picture that looks + + align:start position:0% +turned it into a picture that looks + + + align:start position:0% +turned it into a picture that looks +noisy um there's a way to think about + + align:start position:0% +noisy um there's a way to think about + + + align:start position:0% +noisy um there's a way to think about +how the noise Works imagine that I had a + + align:start position:0% +how the noise Works imagine that I had a + + + align:start position:0% +how the noise Works imagine that I had a +smoothly varying signal showed in blue + + align:start position:0% +smoothly varying signal showed in blue + + + align:start position:0% +smoothly varying signal showed in blue +that was being turned from a a from from + + align:start position:0% +that was being turned from a a from from + + + align:start position:0% +that was being turned from a a from from +a continuous range of amplitudes into a + + align:start position:0% +a continuous range of amplitudes into a + + + align:start position:0% +a continuous range of amplitudes into a +discret range of amplitudes so let's + + align:start position:0% +discret range of amplitudes so let's + + + align:start position:0% +discret range of amplitudes so let's +represent the discret amplitudes by the + + align:start position:0% +represent the discret amplitudes by the + + + align:start position:0% +represent the discret amplitudes by the +dashed red lines then the signal that I + + align:start position:0% +dashed red lines then the signal that I + + + align:start position:0% +dashed red lines then the signal that I +might quantize could look like the red + + align:start position:0% +might quantize could look like the red + + + align:start position:0% +might quantize could look like the red +signal and that's a very graphic + + align:start position:0% +signal and that's a very graphic + + + align:start position:0% +signal and that's a very graphic +representation of where the bands come + + align:start position:0% +representation of where the bands come + + + align:start position:0% +representation of where the bands come +from right so the bands come from the + + align:start position:0% +from right so the bands come from the + + + align:start position:0% +from right so the bands come from the +fact that the original signal sliced + + align:start position:0% +fact that the original signal sliced + + + align:start position:0% +fact that the original signal sliced +through a small number of uh quantized + + align:start position:0% +through a small number of uh quantized + + + align:start position:0% +through a small number of uh quantized +outputs okay everybody see where the + + align:start position:0% +outputs okay everybody see where the + + + align:start position:0% +outputs okay everybody see where the +bands + + align:start position:0% +bands + + + align:start position:0% +bands +are then if I add uh dither I can think + + align:start position:0% +are then if I add uh dither I can think + + + align:start position:0% +are then if I add uh dither I can think +about so so this transformation from + + align:start position:0% +about so so this transformation from + + + align:start position:0% +about so so this transformation from +Blue to Red I can think of that about + + align:start position:0% +Blue to Red I can think of that about + + + align:start position:0% +Blue to Red I can think of that about +that as being y q of X so X is the Blue + + align:start position:0% +that as being y q of X so X is the Blue + + + align:start position:0% +that as being y q of X so X is the Blue +Line Q of X is the red + + align:start position:0% +Line Q of X is the red + + + align:start position:0% +Line Q of X is the red +line down here what I've done is I've + + align:start position:0% +line down here what I've done is I've + + + align:start position:0% +line down here what I've done is I've +taken X and added noise to it then I ran + + align:start position:0% +taken X and added noise to it then I ran + + + align:start position:0% +taken X and added noise to it then I ran +it through the same + + align:start position:0% +it through the same + + + align:start position:0% +it through the same +quantizer and you can see that I've + + align:start position:0% +quantizer and you can see that I've + + + align:start position:0% +quantizer and you can see that I've +broken up the bands but you can see that + + align:start position:0% +broken up the bands but you can see that + + + align:start position:0% +broken up the bands but you can see that +I've added a bunch of noise + + align:start position:0% +I've added a bunch of noise + + + align:start position:0% +I've added a bunch of noise +so there's a slightly more clever thing + + align:start position:0% +so there's a slightly more clever thing + + + align:start position:0% +so there's a slightly more clever thing +that we can do that's called Roberts + + align:start position:0% +that we can do that's called Roberts + + + align:start position:0% +that we can do that's called Roberts +techniques Larry Roberts was a master's + + align:start position:0% +techniques Larry Roberts was a master's + + + align:start position:0% +techniques Larry Roberts was a master's +student here uh he was here before I was + + align:start position:0% +student here uh he was here before I was + + + align:start position:0% +student here uh he was here before I was +here which you know is kind of a + + align:start position:0% +here which you know is kind of a + + + align:start position:0% +here which you know is kind of a +remarkable thing but uh they actually + + align:start position:0% +remarkable thing but uh they actually + + + align:start position:0% +remarkable thing but uh they actually +wrote thesis back then and they used + + align:start position:0% +wrote thesis back then and they used + + + align:start position:0% +wrote thesis back then and they used +paper and you can go to the library and + + align:start position:0% +paper and you can go to the library and + + + align:start position:0% +paper and you can go to the library and +it's still there um and so uh Larry + + align:start position:0% +it's still there um and so uh Larry + + + align:start position:0% +it's still there um and so uh Larry +thought of a method for dealing with + + align:start position:0% +thought of a method for dealing with + + + align:start position:0% +thought of a method for dealing with +this where what you do is + + align:start position:0% +this where what you do is + + + align:start position:0% +this where what you do is +you you take the original signal X you + + align:start position:0% +you you take the original signal X you + + + align:start position:0% +you you take the original signal X you +add n to it and quantize it but then you + + align:start position:0% +add n to it and quantize it but then you + + + align:start position:0% +add n to it and quantize it but then you +subtract n back + + align:start position:0% + + + + align:start position:0% + +off and that's called Roberts technique + + align:start position:0% +off and that's called Roberts technique + + + align:start position:0% +off and that's called Roberts technique +and that's illustrated by this + + align:start position:0% +and that's illustrated by this + + + align:start position:0% +and that's illustrated by this +transformation the good thing about this + + align:start position:0% +transformation the good thing about this + + + align:start position:0% +transformation the good thing about this +transformation is that this so here the + + align:start position:0% +transformation is that this so here the + + + align:start position:0% +transformation is that this so here the +quantization the quantization error was + + align:start position:0% +quantization the quantization error was + + + align:start position:0% +quantization the quantization error was +clearly correlated with the + + align:start position:0% +clearly correlated with the + + + align:start position:0% +clearly correlated with the +signal that's what banding is right + + align:start position:0% +signal that's what banding is right + + + align:start position:0% +signal that's what banding is right +something about the signal turned into + + align:start position:0% +something about the signal turned into + + + align:start position:0% +something about the signal turned into +something about the + + align:start position:0% +something about the + + + align:start position:0% +something about the +error + + align:start position:0% +error + + + align:start position:0% +error +here the error is still correlated with + + align:start position:0% +here the error is still correlated with + + + align:start position:0% +here the error is still correlated with +the + + align:start position:0% +the + + + align:start position:0% +the +signal the correlation is less obvious + + align:start position:0% +signal the correlation is less obvious + + + align:start position:0% +signal the correlation is less obvious +right but here's a range of errors that + + align:start position:0% +right but here's a range of errors that + + + align:start position:0% +right but here's a range of errors that +are all + + align:start position:0% +are all + + + align:start position:0% +are all +positive and here's a range of errors + + align:start position:0% +positive and here's a range of errors + + + align:start position:0% +positive and here's a range of errors +that are all + + align:start position:0% +that are all + + + align:start position:0% +that are all +negative so the errors are still + + align:start position:0% +negative so the errors are still + + + align:start position:0% +negative so the errors are still +correlated with the original + + align:start position:0% +correlated with the original + + + align:start position:0% +correlated with the original +signal so the result and when you do + + align:start position:0% +signal so the result and when you do + + + align:start position:0% +signal so the result and when you do +Robert's technique you destroy the + + align:start position:0% +Robert's technique you destroy the + + + align:start position:0% +Robert's technique you destroy the +correlation so with Robert's technique + + align:start position:0% +correlation so with Robert's technique + + + align:start position:0% +correlation so with Robert's technique +you end up with it's still noisy because + + align:start position:0% +you end up with it's still noisy because + + + align:start position:0% +you end up with it's still noisy because +after all I added noise to it but I've + + align:start position:0% +after all I added noise to it but I've + + + align:start position:0% +after all I added noise to it but I've +added it in a very clever way that + + align:start position:0% +added it in a very clever way that + + + align:start position:0% +added it in a very clever way that +removes the correlation between the + + align:start position:0% +removes the correlation between the + + + align:start position:0% +removes the correlation between the +error and the signal and the result is + + align:start position:0% +error and the signal and the result is + + + align:start position:0% +error and the signal and the result is +that the noise uh seems less so if you + + align:start position:0% +that the noise uh seems less so if you + + + align:start position:0% +that the noise uh seems less so if you +compare six bits with dither to six bits + + align:start position:0% +compare six bits with dither to six bits + + + align:start position:0% +compare six bits with dither to six bits +with Robert's method both pictures are + + align:start position:0% +with Robert's method both pictures are + + + align:start position:0% +with Robert's method both pictures are +represented by six + + align:start position:0% +represented by six + + + align:start position:0% +represented by six +bits five bits five bits four three + + align:start position:0% + + + + align:start position:0% + +so the interesting thing is that the + + align:start position:0% +so the interesting thing is that the + + + align:start position:0% +so the interesting thing is that the +Roberts method looks like less noise + + align:start position:0% +Roberts method looks like less noise + + + align:start position:0% +Roberts method looks like less noise +it's mathematically not mathematically + + align:start position:0% +it's mathematically not mathematically + + + align:start position:0% +it's mathematically not mathematically +you can show that Robert's technique has + + align:start position:0% +you can show that Robert's technique has + + + align:start position:0% +you can show that Robert's technique has +the same energy in the noise as was in + + align:start position:0% +the same energy in the noise as was in + + + align:start position:0% +the same energy in the noise as was in +the dither technique if you just + + align:start position:0% +the dither technique if you just + + + align:start position:0% +the dither technique if you just +calculate the error in the energy in the + + align:start position:0% +calculate the error in the energy in the + + + align:start position:0% +calculate the error in the energy in the +error they're identical but in Robert's + + align:start position:0% +error they're identical but in Robert's + + + align:start position:0% +error they're identical but in Robert's +technique he destroys the correlation + + align:start position:0% +technique he destroys the correlation + + + align:start position:0% +technique he destroys the correlation +and that makes the noise seem smaller + + align:start position:0% +and that makes the noise seem smaller + + + align:start position:0% +and that makes the noise seem smaller +it's psychophysically less + + align:start position:0% + + + + align:start position:0% + +objectionable what's the problem with + + align:start position:0% +objectionable what's the problem with + + + align:start position:0% +objectionable what's the problem with +Robert's + + align:start position:0% + + + + align:start position:0% + +technique if I told you to implement a + + align:start position:0% +technique if I told you to implement a + + + align:start position:0% +technique if I told you to implement a +scheme that + + align:start position:0% +scheme that + + + align:start position:0% +scheme that +um quantized according to Robert's + + align:start position:0% +um quantized according to Robert's + + + align:start position:0% +um quantized according to Robert's +technique and say you're here and you're + + align:start position:0% +technique and say you're here and you're + + + align:start position:0% +technique and say you're here and you're +supposed to quantize a message send it + + align:start position:0% +supposed to quantize a message send it + + + align:start position:0% +supposed to quantize a message send it +over the ethernet and receive it in + + align:start position:0% +over the ethernet and receive it in + + + align:start position:0% +over the ethernet and receive it in +California and you're only supposed to + + align:start position:0% +California and you're only supposed to + + + align:start position:0% +California and you're only supposed to +be sending say a six-bit representation + + align:start position:0% +be sending say a six-bit representation + + + align:start position:0% +be sending say a six-bit representation +instead of a 16bit representation what's + + align:start position:0% +instead of a 16bit representation what's + + + align:start position:0% +instead of a 16bit representation what's +hard about Robert's technique compared + + align:start position:0% +hard about Robert's technique compared + + + align:start position:0% +hard about Robert's technique compared +to dither quantizing is easy right I + + align:start position:0% +to dither quantizing is easy right I + + + align:start position:0% +to dither quantizing is easy right I +take my 16bit + + align:start position:0% +take my 16bit + + + align:start position:0% +take my 16bit +CD I take off the first sample I + + align:start position:0% +CD I take off the first sample I + + + align:start position:0% +CD I take off the first sample I +quantize it I send it across the + + align:start position:0% +quantize it I send it across the + + + align:start position:0% +quantize it I send it across the +internet I take off my second sample I + + align:start position:0% +internet I take off my second sample I + + + align:start position:0% +internet I take off my second sample I +quantize it I send those six bits over + + align:start position:0% +quantize it I send those six bits over + + + align:start position:0% +quantize it I send those six bits over +the Internet Etc dither is sort of the + + align:start position:0% +the Internet Etc dither is sort of the + + + align:start position:0% +the Internet Etc dither is sort of the +same thing I pick up the first sample I + + align:start position:0% +same thing I pick up the first sample I + + + align:start position:0% +same thing I pick up the first sample I +add noise to it I quantize it I send + + align:start position:0% +add noise to it I quantize it I send + + + align:start position:0% +add noise to it I quantize it I send +those 6 six bits over the internet + + align:start position:0% +those 6 six bits over the internet + + + align:start position:0% +those 6 six bits over the internet +what's the hard part of + + align:start position:0% + + + + align:start position:0% + +Roberts + + align:start position:0% +Roberts + + + align:start position:0% +Roberts +yeah you send the noise to I have to + + align:start position:0% +yeah you send the noise to I have to + + + align:start position:0% +yeah you send the noise to I have to +send the noise + + align:start position:0% +send the noise + + + align:start position:0% +send the noise +too I have to know the precise value of + + align:start position:0% +too I have to know the precise value of + + + align:start position:0% +too I have to know the precise value of +the + + align:start position:0% +the + + + align:start position:0% +the +noise that I added a sample n so I can + + align:start position:0% +noise that I added a sample n so I can + + + align:start position:0% +noise that I added a sample n so I can +St subtract it back + + align:start position:0% +St subtract it back + + + align:start position:0% +St subtract it back +out so Robert's technique says I take + + align:start position:0% +out so Robert's technique says I take + + + align:start position:0% +out so Robert's technique says I take +this the value X and I add some amount + + align:start position:0% +this the value X and I add some amount + + + align:start position:0% +this the value X and I add some amount +of noise n n was random number I chose + + align:start position:0% +of noise n n was random number I chose + + + align:start position:0% +of noise n n was random number I chose +it by throwing a die or something I + + align:start position:0% +it by throwing a die or something I + + + align:start position:0% +it by throwing a die or something I +quantize that and then I subtract that + + align:start position:0% +quantize that and then I subtract that + + + align:start position:0% +quantize that and then I subtract that +same number back out well that number + + align:start position:0% +same number back out well that number + + + align:start position:0% +same number back out well that number +has to be precise compared to the + + align:start position:0% +has to be precise compared to the + + + align:start position:0% +has to be precise compared to the +quantization levels so for example + + align:start position:0% +quantization levels so for example + + + align:start position:0% +quantization levels so for example +people would normally use if I'm doing + + align:start position:0% +people would normally use if I'm doing + + + align:start position:0% +people would normally use if I'm doing +16-bit audio people would normally use a + + align:start position:0% +16-bit audio people would normally use a + + + align:start position:0% +16-bit audio people would normally use a +16bit representation for + + align:start position:0% +16bit representation for + + + align:start position:0% +16bit representation for +n which means that I take a 16-bit + + align:start position:0% +n which means that I take a 16-bit + + + align:start position:0% +n which means that I take a 16-bit +number off the + + align:start position:0% +number off the + + + align:start position:0% +number off the +CD I take a random number I add it + + align:start position:0% +CD I take a random number I add it + + + align:start position:0% +CD I take a random number I add it +quantize it and now I can send the sixth + + align:start position:0% +quantize it and now I can send the sixth + + + align:start position:0% +quantize it and now I can send the sixth +bit number but in order for that guy to + + align:start position:0% +bit number but in order for that guy to + + + align:start position:0% +bit number but in order for that guy to +reproduce the answer he has to know n + + align:start position:0% + + + + align:start position:0% + +to everybody see + + align:start position:0% +to everybody see + + + align:start position:0% +to everybody see +that so the problem is how do you send + + align:start position:0% +that so the problem is how do you send + + + align:start position:0% +that so the problem is how do you send +the noise and the trick is that we use + + align:start position:0% +the noise and the trick is that we use + + + align:start position:0% +the noise and the trick is that we use +something called pseudo random noise + + align:start position:0% +something called pseudo random noise + + + align:start position:0% +something called pseudo random noise +pseudo random noise is an algorithm that + + align:start position:0% +pseudo random noise is an algorithm that + + + align:start position:0% +pseudo random noise is an algorithm that +generates a sequence of numbers that + + align:start position:0% +generates a sequence of numbers that + + + align:start position:0% +generates a sequence of numbers that +looks + + align:start position:0% +looks + + + align:start position:0% +looks +random but they were made + + align:start position:0% +random but they were made + + + align:start position:0% +random but they were made +algorithmically so you can independently + + align:start position:0% +algorithmically so you can independently + + + align:start position:0% +algorithmically so you can independently +manufacture the same sequence here and + + align:start position:0% +manufacture the same sequence here and + + + align:start position:0% +manufacture the same sequence here and +there + + align:start position:0% +there + + + align:start position:0% +there +that way if you're using the same if you + + align:start position:0% +that way if you're using the same if you + + + align:start position:0% +that way if you're using the same if you +pre- agree that you're going to use the + + align:start position:0% +pre- agree that you're going to use the + + + align:start position:0% +pre- agree that you're going to use the +same + + align:start position:0% +same + + + align:start position:0% +same +algorithm you can independently generate + + align:start position:0% +algorithm you can independently generate + + + align:start position:0% +algorithm you can independently generate +the same sequence of + + align:start position:0% +the same sequence of + + + align:start position:0% +the same sequence of +ends + + align:start position:0% +ends + + + align:start position:0% +ends +okay okay so + + align:start position:0% +okay okay so + + + align:start position:0% +okay okay so +uh yeah so I jump back to + + align:start position:0% + + + + align:start position:0% + +explain okay so the point is that you + + align:start position:0% +explain okay so the point is that you + + + align:start position:0% +explain okay so the point is that you +can + + align:start position:0% +can + + + align:start position:0% +can +um just like in audio in pictures it's + + align:start position:0% +um just like in audio in pictures it's + + + align:start position:0% +um just like in audio in pictures it's +important how many uh uh bits you ties + + align:start position:0% +important how many uh uh bits you ties + + + align:start position:0% +important how many uh uh bits you ties +to that affects drastically the + + align:start position:0% +to that affects drastically the + + + align:start position:0% +to that affects drastically the +performance of uh Communications or + + align:start position:0% +performance of uh Communications or + + + align:start position:0% +performance of uh Communications or +storage devices how many pictures can + + align:start position:0% +storage devices how many pictures can + + + align:start position:0% +storage devices how many pictures can +you store someplace how many pictures + + align:start position:0% +you store someplace how many pictures + + + align:start position:0% +you store someplace how many pictures +can you put on your iPhone so all of + + align:start position:0% +can you put on your iPhone so all of + + + align:start position:0% +can you put on your iPhone so all of +that matters quite a bit and the code + + align:start position:0% +that matters quite a bit and the code + + + align:start position:0% +that matters quite a bit and the code +that you use is very + + align:start position:0% + + + + align:start position:0% + +important and you're not limited to just + + align:start position:0% +important and you're not limited to just + + + align:start position:0% +important and you're not limited to just +so I have two more examples one of them + + align:start position:0% +so I have two more examples one of them + + + align:start position:0% +so I have two more examples one of them +um so the the simplest possible schemes + + align:start position:0% +um so the the simplest possible schemes + + + align:start position:0% +um so the the simplest possible schemes +are the ones that I've showed so far + + align:start position:0% +are the ones that I've showed so far + + + align:start position:0% +are the ones that I've showed so far +where you think about the uh + + align:start position:0% +where you think about the uh + + + align:start position:0% +where you think about the uh +sampling in time and the quantization in + + align:start position:0% +sampling in time and the quantization in + + + align:start position:0% +sampling in time and the quantization in +amplitude as separate + + align:start position:0% +amplitude as separate + + + align:start position:0% +amplitude as separate +processes you don't have to do that in + + align:start position:0% +processes you don't have to do that in + + + align:start position:0% +processes you don't have to do that in +fact you can get much higher performance + + align:start position:0% +fact you can get much higher performance + + + align:start position:0% +fact you can get much higher performance +if you combine the two so the first + + align:start position:0% +if you combine the two so the first + + + align:start position:0% +if you combine the two so the first +combination I want to think about is uh + + align:start position:0% +combination I want to think about is uh + + + align:start position:0% +combination I want to think about is uh +trading off uh Precision for Speed and + + align:start position:0% +trading off uh Precision for Speed and + + + align:start position:0% +trading off uh Precision for Speed and +that's something that we call + + align:start position:0% +that's something that we call + + + align:start position:0% +that's something that we call +Progressive refinement the idea is + + align:start position:0% +Progressive refinement the idea is + + + align:start position:0% +Progressive refinement the idea is +imagine that I want to make a digital + + align:start position:0% +imagine that I want to make a digital + + + align:start position:0% +imagine that I want to make a digital +representation of all the paintings in + + align:start position:0% +representation of all the paintings in + + + align:start position:0% +representation of all the paintings in +the + + align:start position:0% +the + + + align:start position:0% +the +L okay doesn't make sense to do uh you + + align:start position:0% +L okay doesn't make sense to do uh you + + + align:start position:0% +L okay doesn't make sense to do uh you +know uh 200x 200 at 6bit resolution if + + align:start position:0% +know uh 200x 200 at 6bit resolution if + + + align:start position:0% +know uh 200x 200 at 6bit resolution if +you're looking at pictures in the Loof + + align:start position:0% +you're looking at pictures in the Loof + + + align:start position:0% +you're looking at pictures in the Loof +that doesn't make any sense right you + + align:start position:0% +that doesn't make any sense right you + + + align:start position:0% +that doesn't make any sense right you +would like to see a high resolution + + align:start position:0% +would like to see a high resolution + + + align:start position:0% +would like to see a high resolution +version okay and now you're a user and + + align:start position:0% +version okay and now you're a user and + + + align:start position:0% +version okay and now you're a user and +what you'd like to do is leave through + + align:start position:0% +what you'd like to do is leave through + + + align:start position:0% +what you'd like to do is leave through +them and find uh photos of something or + + align:start position:0% +them and find uh photos of something or + + + align:start position:0% +them and find uh photos of something or +other scenes of some type okay well if + + align:start position:0% +other scenes of some type okay well if + + + align:start position:0% +other scenes of some type okay well if +you've got a high resolution + + align:start position:0% +you've got a high resolution + + + align:start position:0% +you've got a high resolution +representation and you're trying to + + align:start position:0% +representation and you're trying to + + + align:start position:0% +representation and you're trying to +thumb through a lot of images the + + align:start position:0% +thumb through a lot of images the + + + align:start position:0% +thumb through a lot of images the +problem is if each one's represented + + align:start position:0% +problem is if each one's represented + + + align:start position:0% +problem is if each one's represented +with high resolution that can take a + + align:start position:0% +with high resolution that can take a + + + align:start position:0% +with high resolution that can take a +long time so if you didn't do something + + align:start position:0% +long time so if you didn't do something + + + align:start position:0% +long time so if you didn't do something +clever basically you would have to + + align:start position:0% +clever basically you would have to + + + align:start position:0% +clever basically you would have to +download the + + align:start position:0% +download the + + + align:start position:0% +download the +Lou before you could do your search so + + align:start position:0% +Lou before you could do your search so + + + align:start position:0% +Lou before you could do your search so +the idea in Progressive refinement is + + align:start position:0% +the idea in Progressive refinement is + + + align:start position:0% +the idea in Progressive refinement is +first send me a crude + + align:start position:0% +first send me a crude + + + align:start position:0% +first send me a crude +representation and if I haven't uh + + align:start position:0% +representation and if I haven't uh + + + align:start position:0% +representation and if I haven't uh +changed my browser if I'm still looking + + align:start position:0% +changed my browser if I'm still looking + + + align:start position:0% +changed my browser if I'm still looking +at the same picture three seconds later + + align:start position:0% +at the same picture three seconds later + + + align:start position:0% +at the same picture three seconds later +continue to load information that makes + + align:start position:0% +continue to load information that makes + + + align:start position:0% +continue to load information that makes +the picture increasingly precise give me + + align:start position:0% +the picture increasingly precise give me + + + align:start position:0% +the picture increasingly precise give me +a crude representation as soon as you + + align:start position:0% +a crude representation as soon as you + + + align:start position:0% +a crude representation as soon as you +can and then if I sit there give me a + + align:start position:0% +can and then if I sit there give me a + + + align:start position:0% +can and then if I sit there give me a +more and more refined representation but + + align:start position:0% +more and more refined representation but + + + align:start position:0% +more and more refined representation but +if I leave to someplace else stop + + align:start position:0% +if I leave to someplace else stop + + + align:start position:0% +if I leave to someplace else stop +downloading that one and give me a crude + + align:start position:0% +downloading that one and give me a crude + + + align:start position:0% +downloading that one and give me a crude +representation of the new place that's + + align:start position:0% +representation of the new place that's + + + align:start position:0% +representation of the new place that's +the idea so the way you can do that is + + align:start position:0% +the idea so the way you can do that is + + + align:start position:0% +the idea so the way you can do that is +with discrete + + align:start position:0% +with discrete + + + align:start position:0% +with discrete +sampling okay I started with a digital + + align:start position:0% +sampling okay I started with a digital + + + align:start position:0% +sampling okay I started with a digital +representation of a painting in the Lou + + align:start position:0% +representation of a painting in the Lou + + + align:start position:0% +representation of a painting in the Lou +maybe it was 20,000 by 20,000 with 24 + + align:start position:0% +maybe it was 20,000 by 20,000 with 24 + + + align:start position:0% +maybe it was 20,000 by 20,000 with 24 +levels of + + align:start position:0% +levels of + + + align:start position:0% +levels of +color so you know some huge picture so + + align:start position:0% +color so you know some huge picture so + + + align:start position:0% +color so you know some huge picture so +what I'll do is I'll sample it but this + + align:start position:0% +what I'll do is I'll sample it but this + + + align:start position:0% +what I'll do is I'll sample it but this +time it's DT sampling DT sampling you'll + + align:start position:0% +time it's DT sampling DT sampling you'll + + + align:start position:0% +time it's DT sampling DT sampling you'll +be completely shocked to hear this is + + align:start position:0% +be completely shocked to hear this is + + + align:start position:0% +be completely shocked to hear this is +completely analogous to CT sampling it's + + align:start position:0% +completely analogous to CT sampling it's + + + align:start position:0% +completely analogous to CT sampling it's +almost the same thing that shouldn't be + + align:start position:0% +almost the same thing that shouldn't be + + + align:start position:0% +almost the same thing that shouldn't be +too much that shouldn't be too big of a + + align:start position:0% +too much that shouldn't be too big of a + + + align:start position:0% +too much that shouldn't be too big of a +surprise all the different transforms + + align:start position:0% +surprise all the different transforms + + + align:start position:0% +surprise all the different transforms +all the different freier representations + + align:start position:0% +all the different freier representations + + + align:start position:0% +all the different freier representations +that we looked at are almost the same + + align:start position:0% +that we looked at are almost the same + + + align:start position:0% +that we looked at are almost the same +thing so d sampling turns out to work + + align:start position:0% +thing so d sampling turns out to work + + + align:start position:0% +thing so d sampling turns out to work +almost exactly like CT sampling so think + + align:start position:0% +almost exactly like CT sampling so think + + + align:start position:0% +almost exactly like CT sampling so think +about what you would do if you wanted to + + align:start position:0% +about what you would do if you wanted to + + + align:start position:0% +about what you would do if you wanted to +take a + + align:start position:0% +take a + + + align:start position:0% +take a +picture and represent it with a factor + + align:start position:0% +picture and represent it with a factor + + + align:start position:0% +picture and represent it with a factor +of three fewer pixels in the horizontal + + align:start position:0% +of three fewer pixels in the horizontal + + + align:start position:0% +of three fewer pixels in the horizontal +and a factor of three few hor pixels in + + align:start position:0% +and a factor of three few hor pixels in + + + align:start position:0% +and a factor of three few hor pixels in +the vertical well you would sample it in + + align:start position:0% +the vertical well you would sample it in + + + align:start position:0% +the vertical well you would sample it in +CT we would think about multiplying the + + align:start position:0% +CT we would think about multiplying the + + + align:start position:0% +CT we would think about multiplying the +CT signal X of T by an Impulse train + + align:start position:0% +CT signal X of T by an Impulse train + + + align:start position:0% +CT signal X of T by an Impulse train +here we use a unit sample train + + align:start position:0% +here we use a unit sample train + + + align:start position:0% +here we use a unit sample train +so we think about an original signal X + + align:start position:0% +so we think about an original signal X + + + align:start position:0% +so we think about an original signal X +of N and we think about a sampling + + align:start position:0% +of N and we think about a sampling + + + align:start position:0% +of N and we think about a sampling +waveform that's now a an + + align:start position:0% +waveform that's now a an + + + align:start position:0% +waveform that's now a an +infinite unit sample train we used to + + align:start position:0% +infinite unit sample train we used to + + + align:start position:0% +infinite unit sample train we used to +use an infinite impulse train now we're + + align:start position:0% +use an infinite impulse train now we're + + + align:start position:0% +use an infinite impulse train now we're +using an infinite unit sample train so + + align:start position:0% +using an infinite unit sample train so + + + align:start position:0% +using an infinite unit sample train so +we preserve every third sample and throw + + align:start position:0% +we preserve every third sample and throw + + + align:start position:0% +we preserve every third sample and throw +away the ones + + align:start position:0% +away the ones + + + align:start position:0% +away the ones +between so that's a way of generating a + + align:start position:0% +between so that's a way of generating a + + + align:start position:0% +between so that's a way of generating a +new + + align:start position:0% +new + + + align:start position:0% +new +picture that only has onethird of the + + align:start position:0% +picture that only has onethird of the + + + align:start position:0% +picture that only has onethird of the +information that was in the original + + align:start position:0% +information that was in the original + + + align:start position:0% +information that was in the original +picture and as I said before it should + + align:start position:0% +picture and as I said before it should + + + align:start position:0% +picture and as I said before it should +come as no surprise that the math for + + align:start position:0% +come as no surprise that the math for + + + align:start position:0% +come as no surprise that the math for +thinking about this sampling process is + + align:start position:0% +thinking about this sampling process is + + + align:start position:0% +thinking about this sampling process is +virtually identical to the math that you + + align:start position:0% +virtually identical to the math that you + + + align:start position:0% +virtually identical to the math that you +need to think about the CT sampling + + align:start position:0% +need to think about the CT sampling + + + align:start position:0% +need to think about the CT sampling +problem in particular the key is to + + align:start position:0% +problem in particular the key is to + + + align:start position:0% +problem in particular the key is to +think about the frea + + align:start position:0% +think about the frea + + + align:start position:0% +think about the frea +representation if this were the original + + align:start position:0% +representation if this were the original + + + align:start position:0% +representation if this were the original +4A + + align:start position:0% +4A + + + align:start position:0% +4A +signal this if this were the 4A + + align:start position:0% +signal this if this were the 4A + + + align:start position:0% +signal this if this were the 4A +representation of this + + align:start position:0% +representation of this + + + align:start position:0% +representation of this +signal we have to think about the 4A + + align:start position:0% +signal we have to think about the 4A + + + align:start position:0% +signal we have to think about the 4A +representation for the sampling signal + + align:start position:0% +representation for the sampling signal + + + align:start position:0% +representation for the sampling signal +the + + align:start position:0% +the + + + align:start position:0% +the +infinite unit sample + + align:start position:0% +infinite unit sample + + + align:start position:0% +infinite unit sample +train an infinite unit sample train not + + align:start position:0% +train an infinite unit sample train not + + + align:start position:0% +train an infinite unit sample train not +surprisingly the Transformer that's + + align:start position:0% +surprisingly the Transformer that's + + + align:start position:0% +surprisingly the Transformer that's +going to be an infinite impulse + + align:start position:0% +going to be an infinite impulse + + + align:start position:0% +going to be an infinite impulse +train okay all DT signals are periodic + + align:start position:0% +train okay all DT signals are periodic + + + align:start position:0% +train okay all DT signals are periodic +in 2 pi that's a property of DT signals + + align:start position:0% +in 2 pi that's a property of DT signals + + + align:start position:0% +in 2 pi that's a property of DT signals +that's a property of the unit circle + + align:start position:0% +that's a property of the unit circle + + + align:start position:0% +that's a property of the unit circle +right so we're not surprised to see that + + align:start position:0% +right so we're not surprised to see that + + + align:start position:0% +right so we're not surprised to see that +this signal was periodic in 2 pi this + + align:start position:0% +this signal was periodic in 2 pi this + + + align:start position:0% +this signal was periodic in 2 pi this +signal is also periodic in 2 pi that's + + align:start position:0% +signal is also periodic in 2 pi that's + + + align:start position:0% +signal is also periodic in 2 pi that's +because it's DT but it's also periodic + + align:start position:0% +because it's DT but it's also periodic + + + align:start position:0% +because it's DT but it's also periodic +in 1/3 of + + align:start position:0% +in 1/3 of + + + align:start position:0% +in 1/3 of +that that's + + align:start position:0% +that that's + + + align:start position:0% +that that's +because uh of the periodicity + + align:start position:0% +because uh of the periodicity + + + align:start position:0% +because uh of the periodicity +here okay so if we had had a + + align:start position:0% +here okay so if we had had a + + + align:start position:0% +here okay so if we had had a +sample at each one of these then it the + + align:start position:0% +sample at each one of these then it the + + + align:start position:0% +sample at each one of these then it the +base periodicity would have been 2 + + align:start position:0% +base periodicity would have been 2 + + + align:start position:0% +base periodicity would have been 2 +pi but here because of the + + align:start position:0% +pi but here because of the + + + align:start position:0% +pi but here because of the +periodicity being one at every third + + align:start position:0% +periodicity being one at every third + + + align:start position:0% +periodicity being one at every third +sample we get three times that many + + align:start position:0% +sample we get three times that many + + + align:start position:0% +sample we get three times that many +impulses so just like in in CT sampling + + align:start position:0% +impulses so just like in in CT sampling + + + align:start position:0% +impulses so just like in in CT sampling +we multip we think about multiplying the + + align:start position:0% +we multip we think about multiplying the + + + align:start position:0% +we multip we think about multiplying the +original waveform by a sampling waveform + + align:start position:0% +original waveform by a sampling waveform + + + align:start position:0% +original waveform by a sampling waveform +that preserves only the information at + + align:start position:0% +that preserves only the information at + + + align:start position:0% +that preserves only the information at +the samples we do the same thing here + + align:start position:0% +the samples we do the same thing here + + + align:start position:0% +the samples we do the same thing here +multiplication in time is convolution in + + align:start position:0% +multiplication in time is convolution in + + + align:start position:0% +multiplication in time is convolution in +frequency so we take the original signal + + align:start position:0% +frequency so we take the original signal + + + align:start position:0% +frequency so we take the original signal +we convolve it and this is what comes + + align:start position:0% +we convolve it and this is what comes + + + align:start position:0% +we convolve it and this is what comes +out of that sampling + + align:start position:0% +out of that sampling + + + align:start position:0% +out of that sampling +process we get the same + + align:start position:0% +process we get the same + + + align:start position:0% +process we get the same +rule for the sampling theorem that we + + align:start position:0% +rule for the sampling theorem that we + + + align:start position:0% +rule for the sampling theorem that we +got for + + align:start position:0% +got for + + + align:start position:0% +got for +CT + + align:start position:0% +CT + + + align:start position:0% +CT +this process has to be such that when + + align:start position:0% +this process has to be such that when + + + align:start position:0% +this process has to be such that when +you do the convolution the resulting + + align:start position:0% +you do the convolution the resulting + + + align:start position:0% +you do the convolution the resulting +nearest neighbors shouldn't + + align:start position:0% +nearest neighbors shouldn't + + + align:start position:0% +nearest neighbors shouldn't +overlap so there's a maximum frequency + + align:start position:0% +overlap so there's a maximum frequency + + + align:start position:0% +overlap so there's a maximum frequency +for the discrete system just like there + + align:start position:0% +for the discrete system just like there + + + align:start position:0% +for the discrete system just like there +was a maximum frequency for the CT + + align:start position:0% + + + + align:start position:0% + +system there's one more step I obviously + + align:start position:0% +system there's one more step I obviously + + + align:start position:0% +system there's one more step I obviously +if I sample the picture at the Lou I + + align:start position:0% +if I sample the picture at the Lou I + + + align:start position:0% +if I sample the picture at the Lou I +don't want to send the zeros that + + align:start position:0% +don't want to send the zeros that + + + align:start position:0% +don't want to send the zeros that +doesn't make any + + align:start position:0% +doesn't make any + + + align:start position:0% +doesn't make any +sense so in order to not send the zeros + + align:start position:0% +sense so in order to not send the zeros + + + align:start position:0% +sense so in order to not send the zeros +I smash + + align:start position:0% +I smash + + + align:start position:0% +I smash +together the nonzero samples that's + + align:start position:0% +together the nonzero samples that's + + + align:start position:0% +together the nonzero samples that's +Illustrated + + align:start position:0% +Illustrated + + + align:start position:0% +Illustrated +here smashing in time does what in + + align:start position:0% + + + + align:start position:0% + +frequency squish in + + align:start position:0% + + + + align:start position:0% + +Time Stretch in frequency they're + + align:start position:0% +Time Stretch in frequency they're + + + align:start position:0% +Time Stretch in frequency they're +reciprocal spaces right frequency and + + align:start position:0% +reciprocal spaces right frequency and + + + align:start position:0% +reciprocal spaces right frequency and +time are reciprocal spaces Smash in Time + + align:start position:0% +time are reciprocal spaces Smash in Time + + + align:start position:0% +time are reciprocal spaces Smash in Time +Stretch in frequency so the result is + + align:start position:0% +Stretch in frequency so the result is + + + align:start position:0% +Stretch in frequency so the result is +that when you + + align:start position:0% +that when you + + + align:start position:0% +that when you +um smash the zero entries out of the + + align:start position:0% +um smash the zero entries out of the + + + align:start position:0% +um smash the zero entries out of the +signal you stretch the frequency + + align:start position:0% +signal you stretch the frequency + + + align:start position:0% +signal you stretch the frequency +representation by a factor of three and + + align:start position:0% +representation by a factor of three and + + + align:start position:0% +representation by a factor of three and +when you stretch by a factor of three + + align:start position:0% +when you stretch by a factor of three + + + align:start position:0% +when you stretch by a factor of three +this peak which was at 1/3 of 2 pi moves + + align:start position:0% +this peak which was at 1/3 of 2 pi moves + + + align:start position:0% +this peak which was at 1/3 of 2 pi moves +the whole way out to 2 + + align:start position:0% +the whole way out to 2 + + + align:start position:0% +the whole way out to 2 +pi okay so the idea then is that I've + + align:start position:0% +pi okay so the idea then is that I've + + + align:start position:0% +pi okay so the idea then is that I've +got this beautiful picture in the + + align:start position:0% +got this beautiful picture in the + + + align:start position:0% +got this beautiful picture in the +Lou + + align:start position:0% +Lou + + + align:start position:0% +Lou +maybe uh and what I want to do in in + + align:start position:0% +maybe uh and what I want to do in in + + + align:start position:0% +maybe uh and what I want to do in in +order to send a lower resolution version + + align:start position:0% +order to send a lower resolution version + + + align:start position:0% +order to send a lower resolution version +of that what I do is I low pass filter + + align:start position:0% +of that what I do is I low pass filter + + + align:start position:0% +of that what I do is I low pass filter +it because I don't want the frequencies + + align:start position:0% +it because I don't want the frequencies + + + align:start position:0% +it because I don't want the frequencies +to + + align:start position:0% +to + + + align:start position:0% +to +Alias so I low pass filter it that gives + + align:start position:0% +Alias so I low pass filter it that gives + + + align:start position:0% +Alias so I low pass filter it that gives +me a a + + align:start position:0% +me a a + + + align:start position:0% +me a a +representation that I can then down + + align:start position:0% +representation that I can then down + + + align:start position:0% +representation that I can then down +sample okay so this had the same + + align:start position:0% +sample okay so this had the same + + + align:start position:0% +sample okay so this had the same +size but this one has fewer high + + align:start position:0% +size but this one has fewer high + + + align:start position:0% +size but this one has fewer high +frequency components so I can down + + align:start position:0% +frequency components so I can down + + + align:start position:0% +frequency components so I can down +sample which gives me something that can + + align:start position:0% +sample which gives me something that can + + + align:start position:0% +sample which gives me something that can +be represented in the squeezed version + + align:start position:0% +be represented in the squeezed version + + + align:start position:0% +be represented in the squeezed version +with fewer pixels I did a down sample by + + align:start position:0% +with fewer pixels I did a down sample by + + + align:start position:0% +with fewer pixels I did a down sample by +a factor of two in both so that picture + + align:start position:0% +a factor of two in both so that picture + + + align:start position:0% +a factor of two in both so that picture +has 1/4th the number of pixels in + + align:start position:0% +has 1/4th the number of pixels in + + + align:start position:0% +has 1/4th the number of pixels in +it then I can uh low pass filter that + + align:start position:0% +it then I can uh low pass filter that + + + align:start position:0% +it then I can uh low pass filter that +one and uh down sample and low pass + + align:start position:0% +one and uh down sample and low pass + + + align:start position:0% +one and uh down sample and low pass +filter that one and down sample and I + + align:start position:0% +filter that one and down sample and I + + + align:start position:0% +filter that one and down sample and I +end up with a very low resolution image + + align:start position:0% +end up with a very low resolution image + + + align:start position:0% +end up with a very low resolution image +of this um beautiful scene uh that I + + align:start position:0% +of this um beautiful scene uh that I + + + align:start position:0% +of this um beautiful scene uh that I +started with okay so that means + + align:start position:0% +started with okay so that means + + + align:start position:0% +started with okay so that means +that uh I so I start with some number of + + align:start position:0% +that uh I so I start with some number of + + + align:start position:0% +that uh I so I start with some number of +pixels here I have 1/4 as many here I + + align:start position:0% +pixels here I have 1/4 as many here I + + + align:start position:0% +pixels here I have 1/4 as many here I +have 1/4 of that and here I have 1/4 of + + align:start position:0% +have 1/4 of that and here I have 1/4 of + + + align:start position:0% +have 1/4 of that and here I have 1/4 of +that so I have a fourth cubed the + + align:start position:0% +that so I have a fourth cubed the + + + align:start position:0% +that so I have a fourth cubed the +original number of pictures so it'll go + + align:start position:0% +original number of pictures so it'll go + + + align:start position:0% +original number of pictures so it'll go +four cubed faster so it'll take me a lot + + align:start position:0% +four cubed faster so it'll take me a lot + + + align:start position:0% +four cubed faster so it'll take me a lot +less time to get the low res picture so + + align:start position:0% +less time to get the low res picture so + + + align:start position:0% +less time to get the low res picture so +the result then + + align:start position:0% +the result then + + + align:start position:0% +the result then +um skip this for the moment so here's my + + align:start position:0% +um skip this for the moment so here's my + + + align:start position:0% +um skip this for the moment so here's my +low reses + + align:start position:0% +low reses + + + align:start position:0% +low reses +picture with a lot of imagination + + align:start position:0% +picture with a lot of imagination + + + align:start position:0% +picture with a lot of imagination +you can clearly see what that is + + align:start position:0% +you can clearly see what that is + + + align:start position:0% +you can clearly see what that is +right at the next level of refinement + + align:start position:0% +right at the next level of refinement + + + align:start position:0% +right at the next level of refinement +you get this at the next level of + + align:start position:0% +you get this at the next level of + + + align:start position:0% +you get this at the next level of +refinement you get this at the next + + align:start position:0% +refinement you get this at the next + + + align:start position:0% +refinement you get this at the next +level of refinement you get this by now + + align:start position:0% +level of refinement you get this by now + + + align:start position:0% +level of refinement you get this by now +you're tired so you flick on something + + align:start position:0% +you're tired so you flick on something + + + align:start position:0% +you're tired so you flick on something +more interesting no no no you would + + align:start position:0% +more interesting no no no you would + + + align:start position:0% +more interesting no no no you would +continue to look at this right and + + align:start position:0% +continue to look at this right and + + + align:start position:0% +continue to look at this right and +finally you get the original picture so + + align:start position:0% +finally you get the original picture so + + + align:start position:0% +finally you get the original picture so +the idea then is that I want to not only + + align:start position:0% +the idea then is that I want to not only + + + align:start position:0% +the idea then is that I want to not only +transmit but then question is how many + + align:start position:0% +transmit but then question is how many + + + align:start position:0% +transmit but then question is how many +bits do I need to do + + align:start position:0% +bits do I need to do + + + align:start position:0% +bits do I need to do +this right and the answer is is + + align:start position:0% +this right and the answer is is + + + align:start position:0% +this right and the answer is is +that having transmitted this I can use + + align:start position:0% +that having transmitted this I can use + + + align:start position:0% +that having transmitted this I can use +that information to help me generate + + align:start position:0% + + + + align:start position:0% + +this okay so what I + + align:start position:0% +this okay so what I + + + align:start position:0% +this okay so what I +do I run the process + + align:start position:0% +do I run the process + + + align:start position:0% +do I run the process +backwards um let me back + + align:start position:0% +backwards um let me back + + + align:start position:0% +backwards um let me back +up so in order to go forwards I thought + + align:start position:0% +up so in order to go forwards I thought + + + align:start position:0% +up so in order to go forwards I thought +about uh squishing this into a smaller + + align:start position:0% +about uh squishing this into a smaller + + + align:start position:0% +about uh squishing this into a smaller +representation well I can go backwards I + + align:start position:0% +representation well I can go backwards I + + + align:start position:0% +representation well I can go backwards I +can upsample + + align:start position:0% +can upsample + + + align:start position:0% +can upsample +when I upsample all I do is I take all + + align:start position:0% +when I upsample all I do is I take all + + + align:start position:0% +when I upsample all I do is I take all +the pictures in the shrunken verion I + + align:start position:0% +the pictures in the shrunken verion I + + + align:start position:0% +the pictures in the shrunken verion I +stretch them and I put zeros between + + align:start position:0% +stretch them and I put zeros between + + + align:start position:0% +stretch them and I put zeros between +them that gets me + + align:start position:0% +them that gets me + + + align:start position:0% +them that gets me +here but that's not where I want to be I + + align:start position:0% +here but that's not where I want to be I + + + align:start position:0% +here but that's not where I want to be I +want to be up here so how do I go from + + align:start position:0% +want to be up here so how do I go from + + + align:start position:0% +want to be up here so how do I go from +here to + + align:start position:0% +here to + + + align:start position:0% +here to +here so when I put the zeros in it so I + + align:start position:0% +here so when I put the zeros in it so I + + + align:start position:0% +here so when I put the zeros in it so I +started with this I put the zeros in it + + align:start position:0% +started with this I put the zeros in it + + + align:start position:0% +started with this I put the zeros in it +that stretched it in time that + + align:start position:0% +that stretched it in time that + + + align:start position:0% +that stretched it in time that +compressed it in frequency when I + + align:start position:0% +compressed it in frequency when I + + + align:start position:0% +compressed it in frequency when I +compressed this wave form in the + + align:start position:0% +compressed this wave form in the + + + align:start position:0% +compressed this wave form in the +frequency this two Pi Peak ended up at 2 + + align:start position:0% +frequency this two Pi Peak ended up at 2 + + + align:start position:0% +frequency this two Pi Peak ended up at 2 +pi over 3 + + align:start position:0% +pi over 3 + + + align:start position:0% +pi over 3 +so now if I want to get back the + + align:start position:0% +so now if I want to get back the + + + align:start position:0% +so now if I want to get back the +original contribution I have to low pass + + align:start position:0% +original contribution I have to low pass + + + align:start position:0% +original contribution I have to low pass +filter okay everybody see what I'm + + align:start position:0% +filter okay everybody see what I'm + + + align:start position:0% +filter okay everybody see what I'm +doing so the so the final scheme then is + + align:start position:0% +doing so the so the final scheme then is + + + align:start position:0% +doing so the so the final scheme then is +that um + + align:start position:0% +that um + + + align:start position:0% +that um +whoops the final scheme is that I low + + align:start position:0% +whoops the final scheme is that I low + + + align:start position:0% +whoops the final scheme is that I low +pass filter down sample low pass down + + align:start position:0% +pass filter down sample low pass down + + + align:start position:0% +pass filter down sample low pass down +sample low pass down sample down sample + + align:start position:0% +sample low pass down sample down sample + + + align:start position:0% +sample low pass down sample down sample +I can + + align:start position:0% +I can + + + align:start position:0% +I can +upsample by putting zeros between all + + align:start position:0% +upsample by putting zeros between all + + + align:start position:0% +upsample by putting zeros between all +the rows and columns then low pass + + align:start position:0% +the rows and columns then low pass + + + align:start position:0% +the rows and columns then low pass +filter and that gives me this picture so + + align:start position:0% +filter and that gives me this picture so + + + align:start position:0% +filter and that gives me this picture so +what I need to do is also transmit the + + align:start position:0% +what I need to do is also transmit the + + + align:start position:0% +what I need to do is also transmit the +highpass information that I threw + + align:start position:0% +highpass information that I threw + + + align:start position:0% +highpass information that I threw +away so if I separately transmit this + + align:start position:0% +away so if I separately transmit this + + + align:start position:0% +away so if I separately transmit this +picture and the highpass part of this + + align:start position:0% +picture and the highpass part of this + + + align:start position:0% +picture and the highpass part of this +picture then I can combine them to get + + align:start position:0% +picture then I can combine them to get + + + align:start position:0% +picture then I can combine them to get +that + + align:start position:0% +that + + + align:start position:0% +that +picture right and I don't actually need + + align:start position:0% +picture right and I don't actually need + + + align:start position:0% +picture right and I don't actually need +to transmit this + + align:start position:0% +to transmit this + + + align:start position:0% +to transmit this +one so I don't need to transmit this one + + align:start position:0% +one so I don't need to transmit this one + + + align:start position:0% +one so I don't need to transmit this one +either because I can generate so I only + + align:start position:0% +either because I can generate so I only + + + align:start position:0% +either because I can generate so I only +need to send this and + + align:start position:0% +need to send this and + + + align:start position:0% +need to send this and +this then I do the same thing here if I + + align:start position:0% +this then I do the same thing here if I + + + align:start position:0% +this then I do the same thing here if I +take this I put zeros between it low + + align:start position:0% +take this I put zeros between it low + + + align:start position:0% +take this I put zeros between it low +pass filter I can generate this picture + + align:start position:0% +pass filter I can generate this picture + + + align:start position:0% +pass filter I can generate this picture +so I don't need to send + + align:start position:0% +so I don't need to send + + + align:start position:0% +so I don't need to send +it but I do send + + align:start position:0% +it but I do send + + + align:start position:0% +it but I do send +this then I combine these to get that uh + + align:start position:0% +this then I combine these to get that uh + + + align:start position:0% +this then I combine these to get that uh +recurse okay so the result is that I + + align:start position:0% +recurse okay so the result is that I + + + align:start position:0% +recurse okay so the result is that I +send so I don't send + + align:start position:0% +send so I don't send + + + align:start position:0% +send so I don't send +this but I do send this I don't send + + align:start position:0% +this but I do send this I don't send + + + align:start position:0% +this but I do send this I don't send +that because I'm going to regenerate + + align:start position:0% +that because I'm going to regenerate + + + align:start position:0% +that because I'm going to regenerate +it I don't send that I do send this I + + align:start position:0% +it I don't send that I do send this I + + + align:start position:0% +it I don't send that I do send this I +only send this this this and that and + + align:start position:0% +only send this this this and that and + + + align:start position:0% +only send this this this and that and +that's enough + + align:start position:0% +that's enough + + + align:start position:0% +that's enough +to reconstruct the picture right and + + align:start position:0% +to reconstruct the picture right and + + + align:start position:0% +to reconstruct the picture right and +notice it has the hierarchy that you + + align:start position:0% +notice it has the hierarchy that you + + + align:start position:0% +notice it has the hierarchy that you +would expect you can you start with a + + align:start position:0% +would expect you can you start with a + + + align:start position:0% +would expect you can you start with a +low res it takes more bits to make this + + align:start position:0% +low res it takes more bits to make this + + + align:start position:0% +low res it takes more bits to make this +one it takes more bits to make that one + + align:start position:0% +one it takes more bits to make that one + + + align:start position:0% +one it takes more bits to make that one +and it take more bits to make that + + align:start position:0% +and it take more bits to make that + + + align:start position:0% +and it take more bits to make that +one you're worse off if you didn't do + + align:start position:0% +one you're worse off if you didn't do + + + align:start position:0% +one you're worse off if you didn't do +something + + align:start position:0% +something + + + align:start position:0% +something +clever by so I'm sending the full number + + align:start position:0% +clever by so I'm sending the full number + + + align:start position:0% +clever by so I'm sending the full number +of bits here then I'm sending another + + align:start position:0% +of bits here then I'm sending another + + + align:start position:0% +of bits here then I'm sending another +1/4 and then another 116th then another + + align:start position:0% +1/4 and then another 116th then another + + + align:start position:0% +1/4 and then another 116th then another +164th so I'm sending about 33% more bits + + align:start position:0% +164th so I'm sending about 33% more bits + + + align:start position:0% +164th so I'm sending about 33% more bits +total but there's tricks the trick is + + align:start position:0% +total but there's tricks the trick is + + + align:start position:0% +total but there's tricks the trick is +that the I is less sensitive to these + + align:start position:0% +that the I is less sensitive to these + + + align:start position:0% +that the I is less sensitive to these +high frequencies than it is to these so + + align:start position:0% +high frequencies than it is to these so + + + align:start position:0% +high frequencies than it is to these so +I really don't need to send the same + + align:start position:0% +I really don't need to send the same + + + align:start position:0% +I really don't need to send the same +resolution for this so people use this + + align:start position:0% +resolution for this so people use this + + + align:start position:0% +resolution for this so people use this +all the time if you go to a slow website + + align:start position:0% +all the time if you go to a slow website + + + align:start position:0% +all the time if you go to a slow website +you may notice that you you get that + + align:start position:0% +you may notice that you you get that + + + align:start position:0% +you may notice that you you get that +kind of a low res morphing into a higher + + align:start position:0% +kind of a low res morphing into a higher + + + align:start position:0% +kind of a low res morphing into a higher +res and that's exactly this kind of a + + align:start position:0% +res and that's exactly this kind of a + + + align:start position:0% +res and that's exactly this kind of a +scheme but there are cleverer things you + + align:start position:0% +scheme but there are cleverer things you + + + align:start position:0% +scheme but there are cleverer things you +can do so that's already pretty clever + + align:start position:0% +can do so that's already pretty clever + + + align:start position:0% +can do so that's already pretty clever +and that's already something you see in + + align:start position:0% +and that's already something you see in + + + align:start position:0% +and that's already something you see in +today's technology but there are even + + align:start position:0% +today's technology but there are even + + + align:start position:0% +today's technology but there are even +cleverer things that you can do and so + + align:start position:0% +cleverer things that you can do and so + + + align:start position:0% +cleverer things that you can do and so +the last thing I want to talk about is + + align:start position:0% +the last thing I want to talk about is + + + align:start position:0% +the last thing I want to talk about is +jpeg 99% of the images that you download + + align:start position:0% +jpeg 99% of the images that you download + + + align:start position:0% +jpeg 99% of the images that you download +on the on the web are jpeg jpeg is a + + align:start position:0% +on the on the web are jpeg jpeg is a + + + align:start position:0% +on the on the web are jpeg jpeg is a +clever technique that does + + align:start position:0% +clever technique that does + + + align:start position:0% +clever technique that does +quantization in the 4A + + align:start position:0% +quantization in the 4A + + + align:start position:0% +quantization in the 4A +domain okay so the I and that's similar + + align:start position:0% +domain okay so the I and that's similar + + + align:start position:0% +domain okay so the I and that's similar +to what you would want to do in that + + align:start position:0% +to what you would want to do in that + + + align:start position:0% +to what you would want to do in that +Progressive refinement because you would + + align:start position:0% +Progressive refinement because you would + + + align:start position:0% +Progressive refinement because you would +like to separate the frequency + + align:start position:0% +like to separate the frequency + + + align:start position:0% +like to separate the frequency +components and use less resolution for + + align:start position:0% +components and use less resolution for + + + align:start position:0% +components and use less resolution for +the higher frequency components because + + align:start position:0% +the higher frequency components because + + + align:start position:0% +the higher frequency components because +you can't see them as well jpeg is a + + align:start position:0% +you can't see them as well jpeg is a + + + align:start position:0% +you can't see them as well jpeg is a +formalization of that + + align:start position:0% +formalization of that + + + align:start position:0% +formalization of that +idea so this was made by a joint + + align:start position:0% +idea so this was made by a joint + + + align:start position:0% +idea so this was made by a joint +photography group that was very + + align:start position:0% +photography group that was very + + + align:start position:0% +photography group that was very +successful it has four layers of coating + + align:start position:0% +successful it has four layers of coating + + + align:start position:0% +successful it has four layers of coating +first thing you worry about is + + align:start position:0% +first thing you worry about is + + + align:start position:0% +first thing you worry about is +color okay we think we see a broad range + + align:start position:0% +color okay we think we see a broad range + + + align:start position:0% +color okay we think we see a broad range +of colors wrong we only see + + align:start position:0% +of colors wrong we only see + + + align:start position:0% +of colors wrong we only see +three so you can throw away the ones + + align:start position:0% +three so you can throw away the ones + + + align:start position:0% +three so you can throw away the ones +that we can't + + align:start position:0% +that we can't + + + align:start position:0% +that we can't +see so that's the first step is taking + + align:start position:0% +see so that's the first step is taking + + + align:start position:0% +see so that's the first step is taking +advantage of the fact that we really + + align:start position:0% +advantage of the fact that we really + + + align:start position:0% +advantage of the fact that we really +can't see all the different colors we + + align:start position:0% +can't see all the different colors we + + + align:start position:0% +can't see all the different colors we +can really only see three colors so + + align:start position:0% +can really only see three colors so + + + align:start position:0% +can really only see three colors so +there are tricks that you can do to make + + align:start position:0% +there are tricks that you can do to make + + + align:start position:0% +there are tricks that you can do to make +the person think he's seeing the exact + + align:start position:0% +the person think he's seeing the exact + + + align:start position:0% +the person think he's seeing the exact +shade of yellow which we don't see very + + align:start position:0% +shade of yellow which we don't see very + + + align:start position:0% +shade of yellow which we don't see very +well by mixing together a different + + align:start position:0% +well by mixing together a different + + + align:start position:0% +well by mixing together a different +combination of red green and blue right + + align:start position:0% +combination of red green and blue right + + + align:start position:0% +combination of red green and blue right +so what you you get to move the colors + + align:start position:0% +so what you you get to move the colors + + + align:start position:0% +so what you you get to move the colors +around and you can make it + + align:start position:0% +around and you can make it + + + align:start position:0% +around and you can make it +perceptually + + align:start position:0% +perceptually + + + align:start position:0% +perceptually +indistinguishable but easier to code we + + align:start position:0% +indistinguishable but easier to code we + + + align:start position:0% +indistinguishable but easier to code we +won't talk about how you do that but + + align:start position:0% +won't talk about how you do that but + + + align:start position:0% +won't talk about how you do that but +it's a very straightforward process by + + align:start position:0% +it's a very straightforward process by + + + align:start position:0% +it's a very straightforward process by +which you start with one picture and you + + align:start position:0% +which you start with one picture and you + + + align:start position:0% +which you start with one picture and you +change all the colors to make them + + align:start position:0% +change all the colors to make them + + + align:start position:0% +change all the colors to make them +easier to send okay so that's the color + + align:start position:0% +easier to send okay so that's the color + + + align:start position:0% +easier to send okay so that's the color +coding then they do a discrete cosine + + align:start position:0% +coding then they do a discrete cosine + + + align:start position:0% +coding then they do a discrete cosine +transform which is really a for kind of + + align:start position:0% +transform which is really a for kind of + + + align:start position:0% +transform which is really a for kind of +a forier series then they quantize the + + align:start position:0% +a forier series then they quantize the + + + align:start position:0% +a forier series then they quantize the +forier series The + + align:start position:0% +forier series The + + + align:start position:0% +forier series The +DCT and then they uh uh code the + + align:start position:0% +DCT and then they uh uh code the + + + align:start position:0% +DCT and then they uh uh code the +resulting sequence using a lossless + + align:start position:0% +resulting sequence using a lossless + + + align:start position:0% +resulting sequence using a lossless +hufman code so we'll talk about the + + align:start position:0% +hufman code so we'll talk about the + + + align:start position:0% +hufman code so we'll talk about the +middle two steps because that's the fun + + align:start position:0% +middle two steps because that's the fun + + + align:start position:0% +middle two steps because that's the fun +stuff that's the for8 + + align:start position:0% +stuff that's the for8 + + + align:start position:0% +stuff that's the for8 +stuff so the way the DCT works is you + + align:start position:0% +stuff so the way the DCT works is you + + + align:start position:0% +stuff so the way the DCT works is you +take the the image and you break it into + + align:start position:0% +take the the image and you break it into + + + align:start position:0% +take the the image and you break it into +8 by8 pixel squares and then you do the + + align:start position:0% +8 by8 pixel squares and then you do the + + + align:start position:0% +8 by8 pixel squares and then you do the +same processing on each 8 + + align:start position:0% + + + + align:start position:0% + +by8 so here's an example of an 8 by8 + + align:start position:0% +by8 so here's an example of an 8 by8 + + + align:start position:0% +by8 so here's an example of an 8 by8 +image this is a completely trivial one + + align:start position:0% +image this is a completely trivial one + + + align:start position:0% +image this is a completely trivial one +where I have linear taper from black to + + align:start position:0% +where I have linear taper from black to + + + align:start position:0% +where I have linear taper from black to +white linear taper from black to white + + align:start position:0% +white linear taper from black to white + + + align:start position:0% +white linear taper from black to white +the product and all I want to think + + align:start position:0% +the product and all I want to think + + + align:start position:0% +the product and all I want to think +about is what's the DCT and why do they + + align:start position:0% +about is what's the DCT and why do they + + + align:start position:0% +about is what's the DCT and why do they +use a + + align:start position:0% +use a + + + align:start position:0% +use a +DCT instead of a 4A transer + + align:start position:0% +DCT instead of a 4A transer + + + align:start position:0% +DCT instead of a 4A transer +form so just like you would expect from + + align:start position:0% +form so just like you would expect from + + + align:start position:0% +form so just like you would expect from +the other two dimensional image + + align:start position:0% +the other two dimensional image + + + align:start position:0% +the other two dimensional image +processing examples that we've talked + + align:start position:0% +processing examples that we've talked + + + align:start position:0% +processing examples that we've talked +about the way you do this is you do the + + align:start position:0% +about the way you do this is you do the + + + align:start position:0% +about the way you do this is you do the +DCT on all the rows then you do the DCT + + align:start position:0% +DCT on all the rows then you do the DCT + + + align:start position:0% +DCT on all the rows then you do the DCT +on all the columns and then you're done + + align:start position:0% +on all the columns and then you're done + + + align:start position:0% +on all the columns and then you're done +that's a two-dimensional + + align:start position:0% +that's a two-dimensional + + + align:start position:0% +that's a two-dimensional +GCT so here's an example what if I took + + align:start position:0% +GCT so here's an example what if I took + + + align:start position:0% +GCT so here's an example what if I took +my sample image which had this linear + + align:start position:0% +my sample image which had this linear + + + align:start position:0% +my sample image which had this linear +taper so if I think about just one row + + align:start position:0% +taper so if I think about just one row + + + align:start position:0% +taper so if I think about just one row +and I plot brightness on the + + align:start position:0% +and I plot brightness on the + + + align:start position:0% +and I plot brightness on the +vertical then this might be my image + + align:start position:0% +vertical then this might be my image + + + align:start position:0% +vertical then this might be my image +right here and what I do is think about + + align:start position:0% +right here and what I do is think about + + + align:start position:0% +right here and what I do is think about +periodically repeating + + align:start position:0% +periodically repeating + + + align:start position:0% +periodically repeating +it okay the original signal only had + + align:start position:0% +it okay the original signal only had + + + align:start position:0% +it okay the original signal only had +eight numbers in it I'm going to + + align:start position:0% +eight numbers in it I'm going to + + + align:start position:0% +eight numbers in it I'm going to +periodically repeat it because then I + + align:start position:0% +periodically repeat it because then I + + + align:start position:0% +periodically repeat it because then I +can take a fora series okay it's a + + align:start position:0% +can take a fora series okay it's a + + + align:start position:0% +can take a fora series okay it's a +periodic signal it is a 48 series The + + align:start position:0% +periodic signal it is a 48 series The + + + align:start position:0% +periodic signal it is a 48 series The +reason I do that is that the 48 series + + align:start position:0% +reason I do that is that the 48 series + + + align:start position:0% +reason I do that is that the 48 series +only has + + align:start position:0% +only has + + + align:start position:0% +only has +eight uh coefficients right the 48 + + align:start position:0% +eight uh coefficients right the 48 + + + align:start position:0% +eight uh coefficients right the 48 +series of an eight long sequence has uh + + align:start position:0% +series of an eight long sequence has uh + + + align:start position:0% +series of an eight long sequence has uh +eight 48 coefficients + + align:start position:0% +eight 48 coefficients + + + align:start position:0% +eight 48 coefficients +right so the idea is that by taking a + + align:start position:0% +right so the idea is that by taking a + + + align:start position:0% +right so the idea is that by taking a +signal that's only8 samples long I mean + + align:start position:0% +signal that's only8 samples long I mean + + + align:start position:0% +signal that's only8 samples long I mean +the obvious thing you could do is take + + align:start position:0% +the obvious thing you could do is take + + + align:start position:0% +the obvious thing you could do is take +the eight long sample uh the eight long + + align:start position:0% +the eight long sample uh the eight long + + + align:start position:0% +the eight long sample uh the eight long +signal and take a discret Time 4A + + align:start position:0% +signal and take a discret Time 4A + + + align:start position:0% +signal and take a discret Time 4A +transform problem with that is that + + align:start position:0% +transform problem with that is that + + + align:start position:0% +transform problem with that is that +that's a continuous function of Omega + + align:start position:0% +that's a continuous function of Omega + + + align:start position:0% +that's a continuous function of Omega +over 2 pi over the entire unit circle so + + align:start position:0% +over 2 pi over the entire unit circle so + + + align:start position:0% +over 2 pi over the entire unit circle so +you take eight samples and turn it into + + align:start position:0% +you take eight samples and turn it into + + + align:start position:0% +you take eight samples and turn it into +a function of GA with which has lots of + + align:start position:0% +a function of GA with which has lots of + + + align:start position:0% +a function of GA with which has lots of +samples by thinking about the eight + + align:start position:0% +samples by thinking about the eight + + + align:start position:0% +samples by thinking about the eight +samples as having come from a from a + + align:start position:0% +samples as having come from a from a + + + align:start position:0% +samples as having come from a from a +periodic + + align:start position:0% +periodic + + + align:start position:0% +periodic +extension then I don't get a continuous + + align:start position:0% +extension then I don't get a continuous + + + align:start position:0% +extension then I don't get a continuous +range of frequencies between minus pi to + + align:start position:0% +range of frequencies between minus pi to + + + align:start position:0% +range of frequencies between minus pi to +Pi I get exactly eight of them a z + + align:start position:0% +Pi I get exactly eight of them a z + + + align:start position:0% +Pi I get exactly eight of them a z +through + + align:start position:0% +through + + + align:start position:0% +through +A7 okay so the first step is to uh do + + align:start position:0% +A7 okay so the first step is to uh do + + + align:start position:0% +A7 okay so the first step is to uh do +periodic extension on the eight samples + + align:start position:0% +periodic extension on the eight samples + + + align:start position:0% +periodic extension on the eight samples +then I can represent it by 848 + + align:start position:0% +then I can represent it by 848 + + + align:start position:0% +then I can represent it by 848 +coefficients in the DCT they almost do + + align:start position:0% +coefficients in the DCT they almost do + + + align:start position:0% +coefficients in the DCT they almost do +that but instead of writing down the + + align:start position:0% +that but instead of writing down the + + + align:start position:0% +that but instead of writing down the +numbers 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 + + align:start position:0% +numbers 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 + + + align:start position:0% +numbers 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 +1 2 3 4 5 6 78 instead they write 1 2 3 + + align:start position:0% +1 2 3 4 5 6 78 instead they write 1 2 3 + + + align:start position:0% +1 2 3 4 5 6 78 instead they write 1 2 3 +4 5 six 78 87654321 1 2 3 4 5 6 7 8 + + align:start position:0% +4 5 six 78 87654321 1 2 3 4 5 6 7 8 + + + align:start position:0% +4 5 six 78 87654321 1 2 3 4 5 6 7 8 +87654321 now that seems like a dumb + + align:start position:0% +87654321 now that seems like a dumb + + + align:start position:0% +87654321 now that seems like a dumb +thing to do I took an eight long + + align:start position:0% +thing to do I took an eight long + + + align:start position:0% +thing to do I took an eight long +sequence which could be represented with + + align:start position:0% +sequence which could be represented with + + + align:start position:0% +sequence which could be represented with +eight coefficients and I turned it into + + align:start position:0% +eight coefficients and I turned it into + + + align:start position:0% +eight coefficients and I turned it into +a 16 long sequence which now + + align:start position:0% +a 16 long sequence which now + + + align:start position:0% +a 16 long sequence which now +takes 16 coefficients well that's brain + + align:start position:0% +takes 16 coefficients well that's brain + + + align:start position:0% +takes 16 coefficients well that's brain +dead right except that + + align:start position:0% +dead right except that + + + align:start position:0% +dead right except that +it's actually very + + align:start position:0% +it's actually very + + + align:start position:0% +it's actually very +clever of these two signals which has + + align:start position:0% +clever of these two signals which has + + + align:start position:0% +clever of these two signals which has +the higher high frequency + + align:start position:0% + + + + align:start position:0% + +content + + align:start position:0% +content + + + align:start position:0% +content +why sharp drop large amount of high + + align:start position:0% +why sharp drop large amount of high + + + align:start position:0% +why sharp drop large amount of high +frequencies that's the + + align:start position:0% +frequencies that's the + + + align:start position:0% +frequencies that's the +trick so because there's a large amount + + align:start position:0% +trick so because there's a large amount + + + align:start position:0% +trick so because there's a large amount +of high frequencies this signal is hard + + align:start position:0% +of high frequencies this signal is hard + + + align:start position:0% +of high frequencies this signal is hard +to represent with 4A + + align:start position:0% +to represent with 4A + + + align:start position:0% +to represent with 4A +Series this signal is easier because + + align:start position:0% +Series this signal is easier because + + + align:start position:0% +Series this signal is easier because +there's fewer high frequency quencies + + align:start position:0% +there's fewer high frequency quencies + + + align:start position:0% +there's fewer high frequency quencies +you need fewer of those high frequencies + + align:start position:0% +you need fewer of those high frequencies + + + align:start position:0% +you need fewer of those high frequencies +to do a good job of representing the + + align:start position:0% +to do a good job of representing the + + + align:start position:0% +to do a good job of representing the +signal you can throw away the high + + align:start position:0% +signal you can throw away the high + + + align:start position:0% +signal you can throw away the high +frequency stuff and nobody will + + align:start position:0% +frequency stuff and nobody will + + + align:start position:0% +frequency stuff and nobody will +notice + + align:start position:0% +notice + + + align:start position:0% +notice +okay so so the idea then is that um you + + align:start position:0% +okay so so the idea then is that um you + + + align:start position:0% +okay so so the idea then is that um you +use the 16 long sequence but then you + + align:start position:0% +use the 16 long sequence but then you + + + align:start position:0% +use the 16 long sequence but then you +know that whatever a whatever X of 8 was + + align:start position:0% +know that whatever a whatever X of 8 was + + + align:start position:0% +know that whatever a whatever X of 8 was +it's the same as X of 9 because you + + align:start position:0% +it's the same as X of 9 because you + + + align:start position:0% +it's the same as X of 9 because you +always repeat it and X of 7 that's the + + align:start position:0% +always repeat it and X of 7 that's the + + + align:start position:0% +always repeat it and X of 7 that's the +same as uh X of 10 + + align:start position:0% +same as uh X of 10 + + + align:start position:0% +same as uh X of 10 +okay so if you take advantage of knowing + + align:start position:0% +okay so if you take advantage of knowing + + + align:start position:0% +okay so if you take advantage of knowing +that there's a + + align:start position:0% +that there's a + + + align:start position:0% +that there's a +symmetry and if you notice they made it + + align:start position:0% +symmetry and if you notice they made it + + + align:start position:0% +symmetry and if you notice they made it +symmetric so there's an even odd kind of + + align:start position:0% +symmetric so there's an even odd kind of + + + align:start position:0% +symmetric so there's an even odd kind of +symmetry about a weird point it's off by + + align:start position:0% +symmetry about a weird point it's off by + + + align:start position:0% +symmetry about a weird point it's off by +a half but there's a symmetry this way + + align:start position:0% +a half but there's a symmetry this way + + + align:start position:0% +a half but there's a symmetry this way +too if you take those two things into + + align:start position:0% +too if you take those two things into + + + align:start position:0% +too if you take those two things into +account uh you can actually represent + + align:start position:0% +account uh you can actually represent + + + align:start position:0% +account uh you can actually represent +the um 16 length sequence with eight + + align:start position:0% +the um 16 length sequence with eight + + + align:start position:0% +the um 16 length sequence with eight +numbers that's the + + align:start position:0% +numbers that's the + + + align:start position:0% +numbers that's the +DCT it's exact the same as a 4A except + + align:start position:0% +DCT it's exact the same as a 4A except + + + align:start position:0% +DCT it's exact the same as a 4A except +that we're taking the eight non-trivial + + align:start position:0% +that we're taking the eight non-trivial + + + align:start position:0% +that we're taking the eight non-trivial +numbers and putting them together in a + + align:start position:0% +numbers and putting them together in a + + + align:start position:0% +numbers and putting them together in a +funny periodic fashion that's what a DCT + + align:start position:0% +funny periodic fashion that's what a DCT + + + align:start position:0% +funny periodic fashion that's what a DCT +does and the point is that you the DCT + + align:start position:0% +does and the point is that you the DCT + + + align:start position:0% +does and the point is that you the DCT +Maps eight real numbers which are these + + align:start position:0% +Maps eight real numbers which are these + + + align:start position:0% +Maps eight real numbers which are these +uh YN values it Maps eight real numbers + + align:start position:0% +uh YN values it Maps eight real numbers + + + align:start position:0% +uh YN values it Maps eight real numbers +into eight DCT + + align:start position:0% + + + + align:start position:0% + +coefficients and the DCT coefficients + + align:start position:0% +coefficients and the DCT coefficients + + + align:start position:0% +coefficients and the DCT coefficients +unlike the 48 coefficients have real + + align:start position:0% +unlike the 48 coefficients have real + + + align:start position:0% +unlike the 48 coefficients have real +values so because of the trick with all + + align:start position:0% +values so because of the trick with all + + + align:start position:0% +values so because of the trick with all +the symmetries and all that sort of + + align:start position:0% +the symmetries and all that sort of + + + align:start position:0% +the symmetries and all that sort of +stuff they arranged to make a transform + + align:start position:0% +stuff they arranged to make a transform + + + align:start position:0% +stuff they arranged to make a transform +whose imaginary part is guaranteed to be + + align:start position:0% +whose imaginary part is guaranteed to be + + + align:start position:0% +whose imaginary part is guaranteed to be +zero so there's no information explosion + + align:start position:0% +zero so there's no information explosion + + + align:start position:0% +zero so there's no information explosion +in going from the uh 8 to + + align:start position:0% +in going from the uh 8 to + + + align:start position:0% +in going from the uh 8 to +16 and here's the kind of picture that + + align:start position:0% +16 and here's the kind of picture that + + + align:start position:0% +16 and here's the kind of picture that +you can see here's the 48 representation + + align:start position:0% +you can see here's the 48 representation + + + align:start position:0% +you can see here's the 48 representation +for a 2d picture the 4A coefficients are + + align:start position:0% +for a 2d picture the 4A coefficients are + + + align:start position:0% +for a 2d picture the 4A coefficients are +falling off like + + align:start position:0% +falling off like + + + align:start position:0% +falling off like +K here's the DCT where they're falling + + align:start position:0% +K here's the DCT where they're falling + + + align:start position:0% +K here's the DCT where they're falling +off like K squ and the point is you can + + align:start position:0% +off like K squ and the point is you can + + + align:start position:0% +off like K squ and the point is you can +throw those away in the picture and + + align:start position:0% +throw those away in the picture and + + + align:start position:0% +throw those away in the picture and +barely tell that they're even there that + + align:start position:0% +barely tell that they're even there that + + + align:start position:0% +barely tell that they're even there that +they're even gone so what they do then + + align:start position:0% +they're even gone so what they do then + + + align:start position:0% +they're even gone so what they do then +is they quantize the 48 coefficients at + + align:start position:0% +is they quantize the 48 coefficients at + + + align:start position:0% +is they quantize the 48 coefficients at +different + + align:start position:0% +different + + + align:start position:0% +different +levels so you divide the z00 coefficient + + align:start position:0% +levels so you divide the z00 coefficient + + + align:start position:0% +levels so you divide the z00 coefficient +by 16 and send the whole part you divide + + align:start position:0% +by 16 and send the whole part you divide + + + align:start position:0% +by 16 and send the whole part you divide +the one Z by 11 you divide this guy by + + align:start position:0% +the one Z by 11 you divide this guy by + + + align:start position:0% +the one Z by 11 you divide this guy by +61 so you use much less resolution by a + + align:start position:0% +61 so you use much less resolution by a + + + align:start position:0% +61 so you use much less resolution by a +factor of + + align:start position:0% + + + + align:start position:0% + +four because then those numbers were + + align:start position:0% +four because then those numbers were + + + align:start position:0% +four because then those numbers were +chosen so that they are they give rise + + align:start position:0% +chosen so that they are they give rise + + + align:start position:0% +chosen so that they are they give rise +to coefficients that are equally + + align:start position:0% +to coefficients that are equally + + + align:start position:0% +to coefficients that are equally +visually distinct the result is + + align:start position:0% +visually distinct the result is + + + align:start position:0% +visually distinct the result is +that you get very high resolution with a + + align:start position:0% +that you get very high resolution with a + + + align:start position:0% +that you get very high resolution with a +very small number of bits so here's U + + align:start position:0% +very small number of bits so here's U + + + align:start position:0% +very small number of bits so here's U +here's an + + align:start position:0% +here's an + + + align:start position:0% +here's an +original this picture has 4 47 kilobits + + align:start position:0% +original this picture has 4 47 kilobits + + + align:start position:0% +original this picture has 4 47 kilobits +kilobytes of data in + + align:start position:0% +kilobytes of data in + + + align:start position:0% +kilobytes of data in +it and when you change Q the quality of + + align:start position:0% +it and when you change Q the quality of + + + align:start position:0% +it and when you change Q the quality of +jpeg what you're really doing is + + align:start position:0% +jpeg what you're really doing is + + + align:start position:0% +jpeg what you're really doing is +choosing those + + align:start position:0% +choosing those + + + align:start position:0% +choosing those +tables so when you use a high Q you get + + align:start position:0% +tables so when you use a high Q you get + + + align:start position:0% +tables so when you use a high Q you get +a good representation when you use a low + + align:start position:0% +a good representation when you use a low + + + align:start position:0% +a good representation when you use a low +Q you're throwing away more data and you + + align:start position:0% +Q you're throwing away more data and you + + + align:start position:0% +Q you're throwing away more data and you +can see that you can throw away um so + + align:start position:0% +can see that you can throw away um so + + + align:start position:0% +can see that you can throw away um so +47k down to 2K you can throw away uh 19 + + align:start position:0% +47k down to 2K you can throw away uh 19 + + + align:start position:0% +47k down to 2K you can throw away uh 19 +pieces of data out of 20 and you still + + align:start position:0% +pieces of data out of 20 and you still + + + align:start position:0% +pieces of data out of 20 and you still +get a very good resolution picture and + + align:start position:0% +get a very good resolution picture and + + + align:start position:0% +get a very good resolution picture and +that's because the quantization is + + align:start position:0% +that's because the quantization is + + + align:start position:0% +that's because the quantization is +happening in the forier domain and you + + align:start position:0% +happening in the forier domain and you + + + align:start position:0% +happening in the forier domain and you +can match the forier resolution better + + align:start position:0% +can match the forier resolution better + + + align:start position:0% +can match the forier resolution better +to the psychophysical properties of the + + align:start position:0% +to the psychophysical properties of the + + + align:start position:0% +to the psychophysical properties of the +eye so the point is to tell you how to + + align:start position:0% +eye so the point is to tell you how to + + + align:start position:0% +eye so the point is to tell you how to +represent signals in discrete time in a + + align:start position:0% +represent signals in discrete time in a + + + align:start position:0% +represent signals in discrete time in a +way that the errors are as imperceptible + + align:start position:0% +way that the errors are as imperceptible + + + align:start position:0% +way that the errors are as imperceptible +as possible and to demonstrate how the + + align:start position:0% +as possible and to demonstrate how the + + + align:start position:0% +as possible and to demonstrate how the +4A transform uh let you do that okay + + align:start position:0% +4A transform uh let you do that okay + + + align:start position:0% +4A transform uh let you do that okay +thanks see you + + align:start position:0% +thanks see you + + + align:start position:0% +thanks see you +later \ No newline at end of file diff --git a/bV8-5sce5nw.txt b/bV8-5sce5nw.txt new file mode 100644 index 0000000000000000000000000000000000000000..764b078182979db736eb637472611e07fbc03c42 --- /dev/null +++ b/bV8-5sce5nw.txt @@ -0,0 +1,659 @@ +align:start position:0% + +Episode + + align:start position:0% + + + + align:start position:0% + +9. All there is to unlearn. + + align:start position:0% +9. All there is to unlearn. + + + align:start position:0% +9. All there is to unlearn. +Old habits die hard. We have all + + align:start position:0% +Old habits die hard. We have all + + + align:start position:0% +Old habits die hard. We have all +invested a lifetime learning with the + + align:start position:0% +invested a lifetime learning with the + + + align:start position:0% +invested a lifetime learning with the +sole objective of trying to be right. + + align:start position:0% +sole objective of trying to be right. + + + align:start position:0% +sole objective of trying to be right. +Often our jobs require that we be always + + align:start position:0% +Often our jobs require that we be always + + + align:start position:0% +Often our jobs require that we be always +right and that we certify our expertise. + + align:start position:0% +right and that we certify our expertise. + + + align:start position:0% +right and that we certify our expertise. +But in this new mindset, to even start + + align:start position:0% +But in this new mindset, to even start + + + align:start position:0% +But in this new mindset, to even start +innovating, you may need to accept that + + align:start position:0% +innovating, you may need to accept that + + + align:start position:0% +innovating, you may need to accept that +you are most likely wrong from the + + align:start position:0% +you are most likely wrong from the + + + align:start position:0% +you are most likely wrong from the +start. It will take some unlearning. + + align:start position:0% +start. It will take some unlearning. + + + align:start position:0% +start. It will take some unlearning. +Each video in this series introduces one + + align:start position:0% +Each video in this series introduces one + + + align:start position:0% +Each video in this series introduces one +idea to help you wrestle with what you + + align:start position:0% +idea to help you wrestle with what you + + + align:start position:0% +idea to help you wrestle with what you +may need to unlearn. The following ideas + + align:start position:0% +may need to unlearn. The following ideas + + + align:start position:0% +may need to unlearn. The following ideas +extracted from the videos you have just + + align:start position:0% +extracted from the videos you have just + + + align:start position:0% +extracted from the videos you have just +seen can help. One, I have hinted that + + align:start position:0% +seen can help. One, I have hinted that + + + align:start position:0% +seen can help. One, I have hinted that +innovating is a process of exploration. + + align:start position:0% +innovating is a process of exploration. + + + align:start position:0% +innovating is a process of exploration. +The difficulty with any kind of + + align:start position:0% +The difficulty with any kind of + + + align:start position:0% +The difficulty with any kind of +exploration is keeping yourself honest + + align:start position:0% +exploration is keeping yourself honest + + + align:start position:0% +exploration is keeping yourself honest +and open-minded. I find it useful to + + align:start position:0% +and open-minded. I find it useful to + + + align:start position:0% +and open-minded. I find it useful to +remind myself that there's a few things + + align:start position:0% +remind myself that there's a few things + + + align:start position:0% +remind myself that there's a few things +we humans are really bad at and some + + align:start position:0% +we humans are really bad at and some + + + align:start position:0% +we humans are really bad at and some +that we are really good at. Here they + + align:start position:0% +that we are really good at. Here they + + + align:start position:0% +that we are really good at. Here they +go. We're notoriously bad at having good + + align:start position:0% +go. We're notoriously bad at having good + + + align:start position:0% +go. We're notoriously bad at having good +ideas in just one go. + + align:start position:0% +ideas in just one go. + + + align:start position:0% +ideas in just one go. +We're bad at inventing something + + align:start position:0% +We're bad at inventing something + + + align:start position:0% +We're bad at inventing something +entirely from scratch. + + align:start position:0% +entirely from scratch. + + + align:start position:0% +entirely from scratch. +We are horrible at predicting the + + align:start position:0% +We are horrible at predicting the + + + align:start position:0% +We are horrible at predicting the +future. And we're even worse at + + align:start position:0% +future. And we're even worse at + + + align:start position:0% +future. And we're even worse at +remembering how bad we are at predicting + + align:start position:0% +remembering how bad we are at predicting + + + align:start position:0% +remembering how bad we are at predicting +the future. + + align:start position:0% +the future. + + + align:start position:0% +the future. +And then there is the things we are + + align:start position:0% +And then there is the things we are + + + align:start position:0% +And then there is the things we are +actually good at. We are really good at + + align:start position:0% +actually good at. We are really good at + + + align:start position:0% +actually good at. We are really good at +coming up with hunches. + + align:start position:0% +coming up with hunches. + + + align:start position:0% +coming up with hunches. +We're really good at reusing stuff. We + + align:start position:0% +We're really good at reusing stuff. We + + + align:start position:0% +We're really good at reusing stuff. We +excel at saying that something will not + + align:start position:0% +excel at saying that something will not + + + align:start position:0% +excel at saying that something will not +work. And we truly enjoy storytelling. + + align:start position:0% +work. And we truly enjoy storytelling. + + + align:start position:0% +work. And we truly enjoy storytelling. +Two, I invited you to let go of the idea + + align:start position:0% +Two, I invited you to let go of the idea + + + align:start position:0% +Two, I invited you to let go of the idea +of fail fast and to replace it for a + + align:start position:0% +of fail fast and to replace it for a + + + align:start position:0% +of fail fast and to replace it for a +pursuit of excellence. What I'm asking + + align:start position:0% +pursuit of excellence. What I'm asking + + + align:start position:0% +pursuit of excellence. What I'm asking +you to do is to build companies and + + align:start position:0% +you to do is to build companies and + + + align:start position:0% +you to do is to build companies and +projects that fail to fail. + + align:start position:0% +projects that fail to fail. + + + align:start position:0% +projects that fail to fail. +Three. + + align:start position:0% +Three. + + + align:start position:0% +Three. +I have offered you an alternative to all + + align:start position:0% +I have offered you an alternative to all + + + align:start position:0% +I have offered you an alternative to all +the innovation entrepreneurship + + align:start position:0% +the innovation entrepreneurship + + + align:start position:0% +the innovation entrepreneurship +frameworks that require you to settle on + + align:start position:0% +frameworks that require you to settle on + + + align:start position:0% +frameworks that require you to settle on +the product and the user before you even + + align:start position:0% +the product and the user before you even + + + align:start position:0% +the product and the user before you even +start. We spoke about prototyping + + align:start position:0% +start. We spoke about prototyping + + + align:start position:0% +start. We spoke about prototyping +problems and advancing a portfolio of + + align:start position:0% +problems and advancing a portfolio of + + + align:start position:0% +problems and advancing a portfolio of +solutions. + + align:start position:0% +solutions. + + + align:start position:0% +solutions. +Four, we distinguish between focusing + + align:start position:0% +Four, we distinguish between focusing + + + align:start position:0% +Four, we distinguish between focusing +and narrowing. You can focus on the + + align:start position:0% +and narrowing. You can focus on the + + + align:start position:0% +and narrowing. You can focus on the +problem and keep a space of options + + align:start position:0% +problem and keep a space of options + + + align:start position:0% +problem and keep a space of options +open. Your risk goes up if you narrow + + align:start position:0% +open. Your risk goes up if you narrow + + + align:start position:0% +open. Your risk goes up if you narrow +your options. + + align:start position:0% +your options. + + + align:start position:0% +your options. +Five. Our own garage story suggests that + + align:start position:0% +Five. Our own garage story suggests that + + + align:start position:0% +Five. Our own garage story suggests that +there was a time in which we did not + + align:start position:0% +there was a time in which we did not + + + align:start position:0% +there was a time in which we did not +believe that spending little by little + + align:start position:0% +believe that spending little by little + + + align:start position:0% +believe that spending little by little +was how you founded big projects. + + align:start position:0% +was how you founded big projects. + + + align:start position:0% +was how you founded big projects. +This may have important implications for + + align:start position:0% +This may have important implications for + + + align:start position:0% +This may have important implications for +how you decide to fund projects going + + align:start position:0% +how you decide to fund projects going + + + align:start position:0% +how you decide to fund projects going +forward. At the very least, it may help + + align:start position:0% +forward. At the very least, it may help + + + align:start position:0% +forward. At the very least, it may help +calibrate the real risk behind the + + align:start position:0% +calibrate the real risk behind the + + + align:start position:0% +calibrate the real risk behind the +stringing along projects with little + + align:start position:0% +stringing along projects with little + + + align:start position:0% +stringing along projects with little +amounts of funding. + + align:start position:0% +amounts of funding. + + + align:start position:0% +amounts of funding. +Six. There's many more ideas we only + + align:start position:0% +Six. There's many more ideas we only + + + align:start position:0% +Six. There's many more ideas we only +touched on partially like how to create + + align:start position:0% +touched on partially like how to create + + + align:start position:0% +touched on partially like how to create +value from the technology shelf, + + align:start position:0% +value from the technology shelf, + + + align:start position:0% +value from the technology shelf, +repurposing technologies, other ways to + + align:start position:0% +repurposing technologies, other ways to + + + align:start position:0% +repurposing technologies, other ways to +prototype problems, the difference + + align:start position:0% +prototype problems, the difference + + + align:start position:0% +prototype problems, the difference +between precision and accuracy, the + + align:start position:0% +between precision and accuracy, the + + + align:start position:0% +between precision and accuracy, the +curse of hindsight, and the true meaning + + align:start position:0% +curse of hindsight, and the true meaning + + + align:start position:0% +curse of hindsight, and the true meaning +of scale up to name some. You can learn + + align:start position:0% +of scale up to name some. You can learn + + + align:start position:0% +of scale up to name some. You can learn +more about many of those from the book + + align:start position:0% +more about many of those from the book + + + align:start position:0% +more about many of those from the book +Innovating Ador's Manifesto or following + + align:start position:0% +Innovating Ador's Manifesto or following + + + align:start position:0% +Innovating Ador's Manifesto or following +my work. + + align:start position:0% +my work. + + + align:start position:0% +my work. +There is just this one idea I told you + + align:start position:0% +There is just this one idea I told you + + + align:start position:0% +There is just this one idea I told you +about at the very start of this series + + align:start position:0% +about at the very start of this series + + + align:start position:0% +about at the very start of this series +of videos that I would like to come back + + align:start position:0% +of videos that I would like to come back + + + align:start position:0% +of videos that I would like to come back +to. We are sitting on a gold mine of + + align:start position:0% +to. We are sitting on a gold mine of + + + align:start position:0% +to. We are sitting on a gold mine of +underutilized technologies. That's the + + align:start position:0% +underutilized technologies. That's the + + + align:start position:0% +underutilized technologies. That's the +last video in this series. + + align:start position:0% + + + + align:start position:0% + +[Music] \ No newline at end of file diff --git a/c5yzy1S3gPg.txt b/c5yzy1S3gPg.txt new file mode 100644 index 0000000000000000000000000000000000000000..8ebe7c0fdafda3137562ed19395d3e19d419bd37 --- /dev/null +++ b/c5yzy1S3gPg.txt @@ -0,0 +1,1227 @@ +align:start position:0% + +let me discuss for a second effective + + align:start position:0% +let me discuss for a second effective + + + align:start position:0% +let me discuss for a second effective +potential potential and up actually let + + align:start position:0% +potential potential and up actually let + + + align:start position:0% +potential potential and up actually let +me ask you a question to get you start + + align:start position:0% +me ask you a question to get you start + + + align:start position:0% +me ask you a question to get you start +we're going to look at high-end and so + + align:start position:0% +we're going to look at high-end and so + + + align:start position:0% +we're going to look at high-end and so +am say a hundred and then L will go from + + align:start position:0% +am say a hundred and then L will go from + + + align:start position:0% +am say a hundred and then L will go from +0 up to 99 very high else what's going + + align:start position:0% +0 up to 99 very high else what's going + + + align:start position:0% +0 up to 99 very high else what's going +to be the difference from them well here + + align:start position:0% +to be the difference from them well here + + + align:start position:0% +to be the difference from them well here +it here is one possibility and that's + + align:start position:0% +it here is one possibility and that's + + + align:start position:0% +it here is one possibility and that's +the possibility that happens the orbits + + align:start position:0% +the possibility that happens the orbits + + + align:start position:0% +the possibility that happens the orbits +are going to go from being circular to + + align:start position:0% +are going to go from being circular to + + + align:start position:0% +are going to go from being circular to +being elliptical as you change L and I + + align:start position:0% +being elliptical as you change L and I + + + align:start position:0% +being elliptical as you change L and I +ask you which L would correspond to + + align:start position:0% +ask you which L would correspond to + + + align:start position:0% +ask you which L would correspond to +circular orbits and which L would + + align:start position:0% +circular orbits and which L would + + + align:start position:0% +circular orbits and which L would +correspond to the most elliptical orbit + + align:start position:0% +correspond to the most elliptical orbit + + + align:start position:0% +correspond to the most elliptical orbit +so let's take a pause so most circular + + align:start position:0% +so let's take a pause so most circular + + + align:start position:0% +so let's take a pause so most circular +orbit orbit is it L equals 0 or L equals + + align:start position:0% +orbit orbit is it L equals 0 or L equals + + + align:start position:0% +orbit orbit is it L equals 0 or L equals +99 who votes for l equals 0 for the most + + align:start position:0% +99 who votes for l equals 0 for the most + + + align:start position:0% +99 who votes for l equals 0 for the most +circular orbit I have about half of them + + align:start position:0% +circular orbit I have about half of them + + + align:start position:0% +circular orbit I have about half of them +a little bit more than half okay who + + align:start position:0% +a little bit more than half okay who + + + align:start position:0% +a little bit more than half okay who +votes for l equals 99 voters which is + + align:start position:0% +votes for l equals 99 voters which is + + + align:start position:0% +votes for l equals 99 voters which is +the most area okay this is this is funny + + align:start position:0% +the most area okay this is this is funny + + + align:start position:0% +the most area okay this is this is funny +because we all associate most circular + + align:start position:0% +because we all associate most circular + + + align:start position:0% +because we all associate most circular +with l equals 0 spherically symmetric + + align:start position:0% +with l equals 0 spherically symmetric + + + align:start position:0% +with l equals 0 spherically symmetric +but it's wrong this is a most circular + + align:start position:0% +but it's wrong this is a most circular + + + align:start position:0% +but it's wrong this is a most circular +most you cannot reach article 100 uh + + align:start position:0% +most you cannot reach article 100 uh + + + align:start position:0% +most you cannot reach article 100 uh +actually and this is a most elliptical + + align:start position:0% +actually and this is a most elliptical + + + align:start position:0% +actually and this is a most elliptical +elliptical and you can have the + + align:start position:0% +elliptical and you can have the + + + align:start position:0% +elliptical and you can have the +intuition for that let let let's avoid + + align:start position:0% +intuition for that let let let's avoid + + + align:start position:0% +intuition for that let let let's avoid +the calculation and be intuitive and the + + align:start position:0% +the calculation and be intuitive and the + + + align:start position:0% +the calculation and be intuitive and the +intuition is kind of interesting because + + align:start position:0% + + + + align:start position:0% + +we set effective potential and indeed I + + align:start position:0% +we set effective potential and indeed I + + + align:start position:0% +we set effective potential and indeed I +want to discuss that's what I want to + + align:start position:0% +want to discuss that's what I want to + + + align:start position:0% +want to discuss that's what I want to +understand the effective potential so + + align:start position:0% +understand the effective potential so + + + align:start position:0% +understand the effective potential so +maybe I'll draw this line a little lower + + align:start position:0% +maybe I'll draw this line a little lower + + + align:start position:0% +maybe I'll draw this line a little lower +and what is the effective potential with + + align:start position:0% +and what is the effective potential with + + + align:start position:0% +and what is the effective potential with +written it already many times a is H + + align:start position:0% +written it already many times a is H + + + align:start position:0% +written it already many times a is H +squared L times L plus 1 over 2m R + + align:start position:0% +squared L times L plus 1 over 2m R + + + align:start position:0% +squared L times L plus 1 over 2m R +squared minus e squared over R so the + + align:start position:0% +squared minus e squared over R so the + + + align:start position:0% +squared minus e squared over R so the +minus y squared over R is here yeah + + align:start position:0% +minus y squared over R is here yeah + + + align:start position:0% +minus y squared over R is here yeah +maybe I should draw it in a way that + + align:start position:0% +maybe I should draw it in a way that + + + align:start position:0% +maybe I should draw it in a way that +gives me more room oh my god okay and + + align:start position:0% +gives me more room oh my god okay and + + + align:start position:0% +gives me more room oh my god okay and +then there is the energy level that I'm + + align:start position:0% +then there is the energy level that I'm + + + align:start position:0% +then there is the energy level that I'm +looking at it's some high energy level + + align:start position:0% +looking at it's some high energy level + + + align:start position:0% +looking at it's some high energy level +so I'll put it near here not too near + + align:start position:0% +so I'll put it near here not too near + + + align:start position:0% +so I'll put it near here not too near +that I don't see it but near here here's + + align:start position:0% +that I don't see it but near here here's + + + align:start position:0% +that I don't see it but near here here's +my e M is here okay so the answer is + + align:start position:0% +my e M is here okay so the answer is + + + align:start position:0% +my e M is here okay so the answer is +actually already there not too clearly + + align:start position:0% +actually already there not too clearly + + + align:start position:0% +actually already there not too clearly +but here it is what does a particle do + + align:start position:0% +but here it is what does a particle do + + + align:start position:0% +but here it is what does a particle do +in this potential it goes with lots of + + align:start position:0% +in this potential it goes with lots of + + + align:start position:0% +in this potential it goes with lots of +kinetic energy very fast here and goes + + align:start position:0% +kinetic energy very fast here and goes + + + align:start position:0% +kinetic energy very fast here and goes +from here to here here to here + + align:start position:0% +from here to here here to here + + + align:start position:0% +from here to here here to here +but what does that mean that the radius + + align:start position:0% +but what does that mean that the radius + + + align:start position:0% +but what does that mean that the radius +is changing from R to some other value + + align:start position:0% +is changing from R to some other value + + + align:start position:0% +is changing from R to some other value +of R from R equals 0 to some other value + + align:start position:0% +of R from R equals 0 to some other value + + + align:start position:0% +of R from R equals 0 to some other value +of R so what could what looks like an + + align:start position:0% +of R so what could what looks like an + + + align:start position:0% +of R so what could what looks like an +orbit if you have a planet going around + + align:start position:0% +orbit if you have a planet going around + + + align:start position:0% +orbit if you have a planet going around +the Sun and at some point it seems to + + align:start position:0% +the Sun and at some point it seems to + + + align:start position:0% +the Sun and at some point it seems to +reach the Sun and at some point it goes + + align:start position:0% +reach the Sun and at some point it goes + + + align:start position:0% +reach the Sun and at some point it goes +far here is the Sun then the orbit must + + align:start position:0% +far here is the Sun then the orbit must + + + align:start position:0% +far here is the Sun then the orbit must +be like this that's likely to be the + + align:start position:0% +be like this that's likely to be the + + + align:start position:0% +be like this that's likely to be the +orbit on the other hand as soon as L is + + align:start position:0% +orbit on the other hand as soon as L is + + + align:start position:0% +orbit on the other hand as soon as L is +equal to 1 you have a part of the + + align:start position:0% +equal to 1 you have a part of the + + + align:start position:0% +equal to 1 you have a part of the +contribution to effective potential you + + align:start position:0% +contribution to effective potential you + + + align:start position:0% +contribution to effective potential you +have a 1 over R squared like this and + + align:start position:0% +have a 1 over R squared like this and + + + align:start position:0% +have a 1 over R squared like this and +then the total potential which is the + + align:start position:0% +then the total potential which is the + + + align:start position:0% +then the total potential which is the +original term Plus that will have + + align:start position:0% +original term Plus that will have + + + align:start position:0% +original term Plus that will have +something that looks like this and go + + align:start position:0% +something that looks like this and go + + + align:start position:0% +something that looks like this and go +like that and then this orbit is going + + align:start position:0% +like that and then this orbit is going + + + align:start position:0% +like that and then this orbit is going +to go from some small value of R but + + align:start position:0% +to go from some small value of R but + + + align:start position:0% +to go from some small value of R but +different from 0 to another one so those + + align:start position:0% +different from 0 to another one so those + + + align:start position:0% +different from 0 to another one so those +are all elliptical orbits because the + + align:start position:0% +are all elliptical orbits because the + + + align:start position:0% +are all elliptical orbits because the +radius is not constant and then this + + align:start position:0% +radius is not constant and then this + + + align:start position:0% +radius is not constant and then this +orbit it goes like that now look at it + + align:start position:0% +orbit it goes like that now look at it + + + align:start position:0% +orbit it goes like that now look at it +if you have some elliptical orbit so + + align:start position:0% +if you have some elliptical orbit so + + + align:start position:0% +if you have some elliptical orbit so +then after that time it just becomes a + + align:start position:0% +then after that time it just becomes a + + + align:start position:0% +then after that time it just becomes a +little more like this in which the + + align:start position:0% +little more like this in which the + + + align:start position:0% +little more like this in which the +minimum radius for say L equal 1 is here + + align:start position:0% +minimum radius for say L equal 1 is here + + + align:start position:0% +minimum radius for say L equal 1 is here +and the maximum radius has been reduced + + align:start position:0% +and the maximum radius has been reduced + + + align:start position:0% +and the maximum radius has been reduced +L equal to L equal 3 they all produce + + align:start position:0% +L equal to L equal 3 they all produce + + + align:start position:0% +L equal to L equal 3 they all produce +different ones my graph is not perfect + + align:start position:0% +different ones my graph is not perfect + + + align:start position:0% +different ones my graph is not perfect +different ones + + align:start position:0% +different ones + + + align:start position:0% +different ones +different ones and finally one that just + + align:start position:0% +different ones and finally one that just + + + align:start position:0% +different ones and finally one that just +touches it and that one the radius is + + align:start position:0% +touches it and that one the radius is + + + align:start position:0% +touches it and that one the radius is +fixed the particle is moving like that + + align:start position:0% +fixed the particle is moving like that + + + align:start position:0% +fixed the particle is moving like that +and + + align:start position:0% +and + + + align:start position:0% +and +that is your spherical orbit and if you + + align:start position:0% +that is your spherical orbit and if you + + + align:start position:0% +that is your spherical orbit and if you +increase L a little more no more + + align:start position:0% +increase L a little more no more + + + align:start position:0% +increase L a little more no more +solution so is the top L that produces + + align:start position:0% +solution so is the top L that produces + + + align:start position:0% +solution so is the top L that produces +this is already almost circular and this + + align:start position:0% +this is already almost circular and this + + + align:start position:0% +this is already almost circular and this +is perfectly circular so then it goes + + align:start position:0% +is perfectly circular so then it goes + + + align:start position:0% +is perfectly circular so then it goes +like this and then eventually it goes + + align:start position:0% +like this and then eventually it goes + + + align:start position:0% +like this and then eventually it goes +like this and finally at the end it goes + + align:start position:0% +like this and finally at the end it goes + + + align:start position:0% +like this and finally at the end it goes +like that and it's circular at the last + + align:start position:0% +like that and it's circular at the last + + + align:start position:0% +like that and it's circular at the last +case for the most L you finally get your + + align:start position:0% +case for the most L you finally get your + + + align:start position:0% +case for the most L you finally get your +circular orbit and also the intuition is + + align:start position:0% +circular orbit and also the intuition is + + + align:start position:0% +circular orbit and also the intuition is +clear if you have a circular orbit you + + align:start position:0% +clear if you have a circular orbit you + + + align:start position:0% +clear if you have a circular orbit you +have lots of angular momentum our cross + + align:start position:0% +have lots of angular momentum our cross + + + align:start position:0% +have lots of angular momentum our cross +P is very good when two vectors are + + align:start position:0% +P is very good when two vectors are + + + align:start position:0% +P is very good when two vectors are +orthogonal the cross product of r and + + align:start position:0% +orthogonal the cross product of r and + + + align:start position:0% +orthogonal the cross product of r and +the momentum is large but look here here + + align:start position:0% +the momentum is large but look here here + + + align:start position:0% +the momentum is large but look here here +is our for the shortest orbit and piece + + align:start position:0% +is our for the shortest orbit and piece + + + align:start position:0% +is our for the shortest orbit and piece +in that direction R cross P almost like + + align:start position:0% +in that direction R cross P almost like + + + align:start position:0% +in that direction R cross P almost like +that this is a very low angular momentum + + align:start position:0% +that this is a very low angular momentum + + + align:start position:0% +that this is a very low angular momentum +orbit so l equals zero is the most + + align:start position:0% +orbit so l equals zero is the most + + + align:start position:0% +orbit so l equals zero is the most +elliptical orbit l equal very high is + + align:start position:0% +elliptical orbit l equal very high is + + + align:start position:0% +elliptical orbit l equal very high is +the most circular orbit there's one + + align:start position:0% +the most circular orbit there's one + + + align:start position:0% +the most circular orbit there's one +thing calculation maybe I'll use 10 + + align:start position:0% +thing calculation maybe I'll use 10 + + + align:start position:0% +thing calculation maybe I'll use 10 +minutes next time is to show that + + align:start position:0% +minutes next time is to show that + + + align:start position:0% +minutes next time is to show that +there's two turning points here an + + align:start position:0% +there's two turning points here an + + + align:start position:0% +there's two turning points here an +hour-plus and an arm - so there's an + + align:start position:0% +hour-plus and an arm - so there's an + + + align:start position:0% +hour-plus and an arm - so there's an +hour-plus for one solution and an hour - + + align:start position:0% +hour-plus for one solution and an hour - + + + align:start position:0% +hour-plus for one solution and an hour - +and it goes like that + + align:start position:0% +and it goes like that + + + align:start position:0% +and it goes like that +so there are pluses and the r minuses + + align:start position:0% +so there are pluses and the r minuses + + + align:start position:0% +so there are pluses and the r minuses +corresponds to an ellipse that here is + + align:start position:0% +corresponds to an ellipse that here is + + + align:start position:0% +corresponds to an ellipse that here is +the center that's where the proton sits + + align:start position:0% +the center that's where the proton sits + + + align:start position:0% +the center that's where the proton sits +and you go our plus out is the maximum + + align:start position:0% +and you go our plus out is the maximum + + + align:start position:0% +and you go our plus out is the maximum +and our minus is here so the two turning + + align:start position:0% +and our minus is here so the two turning + + + align:start position:0% +and our minus is here so the two turning +points that define the maximum R and + + align:start position:0% +points that define the maximum R and + + + align:start position:0% +points that define the maximum R and +minimum R tell you about the lips and + + align:start position:0% +minimum R tell you about the lips and + + + align:start position:0% +minimum R tell you about the lips and +these are plus plus or minus and when + + align:start position:0% +these are plus plus or minus and when + + + align:start position:0% +these are plus plus or minus and when +you find + + align:start position:0% +you find + + + align:start position:0% +you find +those critical points and do the + + align:start position:0% +those critical points and do the + + + align:start position:0% +those critical points and do the +calculation you in fact can show that + + align:start position:0% +calculation you in fact can show that + + + align:start position:0% +calculation you in fact can show that +our plus plus our minus is indeed equal + + align:start position:0% +our plus plus our minus is indeed equal + + + align:start position:0% +our plus plus our minus is indeed equal +to N squared a zero I think that number + + align:start position:0% +to N squared a zero I think that number + + + align:start position:0% +to N squared a zero I think that number +comes out exactly there X plus R plus + + align:start position:0% +comes out exactly there X plus R plus + + + align:start position:0% +comes out exactly there X plus R plus +plus or minus over to the average is + + align:start position:0% +plus or minus over to the average is + + + align:start position:0% +plus or minus over to the average is +exactly that so the the roots the two + + align:start position:0% +exactly that so the the roots the two + + + align:start position:0% +exactly that so the the roots the two +roots are such that their average is + + align:start position:0% +roots are such that their average is + + + align:start position:0% +roots are such that their average is +always the same so this is not I'm not + + align:start position:0% +always the same so this is not I'm not + + + align:start position:0% +always the same so this is not I'm not +sure I get it right with my graph but it + + align:start position:0% +sure I get it right with my graph but it + + + align:start position:0% +sure I get it right with my graph but it +should be that if you take the average + + align:start position:0% +should be that if you take the average + + + align:start position:0% +should be that if you take the average +of the intersection points are always at + + align:start position:0% +of the intersection points are always at + + + align:start position:0% +of the intersection points are always at +the same point and so that's how it + + align:start position:0% +the same point and so that's how it + + + align:start position:0% +the same point and so that's how it +happens and there's an analog in so you + + align:start position:0% +happens and there's an analog in so you + + + align:start position:0% +happens and there's an analog in so you +get the intuition here here are your + + align:start position:0% +get the intuition here here are your + + + align:start position:0% +get the intuition here here are your +orbits and these are equal energy orbit + + align:start position:0% +orbits and these are equal energy orbit + + + align:start position:0% +orbits and these are equal energy orbit +of different eccentricity as you go in + + align:start position:0% +of different eccentricity as you go in + + + align:start position:0% +of different eccentricity as you go in +there and even Kepler knew that because + + align:start position:0% +there and even Kepler knew that because + + + align:start position:0% +there and even Kepler knew that because +Kepler figured out that the time that it + + align:start position:0% +Kepler figured out that the time that it + + + align:start position:0% +Kepler figured out that the time that it +takes the planet to go around depends + + align:start position:0% +takes the planet to go around depends + + + align:start position:0% +takes the planet to go around depends +only on the sum of these two things the + + align:start position:0% +only on the sum of these two things the + + + align:start position:0% +only on the sum of these two things the +major diameter so all these solutions + + align:start position:0% +major diameter so all these solutions + + + align:start position:0% +major diameter so all these solutions +over here if they were planets would + + align:start position:0% +over here if they were planets would + + + align:start position:0% +over here if they were planets would +take the same time to go around the Sun + + align:start position:0% +take the same time to go around the Sun + + + align:start position:0% +take the same time to go around the Sun +so they all in quantum mechanics have + + align:start position:0% +so they all in quantum mechanics have + + + align:start position:0% +so they all in quantum mechanics have +the same energy and they're therefore + + align:start position:0% +the same energy and they're therefore + + + align:start position:0% +the same energy and they're therefore +degenerate so the mystery of the + + align:start position:0% +degenerate so the mystery of the + + + align:start position:0% +degenerate so the mystery of the +quadratic potential that makes all of + + align:start position:0% +quadratic potential that makes all of + + + align:start position:0% +quadratic potential that makes all of +these periods to be the same is the + + align:start position:0% +these periods to be the same is the + + + align:start position:0% +these periods to be the same is the +mystery that is making the energy is the + + align:start position:0% +mystery that is making the energy is the + + + align:start position:0% +mystery that is making the energy is the +same in all these orbits so we'll + + align:start position:0% +same in all these orbits so we'll + + + align:start position:0% +same in all these orbits so we'll +finalize the story next time and do some + + align:start position:0% +finalize the story next time and do some + + + align:start position:0% +finalize the story next time and do some +other fun things \ No newline at end of file diff --git a/c6-ybCfU6Zc.txt b/c6-ybCfU6Zc.txt new file mode 100644 index 0000000000000000000000000000000000000000..7e92ad3b1315fb4d4e72fb16bf4c34e801917fce --- /dev/null +++ b/c6-ybCfU6Zc.txt @@ -0,0 +1,6451 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +okay so we're going to talk about Six + + align:start position:0% +okay so we're going to talk about Six + + + align:start position:0% +okay so we're going to talk about Six +Sigma now if you've seen the course is + + align:start position:0% +Sigma now if you've seen the course is + + + align:start position:0% +Sigma now if you've seen the course is +heavily weighted towards lean with a + + align:start position:0% +heavily weighted towards lean with a + + + align:start position:0% +heavily weighted towards lean with a +little bit of Six Sigma and we think + + align:start position:0% +little bit of Six Sigma and we think + + + align:start position:0% +little bit of Six Sigma and we think +that's the appropriate place to start so + + align:start position:0% +that's the appropriate place to start so + + + align:start position:0% +that's the appropriate place to start so +but we need to we need to kind of get + + align:start position:0% +but we need to we need to kind of get + + + align:start position:0% +but we need to we need to kind of get +you started on Six Sigma and so learning + + align:start position:0% +you started on Six Sigma and so learning + + + align:start position:0% +you started on Six Sigma and so learning +objectives here are is that Six Sigma is + + align:start position:0% +objectives here are is that Six Sigma is + + + align:start position:0% +objectives here are is that Six Sigma is +a valuable approach for improving + + align:start position:0% +a valuable approach for improving + + + align:start position:0% +a valuable approach for improving +process quality okay and we'll try to + + align:start position:0% +process quality okay and we'll try to + + + align:start position:0% +process quality okay and we'll try to +explain a little bit more about that + + align:start position:0% +explain a little bit more about that + + + align:start position:0% +explain a little bit more about that +we're going to have you be able to + + align:start position:0% +we're going to have you be able to + + + align:start position:0% +we're going to have you be able to +interpret a basical statical process + + align:start position:0% +interpret a basical statical process + + + align:start position:0% +interpret a basical statical process +control chart that's what the active + + align:start position:0% +control chart that's what the active + + + align:start position:0% +control chart that's what the active +learning experiments about we're going + + align:start position:0% +learning experiments about we're going + + + align:start position:0% +learning experiments about we're going +to talk about difference between process + + align:start position:0% +to talk about difference between process + + + align:start position:0% +to talk about difference between process +control limits and specified control + + align:start position:0% +control limits and specified control + + + align:start position:0% +control limits and specified control +limits and you'll be able to describe + + align:start position:0% +limits and you'll be able to describe + + + align:start position:0% +limits and you'll be able to describe +what a capable process is okay so Six + + align:start position:0% +what a capable process is okay so Six + + + align:start position:0% +what a capable process is okay so Six +Sigma is a strategy to improve process + + align:start position:0% +Sigma is a strategy to improve process + + + align:start position:0% +Sigma is a strategy to improve process +quality by identifying and eliminating + + align:start position:0% +quality by identifying and eliminating + + + align:start position:0% +quality by identifying and eliminating +defects in defects in the broadest + + align:start position:0% +defects in defects in the broadest + + + align:start position:0% +defects in defects in the broadest +possible sense not just defects in the + + align:start position:0% +possible sense not just defects in the + + + align:start position:0% +possible sense not just defects in the +size of a hole being drilled + + align:start position:0% +size of a hole being drilled + + + align:start position:0% +size of a hole being drilled +but defect in something that you want to + + align:start position:0% +but defect in something that you want to + + + align:start position:0% +but defect in something that you want to +deliver your customer is not what they + + align:start position:0% +deliver your customer is not what they + + + align:start position:0% +deliver your customer is not what they +want that's a defense okay it's a very + + align:start position:0% +want that's a defense okay it's a very + + + align:start position:0% +want that's a defense okay it's a very +data-driven approach + + align:start position:0% +data-driven approach + + + align:start position:0% +data-driven approach +so you've seen lean in fact one of the + + align:start position:0% +so you've seen lean in fact one of the + + + align:start position:0% +so you've seen lean in fact one of the +comments we got back on the feedback + + align:start position:0% +comments we got back on the feedback + + + align:start position:0% +comments we got back on the feedback +sheet is it's kind of a lot of + + align:start position:0% +sheet is it's kind of a lot of + + + align:start position:0% +sheet is it's kind of a lot of +touchy-feely stuff you're covering and + + align:start position:0% +touchy-feely stuff you're covering and + + + align:start position:0% +touchy-feely stuff you're covering and +lean is a lot of in some ways a lot of + + align:start position:0% +lean is a lot of in some ways a lot of + + + align:start position:0% +lean is a lot of in some ways a lot of +touchy-feely stuff because of the + + align:start position:0% +touchy-feely stuff because of the + + + align:start position:0% +touchy-feely stuff because of the +importance of people Six Sigma if you + + align:start position:0% +importance of people Six Sigma if you + + + align:start position:0% +importance of people Six Sigma if you +read the literature on Six Sigma at + + align:start position:0% +read the literature on Six Sigma at + + + align:start position:0% +read the literature on Six Sigma at +least the literature I've read people + + align:start position:0% +least the literature I've read people + + + align:start position:0% +least the literature I've read people +are never mentioned okay it's about it's + + align:start position:0% +are never mentioned okay it's about it's + + + align:start position:0% +are never mentioned okay it's about it's +about a a problem solving process and + + align:start position:0% +about a a problem solving process and + + + align:start position:0% +about a a problem solving process and +that's important but it it has its + + align:start position:0% +that's important but it it has its + + + align:start position:0% +that's important but it it has its +limitations okay and and importantly + + align:start position:0% +limitations okay and and importantly + + + align:start position:0% +limitations okay and and importantly +it's know when to use it and how it fits + + align:start position:0% +it's know when to use it and how it fits + + + align:start position:0% +it's know when to use it and how it fits +in with a more holistic lean approach + + align:start position:0% +in with a more holistic lean approach + + + align:start position:0% +in with a more holistic lean approach +and it's a very structured + + align:start position:0% +and it's a very structured + + + align:start position:0% +and it's a very structured +implementation approach with certified + + align:start position:0% +implementation approach with certified + + + align:start position:0% +implementation approach with certified +experts you probably have heard of black + + align:start position:0% +experts you probably have heard of black + + + align:start position:0% +experts you probably have heard of black +belts and green belts and things like + + align:start position:0% +belts and green belts and things like + + + align:start position:0% +belts and green belts and things like +that + + align:start position:0% +that + + + align:start position:0% +that +okay so Six Sigma has this hierarchy of + + align:start position:0% +okay so Six Sigma has this hierarchy of + + + align:start position:0% +okay so Six Sigma has this hierarchy of +experts and it's a little bit that's + + align:start position:0% +experts and it's a little bit that's + + + align:start position:0% +experts and it's a little bit that's +really kind of not the mindset of lean + + align:start position:0% +really kind of not the mindset of lean + + + align:start position:0% +really kind of not the mindset of lean +the mindset of lean is the you know the + + align:start position:0% +the mindset of lean is the you know the + + + align:start position:0% +the mindset of lean is the you know the +experts the coach not not the person who + + align:start position:0% +experts the coach not not the person who + + + align:start position:0% +experts the coach not not the person who +knows the most it's the person who gets + + align:start position:0% +knows the most it's the person who gets + + + align:start position:0% +knows the most it's the person who gets +the most out of the people there so + + align:start position:0% +the most out of the people there so + + + align:start position:0% +the most out of the people there so +there's some some big cultural + + align:start position:0% +there's some some big cultural + + + align:start position:0% +there's some some big cultural +differences between Six Sigma and lean + + align:start position:0% +differences between Six Sigma and lean + + + align:start position:0% +differences between Six Sigma and lean +but they've come together and the + + align:start position:0% +but they've come together and the + + + align:start position:0% +but they've come together and the +important thing is to try to understand + + align:start position:0% +important thing is to try to understand + + + align:start position:0% +important thing is to try to understand +that now or + + align:start position:0% +that now or + + + align:start position:0% +that now or +the word Sigma comes from well it's a + + align:start position:0% +the word Sigma comes from well it's a + + + align:start position:0% +the word Sigma comes from well it's a +pretty analytical group so you probably + + align:start position:0% +pretty analytical group so you probably + + + align:start position:0% +pretty analytical group so you probably +all know this but a normal distribution + + align:start position:0% +all know this but a normal distribution + + + align:start position:0% +all know this but a normal distribution +something like what you just saw with + + align:start position:0% +something like what you just saw with + + + align:start position:0% +something like what you just saw with +the M&Ms although that wasn't quite + + align:start position:0% +the M&Ms although that wasn't quite + + + align:start position:0% +the M&Ms although that wasn't quite +normal but it was somewhat close to that + + align:start position:0% +normal but it was somewhat close to that + + + align:start position:0% +normal but it was somewhat close to that +you know it's defined by the standard + + align:start position:0% +you know it's defined by the standard + + + align:start position:0% +you know it's defined by the standard +deviation which is Sigma and in this + + align:start position:0% +deviation which is Sigma and in this + + + align:start position:0% +deviation which is Sigma and in this +chart so this is one standard deviation + + align:start position:0% +chart so this is one standard deviation + + + align:start position:0% +chart so this is one standard deviation +from the mean two standard deviations + + align:start position:0% +from the mean two standard deviations + + + align:start position:0% +from the mean two standard deviations +and three and six Sigma would be six + + align:start position:0% +and three and six Sigma would be six + + + align:start position:0% +and three and six Sigma would be six +standard deviations and just keep this + + align:start position:0% +standard deviations and just keep this + + + align:start position:0% +standard deviations and just keep this +in mind we're going to deal with some + + align:start position:0% +in mind we're going to deal with some + + + align:start position:0% +in mind we're going to deal with some +three Sigma in a little bit coming up + + align:start position:0% +three Sigma in a little bit coming up + + + align:start position:0% +three Sigma in a little bit coming up +here three Sigma is 99.73% of the area + + align:start position:0% +here three Sigma is 99.73% of the area + + + align:start position:0% +here three Sigma is 99.73% of the area +under under a normal distribution would + + align:start position:0% +under under a normal distribution would + + + align:start position:0% +under under a normal distribution would +be within a three sigma band okay an + + align:start position:0% +be within a three sigma band okay an + + + align:start position:0% +be within a three sigma band okay an +important part of Six Sigma is defects + + align:start position:0% +important part of Six Sigma is defects + + + align:start position:0% +important part of Six Sigma is defects +because what you want to do is reduce + + align:start position:0% +because what you want to do is reduce + + + align:start position:0% +because what you want to do is reduce +the the goal of Six Sigma is to reduce + + align:start position:0% +the the goal of Six Sigma is to reduce + + + align:start position:0% +the the goal of Six Sigma is to reduce +the number of defects per million + + align:start position:0% +the number of defects per million + + + align:start position:0% +the number of defects per million +opportunities and a defect is defined as + + align:start position:0% +opportunities and a defect is defined as + + + align:start position:0% +opportunities and a defect is defined as +any process output that does not meet + + align:start position:0% +any process output that does not meet + + + align:start position:0% +any process output that does not meet +the customer specifications as I + + align:start position:0% +the customer specifications as I + + + align:start position:0% +the customer specifications as I +mentioned earlier in a very broad sense + + align:start position:0% +mentioned earlier in a very broad sense + + + align:start position:0% +mentioned earlier in a very broad sense +okay and so you got two things here you + + align:start position:0% +okay and so you got two things here you + + + align:start position:0% +okay and so you got two things here you +got opportunities of defects so you want + + align:start position:0% +got opportunities of defects so you want + + + align:start position:0% +got opportunities of defects so you want +to reduce the defects but you also in + + align:start position:0% +to reduce the defects but you also in + + + align:start position:0% +to reduce the defects but you also in +many ways you want to reduce the number + + align:start position:0% +many ways you want to reduce the number + + + align:start position:0% +many ways you want to reduce the number +of opportunities to have defects + + align:start position:0% +of opportunities to have defects + + + align:start position:0% +of opportunities to have defects +okay so reducing the number of handoffs + + align:start position:0% +okay so reducing the number of handoffs + + + align:start position:0% +okay so reducing the number of handoffs +su mentioned the baton okay handoffs + + align:start position:0% +su mentioned the baton okay handoffs + + + align:start position:0% +su mentioned the baton okay handoffs +handoffs between people are always a + + align:start position:0% +handoffs between people are always a + + + align:start position:0% +handoffs between people are always a +potential source of mistakes or errors + + align:start position:0% +potential source of mistakes or errors + + + align:start position:0% +potential source of mistakes or errors +or misunderstandings okay just think + + align:start position:0% +or misunderstandings okay just think + + + align:start position:0% +or misunderstandings okay just think +about how many miscommunications have + + align:start position:0% +about how many miscommunications have + + + align:start position:0% +about how many miscommunications have +you had with your boyfriend or + + align:start position:0% +you had with your boyfriend or + + + align:start position:0% +you had with your boyfriend or +girlfriend or parents or best friends + + align:start position:0% +girlfriend or parents or best friends + + + align:start position:0% +girlfriend or parents or best friends +you know + + align:start position:0% +you know + + + align:start position:0% +you know +so handoffs of any kind or something + + align:start position:0% +so handoffs of any kind or something + + + align:start position:0% +so handoffs of any kind or something +that you want to minimize I just read + + align:start position:0% +that you want to minimize I just read + + + align:start position:0% +that you want to minimize I just read +some literature I'm going to share this + + align:start position:0% +some literature I'm going to share this + + + align:start position:0% +some literature I'm going to share this +with you since we're in the aviation + + align:start position:0% +with you since we're in the aviation + + + align:start position:0% +with you since we're in the aviation +field I'm in the aviation field the data + + align:start position:0% +field I'm in the aviation field the data + + + align:start position:0% +field I'm in the aviation field the data +from last year's commercial air travel + + align:start position:0% +from last year's commercial air travel + + + align:start position:0% +from last year's commercial air travel +in the US was there were point oh two + + align:start position:0% +in the US was there were point oh two + + + align:start position:0% +in the US was there were point oh two +fatalities for every million boardings + + align:start position:0% +fatalities for every million boardings + + + align:start position:0% +fatalities for every million boardings +0.02 I think that's ten I think that's a + + align:start position:0% +0.02 I think that's ten I think that's a + + + align:start position:0% +0.02 I think that's ten I think that's a +9 Sigma I'm not yeah ok so that gives + + align:start position:0% +9 Sigma I'm not yeah ok so that gives + + + align:start position:0% +9 Sigma I'm not yeah ok so that gives +you a kind of a benchmark or something + + align:start position:0% +you a kind of a benchmark or something + + + align:start position:0% +you a kind of a benchmark or something +being really good but how good is good + + align:start position:0% +being really good but how good is good + + + align:start position:0% +being really good but how good is good +some people say you know 99% is good I + + align:start position:0% +some people say you know 99% is good I + + + align:start position:0% +some people say you know 99% is good I +mean if my car starts 99% of the time + + align:start position:0% +mean if my car starts 99% of the time + + + align:start position:0% +mean if my car starts 99% of the time +you know and it's an old car that's good + + align:start position:0% +you know and it's an old car that's good + + + align:start position:0% +you know and it's an old car that's good +but that's three days out of the year + + align:start position:0% +but that's three days out of the year + + + align:start position:0% +but that's three days out of the year +I'm not going to get out of my garage + + align:start position:0% +I'm not going to get out of my garage + + + align:start position:0% +I'm not going to get out of my garage +and I'm going to miss get into my + + align:start position:0% +and I'm going to miss get into my + + + align:start position:0% +and I'm going to miss get into my +appointment okay that's not so good okay + + align:start position:0% +appointment okay that's not so good okay + + + align:start position:0% +appointment okay that's not so good okay +so 99% you might think is good but + + align:start position:0% +so 99% you might think is good but + + + align:start position:0% +so 99% you might think is good but +that's 20,000 lost article of mail per + + align:start position:0% +that's 20,000 lost article of mail per + + + align:start position:0% +that's 20,000 lost article of mail per +hour + + align:start position:0% +hour + + + align:start position:0% +hour +you know unsafe drinking water 15 would + + align:start position:0% +you know unsafe drinking water 15 would + + + align:start position:0% +you know unsafe drinking water 15 would +say in this light it's 5,000 incorrect + + align:start position:0% +say in this light it's 5,000 incorrect + + + align:start position:0% +say in this light it's 5,000 incorrect +surgical operations per week okay too + + align:start position:0% +surgical operations per week okay too + + + align:start position:0% +surgical operations per week okay too +short or long landings at a major + + align:start position:0% +short or long landings at a major + + + align:start position:0% +short or long landings at a major +airport each day 200,000 wrong drug + + align:start position:0% +airport each day 200,000 wrong drug + + + align:start position:0% +airport each day 200,000 wrong drug +prescriptions a year okay that's not + + align:start position:0% +prescriptions a year okay that's not + + + align:start position:0% +prescriptions a year okay that's not +really very good ninety nine percent + + align:start position:0% +really very good ninety nine percent + + + align:start position:0% +really very good ninety nine percent +ninety nine point six sigma okay so this + + align:start position:0% +ninety nine point six sigma okay so this + + + align:start position:0% +ninety nine point six sigma okay so this +is kind of what you're looking for + + align:start position:0% +is kind of what you're looking for + + + align:start position:0% +is kind of what you're looking for +okay well you know 1.7 incorrect + + align:start position:0% +okay well you know 1.7 incorrect + + + align:start position:0% +okay well you know 1.7 incorrect +operations per week even that's too much + + align:start position:0% +operations per week even that's too much + + + align:start position:0% +operations per week even that's too much +but boy that's a lot better than 5,000 + + align:start position:0% +but boy that's a lot better than 5,000 + + + align:start position:0% +but boy that's a lot better than 5,000 +okay if you're the one of those 1.7 + + align:start position:0% +okay if you're the one of those 1.7 + + + align:start position:0% +okay if you're the one of those 1.7 +people you don't care what Sigma it is + + align:start position:0% +people you don't care what Sigma it is + + + align:start position:0% +people you don't care what Sigma it is +you know you just got same here and as I + + align:start position:0% +you know you just got same here and as I + + + align:start position:0% +you know you just got same here and as I +mentioned airline travels like nine + + align:start position:0% +mentioned airline travels like nine + + + align:start position:0% +mentioned airline travels like nine +Sigma for safety so okay so a a basic + + align:start position:0% +Sigma for safety so okay so a a basic + + + align:start position:0% +Sigma for safety so okay so a a basic +tool in Six Sigma is called the + + align:start position:0% +tool in Six Sigma is called the + + + align:start position:0% +tool in Six Sigma is called the +statistical process control chart so + + align:start position:0% +statistical process control chart so + + + align:start position:0% +statistical process control chart so +chart show so it's a sequence it's is a + + align:start position:0% +chart show so it's a sequence it's is a + + + align:start position:0% +chart show so it's a sequence it's is a +time chart we're going to build one just + + align:start position:0% +time chart we're going to build one just + + + align:start position:0% +time chart we're going to build one just +shortly it's time and this is some + + align:start position:0% +shortly it's time and this is some + + + align:start position:0% +shortly it's time and this is some +measurement and this shows you know how + + align:start position:0% +measurement and this shows you know how + + + align:start position:0% +measurement and this shows you know how +how stable it is how much it's tending + + align:start position:0% +how stable it is how much it's tending + + + align:start position:0% +how stable it is how much it's tending +to be around the center of the chart + + align:start position:0% +to be around the center of the chart + + + align:start position:0% +to be around the center of the chart +it's a very common chart and in both + + align:start position:0% +it's a very common chart and in both + + + align:start position:0% +it's a very common chart and in both +fields if you go into a production + + align:start position:0% +fields if you go into a production + + + align:start position:0% +fields if you go into a production +facility and engineering production + + align:start position:0% +facility and engineering production + + + align:start position:0% +facility and engineering production +facility now the operator will be + + align:start position:0% +facility now the operator will be + + + align:start position:0% +facility now the operator will be +showing you there's their control chart + + align:start position:0% +showing you there's their control chart + + + align:start position:0% +showing you there's their control chart +you know their I couldn't believe when I + + align:start position:0% +you know their I couldn't believe when I + + + align:start position:0% +you know their I couldn't believe when I +first went in and saw you know the + + align:start position:0% +first went in and saw you know the + + + align:start position:0% +first went in and saw you know the +Machinists proudly or the machine + + align:start position:0% +Machinists proudly or the machine + + + align:start position:0% +Machinists proudly or the machine +operator showing me their control chart + + align:start position:0% +operator showing me their control chart + + + align:start position:0% +operator showing me their control chart +okay I see control charts all through + + align:start position:0% +okay I see control charts all through + + + align:start position:0% +okay I see control charts all through +healthcare okay so let's make a control + + align:start position:0% +healthcare okay so let's make a control + + + align:start position:0% +healthcare okay so let's make a control +chart okay so we're going to do a little + + align:start position:0% +chart okay so we're going to do a little + + + align:start position:0% +chart okay so we're going to do a little +experiment a little thing here we're + + align:start position:0% +experiment a little thing here we're + + + align:start position:0% +experiment a little thing here we're +going to put it in the framework of a + + align:start position:0% +going to put it in the framework of a + + + align:start position:0% +going to put it in the framework of a +pharmacy for those of you who are not + + align:start position:0% +pharmacy for those of you who are not + + + align:start position:0% +pharmacy for those of you who are not +kind of in the framework of healthcare + + align:start position:0% +kind of in the framework of healthcare + + + align:start position:0% +kind of in the framework of healthcare +you could think of another application + + align:start position:0% +you could think of another application + + + align:start position:0% +you could think of another application +where you're you're getting something + + align:start position:0% +where you're you're getting something + + + align:start position:0% +where you're you're getting something +but our pharmacy here dispenses a + + align:start position:0% +but our pharmacy here dispenses a + + + align:start position:0% +but our pharmacy here dispenses a +medicine called a white bean medicine + + align:start position:0% +medicine called a white bean medicine + + + align:start position:0% +medicine called a white bean medicine +okay and we get it in bulk from two + + align:start position:0% +okay and we get it in bulk from two + + + align:start position:0% +okay and we get it in bulk from two +different suppliers + + align:start position:0% +different suppliers + + + align:start position:0% +different suppliers +this is our + + align:start position:0% +this is our + + + align:start position:0% +this is our +brand name supplier Goa and it appears + + align:start position:0% +brand name supplier Goa and it appears + + + align:start position:0% +brand name supplier Goa and it appears +to be come from Spain it's a little hard + + align:start position:0% +to be come from Spain it's a little hard + + + align:start position:0% +to be come from Spain it's a little hard +to tell what the original source is here + + align:start position:0% +to tell what the original source is here + + + align:start position:0% +to tell what the original source is here +but at the end of it ice there's some + + align:start position:0% +but at the end of it ice there's some + + + align:start position:0% +but at the end of it ice there's some +Spanish inside the unit comes from Spain + + align:start position:0% +Spanish inside the unit comes from Spain + + + align:start position:0% +Spanish inside the unit comes from Spain +and this is our generic supplier Shaw's + + align:start position:0% +and this is our generic supplier Shaw's + + + align:start position:0% +and this is our generic supplier Shaw's +and they so we get these two suppliers + + align:start position:0% +and they so we get these two suppliers + + + align:start position:0% +and they so we get these two suppliers +and if you read the back of the Shaw's + + align:start position:0% +and if you read the back of the Shaw's + + + align:start position:0% +and if you read the back of the Shaw's +well you can read the back of the labels + + align:start position:0% +well you can read the back of the labels + + + align:start position:0% +well you can read the back of the labels +can you two later so our pharmacy gets + + align:start position:0% +can you two later so our pharmacy gets + + + align:start position:0% +can you two later so our pharmacy gets +it and puts it in these bins and then + + align:start position:0% +it and puts it in these bins and then + + + align:start position:0% +it and puts it in these bins and then +they've decided to measure dosages by + + align:start position:0% +they've decided to measure dosages by + + + align:start position:0% +they've decided to measure dosages by +volume now it usually a dosages by + + align:start position:0% +volume now it usually a dosages by + + + align:start position:0% +volume now it usually a dosages by +weight okay + + align:start position:0% +weight okay + + + align:start position:0% +weight okay +but weights lot you know it's much + + align:start position:0% +but weights lot you know it's much + + + align:start position:0% +but weights lot you know it's much +easier just to kind of scoop this up and + + align:start position:0% +easier just to kind of scoop this up and + + + align:start position:0% +easier just to kind of scoop this up and +fill it then scoop it up and fill it + + align:start position:0% +fill it then scoop it up and fill it + + + align:start position:0% +fill it then scoop it up and fill it +away and so on so we're doing it by + + align:start position:0% +away and so on so we're doing it by + + + align:start position:0% +away and so on so we're doing it by +volume and what we want to do is to + + align:start position:0% +volume and what we want to do is to + + + align:start position:0% +volume and what we want to do is to +track our pharmacy dispensary to be sure + + align:start position:0% +track our pharmacy dispensary to be sure + + + align:start position:0% +track our pharmacy dispensary to be sure +that the regained consistent weight okay + + align:start position:0% +that the regained consistent weight okay + + + align:start position:0% +that the regained consistent weight okay +and so our pharmacy this is a this is + + align:start position:0% +and so our pharmacy this is a this is + + + align:start position:0% +and so our pharmacy this is a this is +not a critical medicine but it's widely + + align:start position:0% +not a critical medicine but it's widely + + + align:start position:0% +not a critical medicine but it's widely +used in our facility so we dispense a + + align:start position:0% +used in our facility so we dispense a + + + align:start position:0% +used in our facility so we dispense a +lot of it each day and so what we've + + align:start position:0% +lot of it each day and so what we've + + + align:start position:0% +lot of it each day and so what we've +done in our pharmacy is our pharmacy is + + align:start position:0% +done in our pharmacy is our pharmacy is + + + align:start position:0% +done in our pharmacy is our pharmacy is +going to take three samples of this + + align:start position:0% +going to take three samples of this + + + align:start position:0% +going to take three samples of this +medicine each day and weigh it and the + + align:start position:0% +medicine each day and weigh it and the + + + align:start position:0% +medicine each day and weigh it and the +next day I'll take three more samples + + align:start position:0% +next day I'll take three more samples + + + align:start position:0% +next day I'll take three more samples +and weigh it and we're going to build + + align:start position:0% +and weigh it and we're going to build + + + align:start position:0% +and weigh it and we're going to build +this chart to see what's like and the + + align:start position:0% +this chart to see what's like and the + + + align:start position:0% +this chart to see what's like and the +pharmacy has been very cooperative + + align:start position:0% +pharmacy has been very cooperative + + + align:start position:0% +pharmacy has been very cooperative +they've given us 20 samples that are + + align:start position:0% +they've given us 20 samples that are + + + align:start position:0% +they've given us 20 samples that are +already on your table okay so a minute + + align:start position:0% +already on your table okay so a minute + + + align:start position:0% +already on your table okay so a minute +I'm going to tell you what to do we're + + align:start position:0% +I'm going to tell you what to do we're + + + align:start position:0% +I'm going to tell you what to do we're +going to enter this data so we got a + + align:start position:0% +going to enter this data so we got a + + + align:start position:0% +going to enter this data so we got a +three cup sample we're going to enter + + align:start position:0% +three cup sample we're going to enter + + + align:start position:0% +three cup sample we're going to enter +data into control charts one for the + + align:start position:0% +data into control charts one for the + + + align:start position:0% +data into control charts one for the +average weight and one for the range of + + align:start position:0% +average weight and one for the range of + + + align:start position:0% +average weight and one for the range of +the weight of the three cups and we're + + align:start position:0% +the weight of the three cups and we're + + + align:start position:0% +the weight of the three cups and we're +going to use it for 20 days to establish + + align:start position:0% +going to use it for 20 days to establish + + + align:start position:0% +going to use it for 20 days to establish +our process capability so we're going to + + align:start position:0% +our process capability so we're going to + + + align:start position:0% +our process capability so we're going to +measure for 20 days and then that's + + align:start position:0% +measure for 20 days and then that's + + + align:start position:0% +measure for 20 days and then that's +going to tell us do we have a stable + + align:start position:0% +going to tell us do we have a stable + + + align:start position:0% +going to tell us do we have a stable +process then we can monitor after that + + align:start position:0% +process then we can monitor after that + + + align:start position:0% +process then we can monitor after that +and so that's what we're going to do so + + align:start position:0% +and so that's what we're going to do so + + + align:start position:0% +and so that's what we're going to do so +our first phase is now each of you are + + align:start position:0% +our first phase is now each of you are + + + align:start position:0% +our first phase is now each of you are +going to weigh this you each have four + + align:start position:0% +going to weigh this you each have four + + + align:start position:0% +going to weigh this you each have four +days in the center of your table you + + align:start position:0% +days in the center of your table you + + + align:start position:0% +days in the center of your table you +have 12 cups and the cups go there are + + align:start position:0% +have 12 cups and the cups go there are + + + align:start position:0% +have 12 cups and the cups go there are +3-3 cups for each day it says right on + + align:start position:0% +3-3 cups for each day it says right on + + + align:start position:0% +3-3 cups for each day it says right on +there this is day 16 there three day 16 + + align:start position:0% +there this is day 16 there three day 16 + + + align:start position:0% +there this is day 16 there three day 16 +cups and you have a sheet and your sheet + + align:start position:0% +cups and you have a sheet and your sheet + + + align:start position:0% +cups and you have a sheet and your sheet +says here's day 16 so you measure cup + + align:start position:0% +says here's day 16 so you measure cup + + + align:start position:0% +says here's day 16 so you measure cup +ABC you compute the average we can get + + align:start position:0% +ABC you compute the average we can get + + + align:start position:0% +ABC you compute the average we can get +some calculators if you need it + + align:start position:0% +some calculators if you need it + + + align:start position:0% +some calculators if you need it +the max and the min and then the range + + align:start position:0% +the max and the min and then the range + + + align:start position:0% +the max and the min and then the range +which is the max minus the min and then + + align:start position:0% +which is the max minus the min and then + + + align:start position:0% +which is the max minus the min and then +you bring that up here to data central + + align:start position:0% +you bring that up here to data central + + + align:start position:0% +you bring that up here to data central +and will will record it and you have a + + align:start position:0% +and will will record it and you have a + + + align:start position:0% +and will will record it and you have a +scale and you want to use grams this is + + align:start position:0% +scale and you want to use grams this is + + + align:start position:0% +scale and you want to use grams this is +in kilogram of pounds and kilograms you + + align:start position:0% +in kilogram of pounds and kilograms you + + + align:start position:0% +in kilogram of pounds and kilograms you +want to use the kilogram scale to get it + + align:start position:0% +want to use the kilogram scale to get it + + + align:start position:0% +want to use the kilogram scale to get it +in grams and don't use this now but when + + align:start position:0% +in grams and don't use this now but when + + + align:start position:0% +in grams and don't use this now but when +we're all finished we'll dump the beans + + align:start position:0% +we're all finished we'll dump the beans + + + align:start position:0% +we're all finished we'll dump the beans +in there but don't do it now because we + + align:start position:0% +in there but don't do it now because we + + + align:start position:0% +in there but don't do it now because we +want to we may need to go back and look + + align:start position:0% +want to we may need to go back and look + + + align:start position:0% +want to we may need to go back and look +at do some second measurements okay so + + align:start position:0% +at do some second measurements okay so + + + align:start position:0% +at do some second measurements okay so +please now start at your tables + + align:start position:0% +please now start at your tables + + + align:start position:0% +please now start at your tables +measuring these samples filling out the + + align:start position:0% +measuring these samples filling out the + + + align:start position:0% +measuring these samples filling out the +chart and bringing it up here + + align:start position:0% + + + + align:start position:0% + +excellent very welcome okay so we have + + align:start position:0% +excellent very welcome okay so we have + + + align:start position:0% +excellent very welcome okay so we have +all the data and our my helper over here + + align:start position:0% +all the data and our my helper over here + + + align:start position:0% +all the data and our my helper over here +is going to enter it day by day so it + + align:start position:0% +is going to enter it day by day so it + + + align:start position:0% +is going to enter it day by day so it +kind of unfolds like you would see a + + align:start position:0% +kind of unfolds like you would see a + + + align:start position:0% +kind of unfolds like you would see a +normal control chart if you're watching + + align:start position:0% +normal control chart if you're watching + + + align:start position:0% +normal control chart if you're watching +it day by day so II now on day five now + + align:start position:0% +it day by day so II now on day five now + + + align:start position:0% +it day by day so II now on day five now +what we have this is the mean average + + align:start position:0% +what we have this is the mean average + + + align:start position:0% +what we have this is the mean average +and this is okay this is the average and + + align:start position:0% +and this is okay this is the average and + + + align:start position:0% +and this is okay this is the average and +this is the range and this is the mean + + align:start position:0% +this is the range and this is the mean + + + align:start position:0% +this is the range and this is the mean +of the average and this is the mean of + + align:start position:0% +of the average and this is the mean of + + + align:start position:0% +of the average and this is the mean of +the range okay + + align:start position:0% +the range okay + + + align:start position:0% +the range okay +and then what we have here these red + + align:start position:0% +and then what we have here these red + + + align:start position:0% +and then what we have here these red +lines are the three sigma lines + + align:start position:0% +lines are the three sigma lines + + + align:start position:0% +lines are the three sigma lines +memorized on the normal distribution i + + align:start position:0% +memorized on the normal distribution i + + + align:start position:0% +memorized on the normal distribution i +said three sigma so so the way these + + align:start position:0% +said three sigma so so the way these + + + align:start position:0% +said three sigma so so the way these +control charts work is you get this data + + align:start position:0% +control charts work is you get this data + + + align:start position:0% +control charts work is you get this data +it's it sort of been established that + + align:start position:0% +it's it sort of been established that + + + align:start position:0% +it's it sort of been established that +the process is you look at a three sigma + + align:start position:0% +the process is you look at a three sigma + + + align:start position:0% +the process is you look at a three sigma +deviation and as long as you're within + + align:start position:0% +deviation and as long as you're within + + + align:start position:0% +deviation and as long as you're within +that three sigma deviation your process + + align:start position:0% +that three sigma deviation your process + + + align:start position:0% +that three sigma deviation your process +is under control okay that's just sort + + align:start position:0% +is under control okay that's just sort + + + align:start position:0% +is under control okay that's just sort +of the what's evolved and and of course + + align:start position:0% +of the what's evolved and and of course + + + align:start position:0% +of the what's evolved and and of course +this these red lines will change as he + + align:start position:0% +this these red lines will change as he + + + align:start position:0% +this these red lines will change as he +enters the data because he's getting + + align:start position:0% +enters the data because he's getting + + + align:start position:0% +enters the data because he's getting +more and more samples so this is like + + align:start position:0% +more and more samples so this is like + + + align:start position:0% +more and more samples so this is like +you know watching the election returns + + align:start position:0% +you know watching the election returns + + + align:start position:0% +you know watching the election returns +on election eve okay okay so we're up to + + align:start position:0% +on election eve okay okay so we're up to + + + align:start position:0% +on election eve okay okay so we're up to +day ten okay and what's going on the + + align:start position:0% +day ten okay and what's going on the + + + align:start position:0% +day ten okay and what's going on the +background one of our colleagues at cal + + align:start position:0% +background one of our colleagues at cal + + + align:start position:0% +background one of our colleagues at cal +poly put this spreadsheet together so + + align:start position:0% +poly put this spreadsheet together so + + + align:start position:0% +poly put this spreadsheet together so +this shows the the app the mean what's + + align:start position:0% +this shows the the app the mean what's + + + align:start position:0% +this shows the the app the mean what's +called x-bar this is X bar and this is + + align:start position:0% +called x-bar this is X bar and this is + + + align:start position:0% +called x-bar this is X bar and this is +our bar x is the average of the in R is + + align:start position:0% +our bar x is the average of the in R is + + + align:start position:0% +our bar x is the average of the in R is +the range and then we got the upper and + + align:start position:0% +the range and then we got the upper and + + + align:start position:0% +the range and then we got the upper and +lower control limits these are called + + align:start position:0% +lower control limits these are called + + + align:start position:0% +lower control limits these are called +upper control limits and lower control + + align:start position:0% +upper control limits and lower control + + + align:start position:0% +upper control limits and lower control +limits got the upper and lower control + + align:start position:0% +limits got the upper and lower control + + + align:start position:0% +limits got the upper and lower control +limits for the average and for the range + + align:start position:0% +limits for the average and for the range + + + align:start position:0% +limits for the average and for the range +and usually it's the way this field + + align:start position:0% +and usually it's the way this field + + + align:start position:0% +and usually it's the way this field +works is 20 samples is considered a good + + align:start position:0% +works is 20 samples is considered a good + + + align:start position:0% +works is 20 samples is considered a good +enough baseline to establish the process + + align:start position:0% +enough baseline to establish the process + + + align:start position:0% +enough baseline to establish the process +capability so Oh + + align:start position:0% + + + + align:start position:0% + +did you jolt can you double-check that + + align:start position:0% + + + + align:start position:0% + +okay well let's finish it off let's keep + + align:start position:0% +okay well let's finish it off let's keep + + + align:start position:0% +okay well let's finish it off let's keep +going okay so something's obviously + + align:start position:0% +going okay so something's obviously + + + align:start position:0% +going okay so something's obviously +funny with day 15 so when you have some + + align:start position:0% +funny with day 15 so when you have some + + + align:start position:0% +funny with day 15 so when you have some +funny data what do you do go to the + + align:start position:0% +funny data what do you do go to the + + + align:start position:0% +funny data what do you do go to the +gemba so where is 15 okay so let's go + + align:start position:0% +gemba so where is 15 okay so let's go + + + align:start position:0% +gemba so where is 15 okay so let's go +take a look at 15 what's going on here + + align:start position:0% +take a look at 15 what's going on here + + + align:start position:0% +take a look at 15 what's going on here +can you weigh it again it's not it + + align:start position:0% +can you weigh it again it's not it + + + align:start position:0% +can you weigh it again it's not it +doesn't look quite full does it you want + + align:start position:0% +doesn't look quite full does it you want + + + align:start position:0% +doesn't look quite full does it you want +to want you put some more beans in there + + align:start position:0% + + + + align:start position:0% + +just fill it up you know kind of like + + align:start position:0% +just fill it up you know kind of like + + + align:start position:0% +just fill it up you know kind of like +the rest of these what's now 73 okay so + + align:start position:0% +the rest of these what's now 73 okay so + + + align:start position:0% +the rest of these what's now 73 okay so +okay so now here's on day 15 something + + align:start position:0% +okay so now here's on day 15 something + + + align:start position:0% +okay so now here's on day 15 something +happened in the pharmacy and all three + + align:start position:0% +happened in the pharmacy and all three + + + align:start position:0% +happened in the pharmacy and all three +cups are shy by quarter-inch eighth inch + + align:start position:0% +cups are shy by quarter-inch eighth inch + + + align:start position:0% +cups are shy by quarter-inch eighth inch +something like that so what we would + + align:start position:0% +something like that so what we would + + + align:start position:0% +something like that so what we would +probably do is go back to the pharmacy + + align:start position:0% +probably do is go back to the pharmacy + + + align:start position:0% +probably do is go back to the pharmacy +records and see what happened and we + + align:start position:0% +records and see what happened and we + + + align:start position:0% +records and see what happened and we +might find out for example that some + + align:start position:0% +might find out for example that some + + + align:start position:0% +might find out for example that some +employee had been ill that day and it + + align:start position:0% +employee had been ill that day and it + + + align:start position:0% +employee had been ill that day and it +hired a temp or fill in wasn't cross + + align:start position:0% +hired a temp or fill in wasn't cross + + + align:start position:0% +hired a temp or fill in wasn't cross +trained properly and they thought this + + align:start position:0% +trained properly and they thought this + + + align:start position:0% +trained properly and they thought this +was a full cup a full dosage so we can + + align:start position:0% +was a full cup a full dosage so we can + + + align:start position:0% +was a full cup a full dosage so we can +eliminate so let's delete that point we + + align:start position:0% +eliminate so let's delete that point we + + + align:start position:0% +eliminate so let's delete that point we +know that that point is no good because + + align:start position:0% +know that that point is no good because + + + align:start position:0% +know that that point is no good because +for certain we can see it we can verify + + align:start position:0% +for certain we can see it we can verify + + + align:start position:0% +for certain we can see it we can verify +it's no good so okay that's fine okay no + + align:start position:0% +it's no good so okay that's fine okay no + + + align:start position:0% +it's no good so okay that's fine okay no +that's fine no no it's fine it's fine + + align:start position:0% +that's fine no no it's fine it's fine + + + align:start position:0% +that's fine no no it's fine it's fine +yeah thank you sir yep okay so now we've + + align:start position:0% +yeah thank you sir yep okay so now we've + + + align:start position:0% +yeah thank you sir yep okay so now we've +got our process capability established + + align:start position:0% +got our process capability established + + + align:start position:0% +got our process capability established +we got 20 days - the one bogus day and + + align:start position:0% +we got 20 days - the one bogus day and + + + align:start position:0% +we got 20 days - the one bogus day and +our upper and lower control limits or we + + align:start position:0% +our upper and lower control limits or we + + + align:start position:0% +our upper and lower control limits or we +know now for our process at 75 and 69 + + align:start position:0% +know now for our process at 75 and 69 + + + align:start position:0% +know now for our process at 75 and 69 +and we got them for the range okay okay + + align:start position:0% +and we got them for the range okay okay + + + align:start position:0% +and we got them for the range okay okay +so good thank you so that's how we would + + align:start position:0% +so good thank you so that's how we would + + + align:start position:0% +so good thank you so that's how we would +build a control chart so now we're going + + align:start position:0% +build a control chart so now we're going + + + align:start position:0% +build a control chart so now we're going +to do a little bit more slides then + + align:start position:0% +to do a little bit more slides then + + + align:start position:0% +to do a little bit more slides then +we're going to come back to see how we + + align:start position:0% +we're going to come back to see how we + + + align:start position:0% +we're going to come back to see how we +use this control chart so I'm going to + + align:start position:0% +use this control chart so I'm going to + + + align:start position:0% +use this control chart so I'm going to +change now + + align:start position:0% +change now + + + align:start position:0% +change now +from the sort of basic control charting + + align:start position:0% +from the sort of basic control charting + + + align:start position:0% +from the sort of basic control charting +to a little bit about the basic Six + + align:start position:0% +to a little bit about the basic Six + + + align:start position:0% +to a little bit about the basic Six +Sigma method called de mayic and Omega + + align:start position:0% +Sigma method called de mayic and Omega + + + align:start position:0% +Sigma method called de mayic and Omega +is another Deming cycle is like plan do + + align:start position:0% +is another Deming cycle is like plan do + + + align:start position:0% +is another Deming cycle is like plan do +study act except it's slightly different + + align:start position:0% +study act except it's slightly different + + + align:start position:0% +study act except it's slightly different +it's called define measure analyze + + align:start position:0% +it's called define measure analyze + + + align:start position:0% +it's called define measure analyze +improve and control and so the Mayock is + + align:start position:0% +improve and control and so the Mayock is + + + align:start position:0% +improve and control and so the Mayock is +easy one thing to remember so so if + + align:start position:0% +easy one thing to remember so so if + + + align:start position:0% +easy one thing to remember so so if +you're doing a Six Sigma + + align:start position:0% +you're doing a Six Sigma + + + align:start position:0% +you're doing a Six Sigma +intervention like in our pharmacy we + + align:start position:0% +intervention like in our pharmacy we + + + align:start position:0% +intervention like in our pharmacy we +would have to define who are the + + align:start position:0% +would have to define who are the + + + align:start position:0% +would have to define who are the +customers and what are their + + align:start position:0% +customers and what are their + + + align:start position:0% +customers and what are their +requirements so in the case of the + + align:start position:0% +requirements so in the case of the + + + align:start position:0% +requirements so in the case of the +pharmacy the customers would be + + align:start position:0% +pharmacy the customers would be + + + align:start position:0% +pharmacy the customers would be +whoever's ordered the medicine in they + + align:start position:0% +whoever's ordered the medicine in they + + + align:start position:0% +whoever's ordered the medicine in they +have some requirements and then we want + + align:start position:0% +have some requirements and then we want + + + align:start position:0% +have some requirements and then we want +to know what the key characteristics are + + align:start position:0% +to know what the key characteristics are + + + align:start position:0% +to know what the key characteristics are +important to the customer while the + + align:start position:0% +important to the customer while the + + + align:start position:0% +important to the customer while the +customer for medication is really + + align:start position:0% +customer for medication is really + + + align:start position:0% +customer for medication is really +interested in weight you know they don't + + align:start position:0% +interested in weight you know they don't + + + align:start position:0% +interested in weight you know they don't +care too much what it looks like they + + align:start position:0% +care too much what it looks like they + + + align:start position:0% +care too much what it looks like they +really don't care how it's packed in the + + align:start position:0% +really don't care how it's packed in the + + + align:start position:0% +really don't care how it's packed in the +cup things like that but they're they're + + align:start position:0% +cup things like that but they're they're + + + align:start position:0% +cup things like that but they're they're +really interested in weight and of + + align:start position:0% +really interested in weight and of + + + align:start position:0% +really interested in weight and of +course we're we're using volume because + + align:start position:0% +course we're we're using volume because + + + align:start position:0% +course we're we're using volume because +it's a little quicker but they're + + align:start position:0% +it's a little quicker but they're + + + align:start position:0% +it's a little quicker but they're +interested in weight so okay then you + + align:start position:0% +interested in weight so okay then you + + + align:start position:0% +interested in weight so okay then you +measure so once we know the key + + align:start position:0% +measure so once we know the key + + + align:start position:0% +measure so once we know the key +characterized characteristics then you + + align:start position:0% +characterized characteristics then you + + + align:start position:0% +characterized characteristics then you +what are the key input and output + + align:start position:0% +what are the key input and output + + + align:start position:0% +what are the key input and output +characteristics and you want to verify + + align:start position:0% +characteristics and you want to verify + + + align:start position:0% +characteristics and you want to verify +the measurement system so here are + + align:start position:0% +the measurement system so here are + + + align:start position:0% +the measurement system so here are +output characteristics is the weight of + + align:start position:0% +output characteristics is the weight of + + + align:start position:0% +output characteristics is the weight of +the cup that's what we're measuring + + align:start position:0% +the cup that's what we're measuring + + + align:start position:0% +the cup that's what we're measuring +later on we might get more sophisticated + + align:start position:0% +later on we might get more sophisticated + + + align:start position:0% +later on we might get more sophisticated +and measure the input characteristics + + align:start position:0% +and measure the input characteristics + + + align:start position:0% +and measure the input characteristics +like you know we might we might weigh + + align:start position:0% +like you know we might we might weigh + + + align:start position:0% +like you know we might we might weigh +these two samples or something like that + + align:start position:0% +these two samples or something like that + + + align:start position:0% +these two samples or something like that +but right now we're just focused on the + + align:start position:0% +but right now we're just focused on the + + + align:start position:0% +but right now we're just focused on the +output characteristics and we collect + + align:start position:0% +output characteristics and we collect + + + align:start position:0% +output characteristics and we collect +the data and establish the baseline + + align:start position:0% +the data and establish the baseline + + + align:start position:0% +the data and establish the baseline +performance that's what we've done okay + + align:start position:0% +performance that's what we've done okay + + + align:start position:0% +performance that's what we've done okay +and then we've done that so far then + + align:start position:0% +and then we've done that so far then + + + align:start position:0% +and then we've done that so far then +we're going to look at the raw data we + + align:start position:0% +we're going to look at the raw data we + + + align:start position:0% +we're going to look at the raw data we +convert the raw data information and see + + align:start position:0% +convert the raw data information and see + + + align:start position:0% +convert the raw data information and see +get insights into the process where we + + align:start position:0% +get insights into the process where we + + + align:start position:0% +get insights into the process where we +already found out we had something wrong + + align:start position:0% +already found out we had something wrong + + + align:start position:0% +already found out we had something wrong +with you know poor Molly on day 15 she + + align:start position:0% +with you know poor Molly on day 15 she + + + align:start position:0% +with you know poor Molly on day 15 she +got the flu and and we had a good + + align:start position:0% +got the flu and and we had a good + + + align:start position:0% +got the flu and and we had a good +template we didn't train the temp so + + align:start position:0% +template we didn't train the temp so + + + align:start position:0% +template we didn't train the temp so +we've learned now the training is + + align:start position:0% +we've learned now the training is + + + align:start position:0% +we've learned now the training is +important so we don't dispense the wrong + + align:start position:0% +important so we don't dispense the wrong + + + align:start position:0% +important so we don't dispense the wrong +medication okay now we we've improved + + align:start position:0% +medication okay now we we've improved + + + align:start position:0% +medication okay now we we've improved +you know we've developed a solution and + + align:start position:0% +you know we've developed a solution and + + + align:start position:0% +you know we've developed a solution and +now we want to put our process under + + align:start position:0% +now we want to put our process under + + + align:start position:0% +now we want to put our process under +process control mean under process + + align:start position:0% +process control mean under process + + + align:start position:0% +process control mean under process +control we're going to now monitor eat + + align:start position:0% +control we're going to now monitor eat + + + align:start position:0% +control we're going to now monitor eat +day by day that the medication + + align:start position:0% +day by day that the medication + + + align:start position:0% +day by day that the medication +dispensing + + align:start position:0% +dispensing + + + align:start position:0% +dispensing +and see if it stays within control + + align:start position:0% +and see if it stays within control + + + align:start position:0% +and see if it stays within control +that's the Mayock so here's a simple + + align:start position:0% +that's the Mayock so here's a simple + + + align:start position:0% +that's the Mayock so here's a simple +example you have a process so you have a + + align:start position:0% +example you have a process so you have a + + + align:start position:0% +example you have a process so you have a +defined process with an input and an + + align:start position:0% +defined process with an input and an + + + align:start position:0% +defined process with an input and an +output you measure the weight with a + + align:start position:0% +output you measure the weight with a + + + align:start position:0% +output you measure the weight with a +scale you analyze the data with the + + align:start position:0% +scale you analyze the data with the + + + align:start position:0% +scale you analyze the data with the +control chart and you want to improve + + align:start position:0% +control chart and you want to improve + + + align:start position:0% +control chart and you want to improve +the process we just talked about + + align:start position:0% +the process we just talked about + + + align:start position:0% +the process we just talked about +training is one improvement and then you + + align:start position:0% +training is one improvement and then you + + + align:start position:0% +training is one improvement and then you +put it under process control okay + + align:start position:0% +put it under process control okay + + + align:start position:0% +put it under process control okay +so that's kind of that's the basic Six + + align:start position:0% +so that's kind of that's the basic Six + + + align:start position:0% +so that's kind of that's the basic Six +Sigma cycle this is one area where I + + align:start position:0% +Sigma cycle this is one area where I + + + align:start position:0% +Sigma cycle this is one area where I +said in lean if when you came out of + + align:start position:0% +said in lean if when you came out of + + + align:start position:0% +said in lean if when you came out of +this course you could probably pick up + + align:start position:0% +this course you could probably pick up + + + align:start position:0% +this course you could probably pick up +any book and lean and you'd go for it if + + align:start position:0% +any book and lean and you'd go for it if + + + align:start position:0% +any book and lean and you'd go for it if +you pick up Six Sigma books they do a + + align:start position:0% +you pick up Six Sigma books they do a + + + align:start position:0% +you pick up Six Sigma books they do a +deep dive into a lot of math so it's + + align:start position:0% +deep dive into a lot of math so it's + + + align:start position:0% +deep dive into a lot of math so it's +very lot of statistical mathematics so + + align:start position:0% +very lot of statistical mathematics so + + + align:start position:0% +very lot of statistical mathematics so +you may need more than what we've taught + + align:start position:0% +you may need more than what we've taught + + + align:start position:0% +you may need more than what we've taught +you because we're not focusing on math + + align:start position:0% +you because we're not focusing on math + + + align:start position:0% +you because we're not focusing on math +okay it's easy to see in a process + + align:start position:0% +okay it's easy to see in a process + + + align:start position:0% +okay it's easy to see in a process +control application like this it may get + + align:start position:0% +control application like this it may get + + + align:start position:0% +control application like this it may get +more complicated if you're looking at + + align:start position:0% +more complicated if you're looking at + + + align:start position:0% +more complicated if you're looking at +something that's not quite so visual but + + align:start position:0% +something that's not quite so visual but + + + align:start position:0% +something that's not quite so visual but +anyway that's what it's now okay now + + align:start position:0% +anyway that's what it's now okay now + + + align:start position:0% +anyway that's what it's now okay now +there's certain kind of variation in the + + align:start position:0% +there's certain kind of variation in the + + + align:start position:0% +there's certain kind of variation in the +process and actually our control chart + + align:start position:0% +process and actually our control chart + + + align:start position:0% +process and actually our control chart +was a good example of that there's + + align:start position:0% +was a good example of that there's + + + align:start position:0% +was a good example of that there's +what's called common cause variation and + + align:start position:0% +what's called common cause variation and + + + align:start position:0% +what's called common cause variation and +this is kind of just the sort of + + align:start position:0% +this is kind of just the sort of + + + align:start position:0% +this is kind of just the sort of +randomness in the system you know that + + align:start position:0% +randomness in the system you know that + + + align:start position:0% +randomness in the system you know that +the things that affect all the samples + + align:start position:0% +the things that affect all the samples + + + align:start position:0% +the things that affect all the samples +and and then you have special cause + + align:start position:0% +and and then you have special cause + + + align:start position:0% +and and then you have special cause +variation and we just had an example + + align:start position:0% +variation and we just had an example + + + align:start position:0% +variation and we just had an example +that common cause was the it was the + + align:start position:0% +that common cause was the it was the + + + align:start position:0% +that common cause was the it was the +different variations of nineteen to the + + align:start position:0% +different variations of nineteen to the + + + align:start position:0% +different variations of nineteen to the +twenty days and then we had one case + + align:start position:0% +twenty days and then we had one case + + + align:start position:0% +twenty days and then we had one case +which was a special cause variation we + + align:start position:0% +which was a special cause variation we + + + align:start position:0% +which was a special cause variation we +sort of went out of bounds in that we + + align:start position:0% +sort of went out of bounds in that we + + + align:start position:0% +sort of went out of bounds in that we +went we could go in and we can intervene + + align:start position:0% +went we could go in and we can intervene + + + align:start position:0% +went we could go in and we can intervene +fairly quickly and correct to get our + + align:start position:0% +fairly quickly and correct to get our + + + align:start position:0% +fairly quickly and correct to get our +common cause variation down we're going + + align:start position:0% +common cause variation down we're going + + + align:start position:0% +common cause variation down we're going +to have to do something different you + + align:start position:0% +to have to do something different you + + + align:start position:0% +to have to do something different you +know we're going to have to be much more + + align:start position:0% +know we're going to have to be much more + + + align:start position:0% +know we're going to have to be much more +careful about how we fill the cups and + + align:start position:0% +careful about how we fill the cups and + + + align:start position:0% +careful about how we fill the cups and +stuff like that we might have to work + + align:start position:0% +stuff like that we might have to work + + + align:start position:0% +stuff like that we might have to work +careful procedures but the the sort of + + align:start position:0% +careful procedures but the the sort of + + + align:start position:0% +careful procedures but the the sort of +special cause variation we want to drive + + align:start position:0% +special cause variation we want to drive + + + align:start position:0% +special cause variation we want to drive +out of the system and the control charts + + align:start position:0% +out of the system and the control charts + + + align:start position:0% +out of the system and the control charts +give you a way to quickly see the + + align:start position:0% +give you a way to quickly see the + + + align:start position:0% +give you a way to quickly see the +differences between these two so let's + + align:start position:0% +differences between these two so let's + + + align:start position:0% +differences between these two so let's +look at an example this is actual data + + align:start position:0% +look at an example this is actual data + + + align:start position:0% +look at an example this is actual data +for patient Falls I've forgotten the + + align:start position:0% +for patient Falls I've forgotten the + + + align:start position:0% +for patient Falls I've forgotten the +facility anyway the reference is just + + align:start position:0% +facility anyway the reference is just + + + align:start position:0% +facility anyway the reference is just +off the back of this bottom of the + + align:start position:0% +off the back of this bottom of the + + + align:start position:0% +off the back of this bottom of the +screen here + + align:start position:0% +screen here + + + align:start position:0% +screen here +but this is a patient Falls and we've + + align:start position:0% +but this is a patient Falls and we've + + + align:start position:0% +but this is a patient Falls and we've +heard sue mentioned this morning how how + + align:start position:0% +heard sue mentioned this morning how how + + + align:start position:0% +heard sue mentioned this morning how how +patient Falls are you had a slide was + + align:start position:0% +patient Falls are you had a slide was + + + align:start position:0% +patient Falls are you had a slide was +something about their main a source of + + align:start position:0% +something about their main a source of + + + align:start position:0% +something about their main a source of +waste or something to it patient Falls + + align:start position:0% +waste or something to it patient Falls + + + align:start position:0% +waste or something to it patient Falls +are are considered and never event + + align:start position:0% +are are considered and never event + + + align:start position:0% +are are considered and never event +something never been right never read + + align:start position:0% +something never been right never read + + + align:start position:0% +something never been right never read +okay and here we got in this facility + + align:start position:0% +okay and here we got in this facility + + + align:start position:0% +okay and here we got in this facility +this is by month and you know we got an + + align:start position:0% +this is by month and you know we got an + + + align:start position:0% +this is by month and you know we got an +average of about six patient Falls a + + align:start position:0% +average of about six patient Falls a + + + align:start position:0% +average of about six patient Falls a +month okay and and they've been charting + + align:start position:0% +month okay and and they've been charting + + + align:start position:0% +month okay and and they've been charting +it and we have an upper control limit of + + align:start position:0% +it and we have an upper control limit of + + + align:start position:0% +it and we have an upper control limit of +about eight and a lower control limit of + + align:start position:0% +about eight and a lower control limit of + + + align:start position:0% +about eight and a lower control limit of +about four how many patient Falls would + + align:start position:0% +about four how many patient Falls would + + + align:start position:0% +about four how many patient Falls would +you want none okay that's a customer + + align:start position:0% +you want none okay that's a customer + + + align:start position:0% +you want none okay that's a customer +specified limit okay there's a + + align:start position:0% +specified limit okay there's a + + + align:start position:0% +specified limit okay there's a +difference between your process limit + + align:start position:0% +difference between your process limit + + + align:start position:0% +difference between your process limit +this is your as is process in this case + + align:start position:0% +this is your as is process in this case + + + align:start position:0% +this is your as is process in this case +your process is not very capable in the + + align:start position:0% +your process is not very capable in the + + + align:start position:0% +your process is not very capable in the +eyes of the customer okay so we're going + + align:start position:0% +eyes of the customer okay so we're going + + + align:start position:0% +eyes of the customer okay so we're going +to get into this towards the back end of + + align:start position:0% +to get into this towards the back end of + + + align:start position:0% +to get into this towards the back end of +the module about the during the process + + align:start position:0% +the module about the during the process + + + align:start position:0% +the module about the during the process +capability the upper and lower control + + align:start position:0% +capability the upper and lower control + + + align:start position:0% +capability the upper and lower control +limits and the upper and lower specified + + align:start position:0% +limits and the upper and lower specified + + + align:start position:0% +limits and the upper and lower specified +limits so I just kind of reduce it here + + align:start position:0% +limits so I just kind of reduce it here + + + align:start position:0% +limits so I just kind of reduce it here +as a teaser so you don't fall asleep + + align:start position:0% +as a teaser so you don't fall asleep + + + align:start position:0% +as a teaser so you don't fall asleep +okay so now we in this facility they + + align:start position:0% +okay so now we in this facility they + + + align:start position:0% +okay so now we in this facility they +they they tracked it for twenty days + + align:start position:0% +they they tracked it for twenty days + + + align:start position:0% +they they tracked it for twenty days +then they kept tracking it and then + + align:start position:0% +then they kept tracking it and then + + + align:start position:0% +then they kept tracking it and then +something starts going kind of bad here + + align:start position:0% +something starts going kind of bad here + + + align:start position:0% +something starts going kind of bad here +towards the end of the around twenty + + align:start position:0% +towards the end of the around twenty + + + align:start position:0% +towards the end of the around twenty +eighth month you know we got something + + align:start position:0% +eighth month you know we got something + + + align:start position:0% +eighth month you know we got something +that's kind of getting up to the control + + align:start position:0% +that's kind of getting up to the control + + + align:start position:0% +that's kind of getting up to the control +limits and then we got something that's + + align:start position:0% +limits and then we got something that's + + + align:start position:0% +limits and then we got something that's +going outside the control limits and + + align:start position:0% +going outside the control limits and + + + align:start position:0% +going outside the control limits and +this is when the red flags start saying + + align:start position:0% +this is when the red flags start saying + + + align:start position:0% +this is when the red flags start saying +okay we're outside the normal bounds we + + align:start position:0% +okay we're outside the normal bounds we + + + align:start position:0% +okay we're outside the normal bounds we +can consider acceptable we better go + + align:start position:0% +can consider acceptable we better go + + + align:start position:0% +can consider acceptable we better go +investigate what's happening here and + + align:start position:0% +investigate what's happening here and + + + align:start position:0% +investigate what's happening here and +that's what we did with with our + + align:start position:0% +that's what we did with with our + + + align:start position:0% +that's what we did with with our +pharmacy thing okay so now what we're + + align:start position:0% +pharmacy thing okay so now what we're + + + align:start position:0% +pharmacy thing okay so now what we're +going to do is continue our our exercise + + align:start position:0% +going to do is continue our our exercise + + + align:start position:0% +going to do is continue our our exercise +and the first thing I'd like you to do + + align:start position:0% +and the first thing I'd like you to do + + + align:start position:0% +and the first thing I'd like you to do +is take the cups and there's a white + + align:start position:0% +is take the cups and there's a white + + + align:start position:0% +is take the cups and there's a white +tray in here and dump all the beans that + + align:start position:0% +tray in here and dump all the beans that + + + align:start position:0% +tray in here and dump all the beans that +you have into there and just Ness the + + align:start position:0% +you have into there and just Ness the + + + align:start position:0% +you have into there and just Ness the +cups back together and then the pharmacy + + align:start position:0% +cups back together and then the pharmacy + + + align:start position:0% +cups back together and then the pharmacy +is going to bring you a new a new batch + + align:start position:0% +is going to bring you a new a new batch + + + align:start position:0% +is going to bring you a new a new batch +of cups let's get these out of the way + + align:start position:0% +of cups let's get these out of the way + + + align:start position:0% +of cups let's get these out of the way +first + + align:start position:0% +first + + + align:start position:0% +first +okay so while the well we gained some + + align:start position:0% +okay so while the well we gained some + + + align:start position:0% +okay so while the well we gained some +help here what's going to happen is each + + align:start position:0% +help here what's going to happen is each + + + align:start position:0% +help here what's going to happen is each +of the stations on their easel has a + + align:start position:0% +of the stations on their easel has a + + + align:start position:0% +of the stations on their easel has a +chart for the average in the range and + + align:start position:0% +chart for the average in the range and + + + align:start position:0% +chart for the average in the range and +what I want you to do is to put comments + + align:start position:0% +what I want you to do is to put comments + + + align:start position:0% +what I want you to do is to put comments +put you know come put a scale on this + + align:start position:0% +put you know come put a scale on this + + + align:start position:0% +put you know come put a scale on this +where you're going to put the okay the + + align:start position:0% +where you're going to put the okay the + + + align:start position:0% +where you're going to put the okay the +upper control limits we don't have to be + + align:start position:0% +upper control limits we don't have to be + + + align:start position:0% +upper control limits we don't have to be +accurate to the second decimal place + + align:start position:0% +accurate to the second decimal place + + + align:start position:0% +accurate to the second decimal place +here okay it's about seventy five point + + align:start position:0% +here okay it's about seventy five point + + + align:start position:0% +here okay it's about seventy five point +four and sixty nine point five so we + + align:start position:0% +four and sixty nine point five so we + + + align:start position:0% +four and sixty nine point five so we +want to do something like this let's go + + align:start position:0% +want to do something like this let's go + + + align:start position:0% +want to do something like this let's go +first well let's get the mean I'll just + + align:start position:0% +first well let's get the mean I'll just + + + align:start position:0% +first well let's get the mean I'll just +do one and I'll let the other the other + + align:start position:0% +do one and I'll let the other the other + + + align:start position:0% +do one and I'll let the other the other +tables do their so this is like seventy + + align:start position:0% +tables do their so this is like seventy + + + align:start position:0% +tables do their so this is like seventy +two point five that's the mean and then + + align:start position:0% +two point five that's the mean and then + + + align:start position:0% +two point five that's the mean and then +the upper control limit is about seventy + + align:start position:0% +the upper control limit is about seventy + + + align:start position:0% +the upper control limit is about seventy +five point four so we'll just put that + + align:start position:0% +five point four so we'll just put that + + + align:start position:0% +five point four so we'll just put that +here in the lower control limit is sixty + + align:start position:0% +here in the lower control limit is sixty + + + align:start position:0% +here in the lower control limit is sixty +nine point five so okay so you're going + + align:start position:0% +nine point five so okay so you're going + + + align:start position:0% +nine point five so okay so you're going +to want to finish that for this is for + + align:start position:0% +to want to finish that for this is for + + + align:start position:0% +to want to finish that for this is for +the average and this is for the range + + align:start position:0% +the average and this is for the range + + + align:start position:0% +the average and this is for the range +and I'll let each team finish their own + + align:start position:0% +and I'll let each team finish their own + + + align:start position:0% +and I'll let each team finish their own +and you can come up here and get the + + align:start position:0% +and you can come up here and get the + + + align:start position:0% +and you can come up here and get the +data if you need to and then so we want + + align:start position:0% +data if you need to and then so we want + + + align:start position:0% +data if you need to and then so we want +to draw the control limits on our chart + + align:start position:0% +to draw the control limits on our chart + + + align:start position:0% +to draw the control limits on our chart +that's now fixed that's our process + + align:start position:0% +that's now fixed that's our process + + + align:start position:0% +that's now fixed that's our process +capability and now we're going to start + + align:start position:0% +capability and now we're going to start + + + align:start position:0% +capability and now we're going to start +monitoring it for days twenty one twenty + + align:start position:0% +monitoring it for days twenty one twenty + + + align:start position:0% +monitoring it for days twenty one twenty +two twenty three twenty four but you're + + align:start position:0% +two twenty three twenty four but you're + + + align:start position:0% +two twenty three twenty four but you're +each going to do it you're going to do + + align:start position:0% +each going to do it you're going to do + + + align:start position:0% +each going to do it you're going to do +twenty one twenty two twenty three forty + + align:start position:0% +twenty one twenty two twenty three forty + + + align:start position:0% +twenty one twenty two twenty three forty +four word you're going to twenty one + + align:start position:0% +four word you're going to twenty one + + + align:start position:0% +four word you're going to twenty one +twenty two twenty three twenty four okay + + align:start position:0% +twenty two twenty three twenty four okay + + + align:start position:0% +twenty two twenty three twenty four okay +and you're going to measure three + + align:start position:0% +and you're going to measure three + + + align:start position:0% +and you're going to measure three +samples each day and plot the data on + + align:start position:0% +samples each day and plot the data on + + + align:start position:0% +samples each day and plot the data on +your control chart so whatever the date + + align:start position:0% +your control chart so whatever the date + + + align:start position:0% +your control chart so whatever the date +is for the average on twenty one on day + + align:start position:0% +is for the average on twenty one on day + + + align:start position:0% +is for the average on twenty one on day +21 you put here in the range on day + + align:start position:0% +21 you put here in the range on day + + + align:start position:0% +21 you put here in the range on day +twenty when you put here okay and you're + + align:start position:0% +twenty when you put here okay and you're + + + align:start position:0% +twenty when you put here okay and you're +going to look at it and you're going to + + align:start position:0% +going to look at it and you're going to + + + align:start position:0% +going to look at it and you're going to +see whether your process stays under + + align:start position:0% +see whether your process stays under + + + align:start position:0% +see whether your process stays under +control or whether it you know is it is + + align:start position:0% +control or whether it you know is it is + + + align:start position:0% +control or whether it you know is it is +it doing this or is it doing that or + + align:start position:0% +it doing this or is it doing that or + + + align:start position:0% +it doing this or is it doing that or +that or something else and if it starts + + align:start position:0% +that or something else and if it starts + + + align:start position:0% +that or something else and if it starts +going out of control once you've decided + + align:start position:0% +going out of control once you've decided + + + align:start position:0% +going out of control once you've decided +it's out of control you know you may + + align:start position:0% +it's out of control you know you may + + + align:start position:0% +it's out of control you know you may +have to watch a little bit then it's + + align:start position:0% +have to watch a little bit then it's + + + align:start position:0% +have to watch a little bit then it's +time to stop to investigate and what the + + align:start position:0% +time to stop to investigate and what the + + + align:start position:0% +time to stop to investigate and what the +root cause is just like we did here we + + align:start position:0% +root cause is just like we did here we + + + align:start position:0% +root cause is just like we did here we +went to + + align:start position:0% +went to + + + align:start position:0% +went to +find out the root cause was it wasn't + + align:start position:0% +find out the root cause was it wasn't + + + align:start position:0% +find out the root cause was it wasn't +filled but we want you to do this in a + + align:start position:0% +filled but we want you to do this in a + + + align:start position:0% +filled but we want you to do this in a +structured way okay the tendency you're + + align:start position:0% +structured way okay the tendency you're + + + align:start position:0% +structured way okay the tendency you're +all going to have to say I know what the + + align:start position:0% +all going to have to say I know what the + + + align:start position:0% +all going to have to say I know what the +root cause is somebody didn't fill it + + align:start position:0% +root cause is somebody didn't fill it + + + align:start position:0% +root cause is somebody didn't fill it +okay but maybe or maybe not so we're + + align:start position:0% +okay but maybe or maybe not so we're + + + align:start position:0% +okay but maybe or maybe not so we're +going to ask you to use the fishbone + + align:start position:0% +going to ask you to use the fishbone + + + align:start position:0% +going to ask you to use the fishbone +diagram that annalisa just told you + + align:start position:0% +diagram that annalisa just told you + + + align:start position:0% +diagram that annalisa just told you +about and that's on the second page and + + align:start position:0% +about and that's on the second page and + + + align:start position:0% +about and that's on the second page and +start thinking about all the reasons + + align:start position:0% +start thinking about all the reasons + + + align:start position:0% +start thinking about all the reasons +that the behavior you're observing might + + align:start position:0% +that the behavior you're observing might + + + align:start position:0% +that the behavior you're observing might +be happening you know for instance could + + align:start position:0% +be happening you know for instance could + + + align:start position:0% +be happening you know for instance could +it be that all BRE was thinking about + + align:start position:0% +it be that all BRE was thinking about + + + align:start position:0% +it be that all BRE was thinking about +something else and didn't weigh it right + + align:start position:0% +something else and didn't weigh it right + + + align:start position:0% +something else and didn't weigh it right +maybe maybe it's a person maybe it's a + + align:start position:0% +maybe maybe it's a person maybe it's a + + + align:start position:0% +maybe maybe it's a person maybe it's a +measurement thing so you that's a would + + align:start position:0% +measurement thing so you that's a would + + + align:start position:0% +measurement thing so you that's a would +be personnel or maybe maybe you got a + + align:start position:0% +be personnel or maybe maybe you got a + + + align:start position:0% +be personnel or maybe maybe you got a +crummy wayne scale that's a machine okay + + align:start position:0% +crummy wayne scale that's a machine okay + + + align:start position:0% +crummy wayne scale that's a machine okay +so start filling out all the things you + + align:start position:0% +so start filling out all the things you + + + align:start position:0% +so start filling out all the things you +can and then when you get those filled + + align:start position:0% +can and then when you get those filled + + + align:start position:0% +can and then when you get those filled +out then start looking at them + + align:start position:0% +out then start looking at them + + + align:start position:0% +out then start looking at them +systematically which one do you think is + + align:start position:0% +systematically which one do you think is + + + align:start position:0% +systematically which one do you think is +most likely okay so it's a detective + + align:start position:0% +most likely okay so it's a detective + + + align:start position:0% +most likely okay so it's a detective +operation so there's now you're going to + + align:start position:0% +operation so there's now you're going to + + + align:start position:0% +operation so there's now you're going to +actually do a root cause analysis okay + + align:start position:0% +actually do a root cause analysis okay + + + align:start position:0% +actually do a root cause analysis okay +okay + + align:start position:0% +okay + + + align:start position:0% +okay +everybody has anybody have any questions + + align:start position:0% +everybody has anybody have any questions + + + align:start position:0% +everybody has anybody have any questions +about yeah we established our baseline + + align:start position:0% +about yeah we established our baseline + + + align:start position:0% +about yeah we established our baseline +yeah so that's not going to change + + align:start position:0% +yeah so that's not going to change + + + align:start position:0% +yeah so that's not going to change +anything you all use the same one but + + align:start position:0% +anything you all use the same one but + + + align:start position:0% +anything you all use the same one but +it'd help if I write down those numbers + + align:start position:0% +it'd help if I write down those numbers + + + align:start position:0% +it'd help if I write down those numbers +yes yeah can you see them before yeah so + + align:start position:0% +yes yeah can you see them before yeah so + + + align:start position:0% +yes yeah can you see them before yeah so +oh you got to dive and just be with + + align:start position:0% +oh you got to dive and just be with + + + align:start position:0% +oh you got to dive and just be with +young people okay now you just operate + + align:start position:0% +young people okay now you just operate + + + align:start position:0% +young people okay now you just operate +on your own you're all independent think + + align:start position:0% +on your own you're all independent think + + + align:start position:0% +on your own you're all independent think +of yourself as the independent + + align:start position:0% +of yourself as the independent + + + align:start position:0% +of yourself as the independent +measurement the quality control group of + + align:start position:0% +measurement the quality control group of + + + align:start position:0% +measurement the quality control group of +the pharmacy okay + + align:start position:0% + + + + align:start position:0% + +7480 tears there's a rock and I totally + + align:start position:0% + + + + align:start position:0% + +ravaged of 71 + + align:start position:0% + + + + align:start position:0% + +and are the machines that you move for + + align:start position:0% +and are the machines that you move for + + + align:start position:0% +and are the machines that you move for +calculus good so let's talk about how + + align:start position:0% +calculus good so let's talk about how + + + align:start position:0% +calculus good so let's talk about how +those write up an issue okay + + align:start position:0% +those write up an issue okay + + + align:start position:0% +those write up an issue okay +and time on materials the cup itself yes + + align:start position:0% +and time on materials the cup itself yes + + + align:start position:0% +and time on materials the cup itself yes +yes okay so how they come is nothing to + + align:start position:0% +yes okay so how they come is nothing to + + + align:start position:0% +yes okay so how they come is nothing to +marry engineer so you want to write your + + align:start position:0% +marry engineer so you want to write your + + + align:start position:0% +marry engineer so you want to write your +right goes down with quality of scale + + align:start position:0% +right goes down with quality of scale + + + align:start position:0% +right goes down with quality of scale +machine we can submit if I'm lucky but + + align:start position:0% +machine we can submit if I'm lucky but + + + align:start position:0% +machine we can submit if I'm lucky but +door our nation's well I just did I just + + align:start position:0% +door our nation's well I just did I just + + + align:start position:0% +door our nation's well I just did I just +sample three different ones + + align:start position:0% + + + + align:start position:0% + +three full okay well let's see Oh + + align:start position:0% +three full okay well let's see Oh + + + align:start position:0% +three full okay well let's see Oh +try pumping her out about okay so going + + align:start position:0% +try pumping her out about okay so going + + + align:start position:0% +try pumping her out about okay so going +around the room we had a range of root + + align:start position:0% +around the room we had a range of root + + + align:start position:0% +around the room we had a range of root +cause analysis things rate ranging from + + align:start position:0% +cause analysis things rate ranging from + + + align:start position:0% +cause analysis things rate ranging from +this table just said we think this is + + align:start position:0% +this table just said we think this is + + + align:start position:0% +this table just said we think this is +the cause and they tested and that was + + align:start position:0% +the cause and they tested and that was + + + align:start position:0% +the cause and they tested and that was +the cause so they just jumped right to a + + align:start position:0% +the cause so they just jumped right to a + + + align:start position:0% +the cause so they just jumped right to a +conclusion we had a very structured + + align:start position:0% +conclusion we had a very structured + + + align:start position:0% +conclusion we had a very structured +process over here but this is a way to + + align:start position:0% +process over here but this is a way to + + + align:start position:0% +process over here but this is a way to +make it visible if you go into a + + align:start position:0% +make it visible if you go into a + + + align:start position:0% +make it visible if you go into a +facilities under statistical process + + align:start position:0% +facilities under statistical process + + + align:start position:0% +facilities under statistical process +control the employees are trained on + + align:start position:0% +control the employees are trained on + + + align:start position:0% +control the employees are trained on +this and they're trained to recognize + + align:start position:0% +this and they're trained to recognize + + + align:start position:0% +this and they're trained to recognize +this kind of deviation and then they do + + align:start position:0% +this kind of deviation and then they do + + + align:start position:0% +this kind of deviation and then they do +something about it okay here's the chart + + align:start position:0% +something about it okay here's the chart + + + align:start position:0% +something about it okay here's the chart +for resident Falls in a long-term care + + align:start position:0% +for resident Falls in a long-term care + + + align:start position:0% +for resident Falls in a long-term care +facility control chart and here's their + + align:start position:0% +facility control chart and here's their + + + align:start position:0% +facility control chart and here's their +twenty days and this was there + + align:start position:0% +twenty days and this was there + + + align:start position:0% +twenty days and this was there +this was their control then they want + + align:start position:0% +this was their control then they want + + + align:start position:0% +this was their control then they want +now in this case that they were + + align:start position:0% +now in this case that they were + + + align:start position:0% +now in this case that they were +intervening to try to reduce patient + + align:start position:0% +intervening to try to reduce patient + + + align:start position:0% +intervening to try to reduce patient +falls so this is not now just doing + + align:start position:0% +falls so this is not now just doing + + + align:start position:0% +falls so this is not now just doing +nothing they're doing a bunch of + + align:start position:0% +nothing they're doing a bunch of + + + align:start position:0% +nothing they're doing a bunch of +interventions and these are different + + align:start position:0% +interventions and these are different + + + align:start position:0% +interventions and these are different +interventions actually what they did + + align:start position:0% +interventions actually what they did + + + align:start position:0% +interventions actually what they did +here was it doesn't it's not on the + + align:start position:0% +here was it doesn't it's not on the + + + align:start position:0% +here was it doesn't it's not on the +chart but what they did was they just + + align:start position:0% +chart but what they did was they just + + + align:start position:0% +chart but what they did was they just +simply identified the patients in this + + align:start position:0% +simply identified the patients in this + + + align:start position:0% +simply identified the patients in this +long-term care facility who were + + align:start position:0% +long-term care facility who were + + + align:start position:0% +long-term care facility who were +susceptible to falling and they put + + align:start position:0% +susceptible to falling and they put + + + align:start position:0% +susceptible to falling and they put +stickers on their wheelchairs or their + + align:start position:0% +stickers on their wheelchairs or their + + + align:start position:0% +stickers on their wheelchairs or their +walkers in their room and on their + + align:start position:0% +walkers in their room and on their + + + align:start position:0% +walkers in their room and on their +charts and they picked stickers that + + align:start position:0% +charts and they picked stickers that + + + align:start position:0% +charts and they picked stickers that +were so interesting that the residents + + align:start position:0% +were so interesting that the residents + + + align:start position:0% +were so interesting that the residents +who weren't in danger wanted the + + align:start position:0% +who weren't in danger wanted the + + + align:start position:0% +who weren't in danger wanted the +stickers to you know but just being + + align:start position:0% +stickers to you know but just being + + + align:start position:0% +stickers to you know but just being +conscious of the those were at the at + + align:start position:0% +conscious of the those were at the at + + + align:start position:0% +conscious of the those were at the at +risk patients started to drop it and you + + align:start position:0% +risk patients started to drop it and you + + + align:start position:0% +risk patients started to drop it and you +can see their interventions lower the + + align:start position:0% +can see their interventions lower the + + + align:start position:0% +can see their interventions lower the +the mean and lower the control limits + + align:start position:0% +the mean and lower the control limits + + + align:start position:0% +the mean and lower the control limits +and lower them again and this is this + + align:start position:0% +and lower them again and this is this + + + align:start position:0% +and lower them again and this is this +was a process improvement study that I + + align:start position:0% +was a process improvement study that I + + + align:start position:0% +was a process improvement study that I +actually heard the last I H I'm eating + + align:start position:0% +actually heard the last I H I'm eating + + + align:start position:0% +actually heard the last I H I'm eating +okay so now our last topic this is + + align:start position:0% +okay so now our last topic this is + + + align:start position:0% +okay so now our last topic this is +process capability ok process + + align:start position:0% +process capability ok process + + + align:start position:0% +process capability ok process +capabilities define is the ability of a + + align:start position:0% +capabilities define is the ability of a + + + align:start position:0% +capabilities define is the ability of a +process to meet the customer + + align:start position:0% +process to meet the customer + + + align:start position:0% +process to meet the customer +expectations and and what we have here + + align:start position:0% +expectations and and what we have here + + + align:start position:0% +expectations and and what we have here +is we have we know what the capabilities + + align:start position:0% +is we have we know what the capabilities + + + align:start position:0% +is we have we know what the capabilities +but we don't know whether it meets the + + align:start position:0% +but we don't know whether it meets the + + + align:start position:0% +but we don't know whether it meets the +customer expectations and to get the + + align:start position:0% +customer expectations and to get the + + + align:start position:0% +customer expectations and to get the +customer expectations on there we have + + align:start position:0% +customer expectations on there we have + + + align:start position:0% +customer expectations on there we have +to find out what they want a customer + + align:start position:0% +to find out what they want a customer + + + align:start position:0% +to find out what they want a customer +determined limit the spec limits are + + align:start position:0% +determined limit the spec limits are + + + align:start position:0% +determined limit the spec limits are +essentially what the cuss + + align:start position:0% +essentially what the cuss + + + align:start position:0% +essentially what the cuss +once the upper and lower values between + + align:start position:0% +once the upper and lower values between + + + align:start position:0% +once the upper and lower values between +which a process much must be controlled + + align:start position:0% +which a process much must be controlled + + + align:start position:0% +which a process much must be controlled +that's what the customer wants the + + align:start position:0% +that's what the customer wants the + + + align:start position:0% +that's what the customer wants the +bounds in which we choose to control the + + align:start position:0% +bounds in which we choose to control the + + + align:start position:0% +bounds in which we choose to control the +process or which we try to control the + + align:start position:0% +process or which we try to control the + + + align:start position:0% +process or which we try to control the +process or the upper and lower control + + align:start position:0% +process or the upper and lower control + + + align:start position:0% +process or the upper and lower control +limits of the of the process so how do + + align:start position:0% +limits of the of the process so how do + + + align:start position:0% +limits of the of the process so how do +we measure given those two definitions + + align:start position:0% +we measure given those two definitions + + + align:start position:0% +we measure given those two definitions +the process capability one way to do it + + align:start position:0% +the process capability one way to do it + + + align:start position:0% +the process capability one way to do it +is to think about the process and again + + align:start position:0% +is to think about the process and again + + + align:start position:0% +is to think about the process and again +this is an approximation but it's but + + align:start position:0% +this is an approximation but it's but + + + align:start position:0% +this is an approximation but it's but +it's a pretty good one under a lot of + + align:start position:0% +it's a pretty good one under a lot of + + + align:start position:0% +it's a pretty good one under a lot of +circumstances the process is having a + + align:start position:0% +circumstances the process is having a + + + align:start position:0% +circumstances the process is having a +normally distributed behavior so if we + + align:start position:0% +normally distributed behavior so if we + + + align:start position:0% +normally distributed behavior so if we +collect some data we can assume a normal + + align:start position:0% +collect some data we can assume a normal + + + align:start position:0% +collect some data we can assume a normal +distribution do some statistics using + + align:start position:0% +distribution do some statistics using + + + align:start position:0% +distribution do some statistics using +our statistical tools and decide how + + align:start position:0% +our statistical tools and decide how + + + align:start position:0% +our statistical tools and decide how +good or bad the process is and if we + + align:start position:0% +good or bad the process is and if we + + + align:start position:0% +good or bad the process is and if we +have a normally distributed process it's + + align:start position:0% +have a normally distributed process it's + + + align:start position:0% +have a normally distributed process it's +it's a behavior is going to be + + align:start position:0% +it's a behavior is going to be + + + align:start position:0% +it's a behavior is going to be +characterized by its standard deviation + + align:start position:0% +characterized by its standard deviation + + + align:start position:0% +characterized by its standard deviation +Sigma and if we draw our spec limits + + align:start position:0% +Sigma and if we draw our spec limits + + + align:start position:0% +Sigma and if we draw our spec limits +around that normal distribution here's + + align:start position:0% +around that normal distribution here's + + + align:start position:0% +around that normal distribution here's +our lower spec limit here's our upper + + align:start position:0% +our lower spec limit here's our upper + + + align:start position:0% +our lower spec limit here's our upper +spec limit we can up we can define a + + align:start position:0% +spec limit we can up we can define a + + + align:start position:0% +spec limit we can up we can define a +quantity called CP the process + + align:start position:0% +quantity called CP the process + + + align:start position:0% +quantity called CP the process +capability which is essentially this + + align:start position:0% +capability which is essentially this + + + align:start position:0% +capability which is essentially this +distance here the upper limit less this + + align:start position:0% +distance here the upper limit less this + + + align:start position:0% +distance here the upper limit less this +lower spec limit so that the range which + + align:start position:0% +lower spec limit so that the range which + + + align:start position:0% +lower spec limit so that the range which +is acceptable divided by the six six + + align:start position:0% +is acceptable divided by the six six + + + align:start position:0% +is acceptable divided by the six six +sigma of the process and if we have say + + align:start position:0% +sigma of the process and if we have say + + + align:start position:0% +sigma of the process and if we have say +a CP of two that's a very tight + + align:start position:0% +a CP of two that's a very tight + + + align:start position:0% +a CP of two that's a very tight +basically the spec limits are twice Six + + align:start position:0% +basically the spec limits are twice Six + + + align:start position:0% +basically the spec limits are twice Six +Sigma of the process then it's a very + + align:start position:0% +Sigma of the process then it's a very + + + align:start position:0% +Sigma of the process then it's a very +tight distribution inside the spec + + align:start position:0% +tight distribution inside the spec + + + align:start position:0% +tight distribution inside the spec +limits and the chance of something bad + + align:start position:0% +limits and the chance of something bad + + + align:start position:0% +limits and the chance of something bad +happening over every small chance of + + align:start position:0% +happening over every small chance of + + + align:start position:0% +happening over every small chance of +going out so so a CP of two is a very + + align:start position:0% +going out so so a CP of two is a very + + + align:start position:0% +going out so so a CP of two is a very +good process that in fact yes that's + + align:start position:0% +good process that in fact yes that's + + + align:start position:0% +good process that in fact yes that's +right six standard deviations on either + + align:start position:0% +right six standard deviations on either + + + align:start position:0% +right six standard deviations on either +side of the of the mean right so a CP of + + align:start position:0% +side of the of the mean right so a CP of + + + align:start position:0% +side of the of the mean right so a CP of +two would be a Six Sigma process in that + + align:start position:0% +two would be a Six Sigma process in that + + + align:start position:0% +two would be a Six Sigma process in that +sense be a very good one and just + + align:start position:0% +sense be a very good one and just + + + align:start position:0% +sense be a very good one and just +graphically you can just see there's + + align:start position:0% +graphically you can just see there's + + + align:start position:0% +graphically you can just see there's +basically no tail sticking out of the + + align:start position:0% +basically no tail sticking out of the + + + align:start position:0% +basically no tail sticking out of the +bad done CP of one means you've got + + align:start position:0% +bad done CP of one means you've got + + + align:start position:0% +bad done CP of one means you've got +three sigma on each side three sigma + + align:start position:0% +three sigma on each side three sigma + + + align:start position:0% +three sigma on each side three sigma +you've got ninety seven point whatever + + align:start position:0% +you've got ninety seven point whatever + + + align:start position:0% +you've got ninety seven point whatever +percent of the of the the process + + align:start position:0% +percent of the of the the process + + + align:start position:0% +percent of the of the the process +falling in that range so the chance of + + align:start position:0% +falling in that range so the chance of + + + align:start position:0% +falling in that range so the chance of +something falling + + align:start position:0% +something falling + + + align:start position:0% +something falling +outside the range is quite small but + + align:start position:0% +outside the range is quite small but + + + align:start position:0% +outside the range is quite small but +it's not zero we can see a little bit of + + align:start position:0% +it's not zero we can see a little bit of + + + align:start position:0% +it's not zero we can see a little bit of +ink here outside of that outside of the + + align:start position:0% +ink here outside of that outside of the + + + align:start position:0% +ink here outside of that outside of the +acceptable range and once we get below + + align:start position:0% +acceptable range and once we get below + + + align:start position:0% +acceptable range and once we get below +one it starts getting ugly we really + + align:start position:0% +one it starts getting ugly we really + + + align:start position:0% +one it starts getting ugly we really +don't want to even talk about that + + align:start position:0% +don't want to even talk about that + + + align:start position:0% +don't want to even talk about that +so from a statistical process control + + align:start position:0% +so from a statistical process control + + + align:start position:0% +so from a statistical process control +point of view another issue which one + + align:start position:0% +point of view another issue which one + + + align:start position:0% +point of view another issue which one +can ignore is the fact that we may not + + align:start position:0% +can ignore is the fact that we may not + + + align:start position:0% +can ignore is the fact that we may not +be centered and we can actually redefine + + align:start position:0% +be centered and we can actually redefine + + + align:start position:0% +be centered and we can actually redefine +our process capability using a metric + + align:start position:0% +our process capability using a metric + + + align:start position:0% +our process capability using a metric +called CPK which takes into a fact that + + align:start position:0% +called CPK which takes into a fact that + + + align:start position:0% +called CPK which takes into a fact that +we may drift off mean and it's defined + + align:start position:0% +we may drift off mean and it's defined + + + align:start position:0% +we may drift off mean and it's defined +this way it's basically the distance to + + align:start position:0% +this way it's basically the distance to + + + align:start position:0% +this way it's basically the distance to +the closer boundary from the from where + + align:start position:0% +the closer boundary from the from where + + + align:start position:0% +the closer boundary from the from where +we are divided by 3 Sigma and it's + + align:start position:0% +we are divided by 3 Sigma and it's + + + align:start position:0% +we are divided by 3 Sigma and it's +whichever one of those is worse and + + align:start position:0% +whichever one of those is worse and + + + align:start position:0% +whichever one of those is worse and +those same curves shifted over one and a + + align:start position:0% +those same curves shifted over one and a + + + align:start position:0% +those same curves shifted over one and a +half Sigma look a lot less pretty our + + align:start position:0% +half Sigma look a lot less pretty our + + + align:start position:0% +half Sigma look a lot less pretty our +former Six Sigma process now has a CPK + + align:start position:0% +former Six Sigma process now has a CPK + + + align:start position:0% +former Six Sigma process now has a CPK +of 1.5 but it's still ok there's a tiny + + align:start position:0% +of 1.5 but it's still ok there's a tiny + + + align:start position:0% +of 1.5 but it's still ok there's a tiny +tiny there's a couple like 2 pixels + + align:start position:0% +tiny there's a couple like 2 pixels + + + align:start position:0% +tiny there's a couple like 2 pixels +worth the ink sticking out there the + + align:start position:0% +worth the ink sticking out there the + + + align:start position:0% +worth the ink sticking out there the +chance of of a defect is still very very + + align:start position:0% +chance of of a defect is still very very + + + align:start position:0% +chance of of a defect is still very very +small but our formally okay-looking CP + + align:start position:0% +small but our formally okay-looking CP + + + align:start position:0% +small but our formally okay-looking CP +of one process now has quite a quite a + + align:start position:0% +of one process now has quite a quite a + + + align:start position:0% +of one process now has quite a quite a +bad looking tail and our process that + + align:start position:0% +bad looking tail and our process that + + + align:start position:0% +bad looking tail and our process that +was bad is now horrible our relatively + + align:start position:0% +was bad is now horrible our relatively + + + align:start position:0% +was bad is now horrible our relatively +uncontrolled process so that's a + + align:start position:0% +uncontrolled process so that's a + + + align:start position:0% +uncontrolled process so that's a +different way of measuring process + + align:start position:0% +different way of measuring process + + + align:start position:0% +different way of measuring process +capability which takes into account the + + align:start position:0% +capability which takes into account the + + + align:start position:0% +capability which takes into account the +fact that the mean may not be on the + + align:start position:0% +fact that the mean may not be on the + + + align:start position:0% +fact that the mean may not be on the +center what we do with these two + + align:start position:0% +center what we do with these two + + + align:start position:0% +center what we do with these two +measures is um different here we have a + + align:start position:0% +measures is um different here we have a + + + align:start position:0% +measures is um different here we have a +archery example this is a classic + + align:start position:0% +archery example this is a classic + + + align:start position:0% +archery example this is a classic +statistically characterizes we have + + align:start position:0% +statistically characterizes we have + + + align:start position:0% +statistically characterizes we have +shots that are both widely dispersed and + + align:start position:0% +shots that are both widely dispersed and + + + align:start position:0% +shots that are both widely dispersed and +off center so how would we characterize + + align:start position:0% +off center so how would we characterize + + + align:start position:0% +off center so how would we characterize +that it's basically low on both metrics + + align:start position:0% +that it's basically low on both metrics + + + align:start position:0% +that it's basically low on both metrics +right it's widely dispersed and it's off + + align:start position:0% +right it's widely dispersed and it's off + + + align:start position:0% +right it's widely dispersed and it's off +center here's another here's another + + align:start position:0% +center here's another here's another + + + align:start position:0% +center here's another here's another +Archer it is has a tight distribution + + align:start position:0% +Archer it is has a tight distribution + + + align:start position:0% +Archer it is has a tight distribution +but it's way off center so CP is high + + align:start position:0% +but it's way off center so CP is high + + + align:start position:0% +but it's way off center so CP is high +and CPK is low that's right so this + + align:start position:0% +and CPK is low that's right so this + + + align:start position:0% +and CPK is low that's right so this +that's the sort of the difference + + align:start position:0% +that's the sort of the difference + + + align:start position:0% +that's the sort of the difference +between those metrics on this metric it + + align:start position:0% +between those metrics on this metric it + + + align:start position:0% +between those metrics on this metric it +looks great on that metric it does not + + align:start position:0% +looks great on that metric it does not + + + align:start position:0% +looks great on that metric it does not +and this of course is what we want if + + align:start position:0% +and this of course is what we want if + + + align:start position:0% +and this of course is what we want if +you're an archer or any other person who + + align:start position:0% +you're an archer or any other person who + + + align:start position:0% +you're an archer or any other person who +needs to control their process what do + + align:start position:0% +needs to control their process what do + + + align:start position:0% +needs to control their process what do +you do first + + align:start position:0% +you do first + + + align:start position:0% +you do first +yeah I'm cheating a little bit on this + + align:start position:0% +yeah I'm cheating a little bit on this + + + align:start position:0% +yeah I'm cheating a little bit on this +one I do our tree sometimes not very + + align:start position:0% +one I do our tree sometimes not very + + + align:start position:0% +one I do our tree sometimes not very +much but you have to do this first + + align:start position:0% +much but you have to do this first + + + align:start position:0% +much but you have to do this first +actually you have to get your process + + align:start position:0% +actually you have to get your process + + + align:start position:0% +actually you have to get your process +repeatable even if the mean is way off + + align:start position:0% +repeatable even if the mean is way off + + + align:start position:0% +repeatable even if the mean is way off +because if you're correcting every time + + align:start position:0% +because if you're correcting every time + + + align:start position:0% +because if you're correcting every time +then it just goes all over the place but + + align:start position:0% +then it just goes all over the place but + + + align:start position:0% +then it just goes all over the place but +if you just go okay same thing every + + align:start position:0% +if you just go okay same thing every + + + align:start position:0% +if you just go okay same thing every +time okay five times in a row I've hit + + align:start position:0% +time okay five times in a row I've hit + + + align:start position:0% +time okay five times in a row I've hit +up into the right now I'm going to + + align:start position:0% +up into the right now I'm going to + + + align:start position:0% +up into the right now I'm going to +adjust right so so often you concentrate + + align:start position:0% +adjust right so so often you concentrate + + + align:start position:0% +adjust right so so often you concentrate +on knocking your CP down first to + + align:start position:0% +on knocking your CP down first to + + + align:start position:0% +on knocking your CP down first to +understand your process to see where the + + align:start position:0% +understand your process to see where the + + + align:start position:0% +understand your process to see where the +mean is because it can't really measure + + align:start position:0% +mean is because it can't really measure + + + align:start position:0% +mean is because it can't really measure +the mean in it in a situation you can't + + align:start position:0% +the mean in it in a situation you can't + + + align:start position:0% +the mean in it in a situation you can't +statistically but it's hard okay enough + + align:start position:0% +statistically but it's hard okay enough + + + align:start position:0% +statistically but it's hard okay enough +of that this this actually remember we + + align:start position:0% +of that this this actually remember we + + + align:start position:0% +of that this this actually remember we +said we would I tell you where the + + align:start position:0% +said we would I tell you where the + + + align:start position:0% +said we would I tell you where the +definition of Six Sigma comes from + + align:start position:0% +definition of Six Sigma comes from + + + align:start position:0% +definition of Six Sigma comes from +interestingly it comes from a process + + align:start position:0% +interestingly it comes from a process + + + align:start position:0% +interestingly it comes from a process +with a mean shift of one and a half + + align:start position:0% +with a mean shift of one and a half + + + align:start position:0% +with a mean shift of one and a half +which would give you three defects per + + align:start position:0% +which would give you three defects per + + + align:start position:0% +which would give you three defects per +million opportunities so if you have a + + align:start position:0% +million opportunities so if you have a + + + align:start position:0% +million opportunities so if you have a +very good process but you still don't + + align:start position:0% +very good process but you still don't + + + align:start position:0% +very good process but you still don't +control your mean to more than a one and + + align:start position:0% +control your mean to more than a one and + + + align:start position:0% +control your mean to more than a one and +a half Sigma you still have a very very + + align:start position:0% +a half Sigma you still have a very very + + + align:start position:0% +a half Sigma you still have a very very +low defects per million that's where + + align:start position:0% +low defects per million that's where + + + align:start position:0% +low defects per million that's where +that idea comes from those are some of + + align:start position:0% +that idea comes from those are some of + + + align:start position:0% +that idea comes from those are some of +the concepts that we use to get + + align:start position:0% +the concepts that we use to get + + + align:start position:0% +the concepts that we use to get +processes under control and keep them + + align:start position:0% +processes under control and keep them + + + align:start position:0% +processes under control and keep them +there and six Six Sigma as an overall + + align:start position:0% +there and six Six Sigma as an overall + + + align:start position:0% +there and six Six Sigma as an overall +method is is very useful for taking + + align:start position:0% +method is is very useful for taking + + + align:start position:0% +method is is very useful for taking +variation down especially in critical + + align:start position:0% +variation down especially in critical + + + align:start position:0% +variation down especially in critical +applications like like large-scale + + align:start position:0% +applications like like large-scale + + + align:start position:0% +applications like like large-scale +manufacturing or healthcare where you + + align:start position:0% +manufacturing or healthcare where you + + + align:start position:0% +manufacturing or healthcare where you +want your your defects to be very low + + align:start position:0% +want your your defects to be very low + + + align:start position:0% +want your your defects to be very low +the variation be very low we've taught + + align:start position:0% +the variation be very low we've taught + + + align:start position:0% +the variation be very low we've taught +you about control charts which is a + + align:start position:0% +you about control charts which is a + + + align:start position:0% +you about control charts which is a +great place to start + + align:start position:0% +great place to start + + + align:start position:0% +great place to start +it's not the end and we've sort of + + align:start position:0% +it's not the end and we've sort of + + + align:start position:0% +it's not the end and we've sort of +glossed over all the statistical tools + + align:start position:0% +glossed over all the statistical tools + + + align:start position:0% +glossed over all the statistical tools +you need to really understand the + + align:start position:0% +you need to really understand the + + + align:start position:0% +you need to really understand the +numbers but the visual is really is + + align:start position:0% +numbers but the visual is really is + + + align:start position:0% +numbers but the visual is really is +very powerful in and of itself even if + + align:start position:0% +very powerful in and of itself even if + + + align:start position:0% +very powerful in and of itself even if +you don't do the statistics having the + + align:start position:0% +you don't do the statistics having the + + + align:start position:0% +you don't do the statistics having the +visual evidence of what your process can + + align:start position:0% +visual evidence of what your process can + + + align:start position:0% +visual evidence of what your process can +do and whether it's deviating is very + + align:start position:0% +do and whether it's deviating is very + + + align:start position:0% +do and whether it's deviating is very +powerful and and and once we understand + + align:start position:0% +powerful and and and once we understand + + + align:start position:0% +powerful and and and once we understand +what our process can do we can compare + + align:start position:0% +what our process can do we can compare + + + align:start position:0% +what our process can do we can compare +that to what the customer wants and + + align:start position:0% +that to what the customer wants and + + + align:start position:0% +that to what the customer wants and +understand the capabilities are a + + align:start position:0% +understand the capabilities are a + + + align:start position:0% +understand the capabilities are a +process and whether they're acceptable + + align:start position:0% +process and whether they're acceptable + + + align:start position:0% +process and whether they're acceptable +or not + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/cJiOSI6df4o.txt b/cJiOSI6df4o.txt new file mode 100644 index 0000000000000000000000000000000000000000..d022fb58d0ec30e3e1f451219b9b4434da6e46c9 --- /dev/null +++ b/cJiOSI6df4o.txt @@ -0,0 +1,9235 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +so as I think you know uh today again + + align:start position:0% +so as I think you know uh today again + + + align:start position:0% +so as I think you know uh today again +we're going to have just an informal + + align:start position:0% +we're going to have just an informal + + + align:start position:0% +we're going to have just an informal +um optional discussion you've all come + + align:start position:0% +um optional discussion you've all come + + + align:start position:0% +um optional discussion you've all come +so I guess you've exercised your option + + align:start position:0% +so I guess you've exercised your option + + + align:start position:0% +so I guess you've exercised your option +but um when we're talking today in 8225 + + align:start position:0% +but um when we're talking today in 8225 + + + align:start position:0% +but um when we're talking today in 8225 +sjs042 uh about some of the themes + + align:start position:0% +sjs042 uh about some of the themes + + + align:start position:0% +sjs042 uh about some of the themes +raised by that second documentary film + + align:start position:0% +raised by that second documentary film + + + align:start position:0% +raised by that second documentary film +that that hopefully had a chance to + + align:start position:0% +that that hopefully had a chance to + + + align:start position:0% +that that hopefully had a chance to +watch uh the film called containment + + align:start position:0% +watch uh the film called containment + + + align:start position:0% +watch uh the film called containment +a film made by uh Peter Gallison and Rob + + align:start position:0% +a film made by uh Peter Gallison and Rob + + + align:start position:0% +a film made by uh Peter Gallison and Rob +moss and and their and their team their + + align:start position:0% +moss and and their and their team their + + + align:start position:0% +moss and and their and their team their +whole team + + align:start position:0% +whole team + + + align:start position:0% +whole team +um + + align:start position:0% +um + + + align:start position:0% +um +and like last time like like our + + align:start position:0% +and like last time like like our + + + align:start position:0% +and like last time like like our +discussion after the film The Day After + + align:start position:0% +discussion after the film The Day After + + + align:start position:0% +discussion after the film The Day After +Trinity + + align:start position:0% +Trinity + + + align:start position:0% +Trinity +um sort of the floors open so I'm just + + align:start position:0% +um sort of the floors open so I'm just + + + align:start position:0% +um sort of the floors open so I'm just +curious + + align:start position:0% +curious + + + align:start position:0% +curious +um + + align:start position:0% +um + + + align:start position:0% +um +you know what what people make of it + + align:start position:0% +you know what what people make of it + + + align:start position:0% +you know what what people make of it +let me let me ask a more specific + + align:start position:0% +let me let me ask a more specific + + + align:start position:0% +let me let me ask a more specific +question was there anything in the film + + align:start position:0% +question was there anything in the film + + + align:start position:0% +question was there anything in the film +that surprised you that you really + + align:start position:0% +that surprised you that you really + + + align:start position:0% +that surprised you that you really +didn't expect uh or that you hadn't seen + + align:start position:0% +didn't expect uh or that you hadn't seen + + + align:start position:0% +didn't expect uh or that you hadn't seen +or you did something about but this this + + align:start position:0% +or you did something about but this this + + + align:start position:0% +or you did something about but this this +you know uh looked at it from different + + align:start position:0% +you know uh looked at it from different + + + align:start position:0% +you know uh looked at it from different +angles or something like that + + align:start position:0% + + + + align:start position:0% + +you might know it might not have been so + + align:start position:0% +you might know it might not have been so + + + align:start position:0% +you might know it might not have been so +clear it might I can't remember you know + + align:start position:0% +clear it might I can't remember you know + + + align:start position:0% +clear it might I can't remember you know +that uh Peter and Rob the filmmakers + + align:start position:0% +that uh Peter and Rob the filmmakers + + + align:start position:0% +that uh Peter and Rob the filmmakers +were working on this project + + align:start position:0% +were working on this project + + + align:start position:0% +were working on this project +um before the Fukushima uh earthquake + + align:start position:0% +um before the Fukushima uh earthquake + + + align:start position:0% +um before the Fukushima uh earthquake +and reactor uh meltdown they were + + align:start position:0% +and reactor uh meltdown they were + + + align:start position:0% +and reactor uh meltdown they were +already immersed in this project and + + align:start position:0% +already immersed in this project and + + + align:start position:0% +already immersed in this project and +they were already actively filming and + + align:start position:0% +they were already actively filming and + + + align:start position:0% +they were already actively filming and +then uh the earthquake in March 2011 + + align:start position:0% +then uh the earthquake in March 2011 + + + align:start position:0% +then uh the earthquake in March 2011 +occurred so in some sense that the film + + align:start position:0% +occurred so in some sense that the film + + + align:start position:0% +occurred so in some sense that the film +took a turn uh while they were already + + align:start position:0% +took a turn uh while they were already + + + align:start position:0% +took a turn uh while they were already +kind of immersed in it I don't know if + + align:start position:0% +kind of immersed in it I don't know if + + + align:start position:0% +kind of immersed in it I don't know if +considering how squarely the film kind + + align:start position:0% +considering how squarely the film kind + + + align:start position:0% +considering how squarely the film kind +of begins and ends with a lot of + + align:start position:0% +of begins and ends with a lot of + + + align:start position:0% +of begins and ends with a lot of +material about very fairly recent + + align:start position:0% +material about very fairly recent + + + align:start position:0% +material about very fairly recent +developments in Japan + + align:start position:0% +developments in Japan + + + align:start position:0% +developments in Japan +I was just curious uh if that if that + + align:start position:0% +I was just curious uh if that if that + + + align:start position:0% +I was just curious uh if that if that +shows in your viewing because the film + + align:start position:0% +shows in your viewing because the film + + + align:start position:0% +shows in your viewing because the film +originally of course I didn't know that + + align:start position:0% +originally of course I didn't know that + + + align:start position:0% +originally of course I didn't know that +was coming they were starting the film + + align:start position:0% +was coming they were starting the film + + + align:start position:0% +was coming they were starting the film +they were working on the film before + + align:start position:0% +they were working on the film before + + + align:start position:0% +they were working on the film before +that even had occurred + + align:start position:0% +that even had occurred + + + align:start position:0% +that even had occurred +did that + + align:start position:0% +did that + + + align:start position:0% +did that +did the film hold together did that seem + + align:start position:0% +did the film hold together did that seem + + + align:start position:0% +did the film hold together did that seem +like it was tacked on I'm just curious + + align:start position:0% +like it was tacked on I'm just curious + + + align:start position:0% +like it was tacked on I'm just curious +you know what what people make of of + + align:start position:0% +you know what what people make of of + + + align:start position:0% +you know what what people make of of +this body of material + + align:start position:0% + + + + align:start position:0% + +thank you Alex let's sit with frv so + + align:start position:0% +thank you Alex let's sit with frv so + + + align:start position:0% +thank you Alex let's sit with frv so +they were Peter and Rob already were + + align:start position:0% +they were Peter and Rob already were + + + align:start position:0% +they were Peter and Rob already were +quite interested in uh areas that do + + align:start position:0% +quite interested in uh areas that do + + + align:start position:0% +quite interested in uh areas that do +show up a lot of the film like the um + + align:start position:0% +show up a lot of the film like the um + + + align:start position:0% +show up a lot of the film like the um +the kind of waste storage facilities uh + + align:start position:0% +the kind of waste storage facilities uh + + + align:start position:0% +the kind of waste storage facilities uh +in the continent of the United States + + align:start position:0% +in the continent of the United States + + + align:start position:0% +in the continent of the United States +and as many of you might know they've + + align:start position:0% +and as many of you might know they've + + + align:start position:0% +and as many of you might know they've +been long long I'm saying decades-long + + align:start position:0% +been long long I'm saying decades-long + + + align:start position:0% +been long long I'm saying decades-long +debates just within the U.S context + + align:start position:0% +debates just within the U.S context + + + align:start position:0% +debates just within the U.S context +about how where whether to to develop a + + align:start position:0% +about how where whether to to develop a + + + align:start position:0% +about how where whether to to develop a +domestic storage facility we should be + + align:start position:0% +domestic storage facility we should be + + + align:start position:0% +domestic storage facility we should be +at a Yucca Mountain should it be some + + align:start position:0% +at a Yucca Mountain should it be some + + + align:start position:0% +at a Yucca Mountain should it be some +other site the so-called wit facility + + align:start position:0% +other site the so-called wit facility + + + align:start position:0% +other site the so-called wit facility +was already then well under + + align:start position:0% +was already then well under + + + align:start position:0% +was already then well under +Stephanie my apologies my the power went + + align:start position:0% +Stephanie my apologies my the power went + + + align:start position:0% +Stephanie my apologies my the power went +out of my house temporarily so I and + + align:start position:0% +out of my house temporarily so I and + + + align:start position:0% +out of my house temporarily so I and +here I am it's clearly just a little + + align:start position:0% +here I am it's clearly just a little + + + align:start position:0% +here I am it's clearly just a little +blip anyway sorry about that + + align:start position:0% +blip anyway sorry about that + + + align:start position:0% +blip anyway sorry about that +um + + align:start position:0% +um + + + align:start position:0% +um +so um + + align:start position:0% +so um + + + align:start position:0% +so um +I have to say I I might be repeating + + align:start position:0% +I have to say I I might be repeating + + + align:start position:0% +I have to say I I might be repeating +things that I missed when I was offline + + align:start position:0% +things that I missed when I was offline + + + align:start position:0% +things that I missed when I was offline +for a moment one of the parts of film + + align:start position:0% +for a moment one of the parts of film + + + align:start position:0% +for a moment one of the parts of film +that I do find Most Fascinating are + + align:start position:0% +that I do find Most Fascinating are + + + align:start position:0% +that I do find Most Fascinating are +these efforts to get a range of types of + + align:start position:0% +these efforts to get a range of types of + + + align:start position:0% +these efforts to get a range of types of +specialists + + align:start position:0% +specialists + + + align:start position:0% +specialists +to design some corn some kind of symbol + + align:start position:0% +to design some corn some kind of symbol + + + align:start position:0% +to design some corn some kind of symbol +system or communication system that + + align:start position:0% +system or communication system that + + + align:start position:0% +system or communication system that +could plausibly and reliably be legible + + align:start position:0% +could plausibly and reliably be legible + + + align:start position:0% +could plausibly and reliably be legible +you know be readable + + align:start position:0% +you know be readable + + + align:start position:0% +you know be readable +to people + + align:start position:0% +to people + + + align:start position:0% +to people +hundreds of thousands of years in the + + align:start position:0% +hundreds of thousands of years in the + + + align:start position:0% +hundreds of thousands of years in the +future + + align:start position:0% +future + + + align:start position:0% +future +um + + align:start position:0% +um + + + align:start position:0% +um +whether it's you know archaeologists and + + align:start position:0% +whether it's you know archaeologists and + + + align:start position:0% +whether it's you know archaeologists and +linguists or other kinds of + + align:start position:0% +linguists or other kinds of + + + align:start position:0% +linguists or other kinds of +anthropologists or experts in seti the + + align:start position:0% +anthropologists or experts in seti the + + + align:start position:0% +anthropologists or experts in seti the +search for extraterrestrial intelligence + + align:start position:0% +search for extraterrestrial intelligence + + + align:start position:0% +search for extraterrestrial intelligence +or you know sculptors or all these kinds + + align:start position:0% +or you know sculptors or all these kinds + + + align:start position:0% +or you know sculptors or all these kinds +of range of people say how do we make + + align:start position:0% +of range of people say how do we make + + + align:start position:0% +of range of people say how do we make +something that can be that will tell + + align:start position:0% +something that can be that will tell + + + align:start position:0% +something that can be that will tell +people still still don't dig here + + align:start position:0% +people still still don't dig here + + + align:start position:0% +people still still don't dig here +because some of these uh highly + + align:start position:0% +because some of these uh highly + + + align:start position:0% +because some of these uh highly +poisonous to humans at least highly + + align:start position:0% +poisonous to humans at least highly + + + align:start position:0% +poisonous to humans at least highly +poisonous + + align:start position:0% +poisonous + + + align:start position:0% +poisonous +radioactive isotopes have half-lives in + + align:start position:0% +radioactive isotopes have half-lives in + + + align:start position:0% +radioactive isotopes have half-lives in +the tens of thousands uh multiple tens + + align:start position:0% +the tens of thousands uh multiple tens + + + align:start position:0% +the tens of thousands uh multiple tens +of thousands of years and so if you need + + align:start position:0% +of thousands of years and so if you need + + + align:start position:0% +of thousands of years and so if you need +activity levels to Fall by many + + align:start position:0% +activity levels to Fall by many + + + align:start position:0% +activity levels to Fall by many +half-lives worth you're looking at you + + align:start position:0% +half-lives worth you're looking at you + + + align:start position:0% +half-lives worth you're looking at you +know 300 000 year time Horizons into the + + align:start position:0% +know 300 000 year time Horizons into the + + + align:start position:0% +know 300 000 year time Horizons into the +future and you think about you know + + align:start position:0% +future and you think about you know + + + align:start position:0% +future and you think about you know +we've had the printing press since um + + align:start position:0% +we've had the printing press since um + + + align:start position:0% +we've had the printing press since um +you know approximately 1450 plus or + + align:start position:0% +you know approximately 1450 plus or + + + align:start position:0% +you know approximately 1450 plus or +minus or 13.50 anyway you know we can + + align:start position:0% +minus or 13.50 anyway you know we can + + + align:start position:0% +minus or 13.50 anyway you know we can +measure that expense in a couple + + align:start position:0% +measure that expense in a couple + + + align:start position:0% +measure that expense in a couple +thousand years not a couple tens of + + align:start position:0% +thousand years not a couple tens of + + + align:start position:0% +thousand years not a couple tens of +thousands of years you know the kind of + + align:start position:0% +thousands of years you know the kind of + + + align:start position:0% +thousands of years you know the kind of +latinate alphabet uh dates to again on + + align:start position:0% +latinate alphabet uh dates to again on + + + align:start position:0% +latinate alphabet uh dates to again on +the order of maybe I don't know 5 000 + + align:start position:0% +the order of maybe I don't know 5 000 + + + align:start position:0% +the order of maybe I don't know 5 000 +years something like that these are + + align:start position:0% +years something like that these are + + + align:start position:0% +years something like that these are +these are a drop in the bucket time + + align:start position:0% +these are a drop in the bucket time + + + align:start position:0% +these are a drop in the bucket time +scale wise compared to a 300 000 year + + align:start position:0% +scale wise compared to a 300 000 year + + + align:start position:0% +scale wise compared to a 300 000 year +projection into the future and I found + + align:start position:0% +projection into the future and I found + + + align:start position:0% +projection into the future and I found +that part of the of the film really + + align:start position:0% +that part of the of the film really + + + align:start position:0% +that part of the of the film really +um just is fascinating how it just as a + + align:start position:0% +um just is fascinating how it just as a + + + align:start position:0% +um just is fascinating how it just as a +you know it's it's I think in part of + + align:start position:0% +you know it's it's I think in part of + + + align:start position:0% +you know it's it's I think in part of +the interview that was also on the + + align:start position:0% +the interview that was also on the + + + align:start position:0% +the interview that was also on the +readings for for today an interview that + + align:start position:0% +readings for for today an interview that + + + align:start position:0% +readings for for today an interview that +Peter Gallison had done + + align:start position:0% +Peter Gallison had done + + + align:start position:0% +Peter Gallison had done +while he's working on the film it's sort + + align:start position:0% +while he's working on the film it's sort + + + align:start position:0% +while he's working on the film it's sort +of part Science Fiction it's an + + align:start position:0% +of part Science Fiction it's an + + + align:start position:0% +of part Science Fiction it's an +interesting + + align:start position:0% +interesting + + + align:start position:0% +interesting +thoughtics are just to imagine a kind of + + align:start position:0% +thoughtics are just to imagine a kind of + + + align:start position:0% +thoughtics are just to imagine a kind of +communicative system for our uh vastly + + align:start position:0% +communicative system for our uh vastly + + + align:start position:0% +communicative system for our uh vastly +future selves + + align:start position:0% +future selves + + + align:start position:0% +future selves +so it's partly science fiction also like + + align:start position:0% +so it's partly science fiction also like + + + align:start position:0% +so it's partly science fiction also like +really deadly serious like this stuff + + align:start position:0% +really deadly serious like this stuff + + + align:start position:0% +really deadly serious like this stuff +will still be harmful to humans and even + + align:start position:0% +will still be harmful to humans and even + + + align:start position:0% +will still be harmful to humans and even +you know human-like creatures uh + + align:start position:0% +you know human-like creatures uh + + + align:start position:0% +you know human-like creatures uh +plausibly in + + align:start position:0% +plausibly in + + + align:start position:0% +plausibly in +you know end Generations forward so + + align:start position:0% +you know end Generations forward so + + + align:start position:0% +you know end Generations forward so +anyway I found that part of the film + + align:start position:0% +anyway I found that part of the film + + + align:start position:0% +anyway I found that part of the film +that's something I didn't know much + + align:start position:0% +that's something I didn't know much + + + align:start position:0% +that's something I didn't know much +about before learning about it from + + align:start position:0% +about before learning about it from + + + align:start position:0% +about before learning about it from +Peter and he's working on the film that + + align:start position:0% +Peter and he's working on the film that + + + align:start position:0% +Peter and he's working on the film that +really stuck with me quite uh quite + + align:start position:0% +really stuck with me quite uh quite + + + align:start position:0% +really stuck with me quite uh quite +hauntingly + + align:start position:0% +hauntingly + + + align:start position:0% +hauntingly +any other thoughts on on the material it + + align:start position:0% +any other thoughts on on the material it + + + align:start position:0% +any other thoughts on on the material it +doesn't be limited to the film other + + align:start position:0% +doesn't be limited to the film other + + + align:start position:0% +doesn't be limited to the film other +things we talked about in class recently + + align:start position:0% +things we talked about in class recently + + + align:start position:0% +things we talked about in class recently +as well it's totally fair game as well + + align:start position:0% + + + + align:start position:0% + +yes uh + + align:start position:0% +yes uh + + + align:start position:0% +yes uh +worked with a number of students and + + align:start position:0% +worked with a number of students and + + + align:start position:0% +worked with a number of students and +colleagues who thought very hard about + + align:start position:0% +colleagues who thought very hard about + + + align:start position:0% +colleagues who thought very hard about +seti as um as from an astronomical point + + align:start position:0% +seti as um as from an astronomical point + + + align:start position:0% +seti as um as from an astronomical point +of view but also as historians or + + align:start position:0% +of view but also as historians or + + + align:start position:0% +of view but also as historians or +anthropologists of science studying + + align:start position:0% +anthropologists of science studying + + + align:start position:0% +anthropologists of science studying +these communities in present day + + align:start position:0% +these communities in present day + + + align:start position:0% +these communities in present day +and you know it does feel like it that + + align:start position:0% +and you know it does feel like it that + + + align:start position:0% +and you know it does feel like it that +work is often a kind of projection of + + align:start position:0% +work is often a kind of projection of + + + align:start position:0% +work is often a kind of projection of +our assumptions about ourselves what + + align:start position:0% +our assumptions about ourselves what + + + align:start position:0% +our assumptions about ourselves what +will the others look like well we have a + + align:start position:0% +will the others look like well we have a + + + align:start position:0% +will the others look like well we have a +range of experience to base that on + + align:start position:0% +range of experience to base that on + + + align:start position:0% +range of experience to base that on +which is what we know about + + align:start position:0% +which is what we know about + + + align:start position:0% +which is what we know about +um + + align:start position:0% +um + + + align:start position:0% +um +and and so it does have a similar kind + + align:start position:0% +and and so it does have a similar kind + + + align:start position:0% +and and so it does have a similar kind +of um + + align:start position:0% +of um + + + align:start position:0% +of um +ambition and yet maybe limitation from + + align:start position:0% +ambition and yet maybe limitation from + + + align:start position:0% +ambition and yet maybe limitation from +from our from just the Horizon of our + + align:start position:0% +from our from just the Horizon of our + + + align:start position:0% +from our from just the Horizon of our +own imaginations uh and so I think it's + + align:start position:0% +own imaginations uh and so I think it's + + + align:start position:0% +own imaginations uh and so I think it's +totally it struck me as totally + + align:start position:0% +totally it struck me as totally + + + align:start position:0% +totally it struck me as totally +appropriate once I learned it from from + + align:start position:0% +appropriate once I learned it from from + + + align:start position:0% +appropriate once I learned it from from +say Peter and Rob's film + + align:start position:0% +say Peter and Rob's film + + + align:start position:0% +say Peter and Rob's film +that these Department of energy experts + + align:start position:0% +that these Department of energy experts + + + align:start position:0% +that these Department of energy experts +would call on seti Experts because the + + align:start position:0% +would call on seti Experts because the + + + align:start position:0% +would call on seti Experts because the +the the nature of the intellectual + + align:start position:0% +the the nature of the intellectual + + + align:start position:0% +the the nature of the intellectual +challenge does seem quite similar at the + + align:start position:0% +challenge does seem quite similar at the + + + align:start position:0% +challenge does seem quite similar at the +same time it also feels + + align:start position:0% +same time it also feels + + + align:start position:0% +same time it also feels +you know exactly as well as big + + align:start position:0% +you know exactly as well as big + + + align:start position:0% +you know exactly as well as big +remaining challenge as it is for + + align:start position:0% +remaining challenge as it is for + + + align:start position:0% +remaining challenge as it is for +anything else because the seti folks + + align:start position:0% +anything else because the seti folks + + + align:start position:0% +anything else because the seti folks +have you know are also dealing with what + + align:start position:0% +have you know are also dealing with what + + + align:start position:0% +have you know are also dealing with what +what they know about what they've + + align:start position:0% +what they know about what they've + + + align:start position:0% +what they know about what they've +experienced what they can even imagine + + align:start position:0% +experienced what they can even imagine + + + align:start position:0% +experienced what they can even imagine +the horizons even of their imaginations + + align:start position:0% +the horizons even of their imaginations + + + align:start position:0% +the horizons even of their imaginations +so in that sense it does feel like a + + align:start position:0% +so in that sense it does feel like a + + + align:start position:0% +so in that sense it does feel like a +remarkably similar + + align:start position:0% +remarkably similar + + + align:start position:0% +remarkably similar +uh exercise + + align:start position:0% + + + + align:start position:0% + +there's also we I mean I wrote a little + + align:start position:0% +there's also we I mean I wrote a little + + + align:start position:0% +there's also we I mean I wrote a little +piece about this some years ago as many + + align:start position:0% +piece about this some years ago as many + + + align:start position:0% +piece about this some years ago as many +of you might know is a bit of an aside + + align:start position:0% +of you might know is a bit of an aside + + + align:start position:0% +of you might know is a bit of an aside +but + + align:start position:0% +but + + + align:start position:0% +but +a large part of the study work is + + align:start position:0% +a large part of the study work is + + + align:start position:0% +a large part of the study work is +focused on something called the Drake + + align:start position:0% +focused on something called the Drake + + + align:start position:0% +focused on something called the Drake +equation named for astronomer and Frank + + align:start position:0% +equation named for astronomer and Frank + + + align:start position:0% +equation named for astronomer and Frank +Drake back in 1961. and there was an + + align:start position:0% +Drake back in 1961. and there was an + + + align:start position:0% +Drake back in 1961. and there was an +effort to try to quantify and estimate + + align:start position:0% +effort to try to quantify and estimate + + + align:start position:0% +effort to try to quantify and estimate +admittedly very loose estimates How + + align:start position:0% +admittedly very loose estimates How + + + align:start position:0% +admittedly very loose estimates How +likely a signal might actually be + + align:start position:0% +likely a signal might actually be + + + align:start position:0% +likely a signal might actually be +expected to be from say an intelligent + + align:start position:0% +expected to be from say an intelligent + + + align:start position:0% +expected to be from say an intelligent +extraterrestrial civilization + + align:start position:0% +extraterrestrial civilization + + + align:start position:0% +extraterrestrial civilization +and the last term in this equation is + + align:start position:0% +and the last term in this equation is + + + align:start position:0% +and the last term in this equation is +always the kind of expected lifetime of + + align:start position:0% +always the kind of expected lifetime of + + + align:start position:0% +always the kind of expected lifetime of +the civilization that would have been + + align:start position:0% +the civilization that would have been + + + align:start position:0% +the civilization that would have been +sending the putative signals and in the + + align:start position:0% +sending the putative signals and in the + + + align:start position:0% +sending the putative signals and in the +cold war in the exactly period we have + + align:start position:0% +cold war in the exactly period we have + + + align:start position:0% +cold war in the exactly period we have +our heads in the middle of in this class + + align:start position:0% +our heads in the middle of in this class + + + align:start position:0% +our heads in the middle of in this class +that last term in the Drake equation + + align:start position:0% +that last term in the Drake equation + + + align:start position:0% +that last term in the Drake equation +capital L always was a stand-in for to + + align:start position:0% +capital L always was a stand-in for to + + + align:start position:0% +capital L always was a stand-in for to +those thinking about in time for + + align:start position:0% +those thinking about in time for + + + align:start position:0% +those thinking about in time for +all-out nuclear Holocaust so it wasn't + + align:start position:0% +all-out nuclear Holocaust so it wasn't + + + align:start position:0% +all-out nuclear Holocaust so it wasn't +that there was a kind of biological you + + align:start position:0% +that there was a kind of biological you + + + align:start position:0% +that there was a kind of biological you +know uh lifespan they thought it was + + align:start position:0% +know uh lifespan they thought it was + + + align:start position:0% +know uh lifespan they thought it was +really did did the civilization blow + + align:start position:0% +really did did the civilization blow + + + align:start position:0% +really did did the civilization blow +itself to bits the way it seemed to many + + align:start position:0% +itself to bits the way it seemed to many + + + align:start position:0% +itself to bits the way it seemed to many +people at the time that maybe people on + + align:start position:0% +people at the time that maybe people on + + + align:start position:0% +people at the time that maybe people on +Earth were about to do were poised to do + + align:start position:0% +Earth were about to do were poised to do + + + align:start position:0% +Earth were about to do were poised to do +so there's there's actually a high kind + + align:start position:0% +so there's there's actually a high kind + + + align:start position:0% +so there's there's actually a high kind +of nuclear component even to seti as + + align:start position:0% +of nuclear component even to seti as + + + align:start position:0% +of nuclear component even to seti as +well the the community had already been + + align:start position:0% +well the the community had already been + + + align:start position:0% +well the the community had already been +thinking about it kind of knife edge of + + align:start position:0% +thinking about it kind of knife edge of + + + align:start position:0% +thinking about it kind of knife edge of +survival in a nuclear age + + align:start position:0% +survival in a nuclear age + + + align:start position:0% +survival in a nuclear age +is what they consider to be knife edge + + align:start position:0% +is what they consider to be knife edge + + + align:start position:0% +is what they consider to be knife edge +at the same time there have been all + + align:start position:0% +at the same time there have been all + + + align:start position:0% +at the same time there have been all +these kind of technological spin-offs uh + + align:start position:0% +these kind of technological spin-offs uh + + + align:start position:0% +these kind of technological spin-offs uh +for certain kinds of multi-channel + + align:start position:0% +for certain kinds of multi-channel + + + align:start position:0% +for certain kinds of multi-channel +analyzers and other technological kind + + align:start position:0% +analyzers and other technological kind + + + align:start position:0% +analyzers and other technological kind +of um uh fancy electronics and code that + + align:start position:0% +of um uh fancy electronics and code that + + + align:start position:0% +of um uh fancy electronics and code that +was developed first for study how do you + + align:start position:0% +was developed first for study how do you + + + align:start position:0% +was developed first for study how do you +sift through millions of channels at + + align:start position:0% +sift through millions of channels at + + + align:start position:0% +sift through millions of channels at +once millions of frequency bands say and + + align:start position:0% +once millions of frequency bands say and + + + align:start position:0% +once millions of frequency bands say and +those some of those were brought back so + + align:start position:0% +those some of those were brought back so + + + align:start position:0% +those some of those were brought back so +to speak behind the fence into certain + + align:start position:0% +to speak behind the fence into certain + + + align:start position:0% +to speak behind the fence into certain +kinds of very sophisticated nuclear + + align:start position:0% +kinds of very sophisticated nuclear + + + align:start position:0% +kinds of very sophisticated nuclear +testing especially after the ban on on + + align:start position:0% +testing especially after the ban on on + + + align:start position:0% +testing especially after the ban on on +actual test blasts and this area of what + + align:start position:0% +actual test blasts and this area of what + + + align:start position:0% +actual test blasts and this area of what +what's now called + + align:start position:0% +what's now called + + + align:start position:0% +what's now called +um stockpile stewardship so he seems + + align:start position:0% +um stockpile stewardship so he seems + + + align:start position:0% +um stockpile stewardship so he seems +like it's always about the far away the + + align:start position:0% +like it's always about the far away the + + + align:start position:0% +like it's always about the far away the +distance a little extra Galactic or or + + align:start position:0% +distance a little extra Galactic or or + + + align:start position:0% +distance a little extra Galactic or or +certainly extraterrestrial + + align:start position:0% +certainly extraterrestrial + + + align:start position:0% +certainly extraterrestrial +and yet it's its own history has been + + align:start position:0% +and yet it's its own history has been + + + align:start position:0% +and yet it's its own history has been +kind of grounded and intertwined with + + align:start position:0% +kind of grounded and intertwined with + + + align:start position:0% +kind of grounded and intertwined with +with a kind of cold war nuclear um age + + align:start position:0% +with a kind of cold war nuclear um age + + + align:start position:0% +with a kind of cold war nuclear um age +from from its own beginning so maybe all + + align:start position:0% +from from its own beginning so maybe all + + + align:start position:0% +from from its own beginning so maybe all +the more appropriate then that some + + align:start position:0% +the more appropriate then that some + + + align:start position:0% +the more appropriate then that some +study experts as well as linguists and + + align:start position:0% +study experts as well as linguists and + + + align:start position:0% +study experts as well as linguists and +and philosophers and sculptors would be + + align:start position:0% +and philosophers and sculptors would be + + + align:start position:0% +and philosophers and sculptors would be +we'll be working with the Department of + + align:start position:0% +we'll be working with the Department of + + + align:start position:0% +we'll be working with the Department of +energy to think about symbol systems for + + align:start position:0% +energy to think about symbol systems for + + + align:start position:0% +energy to think about symbol systems for +300 000 years hence + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +were there parts of the the whip + + align:start position:0% +were there parts of the the whip + + + align:start position:0% +were there parts of the the whip +facility uh was it called was it + + align:start position:0% +facility uh was it called was it + + + align:start position:0% +facility uh was it called was it +I can't remember what whip stands for + + align:start position:0% +I can't remember what whip stands for + + + align:start position:0% +I can't remember what whip stands for +Waste injection + + align:start position:0% +Waste injection + + + align:start position:0% +Waste injection +pilot project something like that + + align:start position:0% + + + + align:start position:0% + +that's a great question Alex I I don't + + align:start position:0% +that's a great question Alex I I don't + + + align:start position:0% +that's a great question Alex I I don't +remember the specifics thank you for + + align:start position:0% +remember the specifics thank you for + + + align:start position:0% +remember the specifics thank you for +asking it so I think in general it's + + align:start position:0% +asking it so I think in general it's + + + align:start position:0% +asking it so I think in general it's +smaller I think the ideas for Yucca + + align:start position:0% +smaller I think the ideas for Yucca + + + align:start position:0% +smaller I think the ideas for Yucca +Mountain + + align:start position:0% +Mountain + + + align:start position:0% +Mountain +um were were ultimately much + + align:start position:0% +um were were ultimately much + + + align:start position:0% +um were were ultimately much +um more Grand it would have had a much + + align:start position:0% +um more Grand it would have had a much + + + align:start position:0% +um more Grand it would have had a much +higher storage capacity for example who + + align:start position:0% +higher storage capacity for example who + + + align:start position:0% +higher storage capacity for example who +at least it never got past kind of + + align:start position:0% +at least it never got past kind of + + + align:start position:0% +at least it never got past kind of +design specs but that was the the + + align:start position:0% +design specs but that was the the + + + align:start position:0% +design specs but that was the the +ambition for Yucca Mountain was it + + align:start position:0% +ambition for Yucca Mountain was it + + + align:start position:0% +ambition for Yucca Mountain was it +really was supposed to be like a + + align:start position:0% +really was supposed to be like a + + + align:start position:0% +really was supposed to be like a +One-Stop shop and we solved it like + + align:start position:0% +One-Stop shop and we solved it like + + + align:start position:0% +One-Stop shop and we solved it like +that's it we have enough capacity sort + + align:start position:0% +that's it we have enough capacity sort + + + align:start position:0% +that's it we have enough capacity sort +of for the indefinite future and I don't + + align:start position:0% +of for the indefinite future and I don't + + + align:start position:0% +of for the indefinite future and I don't +think anyone at whip ever thought that I + + align:start position:0% +think anyone at whip ever thought that I + + + align:start position:0% +think anyone at whip ever thought that I +think whip was always seen as + + align:start position:0% +think whip was always seen as + + + align:start position:0% +think whip was always seen as +um the kind of proof of principal Center + + align:start position:0% +um the kind of proof of principal Center + + + align:start position:0% +um the kind of proof of principal Center +and alone hopefully reminds us what + + align:start position:0% +and alone hopefully reminds us what + + + align:start position:0% +and alone hopefully reminds us what +thank you waste isolation pilot plant + + align:start position:0% +thank you waste isolation pilot plant + + + align:start position:0% +thank you waste isolation pilot plant +okay good thank you so whip whip wasn't + + align:start position:0% +okay good thank you so whip whip wasn't + + + align:start position:0% +okay good thank you so whip whip wasn't +in I think was was built to be as as his + + align:start position:0% +in I think was was built to be as as his + + + align:start position:0% +in I think was was built to be as as his +name uh even implies a kind of pilot + + align:start position:0% +name uh even implies a kind of pilot + + + align:start position:0% +name uh even implies a kind of pilot +project for something that could + + align:start position:0% +project for something that could + + + align:start position:0% +project for something that could +potentially later be scaled up and then + + align:start position:0% +potentially later be scaled up and then + + + align:start position:0% +potentially later be scaled up and then +as it turns out they're you know + + align:start position:0% +as it turns out they're you know + + + align:start position:0% +as it turns out they're you know +um some real uh technical challenges + + align:start position:0% +um some real uh technical challenges + + + align:start position:0% +um some real uh technical challenges +even with a pilot design is that's why I + + align:start position:0% +even with a pilot design is that's why I + + + align:start position:0% +even with a pilot design is that's why I +build Pilots I guess you find out what + + align:start position:0% +build Pilots I guess you find out what + + + align:start position:0% +build Pilots I guess you find out what +what might not work the way you think it + + align:start position:0% +what might not work the way you think it + + + align:start position:0% +what might not work the way you think it +would just for the engineering specs + + align:start position:0% +would just for the engineering specs + + + align:start position:0% +would just for the engineering specs +but I think in general the plans for + + align:start position:0% +but I think in general the plans for + + + align:start position:0% +but I think in general the plans for +Yucca Mountain were were to be + + align:start position:0% +Yucca Mountain were were to be + + + align:start position:0% +Yucca Mountain were were to be +um like forever like we've solved it it + + align:start position:0% +um like forever like we've solved it it + + + align:start position:0% +um like forever like we've solved it it +was was the ambition or the hope that + + align:start position:0% +was was the ambition or the hope that + + + align:start position:0% +was was the ambition or the hope that +would be the one place with enough + + align:start position:0% +would be the one place with enough + + + align:start position:0% +would be the one place with enough +capacity with uh presumed geological + + align:start position:0% +capacity with uh presumed geological + + + align:start position:0% +capacity with uh presumed geological +stability that could be that could be + + align:start position:0% +stability that could be that could be + + + align:start position:0% +stability that could be that could be +estimated again in the hundreds of + + align:start position:0% +estimated again in the hundreds of + + + align:start position:0% +estimated again in the hundreds of +thousands of years time frame I don't + + align:start position:0% +thousands of years time frame I don't + + + align:start position:0% +thousands of years time frame I don't +know how one could ever have that + + align:start position:0% +know how one could ever have that + + + align:start position:0% +know how one could ever have that +confidence but that was at least + + align:start position:0% +confidence but that was at least + + + align:start position:0% +confidence but that was at least +something people were thinking about + + align:start position:0% +something people were thinking about + + + align:start position:0% +something people were thinking about +uh and that it would be the one site + + align:start position:0% +uh and that it would be the one site + + + align:start position:0% +uh and that it would be the one site +needed uh at least for the domestic + + align:start position:0% +needed uh at least for the domestic + + + align:start position:0% +needed uh at least for the domestic +United you know uh continental United + + align:start position:0% +United you know uh continental United + + + align:start position:0% +United you know uh continental United +States maybe even for for worldwide and + + align:start position:0% +States maybe even for for worldwide and + + + align:start position:0% +States maybe even for for worldwide and +I think that certainly has not yet come + + align:start position:0% +I think that certainly has not yet come + + + align:start position:0% +I think that certainly has not yet come +to be to put it mildly + + align:start position:0% + + + + align:start position:0% + +and there's there's that I think really + + align:start position:0% +and there's there's that I think really + + + align:start position:0% +and there's there's that I think really +interesting footage in the film about + + align:start position:0% +interesting footage in the film about + + + align:start position:0% +interesting footage in the film about +some of the local kind of town hall + + align:start position:0% +some of the local kind of town hall + + + align:start position:0% +some of the local kind of town hall +meetings + + align:start position:0% +meetings + + + align:start position:0% +meetings +in and around where the facility I think + + align:start position:0% +in and around where the facility I think + + + align:start position:0% +in and around where the facility I think +was ultimately made uh + + align:start position:0% +was ultimately made uh + + + align:start position:0% +was ultimately made uh +well you can see you know there there's + + align:start position:0% +well you can see you know there there's + + + align:start position:0% +well you can see you know there there's +a there's a robust range of opinions is + + align:start position:0% +a there's a robust range of opinions is + + + align:start position:0% +a there's a robust range of opinions is +it good for the local economy in the + + align:start position:0% +it good for the local economy in the + + + align:start position:0% +it good for the local economy in the +short term does it make good you know + + align:start position:0% +short term does it make good you know + + + align:start position:0% +short term does it make good you know +secure well-paying jobs + + align:start position:0% +secure well-paying jobs + + + align:start position:0% +secure well-paying jobs +um you know does it improve the kind of + + align:start position:0% +um you know does it improve the kind of + + + align:start position:0% +um you know does it improve the kind of +local tax base those kinds of arguments + + align:start position:0% +local tax base those kinds of arguments + + + align:start position:0% +local tax base those kinds of arguments +uh and uh other concerns that are raised + + align:start position:0% +uh and uh other concerns that are raised + + + align:start position:0% +uh and uh other concerns that are raised +about uh is that is that a worthwhile + + align:start position:0% +about uh is that is that a worthwhile + + + align:start position:0% +about uh is that is that a worthwhile +trade-off and that's just for again this + + align:start position:0% +trade-off and that's just for again this + + + align:start position:0% +trade-off and that's just for again this +kind of pilot facility in one kind of + + align:start position:0% +kind of pilot facility in one kind of + + + align:start position:0% +kind of pilot facility in one kind of +um in one area + + align:start position:0% +um in one area + + + align:start position:0% +um in one area +um + + align:start position:0% +um + + + align:start position:0% +um +it it is a fascinating question if you + + align:start position:0% +it it is a fascinating question if you + + + align:start position:0% +it it is a fascinating question if you +get to kind of + + align:start position:0% +get to kind of + + + align:start position:0% +get to kind of +participatory democracy for the Here and + + align:start position:0% +participatory democracy for the Here and + + + align:start position:0% +participatory democracy for the Here and +Now is already really hard I think again + + align:start position:0% +Now is already really hard I think again + + + align:start position:0% +Now is already really hard I think again +we're kind of getting reminded of every + + align:start position:0% +we're kind of getting reminded of every + + + align:start position:0% +we're kind of getting reminded of every +day now imagine this when you're trying + + align:start position:0% +day now imagine this when you're trying + + + align:start position:0% +day now imagine this when you're trying +to make decisions I think as you're + + align:start position:0% +to make decisions I think as you're + + + align:start position:0% +to make decisions I think as you're +saying the live implications for + + align:start position:0% +saying the live implications for + + + align:start position:0% +saying the live implications for +generations to you know to come + + align:start position:0% +generations to you know to come + + + align:start position:0% +generations to you know to come +um what what's the who has say for on + + align:start position:0% +um what what's the who has say for on + + + align:start position:0% +um what what's the who has say for on +behalf of them how do you even + + align:start position:0% +behalf of them how do you even + + + align:start position:0% +behalf of them how do you even +incorporate that let alone the the sort + + align:start position:0% +incorporate that let alone the the sort + + + align:start position:0% +incorporate that let alone the the sort +of next five year ten year plan will + + align:start position:0% +of next five year ten year plan will + + + align:start position:0% +of next five year ten year plan will +this be + + align:start position:0% +this be + + + align:start position:0% +this be +um better or worse for the for the local + + align:start position:0% +um better or worse for the for the local + + + align:start position:0% +um better or worse for the for the local +community + + align:start position:0% + + + + align:start position:0% + +yeah yeah + + align:start position:0% +yeah yeah + + + align:start position:0% +yeah yeah +and again there's something much like + + align:start position:0% +and again there's something much like + + + align:start position:0% +and again there's something much like +with Fukushima obviously the filmmakers + + align:start position:0% +with Fukushima obviously the filmmakers + + + align:start position:0% +with Fukushima obviously the filmmakers +were immersed in the project long before + + align:start position:0% +were immersed in the project long before + + + align:start position:0% +were immersed in the project long before +that had occurred so the film was itself + + align:start position:0% +that had occurred so the film was itself + + + align:start position:0% +that had occurred so the film was itself +a kind of moving not a moving Target but + + align:start position:0% +a kind of moving not a moving Target but + + + align:start position:0% +a kind of moving not a moving Target but +the film evolved more over the course of + + align:start position:0% +the film evolved more over the course of + + + align:start position:0% +the film evolved more over the course of +its making than I think films otherwise + + align:start position:0% +its making than I think films otherwise + + + align:start position:0% +its making than I think films otherwise +often do and that's again it was it was + + align:start position:0% +often do and that's again it was it was + + + align:start position:0% +often do and that's again it was it was +a genuine surprise surprise to still + + align:start position:0% +a genuine surprise surprise to still + + + align:start position:0% +a genuine surprise surprise to still +make a surprise of course to many of The + + align:start position:0% +make a surprise of course to many of The + + + align:start position:0% +make a surprise of course to many of The +Operators and the locals + + align:start position:0% +Operators and the locals + + + align:start position:0% +Operators and the locals +um + + align:start position:0% +um + + + align:start position:0% +um +and again one could say well that's why + + align:start position:0% +and again one could say well that's why + + + align:start position:0% +and again one could say well that's why +you do small scale engineering pilot + + align:start position:0% +you do small scale engineering pilot + + + align:start position:0% +you do small scale engineering pilot +projects you want to learn from these + + align:start position:0% +projects you want to learn from these + + + align:start position:0% +projects you want to learn from these +and hopefully you know get better and + + align:start position:0% +and hopefully you know get better and + + + align:start position:0% +and hopefully you know get better and +better and maybe it'll scale but it does + + align:start position:0% +better and maybe it'll scale but it does + + + align:start position:0% +better and maybe it'll scale but it does +it raises some extraordinarily difficult + + align:start position:0% +it raises some extraordinarily difficult + + + align:start position:0% +it raises some extraordinarily difficult +questions if if I just say on a kind of + + align:start position:0% +questions if if I just say on a kind of + + + align:start position:0% +questions if if I just say on a kind of +decade-long time scale let alone you + + align:start position:0% +decade-long time scale let alone you + + + align:start position:0% +decade-long time scale let alone you +know 10 10 to the power 10 to the one + + align:start position:0% +know 10 10 to the power 10 to the one + + + align:start position:0% +know 10 10 to the power 10 to the one +years as opposed to 10 to the five years + + align:start position:0% +years as opposed to 10 to the five years + + + align:start position:0% +years as opposed to 10 to the five years +that's that's a big change uh can we can + + align:start position:0% +that's that's a big change uh can we can + + + align:start position:0% +that's that's a big change uh can we can +we get 10 to the one years done or even + + align:start position:0% +we get 10 to the one years done or even + + + align:start position:0% +we get 10 to the one years done or even +a century let alone uh you know a + + align:start position:0% +a century let alone uh you know a + + + align:start position:0% +a century let alone uh you know a +hundred thousand years + + align:start position:0% +hundred thousand years + + + align:start position:0% +hundred thousand years +so yeah I was surprised at it too um + + align:start position:0% +so yeah I was surprised at it too um + + + align:start position:0% +so yeah I was surprised at it too um +yeah + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +some of the sort of scenes within kind + + align:start position:0% +some of the sort of scenes within kind + + + align:start position:0% +some of the sort of scenes within kind +of active reactors just this just the + + align:start position:0% +of active reactors just this just the + + + align:start position:0% +of active reactors just this just the +scenes of the kind of Machinery of of + + align:start position:0% +scenes of the kind of Machinery of of + + + align:start position:0% +scenes of the kind of Machinery of of +what it's like for humans to be + + align:start position:0% +what it's like for humans to be + + + align:start position:0% +what it's like for humans to be +interacting with these with these very + + align:start position:0% +interacting with these with these very + + + align:start position:0% +interacting with these with these very +hot materials hot in many ways + + align:start position:0% +hot materials hot in many ways + + + align:start position:0% +hot materials hot in many ways +um you know I don't think I'd ever seen + + align:start position:0% +um you know I don't think I'd ever seen + + + align:start position:0% +um you know I don't think I'd ever seen +moving picture of that uh before myself + + align:start position:0% +moving picture of that uh before myself + + + align:start position:0% +moving picture of that uh before myself +before seeing the film just even in a in + + align:start position:0% +before seeing the film just even in a in + + + align:start position:0% +before seeing the film just even in a in +a reactor site that's operating you know + + align:start position:0% +a reactor site that's operating you know + + + align:start position:0% +a reactor site that's operating you know +perfectly appropriately perfectly + + align:start position:0% +perfectly appropriately perfectly + + + align:start position:0% +perfectly appropriately perfectly +canonically just you know how do you + + align:start position:0% +canonically just you know how do you + + + align:start position:0% +canonically just you know how do you +deal with these with these sort of spent + + align:start position:0% +deal with these with these sort of spent + + + align:start position:0% +deal with these with these sort of spent +fuel rods and all these kinds of just + + align:start position:0% +fuel rods and all these kinds of just + + + align:start position:0% +fuel rods and all these kinds of just +getting a visual of that and the scale + + align:start position:0% +getting a visual of that and the scale + + + align:start position:0% +getting a visual of that and the scale +of it + + align:start position:0% +of it + + + align:start position:0% +of it +um what it's like with all the benefits + + align:start position:0% +um what it's like with all the benefits + + + align:start position:0% +um what it's like with all the benefits +of our own kind of present day high + + align:start position:0% +of our own kind of present day high + + + align:start position:0% +of our own kind of present day high +technology let alone when people are + + align:start position:0% +technology let alone when people are + + + align:start position:0% +technology let alone when people are +doing this you know back in the 40s and + + align:start position:0% +doing this you know back in the 40s and + + + align:start position:0% +doing this you know back in the 40s and +50s + + align:start position:0% +50s + + + align:start position:0% +50s +I found that really + + align:start position:0% +I found that really + + + align:start position:0% +I found that really +um actually pretty riveting too just + + align:start position:0% +um actually pretty riveting too just + + + align:start position:0% +um actually pretty riveting too just +just sort of visually viscerally what's + + align:start position:0% +just sort of visually viscerally what's + + + align:start position:0% +just sort of visually viscerally what's +it like to be working in a site like + + align:start position:0% +it like to be working in a site like + + + align:start position:0% +it like to be working in a site like +that when things are going right when + + align:start position:0% +that when things are going right when + + + align:start position:0% +that when things are going right when +things are going perfectly as the + + align:start position:0% +things are going perfectly as the + + + align:start position:0% +things are going perfectly as the +engineers you know and scientists had + + align:start position:0% +engineers you know and scientists had + + + align:start position:0% +engineers you know and scientists had +had hoped + + align:start position:0% + + + + align:start position:0% + +I don't know Alex it's a great question + + align:start position:0% +I don't know Alex it's a great question + + + align:start position:0% +I don't know Alex it's a great question +I don't know if anyone else on on the + + align:start position:0% +I don't know if anyone else on on the + + + align:start position:0% +I don't know if anyone else on on the +conversation knows about that I bet we + + align:start position:0% +conversation knows about that I bet we + + + align:start position:0% +conversation knows about that I bet we +could find out with some quick Googling + + align:start position:0% +could find out with some quick Googling + + + align:start position:0% +could find out with some quick Googling +but I don't know offhand + + align:start position:0% +but I don't know offhand + + + align:start position:0% +but I don't know offhand +um yeah + + align:start position:0% + + + + align:start position:0% + +you know I think as you as you may know + + align:start position:0% +you know I think as you as you may know + + + align:start position:0% +you know I think as you as you may know +there was a time in the + + align:start position:0% +there was a time in the + + + align:start position:0% +there was a time in the +starting in the late 1940s the early + + align:start position:0% +starting in the late 1940s the early + + + align:start position:0% +starting in the late 1940s the early +years after the second world war and + + align:start position:0% +years after the second world war and + + + align:start position:0% +years after the second world war and +really accelerating throughout the 50s + + align:start position:0% +really accelerating throughout the 50s + + + align:start position:0% +really accelerating throughout the 50s +when many many you know very small-scale + + align:start position:0% +when many many you know very small-scale + + + align:start position:0% +when many many you know very small-scale +research reactors + + align:start position:0% +research reactors + + + align:start position:0% +research reactors +were built on University campuses across + + align:start position:0% +were built on University campuses across + + + align:start position:0% +were built on University campuses across +the country mits was in in that sense + + align:start position:0% +the country mits was in in that sense + + + align:start position:0% +the country mits was in in that sense +MIT is unusual for having survived so + + align:start position:0% +MIT is unusual for having survived so + + + align:start position:0% +MIT is unusual for having survived so +long not for having been built when it + + align:start position:0% +long not for having been built when it + + + align:start position:0% +long not for having been built when it +was and so I don't know what the longest + + align:start position:0% +was and so I don't know what the longest + + + align:start position:0% +was and so I don't know what the longest +the with a larger original plan was + + align:start position:0% +the with a larger original plan was + + + align:start position:0% +the with a larger original plan was +for you know collection and containment + + align:start position:0% +for you know collection and containment + + + align:start position:0% +for you know collection and containment +of these um unavoidable waste products + + align:start position:0% +of these um unavoidable waste products + + + align:start position:0% +of these um unavoidable waste products +the the atomic energy commission the + + align:start position:0% +the the atomic energy commission the + + + align:start position:0% +the the atomic energy commission the +kind of successor to the wartime + + align:start position:0% +kind of successor to the wartime + + + align:start position:0% +kind of successor to the wartime +Manhattan Project really had a very very + + align:start position:0% +Manhattan Project really had a very very + + + align:start position:0% +Manhattan Project really had a very very +kind of + + align:start position:0% +kind of + + + align:start position:0% +kind of +at the time seemed very generous program + + align:start position:0% +at the time seemed very generous program + + + align:start position:0% +at the time seemed very generous program +to build these facilities small scale + + align:start position:0% +to build these facilities small scale + + + align:start position:0% +to build these facilities small scale +facilities + + align:start position:0% +facilities + + + align:start position:0% +facilities +I mean just by the dozens and dozens + + align:start position:0% +I mean just by the dozens and dozens + + + align:start position:0% +I mean just by the dozens and dozens +across um you know liberal arts campuses + + align:start position:0% +across um you know liberal arts campuses + + + align:start position:0% +across um you know liberal arts campuses +big research universities instead of + + align:start position:0% +big research universities instead of + + + align:start position:0% +big research universities instead of +everything between + + align:start position:0% +everything between + + + align:start position:0% +everything between +and so I don't know what the plans were + + align:start position:0% +and so I don't know what the plans were + + + align:start position:0% +and so I don't know what the plans were +for that larger collection of stuff let + + align:start position:0% +for that larger collection of stuff let + + + align:start position:0% +for that larger collection of stuff let +alone what we've been doing you know + + align:start position:0% +alone what we've been doing you know + + + align:start position:0% +alone what we've been doing you know +very locally + + align:start position:0% +very locally + + + align:start position:0% +very locally +looks it looked like you were about to + + align:start position:0% +looks it looked like you were about to + + + align:start position:0% +looks it looked like you were about to +jump in as well I cut you off I think + + align:start position:0% + + + + align:start position:0% + +yeah especially I mean by now it sort of + + align:start position:0% +yeah especially I mean by now it sort of + + + align:start position:0% +yeah especially I mean by now it sort of +Fades into the background we've all been + + align:start position:0% +Fades into the background we've all been + + + align:start position:0% +Fades into the background we've all been +used to there's the basic knowledge that + + align:start position:0% +used to there's the basic knowledge that + + + align:start position:0% +used to there's the basic knowledge that +has been there seemingly Forever at + + align:start position:0% +has been there seemingly Forever at + + + align:start position:0% +has been there seemingly Forever at +least for you know for Generations by + + align:start position:0% +least for you know for Generations by + + + align:start position:0% +least for you know for Generations by +now + + align:start position:0% +now + + + align:start position:0% +now +there was as many of the folks at the + + align:start position:0% +there was as many of the folks at the + + + align:start position:0% +there was as many of the folks at the +Tas certainly won't remember this + + align:start position:0% +Tas certainly won't remember this + + + align:start position:0% +Tas certainly won't remember this +one time when Cambridge residents did + + align:start position:0% +one time when Cambridge residents did + + + align:start position:0% +one time when Cambridge residents did +have a reason to recognize these things + + align:start position:0% +have a reason to recognize these things + + + align:start position:0% +have a reason to recognize these things +was not + + align:start position:0% +was not + + + align:start position:0% +was not +an accident at the MIT reactor + + align:start position:0% +an accident at the MIT reactor + + + align:start position:0% +an accident at the MIT reactor +thankfully but at what had been a + + align:start position:0% +thankfully but at what had been a + + + align:start position:0% +thankfully but at what had been a +particle accelerator uh closer to + + align:start position:0% +particle accelerator uh closer to + + + align:start position:0% +particle accelerator uh closer to +Harvard's Camp is actually really + + align:start position:0% +Harvard's Camp is actually really + + + align:start position:0% +Harvard's Camp is actually really +contiguous with Harvard was at the time + + align:start position:0% +contiguous with Harvard was at the time + + + align:start position:0% +contiguous with Harvard was at the time +called the Cambridge electron + + align:start position:0% +called the Cambridge electron + + + align:start position:0% +called the Cambridge electron +accelerator or the cea and also one of + + align:start position:0% +accelerator or the cea and also one of + + + align:start position:0% +accelerator or the cea and also one of +these things MIT also had one + + align:start position:0% +these things MIT also had one + + + align:start position:0% +these things MIT also had one +the atomic energy commission had also + + align:start position:0% +the atomic energy commission had also + + + align:start position:0% +the atomic energy commission had also +subsidized the construction of dozens + + align:start position:0% +subsidized the construction of dozens + + + align:start position:0% +subsidized the construction of dozens +and dozens of research accelerators so + + align:start position:0% +and dozens of research accelerators so + + + align:start position:0% +and dozens of research accelerators so +particle accelerators not just reactors + + align:start position:0% +particle accelerators not just reactors + + + align:start position:0% +particle accelerators not just reactors +uh and the one in Cambridge close to + + align:start position:0% +uh and the one in Cambridge close to + + + align:start position:0% +uh and the one in Cambridge close to +Harvard + + align:start position:0% +Harvard + + + align:start position:0% +Harvard +was one of that set and in I think it + + align:start position:0% +was one of that set and in I think it + + + align:start position:0% +was one of that set and in I think it +was 1965 or 66 mid 60s uh there was an + + align:start position:0% +was 1965 or 66 mid 60s uh there was an + + + align:start position:0% +was 1965 or 66 mid 60s uh there was an +explosion that actually killed a + + align:start position:0% +explosion that actually killed a + + + align:start position:0% +explosion that actually killed a +graduate student did an enormous amount + + align:start position:0% +graduate student did an enormous amount + + + align:start position:0% +graduate student did an enormous amount +of damage uh property damage as well as + + align:start position:0% +of damage uh property damage as well as + + + align:start position:0% +of damage uh property damage as well as +the loss of life uh from the um from the + + align:start position:0% +the loss of life uh from the um from the + + + align:start position:0% +the loss of life uh from the um from the +accelerator so basically a lot of the um + + align:start position:0% +accelerator so basically a lot of the um + + + align:start position:0% +accelerator so basically a lot of the um +at the time + + align:start position:0% +at the time + + + align:start position:0% +at the time +a lot of the detectors required + + align:start position:0% +a lot of the detectors required + + + align:start position:0% +a lot of the detectors required +cryogenic cooling keep these things + + align:start position:0% +cryogenic cooling keep these things + + + align:start position:0% +cryogenic cooling keep these things +really cold and that often required lots + + align:start position:0% +really cold and that often required lots + + + align:start position:0% +really cold and that often required lots +of kind of volatile gases Under Pressure + + align:start position:0% +of kind of volatile gases Under Pressure + + + align:start position:0% +of kind of volatile gases Under Pressure +uh and so these so-called bubble + + align:start position:0% +uh and so these so-called bubble + + + align:start position:0% +uh and so these so-called bubble +Chambers and I believe it was a case of + + align:start position:0% +Chambers and I believe it was a case of + + + align:start position:0% +Chambers and I believe it was a case of +others on the call Tiffany or Julia or + + align:start position:0% +others on the call Tiffany or Julia or + + + align:start position:0% +others on the call Tiffany or Julia or +others might remember better uh Peter + + align:start position:0% +others might remember better uh Peter + + + align:start position:0% +others might remember better uh Peter +gals has written about this in one of + + align:start position:0% +gals has written about this in one of + + + align:start position:0% +gals has written about this in one of +his older books so I think what happened + + align:start position:0% +his older books so I think what happened + + + align:start position:0% +his older books so I think what happened +with the cea explosion was I think it + + align:start position:0% +with the cea explosion was I think it + + + align:start position:0% +with the cea explosion was I think it +was part of the cryogenic system that + + align:start position:0% +was part of the cryogenic system that + + + align:start position:0% +was part of the cryogenic system that +blew it blew the roof off this + + align:start position:0% +blew it blew the roof off this + + + align:start position:0% +blew it blew the roof off this +factory-sized building as I think at + + align:start position:0% +factory-sized building as I think at + + + align:start position:0% +factory-sized building as I think at +least one graduate was killed in + + align:start position:0% +least one graduate was killed in + + + align:start position:0% +least one graduate was killed in +explosion I think only one loss of one + + align:start position:0% +explosion I think only one loss of one + + + align:start position:0% +explosion I think only one loss of one +person killed + + align:start position:0% +person killed + + + align:start position:0% +person killed +um but that that's a wake-up call to the + + align:start position:0% +um but that that's a wake-up call to the + + + align:start position:0% +um but that that's a wake-up call to the +neighborhood in a big way like wait what + + align:start position:0% +neighborhood in a big way like wait what + + + align:start position:0% +neighborhood in a big way like wait what +that that little quiet sleepy Factory + + align:start position:0% +that that little quiet sleepy Factory + + + align:start position:0% +that that little quiet sleepy Factory +looking non-descript building you know + + align:start position:0% +looking non-descript building you know + + + align:start position:0% +looking non-descript building you know +practically contiguous with Harvard's + + align:start position:0% +practically contiguous with Harvard's + + + align:start position:0% +practically contiguous with Harvard's +campus they're doing what with what + + align:start position:0% +campus they're doing what with what + + + align:start position:0% +campus they're doing what with what +bottles of materials it could really do + + align:start position:0% +bottles of materials it could really do + + + align:start position:0% +bottles of materials it could really do +what so there's only been moments in + + align:start position:0% +what so there's only been moments in + + + align:start position:0% +what so there's only been moments in +cambridge's own in our own Cambridge + + align:start position:0% +cambridge's own in our own Cambridge + + + align:start position:0% +cambridge's own in our own Cambridge +history going back you know not super + + align:start position:0% +history going back you know not super + + + align:start position:0% +history going back you know not super +long ago going that's you know 60 and + + align:start position:0% +long ago going that's you know 60 and + + + align:start position:0% +long ago going that's you know 60 and +not quite 55 years or so where things + + align:start position:0% +not quite 55 years or so where things + + + align:start position:0% +not quite 55 years or so where things +you know where accidents happen right + + align:start position:0% +you know where accidents happen right + + + align:start position:0% +you know where accidents happen right +all these things are built designed and + + align:start position:0% +all these things are built designed and + + + align:start position:0% +all these things are built designed and +built by humans uh none of us it turns + + align:start position:0% +built by humans uh none of us it turns + + + align:start position:0% +built by humans uh none of us it turns +out is perfect uh and uh when you build + + align:start position:0% +out is perfect uh and uh when you build + + + align:start position:0% +out is perfect uh and uh when you build +lots and lots of these things in you + + align:start position:0% +lots and lots of these things in you + + + align:start position:0% +lots and lots of these things in you +know sometimes in pretty + + align:start position:0% +know sometimes in pretty + + + align:start position:0% +know sometimes in pretty +um dense kind of quasi-urban settings + + align:start position:0% +um dense kind of quasi-urban settings + + + align:start position:0% +um dense kind of quasi-urban settings +you know that can be a bad recipe uh now + + align:start position:0% +you know that can be a bad recipe uh now + + + align:start position:0% +you know that can be a bad recipe uh now +it was nothing like the enormous + + align:start position:0% +it was nothing like the enormous + + + align:start position:0% +it was nothing like the enormous +accelerators that were built with much + + align:start position:0% +accelerators that were built with much + + + align:start position:0% +accelerators that were built with much +more careful shielding and site + + align:start position:0% +more careful shielding and site + + + align:start position:0% +more careful shielding and site +selection all that kind of stuff it + + align:start position:0% +selection all that kind of stuff it + + + align:start position:0% +selection all that kind of stuff it +wasn't like it was fermilab or the + + align:start position:0% +wasn't like it was fermilab or the + + + align:start position:0% +wasn't like it was fermilab or the +Stanford accelerator was just pushed far + + align:start position:0% +Stanford accelerator was just pushed far + + + align:start position:0% +Stanford accelerator was just pushed far +away from campus this one was really um + + align:start position:0% +away from campus this one was really um + + + align:start position:0% +away from campus this one was really um +you know uh right right near + + align:start position:0% +you know uh right right near + + + align:start position:0% +you know uh right right near +highly populated parts of Cambridge so + + align:start position:0% +highly populated parts of Cambridge so + + + align:start position:0% +highly populated parts of Cambridge so +things like that certainly have happened + + align:start position:0% +things like that certainly have happened + + + align:start position:0% +things like that certainly have happened +luckily that that did not I don't think + + align:start position:0% +luckily that that did not I don't think + + + align:start position:0% +luckily that that did not I don't think +there was a concern about kind of + + align:start position:0% +there was a concern about kind of + + + align:start position:0% +there was a concern about kind of +radioactive waste being spread by that I + + align:start position:0% +radioactive waste being spread by that I + + + align:start position:0% +radioactive waste being spread by that I +think that was a + + align:start position:0% +think that was a + + + align:start position:0% +think that was a +volatile set of chemicals that exploded + + align:start position:0% +volatile set of chemicals that exploded + + + align:start position:0% +volatile set of chemicals that exploded +and the damage was immediate but not + + align:start position:0% +and the damage was immediate but not + + + align:start position:0% +and the damage was immediate but not +showering immediate land with with + + align:start position:0% +showering immediate land with with + + + align:start position:0% +showering immediate land with with +things with Isotopes it would be here + + align:start position:0% +things with Isotopes it would be here + + + align:start position:0% +things with Isotopes it would be here +for another through the next ice age so + + align:start position:0% +for another through the next ice age so + + + align:start position:0% +for another through the next ice age so +in that sense it's not like a reactor + + align:start position:0% +in that sense it's not like a reactor + + + align:start position:0% +in that sense it's not like a reactor +meltdown but still you know dangerous + + align:start position:0% +meltdown but still you know dangerous + + + align:start position:0% +meltdown but still you know dangerous +stuff uh that really is + + align:start position:0% +stuff uh that really is + + + align:start position:0% +stuff uh that really is +every now and then unfortunately uh you + + align:start position:0% +every now and then unfortunately uh you + + + align:start position:0% +every now and then unfortunately uh you +know doesn't operate as as designed + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% +yes + + + align:start position:0% +yes +and and is that a different kind of is + + align:start position:0% +and and is that a different kind of is + + + align:start position:0% +and and is that a different kind of is +is the threat different today in a kind + + align:start position:0% +is the threat different today in a kind + + + align:start position:0% +is the threat different today in a kind +of um you know Google Earth everything's + + align:start position:0% +of um you know Google Earth everything's + + + align:start position:0% +of um you know Google Earth everything's +in principle under kind of some kind of + + align:start position:0% +in principle under kind of some kind of + + + align:start position:0% +in principle under kind of some kind of +camera surveillance anyone could map + + align:start position:0% +camera surveillance anyone could map + + + align:start position:0% +camera surveillance anyone could map +anything anywhere in principle is that + + align:start position:0% +anything anywhere in principle is that + + + align:start position:0% +anything anywhere in principle is that +different than when these things when it + + align:start position:0% +different than when these things when it + + + align:start position:0% +different than when these things when it +took work to identify where these things + + align:start position:0% +took work to identify where these things + + + align:start position:0% +took work to identify where these things +even were uh no one had automatic GPS + + align:start position:0% +even were uh no one had automatic GPS + + + align:start position:0% +even were uh no one had automatic GPS +coordinates you know downloadable so I + + align:start position:0% +coordinates you know downloadable so I + + + align:start position:0% +coordinates you know downloadable so I +do think I think the nature of that + + align:start position:0% +do think I think the nature of that + + + align:start position:0% +do think I think the nature of that +challenge + + align:start position:0% +challenge + + + align:start position:0% +challenge +um has has changed in the last let's say + + align:start position:0% +um has has changed in the last let's say + + + align:start position:0% +um has has changed in the last let's say +20 years as well Tiffany you mentioned + + align:start position:0% +20 years as well Tiffany you mentioned + + + align:start position:0% +20 years as well Tiffany you mentioned +the chat about Lake Anna originally I + + align:start position:0% +the chat about Lake Anna originally I + + + align:start position:0% +the chat about Lake Anna originally I +actually don't know about that one you + + align:start position:0% +actually don't know about that one you + + + align:start position:0% +actually don't know about that one you +want to tell us about it + + align:start position:0% + + + + align:start position:0% + +yeah I I didn't realize I've never been + + align:start position:0% +yeah I I didn't realize I've never been + + + align:start position:0% +yeah I I didn't realize I've never been +to the whip facility I have a number of + + align:start position:0% +to the whip facility I have a number of + + + align:start position:0% +to the whip facility I have a number of +colleagues from mitu have been because + + align:start position:0% +colleagues from mitu have been because + + + align:start position:0% +colleagues from mitu have been because +as good as you may know and maybe they + + align:start position:0% +as good as you may know and maybe they + + + align:start position:0% +as good as you may know and maybe they +mentioned in the film that was a site + + align:start position:0% +mentioned in the film that was a site + + + align:start position:0% +mentioned in the film that was a site +for a bunch of underground um kind of + + align:start position:0% +for a bunch of underground um kind of + + + align:start position:0% +for a bunch of underground um kind of +fundamental physics experiments as well + + align:start position:0% +fundamental physics experiments as well + + + align:start position:0% +fundamental physics experiments as well +you want to be shielded from cosmic rays + + align:start position:0% +you want to be shielded from cosmic rays + + + align:start position:0% +you want to be shielded from cosmic rays +and lots and lots of physics experiments + + align:start position:0% +and lots and lots of physics experiments + + + align:start position:0% +and lots and lots of physics experiments +this is a Julia's mind very directly but + + align:start position:0% +this is a Julia's mind very directly but + + + align:start position:0% +this is a Julia's mind very directly but +for Generations lots of fundamental + + align:start position:0% +for Generations lots of fundamental + + + align:start position:0% +for Generations lots of fundamental +physics experiments have been in + + align:start position:0% +physics experiments have been in + + + align:start position:0% +physics experiments have been in +abandoned or no longer used Minds + + align:start position:0% +abandoned or no longer used Minds + + + align:start position:0% +abandoned or no longer used Minds +because you want to get underground for + + align:start position:0% +because you want to get underground for + + + align:start position:0% +because you want to get underground for +various shielding reasons so I have many + + align:start position:0% +various shielding reasons so I have many + + + align:start position:0% +various shielding reasons so I have many +several colleagues who had been at whip + + align:start position:0% +several colleagues who had been at whip + + + align:start position:0% +several colleagues who had been at whip +regularly for like neutrino experiments + + align:start position:0% +regularly for like neutrino experiments + + + align:start position:0% +regularly for like neutrino experiments +or other kinds of particle physics + + align:start position:0% +or other kinds of particle physics + + + align:start position:0% +or other kinds of particle physics +things + + align:start position:0% +things + + + align:start position:0% +things +um so they've been there I've never I've + + align:start position:0% +um so they've been there I've never I've + + + align:start position:0% +um so they've been there I've never I've +never been there let alone driven past + + align:start position:0% +never been there let alone driven past + + + align:start position:0% +never been there let alone driven past +it going to or from Vegas but Tiffany + + align:start position:0% +it going to or from Vegas but Tiffany + + + align:start position:0% +it going to or from Vegas but Tiffany +you're coming also reminds me something + + align:start position:0% +you're coming also reminds me something + + + align:start position:0% +you're coming also reminds me something +I I I didn't have a chance to really + + align:start position:0% +I I I didn't have a chance to really + + + align:start position:0% +I I I didn't have a chance to really +Linger on in uh in the class material + + align:start position:0% +Linger on in uh in the class material + + + align:start position:0% +Linger on in uh in the class material +but for for uh + + align:start position:0% +but for for uh + + + align:start position:0% +but for for uh +for many years when uh nuclear weapons + + align:start position:0% +for many years when uh nuclear weapons + + + align:start position:0% +for many years when uh nuclear weapons +tests were still above ground before + + align:start position:0% +tests were still above ground before + + + align:start position:0% +tests were still above ground before +they before they went underground with + + align:start position:0% +they before they went underground with + + + align:start position:0% +they before they went underground with +the limited tests being treated in the + + align:start position:0% +the limited tests being treated in the + + + align:start position:0% +the limited tests being treated in the +early 60s these things were often pegged + + align:start position:0% +early 60s these things were often pegged + + + align:start position:0% +early 60s these things were often pegged +as tourist attractions so obviously not + + align:start position:0% +as tourist attractions so obviously not + + + align:start position:0% +as tourist attractions so obviously not +to get too close to them but in Vegas in + + align:start position:0% +to get too close to them but in Vegas in + + + align:start position:0% +to get too close to them but in Vegas in +particular that was within sight lines + + align:start position:0% +particular that was within sight lines + + + align:start position:0% +particular that was within sight lines +of one of the continental testing + + align:start position:0% +of one of the continental testing + + + align:start position:0% +of one of the continental testing +grounds um + + align:start position:0% +grounds um + + + align:start position:0% +grounds um +and so they would the casinos and the + + align:start position:0% +and so they would the casinos and the + + + align:start position:0% +and so they would the casinos and the +hotels would actually sell like + + align:start position:0% +hotels would actually sell like + + + align:start position:0% +hotels would actually sell like +advertising come this weekend because + + align:start position:0% +advertising come this weekend because + + + align:start position:0% +advertising come this weekend because +you'll get to see an explosion off on + + align:start position:0% +you'll get to see an explosion off on + + + align:start position:0% +you'll get to see an explosion off on +the horizon it won't you know it won't + + align:start position:0% +the horizon it won't you know it won't + + + align:start position:0% +the horizon it won't you know it won't +be in your hotel room but it'll be you + + align:start position:0% +be in your hotel room but it'll be you + + + align:start position:0% +be in your hotel room but it'll be you +could have a clear view of this you know + + align:start position:0% +could have a clear view of this you know + + + align:start position:0% +could have a clear view of this you know +a temporary + + align:start position:0% +a temporary + + + align:start position:0% +a temporary +uh display out the window it was seen as + + align:start position:0% +uh display out the window it was seen as + + + align:start position:0% +uh display out the window it was seen as +um as not just something to be tolerated + + align:start position:0% +um as not just something to be tolerated + + + align:start position:0% +um as not just something to be tolerated +or otherwise based on what seemed like + + align:start position:0% +or otherwise based on what seemed like + + + align:start position:0% +or otherwise based on what seemed like +cold war realities but really + + align:start position:0% +cold war realities but really + + + align:start position:0% +cold war realities but really +I don't know if we'd say celebrated but + + align:start position:0% +I don't know if we'd say celebrated but + + + align:start position:0% +I don't know if we'd say celebrated but +but seen as a kind of as a tourist + + align:start position:0% +but seen as a kind of as a tourist + + + align:start position:0% +but seen as a kind of as a tourist +attraction I mean something that would + + align:start position:0% +attraction I mean something that would + + + align:start position:0% +attraction I mean something that would +help you sell hotel rooms and like you + + align:start position:0% +help you sell hotel rooms and like you + + + align:start position:0% +help you sell hotel rooms and like you +know come to Vegas this weekend kind of + + align:start position:0% +know come to Vegas this weekend kind of + + + align:start position:0% +know come to Vegas this weekend kind of +thing + + align:start position:0% +thing + + + align:start position:0% +thing +I just find that chilling I mean it's + + align:start position:0% +I just find that chilling I mean it's + + + align:start position:0% +I just find that chilling I mean it's +just astonishing + + align:start position:0% +just astonishing + + + align:start position:0% +just astonishing +um the way the way the in this case a + + align:start position:0% +um the way the way the in this case a + + + align:start position:0% +um the way the way the in this case a +weapons not even reactors weapons were + + align:start position:0% +weapons not even reactors weapons were + + + align:start position:0% +weapons not even reactors weapons were +um + + align:start position:0% +um + + + align:start position:0% +um +we're seeing in a kind of popular + + align:start position:0% +we're seeing in a kind of popular + + + align:start position:0% +we're seeing in a kind of popular +culture it wasn't so again coming back + + align:start position:0% +culture it wasn't so again coming back + + + align:start position:0% +culture it wasn't so again coming back +maybe to Lucas's points not only were + + align:start position:0% +maybe to Lucas's points not only were + + + align:start position:0% +maybe to Lucas's points not only were +they not trying to keep secret when the + + align:start position:0% +they not trying to keep secret when the + + + align:start position:0% +they not trying to keep secret when the +blast would be you think well are you + + align:start position:0% +blast would be you think well are you + + + align:start position:0% +blast would be you think well are you +worried about any kind of um Bad actors + + align:start position:0% +worried about any kind of um Bad actors + + + align:start position:0% +worried about any kind of um Bad actors +messing around with these with these + + align:start position:0% +messing around with these with these + + + align:start position:0% +messing around with these with these +nukes not only does not worry about + + align:start position:0% +nukes not only does not worry about + + + align:start position:0% +nukes not only does not worry about +keeping the date and time secret they + + align:start position:0% +keeping the date and time secret they + + + align:start position:0% +keeping the date and time secret they +were actually advertising it as if they + + align:start position:0% +were actually advertising it as if they + + + align:start position:0% +were actually advertising it as if they +could almost sell tickets + + align:start position:0% +could almost sell tickets + + + align:start position:0% +could almost sell tickets +um I again just our added our attitudes + + align:start position:0% +um I again just our added our attitudes + + + align:start position:0% +um I again just our added our attitudes +toward these things over the last 50 or + + align:start position:0% +toward these things over the last 50 or + + + align:start position:0% +toward these things over the last 50 or +60 years + + align:start position:0% +60 years + + + align:start position:0% +60 years +I find that study + + align:start position:0% + + + + align:start position:0% + +yes I mean maybe as you're saying to me + + align:start position:0% +yes I mean maybe as you're saying to me + + + align:start position:0% +yes I mean maybe as you're saying to me +there there's like I don't know if we + + align:start position:0% +there there's like I don't know if we + + + align:start position:0% +there there's like I don't know if we +call it flourishing but there is an + + align:start position:0% +call it flourishing but there is an + + + align:start position:0% +call it flourishing but there is an +actual like nuclear tourism + + align:start position:0% +actual like nuclear tourism + + + align:start position:0% +actual like nuclear tourism +oh maybe we can call it industry one of + + align:start position:0% +oh maybe we can call it industry one of + + + align:start position:0% +oh maybe we can call it industry one of +my colleagues wrote a book a very + + align:start position:0% +my colleagues wrote a book a very + + + align:start position:0% +my colleagues wrote a book a very +interesting book a few years ago + + align:start position:0% +interesting book a few years ago + + + align:start position:0% +interesting book a few years ago +um called the nuclear family vacation + + align:start position:0% +um called the nuclear family vacation + + + align:start position:0% +um called the nuclear family vacation +which is a pretty fun punch she and her + + align:start position:0% +which is a pretty fun punch she and her + + + align:start position:0% +which is a pretty fun punch she and her +husband went traveling because it was + + align:start position:0% +husband went traveling because it was + + + align:start position:0% +husband went traveling because it was +like a nuclear family that also went to + + align:start position:0% +like a nuclear family that also went to + + + align:start position:0% +like a nuclear family that also went to +all these nuclear families okay they + + align:start position:0% +all these nuclear families okay they + + + align:start position:0% +all these nuclear families okay they +went to visit nuclear sites actually + + align:start position:0% +went to visit nuclear sites actually + + + align:start position:0% +went to visit nuclear sites actually +around the world including I can't + + align:start position:0% +around the world including I can't + + + align:start position:0% +around the world including I can't +remember the Chernobyl site but they + + align:start position:0% +remember the Chernobyl site but they + + + align:start position:0% +remember the Chernobyl site but they +only went to many places in + + align:start position:0% +only went to many places in + + + align:start position:0% +only went to many places in +uh the former Soviet Union as well as um + + align:start position:0% +uh the former Soviet Union as well as um + + + align:start position:0% +uh the former Soviet Union as well as um +I think Eastern Europe and and + + align:start position:0% +I think Eastern Europe and and + + + align:start position:0% +I think Eastern Europe and and +throughout the United States + + align:start position:0% +throughout the United States + + + align:start position:0% +throughout the United States +um and she and they wrote She Wrote I + + align:start position:0% +um and she and they wrote She Wrote I + + + align:start position:0% +um and she and they wrote She Wrote I +can't remember they co-writted together + + align:start position:0% +can't remember they co-writted together + + + align:start position:0% +can't remember they co-writted together +they're both journalists excellent + + align:start position:0% +they're both journalists excellent + + + align:start position:0% +they're both journalists excellent +writers anyway um just how many of these + + align:start position:0% +writers anyway um just how many of these + + + align:start position:0% +writers anyway um just how many of these +sites are accessible in general and + + align:start position:0% +sites are accessible in general and + + + align:start position:0% +sites are accessible in general and +what's the appeal to go to right you + + align:start position:0% +what's the appeal to go to right you + + + align:start position:0% +what's the appeal to go to right you +want to go see like like collect them + + align:start position:0% +want to go see like like collect them + + + align:start position:0% +want to go see like like collect them +all like I've seen this one and this one + + align:start position:0% +all like I've seen this one and this one + + + align:start position:0% +all like I've seen this one and this one +this one this one like like other + + align:start position:0% +this one this one like like other + + + align:start position:0% +this one this one like like other +families might try to go to all the you + + align:start position:0% +families might try to go to all the you + + + align:start position:0% +families might try to go to all the you +know national parks and you know in some + + align:start position:0% +know national parks and you know in some + + + align:start position:0% +know national parks and you know in some +region of the country they were going to + + align:start position:0% +region of the country they were going to + + + align:start position:0% +region of the country they were going to +tick off all of these kind of uh nuclear + + align:start position:0% +tick off all of these kind of uh nuclear + + + align:start position:0% +tick off all of these kind of uh nuclear +related sites + + align:start position:0% +related sites + + + align:start position:0% +related sites +um as a kind of uh you know kind of + + align:start position:0% +um as a kind of uh you know kind of + + + align:start position:0% +um as a kind of uh you know kind of +Tourism + + align:start position:0% + + + + align:start position:0% + +yeah thank you I + + align:start position:0% +yeah thank you I + + + align:start position:0% +yeah thank you I +I agree I find that very hard to watch + + align:start position:0% +I agree I find that very hard to watch + + + align:start position:0% +I agree I find that very hard to watch +myself I'm not an expert at all in + + align:start position:0% +myself I'm not an expert at all in + + + align:start position:0% +myself I'm not an expert at all in +the present day kind of biomedical + + align:start position:0% +the present day kind of biomedical + + + align:start position:0% +the present day kind of biomedical +hazards and what precautions are + + align:start position:0% +hazards and what precautions are + + + align:start position:0% +hazards and what precautions are +actually being taken that + + align:start position:0% +actually being taken that + + + align:start position:0% +actually being taken that +um so I I don't know but I like I think + + align:start position:0% +um so I I don't know but I like I think + + + align:start position:0% +um so I I don't know but I like I think +I mentioned briefly in a previous + + align:start position:0% +I mentioned briefly in a previous + + + align:start position:0% +I mentioned briefly in a previous +discussion I know that there was a there + + align:start position:0% +discussion I know that there was a there + + + align:start position:0% +discussion I know that there was a there +was a a very Cavalier attitude toward + + align:start position:0% +was a a very Cavalier attitude toward + + + align:start position:0% +was a a very Cavalier attitude toward +these things uh during the second world + + align:start position:0% +these things uh during the second world + + + align:start position:0% +these things uh during the second world +war and in the early years afterwards + + align:start position:0% +war and in the early years afterwards + + + align:start position:0% +war and in the early years afterwards +and often the cavalierness was not + + align:start position:0% +and often the cavalierness was not + + + align:start position:0% +and often the cavalierness was not +telling workers enough to inform them of + + align:start position:0% +telling workers enough to inform them of + + + align:start position:0% +telling workers enough to inform them of +risks that actually were otherwise well + + align:start position:0% +risks that actually were otherwise well + + + align:start position:0% +risks that actually were otherwise well +known by other experts let alone the + + align:start position:0% +known by other experts let alone the + + + align:start position:0% +known by other experts let alone the +experts deciding to take + + align:start position:0% +experts deciding to take + + + align:start position:0% +experts deciding to take +their own risks or to you behave certain + + align:start position:0% +their own risks or to you behave certain + + + align:start position:0% +their own risks or to you behave certain +ways uh and so I don't know what the + + align:start position:0% +ways uh and so I don't know what the + + + align:start position:0% +ways uh and so I don't know what the +what the current um you know training is + + align:start position:0% +what the current um you know training is + + + align:start position:0% +what the current um you know training is +like and so on but + + align:start position:0% +like and so on but + + + align:start position:0% +like and so on but +3.6 rankings not great not terrible I + + align:start position:0% +3.6 rankings not great not terrible I + + + align:start position:0% +3.6 rankings not great not terrible I +don't I don't remember what what kind of + + align:start position:0% +don't I don't remember what what kind of + + + align:start position:0% +don't I don't remember what what kind of +exposure would would amount to 3.6 + + align:start position:0% +exposure would would amount to 3.6 + + + align:start position:0% +exposure would would amount to 3.6 +rankings I don't remember the scales you + + align:start position:0% +rankings I don't remember the scales you + + + align:start position:0% +rankings I don't remember the scales you +know what to expect do you remember we + + align:start position:0% +know what to expect do you remember we + + + align:start position:0% +know what to expect do you remember we +can look it up + + align:start position:0% + + + + align:start position:0% + +right thank you I I missed the reference + + align:start position:0% +right thank you I I missed the reference + + + align:start position:0% +right thank you I I missed the reference +very good yeah + + align:start position:0% +very good yeah + + + align:start position:0% +very good yeah +right + + align:start position:0% + + + + align:start position:0% + +I agree as well as well right let's + + align:start position:0% +I agree as well as well right let's + + + align:start position:0% +I agree as well as well right let's +let's Hawk all of Kate's books excuse me + + align:start position:0% +let's Hawk all of Kate's books excuse me + + + align:start position:0% +let's Hawk all of Kate's books excuse me +Kate's most recent book + + align:start position:0% +Kate's most recent book + + + align:start position:0% +Kate's most recent book +um + + align:start position:0% +um + + + align:start position:0% +um +oh what's the title + + align:start position:0% +oh what's the title + + + align:start position:0% +oh what's the title +and that just came out roughly a year + + align:start position:0% +and that just came out roughly a year + + + align:start position:0% +and that just came out roughly a year +ago there were a bunch there was a kind + + align:start position:0% +ago there were a bunch there was a kind + + + align:start position:0% +ago there were a bunch there was a kind +of a collection of Chernobyl related + + align:start position:0% +of a collection of Chernobyl related + + + align:start position:0% +of a collection of Chernobyl related +books came out around the same time one + + align:start position:0% +books came out around the same time one + + + align:start position:0% +books came out around the same time one +of which was was Kate Brown she's now as + + align:start position:0% +of which was was Kate Brown she's now as + + + align:start position:0% +of which was was Kate Brown she's now as +you may know okay it's a member of the + + align:start position:0% +you may know okay it's a member of the + + + align:start position:0% +you may know okay it's a member of the +MIT faculty she moved here uh roughly a + + align:start position:0% +MIT faculty she moved here uh roughly a + + + align:start position:0% +MIT faculty she moved here uh roughly a +year ago uh the real expert on uh well + + align:start position:0% +year ago uh the real expert on uh well + + + align:start position:0% +year ago uh the real expert on uh well +both on the Hanford site and the kind of + + align:start position:0% +both on the Hanford site and the kind of + + + align:start position:0% +both on the Hanford site and the kind of +longer term historical development of + + align:start position:0% +longer term historical development of + + + align:start position:0% +longer term historical development of +nuclear projects in the United States + + align:start position:0% +nuclear projects in the United States + + + align:start position:0% +nuclear projects in the United States +she's also trained as a Russian and + + align:start position:0% +she's also trained as a Russian and + + + align:start position:0% +she's also trained as a Russian and +Soviet historian + + align:start position:0% +Soviet historian + + + align:start position:0% +Soviet historian +uh an environmental historian she's done + + align:start position:0% +uh an environmental historian she's done + + + align:start position:0% +uh an environmental historian she's done +a lot of original work on in Russia + + align:start position:0% +a lot of original work on in Russia + + + align:start position:0% +a lot of original work on in Russia +Ukraine and + + align:start position:0% +Ukraine and + + + align:start position:0% +Ukraine and +and uh and many many + + align:start position:0% +and uh and many many + + + align:start position:0% +and uh and many many +um non-english language sources which I + + align:start position:0% +um non-english language sources which I + + + align:start position:0% +um non-english language sources which I +can't do she does marvelously so she's + + align:start position:0% +can't do she does marvelously so she's + + + align:start position:0% +can't do she does marvelously so she's +really a remarkable scholar of kind of + + align:start position:0% +really a remarkable scholar of kind of + + + align:start position:0% +really a remarkable scholar of kind of +comparative views of uh + + align:start position:0% +comparative views of uh + + + align:start position:0% +comparative views of uh +of a lot of these these materials + + align:start position:0% + + + + align:start position:0% + +yeah I I don't know + + align:start position:0% +yeah I I don't know + + + align:start position:0% +yeah I I don't know +um and this does raise the other + + align:start position:0% +um and this does raise the other + + + align:start position:0% +um and this does raise the other +questions I mean this came up a lot + + align:start position:0% +questions I mean this came up a lot + + + align:start position:0% +questions I mean this came up a lot +during the debates over Yucca Mountain + + align:start position:0% +during the debates over Yucca Mountain + + + align:start position:0% +during the debates over Yucca Mountain +um when it was still considered a live + + align:start position:0% +um when it was still considered a live + + + align:start position:0% +um when it was still considered a live +Prospect is you know let's say you have + + align:start position:0% +Prospect is you know let's say you have + + + align:start position:0% +Prospect is you know let's say you have +sufficient geological stability you can + + align:start position:0% +sufficient geological stability you can + + + align:start position:0% +sufficient geological stability you can +you can somehow estimate for an + + align:start position:0% +you can somehow estimate for an + + + align:start position:0% +you can somehow estimate for an +unbelievably long time scale and unless + + align:start position:0% +unbelievably long time scale and unless + + + align:start position:0% +unbelievably long time scale and unless +you have enough sufficient storage and + + align:start position:0% +you have enough sufficient storage and + + + align:start position:0% +you have enough sufficient storage and +containment how do you get the stuff + + align:start position:0% +containment how do you get the stuff + + + align:start position:0% +containment how do you get the stuff +there I mean do you put this on + + align:start position:0% +there I mean do you put this on + + + align:start position:0% +there I mean do you put this on +Commercial Railway you know cars coming + + align:start position:0% +Commercial Railway you know cars coming + + + align:start position:0% +Commercial Railway you know cars coming +back to you know Lucas's point before if + + align:start position:0% +back to you know Lucas's point before if + + + align:start position:0% +back to you know Lucas's point before if +someone knows there's some bad stuff on + + align:start position:0% +someone knows there's some bad stuff on + + + align:start position:0% +someone knows there's some bad stuff on +that tray and why don't you just knock + + align:start position:0% +that tray and why don't you just knock + + + align:start position:0% +that tray and why don't you just knock +out the trade and have some horrible + + align:start position:0% +out the trade and have some horrible + + + align:start position:0% +out the trade and have some horrible +kind of dirty bomb type attack + + align:start position:0% +kind of dirty bomb type attack + + + align:start position:0% +kind of dirty bomb type attack +so how do you how do you move the stuff + + align:start position:0% +so how do you how do you move the stuff + + + align:start position:0% +so how do you how do you move the stuff +I don't know what form is this stuff + + align:start position:0% +I don't know what form is this stuff + + + align:start position:0% +I don't know what form is this stuff +kind of most stable and most easy to + + align:start position:0% +kind of most stable and most easy to + + + align:start position:0% +kind of most stable and most easy to +move and uh there are plenty of experts + + align:start position:0% +move and uh there are plenty of experts + + + align:start position:0% +move and uh there are plenty of experts +who study this full-time I'm absolutely + + align:start position:0% +who study this full-time I'm absolutely + + + align:start position:0% +who study this full-time I'm absolutely +not one of them I don't know what the + + align:start position:0% +not one of them I don't know what the + + + align:start position:0% +not one of them I don't know what the +current best practices are but I know + + align:start position:0% +current best practices are but I know + + + align:start position:0% +current best practices are but I know +these were the kinds of things that had + + align:start position:0% +these were the kinds of things that had + + + align:start position:0% +these were the kinds of things that had +to be thought through not just + + align:start position:0% +to be thought through not just + + + align:start position:0% +to be thought through not just +can you predict the geological stability + + align:start position:0% +can you predict the geological stability + + + align:start position:0% +can you predict the geological stability +in the groundwater flow over you know + + align:start position:0% +in the groundwater flow over you know + + + align:start position:0% +in the groundwater flow over you know +multiple Millennia I think the answer to + + align:start position:0% +multiple Millennia I think the answer to + + + align:start position:0% +multiple Millennia I think the answer to +that is not with sufficient confidence + + align:start position:0% +that is not with sufficient confidence + + + align:start position:0% +that is not with sufficient confidence +right that's already just incredibly + + align:start position:0% +right that's already just incredibly + + + align:start position:0% +right that's already just incredibly +hard just just as a kind of narrow + + align:start position:0% +hard just just as a kind of narrow + + + align:start position:0% +hard just just as a kind of narrow +scientific question and then you start + + align:start position:0% +scientific question and then you start + + + align:start position:0% +scientific question and then you start +getting into practical terms like well + + align:start position:0% +getting into practical terms like well + + + align:start position:0% +getting into practical terms like well +this stuff has to travel you know two + + align:start position:0% +this stuff has to travel you know two + + + align:start position:0% +this stuff has to travel you know two +thousand three thousand miles two + + align:start position:0% +thousand three thousand miles two + + + align:start position:0% +thousand three thousand miles two +thousand miles + + align:start position:0% +thousand miles + + + align:start position:0% +thousand miles +um + + align:start position:0% +um + + + align:start position:0% +um +how do you how do you get it there right + + align:start position:0% +how do you how do you get it there right + + + align:start position:0% +how do you how do you get it there right +what do you what happens along the way + + align:start position:0% +what do you what happens along the way + + + align:start position:0% +what do you what happens along the way +uh and those where let's just say as + + align:start position:0% +uh and those where let's just say as + + + align:start position:0% +uh and those where let's just say as +again as a visit in the physicist + + align:start position:0% +again as a visit in the physicist + + + align:start position:0% +again as a visit in the physicist +terminology non-trivial which is code + + align:start position:0% +terminology non-trivial which is code + + + align:start position:0% +terminology non-trivial which is code +for like I have no idea it's really hard + + align:start position:0% +for like I have no idea it's really hard + + + align:start position:0% +for like I have no idea it's really hard +uh and prone to all kinds of additional + + align:start position:0% +uh and prone to all kinds of additional + + + align:start position:0% +uh and prone to all kinds of additional +worries and concerns + + align:start position:0% +worries and concerns + + + align:start position:0% +worries and concerns +because even for the best intentioned + + align:start position:0% +because even for the best intentioned + + + align:start position:0% +because even for the best intentioned +humans we're still human you know let + + align:start position:0% +humans we're still human you know let + + + align:start position:0% +humans we're still human you know let +alone any kind of Nefarious things that + + align:start position:0% +alone any kind of Nefarious things that + + + align:start position:0% +alone any kind of Nefarious things that +could interrupted so I know those kinds + + align:start position:0% +could interrupted so I know those kinds + + + align:start position:0% +could interrupted so I know those kinds +of considerations have been live issues + + align:start position:0% +of considerations have been live issues + + + align:start position:0% +of considerations have been live issues +since the 70s or 80s let alone in more + + align:start position:0% +since the 70s or 80s let alone in more + + + align:start position:0% +since the 70s or 80s let alone in more +recent times but to Tiffany's direct + + align:start position:0% +recent times but to Tiffany's direct + + + align:start position:0% +recent times but to Tiffany's direct +question I actually have no idea how how + + align:start position:0% +question I actually have no idea how how + + + align:start position:0% +question I actually have no idea how how +that set of you know kind of decisions + + align:start position:0% +that set of you know kind of decisions + + + align:start position:0% +that set of you know kind of decisions +were made is this format more stable to + + align:start position:0% +were made is this format more stable to + + + align:start position:0% +were made is this format more stable to +handle than others of that as well + + align:start position:0% +handle than others of that as well + + + align:start position:0% +handle than others of that as well +beyond anything I know about directly + + align:start position:0% + + + + align:start position:0% + +there some years ago I mean maybe 15 + + align:start position:0% +there some years ago I mean maybe 15 + + + align:start position:0% +there some years ago I mean maybe 15 +years ago by now I've lost track again a + + align:start position:0% +years ago by now I've lost track again a + + + align:start position:0% +years ago by now I've lost track again a +little off topic but um it was another + + align:start position:0% +little off topic but um it was another + + + align:start position:0% +little off topic but um it was another +historian of kind of cold war nuclear + + align:start position:0% +historian of kind of cold war nuclear + + + align:start position:0% +historian of kind of cold war nuclear +age stuff who put a petition together + + align:start position:0% +age stuff who put a petition together + + + align:start position:0% +age stuff who put a petition together +because they were speaking about Hanford + + align:start position:0% +because they were speaking about Hanford + + + align:start position:0% +because they were speaking about Hanford +there was a move to let's see if I can + + align:start position:0% +there was a move to let's see if I can + + + align:start position:0% +there was a move to let's see if I can +get the story right + + align:start position:0% +get the story right + + + align:start position:0% +get the story right +the local Department of energy + + align:start position:0% +the local Department of energy + + + align:start position:0% +the local Department of energy +um administrators were going to + + align:start position:0% +um administrators were going to + + + align:start position:0% +um administrators were going to +basically incinerate a bunch of of + + align:start position:0% +basically incinerate a bunch of of + + + align:start position:0% +basically incinerate a bunch of of +literally garbage from Mostly from World + + align:start position:0% +literally garbage from Mostly from World + + + align:start position:0% +literally garbage from Mostly from World +War II era or early post World War II + + align:start position:0% +War II era or early post World War II + + + align:start position:0% +War II era or early post World War II +times uh and this other historian + + align:start position:0% +times uh and this other historian + + + align:start position:0% +times uh and this other historian +colleague of mine started to kind of + + align:start position:0% +colleague of mine started to kind of + + + align:start position:0% +colleague of mine started to kind of +petition to say please don't burn that + + align:start position:0% +petition to say please don't burn that + + + align:start position:0% +petition to say please don't burn that +stuff historians can learn so much about + + align:start position:0% +stuff historians can learn so much about + + + align:start position:0% +stuff historians can learn so much about +what it was like to live on the site + + align:start position:0% +what it was like to live on the site + + + align:start position:0% +what it was like to live on the site +from you know the crumpled up cigarette + + align:start position:0% +from you know the crumpled up cigarette + + + align:start position:0% +from you know the crumpled up cigarette +rappers it wasn't like + + align:start position:0% +rappers it wasn't like + + + align:start position:0% +rappers it wasn't like +the the kind of radioactive + + align:start position:0% +the the kind of radioactive + + + align:start position:0% +the the kind of radioactive +um + + align:start position:0% +um + + + align:start position:0% +um +sludge it was like signs of human + + align:start position:0% +sludge it was like signs of human + + + align:start position:0% +sludge it was like signs of human +encampments it was like the one of the + + align:start position:0% +encampments it was like the one of the + + + align:start position:0% +encampments it was like the one of the +workers there what was their life like + + align:start position:0% +workers there what was their life like + + + align:start position:0% +workers there what was their life like +and you know you can learn a lot from + + align:start position:0% +and you know you can learn a lot from + + + align:start position:0% +and you know you can learn a lot from +going through someone else's garbage + + align:start position:0% +going through someone else's garbage + + + align:start position:0% +going through someone else's garbage +right so so this effort to save the + + align:start position:0% +right so so this effort to save the + + + align:start position:0% +right so so this effort to save the +Hanford garbage which sounds a little + + align:start position:0% +Hanford garbage which sounds a little + + + align:start position:0% +Hanford garbage which sounds a little +you know like tongue-in-cheek but it was + + align:start position:0% +you know like tongue-in-cheek but it was + + + align:start position:0% +you know like tongue-in-cheek but it was +a real it was a robust effort to say we + + align:start position:0% +a real it was a robust effort to say we + + + align:start position:0% +a real it was a robust effort to say we +need to learn about what it was like + + align:start position:0% +need to learn about what it was like + + + align:start position:0% +need to learn about what it was like +for for all kinds of uh laborers and + + align:start position:0% +for for all kinds of uh laborers and + + + align:start position:0% +for for all kinds of uh laborers and +other staff on the site so please don't + + align:start position:0% +other staff on the site so please don't + + + align:start position:0% +other staff on the site so please don't +burn their old their their at that point + + align:start position:0% +burn their old their their at that point + + + align:start position:0% +burn their old their their at that point +you know merely 50 year old or 60 year + + align:start position:0% +you know merely 50 year old or 60 year + + + align:start position:0% +you know merely 50 year old or 60 year +old garbage and actually don't know + + align:start position:0% +old garbage and actually don't know + + + align:start position:0% +old garbage and actually don't know +whatever happened I don't remember the + + align:start position:0% +whatever happened I don't remember the + + + align:start position:0% +whatever happened I don't remember the +follow-up whether that succeeded in in + + align:start position:0% +follow-up whether that succeeded in in + + + align:start position:0% +follow-up whether that succeeded in in +Saving the uh historical garbage or not + + align:start position:0% +Saving the uh historical garbage or not + + + align:start position:0% +Saving the uh historical garbage or not +but + + align:start position:0% +but + + + align:start position:0% +but +I found that an interesting effort + + align:start position:0% + + + + align:start position:0% + +think about the longest earliest known + + align:start position:0% +think about the longest earliest known + + + align:start position:0% +think about the longest earliest known +kind of human stories that we still know + + align:start position:0% +kind of human stories that we still know + + + align:start position:0% +kind of human stories that we still know +anything about + + align:start position:0% +anything about + + + align:start position:0% +anything about +and just to to your point they haven't + + align:start position:0% +and just to to your point they haven't + + + align:start position:0% +and just to to your point they haven't +been unchanging in interpreted meaning + + align:start position:0% +been unchanging in interpreted meaning + + + align:start position:0% +been unchanging in interpreted meaning +imputed meaning right and that's over + + align:start position:0% +imputed meaning right and that's over + + + align:start position:0% +imputed meaning right and that's over +not even 10 000 Years baby five thousand + + align:start position:0% +not even 10 000 Years baby five thousand + + + align:start position:0% +not even 10 000 Years baby five thousand +right on the order of five thousand I + + align:start position:0% +right on the order of five thousand I + + + align:start position:0% +right on the order of five thousand I +mean who we don't we don't teach you + + align:start position:0% +mean who we don't we don't teach you + + + align:start position:0% +mean who we don't we don't teach you +know the ancient you know uh Greek + + align:start position:0% +know the ancient you know uh Greek + + + align:start position:0% +know the ancient you know uh Greek +stories say this was their meeting right + + align:start position:0% +stories say this was their meeting right + + + align:start position:0% +stories say this was their meeting right +we teach them to say look at the + + align:start position:0% +we teach them to say look at the + + + align:start position:0% +we teach them to say look at the +plethora of meanings of people who might + + align:start position:0% +plethora of meanings of people who might + + + align:start position:0% +plethora of meanings of people who might +then or might still make of them or and + + align:start position:0% +then or might still make of them or and + + + align:start position:0% +then or might still make of them or and +think about you know tall muted + + align:start position:0% +think about you know tall muted + + + align:start position:0% +think about you know tall muted +commentary any any Traditions they're + + align:start position:0% +commentary any any Traditions they're + + + align:start position:0% +commentary any any Traditions they're +they're treated as kind of living + + align:start position:0% +they're treated as kind of living + + + align:start position:0% +they're treated as kind of living +interpretive Traditions often at least + + align:start position:0% +interpretive Traditions often at least + + + align:start position:0% +interpretive Traditions often at least +precisely because the single unambiguous + + align:start position:0% +precisely because the single unambiguous + + + align:start position:0% +precisely because the single unambiguous +meaning is is not what people seem to + + align:start position:0% +meaning is is not what people seem to + + + align:start position:0% +meaning is is not what people seem to +reach for or identify and now multiply + + align:start position:0% +reach for or identify and now multiply + + + align:start position:0% +reach for or identify and now multiply +that by a factor of 30 right now do that + + align:start position:0% +that by a factor of 30 right now do that + + + align:start position:0% +that by a factor of 30 right now do that +not for ten thousand years but 300 000 + + align:start position:0% +not for ten thousand years but 300 000 + + + align:start position:0% +not for ten thousand years but 300 000 +years I just find that just utterly + + align:start position:0% +years I just find that just utterly + + + align:start position:0% +years I just find that just utterly +mind-boggling I um + + align:start position:0% +mind-boggling I um + + + align:start position:0% +mind-boggling I um +so anyway I share I share your + + align:start position:0% +so anyway I share I share your + + + align:start position:0% +so anyway I share I share your +observation a lot of that it is an + + align:start position:0% +observation a lot of that it is an + + + align:start position:0% +observation a lot of that it is an +interesting that that's what people I + + align:start position:0% +interesting that that's what people I + + + align:start position:0% +interesting that that's what people I +take that maybe as a sign of we might + + align:start position:0% +take that maybe as a sign of we might + + + align:start position:0% +take that maybe as a sign of we might +call it desperation that will they'll + + align:start position:0% +call it desperation that will they'll + + + align:start position:0% +call it desperation that will they'll +even go for that as opposed to any other + + align:start position:0% +even go for that as opposed to any other + + + align:start position:0% +even go for that as opposed to any other +like Tiffany saying kind of recognizably + + align:start position:0% +like Tiffany saying kind of recognizably + + + align:start position:0% +like Tiffany saying kind of recognizably +High-Tech high modernist uh + + align:start position:0% +High-Tech high modernist uh + + + align:start position:0% +High-Tech high modernist uh +interventions and think about you know I + + align:start position:0% +interventions and think about you know I + + + align:start position:0% +interventions and think about you know I +I can I can't open + + align:start position:0% +I can I can't open + + + align:start position:0% +I can I can't open +documents that I wrote in college + + align:start position:0% +documents that I wrote in college + + + align:start position:0% +documents that I wrote in college +because of technological creep right I + + align:start position:0% +because of technological creep right I + + + align:start position:0% +because of technological creep right I +was actually using Microsoft Word + + align:start position:0% +was actually using Microsoft Word + + + align:start position:0% +was actually using Microsoft Word +because you know it might whereas my + + align:start position:0% +because you know it might whereas my + + + align:start position:0% +because you know it might whereas my +teachers weren't so I I there was + + align:start position:0% +teachers weren't so I I there was + + + align:start position:0% +teachers weren't so I I there was +actually a level of continuity with my + + align:start position:0% +actually a level of continuity with my + + + align:start position:0% +actually a level of continuity with my +machines and my software and yet I can't + + align:start position:0% +machines and my software and yet I can't + + + align:start position:0% +machines and my software and yet I can't +open documents from like the early uh + + align:start position:0% +open documents from like the early uh + + + align:start position:0% +open documents from like the early uh +90s + + align:start position:0% +90s + + + align:start position:0% +90s +so talk about think about that level of + + align:start position:0% +so talk about think about that level of + + + align:start position:0% +so talk about think about that level of +kind of just getting a a message to + + align:start position:0% +kind of just getting a a message to + + + align:start position:0% +kind of just getting a a message to +persist and be and be readable + + align:start position:0% +persist and be and be readable + + + align:start position:0% +persist and be and be readable +over again ten tens of years not + + align:start position:0% +over again ten tens of years not + + + align:start position:0% +over again ten tens of years not +hundreds or hundreds of thousands + + align:start position:0% +hundreds or hundreds of thousands + + + align:start position:0% +hundreds or hundreds of thousands +right exactly yes no I think I I totally + + align:start position:0% +right exactly yes no I think I I totally + + + align:start position:0% +right exactly yes no I think I I totally +agree uh these if not if not literally + + align:start position:0% +agree uh these if not if not literally + + + align:start position:0% +agree uh these if not if not literally +invitations to take there at least not + + align:start position:0% +invitations to take there at least not + + + align:start position:0% +invitations to take there at least not +very good at stopping people from + + align:start position:0% +very good at stopping people from + + + align:start position:0% +very good at stopping people from +digging + + align:start position:0% + + + + align:start position:0% + +maybe remember our our base license + + align:start position:0% +maybe remember our our base license + + + align:start position:0% +maybe remember our our base license +Chernobyl is approximately 30 years 33 + + align:start position:0% +Chernobyl is approximately 30 years 33 + + + align:start position:0% +Chernobyl is approximately 30 years 33 +. um and again I'm a little cautious of + + align:start position:0% +. um and again I'm a little cautious of + + + align:start position:0% +. um and again I'm a little cautious of +making the leap from 30 years to 300 000 + + align:start position:0% +making the leap from 30 years to 300 000 + + + align:start position:0% +making the leap from 30 years to 300 000 +years so so I guess you know I don't + + align:start position:0% +years so so I guess you know I don't + + + align:start position:0% +years so so I guess you know I don't +know + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +but also I mean I've seen some of these + + align:start position:0% +but also I mean I've seen some of these + + + align:start position:0% +but also I mean I've seen some of these +terracotta warriors so clearly part of + + align:start position:0% +terracotta warriors so clearly part of + + + align:start position:0% +terracotta warriors so clearly part of +the site has been has been not just you + + align:start position:0% +the site has been has been not just you + + + align:start position:0% +the site has been has been not just you +know uh investigative but actually Parts + + align:start position:0% +know uh investigative but actually Parts + + + align:start position:0% +know uh investigative but actually Parts +removed right moved around the world so + + align:start position:0% +removed right moved around the world so + + + align:start position:0% +removed right moved around the world so +uh I don't remember the full details of + + align:start position:0% +uh I don't remember the full details of + + + align:start position:0% +uh I don't remember the full details of +it again it wasn't like the entire site + + align:start position:0% +it again it wasn't like the entire site + + + align:start position:0% +it again it wasn't like the entire site +was left kind of untouched and pristine + + align:start position:0% + + + + align:start position:0% + +yeah no again I take it as a sign of the + + align:start position:0% +yeah no again I take it as a sign of the + + + align:start position:0% +yeah no again I take it as a sign of the +kind of desperation the nature of the + + align:start position:0% +kind of desperation the nature of the + + + align:start position:0% +kind of desperation the nature of the +challenge and the need to do so out of + + align:start position:0% +challenge and the need to do so out of + + + align:start position:0% +challenge and the need to do so out of +the box thinking but I'm not sure that + + align:start position:0% +the box thinking but I'm not sure that + + + align:start position:0% +the box thinking but I'm not sure that +they found compelling answers even with + + align:start position:0% +they found compelling answers even with + + + align:start position:0% +they found compelling answers even with +these wild exercises + + align:start position:0% + + + + align:start position:0% + +and also like how many Cults have + + align:start position:0% +and also like how many Cults have + + + align:start position:0% +and also like how many Cults have +survived for 300 000 years or ten + + align:start position:0% +survived for 300 000 years or ten + + + align:start position:0% +survived for 300 000 years or ten +thousand years right let alone just the + + align:start position:0% +thousand years right let alone just the + + + align:start position:0% +thousand years right let alone just the +mismatch in time scales I just find + + align:start position:0% +mismatch in time scales I just find + + + align:start position:0% +mismatch in time scales I just find +utterly mind-boggling + + align:start position:0% + + + + align:start position:0% + +and and as a good example where I I + + align:start position:0% +and and as a good example where I I + + + align:start position:0% +and and as a good example where I I +think it's safe to say that at each + + align:start position:0% +think it's safe to say that at each + + + align:start position:0% +think it's safe to say that at each +moment in the 2000 years there hasn't + + align:start position:0% +moment in the 2000 years there hasn't + + + align:start position:0% +moment in the 2000 years there hasn't +been a single unified interpretation of + + align:start position:0% +been a single unified interpretation of + + + align:start position:0% +been a single unified interpretation of +what that body of practices and belief + + align:start position:0% +what that body of practices and belief + + + align:start position:0% +what that body of practices and belief +seems to mean uh and that's a mere 2000 + + align:start position:0% +seems to mean uh and that's a mere 2000 + + + align:start position:0% +seems to mean uh and that's a mere 2000 +years let alone + + align:start position:0% +years let alone + + + align:start position:0% +years let alone +so + + align:start position:0% + + + + align:start position:0% + +or or how many of the interpretations + + align:start position:0% +or or how many of the interpretations + + + align:start position:0% +or or how many of the interpretations +are they even frequency seriously how + + align:start position:0% +are they even frequency seriously how + + + align:start position:0% +are they even frequency seriously how +many of them line up with the kind of uh + + align:start position:0% +many of them line up with the kind of uh + + + align:start position:0% +many of them line up with the kind of uh +original intentions or the hope for + + align:start position:0% +original intentions or the hope for + + + align:start position:0% +original intentions or the hope for +message back back some generations ago + + align:start position:0% +message back back some generations ago + + + align:start position:0% +message back back some generations ago +you know they're interpretive moving + + align:start position:0% +you know they're interpretive moving + + + align:start position:0% +you know they're interpretive moving +targets we're people who make who make + + align:start position:0% +targets we're people who make who make + + + align:start position:0% +targets we're people who make who make +meetings + + align:start position:0% +meetings + + + align:start position:0% +meetings +uh so that means the meetings will + + align:start position:0% +uh so that means the meetings will + + + align:start position:0% +uh so that means the meetings will +change + + align:start position:0% + + + + align:start position:0% + +you think would be the pyramids all over + + align:start position:0% +you think would be the pyramids all over + + + align:start position:0% +you think would be the pyramids all over +again in other words right so build some + + align:start position:0% +again in other words right so build some + + + align:start position:0% +again in other words right so build some +your you know kind of Fairground type + + align:start position:0% +your you know kind of Fairground type + + + align:start position:0% +your you know kind of Fairground type +marker and that's going to drop that + + align:start position:0% +marker and that's going to drop that + + + align:start position:0% +marker and that's going to drop that +could draw people in they're supposed to + + align:start position:0% +could draw people in they're supposed to + + + align:start position:0% +could draw people in they're supposed to +tell them to stay away + + align:start position:0% + + + + align:start position:0% + +that that might buy you a thousand years + + align:start position:0% +that that might buy you a thousand years + + + align:start position:0% +that that might buy you a thousand years +you know in round numbers you know Notre + + align:start position:0% +you know in round numbers you know Notre + + + align:start position:0% +you know in round numbers you know Notre +Dame or the Durham uh you know I'm sure + + align:start position:0% +Dame or the Durham uh you know I'm sure + + + align:start position:0% +Dame or the Durham uh you know I'm sure +many structures in other parts of the + + align:start position:0% +many structures in other parts of the + + + align:start position:0% +many structures in other parts of the +world that I don't know about you know + + align:start position:0% +world that I don't know about you know + + + align:start position:0% +world that I don't know about you know +Thousand Years pyramids four thousand + + align:start position:0% +Thousand Years pyramids four thousand + + + align:start position:0% +Thousand Years pyramids four thousand +years + + align:start position:0% +years + + + align:start position:0% +years +we're still we're still missing some + + align:start position:0% +we're still we're still missing some + + + align:start position:0% +we're still we're still missing some +zeros right on that + + align:start position:0% + + + + align:start position:0% + +yes unlike the Sphinx of course which + + align:start position:0% +yes unlike the Sphinx of course which + + + align:start position:0% +yes unlike the Sphinx of course which +nearby which lost a nose to you know uh + + align:start position:0% +nearby which lost a nose to you know uh + + + align:start position:0% +nearby which lost a nose to you know uh +over eager Soldiers with machine guns + + align:start position:0% +over eager Soldiers with machine guns + + + align:start position:0% +over eager Soldiers with machine guns +so + + align:start position:0% +so + + + align:start position:0% +so +yeah + + align:start position:0% + + + + align:start position:0% + +any other parts I mean we're we're we're + + align:start position:0% +any other parts I mean we're we're we're + + + align:start position:0% +any other parts I mean we're we're we're +focusing a lot on this 300 000 years + + align:start position:0% +focusing a lot on this 300 000 years + + + align:start position:0% +focusing a lot on this 300 000 years +time scale because I keep + + align:start position:0% +time scale because I keep + + + align:start position:0% +time scale because I keep +harping on it because I find it so + + align:start position:0% +harping on it because I find it so + + + align:start position:0% +harping on it because I find it so +mind-bogging any other parts of the film + + align:start position:0% +mind-bogging any other parts of the film + + + align:start position:0% +mind-bogging any other parts of the film +other themes or questions that that it + + align:start position:0% +other themes or questions that that it + + + align:start position:0% +other themes or questions that that it +raised or brought to mind things that + + align:start position:0% +raised or brought to mind things that + + + align:start position:0% +raised or brought to mind things that +were unexpected + + align:start position:0% + + + + align:start position:0% + +so that's a really interesting question + + align:start position:0% +so that's a really interesting question + + + align:start position:0% +so that's a really interesting question +I was I don't know what we mean by + + align:start position:0% +I was I don't know what we mean by + + + align:start position:0% +I was I don't know what we mean by +safest or what the Met what the metric + + align:start position:0% +safest or what the Met what the metric + + + align:start position:0% +safest or what the Met what the metric +would be + + align:start position:0% +would be + + + align:start position:0% +would be +um so I I do know we have you know any + + align:start position:0% +um so I I do know we have you know any + + + align:start position:0% +um so I I do know we have you know any +colleagues at MIT who are very very + + align:start position:0% +colleagues at MIT who are very very + + + align:start position:0% +colleagues at MIT who are very very +concerned about climate change + + align:start position:0% +concerned about climate change + + + align:start position:0% +concerned about climate change +that's true broadly and some subset of + + align:start position:0% +that's true broadly and some subset of + + + align:start position:0% +that's true broadly and some subset of +them are very concerned that if we're + + align:start position:0% +them are very concerned that if we're + + + align:start position:0% +them are very concerned that if we're +not trying to figure out + + align:start position:0% +not trying to figure out + + + align:start position:0% +not trying to figure out +um kind of safe and reliable nuclear + + align:start position:0% +um kind of safe and reliable nuclear + + + align:start position:0% +um kind of safe and reliable nuclear +power then is there a longer term + + align:start position:0% +power then is there a longer term + + + align:start position:0% +power then is there a longer term +viability to address climate change to + + align:start position:0% +viability to address climate change to + + + align:start position:0% +viability to address climate change to +get off of such a dominance of fossil + + align:start position:0% +get off of such a dominance of fossil + + + align:start position:0% +get off of such a dominance of fossil +fuels I'm agnostic I'm just personally + + align:start position:0% +fuels I'm agnostic I'm just personally + + + align:start position:0% +fuels I'm agnostic I'm just personally +to share I I just don't consider myself + + align:start position:0% +to share I I just don't consider myself + + + align:start position:0% +to share I I just don't consider myself +an expert enough on that to really + + align:start position:0% +an expert enough on that to really + + + align:start position:0% +an expert enough on that to really +understand the layers of trade-offs but + + align:start position:0% +understand the layers of trade-offs but + + + align:start position:0% +understand the layers of trade-offs but +I know that there are plenty of our + + align:start position:0% +I know that there are plenty of our + + + align:start position:0% +I know that there are plenty of our +neighbors I mean at MIT live on in The + + align:start position:0% +neighbors I mean at MIT live on in The + + + align:start position:0% +neighbors I mean at MIT live on in The +Wider world + + align:start position:0% +Wider world + + + align:start position:0% +Wider world +who who + + align:start position:0% +who who + + + align:start position:0% +who who +would answer your question in the + + align:start position:0% +would answer your question in the + + + align:start position:0% +would answer your question in the +affirmative and I don't know enough to + + align:start position:0% +affirmative and I don't know enough to + + + align:start position:0% +affirmative and I don't know enough to +give it kind of Thoroughly independent + + align:start position:0% +give it kind of Thoroughly independent + + + align:start position:0% +give it kind of Thoroughly independent +answer I can I can understand at least + + align:start position:0% +answer I can I can understand at least + + + align:start position:0% +answer I can I can understand at least +where they're coming from + + align:start position:0% +where they're coming from + + + align:start position:0% +where they're coming from +um and you know and I think that the + + align:start position:0% +um and you know and I think that the + + + align:start position:0% +um and you know and I think that the +challenge then becomes + + align:start position:0% +challenge then becomes + + + align:start position:0% +challenge then becomes +if that if that is the case and Isaiah I + + align:start position:0% +if that if that is the case and Isaiah I + + + align:start position:0% +if that if that is the case and Isaiah I +don't know how do we learn from the past + + align:start position:0% +don't know how do we learn from the past + + + align:start position:0% +don't know how do we learn from the past +to not keep replicating the unintended + + align:start position:0% +to not keep replicating the unintended + + + align:start position:0% +to not keep replicating the unintended +consequences that that have surrounded + + align:start position:0% +consequences that that have surrounded + + + align:start position:0% +consequences that that have surrounded +that body of work to date and again + + align:start position:0% +that body of work to date and again + + + align:start position:0% +that body of work to date and again +we're not talking about a thousand + + align:start position:0% +we're not talking about a thousand + + + align:start position:0% +we're not talking about a thousand +you're talking about you know 50 to 70 + + align:start position:0% +you're talking about you know 50 to 70 + + + align:start position:0% +you're talking about you know 50 to 70 +years and the number of instances with + + align:start position:0% +years and the number of instances with + + + align:start position:0% +years and the number of instances with +where + + align:start position:0% +where + + + align:start position:0% +where +safeguards weren't put in where human + + align:start position:0% +safeguards weren't put in where human + + + align:start position:0% +safeguards weren't put in where human +error was was nonetheless you know not + + align:start position:0% +error was was nonetheless you know not + + + align:start position:0% +error was was nonetheless you know not +sufficiently guarded against where you + + align:start position:0% +sufficiently guarded against where you + + + align:start position:0% +sufficiently guarded against where you +know bad stuff happened even with the + + align:start position:0% +know bad stuff happened even with the + + + align:start position:0% +know bad stuff happened even with the +best of intentions + + align:start position:0% +best of intentions + + + align:start position:0% +best of intentions +uh + + align:start position:0% +uh + + + align:start position:0% +uh +then then I think that rate that that + + align:start position:0% +then then I think that rate that that + + + align:start position:0% +then then I think that rate that that +makes other of my friends and colleagues + + align:start position:0% +makes other of my friends and colleagues + + + align:start position:0% +makes other of my friends and colleagues +concerned about saying well there's the + + align:start position:0% +concerned about saying well there's the + + + align:start position:0% +concerned about saying well there's the +answer let's just put all our eggs in + + align:start position:0% +answer let's just put all our eggs in + + + align:start position:0% +answer let's just put all our eggs in +that basket let's go charge right ahead + + align:start position:0% +that basket let's go charge right ahead + + + align:start position:0% +that basket let's go charge right ahead +so I I guess I sit + + align:start position:0% +so I I guess I sit + + + align:start position:0% +so I I guess I sit +stride a lot of these discussions and I + + align:start position:0% +stride a lot of these discussions and I + + + align:start position:0% +stride a lot of these discussions and I +genuine personally genuinely just just + + align:start position:0% +genuine personally genuinely just just + + + align:start position:0% +genuine personally genuinely just just +sort of you know + + align:start position:0% +sort of you know + + + align:start position:0% +sort of you know +stock which is really stuck because I + + align:start position:0% +stock which is really stuck because I + + + align:start position:0% +stock which is really stuck because I +can really appreciate + + align:start position:0% +can really appreciate + + + align:start position:0% +can really appreciate +um the impetus in especially in terms of + + align:start position:0% +um the impetus in especially in terms of + + + align:start position:0% +um the impetus in especially in terms of +climate change and sustainability + + align:start position:0% +climate change and sustainability + + + align:start position:0% +climate change and sustainability +and yet also you know really share the + + align:start position:0% +and yet also you know really share the + + + align:start position:0% +and yet also you know really share the +worries that people who knew better in + + align:start position:0% +worries that people who knew better in + + + align:start position:0% +worries that people who knew better in +the past didn't always do better people + + align:start position:0% +the past didn't always do better people + + + align:start position:0% +the past didn't always do better people +didn't always know better what don't we + + align:start position:0% +didn't always know better what don't we + + + align:start position:0% +didn't always know better what don't we +even know today to even worry about let + + align:start position:0% +even know today to even worry about let + + + align:start position:0% +even know today to even worry about let +alone what do we do know and still + + align:start position:0% +alone what do we do know and still + + + align:start position:0% +alone what do we do know and still +haven't adequately uh really addressed + + align:start position:0% +haven't adequately uh really addressed + + + align:start position:0% +haven't adequately uh really addressed +in a systematic way so I just feel + + align:start position:0% +in a systematic way so I just feel + + + align:start position:0% +in a systematic way so I just feel +paralyzed first I mean personally even + + align:start position:0% +paralyzed first I mean personally even + + + align:start position:0% +paralyzed first I mean personally even +though I know they're strongly held um + + align:start position:0% +though I know they're strongly held um + + + align:start position:0% +though I know they're strongly held um +arguments on on a whole range it's not + + align:start position:0% +arguments on on a whole range it's not + + + align:start position:0% +arguments on on a whole range it's not +like it's one Cypress the other but a + + align:start position:0% +like it's one Cypress the other but a + + + align:start position:0% +like it's one Cypress the other but a +whole Spectrum + + align:start position:0% +whole Spectrum + + + align:start position:0% +whole Spectrum +um + + align:start position:0% +um + + + align:start position:0% +um +so I don't know I mean I don't know if + + align:start position:0% +so I don't know I mean I don't know if + + + align:start position:0% +so I don't know I mean I don't know if +we had a Flawless history for even five + + align:start position:0% +we had a Flawless history for even five + + + align:start position:0% +we had a Flawless history for even five +year stretches let alone 50. then I then + + align:start position:0% +year stretches let alone 50. then I then + + + align:start position:0% +year stretches let alone 50. then I then +maybe I'd have more reason for + + align:start position:0% +maybe I'd have more reason for + + + align:start position:0% +maybe I'd have more reason for +confidence but personally I don't I I + + align:start position:0% +confidence but personally I don't I I + + + align:start position:0% +confidence but personally I don't I I +see I see that the flaws and the + + align:start position:0% +see I see that the flaws and the + + + align:start position:0% +see I see that the flaws and the +unintended consequences pretty sharply + + align:start position:0% +unintended consequences pretty sharply + + + align:start position:0% +unintended consequences pretty sharply +uh just personally from where I sit + + align:start position:0% +uh just personally from where I sit + + + align:start position:0% +uh just personally from where I sit +partly maybe because you know being a + + align:start position:0% +partly maybe because you know being a + + + align:start position:0% +partly maybe because you know being a +historic focus is a lot of the Cold War + + align:start position:0% +historic focus is a lot of the Cold War + + + align:start position:0% +historic focus is a lot of the Cold War +and there are a lot of things that that + + align:start position:0% +and there are a lot of things that that + + + align:start position:0% +and there are a lot of things that that +people did know better about back then + + align:start position:0% +people did know better about back then + + + align:start position:0% +people did know better about back then +and yet nonetheless you know citing + + align:start position:0% +and yet nonetheless you know citing + + + align:start position:0% +and yet nonetheless you know citing +National Security citing you know + + align:start position:0% +National Security citing you know + + + align:start position:0% +National Security citing you know +pressing demands and needs we kind of + + align:start position:0% +pressing demands and needs we kind of + + + align:start position:0% +pressing demands and needs we kind of +cut corners or not tell people the full + + align:start position:0% +cut corners or not tell people the full + + + align:start position:0% +cut corners or not tell people the full +uh story and come out only later so I + + align:start position:0% +uh story and come out only later so I + + + align:start position:0% +uh story and come out only later so I +guess I come to some of these things + + align:start position:0% +guess I come to some of these things + + + align:start position:0% +guess I come to some of these things +with a bit of a jaundiced eye that's + + align:start position:0% +with a bit of a jaundiced eye that's + + + align:start position:0% +with a bit of a jaundiced eye that's +just me + + align:start position:0% +just me + + + align:start position:0% +just me +um personally + + align:start position:0% +um personally + + + align:start position:0% +um personally +so that's where that's where I get I get + + align:start position:0% +so that's where that's where I get I get + + + align:start position:0% +so that's where that's where I get I get +stuck I will I will just simply say I + + align:start position:0% +stuck I will I will just simply say I + + + align:start position:0% +stuck I will I will just simply say I +get stuck + + align:start position:0% + + + + align:start position:0% + +I mean it's it's a great Point Lucas and + + align:start position:0% +I mean it's it's a great Point Lucas and + + + align:start position:0% +I mean it's it's a great Point Lucas and +even stepping away from the nuclear side + + align:start position:0% +even stepping away from the nuclear side + + + align:start position:0% +even stepping away from the nuclear side +I mean again you can find these very you + + align:start position:0% +I mean again you can find these very you + + + align:start position:0% +I mean again you can find these very you +know Earnest debates + + align:start position:0% +know Earnest debates + + + align:start position:0% +know Earnest debates +about kind of + + align:start position:0% +about kind of + + + align:start position:0% +about kind of +um you know cost benefit analyzes and + + align:start position:0% +um you know cost benefit analyzes and + + + align:start position:0% +um you know cost benefit analyzes and +risk trade-offs about let's say ethanol + + align:start position:0% +risk trade-offs about let's say ethanol + + + align:start position:0% +risk trade-offs about let's say ethanol +it's gonna you know other other efforts + + align:start position:0% +it's gonna you know other other efforts + + + align:start position:0% +it's gonna you know other other efforts +to to focus on say fossil fuel users oh + + align:start position:0% +to to focus on say fossil fuel users oh + + + align:start position:0% +to to focus on say fossil fuel users oh +we'll use you know bioorganic this or + + align:start position:0% +we'll use you know bioorganic this or + + + align:start position:0% +we'll use you know bioorganic this or +that and then you try to cost in all of + + align:start position:0% +that and then you try to cost in all of + + + align:start position:0% +that and then you try to cost in all of +the + + align:start position:0% +the + + + align:start position:0% +the +fossil fuel based fertilizer that's + + align:start position:0% +fossil fuel based fertilizer that's + + + align:start position:0% +fossil fuel based fertilizer that's +needed or you know all the other thing + + align:start position:0% +needed or you know all the other thing + + + align:start position:0% +needed or you know all the other thing +beyond the kind of that product narrowly + + align:start position:0% +beyond the kind of that product narrowly + + + align:start position:0% +beyond the kind of that product narrowly +construed and then you find that at very + + align:start position:0% +construed and then you find that at very + + + align:start position:0% +construed and then you find that at very +least it becomes murky the answer + + align:start position:0% +least it becomes murky the answer + + + align:start position:0% +least it becomes murky the answer +becomes pretty + + align:start position:0% +becomes pretty + + + align:start position:0% +becomes pretty +unclear at least to me uh and I think + + align:start position:0% +unclear at least to me uh and I think + + + align:start position:0% +unclear at least to me uh and I think +that is all the more so amidst these + + align:start position:0% +that is all the more so amidst these + + + align:start position:0% +that is all the more so amidst these +uncertainties like you know what do you + + align:start position:0% +uncertainties like you know what do you + + + align:start position:0% +uncertainties like you know what do you +do with all this nuclear waste it's not + + align:start position:0% +do with all this nuclear waste it's not + + + align:start position:0% +do with all this nuclear waste it's not +going to go away anytime soon let me + + align:start position:0% +going to go away anytime soon let me + + + align:start position:0% +going to go away anytime soon let me +come back to the question about about + + align:start position:0% +come back to the question about about + + + align:start position:0% +come back to the question about about +nuclear power so that doesn't mean the + + align:start position:0% +nuclear power so that doesn't mean the + + + align:start position:0% +nuclear power so that doesn't mean the +answer can never ever be nuclear power + + align:start position:0% +answer can never ever be nuclear power + + + align:start position:0% +answer can never ever be nuclear power +but I mean it just the the tendrils the + + align:start position:0% +but I mean it just the the tendrils the + + + align:start position:0% +but I mean it just the the tendrils the +extent of this very extensive system as + + align:start position:0% +extent of this very extensive system as + + + align:start position:0% +extent of this very extensive system as +opposed to like the safety Protocols of + + align:start position:0% +opposed to like the safety Protocols of + + + align:start position:0% +opposed to like the safety Protocols of +a given reactor design + + align:start position:0% +a given reactor design + + + align:start position:0% +a given reactor design +I think the the breadth of those uh of + + align:start position:0% +I think the the breadth of those uh of + + + align:start position:0% +I think the the breadth of those uh of +the of the range of questions makes me + + align:start position:0% +the of the range of questions makes me + + + align:start position:0% +the of the range of questions makes me +um skeptical that we're going to find a + + align:start position:0% +um skeptical that we're going to find a + + + align:start position:0% +um skeptical that we're going to find a +clear answer a clear metric that says + + align:start position:0% +clear answer a clear metric that says + + + align:start position:0% +clear answer a clear metric that says +yeah that says at the end of the day yes + + align:start position:0% +yeah that says at the end of the day yes + + + align:start position:0% +yeah that says at the end of the day yes +green light the answer is plus seven you + + align:start position:0% +green light the answer is plus seven you + + + align:start position:0% +green light the answer is plus seven you +know go forward and that's where I get + + align:start position:0% +know go forward and that's where I get + + + align:start position:0% +know go forward and that's where I get +more skeptical + + align:start position:0% + + + + align:start position:0% + +and what are the competing incentive + + align:start position:0% +and what are the competing incentive + + + align:start position:0% +and what are the competing incentive +structures instructors and I'm not + + align:start position:0% +structures instructors and I'm not + + + align:start position:0% +structures instructors and I'm not +saying is one's clearly the right answer + + align:start position:0% +saying is one's clearly the right answer + + + align:start position:0% +saying is one's clearly the right answer +but we have to worry about the + + align:start position:0% +but we have to worry about the + + + align:start position:0% +but we have to worry about the +what decisions being made by according + + align:start position:0% +what decisions being made by according + + + align:start position:0% +what decisions being made by according +again to what measures and what metrics + + align:start position:0% +again to what measures and what metrics + + + align:start position:0% +again to what measures and what metrics +what are the incentives + + align:start position:0% + + + + align:start position:0% + +okay so we use + + align:start position:0% +okay so we use + + + align:start position:0% +okay so we use +oh that's interesting I again others on + + align:start position:0% +oh that's interesting I again others on + + + align:start position:0% +oh that's interesting I again others on +the call might have a better answer but + + align:start position:0% +the call might have a better answer but + + + align:start position:0% +the call might have a better answer but +I think + + align:start position:0% +I think + + + align:start position:0% +I think +um the reactors that I'm familiar with + + align:start position:0% +um the reactors that I'm familiar with + + + align:start position:0% +um the reactors that I'm familiar with +are usually trying to you know very + + align:start position:0% +are usually trying to you know very + + + align:start position:0% +are usually trying to you know very +specific kinds of reactions to the + + align:start position:0% +specific kinds of reactions to the + + + align:start position:0% +specific kinds of reactions to the +alternative extract excess energy + + align:start position:0% +alternative extract excess energy + + + align:start position:0% +alternative extract excess energy +and not everything is radioactive will + + align:start position:0% +and not everything is radioactive will + + + align:start position:0% +and not everything is radioactive will +contribute to that energy balance so + + align:start position:0% +contribute to that energy balance so + + + align:start position:0% +contribute to that energy balance so +Things become radioactive as a + + align:start position:0% +Things become radioactive as a + + + align:start position:0% +Things become radioactive as a +consequence of these reactions again + + align:start position:0% +consequence of these reactions again + + + align:start position:0% +consequence of these reactions again +from which one can extract energy + + align:start position:0% +from which one can extract energy + + + align:start position:0% +from which one can extract energy +but I think the most + + align:start position:0% +but I think the most + + + align:start position:0% +but I think the most +um well understood and as far as I know + + align:start position:0% +um well understood and as far as I know + + + align:start position:0% +um well understood and as far as I know +the most efficient reactions that will + + align:start position:0% +the most efficient reactions that will + + + align:start position:0% +the most efficient reactions that will +produce the excess energy ultimately uh + + align:start position:0% +produce the excess energy ultimately uh + + + align:start position:0% +produce the excess energy ultimately uh +involve very specific kinds of + + align:start position:0% +involve very specific kinds of + + + align:start position:0% +involve very specific kinds of +ingredients let's say very specific + + align:start position:0% +ingredients let's say very specific + + + align:start position:0% +ingredients let's say very specific +kinds of Target nuclei to start from + + align:start position:0% +kinds of Target nuclei to start from + + + align:start position:0% +kinds of Target nuclei to start from +and so others that's why I think it's + + align:start position:0% +and so others that's why I think it's + + + align:start position:0% +and so others that's why I think it's +called waste and the the other thing is + + align:start position:0% +called waste and the the other thing is + + + align:start position:0% +called waste and the the other thing is +that become radioactive are not the ones + + align:start position:0% +that become radioactive are not the ones + + + align:start position:0% +that become radioactive are not the ones +that one can nonetheless + + align:start position:0% +that one can nonetheless + + + align:start position:0% +that one can nonetheless +um you know put back in the reactor and + + align:start position:0% +um you know put back in the reactor and + + + align:start position:0% +um you know put back in the reactor and +extract uh excess energy from in any in + + align:start position:0% +extract uh excess energy from in any in + + + align:start position:0% +extract uh excess energy from in any in +any + + align:start position:0% +any + + + align:start position:0% +any +scalable way I was a very abstract + + align:start position:0% +scalable way I was a very abstract + + + align:start position:0% +scalable way I was a very abstract +answer I'd have to learn more about the + + align:start position:0% +answer I'd have to learn more about the + + + align:start position:0% +answer I'd have to learn more about the +particular Isotopes in particular + + align:start position:0% +particular Isotopes in particular + + + align:start position:0% +particular Isotopes in particular +reactions which is not what I work on at + + align:start position:0% +reactions which is not what I work on at + + + align:start position:0% +reactions which is not what I work on at +all directly but I think the basic point + + align:start position:0% +all directly but I think the basic point + + + align:start position:0% +all directly but I think the basic point +is that + + align:start position:0% +is that + + + align:start position:0% +is that +for these fission reactions you know not + + align:start position:0% +for these fission reactions you know not + + + align:start position:0% +for these fission reactions you know not +everything's radioactive is is highly + + align:start position:0% +everything's radioactive is is highly + + + align:start position:0% +everything's radioactive is is highly +fissionable + + align:start position:0% +fissionable + + + align:start position:0% +fissionable +uh and yet it still could be dangerous + + align:start position:0% +uh and yet it still could be dangerous + + + align:start position:0% +uh and yet it still could be dangerous +because still emitting junk that could + + align:start position:0% +because still emitting junk that could + + + align:start position:0% +because still emitting junk that could +hurt you know people and plants in the + + align:start position:0% +hurt you know people and plants in the + + + align:start position:0% +hurt you know people and plants in the +in the in the environment + + align:start position:0% +in the in the environment + + + align:start position:0% +in the in the environment +uh I think that's that's the upshot so + + align:start position:0% +uh I think that's that's the upshot so + + + align:start position:0% +uh I think that's that's the upshot so +only if a small set of these Isotopes + + align:start position:0% +only if a small set of these Isotopes + + + align:start position:0% +only if a small set of these Isotopes +will actually + + align:start position:0% +will actually + + + align:start position:0% +will actually +um fission upon being struck by neutrons + + align:start position:0% +um fission upon being struck by neutrons + + + align:start position:0% +um fission upon being struck by neutrons +of a certain characteristic and then + + align:start position:0% +of a certain characteristic and then + + + align:start position:0% +of a certain characteristic and then +release the excess energy + + align:start position:0% +release the excess energy + + + align:start position:0% +release the excess energy +the others are shooting out alpha + + align:start position:0% +the others are shooting out alpha + + + align:start position:0% +the others are shooting out alpha +particles and beta rays and Gammas but + + align:start position:0% +particles and beta rays and Gammas but + + + align:start position:0% +particles and beta rays and Gammas but +but not + + align:start position:0% +but not + + + align:start position:0% +but not +um + + align:start position:0% +um + + + align:start position:0% +um +not not splitting a nucleus from which + + align:start position:0% +not not splitting a nucleus from which + + + align:start position:0% +not not splitting a nucleus from which +there'll be this large excess energy for + + align:start position:0% +there'll be this large excess energy for + + + align:start position:0% +there'll be this large excess energy for +splitting provision event + + align:start position:0% + + + + align:start position:0% + +so these uranium boosted um armaments + + align:start position:0% +so these uranium boosted um armaments + + + align:start position:0% +so these uranium boosted um armaments +these kinds of things + + align:start position:0% +these kinds of things + + + align:start position:0% +these kinds of things +yeah yeah + + align:start position:0% +yeah yeah + + + align:start position:0% +yeah yeah +I don't know Nixon's book right I + + align:start position:0% +I don't know Nixon's book right I + + + align:start position:0% +I don't know Nixon's book right I +remember reading at least some of the + + align:start position:0% +remember reading at least some of the + + + align:start position:0% +remember reading at least some of the +journalistic accounts about more recent + + align:start position:0% +journalistic accounts about more recent + + + align:start position:0% +journalistic accounts about more recent +concerns about uses of uranium doped + + align:start position:0% +concerns about uses of uranium doped + + + align:start position:0% +concerns about uses of uranium doped +armaments basically + + align:start position:0% + + + + align:start position:0% + +good well we we can pause there we don't + + align:start position:0% +good well we we can pause there we don't + + + align:start position:0% +good well we we can pause there we don't +have to run down the clock uh we cover a + + align:start position:0% +have to run down the clock uh we cover a + + + align:start position:0% +have to run down the clock uh we cover a +lot of ground already + + align:start position:0% +lot of ground already + + + align:start position:0% +lot of ground already +um + + align:start position:0% + + + + align:start position:0% + +thanks thanks for joining the discussion + + align:start position:0% +thanks thanks for joining the discussion + + + align:start position:0% +thanks thanks for joining the discussion +I thought that was really interesting + + align:start position:0% +I thought that was really interesting + + + align:start position:0% +I thought that was really interesting +um we'll go back to the kind of regular + + align:start position:0% +um we'll go back to the kind of regular + + + align:start position:0% +um we'll go back to the kind of regular +format on Wednesday + + align:start position:0% +format on Wednesday + + + align:start position:0% +format on Wednesday +um and thereafter of course + + align:start position:0% +um and thereafter of course + + + align:start position:0% +um and thereafter of course +um and then we'll go from there if you + + align:start position:0% +um and then we'll go from there if you + + + align:start position:0% +um and then we'll go from there if you +have any other questions of course + + align:start position:0% +have any other questions of course + + + align:start position:0% +have any other questions of course +please don't hesitate to email me or any + + align:start position:0% +please don't hesitate to email me or any + + + align:start position:0% +please don't hesitate to email me or any +of the Tas I'll have my regular office + + align:start position:0% +of the Tas I'll have my regular office + + + align:start position:0% +of the Tas I'll have my regular office +hours Wednesday morning at 11 and all + + align:start position:0% +hours Wednesday morning at 11 and all + + + align:start position:0% +hours Wednesday morning at 11 and all +that good stuff \ No newline at end of file diff --git a/cT_qwkTigv4.txt b/cT_qwkTigv4.txt new file mode 100644 index 0000000000000000000000000000000000000000..c55c834c5f39e027e11f306cce0eda4909dc15e0 --- /dev/null +++ b/cT_qwkTigv4.txt @@ -0,0 +1,17243 @@ +align:start position:0% + +so we've been talking about + + align:start position:0% + + + + align:start position:0% + +p and np + + align:start position:0% +p and np + + + align:start position:0% +p and np +and the time complexity classes + + align:start position:0% +and the time complexity classes + + + align:start position:0% +and the time complexity classes +and today we're going to shift gear + + align:start position:0% +and today we're going to shift gear + + + align:start position:0% +and today we're going to shift gear +we're going to talk about uh space + + align:start position:0% +we're going to talk about uh space + + + align:start position:0% +we're going to talk about uh space +complexity or memory complexity as uh + + align:start position:0% +complexity or memory complexity as uh + + + align:start position:0% +complexity or memory complexity as uh +space complexity is what complexity + + align:start position:0% +space complexity is what complexity + + + align:start position:0% +space complexity is what complexity +theorists uh usually refer + + align:start position:0% +theorists uh usually refer + + + align:start position:0% +theorists uh usually refer +refer to it as + + align:start position:0% +refer to it as + + + align:start position:0% +refer to it as +um + + align:start position:0% +um + + + align:start position:0% +um +and um + + align:start position:0% +and um + + + align:start position:0% +and um +you know time and space are the two + + align:start position:0% +you know time and space are the two + + + align:start position:0% +you know time and space are the two +basic most basic measures of complexity + + align:start position:0% +basic most basic measures of complexity + + + align:start position:0% +basic most basic measures of complexity +that uh that we consider and so um today + + align:start position:0% +that uh that we consider and so um today + + + align:start position:0% +that uh that we consider and so um today +we're going to look at the the second of + + align:start position:0% +we're going to look at the the second of + + + align:start position:0% +we're going to look at the the second of +those two um the space complexity + + align:start position:0% +those two um the space complexity + + + align:start position:0% +those two um the space complexity +uh so we will + + align:start position:0% +uh so we will + + + align:start position:0% +uh so we will +define + + align:start position:0% +define + + + align:start position:0% +define +a lot of this is going to be + + align:start position:0% +a lot of this is going to be + + + align:start position:0% +a lot of this is going to be +by analogy with what + + align:start position:0% +by analogy with what + + + align:start position:0% +by analogy with what +we did for time complexity we're going + + align:start position:0% +we did for time complexity we're going + + + align:start position:0% +we did for time complexity we're going +to define complexity classes we'll talk + + align:start position:0% +to define complexity classes we'll talk + + + align:start position:0% +to define complexity classes we'll talk +about + + align:start position:0% +about + + + align:start position:0% +about +polynomial space and non-deterministic + + align:start position:0% +polynomial space and non-deterministic + + + align:start position:0% +polynomial space and non-deterministic +polynomial space + + align:start position:0% +polynomial space + + + align:start position:0% +polynomial space +um see how those + + align:start position:0% +um see how those + + + align:start position:0% +um see how those +classes connect up with the time + + align:start position:0% +classes connect up with the time + + + align:start position:0% +classes connect up with the time +complexity classes that we've already + + align:start position:0% +complexity classes that we've already + + + align:start position:0% +complexity classes that we've already +defined + + align:start position:0% +defined + + + align:start position:0% +defined +and we'll do some examples that will be + + align:start position:0% +and we'll do some examples that will be + + + align:start position:0% +and we'll do some examples that will be +setting us up for our + + align:start position:0% +setting us up for our + + + align:start position:0% +setting us up for our +further discussion about space + + align:start position:0% +further discussion about space + + + align:start position:0% +further discussion about space +complexity next week + + align:start position:0% +complexity next week + + + align:start position:0% +complexity next week +so + + align:start position:0% +so + + + align:start position:0% +so +we're going to talk about first of all + + align:start position:0% +we're going to talk about first of all + + + align:start position:0% +we're going to talk about first of all +what it means for a turing machine + + align:start position:0% +what it means for a turing machine + + + align:start position:0% +what it means for a turing machine +to run in a certain + + align:start position:0% +to run in a certain + + + align:start position:0% +to run in a certain +certain amount of space + + align:start position:0% +certain amount of space + + + align:start position:0% +certain amount of space +and that's simply going to be counting + + align:start position:0% +and that's simply going to be counting + + + align:start position:0% +and that's simply going to be counting +the number of cells that the turing + + align:start position:0% +the number of cells that the turing + + + align:start position:0% +the number of cells that the turing +machine + + align:start position:0% +machine + + + align:start position:0% +machine +scans over + + align:start position:0% +scans over + + + align:start position:0% +scans over +on its tape during the course of its + + align:start position:0% +on its tape during the course of its + + + align:start position:0% +on its tape during the course of its +computation you might be reading that + + align:start position:0% +computation you might be reading that + + + align:start position:0% +computation you might be reading that +cell might be writing on that cell but + + align:start position:0% +cell might be writing on that cell but + + + align:start position:0% +cell might be writing on that cell but +the total number of cells that it + + align:start position:0% +the total number of cells that it + + + align:start position:0% +the total number of cells that it +actually um + + align:start position:0% +actually um + + + align:start position:0% +actually um +visits + + align:start position:0% +visits + + + align:start position:0% +visits +um of course visiting the same cell + + align:start position:0% +um of course visiting the same cell + + + align:start position:0% +um of course visiting the same cell +multiple times only counts once because + + align:start position:0% +multiple times only counts once because + + + align:start position:0% +multiple times only counts once because +space can be reused + + align:start position:0% +space can be reused + + + align:start position:0% +space can be reused +but we're going to count the number of + + align:start position:0% +but we're going to count the number of + + + align:start position:0% +but we're going to count the number of +cells that the turing machine visits + + align:start position:0% +cells that the turing machine visits + + + align:start position:0% +cells that the turing machine visits +during the course of its computation and + + align:start position:0% +during the course of its computation and + + + align:start position:0% +during the course of its computation and +then define + + align:start position:0% +then define + + + align:start position:0% +then define +the space utilization by analogy with + + align:start position:0% +the space utilization by analogy with + + + align:start position:0% +the space utilization by analogy with +what we did for time so we'll say a + + align:start position:0% +what we did for time so we'll say a + + + align:start position:0% +what we did for time so we'll say a +turing machine runs in a certain amount + + align:start position:0% +turing machine runs in a certain amount + + + align:start position:0% +turing machine runs in a certain amount +of space f n we'll say + + align:start position:0% +of space f n we'll say + + + align:start position:0% +of space f n we'll say +if first of all it has to always hold so + + align:start position:0% +if first of all it has to always hold so + + + align:start position:0% +if first of all it has to always hold so +all of the machines are deciders + + align:start position:0% +all of the machines are deciders + + + align:start position:0% +all of the machines are deciders +and it uses at most + + align:start position:0% +and it uses at most + + + align:start position:0% +and it uses at most +that much uh tape that much that + + align:start position:0% +that much uh tape that much that + + + align:start position:0% +that much uh tape that much that +it visits that number of cells + + align:start position:0% +it visits that number of cells + + + align:start position:0% +it visits that number of cells +on all + + align:start position:0% +on all + + + align:start position:0% +on all +inputs of length n + + align:start position:0% +inputs of length n + + + align:start position:0% +inputs of length n +so just like we said for time complexity + + align:start position:0% +so just like we said for time complexity + + + align:start position:0% +so just like we said for time complexity +the machine has to run within + + align:start position:0% +the machine has to run within + + + align:start position:0% +the machine has to run within +t of n time + + align:start position:0% +t of n time + + + align:start position:0% +t of n time +on all inputs + + align:start position:0% +on all inputs + + + align:start position:0% +on all inputs +of length n here it's going to have to + + align:start position:0% +of length n here it's going to have to + + + align:start position:0% +of length n here it's going to have to +use at most f of n + + align:start position:0% +use at most f of n + + + align:start position:0% +use at most f of n +cells + + align:start position:0% +cells + + + align:start position:0% +cells +on all inputs of length n in order for + + align:start position:0% +on all inputs of length n in order for + + + align:start position:0% +on all inputs of length n in order for +it to be running in space f n + + align:start position:0% + + + + align:start position:0% + +okay a tape cell is simply a little + + align:start position:0% +okay a tape cell is simply a little + + + align:start position:0% +okay a tape cell is simply a little +square of the tape where you can write a + + align:start position:0% +square of the tape where you can write a + + + align:start position:0% +square of the tape where you can write a +symbol + + align:start position:0% + + + + align:start position:0% + +okay answering a question that good + + align:start position:0% +okay answering a question that good + + + align:start position:0% +okay answering a question that good +question that came in from the chat + + align:start position:0% +question that came in from the chat + + + align:start position:0% +question that came in from the chat +so um you know + + align:start position:0% +so um you know + + + align:start position:0% +so um you know +uh + + align:start position:0% +uh + + + align:start position:0% +uh +i'm not sure we have i have a + + align:start position:0% +i'm not sure we have i have a + + + align:start position:0% +i'm not sure we have i have a +diagram for that but the um in each of + + align:start position:0% +diagram for that but the um in each of + + + align:start position:0% +diagram for that but the um in each of +the little squares on the tape are going + + align:start position:0% +the little squares on the tape are going + + + align:start position:0% +the little squares on the tape are going +to be the tape cells + + align:start position:0% +to be the tape cells + + + align:start position:0% +to be the tape cells +generally we're going to be sticking to + + align:start position:0% +generally we're going to be sticking to + + + align:start position:0% +generally we're going to be sticking to +one tape turing machines but i'll make a + + align:start position:0% +one tape turing machines but i'll make a + + + align:start position:0% +one tape turing machines but i'll make a +brief remark about multi-tape during + + align:start position:0% +brief remark about multi-tape during + + + align:start position:0% +brief remark about multi-tape during +machining shortly + + align:start position:0% +machining shortly + + + align:start position:0% +machining shortly +better take cells + + align:start position:0% +better take cells + + + align:start position:0% +better take cells +sorry + + align:start position:0% +sorry + + + align:start position:0% +sorry +uh on all inputs of length n + + align:start position:0% +uh on all inputs of length n + + + align:start position:0% +uh on all inputs of length n +uh so return + + align:start position:0% +uh so return + + + align:start position:0% +uh so return +now okay so that's for deterministic uh + + align:start position:0% +now okay so that's for deterministic uh + + + align:start position:0% +now okay so that's for deterministic uh +turing machines + + align:start position:0% +turing machines + + + align:start position:0% +turing machines +for non-deterministic touring machines + + align:start position:0% +for non-deterministic touring machines + + + align:start position:0% +for non-deterministic touring machines +we will say uh that it + + align:start position:0% +we will say uh that it + + + align:start position:0% +we will say uh that it +also runs in a certain amount of space + + align:start position:0% +also runs in a certain amount of space + + + align:start position:0% +also runs in a certain amount of space +so for a + + align:start position:0% +so for a + + + align:start position:0% +so for a +non-deterministic machine + + align:start position:0% +non-deterministic machine + + + align:start position:0% +non-deterministic machine +it has to + + align:start position:0% + + + + align:start position:0% + +use + + align:start position:0% +use + + + align:start position:0% +use +at most + + align:start position:0% +at most + + + align:start position:0% +at most +that many tape cells + + align:start position:0% +that many tape cells + + + align:start position:0% +that many tape cells +on each branch of its computation + + align:start position:0% +on each branch of its computation + + + align:start position:0% +on each branch of its computation +separately you don't add up the total + + align:start position:0% +separately you don't add up the total + + + align:start position:0% +separately you don't add up the total +number of cells used across all of the + + align:start position:0% +number of cells used across all of the + + + align:start position:0% +number of cells used across all of the +branches just like we don't add up the + + align:start position:0% +branches just like we don't add up the + + + align:start position:0% +branches just like we don't add up the +total amount of time the machine + + align:start position:0% +total amount of time the machine + + + align:start position:0% +total amount of time the machine +uses across all of its branches for the + + align:start position:0% +uses across all of its branches for the + + + align:start position:0% +uses across all of its branches for the +machine to be running in say space n + + align:start position:0% +machine to be running in say space n + + + align:start position:0% +machine to be running in say space n +squared + + align:start position:0% +squared + + + align:start position:0% +squared +it has to be using it most n squared + + align:start position:0% +it has to be using it most n squared + + + align:start position:0% +it has to be using it most n squared +cells + + align:start position:0% +cells + + + align:start position:0% +cells +or order n squared cells on each one of + + align:start position:0% +or order n squared cells on each one of + + + align:start position:0% +or order n squared cells on each one of +its non-deterministic branches + + align:start position:0% +its non-deterministic branches + + + align:start position:0% +its non-deterministic branches +separately + + align:start position:0% +separately + + + align:start position:0% +separately +there might be exponentially many + + align:start position:0% +there might be exponentially many + + + align:start position:0% +there might be exponentially many +branches but that's okay + + align:start position:0% +branches but that's okay + + + align:start position:0% +branches but that's okay +but on each branch it's going to be + + align:start position:0% +but on each branch it's going to be + + + align:start position:0% +but on each branch it's going to be +using at most n squared or order n + + align:start position:0% +using at most n squared or order n + + + align:start position:0% +using at most n squared or order n +squared cells + + align:start position:0% +squared cells + + + align:start position:0% +squared cells +importantly though that still the + + align:start position:0% +importantly though that still the + + + align:start position:0% +importantly though that still the +machine has to be a decider + + align:start position:0% +machine has to be a decider + + + align:start position:0% +machine has to be a decider +it's not enough to be looping forever + + align:start position:0% +it's not enough to be looping forever + + + align:start position:0% +it's not enough to be looping forever +and using a small amount of space + + align:start position:0% +and using a small amount of space + + + align:start position:0% +and using a small amount of space +it could do that but that's not going to + + align:start position:0% +it could do that but that's not going to + + + align:start position:0% +it could do that but that's not going to +count toward the machine contributing to + + align:start position:0% +count toward the machine contributing to + + + align:start position:0% +count toward the machine contributing to +its um + + align:start position:0% +its um + + + align:start position:0% +its um +space complexity of that language so for + + align:start position:0% +space complexity of that language so for + + + align:start position:0% +space complexity of that language so for +the machine to be running in a certain + + align:start position:0% +the machine to be running in a certain + + + align:start position:0% +the machine to be running in a certain +amount of space we say that the machine + + align:start position:0% +amount of space we say that the machine + + + align:start position:0% +amount of space we say that the machine +holds on all of its branches + + align:start position:0% +holds on all of its branches + + + align:start position:0% +holds on all of its branches +and each one of its branches uses at + + align:start position:0% +and each one of its branches uses at + + + align:start position:0% +and each one of its branches uses at +most + + align:start position:0% +most + + + align:start position:0% +most +that much space okay + + align:start position:0% +that much space okay + + + align:start position:0% +that much space okay +again + + align:start position:0% + + + + align:start position:0% + +i can see lots of typos here thank you + + align:start position:0% +i can see lots of typos here thank you + + + align:start position:0% +i can see lots of typos here thank you +um + + align:start position:0% +um + + + align:start position:0% +um +i messed this all up today + + align:start position:0% +i messed this all up today + + + align:start position:0% +i messed this all up today +uh + + align:start position:0% +uh + + + align:start position:0% +uh +some non-deterministic + + align:start position:0% + + + + align:start position:0% + +good thank you + + align:start position:0% +good thank you + + + align:start position:0% +good thank you +um + + align:start position:0% + + + + align:start position:0% + +all right so we're going to define the + + align:start position:0% +all right so we're going to define the + + + align:start position:0% +all right so we're going to define the +space complexity classes analogous to + + align:start position:0% +space complexity classes analogous to + + + align:start position:0% +space complexity classes analogous to +this time complexity classes so these + + align:start position:0% +this time complexity classes so these + + + align:start position:0% +this time complexity classes so these +are languages + + align:start position:0% +are languages + + + align:start position:0% +are languages +that you can do + + align:start position:0% +that you can do + + + align:start position:0% +that you can do +with machines + + align:start position:0% +with machines + + + align:start position:0% +with machines +that run within that space bound + + align:start position:0% +that run within that space bound + + + align:start position:0% +that run within that space bound +so + + align:start position:0% +so + + + align:start position:0% +so +um space f n you can think of space n + + align:start position:0% +um space f n you can think of space n + + + align:start position:0% +um space f n you can think of space n +squared + + align:start position:0% +squared + + + align:start position:0% +squared +um is all of the languages + + align:start position:0% +um is all of the languages + + + align:start position:0% +um is all of the languages +that a deterministic one tape turing + + align:start position:0% +that a deterministic one tape turing + + + align:start position:0% +that a deterministic one tape turing +machine + + align:start position:0% +machine + + + align:start position:0% +machine +um can do + + align:start position:0% +um can do + + + align:start position:0% +um can do +within uh can decide within by using in + + align:start position:0% +within uh can decide within by using in + + + align:start position:0% +within uh can decide within by using in +most n-squared tape cells or order + + align:start position:0% +most n-squared tape cells or order + + + align:start position:0% +most n-squared tape cells or order +n-squared tape cells similarly the + + align:start position:0% +n-squared tape cells similarly the + + + align:start position:0% +n-squared tape cells similarly the +non-deterministic space + + align:start position:0% +non-deterministic space + + + align:start position:0% +non-deterministic space +complexity class are all of the + + align:start position:0% +complexity class are all of the + + + align:start position:0% +complexity class are all of the +languages that are non-deterministic one + + align:start position:0% +languages that are non-deterministic one + + + align:start position:0% +languages that are non-deterministic one +tape turing machine can decide + + align:start position:0% +tape turing machine can decide + + + align:start position:0% +tape turing machine can decide +running within that amount of space + + align:start position:0% +running within that amount of space + + + align:start position:0% +running within that amount of space +okay + + align:start position:0% + + + + align:start position:0% + +and lastly + + align:start position:0% +and lastly + + + align:start position:0% +and lastly +we have a polynomial space + + align:start position:0% +we have a polynomial space + + + align:start position:0% +we have a polynomial space +so that's the union over all polynomial + + align:start position:0% +so that's the union over all polynomial + + + align:start position:0% +so that's the union over all polynomial +space bounds of the space complexity + + align:start position:0% +space bounds of the space complexity + + + align:start position:0% +space bounds of the space complexity +class and non-deterministic polynomial + + align:start position:0% +class and non-deterministic polynomial + + + align:start position:0% +class and non-deterministic polynomial +space + + align:start position:0% +space + + + align:start position:0% +space +it's the same for all of the + + align:start position:0% +it's the same for all of the + + + align:start position:0% +it's the same for all of the +non-deterministic + + align:start position:0% +non-deterministic + + + align:start position:0% +non-deterministic +uh polynomial space classes + + align:start position:0% +uh polynomial space classes + + + align:start position:0% +uh polynomial space classes +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so i think i do have a check-in on this + + align:start position:0% +so i think i do have a check-in on this + + + align:start position:0% +so i think i do have a check-in on this +um + + align:start position:0% +um + + + align:start position:0% +um +whoops + + align:start position:0% + + + + align:start position:0% + +which talks about + + align:start position:0% +which talks about + + + align:start position:0% +which talks about +uh multi-tape turing machines + + align:start position:0% + + + + align:start position:0% + +so we could define + + align:start position:0% +so we could define + + + align:start position:0% +so we could define +space complexity for multi-tape turing + + align:start position:0% +space complexity for multi-tape turing + + + align:start position:0% +space complexity for multi-tape turing +machines just as we've been doing which + + align:start position:0% +machines just as we've been doing which + + + align:start position:0% +machines just as we've been doing which +is we did for one tape turning machines + + align:start position:0% +is we did for one tape turning machines + + + align:start position:0% +is we did for one tape turning machines +and then define the associated space + + align:start position:0% +and then define the associated space + + + align:start position:0% +and then define the associated space +complexity classes and then define + + align:start position:0% +complexity classes and then define + + + align:start position:0% +complexity classes and then define +the class p space but that would be for + + align:start position:0% +the class p space but that would be for + + + align:start position:0% +the class p space but that would be for +multi-turing machines + + align:start position:0% +multi-turing machines + + + align:start position:0% +multi-turing machines +now for time + + align:start position:0% +now for time + + + align:start position:0% +now for time +uh + + align:start position:0% +uh + + + align:start position:0% +uh +remember that the class p + + align:start position:0% +remember that the class p + + + align:start position:0% +remember that the class p +that you would get from multitape turing + + align:start position:0% +that you would get from multitape turing + + + align:start position:0% +that you would get from multitape turing +machines is exactly the same as the + + align:start position:0% +machines is exactly the same as the + + + align:start position:0% +machines is exactly the same as the +class p that we got for one tape turing + + align:start position:0% +class p that we got for one tape turing + + + align:start position:0% +class p that we got for one tape turing +machines um that was part of the + + align:start position:0% +machines um that was part of the + + + align:start position:0% +machines um that was part of the +nice + + align:start position:0% +nice + + + align:start position:0% +nice +quality of the class p it's robust in + + align:start position:0% +quality of the class p it's robust in + + + align:start position:0% +quality of the class p it's robust in +that sense a natural so how about for p + + align:start position:0% +that sense a natural so how about for p + + + align:start position:0% +that sense a natural so how about for p +space um what do you think do we get the + + align:start position:0% +space um what do you think do we get the + + + align:start position:0% +space um what do you think do we get the +same class + + align:start position:0% +same class + + + align:start position:0% +same class +um + + align:start position:0% +um + + + align:start position:0% +um +no maybe + + align:start position:0% +no maybe + + + align:start position:0% +no maybe +or + + align:start position:0% +or + + + align:start position:0% +or +yes because we can convert a multi-tape + + align:start position:0% +yes because we can convert a multi-tape + + + align:start position:0% +yes because we can convert a multi-tape +turning machine to a single tape turning + + align:start position:0% +turning machine to a single tape turning + + + align:start position:0% +turning machine to a single tape turning +machine by only squaring the amount of + + align:start position:0% +machine by only squaring the amount of + + + align:start position:0% +machine by only squaring the amount of +space + + align:start position:0% +space + + + align:start position:0% +space +um + + align:start position:0% +um + + + align:start position:0% +um +that was what happened with time as you + + align:start position:0% +that was what happened with time as you + + + align:start position:0% +that was what happened with time as you +remember + + align:start position:0% +remember + + + align:start position:0% +remember +or maybe we can do even better + + align:start position:0% +or maybe we can do even better + + + align:start position:0% +or maybe we can do even better +converting a multi-tape touring machine + + align:start position:0% +converting a multi-tape touring machine + + + align:start position:0% +converting a multi-tape touring machine +to single tape only increases it by by + + align:start position:0% +to single tape only increases it by by + + + align:start position:0% +to single tape only increases it by by +less by say a constant factor here + + align:start position:0% +less by say a constant factor here + + + align:start position:0% +less by say a constant factor here +remember how this is how we're defining + + align:start position:0% +remember how this is how we're defining + + + align:start position:0% +remember how this is how we're defining +space complexity for multi-tape turing + + align:start position:0% +space complexity for multi-tape turing + + + align:start position:0% +space complexity for multi-tape turing +machines we're taking the sum of all the + + align:start position:0% +machines we're taking the sum of all the + + + align:start position:0% +machines we're taking the sum of all the +cells used on all of the tapes + + align:start position:0% + + + + align:start position:0% + +all right so + + align:start position:0% +all right so + + + align:start position:0% +all right so +let's launch that poll and see what you + + align:start position:0% +let's launch that poll and see what you + + + align:start position:0% +let's launch that poll and see what you +think + + align:start position:0% + + + + align:start position:0% + +hopefully this is not + + align:start position:0% +hopefully this is not + + + align:start position:0% +hopefully this is not +too + + align:start position:0% +too + + + align:start position:0% +too +hard um + + align:start position:0% +hard um + + + align:start position:0% +hard um +yeah i think most of you have got the + + align:start position:0% +yeah i think most of you have got the + + + align:start position:0% +yeah i think most of you have got the +idea though some of you are + + align:start position:0% +idea though some of you are + + + align:start position:0% +idea though some of you are +i worry sometimes about some of the + + align:start position:0% +i worry sometimes about some of the + + + align:start position:0% +i worry sometimes about some of the +answers that i get + + align:start position:0% +answers that i get + + + align:start position:0% +answers that i get +i don't know if you're serious or + + align:start position:0% +i don't know if you're serious or + + + align:start position:0% +i don't know if you're serious or +you're really com + + align:start position:0% +you're really com + + + align:start position:0% +you're really com +badly confused + + align:start position:0% + + + + align:start position:0% + +but anyway let's + + align:start position:0% +but anyway let's + + + align:start position:0% +but anyway let's +let's wrap this up another + + align:start position:0% + + + + align:start position:0% + +10 seconds or so + + align:start position:0% + + + + align:start position:0% + +let's call + + align:start position:0% + + + + align:start position:0% + +okay i'm gonna end it + + align:start position:0% + + + + align:start position:0% + +yeah i mean i + + align:start position:0% + + + + align:start position:0% + +uh i think + + align:start position:0% +uh i think + + + align:start position:0% +uh i think +answer b is a reasonable answer in fact + + align:start position:0% +answer b is a reasonable answer in fact + + + align:start position:0% +answer b is a reasonable answer in fact +uh answer c is the correct answer uh you + + align:start position:0% +uh answer c is the correct answer uh you + + + align:start position:0% +uh answer c is the correct answer uh you +can if you just look at the same + + align:start position:0% +can if you just look at the same + + + align:start position:0% +can if you just look at the same +simulation from multi-tape to single + + align:start position:0% +simulation from multi-tape to single + + + align:start position:0% +simulation from multi-tape to single +tape + + align:start position:0% +tape + + + align:start position:0% +tape +and how much space overhead that + + align:start position:0% +and how much space overhead that + + + align:start position:0% +and how much space overhead that +simulation introduces + + align:start position:0% +simulation introduces + + + align:start position:0% +simulation introduces +um it's only linear you're basically + + align:start position:0% +um it's only linear you're basically + + + align:start position:0% +um it's only linear you're basically +just taking all of the tapes of the + + align:start position:0% +just taking all of the tapes of the + + + align:start position:0% +just taking all of the tapes of the +multitape machine and writing them down + + align:start position:0% +multitape machine and writing them down + + + align:start position:0% +multitape machine and writing them down +next to one another + + align:start position:0% +next to one another + + + align:start position:0% +next to one another +obviously you know ignoring all the + + align:start position:0% +obviously you know ignoring all the + + + align:start position:0% +obviously you know ignoring all the +infinite infinitely many blanks we're + + align:start position:0% +infinite infinitely many blanks we're + + + align:start position:0% +infinite infinitely many blanks we're +just taking the active portion of the + + align:start position:0% +just taking the active portion of the + + + align:start position:0% +just taking the active portion of the +tapes writing them down next to each + + align:start position:0% +tapes writing them down next to each + + + align:start position:0% +tapes writing them down next to each +other so the total amount used is just + + align:start position:0% +other so the total amount used is just + + + align:start position:0% +other so the total amount used is just +going to be the sum + + align:start position:0% +going to be the sum + + + align:start position:0% +going to be the sum +on the single tape of what was used on + + align:start position:0% +on the single tape of what was used on + + + align:start position:0% +on the single tape of what was used on +each of the + + align:start position:0% +each of the + + + align:start position:0% +each of the +individual multitapes in the original + + align:start position:0% +individual multitapes in the original + + + align:start position:0% +individual multitapes in the original +machine + + align:start position:0% +machine + + + align:start position:0% +machine +so there's just a linear cost overhead + + align:start position:0% +so there's just a linear cost overhead + + + align:start position:0% +so there's just a linear cost overhead +by converting from multi-tape to single + + align:start position:0% +by converting from multi-tape to single + + + align:start position:0% +by converting from multi-tape to single +tape when you're looking at space the + + align:start position:0% +tape when you're looking at space the + + + align:start position:0% +tape when you're looking at space the +amount of memory that's used + + align:start position:0% +amount of memory that's used + + + align:start position:0% +amount of memory that's used +for time remember there was some + + align:start position:0% +for time remember there was some + + + align:start position:0% +for time remember there was some +additional overhead because we had to be + + align:start position:0% +additional overhead because we had to be + + + align:start position:0% +additional overhead because we had to be +uh updating um where the virtual heads + + align:start position:0% +uh updating um where the virtual heads + + + align:start position:0% +uh updating um where the virtual heads +were and that uh cost extra time to move + + align:start position:0% +were and that uh cost extra time to move + + + align:start position:0% +were and that uh cost extra time to move +our single head around to do that but + + align:start position:0% +our single head around to do that but + + + align:start position:0% +our single head around to do that but +for space + + align:start position:0% +for space + + + align:start position:0% +for space +the amount of time that's introduced is + + align:start position:0% +the amount of time that's introduced is + + + align:start position:0% +the amount of time that's introduced is +not as irrelevant we're only looking at + + align:start position:0% +not as irrelevant we're only looking at + + + align:start position:0% +not as irrelevant we're only looking at +the amount of memory and so that's a um + + align:start position:0% +the amount of memory and so that's a um + + + align:start position:0% +the amount of memory and so that's a um +link going to just uh you know + + align:start position:0% +link going to just uh you know + + + align:start position:0% +link going to just uh you know +the overhead on that is very low + + align:start position:0% +the overhead on that is very low + + + align:start position:0% +the overhead on that is very low +i would do worry about the folks who are + + align:start position:0% +i would do worry about the folks who are + + + align:start position:0% +i would do worry about the folks who are +answering a for example in this uh for + + align:start position:0% +answering a for example in this uh for + + + align:start position:0% +answering a for example in this uh for +this question you should be + + align:start position:0% +this question you should be + + + align:start position:0% +this question you should be +rethinking + + align:start position:0% +rethinking + + + align:start position:0% +rethinking +what's what what's really going on here + + align:start position:0% +what's what what's really going on here + + + align:start position:0% +what's what what's really going on here +um + + align:start position:0% +um + + + align:start position:0% +um +uh so + + align:start position:0% +uh so + + + align:start position:0% +uh so +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +now + + align:start position:0% +now + + + align:start position:0% +now +let us + + align:start position:0% +let us + + + align:start position:0% +let us +um + + align:start position:0% +um + + + align:start position:0% +um +move on here from from that to our next + + align:start position:0% +move on here from from that to our next + + + align:start position:0% +move on here from from that to our next +uh slide + + align:start position:0% +uh slide + + + align:start position:0% +uh slide +and + + align:start position:0% +and + + + align:start position:0% +and +compare + + align:start position:0% +compare + + + align:start position:0% +compare +uh the time and space complexity classes + + align:start position:0% +uh the time and space complexity classes + + + align:start position:0% +uh the time and space complexity classes +you know or time and space complexity + + align:start position:0% +you know or time and space complexity + + + align:start position:0% +you know or time and space complexity +how do they relate to one another + + align:start position:0% +how do they relate to one another + + + align:start position:0% +how do they relate to one another +and so first of all we're going to point + + align:start position:0% +and so first of all we're going to point + + + align:start position:0% +and so first of all we're going to point +out + + align:start position:0% +out + + + align:start position:0% +out +um + + align:start position:0% +um + + + align:start position:0% +um +let's + + align:start position:0% +let's + + + align:start position:0% +let's +uh start out + + align:start position:0% +uh start out + + + align:start position:0% +uh start out +here + + align:start position:0% +here + + + align:start position:0% +here +t of n is going to be represent some + + align:start position:0% +t of n is going to be represent some + + + align:start position:0% +t of n is going to be represent some +bound either on the time or the amount + + align:start position:0% +bound either on the time or the amount + + + align:start position:0% +bound either on the time or the amount +of space and generally at least up till + + align:start position:0% +of space and generally at least up till + + + align:start position:0% +of space and generally at least up till +this point um and most of the mostly + + align:start position:0% +this point um and most of the mostly + + + align:start position:0% +this point um and most of the mostly +going forward though there's going to be + + align:start position:0% +going forward though there's going to be + + + align:start position:0% +going forward though there's going to be +one + + align:start position:0% +one + + + align:start position:0% +one +variation on that a little later but + + align:start position:0% +variation on that a little later but + + + align:start position:0% +variation on that a little later but +we're going to be focusing on + + align:start position:0% +we're going to be focusing on + + + align:start position:0% +we're going to be focusing on +uh bounds which are at least + + align:start position:0% +uh bounds which are at least + + + align:start position:0% +uh bounds which are at least +big enough to either read the input or + + align:start position:0% +big enough to either read the input or + + + align:start position:0% +big enough to either read the input or +at least hold the input that's why we + + align:start position:0% +at least hold the input that's why we + + + align:start position:0% +at least hold the input that's why we +we refer to t of n being at least n + + align:start position:0% +we refer to t of n being at least n + + + align:start position:0% +we refer to t of n being at least n +um + + align:start position:0% +um + + + align:start position:0% +um +so now if we + + align:start position:0% +so now if we + + + align:start position:0% +so now if we +look at + + align:start position:0% +look at + + + align:start position:0% +look at +uh the time complexity class t of n + + align:start position:0% +uh the time complexity class t of n + + + align:start position:0% +uh the time complexity class t of n +think of that t of n like typically + + align:start position:0% +think of that t of n like typically + + + align:start position:0% +think of that t of n like typically +would be say n squared maybe + + align:start position:0% +would be say n squared maybe + + + align:start position:0% +would be say n squared maybe +and the things that you can do + + align:start position:0% +and the things that you can do + + + align:start position:0% +and the things that you can do +in n squared time + + align:start position:0% +in n squared time + + + align:start position:0% +in n squared time +i claim you can also do in n squared + + align:start position:0% +i claim you can also do in n squared + + + align:start position:0% +i claim you can also do in n squared +space + + align:start position:0% +space + + + align:start position:0% +space +um + + align:start position:0% +um + + + align:start position:0% +um +and basically + + align:start position:0% +and basically + + + align:start position:0% +and basically +um it's just using the very same machine + + align:start position:0% +um it's just using the very same machine + + + align:start position:0% +um it's just using the very same machine +suppose you have a machine that runs in + + align:start position:0% +suppose you have a machine that runs in + + + align:start position:0% +suppose you have a machine that runs in +n squared time how could it possibly use + + align:start position:0% +n squared time how could it possibly use + + + align:start position:0% +n squared time how could it possibly use +say n square n cubed space if it's + + align:start position:0% +say n square n cubed space if it's + + + align:start position:0% +say n square n cubed space if it's +running only in n square time + + align:start position:0% +running only in n square time + + + align:start position:0% +running only in n square time +even if it tries to use as much state as + + align:start position:0% +even if it tries to use as much state as + + + align:start position:0% +even if it tries to use as much state as +it possibly could as many tape cells as + + align:start position:0% +it possibly could as many tape cells as + + + align:start position:0% +it possibly could as many tape cells as +it possibly could + + align:start position:0% +it possibly could + + + align:start position:0% +it possibly could +and you know sending its head cruising + + align:start position:0% +and you know sending its head cruising + + + align:start position:0% +and you know sending its head cruising +out um into the blind portion of the + + align:start position:0% +out um into the blind portion of the + + + align:start position:0% +out um into the blind portion of the +tape chewing up as much uh as many tape + + align:start position:0% +tape chewing up as much uh as many tape + + + align:start position:0% +tape chewing up as much uh as many tape +cells as it possibly can in in n squared + + align:start position:0% +cells as it possibly can in in n squared + + + align:start position:0% +cells as it possibly can in in n squared +time it's only going to be able to use n + + align:start position:0% +time it's only going to be able to use n + + + align:start position:0% +time it's only going to be able to use n +squared space so the very same machine + + align:start position:0% +squared space so the very same machine + + + align:start position:0% +squared space so the very same machine +that runs in t of n time is also going + + align:start position:0% +that runs in t of n time is also going + + + align:start position:0% +that runs in t of n time is also going +to run in t event space um so this + + align:start position:0% +to run in t event space um so this + + + align:start position:0% +to run in t event space um so this +containment here + + align:start position:0% +containment here + + + align:start position:0% +containment here +follows you know really without doing um + + align:start position:0% +follows you know really without doing um + + + align:start position:0% +follows you know really without doing um +any work at all um + + align:start position:0% +any work at all um + + + align:start position:0% +any work at all um +so just re restating that here um a + + align:start position:0% +so just re restating that here um a + + + align:start position:0% +so just re restating that here um a +uh turing machine that runs in t of n + + align:start position:0% +uh turing machine that runs in t of n + + + align:start position:0% +uh turing machine that runs in t of n +steps cannot use more than t of n tape + + align:start position:0% +steps cannot use more than t of n tape + + + align:start position:0% +steps cannot use more than t of n tape +cells + + align:start position:0% +cells + + + align:start position:0% +cells +okay so right now we're focusing on we + + align:start position:0% +okay so right now we're focusing on we + + + align:start position:0% +okay so right now we're focusing on we +could prove some analogous statements + + align:start position:0% +could prove some analogous statements + + + align:start position:0% +could prove some analogous statements +about + + align:start position:0% +about + + + align:start position:0% +about +non-deterministic complexity um but + + align:start position:0% +non-deterministic complexity um but + + + align:start position:0% +non-deterministic complexity um but +let's focus here on the deterministic + + align:start position:0% +let's focus here on the deterministic + + + align:start position:0% +let's focus here on the deterministic +complexity + + align:start position:0% +complexity + + + align:start position:0% +complexity +now let's look at going the other + + align:start position:0% +now let's look at going the other + + + align:start position:0% +now let's look at going the other +direction suppose we have a turing + + align:start position:0% +direction suppose we have a turing + + + align:start position:0% +direction suppose we have a turing +machine + + align:start position:0% +machine + + + align:start position:0% +machine +that uses t of n + + align:start position:0% +that uses t of n + + + align:start position:0% +that uses t of n +space now + + align:start position:0% +space now + + + align:start position:0% +space now +does that immediately imply it's using + + align:start position:0% +does that immediately imply it's using + + + align:start position:0% +does that immediately imply it's using +only t of n and time + + align:start position:0% +only t of n and time + + + align:start position:0% +only t of n and time +and that's + + align:start position:0% +and that's + + + align:start position:0% +and that's +uh not so clear and in fact probably not + + align:start position:0% +uh not so clear and in fact probably not + + + align:start position:0% +uh not so clear and in fact probably not +true + + align:start position:0% +true + + + align:start position:0% +true +because + + align:start position:0% +because + + + align:start position:0% +because +a space appears to be much more powerful + + align:start position:0% +a space appears to be much more powerful + + + align:start position:0% +a space appears to be much more powerful +than time and within a certain amount of + + align:start position:0% +than time and within a certain amount of + + + align:start position:0% +than time and within a certain amount of +space you can run for much longer than + + align:start position:0% +space you can run for much longer than + + + align:start position:0% +space you can run for much longer than +that same amount of time um so how long + + align:start position:0% +that same amount of time um so how long + + + align:start position:0% +that same amount of time um so how long +could you run + + align:start position:0% + + + + align:start position:0% + +so what which you can + + align:start position:0% +so what which you can + + + align:start position:0% +so what which you can +show is that if you're running uh within + + align:start position:0% +show is that if you're running uh within + + + align:start position:0% +show is that if you're running uh within +a certain amount of space t event space + + align:start position:0% +a certain amount of space t event space + + + align:start position:0% +a certain amount of space t event space +let's say + + align:start position:0% +let's say + + + align:start position:0% +let's say +n squared space for example + + align:start position:0% +n squared space for example + + + align:start position:0% +n squared space for example +the amount of time you could use is + + align:start position:0% +the amount of time you could use is + + + align:start position:0% +the amount of time you could use is +going to be exponential in n squared a 2 + + align:start position:0% +going to be exponential in n squared a 2 + + + align:start position:0% +going to be exponential in n squared a 2 +to the order n squared + + align:start position:0% + + + + align:start position:0% + +sometimes we also write that as + + align:start position:0% +sometimes we also write that as + + + align:start position:0% +sometimes we also write that as +the union of + + align:start position:0% +the union of + + + align:start position:0% +the union of +c to the um n squared by sort of pulling + + align:start position:0% +c to the um n squared by sort of pulling + + + align:start position:0% +c to the um n squared by sort of pulling +down that constant here if you want well + + align:start position:0% +down that constant here if you want well + + + align:start position:0% +down that constant here if you want well +it's also just to understand what we + + align:start position:0% +it's also just to understand what we + + + align:start position:0% +it's also just to understand what we +mean by order t of n up in the exponent + + align:start position:0% +mean by order t of n up in the exponent + + + align:start position:0% +mean by order t of n up in the exponent +it means that + + align:start position:0% +it means that + + + align:start position:0% +it means that +the union over c to the t of n for all c + + align:start position:0% +the union over c to the t of n for all c + + + align:start position:0% +the union over c to the t of n for all c +either of these are just completely + + align:start position:0% +either of these are just completely + + + align:start position:0% +either of these are just completely +equivalent so whichever one you're more + + align:start position:0% +equivalent so whichever one you're more + + + align:start position:0% +equivalent so whichever one you're more +comfortable with + + align:start position:0% +comfortable with + + + align:start position:0% +comfortable with +but why is this going to be true why + + align:start position:0% +but why is this going to be true why + + + align:start position:0% +but why is this going to be true why +does a turing machine that runs in say + + align:start position:0% +does a turing machine that runs in say + + + align:start position:0% +does a turing machine that runs in say +um + + align:start position:0% +um + + + align:start position:0% +um +uh + + align:start position:0% + + + + align:start position:0% + +say n squared space + + align:start position:0% +say n squared space + + + align:start position:0% +say n squared space +use + + align:start position:0% +use + + + align:start position:0% +use +at most + + align:start position:0% +at most + + + align:start position:0% +at most +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh + + align:start position:0% +uh + + + align:start position:0% +uh +two to the order n squared time + + align:start position:0% +two to the order n squared time + + + align:start position:0% +two to the order n squared time +and that's because if you look at how + + align:start position:0% +and that's because if you look at how + + + align:start position:0% +and that's because if you look at how +many possible configurations the machine + + align:start position:0% +many possible configurations the machine + + + align:start position:0% +many possible configurations the machine +can have + + align:start position:0% +can have + + + align:start position:0% +can have +remember that a configuration is is + + align:start position:0% +remember that a configuration is is + + + align:start position:0% +remember that a configuration is is +essentially + + align:start position:0% +essentially + + + align:start position:0% +essentially +the contents of the tape this is also + + align:start position:0% +the contents of the tape this is also + + + align:start position:0% +the contents of the tape this is also +the head position and the state but the + + align:start position:0% +the head position and the state but the + + + align:start position:0% +the head position and the state but the +dominant um + + align:start position:0% +dominant um + + + align:start position:0% +dominant um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the dominant aspect of a configuration + + align:start position:0% +the dominant aspect of a configuration + + + align:start position:0% +the dominant aspect of a configuration +is the tape and so how many different + + align:start position:0% +is the tape and so how many different + + + align:start position:0% +is the tape and so how many different +tape contents can you have + + align:start position:0% +tape contents can you have + + + align:start position:0% +tape contents can you have +well it's going to be exponential in the + + align:start position:0% +well it's going to be exponential in the + + + align:start position:0% +well it's going to be exponential in the +saw in the length of that tape + + align:start position:0% +saw in the length of that tape + + + align:start position:0% +saw in the length of that tape +because you know each cell can have some + + align:start position:0% +because you know each cell can have some + + + align:start position:0% +because you know each cell can have some +fixed number of symbols in it + + align:start position:0% +fixed number of symbols in it + + + align:start position:0% +fixed number of symbols in it +if a machine + + align:start position:0% +if a machine + + + align:start position:0% +if a machine +repeats a configuration it's going to go + + align:start position:0% +repeats a configuration it's going to go + + + align:start position:0% +repeats a configuration it's going to go +forever which we're forbidding um in uh + + align:start position:0% +forever which we're forbidding um in uh + + + align:start position:0% +forever which we're forbidding um in uh +you know in the in these machines + + align:start position:0% +you know in the in these machines + + + align:start position:0% +you know in the in these machines +because they're all going to be deciders + + align:start position:0% +because they're all going to be deciders + + + align:start position:0% +because they're all going to be deciders +so they can only run + + align:start position:0% +so they can only run + + + align:start position:0% +so they can only run +um + + align:start position:0% +um + + + align:start position:0% +um +uh for an amount of time which is + + align:start position:0% +uh for an amount of time which is + + + align:start position:0% +uh for an amount of time which is +bounded by the number of configurations + + align:start position:0% +bounded by the number of configurations + + + align:start position:0% +bounded by the number of configurations +that the machine can have + + align:start position:0% +that the machine can have + + + align:start position:0% +that the machine can have +and so the machine can have + + align:start position:0% + + + + align:start position:0% + +you know if it's running in t of n space + + align:start position:0% +you know if it's running in t of n space + + + align:start position:0% +you know if it's running in t of n space +then the amount of + + align:start position:0% +then the amount of + + + align:start position:0% +then the amount of +time that it could be running is going + + align:start position:0% +time that it could be running is going + + + align:start position:0% +time that it could be running is going +to be at most some constant to the t of + + align:start position:0% +to be at most some constant to the t of + + + align:start position:0% +to be at most some constant to the t of +n + + align:start position:0% +n + + + align:start position:0% +n +or two to the order of t events saying + + align:start position:0% +or two to the order of t events saying + + + align:start position:0% +or two to the order of t events saying +the same thing + + align:start position:0% +the same thing + + + align:start position:0% +the same thing +uh uh you know unless it's going to + + align:start position:0% +uh uh you know unless it's going to + + + align:start position:0% +uh uh you know unless it's going to +repeat a configuration and end up + + align:start position:0% +repeat a configuration and end up + + + align:start position:0% +repeat a configuration and end up +looping + + align:start position:0% + + + + align:start position:0% + +okay so these are the two fundamental + + align:start position:0% +okay so these are the two fundamental + + + align:start position:0% +okay so these are the two fundamental +connections between time and space + + align:start position:0% +connections between time and space + + + align:start position:0% +connections between time and space +time is contained within the same amount + + align:start position:0% +time is contained within the same amount + + + align:start position:0% +time is contained within the same amount +of space space is contained within that + + align:start position:0% +of space space is contained within that + + + align:start position:0% +of space space is contained within that +amount of time exponentiated + + align:start position:0% + + + + align:start position:0% + +okay um so one car reliary of that is + + align:start position:0% +okay um so one car reliary of that is + + + align:start position:0% +okay um so one car reliary of that is +that the class p is contained within p + + align:start position:0% +that the class p is contained within p + + + align:start position:0% +that the class p is contained within p +space + + align:start position:0% + + + + align:start position:0% + +similarly np is going to be contained + + align:start position:0% +similarly np is going to be contained + + + align:start position:0% +similarly np is going to be contained +within an np space for the very same + + align:start position:0% +within an np space for the very same + + + align:start position:0% +within an np space for the very same +reason + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +okay is this + + align:start position:0% +okay is this + + + align:start position:0% +okay is this +um + + align:start position:0% +um + + + align:start position:0% +um +understandable + + align:start position:0% +understandable + + + align:start position:0% +understandable +you know this is this is a good place or + + align:start position:0% +you know this is this is a good place or + + + align:start position:0% +you know this is this is a good place or +in a moment to have one more line to + + align:start position:0% +in a moment to have one more line to + + + align:start position:0% +in a moment to have one more line to +to to to tell you about but leading into + + align:start position:0% +to to to tell you about but leading into + + + align:start position:0% +to to to tell you about but leading into +the next slide so + + align:start position:0% +the next slide so + + + align:start position:0% +the next slide so +if you understand the definitions + + align:start position:0% +if you understand the definitions + + + align:start position:0% +if you understand the definitions +of what we've done so far + + align:start position:0% +of what we've done so far + + + align:start position:0% +of what we've done so far +all of the the the this is a this is a + + align:start position:0% +all of the the the this is a this is a + + + align:start position:0% +all of the the the this is a this is a +fairly straightforward theorem and the + + align:start position:0% +fairly straightforward theorem and the + + + align:start position:0% +fairly straightforward theorem and the +and the corollary is immediate + + align:start position:0% +and the corollary is immediate + + + align:start position:0% +and the corollary is immediate +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +um + + align:start position:0% +um + + + align:start position:0% +um +anything that you can do in n squared + + align:start position:0% +anything that you can do in n squared + + + align:start position:0% +anything that you can do in n squared +time you can do an n squared space and + + align:start position:0% +time you can do an n squared space and + + + align:start position:0% +time you can do an n squared space and +so for if anything you can do in + + align:start position:0% +so for if anything you can do in + + + align:start position:0% +so for if anything you can do in +polynomial time you can also do in + + align:start position:0% +polynomial time you can also do in + + + align:start position:0% +polynomial time you can also do in +polynomial space + + align:start position:0% +polynomial space + + + align:start position:0% +polynomial space +yes c somebody's asking me you know what + + align:start position:0% +yes c somebody's asking me you know what + + + align:start position:0% +yes c somebody's asking me you know what +is the c c is essentially going to be + + align:start position:0% +is the c c is essentially going to be + + + align:start position:0% +is the c c is essentially going to be +the size of the tape alphabet + + align:start position:0% +the size of the tape alphabet + + + align:start position:0% +the size of the tape alphabet +um + + align:start position:0% +um + + + align:start position:0% +um +because that's going to govern how many + + align:start position:0% +because that's going to govern how many + + + align:start position:0% +because that's going to govern how many +different configurations you have + + align:start position:0% +different configurations you have + + + align:start position:0% +different configurations you have +there's a slight extra uh factor it's + + align:start position:0% +there's a slight extra uh factor it's + + + align:start position:0% +there's a slight extra uh factor it's +like you know slight extra factor for + + align:start position:0% +like you know slight extra factor for + + + align:start position:0% +like you know slight extra factor for +the tape um + + align:start position:0% +the tape um + + + align:start position:0% +the tape um +the the head location and also the + + align:start position:0% +the the head location and also the + + + align:start position:0% +the the head location and also the +um state but uh the the main thing is + + align:start position:0% +um state but uh the the main thing is + + + align:start position:0% +um state but uh the the main thing is +going to be the + + align:start position:0% +going to be the + + + align:start position:0% +going to be the +number of tape symbols and the length of + + align:start position:0% +number of tape symbols and the length of + + + align:start position:0% +number of tape symbols and the length of +the tape + + align:start position:0% + + + + align:start position:0% + +okay but what's going to come next is + + align:start position:0% +okay but what's going to come next is + + + align:start position:0% +okay but what's going to come next is +we're going to prove something more + + align:start position:0% +we're going to prove something more + + + align:start position:0% +we're going to prove something more +powerful than + + align:start position:0% +powerful than + + + align:start position:0% +powerful than +this corollary that p is contained in p + + align:start position:0% +this corollary that p is contained in p + + + align:start position:0% +this corollary that p is contained in p +space because not only is p contained in + + align:start position:0% +space because not only is p contained in + + + align:start position:0% +space because not only is p contained in +p space but np is also contained in p + + align:start position:0% +p space but np is also contained in p + + + align:start position:0% +p space but np is also contained in p +space and for that we're going to have + + align:start position:0% +space and for that we're going to have + + + align:start position:0% +space and for that we're going to have +to do more work + + align:start position:0% + + + + align:start position:0% + +so somebody's asking me about the number + + align:start position:0% +so somebody's asking me about the number + + + align:start position:0% +so somebody's asking me about the number +of states the number of states + + align:start position:0% +of states the number of states + + + align:start position:0% +of states the number of states +is going to be indep is fixed depend + + align:start position:0% +is going to be indep is fixed depend + + + align:start position:0% +is going to be indep is fixed depend +upon depending on the machine only + + align:start position:0% +upon depending on the machine only + + + align:start position:0% +upon depending on the machine only +so um + + align:start position:0% +so um + + + align:start position:0% +so um +they it doesn't depend upon the + + align:start position:0% +they it doesn't depend upon the + + + align:start position:0% +they it doesn't depend upon the +uh depend up on n so it could in most + + align:start position:0% +uh depend up on n so it could in most + + + align:start position:0% +uh depend up on n so it could in most +affect + + align:start position:0% +affect + + + align:start position:0% +affect +the + + align:start position:0% +the + + + align:start position:0% +the +number configurations by a constant + + align:start position:0% +number configurations by a constant + + + align:start position:0% +number configurations by a constant +factor + + align:start position:0% +factor + + + align:start position:0% +factor +and those constant factors are going to + + align:start position:0% +and those constant factors are going to + + + align:start position:0% +and those constant factors are going to +be absorbed + + align:start position:0% +be absorbed + + + align:start position:0% +be absorbed +within the definitions of these uh + + align:start position:0% +within the definitions of these uh + + + align:start position:0% +within the definitions of these uh +complexity classes because that's how we + + align:start position:0% +complexity classes because that's how we + + + align:start position:0% +complexity classes because that's how we +would define them to be um + + align:start position:0% +would define them to be um + + + align:start position:0% +would define them to be um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +you know + + align:start position:0% +you know + + + align:start position:0% +you know +ignoring the constant factors + + align:start position:0% + + + + align:start position:0% + +but you know + + align:start position:0% +but you know + + + align:start position:0% +but you know +why don't we just take a + + align:start position:0% +why don't we just take a + + + align:start position:0% +why don't we just take a +you know this may be a good place to + + align:start position:0% +you know this may be a good place to + + + align:start position:0% +you know this may be a good place to +pause for a second and see if there's + + align:start position:0% +pause for a second and see if there's + + + align:start position:0% +pause for a second and see if there's +any questions + + align:start position:0% + + + + align:start position:0% + +because you know + + align:start position:0% +because you know + + + align:start position:0% +because you know +i think for some of you this may be um + + align:start position:0% +i think for some of you this may be um + + + align:start position:0% +i think for some of you this may be um +straightforward but you know i i think + + align:start position:0% +straightforward but you know i i think + + + align:start position:0% +straightforward but you know i i think +it's less common to be measuring + + align:start position:0% +it's less common to be measuring + + + align:start position:0% +it's less common to be measuring +thinking about uh + + align:start position:0% +thinking about uh + + + align:start position:0% +thinking about uh +the amount of memory as a complexity + + align:start position:0% +the amount of memory as a complexity + + + align:start position:0% +the amount of memory as a complexity +measure um so this is perhaps a little + + align:start position:0% +measure um so this is perhaps a little + + + align:start position:0% +measure um so this is perhaps a little +less familiar some of you have seen + + align:start position:0% +less familiar some of you have seen + + + align:start position:0% +less familiar some of you have seen +measuring time and other classes but + + align:start position:0% +measuring time and other classes but + + + align:start position:0% +measuring time and other classes but +remember + + align:start position:0% +remember + + + align:start position:0% +remember +measuring the the amount of space that + + align:start position:0% +measuring the the amount of space that + + + align:start position:0% +measuring the the amount of space that +the algorithm uses probably is a little + + align:start position:0% +the algorithm uses probably is a little + + + align:start position:0% +the algorithm uses probably is a little +less familiar and maybe that's it's + + align:start position:0% +less familiar and maybe that's it's + + + align:start position:0% +less familiar and maybe that's it's +worth spending a moment or two answering + + align:start position:0% +worth spending a moment or two answering + + + align:start position:0% +worth spending a moment or two answering +questions about that + + align:start position:0% + + + + align:start position:0% + +so i'm not sure i understand the + + align:start position:0% +so i'm not sure i understand the + + + align:start position:0% +so i'm not sure i understand the +question that just came in but i'll i'll + + align:start position:0% +question that just came in but i'll i'll + + + align:start position:0% +question that just came in but i'll i'll +read it out there is it possible that a + + align:start position:0% +read it out there is it possible that a + + + align:start position:0% +read it out there is it possible that a +turing machine can loop forever + + align:start position:0% +turing machine can loop forever + + + align:start position:0% +turing machine can loop forever +absolutely but a turing machine that + + align:start position:0% +absolutely but a turing machine that + + + align:start position:0% +absolutely but a turing machine that +loops forever does not count as one that + + align:start position:0% +loops forever does not count as one that + + + align:start position:0% +loops forever does not count as one that +runs within the space bound to run + + align:start position:0% +runs within the space bound to run + + + align:start position:0% +runs within the space bound to run +within the space bound the machine must + + align:start position:0% +within the space bound the machine must + + + align:start position:0% +within the space bound the machine must +halt on every input it has to be a + + align:start position:0% +halt on every input it has to be a + + + align:start position:0% +halt on every input it has to be a +decider we're only considering deciders + + align:start position:0% +decider we're only considering deciders + + + align:start position:0% +decider we're only considering deciders +here + + align:start position:0% +here + + + align:start position:0% +here +so is it possible that turn machine can + + align:start position:0% +so is it possible that turn machine can + + + align:start position:0% +so is it possible that turn machine can +look forever yes isn't the turing + + align:start position:0% +look forever yes isn't the turing + + + align:start position:0% +look forever yes isn't the turing +machine we're talking about a member of + + align:start position:0% +machine we're talking about a member of + + + align:start position:0% +machine we're talking about a member of +space and thus a decider + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +not totally sure i understand the + + align:start position:0% +not totally sure i understand the + + + align:start position:0% +not totally sure i understand the +question but + + align:start position:0% +question but + + + align:start position:0% +question but +if a + + align:start position:0% +if a + + + align:start position:0% +if a +turing machine is + + align:start position:0% + + + + align:start position:0% + +not + + align:start position:0% +not + + + align:start position:0% +not +halting on all inputs it's not a decider + + align:start position:0% +halting on all inputs it's not a decider + + + align:start position:0% +halting on all inputs it's not a decider +that's our definition + + align:start position:0% +that's our definition + + + align:start position:0% +that's our definition +um + + align:start position:0% + + + + align:start position:0% + +are we good and we're not getting very + + align:start position:0% +are we good and we're not getting very + + + align:start position:0% +are we good and we're not getting very +many questions here so i'm assuming + + align:start position:0% +many questions here so i'm assuming + + + align:start position:0% +many questions here so i'm assuming +you're all with me + + align:start position:0% +you're all with me + + + align:start position:0% +you're all with me +or + + align:start position:0% +or + + + align:start position:0% +or +so lost you don't even know what to ask + + align:start position:0% +so lost you don't even know what to ask + + + align:start position:0% +so lost you don't even know what to ask +which is not good + + align:start position:0% +which is not good + + + align:start position:0% +which is not good +um so be bold if you're confused throw + + align:start position:0% +um so be bold if you're confused throw + + + align:start position:0% +um so be bold if you're confused throw +our question out there because i'm i i + + align:start position:0% +our question out there because i'm i i + + + align:start position:0% +our question out there because i'm i i +don't want to race through this lecture + + align:start position:0% +don't want to race through this lecture + + + align:start position:0% +don't want to race through this lecture +since it's it's maybe a little less + + align:start position:0% +since it's it's maybe a little less + + + align:start position:0% +since it's it's maybe a little less +familiar to some of you + + align:start position:0% +familiar to some of you + + + align:start position:0% +familiar to some of you +okay so let's move on + + align:start position:0% +okay so let's move on + + + align:start position:0% +okay so let's move on +um + + align:start position:0% +um + + + align:start position:0% +um +as promised i'm going to show you now + + align:start position:0% +as promised i'm going to show you now + + + align:start position:0% +as promised i'm going to show you now +that np + + align:start position:0% +that np + + + align:start position:0% +that np +not only p as is kind of happens + + align:start position:0% +not only p as is kind of happens + + + align:start position:0% +not only p as is kind of happens +immediately but np + + align:start position:0% +immediately but np + + + align:start position:0% +immediately but np +is contained as a subset of a p space + + align:start position:0% + + + + align:start position:0% + +so that is oh + + align:start position:0% +so that is oh + + + align:start position:0% +so that is oh +i didn't get a question i + + align:start position:0% +i didn't get a question i + + + align:start position:0% +i didn't get a question i +moved on before i answered this question + + align:start position:0% +moved on before i answered this question + + + align:start position:0% +moved on before i answered this question +can i explain part two of the proof + + align:start position:0% +can i explain part two of the proof + + + align:start position:0% +can i explain part two of the proof +again part two okay let's just do it um + + align:start position:0% +again part two okay let's just do it um + + + align:start position:0% +again part two okay let's just do it um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +if something runs in a certain amount of + + align:start position:0% +if something runs in a certain amount of + + + align:start position:0% +if something runs in a certain amount of +space you have to just think about how + + align:start position:0% +space you have to just think about how + + + align:start position:0% +space you have to just think about how +many different configurations the + + align:start position:0% +many different configurations the + + + align:start position:0% +many different configurations the +machine can have within that amount of + + align:start position:0% +machine can have within that amount of + + + align:start position:0% +machine can have within that amount of +space remember the configurations that + + align:start position:0% +space remember the configurations that + + + align:start position:0% +space remember the configurations that +we defined way back at lbas + + align:start position:0% +we defined way back at lbas + + + align:start position:0% +we defined way back at lbas +um + + align:start position:0% +um + + + align:start position:0% +um +so the number of configurations the + + align:start position:0% +so the number of configurations the + + + align:start position:0% +so the number of configurations the +machine can have depends on how much + + align:start position:0% +machine can have depends on how much + + + align:start position:0% +machine can have depends on how much +space it's allocated + + align:start position:0% +space it's allocated + + + align:start position:0% +space it's allocated +like the lbas they had a fixed number of + + align:start position:0% +like the lbas they had a fixed number of + + + align:start position:0% +like the lbas they had a fixed number of +configurations and we gave a calculation + + align:start position:0% +configurations and we gave a calculation + + + align:start position:0% +configurations and we gave a calculation +for that + + align:start position:0% +for that + + + align:start position:0% +for that +um + + align:start position:0% +um + + + align:start position:0% +um +which is basically an exponential in the + + align:start position:0% +which is basically an exponential in the + + + align:start position:0% +which is basically an exponential in the +amount of space that's how many + + align:start position:0% +amount of space that's how many + + + align:start position:0% +amount of space that's how many +configurations the machine can have + + align:start position:0% +configurations the machine can have + + + align:start position:0% +configurations the machine can have +so + + align:start position:0% +so + + + align:start position:0% +so +if the machine is not a is not looping + + align:start position:0% +if the machine is not a is not looping + + + align:start position:0% +if the machine is not a is not looping +if it's a decider it can never repeat a + + align:start position:0% +if it's a decider it can never repeat a + + + align:start position:0% +if it's a decider it can never repeat a +configuration and that's going to tell + + align:start position:0% +configuration and that's going to tell + + + align:start position:0% +configuration and that's going to tell +us how long the machine can possibly run + + align:start position:0% +us how long the machine can possibly run + + + align:start position:0% +us how long the machine can possibly run +for + + align:start position:0% + + + + align:start position:0% + +you know it's a + + align:start position:0% +you know it's a + + + align:start position:0% +you know it's a +it's it's it's important to understand + + align:start position:0% +it's it's it's important to understand + + + align:start position:0% +it's it's it's important to understand +i'm not sure if i knew how to say that + + align:start position:0% +i'm not sure if i knew how to say that + + + align:start position:0% +i'm not sure if i knew how to say that +in any way be that different from what i + + align:start position:0% +in any way be that different from what i + + + align:start position:0% +in any way be that different from what i +said before but um + + align:start position:0% +said before but um + + + align:start position:0% +said before but um +okay getting back now + + align:start position:0% +okay getting back now + + + align:start position:0% +okay getting back now +to proving that np is a subset of p + + align:start position:0% +to proving that np is a subset of p + + + align:start position:0% +to proving that np is a subset of p +space so now we're going to have to do + + align:start position:0% +space so now we're going to have to do + + + align:start position:0% +space so now we're going to have to do +something that's sort of in a way uh + + align:start position:0% +something that's sort of in a way uh + + + align:start position:0% +something that's sort of in a way uh +different from what we did on the + + align:start position:0% +different from what we did on the + + + align:start position:0% +different from what we did on the +previous slide because now + + align:start position:0% +previous slide because now + + + align:start position:0% +previous slide because now +it's not going to be enough to work with + + align:start position:0% +it's not going to be enough to work with + + + align:start position:0% +it's not going to be enough to work with +the same machine before when we were + + align:start position:0% +the same machine before when we were + + + align:start position:0% +the same machine before when we were +converting we're showing that a certain + + align:start position:0% +converting we're showing that a certain + + + align:start position:0% +converting we're showing that a certain +amount of time time classes contained + + align:start position:0% +amount of time time classes contained + + + align:start position:0% +amount of time time classes contained +within a spaceclass it was by virtue of + + align:start position:0% +within a spaceclass it was by virtue of + + + align:start position:0% +within a spaceclass it was by virtue of +the very same machine by just showing + + align:start position:0% +the very same machine by just showing + + + align:start position:0% +the very same machine by just showing +that if it's running within a certain + + align:start position:0% +that if it's running within a certain + + + align:start position:0% +that if it's running within a certain +amount of time then it has to be running + + align:start position:0% +amount of time then it has to be running + + + align:start position:0% +amount of time then it has to be running +within that same amount of sp within + + align:start position:0% +within that same amount of sp within + + + align:start position:0% +within that same amount of sp within +that same amount of space um + + align:start position:0% +that same amount of space um + + + align:start position:0% +that same amount of space um +or in terms of the space it was in the x + + align:start position:0% +or in terms of the space it was in the x + + + align:start position:0% +or in terms of the space it was in the x +given a certain amount of space it has + + align:start position:0% +given a certain amount of space it has + + + align:start position:0% +given a certain amount of space it has +to be running that same machine within a + + align:start position:0% +to be running that same machine within a + + + align:start position:0% +to be running that same machine within a +certain amount of time + + align:start position:0% + + + + align:start position:0% + +here we're going to mixing + + align:start position:0% +here we're going to mixing + + + align:start position:0% +here we're going to mixing +non-determinism and determinism so we're + + align:start position:0% +non-determinism and determinism so we're + + + align:start position:0% +non-determinism and determinism so we're +going to have to take a machine that's + + align:start position:0% +going to have to take a machine that's + + + align:start position:0% +going to have to take a machine that's +in uh an np type machine a + + align:start position:0% +in uh an np type machine a + + + align:start position:0% +in uh an np type machine a +non-deterministic polynomial time + + align:start position:0% +non-deterministic polynomial time + + + align:start position:0% +non-deterministic polynomial time +machine + + align:start position:0% +machine + + + align:start position:0% +machine +and convert it into a deterministic + + align:start position:0% +and convert it into a deterministic + + + align:start position:0% +and convert it into a deterministic +machine that doesn't use a whole lot of + + align:start position:0% +machine that doesn't use a whole lot of + + + align:start position:0% +machine that doesn't use a whole lot of +space + + align:start position:0% +space + + + align:start position:0% +space +so there's + + align:start position:0% +so there's + + + align:start position:0% +so there's +a difference in the + + align:start position:0% +a difference in the + + + align:start position:0% +a difference in the +character of this theorem because we + + align:start position:0% +character of this theorem because we + + + align:start position:0% +character of this theorem because we +have to introduce a new machine + + align:start position:0% +have to introduce a new machine + + + align:start position:0% +have to introduce a new machine +um + + align:start position:0% +um + + + align:start position:0% +um +and the way we're going to prove that um + + align:start position:0% + + + + align:start position:0% + +i i'm going to take advantage of some of + + align:start position:0% +i i'm going to take advantage of some of + + + align:start position:0% +i i'm going to take advantage of some of +the things we've already shown + + align:start position:0% +the things we've already shown + + + align:start position:0% +the things we've already shown +to prove this one could also prove it a + + align:start position:0% +to prove this one could also prove it a + + + align:start position:0% +to prove this one could also prove it a +little bit more directly and maybe it's + + align:start position:0% +little bit more directly and maybe it's + + + align:start position:0% +little bit more directly and maybe it's +worth understanding making sure you + + align:start position:0% +worth understanding making sure you + + + align:start position:0% +worth understanding making sure you +understand both proofs + + align:start position:0% +understand both proofs + + + align:start position:0% +understand both proofs +so the first thing i'm going to observe + + align:start position:0% + + + + align:start position:0% + +is that sat + + align:start position:0% +is that sat + + + align:start position:0% +is that sat +our np complete language + + align:start position:0% +our np complete language + + + align:start position:0% +our np complete language +um the satisfiability language + + align:start position:0% +um the satisfiability language + + + align:start position:0% +um the satisfiability language +itself is a member of p space + + align:start position:0% + + + + align:start position:0% + +and the reason for that is + + align:start position:0% +and the reason for that is + + + align:start position:0% +and the reason for that is +um when you're given + + align:start position:0% +um when you're given + + + align:start position:0% +um when you're given +a formula + + align:start position:0% +a formula + + + align:start position:0% +a formula +and now you want to test if that formula + + align:start position:0% +and now you want to test if that formula + + + align:start position:0% +and now you want to test if that formula +is satisfiable + + align:start position:0% + + + + align:start position:0% + +one way to do it + + align:start position:0% +one way to do it + + + align:start position:0% +one way to do it +the most obvious way to do it is try all + + align:start position:0% +the most obvious way to do it is try all + + + align:start position:0% +the most obvious way to do it is try all +assignments + + align:start position:0% +assignments + + + align:start position:0% +assignments +one by one + + align:start position:0% +one by one + + + align:start position:0% +one by one +and see if any of them satisfy the + + align:start position:0% +and see if any of them satisfy the + + + align:start position:0% +and see if any of them satisfy the +formula + + align:start position:0% + + + + align:start position:0% + +now that's going to take a lot of time + + align:start position:0% +now that's going to take a lot of time + + + align:start position:0% +now that's going to take a lot of time +but how much space does it use + + align:start position:0% +but how much space does it use + + + align:start position:0% +but how much space does it use +i have in mind reusing the space every + + align:start position:0% +i have in mind reusing the space every + + + align:start position:0% +i have in mind reusing the space every +time we try the next assignment + + align:start position:0% +time we try the next assignment + + + align:start position:0% +time we try the next assignment +think of going through all of the + + align:start position:0% +think of going through all of the + + + align:start position:0% +think of going through all of the +assignments the way an odometer would + + align:start position:0% +assignments the way an odometer would + + + align:start position:0% +assignments the way an odometer would +work + + align:start position:0% +work + + + align:start position:0% +work +just trying every possible assignment + + align:start position:0% +just trying every possible assignment + + + align:start position:0% +just trying every possible assignment +but reusing the space where you're going + + align:start position:0% +but reusing the space where you're going + + + align:start position:0% +but reusing the space where you're going +to write that assignment down + + align:start position:0% +to write that assignment down + + + align:start position:0% +to write that assignment down +um + + align:start position:0% +um + + + align:start position:0% +um +sort of incrementing it like like a + + align:start position:0% +sort of incrementing it like like a + + + align:start position:0% +sort of incrementing it like like a +number um written in binary if you wish + + align:start position:0% +number um written in binary if you wish + + + align:start position:0% +number um written in binary if you wish +um + + align:start position:0% +um + + + align:start position:0% +um +going through all the possible + + align:start position:0% +going through all the possible + + + align:start position:0% +going through all the possible +assignments every time you get in the + + align:start position:0% +assignments every time you get in the + + + align:start position:0% +assignments every time you get in the +next assignment you plug it into the + + align:start position:0% +next assignment you plug it into the + + + align:start position:0% +next assignment you plug it into the +formula and see if the formula is + + align:start position:0% +formula and see if the formula is + + + align:start position:0% +formula and see if the formula is +satisfied if it is then you can accept + + align:start position:0% +satisfied if it is then you can accept + + + align:start position:0% +satisfied if it is then you can accept +immediately if not you go on to the next + + align:start position:0% +immediately if not you go on to the next + + + align:start position:0% +immediately if not you go on to the next +assignment and only when you've gone + + align:start position:0% +assignment and only when you've gone + + + align:start position:0% +assignment and only when you've gone +through all the assignments in that way + + align:start position:0% +through all the assignments in that way + + + align:start position:0% +through all the assignments in that way +and none of them have satisfied the + + align:start position:0% +and none of them have satisfied the + + + align:start position:0% +and none of them have satisfied the +formula then you can reject so how much + + align:start position:0% +formula then you can reject so how much + + + align:start position:0% +formula then you can reject so how much +space does that use + + align:start position:0% +space does that use + + + align:start position:0% +space does that use +that doesn't use a whole lot of space + + align:start position:0% +that doesn't use a whole lot of space + + + align:start position:0% +that doesn't use a whole lot of space +because you're reusing the space + + align:start position:0% +because you're reusing the space + + + align:start position:0% +because you're reusing the space +um to write down one assignment after + + align:start position:0% +um to write down one assignment after + + + align:start position:0% +um to write down one assignment after +the next okay it's only going to be + + align:start position:0% +the next okay it's only going to be + + + align:start position:0% +the next okay it's only going to be +using an amount of space which is big + + align:start position:0% +using an amount of space which is big + + + align:start position:0% +using an amount of space which is big +enough to hold an assignment which is + + align:start position:0% +enough to hold an assignment which is + + + align:start position:0% +enough to hold an assignment which is +basically linear because it's the size + + align:start position:0% +basically linear because it's the size + + + align:start position:0% +basically linear because it's the size +of the number of variables of the + + align:start position:0% +of the number of variables of the + + + align:start position:0% +of the number of variables of the +formula so + + align:start position:0% +formula so + + + align:start position:0% +formula so +that's going to be a linear amount of + + align:start position:0% +that's going to be a linear amount of + + + align:start position:0% +that's going to be a linear amount of +space to solve the satisfiability + + align:start position:0% +space to solve the satisfiability + + + align:start position:0% +space to solve the satisfiability +problem and so the satisfiability + + align:start position:0% +problem and so the satisfiability + + + align:start position:0% +problem and so the satisfiability +problem is certainly in p space + + align:start position:0% +problem is certainly in p space + + + align:start position:0% +problem is certainly in p space +um + + align:start position:0% +um + + + align:start position:0% +um +step one + + align:start position:0% + + + + align:start position:0% + +step two + + align:start position:0% +step two + + + align:start position:0% +step two +is we're going to take advantage + + align:start position:0% +is we're going to take advantage + + + align:start position:0% +is we're going to take advantage +of what we know about reducibility + + align:start position:0% +of what we know about reducibility + + + align:start position:0% +of what we know about reducibility +um so if a is polynomial time reducible + + align:start position:0% +um so if a is polynomial time reducible + + + align:start position:0% +um so if a is polynomial time reducible +to b + + align:start position:0% +to b + + + align:start position:0% +to b +we've already commented we didn't say + + align:start position:0% +we've already commented we didn't say + + + align:start position:0% +we've already commented we didn't say +this exactly in this way but you know + + align:start position:0% +this exactly in this way but you know + + + align:start position:0% +this exactly in this way but you know +it's still going to follow that anything + + align:start position:0% +it's still going to follow that anything + + + align:start position:0% +it's still going to follow that anything +you can do in a certain amount of time + + align:start position:0% +you can do in a certain amount of time + + + align:start position:0% +you can do in a certain amount of time +you can also do in that amount of space + + align:start position:0% +you can also do in that amount of space + + + align:start position:0% +you can also do in that amount of space +because there's a very same machine um + + align:start position:0% +because there's a very same machine um + + + align:start position:0% +because there's a very same machine um +doesn't can't use any more space than + + align:start position:0% +doesn't can't use any more space than + + + align:start position:0% +doesn't can't use any more space than +the amount of time it was allocated + + align:start position:0% +the amount of time it was allocated + + + align:start position:0% +the amount of time it was allocated +so if a is polynomial time reducible to + + align:start position:0% +so if a is polynomial time reducible to + + + align:start position:0% +so if a is polynomial time reducible to +b + + align:start position:0% +b + + + align:start position:0% +b +it's also going to be reducible in + + align:start position:0% +it's also going to be reducible in + + + align:start position:0% +it's also going to be reducible in +polynomial space the a polynomial space + + align:start position:0% +polynomial space the a polynomial space + + + align:start position:0% +polynomial space the a polynomial space +machine could do the reduction + + align:start position:0% + + + + align:start position:0% + +so that means if a + + align:start position:0% +so that means if a + + + align:start position:0% +so that means if a +is polynomial time reducible to b and b + + align:start position:0% +is polynomial time reducible to b and b + + + align:start position:0% +is polynomial time reducible to b and b +is in polynomial space then a is also in + + align:start position:0% +is in polynomial space then a is also in + + + align:start position:0% +is in polynomial space then a is also in +polynomial space + + align:start position:0% + + + + align:start position:0% + +but we know + + align:start position:0% +but we know + + + align:start position:0% +but we know +because satisfiability is np-complete + + align:start position:0% +because satisfiability is np-complete + + + align:start position:0% +because satisfiability is np-complete +that every language of np + + align:start position:0% +that every language of np + + + align:start position:0% +that every language of np +is reducible to sat so put sat in place + + align:start position:0% +is reducible to sat so put sat in place + + + align:start position:0% +is reducible to sat so put sat in place +of b every np language is polynomial + + align:start position:0% +of b every np language is polynomial + + + align:start position:0% +of b every np language is polynomial +time reducible to sat + + align:start position:0% +time reducible to sat + + + align:start position:0% +time reducible to sat +and we now know that sat is in p space + + align:start position:0% +and we now know that sat is in p space + + + align:start position:0% +and we now know that sat is in p space +so therefore every language in np is in + + align:start position:0% +so therefore every language in np is in + + + align:start position:0% +so therefore every language in np is in +p space because they're all polynomial + + align:start position:0% +p space because they're all polynomial + + + align:start position:0% +p space because they're all polynomial +time reducible to set + + align:start position:0% + + + + align:start position:0% + +okay so just by using some of the + + align:start position:0% +okay so just by using some of the + + + align:start position:0% +okay so just by using some of the +technology we've developed + + align:start position:0% +technology we've developed + + + align:start position:0% +technology we've developed +namely the notion of completeness sort + + align:start position:0% +namely the notion of completeness sort + + + align:start position:0% +namely the notion of completeness sort +of shows us some of its power that if + + align:start position:0% +of shows us some of its power that if + + + align:start position:0% +of shows us some of its power that if +you want to + + align:start position:0% +you want to + + + align:start position:0% +you want to +conclude something about an entire class + + align:start position:0% +conclude something about an entire class + + + align:start position:0% +conclude something about an entire class +an entire complexity class if you have a + + align:start position:0% +an entire complexity class if you have a + + + align:start position:0% +an entire complexity class if you have a +complete problem for that complexity + + align:start position:0% +complete problem for that complexity + + + align:start position:0% +complete problem for that complexity +class often it's enough just to work + + align:start position:0% +class often it's enough just to work + + + align:start position:0% +class often it's enough just to work +with the complete problem and then + + align:start position:0% +with the complete problem and then + + + align:start position:0% +with the complete problem and then +everything else by virtue of the + + align:start position:0% +everything else by virtue of the + + + align:start position:0% +everything else by virtue of the +reducibility is going to + + align:start position:0% +reducibility is going to + + + align:start position:0% +reducibility is going to +inherit the same property it doesn't + + align:start position:0% +inherit the same property it doesn't + + + align:start position:0% +inherit the same property it doesn't +work in all cases but in many of the + + align:start position:0% +work in all cases but in many of the + + + align:start position:0% +work in all cases but in many of the +cases as long as the um you know the + + align:start position:0% +cases as long as the um you know the + + + align:start position:0% +cases as long as the um you know the +reducibility can be computed by the um + + align:start position:0% +reducibility can be computed by the um + + + align:start position:0% +reducibility can be computed by the um +by the + + align:start position:0% +by the + + + align:start position:0% +by the +the type of procedure you're working + + align:start position:0% +the type of procedure you're working + + + align:start position:0% +the type of procedure you're working +with um then you can then it follows + + align:start position:0% +with um then you can then it follows + + + align:start position:0% +with um then you can then it follows +uh you know you could also prove this + + align:start position:0% +uh you know you could also prove this + + + align:start position:0% +uh you know you could also prove this +more directly i think it's in some ways + + align:start position:0% +more directly i think it's in some ways + + + align:start position:0% +more directly i think it's in some ways +a little clumsy or a little bit um + + align:start position:0% +a little clumsy or a little bit um + + + align:start position:0% +a little clumsy or a little bit um +less elegant but you can say well let me + + align:start position:0% +less elegant but you can say well let me + + + align:start position:0% +less elegant but you can say well let me +just take my + + align:start position:0% +just take my + + + align:start position:0% +just take my +um + + align:start position:0% +um + + + align:start position:0% +um +uh take a language that's in np it has a + + align:start position:0% +uh take a language that's in np it has a + + + align:start position:0% +uh take a language that's in np it has a +non-deterministic polynomial time + + align:start position:0% +non-deterministic polynomial time + + + align:start position:0% +non-deterministic polynomial time +algorithm + + align:start position:0% +algorithm + + + align:start position:0% +algorithm +and then give a deterministic polynomial + + align:start position:0% +and then give a deterministic polynomial + + + align:start position:0% +and then give a deterministic polynomial +space algorithm simulates that + + align:start position:0% +space algorithm simulates that + + + align:start position:0% +space algorithm simulates that +np algorithm just by going through all + + align:start position:0% +np algorithm just by going through all + + + align:start position:0% +np algorithm just by going through all +the different branches but making sure + + align:start position:0% +the different branches but making sure + + + align:start position:0% +the different branches but making sure +that going through all those different + + align:start position:0% +that going through all those different + + + align:start position:0% +that going through all those different +branches you're reusing the space and + + align:start position:0% +branches you're reusing the space and + + + align:start position:0% +branches you're reusing the space and +not using new space every time you're + + align:start position:0% +not using new space every time you're + + + align:start position:0% +not using new space every time you're +going through a different branch and you + + align:start position:0% +going through a different branch and you + + + align:start position:0% +going through a different branch and you +can arrange things if you're just a + + align:start position:0% +can arrange things if you're just a + + + align:start position:0% +can arrange things if you're just a +little bit careful to do it that way so + + align:start position:0% +little bit careful to do it that way so + + + align:start position:0% +little bit careful to do it that way so +you could give a direct simulation in + + align:start position:0% +you could give a direct simulation in + + + align:start position:0% +you could give a direct simulation in +polynomial space of any + + align:start position:0% +polynomial space of any + + + align:start position:0% +polynomial space of any +uh np turing machine so that i mean + + align:start position:0% +uh np turing machine so that i mean + + + align:start position:0% +uh np turing machine so that i mean +that's also completely satisfactory but + + align:start position:0% +that's also completely satisfactory but + + + align:start position:0% +that's also completely satisfactory but +i think this is a little more elegant + + align:start position:0% +i think this is a little more elegant + + + align:start position:0% +i think this is a little more elegant +so now let's also this + + align:start position:0% +so now let's also this + + + align:start position:0% +so now let's also this +furthermore is going to allow us to + + align:start position:0% +furthermore is going to allow us to + + + align:start position:0% +furthermore is going to allow us to +conclude some additional + + align:start position:0% +conclude some additional + + + align:start position:0% +conclude some additional +languages are in p space + + align:start position:0% +languages are in p space + + + align:start position:0% +languages are in p space +let's define a class we have not yet + + align:start position:0% +let's define a class we have not yet + + + align:start position:0% +let's define a class we have not yet +seen though maybe you've seen this i + + align:start position:0% +seen though maybe you've seen this i + + + align:start position:0% +seen though maybe you've seen this i +think we've talked about this this + + align:start position:0% +think we've talked about this this + + + align:start position:0% +think we've talked about this this +notion of uh + + align:start position:0% +notion of uh + + + align:start position:0% +notion of uh +co + + align:start position:0% +co + + + align:start position:0% +co +before um i think we talked about + + align:start position:0% +before um i think we talked about + + + align:start position:0% +before um i think we talked about +co-touring reducib + + align:start position:0% +co-touring reducib + + + align:start position:0% +co-touring reducib +co touring recognizable um so + + align:start position:0% +co touring recognizable um so + + + align:start position:0% +co touring recognizable um so +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the class + + align:start position:0% +the class + + + align:start position:0% +the class +those are the class of languages whose + + align:start position:0% +those are the class of languages whose + + + align:start position:0% +those are the class of languages whose +complements are turning recognizable and + + align:start position:0% +complements are turning recognizable and + + + align:start position:0% +complements are turning recognizable and +the same for co and p + + align:start position:0% +the same for co and p + + + align:start position:0% +the same for co and p +this is the class of languages whose + + align:start position:0% +this is the class of languages whose + + + align:start position:0% +this is the class of languages whose +complements are in np + + align:start position:0% + + + + align:start position:0% + +so you take the complement of every + + align:start position:0% +so you take the complement of every + + + align:start position:0% +so you take the complement of every +language that's in np and now you get + + align:start position:0% +language that's in np and now you get + + + align:start position:0% +language that's in np and now you get +all the languages that are in this class + + align:start position:0% +all the languages that are in this class + + + align:start position:0% +all the languages that are in this class +co np + + align:start position:0% +co np + + + align:start position:0% +co np +complement of np + + align:start position:0% +complement of np + + + align:start position:0% +complement of np +um + + align:start position:0% +um + + + align:start position:0% +um +so for example the complement of the + + align:start position:0% +so for example the complement of the + + + align:start position:0% +so for example the complement of the +hand handpath problem so all the graphs + + align:start position:0% +hand handpath problem so all the graphs + + + align:start position:0% +hand handpath problem so all the graphs +which don't have + + align:start position:0% +which don't have + + + align:start position:0% +which don't have +hamiltonian paths from uh you know + + align:start position:0% +hamiltonian paths from uh you know + + + align:start position:0% +hamiltonian paths from uh you know +esthetic so the the the non-hamiltonian + + align:start position:0% +esthetic so the the the non-hamiltonian + + + align:start position:0% +esthetic so the the the non-hamiltonian +uh graph uh the non-hamiltonian path + + align:start position:0% +uh graph uh the non-hamiltonian path + + + align:start position:0% +uh graph uh the non-hamiltonian path +problem + + align:start position:0% +problem + + + align:start position:0% +problem +that's a cohen p problem + + align:start position:0% +that's a cohen p problem + + + align:start position:0% +that's a cohen p problem +um well here's a language we haven't + + align:start position:0% +um well here's a language we haven't + + + align:start position:0% +um well here's a language we haven't +i'm not going to define + + align:start position:0% +i'm not going to define + + + align:start position:0% +i'm not going to define +uh as in terms of its complement it's a + + align:start position:0% +uh as in terms of its complement it's a + + + align:start position:0% +uh as in terms of its complement it's a +the tautology problem so these are the + + align:start position:0% +the tautology problem so these are the + + + align:start position:0% +the tautology problem so these are the +problem language + + align:start position:0% +problem language + + + align:start position:0% +problem language +these are all formulas or these are the + + align:start position:0% +these are all formulas or these are the + + + align:start position:0% +these are all formulas or these are the +formulas where all assignments satisfy + + align:start position:0% +formulas where all assignments satisfy + + + align:start position:0% +formulas where all assignments satisfy +the formula all assignments make the + + align:start position:0% +the formula all assignments make the + + + align:start position:0% +the formula all assignments make the +formula true + + align:start position:0% +formula true + + + align:start position:0% +formula true +um so a tautology is a statement that's + + align:start position:0% +um so a tautology is a statement that's + + + align:start position:0% +um so a tautology is a statement that's +always true + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +no matter how you plug in the variables + + align:start position:0% +no matter how you plug in the variables + + + align:start position:0% +no matter how you plug in the variables +so + + align:start position:0% +so + + + align:start position:0% +so +the the tautology tautology language is + + align:start position:0% +the the tautology tautology language is + + + align:start position:0% +the the tautology tautology language is +in co-np + + align:start position:0% +in co-np + + + align:start position:0% +in co-np +um because it's complement which is the + + align:start position:0% +um because it's complement which is the + + + align:start position:0% +um because it's complement which is the +non-tautologies those are the + + align:start position:0% +non-tautologies those are the + + + align:start position:0% +non-tautologies those are the +formulas for which + + align:start position:0% +formulas for which + + + align:start position:0% +formulas for which +um there's some assignment which makes + + align:start position:0% +um there's some assignment which makes + + + align:start position:0% +um there's some assignment which makes +it false so that's going to be clearly + + align:start position:0% +it false so that's going to be clearly + + + align:start position:0% +it false so that's going to be clearly +an np language + + align:start position:0% +an np language + + + align:start position:0% +an np language +so tautology is a co and p language + + align:start position:0% +so tautology is a co and p language + + + align:start position:0% +so tautology is a co and p language +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% + + + + align:start position:0% + +now one thing that we + + align:start position:0% +now one thing that we + + + align:start position:0% +now one thing that we +get immediately from the theorem as a + + align:start position:0% +get immediately from the theorem as a + + + align:start position:0% +get immediately from the theorem as a +corollary really should write this as a + + align:start position:0% +corollary really should write this as a + + + align:start position:0% +corollary really should write this as a +corollary is that cohen p + + align:start position:0% +corollary is that cohen p + + + align:start position:0% +corollary is that cohen p +is also a subset of p space + + align:start position:0% +is also a subset of p space + + + align:start position:0% +is also a subset of p space +and the reason for that is and this is + + align:start position:0% +and the reason for that is and this is + + + align:start position:0% +and the reason for that is and this is +something that + + align:start position:0% +something that + + + align:start position:0% +something that +you know it's um + + align:start position:0% +you know it's um + + + align:start position:0% +you know it's um +again + + align:start position:0% +again + + + align:start position:0% +again +easy but make sure you understand it + + align:start position:0% +easy but make sure you understand it + + + align:start position:0% +easy but make sure you understand it +is that + + align:start position:0% +is that + + + align:start position:0% +is that +p space itself is closed under + + align:start position:0% +p space itself is closed under + + + align:start position:0% +p space itself is closed under +complement + + align:start position:0% +complement + + + align:start position:0% +complement +because it is + + align:start position:0% +because it is + + + align:start position:0% +because it is +defined in terms of deterministic + + align:start position:0% +defined in terms of deterministic + + + align:start position:0% +defined in terms of deterministic +machines and deterministic machines you + + align:start position:0% +machines and deterministic machines you + + + align:start position:0% +machines and deterministic machines you +can always flip the answer + + align:start position:0% +can always flip the answer + + + align:start position:0% +can always flip the answer +and get a machine + + align:start position:0% +and get a machine + + + align:start position:0% +and get a machine +of the same type + + align:start position:0% +of the same type + + + align:start position:0% +of the same type +which um + + align:start position:0% +which um + + + align:start position:0% +which um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh will decide the complementary + + align:start position:0% +uh will decide the complementary + + + align:start position:0% +uh will decide the complementary +language + + align:start position:0% +language + + + align:start position:0% +language +so for deterministic machines + + align:start position:0% +so for deterministic machines + + + align:start position:0% +so for deterministic machines +deterministic deciders i should say um + + align:start position:0% +deterministic deciders i should say um + + + align:start position:0% +deterministic deciders i should say um +you can always flip the answer + + align:start position:0% +you can always flip the answer + + + align:start position:0% +you can always flip the answer +um + + align:start position:0% +um + + + align:start position:0% +um +now + + align:start position:0% + + + + align:start position:0% + +so here we have anything that's in p + + align:start position:0% +so here we have anything that's in p + + + align:start position:0% +so here we have anything that's in p +space + + align:start position:0% +space + + + align:start position:0% +space +it has a deterministic polynomial time a + + align:start position:0% +it has a deterministic polynomial time a + + + align:start position:0% +it has a deterministic polynomial time a +polynomial space uh machine and so its + + align:start position:0% +polynomial space uh machine and so its + + + align:start position:0% +polynomial space uh machine and so its +complementary line which is also going + + align:start position:0% +complementary line which is also going + + + align:start position:0% +complementary line which is also going +to be in p space so p space and cos base + + align:start position:0% +to be in p space so p space and cos base + + + align:start position:0% +to be in p space so p space and cos base +p co p space are equal and so that's why + + align:start position:0% +p co p space are equal and so that's why + + + align:start position:0% +p co p space are equal and so that's why +coen p + + align:start position:0% +coen p + + + align:start position:0% +coen p +uh is going to be in p space it's going + + align:start position:0% +uh is going to be in p space it's going + + + align:start position:0% +uh is going to be in p space it's going +to be a subset of p space + + align:start position:0% +to be a subset of p space + + + align:start position:0% +to be a subset of p space +okay i hope that's + + align:start position:0% +okay i hope that's + + + align:start position:0% +okay i hope that's +not getting mixed up by all of the + + align:start position:0% +not getting mixed up by all of the + + + align:start position:0% +not getting mixed up by all of the +different uh + + align:start position:0% +different uh + + + align:start position:0% +different uh +alphabet soup here but um + + align:start position:0% +alphabet soup here but um + + + align:start position:0% +alphabet soup here but um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +here is maybe a picture maybe that'll be + + align:start position:0% +here is maybe a picture maybe that'll be + + + align:start position:0% +here is maybe a picture maybe that'll be +helpful uh of how the world looks for + + align:start position:0% +helpful uh of how the world looks for + + + align:start position:0% +helpful uh of how the world looks for +the time and spice uh complexity classes + + align:start position:0% +the time and spice uh complexity classes + + + align:start position:0% +the time and spice uh complexity classes +um so far + + align:start position:0% +um so far + + + align:start position:0% +um so far +uh so + + align:start position:0% +uh so + + + align:start position:0% +uh so +we have p + + align:start position:0% +we have p + + + align:start position:0% +we have p +is a subset of np it's also a subset of + + align:start position:0% +is a subset of np it's also a subset of + + + align:start position:0% +is a subset of np it's also a subset of +co np + + align:start position:0% +co np + + + align:start position:0% +co np +um + + align:start position:0% +um + + + align:start position:0% +um +again for the same reason that p and co + + align:start position:0% +again for the same reason that p and co + + + align:start position:0% +again for the same reason that p and co +p are equal we never never even really + + align:start position:0% +p are equal we never never even really + + + align:start position:0% +p are equal we never never even really +talk about copy because it's the same as + + align:start position:0% +talk about copy because it's the same as + + + align:start position:0% +talk about copy because it's the same as +p + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +uh but np and cohen p + + align:start position:0% +uh but np and cohen p + + + align:start position:0% +uh but np and cohen p +that those are two classes where we + + align:start position:0% +that those are two classes where we + + + align:start position:0% +that those are two classes where we +don't know whether they're equal or not + + align:start position:0% +don't know whether they're equal or not + + + align:start position:0% +don't know whether they're equal or not +uh because an np machine + + align:start position:0% +uh because an np machine + + + align:start position:0% +uh because an np machine +um + + align:start position:0% +um + + + align:start position:0% +um +you know you can't necessarily + + align:start position:0% +you know you can't necessarily + + + align:start position:0% +you know you can't necessarily +complement the + + align:start position:0% +complement the + + + align:start position:0% +complement the +behavior of an np machine and end up + + align:start position:0% +behavior of an np machine and end up + + + align:start position:0% +behavior of an np machine and end up +with an np machine + + align:start position:0% +with an np machine + + + align:start position:0% +with an np machine +so a question how do we know that cohen + + align:start position:0% +so a question how do we know that cohen + + + align:start position:0% +so a question how do we know that cohen +p is a complete class of problems i + + align:start position:0% +p is a complete class of problems i + + + align:start position:0% +p is a complete class of problems i +didn't say that there's anything about + + align:start position:0% +didn't say that there's anything about + + + align:start position:0% +didn't say that there's anything about +completeness and cohen p is just a + + align:start position:0% +completeness and cohen p is just a + + + align:start position:0% +completeness and cohen p is just a +collection of languages i'm not saying + + align:start position:0% +collection of languages i'm not saying + + + align:start position:0% +collection of languages i'm not saying +it's anything any particular feature + + align:start position:0% +it's anything any particular feature + + + align:start position:0% +it's anything any particular feature +about it in fact it does have a complete + + align:start position:0% +about it in fact it does have a complete + + + align:start position:0% +about it in fact it does have a complete +problem just like np has a complete + + align:start position:0% +problem just like np has a complete + + + align:start position:0% +problem just like np has a complete +complete problem the complements + + align:start position:0% +complete problem the complements + + + align:start position:0% +complete problem the complements +and i'm not going to prove this right + + align:start position:0% +and i'm not going to prove this right + + + align:start position:0% +and i'm not going to prove this right +here but though it's pretty + + align:start position:0% +here but though it's pretty + + + align:start position:0% +here but though it's pretty +straightforward + + align:start position:0% +straightforward + + + align:start position:0% +straightforward +complements of all the np-complete + + align:start position:0% +complements of all the np-complete + + + align:start position:0% +complements of all the np-complete +languages are going to be co-np-complete + + align:start position:0% +languages are going to be co-np-complete + + + align:start position:0% +languages are going to be co-np-complete +languages + + align:start position:0% +languages + + + align:start position:0% +languages +um + + align:start position:0% + + + + align:start position:0% + +and um + + align:start position:0% +and um + + + align:start position:0% +and um +so + + align:start position:0% +so + + + align:start position:0% +so +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so i'm getting so okay so let's + + align:start position:0% +so i'm getting so okay so let's + + + align:start position:0% +so i'm getting so okay so let's +i will answer some of the questions + + align:start position:0% +i will answer some of the questions + + + align:start position:0% +i will answer some of the questions +about or about + + align:start position:0% +about or about + + + align:start position:0% +about or about +possible alternate worlds this is how we + + align:start position:0% +possible alternate worlds this is how we + + + align:start position:0% +possible alternate worlds this is how we +believe the world looks like + + align:start position:0% +believe the world looks like + + + align:start position:0% +believe the world looks like +with each one of these regions being + + align:start position:0% +with each one of these regions being + + + align:start position:0% +with each one of these regions being +separated from one another including + + align:start position:0% +separated from one another including + + + align:start position:0% +separated from one another including +this little + + align:start position:0% +this little + + + align:start position:0% +this little +corner of the world here np and + + align:start position:0% +corner of the world here np and + + + align:start position:0% +corner of the world here np and +intersect co-np which is not um there + + align:start position:0% +intersect co-np which is not um there + + + align:start position:0% +intersect co-np which is not um there +might be languages in here which are not + + align:start position:0% +might be languages in here which are not + + + align:start position:0% +might be languages in here which are not +in p and we actually believe there are + + align:start position:0% +in p and we actually believe there are + + + align:start position:0% +in p and we actually believe there are +such languages but again all of this is + + align:start position:0% +such languages but again all of this is + + + align:start position:0% +such languages but again all of this is +conjectural um and even whether p and p + + align:start position:0% +conjectural um and even whether p and p + + + align:start position:0% +conjectural um and even whether p and p +space are the same or different is an un + + align:start position:0% +space are the same or different is an un + + + align:start position:0% +space are the same or different is an un +is an open question + + align:start position:0% +is an open question + + + align:start position:0% +is an open question +we don't even know the answer to that + + align:start position:0% +we don't even know the answer to that + + + align:start position:0% +we don't even know the answer to that +which is perhaps even more shocking that + + align:start position:0% +which is perhaps even more shocking that + + + align:start position:0% +which is perhaps even more shocking that +we don't know how to solve pnn + + align:start position:0% +we don't know how to solve pnn + + + align:start position:0% +we don't know how to solve pnn +you know proved p different from np that + + align:start position:0% +you know proved p different from np that + + + align:start position:0% +you know proved p different from np that +we don't know how to prove p different + + align:start position:0% +we don't know how to prove p different + + + align:start position:0% +we don't know how to prove p different +from p space which seems to be a much + + align:start position:0% +from p space which seems to be a much + + + align:start position:0% +from p space which seems to be a much +bigger class + + align:start position:0% +bigger class + + + align:start position:0% +bigger class +uh it would be incredible that anything + + align:start position:0% +uh it would be incredible that anything + + + align:start position:0% +uh it would be incredible that anything +you can do with a polynomial amount of + + align:start position:0% +you can do with a polynomial amount of + + + align:start position:0% +you can do with a polynomial amount of +space + + align:start position:0% +space + + + align:start position:0% +space +uh you can also do with a polynomial + + align:start position:0% +uh you can also do with a polynomial + + + align:start position:0% +uh you can also do with a polynomial +amount of time + + align:start position:0% +amount of time + + + align:start position:0% +amount of time +um but + + align:start position:0% +um but + + + align:start position:0% +um but +i don't know how to prove that they're + + align:start position:0% +i don't know how to prove that they're + + + align:start position:0% +i don't know how to prove that they're +different and in fact so this is how the + + align:start position:0% +different and in fact so this is how the + + + align:start position:0% +different and in fact so this is how the +world could look + + align:start position:0% +world could look + + + align:start position:0% +world could look +um + + align:start position:0% + + + + align:start position:0% + +everything could collapse down p could + + align:start position:0% +everything could collapse down p could + + + align:start position:0% +everything could collapse down p could +equal p space + + align:start position:0% +equal p space + + + align:start position:0% +equal p space +and then all of these classes would be + + align:start position:0% +and then all of these classes would be + + + align:start position:0% +and then all of these classes would be +the same + + align:start position:0% +the same + + + align:start position:0% +the same +um + + align:start position:0% +um + + + align:start position:0% +um +and i should also mention i don't have + + align:start position:0% +and i should also mention i don't have + + + align:start position:0% +and i should also mention i don't have +this as another diagram here but just to + + align:start position:0% +this as another diagram here but just to + + + align:start position:0% +this as another diagram here but just to +answer + + align:start position:0% +answer + + + align:start position:0% +answer +you know there's also another pos + + align:start position:0% +you know there's also another pos + + + align:start position:0% +you know there's also another pos +there's other possibilities for example + + align:start position:0% +there's other possibilities for example + + + align:start position:0% +there's other possibilities for example +um + + align:start position:0% +um + + + align:start position:0% +um +p could equal np + + align:start position:0% +p could equal np + + + align:start position:0% +p could equal np +without it being equal to p space + + align:start position:0% +without it being equal to p space + + + align:start position:0% +without it being equal to p space +and then you'd have a different looking + + align:start position:0% +and then you'd have a different looking + + + align:start position:0% +and then you'd have a different looking +venn diagram here where there'd be just + + align:start position:0% +venn diagram here where there'd be just + + + align:start position:0% +venn diagram here where there'd be just +two classes p np and co np would all be + + align:start position:0% +two classes p np and co np would all be + + + align:start position:0% +two classes p np and co np would all be +the same p space would be different + + align:start position:0% +the same p space would be different + + + align:start position:0% +the same p space would be different +that's possible + + align:start position:0% +that's possible + + + align:start position:0% +that's possible +at least we have no idea + + align:start position:0% +at least we have no idea + + + align:start position:0% +at least we have no idea +uh had a head of m + + align:start position:0% +uh had a head of m + + + align:start position:0% +uh had a head of m +a a lot of these things can collapse in + + align:start position:0% +a a lot of these things can collapse in + + + align:start position:0% +a a lot of these things can collapse in +in various ways + + align:start position:0% +in various ways + + + align:start position:0% +in various ways +um and you just have to make sure that + + align:start position:0% +um and you just have to make sure that + + + align:start position:0% +um and you just have to make sure that +you you know there are some collapses + + align:start position:0% +you you know there are some collapses + + + align:start position:0% +you you know there are some collapses +that obviously could not uh occur like p + + align:start position:0% +that obviously could not uh occur like p + + + align:start position:0% +that obviously could not uh occur like p +if p equals np it's also going to equal + + align:start position:0% +if p equals np it's also going to equal + + + align:start position:0% +if p equals np it's also going to equal +cohen p + + align:start position:0% +cohen p + + + align:start position:0% +cohen p +um so you can't get some there are + + align:start position:0% +um so you can't get some there are + + + align:start position:0% +um so you can't get some there are +obviously some crazy collapses which + + align:start position:0% +obviously some crazy collapses which + + + align:start position:0% +obviously some crazy collapses which +could not + + align:start position:0% +could not + + + align:start position:0% +could not +uh happen that p collapsing p and np + + align:start position:0% +uh happen that p collapsing p and np + + + align:start position:0% +uh happen that p collapsing p and np +being the same but different from cohen + + align:start position:0% +being the same but different from cohen + + + align:start position:0% +being the same but different from cohen +b that can't happen + + align:start position:0% +b that can't happen + + + align:start position:0% +b that can't happen +but um + + align:start position:0% + + + + align:start position:0% + +avoiding some obvious contradictory + + align:start position:0% +avoiding some obvious contradictory + + + align:start position:0% +avoiding some obvious contradictory +situations everything else is possible + + align:start position:0% +situations everything else is possible + + + align:start position:0% +situations everything else is possible +so somebody said so well here's a + + align:start position:0% +so somebody said so well here's a + + + align:start position:0% +so somebody said so well here's a +question let me just answer a few of + + align:start position:0% +question let me just answer a few of + + + align:start position:0% +question let me just answer a few of +these + + align:start position:0% +these + + + align:start position:0% +these +did we use the completeness of co np to + + align:start position:0% +did we use the completeness of co np to + + + align:start position:0% +did we use the completeness of co np to +show that cohen p is + + align:start position:0% +show that cohen p is + + + align:start position:0% +show that cohen p is +a subset of co-p space no we didn't do + + align:start position:0% +a subset of co-p space no we didn't do + + + align:start position:0% +a subset of co-p space no we didn't do +it that way + + align:start position:0% + + + + align:start position:0% + +we showed that uh co-np + + align:start position:0% +we showed that uh co-np + + + align:start position:0% +we showed that uh co-np +um + + align:start position:0% +um + + + align:start position:0% +um +uh + + align:start position:0% + + + + align:start position:0% + +well let's see didn't we is that fair um + + align:start position:0% + + + + align:start position:0% + +well i i suppose you know np of subset + + align:start position:0% +well i i suppose you know np of subset + + + align:start position:0% +well i i suppose you know np of subset +of p space immediately implies because + + align:start position:0% +of p space immediately implies because + + + align:start position:0% +of p space immediately implies because +he's complementing both sides that cohen + + align:start position:0% +he's complementing both sides that cohen + + + align:start position:0% +he's complementing both sides that cohen +p is a subset of copy space + + align:start position:0% +p is a subset of copy space + + + align:start position:0% +p is a subset of copy space +so you don't have to deal with + + align:start position:0% +so you don't have to deal with + + + align:start position:0% +so you don't have to deal with +the complete problems on the other side + + align:start position:0% +the complete problems on the other side + + + align:start position:0% +the complete problems on the other side +that's too complicated to get into here + + align:start position:0% +that's too complicated to get into here + + + align:start position:0% +that's too complicated to get into here +but you don't you don't need to talk + + align:start position:0% +but you don't you don't need to talk + + + align:start position:0% +but you don't you don't need to talk +about + + align:start position:0% +about + + + align:start position:0% +about +co-empty complete problems um though + + align:start position:0% +co-empty complete problems um though + + + align:start position:0% +co-empty complete problems um though +again those are very simple to to get + + align:start position:0% +again those are very simple to to get + + + align:start position:0% +again those are very simple to to get +from np complete problems + + align:start position:0% +from np complete problems + + + align:start position:0% +from np complete problems +um + + align:start position:0% +um + + + align:start position:0% +um +let's see what else is here + + align:start position:0% +let's see what else is here + + + align:start position:0% +let's see what else is here +uh + + align:start position:0% +uh + + + align:start position:0% +uh +are there np complete problems that are + + align:start position:0% +are there np complete problems that are + + + align:start position:0% +are there np complete problems that are +in co-np + + align:start position:0% +in co-np + + + align:start position:0% +in co-np +so the answer to that is no + + align:start position:0% +so the answer to that is no + + + align:start position:0% +so the answer to that is no +not as far as well i mean there would be + + align:start position:0% +not as far as well i mean there would be + + + align:start position:0% +not as far as well i mean there would be +if there was an np complete problem in + + align:start position:0% +if there was an np complete problem in + + + align:start position:0% +if there was an np complete problem in +co-np then all of np would be in cohen p + + align:start position:0% +co-np then all of np would be in cohen p + + + align:start position:0% +co-np then all of np would be in cohen p +and they would be equal + + align:start position:0% +and they would be equal + + + align:start position:0% +and they would be equal +so we suspect the np complete problems + + align:start position:0% +so we suspect the np complete problems + + + align:start position:0% +so we suspect the np complete problems +are not in co and p but don't know how + + align:start position:0% +are not in co and p but don't know how + + + align:start position:0% +are not in co and p but don't know how +to prove that + + align:start position:0% + + + + align:start position:0% + +so why is tautology + + align:start position:0% +so why is tautology + + + align:start position:0% +so why is tautology +in cohen p so here is tautology sits in + + align:start position:0% +in cohen p so here is tautology sits in + + + align:start position:0% +in cohen p so here is tautology sits in +this class here the reason is that its + + align:start position:0% +this class here the reason is that its + + + align:start position:0% +this class here the reason is that its +complementary language is an np the + + align:start position:0% +complementary language is an np the + + + align:start position:0% +complementary language is an np the +complement of tautology + + align:start position:0% +complement of tautology + + + align:start position:0% +complement of tautology +are the languages where there is some + + align:start position:0% +are the languages where there is some + + + align:start position:0% +are the languages where there is some +assignment + + align:start position:0% +assignment + + + align:start position:0% +assignment +which makes the formula false + + align:start position:0% +which makes the formula false + + + align:start position:0% +which makes the formula false +so with a with an np machine you can + + align:start position:0% +so with a with an np machine you can + + + align:start position:0% +so with a with an np machine you can +just guess that assignment and check + + align:start position:0% +just guess that assignment and check + + + align:start position:0% +just guess that assignment and check +that it makes the formula false + + align:start position:0% +that it makes the formula false + + + align:start position:0% +that it makes the formula false +so the complement of tautology + + align:start position:0% +so the complement of tautology + + + align:start position:0% +so the complement of tautology +is an np language and so tautology is a + + align:start position:0% +is an np language and so tautology is a + + + align:start position:0% +is an np language and so tautology is a +co-np language + + align:start position:0% +co-np language + + + align:start position:0% +co-np language +um + + align:start position:0% + + + + align:start position:0% + +okay uh + + align:start position:0% +okay uh + + + align:start position:0% +okay uh +so somebody's asking about p space and + + align:start position:0% +so somebody's asking about p space and + + + align:start position:0% +so somebody's asking about p space and +np-space and how do those relate to one + + align:start position:0% +np-space and how do those relate to one + + + align:start position:0% +np-space and how do those relate to one +another so that's looking ahead um to + + align:start position:0% +another so that's looking ahead um to + + + align:start position:0% +another so that's looking ahead um to +what we're going to be doing next week + + align:start position:0% +what we're going to be doing next week + + + align:start position:0% +what we're going to be doing next week +but i'll give you a preview + + align:start position:0% + + + + align:start position:0% + +an old but at the time surprising + + align:start position:0% +an old but at the time surprising + + + align:start position:0% +an old but at the time surprising +theorem was that + + align:start position:0% +theorem was that + + + align:start position:0% +theorem was that +piece base and np space actually are + + align:start position:0% +piece base and np space actually are + + + align:start position:0% +piece base and np space actually are +equal + + align:start position:0% +equal + + + align:start position:0% +equal +so there this analogy with time breaks + + align:start position:0% +so there this analogy with time breaks + + + align:start position:0% +so there this analogy with time breaks +down + + align:start position:0% +down + + + align:start position:0% +down +so polynomial space and + + align:start position:0% +so polynomial space and + + + align:start position:0% +so polynomial space and +non-deterministic polynomial space do + + align:start position:0% +non-deterministic polynomial space do + + + align:start position:0% +non-deterministic polynomial space do +turn out to be equal + + align:start position:0% +turn out to be equal + + + align:start position:0% +turn out to be equal +the most obvious way of proving of + + align:start position:0% +the most obvious way of proving of + + + align:start position:0% +the most obvious way of proving of +trying to simulate an np an np space + + align:start position:0% +trying to simulate an np an np space + + + align:start position:0% +trying to simulate an np an np space +machine would be give you an exponential + + align:start position:0% +machine would be give you an exponential + + + align:start position:0% +machine would be give you an exponential +deterministic space algorithm uh so + + align:start position:0% +deterministic space algorithm uh so + + + align:start position:0% +deterministic space algorithm uh so +we'll go through that but there is an + + align:start position:0% +we'll go through that but there is an + + + align:start position:0% +we'll go through that but there is an +algorithm which + + align:start position:0% +algorithm which + + + align:start position:0% +algorithm which +collapses + + align:start position:0% +collapses + + + align:start position:0% +collapses +non-deterministic polynomial space down + + align:start position:0% +non-deterministic polynomial space down + + + align:start position:0% +non-deterministic polynomial space down +to deterministic polynomial space which + + align:start position:0% +to deterministic polynomial space which + + + align:start position:0% +to deterministic polynomial space which +again at the time was kind of surprising + + align:start position:0% +again at the time was kind of surprising + + + align:start position:0% +again at the time was kind of surprising +uh + + align:start position:0% + + + + align:start position:0% + +and so last question i'll take here is + + align:start position:0% +and so last question i'll take here is + + + align:start position:0% +and so last question i'll take here is +there some equivalent concept to the + + align:start position:0% +there some equivalent concept to the + + + align:start position:0% +there some equivalent concept to the +idea of a certificate for co-np + + align:start position:0% +idea of a certificate for co-np + + + align:start position:0% +idea of a certificate for co-np +yes there is a notion of a certificate + + align:start position:0% +yes there is a notion of a certificate + + + align:start position:0% +yes there is a notion of a certificate +but now it's going to be a certificate + + align:start position:0% +but now it's going to be a certificate + + + align:start position:0% +but now it's going to be a certificate +that you're not in the language instead + + align:start position:0% +that you're not in the language instead + + + align:start position:0% +that you're not in the language instead +of a certificate that you're in the + + align:start position:0% +of a certificate that you're in the + + + align:start position:0% +of a certificate that you're in the +language + + align:start position:0% +language + + + align:start position:0% +language +and then again works for the very same + + align:start position:0% +and then again works for the very same + + + align:start position:0% +and then again works for the very same +reason that we had certificates for np + + align:start position:0% +reason that we had certificates for np + + + align:start position:0% +reason that we had certificates for np +languages where you had certificate for + + align:start position:0% +languages where you had certificate for + + + align:start position:0% +languages where you had certificate for +membership for cohenp you have a + + align:start position:0% +membership for cohenp you have a + + + align:start position:0% +membership for cohenp you have a +certificate for non-membership i don't + + align:start position:0% +certificate for non-membership i don't + + + align:start position:0% +certificate for non-membership i don't +know if there's no other certificate for + + align:start position:0% +know if there's no other certificate for + + + align:start position:0% +know if there's no other certificate for +membership in co mp + + align:start position:0% +membership in co mp + + + align:start position:0% +membership in co mp +um okay so let's move on + + align:start position:0% +um okay so let's move on + + + align:start position:0% +um okay so let's move on +um + + align:start position:0% + + + + align:start position:0% + +okay so now we're going to introduce + + align:start position:0% +okay so now we're going to introduce + + + align:start position:0% +okay so now we're going to introduce +we're going to look at some important + + align:start position:0% +we're going to look at some important + + + align:start position:0% +we're going to look at some important +examples these are examples that we're + + align:start position:0% +examples these are examples that we're + + + align:start position:0% +examples these are examples that we're +going to um i'm going to give you two + + align:start position:0% +going to um i'm going to give you two + + + align:start position:0% +going to um i'm going to give you two +examples first one called tqbf + + align:start position:0% +examples first one called tqbf + + + align:start position:0% +examples first one called tqbf +and then we're going to have a second + + align:start position:0% +and then we're going to have a second + + + align:start position:0% +and then we're going to have a second +example both of those + + align:start position:0% +example both of those + + + align:start position:0% +example both of those +we're going to + + align:start position:0% +we're going to + + + align:start position:0% +we're going to +one of them is going to be an example of + + align:start position:0% +one of them is going to be an example of + + + align:start position:0% +one of them is going to be an example of +a problem in + + align:start position:0% +a problem in + + + align:start position:0% +a problem in +p space the other one is going to be an + + align:start position:0% +p space the other one is going to be an + + + align:start position:0% +p space the other one is going to be an +example of a problem in np space um and + + align:start position:0% +example of a problem in np space um and + + + align:start position:0% +example of a problem in np space um and +it's these are going to be important + + align:start position:0% +it's these are going to be important + + + align:start position:0% +it's these are going to be important +languages for us so they're not just + + align:start position:0% +languages for us so they're not just + + + align:start position:0% +languages for us so they're not just +going to serve as examples for today but + + align:start position:0% +going to serve as examples for today but + + + align:start position:0% +going to serve as examples for today but +you know um they're going to be + + align:start position:0% +you know um they're going to be + + + align:start position:0% +you know um they're going to be +useful languages for us later on so just + + align:start position:0% +useful languages for us later on so just + + + align:start position:0% +useful languages for us later on so just +keep that in mind as we're going through + + align:start position:0% +keep that in mind as we're going through + + + align:start position:0% +keep that in mind as we're going through +going through it + + align:start position:0% +going through it + + + align:start position:0% +going through it +so + + align:start position:0% +so + + + align:start position:0% +so +to understand tqbf you have to + + align:start position:0% +to understand tqbf you have to + + + align:start position:0% +to understand tqbf you have to +understand um + + align:start position:0% +understand um + + + align:start position:0% +understand um +what are called quantified boolean + + align:start position:0% +what are called quantified boolean + + + align:start position:0% +what are called quantified boolean +formulas + + align:start position:0% +formulas + + + align:start position:0% +formulas +or qbfs + + align:start position:0% + + + + align:start position:0% + +so those are boolean formulas just like + + align:start position:0% +so those are boolean formulas just like + + + align:start position:0% +so those are boolean formulas just like +the ones we've been seeing we've been + + align:start position:0% +the ones we've been seeing we've been + + + align:start position:0% +the ones we've been seeing we've been +talking about with boolean variables and + + align:start position:0% +talking about with boolean variables and + + + align:start position:0% +talking about with boolean variables and +the ands ors and and negated variables + + align:start position:0% +the ands ors and and negated variables + + + align:start position:0% +the ands ors and and negated variables +um but now you're going to add + + align:start position:0% +um but now you're going to add + + + align:start position:0% +um but now you're going to add +quantifiers + + align:start position:0% +quantifiers + + + align:start position:0% +quantifiers +exist quantifiers for all quantifiers + + align:start position:0% +exist quantifiers for all quantifiers + + + align:start position:0% +exist quantifiers for all quantifiers +if you haven't seen quantifiers you you + + align:start position:0% +if you haven't seen quantifiers you you + + + align:start position:0% +if you haven't seen quantifiers you you +need to go back and re you know review + + align:start position:0% +need to go back and re you know review + + + align:start position:0% +need to go back and re you know review +those um + + align:start position:0% +those um + + + align:start position:0% +those um +you know i think that we already kind of + + align:start position:0% +you know i think that we already kind of + + + align:start position:0% +you know i think that we already kind of +introduced talked about them briefly + + align:start position:0% +introduced talked about them briefly + + + align:start position:0% +introduced talked about them briefly +earlier in the in the term + + align:start position:0% +earlier in the in the term + + + align:start position:0% +earlier in the in the term +but um + + align:start position:0% +but um + + + align:start position:0% +but um +this is part of the basic math that you + + align:start position:0% +this is part of the basic math that you + + + align:start position:0% +this is part of the basic math that you +need to know + + align:start position:0% + + + + align:start position:0% + +maybe you'll + + align:start position:0% +maybe you'll + + + align:start position:0% +maybe you'll +not comfortable with them you'll + + align:start position:0% +not comfortable with them you'll + + + align:start position:0% +not comfortable with them you'll +pick it up somewhat during the course of + + align:start position:0% +pick it up somewhat during the course of + + + align:start position:0% +pick it up somewhat during the course of +the today's and the next few lectures + + align:start position:0% +the today's and the next few lectures + + + align:start position:0% +the today's and the next few lectures +but anyway + + align:start position:0% +but anyway + + + align:start position:0% +but anyway +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so if you have a boolean formula formula + + align:start position:0% +so if you have a boolean formula formula + + + align:start position:0% +so if you have a boolean formula formula +i'll give you some examples that has + + align:start position:0% +i'll give you some examples that has + + + align:start position:0% +i'll give you some examples that has +exist and for all quantifiers one of the + + align:start position:0% +exist and for all quantifiers one of the + + + align:start position:0% +exist and for all quantifiers one of the +requirement for it to be a qbf is that + + align:start position:0% +requirement for it to be a qbf is that + + + align:start position:0% +requirement for it to be a qbf is that +all of the variables have to be + + align:start position:0% +all of the variables have to be + + + align:start position:0% +all of the variables have to be +within the scope of one of the + + align:start position:0% +within the scope of one of the + + + align:start position:0% +within the scope of one of the +quantifiers + + align:start position:0% +quantifiers + + + align:start position:0% +quantifiers +so you + + align:start position:0% +so you + + + align:start position:0% +so you +all of the variables of the formula have + + align:start position:0% +all of the variables of the formula have + + + align:start position:0% +all of the variables of the formula have +to be quantified + + align:start position:0% +to be quantified + + + align:start position:0% +to be quantified +by one of the quantifiers and the we're + + align:start position:0% +by one of the quantifiers and the we're + + + align:start position:0% +by one of the quantifiers and the we're +going to assume the quantifiers are in + + align:start position:0% +going to assume the quantifiers are in + + + align:start position:0% +going to assume the quantifiers are in +front are sort of leading quantifiers in + + align:start position:0% +front are sort of leading quantifiers in + + + align:start position:0% +front are sort of leading quantifiers in +front of the rest of the uh + + align:start position:0% +front of the rest of the uh + + + align:start position:0% +front of the rest of the uh +of the of the rest of the expression + + align:start position:0% + + + + align:start position:0% + +so because all of the variables have + + align:start position:0% +so because all of the variables have + + + align:start position:0% +so because all of the variables have +been quantified + + align:start position:0% +been quantified + + + align:start position:0% +been quantified +then a quantified boolean formula is + + align:start position:0% +then a quantified boolean formula is + + + align:start position:0% +then a quantified boolean formula is +going to be either true or false + + align:start position:0% +going to be either true or false + + + align:start position:0% +going to be either true or false +following the meaning of the quantifiers + + align:start position:0% +following the meaning of the quantifiers + + + align:start position:0% +following the meaning of the quantifiers +um and again some of this may become + + align:start position:0% +um and again some of this may become + + + align:start position:0% +um and again some of this may become +clear as we do some examples uh + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so here are some examples coming + + align:start position:0% +so here are some examples coming + + + align:start position:0% +so here are some examples coming +so here is one + + align:start position:0% +so here is one + + + align:start position:0% +so here is one +here is a qbf + + align:start position:0% +here is a qbf + + + align:start position:0% +here is a qbf +so all of the variables the which are + + align:start position:0% +so all of the variables the which are + + + align:start position:0% +so all of the variables the which are +just x and y they both appear in front + + align:start position:0% +just x and y they both appear in front + + + align:start position:0% +just x and y they both appear in front +of + + align:start position:0% +of + + + align:start position:0% +of +uh next to some quantifier so that's + + align:start position:0% +uh next to some quantifier so that's + + + align:start position:0% +uh next to some quantifier so that's +going to be that's a requirement uh if + + align:start position:0% +going to be that's a requirement uh if + + + align:start position:0% +going to be that's a requirement uh if +we have a + + align:start position:0% +we have a + + + align:start position:0% +we have a +qbf + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +so this says for all x there exists a y + + align:start position:0% +so this says for all x there exists a y + + + align:start position:0% +so this says for all x there exists a y +this expression + + align:start position:0% +this expression + + + align:start position:0% +this expression +holds + + align:start position:0% +holds + + + align:start position:0% +holds +so + + align:start position:0% +so + + + align:start position:0% +so +we need to kind of unpack that and + + align:start position:0% +we need to kind of unpack that and + + + align:start position:0% +we need to kind of unpack that and +understand what it means it says for + + align:start position:0% +understand what it means it says for + + + align:start position:0% +understand what it means it says for +every x + + align:start position:0% +every x + + + align:start position:0% +every x +for every for every way of assigning + + align:start position:0% +for every for every way of assigning + + + align:start position:0% +for every for every way of assigning +a boolean value to x so + + align:start position:0% +a boolean value to x so + + + align:start position:0% +a boolean value to x so +uh x is going to be either true or false + + align:start position:0% +uh x is going to be either true or false + + + align:start position:0% +uh x is going to be either true or false +there exists a way of assigning a + + align:start position:0% +there exists a way of assigning a + + + align:start position:0% +there exists a way of assigning a +boolean value for y to make this true + + align:start position:0% +boolean value for y to make this true + + + align:start position:0% +boolean value for y to make this true +determined to to make the rest of the + + align:start position:0% +determined to to make the rest of the + + + align:start position:0% +determined to to make the rest of the +expression hold true + + align:start position:0% +expression hold true + + + align:start position:0% +expression hold true +um and + + align:start position:0% +um and + + + align:start position:0% +um and +we'll go through that but + + align:start position:0% +we'll go through that but + + + align:start position:0% +we'll go through that but +let's let's uh contrast + + align:start position:0% +let's let's uh contrast + + + align:start position:0% +let's let's uh contrast +that with the second example where i + + align:start position:0% +that with the second example where i + + + align:start position:0% +that with the second example where i +invert the order of the quantifiers + + align:start position:0% +invert the order of the quantifiers + + + align:start position:0% +invert the order of the quantifiers +because that's going to be important + + align:start position:0% + + + + align:start position:0% + +for the meaning of the formula + + align:start position:0% + + + + align:start position:0% + +so if i say for every x there is a y + + align:start position:0% +so if i say for every x there is a y + + + align:start position:0% +so if i say for every x there is a y +which makes this the rest of it true + + align:start position:0% +which makes this the rest of it true + + + align:start position:0% +which makes this the rest of it true +that says well no matter how i set x + + align:start position:0% +that says well no matter how i set x + + + align:start position:0% +that says well no matter how i set x +there's going to be a way to set y to + + align:start position:0% +there's going to be a way to set y to + + + align:start position:0% +there's going to be a way to set y to +make this true so that says well if i + + align:start position:0% +make this true so that says well if i + + + align:start position:0% +make this true so that says well if i +set x to true + + align:start position:0% +set x to true + + + align:start position:0% +set x to true +it's got to be some way to set y to make + + align:start position:0% +it's got to be some way to set y to make + + + align:start position:0% +it's got to be some way to set y to make +to make the the the remaining expression + + align:start position:0% +to make the the the remaining expression + + + align:start position:0% +to make the the the remaining expression +hold + + align:start position:0% +hold + + + align:start position:0% +hold +um so if i said x to true what should i + + align:start position:0% +um so if i said x to true what should i + + + align:start position:0% +um so if i said x to true what should i +set y to be + + align:start position:0% +set y to be + + + align:start position:0% +set y to be +um + + align:start position:0% +um + + + align:start position:0% +um +well + + align:start position:0% +well + + + align:start position:0% +well +uh + + align:start position:0% +uh + + + align:start position:0% +uh +if i said x to be true and maybe i said + + align:start position:0% +if i said x to be true and maybe i said + + + align:start position:0% +if i said x to be true and maybe i said +y to be true + + align:start position:0% +y to be true + + + align:start position:0% +y to be true +well then this this clause is uh + + align:start position:0% +well then this this clause is uh + + + align:start position:0% +well then this this clause is uh +satisfied but this clause won't be + + align:start position:0% +satisfied but this clause won't be + + + align:start position:0% +satisfied but this clause won't be +satisfied so setting y to be true is not + + align:start position:0% +satisfied so setting y to be true is not + + + align:start position:0% +satisfied so setting y to be true is not +it won't work but for every x i'm + + align:start position:0% +it won't work but for every x i'm + + + align:start position:0% +it won't work but for every x i'm +only need to show there exists some y so + + align:start position:0% +only need to show there exists some y so + + + align:start position:0% +only need to show there exists some y so +if i pick x to be true i can say y to be + + align:start position:0% +if i pick x to be true i can say y to be + + + align:start position:0% +if i pick x to be true i can say y to be +false + + align:start position:0% +false + + + align:start position:0% +false +um + + align:start position:0% +um + + + align:start position:0% +um +and now this one is this one holds and + + align:start position:0% +and now this one is this one holds and + + + align:start position:0% +and now this one is this one holds and +this one holds and the formula holds but + + align:start position:0% +this one holds and the formula holds but + + + align:start position:0% +this one holds and the formula holds but +i have to make sure that that's going to + + align:start position:0% +i have to make sure that that's going to + + + align:start position:0% +i have to make sure that that's going to +be the case for both settings of x + + align:start position:0% +be the case for both settings of x + + + align:start position:0% +be the case for both settings of x +because + + align:start position:0% +because + + + align:start position:0% +because +i'm saying for all x so if i said x not + + align:start position:0% +i'm saying for all x so if i said x not + + + align:start position:0% +i'm saying for all x so if i said x not +a false because i already showed that it + + align:start position:0% +a false because i already showed that it + + + align:start position:0% +a false because i already showed that it +works for x equal to true if i set x to + + align:start position:0% +works for x equal to true if i set x to + + + align:start position:0% +works for x equal to true if i set x to +false if i set now y to be true + + align:start position:0% +false if i set now y to be true + + + align:start position:0% +false if i set now y to be true +this is going to hold + + align:start position:0% +this is going to hold + + + align:start position:0% +this is going to hold +so this + + align:start position:0% +so this + + + align:start position:0% +so this +expression is true + + align:start position:0% +expression is true + + + align:start position:0% +expression is true +because it is the case that for every + + align:start position:0% +because it is the case that for every + + + align:start position:0% +because it is the case that for every +way to set x there is a way to set y + + align:start position:0% +way to set x there is a way to set y + + + align:start position:0% +way to set x there is a way to set y +so this part holds + + align:start position:0% +so this part holds + + + align:start position:0% +so this part holds +let's look at let's compare that with + + align:start position:0% +let's look at let's compare that with + + + align:start position:0% +let's look at let's compare that with +this case + + align:start position:0% +this case + + + align:start position:0% +this case +is there some way to set y + + align:start position:0% +is there some way to set y + + + align:start position:0% +is there some way to set y +such that no matter how i said x + + align:start position:0% +such that no matter how i said x + + + align:start position:0% +such that no matter how i said x +this is going to hold + + align:start position:0% +this is going to hold + + + align:start position:0% +this is going to hold +and that's not going to be true no + + align:start position:0% +and that's not going to be true no + + + align:start position:0% +and that's not going to be true no +matter what you pick for y + + align:start position:0% +matter what you pick for y + + + align:start position:0% +matter what you pick for y +um there is going to be some way to set + + align:start position:0% +um there is going to be some way to set + + + align:start position:0% +um there is going to be some way to set +x to make this false + + align:start position:0% +x to make this false + + + align:start position:0% +x to make this false +so does it resist a y such that every x + + align:start position:0% +so does it resist a y such that every x + + + align:start position:0% +so does it resist a y such that every x +makes us true no + + align:start position:0% +makes us true no + + + align:start position:0% +makes us true no +if you try x equal to true it's not + + align:start position:0% +if you try x equal to true it's not + + + align:start position:0% +if you try x equal to true it's not +going to work if you try x equal to + + align:start position:0% +going to work if you try x equal to + + + align:start position:0% +going to work if you try x equal to +false it's not going to work + + align:start position:0% +false it's not going to work + + + align:start position:0% +false it's not going to work +so this + + align:start position:0% +so this + + + align:start position:0% +so this +second fi2 + + align:start position:0% +second fi2 + + + align:start position:0% +second fi2 +expression quantified qbf is false + + align:start position:0% +expression quantified qbf is false + + + align:start position:0% +expression quantified qbf is false +okay + + align:start position:0% +okay + + + align:start position:0% +okay +we're going to be playing with these a + + align:start position:0% +we're going to be playing with these a + + + align:start position:0% +we're going to be playing with these a +lot + + align:start position:0% +lot + + + align:start position:0% +lot +so it's important to understand + + align:start position:0% +so it's important to understand + + + align:start position:0% +so it's important to understand +how this + + align:start position:0% +how this + + + align:start position:0% +how this +this quantification works + + align:start position:0% +this quantification works + + + align:start position:0% +this quantification works +um + + align:start position:0% +um + + + align:start position:0% +um +so tqbf + + align:start position:0% +so tqbf + + + align:start position:0% +so tqbf +is the problem of testing + + align:start position:0% +is the problem of testing + + + align:start position:0% +is the problem of testing +whether one of these qbfs is true + + align:start position:0% +whether one of these qbfs is true + + + align:start position:0% +whether one of these qbfs is true +or + + align:start position:0% +or + + + align:start position:0% +or +phrased as a language it's the + + align:start position:0% +phrased as a language it's the + + + align:start position:0% +phrased as a language it's the +collection of true qb + + align:start position:0% +collection of true qb + + + align:start position:0% +collection of true qb +true qbfs and that's where we get the um + + align:start position:0% +true qbfs and that's where we get the um + + + align:start position:0% +true qbfs and that's where we get the um +uh the uh acronym tqbf not acronym the + + align:start position:0% +uh the uh acronym tqbf not acronym the + + + align:start position:0% +uh the uh acronym tqbf not acronym the +the the abbreviation tqbf for the true + + align:start position:0% +the the abbreviation tqbf for the true + + + align:start position:0% +the the abbreviation tqbf for the true +quantified boolean formulas + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +going back to that example p1 is a true + + align:start position:0% +going back to that example p1 is a true + + + align:start position:0% +going back to that example p1 is a true +quantified boolean formula and v2 is not + + align:start position:0% +quantified boolean formula and v2 is not + + + align:start position:0% +quantified boolean formula and v2 is not +a true quantified building formula so + + align:start position:0% +a true quantified building formula so + + + align:start position:0% +a true quantified building formula so +that's why + + align:start position:0% +that's why + + + align:start position:0% +that's why +p1 is in the language v2 is not in the + + align:start position:0% +p1 is in the language v2 is not in the + + + align:start position:0% +p1 is in the language v2 is not in the +language + + align:start position:0% + + + + align:start position:0% + +now our computational problem is to test + + align:start position:0% +now our computational problem is to test + + + align:start position:0% +now our computational problem is to test +whether + + align:start position:0% +whether + + + align:start position:0% +whether +quantified boolean formulas are true or + + align:start position:0% +quantified boolean formulas are true or + + + align:start position:0% +quantified boolean formulas are true or +not + + align:start position:0% +not + + + align:start position:0% +not +and now we can do in polynomial space + + align:start position:0% +and now we can do in polynomial space + + + align:start position:0% +and now we can do in polynomial space +oh there's a check in first + + align:start position:0% + + + + align:start position:0% + +i claim that sat is a special case of + + align:start position:0% +i claim that sat is a special case of + + + align:start position:0% +i claim that sat is a special case of +tqbf + + align:start position:0% + + + + align:start position:0% + +why is that + + align:start position:0% +why is that + + + align:start position:0% +why is that +how can we + + align:start position:0% +how can we + + + align:start position:0% +how can we +um + + align:start position:0% +um + + + align:start position:0% +um +think of sat + + align:start position:0% +think of sat + + + align:start position:0% +think of sat +as a special case if i give you a sat + + align:start position:0% +as a special case if i give you a sat + + + align:start position:0% +as a special case if i give you a sat +formula + + align:start position:0% +formula + + + align:start position:0% +formula +how can i see that as also a tqbf + + align:start position:0% +how can i see that as also a tqbf + + + align:start position:0% +how can i see that as also a tqbf +problem if you want to test if that + + align:start position:0% +problem if you want to test if that + + + align:start position:0% +problem if you want to test if that +formula is + + align:start position:0% +formula is + + + align:start position:0% +formula is +true what would you say remove all the + + align:start position:0% +true what would you say remove all the + + + align:start position:0% +true what would you say remove all the +quantifiers + + align:start position:0% +quantifiers + + + align:start position:0% +quantifiers +or add some quantifiers and what kind of + + align:start position:0% +or add some quantifiers and what kind of + + + align:start position:0% +or add some quantifiers and what kind of +quantifiers maybe um + + align:start position:0% + + + + align:start position:0% + +uh how is sat + + align:start position:0% +uh how is sat + + + align:start position:0% +uh how is sat +just testing a formula satisfiable + + align:start position:0% +just testing a formula satisfiable + + + align:start position:0% +just testing a formula satisfiable +a special case of this + + align:start position:0% +a special case of this + + + align:start position:0% +a special case of this +what i claim is a more general problem + + align:start position:0% +what i claim is a more general problem + + + align:start position:0% +what i claim is a more general problem +of solving these + + align:start position:0% +of solving these + + + align:start position:0% +of solving these +tqbf problems + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +closing down + + align:start position:0% +closing down + + + align:start position:0% +closing down +let's call + + align:start position:0% + + + + align:start position:0% + +yes indeed you know satisfiability + + align:start position:0% +yes indeed you know satisfiability + + + align:start position:0% +yes indeed you know satisfiability +so c is correct + + align:start position:0% +so c is correct + + + align:start position:0% +so c is correct +when you're talking about a + + align:start position:0% +when you're talking about a + + + align:start position:0% +when you're talking about a +satisfiability problem you're saying is + + align:start position:0% +satisfiability problem you're saying is + + + align:start position:0% +satisfiability problem you're saying is +there a satisfying assignment another + + align:start position:0% +there a satisfying assignment another + + + align:start position:0% +there a satisfying assignment another +way of writing that down is + + align:start position:0% +way of writing that down is + + + align:start position:0% +way of writing that down is +take the boolean formula represent take + + align:start position:0% +take the boolean formula represent take + + + align:start position:0% +take the boolean formula represent take +that boolean formula and put + + align:start position:0% +that boolean formula and put + + + align:start position:0% +that boolean formula and put +exists in front of all the variables + + align:start position:0% +exists in front of all the variables + + + align:start position:0% +exists in front of all the variables +saying the is there a is there exists + + align:start position:0% +saying the is there a is there exists + + + align:start position:0% +saying the is there a is there exists +does there exist a way to set x1 and x2 + + align:start position:0% +does there exist a way to set x1 and x2 + + + align:start position:0% +does there exist a way to set x1 and x2 +and x3 and x4 to make the formula + + align:start position:0% +and x3 and x4 to make the formula + + + align:start position:0% +and x3 and x4 to make the formula +true make your formula hold + + align:start position:0% +true make your formula hold + + + align:start position:0% +true make your formula hold +so um sat is a special case by adding + + align:start position:0% +so um sat is a special case by adding + + + align:start position:0% +so um sat is a special case by adding +exist quantifiers + + align:start position:0% +exist quantifiers + + + align:start position:0% +exist quantifiers +of a tqbf problem + + align:start position:0% +of a tqbf problem + + + align:start position:0% +of a tqbf problem +so c is correct + + align:start position:0% +so c is correct + + + align:start position:0% +so c is correct +um + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so why is this problem in p space + + align:start position:0% +so why is this problem in p space + + + align:start position:0% +so why is this problem in p space +as i claimed and for that we're going to + + align:start position:0% +as i claimed and for that we're going to + + + align:start position:0% +as i claimed and for that we're going to +give a simple recursive algorithm + + align:start position:0% +give a simple recursive algorithm + + + align:start position:0% +give a simple recursive algorithm +um + + align:start position:0% +um + + + align:start position:0% +um +in any + + align:start position:0% +in any + + + align:start position:0% +in any +uh a quantified boolean formula now if + + align:start position:0% +uh a quantified boolean formula now if + + + align:start position:0% +uh a quantified boolean formula now if +you want to test if it's true or not you + + align:start position:0% +you want to test if it's true or not you + + + align:start position:0% +you want to test if it's true or not you +know we're going to basically strip off + + align:start position:0% +know we're going to basically strip off + + + align:start position:0% +know we're going to basically strip off +the leading + + align:start position:0% +the leading + + + align:start position:0% +the leading +quantifiers + + align:start position:0% +quantifiers + + + align:start position:0% +quantifiers +so if it's an exist quantifier we'll + + align:start position:0% +so if it's an exist quantifier we'll + + + align:start position:0% +so if it's an exist quantifier we'll +remove it and plug in true and false + + align:start position:0% +remove it and plug in true and false + + + align:start position:0% +remove it and plug in true and false +associated to its + + align:start position:0% +associated to its + + + align:start position:0% +associated to its +variable + + align:start position:0% +variable + + + align:start position:0% +variable +and then solve those problems + + align:start position:0% +and then solve those problems + + + align:start position:0% +and then solve those problems +recursively + + align:start position:0% + + + + align:start position:0% + +okay so this is just going to be a + + align:start position:0% +okay so this is just going to be a + + + align:start position:0% +okay so this is just going to be a +recursive procedure for solving + + align:start position:0% +recursive procedure for solving + + + align:start position:0% +recursive procedure for solving +tqbf problems + + align:start position:0% +tqbf problems + + + align:start position:0% +tqbf problems +operating by stripping off the the + + align:start position:0% +operating by stripping off the the + + + align:start position:0% +operating by stripping off the the +quantifiers in front + + align:start position:0% +quantifiers in front + + + align:start position:0% +quantifiers in front +and uh getting smaller and smaller + + align:start position:0% +and uh getting smaller and smaller + + + align:start position:0% +and uh getting smaller and smaller +formulas but now we're going to be + + align:start position:0% +formulas but now we're going to be + + + align:start position:0% +formulas but now we're going to be +plugging in uh values true and false um + + align:start position:0% +plugging in uh values true and false um + + + align:start position:0% +plugging in uh values true and false um +instead of relying on the quantifier uh + + align:start position:0% +instead of relying on the quantifier uh + + + align:start position:0% +instead of relying on the quantifier uh +to um uh to to to uh + + align:start position:0% +to um uh to to to uh + + + align:start position:0% +to um uh to to to uh +give us the meaning of the formula + + align:start position:0% +give us the meaning of the formula + + + align:start position:0% +give us the meaning of the formula +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so first of all if there are no + + align:start position:0% +so first of all if there are no + + + align:start position:0% +so first of all if there are no +quantifiers then there are no variables + + align:start position:0% +quantifiers then there are no variables + + + align:start position:0% +quantifiers then there are no variables +because all variables have to be bound + + align:start position:0% +because all variables have to be bound + + + align:start position:0% +because all variables have to be bound +within quantifiers and in that case the + + align:start position:0% +within quantifiers and in that case the + + + align:start position:0% +within quantifiers and in that case the +uh that quantified boolean formula has + + align:start position:0% +uh that quantified boolean formula has + + + align:start position:0% +uh that quantified boolean formula has +to simply be the statement true or the + + align:start position:0% +to simply be the statement true or the + + + align:start position:0% +to simply be the statement true or the +statement false and so you're going to + + align:start position:0% +statement false and so you're going to + + + align:start position:0% +statement false and so you're going to +output accordingly because that's all it + + align:start position:0% +output accordingly because that's all it + + + align:start position:0% +output accordingly because that's all it +can be if you have no variables + + align:start position:0% +can be if you have no variables + + + align:start position:0% +can be if you have no variables +um + + align:start position:0% +um + + + align:start position:0% +um +if the formula starts with an exist + + align:start position:0% +if the formula starts with an exist + + + align:start position:0% +if the formula starts with an exist +quantifier + + align:start position:0% +quantifier + + + align:start position:0% +quantifier +what you're going to do + + align:start position:0% +what you're going to do + + + align:start position:0% +what you're going to do +so here psi is the remainder of the + + align:start position:0% +so here psi is the remainder of the + + + align:start position:0% +so here psi is the remainder of the +formula after you strip off that exist + + align:start position:0% +formula after you strip off that exist + + + align:start position:0% +formula after you strip off that exist +quantifier + + align:start position:0% +quantifier + + + align:start position:0% +quantifier +so you're going to evaluate psi now but + + align:start position:0% +so you're going to evaluate psi now but + + + align:start position:0% +so you're going to evaluate psi now but +take that variable that was bound by the + + align:start position:0% +take that variable that was bound by the + + + align:start position:0% +take that variable that was bound by the +exist and just plug in true + + align:start position:0% +exist and just plug in true + + + align:start position:0% +exist and just plug in true +um + + align:start position:0% +um + + + align:start position:0% +um +or and false respectively so you're + + align:start position:0% +or and false respectively so you're + + + align:start position:0% +or and false respectively so you're +going to get two two now new problems + + align:start position:0% +going to get two two now new problems + + + align:start position:0% +going to get two two now new problems +um + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +uh + + align:start position:0% +uh + + + align:start position:0% +uh +run them + + align:start position:0% +run them + + + align:start position:0% +run them +uh and evaluate them using the same + + align:start position:0% +uh and evaluate them using the same + + + align:start position:0% +uh and evaluate them using the same +procedure recursively uh but now with x + + align:start position:0% +procedure recursively uh but now with x + + + align:start position:0% +procedure recursively uh but now with x +plugged in for true plugged in for x and + + align:start position:0% +plugged in for true plugged in for x and + + + align:start position:0% +plugged in for true plugged in for x and +also then with false plug in for x + + align:start position:0% +also then with false plug in for x + + + align:start position:0% +also then with false plug in for x +and + + align:start position:0% +and + + + align:start position:0% +and +get the answers for those two cases and + + align:start position:0% +get the answers for those two cases and + + + align:start position:0% +get the answers for those two cases and +if either one of them ended up accepting + + align:start position:0% +if either one of them ended up accepting + + + align:start position:0% +if either one of them ended up accepting +then you're going to accept because you + + align:start position:0% +then you're going to accept because you + + + align:start position:0% +then you're going to accept because you +know there exists a value + + align:start position:0% +know there exists a value + + + align:start position:0% +know there exists a value +uh for x which makes the whole thing + + align:start position:0% +uh for x which makes the whole thing + + + align:start position:0% +uh for x which makes the whole thing +true because you you you just + + align:start position:0% +true because you you you just + + + align:start position:0% +true because you you you just +recursively + + align:start position:0% +recursively + + + align:start position:0% +recursively +showed that there was such a value you + + align:start position:0% +showed that there was such a value you + + + align:start position:0% +showed that there was such a value you +know either true or false the thing is + + align:start position:0% +know either true or false the thing is + + + align:start position:0% +know either true or false the thing is +has accepted and if both of them fail + + align:start position:0% +has accepted and if both of them fail + + + align:start position:0% +has accepted and if both of them fail +then you're going to reject and the very + + align:start position:0% +then you're going to reject and the very + + + align:start position:0% +then you're going to reject and the very +same idea if you have a for all + + align:start position:0% +same idea if you have a for all + + + align:start position:0% +same idea if you have a for all +quantifier + + align:start position:0% +quantifier + + + align:start position:0% +quantifier +you're going to evaluate + + align:start position:0% +you're going to evaluate + + + align:start position:0% +you're going to evaluate +the remainder of the formula + + align:start position:0% +the remainder of the formula + + + align:start position:0% +the remainder of the formula +again with x equal to true and false so + + align:start position:0% +again with x equal to true and false so + + + align:start position:0% +again with x equal to true and false so +as two subproblems + + align:start position:0% +as two subproblems + + + align:start position:0% +as two subproblems +but now you're going to require them + + align:start position:0% +but now you're going to require them + + + align:start position:0% +but now you're going to require them +both to accept because that's the + + align:start position:0% +both to accept because that's the + + + align:start position:0% +both to accept because that's the +meaning of for all that both assignments + + align:start position:0% +meaning of for all that both assignments + + + align:start position:0% +meaning of for all that both assignments +to x have to make the formula true so + + align:start position:0% +to x have to make the formula true so + + + align:start position:0% +to x have to make the formula true so +you're going to + + align:start position:0% +you're going to + + + align:start position:0% +you're going to +evaluate them recursively and accept + + align:start position:0% +evaluate them recursively and accept + + + align:start position:0% +evaluate them recursively and accept +both of them are true as determined by + + align:start position:0% +both of them are true as determined by + + + align:start position:0% +both of them are true as determined by +your recursive your recursion + + align:start position:0% +your recursive your recursion + + + align:start position:0% +your recursive your recursion +okay so how much space does this use + + align:start position:0% +okay so how much space does this use + + + align:start position:0% +okay so how much space does this use +um i'm not going to go through this in + + align:start position:0% +um i'm not going to go through this in + + + align:start position:0% +um i'm not going to go through this in +great detail but uh + + align:start position:0% +great detail but uh + + + align:start position:0% +great detail but uh +each recursive level uses just a + + align:start position:0% +each recursive level uses just a + + + align:start position:0% +each recursive level uses just a +constant amount of space so every time + + align:start position:0% +constant amount of space so every time + + + align:start position:0% +constant amount of space so every time +you do a recursion you have to remember + + align:start position:0% +you do a recursion you have to remember + + + align:start position:0% +you do a recursion you have to remember +that uh + + align:start position:0% +that uh + + + align:start position:0% +that uh +that value uh that assignment to that to + + align:start position:0% +that value uh that assignment to that to + + + align:start position:0% +that value uh that assignment to that to +that variable + + align:start position:0% +that variable + + + align:start position:0% +that variable +you want to think of recursion as being + + align:start position:0% +you want to think of recursion as being + + + align:start position:0% +you want to think of recursion as being +implemented on a stack so you're just + + align:start position:0% +implemented on a stack so you're just + + + align:start position:0% +implemented on a stack so you're just +going to pop push on the stack that + + align:start position:0% +going to pop push on the stack that + + + align:start position:0% +going to pop push on the stack that +value of that variable + + align:start position:0% +value of that variable + + + align:start position:0% +value of that variable +which is that true or false so basically + + align:start position:0% +which is that true or false so basically + + + align:start position:0% +which is that true or false so basically +it's one bit of memory uh + + align:start position:0% +it's one bit of memory uh + + + align:start position:0% +it's one bit of memory uh +that you're going to require every time + + align:start position:0% +that you're going to require every time + + + align:start position:0% +that you're going to require every time +you're going down the recursion you just + + align:start position:0% +you're going down the recursion you just + + + align:start position:0% +you're going down the recursion you just +have to remember what um + + align:start position:0% +have to remember what um + + + align:start position:0% +have to remember what um +you know + + align:start position:0% +you know + + + align:start position:0% +you know +which case you're working on whether + + align:start position:0% +which case you're working on whether + + + align:start position:0% +which case you're working on whether +x equal to true or x equal to false + + align:start position:0% +x equal to true or x equal to false + + + align:start position:0% +x equal to true or x equal to false +uh and + + align:start position:0% +uh and + + + align:start position:0% +uh and +um so each recursive level just involves + + align:start position:0% +um so each recursive level just involves + + + align:start position:0% +um so each recursive level just involves +constant space + + align:start position:0% +constant space + + + align:start position:0% +constant space +and the depth of the recursion you know + + align:start position:0% +and the depth of the recursion you know + + + align:start position:0% +and the depth of the recursion you know +how far how much might you have to + + align:start position:0% +how far how much might you have to + + + align:start position:0% +how far how much might you have to +remember well it's going to be at most + + align:start position:0% +remember well it's going to be at most + + + align:start position:0% +remember well it's going to be at most +one for every quantifier um + + align:start position:0% +one for every quantifier um + + + align:start position:0% +one for every quantifier um +because that's you know you're stripping + + align:start position:0% +because that's you know you're stripping + + + align:start position:0% +because that's you know you're stripping +them off as you're going down the + + align:start position:0% +them off as you're going down the + + + align:start position:0% +them off as you're going down the +recursion so that's going to be at most + + align:start position:0% +recursion so that's going to be at most + + + align:start position:0% +recursion so that's going to be at most +the length of the formula that says most + + align:start position:0% +the length of the formula that says most + + + align:start position:0% +the length of the formula that says most +of the number of quantifiers you can + + align:start position:0% +of the number of quantifiers you can + + + align:start position:0% +of the number of quantifiers you can +have + + align:start position:0% +have + + + align:start position:0% +have +and so + + align:start position:0% +and so + + + align:start position:0% +and so +uh the total amount of space used by + + align:start position:0% +uh the total amount of space used by + + + align:start position:0% +uh the total amount of space used by +this is going to be um just n order n + + align:start position:0% +this is going to be um just n order n + + + align:start position:0% +this is going to be um just n order n +okay so this + + align:start position:0% +okay so this + + + align:start position:0% +okay so this +problem is solved in uh + + align:start position:0% +problem is solved in uh + + + align:start position:0% +problem is solved in uh +in n space + + align:start position:0% +in n space + + + align:start position:0% +in n space +and so that's why it's in p space + + align:start position:0% +and so that's why it's in p space + + + align:start position:0% +and so that's why it's in p space +okay i think that's + + align:start position:0% +okay i think that's + + + align:start position:0% +okay i think that's +all i wanted to say about this + + align:start position:0% + + + + align:start position:0% + +okay if we've got the tape and a turning + + align:start position:0% +okay if we've got the tape and a turning + + + align:start position:0% +okay if we've got the tape and a turning +machine as memory + + align:start position:0% +machine as memory + + + align:start position:0% +machine as memory +in a modern computer what does the + + align:start position:0% +in a modern computer what does the + + + align:start position:0% +in a modern computer what does the +finite control correspond to the finite + + align:start position:0% +finite control correspond to the finite + + + align:start position:0% +finite control correspond to the finite +control corresponds to just a finite + + align:start position:0% +control corresponds to just a finite + + + align:start position:0% +control corresponds to just a finite +additional memory um the tape is an + + align:start position:0% +additional memory um the tape is an + + + align:start position:0% +additional memory um the tape is an +unlimited amount of memory uh or if + + align:start position:0% +unlimited amount of memory uh or if + + + align:start position:0% +unlimited amount of memory uh or if +we're putting bounds you know the amount + + align:start position:0% +we're putting bounds you know the amount + + + align:start position:0% +we're putting bounds you know the amount +of tape is going to be + + align:start position:0% +of tape is going to be + + + align:start position:0% +of tape is going to be +say n squared memory where n is the + + align:start position:0% +say n squared memory where n is the + + + align:start position:0% +say n squared memory where n is the +length of n n is the length of the input + + align:start position:0% +length of n n is the length of the input + + + align:start position:0% +length of n n is the length of the input +so um + + align:start position:0% +so um + + + align:start position:0% +so um +yeah they're both memories but um + + align:start position:0% +yeah they're both memories but um + + + align:start position:0% +yeah they're both memories but um +the finite control is + + align:start position:0% +the finite control is + + + align:start position:0% +the finite control is +it doesn't grow with n so that's going + + align:start position:0% +it doesn't grow with n so that's going + + + align:start position:0% +it doesn't grow with n so that's going +to be just a you know some constant + + align:start position:0% +to be just a you know some constant + + + align:start position:0% +to be just a you know some constant +amount of memory + + align:start position:0% +amount of memory + + + align:start position:0% +amount of memory +what would be the time complexity of + + align:start position:0% +what would be the time complexity of + + + align:start position:0% +what would be the time complexity of +this album time complexity would be bad + + align:start position:0% +this album time complexity would be bad + + + align:start position:0% +this album time complexity would be bad +it's going to be exponential so you'd + + align:start position:0% +it's going to be exponential so you'd + + + align:start position:0% +it's going to be exponential so you'd +have to just double check that but it's + + align:start position:0% +have to just double check that but it's + + + align:start position:0% +have to just double check that but it's +going to be something like 2 + + align:start position:0% +going to be something like 2 + + + align:start position:0% +going to be something like 2 +to the + + align:start position:0% +to the + + + align:start position:0% +to the +number of variables that you have two to + + align:start position:0% +number of variables that you have two to + + + align:start position:0% +number of variables that you have two to +the number of quantifiers + + align:start position:0% +the number of quantifiers + + + align:start position:0% +the number of quantifiers +plus some small overhead for evaluating + + align:start position:0% +plus some small overhead for evaluating + + + align:start position:0% +plus some small overhead for evaluating +the formula multiple time but it's going + + align:start position:0% +the formula multiple time but it's going + + + align:start position:0% +the formula multiple time but it's going +to be exponential + + align:start position:0% +to be exponential + + + align:start position:0% +to be exponential +um + + align:start position:0% + + + + align:start position:0% + +that's going to answer for you + + align:start position:0% + + + + align:start position:0% + +so someone is asking going back again to + + align:start position:0% +so someone is asking going back again to + + + align:start position:0% +so someone is asking going back again to +co-np and how do we know there exists a + + align:start position:0% +co-np and how do we know there exists a + + + align:start position:0% +co-np and how do we know there exists a +problem in cohen p that is co and p + + align:start position:0% +problem in cohen p that is co and p + + + align:start position:0% +problem in cohen p that is co and p +complete we didn't define even what that + + align:start position:0% +complete we didn't define even what that + + + align:start position:0% +complete we didn't define even what that +means + + align:start position:0% +means + + + align:start position:0% +means +but uh co-np-complete + + align:start position:0% +but uh co-np-complete + + + align:start position:0% +but uh co-np-complete +means + + align:start position:0% +means + + + align:start position:0% +means +we're going to start seeing other + + align:start position:0% +we're going to start seeing other + + + align:start position:0% +we're going to start seeing other +examples of completeness for different + + align:start position:0% +examples of completeness for different + + + align:start position:0% +examples of completeness for different +complexity classes in particular one of + + align:start position:0% +complexity classes in particular one of + + + align:start position:0% +complexity classes in particular one of +one thing that's going to happen on + + align:start position:0% +one thing that's going to happen on + + + align:start position:0% +one thing that's going to happen on +tuesdays we'll see + + align:start position:0% +tuesdays we'll see + + + align:start position:0% +tuesdays we'll see +a problem that's complete for p space + + align:start position:0% +a problem that's complete for p space + + + align:start position:0% +a problem that's complete for p space +in fact it's going to be tq tqbf + + align:start position:0% +in fact it's going to be tq tqbf + + + align:start position:0% +in fact it's going to be tq tqbf +sort of looking ahead is going to + + align:start position:0% +sort of looking ahead is going to + + + align:start position:0% +sort of looking ahead is going to +be a piece based complete problem + + align:start position:0% +be a piece based complete problem + + + align:start position:0% +be a piece based complete problem +but + + align:start position:0% +but + + + align:start position:0% +but +we even have to have the notion of what + + align:start position:0% +we even have to have the notion of what + + + align:start position:0% +we even have to have the notion of what +we mean by uh complete for these other + + align:start position:0% +we mean by uh complete for these other + + + align:start position:0% +we mean by uh complete for these other +classes + + align:start position:0% +classes + + + align:start position:0% +classes +and in the case of co np a problem is co + + align:start position:0% +and in the case of co np a problem is co + + + align:start position:0% +and in the case of co np a problem is co +and p complete if it's in in co np and + + align:start position:0% +and p complete if it's in in co np and + + + align:start position:0% +and p complete if it's in in co np and +every other co np problem is polynomial + + align:start position:0% +every other co np problem is polynomial + + + align:start position:0% +every other co np problem is polynomial +time reducible to it so just exactly the + + align:start position:0% +time reducible to it so just exactly the + + + align:start position:0% +time reducible to it so just exactly the +same as we have for np just plugging in + + align:start position:0% +same as we have for np just plugging in + + + align:start position:0% +same as we have for np just plugging in +co np instead + + align:start position:0% +co np instead + + + align:start position:0% +co np instead +and + + align:start position:0% + + + + align:start position:0% + +you just have to work through the logic + + align:start position:0% +you just have to work through the logic + + + align:start position:0% +you just have to work through the logic +but it's pretty straightforward + + align:start position:0% +but it's pretty straightforward + + + align:start position:0% +but it's pretty straightforward +the complement of any np complete + + align:start position:0% +the complement of any np complete + + + align:start position:0% +the complement of any np complete +problem is going to be a co-np-complete + + align:start position:0% +problem is going to be a co-np-complete + + + align:start position:0% +problem is going to be a co-np-complete +problem using that definition um + + align:start position:0% +problem using that definition um + + + align:start position:0% +problem using that definition um +uh so + + align:start position:0% +uh so + + + align:start position:0% +uh so +just i i don't want to go through + + align:start position:0% +just i i don't want to go through + + + align:start position:0% +just i i don't want to go through +through that those simple steps but + + align:start position:0% +through that those simple steps but + + + align:start position:0% +through that those simple steps but +you just can go and verify that offline + + align:start position:0% +you just can go and verify that offline + + + align:start position:0% +you just can go and verify that offline +that that's + + align:start position:0% +that that's + + + align:start position:0% +that that's +going to be true and i think we're going + + align:start position:0% +going to be true and i think we're going + + + align:start position:0% +going to be true and i think we're going +to probably talk about that later in the + + align:start position:0% +to probably talk about that later in the + + + align:start position:0% +to probably talk about that later in the +semester too + + align:start position:0% +semester too + + + align:start position:0% +semester too +um + + align:start position:0% + + + + align:start position:0% + +so another question how does the tqbf + + align:start position:0% +so another question how does the tqbf + + + align:start position:0% +so another question how does the tqbf +algorithm + + align:start position:0% + + + + align:start position:0% + +ah that is a good question here um + + align:start position:0% +ah that is a good question here um + + + align:start position:0% +ah that is a good question here um +why is the tqbf algorithm that i just + + align:start position:0% +why is the tqbf algorithm that i just + + + align:start position:0% +why is the tqbf algorithm that i just +described in p space doesn't the thing + + align:start position:0% +described in p space doesn't the thing + + + align:start position:0% +described in p space doesn't the thing +every time i'm doing the recursion + + align:start position:0% +every time i'm doing the recursion + + + align:start position:0% +every time i'm doing the recursion +doesn't things branch out so that i end + + align:start position:0% +doesn't things branch out so that i end + + + align:start position:0% +doesn't things branch out so that i end +up using exponential space + + align:start position:0% +up using exponential space + + + align:start position:0% +up using exponential space +critical thing which + + align:start position:0% +critical thing which + + + align:start position:0% +critical thing which +i don't i actually don't think i + + align:start position:0% +i don't i actually don't think i + + + align:start position:0% +i don't i actually don't think i +mentioned which i think is important to + + align:start position:0% +mentioned which i think is important to + + + align:start position:0% +mentioned which i think is important to +observe is that when you're doing those + + align:start position:0% +observe is that when you're doing those + + + align:start position:0% +observe is that when you're doing those +two recursive calls when you set x equal + + align:start position:0% +two recursive calls when you set x equal + + + align:start position:0% +two recursive calls when you set x equal +to true and set x equal to false + + align:start position:0% +to true and set x equal to false + + + align:start position:0% +to true and set x equal to false +after you've determined that the the + + align:start position:0% +after you've determined that the the + + + align:start position:0% +after you've determined that the the +answer for when you set x equal to true + + align:start position:0% +answer for when you set x equal to true + + + align:start position:0% +answer for when you set x equal to true +now you reuse that space + + align:start position:0% +now you reuse that space + + + align:start position:0% +now you reuse that space +that very same space + + align:start position:0% +that very same space + + + align:start position:0% +that very same space +to test what happens when you have x + + align:start position:0% +to test what happens when you have x + + + align:start position:0% +to test what happens when you have x +equal to false + + align:start position:0% +equal to false + + + align:start position:0% +equal to false +so that's that's the power of space + + align:start position:0% +so that's that's the power of space + + + align:start position:0% +so that's that's the power of space +which makes it different from time is + + align:start position:0% +which makes it different from time is + + + align:start position:0% +which makes it different from time is +that it can be reused + + align:start position:0% +that it can be reused + + + align:start position:0% +that it can be reused +so after you've got the answer for when + + align:start position:0% +so after you've got the answer for when + + + align:start position:0% +so after you've got the answer for when +you have x equal to true now you free up + + align:start position:0% +you have x equal to true now you free up + + + align:start position:0% +you have x equal to true now you free up +that space that's no longer needed + + align:start position:0% +that space that's no longer needed + + + align:start position:0% +that space that's no longer needed +anymore you just remember the answer and + + align:start position:0% +anymore you just remember the answer and + + + align:start position:0% +anymore you just remember the answer and +now you see what happens when you have x + + align:start position:0% +now you see what happens when you have x + + + align:start position:0% +now you see what happens when you have x +equal to false using that same space so + + align:start position:0% +equal to false using that same space so + + + align:start position:0% +equal to false using that same space so +there's no exponential blow-up that's + + align:start position:0% +there's no exponential blow-up that's + + + align:start position:0% +there's no exponential blow-up that's +that's an important point i'm glad you + + align:start position:0% +that's an important point i'm glad you + + + align:start position:0% +that's an important point i'm glad you +gave me the chance to to say it + + align:start position:0% +gave me the chance to to say it + + + align:start position:0% +gave me the chance to to say it +so somebody's asking about + + align:start position:0% +so somebody's asking about + + + align:start position:0% +so somebody's asking about +defining time of an undetermined turing + + align:start position:0% +defining time of an undetermined turing + + + align:start position:0% +defining time of an undetermined turing +machine to the maximum + + align:start position:0% +machine to the maximum + + + align:start position:0% +machine to the maximum +time + + align:start position:0% +time + + + align:start position:0% +time +of each branch well that's sort of what + + align:start position:0% +of each branch well that's sort of what + + + align:start position:0% +of each branch well that's sort of what +we have done maybe i don't understand + + align:start position:0% +we have done maybe i don't understand + + + align:start position:0% +we have done maybe i don't understand +your question but you'll have to ask it + + align:start position:0% +your question but you'll have to ask it + + + align:start position:0% +your question but you'll have to ask it +after after um afterwards because i want + + align:start position:0% +after after um afterwards because i want + + + align:start position:0% +after after um afterwards because i want +to i don't want to be delaying any more + + align:start position:0% +to i don't want to be delaying any more + + + align:start position:0% +to i don't want to be delaying any more +than we + + align:start position:0% +than we + + + align:start position:0% +than we +that we have + + align:start position:0% +that we have + + + align:start position:0% +that we have +so + + align:start position:0% +so + + + align:start position:0% +so +we're going to we're going to go back + + align:start position:0% +we're going to we're going to go back + + + align:start position:0% +we're going to we're going to go back +and + + align:start position:0% +and + + + align:start position:0% +and +um move on here + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +second + + align:start position:0% +second + + + align:start position:0% +second +example + + align:start position:0% +example + + + align:start position:0% +example +um and this one is a kind of a fun + + align:start position:0% +um and this one is a kind of a fun + + + align:start position:0% +um and this one is a kind of a fun +example but it's also going to be an + + align:start position:0% +example but it's also going to be an + + + align:start position:0% +example but it's also going to be an +important one for us um it's called the + + align:start position:0% +important one for us um it's called the + + + align:start position:0% +important one for us um it's called the +latter problem + + align:start position:0% +latter problem + + + align:start position:0% +latter problem +now so you may have seen something + + align:start position:0% +now so you may have seen something + + + align:start position:0% +now so you may have seen something +called the word ladder + + align:start position:0% +called the word ladder + + + align:start position:0% +called the word ladder +but in general a ladder is a sequence of + + align:start position:0% +but in general a ladder is a sequence of + + + align:start position:0% +but in general a ladder is a sequence of +strings + + align:start position:0% +strings + + + align:start position:0% +strings +which are all of the same length + + align:start position:0% +which are all of the same length + + + align:start position:0% +which are all of the same length +but where consecutive strings differ in + + align:start position:0% +but where consecutive strings differ in + + + align:start position:0% +but where consecutive strings differ in +a single + + align:start position:0% +a single + + + align:start position:0% +a single +symbol um + + align:start position:0% +symbol um + + + align:start position:0% +symbol um +so + + align:start position:0% + + + + align:start position:0% + +so for example if you have a word letter + + align:start position:0% +so for example if you have a word letter + + + align:start position:0% +so for example if you have a word letter +for english it's going to be a ladder + + align:start position:0% +for english it's going to be a ladder + + + align:start position:0% +for english it's going to be a ladder +where all the words are english all of + + align:start position:0% +where all the words are english all of + + + align:start position:0% +where all the words are english all of +the um strings are english words so + + align:start position:0% +the um strings are english words so + + + align:start position:0% +the um strings are english words so +here's an example + + align:start position:0% + + + + align:start position:0% + +i thought i fixed that okay here is here + + align:start position:0% +i thought i fixed that okay here is here + + + align:start position:0% +i thought i fixed that okay here is here +is a + + align:start position:0% + + + + align:start position:0% + +a + + align:start position:0% +a + + + align:start position:0% +a +word ladder for english and maybe you've + + align:start position:0% +word ladder for english and maybe you've + + + align:start position:0% +word ladder for english and maybe you've +seen these suppose i want to try to get + + align:start position:0% +seen these suppose i want to try to get + + + align:start position:0% +seen these suppose i want to try to get +from work to play + + align:start position:0% +from work to play + + + align:start position:0% +from work to play +but all of the intermediate + + align:start position:0% +but all of the intermediate + + + align:start position:0% +but all of the intermediate +uh + + align:start position:0% +uh + + + align:start position:0% +uh +strings should be + + align:start position:0% +strings should be + + + align:start position:0% +strings should be +english words + + align:start position:0% +english words + + + align:start position:0% +english words +with four letters + + align:start position:0% +with four letters + + + align:start position:0% +with four letters +that differ from their previous one in + + align:start position:0% +that differ from their previous one in + + + align:start position:0% +that differ from their previous one in +only a single letter + + align:start position:0% +only a single letter + + + align:start position:0% +only a single letter +and i want to somehow change the word + + align:start position:0% +and i want to somehow change the word + + + align:start position:0% +and i want to somehow change the word +work + + align:start position:0% +work + + + align:start position:0% +work +to the word play so i don't know if + + align:start position:0% +to the word play so i don't know if + + + align:start position:0% +to the word play so i don't know if +you know so for example i can change + + align:start position:0% +you know so for example i can change + + + align:start position:0% +you know so for example i can change +work to pork + + align:start position:0% +work to pork + + + align:start position:0% +work to pork +so here's just one letter difference + + align:start position:0% +so here's just one letter difference + + + align:start position:0% +so here's just one letter difference +um which looks like it's an improvement + + align:start position:0% +um which looks like it's an improvement + + + align:start position:0% +um which looks like it's an improvement +because now i have the i'm agree an + + align:start position:0% +because now i have the i'm agree an + + + align:start position:0% +because now i have the i'm agree an +agreement on the play + + align:start position:0% +agreement on the play + + + align:start position:0% +agreement on the play +um but sometimes you know you might + + align:start position:0% +um but sometimes you know you might + + + align:start position:0% +um but sometimes you know you might +change it you might have a good change + + align:start position:0% +change it you might have a good change + + + align:start position:0% +change it you might have a good change +and then you have to undo it later which + + align:start position:0% +and then you have to undo it later which + + + align:start position:0% +and then you have to undo it later which +i think actually happens here um + + align:start position:0% +i think actually happens here um + + + align:start position:0% +i think actually happens here um +so pork then this port but then we gave + + align:start position:0% +so pork then this port but then we gave + + + align:start position:0% +so pork then this port but then we gave +up that progress we made port + + align:start position:0% +up that progress we made port + + + align:start position:0% +up that progress we made port +to sort + + align:start position:0% +to sort + + + align:start position:0% +to sort +to suit + + align:start position:0% +to suit + + + align:start position:0% +to suit +to slot you understand again you + + align:start position:0% +to slot you understand again you + + + align:start position:0% +to slot you understand again you +understand what i'm doing here each case + + align:start position:0% +understand what i'm doing here each case + + + align:start position:0% +understand what i'm doing here each case +i'm just changing a single letter + + align:start position:0% +i'm just changing a single letter + + + align:start position:0% +i'm just changing a single letter +but all of these words all of these have + + align:start position:0% +but all of these words all of these have + + + align:start position:0% +but all of these words all of these have +to be legitimate english words of length + + align:start position:0% +to be legitimate english words of length + + + align:start position:0% +to be legitimate english words of length +four + + align:start position:0% +four + + + align:start position:0% +four +plot + + align:start position:0% +plot + + + align:start position:0% +plot +ploy + + align:start position:0% +ploy + + + align:start position:0% +ploy +and then play + + align:start position:0% +and then play + + + align:start position:0% +and then play +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that's what a word lighter in english + + align:start position:0% +so that's what a word lighter in english + + + align:start position:0% +so that's what a word lighter in english +would be of course you can do it in + + align:start position:0% +would be of course you can do it in + + + align:start position:0% +would be of course you can do it in +different languages and i'm going to + + align:start position:0% +different languages and i'm going to + + + align:start position:0% +different languages and i'm going to +talk about it abstractly where + + align:start position:0% +talk about it abstractly where + + + align:start position:0% +talk about it abstractly where +instead of having any natural human + + align:start position:0% +instead of having any natural human + + + align:start position:0% +instead of having any natural human +language as being the uh test for a word + + align:start position:0% +language as being the uh test for a word + + + align:start position:0% +language as being the uh test for a word +b for being a string being legitimate + + align:start position:0% +b for being a string being legitimate + + + align:start position:0% +b for being a string being legitimate +i'm going to define a + + align:start position:0% +i'm going to define a + + + align:start position:0% +i'm going to define a +um + + align:start position:0% +um + + + align:start position:0% +um +any old language + + align:start position:0% +any old language + + + align:start position:0% +any old language +uh let's let's say it's a is going to be + + align:start position:0% +uh let's let's say it's a is going to be + + + align:start position:0% +uh let's let's say it's a is going to be +some language some set of strings and + + align:start position:0% +some language some set of strings and + + + align:start position:0% +some language some set of strings and +the and the + + align:start position:0% +the and the + + + align:start position:0% +the and the +those are going to be the legal strings + + align:start position:0% +those are going to be the legal strings + + + align:start position:0% +those are going to be the legal strings +that can be in the ladder + + align:start position:0% +that can be in the ladder + + + align:start position:0% +that can be in the ladder +so a ladder in a is a lot of strings + + align:start position:0% +so a ladder in a is a lot of strings + + + align:start position:0% +so a ladder in a is a lot of strings +that are all members of a + + align:start position:0% +that are all members of a + + + align:start position:0% +that are all members of a +um + + align:start position:0% +um + + + align:start position:0% +um +and now the + + align:start position:0% +and now the + + + align:start position:0% +and now the +the + + align:start position:0% +the + + + align:start position:0% +the +latter dfa problem is + + align:start position:0% +latter dfa problem is + + + align:start position:0% +latter dfa problem is +a is going to be the language of some + + align:start position:0% +a is going to be the language of some + + + align:start position:0% +a is going to be the language of some +dfa + + align:start position:0% +dfa + + + align:start position:0% +dfa +so i'm giving you b + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +and so i want and then a start string + + align:start position:0% +and so i want and then a start string + + + align:start position:0% +and so i want and then a start string +and an n string so this is like work and + + align:start position:0% +and an n string so this is like work and + + + align:start position:0% +and an n string so this is like work and +play u and v are like work and play so + + align:start position:0% +play u and v are like work and play so + + + align:start position:0% +play u and v are like work and play so +where b is a dfa + + align:start position:0% +where b is a dfa + + + align:start position:0% +where b is a dfa +and its language has a ladder that goes + + align:start position:0% +and its language has a ladder that goes + + + align:start position:0% +and its language has a ladder that goes +from u to v + + align:start position:0% +from u to v + + + align:start position:0% +from u to v +here are the intermediate strings + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +all right um + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +i'm going to show you that this latter + + align:start position:0% +i'm going to show you that this latter + + + align:start position:0% +i'm going to show you that this latter +dfa problem is in np space + + align:start position:0% +dfa problem is in np space + + + align:start position:0% +dfa problem is in np space +okay and it's not this is not super hard + + align:start position:0% +okay and it's not this is not super hard + + + align:start position:0% +okay and it's not this is not super hard +because basically + + align:start position:0% +because basically + + + align:start position:0% +because basically +uh well + + align:start position:0% +uh well + + + align:start position:0% +uh well +let's just actually + + align:start position:0% +let's just actually + + + align:start position:0% +let's just actually +look at the slide here + + align:start position:0% +look at the slide here + + + align:start position:0% +look at the slide here +the way it's going to work is it's not + + align:start position:0% +the way it's going to work is it's not + + + align:start position:0% +the way it's going to work is it's not +deterministically going to guess that + + align:start position:0% +deterministically going to guess that + + + align:start position:0% +deterministically going to guess that +sequence from u to v + + align:start position:0% +sequence from u to v + + + align:start position:0% +sequence from u to v +so if i if i'm trying to get from work + + align:start position:0% +so if i if i'm trying to get from work + + + align:start position:0% +so if i if i'm trying to get from work +to play imagine those i'm going to be + + align:start position:0% +to play imagine those i'm going to be + + + align:start position:0% +to play imagine those i'm going to be +using this as um + + align:start position:0% +using this as um + + + align:start position:0% +using this as um +you know + + align:start position:0% +you know + + + align:start position:0% +you know +in place of the + + align:start position:0% +in place of the + + + align:start position:0% +in place of the +uh the + + align:start position:0% +uh the + + + align:start position:0% +uh the +of the language of my fine art automaton + + align:start position:0% +of the language of my fine art automaton + + + align:start position:0% +of the language of my fine art automaton +just because this is easier to talk + + align:start position:0% +just because this is easier to talk + + + align:start position:0% +just because this is easier to talk +about but imagine these are being + + align:start position:0% +about but imagine these are being + + + align:start position:0% +about but imagine these are being +strings that are that are accepted by + + align:start position:0% +strings that are that are accepted by + + + align:start position:0% +strings that are that are accepted by +that that dfa + + align:start position:0% +that that dfa + + + align:start position:0% +that that dfa +um so now i'm trying to get from my + + align:start position:0% +um so now i'm trying to get from my + + + align:start position:0% +um so now i'm trying to get from my +string u to the string v and i want to + + align:start position:0% +string u to the string v and i want to + + + align:start position:0% +string u to the string v and i want to +test can i get there + + align:start position:0% +test can i get there + + + align:start position:0% +test can i get there +by some + + align:start position:0% +by some + + + align:start position:0% +by some +uh changing one letter at a time but + + align:start position:0% +uh changing one letter at a time but + + + align:start position:0% +uh changing one letter at a time but +staying as strings that are accepted by + + align:start position:0% +staying as strings that are accepted by + + + align:start position:0% +staying as strings that are accepted by +the dfa + + align:start position:0% +the dfa + + + align:start position:0% +the dfa +um + + align:start position:0% +um + + + align:start position:0% +um +i'm just going to guess that sequence + + align:start position:0% +i'm just going to guess that sequence + + + align:start position:0% +i'm just going to guess that sequence +non-deterministically + + align:start position:0% +non-deterministically + + + align:start position:0% +non-deterministically +but i have to make sure careful of two + + align:start position:0% +but i have to make sure careful of two + + + align:start position:0% +but i have to make sure careful of two +things um + + align:start position:0% +things um + + + align:start position:0% +things um +i don't want to guess the sequence solid + + align:start position:0% +i don't want to guess the sequence solid + + + align:start position:0% +i don't want to guess the sequence solid +in advance because that sequence might + + align:start position:0% +in advance because that sequence might + + + align:start position:0% +in advance because that sequence might +be exponentially long + + align:start position:0% +be exponentially long + + + align:start position:0% +be exponentially long +you have to calculate how long it could + + align:start position:0% +you have to calculate how long it could + + + align:start position:0% +you have to calculate how long it could +possibly be but you might + + align:start position:0% +possibly be but you might + + + align:start position:0% +possibly be but you might +might you know you might change to one + + align:start position:0% +might you know you might change to one + + + align:start position:0% +might you know you might change to one +symbol then change it to a different + + align:start position:0% +symbol then change it to a different + + + align:start position:0% +symbol then change it to a different +symbol then change it back to that + + align:start position:0% +symbol then change it back to that + + + align:start position:0% +symbol then change it back to that +original symbol or + + align:start position:0% +original symbol or + + + align:start position:0% +original symbol or +so + + align:start position:0% +so + + + align:start position:0% +so +the the only bound that you can write + + align:start position:0% +the the only bound that you can write + + + align:start position:0% +the the only bound that you can write +down is the number of possible strings + + align:start position:0% +down is the number of possible strings + + + align:start position:0% +down is the number of possible strings +that you can have of that length + + align:start position:0% +that you can have of that length + + + align:start position:0% +that you can have of that length +um so it might be exponential uh you + + align:start position:0% +um so it might be exponential uh you + + + align:start position:0% +um so it might be exponential uh you +don't want to write down that whole + + align:start position:0% +don't want to write down that whole + + + align:start position:0% +don't want to write down that whole +thing because that's going to be + + align:start position:0% +thing because that's going to be + + + align:start position:0% +thing because that's going to be +exceeding your space bound + + align:start position:0% +exceeding your space bound + + + align:start position:0% +exceeding your space bound +but what you don't need to you're just + + align:start position:0% +but what you don't need to you're just + + + align:start position:0% +but what you don't need to you're just +going to guess them one at a time + + align:start position:0% +going to guess them one at a time + + + align:start position:0% +going to guess them one at a time +forgetting about the previous ones just + + align:start position:0% +forgetting about the previous ones just + + + align:start position:0% +forgetting about the previous ones just +keep guessing the next uh one in the + + align:start position:0% +keep guessing the next uh one in the + + + align:start position:0% +keep guessing the next uh one in the +sequence and only remembering that one + + align:start position:0% +sequence and only remembering that one + + + align:start position:0% +sequence and only remembering that one +and seeing if uh + + align:start position:0% +and seeing if uh + + + align:start position:0% +and seeing if uh +you're ever get to the the string your + + align:start position:0% +you're ever get to the the string your + + + align:start position:0% +you're ever get to the the string your +you your target string + + align:start position:0% +you your target string + + + align:start position:0% +you your target string +but then when you do that you have to + + align:start position:0% +but then when you do that you have to + + + align:start position:0% +but then when you do that you have to +make sure that you don't end up going + + align:start position:0% +make sure that you don't end up going + + + align:start position:0% +make sure that you don't end up going +forever + + align:start position:0% +forever + + + align:start position:0% +forever +um because that's not allowed + + align:start position:0% +um because that's not allowed + + + align:start position:0% +um because that's not allowed +in your uh in your um + + align:start position:0% +in your uh in your um + + + align:start position:0% +in your uh in your um +in your np space algorithm + + align:start position:0% +in your np space algorithm + + + align:start position:0% +in your np space algorithm +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so + + align:start position:0% +so + + + align:start position:0% +so +you're going to have to keep a counter + + align:start position:0% +you're going to have to keep a counter + + + align:start position:0% +you're going to have to keep a counter +to make sure that if you go beyond that + + align:start position:0% +to make sure that if you go beyond that + + + align:start position:0% +to make sure that if you go beyond that +bound which is going to be the maximum + + align:start position:0% +bound which is going to be the maximum + + + align:start position:0% +bound which is going to be the maximum +number of strings you could possibly + + align:start position:0% +number of strings you could possibly + + + align:start position:0% +number of strings you could possibly +have then you're going to just shot that + + align:start position:0% +have then you're going to just shot that + + + align:start position:0% +have then you're going to just shot that +branch of the non-determinism off + + align:start position:0% +branch of the non-determinism off + + + align:start position:0% +branch of the non-determinism off +you're going to just reject on that + + align:start position:0% +you're going to just reject on that + + + align:start position:0% +you're going to just reject on that +branch + + align:start position:0% +branch + + + align:start position:0% +branch +okay so here is i'm going to write to + + align:start position:0% +okay so here is i'm going to write to + + + align:start position:0% +okay so here is i'm going to write to +say this here + + align:start position:0% + + + + align:start position:0% + +here is my non-deterministic uh + + align:start position:0% +here is my non-deterministic uh + + + align:start position:0% +here is my non-deterministic uh +you know polynomial space procedure + + align:start position:0% +you know polynomial space procedure + + + align:start position:0% +you know polynomial space procedure +um i'm given my language my dfab and my + + align:start position:0% +um i'm given my language my dfab and my + + + align:start position:0% +um i'm given my language my dfab and my +start and end strings + + align:start position:0% +start and end strings + + + align:start position:0% +start and end strings +i let y equal the start string + + align:start position:0% +i let y equal the start string + + + align:start position:0% +i let y equal the start string +write down the length of my strings that + + align:start position:0% +write down the length of my strings that + + + align:start position:0% +write down the length of my strings that +i'm going to have to keep + + align:start position:0% +i'm going to have to keep + + + align:start position:0% +i'm going to have to keep +in mind all the way through + + align:start position:0% +in mind all the way through + + + align:start position:0% +in mind all the way through +and then i'm going to just repeat the + + align:start position:0% +and then i'm going to just repeat the + + + align:start position:0% +and then i'm going to just repeat the +following t times where t is the maximum + + align:start position:0% +following t times where t is the maximum + + + align:start position:0% +following t times where t is the maximum +length as can be which is the the size + + align:start position:0% +length as can be which is the the size + + + align:start position:0% +length as can be which is the the size +of the alphabet of these of these things + + align:start position:0% +of the alphabet of these of these things + + + align:start position:0% +of the alphabet of these of these things +to the nth power where m is the length + + align:start position:0% +to the nth power where m is the length + + + align:start position:0% +to the nth power where m is the length +of those strings + + align:start position:0% +of those strings + + + align:start position:0% +of those strings +uh and i'm just going to not + + align:start position:0% +uh and i'm just going to not + + + align:start position:0% +uh and i'm just going to not +deterministically change one symbol + + align:start position:0% +deterministically change one symbol + + + align:start position:0% +deterministically change one symbol +at a time + + align:start position:0% +at a time + + + align:start position:0% +at a time +making sure that i'm staying in the + + align:start position:0% +making sure that i'm staying in the + + + align:start position:0% +making sure that i'm staying in the +language + + align:start position:0% +language + + + align:start position:0% +language +so rejecting immediately if that change + + align:start position:0% +so rejecting immediately if that change + + + align:start position:0% +so rejecting immediately if that change +introduced a + + align:start position:0% +introduced a + + + align:start position:0% +introduced a +string outside the language + + align:start position:0% +string outside the language + + + align:start position:0% +string outside the language +and accepting if that string that i get + + align:start position:0% +and accepting if that string that i get + + + align:start position:0% +and accepting if that string that i get +by changing that single symbol + + align:start position:0% +by changing that single symbol + + + align:start position:0% +by changing that single symbol +is now my target + + align:start position:0% +is now my target + + + align:start position:0% +is now my target +um + + align:start position:0% +um + + + align:start position:0% +um +and if i've gone through my bound and i + + align:start position:0% +and if i've gone through my bound and i + + + align:start position:0% +and if i've gone through my bound and i +haven't managed to reach + + align:start position:0% +haven't managed to reach + + + align:start position:0% +haven't managed to reach +that target then i'm just going to + + align:start position:0% +that target then i'm just going to + + + align:start position:0% +that target then i'm just going to +reject + + align:start position:0% + + + + align:start position:0% + +and we just have to observe that this + + align:start position:0% +and we just have to observe that this + + + align:start position:0% +and we just have to observe that this +algorithm + + align:start position:0% +algorithm + + + align:start position:0% +algorithm +doesn't use too much space + + align:start position:0% +doesn't use too much space + + + align:start position:0% +doesn't use too much space +so if you imagine what we need here + + align:start position:0% +so if you imagine what we need here + + + align:start position:0% +so if you imagine what we need here +here's my input unv + + align:start position:0% +here's my input unv + + + align:start position:0% +here's my input unv +which is of length n + + align:start position:0% +which is of length n + + + align:start position:0% +which is of length n +and the total amount of space i just + + align:start position:0% +and the total amount of space i just + + + align:start position:0% +and the total amount of space i just +have to remember the current y + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +and um + + align:start position:0% +and um + + + align:start position:0% +and um +and also my counter t my counter up to t + + align:start position:0% +and also my counter t my counter up to t + + + align:start position:0% +and also my counter t my counter up to t +so um each of those can be written down + + align:start position:0% +so um each of those can be written down + + + align:start position:0% +so um each of those can be written down +with it with uh essentially in space so + + align:start position:0% +with it with uh essentially in space so + + + align:start position:0% +with it with uh essentially in space so +the total amount is going to be order n + + align:start position:0% +the total amount is going to be order n + + + align:start position:0% +the total amount is going to be order n +space + + align:start position:0% +space + + + align:start position:0% +space +um + + align:start position:0% +um + + + align:start position:0% +um +so that shows that uh this latter dfa + + align:start position:0% +so that shows that uh this latter dfa + + + align:start position:0% +so that shows that uh this latter dfa +problem is actually in non-deterministic + + align:start position:0% +problem is actually in non-deterministic + + + align:start position:0% +problem is actually in non-deterministic +space n + + align:start position:0% +space n + + + align:start position:0% +space n +not deterministic linear space + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +and what we're going to show next + + align:start position:0% +and what we're going to show next + + + align:start position:0% +and what we're going to show next +um + + align:start position:0% +um + + + align:start position:0% +um +is that this language is actually + + align:start position:0% +is that this language is actually + + + align:start position:0% +is that this language is actually +solvable in deterministic space and this + + align:start position:0% +solvable in deterministic space and this + + + align:start position:0% +solvable in deterministic space and this +is kind of perhaps a bit of a surprise + + align:start position:0% +is kind of perhaps a bit of a surprise + + + align:start position:0% +is kind of perhaps a bit of a surprise +okay um + + align:start position:0% + + + + align:start position:0% + +so what's the size of the input the size + + align:start position:0% +so what's the size of the input the size + + + align:start position:0% +so what's the size of the input the size +of the input is + + align:start position:0% +of the input is + + + align:start position:0% +of the input is +uh going to be what it takes to write + + align:start position:0% +uh going to be what it takes to write + + + align:start position:0% +uh going to be what it takes to write +down the uh the dfa and the uh the two + + align:start position:0% +down the uh the dfa and the uh the two + + + align:start position:0% +down the uh the dfa and the uh the two +strings u and v um + + align:start position:0% +strings u and v um + + + align:start position:0% +strings u and v um +so uh + + align:start position:0% + + + + align:start position:0% + +um here + + align:start position:0% +um here + + + align:start position:0% +um here +uh + + align:start position:0% +uh + + + align:start position:0% +uh +yeah i mean i i should have also + + align:start position:0% +yeah i mean i i should have also + + + align:start position:0% +yeah i mean i i should have also +included as part of the input + + align:start position:0% +included as part of the input + + + align:start position:0% +included as part of the input +the the description of b itself + + align:start position:0% +the the description of b itself + + + align:start position:0% +the the description of b itself +but um + + align:start position:0% +but um + + + align:start position:0% +but um +uh so + + align:start position:0% +uh so + + + align:start position:0% +uh so +but that's going to even work in my + + align:start position:0% +but that's going to even work in my + + + align:start position:0% +but that's going to even work in my +favor because um + + align:start position:0% +favor because um + + + align:start position:0% +favor because um +so this this is slightly incorrect + + align:start position:0% +so this this is slightly incorrect + + + align:start position:0% +so this this is slightly incorrect +because b itself has to appear as part + + align:start position:0% +because b itself has to appear as part + + + align:start position:0% +because b itself has to appear as part +of the input so apologies for that but + + align:start position:0% +of the input so apologies for that but + + + align:start position:0% +of the input so apologies for that but +still the amount of uh space used is + + align:start position:0% +still the amount of uh space used is + + + align:start position:0% +still the amount of uh space used is +going to be order n + + align:start position:0% +going to be order n + + + align:start position:0% +going to be order n +um because these are going to be + + align:start position:0% +um because these are going to be + + + align:start position:0% +um because these are going to be +actually less than n + + align:start position:0% +actually less than n + + + align:start position:0% +actually less than n +um + + align:start position:0% +um + + + align:start position:0% +um +so let me + + align:start position:0% +so let me + + + align:start position:0% +so let me +jump be so we don't run out of time for + + align:start position:0% +jump be so we don't run out of time for + + + align:start position:0% +jump be so we don't run out of time for +the lecture we can save additional + + align:start position:0% +the lecture we can save additional + + + align:start position:0% +the lecture we can save additional +questions for + + align:start position:0% +questions for + + + align:start position:0% +questions for +afterward i'll stick around for a few + + align:start position:0% +afterward i'll stick around for a few + + + align:start position:0% +afterward i'll stick around for a few +minutes i just really have one more + + align:start position:0% +minutes i just really have one more + + + align:start position:0% +minutes i just really have one more +slide here um and that is proving this + + align:start position:0% +slide here um and that is proving this + + + align:start position:0% +slide here um and that is proving this +theorem that ladder can be done in + + align:start position:0% +theorem that ladder can be done in + + + align:start position:0% +theorem that ladder can be done in +deterministically in polynomial space + + align:start position:0% +deterministically in polynomial space + + + align:start position:0% +deterministically in polynomial space +and that's going to be + + align:start position:0% +and that's going to be + + + align:start position:0% +and that's going to be +important as a kind of a + + align:start position:0% +important as a kind of a + + + align:start position:0% +important as a kind of a +preview of what we're going to be doing + + align:start position:0% +preview of what we're going to be doing + + + align:start position:0% +preview of what we're going to be doing +on tuesday + + align:start position:0% + + + + align:start position:0% + +and you know + + align:start position:0% + + + + align:start position:0% + +if this goes a little fast i'll go over + + align:start position:0% +if this goes a little fast i'll go over + + + align:start position:0% +if this goes a little fast i'll go over +it again on tuesday so let's just see + + align:start position:0% +it again on tuesday so let's just see + + + align:start position:0% +it again on tuesday so let's just see +how it goes so i'm going to show the + + align:start position:0% +how it goes so i'm going to show the + + + align:start position:0% +how it goes so i'm going to show the +same ladder dfa problem + + align:start position:0% + + + + align:start position:0% + +is solvable deterministically + + align:start position:0% +is solvable deterministically + + + align:start position:0% +is solvable deterministically +in + + align:start position:0% +in + + + align:start position:0% +in +polynomial space and but this time it's + + align:start position:0% +polynomial space and but this time it's + + + align:start position:0% +polynomial space and but this time it's +going to be in squared space instead of + + align:start position:0% +going to be in squared space instead of + + + align:start position:0% +going to be in squared space instead of +non-deterministically in end space so + + align:start position:0% +non-deterministically in end space so + + + align:start position:0% +non-deterministically in end space so +there's going to be some cost but it's + + align:start position:0% +there's going to be some cost but it's + + + align:start position:0% +there's going to be some cost but it's +only going to be a squaring + + align:start position:0% +only going to be a squaring + + + align:start position:0% +only going to be a squaring +so remember what the problem is + + align:start position:0% +so remember what the problem is + + + align:start position:0% +so remember what the problem is +you know i'm giving you that dfa + + align:start position:0% +you know i'm giving you that dfa + + + align:start position:0% +you know i'm giving you that dfa +and giving you two strings in the + + align:start position:0% +and giving you two strings in the + + + align:start position:0% +and giving you two strings in the +language of that dfa and i want to know + + align:start position:0% +language of that dfa and i want to know + + + align:start position:0% +language of that dfa and i want to know +can i get + + align:start position:0% +can i get + + + align:start position:0% +can i get +from one + + align:start position:0% +from one + + + align:start position:0% +from one +the first string to the second string by + + align:start position:0% +the first string to the second string by + + + align:start position:0% +the first string to the second string by +changing one symbol at a time but always + + align:start position:0% +changing one symbol at a time but always + + + align:start position:0% +changing one symbol at a time but always +making sure that the strings are + + align:start position:0% +making sure that the strings are + + + align:start position:0% +making sure that the strings are +along the way are accepted by that dfa + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so i'm going to introduce notation + + align:start position:0% +so i'm going to introduce notation + + + align:start position:0% +so i'm going to introduce notation +saying + + align:start position:0% +saying + + + align:start position:0% +saying +can i get from string u to v by a ladder + + align:start position:0% +can i get from string u to v by a ladder + + + align:start position:0% +can i get from string u to v by a ladder +but now i'm limiting how many steps i + + align:start position:0% +but now i'm limiting how many steps i + + + align:start position:0% +but now i'm limiting how many steps i +can take so i'm writing u to v but doing + + align:start position:0% +can take so i'm writing u to v but doing + + + align:start position:0% +can take so i'm writing u to v but doing +it only within b + + align:start position:0% +it only within b + + + align:start position:0% +it only within b +b intermediate strings b steps + + align:start position:0% +b intermediate strings b steps + + + align:start position:0% +b intermediate strings b steps +so is there a ladder from u to v of + + align:start position:0% +so is there a ladder from u to v of + + + align:start position:0% +so is there a ladder from u to v of +length at most b + + align:start position:0% +length at most b + + + align:start position:0% +length at most b +that's what it means to write this + + align:start position:0% +that's what it means to write this + + + align:start position:0% +that's what it means to write this +notation down + + align:start position:0% + + + + align:start position:0% + +so i'm going to + + align:start position:0% +so i'm going to + + + align:start position:0% +so i'm going to +uh give you a recursive procedure to + + align:start position:0% +uh give you a recursive procedure to + + + align:start position:0% +uh give you a recursive procedure to +solve + + align:start position:0% +solve + + + align:start position:0% +solve +the bounded ladder problem where it's + + align:start position:0% +the bounded ladder problem where it's + + + align:start position:0% +the bounded ladder problem where it's +just like the before but now i'm going + + align:start position:0% +just like the before but now i'm going + + + align:start position:0% +just like the before but now i'm going +to + + align:start position:0% +to + + + align:start position:0% +to +say not only does there a ladder from u + + align:start position:0% +say not only does there a ladder from u + + + align:start position:0% +say not only does there a ladder from u +to v but there's a ladder of length at + + align:start position:0% +to v but there's a ladder of length at + + + align:start position:0% +to v but there's a ladder of length at +most b + + align:start position:0% + + + + align:start position:0% + +okay so that's going to allow me to + + align:start position:0% +okay so that's going to allow me to + + + align:start position:0% +okay so that's going to allow me to +solve the latter problem recursively by + + align:start position:0% +solve the latter problem recursively by + + + align:start position:0% +solve the latter problem recursively by +shrinking the size of b + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +okay + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% +so um + + + align:start position:0% +so um +let's how is this going to work + + align:start position:0% +let's how is this going to work + + + align:start position:0% +let's how is this going to work +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um + + align:start position:0% +um + + + align:start position:0% +um +well here's going to be the idea + + align:start position:0% +well here's going to be the idea + + + align:start position:0% +well here's going to be the idea +so here is my u and my v + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +and the procedure is going to work by + + align:start position:0% +and the procedure is going to work by + + + align:start position:0% +and the procedure is going to work by +instead of + + align:start position:0% +instead of + + + align:start position:0% +instead of +non-deterministically guessing + + align:start position:0% +non-deterministically guessing + + + align:start position:0% +non-deterministically guessing +the steps that take me from work to play + + align:start position:0% +the steps that take me from work to play + + + align:start position:0% +the steps that take me from work to play +because i don't have non-determinism + + align:start position:0% +because i don't have non-determinism + + + align:start position:0% +because i don't have non-determinism +anymore i have to operate + + align:start position:0% +anymore i have to operate + + + align:start position:0% +anymore i have to operate +deterministically + + align:start position:0% +deterministically + + + align:start position:0% +deterministically +what i'm going to do is + + align:start position:0% +what i'm going to do is + + + align:start position:0% +what i'm going to do is +work instead of + + align:start position:0% +work instead of + + + align:start position:0% +work instead of +um + + align:start position:0% +um + + + align:start position:0% +um +i'm going to instead of going from + + align:start position:0% +i'm going to instead of going from + + + align:start position:0% +i'm going to instead of going from +looking at the very first + + align:start position:0% +looking at the very first + + + align:start position:0% +looking at the very first +thing that follows from from you i'm + + align:start position:0% +thing that follows from from you i'm + + + align:start position:0% +thing that follows from from you i'm +going to jump right to the middle + + align:start position:0% +going to jump right to the middle + + + align:start position:0% +going to jump right to the middle +and try every possible middle string + + align:start position:0% + + + + align:start position:0% + +oh i have no clue even what that middle + + align:start position:0% +oh i have no clue even what that middle + + + align:start position:0% +oh i have no clue even what that middle +string should look like so i'm going to + + align:start position:0% +string should look like so i'm going to + + + align:start position:0% +string should look like so i'm going to +try all possibilities in the sequence + + align:start position:0% + + + + align:start position:0% + +but then i'm going to use once i have + + align:start position:0% +but then i'm going to use once i have + + + align:start position:0% +but then i'm going to use once i have +one of those possibilities i'm going to + + align:start position:0% +one of those possibilities i'm going to + + + align:start position:0% +one of those possibilities i'm going to +recursively try to solve the problem by + + align:start position:0% +recursively try to solve the problem by + + + align:start position:0% +recursively try to solve the problem by +splitting that now but i'm now going to + + align:start position:0% +splitting that now but i'm now going to + + + align:start position:0% +splitting that now but i'm now going to +divide that b value in half + + align:start position:0% +divide that b value in half + + + align:start position:0% +divide that b value in half +okay so here is the maximum value we can + + align:start position:0% +okay so here is the maximum value we can + + + align:start position:0% +okay so here is the maximum value we can +have this is the t from the previous + + align:start position:0% +have this is the t from the previous + + + align:start position:0% +have this is the t from the previous +slide which is the maximum length um + + align:start position:0% +slide which is the maximum length um + + + align:start position:0% +slide which is the maximum length um +and i uh + + align:start position:0% +and i uh + + + align:start position:0% +and i uh +here i'm going to try every possible + + align:start position:0% +here i'm going to try every possible + + + align:start position:0% +here i'm going to try every possible +intermediate let's start off with a + + align:start position:0% +intermediate let's start off with a + + + align:start position:0% +intermediate let's start off with a +all a's + + align:start position:0% +all a's + + + align:start position:0% +all a's +um + + align:start position:0% +um + + + align:start position:0% +um +and now i cut the problem in half can i + + align:start position:0% +and now i cut the problem in half can i + + + align:start position:0% +and now i cut the problem in half can i +get from work to all a's and all a's to + + align:start position:0% +get from work to all a's and all a's to + + + align:start position:0% +get from work to all a's and all a's to +play well very first thing i should + + align:start position:0% +play well very first thing i should + + + align:start position:0% +play well very first thing i should +check is making sure that all a's + + align:start position:0% +check is making sure that all a's + + + align:start position:0% +check is making sure that all a's +in fact is a string uh in the language + + align:start position:0% +in fact is a string uh in the language + + + align:start position:0% +in fact is a string uh in the language +and if we're thinking of the languages + + align:start position:0% +and if we're thinking of the languages + + + align:start position:0% +and if we're thinking of the languages +sort of you know matching it's like + + align:start position:0% +sort of you know matching it's like + + + align:start position:0% +sort of you know matching it's like +english all a's is not + + align:start position:0% +english all a's is not + + + align:start position:0% +english all a's is not +a legitimate word so you try the next + + align:start position:0% +a legitimate word so you try the next + + + align:start position:0% +a legitimate word so you try the next +one + + align:start position:0% +one + + + align:start position:0% +one +aab and this is how it's going to work + + align:start position:0% +aab and this is how it's going to work + + + align:start position:0% +aab and this is how it's going to work +but now you're going to be instead of + + align:start position:0% +but now you're going to be instead of + + + align:start position:0% +but now you're going to be instead of +using english you're going to feed it + + align:start position:0% +using english you're going to feed it + + + align:start position:0% +using english you're going to feed it +into the finite automaton just one after + + align:start position:0% +into the finite automaton just one after + + + align:start position:0% +into the finite automaton just one after +the next trying every possibility until + + align:start position:0% +the next trying every possibility until + + + align:start position:0% +the next trying every possibility until +you know like a clock + + align:start position:0% +you know like a clock + + + align:start position:0% +you know like a clock +like a like an odometer + + align:start position:0% +like a like an odometer + + + align:start position:0% +like a like an odometer +trying them all + + align:start position:0% +trying them all + + + align:start position:0% +trying them all +until eventually you find a string + + align:start position:0% +until eventually you find a string + + + align:start position:0% +until eventually you find a string +that's in the language + + align:start position:0% +that's in the language + + + align:start position:0% +that's in the language +sort of i'm representing that by an + + align:start position:0% +sort of i'm representing that by an + + + align:start position:0% +sort of i'm representing that by an +english word able maybe that's the first + + align:start position:0% +english word able maybe that's the first + + + align:start position:0% +english word able maybe that's the first +word that you would have found and then + + align:start position:0% +word that you would have found and then + + + align:start position:0% +word that you would have found and then +once you find that you're gonna + + align:start position:0% +once you find that you're gonna + + + align:start position:0% +once you find that you're gonna +can i get from work to able and able to + + align:start position:0% +can i get from work to able and able to + + + align:start position:0% +can i get from work to able and able to +play recursively reusing the space again + + align:start position:0% +play recursively reusing the space again + + + align:start position:0% +play recursively reusing the space again +but now where the bound is cut in half + + align:start position:0% +but now where the bound is cut in half + + + align:start position:0% +but now where the bound is cut in half +okay so that's that's the whole album + + align:start position:0% +okay so that's that's the whole album + + + align:start position:0% +okay so that's that's the whole album +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +just going through it quickly and we'll + + align:start position:0% +just going through it quickly and we'll + + + align:start position:0% +just going through it quickly and we'll +do this again um + + align:start position:0% +do this again um + + + align:start position:0% +do this again um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +here is my + + align:start position:0% +here is my + + + align:start position:0% +here is my +dfa going from u to v within b steps + + align:start position:0% +dfa going from u to v within b steps + + + align:start position:0% +dfa going from u to v within b steps +first of all + + align:start position:0% +first of all + + + align:start position:0% +first of all +oh this is bad uh t should not be one b + + align:start position:0% +oh this is bad uh t should not be one b + + + align:start position:0% +oh this is bad uh t should not be one b +this should be b if b is one um + + align:start position:0% +this should be b if b is one um + + + align:start position:0% +this should be b if b is one um +can i quickly fix that + + align:start position:0% +can i quickly fix that + + + align:start position:0% +can i quickly fix that +uh so these t's should be b's my + + align:start position:0% +uh so these t's should be b's my + + + align:start position:0% +uh so these t's should be b's my +apologies + + align:start position:0% +apologies + + + align:start position:0% +apologies +um + + align:start position:0% + + + + align:start position:0% + +so if t is one if b is one + + align:start position:0% +so if t is one if b is one + + + align:start position:0% +so if t is one if b is one +then they have to d then i'm only + + align:start position:0% +then they have to d then i'm only + + + align:start position:0% +then they have to d then i'm only +allowed a a ladder of length one now i + + align:start position:0% +allowed a a ladder of length one now i + + + align:start position:0% +allowed a a ladder of length one now i +just check at the media directly do you + + align:start position:0% +just check at the media directly do you + + + align:start position:0% +just check at the media directly do you +and v different in just + + align:start position:0% +and v different in just + + + align:start position:0% +and v different in just +in one place + + align:start position:0% +in one place + + + align:start position:0% +in one place +if yes then accept else i reject + + align:start position:0% +if yes then accept else i reject + + + align:start position:0% +if yes then accept else i reject +uh if it's greater than one now i'm + + align:start position:0% +uh if it's greater than one now i'm + + + align:start position:0% +uh if it's greater than one now i'm +going to do this procedure that i + + align:start position:0% +going to do this procedure that i + + + align:start position:0% +going to do this procedure that i +described i'm going to try for each + + align:start position:0% +described i'm going to try for each + + + align:start position:0% +described i'm going to try for each +possible w + + align:start position:0% +possible w + + + align:start position:0% +possible w +uh + + align:start position:0% +uh + + + align:start position:0% +uh +in the middle + + align:start position:0% +in the middle + + + align:start position:0% +in the middle +um + + align:start position:0% +um + + + align:start position:0% +um +i'm gonna + + align:start position:0% + + + + align:start position:0% + +try that w test whether i can get from u + + align:start position:0% +try that w test whether i can get from u + + + align:start position:0% +try that w test whether i can get from u +to w in half the number of steps and + + align:start position:0% +to w in half the number of steps and + + + align:start position:0% +to w in half the number of steps and +from w to v in half the number of steps + + align:start position:0% +from w to v in half the number of steps + + + align:start position:0% +from w to v in half the number of steps +and except if they both accept um + + align:start position:0% +and except if they both accept um + + + align:start position:0% +and except if they both accept um +and if trying all possible w's + + align:start position:0% +and if trying all possible w's + + + align:start position:0% +and if trying all possible w's +none of them work then i know that + + align:start position:0% +none of them work then i know that + + + align:start position:0% +none of them work then i know that +there's no way to get from u to v and b + + align:start position:0% +there's no way to get from u to v and b + + + align:start position:0% +there's no way to get from u to v and b +steps and so then i reject + + align:start position:0% +steps and so then i reject + + + align:start position:0% +steps and so then i reject +okay and then to do + + align:start position:0% +okay and then to do + + + align:start position:0% +okay and then to do +the original problem which was not the + + align:start position:0% +the original problem which was not the + + + align:start position:0% +the original problem which was not the +bounded ladder problem i just do the + + align:start position:0% +bounded ladder problem i just do the + + + align:start position:0% +bounded ladder problem i just do the +bounded line i do the bounded ladder + + align:start position:0% +bounded line i do the bounded ladder + + + align:start position:0% +bounded line i do the bounded ladder +problem + + align:start position:0% +problem + + + align:start position:0% +problem +where i put in t which is the maximum + + align:start position:0% +where i put in t which is the maximum + + + align:start position:0% +where i put in t which is the maximum +possible length that it could be to get + + align:start position:0% +possible length that it could be to get + + + align:start position:0% +possible length that it could be to get +from work to play out to get from u to v + + align:start position:0% +from work to play out to get from u to v + + + align:start position:0% +from work to play out to get from u to v +okay so the space analysis + + align:start position:0% +okay so the space analysis + + + align:start position:0% +okay so the space analysis +um + + align:start position:0% +um + + + align:start position:0% +um +well i'm kind of out of time here so + + align:start position:0% +well i'm kind of out of time here so + + + align:start position:0% +well i'm kind of out of time here so +we're going to go through this again + + align:start position:0% +we're going to go through this again + + + align:start position:0% +we're going to go through this again +next time + + align:start position:0% +next time + + + align:start position:0% +next time +we have a very quick + + align:start position:0% +we have a very quick + + + align:start position:0% +we have a very quick +so let me skip that uh analysis i'll + + align:start position:0% +so let me skip that uh analysis i'll + + + align:start position:0% +so let me skip that uh analysis i'll +review this next time i have a very + + align:start position:0% +review this next time i have a very + + + align:start position:0% +review this next time i have a very +quick check-in i just want to get to you + + align:start position:0% +quick check-in i just want to get to you + + + align:start position:0% +quick check-in i just want to get to you +get get here + + align:start position:0% +get get here + + + align:start position:0% +get get here +um + + align:start position:0% +um + + + align:start position:0% +um +find an english word + + align:start position:0% +find an english word + + + align:start position:0% +find an english word +letter that connects the word must to + + align:start position:0% +letter that connects the word must to + + + align:start position:0% +letter that connects the word must to +the word vote + + align:start position:0% +the word vote + + + align:start position:0% +the word vote +you can think about that i mean i it's + + align:start position:0% +you can think about that i mean i it's + + + align:start position:0% +you can think about that i mean i it's +not that hard to come up with such a + + align:start position:0% +not that hard to come up with such a + + + align:start position:0% +not that hard to come up with such a +word ladder uh so i encourage you + + align:start position:0% +word ladder uh so i encourage you + + + align:start position:0% +word ladder uh so i encourage you +to think about that also to think about + + align:start position:0% +to think about that also to think about + + + align:start position:0% +to think about that also to think about +voting which is also important + + align:start position:0% +voting which is also important + + + align:start position:0% +voting which is also important +that's coming up + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +okay another five seconds here + + align:start position:0% +okay another five seconds here + + + align:start position:0% +okay another five seconds here +um + + align:start position:0% + + + + align:start position:0% + +okay i'm gonna end this so make sure you + + align:start position:0% +okay i'm gonna end this so make sure you + + + align:start position:0% +okay i'm gonna end this so make sure you +get your credit for the check-in + + align:start position:0% + + + + align:start position:0% + +okay so uh we're at the end of the hour + + align:start position:0% +okay so uh we're at the end of the hour + + + align:start position:0% +okay so uh we're at the end of the hour +um + + align:start position:0% +um + + + align:start position:0% +um +into the end of the night + + align:start position:0% +into the end of the night + + + align:start position:0% +into the end of the night +end of the 80 minutes anyway uh so this + + align:start position:0% +end of the 80 minutes anyway uh so this + + + align:start position:0% +end of the 80 minutes anyway uh so this +is what we did today + + align:start position:0% +is what we did today + + + align:start position:0% +is what we did today +um + + align:start position:0% +um + + + align:start position:0% +um +and + + align:start position:0% +and + + + align:start position:0% +and +looks like i ran over by a minute so my + + align:start position:0% +looks like i ran over by a minute so my + + + align:start position:0% +looks like i ran over by a minute so my +apologies + + align:start position:0% +apologies + + + align:start position:0% +apologies +and but i'll stick around here um if any + + align:start position:0% +and but i'll stick around here um if any + + + align:start position:0% +and but i'll stick around here um if any +of you have any further questions so but + + align:start position:0% +of you have any further questions so but + + + align:start position:0% +of you have any further questions so but +otherwise + + align:start position:0% +otherwise + + + align:start position:0% +otherwise +uh lecture is over + + align:start position:0% +uh lecture is over + + + align:start position:0% +uh lecture is over +uh see you guys + + align:start position:0% +uh see you guys + + + align:start position:0% +uh see you guys +do we know anything about ladder for + + align:start position:0% +do we know anything about ladder for + + + align:start position:0% +do we know anything about ladder for +other kinds of languages + + align:start position:0% +other kinds of languages + + + align:start position:0% +other kinds of languages +i i don't know + + align:start position:0% +i i don't know + + + align:start position:0% +i i don't know +um uh interesting question whether you + + align:start position:0% +um uh interesting question whether you + + + align:start position:0% +um uh interesting question whether you +can say uh some nice things about the + + align:start position:0% +can say uh some nice things about the + + + align:start position:0% +can say uh some nice things about the +latter + + align:start position:0% +latter + + + align:start position:0% +latter +um + + align:start position:0% +um + + + align:start position:0% +um +the latter um problem in other in other + + align:start position:0% +the latter um problem in other in other + + + align:start position:0% +the latter um problem in other in other +cases i don't know + + align:start position:0% +cases i don't know + + + align:start position:0% +cases i don't know +okay why is t here this value of t + + align:start position:0% +okay why is t here this value of t + + + align:start position:0% +okay why is t here this value of t +sigma to the m the maximum length + + align:start position:0% +sigma to the m the maximum length + + + align:start position:0% +sigma to the m the maximum length +of a um of a word letter so what did + + align:start position:0% +of a um of a word letter so what did + + + align:start position:0% +of a um of a word letter so what did +what first of all we have to m maybe i + + align:start position:0% +what first of all we have to m maybe i + + + align:start position:0% +what first of all we have to m maybe i +should have written this down m is the + + align:start position:0% +should have written this down m is the + + + align:start position:0% +should have written this down m is the +the the length + + align:start position:0% +the the length + + + align:start position:0% +the the length +of the words + + align:start position:0% +of the words + + + align:start position:0% +of the words +uh sigma is the alphabet + + align:start position:0% +uh sigma is the alphabet + + + align:start position:0% +uh sigma is the alphabet +of the words + + align:start position:0% +of the words + + + align:start position:0% +of the words +um + + align:start position:0% +um + + + align:start position:0% +um +so the number of possible different + + align:start position:0% +so the number of possible different + + + align:start position:0% +so the number of possible different +words is sigma to the m + + align:start position:0% +words is sigma to the m + + + align:start position:0% +words is sigma to the m +these are all possible words that there + + align:start position:0% +these are all possible words that there + + + align:start position:0% +these are all possible words that there +could possibly be + + align:start position:0% +could possibly be + + + align:start position:0% +could possibly be +so uh + + align:start position:0% +so uh + + + align:start position:0% +so uh +there's no + + align:start position:0% +there's no + + + align:start position:0% +there's no +reason in a word like + + align:start position:0% +reason in a word like + + + align:start position:0% +reason in a word like +or ever to repeat the word because you + + align:start position:0% +or ever to repeat the word because you + + + align:start position:0% +or ever to repeat the word because you +can just find a shorter word ladder that + + align:start position:0% +can just find a shorter word ladder that + + + align:start position:0% +can just find a shorter word ladder that +still does the job of connecting to + + align:start position:0% +still does the job of connecting to + + + align:start position:0% +still does the job of connecting to +connecting + + align:start position:0% +connecting + + + align:start position:0% +connecting +a start in the end + + align:start position:0% +a start in the end + + + align:start position:0% +a start in the end +so you can just cut out that middle + + align:start position:0% +so you can just cut out that middle + + + align:start position:0% +so you can just cut out that middle +part um the repeated part + + align:start position:0% +part um the repeated part + + + align:start position:0% +part um the repeated part +so + + align:start position:0% +so + + + align:start position:0% +so +in that case + + align:start position:0% +in that case + + + align:start position:0% +in that case +the longest possible + + align:start position:0% +the longest possible + + + align:start position:0% +the longest possible +word letter is going to be the total + + align:start position:0% +word letter is going to be the total + + + align:start position:0% +word letter is going to be the total +number of possible words that you can + + align:start position:0% +number of possible words that you can + + + align:start position:0% +number of possible words that you can +have which is going to be sigma the size + + align:start position:0% +have which is going to be sigma the size + + + align:start position:0% +have which is going to be sigma the size +of sigma to the m + + align:start position:0% +of sigma to the m + + + align:start position:0% +of sigma to the m +explain again why cohen p is a subset of + + align:start position:0% +explain again why cohen p is a subset of + + + align:start position:0% +explain again why cohen p is a subset of +p space + + align:start position:0% +p space + + + align:start position:0% +p space +um + + align:start position:0% + + + + align:start position:0% + +well + + align:start position:0% +well + + + align:start position:0% +well +maybe i'll say it this way + + align:start position:0% +maybe i'll say it this way + + + align:start position:0% +maybe i'll say it this way +take the + + align:start position:0% +take the + + + align:start position:0% +take the +why is + + align:start position:0% +why is + + + align:start position:0% +why is +why is every co np language also in pd + + align:start position:0% +why is every co np language also in pd + + + align:start position:0% +why is every co np language also in pd +space + + align:start position:0% +space + + + align:start position:0% +space +well take the complement of your co-mp + + align:start position:0% +well take the complement of your co-mp + + + align:start position:0% +well take the complement of your co-mp +language that's an np language + + align:start position:0% +language that's an np language + + + align:start position:0% +language that's an np language +an np language is in p space because we + + align:start position:0% +an np language is in p space because we + + + align:start position:0% +an np language is in p space because we +proved that that's what we proved um + + align:start position:0% +proved that that's what we proved um + + + align:start position:0% +proved that that's what we proved um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +but if a language is in p space its + + align:start position:0% +but if a language is in p space its + + + align:start position:0% +but if a language is in p space its +complement is also in p space because + + align:start position:0% +complement is also in p space because + + + align:start position:0% +complement is also in p space because +for a deterministic procedure you can + + align:start position:0% +for a deterministic procedure you can + + + align:start position:0% +for a deterministic procedure you can +just flip the answer of the machine + + align:start position:0% +just flip the answer of the machine + + + align:start position:0% +just flip the answer of the machine +um so now you get + + align:start position:0% +um so now you get + + + align:start position:0% +um so now you get +you know if so if b language b is in + + align:start position:0% +you know if so if b language b is in + + + align:start position:0% +you know if so if b language b is in +cohen p its complement b b complement is + + align:start position:0% +cohen p its complement b b complement is + + + align:start position:0% +cohen p its complement b b complement is +an np which is in p space but now so b + + align:start position:0% +an np which is in p space but now so b + + + align:start position:0% +an np which is in p space but now so b +complement is in p space so now + + align:start position:0% +complement is in p space so now + + + align:start position:0% +complement is in p space so now +p space you can invert the answer and + + align:start position:0% +p space you can invert the answer and + + + align:start position:0% +p space you can invert the answer and +now b is also in p space i hope that + + align:start position:0% +now b is also in p space i hope that + + + align:start position:0% +now b is also in p space i hope that +helps um + + align:start position:0% +helps um + + + align:start position:0% +helps um +somebody's giving me the answer to get + + align:start position:0% +somebody's giving me the answer to get + + + align:start position:0% +somebody's giving me the answer to get +from uh + + align:start position:0% +from uh + + + align:start position:0% +from uh +uh must to vote but you know i i i've + + align:start position:0% +uh must to vote but you know i i i've + + + align:start position:0% +uh must to vote but you know i i i've +seen an answer and that's you know there + + align:start position:0% +seen an answer and that's you know there + + + align:start position:0% +seen an answer and that's you know there +are online tools + + align:start position:0% +are online tools + + + align:start position:0% +are online tools +that will answer word letters um + + align:start position:0% +that will answer word letters um + + + align:start position:0% +that will answer word letters um +so you just + + align:start position:0% +so you just + + + align:start position:0% +so you just +plug in the two you know + + align:start position:0% +plug in the two you know + + + align:start position:0% +plug in the two you know +where the start and the finish and it'll + + align:start position:0% +where the start and the finish and it'll + + + align:start position:0% +where the start and the finish and it'll +give you the word ladder and then the + + align:start position:0% +give you the word ladder and then the + + + align:start position:0% +give you the word ladder and then the +one that this person is + + align:start position:0% +one that this person is + + + align:start position:0% +one that this person is +sent me is the one you get from that + + align:start position:0% +sent me is the one you get from that + + + align:start position:0% +sent me is the one you get from that +that tool so i suspect it didn't find it + + align:start position:0% +that tool so i suspect it didn't find it + + + align:start position:0% +that tool so i suspect it didn't find it +himself i i actually uh before lecture i + + align:start position:0% +himself i i actually uh before lecture i + + + align:start position:0% +himself i i actually uh before lecture i +actually saw that on my own besides the + + align:start position:0% +actually saw that on my own besides the + + + align:start position:0% +actually saw that on my own besides the +one that i know the one that the one + + align:start position:0% +one that i know the one that the one + + + align:start position:0% +one that i know the one that the one +that the tool will give you so that tool + + align:start position:0% +that the tool will give you so that tool + + + align:start position:0% +that the tool will give you so that tool +gives one in uh i think five steps and i + + align:start position:0% +gives one in uh i think five steps and i + + + align:start position:0% +gives one in uh i think five steps and i +found one on my own of six steps it's + + align:start position:0% +found one on my own of six steps it's + + + align:start position:0% +found one on my own of six steps it's +not that hard but yeah must + + align:start position:0% +not that hard but yeah must + + + align:start position:0% +not that hard but yeah must +most + + align:start position:0% +most + + + align:start position:0% +most +lost lose + + align:start position:0% +lost lose + + + align:start position:0% +lost lose +rose wrote and vote + + align:start position:0% +rose wrote and vote + + + align:start position:0% +rose wrote and vote +i think maybe that's seven steps + + align:start position:0% +i think maybe that's seven steps + + + align:start position:0% +i think maybe that's seven steps +um + + align:start position:0% +um + + + align:start position:0% +um +anyway you see you can solve the for + + align:start position:0% +anyway you see you can solve the for + + + align:start position:0% +anyway you see you can solve the for +short words you can solve these + + align:start position:0% +short words you can solve these + + + align:start position:0% +short words you can solve these +generally pretty quickly on your own + + align:start position:0% +generally pretty quickly on your own + + + align:start position:0% +generally pretty quickly on your own +um + + align:start position:0% +um + + + align:start position:0% +um +what else what else can i do for you + + align:start position:0% +what else what else can i do for you + + + align:start position:0% +what else what else can i do for you +um + + align:start position:0% + + + + align:start position:0% + +do we need to worry about coming back to + + align:start position:0% +do we need to worry about coming back to + + + align:start position:0% +do we need to worry about coming back to +a previously visited word visited word + + align:start position:0% +a previously visited word visited word + + + align:start position:0% +a previously visited word visited word +on the construction on this page + + align:start position:0% +on the construction on this page + + + align:start position:0% +on the construction on this page +no we don't have to worry about coming + + align:start position:0% +no we don't have to worry about coming + + + align:start position:0% +no we don't have to worry about coming +back to a previously visited word all + + align:start position:0% +back to a previously visited word all + + + align:start position:0% +back to a previously visited word all +you need to worry about is making sure + + align:start position:0% +you need to worry about is making sure + + + align:start position:0% +you need to worry about is making sure +that you bound how long you're going to + + align:start position:0% +that you bound how long you're going to + + + align:start position:0% +that you bound how long you're going to +go for + + align:start position:0% +go for + + + align:start position:0% +go for +and that's where the previously visited + + align:start position:0% +and that's where the previously visited + + + align:start position:0% +and that's where the previously visited +issue + + align:start position:0% +issue + + + align:start position:0% +issue +comes in + + align:start position:0% +comes in + + + align:start position:0% +comes in +you know if the + + align:start position:0% +you know if the + + + align:start position:0% +you know if the +um + + align:start position:0% +um + + + align:start position:0% +um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +if the word letter that you found + + align:start position:0% +if the word letter that you found + + + align:start position:0% +if the word letter that you found +repeats some word + + align:start position:0% +repeats some word + + + align:start position:0% +repeats some word +well then there would would have been a + + align:start position:0% +well then there would would have been a + + + align:start position:0% +well then there would would have been a +shorter word ladder that would have also + + align:start position:0% +shorter word ladder that would have also + + + align:start position:0% +shorter word ladder that would have also +worked but uh + + align:start position:0% +worked but uh + + + align:start position:0% +worked but uh +you know it still shows that it's + + align:start position:0% +you know it still shows that it's + + + align:start position:0% +you know it still shows that it's +possible to get from the + + align:start position:0% +possible to get from the + + + align:start position:0% +possible to get from the +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the start word to the finish word um + + align:start position:0% +the start word to the finish word um + + + align:start position:0% +the start word to the finish word um +if you if you're if you have a repeated + + align:start position:0% +if you if you're if you have a repeated + + + align:start position:0% +if you if you're if you have a repeated +one in between so that that doesn't + + align:start position:0% +one in between so that that doesn't + + + align:start position:0% +one in between so that that doesn't +matter + + align:start position:0% +matter + + + align:start position:0% +matter +we don't have to worry about that + + align:start position:0% +we don't have to worry about that + + + align:start position:0% +we don't have to worry about that +if you did then it would be a problem + + align:start position:0% +if you did then it would be a problem + + + align:start position:0% +if you did then it would be a problem +so i think i will it's four or five i + + align:start position:0% +so i think i will it's four or five i + + + align:start position:0% +so i think i will it's four or five i +think i want to head out uh + + align:start position:0% +think i want to head out uh + + + align:start position:0% +think i want to head out uh +see you all guys and i'm going to join + + align:start position:0% +see you all guys and i'm going to join + + + align:start position:0% +see you all guys and i'm going to join +my tas in the meeting shortly so bye-bye + + align:start position:0% +my tas in the meeting shortly so bye-bye + + + align:start position:0% +my tas in the meeting shortly so bye-bye +thank you for being here + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/cph71QcwHeQ.txt b/cph71QcwHeQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..a3d6f021b823ea13c3ba3b464fc50d399c6dc2d6 --- /dev/null +++ b/cph71QcwHeQ.txt @@ -0,0 +1,1027 @@ +align:start position:0% + +Markov processes can be very general + + align:start position:0% +Markov processes can be very general + + + align:start position:0% +Markov processes can be very general +they can run in continuous or discrete + + align:start position:0% +they can run in continuous or discrete + + + align:start position:0% +they can run in continuous or discrete +time can have a discrete or a continuous + + align:start position:0% +time can have a discrete or a continuous + + + align:start position:0% +time can have a discrete or a continuous +state space in this class will restrict + + align:start position:0% +state space in this class will restrict + + + align:start position:0% +state space in this class will restrict +ourselves to discrete time discrete + + align:start position:0% +ourselves to discrete time discrete + + + align:start position:0% +ourselves to discrete time discrete +state Markov chains these are the + + align:start position:0% +state Markov chains these are the + + + align:start position:0% +state Markov chains these are the +simplest cases and are the best to build + + align:start position:0% +simplest cases and are the best to build + + + align:start position:0% +simplest cases and are the best to build +our intuition so the state space is + + align:start position:0% +our intuition so the state space is + + + align:start position:0% +our intuition so the state space is +discrete here finite with M States and + + align:start position:0% +discrete here finite with M States and + + + align:start position:0% +discrete here finite with M States and +time is discrete that is at any discrete + + align:start position:0% +time is discrete that is at any discrete + + + align:start position:0% +time is discrete that is at any discrete +point in time the process is in one of + + align:start position:0% +point in time the process is in one of + + + align:start position:0% +point in time the process is in one of +these M States and let's say here at a + + align:start position:0% +these M States and let's say here at a + + + align:start position:0% +these M States and let's say here at a +given time s and again time is discrete + + align:start position:0% +given time s and again time is discrete + + + align:start position:0% +given time s and again time is discrete +so think about the following process you + + align:start position:0% +so think about the following process you + + + align:start position:0% +so think about the following process you +have someone hitting a drum indicating + + align:start position:0% +have someone hitting a drum indicating + + + align:start position:0% +have someone hitting a drum indicating +that a transition occurs and what it + + align:start position:0% +that a transition occurs and what it + + + align:start position:0% +that a transition occurs and what it +means is that the chain that was here + + align:start position:0% +means is that the chain that was here + + + align:start position:0% +means is that the chain that was here +will then jump let's say to another + + align:start position:0% +will then jump let's say to another + + + align:start position:0% +will then jump let's say to another +stage a at the next time so when the + + align:start position:0% +stage a at the next time so when the + + + align:start position:0% +stage a at the next time so when the +Markov chain jumps it can jump on itself + + align:start position:0% +Markov chain jumps it can jump on itself + + + align:start position:0% +Markov chain jumps it can jump on itself +or jump to another state like here or + + align:start position:0% +or jump to another state like here or + + + align:start position:0% +or jump to another state like here or +here and then you know at time s plus 1 + + align:start position:0% +here and then you know at time s plus 1 + + + align:start position:0% +here and then you know at time s plus 1 +someone hit the drum and you jump again + + align:start position:0% +someone hit the drum and you jump again + + + align:start position:0% +someone hit the drum and you jump again +and so on and so forth you can think of + + align:start position:0% +and so on and so forth you can think of + + + align:start position:0% +and so on and so forth you can think of +a very active frog jumping from lilies + + align:start position:0% +a very active frog jumping from lilies + + + align:start position:0% +a very active frog jumping from lilies +to lilies on the pond and following a + + align:start position:0% +to lilies on the pond and following a + + + align:start position:0% +to lilies on the pond and following a +regular drum beat so what is left to + + align:start position:0% +regular drum beat so what is left to + + + align:start position:0% +regular drum beat so what is left to +define are the various probability of + + align:start position:0% +define are the various probability of + + + align:start position:0% +define are the various probability of +transitions such as the transition from + + align:start position:0% +transitions such as the transition from + + + align:start position:0% +transitions such as the transition from +I to J and the notation is we're going + + align:start position:0% +I to J and the notation is we're going + + + align:start position:0% +I to J and the notation is we're going +to use is P IJ which by definition is + + align:start position:0% +to use is P IJ which by definition is + + + align:start position:0% +to use is P IJ which by definition is +that transition probability here + + align:start position:0% + + + + align:start position:0% + +right so given that you are in state I + + align:start position:0% +right so given that you are in state I + + + align:start position:0% +right so given that you are in state I +at time s what is the priority that you + + align:start position:0% +at time s what is the priority that you + + + align:start position:0% +at time s what is the priority that you +end up in state J at time s plus one + + align:start position:0% +end up in state J at time s plus one + + + align:start position:0% +end up in state J at time s plus one +notice that these transition + + align:start position:0% +notice that these transition + + + align:start position:0% +notice that these transition +probabilities here P IJ are not function + + align:start position:0% +probabilities here P IJ are not function + + + align:start position:0% +probabilities here P IJ are not function +of s so irrespective of what the term s + + align:start position:0% +of s so irrespective of what the term s + + + align:start position:0% +of s so irrespective of what the term s +that we are talking about these + + align:start position:0% +that we are talking about these + + + align:start position:0% +that we are talking about these +transition probabilities are the same so + + align:start position:0% +transition probabilities are the same so + + + align:start position:0% +transition probabilities are the same so +this is what we mean by a time + + align:start position:0% +this is what we mean by a time + + + align:start position:0% +this is what we mean by a time +homogeneous Markov chain in other words + + align:start position:0% +homogeneous Markov chain in other words + + + align:start position:0% +homogeneous Markov chain in other words +these are valid for s equals 0 1 2 and + + align:start position:0% +these are valid for s equals 0 1 2 and + + + align:start position:0% +these are valid for s equals 0 1 2 and +so and so forth so the defining feature + + align:start position:0% +so and so forth so the defining feature + + + align:start position:0% +so and so forth so the defining feature +of a Markov chain is the Markov property + + align:start position:0% +of a Markov chain is the Markov property + + + align:start position:0% +of a Markov chain is the Markov property +and the Markov property essentially says + + align:start position:0% +and the Markov property essentially says + + + align:start position:0% +and the Markov property essentially says +that the past is not really important in + + align:start position:0% +that the past is not really important in + + + align:start position:0% +that the past is not really important in +order to predict the future as long as + + align:start position:0% +order to predict the future as long as + + + align:start position:0% +order to predict the future as long as +you know where you are now another way + + align:start position:0% +you know where you are now another way + + + align:start position:0% +you know where you are now another way +of saying it is that if you look at the + + align:start position:0% +of saying it is that if you look at the + + + align:start position:0% +of saying it is that if you look at the +probability of going next in stage a + + align:start position:0% +probability of going next in stage a + + + align:start position:0% +probability of going next in stage a +even that you are now in state high and + + align:start position:0% +even that you are now in state high and + + + align:start position:0% +even that you are now in state high and +that I give you in addition the anti + + align:start position:0% +that I give you in addition the anti + + + align:start position:0% +that I give you in addition the anti +trajectory so I tell you that it was in + + align:start position:0% +trajectory so I tell you that it was in + + + align:start position:0% +trajectory so I tell you that it was in +eysie row at that time and so and so + + align:start position:0% +eysie row at that time and so and so + + + align:start position:0% +eysie row at that time and so and so +forth all the way up to time s minus 1 + + align:start position:0% +forth all the way up to time s minus 1 + + + align:start position:0% +forth all the way up to time s minus 1 +where it was in I s minus 1 so I give + + align:start position:0% +where it was in I s minus 1 so I give + + + align:start position:0% +where it was in I s minus 1 so I give +you the anti trajectory of the chain up + + align:start position:0% +you the anti trajectory of the chain up + + + align:start position:0% +you the anti trajectory of the chain up +to s and now I'm asking you what is the + + align:start position:0% +to s and now I'm asking you what is the + + + align:start position:0% +to s and now I'm asking you what is the +priority that you're going to go to s + + align:start position:0% +priority that you're going to go to s + + + align:start position:0% +priority that you're going to go to s +plus 1 the Markov property here simply + + align:start position:0% +plus 1 the Markov property here simply + + + align:start position:0% +plus 1 the Markov property here simply +says that that probability here is again + + align:start position:0% +says that that probability here is again + + + align:start position:0% +says that that probability here is again +p IJ so in other words all this + + align:start position:0% +p IJ so in other words all this + + + align:start position:0% +p IJ so in other words all this +information here is of no use to compute + + align:start position:0% +information here is of no use to compute + + + align:start position:0% +information here is of no use to compute +this probability now note that this + + align:start position:0% +this probability now note that this + + + align:start position:0% +this probability now note that this +transition probabilities are really + + align:start position:0% +transition probabilities are really + + + align:start position:0% +transition probabilities are really +probabilities in the following sense + + align:start position:0% +probabilities in the following sense + + + align:start position:0% +probabilities in the following sense +right so you are in I and then at the + + align:start position:0% +right so you are in I and then at the + + + align:start position:0% +right so you are in I and then at the +next time step you will definitely jump + + align:start position:0% +next time step you will definitely jump + + + align:start position:0% +next time step you will definitely jump +with Priority One and where are you + + align:start position:0% +with Priority One and where are you + + + align:start position:0% +with Priority One and where are you +going to jump or the pan but the + + align:start position:0% +going to jump or the pan but the + + + align:start position:0% +going to jump or the pan but the +summation of all possibilities have to + + align:start position:0% +summation of all possibilities have to + + + align:start position:0% +summation of all possibilities have to +sum up to one so from J equals 1 to n + + align:start position:0% +sum up to one so from J equals 1 to n + + + align:start position:0% +sum up to one so from J equals 1 to n +has to be 1 + + align:start position:0% +has to be 1 + + + align:start position:0% +has to be 1 +so now that we have introduced the main + + align:start position:0% +so now that we have introduced the main + + + align:start position:0% +so now that we have introduced the main +ingredients usually we are very + + align:start position:0% +ingredients usually we are very + + + align:start position:0% +ingredients usually we are very +interested in knowing what a Markov + + align:start position:0% +interested in knowing what a Markov + + + align:start position:0% +interested in knowing what a Markov +chain is going to do in the long run we + + align:start position:0% +chain is going to do in the long run we + + + align:start position:0% +chain is going to do in the long run we +are interested in finding the + + align:start position:0% +are interested in finding the + + + align:start position:0% +are interested in finding the +probability that the chain is in a state + + align:start position:0% +probability that the chain is in a state + + + align:start position:0% +probability that the chain is in a state +J after n transitions given that it is + + align:start position:0% +J after n transitions given that it is + + + align:start position:0% +J after n transitions given that it is +now in state I now because of the time + + align:start position:0% +now in state I now because of the time + + + align:start position:0% +now in state I now because of the time +of more genius this is the same thing as + + align:start position:0% +of more genius this is the same thing as + + + align:start position:0% +of more genius this is the same thing as +that in other words the current time + + align:start position:0% +that in other words the current time + + + align:start position:0% +that in other words the current time +could be an any time s we just have to + + align:start position:0% +could be an any time s we just have to + + + align:start position:0% +could be an any time s we just have to +add s here and again that is nothing + + align:start position:0% +add s here and again that is nothing + + + align:start position:0% +add s here and again that is nothing +else than this property right so we are + + align:start position:0% +else than this property right so we are + + + align:start position:0% +else than this property right so we are +interested in calculating our I G of n + + align:start position:0% +interested in calculating our I G of n + + + align:start position:0% +interested in calculating our I G of n +for any n for N equals 1 this is nothing + + align:start position:0% +for any n for N equals 1 this is nothing + + + align:start position:0% +for any n for N equals 1 this is nothing +else than our i G of 1 is the same as + + align:start position:0% +else than our i G of 1 is the same as + + + align:start position:0% +else than our i G of 1 is the same as +these transition probabilities that we + + align:start position:0% +these transition probabilities that we + + + align:start position:0% +these transition probabilities that we +have defined but for N greater than + + align:start position:0% +have defined but for N greater than + + + align:start position:0% +have defined but for N greater than +equals to do what we have seen is the + + align:start position:0% +equals to do what we have seen is the + + + align:start position:0% +equals to do what we have seen is the +introduction of a key recursion here and + + align:start position:0% +introduction of a key recursion here and + + + align:start position:0% +introduction of a key recursion here and +this is what how you would be able to + + align:start position:0% +this is what how you would be able to + + + align:start position:0% +this is what how you would be able to +calculate these probabilities now how + + align:start position:0% +calculate these probabilities now how + + + align:start position:0% +calculate these probabilities now how +did we come up with this recursion well + + align:start position:0% +did we come up with this recursion well + + + align:start position:0% +did we come up with this recursion well +it's based on a classical divide and + + align:start position:0% +it's based on a classical divide and + + + align:start position:0% +it's based on a classical divide and +conquer and essentially the use of the + + align:start position:0% +conquer and essentially the use of the + + + align:start position:0% +conquer and essentially the use of the +topology theorem essentially you have + + align:start position:0% +topology theorem essentially you have + + + align:start position:0% +topology theorem essentially you have +the time step here this is the current + + align:start position:0% +the time step here this is the current + + + align:start position:0% +the time step here this is the current +time s you are interested in what's + + align:start position:0% +time s you are interested in what's + + + align:start position:0% +time s you are interested in what's +gonna happen at n plus s that means n + + align:start position:0% +gonna happen at n plus s that means n + + + align:start position:0% +gonna happen at n plus s that means n +steps later here you are in state I you + + align:start position:0% +steps later here you are in state I you + + + align:start position:0% +steps later here you are in state I you +are interested in knowing what is the + + align:start position:0% +are interested in knowing what is the + + + align:start position:0% +are interested in knowing what is the +probability of being in state G at that + + align:start position:0% +probability of being in state G at that + + + align:start position:0% +probability of being in state G at that +time and what you simply do is you look + + align:start position:0% +time and what you simply do is you look + + + align:start position:0% +time and what you simply do is you look +at the step n plus n minus 1 just before + + align:start position:0% +at the step n plus n minus 1 just before + + + align:start position:0% +at the step n plus n minus 1 just before +the last one and then you say well let + + align:start position:0% +the last one and then you say well let + + + align:start position:0% +the last one and then you say well let +me do a divide and conquer this is K + + align:start position:0% +me do a divide and conquer this is K + + + align:start position:0% +me do a divide and conquer this is K +here and I'm going to look at evaluating + + align:start position:0% +here and I'm going to look at evaluating + + + align:start position:0% +here and I'm going to look at evaluating +that probability and then once I have + + align:start position:0% +that probability and then once I have + + + align:start position:0% +that probability and then once I have +that I will simply multiply by this + + align:start position:0% +that I will simply multiply by this + + + align:start position:0% +that I will simply multiply by this +transition here and what happened is + + align:start position:0% +transition here and what happened is + + + align:start position:0% +transition here and what happened is +that this here is nothing else than this + + align:start position:0% +that this here is nothing else than this + + + align:start position:0% +that this here is nothing else than this +calculation that we have here and that's + + align:start position:0% +calculation that we have here and that's + + + align:start position:0% +calculation that we have here and that's +the same thing and here this is the + + align:start position:0% +the same thing and here this is the + + + align:start position:0% +the same thing and here this is the +parity of one step transition and of + + align:start position:0% +parity of one step transition and of + + + align:start position:0% +parity of one step transition and of +course we have conditioned on the fact + + align:start position:0% +course we have conditioned on the fact + + + align:start position:0% +course we have conditioned on the fact +that we would be in a state K here but K + + align:start position:0% +that we would be in a state K here but K + + + align:start position:0% +that we would be in a state K here but K +could be any of these states rights and + + align:start position:0% +could be any of these states rights and + + + align:start position:0% +could be any of these states rights and +there are M of them and this is why we + + align:start position:0% +there are M of them and this is why we + + + align:start position:0% +there are M of them and this is why we +son from K equals 1 to M so it's + + align:start position:0% +son from K equals 1 to M so it's + + + align:start position:0% +son from K equals 1 to M so it's +actually this is how the scary question + + align:start position:0% +actually this is how the scary question + + + align:start position:0% +actually this is how the scary question +has been put together and we have used + + align:start position:0% +has been put together and we have used + + + align:start position:0% +has been put together and we have used +of course the + + align:start position:0% +of course the + + + align:start position:0% +of course the +property in order to do that let's do + + align:start position:0% +property in order to do that let's do + + + align:start position:0% +property in order to do that let's do +now a little bit of warm-up in terms of + + align:start position:0% +now a little bit of warm-up in terms of + + + align:start position:0% +now a little bit of warm-up in terms of +calculation and apply these concepts \ No newline at end of file diff --git a/csRRQOyl5kM.txt b/csRRQOyl5kM.txt new file mode 100644 index 0000000000000000000000000000000000000000..ce0a7517d9f75981abc88c15ac1e6b6072ef427f --- /dev/null +++ b/csRRQOyl5kM.txt @@ -0,0 +1,12251 @@ +align:start position:0% + +yes of course if we argue if we want to + + align:start position:0% +yes of course if we argue if we want to + + + align:start position:0% +yes of course if we argue if we want to +prove to him that X is in the language + + align:start position:0% +prove to him that X is in the language + + + align:start position:0% +prove to him that X is in the language +it's essentially we're saying telling + + align:start position:0% +it's essentially we're saying telling + + + align:start position:0% +it's essentially we're saying telling +him if you evaluate X on circuit C + + align:start position:0% +him if you evaluate X on circuit C + + + align:start position:0% +him if you evaluate X on circuit C +you'll get one or maybe if there exists + + align:start position:0% +you'll get one or maybe if there exists + + + align:start position:0% +you'll get one or maybe if there exists +a witness of that c of the witness c and + + align:start position:0% +a witness of that c of the witness c and + + + align:start position:0% +a witness of that c of the witness c and +x and the witness gives you one of + + align:start position:0% +x and the witness gives you one of + + + align:start position:0% +x and the witness gives you one of +course we assume the verifier knows + + align:start position:0% +course we assume the verifier knows + + + align:start position:0% +course we assume the verifier knows +description of this circuit C and + + align:start position:0% +description of this circuit C and + + + align:start position:0% +description of this circuit C and +usually and for our purposes you think + + align:start position:0% +usually and for our purposes you think + + + align:start position:0% +usually and for our purposes you think +of C as being a uniform like a a tring + + align:start position:0% +of C as being a uniform like a a tring + + + align:start position:0% +of C as being a uniform like a a tring +machine okay so it's a it can be + + align:start position:0% +machine okay so it's a it can be + + + align:start position:0% +machine okay so it's a it can be +generated efficiently from a training + + align:start position:0% +generated efficiently from a training + + + align:start position:0% +generated efficiently from a training +machine but yes the verifier can + + align:start position:0% +machine but yes the verifier can + + + align:start position:0% +machine but yes the verifier can +generate can both the prover and + + align:start position:0% +generate can both the prover and + + + align:start position:0% +generate can both the prover and +verifier can generate the circuit that's + + align:start position:0% +verifier can generate the circuit that's + + + align:start position:0% +verifier can generate the circuit that's +uh so if you think of three s you know + + align:start position:0% +uh so if you think of three s you know + + + align:start position:0% +uh so if you think of three s you know +the circuit is takes input all the + + align:start position:0% +the circuit is takes input all the + + + align:start position:0% +the circuit is takes input all the +assignments and it checks that all the + + align:start position:0% +assignments and it checks that all the + + + align:start position:0% +assignments and it checks that all the +uh uh Clauses are satisfied + + align:start position:0% +uh uh Clauses are satisfied + + + align:start position:0% +uh uh Clauses are satisfied +that's an example of circuit + + align:start position:0% +that's an example of circuit + + + align:start position:0% +that's an example of circuit +yeah is that simar to running + + align:start position:0% +yeah is that simar to running + + + align:start position:0% +yeah is that simar to running +that yeah it's like just yeah so so the + + align:start position:0% +that yeah it's like just yeah so so the + + + align:start position:0% +that yeah it's like just yeah so so the +prover essentially computes the circuit + + align:start position:0% +prover essentially computes the circuit + + + align:start position:0% +prover essentially computes the circuit +all the gates in the circuit hashes it + + align:start position:0% +all the gates in the circuit hashes it + + + align:start position:0% +all the gates in the circuit hashes it +and then gives a bar that each and every + + align:start position:0% +and then gives a bar that each and every + + + align:start position:0% +and then gives a bar that each and every +gate of the circuit is satisfied that + + align:start position:0% +gate of the circuit is satisfied that + + + align:start position:0% +gate of the circuit is satisfied that +the value he hased satisfy + + align:start position:0% +the value he hased satisfy + + + align:start position:0% +the value he hased satisfy +each uh respect each gate + + align:start position:0% + + + + align:start position:0% + +because okay so the verifier doesn't + + align:start position:0% +because okay so the verifier doesn't + + + align:start position:0% +because okay so the verifier doesn't +know all these values all these bits + + align:start position:0% +know all these values all these bits + + + align:start position:0% +know all these values all these bits +he's getting just the the the verifier + + align:start position:0% +he's getting just the the the verifier + + + align:start position:0% +he's getting just the the the verifier +only knows the hash he gets only V he + + align:start position:0% +only knows the hash he gets only V he + + + align:start position:0% +only knows the hash he gets only V he +doesn't know all these things he and he + + align:start position:0% +doesn't know all these things he and he + + + align:start position:0% +doesn't know all these things he and he +can't it's there too many of them he + + align:start position:0% +can't it's there too many of them he + + + align:start position:0% +can't it's there too many of them he +doesn't he he can he knows what the + + align:start position:0% +doesn't he he can he knows what the + + + align:start position:0% +doesn't he he can he knows what the +circuit is but he doesn't run in time + + align:start position:0% +circuit is but he doesn't run in time + + + align:start position:0% +circuit is but he doesn't run in time +that depends on the circuit the circuit + + align:start position:0% +that depends on the circuit the circuit + + + align:start position:0% +that depends on the circuit the circuit +is too big he just kind of knows in his + + align:start position:0% +is too big he just kind of knows in his + + + align:start position:0% +is too big he just kind of knows in his +head how to generate each gate in the + + align:start position:0% +head how to generate each gate in the + + + align:start position:0% +head how to generate each gate in the +circuit but he can't uh so he doesn't + + align:start position:0% +circuit but he can't uh so he doesn't + + + align:start position:0% +circuit but he can't uh so he doesn't +know these bits all he knows is the hash + + align:start position:0% +know these bits all he knows is the hash + + + align:start position:0% +know these bits all he knows is the hash +value and the bar which is + + align:start position:0% +value and the bar which is + + + align:start position:0% +value and the bar which is +succinct + + align:start position:0% +succinct + + + align:start position:0% +succinct +okay any yeah security is going to give + + align:start position:0% +okay any yeah security is going to give + + + align:start position:0% +okay any yeah security is going to give +us some lower bound on L right it just + + align:start position:0% +us some lower bound on L right it just + + + align:start position:0% +us some lower bound on L right it just +happens a lower bound on what on L and L + + align:start position:0% +happens a lower bound on what on L and L + + + align:start position:0% +happens a lower bound on what on L and L +yes yeah okay yeah we're going to yeah + + align:start position:0% +yes yeah okay yeah we're going to yeah + + + align:start position:0% +yes yeah okay yeah we're going to yeah +yeah yeah we're going to talk now we're + + align:start position:0% +yeah yeah we're going to talk now we're + + + align:start position:0% +yeah yeah we're going to talk now we're +going to talk about sec a soundness so + + align:start position:0% +going to talk about sec a soundness so + + + align:start position:0% +going to talk about sec a soundness so +we'll see uh one thing I want to say + + align:start position:0% +we'll see uh one thing I want to say + + + align:start position:0% +we'll see uh one thing I want to say +before we we jump to soundness Just note + + align:start position:0% +before we we jump to soundness Just note + + + align:start position:0% +before we we jump to soundness Just note +because I said uh the CRS of the bar + + align:start position:0% +because I said uh the CRS of the bar + + + align:start position:0% +because I said uh the CRS of the bar +it's we generated with security + + align:start position:0% +it's we generated with security + + + align:start position:0% +it's we generated with security +parameter Lambda K which is the number + + align:start position:0% +parameter Lambda K which is the number + + + align:start position:0% +parameter Lambda K which is the number +of gates and then I said n Prime we'll + + align:start position:0% +of gates and then I said n Prime we'll + + + align:start position:0% +of gates and then I said n Prime we'll +see we'll see what n Prime is I just I + + align:start position:0% +see we'll see what n Prime is I just I + + + align:start position:0% +see we'll see what n Prime is I just I +forgot to this is n Prime it's just + + align:start position:0% +forgot to this is n Prime it's just + + + align:start position:0% +forgot to this is n Prime it's just +security parameter it's like the length + + align:start position:0% +security parameter it's like the length + + + align:start position:0% +security parameter it's like the length +of not n Prime will be the length of the + + align:start position:0% +of not n Prime will be the length of the + + + align:start position:0% +of not n Prime will be the length of the +hash key the length of V which grows + + align:start position:0% +hash key the length of V which grows + + + align:start position:0% +hash key the length of V which grows +with L and J that's kind of the N Prime + + align:start position:0% +with L and J that's kind of the N Prime + + + align:start position:0% +with L and J that's kind of the N Prime +I I'm just mentioning it because I + + align:start position:0% +I I'm just mentioning it because I + + + align:start position:0% +I I'm just mentioning it because I +forgot to Circle back to + + align:start position:0% +forgot to Circle back to + + + align:start position:0% +forgot to Circle back to +it okay are you ready to talk about + + align:start position:0% +it okay are you ready to talk about + + + align:start position:0% +it okay are you ready to talk about +analyzing this because that's actually + + align:start position:0% +analyzing this because that's actually + + + align:start position:0% +analyzing this because that's actually +the very interesting part okay so let's + + align:start position:0% +the very interesting part okay so let's + + + align:start position:0% +the very interesting part okay so let's +analyze + + align:start position:0% + + + + align:start position:0% + +a so okay we need to argue completeness + + align:start position:0% +a so okay we need to argue completeness + + + align:start position:0% +a so okay we need to argue completeness +and + + align:start position:0% +and + + + align:start position:0% +and +soundness completeness I don't want to + + align:start position:0% +soundness completeness I don't want to + + + align:start position:0% +soundness completeness I don't want to +waste our time because it's just trivial + + align:start position:0% +waste our time because it's just trivial + + + align:start position:0% +waste our time because it's just trivial +it just completeness just follows from + + align:start position:0% +it just completeness just follows from + + + align:start position:0% +it just completeness just follows from +the completeness of the bar and + + align:start position:0% +the completeness of the bar and + + + align:start position:0% +the completeness of the bar and +completeness of of the summer + + align:start position:0% +completeness of of the summer + + + align:start position:0% +completeness of of the summer +extractible hash okay so essentially if + + align:start position:0% +extractible hash okay so essentially if + + + align:start position:0% +extractible hash okay so essentially if +you're honest if x is in the language + + align:start position:0% +you're honest if x is in the language + + + align:start position:0% +you're honest if x is in the language +you compute all the wires + + align:start position:0% +you compute all the wires + + + align:start position:0% +you compute all the wires +correctly uh you hashed all the wires + + align:start position:0% +correctly uh you hashed all the wires + + + align:start position:0% +correctly uh you hashed all the wires +and you g if you hated all the wires + + align:start position:0% +and you g if you hated all the wires + + + align:start position:0% +and you g if you hated all the wires +correctly then you have a valid witness + + align:start position:0% +correctly then you have a valid witness + + + align:start position:0% +correctly then you have a valid witness +for all the wires so your bug will be + + align:start position:0% +for all the wires so your bug will be + + + align:start position:0% +for all the wires so your bug will be +accepted if you did everything correctly + + align:start position:0% +accepted if you did everything correctly + + + align:start position:0% +accepted if you did everything correctly +everything is going to be accepted + + align:start position:0% +everything is going to be accepted + + + align:start position:0% +everything is going to be accepted +because the completeness of the + + align:start position:0% +because the completeness of the + + + align:start position:0% +because the completeness of the +underlying primitive okay there's + + align:start position:0% +underlying primitive okay there's + + + align:start position:0% +underlying primitive okay there's +nothing interesting going on the + + align:start position:0% +nothing interesting going on the + + + align:start position:0% +nothing interesting going on the +interesting part is soundness okay so + + align:start position:0% +interesting part is soundness okay so + + + align:start position:0% +interesting part is soundness okay so +how do we know you cannot + + align:start position:0% +how do we know you cannot + + + align:start position:0% +how do we know you cannot +cheat + + align:start position:0% +cheat + + + align:start position:0% +cheat +and let me even jump and tell + + align:start position:0% +and let me even jump and tell + + + align:start position:0% +and let me even jump and tell +you this thing is not really + + align:start position:0% +you this thing is not really + + + align:start position:0% +you this thing is not really +sound + + align:start position:0% + + + + align:start position:0% + +but but we'll make it + + align:start position:0% +but but we'll make it + + + align:start position:0% +but but we'll make it +sound uh okay so let me okay so what do + + align:start position:0% +sound uh okay so let me okay so what do + + + align:start position:0% +sound uh okay so let me okay so what do +we know so sound this so what do we want + + align:start position:0% +we know so sound this so what do we want + + + align:start position:0% +we know so sound this so what do we want +to prove + + align:start position:0% + + + + align:start position:0% + +let's hope let's try to hope for so + + align:start position:0% +let's hope let's try to hope for so + + + align:start position:0% +let's hope let's try to hope for so +again there's non-adaptive and adaptive + + align:start position:0% +again there's non-adaptive and adaptive + + + align:start position:0% +again there's non-adaptive and adaptive +you can think of both but let's talk + + align:start position:0% +you can think of both but let's talk + + + align:start position:0% +you can think of both but let's talk +about what does it mean to be let's say + + align:start position:0% +about what does it mean to be let's say + + + align:start position:0% +about what does it mean to be let's say +adaptively sound so we need to prove + + align:start position:0% +adaptively sound so we need to prove + + + align:start position:0% +adaptively sound so we need to prove +that for any polinomial size cheating + + align:start position:0% +that for any polinomial size cheating + + + align:start position:0% +that for any polinomial size cheating +prover we want to say the + + align:start position:0% +prover we want to say the + + + align:start position:0% +prover we want to say the +probability that P star takes a + + align:start position:0% +probability that P star takes a + + + align:start position:0% +probability that P star takes a +CRS of the bar of the as snar so hash + + align:start position:0% +CRS of the bar of the as snar so hash + + + align:start position:0% +CRS of the bar of the as snar so hash +and CRS for the VAR okay takes the CRS + + align:start position:0% +and CRS for the VAR okay takes the CRS + + + align:start position:0% +and CRS for the VAR okay takes the CRS +it outputs some X and + + align:start position:0% +it outputs some X and + + + align:start position:0% +it outputs some X and +Pi such that X is not in the + + align:start position:0% +Pi such that X is not in the + + + align:start position:0% +Pi such that X is not in the +language and Pi the the snar is + + align:start position:0% +language and Pi the the snar is + + + align:start position:0% +language and Pi the the snar is +satisfied V on CRS x Pi outputs + + align:start position:0% +satisfied V on CRS x Pi outputs + + + align:start position:0% +satisfied V on CRS x Pi outputs +one you want to say that this is + + align:start position:0% + + + + align:start position:0% + +negligible that's we need to prove okay + + align:start position:0% +negligible that's we need to prove okay + + + align:start position:0% +negligible that's we need to prove okay +the probability that a cheating prover + + align:start position:0% +the probability that a cheating prover + + + align:start position:0% +the probability that a cheating prover +gets a + + align:start position:0% +gets a + + + align:start position:0% +gets a +CRS and generates any ex that's not in + + align:start position:0% +CRS and generates any ex that's not in + + + align:start position:0% +CRS and generates any ex that's not in +the language and a + + align:start position:0% +the language and a + + + align:start position:0% +the language and a +proof that's + + align:start position:0% +proof that's + + + align:start position:0% +proof that's +accepted you can't do that okay you can + + align:start position:0% +accepted you can't do that okay you can + + + align:start position:0% +accepted you can't do that okay you can +do that only with neg + + align:start position:0% +do that only with neg + + + align:start position:0% +do that only with neg +probability let me just mention another + + align:start position:0% +probability let me just mention another + + + align:start position:0% +probability let me just mention another +uh more uh a weaker definition is the + + align:start position:0% +uh more uh a weaker definition is the + + + align:start position:0% +uh more uh a weaker definition is the +non Adept which says for any p and for + + align:start position:0% +non Adept which says for any p and for + + + align:start position:0% +non Adept which says for any p and for +every X not so he gives X ahead of time + + align:start position:0% +every X not so he gives X ahead of time + + + align:start position:0% +every X not so he gives X ahead of time +for any P star + + align:start position:0% +for any P star + + + align:start position:0% +for any P star +and for any X not in the language when + + align:start position:0% +and for any X not in the language when + + + align:start position:0% +and for any X not in the language when +he gets a random CRS the probability + + align:start position:0% +he gets a random CRS the probability + + + align:start position:0% +he gets a random CRS the probability +that he manages to generate a fake proof + + align:start position:0% +that he manages to generate a fake proof + + + align:start position:0% +that he manages to generate a fake proof +that's accepted is negligible so there's + + align:start position:0% +that's accepted is negligible so there's + + + align:start position:0% +that's accepted is negligible so there's +two variants one one he needs to choose + + align:start position:0% +two variants one one he needs to choose + + + align:start position:0% +two variants one one he needs to choose +the X a given X for all the crs's or he + + align:start position:0% +the X a given X for all the crs's or he + + + align:start position:0% +the X a given X for all the crs's or he +can choose an X depending on the + + align:start position:0% +can choose an X depending on the + + + align:start position:0% +can choose an X depending on the +CRS let's talk about the Adaptive + + align:start position:0% +CRS let's talk about the Adaptive + + + align:start position:0% +CRS let's talk about the Adaptive +because it's just uh stronger and we can + + align:start position:0% +because it's just uh stronger and we can + + + align:start position:0% +because it's just uh stronger and we can +get it okay at least in some cases so + + align:start position:0% +get it okay at least in some cases so + + + align:start position:0% +get it okay at least in some cases so +today the snars in the literature some + + align:start position:0% +today the snars in the literature some + + + align:start position:0% +today the snars in the literature some +achieve adaptive some achieve + + align:start position:0% +achieve adaptive some achieve + + + align:start position:0% +achieve adaptive some achieve +nonadaptive and in general the the ones + + align:start position:0% +nonadaptive and in general the the ones + + + align:start position:0% +nonadaptive and in general the the ones +for the teristic computations are + + align:start position:0% +for the teristic computations are + + + align:start position:0% +for the teristic computations are +adaptive the one for nistic computations + + align:start position:0% +adaptive the one for nistic computations + + + align:start position:0% +adaptive the one for nistic computations +are more on the non-adaptive side and we + + align:start position:0% +are more on the non-adaptive side and we + + + align:start position:0% +are more on the non-adaptive side and we +don't have SN NP so at the end of the + + align:start position:0% +don't have SN NP so at the end of the + + + align:start position:0% +don't have SN NP so at the end of the +talk at the end of the class I'll leave + + align:start position:0% +talk at the end of the class I'll leave + + + align:start position:0% +talk at the end of the class I'll leave +kind of like 10 minutes to talk about + + align:start position:0% +kind of like 10 minutes to talk about + + + align:start position:0% +kind of like 10 minutes to talk about +kind of where we're standing as a + + align:start position:0% +kind of where we're standing as a + + + align:start position:0% +kind of where we're standing as a +community but um but both of them are + + align:start position:0% +community but um but both of them are + + + align:start position:0% +community but um but both of them are +kind of both definitions are relevant + + align:start position:0% +kind of both definitions are relevant + + + align:start position:0% +kind of both definitions are relevant +and we have results in both settings + + align:start position:0% +and we have results in both settings + + + align:start position:0% +and we have results in both settings +that adap in the non-adaptive but let's + + align:start position:0% +that adap in the non-adaptive but let's + + + align:start position:0% +that adap in the non-adaptive but let's +talk today uh on the Adaptive setting + + align:start position:0% +talk today uh on the Adaptive setting + + + align:start position:0% +talk today uh on the Adaptive setting +okay so that's what we want but the + + align:start position:0% +okay so that's what we want but the + + + align:start position:0% +okay so that's what we want but the +question do we get this so let's try to + + align:start position:0% +question do we get this so let's try to + + + align:start position:0% +question do we get this so let's try to +see what this construction actually + + align:start position:0% +see what this construction actually + + + align:start position:0% +see what this construction actually +gives us okay so what I'm going to argue + + align:start position:0% +gives us okay so what I'm going to argue + + + align:start position:0% +gives us okay so what I'm going to argue +is actually this construction does not + + align:start position:0% +is actually this construction does not + + + align:start position:0% +is actually this construction does not +give us soundness it doesn't give us + + align:start position:0% +give us soundness it doesn't give us + + + align:start position:0% +give us soundness it doesn't give us +what it gives us is kind of a a form of + + align:start position:0% +what it gives us is kind of a a form of + + + align:start position:0% +what it gives us is kind of a a form of +local soundness so I'll explain what + + align:start position:0% +local soundness so I'll explain what + + + align:start position:0% +local soundness so I'll explain what +this means so what I'm going to argue is + + align:start position:0% +this means so what I'm going to argue is + + + align:start position:0% +this means so what I'm going to argue is +that so + + align:start position:0% + + + + align:start position:0% + +claim the snar that I just + + align:start position:0% +claim the snar that I just + + + align:start position:0% +claim the snar that I just +constructed is let me call it + + align:start position:0% +constructed is let me call it + + + align:start position:0% +constructed is let me call it +locally + + align:start position:0% +locally + + + align:start position:0% +locally +sound or locally consistent it's also + + align:start position:0% +sound or locally consistent it's also + + + align:start position:0% +sound or locally consistent it's also +people call locally + + align:start position:0% +people call locally + + + align:start position:0% +people call locally +consistent and I'll explain what it + + align:start position:0% +consistent and I'll explain what it + + + align:start position:0% +consistent and I'll explain what it +is okay we want to prove something so + + align:start position:0% +is okay we want to prove something so + + + align:start position:0% +is okay we want to prove something so +what do we want to prove we want to + + align:start position:0% +what do we want to prove we want to + + + align:start position:0% +what do we want to prove we want to +prove + + align:start position:0% +prove + + + align:start position:0% +prove +that this nnar if you manage to say that + + align:start position:0% +that this nnar if you manage to say that + + + align:start position:0% +that this nnar if you manage to say that +the output is one there's actually an + + align:start position:0% +the output is one there's actually an + + + align:start position:0% +the output is one there's actually an +assignment to all the wires that give + + align:start position:0% +assignment to all the wires that give + + + align:start position:0% +assignment to all the wires that give +you one that means it's + + align:start position:0% +you one that means it's + + + align:start position:0% +you one that means it's +sound we can't prove + + align:start position:0% +sound we can't prove + + + align:start position:0% +sound we can't prove +that what can we + + align:start position:0% +that what can we + + + align:start position:0% +that what can we +prove we can prove that if you argue + + align:start position:0% +prove we can prove that if you argue + + + align:start position:0% +prove we can prove that if you argue +that the value is + + align:start position:0% +that the value is + + + align:start position:0% +that the value is +one I can use you to extract the value + + align:start position:0% +one I can use you to extract the value + + + align:start position:0% +one I can use you to extract the value +of any small set of wires how many l so + + align:start position:0% +of any small set of wires how many l so + + + align:start position:0% +of any small set of wires how many l so +remember our snar we're binding on + + align:start position:0% +remember our snar we're binding on + + + align:start position:0% +remember our snar we're binding on +allocations these allocation I can + + align:start position:0% +allocations these allocation I can + + + align:start position:0% +allocations these allocation I can +extract you gave me a v that's binding + + align:start position:0% +extract you gave me a v that's binding + + + align:start position:0% +extract you gave me a v that's binding +allocation I can extract I can get from + + align:start position:0% +allocation I can extract I can get from + + + align:start position:0% +allocation I can extract I can get from +you the L wire + + align:start position:0% +you the L wire + + + align:start position:0% +you the L wire +values so I get L wire's values from you + + align:start position:0% +values so I get L wire's values from you + + + align:start position:0% +values so I get L wire's values from you +what I can argue about these L wire + + align:start position:0% +what I can argue about these L wire + + + align:start position:0% +what I can argue about these L wire +values is that locally they're + + align:start position:0% +values is that locally they're + + + align:start position:0% +values is that locally they're +consistent so if there's a gate if if I + + align:start position:0% +consistent so if there's a gate if if I + + + align:start position:0% +consistent so if there's a gate if if I +if the l y vales three of them are + + align:start position:0% +if the l y vales three of them are + + + align:start position:0% +if the l y vales three of them are +connected with a gate I can argue that + + align:start position:0% +connected with a gate I can argue that + + + align:start position:0% +connected with a gate I can argue that +this gate is + + align:start position:0% +this gate is + + + align:start position:0% +this gate is +satisfied so I can argue this form with + + align:start position:0% +satisfied so I can argue this form with + + + align:start position:0% +satisfied so I can argue this form with +local + + align:start position:0% + + + + align:start position:0% + +consistency so I'm going to Define what + + align:start position:0% +consistency so I'm going to Define what + + + align:start position:0% +consistency so I'm going to Define what +local consistency is but just kind of + + align:start position:0% +local consistency is but just kind of + + + align:start position:0% +local consistency is but just kind of +high level what I can argue is not that + + align:start position:0% +high level what I can argue is not that + + + align:start position:0% +high level what I can argue is not that +I have a uh assignment of all the wires + + align:start position:0% +I have a uh assignment of all the wires + + + align:start position:0% +I have a uh assignment of all the wires +that kind of are consistent inside the + + align:start position:0% +that kind of are consistent inside the + + + align:start position:0% +that kind of are consistent inside the +output is is one which is what I want to + + align:start position:0% +output is is one which is what I want to + + + align:start position:0% +output is is one which is what I want to +argue I can argue that I have an + + align:start position:0% +argue I can argue that I have an + + + align:start position:0% +argue I can argue that I have an +assignment that I can kind of have a + + align:start position:0% +assignment that I can kind of have a + + + align:start position:0% +assignment that I can kind of have a +small window to the wires a window of + + align:start position:0% +small window to the wires a window of + + + align:start position:0% +small window to the wires a window of +size l so I can look at these L wires + + align:start position:0% +size l so I can look at these L wires + + + align:start position:0% +size l so I can look at these L wires +and they look consistent and I can look + + align:start position:0% +and they look consistent and I can look + + + align:start position:0% +and they look consistent and I can look +at these L wires and they look + + align:start position:0% +at these L wires and they look + + + align:start position:0% +at these L wires and they look +consistent and output is + + align:start position:0% +consistent and output is + + + align:start position:0% +consistent and output is +one so it seems like okay local now + + align:start position:0% +one so it seems like okay local now + + + align:start position:0% +one so it seems like okay local now +let's we only need to stitch all them + + align:start position:0% +let's we only need to stitch all them + + + align:start position:0% +let's we only need to stitch all them +together to get kind of a final + + align:start position:0% +together to get kind of a final + + + align:start position:0% +together to get kind of a final +assignment and we're done so the goal is + + align:start position:0% +assignment and we're done so the goal is + + + align:start position:0% +assignment and we're done so the goal is +we're going to say locally we're + + align:start position:0% +we're going to say locally we're + + + align:start position:0% +we're going to say locally we're +consistent and local consistency implies + + align:start position:0% +consistent and local consistency implies + + + align:start position:0% +consistent and local consistency implies +kind of global consistency and so we get + + align:start position:0% +kind of global consistency and so we get + + + align:start position:0% +kind of global consistency and so we get +to + + align:start position:0% +to + + + align:start position:0% +to +this okay so the plan we are going to + + align:start position:0% +this okay so the plan we are going to + + + align:start position:0% +this okay so the plan we are going to +prove local consistency so that's check + + align:start position:0% +prove local consistency so that's check + + + align:start position:0% +prove local consistency so that's check +and we're going to Define it and prove + + align:start position:0% +and we're going to Define it and prove + + + align:start position:0% +and we're going to Define it and prove +it the local consistency ples + + align:start position:0% +it the local consistency ples + + + align:start position:0% +it the local consistency ples +Global that turns out to be much more + + align:start position:0% +Global that turns out to be much more + + + align:start position:0% +Global that turns out to be much more +difficult than we thought so when we + + align:start position:0% +difficult than we thought so when we + + + align:start position:0% +difficult than we thought so when we +started working on this we're like oh + + align:start position:0% +started working on this we're like oh + + + align:start position:0% +started working on this we're like oh +local consistency yeah shouldn't PL glob + + align:start position:0% +local consistency yeah shouldn't PL glob + + + align:start position:0% +local consistency yeah shouldn't PL glob +that should be good so we worked really + + align:start position:0% +that should be good so we worked really + + + align:start position:0% +that should be good so we worked really +hard local local and then turns out + + align:start position:0% +hard local local and then turns out + + + align:start position:0% +hard local local and then turns out +local to Global was another 10 years of + + align:start position:0% +local to Global was another 10 years of + + + align:start position:0% +local to Global was another 10 years of +work and we're still we're in progress + + align:start position:0% +work and we're still we're in progress + + + align:start position:0% +work and we're still we're in progress +in progress so so that's what so what + + align:start position:0% +in progress so so that's what so what + + + align:start position:0% +in progress so so that's what so what +we're going to see today is how to get + + align:start position:0% +we're going to see today is how to get + + + align:start position:0% +we're going to see today is how to get +local consistency we're going to talk a + + align:start position:0% +local consistency we're going to talk a + + + align:start position:0% +local consistency we're going to talk a +little bit about why local implies + + align:start position:0% +little bit about why local implies + + + align:start position:0% +little bit about why local implies +Global and why not okay why is it + + align:start position:0% +Global and why not okay why is it + + + align:start position:0% +Global and why not okay why is it +doesn't it always imply Global and + + align:start position:0% +doesn't it always imply Global and + + + align:start position:0% +doesn't it always imply Global and +hopefully it will give you some food for + + align:start position:0% +hopefully it will give you some food for + + + align:start position:0% +hopefully it will give you some food for +thoughts okay so so so I'm G to argue + + align:start position:0% +thoughts okay so so so I'm G to argue + + + align:start position:0% +thoughts okay so so so I'm G to argue +that it's locally sound and let me tell + + align:start position:0% +that it's locally sound and let me tell + + + align:start position:0% +that it's locally sound and let me tell +you what locally sound means let me + + align:start position:0% +you what locally sound means let me + + + align:start position:0% +you what locally sound means let me +first Define it okay so the definition + + align:start position:0% +first Define it okay so the definition + + + align:start position:0% +first Define it okay so the definition +so + + align:start position:0% + + + + align:start position:0% + +okay so here's what it + + align:start position:0% +okay so here's what it + + + align:start position:0% +okay so here's what it +means it means that there exists so this + + align:start position:0% +means it means that there exists so this + + + align:start position:0% +means it means that there exists so this +is I'm now defining what this means it + + align:start position:0% +is I'm now defining what this means it + + + align:start position:0% +is I'm now defining what this means it +means that there + + align:start position:0% +means that there + + + align:start position:0% +means that there +exists an extractor we call sometime + + align:start position:0% +exists an extractor we call sometime + + + align:start position:0% +exists an extractor we call sometime +sometimes a local assignment it kind of + + align:start position:0% +sometimes a local assignment it kind of + + + align:start position:0% +sometimes a local assignment it kind of +so some extractor a + + align:start position:0% +so some extractor a + + + align:start position:0% +so some extractor a +local + + align:start position:0% + + + + align:start position:0% + +assignment generator that's another name + + align:start position:0% +assignment generator that's another name + + + align:start position:0% +assignment generator that's another name +we use + + align:start position:0% +we use + + + align:start position:0% +we use +e so we have an kind of an extractor + + align:start position:0% +e so we have an kind of an extractor + + + align:start position:0% +e so we have an kind of an extractor +that generates assignments for us this + + align:start position:0% +that generates assignments for us this + + + align:start position:0% +that generates assignments for us this +assignment takes only L wire values on + + align:start position:0% +assignment takes only L wire values on + + + align:start position:0% +assignment takes only L wire values on +the circuit so we have a circuit C okay + + align:start position:0% +the circuit so we have a circuit C okay + + + align:start position:0% +the circuit so we have a circuit C okay +this this uh extractor or local + + align:start position:0% +this this uh extractor or local + + + align:start position:0% +this this uh extractor or local +assignment generator it gets L wires i1 + + align:start position:0% +assignment generator it gets L wires i1 + + + align:start position:0% +assignment generator it gets L wires i1 +up to I L they're all in uh the wires + + align:start position:0% +up to I L they're all in uh the wires + + + align:start position:0% +up to I L they're all in uh the wires +which we denoted by n okay so it takes L + + align:start position:0% +which we denoted by n okay so it takes L + + + align:start position:0% +which we denoted by n okay so it takes L +wires and it + + align:start position:0% +wires and it + + + align:start position:0% +wires and it +outputs some xar an in an + + align:start position:0% +outputs some xar an in an + + + align:start position:0% +outputs some xar an in an +instance and Y values and values wi i1 + + align:start position:0% +instance and Y values and values wi i1 + + + align:start position:0% +instance and Y values and values wi i1 +up to w i this is what our our local + + align:start position:0% +up to w i this is what our our local + + + align:start position:0% +up to w i this is what our our local +assignment generator outputs for any i1 + + align:start position:0% +assignment generator outputs for any i1 + + + align:start position:0% +assignment generator outputs for any i1 +up to I it outputs some instance and Y + + align:start position:0% +up to I it outputs some instance and Y + + + align:start position:0% +up to I it outputs some instance and Y +values that satisfy the following such + + align:start position:0% +values that satisfy the following such + + + align:start position:0% +values that satisfy the following such +that + + align:start position:0% + + + + align:start position:0% + +one is local + + align:start position:0% + + + + align:start position:0% + +consistency which means any two wires + + align:start position:0% +consistency which means any two wires + + + align:start position:0% +consistency which means any two wires +any any wires that are connected by a + + align:start position:0% +any any wires that are connected by a + + + align:start position:0% +any any wires that are connected by a +gate satisfy the gate and the output + + align:start position:0% +gate satisfy the gate and the output + + + align:start position:0% +gate satisfy the gate and the output +wire is a one and if one of them are + + align:start position:0% +wire is a one and if one of them are + + + align:start position:0% +wire is a one and if one of them are +connected to input wires then it's it's + + align:start position:0% +connected to input wires then it's it's + + + align:start position:0% +connected to input wires then it's it's +consistent with the input Wire yeah so + + align:start position:0% +consistent with the input Wire yeah so + + + align:start position:0% +consistent with the input Wire yeah so +local consistency just means it respects + + align:start position:0% + + + + align:start position:0% + +all + + align:start position:0% + + + + align:start position:0% + +Gates + + align:start position:0% +Gates + + + align:start position:0% +Gates +consistent with X1 up to xn and out + + align:start position:0% +consistent with X1 up to xn and out + + + align:start position:0% +consistent with X1 up to xn and out +and you know output + + align:start position:0% + + + + align:start position:0% + +one okay so of course if you just read + + align:start position:0% +one okay so of course if you just read + + + align:start position:0% +one okay so of course if you just read +wires here and here like uh very spread + + align:start position:0% +wires here and here like uh very spread + + + align:start position:0% +wires here and here like uh very spread +that are not connected with any Gates + + align:start position:0% +that are not connected with any Gates + + + align:start position:0% +that are not connected with any Gates +then the local consistency doesn't say + + align:start position:0% +then the local consistency doesn't say + + + align:start position:0% +then the local consistency doesn't say +anything because you can determine the + + align:start position:0% +anything because you can determine the + + + align:start position:0% +anything because you can determine the +value of any gate you don't but any gate + + align:start position:0% +value of any gate you don't but any gate + + + align:start position:0% +value of any gate you don't but any gate +for which you have any gate for which + + align:start position:0% +for which you have any gate for which + + + align:start position:0% +for which you have any gate for which +the input and output wires are these or + + align:start position:0% +the input and output wires are these or + + + align:start position:0% +the input and output wires are these or +the output wire or the input wires the + + align:start position:0% +the output wire or the input wires the + + + align:start position:0% +the output wire or the input wires the +gate should be + + align:start position:0% +gate should be + + + align:start position:0% +gate should be +satisfied okay that's number one and + + align:start position:0% +satisfied okay that's number one and + + + align:start position:0% +satisfied okay that's number one and +number + + align:start position:0% +number + + + align:start position:0% +number +two is what we call non- signaling I'll + + align:start position:0% + + + + align:start position:0% + +explain number the number two says the + + align:start position:0% +explain number the number two says the + + + align:start position:0% +explain number the number two says the +the Y values that he gives here that the + + align:start position:0% +the Y values that he gives here that the + + + align:start position:0% +the Y values that he gives here that the +extractor the local assignment + + align:start position:0% +extractor the local assignment + + + align:start position:0% +extractor the local assignment +assignment generator + + align:start position:0% +assignment generator + + + align:start position:0% +assignment generator +gives the distribution so this is an a + + align:start position:0% +gives the distribution so this is an a + + + align:start position:0% +gives the distribution so this is an a +randomized algorithm this extractor is a + + align:start position:0% +randomized algorithm this extractor is a + + + align:start position:0% +randomized algorithm this extractor is a +randomized algorithm he gives he gives + + align:start position:0% +randomized algorithm he gives he gives + + + align:start position:0% +randomized algorithm he gives he gives +given these wire he gives a distribution + + align:start position:0% +given these wire he gives a distribution + + + align:start position:0% +given these wire he gives a distribution +over xar and wire values the claim is + + align:start position:0% +over xar and wire values the claim is + + + align:start position:0% +over xar and wire values the claim is +the distribution of xar for + + align:start position:0% +the distribution of xar for + + + align:start position:0% +the distribution of xar for +example doesn't depend on i1 up to I so + + align:start position:0% +example doesn't depend on i1 up to I so + + + align:start position:0% +example doesn't depend on i1 up to I so +the distribution xar in + + align:start position:0% +the distribution xar in + + + align:start position:0% +the distribution xar in +computationally looks the same no matter + + align:start position:0% +computationally looks the same no matter + + + align:start position:0% +computationally looks the same no matter +which uh wires you give moreover the + + align:start position:0% +which uh wires you give moreover the + + + align:start position:0% +which uh wires you give moreover the +distribution of wi + + align:start position:0% +distribution of wi + + + align:start position:0% +distribution of wi +i1 doesn't depend on I2 up to I so let + + align:start position:0% +i1 doesn't depend on I2 up to I so let + + + align:start position:0% +i1 doesn't depend on I2 up to I so let +me say this + + align:start position:0% +me say this + + + align:start position:0% +me say this +formally formally for every set I and + + align:start position:0% +formally formally for every set I and + + + align:start position:0% +formally formally for every set I and +J of + + align:start position:0% +J of + + + align:start position:0% +J of +size L uh let me sorry for any I and J + + align:start position:0% +size L uh let me sorry for any I and J + + + align:start position:0% +size L uh let me sorry for any I and J +subset of n so for any set of wires of + + align:start position:0% +subset of n so for any set of wires of + + + align:start position:0% +subset of n so for any set of wires of +size l so take any set of wires like I + + align:start position:0% +size l so take any set of wires like I + + + align:start position:0% +size l so take any set of wires like I +went up to I L let me call the first set + + align:start position:0% +went up to I L let me call the first set + + + align:start position:0% +went up to I L let me call the first set +I the second set + + align:start position:0% +I the second set + + + align:start position:0% +I the second set +J what and what we know is if you look + + align:start position:0% +J what and what we know is if you look + + + align:start position:0% +J what and what we know is if you look +at the intersection of so if you look at + + align:start position:0% +at the intersection of so if you look at + + + align:start position:0% +at the intersection of so if you look at +um + + align:start position:0% +um + + + align:start position:0% +um +a how would I one second just think of + + align:start position:0% +a how would I one second just think of + + + align:start position:0% +a how would I one second just think of +notation so think of let's look at if + + align:start position:0% +notation so think of let's look at if + + + align:start position:0% +notation so think of let's look at if +you look at extractor and I but only + + align:start position:0% +you look at extractor and I but only + + + align:start position:0% +you look at extractor and I but only +restricted the coordinate in I intersect + + align:start position:0% +restricted the coordinate in I intersect + + + align:start position:0% +restricted the coordinate in I intersect +J so the W's there's many there's W for + + align:start position:0% +J so the W's there's many there's W for + + + align:start position:0% +J so the W's there's many there's W for +i1 I2 let's look only the W's and the + + align:start position:0% +i1 I2 let's look only the W's and the + + + align:start position:0% +i1 I2 let's look only the W's and the +location that are both in I and in + + align:start position:0% + + + + align:start position:0% + +J the + + align:start position:0% + + + + align:start position:0% + +distribution of them + + align:start position:0% +distribution of them + + + align:start position:0% +distribution of them +looks like it looks it's inting from the + + align:start position:0% +looks like it looks it's inting from the + + + align:start position:0% +looks like it looks it's inting from the +distribution if you looked at this these + + align:start position:0% +distribution if you looked at this these + + + align:start position:0% +distribution if you looked at this these +coordinates with set J in other words + + align:start position:0% +coordinates with set J in other words + + + align:start position:0% +coordinates with set J in other words +let's say the intersection of I and J or + + align:start position:0% +let's say the intersection of I and J or + + + align:start position:0% +let's say the intersection of I and J or +I don't know some set of wires put the + + align:start position:0% +I don't know some set of wires put the + + + align:start position:0% +I don't know some set of wires put the +set of wires in the + + align:start position:0% +set of wires in the + + + align:start position:0% +set of wires in the +beginning okay it the rest of the so if + + align:start position:0% +beginning okay it the rest of the so if + + + align:start position:0% +beginning okay it the rest of the so if +you look at a set of wires look at their + + align:start position:0% +you look at a set of wires look at their + + + align:start position:0% +you look at a set of wires look at their +distribution their + + align:start position:0% +distribution their + + + align:start position:0% +distribution their +distribution does not depend and what + + align:start position:0% +distribution does not depend and what + + + align:start position:0% +distribution does not depend and what +the other wires are if you look at the + + align:start position:0% +the other wires are if you look at the + + + align:start position:0% +the other wires are if you look at the +distribution of these they will look the + + align:start position:0% +distribution of these they will look the + + + align:start position:0% +distribution of these they will look the +same whether the rest of the eyes were + + align:start position:0% +same whether the rest of the eyes were + + + align:start position:0% +same whether the rest of the eyes were +have one form or another form at least + + align:start position:0% +have one form or another form at least + + + align:start position:0% +have one form or another form at least +computationally they look the same they + + align:start position:0% +computationally they look the same they + + + align:start position:0% +computationally they look the same they +they need not be exactly the same but + + align:start position:0% +they need not be exactly the same but + + + align:start position:0% +they need not be exactly the same but +nobody can distinguish between the + + align:start position:0% +nobody can distinguish between the + + + align:start position:0% +nobody can distinguish between the +two okay and this is including this this + + align:start position:0% +two okay and this is including this this + + + align:start position:0% +two okay and this is including this this +is including the xar okay so e is like + + align:start position:0% +is including the xar okay so e is like + + + align:start position:0% +is including the xar okay so e is like +uh when I when the extractor here it + + align:start position:0% +uh when I when the extractor here it + + + align:start position:0% +uh when I when the extractor here it +means kind of X star and the + + align:start position:0% +means kind of X star and the + + + align:start position:0% +means kind of X star and the +w i j + + align:start position:0% +w i j + + + align:start position:0% +w i j +for i j in in I so I include the xar so + + align:start position:0% +for i j in in I so I include the xar so + + + align:start position:0% +for i j in in I so I include the xar so +even with xar the xar here the xar here + + align:start position:0% +even with xar the xar here the xar here + + + align:start position:0% +even with xar the xar here the xar here +are + + align:start position:0% +are + + + align:start position:0% +are +indistinguishable okay xar I always + + align:start position:0% +indistinguishable okay xar I always + + + align:start position:0% +indistinguishable okay xar I always +include even if it's empty I include + + align:start position:0% +include even if it's empty I include + + + align:start position:0% +include even if it's empty I include +xar okay so that's a non signaling the + + align:start position:0% +xar okay so that's a non signaling the + + + align:start position:0% +xar okay so that's a non signaling the +distributions are + + align:start position:0% +distributions are + + + align:start position:0% +distributions are +indistinguishable and now I want to + + align:start position:0% +indistinguishable and now I want to + + + align:start position:0% +indistinguishable and now I want to +argue that we get I can I have this + + align:start position:0% +argue that we get I can I have this + + + align:start position:0% +argue that we get I can I have this +extractor I'm going to show you I'm + + align:start position:0% +extractor I'm going to show you I'm + + + align:start position:0% +extractor I'm going to show you I'm +going to construct this extractor + + align:start position:0% +going to construct this extractor + + + align:start position:0% +going to construct this extractor +actually very easy to construct this + + align:start position:0% +actually very easy to construct this + + + align:start position:0% +actually very easy to construct this +extractor so if you give me a cheating + + align:start position:0% +extractor so if you give me a cheating + + + align:start position:0% +extractor so if you give me a cheating +prover if you give me any prover forget + + align:start position:0% +prover if you give me any prover forget + + + align:start position:0% +prover if you give me any prover forget +about cheating you give me aover I can + + align:start position:0% +about cheating you give me aover I can + + + align:start position:0% +about cheating you give me aover I can +construct this local assignment + + align:start position:0% +construct this local assignment + + + align:start position:0% +construct this local assignment +generator from him and then all I need + + align:start position:0% +generator from him and then all I need + + + align:start position:0% +generator from him and then all I need +to do is argue that a local assignment + + align:start position:0% +to do is argue that a local assignment + + + align:start position:0% +to do is argue that a local assignment +gener implies that I can kind of I have + + align:start position:0% +gener implies that I can kind of I have + + + align:start position:0% +gener implies that I can kind of I have +a a a assignment for all like a not just + + align:start position:0% +a a a assignment for all like a not just + + + align:start position:0% +a a a assignment for all like a not just +locally cons consistent but a fully + + align:start position:0% +locally cons consistent but a fully + + + align:start position:0% +locally cons consistent but a fully +consistent assignment to all the wires + + align:start position:0% +consistent assignment to all the wires + + + align:start position:0% +consistent assignment to all the wires +that give give Alpha One and therefore X + + align:start position:0% +that give give Alpha One and therefore X + + + align:start position:0% +that give give Alpha One and therefore X +needs to be in the + + align:start position:0% +needs to be in the + + + align:start position:0% +needs to be in the +language that's kind of the proof + + align:start position:0% + + + + align:start position:0% + +strategy so what I'm going to do first + + align:start position:0% +strategy so what I'm going to do first + + + align:start position:0% +strategy so what I'm going to do first +is show you how we get so we're going to + + align:start position:0% +is show you how we get so we're going to + + + align:start position:0% +is show you how we get so we're going to +show how given any P star we can + + align:start position:0% +show how given any P star we can + + + align:start position:0% +show how given any P star we can +generate a local assignment generator we + + align:start position:0% +generate a local assignment generator we + + + align:start position:0% +generate a local assignment generator we +can give kind of local assignment to all + + align:start position:0% +can give kind of local assignment to all + + + align:start position:0% +can give kind of local assignment to all +the wires that are consistent and + + align:start position:0% +the wires that are consistent and + + + align:start position:0% +the wires that are consistent and +satisfy this kind of noning property and + + align:start position:0% +satisfy this kind of noning property and + + + align:start position:0% +satisfy this kind of noning property and +then we're going to show how to use this + + align:start position:0% +then we're going to show how to use this + + + align:start position:0% +then we're going to show how to use this +this local assignment generator to get + + align:start position:0% +this local assignment generator to get + + + align:start position:0% +this local assignment generator to get +soundness questions yeah is another + + align:start position:0% +soundness questions yeah is another + + + align:start position:0% +soundness questions yeah is another +issue with obtaining this + + align:start position:0% +issue with obtaining this + + + align:start position:0% +issue with obtaining this +sound comes + + align:start position:0% + + + + align:start position:0% + +fromi the the actually the semi adaptive + + align:start position:0% +fromi the the actually the semi adaptive + + + align:start position:0% +fromi the the actually the semi adaptive +soundness of bar is enough for me it's I + + align:start position:0% +soundness of bar is enough for me it's I + + + align:start position:0% +soundness of bar is enough for me it's I +I don't need to use you'll see actually + + align:start position:0% +I don't need to use you'll see actually + + + align:start position:0% +I don't need to use you'll see actually +I don't need full adaptive bars it's not + + align:start position:0% +I don't need full adaptive bars it's not + + + align:start position:0% +I don't need full adaptive bars it's not +it's I never use it I don't it's enough + + align:start position:0% +it's I never use it I don't it's enough + + + align:start position:0% +it's I never use it I don't it's enough +for me that the bar only has semi even + + align:start position:0% +for me that the bar only has semi even + + + align:start position:0% +for me that the bar only has semi even +though okay that's a good point note I + + align:start position:0% +though okay that's a good point note I + + + align:start position:0% +though okay that's a good point note I +want I'm going to prove adaptive + + align:start position:0% +want I'm going to prove adaptive + + + align:start position:0% +want I'm going to prove adaptive +soundness and what you're saying wait + + align:start position:0% +soundness and what you're saying wait + + + align:start position:0% +soundness and what you're saying wait +but the bar only has semi adaptive + + align:start position:0% +but the bar only has semi adaptive + + + align:start position:0% +but the bar only has semi adaptive +soundness is that enough is it enough to + + align:start position:0% +soundness is that enough is it enough to + + + align:start position:0% +soundness is that enough is it enough to +use only semi-adaptive bar and get fully + + align:start position:0% +use only semi-adaptive bar and get fully + + + align:start position:0% +use only semi-adaptive bar and get fully +adaptive snar yes I will not need the + + align:start position:0% +adaptive snar yes I will not need the + + + align:start position:0% +adaptive snar yes I will not need the +full adaptivity of the bar we'll see as + + align:start position:0% +full adaptivity of the bar we'll see as + + + align:start position:0% +full adaptivity of the bar we'll see as +we'll see it next I'll use it you'll see + + align:start position:0% +we'll see it next I'll use it you'll see + + + align:start position:0% +we'll see it next I'll use it you'll see +it doesn't come up so it's enough the + + align:start position:0% +it doesn't come up so it's enough the + + + align:start position:0% +it doesn't come up so it's enough the +problem is to to get this the local + + align:start position:0% +problem is to to get this the local + + + align:start position:0% +problem is to to get this the local +assignment I can get the problem why + + align:start position:0% +assignment I can get the problem why + + + align:start position:0% +assignment I can get the problem why +this kind of implies global so we'll see + + align:start position:0% +this kind of implies global so we'll see + + + align:start position:0% +this kind of implies global so we'll see +that but the semi it seems it seems + + align:start position:0% +that but the semi it seems it seems + + + align:start position:0% +that but the semi it seems it seems +counterintuitive but actually it's + + align:start position:0% +counterintuitive but actually it's + + + align:start position:0% +counterintuitive but actually it's +enough was there another question you + + align:start position:0% +enough was there another question you + + + align:start position:0% +enough was there another question you +have question yeah remember like the X + + align:start position:0% +have question yeah remember like the X + + + align:start position:0% +have question yeah remember like the X +star oh good good good this is any okay + + align:start position:0% +star oh good good good this is any okay + + + align:start position:0% +star oh good good good this is any okay +so the good what is xar no sorry + + align:start position:0% +so the good what is xar no sorry + + + align:start position:0% +so the good what is xar no sorry +okay it's okay yeah let me call XA uh + + align:start position:0% +okay it's okay yeah let me call XA uh + + + align:start position:0% +okay it's okay yeah let me call XA uh +this sorry let me you're right uh the + + align:start position:0% +this sorry let me you're right uh the + + + align:start position:0% +this sorry let me you're right uh the +extract okay + + align:start position:0% +extract okay + + + align:start position:0% +extract okay +yeah okay so let's think P star output's + + align:start position:0% +yeah okay so let's think P star output's + + + align:start position:0% +yeah okay so let's think P star output's +kind of a x tlda Crooked Kind of you + + align:start position:0% +kind of a x tlda Crooked Kind of you + + + align:start position:0% +kind of a x tlda Crooked Kind of you +know a cheating X so let's use Cricket + + align:start position:0% +know a cheating X so let's use Cricket + + + align:start position:0% +know a cheating X so let's use Cricket +like Tilda to den knowe kind of a + + align:start position:0% +like Tilda to den knowe kind of a + + + align:start position:0% +like Tilda to den knowe kind of a +cricket cheating thing and he's also + + align:start position:0% +cricket cheating thing and he's also + + + align:start position:0% +cricket cheating thing and he's also +gonna output some + + align:start position:0% +gonna output some + + + align:start position:0% +gonna output some +Tilda because it he his is also crooked + + align:start position:0% +Tilda because it he his is also crooked + + + align:start position:0% +Tilda because it he his is also crooked +and we want to argue that this crooked X + + align:start position:0% +and we want to argue that this crooked X + + + align:start position:0% +and we want to argue that this crooked X +is indistinguishable from the Crooked ax + + align:start position:0% +is indistinguishable from the Crooked ax + + + align:start position:0% +is indistinguishable from the Crooked ax +given by the cheating prover we're going + + align:start position:0% +given by the cheating prover we're going + + + align:start position:0% +given by the cheating prover we're going +to yeah and oh yeah so I need to say + + align:start position:0% +to yeah and oh yeah so I need to say + + + align:start position:0% +to yeah and oh yeah so I need to say +that sorry so good so let's say again + + align:start position:0% +that sorry so good so let's say again + + + align:start position:0% +that sorry so good so let's say again +the local assignment generator it + + align:start position:0% +the local assignment generator it + + + align:start position:0% +the local assignment generator it +outputs x a crooked x with assignments + + align:start position:0% +outputs x a crooked x with assignments + + + align:start position:0% +outputs x a crooked x with assignments +partial assignments to some of the wires + + align:start position:0% +partial assignments to some of the wires + + + align:start position:0% +partial assignments to some of the wires +to the L wires such + + align:start position:0% +to the L wires such + + + align:start position:0% +to the L wires such +that you it's + + align:start position:0% +that you it's + + + align:start position:0% +that you it's +consistent uh non- signaling and it's + + align:start position:0% +consistent uh non- signaling and it's + + + align:start position:0% +consistent uh non- signaling and it's +also non and sorry + + align:start position:0% +also non and sorry + + + align:start position:0% +also non and sorry +and X Tilda is indistinguishable from + + align:start position:0% +and X Tilda is indistinguishable from + + + align:start position:0% +and X Tilda is indistinguishable from +the X Tilda P star so P star also + + align:start position:0% +the X Tilda P star so P star also + + + align:start position:0% +the X Tilda P star so P star also +outputs X Delta they look the + + align:start position:0% +outputs X Delta they look the + + + align:start position:0% +outputs X Delta they look the +same note and if if it was non adaptive + + align:start position:0% +same note and if if it was non adaptive + + + align:start position:0% +same note and if if it was non adaptive +it would be fixed so then X XA is fixed + + align:start position:0% +it would be fixed so then X XA is fixed + + + align:start position:0% +it would be fixed so then X XA is fixed +ahead of time nobody will need to + + align:start position:0% +ahead of time nobody will need to + + + align:start position:0% +ahead of time nobody will need to +generate them anymore it's fixed and the + + align:start position:0% +generate them anymore it's fixed and the + + + align:start position:0% +generate them anymore it's fixed and the +and the extractor the local assignment + + align:start position:0% +and the extractor the local assignment + + + align:start position:0% +and the extractor the local assignment +generator will only give values to the + + align:start position:0% +generator will only give values to the + + + align:start position:0% +generator will only give values to the +wires but in the Adaptive setting the P + + align:start position:0% +wires but in the Adaptive setting the P + + + align:start position:0% +wires but in the Adaptive setting the P +star you give him CRS he gives you a + + align:start position:0% +star you give him CRS he gives you a + + + align:start position:0% +star you give him CRS he gives you a +different X star the X Tilda sorry now + + align:start position:0% +different X star the X Tilda sorry now + + + align:start position:0% +different X star the X Tilda sorry now +okay he gives you a different a + + align:start position:0% +okay he gives you a different a + + + align:start position:0% +okay he gives you a different a +different ex Tilda so every time he + + align:start position:0% +different ex Tilda so every time he + + + align:start position:0% +different ex Tilda so every time he +gives you a local kind of window it will + + align:start position:0% +gives you a local kind of window it will + + + align:start position:0% +gives you a local kind of window it will +be for a with a different X dilda + + align:start position:0% +be for a with a different X dilda + + + align:start position:0% +be for a with a different X dilda +possibly uh uh in the Adaptive setting + + align:start position:0% +possibly uh uh in the Adaptive setting + + + align:start position:0% +possibly uh uh in the Adaptive setting +in the nonadaptive setting it's always + + align:start position:0% +in the nonadaptive setting it's always + + + align:start position:0% +in the nonadaptive setting it's always +going to be with the same X + + align:start position:0% +going to be with the same X + + + align:start position:0% +going to be with the same X +till okay any any + + align:start position:0% + + + + align:start position:0% + +questions okay let's try to see why we + + align:start position:0% +questions okay let's try to see why we + + + align:start position:0% +questions okay let's try to see why we +get local how we can construct this + + align:start position:0% +get local how we can construct this + + + align:start position:0% +get local how we can construct this +local assignment + + align:start position:0% +local assignment + + + align:start position:0% +local assignment +generator okay so I have a cheating Pro + + align:start position:0% +generator okay so I have a cheating Pro + + + align:start position:0% +generator okay so I have a cheating Pro +so fix so + + align:start position:0% +so fix so + + + align:start position:0% +so fix so +proof so fix P star fix a poly + + align:start position:0% + + + + align:start position:0% + +size P + + align:start position:0% +size P + + + align:start position:0% +size P +star I want to get an assign uh kind of + + align:start position:0% +star I want to get an assign uh kind of + + + align:start position:0% +star I want to get an assign uh kind of +a window to the there's the circuit we + + align:start position:0% +a window to the there's the circuit we + + + align:start position:0% +a window to the there's the circuit we +have the circuit + + align:start position:0% +have the circuit + + + align:start position:0% +have the circuit +C that has X maybe a witness I want use + + align:start position:0% +C that has X maybe a witness I want use + + + align:start position:0% +C that has X maybe a witness I want use +the C star the P the cheating prover + + align:start position:0% +the C star the P the cheating prover + + + align:start position:0% +the C star the P the cheating prover +well he so he's going to give me okay so + + align:start position:0% +well he so he's going to give me okay so + + + align:start position:0% +well he so he's going to give me okay so +fix P star for any CRS he's going to + + align:start position:0% +fix P star for any CRS he's going to + + + align:start position:0% +fix P star for any CRS he's going to +give me X I'm going to get from him an X + + align:start position:0% +give me X I'm going to get from him an X + + + align:start position:0% +give me X I'm going to get from him an X +and a window to some of the wires of the + + align:start position:0% +and a window to some of the wires of the + + + align:start position:0% +and a window to some of the wires of the +circuit so let's see how so here's my + + align:start position:0% +circuit so let's see how so here's my + + + align:start position:0% +circuit so let's see how so here's my +extractor the extractor or the local + + align:start position:0% +extractor the extractor or the local + + + align:start position:0% +extractor the extractor or the local +assignment gener it's going to use P + + align:start position:0% +assignment gener it's going to use P + + + align:start position:0% +assignment gener it's going to use P +Star as an oracle it's going to make + + align:start position:0% +Star as an oracle it's going to make + + + align:start position:0% +Star as an oracle it's going to make +it's going to make use of P star he's + + align:start position:0% +it's going to make use of P star he's + + + align:start position:0% +it's going to make use of P star he's +going to get i1 up to I what does he do + + align:start position:0% +going to get i1 up to I what does he do + + + align:start position:0% +going to get i1 up to I what does he do +he wants to get the values of these + + align:start position:0% +he wants to get the values of these + + + align:start position:0% +he wants to get the values of these +wires okay what does he do he's going to + + align:start position:0% +wires okay what does he do he's going to + + + align:start position:0% +wires okay what does he do he's going to +run P star he's going to run P star in a + + align:start position:0% +run P star he's going to run P star in a + + + align:start position:0% +run P star he's going to run P star in a +CRS that he chooses so he's going to + + align:start position:0% + + + + align:start position:0% + +generate CRS we'll see how in a second + + align:start position:0% +generate CRS we'll see how in a second + + + align:start position:0% +generate CRS we'll see how in a second +and then he's going to run P star on the + + align:start position:0% +and then he's going to run P star on the + + + align:start position:0% +and then he's going to run P star on the +CRS to get a value and a snar and then + + align:start position:0% +CRS to get a value and a snar and then + + + align:start position:0% +CRS to get a value and a snar and then +he's going to kind of extract the wires + + align:start position:0% +he's going to kind of extract the wires + + + align:start position:0% +he's going to kind of extract the wires +from this hash value okay so let's see + + align:start position:0% +from this hash value okay so let's see + + + align:start position:0% +from this hash value okay so let's see +so how does he generate the CRS CRS is + + align:start position:0% +so how does he generate the CRS CRS is + + + align:start position:0% +so how does he generate the CRS CRS is +going to be a piie for uh um CRS bargain + + align:start position:0% +going to be a piie for uh um CRS bargain + + + align:start position:0% +going to be a piie for uh um CRS bargain +hash key yeah so he's going to + + align:start position:0% +hash key yeah so he's going to + + + align:start position:0% +hash key yeah so he's going to +generate he's going to generate hash Key + + align:start position:0% +generate he's going to generate hash Key + + + align:start position:0% +generate he's going to generate hash Key +by you by running gen on this location I + + align:start position:0% +by you by running gen on this location I + + + align:start position:0% +by you by running gen on this location I +went up to I so what is it so let me + + align:start position:0% +went up to I so what is it so let me + + + align:start position:0% +went up to I so what is it so let me +actually he's going to first generate + + align:start position:0% +actually he's going to first generate + + + align:start position:0% +actually he's going to first generate +hash key and trapo + + align:start position:0% + + + + align:start position:0% + +and gen Sumer extractable hash with uh + + align:start position:0% +and gen Sumer extractable hash with uh + + + align:start position:0% +and gen Sumer extractable hash with uh +one to the Lambda number of wires in C + + align:start position:0% +one to the Lambda number of wires in C + + + align:start position:0% +one to the Lambda number of wires in C +in the circuit and i1 up to I L these + + align:start position:0% +in the circuit and i1 up to I L these + + + align:start position:0% +in the circuit and i1 up to I L these +are the wires he wants to extract okay + + align:start position:0% +are the wires he wants to extract okay + + + align:start position:0% +are the wires he wants to extract okay +because he has I went up to I L he wants + + align:start position:0% +because he has I went up to I L he wants + + + align:start position:0% +because he has I went up to I L he wants +to extract the values of these wires so + + align:start position:0% +to extract the values of these wires so + + + align:start position:0% +to extract the values of these wires so +he's going to give you a hash key that's + + align:start position:0% +he's going to give you a hash key that's + + + align:start position:0% +he's going to give you a hash key that's +extractable on these + + align:start position:0% +extractable on these + + + align:start position:0% +extractable on these +locations and then it's also going to + + align:start position:0% +locations and then it's also going to + + + align:start position:0% +locations and then it's also going to +generate uh gen for the bar to get H CRS + + align:start position:0% +generate uh gen for the bar to get H CRS + + + align:start position:0% +generate uh gen for the bar to get H CRS +bar he's just going to do this honestly + + align:start position:0% +bar he's just going to do this honestly + + + align:start position:0% +bar he's just going to do this honestly +here we has one to the Lambda K and + + align:start position:0% +here we has one to the Lambda K and + + + align:start position:0% +here we has one to the Lambda K and +N and or this is n Prime the N Prime you + + align:start position:0% +N and or this is n Prime the N Prime you + + + align:start position:0% +N and or this is n Prime the N Prime you +know the he's going to generate exactly + + align:start position:0% +know the he's going to generate exactly + + + align:start position:0% +know the he's going to generate exactly +as as in the construction and then he + + align:start position:0% +as as in the construction and then he + + + align:start position:0% +as as in the construction and then he +gives he runs now + + align:start position:0% +gives he runs now + + + align:start position:0% +gives he runs now +run P star with hash key and CRS bar + + align:start position:0% +run P star with hash key and CRS bar + + + align:start position:0% +run P star with hash key and CRS bar +that's the CRS he gives P + + align:start position:0% + + + + align:start position:0% + +star and get V and Pi barg that's + + align:start position:0% +star and get V and Pi barg that's + + + align:start position:0% +star and get V and Pi barg that's +what the P star gives + + align:start position:0% +what the P star gives + + + align:start position:0% +what the P star gives +you + + align:start position:0% +you + + + align:start position:0% +you +now if this is rejected start again so + + align:start position:0% +now if this is rejected start again so + + + align:start position:0% +now if this is rejected start again so +if Pi Bar or if if V and Pi + + align:start position:0% +if Pi Bar or if if V and Pi + + + align:start position:0% +if Pi Bar or if if V and Pi +Bar so you know if the verifier with + + align:start position:0% +Bar so you know if the verifier with + + + align:start position:0% +Bar so you know if the verifier with +input oh wait sorry X star also X Tilda + + align:start position:0% +input oh wait sorry X star also X Tilda + + + align:start position:0% +input oh wait sorry X star also X Tilda +sorry he G so he G the P star gives what + + align:start position:0% +sorry he G so he G the P star gives what + + + align:start position:0% +sorry he G so he G the P star gives what +some X TAA because it's adaptive he + + align:start position:0% +some X TAA because it's adaptive he + + + align:start position:0% +some X TAA because it's adaptive he +gives him some X and a + + align:start position:0% +gives him some X and a + + + align:start position:0% +gives him some X and a +proof the proof is is a hash value and + + align:start position:0% +proof the proof is is a hash value and + + + align:start position:0% +proof the proof is is a hash value and +the bar that's what the proof is now he + + align:start position:0% +the bar that's what the proof is now he + + + align:start position:0% +the bar that's what the proof is now he +checks if V if the verifier rejects this + + align:start position:0% +checks if V if the verifier rejects this + + + align:start position:0% +checks if V if the verifier rejects this +proof it's it's not a good proof so if + + align:start position:0% +proof it's it's not a good proof so if + + + align:start position:0% +proof it's it's not a good proof so if +if V + + align:start position:0% +if V + + + align:start position:0% +if V +given CRS which is these two this is the + + align:start position:0% +given CRS which is these two this is the + + + align:start position:0% +given CRS which is these two this is the +CRS given CRS given X Tilda and given Pi + + align:start position:0% +CRS given CRS given X Tilda and given Pi + + + align:start position:0% +CRS given CRS given X Tilda and given Pi +this is + + align:start position:0% +this is + + + align:start position:0% +this is +pi output zero if it rejects try + + align:start position:0% + + + + align:start position:0% + +again what I mean by try again again + + align:start position:0% +again what I mean by try again again + + + align:start position:0% +again what I mean by try again again +generate a hash key generate a bar + + align:start position:0% +generate a hash key generate a bar + + + align:start position:0% +generate a hash key generate a bar +run if this is accept if it's rejected + + align:start position:0% +run if this is accept if it's rejected + + + align:start position:0% +run if this is accept if it's rejected +try again + + align:start position:0% + + + + align:start position:0% + +until I get something + + align:start position:0% +until I get something + + + align:start position:0% +until I get something +good okay now okay we want we okay until + + align:start position:0% +good okay now okay we want we okay until + + + align:start position:0% +good okay now okay we want we okay until +you get something good once you get + + align:start position:0% +you get something good once you get + + + align:start position:0% +you get something good once you get +something good you're happy what then + + align:start position:0% +something good you're happy what then + + + align:start position:0% +something good you're happy what then +what do you do you output so try again + + align:start position:0% +what do you do you output so try again + + + align:start position:0% +what do you do you output so try again +uh if + + align:start position:0% + + + + align:start position:0% + +success then + + align:start position:0% + + + + align:start position:0% + +output the X + + align:start position:0% +output the X + + + align:start position:0% +output the X +Tilda and what y values extract from the + + align:start position:0% +Tilda and what y values extract from the + + + align:start position:0% +Tilda and what y values extract from the +V so remember this V is Hash of all the + + align:start position:0% +V so remember this V is Hash of all the + + + align:start position:0% +V so remember this V is Hash of all the +wires of the + + align:start position:0% +wires of the + + + align:start position:0% +wires of the +circuit extract you'll get the wires + + align:start position:0% +circuit extract you'll get the wires + + + align:start position:0% +circuit extract you'll get the wires +corresponding to i1 of I so outut this + + align:start position:0% +corresponding to i1 of I so outut this + + + align:start position:0% +corresponding to i1 of I so outut this +and I'll put + + align:start position:0% + + + + align:start position:0% + +extract with + + align:start position:0% + + + + align:start position:0% + +trapo the value V to get W i1 up to W + + align:start position:0% +trapo the value V to get W i1 up to W + + + align:start position:0% +trapo the value V to get W i1 up to W +iil that's it that's what the extractor + + align:start position:0% +iil that's it that's what the extractor + + + align:start position:0% +iil that's it that's what the extractor +the local assignment generator does why + + align:start position:0% +the local assignment generator does why + + + align:start position:0% +the local assignment generator does why +can you do this I + + align:start position:0% +can you do this I + + + align:start position:0% +can you do this I +thought was adaptive so if you change + + align:start position:0% +thought was adaptive so if you change + + + align:start position:0% +thought was adaptive so if you change +CRS why can you fix it s no it's not + + align:start position:0% +CRS why can you fix it s no it's not + + + align:start position:0% +CRS why can you fix it s no it's not +fixed you're right so what do I do I + + align:start position:0% +fixed you're right so what do I do I + + + align:start position:0% +fixed you're right so what do I do I +generate hash key and a bar I run him he + + align:start position:0% +generate hash key and a bar I run him he + + + align:start position:0% +generate hash key and a bar I run him he +gives me XA if I'm happy with X if I'm + + align:start position:0% +gives me XA if I'm happy with X if I'm + + + align:start position:0% +gives me XA if I'm happy with X if I'm +happy with this proof I output XA the XA + + align:start position:0% +happy with this proof I output XA the XA + + + align:start position:0% +happy with this proof I output XA the XA +dependent on CRS so given I want to I + + align:start position:0% +dependent on CRS so given I want to I + + + align:start position:0% +dependent on CRS so given I want to I +I'm going to get a different I'm going + + align:start position:0% +I'm going to get a different I'm going + + + align:start position:0% +I'm going to get a different I'm going +to get a different X still the + + align:start position:0% +to get a different X still the + + + align:start position:0% +to get a different X still the +every time I get up i1 I generate H CRS + + align:start position:0% +every time I get up i1 I generate H CRS + + + align:start position:0% +every time I get up i1 I generate H CRS +for my + + align:start position:0% +for my + + + align:start position:0% +for my +snar I run the pro I get xtia and a + + align:start position:0% +snar I run the pro I get xtia and a + + + align:start position:0% +snar I run the pro I get xtia and a +proof If I'm happy with the proof I + + align:start position:0% +proof If I'm happy with the proof I + + + align:start position:0% +proof If I'm happy with the proof I +output xtia and the extracted wires W's + + align:start position:0% +output xtia and the extracted wires W's + + + align:start position:0% +output xtia and the extracted wires W's +are just wire values they're not + + align:start position:0% +are just wire values they're not + + + align:start position:0% +are just wire values they're not +Witnesses no they're wire values sorry + + align:start position:0% +Witnesses no they're wire values sorry + + + align:start position:0% +Witnesses no they're wire values sorry +these are not Witnesses yeah uh yeah I + + align:start position:0% +these are not Witnesses yeah uh yeah I + + + align:start position:0% +these are not Witnesses yeah uh yeah I +use W for you know wires but it's also + + align:start position:0% +use W for you know wires but it's also + + + align:start position:0% +use W for you know wires but it's also +witness it's + + align:start position:0% +witness it's + + + align:start position:0% +witness it's +a uh so + + align:start position:0% +a uh so + + + align:start position:0% +a uh so +sorry + + align:start position:0% +sorry + + + align:start position:0% +sorry +a a bit of abuse of notation sorry these + + align:start position:0% +a a bit of abuse of notation sorry these + + + align:start position:0% +a a bit of abuse of notation sorry these +are yre values okay forget about witness + + align:start position:0% +are yre values okay forget about witness + + + align:start position:0% +are yre values okay forget about witness +there's no Witnesses now just wires yeah + + align:start position:0% +there's no Witnesses now just wires yeah + + + align:start position:0% +there's no Witnesses now just wires yeah +yeah if you're like projection sampling + + align:start position:0% +yeah if you're like projection sampling + + + align:start position:0% +yeah if you're like projection sampling +until you get the verifi to accept then + + align:start position:0% +until you get the verifi to accept then + + + align:start position:0% +until you get the verifi to accept then +how is the distribution of X be the + + align:start position:0% +how is the distribution of X be the + + + align:start position:0% +how is the distribution of X be the +distribution of okay uh uh okay that's + + align:start position:0% +distribution of okay uh uh okay that's + + + align:start position:0% +distribution of okay uh uh okay that's +good so I'm gonna answer did you you + + align:start position:0% +good so I'm gonna answer did you you + + + align:start position:0% +good so I'm gonna answer did you you +it's a different question a different + + align:start position:0% +it's a different question a different + + + align:start position:0% +it's a different question a different +question okay let me first answer this + + align:start position:0% +question okay let me first answer this + + + align:start position:0% +question okay let me first answer this +question so okay I'm GNA um + + align:start position:0% +question so okay I'm GNA um + + + align:start position:0% +question so okay I'm GNA um +the question was first there's a couple + + align:start position:0% +the question was first there's a couple + + + align:start position:0% +the question was first there's a couple +issues first of all how many times am am + + align:start position:0% +issues first of all how many times am am + + + align:start position:0% +issues first of all how many times am am +I going to do this rejection sampling + + align:start position:0% +I going to do this rejection sampling + + + align:start position:0% +I going to do this rejection sampling +okay am I going to run forever what's + + align:start position:0% +okay am I going to run forever what's + + + align:start position:0% +okay am I going to run forever what's +going on here and the answer is no + + align:start position:0% +going on here and the answer is no + + + align:start position:0% +going on here and the answer is no +actually I'm not not going to run + + align:start position:0% +actually I'm not not going to run + + + align:start position:0% +actually I'm not not going to run +forever so fix a p star that let's say + + align:start position:0% +forever so fix a p star that let's say + + + align:start position:0% +forever so fix a p star that let's say +is + + align:start position:0% +is + + + align:start position:0% +is +accepted with non-n + + align:start position:0% + + + + align:start position:0% + +probability Epsilon okay Epsilon is not + + align:start position:0% +probability Epsilon okay Epsilon is not + + + align:start position:0% +probability Epsilon okay Epsilon is not +negligible + + align:start position:0% +negligible + + + align:start position:0% +negligible +I'm going to try again at + + align:start position:0% + + + + align:start position:0% + +most a I know poly in Lambda and 1 over + + align:start position:0% +most a I know poly in Lambda and 1 over + + + align:start position:0% +most a I know poly in Lambda and 1 over +Epsilon + + align:start position:0% + + + + align:start position:0% + +times so I'm going to do this only poom + + align:start position:0% +times so I'm going to do this only poom + + + align:start position:0% +times so I'm going to do this only poom +many times okay think of Epsilon as one + + align:start position:0% +many times okay think of Epsilon as one + + + align:start position:0% +many times okay think of Epsilon as one +over poly Lambda so I'm going to run in + + align:start position:0% +over poly Lambda so I'm going to run in + + + align:start position:0% +over poly Lambda so I'm going to run in +time poly in + + align:start position:0% +time poly in + + + align:start position:0% +time poly in +Lambda + + align:start position:0% +Lambda + + + align:start position:0% +Lambda +okay now given that and okay so the + + align:start position:0% +okay now given that and okay so the + + + align:start position:0% +okay now given that and okay so the +first thing I want to argue you is the + + align:start position:0% +first thing I want to argue you is the + + + align:start position:0% +first thing I want to argue you is the +probability that I will and so I'm going + + align:start position:0% +probability that I will and so I'm going + + + align:start position:0% +probability that I will and so I'm going +to run the most poly Lambda one overs on + + align:start position:0% +to run the most poly Lambda one overs on + + + align:start position:0% +to run the most poly Lambda one overs on +time that's it and you say what if all + + align:start position:0% +time that's it and you say what if all + + + align:start position:0% +time that's it and you say what if all +of them are reject then I'm going to say + + align:start position:0% +of them are reject then I'm going to say + + + align:start position:0% +of them are reject then I'm going to say +okay I I Was + + align:start position:0% +okay I I Was + + + align:start position:0% +okay I I Was +Defeated okay what is the probability + + align:start position:0% +Defeated okay what is the probability + + + align:start position:0% +Defeated okay what is the probability +that I'll be defeated negligible because + + align:start position:0% +that I'll be defeated negligible because + + + align:start position:0% +that I'll be defeated negligible because +each time I'm starting fresh and the + + align:start position:0% +each time I'm starting fresh and the + + + align:start position:0% +each time I'm starting fresh and the +probability of defeat is only ABS is is + + align:start position:0% +probability of defeat is only ABS is is + + + align:start position:0% +probability of defeat is only ABS is is +uh is one over ah the okay I'm re + + align:start position:0% +uh is one over ah the okay I'm re + + + align:start position:0% +uh is one over ah the okay I'm re +I'm I'm accepted I'm I'm okay I'm + + align:start position:0% +I'm I'm accepted I'm I'm okay I'm + + + align:start position:0% +I'm I'm accepted I'm I'm okay I'm +accepted with probability Epsilon if I + + align:start position:0% +accepted with probability Epsilon if I + + + align:start position:0% +accepted with probability Epsilon if I +repeat it you know Lambda over Epsilon + + align:start position:0% +repeat it you know Lambda over Epsilon + + + align:start position:0% +repeat it you know Lambda over Epsilon +Times by just concentration Bound by + + align:start position:0% +Times by just concentration Bound by + + + align:start position:0% +Times by just concentration Bound by +turn of bound I'm going to be accepted + + align:start position:0% +turn of bound I'm going to be accepted + + + align:start position:0% +turn of bound I'm going to be accepted +in one of them with very very high + + align:start position:0% +in one of them with very very high + + + align:start position:0% +in one of them with very very high +probability okay exponential like + + align:start position:0% +probability okay exponential like + + + align:start position:0% +probability okay exponential like +exponential in one like two the minus + + align:start position:0% +exponential in one like two the minus + + + align:start position:0% +exponential in one like two the minus +Lambda or something like that so if I + + align:start position:0% +Lambda or something like that so if I + + + align:start position:0% +Lambda or something like that so if I +repeat it enough times one of them I'm + + align:start position:0% +repeat it enough times one of them I'm + + + align:start position:0% +repeat it enough times one of them I'm +going to the probability of of Bot of me + + align:start position:0% +going to the probability of of Bot of me + + + align:start position:0% +going to the probability of of Bot of me +kind of being defeated is negligible + + align:start position:0% +kind of being defeated is negligible + + + align:start position:0% +kind of being defeated is negligible +okay so now then but now going back to + + align:start position:0% +okay so now then but now going back to + + + align:start position:0% +okay so now then but now going back to +your question the question is how do I + + align:start position:0% +your question the question is how do I + + + align:start position:0% +your question the question is how do I +know that XA here has the same + + align:start position:0% +know that XA here has the same + + + align:start position:0% +know that XA here has the same +distribution as the x of P star yeah + + align:start position:0% +distribution as the x of P star yeah + + + align:start position:0% +distribution as the x of P star yeah +that's the question + + align:start position:0% +that's the question + + + align:start position:0% +that's the question +so a good so + + align:start position:0% +so a good so + + + align:start position:0% +so a good so +a actually I was a bit sloppy when I say + + align:start position:0% +a actually I was a bit sloppy when I say + + + align:start position:0% +a actually I was a bit sloppy when I say +XA is inting from this I mean in the for + + align:start position:0% +XA is inting from this I mean in the for + + + align:start position:0% +XA is inting from this I mean in the for +XA condition and accept sorry yeah this + + align:start position:0% +XA condition and accept sorry yeah this + + + align:start position:0% +XA condition and accept sorry yeah this +is + + align:start position:0% +is + + + align:start position:0% +is +condition on P star + + align:start position:0% +condition on P star + + + align:start position:0% +condition on P star +accepting so p i can assume without loss + + align:start position:0% +accepting so p i can assume without loss + + + align:start position:0% +accepting so p i can assume without loss +of yeah so and let's think of P star + + align:start position:0% +of yeah so and let's think of P star + + + align:start position:0% +of yeah so and let's think of P star +either is outting bot there's no point + + align:start position:0% +either is outting bot there's no point + + + align:start position:0% +either is outting bot there's no point +in him giving a bad proof like he's + + align:start position:0% +in him giving a bad proof like he's + + + align:start position:0% +in him giving a bad proof like he's +going to be rejected either is like + + align:start position:0% +going to be rejected either is like + + + align:start position:0% +going to be rejected either is like +defeat or give x with a good proof okay + + align:start position:0% +defeat or give x with a good proof okay + + + align:start position:0% +defeat or give x with a good proof okay +so the pro so uh my X I always output XA + + align:start position:0% +so the pro so uh my X I always output XA + + + align:start position:0% +so the pro so uh my X I always output XA +with property one minus negligible and + + align:start position:0% +with property one minus negligible and + + + align:start position:0% +with property one minus negligible and +this XA is going to be distributed like + + align:start position:0% +this XA is going to be distributed like + + + align:start position:0% +this XA is going to be distributed like +X zilda condition on n on the P star not + + align:start position:0% +X zilda condition on n on the P star not + + + align:start position:0% +X zilda condition on n on the P star not +a boarding yeah those two distribs + + align:start position:0% +a boarding yeah those two distribs + + + align:start position:0% +a boarding yeah those two distribs +actually idal right up to the SL + + align:start position:0% +actually idal right up to the SL + + + align:start position:0% +actually idal right up to the SL +probability that you give up at the end + + align:start position:0% +probability that you give up at the end + + + align:start position:0% +probability that you give up at the end +no it's uh okay so the question one is + + align:start position:0% +no it's uh okay so the question one is + + + align:start position:0% +no it's uh okay so the question one is +the X Tilla of P star actually identical + + align:start position:0% +the X Tilla of P star actually identical + + + align:start position:0% +the X Tilla of P star actually identical +to the X Tilda of the extractor and the + + align:start position:0% +to the X Tilda of the extractor and the + + + align:start position:0% +to the X Tilda of the extractor and the +answer is not quite because the xti of + + align:start position:0% +answer is not quite because the xti of + + + align:start position:0% +answer is not quite because the xti of +the extractor runs gen with these + + align:start position:0% +the extractor runs gen with these + + + align:start position:0% +the extractor runs gen with these +specific + + align:start position:0% +specific + + + align:start position:0% +specific +eyes and X Tilda is run with P star with + + align:start position:0% +eyes and X Tilda is run with P star with + + + align:start position:0% +eyes and X Tilda is run with P star with +let's say one two three up to L I don't + + align:start position:0% +let's say one two three up to L I don't + + + align:start position:0% +let's say one two three up to L I don't +know like a fixed uh and this kind of + + align:start position:0% +know like a fixed uh and this kind of + + + align:start position:0% +know like a fixed uh and this kind of +the eyes change that's the only + + align:start position:0% +the eyes change that's the only + + + align:start position:0% +the eyes change that's the only +difference and that's why it's + + align:start position:0% +difference and that's why it's + + + align:start position:0% +difference and that's why it's +indistinguishable because the p star + + align:start position:0% +indistinguishable because the p star + + + align:start position:0% +indistinguishable because the p star +doesn't know that because of the index + + align:start position:0% +doesn't know that because of the index + + + align:start position:0% +doesn't know that because of the index +hiding P star has no idea what the indic + + align:start position:0% +hiding P star has no idea what the indic + + + align:start position:0% +hiding P star has no idea what the indic +which indices are sitting behind the + + align:start position:0% +which indices are sitting behind the + + + align:start position:0% +which indices are sitting behind the +hash key so the Exel that he he's given + + align:start position:0% +hash key so the Exel that he he's given + + + align:start position:0% +hash key so the Exel that he he's given +he gives is the same is + + align:start position:0% +he gives is the same is + + + align:start position:0% +he gives is the same is +indistinguishable nikan did you are + + align:start position:0% +indistinguishable nikan did you are + + + align:start position:0% +indistinguishable nikan did you are +you make sure last Point each trial here + + align:start position:0% +you make sure last Point each trial here + + + align:start position:0% +you make sure last Point each trial here +will work with probability Epsilon minus + + align:start position:0% +will work with probability Epsilon minus + + + align:start position:0% +will work with probability Epsilon minus +because of the index hiding right + + align:start position:0% +because of the index hiding right + + + align:start position:0% +because of the index hiding right +exactly you're right yeah you're right + + align:start position:0% +exactly you're right yeah you're right + + + align:start position:0% +exactly you're right yeah you're right +exactly Epson minus that's why the + + align:start position:0% +exactly Epson minus that's why the + + + align:start position:0% +exactly Epson minus that's why the +Epsilon has to be non- negligible + + align:start position:0% +Epsilon has to be non- negligible + + + align:start position:0% +Epsilon has to be non- negligible +because you lose negligible and if if + + align:start position:0% +because you lose negligible and if if + + + align:start position:0% +because you lose negligible and if if +you know it needs to be negligible + + align:start position:0% +you know it needs to be negligible + + + align:start position:0% +you know it needs to be negligible +compared to the + + align:start position:0% +compared to the + + + align:start position:0% +compared to the +Epsilon so my question was the extract + + align:start position:0% +Epsilon so my question was the extract + + + align:start position:0% +Epsilon so my question was the extract +algorithm for the is only required to + + align:start position:0% +algorithm for the is only required to + + + align:start position:0% +algorithm for the is only required to +extract when V is an eval of X + + align:start position:0% +extract when V is an eval of X + + + align:start position:0% +extract when V is an eval of X +right is that true or is that not true a + + align:start position:0% +right is that true or is that not true a + + + align:start position:0% +right is that true or is that not true a +okay one second + + align:start position:0% + + + + align:start position:0% + +good point uh no um okay the no the + + align:start position:0% +good point uh no um okay the no the + + + align:start position:0% +good point uh no um okay the no the +completeness was assuming you know holds + + align:start position:0% +completeness was assuming you know holds + + + align:start position:0% +completeness was assuming you know holds +but + + align:start position:0% +but + + + align:start position:0% +but +uh I didn't write it actually down good + + align:start position:0% +uh I didn't write it actually down good + + + align:start position:0% +uh I didn't write it actually down good +point Nikon thank you + + align:start position:0% + + + + align:start position:0% + +a the uh the summer extractable hash I + + align:start position:0% +a the uh the summer extractable hash I + + + align:start position:0% +a the uh the summer extractable hash I +didn't say soundness of the I didn't + + align:start position:0% +didn't say soundness of the I didn't + + + align:start position:0% +didn't say soundness of the I didn't +write like the soundness of this extract + + align:start position:0% +write like the soundness of this extract + + + align:start position:0% +write like the soundness of this extract +so + + align:start position:0% +so + + + align:start position:0% +so +uh the extract has the the following + + align:start position:0% +uh the extract has the the following + + + align:start position:0% +uh the extract has the the following +property if the cheating + + align:start position:0% + + + + align:start position:0% + +a if the cheating + + align:start position:0% +a if the cheating + + + align:start position:0% +a if the cheating +prover gives any hold on let me think + + align:start position:0% +prover gives any hold on let me think + + + align:start position:0% +prover gives any hold on let me think +for a second + + align:start position:0% + + + + align:start position:0% + +if the cheating prover gives an opening + + align:start position:0% +if the cheating prover gives an opening + + + align:start position:0% +if the cheating prover gives an opening +if if you're extract if the hash key + + align:start position:0% +if if you're extract if the hash key + + + align:start position:0% +if if you're extract if the hash key +okay thank you if the hash key is + + align:start position:0% +okay thank you if the hash key is + + + align:start position:0% +okay thank you if the hash key is +generated with Gen of I and if an + + align:start position:0% +generated with Gen of I and if an + + + align:start position:0% +generated with Gen of I and if an +adversary generated an opening of I a + + align:start position:0% +adversary generated an opening of I a + + + align:start position:0% +adversary generated an opening of I a +valid opening so he successfully opened + + align:start position:0% +valid opening so he successfully opened + + + align:start position:0% +valid opening so he successfully opened +the I + + align:start position:0% +the I + + + align:start position:0% +the I +bit somehow with a B then the extract + + align:start position:0% +bit somehow with a B then the extract + + + align:start position:0% +bit somehow with a B then the extract +will work and give you that same + + align:start position:0% +will work and give you that same + + + align:start position:0% +will work and give you that same +B so let me let me write it down because + + align:start position:0% +B so let me let me write it down because + + + align:start position:0% +B so let me let me write it down because +actually we need it here so uh + + align:start position:0% + + + + align:start position:0% + +okay okay uh for + + align:start position:0% +okay okay uh for + + + align:start position:0% +okay okay uh for +any + + align:start position:0% + + + + align:start position:0% + +uh for any a adversary and for every + + align:start position:0% +uh for any a adversary and for every + + + align:start position:0% +uh for any a adversary and for every +I the probability + + align:start position:0% +I the probability + + + align:start position:0% +I the probability +that a and hash key where the hash key + + align:start position:0% +that a and hash key where the hash key + + + align:start position:0% +that a and hash key where the hash key +is generated with I so hash key trapd + + align:start position:0% +is generated with I so hash key trapd + + + align:start position:0% +is generated with I so hash key trapd +door they're generated with Gen with uh + + align:start position:0% +door they're generated with Gen with uh + + + align:start position:0% +door they're generated with Gen with uh +one to the Lambda n and + + align:start position:0% +one to the Lambda n and + + + align:start position:0% +one to the Lambda n and +I if this if he managed to give me a + + align:start position:0% +I if this if he managed to give me a + + + align:start position:0% +I if this if he managed to give me a +value adversarial value but he manages + + align:start position:0% +value adversarial value but he manages + + + align:start position:0% +value adversarial value but he manages +to open with a a b and row so let me + + align:start position:0% +to open with a a b and row so let me + + + align:start position:0% +to open with a a b and row so let me +call it it b i and row I such + + align:start position:0% +call it it b i and row I such + + + align:start position:0% +call it it b i and row I such +that the verifier accept it such that + + align:start position:0% +that the verifier accept it such that + + + align:start position:0% +that the verifier accept it such that +ver so the probability that he gives me + + align:start position:0% +ver so the probability that he gives me + + + align:start position:0% +ver so the probability that he gives me +a verify uh um a tuple that verifies so + + align:start position:0% +a verify uh um a tuple that verifies so + + + align:start position:0% +a verify uh um a tuple that verifies so +hash key + + align:start position:0% +hash key + + + align:start position:0% +hash key +v i b row is + + align:start position:0% +v i b row is + + + align:start position:0% +v i b row is +one and but extraction fails is + + align:start position:0% +one and but extraction fails is + + + align:start position:0% +one and but extraction fails is +negligible so the probability that this + + align:start position:0% +negligible so the probability that this + + + align:start position:0% +negligible so the probability that this +accept but extract + + align:start position:0% + + + + align:start position:0% + +a is not + + align:start position:0% +a is not + + + align:start position:0% +a is not +b bi is + + align:start position:0% + + + + align:start position:0% + +negligible so if you opened it must be + + align:start position:0% +negligible so if you opened it must be + + + align:start position:0% +negligible so if you opened it must be +valid and if you think about the + + align:start position:0% +valid and if you think about the + + + align:start position:0% +valid and if you think about the +construction if you open it's like + + align:start position:0% +construction if you open it's like + + + align:start position:0% +construction if you open it's like +everything is in the correct encryption + + align:start position:0% +everything is in the correct encryption + + + align:start position:0% +everything is in the correct encryption +encryption encryption the encryption + + align:start position:0% +encryption encryption the encryption + + + align:start position:0% +encryption encryption the encryption +must be correct and the extractor will + + align:start position:0% +must be correct and the extractor will + + + align:start position:0% +must be correct and the extractor will +will + + align:start position:0% +will + + + align:start position:0% +will +decrypted that's kind of the a + + align:start position:0% +decrypted that's kind of the a + + + align:start position:0% +decrypted that's kind of the a +yeah so if he doesn't open anything V + + align:start position:0% +yeah so if he doesn't open anything V + + + align:start position:0% +yeah so if he doesn't open anything V +can be whatever you may not be able to + + align:start position:0% +can be whatever you may not be able to + + + align:start position:0% +can be whatever you may not be able to +extract but as long as he gave you uh + + align:start position:0% +extract but as long as he gave you uh + + + align:start position:0% +extract but as long as he gave you uh +the correct path then then okay so we'll + + align:start position:0% +the correct path then then okay so we'll + + + align:start position:0% +the correct path then then okay so we'll +use it here thank + + align:start position:0% +use it here thank + + + align:start position:0% +use it here thank +you okay uh okay so now let's see why is + + align:start position:0% +you okay uh okay so now let's see why is + + + align:start position:0% +you okay uh okay so now let's see why is +so this is but this is the extraction + + align:start position:0% +so this is but this is the extraction + + + align:start position:0% +so this is but this is the extraction +procedure okay we'll analyze it in a + + align:start position:0% +procedure okay we'll analyze it in a + + + align:start position:0% +procedure okay we'll analyze it in a +second we'll see why this is used but + + align:start position:0% +second we'll see why this is used but + + + align:start position:0% +second we'll see why this is used but +again let me let's just kind of R kind + + align:start position:0% +again let me let's just kind of R kind + + + align:start position:0% +again let me let's just kind of R kind +of uh recall what so what is the local + + align:start position:0% +of uh recall what so what is the local + + + align:start position:0% +of uh recall what so what is the local +assignment generator it takes L + + align:start position:0% +assignment generator it takes L + + + align:start position:0% +assignment generator it takes L +wires he will generate a CRS and give it + + align:start position:0% +wires he will generate a CRS and give it + + + align:start position:0% +wires he will generate a CRS and give it +to the cheating po the CRS he generates + + align:start position:0% +to the cheating po the CRS he generates + + + align:start position:0% +to the cheating po the CRS he generates +consists of a hash key and a bar and a + + align:start position:0% +consists of a hash key and a bar and a + + + align:start position:0% +consists of a hash key and a bar and a +CRS for the bar the CRS for the bar he + + align:start position:0% +CRS for the bar the CRS for the bar he + + + align:start position:0% +CRS for the bar the CRS for the bar he +just generates and the s for the hash + + align:start position:0% +just generates and the s for the hash + + + align:start position:0% +just generates and the s for the hash +key he generates with a trapo with + + align:start position:0% +key he generates with a trapo with + + + align:start position:0% +key he generates with a trapo with +respect to the wires that he needs to + + align:start position:0% +respect to the wires that he needs to + + + align:start position:0% +respect to the wires that he needs to +extract he gives this to the prover and + + align:start position:0% +extract he gives this to the prover and + + + align:start position:0% +extract he gives this to the prover and +the prover gives him + + align:start position:0% +the prover gives him + + + align:start position:0% +the prover gives him +hash value that's extractable on these + + align:start position:0% +hash value that's extractable on these + + + align:start position:0% +hash value that's extractable on these +wires and a bark proof If the bark proof + + align:start position:0% +wires and a bark proof If the bark proof + + + align:start position:0% +wires and a bark proof If the bark proof +is rejected he starts all over so we're + + align:start position:0% +is rejected he starts all over so we're + + + align:start position:0% +is rejected he starts all over so we're +going to do it until we have something + + align:start position:0% +going to do it until we have something + + + align:start position:0% +going to do it until we have something +accepted once it's accepted we're going + + align:start position:0% +accepted once it's accepted we're going + + + align:start position:0% +accepted once it's accepted we're going +to just extract these W these uh wires + + align:start position:0% +to just extract these W these uh wires + + + align:start position:0% +to just extract these W these uh wires +because we we have the trapo the the + + align:start position:0% +because we we have the trapo the the + + + align:start position:0% +because we we have the trapo the the +extractor has the trapo we're going to + + align:start position:0% +extractor has the trapo we're going to + + + align:start position:0% +extractor has the trapo we're going to +or the E here we're going to extract uh + + align:start position:0% +or the E here we're going to extract uh + + + align:start position:0% +or the E here we're going to extract uh +the wires and that's what we're going to + + align:start position:0% +the wires and that's what we're going to + + + align:start position:0% +the wires and that's what we're going to +Output okay the XA and the + + align:start position:0% +Output okay the XA and the + + + align:start position:0% +Output okay the XA and the +wires Okay so so now we need to argue + + align:start position:0% +wires Okay so so now we need to argue + + + align:start position:0% +wires Okay so so now we need to argue +non- signaling and we need to argue + + align:start position:0% +non- signaling and we need to argue + + + align:start position:0% +non- signaling and we need to argue +local + + align:start position:0% +local + + + align:start position:0% +local +consistency any questions before I go + + align:start position:0% +consistency any questions before I go + + + align:start position:0% +consistency any questions before I go +ahead and do + + align:start position:0% + + + + align:start position:0% + +it okay so let's see let's start with um + + align:start position:0% +it okay so let's see let's start with um + + + align:start position:0% +it okay so let's see let's start with um +with local consistency okay why why are + + align:start position:0% +with local consistency okay why why are + + + align:start position:0% +with local consistency okay why why are +things locally + + align:start position:0% +things locally + + + align:start position:0% +things locally +consistent so the I claim that local + + align:start position:0% +consistent so the I claim that local + + + align:start position:0% +consistent so the I claim that local +consistency follows from the soundness + + align:start position:0% +consistency follows from the soundness + + + align:start position:0% +consistency follows from the soundness +of the bar okay so let's see why this is + + align:start position:0% +of the bar okay so let's see why this is + + + align:start position:0% +of the bar okay so let's see why this is +um + + align:start position:0% + + + + align:start position:0% + +I want of + + align:start position:0% + + + + align:start position:0% + +okay what do we have + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% + + + + align:start position:0% + +a okay oh well I'm just + + align:start position:0% +a okay oh well I'm just + + + align:start position:0% +a okay oh well I'm just +gonna we're going to kind of needed but + + align:start position:0% +gonna we're going to kind of needed but + + + align:start position:0% +gonna we're going to kind of needed but +it's + + align:start position:0% +it's + + + align:start position:0% +it's +okay okay so + + align:start position:0% + + + + align:start position:0% + +so local consistency I want to argue + + align:start position:0% +so local consistency I want to argue + + + align:start position:0% +so local consistency I want to argue +follows from the correctness of the bar + + align:start position:0% +follows from the correctness of the bar + + + align:start position:0% +follows from the correctness of the bar +from the soundness of the bar why + + align:start position:0% +from the soundness of the bar why + + + align:start position:0% +from the soundness of the bar why +suppose for + + align:start position:0% + + + + align:start position:0% + +contradiction so suppose at the + + align:start position:0% +contradiction so suppose at the + + + align:start position:0% +contradiction so suppose at the +extractor output X TAA and l y values + + align:start position:0% +extractor output X TAA and l y values + + + align:start position:0% +extractor output X TAA and l y values +the not + + align:start position:0% +the not + + + align:start position:0% +the not +consistent okay so the ly values are not + + align:start position:0% +consistent okay so the ly values are not + + + align:start position:0% +consistent okay so the ly values are not +consistent then what does they mean + + align:start position:0% +consistent then what does they mean + + + align:start position:0% +consistent then what does they mean +they're not consistent there's one gate + + align:start position:0% +they're not consistent there's one gate + + + align:start position:0% +they're not consistent there's one gate +that they don't + + align:start position:0% +that they don't + + + align:start position:0% +that they don't +respect + + align:start position:0% +respect + + + align:start position:0% +respect +now remember so okay so there's one gate + + align:start position:0% +now remember so okay so there's one gate + + + align:start position:0% +now remember so okay so there's one gate +that they don't respect so + + align:start position:0% + + + + align:start position:0% + +suppose e an input i1 up to I L output + + align:start position:0% + + + + align:start position:0% + +like W1 up to W i1 up to w i + + align:start position:0% +like W1 up to W i1 up to w i + + + align:start position:0% +like W1 up to W i1 up to w i +l that do not + + align:start position:0% + + + + align:start position:0% + +respect some gate let's fix a gate some + + align:start position:0% +respect some gate let's fix a gate some + + + align:start position:0% +respect some gate let's fix a gate some +gate J with non- Neal probability if + + align:start position:0% +gate J with non- Neal probability if + + + align:start position:0% +gate J with non- Neal probability if +there's one gate doesn't respect choose + + align:start position:0% +there's one gate doesn't respect choose + + + align:start position:0% +there's one gate doesn't respect choose +it one at random so won't respect this + + align:start position:0% +it one at random so won't respect this + + + align:start position:0% +it one at random so won't respect this +random one with probability I mean there + + align:start position:0% +random one with probability I mean there + + + align:start position:0% +random one with probability I mean there +exists one gate that's not respect + + align:start position:0% +exists one gate that's not respect + + + align:start position:0% +exists one gate that's not respect +probability one over poly + + align:start position:0% +probability one over poly + + + align:start position:0% +probability one over poly +okay Suppose there exist some GJ that + + align:start position:0% +okay Suppose there exist some GJ that + + + align:start position:0% +okay Suppose there exist some GJ that +this does not with + + align:start position:0% + + + + align:start position:0% + +probability one over + + align:start position:0% +probability one over + + + align:start position:0% +probability one over +poly now let's look at the bar what does + + align:start position:0% +poly now let's look at the bar what does + + + align:start position:0% +poly now let's look at the bar what does +the bar say the bar tells me that all + + align:start position:0% +the bar say the bar tells me that all + + + align:start position:0% +the bar say the bar tells me that all +the gates are + + align:start position:0% +the gates are + + + align:start position:0% +the gates are +respected so what I'm going to do in the + + align:start position:0% +respected so what I'm going to do in the + + + align:start position:0% +respected so what I'm going to do in the +bar I'm going to so remember in the bar + + align:start position:0% +bar I'm going to so remember in the bar + + + align:start position:0% +bar I'm going to so remember in the bar +a I have this somewhere now I'm to the + + align:start position:0% +a I have this somewhere now I'm to the + + + align:start position:0% +a I have this somewhere now I'm to the +Adaptive versus the why some more + + align:start position:0% +Adaptive versus the why some more + + + align:start position:0% +Adaptive versus the why some more +adaptive soundless of bar is enough why + + align:start position:0% +adaptive soundless of bar is enough why + + + align:start position:0% +adaptive soundless of bar is enough why +if there's some gay J that's not + + align:start position:0% +if there's some gay J that's not + + + align:start position:0% +if there's some gay J that's not +responsibility one over poly in the bar + + align:start position:0% +responsibility one over poly in the bar + + + align:start position:0% +responsibility one over poly in the bar +Construction in the CRS I'm going to + + align:start position:0% +Construction in the CRS I'm going to + + + align:start position:0% +Construction in the CRS I'm going to +hard why I'm so sorry I'm gonna okay let + + align:start position:0% +hard why I'm so sorry I'm gonna okay let + + + align:start position:0% +hard why I'm so sorry I'm gonna okay let +me construct a cheating prover for the + + align:start position:0% +me construct a cheating prover for the + + + align:start position:0% +me construct a cheating prover for the +bar okay so we're going to + + align:start position:0% + + + + align:start position:0% + +construct cheating prover + + align:start position:0% + + + + align:start position:0% + +for + + align:start position:0% + + + + align:start position:0% + +bar that + + align:start position:0% + + + + align:start position:0% + +cheats he's going to be somewhere + + align:start position:0% +cheats he's going to be somewhere + + + align:start position:0% +cheats he's going to be somewhere +adaptive sound is and he's going to + + align:start position:0% +adaptive sound is and he's going to + + + align:start position:0% +adaptive sound is and he's going to +cheat on + + align:start position:0% +cheat on + + + align:start position:0% +cheat on +J and this specific J I don't care about + + align:start position:0% +J and this specific J I don't care about + + + align:start position:0% +J and this specific J I don't care about +what the CRS is yet I'm going to be semi + + align:start position:0% +what the CRS is yet I'm going to be semi + + + align:start position:0% +what the CRS is yet I'm going to be semi +adaptive so I'm going to tell you my + + align:start position:0% +adaptive so I'm going to tell you my + + + align:start position:0% +adaptive so I'm going to tell you my +chover he may choose the X1 star of to x + + align:start position:0% +chover he may choose the X1 star of to x + + + align:start position:0% +chover he may choose the X1 star of to x +k star the actual instances later but + + align:start position:0% +k star the actual instances later but + + + align:start position:0% +k star the actual instances later but +which one he's going to choose he's + + align:start position:0% +which one he's going to choose he's + + + align:start position:0% +which one he's going to choose he's +going to cheat on I'm going to tell you + + align:start position:0% +going to cheat on I'm going to tell you + + + align:start position:0% +going to cheat on I'm going to tell you +now it's j so it's going to be S like + + align:start position:0% +now it's j so it's going to be S like + + + align:start position:0% +now it's j so it's going to be S like +it's going to be nonadaptive and where + + align:start position:0% +it's going to be nonadaptive and where + + + align:start position:0% +it's going to be nonadaptive and where +he's cheating that's kind of the + + align:start position:0% +he's cheating that's kind of the + + + align:start position:0% +he's cheating that's kind of the +semi-adaptive + + align:start position:0% + + + + align:start position:0% + +yeah loal consistency is a statement + + align:start position:0% +yeah loal consistency is a statement + + + align:start position:0% +yeah loal consistency is a statement +that the extractor out is that the same + + align:start position:0% +that the extractor out is that the same + + + align:start position:0% +that the extractor out is that the same +as the statement + + align:start position:0% +as the statement + + + align:start position:0% +as the statement +that okay so let me tell okay so let me + + align:start position:0% +that okay so let me tell okay so let me + + + align:start position:0% +that okay so let me tell okay so let me +so you're asking is there a match how do + + align:start position:0% +so you're asking is there a match how do + + + align:start position:0% +so you're asking is there a match how do +we match these two so let me okay so + + align:start position:0% +we match these two so let me okay so + + + align:start position:0% +we match these two so let me okay so +wait let me tell you the cheating prover + + align:start position:0% +wait let me tell you the cheating prover + + + align:start position:0% +wait let me tell you the cheating prover +so I'm going to construct a cheating + + align:start position:0% +so I'm going to construct a cheating + + + align:start position:0% +so I'm going to construct a cheating +prover let's say Pou star for the bar + + align:start position:0% +prover let's say Pou star for the bar + + + align:start position:0% +prover let's say Pou star for the bar +okay here's what my pble star does my + + align:start position:0% +okay here's what my pble star does my + + + align:start position:0% +okay here's what my pble star does my +pble star he gets CRS of + + align:start position:0% + + + + align:start position:0% + +bar what he's going to do he's gonna + + align:start position:0% +bar what he's going to do he's gonna + + + align:start position:0% +bar what he's going to do he's gonna +a uh run piece he's going to generate + + align:start position:0% +a uh run piece he's going to generate + + + align:start position:0% +a uh run piece he's going to generate +hash key on his own okay and he's going + + align:start position:0% +hash key on his own okay and he's going + + + align:start position:0% +hash key on his own okay and he's going +to + + align:start position:0% +to + + + align:start position:0% +to +run P star on the CRS + + align:start position:0% + + + + align:start position:0% + +bar and the hash key that he gives him + + align:start position:0% +bar and the hash key that he gives him + + + align:start position:0% +bar and the hash key that he gives him +he's going to get + + align:start position:0% +he's going to get + + + align:start position:0% +he's going to get +V and Pi + + align:start position:0% + + + + align:start position:0% + +Bar and now he's going to cheat pble + + align:start position:0% +Bar and now he's going to cheat pble + + + align:start position:0% +Bar and now he's going to cheat pble +star will + + align:start position:0% +star will + + + align:start position:0% +star will +cheat and here's the instances that he + + align:start position:0% +cheat and here's the instances that he + + + align:start position:0% +cheat and here's the instances that he +gives so he's going to give the + + align:start position:0% +gives so he's going to give the + + + align:start position:0% +gives so he's going to give the +instances adaptively the instances are + + align:start position:0% +instances adaptively the instances are + + + align:start position:0% +instances adaptively the instances are +going to be hash key V and + + align:start position:0% +going to be hash key V and + + + align:start position:0% +going to be hash key V and +J for J goes from one to uh K the number + + align:start position:0% +J for J goes from one to uh K the number + + + align:start position:0% +J for J goes from one to uh K the number +of + + align:start position:0% +of + + + align:start position:0% +of +gates these are going to be the instance + + align:start position:0% +gates these are going to be the instance + + + align:start position:0% +gates these are going to be the instance +so this is going to be XJ + + align:start position:0% +so this is going to be XJ + + + align:start position:0% +so this is going to be XJ +star or x i sorry that's a third go + + align:start position:0% + + + + align:start position:0% + +I so that's the XI star and the bar is + + align:start position:0% +I so that's the XI star and the bar is + + + align:start position:0% +I so that's the XI star and the bar is +going to be + + align:start position:0% + + + + align:start position:0% + +this so that time that time cheating + + align:start position:0% +this so that time that time cheating + + + align:start position:0% +this so that time that time cheating +okay I + + align:start position:0% +okay I + + + align:start position:0% +okay I +have K instances that I chose adaptively + + align:start position:0% +have K instances that I chose adaptively + + + align:start position:0% +have K instances that I chose adaptively +but I'm arguing that the J one which + + align:start position:0% +but I'm arguing that the J one which + + + align:start position:0% +but I'm arguing that the J one which +corresponds to gate + + align:start position:0% +corresponds to gate + + + align:start position:0% +corresponds to gate +J is actually it's false this XJ star is + + align:start position:0% +J is actually it's false this XJ star is + + + align:start position:0% +J is actually it's false this XJ star is +not in the language because I'm + + align:start position:0% +not in the language because I'm + + + align:start position:0% +not in the language because I'm +binding on this J and what's sitting + + align:start position:0% +binding on this J and what's sitting + + + align:start position:0% +binding on this J and what's sitting +there is false so even if you're just + + align:start position:0% +there is false so even if you're just + + + align:start position:0% +there is false so even if you're just +does not exist of an opening because I'm + + align:start position:0% +does not exist of an opening because I'm + + + align:start position:0% +does not exist of an opening because I'm +binding on these locations what I know + + align:start position:0% +binding on these locations what I know + + + align:start position:0% +binding on these locations what I know +from The Binding condition which + + align:start position:0% +from The Binding condition which + + + align:start position:0% +from The Binding condition which +is here what I know from The Binding + + align:start position:0% +is here what I know from The Binding + + + align:start position:0% +is here what I know from The Binding +condition there is no opening for the + + align:start position:0% +condition there is no opening for the + + + align:start position:0% +condition there is no opening for the +wrong value it just doesn't exist so + + align:start position:0% +wrong value it just doesn't exist so + + + align:start position:0% +wrong value it just doesn't exist so +there is no + + align:start position:0% +there is no + + + align:start position:0% +there is no +witness for x uh for XJ star but look I + + align:start position:0% +witness for x uh for XJ star but look I + + + align:start position:0% +witness for x uh for XJ star but look I +pble star managed to come up with a + + align:start position:0% +pble star managed to come up with a + + + align:start position:0% +pble star managed to come up with a +proof even though before in the semi + + align:start position:0% +proof even though before in the semi + + + align:start position:0% +proof even though before in the semi +adaptive way he gave me a j a gate + + align:start position:0% +adaptive way he gave me a j a gate + + + align:start position:0% +adaptive way he gave me a j a gate +before I got even the CRS he gave me a + + align:start position:0% +before I got even the CRS he gave me a + + + align:start position:0% +before I got even the CRS he gave me a +gate and nevertheless manages managed to + + align:start position:0% +gate and nevertheless manages managed to + + + align:start position:0% +gate and nevertheless manages managed to +produce a bar that all my xar and and a + + align:start position:0% +produce a bar that all my xar and and a + + + align:start position:0% +produce a bar that all my xar and and a +bunch of + + align:start position:0% +bunch of + + + align:start position:0% +bunch of +xstar and the bar is satisfied but the + + align:start position:0% +xstar and the bar is satisfied but the + + + align:start position:0% +xstar and the bar is satisfied but the +J A instance is does not have a witness + + align:start position:0% + + + + align:start position:0% + +contradiction so so the local + + align:start position:0% +contradiction so so the local + + + align:start position:0% +contradiction so so the local +consistency really follows from the + + align:start position:0% +consistency really follows from the + + + align:start position:0% +consistency really follows from the +soundness of the bar and all we need is + + align:start position:0% +soundness of the bar and all we need is + + + align:start position:0% +soundness of the bar and all we need is +is a a semi-adaptive soundness of the + + align:start position:0% +is a a semi-adaptive soundness of the + + + align:start position:0% +is a a semi-adaptive soundness of the +bar because if you're somewhere not + + align:start position:0% +bar because if you're somewhere not + + + align:start position:0% +bar because if you're somewhere not +local consistency not not local + + align:start position:0% +local consistency not not local + + + align:start position:0% +local consistency not not local +consistent even if there's you don't + + align:start position:0% +consistent even if there's you don't + + + align:start position:0% +consistent even if there's you don't +need to be even if there's one gate and + + align:start position:0% +need to be even if there's one gate and + + + align:start position:0% +need to be even if there's one gate and +which you're not local consistency only + + align:start position:0% +which you're not local consistency only + + + align:start position:0% +which you're not local consistency only +probility Epsilon Epson can be one overk + + align:start position:0% +probility Epsilon Epson can be one overk + + + align:start position:0% +probility Epsilon Epson can be one overk +can be very + + align:start position:0% +can be very + + + align:start position:0% +can be very +small i i i the the claim is on each and + + align:start position:0% +small i i i the the claim is on each and + + + align:start position:0% +small i i i the the claim is on each and +every gate local consisten hold this + + align:start position:0% +every gate local consisten hold this + + + align:start position:0% +every gate local consisten hold this +property one man is + + align:start position:0% + + + + align:start position:0% + +negligible because otherwise take that + + align:start position:0% +negligible because otherwise take that + + + align:start position:0% +negligible because otherwise take that +gate and then that gate we're gonna kind + + align:start position:0% +gate and then that gate we're gonna kind + + + align:start position:0% +gate and then that gate we're gonna kind +of cheat in the barg that's the instance + + align:start position:0% +of cheat in the barg that's the instance + + + align:start position:0% +of cheat in the barg that's the instance +that in which we're going to cheat on + + align:start position:0% +that in which we're going to cheat on + + + align:start position:0% +that in which we're going to cheat on +the + + align:start position:0% + + + + align:start position:0% + +bar so that's uh that's local + + align:start position:0% +bar so that's uh that's local + + + align:start position:0% +bar so that's uh that's local +consistency and now you can ask what + + align:start position:0% +consistency and now you can ask what + + + align:start position:0% +consistency and now you can ask what +about the non- signaling and the non + + align:start position:0% +about the non- signaling and the non + + + align:start position:0% +about the non- signaling and the non +signaling really follows from the fact + + align:start position:0% +signaling really follows from the fact + + + align:start position:0% +signaling really follows from the fact +from the index + + align:start position:0% +from the index + + + align:start position:0% +from the index +hiding and and so okay so let's go to + + align:start position:0% +hiding and and so okay so let's go to + + + align:start position:0% +hiding and and so okay so let's go to +the N so are we okay with local + + align:start position:0% + + + + align:start position:0% + +consistency okay any questions before I + + align:start position:0% +consistency okay any questions before I + + + align:start position:0% +consistency okay any questions before I +run actually + + align:start position:0% + + + + align:start position:0% + +yeah okay oh sorry I changed yeah sorry + + align:start position:0% +yeah okay oh sorry I changed yeah sorry + + + align:start position:0% +yeah okay oh sorry I changed yeah sorry +this is J thanks sorry about that this + + align:start position:0% +this is J thanks sorry about that this + + + align:start position:0% +this is J thanks sorry about that this +is yeah so I I give you all this is kind + + align:start position:0% +is yeah so I I give you all this is kind + + + align:start position:0% +is yeah so I I give you all this is kind +of an index uh language so I give the + + align:start position:0% +of an index uh language so I give the + + + align:start position:0% +of an index uh language so I give the +instances are oh ah sorry no these are + + align:start position:0% +instances are oh ah sorry no these are + + + align:start position:0% +instances are oh ah sorry no these are +all for all I I just J is a specific J + + align:start position:0% +all for all I I just J is a specific J + + + align:start position:0% +all for all I I just J is a specific J +so I don't want to J is the one that I'm + + align:start position:0% +so I don't want to J is the one that I'm + + + align:start position:0% +so I don't want to J is the one that I'm +binding on but I give + + align:start position:0% +binding on but I give + + + align:start position:0% +binding on but I give +you the the instances are yeah all of + + align:start position:0% +you the the instances are yeah all of + + + align:start position:0% +you the the instances are yeah all of +them are I sorry j is the specific one + + align:start position:0% +them are I sorry j is the specific one + + + align:start position:0% +them are I sorry j is the specific one +on which I'm G to be uh I'm G to cheat + + align:start position:0% +on which I'm G to be uh I'm G to cheat + + + align:start position:0% +on which I'm G to be uh I'm G to cheat +on all all them are sorry about the + + align:start position:0% + + + + align:start position:0% + +yeah any any other questions + + align:start position:0% + + + + align:start position:0% + +okay so so now the question is uh now + + align:start position:0% +okay so so now the question is uh now + + + align:start position:0% +okay so so now the question is uh now +what about non- signaling and non thing + + align:start position:0% +what about non- signaling and non thing + + + align:start position:0% +what about non- signaling and non thing +I don't want to go into a lot of depth + + align:start position:0% +I don't want to go into a lot of depth + + + align:start position:0% +I don't want to go into a lot of depth +but um let me be handwavy here uh the + + align:start position:0% +but um let me be handwavy here uh the + + + align:start position:0% +but um let me be handwavy here uh the +idea why we're non so we want to argue + + align:start position:0% +idea why we're non so we want to argue + + + align:start position:0% +idea why we're non so we want to argue +that the local assignment generator the + + align:start position:0% +that the local assignment generator the + + + align:start position:0% +that the local assignment generator the +the assignment values that he gives for + + align:start position:0% +the assignment values that he gives for + + + align:start position:0% +the assignment values that he gives for +any subset of wires do not depend on the + + align:start position:0% +any subset of wires do not depend on the + + + align:start position:0% +any subset of wires do not depend on the +other wires that is given to him okay so + + align:start position:0% +other wires that is given to him okay so + + + align:start position:0% +other wires that is given to him okay so +if we look if the extractor is given a + + align:start position:0% +if we look if the extractor is given a + + + align:start position:0% +if we look if the extractor is given a +bunch of wires and you look at the + + align:start position:0% +bunch of wires and you look at the + + + align:start position:0% +bunch of wires and you look at the +assignment on a + + align:start position:0% +assignment on a + + + align:start position:0% +assignment on a +subset the the distribution of the + + align:start position:0% +subset the the distribution of the + + + align:start position:0% +subset the the distribution of the +assignment that the that you get it it + + align:start position:0% +assignment that the that you get it it + + + align:start position:0% +assignment that the that you get it it +looks the same no matter what the other + + align:start position:0% +looks the same no matter what the other + + + align:start position:0% +looks the same no matter what the other +the rest of the the wires + + align:start position:0% +the rest of the the wires + + + align:start position:0% +the rest of the the wires +are and why is that it just follows from + + align:start position:0% +are and why is that it just follows from + + + align:start position:0% +are and why is that it just follows from +the fact that um did I I just erased it + + align:start position:0% +the fact that um did I I just erased it + + + align:start position:0% +the fact that um did I I just erased it +here uh so it follows from the fact + + align:start position:0% +here uh so it follows from the fact + + + align:start position:0% +here uh so it follows from the fact +that when we do a summer extractable + + align:start position:0% +that when we do a summer extractable + + + align:start position:0% +that when we do a summer extractable +hash with many when we uh construct a + + align:start position:0% +hash with many when we uh construct a + + + align:start position:0% +hash with many when we uh construct a +somewh extractable hash with many + + align:start position:0% +somewh extractable hash with many + + + align:start position:0% +somewh extractable hash with many +indices that were extractable on many + + align:start position:0% +indices that were extractable on many + + + align:start position:0% +indices that were extractable on many +indices we want to have the + + align:start position:0% +indices we want to have the + + + align:start position:0% +indices we want to have the +property that even if we extracted on + + align:start position:0% +property that even if we extracted on + + + align:start position:0% +property that even if we extracted on +some + + align:start position:0% + + + + align:start position:0% + +indices the the index hiding still holds + + align:start position:0% +indices the the index hiding still holds + + + align:start position:0% +indices the the index hiding still holds +for the other so in other words think of + + align:start position:0% +for the other so in other words think of + + + align:start position:0% +for the other so in other words think of +where the way we're going to construct + + align:start position:0% +where the way we're going to construct + + + align:start position:0% +where the way we're going to construct +the sum extractible hash is by + + align:start position:0% +the sum extractible hash is by + + + align:start position:0% +the sum extractible hash is by +repetition okay we're going to repeat it + + align:start position:0% +repetition okay we're going to repeat it + + + align:start position:0% +repetition okay we're going to repeat it +many many times so even if even if you + + align:start position:0% +many many times so even if even if you + + + align:start position:0% +many many times so even if even if you +saw if I extracted wire i1 wire I2 wire + + align:start position:0% +saw if I extracted wire i1 wire I2 wire + + + align:start position:0% +saw if I extracted wire i1 wire I2 wire +I3 the indexes indices behind the other + + align:start position:0% +I3 the indexes indices behind the other + + + align:start position:0% +I3 the indexes indices behind the other +wires are completely + + align:start position:0% +wires are completely + + + align:start position:0% +wires are completely +hidden okay so here when when uh when I + + align:start position:0% +hidden okay so here when when uh when I + + + align:start position:0% +hidden okay so here when when uh when I +when you look at extract and subset of + + align:start position:0% +when you look at extract and subset of + + + align:start position:0% +when you look at extract and subset of +witnesses how do you find extract on + + align:start position:0% +witnesses how do you find extract on + + + align:start position:0% +witnesses how do you find extract on +these + + align:start position:0% +these + + + align:start position:0% +these +how how does the how does the local + + align:start position:0% +how how does the how does the local + + + align:start position:0% +how how does the how does the local +assignment generator generate these + + align:start position:0% +assignment generator generate these + + + align:start position:0% +assignment generator generate these +these wires he gener these wires using + + align:start position:0% +these wires he gener these wires using + + + align:start position:0% +these wires he gener these wires using +the corresponding trap + + align:start position:0% +the corresponding trap + + + align:start position:0% +the corresponding trap +doors without the other trap doors so he + + align:start position:0% +doors without the other trap doors so he + + + align:start position:0% +doors without the other trap doors so he +actually has no + + align:start position:0% + + + + align:start position:0% + +idea this should not signal anything + + align:start position:0% +idea this should not signal anything + + + align:start position:0% +idea this should not signal anything +about the other the other the value of + + align:start position:0% +about the other the other the value of + + + align:start position:0% +about the other the other the value of +the other wires okay so again let me say + + align:start position:0% +the other wires okay so again let me say + + + align:start position:0% +the other wires okay so again let me say +it again the maybe I didn't say say it + + align:start position:0% +it again the maybe I didn't say say it + + + align:start position:0% +it again the maybe I didn't say say it +quite right but the local assignment + + align:start position:0% +quite right but the local assignment + + + align:start position:0% +quite right but the local assignment +generator when he he runs the cheating + + align:start position:0% +generator when he he runs the cheating + + + align:start position:0% +generator when he he runs the cheating +prover and the cheating prover he when + + align:start position:0% +prover and the cheating prover he when + + + align:start position:0% +prover and the cheating prover he when +you extract from the cheating + + align:start position:0% +you extract from the cheating + + + align:start position:0% +you extract from the cheating +prover the value of some of the wires + + align:start position:0% +prover the value of some of the wires + + + align:start position:0% +prover the value of some of the wires +you need only to do that using the trap + + align:start position:0% +you need only to do that using the trap + + + align:start position:0% +you need only to do that using the trap +doors for these + + align:start position:0% +doors for these + + + align:start position:0% +doors for these +wires the cheating Prov has no idea what + + align:start position:0% +wires the cheating Prov has no idea what + + + align:start position:0% +wires the cheating Prov has no idea what +the other wires what the trap door of + + align:start position:0% +the other wires what the trap door of + + + align:start position:0% +the other wires what the trap door of +the other wires are so these values + + align:start position:0% +the other wires are so these values + + + align:start position:0% +the other wires are so these values +should not depend at all about the other + + align:start position:0% +should not depend at all about the other + + + align:start position:0% +should not depend at all about the other +a indices + + align:start position:0% +a indices + + + align:start position:0% +a indices +used in the other repetitions otherwise + + align:start position:0% +used in the other repetitions otherwise + + + align:start position:0% +used in the other repetitions otherwise +you broke IND ex hiding for these + + align:start position:0% +you broke IND ex hiding for these + + + align:start position:0% +you broke IND ex hiding for these +repetitions okay so so the point is the + + align:start position:0% +repetitions okay so so the point is the + + + align:start position:0% +repetitions okay so so the point is the +the the a non signaling really follows + + align:start position:0% +the the a non signaling really follows + + + align:start position:0% +the the a non signaling really follows +in a sense from the non- signaling in + + align:start position:0% +in a sense from the non- signaling in + + + align:start position:0% +in a sense from the non- signaling in +the in in the summer extractable hash + + align:start position:0% +the in in the summer extractable hash + + + align:start position:0% +the in in the summer extractable hash +the summer extractable hash when we + + align:start position:0% +the summer extractable hash when we + + + align:start position:0% +the summer extractable hash when we +repeat when we do repetition what we can + + align:start position:0% +repeat when we do repetition what we can + + + align:start position:0% +repeat when we do repetition what we can +argue is any cheating prover who given + + align:start position:0% +argue is any cheating prover who given + + + align:start position:0% +argue is any cheating prover who given +uh + + align:start position:0% +uh + + + align:start position:0% +uh +hash key generates a + + align:start position:0% +hash key generates a + + + align:start position:0% +hash key generates a +value if you extract some of the + + align:start position:0% +value if you extract some of the + + + align:start position:0% +value if you extract some of the +wir the value you get do not depend on + + align:start position:0% +wir the value you get do not depend on + + + align:start position:0% +wir the value you get do not depend on +the other indices this is kind of a + + align:start position:0% +the other indices this is kind of a + + + align:start position:0% +the other indices this is kind of a +property of the Su extractable hash so + + align:start position:0% +property of the Su extractable hash so + + + align:start position:0% +property of the Su extractable hash so +non signaling here falls directly from + + align:start position:0% +non signaling here falls directly from + + + align:start position:0% +non signaling here falls directly from +the non- signaling of the Su extractable + + align:start position:0% +the non- signaling of the Su extractable + + + align:start position:0% +the non- signaling of the Su extractable +hash okay so I'm running out of time I + + align:start position:0% +hash okay so I'm running out of time I + + + align:start position:0% +hash okay so I'm running out of time I +don't want to go too much in in depth + + align:start position:0% +don't want to go too much in in depth + + + align:start position:0% +don't want to go too much in in depth +because I find I think it's not as + + align:start position:0% +because I find I think it's not as + + + align:start position:0% +because I find I think it's not as +interesting I want to actually go and + + align:start position:0% +interesting I want to actually go and + + + align:start position:0% +interesting I want to actually go and +talk about why is this not sufficient + + align:start position:0% +talk about why is this not sufficient + + + align:start position:0% +talk about why is this not sufficient +and when is it + + align:start position:0% +and when is it + + + align:start position:0% +and when is it +sufficient okay so let's so let's call + + align:start position:0% +sufficient okay so let's so let's call + + + align:start position:0% +sufficient okay so let's so let's call +let's say okay so we have suppose we we + + align:start position:0% +let's say okay so we have suppose we we + + + align:start position:0% +let's say okay so we have suppose we we +have a cheating prover we manag to to + + align:start position:0% +have a cheating prover we manag to to + + + align:start position:0% +have a cheating prover we manag to to +construct from him this local assignment + + align:start position:0% +construct from him this local assignment + + + align:start position:0% +construct from him this local assignment +generator so we have the + + align:start position:0% +generator so we have the + + + align:start position:0% +generator so we have the +circuit we want to we we have a cheating + + align:start position:0% +circuit we want to we we have a cheating + + + align:start position:0% +circuit we want to we we have a cheating +prover he gave me an X we want to argue + + align:start position:0% +prover he gave me an X we want to argue + + + align:start position:0% +prover he gave me an X we want to argue +it's in the language it must if he + + align:start position:0% +it's in the language it must if he + + + align:start position:0% +it's in the language it must if he +convinced me it must me the language + + align:start position:0% +convinced me it must me the language + + + align:start position:0% +convinced me it must me the language +that's what soundness means what do we + + align:start position:0% +that's what soundness means what do we + + + align:start position:0% +that's what soundness means what do we +know we know when we look at any window + + align:start position:0% +know we know when we look at any window + + + align:start position:0% +know we know when we look at any window +everything looks good and when you look + + align:start position:0% +everything looks good and when you look + + + align:start position:0% +everything looks good and when you look +at the window that contains the output + + align:start position:0% +at the window that contains the output + + + align:start position:0% +at the window that contains the output +it's + + align:start position:0% +it's + + + align:start position:0% +it's +one does that mean we can have like an + + align:start position:0% +one does that mean we can have like an + + + align:start position:0% +one does that mean we can have like an +entire uh assignment to all the wires + + align:start position:0% +entire uh assignment to all the wires + + + align:start position:0% +entire uh assignment to all the wires +that everything is consistent in which + + align:start position:0% +that everything is consistent in which + + + align:start position:0% +that everything is consistent in which +case we can then + + align:start position:0% +case we can then + + + align:start position:0% +case we can then +sound so can we piece these things + + align:start position:0% +sound so can we piece these things + + + align:start position:0% +sound so can we piece these things +together okay so a + + align:start position:0% + + + + align:start position:0% + +so the answer is yes and + + align:start position:0% +so the answer is yes and + + + align:start position:0% +so the answer is yes and +no okay so in general for + + align:start position:0% +no okay so in general for + + + align:start position:0% +no okay so in general for +NP the answer is no we don't know how to + + align:start position:0% +NP the answer is no we don't know how to + + + align:start position:0% +NP the answer is no we don't know how to +piece it together moreover we believe + + align:start position:0% +piece it together moreover we believe + + + align:start position:0% +piece it together moreover we believe +that you can't piece it together for any + + align:start position:0% +that you can't piece it together for any + + + align:start position:0% +that you can't piece it together for any +NP language like we + + align:start position:0% +NP language like we + + + align:start position:0% +NP language like we +believe + + align:start position:0% +believe + + + align:start position:0% +believe +that it's just there exist very hard NP + + align:start position:0% +that it's just there exist very hard NP + + + align:start position:0% +that it's just there exist very hard NP +languages that there's no way you can + + align:start position:0% +languages that there's no way you can + + + align:start position:0% +languages that there's no way you can +piece it together but let me tell you + + align:start position:0% +piece it together but let me tell you + + + align:start position:0% +piece it together but let me tell you +why why does why is it hard to piece + + align:start position:0% +why why does why is it hard to piece + + + align:start position:0% +why why does why is it hard to piece +things + + align:start position:0% +things + + + align:start position:0% +things +together and the reason is even you know + + align:start position:0% +together and the reason is even you know + + + align:start position:0% +together and the reason is even you know +let's even think now for Simplicity I + + align:start position:0% +let's even think now for Simplicity I + + + align:start position:0% +let's even think now for Simplicity I +think it would be easier to think let's + + align:start position:0% +think it would be easier to think let's + + + align:start position:0% +think it would be easier to think let's +say even in the non-adaptive version X + + align:start position:0% +say even in the non-adaptive version X + + + align:start position:0% +say even in the non-adaptive version X +is fixed can we argue that for this + + align:start position:0% +is fixed can we argue that for this + + + align:start position:0% +is fixed can we argue that for this +fixed X we have a like we can we can uh + + align:start position:0% +fixed X we have a like we can we can uh + + + align:start position:0% +fixed X we have a like we can we can uh +a piece everything together and the + + align:start position:0% +a piece everything together and the + + + align:start position:0% +a piece everything together and the +reason why it's hard to piece everything + + align:start position:0% +reason why it's hard to piece everything + + + align:start position:0% +reason why it's hard to piece everything +together is because because this local + + align:start position:0% +together is because because this local + + + align:start position:0% +together is because because this local +assignment generator every time you give + + align:start position:0% +assignment generator every time you give + + + align:start position:0% +assignment generator every time you give +him a bunch of + + align:start position:0% +him a bunch of + + + align:start position:0% +him a bunch of +wires he even think think of a a even a + + align:start position:0% +wires he even think think of a a even a + + + align:start position:0% +wires he even think think of a a even a +valid kind of approver okay this think + + align:start position:0% +valid kind of approver okay this think + + + align:start position:0% +valid kind of approver okay this think +of a valid prover every time you run him + + align:start position:0% +of a valid prover every time you run him + + + align:start position:0% +of a valid prover every time you run him +he uses different Witnesses maybe has + + align:start position:0% +he uses different Witnesses maybe has + + + align:start position:0% +he uses different Witnesses maybe has +many many witnesses in his disposal + + align:start position:0% +many many witnesses in his disposal + + + align:start position:0% +many many witnesses in his disposal +every time you run him he's honest but + + align:start position:0% +every time you run him he's honest but + + + align:start position:0% +every time you run him he's honest but +with a different witness okay so it's + + align:start position:0% +with a different witness okay so it's + + + align:start position:0% +with a different witness okay so it's +actually in the language but the + + align:start position:0% +actually in the language but the + + + align:start position:0% +actually in the language but the +question is are we able to construct + + align:start position:0% +question is are we able to construct + + + align:start position:0% +question is are we able to construct +kind of a satisfying assignment and the + + align:start position:0% +kind of a satisfying assignment and the + + + align:start position:0% +kind of a satisfying assignment and the +reason why this is hard is or seems hard + + align:start position:0% +reason why this is hard is or seems hard + + + align:start position:0% +reason why this is hard is or seems hard +is + + align:start position:0% +is + + + align:start position:0% +is +because okay we have our local local + + align:start position:0% +because okay we have our local local + + + align:start position:0% +because okay we have our local local +assignment generator we give him a bunch + + align:start position:0% +assignment generator we give him a bunch + + + align:start position:0% +assignment generator we give him a bunch +of wires he chooses one of his Witnesses + + align:start position:0% +of wires he chooses one of his Witnesses + + + align:start position:0% +of wires he chooses one of his Witnesses +at random because that's what the + + align:start position:0% +at random because that's what the + + + align:start position:0% +at random because that's what the +cheating prover does and gives an + + align:start position:0% +cheating prover does and gives an + + + align:start position:0% +cheating prover does and gives an +assignment with this the witness okay + + align:start position:0% +assignment with this the witness okay + + + align:start position:0% +assignment with this the witness okay +local consistent we're fine we're happy + + align:start position:0% +local consistent we're fine we're happy + + + align:start position:0% +local consistent we're fine we're happy +now we run him again he uses a different + + align:start position:0% +now we run him again he uses a different + + + align:start position:0% +now we run him again he uses a different +witness it doesn't match things like you + + align:start position:0% +witness it doesn't match things like you + + + align:start position:0% +witness it doesn't match things like you +know how do we match things together so + + align:start position:0% +know how do we match things together so + + + align:start position:0% +know how do we match things together so +that's why in the non-deterministic case + + align:start position:0% +that's why in the non-deterministic case + + + align:start position:0% +that's why in the non-deterministic case +things are really difficult okay and we + + align:start position:0% +things are really difficult okay and we + + + align:start position:0% +things are really difficult okay and we +do have some results but for very + + align:start position:0% +do have some results but for very + + + align:start position:0% +do have some results but for very +specific languages let me not go into + + align:start position:0% +specific languages let me not go into + + + align:start position:0% +specific languages let me not go into +that let's talk about the teristic + + align:start position:0% +that let's talk about the teristic + + + align:start position:0% +that let's talk about the teristic +languages that seems to be much easier + + align:start position:0% +languages that seems to be much easier + + + align:start position:0% +languages that seems to be much easier +so let me first convince you that we can + + align:start position:0% +so let me first convince you that we can + + + align:start position:0% +so let me first convince you that we can +do it and then I'll show you where I + + align:start position:0% +do it and then I'll show you where I + + + align:start position:0% +do it and then I'll show you where I +cheated okay so let's first take a a + + align:start position:0% +cheated okay so let's first take a a + + + align:start position:0% +cheated okay so let's first take a a +circuit we have a local assignment + + align:start position:0% +circuit we have a local assignment + + + align:start position:0% +circuit we have a local assignment +generator so let me convince you that + + align:start position:0% +generator so let me convince you that + + + align:start position:0% +generator so let me convince you that +that one must be one okay so we have an + + align:start position:0% +that one must be one okay so we have an + + + align:start position:0% +that one must be one okay so we have an +input X1 up to xn + + align:start position:0% + + + + align:start position:0% + +okay I'm going to call my local + + align:start position:0% +okay I'm going to call my local + + + align:start position:0% +okay I'm going to call my local +assignment generator I'm going to tell + + align:start position:0% +assignment generator I'm going to tell + + + align:start position:0% +assignment generator I'm going to tell +them give me the values + + align:start position:0% +them give me the values + + + align:start position:0% +them give me the values +here or here let me I have L right so + + align:start position:0% +here or here let me I have L right so + + + align:start position:0% +here or here let me I have L right so +let me use my L here here and here I + + align:start position:0% +let me use my L here here and here I + + + align:start position:0% +let me use my L here here and here I +don't know he gives me values now this + + align:start position:0% +don't know he gives me values now this + + + align:start position:0% +don't know he gives me values now this +must be consistent because I know local + + align:start position:0% +must be consistent because I know local + + + align:start position:0% +must be consistent because I know local +consistency hold to one minus negligible + + align:start position:0% +consistency hold to one minus negligible + + + align:start position:0% +consistency hold to one minus negligible +so and all of them are consistent okay + + align:start position:0% +so and all of them are consistent okay + + + align:start position:0% +so and all of them are consistent okay +which means these are the correct values + + align:start position:0% +which means these are the correct values + + + align:start position:0% +which means these are the correct values +now we're deterministic okay we're + + align:start position:0% +now we're deterministic okay we're + + + align:start position:0% +now we're deterministic okay we're +talking about a deterministic circuit + + align:start position:0% +talking about a deterministic circuit + + + align:start position:0% +talking about a deterministic circuit +so if this is locally consistent it + + align:start position:0% +so if this is locally consistent it + + + align:start position:0% +so if this is locally consistent it +means this is the correct value I know + + align:start position:0% +means this is the correct value I know + + + align:start position:0% +means this is the correct value I know +if it's an and it's an and whatever it + + align:start position:0% +if it's an and it's an and whatever it + + + align:start position:0% +if it's an and it's an and whatever it +is so all these are correct I can argue + + align:start position:0% +is so all these are correct I can argue + + + align:start position:0% +is so all these are correct I can argue +when I run the cheating the assignment J + + align:start position:0% +when I run the cheating the assignment J + + + align:start position:0% +when I run the cheating the assignment J +so I want to argue essentially + + align:start position:0% +so I want to argue essentially + + + align:start position:0% +so I want to argue essentially +any the local assignment generator every + + align:start position:0% +any the local assignment generator every + + + align:start position:0% +any the local assignment generator every +wire he gives me must be the correct one + + align:start position:0% +wire he gives me must be the correct one + + + align:start position:0% +wire he gives me must be the correct one +and then I'm done because the output is + + align:start position:0% +and then I'm done because the output is + + + align:start position:0% +and then I'm done because the output is +the correct and if he gives me output + + align:start position:0% +the correct and if he gives me output + + + align:start position:0% +the correct and if he gives me output +one voila it's the correct I'm + + align:start position:0% +one voila it's the correct I'm + + + align:start position:0% +one voila it's the correct I'm +done so I'm going to argue kind of by + + align:start position:0% +done so I'm going to argue kind of by + + + align:start position:0% +done so I'm going to argue kind of by +induction that every y or given me must + + align:start position:0% +induction that every y or given me must + + + align:start position:0% +induction that every y or given me must +be the correct one why okay let's try + + align:start position:0% +be the correct one why okay let's try + + + align:start position:0% +be the correct one why okay let's try +layer layer so I'm going to argue kind + + align:start position:0% +layer layer so I'm going to argue kind + + + align:start position:0% +layer layer so I'm going to argue kind +of layer by the induction is going to be + + align:start position:0% +of layer by the induction is going to be + + + align:start position:0% +of layer by the induction is going to be +by the think of the uh circuit as + + align:start position:0% +by the think of the uh circuit as + + + align:start position:0% +by the think of the uh circuit as +layered and I'm going to argue this by + + align:start position:0% +layered and I'm going to argue this by + + + align:start position:0% +layered and I'm going to argue this by +induction on the layers okay layer one + + align:start position:0% +induction on the layers okay layer one + + + align:start position:0% +induction on the layers okay layer one +what does the cheating prover gives me + + align:start position:0% +what does the cheating prover gives me + + + align:start position:0% +what does the cheating prover gives me +he gives me assignment now I know I + + align:start position:0% +he gives me assignment now I know I + + + align:start position:0% +he gives me assignment now I know I +proved it's locally satisfiable which + + align:start position:0% +proved it's locally satisfiable which + + + align:start position:0% +proved it's locally satisfiable which +means it satisfies the gate so it's + + align:start position:0% +means it satisfies the gate so it's + + + align:start position:0% +means it satisfies the gate so it's +correct so layer one correct let's go to + + align:start position:0% +correct so layer one correct let's go to + + + align:start position:0% +correct so layer one correct let's go to +Layer Two + + align:start position:0% +Layer Two + + + align:start position:0% +Layer Two +Layer Two he G now I I'm going to ask + + align:start position:0% +Layer Two he G now I I'm going to ask + + + align:start position:0% +Layer Two he G now I I'm going to ask +him this let's say I'm going to ask him + + align:start position:0% +him this let's say I'm going to ask him + + + align:start position:0% +him this let's say I'm going to ask him +these I want to argue that this is + + align:start position:0% +these I want to argue that this is + + + align:start position:0% +these I want to argue that this is +correct all I know is that it's locally + + align:start position:0% +correct all I know is that it's locally + + + align:start position:0% +correct all I know is that it's locally +consistent but I know that these are + + align:start position:0% +consistent but I know that these are + + + align:start position:0% +consistent but I know that these are +correct why are these correct because of + + align:start position:0% +correct why are these correct because of + + + align:start position:0% +correct why are these correct because of +the non signaling I know if I asked give + + align:start position:0% +the non signaling I know if I asked give + + + align:start position:0% +the non signaling I know if I asked give +me kind of these wires uh give me these + + align:start position:0% +me kind of these wires uh give me these + + + align:start position:0% +me kind of these wires uh give me these +wires with kind of the input it was + + align:start position:0% +wires with kind of the input it was + + + align:start position:0% +wires with kind of the input it was +correct I got the the correct + + align:start position:0% +correct I got the the correct + + + align:start position:0% +correct I got the the correct +answer so now when I ask the extract the + + align:start position:0% +answer so now when I ask the extract the + + + align:start position:0% +answer so now when I ask the extract the +local assignment generator give me these + + align:start position:0% +local assignment generator give me these + + + align:start position:0% +local assignment generator give me these +wires with + + align:start position:0% +wires with + + + align:start position:0% +wires with +these that we said the distribution is + + align:start position:0% +these that we said the distribution is + + + align:start position:0% +these that we said the distribution is +the same up to computationally + + align:start position:0% +the same up to computationally + + + align:start position:0% +the same up to computationally +distinguishable so when I asked him give + + align:start position:0% +distinguishable so when I asked him give + + + align:start position:0% +distinguishable so when I asked him give +me kind of uh the value of this wire + + align:start position:0% +me kind of uh the value of this wire + + + align:start position:0% +me kind of uh the value of this wire +when I asked with the kind of with the + + align:start position:0% +when I asked with the kind of with the + + + align:start position:0% +when I asked with the kind of with the +inputs or and I asked give me these + + align:start position:0% +inputs or and I asked give me these + + + align:start position:0% +inputs or and I asked give me these +wires with this it's the same + + align:start position:0% +wires with this it's the same + + + align:start position:0% +wires with this it's the same +distribution was correct before it's + + align:start position:0% +distribution was correct before it's + + + align:start position:0% +distribution was correct before it's +correct now so these are correct and + + align:start position:0% +correct now so these are correct and + + + align:start position:0% +correct now so these are correct and +this is locally consistent so this is + + align:start position:0% +this is locally consistent so this is + + + align:start position:0% +this is locally consistent so this is +also correct so these layers are correct + + align:start position:0% +also correct so these layers are correct + + + align:start position:0% +also correct so these layers are correct +and and and again now let's look at + + align:start position:0% +and and and again now let's look at + + + align:start position:0% +and and and again now let's look at +these is this correct yeah because this + + align:start position:0% +these is this correct yeah because this + + + align:start position:0% +these is this correct yeah because this +these still need to be correct because + + align:start position:0% +these still need to be correct because + + + align:start position:0% +these still need to be correct because +we argued it's correct and it doesn't + + align:start position:0% +we argued it's correct and it doesn't + + + align:start position:0% +we argued it's correct and it doesn't +depend on the distribution it doesn't + + align:start position:0% +depend on the distribution it doesn't + + + align:start position:0% +depend on the distribution it doesn't +depend on the every time I ask him this + + align:start position:0% +depend on the every time I ask him this + + + align:start position:0% +depend on the every time I ask him this +I get corre one minus negligible so + + align:start position:0% +I get corre one minus negligible so + + + align:start position:0% +I get corre one minus negligible so +correct so this is + + align:start position:0% +correct so this is + + + align:start position:0% +correct so this is +correct by induction the output is + + align:start position:0% +correct by induction the output is + + + align:start position:0% +correct by induction the output is +correct I know it's one that's what the + + align:start position:0% +correct I know it's one that's what the + + + align:start position:0% +correct I know it's one that's what the +the local generator promised me so it's + + align:start position:0% +the local generator promised me so it's + + + align:start position:0% +the local generator promised me so it's +one and correct I'm + + align:start position:0% + + + + align:start position:0% + +done + + align:start position:0% +done + + + align:start position:0% +done +okay that's the proof moreover let me + + align:start position:0% +okay that's the proof moreover let me + + + align:start position:0% +okay that's the proof moreover let me +tell you something when we wrote this + + align:start position:0% +tell you something when we wrote this + + + align:start position:0% +tell you something when we wrote this +proof we wrote it we were happy with it + + align:start position:0% +proof we wrote it we were happy with it + + + align:start position:0% +proof we wrote it we were happy with it +we literally almost submitted this thing + + align:start position:0% +we literally almost submitted this thing + + + align:start position:0% +we literally almost submitted this thing +a couple days before the deadline we + + align:start position:0% +a couple days before the deadline we + + + align:start position:0% +a couple days before the deadline we +noticed there's a bug this is wrong this + + align:start position:0% +noticed there's a bug this is wrong this + + + align:start position:0% +noticed there's a bug this is wrong this +does not + + align:start position:0% +does not + + + align:start position:0% +does not +work okay I'll tell you why it doesn't + + align:start position:0% +work okay I'll tell you why it doesn't + + + align:start position:0% +work okay I'll tell you why it doesn't +work as a suppos to asking because I + + align:start position:0% +work as a suppos to asking because I + + + align:start position:0% +work as a suppos to asking because I +think it's so subtle but if does anybody + + align:start position:0% +think it's so subtle but if does anybody + + + align:start position:0% +think it's so subtle but if does anybody +see why it doesn't it's very very hard + + align:start position:0% +see why it doesn't it's very very hard + + + align:start position:0% +see why it doesn't it's very very hard +to see in my opinion but uh I mean + + align:start position:0% +to see in my opinion but uh I mean + + + align:start position:0% +to see in my opinion but uh I mean +clearly I didn't see it but anybody see + + align:start position:0% +clearly I didn't see it but anybody see + + + align:start position:0% +clearly I didn't see it but anybody see +why why I cheated + + align:start position:0% +why why I cheated + + + align:start position:0% +why why I cheated +here + + align:start position:0% +here + + + align:start position:0% +here +yeah restricted + + align:start position:0% + + + + align:start position:0% + +deterministic inut yeah so what why yeah + + align:start position:0% +deterministic inut yeah so what why yeah + + + align:start position:0% +deterministic inut yeah so what why yeah +there's only the input the actually the + + align:start position:0% +there's only the input the actually the + + + align:start position:0% +there's only the input the actually the +fact that there's deterministic it's + + align:start position:0% +fact that there's deterministic it's + + + align:start position:0% +fact that there's deterministic it's +helpful for us because now there's a + + align:start position:0% +helpful for us because now there's a + + + align:start position:0% +helpful for us because now there's a +notion of correctness once there's a + + align:start position:0% +notion of correctness once there's a + + + align:start position:0% +notion of correctness once there's a +there's no what do you mean correct + + align:start position:0% +there's no what do you mean correct + + + align:start position:0% +there's no what do you mean correct +depends on the witness every wire has + + align:start position:0% +depends on the witness every wire has + + + align:start position:0% +depends on the witness every wire has +like if use this witness it can be this + + align:start position:0% +like if use this witness it can be this + + + align:start position:0% +like if use this witness it can be this +value here because it's deterministic + + align:start position:0% +value here because it's deterministic + + + align:start position:0% +value here because it's deterministic +there's only one value for each wire and + + align:start position:0% +there's only one value for each wire and + + + align:start position:0% +there's only one value for each wire and +so there's the notion of + + align:start position:0% +so there's the notion of + + + align:start position:0% +so there's the notion of +correct + + align:start position:0% +correct + + + align:start position:0% +correct +value and I can argue by induction that + + align:start position:0% +value and I can argue by induction that + + + align:start position:0% +value and I can argue by induction that +everything is + + align:start position:0% + + + + align:start position:0% + +correct okay I um a so I'll tell + + align:start position:0% +correct okay I um a so I'll tell + + + align:start position:0% +correct okay I um a so I'll tell +you why I you know I I I suffered + + align:start position:0% +you why I you know I I I suffered + + + align:start position:0% +you why I you know I I I suffered +through this I I have the like desire to + + align:start position:0% +through this I I have the like desire to + + + align:start position:0% +through this I I have the like desire to +have you like to torture you a little + + align:start position:0% +have you like to torture you a little + + + align:start position:0% +have you like to torture you a little +bit to see why and so like I like the + + align:start position:0% +bit to see why and so like I like the + + + align:start position:0% +bit to see why and so like I like the +experience I had but I'll given that you + + align:start position:0% +experience I had but I'll given that you + + + align:start position:0% +experience I had but I'll given that you +only have like 10 minutes left I'll tell + + align:start position:0% +only have like 10 minutes left I'll tell + + + align:start position:0% +only have like 10 minutes left I'll tell +you so okay so here's + + align:start position:0% + + + + align:start position:0% + +why + + align:start position:0% + + + + align:start position:0% + +so local + + align:start position:0% +so local + + + align:start position:0% +so local +consistency holds or or yeah everything + + align:start position:0% +consistency holds or or yeah everything + + + align:start position:0% +consistency holds or or yeah everything +like local consistency holds with + + align:start position:0% +like local consistency holds with + + + align:start position:0% +like local consistency holds with +probability or or the noning everything + + align:start position:0% +probability or or the noning everything + + + align:start position:0% +probability or or the noning everything +holds with probability one minus + + align:start position:0% +holds with probability one minus + + + align:start position:0% +holds with probability one minus +negligible not with probability one if + + align:start position:0% +negligible not with probability one if + + + align:start position:0% +negligible not with probability one if +everything was with probability one one + + align:start position:0% +everything was with probability one one + + + align:start position:0% +everything was with probability one one +you know local consistency this then + + align:start position:0% +you know local consistency this then + + + align:start position:0% +you know local consistency this then +this cons probility one this then + + align:start position:0% +this cons probility one this then + + + align:start position:0% +this cons probility one this then +everything would work out okay if if I + + align:start position:0% +everything would work out okay if if I + + + align:start position:0% +everything would work out okay if if I +promised you local cons probability one + + align:start position:0% +promised you local cons probability one + + + align:start position:0% +promised you local cons probability one +and non signability one like it's + + align:start position:0% +and non signability one like it's + + + align:start position:0% +and non signability one like it's +exactly the same we're good then I can + + align:start position:0% +exactly the same we're good then I can + + + align:start position:0% +exactly the same we're good then I can +Pro + + align:start position:0% +Pro + + + align:start position:0% +Pro +now it's you in cryptography oh command + + align:start position:0% +now it's you in cryptography oh command + + + align:start position:0% +now it's you in cryptography oh command +negligible it's zero okay here it's not + + align:start position:0% +negligible it's zero okay here it's not + + + align:start position:0% +negligible it's zero okay here it's not +zero turns out negligible is a pain this + + align:start position:0% +zero turns out negligible is a pain this + + + align:start position:0% +zero turns out negligible is a pain this +is the entire problem the negligible and + + align:start position:0% +is the entire problem the negligible and + + + align:start position:0% +is the entire problem the negligible and +I'll tell you why it seems weird but + + align:start position:0% +I'll tell you why it seems weird but + + + align:start position:0% +I'll tell you why it seems weird but +here is why the reason + + align:start position:0% +here is why the reason + + + align:start position:0% +here is why the reason +is this is correct with all the ne + + align:start position:0% +is this is correct with all the ne + + + align:start position:0% +is this is correct with all the ne +probability so this is correct except + + align:start position:0% +probability so this is correct except + + + align:start position:0% +probability so this is correct except +probability + + align:start position:0% +probability + + + align:start position:0% +probability +mu this is correct except with + + align:start position:0% +mu this is correct except with + + + align:start position:0% +mu this is correct except with +probability + + align:start position:0% +probability + + + align:start position:0% +probability +me but now + + align:start position:0% +me but now + + + align:start position:0% +me but now +this is correct if this needs to be + + align:start position:0% +this is correct if this needs to be + + + align:start position:0% +this is correct if this needs to be +correct and this needs to be correct if + + align:start position:0% +correct and this needs to be correct if + + + align:start position:0% +correct and this needs to be correct if +one of them is incorrect you're not + + align:start position:0% +one of them is incorrect you're not + + + align:start position:0% +one of them is incorrect you're not +correct so this is correct probity + + align:start position:0% +correct so this is correct probity + + + align:start position:0% +correct so this is correct probity +correct exact probability to + + align:start position:0% +correct exact probability to + + + align:start position:0% +correct exact probability to +Mu so here you have two mu now two mu is + + align:start position:0% +Mu so here you have two mu now two mu is + + + align:start position:0% +Mu so here you have two mu now two mu is +also + + align:start position:0% +also + + + align:start position:0% +also +negligible this is also corre except 2 + + align:start position:0% +negligible this is also corre except 2 + + + align:start position:0% +negligible this is also corre except 2 +mu but this for this to be correct both + + align:start position:0% +mu but this for this to be correct both + + + align:start position:0% +mu but this for this to be correct both +of them need to be correct so here you + + align:start position:0% +of them need to be correct so here you + + + align:start position:0% +of them need to be correct so here you +have four mu and then 8 mu you're going + + align:start position:0% +have four mu and then 8 mu you're going + + + align:start position:0% +have four mu and then 8 mu you're going +to get two to the depth times + + align:start position:0% +to get two to the depth times + + + align:start position:0% +to get two to the depth times +mu now if the depth is more than + + align:start position:0% + + + + align:start position:0% + +log it's not negligible + + align:start position:0% + + + + align:start position:0% + +anymore so the problem is two to depth + + align:start position:0% +anymore so the problem is two to depth + + + align:start position:0% +anymore so the problem is two to depth +may be much bigger than one over + + align:start position:0% + + + + align:start position:0% + +mu so it's this kind of there's this + + align:start position:0% +mu so it's this kind of there's this + + + align:start position:0% +mu so it's this kind of there's this +exponential + + align:start position:0% +exponential + + + align:start position:0% +exponential +curse of of of we carry kind of the air + + align:start position:0% +curse of of of we carry kind of the air + + + align:start position:0% +curse of of of we carry kind of the air +Grows by factor of two each time and + + align:start position:0% +Grows by factor of two each time and + + + align:start position:0% +Grows by factor of two each time and +eventually can kill + + align:start position:0% +eventually can kill + + + align:start position:0% +eventually can kill +us that's the bug so this works if it's + + align:start position:0% +us that's the bug so this works if it's + + + align:start position:0% +us that's the bug so this works if it's +bounded depth log depth yes more than + + align:start position:0% +bounded depth log depth yes more than + + + align:start position:0% +bounded depth log depth yes more than +that not + + align:start position:0% +that not + + + align:start position:0% +that not +clear + + align:start position:0% +clear + + + align:start position:0% +clear +okay so what do we do so to fix + + align:start position:0% +okay so what do we do so to fix + + + align:start position:0% +okay so what do we do so to fix +this there is two ways to fix this + + align:start position:0% +this there is two ways to fix this + + + align:start position:0% +this there is two ways to fix this +option number one which is what we did + + align:start position:0% +option number one which is what we did + + + align:start position:0% +option number one which is what we did +originally cuz we we didn't have a + + align:start position:0% +originally cuz we we didn't have a + + + align:start position:0% +originally cuz we we didn't have a +better idea is we said you know what + + align:start position:0% +better idea is we said you know what + + + align:start position:0% +better idea is we said you know what +let's assume that the circuit is very + + align:start position:0% +let's assume that the circuit is very + + + align:start position:0% +let's assume that the circuit is very +narrow like think of bound depth + + align:start position:0% +narrow like think of bound depth + + + align:start position:0% +narrow like think of bound depth +deterministic computations okay where + + align:start position:0% +deterministic computations okay where + + + align:start position:0% +deterministic computations okay where +not sorry bounded space so think of DET + + align:start position:0% +not sorry bounded space so think of DET + + + align:start position:0% +not sorry bounded space so think of DET +computation where each configuration is + + align:start position:0% +computation where each configuration is + + + align:start position:0% +computation where each configuration is +like very small so like a TR machine you + + align:start position:0% +like very small so like a TR machine you + + + align:start position:0% +like very small so like a TR machine you +know that has very uh it's kind of the + + align:start position:0% +know that has very uh it's kind of the + + + align:start position:0% +know that has very uh it's kind of the +Tableau is very thin and long and then + + align:start position:0% +Tableau is very thin and long and then + + + align:start position:0% +Tableau is very thin and long and then +we said you know what let's make L like + + align:start position:0% +we said you know what let's make L like + + + align:start position:0% +we said you know what let's make L like +where you're statistically bound it on + + align:start position:0% +where you're statistically bound it on + + + align:start position:0% +where you're statistically bound it on +let's make it an entire configuration so + + align:start position:0% +let's make it an entire configuration so + + + align:start position:0% +let's make it an entire configuration so +yeah you pay with an entire kind of with + + align:start position:0% +yeah you pay with an entire kind of with + + + align:start position:0% +yeah you pay with an entire kind of with +a space the snar the proof will grow + + align:start position:0% +a space the snar the proof will grow + + + align:start position:0% +a space the snar the proof will grow +with the space but now we say you can + + align:start position:0% +with the space but now we say you can + + + align:start position:0% +with the space but now we say you can +read the entire thing you can read so + + align:start position:0% +read the entire thing you can read so + + + align:start position:0% +read the entire thing you can read so +here here is the Tableau you can read + + align:start position:0% +here here is the Tableau you can read + + + align:start position:0% +here here is the Tableau you can read +the entire computation you can read the + + align:start position:0% +the entire computation you can read the + + + align:start position:0% +the entire computation you can read the +entire configuration and now we say the + + align:start position:0% +entire configuration and now we say the + + + align:start position:0% +entire configuration and now we say the +first configuration is correct probility + + align:start position:0% +first configuration is correct probility + + + align:start position:0% +first configuration is correct probility +mu the second configuration if this was + + align:start position:0% +mu the second configuration if this was + + + align:start position:0% +mu the second configuration if this was +correct it's this is two Mew three me + + align:start position:0% +correct it's this is two Mew three me + + + align:start position:0% +correct it's this is two Mew three me +four me it doesn't grow exponential + + align:start position:0% +four me it doesn't grow exponential + + + align:start position:0% +four me it doesn't grow exponential +anymore cuz you read the entire thing so + + align:start position:0% +anymore cuz you read the entire thing so + + + align:start position:0% +anymore cuz you read the entire thing so +I'm going to read these two + + align:start position:0% +I'm going to read these two + + + align:start position:0% +I'm going to read these two +configurations together if this was + + align:start position:0% +configurations together if this was + + + align:start position:0% +configurations together if this was +consistent this is consistent there's + + align:start position:0% +consistent this is consistent there's + + + align:start position:0% +consistent this is consistent there's +always an usability of error that I'm in + + align:start position:0% +always an usability of error that I'm in + + + align:start position:0% +always an usability of error that I'm in +cran fine but it doesn't double because + + align:start position:0% +cran fine but it doesn't double because + + + align:start position:0% +cran fine but it doesn't double because +I'm reading the entire thing I said if + + align:start position:0% +I'm reading the entire thing I said if + + + align:start position:0% +I'm reading the entire thing I said if +this was a a correct + + align:start position:0% +this was a a correct + + + align:start position:0% +this was a a correct +configuration then when I read this with + + align:start position:0% +configuration then when I read this with + + + align:start position:0% +configuration then when I read this with +this this is going to be correct + + align:start position:0% +this this is going to be correct + + + align:start position:0% +this this is going to be correct +configuration but I read the entire + + align:start position:0% +configuration but I read the entire + + + align:start position:0% +configuration but I read the entire +thing so I don't double up + + align:start position:0% +thing so I don't double up + + + align:start position:0% +thing so I don't double up +things so we get we get snark for any + + align:start position:0% +things so we get we get snark for any + + + align:start position:0% +things so we get we get snark for any +computation that's bounded space where + + align:start position:0% +computation that's bounded space where + + + align:start position:0% +computation that's bounded space where +the snar grows with the + + align:start position:0% +the snar grows with the + + + align:start position:0% +the snar grows with the +space okay but let me tell you we can do + + align:start position:0% +space okay but let me tell you we can do + + + align:start position:0% +space okay but let me tell you we can do +better we can actually we don't need to + + align:start position:0% +better we can actually we don't need to + + + align:start position:0% +better we can actually we don't need to +grow with the + + align:start position:0% +grow with the + + + align:start position:0% +grow with the +space so I'll just say a word because + + align:start position:0% +space so I'll just say a word because + + + align:start position:0% +space so I'll just say a word because +I'm running out of time and I want to + + align:start position:0% +I'm running out of time and I want to + + + align:start position:0% +I'm running out of time and I want to +kind of do a quick summary so but the + + align:start position:0% +kind of do a quick summary so but the + + + align:start position:0% +kind of do a quick summary so but the +idea of not running into this + + align:start position:0% +idea of not running into this + + + align:start position:0% +idea of not running into this +exponential curse idea is to say the + + align:start position:0% +exponential curse idea is to say the + + + align:start position:0% +exponential curse idea is to say the +following you know let's do this hash + + align:start position:0% +following you know let's do this hash + + + align:start position:0% +following you know let's do this hash +and Bar so what did we do this this snar + + align:start position:0% +and Bar so what did we do this this snar + + + align:start position:0% +and Bar so what did we do this this snar +is like hash all the wires and then bar + + align:start position:0% +is like hash all the wires and then bar + + + align:start position:0% +is like hash all the wires and then bar +the idea is don't do hash and Bar in the + + align:start position:0% +the idea is don't do hash and Bar in the + + + align:start position:0% +the idea is don't do hash and Bar in the +original circuit don't just do hash and + + align:start position:0% +original circuit don't just do hash and + + + align:start position:0% +original circuit don't just do hash and +Bar in the verification circuit do hash + + align:start position:0% +Bar in the verification circuit do hash + + + align:start position:0% +Bar in the verification circuit do hash +and bar on an extended circuit change + + align:start position:0% +and bar on an extended circuit change + + + align:start position:0% +and bar on an extended circuit change +the circuit do hash and a slightly more + + align:start position:0% +the circuit do hash and a slightly more + + + align:start position:0% +the circuit do hash and a slightly more +elaborate circuit so what is the more + + align:start position:0% +elaborate circuit so what is the more + + + align:start position:0% +elaborate circuit so what is the more +elaborate circuit let me give you an + + align:start position:0% +elaborate circuit let me give you an + + + align:start position:0% +elaborate circuit let me give you an +example one example you can + + align:start position:0% +example one example you can + + + align:start position:0% +example one example you can +do take each kind of um layer here and + + align:start position:0% +do take each kind of um layer here and + + + align:start position:0% +do take each kind of um layer here and +add a miracle hash in the + + align:start position:0% +add a miracle hash in the + + + align:start position:0% +add a miracle hash in the +circuit so now before you had a a + + align:start position:0% +circuit so now before you had a a + + + align:start position:0% +circuit so now before you had a a +verification circuit change it a little + + align:start position:0% +verification circuit change it a little + + + align:start position:0% +verification circuit change it a little +bit how how do you change it you compute + + align:start position:0% +bit how how do you change it you compute + + + align:start position:0% +bit how how do you change it you compute +each one and then you compute kind of a + + align:start position:0% +each one and then you compute kind of a + + + align:start position:0% +each one and then you compute kind of a +miracle hash compute the next layer and + + align:start position:0% +miracle hash compute the next layer and + + + align:start position:0% +miracle hash compute the next layer and +compute a miracle hash compute the next + + align:start position:0% +compute a miracle hash compute the next + + + align:start position:0% +compute a miracle hash compute the next +layer compute a mle hash it's weird like + + align:start position:0% +layer compute a mle hash it's weird like + + + align:start position:0% +layer compute a mle hash it's weird like +why would you do that do that moreover + + align:start position:0% +why would you do that do that moreover + + + align:start position:0% +why would you do that do that moreover +also compute for every wire like the + + align:start position:0% +also compute for every wire like the + + + align:start position:0% +also compute for every wire like the +opening of the Merkel + + align:start position:0% +opening of the Merkel + + + align:start position:0% +opening of the Merkel +hash add add all these Merkel hashes and + + align:start position:0% +hash add add all these Merkel hashes and + + + align:start position:0% +hash add add all these Merkel hashes and +add all these opening to the circle + + align:start position:0% +add all these opening to the circle + + + align:start position:0% +add all these opening to the circle +circuit now that seems a ridiculous + + align:start position:0% +circuit now that seems a ridiculous + + + align:start position:0% +circuit now that seems a ridiculous +thing to do why would you add to the + + align:start position:0% +thing to do why would you add to the + + + align:start position:0% +thing to do why would you add to the +Circuit that you're trying to verify + + align:start position:0% +Circuit that you're trying to verify + + + align:start position:0% +Circuit that you're trying to verify +that it's correct for each wire Merle + + align:start position:0% +that it's correct for each wire Merle + + + align:start position:0% +that it's correct for each wire Merle +has all the wires and add kind of wires + + align:start position:0% +has all the wires and add kind of wires + + + align:start position:0% +has all the wires and add kind of wires +that check opening like what this sounds + + align:start position:0% +that check opening like what this sounds + + + align:start position:0% +that check opening like what this sounds +really weird and not a very like a weird + + align:start position:0% +really weird and not a very like a weird + + + align:start position:0% +really weird and not a very like a weird +thing to do or sorry you know you don't + + align:start position:0% +thing to do or sorry you know you don't + + + align:start position:0% +thing to do or sorry you know you don't +need to check opening just add Merkel + + align:start position:0% +need to check opening just add Merkel + + + align:start position:0% +need to check opening just add Merkel +hashes add for each wire add moral hash + + align:start position:0% +hashes add for each wire add moral hash + + + align:start position:0% +hashes add for each wire add moral hash +to the wire for each layer add a miracle + + align:start position:0% +to the wire for each layer add a miracle + + + align:start position:0% +to the wire for each layer add a miracle +hash so on so forth why is adding + + align:start position:0% +hash so on so forth why is adding + + + align:start position:0% +hash so on so forth why is adding +hashes helpful at + + align:start position:0% +hashes helpful at + + + align:start position:0% +hashes helpful at +all so I'll tell you why it's helpful + + align:start position:0% +all so I'll tell you why it's helpful + + + align:start position:0% +all so I'll tell you why it's helpful +because now we have the local assignment + + align:start position:0% +because now we have the local assignment + + + align:start position:0% +because now we have the local assignment +generator and now in the local + + align:start position:0% +generator and now in the local + + + align:start position:0% +generator and now in the local +assignment generator what we can do we + + align:start position:0% +assignment generator what we can do we + + + align:start position:0% +assignment generator what we can do we +said the first layer each one is + + align:start position:0% +said the first layer each one is + + + align:start position:0% +said the first layer each one is +correct now we're going to argue this + + align:start position:0% +correct now we're going to argue this + + + align:start position:0% +correct now we're going to argue this +implies that the meracle root is + + align:start position:0% +implies that the meracle root is + + + align:start position:0% +implies that the meracle root is +correct that this must be correct now + + align:start position:0% +correct that this must be correct now + + + align:start position:0% +correct that this must be correct now +when we argue it we do pay exponential + + align:start position:0% +when we argue it we do pay exponential + + + align:start position:0% +when we argue it we do pay exponential +with the depth so this is a computation + + align:start position:0% +with the depth so this is a computation + + + align:start position:0% +with the depth so this is a computation +and the air does grow but the depth is + + align:start position:0% +and the air does grow but the depth is + + + align:start position:0% +and the air does grow but the depth is +long Miracle hash is a very low depth + + align:start position:0% +long Miracle hash is a very low depth + + + align:start position:0% +long Miracle hash is a very low depth +computation so it grows but perally it's + + align:start position:0% +computation so it grows but perally it's + + + align:start position:0% +computation so it grows but perally it's +okay now when we read things here we're + + align:start position:0% +okay now when we read things here we're + + + align:start position:0% +okay now when we read things here we're +going to read them together with a root + + align:start position:0% +going to read them together with a root + + + align:start position:0% +going to read them together with a root +we're not going to just we're going to + + align:start position:0% +we're not going to just we're going to + + + align:start position:0% +we're not going to just we're going to +say the when we ask the local assignment + + align:start position:0% +say the when we ask the local assignment + + + align:start position:0% +say the when we ask the local assignment +generator what is the value give me the + + align:start position:0% +generator what is the value give me the + + + align:start position:0% +generator what is the value give me the +value here here here we're gonna also + + align:start position:0% +value here here here we're gonna also + + + align:start position:0% +value here here here we're gonna also +say and + + align:start position:0% +say and + + + align:start position:0% +say and +give me the value of the root and the + + align:start position:0% +give me the value of the root and the + + + align:start position:0% +give me the value of the root and the +and the paths corresponding to this and + + align:start position:0% +and the paths corresponding to this and + + + align:start position:0% +and the paths corresponding to this and +this and now the thing is the following + + align:start position:0% +this and now the thing is the following + + + align:start position:0% +this and now the thing is the following +if the root was + + align:start position:0% +if the root was + + + align:start position:0% +if the root was +correct both of them have to be correct + + align:start position:0% +correct both of them have to be correct + + + align:start position:0% +correct both of them have to be correct +unless you broke the hash + + align:start position:0% +unless you broke the hash + + + align:start position:0% +unless you broke the hash +function so you you don't need to get + + align:start position:0% +function so you you don't need to get + + + align:start position:0% +function so you you don't need to get +this Independence before we were like oh + + align:start position:0% +this Independence before we were like oh + + + align:start position:0% +this Independence before we were like oh +we needed this to be correct and this to + + align:start position:0% +we needed this to be correct and this to + + + align:start position:0% +we needed this to be correct and this to +be correct and things doubl here we can + + align:start position:0% +be correct and things doubl here we can + + + align:start position:0% +be correct and things doubl here we can +say if the root is correct we know that + + align:start position:0% +say if the root is correct we know that + + + align:start position:0% +say if the root is correct we know that +both of them have to be correct + + align:start position:0% +both of them have to be correct + + + align:start position:0% +both of them have to be correct +so it's enough to argue that the root is + + align:start position:0% +so it's enough to argue that the root is + + + align:start position:0% +so it's enough to argue that the root is +correct so it's kind of a little bit + + align:start position:0% +correct so it's kind of a little bit + + + align:start position:0% +correct so it's kind of a little bit +simulates the case of like reading the + + align:start position:0% +simulates the case of like reading the + + + align:start position:0% +simulates the case of like reading the +entire config the entire configuration + + align:start position:0% +entire config the entire configuration + + + align:start position:0% +entire config the entire configuration +or an entire layer which is what we did + + align:start position:0% +or an entire layer which is what we did + + + align:start position:0% +or an entire layer which is what we did +in the bounded + + align:start position:0% +in the bounded + + + align:start position:0% +in the bounded +space so I don't want to go I think + + align:start position:0% +space so I don't want to go I think + + + align:start position:0% +space so I don't want to go I think +that's all I want to say but essentially + + align:start position:0% +that's all I want to say but essentially + + + align:start position:0% +that's all I want to say but essentially +what I want to mention is this local + + align:start position:0% +what I want to mention is this local + + + align:start position:0% +what I want to mention is this local +satisfiability or local soundness or + + align:start position:0% +satisfiability or local soundness or + + + align:start position:0% +satisfiability or local soundness or +local uh uh a consistency + + align:start position:0% +local uh uh a consistency + + + align:start position:0% +local uh uh a consistency +does not necessarily imply Global + + align:start position:0% +does not necessarily imply Global + + + align:start position:0% +does not necessarily imply Global +correctness actually to use it to get + + align:start position:0% +correctness actually to use it to get + + + align:start position:0% +correctness actually to use it to get +Global correctness often we need to kind + + align:start position:0% +Global correctness often we need to kind + + + align:start position:0% +Global correctness often we need to kind +of change the circuit and kind of do + + align:start position:0% +of change the circuit and kind of do + + + align:start position:0% +of change the circuit and kind of do +kind of circuit gymnastics in weird ways + + align:start position:0% +kind of circuit gymnastics in weird ways + + + align:start position:0% +kind of circuit gymnastics in weird ways +to get it to work and this is still kind + + align:start position:0% +to get it to work and this is still kind + + + align:start position:0% +to get it to work and this is still kind +of work in progress it's still kind of + + align:start position:0% +of work in progress it's still kind of + + + align:start position:0% +of work in progress it's still kind of +uh us as a community are still uh + + align:start position:0% +uh us as a community are still uh + + + align:start position:0% +uh us as a community are still uh +combating with this I see smiled because + + align:start position:0% +combating with this I see smiled because + + + align:start position:0% +combating with this I see smiled because +my students have been suffering with me + + align:start position:0% +my students have been suffering with me + + + align:start position:0% +my students have been suffering with me +through this L's like I don't know half + + align:start position:0% +through this L's like I don't know half + + + align:start position:0% +through this L's like I don't know half +smiling half + + align:start position:0% +smiling half + + + align:start position:0% +smiling half +crying but but + + align:start position:0% +crying but but + + + align:start position:0% +crying but but +uh uh yeah so that's kind of uh where we + + align:start position:0% +uh uh yeah so that's kind of uh where we + + + align:start position:0% +uh uh yeah so that's kind of uh where we +are today so let me use the last 3 + + align:start position:0% +are today so let me use the last 3 + + + align:start position:0% +are today so let me use the last 3 +minutes or so to do kind of a quick + + align:start position:0% +minutes or so to do kind of a quick + + + align:start position:0% +minutes or so to do kind of a quick +summary so first of all before I + + align:start position:0% +summary so first of all before I + + + align:start position:0% +summary so first of all before I +summarize there's um a if you have any + + align:start position:0% +summarize there's um a if you have any + + + align:start position:0% +summarize there's um a if you have any +feedback there's feedback forms please + + align:start position:0% +feedback there's feedback forms please + + + align:start position:0% +feedback there's feedback forms please +submit so I you know I'll improve uh uh + + align:start position:0% +submit so I you know I'll improve uh uh + + + align:start position:0% +submit so I you know I'll improve uh uh +or I'll keep on doing things that worked + + align:start position:0% +or I'll keep on doing things that worked + + + align:start position:0% +or I'll keep on doing things that worked +to try not to do things that didn't work + + align:start position:0% +to try not to do things that didn't work + + + align:start position:0% +to try not to do things that didn't work +so uh it's it'll be great great great if + + align:start position:0% +so uh it's it'll be great great great if + + + align:start position:0% +so uh it's it'll be great great great if +you if uh you can submit the feedback + + align:start position:0% +you if uh you can submit the feedback + + + align:start position:0% +you if uh you can submit the feedback +form that would be really really helpful + + align:start position:0% +form that would be really really helpful + + + align:start position:0% +form that would be really really helpful +uh and okay so with that uh let me just + + align:start position:0% +uh and okay so with that uh let me just + + + align:start position:0% +uh and okay so with that uh let me just +I want to kind of reflect a couple + + align:start position:0% +I want to kind of reflect a couple + + + align:start position:0% +I want to kind of reflect a couple +minutes on this journey and and where we + + align:start position:0% +minutes on this journey and and where we + + + align:start position:0% +minutes on this journey and and where we +are and how you know so if you remember + + align:start position:0% +are and how you know so if you remember + + + align:start position:0% +are and how you know so if you remember +you know we started by saying look + + align:start position:0% +you know we started by saying look + + + align:start position:0% +you know we started by saying look +proofs has been has been something that + + align:start position:0% +proofs has been has been something that + + + align:start position:0% +proofs has been has been something that +you know uh mathematicians have been + + align:start position:0% +you know uh mathematicians have been + + + align:start position:0% +you know uh mathematicians have been +working with and uh thinking about for + + align:start position:0% +working with and uh thinking about for + + + align:start position:0% +working with and uh thinking about for +thousands of years and proofs have + + align:start position:0% +thousands of years and proofs have + + + align:start position:0% +thousands of years and proofs have +always been very specific form of like + + align:start position:0% +always been very specific form of like + + + align:start position:0% +always been very specific form of like +logic deductions and this changed kind + + align:start position:0% +logic deductions and this changed kind + + + align:start position:0% +logic deductions and this changed kind +of the cryptography changed this with + + align:start position:0% +of the cryptography changed this with + + + align:start position:0% +of the cryptography changed this with +the introduction with the thinking about + + align:start position:0% +the introduction with the thinking about + + + align:start position:0% +the introduction with the thinking about +zero knowledge proofs they defined this + + align:start position:0% +zero knowledge proofs they defined this + + + align:start position:0% +zero knowledge proofs they defined this +notion of interactive proof a new proof + + align:start position:0% +notion of interactive proof a new proof + + + align:start position:0% +notion of interactive proof a new proof +model and this new way of thinking about + + align:start position:0% +model and this new way of thinking about + + + align:start position:0% +model and this new way of thinking about +proofs was kind of a a huge huge success + + align:start position:0% +proofs was kind of a a huge huge success + + + align:start position:0% +proofs was kind of a a huge huge success +story for cryptography for complexity um + + align:start position:0% +story for cryptography for complexity um + + + align:start position:0% +story for cryptography for complexity um +and it kind of we noticed that these + + align:start position:0% +and it kind of we noticed that these + + + align:start position:0% +and it kind of we noticed that these +interactive proof systems turned out to + + align:start position:0% +interactive proof systems turned out to + + + align:start position:0% +interactive proof systems turned out to +be very very powerful and this kind of + + align:start position:0% +be very very powerful and this kind of + + + align:start position:0% +be very very powerful and this kind of +the main work that kind of uh + + align:start position:0% +the main work that kind of uh + + + align:start position:0% +the main work that kind of uh +demonstrated that was the uh um sub Che + + align:start position:0% +demonstrated that was the uh um sub Che + + + align:start position:0% +demonstrated that was the uh um sub Che +protocol that was kind of the first + + align:start position:0% +protocol that was kind of the first + + + align:start position:0% +protocol that was kind of the first +protocol that wow you can do something + + align:start position:0% +protocol that wow you can do something + + + align:start position:0% +protocol that wow you can do something +that we have no idea how to do + + align:start position:0% +that we have no idea how to do + + + align:start position:0% +that we have no idea how to do +classically and that kind of gave birth + + align:start position:0% +classically and that kind of gave birth + + + align:start position:0% +classically and that kind of gave birth +to the IP equals peace space theorem + + align:start position:0% +to the IP equals peace space theorem + + + align:start position:0% +to the IP equals peace space theorem +once you had the the Su check from that + + align:start position:0% +once you had the the Su check from that + + + align:start position:0% +once you had the the Su check from that +kind of uh with a little more work uh + + align:start position:0% +kind of uh with a little more work uh + + + align:start position:0% +kind of uh with a little more work uh +you can do the IP equals uh P space uh + + align:start position:0% +you can do the IP equals uh P space uh + + + align:start position:0% +you can do the IP equals uh P space uh +theorem and what we showed in this class + + align:start position:0% +theorem and what we showed in this class + + + align:start position:0% +theorem and what we showed in this class +is actually we kind of went through uh + + align:start position:0% +is actually we kind of went through uh + + + align:start position:0% +is actually we kind of went through uh +gkr so we we we showed that if you have + + align:start position:0% +gkr so we we we showed that if you have + + + align:start position:0% +gkr so we we we showed that if you have +a su check you can get actually a just + + align:start position:0% +a su check you can get actually a just + + + align:start position:0% +a su check you can get actually a just +by a very simple idea of kind of uh + + align:start position:0% +by a very simple idea of kind of uh + + + align:start position:0% +by a very simple idea of kind of uh +doing snar H Su check layer by layer you + + align:start position:0% +doing snar H Su check layer by layer you + + + align:start position:0% +doing snar H Su check layer by layer you +can get an interactive a succinct + + align:start position:0% +can get an interactive a succinct + + + align:start position:0% +can get an interactive a succinct +interactive proof for any bound to depth + + align:start position:0% +interactive proof for any bound to depth + + + align:start position:0% +interactive proof for any bound to depth +computation that's doubly efficient so + + align:start position:0% +computation that's doubly efficient so + + + align:start position:0% +computation that's doubly efficient so +the pro is efficient + + align:start position:0% +the pro is efficient + + + align:start position:0% +the pro is efficient +and the verifier is is uh succinct or + + align:start position:0% +and the verifier is is uh succinct or + + + align:start position:0% +and the verifier is is uh succinct or +very + + align:start position:0% +very + + + align:start position:0% +very +efficient and then we showed kind of the + + align:start position:0% +efficient and then we showed kind of the + + + align:start position:0% +efficient and then we showed kind of the +IP equals P space as a quary showed that + + align:start position:0% +IP equals P space as a quary showed that + + + align:start position:0% +IP equals P space as a quary showed that +you can get PCP from it uh and then we + + align:start position:0% +you can get PCP from it uh and then we + + + align:start position:0% +you can get PCP from it uh and then we +moved to arguments said well okay that's + + align:start position:0% +moved to arguments said well okay that's + + + align:start position:0% +moved to arguments said well okay that's +where we are with proofs uh with + + align:start position:0% +where we are with proofs uh with + + + align:start position:0% +where we are with proofs uh with +statistical soundness and then we said + + align:start position:0% +statistical soundness and then we said + + + align:start position:0% +statistical soundness and then we said +well if you're willing to rely to to + + align:start position:0% +well if you're willing to rely to to + + + align:start position:0% +well if you're willing to rely to to +reduce soundness to computational + + align:start position:0% +reduce soundness to computational + + + align:start position:0% +reduce soundness to computational +soundness then we saw the kilan mik you + + align:start position:0% +soundness then we saw the kilan mik you + + + align:start position:0% +soundness then we saw the kilan mik you +can get everything like really efficient + + align:start position:0% +can get everything like really efficient + + + align:start position:0% +can get everything like really efficient +uh Interactive arguments by T think PCP + + align:start position:0% +uh Interactive arguments by T think PCP + + + align:start position:0% +uh Interactive arguments by T think PCP +and kind of hashing them + + align:start position:0% +and kind of hashing them + + + align:start position:0% +and kind of hashing them +down and then there was a question okay + + align:start position:0% +down and then there was a question okay + + + align:start position:0% +down and then there was a question okay +we can have intractive arguments can we + + align:start position:0% +we can have intractive arguments can we + + + align:start position:0% +we can have intractive arguments can we +have + + align:start position:0% +have + + + align:start position:0% +have +snars can we eliminate intraction and + + align:start position:0% +snars can we eliminate intraction and + + + align:start position:0% +snars can we eliminate intraction and +then we talked about F uh kind of went + + align:start position:0% +then we talked about F uh kind of went + + + align:start position:0% +then we talked about F uh kind of went +through kind of zero knowledge a little + + align:start position:0% +through kind of zero knowledge a little + + + align:start position:0% +through kind of zero knowledge a little +bit because that's the first time where + + align:start position:0% +bit because that's the first time where + + + align:start position:0% +bit because that's the first time where +F proved security of it was uh in the + + align:start position:0% +F proved security of it was uh in the + + + align:start position:0% +F proved security of it was uh in the +context of zero + + align:start position:0% +context of zero + + + align:start position:0% +context of zero +knowledge but then we showed or Jen Jang + + align:start position:0% +knowledge but then we showed or Jen Jang + + + align:start position:0% +knowledge but then we showed or Jen Jang +showed that actually you can do F also + + align:start position:0% +showed that actually you can do F also + + + align:start position:0% +showed that actually you can do F also +the context of bars so we have an + + align:start position:0% +the context of bars so we have an + + + align:start position:0% +the context of bars so we have an +interactive uh batch argument and you + + align:start position:0% +interactive uh batch argument and you + + + align:start position:0% +interactive uh batch argument and you +can or a constructed interractive batch + + align:start position:0% +can or a constructed interractive batch + + + align:start position:0% +can or a constructed interractive batch +argument showed you can use I don't know + + align:start position:0% +argument showed you can use I don't know + + + align:start position:0% +argument showed you can use I don't know +it didn't get into detail but turns out + + align:start position:0% +it didn't get into detail but turns out + + + align:start position:0% +it didn't get into detail but turns out +you can use similar techniques to uh to + + align:start position:0% +you can use similar techniques to uh to + + + align:start position:0% +you can use similar techniques to uh to +show F secure or these techniques Plus+ + + align:start position:0% +show F secure or these techniques Plus+ + + + align:start position:0% +show F secure or these techniques Plus+ +to show that F secure when apply to the + + align:start position:0% +to show that F secure when apply to the + + + align:start position:0% +to show that F secure when apply to the +interactive batch argument and then you + + align:start position:0% +interactive batch argument and then you + + + align:start position:0% +interactive batch argument and then you +get like a this non- interractive + + align:start position:0% +get like a this non- interractive + + + align:start position:0% +get like a this non- interractive +bar and today kind of to close the this + + align:start position:0% +bar and today kind of to close the this + + + align:start position:0% +bar and today kind of to close the this +entire Journey we showed how to get uh + + align:start position:0% +entire Journey we showed how to get uh + + + align:start position:0% +entire Journey we showed how to get uh +snars from these bars and as I said we + + align:start position:0% +snars from these bars and as I said we + + + align:start position:0% +snars from these bars and as I said we +have it for deterministic computation we + + align:start position:0% +have it for deterministic computation we + + + align:start position:0% +have it for deterministic computation we +have it for some non-deterministic + + align:start position:0% +have it for some non-deterministic + + + align:start position:0% +have it for some non-deterministic +computation constructing it for all of + + align:start position:0% +computation constructing it for all of + + + align:start position:0% +computation constructing it for all of +NP is still a major open question uh so + + align:start position:0% +NP is still a major open question uh so + + + align:start position:0% +NP is still a major open question uh so +you know I invite you all to work on it + + align:start position:0% +you know I invite you all to work on it + + + align:start position:0% +you know I invite you all to work on it +with me but I want to say one more thing + + align:start position:0% +with me but I want to say one more thing + + + align:start position:0% +with me but I want to say one more thing +about this area which is it's really + + align:start position:0% +about this area which is it's really + + + align:start position:0% +about this area which is it's really +nice because this is one example where + + align:start position:0% +nice because this is one example where + + + align:start position:0% +nice because this is one example where +this area has a beautiful beautiful math + + align:start position:0% +this area has a beautiful beautiful math + + + align:start position:0% +this area has a beautiful beautiful math +in my opinion so it's very theoretical + + align:start position:0% +in my opinion so it's very theoretical + + + align:start position:0% +in my opinion so it's very theoretical +with beautiful mathematical ideas and + + align:start position:0% +with beautiful mathematical ideas and + + + align:start position:0% +with beautiful mathematical ideas and +applied so this is kind of this area has + + align:start position:0% +applied so this is kind of this area has + + + align:start position:0% +applied so this is kind of this area has +been a really nice kind of bonding + + align:start position:0% +been a really nice kind of bonding + + + align:start position:0% +been a really nice kind of bonding +between kind of theoreticians and + + align:start position:0% +between kind of theoreticians and + + + align:start position:0% +between kind of theoreticians and +practitioners these things are used uh + + align:start position:0% +practitioners these things are used uh + + + align:start position:0% +practitioners these things are used uh +in particular by a lot of bankers and uh + + align:start position:0% +in particular by a lot of bankers and uh + + + align:start position:0% +in particular by a lot of bankers and uh +you know people started using + + align:start position:0% +you know people started using + + + align:start position:0% +you know people started using +blockchains and now B Bank systems and + + align:start position:0% +blockchains and now B Bank systems and + + + align:start position:0% +blockchains and now B Bank systems and +so on are interested in it so it's been + + align:start position:0% +so on are interested in it so it's been + + + align:start position:0% +so on are interested in it so it's been +kind of um a really nice a example where + + align:start position:0% +kind of um a really nice a example where + + + align:start position:0% +kind of um a really nice a example where +really beautiful theory is is used like + + align:start position:0% +really beautiful theory is is used like + + + align:start position:0% +really beautiful theory is is used like +the theory itself is really uh deployed + + align:start position:0% +the theory itself is really uh deployed + + + align:start position:0% +the theory itself is really uh deployed +and used so it's um it's kind of uh I + + align:start position:0% +and used so it's um it's kind of uh I + + + align:start position:0% +and used so it's um it's kind of uh I +think this is an example of success + + align:start position:0% +think this is an example of success + + + align:start position:0% +think this is an example of success +story for theoretical + + align:start position:0% +story for theoretical + + + align:start position:0% +story for theoretical +cryptography okay thank you guys it was + + align:start position:0% +cryptography okay thank you guys it was + + + align:start position:0% +cryptography okay thank you guys it was +really really fun teaching you thank you \ No newline at end of file diff --git a/dKLkXQEN9XU.txt b/dKLkXQEN9XU.txt new file mode 100644 index 0000000000000000000000000000000000000000..5b948f283fb055c150de0288d2169021172bd095 --- /dev/null +++ b/dKLkXQEN9XU.txt @@ -0,0 +1,7707 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu all right let's look at some + + align:start position:0% +ocw.mit.edu all right let's look at some + + + align:start position:0% +ocw.mit.edu all right let's look at some +of your questions + + align:start position:0% + + + + align:start position:0% + +a bunch of them I'll you know what I'm + + align:start position:0% +a bunch of them I'll you know what I'm + + + align:start position:0% +a bunch of them I'll you know what I'm +probably going to use that screen most + + align:start position:0% +probably going to use that screen most + + + align:start position:0% +probably going to use that screen most +of the time because this one's not + + align:start position:0% +of the time because this one's not + + + align:start position:0% +of the time because this one's not +fitting but let's look on this + + align:start position:0% +fitting but let's look on this + + + align:start position:0% +fitting but let's look on this +screen your questions really focused + + align:start position:0% +screen your questions really focused + + + align:start position:0% +screen your questions really focused +around IPS + + align:start position:0% +around IPS + + + align:start position:0% +around IPS +cells and the kind of magic of ips + + align:start position:0% +cells and the kind of magic of ips + + + align:start position:0% +cells and the kind of magic of ips +cells and there were a couple of major + + align:start position:0% +cells and there were a couple of major + + + align:start position:0% +cells and there were a couple of major +questions that came + + align:start position:0% +questions that came + + + align:start position:0% +questions that came +up what's the problem with using IPS + + align:start position:0% +up what's the problem with using IPS + + + align:start position:0% +up what's the problem with using IPS +cells therapeutically well they're a + + align:start position:0% +cells therapeutically well they're a + + + align:start position:0% +cells therapeutically well they're a +number one they're so new that really we + + align:start position:0% +number one they're so new that really we + + + align:start position:0% +number one they're so new that really we +don't know what kinds of cell types + + align:start position:0% +don't know what kinds of cell types + + + align:start position:0% +don't know what kinds of cell types +these IPS cells can make so it's not + + align:start position:0% +these IPS cells can make so it's not + + + align:start position:0% +these IPS cells can make so it's not +clear how to use them another problem + + align:start position:0% +clear how to use them another problem + + + align:start position:0% +clear how to use them another problem +actually which my colleague Professor + + align:start position:0% +actually which my colleague Professor + + + align:start position:0% +actually which my colleague Professor +yanish works on is the question of how + + align:start position:0% +yanish works on is the question of how + + + align:start position:0% +yanish works on is the question of how +to actually grow these + + align:start position:0% + + + + align:start position:0% + +cells I have a voice issue this morning + + align:start position:0% +cells I have a voice issue this morning + + + align:start position:0% +cells I have a voice issue this morning +so you know the quieter you are the more + + align:start position:0% +so you know the quieter you are the more + + + align:start position:0% +so you know the quieter you are the more +you'll be able to hear my + + align:start position:0% +you'll be able to hear my + + + align:start position:0% +you'll be able to hear my +words IPS cells human cells grow very + + align:start position:0% +words IPS cells human cells grow very + + + align:start position:0% +words IPS cells human cells grow very +slowly in the laboratory and it's very + + align:start position:0% +slowly in the laboratory and it's very + + + align:start position:0% +slowly in the laboratory and it's very +difficult to grow them so there are some + + align:start position:0% +difficult to grow them so there are some + + + align:start position:0% +difficult to grow them so there are some +basic questions in biology as to how to + + align:start position:0% +basic questions in biology as to how to + + + align:start position:0% +basic questions in biology as to how to +grow these cells to enough numbers that + + align:start position:0% +grow these cells to enough numbers that + + + align:start position:0% +grow these cells to enough numbers that +they'd actually be useful but here's + + align:start position:0% +they'd actually be useful but here's + + + align:start position:0% +they'd actually be useful but here's +another one that's very important the + + align:start position:0% +another one that's very important the + + + align:start position:0% +another one that's very important the +transcription factors that were used to + + align:start position:0% +transcription factors that were used to + + + align:start position:0% +transcription factors that were used to +convert adult cells into IPS cells + + align:start position:0% +convert adult cells into IPS cells + + + align:start position:0% +convert adult cells into IPS cells +included an enag Gene called + + align:start position:0% +included an enag Gene called + + + align:start position:0% +included an enag Gene called +CCH and MCH is the the kind of Gene you + + align:start position:0% +CCH and MCH is the the kind of Gene you + + + align:start position:0% +CCH and MCH is the the kind of Gene you +don't want floating around your body + + align:start position:0% +don't want floating around your body + + + align:start position:0% +don't want floating around your body +nice and active in your cells because + + align:start position:0% +nice and active in your cells because + + + align:start position:0% +nice and active in your cells because +it'll give you cancer so the challenge + + align:start position:0% +it'll give you cancer so the challenge + + + align:start position:0% +it'll give you cancer so the challenge +is how to actually use Mech and other + + align:start position:0% +is how to actually use Mech and other + + + align:start position:0% +is how to actually use Mech and other +potent transcription factors to turn + + align:start position:0% +potent transcription factors to turn + + + align:start position:0% +potent transcription factors to turn +adult cells into stem cells but not have + + align:start position:0% +adult cells into stem cells but not have + + + align:start position:0% +adult cells into stem cells but not have +the stem cells give the recipient cancer + + align:start position:0% +the stem cells give the recipient cancer + + + align:start position:0% +the stem cells give the recipient cancer +and there's some very clever ways that + + align:start position:0% +and there's some very clever ways that + + + align:start position:0% +and there's some very clever ways that +people are trying to get around this + + align:start position:0% + + + + align:start position:0% + +it is really impossible to teach you if + + align:start position:0% +it is really impossible to teach you if + + + align:start position:0% +it is really impossible to teach you if +there are groups of you + + align:start position:0% +there are groups of you + + + align:start position:0% +there are groups of you +talking I just cannot do it so those of + + align:start position:0% +talking I just cannot do it so those of + + + align:start position:0% +talking I just cannot do it so those of +you + + align:start position:0% +you + + + align:start position:0% +you +talking please don't thank + + align:start position:0% +talking please don't thank + + + align:start position:0% +talking please don't thank +you all right so what's the big deal + + align:start position:0% +you all right so what's the big deal + + + align:start position:0% +you all right so what's the big deal +about IPS cells well the big deal is + + align:start position:0% +about IPS cells well the big deal is + + + align:start position:0% +about IPS cells well the big deal is +they can be your own in theory and maybe + + align:start position:0% +they can be your own in theory and maybe + + + align:start position:0% +they can be your own in theory and maybe +in practice a decade five years maybe + + align:start position:0% +in practice a decade five years maybe + + + align:start position:0% +in practice a decade five years maybe +from now + + align:start position:0% +from now + + + align:start position:0% +from now +your own cells your skin cells could be + + align:start position:0% +your own cells your skin cells could be + + + align:start position:0% +your own cells your skin cells could be +removed from you could be dealt with in + + align:start position:0% +removed from you could be dealt with in + + + align:start position:0% +removed from you could be dealt with in +the laboratory turned into your own stem + + align:start position:0% +the laboratory turned into your own stem + + + align:start position:0% +the laboratory turned into your own stem +cells and put back into your own body + + align:start position:0% +cells and put back into your own body + + + align:start position:0% +cells and put back into your own body +and they'd be your own so of course they + + align:start position:0% +and they'd be your own so of course they + + + align:start position:0% +and they'd be your own so of course they +wouldn't be rejected by you and that is + + align:start position:0% +wouldn't be rejected by you and that is + + + align:start position:0% +wouldn't be rejected by you and that is +an enormous deal they're called + + align:start position:0% +an enormous deal they're called + + + align:start position:0% +an enormous deal they're called +autologous + + align:start position:0% +autologous + + + align:start position:0% +autologous +cells there's an ethical issue in that + + align:start position:0% +cells there's an ethical issue in that + + + align:start position:0% +cells there's an ethical issue in that +you don't have to harvest any embryos to + + align:start position:0% +you don't have to harvest any embryos to + + + align:start position:0% +you don't have to harvest any embryos to +get stem cell + + align:start position:0% +get stem cell + + + align:start position:0% +get stem cell +lines and that's a big deal and here's a + + align:start position:0% +lines and that's a big deal and here's a + + + align:start position:0% +lines and that's a big deal and here's a +conceptual deal + + align:start position:0% +conceptual deal + + + align:start position:0% +conceptual deal +when we talked about development we + + align:start position:0% +when we talked about development we + + + align:start position:0% +when we talked about development we +talked about this directional pathway + + align:start position:0% +talked about this directional pathway + + + align:start position:0% +talked about this directional pathway +where uncommitted cells became committed + + align:start position:0% +where uncommitted cells became committed + + + align:start position:0% +where uncommitted cells became committed +became + + align:start position:0% +became + + + align:start position:0% +became +differentiated it was really thought + + align:start position:0% +differentiated it was really thought + + + align:start position:0% +differentiated it was really thought +that that was a one-way pathway but what + + align:start position:0% +that that was a one-way pathway but what + + + align:start position:0% +that that was a one-way pathway but what +IPS cell technology has shown let's look + + align:start position:0% +IPS cell technology has shown let's look + + + align:start position:0% +IPS cell technology has shown let's look +at + + align:start position:0% +at + + + align:start position:0% +at +this all right we can we can get the + + align:start position:0% +this all right we can we can get the + + + align:start position:0% +this all right we can we can get the +idea from one of these two screens what + + align:start position:0% +idea from one of these two screens what + + + align:start position:0% +idea from one of these two screens what +IPS cell technology has shown is that + + align:start position:0% +IPS cell technology has shown is that + + + align:start position:0% +IPS cell technology has shown is that +you can reverse differentiation you can + + align:start position:0% +you can reverse differentiation you can + + + align:start position:0% +you can reverse differentiation you can +take differentiated adult cells and with + + align:start position:0% +take differentiated adult cells and with + + + align:start position:0% +take differentiated adult cells and with +the right regulatory factors you can + + align:start position:0% +the right regulatory factors you can + + + align:start position:0% +the right regulatory factors you can +turn them into stem cells okay and so + + align:start position:0% +turn them into stem cells okay and so + + + align:start position:0% +turn them into stem cells okay and so +conceptually that's a big + + align:start position:0% +conceptually that's a big + + + align:start position:0% +conceptually that's a big +deal very good great + + align:start position:0% +deal very good great + + + align:start position:0% +deal very good great +questions my next office hour is on are + + align:start position:0% +questions my next office hour is on are + + + align:start position:0% +questions my next office hour is on are +on Monday 12 to1 come along or email + + align:start position:0% +on Monday 12 to1 come along or email + + + align:start position:0% +on Monday 12 to1 come along or email +me but now we're going to turn to a new + + align:start position:0% +me but now we're going to turn to a new + + + align:start position:0% +me but now we're going to turn to a new +module and that is the nervous system + + align:start position:0% +module and that is the nervous system + + + align:start position:0% +module and that is the nervous system +and this is where we are in the + + align:start position:0% +and this is where we are in the + + + align:start position:0% +and this is where we are in the +course we've told you've done all the + + align:start position:0% +course we've told you've done all the + + + align:start position:0% +course we've told you've done all the +foundational material we've talked about + + align:start position:0% +foundational material we've talked about + + + align:start position:0% +foundational material we've talked about +formation and now we're going to talk + + align:start position:0% +formation and now we're going to talk + + + align:start position:0% +formation and now we're going to talk +about systems and the nervous system in + + align:start position:0% +about systems and the nervous system in + + + align:start position:0% +about systems and the nervous system in +particular let's start with the question + + align:start position:0% +particular let's start with the question + + + align:start position:0% +particular let's start with the question +of what a system + + align:start position:0% + + + + align:start position:0% + +is building up the complexity of what + + align:start position:0% +is building up the complexity of what + + + align:start position:0% +is building up the complexity of what +we're talking about in life a system + + align:start position:0% +we're talking about in life a system + + + align:start position:0% +we're talking about in life a system +refers to many organs that work together + + align:start position:0% +refers to many organs that work together + + + align:start position:0% +refers to many organs that work together +with one common function + + align:start position:0% + + + + align:start position:0% + +many organs working together with one + + align:start position:0% +many organs working together with one + + + align:start position:0% +many organs working together with one +overall + + align:start position:0% +overall + + + align:start position:0% +overall +function and you'll talk about two in + + align:start position:0% +function and you'll talk about two in + + + align:start position:0% +function and you'll talk about two in +the course you'll talk about the nervous + + align:start position:0% +the course you'll talk about the nervous + + + align:start position:0% +the course you'll talk about the nervous +system and the immune system with + + align:start position:0% +system and the immune system with + + + align:start position:0% +system and the immune system with +Professor Jax the nervous system which + + align:start position:0% +Professor Jax the nervous system which + + + align:start position:0% +Professor Jax the nervous system which +is the topic of the next three lectures + + align:start position:0% +is the topic of the next three lectures + + + align:start position:0% +is the topic of the next three lectures +has to do with communication has to do + + align:start position:0% +has to do with communication has to do + + + align:start position:0% +has to do with communication has to do +with communication from the outside to + + align:start position:0% +with communication from the outside to + + + align:start position:0% +with communication from the outside to +the inside of an animal's body has to do + + align:start position:0% +the inside of an animal's body has to do + + + align:start position:0% +the inside of an animal's body has to do +with communication within the body and + + align:start position:0% +with communication within the body and + + + align:start position:0% +with communication within the body and +has to do with communication to get the + + align:start position:0% +has to do with communication to get the + + + align:start position:0% +has to do with communication to get the +organism the animal because plants don't + + align:start position:0% +organism the animal because plants don't + + + align:start position:0% +organism the animal because plants don't +have nervous system the animal to do + + align:start position:0% +have nervous system the animal to do + + + align:start position:0% +have nervous system the animal to do +something so the nervous + + align:start position:0% + + + + align:start position:0% + +system is + + align:start position:0% +system is + + + align:start position:0% +system is +about communication + + align:start position:0% + + + + align:start position:0% + +to or + + align:start position:0% + + + + align:start position:0% + +from or + + align:start position:0% +from or + + + align:start position:0% +from or +within the body of an + + align:start position:0% + + + + align:start position:0% + +animal we've had a number of electrical + + align:start position:0% +animal we've had a number of electrical + + + align:start position:0% +animal we've had a number of electrical +analogies in the course you will + + align:start position:0% +analogies in the course you will + + + align:start position:0% +analogies in the course you will +remember the famous signaling analogy of + + align:start position:0% +remember the famous signaling analogy of + + + align:start position:0% +remember the famous signaling analogy of +turning on the light switch over there + + align:start position:0% +turning on the light switch over there + + + align:start position:0% +turning on the light switch over there +on the wall but now we move on to + + align:start position:0% +on the wall but now we move on to + + + align:start position:0% +on the wall but now we move on to +another electrical analogy which is + + align:start position:0% +another electrical analogy which is + + + align:start position:0% +another electrical analogy which is +actually a trer one and I'm going to use + + align:start position:0% +actually a trer one and I'm going to use + + + align:start position:0% +actually a trer one and I'm going to use +the analogy for the nervous system of + + align:start position:0% +the analogy for the nervous system of + + + align:start position:0% +the analogy for the nervous system of +talking about wires that transmit the + + align:start position:0% +talking about wires that transmit the + + + align:start position:0% +talking about wires that transmit the +signal by which cells communicate I'm + + align:start position:0% +signal by which cells communicate I'm + + + align:start position:0% +signal by which cells communicate I'm +going to talk about connectors between + + align:start position:0% +going to talk about connectors between + + + align:start position:0% +going to talk about connectors between +the wires and then I'm going to talk + + align:start position:0% +the wires and then I'm going to talk + + + align:start position:0% +the wires and then I'm going to talk +about circuits and those are going to be + + align:start position:0% +about circuits and those are going to be + + + align:start position:0% +about circuits and those are going to be +the topics of the next three lectures so + + align:start position:0% + + + + align:start position:0% + +wires + + align:start position:0% + + + + align:start position:0% + +connectors and + + align:start position:0% + + + + align:start position:0% + +circuits and those will be ner system 1 + + align:start position:0% +circuits and those will be ner system 1 + + + align:start position:0% +circuits and those will be ner system 1 +to three the lectures in this module + + align:start position:0% +to three the lectures in this module + + + align:start position:0% +to three the lectures in this module +today we're going to talk about the + + align:start position:0% + + + + align:start position:0% + +wires and there'll be three topics the + + align:start position:0% +wires and there'll be three topics the + + + align:start position:0% +wires and there'll be three topics the +first is the cell + + align:start position:0% +first is the cell + + + align:start position:0% +first is the cell +type that's got something to do with the + + align:start position:0% +type that's got something to do with the + + + align:start position:0% +type that's got something to do with the +wiring for this communication the second + + align:start position:0% +wiring for this communication the second + + + align:start position:0% +wiring for this communication the second +is something called the action + + align:start position:0% +is something called the action + + + align:start position:0% +is something called the action +potential which is the signal by which + + align:start position:0% +potential which is the signal by which + + + align:start position:0% +potential which is the signal by which +cells communicate within the + + align:start position:0% +cells communicate within the + + + align:start position:0% +cells communicate within the +themselves and the third has to do with + + align:start position:0% +themselves and the third has to do with + + + align:start position:0% +themselves and the third has to do with +iron channels and + + align:start position:0% + + + + align:start position:0% + +pumps but let's start by phrasing the + + align:start position:0% +pumps but let's start by phrasing the + + + align:start position:0% +pumps but let's start by phrasing the +problem in a kind of a cool + + align:start position:0% +problem in a kind of a cool + + + align:start position:0% +problem in a kind of a cool +way if you look in the + + align:start position:0% +way if you look in the + + + align:start position:0% +way if you look in the +human let's look on this screen if you + + align:start position:0% +human let's look on this screen if you + + + align:start position:0% +human let's look on this screen if you +look in the human and you outline the + + align:start position:0% +look in the human and you outline the + + + align:start position:0% +look in the human and you outline the +nerves and if you went to see the living + + align:start position:0% +nerves and if you went to see the living + + + align:start position:0% +nerves and if you went to see the living +plasticized human exhibits you would + + align:start position:0% +plasticized human exhibits you would + + + align:start position:0% +plasticized human exhibits you would +have seen the plasticized nerves they're + + align:start position:0% +have seen the plasticized nerves they're + + + align:start position:0% +have seen the plasticized nerves they're +really extraordinary the network of + + align:start position:0% +really extraordinary the network of + + + align:start position:0% +really extraordinary the network of +nerves which are the unit of + + align:start position:0% +nerves which are the unit of + + + align:start position:0% +nerves which are the unit of +communication throughout the body is + + align:start position:0% +communication throughout the body is + + + align:start position:0% +communication throughout the body is +enormous and it Embraces every single + + align:start position:0% +enormous and it Embraces every single + + + align:start position:0% +enormous and it Embraces every single +part of the + + align:start position:0% +part of the + + + align:start position:0% +part of the +body + + align:start position:0% +body + + + align:start position:0% +body +almost the cell that's involved in + + align:start position:0% +almost the cell that's involved in + + + align:start position:0% +almost the cell that's involved in +communication we'll draw this out in a + + align:start position:0% +communication we'll draw this out in a + + + align:start position:0% +communication we'll draw this out in a +moment is the neuron and one of the + + align:start position:0% +moment is the neuron and one of the + + + align:start position:0% +moment is the neuron and one of the +things about neurons is that they've got + + align:start position:0% +things about neurons is that they've got + + + align:start position:0% +things about neurons is that they've got +very long processes called axons that we + + align:start position:0% +very long processes called axons that we + + + align:start position:0% +very long processes called axons that we +will deal with in depth today but let's + + align:start position:0% +will deal with in depth today but let's + + + align:start position:0% +will deal with in depth today but let's +phrase + + align:start position:0% +phrase + + + align:start position:0% +phrase +things more intuitively this is what our + + align:start position:0% +things more intuitively this is what our + + + align:start position:0% +things more intuitively this is what our +brains look like they in fact do not + + align:start position:0% +brains look like they in fact do not + + + align:start position:0% +brains look like they in fact do not +have nerves innovating them and so if + + align:start position:0% +have nerves innovating them and so if + + + align:start position:0% +have nerves innovating them and so if +you actually have brain surgery you can + + align:start position:0% +you actually have brain surgery you can + + + align:start position:0% +you actually have brain surgery you can +really be awake during surgery because + + align:start position:0% +really be awake during surgery because + + + align:start position:0% +really be awake during surgery because +there are no nerves within the brain or + + align:start position:0% +there are no nerves within the brain or + + + align:start position:0% +there are no nerves within the brain or +at least no pain receptors within the + + align:start position:0% +at least no pain receptors within the + + + align:start position:0% +at least no pain receptors within the +brain of course the brain is nerves but + + align:start position:0% +brain of course the brain is nerves but + + + align:start position:0% +brain of course the brain is nerves but +there are no pain receptors in the brain + + align:start position:0% +there are no pain receptors in the brain + + + align:start position:0% +there are no pain receptors in the brain +okay human brain + + align:start position:0% +okay human brain + + + align:start position:0% +okay human brain +billions and billions and trillions of + + align:start position:0% +billions and billions and trillions of + + + align:start position:0% +billions and billions and trillions of +neurons we'll talk about numbers in + + align:start position:0% +neurons we'll talk about numbers in + + + align:start position:0% +neurons we'll talk about numbers in +future lectures but + + align:start position:0% +future lectures but + + + align:start position:0% +future lectures but +let's look a little more deeply in the + + align:start position:0% +let's look a little more deeply in the + + + align:start position:0% +let's look a little more deeply in the +brain so you can see how packed it is + + align:start position:0% +brain so you can see how packed it is + + + align:start position:0% +brain so you can see how packed it is +with neurons and how the connections + + align:start position:0% +with neurons and how the connections + + + align:start position:0% +with neurons and how the connections +between the neurons are so unbelievably + + align:start position:0% +between the neurons are so unbelievably + + + align:start position:0% +between the neurons are so unbelievably +complex that thinking about how you use + + align:start position:0% +complex that thinking about how you use + + + align:start position:0% +complex that thinking about how you use +circuitry to construct the human nervous + + align:start position:0% +circuitry to construct the human nervous + + + align:start position:0% +circuitry to construct the human nervous +system or indeed that of most animals is + + align:start position:0% +system or indeed that of most animals is + + + align:start position:0% +system or indeed that of most animals is +an enormous problem professor Sebastian + + align:start position:0% +an enormous problem professor Sebastian + + + align:start position:0% +an enormous problem professor Sebastian +Sun here whose name is off the screen + + align:start position:0% +Sun here whose name is off the screen + + + align:start position:0% +Sun here whose name is off the screen +and I apologize to him it's the screen + + align:start position:0% +and I apologize to him it's the screen + + + align:start position:0% +and I apologize to him it's the screen +snafu it'll be on your um PowerPoints + + align:start position:0% +snafu it'll be on your um PowerPoints + + + align:start position:0% +snafu it'll be on your um PowerPoints +when you download these from the web has + + align:start position:0% +when you download these from the web has + + + align:start position:0% +when you download these from the web has +been or is working on the task of + + align:start position:0% +been or is working on the task of + + + align:start position:0% +been or is working on the task of +putting together all the connections in + + align:start position:0% +putting together all the connections in + + + align:start position:0% +putting together all the connections in +the human brain and starting with a + + align:start position:0% +the human brain and starting with a + + + align:start position:0% +the human brain and starting with a +little cube of brain this is about a 100 + + align:start position:0% +little cube of brain this is about a 100 + + + align:start position:0% +little cube of brain this is about a 100 +microns it's not quite a cube but it's + + align:start position:0% +microns it's not quite a cube but it's + + + align:start position:0% +microns it's not quite a cube but it's +approximately 100 Micron + + align:start position:0% +approximately 100 Micron + + + align:start position:0% +approximately 100 Micron +Cube he's worked to try try to figure + + align:start position:0% +Cube he's worked to try try to figure + + + align:start position:0% +Cube he's worked to try try to figure +out what all the cell connections are + + align:start position:0% +out what all the cell connections are + + + align:start position:0% +out what all the cell connections are +and what all the cells are within this + + align:start position:0% +and what all the cells are within this + + + align:start position:0% +and what all the cells are within this +little tiny cube of brain which is just + + align:start position:0% +little tiny cube of brain which is just + + + align:start position:0% +little tiny cube of brain which is just +a tiny tiny fraction of your + + align:start position:0% +a tiny tiny fraction of your + + + align:start position:0% +a tiny tiny fraction of your +brain so look at this this is an + + align:start position:0% +brain so look at this this is an + + + align:start position:0% +brain so look at this this is an +electron + + align:start position:0% +electron + + + align:start position:0% +electron +micrograph that he's put a bunch of + + align:start position:0% +micrograph that he's put a bunch of + + + align:start position:0% +micrograph that he's put a bunch of +electron micrographs together to build + + align:start position:0% +electron micrographs together to build + + + align:start position:0% +electron micrographs together to build +this 3D structure and now his students + + align:start position:0% +this 3D structure and now his students + + + align:start position:0% +this 3D structure and now his students +and those of professor lickman at + + align:start position:0% +and those of professor lickman at + + + align:start position:0% +and those of professor lickman at +Harvard go and outline a particular cell + + align:start position:0% +Harvard go and outline a particular cell + + + align:start position:0% +Harvard go and outline a particular cell +in serial sections through this Cube + + align:start position:0% +in serial sections through this Cube + + + align:start position:0% +in serial sections through this Cube +these are very tiny sections these are + + align:start position:0% +these are very tiny sections these are + + + align:start position:0% +these are very tiny sections these are +about five nanometer sections and then + + align:start position:0% +about five nanometer sections and then + + + align:start position:0% +about five nanometer sections and then +they put these sections together and you + + align:start position:0% +they put these sections together and you + + + align:start position:0% +they put these sections together and you +can get the three-dimensional structure + + align:start position:0% +can get the three-dimensional structure + + + align:start position:0% +can get the three-dimensional structure +of the neuron as it's going through the + + align:start position:0% +of the neuron as it's going through the + + + align:start position:0% +of the neuron as it's going through the +through the cube and you can start to + + align:start position:0% +through the cube and you can start to + + + align:start position:0% +through the cube and you can start to +map how this neuron lies next to other + + align:start position:0% +map how this neuron lies next to other + + + align:start position:0% +map how this neuron lies next to other +neurons okay there it's going + + align:start position:0% +neurons okay there it's going + + + align:start position:0% +neurons okay there it's going +backwards and there are two cells lying + + align:start position:0% +backwards and there are two cells lying + + + align:start position:0% +backwards and there are two cells lying +next to one another that you can get in + + align:start position:0% +next to one another that you can get in + + + align:start position:0% +next to one another that you can get in +3D rendering with this very painstaking + + align:start position:0% +3D rendering with this very painstaking + + + align:start position:0% +3D rendering with this very painstaking +process of first getting sections of the + + align:start position:0% +process of first getting sections of the + + + align:start position:0% +process of first getting sections of the +brain putting them all together into a + + align:start position:0% +brain putting them all together into a + + + align:start position:0% +brain putting them all together into a +chunk and then deconstructing the + + align:start position:0% +chunk and then deconstructing the + + + align:start position:0% +chunk and then deconstructing the +individual cell shapes within that chunk + + align:start position:0% +individual cell shapes within that chunk + + + align:start position:0% +individual cell shapes within that chunk +if you do that for the whole chunk of + + align:start position:0% +if you do that for the whole chunk of + + + align:start position:0% +if you do that for the whole chunk of +tissue this is what you get there's that + + align:start position:0% +tissue this is what you get there's that + + + align:start position:0% +tissue this is what you get there's that +red and that green neuron here's a blue + + align:start position:0% +red and that green neuron here's a blue + + + align:start position:0% +red and that green neuron here's a blue +one there's a yellow one lime purple + + align:start position:0% +one there's a yellow one lime purple + + + align:start position:0% +one there's a yellow one lime purple +red dark blue yellow orang Orange it's + + align:start position:0% +red dark blue yellow orang Orange it's + + + align:start position:0% +red dark blue yellow orang Orange it's +daunting + + align:start position:0% +daunting + + + align:start position:0% +daunting +okay there you go in that tiny little + + align:start position:0% +okay there you go in that tiny little + + + align:start position:0% +okay there you go in that tiny little +chunk of brain that is how packed the + + align:start position:0% +chunk of brain that is how packed the + + + align:start position:0% +chunk of brain that is how packed the +cells are and the connections between + + align:start position:0% +cells are and the connections between + + + align:start position:0% +cells are and the connections between +them are enormous and that is just less + + align:start position:0% +them are enormous and that is just less + + + align:start position:0% +them are enormous and that is just less +than a millionth of your brain so to + + align:start position:0% +than a millionth of your brain so to + + + align:start position:0% +than a millionth of your brain so to +figure out all the connections all the + + align:start position:0% +figure out all the connections all the + + + align:start position:0% +figure out all the connections all the +circuitry in the nervous system is an + + align:start position:0% +circuitry in the nervous system is an + + + align:start position:0% +circuitry in the nervous system is an +enormous task and we don't know it we'll + + align:start position:0% +enormous task and we don't know it we'll + + + align:start position:0% +enormous task and we don't know it we'll +talk about what we do know later on but + + align:start position:0% +talk about what we do know later on but + + + align:start position:0% +talk about what we do know later on but +I wanted to frame the problem for you so + + align:start position:0% +I wanted to frame the problem for you so + + + align:start position:0% +I wanted to frame the problem for you so +that you have a sense of where we're + + align:start position:0% +that you have a sense of where we're + + + align:start position:0% +that you have a sense of where we're +trying to go all right let's go back to + + align:start position:0% +trying to go all right let's go back to + + + align:start position:0% +trying to go all right let's go back to +the + + align:start position:0% +the + + + align:start position:0% +the +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +neuron and let's talk about cell type + + align:start position:0% +neuron and let's talk about cell type + + + align:start position:0% +neuron and let's talk about cell type +and how cell + + align:start position:0% +and how cell + + + align:start position:0% +and how cell +type is important for thinking about + + align:start position:0% +type is important for thinking about + + + align:start position:0% +type is important for thinking about +signaling in the nervous + + align:start position:0% +signaling in the nervous + + + align:start position:0% +signaling in the nervous +system so like everything else in the + + align:start position:0% +system so like everything else in the + + + align:start position:0% +system so like everything else in the +body + + align:start position:0% +body + + + align:start position:0% +body +communication uses cells as its currency + + align:start position:0% +communication uses cells as its currency + + + align:start position:0% +communication uses cells as its currency +and the cell type + + align:start position:0% +and the cell type + + + align:start position:0% +and the cell type +is the special car is a special kind of + + align:start position:0% +is the special car is a special kind of + + + align:start position:0% +is the special car is a special kind of +cell + + align:start position:0% +cell + + + align:start position:0% +cell +type which is the + + align:start position:0% + + + + align:start position:0% + +neuron so + + align:start position:0% +neuron so + + + align:start position:0% +neuron so +neurons are the + + align:start position:0% + + + + align:start position:0% + +connecting + + align:start position:0% +connecting + + + align:start position:0% +connecting +wiring + + align:start position:0% +wiring + + + align:start position:0% +wiring +cells there's a second type of cell in + + align:start position:0% +cells there's a second type of cell in + + + align:start position:0% +cells there's a second type of cell in +the nervous system that is really + + align:start position:0% +the nervous system that is really + + + align:start position:0% +the nervous system that is really +pivotal for nervous system function that + + align:start position:0% +pivotal for nervous system function that + + + align:start position:0% +pivotal for nervous system function that +are called + + align:start position:0% +are called + + + align:start position:0% +are called +Gia and these are cells which are + + align:start position:0% +Gia and these are cells which are + + + align:start position:0% +Gia and these are cells which are +referred to as support cells but that's + + align:start position:0% +referred to as support cells but that's + + + align:start position:0% +referred to as support cells but that's +not really fair they guide neurons and + + align:start position:0% +not really fair they guide neurons and + + + align:start position:0% +not really fair they guide neurons and +as we'll mention later they also + + align:start position:0% +as we'll mention later they also + + + align:start position:0% +as we'll mention later they also +insulate neurons so that the wires don't + + align:start position:0% +insulate neurons so that the wires don't + + + align:start position:0% +insulate neurons so that the wires don't +short circuit so they guide and insulate + + align:start position:0% + + + + align:start position:0% + +neurons the structure of the neuron is + + align:start position:0% +neurons the structure of the neuron is + + + align:start position:0% +neurons the structure of the neuron is +important for to understand its function + + align:start position:0% +important for to understand its function + + + align:start position:0% +important for to understand its function +like all cells it's + + align:start position:0% +like all cells it's + + + align:start position:0% +like all cells it's +got a nucleus and + + align:start position:0% +got a nucleus and + + + align:start position:0% +got a nucleus and +cytoplasm and here it is the nucleus the + + align:start position:0% +cytoplasm and here it is the nucleus the + + + align:start position:0% +cytoplasm and here it is the nucleus the +cytoplasm and this region of the neuron + + align:start position:0% +cytoplasm and this region of the neuron + + + align:start position:0% +cytoplasm and this region of the neuron +is called the cell + + align:start position:0% + + + + align:start position:0% + +body but unlike other cells coming out + + align:start position:0% +body but unlike other cells coming out + + + align:start position:0% +body but unlike other cells coming out +from this cell body there are processes + + align:start position:0% +from this cell body there are processes + + + align:start position:0% +from this cell body there are processes +and they are very substantial processes + + align:start position:0% +and they are very substantial processes + + + align:start position:0% +and they are very substantial processes +on one side of the cell body are usually + + align:start position:0% +on one side of the cell body are usually + + + align:start position:0% +on one side of the cell body are usually +fairly short + + align:start position:0% +fairly short + + + align:start position:0% +fairly short +processes they could be branched and + + align:start position:0% +processes they could be branched and + + + align:start position:0% +processes they could be branched and +there can be Bunches of them and these + + align:start position:0% +there can be Bunches of them and these + + + align:start position:0% +there can be Bunches of them and these +are called + + align:start position:0% + + + + align:start position:0% + +dendrites okay dandrites are processes + + align:start position:0% +dendrites okay dandrites are processes + + + align:start position:0% +dendrites okay dandrites are processes +that receive a signal so they are the + + align:start position:0% +that receive a signal so they are the + + + align:start position:0% +that receive a signal so they are the +place where there is a + + align:start position:0% +place where there is a + + + align:start position:0% +place where there is a +signaling I'm going to get rid of that + + align:start position:0% +signaling I'm going to get rid of that + + + align:start position:0% +signaling I'm going to get rid of that +dendr there is a sign sign in + + align:start position:0% + + + + align:start position:0% + +input the signal that dendrites receive + + align:start position:0% +input the signal that dendrites receive + + + align:start position:0% +input the signal that dendrites receive +moves through the cell body and into + + align:start position:0% +moves through the cell body and into + + + align:start position:0% +moves through the cell body and into +another process which is called the axon + + align:start position:0% +another process which is called the axon + + + align:start position:0% +another process which is called the axon +and is very + + align:start position:0% +and is very + + + align:start position:0% +and is very +long and the fact that it is very + + align:start position:0% +long and the fact that it is very + + + align:start position:0% +long and the fact that it is very +long is actually what this lecture is + + align:start position:0% +long is actually what this lecture is + + + align:start position:0% +long is actually what this lecture is +all about so the axon is the wire axons + + align:start position:0% +all about so the axon is the wire axons + + + align:start position:0% +all about so the axon is the wire axons +can be up to a meter long + + align:start position:0% +can be up to a meter long + + + align:start position:0% +can be up to a meter long +so here's the + + align:start position:0% + + + + align:start position:0% + +axon and there are axons that start in + + align:start position:0% +axon and there are axons that start in + + + align:start position:0% +axon and there are axons that start in +your spinal cord and move all the way + + align:start position:0% +your spinal cord and move all the way + + + align:start position:0% +your spinal cord and move all the way +down your leg from a single cell okay + + align:start position:0% +down your leg from a single cell okay + + + align:start position:0% +down your leg from a single cell okay +we'll talk about why that is in a moment + + align:start position:0% +we'll talk about why that is in a moment + + + align:start position:0% +we'll talk about why that is in a moment +these axons Branch at their + + align:start position:0% +these axons Branch at their + + + align:start position:0% +these axons Branch at their +ends and they connect to another neuron + + align:start position:0% +ends and they connect to another neuron + + + align:start position:0% +ends and they connect to another neuron +or something else but we'll draw another + + align:start position:0% +or something else but we'll draw another + + + align:start position:0% +or something else but we'll draw another +neuron here's another + + align:start position:0% +neuron here's another + + + align:start position:0% +neuron here's another +neuron with its + + align:start position:0% +neuron with its + + + align:start position:0% +neuron with its +dendrites and another + + align:start position:0% +dendrites and another + + + align:start position:0% +dendrites and another +axon the connection oh here's neuron + + align:start position:0% + + + + align:start position:0% + +one and neuron + + align:start position:0% + + + + align:start position:0% + +2 and the connection between axons and + + align:start position:0% +2 and the connection between axons and + + + align:start position:0% +2 and the connection between axons and +dendrites or as you'll discover axons in + + align:start position:0% +dendrites or as you'll discover axons in + + + align:start position:0% +dendrites or as you'll discover axons in +the cell body is called a + + align:start position:0% +the cell body is called a + + + align:start position:0% +the cell body is called a +synapse some people say + + align:start position:0% +synapse some people say + + + align:start position:0% +synapse some people say +syapse that's the + + align:start position:0% +syapse that's the + + + align:start position:0% +syapse that's the +connection either is + + align:start position:0% + + + + align:start position:0% + +okay and the thing + + align:start position:0% +okay and the thing + + + align:start position:0% +okay and the thing +is that this input that is way over on + + align:start position:0% +is that this input that is way over on + + + align:start position:0% +is that this input that is way over on +the left hand side of the board is + + align:start position:0% +the left hand side of the board is + + + align:start position:0% +the left hand side of the board is +transmitted along the Axon + + align:start position:0% + + + + align:start position:0% + +into the next + + align:start position:0% + + + + align:start position:0% + +neuron and then along the next + + align:start position:0% +neuron and then along the next + + + align:start position:0% +neuron and then along the next +neuron this is the + + align:start position:0% + + + + align:start position:0% + +signal and we have to think about why + + align:start position:0% +signal and we have to think about why + + + align:start position:0% +signal and we have to think about why +cells might want to have these very long + + align:start position:0% +cells might want to have these very long + + + align:start position:0% +cells might want to have these very long +processes to do this and then how the + + align:start position:0% +processes to do this and then how the + + + align:start position:0% +processes to do this and then how the +signal is + + align:start position:0% + + + + align:start position:0% + +transmitted the reason that cells have + + align:start position:0% +transmitted the reason that cells have + + + align:start position:0% +transmitted the reason that cells have +got these long processes rather than + + align:start position:0% +got these long processes rather than + + + align:start position:0% +got these long processes rather than +well well let's actually step back a + + align:start position:0% +well well let's actually step back a + + + align:start position:0% +well well let's actually step back a +moment okay let's think about how cells + + align:start position:0% +moment okay let's think about how cells + + + align:start position:0% +moment okay let's think about how cells +might communicate with one another you + + align:start position:0% +might communicate with one another you + + + align:start position:0% +might communicate with one another you +could imagine a whole bunch of little + + align:start position:0% +could imagine a whole bunch of little + + + align:start position:0% +could imagine a whole bunch of little +round cells all lined up so that there's + + align:start position:0% +round cells all lined up so that there's + + + align:start position:0% +round cells all lined up so that there's +a meter of them that go from your spinal + + align:start position:0% +a meter of them that go from your spinal + + + align:start position:0% +a meter of them that go from your spinal +cord down to your leg okay and that + + align:start position:0% +cord down to your leg okay and that + + + align:start position:0% +cord down to your leg okay and that +would give you a chain of communication + + align:start position:0% +would give you a chain of communication + + + align:start position:0% +would give you a chain of communication +from your spinal cord to your leg and + + align:start position:0% +from your spinal cord to your leg and + + + align:start position:0% +from your spinal cord to your leg and +you could have one back to your brain + + align:start position:0% +you could have one back to your brain + + + align:start position:0% +you could have one back to your brain +and so on and that in theory would work + + align:start position:0% +and so on and that in theory would work + + + align:start position:0% +and so on and that in theory would work +okay but it turns out that cell cell + + align:start position:0% +okay but it turns out that cell cell + + + align:start position:0% +okay but it turns out that cell cell +communication is very slow + + align:start position:0% +communication is very slow + + + align:start position:0% +communication is very slow +and that cells have figured out a way to + + align:start position:0% +and that cells have figured out a way to + + + align:start position:0% +and that cells have figured out a way to +transmit a signal along their own length + + align:start position:0% +transmit a signal along their own length + + + align:start position:0% +transmit a signal along their own length +that is very rapid you know that there + + align:start position:0% +that is very rapid you know that there + + + align:start position:0% +that is very rapid you know that there +is a finite time between getting a + + align:start position:0% +is a finite time between getting a + + + align:start position:0% +is a finite time between getting a +stimulus and a response you know you + + align:start position:0% +stimulus and a response you know you + + + align:start position:0% +stimulus and a response you know you +touch something hot you can tell it + + align:start position:0% +touch something hot you can tell it + + + align:start position:0% +touch something hot you can tell it +actually takes a moment before you + + align:start position:0% +actually takes a moment before you + + + align:start position:0% +actually takes a moment before you +figure out it's hot that's a speed of + + align:start position:0% +figure out it's hot that's a speed of + + + align:start position:0% +figure out it's hot that's a speed of +transmission of the signal up into your + + align:start position:0% +transmission of the signal up into your + + + align:start position:0% +transmission of the signal up into your +brain and you say wow that's hot move my + + align:start position:0% +brain and you say wow that's hot move my + + + align:start position:0% +brain and you say wow that's hot move my +finger okay if you had cells that were + + align:start position:0% +finger okay if you had cells that were + + + align:start position:0% +finger okay if you had cells that were +connecting rather than long processes of + + align:start position:0% +connecting rather than long processes of + + + align:start position:0% +connecting rather than long processes of +one one cell it would take you that much + + align:start position:0% +one one cell it would take you that much + + + align:start position:0% +one one cell it would take you that much +longer to actually make that maybe 10 + + align:start position:0% +longer to actually make that maybe 10 + + + align:start position:0% +longer to actually make that maybe 10 +times longer to make that connection and + + align:start position:0% +times longer to make that connection and + + + align:start position:0% +times longer to make that connection and +you'd get a badly burnt finger excuse me + + align:start position:0% +you'd get a badly burnt finger excuse me + + + align:start position:0% +you'd get a badly burnt finger excuse me +all right so the axon is the thing that + + align:start position:0% +all right so the axon is the thing that + + + align:start position:0% +all right so the axon is the thing that +allows rapid transmission of the + + align:start position:0% + + + + align:start position:0% + +signal so the axon is + + align:start position:0% +signal so the axon is + + + align:start position:0% +signal so the axon is +long it leads to to an intracellular + + align:start position:0% + + + + align:start position:0% + +signal and this is very + + align:start position:0% + + + + align:start position:0% + +rapid relative to an inter cellular + + align:start position:0% + + + + align:start position:0% + +signal but how do you transmit a signal + + align:start position:0% +signal but how do you transmit a signal + + + align:start position:0% +signal but how do you transmit a signal +along a + + align:start position:0% +along a + + + align:start position:0% +along a +cell while axon used to do this by using + + align:start position:0% +cell while axon used to do this by using + + + align:start position:0% +cell while axon used to do this by using +movement of + + align:start position:0% + + + + align:start position:0% + +ions so the signal along the axon is due + + align:start position:0% +ions so the signal along the axon is due + + + align:start position:0% +ions so the signal along the axon is due +to movement of + + align:start position:0% +to movement of + + + align:start position:0% +to movement of +ions and this is + + align:start position:0% +ions and this is + + + align:start position:0% +ions and this is +called an action + + align:start position:0% +called an action + + + align:start position:0% +called an action +potential as we will discuss + + align:start position:0% + + + + align:start position:0% + +and this process draws on a property of + + align:start position:0% +and this process draws on a property of + + + align:start position:0% +and this process draws on a property of +all cells that neurons have capitalized + + align:start position:0% +all cells that neurons have capitalized + + + align:start position:0% +all cells that neurons have capitalized +on so almost all cells have got a + + align:start position:0% +on so almost all cells have got a + + + align:start position:0% +on so almost all cells have got a +potential difference across their + + align:start position:0% +potential difference across their + + + align:start position:0% +potential difference across their +membrane because there's a charge + + align:start position:0% +membrane because there's a charge + + + align:start position:0% +membrane because there's a charge +difference across the plasma + + align:start position:0% + + + + align:start position:0% + +membrane so almost all cells have what + + align:start position:0% +membrane so almost all cells have what + + + align:start position:0% +membrane so almost all cells have what +is called a membrane potential + + align:start position:0% +is called a membrane potential + + + align:start position:0% +is called a membrane potential +which is a membrane potential + + align:start position:0% + + + + align:start position:0% + +difference and in + + align:start position:0% +difference and in + + + align:start position:0% +difference and in +general cells are more positive outside + + align:start position:0% +general cells are more positive outside + + + align:start position:0% +general cells are more positive outside +than they are inside so outside the + + align:start position:0% + + + + align:start position:0% + +cell and this is worth your + + align:start position:0% +cell and this is worth your + + + align:start position:0% +cell and this is worth your +remembering it is more + + align:start position:0% +remembering it is more + + + align:start position:0% +remembering it is more +positive and it's more positive because + + align:start position:0% +positive and it's more positive because + + + align:start position:0% +positive and it's more positive because +there's a lot of sodium ion + + align:start position:0% +there's a lot of sodium ion + + + align:start position:0% +there's a lot of sodium ion +you'll see why this is important there's + + align:start position:0% +you'll see why this is important there's + + + align:start position:0% +you'll see why this is important there's +low potassium ion and there's some high + + align:start position:0% +low potassium ion and there's some high + + + align:start position:0% +low potassium ion and there's some high +chloride + + align:start position:0% +chloride + + + align:start position:0% +chloride +ion but really the thing that's + + align:start position:0% +ion but really the thing that's + + + align:start position:0% +ion but really the thing that's +important is that there's very + + align:start position:0% + + + + align:start position:0% + +high sodium concentration outside the + + align:start position:0% +high sodium concentration outside the + + + align:start position:0% +high sodium concentration outside the +cell conversely inside the + + align:start position:0% +cell conversely inside the + + + align:start position:0% +cell conversely inside the +cell is obviously more + + align:start position:0% + + + + align:start position:0% + +negative sodium is low + + align:start position:0% + + + + align:start position:0% + +potassium is + + align:start position:0% +potassium is + + + align:start position:0% +potassium is +higher but still not very high and + + align:start position:0% +higher but still not very high and + + + align:start position:0% +higher but still not very high and +there's a bunch of + + align:start position:0% +there's a bunch of + + + align:start position:0% +there's a bunch of +anions that are kind of Trapped in the + + align:start position:0% +anions that are kind of Trapped in the + + + align:start position:0% +anions that are kind of Trapped in the +cell + + align:start position:0% +cell + + + align:start position:0% +cell +okay why is this + + align:start position:0% +okay why is this + + + align:start position:0% +okay why is this +important let me see what I have next + + align:start position:0% +important let me see what I have next + + + align:start position:0% +important let me see what I have next +here okay most cells show a potential + + align:start position:0% +here okay most cells show a potential + + + align:start position:0% +here okay most cells show a potential +difference here it is here has written + + align:start position:0% +difference here it is here has written + + + align:start position:0% +difference here it is here has written +the potential difference neurons are + + align:start position:0% +the potential difference neurons are + + + align:start position:0% +the potential difference neurons are +somewhere between -70 and -60 molts + + align:start position:0% +somewhere between -70 and -60 molts + + + align:start position:0% +somewhere between -70 and -60 molts +where where you're talking about the + + align:start position:0% +where where you're talking about the + + + align:start position:0% +where where you're talking about the +relative potential difference inside to + + align:start position:0% +relative potential difference inside to + + + align:start position:0% +relative potential difference inside to +outside that's why it's negative and you + + align:start position:0% +outside that's why it's negative and you + + + align:start position:0% +outside that's why it's negative and you +can see tumor cells actually have got a + + align:start position:0% +can see tumor cells actually have got a + + + align:start position:0% +can see tumor cells actually have got a +very low membrane potential which may or + + align:start position:0% +very low membrane potential which may or + + + align:start position:0% +very low membrane potential which may or +may not be + + align:start position:0% + + + + align:start position:0% + +significant what is the nature of the + + align:start position:0% +significant what is the nature of the + + + align:start position:0% +significant what is the nature of the +signal that neurons use to + + align:start position:0% +signal that neurons use to + + + align:start position:0% +signal that neurons use to +transmit from from the input along the + + align:start position:0% +transmit from from the input along the + + + align:start position:0% +transmit from from the input along the +axon to the next cell + + align:start position:0% +axon to the next cell + + + align:start position:0% +axon to the next cell +particularly what is the signal that's + + align:start position:0% +particularly what is the signal that's + + + align:start position:0% +particularly what is the signal that's +transmitted along the axon and the + + align:start position:0% +transmitted along the axon and the + + + align:start position:0% +transmitted along the axon and the +answer is something called an action + + align:start position:0% +answer is something called an action + + + align:start position:0% +answer is something called an action +potential it's the + + align:start position:0% +potential it's the + + + align:start position:0% +potential it's the +signal transmitted along the + + align:start position:0% + + + + align:start position:0% + +axon the + + align:start position:0% +axon the + + + align:start position:0% +axon the +wire that I referred to + + align:start position:0% +wire that I referred to + + + align:start position:0% +wire that I referred to +and an action potential which I'm going + + align:start position:0% +and an action potential which I'm going + + + align:start position:0% +and an action potential which I'm going +to + + align:start position:0% +to + + + align:start position:0% +to +abbreviate as + + align:start position:0% +abbreviate as + + + align:start position:0% +abbreviate as +AP will Define and you'll you'll + + align:start position:0% +AP will Define and you'll you'll + + + align:start position:0% +AP will Define and you'll you'll +understand this in a moment as a local + + align:start position:0% +understand this in a moment as a local + + + align:start position:0% +understand this in a moment as a local +transient + + align:start position:0% + + + + align:start position:0% + +depolarization local transient just + + align:start position:0% +depolarization local transient just + + + align:start position:0% +depolarization local transient just +lasts a moment + + align:start position:0% +lasts a moment + + + align:start position:0% +lasts a moment +depolarization change in membrane + + align:start position:0% +depolarization change in membrane + + + align:start position:0% +depolarization change in membrane +potential + + align:start position:0% + + + + align:start position:0% + +all right and I'm going to do most of + + align:start position:0% +all right and I'm going to do most of + + + align:start position:0% +all right and I'm going to do most of +this on the board you have a handout but + + align:start position:0% +this on the board you have a handout but + + + align:start position:0% +this on the board you have a handout but +I'm going to do most of this on the + + align:start position:0% +I'm going to do most of this on the + + + align:start position:0% +I'm going to do most of this on the +board because it works better as a + + align:start position:0% +board because it works better as a + + + align:start position:0% +board because it works better as a +conversation than a demonstration let's + + align:start position:0% +conversation than a demonstration let's + + + align:start position:0% +conversation than a demonstration let's +draw a bit of an + + align:start position:0% +draw a bit of an + + + align:start position:0% +draw a bit of an +axon here's the axon two plasma + + align:start position:0% +axon here's the axon two plasma + + + align:start position:0% +axon here's the axon two plasma +membranes + + align:start position:0% +membranes + + + align:start position:0% +membranes +outside + + align:start position:0% +outside + + + align:start position:0% +outside +inside + + align:start position:0% +inside + + + align:start position:0% +inside +outside so this is the + + align:start position:0% + + + + align:start position:0% + +axon plasma membrane PM pm and what we + + align:start position:0% +axon plasma membrane PM pm and what we + + + align:start position:0% +axon plasma membrane PM pm and what we +are going to do and here's a + + align:start position:0% +are going to do and here's a + + + align:start position:0% +are going to do and here's a +cytoplasm what we are going to do is + + align:start position:0% +cytoplasm what we are going to do is + + + align:start position:0% +cytoplasm what we are going to do is +take a chunk of the axon and blow it up + + align:start position:0% +take a chunk of the axon and blow it up + + + align:start position:0% +take a chunk of the axon and blow it up +and focus on just one plasma membrane on + + align:start position:0% +and focus on just one plasma membrane on + + + align:start position:0% +and focus on just one plasma membrane on +one side of the axon and look and see in + + align:start position:0% +one side of the axon and look and see in + + + align:start position:0% +one side of the axon and look and see in +detail what is going on there so let's + + align:start position:0% +detail what is going on there so let's + + + align:start position:0% +detail what is going on there so let's +take this chunk and blow it up so that + + align:start position:0% +take this chunk and blow it up so that + + + align:start position:0% +take this chunk and blow it up so that +we now have the plasma + + align:start position:0% +we now have the plasma + + + align:start position:0% +we now have the plasma +membrane and you remember it's a lipid + + align:start position:0% +membrane and you remember it's a lipid + + + align:start position:0% +membrane and you remember it's a lipid +bilayer but I'm drawing it as a single + + align:start position:0% +bilayer but I'm drawing it as a single + + + align:start position:0% +bilayer but I'm drawing it as a single +line because it's really a pain to draw + + align:start position:0% +line because it's really a pain to draw + + + align:start position:0% +line because it's really a pain to draw +it as a lipid bilayer but you know it's + + align:start position:0% +it as a lipid bilayer but you know it's + + + align:start position:0% +it as a lipid bilayer but you know it's +a lipid + + align:start position:0% +a lipid + + + align:start position:0% +a lipid +bilayer on one side and here's outside + + align:start position:0% +bilayer on one side and here's outside + + + align:start position:0% +bilayer on one side and here's outside +the cell and inside the cell on one + + align:start position:0% +the cell and inside the cell on one + + + align:start position:0% +the cell and inside the cell on one +side there are lots of positive + + align:start position:0% +side there are lots of positive + + + align:start position:0% +side there are lots of positive +charges and on the other side there are + + align:start position:0% +charges and on the other side there are + + + align:start position:0% +charges and on the other side there are +fewer and more relatively more negative + + align:start position:0% +fewer and more relatively more negative + + + align:start position:0% +fewer and more relatively more negative +charges + + align:start position:0% +charges + + + align:start position:0% +charges +okay when the axon looks like this with + + align:start position:0% +okay when the axon looks like this with + + + align:start position:0% +okay when the axon looks like this with +this balance of positive and negative + + align:start position:0% +this balance of positive and negative + + + align:start position:0% +this balance of positive and negative +charges it's said to be at resting + + align:start position:0% + + + + align:start position:0% + +potential and resting + + align:start position:0% +potential and resting + + + align:start position:0% +potential and resting +potential is about- 60 + + align:start position:0% + + + + align:start position:0% + +molts okay what's our goal our goal is + + align:start position:0% +molts okay what's our goal our goal is + + + align:start position:0% +molts okay what's our goal our goal is +to start + + align:start position:0% + + + + align:start position:0% + +here at this asterisk and to transmit a + + align:start position:0% +here at this asterisk and to transmit a + + + align:start position:0% +here at this asterisk and to transmit a +signal along the length of this piece of + + align:start position:0% +signal along the length of this piece of + + + align:start position:0% +signal along the length of this piece of +axon and to transmit the signal in a + + align:start position:0% +axon and to transmit the signal in a + + + align:start position:0% +axon and to transmit the signal in a +directional + + align:start position:0% +directional + + + align:start position:0% +directional +way so our goal excuse me is to transmit + + align:start position:0% +way so our goal excuse me is to transmit + + + align:start position:0% +way so our goal excuse me is to transmit +a directional signal + + align:start position:0% + + + + align:start position:0% + +let's draw three time points Each of + + align:start position:0% +let's draw three time points Each of + + + align:start position:0% +let's draw three time points Each of +which have a plasma membrane of this + + align:start position:0% +which have a plasma membrane of this + + + align:start position:0% +which have a plasma membrane of this +particular segment of axon okay and let + + align:start position:0% +particular segment of axon okay and let + + + align:start position:0% +particular segment of axon okay and let +us I'm going to move over a bit to this + + align:start position:0% +us I'm going to move over a bit to this + + + align:start position:0% +us I'm going to move over a bit to this +side of the + + align:start position:0% +side of the + + + align:start position:0% +side of the +board let's have them + + align:start position:0% + + + + align:start position:0% + +here here + + align:start position:0% +here here + + + align:start position:0% +here here +and + + align:start position:0% +and + + + align:start position:0% +and +here okay and so we're going to have a + + align:start position:0% +here okay and so we're going to have a + + + align:start position:0% +here okay and so we're going to have a +Time Vector going diagonally across the + + align:start position:0% +Time Vector going diagonally across the + + + align:start position:0% +Time Vector going diagonally across the +board and we started off with + + align:start position:0% +board and we started off with + + + align:start position:0% +board and we started off with +a something that looked like it did on + + align:start position:0% +a something that looked like it did on + + + align:start position:0% +a something that looked like it did on +the board above at resting potential and + + align:start position:0% +the board above at resting potential and + + + align:start position:0% +the board above at resting potential and +now we're going to over a very short + + align:start position:0% +now we're going to over a very short + + + align:start position:0% +now we're going to over a very short +segment of membrane we're going to + + align:start position:0% +segment of membrane we're going to + + + align:start position:0% +segment of membrane we're going to +reverse the membrane charge or the + + align:start position:0% +reverse the membrane charge or the + + + align:start position:0% +reverse the membrane charge or the +cell's going to do it so that on the + + align:start position:0% +cell's going to do it so that on the + + + align:start position:0% +cell's going to do it so that on the +outside now there's a little part of the + + align:start position:0% +outside now there's a little part of the + + + align:start position:0% +outside now there's a little part of the +membrane that's negative outside and + + align:start position:0% +membrane that's negative outside and + + + align:start position:0% +membrane that's negative outside and +positive inside and the rest is positive + + align:start position:0% +positive inside and the rest is positive + + + align:start position:0% +positive inside and the rest is positive +outside and negative + + align:start position:0% +outside and negative + + + align:start position:0% +outside and negative +inside over + + align:start position:0% +inside over + + + align:start position:0% +inside over +time this is called a + + align:start position:0% + + + + align:start position:0% + +depolarization a reversal of the + + align:start position:0% +depolarization a reversal of the + + + align:start position:0% +depolarization a reversal of the +membrane potential + + align:start position:0% +membrane potential + + + align:start position:0% +membrane potential +over + + align:start position:0% +over + + + align:start position:0% +over +time that depolarization that initial + + align:start position:0% +time that depolarization that initial + + + align:start position:0% +time that depolarization that initial +depolarization is going to rectify it's + + align:start position:0% +depolarization is going to rectify it's + + + align:start position:0% +depolarization is going to rectify it's +going to go back to how it was so you'll + + align:start position:0% +going to go back to how it was so you'll + + + align:start position:0% +going to go back to how it was so you'll +get positive charges outside + + align:start position:0% +get positive charges outside + + + align:start position:0% +get positive charges outside +again but the segment of membrane next + + align:start position:0% +again but the segment of membrane next + + + align:start position:0% +again but the segment of membrane next +door is going to + + align:start position:0% +door is going to + + + align:start position:0% +door is going to +depolarize so it now becomes negative + + align:start position:0% +depolarize so it now becomes negative + + + align:start position:0% +depolarize so it now becomes negative +outside and positive + + align:start position:0% +outside and positive + + + align:start position:0% +outside and positive +inside and the rest is positive outside + + align:start position:0% +inside and the rest is positive outside + + + align:start position:0% +inside and the rest is positive outside +and negative inside + + align:start position:0% +and negative inside + + + align:start position:0% +and negative inside +that little piece of membrane the second + + align:start position:0% +that little piece of membrane the second + + + align:start position:0% +that little piece of membrane the second +so that's depolarization one here's + + align:start position:0% +so that's depolarization one here's + + + align:start position:0% +so that's depolarization one here's +depolarization + + align:start position:0% +depolarization + + + align:start position:0% +depolarization +two again over time you're going to get + + align:start position:0% +two again over time you're going to get + + + align:start position:0% +two again over time you're going to get +rectification of that second + + align:start position:0% +rectification of that second + + + align:start position:0% +rectification of that second +depolarization and you got the idea now + + align:start position:0% +depolarization and you got the idea now + + + align:start position:0% +depolarization and you got the idea now +it's going to + + align:start position:0% +it's going to + + + align:start position:0% +it's going to +move further down the axon so here is + + align:start position:0% +move further down the axon so here is + + + align:start position:0% +move further down the axon so here is +depolarization + + align:start position:0% + + + + align:start position:0% + +three and you recall that this is + + align:start position:0% +three and you recall that this is + + + align:start position:0% +three and you recall that this is +outside and inside the axon so if you + + align:start position:0% +outside and inside the axon so if you + + + align:start position:0% +outside and inside the axon so if you +look at my diagram I haven't given you + + align:start position:0% +look at my diagram I haven't given you + + + align:start position:0% +look at my diagram I haven't given you +any mechanism but you can see here we + + align:start position:0% +any mechanism but you can see here we + + + align:start position:0% +any mechanism but you can see here we +have got a + + align:start position:0% +have got a + + + align:start position:0% +have got a +signal that is + + align:start position:0% +signal that is + + + align:start position:0% +signal that is +moving in this direction along the + + align:start position:0% +moving in this direction along the + + + align:start position:0% +moving in this direction along the +axon each of these depolarizations that + + align:start position:0% +axon each of these depolarizations that + + + align:start position:0% +axon each of these depolarizations that +I've drawn is called an action potential + + align:start position:0% + + + + align:start position:0% + +and I'll give you in a moment some more + + align:start position:0% +and I'll give you in a moment some more + + + align:start position:0% +and I'll give you in a moment some more +properties so that you'll know an action + + align:start position:0% +properties so that you'll know an action + + + align:start position:0% +properties so that you'll know an action +potential when you see one but there are + + align:start position:0% +potential when you see one but there are + + + align:start position:0% +potential when you see one but there are +a couple of questions that arise from + + align:start position:0% +a couple of questions that arise from + + + align:start position:0% +a couple of questions that arise from +this easy to draw diagram firstly how + + align:start position:0% +this easy to draw diagram firstly how + + + align:start position:0% +this easy to draw diagram firstly how +does this really happen how does the + + align:start position:0% +does this really happen how does the + + + align:start position:0% +does this really happen how does the +charges reverse across the membrane + + align:start position:0% +charges reverse across the membrane + + + align:start position:0% +charges reverse across the membrane +secondly why is the signal + + align:start position:0% +secondly why is the signal + + + align:start position:0% +secondly why is the signal +unidirectional why doesn't it go + + align:start position:0% +unidirectional why doesn't it go + + + align:start position:0% +unidirectional why doesn't it go +backwards and thirdly how do you reset + + align:start position:0% +backwards and thirdly how do you reset + + + align:start position:0% +backwards and thirdly how do you reset +the depolarization once it's happened + + align:start position:0% +the depolarization once it's happened + + + align:start position:0% +the depolarization once it's happened +and all of these things you'll see are + + align:start position:0% +and all of these things you'll see are + + + align:start position:0% +and all of these things you'll see are +connected but let's raise these + + align:start position:0% +connected but let's raise these + + + align:start position:0% +connected but let's raise these +questions so how does this + + align:start position:0% + + + + align:start position:0% + +happen why is it + + align:start position:0% + + + + align:start position:0% + +unidirectional and what does it + + align:start position:0% +unidirectional and what does it + + + align:start position:0% +unidirectional and what does it +mean or what is the mechanism of + + align:start position:0% +mean or what is the mechanism of + + + align:start position:0% +mean or what is the mechanism of +resetting the membrane potential after a + + align:start position:0% +resetting the membrane potential after a + + + align:start position:0% +resetting the membrane potential after a +depolarization has happened as for + + align:start position:0% +depolarization has happened as for + + + align:start position:0% +depolarization has happened as for +example + + align:start position:0% +example + + + align:start position:0% +example +here you have + + align:start position:0% +here you have + + + align:start position:0% +here you have +reset the membrane + + align:start position:0% + + + + align:start position:0% + +potential + + align:start position:0% + + + + align:start position:0% + +okay so the answer to all of this you + + align:start position:0% +okay so the answer to all of this you + + + align:start position:0% +okay so the answer to all of this you +know is complex and we'll ask we'll + + align:start position:0% +know is complex and we'll ask we'll + + + align:start position:0% +know is complex and we'll ask we'll +answer it in chunks as we tend to do in + + align:start position:0% +answer it in chunks as we tend to do in + + + align:start position:0% +answer it in chunks as we tend to do in +this class and the first thing we'll + + align:start position:0% +this class and the first thing we'll + + + align:start position:0% +this class and the first thing we'll +answer it with respect to is changing + + align:start position:0% +answer it with respect to is changing + + + align:start position:0% +answer it with respect to is changing +membrane + + align:start position:0% + + + + align:start position:0% + +potential well let's start off + + align:start position:0% +potential well let's start off + + + align:start position:0% +potential well let's start off +again with our axon + + align:start position:0% +again with our axon + + + align:start position:0% +again with our axon +chunk with outside and + + align:start position:0% + + + + align:start position:0% + +inside and the charge + + align:start position:0% +inside and the charge + + + align:start position:0% +inside and the charge +distribution that is at resting + + align:start position:0% +distribution that is at resting + + + align:start position:0% +distribution that is at resting +potential + + align:start position:0% + + + + align:start position:0% + +and along comes some kind of input it + + align:start position:0% +and along comes some kind of input it + + + align:start position:0% +and along comes some kind of input it +might be touch it might be another + + align:start position:0% +might be touch it might be another + + + align:start position:0% +might be touch it might be another +neuron touching a second neuron it might + + align:start position:0% +neuron touching a second neuron it might + + + align:start position:0% +neuron touching a second neuron it might +be Vision light that comes along some + + align:start position:0% +be Vision light that comes along some + + + align:start position:0% +be Vision light that comes along some +kind of + + align:start position:0% +kind of + + + align:start position:0% +kind of +input here it + + align:start position:0% +input here it + + + align:start position:0% +input here it +is and this input acts on a very local + + align:start position:0% +is and this input acts on a very local + + + align:start position:0% +is and this input acts on a very local +part of the membrane and it changes the + + align:start position:0% +part of the membrane and it changes the + + + align:start position:0% +part of the membrane and it changes the +membrane potential just a tiny bit such + + align:start position:0% +membrane potential just a tiny bit such + + + align:start position:0% +membrane potential just a tiny bit such +that the membrane potential might reach + + align:start position:0% +that the membrane potential might reach + + + align:start position:0% +that the membrane potential might reach +something called threshold + + align:start position:0% +something called threshold + + + align:start position:0% +something called threshold +potential so let's look let's draw it + + align:start position:0% +potential so let's look let's draw it + + + align:start position:0% +potential so let's look let's draw it +out here it + + align:start position:0% +out here it + + + align:start position:0% +out here it +is just over one little tiny bit of the + + align:start position:0% +is just over one little tiny bit of the + + + align:start position:0% +is just over one little tiny bit of the +membrane there's some kind of charge + + align:start position:0% +membrane there's some kind of charge + + + align:start position:0% +membrane there's some kind of charge +reversal the positive charges come from + + align:start position:0% +reversal the positive charges come from + + + align:start position:0% +reversal the positive charges come from +outside and they move + + align:start position:0% + + + + align:start position:0% + +inside and we'll call this potential + + align:start position:0% +inside and we'll call this potential + + + align:start position:0% +inside and we'll call this potential +difference threshold + + align:start position:0% + + + + align:start position:0% + +potential and if you want to number it's + + align:start position:0% +potential and if you want to number it's + + + align:start position:0% +potential and if you want to number it's +about minus 55 + + align:start position:0% +about minus 55 + + + align:start position:0% +about minus 55 +molts + + align:start position:0% +molts + + + align:start position:0% +molts +okay what happens off to threshold well + + align:start position:0% +okay what happens off to threshold well + + + align:start position:0% +okay what happens off to threshold well +threshold you understand what threshold + + align:start position:0% +threshold you understand what threshold + + + align:start position:0% +threshold you understand what threshold +is it means something happens because + + align:start position:0% +is it means something happens because + + + align:start position:0% +is it means something happens because +you've reached a point of no return and + + align:start position:0% +you've reached a point of no return and + + + align:start position:0% +you've reached a point of no return and +what happens is that there is now an + + align:start position:0% +what happens is that there is now an + + + align:start position:0% +what happens is that there is now an +action potential and there is a massive + + align:start position:0% +action potential and there is a massive + + + align:start position:0% +action potential and there is a massive +movement of the positive sodium ions + + align:start position:0% +movement of the positive sodium ions + + + align:start position:0% +movement of the positive sodium ions +into the cell so that from threshold + + align:start position:0% +into the cell so that from threshold + + + align:start position:0% +into the cell so that from threshold +potential there + + align:start position:0% +potential there + + + align:start position:0% +potential there +is a massive + + align:start position:0% + + + + align:start position:0% + +movement again out and + + align:start position:0% + + + + align:start position:0% + +in so now you've got instead of this + + align:start position:0% +in so now you've got instead of this + + + align:start position:0% +in so now you've got instead of this +little tiny region of depolarization + + align:start position:0% +little tiny region of depolarization + + + align:start position:0% +little tiny region of depolarization +you've got a large region of + + align:start position:0% +you've got a large region of + + + align:start position:0% +you've got a large region of +depolarization so this is a + + align:start position:0% +depolarization so this is a + + + align:start position:0% +depolarization so this is a +small deole for + + align:start position:0% +small deole for + + + align:start position:0% +small deole for +depolarization leading to a very large + + align:start position:0% +depolarization leading to a very large + + + align:start position:0% +depolarization leading to a very large +depolarization of the kind that I drew + + align:start position:0% +depolarization of the kind that I drew + + + align:start position:0% +depolarization of the kind that I drew +on the board + + align:start position:0% +on the board + + + align:start position:0% +on the board +before this large + + align:start position:0% +before this large + + + align:start position:0% +before this large +depolarization is called the action + + align:start position:0% +depolarization is called the action + + + align:start position:0% +depolarization is called the action +potential + + align:start position:0% + + + + align:start position:0% + +and it has several properties the action + + align:start position:0% +and it has several properties the action + + + align:start position:0% +and it has several properties the action +potential reverses the membrane + + align:start position:0% +potential reverses the membrane + + + align:start position:0% +potential reverses the membrane +potential almost completely so now it's + + align:start position:0% +potential almost completely so now it's + + + align:start position:0% +potential almost completely so now it's +at in this region of the membrane it's + + align:start position:0% +at in this region of the membrane it's + + + align:start position:0% +at in this region of the membrane it's +at about plus 60 M volts so it's a + + align:start position:0% +at about plus 60 M volts so it's a + + + align:start position:0% +at about plus 60 M volts so it's a +massive depolarization you completely + + align:start position:0% +massive depolarization you completely + + + align:start position:0% +massive depolarization you completely +reverse the ion distribution over a + + align:start position:0% +reverse the ion distribution over a + + + align:start position:0% +reverse the ion distribution over a +small region of the of the + + align:start position:0% +small region of the of the + + + align:start position:0% +small region of the of the +membrane it's very local however + + align:start position:0% +membrane it's very local however + + + align:start position:0% +membrane it's very local however +an action + + align:start position:0% +an action + + + align:start position:0% +an action +potential occurs over or the this + + align:start position:0% +potential occurs over or the this + + + align:start position:0% +potential occurs over or the this +massive + + align:start position:0% +massive + + + align:start position:0% +massive +depolarization occurs over about a + + align:start position:0% +depolarization occurs over about a + + + align:start position:0% +depolarization occurs over about a +micron of + + align:start position:0% +micron of + + + align:start position:0% +micron of +membrane it takes one to two + + align:start position:0% +membrane it takes one to two + + + align:start position:0% +membrane it takes one to two +milliseconds to set up it involves the + + align:start position:0% +milliseconds to set up it involves the + + + align:start position:0% +milliseconds to set up it involves the +movement of about 10 to the fifth ions + + align:start position:0% +movement of about 10 to the fifth ions + + + align:start position:0% +movement of about 10 to the fifth ions +from the outside + + align:start position:0% + + + + align:start position:0% + +in and I've told you the potential the + + align:start position:0% +in and I've told you the potential the + + + align:start position:0% +in and I've told you the potential the +other thing that is really critical that + + align:start position:0% +other thing that is really critical that + + + align:start position:0% +other thing that is really critical that +you have to understand is something + + align:start position:0% +you have to understand is something + + + align:start position:0% +you have to understand is something +called all or + + align:start position:0% + + + + align:start position:0% + +none the depolarization you get with an + + align:start position:0% +none the depolarization you get with an + + + align:start position:0% +none the depolarization you get with an +action potential is either complete or + + align:start position:0% +action potential is either complete or + + + align:start position:0% +action potential is either complete or +it doesn't happen if you reach threshold + + align:start position:0% +it doesn't happen if you reach threshold + + + align:start position:0% +it doesn't happen if you reach threshold +you reverse polarity and you get this + + align:start position:0% +you reverse polarity and you get this + + + align:start position:0% +you reverse polarity and you get this +complete depolarization to plus 60 M + + align:start position:0% +complete depolarization to plus 60 M + + + align:start position:0% +complete depolarization to plus 60 M +volts from minus 60 you do not get a + + align:start position:0% +volts from minus 60 you do not get a + + + align:start position:0% +volts from minus 60 you do not get a +partial depolarization to plus 10 + + align:start position:0% +partial depolarization to plus 10 + + + align:start position:0% +partial depolarization to plus 10 +or 20 or 30 sometimes or + + align:start position:0% +or 20 or 30 sometimes or + + + align:start position:0% +or 20 or 30 sometimes or +35 for a given neuron you get a specific + + align:start position:0% +35 for a given neuron you get a specific + + + align:start position:0% +35 for a given neuron you get a specific +action potential and it either happens + + align:start position:0% +action potential and it either happens + + + align:start position:0% +action potential and it either happens +or it doesn't happen Okay so all or + + align:start position:0% + + + + align:start position:0% + +none very important no little or big + + align:start position:0% +none very important no little or big + + + align:start position:0% +none very important no little or big +Action + + align:start position:0% + + + + align:start position:0% + +potentials and + + align:start position:0% +potentials and + + + align:start position:0% +potentials and +now we've got a depolarization but we + + align:start position:0% +now we've got a depolarization but we + + + align:start position:0% +now we've got a depolarization but we +haven't answered two questions we + + align:start position:0% +haven't answered two questions we + + + align:start position:0% +haven't answered two questions we +haven't answered the question of + + align:start position:0% +haven't answered the question of + + + align:start position:0% +haven't answered the question of +unidirection and we haven't answered the + + align:start position:0% +unidirection and we haven't answered the + + + align:start position:0% +unidirection and we haven't answered the +question of resetting so let's do that + + align:start position:0% +question of resetting so let's do that + + + align:start position:0% +question of resetting so let's do that +on the next board and let's start off + + align:start position:0% +on the next board and let's start off + + + align:start position:0% +on the next board and let's start off +actually with an action + + align:start position:0% + + + + align:start position:0% + +potential and I'm actually going to draw + + align:start position:0% +potential and I'm actually going to draw + + + align:start position:0% +potential and I'm actually going to draw +an action + + align:start position:0% +an action + + + align:start position:0% +an action +potential kind of in the + + align:start position:0% +potential kind of in the + + + align:start position:0% +potential kind of in the +middle of this Axon + + align:start position:0% + + + + align:start position:0% + +you'll see + + align:start position:0% +you'll see + + + align:start position:0% +you'll see +why when you get an action potential + + align:start position:0% +why when you get an action potential + + + align:start position:0% +why when you get an action potential +what's happening is that sodium ions are + + align:start position:0% +what's happening is that sodium ions are + + + align:start position:0% +what's happening is that sodium ions are +moving from the outside inside and those + + align:start position:0% +moving from the outside inside and those + + + align:start position:0% +moving from the outside inside and those +sodium ions because they're just ions + + align:start position:0% +sodium ions because they're just ions + + + align:start position:0% +sodium ions because they're just ions +will start to diffuse in the + + align:start position:0% +will start to diffuse in the + + + align:start position:0% +will start to diffuse in the +cytoplasm and as they diffuse next door + + align:start position:0% +cytoplasm and as they diffuse next door + + + align:start position:0% +cytoplasm and as they diffuse next door +they'll change the membrane potential + + align:start position:0% +they'll change the membrane potential + + + align:start position:0% +they'll change the membrane potential +which will reach threshold which will + + align:start position:0% +which will reach threshold which will + + + align:start position:0% +which will reach threshold which will +trigger an action potential in the + + align:start position:0% +trigger an action potential in the + + + align:start position:0% +trigger an action potential in the +membrane chunk next door and then those + + align:start position:0% +membrane chunk next door and then those + + + align:start position:0% +membrane chunk next door and then those +ions will diffuse to make the chunk chk + + align:start position:0% +ions will diffuse to make the chunk chk + + + align:start position:0% +ions will diffuse to make the chunk chk +of membrane next door reach threshold + + align:start position:0% +of membrane next door reach threshold + + + align:start position:0% +of membrane next door reach threshold +potential and you'll get an action + + align:start position:0% +potential and you'll get an action + + + align:start position:0% +potential and you'll get an action +potential triggered and so on but the + + align:start position:0% +potential triggered and so on but the + + + align:start position:0% +potential triggered and so on but the +ions of course because they're just ions + + align:start position:0% +ions of course because they're just ions + + + align:start position:0% +ions of course because they're just ions +can move in either direction so the ions + + align:start position:0% +can move in either direction so the ions + + + align:start position:0% +can move in either direction so the ions +can move back if this is where your + + align:start position:0% +can move back if this is where your + + + align:start position:0% +can move back if this is where your +action potential took place the ions + + align:start position:0% +action potential took place the ions + + + align:start position:0% +action potential took place the ions +could move in that direction and trigger + + align:start position:0% +could move in that direction and trigger + + + align:start position:0% +could move in that direction and trigger +an action potential going back up the + + align:start position:0% +an action potential going back up the + + + align:start position:0% +an action potential going back up the +axon towards the cell body why doesn't + + align:start position:0% +axon towards the cell body why doesn't + + + align:start position:0% +axon towards the cell body why doesn't +that happen it doesn't happen because + + align:start position:0% +that happen it doesn't happen because + + + align:start position:0% +that happen it doesn't happen because +once you've triggered an action + + align:start position:0% +once you've triggered an action + + + align:start position:0% +once you've triggered an action +potential that membrane becomes + + align:start position:0% +potential that membrane becomes + + + align:start position:0% +potential that membrane becomes +refractory unable to trigger another + + align:start position:0% +refractory unable to trigger another + + + align:start position:0% +refractory unable to trigger another +action potential for a while and during + + align:start position:0% +action potential for a while and during + + + align:start position:0% +action potential for a while and during +that time where the membrane is unable + + align:start position:0% +that time where the membrane is unable + + + align:start position:0% +that time where the membrane is unable +to respond and make another action + + align:start position:0% +to respond and make another action + + + align:start position:0% +to respond and make another action +potential the ions have diffused away + + align:start position:0% +potential the ions have diffused away + + + align:start position:0% +potential the ions have diffused away +and gone on down the axon and so you get + + align:start position:0% +and gone on down the axon and so you get + + + align:start position:0% +and gone on down the axon and so you get +a + + align:start position:0% +a + + + align:start position:0% +a +unidirectional propagation let's try to + + align:start position:0% +unidirectional propagation let's try to + + + align:start position:0% +unidirectional propagation let's try to +draw that out so here's an action + + align:start position:0% + + + + align:start position:0% + +potential and the ions + + align:start position:0% + + + + align:start position:0% + +that a moving + + align:start position:0% +that a moving + + + align:start position:0% +that a moving +in will + + align:start position:0% + + + + align:start position:0% + +diffuse and they will take the membrane + + align:start position:0% +diffuse and they will take the membrane + + + align:start position:0% +diffuse and they will take the membrane +next + + align:start position:0% +next + + + align:start position:0% +next +door to + + align:start position:0% + + + + align:start position:0% + +threshold and so they'll trigger + + align:start position:0% + + + + align:start position:0% + +an action + + align:start position:0% +an action + + + align:start position:0% +an action +potential next + + align:start position:0% + + + + align:start position:0% + +door those ions fusing backwards can't + + align:start position:0% +door those ions fusing backwards can't + + + align:start position:0% +door those ions fusing backwards can't +do anything because once the membrane + + align:start position:0% +do anything because once the membrane + + + align:start position:0% +do anything because once the membrane +has had an action potential it can't + + align:start position:0% +has had an action potential it can't + + + align:start position:0% +has had an action potential it can't +have another one for a while so this + + align:start position:0% +have another one for a while so this + + + align:start position:0% +have another one for a while so this +membrane here next door to the action + + align:start position:0% +membrane here next door to the action + + + align:start position:0% +membrane here next door to the action +potential + + align:start position:0% +potential + + + align:start position:0% +potential +is + + align:start position:0% + + + + align:start position:0% + +refractory to + + align:start position:0% + + + + align:start position:0% + +depolarization + + align:start position:0% + + + + align:start position:0% + +depolarization that is a really + + align:start position:0% +depolarization that is a really + + + align:start position:0% +depolarization that is a really +horrendous spelling job there + + align:start position:0% + + + + align:start position:0% + +depolarization for some period of time + + align:start position:0% +depolarization for some period of time + + + align:start position:0% +depolarization for some period of time +let's say for about a second + + align:start position:0% +let's say for about a second + + + align:start position:0% +let's say for about a second +or little less than that but somewhere + + align:start position:0% +or little less than that but somewhere + + + align:start position:0% +or little less than that but somewhere +around there okay and so that means that + + align:start position:0% +around there okay and so that means that + + + align:start position:0% +around there okay and so that means that +the action potential is unidirectional + + align:start position:0% +the action potential is unidirectional + + + align:start position:0% +the action potential is unidirectional +the ions can diffuse in both directions + + align:start position:0% +the ions can diffuse in both directions + + + align:start position:0% +the ions can diffuse in both directions +but the action potential can only go in + + align:start position:0% +but the action potential can only go in + + + align:start position:0% +but the action potential can only go in +one okay so that gives you a + + align:start position:0% +one okay so that gives you a + + + align:start position:0% +one okay so that gives you a +direction of your + + align:start position:0% +direction of your + + + align:start position:0% +direction of your +signal and also I have cavalierly drawn + + align:start position:0% +signal and also I have cavalierly drawn + + + align:start position:0% +signal and also I have cavalierly drawn +on there that the membrane potential + + align:start position:0% +on there that the membrane potential + + + align:start position:0% +on there that the membrane potential +reverses and resets itself where the + + align:start position:0% +reverses and resets itself where the + + + align:start position:0% +reverses and resets itself where the +action potential previously occurred and + + align:start position:0% +action potential previously occurred and + + + align:start position:0% +action potential previously occurred and +we'll talk about that more in a moment + + align:start position:0% +we'll talk about that more in a moment + + + align:start position:0% +we'll talk about that more in a moment +so here the membrane potential has + + align:start position:0% + + + + align:start position:0% + +reset okay so this is a theoretical walk + + align:start position:0% +reset okay so this is a theoretical walk + + + align:start position:0% +reset okay so this is a theoretical walk +through Action potentials and I gave you + + align:start position:0% +through Action potentials and I gave you + + + align:start position:0% +through Action potentials and I gave you +a bunch of handouts but I am not going + + align:start position:0% +a bunch of handouts but I am not going + + + align:start position:0% +a bunch of handouts but I am not going +to go through them because you can use + + align:start position:0% +to go through them because you can use + + + align:start position:0% +to go through them because you can use +them as a test or as an exercise after + + align:start position:0% +them as a test or as an exercise after + + + align:start position:0% +them as a test or as an exercise after +class to see how much you + + align:start position:0% +class to see how much you + + + align:start position:0% +class to see how much you +understood one of the things about about + + align:start position:0% +understood one of the things about about + + + align:start position:0% +understood one of the things about about +conductance along an axon is that it's + + align:start position:0% +conductance along an axon is that it's + + + align:start position:0% +conductance along an axon is that it's +very quick it takes a very short time + + align:start position:0% +very quick it takes a very short time + + + align:start position:0% +very quick it takes a very short time +from touching that hot thing to + + align:start position:0% +from touching that hot thing to + + + align:start position:0% +from touching that hot thing to +realizing you've touched it but one of + + align:start position:0% +realizing you've touched it but one of + + + align:start position:0% +realizing you've touched it but one of +the reasons it's so short is because + + align:start position:0% +the reasons it's so short is because + + + align:start position:0% +the reasons it's so short is because +you're not sending an action potential + + align:start position:0% +you're not sending an action potential + + + align:start position:0% +you're not sending an action potential +all the way along an axon like we're + + align:start position:0% +all the way along an axon like we're + + + align:start position:0% +all the way along an axon like we're +drawing you don't really get successive + + align:start position:0% +drawing you don't really get successive + + + align:start position:0% +drawing you don't really get successive +parts of the membrane + + align:start position:0% +parts of the membrane + + + align:start position:0% +parts of the membrane +depolarizing because that actually + + align:start position:0% +depolarizing because that actually + + + align:start position:0% +depolarizing because that actually +although it's faster than intercellular + + align:start position:0% +although it's faster than intercellular + + + align:start position:0% +although it's faster than intercellular +connections is still quite slow + + align:start position:0% +connections is still quite slow + + + align:start position:0% +connections is still quite slow +so there's a way that a cell insulates + + align:start position:0% +so there's a way that a cell insulates + + + align:start position:0% +so there's a way that a cell insulates +itself and axon insulates itself to give + + align:start position:0% +itself and axon insulates itself to give + + + align:start position:0% +itself and axon insulates itself to give +you Action potentials just a particular + + align:start position:0% +you Action potentials just a particular + + + align:start position:0% +you Action potentials just a particular +places and that really speeds up the + + align:start position:0% +places and that really speeds up the + + + align:start position:0% +places and that really speeds up the +rate of transmission of an action + + align:start position:0% +rate of transmission of an action + + + align:start position:0% +rate of transmission of an action +potential and I've got that on the slide + + align:start position:0% +potential and I've got that on the slide + + + align:start position:0% +potential and I've got that on the slide +here and we'll write on the board so + + align:start position:0% +here and we'll write on the board so + + + align:start position:0% +here and we'll write on the board so +that + + align:start position:0% + + + + align:start position:0% + +during + + align:start position:0% + + + + align:start position:0% + +depolarization and after + + align:start position:0% +depolarization and after + + + align:start position:0% +depolarization and after +and all the + + align:start position:0% +and all the + + + align:start position:0% +and all the +time ions + + align:start position:0% +time ions + + + align:start position:0% +time ions +leak from the + + align:start position:0% + + + + align:start position:0% + +axon and this decreases the frequency of + + align:start position:0% +axon and this decreases the frequency of + + + align:start position:0% +axon and this decreases the frequency of +action + + align:start position:0% +action + + + align:start position:0% +action +potential + + align:start position:0% + + + + align:start position:0% + +formation and so what cells + + align:start position:0% +formation and so what cells + + + align:start position:0% +formation and so what cells +do it's kind of like a short not it's + + align:start position:0% +do it's kind of like a short not it's + + + align:start position:0% +do it's kind of like a short not it's +not quite short circuiting but it's it's + + align:start position:0% +not quite short circuiting but it's it's + + + align:start position:0% +not quite short circuiting but it's it's +a bad Electric wire and so what the cell + + align:start position:0% +a bad Electric wire and so what the cell + + + align:start position:0% +a bad Electric wire and so what the cell +has done is to insulate + + align:start position:0% + + + + align:start position:0% + +itself with layers of fatty cells and + + align:start position:0% +itself with layers of fatty cells and + + + align:start position:0% +itself with layers of fatty cells and +these cells are really kind of + + align:start position:0% +these cells are really kind of + + + align:start position:0% +these cells are really kind of +amazing most of the cells that insulate + + align:start position:0% +amazing most of the cells that insulate + + + align:start position:0% +amazing most of the cells that insulate +the neurons in the nervous system wrap + + align:start position:0% +the neurons in the nervous system wrap + + + align:start position:0% +the neurons in the nervous system wrap +around the neurons as in this diagram + + align:start position:0% +around the neurons as in this diagram + + + align:start position:0% +around the neurons as in this diagram +you can see here is a cell and these + + align:start position:0% +you can see here is a cell and these + + + align:start position:0% +you can see here is a cell and these +lines are because a single cell has + + align:start position:0% +lines are because a single cell has + + + align:start position:0% +lines are because a single cell has +wrapped itself around the neuron you + + align:start position:0% +wrapped itself around the neuron you + + + align:start position:0% +wrapped itself around the neuron you +know that the plasma membrane is lipid + + align:start position:0% +know that the plasma membrane is lipid + + + align:start position:0% +know that the plasma membrane is lipid +it doesn't conduct ions and so you've + + align:start position:0% +it doesn't conduct ions and so you've + + + align:start position:0% +it doesn't conduct ions and so you've +got really a fatty layer of + + align:start position:0% + + + + align:start position:0% + +insulation and the + + align:start position:0% +insulation and the + + + align:start position:0% +insulation and the +thing that insulates the cells is + + align:start position:0% +thing that insulates the cells is + + + align:start position:0% +thing that insulates the cells is +something called ayin sheath which is + + align:start position:0% +something called ayin sheath which is + + + align:start position:0% +something called ayin sheath which is +lipid plus some protein but it's a + + align:start position:0% +lipid plus some protein but it's a + + + align:start position:0% +lipid plus some protein but it's a +really hydrophobic + + align:start position:0% +really hydrophobic + + + align:start position:0% +really hydrophobic +layer that wraps around the neur neurons + + align:start position:0% +layer that wraps around the neur neurons + + + align:start position:0% +layer that wraps around the neur neurons +and insulates them along the neurons + + align:start position:0% +and insulates them along the neurons + + + align:start position:0% +and insulates them along the neurons +that are insulated there are specific + + align:start position:0% +that are insulated there are specific + + + align:start position:0% +that are insulated there are specific +places where there's no insulation and + + align:start position:0% +places where there's no insulation and + + + align:start position:0% +places where there's no insulation and +that's where Action potentials take + + align:start position:0% +that's where Action potentials take + + + align:start position:0% +that's where Action potentials take +place so Action + + align:start position:0% +place so Action + + + align:start position:0% +place so Action +potentials take + + align:start position:0% + + + + align:start position:0% + +place at + + align:start position:0% + + + + align:start position:0% + +nodes without myelin + + align:start position:0% + + + + align:start position:0% + +okay and this is one way that neurons + + align:start position:0% +okay and this is one way that neurons + + + align:start position:0% +okay and this is one way that neurons +really speed up their conductance rate + + align:start position:0% +really speed up their conductance rate + + + align:start position:0% +really speed up their conductance rate +and so I put here action potential + + align:start position:0% +and so I put here action potential + + + align:start position:0% +and so I put here action potential +frequency but actually that's not + + align:start position:0% + + + + align:start position:0% + +correct I'm going to talk about + + align:start position:0% +correct I'm going to talk about + + + align:start position:0% +correct I'm going to talk about +rate of + + align:start position:0% + + + + align:start position:0% + +transmission all right so how does this + + align:start position:0% +transmission all right so how does this + + + align:start position:0% +transmission all right so how does this +all go together let's look at a movie + + align:start position:0% + + + + align:start position:0% + +where here's the neuron and here is the + + align:start position:0% +where here's the neuron and here is the + + + align:start position:0% +where here's the neuron and here is the +axon transmitting an action potential + + align:start position:0% +axon transmitting an action potential + + + align:start position:0% +axon transmitting an action potential +along its length Okay and here's a + + align:start position:0% +along its length Okay and here's a + + + align:start position:0% +along its length Okay and here's a +different way of depicting the action + + align:start position:0% +different way of depicting the action + + + align:start position:0% +different way of depicting the action +potential as a graph of voltage against + + align:start position:0% +potential as a graph of voltage against + + + align:start position:0% +potential as a graph of voltage against +time and that's you'll something that + + align:start position:0% +time and that's you'll something that + + + align:start position:0% +time and that's you'll something that +you'll practice in section but what I + + align:start position:0% +you'll practice in section but what I + + + align:start position:0% +you'll practice in section but what I +want you to see is that there's an + + align:start position:0% +want you to see is that there's an + + + align:start position:0% +want you to see is that there's an +action potential moving along the + + align:start position:0% +action potential moving along the + + + align:start position:0% +action potential moving along the +axon and the axon can transmit many many + + align:start position:0% +axon and the axon can transmit many many + + + align:start position:0% +axon and the axon can transmit many many +action potentials one after the other + + align:start position:0% +action potentials one after the other + + + align:start position:0% +action potentials one after the other +with a short recovery period in + + align:start position:0% +with a short recovery period in + + + align:start position:0% +with a short recovery period in +between + + align:start position:0% + + + + align:start position:0% + +okay we still have not answered quite + + align:start position:0% +okay we still have not answered quite + + + align:start position:0% +okay we still have not answered quite +the question of how Action potentials + + align:start position:0% +the question of how Action potentials + + + align:start position:0% +the question of how Action potentials +work and the answer to that is to + + align:start position:0% +work and the answer to that is to + + + align:start position:0% +work and the answer to that is to +consider ion + + align:start position:0% + + + + align:start position:0% + +channels and pump + + align:start position:0% + + + + align:start position:0% + +because all of this charge distribution + + align:start position:0% +because all of this charge distribution + + + align:start position:0% +because all of this charge distribution +doesn't just happen it's set up by the + + align:start position:0% +doesn't just happen it's set up by the + + + align:start position:0% +doesn't just happen it's set up by the +cell and it's set up by Iron channels + + align:start position:0% +cell and it's set up by Iron channels + + + align:start position:0% +cell and it's set up by Iron channels +and pumps which we can write + + align:start position:0% +and pumps which we can write + + + align:start position:0% +and pumps which we can write +regulate membrane + + align:start position:0% +regulate membrane + + + align:start position:0% +regulate membrane +potential let's review very briefly what + + align:start position:0% +potential let's review very briefly what + + + align:start position:0% +potential let's review very briefly what +ion channels and pumps are we've talked + + align:start position:0% +ion channels and pumps are we've talked + + + align:start position:0% +ion channels and pumps are we've talked +about the a bunch but you need to know + + align:start position:0% +about the a bunch but you need to know + + + align:start position:0% +about the a bunch but you need to know +some Essences for this particular module + + align:start position:0% +some Essences for this particular module + + + align:start position:0% +some Essences for this particular module +ion channels allow ions across the + + align:start position:0% +ion channels allow ions across the + + + align:start position:0% +ion channels allow ions across the +membrane by + + align:start position:0% + + + + align:start position:0% + +diffusion so here's an ion Channel and + + align:start position:0% +diffusion so here's an ion Channel and + + + align:start position:0% +diffusion so here's an ion Channel and +I'm drawing a channel which is + + align:start position:0% + + + + align:start position:0% + +open and the ions move by + + align:start position:0% +open and the ions move by + + + align:start position:0% +open and the ions move by +diffusion across the channel + + align:start position:0% +diffusion across the channel + + + align:start position:0% +diffusion across the channel +but there are other classes of pump of + + align:start position:0% +but there are other classes of pump of + + + align:start position:0% +but there are other classes of pump of +iron channels which are not always open + + align:start position:0% +iron channels which are not always open + + + align:start position:0% +iron channels which are not always open +they're called gated and we talked about + + align:start position:0% +they're called gated and we talked about + + + align:start position:0% +they're called gated and we talked about +them when we talked about protein + + align:start position:0% +them when we talked about protein + + + align:start position:0% +them when we talked about protein +secretion protein + + align:start position:0% + + + + align:start position:0% + +localization so + + align:start position:0% +localization so + + + align:start position:0% +localization so +gated + + align:start position:0% +gated + + + align:start position:0% +gated +channels under a particular + + align:start position:0% +channels under a particular + + + align:start position:0% +channels under a particular +stimulus are can be closed + + align:start position:0% +stimulus are can be closed + + + align:start position:0% +stimulus are can be closed +and then change to the open + + align:start position:0% + + + + align:start position:0% + +confirmation after they've been given + + align:start position:0% +confirmation after they've been given + + + align:start position:0% +confirmation after they've been given +the appropriate + + align:start position:0% +the appropriate + + + align:start position:0% +the appropriate +stimulus okay so here there's some kind + + align:start position:0% +stimulus okay so here there's some kind + + + align:start position:0% +stimulus okay so here there's some kind +of + + align:start position:0% +of + + + align:start position:0% +of +stimulus and a channel that is gated + + align:start position:0% +stimulus and a channel that is gated + + + align:start position:0% +stimulus and a channel that is gated +will + + align:start position:0% +will + + + align:start position:0% +will +open a third kind of way of getting ions + + align:start position:0% +open a third kind of way of getting ions + + + align:start position:0% +open a third kind of way of getting ions +across the membrane is to use a + + align:start position:0% +across the membrane is to use a + + + align:start position:0% +across the membrane is to use a +pump where a pump is localized in the + + align:start position:0% +pump where a pump is localized in the + + + align:start position:0% +pump where a pump is localized in the +plas plasma membrane as + + align:start position:0% +plas plasma membrane as + + + align:start position:0% +plas plasma membrane as +well but instead of a diffusion governed + + align:start position:0% +well but instead of a diffusion governed + + + align:start position:0% +well but instead of a diffusion governed +process to get ions across the membrane + + align:start position:0% +process to get ions across the membrane + + + align:start position:0% +process to get ions across the membrane +the pump is actively moving ions across + + align:start position:0% +the pump is actively moving ions across + + + align:start position:0% +the pump is actively moving ions across +the membrane so ion + + align:start position:0% +the membrane so ion + + + align:start position:0% +the membrane so ion +pumps actively transport + + align:start position:0% + + + + align:start position:0% + +ions and they generally require energy + + align:start position:0% +ions and they generally require energy + + + align:start position:0% +ions and they generally require energy +ATP in order to do so and all of these + + align:start position:0% +ATP in order to do so and all of these + + + align:start position:0% +ATP in order to do so and all of these +things are essential to set the membrane + + align:start position:0% +things are essential to set the membrane + + + align:start position:0% +things are essential to set the membrane +potential and to change it during action + + align:start position:0% +potential and to change it during action + + + align:start position:0% +potential and to change it during action +potential + + align:start position:0% +potential + + + align:start position:0% +potential +formation if we consider the resting + + align:start position:0% +formation if we consider the resting + + + align:start position:0% +formation if we consider the resting +potential actually let me see what I + + align:start position:0% +potential actually let me see what I + + + align:start position:0% +potential actually let me see what I +have on the slides + + align:start position:0% + + + + align:start position:0% + +here this is a really cool thing all + + align:start position:0% +here this is a really cool thing all + + + align:start position:0% +here this is a really cool thing all +right let me let me though get through + + align:start position:0% +right let me let me though get through + + + align:start position:0% +right let me let me though get through +our board work and then we'll do what is + + align:start position:0% +our board work and then we'll do what is + + + align:start position:0% +our board work and then we'll do what is +really + + align:start position:0% +really + + + align:start position:0% +really +cool after okay + + align:start position:0% + + + + align:start position:0% + +or on + + align:start position:0% + + + + align:start position:0% + +Monday in order to set up the resting + + align:start position:0% +Monday in order to set up the resting + + + align:start position:0% +Monday in order to set up the resting +potential there are several kinds of + + align:start position:0% +potential there are several kinds of + + + align:start position:0% +potential there are several kinds of +channels and pumps that you need to be + + align:start position:0% +channels and pumps that you need to be + + + align:start position:0% +channels and pumps that you need to be +aware of one of them which is a biggie + + align:start position:0% +aware of one of them which is a biggie + + + align:start position:0% +aware of one of them which is a biggie +and for which a Nobel Prize was given + + align:start position:0% +and for which a Nobel Prize was given + + + align:start position:0% +and for which a Nobel Prize was given +some decades ago is called the sodium + + align:start position:0% +some decades ago is called the sodium + + + align:start position:0% +some decades ago is called the sodium +pottassium + + align:start position:0% + + + + align:start position:0% + +pump and this is really a big thing it's + + align:start position:0% +pump and this is really a big thing it's + + + align:start position:0% +pump and this is really a big thing it's +also called the sodium pot cassium + + align:start position:0% +also called the sodium pot cassium + + + align:start position:0% +also called the sodium pot cassium +atpa and what it does is to + + align:start position:0% +atpa and what it does is to + + + align:start position:0% +atpa and what it does is to +pump three sodium ions out of the + + align:start position:0% +pump three sodium ions out of the + + + align:start position:0% +pump three sodium ions out of the +cell and put two potassium ions into the + + align:start position:0% +cell and put two potassium ions into the + + + align:start position:0% +cell and put two potassium ions into the +cell and this is an enormously important + + align:start position:0% +cell and this is an enormously important + + + align:start position:0% +cell and this is an enormously important +pump for life and you can see what it + + align:start position:0% +pump for life and you can see what it + + + align:start position:0% +pump for life and you can see what it +does is to increase the sodium + + align:start position:0% +does is to increase the sodium + + + align:start position:0% +does is to increase the sodium +concentration outside the cell and + + align:start position:0% +concentration outside the cell and + + + align:start position:0% +concentration outside the cell and +increase the potassium concentration + + align:start position:0% +increase the potassium concentration + + + align:start position:0% +increase the potassium concentration +inside there is also something called an + + align:start position:0% +inside there is also something called an + + + align:start position:0% +inside there is also something called an +open pottassium + + align:start position:0% + + + + align:start position:0% + +Channel that will allow all this + + align:start position:0% +Channel that will allow all this + + + align:start position:0% +Channel that will allow all this +pottassium that's being pumped in by the + + align:start position:0% +pottassium that's being pumped in by the + + + align:start position:0% +pottassium that's being pumped in by the +sodium potassium pump to start diffusing + + align:start position:0% +sodium potassium pump to start diffusing + + + align:start position:0% +sodium potassium pump to start diffusing +out of the cell but in actual fact it + + align:start position:0% +out of the cell but in actual fact it + + + align:start position:0% +out of the cell but in actual fact it +doesn't all diffuse out because it hits + + align:start position:0% +doesn't all diffuse out because it hits + + + align:start position:0% +doesn't all diffuse out because it hits +the positive charges of the sodium ions + + align:start position:0% +the positive charges of the sodium ions + + + align:start position:0% +the positive charges of the sodium ions +on the outside and there's an + + align:start position:0% +on the outside and there's an + + + align:start position:0% +on the outside and there's an +electrostatic repulsion and so that + + align:start position:0% +electrostatic repulsion and so that + + + align:start position:0% +electrostatic repulsion and so that +limits how much pottassium + + align:start position:0% +limits how much pottassium + + + align:start position:0% +limits how much pottassium +by Monday I may I I will either be able + + align:start position:0% +by Monday I may I I will either be able + + + align:start position:0% +by Monday I may I I will either be able +to speak by Monday oh while I've + + align:start position:0% +to speak by Monday oh while I've + + + align:start position:0% +to speak by Monday oh while I've +completely lost my voice okay we can + + align:start position:0% +completely lost my voice okay we can + + + align:start position:0% +completely lost my voice okay we can +well you you'll have the option okay so + + align:start position:0% +well you you'll have the option okay so + + + align:start position:0% +well you you'll have the option okay so +the open potassium Channel allows + + align:start position:0% +the open potassium Channel allows + + + align:start position:0% +the open potassium Channel allows +potassium + + align:start position:0% +potassium + + + align:start position:0% +potassium +out by + + align:start position:0% +out by + + + align:start position:0% +out by +diffusion until it is + + align:start position:0% + + + + align:start position:0% + +repelled or + + align:start position:0% +repelled or + + + align:start position:0% +repelled or +stopped by electrostatic forces coming + + align:start position:0% +stopped by electrostatic forces coming + + + align:start position:0% +stopped by electrostatic forces coming +from the sodium ions + + align:start position:0% + + + + align:start position:0% + +okay and then a third ion that's open an + + align:start position:0% +okay and then a third ion that's open an + + + align:start position:0% +okay and then a third ion that's open an +ion Channel that's open is the chloride + + align:start position:0% +ion Channel that's open is the chloride + + + align:start position:0% +ion Channel that's open is the chloride +Channel which we won't discuss right + + align:start position:0% + + + + align:start position:0% + +now during the action potential there is + + align:start position:0% +now during the action potential there is + + + align:start position:0% +now during the action potential there is +an enormously important ION channel that + + align:start position:0% +an enormously important ION channel that + + + align:start position:0% +an enormously important ION channel that +is the last thing I'll mention + + align:start position:0% +is the last thing I'll mention + + + align:start position:0% +is the last thing I'll mention +today and that's called the voltage ated + + align:start position:0% +today and that's called the voltage ated + + + align:start position:0% +today and that's called the voltage ated +sodium + + align:start position:0% + + + + align:start position:0% + +Channel this is an ion channel that like + + align:start position:0% +Channel this is an ion channel that like + + + align:start position:0% +Channel this is an ion channel that like +many ion channels consists of a complex + + align:start position:0% +many ion channels consists of a complex + + + align:start position:0% +many ion channels consists of a complex +of + + align:start position:0% +of + + + align:start position:0% +of +proteins we'll make a note of that I'll + + align:start position:0% +proteins we'll make a note of that I'll + + + align:start position:0% +proteins we'll make a note of that I'll +make a note of that next time but the + + align:start position:0% +make a note of that next time but the + + + align:start position:0% +make a note of that next time but the +voltage gate sodium channel is sensitive + + align:start position:0% +voltage gate sodium channel is sensitive + + + align:start position:0% +voltage gate sodium channel is sensitive +to membrane potential and when threshold + + align:start position:0% +to membrane potential and when threshold + + + align:start position:0% +to membrane potential and when threshold +potential is reached there is a change + + align:start position:0% +potential is reached there is a change + + + align:start position:0% +potential is reached there is a change +in the confirmation of this channel + + align:start position:0% +in the confirmation of this channel + + + align:start position:0% +in the confirmation of this channel +which is closed + + align:start position:0% +which is closed + + + align:start position:0% +which is closed +normally at resting + + align:start position:0% + + + + align:start position:0% + +potential but becomes + + align:start position:0% +potential but becomes + + + align:start position:0% +potential but becomes +open at + + align:start position:0% +open at + + + align:start position:0% +open at +threshold + + align:start position:0% +threshold + + + align:start position:0% +threshold +potential to lead to the action + + align:start position:0% +potential to lead to the action + + + align:start position:0% +potential to lead to the action +potential + + align:start position:0% + + + + align:start position:0% + +and it becomes open through actually the + + align:start position:0% +and it becomes open through actually the + + + align:start position:0% +and it becomes open through actually the +sliding of one of the alha helices that + + align:start position:0% +sliding of one of the alha helices that + + + align:start position:0% +sliding of one of the alha helices that +make up the proteins of the channel and + + align:start position:0% +make up the proteins of the channel and + + + align:start position:0% +make up the proteins of the channel and +the sliding Alpha helices slide because + + align:start position:0% +the sliding Alpha helices slide because + + + align:start position:0% +the sliding Alpha helices slide because +their charges change the charges of the + + align:start position:0% +their charges change the charges of the + + + align:start position:0% +their charges change the charges of the +amino acids change and that opens up the + + align:start position:0% +amino acids change and that opens up the + + + align:start position:0% +amino acids change and that opens up the +channel so I'm going to show you one + + align:start position:0% +channel so I'm going to show you one + + + align:start position:0% +channel so I'm going to show you one +picture of the last of the sodium + + align:start position:0% +picture of the last of the sodium + + + align:start position:0% +picture of the last of the sodium +channel the sodium the voltage gated + + align:start position:0% +channel the sodium the voltage gated + + + align:start position:0% +channel the sodium the voltage gated +sodium Channel + + align:start position:0% + + + + align:start position:0% + +here it is and then we'll finish take a + + align:start position:0% +here it is and then we'll finish take a + + + align:start position:0% +here it is and then we'll finish take a +look at this + + align:start position:0% +look at this + + + align:start position:0% +look at this +quickly here is the voltage gated sodium + + align:start position:0% +quickly here is the voltage gated sodium + + + align:start position:0% +quickly here is the voltage gated sodium +Channel + + align:start position:0% +Channel + + + align:start position:0% +Channel +closed amino acids blocking up the pore + + align:start position:0% +closed amino acids blocking up the pore + + + align:start position:0% +closed amino acids blocking up the pore +and there it opens up to let the ions in + + align:start position:0% +and there it opens up to let the ions in + + + align:start position:0% +and there it opens up to let the ions in +and we'll finish this on Monday \ No newline at end of file diff --git a/dvPJj-5X_uU.txt b/dvPJj-5X_uU.txt new file mode 100644 index 0000000000000000000000000000000000000000..7cd76d7571ad516c77f637645b87f7f48355c33e --- /dev/null +++ b/dvPJj-5X_uU.txt @@ -0,0 +1,4547 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +SAMAN AMARASINGHE: Welcome +to the final competition. + +So you guys survived this far. + +And I don't know how. + +I think, probably, with +very little sleep. + +And knowing all the emails that +I have seen and all the + +check-ins.-- + +I don't know how many +people had-- + +Who had any sleep within +last 24 hours? + +AUDIENCE: Haha. + +SAMAN AMARASINGHE: Oh, OK. + +[LAUGHTER] + +OK. + +And also what we looked at was +the quality of the results + +keep improving because he was +running tests to check + +what's going on. + +And when we moved to +a machine, the + +things ran very fast. + +We're like, wait a minute. + +Why is this running that fast? + +Because people had checked in +more and more, faster and + +faster versions. + +So things improved, not because +we checked in faster + +machines, but you guys actually +did a lot of work. + +So first before we +get started, I + +want to thank Akamai. + +So we and Akamai got +this nice place. + +And then we are going +to give a demo. + +And we're going to have a party +sponsored by Akamai, + +which is really cool. + +So you guys actually +see something-- + +what the real-life people who +care about performance do. + +So it will be really fun. + +And also, I also want to thank +most of our MIT POSSE that + +help you guys a lot in meeting +with you individually. + +So we have people from Akamai, +[UNINTELLIGIBLE] + +Digital, Google, Lockheed +Martin, MathWorks, Wordica, + +VMWare and couple of independent +consultants who + +basically put lot of their +sweat and edge + +in helping you guys. + +CHARLES LEISERSON: +And Microsoft. + +SAMAN AMARASINGHE: +And Microsoft. + +CHARLES LEISERSON: So let's +give a hand for + +the posse, MIT POSSE. + +[LAUGHTER] + +CHARLES LEISERSON: And a +couple of the sponsors. + +SAMAN AMARASINGHE: So here +is the process we + +are going to do today. + +Today's about the competition. + +So we've set up a very strict +set of rules that we are going + +to go through, which is not +going to be the way we are + +going to grade you guys. + +Because we are going to be +little bit more lenient. + +So this is the set of rules +we are going to do. + +So we had a lot of these images +that you get submitted. + +And some images were +not exactly same. + +People did little bit things. + +They made them look little +bit different. + +So what they said was instead +of we're deciding. + +We will let you guys work on +images which can participate. + +OK? + +So don't be harsh +to your friends. + +So what we'll do, we'll first +go through the images. + +And then well you guys can say +which images should be part of + +the competition. + +This is for the competition. + +Then at the end, after you get +the Akamai sponsored prize-- + +not for the grading. + +So the fact that the images +start to count, that doesn't + +mean you get zero +in the grade. + +But you won't get to +participate in the + +competition. + +So after that, what +we have done is we + +looked at all your projects. + +Ran them on our 12 +core machine. + +And we will show you +and seed them. + +We'll say here is the order +of everything happening. + +And there are-- + +AUDIENCE: [LAUGHTER] + +SAMAN AMARASINGHE: +There are some-- + +Basically, what we'll do is +we'll pick out the top set of + +seeds in them because +we don't have time + +to run through everybody. + +And basically, a lot of these +things live are not for the 48 + +core machine. + +And then the-- + +accepted image that ran faster, +got generated faster + +in the 48 core machine, +wins the prize. + +So that doesn't mean that when +you start grading, we will + +look at all the images and we +will do some averaging. + +We will do a lot more fair. + +But hey, this is +a competition. + +We just need to find the top +guy so we have a top group. + +So we have a much more +faster thing. + +SAMAN AMARASINGHE: So +to get started. + +So here are some of the images +people generated. + +So what we want to do is show +the reference image. + +That's the reference image. + +And what we'll do is we'll first +go through everybody's + +images generated, so you +get a feel for all the + +variations out there. + +And then after that, we'll +ask you to go out. + +We'll ask you if you don't +want that image + +to be part of this. + +[LAUGHTER] + +SAMAN AMARASINGHE: You'll see. + +OK. + +So this is the reference +image. + +Why don't you go through-- + +Charles. + +Mike. + +AUDIENCE: Yep? + +SAMAN AMARASINGHE: Why +don't you go through + +the rest of the images. + +AUDIENCE: OK. + +So before we we get into the +images that we actually + +rendered in the last few hours, +I just wanted to like + +honorable mention for this. + +I think this is the coolest. + +I'm sure you guys have been +looking at a whole variety of + +broken ray tracer images But I +think this is pretty much the + +coolest thing I've seen. + +So honorable mention for that. + +And so now let's look +at things that + +people actually submitted. + +First we're going to go through +all the images and + +sort of look at the range. + +And then we'll go back +and vote on them. + +And so I'm just going to flip +through the ones on the right + +and give a couple +seconds to each. + +SAMAN AMARASINGHE: So +see if they can + +identify the artifacts. + +AUDIENCE: Which one? + +CHARLES LEISERSON: You got to +say when you're going because + +otherwise people aren't going +to realize that you've been + +through three of them already. + +Here's image one. + +SAMAN AMARASINGHE: Image-- + +AUDIENCE: Here's the next one. + +SAMAN AMARASINGHE: Image two. + +CHARLES LEISERSON: +That's five. + +Four, five. + +SAMAN AMARASINGHE: +Image three. + +image four, image five, image +six, seven, eight, nine, ten, + +11, SAMAN AMARASINGHE: 12, +13, 14, 15, OK, 15. + +There are some groups that we +could not get the rendering. + +Either it crashed, or after +ten minutes it was still + +hadn't produced an image. + +So they're not a part +of the competition. + +And of course we run them +for the finals. + +OK, now the vote time. + +OK, so this image, in or out? + +Who thinks out? + +Whoa, you guys are +a harsh crowd. + +OK. + +[LAUGHTER] + +CHARLES LEISERSON: +Who thinks in? + +Who thinks in? + +SAMAN AMARASINGHE: +Who thinks in? + +CHARLES LEISERSON: We've +got to get you both. + +Who thinks in? + +SAMAN AMARASINGHE: +So we know-- + +AUDIENCE: Do we get +screwed for this? + +[LAUGHTER] + +SAMAN AMARASINGHE: +Imagine that. + +OK. + +That image is out. + +You can take notes, OK. + +[INTERPOSING VOICES] + +SAMAN AMARASINGHE: +OK, next image. + +AUDIENCE: Number one's out. + +SAMAN AMARASINGHE: OK, +this one, in or out? + +Out. + +OK. + +AUDIENCE: Probably the same. + +SAMAN AMARASINGHE: +OK, it's out. + +AUDIENCE: It's got the funny +ring at the bottom, which I + +guess that's what most of +you are picking up on. + +I think that's kind of +disqualifying for the derby. + +SAMAN AMARASINGHE: OK, +how about this? + +Out? + +In or out? + +AUDIENCE: Out. + +SAMAN AMARASINGHE: Out. + +Whoa. + +CHARLES LEISERSON: Wow, +you guys are vicious. + +SAMAN AMARASINGHE: Exactly. + +OK, how about this? + +How many people think +they should be out? + +OK, I guess that'll +get in here. + +I guess-- + +OK, that image is in. + +OK. + +Make sure it's in. + +How about this one? + +AUDIENCE: It's okay. + +SAMAN AMARASINGHE: Who +says it's out? + +AUDIENCE: [INTERPOSING VOICES] + +SAMAN AMARASINGHE: OK, +Who says it's in? + +I think it's in. + +CHARLES LEISERSON: You should +look at the water. + +SAMAN AMARASINGHE: Water. + +AUDIENCE: The water has holes. + +CHARLES LEISERSON: The +water has holes. + +That's what's going on. + +The water has holes. + +AUDIENCE: [INTERPOSING VOICES] + +It's the only one we're going +to be able to reference. + +SAMAN AMARASINGHE: OK, so what's +the this is in charge? + +CHARLES LEISERSON: Let's +do it again. + +SAMAN AMARASINGHE: OK. + +CHARLES LEISERSON: OK, you +have to point out-- + +SAMAN AMARASINGHE: What's +the problem? + +CHARLES LEISERSON: --what's +going on in the image. + +AUDIENCE: Yeah. + +I think we should-- + +I mean, do we want to get people +to like say why they + +think it's in or out? + +CHARLES LEISERSON: It's helpful +to say what's in the + +image, though. + +AUDIENCE: Yeah. + +SAMAN AMARASINGHE: OK. + +Let's take a vote again. + +How many people think +it should be out? + +AUDIENCE: OK, that's out. + +OK, yeah. + +SAMAN AMARASINGHE: +OK, next image. + +AUDIENCE: Number 5, +on the slide. + +SAMAN AMARASINGHE: +OK, in or out? + +How many people think +this should be out? + +AUDIENCE: Is there +any problem? + +I mean, what's the-- + +[INTERPOSING VOICES] + +[LAUGHTER] + +SAMAN AMARASINGHE: I don't +think there's a problem. + +OK, good. + +Next one. + +How many think this +should be-- + +OK. + +That's unanimous, that's out. + +How many think this +should be out? + +OK, I guess that's in. + +This another one? + +AUDIENCE: Yeah, I think it's +interesting to flip back and + +forth and see the difference +between these two. + +Like, these are very +close, right? + +AUDIENCE: Yeah. + +It's obvious they're +using this one. + +[LAUGHTER] + +SAMAN AMARASINGHE: OK, +how many think they + +should be be out? + +That group once is going +to kill everybody. + +[INTERPOSING VOICES] + +SAMAN AMARASINGHE: How +about this one? + +How many people think +this should be out? + +AUDIENCE: There's not +enough caustics. + +You don't see the floor. + +AUDIENCE: Yeah, that's +an interesting point. + +[INTERPOSING VOICES] + +AUDIENCE: Say what? + +AUDIENCE: We went past ones +that look the same. + +[INTERPOSING VOICES] + +AUDIENCE: It's really +not fair. + +When you have an image and +then put that image right + +after that it's not fair. + +SAMAN AMARASINGHE: We will keep +this in because there's + +few people want it out, but +it looks pretty good. + +OK, next image. + +OK, how many people think +this should be-- + +OK, that's a clear out. + +How about this image? + +AUDIENCE: It looks OK. + +It's fine. + +SAMAN AMARASINGHE: It's fine. + +OK, anybody want it out? + +No? + +OK, good. + +That's in. + +Next image. + +How about this image? + +[INTERPOSING VOICES] + +[LAUGHTER] + +[INTERPOSING VOICES] + +CHARLES LEISERSON: We really +should start the reference-- + +SAMAN AMARASINGHE: We need +another slide to see how many + +people want that out. + +CHARLES LEISERSON: --identical +images and + +people could be voting. + +[LAUGHTER] + +AUDIENCE: Is there an +explanation why all of the + +yellows have been so +far different from + +the reference image? + +[INTERPOSING VOICES] + +[LAUGHTER] + +SAMAN AMARASINGHE: So I guess +this image is in. + +OK, next one. + +How about this image? + +AUDIENCE: It's fine. + +SAMAN AMARASINGHE: Fine. + +OK, anybody want it out? + +No? + +OK. + +How about next one? + +[INTERPOSING VOICES] + +SAMAN AMARASINGHE: It +looks pretty good. + +AUDIENCE: It's pretty good. + +AUDIENCE: It's messed up on +the left and the right. + +SAMAN AMARASINGHE: +How many people-- + +We have to count this one. + +This is too close. + +One, two, three, four, five, +six, seven, eight, nine, 10, + +11, 12, 13, 14, 15, +16, 17, 18, 19. + +19 out. + +Who says it should be in? + +[INTERPOSING VOICES] + +SAMAN AMARASINGHE: Oh, +I guess it's out. + +AUDIENCE: Oh, the number of +hands is more for out. + +AUDIENCE: OK, and that's it. + +SAMAN AMARASINGHE: That's it. + +So now, next thing we are going +to do is, we are going + +to show you a rank +in our seating. + +AUDIENCE: Yeah, so we +seeded you guys + +on the 12 core machines. + +So we seeded you guys based on +the time that it took for + +scene three on the +12 core machines. + +So here is the ranking so far. + +Top one is number one team. + +And we ranked about +the top 10 or so. + +SAMAN AMARASINGHE: Show +the real run time. + +AUDIENCE: I don't have the run +time, actually, for the seat. + +AUDIENCE: For scene one? + +AUDIENCE: Yeah. + +Actually, I can get +it real quick. + +SAMAN AMARASINGHE: You had +the graph, didn't you? + +AUDIENCE: I don't +have a graph. + +SAMAN AMARASINGHE: So here are +the rankings of the top ten. + +Do we have that graph? + +AUDIENCE: What? + +I don't have a graph. + +AUDIENCE: He has numbers. + +AUDIENCE: I just have +the numbers. + +[INTERPOSING VOICES] + +AUDIENCE: There's all kinds +of other numbers, too. + +[INTERPOSING VOICES] + +AUDIENCE: We'll say +unplug this. + +SAMAN AMARASINGHE: No, +nobody can see it. + +CHARLES LEISERSON: It's okay. + +AUDIENCE: Do we want to +get the rankings? + +SAMAN AMARASINGHE: No. + +Now, what we're going to do is +we're going to start from the + +bottom and start running it +on our 48 core machine. + +And while it's running, we want +that team to say a little + +bit about what they did to +get their performance. + +So-- + +CHARLES LEISERSON: We need +to knock out the one-- + +[INTERPOSING VOICES] + +SAMAN AMARASINGHE: Either come +prepared when you have formed + +your presentation, or make +your image run very slow. + +So you don't have to. + +So I guess-- + +CHARLES LEISERSON: First of all +we have to knock out the + +ones whose images +did not render. + +SAMAN AMARASINGHE: +Oh, that's true. + +That's true. + +That's true. + +CHARLES LEISERSON: So maybe +they all get knocked out. + +And then everybody goes +home with an iPod. + +SAMAN AMARASINGHE: Or nobody. + +[LAUGHTER] + +AUDIENCE: Can we just +put the next one up? + +Here we go. + +Now we have time +for everybody. + +SAMAN AMARASINGHE: +OK, there we go. + +So this is the time for +all the images. + +So is there any of these images +today getting knocked + +out, can you check that? + +AUDIENCE: We're pretty close. + +SAMAN AMARASINGHE: Which +images get knocked out? + +AUDIENCE: So I'm looking at +them from bottom to top. + +AUDIENCE: This is the-- + +I think this one's +knocked out. + +AUDIENCE: Number one, +two, and three. + +[INTERPOSING VOICES] + +AUDIENCE: I think David +Lamb and Victor + +Wang got knocked out. + +Because this is their +image here. + +SAMAN AMARASINGHE: That +got knocked out. + +The last image got +knocked out. + +[INTERPOSING VOICES] + +SAMAN AMARASINGHE: What's +the next group? + +AUDIENCE: In between-- + +the A group-- + +[INAUDIBLE] + +[INTERPOSING VOICES] + +AUDIENCE: This one +was the water. + +19. + +AUDIENCE: Yeah, that was. + +[INTERPOSING VOICES] + +SAMAN AMARASINGHE: Uh-oh, +they're getting knocked out. + +[INTERPOSING VOICES] + +SAMAN AMARASINGHE: OK, that +got knocked out, too. + +[INTERPOSING VOICES] + +SAMAN AMARASINGHE: Oh, man. + +Yeah, nobody competing +at this point. + +[LAUGHTER] + +[INTERPOSING VOICES] + +SAMAN AMARASINGHE: +That survives. + +That survives. + +Push! + +We have a survivor. + +So that might be a knockout +by default. + +[INTERPOSING VOICES] + +SAMAN AMARASINGHE: +Oh, that is out. + +Oh, man. + +AUDIENCE: Ours is +so close though. + +[LAUGHTER] + +[INTERPOSING VOICES] + +SAMAN AMARASINGHE: +That's all right. + +OK, I at least we have +two people right now. + +AUDIENCE: Wasn't that the one +that was really dark? + +AUDIENCE: This is the one that +was sort of darker-- + +[INTERPOSING VOICES] + +AUDIENCE: Like they +don't have enough. + +[INTERPOSING VOICES] + +AUDIENCE: So here's the +two reference images. + +SAMAN AMARASINGHE: +We already voted. + +We can't vote again. + +[INTERPOSING VOICES] + +SAMAN AMARASINGHE: No-- + +leave them knocked out. + +AUDIENCE: Some people voted +against it, but-- + +[INTERPOSING VOICES] + +SAMAN AMARASINGHE: Yeah, but +it didn't get the quorum. + +It didn't get a quorum +to get voted out. + +[INTERPOSING VOICES] + +SAMAN AMARASINGHE: How +about other group? + +First one, let's look at that. + +AUDIENCE: Who's this? + +[INTERPOSING VOICES] + +SAMAN AMARASINGHE: OK, +that survives. + +That's good. + +Mangpo. + +OK. + +That survived, too. + +Two. + +That's all right. + +Li Chen. + +[INTERPOSING VOICES] + +SAMAN AMARASINGHE: Ooooo. + +[LAUGHTER] + +SAMAN AMARASINGHE: Oh, man. + +That's a... + +So that is a knockout +blow there. + +Now what we're going to do is, +we're going to run it on from + +48 core machine from +the bottom. + +So we will let other teams also, +if we have time, to come + +and explain what they did. + +We are running-- + +who's now? + +AUDIENCE: This is a Dobs. + +SAMAN AMARASINGHE: Dobs. + +OK, why don't you guys +explain what you did. + +AUDIENCE: Come up here. + +AUDIENCE: Need the mic? + +AUDIENCE: I think +the mic is off. + +CHARLES LEISERSON: The +mic is on, but it's + +only for the video. + +SAMAN AMARASINGHE: Video. + +CHARLES LEISERSON: You have to +use the mic but you can't hear + +the speaking. + +AUDIENCE: So we parallelized +the ray tracing part. + +The two for loops for going +through all the + +pixels on the screen. + +And then we also parallelized +the main loop for caustic + +elimination. + +And we changed the-- + +sort of the data structure-- + +how that works. + +Used some like bounding +boxes to make the + +intersection faster. + +I don't know what else we did. + +AUDIENCE: We found ways +to get rid of-- + +AUDIENCE: Mic, please. + +AUDIENCE: We found ways to get +rid of a lot of trigonometry, + +which actually helped a lot. + +And we got rid of the recursion +in locate photons, + +which was a major roadblock. + +SAMAN AMARASINGHE: Question. + +AUDIENCE: What did +you do for that? + +How'd you get rid of the trig? + +AUDIENCE: Repeat the question. + +AUDIENCE: They were converting +from XYZ coordinates into + +spherical coordinates and then +back again, over and over. + +So we just didn't do that. + +[INTERPOSING VOICES] + +[LAUGHTER] + +AUDIENCE: Slow down. + +SAMAN AMARASINGHE: +It slow down. + +Uh-oh. + +AUDIENCE: No. + +The seating was done +on scene one. + +Right? + +AUDIENCE: Oh, yeah. + +Oh. + +Wait-- + +Apples and oranges. + +[INTERPOSING VOICES] + +I just ran scene three. + +[INTERPOSING VOICES] + +48. + +Scene three. + +So there might have +been a slip. + +SAMAN AMARASINGHE: No. + +But this scene one is +much more simpler. + +OK, good. + +So you're on the board now? + +[INTERPOSING VOICES] + +AUDIENCE: How is the seating +being done in scene one if it + +doesn't have a surface +that's-- + +[INTERPOSING VOICES] + +AUDIENCE: --caustics. + +It might be that some +people did really + +fast on that one and-- + +AUDIENCE: Because we ran +everybody's scene three. + +And we guarantee that the +top end teams are on it. + +[LAUGHTER] + +AUDIENCE: The results +are rigged. + +[LAUGHTER] + +SAMAN AMARASINGHE: He +detained the tape. + +OK, good. + +First team is in. + +Then the next team. + +AUDIENCE: That's Elizabeth. + +SAMAN AMARASINGHE: Elizabeth-- + +AUDIENCE: Scott, right? + +SAMAN AMARASINGHE: +There we go. + +Why their thing is being run. + +AUDIENCE: Are you running it? + +AUDIENCE: All right. + +So I guess for the display +surface, the main optimization + +there was imagining two planes +at the top bound and the + +bottom bound and seeing if a +ray passed through them and + +then only checking that +section of the grid. + +And then even within like that +square bounding box-- + +AUDIENCE: Like if there's a +square, and then the ray's + +going through like +that, there's a + +bunch of grid squares-- + +AUDIENCE: Could you use +the mic, please? + +AUDIENCE: Like if a ray's +intersecting a square, there's + +still a bunch of grid squares +above and below it that you + +don't have to check. + +So we kind of imagined +it as a-- + +projected it onto +a 2D surface. + +So we didn't check additional +superfluous grid squares. + +We also did the thing where +we got rid of the trig by + +transforming from polar +coordinates to XYZ + +coordinates. + +Although, before that, we used +the fast sign and cosign + +approximation, which +was almost as fast. + +Using a quadratic curve, +which was kind of cool. + +AUDIENCE: I think those +are the main-- + +AUDIENCE: We did an SSE matrix +multiply, which barely speeded + +it up, but whatever. + +[LAUGHTER] + +AUDIENCE: We moved +stuff into... + +SAMAN AMARASINGHE: So you are +the team that had issue going + +to Intel to AMD. + +[INTERPOSING VOICES] + +AUDIENCE: Yeah, we were +complaining about-- + +[INTERPOSING VOICES] + +SAMAN AMARASINGHE: If you use +Intel, certain instruction is + +not the same in AMD. + +OK, good. + +So we are waiting for +the time to come? + +AUDIENCE: So we ran it once, +but we forgot to time it. + +[LAUGHTER] + +AUDIENCE: It was fast enough +that we could run it again-- + +[INTERPOSING VOICES] + +SAMAN AMARASINGHE: So by the +way, I want to give a chance + +for the top team that +get knocked out, + +explain what they did. + +Even though they are not in +competition because they ran + +much faster in the same run. + +Who's the top team? + +AUDIENCE: [UNINTELLIGIBLE] + +SAMAN AMARASINGHE: Who's +the top team up there? + +[INTERPOSING VOICES] + +CHARLES LEISERSON: They're +getting sleep. + +[LAUGHTER] + +SAMAN AMARASINGHE: OK, 59. + +Uh-oh, now we-- + +Oops. + +OK. + +AUDIENCE: Ooo... + +SAMAN AMARASINGHE: Inversion +off that. + +OK, next team. + +AUDIENCE: So our team also +did a same trick. + +That was done in the +previous two teams. + +We got rid of the +trigonometry. + +And also used a bounding box. + +Basically described in +the previous team. + +And we also tried to use SSE. + +But as soon as the news +about an AMD machine, + +we got rid of that. + +[LAUGHTER] + +SAMAN AMARASINGHE: Oh, my +look at that speed. + +AUDIENCE: Whoa. + +SAMAN AMARASINGHE: Whoa. + +Woo! + +[LAUGHTER] + +OK. + +AUDIENCE: If you want to take-- +could we take more time + +to talk about it-- + +SAMAN AMARASINGHE: Yeah, sure. + +Yes. + +AUDIENCE: Because I'm sure you +guys have some things that are + +different than everybody +else's. + +In fact, I know it. + +AUDIENCE: It's on. + +It's just on. + +SAMAN AMARASINGHE: It's on. + +It's on. + +It's already recording. + +So for the cache I use like +a three-dimensional grid. + +Because I realized that as the +old times, the torrents is + +like usually one, unless +there's some outlier. + +But I don't see one +in my case. + +So I use a three-dimensional +grid. + +And use a lot of locks to +prevent contention. + +So I do the same thing +for photon map. + +I basically implement my +own photon map and + +just get rid of theirs. + +And also, the same thing, +like using a grid. + +And I spent a lot of +time debugging. + +[LAUGHTER] + +AUDIENCE: And we also do some +minor optimization. + +We implement the rendering +crest as a reducer. + +So that we-- + +a hyper rod object So that every +time Cilk steals some + +other's job, you will create +a local view of + +the rendered object. + +And we found there is a artifact +that-- because we are + +seeding the rendered object. + +The default that seed +is two, right? + +And it will create some artifact +in our image, so we + +use a random number to seed +that rendered object. + +That's what we do. + +And also, we do something +like we change the-- + +no, we don't have +locate photon. + +Yeah OK. + +So we have done a lot of thing +to improve the original photon + +med but after that we decide to +change our implementation + +of photon med so we +don't use that. + +OK. + +PROFESSOR 1: OK, good. + +Thank you. + +OK. + +OK, the suspense is on. + +So the final team. + +OK. + +STUDENT 8: So one of the first +things that happened is that + +we looked at the code and, like, +it was all a KD tree. + +And we're like, what's that? + +So we got rid of that +immediately and we turned it + +into something-- + +I think the other groups might +have talked about it, but we + +gave it a nifty marketing +name, we + +called it a photon cube. + +And so we created +lots of these. + +We partitioned the large cube +environment into many small + +photon cubes so we could just +jump in and look in the + +relative air vicinity +of photons that + +you're looking for. + +STUDENT 9: Yeah. + +So this is like, when you do +locate photon, you know the + +reference photon and you +can create a sphere. + +So we can do constant time to +find the boundary of the + +photon cube. + +Like go from x1 to x something, +y to y and z to z. + +So then we don't have to +traverse the tree. + +And we basically parallelized +two part, so the one in render + +and another one in the trace +photon that when we try to put + +the photon in the map. + +And also when we create a photon +to the cube, there is a + +reused vector to start a +photon in each cube. + +But then it's not really good, +because when you put the + +photon in the cube, you have +to, like, new photon. + +Which means that the memory, +it's like spurts throughout + +your program. + +So after that we convert that +into a block of memory. + +And we use that when we +call locate photon. + +STUDENT 10: And for the last, +about surfaces that intersect. + +There were four kinds +of optimizations. + +First one is checking if the +origin of ray is outside of + +the maximum bound and lower +bound of surface, then and + +check whether by direction is +outside or if it's toward the + +outside then we don't have to +check, just return false. + +And second thing is like +the square cube thing. + +When rays intersect we can make +a boundary by directly + +mapping to the XYZ at the +surface at the maximum + +boundary and lower boundary +of the surface. + +And also when you iterate +through the x index, we can + +cut off again because +a bitmap. + +We only have to check with the +indexes which correspond to + +ray's z index at that cube, +at that x location. + +And the last thing was for each +square we pre-computed + +the minimum value and maximum +value of y and we compared the + +rays by value within +that range. + +And we just cut off if +it doesn't intersect. + +It doesn't overlap. + +PROFESSOR 1: OK. + +Good. + +OK, now this is the +suspense part. + +OK. + +We are going to run +this and see. + +The time to beat is 18.7. + +OK, right? + +Again. + +OK. + +There we go. + +Let's see. + +How many people think it's +going to beat 18.7. + +18.6. + +OK. + +AUDIENCE: 8, 9, 10-- + +PROFESSOR 1: It's +the excitement. + +Keep counting. + +OK. + +There we go. + +AUDIENCE: 13, 14, 15, +16, 17, 18, 19-- + +PROFESSOR 1: Oh, oh, oh. + +AUDIENCE: 21, 22, +23, 24, 25, 26. + +PROFESSOR 1: Oh, OK. + +It came out as 26.41. + +OK. + +[APPLAUSE] + +PROFESSOR 1: So you guys +are the winners. + +Come up here. + +AUDIENCE: Danielle. + +PROFESSOR 1: Where's Danielle? + +AUDIENCE: Uh, Danielle +disappeared. + +AUDIENCE: Yes, she did. + +PROFESSOR 1: OK. + +Let's see whether she +can find her, so OK. + +Just hold on a second until-- + +AUDIENCE: Yep, there we go. + +PROFESSOR 1: You can put +it down now, though. + +PRESENTER: So this one's +the reference. + +PROFESSOR 1: Put a text meter +in, that's better. + +AUDIENCE: Which one's +reference? + +PRESENTER: This one's +the reference. + +PROFESSOR 1: I think +they don't align. + +Can you align them? + +PRESENTER: There we go. + +PROFESSOR 1: OK, so we +have a winning team. + +PROFESSOR 2: We have +a winning team. + +And so it's my pleasure to +introduce Danielle Smith, who + +is the University relations for +Akamai, and she's here to + +give you guys your prize. + +So we have three winners. + +DANIELLE: I just wanted +to make an entrance + +is why I came in. + +Thank you. + +First of all, welcome to all of +you guys for coming in, and + +we wanted to give you +these prizes. + +So we have some cool iPod Nanos, +which you may or may + +not have already, but it can't +hurt to have another. + +They kind of burn out +or you lose one or + +someone steps on it. + +[APPLAUSE] + +DANIELLE: Congratulations. + +You guys have worked +really hard. + +PROFESSOR 1: Congratulations. + +Congratulations. + +Congratulations. + +OK. + +So what's next. + +That's it. + +We are done? + +DANIELLE: All righty. + +So we have plenty of food, +it's going to be + +right on the atrium. + +I know that's the most +exciting part. + +But it should be arriving in the +next 10 to 15 minutes, so + +we have a few minutes. + +I thought maybe this would +go a little bit longer. + +PROFESSOR 1: We do +have a couple of + +things we can chat about. + +DANIELLE: Yeah. + +So just a couple of housekeeping +things. + +If you need to use the ladies' +room or the men's room, it's + +actually right outside +that door. + +Out the double doors, you'll +see it right there. + +I have invited some other Akamai +employees to come and + +mingle and say hello to you +guys, so I encourage you, if + +you see any faces that aren't +familiar, to kind of go up and + +talk about your projects +and introduce yourself. + +And thanks for coming. + +I know we wanted to switch it up +a little bit because it was + +the last class. + +We wanted to get you out of the +classroom and just kind of + +shake it up. + +So I'm glad that you +came to join. + +PROFESSOR 1: And the +knock tours. + +DANIELLE: And the knock tours. + +Thank you. + +So on the back of your name +tags, there's a number, one, + +two or three. + +One, two or three. + +So that correlates with +the knock tour that + +you're going to be on. + +We have to keep it to relatively +small groups. + +So the first tour will be at 10 +past 4, the second one will + +be at 4:40, and the last +one will be at 5:10. + +PROFESSOR 1: I guess if we don't +have too many people we + +might be able to +compress some-- + +DANIELLE: Yes. + +PROFESSOR 1: So we'll +see whether we + +can do that, compress-- + +DANIELLE: Yes. + +So I'll just call the first tour +and you guys can go down. + +And obviously it's optional. + +Don't feel-- if you're not +interested, you don't have to + +go on the knock tour. + +I think that's it. + +PROFESSOR 1: Good. + +Thank you. + +[APPLAUSE] + +PROFESSOR 1: We can talk +about a little bit. + +So one thing. + +We are trying to get HKN +feedback up to hopefully 90%, + +and we are right now +at what, 11? + +PROFESSOR 2: No, we're +a little bit higher. + +We're now at about 16 or so. + +PROFESSOR 1: 16. + +So that's a little more way +to go from 16 to 90. + +I hope you guys go back and +then fill out this survey. + +Very important. + +PROFESSOR 2: Please take a +few minutes to do that. + +It really helps us in, +even if you want to + +say bad things, OK? + +It really helps overall to +give feedback and the + +department likes to +see these things. + +Oh yeah, thanks. + +Likes to see how it +is that people are + +responding to the courses. + +So if you hated the course, if +you liked the course, in + +particular, we have some +questions on there that are + +specific to how we teach +the course next year. + +One of the ideas we have for +next year is to introduce our + +recitation sections, +which would focus + +on the use of tools. + +OK? + +So basically the conceptual +stuff, much as we have the + +lectures now, but then also +having something where it + +really takes you through each +tool, and teaches how the use + +of those tools which would +be taught once a week. + +So if you think that's a good +idea, that's going to really + +help to have that kind +of feedback. + +And it will certainly help the +students who take it next year + +if we can persuade the +department that that's worth + +staffing the sections +next year. + +Also if you have any positive +things to say about teaching + +assistants, that's a great +place to put it. + +OK? + +If they helped you get through +this term, this is a great + +place to say thank you and it +only takes a few minutes. + +OK? + +So I'm sure that some of the +TAs put in more than a few + +minutes, OK, on your thing. + +So to take a few minutes +and say thank you on + +that form would be-- + +I'm sure they would very, +very much appreciate. + +PROFESSOR 1: One thing, as +Charles mentioned, what we are + +trying to do in recitation is do +a little bit of programmer + +life skills. + +So I know all of you guys are +probably very smart, can think + +about the complex algorithms +and stuff like that. + +But there are a lot of tools +that, it's not the smartness + +but you can spend hours +trying to figure out. + +But if you know it, +it will be useful. + +So what we are trying to do is +have these recitations to say + +OK, how to use a debugger. + +And even how to change +a makefile. + +Things like that. + +So one thing, until the food +arrives, I'd like to say is, + +get some feedback. + +Think of what is a tool you'd +like to know or like to learn, + +or something you think is very +useful for people coming next + +year to learn. + +That if you have spent a lot of +time worrying and you think + +you spent way too much time +trying to understand, it would + +be easier for us to +think about that. + +I mean, I would like to +get your feedback. + +And also some of you probably +will open up with some general + +feedback on class. + +AUDIENCE: I don't know if +you want to repeat that. + +A more in depth thing +on how to use git + +would be really useful. + +Because I know it has things to +make your life easier, but + +I don't know how to +use any of them. + +AUDIENCE: Yeah. women are always +breaking the branches. + +And it's like, yeah, we maybe +know how to do this and it is + +really easy. + +And then we're like, use +this git command. + +And it's like, now your +branch is broken. + +[LAUGHTER] + +PROFESSOR 2: Good. + +So git + +PROFESSOR 1: Yeah. + +I mean that's because those are +interesting tools because, + +if you know everything +right, you can do + +a lot of fun things. + +But if you do it wrong, you end +up in huge mess that all + +you do is scored all over the +place and you don't know. + +So yes. + +I mean I can relate to that. + +AUDIENCE: If you use git +correctly, if you + +know how to use git-- + +If you learn how to use git you +will find yourself using + +it even when you're working +on a one person project. + +git is awesome. + +I can highly recommend +learning it. + +AUDIENCE: What would be helpful +is that telling us + +that you are running on an AMD +box and AMD doesn't support + +SSE 4.1 instructions. + +[LAUGHTER] + +PROFESSOR 1: Yeah, I mean, this +is supposed to be X86 + +compatible, all those things. + +But I mean, some people learn +the hard way that, OK, the + +word is not the same +even though-- + +PROFESSOR 2: But that is part +of the lesson of the course, + +is how do you make high +performance portable? + +OK? + +And so what you choose or +don't choose to use is-- + +But I agree. + +PROFESSOR 1: That's why we ran, +we want to run it the + +night before because we knew +things like this would happen. + +So we can at least give some +time to say OK, look. + +Go change something. + +Were you able to fix that? + +OK. + +Good. + +So yes. + +PROFESSOR 2: Good. + +PROFESSOR 1: And sometimes the +problem is, a lot of these + +small changes you don't know +until you run into things like + +this and oh, somewhere in page +256 in the manual that there's + +a footnote say, oh, +by the way. + +And that's what happens +in there. + +I mean if you had listed +everything that would be + +probably and entire encyclopedia +of things that + +you will see. + +PROFESSOR 2: So one other thing +that people ask about + +is, what comes after +this course? + +OK? + +So next term Saman is teaching +the compiler course. + +PROFESSOR 1: It's Martin. + +PROFESSOR 2: Are you +teaching with him? + +PROFESSOR 1: No. + +PROFESSOR 2: Oh, you're +not teaching. + +OK. + +I thought you were. + +OK. + +So in any case, compiler +course is a + +good follow-on course. + +For those who haven't done +6.046, that's a good course + +and I'll be teaching that +course next term. + +In addition, how many people +here have done a UROP? + +Few of you. + +So let me encourage you +to look for UROPs. + +You now have some skills that +will make you really valuable. + +And in particular my group +is looking for-- + +[LAUGHTER] + +PROFESSOR 2: Probably two more +UROPs than I have already. + +Already Boone is one of my +UROPs, started just a + +couple weeks ago. + +And so we do have some other +projects in both architecture + +and in software-related things. + +And so. + +if you're interested, you go +to my group's web page. + +It tells you five things you +have to submit if you want to + +work in my group. + +OK? + +That includes things like +samples of your code. + +Well, you ought to +have that by now. + +And so forth. + +So let me encourage +you to do that. + +And Saman also has active +participation of + +UROPs in his group. + +PROFESSOR 1: Yeah. + +So my employees already +started doing a + +project in my group. + +And I'm also looking for a +couple more people to do some + +compiler, runtime system, and +a bunch of high performance + +type projects I have. + +And also for future course, +one course I want to also + +mention is this IAP. + +There's a course that is done +with collaboration with VMware + +to look at how to build scalable +large systems using + +this the Spring and +Java platforms. + +So if they're interested in +trying to see how things were + +running on one machine and run +something that can scale up to + +hundreds of machines. + +If you have ideas of creating +an I 8 with web 2.0, + +interesting thing. + +Here is an opportunity +to do that. + +So if you're looking +for interesting IAP + +courses, this is great. + +PROFESSOR 2: I really encourage +every single person + +who completed this class +to do a UROP with + +somebody before you leave. + +It's really a way of integrating +your knowledge. + +And it is one of the most +valuable experiences that you + +can have at MIT is to do a UROP +for a professor and get + +involved in the research +of a group. + +Because in some ways it's like +this course, in that it + +integrates knowledge from a +lot of different sources. + +And it isn't just one thing. + +But even more than +this course. + +This course we still +are dealing + +with artificial things. + +And in the researcher +arena, you're + +dealing with real problems. + +So let me just once again +encourage you to spend some + +time getting a UROP and +certainly looking + +for AUPs and MEng. + +How many people here are +looking at MEng as a + +possibility? + +So a fair number. + +Yeah, that's good. + +That's great. + +PROFESSOR 1: I want +to add to that. + +So these days there has been a +big philosophical discussion + +saying why do you have +to have universities? + +You go to OCW and sit home in +your bedroom and you can + +follow all these courses, +and you don't have to + +pay a mighty tuition. + +And wouldn't that +be good enough? + +One part that's not good +enough is this class. + +So I mean think about it. + +I mean you can't go get the OCW +catalog and have this kind + +of a dynamic. + +There's no seventh floor. + +All in OCW. + +And you have from there to +go and get motivated. + +So that's one part of that. + +PROFESSOR 2: There's no John +or Reed or Eric or Josh to + +respond quickly about +what's going on. + +PROFESSOR 1: That's one. + +But I think one other thing that +a lot of people miss when + +they look at all of the +curriculum and stuff like that + +is the UROP ability. + +So a lot of these people, that +is something, it's very unique + +to MIT and a lot of people +benefit hugely with UROPs. + +I have had UROPs who started +with me as seniors. + +By the time they are graduating +with their MEng + +they have two first out +papers in the best + +conference out there. + +And everybody thinks, when they +say they are looking for + +a job, they are finishing their +Ph.D and looking for + +academic jobs. + +No. + +They are just finishing +up their masters. + +And I have a couple of students +that managed to + +become really expert in an +area by being a UROP. + +So they are finishing up at MIT +as a generalist, saying + +give me a job. + +But you're finishing up +and have some deep + +knowledge in some area. + +Sitting in and at the same level +as most Ph.Ds or most + +really deep practicing engineers +in that area. + +So that level, even if you don't +do that, just seeing + +what happens in a research +group, being + +participating on that. + +Pushing, seeing something +to the maximum limit. + +I mean in the class, +that's a limit. + +I mean even though this class is +somewhat open, says make it + +run as fast as possible. + +But most of the time in the +class, it's like, we give you + +something, if you made that, +OK, you're done with it. + +In research, there's no limit. + +You really, really push +your boundaries. + +What's that? + +PROFESSOR 2: So what do +we have here, John? + +JOHN: I counted in my mailbox +how many messages came from + +6.172 staff, and it's +about 3,500 over the + +course of this term. + +PROFESSOR 2: Wow. + +[APPLAUSE] + +PROFESSOR 1: How much time-- + +PROFESSOR 2: So, this is also, +as Saman mentions, a + +programmer life skills course. + +And one of the things that you +should get used to in life is + +thanking people who help you. + +OK? + +I think that all of the MIT +POSSE members, all the people + +who devoted, volunteered their +time to help you, could really + +appreciate an email that says +thank you and what exactly you + +feel you learned from them. + +OK? + +Because it's one thing +to just say + +thanks, so long, et cetera. + +In addition, these people are +contacts, part of your network + +of understanding what the world +of software developers + +is all about, and can serve as +useful contacts to keep. + +How many people use a service +like LinkedIn + +or something to-- + +You probably all you mostly +use Facebook. + +Anybody use LinkedIn +at this point? + +So many professionals use-- + +I don't want to pitch for +LinkedIn, but it is one of the + +services that lots +of people are on. + +So what are some of the other +services that people use for + +professional contacts? + +AUDIENCE: The only thing +people try to + +contact me on is LinkedIn. + +PROFESSOR 2: Yeah. + +So, good idea to start +connecting and building a + +network of people who you +know and who can answer + +questions for you. + +OK? + +Such as, gee, I'm considering +these two kinds of job offers. + +What should I be looking for? + +It might be good to get a +professional software + +engineer's input to that. + +OK? + +Because you know these folks. + +You've had a few meetings +with them. + +OK? + +And they know you. + +And they may be able to say +here's my take on that, as + +well as getting input from your +family and your friends + +and your professors and other +people that you know. + +But I do think that courtesy +goes a long way in life. + +And they really have, these are +all people, as I say, who + +spent time looking +over your code. + +And you should have heard some +of the comments we got from + +them after project one. + +Oh my God, they have a single +letter variable names for the + +whole thing. + +Or, what are you teaching +these students? + +And I said no, this is exactly +why we want you there. + +OK? + +So I think that if you feel in +particular, whether or not you + +feel you got anything +out of it, OK? + +But in particular, if you did +get something out of it, it + +would be really good idea to not +forget to send some email + +off to thank them. + +PROFESSOR 1: OK, we want to get +some feedback from them. + +PROFESSOR 2: Sure. + +PROFESSOR 1: Have open mic? + +PROFESSOR 2: Open mic? + +PROFESSOR 1: Yeah. + +PROFESSOR 2: Actually, open mic, +let's do it like this. + +Because I think it'll be easier +and better for the + +video if we just have +people come up and-- + +PROFESSOR 1: I don't know that +they're going to be too + +intimidating. + +PROFESSOR 2: That's OK. + +They can handle it. + +These are seasoned-- + +So, comments about the class. + +PROFESSOR 1: How +we can improve? + +We'd really like to hear that. + +I mean things you liked +and didn't like. + +For example, these absolute +gradings we did for projects + +had passionate support and +control let's say before. + +I mean, did you guys feel giving +the top marke for the + +fastest and having at least a +log scale, no, we didn't do a + +linear scale going down. + +I mean, hey. + +Was it motivating +or demotivating? + +PROFESSOR 2: So what do people +think was the most valuable + +thing out of the course? + +I've had dinner with a few +of you, and you were very + +opinionated over dinner. + +So I don't mind hearing those +comments again, but making + +them for other people. + +So I know it's intimidating, +but what I want + +to do is get a line. + +As one person's talking +I want other + +people to line up behind. + +And just give us +some feedback. + +PROFESSOR 1: Come on. + +PROFESSOR 2: OK, come on, come +on, come on, come on. + +Who's brave? + +Yeah, yeah, yeah yeah. + +You got halfway of your seat. + +Yeah. + +PROFESSOR 1: Yeah, come on. + +PROFESSOR 2: I'm sure +you have an opinion. + +Who here does not +have an opinion? + +PROFESSOR 1: Sure. + +Yeah. + +PROFESSOR 2: Yeah, yeah, good. + +And then you can +line up right-- + +there you go. + +OK? + +There you go. + +And then others can come up +behind as they're motivated. + +AUDIENCE: Good afternoon. + +First of all, I'd like to thank +the professors and the + +TAs for this opportunity. + +This is absolutely wonderful. + +And all the students +I worked with. + +You were all great. + +I just wanted to say when you +were talking about what the + +most valuable thing in the class +people thought was, I + +don't even know how to pick. + +Of the projects that we worked +on, or that they worked on, I + +looked at every one and just +thought, what of the content + +of this project have I used +just in the past year? + +And the amount of stuff that +I've made significant use of + +that you guys covered has been +at least 75%, maybe even more, + +of the material of the class. + +And that means that if you look +over multiple engineers, + +you probably pretty quickly get +coverage of 100% of it. + +All these projects, profiling, +parallelism, algorithms, bit + +hacks, these are all things +that I use on. + +if not a daily basis, +then a weekly basis. + +PROFESSOR 2: OK. + +Good. + +Thanks. + +Thank you. + +[APPLAUSE] + +AUDIENCE: So for me, like, I +really had no experience with + +C or C++ or really distributed +version + +control before this class. + +So a lot of my time I think was +spent kind of learning the + +basics of that. + +I spent a lot of time initially +learning the basics + +like pointer arithmetic and +that kind of stuff. + +And then a lot of time learning +the profiling tools. + +So I wish, I really do wish more +time was spent kind of-- + +well, your recitation, I think, +would be a good way to + +really get that out +of the way. + +Because the algorithmic stuff +was more easy for me, which I + +thought was kind of ridiculous. + +You know? + +[LAUGHTER] + +AUDIENCE: The fact that these +tools are what's holding back, + +that I have to spend a +lot of time learning. + +PROFESSOR 1: This is actually +something very interesting + +people have observed. + +So if you do physics problems +or math problems, if you run + +into an issue, after a certain +amount of time you will just + +go ask somebody. + +But in programming, people seem +to go on and on and on + +trying to debug this +simple thing. + +And part of that, part of what +we try to get is also not just + +all the cool algorithms +and stuff like that. + +To give you a process. + +Because there are times when you +start saying this program + +is slow, what you do? + +And I think that's a missing +part sometimes about the + +process of debugging. + +If the program doesn't +work, what do you do? + +Where do you start? + +I think that's why we are trying +to do a little bit of, + +basically, these life skills. + +AUDIENCE: It was great to +learn but it was more + +stressful to learn. + +I'm not as willing to ask as a +lot of people, so it's hard + +for me to-- + +PROFESSOR 1: So one thing we're + +trying to do is probably-- + +PROFESSOR 2: That's +great feedback. + +PROFESSOR 2: We will try to +formalize next year the + +seventh floor lounge, because +a lot of people + +who came there benefited. + +But have it a little bit more. + +And also get a little bit +more life skills type + +things early on. + +Like if you find a problem, +what will happen? + +AUDIENCE: It could be a +lot longer than that. + +PROFESSOR 1: Yeah. + +PROFESSOR 2: Yes, so that's +our goal, is to make it so + +that people come up to +speed more quickly. + +But in some sense, another goal +but I have here, next + +year, is that the C students +will stay in the class. + +OK? + +So what happened is most of the +C students dropped out. + +So in case you want to know, +most people are going to get + +A's and B's. + +OK? + +So most of the C students +dropped out. + +And I would like to have people +complete the course, + +even the C students, feeling +that it's useful to complete + +the course. + +AUDIENCE: So I think again, +as the person before me, I + +learned a lot. + +I hadn't had almost any +experience in C or + +C++ before the class. + +I had some experience +with git. + +But I think that the class +has a lot to offer. + +There's a lot of content +covered. + +And I wish that, for example, +there are things that I wish + +that I could have learned more +about, how to implement in a + +formal way. + +Things like SSE instructions. + +So I feel that like there was a +clear cut off of people who + +had a lot of experience and they +could be like, OK, I know + +how to do assembly, I know how +to do other things, and if I + +want to optimize this function +I can, whatever. + +Write it down. + +And then there's these other +people that don't have that + +much experience that in a class +it mentions this is how + +you use SSE or compiler +optimizations. + +It's kind of mentioned but +not really more in depth. + +This is a case of how do you +actually do this in real life? + +I mean, I think maybe the +examples given in class were + +useful but very superfluous. + +Like you don't really know. + +I know that I was looking +through other projects that + +were similar to ours +for the final. + +And I think it's a class +that you taught in IAP. + +There was a team of people that +did a ray tracer in the + +multi-programming. + +And they used SSE and +CMD everywhere. + +They packaged everything. + +But that's something that I +said, it'll be really awesome + +to do, but I have no idea +how to start doing it. + +And I think that there's still +a lot of room to actually + +apply the concepts that are +trying to be taught. + +PROFESSOR 2: I think it's our +intention actually to increase + +that part of the course, +the data + +parallel part of the course. + +Which I think we'll +be able to do. + +One of our concerns about adding +material has been, OK, + +that means you guys have +to learn it too. + +But I think that if we're able +to reduce the workload of the + +learning of the tools by having +recitations, we then + +can look at adding other +material, and expect that the + +load on students won't go up. + +AUDIENCE: Right. + +I mean even what +I want to say. + +It's not even adding material, +what I think. + +I feel that I was going to +class, learning all of these + +cool things. + +And then I was looking at my +project and it's like well, + +these are the things that +I know how to do. + +And I know that they +mentioned all these + +other things in class. + +I don't know how to make +them in my project. + +PROFESSOR 2: Great comment. + +PROFESSOR 1: So I think one +thing both good and bad about + +this class is what +happened in-- + +I think it applied +to all of you. + +When you try to teach computer +science, you get people who + +are for the first time they are +writing any piece of code + +more than 20 lines. + +And you get people who are +checking in code for Apache. + +And you have that entire range +of people in the class. + +So how do you teach everybody? + +And a lot of times when you give +a fixed project, either + +somebody's completely struggling +to finish that, or + +they are like in +a day is done. + +They are like, so what's this? + +What's new? + +The thing about performance +is, asked lot of people, + +figured out there's +no end to it. + +And you can keep doing +it, you can do more, + +you can do more deeper. + +So the nice thing about-- + +one thing about this class is +that there's something for + +everybody in that. + +So if you are struggling still, +if you're learning, you + +can still get to someplace, +learn a lot. + +But if you have done that when +you are in the fourth grade, + +you can still go and do +something more, push that. + +So we try to keep that +balance in there. + +So we don't want to +bore anybody. + +And also we don't want a lot of +people dropping out of the + +class either. + +AUDIENCE: So continuing on with +what other people said, I + +also ran into the same +problems with that. + +Just the syntax, +just the tools. + +So I guess I'll start off +thanking John and Reed, + +they're really fast and good +at what they're doing. + +And I feel like I've asked a +lot of dumb questions, and + +they're good at answering +those. + +[APPLAUSE] + +PROFESSOR 2: So John and +Reed and Josh all took + +the class last year. + +OK? + +And it's amazing, if you +ask John how he did + +on the final project-- + +[LAUGHTER] + +PROFESSOR 2: He didn't +do so well. + +OK? + +But it's amazing. + +You'll discover, it's amazing +what you guys are going to + +learn next semester after +being out of the class. + +Because you're on a path to +learning this stuff for + +yourself now. + +OK? + +And you'll find that in all +kinds of things you do that + +all these skills, you can +keep building them. + +We will definitely be looking +for TAs next fall. + +And so people who are +interested should-- + +who are going to be +MENGs should-- + +and even if you're +undergraduate, you're still + +allowed to work hourly +for the class. + +In fact, that's what +John is doing. + +So if you're interested, +please let us know. + +Please let us know. + +PROFESSOR 1: So you can have +this nice experience as a TA. + +AUDIENCE: Yeah, so, and then I +want to say something that I + +really love about this course. + +I feel like it's such an +integrated experience. + +It's, maybe except project one, +everything after that is, + +you get a piece of code, as you +would normally, and then + +everything is within +your bounds of-- + +you can do anything +that you want. + +So I really like how it's not +limited to like, oh, we're on + +this topic so we're going to +write a little algorithm that + +implements this particular +algorithm, and then move on to + +next unit, and then nothing +ever comes together. + +So that's something I really +love about this course. + +And the next thing I want to +say is the beta grading. + +For project three, I was working +with Angela, I feel + +like from beta to final, because +I don't have much + +experience with C, so it takes +me so long to just get the + +syntax right, to get +my own going. + +So for beta, we didn't have +anything working. + +It doesn't even build. + +But with two or three more +hours, we got it working. + +It's not super fast, but +we kept working on it. + +And by the final we have +something I felt pretty proud. + +But the beta grading doesn't +take that into account. + +Like if you are not very +experienced with C, it takes + +you a long time, longer than +other people have experienced + +to get something going +in the first place. + +But beta kind of penalizes you +for just not having enough + +time to do things you want. + +PROFESSOR 1: I think it's +a double-edged sword. + +Because if you don't do beta, +then you have very harsh. + +You have one time code, +it's in and out. + +If you just really don't do, +give that much grading for + +beta and make it optional +and stuff like that, + +people just drop beta. + +They don't just do +anything in it. + +So we try to do something, give +everybody a true chance + +and get everybody a real +motivation to actually work + +for both sides. + +Because for a lot of you +guys, beta defined and + +you learned a lot. + +Because you got something +in beta. + +And for most of the classes I +have, we had things called + +checkpoints. + +For example, compiler class, you +had to do a checkpoint and + +checkpoint will be used more +like subjectivity to grade. + +We don't say how many grade +percent checkpoint. + +But if checkpoint has nothing, +then we'll be very harsh + +grading later. + +We always provide that. + +But still, people don't take +checkpoint that seriously. + +But here we have to try to make +something to make people + +get beta seriously, do something +there, and then give + +them the opportunity +to improve. + +I think there's a balance +in that somewhere. + +PROFESSOR 2: And I wouldn't +worry about your grade. + +[LAUGHTER] + +AUDIENCE: Maybe like one idea +I was thinking is maybe + +there's some component +of improvement + +from beta to final. + +Like the proportional +improvement that you made from + +beta to final. + +PROFESSOR 2: Oh, that's +a good idea, actually. + +That's a good idea. + +Yeah, to say, if you made a-- + +Although you want to be +careful about people + +sandbagging. + +[LAUGHTER] + +PROFESSOR 1: Exactly. + +AUDIENCE: And then one +last small thing-- + +PROFESSOR 2: I want to make +sure we get to everybody. + +AUDIENCE: OK, sorry. + +PROFESSOR 2: So if you +want to go around to + +the end of the line. + +AUDIENCE: That's actually +mostly all of it. + +PROFESSOR 2: OK. + +Thank you. + +AUDIENCE: So I've said some of +this on my evaluation, which I + +already turned in. + +But I'll repeat it for +everyone else. + +[APPLAUSE] + +AUDIENCE: A couple things. + +One relating to the grading +which you mentioned. + +Honestly, I found it incredibly +stressful knowing + +that it was competitive +grading. + +Because we had no idea where +the benchmark was. + +So it's like, well we've +improved it. + +But did we improve it enough? + +Did everyone else not improve +it any more than we did? + +And it was just like having it +be a complete unknown was + +pretty stressful. + +So I don't know if there's some +way you could do like a-- + +like maybe the TAs got some +speed up, and that's the + +benchmark to start with +or something. + +PROFESSOR 1: I guess what we did +this time is basically we + +gave the best grade as a +benchmark for the final. + +And if you go above that, it's +just bragging rights. + +AUDIENCE: I mean, when you're +working on the beta, you have + +no idea what's going on. + +But I did like that. + +Once you know where the +benchmark is, then it's nice + +to know what you're +aiming for. + +PROFESSOR 1: So the thing about +that is, the flip side + +of that is, we don't want +somebody that a lot of courses + +they say OK, I'm done. + +When you go there something, Oh +yeah, I met the thing, OK, + +I'm getting a good grade, +OK, I move on. + +I mean, we want people kind of +to keep pushing in time. + +Because sometimes +the thing is-- + +If I have a minute, I'll +tell the story. + +There's this guy named Tony +Danzig who basically invented + +the simplex method. + +His thing was, he was always +late to class. + +He went to class one +day and there was-- + +normally the professor writes +the problems on the board. + +So he copied the problems +down and went home. + +And they were really +hard problems. + +And so he was like, damn. + +I don't know how +to solve this. + +And he worked very hard +and solved it. + +And wrote a note to the +professor saying I'm sorry + +this is late, and put +it on his desk. + +And a couple of hours later he +gets this excited professor + +running around trying +to find him. + +Because what the professor had +done is written two unsolved + +problems on the board. + +He came late to the class, he +didn't know that, he had two + +problems, he copied them down. + +He worked very hard +and solved it. + +[LAUGHTER] + +PROFESSOR 1: And so the +professor said divide this up, + +you get your pay at the end. + +Then there's lots of it. + +So this is something +like that. + +If you give the thing, if you +know where we are going, for + +some people it will +be a hard climb. + +But other people, they will get +there faster, they'll say + +OK, I'm done. + +And what we want to do is give +them the ability to kind of + +really push to their limits, +not some artificial limit. + +But not to penalize +too much for that. + +We try to balance this out. + +So I want everybody to go +to their best limits. + +AUDIENCE: I had one other +thing to say. + +Have you considered or would +it be possible to make the + +class more than a 12 +credit course? + +[LAUGHTER] + +AUDIENCE: No, seriously. + +Since there is so much material +and we keep talking + +about wouldn't it be nice to +add this and add that. + +But I don't know about you, but +I spend a lot of time in + +this course already. + +And I mean, I think it's the +kind of class where you could + +pack 16 or 18 credits worth +of material into it. + +PROFESSOR 2: More realistic +would be to have a follow-on. + +PROFESSOR 1: Try to make +it as two classes. + +PROFESSOR 2: To make a +two-semester sequence. + +But I think Saman and I still +feel that this, it's like, OK, + +that's a new development +effort. + +That this class still-- + +I think we feel that there's +more than incremental + +improvement we can do to make +the class teachable. + +For example, by introducing +recitations. + +And so I think once-- + +maybe after next semester, +next fall we can we can-- + +But thank you, because I think +that that would be good. + +And the whole idea of the +sections is to try + +to reduce your load. + +There used to be a thing that +was on all the evaluations + +that they no longer do. + +And this is actually before +I got to MIT. + +They had a measure called +cums per tooling hour. + +OK? + +So a cum is how many units of +knowledge you're using in + +whatever measure, and tooling +hours, like how hard you work. + +And they got rid of it because +they said it was not + +quantitative. + +After all, what's a cum? + +All right. + +Well, regardless of the fact +they got rid of that, because + +I think that it actually was a +very useful measure, even if + +people are subjective +about it. + +That's our goal in the course. + +It's not to make people spend +a lot of time and then have + +learned epsilon. + +It's to have them, for the time +they put in, learn as + +much as possible. + +And so I think that we recognize +it's a lot more work + +right now that you folks +are going through. + +We hope that it's +rewarding work. + +But we hope we can do even +better in terms of giving + +people the opportunity to +learn these things. + +PROFESSOR 1: So we are thinking +about cutting things. + +We all are thinking about +what to eliminate + +even if we add something. + +It's very hard because we +think a lot things are + +useful-- important. + +But something has to give. + +So that's the hard decision. + +PROFESSOR 2: Yeah, we're +thinking of cutting caching + +and parallelism. + +[LAUGHTER] + +PROFESSOR 1: OK. + +PROFESSOR 2: OK. + +We have to hurry because we +gotta be out of the room by 4. + +AUDIENCE: I just wanted +to say that I agree. + +That I didn't really like the +way the course was graded. + +But I did like the material +in the course a lot. + +So that was good. + +But for one thing, the thing +about the competitive grading + +was that it was way more +stressful than necessary. + +My luck was good because +we had the kind + +of benchmark thing. + +It was a reasonable high +performance to attain. + +And also I didn't like +the way some of + +the stuff was weighted. + +For example, it didn't really +correspond to how much time I + +spent on it. + +The pset was worth like 3% or +4% of the grade and it took + +like hours, I think. + +Many, many hours. + +That's all. + +PROFESSOR 1: OK, thank you. + +PROFESSOR 2: OK. + +AUDIENCE: There is one thing +that's pretty general about + +course six, I guess, +is that they're + +really lenient on prereqs. + +Since I've only been at MIT +for like three months. + +[LAUGHTER] + +AUDIENCE: So yes, +I'm a freshman. + +PROFESSOR 1: One freshman +in the class. + +There you go. + +AUDIENCE: I'm really thankful +that Professor Leiserson and + +Professor Amarasinghe +let me into the + +course without any prereqs. + +And I like the breadth +of the topics. + +But I think with office hours +we could have gotten a bit + +deeper into them. + +And one suggestion I'd like to +make is that get the nightly + +builds working. + +It was there for one night for +project one, and that was it. + +[LAUGHTER] + +AUDIENCE: So I decided +this is my last-- + +PROFESSOR 2: Can you +talk in the mic? + +AUDIENCE: So this is my +last term at MIT. + +And I decided to take things +easy by not taking that many + +courses and TAing this course. + +[LAUGHTER] + +AUDIENCE: So yeah. + +It would be nice to have +48 unit TA shifts too. + +PROFESSOR 2: Thank you. + +AUDIENCE: I just want to say +that this was like-- + +should I take it? + +PROFESSOR 1: Sure. + +AUDIENCE: OK. + +That this was like +an amazing class. + +I think everyone can agree that +we learned so much that + +is not found in textbooks. + +And what I thought was really +weird is that every little + +random thing I've ever read +on the internet related to + +coding, I guess, has come up in +this class in like, useful, + +come up like useful +in this class. + +Like every little bit of outside +knowledge that you + +take yourself has appeared +useful in this class later on. + +And I thought was really cool. + +And related to the hardness that +people are talking about. + +I think everyone came into the +class bracing for the absolute + +worst, because we've heard +about you guys. + +[LAUGHTER] + +AUDIENCE: But, yeah. + +I was actually really pleasantly +surprised that + +there were helpful TAs waiting +in the G7 lounge for you, even + +before office hours start. + +And so I was actually really +pleasantly surprised by-- + +just like everyone, the class. + +I feel like everyone who has +survived until this point has + +some sort of magic skill. + +That you really learn a lot +by working with them + +on the group projects. + +And so I was just +really inspired. + +And I thought it was +a great class. + +PROFESSOR 1: Thank you. + +PROFESSOR 2: Thank you. + +[APPLAUSE] + +AUDIENCE: Hi. + +I love the class. + +I appreciate you Professor +Leiserson, and everything that + +everybody else before me said. + +I just wanted to mention +two things I + +don't think were mentioned. + +Beta programming, to be honest, +was amazing because + +except the final project, +everything I did was beta + +programming in the projects. + +And the amount of bugs that we +avoided because of that is + +ridiculous. + +Especially when we're doing +pointers, and if it doesn't + +work, make it a pointer, and all +those philosophies that we + +came up with. + +That's the first thing. + +Second thing is, and I've +already mentioned this. + +A book or readings for +this class or links. + +Because as amazing as the +lecture slides are, a lot of + +work done there, so +thanks a lot. + +They're hard to connect +together, especially when + +you're trying to figure out +what our cache-oblivious + +algorithm is trying +to do with those. + +So that's pretty much it. + +Are you telling me the +stack overflow is as + +much as this course? + +Well, thanks a lot again +for the TAs. + +Most of my learning came from +them, to be honest. + +[LAUGHTER] + +[APPLAUSE] + +AUDIENCE: Hands on learning. + +Hands on. + +Thank you. + +[LAUGHTER] + +GUEST SPEAKER: Hi. + +my name is Harold Pokob, +I'm the head of + +engineering at Akamai. + +So I wanted to use the +opportunity to thank all of + +you for taking the class. + +Charles was my adviser when I +was at MIT and he told me + +about his plans for the class. + +I thought it was a great idea. + +Getting a lot more hands-on +experience going. + +Back when I spent time at MIT, +it was a lot more theory, and + +Scheme was one of the main +programming languages. + +So in that context I really +like this type of class. + +And I'm glad MIT is investing +in that and + +supported from Akamai. + +So I'm honored that we +could sponsor it. + +I'm very happy you're here. + +There is, I think, refreshments +downstairs in a + +few minutes. + +PROFESSOR 2: Yeah. + +I'd also like to ask Harold to +say what the topic of his + +master's thesis was. + +[LAUGHTER] + +GUEST SPEAKER: My master's +thesis was cache oblivious + +algorithms. + +[LAUGHTER] + +PROFESSOR 2: So you have Harold +to thank for one of the + +papers that you read +during the term. + +GUEST SPEAKER: It's nice that +something that I did in + +academia is still used. + +Not all now practical business +stuff that I do these days. + +Great to have you here, and +I hope to see some of you + +downstairs. + +And I've got to actually go +into a meeting at 4:00 for + +half an hour, but I'll be +back down afterwards. + +Thank you. + +PROFESSOR 1: Thank you very much +for sponsoring this event + +and getting all the food. + +[APPLAUSE] + +PROFESSOR 1: OK. + +Now we have food. + +AUDIENCE: We also have +quizzes here. + +[LAUGHTER] \ No newline at end of file diff --git a/e2CGPcPNldA.txt b/e2CGPcPNldA.txt new file mode 100644 index 0000000000000000000000000000000000000000..b7b52578941606f4b5991c0d2d57c284ca96187b --- /dev/null +++ b/e2CGPcPNldA.txt @@ -0,0 +1,7872 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu all right + + align:start position:0% + + + + align:start position:0% + +um I am relatively + + align:start position:0% +um I am relatively + + + align:start position:0% +um I am relatively +famous for not just doing spectroscopy + + align:start position:0% +famous for not just doing spectroscopy + + + align:start position:0% +famous for not just doing spectroscopy +but + + align:start position:0% +but + + + align:start position:0% +but +Dynamics and now it may be that the kind + + align:start position:0% +Dynamics and now it may be that the kind + + + align:start position:0% +Dynamics and now it may be that the kind +of dynamics that I talk about is pretty + + align:start position:0% +of dynamics that I talk about is pretty + + + align:start position:0% +of dynamics that I talk about is pretty +childish but I think it's important for + + align:start position:0% +childish but I think it's important for + + + align:start position:0% +childish but I think it's important for +people whose main business is frequency + + align:start position:0% +people whose main business is frequency + + + align:start position:0% +people whose main business is frequency +domain spectroscopy to make a meaningful + + align:start position:0% +domain spectroscopy to make a meaningful + + + align:start position:0% +domain spectroscopy to make a meaningful +contact with dynamical quantities and so + + align:start position:0% +contact with dynamical quantities and so + + + align:start position:0% +contact with dynamical quantities and so +this in the next lecture is a is my my + + align:start position:0% +this in the next lecture is a is my my + + + align:start position:0% +this in the next lecture is a is my my +feeble attempt to make that + + align:start position:0% +feeble attempt to make that + + + align:start position:0% +feeble attempt to make that +connection + + align:start position:0% + + + + align:start position:0% + +um a spectrum consists of transitions + + align:start position:0% +um a spectrum consists of transitions + + + align:start position:0% +um a spectrum consists of transitions +between igen states and igen states are + + align:start position:0% +between igen states and igen states are + + + align:start position:0% +between igen states and igen states are +stationary we all know that there's no + + align:start position:0% +stationary we all know that there's no + + + align:start position:0% +stationary we all know that there's no +motion but + + align:start position:0% +motion but + + + align:start position:0% +motion but +somehow the collection of igen states + + align:start position:0% +somehow the collection of igen states + + + align:start position:0% +somehow the collection of igen states +that we sample in a spectrum encodes + + align:start position:0% +that we sample in a spectrum encodes + + + align:start position:0% +that we sample in a spectrum encodes +motion and how do we uh extract this + + align:start position:0% +motion and how do we uh extract this + + + align:start position:0% +motion and how do we uh extract this +motion and why do we + + align:start position:0% +motion and why do we + + + align:start position:0% +motion and why do we +care + + align:start position:0% +care + + + align:start position:0% +care +so today I'm going to be talking about + + align:start position:0% +so today I'm going to be talking about + + + align:start position:0% +so today I'm going to be talking about +this famous relationship between the + + align:start position:0% +this famous relationship between the + + + align:start position:0% +this famous relationship between the +spectrum of an electronic + + align:start position:0% +spectrum of an electronic + + + align:start position:0% +spectrum of an electronic +transition uh and the 4A transform of an + + align:start position:0% +transition uh and the 4A transform of an + + + align:start position:0% +transition uh and the 4A transform of an +autocorrelation + + align:start position:0% +autocorrelation + + + align:start position:0% +autocorrelation +function + + align:start position:0% +function + + + align:start position:0% +function +this uh approach or this idea that you + + align:start position:0% +this uh approach or this idea that you + + + align:start position:0% +this uh approach or this idea that you +can think of the spectrum as the 4A + + align:start position:0% +can think of the spectrum as the 4A + + + align:start position:0% +can think of the spectrum as the 4A +transform of an autocorrelation function + + align:start position:0% +transform of an autocorrelation function + + + align:start position:0% +transform of an autocorrelation function +is was really important + + align:start position:0% +is was really important + + + align:start position:0% +is was really important +in uh changing the way we think about + + align:start position:0% +in uh changing the way we think about + + + align:start position:0% +in uh changing the way we think about +Spectra + + align:start position:0% + + + + align:start position:0% + +um in the frequency + + align:start position:0% +um in the frequency + + + align:start position:0% +um in the frequency +domain we think about a spectrum as a + + align:start position:0% +domain we think about a spectrum as a + + + align:start position:0% +domain we think about a spectrum as a +bunch of energy levels and a bunch of + + align:start position:0% +bunch of energy levels and a bunch of + + + align:start position:0% +bunch of energy levels and a bunch of +wave + + align:start position:0% +wave + + + align:start position:0% +wave +functions and the in the Spectrum we see + + align:start position:0% +functions and the in the Spectrum we see + + + align:start position:0% +functions and the in the Spectrum we see +some intensities and we often call those + + align:start position:0% +some intensities and we often call those + + + align:start position:0% +some intensities and we often call those +frankon factors or some other factor + + align:start position:0% +frankon factors or some other factor + + + align:start position:0% +frankon factors or some other factor +that comes from an integral between two + + align:start position:0% +that comes from an integral between two + + + align:start position:0% +that comes from an integral between two +igen states + + align:start position:0% +igen states + + + align:start position:0% +igen states +um and uh we are content with that and + + align:start position:0% +um and uh we are content with that and + + + align:start position:0% +um and uh we are content with that and +in in fact it provides a fairly complete + + align:start position:0% +in in fact it provides a fairly complete + + + align:start position:0% +in in fact it provides a fairly complete +picture of anything that we would care + + align:start position:0% +picture of anything that we would care + + + align:start position:0% +picture of anything that we would care +about however when you ask about an Igan + + align:start position:0% +about however when you ask about an Igan + + + align:start position:0% +about however when you ask about an Igan +State this igen state is spread out over + + align:start position:0% +State this igen state is spread out over + + + align:start position:0% +State this igen state is spread out over +a lot of coordinate and momentum space + + align:start position:0% +a lot of coordinate and momentum space + + + align:start position:0% +a lot of coordinate and momentum space +it samples not a little tiny region of + + align:start position:0% +it samples not a little tiny region of + + + align:start position:0% +it samples not a little tiny region of +the potential but it samples pretty + + align:start position:0% +the potential but it samples pretty + + + align:start position:0% +the potential but it samples pretty +globally the + + align:start position:0% +globally the + + + align:start position:0% +globally the +potential + + align:start position:0% + + + + align:start position:0% + +um we also use quantum mechanics and + + align:start position:0% +um we also use quantum mechanics and + + + align:start position:0% +um we also use quantum mechanics and +quantum mechanics prohibits us from + + align:start position:0% +quantum mechanics prohibits us from + + + align:start position:0% +quantum mechanics prohibits us from +talking about coordinates and momenta + + align:start position:0% +talking about coordinates and momenta + + + align:start position:0% +talking about coordinates and momenta +simultaneously and one can do + + align:start position:0% +simultaneously and one can do + + + align:start position:0% +simultaneously and one can do +complicated things and describe + + align:start position:0% +complicated things and describe + + + align:start position:0% +complicated things and describe +functions which are localized in both + + align:start position:0% +functions which are localized in both + + + align:start position:0% +functions which are localized in both +coordinate and momentum space and uh we + + align:start position:0% +coordinate and momentum space and uh we + + + align:start position:0% +coordinate and momentum space and uh we +can talk about that but generally uh we + + align:start position:0% +can talk about that but generally uh we + + + align:start position:0% +can talk about that but generally uh we +just accept what quantum mechanics tells + + align:start position:0% +just accept what quantum mechanics tells + + + align:start position:0% +just accept what quantum mechanics tells +us and uh we think about uh um wave + + align:start position:0% +us and uh we think about uh um wave + + + align:start position:0% +us and uh we think about uh um wave +functions in either coordinate or + + align:start position:0% +functions in either coordinate or + + + align:start position:0% +functions in either coordinate or +momentum space + + align:start position:0% +momentum space + + + align:start position:0% +momentum space +and when we do that we don't have any + + align:start position:0% +and when we do that we don't have any + + + align:start position:0% +and when we do that we don't have any +idea about the mechanisms by which uh + + align:start position:0% +idea about the mechanisms by which uh + + + align:start position:0% +idea about the mechanisms by which uh +energy moves around in a + + align:start position:0% +energy moves around in a + + + align:start position:0% +energy moves around in a +molecule we we can describe it in terms + + align:start position:0% +molecule we we can describe it in terms + + + align:start position:0% +molecule we we can describe it in terms +of wave functions but we don't really + + align:start position:0% +of wave functions but we don't really + + + align:start position:0% +of wave functions but we don't really +have a good idea of what the molecule is + + align:start position:0% +have a good idea of what the molecule is + + + align:start position:0% +have a good idea of what the molecule is +doing and since our reality is based on + + align:start position:0% +doing and since our reality is based on + + + align:start position:0% +doing and since our reality is based on +watching things move and not having to + + align:start position:0% +watching things move and not having to + + + align:start position:0% +watching things move and not having to +close our eyes and open them at certain + + align:start position:0% +close our eyes and open them at certain + + + align:start position:0% +close our eyes and open them at certain +times uh that we think of these things + + align:start position:0% +times uh that we think of these things + + + align:start position:0% +times uh that we think of these things +as localized and moving because some + + align:start position:0% +as localized and moving because some + + + align:start position:0% +as localized and moving because some +force was applied and we have some + + align:start position:0% +force was applied and we have some + + + align:start position:0% +force was applied and we have some +pretty good predictors about if we do + + align:start position:0% +pretty good predictors about if we do + + + align:start position:0% +pretty good predictors about if we do +close our eyes and open them where + + align:start position:0% +close our eyes and open them where + + + align:start position:0% +close our eyes and open them where +things will be and why they got there um + + align:start position:0% +things will be and why they got there um + + + align:start position:0% +things will be and why they got there um +and this is + + align:start position:0% +and this is + + + align:start position:0% +and this is +totally uh illegal in the standard view + + align:start position:0% +totally uh illegal in the standard view + + + align:start position:0% +totally uh illegal in the standard view +of quantum mechanics now of course we + + align:start position:0% +of quantum mechanics now of course we + + + align:start position:0% +of quantum mechanics now of course we +can always uh we can always compute + + align:start position:0% +can always uh we can always compute + + + align:start position:0% +can always uh we can always compute +Quantum mechanically any any quantity we + + align:start position:0% +Quantum mechanically any any quantity we + + + align:start position:0% +Quantum mechanically any any quantity we +want but we can't we're not supposed to + + align:start position:0% +want but we can't we're not supposed to + + + align:start position:0% +want but we can't we're not supposed to +think about uh localized + + align:start position:0% + + + + align:start position:0% + +events and if we can't think about + + align:start position:0% +events and if we can't think about + + + align:start position:0% +events and if we can't think about +localized events we can't really think + + align:start position:0% +localized events we can't really think + + + align:start position:0% +localized events we can't really think +about forces operating and + + align:start position:0% +about forces operating and + + + align:start position:0% +about forces operating and +causing uh motion to occur in some + + align:start position:0% +causing uh motion to occur in some + + + align:start position:0% +causing uh motion to occur in some +mechanistically predictable + + align:start position:0% + + + + align:start position:0% + +way but we've had some + + align:start position:0% +way but we've had some + + + align:start position:0% +way but we've had some +hints uh + + align:start position:0% +hints uh + + + align:start position:0% +hints uh +in at least in some of my lectures this + + align:start position:0% +in at least in some of my lectures this + + + align:start position:0% +in at least in some of my lectures this +semester + + align:start position:0% +semester + + + align:start position:0% +semester +uh about the stationary phase + + align:start position:0% + + + + align:start position:0% + +approximation the integrals from quantum + + align:start position:0% +approximation the integrals from quantum + + + align:start position:0% +approximation the integrals from quantum +mechanics that we uh use like Frank + + align:start position:0% +mechanics that we uh use like Frank + + + align:start position:0% +mechanics that we uh use like Frank +Condon + + align:start position:0% +Condon + + + align:start position:0% +Condon +overlaps uh these integrals + + align:start position:0% +overlaps uh these integrals + + + align:start position:0% +overlaps uh these integrals +accumulate in very restricted regions of + + align:start position:0% + + + + align:start position:0% + +space easily predictable regions of + + align:start position:0% +space easily predictable regions of + + + align:start position:0% +space easily predictable regions of +space they the integrals accumulate they + + align:start position:0% +space they the integrals accumulate they + + + align:start position:0% +space they the integrals accumulate they +reach their final value + + align:start position:0% +reach their final value + + + align:start position:0% +reach their final value +from zero to the final value over a very + + align:start position:0% +from zero to the final value over a very + + + align:start position:0% +from zero to the final value over a very +limited region of coordinate space when + + align:start position:0% +limited region of coordinate space when + + + align:start position:0% +limited region of coordinate space when +the process involve conserves + + align:start position:0% +the process involve conserves + + + align:start position:0% +the process involve conserves +momentum and + + align:start position:0% +momentum and + + + align:start position:0% +momentum and +so the stationary phase + + align:start position:0% +so the stationary phase + + + align:start position:0% +so the stationary phase +ideas enable us to think about + + align:start position:0% +ideas enable us to think about + + + align:start position:0% +ideas enable us to think about +coordinates and momentum and + + align:start position:0% +coordinates and momentum and + + + align:start position:0% +coordinates and momentum and +localization + + align:start position:0% +localization + + + align:start position:0% +localization +simultaneously and so all of + + align:start position:0% +simultaneously and so all of + + + align:start position:0% +simultaneously and so all of +this uh is really brought out in this + + align:start position:0% +this uh is really brought out in this + + + align:start position:0% +this uh is really brought out in this +wave packet picture of uh Spectra or + + align:start position:0% +wave packet picture of uh Spectra or + + + align:start position:0% +wave packet picture of uh Spectra or +more particularly the spectrum is the + + align:start position:0% +more particularly the spectrum is the + + + align:start position:0% +more particularly the spectrum is the +autocorrelation is the fora transform of + + align:start position:0% +autocorrelation is the fora transform of + + + align:start position:0% +autocorrelation is the fora transform of +an autocorrelation function + + align:start position:0% +an autocorrelation function + + + align:start position:0% +an autocorrelation function +so I'm going to talk about wave packets + + align:start position:0% +so I'm going to talk about wave packets + + + align:start position:0% +so I'm going to talk about wave packets +and I'm going to talk about the Spectrum + + align:start position:0% +and I'm going to talk about the Spectrum + + + align:start position:0% +and I'm going to talk about the Spectrum +as the autocorrelation and uh I'm going + + align:start position:0% +as the autocorrelation and uh I'm going + + + align:start position:0% +as the autocorrelation and uh I'm going +to try to make some sense of this and to + + align:start position:0% +to try to make some sense of this and to + + + align:start position:0% +to try to make some sense of this and to +give some insights + + align:start position:0% +give some insights + + + align:start position:0% +give some insights +uh you have in addition to the notes um + + align:start position:0% +uh you have in addition to the notes um + + + align:start position:0% +uh you have in addition to the notes um +some pages from uh my book the next + + align:start position:0% +some pages from uh my book the next + + + align:start position:0% +some pages from uh my book the next +lecture is going to be some more pages + + align:start position:0% +lecture is going to be some more pages + + + align:start position:0% +lecture is going to be some more pages +from the book and and measures of + + align:start position:0% +from the book and and measures of + + + align:start position:0% +from the book and and measures of +Dynamics and you have those as a + + align:start position:0% +Dynamics and you have those as a + + + align:start position:0% +Dynamics and you have those as a +supplement as a separate hand up okay + + align:start position:0% +supplement as a separate hand up okay + + + align:start position:0% +supplement as a separate hand up okay +so this is the famous equation that + + align:start position:0% +so this is the famous equation that + + + align:start position:0% +so this is the famous equation that +tells us + + align:start position:0% +tells us + + + align:start position:0% +tells us +that the Spectrum I of Omega the + + align:start position:0% +that the Spectrum I of Omega the + + + align:start position:0% +that the Spectrum I of Omega the +frequency domain spectrum + + align:start position:0% +frequency domain spectrum + + + align:start position:0% +frequency domain spectrum +is the 4A transform of + + align:start position:0% +is the 4A transform of + + + align:start position:0% +is the 4A transform of +something and that something + + align:start position:0% + + + + align:start position:0% + +is oops that so I guess I need a + + align:start position:0% +is oops that so I guess I need a + + + align:start position:0% +is oops that so I guess I need a +DT so this tells us to take the 4A + + align:start position:0% +DT so this tells us to take the 4A + + + align:start position:0% +DT so this tells us to take the 4A +transform of this object this is the + + align:start position:0% +transform of this object this is the + + + align:start position:0% +transform of this object this is the +auto correlation function this is the + + align:start position:0% +auto correlation function this is the + + + align:start position:0% +auto correlation function this is the +initially prepared wave function and + + align:start position:0% +initially prepared wave function and + + + align:start position:0% +initially prepared wave function and +this this is the wave function uh that + + align:start position:0% +this this is the wave function uh that + + + align:start position:0% +this this is the wave function uh that +was initially prepared uh evolving in + + align:start position:0% +was initially prepared uh evolving in + + + align:start position:0% +was initially prepared uh evolving in +time so and in chemistry or theoretical + + align:start position:0% +time so and in chemistry or theoretical + + + align:start position:0% +time so and in chemistry or theoretical +chemistry is full of autocorrelation + + align:start position:0% +chemistry is full of autocorrelation + + + align:start position:0% +chemistry is full of autocorrelation +functions and I am innocent of all but + + align:start position:0% +functions and I am innocent of all but + + + align:start position:0% +functions and I am innocent of all but +this + + align:start position:0% +this + + + align:start position:0% +this +one but it's a it's a an a when you have + + align:start position:0% +one but it's a it's a an a when you have + + + align:start position:0% +one but it's a it's a an a when you have +complicated Dynamics it is a very + + align:start position:0% +complicated Dynamics it is a very + + + align:start position:0% +complicated Dynamics it is a very +insightful thing to say okay here is the + + align:start position:0% +insightful thing to say okay here is the + + + align:start position:0% +insightful thing to say okay here is the +initial State here is its Evolution the + + align:start position:0% +initial State here is its Evolution the + + + align:start position:0% +initial State here is its Evolution the +overlap between these two tells you + + align:start position:0% +overlap between these two tells you + + + align:start position:0% +overlap between these two tells you +something that you want to know and it's + + align:start position:0% +something that you want to know and it's + + + align:start position:0% +something that you want to know and it's +a way of taking a huge amount of + + align:start position:0% +a way of taking a huge amount of + + + align:start position:0% +a way of taking a huge amount of +information and compressing it to a + + align:start position:0% +information and compressing it to a + + + align:start position:0% +information and compressing it to a +small amount of information that begs to + + align:start position:0% +small amount of information that begs to + + + align:start position:0% +small amount of information that begs to +be understood so this is the thing that + + align:start position:0% +be understood so this is the thing that + + + align:start position:0% +be understood so this is the thing that +is supposedly equivalent to the for + + align:start position:0% +is supposedly equivalent to the for + + + align:start position:0% +is supposedly equivalent to the for +the uh usual spectroscopic picture of + + align:start position:0% +the uh usual spectroscopic picture of + + + align:start position:0% +the uh usual spectroscopic picture of +the spectrum the usual spectroscopic + + align:start position:0% +the spectrum the usual spectroscopic + + + align:start position:0% +the spectrum the usual spectroscopic +picture of the wave function can be + + align:start position:0% +picture of the wave function can be + + + align:start position:0% +picture of the wave function can be +expressed as a sum over + + align:start position:0% +expressed as a sum over + + + align:start position:0% +expressed as a sum over +intensities times a Delta + + align:start position:0% + + + + align:start position:0% + +function so this is a bunch of spectral + + align:start position:0% +function so this is a bunch of spectral + + + align:start position:0% +function so this is a bunch of spectral +lines at frequencies Omega + + align:start position:0% +lines at frequencies Omega + + + align:start position:0% +lines at frequencies Omega +J and intensities i j okay so this is an + + align:start position:0% +J and intensities i j okay so this is an + + + align:start position:0% +J and intensities i j okay so this is an +idealization of the spectrum it's + + align:start position:0% +idealization of the spectrum it's + + + align:start position:0% +idealization of the spectrum it's +treating the lines in the Spectrum as + + align:start position:0% +treating the lines in the Spectrum as + + + align:start position:0% +treating the lines in the Spectrum as +infinitely sharp and for the the the + + align:start position:0% +infinitely sharp and for the the the + + + align:start position:0% +infinitely sharp and for the the the +what I'm going to do today we're going + + align:start position:0% +what I'm going to do today we're going + + + align:start position:0% +what I'm going to do today we're going +to neglect rotational structure we're + + align:start position:0% +to neglect rotational structure we're + + + align:start position:0% +to neglect rotational structure we're +just going to talk about vibrational + + align:start position:0% +just going to talk about vibrational + + + align:start position:0% +just going to talk about vibrational +Spectrum okay so I want to get from here + + align:start position:0% +Spectrum okay so I want to get from here + + + align:start position:0% +Spectrum okay so I want to get from here +to here using familiar uh + + align:start position:0% +to here using familiar uh + + + align:start position:0% +to here using familiar uh +quantities + + align:start position:0% + + + + align:start position:0% + +okay first of + + align:start position:0% +okay first of + + + align:start position:0% +okay first of +all Omega J is just + + align:start position:0% +all Omega J is just + + + align:start position:0% +all Omega J is just +e v Prime J minus E V Prime over + + align:start position:0% + + + + align:start position:0% + +HR okay so this is the energy of the + + align:start position:0% +HR okay so this is the energy of the + + + align:start position:0% +HR okay so this is the energy of the +excited state this is the energy of the + + align:start position:0% +excited state this is the energy of the + + + align:start position:0% +excited state this is the energy of the +initial State we divide by har and + + align:start position:0% +initial State we divide by har and + + + align:start position:0% +initial State we divide by har and +that's that has unit of angular + + align:start position:0% +that's that has unit of angular + + + align:start position:0% +that's that has unit of angular +frequency and we're going to abbreviate + + align:start position:0% +frequency and we're going to abbreviate + + + align:start position:0% +frequency and we're going to abbreviate +this by + + align:start position:0% + + + + align:start position:0% + +that we can also call this whenever we + + align:start position:0% +that we can also call this whenever we + + + align:start position:0% +that we can also call this whenever we +need to EJ over Harr even though this is + + align:start position:0% +need to EJ over Harr even though this is + + + align:start position:0% +need to EJ over Harr even though this is +not really an energy this is a + + align:start position:0% +not really an energy this is a + + + align:start position:0% +not really an energy this is a +difference in energy and uh but often we + + align:start position:0% +difference in energy and uh but often we + + + align:start position:0% +difference in energy and uh but often we +implicitly define the zero of energy + + align:start position:0% +implicitly define the zero of energy + + + align:start position:0% +implicitly define the zero of energy +somewhere we have to know where that is + + align:start position:0% +somewhere we have to know where that is + + + align:start position:0% +somewhere we have to know where that is +and then we can talk about that as an + + align:start position:0% +and then we can talk about that as an + + + align:start position:0% +and then we can talk about that as an +energy okay + + align:start position:0% +energy okay + + + align:start position:0% +energy okay +okay so we + + align:start position:0% +okay so we + + + align:start position:0% +okay so we +have one + + align:start position:0% + + + + align:start position:0% + +quantity well we normally think of + + align:start position:0% +quantity well we normally think of + + + align:start position:0% +quantity well we normally think of +intensities as frankon + + align:start position:0% +intensities as frankon + + + align:start position:0% +intensities as frankon +factors so the intensities + + align:start position:0% +factors so the intensities + + + align:start position:0% +factors so the intensities +are an electronic Matrix element the + + align:start position:0% +are an electronic Matrix element the + + + align:start position:0% +are an electronic Matrix element the +transition moment Matrix element Square + + align:start position:0% +transition moment Matrix element Square + + + align:start position:0% +transition moment Matrix element Square +modulus times the Frank Condon Factor Q + + align:start position:0% +modulus times the Frank Condon Factor Q + + + align:start position:0% +modulus times the Frank Condon Factor Q +VJ Prime V + + align:start position:0% +VJ Prime V + + + align:start position:0% +VJ Prime V +uh + + align:start position:0% +uh + + + align:start position:0% +uh +Prime so this is the square of an + + align:start position:0% +Prime so this is the square of an + + + align:start position:0% +Prime so this is the square of an +overlap and this is some electronic + + align:start position:0% +overlap and this is some electronic + + + align:start position:0% +overlap and this is some electronic +Matrix element so this is what we mean + + align:start position:0% +Matrix element so this is what we mean + + + align:start position:0% +Matrix element so this is what we mean +by + + align:start position:0% +by + + + align:start position:0% +by +intensities and this would be the + + align:start position:0% +intensities and this would be the + + + align:start position:0% +intensities and this would be the +intensities in an absorption + + align:start position:0% +intensities in an absorption + + + align:start position:0% +intensities in an absorption +Spectrum uh so there's no frequency Cube + + align:start position:0% +Spectrum uh so there's no frequency Cube + + + align:start position:0% +Spectrum uh so there's no frequency Cube +Factor we're also we're being very + + align:start position:0% +Factor we're also we're being very + + + align:start position:0% +Factor we're also we're being very +sloppy about uh um spectral density + + align:start position:0% +sloppy about uh um spectral density + + + align:start position:0% +sloppy about uh um spectral density +versus delta function so but this is + + align:start position:0% +versus delta function so but this is + + + align:start position:0% +versus delta function so but this is +okay all right + + align:start position:0% +okay all right + + + align:start position:0% +okay all right +so and Q VJ I haven't put that in yet VJ + + align:start position:0% +so and Q VJ I haven't put that in yet VJ + + + align:start position:0% +so and Q VJ I haven't put that in yet VJ +V Prime is just the overlap integral V + + align:start position:0% +V Prime is just the overlap integral V + + + align:start position:0% +V Prime is just the overlap integral V +Prime v + + align:start position:0% +Prime v + + + align:start position:0% +Prime v +j + + align:start position:0% + + + + align:start position:0% + +squared + + align:start position:0% +squared + + + align:start position:0% +squared +now we should also be a little bit + + align:start position:0% +now we should also be a little bit + + + align:start position:0% +now we should also be a little bit +careful because as soon as + + align:start position:0% +careful because as soon as + + + align:start position:0% +careful because as soon as +we go away from this formal thing where + + align:start position:0% +we go away from this formal thing where + + + align:start position:0% +we go away from this formal thing where +we talk about the autocorrelation + + align:start position:0% +we talk about the autocorrelation + + + align:start position:0% +we talk about the autocorrelation +function which is an + + align:start position:0% +function which is an + + + align:start position:0% +function which is an +integral and it's a function in state + + align:start position:0% +integral and it's a function in state + + + align:start position:0% +integral and it's a function in state +space we don't + + align:start position:0% +space we don't + + + align:start position:0% +space we don't +necessarily think about it as having any + + align:start position:0% +necessarily think about it as having any + + + align:start position:0% +necessarily think about it as having any +coordinate nature to it at all we're + + align:start position:0% +coordinate nature to it at all we're + + + align:start position:0% +coordinate nature to it at all we're +going to be going from states to + + align:start position:0% +going to be going from states to + + + align:start position:0% +going to be going from states to +coordinate space pictures and so a + + align:start position:0% +coordinate space pictures and so a + + + align:start position:0% +coordinate space pictures and so a +vibrational wave + + align:start position:0% +vibrational wave + + + align:start position:0% +vibrational wave +function will have + + align:start position:0% +function will have + + + align:start position:0% +function will have +the + + align:start position:0% + + + + align:start position:0% + +form where this is State space this is + + align:start position:0% +form where this is State space this is + + + align:start position:0% +form where this is State space this is +coordinate space this is how we write a + + align:start position:0% +coordinate space this is how we write a + + + align:start position:0% +coordinate space this is how we write a +wave function and we can put our in and + + align:start position:0% +wave function and we can put our in and + + + align:start position:0% +wave function and we can put our in and +out as we as we wish as long as we obey + + align:start position:0% +out as we as we wish as long as we obey + + + align:start position:0% +out as we as we wish as long as we obey +completeness so when we put an r in we + + align:start position:0% +completeness so when we put an r in we + + + align:start position:0% +completeness so when we put an r in we +have to really do something like this + + align:start position:0% + + + + align:start position:0% + +Dr + + align:start position:0% +Dr + + + align:start position:0% +Dr +okay uh but for the initial part I we + + align:start position:0% +okay uh but for the initial part I we + + + align:start position:0% +okay uh but for the initial part I we +don't really need to say anything about + + align:start position:0% +don't really need to say anything about + + + align:start position:0% +don't really need to say anything about +the + + align:start position:0% + + + + align:start position:0% + +coordinates all right so we've got all + + align:start position:0% +coordinates all right so we've got all + + + align:start position:0% +coordinates all right so we've got all +the pieces together and now let's + + align:start position:0% +the pieces together and now let's + + + align:start position:0% +the pieces together and now let's +describe SI + + align:start position:0% +describe SI + + + align:start position:0% +describe SI +Z and Si Z is going to be the + + align:start position:0% +Z and Si Z is going to be the + + + align:start position:0% +Z and Si Z is going to be the +vibrational wave function on the Lower + + align:start position:0% +vibrational wave function on the Lower + + + align:start position:0% +vibrational wave function on the Lower +State multiplied by this transition + + align:start position:0% +State multiplied by this transition + + + align:start position:0% +State multiplied by this transition +moment which you can think of as + + align:start position:0% +moment which you can think of as + + + align:start position:0% +moment which you can think of as +formally transferring the initial State + + align:start position:0% +formally transferring the initial State + + + align:start position:0% +formally transferring the initial State +vibrational wave function from the + + align:start position:0% +vibrational wave function from the + + + align:start position:0% +vibrational wave function from the +ground state to the electronically + + align:start position:0% +ground state to the electronically + + + align:start position:0% +ground state to the electronically +excited state now in my notes in my book + + align:start position:0% +excited state now in my notes in my book + + + align:start position:0% +excited state now in my notes in my book +I do this more carefully and but that + + align:start position:0% +I do this more carefully and but that + + + align:start position:0% +I do this more carefully and but that +means longer formulas and more rigorous + + align:start position:0% +means longer formulas and more rigorous + + + align:start position:0% +means longer formulas and more rigorous +derivations and I think the big picture + + align:start position:0% +derivations and I think the big picture + + + align:start position:0% +derivations and I think the big picture +is okay in this abbreviated simplified + + align:start position:0% +is okay in this abbreviated simplified + + + align:start position:0% +is okay in this abbreviated simplified +form formulation so we have an initial + + align:start position:0% +form formulation so we have an initial + + + align:start position:0% +form formulation so we have an initial +wave function which has a factor that + + align:start position:0% +wave function which has a factor that + + + align:start position:0% +wave function which has a factor that +that symbolically involves exitation + + align:start position:0% +that symbolically involves exitation + + + align:start position:0% +that symbolically involves exitation +from the Lower State to the Upper State + + align:start position:0% +from the Lower State to the Upper State + + + align:start position:0% +from the Lower State to the Upper State +and it has a wave function a vibrational + + align:start position:0% +and it has a wave function a vibrational + + + align:start position:0% +and it has a wave function a vibrational +State function which is the Lower State + + align:start position:0% +State function which is the Lower State + + + align:start position:0% +State function which is the Lower State +vibrational wave function and so that + + align:start position:0% +vibrational wave function and so that + + + align:start position:0% +vibrational wave function and so that +we'd like to fix by using completeness + + align:start position:0% +we'd like to fix by using completeness + + + align:start position:0% +we'd like to fix by using completeness +and so we have a sum over J of + + align:start position:0% +and so we have a sum over J of + + + align:start position:0% +and so we have a sum over J of +v + + align:start position:0% +v + + + align:start position:0% +v +v j + + align:start position:0% +v j + + + align:start position:0% +v j +the + + align:start position:0% +the + + + align:start position:0% +the +whoops I knew I was having trouble + + align:start position:0% +whoops I knew I was having trouble + + + align:start position:0% +whoops I knew I was having trouble +writing this because I was writing it + + align:start position:0% +writing this because I was writing it + + + align:start position:0% +writing this because I was writing it +wrong so completeness is VJ Prime v j + + align:start position:0% +wrong so completeness is VJ Prime v j + + + align:start position:0% +wrong so completeness is VJ Prime v j +Prime and then we have V + + align:start position:0% +Prime and then we have V + + + align:start position:0% +Prime and then we have V +Prime okay so this is the overlap + + align:start position:0% +Prime okay so this is the overlap + + + align:start position:0% +Prime okay so this is the overlap +integral and this is the Upper State + + align:start position:0% +integral and this is the Upper State + + + align:start position:0% +integral and this is the Upper State +wave function and this is just + + align:start position:0% + + + + align:start position:0% + +completeness and so that that's a sum or + + align:start position:0% +completeness and so that that's a sum or + + + align:start position:0% +completeness and so that that's a sum or +some at an integral but we have a + + align:start position:0% +some at an integral but we have a + + + align:start position:0% +some at an integral but we have a +complete set of functions and we're just + + align:start position:0% +complete set of functions and we're just + + + align:start position:0% +complete set of functions and we're just +expressing the Lower State vibrational + + align:start position:0% +expressing the Lower State vibrational + + + align:start position:0% +expressing the Lower State vibrational +wave function formally in this + + align:start position:0% + + + + align:start position:0% + +way so + + align:start position:0% +way so + + + align:start position:0% +way so +uh that means that we can uh write uh + + align:start position:0% +uh that means that we can uh write uh + + + align:start position:0% +uh that means that we can uh write uh +and I still need the + + align:start position:0% + + + + align:start position:0% + +M okay and so we can also write s of + + align:start position:0% +M okay and so we can also write s of + + + align:start position:0% +M okay and so we can also write s of +T and uh or more specific speically we I + + align:start position:0% +T and uh or more specific speically we I + + + align:start position:0% +T and uh or more specific speically we I +should have been writing this this way + + align:start position:0% +should have been writing this this way + + + align:start position:0% +should have been writing this this way +anyway this is a state Vector because + + align:start position:0% +anyway this is a state Vector because + + + align:start position:0% +anyway this is a state Vector because +I've written it entirely in terms of + + align:start position:0% +I've written it entirely in terms of + + + align:start position:0% +I've written it entirely in terms of +State vectors there's no function and as + + align:start position:0% +State vectors there's no function and as + + + align:start position:0% +State vectors there's no function and as +soon if we don't put the the the symbol + + align:start position:0% +soon if we don't put the the the symbol + + + align:start position:0% +soon if we don't put the the the symbol +of a state Vector around this we think + + align:start position:0% +of a state Vector around this we think + + + align:start position:0% +of a state Vector around this we think +of a wave function so I okay so now we + + align:start position:0% +of a wave function so I okay so now we + + + align:start position:0% +of a wave function so I okay so now we +want this guy the time evolving form of + + align:start position:0% +want this guy the time evolving form of + + + align:start position:0% +want this guy the time evolving form of +this and so that means well first of all + + align:start position:0% +this and so that means well first of all + + + align:start position:0% +this and so that means well first of all +we have instead of + + align:start position:0% +we have instead of + + + align:start position:0% +we have instead of +uh the Cat symbol we have a bra symbol + + align:start position:0% +uh the Cat symbol we have a bra symbol + + + align:start position:0% +uh the Cat symbol we have a bra symbol +and that means we have to take the + + align:start position:0% +and that means we have to take the + + + align:start position:0% +and that means we have to take the +conjugate transpose of everything and so + + align:start position:0% +conjugate transpose of everything and so + + + align:start position:0% +conjugate transpose of everything and so +we have M Star first then we have J and + + align:start position:0% +we have M Star first then we have J and + + + align:start position:0% +we have M Star first then we have J and +we have + + align:start position:0% + + + + align:start position:0% + +the but now we also have to write the + + align:start position:0% +the but now we also have to write the + + + align:start position:0% +the but now we also have to write the +energy and fortunately these are IG + + align:start position:0% +energy and fortunately these are IG + + + align:start position:0% +energy and fortunately these are IG +States and so we know their energies and + + align:start position:0% +States and so we know their energies and + + + align:start position:0% +States and so we know their energies and +uh so + + align:start position:0% +uh so + + + align:start position:0% +uh so +and we've taken the complex conjugate so + + align:start position:0% +and we've taken the complex conjugate so + + + align:start position:0% +and we've taken the complex conjugate so +instead of having e to the minus it's e + + align:start position:0% +instead of having e to the minus it's e + + + align:start position:0% +instead of having e to the minus it's e +to the plus + + align:start position:0% +to the plus + + + align:start position:0% +to the plus +i e z t over H + + align:start position:0% + + + + align:start position:0% + +bar okay so now we just put it all + + align:start position:0% +bar okay so now we just put it all + + + align:start position:0% +bar okay so now we just put it all +together and we have the auto coration + + align:start position:0% + + + + align:start position:0% + +function and you usually people write it + + align:start position:0% +function and you usually people write it + + + align:start position:0% +function and you usually people write it +the other way around and I don't know + + align:start position:0% +the other way around and I don't know + + + align:start position:0% +the other way around and I don't know +why I write it this way around doesn't + + align:start position:0% +why I write it this way around doesn't + + + align:start position:0% +why I write it this way around doesn't +really matter uh we + + align:start position:0% +really matter uh we + + + align:start position:0% +really matter uh we +have + + align:start position:0% + + + + align:start position:0% + +mstar sum over J and K of V Prime V + + align:start position:0% +mstar sum over J and K of V Prime V + + + align:start position:0% +mstar sum over J and K of V Prime V +Prime + + align:start position:0% +Prime + + + align:start position:0% +Prime +J V Prime + + align:start position:0% +J V Prime + + + align:start position:0% +J V Prime +J and then we have the other guy and + + align:start position:0% +J and then we have the other guy and + + + align:start position:0% +J and then we have the other guy and +that has to be a different + + align:start position:0% +that has to be a different + + + align:start position:0% +that has to be a different +summation but it goes away + + align:start position:0% + + + + align:start position:0% + +so this is the whole + + align:start position:0% +so this is the whole + + + align:start position:0% +so this is the whole +picture okay first of all these are igen + + align:start position:0% +picture okay first of all these are igen + + + align:start position:0% +picture okay first of all these are igen +functions in the same basis set and so J + + align:start position:0% +functions in the same basis set and so J + + + align:start position:0% +functions in the same basis set and so J +has to be equal to K and so this just + + align:start position:0% +has to be equal to K and so this just + + + align:start position:0% +has to be equal to K and so this just +becomes then M Star sum over + + align:start position:0% +becomes then M Star sum over + + + align:start position:0% +becomes then M Star sum over +J V Prime + + align:start position:0% + + + + align:start position:0% + +VJ and I've lost my e to + + align:start position:0% + + + + align:start position:0% + +the sorry about + + align:start position:0% + + + + align:start position:0% + +that that was in the middle okay well + + align:start position:0% +that that was in the middle okay well + + + align:start position:0% +that that was in the middle okay well +um so this all simplifies to + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% + + + + align:start position:0% + +I forgot the T how many times did I + + align:start position:0% +I forgot the T how many times did I + + + align:start position:0% +I forgot the T how many times did I +forget the T well just that + + align:start position:0% + + + + align:start position:0% + +time and then + + align:start position:0% + + + + align:start position:0% + +a okay + + align:start position:0% +a okay + + + align:start position:0% +a okay +so + + align:start position:0% +so + + + align:start position:0% +so +um this is just the Frank conon + + align:start position:0% +um this is just the Frank conon + + + align:start position:0% +um this is just the Frank conon +factor and this is just the transition + + align:start position:0% +factor and this is just the transition + + + align:start position:0% +factor and this is just the transition +moment squared and so we have m q v j + + align:start position:0% +moment squared and so we have m q v j + + + align:start position:0% +moment squared and so we have m q v j +Prime V Prime and then we have this + + align:start position:0% +Prime V Prime and then we have this + + + align:start position:0% +Prime V Prime and then we have this +oscillating thing e the I EJ T over H + + align:start position:0% + + + + align:start position:0% + +bar + + align:start position:0% +bar + + + align:start position:0% +bar +so + + align:start position:0% +so + + + align:start position:0% +so +um now we want to take the fora + + align:start position:0% +um now we want to take the fora + + + align:start position:0% +um now we want to take the fora +transform of the order correlation + + align:start position:0% +transform of the order correlation + + + align:start position:0% +transform of the order correlation +function to cancel this oscillation + + align:start position:0% +function to cancel this oscillation + + + align:start position:0% +function to cancel this oscillation +or we take the fora transform and + + align:start position:0% +or we take the fora transform and + + + align:start position:0% +or we take the fora transform and +whenever the frequency is equal to EJ + + align:start position:0% +whenever the frequency is equal to EJ + + + align:start position:0% +whenever the frequency is equal to EJ +over H we get something that survives + + align:start position:0% +over H we get something that survives + + + align:start position:0% +over H we get something that survives +and everywhere else we get destruction + + align:start position:0% +and everywhere else we get destruction + + + align:start position:0% +and everywhere else we get destruction +so we take the 4A transform with the aut + + align:start position:0% +so we take the 4A transform with the aut + + + align:start position:0% +so we take the 4A transform with the aut +correlation function and so that's + + align:start position:0% +correlation function and so that's + + + align:start position:0% +correlation function and so that's +integral minus infinity to Infinity e to + + align:start position:0% +integral minus infinity to Infinity e to + + + align:start position:0% +integral minus infinity to Infinity e to +the minus I Omega + + align:start position:0% +the minus I Omega + + + align:start position:0% +the minus I Omega +T so i + + align:start position:0% +T so i + + + align:start position:0% +T so i +t i + + align:start position:0% +t i + + + align:start position:0% +t i +z and we carry all this out there some + + align:start position:0% +z and we carry all this out there some + + + align:start position:0% +z and we carry all this out there some +steps and we have a sum j i + + align:start position:0% +steps and we have a sum j i + + + align:start position:0% +steps and we have a sum j i +j Delta Omega J minus + + align:start position:0% +j Delta Omega J minus + + + align:start position:0% +j Delta Omega J minus +Omega so we have the intended result + + align:start position:0% +Omega so we have the intended result + + + align:start position:0% +Omega so we have the intended result +that the 4A transform of the aut + + align:start position:0% +that the 4A transform of the aut + + + align:start position:0% +that the 4A transform of the aut +correlation function is just the some a + + align:start position:0% +correlation function is just the some a + + + align:start position:0% +correlation function is just the some a +bunch of lines at the known transition + + align:start position:0% +bunch of lines at the known transition + + + align:start position:0% +bunch of lines at the known transition +frequencies with the Frank Condon + + align:start position:0% +frequencies with the Frank Condon + + + align:start position:0% +frequencies with the Frank Condon +factors so these two pictures are + + align:start position:0% +factors so these two pictures are + + + align:start position:0% +factors so these two pictures are +equivalent and one one response is so + + align:start position:0% +equivalent and one one response is so + + + align:start position:0% +equivalent and one one response is so +what we already had a perfectly good way + + align:start position:0% +what we already had a perfectly good way + + + align:start position:0% +what we already had a perfectly good way +of understanding Spectra we know how to + + align:start position:0% +of understanding Spectra we know how to + + + align:start position:0% +of understanding Spectra we know how to +calculate Frank kindon + + align:start position:0% +calculate Frank kindon + + + align:start position:0% +calculate Frank kindon +factors + + align:start position:0% +factors + + + align:start position:0% +factors +uh at least in + + align:start position:0% +uh at least in + + + align:start position:0% +uh at least in +principal and that's the rub because in + + align:start position:0% +principal and that's the rub because in + + + align:start position:0% +principal and that's the rub because in +principal is uh is not good enough + + align:start position:0% +principal is uh is not good enough + + + align:start position:0% +principal is uh is not good enough +because usually when we start out with a + + align:start position:0% +because usually when we start out with a + + + align:start position:0% +because usually when we start out with a +spectrum we we get a spectrum we get + + align:start position:0% +spectrum we we get a spectrum we get + + + align:start position:0% +spectrum we we get a spectrum we get +intensities we know the intensities are + + align:start position:0% +intensities we know the intensities are + + + align:start position:0% +intensities we know the intensities are +related to Frank con factors but we + + align:start position:0% +related to Frank con factors but we + + + align:start position:0% +related to Frank con factors but we +don't know the potential surfaces so we + + align:start position:0% +don't know the potential surfaces so we + + + align:start position:0% +don't know the potential surfaces so we +can't calculate the frankc factors and + + align:start position:0% +can't calculate the frankc factors and + + + align:start position:0% +can't calculate the frankc factors and +the problem + + align:start position:0% +the problem + + + align:start position:0% +the problem +is + + align:start position:0% +is + + + align:start position:0% +is +the we don't know anything about the + + align:start position:0% +the we don't know anything about the + + + align:start position:0% +the we don't know anything about the +potential to calculate Frank kind + + align:start position:0% +potential to calculate Frank kind + + + align:start position:0% +potential to calculate Frank kind +factors we have to know pretty much + + align:start position:0% +factors we have to know pretty much + + + align:start position:0% +factors we have to know pretty much +everything + + align:start position:0% +everything + + + align:start position:0% +everything +and so what ends up happening is what we + + align:start position:0% +and so what ends up happening is what we + + + align:start position:0% +and so what ends up happening is what we +need to know requires Global Information + + align:start position:0% +need to know requires Global Information + + + align:start position:0% +need to know requires Global Information +about the + + align:start position:0% +about the + + + align:start position:0% +about the +potential but what we really only + + align:start position:0% +potential but what we really only + + + align:start position:0% +potential but what we really only +need and only this picture tells us is + + align:start position:0% +need and only this picture tells us is + + + align:start position:0% +need and only this picture tells us is +uh we only need local information about + + align:start position:0% +uh we only need local information about + + + align:start position:0% +uh we only need local information about +the + + align:start position:0% +the + + + align:start position:0% +the +potential that uh somehow the spectrum + + align:start position:0% +potential that uh somehow the spectrum + + + align:start position:0% +potential that uh somehow the spectrum +is going to tell us stuff about a region + + align:start position:0% +is going to tell us stuff about a region + + + align:start position:0% +is going to tell us stuff about a region +of the + + align:start position:0% +of the + + + align:start position:0% +of the +potential that we want to know about and + + align:start position:0% +potential that we want to know about and + + + align:start position:0% +potential that we want to know about and +I mean basically you start out from a + + align:start position:0% +I mean basically you start out from a + + + align:start position:0% +I mean basically you start out from a +molecule in its ground state and we know + + align:start position:0% +molecule in its ground state and we know + + + align:start position:0% +molecule in its ground state and we know +a lot about the ground + + align:start position:0% +a lot about the ground + + + align:start position:0% +a lot about the ground +state um and and so we have a wave + + align:start position:0% +state um and and so we have a wave + + + align:start position:0% +state um and and so we have a wave +function which is localized in a very + + align:start position:0% +function which is localized in a very + + + align:start position:0% +function which is localized in a very +small and perfectly known region of + + align:start position:0% +small and perfectly known region of + + + align:start position:0% +small and perfectly known region of +space and it's also even because it's a + + align:start position:0% +space and it's also even because it's a + + + align:start position:0% +space and it's also even because it's a +low vibrational level of the first + + align:start position:0% +low vibrational level of the first + + + align:start position:0% +low vibrational level of the first +Electronics State it's pretty gaussian + + align:start position:0% +Electronics State it's pretty gaussian + + + align:start position:0% +Electronics State it's pretty gaussian +so we know the wave function without + + align:start position:0% +so we know the wave function without + + + align:start position:0% +so we know the wave function without +very much work at all the initial State + + align:start position:0% +very much work at all the initial State + + + align:start position:0% +very much work at all the initial State +extremely + + align:start position:0% + + + + align:start position:0% + +well and so this + + align:start position:0% +well and so this + + + align:start position:0% +well and so this +Factor + + align:start position:0% +Factor + + + align:start position:0% +Factor +Here is + + align:start position:0% +Here is + + + align:start position:0% +Here is +known and this Factor well there's a lot + + align:start position:0% +known and this Factor well there's a lot + + + align:start position:0% +known and this Factor well there's a lot +that we know because in the Spectrum we + + align:start position:0% +that we know because in the Spectrum we + + + align:start position:0% +that we know because in the Spectrum we +know the frequencies + + align:start position:0% +know the frequencies + + + align:start position:0% +know the frequencies +and so there's only a little bit about + + align:start position:0% +and so there's only a little bit about + + + align:start position:0% +and so there's only a little bit about +the potential we want to know about + + align:start position:0% +the potential we want to know about + + + align:start position:0% +the potential we want to know about +and so you our our Frank Conan principle + + align:start position:0% +and so you our our Frank Conan principle + + + align:start position:0% +and so you our our Frank Conan principle +says draw a vertical + + align:start position:0% +says draw a vertical + + + align:start position:0% +says draw a vertical +line what does the vertical line do it + + align:start position:0% +line what does the vertical line do it + + + align:start position:0% +line what does the vertical line do it +tells you where the stationary face + + align:start position:0% +tells you where the stationary face + + + align:start position:0% +tells you where the stationary face +point is it says everything about the + + align:start position:0% +point is it says everything about the + + + align:start position:0% +point is it says everything about the +upper potential that we need to know is + + align:start position:0% +upper potential that we need to know is + + + align:start position:0% +upper potential that we need to know is +given to us by the shape of the potent + + align:start position:0% +given to us by the shape of the potent + + + align:start position:0% +given to us by the shape of the potent +the slope of the + + align:start position:0% +the slope of the + + + align:start position:0% +the slope of the +potential we don't don't need to know + + align:start position:0% +potential we don't don't need to know + + + align:start position:0% +potential we don't don't need to know +the whole thing we need to know + + align:start position:0% +the whole thing we need to know + + + align:start position:0% +the whole thing we need to know +basically the slope of the + + align:start position:0% +basically the slope of the + + + align:start position:0% +basically the slope of the +potential now this could be a repulsive + + align:start position:0% +potential now this could be a repulsive + + + align:start position:0% +potential now this could be a repulsive +state or it could be a bounce State and + + align:start position:0% +state or it could be a bounce State and + + + align:start position:0% +state or it could be a bounce State and +so if it's a repulsive State then + + align:start position:0% +so if it's a repulsive State then + + + align:start position:0% +so if it's a repulsive State then +everything we're really allowed to know + + align:start position:0% +everything we're really allowed to know + + + align:start position:0% +everything we're really allowed to know +is confined to this region where the + + align:start position:0% +is confined to this region where the + + + align:start position:0% +is confined to this region where the +wave P packet gets launched into the + + align:start position:0% +wave P packet gets launched into the + + + align:start position:0% +wave P packet gets launched into the +Continuum if it's a bounce State well + + align:start position:0% +Continuum if it's a bounce State well + + + align:start position:0% +Continuum if it's a bounce State well +we're going to have a wave function and + + align:start position:0% +we're going to have a wave function and + + + align:start position:0% +we're going to have a wave function and +it's going to be bouncing back and forth + + align:start position:0% +it's going to be bouncing back and forth + + + align:start position:0% +it's going to be bouncing back and forth +and so as it bounces back and forth uh + + align:start position:0% +and so as it bounces back and forth uh + + + align:start position:0% +and so as it bounces back and forth uh +it tells us + + align:start position:0% +it tells us + + + align:start position:0% +it tells us +frequencies which are related to the + + align:start position:0% +frequencies which are related to the + + + align:start position:0% +frequencies which are related to the +width of the potential and now this is a + + align:start position:0% +width of the potential and now this is a + + + align:start position:0% +width of the potential and now this is a +one-dimensional picture of a + + align:start position:0% +one-dimensional picture of a + + + align:start position:0% +one-dimensional picture of a +many-dimensional object there will be + + align:start position:0% +many-dimensional object there will be + + + align:start position:0% +many-dimensional object there will be +many different bouncing back and forth + + align:start position:0% +many different bouncing back and forth + + + align:start position:0% +many different bouncing back and forth +and there'll be uh um information every + + align:start position:0% +and there'll be uh um information every + + + align:start position:0% +and there'll be uh um information every +time the wave function comes back the + + align:start position:0% +time the wave function comes back the + + + align:start position:0% +time the wave function comes back the +wave packet comes back to where it + + align:start position:0% +wave packet comes back to where it + + + align:start position:0% +wave packet comes back to where it +started there's a little uh blip in the + + align:start position:0% +started there's a little uh blip in the + + + align:start position:0% +started there's a little uh blip in the +autocorrelation function and so we know + + align:start position:0% +autocorrelation function and so we know + + + align:start position:0% +autocorrelation function and so we know +there's going to be periodic structures + + align:start position:0% +there's going to be periodic structures + + + align:start position:0% +there's going to be periodic structures +in the autocorrelation function that + + align:start position:0% +in the autocorrelation function that + + + align:start position:0% +in the autocorrelation function that +relate to the normal modes the normal + + align:start position:0% +relate to the normal modes the normal + + + align:start position:0% +relate to the normal modes the normal +mode frequencies they're very very + + align:start position:0% +mode frequencies they're very very + + + align:start position:0% +mode frequencies they're very very +sensitive to the slope of the + + align:start position:0% +sensitive to the slope of the + + + align:start position:0% +sensitive to the slope of the +potential this is a many dimensional + + align:start position:0% +potential this is a many dimensional + + + align:start position:0% +potential this is a many dimensional +potential so there will be slopes along + + align:start position:0% +potential so there will be slopes along + + + align:start position:0% +potential so there will be slopes along +each of the normal + + align:start position:0% +each of the normal + + + align:start position:0% +each of the normal +coordinates and so now you're beginning + + align:start position:0% +coordinates and so now you're beginning + + + align:start position:0% +coordinates and so now you're beginning +to say oh well maybe this is a good way + + align:start position:0% +to say oh well maybe this is a good way + + + align:start position:0% +to say oh well maybe this is a good way +of thinking about the potential because + + align:start position:0% +of thinking about the potential because + + + align:start position:0% +of thinking about the potential because +because if I uh if I do something about + + align:start position:0% +because if I uh if I do something about + + + align:start position:0% +because if I uh if I do something about +uh uh if I go from the Spectrum to + + align:start position:0% +uh uh if I go from the Spectrum to + + + align:start position:0% +uh uh if I go from the Spectrum to +frequencies and intensities I'm going to + + align:start position:0% +frequencies and intensities I'm going to + + + align:start position:0% +frequencies and intensities I'm going to +be learning something about the slope of + + align:start position:0% +be learning something about the slope of + + + align:start position:0% +be learning something about the slope of +the potential in the Frank Condon region + + align:start position:0% +the potential in the Frank Condon region + + + align:start position:0% +the potential in the Frank Condon region +and maybe something + + align:start position:0% +and maybe something + + + align:start position:0% +and maybe something +else and so and it turns out this is + + align:start position:0% +else and so and it turns out this is + + + align:start position:0% +else and so and it turns out this is +true this is why people really get + + align:start position:0% +true this is why people really get + + + align:start position:0% +true this is why people really get +excited about the wave pack and approach + + align:start position:0% +excited about the wave pack and approach + + + align:start position:0% +excited about the wave pack and approach +and this spectrum is the forier + + align:start position:0% +and this spectrum is the forier + + + align:start position:0% +and this spectrum is the forier +transform autocorrelation function + + align:start position:0% +transform autocorrelation function + + + align:start position:0% +transform autocorrelation function +because this really samples local + + align:start position:0% +because this really samples local + + + align:start position:0% +because this really samples local +information and early time information + + align:start position:0% +information and early time information + + + align:start position:0% +information and early time information +and it uses what you knew + + align:start position:0% + + + + align:start position:0% + +already and this + + align:start position:0% +already and this + + + align:start position:0% +already and this +is uh it's really + + align:start position:0% +is uh it's really + + + align:start position:0% +is uh it's really +beautiful + + align:start position:0% + + + + align:start position:0% + +um Okay so + + align:start position:0% + + + + align:start position:0% + +this picture says well this + + align:start position:0% +this picture says well this + + + align:start position:0% +this picture says well this +autocorrelation function is really + + align:start position:0% +autocorrelation function is really + + + align:start position:0% +autocorrelation function is really +important but maybe we should talk about + + align:start position:0% +important but maybe we should talk about + + + align:start position:0% +important but maybe we should talk about +uh something that looks like + + align:start position:0% + + + + align:start position:0% + +this just the time evolving wave + + align:start position:0% +this just the time evolving wave + + + align:start position:0% +this just the time evolving wave +function because this is going to + + align:start position:0% +function because this is going to + + + align:start position:0% +function because this is going to +provide the physical picture of of what + + align:start position:0% +provide the physical picture of of what + + + align:start position:0% +provide the physical picture of of what +you made at T equals + + align:start position:0% +you made at T equals + + + align:start position:0% +you made at T equals +z and it will give you a little bit of a + + align:start position:0% +z and it will give you a little bit of a + + + align:start position:0% +z and it will give you a little bit of a +physical picture of what's behind this + + align:start position:0% +physical picture of what's behind this + + + align:start position:0% +physical picture of what's behind this +now this is an integral this is not a + + align:start position:0% +now this is an integral this is not a + + + align:start position:0% +now this is an integral this is not a +function it's not a function of space + + align:start position:0% +function it's not a function of space + + + align:start position:0% +function it's not a function of space +it's a function of time so this is just + + align:start position:0% +it's a function of time so this is just + + + align:start position:0% +it's a function of time so this is just +one number as a function of time whereas + + align:start position:0% +one number as a function of time whereas + + + align:start position:0% +one number as a function of time whereas +this is a picture a many dimensional + + align:start position:0% +this is a picture a many dimensional + + + align:start position:0% +this is a picture a many dimensional +picture because it's not integral + + align:start position:0% +picture because it's not integral + + + align:start position:0% +picture because it's not integral +integrated over space which Chang Es as + + align:start position:0% +integrated over space which Chang Es as + + + align:start position:0% +integrated over space which Chang Es as +a function of time and we already know + + align:start position:0% +a function of time and we already know + + + align:start position:0% +a function of time and we already know +about wave packets we know how to build + + align:start position:0% +about wave packets we know how to build + + + align:start position:0% +about wave packets we know how to build +this time evolving wave packet and if we + + align:start position:0% +this time evolving wave packet and if we + + + align:start position:0% +this time evolving wave packet and if we +have + + align:start position:0% +have + + + align:start position:0% +have +a uh picture like this we we have the + + align:start position:0% +a uh picture like this we we have the + + + align:start position:0% +a uh picture like this we we have the +sense that at T equals z we create a + + align:start position:0% +sense that at T equals z we create a + + + align:start position:0% +sense that at T equals z we create a +replica of the initial State operating + + align:start position:0% +replica of the initial State operating + + + align:start position:0% +replica of the initial State operating +on the upper State potential and this is + + align:start position:0% +on the upper State potential and this is + + + align:start position:0% +on the upper State potential and this is +something that you get from proper + + align:start position:0% +something that you get from proper + + + align:start position:0% +something that you get from proper +analysis of this and saying okay here's + + align:start position:0% +analysis of this and saying okay here's + + + align:start position:0% +analysis of this and saying okay here's +a bunch of symbols this you can regard + + align:start position:0% +a bunch of symbols this you can regard + + + align:start position:0% +a bunch of symbols this you can regard +as the + + align:start position:0% +as the + + + align:start position:0% +as the +propagator uh on the oper electronic + + align:start position:0% +propagator uh on the oper electronic + + + align:start position:0% +propagator uh on the oper electronic +State I don't want to talk about that + + align:start position:0% +State I don't want to talk about that + + + align:start position:0% +State I don't want to talk about that +because the simple idea is okay this + + align:start position:0% +because the simple idea is okay this + + + align:start position:0% +because the simple idea is okay this +tells us that uh this is equivalent to + + align:start position:0% +tells us that uh this is equivalent to + + + align:start position:0% +tells us that uh this is equivalent to +what we're used to and it's related to + + align:start position:0% +what we're used to and it's related to + + + align:start position:0% +what we're used to and it's related to +this and now we're starting to talk + + align:start position:0% +this and now we're starting to talk + + + align:start position:0% +this and now we're starting to talk +about things + + align:start position:0% +about things + + + align:start position:0% +about things +moving localized objects moving + + align:start position:0% +moving localized objects moving + + + align:start position:0% +moving localized objects moving +spreading uh behaving uh in ways that we + + align:start position:0% +spreading uh behaving uh in ways that we + + + align:start position:0% +spreading uh behaving uh in ways that we +can understand and because it's we start + + align:start position:0% +can understand and because it's we start + + + align:start position:0% +can understand and because it's we start +with a localized pluck of the + + align:start position:0% +with a localized pluck of the + + + align:start position:0% +with a localized pluck of the +system we know that the + + align:start position:0% +system we know that the + + + align:start position:0% +system we know that the +initial state of the system is perfectly + + align:start position:0% +initial state of the system is perfectly + + + align:start position:0% +initial state of the system is perfectly +described and for a short time we can + + align:start position:0% +described and for a short time we can + + + align:start position:0% +described and for a short time we can +understand everything in terms of how + + align:start position:0% +understand everything in terms of how + + + align:start position:0% +understand everything in terms of how +does this thing get away from + + align:start position:0% + + + + align:start position:0% + +itself how fast does this wave packet + + align:start position:0% +itself how fast does this wave packet + + + align:start position:0% +itself how fast does this wave packet +move away from its initial + + align:start position:0% +move away from its initial + + + align:start position:0% +move away from its initial +position and we can use all sorts of + + align:start position:0% +position and we can use all sorts of + + + align:start position:0% +position and we can use all sorts of +simple ideas to do + + align:start position:0% + + + + align:start position:0% + +that okay so we we're going to want to + + align:start position:0% +that okay so we we're going to want to + + + align:start position:0% +that okay so we we're going to want to +know about how fast does the wave packet + + align:start position:0% +know about how fast does the wave packet + + + align:start position:0% +know about how fast does the wave packet +move away or how fast does the auto + + align:start position:0% +move away or how fast does the auto + + + align:start position:0% +move away or how fast does the auto +correlation function + + align:start position:0% +correlation function + + + align:start position:0% +correlation function +Decay and what about + + align:start position:0% +Decay and what about + + + align:start position:0% +Decay and what about +recurrences how what is the time what + + align:start position:0% +recurrences how what is the time what + + + align:start position:0% +recurrences how what is the time what +when do recurrences occur and what is + + align:start position:0% +when do recurrences occur and what is + + + align:start position:0% +when do recurrences occur and what is +their amplitude and stuff like that that + + align:start position:0% +their amplitude and stuff like that that + + + align:start position:0% +their amplitude and stuff like that that +know potential not just the + + align:start position:0% +know potential not just the + + + align:start position:0% +know potential not just the +SL well the initial Decay is entirely + + align:start position:0% +SL well the initial Decay is entirely + + + align:start position:0% +SL well the initial Decay is entirely +the slope at the Frank conon point the + + align:start position:0% +the slope at the Frank conon point the + + + align:start position:0% +the slope at the Frank conon point the +whole potential + + align:start position:0% +whole potential + + + align:start position:0% +whole potential +uh you need to know the whole potential + + align:start position:0% +uh you need to know the whole potential + + + align:start position:0% +uh you need to know the whole potential +to know the amplitudes of + + align:start position:0% +to know the amplitudes of + + + align:start position:0% +to know the amplitudes of +recurrences + + align:start position:0% + + + + align:start position:0% + +but you don't need to know the whole + + align:start position:0% +but you don't need to know the whole + + + align:start position:0% +but you don't need to know the whole +potential to know what to do with the + + align:start position:0% +potential to know what to do with the + + + align:start position:0% +potential to know what to do with the +recurrences because those are the normal + + align:start position:0% +recurrences because those are the normal + + + align:start position:0% +recurrences because those are the normal +mode frequencies or the anharmonic mode + + align:start position:0% +mode frequencies or the anharmonic mode + + + align:start position:0% +mode frequencies or the anharmonic mode +frequencies and uh uh so the intensities + + align:start position:0% +frequencies and uh uh so the intensities + + + align:start position:0% +frequencies and uh uh so the intensities +or the the amplitudes of the recurrences + + align:start position:0% +or the the amplitudes of the recurrences + + + align:start position:0% +or the the amplitudes of the recurrences +are something that tell you about the + + align:start position:0% +are something that tell you about the + + + align:start position:0% +are something that tell you about the +anharmonicity of the potential and + + align:start position:0% +anharmonicity of the potential and + + + align:start position:0% +anharmonicity of the potential and +because you know you can do all sorts of + + align:start position:0% +because you know you can do all sorts of + + + align:start position:0% +because you know you can do all sorts of +numerical experiments and maybe I'll be + + align:start position:0% +numerical experiments and maybe I'll be + + + align:start position:0% +numerical experiments and maybe I'll be +talking about this on Wednesday but if + + align:start position:0% +talking about this on Wednesday but if + + + align:start position:0% +talking about this on Wednesday but if +you have a harmonic potential the wave + + align:start position:0% +you have a harmonic potential the wave + + + align:start position:0% +you have a harmonic potential the wave +function the wave you start a wave + + align:start position:0% +function the wave you start a wave + + + align:start position:0% +function the wave you start a wave +packet at the left turning point it + + align:start position:0% +packet at the left turning point it + + + align:start position:0% +packet at the left turning point it +might do complicated stuff but but when + + align:start position:0% +might do complicated stuff but but when + + + align:start position:0% +might do complicated stuff but but when +it comes back it's exactly the way it + + align:start position:0% +it comes back it's exactly the way it + + + align:start position:0% +it comes back it's exactly the way it +was when it + + align:start position:0% +was when it + + + align:start position:0% +was when it +started uh if it's anharmonic it's not + + align:start position:0% +started uh if it's anharmonic it's not + + + align:start position:0% +started uh if it's anharmonic it's not +back the way it was when it started it's + + align:start position:0% +back the way it was when it started it's + + + align:start position:0% +back the way it was when it started it's +been stretched and so the successive + + align:start position:0% +been stretched and so the successive + + + align:start position:0% +been stretched and so the successive +recurrences are decreased in + + align:start position:0% +recurrences are decreased in + + + align:start position:0% +recurrences are decreased in +amplitude + + align:start position:0% + + + + align:start position:0% + +so how much time do I + + align:start position:0% + + + + align:start position:0% + +have okay um there's all sorts of things + + align:start position:0% +have okay um there's all sorts of things + + + align:start position:0% +have okay um there's all sorts of things +we + + align:start position:0% +we + + + align:start position:0% +we +know well let me just finish the + + align:start position:0% +know well let me just finish the + + + align:start position:0% +know well let me just finish the +derivation + + align:start position:0% +derivation + + + align:start position:0% +derivation +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um suppose we wanted to + + align:start position:0% +um suppose we wanted to + + + align:start position:0% +um suppose we wanted to +calculate how long it takes for a wave + + align:start position:0% +calculate how long it takes for a wave + + + align:start position:0% +calculate how long it takes for a wave + to move by half its + + align:start position:0% + to move by half its + + + align:start position:0% + to move by half its +width which corresponds to the time at + + align:start position:0% +width which corresponds to the time at + + + align:start position:0% +width which corresponds to the time at +which the autocorrelation function has + + align:start position:0% +which the autocorrelation function has + + + align:start position:0% +which the autocorrelation function has +reduced from one to a + + align:start position:0% +reduced from one to a + + + align:start position:0% +reduced from one to a +half + + align:start position:0% +half + + + align:start position:0% +half +approximately so we we want to know + + align:start position:0% +approximately so we we want to know + + + align:start position:0% +approximately so we we want to know +something about uh uh the the various + + align:start position:0% +something about uh uh the the various + + + align:start position:0% +something about uh uh the the various +quantities that we need to describe this + + align:start position:0% +quantities that we need to describe this + + + align:start position:0% +quantities that we need to describe this +okay well first of all uh we have + + align:start position:0% +okay well first of all uh we have + + + align:start position:0% +okay well first of all uh we have +recurrences which occur + + align:start position:0% +recurrences which occur + + + align:start position:0% +recurrences which occur +at uh the period of an + + align:start position:0% +at uh the period of an + + + align:start position:0% +at uh the period of an +oscillation and The Classical period of + + align:start position:0% + + + + align:start position:0% + +oscillation it's given by this or 1 over + + align:start position:0% +oscillation it's given by this or 1 over + + + align:start position:0% +oscillation it's given by this or 1 over +Omega e * + + align:start position:0% + + + + align:start position:0% + +C you have to be careful and I keep + + align:start position:0% +C you have to be careful and I keep + + + align:start position:0% +C you have to be careful and I keep +getting confused this is a frequency + + align:start position:0% +getting confused this is a frequency + + + align:start position:0% +getting confused this is a frequency +this is a wave number which is a + + align:start position:0% +this is a wave number which is a + + + align:start position:0% +this is a wave number which is a +frequency divided by C even though it's + + align:start position:0% +frequency divided by C even though it's + + + align:start position:0% +frequency divided by C even though it's +Omega there's no two Pi + + align:start position:0% + + + + align:start position:0% + +involved okay so the initial Decay has + + align:start position:0% +involved okay so the initial Decay has + + + align:start position:0% +involved okay so the initial Decay has +to do we have a a wave packet and it's + + align:start position:0% +to do we have a a wave packet and it's + + + align:start position:0% +to do we have a a wave packet and it's +sitting at rest at a center at a at a + + align:start position:0% +sitting at rest at a center at a at a + + + align:start position:0% +sitting at rest at a center at a at a +coordinate we know because it's a + + align:start position:0% +coordinate we know because it's a + + + align:start position:0% +coordinate we know because it's a +vertical transition and at T equals z + + align:start position:0% +vertical transition and at T equals z + + + align:start position:0% +vertical transition and at T equals z +that's where it is and it has zero + + align:start position:0% +that's where it is and it has zero + + + align:start position:0% +that's where it is and it has zero +momentum so now we use classical + + align:start position:0% +momentum so now we use classical + + + align:start position:0% +momentum so now we use classical +mechanics we have the for force is equal + + align:start position:0% +mechanics we have the for force is equal + + + align:start position:0% +mechanics we have the for force is equal +to the gradient minus the gradient of + + align:start position:0% +to the gradient minus the gradient of + + + align:start position:0% +to the gradient minus the gradient of +the + + align:start position:0% +the + + + align:start position:0% +the +potential and and that's equal to the + + align:start position:0% +potential and and that's equal to the + + + align:start position:0% +potential and and that's equal to the +mass times the + + align:start position:0% +mass times the + + + align:start position:0% +mass times the +acceleration so we have uh an equation + + align:start position:0% +acceleration so we have uh an equation + + + align:start position:0% +acceleration so we have uh an equation +of motion initial condition r0 is + + align:start position:0% +of motion initial condition r0 is + + + align:start position:0% +of motion initial condition r0 is +usually a turning point so we can use + + align:start position:0% +usually a turning point so we can use + + + align:start position:0% +usually a turning point so we can use +say it's the left turning + + align:start position:0% +say it's the left turning + + + align:start position:0% +say it's the left turning +point + + align:start position:0% +point + + + align:start position:0% +point +and the velocity at t equal 0 is + + align:start position:0% +and the velocity at t equal 0 is + + + align:start position:0% +and the velocity at t equal 0 is +zero and so now we can uh we can take + + align:start position:0% +zero and so now we can uh we can take + + + align:start position:0% +zero and so now we can uh we can take +this equation of motion and we can + + align:start position:0% +this equation of motion and we can + + + align:start position:0% +this equation of motion and we can +integrate this equation of motion and so + + align:start position:0% +integrate this equation of motion and so + + + align:start position:0% +integrate this equation of motion and so +we get r dot of T is going to be equal + + align:start position:0% +we get r dot of T is going to be equal + + + align:start position:0% +we get r dot of T is going to be equal +to minus one over the + + align:start position:0% +to minus one over the + + + align:start position:0% +to minus one over the +masstimes the gradient of the + + align:start position:0% +masstimes the gradient of the + + + align:start position:0% +masstimes the gradient of the +potential time T evaluated at our + + align:start position:0% +potential time T evaluated at our + + + align:start position:0% +potential time T evaluated at our +turning point so this is the derivative + + align:start position:0% +turning point so this is the derivative + + + align:start position:0% +turning point so this is the derivative +of the potential evaluated at the place + + align:start position:0% +of the potential evaluated at the place + + + align:start position:0% +of the potential evaluated at the place +where the wave packet was initially + + align:start position:0% +where the wave packet was initially + + + align:start position:0% +where the wave packet was initially +put so this is this is essentially the + + align:start position:0% +put so this is this is essentially the + + + align:start position:0% +put so this is this is essentially the +same thing well took the M over here + + align:start position:0% +same thing well took the M over here + + + align:start position:0% +same thing well took the M over here +it's the momentum as a function of time + + align:start position:0% +it's the momentum as a function of time + + + align:start position:0% +it's the momentum as a function of time +and so the + + align:start position:0% +and so the + + + align:start position:0% +and so the +momentum increases linearly in + + align:start position:0% +momentum increases linearly in + + + align:start position:0% +momentum increases linearly in +time and the coefficient of that linear + + align:start position:0% +time and the coefficient of that linear + + + align:start position:0% +time and the coefficient of that linear +increase is the slope so if the + + align:start position:0% +increase is the slope so if the + + + align:start position:0% +increase is the slope so if the +potential is very + + align:start position:0% +potential is very + + + align:start position:0% +potential is very +vertical the slope is large the momentum + + align:start position:0% +vertical the slope is large the momentum + + + align:start position:0% +vertical the slope is large the momentum +increases rapidly and if this slope if + + align:start position:0% +increases rapidly and if this slope if + + + align:start position:0% +increases rapidly and if this slope if +the potential is very horizontal or soft + + align:start position:0% +the potential is very horizontal or soft + + + align:start position:0% +the potential is very horizontal or soft +the uh momentum increases very + + align:start position:0% + + + + align:start position:0% + +slowly we can integrate + + align:start position:0% +slowly we can integrate + + + align:start position:0% +slowly we can integrate +again and so we can get the coordinate + + align:start position:0% +again and so we can get the coordinate + + + align:start position:0% +again and so we can get the coordinate +as a function of time and that's 1 over + + align:start position:0% +as a function of time and that's 1 over + + + align:start position:0% +as a function of time and that's 1 over + + align:start position:0% + + + align:start position:0% +m d + + align:start position:0% + + + + align:start position:0% + +v Dr again evaluated at the turning + + align:start position:0% +v Dr again evaluated at the turning + + + align:start position:0% +v Dr again evaluated at the turning +point t^2 plus the turning + + align:start position:0% +point t^2 plus the turning + + + align:start position:0% +point t^2 plus the turning +point so at Early times we know how the + + align:start position:0% +point so at Early times we know how the + + + align:start position:0% +point so at Early times we know how the +momentum and the coordinate change Early + + align:start position:0% +momentum and the coordinate change Early + + + align:start position:0% +momentum and the coordinate change Early +Times means this is + + align:start position:0% +Times means this is + + + align:start position:0% +Times means this is +small so the main action in the wave + + align:start position:0% +small so the main action in the wave + + + align:start position:0% +small so the main action in the wave +packet is on the momentum part of it not + + align:start position:0% +packet is on the momentum part of it not + + + align:start position:0% +packet is on the momentum part of it not +the coordinate part of + + align:start position:0% +the coordinate part of + + + align:start position:0% +the coordinate part of +it I'm going to ignore that and I'm + + align:start position:0% +it I'm going to ignore that and I'm + + + align:start position:0% +it I'm going to ignore that and I'm +going to talk entirely about the + + align:start position:0% +going to talk entirely about the + + + align:start position:0% +going to talk entirely about the +coordinate + + align:start position:0% +coordinate + + + align:start position:0% +coordinate +part uh and in the uh + + align:start position:0% +part uh and in the uh + + + align:start position:0% +part uh and in the uh +handout + + align:start position:0% +handout + + + align:start position:0% +handout +um there is the uh the equation for a + + align:start position:0% +um there is the uh the equation for a + + + align:start position:0% +um there is the uh the equation for a +gaussian wave + + align:start position:0% +gaussian wave + + + align:start position:0% +gaussian wave +packet which is uh so the gaussian wave + + align:start position:0% +packet which is uh so the gaussian wave + + + align:start position:0% +packet which is uh so the gaussian wave +packet has a real part and imaginary + + align:start position:0% +packet has a real part and imaginary + + + align:start position:0% +packet has a real part and imaginary +part and the real part encodes + + align:start position:0% +part and the real part encodes + + + align:start position:0% +part and the real part encodes +coordinate and the imaginary part + + align:start position:0% +coordinate and the imaginary part + + + align:start position:0% +coordinate and the imaginary part +encodes + + align:start position:0% +encodes + + + align:start position:0% +encodes +momentum and we know wave packets are + + align:start position:0% +momentum and we know wave packets are + + + align:start position:0% +momentum and we know wave packets are +going to + + align:start position:0% +going to + + + align:start position:0% +going to +move and they're going to + + align:start position:0% +move and they're going to + + + align:start position:0% +move and they're going to +broaden or maybe + + align:start position:0% +broaden or maybe + + + align:start position:0% +broaden or maybe +sometimes Focus but uh uh and so we're + + align:start position:0% +sometimes Focus but uh uh and so we're + + + align:start position:0% +sometimes Focus but uh uh and so we're +going to uh and the uh the velocity uh + + align:start position:0% +going to uh and the uh the velocity uh + + + align:start position:0% +going to uh and the uh the velocity uh +or moment + + align:start position:0% +or moment + + + align:start position:0% +or moment +doesn't have to be constant but this is + + align:start position:0% +doesn't have to be constant but this is + + + align:start position:0% +doesn't have to be constant but this is +an this is a localized early Time + + align:start position:0% +an this is a localized early Time + + + align:start position:0% +an this is a localized early Time +picture and what we really want is to be + + align:start position:0% +picture and what we really want is to be + + + align:start position:0% +picture and what we really want is to be +able to understand what happens first + + align:start position:0% +able to understand what happens first + + + align:start position:0% +able to understand what happens first +yeah so suppose the uh potential is Sly + + align:start position:0% +yeah so suppose the uh potential is Sly + + + align:start position:0% +yeah so suppose the uh potential is Sly +on classically speaking You can predict + + align:start position:0% +on classically speaking You can predict + + + align:start position:0% +on classically speaking You can predict +the uh shape of the wave packet in the + + align:start position:0% +the uh shape of the wave packet in the + + + align:start position:0% +the uh shape of the wave packet in the +middle but when it just uh goes towards + + align:start position:0% +middle but when it just uh goes towards + + + align:start position:0% +middle but when it just uh goes towards +the other end uh just by knowing the + + align:start position:0% +the other end uh just by knowing the + + + align:start position:0% +the other end uh just by knowing the +initial slope uh can you do that quum + + align:start position:0% +initial slope uh can you do that quum + + + align:start position:0% +initial slope uh can you do that quum +mechanically would it feel the anonity + + align:start position:0% +mechanically would it feel the anonity + + + align:start position:0% +mechanically would it feel the anonity +on the other side you know before it + + align:start position:0% +on the other side you know before it + + + align:start position:0% +on the other side you know before it +reached + + align:start position:0% +reached + + + align:start position:0% +reached +there I believe so I believe that the + + align:start position:0% +there I believe so I believe that the + + + align:start position:0% +there I believe so I believe that the +quantum mechanics is is is more Global + + align:start position:0% +quantum mechanics is is is more Global + + + align:start position:0% +quantum mechanics is is is more Global +than the classical mechanics that I mean + + align:start position:0% +than the classical mechanics that I mean + + + align:start position:0% +than the classical mechanics that I mean +the classical mechanics you're you're + + align:start position:0% +the classical mechanics you're you're + + + align:start position:0% +the classical mechanics you're you're +basically uh well here we're just + + align:start position:0% +basically uh well here we're just + + + align:start position:0% +basically uh well here we're just +sampling the potential at a + + align:start position:0% +sampling the potential at a + + + align:start position:0% +sampling the potential at a +point uh we could do this more + + align:start position:0% +point uh we could do this more + + + align:start position:0% +point uh we could do this more +rigorously and you know we could we + + align:start position:0% +rigorously and you know we could we + + + align:start position:0% +rigorously and you know we could we +could say okay uh so you have only one + + align:start position:0% +could say okay uh so you have only one + + + align:start position:0% +could say okay uh so you have only one +condition initial one that's that's + + align:start position:0% +condition initial one that's that's + + + align:start position:0% +condition initial one that's that's +right I what I'm going to say is + + align:start position:0% +right I what I'm going to say is + + + align:start position:0% +right I what I'm going to say is +eventually the wave packet hits the + + align:start position:0% +eventually the wave packet hits the + + + align:start position:0% +eventually the wave packet hits the +other wall and comes back and its Center + + align:start position:0% +other wall and comes back and its Center + + + align:start position:0% +other wall and comes back and its Center +will come back at a time which + + align:start position:0% +will come back at a time which + + + align:start position:0% +will come back at a time which +corresponds to the period of oscillation + + align:start position:0% +corresponds to the period of oscillation + + + align:start position:0% +corresponds to the period of oscillation +but it will have been messed up the wave + + align:start position:0% +but it will have been messed up the wave + + + align:start position:0% +but it will have been messed up the wave +packet will have a complicated structure + + align:start position:0% +packet will have a complicated structure + + + align:start position:0% +packet will have a complicated structure +which we will not pay attention to its + + align:start position:0% +which we will not pay attention to its + + + align:start position:0% +which we will not pay attention to its +zero order in a real calculation you + + align:start position:0% +zero order in a real calculation you + + + align:start position:0% +zero order in a real calculation you +would pay attention to it but basically + + align:start position:0% +would pay attention to it but basically + + + align:start position:0% +would pay attention to it but basically +air infest theorem tells you what you + + align:start position:0% +air infest theorem tells you what you + + + align:start position:0% +air infest theorem tells you what you +follow is the center of the wave packet + + align:start position:0% +follow is the center of the wave packet + + + align:start position:0% +follow is the center of the wave packet +and that tells you what you want it's + + align:start position:0% +and that tells you what you want it's + + + align:start position:0% +and that tells you what you want it's +rare that a wave packet will develop + + align:start position:0% +rare that a wave packet will develop + + + align:start position:0% +rare that a wave packet will develop +structure so that one wave packet one + + align:start position:0% +structure so that one wave packet one + + + align:start position:0% +structure so that one wave packet one +localized wave packet going out and + + align:start position:0% +localized wave packet going out and + + + align:start position:0% +localized wave packet going out and +coming back will do anything but go up + + align:start position:0% +coming back will do anything but go up + + + align:start position:0% +coming back will do anything but go up +and go down it will have a you know it + + align:start position:0% +and go down it will have a you know it + + + align:start position:0% +and go down it will have a you know it +will have a perhaps a little bit + + align:start position:0% +will have a perhaps a little bit + + + align:start position:0% +will have a perhaps a little bit +complicated structure but it won't look + + align:start position:0% +complicated structure but it won't look + + + align:start position:0% +complicated structure but it won't look +like several different + + align:start position:0% + + + + align:start position:0% + +frequencies okay so we have this picture + + align:start position:0% +frequencies okay so we have this picture + + + align:start position:0% +frequencies okay so we have this picture +and + + align:start position:0% +and + + + align:start position:0% +and +so uh this T12 the time it takes for the + + align:start position:0% +so uh this T12 the time it takes for the + + + align:start position:0% +so uh this T12 the time it takes for the +autocorrelation function to reduce by a + + align:start position:0% +autocorrelation function to reduce by a + + + align:start position:0% +autocorrelation function to reduce by a +factor of two and whether that's a + + align:start position:0% +factor of two and whether that's a + + + align:start position:0% +factor of two and whether that's a +factor of two or the square root of two + + align:start position:0% +factor of two or the square root of two + + + align:start position:0% +factor of two or the square root of two +doesn't really matter uh we can just say + + align:start position:0% +doesn't really matter uh we can just say + + + align:start position:0% +doesn't really matter uh we can just say +we're interested in the W picket moving + + align:start position:0% +we're interested in the W picket moving + + + align:start position:0% +we're interested in the W picket moving +by half its width and that's the + + align:start position:0% +by half its width and that's the + + + align:start position:0% +by half its width and that's the +quantity we're interested in and so we + + align:start position:0% +quantity we're interested in and so we + + + align:start position:0% +quantity we're interested in and so we +can calculate then what that is and that + + align:start position:0% +can calculate then what that is and that + + + align:start position:0% +can calculate then what that is and that +becomes uh + + align:start position:0% +becomes uh + + + align:start position:0% +becomes uh +Delta over the the + + align:start position:0% + + + + align:start position:0% + +slope square + + align:start position:0% +slope square + + + align:start position:0% +slope square +root you can calculate this it's a + + align:start position:0% +root you can calculate this it's a + + + align:start position:0% +root you can calculate this it's a +simple thing so that's how far it has to + + align:start position:0% +simple thing so that's how far it has to + + + align:start position:0% +simple thing so that's how far it has to +move and now what we want to do is say + + align:start position:0% +move and now what we want to do is say + + + align:start position:0% +move and now what we want to do is say +okay what goes into this how broad is + + align:start position:0% +okay what goes into this how broad is + + + align:start position:0% +okay what goes into this how broad is +the W the initial wave packet and what + + align:start position:0% +the W the initial wave packet and what + + + align:start position:0% +the W the initial wave packet and what +goes into + + align:start position:0% +goes into + + + align:start position:0% +goes into +this and what goes into this is going to + + align:start position:0% +this and what goes into this is going to + + + align:start position:0% +this and what goes into this is going to +be the + + align:start position:0% +be the + + + align:start position:0% +be the +um the harmonic + + align:start position:0% +um the harmonic + + + align:start position:0% +um the harmonic +frequency and the distance from + + align:start position:0% +frequency and the distance from + + + align:start position:0% +frequency and the distance from +equilibrium and so from this simple + + align:start position:0% +equilibrium and so from this simple + + + align:start position:0% +equilibrium and so from this simple +formula we can uh we can write a more + + align:start position:0% +formula we can uh we can write a more + + + align:start position:0% +formula we can uh we can write a more +useful formula and I'm skipping steps + + align:start position:0% +useful formula and I'm skipping steps + + + align:start position:0% +useful formula and I'm skipping steps +because I'm getting lazy and we're + + align:start position:0% +because I'm getting lazy and we're + + + align:start position:0% +because I'm getting lazy and we're +running out of time and I want to show + + align:start position:0% +running out of time and I want to show + + + align:start position:0% +running out of time and I want to show +some pretty + + align:start position:0% +some pretty + + + align:start position:0% +some pretty +pictures + + align:start position:0% +pictures + + + align:start position:0% +pictures +so + + align:start position:0% +so + + + align:start position:0% +so +T12 can be shown to be 1 over 2 + + align:start position:0% +T12 can be shown to be 1 over 2 + + + align:start position:0% +T12 can be shown to be 1 over 2 +pi C Omega e Prime so we we're treating + + align:start position:0% +pi C Omega e Prime so we we're treating + + + align:start position:0% +pi C Omega e Prime so we we're treating +the Lower State potential and the Upper + + align:start position:0% +the Lower State potential and the Upper + + + align:start position:0% +the Lower State potential and the Upper +State potential is harmonic so this is + + align:start position:0% +State potential is harmonic so this is + + + align:start position:0% +State potential is harmonic so this is +the harmonic + + align:start position:0% +the harmonic + + + align:start position:0% +the harmonic +frequency + + align:start position:0% + + + + align:start position:0% + +uh of the uh upper potential and then + + align:start position:0% +uh of the uh upper potential and then + + + align:start position:0% +uh of the uh upper potential and then +this is the width of the wave packet Rus + + align:start position:0% +this is the width of the wave packet Rus + + + align:start position:0% +this is the width of the wave packet Rus +r e Prime D you know square + + align:start position:0% +r e Prime D you know square + + + align:start position:0% +r e Prime D you know square +root now normally we're starting out at + + align:start position:0% +root now normally we're starting out at + + + align:start position:0% +root now normally we're starting out at +r e + + align:start position:0% + + + + align:start position:0% + +Prime and so you already see that the + + align:start position:0% +Prime and so you already see that the + + + align:start position:0% +Prime and so you already see that the +time that it takes for the wave function + + align:start position:0% +time that it takes for the wave function + + + align:start position:0% +time that it takes for the wave function +to get away from + + align:start position:0% +to get away from + + + align:start position:0% +to get away from +itself gives you an information about + + align:start position:0% +itself gives you an information about + + + align:start position:0% +itself gives you an information about +the uh frequency + + align:start position:0% +the uh frequency + + + align:start position:0% +the uh frequency +a high frequency means short time a + + align:start position:0% +a high frequency means short time a + + + align:start position:0% +a high frequency means short time a +large distance away from equilibrium + + align:start position:0% +large distance away from equilibrium + + + align:start position:0% +large distance away from equilibrium +also means a short + + align:start position:0% + + + + align:start position:0% + +time so and I could also just calc show + + align:start position:0% +time so and I could also just calc show + + + align:start position:0% +time so and I could also just calc show +you Delta the width of the Lower State + + align:start position:0% +you Delta the width of the Lower State + + + align:start position:0% +you Delta the width of the Lower State +wave function is 1 over + + align:start position:0% +wave function is 1 over + + + align:start position:0% +wave function is 1 over +Pi H over + + align:start position:0% +Pi H over + + + align:start position:0% +Pi H over +m c Omega e Prime square + + align:start position:0% +m c Omega e Prime square + + + align:start position:0% +m c Omega e Prime square +root + + align:start position:0% +root + + + align:start position:0% +root +so this + + align:start position:0% +so this + + + align:start position:0% +so this +thing uh basically reflects the the + + align:start position:0% +thing uh basically reflects the the + + + align:start position:0% +thing uh basically reflects the the +Lower State + + align:start position:0% +Lower State + + + align:start position:0% +Lower State +frequency and if the Lower State + + align:start position:0% +frequency and if the Lower State + + + align:start position:0% +frequency and if the Lower State +frequency is + + align:start position:0% +frequency is + + + align:start position:0% +frequency is +high also uh uh the uh uh wave packet + + align:start position:0% +high also uh uh the uh uh wave packet + + + align:start position:0% +high also uh uh the uh uh wave packet +moves away from + + align:start position:0% +moves away from + + + align:start position:0% +moves away from +itself + + align:start position:0% +itself + + + align:start position:0% +itself +fast because Delta is + + align:start position:0% +fast because Delta is + + + align:start position:0% +fast because Delta is +small so we have a lot of stuff here and + + align:start position:0% +small so we have a lot of stuff here and + + + align:start position:0% +small so we have a lot of stuff here and +and we haven't looked at any recurrences + + align:start position:0% +and we haven't looked at any recurrences + + + align:start position:0% +and we haven't looked at any recurrences +yet we we see that the wave function the + + align:start position:0% +yet we we see that the wave function the + + + align:start position:0% +yet we we see that the wave function the +the autocorrelation function is going to + + align:start position:0% +the autocorrelation function is going to + + + align:start position:0% +the autocorrelation function is going to +Decay at a rate which is determined by + + align:start position:0% +Decay at a rate which is determined by + + + align:start position:0% +Decay at a rate which is determined by +how far away from equilibrium and uh the + + align:start position:0% +how far away from equilibrium and uh the + + + align:start position:0% +how far away from equilibrium and uh the +frequencies of the upper and lower + + align:start position:0% + + + + align:start position:0% + +States so all sorts of spectroscopic + + align:start position:0% +States so all sorts of spectroscopic + + + align:start position:0% +States so all sorts of spectroscopic +stuff is coming in + + align:start position:0% + + + + align:start position:0% + +here now we already know that they're + + align:start position:0% +here now we already know that they're + + + align:start position:0% +here now we already know that they're +going to be recurrences and the + + align:start position:0% +going to be recurrences and the + + + align:start position:0% +going to be recurrences and the +recurrences are going to tell us about + + align:start position:0% +recurrences are going to tell us about + + + align:start position:0% +recurrences are going to tell us about +these + + align:start position:0% +these + + + align:start position:0% +these +things and so uh uh we know about the + + align:start position:0% +things and so uh uh we know about the + + + align:start position:0% +things and so uh uh we know about the +initial wave function so we know what + + align:start position:0% +initial wave function so we know what + + + align:start position:0% +initial wave function so we know what +this is and and so then it's going to + + align:start position:0% +this is and and so then it's going to + + + align:start position:0% +this is and and so then it's going to +give us a little bit of a clue about how + + align:start position:0% +give us a little bit of a clue about how + + + align:start position:0% +give us a little bit of a clue about how +far up this the inner or outer wall we + + align:start position:0% +far up this the inner or outer wall we + + + align:start position:0% +far up this the inner or outer wall we +are and that's an awful lot of + + align:start position:0% +are and that's an awful lot of + + + align:start position:0% +are and that's an awful lot of +information uh now I mean suppose you + + align:start position:0% +information uh now I mean suppose you + + + align:start position:0% +information uh now I mean suppose you +had a uh uh + + align:start position:0% +had a uh uh + + + align:start position:0% +had a uh uh +all right I I I want to go to the + + align:start position:0% +all right I I I want to go to the + + + align:start position:0% +all right I I I want to go to the +pictures + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +um suppose you had a potential + + align:start position:0% + + + + align:start position:0% + +surface which is bound in one coordinate + + align:start position:0% +surface which is bound in one coordinate + + + align:start position:0% +surface which is bound in one coordinate +and repulsive in another coordinate so + + align:start position:0% +and repulsive in another coordinate so + + + align:start position:0% +and repulsive in another coordinate so +this + + align:start position:0% +this + + + align:start position:0% +this +is + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% + + + + align:start position:0% + +okay so here is a picture uh the + + align:start position:0% +okay so here is a picture uh the + + + align:start position:0% +okay so here is a picture uh the +potential is bound in this + + align:start position:0% +potential is bound in this + + + align:start position:0% +potential is bound in this +direction and it's repulsive in this + + align:start position:0% +direction and it's repulsive in this + + + align:start position:0% +direction and it's repulsive in this +direction and so this is T equals z this + + align:start position:0% +direction and so this is T equals z this + + + align:start position:0% +direction and so this is T equals z this +is a later time and so here you've + + align:start position:0% +is a later time and so here you've + + + align:start position:0% +is a later time and so here you've +created the wave function at a at a + + align:start position:0% +created the wave function at a at a + + + align:start position:0% +created the wave function at a at a +turning point here the wave function has + + align:start position:0% +turning point here the wave function has + + + align:start position:0% +turning point here the wave function has +moved away from + + align:start position:0% +moved away from + + + align:start position:0% +moved away from +itself and has spread along the uh uh + + align:start position:0% +itself and has spread along the uh uh + + + align:start position:0% +itself and has spread along the uh uh +Unbound coordinate here the wave + + align:start position:0% + + + + align:start position:0% + +function is it really as terrible as + + align:start position:0% +function is it really as terrible as + + + align:start position:0% +function is it really as terrible as +that that you can't that's a little + + align:start position:0% +that that you can't that's a little + + + align:start position:0% +that that you can't that's a little +better okay so here it's continuing to + + align:start position:0% +better okay so here it's continuing to + + + align:start position:0% +better okay so here it's continuing to +move and + + align:start position:0% +move and + + + align:start position:0% +move and +spread and now comes + + align:start position:0% +spread and now comes + + + align:start position:0% +spread and now comes +back and it starts to overlap with + + align:start position:0% +back and it starts to overlap with + + + align:start position:0% +back and it starts to overlap with +itself having spread it should should + + align:start position:0% +itself having spread it should should + + + align:start position:0% +itself having spread it should should +have shown uh more spre I don't see why + + align:start position:0% +have shown uh more spre I don't see why + + + align:start position:0% +have shown uh more spre I don't see why +it would decrease its spread but and now + + align:start position:0% +it would decrease its spread but and now + + + align:start position:0% +it would decrease its spread but and now +here is the uh spreaded the spread wave + + align:start position:0% +here is the uh spreaded the spread wave + + + align:start position:0% +here is the uh spreaded the spread wave +packet now overlapping with itself and + + align:start position:0% +packet now overlapping with itself and + + + align:start position:0% +packet now overlapping with itself and +the recurrence can only be a relatively + + align:start position:0% +the recurrence can only be a relatively + + + align:start position:0% +the recurrence can only be a relatively +small value because most of it spread + + align:start position:0% +small value because most of it spread + + + align:start position:0% +small value because most of it spread +out and here it now moves away again and + + align:start position:0% +out and here it now moves away again and + + + align:start position:0% +out and here it now moves away again and +so you have a + + align:start position:0% +so you have a + + + align:start position:0% +so you have a +recurrence and you have a + + align:start position:0% +recurrence and you have a + + + align:start position:0% +recurrence and you have a +width and uh uh those things appear in + + align:start position:0% +width and uh uh those things appear in + + + align:start position:0% +width and uh uh those things appear in +this + + align:start position:0% + + + + align:start position:0% + +picture so up here is the + + align:start position:0% +picture so up here is the + + + align:start position:0% +picture so up here is the +autocorrelation function and this is + + align:start position:0% +autocorrelation function and this is + + + align:start position:0% +autocorrelation function and this is +time equals zero and so uh we we start + + align:start position:0% +time equals zero and so uh we we start + + + align:start position:0% +time equals zero and so uh we we start +here and it deases goes way and so this + + align:start position:0% +here and it deases goes way and so this + + + align:start position:0% +here and it deases goes way and so this +was the initial picture this is uh the + + align:start position:0% +was the initial picture this is uh the + + + align:start position:0% +was the initial picture this is uh the +wave function have moved away from + + align:start position:0% +wave function have moved away from + + + align:start position:0% +wave function have moved away from +itself uh this is the wave function + + align:start position:0% +itself uh this is the wave function + + + align:start position:0% +itself uh this is the wave function +continuing to move away and there's + + align:start position:0% +continuing to move away and there's + + + align:start position:0% +continuing to move away and there's +nothing there and then it's starting to + + align:start position:0% +nothing there and then it's starting to + + + align:start position:0% +nothing there and then it's starting to +come back here it's uh on top of itself + + align:start position:0% +come back here it's uh on top of itself + + + align:start position:0% +come back here it's uh on top of itself +but the amplitude is + + align:start position:0% +but the amplitude is + + + align:start position:0% +but the amplitude is +smaller and uh it's moved away again and + + align:start position:0% +smaller and uh it's moved away again and + + + align:start position:0% +smaller and uh it's moved away again and +then another + + align:start position:0% +then another + + + align:start position:0% +then another +recurrence now we can take the forier + + align:start position:0% +recurrence now we can take the forier + + + align:start position:0% +recurrence now we can take the forier +transform of this and so we have + + align:start position:0% +transform of this and so we have + + + align:start position:0% +transform of this and so we have +periodic + + align:start position:0% +periodic + + + align:start position:0% +periodic +recurrences and so when we take the for + + align:start position:0% +recurrences and so when we take the for + + + align:start position:0% +recurrences and so when we take the for +a transform we're going to have + + align:start position:0% +a transform we're going to have + + + align:start position:0% +a transform we're going to have +something that reflects those + + align:start position:0% +something that reflects those + + + align:start position:0% +something that reflects those +recurrences and that's + + align:start position:0% +recurrences and that's + + + align:start position:0% +recurrences and that's +this this + + align:start position:0% +this this + + + align:start position:0% +this this +pattern and there's going to be + + align:start position:0% +pattern and there's going to be + + + align:start position:0% +pattern and there's going to be +something that reflects the the time it + + align:start position:0% +something that reflects the the time it + + + align:start position:0% +something that reflects the the time it +takes for the wave packet to move away + + align:start position:0% +takes for the wave packet to move away + + + align:start position:0% +takes for the wave packet to move away +from itself and that's + + align:start position:0% + + + + align:start position:0% + +this and so this provides you with a + + align:start position:0% +this and so this provides you with a + + + align:start position:0% +this and so this provides you with a +kind of a picture of + + align:start position:0% +kind of a picture of + + + align:start position:0% +kind of a picture of +um what is the uh Spectrum + + align:start position:0% +um what is the uh Spectrum + + + align:start position:0% +um what is the uh Spectrum +going to look like if you have a bound + + align:start position:0% +going to look like if you have a bound + + + align:start position:0% +going to look like if you have a bound +State a bound mode and a repulsive mode + + align:start position:0% +State a bound mode and a repulsive mode + + + align:start position:0% +State a bound mode and a repulsive mode +you're going to have a big broad thing + + align:start position:0% +you're going to have a big broad thing + + + align:start position:0% +you're going to have a big broad thing +with some Wiggles on top of it now you + + align:start position:0% +with some Wiggles on top of it now you + + + align:start position:0% +with some Wiggles on top of it now you +wouldn't have been able to do that + + align:start position:0% +wouldn't have been able to do that + + + align:start position:0% +wouldn't have been able to do that +without a lengthy calculation if you + + align:start position:0% +without a lengthy calculation if you + + + align:start position:0% +without a lengthy calculation if you +were starting from the full potential + + align:start position:0% +were starting from the full potential + + + align:start position:0% +were starting from the full potential +but these simple ideas are uh you know + + align:start position:0% +but these simple ideas are uh you know + + + align:start position:0% +but these simple ideas are uh you know +it's very you know very simple to to + + align:start position:0% +it's very you know very simple to to + + + align:start position:0% +it's very you know very simple to to +figure out what this is and to uh and to + + align:start position:0% +figure out what this is and to uh and to + + + align:start position:0% +figure out what this is and to uh and to +see in the Spectrum um uh the the fre + + align:start position:0% +see in the Spectrum um uh the the fre + + + align:start position:0% +see in the Spectrum um uh the the fre +frequencies and that's just you know + + align:start position:0% +frequencies and that's just you know + + + align:start position:0% +frequencies and that's just you know +that's a fantastic thing now here is + + align:start position:0% +that's a fantastic thing now here is + + + align:start position:0% +that's a fantastic thing now here is +another + + align:start position:0% + + + + align:start position:0% + +picture and this has a lot of + + align:start position:0% +picture and this has a lot of + + + align:start position:0% +picture and this has a lot of +information in it so here is just IOD we + + align:start position:0% +information in it so here is just IOD we + + + align:start position:0% +information in it so here is just IOD we +excite iodine from the ground state V + + align:start position:0% +excite iodine from the ground state V + + + align:start position:0% +excite iodine from the ground state V +equals z to an excited state which is + + align:start position:0% +equals z to an excited state which is + + + align:start position:0% +equals z to an excited state which is +not bound to onedimensional + + align:start position:0% +not bound to onedimensional + + + align:start position:0% +not bound to onedimensional +and so at T equals z the wave packet is + + align:start position:0% +and so at T equals z the wave packet is + + + align:start position:0% +and so at T equals z the wave packet is +localized here and with time the way + + align:start position:0% +localized here and with time the way + + + align:start position:0% +localized here and with time the way +packet + + align:start position:0% +packet + + + align:start position:0% +packet +spreads and uh so there's lots of things + + align:start position:0% +spreads and uh so there's lots of things + + + align:start position:0% +spreads and uh so there's lots of things +you can do to monitor the + + align:start position:0% +you can do to monitor the + + + align:start position:0% +you can do to monitor the +Dynamics and people have done all of + + align:start position:0% +Dynamics and people have done all of + + + align:start position:0% +Dynamics and people have done all of +them uh so one of the things you can do + + align:start position:0% +them uh so one of the things you can do + + + align:start position:0% +them uh so one of the things you can do +is to look at uh the states of AAR and + + align:start position:0% +is to look at uh the states of AAR and + + + align:start position:0% +is to look at uh the states of AAR and +BC BC has vibrational structure and so + + align:start position:0% +BC BC has vibrational structure and so + + + align:start position:0% +BC BC has vibrational structure and so +uh there'll be some about the state + + align:start position:0% +uh there'll be some about the state + + + align:start position:0% +uh there'll be some about the state +distribution that tells you what + + align:start position:0% +distribution that tells you what + + + align:start position:0% +distribution that tells you what +happened in the + + align:start position:0% +happened in the + + + align:start position:0% +happened in the +Dynamics + + align:start position:0% +Dynamics + + + align:start position:0% +Dynamics +um now as this wave packet + + align:start position:0% +um now as this wave packet + + + align:start position:0% +um now as this wave packet +moves the wave packet is resonant with + + align:start position:0% +moves the wave packet is resonant with + + + align:start position:0% +moves the wave packet is resonant with +various outer turning points on this + + align:start position:0% +various outer turning points on this + + + align:start position:0% +various outer turning points on this +well and every time the wave packet + + align:start position:0% +well and every time the wave packet + + + align:start position:0% +well and every time the wave packet +passes through a stationary phase uh + + align:start position:0% +passes through a stationary phase uh + + + align:start position:0% +passes through a stationary phase uh +stay it passes through a uh um + + align:start position:0% +stay it passes through a uh um + + + align:start position:0% +stay it passes through a uh um +a turning + + align:start position:0% +a turning + + + align:start position:0% +a turning +point uh you expect that something will + + align:start position:0% +point uh you expect that something will + + + align:start position:0% +point uh you expect that something will +happen now this wave packet is not + + align:start position:0% +happen now this wave packet is not + + + align:start position:0% +happen now this wave packet is not +moving at zero momentum it has momentum + + align:start position:0% +moving at zero momentum it has momentum + + + align:start position:0% +moving at zero momentum it has momentum +and so stationary phase is a little bit + + align:start position:0% +and so stationary phase is a little bit + + + align:start position:0% +and so stationary phase is a little bit +more complicated but what you end up + + align:start position:0% +more complicated but what you end up + + + align:start position:0% +more complicated but what you end up +seeing is that there at various times + + align:start position:0% +seeing is that there at various times + + + align:start position:0% +seeing is that there at various times +there will be different frequency + + align:start position:0% + + + + align:start position:0% + +emission and but if you don't resolve + + align:start position:0% +emission and but if you don't resolve + + + align:start position:0% +emission and but if you don't resolve +time you get a spectrum which contains + + align:start position:0% +time you get a spectrum which contains + + + align:start position:0% +time you get a spectrum which contains +the emission to the various vibrational + + align:start position:0% +the emission to the various vibrational + + + align:start position:0% +the emission to the various vibrational +levels now you say well this is + + align:start position:0% +levels now you say well this is + + + align:start position:0% +levels now you say well this is +ridiculous up this thing is is not + + align:start position:0% +ridiculous up this thing is is not + + + align:start position:0% +ridiculous up this thing is is not +bound so how am I going to get + + align:start position:0% +bound so how am I going to get + + + align:start position:0% +bound so how am I going to get +fluoresence that looks bound how am I + + align:start position:0% +fluoresence that looks bound how am I + + + align:start position:0% +fluoresence that looks bound how am I +going to get fluoresence at all well uh + + align:start position:0% +going to get fluoresence at all well uh + + + align:start position:0% +going to get fluoresence at all well uh +it's + + align:start position:0% +it's + + + align:start position:0% +it's +weak but you have energy conservation it + + align:start position:0% +weak but you have energy conservation it + + + align:start position:0% +weak but you have energy conservation it +doesn't matter that this isn't bound + + align:start position:0% +doesn't matter that this isn't bound + + + align:start position:0% +doesn't matter that this isn't bound +it's excited at a definite energy and + + align:start position:0% +it's excited at a definite energy and + + + align:start position:0% +it's excited at a definite energy and +it's sampling the level structure here + + align:start position:0% +it's sampling the level structure here + + + align:start position:0% +it's sampling the level structure here +and so you do get uh a spectrum with + + align:start position:0% +and so you do get uh a spectrum with + + + align:start position:0% +and so you do get uh a spectrum with +frequencies and + + align:start position:0% +frequencies and + + + align:start position:0% +frequencies and +intensities + + align:start position:0% + + + + align:start position:0% + +um this is a picture of the absorption + + align:start position:0% +um this is a picture of the absorption + + + align:start position:0% +um this is a picture of the absorption +Spectrum the absorption Spectrum from + + align:start position:0% +Spectrum the absorption Spectrum from + + + align:start position:0% +Spectrum the absorption Spectrum from +here is just a lump but that lump is + + align:start position:0% +here is just a lump but that lump is + + + align:start position:0% +here is just a lump but that lump is +basically telling you about the slope of + + align:start position:0% +basically telling you about the slope of + + + align:start position:0% +basically telling you about the slope of +the potential at the uh uh vertically + + align:start position:0% +the potential at the uh uh vertically + + + align:start position:0% +the potential at the uh uh vertically +above of uh the initial State that's + + align:start position:0% +above of uh the initial State that's + + + align:start position:0% +above of uh the initial State that's +basically the reflection principle and + + align:start position:0% +basically the reflection principle and + + + align:start position:0% +basically the reflection principle and +if you were to excite from here you + + align:start position:0% +if you were to excite from here you + + + align:start position:0% +if you were to excite from here you +would see a different shape of the + + align:start position:0% +would see a different shape of the + + + align:start position:0% +would see a different shape of the +absorption Spectrum with with two lumps + + align:start position:0% +absorption Spectrum with with two lumps + + + align:start position:0% +absorption Spectrum with with two lumps +associated with the inner and the outer + + align:start position:0% +associated with the inner and the outer + + + align:start position:0% +associated with the inner and the outer +turning point so there are all sorts of + + align:start position:0% +turning point so there are all sorts of + + + align:start position:0% +turning point so there are all sorts of +ways of looking at this and there's also + + align:start position:0% +ways of looking at this and there's also + + + align:start position:0% +ways of looking at this and there's also +ways of saying okay suppose I launch a + + align:start position:0% +ways of saying okay suppose I launch a + + + align:start position:0% +ways of saying okay suppose I launch a +wave packet and it's doing something + + align:start position:0% +wave packet and it's doing something + + + align:start position:0% +wave packet and it's doing something +it's broad it's moving and Broad and and + + align:start position:0% +it's broad it's moving and Broad and and + + + align:start position:0% +it's broad it's moving and Broad and and +and getting + + align:start position:0% +and getting + + + align:start position:0% +and getting +broader can I + + align:start position:0% +broader can I + + + align:start position:0% +broader can I +sample what's going on suppose I + + align:start position:0% +sample what's going on suppose I + + + align:start position:0% +sample what's going on suppose I +have a bound State a repulsive State and + + align:start position:0% +have a bound State a repulsive State and + + + align:start position:0% +have a bound State a repulsive State and +another bound State and suppose I do + + align:start position:0% +another bound State and suppose I do + + + align:start position:0% +another bound State and suppose I do +some kind of a wave packet experiment uh + + align:start position:0% +some kind of a wave packet experiment uh + + + align:start position:0% +some kind of a wave packet experiment uh +I short pulse create a wave packet it's + + align:start position:0% +I short pulse create a wave packet it's + + + align:start position:0% +I short pulse create a wave packet it's +going away another pulse coming in at + + align:start position:0% +going away another pulse coming in at + + + align:start position:0% +going away another pulse coming in at +some time and so depending on the the + + align:start position:0% +some time and so depending on the the + + + align:start position:0% +some time and so depending on the the +delay you can you're going to see + + align:start position:0% +delay you can you're going to see + + + align:start position:0% +delay you can you're going to see +different frequencies in the uh suppose + + align:start position:0% +different frequencies in the uh suppose + + + align:start position:0% +different frequencies in the uh suppose +this fluoresence so you could look at + + align:start position:0% +this fluoresence so you could look at + + + align:start position:0% +this fluoresence so you could look at +pump prob two short pulses delayed uh + + align:start position:0% +pump prob two short pulses delayed uh + + + align:start position:0% +pump prob two short pulses delayed uh +and the fluorescent spectrum that you + + align:start position:0% +and the fluorescent spectrum that you + + + align:start position:0% +and the fluorescent spectrum that you +would see as the delay is increased will + + align:start position:0% +would see as the delay is increased will + + + align:start position:0% +would see as the delay is increased will +change because you're primarily exciting + + align:start position:0% +change because you're primarily exciting + + + align:start position:0% +change because you're primarily exciting +different vibrational levels and this is + + align:start position:0% +different vibrational levels and this is + + + align:start position:0% +different vibrational levels and this is +pretty much what uh uh Zoel got the + + align:start position:0% +pretty much what uh uh Zoel got the + + + align:start position:0% +pretty much what uh uh Zoel got the +Nobel Prize + + align:start position:0% + + + + align:start position:0% + +for so there's all sorts of wonderful + + align:start position:0% +for so there's all sorts of wonderful + + + align:start position:0% +for so there's all sorts of wonderful +stuff that you can you can understand by + + align:start position:0% +stuff that you can you can understand by + + + align:start position:0% +stuff that you can you can understand by +think thinking about + + align:start position:0% +think thinking about + + + align:start position:0% +think thinking about +localized things moving according to the + + align:start position:0% +localized things moving according to the + + + align:start position:0% +localized things moving according to the +laws that we've known ever since we've + + align:start position:0% +laws that we've known ever since we've + + + align:start position:0% +laws that we've known ever since we've +observed uh a + + align:start position:0% +observed uh a + + + align:start position:0% +observed uh a +baseball and uh I think this is + + align:start position:0% +baseball and uh I think this is + + + align:start position:0% +baseball and uh I think this is +wonderful so + + align:start position:0% +wonderful so + + + align:start position:0% +wonderful so +um next uh time I'll talk about + + align:start position:0% +um next uh time I'll talk about + + + align:start position:0% +um next uh time I'll talk about +different dynamical quantities but I I + + align:start position:0% +different dynamical quantities but I I + + + align:start position:0% +different dynamical quantities but I I +think that you know this the wave + + align:start position:0% +think that you know this the wave + + + align:start position:0% +think that you know this the wave +function the the spectrum is the + + align:start position:0% +function the the spectrum is the + + + align:start position:0% +function the the spectrum is the +autocorrelation of an is the for8 + + align:start position:0% +autocorrelation of an is the for8 + + + align:start position:0% +autocorrelation of an is the for8 +transform of an autocorrelation function + + align:start position:0% +transform of an autocorrelation function + + + align:start position:0% +transform of an autocorrelation function +this was an idea that Rick + + align:start position:0% +this was an idea that Rick + + + align:start position:0% +this was an idea that Rick +heler uh popularized in the early 80s + + align:start position:0% +heler uh popularized in the early 80s + + + align:start position:0% +heler uh popularized in the early 80s +and it completely changed the way we + + align:start position:0% +and it completely changed the way we + + + align:start position:0% +and it completely changed the way we +think about + + align:start position:0% + + + + align:start position:0% + +spectroscopy and uh uh he probably + + align:start position:0% +spectroscopy and uh uh he probably + + + align:start position:0% +spectroscopy and uh uh he probably +should have gotten a Nobel Prize for + + align:start position:0% +should have gotten a Nobel Prize for + + + align:start position:0% +should have gotten a Nobel Prize for +that anyway so that's all I have to say \ No newline at end of file diff --git a/e9oP4O0P2R8.txt b/e9oP4O0P2R8.txt new file mode 100644 index 0000000000000000000000000000000000000000..d4976a9eca1c86f880130231deafbb231c5bf0fa --- /dev/null +++ b/e9oP4O0P2R8.txt @@ -0,0 +1,10080 @@ +align:start position:0% + +certainly ties to lecture + + align:start position:0% +certainly ties to lecture + + + align:start position:0% +certainly ties to lecture +five okay so I'm using the Matrix I'm + + align:start position:0% +five okay so I'm using the Matrix I'm + + + align:start position:0% +five okay so I'm using the Matrix I'm +calling K because I have in mind one of + + align:start position:0% +calling K because I have in mind one of + + + align:start position:0% +calling K because I have in mind one of +our stiffness matrices one of our a + + align:start position:0% +our stiffness matrices one of our a + + + align:start position:0% +our stiffness matrices one of our a +transpose a or a transpose CA symmetric + + align:start position:0% +transpose a or a transpose CA symmetric + + + align:start position:0% +transpose a or a transpose CA symmetric +positive definite so so this this uh + + align:start position:0% +positive definite so so this this uh + + + align:start position:0% +positive definite so so this this uh +this is a nice + + align:start position:0% +this is a nice + + + align:start position:0% +this is a nice +Matrix and we know from lecture five + + align:start position:0% +Matrix and we know from lecture five + + + align:start position:0% +Matrix and we know from lecture five +it's I values are + + align:start position:0% +it's I values are + + + align:start position:0% +it's I values are +real and its igen vectors are or can be + + align:start position:0% +real and its igen vectors are or can be + + + align:start position:0% +real and its igen vectors are or can be +chosen orthonormal and and more than + + align:start position:0% +chosen orthonormal and and more than + + + align:start position:0% +chosen orthonormal and and more than +that we know more about a transpose a + + align:start position:0% +that we know more about a transpose a + + + align:start position:0% +that we know more about a transpose a +and a transpose CA don't + + align:start position:0% +and a transpose CA don't + + + align:start position:0% +and a transpose CA don't +we uh those are symmetric and positive + + align:start position:0% +we uh those are symmetric and positive + + + align:start position:0% +we uh those are symmetric and positive +definite or or at least positive + + align:start position:0% +definite or or at least positive + + + align:start position:0% +definite or or at least positive +semi-definite so so I'm thinking of uh + + align:start position:0% +semi-definite so so I'm thinking of uh + + + align:start position:0% +semi-definite so so I'm thinking of uh +here as K as being symmetric let's say + + align:start position:0% +here as K as being symmetric let's say + + + align:start position:0% +here as K as being symmetric let's say +positive + + align:start position:0% +positive + + + align:start position:0% +positive +definite and and that tells me that the + + align:start position:0% +definite and and that tells me that the + + + align:start position:0% +definite and and that tells me that the +the the Symmetry tells me tells me that + + align:start position:0% +the the Symmetry tells me tells me that + + + align:start position:0% +the the Symmetry tells me tells me that +the X's are orthonormal as + + align:start position:0% +the X's are orthonormal as + + + align:start position:0% +the X's are orthonormal as +always and the igen values are real as + + align:start position:0% +always and the igen values are real as + + + align:start position:0% +always and the igen values are real as +always but now the positive definite + + align:start position:0% +always but now the positive definite + + + align:start position:0% +always but now the positive definite +part tells me the lambdas are all + + align:start position:0% +part tells me the lambdas are all + + + align:start position:0% +part tells me the lambdas are all +positive okay so uh that's that's a a + + align:start position:0% +positive okay so uh that's that's a a + + + align:start position:0% +positive okay so uh that's that's a a +nice situation to be starting in no no + + align:start position:0% +nice situation to be starting in no no + + + align:start position:0% +nice situation to be starting in no no +problems so how do we use them suppose + + align:start position:0% +problems so how do we use them suppose + + + align:start position:0% +problems so how do we use them suppose +we found them + + align:start position:0% +we found them + + + align:start position:0% +we found them +suppose we've we've got these + + align:start position:0% +suppose we've we've got these + + + align:start position:0% +suppose we've we've got these +guys x's and + + align:start position:0% +guys x's and + + + align:start position:0% +guys x's and +lambdas and just a + + align:start position:0% +lambdas and just a + + + align:start position:0% +lambdas and just a +complete uh thought that came up in + + align:start position:0% +complete uh thought that came up in + + + align:start position:0% +complete uh thought that came up in +discussion uh those were very special + + align:start position:0% +discussion uh those were very special + + + align:start position:0% +discussion uh those were very special +matrices in the last lecture normally I + + align:start position:0% +matrices in the last lecture normally I + + + align:start position:0% +matrices in the last lecture normally I +couldn't write down a matrix and write + + align:start position:0% +couldn't write down a matrix and write + + + align:start position:0% +couldn't write down a matrix and write +down start say what are its igen values + + align:start position:0% +down start say what are its igen values + + + align:start position:0% +down start say what are its igen values +what are its igen vectors but for those + + align:start position:0% +what are its igen vectors but for those + + + align:start position:0% +what are its igen vectors but for those +particular matrices we could do it and I + + align:start position:0% +particular matrices we could do it and I + + + align:start position:0% +particular matrices we could do it and I +felt it was was worth doing + + align:start position:0% +felt it was was worth doing + + + align:start position:0% +felt it was was worth doing +because special matrices are what come + + align:start position:0% +because special matrices are what come + + + align:start position:0% +because special matrices are what come +up in reality uh even if it's not the + + align:start position:0% +up in reality uh even if it's not the + + + align:start position:0% +up in reality uh even if it's not the +most General mathematical case it's what + + align:start position:0% +most General mathematical case it's what + + + align:start position:0% +most General mathematical case it's what +you see in in practice okay so uh you + + align:start position:0% +you see in in practice okay so uh you + + + align:start position:0% +you see in in practice okay so uh you +could keep those matrices in mind but + + align:start position:0% +could keep those matrices in mind but + + + align:start position:0% +could keep those matrices in mind but +how do we + + align:start position:0% +how do we + + + align:start position:0% +how do we +solve uh so what I'm going to to to to + + align:start position:0% +solve uh so what I'm going to to to to + + + align:start position:0% +solve uh so what I'm going to to to to +give you an advanced shot at the lecture + + align:start position:0% +give you an advanced shot at the lecture + + + align:start position:0% +give you an advanced shot at the lecture +this the igen values and igen vectors + + align:start position:0% +this the igen values and igen vectors + + + align:start position:0% +this the igen values and igen vectors +are going to + + align:start position:0% +are going to + + + align:start position:0% +are going to +solve this ordinary first derivative + + align:start position:0% +solve this ordinary first derivative + + + align:start position:0% +solve this ordinary first derivative +that's dudt this means dudt U dot I + + align:start position:0% +that's dudt this means dudt U dot I + + + align:start position:0% +that's dudt this means dudt U dot I +could also put U sub subscript + + align:start position:0% +could also put U sub subscript + + + align:start position:0% +could also put U sub subscript +t uh derivative of U equal + + align:start position:0% +t uh derivative of U equal + + + align:start position:0% +t uh derivative of U equal +KU and they will also solve second + + align:start position:0% +KU and they will also solve second + + + align:start position:0% +KU and they will also solve second +derivative of U and then it's more + + align:start position:0% +derivative of U and then it's more + + + align:start position:0% +derivative of U and then it's more +natural to have the KU on this + + align:start position:0% +natural to have the KU on this + + + align:start position:0% +natural to have the KU on this +side now if the real the most + + align:start position:0% +side now if the real the most + + + align:start position:0% +side now if the real the most +fundamental equation in dynamic dyamics + + align:start position:0% +fundamental equation in dynamic dyamics + + + align:start position:0% +fundamental equation in dynamic dyamics +is Newton's law Newton's law WIS of + + align:start position:0% +is Newton's law Newton's law WIS of + + + align:start position:0% +is Newton's law Newton's law WIS of +course okay so what's Newton's law well + + align:start position:0% +course okay so what's Newton's law well + + + align:start position:0% +course okay so what's Newton's law well +Newton's law includes mass times + + align:start position:0% +Newton's law includes mass times + + + align:start position:0% +Newton's law includes mass times +acceleration so there is a mass here if + + align:start position:0% +acceleration so there is a mass here if + + + align:start position:0% +acceleration so there is a mass here if +all the masses in our spring system were + + align:start position:0% +all the masses in our spring system were + + + align:start position:0% +all the masses in our spring system were +equal then of course that would be just + + align:start position:0% +equal then of course that would be just + + + align:start position:0% +equal then of course that would be just +a multiple of the identity and we could + + align:start position:0% +a multiple of the identity and we could + + + align:start position:0% +a multiple of the identity and we could +get back to this one but the physical + + align:start position:0% +get back to this one but the physical + + + align:start position:0% +get back to this one but the physical +problem has got a mass Matrix as well as + + align:start position:0% +problem has got a mass Matrix as well as + + + align:start position:0% +problem has got a mass Matrix as well as +a stiffness Matrix and of course it + + align:start position:0% +a stiffness Matrix and of course it + + + align:start position:0% +a stiffness Matrix and of course it +might have a right hand side there might + + align:start position:0% +might have a right hand side there might + + + align:start position:0% +might have a right hand side there might +be an external driving force as well as + + align:start position:0% +be an external driving force as well as + + + align:start position:0% +be an external driving force as well as +uh the free oscillations that would come + + align:start position:0% +uh the free oscillations that would come + + + align:start position:0% +uh the free oscillations that would come +from uh with no Force okay so we're + + align:start position:0% +from uh with no Force okay so we're + + + align:start position:0% +from uh with no Force okay so we're +talking here about + + align:start position:0% +talking here about + + + align:start position:0% +talking here about +oscillations + + align:start position:0% +oscillations + + + align:start position:0% +oscillations +oscillations and hear about more of a + + align:start position:0% +oscillations and hear about more of a + + + align:start position:0% +oscillations and hear about more of a +diffusion type equation so this is more + + align:start position:0% +diffusion type equation so this is more + + + align:start position:0% +diffusion type equation so this is more +like a heat equation these are like just + + align:start position:0% +like a heat equation these are like just + + + align:start position:0% +like a heat equation these are like just +just finite dimensional wave equation + + align:start position:0% +just finite dimensional wave equation + + + align:start position:0% +just finite dimensional wave equation +equ and then the other point to see in + + align:start position:0% +equ and then the other point to see in + + + align:start position:0% +equ and then the other point to see in +to mention in advance is when we have + + align:start position:0% +to mention in advance is when we have + + + align:start position:0% +to mention in advance is when we have +two matrixes in the differential + + align:start position:0% +two matrixes in the differential + + + align:start position:0% +two matrixes in the differential +equation then we're going to have two + + align:start position:0% +equation then we're going to have two + + + align:start position:0% +equation then we're going to have two +matrices in the igen value problem and + + align:start position:0% +matrices in the igen value problem and + + + align:start position:0% +matrices in the igen value problem and +it often gets called the generalized ion + + align:start position:0% +it often gets called the generalized ion + + + align:start position:0% +it often gets called the generalized ion +value problem we hope that this Matrix m + + align:start position:0% +value problem we hope that this Matrix m + + + align:start position:0% +value problem we hope that this Matrix m +is extremely nice possibly even diagonal + + align:start position:0% +is extremely nice possibly even diagonal + + + align:start position:0% +is extremely nice possibly even diagonal +positive diagonal um masses there and uh + + align:start position:0% +positive diagonal um masses there and uh + + + align:start position:0% +positive diagonal um masses there and uh +gives us not much trouble but uh really + + align:start position:0% +gives us not much trouble but uh really + + + align:start position:0% +gives us not much trouble but uh really +it's that problem + + align:start position:0% +it's that problem + + + align:start position:0% +it's that problem +okay so now you see what's coming now + + align:start position:0% +okay so now you see what's coming now + + + align:start position:0% +okay so now you see what's coming now +let's see it come uh how how do you + + align:start position:0% +let's see it come uh how how do you + + + align:start position:0% +let's see it come uh how how do you +solve get let's find some solutions + + align:start position:0% +solve get let's find some solutions + + + align:start position:0% +solve get let's find some solutions +special solutions to that differential + + align:start position:0% +special solutions to that differential + + + align:start position:0% +special solutions to that differential +equation so so so + + align:start position:0% +equation so so so + + + align:start position:0% +equation so so so +Solutions + + align:start position:0% +Solutions + + + align:start position:0% +Solutions +Solutions what's one + + align:start position:0% +Solutions what's one + + + align:start position:0% +Solutions what's one +solution one solution is to follow + + align:start position:0% +solution one solution is to follow + + + align:start position:0% +solution one solution is to follow +follow is to stay with one of the igen + + align:start position:0% +follow is to stay with one of the igen + + + align:start position:0% +follow is to stay with one of the igen +vectors of course we've got n igen + + align:start position:0% +vectors of course we've got n igen + + + align:start position:0% +vectors of course we've got n igen +Vector so I really should put subscripts + + align:start position:0% +Vector so I really should put subscripts + + + align:start position:0% +Vector so I really should put subscripts +as as we saw in the last lecture there's + + align:start position:0% +as as we saw in the last lecture there's + + + align:start position:0% +as as we saw in the last lecture there's +n of these I vectors and I values and so + + align:start position:0% +n of these I vectors and I values and so + + + align:start position:0% +n of these I vectors and I values and so +this I goes from one to n and similarly + + align:start position:0% +this I goes from one to n and similarly + + + align:start position:0% +this I goes from one to n and similarly +there kxi will be Lambda i + + align:start position:0% +there kxi will be Lambda i + + + align:start position:0% +there kxi will be Lambda i +mxi n of them okay so focus on one of + + align:start position:0% +mxi n of them okay so focus on one of + + + align:start position:0% +mxi n of them okay so focus on one of +them say the first one + + align:start position:0% +them say the first one + + + align:start position:0% +them say the first one +X1 okay that's a vector + + align:start position:0% +X1 okay that's a vector + + + align:start position:0% +X1 okay that's a vector +fixed now how can we use that to solve + + align:start position:0% +fixed now how can we use that to solve + + + align:start position:0% +fixed now how can we use that to solve +this differential equation so I'm + + align:start position:0% +this differential equation so I'm + + + align:start position:0% +this differential equation so I'm +looking for some solutions U of + + align:start position:0% +looking for some solutions U of + + + align:start position:0% +looking for some solutions U of +T that Vector times e times a the whole + + align:start position:0% +T that Vector times e times a the whole + + + align:start position:0% +T that Vector times e times a the whole +point of course about pinning down an IG + + align:start position:0% +point of course about pinning down an IG + + + align:start position:0% +point of course about pinning down an IG +Vector is + + align:start position:0% +Vector is + + + align:start position:0% +Vector is +that for that special Vector our Matrix + + align:start position:0% +that for that special Vector our Matrix + + + align:start position:0% +that for that special Vector our Matrix +is just actually like a number so we + + align:start position:0% +is just actually like a number so we + + + align:start position:0% +is just actually like a number so we +could pretend we were solving this + + align:start position:0% +could pretend we were solving this + + + align:start position:0% +could pretend we were solving this +equation with a number on the right side + + align:start position:0% +equation with a number on the right side + + + align:start position:0% +equation with a number on the right side +like + + align:start position:0% +like + + + align:start position:0% +like +Lambda so what would be the what would + + align:start position:0% +Lambda so what would be the what would + + + align:start position:0% +Lambda so what would be the what would +be the solution to our differential + + align:start position:0% +be the solution to our differential + + + align:start position:0% +be the solution to our differential +equation the derivative equals Lambda + + align:start position:0% +equation the derivative equals Lambda + + + align:start position:0% +equation the derivative equals Lambda +time the + + align:start position:0% +time the + + + align:start position:0% +time the +function so that's the most basic first + + align:start position:0% +function so that's the most basic first + + + align:start position:0% +function so that's the most basic first +order differential equation derivative + + align:start position:0% +order differential equation derivative + + + align:start position:0% +order differential equation derivative +equals Lambda time function it's + + align:start position:0% +equals Lambda time function it's + + + align:start position:0% +equals Lambda time function it's +exponential that's where e you know the + + align:start position:0% +exponential that's where e you know the + + + align:start position:0% +exponential that's where e you know the +most important function of calculus + + align:start position:0% +most important function of calculus + + + align:start position:0% +most important function of calculus +comes from the fact that the Der is the + + align:start position:0% +comes from the fact that the Der is the + + + align:start position:0% +comes from the fact that the Der is the +function or a multiple of the function + + align:start position:0% +function or a multiple of the function + + + align:start position:0% +function or a multiple of the function +we just need e to the Lambda 1 T because + + align:start position:0% +we just need e to the Lambda 1 T because + + + align:start position:0% +we just need e to the Lambda 1 T because +of course it's the Lambda one that goes + + align:start position:0% +of course it's the Lambda one that goes + + + align:start position:0% +of course it's the Lambda one that goes +with the + + align:start position:0% +with the + + + align:start position:0% +with the +X1 that solves as one solu it's if we + + align:start position:0% +X1 that solves as one solu it's if we + + + align:start position:0% +X1 that solves as one solu it's if we +substitute it for + + align:start position:0% +substitute it for + + + align:start position:0% +substitute it for +U or any multiple of it so I could + + align:start position:0% +U or any multiple of it so I could + + + align:start position:0% +U or any multiple of it so I could +multiply it by any number C1 right + + align:start position:0% +multiply it by any number C1 right + + + align:start position:0% +multiply it by any number C1 right +because this equation homogeneous If I + + align:start position:0% +because this equation homogeneous If I + + + align:start position:0% +because this equation homogeneous If I +multiply both sides by C1 I'm still fine + + align:start position:0% +multiply both sides by C1 I'm still fine + + + align:start position:0% +multiply both sides by C1 I'm still fine +so there is a special you could say + + align:start position:0% +so there is a special you could say + + + align:start position:0% +so there is a special you could say +special pure exponential solution we + + align:start position:0% +special pure exponential solution we + + + align:start position:0% +special pure exponential solution we +ought to we ought to be able to plug it + + align:start position:0% +ought to we ought to be able to plug it + + + align:start position:0% +ought to we ought to be able to plug it +into that equation and see that it + + align:start position:0% +into that equation and see that it + + + align:start position:0% +into that equation and see that it +works can we plug that into plug that + + align:start position:0% +works can we plug that into plug that + + + align:start position:0% +works can we plug that into plug that +into this equation just to see that it + + align:start position:0% +into this equation just to see that it + + + align:start position:0% +into this equation just to see that it +works what's the left hand + + align:start position:0% +works what's the left hand + + + align:start position:0% +works what's the left hand +side if I take the time derivative of + + align:start position:0% +side if I take the time derivative of + + + align:start position:0% +side if I take the time derivative of +this thing what do I get Lambda 1 times + + align:start position:0% +this thing what do I get Lambda 1 times + + + align:start position:0% +this thing what do I get Lambda 1 times +what I've got right the time to + + align:start position:0% +what I've got right the time to + + + align:start position:0% +what I've got right the time to +derivative will bring down to Lambda + + align:start position:0% +derivative will bring down to Lambda + + + align:start position:0% +derivative will bring down to Lambda + + align:start position:0% + + + align:start position:0% +U I'll write U for the whole deal for + + align:start position:0% +U I'll write U for the whole deal for + + + align:start position:0% +U I'll write U for the whole deal for +the moment and now on the right hand + + align:start position:0% +the moment and now on the right hand + + + align:start position:0% +the moment and now on the right hand +side what happens if I multiply by + + align:start position:0% +side what happens if I multiply by + + + align:start position:0% +side what happens if I multiply by +k k times this what's K * + + align:start position:0% + + + + align:start position:0% + +that so I'm multiply a matrix this is a + + align:start position:0% +that so I'm multiply a matrix this is a + + + align:start position:0% +that so I'm multiply a matrix this is a +vector of course everything's a vector + + align:start position:0% +vector of course everything's a vector + + + align:start position:0% +vector of course everything's a vector +here U is a vector X is a vector well + + align:start position:0% +here U is a vector X is a vector well + + + align:start position:0% +here U is a vector X is a vector well +not everything those are scalers that U + + align:start position:0% +not everything those are scalers that U + + + align:start position:0% +not everything those are scalers that U +is a vector X is a vector now what + + align:start position:0% +is a vector X is a vector now what + + + align:start position:0% +is a vector X is a vector now what +happens if I multiply this by K what + + align:start position:0% +happens if I multiply this by K what + + + align:start position:0% +happens if I multiply this by K what +happens well these are numbers they just + + align:start position:0% +happens well these are numbers they just + + + align:start position:0% +happens well these are numbers they just +Factor write out and I have kx1 which + + align:start position:0% +Factor write out and I have kx1 which + + + align:start position:0% +Factor write out and I have kx1 which +is Lambda 1 X1 right so when I multiply + + align:start position:0% +is Lambda 1 X1 right so when I multiply + + + align:start position:0% +is Lambda 1 X1 right so when I multiply +by + + align:start position:0% +by + + + align:start position:0% +by +K all this is not Chang only thing comes + + align:start position:0% +K all this is not Chang only thing comes + + + align:start position:0% +K all this is not Chang only thing comes +out is a Lambda one comes out it it + + align:start position:0% +out is a Lambda one comes out it it + + + align:start position:0% +out is a Lambda one comes out it it +works it works if I take the time + + align:start position:0% +works it works if I take the time + + + align:start position:0% +works it works if I take the time +derivative a Lambda 1 comes out if I + + align:start position:0% +derivative a Lambda 1 comes out if I + + + align:start position:0% +derivative a Lambda 1 comes out if I +multiply by K A Lambda 1 comes out so it + + align:start position:0% +multiply by K A Lambda 1 comes out so it + + + align:start position:0% +multiply by K A Lambda 1 comes out so it +solves the equation okay tell me a + + align:start position:0% +solves the equation okay tell me a + + + align:start position:0% +solves the equation okay tell me a +second solution to the differential + + align:start position:0% +second solution to the differential + + + align:start position:0% +second solution to the differential +equation well the same thing with + + align:start position:0% +equation well the same thing with + + + align:start position:0% +equation well the same thing with +two and the same thing with three so the + + align:start position:0% +two and the same thing with three so the + + + align:start position:0% +two and the same thing with three so the +solution could be a combination of these + + align:start position:0% +solution could be a combination of these + + + align:start position:0% +solution could be a combination of these +guys all the way up to any multiple of e + + align:start position:0% +guys all the way up to any multiple of e + + + align:start position:0% +guys all the way up to any multiple of e +to the Lambda n t times the it Vector X + + align:start position:0% +to the Lambda n t times the it Vector X + + + align:start position:0% +to the Lambda n t times the it Vector X +so again these are vectors U is a vector + + align:start position:0% +so again these are vectors U is a vector + + + align:start position:0% +so again these are vectors U is a vector +X1 is a vector xn is a + + align:start position:0% +X1 is a vector xn is a + + + align:start position:0% +X1 is a vector xn is a +vector and that's the general solution + + align:start position:0% +vector and that's the general solution + + + align:start position:0% +vector and that's the general solution +it's got n constants to play + + align:start position:0% + + + + align:start position:0% + +with it's like it's the null space of U + + align:start position:0% +with it's like it's the null space of U + + + align:start position:0% +with it's like it's the null space of U +Prime minus KU it's the if I put U Prime + + align:start position:0% +Prime minus KU it's the if I put U Prime + + + align:start position:0% +Prime minus KU it's the if I put U Prime +minus KU on one side I found all + + align:start position:0% +minus KU on one side I found all + + + align:start position:0% +minus KU on one side I found all +everything in the null space all the + + align:start position:0% +everything in the null space all the + + + align:start position:0% +everything in the null space all the +solutions and what would I use them for + + align:start position:0% +solutions and what would I use them for + + + align:start position:0% +solutions and what would I use them for +well what how would I use these C1 C2 up + + align:start position:0% +well what how would I use these C1 C2 up + + + align:start position:0% +well what how would I use these C1 C2 up +to CN there I've got n numbers still to + + align:start position:0% +to CN there I've got n numbers still to + + + align:start position:0% +to CN there I've got n numbers still to +play + + align:start position:0% +play + + + align:start position:0% +play +with well they would they would I would + + align:start position:0% +with well they would they would I would + + + align:start position:0% +with well they would they would I would +use those to match initial conditions so + + align:start position:0% +use those to match initial conditions so + + + align:start position:0% +use those to match initial conditions so +I would these equations come with U at + + align:start position:0% +I would these equations come with U at + + + align:start position:0% +I would these equations come with U at +zero is + + align:start position:0% + + + + align:start position:0% + +given so at T equals z all all these e + + align:start position:0% +given so at T equals z all all these e + + + align:start position:0% +given so at T equals z all all these e +of the t's are all ones so I just have + + align:start position:0% +of the t's are all ones so I just have + + + align:start position:0% +of the t's are all ones so I just have +C1 X1 and C2 X2 and + + align:start position:0% +C1 X1 and C2 X2 and + + + align:start position:0% +C1 X1 and C2 X2 and +cnxn have to agree with u u of zero + + align:start position:0% +cnxn have to agree with u u of zero + + + align:start position:0% +cnxn have to agree with u u of zero +right so that would so then the so that + + align:start position:0% +right so that would so then the so that + + + align:start position:0% +right so that would so then the so that +equation + + align:start position:0% +equation + + + align:start position:0% +equation +satisfied and then use the C1 up to CN + + align:start position:0% +satisfied and then use the C1 up to CN + + + align:start position:0% +satisfied and then use the C1 up to CN +to + + align:start position:0% +to + + + align:start position:0% +to +match the + + align:start position:0% +match the + + + align:start position:0% +match the +given initial condition U of zero good I + + align:start position:0% +given initial condition U of zero good I + + + align:start position:0% +given initial condition U of zero good I +I don't think I want to I mean I haven't + + align:start position:0% +I don't think I want to I mean I haven't + + + align:start position:0% +I don't think I want to I mean I haven't +done + + align:start position:0% +done + + + align:start position:0% +done +examples this whole top this whole + + align:start position:0% +examples this whole top this whole + + + align:start position:0% +examples this whole top this whole +lecture that is lecture five and this + + align:start position:0% +lecture that is lecture five and this + + + align:start position:0% +lecture that is lecture five and this +part is in section + + align:start position:0% +part is in section + + + align:start position:0% +part is in section +1.5 well maybe that's not there but this + + align:start position:0% +1.5 well maybe that's not there but this + + + align:start position:0% +1.5 well maybe that's not there but this +is so can I put maybe at the top here + + align:start position:0% +is so can I put maybe at the top here + + + align:start position:0% +is so can I put maybe at the top here +section 1.5 of the applied math + + align:start position:0% +section 1.5 of the applied math + + + align:start position:0% +section 1.5 of the applied math +book and I'll suggest some + + align:start position:0% +book and I'll suggest some + + + align:start position:0% +book and I'll suggest some +uh particular exercises out of that + + align:start position:0% +uh particular exercises out of that + + + align:start position:0% +uh particular exercises out of that +section uh which would allow you to + + align:start position:0% +section uh which would allow you to + + + align:start position:0% +section uh which would allow you to +execute these steps all I'm doing here + + align:start position:0% +execute these steps all I'm doing here + + + align:start position:0% +execute these steps all I'm doing here +is + + align:start position:0% +is + + + align:start position:0% +is +saying igen values and igen vectors give + + align:start position:0% +saying igen values and igen vectors give + + + align:start position:0% +saying igen values and igen vectors give +us a great bunch of special Solutions + + align:start position:0% +us a great bunch of special Solutions + + + align:start position:0% +us a great bunch of special Solutions +some very convenient ones normal modes + + align:start position:0% +some very convenient ones normal modes + + + align:start position:0% +some very convenient ones normal modes +these are called yeah what oh let's tie + + align:start position:0% +these are called yeah what oh let's tie + + + align:start position:0% +these are called yeah what oh let's tie +them to to let's connect this oh haven't + + align:start position:0% +them to to let's connect this oh haven't + + + align:start position:0% +them to to let's connect this oh haven't +got anything oscillating yet until I get + + align:start position:0% +got anything oscillating yet until I get + + + align:start position:0% +got anything oscillating yet until I get +to second derivative so let me let me + + align:start position:0% +to second derivative so let me let me + + + align:start position:0% +to second derivative so let me let me +move on to Second derivatives so now I'm + + align:start position:0% +move on to Second derivatives so now I'm + + + align:start position:0% +move on to Second derivatives so now I'm +ready for this + + align:start position:0% +ready for this + + + align:start position:0% +ready for this +guy okay so this was number one you + + align:start position:0% +guy okay so this was number one you + + + align:start position:0% +guy okay so this was number one you +here okay that that led to here okay now + + align:start position:0% +here okay that that led to here okay now + + + align:start position:0% +here okay that that led to here okay now +I'm ready to to tackle the second + + align:start position:0% +I'm ready to to tackle the second + + + align:start position:0% +I'm ready to to tackle the second +equation what are the special solutions + + align:start position:0% +equation what are the special solutions + + + align:start position:0% +equation what are the special solutions +for this now U of T is + + align:start position:0% +for this now U of T is + + + align:start position:0% +for this now U of T is +something and and tell me what + + align:start position:0% +something and and tell me what + + + align:start position:0% +something and and tell me what +special Solutions now I want the second + + align:start position:0% +special Solutions now I want the second + + + align:start position:0% +special Solutions now I want the second +derivative so now I'm going to take + + align:start position:0% +derivative so now I'm going to take + + + align:start position:0% +derivative so now I'm going to take +second derivatives + + align:start position:0% +second derivatives + + + align:start position:0% +second derivatives +well you hope I'm going to it's going to + + align:start position:0% +well you hope I'm going to it's going to + + + align:start position:0% +well you hope I'm going to it's going to +be something times the first IG Vector + + align:start position:0% +be something times the first IG Vector + + + align:start position:0% +be something times the first IG Vector +right that was what made everything + + align:start position:0% +right that was what made everything + + + align:start position:0% +right that was what made everything +great is that we used we followed the + + align:start position:0% +great is that we used we followed the + + + align:start position:0% +great is that we used we followed the +igen vectors we're following these + + align:start position:0% +igen vectors we're following these + + + align:start position:0% +igen vectors we're following these +normal modes of motion so + + align:start position:0% +normal modes of motion so + + + align:start position:0% +normal modes of motion so +X1 but now what can I and of course I + + align:start position:0% +X1 but now what can I and of course I + + + align:start position:0% +X1 but now what can I and of course I +can multiply by a C1 because again + + align:start position:0% +can multiply by a C1 because again + + + align:start position:0% +can multiply by a C1 because again +they're multiplying through by C1 no + + align:start position:0% +they're multiplying through by C1 no + + + align:start position:0% +they're multiplying through by C1 no +problem but but what do I have I don't + + align:start position:0% +problem but but what do I have I don't + + + align:start position:0% +problem but but what do I have I don't +have exponentials + + align:start position:0% +have exponentials + + + align:start position:0% +have exponentials +anymore I've got signs and cosiness SS + + align:start position:0% +anymore I've got signs and cosiness SS + + + align:start position:0% +anymore I've got signs and cosiness SS +and + + align:start position:0% +and + + + align:start position:0% +and +cosiness so why let's put them in and + + align:start position:0% +cosiness so why let's put them in and + + + align:start position:0% +cosiness so why let's put them in and +see why let me just take a sign for + + align:start position:0% +see why let me just take a sign for + + + align:start position:0% +see why let me just take a sign for +example C1 s of something T instead + + align:start position:0% +example C1 s of something T instead + + + align:start position:0% +example C1 s of something T instead +of and we have to think of what's that + + align:start position:0% +of and we have to think of what's that + + + align:start position:0% +of and we have to think of what's that +something times the first ion Vector we + + align:start position:0% +something times the first ion Vector we + + + align:start position:0% +something times the first ion Vector we +want that to + + align:start position:0% +want that to + + + align:start position:0% +want that to +work so let's plug it in and make it go + + align:start position:0% +work so let's plug it in and make it go + + + align:start position:0% +work so let's plug it in and make it go +what will happen + + align:start position:0% +what will happen + + + align:start position:0% +what will happen +here I'm this is a question mark at the + + align:start position:0% +here I'm this is a question mark at the + + + align:start position:0% +here I'm this is a question mark at the +moment okay what what's going to work + + align:start position:0% +moment okay what what's going to work + + + align:start position:0% +moment okay what what's going to work +there well just plug in this form into + + align:start position:0% +there well just plug in this form into + + + align:start position:0% +there well just plug in this form into +the equation and see what we need the + + align:start position:0% +the equation and see what we need the + + + align:start position:0% +the equation and see what we need the +second time derivative will be + + align:start position:0% + + + + align:start position:0% + +what it'll be a minus because there's a + + align:start position:0% +what it'll be a minus because there's a + + + align:start position:0% +what it'll be a minus because there's a +second derivative it'll still be the + + align:start position:0% +second derivative it'll still be the + + + align:start position:0% +second derivative it'll still be the +sign right the time derivative is only + + align:start position:0% +sign right the time derivative is only + + + align:start position:0% +sign right the time derivative is only +this is constant that's constant + + align:start position:0% +this is constant that's constant + + + align:start position:0% +this is constant that's constant +so what do I want + + align:start position:0% +so what do I want + + + align:start position:0% +so what do I want +there do I want a square root of + + align:start position:0% +there do I want a square root of + + + align:start position:0% +there do I want a square root of +Lambda then when I do this + + align:start position:0% +Lambda then when I do this + + + align:start position:0% +Lambda then when I do this +term what will happen when I multiply by + + align:start position:0% +term what will happen when I multiply by + + + align:start position:0% +term what will happen when I multiply by +K that'll bring a Lambda + + align:start position:0% +K that'll bring a Lambda + + + align:start position:0% +K that'll bring a Lambda +right so the way I've got the signs I + + align:start position:0% +right so the way I've got the signs I + + + align:start position:0% +right so the way I've got the signs I +want I want a I think I want a square + + align:start position:0% +want I want a I think I want a square + + + align:start position:0% +want I want a I think I want a square +root of minus Lambda + + align:start position:0% +root of minus Lambda + + + align:start position:0% +root of minus Lambda +wait a + + align:start position:0% +wait a + + + align:start position:0% +wait a +minute have I let's + + align:start position:0% +minute have I let's + + + align:start position:0% +minute have I let's +see uh I the way I've chosen K and let's + + align:start position:0% +see uh I the way I've chosen K and let's + + + align:start position:0% +see uh I the way I've chosen K and let's +settle on that same K yeah should I am I + + align:start position:0% +settle on that same K yeah should I am I + + + align:start position:0% +settle on that same K yeah should I am I +better with + + align:start position:0% +better with + + + align:start position:0% +better with +it with + + align:start position:0% + + + + align:start position:0% + +i h yes right right so what do I want + + align:start position:0% +i h yes right right so what do I want + + + align:start position:0% +i h yes right right so what do I want +here square root of Lambda oh thanks go + + align:start position:0% +here square root of Lambda oh thanks go + + + align:start position:0% +here square root of Lambda oh thanks go +sorry I made that harder than it should + + align:start position:0% +sorry I made that harder than it should + + + align:start position:0% +sorry I made that harder than it should +have been Square Ro of Lambda 1 right + + align:start position:0% +have been Square Ro of Lambda 1 right + + + align:start position:0% +have been Square Ro of Lambda 1 right +now did it + + align:start position:0% +now did it + + + align:start position:0% +now did it +work yes right thanks I'm in your dead + + align:start position:0% +work yes right thanks I'm in your dead + + + align:start position:0% +work yes right thanks I'm in your dead +the second derivative will will produce + + align:start position:0% +the second derivative will will produce + + + align:start position:0% +the second derivative will will produce +a minus sign and then k x will produce + + align:start position:0% +a minus sign and then k x will produce + + + align:start position:0% +a minus sign and then k x will produce +the Lambda so the so we'll get a Lambda + + align:start position:0% +the Lambda so the so we'll get a Lambda + + + align:start position:0% +the Lambda so the so we'll get a Lambda +one coming out of both minus Lambda 1 + + align:start position:0% +one coming out of both minus Lambda 1 + + + align:start position:0% +one coming out of both minus Lambda 1 +from one term and a Lambda one from the + + align:start position:0% +from one term and a Lambda one from the + + + align:start position:0% +from one term and a Lambda one from the +other perfect or cosine so we could have + + align:start position:0% +other perfect or cosine so we could have + + + align:start position:0% +other perfect or cosine so we could have +a C1 and maybe a + + align:start position:0% +a C1 and maybe a + + + align:start position:0% +a C1 and maybe a +D1 s + + align:start position:0% +D1 s + + + align:start position:0% +D1 s +cosine wouldn't that do just as well + + align:start position:0% +cosine wouldn't that do just as well + + + align:start position:0% +cosine wouldn't that do just as well +root of Lambda 1 T + + align:start position:0% +root of Lambda 1 T + + + align:start position:0% +root of Lambda 1 T +X1 + + align:start position:0% +X1 + + + align:start position:0% +X1 +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so what's happening here I'm getting + + align:start position:0% +so what's happening here I'm getting + + + align:start position:0% +so what's happening here I'm getting +two special solutions for + + align:start position:0% +two special solutions for + + + align:start position:0% +two special solutions for +every igen Vector over here I got one + + align:start position:0% +every igen Vector over here I got one + + + align:start position:0% +every igen Vector over here I got one +special guy now I'm getting two special + + align:start position:0% +special guy now I'm getting two special + + + align:start position:0% +special guy now I'm getting two special +guys and then plus so on plus there will + + align:start position:0% +guys and then plus so on plus there will + + + align:start position:0% +guys and then plus so on plus there will +be a + + align:start position:0% +be a + + + align:start position:0% +be a +CN s of square root of Lambda n t + + align:start position:0% +CN s of square root of Lambda n t + + + align:start position:0% +CN s of square root of Lambda n t +xn and also just as well could have + + align:start position:0% +xn and also just as well could have + + + align:start position:0% +xn and also just as well could have +cosine of square root of Lambda n + + align:start position:0% +cosine of square root of Lambda n + + + align:start position:0% +cosine of square root of Lambda n +t + + align:start position:0% +t + + + align:start position:0% +t +xn so each hon Vector is like producing + + align:start position:0% +xn so each hon Vector is like producing + + + align:start position:0% +xn so each hon Vector is like producing +two solutions and now I've got how many + + align:start position:0% +two solutions and now I've got how many + + + align:start position:0% +two solutions and now I've got how many +constants have I got + + align:start position:0% +constants have I got + + + align:start position:0% +constants have I got +2 N + + align:start position:0% +2 N + + + align:start position:0% +2 N +right I've got all the C's and all the + + align:start position:0% +right I've got all the C's and all the + + + align:start position:0% +right I've got all the C's and all the +D's now so what do I do with 2N + + align:start position:0% + + + + align:start position:0% + +constants I'm matching instead of just + + align:start position:0% +constants I'm matching instead of just + + + align:start position:0% +constants I'm matching instead of just +matching the initial so I'll use the use + + align:start position:0% +matching the initial so I'll use the use + + + align:start position:0% +matching the initial so I'll use the use +the + + align:start position:0% +the + + + align:start position:0% +the +C's and + + align:start position:0% +C's and + + + align:start position:0% +C's and +D's to + + align:start position:0% +D's to + + + align:start position:0% +D's to +match what the initial Vector U of zero + + align:start position:0% +match what the initial Vector U of zero + + + align:start position:0% +match what the initial Vector U of zero +and and U Prime so there I've got n u + + align:start position:0% +and and U Prime so there I've got n u + + + align:start position:0% +and and U Prime so there I've got n u +Prime the initial velocity so here I + + align:start position:0% +Prime the initial velocity so here I + + + align:start position:0% +Prime the initial velocity so here I +have a I've got a line of + + align:start position:0% +have a I've got a line of + + + align:start position:0% +have a I've got a line of +Springs I've got a line of Springs and + + align:start position:0% +Springs I've got a line of Springs and + + + align:start position:0% +Springs I've got a line of Springs and +what what am I doing physically with + + align:start position:0% +what what am I doing physically with + + + align:start position:0% +what what am I doing physically with +this line of Springs here so here's our + + align:start position:0% +this line of Springs here so here's our + + + align:start position:0% +this line of Springs here so here's our +like line of + + align:start position:0% +like line of + + + align:start position:0% +like line of +Springs there's a spring and a mass and + + align:start position:0% +Springs there's a spring and a mass and + + + align:start position:0% +Springs there's a spring and a mass and +a spring and a mass and a spring and a + + align:start position:0% +a spring and a mass and a spring and a + + + align:start position:0% +a spring and a mass and a spring and a +mass Mass let's say suppose I did it + + align:start position:0% +mass Mass let's say suppose I did it + + + align:start position:0% +mass Mass let's say suppose I did it +with the uh that would be the B Matrix + + align:start position:0% +with the uh that would be the B Matrix + + + align:start position:0% +with the uh that would be the B Matrix +right no the T yeah that would be like + + align:start position:0% +right no the T yeah that would be like + + + align:start position:0% +right no the T yeah that would be like +the T Matrix where the well it would be + + align:start position:0% +the T Matrix where the well it would be + + + align:start position:0% +the T Matrix where the well it would be +fixed free if if you want me to get to + + align:start position:0% +fixed free if if you want me to get to + + + align:start position:0% +fixed free if if you want me to get to +the K Matrix I fix the last one but what + + align:start position:0% +the K Matrix I fix the last one but what + + + align:start position:0% +the K Matrix I fix the last one but what +what's the physical problem now that + + align:start position:0% +what's the physical problem now that + + + align:start position:0% +what's the physical problem now that +that's that's that that's that I'm close + + align:start position:0% +that's that's that that's that I'm close + + + align:start position:0% +that's that's that that's that I'm close +to here it's it's a + + align:start position:0% +to here it's it's a + + + align:start position:0% +to here it's it's a +I move the Springs away from equilibrium + + align:start position:0% +I move the Springs away from equilibrium + + + align:start position:0% +I move the Springs away from equilibrium +and let go they oscillate right they + + align:start position:0% +and let go they oscillate right they + + + align:start position:0% +and let go they oscillate right they +they oscillate uh indefinitely no + + align:start position:0% +they oscillate uh indefinitely no + + + align:start position:0% +they oscillate uh indefinitely no +friction no + + align:start position:0% +friction no + + + align:start position:0% +friction no +damping a damping term would be probably + + align:start position:0% +damping a damping term would be probably + + + align:start position:0% +damping a damping term would be probably +involve a first derivative a velocity + + align:start position:0% +involve a first derivative a velocity + + + align:start position:0% +involve a first derivative a velocity +but here that's this is a totally + + align:start position:0% +but here that's this is a totally + + + align:start position:0% +but here that's this is a totally +conservative system and uh the the + + align:start position:0% +conservative system and uh the the + + + align:start position:0% +conservative system and uh the the +Springs will just oscillate forever and + + align:start position:0% +Springs will just oscillate forever and + + + align:start position:0% +Springs will just oscillate forever and +with what frequencies + + align:start position:0% +with what frequencies + + + align:start position:0% +with what frequencies +with these frequencies square roots of + + align:start position:0% +with these frequencies square roots of + + + align:start position:0% +with these frequencies square roots of +the igen + + align:start position:0% +the igen + + + align:start position:0% +the igen +values and it's we're happy to know that + + align:start position:0% +values and it's we're happy to know that + + + align:start position:0% +values and it's we're happy to know that +those igen values are positive so we can + + align:start position:0% +those igen values are positive so we can + + + align:start position:0% +those igen values are positive so we can +take their square roots right is that so + + align:start position:0% +take their square roots right is that so + + + align:start position:0% +take their square roots right is that so +there is a mechanical engineering + + align:start position:0% +there is a mechanical engineering + + + align:start position:0% +there is a mechanical engineering +absolutely prototype problem of uh + + align:start position:0% +absolutely prototype problem of uh + + + align:start position:0% +absolutely prototype problem of uh +Springs with identical masses with + + align:start position:0% +Springs with identical masses with + + + align:start position:0% +Springs with identical masses with +identical masses so that there's so we + + align:start position:0% +identical masses so that there's so we + + + align:start position:0% +identical masses so that there's so we +don't have to worry about a mass Mass + + align:start position:0% +don't have to worry about a mass Mass + + + align:start position:0% +don't have to worry about a mass Mass +Matrix + + align:start position:0% +Matrix + + + align:start position:0% +Matrix +now are you ready to worry about the + + align:start position:0% +now are you ready to worry about the + + + align:start position:0% +now are you ready to worry about the +mass + + align:start position:0% +mass + + + align:start position:0% +mass +Matrix this says our third example + + align:start position:0% +Matrix this says our third example + + + align:start position:0% +Matrix this says our third example +suppose these masses are now + + align:start position:0% + + + + align:start position:0% + +different of course we had our spring + + align:start position:0% +different of course we had our spring + + + align:start position:0% +different of course we had our spring +constants they go into the + + align:start position:0% +constants they go into the + + + align:start position:0% +constants they go into the +K right remember the K is our a + + align:start position:0% +K right remember the K is our a + + + align:start position:0% +K right remember the K is our a +transpose CA no change but now we have a + + align:start position:0% +transpose CA no change but now we have a + + + align:start position:0% +transpose CA no change but now we have a +mass Matrix + + align:start position:0% +mass Matrix + + + align:start position:0% +mass Matrix +which would be M1 M2 + + align:start position:0% + + + + align:start position:0% + +M3 diagonal in this + + align:start position:0% +M3 diagonal in this + + + align:start position:0% +M3 diagonal in this +case where is that coming from Newton's + + align:start position:0% +case where is that coming from Newton's + + + align:start position:0% +case where is that coming from Newton's +law Newton's law is I mean that's what's + + align:start position:0% +law Newton's law is I mean that's what's + + + align:start position:0% +law Newton's law is I mean that's what's +governing the motion of these Springs + + align:start position:0% +governing the motion of these Springs + + + align:start position:0% +governing the motion of these Springs +the mass times the acceleration equal + + align:start position:0% +the mass times the acceleration equal + + + align:start position:0% +the mass times the acceleration equal +the + + align:start position:0% +the + + + align:start position:0% +the +force okay and what's the + + align:start position:0% +force okay and what's the + + + align:start position:0% +force okay and what's the +force the force is partly an ex external + + align:start position:0% +force the force is partly an ex external + + + align:start position:0% +force the force is partly an ex external +Force + + align:start position:0% +Force + + + align:start position:0% +Force +F but partly an internal Force coming + + align:start position:0% +F but partly an internal Force coming + + + align:start position:0% +F but partly an internal Force coming +from where so what are the forces on + + align:start position:0% +from where so what are the forces on + + + align:start position:0% +from where so what are the forces on +those on those masses that are making + + align:start position:0% +those on those masses that are making + + + align:start position:0% +those on those masses that are making +them move the Springs the Springs so + + align:start position:0% +them move the Springs the Springs so + + + align:start position:0% +them move the Springs the Springs so +these are in this is internal force from + + align:start position:0% +these are in this is internal force from + + + align:start position:0% +these are in this is internal force from +the Springs this is external force + + align:start position:0% +the Springs this is external force + + + align:start position:0% +the Springs this is external force +from uh whatever we we might do it could + + align:start position:0% +from uh whatever we we might do it could + + + align:start position:0% +from uh whatever we we might do it could +be zero if it is zero then it's just + + align:start position:0% +be zero if it is zero then it's just + + + align:start position:0% +be zero if it is zero then it's just +purely a a closed + + align:start position:0% +purely a a closed + + + align:start position:0% +purely a a closed +system and the energy would be conserved + + align:start position:0% +system and the energy would be conserved + + + align:start position:0% +system and the energy would be conserved +and we could it would come out of the + + align:start position:0% +and we could it would come out of the + + + align:start position:0% +and we could it would come out of the +differential equation that the energy + + align:start position:0% +differential equation that the energy + + + align:start position:0% +differential equation that the energy +was conserved the + + align:start position:0% +was conserved the + + + align:start position:0% +was conserved the +total energy in the springs plus the + + align:start position:0% +total energy in the springs plus the + + + align:start position:0% +total energy in the springs plus the +energy in the masses so let's just I'll + + align:start position:0% +energy in the masses so let's just I'll + + + align:start position:0% +energy in the masses so let's just I'll +just note that down if this was + + align:start position:0% +just note that down if this was + + + align:start position:0% +just note that down if this was +Zero then the this is + + align:start position:0% + + + + align:start position:0% + +conservative don't know if it's + + align:start position:0% +conservative don't know if it's + + + align:start position:0% +conservative don't know if it's +compassionate or not but it's + + align:start position:0% +compassionate or not but it's + + + align:start position:0% +compassionate or not but it's +conservative uh so the kinetic energy + + align:start position:0% +conservative uh so the kinetic energy + + + align:start position:0% +conservative uh so the kinetic energy +that's in the + + align:start position:0% +that's in the + + + align:start position:0% +that's in the +masses plus the potential energy strain + + align:start position:0% +masses plus the potential energy strain + + + align:start position:0% +masses plus the potential energy strain +energy in the + + align:start position:0% + + + + align:start position:0% + +springs would be + + align:start position:0% +springs would be + + + align:start position:0% +springs would be +constant constant + + align:start position:0% +constant constant + + + align:start position:0% +constant constant +energy okay I I we could the notes will + + align:start position:0% +energy okay I I we could the notes will + + + align:start position:0% +energy okay I I we could the notes will +uh derive that fact from the + + align:start position:0% +uh derive that fact from the + + + align:start position:0% +uh derive that fact from the +differential equation I I just think + + align:start position:0% +differential equation I I just think + + + align:start position:0% +differential equation I I just think +maybe it's + + align:start position:0% +maybe it's + + + align:start position:0% +maybe it's +I know you guys are not doing mechanical + + align:start position:0% +I know you guys are not doing mechanical + + + align:start position:0% +I know you guys are not doing mechanical +engineering uh or at least uh some maybe + + align:start position:0% +engineering uh or at least uh some maybe + + + align:start position:0% +engineering uh or at least uh some maybe +but not but a lot uh looking at other + + align:start position:0% +but not but a lot uh looking at other + + + align:start position:0% +but not but a lot uh looking at other +parts of mathematics but and and and not + + align:start position:0% +parts of mathematics but and and and not + + + align:start position:0% +parts of mathematics but and and and not +masses and springs but this is really + + align:start position:0% +masses and springs but this is really + + + align:start position:0% +masses and springs but this is really +the fundamental equation of motion + + align:start position:0% +the fundamental equation of motion + + + align:start position:0% +the fundamental equation of motion +Newton's law ma equal + + align:start position:0% +Newton's law ma equal + + + align:start position:0% +Newton's law ma equal +force and how would we solve it + + align:start position:0% +force and how would we solve it + + + align:start position:0% +force and how would we solve it +I'm let's solve it when I say solve it I + + align:start position:0% +I'm let's solve it when I say solve it I + + + align:start position:0% +I'm let's solve it when I say solve it I +I really mean how could we write down a + + align:start position:0% +I really mean how could we write down a + + + align:start position:0% +I really mean how could we write down a +formula for the + + align:start position:0% +formula for the + + + align:start position:0% +formula for the +answer I to solve something really has + + align:start position:0% +answer I to solve something really has + + + align:start position:0% +answer I to solve something really has +two meanings here in in this course we + + align:start position:0% +two meanings here in in this course we + + + align:start position:0% +two meanings here in in this course we +either solve it by a + + align:start position:0% +either solve it by a + + + align:start position:0% +either solve it by a +formula or we solve it by an + + align:start position:0% +formula or we solve it by an + + + align:start position:0% +formula or we solve it by an +algorithm + + align:start position:0% +algorithm + + + align:start position:0% +algorithm +and we really ought to know something + + align:start position:0% +and we really ought to know something + + + align:start position:0% +and we really ought to know something +about + + align:start position:0% +about + + + align:start position:0% +about +both um the formula of course is going + + align:start position:0% +both um the formula of course is going + + + align:start position:0% +both um the formula of course is going +to be like limited to cases where we + + align:start position:0% +to be like limited to cases where we + + + align:start position:0% +to be like limited to cases where we +have uh everything + + align:start position:0% + + + + align:start position:0% + +beautiful where uh the algorithm has to + + align:start position:0% +beautiful where uh the algorithm has to + + + align:start position:0% +beautiful where uh the algorithm has to +be prepared for whatever the the the + + align:start position:0% +be prepared for whatever the the the + + + align:start position:0% +be prepared for whatever the the the +real problem is so in these early + + align:start position:0% +real problem is so in these early + + + align:start position:0% +real problem is so in these early +lectures in the course we're talking + + align:start position:0% +lectures in the course we're talking + + + align:start position:0% +lectures in the course we're talking +mostly about formulas you know + + align:start position:0% +mostly about formulas you know + + + align:start position:0% +mostly about formulas you know +occasionally I'll + + align:start position:0% +occasionally I'll + + + align:start position:0% +occasionally I'll +say wait a minute here's a comment on an + + align:start position:0% +say wait a minute here's a comment on an + + + align:start position:0% +say wait a minute here's a comment on an +algorithm like Computing igen values I + + align:start position:0% +algorithm like Computing igen values I + + + align:start position:0% +algorithm like Computing igen values I +said you don't use a determinative a + + align:start position:0% +said you don't use a determinative a + + + align:start position:0% +said you don't use a determinative a +minus Lambda I unless the Matrix is like + + align:start position:0% +minus Lambda I unless the Matrix is like + + + align:start position:0% +minus Lambda I unless the Matrix is like +2x two or something or or unless the + + align:start position:0% +2x two or something or or unless the + + + align:start position:0% +2x two or something or or unless the +professor has cooked up a 3X3 but not + + align:start position:0% +professor has cooked up a 3X3 but not + + + align:start position:0% +professor has cooked up a 3X3 but not +not in reality and similarly here uh + + align:start position:0% +not in reality and similarly here uh + + + align:start position:0% +not in reality and similarly here uh +well only in only in the most beautiful + + align:start position:0% +well only in only in the most beautiful + + + align:start position:0% +well only in only in the most beautiful +cases what I expect to uh get everything + + align:start position:0% +cases what I expect to uh get everything + + + align:start position:0% +cases what I expect to uh get everything +from these from these simple formulas + + align:start position:0% +from these from these simple formulas + + + align:start position:0% +from these from these simple formulas +now just to complete how does this + + align:start position:0% +now just to complete how does this + + + align:start position:0% +now just to complete how does this +problem why does this problem produ + + align:start position:0% +problem why does this problem produ + + + align:start position:0% +problem why does this problem produ +connect to this equation well of course + + align:start position:0% +connect to this equation well of course + + + align:start position:0% +connect to this equation well of course +I just want so what are my special + + align:start position:0% +I just want so what are my special + + + align:start position:0% +I just want so what are my special +solutions to this + + align:start position:0% + + + + align:start position:0% + +one I think they'll look just the same + + align:start position:0% +one I think they'll look just the same + + + align:start position:0% +one I think they'll look just the same +they'll be identical it's just that when + + align:start position:0% +they'll be identical it's just that when + + + align:start position:0% +they'll be identical it's just that when +I plug them into this + + align:start position:0% + + + + align:start position:0% + +equation I I better the lambdas better + + align:start position:0% +equation I I better the lambdas better + + + align:start position:0% +equation I I better the lambdas better +come out of that igen value problem do + + align:start position:0% +come out of that igen value problem do + + + align:start position:0% +come out of that igen value problem do +you see what what happened happens so + + align:start position:0% +you see what what happened happens so + + + align:start position:0% +you see what what happened happens so +let's let's plug one in let's see if I + + align:start position:0% +let's let's plug one in let's see if I + + + align:start position:0% +let's let's plug one in let's see if I +plug that into this + + align:start position:0% + + + + align:start position:0% + +equation so what + + align:start position:0% +equation so what + + + align:start position:0% +equation so what +happens let's + + align:start position:0% +happens let's + + + align:start position:0% +happens let's +see when I plug this in multiply by K + + align:start position:0% +see when I plug this in multiply by K + + + align:start position:0% +see when I plug this in multiply by K +then I get + + align:start position:0% +then I get + + + align:start position:0% +then I get +kx1 and by my special igen vectors + + align:start position:0% +kx1 and by my special igen vectors + + + align:start position:0% +kx1 and by my special igen vectors +that's the same as Lambda 1 + + align:start position:0% +that's the same as Lambda 1 + + + align:start position:0% +that's the same as Lambda 1 +mx1 and when I plug it into that term I + + align:start position:0% +mx1 and when I plug it into that term I + + + align:start position:0% +mx1 and when I plug it into that term I +get the Lambda and the minus and the m + + align:start position:0% +get the Lambda and the minus and the m + + + align:start position:0% +get the Lambda and the minus and the m +so do you see it works you see that you + + align:start position:0% +so do you see it works you see that you + + + align:start position:0% +so do you see it works you see that you +see that it's the same idea I don't even + + align:start position:0% +see that it's the same idea I don't even + + + align:start position:0% +see that it's the same idea I don't even +have to write a new solution the same + + align:start position:0% +have to write a new solution the same + + + align:start position:0% +have to write a new solution the same +form but the X1 and the Lambda one have + + align:start position:0% +form but the X1 and the Lambda one have + + + align:start position:0% +form but the X1 and the Lambda one have +to come from this generalized ion value + + align:start position:0% +to come from this generalized ion value + + + align:start position:0% +to come from this generalized ion value +problem if we're going to be okay with + + align:start position:0% +problem if we're going to be okay with + + + align:start position:0% +problem if we're going to be okay with +that m in the + + align:start position:0% + + + + align:start position:0% + +equation + + align:start position:0% +equation + + + align:start position:0% +equation +okay yeah good question now what if + + align:start position:0% +okay yeah good question now what if + + + align:start position:0% +okay yeah good question now what if +I can I can I get back to my so the + + align:start position:0% +I can I can I get back to my so the + + + align:start position:0% +I can I can I get back to my so the +question was shall I just multiply by m + + align:start position:0% +question was shall I just multiply by m + + + align:start position:0% +question was shall I just multiply by m +inverse that would wouldn't be a bad + + align:start position:0% +inverse that would wouldn't be a bad + + + align:start position:0% +inverse that would wouldn't be a bad +idea let me let me just make a few + + align:start position:0% +idea let me let me just make a few + + + align:start position:0% +idea let me let me just make a few +comments on this problem okay how could + + align:start position:0% +comments on this problem okay how could + + + align:start position:0% +comments on this problem okay how could +so that was the m and it probably had a + + align:start position:0% +so that was the m and it probably had a + + + align:start position:0% +so that was the m and it probably had a +very simple form so uh so what comments + + align:start position:0% +very simple form so uh so what comments + + + align:start position:0% +very simple form so uh so what comments +on this KX equal how would you tackle KX + + align:start position:0% +on this KX equal how would you tackle KX + + + align:start position:0% +on this KX equal how would you tackle KX +equal Lambda MX + + align:start position:0% + + + + align:start position:0% + +well as you say one way the sort of + + align:start position:0% +well as you say one way the sort of + + + align:start position:0% +well as you say one way the sort of +first idea would be if m is simple + + align:start position:0% +first idea would be if m is simple + + + align:start position:0% +first idea would be if m is simple +multiply by m + + align:start position:0% +multiply by m + + + align:start position:0% +multiply by m +inverse and we've got back to a standard + + align:start position:0% +inverse and we've got back to a standard + + + align:start position:0% +inverse and we've got back to a standard +problem + + align:start position:0% +problem + + + align:start position:0% +problem +now why should I quibble with + + align:start position:0% +now why should I quibble with + + + align:start position:0% +now why should I quibble with +that it might be but probably so it + + align:start position:0% +that it might be but probably so it + + + align:start position:0% +that it might be but probably so it +might be hard to find M inverse but in a + + align:start position:0% +might be hard to find M inverse but in a + + + align:start position:0% +might be hard to find M inverse but in a +lot of cases it's diagonal or nearly + + align:start position:0% +lot of cases it's diagonal or nearly + + + align:start position:0% +lot of cases it's diagonal or nearly +because it's coming from these masses + + align:start position:0% +because it's coming from these masses + + + align:start position:0% +because it's coming from these masses +and not you know it's a separate Mass + + align:start position:0% +and not you know it's a separate Mass + + + align:start position:0% +and not you know it's a separate Mass +matrix it's just like Newton's law so + + align:start position:0% +matrix it's just like Newton's law so + + + align:start position:0% +matrix it's just like Newton's law so +what's what's my little objection to + + align:start position:0% +what's what's my little objection to + + + align:start position:0% +what's what's my little objection to +this problem it's not symmetric that's + + align:start position:0% +this problem it's not symmetric that's + + + align:start position:0% +this problem it's not symmetric that's +my little objection it's it's so like + + align:start position:0% +my little objection it's it's so like + + + align:start position:0% +my little objection it's it's so like +you know it's a good friend of a + + align:start position:0% +you know it's a good friend of a + + + align:start position:0% +you know it's a good friend of a +symmetric problem I mean where this one + + align:start position:0% +symmetric problem I mean where this one + + + align:start position:0% +symmetric problem I mean where this one +was had symmetric matrices in it m + + align:start position:0% +was had symmetric matrices in it m + + + align:start position:0% +was had symmetric matrices in it m +inverse time K If I multiply right if I + + align:start position:0% +inverse time K If I multiply right if I + + + align:start position:0% +inverse time K If I multiply right if I +you see that if I had my so it might be + + align:start position:0% +you see that if I had my so it might be + + + align:start position:0% +you see that if I had my so it might be +my 2 - one's + + align:start position:0% +my 2 - one's + + + align:start position:0% +my 2 - one's +Matrix and then if I multiply by m + + align:start position:0% +Matrix and then if I multiply by m + + + align:start position:0% +Matrix and then if I multiply by m +inverse so 1 over M1 1 over M2 1 over M3 + + align:start position:0% +inverse so 1 over M1 1 over M2 1 over M3 + + + align:start position:0% +inverse so 1 over M1 1 over M2 1 over M3 +now I've screwed up the Symmetry right + + align:start position:0% +now I've screwed up the Symmetry right + + + align:start position:0% +now I've screwed up the Symmetry right +the this will put a a one over m one + + align:start position:0% +the this will put a a one over m one + + + align:start position:0% +the this will put a a one over m one +over M1 here and on the other side of + + align:start position:0% +over M1 here and on the other side of + + + align:start position:0% +over M1 here and on the other side of +the diagonal will come the 1 over M2 uh + + align:start position:0% +the diagonal will come the 1 over M2 uh + + + align:start position:0% +the diagonal will come the 1 over M2 uh +can you suggest how I could fix it I + + align:start position:0% +can you suggest how I could fix it I + + + align:start position:0% +can you suggest how I could fix it I +would + + align:start position:0% +would + + + align:start position:0% +would +like my problem to be symmetric why + + align:start position:0% +like my problem to be symmetric why + + + align:start position:0% +like my problem to be symmetric why +would I like it to be symmetric well + + align:start position:0% +would I like it to be symmetric well + + + align:start position:0% +would I like it to be symmetric well +first matlb has a special algorithm for + + align:start position:0% +first matlb has a special algorithm for + + + align:start position:0% +first matlb has a special algorithm for +symmetric igon value + + align:start position:0% +symmetric igon value + + + align:start position:0% +symmetric igon value +problems and the igen vectors are + + align:start position:0% +problems and the igen vectors are + + + align:start position:0% +problems and the igen vectors are +orthogonal like you know everything nice + + align:start position:0% +orthogonal like you know everything nice + + + align:start position:0% +orthogonal like you know everything nice +that I know came from that symmetric + + align:start position:0% +that I know came from that symmetric + + + align:start position:0% +that I know came from that symmetric +case but I could I could get this to be + + align:start position:0% +case but I could I could get this to be + + + align:start position:0% +case but I could I could get this to be +symmetric just with a little + + align:start position:0% +symmetric just with a little + + + align:start position:0% +symmetric just with a little +effort + + align:start position:0% +effort + + + align:start position:0% +effort +uh how to do + + align:start position:0% +uh how to do + + + align:start position:0% +uh how to do +it let's see I could somehow I want to + + align:start position:0% +it let's see I could somehow I want to + + + align:start position:0% +it let's see I could somehow I want to +put half of am on each side of K so what + + align:start position:0% +put half of am on each side of K so what + + + align:start position:0% +put half of am on each side of K so what +really I would really be + + align:start position:0% +really I would really be + + + align:start position:0% +really I would really be +happier I could like change variables I + + align:start position:0% +happier I could like change variables I + + + align:start position:0% +happier I could like change variables I +could let like I could let square root + + align:start position:0% +could let like I could let square root + + + align:start position:0% +could let like I could let square root +of M can I write square root of M or M + + align:start position:0% +of M can I write square root of M or M + + + align:start position:0% +of M can I write square root of M or M +to the2 it's just going to be the square + + align:start position:0% +to the2 it's just going to be the square + + + align:start position:0% +to the2 it's just going to be the square +root of + + align:start position:0% +root of + + + align:start position:0% +root of +each + + align:start position:0% +each + + + align:start position:0% +each +term so let me call it m to the one2 + + align:start position:0% +term so let me call it m to the one2 + + + align:start position:0% +term so let me call it m to the one2 +m to the 12 let let X be let M introduce + + align:start position:0% +m to the 12 let let X be let M introduce + + + align:start position:0% +m to the 12 let let X be let M introduce +a new + + align:start position:0% +a new + + + align:start position:0% +a new +variable in place of + + align:start position:0% +variable in place of + + + align:start position:0% +variable in place of +X you see I'm just I'm just normalizing + + align:start position:0% +X you see I'm just I'm just normalizing + + + align:start position:0% +X you see I'm just I'm just normalizing +or or + + align:start position:0% +or or + + + align:start position:0% +or or +rescaling X the components of X so in + + align:start position:0% +rescaling X the components of X so in + + + align:start position:0% +rescaling X the components of X so in +place of X I put M the 12 y so this is + + align:start position:0% +place of X I put M the 12 y so this is + + + align:start position:0% +place of X I put M the 12 y so this is +this is k m to the one o do I want it + + align:start position:0% +this is k m to the one o do I want it + + + align:start position:0% +this is k m to the one o do I want it +maybe I want M Theus 12 1 right because + + align:start position:0% +maybe I want M Theus 12 1 right because + + + align:start position:0% +maybe I want M Theus 12 1 right because +I wanted a minus a half to appear here + + align:start position:0% +I wanted a minus a half to appear here + + + align:start position:0% +I wanted a minus a half to appear here +so so my X I'm now cooking up a y y is M + + align:start position:0% +so so my X I'm now cooking up a y y is M + + + align:start position:0% +so so my X I'm now cooking up a y y is M +the 12 X or X is M the minus one2 y so + + align:start position:0% +the 12 X or X is M the minus one2 y so + + + align:start position:0% +the 12 X or X is M the minus one2 y so +for that X I'll put in M -2 Y and this + + align:start position:0% +for that X I'll put in M -2 Y and this + + + align:start position:0% +for that X I'll put in M -2 Y and this +is Lambda m m to the + + align:start position:0% +is Lambda m m to the + + + align:start position:0% +is Lambda m m to the +-2 y was that all right I'm making this + + align:start position:0% +-2 y was that all right I'm making this + + + align:start position:0% +-2 y was that all right I'm making this +look more complicated I'm just I'm just + + align:start position:0% +look more complicated I'm just I'm just + + + align:start position:0% +look more complicated I'm just I'm just +rescaling the + + align:start position:0% +rescaling the + + + align:start position:0% +rescaling the +ex it's like noise whitening it's like + + align:start position:0% +ex it's like noise whitening it's like + + + align:start position:0% +ex it's like noise whitening it's like +it's like we just uh we always have a + + align:start position:0% +it's like we just uh we always have a + + + align:start position:0% +it's like we just uh we always have a +choice do we deal with a slightly + + align:start position:0% +choice do we deal with a slightly + + + align:start position:0% +choice do we deal with a slightly +lopsided problem or in the in the + + align:start position:0% +lopsided problem or in the in the + + + align:start position:0% +lopsided problem or in the in the +estimation of the of last week uh we + + align:start position:0% +estimation of the of last week uh we + + + align:start position:0% +estimation of the of last week uh we +needed a waiting Matrix so it's like m + + align:start position:0% +needed a waiting Matrix so it's like m + + + align:start position:0% +needed a waiting Matrix so it's like m +is our waiting Matrix well if we jiggle + + align:start position:0% +is our waiting Matrix well if we jiggle + + + align:start position:0% +is our waiting Matrix well if we jiggle +around slightly and use a different + + align:start position:0% +around slightly and use a different + + + align:start position:0% +around slightly and use a different +unknown we can get back to the the best + + align:start position:0% +unknown we can get back to the the best + + + align:start position:0% +unknown we can get back to the the best +case and do you see that we does that + + align:start position:0% +case and do you see that we does that + + + align:start position:0% +case and do you see that we does that +look better or + + align:start position:0% +look better or + + + align:start position:0% +look better or +worse do you see that that is actually + + align:start position:0% +worse do you see that that is actually + + + align:start position:0% +worse do you see that that is actually +better what's better about + + align:start position:0% +better what's better about + + + align:start position:0% +better what's better about +that everybody everybody sees that I + + align:start position:0% +that everybody everybody sees that I + + + align:start position:0% +that everybody everybody sees that I +just took my problem here I didn't want + + align:start position:0% +just took my problem here I didn't want + + + align:start position:0% +just took my problem here I didn't want +to go this way I didn't really want to + + align:start position:0% +to go this way I didn't really want to + + + align:start position:0% +to go this way I didn't really want to +do it but I wanted to I wanted to I + + align:start position:0% +do it but I wanted to I wanted to I + + + align:start position:0% +do it but I wanted to I wanted to I +wanted to get it now now what have I got + + align:start position:0% +wanted to get it now now what have I got + + + align:start position:0% +wanted to get it now now what have I got +here that's M * m -2 so what is that + + align:start position:0% +here that's M * m -2 so what is that + + + align:start position:0% +here that's M * m -2 so what is that +that's that's M to + + align:start position:0% +that's that's M to + + + align:start position:0% +that's that's M to +the2 and then when I bring it on the + + align:start position:0% +the2 and then when I bring it on the + + + align:start position:0% +the2 and then when I bring it on the +other side I finally got what I + + align:start position:0% +other side I finally got what I + + + align:start position:0% +other side I finally got what I +want k m to the one M the minus a + + align:start position:0% +want k m to the one M the minus a + + + align:start position:0% +want k m to the one M the minus a +half y = Lambda + + align:start position:0% + + + + align:start position:0% + +y you can look at that on the video + + align:start position:0% +y you can look at that on the video + + + align:start position:0% +y you can look at that on the video +those steps are just straight forward + + align:start position:0% +those steps are just straight forward + + + align:start position:0% +those steps are just straight forward +and the result was that we have this + + align:start position:0% +and the result was that we have this + + + align:start position:0% +and the result was that we have this +nice Matrix which is + + align:start position:0% +nice Matrix which is + + + align:start position:0% +nice Matrix which is +symmetric and will still be positive + + align:start position:0% +symmetric and will still be positive + + + align:start position:0% +symmetric and will still be positive +definite so it's sort of our our wise + + align:start position:0% +definite so it's sort of our our wise + + + align:start position:0% +definite so it's sort of our our wise +then are these nice orthonormal guys all + + align:start position:0% +then are these nice orthonormal guys all + + + align:start position:0% +then are these nice orthonormal guys all +we did and I just mention it + + align:start position:0% +we did and I just mention it + + + align:start position:0% +we did and I just mention it +because this generalized zigen value + + align:start position:0% +because this generalized zigen value + + + align:start position:0% +because this generalized zigen value +problem really does come up in a lot of + + align:start position:0% +problem really does come up in a lot of + + + align:start position:0% +problem really does come up in a lot of +not only in + + align:start position:0% +not only in + + + align:start position:0% +not only in +mechanics but that was you see that + + align:start position:0% +mechanics but that was you see that + + + align:start position:0% +mechanics but that was you see that +point that that all I've done is by + + align:start position:0% +point that that all I've done is by + + + align:start position:0% +point that that all I've done is by +adjusting the problem get half of M + + align:start position:0% +adjusting the problem get half of M + + + align:start position:0% +adjusting the problem get half of M +inverse on one side and the and the same + + align:start position:0% +inverse on one side and the and the same + + + align:start position:0% +inverse on one side and the and the same +thing on the other side and kept the + + align:start position:0% +thing on the other side and kept the + + + align:start position:0% +thing on the other side and kept the +Symmetry + + align:start position:0% +Symmetry + + + align:start position:0% +Symmetry +okay okay but either way I get these + + align:start position:0% +okay okay but either way I get these + + + align:start position:0% +okay okay but either way I get these +lambdas and I I've got the + + align:start position:0% +lambdas and I I've got the + + + align:start position:0% +lambdas and I I've got the +solution I'm I'm this is exactly half + + align:start position:0% +solution I'm I'm this is exactly half + + + align:start position:0% +solution I'm I'm this is exactly half +half hour into lecture six and that's + + align:start position:0% +half hour into lecture six and that's + + + align:start position:0% +half hour into lecture six and that's +really what I want wanted to do with + + align:start position:0% +really what I want wanted to do with + + + align:start position:0% +really what I want wanted to do with +differential equations because I wanted + + align:start position:0% +differential equations because I wanted + + + align:start position:0% +differential equations because I wanted +you to see what are these igen values + + align:start position:0% +you to see what are these igen values + + + align:start position:0% +you to see what are these igen values +and igen vectors good for and they + + align:start position:0% +and igen vectors good for and they + + + align:start position:0% +and igen vectors good for and they +really pay off + + align:start position:0% +really pay off + + + align:start position:0% +really pay off +in initial value Dynamic problems + + align:start position:0% +in initial value Dynamic problems + + + align:start position:0% +in initial value Dynamic problems +because we can follow one normal fixed + + align:start position:0% +because we can follow one normal fixed + + + align:start position:0% +because we can follow one normal fixed +mode and it has a simple + + align:start position:0% +mode and it has a simple + + + align:start position:0% +mode and it has a simple +evolution of course if the problem's + + align:start position:0% +evolution of course if the problem's + + + align:start position:0% +evolution of course if the problem's +nonlinear or even if the coefficients + + align:start position:0% +nonlinear or even if the coefficients + + + align:start position:0% +nonlinear or even if the coefficients +are variable and changing with time + + align:start position:0% +are variable and changing with time + + + align:start position:0% +are variable and changing with time +that's + + align:start position:0% +that's + + + align:start position:0% +that's +shot so this this pure stuff is these + + align:start position:0% +shot so this this pure stuff is these + + + align:start position:0% +shot so this this pure stuff is these +pure exponentials are really coming from + + align:start position:0% +pure exponentials are really coming from + + + align:start position:0% +pure exponentials are really coming from +the first order equation U Prime equal + + align:start position:0% +the first order equation U Prime equal + + + align:start position:0% +the first order equation U Prime equal +Lambda + + align:start position:0% +Lambda + + + align:start position:0% +Lambda +u i mean that's the that's the Prototype + + align:start position:0% +u i mean that's the that's the Prototype + + + align:start position:0% +u i mean that's the that's the Prototype +equation U Prime equal lamb U and our + + align:start position:0% +equation U Prime equal lamb U and our + + + align:start position:0% +equation U Prime equal lamb U and our +system reduces to n of these + + align:start position:0% +system reduces to n of these + + + align:start position:0% +system reduces to n of these +because each we follow each I Vector + + align:start position:0% +because each we follow each I Vector + + + align:start position:0% +because each we follow each I Vector +separately + + align:start position:0% +separately + + + align:start position:0% +separately +okay you you see that idea could I uh + + align:start position:0% +okay you you see that idea could I uh + + + align:start position:0% +okay you you see that idea could I uh +now what I had in mind for + + align:start position:0% +now what I had in mind for + + + align:start position:0% +now what I had in mind for +this + + align:start position:0% +this + + + align:start position:0% +this +um to take half an hour more on the + + align:start position:0% +um to take half an hour more on the + + + align:start position:0% +um to take half an hour more on the +General on on on other topics + + align:start position:0% +General on on on other topics + + + align:start position:0% +General on on on other topics +in uh linear + + align:start position:0% +in uh linear + + + align:start position:0% +in uh linear +algebra okay and here on this board I + + align:start position:0% +algebra okay and here on this board I + + + align:start position:0% +algebra okay and here on this board I +wrote the the two big the two big guys + + align:start position:0% +wrote the the two big the two big guys + + + align:start position:0% +wrote the the two big the two big guys +that we've got for the + + align:start position:0% +that we've got for the + + + align:start position:0% +that we've got for the +for the + + align:start position:0% +for the + + + align:start position:0% +for the +symmetric case especially symmetric + + align:start position:0% +symmetric case especially symmetric + + + align:start position:0% +symmetric case especially symmetric +positive definite case or what did what + + align:start position:0% +positive definite case or what did what + + + align:start position:0% +positive definite case or what did what +does LDL transpose come from can can you + + align:start position:0% +does LDL transpose come from can can you + + + align:start position:0% +does LDL transpose come from can can you +have a look at that board just as I make + + align:start position:0% +have a look at that board just as I make + + + align:start position:0% +have a look at that board just as I make +some space here on this + + align:start position:0% + + + + align:start position:0% + +one so now we're at the top half of that + + align:start position:0% + + + + align:start position:0% + +board and I guess what I'm trying to say + + align:start position:0% +board and I guess what I'm trying to say + + + align:start position:0% +board and I guess what I'm trying to say +there so this is + + align:start position:0% +there so this is + + + align:start position:0% +there so this is +now + + align:start position:0% +now + + + align:start position:0% +now +uh this is + + align:start position:0% +uh this is + + + align:start position:0% +uh this is +now linear algebra factorizations in + + align:start position:0% +now linear algebra factorizations in + + + align:start position:0% +now linear algebra factorizations in +linear + + align:start position:0% + + + + align:start position:0% + +algebra or factorizations every + + align:start position:0% +algebra or factorizations every + + + align:start position:0% +algebra or factorizations every +factorization representing some + + align:start position:0% +factorization representing some + + + align:start position:0% +factorization representing some +important + + align:start position:0% +important + + + align:start position:0% +important +algorithm in linear algebra okay okay so + + align:start position:0% +algorithm in linear algebra okay okay so + + + align:start position:0% +algorithm in linear algebra okay okay so +I + + align:start position:0% +I + + + align:start position:0% +I +start with the these two guys that we've + + align:start position:0% +start with the these two guys that we've + + + align:start position:0% +start with the these two guys that we've +seen k equal l d l transpose that's a + + align:start position:0% +seen k equal l d l transpose that's a + + + align:start position:0% +seen k equal l d l transpose that's a +factorization into lower triangular + + align:start position:0% +factorization into lower triangular + + + align:start position:0% +factorization into lower triangular +diagonal upper triangular and what was + + align:start position:0% +diagonal upper triangular and what was + + + align:start position:0% +diagonal upper triangular and what was +the algorithm that this factorization + + align:start position:0% +the algorithm that this factorization + + + align:start position:0% +the algorithm that this factorization +came from + + align:start position:0% +came from + + + align:start position:0% +came from +elimination so that's from + + align:start position:0% +elimination so that's from + + + align:start position:0% +elimination so that's from +elimination on a on a symmetric positive + + align:start position:0% +elimination on a on a symmetric positive + + + align:start position:0% +elimination on a on a symmetric positive +definite + + align:start position:0% +definite + + + align:start position:0% +definite +Matrix okay and the second one we just + + align:start position:0% +Matrix okay and the second one we just + + + align:start position:0% +Matrix okay and the second one we just +got + + align:start position:0% +got + + + align:start position:0% +got +is Q Lambda Q + + align:start position:0% +is Q Lambda Q + + + align:start position:0% +is Q Lambda Q +transpose and what algorithm or + + align:start position:0% +transpose and what algorithm or + + + align:start position:0% +transpose and what algorithm or +what problem led us to that + + align:start position:0% +what problem led us to that + + + align:start position:0% +what problem led us to that +factorization of what was this + + align:start position:0% +factorization of what was this + + + align:start position:0% +factorization of what was this +factorization this was an orthogonal + + align:start position:0% +factorization this was an orthogonal + + + align:start position:0% +factorization this was an orthogonal +Matrix times a diagonal times a + + align:start position:0% +Matrix times a diagonal times a + + + align:start position:0% +Matrix times a diagonal times a +transpose of of the orthogonal so + + align:start position:0% +transpose of of the orthogonal so + + + align:start position:0% +transpose of of the orthogonal so +another orthogonal + + align:start position:0% +another orthogonal + + + align:start position:0% +another orthogonal +Matrix what led us to that the igen + + align:start position:0% +Matrix what led us to that the igen + + + align:start position:0% +Matrix what led us to that the igen +value problem so this was this is this + + align:start position:0% +value problem so this was this is this + + + align:start position:0% +value problem so this was this is this +is what we've got the two e + + align:start position:0% +is what we've got the two e + + + align:start position:0% +is what we've got the two e +eliminations and + + align:start position:0% +eliminations and + + + align:start position:0% +eliminations and +IG of course in reality this one + + align:start position:0% +IG of course in reality this one + + + align:start position:0% +IG of course in reality this one +numerically is much harder than this one + + align:start position:0% +numerically is much harder than this one + + + align:start position:0% +numerically is much harder than this one +this one is just mechanical dot dot dot + + align:start position:0% +this one is just mechanical dot dot dot + + + align:start position:0% +this one is just mechanical dot dot dot +dot dot and you got + + align:start position:0% +dot dot and you got + + + align:start position:0% +dot dot and you got +it + + align:start position:0% +it + + + align:start position:0% +it +in some fixed number of steps you got it + + align:start position:0% +in some fixed number of steps you got it + + + align:start position:0% +in some fixed number of steps you got it +exactly this one you can't get exactly + + align:start position:0% +exactly this one you can't get exactly + + + align:start position:0% +exactly this one you can't get exactly +in a fixed number of steps because you + + align:start position:0% +in a fixed number of steps because you + + + align:start position:0% +in a fixed number of steps because you +can't find the roots of a polinomial in + + align:start position:0% +can't find the roots of a polinomial in + + + align:start position:0% +can't find the roots of a polinomial in +a fixed number of steps + + align:start position:0% +a fixed number of steps + + + align:start position:0% +a fixed number of steps +galwad died in uh after + + align:start position:0% +galwad died in uh after + + + align:start position:0% +galwad died in uh after +uh after he proved + + align:start position:0% +uh after he proved + + + align:start position:0% +uh after he proved +that and well not that wasn't cause and + + align:start position:0% +that and well not that wasn't cause and + + + align:start position:0% +that and well not that wasn't cause and +effect he was killed in a jewel and we + + align:start position:0% +effect he was killed in a jewel and we + + + align:start position:0% +effect he was killed in a jewel and we +regret it very + + align:start position:0% +regret it very + + + align:start position:0% +regret it very +much + + align:start position:0% +much + + + align:start position:0% +much +uh yeah he was the best graduate student + + align:start position:0% +uh yeah he was the best graduate student + + + align:start position:0% +uh yeah he was the best graduate student +I know of and U never finish okay so now + + align:start position:0% +I know of and U never finish okay so now + + + align:start position:0% +I know of and U never finish okay so now +there are two more + + align:start position:0% +there are two more + + + align:start position:0% +there are two more +factorizations of fundamental importance + + align:start position:0% +factorizations of fundamental importance + + + align:start position:0% +factorizations of fundamental importance +in linear algebra these are about Square + + align:start position:0% +in linear algebra these are about Square + + + align:start position:0% +in linear algebra these are about Square +matrices so just to emphasize that these + + align:start position:0% +matrices so just to emphasize that these + + + align:start position:0% +matrices so just to emphasize that these +are about square and actually positive + + align:start position:0% +are about square and actually positive + + + align:start position:0% +are about square and actually positive +definite square and actually positive + + align:start position:0% +definite square and actually positive + + + align:start position:0% +definite square and actually positive +definite + + align:start position:0% +definite + + + align:start position:0% +definite +matrices okay now I want to consider + + align:start position:0% +matrices okay now I want to consider + + + align:start position:0% +matrices okay now I want to consider +General rectangular any + + align:start position:0% +General rectangular any + + + align:start position:0% +General rectangular any +rectangular + + align:start position:0% + + + + align:start position:0% + +Matrix M and that I'll call a so I have + + align:start position:0% +Matrix M and that I'll call a so I have + + + align:start position:0% +Matrix M and that I'll call a so I have +two factorizations to tell you + + align:start position:0% + + + + align:start position:0% + +about corresponding so you're you're + + align:start position:0% +about corresponding so you're you're + + + align:start position:0% +about corresponding so you're you're +getting linear algebra in a nutshell + + align:start position:0% +getting linear algebra in a nutshell + + + align:start position:0% +getting linear algebra in a nutshell +here the the the sort of Heart of linear + + align:start position:0% +here the the the sort of Heart of linear + + + align:start position:0% +here the the the sort of Heart of linear +algebra is in these + + align:start position:0% +algebra is in these + + + align:start position:0% +algebra is in these +four + + align:start position:0% +four + + + align:start position:0% +four +and this + + align:start position:0% +and this + + + align:start position:0% +and this +one is + + align:start position:0% +one is + + + align:start position:0% +one is +a let's + + align:start position:0% +a let's + + + align:start position:0% +a let's +see well everybody is everybody + + align:start position:0% +see well everybody is everybody + + + align:start position:0% +see well everybody is everybody +describes it as QR a equal + + align:start position:0% +describes it as QR a equal + + + align:start position:0% +describes it as QR a equal +QR so I have to tell you what the Q is + + align:start position:0% +QR so I have to tell you what the Q is + + + align:start position:0% +QR so I have to tell you what the Q is +and the R so this is + + align:start position:0% +and the R so this is + + + align:start position:0% +and the R so this is +orthogonal + + align:start position:0% + + + + align:start position:0% + +Matrix times R sort of for right upper + + align:start position:0% +Matrix times R sort of for right upper + + + align:start position:0% +Matrix times R sort of for right upper +times upper + + align:start position:0% + + + + align:start position:0% + +triangular + + align:start position:0% +triangular + + + align:start position:0% +triangular +okay it's a different + + align:start position:0% +okay it's a different + + + align:start position:0% +okay it's a different +Q I'm tempted to write + + align:start position:0% +Q I'm tempted to write + + + align:start position:0% +Q I'm tempted to write +o but then you won't think it's zero + + align:start position:0% +o but then you won't think it's zero + + + align:start position:0% +o but then you won't think it's zero +right I I I would like it not to get + + align:start position:0% +right I I I would like it not to get + + + align:start position:0% +right I I I would like it not to get +confused with that q and everybody write + + align:start position:0% +confused with that q and everybody write + + + align:start position:0% +confused with that q and everybody write +calls it q but can I call it o for the + + align:start position:0% +calls it q but can I call it o for the + + + align:start position:0% +calls it q but can I call it o for the +moment so this is the orthogonal it's an + + align:start position:0% +moment so this is the orthogonal it's an + + + align:start position:0% +moment so this is the orthogonal it's an +orthogonal Matrix times this Matrix up + + align:start position:0% +orthogonal Matrix times this Matrix up + + + align:start position:0% +orthogonal Matrix times this Matrix up +to the right and uh this is a + + align:start position:0% +to the right and uh this is a + + + align:start position:0% +to the right and uh this is a +fundamental + + align:start position:0% +fundamental + + + align:start position:0% +fundamental +step this means you you you you uh + + align:start position:0% +step this means you you you you uh + + + align:start position:0% +step this means you you you you uh +you're orthogonal so it's associated + + align:start position:0% +you're orthogonal so it's associated + + + align:start position:0% +you're orthogonal so it's associated +with this famous two guys Graham + + align:start position:0% + + + + align:start position:0% + +Schmidt two guys with one idea okay and + + align:start position:0% +Schmidt two guys with one idea okay and + + + align:start position:0% +Schmidt two guys with one idea okay and +this this expresses their idea that if I + + align:start position:0% +this this expresses their idea that if I + + + align:start position:0% +this this expresses their idea that if I +have a bunch of vectors say The Columns + + align:start position:0% +have a bunch of vectors say The Columns + + + align:start position:0% +have a bunch of vectors say The Columns +of a so can I start with The Columns of + + align:start position:0% +of a so can I start with The Columns of + + + align:start position:0% +of a so can I start with The Columns of +a so suppose it just has two + + align:start position:0% +a so suppose it just has two + + + align:start position:0% +a so suppose it just has two +columns there's here's the Matrix a + + align:start position:0% +columns there's here's the Matrix a + + + align:start position:0% +columns there's here's the Matrix a +here's column 1 here's column + + align:start position:0% +here's column 1 here's column + + + align:start position:0% +here's column 1 here's column +two so what's we want to get to this + + align:start position:0% +two so what's we want to get to this + + + align:start position:0% +two so what's we want to get to this +Matrix o or + + align:start position:0% +Matrix o or + + + align:start position:0% +Matrix o or +q and what tell me about its columns + + align:start position:0% +q and what tell me about its columns + + + align:start position:0% +q and what tell me about its columns +what's the deal with the columns of of + + align:start position:0% +what's the deal with the columns of of + + + align:start position:0% +what's the deal with the columns of of +the orthogonal + + align:start position:0% + + + + align:start position:0% + +Matrix they're they're at a right angle + + align:start position:0% +Matrix they're they're at a right angle + + + align:start position:0% +Matrix they're they're at a right angle +they're unit vectors so now we would + + align:start position:0% +they're unit vectors so now we would + + + align:start position:0% +they're unit vectors so now we would +like to have unit vectors May maybe this + + align:start position:0% +like to have unit vectors May maybe this + + + align:start position:0% +like to have unit vectors May maybe this +first direction is fine but the second + + align:start position:0% +first direction is fine but the second + + + align:start position:0% +first direction is fine but the second +direction should be like that + + align:start position:0% +direction should be like that + + + align:start position:0% +direction should be like that +right so this would be the q1 and Q2 + + align:start position:0% +right so this would be the q1 and Q2 + + + align:start position:0% +right so this would be the q1 and Q2 +vectors The Columns of + + align:start position:0% +vectors The Columns of + + + align:start position:0% +vectors The Columns of +O what's the gram Schmid idea if I gave + + align:start position:0% +O what's the gram Schmid idea if I gave + + + align:start position:0% +O what's the gram Schmid idea if I gave +you those two columns or if I gave them + + align:start position:0% +you those two columns or if I gave them + + + align:start position:0% +you those two columns or if I gave them +to Graham and Schmidt and let them have + + align:start position:0% +to Graham and Schmidt and let them have + + + align:start position:0% +to Graham and Schmidt and let them have +a contest uh what would they do how + + align:start position:0% +a contest uh what would they do how + + + align:start position:0% +a contest uh what would they do how +would they produce q1 from the from the + + align:start position:0% +would they produce q1 from the from the + + + align:start position:0% +would they produce q1 from the from the +given + + align:start position:0% +given + + + align:start position:0% +given +a normalize it to a unit Vector that's + + align:start position:0% +a normalize it to a unit Vector that's + + + align:start position:0% +a normalize it to a unit Vector that's +all there'd be to + + align:start position:0% +all there'd be to + + + align:start position:0% +all there'd be to +do how would they produce + + align:start position:0% + + + + align:start position:0% + +Q2 they would Z they they column two is + + align:start position:0% +Q2 they would Z they they column two is + + + align:start position:0% +Q2 they would Z they they column two is +not at a right + + align:start position:0% +not at a right + + + align:start position:0% +not at a right +angle so they project somehow I mean + + align:start position:0% +angle so they project somehow I mean + + + align:start position:0% +angle so they project somehow I mean +geometrically they would figure out the + + align:start position:0% +geometrically they would figure out the + + + align:start position:0% +geometrically they would figure out the +they' figure out this projection but + + align:start position:0% +they' figure out this projection but + + + align:start position:0% +they' figure out this projection but +it's really that part they want it's the + + align:start position:0% +it's really that part they want it's the + + + align:start position:0% +it's really that part they want it's the +E part the error + + align:start position:0% +E part the error + + + align:start position:0% +E part the error +part that they would + + align:start position:0% +part that they would + + + align:start position:0% +part that they would +identify and then what final step would + + align:start position:0% +identify and then what final step would + + + align:start position:0% +identify and then what final step would +be normalize to length one okay so what + + align:start position:0% +be normalize to length one okay so what + + + align:start position:0% +be normalize to length one okay so what +Matrix is going to go into this process + + align:start position:0% +Matrix is going to go into this process + + + align:start position:0% +Matrix is going to go into this process +what Matrix does Graham do Graham and + + align:start position:0% +what Matrix does Graham do Graham and + + + align:start position:0% +what Matrix does Graham do Graham and +Schmidt have to ultimately + + align:start position:0% + + + + align:start position:0% + +use they're they're projecting and and + + align:start position:0% +use they're they're projecting and and + + + align:start position:0% +use they're they're projecting and and +what was The Matrix what was the + + align:start position:0% +what was The Matrix what was the + + + align:start position:0% +what was The Matrix what was the +equation that we got to in deal in doing + + align:start position:0% +equation that we got to in deal in doing + + + align:start position:0% +equation that we got to in deal in doing +projections this isn't weighted now it's + + align:start position:0% +projections this isn't weighted now it's + + + align:start position:0% +projections this isn't weighted now it's +just regular projections it was a + + align:start position:0% +just regular projections it was a + + + align:start position:0% +just regular projections it was a +transpose + + align:start position:0% +transpose + + + align:start position:0% +transpose +a somewhere in in this process comes a + + align:start position:0% +a somewhere in in this process comes a + + + align:start position:0% +a somewhere in in this process comes a +transpose + + align:start position:0% +transpose + + + align:start position:0% +transpose +a which is our K so what I want to do is + + align:start position:0% +a which is our K so what I want to do is + + + align:start position:0% +a which is our K so what I want to do is +show how this K will be this will be our + + align:start position:0% +show how this K will be this will be our + + + align:start position:0% +show how this K will be this will be our +a transpose + + align:start position:0% + + + + align:start position:0% + +a what I'm trying to do is say that + + align:start position:0% +a what I'm trying to do is say that + + + align:start position:0% +a what I'm trying to do is say that +these two come from these + + align:start position:0% +these two come from these + + + align:start position:0% +these two come from these +two these two well said what this is + + align:start position:0% +two these two well said what this is + + + align:start position:0% +two these two well said what this is +it's going to be the singular value + + align:start position:0% +it's going to be the singular value + + + align:start position:0% +it's going to be the singular value +decomposition let me fill that fill this + + align:start position:0% +decomposition let me fill that fill this + + + align:start position:0% +decomposition let me fill that fill this +in this is the other great and more and + + align:start position:0% +in this is the other great and more and + + + align:start position:0% +in this is the other great and more and +more famous uh factorization into + + align:start position:0% +more famous uh factorization into + + + align:start position:0% +more famous uh factorization into +orthogonal + + align:start position:0% + + + + align:start position:0% + +diagonal + + align:start position:0% + + + + align:start position:0% + +orthogonal you might say the number of + + align:start position:0% +orthogonal you might say the number of + + + align:start position:0% +orthogonal you might say the number of +ideas here the number of rearrangements + + align:start position:0% +ideas here the number of rearrangements + + + align:start position:0% +ideas here the number of rearrangements +is pretty small because we're always + + align:start position:0% +is pretty small because we're always + + + align:start position:0% +is pretty small because we're always +working with triangular + + align:start position:0% +working with triangular + + + align:start position:0% +working with triangular +matrices orthogonal + + align:start position:0% +matrices orthogonal + + + align:start position:0% +matrices orthogonal +matrices diagonal + + align:start position:0% +matrices diagonal + + + align:start position:0% +matrices diagonal +matrices we're + + align:start position:0% +matrices we're + + + align:start position:0% +matrices we're +just playing all the possible + + align:start position:0% +just playing all the possible + + + align:start position:0% +just playing all the possible +combinations but this is a highly + + align:start position:0% +combinations but this is a highly + + + align:start position:0% +combinations but this is a highly +important one and it's called so it's + + align:start position:0% +important one and it's called so it's + + + align:start position:0% +important one and it's called so it's +orthogonal + + align:start position:0% +orthogonal + + + align:start position:0% +orthogonal +orthogonal times + + align:start position:0% +orthogonal times + + + align:start position:0% +orthogonal times +diagonal time + + align:start position:0% +diagonal time + + + align:start position:0% +diagonal time +orthogonal and it's known as + + align:start position:0% +orthogonal and it's known as + + + align:start position:0% +orthogonal and it's known as +the + + align:start position:0% +the + + + align:start position:0% +the +singular value decomposition + + align:start position:0% +singular value decomposition + + + align:start position:0% +singular value decomposition +the + + align:start position:0% + + + + align:start position:0% + +SVD so that's a a + + align:start position:0% +SVD so that's a a + + + align:start position:0% +SVD so that's a a +terrific + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +um terrifically useful uh + + align:start position:0% +um terrifically useful uh + + + align:start position:0% +um terrifically useful uh +factorization it's a nice thing to know + + align:start position:0% +factorization it's a nice thing to know + + + align:start position:0% +factorization it's a nice thing to know +now of course sometimes those fact you + + align:start position:0% +now of course sometimes those fact you + + + align:start position:0% +now of course sometimes those fact you +could say wait a minute we've seen + + align:start position:0% +could say wait a minute we've seen + + + align:start position:0% +could say wait a minute we've seen +orthogonal time diagonal time orthogonal + + align:start position:0% +orthogonal time diagonal time orthogonal + + + align:start position:0% +orthogonal time diagonal time orthogonal +before where did we see it before + + align:start position:0% +before where did we see it before + + + align:start position:0% +before where did we see it before +we saw it up + + align:start position:0% +we saw it up + + + align:start position:0% +we saw it up +here that's orthogonal time diagonal + + align:start position:0% +here that's orthogonal time diagonal + + + align:start position:0% +here that's orthogonal time diagonal +time + + align:start position:0% +time + + + align:start position:0% +time +orthogonal but what's the difference + + align:start position:0% +orthogonal but what's the difference + + + align:start position:0% +orthogonal but what's the difference +then between here and + + align:start position:0% +then between here and + + + align:start position:0% +then between here and +here one well that's right this is for + + align:start position:0% +here one well that's right this is for + + + align:start position:0% +here one well that's right this is for +square matrices but anyway this could + + align:start position:0% +square matrices but anyway this could + + + align:start position:0% +square matrices but anyway this could +this would rectangular or this this + + align:start position:0% +this would rectangular or this this + + + align:start position:0% +this would rectangular or this this +Matrix could be square if it was Square + + align:start position:0% +Matrix could be square if it was Square + + + align:start position:0% +Matrix could be square if it was Square +how would there there still would be a + + align:start position:0% +how would there there still would be a + + + align:start position:0% +how would there there still would be a +difference between the two different + + align:start position:0% +difference between the two different + + + align:start position:0% +difference between the two different +yeah different or this was the same + + align:start position:0% +yeah different or this was the same + + + align:start position:0% +yeah different or this was the same +orthogonal Matrix and that was because + + align:start position:0% +orthogonal Matrix and that was because + + + align:start position:0% +orthogonal Matrix and that was because +why because the Matrix was symmetric + + align:start position:0% +why because the Matrix was symmetric + + + align:start position:0% +why because the Matrix was symmetric +right because the Matrix was symmetric + + align:start position:0% +right because the Matrix was symmetric + + + align:start position:0% +right because the Matrix was symmetric +here we're taking some other Matrix not + + align:start position:0% +here we're taking some other Matrix not + + + align:start position:0% +here we're taking some other Matrix not +symmetric anymore let's just + + align:start position:0% +symmetric anymore let's just + + + align:start position:0% +symmetric anymore let's just +say 2 one one oh don't make it symmetric + + align:start position:0% +say 2 one one oh don't make it symmetric + + + align:start position:0% +say 2 one one oh don't make it symmetric +I can't help myself uh zero one okay + + align:start position:0% +I can't help myself uh zero one okay + + + align:start position:0% +I can't help myself uh zero one okay +there is a matrix not symmetric that's + + align:start position:0% +there is a matrix not symmetric that's + + + align:start position:0% +there is a matrix not symmetric that's +my a and but it can be factored into + + align:start position:0% +my a and but it can be factored into + + + align:start position:0% +my a and but it can be factored into +orthogonal time diagonal time orthogonal + + align:start position:0% +orthogonal time diagonal time orthogonal + + + align:start position:0% +orthogonal time diagonal time orthogonal +but these + + align:start position:0% +but these + + + align:start position:0% +but these +um two orthogonal matrices will be + + align:start position:0% +um two orthogonal matrices will be + + + align:start position:0% +um two orthogonal matrices will be +different they couldn't be the same or I + + align:start position:0% +different they couldn't be the same or I + + + align:start position:0% +different they couldn't be the same or I +would have a I would have an + + align:start position:0% +would have a I would have an + + + align:start position:0% +would have a I would have an +automatically symmetric + + align:start position:0% +automatically symmetric + + + align:start position:0% +automatically symmetric +Matrix and what are the numbers that go + + align:start position:0% +Matrix and what are the numbers that go + + + align:start position:0% +Matrix and what are the numbers that go +on in this diagonal matrix up here the + + align:start position:0% +on in this diagonal matrix up here the + + + align:start position:0% +on in this diagonal matrix up here the +numbers that went in here were the I + + align:start position:0% +numbers that went in here were the I + + + align:start position:0% +numbers that went in here were the I +values in here the numbers that go in + + align:start position:0% +values in here the numbers that go in + + + align:start position:0% +values in here the numbers that go in +here are called the singular values so + + align:start position:0% +here are called the singular values so + + + align:start position:0% +here are called the singular values so +that's why it's called the singular + + align:start position:0% +that's why it's called the singular + + + align:start position:0% +that's why it's called the singular +value + + align:start position:0% + + + + align:start position:0% + +decomposition + + align:start position:0% +decomposition + + + align:start position:0% +decomposition +okay and my point + + align:start position:0% +okay and my point + + + align:start position:0% +okay and my point +is that this factorization for a square + + align:start position:0% +is that this factorization for a square + + + align:start position:0% +is that this factorization for a square +a for for for a rectangular a the SBD + + align:start position:0% +a for for for a rectangular a the SBD + + + align:start position:0% +a for for for a rectangular a the SBD +comes from this factorization for a + + align:start position:0% +comes from this factorization for a + + + align:start position:0% +comes from this factorization for a +transpose a should I write that down + + align:start position:0% +transpose a should I write that down + + + align:start position:0% +transpose a should I write that down +because I I'm afraid that that's not in + + align:start position:0% +because I I'm afraid that that's not in + + + align:start position:0% +because I I'm afraid that that's not in +the book it'll be in the next book but + + align:start position:0% +the book it'll be in the next book but + + + align:start position:0% +the book it'll be in the next book but +it's not in this one so so the point + + align:start position:0% +it's not in this one so so the point + + + align:start position:0% +it's not in this one so so the point +about this was um that LDL + + align:start position:0% +about this was um that LDL + + + align:start position:0% +about this was um that LDL +transpose for a transpose + + align:start position:0% +transpose for a transpose + + + align:start position:0% +transpose for a transpose +a connected + + align:start position:0% +a connected + + + align:start position:0% +a connected +to QR or o r whatever we're calling it + + align:start position:0% +to QR or o r whatever we're calling it + + + align:start position:0% +to QR or o r whatever we're calling it +for a + + align:start position:0% +for a + + + align:start position:0% +for a +and then the point about the second guy + + align:start position:0% +and then the point about the second guy + + + align:start position:0% +and then the point about the second guy +is that that Q Lambda Q transpose for a + + align:start position:0% +is that that Q Lambda Q transpose for a + + + align:start position:0% +is that that Q Lambda Q transpose for a +transpose a that'll be our K connects + + align:start position:0% +transpose a that'll be our K connects + + + align:start position:0% +transpose a that'll be our K connects +to U Sigma V transpose for our a that's + + align:start position:0% +to U Sigma V transpose for our a that's + + + align:start position:0% +to U Sigma V transpose for our a that's +uh I'm proved a thing here but I'm + + align:start position:0% +uh I'm proved a thing here but I'm + + + align:start position:0% +uh I'm proved a thing here but I'm +trying to say that we really have got in + + align:start position:0% +trying to say that we really have got in + + + align:start position:0% +trying to say that we really have got in +our + + align:start position:0% +our + + + align:start position:0% +our +grasp not only the first two which we've + + align:start position:0% +grasp not only the first two which we've + + + align:start position:0% +grasp not only the first two which we've +done in detail but we can use those to + + align:start position:0% +done in detail but we can use those to + + + align:start position:0% +done in detail but we can use those to +capture the second two and then we've + + align:start position:0% +capture the second two and then we've + + + align:start position:0% +capture the second two and then we've +got the whole thing just by applying the + + align:start position:0% +got the whole thing just by applying the + + + align:start position:0% +got the whole thing just by applying the +first two to k equal a transpose which + + align:start position:0% +first two to k equal a transpose which + + + align:start position:0% +first two to k equal a transpose which +is our symmetric positive definite + + align:start position:0% +is our symmetric positive definite + + + align:start position:0% +is our symmetric positive definite +Matrix + + align:start position:0% +Matrix + + + align:start position:0% +Matrix +okay so how do I make that connection + + align:start position:0% +okay so how do I make that connection + + + align:start position:0% +okay so how do I make that connection +but between the the the a transpose a + + align:start position:0% +but between the the the a transpose a + + + align:start position:0% +but between the the the a transpose a +factorization and the a alone + + align:start position:0% +factorization and the a alone + + + align:start position:0% +factorization and the a alone +factorizations okay I've got two to + + align:start position:0% +factorizations okay I've got two to + + + align:start position:0% +factorizations okay I've got two to +do I've got to connect this one to this + + align:start position:0% +do I've got to connect this one to this + + + align:start position:0% +do I've got to connect this one to this +one this one to this + + align:start position:0% +one this one to this + + + align:start position:0% +one this one to this +one and I've got to connect this one to + + align:start position:0% +one and I've got to connect this one to + + + align:start position:0% +one and I've got to connect this one to +this + + align:start position:0% +this + + + align:start position:0% +this +one right that's the that's the + + align:start position:0% +one right that's the that's the + + + align:start position:0% +one right that's the that's the +job and an + + align:start position:0% +job and an + + + align:start position:0% +job and an +important facts come out from that this + + align:start position:0% +important facts come out from that this + + + align:start position:0% +important facts come out from that this +Graham Schmidt will + + align:start position:0% +Graham Schmidt will + + + align:start position:0% +Graham Schmidt will +be finite steps in a finite number of + + align:start position:0% +be finite steps in a finite number of + + + align:start position:0% +be finite steps in a finite number of +steps + + align:start position:0% +steps + + + align:start position:0% +steps +we orthogonalize those vectors into this + + align:start position:0% +we orthogonalize those vectors into this + + + align:start position:0% +we orthogonalize those vectors into this +one into these + + align:start position:0% +one into these + + + align:start position:0% +one into these +vectors + + align:start position:0% +vectors + + + align:start position:0% +vectors +so so Graham Schmidt is just a SE + + align:start position:0% +so so Graham Schmidt is just a SE + + + align:start position:0% +so so Graham Schmidt is just a SE +sequence of steps we could you know we + + align:start position:0% +sequence of steps we could you know we + + + align:start position:0% +sequence of steps we could you know we +could write out a code to do + + align:start position:0% +could write out a code to do + + + align:start position:0% +could write out a code to do +it this one and this one can't be done + + align:start position:0% +it this one and this one can't be done + + + align:start position:0% +it this one and this one can't be done +in a finite number of steps that's + + align:start position:0% +in a finite number of steps that's + + + align:start position:0% +in a finite number of steps that's +that's what galwas said uh so we can't + + align:start position:0% +that's what galwas said uh so we can't + + + align:start position:0% +that's what galwas said uh so we can't +find the singular value decomposition + + align:start position:0% +find the singular value decomposition + + + align:start position:0% +find the singular value decomposition +exactly in a in a fixed set of steps but + + align:start position:0% +exactly in a in a fixed set of steps but + + + align:start position:0% +exactly in a in a fixed set of steps but +of course numerical linear algebra is + + align:start position:0% +of course numerical linear algebra is + + + align:start position:0% +of course numerical linear algebra is +highly occupied with doing this fast a + + align:start position:0% +highly occupied with doing this fast a + + + align:start position:0% +highly occupied with doing this fast a +fast algorithm that gets it gets gets uh + + align:start position:0% +fast algorithm that gets it gets gets uh + + + align:start position:0% +fast algorithm that gets it gets gets uh +um all the accuracy you want so we're + + align:start position:0% +um all the accuracy you want so we're + + + align:start position:0% +um all the accuracy you want so we're +fast methods for and and people come up + + align:start position:0% +fast methods for and and people come up + + + align:start position:0% +fast methods for and and people come up +with new ideas and and you know that's a + + align:start position:0% +with new ideas and and you know that's a + + + align:start position:0% +with new ideas and and you know that's a +crucial um + + align:start position:0% +crucial um + + + align:start position:0% +crucial um +um crucial step in in this subject is to + + align:start position:0% +um crucial step in in this subject is to + + + align:start position:0% +um crucial step in in this subject is to +find new ways maybe for certain classes + + align:start position:0% +find new ways maybe for certain classes + + + align:start position:0% +find new ways maybe for certain classes +of matrices okay so now let me try to + + align:start position:0% +of matrices okay so now let me try to + + + align:start position:0% +of matrices okay so now let me try to +make this + + align:start position:0% +make this + + + align:start position:0% +make this +connection suppose I suppose I'm looking + + align:start position:0% +connection suppose I suppose I'm looking + + + align:start position:0% +connection suppose I suppose I'm looking +for + + align:start position:0% + + + + align:start position:0% + +that okay U let me suppose I'm I'm I'm + + align:start position:0% +that okay U let me suppose I'm I'm I'm + + + align:start position:0% +that okay U let me suppose I'm I'm I'm +trying to get hold of that then what + + align:start position:0% +trying to get hold of that then what + + + align:start position:0% +trying to get hold of that then what +will a transpose a be can can you just + + align:start position:0% +will a transpose a be can can you just + + + align:start position:0% +will a transpose a be can can you just +take that this thing that I'm hoping for + + align:start position:0% +take that this thing that I'm hoping for + + + align:start position:0% +take that this thing that I'm hoping for +and say what would a transpose a + + align:start position:0% +and say what would a transpose a + + + align:start position:0% +and say what would a transpose a +be just if I have that what what would + + align:start position:0% +be just if I have that what what would + + + align:start position:0% +be just if I have that what what would +the what would that lead me to a + + align:start position:0% +the what would that lead me to a + + + align:start position:0% +the what would that lead me to a +transpose a and then I'll match with + + align:start position:0% +transpose a and then I'll match with + + + align:start position:0% +transpose a and then I'll match with +this can can you just take a what's a + + align:start position:0% +this can can you just take a what's a + + + align:start position:0% +this can can you just take a what's a +transpose v v Sigma + + align:start position:0% +transpose v v Sigma + + + align:start position:0% +transpose v v Sigma +transpose U transpose right and now I'll + + align:start position:0% +transpose U transpose right and now I'll + + + align:start position:0% +transpose U transpose right and now I'll +put in a which is U Sigma V + + align:start position:0% + + + + align:start position:0% + +transpose okay now I got six things on + + align:start position:0% +transpose okay now I got six things on + + + align:start position:0% +transpose okay now I got six things on +the right but what's the what's the good + + align:start position:0% +the right but what's the what's the good + + + align:start position:0% +the right but what's the what's the good +point here U transpose U is i u + + align:start position:0% +point here U transpose U is i u + + + align:start position:0% +point here U transpose U is i u +transpose U that was the point of + + align:start position:0% +transpose U that was the point of + + + align:start position:0% +transpose U that was the point of +orthogonal matrices U transpose U was I + + align:start position:0% +orthogonal matrices U transpose U was I + + + align:start position:0% +orthogonal matrices U transpose U was I +so this is the identity + + align:start position:0% +so this is the identity + + + align:start position:0% +so this is the identity +so I don't even write it in let me just + + align:start position:0% +so I don't even write it in let me just + + + align:start position:0% +so I don't even write it in let me just +close that + + align:start position:0% +close that + + + align:start position:0% +close that +Gap okay now compare that with the with + + align:start position:0% +Gap okay now compare that with the with + + + align:start position:0% +Gap okay now compare that with the with +the regular what what's what's + + align:start position:0% +the regular what what's what's + + + align:start position:0% +the regular what what's what's +up I can + + align:start position:0% +up I can + + + align:start position:0% +up I can +identify what's the V that I'm looking + + align:start position:0% +identify what's the V that I'm looking + + + align:start position:0% +identify what's the V that I'm looking +for here in the singular value + + align:start position:0% +for here in the singular value + + + align:start position:0% +for here in the singular value +decomposition it's the + + align:start position:0% +decomposition it's the + + + align:start position:0% +decomposition it's the +Q V is the Q V is the + + align:start position:0% +Q V is the Q V is the + + + align:start position:0% +Q V is the Q V is the +Q V for a is the Q for a transpose + + align:start position:0% + + + + align:start position:0% + +a and what about the + + align:start position:0% +a and what about the + + + align:start position:0% +a and what about the +Lambda and the + + align:start position:0% +Lambda and the + + + align:start position:0% +Lambda and the +sigma well lambda's got to match right + + align:start position:0% +sigma well lambda's got to match right + + + align:start position:0% +sigma well lambda's got to match right +the v's match the Q and The Q transpose + + align:start position:0% +the v's match the Q and The Q transpose + + + align:start position:0% +the v's match the Q and The Q transpose +matches the V transpose that's got to be + + align:start position:0% +matches the V transpose that's got to be + + + align:start position:0% +matches the V transpose that's got to be +match the + + align:start position:0% +match the + + + align:start position:0% +match the +Lambda so these singular values on the + + align:start position:0% +Lambda so these singular values on the + + + align:start position:0% +Lambda so these singular values on the +diagonal + + align:start position:0% + + + + align:start position:0% + +squared are the igen values of a + + align:start position:0% +squared are the igen values of a + + + align:start position:0% +squared are the igen values of a +transpose a these are the singular + + align:start position:0% +transpose a these are the singular + + + align:start position:0% +transpose a these are the singular +values of a these come from singular + + align:start position:0% +values of a these come from singular + + + align:start position:0% +values of a these come from singular +values of a and these guys come from a + + align:start position:0% +values of a and these guys come from a + + + align:start position:0% +values of a and these guys come from a +transpose a and of course we don't + + align:start position:0% +transpose a and of course we don't + + + align:start position:0% +transpose a and of course we don't +surprise to see a square because we sort + + align:start position:0% +surprise to see a square because we sort + + + align:start position:0% +surprise to see a square because we sort +of squared + + align:start position:0% +of squared + + + align:start position:0% +of squared +a we didn't literally square a we took a + + align:start position:0% +a we didn't literally square a we took a + + + align:start position:0% +a we didn't literally square a we took a +transpose a which was the right way + + align:start position:0% +transpose a which was the right way + + + align:start position:0% +transpose a which was the right way +there + + align:start position:0% +there + + + align:start position:0% +there +Square okay how about let's see I guess + + align:start position:0% +Square okay how about let's see I guess + + + align:start position:0% +Square okay how about let's see I guess +we still have a u would you want to so + + align:start position:0% +we still have a u would you want to so + + + align:start position:0% +we still have a u would you want to so +so what did we discover then describe V + + align:start position:0% +so what did we discover then describe V + + + align:start position:0% +so what did we discover then describe V +now what what did we learn here that the + + align:start position:0% +now what what did we learn here that the + + + align:start position:0% +now what what did we learn here that the +v in this is what what Matrix is it it's + + align:start position:0% +v in this is what what Matrix is it it's + + + align:start position:0% +v in this is what what Matrix is it it's +the Q what was the + + align:start position:0% +the Q what was the + + + align:start position:0% +the Q what was the +Q it was the I vectors of a transpose a + + align:start position:0% +Q it was the I vectors of a transpose a + + + align:start position:0% +Q it was the I vectors of a transpose a +right the V here should be the I vectors + + align:start position:0% +right the V here should be the I vectors + + + align:start position:0% +right the V here should be the I vectors +of a transpose a now would you want to + + align:start position:0% +of a transpose a now would you want to + + + align:start position:0% +of a transpose a now would you want to +make a shot at the U + + align:start position:0% +make a shot at the U + + + align:start position:0% +make a shot at the U +at the other piece how could we get V + + align:start position:0% +at the other piece how could we get V + + + align:start position:0% +at the other piece how could we get V +out of the picture and U in the + + align:start position:0% +out of the picture and U in the + + + align:start position:0% +out of the picture and U in the +picture a a transpose that's the bright + + align:start position:0% +picture a a transpose that's the bright + + + align:start position:0% +picture a a transpose that's the bright +idea exactly if I take a a + + align:start position:0% +idea exactly if I take a a + + + align:start position:0% +idea exactly if I take a a +transpose which is another k a different + + align:start position:0% +transpose which is another k a different + + + align:start position:0% +transpose which is another k a different +K by the + + align:start position:0% +K by the + + + align:start position:0% +K by the +way now let's write a a transpose U + + align:start position:0% +way now let's write a a transpose U + + + align:start position:0% +way now let's write a a transpose U +Sigma V transpose and now I'm ready for + + align:start position:0% +Sigma V transpose and now I'm ready for + + + align:start position:0% +Sigma V transpose and now I'm ready for +the transpose V Sigma transpose + + align:start position:0% +the transpose V Sigma transpose + + + align:start position:0% +the transpose V Sigma transpose +U + + align:start position:0% +U + + + align:start position:0% +U +transpose now sorry + + align:start position:0% +transpose now sorry + + + align:start position:0% +transpose now sorry +that looks a little raced but what's + + align:start position:0% +that looks a little raced but what's + + + align:start position:0% +that looks a little raced but what's +good + + align:start position:0% +good + + + align:start position:0% +good +there it's just like the one above but + + align:start position:0% +there it's just like the one above but + + + align:start position:0% +there it's just like the one above but +sort of everything in the opposite order + + align:start position:0% +sort of everything in the opposite order + + + align:start position:0% +sort of everything in the opposite order +so what's up V transpose V in the middle + + align:start position:0% +so what's up V transpose V in the middle + + + align:start position:0% +so what's up V transpose V in the middle +is the identity so again I can just + + align:start position:0% +is the identity so again I can just + + + align:start position:0% +is the identity so again I can just +erase it so I've learned What U + + align:start position:0% +erase it so I've learned What U + + + align:start position:0% +erase it so I've learned What U +is U is + + align:start position:0% + + + + align:start position:0% + +the V is the Q this this came for a + + align:start position:0% +the V is the Q this this came for a + + + align:start position:0% +the V is the Q this this came for a +transpose + + align:start position:0% +transpose + + + align:start position:0% +transpose +a and what is U you see it see what I'm + + align:start position:0% +a and what is U you see it see what I'm + + + align:start position:0% +a and what is U you see it see what I'm +what I'm barely got room to put what's + + align:start position:0% +what I'm barely got room to put what's + + + align:start position:0% +what I'm barely got room to put what's +the U for what this U is I'm seeing it + + align:start position:0% +the U for what this U is I'm seeing it + + + align:start position:0% +the U for what this U is I'm seeing it +here it's the U this is my this is my + + align:start position:0% +here it's the U this is my this is my + + + align:start position:0% +here it's the U this is my this is my +Lambda this is my U transpose so match + + align:start position:0% +Lambda this is my U transpose so match + + + align:start position:0% +Lambda this is my U transpose so match +it + + align:start position:0% +it + + + align:start position:0% +it +with + + align:start position:0% +with + + + align:start position:0% +with +it's it's not coming from a transpose a + + align:start position:0% +it's it's not coming from a transpose a + + + align:start position:0% +it's it's not coming from a transpose a +it's coming from a a transpose right + + align:start position:0% +it's coming from a a transpose right + + + align:start position:0% +it's coming from a a transpose right +it's the U is coming is the igen vector + + align:start position:0% +it's the U is coming is the igen vector + + + align:start position:0% +it's the U is coming is the igen vector +Matrix + + align:start position:0% +Matrix + + + align:start position:0% +Matrix +of a a + + align:start position:0% +of a a + + + align:start position:0% +of a a +transpose where what I really should + + align:start position:0% +transpose where what I really should + + + align:start position:0% +transpose where what I really should +have said here is V is the IG Vector ion + + align:start position:0% +have said here is V is the IG Vector ion + + + align:start position:0% +have said here is V is the IG Vector ion +Vector + + align:start position:0% + + + + align:start position:0% + +Matrix for a transpose a and the point + + align:start position:0% +Matrix for a transpose a and the point + + + align:start position:0% +Matrix for a transpose a and the point +is in a rectangular typical case those + + align:start position:0% +is in a rectangular typical case those + + + align:start position:0% +is in a rectangular typical case those +are different let me just make sure we + + align:start position:0% +are different let me just make sure we + + + align:start position:0% +are different let me just make sure we +know that here was a typical + + align:start position:0% + + + + align:start position:0% + +a let's take a transpose a a transpose a + + align:start position:0% +a let's take a transpose a a transpose a + + + align:start position:0% +a let's take a transpose a a transpose a +is to what please transpose that + + align:start position:0% +is to what please transpose that + + + align:start position:0% +is to what please transpose that +Matrix so what do I get for a transpose + + align:start position:0% +Matrix so what do I get for a transpose + + + align:start position:0% +Matrix so what do I get for a transpose +a I get 4 2 2 two is that + + align:start position:0% +a I get 4 2 2 two is that + + + align:start position:0% +a I get 4 2 2 two is that +right + + align:start position:0% +right + + + align:start position:0% +right +what's remarkable about that Matrix so + + align:start position:0% +what's remarkable about that Matrix so + + + align:start position:0% +what's remarkable about that Matrix so +here's my + + align:start position:0% +here's my + + + align:start position:0% +here's my +a here's my a + + align:start position:0% +a here's my a + + + align:start position:0% +a here's my a +transpose what's what can you tell me + + align:start position:0% +transpose what's what can you tell me + + + align:start position:0% +transpose what's what can you tell me +about that Matrix sprit symetric for + + align:start position:0% +about that Matrix sprit symetric for + + + align:start position:0% +about that Matrix sprit symetric for +sure and positive definite but is it the + + align:start position:0% +sure and positive definite but is it the + + + align:start position:0% +sure and positive definite but is it the +same as AA transpose I doubt it let's + + align:start position:0% +same as AA transpose I doubt it let's + + + align:start position:0% +same as AA transpose I doubt it let's +put them in the opposite order two 0 1 1 + + align:start position:0% +put them in the opposite order two 0 1 1 + + + align:start position:0% +put them in the opposite order two 0 1 1 +coming on this side of + + align:start position:0% +coming on this side of + + + align:start position:0% +coming on this side of +211 do the + + align:start position:0% +211 do the + + + align:start position:0% +211 do the +multiplication + + align:start position:0% +multiplication + + + align:start position:0% +multiplication +and what do I get I hope it's not the + + align:start position:0% +and what do I get I hope it's not the + + + align:start position:0% +and what do I get I hope it's not the +same five good five + + align:start position:0% +same five good five + + + align:start position:0% +same five good five +one one and + + align:start position:0% +one one and + + + align:start position:0% +one one and +one + + align:start position:0% +one + + + align:start position:0% +one +okay different Matrix that's the AA + + align:start position:0% +okay different Matrix that's the AA + + + align:start position:0% +okay different Matrix that's the AA +transpose Matrix so that so it will have + + align:start position:0% +transpose Matrix so that so it will have + + + align:start position:0% +transpose Matrix so that so it will have +different igen vectors but same igen + + align:start position:0% +different igen vectors but same igen + + + align:start position:0% +different igen vectors but same igen +values actually notice that we that had + + align:start position:0% +values actually notice that we that had + + + align:start position:0% +values actually notice that we that had +to happen here because one case we had + + align:start position:0% +to happen here because one case we had + + + align:start position:0% +to happen here because one case we had +anyway you know one case we had igen + + align:start position:0% +anyway you know one case we had igen + + + align:start position:0% +anyway you know one case we had igen +values of this and other case we had + + align:start position:0% +values of this and other case we had + + + align:start position:0% +values of this and other case we had +igen values of that and the beauty is + + align:start position:0% +igen values of that and the beauty is + + + align:start position:0% +igen values of that and the beauty is +that they're the same the igen values do + + align:start position:0% +that they're the same the igen values do + + + align:start position:0% +that they're the same the igen values do +do you any idea why the igen values of + + align:start position:0% +do you any idea why the igen values of + + + align:start position:0% +do you any idea why the igen values of +those two matrices if I if I reverse the + + align:start position:0% +those two matrices if I if I reverse the + + + align:start position:0% +those two matrices if I if I reverse the +order of + + align:start position:0% +order of + + + align:start position:0% +order of +multiplication I get a different Matrix + + align:start position:0% +multiplication I get a different Matrix + + + align:start position:0% +multiplication I get a different Matrix +but the IG values don't change so that's + + align:start position:0% +but the IG values don't change so that's + + + align:start position:0% +but the IG values don't change so that's +just good luck a and a a transpose a and + + align:start position:0% +just good luck a and a a transpose a and + + + align:start position:0% +just good luck a and a a transpose a and +a a transpose have the same I value so + + align:start position:0% +a a transpose have the same I value so + + + align:start position:0% +a a transpose have the same I value so +those I values are the singular values + + align:start position:0% +those I values are the singular values + + + align:start position:0% +those I values are the singular values +squared uh how would + + align:start position:0% +squared uh how would + + + align:start position:0% +squared uh how would +you convince me that those matrices had + + align:start position:0% +you convince me that those matrices had + + + align:start position:0% +you convince me that those matrices had +the same I values without actually + + align:start position:0% +the same I values without actually + + + align:start position:0% +the same I values without actually +Computing + + align:start position:0% + + + + align:start position:0% + +them you somebody would take + + align:start position:0% +them you somebody would take + + + align:start position:0% +them you somebody would take +the the sum the trace would be a good if + + align:start position:0% +the the sum the trace would be a good if + + + align:start position:0% +the the sum the trace would be a good if +that doesn't work we we we won't make it + + align:start position:0% +that doesn't work we we we won't make it + + + align:start position:0% +that doesn't work we we we won't make it +what's the trace of the two + + align:start position:0% +what's the trace of the two + + + align:start position:0% +what's the trace of the two +matrices both six so the igen values add + + align:start position:0% +matrices both six so the igen values add + + + align:start position:0% +matrices both six so the igen values add +up to this the same thing now I need one + + align:start position:0% +up to this the same thing now I need one + + + align:start position:0% +up to this the same thing now I need one +more fact of course to really be sure + + align:start position:0% +more fact of course to really be sure + + + align:start position:0% +more fact of course to really be sure +that they're the + + align:start position:0% +that they're the + + + align:start position:0% +that they're the +same it would be nice like if I knew the + + align:start position:0% +same it would be nice like if I knew the + + + align:start position:0% +same it would be nice like if I knew the +product of the igen + + align:start position:0% +product of the igen + + + align:start position:0% +product of the igen +values and that's the + + align:start position:0% +values and that's the + + + align:start position:0% +values and that's the +determinant so the sum of the igen + + align:start position:0% +determinant so the sum of the igen + + + align:start position:0% +determinant so the sum of the igen +values let me write that let me write + + align:start position:0% +values let me write that let me write + + + align:start position:0% +values let me write that let me write +those wonderful facts we we wrote before + + align:start position:0% +those wonderful facts we we wrote before + + + align:start position:0% +those wonderful facts we we wrote before +that the sum of the I values was the + + align:start position:0% +that the sum of the I values was the + + + align:start position:0% +that the sum of the I values was the +trace the sum down the equals the sum + + align:start position:0% +trace the sum down the equals the sum + + + align:start position:0% +trace the sum down the equals the sum +down the diagonal and the product of the + + align:start position:0% +down the diagonal and the product of the + + + align:start position:0% +down the diagonal and the product of the +IG value is the + + align:start position:0% +IG value is the + + + align:start position:0% +IG value is the +determinant those are the two decent + + align:start position:0% +determinant those are the two decent + + + align:start position:0% +determinant those are the two decent +facts about so and I hope that those + + align:start position:0% +facts about so and I hope that those + + + align:start position:0% +facts about so and I hope that those +matrices have the same + + align:start position:0% + + + + align:start position:0% + +determinant in fact yeah what's the + + align:start position:0% +determinant in fact yeah what's the + + + align:start position:0% +determinant in fact yeah what's the +determinant here four 5 minus one 8 + + align:start position:0% +determinant here four 5 minus one 8 + + + align:start position:0% +determinant here four 5 minus one 8 +minus 4 so in both cases the determinant + + align:start position:0% +minus 4 so in both cases the determinant + + + align:start position:0% +minus 4 so in both cases the determinant +is four and the trace is + + align:start position:0% +is four and the trace is + + + align:start position:0% +is four and the trace is +six and the igen values are whatever the + + align:start position:0% +six and the igen values are whatever the + + + align:start position:0% +six and the igen values are whatever the +two magic numbers are that multiply to + + align:start position:0% +two magic numbers are that multiply to + + + align:start position:0% +two magic numbers are that multiply to +give six and multiply to give four and + + align:start position:0% +give six and multiply to give four and + + + align:start position:0% +give six and multiply to give four and +add to give + + align:start position:0% +add to give + + + align:start position:0% +add to give +six that that's uh there' be some square + + align:start position:0% +six that that's uh there' be some square + + + align:start position:0% +six that that's uh there' be some square +roots in there but whatever they're the + + align:start position:0% +roots in there but whatever they're the + + + align:start position:0% +roots in there but whatever they're the +same okay so + + align:start position:0% +same okay so + + + align:start position:0% +same okay so +that well I have I've just sort of + + align:start position:0% +that well I have I've just sort of + + + align:start position:0% +that well I have I've just sort of +claimed that the SVD was worth your + + align:start position:0% +claimed that the SVD was worth your + + + align:start position:0% +claimed that the SVD was worth your +attention and I wanted to show that it + + align:start position:0% +attention and I wanted to show that it + + + align:start position:0% +attention and I wanted to show that it +came from the one we + + align:start position:0% +came from the one we + + + align:start position:0% +came from the one we +know now I guess I + + align:start position:0% +know now I guess I + + + align:start position:0% +know now I guess I +if time allows I ought to to be + + align:start position:0% +if time allows I ought to to be + + + align:start position:0% +if time allows I ought to to be +systematic + + align:start position:0% +systematic + + + align:start position:0% +systematic +here I should also show how this one + + align:start position:0% +here I should also show how this one + + + align:start position:0% +here I should also show how this one +connects to this one is that right I + + align:start position:0% +connects to this one is that right I + + + align:start position:0% +connects to this one is that right I +you're getting a lot of letters in this + + align:start position:0% +you're getting a lot of letters in this + + + align:start position:0% +you're getting a lot of letters in this +uh and not many numbers this was like a + + align:start position:0% +uh and not many numbers this was like a + + + align:start position:0% +uh and not many numbers this was like a +breather here to to uh do + + align:start position:0% +breather here to to uh do + + + align:start position:0% +breather here to to uh do +numbers uh but actually yeah maybe I + + align:start position:0% +numbers uh but actually yeah maybe I + + + align:start position:0% +numbers uh but actually yeah maybe I +could use that same example here yeah + + align:start position:0% +could use that same example here yeah + + + align:start position:0% +could use that same example here yeah +let me let me let let's get + + align:start position:0% +let me let me let let's get + + + align:start position:0% +let me let me let let's get +some numbers all right I I have to tell + + align:start position:0% +some numbers all right I I have to tell + + + align:start position:0% +some numbers all right I I have to tell +you that u i so I taught linear algebra + + align:start position:0% +you that u i so I taught linear algebra + + + align:start position:0% +you that u i so I taught linear algebra +this fall at MIT created a final exam + + align:start position:0% +this fall at MIT created a final exam + + + align:start position:0% +this fall at MIT created a final exam +got all typed up you know 280 copies + + align:start position:0% +got all typed up you know 280 copies + + + align:start position:0% +got all typed up you know 280 copies +Xerox and then went to sleep and I woke + + align:start position:0% +Xerox and then went to sleep and I woke + + + align:start position:0% +Xerox and then went to sleep and I woke +up early thinking I made that exam too + + align:start position:0% +up early thinking I made that exam too + + + align:start position:0% +up early thinking I made that exam too +hard uh this is this is like horrible uh + + align:start position:0% +hard uh this is this is like horrible uh + + + align:start position:0% +hard uh this is this is like horrible uh +because you spend a whole semester with + + align:start position:0% +because you spend a whole semester with + + + align:start position:0% +because you spend a whole semester with +a class your your friend you hope and uh + + align:start position:0% +a class your your friend you hope and uh + + + align:start position:0% +a class your your friend you hope and uh +and they're all coming to that exam at + + align:start position:0% +and they're all coming to that exam at + + + align:start position:0% +and they're all coming to that exam at +the end of December where their bag + + align:start position:0% +the end of December where their bag + + + align:start position:0% +the end of December where their bag +right you know their suitcase next to + + align:start position:0% +right you know their suitcase next to + + + align:start position:0% +right you know their suitcase next to +them they're going to The Plight and if + + align:start position:0% +them they're going to The Plight and if + + + align:start position:0% +them they're going to The Plight and if +you uh have made the exam too hard + + align:start position:0% +you uh have made the exam too hard + + + align:start position:0% +you uh have made the exam too hard +they're just uh not happy their whole + + align:start position:0% +they're just uh not happy their whole + + + align:start position:0% +they're just uh not happy their whole +Christmas is spoiled uh so + + align:start position:0% +Christmas is spoiled uh so + + + align:start position:0% +Christmas is spoiled uh so +um uh so I changed it a little to make + + align:start position:0% +um uh so I changed it a little to make + + + align:start position:0% +um uh so I changed it a little to make +it okay uh but still it was a bit on the + + align:start position:0% +it okay uh but still it was a bit on the + + + align:start position:0% +it okay uh but still it was a bit on the +hard side + + align:start position:0% +hard side + + + align:start position:0% +hard side +and it was mostly letters where I love + + align:start position:0% +and it was mostly letters where I love + + + align:start position:0% +and it was mostly letters where I love +to give examples I just messed up I just + + align:start position:0% +to give examples I just messed up I just + + + align:start position:0% +to give examples I just messed up I just +thought of too many problems in fact the + + align:start position:0% +thought of too many problems in fact the + + + align:start position:0% +thought of too many problems in fact the +first problem was the one that I'm going + + align:start position:0% +first problem was the one that I'm going + + + align:start position:0% +first problem was the one that I'm going +to tell you about if time allows the + + align:start position:0% +to tell you about if time allows the + + + align:start position:0% +to tell you about if time allows the +connection of that to that anyway too + + align:start position:0% +connection of that to that anyway too + + + align:start position:0% +connection of that to that anyway too +many letters and and and as they passed + + align:start position:0% +many letters and and and as they passed + + + align:start position:0% +many letters and and and as they passed +in the papers one of one guy in the + + align:start position:0% +in the papers one of one guy in the + + + align:start position:0% +in the papers one of one guy in the +class good humored guy said what have + + align:start position:0% +class good humored guy said what have + + + align:start position:0% +class good humored guy said what have +you got against numbers and I thought + + align:start position:0% +you got against numbers and I thought + + + align:start position:0% +you got against numbers and I thought +wait a minute to say that to a + + align:start position:0% +wait a minute to say that to a + + + align:start position:0% +wait a minute to say that to a +mathematician is really cruel but uh uh + + align:start position:0% +mathematician is really cruel but uh uh + + + align:start position:0% +mathematician is really cruel but uh uh +he was totally right that that the exam + + align:start position:0% +he was totally right that that the exam + + + align:start position:0% +he was totally right that that the exam +had been uh letters so and this was one + + align:start position:0% +had been uh letters so and this was one + + + align:start position:0% +had been uh letters so and this was one +of the questions so let me do it first + + align:start position:0% +of the questions so let me do it first + + + align:start position:0% +of the questions so let me do it first +with numbers here's our Matrix a what's + + align:start position:0% +with numbers here's our Matrix a what's + + + align:start position:0% +with numbers here's our Matrix a what's +what are the or now everybody spotting + + align:start position:0% +what are the or now everybody spotting + + + align:start position:0% +what are the or now everybody spotting +on the board what I'm doing I'm now + + align:start position:0% +on the board what I'm doing I'm now + + + align:start position:0% +on the board what I'm doing I'm now +doing the the orthogonal times upper + + align:start position:0% +doing the the orthogonal times upper + + + align:start position:0% +doing the the orthogonal times upper +triangular could you factor that one + + align:start position:0% +triangular could you factor that one + + + align:start position:0% +triangular could you factor that one +into an orthogonal times an upper + + align:start position:0% +into an orthogonal times an upper + + + align:start position:0% +into an orthogonal times an upper +triangular + + align:start position:0% +triangular + + + align:start position:0% +triangular +so it's like it's like the first this + + align:start position:0% +so it's like it's like the first this + + + align:start position:0% +so it's like it's like the first this +First Column is the two + + align:start position:0% + + + + align:start position:0% + +vector and the second column is the one + + align:start position:0% +vector and the second column is the one + + + align:start position:0% +vector and the second column is the one +one vector yeah look our pictures fits + + align:start position:0% +one vector yeah look our pictures fits + + + align:start position:0% +one vector yeah look our pictures fits +the + + align:start position:0% +the + + + align:start position:0% +the +problem what's what are the what's the + + align:start position:0% +problem what's what are the what's the + + + align:start position:0% +problem what's what are the what's the +what are what are the orthogonal guys + + align:start position:0% +what are what are the orthogonal guys + + + align:start position:0% +what are what are the orthogonal guys +that Graham Schmidt would struggle to + + align:start position:0% +that Graham Schmidt would struggle to + + + align:start position:0% +that Graham Schmidt would struggle to +find tell tell me what the orthogonal + + align:start position:0% +find tell tell me what the orthogonal + + + align:start position:0% +find tell tell me what the orthogonal +Matrix is that comes from that okay + + align:start position:0% +Matrix is that comes from that okay + + + align:start position:0% +Matrix is that comes from that okay +what's the what's the guy in this + + align:start position:0% +what's the what's the guy in this + + + align:start position:0% +what's the what's the guy in this +Direction one zero right because we want + + align:start position:0% +Direction one zero right because we want + + + align:start position:0% +Direction one zero right because we want +a unit Factor so we just scale it what's + + align:start position:0% +a unit Factor so we just scale it what's + + + align:start position:0% +a unit Factor so we just scale it what's +the other + + align:start position:0% +the other + + + align:start position:0% +the other +one 01 because it's the projection it's + + align:start position:0% +one 01 because it's the projection it's + + + align:start position:0% +one 01 because it's the projection it's +the guy in this direction and then + + align:start position:0% +the guy in this direction and then + + + align:start position:0% +the guy in this direction and then +stretched out to a unit Vector so + + align:start position:0% +stretched out to a unit Vector so + + + align:start position:0% +stretched out to a unit Vector so +01 so what's our Matrix Q in this case + + align:start position:0% +01 so what's our Matrix Q in this case + + + align:start position:0% +01 so what's our Matrix Q in this case +oh I've got to got to got the whole + + align:start position:0% +oh I've got to got to got the whole + + + align:start position:0% +oh I've got to got to got the whole +thing here here's our + + align:start position:0% +thing here here's our + + + align:start position:0% +thing here here's our +Matrix and I'm factoring it into + + align:start position:0% + + + + align:start position:0% + +into uh what's the orthogonal Matrix and + + align:start position:0% +into uh what's the orthogonal Matrix and + + + align:start position:0% +into uh what's the orthogonal Matrix and +what's the upper + + align:start position:0% +what's the upper + + + align:start position:0% +what's the upper +triangle so that was this was the one + + align:start position:0% +triangle so that was this was the one + + + align:start position:0% +triangle so that was this was the one +zero okay well everybody knows what that + + align:start position:0% +zero okay well everybody knows what that + + + align:start position:0% +zero okay well everybody knows what that +orthogonal Matrix has turned out to + + align:start position:0% + + + + align:start position:0% + +be oh God this is falling apart isn't it + + align:start position:0% +be oh God this is falling apart isn't it + + + align:start position:0% +be oh God this is falling apart isn't it +uh what's the what I'm upper triangular + + align:start position:0% +uh what's the what I'm upper triangular + + + align:start position:0% +uh what's the what I'm upper triangular +to start + + align:start position:0% +to start + + + align:start position:0% +to start +with oh jeez take that off the tape uh + + align:start position:0% +with oh jeez take that off the tape uh + + + align:start position:0% +with oh jeez take that off the tape uh +uh SE triangular of course this is the + + align:start position:0% +uh SE triangular of course this is the + + + align:start position:0% +uh SE triangular of course this is the +that's the orthogonal Matrix and then + + align:start position:0% +that's the orthogonal Matrix and then + + + align:start position:0% +that's the orthogonal Matrix and then +here's my happy little matric again okay + + align:start position:0% +here's my happy little matric again okay + + + align:start position:0% +here's my happy little matric again okay +well that was a brilliant + + align:start position:0% +well that was a brilliant + + + align:start position:0% +well that was a brilliant +factorization okay that goes down in + + align:start position:0% +factorization okay that goes down in + + + align:start position:0% +factorization okay that goes down in +history unfortunately all right now + + align:start position:0% +history unfortunately all right now + + + align:start position:0% +history unfortunately all right now +what's the connection with uh with + + align:start position:0% +what's the connection with uh with + + + align:start position:0% +what's the connection with uh with +um so the idea is that that should + + align:start position:0% +um so the idea is that that should + + + align:start position:0% +um so the idea is that that should +somehow connect with the LDL transpose + + align:start position:0% +somehow connect with the LDL transpose + + + align:start position:0% +somehow connect with the LDL transpose +for or a transpose a holy + + align:start position:0% +for or a transpose a holy + + + align:start position:0% +for or a transpose a holy +Moses + + align:start position:0% +Moses + + + align:start position:0% +Moses +uh yes I have a square Matrix right I + + align:start position:0% +uh yes I have a square Matrix right I + + + align:start position:0% +uh yes I have a square Matrix right I +have a square Matrix that's not anything + + align:start position:0% +have a square Matrix that's not anything + + + align:start position:0% +have a square Matrix that's not anything +nice hasn't got any it's square + + align:start position:0% +nice hasn't got any it's square + + + align:start position:0% +nice hasn't got any it's square +but it's not it NE it happened to be + + align:start position:0% +but it's not it NE it happened to be + + + align:start position:0% +but it's not it NE it happened to be +upper triangular yeah that that's I + + align:start position:0% +upper triangular yeah that that's I + + + align:start position:0% +upper triangular yeah that that's I +should have made it maybe like Z2 then + + align:start position:0% +should have made it maybe like Z2 then + + + align:start position:0% +should have made it maybe like Z2 then +then at least it would have been a + + align:start position:0% +then at least it would have been a + + + align:start position:0% +then at least it would have been a +little little something to + + align:start position:0% +little little something to + + + align:start position:0% +little little something to +do which is like to close with see I've + + align:start position:0% +do which is like to close with see I've + + + align:start position:0% +do which is like to close with see I've +got 30 seconds I I could let me let me + + align:start position:0% +got 30 seconds I I could let me let me + + + align:start position:0% +got 30 seconds I I could let me let me +tell you on the on the notes for the + + align:start position:0% +tell you on the on the notes for the + + + align:start position:0% +tell you on the on the notes for the +lecture rather than just like you can + + align:start position:0% +lecture rather than just like you can + + + align:start position:0% +lecture rather than just like you can +only take in so much in these two hours + + align:start position:0% +only take in so much in these two hours + + + align:start position:0% +only take in so much in these two hours +I think you guys are terrific uh + + align:start position:0% +I think you guys are terrific uh + + + align:start position:0% +I think you guys are terrific uh +um so let me put in the notes that this + + align:start position:0% +um so let me put in the notes that this + + + align:start position:0% +um so let me put in the notes that this +that this triangular factor is + + align:start position:0% +that this triangular factor is + + + align:start position:0% +that this triangular factor is +associated with this + + align:start position:0% +associated with this + + + align:start position:0% +associated with this +guy in fact I need I'll take a square + + align:start position:0% +guy in fact I need I'll take a square + + + align:start position:0% +guy in fact I need I'll take a square +root of D over so the are R here that's + + align:start position:0% +root of D over so the are R here that's + + + align:start position:0% +root of D over so the are R here that's +the connection is the r here is the + + align:start position:0% +the connection is the r here is the + + + align:start position:0% +the connection is the r here is the +square root of D so I I I need I just + + align:start position:0% +square root of D so I I I need I just + + + align:start position:0% +square root of D so I I I need I just +need to split this apart into D the one + + align:start position:0% +need to split this apart into D the one + + + align:start position:0% +need to split this apart into D the one +d the2 d the2 + + align:start position:0% + + + + align:start position:0% + +here I need to just just taking square + + align:start position:0% +here I need to just just taking square + + + align:start position:0% +here I need to just just taking square +roots of those pivots and I wanted them + + align:start position:0% +roots of those pivots and I wanted them + + + align:start position:0% +roots of those pivots and I wanted them +to be positive of course to take the + + align:start position:0% +to be positive of course to take the + + + align:start position:0% +to be positive of course to take the +square roots that's why I'm happy that + + align:start position:0% +square roots that's why I'm happy that + + + align:start position:0% +square roots that's why I'm happy that +have this positive so there's my + + align:start position:0% +have this positive so there's my + + + align:start position:0% +have this positive so there's my +r there's my R that's the connection + + align:start position:0% +r there's my R that's the connection + + + align:start position:0% +r there's my R that's the connection +there and then and then this guy is + + align:start position:0% +there and then and then this guy is + + + align:start position:0% +there and then and then this guy is +whatever it has to be I started with an + + align:start position:0% +whatever it has to be I started with an + + + align:start position:0% +whatever it has to be I started with an +a the r is this and then whatever is + + align:start position:0% +a the r is this and then whatever is + + + align:start position:0% +a the r is this and then whatever is +left is that and it turns out to be + + align:start position:0% +left is that and it turns out to be + + + align:start position:0% +left is that and it turns out to be +orthod I'll put that in the + + align:start position:0% +orthod I'll put that in the + + + align:start position:0% +orthod I'll put that in the +notes stay with me one more moment just + + align:start position:0% +notes stay with me one more moment just + + + align:start position:0% +notes stay with me one more moment just +so I don't go down with such a + + align:start position:0% +so I don't go down with such a + + + align:start position:0% +so I don't go down with such a +contemptible example uh and I'll I'll + + align:start position:0% +contemptible example uh and I'll I'll + + + align:start position:0% +contemptible example uh and I'll I'll +just uh I'll just just all I'll do is uh + + align:start position:0% +just uh I'll just just all I'll do is uh + + + align:start position:0% +just uh I'll just just all I'll do is uh +do the same example with + + align:start position:0% +do the same example with + + + align:start position:0% +do the same example with +uh with a matrix that's not + + align:start position:0% +uh with a matrix that's not + + + align:start position:0% +uh with a matrix that's not +quite + + align:start position:0% +quite + + + align:start position:0% +quite +um upper triangular already I'll make it + + align:start position:0% +um upper triangular already I'll make it + + + align:start position:0% +um upper triangular already I'll make it +this + + align:start position:0% +this + + + align:start position:0% +this +one okay so my two vectors are yeah tell + + align:start position:0% +one okay so my two vectors are yeah tell + + + align:start position:0% +one okay so my two vectors are yeah tell +me now my two orthogonal vectors and my + + align:start position:0% +me now my two orthogonal vectors and my + + + align:start position:0% +me now my two orthogonal vectors and my +upper triangular + + align:start position:0% + + + + align:start position:0% + +guy + + align:start position:0% +guy + + + align:start position:0% +guy +okay do Graham Schmidt so the first + + align:start position:0% +okay do Graham Schmidt so the first + + + align:start position:0% +okay do Graham Schmidt so the first +Vector is 02 and I want it to normalize + + align:start position:0% +Vector is 02 and I want it to normalize + + + align:start position:0% +Vector is 02 and I want it to normalize +it to be + + align:start position:0% +it to be + + + align:start position:0% +it to be +01 and then the other guy you can pretty + + align:start position:0% +01 and then the other guy you can pretty + + + align:start position:0% +01 and then the other guy you can pretty +well + + align:start position:0% +well + + + align:start position:0% +well +guess it'll be + + align:start position:0% +guess it'll be + + + align:start position:0% +guess it'll be +orthonormal so it'll be one + + align:start position:0% + + + + align:start position:0% + +zero and now what's this Matrix come out + + align:start position:0% +zero and now what's this Matrix come out + + + align:start position:0% +zero and now what's this Matrix come out +to + + align:start position:0% +to + + + align:start position:0% +to +be let's see this is just going to + + align:start position:0% +be let's see this is just going to + + + align:start position:0% +be let's see this is just going to +exchange the rows right + + align:start position:0% +exchange the rows right + + + align:start position:0% +exchange the rows right +so I better exchange those + + align:start position:0% +so I better exchange those + + + align:start position:0% +so I better exchange those +rows to uh + + align:start position:0% +rows to uh + + + align:start position:0% +rows to uh +yeah so that example is marginally + + align:start position:0% +yeah so that example is marginally + + + align:start position:0% +yeah so that example is marginally +better uh at least I didn't have the + + align:start position:0% +better uh at least I didn't have the + + + align:start position:0% +better uh at least I didn't have the +identity Matrix and I did have to + + align:start position:0% +identity Matrix and I did have to + + + align:start position:0% +identity Matrix and I did have to +exchange rows but of course if I change + + align:start position:0% +exchange rows but of course if I change + + + align:start position:0% +exchange rows but of course if I change +that zero to a six I'll have all sorts + + align:start position:0% +that zero to a six I'll have all sorts + + + align:start position:0% +that zero to a six I'll have all sorts +of square roots and so on because Graham + + align:start position:0% +of square roots and so on because Graham + + + align:start position:0% +of square roots and so on because Graham +Schmidt always produces square roots + + align:start position:0% +Schmidt always produces square roots + + + align:start position:0% +Schmidt always produces square roots +because it when as soon as you normalize + + align:start position:0% +because it when as soon as you normalize + + + align:start position:0% +because it when as soon as you normalize +a length one you have to divide by a + + align:start position:0% +a length one you have to divide by a + + + align:start position:0% +a length one you have to divide by a +length a square root and and uh it + + align:start position:0% +length a square root and and uh it + + + align:start position:0% +length a square root and and uh it +doesn't look so beautiful so this was a + + align:start position:0% +doesn't look so beautiful so this was a + + + align:start position:0% +doesn't look so beautiful so this was a +beautiful but almost as uh special a + + align:start position:0% +beautiful but almost as uh special a + + + align:start position:0% +beautiful but almost as uh special a +case as the first one okay uh we + + align:start position:0% +case as the first one okay uh we + + + align:start position:0% +case as the first one okay uh we +will have separate discussion + + align:start position:0% +will have separate discussion + + + align:start position:0% +will have separate discussion +of the uses of QR Graham Schmid and the + + align:start position:0% +of the uses of QR Graham Schmid and the + + + align:start position:0% +of the uses of QR Graham Schmid and the +uses of + + align:start position:0% +uses of + + + align:start position:0% +uses of +SVD this guy so uh this isn't our last + + align:start position:0% +SVD this guy so uh this isn't our last + + + align:start position:0% +SVD this guy so uh this isn't our last +look by any means at these uh at these + + align:start position:0% +look by any means at these uh at these + + + align:start position:0% +look by any means at these uh at these +four Central factorizations of linear + + align:start position:0% +four Central factorizations of linear + + + align:start position:0% +four Central factorizations of linear +algebra okay so I'll put more into the + + align:start position:0% +algebra okay so I'll put more into the + + + align:start position:0% +algebra okay so I'll put more into the +notes including the connection there + + align:start position:0% +notes including the connection there + + + align:start position:0% +notes including the connection there +that didn't make it into the + + align:start position:0% +that didn't make it into the + + + align:start position:0% +that didn't make it into the +presentation but uh um so that and I'll + + align:start position:0% +presentation but uh um so that and I'll + + + align:start position:0% +presentation but uh um so that and I'll +suggest some uh exercises too in the + + align:start position:0% +suggest some uh exercises too in the + + + align:start position:0% +suggest some uh exercises too in the +notes Okay so you next Thursday then + + align:start position:0% +notes Okay so you next Thursday then + + + align:start position:0% +notes Okay so you next Thursday then +good \ No newline at end of file diff --git a/ehZgJ8Y2UJI.txt b/ehZgJ8Y2UJI.txt new file mode 100644 index 0000000000000000000000000000000000000000..f28a9fcaddf3e64d80daccecb947a3739a973419 --- /dev/null +++ b/ehZgJ8Y2UJI.txt @@ -0,0 +1,1507 @@ +align:start position:0% + +hello my name is siin I am a visiting + + align:start position:0% +hello my name is siin I am a visiting + + + align:start position:0% +hello my name is siin I am a visiting +scholar in am it UTM sustainable City + + align:start position:0% +scholar in am it UTM sustainable City + + + align:start position:0% +scholar in am it UTM sustainable City +program in this video I will be + + align:start position:0% +program in this video I will be + + + align:start position:0% +program in this video I will be +reviewing the Sid River restoration + + align:start position:0% +reviewing the Sid River restoration + + + align:start position:0% +reviewing the Sid River restoration +project as a good example of sustainable + + align:start position:0% +project as a good example of sustainable + + + align:start position:0% +project as a good example of sustainable +City tourism development in Malaysia for + + align:start position:0% +City tourism development in Malaysia for + + + align:start position:0% +City tourism development in Malaysia for +Cent people have live along rivers + + align:start position:0% +Cent people have live along rivers + + + align:start position:0% +Cent people have live along rivers +rivers are a source of Life they provide + + align:start position:0% +rivers are a source of Life they provide + + + align:start position:0% +rivers are a source of Life they provide +water food + + align:start position:0% +water food + + + align:start position:0% +water food +Transportation places for recreation and + + align:start position:0% +Transportation places for recreation and + + + align:start position:0% +Transportation places for recreation and +much more for these reasons cities + + align:start position:0% +much more for these reasons cities + + + align:start position:0% +much more for these reasons cities +around the world are connected to Rivers + + align:start position:0% +around the world are connected to Rivers + + + align:start position:0% +around the world are connected to Rivers +as more and more people seek to live in + + align:start position:0% +as more and more people seek to live in + + + align:start position:0% +as more and more people seek to live in +cities driving up land prices many Urban + + align:start position:0% +cities driving up land prices many Urban + + + align:start position:0% +cities driving up land prices many Urban +Rivers has been filled in to make space + + align:start position:0% +Rivers has been filled in to make space + + + align:start position:0% +Rivers has been filled in to make space +for growing + + align:start position:0% +for growing + + + align:start position:0% +for growing +populations unfortunately filling in + + align:start position:0% +populations unfortunately filling in + + + align:start position:0% +populations unfortunately filling in +rivers conversion flooding and water + + align:start position:0% +rivers conversion flooding and water + + + align:start position:0% +rivers conversion flooding and water +pollution problems some country regret + + align:start position:0% +pollution problems some country regret + + + align:start position:0% +pollution problems some country regret +having fill in their rivers and are + + align:start position:0% +having fill in their rivers and are + + + align:start position:0% +having fill in their rivers and are +trying to restore them Malaysia is one + + align:start position:0% +trying to restore them Malaysia is one + + + align:start position:0% +trying to restore them Malaysia is one +such example the SED River flow through + + align:start position:0% +such example the SED River flow through + + + align:start position:0% +such example the SED River flow through +the center of Cho baru the capital of + + align:start position:0% +the center of Cho baru the capital of + + + align:start position:0% +the center of Cho baru the capital of +Cho state in Malaysia the senit river + + align:start position:0% +Cho state in Malaysia the senit river + + + align:start position:0% +Cho state in Malaysia the senit river +used to be the primary water way and a + + align:start position:0% +used to be the primary water way and a + + + align:start position:0% +used to be the primary water way and a +source of life for many people when + + align:start position:0% +source of life for many people when + + + align:start position:0% +source of life for many people when +chobu was a small town people sold their + + align:start position:0% +chobu was a small town people sold their + + + align:start position:0% +chobu was a small town people sold their +products from their boats for many the + + align:start position:0% +products from their boats for many the + + + align:start position:0% +products from their boats for many the +senit river was a source of their + + align:start position:0% +senit river was a source of their + + + align:start position:0% +senit river was a source of their +cultural identity joob baru has become + + align:start position:0% +cultural identity joob baru has become + + + align:start position:0% +cultural identity joob baru has become +the second largest city in Malaysia it + + align:start position:0% +the second largest city in Malaysia it + + + align:start position:0% +the second largest city in Malaysia it +was also seriously polluted many people + + align:start position:0% +was also seriously polluted many people + + + align:start position:0% +was also seriously polluted many people +avoided going near the river because of + + align:start position:0% +avoided going near the river because of + + + align:start position:0% +avoided going near the river because of +its strong order tourists had no + + align:start position:0% +its strong order tourists had no + + + align:start position:0% +its strong order tourists had no +interest in coming to the city they used + + align:start position:0% +interest in coming to the city they used + + + align:start position:0% +interest in coming to the city they used +it only as a layover on their way to + + align:start position:0% +it only as a layover on their way to + + + align:start position:0% +it only as a layover on their way to +Singapore kalal lumur or Mala in 2005 + + align:start position:0% +Singapore kalal lumur or Mala in 2005 + + + align:start position:0% +Singapore kalal lumur or Mala in 2005 +the city decided to cover up the river + + align:start position:0% +the city decided to cover up the river + + + align:start position:0% +the city decided to cover up the river +to use it as a sewage system and a main + + align:start position:0% +to use it as a sewage system and a main + + + align:start position:0% +to use it as a sewage system and a main +road when the cover was added flooding + + align:start position:0% +road when the cover was added flooding + + + align:start position:0% +road when the cover was added flooding +version now joobu wants to become a + + align:start position:0% +version now joobu wants to become a + + + align:start position:0% +version now joobu wants to become a +world- class City it seek to expand + + align:start position:0% +world- class City it seek to expand + + + align:start position:0% +world- class City it seek to expand +tourism to achieve this goal the city + + align:start position:0% +tourism to achieve this goal the city + + + align:start position:0% +tourism to achieve this goal the city +want to restore the sinked river to do + + align:start position:0% +want to restore the sinked river to do + + + align:start position:0% +want to restore the sinked river to do +this it will take the cover of build + + align:start position:0% +this it will take the cover of build + + + align:start position:0% +this it will take the cover of build +water treatment plans introduce flood + + align:start position:0% +water treatment plans introduce flood + + + align:start position:0% +water treatment plans introduce flood +mitigation system + + align:start position:0% +mitigation system + + + align:start position:0% +mitigation system +and beautify the river making it + + align:start position:0% +and beautify the river making it + + + align:start position:0% +and beautify the river making it +attractive for recreation and business + + align:start position:0% +attractive for recreation and business + + + align:start position:0% +attractive for recreation and business +Mr abim a project management officer + + align:start position:0% +Mr abim a project management officer + + + align:start position:0% +Mr abim a project management officer +from the iscandal regional Development + + align:start position:0% +from the iscandal regional Development + + + align:start position:0% +from the iscandal regional Development +Authority explain the rational we + + align:start position:0% +Authority explain the rational we + + + align:start position:0% +Authority explain the rational we +identify that joobu uh suffers we what + + align:start position:0% +identify that joobu uh suffers we what + + + align:start position:0% +identify that joobu uh suffers we what +we call it Urban Decay syndrome where + + align:start position:0% +we call it Urban Decay syndrome where + + + align:start position:0% +we call it Urban Decay syndrome where +there's no population declining + + align:start position:0% +there's no population declining + + + align:start position:0% +there's no population declining +businesses and then uh no + + align:start position:0% +businesses and then uh no + + + align:start position:0% +businesses and then uh no +activities uh + + align:start position:0% +activities uh + + + align:start position:0% +activities uh +Su seate is heavily polluted and they + + align:start position:0% +Su seate is heavily polluted and they + + + align:start position:0% +Su seate is heavily polluted and they +they say that joho is Melly because of + + align:start position:0% +they say that joho is Melly because of + + + align:start position:0% +they say that joho is Melly because of +untreated uh point source of pollution + + align:start position:0% +untreated uh point source of pollution + + + align:start position:0% +untreated uh point source of pollution +again no pollution no business and all + + align:start position:0% +again no pollution no business and all + + + align:start position:0% +again no pollution no business and all +that so uh with that U issues or what we + + align:start position:0% +that so uh with that U issues or what we + + + align:start position:0% +that so uh with that U issues or what we +call it Urban uh Decay syndrome we + + align:start position:0% +call it Urban uh Decay syndrome we + + + align:start position:0% +call it Urban uh Decay syndrome we +initiated this jaru transformation + + align:start position:0% +initiated this jaru transformation + + + align:start position:0% +initiated this jaru transformation +program uh and then we seek Government + + align:start position:0% +program uh and then we seek Government + + + align:start position:0% +program uh and then we seek Government +funding uh Federal govern + + align:start position:0% +funding uh Federal govern + + + align:start position:0% +funding uh Federal govern +funding uh in uh this initiative started + + align:start position:0% +funding uh in uh this initiative started + + + align:start position:0% +funding uh in uh this initiative started +2010 uh in detail we do the all the + + align:start position:0% +2010 uh in detail we do the all the + + + align:start position:0% +2010 uh in detail we do the all the +design calculation design detailing so + + align:start position:0% +design calculation design detailing so + + + align:start position:0% +design calculation design detailing so +uh alhamdulillah we successfully secure + + align:start position:0% +uh alhamdulillah we successfully secure + + + align:start position:0% +uh alhamdulillah we successfully secure +Government funding about a seeding cost + + align:start position:0% +Government funding about a seeding cost + + + align:start position:0% +Government funding about a seeding cost +about 240 million for this project at + + align:start position:0% +about 240 million for this project at + + + align:start position:0% +about 240 million for this project at +first up the river in the middle + + align:start position:0% +first up the river in the middle + + + align:start position:0% +first up the river in the middle +of the city sounded like a crazy idea + + align:start position:0% +of the city sounded like a crazy idea + + + align:start position:0% +of the city sounded like a crazy idea +the cost would be substantial and a lot + + align:start position:0% +the cost would be substantial and a lot + + + align:start position:0% +the cost would be substantial and a lot +of people would be affected my recent + + align:start position:0% +of people would be affected my recent + + + align:start position:0% +of people would be affected my recent +study of Cho's effort to promote + + align:start position:0% +study of Cho's effort to promote + + + align:start position:0% +study of Cho's effort to promote +sustainable City tourism found that the + + align:start position:0% +sustainable City tourism found that the + + + align:start position:0% +sustainable City tourism found that the +senit river restoration project is a + + align:start position:0% +senit river restoration project is a + + + align:start position:0% +senit river restoration project is a +valuable and noteworthy idea Mrs noai + + align:start position:0% +valuable and noteworthy idea Mrs noai + + + align:start position:0% +valuable and noteworthy idea Mrs noai +Sur benti a city planner explained how + + align:start position:0% +Sur benti a city planner explained how + + + align:start position:0% +Sur benti a city planner explained how +chob Bahu is seeking to promote + + align:start position:0% +chob Bahu is seeking to promote + + + align:start position:0% +chob Bahu is seeking to promote +Environmental and Cultural conservation + + align:start position:0% +Environmental and Cultural conservation + + + align:start position:0% +Environmental and Cultural conservation +Foster Economic Development and ensure + + align:start position:0% +Foster Economic Development and ensure + + + align:start position:0% +Foster Economic Development and ensure +physical connectivity and workability so + + align:start position:0% +physical connectivity and workability so + + + align:start position:0% +physical connectivity and workability so +the lesson learn by covering the river + + align:start position:0% +the lesson learn by covering the river + + + align:start position:0% +the lesson learn by covering the river +is is only the the the shortterm + + align:start position:0% +is is only the the the shortterm + + + align:start position:0% +is is only the the the shortterm +shortterm solution yeah for the + + align:start position:0% +shortterm solution yeah for the + + + align:start position:0% +shortterm solution yeah for the +long-term + + align:start position:0% +long-term + + + align:start position:0% +long-term +solution this is what we did on the side + + align:start position:0% +solution this is what we did on the side + + + align:start position:0% +solution this is what we did on the side +we try to settle the environment issue + + align:start position:0% +we try to settle the environment issue + + + align:start position:0% +we try to settle the environment issue +the flood issue we try to make it the + + align:start position:0% +the flood issue we try to make it the + + + align:start position:0% +the flood issue we try to make it the +river as a The Heart of the City to make + + align:start position:0% +river as a The Heart of the City to make + + + align:start position:0% +river as a The Heart of the City to make +it vibrant City we have to do that + + align:start position:0% +it vibrant City we have to do that + + + align:start position:0% +it vibrant City we have to do that +there's a lot of history for + + align:start position:0% +there's a lot of history for + + + align:start position:0% +there's a lot of history for +Center so it's so important for JBC + + align:start position:0% +Center so it's so important for JBC + + + align:start position:0% +Center so it's so important for JBC +Center actually we want to to increase + + align:start position:0% +Center actually we want to to increase + + + align:start position:0% +Center actually we want to to increase +the economic value environment and the + + align:start position:0% +the economic value environment and the + + + align:start position:0% +the economic value environment and the +identity of joobu and now we are trying + + align:start position:0% +identity of joobu and now we are trying + + + align:start position:0% +identity of joobu and now we are trying +to rebranding the image and identity of + + align:start position:0% +to rebranding the image and identity of + + + align:start position:0% +to rebranding the image and identity of +joob baru we want the new brand for joob + + align:start position:0% +joob baru we want the new brand for joob + + + align:start position:0% +joob baru we want the new brand for joob +baru City Center so we Benchmark at + + align:start position:0% +baru City Center so we Benchmark at + + + align:start position:0% +baru City Center so we Benchmark at +Korea just exactly like that we want to + + align:start position:0% +Korea just exactly like that we want to + + + align:start position:0% +Korea just exactly like that we want to +to promote uh Su SE as a new product in + + align:start position:0% +to promote uh Su SE as a new product in + + + align:start position:0% +to promote uh Su SE as a new product in +JBC Center must + + align:start position:0% +JBC Center must + + + align:start position:0% +JBC Center must +visit uh it's good for environment it's + + align:start position:0% +visit uh it's good for environment it's + + + align:start position:0% +visit uh it's good for environment it's +good for the image of the city it's good + + align:start position:0% +good for the image of the city it's good + + + align:start position:0% +good for the image of the city it's good +for the public the tourist if you can + + align:start position:0% +for the public the tourist if you can + + + align:start position:0% +for the public the tourist if you can +see the future image for Su SE I think + + align:start position:0% +see the future image for Su SE I think + + + align:start position:0% +see the future image for Su SE I think +all the joran will be proud yes the s + + align:start position:0% +all the joran will be proud yes the s + + + align:start position:0% +all the joran will be proud yes the s +River restoration projects also + + align:start position:0% +River restoration projects also + + + align:start position:0% +River restoration projects also +illustrate important of democratic + + align:start position:0% +illustrate important of democratic + + + align:start position:0% +illustrate important of democratic +governance as a part of sustainable City + + align:start position:0% +governance as a part of sustainable City + + + align:start position:0% +governance as a part of sustainable City +tourism development chob baru has been + + align:start position:0% +tourism development chob baru has been + + + align:start position:0% +tourism development chob baru has been +able to make great stries by Consulting + + align:start position:0% +able to make great stries by Consulting + + + align:start position:0% +able to make great stries by Consulting +with stakeholders minimizing social + + align:start position:0% +with stakeholders minimizing social + + + align:start position:0% +with stakeholders minimizing social +impacts providing Fair compensation and + + align:start position:0% +impacts providing Fair compensation and + + + align:start position:0% +impacts providing Fair compensation and +building strong Partnerships Mr AB halim + + align:start position:0% +building strong Partnerships Mr AB halim + + + align:start position:0% +building strong Partnerships Mr AB halim +explain how Democratic governance has + + align:start position:0% +explain how Democratic governance has + + + align:start position:0% +explain how Democratic governance has +been used to win the public support we + + align:start position:0% +been used to win the public support we + + + align:start position:0% +been used to win the public support we +do a lot of Engagement with her + + align:start position:0% +do a lot of Engagement with her + + + align:start position:0% +do a lot of Engagement with her +stakeholders we call it a focus group + + align:start position:0% +stakeholders we call it a focus group + + + align:start position:0% +stakeholders we call it a focus group +discussion meetings and workshop and + + align:start position:0% +discussion meetings and workshop and + + + align:start position:0% +discussion meetings and workshop and +onetoone discussion the first one uh we + + align:start position:0% +onetoone discussion the first one uh we + + + align:start position:0% +onetoone discussion the first one uh we +started with all the building owners the + + align:start position:0% +started with all the building owners the + + + align:start position:0% +started with all the building owners the +big big players like uh + + align:start position:0% +big big players like uh + + + align:start position:0% +big big players like uh +kta uh City Square public bank and all + + align:start position:0% +kta uh City Square public bank and all + + + align:start position:0% +kta uh City Square public bank and all +the big big business owners in this area + + align:start position:0% +the big big business owners in this area + + + align:start position:0% +the big big business owners in this area +so we want to know what is their + + align:start position:0% +so we want to know what is their + + + align:start position:0% +so we want to know what is their +acceptance towards this uh project + + align:start position:0% +acceptance towards this uh project + + + align:start position:0% +acceptance towards this uh project +including what kind of environment that + + align:start position:0% +including what kind of environment that + + + align:start position:0% +including what kind of environment that +they want to see within this area the + + align:start position:0% +they want to see within this area the + + + align:start position:0% +they want to see within this area the +first uh proposal uh designed for this + + align:start position:0% +first uh proposal uh designed for this + + + align:start position:0% +first uh proposal uh designed for this +area it want to make it as fully + + align:start position:0% +area it want to make it as fully + + + align:start position:0% +area it want to make it as fully +pedestrianized there's no Moto uh + + align:start position:0% +pedestrianized there's no Moto uh + + + align:start position:0% +pedestrianized there's no Moto uh +vehicle to be uh at Jalan war of so we + + align:start position:0% +vehicle to be uh at Jalan war of so we + + + align:start position:0% +vehicle to be uh at Jalan war of so we +want to make it fiz so after we engage + + align:start position:0% +want to make it fiz so after we engage + + + align:start position:0% +want to make it fiz so after we engage +with all the stakeholders they not agree + + align:start position:0% +with all the stakeholders they not agree + + + align:start position:0% +with all the stakeholders they not agree +they say that the jalam AFU is a main + + align:start position:0% +they say that the jalam AFU is a main + + + align:start position:0% +they say that the jalam AFU is a main +terare of joobu there's no uh benefit of + + align:start position:0% +terare of joobu there's no uh benefit of + + + align:start position:0% +terare of joobu there's no uh benefit of +doing this so we come back to uh + + align:start position:0% +doing this so we come back to uh + + + align:start position:0% +doing this so we come back to uh +combination of uh River Rejuvenation and + + align:start position:0% +combination of uh River Rejuvenation and + + + align:start position:0% +combination of uh River Rejuvenation and +uh some sort of uh public transport + + align:start position:0% +uh some sort of uh public transport + + + align:start position:0% +uh some sort of uh public transport +though his shop was badly affected by + + align:start position:0% +though his shop was badly affected by + + + align:start position:0% +though his shop was badly affected by +the construction Mr Chan liim was happy + + align:start position:0% +the construction Mr Chan liim was happy + + + align:start position:0% +the construction Mr Chan liim was happy +with the + + align:start position:0% + + + + align:start position:0% + +project minimizing social impact is + + align:start position:0% +project minimizing social impact is + + + align:start position:0% +project minimizing social impact is +important for public project management + + align:start position:0% +important for public project management + + + align:start position:0% +important for public project management +but having a long-term plan such as a + + align:start position:0% +but having a long-term plan such as a + + + align:start position:0% +but having a long-term plan such as a +city master plan is a major asset for + + align:start position:0% +city master plan is a major asset for + + + align:start position:0% +city master plan is a major asset for +the project the plan provides an overall + + align:start position:0% +the project the plan provides an overall + + + align:start position:0% +the project the plan provides an overall +framework and TR resources Mr Adam leave + + align:start position:0% +framework and TR resources Mr Adam leave + + + align:start position:0% +framework and TR resources Mr Adam leave +a board member of Cho area + + align:start position:0% +a board member of Cho area + + + align:start position:0% +a board member of Cho area +Rehabilitation organization a local + + align:start position:0% +Rehabilitation organization a local + + + align:start position:0% +Rehabilitation organization a local +Social Service NGO has a great hope for + + align:start position:0% +Social Service NGO has a great hope for + + + align:start position:0% +Social Service NGO has a great hope for +the city plan but now we got great plans + + align:start position:0% +the city plan but now we got great plans + + + align:start position:0% +the city plan but now we got great plans +we could have like Venice you + + align:start position:0% +we could have like Venice you + + + align:start position:0% +we could have like Venice you +know this River restoration project in + + align:start position:0% +know this River restoration project in + + + align:start position:0% +know this River restoration project in +chobu offers six lessons for other city + + align:start position:0% +chobu offers six lessons for other city + + + align:start position:0% +chobu offers six lessons for other city +in developing World seeking to promote + + align:start position:0% +in developing World seeking to promote + + + align:start position:0% +in developing World seeking to promote +sustainable City + + align:start position:0% +sustainable City + + + align:start position:0% +sustainable City +tourism first conserving and beautifying + + align:start position:0% +tourism first conserving and beautifying + + + align:start position:0% +tourism first conserving and beautifying +Urban environment is a key to promoting + + align:start position:0% +Urban environment is a key to promoting + + + align:start position:0% +Urban environment is a key to promoting +sustainable City tourism this may + + align:start position:0% +sustainable City tourism this may + + + align:start position:0% +sustainable City tourism this may +involve restoring ecological features + + align:start position:0% +involve restoring ecological features + + + align:start position:0% +involve restoring ecological features +for use by both City resident and + + align:start position:0% +for use by both City resident and + + + align:start position:0% +for use by both City resident and +tourists second sustainable City tourism + + align:start position:0% +tourists second sustainable City tourism + + + align:start position:0% +tourists second sustainable City tourism +need to conserve Urban cultural heritage + + align:start position:0% +need to conserve Urban cultural heritage + + + align:start position:0% +need to conserve Urban cultural heritage +this is what makes each City unique + + align:start position:0% +this is what makes each City unique + + + align:start position:0% +this is what makes each City unique +cultural heritage attracts tourist third + + align:start position:0% +cultural heritage attracts tourist third + + + align:start position:0% +cultural heritage attracts tourist third +physical connectivity particularly vocab + + align:start position:0% +physical connectivity particularly vocab + + + align:start position:0% +physical connectivity particularly vocab +is at the heart of sustainable City + + align:start position:0% +is at the heart of sustainable City + + + align:start position:0% +is at the heart of sustainable City +tourism tourists must be able to walk + + align:start position:0% +tourism tourists must be able to walk + + + align:start position:0% +tourism tourists must be able to walk +around the city to enjoy it fourth + + align:start position:0% +around the city to enjoy it fourth + + + align:start position:0% +around the city to enjoy it fourth +sustainable City tourism can and should + + align:start position:0% +sustainable City tourism can and should + + + align:start position:0% +sustainable City tourism can and should +expand the economy of the city the goal + + align:start position:0% +expand the economy of the city the goal + + + align:start position:0% +expand the economy of the city the goal +is to enhance the wellbeing of both + + align:start position:0% +is to enhance the wellbeing of both + + + align:start position:0% +is to enhance the wellbeing of both +locals and tourists fifth Democratic + + align:start position:0% +locals and tourists fifth Democratic + + + align:start position:0% +locals and tourists fifth Democratic +governance is crucial to building public + + align:start position:0% +governance is crucial to building public + + + align:start position:0% +governance is crucial to building public +support for sustainable City tourism + + align:start position:0% +support for sustainable City tourism + + + align:start position:0% +support for sustainable City tourism +public investment in infrastructure for + + align:start position:0% +public investment in infrastructure for + + + align:start position:0% +public investment in infrastructure for +example are more likely to serve the + + align:start position:0% +example are more likely to serve the + + + align:start position:0% +example are more likely to serve the +general public when the public is + + align:start position:0% +general public when the public is + + + align:start position:0% +general public when the public is +consulted on design and finance + + align:start position:0% +consulted on design and finance + + + align:start position:0% +consulted on design and finance +strategies last and most important never + + align:start position:0% +strategies last and most important never + + + align:start position:0% +strategies last and most important never +mess up your River the river will take + + align:start position:0% +mess up your River the river will take + + + align:start position:0% +mess up your River the river will take +good care of us if we take good care of + + align:start position:0% +good care of us if we take good care of + + + align:start position:0% +good care of us if we take good care of +it + + align:start position:0% + + + + align:start position:0% + +[Music] \ No newline at end of file diff --git a/fN1uPAtLatY.txt b/fN1uPAtLatY.txt new file mode 100644 index 0000000000000000000000000000000000000000..435fc99576a3f8f1eac53775bd074721f23a38e7 --- /dev/null +++ b/fN1uPAtLatY.txt @@ -0,0 +1,5931 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license + + align:start position:0% +a Creative Commons license + + + align:start position:0% +a Creative Commons license +your support will help MIT + + align:start position:0% +your support will help MIT + + + align:start position:0% +your support will help MIT +OpenCourseWare continue to offer high + + align:start position:0% +OpenCourseWare continue to offer high + + + align:start position:0% +OpenCourseWare continue to offer high +quality educational resources for free + + align:start position:0% +quality educational resources for free + + + align:start position:0% +quality educational resources for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +all of the lab and we at the Royal + + align:start position:0% +all of the lab and we at the Royal + + + align:start position:0% +all of the lab and we at the Royal +Danish Academy see it's a long service + + align:start position:0% +Danish Academy see it's a long service + + + align:start position:0% +Danish Academy see it's a long service +and take you longer than the Royal + + align:start position:0% +and take you longer than the Royal + + + align:start position:0% +and take you longer than the Royal +Danish Academy of Fine Arts schools and + + align:start position:0% +Danish Academy of Fine Arts schools and + + + align:start position:0% +Danish Academy of Fine Arts schools and +architecture conservation and Design + + align:start position:0% +architecture conservation and Design + + + align:start position:0% +architecture conservation and Design +common School of Design right you you've + + align:start position:0% +common School of Design right you you've + + + align:start position:0% +common School of Design right you you've +also taught at NYU you're a visiting + + align:start position:0% +also taught at NYU you're a visiting + + + align:start position:0% +also taught at NYU you're a visiting +professor here and given my game scholar + + align:start position:0% +professor here and given my game scholar + + + align:start position:0% +professor here and given my game scholar +for we if you take a bunch of the + + align:start position:0% +for we if you take a bunch of the + + + align:start position:0% +for we if you take a bunch of the +classes here we sometimes have readings + + align:start position:0% +classes here we sometimes have readings + + + align:start position:0% +classes here we sometimes have readings +from from yes for articles that you've + + align:start position:0% +from from yes for articles that you've + + + align:start position:0% +from from yes for articles that you've +written but I this is another example + + align:start position:0% +written but I this is another example + + + align:start position:0% +written but I this is another example +two of the talks that we've been having + + align:start position:0% +two of the talks that we've been having + + + align:start position:0% +two of the talks that we've been having +on this is what people do once they + + align:start position:0% +on this is what people do once they + + + align:start position:0% +on this is what people do once they +understand game design right some people + + align:start position:0% +understand game design right some people + + + align:start position:0% +understand game design right some people +study games + + align:start position:0% +study games + + + align:start position:0% +study games +some people do research write books + + align:start position:0% +some people do research write books + + + align:start position:0% +some people do research write books +about and ask interesting questions that + + align:start position:0% +about and ask interesting questions that + + + align:start position:0% +about and ask interesting questions that +try to find out more about what makes + + align:start position:0% +try to find out more about what makes + + + align:start position:0% +try to find out more about what makes +games fascinating or what makes the + + align:start position:0% +games fascinating or what makes the + + + align:start position:0% +games fascinating or what makes the +environment in which we create games so + + align:start position:0% +environment in which we create games so + + + align:start position:0% +environment in which we create games so +we play games it's interesting so so a + + align:start position:0% +we play games it's interesting so so a + + + align:start position:0% +we play games it's interesting so so a +book with that I can hand it over + + align:start position:0% +book with that I can hand it over + + + align:start position:0% +book with that I can hand it over +yes per hand this is fine this is game + + align:start position:0% +yes per hand this is fine this is game + + + align:start position:0% +yes per hand this is fine this is game +design 608 a little game design security + + align:start position:0% +design 608 a little game design security + + + align:start position:0% +design 608 a little game design security +yeah I guess yeah so how many of you are + + align:start position:0% +yeah I guess yeah so how many of you are + + + align:start position:0% +yeah I guess yeah so how many of you are +you doing digital games + + align:start position:0% +you doing digital games + + + align:start position:0% +you doing digital games +games or oh yeah all right yeah so I + + align:start position:0% +games or oh yeah all right yeah so I + + + align:start position:0% +games or oh yeah all right yeah so I +think I'm most of you talking probably + + align:start position:0% +think I'm most of you talking probably + + + align:start position:0% +think I'm most of you talking probably +most about digital games right right now + + align:start position:0% +most about digital games right right now + + + align:start position:0% +most about digital games right right now +but but I think it probably applies to + + align:start position:0% +but but I think it probably applies to + + + align:start position:0% +but but I think it probably applies to +some extent as Sophie Lee introduced me + + align:start position:0% +some extent as Sophie Lee introduced me + + + align:start position:0% +some extent as Sophie Lee introduced me +so so nicely and so this is really a + + align:start position:0% +so so nicely and so this is really a + + + align:start position:0% +so so nicely and so this is really a +part of a conference presentation that I + + align:start position:0% +part of a conference presentation that I + + + align:start position:0% +part of a conference presentation that I +did earlier this no earlier in April and + + align:start position:0% +did earlier this no earlier in April and + + + align:start position:0% +did earlier this no earlier in April and +so if you if you're interested in + + align:start position:0% +so if you if you're interested in + + + align:start position:0% +so if you if you're interested in +reading the full paper it's on my + + align:start position:0% +reading the full paper it's on my + + + align:start position:0% +reading the full paper it's on my +website and it's kind of URL independent + + align:start position:0% +website and it's kind of URL independent + + + align:start position:0% +website and it's kind of URL independent +style so and if you just go to slash + + align:start position:0% +style so and if you just go to slash + + + align:start position:0% +style so and if you just go to slash +text you can see some of the other stuff + + align:start position:0% +text you can see some of the other stuff + + + align:start position:0% +text you can see some of the other stuff +I've written and I've written there + + align:start position:0% +I've written and I've written there + + + align:start position:0% +I've written and I've written there +alphaman a few books I'd say about about + + align:start position:0% +alphaman a few books I'd say about about + + + align:start position:0% +alphaman a few books I'd say about about +video games so so one I wrote one about + + align:start position:0% +video games so so one I wrote one about + + + align:start position:0% +video games so so one I wrote one about +video games and storytelling and one + + align:start position:0% +video games and storytelling and one + + + align:start position:0% +video games and storytelling and one +about casual games and my most recent + + align:start position:0% +about casual games and my most recent + + + align:start position:0% +about casual games and my most recent +one called the art of failure is in a + + align:start position:0% +one called the art of failure is in a + + + align:start position:0% +one called the art of failure is in a +way about being a sore loser so it's a + + align:start position:0% +way about being a sore loser so it's a + + + align:start position:0% +way about being a sore loser so it's a +called an essay on the pain of playing + + align:start position:0% +called an essay on the pain of playing + + + align:start position:0% +called an essay on the pain of playing +video games so that's an iBook on this + + align:start position:0% +video games so that's an iBook on this + + + align:start position:0% +video games so that's an iBook on this +question of why we claim we enjoy be + + align:start position:0% +question of why we claim we enjoy be + + + align:start position:0% +question of why we claim we enjoy be +unions even though if you look at people + + align:start position:0% +unions even though if you look at people + + + align:start position:0% +unions even though if you look at people +playing they often look quite unhappy + + align:start position:0% +playing they often look quite unhappy + + + align:start position:0% +playing they often look quite unhappy +Act so it's a discussion like that but + + align:start position:0% +Act so it's a discussion like that but + + + align:start position:0% +Act so it's a discussion like that but +this one is especially slightly kind of + + align:start position:0% +this one is especially slightly kind of + + + align:start position:0% +this one is especially slightly kind of +different things different thing the + + align:start position:0% +different things different thing the + + + align:start position:0% +different things different thing the +president of independent games and so so + + align:start position:0% +president of independent games and so so + + + align:start position:0% +president of independent games and so so +if you I think that there seems to be a + + align:start position:0% +if you I think that there seems to be a + + + align:start position:0% +if you I think that there seems to be a +kind of consensus that independent games + + align:start position:0% +kind of consensus that independent games + + + align:start position:0% +kind of consensus that independent games +have become a kind of important aspect + + align:start position:0% +have become a kind of important aspect + + + align:start position:0% +have become a kind of important aspect +of game culture and you can see this in + + align:start position:0% +of game culture and you can see this in + + + align:start position:0% +of game culture and you can see this in +in several ways but here's the cheap + + align:start position:0% +in several ways but here's the cheap + + + align:start position:0% +in several ways but here's the cheap +very cheap + + align:start position:0% +very cheap + + + align:start position:0% +very cheap +we'll integrand way of showing that + + align:start position:0% +we'll integrand way of showing that + + + align:start position:0% +we'll integrand way of showing that +something is popular + + align:start position:0% +something is popular + + + align:start position:0% +something is popular +I don't anybody notice whites white + + align:start position:0% +I don't anybody notice whites white + + + align:start position:0% +I don't anybody notice whites white +White's never fled this curve to + + align:start position:0% +White's never fled this curve to + + + align:start position:0% +White's never fled this curve to +somebody no so it's an economic game + + align:start position:0% +somebody no so it's an economic game + + + align:start position:0% +somebody no so it's an economic game +theory that's actually a concept called + + align:start position:0% +theory that's actually a concept called + + + align:start position:0% +theory that's actually a concept called +independent game so it means like a game + + align:start position:0% +independent game so it means like a game + + + align:start position:0% +independent game so it means like a game +that's not attached to two other games + + align:start position:0% +that's not attached to two other games + + + align:start position:0% +that's not attached to two other games +so that's why it's never quite fled the + + align:start position:0% +so that's why it's never quite fled the + + + align:start position:0% +so that's why it's never quite fled the +curve but but today it shows you that in + + align:start position:0% +curve but but today it shows you that in + + + align:start position:0% +curve but but today it shows you that in +two thousand on people started talking + + align:start position:0% +two thousand on people started talking + + + align:start position:0% +two thousand on people started talking +about independent game and you doesn't + + align:start position:0% +about independent game and you doesn't + + + align:start position:0% +about independent game and you doesn't +see that the same Sony and Microsoft + + align:start position:0% +see that the same Sony and Microsoft + + + align:start position:0% +see that the same Sony and Microsoft +actually spend a good deal of energy and + + align:start position:0% +actually spend a good deal of energy and + + + align:start position:0% +actually spend a good deal of energy and +these two claim power independent game + + align:start position:0% +these two claim power independent game + + + align:start position:0% +these two claim power independent game +friendly they are with the new consoles + + align:start position:0% +friendly they are with the new consoles + + + align:start position:0% +friendly they are with the new consoles +soon is sustainable and we can tell + + align:start position:0% +soon is sustainable and we can tell + + + align:start position:0% +soon is sustainable and we can tell +whether there's a few different reasons + + align:start position:0% +whether there's a few different reasons + + + align:start position:0% +whether there's a few different reasons +while we talk about independent games + + align:start position:0% +while we talk about independent games + + + align:start position:0% +while we talk about independent games +and one of them may be that the budgets + + align:start position:0% +and one of them may be that the budgets + + + align:start position:0% +and one of them may be that the budgets +have become too big to play development + + align:start position:0% +have become too big to play development + + + align:start position:0% +have become too big to play development +so this is kind of opening for games and + + align:start position:0% +so this is kind of opening for games and + + + align:start position:0% +so this is kind of opening for games and +it's made on a smaller budget and also + + align:start position:0% +it's made on a smaller budget and also + + + align:start position:0% +it's made on a smaller budget and also +that that it's become easier to + + align:start position:0% +that that it's become easier to + + + align:start position:0% +that that it's become easier to +distribute games so it used to be you + + align:start position:0% +distribute games so it used to be you + + + align:start position:0% +distribute games so it used to be you +know the distributor gaming on a disc + + align:start position:0% +know the distributor gaming on a disc + + + align:start position:0% +know the distributor gaming on a disc +and in a box and that's no longer true + + align:start position:0% +and in a box and that's no longer true + + + align:start position:0% +and in a box and that's no longer true +fortunately it just endless means it's + + align:start position:0% +fortunately it just endless means it's + + + align:start position:0% +fortunately it just endless means it's +become possible to make kind of games in + + align:start position:0% +become possible to make kind of games in + + + align:start position:0% +become possible to make kind of games in +different sizes and then also finally + + align:start position:0% +different sizes and then also finally + + + align:start position:0% +different sizes and then also finally +but that's the thing that could sound + + align:start position:0% +but that's the thing that could sound + + + align:start position:0% +but that's the thing that could sound +kind of weird that in a way the + + align:start position:0% +kind of weird that in a way the + + + align:start position:0% +kind of weird that in a way the +independent games and way presuppose the + + align:start position:0% +independent games and way presuppose the + + + align:start position:0% +independent games and way presuppose the +idea of independent games means so it + + align:start position:0% +idea of independent games means so it + + + align:start position:0% +idea of independent games means so it +said if you're if you're making a game + + align:start position:0% +said if you're if you're making a game + + + align:start position:0% +said if you're if you're making a game +on a small budget one of the things you + + align:start position:0% +on a small budget one of the things you + + + align:start position:0% +on a small budget one of the things you +need to be able to be sure of is that + + align:start position:0% +need to be able to be sure of is that + + + align:start position:0% +need to be able to be sure of is that +people who see your game don't just + + align:start position:0% +people who see your game don't just + + + align:start position:0% +people who see your game don't just +think of it as a game with two smaller + + align:start position:0% +think of it as a game with two smaller + + + align:start position:0% +think of it as a game with two smaller +budgets but that that they understand + + align:start position:0% +budgets but that that they understand + + + align:start position:0% +budgets but that that they understand +that this is a game and it has some + + align:start position:0% +that this is a game and it has some + + + align:start position:0% +that this is a game and it has some +positive qualities to it or that there's + + align:start position:0% +positive qualities to it or that there's + + + align:start position:0% +positive qualities to it or that there's +particular reason why it has a small + + align:start position:0% +particular reason why it has a small + + + align:start position:0% +particular reason why it has a small +budget or the fact that a bigger budget + + align:start position:0% +budget or the fact that a bigger budget + + + align:start position:0% +budget or the fact that a bigger budget +wouldn't have made this game any better + + align:start position:0% +wouldn't have made this game any better + + + align:start position:0% +wouldn't have made this game any better +and so I think the idea is independent + + align:start position:0% +and so I think the idea is independent + + + align:start position:0% +and so I think the idea is independent +game they like you it's really that idea + + align:start position:0% +game they like you it's really that idea + + + align:start position:0% +game they like you it's really that idea +that you can actually say I'm making an + + align:start position:0% +that you can actually say I'm making an + + + align:start position:0% +that you can actually say I'm making an +independent + + align:start position:0% +independent + + + align:start position:0% +independent +game people understand that this is a + + align:start position:0% +game people understand that this is a + + + align:start position:0% +game people understand that this is a +game that has a particular set of + + align:start position:0% +game that has a particular set of + + + align:start position:0% +game that has a particular set of +qualities where it's a feature the fact + + align:start position:0% +qualities where it's a feature the fact + + + align:start position:0% +qualities where it's a feature the fact +that it's a game with a small budget and + + align:start position:0% +that it's a game with a small budget and + + + align:start position:0% +that it's a game with a small budget and +so it doesn't mean you can see the + + align:start position:0% +so it doesn't mean you can see the + + + align:start position:0% +so it doesn't mean you can see the +questions like what makes people assume + + align:start position:0% +questions like what makes people assume + + + align:start position:0% +questions like what makes people assume +that something isn't it an independent + + align:start position:0% +that something isn't it an independent + + + align:start position:0% +that something isn't it an independent +game when they see it right it's not I + + align:start position:0% +game when they see it right it's not I + + + align:start position:0% +game when they see it right it's not I +don't think it's just that it says + + align:start position:0% +don't think it's just that it says + + + align:start position:0% +don't think it's just that it says +independent game somewhere but I do + + align:start position:0% +independent game somewhere but I do + + + align:start position:0% +independent game somewhere but I do +think there is actually a particular + + align:start position:0% +think there is actually a particular + + + align:start position:0% +think there is actually a particular +style that's coming to independent game + + align:start position:0% +style that's coming to independent game + + + align:start position:0% +style that's coming to independent game +talk about that at first you can see + + align:start position:0% +talk about that at first you can see + + + align:start position:0% +talk about that at first you can see +that when people write about independent + + align:start position:0% +that when people write about independent + + + align:start position:0% +that when people write about independent +games actually the first thing everybody + + align:start position:0% +games actually the first thing everybody + + + align:start position:0% +games actually the first thing everybody +will say is that you can't define it the + + align:start position:0% +will say is that you can't define it the + + + align:start position:0% +will say is that you can't define it the +first thing you have to say and so no + + align:start position:0% +first thing you have to say and so no + + + align:start position:0% +first thing you have to say and so no +it's got people say that you can't + + align:start position:0% +it's got people say that you can't + + + align:start position:0% +it's got people say that you can't +define it because this is creates + + align:start position:0% +define it because this is creates + + + align:start position:0% +define it because this is creates +discord in the game community or sumin + + align:start position:0% +discord in the game community or sumin + + + align:start position:0% +discord in the game community or sumin +talks about independent in different + + align:start position:0% +talks about independent in different + + + align:start position:0% +talks about independent in different +kind of ways economic technological + + align:start position:0% +kind of ways economic technological + + + align:start position:0% +kind of ways economic technological +cultural status and then the several + + align:start position:0% +cultural status and then the several + + + align:start position:0% +cultural status and then the several +people say well it's not pointed trying + + align:start position:0% +people say well it's not pointed trying + + + align:start position:0% +people say well it's not pointed trying +to define independent games in the first + + align:start position:0% +to define independent games in the first + + + align:start position:0% +to define independent games in the first +place + + align:start position:0% +place + + + align:start position:0% +place +so I think that that's actually said a + + align:start position:0% +so I think that that's actually said a + + + align:start position:0% +so I think that that's actually said a +lot on the other hand if you if you look + + align:start position:0% +lot on the other hand if you if you look + + + align:start position:0% +lot on the other hand if you if you look +at what people who make independent + + align:start position:0% +at what people who make independent + + + align:start position:0% +at what people who make independent +games say there's actually a lot of + + align:start position:0% +games say there's actually a lot of + + + align:start position:0% +games say there's actually a lot of +things in common so then cook talks + + align:start position:0% +things in common so then cook talks + + + align:start position:0% +things in common so then cook talks +about that independent games allowed to + + align:start position:0% +about that independent games allowed to + + + align:start position:0% +about that independent games allowed to +be fan of someone who's authentic and + + align:start position:0% +be fan of someone who's authentic and + + + align:start position:0% +be fan of someone who's authentic and +deserving Macmillan X it talks about + + align:start position:0% +deserving Macmillan X it talks about + + + align:start position:0% +deserving Macmillan X it talks about +honesty and speaking from your heart he + + align:start position:0% +honesty and speaking from your heart he + + + align:start position:0% +honesty and speaking from your heart he +made it super meatboy and then cook meat + + align:start position:0% +made it super meatboy and then cook meat + + + align:start position:0% +made it super meatboy and then cook meat +triple time with you + + align:start position:0% +triple time with you + + + align:start position:0% +triple time with you +and Robin Allen talks about more + + align:start position:0% +and Robin Allen talks about more + + + align:start position:0% +and Robin Allen talks about more +personal relationship with the work for + + align:start position:0% +personal relationship with the work for + + + align:start position:0% +personal relationship with the work for +independent games + + align:start position:0% +independent games + + + align:start position:0% +independent games +Chavez the whole discussion preparing + + align:start position:0% +Chavez the whole discussion preparing + + + align:start position:0% +Chavez the whole discussion preparing +independent games to funk music like the + + align:start position:0% +independent games to funk music like the + + + align:start position:0% +independent games to funk music like the +emphasis on become small small kind of + + align:start position:0% +emphasis on become small small kind of + + + align:start position:0% +emphasis on become small small kind of +personal anyone can do do it very kind + + align:start position:0% +personal anyone can do do it very kind + + + align:start position:0% +personal anyone can do do it very kind +of thing and very zen Anthropy has + + align:start position:0% +of thing and very zen Anthropy has + + + align:start position:0% +of thing and very zen Anthropy has +turned about times the smaller budgets + + align:start position:0% +turned about times the smaller budgets + + + align:start position:0% +turned about times the smaller budgets +allowing games to be more personal and + + align:start position:0% +allowing games to be more personal and + + + align:start position:0% +allowing games to be more personal and +more relevant and so I think these + + align:start position:0% +more relevant and so I think these + + + align:start position:0% +more relevant and so I think these +psyche decided these are quite similar + + align:start position:0% +psyche decided these are quite similar + + + align:start position:0% +psyche decided these are quite similar +in some ways right so they talk about + + align:start position:0% +in some ways right so they talk about + + + align:start position:0% +in some ways right so they talk about +this kind of live the honest and the + + align:start position:0% +this kind of live the honest and the + + + align:start position:0% +this kind of live the honest and the +traditional and and what I call this + + align:start position:0% +traditional and and what I call this + + + align:start position:0% +traditional and and what I call this +minimal complexity you can understand of + + align:start position:0% +minimal complexity you can understand of + + + align:start position:0% +minimal complexity you can understand of +understand who made the game and it like + + align:start position:0% +understand who made the game and it like + + + align:start position:0% +understand who made the game and it like +we talked about just before with king's + + align:start position:0% +we talked about just before with king's + + + align:start position:0% +we talked about just before with king's +daughter right that if you if you buy a + + align:start position:0% +daughter right that if you if you buy a + + + align:start position:0% +daughter right that if you if you buy a +triple-a game it's not necessarily clear + + align:start position:0% +triple-a game it's not necessarily clear + + + align:start position:0% +triple-a game it's not necessarily clear +who actually make the game and with + + align:start position:0% +who actually make the game and with + + + align:start position:0% +who actually make the game and with +independent games I think there's much + + align:start position:0% +independent games I think there's much + + + align:start position:0% +independent games I think there's much +more of an idea that you will have a + + align:start position:0% +more of an idea that you will have a + + + align:start position:0% +more of an idea that you will have a +feeling of the of the authors of the + + align:start position:0% +feeling of the of the authors of the + + + align:start position:0% +feeling of the of the authors of the +creator's personality all right so you + + align:start position:0% +creator's personality all right so you + + + align:start position:0% +creator's personality all right so you +can see that these are you tell us about + + align:start position:0% +can see that these are you tell us about + + + align:start position:0% +can see that these are you tell us about +what I call kind of moral and aesthetic + + align:start position:0% +what I call kind of moral and aesthetic + + + align:start position:0% +what I call kind of moral and aesthetic +claims so at the same time so it's not + + align:start position:0% +claims so at the same time so it's not + + + align:start position:0% +claims so at the same time so it's not +just you see if not just saying that + + align:start position:0% +just you see if not just saying that + + + align:start position:0% +just you see if not just saying that +these are better games it's a bit more + + align:start position:0% +these are better games it's a bit more + + + align:start position:0% +these are better games it's a bit more +deep than that right it's also saying + + align:start position:0% +deep than that right it's also saying + + + align:start position:0% +deep than that right it's also saying +anyway that this is a better way of + + align:start position:0% +anyway that this is a better way of + + + align:start position:0% +anyway that this is a better way of +making a game so not that just did it + + align:start position:0% +making a game so not that just did it + + + align:start position:0% +making a game so not that just did it +not just that it'll be a better product + + align:start position:0% +not just that it'll be a better product + + + align:start position:0% +not just that it'll be a better product +but that that even say like the quality + + align:start position:0% +but that that even say like the quality + + + align:start position:0% +but that that even say like the quality +of life if someone makes an indie game + + align:start position:0% +of life if someone makes an indie game + + + align:start position:0% +of life if someone makes an indie game +would be better but also anyway that + + align:start position:0% +would be better but also anyway that + + + align:start position:0% +would be better but also anyway that +we'll all be better off if more people + + align:start position:0% +we'll all be better off if more people + + + align:start position:0% +we'll all be better off if more people +make in the pen + + align:start position:0% +make in the pen + + + align:start position:0% +make in the pen +games who have more communication and + + align:start position:0% +games who have more communication and + + + align:start position:0% +games who have more communication and +more ideas being spread and more more + + align:start position:0% +more ideas being spread and more more + + + align:start position:0% +more ideas being spread and more more +diversity and so on now so the thing is + + align:start position:0% +diversity and so on now so the thing is + + + align:start position:0% +diversity and so on now so the thing is +this is not exactly new so this is said + + align:start position:0% + + + + align:start position:0% + +as I said this is called the shredders + + align:start position:0% +as I said this is called the shredders + + + align:start position:0% +as I said this is called the shredders +wallpaper by William Morris and Phil is + + align:start position:0% +wallpaper by William Morris and Phil is + + + align:start position:0% +wallpaper by William Morris and Phil is +we're from 1862 so I think one of the + + align:start position:0% +we're from 1862 so I think one of the + + + align:start position:0% +we're from 1862 so I think one of the +things that's I think that strikes me + + align:start position:0% +things that's I think that strikes me + + + align:start position:0% +things that's I think that strikes me +with India is that it actually is quite + + align:start position:0% +with India is that it actually is quite + + + align:start position:0% +with India is that it actually is quite +similar to some things that have + + align:start position:0% +similar to some things that have + + + align:start position:0% +similar to some things that have +happened several times but I think + + align:start position:0% +happened several times but I think + + + align:start position:0% +happened several times but I think +particularly happy with with the divet + + align:start position:0% +particularly happy with with the divet + + + align:start position:0% +particularly happy with with the divet +well it's called the Arts and Crafts + + align:start position:0% +well it's called the Arts and Crafts + + + align:start position:0% +well it's called the Arts and Crafts +movement of the 19th century so you can + + align:start position:0% +movement of the 19th century so you can + + + align:start position:0% +movement of the 19th century so you can +see when we talk about independent games + + align:start position:0% +see when we talk about independent games + + + align:start position:0% +see when we talk about independent games +I don't think it ties into several + + align:start position:0% +I don't think it ties into several + + + align:start position:0% +I don't think it ties into several +things such as like the FBI why or the + + align:start position:0% +things such as like the FBI why or the + + + align:start position:0% +things such as like the FBI why or the +maker movement or the idea of kind of + + align:start position:0% +maker movement or the idea of kind of + + + align:start position:0% +maker movement or the idea of kind of +local food production like the local + + align:start position:0% +local food production like the local + + + align:start position:0% +local food production like the local +ball movement this idea that if you go + + align:start position:0% +ball movement this idea that if you go + + + align:start position:0% +ball movement this idea that if you go +to a restaurant you should you should + + align:start position:0% +to a restaurant you should you should + + + align:start position:0% +to a restaurant you should you should +know where where the where the chicken + + align:start position:0% +know where where the where the chicken + + + align:start position:0% +know where where the where the chicken +you ate actually came from so he only + + align:start position:0% +you ate actually came from so he only + + + align:start position:0% +you ate actually came from so he only +yesterday I was a good restaurant called + + align:start position:0% +yesterday I was a good restaurant called + + + align:start position:0% +yesterday I was a good restaurant called +Evo I don't know it makes it lists on + + align:start position:0% +Evo I don't know it makes it lists on + + + align:start position:0% +Evo I don't know it makes it lists on +the left side of a menu like all of the + + align:start position:0% +the left side of a menu like all of the + + + align:start position:0% +the left side of a menu like all of the +farms from food where they get their + + align:start position:0% +farms from food where they get their + + + align:start position:0% +farms from food where they get their +ingredients and it has its kind of like + + align:start position:0% +ingredients and it has its kind of like + + + align:start position:0% +ingredients and it has its kind of like +wow isn't it amazing + + align:start position:0% +wow isn't it amazing + + + align:start position:0% +wow isn't it amazing +and of course I've never heard about any + + align:start position:0% +and of course I've never heard about any + + + align:start position:0% +and of course I've never heard about any +any of those farms have no idea what + + align:start position:0% +any of those farms have no idea what + + + align:start position:0% +any of those farms have no idea what +where they are but it kind of still + + align:start position:0% +where they are but it kind of still + + + align:start position:0% +where they are but it kind of still +works I mean it's gonna fit since that + + align:start position:0% +works I mean it's gonna fit since that + + + align:start position:0% +works I mean it's gonna fit since that +you can understand that this it's kind + + align:start position:0% +you can understand that this it's kind + + + align:start position:0% +you can understand that this it's kind +of honesty or right but but the absolute + + align:start position:0% +of honesty or right but but the absolute + + + align:start position:0% +of honesty or right but but the absolute +Crafts movement I think still we + + align:start position:0% +Crafts movement I think still we + + + align:start position:0% +Crafts movement I think still we +discussed this being this like late 19th + + align:start position:0% +discussed this being this like late 19th + + + align:start position:0% +discussed this being this like late 19th +century movement where people reacted + + align:start position:0% +century movement where people reacted + + + align:start position:0% +century movement where people reacted +against the industrialization and kind + + align:start position:0% +against the industrialization and kind + + + align:start position:0% +against the industrialization and kind +of machine production and they felt that + + align:start position:0% +of machine production and they felt that + + + align:start position:0% +of machine production and they felt that +this included a kind of loss of quality + + align:start position:0% +this included a kind of loss of quality + + + align:start position:0% +this included a kind of loss of quality +or personality so that you didn't even + + align:start position:0% +or personality so that you didn't even + + + align:start position:0% +or personality so that you didn't even +know who made the product and the + + align:start position:0% +know who made the product and the + + + align:start position:0% +know who made the product and the +products themselves would be kind of + + align:start position:0% +products themselves would be kind of + + + align:start position:0% +products themselves would be kind of +worse and then sort of the proponents of + + align:start position:0% +worse and then sort of the proponents of + + + align:start position:0% +worse and then sort of the proponents of +John Ruskin kind of he talks about this + + align:start position:0% +John Ruskin kind of he talks about this + + + align:start position:0% +John Ruskin kind of he talks about this +idea that in medieval times those that + + align:start position:0% +idea that in medieval times those that + + + align:start position:0% +idea that in medieval times those that +was a much better it has a fascinated by + + align:start position:0% +was a much better it has a fascinated by + + + align:start position:0% +was a much better it has a fascinated by +the if the medieval guild + + align:start position:0% +the if the medieval guild + + + align:start position:0% +the if the medieval guild +it's kind of small group of people + + align:start position:0% +it's kind of small group of people + + + align:start position:0% +it's kind of small group of people +making something like a gothic building + + align:start position:0% +making something like a gothic building + + + align:start position:0% +making something like a gothic building +and when the amorous talks about this + + align:start position:0% +and when the amorous talks about this + + + align:start position:0% +and when the amorous talks about this +idea that of handicraft or the or the + + align:start position:0% +idea that of handicraft or the or the + + + align:start position:0% +idea that of handicraft or the or the +crafts person making a something that + + align:start position:0% +crafts person making a something that + + + align:start position:0% +crafts person making a something that +it's kind of much better than what would + + align:start position:0% +it's kind of much better than what would + + + align:start position:0% +it's kind of much better than what would +be made by machine production and again + + align:start position:0% +be made by machine production and again + + + align:start position:0% +be made by machine production and again +not just that not just that it would be + + align:start position:0% +not just that not just that it would be + + + align:start position:0% +not just that not just that it would be +better products but then anyway like + + align:start position:0% +better products but then anyway like + + + align:start position:0% +better products but then anyway like +society at large the world would be a + + align:start position:0% +society at large the world would be a + + + align:start position:0% +society at large the world would be a +better place if we made things that way + + align:start position:0% +better place if we made things that way + + + align:start position:0% +better place if we made things that way +and I do think you'd say that + + align:start position:0% +and I do think you'd say that + + + align:start position:0% +and I do think you'd say that +that that I think is very clear with the + + align:start position:0% +that that I think is very clear with the + + + align:start position:0% +that that I think is very clear with the +idea of independent games it's kind of + + align:start position:0% +idea of independent games it's kind of + + + align:start position:0% +idea of independent games it's kind of +similar in the sense that when they + + align:start position:0% +similar in the sense that when they + + + align:start position:0% +similar in the sense that when they +talked about the revival of see + + align:start position:0% +talked about the revival of see + + + align:start position:0% +talked about the revival of see +craftsmanship and handicraft this + + align:start position:0% +craftsmanship and handicraft this + + + align:start position:0% +craftsmanship and handicraft this +reaction against this kind of big + + align:start position:0% +reaction against this kind of big + + + align:start position:0% +reaction against this kind of big +machine of big corporate productions + + align:start position:0% +machine of big corporate productions + + + align:start position:0% +machine of big corporate productions +omission + + align:start position:0% +omission + + + align:start position:0% +omission +mass production and I think very similar + + align:start position:0% +mass production and I think very similar + + + align:start position:0% +mass production and I think very similar +you could say that independent games we + + align:start position:0% +you could say that independent games we + + + align:start position:0% +you could say that independent games we +actually give us like very large + + align:start position:0% +actually give us like very large + + + align:start position:0% +actually give us like very large +triple-a production teams and so they + + align:start position:0% +triple-a production teams and so they + + + align:start position:0% +triple-a production teams and so they +have this idea that we should be + + align:start position:0% +have this idea that we should be + + + align:start position:0% +have this idea that we should be +returned to these smaller productions + + align:start position:0% +returned to these smaller productions + + + align:start position:0% +returned to these smaller productions +and this will make everybody everything + + align:start position:0% +and this will make everybody everything + + + align:start position:0% +and this will make everybody everything +and a better number of levels does that + + align:start position:0% +and a better number of levels does that + + + align:start position:0% +and a better number of levels does that +make sense today I don't know I don't + + align:start position:0% +make sense today I don't know I don't + + + align:start position:0% +make sense today I don't know I don't +know how do you have firstly the + + align:start position:0% +know how do you have firstly the + + + align:start position:0% +know how do you have firstly the +independent game of you that you get a + + align:start position:0% +independent game of you that you get a + + + align:start position:0% +independent game of you that you get a +joint play playing or + + align:start position:0% + + + + align:start position:0% + +explore mechanics Emily + + align:start position:0% +explore mechanics Emily + + + align:start position:0% +explore mechanics Emily +sort of subway from + + align:start position:0% + + + + align:start position:0% + +million + + align:start position:0% + + + + align:start position:0% + +the market so they + + align:start position:0% + + + + align:start position:0% + +yeah so I found it just for me + + align:start position:0% +yeah so I found it just for me + + + align:start position:0% +yeah so I found it just for me +personally I don't really play games + + align:start position:0% +personally I don't really play games + + + align:start position:0% +personally I don't really play games +unless I'm planning on playing them a + + align:start position:0% +unless I'm planning on playing them a + + + align:start position:0% +unless I'm planning on playing them a +lot so I play like competitively like + + align:start position:0% +lot so I play like competitively like + + + align:start position:0% +lot so I play like competitively like +League of Legends or our Super Smash + + align:start position:0% +League of Legends or our Super Smash + + + align:start position:0% +League of Legends or our Super Smash +Brothers yeah and some one of the + + align:start position:0% +Brothers yeah and some one of the + + + align:start position:0% +Brothers yeah and some one of the +problems I have with independent games + + align:start position:0% +problems I have with independent games + + + align:start position:0% +problems I have with independent games +is that I don't feel like there that's + + align:start position:0% +is that I don't feel like there that's + + + align:start position:0% +is that I don't feel like there that's +developed like their general ones we + + align:start position:0% +developed like their general ones we + + + align:start position:0% +developed like their general ones we +were creative fine which is definitely + + align:start position:0% +were creative fine which is definitely + + + align:start position:0% +were creative fine which is definitely +something appreciable but not something + + align:start position:0% +something appreciable but not something + + + align:start position:0% +something appreciable but not something +that I enjoy prefer like getting very + + align:start position:0% +that I enjoy prefer like getting very + + + align:start position:0% +that I enjoy prefer like getting very +good at like I physically you don't you + + align:start position:0% +good at like I physically you don't you + + + align:start position:0% +good at like I physically you don't you +can mixin yeah I guess especially like + + align:start position:0% +can mixin yeah I guess especially like + + + align:start position:0% +can mixin yeah I guess especially like +the quality play aspect there's nothing + + align:start position:0% +the quality play aspect there's nothing + + + align:start position:0% +the quality play aspect there's nothing +to though I mean there's just new + + align:start position:0% +to though I mean there's just new + + + align:start position:0% +to though I mean there's just new +collection out called sports prince2 + + align:start position:0% + + + + align:start position:0% + +that in the way that the competitive + + align:start position:0% +that in the way that the competitive + + + align:start position:0% +that in the way that the competitive +sports is no not that development and + + align:start position:0% +sports is no not that development and + + + align:start position:0% +sports is no not that development and +it's a game that like me did you see + + align:start position:0% +it's a game that like me did you see + + + align:start position:0% +it's a game that like me did you see +that which has a different way yeah so + + align:start position:0% +that which has a different way yeah so + + + align:start position:0% +that which has a different way yeah so +so that this is this is I think that's + + align:start position:0% +so that this is this is I think that's + + + align:start position:0% +so that this is this is I think that's +kind of part of the also so kind of on + + align:start position:0% +kind of part of the also so kind of on + + + align:start position:0% +kind of part of the also so kind of on +the opposite note I think not all but a + + align:start position:0% +the opposite note I think not all but a + + + align:start position:0% +the opposite note I think not all but a +lot of games while the metal competitive + + align:start position:0% +lot of games while the metal competitive + + + align:start position:0% +lot of games while the metal competitive +aspect might be there that's multiplayer + + align:start position:0% +aspect might be there that's multiplayer + + + align:start position:0% +aspect might be there that's multiplayer +they can be hard single-player mode like + + align:start position:0% +they can be hard single-player mode like + + + align:start position:0% +they can be hard single-player mode like +we make investment stuff so a lot of + + align:start position:0% +we make investment stuff so a lot of + + + align:start position:0% +we make investment stuff so a lot of +people are frustrated when they lose but + + align:start position:0% +people are frustrated when they lose but + + + align:start position:0% +people are frustrated when they lose but +they can explore that and I do think + + align:start position:0% +they can explore that and I do think + + + align:start position:0% +they can explore that and I do think +it's also the same person said you know + + align:start position:0% +it's also the same person said you know + + + align:start position:0% +it's also the same person said you know +Cece with these people you know so come + + align:start position:0% +Cece with these people you know so come + + + align:start position:0% +Cece with these people you know so come +on nostalgia right for an earlier time + + align:start position:0% +on nostalgia right for an earlier time + + + align:start position:0% +on nostalgia right for an earlier time +and I do think that those apart kind of + + align:start position:0% +and I do think that those apart kind of + + + align:start position:0% +and I do think that those apart kind of +question difficulties also part of that + + align:start position:0% +question difficulties also part of that + + + align:start position:0% +question difficulties also part of that +is this the sense that they're like all + + align:start position:0% +is this the sense that they're like all + + + align:start position:0% +is this the sense that they're like all +of the edges of being kind of removed + + align:start position:0% +of the edges of being kind of removed + + + align:start position:0% +of the edges of being kind of removed +the challenge is being removed from big + + align:start position:0% +the challenge is being removed from big + + + align:start position:0% +the challenge is being removed from big +game productions to please everybody + + align:start position:0% +game productions to please everybody + + + align:start position:0% +game productions to please everybody +rather than if you if you making an + + align:start position:0% +rather than if you if you making an + + + align:start position:0% +rather than if you if you making an +indie game you can make something that's + + align:start position:0% +indie game you can make something that's + + + align:start position:0% +indie game you can make something that's +more kind of tied and more more kind of + + align:start position:0% +more kind of tied and more more kind of + + + align:start position:0% +more kind of tied and more more kind of +focused and extreme difficulty was + + align:start position:0% +focused and extreme difficulty was + + + align:start position:0% +focused and extreme difficulty was +incredibly such that you're carving out + + align:start position:0% +incredibly such that you're carving out + + + align:start position:0% +incredibly such that you're carving out +a very small audience and + + align:start position:0% + + + + align:start position:0% + +yeah nobody and so I think this also + + align:start position:0% +yeah nobody and so I think this also + + + align:start position:0% +yeah nobody and so I think this also +bubbles gets it as a bit that that in a + + align:start position:0% +bubbles gets it as a bit that that in a + + + align:start position:0% +bubbles gets it as a bit that that in a +way they had some Crafts movement also + + align:start position:0% +way they had some Crafts movement also + + + align:start position:0% +way they had some Crafts movement also +had this kind of political thing like + + align:start position:0% +had this kind of political thing like + + + align:start position:0% +had this kind of political thing like +that which will be for everybody or like + + align:start position:0% +that which will be for everybody or like + + + align:start position:0% +that which will be for everybody or like +art by the people for the people but the + + align:start position:0% +art by the people for the people but the + + + align:start position:0% +art by the people for the people but the +standard criticism is that it kind of + + align:start position:0% +standard criticism is that it kind of + + + align:start position:0% +standard criticism is that it kind of +ended up making kind of conspicuous + + align:start position:0% +ended up making kind of conspicuous + + + align:start position:0% +ended up making kind of conspicuous +consumption for rich people and you see + + align:start position:0% +consumption for rich people and you see + + + align:start position:0% +consumption for rich people and you see +the same thing I mean it's just a pretty + + align:start position:0% +the same thing I mean it's just a pretty + + + align:start position:0% +the same thing I mean it's just a pretty +expensive age and so it's something that + + align:start position:0% +expensive age and so it's something that + + + align:start position:0% +expensive age and so it's something that +kind of it happens that anyway you can + + align:start position:0% +kind of it happens that anyway you can + + + align:start position:0% +kind of it happens that anyway you can +often have this kind of a deal so for + + align:start position:0% +often have this kind of a deal so for + + + align:start position:0% +often have this kind of a deal so for +broadening things why this kind of + + align:start position:0% +broadening things why this kind of + + + align:start position:0% +broadening things why this kind of +reduction that but often you can also + + align:start position:0% +reduction that but often you can also + + + align:start position:0% +reduction that but often you can also +those who kind of got flip side of + + align:start position:0% +those who kind of got flip side of + + + align:start position:0% +those who kind of got flip side of +actually narrowing it but specially the + + align:start position:0% +actually narrowing it but specially the + + + align:start position:0% +actually narrowing it but specially the +desert one thing that I thought was + + align:start position:0% +desert one thing that I thought was + + + align:start position:0% +desert one thing that I thought was +interesting was to ask if there is any + + align:start position:0% +interesting was to ask if there is any + + + align:start position:0% +interesting was to ask if there is any +anything kind of common in the way just + + align:start position:0% +anything kind of common in the way just + + + align:start position:0% +anything kind of common in the way just +talking about the visual style of + + align:start position:0% +talking about the visual style of + + + align:start position:0% +talking about the visual style of +independent games and and here are three + + align:start position:0% +independent games and and here are three + + + align:start position:0% +independent games and and here are three +games that we often I think talk of as + + align:start position:0% +games that we often I think talk of as + + + align:start position:0% +games that we often I think talk of as +being independent + + align:start position:0% +being independent + + + align:start position:0% +being independent +fee which is kind of pixelated or large + + align:start position:0% +fee which is kind of pixelated or large + + + align:start position:0% +fee which is kind of pixelated or large +pixel style and yet it moves us it's + + align:start position:0% +pixel style and yet it moves us it's + + + align:start position:0% +pixel style and yet it moves us it's +kind of torn paper and printed + + align:start position:0% +kind of torn paper and printed + + + align:start position:0% +kind of torn paper and printed +successful obvious parents drawings and + + align:start position:0% +successful obvious parents drawings and + + + align:start position:0% +successful obvious parents drawings and +so you tell one hand these are kind of + + align:start position:0% +so you tell one hand these are kind of + + + align:start position:0% +so you tell one hand these are kind of +different different graphical styles but + + align:start position:0% +different different graphical styles but + + + align:start position:0% +different different graphical styles but +actually you can see what what they do + + align:start position:0% +actually you can see what what they do + + + align:start position:0% +actually you can see what what they do +have in common is what you can call it + + align:start position:0% +have in common is what you can call it + + + align:start position:0% +have in common is what you can call it +kind of a double layer right it's a it's + + align:start position:0% +kind of a double layer right it's a it's + + + align:start position:0% +kind of a double layer right it's a it's +a representation of a representation and + + align:start position:0% +a representation of a representation and + + + align:start position:0% +a representation of a representation and +so that maybe kind of represents like + + align:start position:0% +so that maybe kind of represents like + + + align:start position:0% +so that maybe kind of represents like +nineteen eighties size pixels which then + + align:start position:0% +nineteen eighties size pixels which then + + + align:start position:0% +nineteen eighties size pixels which then +represent the game world and yet it + + align:start position:0% +represent the game world and yet it + + + align:start position:0% +represent the game world and yet it +moves with the sense paper which then + + align:start position:0% +moves with the sense paper which then + + + align:start position:0% +moves with the sense paper which then +represents the game world and physics + + align:start position:0% +represents the game world and physics + + + align:start position:0% +represents the game world and physics +with us in screens which they represent + + align:start position:0% +with us in screens which they represent + + + align:start position:0% +with us in screens which they represent +a game world and you can compare this to + + align:start position:0% +a game world and you can compare this to + + + align:start position:0% +a game world and you can compare this to +- thank you if you play a kind of modern + + align:start position:0% +- thank you if you play a kind of modern + + + align:start position:0% +- thank you if you play a kind of modern +triple-a game you don't really have that + + align:start position:0% +triple-a game you don't really have that + + + align:start position:0% +triple-a game you don't really have that +wage and you have like it's mini + + align:start position:0% +wage and you have like it's mini + + + align:start position:0% +wage and you have like it's mini +graphics with creepers in the game world + + align:start position:0% +graphics with creepers in the game world + + + align:start position:0% +graphics with creepers in the game world +so I think what you can say that I think + + align:start position:0% +so I think what you can say that I think + + + align:start position:0% +so I think what you can say that I think +that's it's pretty common and I think + + align:start position:0% +that's it's pretty common and I think + + + align:start position:0% +that's it's pretty common and I think +this is not a definition of independent + + align:start position:0% +this is not a definition of independent + + + align:start position:0% +this is not a definition of independent +games I'm saying that I think when we + + align:start position:0% +games I'm saying that I think when we + + + align:start position:0% +games I'm saying that I think when we +usually see a game and recognize it as + + align:start position:0% +usually see a game and recognize it as + + + align:start position:0% +usually see a game and recognize it as +being an independent game I think it's + + align:start position:0% +being an independent game I think it's + + + align:start position:0% +being an independent game I think it's +often because they will have this type + + align:start position:0% +often because they will have this type + + + align:start position:0% +often because they will have this type +of style like a representation of + + align:start position:0% +of style like a representation of + + + align:start position:0% +of style like a representation of +representation so often we will have you + + align:start position:0% +representation so often we will have you + + + align:start position:0% +representation so often we will have you +use something contemporary technology + + align:start position:0% +use something contemporary technology + + + align:start position:0% +use something contemporary technology +obviously but you said to emulate + + align:start position:0% +obviously but you said to emulate + + + align:start position:0% +obviously but you said to emulate +something that's kind of low-tech and + + align:start position:0% +something that's kind of low-tech and + + + align:start position:0% +something that's kind of low-tech and +cheap right so you can see that day you + + align:start position:0% +cheap right so you can see that day you + + + align:start position:0% +cheap right so you can see that day you +can compare this to certain casual + + align:start position:0% +can compare this to certain casual + + + align:start position:0% +can compare this to certain casual +casual games like a matching games with + + align:start position:0% +casual games like a matching games with + + + align:start position:0% +casual games like a matching games with +much which might like sort of signal + + align:start position:0% +much which might like sort of signal + + + align:start position:0% +much which might like sort of signal +like jewels or or diamonds things it's + + align:start position:0% +like jewels or or diamonds things it's + + + align:start position:0% +like jewels or or diamonds things it's +very clear that most kind of independent + + align:start position:0% +very clear that most kind of independent + + + align:start position:0% +very clear that most kind of independent +games tend to to assist to emulate it's + + align:start position:0% +games tend to to assist to emulate it's + + + align:start position:0% +games tend to to assist to emulate it's +kind of very cheap materials like like + + align:start position:0% +kind of very cheap materials like like + + + align:start position:0% +kind of very cheap materials like like +torn paper + + align:start position:0% +torn paper + + + align:start position:0% +torn paper +things like that I think also that the + + align:start position:0% +things like that I think also that the + + + align:start position:0% +things like that I think also that the +reason why people do this is that in any + + align:start position:0% +reason why people do this is that in any + + + align:start position:0% +reason why people do this is that in any +way what you are done is it you're + + align:start position:0% +way what you are done is it you're + + + align:start position:0% +way what you are done is it you're +signaling that that we have made a + + align:start position:0% +signaling that that we have made a + + + align:start position:0% +signaling that that we have made a +deliberate choice to have this style and + + align:start position:0% +deliberate choice to have this style and + + + align:start position:0% +deliberate choice to have this style and +we are listening and so we have + + align:start position:0% +we are listening and so we have + + + align:start position:0% +we are listening and so we have +deliberately chosen to make a game on a + + align:start position:0% +deliberately chosen to make a game on a + + + align:start position:0% +deliberately chosen to make a game on a +small budget I think this is work but I + + align:start position:0% +small budget I think this is work but I + + + align:start position:0% +small budget I think this is work but I +think that what this kind of style + + align:start position:0% +think that what this kind of style + + + align:start position:0% +think that what this kind of style +sickness and it's also signal as this + + align:start position:0% +sickness and it's also signal as this + + + align:start position:0% +sickness and it's also signal as this +thing of these things are talking about + + align:start position:0% +thing of these things are talking about + + + align:start position:0% +thing of these things are talking about +like authenticity or knowing who made + + align:start position:0% +like authenticity or knowing who made + + + align:start position:0% +like authenticity or knowing who made +the game or kind of transparency in the + + align:start position:0% +the game or kind of transparency in the + + + align:start position:0% +the game or kind of transparency in the +production process and so you can think + + align:start position:0% +production process and so you can think + + + align:start position:0% +production process and so you can think +of it like this right that that India's + + align:start position:0% +of it like this right that that India's + + + align:start position:0% +of it like this right that that India's +east in this sense seems to me three + + align:start position:0% +east in this sense seems to me three + + + align:start position:0% +east in this sense seems to me three +different things indeed like on paper + + align:start position:0% +different things indeed like on paper + + + align:start position:0% +different things indeed like on paper +means like an financially independent + + align:start position:0% +means like an financially independent + + + align:start position:0% +means like an financially independent +team then I think there's also you see + + align:start position:0% +team then I think there's also you see + + + align:start position:0% +team then I think there's also you see +that these people talked about in decent + + align:start position:0% +that these people talked about in decent + + + align:start position:0% +that these people talked about in decent +game development community talk about + + align:start position:0% +game development community talk about + + + align:start position:0% +game development community talk about +anyway they was coming morally and + + align:start position:0% +anyway they was coming morally and + + + align:start position:0% +anyway they was coming morally and +politically and aesthetically better not + + align:start position:0% +politically and aesthetically better not + + + align:start position:0% +politically and aesthetically better not +just better games but also know it + + align:start position:0% +just better games but also know it + + + align:start position:0% +just better games but also know it +better for everybody in between games + + align:start position:0% +better for everybody in between games + + + align:start position:0% +better for everybody in between games +are made this way because we can + + align:start position:0% +are made this way because we can + + + align:start position:0% +are made this way because we can +communicate values and ideas and so on + + align:start position:0% +communicate values and ideas and so on + + + align:start position:0% +communicate values and ideas and so on +and then India's a particular kind of + + align:start position:0% +and then India's a particular kind of + + + align:start position:0% +and then India's a particular kind of +style and I think then this kind of + + align:start position:0% +style and I think then this kind of + + + align:start position:0% +style and I think then this kind of +style of having having these kind of + + align:start position:0% +style of having having these kind of + + + align:start position:0% +style of having having these kind of +representation of a representation is + + align:start position:0% +representation of a representation is + + + align:start position:0% +representation of a representation is +one that people used to signal now we're + + align:start position:0% +one that people used to signal now we're + + + align:start position:0% +one that people used to signal now we're +making a game with a small team and it + + align:start position:0% +making a game with a small team and it + + + align:start position:0% +making a game with a small team and it +has these kind of positive values of + + align:start position:0% +has these kind of positive values of + + + align:start position:0% +has these kind of positive values of +being kind of offense again means + + align:start position:0% +being kind of offense again means + + + align:start position:0% +being kind of offense again means +something that you can figure out what's + + align:start position:0% +something that you can figure out what's + + + align:start position:0% +something that you can figure out what's +going on + + align:start position:0% +going on + + + align:start position:0% +going on +who needed disturbed quickly how that + + align:start position:0% +who needed disturbed quickly how that + + + align:start position:0% +who needed disturbed quickly how that +touch style appeared I think and so this + + align:start position:0% +touch style appeared I think and so this + + + align:start position:0% +touch style appeared I think and so this +is looking at the Dino in the + + align:start position:0% +is looking at the Dino in the + + + align:start position:0% +is looking at the Dino in the +independent Games Festival did you + + align:start position:0% +independent Games Festival did you + + + align:start position:0% +independent Games Festival did you +follow that we follow this so that's + + align:start position:0% +follow that we follow this so that's + + + align:start position:0% +follow that we follow this so that's +what Joey Mason said this is a beginner + + align:start position:0% +what Joey Mason said this is a beginner + + + align:start position:0% +what Joey Mason said this is a beginner +house conference every year since 2000 + + align:start position:0% +house conference every year since 2000 + + + align:start position:0% +house conference every year since 2000 +Lisbon is independent Games Festival and + + align:start position:0% +Lisbon is independent Games Festival and + + + align:start position:0% +Lisbon is independent Games Festival and +this is like the longest-running + + align:start position:0% +this is like the longest-running + + + align:start position:0% +this is like the longest-running +festival independent games and that's + + align:start position:0% +festival independent games and that's + + + align:start position:0% +festival independent games and that's +kind of jury based competition and so + + align:start position:0% +kind of jury based competition and so + + + align:start position:0% +kind of jury based competition and so +one things it's interesting I think is + + align:start position:0% +one things it's interesting I think is + + + align:start position:0% +one things it's interesting I think is +looking at the winners of the grand + + align:start position:0% +looking at the winners of the grand + + + align:start position:0% +looking at the winners of the grand +prize in this independent Games Festival + + align:start position:0% +prize in this independent Games Festival + + + align:start position:0% +prize in this independent Games Festival +and one of the things that's kind of + + align:start position:0% +and one of the things that's kind of + + + align:start position:0% +and one of the things that's kind of +artisan if you look at the first five + + align:start position:0% +artisan if you look at the first five + + + align:start position:0% +artisan if you look at the first five +years none of the games I think actually + + align:start position:0% +years none of the games I think actually + + + align:start position:0% +years none of the games I think actually +signal independent very well in a kind + + align:start position:0% +signal independent very well in a kind + + + align:start position:0% +signal independent very well in a kind +of contemporary way so you can see that + + align:start position:0% +of contemporary way so you can see that + + + align:start position:0% +of contemporary way so you can see that +the three of them somewhat regular games + + align:start position:0% +the three of them somewhat regular games + + + align:start position:0% +the three of them somewhat regular games +of armed conflict and then wild earth is + + align:start position:0% +of armed conflict and then wild earth is + + + align:start position:0% +of armed conflict and then wild earth is +a kind of Pokemon snap style game the + + align:start position:0% +a kind of Pokemon snap style game the + + + align:start position:0% +a kind of Pokemon snap style game the +bad milk is this it's kind of weird + + align:start position:0% +bad milk is this it's kind of weird + + + align:start position:0% +bad milk is this it's kind of weird +never released kind of associational + + align:start position:0% +never released kind of associational + + + align:start position:0% +never released kind of associational +cd-rom you click on things and other + + align:start position:0% +cd-rom you click on things and other + + + align:start position:0% +cd-rom you click on things and other +things appear and so on but you can see + + align:start position:0% +things appear and so on but you can see + + + align:start position:0% +things appear and so on but you can see +that that that this in a way seems like + + align:start position:0% +that that that this in a way seems like + + + align:start position:0% +that that that this in a way seems like +it from a different time like if you see + + align:start position:0% +it from a different time like if you see + + + align:start position:0% +it from a different time like if you see +like the picture to select the two top + + align:start position:0% +like the picture to select the two top + + + align:start position:0% +like the picture to select the two top +games there's nothing I think that + + align:start position:0% +games there's nothing I think that + + + align:start position:0% +games there's nothing I think that +signals independent game + + align:start position:0% +signals independent game + + + align:start position:0% +signals independent game +in a kind of modern sense and I think + + align:start position:0% +in a kind of modern sense and I think + + + align:start position:0% +in a kind of modern sense and I think +part is described just because at this + + align:start position:0% +part is described just because at this + + + align:start position:0% +part is described just because at this +time online distribution just wasn't + + align:start position:0% +time online distribution just wasn't + + + align:start position:0% +time online distribution just wasn't +that that big a deal and so when people + + align:start position:0% +that that big a deal and so when people + + + align:start position:0% +that that big a deal and so when people +submit it to a festival like this what + + align:start position:0% +submit it to a festival like this what + + + align:start position:0% +submit it to a festival like this what +they did was sometimes probably just + + align:start position:0% +they did was sometimes probably just + + + align:start position:0% +they did was sometimes probably just +that they hoped that they would notice + + align:start position:0% +that they hoped that they would notice + + + align:start position:0% +that they hoped that they would notice +my publisher who within fun times and we + + align:start position:0% +my publisher who within fun times and we + + + align:start position:0% +my publisher who within fun times and we +could make a very big version of the + + align:start position:0% +could make a very big version of the + + + align:start position:0% +could make a very big version of the +game which could put them just shipped + + align:start position:0% +game which could put them just shipped + + + align:start position:0% +game which could put them just shipped +on a disk and then we see that like from + + align:start position:0% +on a disk and then we see that like from + + + align:start position:0% +on a disk and then we see that like from +2005 on the winners of the Sesto + + align:start position:0% +2005 on the winners of the Sesto + + + align:start position:0% +2005 on the winners of the Sesto +graduated we get more this style and + + align:start position:0% +graduated we get more this style and + + + align:start position:0% +graduated we get more this style and +talking about you see that they kind of + + align:start position:0% +talking about you see that they kind of + + + align:start position:0% +talking about you see that they kind of +paradigmatic like the kind of 2d + + align:start position:0% +paradigmatic like the kind of 2d + + + align:start position:0% +paradigmatic like the kind of 2d +platformer with some kind of twist and + + align:start position:0% +platformer with some kind of twist and + + + align:start position:0% +platformer with some kind of twist and +you dish then with that winner we see a + + align:start position:0% +you dish then with that winner we see a + + + align:start position:0% +you dish then with that winner we see a +kind of a low poly style that today I + + align:start position:0% +kind of a low poly style that today I + + + align:start position:0% +kind of a low poly style that today I +think people can refer Smith to a movie + + align:start position:0% +think people can refer Smith to a movie + + + align:start position:0% +think people can refer Smith to a movie +like Tron and then we see various takes + + align:start position:0% +like Tron and then we see various takes + + + align:start position:0% +like Tron and then we see various takes +on like watercolors and in the kind of + + align:start position:0% +on like watercolors and in the kind of + + + align:start position:0% +on like watercolors and in the kind of +hand drawing and hand-drawn graphics and + + align:start position:0% +hand drawing and hand-drawn graphics and + + + align:start position:0% +hand drawing and hand-drawn graphics and +you see this actually quite sides with a + + align:start position:0% +you see this actually quite sides with a + + + align:start position:0% +you see this actually quite sides with a +kind of gradual rise of digital + + align:start position:0% +kind of gradual rise of digital + + + align:start position:0% +kind of gradual rise of digital +distribution so first in things like + + align:start position:0% +distribution so first in things like + + + align:start position:0% +distribution so first in things like +downloadable casual games that this + + align:start position:0% +downloadable casual games that this + + + align:start position:0% +downloadable casual games that this +becomes possible or and also goes flash + + align:start position:0% +becomes possible or and also goes flash + + + align:start position:0% +becomes possible or and also goes flash +game sites that because more possible to + + align:start position:0% +game sites that because more possible to + + + align:start position:0% +game sites that because more possible to +distribute again without having to put + + align:start position:0% +distribute again without having to put + + + align:start position:0% +distribute again without having to put +in a box and then more recently then we + + align:start position:0% +in a box and then more recently then we + + + align:start position:0% +in a box and then more recently then we +see we still have this kind of pixel + + align:start position:0% +see we still have this kind of pixel + + + align:start position:0% +see we still have this kind of pixel +style but then that gets kind of merged + + align:start position:0% +style but then that gets kind of merged + + + align:start position:0% +style but then that gets kind of merged +with different things like in a game + + align:start position:0% +with different things like in a game + + + align:start position:0% +with different things like in a game +like Monaco it has these various + + align:start position:0% +like Monaco it has these various + + + align:start position:0% +like Monaco it has these various +lighting effects and then in Minecraft + + align:start position:0% +lighting effects and then in Minecraft + + + align:start position:0% +lighting effects and then in Minecraft +and fairs it gets moved into a kind of + + align:start position:0% +and fairs it gets moved into a kind of + + + align:start position:0% +and fairs it gets moved into a kind of +it into a third dimension so not that + + align:start position:0% +it into a third dimension so not that + + + align:start position:0% +it into a third dimension so not that +and this is what I call in color-coded + + align:start position:0% +and this is what I call in color-coded + + + align:start position:0% +and this is what I call in color-coded +kind of counterfactual nostalgia right + + align:start position:0% +kind of counterfactual nostalgia right + + + align:start position:0% +kind of counterfactual nostalgia right +so in a way it is it's pixelated as as + + align:start position:0% +so in a way it is it's pixelated as as + + + align:start position:0% +so in a way it is it's pixelated as as +if there was a time in + + align:start position:0% +if there was a time in + + + align:start position:0% +if there was a time in +1980s when people would make 3d games + + align:start position:0% +1980s when people would make 3d games + + + align:start position:0% +1980s when people would make 3d games +with big pixels like this never happened + + align:start position:0% +with big pixels like this never happened + + + align:start position:0% +with big pixels like this never happened +obviously but anyway it's a has it's + + align:start position:0% +obviously but anyway it's a has it's + + + align:start position:0% +obviously but anyway it's a has it's +kind of it has got Steve Kot steampunk + + align:start position:0% +kind of it has got Steve Kot steampunk + + + align:start position:0% +kind of it has got Steve Kot steampunk +anachronism about it right but still it + + align:start position:0% +anachronism about it right but still it + + + align:start position:0% +anachronism about it right but still it +kind of signals that this is a + + align:start position:0% +kind of signals that this is a + + + align:start position:0% +kind of signals that this is a +particular game and only the a + + align:start position:0% +particular game and only the a + + + align:start position:0% +particular game and only the a +particular style is only used come on + + align:start position:0% +particular style is only used come on + + + align:start position:0% +particular style is only used come on +and effects on it and then the tool and + + align:start position:0% +and effects on it and then the tool and + + + align:start position:0% +and effects on it and then the tool and +last two years still have this kind of + + align:start position:0% +last two years still have this kind of + + + align:start position:0% +last two years still have this kind of +flat and mostly grayscale pixels time + + align:start position:0% +flat and mostly grayscale pixels time + + + align:start position:0% +flat and mostly grayscale pixels time +now but then there's certain things that + + align:start position:0% +now but then there's certain things that + + + align:start position:0% +now but then there's certain things that +seem to be happening in the gameplay + + align:start position:0% +seem to be happening in the gameplay + + + align:start position:0% +seem to be happening in the gameplay +where a cod life assimilates life of a + + align:start position:0% +where a cod life assimilates life of a + + + align:start position:0% +where a cod life assimilates life of a +poor cat vendor and paper please + + align:start position:0% + + + + align:start position:0% + +simulates being a like an immigration + + align:start position:0% +simulates being a like an immigration + + + align:start position:0% +simulates being a like an immigration +officer and so I think also contact to + + align:start position:0% +officer and so I think also contact to + + + align:start position:0% +officer and so I think also contact to +attach with some people talked about + + align:start position:0% +attach with some people talked about + + + align:start position:0% +attach with some people talked about +they've become a moral turn like this + + align:start position:0% +they've become a moral turn like this + + + align:start position:0% +they've become a moral turn like this +lot of discussion about participation in + + align:start position:0% +lot of discussion about participation in + + + align:start position:0% +lot of discussion about participation in +various ways and in games and an + + align:start position:0% +various ways and in games and an + + + align:start position:0% +various ways and in games and an +attorney a lot of emphasis on trying to + + align:start position:0% +attorney a lot of emphasis on trying to + + + align:start position:0% +attorney a lot of emphasis on trying to +make games with more have serious team + + align:start position:0% +make games with more have serious team + + + align:start position:0% +make games with more have serious team +so that would cover a kind of broader + + align:start position:0% +so that would cover a kind of broader + + + align:start position:0% +so that would cover a kind of broader +range of the user until you see you see + + align:start position:0% +range of the user until you see you see + + + align:start position:0% +range of the user until you see you see +and so this is kind of shows you where + + align:start position:0% +and so this is kind of shows you where + + + align:start position:0% +and so this is kind of shows you where +this kind of style comes from the + + align:start position:0% +this kind of style comes from the + + + align:start position:0% +this kind of style comes from the +representation of the representation you + + align:start position:0% +representation of the representation you + + + align:start position:0% +representation of the representation you +can also see that basic actually every + + align:start position:0% +can also see that basic actually every + + + align:start position:0% +can also see that basic actually every +single winner since 2005 + + align:start position:0% +single winner since 2005 + + + align:start position:0% +single winner since 2005 +hesitation Catholics this kind of + + align:start position:0% +hesitation Catholics this kind of + + + align:start position:0% +hesitation Catholics this kind of +petition of representations time all + + align:start position:0% +petition of representations time all + + + align:start position:0% +petition of representations time all +right + + align:start position:0% +right + + + align:start position:0% +right +but what does it mean well there I think + + align:start position:0% +but what does it mean well there I think + + + align:start position:0% +but what does it mean well there I think +there are few kind of contradictions in + + align:start position:0% +there are few kind of contradictions in + + + align:start position:0% +there are few kind of contradictions in +independent games and so one of them has + + align:start position:0% +independent games and so one of them has + + + align:start position:0% +independent games and so one of them has +to do with what he calls like the DIY + + align:start position:0% +to do with what he calls like the DIY + + + align:start position:0% +to do with what he calls like the DIY +movement this idea that anybody can make + + align:start position:0% +movement this idea that anybody can make + + + align:start position:0% +movement this idea that anybody can make +a video game now with independent games + + align:start position:0% +a video game now with independent games + + + align:start position:0% +a video game now with independent games +versus the idea of independent games as + + align:start position:0% +versus the idea of independent games as + + + align:start position:0% +versus the idea of independent games as +being a kind of way for people to do + + align:start position:0% +being a kind of way for people to do + + + align:start position:0% +being a kind of way for people to do +games that have particularly expertly + + align:start position:0% +games that have particularly expertly + + + align:start position:0% +games that have particularly expertly +crafted so so something that was like + + align:start position:0% +crafted so so something that was like + + + align:start position:0% +crafted so so something that was like +Terry Cavanagh and she talking talks + + align:start position:0% +Terry Cavanagh and she talking talks + + + align:start position:0% +Terry Cavanagh and she talking talks +about how it's easy when to make a game + + align:start position:0% +about how it's easy when to make a game + + + align:start position:0% +about how it's easy when to make a game +with this kind of pixel style I think + + align:start position:0% +with this kind of pixel style I think + + + align:start position:0% +with this kind of pixel style I think +because it's nothing he doesn't consider + + align:start position:0% +because it's nothing he doesn't consider + + + align:start position:0% +because it's nothing he doesn't consider +himself that greater graphic artist and + + align:start position:0% +himself that greater graphic artist and + + + align:start position:0% +himself that greater graphic artist and +said way that it's kind of pixel studies + + align:start position:0% +said way that it's kind of pixel studies + + + align:start position:0% +said way that it's kind of pixel studies +easy for him to do to make in a + + align:start position:0% +easy for him to do to make in a + + + align:start position:0% +easy for him to do to make in a +convincing way on the other hand if you + + align:start position:0% +convincing way on the other hand if you + + + align:start position:0% +convincing way on the other hand if you +want to make a game like that in a tool + + align:start position:0% +want to make a game like that in a tool + + + align:start position:0% +want to make a game like that in a tool +like unity3d a default unity3d kind of + + align:start position:0% +like unity3d a default unity3d kind of + + + align:start position:0% +like unity3d a default unity3d kind of +doesn't want you to do that so so by + + align:start position:0% +doesn't want you to do that so so by + + + align:start position:0% +doesn't want you to do that so so by +default unity3d will soon as various + + align:start position:0% +default unity3d will soon as various + + + align:start position:0% +default unity3d will soon as various +filtering things on a new texture so if + + align:start position:0% +filtering things on a new texture so if + + + align:start position:0% +filtering things on a new texture so if +you just don't draw this or something + + align:start position:0% +you just don't draw this or something + + + align:start position:0% +you just don't draw this or something +with big pixels and be very blurry like + + align:start position:0% +with big pixels and be very blurry like + + + align:start position:0% +with big pixels and be very blurry like +under each other left so you have to do + + align:start position:0% +under each other left so you have to do + + + align:start position:0% +under each other left so you have to do +various things about changing the + + align:start position:0% +various things about changing the + + + align:start position:0% +various things about changing the +settings in the rendering of unity + + align:start position:0% +settings in the rendering of unity + + + align:start position:0% +settings in the rendering of unity +speedy track should do pixel style + + align:start position:0% +speedy track should do pixel style + + + align:start position:0% +speedy track should do pixel style +because that's really what the coolest + + align:start position:0% +because that's really what the coolest + + + align:start position:0% +because that's really what the coolest +minute for doing anyway and so this + + align:start position:0% +minute for doing anyway and so this + + + align:start position:0% +minute for doing anyway and so this +gives you the possibility of kind of + + align:start position:0% +gives you the possibility of kind of + + + align:start position:0% +gives you the possibility of kind of +demonstrating technical expertise by do + + align:start position:0% +demonstrating technical expertise by do + + + align:start position:0% +demonstrating technical expertise by do +you're working against intentions of the + + align:start position:0% +you're working against intentions of the + + + align:start position:0% +you're working against intentions of the +tool and that is the kind of that is a + + align:start position:0% +tool and that is the kind of that is a + + + align:start position:0% +tool and that is the kind of that is a +kind of a feature and so I think this is + + align:start position:0% +kind of a feature and so I think this is + + + align:start position:0% +kind of a feature and so I think this is +suddenly that's a kind of conflict in + + align:start position:0% +suddenly that's a kind of conflict in + + + align:start position:0% +suddenly that's a kind of conflict in +independent games between that like + + align:start position:0% +independent games between that like + + + align:start position:0% +independent games between that like +making independent games being these + + align:start position:0% +making independent games being these + + + align:start position:0% +making independent games being these +kind of kind of very small games in + + align:start position:0% +kind of kind of very small games in + + + align:start position:0% +kind of kind of very small games in +which a developer has the opportunity to + + align:start position:0% +which a developer has the opportunity to + + + align:start position:0% +which a developer has the opportunity to +show off how great they are various + + align:start position:0% +show off how great they are various + + + align:start position:0% +show off how great they are various +technical skills and they're balancing + + align:start position:0% +technical skills and they're balancing + + + align:start position:0% +technical skills and they're balancing +always like very small systems versus + + align:start position:0% +always like very small systems versus + + + align:start position:0% +always like very small systems versus +independent + + align:start position:0% +independent + + + align:start position:0% +independent +as being something where that kind of is + + align:start position:0% +as being something where that kind of is + + + align:start position:0% +as being something where that kind of is +open to everybody and so you can take a + + align:start position:0% +open to everybody and so you can take a + + + align:start position:0% +open to everybody and so you can take a +designer like anti entropy you wrote a + + align:start position:0% +designer like anti entropy you wrote a + + + align:start position:0% +designer like anti entropy you wrote a +book called rise of the videogame + + align:start position:0% +book called rise of the videogame + + + align:start position:0% +book called rise of the videogame +seamstress have reached normal to + + align:start position:0% +seamstress have reached normal to + + + align:start position:0% +seamstress have reached normal to +amateurs access prima scrub out squeeze + + align:start position:0% +amateurs access prima scrub out squeeze + + + align:start position:0% +amateurs access prima scrub out squeeze +housewives and people like you are + + align:start position:0% +housewives and people like you are + + + align:start position:0% +housewives and people like you are +taking back an art form I talked about + + align:start position:0% +taking back an art form I talked about + + + align:start position:0% +taking back an art form I talked about +but like making they can give it a + + align:start position:0% +but like making they can give it a + + + align:start position:0% +but like making they can give it a +little more democratic and at the same + + align:start position:0% +little more democratic and at the same + + + align:start position:0% +little more democratic and at the same +time when you see you and empathy skins + + align:start position:0% +time when you see you and empathy skins + + + align:start position:0% +time when you see you and empathy skins +she's actually very very good for sana + + align:start position:0% +she's actually very very good for sana + + + align:start position:0% +she's actually very very good for sana +so he makes these kind of games that are + + align:start position:0% +so he makes these kind of games that are + + + align:start position:0% +so he makes these kind of games that are +very she's good at combining elements + + align:start position:0% +very she's good at combining elements + + + align:start position:0% +very she's good at combining elements +from I'm getting history and introduce + + align:start position:0% +from I'm getting history and introduce + + + align:start position:0% +from I'm getting history and introduce +them in a new way the second element + + align:start position:0% +them in a new way the second element + + + align:start position:0% +them in a new way the second element +same contradiction are things more than + + align:start position:0% +same contradiction are things more than + + + align:start position:0% +same contradiction are things more than +the kind of use and like that that on + + align:start position:0% +the kind of use and like that that on + + + align:start position:0% +the kind of use and like that that on +the one hand on one hand this idea of + + align:start position:0% +the one hand on one hand this idea of + + + align:start position:0% +the one hand on one hand this idea of +independent games tend to have this idea + + align:start position:0% +independent games tend to have this idea + + + align:start position:0% +independent games tend to have this idea +it's kind of the democratization right + + align:start position:0% +it's kind of the democratization right + + + align:start position:0% +it's kind of the democratization right +because games by the people for the + + align:start position:0% +because games by the people for the + + + align:start position:0% +because games by the people for the +people from the other hand I think that + + align:start position:0% +people from the other hand I think that + + + align:start position:0% +people from the other hand I think that +that you can see that now that it's so + + align:start position:0% +that you can see that now that it's so + + + align:start position:0% +that you can see that now that it's so +common to play video games and more than + + align:start position:0% +common to play video games and more than + + + align:start position:0% +common to play video games and more than +50% of the population actually plays + + align:start position:0% +50% of the population actually plays + + + align:start position:0% +50% of the population actually plays +video games on a regular basis then I + + align:start position:0% +video games on a regular basis then I + + + align:start position:0% +video games on a regular basis then I +think also you to some extent indie + + align:start position:0% +think also you to some extent indie + + + align:start position:0% +think also you to some extent indie +games can be this kind of way of showing + + align:start position:0% +games can be this kind of way of showing + + + align:start position:0% +games can be this kind of way of showing +that you have a more sophisticated taste + + align:start position:0% +that you have a more sophisticated taste + + + align:start position:0% +that you have a more sophisticated taste +than the the kind of great masses right + + align:start position:0% +than the the kind of great masses right + + + align:start position:0% +than the the kind of great masses right +there if everybody please if everybody + + align:start position:0% +there if everybody please if everybody + + + align:start position:0% +there if everybody please if everybody +could please these candy crush then you + + align:start position:0% +could please these candy crush then you + + + align:start position:0% +could please these candy crush then you +can show that you're you're playing some + + align:start position:0% +can show that you're you're playing some + + + align:start position:0% +can show that you're you're playing some +obscure game from the from the Humble + + align:start position:0% +obscure game from the from the Humble + + + align:start position:0% +obscure game from the from the Humble +Bundle that sort of regular people don't + + align:start position:0% +Bundle that sort of regular people don't + + + align:start position:0% +Bundle that sort of regular people don't +really add any because Malcolm was kind + + align:start position:0% +really add any because Malcolm was kind + + + align:start position:0% +really add any because Malcolm was kind +of fine kind of wine tasting and so I + + align:start position:0% +of fine kind of wine tasting and so I + + + align:start position:0% +of fine kind of wine tasting and so I +think that + + align:start position:0% + + + + align:start position:0% + +suddenly you have I mean you have kind + + align:start position:0% +suddenly you have I mean you have kind + + + align:start position:0% +suddenly you have I mean you have kind +of breakout indie games life like + + align:start position:0% +of breakout indie games life like + + + align:start position:0% +of breakout indie games life like +Minecraft obviously which of course is a + + align:start position:0% +Minecraft obviously which of course is a + + + align:start position:0% +Minecraft obviously which of course is a +very very broad hit across like in a lot + + align:start position:0% +very very broad hit across like in a lot + + + align:start position:0% +very very broad hit across like in a lot +of countries I don't mean it's all about + + align:start position:0% +of countries I don't mean it's all about + + + align:start position:0% +of countries I don't mean it's all about +15 million copies it is going I'm going + + align:start position:0% +15 million copies it is going I'm going + + + align:start position:0% +15 million copies it is going I'm going +launch and then of course still is still + + align:start position:0% +launch and then of course still is still + + + align:start position:0% +launch and then of course still is still +like that the developer not she still + + align:start position:0% +like that the developer not she still + + + align:start position:0% +like that the developer not she still +asks it's kind of scruffy to himself + + align:start position:0% +asks it's kind of scruffy to himself + + + align:start position:0% +asks it's kind of scruffy to himself +goes from one to the other in fact he + + align:start position:0% +goes from one to the other in fact he + + + align:start position:0% +goes from one to the other in fact he +has a stylist to making sure that's + + align:start position:0% +has a stylist to making sure that's + + + align:start position:0% +has a stylist to making sure that's +making a big scruffy so it kind of keeps + + align:start position:0% +making a big scruffy so it kind of keeps + + + align:start position:0% +making a big scruffy so it kind of keeps +his yes yes yeah but but do you see this + + align:start position:0% +his yes yes yeah but but do you see this + + + align:start position:0% +his yes yes yeah but but do you see this +is that I think this is a kind of + + align:start position:0% +is that I think this is a kind of + + + align:start position:0% +is that I think this is a kind of +ongoing conflict within this independent + + align:start position:0% +ongoing conflict within this independent + + + align:start position:0% +ongoing conflict within this independent +game tried this with it it's something + + align:start position:0% +game tried this with it it's something + + + align:start position:0% +game tried this with it it's something +that is supposed to be kind of very + + align:start position:0% +that is supposed to be kind of very + + + align:start position:0% +that is supposed to be kind of very +broad or whether it's it is its kind of + + align:start position:0% +broad or whether it's it is its kind of + + + align:start position:0% +broad or whether it's it is its kind of +kind of surfing and I'm certain as you + + align:start position:0% +kind of surfing and I'm certain as you + + + align:start position:0% +kind of surfing and I'm certain as you +said this so do you think that that this + + align:start position:0% +said this so do you think that that this + + + align:start position:0% +said this so do you think that that this +you couldn't actually see this as we saw + + align:start position:0% +you couldn't actually see this as we saw + + + align:start position:0% +you couldn't actually see this as we saw +the prospect that so many people are + + align:start position:0% +the prospect that so many people are + + + align:start position:0% +the prospect that so many people are +playing video games right so it used to + + align:start position:0% +playing video games right so it used to + + + align:start position:0% +playing video games right so it used to +be that you could say the fact that you + + align:start position:0% +be that you could say the fact that you + + + align:start position:0% +be that you could say the fact that you +play video games video and belonging to + + align:start position:0% +play video games video and belonging to + + + align:start position:0% +play video games video and belonging to +a particular category of people right + + align:start position:0% +a particular category of people right + + + align:start position:0% +a particular category of people right +but now that video game playing is so + + align:start position:0% +but now that video game playing is so + + + align:start position:0% +but now that video game playing is so +common you need to people need to select + + align:start position:0% +common you need to people need to select + + + align:start position:0% +common you need to people need to select +like a certain subset of video games too + + align:start position:0% +like a certain subset of video games too + + + align:start position:0% +like a certain subset of video games too +we have an identity of this video game + + align:start position:0% +we have an identity of this video game + + + align:start position:0% +we have an identity of this video game +bears and then I think this kind of + + align:start position:0% +bears and then I think this kind of + + + align:start position:0% +bears and then I think this kind of +indie games can be seen as a kind of + + align:start position:0% +indie games can be seen as a kind of + + + align:start position:0% +indie games can be seen as a kind of +response to that it's something yeah it + + align:start position:0% +response to that it's something yeah it + + + align:start position:0% +response to that it's something yeah it +allows you to just kind of feel that you + + align:start position:0% +allows you to just kind of feel that you + + + align:start position:0% +allows you to just kind of feel that you +have a particular taste so a concept art + + align:start position:0% +have a particular taste so a concept art + + + align:start position:0% +have a particular taste so a concept art +activity and + + align:start position:0% + + + + align:start position:0% + +and the second which should Peters in + + align:start position:0% +and the second which should Peters in + + + align:start position:0% +and the second which should Peters in +touch about the idea until authenticity + + align:start position:0% +touch about the idea until authenticity + + + align:start position:0% +touch about the idea until authenticity +work so one of the things he studied + + align:start position:0% +work so one of the things he studied + + + align:start position:0% +work so one of the things he studied +this country music and it looks at how + + align:start position:0% +this country music and it looks at how + + + align:start position:0% +this country music and it looks at how +different how people arguing for for + + align:start position:0% +different how people arguing for for + + + align:start position:0% +different how people arguing for for +various types of country music's being + + align:start position:0% +various types of country music's being + + + align:start position:0% +various types of country music's being +authentic in different ways certainly we + + align:start position:0% +authentic in different ways certainly we + + + align:start position:0% +authentic in different ways certainly we +were thinking in terms of like who who + + align:start position:0% +were thinking in terms of like who who + + + align:start position:0% +were thinking in terms of like who who +recorded it though in terms of style or + + align:start position:0% +recorded it though in terms of style or + + + align:start position:0% +recorded it though in terms of style or +various and she says that authenticity + + align:start position:0% +various and she says that authenticity + + + align:start position:0% +various and she says that authenticity +work is whenever people try to put an + + align:start position:0% +work is whenever people try to put an + + + align:start position:0% +work is whenever people try to put an +effort in order to make something appear + + align:start position:0% +effort in order to make something appear + + + align:start position:0% +effort in order to make something appear +authentic so it's been like like the + + align:start position:0% +authentic so it's been like like the + + + align:start position:0% +authentic so it's been like like the +restaurant that if they actually spend + + align:start position:0% +restaurant that if they actually spend + + + align:start position:0% +restaurant that if they actually spend +spend energy listing all of the places + + align:start position:0% +spend energy listing all of the places + + + align:start position:0% +spend energy listing all of the places +from where they got their ingredients + + align:start position:0% +from where they got their ingredients + + + align:start position:0% +from where they got their ingredients +such as to make the whole continue at + + align:start position:0% +such as to make the whole continue at + + + align:start position:0% +such as to make the whole continue at +people have authentic and low points and + + align:start position:0% +people have authentic and low points and + + + align:start position:0% +people have authentic and low points and +so I kind of critical this particular + + align:start position:0% +so I kind of critical this particular + + + align:start position:0% +so I kind of critical this particular +kind of critical argument against it + + align:start position:0% +kind of critical argument against it + + + align:start position:0% +kind of critical argument against it +saying that if you like this to be + + align:start position:0% +saying that if you like this to be + + + align:start position:0% +saying that if you like this to be +experienced as authentic serving must be + + align:start position:0% +experienced as authentic serving must be + + + align:start position:0% +experienced as authentic serving must be +marked as authentic and this makes it or + + align:start position:0% +marked as authentic and this makes it or + + + align:start position:0% +marked as authentic and this makes it or +temps are not innocent to grab because + + align:start position:0% +temps are not innocent to grab because + + + align:start position:0% +temps are not innocent to grab because +nothing has been done deliberate and you + + align:start position:0% +nothing has been done deliberate and you + + + align:start position:0% +nothing has been done deliberate and you +can certainly see like environment all + + align:start position:0% +can certainly see like environment all + + + align:start position:0% +can certainly see like environment all +kinds of products obviously where where + + align:start position:0% +kinds of products obviously where where + + + align:start position:0% +kinds of products obviously where where +where you can see there's some kind of + + align:start position:0% +where you can see there's some kind of + + + align:start position:0% +where you can see there's some kind of +advertising agency has spent a large + + align:start position:0% +advertising agency has spent a large + + + align:start position:0% +advertising agency has spent a large +amount of time trying to figure out how + + align:start position:0% +amount of time trying to figure out how + + + align:start position:0% +amount of time trying to figure out how +to make that particular thing look + + align:start position:0% +to make that particular thing look + + + align:start position:0% +to make that particular thing look +authentic by changed choosing the right + + align:start position:0% +authentic by changed choosing the right + + + align:start position:0% +authentic by changed choosing the right +font so coloring so making it appear + + align:start position:0% +font so coloring so making it appear + + + align:start position:0% +font so coloring so making it appear +like an old country store or so even + + align:start position:0% +like an old country store or so even + + + align:start position:0% +like an old country store or so even +though it's big multi-billion dollar + + align:start position:0% +though it's big multi-billion dollar + + + align:start position:0% +though it's big multi-billion dollar +corporation and so on and so you can see + + align:start position:0% +corporation and so on and so you can see + + + align:start position:0% +corporation and so on and so you can see +this anyway even think of this would be + + align:start position:0% +this anyway even think of this would be + + + align:start position:0% +this anyway even think of this would be +a kind of critical idea of this would be + + align:start position:0% +a kind of critical idea of this would be + + + align:start position:0% +a kind of critical idea of this would be +kind of critical so you can say about + + align:start position:0% +kind of critical so you can say about + + + align:start position:0% +kind of critical so you can say about +independent games that of course you + + align:start position:0% +independent games that of course you + + + align:start position:0% +independent games that of course you +don't necessarily have to make games + + align:start position:0% +don't necessarily have to make games + + + align:start position:0% +don't necessarily have to make games +with this particular style and then that + + align:start position:0% +with this particular style and then that + + + align:start position:0% +with this particular style and then that +pepcid anyways there's something kind of + + align:start position:0% +pepcid anyways there's something kind of + + + align:start position:0% +pepcid anyways there's something kind of +enough fencing about choosing a kind of + + align:start position:0% +enough fencing about choosing a kind of + + + align:start position:0% +enough fencing about choosing a kind of +style to see authentic right and so that + + align:start position:0% +style to see authentic right and so that + + + align:start position:0% +style to see authentic right and so that +you can so but I think it's also been + + align:start position:0% +you can so but I think it's also been + + + align:start position:0% +you can so but I think it's also been +more complicated like that but because + + align:start position:0% +more complicated like that but because + + + align:start position:0% +more complicated like that but because +anyway just the fact that it's possible + + align:start position:0% +anyway just the fact that it's possible + + + align:start position:0% +anyway just the fact that it's possible +to make a game I choose + + align:start position:0% +to make a game I choose + + + align:start position:0% +to make a game I choose +particular style both actually that + + align:start position:0% +particular style both actually that + + + align:start position:0% +particular style both actually that +status both interesting because + + align:start position:0% +status both interesting because + + + align:start position:0% +status both interesting because +protected cheap it is fairly cheap to + + align:start position:0% +protected cheap it is fairly cheap to + + + align:start position:0% +protected cheap it is fairly cheap to +make games with like large pixels or + + align:start position:0% +make games with like large pixels or + + + align:start position:0% +make games with like large pixels or +scanned paper or things like that + + align:start position:0% +scanned paper or things like that + + + align:start position:0% +scanned paper or things like that +so even though you can say it's not it's + + align:start position:0% +so even though you can say it's not it's + + + align:start position:0% +so even though you can say it's not it's +not it's something that people sort of + + align:start position:0% +not it's something that people sort of + + + align:start position:0% +not it's something that people sort of +deliberately choose and so it's not + + align:start position:0% +deliberately choose and so it's not + + + align:start position:0% +deliberately choose and so it's not +authentic in that sense but it's still + + align:start position:0% +authentic in that sense but it's still + + + align:start position:0% +authentic in that sense but it's still +something that enables cheap did being + + align:start position:0% +something that enables cheap did being + + + align:start position:0% +something that enables cheap did being +development right so it does solve that + + align:start position:0% +development right so it does solve that + + + align:start position:0% +development right so it does solve that +particular problem of how do you make a + + align:start position:0% +particular problem of how do you make a + + + align:start position:0% +particular problem of how do you make a +game on a smaller budget and make it + + align:start position:0% +game on a smaller budget and make it + + + align:start position:0% +game on a smaller budget and make it +appear as a deliberate choice rather + + align:start position:0% +appear as a deliberate choice rather + + + align:start position:0% +appear as a deliberate choice rather +than just a game with two smaller budget + + align:start position:0% +than just a game with two smaller budget + + + align:start position:0% +than just a game with two smaller budget +and instead of you see that this is what + + align:start position:0% +and instead of you see that this is what + + + align:start position:0% +and instead of you see that this is what +that particular style dollars I just say + + align:start position:0% +that particular style dollars I just say + + + align:start position:0% +that particular style dollars I just say +that there are few games that we tend to + + align:start position:0% +that there are few games that we tend to + + + align:start position:0% +that there are few games that we tend to +talk of us independent which don't + + align:start position:0% +talk of us independent which don't + + + align:start position:0% +talk of us independent which don't +doesn't really match this style so free + + align:start position:0% +doesn't really match this style so free + + + align:start position:0% +doesn't really match this style so free +it's particularly interesting case + + align:start position:0% +it's particularly interesting case + + + align:start position:0% +it's particularly interesting case +because it does have this kind of + + align:start position:0% +because it does have this kind of + + + align:start position:0% +because it does have this kind of +representation of a representation style + + align:start position:0% +representation of a representation style + + + align:start position:0% +representation of a representation style +right it looks as a it's made us look at + + align:start position:0% +right it looks as a it's made us look at + + + align:start position:0% +right it looks as a it's made us look at +the painting but in the particular way + + align:start position:0% +the painting but in the particular way + + + align:start position:0% +the painting but in the particular way +it's not meant to look as if somebody's + + align:start position:0% +it's not meant to look as if somebody's + + + align:start position:0% +it's not meant to look as if somebody's +kind of offhand and improvised join this + + align:start position:0% +kind of offhand and improvised join this + + + align:start position:0% +kind of offhand and improvised join this +actually meant to look a bit like fine + + align:start position:0% +actually meant to look a bit like fine + + + align:start position:0% +actually meant to look a bit like fine +art and so you see in anyway it has this + + align:start position:0% +art and so you see in anyway it has this + + + align:start position:0% +art and so you see in anyway it has this +thing of being a representation of + + align:start position:0% +thing of being a representation of + + + align:start position:0% +thing of being a representation of +representation but here it's actually + + align:start position:0% +representation but here it's actually + + + align:start position:0% +representation but here it's actually +supposed to say that this is nothing + + align:start position:0% +supposed to say that this is nothing + + + align:start position:0% +supposed to say that this is nothing +like buying a nice or sophisticated and + + align:start position:0% +like buying a nice or sophisticated and + + + align:start position:0% +like buying a nice or sophisticated and +and I think this kind of match to said + + align:start position:0% +and I think this kind of match to said + + + align:start position:0% +and I think this kind of match to said +did you guys play parade or a video so + + align:start position:0% +did you guys play parade or a video so + + + align:start position:0% +did you guys play parade or a video so +greatest is meant to be a and a scindia + + align:start position:0% +greatest is meant to be a and a scindia + + + align:start position:0% +greatest is meant to be a and a scindia +a kind of work of art with a capital A + + align:start position:0% +a kind of work of art with a capital A + + + align:start position:0% +a kind of work of art with a capital A +and I do think this is why that + + align:start position:0% +and I do think this is why that + + + align:start position:0% +and I do think this is why that +particular style was choosing chosen I + + align:start position:0% +particular style was choosing chosen I + + + align:start position:0% +particular style was choosing chosen I +think it's a bit simplistic and that's \ No newline at end of file diff --git a/fdBTs6D2jpo.txt b/fdBTs6D2jpo.txt new file mode 100644 index 0000000000000000000000000000000000000000..93786734136e10d0f34bc233bf4e9ddae2fe93ca --- /dev/null +++ b/fdBTs6D2jpo.txt @@ -0,0 +1,7144 @@ +align:start position:0% + +the following content is provided by MIT + + align:start position:0% +the following content is provided by MIT + + + align:start position:0% +the following content is provided by MIT +open courseware under a Creative Commons + + align:start position:0% +open courseware under a Creative Commons + + + align:start position:0% +open courseware under a Creative Commons +license additional information about our + + align:start position:0% +license additional information about our + + + align:start position:0% +license additional information about our +license and MIT open courseware in + + align:start position:0% +license and MIT open courseware in + + + align:start position:0% +license and MIT open courseware in +general is available at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu so Monday's class really + + align:start position:0% +ocw.mit.edu so Monday's class really + + + align:start position:0% +ocw.mit.edu so Monday's class really +picks up from the lecture we had this + + align:start position:0% +picks up from the lecture we had this + + + align:start position:0% +picks up from the lecture we had this +past Monday so we started Crystal field + + align:start position:0% +past Monday so we started Crystal field + + + align:start position:0% +past Monday so we started Crystal field +Theory and then uh talked about + + align:start position:0% +Theory and then uh talked about + + + align:start position:0% +Theory and then uh talked about +octahedral shaped molecules and + + align:start position:0% +octahedral shaped molecules and + + + align:start position:0% +octahedral shaped molecules and +splitting of D orbitals and then on + + align:start position:0% +splitting of D orbitals and then on + + + align:start position:0% +splitting of D orbitals and then on +Monday we're going to continue with that + + align:start position:0% +Monday we're going to continue with that + + + align:start position:0% +Monday we're going to continue with that +topic we're going to move in and talk + + align:start position:0% +topic we're going to move in and talk + + + align:start position:0% +topic we're going to move in and talk +about tetrahedral molecules Square + + align:start position:0% +about tetrahedral molecules Square + + + align:start position:0% +about tetrahedral molecules Square +planer molecules and how they're going + + align:start position:0% +planer molecules and how they're going + + + align:start position:0% +planer molecules and how they're going +to uh split the D orbitals and then how + + align:start position:0% +to uh split the D orbitals and then how + + + align:start position:0% +to uh split the D orbitals and then how +that relates to something why we need to + + align:start position:0% +that relates to something why we need to + + + align:start position:0% +that relates to something why we need to +know about any of that and that's + + align:start position:0% +know about any of that and that's + + + align:start position:0% +know about any of that and that's +because it it's able to predict some of + + align:start position:0% +because it it's able to predict some of + + + align:start position:0% +because it it's able to predict some of +the properties of molecules like their + + align:start position:0% +the properties of molecules like their + + + align:start position:0% +the properties of molecules like their +their colors and also uh their their + + align:start position:0% +their colors and also uh their their + + + align:start position:0% +their colors and also uh their their +properties in terms of Spin and using + + align:start position:0% +properties in terms of Spin and using + + + align:start position:0% +properties in terms of Spin and using +various different spectroscopies to + + align:start position:0% +various different spectroscopies to + + + align:start position:0% +various different spectroscopies to +learn about something about particular + + align:start position:0% +learn about something about particular + + + align:start position:0% +learn about something about particular +um molecules coordination complexes so + + align:start position:0% +um molecules coordination complexes so + + + align:start position:0% +um molecules coordination complexes so +before we get into that unit we're going + + align:start position:0% +before we get into that unit we're going + + + align:start position:0% +before we get into that unit we're going +to kind of take a step back and talk + + align:start position:0% +to kind of take a step back and talk + + + align:start position:0% +to kind of take a step back and talk +today about shapes of molecules so we + + align:start position:0% +today about shapes of molecules so we + + + align:start position:0% +today about shapes of molecules so we +introduced octahedral but now we're + + align:start position:0% +introduced octahedral but now we're + + + align:start position:0% +introduced octahedral but now we're +going to talk about all the other kinds + + align:start position:0% +going to talk about all the other kinds + + + align:start position:0% +going to talk about all the other kinds +of of shapes of molecules and uh in in + + align:start position:0% +of of shapes of molecules and uh in in + + + align:start position:0% +of of shapes of molecules and uh in in +today's in today's + + align:start position:0% +today's in today's + + + align:start position:0% +today's in today's +lecture so this is um kind of jumping + + align:start position:0% +lecture so this is um kind of jumping + + + align:start position:0% +lecture so this is um kind of jumping +around in the book a little bit we've + + align:start position:0% +around in the book a little bit we've + + + align:start position:0% +around in the book a little bit we've +been in chapter 16 and now the way the + + align:start position:0% +been in chapter 16 and now the way the + + + align:start position:0% +been in chapter 16 and now the way the +book is divided uh this this particular + + align:start position:0% +book is divided uh this this particular + + + align:start position:0% +book is divided uh this this particular +unit is back in chapter 3 although it's + + align:start position:0% +unit is back in chapter 3 although it's + + + align:start position:0% +unit is back in chapter 3 although it's +referred to a lot in chapter 16 so this + + align:start position:0% +referred to a lot in chapter 16 so this + + + align:start position:0% +referred to a lot in chapter 16 so this +is kind of some of the things that you + + align:start position:0% +is kind of some of the things that you + + + align:start position:0% +is kind of some of the things that you +need to know to finish up chapter 16 and + + align:start position:0% +need to know to finish up chapter 16 and + + + align:start position:0% +need to know to finish up chapter 16 and +then on Monday we'll be back in chapter + + align:start position:0% +then on Monday we'll be back in chapter + + + align:start position:0% +then on Monday we'll be back in chapter +16 as + + align:start position:0% +16 as + + + align:start position:0% +16 as +well so again this is a little bit odd + + align:start position:0% +well so again this is a little bit odd + + + align:start position:0% +well so again this is a little bit odd +order because of the way the calendar + + align:start position:0% +order because of the way the calendar + + + align:start position:0% +order because of the way the calendar +fell this + + align:start position:0% +fell this + + + align:start position:0% +fell this +year all right so Vesper shapes of + + align:start position:0% +year all right so Vesper shapes of + + + align:start position:0% +year all right so Vesper shapes of +molecules why why do we need to know + + align:start position:0% +molecules why why do we need to know + + + align:start position:0% +molecules why why do we need to know +about this + + align:start position:0% +about this + + + align:start position:0% +about this +well as most of you know um I do protein + + align:start position:0% +well as most of you know um I do protein + + + align:start position:0% +well as most of you know um I do protein +crystallography which is all about + + align:start position:0% +crystallography which is all about + + + align:start position:0% +crystallography which is all about +structure so of course I'm going to + + align:start position:0% +structure so of course I'm going to + + + align:start position:0% +structure so of course I'm going to +think that that structure is important + + align:start position:0% +think that that structure is important + + + align:start position:0% +think that that structure is important +that shape and geometry are important + + align:start position:0% +that shape and geometry are important + + + align:start position:0% +that shape and geometry are important +and uh in fact they have an influence on + + align:start position:0% +and uh in fact they have an influence on + + + align:start position:0% +and uh in fact they have an influence on +the physical properties uh and chemical + + align:start position:0% +the physical properties uh and chemical + + + align:start position:0% +the physical properties uh and chemical +properties of molecules so things like + + align:start position:0% +properties of molecules so things like + + + align:start position:0% +properties of molecules so things like +melting points boiling points + + align:start position:0% +melting points boiling points + + + align:start position:0% +melting points boiling points +reactivities and in particular in + + align:start position:0% +reactivities and in particular in + + + align:start position:0% +reactivities and in particular in +biological systems it's important a + + align:start position:0% +biological systems it's important a + + + align:start position:0% +biological systems it's important a +biological system they have particular + + align:start position:0% +biological system they have particular + + + align:start position:0% +biological system they have particular +uh shapes of chyal molecules it's a + + align:start position:0% +uh shapes of chyal molecules it's a + + + align:start position:0% +uh shapes of chyal molecules it's a +chyal environment which we've talked + + align:start position:0% +chyal environment which we've talked + + + align:start position:0% +chyal environment which we've talked +about before and so molecules must fit + + align:start position:0% +about before and so molecules must fit + + + align:start position:0% +about before and so molecules must fit +precisely in that environment often if + + align:start position:0% +precisely in that environment often if + + + align:start position:0% +precisely in that environment often if +you're talking about an inhibitor of an + + align:start position:0% +you're talking about an inhibitor of an + + + align:start position:0% +you're talking about an inhibitor of an +enzyme the inhibitor or the + + align:start position:0% +enzyme the inhibitor or the + + + align:start position:0% +enzyme the inhibitor or the +pharmaceutical drug is designed so it + + align:start position:0% +pharmaceutical drug is designed so it + + + align:start position:0% +pharmaceutical drug is designed so it +specifically fits into a particular + + align:start position:0% +specifically fits into a particular + + + align:start position:0% +specifically fits into a particular +crevice in an active site and blocks + + align:start position:0% +crevice in an active site and blocks + + + align:start position:0% +crevice in an active site and blocks +activity so a lot of the world of + + align:start position:0% +activity so a lot of the world of + + + align:start position:0% +activity so a lot of the world of +pharmaceuticals is all about shape of + + align:start position:0% +pharmaceuticals is all about shape of + + + align:start position:0% +pharmaceuticals is all about shape of +molecules and how you design particular + + align:start position:0% +molecules and how you design particular + + + align:start position:0% +molecules and how you design particular +types of shap shapes of + + align:start position:0% +types of shap shapes of + + + align:start position:0% +types of shap shapes of +molecules so um so we we've learned a + + align:start position:0% +molecules so um so we we've learned a + + + align:start position:0% +molecules so um so we we've learned a +lot about this sort of area already and + + align:start position:0% +lot about this sort of area already and + + + align:start position:0% +lot about this sort of area already and +we found that uh the shapes of molecules + + align:start position:0% +we found that uh the shapes of molecules + + + align:start position:0% +we found that uh the shapes of molecules +can be predicted pretty well using + + align:start position:0% +can be predicted pretty well using + + + align:start position:0% +can be predicted pretty well using +simple methods based on Lewis structures + + align:start position:0% +simple methods based on Lewis structures + + + align:start position:0% +simple methods based on Lewis structures +and also in terms of thinking about sort + + align:start position:0% +and also in terms of thinking about sort + + + align:start position:0% +and also in terms of thinking about sort +of where orbitals are and how that that + + align:start position:0% +of where orbitals are and how that that + + + align:start position:0% +of where orbitals are and how that that +may affect uh the particular shape of + + align:start position:0% +may affect uh the particular shape of + + + align:start position:0% +may affect uh the particular shape of +the molecules so again this is sort of a + + align:start position:0% +the molecules so again this is sort of a + + + align:start position:0% +the molecules so again this is sort of a +simplistic view that works pretty pretty + + align:start position:0% +simplistic view that works pretty pretty + + + align:start position:0% +simplistic view that works pretty pretty +well + + align:start position:0% +well + + + align:start position:0% +well +and it'll be also on the next problem + + align:start position:0% +and it'll be also on the next problem + + + align:start position:0% +and it'll be also on the next problem +set a good opportunity for you to review + + align:start position:0% +set a good opportunity for you to review + + + align:start position:0% +set a good opportunity for you to review +Lewis structures before you take the + + align:start position:0% +Lewis structures before you take the + + + align:start position:0% +Lewis structures before you take the +final so sometimes this unit is with + + align:start position:0% +final so sometimes this unit is with + + + align:start position:0% +final so sometimes this unit is with +Lewis structures um there's some + + align:start position:0% +Lewis structures um there's some + + + align:start position:0% +Lewis structures um there's some +rationale for that but it's also kind of + + align:start position:0% +rationale for that but it's also kind of + + + align:start position:0% +rationale for that but it's also kind of +nice to come back to it later in the + + align:start position:0% +nice to come back to it later in the + + + align:start position:0% +nice to come back to it later in the +semester as a way to review things that + + align:start position:0% +semester as a way to review things that + + + align:start position:0% +semester as a way to review things that +you learned before and get you ready for + + align:start position:0% +you learned before and get you ready for + + + align:start position:0% +you learned before and get you ready for +the final exam all right so the + + align:start position:0% +the final exam all right so the + + + align:start position:0% +the final exam all right so the +particular Theory we're going to talk + + align:start position:0% +particular Theory we're going to talk + + + align:start position:0% +particular Theory we're going to talk +about today is referred to as + + align:start position:0% +about today is referred to as + + + align:start position:0% +about today is referred to as +Vesper and this is the veent shell + + align:start position:0% +Vesper and this is the veent shell + + + align:start position:0% +Vesper and this is the veent shell +electron pair repulsion + + align:start position:0% +electron pair repulsion + + + align:start position:0% +electron pair repulsion +Theory and so like Crystal field Theory + + align:start position:0% +Theory and so like Crystal field Theory + + + align:start position:0% +Theory and so like Crystal field Theory +you're talking about repulsive effects + + align:start position:0% +you're talking about repulsive effects + + + align:start position:0% +you're talking about repulsive effects +so here this is based on a simple + + align:start position:0% +so here this is based on a simple + + + align:start position:0% +so here this is based on a simple +principle that veence uh electron pairs + + align:start position:0% +principle that veence uh electron pairs + + + align:start position:0% +principle that veence uh electron pairs +will repel each other and that the + + align:start position:0% +will repel each other and that the + + + align:start position:0% +will repel each other and that the +geometry around a central atom will be + + align:start position:0% +geometry around a central atom will be + + + align:start position:0% +geometry around a central atom will be +such to minimize that repulsion so this + + align:start position:0% +such to minimize that repulsion so this + + + align:start position:0% +such to minimize that repulsion so this +is a lot like Crystal field Theory where + + align:start position:0% +is a lot like Crystal field Theory where + + + align:start position:0% +is a lot like Crystal field Theory where +we are talking about uh the splitting of + + align:start position:0% +we are talking about uh the splitting of + + + align:start position:0% +we are talking about uh the splitting of +the D orbitals and we're talk calling + + align:start position:0% +the D orbitals and we're talk calling + + + align:start position:0% +the D orbitals and we're talk calling +that ligans as negative point charges + + align:start position:0% +that ligans as negative point charges + + + align:start position:0% +that ligans as negative point charges +heading toward those D orbitals so a lot + + align:start position:0% +heading toward those D orbitals so a lot + + + align:start position:0% +heading toward those D orbitals so a lot +of these theories that work pretty well + + align:start position:0% +of these theories that work pretty well + + + align:start position:0% +of these theories that work pretty well +are just really based on the idea that + + align:start position:0% +are just really based on the idea that + + + align:start position:0% +are just really based on the idea that +you know repulsion is + + align:start position:0% +you know repulsion is + + + align:start position:0% +you know repulsion is +unfavorable uh so it's it's pretty + + align:start position:0% +unfavorable uh so it's it's pretty + + + align:start position:0% +unfavorable uh so it's it's pretty +pretty simple concept which can explain + + align:start position:0% +pretty simple concept which can explain + + + align:start position:0% +pretty simple concept which can explain +a lot in terms of properties of + + align:start position:0% +a lot in terms of properties of + + + align:start position:0% +a lot in terms of properties of +molecules so before we get into this + + align:start position:0% +molecules so before we get into this + + + align:start position:0% +molecules so before we get into this +there's always + + align:start position:0% +there's always + + + align:start position:0% +there's always +nomenclature that uh we must deal with + + align:start position:0% +nomenclature that uh we must deal with + + + align:start position:0% +nomenclature that uh we must deal with +and here's the nomenclature here we have + + align:start position:0% +and here's the nomenclature here we have + + + align:start position:0% +and here's the nomenclature here we have +a as a central + + align:start position:0% +a as a central + + + align:start position:0% +a as a central +a central atom so whatever's in the + + align:start position:0% +a central atom so whatever's in the + + + align:start position:0% +a central atom so whatever's in the +middle which when we're talking about uh + + align:start position:0% +middle which when we're talking about uh + + + align:start position:0% +middle which when we're talking about uh +about transition metals uh complexes + + align:start position:0% +about transition metals uh complexes + + + align:start position:0% +about transition metals uh complexes +would be your metal but uh this works + + align:start position:0% +would be your metal but uh this works + + + align:start position:0% +would be your metal but uh this works +for organic chemistry as well when + + align:start position:0% +for organic chemistry as well when + + + align:start position:0% +for organic chemistry as well when +you're all talking about carbon oxygen + + align:start position:0% +you're all talking about carbon oxygen + + + align:start position:0% +you're all talking about carbon oxygen +Sul for nitrogen and X is going to be + + align:start position:0% +Sul for nitrogen and X is going to be + + + align:start position:0% +Sul for nitrogen and X is going to be +your bound + + align:start position:0% +your bound + + + align:start position:0% +your bound +atom and E will be a lone pair of + + align:start position:0% +atom and E will be a lone pair of + + + align:start position:0% +atom and E will be a lone pair of +electrons hence the uh the + + align:start position:0% + + + + align:start position:0% + +E so there are just a few rules it's not + + align:start position:0% +E so there are just a few rules it's not + + + align:start position:0% +E so there are just a few rules it's not +too bad compared to some of the other + + align:start position:0% +too bad compared to some of the other + + + align:start position:0% +too bad compared to some of the other +things we've done just a handful of + + align:start position:0% +things we've done just a handful of + + + align:start position:0% +things we've done just a handful of +rules that you need to + + align:start position:0% +rules that you need to + + + align:start position:0% +rules that you need to +know first uh you need to know that the + + align:start position:0% +know first uh you need to know that the + + + align:start position:0% +know first uh you need to know that the +steric number abbreviated SN is used to + + align:start position:0% +steric number abbreviated SN is used to + + + align:start position:0% +steric number abbreviated SN is used to +predict geometries and what that steric + + align:start position:0% +predict geometries and what that steric + + + align:start position:0% +predict geometries and what that steric +number refers to so it refers to the + + align:start position:0% +number refers to so it refers to the + + + align:start position:0% +number refers to so it refers to the +number of atoms bound to the central + + align:start position:0% +number of atoms bound to the central + + + align:start position:0% +number of atoms bound to the central +atom plus the number of aone pair + + align:start position:0% +atom plus the number of aone pair + + + align:start position:0% +atom plus the number of aone pair +electrons on the central atom + + align:start position:0% +electrons on the central atom + + + align:start position:0% +electrons on the central atom +so here we're we're not concerned about + + align:start position:0% +so here we're we're not concerned about + + + align:start position:0% +so here we're we're not concerned about +double or triple bonds we're only + + align:start position:0% +double or triple bonds we're only + + + align:start position:0% +double or triple bonds we're only +concerned about how many things are + + align:start position:0% +concerned about how many things are + + + align:start position:0% +concerned about how many things are +around our Central atom both the bonded + + align:start position:0% +around our Central atom both the bonded + + + align:start position:0% +around our Central atom both the bonded +and the lone pairs so whether it's a + + align:start position:0% +and the lone pairs so whether it's a + + + align:start position:0% +and the lone pairs so whether it's a +double or a triple bond doesn't matter + + align:start position:0% +double or a triple bond doesn't matter + + + align:start position:0% +double or a triple bond doesn't matter +at all for these cases so it's the + + align:start position:0% +at all for these cases so it's the + + + align:start position:0% +at all for these cases so it's the +number of atoms bonded not not the + + align:start position:0% +number of atoms bonded not not the + + + align:start position:0% +number of atoms bonded not not the +number of bonds which is important to + + align:start position:0% +number of bonds which is important to + + + align:start position:0% +number of bonds which is important to +remember and so steric number here uh + + align:start position:0% +remember and so steric number here uh + + + align:start position:0% +remember and so steric number here uh +shouldn't be confused with coordination + + align:start position:0% +shouldn't be confused with coordination + + + align:start position:0% +shouldn't be confused with coordination +number which we talked about at + + align:start position:0% +number which we talked about at + + + align:start position:0% +number which we talked about at +transition metals which is just the + + align:start position:0% +transition metals which is just the + + + align:start position:0% +transition metals which is just the +number of lians around the central metal + + align:start position:0% +number of lians around the central metal + + + align:start position:0% +number of lians around the central metal +so there's a number of different things + + align:start position:0% +so there's a number of different things + + + align:start position:0% +so there's a number of different things +that you're going to learn + + align:start position:0% + + + + align:start position:0% + +about all right so if they're uh for + + align:start position:0% +about all right so if they're uh for + + + align:start position:0% +about all right so if they're uh for +Resident structures uh you can imply a + + align:start position:0% +Resident structures uh you can imply a + + + align:start position:0% +Resident structures uh you can imply a +Vesper to any one of them and uh there + + align:start position:0% +Vesper to any one of them and uh there + + + align:start position:0% +Vesper to any one of them and uh there +are two cases that we need to consider + + align:start position:0% +are two cases that we need to consider + + + align:start position:0% +are two cases that we need to consider +today one is the case when there are no + + align:start position:0% +today one is the case when there are no + + + align:start position:0% +today one is the case when there are no +loone paays and another is the case when + + align:start position:0% +loone paays and another is the case when + + + align:start position:0% +loone paays and another is the case when +there are alone pairs so those are all + + align:start position:0% +there are alone pairs so those are all + + + align:start position:0% +there are alone pairs so those are all +the rules it's really not not too + + align:start position:0% +the rules it's really not not too + + + align:start position:0% +the rules it's really not not too +complicated for + + align:start position:0% + + + + align:start position:0% + +this so we're just going to go through + + align:start position:0% +this so we're just going to go through + + + align:start position:0% +this so we're just going to go through +today and look at all these different + + align:start position:0% +today and look at all these different + + + align:start position:0% +today and look at all these different +molecules and consider the + + align:start position:0% +molecules and consider the + + + align:start position:0% +molecules and consider the +nomenclature and the geometry around + + align:start position:0% +nomenclature and the geometry around + + + align:start position:0% +nomenclature and the geometry around +them so first we'll consider formula + + align:start position:0% +them so first we'll consider formula + + + align:start position:0% +them so first we'll consider formula +type and so ax2 would mean that you have + + align:start position:0% +type and so ax2 would mean that you have + + + align:start position:0% +type and so ax2 would mean that you have +a central atom a and we have two atoms + + align:start position:0% +a central atom a and we have two atoms + + + align:start position:0% +a central atom a and we have two atoms +bound to it so two x's and now we're + + align:start position:0% +bound to it so two x's and now we're + + + align:start position:0% +bound to it so two x's and now we're +considering the cases without lone pairs + + align:start position:0% +considering the cases without lone pairs + + + align:start position:0% +considering the cases without lone pairs +of electrons so there won't be any EAS + + align:start position:0% +of electrons so there won't be any EAS + + + align:start position:0% +of electrons so there won't be any EAS +uh until later so then the steric number + + align:start position:0% +uh until later so then the steric number + + + align:start position:0% +uh until later so then the steric number +is going to be two and so here would be + + align:start position:0% +is going to be two and so here would be + + + align:start position:0% +is going to be two and so here would be +the shape of the + + align:start position:0% +the shape of the + + + align:start position:0% +the shape of the +molecule and so we have a center atom + + align:start position:0% +molecule and so we have a center atom + + + align:start position:0% +molecule and so we have a center atom +and two two atoms bound to it it would + + align:start position:0% +and two two atoms bound to it it would + + + align:start position:0% +and two two atoms bound to it it would +have linear geometry and a bond angle of + + align:start position:0% +have linear geometry and a bond angle of + + + align:start position:0% +have linear geometry and a bond angle of +one + + align:start position:0% + + + + align:start position:0% + +80 so that's pretty + + align:start position:0% + + + + align:start position:0% + +simple so now we go to the next category + + align:start position:0% +simple so now we go to the next category + + + align:start position:0% +simple so now we go to the next category +where you have three things bound so + + align:start position:0% +where you have three things bound so + + + align:start position:0% +where you have three things bound so +that would have an SN number of + + align:start position:0% +that would have an SN number of + + + align:start position:0% +that would have an SN number of +three and uh this is going to be the + + align:start position:0% +three and uh this is going to be the + + + align:start position:0% +three and uh this is going to be the +shape of that molecule and what is this + + align:start position:0% +shape of that molecule and what is this + + + align:start position:0% +shape of that molecule and what is this +called trigonal + + align:start position:0% +called trigonal + + + align:start position:0% +called trigonal +planer and what are the + + align:start position:0% +planer and what are the + + + align:start position:0% +planer and what are the +angles 190 or + + align:start position:0% +angles 190 or + + + align:start position:0% +angles 190 or +120 okay so now if we move up to + + align:start position:0% + + + + align:start position:0% + +four and uh this one should be pretty + + align:start position:0% +four and uh this one should be pretty + + + align:start position:0% +four and uh this one should be pretty +familiar to you so if we have four + + align:start position:0% +familiar to you so if we have four + + + align:start position:0% +familiar to you so if we have four +things bound SN number of four this is + + align:start position:0% +things bound SN number of four this is + + + align:start position:0% +things bound SN number of four this is +the molecular shape that we have and you + + align:start position:0% +the molecular shape that we have and you + + + align:start position:0% +the molecular shape that we have and you +all know this as a tetrahedral and the + + align:start position:0% +all know this as a tetrahedral and the + + + align:start position:0% +all know this as a tetrahedral and the +angles of tetrahedral + + align:start position:0% +angles of tetrahedral + + + align:start position:0% +angles of tetrahedral +are + + align:start position:0% +are + + + align:start position:0% +are +109.5 so these are all things you have + + align:start position:0% +109.5 so these are all things you have + + + align:start position:0% +109.5 so these are all things you have +to memorize so it's good uh to uh this + + align:start position:0% +to memorize so it's good uh to uh this + + + align:start position:0% +to memorize so it's good uh to uh this +is written in your notes but if you + + align:start position:0% +is written in your notes but if you + + + align:start position:0% +is written in your notes but if you +don't look at your notes and just try to + + align:start position:0% +don't look at your notes and just try to + + + align:start position:0% +don't look at your notes and just try to +think about it it'll be a good good + + align:start position:0% +think about it it'll be a good good + + + align:start position:0% +think about it it'll be a good good +review uh for uh the next exam on this + + align:start position:0% +review uh for uh the next exam on this + + + align:start position:0% +review uh for uh the next exam on this +topic all right so if we go into the + + align:start position:0% +topic all right so if we go into the + + + align:start position:0% +topic all right so if we go into the +next category when we have five things + + align:start position:0% +next category when we have five things + + + align:start position:0% +next category when we have five things +bound so that would be + + align:start position:0% +bound so that would be + + + align:start position:0% +bound so that would be +ax5 five atoms bound SN number of five + + align:start position:0% +ax5 five atoms bound SN number of five + + + align:start position:0% +ax5 five atoms bound SN number of five +we have this uh trigonal by paramal + + align:start position:0% +we have this uh trigonal by paramal + + + align:start position:0% +we have this uh trigonal by paramal +geometry and what are the what are the + + align:start position:0% +geometry and what are the what are the + + + align:start position:0% +geometry and what are the what are the +angles around the equator here + + align:start position:0% +angles around the equator here + + + align:start position:0% +angles around the equator here +connecting the red atoms 120 and what + + align:start position:0% +connecting the red atoms 120 and what + + + align:start position:0% +connecting the red atoms 120 and what +about red to Black + + align:start position:0% +about red to Black + + + align:start position:0% +about red to Black + + align:start position:0% + + + align:start position:0% +right and uh then if we go to the next + + align:start position:0% +right and uh then if we go to the next + + + align:start position:0% +right and uh then if we go to the next +category when we have six things we + + align:start position:0% +category when we have six things we + + + align:start position:0% +category when we have six things we +talked a lot about this in in the last + + align:start position:0% +talked a lot about this in in the last + + + align:start position:0% +talked a lot about this in in the last +two + + align:start position:0% +two + + + align:start position:0% +two +classes so uh what kind of geometry is + + align:start position:0% + + + + align:start position:0% + +this it's octahedral geometry with + + align:start position:0% +this it's octahedral geometry with + + + align:start position:0% +this it's octahedral geometry with +angles + + align:start position:0% +angles + + + align:start position:0% +angles +of 90 right so these are all the basic + + align:start position:0% +of 90 right so these are all the basic + + + align:start position:0% +of 90 right so these are all the basic +uh shapes when you just have uh two + + align:start position:0% +uh shapes when you just have uh two + + + align:start position:0% +uh shapes when you just have uh two +through six atoms + + align:start position:0% +through six atoms + + + align:start position:0% +through six atoms +bound so let's take a look at a couple + + align:start position:0% +bound so let's take a look at a couple + + + align:start position:0% +bound so let's take a look at a couple +of examples of molecules when we have + + align:start position:0% +of examples of molecules when we have + + + align:start position:0% +of examples of molecules when we have +actual atoms + + align:start position:0% +actual atoms + + + align:start position:0% +actual atoms +listed if we look at + + align:start position:0% +listed if we look at + + + align:start position:0% +listed if we look at +CO2 what is our SN + + align:start position:0% +CO2 what is our SN + + + align:start position:0% +CO2 what is our SN +number two right so we're only + + align:start position:0% +number two right so we're only + + + align:start position:0% +number two right so we're only +considering the number of atoms bound we + + align:start position:0% +considering the number of atoms bound we + + + align:start position:0% +considering the number of atoms bound we +don't care that they're double bonds + + align:start position:0% +don't care that they're double bonds + + + align:start position:0% +don't care that they're double bonds +we're only concerned with the atoms that + + align:start position:0% +we're only concerned with the atoms that + + + align:start position:0% +we're only concerned with the atoms that +are linked to the central atom here so + + align:start position:0% +are linked to the central atom here so + + + align:start position:0% +are linked to the central atom here so +then the geometry is + + align:start position:0% +then the geometry is + + + align:start position:0% +then the geometry is +what linear and + + align:start position:0% +what linear and + + + align:start position:0% +what linear and +angles 180 right so we'll look at + + align:start position:0% +angles 180 right so we'll look at + + + align:start position:0% +angles 180 right so we'll look at +another example here is this one going + + align:start position:0% +another example here is this one going + + + align:start position:0% +another example here is this one going +to be the same or different from the one + + align:start position:0% +to be the same or different from the one + + + align:start position:0% +to be the same or different from the one +above same right because we don't care + + align:start position:0% +above same right because we don't care + + + align:start position:0% +above same right because we don't care +about the double or triple bonds so we + + align:start position:0% +about the double or triple bonds so we + + + align:start position:0% +about the double or triple bonds so we +can go through SN number is still two + + align:start position:0% +can go through SN number is still two + + + align:start position:0% +can go through SN number is still two +it's still linear and the angle is still + + align:start position:0% + + + + align:start position:0% + +180 okay so we move into another example + + align:start position:0% +180 okay so we move into another example + + + align:start position:0% +180 okay so we move into another example +here and I'll just uh I'll just say that + + align:start position:0% +here and I'll just uh I'll just say that + + + align:start position:0% +here and I'll just uh I'll just say that +these lecture handouts have uh this + + align:start position:0% +these lecture handouts have uh this + + + align:start position:0% +these lecture handouts have uh this +information in here this is the most + + align:start position:0% +information in here this is the most + + + align:start position:0% +information in here this is the most +requested lecture handout that I have + + align:start position:0% +requested lecture handout that I have + + + align:start position:0% +requested lecture handout that I have +from people who have been in the classes + + align:start position:0% +from people who have been in the classes + + + align:start position:0% +from people who have been in the classes +who get up to other level classes and + + align:start position:0% +who get up to other level classes and + + + align:start position:0% +who get up to other level classes and +need to know this stuff and for some + + align:start position:0% +need to know this stuff and for some + + + align:start position:0% +need to know this stuff and for some +reason some of them have not kept their + + align:start position:0% +reason some of them have not kept their + + + align:start position:0% +reason some of them have not kept their +511 notes sort of next to their pillow + + align:start position:0% +511 notes sort of next to their pillow + + + align:start position:0% +511 notes sort of next to their pillow +in later years I'm not really sure why + + align:start position:0% +in later years I'm not really sure why + + + align:start position:0% +in later years I'm not really sure why +but sometimes it gets lost and they + + align:start position:0% +but sometimes it gets lost and they + + + align:start position:0% +but sometimes it gets lost and they +request this handout because it's a + + align:start position:0% +request this handout because it's a + + + align:start position:0% +request this handout because it's a +really nice summary of all of these + + align:start position:0% +really nice summary of all of these + + + align:start position:0% +really nice summary of all of these +things so you might want to you know + + align:start position:0% +things so you might want to you know + + + align:start position:0% +things so you might want to you know +keep it in a nice special place for + + align:start position:0% +keep it in a nice special place for + + + align:start position:0% +keep it in a nice special place for +future for future reference all right + + align:start position:0% +future for future reference all right + + + align:start position:0% +future for future reference all right +someday I should bring in what my + + align:start position:0% +someday I should bring in what my + + + align:start position:0% +someday I should bring in what my +freshman chemistry textbook looked like + + align:start position:0% +freshman chemistry textbook looked like + + + align:start position:0% +freshman chemistry textbook looked like +with like everything highlighted and + + align:start position:0% +with like everything highlighted and + + + align:start position:0% +with like everything highlighted and +stuff just for entertainment value all + + align:start position:0% +stuff just for entertainment value all + + + align:start position:0% +stuff just for entertainment value all +right so uh this this molecule here + + align:start position:0% +right so uh this this molecule here + + + align:start position:0% +right so uh this this molecule here +would have an SN number + + align:start position:0% +would have an SN number + + + align:start position:0% +would have an SN number +of of three and it shape + + align:start position:0% +of of three and it shape + + + align:start position:0% +of of three and it shape +again trigonal planer and + + align:start position:0% +again trigonal planer and + + + align:start position:0% +again trigonal planer and +angles 180 by the time we get through + + align:start position:0% +angles 180 by the time we get through + + + align:start position:0% +angles 180 by the time we get through +with lecture today you should have all + + align:start position:0% +with lecture today you should have all + + + align:start position:0% +with lecture today you should have all +of this memorized because we're going to + + align:start position:0% +of this memorized because we're going to + + + align:start position:0% +of this memorized because we're going to +see these a couple more + + align:start position:0% +see these a couple more + + + align:start position:0% +see these a couple more +times all right so this this + + align:start position:0% +times all right so this this + + + align:start position:0% +times all right so this this +one what molecule is this does someone + + align:start position:0% +one what molecule is this does someone + + + align:start position:0% +one what molecule is this does someone +know its name methane right so again + + align:start position:0% +know its name methane right so again + + + align:start position:0% +know its name methane right so again +what's this + + align:start position:0% +what's this + + + align:start position:0% +what's this +geometry tetrahedral SN number of four + + align:start position:0% +geometry tetrahedral SN number of four + + + align:start position:0% +geometry tetrahedral SN number of four +and angles + + align:start position:0% +and angles + + + align:start position:0% +and angles +of + + align:start position:0% +of + + + align:start position:0% +of +right okay now we get into a few more + + align:start position:0% +right okay now we get into a few more + + + align:start position:0% +right okay now we get into a few more +complicated molecules that you don't see + + align:start position:0% +complicated molecules that you don't see + + + align:start position:0% +complicated molecules that you don't see +quite as often although I think we have + + align:start position:0% +quite as often although I think we have + + + align:start position:0% +quite as often although I think we have +seen this one quite often in different + + align:start position:0% +seen this one quite often in different + + + align:start position:0% +seen this one quite often in different +kinds of problems including chemical + + align:start position:0% +kinds of problems including chemical + + + align:start position:0% +kinds of problems including chemical +equilibrium and other things uh so SN + + align:start position:0% +equilibrium and other things uh so SN + + + align:start position:0% +equilibrium and other things uh so SN +number here five geometry + + align:start position:0% + + + + align:start position:0% + +it's hard to say that one in unison we + + align:start position:0% +it's hard to say that one in unison we + + + align:start position:0% +it's hard to say that one in unison we +can work on this for the end of of + + align:start position:0% +can work on this for the end of of + + + align:start position:0% +can work on this for the end of of +lecture that we can all say it in + + align:start position:0% +lecture that we can all say it in + + + align:start position:0% +lecture that we can all say it in +harmony all right and our angles + + align:start position:0% +harmony all right and our angles + + + align:start position:0% +harmony all right and our angles +again + + align:start position:0% +again + + + align:start position:0% +again +yeah okay and one last one this should + + align:start position:0% +yeah okay and one last one this should + + + align:start position:0% +yeah okay and one last one this should +be very familiar to + + align:start position:0% +be very familiar to + + + align:start position:0% +be very familiar to +you so this is uh SN + + align:start position:0% +you so this is uh SN + + + align:start position:0% +you so this is uh SN +number six + + align:start position:0% +number six + + + align:start position:0% +number six +geometry octahedral angles 90 okay okay + + align:start position:0% +geometry octahedral angles 90 okay okay + + + align:start position:0% +geometry octahedral angles 90 okay okay +people are doing well okay so here's + + align:start position:0% +people are doing well okay so here's + + + align:start position:0% +people are doing well okay so here's +some some stuff that you may not um have + + align:start position:0% +some some stuff that you may not um have + + + align:start position:0% +some some stuff that you may not um have +heard before or maybe have in another + + align:start position:0% +heard before or maybe have in another + + + align:start position:0% +heard before or maybe have in another +chemistry course um but now we're going + + align:start position:0% +chemistry course um but now we're going + + + align:start position:0% +chemistry course um but now we're going +to introduce lone Pairs and see what + + align:start position:0% +to introduce lone Pairs and see what + + + align:start position:0% +to introduce lone Pairs and see what +effect this + + align:start position:0% +effect this + + + align:start position:0% +effect this +has so it gets a little bit more + + align:start position:0% +has so it gets a little bit more + + + align:start position:0% +has so it gets a little bit more +complicated at this + + align:start position:0% +complicated at this + + + align:start position:0% +complicated at this +point so for lone pairs we think of them + + align:start position:0% +point so for lone pairs we think of them + + + align:start position:0% +point so for lone pairs we think of them +as as being sort of uh centrally located + + align:start position:0% +as as being sort of uh centrally located + + + align:start position:0% +as as being sort of uh centrally located +and I brought in some props to talk + + align:start position:0% +and I brought in some props to talk + + + align:start position:0% +and I brought in some props to talk +about uh the spatial distribution of + + align:start position:0% +about uh the spatial distribution of + + + align:start position:0% +about uh the spatial distribution of +electrons so one can imagine that the + + align:start position:0% +electrons so one can imagine that the + + + align:start position:0% +electrons so one can imagine that the +electrons are spread out as far as they + + align:start position:0% +electrons are spread out as far as they + + + align:start position:0% +electrons are spread out as far as they +can go and so they like to have a lot of + + align:start position:0% +can go and so they like to have a lot of + + + align:start position:0% +can go and so they like to have a lot of +space and so the lone pair electrons are + + align:start position:0% +space and so the lone pair electrons are + + + align:start position:0% +space and so the lone pair electrons are +going to take up more space and + + align:start position:0% +going to take up more space and + + + align:start position:0% +going to take up more space and +experience more repulsion than when you + + align:start position:0% +experience more repulsion than when you + + + align:start position:0% +experience more repulsion than when you +have the electrons as part of bonds to + + align:start position:0% +have the electrons as part of bonds to + + + align:start position:0% +have the electrons as part of bonds to +atoms so the lone pairs are not sort of + + align:start position:0% +atoms so the lone pairs are not sort of + + + align:start position:0% +atoms so the lone pairs are not sort of +held in as much they're not sort of + + align:start position:0% +held in as much they're not sort of + + + align:start position:0% +held in as much they're not sort of +forced to be in one Loc + + align:start position:0% +forced to be in one Loc + + + align:start position:0% +forced to be in one Loc +so they'll they'll spread out more and + + align:start position:0% +so they'll they'll spread out more and + + + align:start position:0% +so they'll they'll spread out more and +so because this they're spreading out + + align:start position:0% +so because this they're spreading out + + + align:start position:0% +so because this they're spreading out +more they're taking up room they're kind + + align:start position:0% +more they're taking up room they're kind + + + align:start position:0% +more they're taking up room they're kind +of pushing everything away because they + + align:start position:0% +of pushing everything away because they + + + align:start position:0% +of pushing everything away because they +want to have as much room as they + + align:start position:0% +want to have as much room as they + + + align:start position:0% +want to have as much room as they +possibly can so that means that lone + + align:start position:0% +possibly can so that means that lone + + + align:start position:0% +possibly can so that means that lone +pairs are going to be more repulsive + + align:start position:0% +pairs are going to be more repulsive + + + align:start position:0% +pairs are going to be more repulsive +than the atoms that are bound even + + align:start position:0% +than the atoms that are bound even + + + align:start position:0% +than the atoms that are bound even +though electrons are involved in those + + align:start position:0% +though electrons are involved in those + + + align:start position:0% +though electrons are involved in those +bonds they're not quite as bad so the + + align:start position:0% +bonds they're not quite as bad so the + + + align:start position:0% +bonds they're not quite as bad so the +worst thing you can have is two sets of + + align:start position:0% +worst thing you can have is two sets of + + + align:start position:0% +worst thing you can have is two sets of +Lone pairs near each other they want all + + align:start position:0% +Lone pairs near each other they want all + + + align:start position:0% +Lone pairs near each other they want all +the room and so they're going to be sort + + align:start position:0% +the room and so they're going to be sort + + + align:start position:0% +the room and so they're going to be sort +of bumping into each other and trying to + + align:start position:0% +of bumping into each other and trying to + + + align:start position:0% +of bumping into each other and trying to +force the other set farther away see + + align:start position:0% +force the other set farther away see + + + align:start position:0% +force the other set farther away see +these this is much more bulky than if + + align:start position:0% +these this is much more bulky than if + + + align:start position:0% +these this is much more bulky than if +you just have the two two atoms uh bound + + align:start position:0% +you just have the two two atoms uh bound + + + align:start position:0% +you just have the two two atoms uh bound +with bonds to a central atom so the next + + align:start position:0% +with bonds to a central atom so the next + + + align:start position:0% +with bonds to a central atom so the next +would be a lone pair versus a bonding + + align:start position:0% +would be a lone pair versus a bonding + + + align:start position:0% +would be a lone pair versus a bonding +pair and then the least repulsive will + + align:start position:0% +pair and then the least repulsive will + + + align:start position:0% +pair and then the least repulsive will +be two bonding pairs because those + + align:start position:0% +be two bonding pairs because those + + + align:start position:0% +be two bonding pairs because those +electrons are sort of fixed into + + align:start position:0% +electrons are sort of fixed into + + + align:start position:0% +electrons are sort of fixed into +locations for the bonds so they aren't + + align:start position:0% +locations for the bonds so they aren't + + + align:start position:0% +locations for the bonds so they aren't +require iring as much space so they're + + align:start position:0% +require iring as much space so they're + + + align:start position:0% +require iring as much space so they're +not sort of spreading out and taking + + align:start position:0% +not sort of spreading out and taking + + + align:start position:0% +not sort of spreading out and taking +taking over all the space that's + + align:start position:0% +taking over all the space that's + + + align:start position:0% +taking over all the space that's +available so worst is lone pair lone + + align:start position:0% +available so worst is lone pair lone + + + align:start position:0% +available so worst is lone pair lone +pair then lone pair bonding and then + + align:start position:0% +pair then lone pair bonding and then + + + align:start position:0% +pair then lone pair bonding and then +bonding bonding and if you think about + + align:start position:0% +bonding bonding and if you think about + + + align:start position:0% +bonding bonding and if you think about +this sort of simple rule You can predict + + align:start position:0% +this sort of simple rule You can predict + + + align:start position:0% +this sort of simple rule You can predict +a lot about the shapes of + + align:start position:0% +a lot about the shapes of + + + align:start position:0% +a lot about the shapes of +molecules so let's look at what uh shape + + align:start position:0% +molecules so let's look at what uh shape + + + align:start position:0% +molecules so let's look at what uh shape +something will have if it has this sort + + align:start position:0% +something will have if it has this sort + + + align:start position:0% +something will have if it has this sort +of set molecule so again a the central + + align:start position:0% +of set molecule so again a the central + + + align:start position:0% +of set molecule so again a the central +atom X is four atoms that are bonded to + + align:start position:0% +atom X is four atoms that are bonded to + + + align:start position:0% +atom X is four atoms that are bonded to +the central atom and E is one set of + + align:start position:0% +the central atom and E is one set of + + + align:start position:0% +the central atom and E is one set of +lone pair and so this is going to have + + align:start position:0% +lone pair and so this is going to have + + + align:start position:0% +lone pair and so this is going to have +what's known as a seesaw shape and if + + align:start position:0% +what's known as a seesaw shape and if + + + align:start position:0% +what's known as a seesaw shape and if +let's think about why that would be the + + align:start position:0% + + + + align:start position:0% + +case so if we have this sort of central + + align:start position:0% +case so if we have this sort of central + + + align:start position:0% +case so if we have this sort of central +framework but one of these bonded atoms + + align:start position:0% +framework but one of these bonded atoms + + + align:start position:0% +framework but one of these bonded atoms +is now going to be replaced with a lone + + align:start position:0% +is now going to be replaced with a lone + + + align:start position:0% +is now going to be replaced with a lone +pair so they're five things around this + + align:start position:0% +pair so they're five things around this + + + align:start position:0% +pair so they're five things around this +framework one is a lone pair so where + + align:start position:0% +framework one is a lone pair so where + + + align:start position:0% +framework one is a lone pair so where +are you going to put + + align:start position:0% + + + + align:start position:0% + +it so if we put it on + + align:start position:0% +it so if we put it on + + + align:start position:0% +it so if we put it on +top what is the what are the angles + + align:start position:0% +top what is the what are the angles + + + align:start position:0% +top what is the what are the angles +between this lone pairs on top and the + + align:start position:0% +between this lone pairs on top and the + + + align:start position:0% +between this lone pairs on top and the +three red uh bonded atoms 90 so that's + + align:start position:0% +three red uh bonded atoms 90 so that's + + + align:start position:0% +three red uh bonded atoms 90 so that's +kind of close and not so favorable if we + + align:start position:0% +kind of close and not so favorable if we + + + align:start position:0% +kind of close and not so favorable if we +instead put one over here + + align:start position:0% + + + + align:start position:0% + +then then we have still this sort of + + align:start position:0% +then then we have still this sort of + + + align:start position:0% +then then we have still this sort of +negative interaction with the 90 here + + align:start position:0% +negative interaction with the 90 here + + + align:start position:0% +negative interaction with the 90 here +and the 90 here but we only have two of + + align:start position:0% +and the 90 here but we only have two of + + + align:start position:0% +and the 90 here but we only have two of +them instead of three and these guys are + + align:start position:0% +them instead of three and these guys are + + + align:start position:0% +them instead of three and these guys are +120 apart so it's not so bad so there's + + align:start position:0% +120 apart so it's not so bad so there's + + + align:start position:0% +120 apart so it's not so bad so there's +a little bit more space in the + + align:start position:0% +a little bit more space in the + + + align:start position:0% +a little bit more space in the +equatorial position and so that's why + + align:start position:0% +equatorial position and so that's why + + + align:start position:0% +equatorial position and so that's why +you get this this seesaw shape uh + + align:start position:0% +you get this this seesaw shape uh + + + align:start position:0% +you get this this seesaw shape uh +because you would want to put it in the + + align:start position:0% +because you would want to put it in the + + + align:start position:0% +because you would want to put it in the +equatorial position with where there's + + align:start position:0% +equatorial position with where there's + + + align:start position:0% +equatorial position with where there's +only sort of these two rather than three + + align:start position:0% +only sort of these two rather than three + + + align:start position:0% +only sort of these two rather than three +there's just a little bit more space + + align:start position:0% +there's just a little bit more space + + + align:start position:0% +there's just a little bit more space +because these guys are farther away so + + align:start position:0% +because these guys are farther away so + + + align:start position:0% +because these guys are farther away so +that gives rise to seesaw geometry so + + align:start position:0% +that gives rise to seesaw geometry so + + + align:start position:0% +that gives rise to seesaw geometry so +you can sort of again uh these rules are + + align:start position:0% +you can sort of again uh these rules are + + + align:start position:0% +you can sort of again uh these rules are +more to explain in retrospect what's + + align:start position:0% +more to explain in retrospect what's + + + align:start position:0% +more to explain in retrospect what's +observed about those molecules and then + + align:start position:0% +observed about those molecules and then + + + align:start position:0% +observed about those molecules and then +you rationalize but the rationalization + + align:start position:0% +you rationalize but the rationalization + + + align:start position:0% +you rationalize but the rationalization +works pretty well so if we do that if we + + align:start position:0% +works pretty well so if we do that if we + + + align:start position:0% +works pretty well so if we do that if we +put a lone pair then here instead of at + + align:start position:0% +put a lone pair then here instead of at + + + align:start position:0% +put a lone pair then here instead of at +one of the these top positions this we + + align:start position:0% +one of the these top positions this we + + + align:start position:0% +one of the these top positions this we +get this seesaw geometry and so let me + + align:start position:0% +get this seesaw geometry and so let me + + + align:start position:0% +get this seesaw geometry and so let me +help you um remember this so see get the + + align:start position:0% +help you um remember this so see get the + + + align:start position:0% +help you um remember this so see get the +Seesaw + + align:start position:0% + + + + align:start position:0% + +geometry how many of you actually grew + + align:start position:0% +geometry how many of you actually grew + + + align:start position:0% +geometry how many of you actually grew +up with seesaws in the neighborhood + + align:start position:0% +up with seesaws in the neighborhood + + + align:start position:0% +up with seesaws in the neighborhood +playground oh still most people okay + + align:start position:0% +playground oh still most people okay + + + align:start position:0% +playground oh still most people okay +they're actually one of the most + + align:start position:0% +they're actually one of the most + + + align:start position:0% +they're actually one of the most +dangerous toys and I think a lot of + + align:start position:0% +dangerous toys and I think a lot of + + + align:start position:0% +dangerous toys and I think a lot of +playgrounds um have removed them because + + align:start position:0% +playgrounds um have removed them because + + + align:start position:0% +playgrounds um have removed them because +of the uh the one kid who sort of sits + + align:start position:0% +of the uh the one kid who sort of sits + + + align:start position:0% +of the uh the one kid who sort of sits +on it and keeps you like stuck up in the + + align:start position:0% +on it and keeps you like stuck up in the + + + align:start position:0% +on it and keeps you like stuck up in the +air because they're a little heavier + + align:start position:0% +air because they're a little heavier + + + align:start position:0% +air because they're a little heavier +than you are and uh you're stuck there + + align:start position:0% +than you are and uh you're stuck there + + + align:start position:0% +than you are and uh you're stuck there +for a really long time and then + + align:start position:0% +for a really long time and then + + + align:start position:0% +for a really long time and then +eventually they get up and you go + + align:start position:0% +eventually they get up and you go + + + align:start position:0% +eventually they get up and you go +falling and flying so um we may have to + + align:start position:0% +falling and flying so um we may have to + + + align:start position:0% +falling and flying so um we may have to +give this a new name at some point when + + align:start position:0% +give this a new name at some point when + + + align:start position:0% +give this a new name at some point when +all seesaws are removed from playgrounds + + align:start position:0% +all seesaws are removed from playgrounds + + + align:start position:0% +all seesaws are removed from playgrounds +but sounds like it's still it's uh still + + align:start position:0% + + + + align:start position:0% + +usable okay so now if we wanted to put + + align:start position:0% +usable okay so now if we wanted to put + + + align:start position:0% +usable okay so now if we wanted to put +another lone pair on that same uh same + + align:start position:0% +another lone pair on that same uh same + + + align:start position:0% +another lone pair on that same uh same +structure we still have Central atom + + align:start position:0% +structure we still have Central atom + + + align:start position:0% +structure we still have Central atom +three atoms bound now we have two loone + + align:start position:0% +three atoms bound now we have two loone + + + align:start position:0% +three atoms bound now we have two loone +pairs those two loone pairs then will go + + align:start position:0% +pairs those two loone pairs then will go + + + align:start position:0% +pairs those two loone pairs then will go +into the equatorial positions as + + align:start position:0% +into the equatorial positions as + + + align:start position:0% +into the equatorial positions as +well and so you kind of have this sort + + align:start position:0% +well and so you kind of have this sort + + + align:start position:0% +well and so you kind of have this sort +of uh + + align:start position:0% + + + + align:start position:0% + +Arrangement and they were so repulsive + + align:start position:0% +Arrangement and they were so repulsive + + + align:start position:0% +Arrangement and they were so repulsive +they actually made the bond the atom + + align:start position:0% +they actually made the bond the atom + + + align:start position:0% +they actually made the bond the atom +unbonded from it okay so that leaves you + + align:start position:0% +unbonded from it okay so that leaves you + + + align:start position:0% +unbonded from it okay so that leaves you +with uh this shape which is + + align:start position:0% +with uh this shape which is + + + align:start position:0% +with uh this shape which is +a t-shape molecule so again this is a + + align:start position:0% +a t-shape molecule so again this is a + + + align:start position:0% +a t-shape molecule so again this is a +rationalization someone figured out that + + align:start position:0% +rationalization someone figured out that + + + align:start position:0% +rationalization someone figured out that +a molecule like this had this t-shape + + align:start position:0% +a molecule like this had this t-shape + + + align:start position:0% +a molecule like this had this t-shape +and it could be rationalized by the fact + + align:start position:0% +and it could be rationalized by the fact + + + align:start position:0% +and it could be rationalized by the fact +that the lone pairs want to sort of fill + + align:start position:0% +that the lone pairs want to sort of fill + + + align:start position:0% +that the lone pairs want to sort of fill +out in that equatorial uh plane and they + + align:start position:0% +out in that equatorial uh plane and they + + + align:start position:0% +out in that equatorial uh plane and they +could move away slightly from each other + + align:start position:0% +could move away slightly from each other + + + align:start position:0% +could move away slightly from each other +and uh that would minimize the amounts + + align:start position:0% +and uh that would minimize the amounts + + + align:start position:0% +and uh that would minimize the amounts +of + + align:start position:0% + + + + align:start position:0% + +repulsion all right so if we uh keep + + align:start position:0% +repulsion all right so if we uh keep + + + align:start position:0% +repulsion all right so if we uh keep +keep going here and uh look now at a + + align:start position:0% +keep going here and uh look now at a + + + align:start position:0% +keep going here and uh look now at a +molecule with this geometry + + align:start position:0% +molecule with this geometry + + + align:start position:0% +molecule with this geometry +ax4 uh E2 molecule and that's based on + + align:start position:0% +ax4 uh E2 molecule and that's based on + + + align:start position:0% +ax4 uh E2 molecule and that's based on +kind of what structural + + align:start position:0% +kind of what structural + + + align:start position:0% +kind of what structural +framework what's the uh sort of parent + + align:start position:0% +framework what's the uh sort of parent + + + align:start position:0% +framework what's the uh sort of parent +structure when you have four uh when you + + align:start position:0% +structure when you have four uh when you + + + align:start position:0% +structure when you have four uh when you +have six things + + align:start position:0% +have six things + + + align:start position:0% +have six things +bound it's a yeah based on a on an + + align:start position:0% +bound it's a yeah based on a on an + + + align:start position:0% +bound it's a yeah based on a on an +octahedral geometry so if if you take + + align:start position:0% +octahedral geometry so if if you take + + + align:start position:0% +octahedral geometry so if if you take +your + + align:start position:0% +your + + + align:start position:0% +your +octahedral + + align:start position:0% +octahedral + + + align:start position:0% +octahedral +molecule and if you want to figure out + + align:start position:0% +molecule and if you want to figure out + + + align:start position:0% +molecule and if you want to figure out +where you're going to put your loan your + + align:start position:0% +where you're going to put your loan your + + + align:start position:0% +where you're going to put your loan your +loan + + align:start position:0% + + + + align:start position:0% + +pairs you could stick one down here in + + align:start position:0% +pairs you could stick one down here in + + + align:start position:0% +pairs you could stick one down here in +the equatorial but that doesn't do you + + align:start position:0% +the equatorial but that doesn't do you + + + align:start position:0% +the equatorial but that doesn't do you +as much good this time because now your + + align:start position:0% +as much good this time because now your + + + align:start position:0% +as much good this time because now your +other equatorial things are at 90 so + + align:start position:0% +other equatorial things are at 90 so + + + align:start position:0% +other equatorial things are at 90 so +this one would have a lot of crashes + + align:start position:0% +this one would have a lot of crashes + + + align:start position:0% +this one would have a lot of crashes +down here so what ends up happening is + + align:start position:0% +down here so what ends up happening is + + + align:start position:0% +down here so what ends up happening is +that the two loone pairs would go one + + align:start position:0% +that the two loone pairs would go one + + + align:start position:0% +that the two loone pairs would go one +above and one below so they would be as + + align:start position:0% +above and one below so they would be as + + + align:start position:0% +above and one below so they would be as +far away from each other as possible so + + align:start position:0% +far away from each other as possible so + + + align:start position:0% +far away from each other as possible so +you have one below and another one on + + align:start position:0% +you have one below and another one on + + + align:start position:0% +you have one below and another one on +top and remember the worst thing to have + + align:start position:0% +top and remember the worst thing to have + + + align:start position:0% +top and remember the worst thing to have +is a lone pair lone pair so even though + + align:start position:0% +is a lone pair lone pair so even though + + + align:start position:0% +is a lone pair lone pair so even though +you have four atoms at 90 that it's + + align:start position:0% +you have four atoms at 90 that it's + + + align:start position:0% +you have four atoms at 90 that it's +interacting with at least it's far away + + align:start position:0% +interacting with at least it's far away + + + align:start position:0% +interacting with at least it's far away +from the other lone pair so each kind of + + align:start position:0% +from the other lone pair so each kind of + + + align:start position:0% +from the other lone pair so each kind of +gets half the molecule uh one up top one + + align:start position:0% +gets half the molecule uh one up top one + + + align:start position:0% +gets half the molecule uh one up top one +on the bottom so they have the most uh + + align:start position:0% +on the bottom so they have the most uh + + + align:start position:0% +on the bottom so they have the most uh +room those electrons to uh spread out + + align:start position:0% +room those electrons to uh spread out + + + align:start position:0% +room those electrons to uh spread out +and so that gives you uh what kind of + + align:start position:0% +and so that gives you uh what kind of + + + align:start position:0% +and so that gives you uh what kind of +geometry Square planer + + align:start position:0% + + + + align:start position:0% + +right all right so you can uh also + + align:start position:0% +right all right so you can uh also + + + align:start position:0% +right all right so you can uh also +predict something about what what might + + align:start position:0% +predict something about what what might + + + align:start position:0% +predict something about what what might +happen to the angles that you've all now + + align:start position:0% +happen to the angles that you've all now + + + align:start position:0% +happen to the angles that you've all now +pretty much memorized on the uh on the + + align:start position:0% +pretty much memorized on the uh on the + + + align:start position:0% +pretty much memorized on the uh on the +previous uh + + align:start position:0% +previous uh + + + align:start position:0% +previous uh +slides that if you do have a lone pair + + align:start position:0% +slides that if you do have a lone pair + + + align:start position:0% +slides that if you do have a lone pair +and now here we have an + + align:start position:0% +and now here we have an + + + align:start position:0% +and now here we have an +ax3e SN number of four so four things + + align:start position:0% +ax3e SN number of four so four things + + + align:start position:0% +ax3e SN number of four so four things +bound one loone pair and uh three three + + align:start position:0% +bound one loone pair and uh three three + + + align:start position:0% +bound one loone pair and uh three three +atoms and this is based then on what + + align:start position:0% +atoms and this is based then on what + + + align:start position:0% +atoms and this is based then on what +kind of uh + + align:start position:0% + + + + align:start position:0% + +structure with for SN number of four + + align:start position:0% +structure with for SN number of four + + + align:start position:0% +structure with for SN number of four +what's kind of the parent geometry + + align:start position:0% +what's kind of the parent geometry + + + align:start position:0% +what's kind of the parent geometry +there it's yeah tetrahedral is the + + align:start position:0% +there it's yeah tetrahedral is the + + + align:start position:0% +there it's yeah tetrahedral is the +parent geometry and now we've replaced + + align:start position:0% +parent geometry and now we've replaced + + + align:start position:0% +parent geometry and now we've replaced +one of the bonded atoms with a lone pair + + align:start position:0% +one of the bonded atoms with a lone pair + + + align:start position:0% +one of the bonded atoms with a lone pair +and so what that's going to do is that + + align:start position:0% +and so what that's going to do is that + + + align:start position:0% +and so what that's going to do is that +lone pair it's really not in that bad + + align:start position:0% +lone pair it's really not in that bad + + + align:start position:0% +lone pair it's really not in that bad +shape you put it on top you know you + + align:start position:0% +shape you put it on top you know you + + + align:start position:0% +shape you put it on top you know you +have + + align:start position:0% +have + + + align:start position:0% +have +109.5 now between those angles pointing + + align:start position:0% +109.5 now between those angles pointing + + + align:start position:0% +109.5 now between those angles pointing +down in the parent geometry and that was + + align:start position:0% +down in the parent geometry and that was + + + align:start position:0% +down in the parent geometry and that was +better than the others which were at 90 + + align:start position:0% +better than the others which were at 90 + + + align:start position:0% +better than the others which were at 90 +but it's still not good enough for it + + align:start position:0% +but it's still not good enough for it + + + align:start position:0% +but it's still not good enough for it +and so it actually presses down even + + align:start position:0% +and so it actually presses down even + + + align:start position:0% +and so it actually presses down even +more those lone pairs they're going to + + align:start position:0% +more those lone pairs they're going to + + + align:start position:0% +more those lone pairs they're going to +spread out as much as they possibly can + + align:start position:0% +spread out as much as they possibly can + + + align:start position:0% +spread out as much as they possibly can +and repel those bonded atoms away to the + + align:start position:0% +and repel those bonded atoms away to the + + + align:start position:0% +and repel those bonded atoms away to the +extent possible so in this molecule + + align:start position:0% +extent possible so in this molecule + + + align:start position:0% +extent possible so in this molecule +what's observed is that the angles in + + align:start position:0% +what's observed is that the angles in + + + align:start position:0% +what's observed is that the angles in +between here in between the hydrogens + + align:start position:0% +between here in between the hydrogens + + + align:start position:0% +between here in between the hydrogens +instead of being + + align:start position:0% +instead of being + + + align:start position:0% +instead of being +109.5 which is what you'd expect for for + + align:start position:0% +109.5 which is what you'd expect for for + + + align:start position:0% +109.5 which is what you'd expect for for +the uh true tetrahedral geometry they're + + align:start position:0% +the uh true tetrahedral geometry they're + + + align:start position:0% +the uh true tetrahedral geometry they're +106.7 so this lone pair is pressing down + + align:start position:0% +106.7 so this lone pair is pressing down + + + align:start position:0% +106.7 so this lone pair is pressing down +pressing the bonded atoms even closer to + + align:start position:0% +pressing the bonded atoms even closer to + + + align:start position:0% +pressing the bonded atoms even closer to +each other than uh than what is sort of + + align:start position:0% +each other than uh than what is sort of + + + align:start position:0% +each other than uh than what is sort of +the normal framework so this really + + align:start position:0% +the normal framework so this really + + + align:start position:0% +the normal framework so this really +takes up a lot of room here and is + + align:start position:0% +takes up a lot of room here and is + + + align:start position:0% +takes up a lot of room here and is +repulsive toward these bonded angles so + + align:start position:0% +repulsive toward these bonded angles so + + + align:start position:0% +repulsive toward these bonded angles so +again the veser theory can predict these + + align:start position:0% +again the veser theory can predict these + + + align:start position:0% +again the veser theory can predict these +kinds of or really explain these kinds + + align:start position:0% +kinds of or really explain these kinds + + + align:start position:0% +kinds of or really explain these kinds +of changes if You observe the smaller + + align:start position:0% +of changes if You observe the smaller + + + align:start position:0% +of changes if You observe the smaller +angle you can say oh there was a lone + + align:start position:0% +angle you can say oh there was a lone + + + align:start position:0% +angle you can say oh there was a lone +pair that makes sense that it would it + + align:start position:0% +pair that makes sense that it would it + + + align:start position:0% +pair that makes sense that it would it +would be a a smaller angle because + + align:start position:0% +would be a a smaller angle because + + + align:start position:0% +would be a a smaller angle because +there'd be repulsion repulsion + + align:start position:0% +there'd be repulsion repulsion + + + align:start position:0% +there'd be repulsion repulsion +down so again you can think about it you + + align:start position:0% +down so again you can think about it you + + + align:start position:0% +down so again you can think about it you +know you can make make one of these + + align:start position:0% +know you can make make one of these + + + align:start position:0% +know you can make make one of these +loone pairs yourself uh lone Tech and uh + + align:start position:0% +loone pairs yourself uh lone Tech and uh + + + align:start position:0% +loone pairs yourself uh lone Tech and uh +and think about the shapes + + align:start position:0% +and think about the shapes + + + align:start position:0% +and think about the shapes +here all right + + align:start position:0% +here all right + + + align:start position:0% +here all right +so we can also rationalize the + + align:start position:0% +so we can also rationalize the + + + align:start position:0% +so we can also rationalize the +difference between a p ph3 and NH3 + + align:start position:0% +difference between a p ph3 and NH3 + + + align:start position:0% +difference between a p ph3 and NH3 +molecule so they have pretty much the + + align:start position:0% +molecule so they have pretty much the + + + align:start position:0% +molecule so they have pretty much the +same the same framework here BAS based + + align:start position:0% +same the same framework here BAS based + + + align:start position:0% +same the same framework here BAS based +on tetrahedral geometry + + align:start position:0% +on tetrahedral geometry + + + align:start position:0% +on tetrahedral geometry +ax3e SN number of four but now instead + + align:start position:0% +ax3e SN number of four but now instead + + + align:start position:0% +ax3e SN number of four but now instead +of the number for methane that we saw of + + align:start position:0% +of the number for methane that we saw of + + + align:start position:0% +of the number for methane that we saw of +109.5 and instead of the + + align:start position:0% +109.5 and instead of the + + + align:start position:0% +109.5 and instead of the +106.7 for um NH3 we now get a really + + align:start position:0% +106.7 for um NH3 we now get a really + + + align:start position:0% +106.7 for um NH3 we now get a really +small angle between between here between + + align:start position:0% +small angle between between here between + + + align:start position:0% +small angle between between here between +the angle between hydrogen and + + align:start position:0% +the angle between hydrogen and + + + align:start position:0% +the angle between hydrogen and +phosphorus and hydrogen is now 93.3 + + align:start position:0% + + + + align:start position:0% + +so it's even more compressed and the + + align:start position:0% +so it's even more compressed and the + + + align:start position:0% +so it's even more compressed and the +reason why is because we're moving down + + align:start position:0% +reason why is because we're moving down + + + align:start position:0% +reason why is because we're moving down +in the periodic table and so as we move + + align:start position:0% +in the periodic table and so as we move + + + align:start position:0% +in the periodic table and so as we move +down the column in the periodic table + + align:start position:0% +down the column in the periodic table + + + align:start position:0% +down the column in the periodic table +we're going to have lone pairs that he + + align:start position:0% +we're going to have lone pairs that he + + + align:start position:0% +we're going to have lone pairs that he +have even larger uh spatial volumes and + + align:start position:0% +have even larger uh spatial volumes and + + + align:start position:0% +have even larger uh spatial volumes and +so they're going to compress even more + + align:start position:0% +so they're going to compress even more + + + align:start position:0% +so they're going to compress even more +so now it's sort of it's it's an even + + align:start position:0% +so now it's sort of it's it's an even + + + align:start position:0% +so now it's sort of it's it's an even +bigger bigger sort of situation here the + + align:start position:0% +bigger bigger sort of situation here the + + + align:start position:0% +bigger bigger sort of situation here the +lone pairs are trying to fill up up even + + align:start position:0% +lone pairs are trying to fill up up even + + + align:start position:0% +lone pairs are trying to fill up up even +more volume and so they're sort of + + align:start position:0% +more volume and so they're sort of + + + align:start position:0% +more volume and so they're sort of +trying to compress as much as possible + + align:start position:0% +trying to compress as much as possible + + + align:start position:0% +trying to compress as much as possible +these atoms away they're filling up all + + align:start position:0% +these atoms away they're filling up all + + + align:start position:0% +these atoms away they're filling up all +available space and making the angle + + align:start position:0% +available space and making the angle + + + align:start position:0% +available space and making the angle +here even + + align:start position:0% +here even + + + align:start position:0% +here even +smaller and so if ask about this if + + align:start position:0% +smaller and so if ask about this if + + + align:start position:0% +smaller and so if ask about this if +asked to predict you could sort of look + + align:start position:0% +asked to predict you could sort of look + + + align:start position:0% +asked to predict you could sort of look +at where things are in the periodic + + align:start position:0% +at where things are in the periodic + + + align:start position:0% +at where things are in the periodic +table here's nitrogen here's phosphorus + + align:start position:0% +table here's nitrogen here's phosphorus + + + align:start position:0% +table here's nitrogen here's phosphorus +and so if we had uh a compound based on + + align:start position:0% +and so if we had uh a compound based on + + + align:start position:0% +and so if we had uh a compound based on +nitrogen or phosphorus that was based on + + align:start position:0% +nitrogen or phosphorus that was based on + + + align:start position:0% +nitrogen or phosphorus that was based on +tetrahedral geometry + + align:start position:0% +tetrahedral geometry + + + align:start position:0% +tetrahedral geometry +one might expect that the angle becomes + + align:start position:0% +one might expect that the angle becomes + + + align:start position:0% +one might expect that the angle becomes +even smaller as you move down the + + align:start position:0% +even smaller as you move down the + + + align:start position:0% +even smaller as you move down the +periodic table as that lone pair that's + + align:start position:0% +periodic table as that lone pair that's + + + align:start position:0% +periodic table as that lone pair that's +on there is filling up even more and + + align:start position:0% +on there is filling up even more and + + + align:start position:0% +on there is filling up even more and +more spatial volume so this kind of + + align:start position:0% +more spatial volume so this kind of + + + align:start position:0% +more spatial volume so this kind of +combines ideas of Trends in the periodic + + align:start position:0% +combines ideas of Trends in the periodic + + + align:start position:0% +combines ideas of Trends in the periodic +table with shapes of + + align:start position:0% + + + + align:start position:0% + +molecules all right another thing that + + align:start position:0% +molecules all right another thing that + + + align:start position:0% +molecules all right another thing that +you can sometimes predict is about Bond + + align:start position:0% +you can sometimes predict is about Bond + + + align:start position:0% +you can sometimes predict is about Bond +lengths so if you experiment observed + + align:start position:0% +lengths so if you experiment observed + + + align:start position:0% +lengths so if you experiment observed +different Bond lengths in a molecule you + + align:start position:0% +different Bond lengths in a molecule you + + + align:start position:0% +different Bond lengths in a molecule you +could use veser to go back and think + + align:start position:0% +could use veser to go back and think + + + align:start position:0% +could use veser to go back and think +about where where that may have come + + align:start position:0% +about where where that may have come + + + align:start position:0% +about where where that may have come +from so uh what's what's this uh + + align:start position:0% +from so uh what's what's this uh + + + align:start position:0% +from so uh what's what's this uh +geometry + + align:start position:0% +geometry + + + align:start position:0% +geometry +here so the one that's H shown and uh + + align:start position:0% +here so the one that's H shown and uh + + + align:start position:0% +here so the one that's H shown and uh +also the parent geometry so one that's + + align:start position:0% +also the parent geometry so one that's + + + align:start position:0% +also the parent geometry so one that's +shown is what seesaw and the parent + + align:start position:0% + + + + align:start position:0% + +geometry right trigonal by paramal all + + align:start position:0% +geometry right trigonal by paramal all + + + align:start position:0% +geometry right trigonal by paramal all +right so here we have + + align:start position:0% +right so here we have + + + align:start position:0% +right so here we have +ax4e we have an SN number of five we + + align:start position:0% +ax4e we have an SN number of five we + + + align:start position:0% +ax4e we have an SN number of five we +have four atoms bound we have one lone + + align:start position:0% +have four atoms bound we have one lone + + + align:start position:0% +have four atoms bound we have one lone +pair and now it's observed that there + + align:start position:0% +pair and now it's observed that there + + + align:start position:0% +pair and now it's observed that there +two sets of SF bonds one set is 1.54 + + align:start position:0% +two sets of SF bonds one set is 1.54 + + + align:start position:0% +two sets of SF bonds one set is 1.54 +five and one is + + align:start position:0% +five and one is + + + align:start position:0% +five and one is +1.64 + + align:start position:0% +1.64 + + + align:start position:0% +1.64 +6 so what do you think those different + + align:start position:0% +6 so what do you think those different + + + align:start position:0% +6 so what do you think those different +Bond sets there's two types of bonds + + align:start position:0% + + + + align:start position:0% + +two types of bonds we have one sort of + + align:start position:0% +two types of bonds we have one sort of + + + align:start position:0% +two types of bonds we have one sort of +maybe I'll use this one one lone + + align:start position:0% + + + + align:start position:0% + +pair so likely one set would involve the + + align:start position:0% +pair so likely one set would involve the + + + align:start position:0% +pair so likely one set would involve the +gray atoms and the other would be the + + align:start position:0% +gray atoms and the other would be the + + + align:start position:0% +gray atoms and the other would be the +black atoms which do you think would be + + align:start position:0% +black atoms which do you think would be + + + align:start position:0% +black atoms which do you think would be +longer do you think the gray or the + + align:start position:0% +longer do you think the gray or the + + + align:start position:0% +longer do you think the gray or the +black would be longer + + align:start position:0% +black would be longer + + + align:start position:0% +black would be longer +the bond lengths from the central atom + + align:start position:0% +the bond lengths from the central atom + + + align:start position:0% +the bond lengths from the central atom +to the gray or to the black would be + + align:start position:0% +to the gray or to the black would be + + + align:start position:0% +to the gray or to the black would be +longer gray and why is + + align:start position:0% +longer gray and why is + + + align:start position:0% +longer gray and why is +that right because these These are at 90 + + align:start position:0% +that right because these These are at 90 + + + align:start position:0% +that right because these These are at 90 +going down whereas this is at 120 so the + + align:start position:0% +going down whereas this is at 120 so the + + + align:start position:0% +going down whereas this is at 120 so the +90 is more repulsive so it basically + + align:start position:0% +90 is more repulsive so it basically + + + align:start position:0% +90 is more repulsive so it basically +kind of pushes that up farther and down + + align:start position:0% +kind of pushes that up farther and down + + + align:start position:0% +kind of pushes that up farther and down +farther moves them farther away the the + + align:start position:0% +farther moves them farther away the the + + + align:start position:0% +farther moves them farther away the the +black atoms are already farther and + + align:start position:0% +black atoms are already farther and + + + align:start position:0% +black atoms are already farther and +won't feel the repulsion as watch so + + align:start position:0% +won't feel the repulsion as watch so + + + align:start position:0% +won't feel the repulsion as watch so +another way to sort of if you have a + + align:start position:0% +another way to sort of if you have a + + + align:start position:0% +another way to sort of if you have a +lone pair here to uh for the lone pair + + align:start position:0% +lone pair here to uh for the lone pair + + + align:start position:0% +lone pair here to uh for the lone pair +to feel like it really has the space + + align:start position:0% +to feel like it really has the space + + + align:start position:0% +to feel like it really has the space +that it requires is to sort of repel the + + align:start position:0% +that it requires is to sort of repel the + + + align:start position:0% +that it requires is to sort of repel the +atoms that are closer in terms of the of + + align:start position:0% +atoms that are closer in terms of the of + + + align:start position:0% +atoms that are closer in terms of the of +of distance repel them just a little bit + + align:start position:0% +of distance repel them just a little bit + + + align:start position:0% +of distance repel them just a little bit +farther away and then it can kind of + + align:start position:0% +farther away and then it can kind of + + + align:start position:0% +farther away and then it can kind of +fill out and feel like it it has has + + align:start position:0% +fill out and feel like it it has has + + + align:start position:0% +fill out and feel like it it has has +enough + + align:start position:0% +enough + + + align:start position:0% +enough +space so again if you had an observed + + align:start position:0% +space so again if you had an observed + + + align:start position:0% +space so again if you had an observed +experimentally observed uh set of bonds + + align:start position:0% +experimentally observed uh set of bonds + + + align:start position:0% +experimentally observed uh set of bonds +uh Bond lengths you could r + + align:start position:0% +uh Bond lengths you could r + + + align:start position:0% +uh Bond lengths you could r +using Vesper why you would have + + align:start position:0% + + + + align:start position:0% + +this okay so um as as we said more + + align:start position:0% +this okay so um as as we said more + + + align:start position:0% +this okay so um as as we said more +repulsion uh between the lone pair + + align:start position:0% +repulsion uh between the lone pair + + + align:start position:0% +repulsion uh between the lone pair +electrons and the axial ones because + + align:start position:0% +electrons and the axial ones because + + + align:start position:0% +electrons and the axial ones because +those are at 90 so those would move + + align:start position:0% +those are at 90 so those would move + + + align:start position:0% +those are at 90 so those would move +farther + + align:start position:0% +farther + + + align:start position:0% +farther +away okay so that's a lot of the theory + + align:start position:0% +away okay so that's a lot of the theory + + + align:start position:0% +away okay so that's a lot of the theory +and now we're just going to run through + + align:start position:0% +and now we're just going to run through + + + align:start position:0% +and now we're just going to run through +these sheets and talk about the + + align:start position:0% +these sheets and talk about the + + + align:start position:0% +these sheets and talk about the +different types of geometry + + align:start position:0% +different types of geometry + + + align:start position:0% +different types of geometry +the names of different types of + + align:start position:0% +the names of different types of + + + align:start position:0% +the names of different types of +geometries when you have the lone pairs + + align:start position:0% +geometries when you have the lone pairs + + + align:start position:0% +geometries when you have the lone pairs +on there and then look at some examples + + align:start position:0% +on there and then look at some examples + + + align:start position:0% +on there and then look at some examples +and again if you call out the answers + + align:start position:0% +and again if you call out the answers + + + align:start position:0% +and again if you call out the answers +and if we go through this quickly uh + + align:start position:0% +and if we go through this quickly uh + + + align:start position:0% +and if we go through this quickly uh +this is all that we need to go over for + + align:start position:0% +this is all that we need to go over for + + + align:start position:0% +this is all that we need to go over for +today and it'll be a good review uh this + + align:start position:0% +today and it'll be a good review uh this + + + align:start position:0% +today and it'll be a good review uh this +you'll sort of have the opportunity + + align:start position:0% +you'll sort of have the opportunity + + + align:start position:0% +you'll sort of have the opportunity +today to memorize this you might want to + + align:start position:0% +today to memorize this you might want to + + + align:start position:0% +today to memorize this you might want to +go back over it a couple times but + + align:start position:0% +go back over it a couple times but + + + align:start position:0% +go back over it a couple times but +pretty much this is uh this whole unit + + align:start position:0% +pretty much this is uh this whole unit + + + align:start position:0% +pretty much this is uh this whole unit +it's not not too challenging all right + + align:start position:0% +it's not not too challenging all right + + + align:start position:0% +it's not not too challenging all right +so if we have ax2e + + align:start position:0% +so if we have ax2e + + + align:start position:0% +so if we have ax2e +we're going to have an SN number of + + align:start position:0% +we're going to have an SN number of + + + align:start position:0% +we're going to have an SN number of +three and a molecular + + align:start position:0% +three and a molecular + + + align:start position:0% +three and a molecular +shape I'll draw that and what's the name + + align:start position:0% +shape I'll draw that and what's the name + + + align:start position:0% +shape I'll draw that and what's the name +of that + + align:start position:0% +of that + + + align:start position:0% +of that +geometry it's bent and that's because + + align:start position:0% +geometry it's bent and that's because + + + align:start position:0% +geometry it's bent and that's because +you're only considering the bonded atoms + + align:start position:0% +you're only considering the bonded atoms + + + align:start position:0% +you're only considering the bonded atoms +so you're not talking about the lone + + align:start position:0% +so you're not talking about the lone + + + align:start position:0% +so you're not talking about the lone +pair we don't really see the lone pair + + align:start position:0% +pair we don't really see the lone pair + + + align:start position:0% +pair we don't really see the lone pair +there's my bent we don't really see the + + align:start position:0% +there's my bent we don't really see the + + + align:start position:0% +there's my bent we don't really see the +lone the lone pair two bents + + align:start position:0% + + + + align:start position:0% + +and so it would just look bent to us so + + align:start position:0% +and so it would just look bent to us so + + + align:start position:0% +and so it would just look bent to us so +that's uh where that comes from and what + + align:start position:0% +that's uh where that comes from and what + + + align:start position:0% +that's uh where that comes from and what +angles would this have uh for this + + align:start position:0% +angles would this have uh for this + + + align:start position:0% +angles would this have uh for this +particular case SN number + + align:start position:0% + + + + align:start position:0% + +three so okay you have this one + + align:start position:0% +three so okay you have this one + + + align:start position:0% +three so okay you have this one +here so this is going to be um the the + + align:start position:0% +here so this is going to be um the the + + + align:start position:0% +here so this is going to be um the the +sn3 would have a trigonal + + align:start position:0% +sn3 would have a trigonal + + + align:start position:0% +sn3 would have a trigonal +planer parent geometry + + align:start position:0% +planer parent geometry + + + align:start position:0% +planer parent geometry +but if we take a lone + + align:start position:0% +but if we take a lone + + + align:start position:0% +but if we take a lone +pair and put that on instead of an atom + + align:start position:0% +pair and put that on instead of an atom + + + align:start position:0% +pair and put that on instead of an atom +then it will also be somewhat + + align:start position:0% +then it will also be somewhat + + + align:start position:0% +then it will also be somewhat +compressing of those two atoms down + + align:start position:0% +compressing of those two atoms down + + + align:start position:0% +compressing of those two atoms down +there we won't really know without + + align:start position:0% +there we won't really know without + + + align:start position:0% +there we won't really know without +knowing what uh what the central atom is + + align:start position:0% +knowing what uh what the central atom is + + + align:start position:0% +knowing what uh what the central atom is +we can't really predict how bad the + + align:start position:0% +we can't really predict how bad the + + + align:start position:0% +we can't really predict how bad the +compression is going to be so what you + + align:start position:0% +compression is going to be so what you + + + align:start position:0% +compression is going to be so what you +would put is less than 120 here because + + align:start position:0% +would put is less than 120 here because + + + align:start position:0% +would put is less than 120 here because +it would be 120 if this was an atom and + + align:start position:0% +it would be 120 if this was an atom and + + + align:start position:0% +it would be 120 if this was an atom and +not a lone pair so if this is a lone + + align:start position:0% +not a lone pair so if this is a lone + + + align:start position:0% +not a lone pair so if this is a lone +pair then it's less than + + align:start position:0% + + + + align:start position:0% + +120 all right so here is another case + + align:start position:0% +120 all right so here is another case + + + align:start position:0% +120 all right so here is another case +now we have three uh atoms bound one + + align:start position:0% +now we have three uh atoms bound one + + + align:start position:0% +now we have three uh atoms bound one +loone pair SN number of four and our + + align:start position:0% +loone pair SN number of four and our + + + align:start position:0% +loone pair SN number of four and our +parent geometry here would + + align:start position:0% +parent geometry here would + + + align:start position:0% +parent geometry here would +be tetrahedral and uh now we have a lone + + align:start position:0% +be tetrahedral and uh now we have a lone + + + align:start position:0% +be tetrahedral and uh now we have a lone +pair so we saw this uh a little bit + + align:start position:0% +pair so we saw this uh a little bit + + + align:start position:0% +pair so we saw this uh a little bit +before and what is what is that geometry + + align:start position:0% +before and what is what is that geometry + + + align:start position:0% +before and what is what is that geometry +called so here we have + + align:start position:0% +called so here we have + + + align:start position:0% +called so here we have +have this picture what is this + + align:start position:0% + + + + align:start position:0% + +called so we have this and what do you + + align:start position:0% +called so we have this and what do you + + + align:start position:0% +called so we have this and what do you +what would the angles be + + align:start position:0% + + + + align:start position:0% + +here less than 109.5 so all of you + + align:start position:0% +here less than 109.5 so all of you + + + align:start position:0% +here less than 109.5 so all of you +should know the answers because they're + + align:start position:0% +should know the answers because they're + + + align:start position:0% +should know the answers because they're +actually in your handout so um feel free + + align:start position:0% +actually in your handout so um feel free + + + align:start position:0% +actually in your handout so um feel free +and confident to yell them out all right + + align:start position:0% +and confident to yell them out all right + + + align:start position:0% +and confident to yell them out all right +so again this is going to be less than + + align:start position:0% +so again this is going to be less than + + + align:start position:0% +so again this is going to be less than +109.5 because we have a lone pair + + align:start position:0% +109.5 because we have a lone pair + + + align:start position:0% +109.5 because we have a lone pair +pressing down and so you have to in all + + align:start position:0% +pressing down and so you have to in all + + + align:start position:0% +pressing down and so you have to in all +these cases consider what the parent + + align:start position:0% +these cases consider what the parent + + + align:start position:0% +these cases consider what the parent +geometry is and then the angles are + + align:start position:0% +geometry is and then the angles are + + + align:start position:0% +geometry is and then the angles are +going to be a little less than that uh + + align:start position:0% +going to be a little less than that uh + + + align:start position:0% +going to be a little less than that uh +if you have one lone pair sitting on + + align:start position:0% +if you have one lone pair sitting on + + + align:start position:0% +if you have one lone pair sitting on +top all right + + align:start position:0% +top all right + + + align:start position:0% +top all right +ax2 E2 has an SN number of four and uh + + align:start position:0% +ax2 E2 has an SN number of four and uh + + + align:start position:0% +ax2 E2 has an SN number of four and uh +all right so what what geometry is this + + align:start position:0% +all right so what what geometry is this + + + align:start position:0% +all right so what what geometry is this +based + + align:start position:0% +based + + + align:start position:0% +based +on yeah and so tetrahedral again so we + + align:start position:0% +on yeah and so tetrahedral again so we + + + align:start position:0% +on yeah and so tetrahedral again so we +have two lone pairs on that and what + + align:start position:0% +have two lone pairs on that and what + + + align:start position:0% +have two lone pairs on that and what +does that n look like it should be + + align:start position:0% +does that n look like it should be + + + align:start position:0% +does that n look like it should be +called bent as + + align:start position:0% +called bent as + + + align:start position:0% +called bent as +well and now the angles are going to be + + align:start position:0% +well and now the angles are going to be + + + align:start position:0% +well and now the angles are going to be +less than + + align:start position:0% +less than + + + align:start position:0% +less than +109.5 so you see we have two bent + + align:start position:0% +109.5 so you see we have two bent + + + align:start position:0% +109.5 so you see we have two bent +molecules but the angle isn't the same + + align:start position:0% +molecules but the angle isn't the same + + + align:start position:0% +molecules but the angle isn't the same +so it depends on whether it's based on a + + align:start position:0% +so it depends on whether it's based on a + + + align:start position:0% +so it depends on whether it's based on a +trigonal uh planer or it's based on + + align:start position:0% +trigonal uh planer or it's based on + + + align:start position:0% +trigonal uh planer or it's based on +tetrahedral so you need to sort of know + + align:start position:0% +tetrahedral so you need to sort of know + + + align:start position:0% +tetrahedral so you need to sort of know +what the whole molecule was + + align:start position:0% +what the whole molecule was + + + align:start position:0% +what the whole molecule was +uh to figure out um what degree of bent + + align:start position:0% +uh to figure out um what degree of bent + + + align:start position:0% +uh to figure out um what degree of bent +you have in these + + align:start position:0% + + + + align:start position:0% + +two all right ax4 e has SN number + + align:start position:0% +two all right ax4 e has SN number + + + align:start position:0% +two all right ax4 e has SN number +of five and so um our shape here what is + + align:start position:0% +of five and so um our shape here what is + + + align:start position:0% +of five and so um our shape here what is +this one going to + + align:start position:0% +this one going to + + + align:start position:0% +this one going to +be yeah so this is going to be a + + align:start position:0% +be yeah so this is going to be a + + + align:start position:0% +be yeah so this is going to be a +seesaw and uh so what are our angles + + align:start position:0% +seesaw and uh so what are our angles + + + align:start position:0% +seesaw and uh so what are our angles +going to be + + align:start position:0% +going to be + + + align:start position:0% +going to be +right so less than 120 less than 90 it + + align:start position:0% +right so less than 120 less than 90 it + + + align:start position:0% +right so less than 120 less than 90 it +could be that really the 120 are not + + align:start position:0% +could be that really the 120 are not + + + align:start position:0% +could be that really the 120 are not +going to be that affected but that's + + align:start position:0% +going to be that affected but that's + + + align:start position:0% +going to be that affected but that's +what you will uh put put down because + + align:start position:0% +what you will uh put put down because + + + align:start position:0% +what you will uh put put down because +you don't really know this is just a + + align:start position:0% +you don't really know this is just a + + + align:start position:0% +you don't really know this is just a +rough predictor of uh what those are + + align:start position:0% +rough predictor of uh what those are + + + align:start position:0% +rough predictor of uh what those are +going to be so it's less than what the + + align:start position:0% +going to be so it's less than what the + + + align:start position:0% +going to be so it's less than what the +parent molecule + + align:start position:0% +parent molecule + + + align:start position:0% +parent molecule +was all right uh SN number + + align:start position:0% +was all right uh SN number + + + align:start position:0% +was all right uh SN number +of five and so what are what are we + + align:start position:0% +of five and so what are what are we + + + align:start position:0% +of five and so what are what are we +going to be doing here we're going to + + align:start position:0% +going to be doing here we're going to + + + align:start position:0% +going to be doing here we're going to +add another loan take off an atom at + + align:start position:0% +add another loan take off an atom at + + + align:start position:0% +add another loan take off an atom at +another lone pair and what are we going + + align:start position:0% +another lone pair and what are we going + + + align:start position:0% +another lone pair and what are we going +to get here right + + align:start position:0% +to get here right + + + align:start position:0% +to get here right +t-shape and the angles will + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +be so at this point is our + + align:start position:0% +be so at this point is our + + + align:start position:0% +be so at this point is our +t-shaped and so we'll have less than 90 + + align:start position:0% +t-shaped and so we'll have less than 90 + + + align:start position:0% +t-shaped and so we'll have less than 90 +you'll have the two lone pairs in the + + align:start position:0% +you'll have the two lone pairs in the + + + align:start position:0% +you'll have the two lone pairs in the +equatorial position as we talked about + + align:start position:0% +equatorial position as we talked about + + + align:start position:0% +equatorial position as we talked about +before trying to spread out as much as + + align:start position:0% +before trying to spread out as much as + + + align:start position:0% +before trying to spread out as much as +they possibly + + align:start position:0% +they possibly + + + align:start position:0% +they possibly +can and then uh now we're repl replacing + + align:start position:0% +can and then uh now we're repl replacing + + + align:start position:0% +can and then uh now we're repl replacing +another one um with a lone pair another + + align:start position:0% +another one um with a lone pair another + + + align:start position:0% +another one um with a lone pair another +bonded atom so essn number is still five + + align:start position:0% +bonded atom so essn number is still five + + + align:start position:0% +bonded atom so essn number is still five +and what shape are we going to get in + + align:start position:0% +and what shape are we going to get in + + + align:start position:0% +and what shape are we going to get in +that + + align:start position:0% +that + + + align:start position:0% +that +case linear right so they all go in + + align:start position:0% +case linear right so they all go in + + + align:start position:0% +case linear right so they all go in +these equatorial positions um to spread + + align:start position:0% +these equatorial positions um to spread + + + align:start position:0% +these equatorial positions um to spread +out as much as they possibly can and so + + align:start position:0% +out as much as they possibly can and so + + + align:start position:0% +out as much as they possibly can and so +we're going to end up with a linear + + align:start position:0% +we're going to end up with a linear + + + align:start position:0% +we're going to end up with a linear +molecule so we would uh replace here and + + align:start position:0% +molecule so we would uh replace here and + + + align:start position:0% +molecule so we would uh replace here and +what are our angles + + align:start position:0% +what are our angles + + + align:start position:0% +what are our angles +here so they're exactly 180 + + align:start position:0% + + + + align:start position:0% + +yeah it it could be that there would uh + + align:start position:0% +yeah it it could be that there would uh + + + align:start position:0% +yeah it it could be that there would uh +but they'll probably just be really + + align:start position:0% +but they'll probably just be really + + + align:start position:0% +but they'll probably just be really +spreading out around the uh to fill out + + align:start position:0% +spreading out around the uh to fill out + + + align:start position:0% +spreading out around the uh to fill out +as much room as possible around the + + align:start position:0% +as much room as possible around the + + + align:start position:0% +as much room as possible around the +whole equatorial place so you can just + + align:start position:0% +whole equatorial place so you can just + + + align:start position:0% +whole equatorial place so you can just +sort of think about it as if there if + + align:start position:0% +sort of think about it as if there if + + + align:start position:0% +sort of think about it as if there if +there was space they'd move into it so + + align:start position:0% +there was space they'd move into it so + + + align:start position:0% +there was space they'd move into it so +they've really filled up this space and + + align:start position:0% +they've really filled up this space and + + + align:start position:0% +they've really filled up this space and +pretty much you might as well keep them + + align:start position:0% +pretty much you might as well keep them + + + align:start position:0% +pretty much you might as well keep them +there because whichever way they move + + align:start position:0% +there because whichever way they move + + + align:start position:0% +there because whichever way they move +they're just going to get repelled in + + align:start position:0% +they're just going to get repelled in + + + align:start position:0% +they're just going to get repelled in +another + + align:start position:0% +another + + + align:start position:0% +another +Direction so that's kind of the one the + + align:start position:0% +Direction so that's kind of the one the + + + align:start position:0% +Direction so that's kind of the one the +one exception are these ones that that + + align:start position:0% +one exception are these ones that that + + + align:start position:0% +one exception are these ones that that +turn out to be linear there's one other + + align:start position:0% +turn out to be linear there's one other + + + align:start position:0% +turn out to be linear there's one other +exception where the angles aren't going + + align:start position:0% +exception where the angles aren't going + + + align:start position:0% +exception where the angles aren't going +to change as well where you have + + align:start position:0% +to change as well where you have + + + align:start position:0% +to change as well where you have +orbitals on kind of either side that + + align:start position:0% +orbitals on kind of either side that + + + align:start position:0% +orbitals on kind of either side that +counter counteract that's a good + + align:start position:0% +counter counteract that's a good + + + align:start position:0% +counter counteract that's a good +question all right so one more we have + + align:start position:0% +question all right so one more we have + + + align:start position:0% +question all right so one more we have +ax ax5e SN number + + align:start position:0% +ax ax5e SN number + + + align:start position:0% +ax ax5e SN number +of six so this is based on what parent + + align:start position:0% +of six so this is based on what parent + + + align:start position:0% +of six so this is based on what parent +molecule + + align:start position:0% +molecule + + + align:start position:0% +molecule +octahedral so we're going to take off um + + align:start position:0% +octahedral so we're going to take off um + + + align:start position:0% +octahedral so we're going to take off um +one one + + align:start position:0% +one one + + + align:start position:0% +one one +Li and so this would be if we removed + + align:start position:0% +Li and so this would be if we removed + + + align:start position:0% +Li and so this would be if we removed +one of the the lians here and we get + + align:start position:0% +one of the the lians here and we get + + + align:start position:0% +one of the the lians here and we get +this parent shape which is + + align:start position:0% +this parent shape which is + + + align:start position:0% +this parent shape which is +called Square paramal and what are the + + align:start position:0% +called Square paramal and what are the + + + align:start position:0% +called Square paramal and what are the +angles going to be + + align:start position:0% +angles going to be + + + align:start position:0% +angles going to be +here less than + + align:start position:0% +here less than + + + align:start position:0% +here less than +90 okay + + align:start position:0% + + + + align:start position:0% + +so every year uh when I do this unit I + + align:start position:0% +so every year uh when I do this unit I + + + align:start position:0% +so every year uh when I do this unit I +like to reward people who are in class + + align:start position:0% +like to reward people who are in class + + + align:start position:0% +like to reward people who are in class +um and so I give a little hint about the + + align:start position:0% +um and so I give a little hint about the + + + align:start position:0% +um and so I give a little hint about the +final and uh the hint will be that this + + align:start position:0% +final and uh the hint will be that this + + + align:start position:0% +final and uh the hint will be that this +will be on the + + align:start position:0% + + + + align:start position:0% + +final so you might want to put that down + + align:start position:0% +final so you might want to put that down + + + align:start position:0% +final so you might want to put that down +the last couple years I did seesaw which + + align:start position:0% +the last couple years I did seesaw which + + + align:start position:0% +the last couple years I did seesaw which +really is my personal favorite but at + + align:start position:0% +really is my personal favorite but at + + + align:start position:0% +really is my personal favorite but at +some point I have to switch so uh this + + align:start position:0% +some point I have to switch so uh this + + + align:start position:0% +some point I have to switch so uh this +time it will be this one + + align:start position:0% + + + + align:start position:0% + +and it's always so sad to me when people + + align:start position:0% +and it's always so sad to me when people + + + align:start position:0% +and it's always so sad to me when people +get that one wrong so please get that + + align:start position:0% +get that one wrong so please get that + + + align:start position:0% +get that one wrong so please get that +one + + align:start position:0% +one + + + align:start position:0% +one +right + + align:start position:0% + + + + align:start position:0% + +okay so uh let's keep going SN number + + align:start position:0% +okay so uh let's keep going SN number + + + align:start position:0% +okay so uh let's keep going SN number +is six and so we're going to put on + + align:start position:0% +is six and so we're going to put on + + + align:start position:0% +is six and so we're going to put on +another loone pair and where are we + + align:start position:0% +another loone pair and where are we + + + align:start position:0% +another loone pair and where are we +going to put it we're going to try to + + align:start position:0% +going to put it we're going to try to + + + align:start position:0% +going to put it we're going to try to +move it so that there's the least amount + + align:start position:0% +move it so that there's the least amount + + + align:start position:0% +move it so that there's the least amount +of repulsion between the loone pairs so + + align:start position:0% +of repulsion between the loone pairs so + + + align:start position:0% +of repulsion between the loone pairs so +it's going to be up on top so this + + align:start position:0% +it's going to be up on top so this + + + align:start position:0% +it's going to be up on top so this +geometry keeps the lone pairs as far + + align:start position:0% +geometry keeps the lone pairs as far + + + align:start position:0% +geometry keeps the lone pairs as far +away from each other as possible and + + align:start position:0% +away from each other as possible and + + + align:start position:0% +away from each other as possible and +what's the remaining uh thing called + + align:start position:0% +what's the remaining uh thing called + + + align:start position:0% +what's the remaining uh thing called +when you have those loone pairs on + + align:start position:0% + + + + align:start position:0% + +there so that's going to be square + + align:start position:0% +there so that's going to be square + + + align:start position:0% +there so that's going to be square +planer and what about the angles in this + + align:start position:0% + + + + align:start position:0% + +case so in this case they're just 90 + + align:start position:0% +case so in this case they're just 90 + + + align:start position:0% +case so in this case they're just 90 +because you have a lone pair on top + + align:start position:0% +because you have a lone pair on top + + + align:start position:0% +because you have a lone pair on top +pushing down and a lone pair on the + + align:start position:0% +pushing down and a lone pair on the + + + align:start position:0% +pushing down and a lone pair on the +bottom pushing up so this is another + + align:start position:0% +bottom pushing up so this is another + + + align:start position:0% +bottom pushing up so this is another +example where it's not less + + align:start position:0% + + + + align:start position:0% + +than all right so then next one we add + + align:start position:0% +than all right so then next one we add + + + align:start position:0% +than all right so then next one we add +another lone pair and at this point does + + align:start position:0% +another lone pair and at this point does + + + align:start position:0% +another lone pair and at this point does +it matter where you put the lone + + align:start position:0% +it matter where you put the lone + + + align:start position:0% +it matter where you put the lone +pair no it's they're all equivalent + + align:start position:0% +pair no it's they're all equivalent + + + align:start position:0% +pair no it's they're all equivalent +positions so it doesn't make any + + align:start position:0% +positions so it doesn't make any + + + align:start position:0% +positions so it doesn't make any +difference uh so it's going to be one of + + align:start position:0% +difference uh so it's going to be one of + + + align:start position:0% +difference uh so it's going to be one of +these guys gets replaced and so that's + + align:start position:0% +these guys gets replaced and so that's + + + align:start position:0% +these guys gets replaced and so that's +going to leave lead you with the what + + align:start position:0% +going to leave lead you with the what + + + align:start position:0% +going to leave lead you with the what +geometry t-shaped and angle here is + + align:start position:0% +geometry t-shaped and angle here is + + + align:start position:0% +geometry t-shaped and angle here is +going to be this time less than 90 right + + align:start position:0% +going to be this time less than 90 right + + + align:start position:0% +going to be this time less than 90 right +because it will repel this one and this + + align:start position:0% +because it will repel this one and this + + + align:start position:0% +because it will repel this one and this +one if you have a loone big lone pair in + + align:start position:0% +one if you have a loone big lone pair in + + + align:start position:0% +one if you have a loone big lone pair in +this + + align:start position:0% +this + + + align:start position:0% +this +position all right one + + align:start position:0% +position all right one + + + align:start position:0% +position all right one +more uh again the same geometry we take + + align:start position:0% +more uh again the same geometry we take + + + align:start position:0% +more uh again the same geometry we take +another + + align:start position:0% +another + + + align:start position:0% +another +one off another bonded atom off and put + + align:start position:0% +one off another bonded atom off and put + + + align:start position:0% +one off another bonded atom off and put +another lone pair and what are we left + + align:start position:0% +another lone pair and what are we left + + + align:start position:0% +another lone pair and what are we left +with in this case + + align:start position:0% +with in this case + + + align:start position:0% +with in this case +linear and again this is going to be + + align:start position:0% + + + + align:start position:0% + +180 all right so now we've looked at all + + align:start position:0% +180 all right so now we've looked at all + + + align:start position:0% +180 all right so now we've looked at all +of those and we can very quickly go down + + align:start position:0% +of those and we can very quickly go down + + + align:start position:0% +of those and we can very quickly go down +and in this handout I have most of it + + align:start position:0% +and in this handout I have most of it + + + align:start position:0% +and in this handout I have most of it +written I don't have the angles so that + + align:start position:0% +written I don't have the angles so that + + + align:start position:0% +written I don't have the angles so that +you can write the angles in and have + + align:start position:0% +you can write the angles in and have + + + align:start position:0% +you can write the angles in and have +your complete set for this as + + align:start position:0% +your complete set for this as + + + align:start position:0% +your complete set for this as +well so now let's look at Water you did + + align:start position:0% +well so now let's look at Water you did + + + align:start position:0% +well so now let's look at Water you did +the Louis structure for water you'd end + + align:start position:0% +the Louis structure for water you'd end + + + align:start position:0% +the Louis structure for water you'd end +up with two lone pair on the + + align:start position:0% +up with two lone pair on the + + + align:start position:0% +up with two lone pair on the +oxygen and so what formula type would + + align:start position:0% +oxygen and so what formula type would + + + align:start position:0% +oxygen and so what formula type would +this + + align:start position:0% +this + + + align:start position:0% +this +be ax2 E2 s a number of four geometry + + align:start position:0% +be ax2 E2 s a number of four geometry + + + align:start position:0% +be ax2 E2 s a number of four geometry +bent + + align:start position:0% + + + + align:start position:0% + +angle yeah less than 109.5 because this + + align:start position:0% +angle yeah less than 109.5 because this + + + align:start position:0% +angle yeah less than 109.5 because this +is based on that tetrahedral geometry so + + align:start position:0% +is based on that tetrahedral geometry so + + + align:start position:0% +is based on that tetrahedral geometry so +remember bent could either be less than + + align:start position:0% +remember bent could either be less than + + + align:start position:0% +remember bent could either be less than +120 or less than + + align:start position:0% +120 or less than + + + align:start position:0% +120 or less than +109.5 but if you have an SN number of + + align:start position:0% +109.5 but if you have an SN number of + + + align:start position:0% +109.5 but if you have an SN number of +four then it's based on tetrahedral + + align:start position:0% +four then it's based on tetrahedral + + + align:start position:0% +four then it's based on tetrahedral +geometry so it would be less than 109.5 + + align:start position:0% +geometry so it would be less than 109.5 + + + align:start position:0% +geometry so it would be less than 109.5 +which is the tetrahedral + + align:start position:0% + + + + align:start position:0% + +angles okay + + align:start position:0% +angles okay + + + align:start position:0% +angles okay +sf4 so here is our our uh structure + + align:start position:0% +sf4 so here is our our uh structure + + + align:start position:0% +sf4 so here is our our uh structure +formula type for this would + + align:start position:0% +formula type for this would + + + align:start position:0% +formula type for this would +be + + align:start position:0% +be + + + align:start position:0% +be +ax4 e and that's an SN number of five + + align:start position:0% +ax4 e and that's an SN number of five + + + align:start position:0% +ax4 e and that's an SN number of five +and the shape seaw and + + align:start position:0% +and the shape seaw and + + + align:start position:0% +and the shape seaw and +angles yeah less than 90 and less than + + align:start position:0% + + + + align:start position:0% + +120 here's another one brf3 these are + + align:start position:0% +120 here's another one brf3 these are + + + align:start position:0% +120 here's another one brf3 these are +all probably ones that you did leis + + align:start position:0% +all probably ones that you did leis + + + align:start position:0% +all probably ones that you did leis +structures for if not I'm sure you will + + align:start position:0% +structures for if not I'm sure you will + + + align:start position:0% +structures for if not I'm sure you will +uh before the final so uh here's another + + align:start position:0% +uh before the final so uh here's another + + + align:start position:0% +uh before the final so uh here's another +one the formula type for this would + + align:start position:0% +one the formula type for this would + + + align:start position:0% +one the formula type for this would +be X3 + + align:start position:0% +be X3 + + + align:start position:0% +be X3 +e E2 and essn number five and geometry + + align:start position:0% +e E2 and essn number five and geometry + + + align:start position:0% +e E2 and essn number five and geometry +t-shaped + + align:start position:0% +t-shaped + + + align:start position:0% +t-shaped +angles less than + + align:start position:0% + + + + align:start position:0% + +90 okay so if we keep going here's + + align:start position:0% +90 okay so if we keep going here's + + + align:start position:0% +90 okay so if we keep going here's +another example of zenium and fluoride + + align:start position:0% +another example of zenium and fluoride + + + align:start position:0% +another example of zenium and fluoride +and we have three sets of Lone pairs + + align:start position:0% +and we have three sets of Lone pairs + + + align:start position:0% +and we have three sets of Lone pairs +what's the formula + + align:start position:0% + + + + align:start position:0% + +type yep ax2 E3 SN number of five + + align:start position:0% +type yep ax2 E3 SN number of five + + + align:start position:0% +type yep ax2 E3 SN number of five +geometry + + align:start position:0% +geometry + + + align:start position:0% +geometry +linear angle + + align:start position:0% + + + + align:start position:0% + +180 okay + + align:start position:0% +180 okay + + + align:start position:0% +180 okay +brf5 formula + + align:start position:0% + + + + align:start position:0% + +type the + + align:start position:0% +type the + + + align:start position:0% +type the +ax5e SN number six + + align:start position:0% + + + + align:start position:0% + +geometry Square parameter and uh + + align:start position:0% +geometry Square parameter and uh + + + align:start position:0% +geometry Square parameter and uh +angles less than 90 so you want to + + align:start position:0% +angles less than 90 so you want to + + + align:start position:0% +angles less than 90 so you want to +remember that one + + align:start position:0% +remember that one + + + align:start position:0% +remember that one +okay here's another one with an + + align:start position:0% +okay here's another one with an + + + align:start position:0% +okay here's another one with an +additional lone pair formula + + align:start position:0% +additional lone pair formula + + + align:start position:0% +additional lone pair formula +type ax4 E2 essn number six + + align:start position:0% +type ax4 E2 essn number six + + + align:start position:0% +type ax4 E2 essn number six +geometry Square planer angle 90 + + align:start position:0% +geometry Square planer angle 90 + + + align:start position:0% +geometry Square planer angle 90 +exactly all right so that completes that + + align:start position:0% +exactly all right so that completes that + + + align:start position:0% +exactly all right so that completes that +list and again the theory of bper you're + + align:start position:0% +list and again the theory of bper you're + + + align:start position:0% +list and again the theory of bper you're +taking experimental results and then + + align:start position:0% +taking experimental results and then + + + align:start position:0% +taking experimental results and then +trying to apply a theory to it so it's + + align:start position:0% +trying to apply a theory to it so it's + + + align:start position:0% +trying to apply a theory to it so it's +not good at really making exact + + align:start position:0% +not good at really making exact + + + align:start position:0% +not good at really making exact +predictions about things but it's really + + align:start position:0% +predictions about things but it's really + + + align:start position:0% +predictions about things but it's really +good at + + align:start position:0% +good at + + + align:start position:0% +good at +rationalizing uh what what they have all + + align:start position:0% +rationalizing uh what what they have all + + + align:start position:0% +rationalizing uh what what they have all +right so have a wonderful Thanksgiving + + align:start position:0% +right so have a wonderful Thanksgiving + + + align:start position:0% +right so have a wonderful Thanksgiving +everybody + + align:start position:0% + + + + align:start position:0% + +[Applause] \ No newline at end of file diff --git a/fg6QYiiF_c8.txt b/fg6QYiiF_c8.txt new file mode 100644 index 0000000000000000000000000000000000000000..132492286f64f7c880c5691ebd73b683aa6beee0 --- /dev/null +++ b/fg6QYiiF_c8.txt @@ -0,0 +1,64 @@ +Given a probability, p, of an event occurring, +we know that the amount of information that + +you get from being told that a particular +event occurred is log<sub>2</sub>(1/p). + +Using that information, let's try to answer +the following questions. + +Someone picks a name out of a hat known to +contain the names of 5 women and 3 men, and + +tells you a man has been selected. + +How much information have they given you about +the selection? + +The probability of a man being selected in +this problem is 3/8. + +So the amount of information that you have +been given + +is log<sub>2</sub>(1/(3/8)) = log<sub>2</sub>(8/3). + +Another way to think about this is that if +you start off with N choices, and the additional + +information that you are given reduces your +choices to M, then the amount of information + +that you have been given is log<sub>2</sub>(N/M). + +In this example N = 8 because that is the +original number of choices. + +The reduced number of choices once you are +told that a man has been selected is 3, so + +M = 3. + +This means that the amount of information +you received is log<sub>2</sub>(8/3). + +For the second question, you are asked to +guess a random 4-bit 2's complement number. + +I then tell you that the number is greater +than 0. + +How much information have you been given? + +For this problem the original number of choices +is the number of permutations of 4 binary + +bits which is 16, so N = 16. + +Once you are told that the number is greater +than 0, this reduces your choice to 7, so + +M = 7. + +That means that the amount of information +that you have been given is log<sub>2</sub>(16/7). \ No newline at end of file diff --git a/fsbVJxOhRcU.txt b/fsbVJxOhRcU.txt new file mode 100644 index 0000000000000000000000000000000000000000..0c4f17d608811e406071bdaa1beedb98afca4b89 --- /dev/null +++ b/fsbVJxOhRcU.txt @@ -0,0 +1,11083 @@ +align:start position:0% + +Okay. So + + align:start position:0% +Okay. So + + + align:start position:0% +Okay. So +um so right so we're going to prove the + + align:start position:0% +um so right so we're going to prove the + + + align:start position:0% +um so right so we're going to prove the +picard lindel theorem and it may we'll + + align:start position:0% +picard lindel theorem and it may we'll + + + align:start position:0% +picard lindel theorem and it may we'll +see it may take us + + align:start position:0% +see it may take us + + + align:start position:0% +see it may take us +it may um we may need to continue on it + + align:start position:0% +it may um we may need to continue on it + + + align:start position:0% +it may um we may need to continue on it +also on Tuesday and then when we're done + + align:start position:0% +also on Tuesday and then when we're done + + + align:start position:0% +also on Tuesday and then when we're done +with it we will just do review on + + align:start position:0% +with it we will just do review on + + + align:start position:0% +with it we will just do review on +Tuesday but let's see how far we get so + + align:start position:0% +Tuesday but let's see how far we get so + + + align:start position:0% +Tuesday but let's see how far we get so +the picinder theorem + + align:start position:0% + + + + align:start position:0% + +is the following theorem + + align:start position:0% +is the following theorem + + + align:start position:0% +is the following theorem +and it say that uh it's it's a it's a OD + + align:start position:0% +and it say that uh it's it's a it's a OD + + + align:start position:0% +and it say that uh it's it's a it's a OD +so it's a what's called ordinary + + align:start position:0% +so it's a what's called ordinary + + + align:start position:0% +so it's a what's called ordinary +differential equation Okay. + + align:start position:0% + + + + align:start position:0% + +And so again a differential equation is + + align:start position:0% +And so again a differential equation is + + + align:start position:0% +And so again a differential equation is +something about an unknown function and + + align:start position:0% +something about an unknown function and + + + align:start position:0% +something about an unknown function and +its derivative. Right? So differential + + align:start position:0% +its derivative. Right? So differential + + + align:start position:0% +its derivative. Right? So differential +equation just mean it's an equation. So + + align:start position:0% +equation just mean it's an equation. So + + + align:start position:0% +equation just mean it's an equation. So +this here means that it's an equation + + align:start position:0% + + + + align:start position:0% + +in an unknown function + + align:start position:0% + + + + align:start position:0% + +uh and its derivative. + + align:start position:0% + + + + align:start position:0% + +ordinary just as we talked about last + + align:start position:0% +ordinary just as we talked about last + + + align:start position:0% +ordinary just as we talked about last +time ordinary refer to uh that is just + + align:start position:0% +time ordinary refer to uh that is just + + + align:start position:0% +time ordinary refer to uh that is just +of one variable. Okay. And so the OD + + align:start position:0% +of one variable. Okay. And so the OD + + + align:start position:0% +of one variable. Okay. And so the OD +that the picard line theorem is about is + + align:start position:0% +that the picard line theorem is about is + + + align:start position:0% +that the picard line theorem is about is +so the unknown function is y. And the od + + align:start position:0% +so the unknown function is y. And the od + + + align:start position:0% +so the unknown function is y. And the od +is is this that we want the derivative + + align:start position:0% +is is this that we want the derivative + + + align:start position:0% +is is this that we want the derivative +of this unknown function to be equal to + + align:start position:0% +of this unknown function to be equal to + + + align:start position:0% +of this unknown function to be equal to +a function of the unknown function plus + + align:start position:0% +a function of the unknown function plus + + + align:start position:0% +a function of the unknown function plus +another function that just depend on x. + + align:start position:0% +another function that just depend on x. + + + align:start position:0% +another function that just depend on x. +So y here is the unknown function and y + + align:start position:0% +So y here is the unknown function and y + + + align:start position:0% +So y here is the unknown function and y +is a function of x right x is x is a + + align:start position:0% +is a function of x right x is x is a + + + align:start position:0% +is a function of x right x is x is a +real number + + align:start position:0% +real number + + + align:start position:0% +real number +right and and it's just a yeah so this + + align:start position:0% +right and and it's just a yeah so this + + + align:start position:0% +right and and it's just a yeah so this +is the differential equation and then we + + align:start position:0% +is the differential equation and then we + + + align:start position:0% +is the differential equation and then we +have some initial condition so at zero + + align:start position:0% +have some initial condition so at zero + + + align:start position:0% +have some initial condition so at zero +we want it to take a value a okay so + + align:start position:0% +we want it to take a value a okay so + + + align:start position:0% +we want it to take a value a okay so +this is the differential equation and + + align:start position:0% +this is the differential equation and + + + align:start position:0% +this is the differential equation and +what we assume Assume here is so f and g + + align:start position:0% +what we assume Assume here is so f and g + + + align:start position:0% +what we assume Assume here is so f and g +are function on r + + align:start position:0% +are function on r + + + align:start position:0% +are function on r +and you should think about those as + + align:start position:0% +and you should think about those as + + + align:start position:0% +and you should think about those as +being known + + align:start position:0% + + + + align:start position:0% + +and uh they are an f here is + + align:start position:0% +and uh they are an f here is + + + align:start position:0% +and uh they are an f here is +differentiable + + align:start position:0% + + + + align:start position:0% + +and the derivative + + align:start position:0% +and the derivative + + + align:start position:0% +and the derivative +is continuous. + + align:start position:0% + + + + align:start position:0% + +and G is just continuous + + align:start position:0% +and G is just continuous + + + align:start position:0% +and G is just continuous +doesn't need to be differentiable + + align:start position:0% + + + + align:start position:0% + +and the pal Lindel theorem is so the + + align:start position:0% +and the pal Lindel theorem is so the + + + align:start position:0% +and the pal Lindel theorem is so the +again the pard Theorem + + align:start position:0% + + + + align:start position:0% + +is the following + + align:start position:0% +is the following + + + align:start position:0% +is the following +that given + + align:start position:0% +that given + + + align:start position:0% +that given +uh given f + + align:start position:0% +uh given f + + + align:start position:0% +uh given f +uh g as above + + align:start position:0% +uh g as above + + + align:start position:0% +uh g as above +and sorry n a was this constant. It's + + align:start position:0% +and sorry n a was this constant. It's + + + align:start position:0% +and sorry n a was this constant. It's +just a real number as above. + + align:start position:0% + + + + align:start position:0% + +There exist + + align:start position:0% + + + + align:start position:0% + +uh delta greater than zero. + + align:start position:0% +uh delta greater than zero. + + + align:start position:0% +uh delta greater than zero. +Um um such that and and and a solution + + align:start position:0% + + + + align:start position:0% + +why + + align:start position:0% +why + + + align:start position:0% +why +defined on + + align:start position:0% + + + + align:start position:0% + +the integral from minus delta to delta + + align:start position:0% +the integral from minus delta to delta + + + align:start position:0% +the integral from minus delta to delta +and and solution y to uh the OD + + align:start position:0% +and and solution y to uh the OD + + + align:start position:0% +and and solution y to uh the OD +right and so again meaning that is uh + + align:start position:0% +right and so again meaning that is uh + + + align:start position:0% +right and so again meaning that is uh +that is solution that means that at the + + align:start position:0% +that is solution that means that at the + + + align:start position:0% +that is solution that means that at the +in at zero it takes value a and then is + + align:start position:0% +in at zero it takes value a and then is + + + align:start position:0% +in at zero it takes value a and then is +satisfying that equation okay + + align:start position:0% +satisfying that equation okay + + + align:start position:0% +satisfying that equation okay +and Moreover, + + align:start position:0% +and Moreover, + + + align:start position:0% +and Moreover, +and I'll get back to that, but we won't, + + align:start position:0% +and I'll get back to that, but we won't, + + + align:start position:0% +and I'll get back to that, but we won't, +you know, that's it's quite possible. I + + align:start position:0% +you know, that's it's quite possible. I + + + align:start position:0% +you know, that's it's quite possible. I +won't get to that uh today. Moreover, + + align:start position:0% + + + + align:start position:0% + +uh um solutions are unique. + + align:start position:0% + + + + align:start position:0% + +Okay. And so, so right. So this is like + + align:start position:0% +Okay. And so, so right. So this is like + + + align:start position:0% +Okay. And so, so right. So this is like +a standard problem in when you're + + align:start position:0% +a standard problem in when you're + + + align:start position:0% +a standard problem in when you're +looking at differential equations. You + + align:start position:0% +looking at differential equations. You + + + align:start position:0% +looking at differential equations. You +have a differential equation that may + + align:start position:0% +have a differential equation that may + + + align:start position:0% +have a differential equation that may +describe something in nature and you + + align:start position:0% +describe something in nature and you + + + align:start position:0% +describe something in nature and you +wonder does this uh equation have a + + align:start position:0% +wonder does this uh equation have a + + + align:start position:0% +wonder does this uh equation have a +solution + + align:start position:0% +solution + + + align:start position:0% +solution +and uh and if it has a solution or + + align:start position:0% +and uh and if it has a solution or + + + align:start position:0% +and uh and if it has a solution or +solutions unique. Okay. So this is what + + align:start position:0% +solutions unique. Okay. So this is what + + + align:start position:0% +solutions unique. Okay. So this is what +this answer in this case + + align:start position:0% +this answer in this case + + + align:start position:0% +this answer in this case +and the interesting thing or part of the + + align:start position:0% +and the interesting thing or part of the + + + align:start position:0% +and the interesting thing or part of the +interesting thing I mean so this is a + + align:start position:0% +interesting thing I mean so this is a + + + align:start position:0% +interesting thing I mean so this is a +fundamental question u used all over + + align:start position:0% +fundamental question u used all over + + + align:start position:0% +fundamental question u used all over +science and engineering and one of the + + align:start position:0% +science and engineering and one of the + + + align:start position:0% +science and engineering and one of the +interesting things is that it's uses the + + align:start position:0% +interesting things is that it's uses the + + + align:start position:0% +interesting things is that it's uses the +proof of this uses metric spaces and so + + align:start position:0% +proof of this uses metric spaces and so + + + align:start position:0% +proof of this uses metric spaces and so +the proof is has been used you know + + align:start position:0% +the proof is has been used you know + + + align:start position:0% +the proof is has been used you know +various version of the proof have been + + align:start position:0% +various version of the proof have been + + + align:start position:0% +various version of the proof have been +used to prove existence + + align:start position:0% +used to prove existence + + + align:start position:0% +used to prove existence +uh and uniqueness of various + + align:start position:0% +uh and uniqueness of various + + + align:start position:0% +uh and uniqueness of various +differential equations. + + align:start position:0% +differential equations. + + + align:start position:0% +differential equations. +So the pro the proof + + align:start position:0% + + + + align:start position:0% + +uses + + align:start position:0% +uses + + + align:start position:0% +uses +the theory of metric spaces + + align:start position:0% + + + + align:start position:0% + +which is sort of surprising because it + + align:start position:0% +which is sort of surprising because it + + + align:start position:0% +which is sort of surprising because it +seems to have nothing to do with metric + + align:start position:0% +seems to have nothing to do with metric + + + align:start position:0% +seems to have nothing to do with metric +spaces. + + align:start position:0% + + + + align:start position:0% + +And so it uses in particular the metric + + align:start position:0% +And so it uses in particular the metric + + + align:start position:0% +And so it uses in particular the metric +space that it's using is + + align:start position:0% +space that it's using is + + + align:start position:0% +space that it's using is +uh the continuous functions on some + + align:start position:0% +uh the continuous functions on some + + + align:start position:0% +uh the continuous functions on some +interval here + + align:start position:0% + + + + align:start position:0% + +right and on the space of continuous + + align:start position:0% +right and on the space of continuous + + + align:start position:0% +right and on the space of continuous +function we have the metric that we + + align:start position:0% +function we have the metric that we + + + align:start position:0% +function we have the metric that we +talked about the metric so if f and g + + align:start position:0% +talked about the metric so if f and g + + + align:start position:0% +talked about the metric so if f and g +sorry f is so bad uh because it's the + + align:start position:0% +sorry f is so bad uh because it's the + + + align:start position:0% +sorry f is so bad uh because it's the +and g also let's call it h1 H1 and H2. + + align:start position:0% +and g also let's call it h1 H1 and H2. + + + align:start position:0% +and g also let's call it h1 H1 and H2. +Suppose that these are continuous + + align:start position:0% +Suppose that these are continuous + + + align:start position:0% +Suppose that these are continuous +functions. H1 and H2 + + align:start position:0% +functions. H1 and H2 + + + align:start position:0% +functions. H1 and H2 +are continuous functions + + align:start position:0% +are continuous functions + + + align:start position:0% +are continuous functions +on an interval + + align:start position:0% +on an interval + + + align:start position:0% +on an interval +like this. + + align:start position:0% +like this. + + + align:start position:0% +like this. +Then the distance is this that we have + + align:start position:0% +Then the distance is this that we have + + + align:start position:0% +Then the distance is this that we have +considered various times. This is just a + + align:start position:0% +considered various times. This is just a + + + align:start position:0% +considered various times. This is just a +maximum + + align:start position:0% +maximum + + + align:start position:0% +maximum +uh over uh x in this interval here + + align:start position:0% +uh over uh x in this interval here + + + align:start position:0% +uh over uh x in this interval here +of uh f of x of h1 sorry h1 of x minus + + align:start position:0% +of uh f of x of h1 sorry h1 of x minus + + + align:start position:0% +of uh f of x of h1 sorry h1 of x minus +h2 of x and then the absolute value of + + align:start position:0% +h2 of x and then the absolute value of + + + align:start position:0% +h2 of x and then the absolute value of +that right. + + align:start position:0% +that right. + + + align:start position:0% +that right. +So this is the distance on the space of + + align:start position:0% +So this is the distance on the space of + + + align:start position:0% +So this is the distance on the space of +continuous functions that we have looked + + align:start position:0% +continuous functions that we have looked + + + align:start position:0% +continuous functions that we have looked +at a lot. + + align:start position:0% +at a lot. + + + align:start position:0% +at a lot. +Okay. And it's actually not quite this + + align:start position:0% +Okay. And it's actually not quite this + + + align:start position:0% +Okay. And it's actually not quite this +space as I mentioned last time. It's a + + align:start position:0% +space as I mentioned last time. It's a + + + align:start position:0% +space as I mentioned last time. It's a +ball in this space that is using + + align:start position:0% + + + + align:start position:0% + +right okay + + align:start position:0% +right okay + + + align:start position:0% +right okay +so what do we need about this metric + + align:start position:0% +so what do we need about this metric + + + align:start position:0% +so what do we need about this metric +space? So one thing we've proven + + align:start position:0% +space? So one thing we've proven + + + align:start position:0% +space? So one thing we've proven +couple of lectures ago is that uh that + + align:start position:0% +couple of lectures ago is that uh that + + + align:start position:0% +couple of lectures ago is that uh that +this this space here of continuous + + align:start position:0% +this this space here of continuous + + + align:start position:0% +this this space here of continuous +functions + + align:start position:0% + + + + align:start position:0% + +uh with this metric here + + align:start position:0% +uh with this metric here + + + align:start position:0% +uh with this metric here +uh is cushy complete. + + align:start position:0% + + + + align:start position:0% + +So we're going to use that. Okay, + + align:start position:0% +So we're going to use that. Okay, + + + align:start position:0% +So we're going to use that. Okay, +another thing we're going to use is this + + align:start position:0% +another thing we're going to use is this + + + align:start position:0% +another thing we're going to use is this +notion of contracting map. So, um + + align:start position:0% +notion of contracting map. So, um + + + align:start position:0% +notion of contracting map. So, um +another tool + + align:start position:0% +another tool + + + align:start position:0% +another tool +will + + align:start position:0% +will + + + align:start position:0% +will +be that + + align:start position:0% +be that + + + align:start position:0% +be that +of a contracting map. + + align:start position:0% + + + + align:start position:0% + +And so but and remember + + align:start position:0% +And so but and remember + + + align:start position:0% +And so but and remember +this is a number of lectures ago we + + align:start position:0% +this is a number of lectures ago we + + + align:start position:0% +this is a number of lectures ago we +talked about a contracting map but we + + align:start position:0% +talked about a contracting map but we + + + align:start position:0% +talked about a contracting map but we +need a more general notion of + + align:start position:0% +need a more general notion of + + + align:start position:0% +need a more general notion of +contracting map because when we talked + + align:start position:0% +contracting map because when we talked + + + align:start position:0% +contracting map because when we talked +about it we talked about a map from R + + align:start position:0% +about it we talked about a map from R + + + align:start position:0% +about it we talked about a map from R +into R. Uh and then we use this notion + + align:start position:0% +into R. Uh and then we use this notion + + + align:start position:0% +into R. Uh and then we use this notion +of contracting map to u uh in to finding + + align:start position:0% +of contracting map to u uh in to finding + + + align:start position:0% +of contracting map to u uh in to finding +zeros with using Newton's method. Okay. + + align:start position:0% +zeros with using Newton's method. Okay. + + + align:start position:0% +zeros with using Newton's method. Okay. +And but here we're going to use it for + + align:start position:0% +And but here we're going to use it for + + + align:start position:0% +And but here we're going to use it for +something different and so we need a + + align:start position:0% +something different and so we need a + + + align:start position:0% +something different and so we need a +more general notion. So suppose that so + + align:start position:0% +more general notion. So suppose that so + + + align:start position:0% +more general notion. So suppose that so +uh contracting map. + + align:start position:0% + + + + align:start position:0% + +So this is the general version + + align:start position:0% +So this is the general version + + + align:start position:0% +So this is the general version +as opposed to uh the version that we + + align:start position:0% +as opposed to uh the version that we + + + align:start position:0% +as opposed to uh the version that we +talked about already that was for for + + align:start position:0% +talked about already that was for for + + + align:start position:0% +talked about already that was for for +the line for for R. So contracting map + + align:start position:0% +the line for for R. So contracting map + + + align:start position:0% +the line for for R. So contracting map +sorry. + + align:start position:0% + + + + align:start position:0% + +And so this is so you have a metric + + align:start position:0% +And so this is so you have a metric + + + align:start position:0% +And so this is so you have a metric +space XD. This is you know could be like + + align:start position:0% +space XD. This is you know could be like + + + align:start position:0% +space XD. This is you know could be like +this but it also just could be any + + align:start position:0% +this but it also just could be any + + + align:start position:0% +this but it also just could be any +metric space. + + align:start position:0% +metric space. + + + align:start position:0% +metric space. +And then you have a map from this metric + + align:start position:0% +And then you have a map from this metric + + + align:start position:0% +And then you have a map from this metric +space + + align:start position:0% +space + + + align:start position:0% +space +into the self. + + align:start position:0% +into the self. + + + align:start position:0% +into the self. +And T here is set to be T is set to be + + align:start position:0% +And T here is set to be T is set to be + + + align:start position:0% +And T here is set to be T is set to be +contracting. + + align:start position:0% + + + + align:start position:0% + +uh if there exist + + align:start position:0% + + + + align:start position:0% + +uh a constant C less than one such that + + align:start position:0% +uh a constant C less than one such that + + + align:start position:0% +uh a constant C less than one such that +if you're looking at the distance + + align:start position:0% +if you're looking at the distance + + + align:start position:0% +if you're looking at the distance +between the images + + align:start position:0% +between the images + + + align:start position:0% +between the images +then they are squeezed together. So this + + align:start position:0% +then they are squeezed together. So this + + + align:start position:0% +then they are squeezed together. So this +distance here between the images under + + align:start position:0% +distance here between the images under + + + align:start position:0% +distance here between the images under +the map is less or equal to + + align:start position:0% +the map is less or equal to + + + align:start position:0% +the map is less or equal to +this constant that is less than one + + align:start position:0% +this constant that is less than one + + + align:start position:0% +this constant that is less than one +times the distance before you apply the + + align:start position:0% +times the distance before you apply the + + + align:start position:0% +times the distance before you apply the +map. Right? So this means that under the + + align:start position:0% +map. Right? So this means that under the + + + align:start position:0% +map. Right? So this means that under the +map sinks get closer together. Right? + + align:start position:0% +map sinks get closer together. Right? + + + align:start position:0% +map sinks get closer together. Right? +So that's a contracting map. + + align:start position:0% +So that's a contracting map. + + + align:start position:0% +So that's a contracting map. +And so now we proved a theorem when we + + align:start position:0% +And so now we proved a theorem when we + + + align:start position:0% +And so now we proved a theorem when we +did the new measuring we proved a + + align:start position:0% +did the new measuring we proved a + + + align:start position:0% +did the new measuring we proved a +theorem but we needed a about fix points + + align:start position:0% +theorem but we needed a about fix points + + + align:start position:0% +theorem but we needed a about fix points +and we need a generalized version of + + align:start position:0% +and we need a generalized version of + + + align:start position:0% +and we need a generalized version of +that. So um so if you take a map just in + + align:start position:0% +that. So um so if you take a map just in + + + align:start position:0% +that. So um so if you take a map just in +general + + align:start position:0% +general + + + align:start position:0% +general +from a space to a space then a fixed + + align:start position:0% +from a space to a space then a fixed + + + align:start position:0% +from a space to a space then a fixed +point + + align:start position:0% +point + + + align:start position:0% +point +a fixed point + + align:start position:0% + + + + align:start position:0% + +is uh a point + + align:start position:0% + + + + align:start position:0% + +x in the space + + align:start position:0% +x in the space + + + align:start position:0% +x in the space +so that t of x + + align:start position:0% +so that t of x + + + align:start position:0% +so that t of x +so t leaves X invariance. So T of X is + + align:start position:0% +so t leaves X invariance. So T of X is + + + align:start position:0% +so t leaves X invariance. So T of X is +equal to X. That's a fixed point, right? + + align:start position:0% +equal to X. That's a fixed point, right? + + + align:start position:0% +equal to X. That's a fixed point, right? +Okay. And so now if you have a + + align:start position:0% +Okay. And so now if you have a + + + align:start position:0% +Okay. And so now if you have a +contracting map, so if + + align:start position:0% +contracting map, so if + + + align:start position:0% +contracting map, so if +if T here is contracting, + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +T can have at most one fix point. + + align:start position:0% + + + + align:start position:0% + +Why? Because suppose that X so if + + align:start position:0% +Why? Because suppose that X so if + + + align:start position:0% +Why? Because suppose that X so if +if X and Y are both fixed points. + + align:start position:0% + + + + align:start position:0% + +Well, then you have that g of x + + align:start position:0% +Well, then you have that g of x + + + align:start position:0% +Well, then you have that g of x +is equal to g of y. Sorry, g of x is + + align:start position:0% +is equal to g of y. Sorry, g of x is + + + align:start position:0% +is equal to g of y. Sorry, g of x is +equal to tox and t of y is equal to one. + + align:start position:0% +equal to tox and t of y is equal to one. + + + align:start position:0% +equal to tox and t of y is equal to one. +Right? + + align:start position:0% +Right? + + + align:start position:0% +Right? +And so now you have that the distance + + align:start position:0% +And so now you have that the distance + + + align:start position:0% +And so now you have that the distance +between t of x + + align:start position:0% + + + + align:start position:0% + +uh let me make make a little more space. + + align:start position:0% +uh let me make make a little more space. + + + align:start position:0% +uh let me make make a little more space. +Then you have that the actually we just + + align:start position:0% +Then you have that the actually we just + + + align:start position:0% +Then you have that the actually we just +continue down here. So that the distance + + align:start position:0% +continue down here. So that the distance + + + align:start position:0% +continue down here. So that the distance +between t of x + + align:start position:0% +between t of x + + + align:start position:0% +between t of x +comma t of y + + align:start position:0% +comma t of y + + + align:start position:0% +comma t of y +the map is contracting. So this is less + + align:start position:0% +the map is contracting. So this is less + + + align:start position:0% +the map is contracting. So this is less +or equal to this constant times + + align:start position:0% +or equal to this constant times + + + align:start position:0% +or equal to this constant times +this here. On the other hand they're + + align:start position:0% +this here. On the other hand they're + + + align:start position:0% +this here. On the other hand they're +both fixed points. So t of x is x. This + + align:start position:0% +both fixed points. So t of x is x. This + + + align:start position:0% +both fixed points. So t of x is x. This +here is x and this here is y. So if we + + align:start position:0% +here is x and this here is y. So if we + + + align:start position:0% +here is x and this here is y. So if we +write this out so this is x comma y. And + + align:start position:0% +write this out so this is x comma y. And + + + align:start position:0% +write this out so this is x comma y. And +so you see that this thing here is some + + align:start position:0% +so you see that this thing here is some + + + align:start position:0% +so you see that this thing here is some +constant less than one strictly less + + align:start position:0% +constant less than one strictly less + + + align:start position:0% +constant less than one strictly less +than one times itself. So this means of + + align:start position:0% +than one times itself. So this means of + + + align:start position:0% +than one times itself. So this means of +course that this number here this non- + + align:start position:0% +course that this number here this non- + + + align:start position:0% +course that this number here this non- +negative number must be zero. And so + + align:start position:0% +negative number must be zero. And so + + + align:start position:0% +negative number must be zero. And so +this of course implies by the + + align:start position:0% +this of course implies by the + + + align:start position:0% +this of course implies by the +actions of a metric space that X is + + align:start position:0% +actions of a metric space that X is + + + align:start position:0% +actions of a metric space that X is +equal to Y. Right? So a contracting map + + align:start position:0% +equal to Y. Right? So a contracting map + + + align:start position:0% +equal to Y. Right? So a contracting map +has at most one fixed point. + + align:start position:0% +has at most one fixed point. + + + align:start position:0% +has at most one fixed point. +Now the other thing is that if you take + + align:start position:0% +Now the other thing is that if you take + + + align:start position:0% +Now the other thing is that if you take +a metric space + + align:start position:0% +a metric space + + + align:start position:0% +a metric space +um if you take a metric space + + align:start position:0% + + + + align:start position:0% + +right so this here is cushy complete so + + align:start position:0% +right so this here is cushy complete so + + + align:start position:0% +right so this here is cushy complete so +now I'm going to take a cushy complete + + align:start position:0% +now I'm going to take a cushy complete + + + align:start position:0% +now I'm going to take a cushy complete +metric space so it could be continuous + + align:start position:0% +metric space so it could be continuous + + + align:start position:0% +metric space so it could be continuous +function on some closed interval and + + align:start position:0% +function on some closed interval and + + + align:start position:0% +function on some closed interval and +that's how we will apply it but it works + + align:start position:0% +that's how we will apply it but it works + + + align:start position:0% +that's how we will apply it but it works +more generally + + align:start position:0% + + + + align:start position:0% + +So we have a fin. + + align:start position:0% +So we have a fin. + + + align:start position:0% +So we have a fin. +So if + + align:start position:0% + + + + align:start position:0% + +if this here is a complete cushy + + align:start position:0% +if this here is a complete cushy + + + align:start position:0% +if this here is a complete cushy +complete + + align:start position:0% + + + + align:start position:0% + +metric space + + align:start position:0% + + + + align:start position:0% + +uh and t + + align:start position:0% + + + + align:start position:0% + +from x into x + + align:start position:0% +from x into x + + + align:start position:0% +from x into x +is Yeah. Uh contracting map + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +t + + align:start position:0% +t + + + align:start position:0% +t +has a unique fixed bot. We know it only + + align:start position:0% +has a unique fixed bot. We know it only + + + align:start position:0% +has a unique fixed bot. We know it only +have it have at most one. So the + + align:start position:0% +have it have at most one. So the + + + align:start position:0% +have it have at most one. So the +statement really is that that it has one + + align:start position:0% +statement really is that that it has one + + + align:start position:0% +statement really is that that it has one +right? has a unique fix point. + + align:start position:0% + + + + align:start position:0% + +Okay. So, + + align:start position:0% +Okay. So, + + + align:start position:0% +Okay. So, +so let's try to prove this. + + align:start position:0% + + + + align:start position:0% + +And you might remember and if you don't + + align:start position:0% +And you might remember and if you don't + + + align:start position:0% +And you might remember and if you don't +that's fine but you might remember how + + align:start position:0% +that's fine but you might remember how + + + align:start position:0% +that's fine but you might remember how +we used it in the new methods because + + align:start position:0% +we used it in the new methods because + + + align:start position:0% +we used it in the new methods because +the new methods was like it was a + + align:start position:0% +the new methods was like it was a + + + align:start position:0% +the new methods was like it was a +version of this on a + + align:start position:0% +version of this on a + + + align:start position:0% +version of this on a +So you had a map from R to R and to find + + align:start position:0% +So you had a map from R to R and to find + + + align:start position:0% +So you had a map from R to R and to find +the fixed point and so you wondered what + + align:start position:0% +the fixed point and so you wondered what + + + align:start position:0% +the fixed point and so you wondered what +you were there and you knew the message + + align:start position:0% +you were there and you knew the message + + + align:start position:0% +you were there and you knew the message +was something about finding a point + + align:start position:0% +was something about finding a point + + + align:start position:0% +was something about finding a point +where a function vanishes, right? And + + align:start position:0% +where a function vanishes, right? And + + + align:start position:0% +where a function vanishes, right? And +that was set up as a fixed point + + align:start position:0% +that was set up as a fixed point + + + align:start position:0% +that was set up as a fixed point +theorem. And so what you did is you made + + align:start position:0% +theorem. And so what you did is you made + + + align:start position:0% +theorem. And so what you did is you made +a good choice. I mean a choice that look + + align:start position:0% +a good choice. I mean a choice that look + + + align:start position:0% +a good choice. I mean a choice that look +reasonable, right? This is not exactly + + align:start position:0% +reasonable, right? This is not exactly + + + align:start position:0% +reasonable, right? This is not exactly +where the function vanishes, but + + align:start position:0% +where the function vanishes, but + + + align:start position:0% +where the function vanishes, but +something that looks close to where it + + align:start position:0% +something that looks close to where it + + + align:start position:0% +something that looks close to where it +vanish. And then you iterate, you took + + align:start position:0% +vanish. And then you iterate, you took + + + align:start position:0% +vanish. And then you iterate, you took +the image under the map and you iterated + + align:start position:0% +the image under the map and you iterated + + + align:start position:0% +the image under the map and you iterated +this. And so it's the same we're going + + align:start position:0% +this. And so it's the same we're going + + + align:start position:0% +this. And so it's the same we're going +to do here. So, and this time we we we + + align:start position:0% +to do here. So, and this time we we we + + + align:start position:0% +to do here. So, and this time we we we +don't even need to make a good choice. + + align:start position:0% +don't even need to make a good choice. + + + align:start position:0% +don't even need to make a good choice. +So, we just take um we just take let + + align:start position:0% +So, we just take um we just take let + + + align:start position:0% +So, we just take um we just take let +x here be any point in the metric space. + + align:start position:0% +x here be any point in the metric space. + + + align:start position:0% +x here be any point in the metric space. +So, you're just fixing some point in the + + align:start position:0% +So, you're just fixing some point in the + + + align:start position:0% +So, you're just fixing some point in the +metric space. + + align:start position:0% +metric space. + + + align:start position:0% +metric space. +And now you're looking at so you're + + align:start position:0% +And now you're looking at so you're + + + align:start position:0% +And now you're looking at so you're +looking at the sequence x t of x + + align:start position:0% +looking at the sequence x t of x + + + align:start position:0% +looking at the sequence x t of x +and then you apply t to t of x. So this + + align:start position:0% +and then you apply t to t of x. So this + + + align:start position:0% +and then you apply t to t of x. So this +is I write this as this. Then you apply + + align:start position:0% +is I write this as this. Then you apply + + + align:start position:0% +is I write this as this. Then you apply +t to t squared of x. So that's right + + align:start position:0% +t to t squared of x. So that's right + + + align:start position:0% +t to t squared of x. So that's right +like this. And so you keep applying t + + align:start position:0% +like this. And so you keep applying t + + + align:start position:0% +like this. And so you keep applying t +more and more times. + + align:start position:0% +more and more times. + + + align:start position:0% +more and more times. +Right? And so this gives you a sequence + + align:start position:0% +Right? And so this gives you a sequence + + + align:start position:0% +Right? And so this gives you a sequence +and so on. So this gives you a sequence. + + align:start position:0% +and so on. So this gives you a sequence. + + + align:start position:0% +and so on. So this gives you a sequence. +Okay? And now the claim is that this + + align:start position:0% +Okay? And now the claim is that this + + + align:start position:0% +Okay? And now the claim is that this +sequence here. So claim + + align:start position:0% + + + + align:start position:0% + +that this sequence here + + align:start position:0% +that this sequence here + + + align:start position:0% +that this sequence here +converge + + align:start position:0% + + + + align:start position:0% + +to right. So it converge and the limit + + align:start position:0% +to right. So it converge and the limit + + + align:start position:0% +to right. So it converge and the limit +here this here + + align:start position:0% +here this here + + + align:start position:0% +here this here +is a fixed point + + align:start position:0% + + + + align:start position:0% + +for G. So that's a claim. Okay. + + align:start position:0% +for G. So that's a claim. Okay. + + + align:start position:0% +for G. So that's a claim. Okay. +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Now, + + align:start position:0% + + + + align:start position:0% + +so we wanted to prove first that is + + align:start position:0% +so we wanted to prove first that is + + + align:start position:0% +so we wanted to prove first that is +converging. + + align:start position:0% + + + + align:start position:0% + +Okay. So we're going to prove first. So + + align:start position:0% +Okay. So we're going to prove first. So + + + align:start position:0% +Okay. So we're going to prove first. So +we first show + + align:start position:0% + + + + align:start position:0% + +that TN + + align:start position:0% +that TN + + + align:start position:0% +that TN +is a cushy sequence. + + align:start position:0% + + + + align:start position:0% + +Okay. So now let's look at um so we're + + align:start position:0% +Okay. So now let's look at um so we're + + + align:start position:0% +Okay. So now let's look at um so we're +supposed to look if you're looking at a + + align:start position:0% +supposed to look if you're looking at a + + + align:start position:0% +supposed to look if you're looking at a +if you try to prove that something is a + + align:start position:0% +if you try to prove that something is a + + + align:start position:0% +if you try to prove that something is a +cruise sequence then you're looking at + + align:start position:0% +cruise sequence then you're looking at + + + align:start position:0% +cruise sequence then you're looking at +the distance between + + align:start position:0% +the distance between + + + align:start position:0% +the distance between +elements in the sequence + + align:start position:0% +elements in the sequence + + + align:start position:0% +elements in the sequence +where both of these elements is + + align:start position:0% +where both of these elements is + + + align:start position:0% +where both of these elements is +sufficiently far right that's what + + align:start position:0% +sufficiently far right that's what + + + align:start position:0% +sufficiently far right that's what +you're supposed to look at + + align:start position:0% +you're supposed to look at + + + align:start position:0% +you're supposed to look at +and so let me write the m here so I can + + align:start position:0% +and so let me write the m here so I can + + + align:start position:0% +and so let me write the m here so I can +sing about one of them as being further + + align:start position:0% +sing about one of them as being further + + + align:start position:0% +sing about one of them as being further +out than the other one. So I'm going to + + align:start position:0% +out than the other one. So I'm going to + + + align:start position:0% +out than the other one. So I'm going to +think about m here as being n plus some + + align:start position:0% +think about m here as being n plus some + + + align:start position:0% +think about m here as being n plus some +number k, right? Some integer k, right? + + align:start position:0% +number k, right? Some integer k, right? + + + align:start position:0% +number k, right? Some integer k, right? +And so I'm interested in estimating the + + align:start position:0% +And so I'm interested in estimating the + + + align:start position:0% +And so I'm interested in estimating the +distance between tn of x + + align:start position:0% +distance between tn of x + + + align:start position:0% +distance between tn of x +and t n + k + + align:start position:0% +and t n + k + + + align:start position:0% +and t n + k +of x. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Now + + align:start position:0% +Now + + + align:start position:0% +Now +in order to do that let me start with + + align:start position:0% +in order to do that let me start with + + + align:start position:0% +in order to do that let me start with +something + + align:start position:0% +something + + + align:start position:0% +something +simpler first. + + align:start position:0% +simpler first. + + + align:start position:0% +simpler first. +Let me look at the distance + + align:start position:0% +Let me look at the distance + + + align:start position:0% +Let me look at the distance +between T of X + + align:start position:0% +between T of X + + + align:start position:0% +between T of X +uh let me look at the distance between T + + align:start position:0% +uh let me look at the distance between T + + + align:start position:0% +uh let me look at the distance between T +um + + align:start position:0% +um + + + align:start position:0% +um +L of X + + align:start position:0% +L of X + + + align:start position:0% +L of X +and T L + one of X. + + align:start position:0% +and T L + one of X. + + + align:start position:0% +and T L + one of X. +Okay. So two consecutive elements in the + + align:start position:0% +Okay. So two consecutive elements in the + + + align:start position:0% +Okay. So two consecutive elements in the +sequence. Okay. Now I can sing it. So + + align:start position:0% +sequence. Okay. Now I can sing it. So + + + align:start position:0% +sequence. Okay. Now I can sing it. So +this thing here well this is equal to + + align:start position:0% +this thing here well this is equal to + + + align:start position:0% +this thing here well this is equal to +the distance between t of t + + align:start position:0% +the distance between t of t + + + align:start position:0% +the distance between t of t +uh l -1 + + align:start position:0% +uh l -1 + + + align:start position:0% +uh l -1 +of x + + align:start position:0% +of x + + + align:start position:0% +of x +and then uh t of g l of of x like that. + + align:start position:0% +and then uh t of g l of of x like that. + + + align:start position:0% +and then uh t of g l of of x like that. +Right? + + align:start position:0% +Right? + + + align:start position:0% +Right? +I can write it like that. Right? I just + + align:start position:0% +I can write it like that. Right? I just + + + align:start position:0% +I can write it like that. Right? I just +But now of course, so you see here + + align:start position:0% +But now of course, so you see here + + + align:start position:0% +But now of course, so you see here +there's some elements in X in the spa + + align:start position:0% +there's some elements in X in the spa + + + align:start position:0% +there's some elements in X in the spa +space X. Here's another element. + + align:start position:0% +space X. Here's another element. + + + align:start position:0% +space X. Here's another element. +They both have T applied to it. T is + + align:start position:0% +They both have T applied to it. T is + + + align:start position:0% +They both have T applied to it. T is +contracting. So you get C + + align:start position:0% +contracting. So you get C + + + align:start position:0% +contracting. So you get C +T L minus one X + + align:start position:0% +T L minus one X + + + align:start position:0% +T L minus one X +uh TL + + align:start position:0% +uh TL + + + align:start position:0% +uh TL +of X. + + align:start position:0% + + + + align:start position:0% + +So you see that if you take two + + align:start position:0% +So you see that if you take two + + + align:start position:0% +So you see that if you take two +consecutive elements and you're taking + + align:start position:0% +consecutive elements and you're taking + + + align:start position:0% +consecutive elements and you're taking +the distance then it's bounded by + + align:start position:0% +the distance then it's bounded by + + + align:start position:0% +the distance then it's bounded by +this constant C times right where you + + align:start position:0% +this constant C times right where you + + + align:start position:0% +this constant C times right where you +have one less uh where you have have + + align:start position:0% +have one less uh where you have have + + + align:start position:0% +have one less uh where you have have +have applied t one less time on both + + align:start position:0% +have applied t one less time on both + + + align:start position:0% +have applied t one less time on both +right these are again consecutive + + align:start position:0% +right these are again consecutive + + + align:start position:0% +right these are again consecutive +elements but but the highest one is one + + align:start position:0% +elements but but the highest one is one + + + align:start position:0% +elements but but the highest one is one +less right + + align:start position:0% +less right + + + align:start position:0% +less right +okay so now if you iterate this + + align:start position:0% + + + + align:start position:0% + +uh okay so iterating this so let's see + + align:start position:0% +uh okay so iterating this so let's see + + + align:start position:0% +uh okay so iterating this so let's see +maybe maybe okay maybe let me wait with + + align:start position:0% +maybe maybe okay maybe let me wait with + + + align:start position:0% +maybe maybe okay maybe let me wait with +iterating let me just look at at what we + + align:start position:0% +iterating let me just look at at what we + + + align:start position:0% +iterating let me just look at at what we +need so we have this in here + + align:start position:0% +need so we have this in here + + + align:start position:0% +need so we have this in here +and this here I can write as as um so + + align:start position:0% +and this here I can write as as um so + + + align:start position:0% +and this here I can write as as um so +here you see here I can write this as t + + align:start position:0% +here you see here I can write this as t + + + align:start position:0% +here you see here I can write this as t +the distance t and then t n minus one + + align:start position:0% +the distance t and then t n minus one + + + align:start position:0% +the distance t and then t n minus one +x + + align:start position:0% +x + + + align:start position:0% +x +and then t + + align:start position:0% +and then t + + + align:start position:0% +and then t +t n -1 + k + + align:start position:0% +t n -1 + k + + + align:start position:0% +t n -1 + k +x like this right and so here I can + + align:start position:0% +x like this right and so here I can + + + align:start position:0% +x like this right and so here I can +use the same trick that it get c and + + align:start position:0% +use the same trick that it get c and + + + align:start position:0% +use the same trick that it get c and +then d t n minus 1 x comma t n -1 + k + + align:start position:0% +then d t n minus 1 x comma t n -1 + k + + + align:start position:0% +then d t n minus 1 x comma t n -1 + k +of x right + + align:start position:0% + + + + align:start position:0% + +and this one here I can keep going like + + align:start position:0% +and this one here I can keep going like + + + align:start position:0% +and this one here I can keep going like +this right I can keep going until + + align:start position:0% +this right I can keep going until + + + align:start position:0% +this right I can keep going until +there is the I' I've used up all my ends + + align:start position:0% +there is the I' I've used up all my ends + + + align:start position:0% +there is the I' I've used up all my ends +right and so I can keep going and so + + align:start position:0% +right and so I can keep going and so + + + align:start position:0% +right and so I can keep going and so +this is lesser equal to c to the n and + + align:start position:0% +this is lesser equal to c to the n and + + + align:start position:0% +this is lesser equal to c to the n and +then the last one I get is I get x + + align:start position:0% +then the last one I get is I get x + + + align:start position:0% +then the last one I get is I get x +and then I get t k + + align:start position:0% +and then I get t k + + + align:start position:0% +and then I get t k +of x + + align:start position:0% +of x + + + align:start position:0% +of x +right + + align:start position:0% + + + + align:start position:0% + +I want to show that this thing here + + align:start position:0% +I want to show that this thing here + + + align:start position:0% +I want to show that this thing here +becomes small as long as n remember k is + + align:start position:0% +becomes small as long as n remember k is + + + align:start position:0% +becomes small as long as n remember k is +a positive integer as long as n is + + align:start position:0% +a positive integer as long as n is + + + align:start position:0% +a positive integer as long as n is +sufficiently large right so I need but + + align:start position:0% +sufficiently large right so I need but + + + align:start position:0% +sufficiently large right so I need but +this. So this is a hopeful sign because + + align:start position:0% +this. So this is a hopeful sign because + + + align:start position:0% +this. So this is a hopeful sign because +when n get large this here get really + + align:start position:0% +when n get large this here get really + + + align:start position:0% +when n get large this here get really +really small right but I still need to + + align:start position:0% +really small right but I still need to + + + align:start position:0% +really small right but I still need to +estimate this here right now. So how do + + align:start position:0% +estimate this here right now. So how do + + + align:start position:0% +estimate this here right now. So how do +I estimate it? I using what I did over + + align:start position:0% +I estimate it? I using what I did over + + + align:start position:0% +I estimate it? I using what I did over +here. + + align:start position:0% +here. + + + align:start position:0% +here. +So I um so you're looking at + + align:start position:0% + + + + align:start position:0% + +so you have the distance + + align:start position:0% +so you have the distance + + + align:start position:0% +so you have the distance +between x and t k of x + + align:start position:0% + + + + align:start position:0% + +This thing here I can use this triangle + + align:start position:0% +This thing here I can use this triangle + + + align:start position:0% +This thing here I can use this triangle +inequality. So I can say that this is + + align:start position:0% +inequality. So I can say that this is + + + align:start position:0% +inequality. So I can say that this is +less than dx + + align:start position:0% +less than dx + + + align:start position:0% +less than dx +t of x + + align:start position:0% +t of x + + + align:start position:0% +t of x +plus d t of x + + align:start position:0% +plus d t of x + + + align:start position:0% +plus d t of x +g ^2 of x + + align:start position:0% +g ^2 of x + + + align:start position:0% +g ^2 of x +plus + + align:start position:0% +plus + + + align:start position:0% +plus +d t of x, + + align:start position:0% +d t of x, + + + align:start position:0% +d t of x, +you know, like cube of x. and then all + + align:start position:0% +you know, like cube of x. and then all + + + align:start position:0% +you know, like cube of x. and then all +the way up to + + align:start position:0% +the way up to + + + align:start position:0% +the way up to +d + + align:start position:0% +d + + + align:start position:0% +d +t k minus one of x + + align:start position:0% +t k minus one of x + + + align:start position:0% +t k minus one of x +t k of x right so this is just a + + align:start position:0% +t k of x right so this is just a + + + align:start position:0% +t k of x right so this is just a +triangle inequality right + + align:start position:0% +triangle inequality right + + + align:start position:0% +triangle inequality right +now this may seems ra rather bad + + align:start position:0% +now this may seems ra rather bad + + + align:start position:0% +now this may seems ra rather bad +estimate but let's see how bad it is so + + align:start position:0% +estimate but let's see how bad it is so + + + align:start position:0% +estimate but let's see how bad it is so +uh right so now this first thing here + + align:start position:0% +uh right so now this first thing here + + + align:start position:0% +uh right so now this first thing here +I'm just leaving it I can't do anything + + align:start position:0% +I'm just leaving it I can't do anything + + + align:start position:0% +I'm just leaving it I can't do anything +about that so + + align:start position:0% +about that so + + + align:start position:0% +about that so +I need to just take that this one here. + + align:start position:0% +I need to just take that this one here. + + + align:start position:0% +I need to just take that this one here. +So I'm using this with between two + + align:start position:0% +So I'm using this with between two + + + align:start position:0% +So I'm using this with between two +consecutive. So in this case it's just + + align:start position:0% +consecutive. So in this case it's just + + + align:start position:0% +consecutive. So in this case it's just +bounded by C * D X + + align:start position:0% +bounded by C * D X + + + align:start position:0% +bounded by C * D X +right and the next one here + + align:start position:0% +right and the next one here + + + align:start position:0% +right and the next one here +this one here is bounded by C ^ 2 D X GX + + align:start position:0% +this one here is bounded by C ^ 2 D X GX + + + align:start position:0% +this one here is bounded by C ^ 2 D X GX +and then and the next right and so on up + + align:start position:0% +and then and the next right and so on up + + + align:start position:0% +and then and the next right and so on up +to this one here + + align:start position:0% +to this one here + + + align:start position:0% +to this one here +is bounded by uh C K - one + + align:start position:0% +is bounded by uh C K - one + + + align:start position:0% +is bounded by uh C K - one +uh D X T X + + align:start position:0% +uh D X T X + + + align:start position:0% +uh D X T X +right and so you see that now this here + + align:start position:0% +right and so you see that now this here + + + align:start position:0% +right and so you see that now this here +factor out so this here is so this + + align:start position:0% +factor out so this here is so this + + + align:start position:0% +factor out so this here is so this +factor out + + align:start position:0% + + + + align:start position:0% + +and then in this bracket you get 1 + C + + + align:start position:0% +and then in this bracket you get 1 + C + + + + align:start position:0% +and then in this bracket you get 1 + C + +C^ 2 plus all the way up to C K minus + + align:start position:0% +C^ 2 plus all the way up to C K minus + + + align:start position:0% +C^ 2 plus all the way up to C K minus +But this is a geometric series right + + align:start position:0% +But this is a geometric series right + + + align:start position:0% +But this is a geometric series right +this is a geometric series and this is + + align:start position:0% +this is a geometric series and this is + + + align:start position:0% +this is a geometric series and this is +certainly less than when I take remember + + align:start position:0% +certainly less than when I take remember + + + align:start position:0% +certainly less than when I take remember +C is strictly less than one so it's a + + align:start position:0% +C is strictly less than one so it's a + + + align:start position:0% +C is strictly less than one so it's a +geometric series it's a convergent + + align:start position:0% +geometric series it's a convergent + + + align:start position:0% +geometric series it's a convergent +geometric series so this here is less + + align:start position:0% +geometric series so this here is less + + + align:start position:0% +geometric series so this here is less +than d xt of x and then this sum well + + align:start position:0% +than d xt of x and then this sum well + + + align:start position:0% +than d xt of x and then this sum well +it's less than when you're summing it + + align:start position:0% +it's less than when you're summing it + + + align:start position:0% +it's less than when you're summing it +all the way to infinity so this is less + + align:start position:0% +all the way to infinity so this is less + + + align:start position:0% +all the way to infinity so this is less +than one. This is the sum of the + + align:start position:0% +than one. This is the sum of the + + + align:start position:0% +than one. This is the sum of the +geometric series. C is strictly less + + align:start position:0% +geometric series. C is strictly less + + + align:start position:0% +geometric series. C is strictly less +than one, + + align:start position:0% +than one, + + + align:start position:0% +than one, +right? C is positive and is strictly + + align:start position:0% +right? C is positive and is strictly + + + align:start position:0% +right? C is positive and is strictly +less than one. + + align:start position:0% +less than one. + + + align:start position:0% +less than one. +Okay? So you see now that we have + + align:start position:0% +Okay? So you see now that we have + + + align:start position:0% +Okay? So you see now that we have +right so we have that so what we were + + align:start position:0% +right so we have that so what we were + + + align:start position:0% +right so we have that so what we were +interested in is we were interested in + + align:start position:0% +interested in is we were interested in + + + align:start position:0% +interested in is we were interested in +saying that as long as I choose little + + align:start position:0% +saying that as long as I choose little + + + align:start position:0% +saying that as long as I choose little +and sufficiently large then this thing + + align:start position:0% +and sufficiently large then this thing + + + align:start position:0% +and sufficiently large then this thing +here must be very small. Right? + + align:start position:0% +here must be very small. Right? + + + align:start position:0% +here must be very small. Right? +And we know already that it's bounded + + align:start position:0% +And we know already that it's bounded + + + align:start position:0% +And we know already that it's bounded +like this. And now I fill in this and + + align:start position:0% +like this. And now I fill in this and + + + align:start position:0% +like this. And now I fill in this and +you see this here. So this means that + + align:start position:0% +you see this here. So this means that + + + align:start position:0% +you see this here. So this means that +this is less than cn. And then what you + + align:start position:0% +this is less than cn. And then what you + + + align:start position:0% +this is less than cn. And then what you +get here is uh 1 minus c and then times + + align:start position:0% +get here is uh 1 minus c and then times + + + align:start position:0% +get here is uh 1 minus c and then times +d x g of x, + + align:start position:0% +d x g of x, + + + align:start position:0% +d x g of x, +right? x is fixed. + + align:start position:0% +right? x is fixed. + + + align:start position:0% +right? x is fixed. +And so you see that when n little n is + + align:start position:0% +And so you see that when n little n is + + + align:start position:0% +And so you see that when n little n is +sufficiently large then this whole thing + + align:start position:0% +sufficiently large then this whole thing + + + align:start position:0% +sufficiently large then this whole thing +here is as small as you want. Right? So + + align:start position:0% +here is as small as you want. Right? So + + + align:start position:0% +here is as small as you want. Right? So +this means that what we have proven here + + align:start position:0% +this means that what we have proven here + + + align:start position:0% +this means that what we have proven here +is that this sequence here + + align:start position:0% +is that this sequence here + + + align:start position:0% +is that this sequence here +is a cushy sequence. + + align:start position:0% + + + + align:start position:0% + +So we've proven that. Okay. + + align:start position:0% +So we've proven that. Okay. + + + align:start position:0% +So we've proven that. Okay. +Now of course this is where the + + align:start position:0% +Now of course this is where the + + + align:start position:0% +Now of course this is where the +assumption comes in that this metric + + align:start position:0% +assumption comes in that this metric + + + align:start position:0% +assumption comes in that this metric +space is cushy complete + + align:start position:0% +space is cushy complete + + + align:start position:0% +space is cushy complete +right. So, so uh since + + align:start position:0% + + + + align:start position:0% + +x this metric space is cushy complete + + align:start position:0% + + + + align:start position:0% + +and this sequence here + + align:start position:0% + + + + align:start position:0% + +is a cushy sequence. + + align:start position:0% + + + + align:start position:0% + +It is convergent, + + align:start position:0% + + + + align:start position:0% + +>> right? Yeah. + + align:start position:0% +>> right? Yeah. + + + align:start position:0% +>> right? Yeah. +>> I'm sorry. + + align:start position:0% +>> I'm sorry. + + + align:start position:0% +>> I'm sorry. +>> Yep. + + align:start position:0% +>> Yep. + + + align:start position:0% +>> Yep. +>> Are you able to explain again how we got + + align:start position:0% +>> Are you able to explain again how we got + + + align:start position:0% +>> Are you able to explain again how we got +that + + align:start position:0% + + + + align:start position:0% + +for the DXDX or we're just saying that + + align:start position:0% +for the DXDX or we're just saying that + + + align:start position:0% +for the DXDX or we're just saying that +>> right? So I'm saying that X is fixed. + + align:start position:0% +>> right? So I'm saying that X is fixed. + + + align:start position:0% +>> right? So I'm saying that X is fixed. +You you pick any point you want. And I + + align:start position:0% +You you pick any point you want. And I + + + align:start position:0% +You you pick any point you want. And I +claim that if I you know it may be a + + align:start position:0% +claim that if I you know it may be a + + + align:start position:0% +claim that if I you know it may be a +very bad candidate for the fixed point, + + align:start position:0% +very bad candidate for the fixed point, + + + align:start position:0% +very bad candidate for the fixed point, +but it doesn't matter. It's okay. Uh it + + align:start position:0% +but it doesn't matter. It's okay. Uh it + + + align:start position:0% +but it doesn't matter. It's okay. Uh it +may just take you longer to get to the + + align:start position:0% +may just take you longer to get to the + + + align:start position:0% +may just take you longer to get to the +fixed point, but you fix X and then + + align:start position:0% +fixed point, but you fix X and then + + + align:start position:0% +fixed point, but you fix X and then +you're looking at this sequence + + align:start position:0% +you're looking at this sequence + + + align:start position:0% +you're looking at this sequence +and then I claim that this sequence will + + align:start position:0% +and then I claim that this sequence will + + + align:start position:0% +and then I claim that this sequence will +be a cushy sequence, right? And so x is + + align:start position:0% +be a cushy sequence, right? And so x is + + + align:start position:0% +be a cushy sequence, right? And so x is +fixed. And so we have this inequality + + align:start position:0% +fixed. And so we have this inequality + + + align:start position:0% +fixed. And so we have this inequality +here. And what we need is that when + + align:start position:0% +here. And what we need is that when + + + align:start position:0% +here. And what we need is that when +little n is sufficiently far, you know, + + align:start position:0% +little n is sufficiently far, you know, + + + align:start position:0% +little n is sufficiently far, you know, +large, then for all k is positive + + align:start position:0% +large, then for all k is positive + + + align:start position:0% +large, then for all k is positive +integer, right? This here is like + + align:start position:0% +integer, right? This here is like + + + align:start position:0% +integer, right? This here is like +further out than n. Then for all k and + + align:start position:0% +further out than n. Then for all k and + + + align:start position:0% +further out than n. Then for all k and +it should be independent on k. This + + align:start position:0% +it should be independent on k. This + + + align:start position:0% +it should be independent on k. This +thing here is small. But this is + + align:start position:0% +thing here is small. But this is + + + align:start position:0% +thing here is small. But this is +>> get rid of the whole thing from the + + align:start position:0% +>> get rid of the whole thing from the + + + align:start position:0% +>> get rid of the whole thing from the +previous step was now not a TK of X, + + align:start position:0% +previous step was now not a TK of X, + + + align:start position:0% +previous step was now not a TK of X, +right? So, + + align:start position:0% +right? So, + + + align:start position:0% +right? So, +>> so so so since X is fixed, + + align:start position:0% +>> so so so since X is fixed, + + + align:start position:0% +>> so so so since X is fixed, +X is fixed, TX is fixed. + + align:start position:0% +X is fixed, TX is fixed. + + + align:start position:0% +X is fixed, TX is fixed. +>> So, this is just a constant. + + align:start position:0% +>> So, this is just a constant. + + + align:start position:0% +>> So, this is just a constant. +>> Yeah. + + align:start position:0% + + + + align:start position:0% + +Okay. So um right so what we have proven + + align:start position:0% +Okay. So um right so what we have proven + + + align:start position:0% +Okay. So um right so what we have proven +is that so we have so we have this koshi + + align:start position:0% +is that so we have so we have this koshi + + + align:start position:0% +is that so we have so we have this koshi +complete metric space and we have this + + align:start position:0% +complete metric space and we have this + + + align:start position:0% +complete metric space and we have this +sequence x was fixed again that is a + + align:start position:0% +sequence x was fixed again that is a + + + align:start position:0% +sequence x was fixed again that is a +cush sequence and so since this metric + + align:start position:0% +cush sequence and so since this metric + + + align:start position:0% +cush sequence and so since this metric +space is cush complete this is + + align:start position:0% +space is cush complete this is + + + align:start position:0% +space is cush complete this is +convergent and I can denote the limits + + align:start position:0% +convergent and I can denote the limits + + + align:start position:0% +convergent and I can denote the limits +so I just call the limits x infinity + + align:start position:0% +so I just call the limits x infinity + + + align:start position:0% +so I just call the limits x infinity +right so if you have is + + align:start position:0% + + + + align:start position:0% + +now I want to show that uh that uh so so + + align:start position:0% +now I want to show that uh that uh so so + + + align:start position:0% +now I want to show that uh that uh so so +the next claim is + + align:start position:0% + + + + align:start position:0% + +is that x infinity is a fixed point + + align:start position:0% + + + + align:start position:0% + +for for g + + align:start position:0% + + + + align:start position:0% + +okay okay + + align:start position:0% +okay okay + + + align:start position:0% +okay okay +so if I'm looking at this sequence here. + + align:start position:0% +so if I'm looking at this sequence here. + + + align:start position:0% +so if I'm looking at this sequence here. +Suppose I take this sequence and suppose + + align:start position:0% +Suppose I take this sequence and suppose + + + align:start position:0% +Suppose I take this sequence and suppose +I take T of this sequence. + + align:start position:0% + + + + align:start position:0% + +So if I take T of this sequence, this + + align:start position:0% +So if I take T of this sequence, this + + + align:start position:0% +So if I take T of this sequence, this +here is nothing but the next element in + + align:start position:0% +here is nothing but the next element in + + + align:start position:0% +here is nothing but the next element in +the sequence. + + align:start position:0% +the sequence. + + + align:start position:0% +the sequence. +So this one here will still converge to + + align:start position:0% +So this one here will still converge to + + + align:start position:0% +So this one here will still converge to +X infinit, + + align:start position:0% +X infinit, + + + align:start position:0% +X infinit, +right? Because it's just shifted by one. + + align:start position:0% +right? Because it's just shifted by one. + + + align:start position:0% +right? Because it's just shifted by one. +But then on the other hand, so now if + + align:start position:0% +But then on the other hand, so now if + + + align:start position:0% +But then on the other hand, so now if +you're looking at + + align:start position:0% +you're looking at + + + align:start position:0% +you're looking at +um at so so you have that if you're + + align:start position:0% +um at so so you have that if you're + + + align:start position:0% +um at so so you have that if you're +looking at t so you want to we want to + + align:start position:0% +looking at t so you want to we want to + + + align:start position:0% +looking at t so you want to we want to +prove that um + + align:start position:0% +prove that um + + + align:start position:0% +prove that um +right so now uh so now if we're looking + + align:start position:0% +right so now uh so now if we're looking + + + align:start position:0% +right so now uh so now if we're looking +at t of x infinity + + align:start position:0% +at t of x infinity + + + align:start position:0% +at t of x infinity +the distance between t of x infinity + + align:start position:0% +the distance between t of x infinity + + + align:start position:0% +the distance between t of x infinity +and + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +uh and t + + align:start position:0% +uh and t + + + align:start position:0% +uh and t +uh n + one + + align:start position:0% +uh n + one + + + align:start position:0% +uh n + one +of x suppose I'm looking at this + + align:start position:0% +of x suppose I'm looking at this + + + align:start position:0% +of x suppose I'm looking at this +distance here right well this here I can + + align:start position:0% +distance here right well this here I can + + + align:start position:0% +distance here right well this here I can +think about as the distance between t of + + align:start position:0% +think about as the distance between t of + + + align:start position:0% +think about as the distance between t of +x infinity and t of tn of x + + align:start position:0% +x infinity and t of tn of x + + + align:start position:0% +x infinity and t of tn of x +but here there are now both of these + + align:start position:0% +but here there are now both of these + + + align:start position:0% +but here there are now both of these +element you can about this is just some + + align:start position:0% +element you can about this is just some + + + align:start position:0% +element you can about this is just some +element applied t to it. Here there's t + + align:start position:0% +element applied t to it. Here there's t + + + align:start position:0% +element applied t to it. Here there's t +applied to that. So this is less than + + align:start position:0% +applied to that. So this is less than + + + align:start position:0% +applied to that. So this is less than +the distance + + align:start position:0% +the distance + + + align:start position:0% +the distance +x infinity to t n. There's a constant c + + align:start position:0% +x infinity to t n. There's a constant c + + + align:start position:0% +x infinity to t n. There's a constant c +less than one in front. + + align:start position:0% +less than one in front. + + + align:start position:0% +less than one in front. +So like this + + align:start position:0% +So like this + + + align:start position:0% +So like this +right by the contracting map property. + + align:start position:0% +right by the contracting map property. + + + align:start position:0% +right by the contracting map property. +But now you see that as n go to infinity + + align:start position:0% +But now you see that as n go to infinity + + + align:start position:0% +But now you see that as n go to infinity +this thing here goes to zero. Right? So + + align:start position:0% +this thing here goes to zero. Right? So + + + align:start position:0% +this thing here goes to zero. Right? So +this means that this thing here + + align:start position:0% +this means that this thing here + + + align:start position:0% +this means that this thing here +converts to this point. + + align:start position:0% +converts to this point. + + + align:start position:0% +converts to this point. +Right? So you have that. + + align:start position:0% + + + + align:start position:0% + +So you have that + + align:start position:0% + + + + align:start position:0% + +you have that that if you're looking at + + align:start position:0% +you have that that if you're looking at + + + align:start position:0% +you have that that if you're looking at +uh if you're looking at um right again + + align:start position:0% +uh if you're looking at um right again + + + align:start position:0% +uh if you're looking at um right again +as + + align:start position:0% +as + + + align:start position:0% +as +as n go to + + align:start position:0% +as n go to + + + align:start position:0% +as n go to +as n go to infinity + + align:start position:0% +as n go to infinity + + + align:start position:0% +as n go to infinity +uh Since + + align:start position:0% +uh Since + + + align:start position:0% +uh Since +since tn of x converts to x infinity + + align:start position:0% +since tn of x converts to x infinity + + + align:start position:0% +since tn of x converts to x infinity +then we have that the distance this is + + align:start position:0% +then we have that the distance this is + + + align:start position:0% +then we have that the distance this is +equivalent to that the distance + + align:start position:0% +equivalent to that the distance + + + align:start position:0% +equivalent to that the distance +here + + align:start position:0% +here + + + align:start position:0% +here +goes to zero. And then by this + + align:start position:0% +goes to zero. And then by this + + + align:start position:0% +goes to zero. And then by this +inequality it means that the distance + + align:start position:0% +inequality it means that the distance + + + align:start position:0% +inequality it means that the distance +here + + align:start position:0% +here + + + align:start position:0% +here +tx infinity + + align:start position:0% + + + + align:start position:0% + +and t n + one of x goes to zero right + + align:start position:0% +and t n + one of x goes to zero right + + + align:start position:0% +and t n + one of x goes to zero right +and so this means that this is just some + + align:start position:0% +and so this means that this is just some + + + align:start position:0% +and so this means that this is just some +fixed point. It means that this sequence + + align:start position:0% +fixed point. It means that this sequence + + + align:start position:0% +fixed point. It means that this sequence +here, so this implies that this sequence + + align:start position:0% +here, so this implies that this sequence + + + align:start position:0% +here, so this implies that this sequence +here + + align:start position:0% + + + + align:start position:0% + +converge to t of x infinity, right? But + + align:start position:0% +converge to t of x infinity, right? But + + + align:start position:0% +converge to t of x infinity, right? But +on the other hand, we already observe + + align:start position:0% +on the other hand, we already observe + + + align:start position:0% +on the other hand, we already observe +that this sequence also converge + + align:start position:0% +that this sequence also converge + + + align:start position:0% +that this sequence also converge +to x infinity, right? But you can't can + + align:start position:0% +to x infinity, right? But you can't can + + + align:start position:0% +to x infinity, right? But you can't can +you know there's the so it converges to + + align:start position:0% +you know there's the so it converges to + + + align:start position:0% +you know there's the so it converges to +this and it converts to that, but it can + + align:start position:0% +this and it converts to that, but it can + + + align:start position:0% +this and it converts to that, but it can +only have one limit. So those two things + + align:start position:0% +only have one limit. So those two things + + + align:start position:0% +only have one limit. So those two things +are equal. So you conclude that x + + align:start position:0% +are equal. So you conclude that x + + + align:start position:0% +are equal. So you conclude that x +infinity is equal to g of x infinity and + + align:start position:0% +infinity is equal to g of x infinity and + + + align:start position:0% +infinity is equal to g of x infinity and +so x infinity + + align:start position:0% +so x infinity + + + align:start position:0% +so x infinity +is a fixed point. + + align:start position:0% + + + + align:start position:0% + +Right? So this proved this theorem. And + + align:start position:0% +Right? So this proved this theorem. And + + + align:start position:0% +Right? So this proved this theorem. And +again we already knew that the limit was + + align:start position:0% +again we already knew that the limit was + + + align:start position:0% +again we already knew that the limit was +uh was unique. Right? + + align:start position:0% +uh was unique. Right? + + + align:start position:0% +uh was unique. Right? +Okay. So now what how is this related to + + align:start position:0% +Okay. So now what how is this related to + + + align:start position:0% +Okay. So now what how is this related to +the picar linda lift theorem + + align:start position:0% +the picar linda lift theorem + + + align:start position:0% +the picar linda lift theorem +and so it's related in the following way + + align:start position:0% +and so it's related in the following way + + + align:start position:0% +and so it's related in the following way +and again this is uh something that have + + align:start position:0% +and again this is uh something that have + + + align:start position:0% +and again this is uh something that have +been used to solve a lot of differential + + align:start position:0% +been used to solve a lot of differential + + + align:start position:0% +been used to solve a lot of differential +equations + + align:start position:0% +equations + + + align:start position:0% +equations +um + + align:start position:0% + + + + align:start position:0% + +and so we need to define space and a + + align:start position:0% +and so we need to define space and a + + + align:start position:0% +and so we need to define space and a +map. + + align:start position:0% +map. + + + align:start position:0% +map. +the spaces initially but we have to + + align:start position:0% +the spaces initially but we have to + + + align:start position:0% +the spaces initially but we have to +restrict it but initially let's think + + align:start position:0% +restrict it but initially let's think + + + align:start position:0% +restrict it but initially let's think +about some continuous functions + + align:start position:0% + + + + align:start position:0% + +on some interval + + align:start position:0% +on some interval + + + align:start position:0% +on some interval +let's start with just continuous + + align:start position:0% +let's start with just continuous + + + align:start position:0% +let's start with just continuous +function but it's not quite going to be + + align:start position:0% +function but it's not quite going to be + + + align:start position:0% +function but it's not quite going to be +this space I will have to look at a + + align:start position:0% +this space I will have to look at a + + + align:start position:0% +this space I will have to look at a +smaller yeah + + align:start position:0% + + + + align:start position:0% + +Right. That's a good question. So, so + + align:start position:0% +Right. That's a good question. So, so + + + align:start position:0% +Right. That's a good question. So, so +that's right. So, this comes with this + + align:start position:0% +that's right. So, this comes with this + + + align:start position:0% +that's right. So, this comes with this +Newton method. So, we used the so we + + align:start position:0% +Newton method. So, we used the so we + + + align:start position:0% +Newton method. So, we used the so we +used this contracting mapping for R in + + align:start position:0% +used this contracting mapping for R in + + + align:start position:0% +used this contracting mapping for R in +the Newton method to find a zero. Okay. + + align:start position:0% +the Newton method to find a zero. Okay. + + + align:start position:0% +the Newton method to find a zero. Okay. +And to some I mean that was a great + + align:start position:0% +And to some I mean that was a great + + + align:start position:0% +And to some I mean that was a great +idea. Uh Newton was a pretty famous guy + + align:start position:0% +idea. Uh Newton was a pretty famous guy + + + align:start position:0% +idea. Uh Newton was a pretty famous guy +for a good reason. uh but in a way this + + align:start position:0% +for a good reason. uh but in a way this + + + align:start position:0% +for a good reason. uh but in a way this +is more ingenious I think because it's + + align:start position:0% +is more ingenious I think because it's + + + align:start position:0% +is more ingenious I think because it's +like you know metric space what the hell + + align:start position:0% +like you know metric space what the hell + + + align:start position:0% +like you know metric space what the hell +does this have to do with differential + + align:start position:0% +does this have to do with differential + + + align:start position:0% +does this have to do with differential +equation right but and the reason why in + + align:start position:0% +equation right but and the reason why in + + + align:start position:0% +equation right but and the reason why in +the other one we had to restrict it was + + align:start position:0% +the other one we had to restrict it was + + + align:start position:0% +the other one we had to restrict it was +that the map we defined wasn't + + align:start position:0% +that the map we defined wasn't + + + align:start position:0% +that the map we defined wasn't +contracting everywhere it needed sinks + + align:start position:0% +contracting everywhere it needed sinks + + + align:start position:0% +contracting everywhere it needed sinks +to be pretty close initially for for + + align:start position:0% +to be pretty close initially for for + + + align:start position:0% +to be pretty close initially for for +there to exist a c strictly less than + + align:start position:0% +there to exist a c strictly less than + + + align:start position:0% +there to exist a c strictly less than +one right so that's where I came in it + + align:start position:0% +one right so that's where I came in it + + + align:start position:0% +one right so that's where I came in it +wasn't really it wasn't really because + + align:start position:0% +wasn't really it wasn't really because + + + align:start position:0% +wasn't really it wasn't really because +in in N or if Yeah. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So now again so so we need to relate + + align:start position:0% +So now again so so we need to relate + + + align:start position:0% +So now again so so we need to relate +this that seems to have nothing to do + + align:start position:0% +this that seems to have nothing to do + + + align:start position:0% +this that seems to have nothing to do +with differential equation. We need to + + align:start position:0% +with differential equation. We need to + + + align:start position:0% +with differential equation. We need to +relate it to the differential equation. + + align:start position:0% +relate it to the differential equation. + + + align:start position:0% +relate it to the differential equation. +So again what is the space the metric + + align:start position:0% +So again what is the space the metric + + + align:start position:0% +So again what is the space the metric +space that we're going to look at and + + align:start position:0% +space that we're going to look at and + + + align:start position:0% +space that we're going to look at and +again it's not exactly this but it's + + align:start position:0% +again it's not exactly this but it's + + + align:start position:0% +again it's not exactly this but it's +just a subset of it. So, so, so, so it's + + align:start position:0% +just a subset of it. So, so, so, so it's + + + align:start position:0% +just a subset of it. So, so, so, so it's +it's this space and with the usual + + align:start position:0% +it's this space and with the usual + + + align:start position:0% +it's this space and with the usual +metric that we have talked about, right? + + align:start position:0% +metric that we have talked about, right? + + + align:start position:0% +metric that we have talked about, right? +That is going to be the + + align:start position:0% +That is going to be the + + + align:start position:0% +That is going to be the +the metric space. + + align:start position:0% +the metric space. + + + align:start position:0% +the metric space. +Now, what is the map T? + + align:start position:0% +Now, what is the map T? + + + align:start position:0% +Now, what is the map T? +And so the map t is so t here + + align:start position:0% +And so the map t is so t here + + + align:start position:0% +And so the map t is so t here +um so t here is going to be a map from + + align:start position:0% +um so t here is going to be a map from + + + align:start position:0% +um so t here is going to be a map from +continuous functions + + align:start position:0% + + + + align:start position:0% + +uh into the space of continuous + + align:start position:0% +uh into the space of continuous + + + align:start position:0% +uh into the space of continuous +functions + + align:start position:0% + + + + align:start position:0% + +and it's going to be defined + + align:start position:0% + + + + align:start position:0% + +um as follow + + align:start position:0% +um as follow + + + align:start position:0% +um as follow +and if yeah I'll come to this in a + + align:start position:0% +and if yeah I'll come to this in a + + + align:start position:0% +and if yeah I'll come to this in a +second so uh t of x t of y. So y think + + align:start position:0% +second so uh t of x t of y. So y think + + + align:start position:0% +second so uh t of x t of y. So y think +about y as being a continuous function + + align:start position:0% +about y as being a continuous function + + + align:start position:0% +about y as being a continuous function +on this integral, right? And t of y is + + align:start position:0% +on this integral, right? And t of y is + + + align:start position:0% +on this integral, right? And t of y is +now equal to uh a plus and then the + + align:start position:0% +now equal to uh a plus and then the + + + align:start position:0% +now equal to uh a plus and then the +integral in and then right + + align:start position:0% +integral in and then right + + + align:start position:0% +integral in and then right +then the inte uh integral. So this is a + + align:start position:0% +then the inte uh integral. So this is a + + + align:start position:0% +then the inte uh integral. So this is a +so t of y is of an element here. This + + align:start position:0% +so t of y is of an element here. This + + + align:start position:0% +so t of y is of an element here. This +one here is also supposed to be an + + align:start position:0% +one here is also supposed to be an + + + align:start position:0% +one here is also supposed to be an +element here. So this is a function. + + align:start position:0% +element here. So this is a function. + + + align:start position:0% +element here. So this is a function. +So we want to find out what the value is + + align:start position:0% +So we want to find out what the value is + + + align:start position:0% +So we want to find out what the value is +at x. And it's a this constant a plus + + align:start position:0% +at x. And it's a this constant a plus + + + align:start position:0% +at x. And it's a this constant a plus +the integral from zero to x + + align:start position:0% +the integral from zero to x + + + align:start position:0% +the integral from zero to x +uh and then of f of uh y + + align:start position:0% +uh and then of f of uh y + + + align:start position:0% +uh and then of f of uh y +uh plus uh g of x + + align:start position:0% +uh plus uh g of x + + + align:start position:0% +uh plus uh g of x +and this here is a function of x right + + align:start position:0% +and this here is a function of x right + + + align:start position:0% +and this here is a function of x right +also it's like this + + align:start position:0% +also it's like this + + + align:start position:0% +also it's like this +uh and I shouldn't write x because I use + + align:start position:0% +uh and I shouldn't write x because I use + + + align:start position:0% +uh and I shouldn't write x because I use +now x up here + + align:start position:0% +now x up here + + + align:start position:0% +now x up here +so I write it like DF + + align:start position:0% +so I write it like DF + + + align:start position:0% +so I write it like DF +okay that's how the map is going to be + + align:start position:0% +okay that's how the map is going to be + + + align:start position:0% +okay that's how the map is going to be +defined + + align:start position:0% +defined + + + align:start position:0% +defined +so again if you take so y here so y is + + align:start position:0% +so again if you take so y here so y is + + + align:start position:0% +so again if you take so y here so y is +going so y is a continuous function on + + align:start position:0% +going so y is a continuous function on + + + align:start position:0% +going so y is a continuous function on +this interval + + align:start position:0% +this interval + + + align:start position:0% +this interval +and I will have to restrict it and this + + align:start position:0% +and I will have to restrict it and this + + + align:start position:0% +and I will have to restrict it and this +is exactly when you asking what you know + + align:start position:0% +is exactly when you asking what you know + + + align:start position:0% +is exactly when you asking what you know +in Newton methods right why why did we + + align:start position:0% +in Newton methods right why why did we + + + align:start position:0% +in Newton methods right why why did we +have to pick this good choice it's + + align:start position:0% +have to pick this good choice it's + + + align:start position:0% +have to pick this good choice it's +exactly like this that it's this map is + + align:start position:0% +exactly like this that it's this map is + + + align:start position:0% +exactly like this that it's this map is +not contracting on this whole space. + + align:start position:0% +not contracting on this whole space. + + + align:start position:0% +not contracting on this whole space. +Okay. So we have to in a way we have to + + align:start position:0% +Okay. So we have to in a way we have to + + + align:start position:0% +Okay. So we have to in a way we have to +do the same stuff. We have to make a + + align:start position:0% +do the same stuff. We have to make a + + + align:start position:0% +do the same stuff. We have to make a +good choice first and so that's why we + + align:start position:0% +good choice first and so that's why we + + + align:start position:0% +good choice first and so that's why we +have to restrict the space. Okay. And it + + align:start position:0% +have to restrict the space. Okay. And it + + + align:start position:0% +have to restrict the space. Okay. And it +actually is I mean it's part of the + + align:start position:0% +actually is I mean it's part of the + + + align:start position:0% +actually is I mean it's part of the +beauty is that it's pretty much optimal + + align:start position:0% +beauty is that it's pretty much optimal + + + align:start position:0% +beauty is that it's pretty much optimal +this stuff this sort of general + + align:start position:0% +this stuff this sort of general + + + align:start position:0% +this stuff this sort of general +principle uh we can come back to that. + + align:start position:0% +principle uh we can come back to that. + + + align:start position:0% +principle uh we can come back to that. +So this is the map t. + + align:start position:0% +So this is the map t. + + + align:start position:0% +So this is the map t. +And so the first thing that you observe + + align:start position:0% +And so the first thing that you observe + + + align:start position:0% +And so the first thing that you observe +is + + align:start position:0% +is + + + align:start position:0% +is +that t. So this gives you a this + + align:start position:0% +that t. So this gives you a this + + + align:start position:0% +that t. So this gives you a this +function here. + + align:start position:0% +function here. + + + align:start position:0% +function here. +Right? Remember that. So if y is + + align:start position:0% +Right? Remember that. So if y is + + + align:start position:0% +Right? Remember that. So if y is +continuous, + + align:start position:0% +continuous, + + + align:start position:0% +continuous, +g is continuous. If y is continuous, f + + align:start position:0% +g is continuous. If y is continuous, f + + + align:start position:0% +g is continuous. If y is continuous, f +is continuous. Everything here is + + align:start position:0% +is continuous. Everything here is + + + align:start position:0% +is continuous. Everything here is +continuous. And so this means that by + + align:start position:0% +continuous. And so this means that by + + + align:start position:0% +continuous. And so this means that by +the fundamental theorem of calculus this + + align:start position:0% +the fundamental theorem of calculus this + + + align:start position:0% +the fundamental theorem of calculus this +function here is actually even + + align:start position:0% +function here is actually even + + + align:start position:0% +function here is actually even +differentiable right and the derivative + + align:start position:0% +differentiable right and the derivative + + + align:start position:0% +differentiable right and the derivative +this is just a constant so this function + + align:start position:0% +this is just a constant so this function + + + align:start position:0% +this is just a constant so this function +here is differentiable + + align:start position:0% +here is differentiable + + + align:start position:0% +here is differentiable +let alone continuous so it's definitely + + align:start position:0% +let alone continuous so it's definitely + + + align:start position:0% +let alone continuous so it's definitely +in the space and the derivative of this + + align:start position:0% +in the space and the derivative of this + + + align:start position:0% +in the space and the derivative of this +map + + align:start position:0% +map + + + align:start position:0% +map +by the fundamental theorem of calculus + + align:start position:0% +by the fundamental theorem of calculus + + + align:start position:0% +by the fundamental theorem of calculus +This + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% + + + + align:start position:0% + +so by the fundamental of calculus the + + align:start position:0% +so by the fundamental of calculus the + + + align:start position:0% +so by the fundamental of calculus the +derivative is just what is inside here. + + align:start position:0% +derivative is just what is inside here. + + + align:start position:0% +derivative is just what is inside here. +So this is just f of y + + align:start position:0% + + + + align:start position:0% + +plus g of x right and if you want to + + align:start position:0% +plus g of x right and if you want to + + + align:start position:0% +plus g of x right and if you want to +write x in then it should be like this + + align:start position:0% +write x in then it should be like this + + + align:start position:0% +write x in then it should be like this +right + + align:start position:0% + + + + align:start position:0% + +so that's so and then one more thing you + + align:start position:0% +so that's so and then one more thing you + + + align:start position:0% +so that's so and then one more thing you +observe which is also immediate that if + + align:start position:0% +observe which is also immediate that if + + + align:start position:0% +observe which is also immediate that if +you take + + align:start position:0% +you take + + + align:start position:0% +you take +a continuous function like this and now + + align:start position:0% +a continuous function like this and now + + + align:start position:0% +a continuous function like this and now +you evaluate this now you evaluate this + + align:start position:0% +you evaluate this now you evaluate this + + + align:start position:0% +you evaluate this now you evaluate this +at zero right if x is zero but then this + + align:start position:0% +at zero right if x is zero but then this + + + align:start position:0% +at zero right if x is zero but then this +integral it's over just a point so this + + align:start position:0% +integral it's over just a point so this + + + align:start position:0% +integral it's over just a point so this +here is zero so this means that the + + align:start position:0% +here is zero so this means that the + + + align:start position:0% +here is zero so this means that the +value here is a + + align:start position:0% +value here is a + + + align:start position:0% +value here is a +right okay + + align:start position:0% +right okay + + + align:start position:0% +right okay +and so now the next thing you observe is + + align:start position:0% +and so now the next thing you observe is + + + align:start position:0% +and so now the next thing you observe is +that + + align:start position:0% + + + + align:start position:0% + +So the next thing we observe is that um + + align:start position:0% +So the next thing we observe is that um + + + align:start position:0% +So the next thing we observe is that um +that if uh if you have a fixed point so + + align:start position:0% +that if uh if you have a fixed point so + + + align:start position:0% +that if uh if you have a fixed point so +if + + align:start position:0% +if + + + align:start position:0% +if +I mean I think this is another nice + + align:start position:0% +I mean I think this is another nice + + + align:start position:0% +I mean I think this is another nice +thing is that you know that the way it's + + align:start position:0% +thing is that you know that the way it's + + + align:start position:0% +thing is that you know that the way it's +set up is that you just need to use + + align:start position:0% +set up is that you just need to use + + + align:start position:0% +set up is that you just need to use +continuous functions. + + align:start position:0% +continuous functions. + + + align:start position:0% +continuous functions. +Right. But of course, if you want a + + align:start position:0% +Right. But of course, if you want a + + + align:start position:0% +Right. But of course, if you want a +solution to this, it means that the + + align:start position:0% +solution to this, it means that the + + + align:start position:0% +solution to this, it means that the +function must have a derivative. Yeah. + + align:start position:0% + + + + align:start position:0% + +Yeah. We don't know that yet. I mean, + + align:start position:0% +Yeah. We don't know that yet. I mean, + + + align:start position:0% +Yeah. We don't know that yet. I mean, +that's a major point actually, right? + + align:start position:0% +that's a major point actually, right? + + + align:start position:0% +that's a major point actually, right? +And again, just like in the Newton + + align:start position:0% +And again, just like in the Newton + + + align:start position:0% +And again, just like in the Newton +methods, we have to restrict where we're + + align:start position:0% +methods, we have to restrict where we're + + + align:start position:0% +methods, we have to restrict where we're +looking at it. Yeah. Okay. So but but + + align:start position:0% +looking at it. Yeah. Okay. So but but + + + align:start position:0% +looking at it. Yeah. Okay. So but but +the first thing I want to observe is + + align:start position:0% +the first thing I want to observe is + + + align:start position:0% +the first thing I want to observe is +that + + align:start position:0% +that + + + align:start position:0% +that +if uh if y is a fixed point + + align:start position:0% + + + + align:start position:0% + +well then t of y + + align:start position:0% +well then t of y + + + align:start position:0% +well then t of y +is equal to y and so what does this + + align:start position:0% +is equal to y and so what does this + + + align:start position:0% +is equal to y and so what does this +mean? + + align:start position:0% +mean? + + + align:start position:0% +mean? +Well, the derivative. So it means that + + align:start position:0% +Well, the derivative. So it means that + + + align:start position:0% +Well, the derivative. So it means that +if this is the case, + + align:start position:0% +if this is the case, + + + align:start position:0% +if this is the case, +right? + + align:start position:0% +right? + + + align:start position:0% +right? +Then we have that t of y is of this + + align:start position:0% +Then we have that t of y is of this + + + align:start position:0% +Then we have that t of y is of this +form. So it has a derivative and that + + align:start position:0% +form. So it has a derivative and that + + + align:start position:0% +form. So it has a derivative and that +derivative is this. Right? So this means + + align:start position:0% +derivative is this. Right? So this means + + + align:start position:0% +derivative is this. Right? So this means +that y would have it because y is equal + + align:start position:0% +that y would have it because y is equal + + + align:start position:0% +that y would have it because y is equal +to this. So y is differentiable + + align:start position:0% +to this. So y is differentiable + + + align:start position:0% +to this. So y is differentiable +and the derivative is equal to this. + + align:start position:0% + + + + align:start position:0% + +And we always have whether it's a fixed + + align:start position:0% +And we always have whether it's a fixed + + + align:start position:0% +And we always have whether it's a fixed +point or not. We always have that t y of + + align:start position:0% +point or not. We always have that t y of + + + align:start position:0% +point or not. We always have that t y of +zero + + align:start position:0% +zero + + + align:start position:0% +zero +is is a and since it is a fixed point + + align:start position:0% +is is a and since it is a fixed point + + + align:start position:0% +is is a and since it is a fixed point +this is also this. So you see that if it + + align:start position:0% +this is also this. So you see that if it + + + align:start position:0% +this is also this. So you see that if it +is a fixed point then it is a solution + + align:start position:0% +is a fixed point then it is a solution + + + align:start position:0% +is a fixed point then it is a solution +to the differential equation. Okay. + + align:start position:0% +to the differential equation. Okay. + + + align:start position:0% +to the differential equation. Okay. +Now then then the the the point comes in + + align:start position:0% +Now then then the the the point comes in + + + align:start position:0% +Now then then the the the point comes in +the key point comes in with um + + align:start position:0% +the key point comes in with um + + + align:start position:0% +the key point comes in with um +proving that the map is contracting. + + align:start position:0% +proving that the map is contracting. + + + align:start position:0% +proving that the map is contracting. +Okay. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +And so so now so we need to prove + + align:start position:0% +And so so now so we need to prove + + + align:start position:0% +And so so now so we need to prove +need to show + + align:start position:0% + + + + align:start position:0% + +that t + + align:start position:0% +that t + + + align:start position:0% +that t +is a contracting map. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% +So + + + align:start position:0% +So +I define so set I I I I have to define a + + align:start position:0% +I define so set I I I I have to define a + + + align:start position:0% +I define so set I I I I have to define a +number of things because again I have to + + align:start position:0% +number of things because again I have to + + + align:start position:0% +number of things because again I have to +it's not t is not going to be + + align:start position:0% +it's not t is not going to be + + + align:start position:0% +it's not t is not going to be +contracting on the space of continuous + + align:start position:0% +contracting on the space of continuous + + + align:start position:0% +contracting on the space of continuous +function. So I have to look at some + + align:start position:0% +function. So I have to look at some + + + align:start position:0% +function. So I have to look at some +subset of continuous function and the + + align:start position:0% +subset of continuous function and the + + + align:start position:0% +subset of continuous function and the +right subset is just a ball. It's a + + align:start position:0% +right subset is just a ball. It's a + + + align:start position:0% +right subset is just a ball. It's a +closed ball. So it's so + + align:start position:0% +closed ball. So it's so + + + align:start position:0% +closed ball. So it's so +it's going to be so so + + align:start position:0% +it's going to be so so + + + align:start position:0% +it's going to be so so +we're going to maybe I'll just say first + + align:start position:0% +we're going to maybe I'll just say first + + + align:start position:0% +we're going to maybe I'll just say first +that we're going to restrict + + align:start position:0% +that we're going to restrict + + + align:start position:0% +that we're going to restrict +uh t. So t here will be restricted now + + align:start position:0% +uh t. So t here will be restricted now + + + align:start position:0% +uh t. So t here will be restricted now +to we will think about it as a map on + + align:start position:0% +to we will think about it as a map on + + + align:start position:0% +to we will think about it as a map on +some ball + + align:start position:0% +some ball + + + align:start position:0% +some ball +into itself. + + align:start position:0% +into itself. + + + align:start position:0% +into itself. +But it's not at all clear that this map + + align:start position:0% +But it's not at all clear that this map + + + align:start position:0% +But it's not at all clear that this map +takes a ball into itself. Okay. And what + + align:start position:0% +takes a ball into itself. Okay. And what + + + align:start position:0% +takes a ball into itself. Okay. And what +do I mean by ball? So I have this bar up + + align:start position:0% +do I mean by ball? So I have this bar up + + + align:start position:0% +do I mean by ball? So I have this bar up +here. So I just means that this thing + + align:start position:0% +here. So I just means that this thing + + + align:start position:0% +here. So I just means that this thing +here + + align:start position:0% + + + + align:start position:0% + +is going to be the function y that is + + align:start position:0% +is going to be the function y that is + + + align:start position:0% +is going to be the function y that is +continuous. Sorry continuous. + + align:start position:0% + + + + align:start position:0% + +And then it's not quite going to be this + + align:start position:0% +And then it's not quite going to be this + + + align:start position:0% +And then it's not quite going to be this +either. I have to restrict but I'll get + + align:start position:0% +either. I have to restrict but I'll get + + + align:start position:0% +either. I have to restrict but I'll get +to this in a second. So at the moment + + align:start position:0% +to this in a second. So at the moment + + + align:start position:0% +to this in a second. So at the moment +you can think about it as being + + align:start position:0% +you can think about it as being + + + align:start position:0% +you can think about it as being +continuous function on the interval so + + align:start position:0% +continuous function on the interval so + + + align:start position:0% +continuous function on the interval so +that the norm of y at each point x + + align:start position:0% +that the norm of y at each point x + + + align:start position:0% +that the norm of y at each point x +is less or equal to r + + align:start position:0% +is less or equal to r + + + align:start position:0% +is less or equal to r +and this bar here refer to that lesser + + align:start position:0% +and this bar here refer to that lesser + + + align:start position:0% +and this bar here refer to that lesser +that equal is also allowed. Right? Now + + align:start position:0% +that equal is also allowed. Right? Now + + + align:start position:0% +that equal is also allowed. Right? Now +this here is really like the board right + + align:start position:0% +this here is really like the board right + + + align:start position:0% +this here is really like the board right +these are are functions if you're + + align:start position:0% +these are are functions if you're + + + align:start position:0% +these are are functions if you're +thinking about the function in the space + + align:start position:0% +thinking about the function in the space + + + align:start position:0% +thinking about the function in the space +of continuous function that is constant + + align:start position:0% +of continuous function that is constant + + + align:start position:0% +of continuous function that is constant +zero right then these are the functions + + align:start position:0% +zero right then these are the functions + + + align:start position:0% +zero right then these are the functions +whose distance this is the same as the + + align:start position:0% +whose distance this is the same as the + + + align:start position:0% +whose distance this is the same as the +space of continuous functions + + align:start position:0% +space of continuous functions + + + align:start position:0% +space of continuous functions +whose distance to the constant function + + align:start position:0% +whose distance to the constant function + + + align:start position:0% +whose distance to the constant function +zero is at most uh + + align:start position:0% + + + + align:start position:0% + +this is the zero function is less or + + align:start position:0% +this is the zero function is less or + + + align:start position:0% +this is the zero function is less or +equal to sorry this is getting a little + + align:start position:0% +equal to sorry this is getting a little + + + align:start position:0% +equal to sorry this is getting a little +small over here + + align:start position:0% +small over here + + + align:start position:0% +small over here +right so it's just + + align:start position:0% +right so it's just + + + align:start position:0% +right so it's just +okay and again it's not it's going to be + + align:start position:0% +okay and again it's not it's going to be + + + align:start position:0% +okay and again it's not it's going to be +I will have to restrict the interval + + align:start position:0% +I will have to restrict the interval + + + align:start position:0% +I will have to restrict the interval +here to make to make sure that the map + + align:start position:0% +here to make to make sure that the map + + + align:start position:0% +here to make to make sure that the map +is contracted + + align:start position:0% + + + + align:start position:0% + +so but first I want to define and this + + align:start position:0% +so but first I want to define and this + + + align:start position:0% +so but first I want to define and this +radius here. Okay. And so the radius is + + align:start position:0% +radius here. Okay. And so the radius is + + + align:start position:0% +radius here. Okay. And so the radius is +so I'm setting r here equal a was just a + + align:start position:0% +so I'm setting r here equal a was just a + + + align:start position:0% +so I'm setting r here equal a was just a +constant. I take the absolute value of a + + align:start position:0% +constant. I take the absolute value of a + + + align:start position:0% +constant. I take the absolute value of a +and I add two to it. + + align:start position:0% + + + + align:start position:0% + +Then I define two other yeah and there's + + align:start position:0% +Then I define two other yeah and there's + + + align:start position:0% +Then I define two other yeah and there's +no way around it. Uh you have to define + + align:start position:0% +no way around it. Uh you have to define + + + align:start position:0% +no way around it. Uh you have to define +we will require to define several + + align:start position:0% +we will require to define several + + + align:start position:0% +we will require to define several +constants. First + + align:start position:0% + + + + align:start position:0% + +L1 capital L1 is going to be another + + align:start position:0% +L1 capital L1 is going to be another + + + align:start position:0% +L1 capital L1 is going to be another +constant. It's going to be the maximum + + align:start position:0% +constant. It's going to be the maximum + + + align:start position:0% +constant. It's going to be the maximum +and then you take uh then you take of + + align:start position:0% +and then you take uh then you take of + + + align:start position:0% +and then you take uh then you take of +over set where set here is less than R + + align:start position:0% +over set where set here is less than R + + + align:start position:0% +over set where set here is less than R +and then you take the value + + align:start position:0% +and then you take the value + + + align:start position:0% +and then you take the value +like this. + + align:start position:0% +like this. + + + align:start position:0% +like this. +Okay, remember f is continuous. + + align:start position:0% +Okay, remember f is continuous. + + + align:start position:0% +Okay, remember f is continuous. +So if I looking at where the norm of x + + align:start position:0% +So if I looking at where the norm of x + + + align:start position:0% +So if I looking at where the norm of x +is less or equal to some constant + + align:start position:0% +is less or equal to some constant + + + align:start position:0% +is less or equal to some constant +then this the maximum is achieved on + + align:start position:0% +then this the maximum is achieved on + + + align:start position:0% +then this the maximum is achieved on +this. So this a + + align:start position:0% +this. So this a + + + align:start position:0% +this. So this a +just some real number positive real non- + + align:start position:0% +just some real number positive real non- + + + align:start position:0% +just some real number positive real non- +negative non- negative real number + + align:start position:0% +negative non- negative real number + + + align:start position:0% +negative non- negative real number +and then I define L2 to be the maximum + + align:start position:0% +and then I define L2 to be the maximum + + + align:start position:0% +and then I define L2 to be the maximum +of + + align:start position:0% +of + + + align:start position:0% +of +where I of maximum on the unit ball here + + align:start position:0% +where I of maximum on the unit ball here + + + align:start position:0% +where I of maximum on the unit ball here +and where norm of X is less than one of + + align:start position:0% +and where norm of X is less than one of + + + align:start position:0% +and where norm of X is less than one of +G of X + + align:start position:0% +G of X + + + align:start position:0% +G of X +like there. + + align:start position:0% +like there. + + + align:start position:0% +like there. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +And now + + align:start position:0% +And now + + + align:start position:0% +And now +what I want to do is + + align:start position:0% +what I want to do is + + + align:start position:0% +what I want to do is +so the first step is so the first step + + align:start position:0% +so the first step is so the first step + + + align:start position:0% +so the first step is so the first step +is the following. + + align:start position:0% + + + + align:start position:0% + +So first first step + + align:start position:0% + + + + align:start position:0% + +And the proof + + align:start position:0% +And the proof + + + align:start position:0% +And the proof +uh is to prove the following that there + + align:start position:0% +uh is to prove the following that there + + + align:start position:0% +uh is to prove the following that there +exist + + align:start position:0% + + + + align:start position:0% + +there exist + + align:start position:0% + + + + align:start position:0% + +uh uh uh delta zero. This is not the + + align:start position:0% +uh uh uh delta zero. This is not the + + + align:start position:0% +uh uh uh delta zero. This is not the +delta that I will use eventually. Um I + + align:start position:0% +delta that I will use eventually. Um I + + + align:start position:0% +delta that I will use eventually. Um I +would have to restrict it further. There + + align:start position:0% +would have to restrict it further. There + + + align:start position:0% +would have to restrict it further. There +exist delta serum. So that if you're + + align:start position:0% +exist delta serum. So that if you're + + + align:start position:0% +exist delta serum. So that if you're +looking at the space if y here + + align:start position:0% +looking at the space if y here + + + align:start position:0% +looking at the space if y here +is in the space of continuous functions + + align:start position:0% +is in the space of continuous functions + + + align:start position:0% +is in the space of continuous functions +on this interval here + + align:start position:0% + + + + align:start position:0% + +then t of y sorry if y is in this here + + align:start position:0% +then t of y sorry if y is in this here + + + align:start position:0% +then t of y sorry if y is in this here +and y is in the unit form + + align:start position:0% +and y is in the unit form + + + align:start position:0% +and y is in the unit form +and not in the uniform that y here is + + align:start position:0% +and not in the uniform that y here is + + + align:start position:0% +and not in the uniform that y here is +lesser equal to r + + align:start position:0% +lesser equal to r + + + align:start position:0% +lesser equal to r +right so it's a continuous function on + + align:start position:0% +right so it's a continuous function on + + + align:start position:0% +right so it's a continuous function on +this interval and the norm is lesser + + align:start position:0% +this interval and the norm is lesser + + + align:start position:0% +this interval and the norm is lesser +equal to r so this means that so this is + + align:start position:0% +equal to r so this means that so this is + + + align:start position:0% +equal to r so this means that so this is +of course the same as saying that y is + + align:start position:0% +of course the same as saying that y is + + + align:start position:0% +of course the same as saying that y is +in this ball here + + align:start position:0% +in this ball here + + + align:start position:0% +in this ball here +uh when I'm now thinking about this as a + + align:start position:0% +uh when I'm now thinking about this as a + + + align:start position:0% +uh when I'm now thinking about this as a +space but you can forget about that if + + align:start position:0% +space but you can forget about that if + + + align:start position:0% +space but you can forget about that if +you want it's the + + align:start position:0% + + + + align:start position:0% + +Okay. But I and I want to show that t of + + align:start position:0% +Okay. But I and I want to show that t of + + + align:start position:0% +Okay. But I and I want to show that t of +y is in the same space, right? So I need + + align:start position:0% +y is in the same space, right? So I need + + + align:start position:0% +y is in the same space, right? So I need +so t of y. + + align:start position:0% +so t of y. + + + align:start position:0% +so t of y. +So I need so I want to show so want to + + align:start position:0% +So I need so I want to show so want to + + + align:start position:0% +So I need so I want to show so want to +show + + align:start position:0% +show + + + align:start position:0% +show +want to show + + align:start position:0% + + + + align:start position:0% + +that t of y + + align:start position:0% +that t of y + + + align:start position:0% +that t of y +at each x + + align:start position:0% +at each x + + + align:start position:0% +at each x +here the norm is lesser equal to one + + align:start position:0% +here the norm is lesser equal to one + + + align:start position:0% +here the norm is lesser equal to one +right then it if I have that I already + + align:start position:0% +right then it if I have that I already + + + align:start position:0% +right then it if I have that I already +know that this function t of y is + + align:start position:0% +know that this function t of y is + + + align:start position:0% +know that this function t of y is +continuous it's it's actually even + + align:start position:0% +continuous it's it's actually even + + + align:start position:0% +continuous it's it's actually even +differentiable right But it's in + + align:start position:0% +differentiable right But it's in + + + align:start position:0% +differentiable right But it's in +particular continuous. + + align:start position:0% +particular continuous. + + + align:start position:0% +particular continuous. +And if I have this then I know that this + + align:start position:0% +And if I have this then I know that this + + + align:start position:0% +And if I have this then I know that this +space is taking into itself. Right? + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So now how do I do that? + + align:start position:0% +So now how do I do that? + + + align:start position:0% +So now how do I do that? +So I I that's where I need to restrict + + align:start position:0% +So I I that's where I need to restrict + + + align:start position:0% +So I I that's where I need to restrict +the interval that I'm looking on and and + + align:start position:0% +the interval that I'm looking on and and + + + align:start position:0% +the interval that I'm looking on and and +again we'll come back to it but there's + + align:start position:0% +again we'll come back to it but there's + + + align:start position:0% +again we'll come back to it but there's +a good reason to rest that we have to + + align:start position:0% +a good reason to rest that we have to + + + align:start position:0% +a good reason to rest that we have to +restrict otherwise it couldn't be + + align:start position:0% +restrict otherwise it couldn't be + + + align:start position:0% +restrict otherwise it couldn't be +possibly be true. + + align:start position:0% + + + + align:start position:0% + +>> Yeah. to be contracting. Do we need it + + align:start position:0% +>> Yeah. to be contracting. Do we need it + + + align:start position:0% +>> Yeah. to be contracting. Do we need it +strictly less than? + + align:start position:0% +strictly less than? + + + align:start position:0% +strictly less than? +>> So remember contracting means that there + + align:start position:0% +>> So remember contracting means that there + + + align:start position:0% +>> So remember contracting means that there +exist a constant C strictly less than + + align:start position:0% +exist a constant C strictly less than + + + align:start position:0% +exist a constant C strictly less than +one. This here had nothing to do with a + + align:start position:0% +one. This here had nothing to do with a + + + align:start position:0% +one. This here had nothing to do with a +constant C. This here is just the space + + align:start position:0% +constant C. This here is just the space + + + align:start position:0% +constant C. This here is just the space +that we're looking at the map on. Okay. + + align:start position:0% +that we're looking at the map on. Okay. + + + align:start position:0% +that we're looking at the map on. Okay. +So, so, so and the reason why I make + + align:start position:0% +So, so, so and the reason why I make + + + align:start position:0% +So, so, so and the reason why I make +here. So, again, so this have nothing to + + align:start position:0% +here. So, again, so this have nothing to + + + align:start position:0% +here. So, again, so this have nothing to +do with that C. But the reason why I + + align:start position:0% +do with that C. But the reason why I + + + align:start position:0% +do with that C. But the reason why I +want this lesser equal to is that I want + + align:start position:0% +want this lesser equal to is that I want + + + align:start position:0% +want this lesser equal to is that I want +to have that the space is C complete. + + align:start position:0% +to have that the space is C complete. + + + align:start position:0% +to have that the space is C complete. +Okay, sorry. So, let me just try to make + + align:start position:0% +Okay, sorry. So, let me just try to make + + + align:start position:0% +Okay, sorry. So, let me just try to make +that clear. So I take I have a to get a + + align:start position:0% +that clear. So I take I have a to get a + + + align:start position:0% +that clear. So I take I have a to get a +fix point for a contracting map you need + + align:start position:0% +fix point for a contracting map you need + + + align:start position:0% +fix point for a contracting map you need +a space that is cushy complete right + + align:start position:0% +a space that is cushy complete right + + + align:start position:0% +a space that is cushy complete right +that when we prove this for the metric + + align:start position:0% +that when we prove this for the metric + + + align:start position:0% +that when we prove this for the metric +space we have a good candidate right we + + align:start position:0% +space we have a good candidate right we + + + align:start position:0% +space we have a good candidate right we +have the candidate of continuous + + align:start position:0% +have the candidate of continuous + + + align:start position:0% +have the candidate of continuous +functions + + align:start position:0% +functions + + + align:start position:0% +functions +on some closed interval like this right + + align:start position:0% +on some closed interval like this right + + + align:start position:0% +on some closed interval like this right +this is cushy complete right with a + + align:start position:0% +this is cushy complete right with a + + + align:start position:0% +this is cushy complete right with a +usual metric but I'm not going to look + + align:start position:0% +usual metric but I'm not going to look + + + align:start position:0% +usual metric but I'm not going to look +at that space because my map is not + + align:start position:0% +at that space because my map is not + + + align:start position:0% +at that space because my map is not +actually contracting on the case it's + + align:start position:0% +actually contracting on the case it's + + + align:start position:0% +actually contracting on the case it's +contracting on a subset right and so I + + align:start position:0% +contracting on a subset right and so I + + + align:start position:0% +contracting on a subset right and so I +need that subset so so so in the end I + + align:start position:0% +need that subset so so so in the end I + + + align:start position:0% +need that subset so so so in the end I +sort of you know I'm not working on this + + align:start position:0% +sort of you know I'm not working on this + + + align:start position:0% +sort of you know I'm not working on this +but I'm working on a subset right and I + + align:start position:0% +but I'm working on a subset right and I + + + align:start position:0% +but I'm working on a subset right and I +need that subset to be complete so + + align:start position:0% +need that subset to be complete so + + + align:start position:0% +need that subset to be complete so +basically what I have is that this here + + align:start position:0% +basically what I have is that this here + + + align:start position:0% +basically what I have is that this here +is the metric giant metric space I start + + align:start position:0% +is the metric giant metric space I start + + + align:start position:0% +is the metric giant metric space I start +with then I'm looking at a ball in this + + align:start position:0% +with then I'm looking at a ball in this + + + align:start position:0% +with then I'm looking at a ball in this +and if I take the closed ball + + align:start position:0% +and if I take the closed ball + + + align:start position:0% +and if I take the closed ball +and and it happened to be at the origin + + align:start position:0% +and and it happened to be at the origin + + + align:start position:0% +and and it happened to be at the origin +but it could be just at any point right + + align:start position:0% +but it could be just at any point right + + + align:start position:0% +but it could be just at any point right +if you take a metric space and you're + + align:start position:0% +if you take a metric space and you're + + + align:start position:0% +if you take a metric space and you're +taking something like this if the metric + + align:start position:0% +taking something like this if the metric + + + align:start position:0% +taking something like this if the metric +space is cushy complete then this subset + + align:start position:0% +space is cushy complete then this subset + + + align:start position:0% +space is cushy complete then this subset +is also cushy complete and but this + + align:start position:0% +is also cushy complete and but this + + + align:start position:0% +is also cushy complete and but this +require + + align:start position:0% +require + + + align:start position:0% +require +I have less or equal to right because + + align:start position:0% +I have less or equal to right because + + + align:start position:0% +I have less or equal to right because +else it could kind of converge to + + align:start position:0% +else it could kind of converge to + + + align:start position:0% +else it could kind of converge to +something where where you got equality + + align:start position:0% +something where where you got equality + + + align:start position:0% +something where where you got equality +right so so that was why I I do it like + + align:start position:0% + + + + align:start position:0% + +Okay. So um so let's see. So + + align:start position:0% +Okay. So um so let's see. So + + + align:start position:0% +Okay. So um so let's see. So +we are trying we we defined we have + + align:start position:0% +we are trying we we defined we have + + + align:start position:0% +we are trying we we defined we have +already defined this radius capital R + + align:start position:0% +already defined this radius capital R + + + align:start position:0% +already defined this radius capital R +and then we have these two constant + + align:start position:0% +and then we have these two constant + + + align:start position:0% +and then we have these two constant +uh L1 and L2 and what I need to prove is + + align:start position:0% +uh L1 and L2 and what I need to prove is + + + align:start position:0% +uh L1 and L2 and what I need to prove is +the first step here is to prove that if + + align:start position:0% +the first step here is to prove that if + + + align:start position:0% +the first step here is to prove that if +I'm going to look again so the first + + align:start position:0% +I'm going to look again so the first + + + align:start position:0% +I'm going to look again so the first +step is that I need to restrict so I + + align:start position:0% +step is that I need to restrict so I + + + align:start position:0% +step is that I need to restrict so I +need to restrict so I'm going to look at + + align:start position:0% +need to restrict so I'm going to look at + + + align:start position:0% +need to restrict so I'm going to look at +are subs these spaces of + + align:start position:0% +are subs these spaces of + + + align:start position:0% +are subs these spaces of +this is a subset of the continuous + + align:start position:0% +this is a subset of the continuous + + + align:start position:0% +this is a subset of the continuous +functions and I need to prove that if y + + align:start position:0% +functions and I need to prove that if y + + + align:start position:0% +functions and I need to prove that if y +is in here then the image is in the same + + align:start position:0% +is in here then the image is in the same + + + align:start position:0% +is in here then the image is in the same +space. + + align:start position:0% + + + + align:start position:0% + +Okay. And so this is the statement that + + align:start position:0% +Okay. And so this is the statement that + + + align:start position:0% +Okay. And so this is the statement that +if y is continuous + + align:start position:0% +if y is continuous + + + align:start position:0% +if y is continuous +the norm of this function is less or + + align:start position:0% +the norm of this function is less or + + + align:start position:0% +the norm of this function is less or +equal to r. So at each point each x the + + align:start position:0% +equal to r. So at each point each x the + + + align:start position:0% +equal to r. So at each point each x the +absolute value of y of x is less or + + align:start position:0% +absolute value of y of x is less or + + + align:start position:0% +absolute value of y of x is less or +equal to r. Then you have the same for + + align:start position:0% +equal to r. Then you have the same for + + + align:start position:0% +equal to r. Then you have the same for +the image under t. We already know again + + align:start position:0% +the image under t. We already know again + + + align:start position:0% +the image under t. We already know again +that the image under t of y is + + align:start position:0% +that the image under t of y is + + + align:start position:0% +that the image under t of y is +continuous. Okay. + + align:start position:0% +continuous. Okay. + + + align:start position:0% +continuous. Okay. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +And so but I and what I can do is I can + + align:start position:0% +And so but I and what I can do is I can + + + align:start position:0% +And so but I and what I can do is I can +restrict my interval. + + align:start position:0% +restrict my interval. + + + align:start position:0% +restrict my interval. +So + + align:start position:0% +So + + + align:start position:0% +So +I will restrict the interval as follows. + + align:start position:0% +I will restrict the interval as follows. + + + align:start position:0% +I will restrict the interval as follows. +So I'm going to pick delta zero to be + + align:start position:0% +So I'm going to pick delta zero to be + + + align:start position:0% +So I'm going to pick delta zero to be +the minimum + + align:start position:0% + + + + align:start position:0% + +of one + + align:start position:0% +of one + + + align:start position:0% +of one +uh one over + + align:start position:0% +uh one over + + + align:start position:0% +uh one over +L + one. L is non- negative. In + + align:start position:0% +L + one. L is non- negative. In + + + align:start position:0% +L + one. L is non- negative. In +principle it could be zero. I don't want + + align:start position:0% +principle it could be zero. I don't want + + + align:start position:0% +principle it could be zero. I don't want +to worry about that. So I just add one. + + align:start position:0% +to worry about that. So I just add one. + + + align:start position:0% +to worry about that. So I just add one. +And L2 could also be zero. Although it's + + align:start position:0% +And L2 could also be zero. Although it's + + + align:start position:0% +And L2 could also be zero. Although it's +pretty unlikely that any of them are + + align:start position:0% +pretty unlikely that any of them are + + + align:start position:0% +pretty unlikely that any of them are +zero. But I'm just to be safe. if I'm + + align:start position:0% +zero. But I'm just to be safe. if I'm + + + align:start position:0% +zero. But I'm just to be safe. if I'm +just adding so I don't divide by zero. + + align:start position:0% +just adding so I don't divide by zero. + + + align:start position:0% +just adding so I don't divide by zero. +So that's why and the so and and the + + align:start position:0% +So that's why and the so and and the + + + align:start position:0% +So that's why and the so and and the +first thing is that I'm so and then I'm + + align:start position:0% +first thing is that I'm so and then I'm + + + align:start position:0% +first thing is that I'm so and then I'm +going to look at the interval from this + + align:start position:0% +going to look at the interval from this + + + align:start position:0% +going to look at the interval from this +and this is not going to be my final I + + align:start position:0% +and this is not going to be my final I + + + align:start position:0% +and this is not going to be my final I +will have to do some further restriction + + align:start position:0% +will have to do some further restriction + + + align:start position:0% +will have to do some further restriction +but I'm going to look at this interval + + align:start position:0% +but I'm going to look at this interval + + + align:start position:0% +but I'm going to look at this interval +initially okay and the one here just + + align:start position:0% +initially okay and the one here just + + + align:start position:0% +initially okay and the one here just +comes in that I want this here to be a + + align:start position:0% +comes in that I want this here to be a + + + align:start position:0% +comes in that I want this here to be a +sub subset of this unit interval + + align:start position:0% +sub subset of this unit interval + + + align:start position:0% +sub subset of this unit interval +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So now let's let's try. So now we are in + + align:start position:0% +So now let's let's try. So now we are in + + + align:start position:0% +So now let's let's try. So now we are in +good shape here. + + align:start position:0% + + + + align:start position:0% + +So now let's look at t + + align:start position:0% +So now let's look at t + + + align:start position:0% +So now let's look at t +y + + align:start position:0% +y + + + align:start position:0% +y +and we need to estimate this at each x. + + align:start position:0% +and we need to estimate this at each x. + + + align:start position:0% +and we need to estimate this at each x. +Right? We want to say + + align:start position:0% +Right? We want to say + + + align:start position:0% +Right? We want to say +that the norm is less than capital less + + align:start position:0% +that the norm is less than capital less + + + align:start position:0% +that the norm is less than capital less +or equal to capital R. But let's just + + align:start position:0% +or equal to capital R. But let's just + + + align:start position:0% +or equal to capital R. But let's just +look at what this is. This thing here is + + align:start position:0% +look at what this is. This thing here is + + + align:start position:0% +look at what this is. This thing here is +equal to this function t of y is defined + + align:start position:0% +equal to this function t of y is defined + + + align:start position:0% +equal to this function t of y is defined +to be a plus the integral from zero to x + + align:start position:0% +to be a plus the integral from zero to x + + + align:start position:0% +to be a plus the integral from zero to x +of uh f of y of s + + align:start position:0% + + + + align:start position:0% + +plus g + + align:start position:0% +plus g + + + align:start position:0% +plus g +of s + + align:start position:0% +of s + + + align:start position:0% +of s +ds and then I have to have absolute + + align:start position:0% +ds and then I have to have absolute + + + align:start position:0% +ds and then I have to have absolute +value like that. + + align:start position:0% +value like that. + + + align:start position:0% +value like that. +And now I can just use the triangle + + align:start position:0% +And now I can just use the triangle + + + align:start position:0% +And now I can just use the triangle +inequality of course sort of trially. I + + align:start position:0% +inequality of course sort of trially. I + + + align:start position:0% +inequality of course sort of trially. I +get absolute value of this and then plus + + align:start position:0% +get absolute value of this and then plus + + + align:start position:0% +get absolute value of this and then plus +and then the integral here + + align:start position:0% +and then the integral here + + + align:start position:0% +and then the integral here +uh like that. + + align:start position:0% + + + + align:start position:0% + +Oops. + + align:start position:0% + + + + align:start position:0% + +And then I can just take this absolute + + align:start position:0% +And then I can just take this absolute + + + align:start position:0% +And then I can just take this absolute +value in under. So I get less or equal + + align:start position:0% +value in under. So I get less or equal + + + align:start position:0% +value in under. So I get less or equal +to a plus and then the integral + + align:start position:0% +to a plus and then the integral + + + align:start position:0% +to a plus and then the integral +and then the absolute value of f of y of + + align:start position:0% +and then the absolute value of f of y of + + + align:start position:0% +and then the absolute value of f of y of +s. + + align:start position:0% +s. + + + align:start position:0% +s. +And here I can also take the absolute + + align:start position:0% +And here I can also take the absolute + + + align:start position:0% +And here I can also take the absolute +value + + align:start position:0% +value + + + align:start position:0% +value +using the triangle equals on each + + align:start position:0% +using the triangle equals on each + + + align:start position:0% +using the triangle equals on each +individually. + + align:start position:0% + + + + align:start position:0% + +So I can write it like this. + + align:start position:0% +So I can write it like this. + + + align:start position:0% +So I can write it like this. +Now + + align:start position:0% +Now + + + align:start position:0% +Now +this is where I use. So s here will have + + align:start position:0% +this is where I use. So s here will have + + + align:start position:0% +this is where I use. So s here will have +to lie between zero and x right + + align:start position:0% +to lie between zero and x right + + + align:start position:0% +to lie between zero and x right +and so x is between + + align:start position:0% + + + + align:start position:0% + +let me write just draw it here. So here + + align:start position:0% +let me write just draw it here. So here + + + align:start position:0% +let me write just draw it here. So here +I have zero + + align:start position:0% + + + + align:start position:0% + +here I have delta zero and then I have + + align:start position:0% +here I have delta zero and then I have + + + align:start position:0% +here I have delta zero and then I have +this is zero and here I have x. + + align:start position:0% +this is zero and here I have x. + + + align:start position:0% +this is zero and here I have x. +somewhere X, right? + + align:start position:0% +somewhere X, right? + + + align:start position:0% +somewhere X, right? +But since, right? So this means that + + align:start position:0% +But since, right? So this means that + + + align:start position:0% +But since, right? So this means that +that um this means that so here you have + + align:start position:0% +that um this means that so here you have + + + align:start position:0% +that um this means that so here you have +X but but right but X itself X + + align:start position:0% +X but but right but X itself X + + + align:start position:0% +X but but right but X itself X +has to lie X has to lie between + + align:start position:0% +has to lie X has to lie between + + + align:start position:0% +has to lie X has to lie between +delta 0 + + align:start position:0% +delta 0 + + + align:start position:0% +delta 0 +minus delta 0 and delta 0 and S has to + + align:start position:0% +minus delta 0 and delta 0 and S has to + + + align:start position:0% +minus delta 0 and delta 0 and S has to +lie between zero and X. So this means + + align:start position:0% +lie between zero and X. So this means + + + align:start position:0% +lie between zero and X. So this means +that s here lies between like x will lie + + align:start position:0% +that s here lies between like x will lie + + + align:start position:0% +that s here lies between like x will lie +in this interval + + align:start position:0% +in this interval + + + align:start position:0% +in this interval +also + + align:start position:0% +also + + + align:start position:0% +also +right + + align:start position:0% + + + + align:start position:0% + +but now you see that um + + align:start position:0% + + + + align:start position:0% + +so now if we're looking at so we have t + + align:start position:0% +so now if we're looking at so we have t + + + align:start position:0% +so now if we're looking at so we have t +of y in x again remember that x here + + align:start position:0% +of y in x again remember that x here + + + align:start position:0% +of y in x again remember that x here +is less than or equal to delta z. So we + + align:start position:0% +is less than or equal to delta z. So we + + + align:start position:0% +is less than or equal to delta z. So we +have that this thing here is less or + + align:start position:0% +have that this thing here is less or + + + align:start position:0% +have that this thing here is less or +equal to a plus and then the integral + + align:start position:0% +equal to a plus and then the integral + + + align:start position:0% +equal to a plus and then the integral +from 0 to x of f of y of s + + align:start position:0% +from 0 to x of f of y of s + + + align:start position:0% +from 0 to x of f of y of s +plus + + align:start position:0% + + + + align:start position:0% + +g of s + + align:start position:0% +g of s + + + align:start position:0% +g of s +ds. Right? And and the first thing I + + align:start position:0% +ds. Right? And and the first thing I + + + align:start position:0% +ds. Right? And and the first thing I +observe is that s here is is also just + + align:start position:0% +observe is that s here is is also just + + + align:start position:0% +observe is that s here is is also just +because x was in that interval, you also + + align:start position:0% +because x was in that interval, you also + + + align:start position:0% +because x was in that interval, you also +have that s because x is in that + + align:start position:0% +have that s because x is in that + + + align:start position:0% +have that s because x is in that +interval, + + align:start position:0% +interval, + + + align:start position:0% +interval, +s is also in this interval. The second + + align:start position:0% +s is also in this interval. The second + + + align:start position:0% +s is also in this interval. The second +thing I observe is that I'm assuming + + align:start position:0% +thing I observe is that I'm assuming + + + align:start position:0% +thing I observe is that I'm assuming +that the function that I start with at + + align:start position:0% +that the function that I start with at + + + align:start position:0% +that the function that I start with at +each point + + align:start position:0% +each point + + + align:start position:0% +each point +have no less than R. + + align:start position:0% +have no less than R. + + + align:start position:0% +have no less than R. +Now if I using these two things then I + + align:start position:0% +Now if I using these two things then I + + + align:start position:0% +Now if I using these two things then I +have that. So this means that g of s + + align:start position:0% +have that. So this means that g of s + + + align:start position:0% +have that. So this means that g of s +this one here this is how we define l2 + + align:start position:0% +this one here this is how we define l2 + + + align:start position:0% +this one here this is how we define l2 +right because this interval here is + + align:start position:0% +right because this interval here is + + + align:start position:0% +right because this interval here is +contained in the interval between minus1 + + align:start position:0% +contained in the interval between minus1 + + + align:start position:0% +contained in the interval between minus1 +and one this here is contained in the + + align:start position:0% +and one this here is contained in the + + + align:start position:0% +and one this here is contained in the +interval between minus1 and one right so + + align:start position:0% +interval between minus1 and one right so + + + align:start position:0% +interval between minus1 and one right so +we have that g of s + + align:start position:0% +we have that g of s + + + align:start position:0% +we have that g of s +is less than this l2 lesser equal to L2. + + align:start position:0% +is less than this l2 lesser equal to L2. + + + align:start position:0% +is less than this l2 lesser equal to L2. +Right? + + align:start position:0% +Right? + + + align:start position:0% +Right? +The second thing we observe is that + + align:start position:0% +The second thing we observe is that + + + align:start position:0% +The second thing we observe is that +because we have + + align:start position:0% +because we have + + + align:start position:0% +because we have +this here for each S we have this + + align:start position:0% + + + + align:start position:0% + +then it means you see by the first + + align:start position:0% +then it means you see by the first + + + align:start position:0% +then it means you see by the first +by the f by the definition of L1 that uh + + align:start position:0% +by the f by the definition of L1 that uh + + + align:start position:0% +by the f by the definition of L1 that uh +f of y of less + + align:start position:0% +f of y of less + + + align:start position:0% +f of y of less +this thing here is less than L1. + + align:start position:0% +this thing here is less than L1. + + + align:start position:0% +this thing here is less than L1. +Okay, L1 and L2 are are now fixed + + align:start position:0% +Okay, L1 and L2 are are now fixed + + + align:start position:0% +Okay, L1 and L2 are are now fixed +numbers, right? And so you see that this + + align:start position:0% +numbers, right? And so you see that this + + + align:start position:0% +numbers, right? And so you see that this +second thing here I can bound this thing + + align:start position:0% +second thing here I can bound this thing + + + align:start position:0% +second thing here I can bound this thing +here by so this is lesser equal to a uh + + align:start position:0% +here by so this is lesser equal to a uh + + + align:start position:0% +here by so this is lesser equal to a uh +and that should have been an absolute + + align:start position:0% +and that should have been an absolute + + + align:start position:0% +and that should have been an absolute +value somehow lost it when I copied from + + align:start position:0% +value somehow lost it when I copied from + + + align:start position:0% +value somehow lost it when I copied from +this line. + + align:start position:0% +this line. + + + align:start position:0% +this line. +um a absolute value of a and then on the + + align:start position:0% +um a absolute value of a and then on the + + + align:start position:0% +um a absolute value of a and then on the +first one here the length of this + + align:start position:0% +first one here the length of this + + + align:start position:0% +first one here the length of this +interval + + align:start position:0% +interval + + + align:start position:0% +interval +but that is of course bounded by delta + + align:start position:0% +but that is of course bounded by delta + + + align:start position:0% +but that is of course bounded by delta +zero right so this is plus delta 0 and + + align:start position:0% +zero right so this is plus delta 0 and + + + align:start position:0% +zero right so this is plus delta 0 and +then the maximal possible value of this + + align:start position:0% +then the maximal possible value of this + + + align:start position:0% +then the maximal possible value of this +that would be l1 + + align:start position:0% +that would be l1 + + + align:start position:0% +that would be l1 +and then likewise the length of this + + align:start position:0% +and then likewise the length of this + + + align:start position:0% +and then likewise the length of this +interval you're integrating over is at + + align:start position:0% +interval you're integrating over is at + + + align:start position:0% +interval you're integrating over is at +most delta zero and this one here cannot + + align:start position:0% +most delta zero and this one here cannot + + + align:start position:0% +most delta zero and this one here cannot +be larger than L2. So you have this + + align:start position:0% +be larger than L2. So you have this + + + align:start position:0% +be larger than L2. So you have this +right + + align:start position:0% +right + + + align:start position:0% +right +and now remember what delta zero was and + + align:start position:0% +and now remember what delta zero was and + + + align:start position:0% +and now remember what delta zero was and +I will just I have it I think on the + + align:start position:0% +I will just I have it I think on the + + + align:start position:0% +I will just I have it I think on the +both on board below here but let me just + + align:start position:0% +both on board below here but let me just + + + align:start position:0% +both on board below here but let me just +write it here. This here was what delta + + align:start position:0% +write it here. This here was what delta + + + align:start position:0% +write it here. This here was what delta +0 was chosen to be the minimum + + align:start position:0% +0 was chosen to be the minimum + + + align:start position:0% +0 was chosen to be the minimum +1 / l1 + 1 + + align:start position:0% +1 / l1 + 1 + + + align:start position:0% +1 / l1 + 1 +uh 1 / l2 + 1. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +So now, + + align:start position:0% +So now, + + + align:start position:0% +So now, +so now we have that this thing here is + + align:start position:0% +so now we have that this thing here is + + + align:start position:0% +so now we have that this thing here is +less than this here. We just keep + + align:start position:0% +less than this here. We just keep + + + align:start position:0% +less than this here. We just keep +this thing here. + + align:start position:0% +this thing here. + + + align:start position:0% +this thing here. +Well, delta + + align:start position:0% +Well, delta + + + align:start position:0% +Well, delta +is in particular less than this thing + + align:start position:0% +is in particular less than this thing + + + align:start position:0% +is in particular less than this thing +here. + + align:start position:0% +here. + + + align:start position:0% +here. +So you see that if you put plug in this + + align:start position:0% +So you see that if you put plug in this + + + align:start position:0% +So you see that if you put plug in this +so it's like plus 1 L1 + 1 * L1. + + align:start position:0% +so it's like plus 1 L1 + 1 * L1. + + + align:start position:0% +so it's like plus 1 L1 + 1 * L1. +Likewise over here you're using this. So + + align:start position:0% +Likewise over here you're using this. So + + + align:start position:0% +Likewise over here you're using this. So +you're getting 1 / L2 + 1 L2. And now + + align:start position:0% +you're getting 1 / L2 + 1 L2. And now + + + align:start position:0% +you're getting 1 / L2 + 1 L2. And now +you see that this thing here is less + + align:start position:0% +you see that this thing here is less + + + align:start position:0% +you see that this thing here is less +than one. This is less than one. So this + + align:start position:0% +than one. This is less than one. So this + + + align:start position:0% +than one. This is less than one. So this +is less than a. It's actually strictly + + align:start position:0% +is less than a. It's actually strictly + + + align:start position:0% +is less than a. It's actually strictly +less but it doesn't really matter. a + + + align:start position:0% +less but it doesn't really matter. a + + + + align:start position:0% +less but it doesn't really matter. a + +uh plus uh 2 like this. Okay. + + align:start position:0% + + + + align:start position:0% + +So this means that so then but this here + + align:start position:0% +So this means that so then but this here + + + align:start position:0% +So this means that so then but this here +this here was exactly the definition of + + align:start position:0% +this here was exactly the definition of + + + align:start position:0% +this here was exactly the definition of +capital R right and so you have that and + + align:start position:0% +capital R right and so you have that and + + + align:start position:0% +capital R right and so you have that and +when I copied it over I also forgot to + + align:start position:0% +when I copied it over I also forgot to + + + align:start position:0% +when I copied it over I also forgot to +put absolute on here right so you have + + align:start position:0% +put absolute on here right so you have + + + align:start position:0% +put absolute on here right so you have +that the if so you have that if so the + + align:start position:0% +that the if so you have that if so the + + + align:start position:0% +that the if so you have that if so the +conclusion here is that if y here is a + + align:start position:0% +conclusion here is that if y here is a + + + align:start position:0% +conclusion here is that if y here is a +continuous function + + align:start position:0% +continuous function + + + align:start position:0% +continuous function +on this interval here + + align:start position:0% + + + + align:start position:0% + +and the norm of y at each point is less + + align:start position:0% +and the norm of y at each point is less + + + align:start position:0% +and the norm of y at each point is less +or equal to r. Well, then you have that + + align:start position:0% +or equal to r. Well, then you have that + + + align:start position:0% +or equal to r. Well, then you have that +t of y + + align:start position:0% + + + + align:start position:0% + +at each point is lesser now lesser. It's + + align:start position:0% +at each point is lesser now lesser. It's + + + align:start position:0% +at each point is lesser now lesser. It's +actually strictly less, but we don't + + align:start position:0% +actually strictly less, but we don't + + + align:start position:0% +actually strictly less, but we don't +care about that. + + align:start position:0% +care about that. + + + align:start position:0% +care about that. +Okay. So, so, + + align:start position:0% +Okay. So, so, + + + align:start position:0% +Okay. So, so, +so what you have now is, + + align:start position:0% +so what you have now is, + + + align:start position:0% +so what you have now is, +so what we now have proven is that we + + align:start position:0% +so what we now have proven is that we + + + align:start position:0% +so what we now have proven is that we +have this map t + + align:start position:0% +have this map t + + + align:start position:0% +have this map t +and now I'm going to sing about this map + + align:start position:0% +and now I'm going to sing about this map + + + align:start position:0% +and now I'm going to sing about this map +sorry on the space of + + align:start position:0% +sorry on the space of + + + align:start position:0% +sorry on the space of +of y that is continuous + + align:start position:0% +of y that is continuous + + + align:start position:0% +of y that is continuous +on this interval here. + + align:start position:0% + + + + align:start position:0% + +Um and what you have is and also sorry + + align:start position:0% +Um and what you have is and also sorry + + + align:start position:0% +Um and what you have is and also sorry +and I'm thinking about with the norm at + + align:start position:0% +and I'm thinking about with the norm at + + + align:start position:0% +and I'm thinking about with the norm at +each point this here is less than r and + + align:start position:0% +each point this here is less than r and + + + align:start position:0% +each point this here is less than r and +again you can this is really a ball in + + align:start position:0% +again you can this is really a ball in + + + align:start position:0% +again you can this is really a ball in +this metric space but let me just write + + align:start position:0% +this metric space but let me just write + + + align:start position:0% +this metric space but let me just write +it out like this + + align:start position:0% +it out like this + + + align:start position:0% +it out like this +and what you have is that sorry this is + + align:start position:0% +and what you have is that sorry this is + + + align:start position:0% +and what you have is that sorry this is +the space and you have that t of y + + align:start position:0% +the space and you have that t of y + + + align:start position:0% +the space and you have that t of y +if y is in this space then t of y is in + + align:start position:0% +if y is in this space then t of y is in + + + align:start position:0% +if y is in this space then t of y is in +the same space. So t of y is also + + align:start position:0% +the same space. So t of y is also + + + align:start position:0% +the same space. So t of y is also +continuous + + align:start position:0% +continuous + + + align:start position:0% +continuous +on that interval + + align:start position:0% +on that interval + + + align:start position:0% +on that interval +and t of y at each point x is less or + + align:start position:0% +and t of y at each point x is less or + + + align:start position:0% +and t of y at each point x is less or +equal to one. So the map map this space + + align:start position:0% +equal to one. So the map map this space + + + align:start position:0% +equal to one. So the map map this space +into itself. Okay. + + align:start position:0% + + + + align:start position:0% + +Now + + align:start position:0% +Now + + + align:start position:0% +Now +the next thing we will we want to prove + + align:start position:0% +the next thing we will we want to prove + + + align:start position:0% +the next thing we will we want to prove +is that the map is contracting. + + align:start position:0% +is that the map is contracting. + + + align:start position:0% +is that the map is contracting. +Okay. + + align:start position:0% + + + + align:start position:0% + +Right? You see that you need you know if + + align:start position:0% +Right? You see that you need you know if + + + align:start position:0% +Right? You see that you need you know if +this space is not stable right so + + align:start position:0% +this space is not stable right so + + + align:start position:0% +this space is not stable right so +imagine that you take so you we're + + align:start position:0% +imagine that you take so you we're + + + align:start position:0% +imagine that you take so you we're +starting with some giant metric space + + align:start position:0% +starting with some giant metric space + + + align:start position:0% +starting with some giant metric space +this is the continuous function say on + + align:start position:0% +this is the continuous function say on + + + align:start position:0% +this is the continuous function say on +this interval + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% +this + + + align:start position:0% +this +and then we're looking at some subspace + + align:start position:0% +and then we're looking at some subspace + + + align:start position:0% +and then we're looking at some subspace +of that. So these are continuous on a + + align:start position:0% +of that. So these are continuous on a + + + align:start position:0% +of that. So these are continuous on a +smaller interval. Okay. But this + + align:start position:0% +smaller interval. Okay. But this + + + align:start position:0% +smaller interval. Okay. But this +but if the and then we have defined a + + align:start position:0% +but if the and then we have defined a + + + align:start position:0% +but if the and then we have defined a +map + + align:start position:0% +map + + + align:start position:0% +map +but if the you know if if if somehow the + + align:start position:0% +but if the you know if if if somehow the + + + align:start position:0% +but if the you know if if if somehow the +map was taking us out of the space where + + align:start position:0% +map was taking us out of the space where + + + align:start position:0% +map was taking us out of the space where +it's contracting then we couldn't keep + + align:start position:0% +it's contracting then we couldn't keep + + + align:start position:0% +it's contracting then we couldn't keep +applying the contracting map right it + + align:start position:0% +applying the contracting map right it + + + align:start position:0% +applying the contracting map right it +wouldn't anymore be you know by and and + + align:start position:0% +wouldn't anymore be you know by and and + + + align:start position:0% +wouldn't anymore be you know by and and +the thing is that you want to just + + align:start position:0% +the thing is that you want to just + + + align:start position:0% +the thing is that you want to just +iterate. You want to keep you want to + + align:start position:0% +iterate. You want to keep you want to + + + align:start position:0% +iterate. You want to keep you want to +pick some point and then you want to + + align:start position:0% +pick some point and then you want to + + + align:start position:0% +pick some point and then you want to +keep applying the contracting map. So + + align:start position:0% +keep applying the contracting map. So + + + align:start position:0% +keep applying the contracting map. So +you want it to stay in the space where + + align:start position:0% +you want it to stay in the space where + + + align:start position:0% +you want it to stay in the space where +it is contracting, right? And so this is + + align:start position:0% +it is contracting, right? And so this is + + + align:start position:0% +it is contracting, right? And so this is +what we did in one, but we haven't yet + + align:start position:0% +what we did in one, but we haven't yet + + + align:start position:0% +what we did in one, but we haven't yet +proved that the map is contracting. And + + align:start position:0% +proved that the map is contracting. And + + + align:start position:0% +proved that the map is contracting. And +so now to prove that the map is + + align:start position:0% +so now to prove that the map is + + + align:start position:0% +so now to prove that the map is +contracting, we're going to further + + align:start position:0% +contracting, we're going to further + + + align:start position:0% +contracting, we're going to further +restrict the interval. Okay? And so this + + align:start position:0% +restrict the interval. Okay? And so this + + + align:start position:0% +restrict the interval. Okay? And so this +is so I'm going to set I'm going to + + align:start position:0% +is so I'm going to set I'm going to + + + align:start position:0% +is so I'm going to set I'm going to +define now one more constant. Sorry + + align:start position:0% +define now one more constant. Sorry + + + align:start position:0% +define now one more constant. Sorry +about that. So this is m here and m is + + align:start position:0% +about that. So this is m here and m is + + + align:start position:0% +about that. So this is m here and m is +going to be just the max + + align:start position:0% +going to be just the max + + + align:start position:0% +going to be just the max +of fprime + + align:start position:0% + + + + align:start position:0% + +uh of uh fprime of set absolute value of + + align:start position:0% +uh of uh fprime of set absolute value of + + + align:start position:0% +uh of uh fprime of set absolute value of +this where set here is lesser equals + + align:start position:0% +this where set here is lesser equals + + + align:start position:0% +this where set here is lesser equals +one. + + align:start position:0% +one. + + + align:start position:0% +one. +Fine. So this is my uh this is my um + + align:start position:0% +Fine. So this is my uh this is my um + + + align:start position:0% +Fine. So this is my uh this is my um +the the well almost the second last + + align:start position:0% +the the well almost the second last + + + align:start position:0% +the the well almost the second last +constant unfortunately + + align:start position:0% + + + + align:start position:0% + +and now I'm going to define this. So the + + align:start position:0% +and now I'm going to define this. So the + + + align:start position:0% +and now I'm going to define this. So the +last constant is going to be the + + align:start position:0% +last constant is going to be the + + + align:start position:0% +last constant is going to be the +integral that I'm going to work with. + + align:start position:0% +integral that I'm going to work with. + + + align:start position:0% +integral that I'm going to work with. +Right? So remember what I'm trying to do + + align:start position:0% +Right? So remember what I'm trying to do + + + align:start position:0% +Right? So remember what I'm trying to do +is + + align:start position:0% + + + + align:start position:0% + +I have this differential equation and I + + align:start position:0% +I have this differential equation and I + + + align:start position:0% +I have this differential equation and I +want to say that + + align:start position:0% +want to say that + + + align:start position:0% +want to say that +near zero there is a solution but near + + align:start position:0% +near zero there is a solution but near + + + align:start position:0% +near zero there is a solution but near +zero just mean that there exists some + + align:start position:0% +zero just mean that there exists some + + + align:start position:0% +zero just mean that there exists some +tiny interval around zero where I have a + + align:start position:0% +tiny interval around zero where I have a + + + align:start position:0% +tiny interval around zero where I have a +solution and again if I have time or + + align:start position:0% +solution and again if I have time or + + + align:start position:0% +solution and again if I have time or +else I will do it next time I will give + + align:start position:0% +else I will do it next time I will give + + + align:start position:0% +else I will do it next time I will give +an example where you can see that in + + align:start position:0% +an example where you can see that in + + + align:start position:0% +an example where you can see that in +general you would need to look at a very + + align:start position:0% +general you would need to look at a very + + + align:start position:0% +general you would need to look at a very +tiny interval for this to have a + + align:start position:0% +tiny interval for this to have a + + + align:start position:0% +tiny interval for this to have a +solution otherwise it doesn't have a + + align:start position:0% +solution otherwise it doesn't have a + + + align:start position:0% +solution otherwise it doesn't have a +solution on a very large set. + + align:start position:0% + + + + align:start position:0% + +Okay. So I define it like this and then + + align:start position:0% +Okay. So I define it like this and then + + + align:start position:0% +Okay. So I define it like this and then +I define delta here. So delta is now + + align:start position:0% +I define delta here. So delta is now + + + align:start position:0% +I define delta here. So delta is now +going to be the minimum + + align:start position:0% +going to be the minimum + + + align:start position:0% +going to be the minimum +of delta zero the one from before and + + align:start position:0% +of delta zero the one from before and + + + align:start position:0% +of delta zero the one from before and +then 1 over 2 m + one. + + align:start position:0% + + + + align:start position:0% + +And now I want to look at the space. + + align:start position:0% +And now I want to look at the space. + + + align:start position:0% +And now I want to look at the space. +So I want to look at t. + + align:start position:0% +So I want to look at t. + + + align:start position:0% +So I want to look at t. +And then t is going to be a map from the + + align:start position:0% +And then t is going to be a map from the + + + align:start position:0% +And then t is going to be a map from the +continuous functions. So y here is a + + align:start position:0% +continuous functions. So y here is a + + + align:start position:0% +continuous functions. So y here is a +continuous function on now this little + + align:start position:0% +continuous function on now this little + + + align:start position:0% +continuous function on now this little +interval. So this interval here because + + align:start position:0% +interval. So this interval here because + + + align:start position:0% +interval. So this interval here because +it's you have the minimum of this. This + + align:start position:0% +it's you have the minimum of this. This + + + align:start position:0% +it's you have the minimum of this. This +is interval is contained in the + + align:start position:0% +is interval is contained in the + + + align:start position:0% +is interval is contained in the +corresponding interval with the delta to + + align:start position:0% +corresponding interval with the delta to + + + align:start position:0% +corresponding interval with the delta to +zero. So it's y in this space such that + + align:start position:0% +zero. So it's y in this space such that + + + align:start position:0% +zero. So it's y in this space such that +the norm here at each point is lesser + + align:start position:0% +the norm here at each point is lesser + + + align:start position:0% +the norm here at each point is lesser +equal to r. That's a space I'm going to + + align:start position:0% +equal to r. That's a space I'm going to + + + align:start position:0% +equal to r. That's a space I'm going to +look at. And we already know that t maps + + align:start position:0% +look at. And we already know that t maps + + + align:start position:0% +look at. And we already know that t maps +this space into itself, right? Because + + align:start position:0% +this space into itself, right? Because + + + align:start position:0% +this space into itself, right? Because +there's really no new statement if the + + align:start position:0% +there's really no new statement if the + + + align:start position:0% +there's really no new statement if the +function is is right. So as long as you + + align:start position:0% +function is is right. So as long as you + + + align:start position:0% +function is is right. So as long as you +have this here and you apply t on it, t + + align:start position:0% +have this here and you apply t on it, t + + + align:start position:0% +have this here and you apply t on it, t +when you apply t on a function it's + + align:start position:0% +when you apply t on a function it's + + + align:start position:0% +when you apply t on a function it's +defined on the same interval. So it will + + align:start position:0% +defined on the same interval. So it will + + + align:start position:0% +defined on the same interval. So it will +automatically defined on this smaller + + align:start position:0% +automatically defined on this smaller + + + align:start position:0% +automatically defined on this smaller +interval and and we already have this + + align:start position:0% +interval and and we already have this + + + align:start position:0% +interval and and we already have this +property. Okay. So so t maps this space + + align:start position:0% +property. Okay. So so t maps this space + + + align:start position:0% +property. Okay. So so t maps this space +here into itself. Okay. + + align:start position:0% +here into itself. Okay. + + + align:start position:0% +here into itself. Okay. +And now I want to prove I want to + + align:start position:0% +And now I want to prove I want to + + + align:start position:0% +And now I want to prove I want to +estimate. So I take two elements in this + + align:start position:0% +estimate. So I take two elements in this + + + align:start position:0% +estimate. So I take two elements in this +space. + + align:start position:0% +space. + + + align:start position:0% +space. +So I have y1 and y2. So you're looking + + align:start position:0% +So I have y1 and y2. So you're looking + + + align:start position:0% +So I have y1 and y2. So you're looking +at so y1 + + align:start position:0% +at so y1 + + + align:start position:0% +at so y1 +and y2 are in this space. + + align:start position:0% +and y2 are in this space. + + + align:start position:0% +and y2 are in this space. +And you want to look at what is the + + align:start position:0% +And you want to look at what is the + + + align:start position:0% +And you want to look at what is the +distance + + align:start position:0% +distance + + + align:start position:0% +distance +between y1 + + align:start position:0% +between y1 + + + align:start position:0% +between y1 +and y2. + + align:start position:0% + + + + align:start position:0% + +Right? So we want this here and we want + + align:start position:0% +Right? So we want this here and we want + + + align:start position:0% +Right? So we want this here and we want +what I want to prove is + + align:start position:0% +what I want to prove is + + + align:start position:0% +what I want to prove is +that it's contracting. + + align:start position:0% +that it's contracting. + + + align:start position:0% +that it's contracting. +So I want to show + + align:start position:0% + + + + align:start position:0% + +and I want to prove I'm going to prove + + align:start position:0% +and I want to prove I'm going to prove + + + align:start position:0% +and I want to prove I'm going to prove +it. + + align:start position:0% +it. + + + align:start position:0% +it. +You know my constant C will be explicit. + + align:start position:0% +You know my constant C will be explicit. + + + align:start position:0% +You know my constant C will be explicit. +It would be just a half. So that + + align:start position:0% +It would be just a half. So that + + + align:start position:0% +It would be just a half. So that +certainly is less than one. + + align:start position:0% +certainly is less than one. + + + align:start position:0% +certainly is less than one. +And this is what I want. + + align:start position:0% +And this is what I want. + + + align:start position:0% +And this is what I want. +Okay. + + align:start position:0% + + + + align:start position:0% + +So now + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +So now let's look at then. + + align:start position:0% + + + + align:start position:0% + +So t of y1 + + align:start position:0% +So t of y1 + + + align:start position:0% +So t of y1 +minus t of y2. + + align:start position:0% + + + + align:start position:0% + +this thing here y t of y1 is defined to + + align:start position:0% +this thing here y t of y1 is defined to + + + align:start position:0% +this thing here y t of y1 is defined to +be a plus the integral sorry and let me + + align:start position:0% +be a plus the integral sorry and let me + + + align:start position:0% +be a plus the integral sorry and let me +write so I'm going to let me just make a + + align:start position:0% +write so I'm going to let me just make a + + + align:start position:0% +write so I'm going to let me just make a +little more space here I worried I'm + + align:start position:0% +little more space here I worried I'm + + + align:start position:0% +little more space here I worried I'm +running out of time but let's see so + + align:start position:0% +running out of time but let's see so + + + align:start position:0% +running out of time but let's see so +this thing here minus t of y2 and I'm + + align:start position:0% +this thing here minus t of y2 and I'm + + + align:start position:0% +this thing here minus t of y2 and I'm +just looking at the difference in some x + + align:start position:0% +just looking at the difference in some x + + + align:start position:0% +just looking at the difference in some x +and again x here is now in x here will + + align:start position:0% +and again x here is now in x here will + + + align:start position:0% +and again x here is now in x here will +be in the interval + + align:start position:0% +be in the interval + + + align:start position:0% +be in the interval +um you were looking at x in the interval + + align:start position:0% +um you were looking at x in the interval + + + align:start position:0% +um you were looking at x in the interval +in this interval + + align:start position:0% +in this interval + + + align:start position:0% +in this interval +and so I'm just writing down first here + + align:start position:0% +and so I'm just writing down first here + + + align:start position:0% +and so I'm just writing down first here +what this is this is the integral of + + align:start position:0% +what this is this is the integral of + + + align:start position:0% +what this is this is the integral of +from a to x of f of y1 + + align:start position:0% +from a to x of f of y1 + + + align:start position:0% +from a to x of f of y1 +uh s + + align:start position:0% +uh s + + + align:start position:0% +uh s +plus + + align:start position:0% +plus + + + align:start position:0% +plus +g of s + + align:start position:0% + + + + align:start position:0% + +Um and then you have minus + + align:start position:0% +Um and then you have minus + + + align:start position:0% +Um and then you have minus +this is what you get for a2 for y2 a. So + + align:start position:0% +this is what you get for a2 for y2 a. So + + + align:start position:0% +this is what you get for a2 for y2 a. So +minus this thing here. + + align:start position:0% + + + + align:start position:0% + +So this is the difference right. + + align:start position:0% +So this is the difference right. + + + align:start position:0% +So this is the difference right. +And what you see is the first thing you + + align:start position:0% +And what you see is the first thing you + + + align:start position:0% +And what you see is the first thing you +observe is that this a here cancels + + align:start position:0% +observe is that this a here cancels + + + align:start position:0% +observe is that this a here cancels +right but it not only does this cancel + + align:start position:0% +right but it not only does this cancel + + + align:start position:0% +right but it not only does this cancel +but this term here also cancel okay and + + align:start position:0% +but this term here also cancel okay and + + + align:start position:0% +but this term here also cancel okay and +that actually there's a good reason that + + align:start position:0% +that actually there's a good reason that + + + align:start position:0% +that actually there's a good reason that +there are lower order and and the point + + align:start position:0% +there are lower order and and the point + + + align:start position:0% +there are lower order and and the point +here is that right the the the the main + + align:start position:0% +here is that right the the the the main + + + align:start position:0% +here is that right the the the the main +point is in the unknown function anyway + + align:start position:0% +point is in the unknown function anyway + + + align:start position:0% +point is in the unknown function anyway +right and it's it's a what's called a + + align:start position:0% +right and it's it's a what's called a + + + align:start position:0% +right and it's it's a what's called a +nonlinear equation + + align:start position:0% +nonlinear equation + + + align:start position:0% +nonlinear equation +um So that's a difficulty. + + align:start position:0% +um So that's a difficulty. + + + align:start position:0% +um So that's a difficulty. +So but what you then get when you write + + align:start position:0% +So but what you then get when you write + + + align:start position:0% +So but what you then get when you write +when you have when you have after the + + align:start position:0% +when you have when you have after the + + + align:start position:0% +when you have when you have after the +cancellation what you get is f of y1 + + align:start position:0% +cancellation what you get is f of y1 + + + align:start position:0% +cancellation what you get is f of y1 +of s + + align:start position:0% +of s + + + align:start position:0% +of s +minus f of y2 of s + + align:start position:0% +minus f of y2 of s + + + align:start position:0% +minus f of y2 of s +ds. Okay. So you have that. + + align:start position:0% +ds. Okay. So you have that. + + + align:start position:0% +ds. Okay. So you have that. +Now I will now I will + + align:start position:0% +Now I will now I will + + + align:start position:0% +Now I will now I will +look at this thing here and that thing + + align:start position:0% +look at this thing here and that thing + + + align:start position:0% +look at this thing here and that thing +here and I'm going to and you have to + + align:start position:0% +here and I'm going to and you have to + + + align:start position:0% +here and I'm going to and you have to +now abstract. So, so now I'm going to + + align:start position:0% +now abstract. So, so now I'm going to + + + align:start position:0% +now abstract. So, so now I'm going to +look at this difference here. And then + + align:start position:0% +look at this difference here. And then + + + align:start position:0% +look at this difference here. And then +now the thing is that you have to kind + + align:start position:0% +now the thing is that you have to kind + + + align:start position:0% +now the thing is that you have to kind +of abstract from it and you have to + + align:start position:0% +of abstract from it and you have to + + + align:start position:0% +of abstract from it and you have to +think about S as being + + align:start position:0% +think about S as being + + + align:start position:0% +think about S as being +if you think about S as being fixed, + + align:start position:0% +if you think about S as being fixed, + + + align:start position:0% +if you think about S as being fixed, +right? Then this is just two numbers, + + align:start position:0% +right? Then this is just two numbers, + + + align:start position:0% +right? Then this is just two numbers, +right? You could think about this as set + + align:start position:0% +right? You could think about this as set + + + align:start position:0% +right? You could think about this as set +one + + align:start position:0% +one + + + align:start position:0% +one +and this here as set two, right? This is + + align:start position:0% +and this here as set two, right? This is + + + align:start position:0% +and this here as set two, right? This is +set one and this here is set two. So + + align:start position:0% +set one and this here is set two. So + + + align:start position:0% +set one and this here is set two. So +it's like f of set one minus f of set + + align:start position:0% +it's like f of set one minus f of set + + + align:start position:0% +it's like f of set one minus f of set +two. Right? Now the mean value theorem + + align:start position:0% +two. Right? Now the mean value theorem + + + align:start position:0% +two. Right? Now the mean value theorem +tells us that this thing here is equal + + align:start position:0% +tells us that this thing here is equal + + + align:start position:0% +tells us that this thing here is equal +to the derivative at some intermediate + + align:start position:0% +to the derivative at some intermediate + + + align:start position:0% +to the derivative at some intermediate +point. Say let's say set three where set + + align:start position:0% +point. Say let's say set three where set + + + align:start position:0% +point. Say let's say set three where set +three is between + + align:start position:0% +three is between + + + align:start position:0% +three is between +is between + + align:start position:0% + + + + align:start position:0% + +set one and set two, + + align:start position:0% +set one and set two, + + + align:start position:0% +set one and set two, +right? And then times set one minus set + + align:start position:0% +right? And then times set one minus set + + + align:start position:0% +right? And then times set one minus set +two, + + align:start position:0% +two, + + + align:start position:0% +two, +right? + + align:start position:0% +right? + + + align:start position:0% +right? +And but you okay? So this is so this is + + align:start position:0% +And but you okay? So this is so this is + + + align:start position:0% +And but you okay? So this is so this is +just for you just for any xs you have + + align:start position:0% +just for you just for any xs you have + + + align:start position:0% +just for you just for any xs you have +this. Okay, but this means that + + align:start position:0% +this. Okay, but this means that + + + align:start position:0% +this. Okay, but this means that +this means now we almost out of time. Uh + + align:start position:0% +this means now we almost out of time. Uh + + + align:start position:0% +this means now we almost out of time. Uh +so this means that the when you're + + align:start position:0% +so this means that the when you're + + + align:start position:0% +so this means that the when you're +looking at the norm of this + + align:start position:0% +looking at the norm of this + + + align:start position:0% +looking at the norm of this +f of y1 of s minus f of y 2 of s + + align:start position:0% +f of y1 of s minus f of y 2 of s + + + align:start position:0% +f of y1 of s minus f of y 2 of s +right that the norm here is so the norm + + align:start position:0% +right that the norm here is so the norm + + + align:start position:0% +right that the norm here is so the norm +is equal to fprime at set three + + align:start position:0% + + + + align:start position:0% + +times set one which is and set one I can + + align:start position:0% +times set one which is and set one I can + + + align:start position:0% +times set one which is and set one I can +write Again it's really this and this is + + align:start position:0% + + + + align:start position:0% + +set two. + + align:start position:0% +set two. + + + align:start position:0% +set two. +This thing here remember set is some + + align:start position:0% +This thing here remember set is some + + + align:start position:0% +This thing here remember set is some +point in between those two points right? + + align:start position:0% +point in between those two points right? + + + align:start position:0% +point in between those two points right? +But both of these points both of these + + align:start position:0% +But both of these points both of these + + + align:start position:0% +But both of these points both of these +points here both this one here and that + + align:start position:0% +points here both this one here and that + + + align:start position:0% +points here both this one here and that +one here have norm less than r. + + align:start position:0% +one here have norm less than r. + + + align:start position:0% +one here have norm less than r. +Right? + + align:start position:0% +Right? + + + align:start position:0% +Right? +So this here is so but now where the way + + align:start position:0% +So this here is so but now where the way + + + align:start position:0% +So this here is so but now where the way +that m was defined + + align:start position:0% +that m was defined + + + align:start position:0% +that m was defined +uh and it should have been on the same + + align:start position:0% +uh and it should have been on the same + + + align:start position:0% +uh and it should have been on the same +board. + + align:start position:0% +board. + + + align:start position:0% +board. +So m here was defined to be the maximum + + align:start position:0% +So m here was defined to be the maximum + + + align:start position:0% +So m here was defined to be the maximum +of fprime of set + + align:start position:0% +of fprime of set + + + align:start position:0% +of fprime of set +where set was less or equal to one. + + align:start position:0% +where set was less or equal to one. + + + align:start position:0% +where set was less or equal to one. +And so you see that this thing here + + align:start position:0% +And so you see that this thing here + + + align:start position:0% +And so you see that this thing here +where you take the derivative that is + + align:start position:0% +where you take the derivative that is + + + align:start position:0% +where you take the derivative that is +bounded by m right. So this thing here + + align:start position:0% +bounded by m right. So this thing here + + + align:start position:0% +bounded by m right. So this thing here +is less than m y1 s minus y2 + + align:start position:0% +is less than m y1 s minus y2 + + + align:start position:0% +is less than m y1 s minus y2 +of s like that. Okay I so I'm not sure + + align:start position:0% +of s like that. Okay I so I'm not sure + + + align:start position:0% +of s like that. Okay I so I'm not sure +where we should stop. I mean we're over + + align:start position:0% +where we should stop. I mean we're over + + + align:start position:0% +where we should stop. I mean we're over +and I probably need a few more minutes. + + align:start position:0% +and I probably need a few more minutes. + + + align:start position:0% +and I probably need a few more minutes. +Maybe we should stop and it's not a + + align:start position:0% +Maybe we should stop and it's not a + + + align:start position:0% +Maybe we should stop and it's not a +great place to stop, but uh but that's + + align:start position:0% +great place to stop, but uh but that's + + + align:start position:0% +great place to stop, but uh but that's +how it goes. Uh so I will uh keep you in + + align:start position:0% +how it goes. Uh so I will uh keep you in + + + align:start position:0% +how it goes. Uh so I will uh keep you in +suspension + + align:start position:0% +suspension + + + align:start position:0% +suspension +uh and um and so we'll pick up uh from + + align:start position:0% +uh and um and so we'll pick up uh from + + + align:start position:0% +uh and um and so we'll pick up uh from +here on on Tuesday. And so I I want + + align:start position:0% +here on on Tuesday. And so I I want + + + align:start position:0% +here on on Tuesday. And so I I want +anyway to explain to you why actually + + align:start position:0% +anyway to explain to you why actually + + + align:start position:0% +anyway to explain to you why actually +this method which seems a little crazy + + align:start position:0% +this method which seems a little crazy + + + align:start position:0% +this method which seems a little crazy +in a way because it's bringing in all + + align:start position:0% +in a way because it's bringing in all + + + align:start position:0% +in a way because it's bringing in all +these things why it turned out to be + + align:start position:0% +these things why it turned out to be + + + align:start position:0% +these things why it turned out to be +basically optimal. + + align:start position:0% +basically optimal. + + + align:start position:0% +basically optimal. +Okay. And then we'll do a review the + + align:start position:0% +Okay. And then we'll do a review the + + + align:start position:0% +Okay. And then we'll do a review the +rest of the time on on Tuesday. \ No newline at end of file diff --git a/g7frRgUhmeU.txt b/g7frRgUhmeU.txt new file mode 100644 index 0000000000000000000000000000000000000000..515b536471d1ec307910563c6ca7fb3d9493c882 --- /dev/null +++ b/g7frRgUhmeU.txt @@ -0,0 +1,627 @@ +align:start position:0% + +in the second culture you have a couple + + align:start position:0% +in the second culture you have a couple + + + align:start position:0% +in the second culture you have a couple +rows to play you I I give like five + + align:start position:0% +rows to play you I I give like five + + + align:start position:0% +rows to play you I I give like five +levels you can be a + + align:start position:0% +levels you can be a + + + align:start position:0% +levels you can be a +tourist and you can be an observer and + + align:start position:0% +tourist and you can be an observer and + + + align:start position:0% +tourist and you can be an observer and +you can be a participants and you can be + + align:start position:0% +you can be a participants and you can be + + + align:start position:0% +you can be a participants and you can be +a contributor and you can be a + + align:start position:0% +a contributor and you can be a + + + align:start position:0% +a contributor and you can be a +shareholder and I always ask my students + + align:start position:0% +shareholder and I always ask my students + + + align:start position:0% +shareholder and I always ask my students +ask yourself what kind of role you want + + align:start position:0% +ask yourself what kind of role you want + + + align:start position:0% +ask yourself what kind of role you want +to play in the second culture and that + + align:start position:0% +to play in the second culture and that + + + align:start position:0% +to play in the second culture and that +that would that will also guide you + + align:start position:0% +that would that will also guide you + + + align:start position:0% +that would that will also guide you +through when you are learning how to do + + align:start position:0% +through when you are learning how to do + + + align:start position:0% +through when you are learning how to do +these kind of things with the language + + align:start position:0% +these kind of things with the language + + + align:start position:0% +these kind of things with the language +and our goal here for chines 1 and + + align:start position:0% +and our goal here for chines 1 and + + + align:start position:0% +and our goal here for chines 1 and +chines 2 until chines 4 we really push + + align:start position:0% +chines 2 until chines 4 we really push + + + align:start position:0% +chines 2 until chines 4 we really push +we really push our students heart to the + + align:start position:0% +we really push our students heart to the + + + align:start position:0% +we really push our students heart to the +level at Le to be a + + align:start position:0% + + + + align:start position:0% + +participant what is a tourist I mean I + + align:start position:0% +participant what is a tourist I mean I + + + align:start position:0% +participant what is a tourist I mean I +mean being a touris is totally okay so + + align:start position:0% +mean being a touris is totally okay so + + + align:start position:0% +mean being a touris is totally okay so +for example when you go to China you see + + align:start position:0% +for example when you go to China you see + + + align:start position:0% +for example when you go to China you see +so many cars and the air is really bad + + align:start position:0% +so many cars and the air is really bad + + + align:start position:0% +so many cars and the air is really bad +and and so you say as a t said the air + + align:start position:0% +and and so you say as a t said the air + + + align:start position:0% +and and so you say as a t said the air +is so + + align:start position:0% +is so + + + align:start position:0% +is so +bad an utterance like that would not get + + align:start position:0% +bad an utterance like that would not get + + + align:start position:0% +bad an utterance like that would not get +you too far in Communications but if you + + align:start position:0% +you too far in Communications but if you + + + align:start position:0% +you too far in Communications but if you +can start to be Observer for example So + + align:start position:0% +can start to be Observer for example So + + + align:start position:0% +can start to be Observer for example So +You observe what what are the reasons + + align:start position:0% +You observe what what are the reasons + + + align:start position:0% +You observe what what are the reasons +involved and start to give it some time + + align:start position:0% +involved and start to give it some time + + + align:start position:0% +involved and start to give it some time +and absorb them then the next then the + + align:start position:0% +and absorb them then the next then the + + + align:start position:0% +and absorb them then the next then the +next level is you can start to + + align:start position:0% +next level is you can start to + + + align:start position:0% +next level is you can start to +participate in the discussions so that + + align:start position:0% +participate in the discussions so that + + + align:start position:0% +participate in the discussions so that +the words coming from your mouth they're + + align:start position:0% +the words coming from your mouth they're + + + align:start position:0% +the words coming from your mouth they're +much more sophisticated they're much + + align:start position:0% +much more sophisticated they're much + + + align:start position:0% +much more sophisticated they're much +more sophisticated so that the native + + align:start position:0% +more sophisticated so that the native + + + align:start position:0% +more sophisticated so that the native +speakers would have the interest to to + + align:start position:0% +speakers would have the interest to to + + + align:start position:0% +speakers would have the interest to to +speak with you so those are the five + + align:start position:0% +speak with you so those are the five + + + align:start position:0% +speak with you so those are the five +roles I always encourage students that + + align:start position:0% +roles I always encourage students that + + + align:start position:0% +roles I always encourage students that +think about what kind of role you want + + align:start position:0% +think about what kind of role you want + + + align:start position:0% +think about what kind of role you want +to play in the second culture and that + + align:start position:0% +to play in the second culture and that + + + align:start position:0% +to play in the second culture and that +would for the most part determine your + + align:start position:0% +would for the most part determine your + + + align:start position:0% +would for the most part determine your +efforts when you when you are learning + + align:start position:0% +efforts when you when you are learning + + + align:start position:0% +efforts when you when you are learning +the + + align:start position:0% +the + + + align:start position:0% +the +language it can be applied in many in + + align:start position:0% +language it can be applied in many in + + + align:start position:0% +language it can be applied in many in +many many aspects if today the issue is + + align:start position:0% +many many aspects if today the issue is + + + align:start position:0% +many many aspects if today the issue is +really about a l cell for example the + + align:start position:0% +really about a l cell for example the + + + align:start position:0% +really about a l cell for example the +structure is not right I was I was I + + align:start position:0% +structure is not right I was I was I + + + align:start position:0% +structure is not right I was I was I +always ask my students what if what + + align:start position:0% +always ask my students what if what + + + align:start position:0% +always ask my students what if what +would you react if a native if if a + + align:start position:0% +would you react if a native if if a + + + align:start position:0% +would you react if a native if if a +foreigner speaks to you with the English + + align:start position:0% +foreigner speaks to you with the English + + + align:start position:0% +foreigner speaks to you with the English +like + + align:start position:0% +like + + + align:start position:0% +like +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um I go to the park yesterday what would + + align:start position:0% +um I go to the park yesterday what would + + + align:start position:0% +um I go to the park yesterday what would +you react think about a sentence like + + align:start position:0% +you react think about a sentence like + + + align:start position:0% +you react think about a sentence like +this his spe his speed is not is not + + align:start position:0% +this his spe his speed is not is not + + + align:start position:0% +this his spe his speed is not is not +fluence and he has some grammatical errs + + align:start position:0% +fluence and he has some grammatical errs + + + align:start position:0% +fluence and he has some grammatical errs +how would you re Rea react you can still + + align:start position:0% +how would you re Rea react you can still + + + align:start position:0% +how would you re Rea react you can still +react without any difficulties because + + align:start position:0% +react without any difficulties because + + + align:start position:0% +react without any difficulties because +you understand but think about that if + + align:start position:0% +you understand but think about that if + + + align:start position:0% +you understand but think about that if +you have to interact with the person for + + align:start position:0% +you have to interact with the person for + + + align:start position:0% +you have to interact with the person for +30 minutes what is your + + align:start position:0% +30 minutes what is your + + + align:start position:0% +30 minutes what is your +maximum and that would also become the + + align:start position:0% +maximum and that would also become the + + + align:start position:0% +maximum and that would also become the +motivation to work on your language + + align:start position:0% +motivation to work on your language + + + align:start position:0% +motivation to work on your language +forms that's for sure second thing is + + align:start position:0% +forms that's for sure second thing is + + + align:start position:0% +forms that's for sure second thing is +that would also there was that will also + + align:start position:0% +that would also there was that will also + + + align:start position:0% +that would also there was that will also +gives the opportunity to think + + align:start position:0% +gives the opportunity to think + + + align:start position:0% +gives the opportunity to think +about what kind of level and what the + + align:start position:0% +about what kind of level and what the + + + align:start position:0% +about what kind of level and what the +level we're talking about includes + + align:start position:0% +level we're talking about includes + + + align:start position:0% +level we're talking about includes +culture competence and language + + align:start position:0% +culture competence and language + + + align:start position:0% +culture competence and language +proficiency that want you push yourself + + align:start position:0% +proficiency that want you push yourself + + + align:start position:0% +proficiency that want you push yourself +to be but I would say that as long as + + align:start position:0% +to be but I would say that as long as + + + align:start position:0% +to be but I would say that as long as +you put in the efforts it's always + + align:start position:0% +you put in the efforts it's always + + + align:start position:0% +you put in the efforts it's always +reverting it's always reverting and I + + align:start position:0% +reverting it's always reverting and I + + + align:start position:0% +reverting it's always reverting and I +and I'm very happy to say that our + + align:start position:0% +and I'm very happy to say that our + + + align:start position:0% +and I'm very happy to say that our +students they are usually they're + + align:start position:0% +students they are usually they're + + + align:start position:0% +students they are usually they're +usually very good at this regard they + + align:start position:0% +usually very good at this regard they + + + align:start position:0% +usually very good at this regard they +usually find a lot of resources either + + align:start position:0% +usually find a lot of resources either + + + align:start position:0% +usually find a lot of resources either +on campus or the Greater Boston + + align:start position:0% +on campus or the Greater Boston + + + align:start position:0% +on campus or the Greater Boston +Community to interact with them to + + align:start position:0% +Community to interact with them to + + + align:start position:0% +Community to interact with them to +interact with with the speakers of + + align:start position:0% +interact with with the speakers of + + + align:start position:0% +interact with with the speakers of +Chinese \ No newline at end of file diff --git a/h8DKVKfWU_Q.txt b/h8DKVKfWU_Q.txt new file mode 100644 index 0000000000000000000000000000000000000000..abc43202b9393e54869e5aa09fac3f0cfd190089 --- /dev/null +++ b/h8DKVKfWU_Q.txt @@ -0,0 +1,979 @@ +align:start position:0% + +in the discrete case we saw that we + + align:start position:0% +in the discrete case we saw that we + + + align:start position:0% +in the discrete case we saw that we +could recover the PMF of X and the PMF + + align:start position:0% +could recover the PMF of X and the PMF + + + align:start position:0% +could recover the PMF of X and the PMF +of Y from the joint PMF indeed the joint + + align:start position:0% +of Y from the joint PMF indeed the joint + + + align:start position:0% +of Y from the joint PMF indeed the joint +PMF is supposed to contain a complete + + align:start position:0% +PMF is supposed to contain a complete + + + align:start position:0% +PMF is supposed to contain a complete +probabilistic description of the two + + align:start position:0% +probabilistic description of the two + + + align:start position:0% +probabilistic description of the two +random variables it is their probability + + align:start position:0% +random variables it is their probability + + + align:start position:0% +random variables it is their probability +law and any quantity of interest can be + + align:start position:0% +law and any quantity of interest can be + + + align:start position:0% +law and any quantity of interest can be +computed if we know the joint things are + + align:start position:0% +computed if we know the joint things are + + + align:start position:0% +computed if we know the joint things are +similar in the continued setting you can + + align:start position:0% +similar in the continued setting you can + + + align:start position:0% +similar in the continued setting you can +easily guess the formula through the + + align:start position:0% +easily guess the formula through the + + + align:start position:0% +easily guess the formula through the +standard recipe replace sums by + + align:start position:0% +standard recipe replace sums by + + + align:start position:0% +standard recipe replace sums by +integrals and replace pmfs by PDFs but a + + align:start position:0% +integrals and replace pmfs by PDFs but a + + + align:start position:0% +integrals and replace pmfs by PDFs but a +proof of this formula is actually + + align:start position:0% +proof of this formula is actually + + + align:start position:0% +proof of this formula is actually +instructive so let us start by first + + align:start position:0% +instructive so let us start by first + + + align:start position:0% +instructive so let us start by first +finding the CDF of X the CDF of X is by + + align:start position:0% +finding the CDF of X the CDF of X is by + + + align:start position:0% +finding the CDF of X the CDF of X is by +definition the probability that the + + align:start position:0% +definition the probability that the + + + align:start position:0% +definition the probability that the +random variable X takes a value less + + align:start position:0% +random variable X takes a value less + + + align:start position:0% +random variable X takes a value less +than or equal to a certain number little + + align:start position:0% +than or equal to a certain number little + + + align:start position:0% +than or equal to a certain number little +X and this is the probability of a + + align:start position:0% +X and this is the probability of a + + + align:start position:0% +X and this is the probability of a +particular set that we can visualize on + + align:start position:0% +particular set that we can visualize on + + + align:start position:0% +particular set that we can visualize on +the two-dimensional plane if here is the + + align:start position:0% +the two-dimensional plane if here is the + + + align:start position:0% +the two-dimensional plane if here is the +value of little X then we're talking + + align:start position:0% +value of little X then we're talking + + + align:start position:0% +value of little X then we're talking +about the set of all pairs X Y for which + + align:start position:0% +about the set of all pairs X Y for which + + + align:start position:0% +about the set of all pairs X Y for which +the X component is less than or equal to + + align:start position:0% +the X component is less than or equal to + + + align:start position:0% +the X component is less than or equal to +a certain number so we need to integrate + + align:start position:0% +a certain number so we need to integrate + + + align:start position:0% +a certain number so we need to integrate +over this two-dimensional set the joint + + align:start position:0% +over this two-dimensional set the joint + + + align:start position:0% +over this two-dimensional set the joint +density so it will be a double integral + + align:start position:0% +density so it will be a double integral + + + align:start position:0% +density so it will be a double integral +of the joint density over this + + align:start position:0% +of the joint density over this + + + align:start position:0% +of the joint density over this +particular two-dimensional set now since + + align:start position:0% +particular two-dimensional set now since + + + align:start position:0% +particular two-dimensional set now since +we've used the symbol X here to mean + + align:start position:0% +we've used the symbol X here to mean + + + align:start position:0% +we've used the symbol X here to mean +something specific let us use different + + align:start position:0% +something specific let us use different + + + align:start position:0% +something specific let us use different +symbols for the dummy variables that we + + align:start position:0% +symbols for the dummy variables that we + + + align:start position:0% +symbols for the dummy variables that we +will use in the integration and we need + + align:start position:0% +will use in the integration and we need + + + align:start position:0% +will use in the integration and we need +to integrate with respect to the two + + align:start position:0% +to integrate with respect to the two + + + align:start position:0% +to integrate with respect to the two +variables let's say with respect to T + + align:start position:0% +variables let's say with respect to T + + + align:start position:0% +variables let's say with respect to T +and with respect to s the variable T can + + align:start position:0% +and with respect to s the variable T can + + + align:start position:0% +and with respect to s the variable T can +be anything so it ranges from minus + + align:start position:0% +be anything so it ranges from minus + + + align:start position:0% +be anything so it ranges from minus +infinity to infinity but the variable s + + align:start position:0% +infinity to infinity but the variable s + + + align:start position:0% +infinity to infinity but the variable s +the first argument ranges from minus + + align:start position:0% +the first argument ranges from minus + + + align:start position:0% +the first argument ranges from minus +infinity up to + + align:start position:0% +infinity up to + + + align:start position:0% +infinity up to +point which is X think of this double + + align:start position:0% +point which is X think of this double + + + align:start position:0% +point which is X think of this double +integral has an integral with respect to + + align:start position:0% +integral has an integral with respect to + + + align:start position:0% +integral has an integral with respect to +the variable s of this complicated + + align:start position:0% +the variable s of this complicated + + + align:start position:0% +the variable s of this complicated +function inside the brackets now to find + + align:start position:0% +function inside the brackets now to find + + + align:start position:0% +function inside the brackets now to find +the density of X all we need to do is to + + align:start position:0% +the density of X all we need to do is to + + + align:start position:0% +the density of X all we need to do is to +differentiate the CDF of X and when we + + align:start position:0% +differentiate the CDF of X and when we + + + align:start position:0% +differentiate the CDF of X and when we +have an integral of this kind and we + + align:start position:0% +have an integral of this kind and we + + + align:start position:0% +have an integral of this kind and we +differentiate with respect to the upper + + align:start position:0% +differentiate with respect to the upper + + + align:start position:0% +differentiate with respect to the upper +limit of the integration what we are + + align:start position:0% +limit of the integration what we are + + + align:start position:0% +limit of the integration what we are +left with is the integrand that is this + + align:start position:0% +left with is the integrand that is this + + + align:start position:0% +left with is the integrand that is this +expression here it is an integral with + + align:start position:0% +expression here it is an integral with + + + align:start position:0% +expression here it is an integral with +respect to the second variable and it's + + align:start position:0% +respect to the second variable and it's + + + align:start position:0% +respect to the second variable and it's +an integral over the entire space from + + align:start position:0% +an integral over the entire space from + + + align:start position:0% +an integral over the entire space from +minus infinity to plus infinity here is + + align:start position:0% +minus infinity to plus infinity here is + + + align:start position:0% +minus infinity to plus infinity here is +an example the simplest kind of a joint + + align:start position:0% +an example the simplest kind of a joint + + + align:start position:0% +an example the simplest kind of a joint +PDF is a PDF that is constant on a + + align:start position:0% +PDF is a PDF that is constant on a + + + align:start position:0% +PDF is a PDF that is constant on a +certain set s and is 0 outside that set + + align:start position:0% +certain set s and is 0 outside that set + + + align:start position:0% +certain set s and is 0 outside that set +so the overall probability 1 unit of + + align:start position:0% +so the overall probability 1 unit of + + + align:start position:0% +so the overall probability 1 unit of +probability is spread uniformly over + + align:start position:0% +probability is spread uniformly over + + + align:start position:0% +probability is spread uniformly over +that set because the total volume under + + align:start position:0% +that set because the total volume under + + + align:start position:0% +that set because the total volume under +the joint PDF must be equal to 1 the + + align:start position:0% +the joint PDF must be equal to 1 the + + + align:start position:0% +the joint PDF must be equal to 1 the +height of the PDF must be equal to 1 + + align:start position:0% +height of the PDF must be equal to 1 + + + align:start position:0% +height of the PDF must be equal to 1 +over the area to calculate the + + align:start position:0% +over the area to calculate the + + + align:start position:0% +over the area to calculate the +probability of a certain set a we want + + align:start position:0% +probability of a certain set a we want + + + align:start position:0% +probability of a certain set a we want +to ask how much volume is sitting on top + + align:start position:0% +to ask how much volume is sitting on top + + + align:start position:0% +to ask how much volume is sitting on top +of that set and because in this case the + + align:start position:0% +of that set and because in this case the + + + align:start position:0% +of that set and because in this case the +PDF is constant we need to take the + + align:start position:0% +PDF is constant we need to take the + + + align:start position:0% +PDF is constant we need to take the +height of the PDF times the relevant + + align:start position:0% +height of the PDF times the relevant + + + align:start position:0% +height of the PDF times the relevant +area what is the relevant area + + align:start position:0% +area what is the relevant area + + + align:start position:0% +area what is the relevant area +well actually the PDF is 0 outside the + + align:start position:0% +well actually the PDF is 0 outside the + + + align:start position:0% +well actually the PDF is 0 outside the +set s so the relevant area is only this + + align:start position:0% +set s so the relevant area is only this + + + align:start position:0% +set s so the relevant area is only this +part here which is the intersection of + + align:start position:0% +part here which is the intersection of + + + align:start position:0% +part here which is the intersection of +the two sets s and a so the total volume + + align:start position:0% +the two sets s and a so the total volume + + + align:start position:0% +the two sets s and a so the total volume +sitting on top of this little set is + + align:start position:0% +sitting on top of this little set is + + + align:start position:0% +sitting on top of this little set is +going to be the + + align:start position:0% +going to be the + + + align:start position:0% +going to be the +basse the area of the base which is the + + align:start position:0% +basse the area of the base which is the + + + align:start position:0% +basse the area of the base which is the +area of a intersection s times the + + align:start position:0% +area of a intersection s times the + + + align:start position:0% +area of a intersection s times the +height of the PDF at those places now + + align:start position:0% +height of the PDF at those places now + + + align:start position:0% +height of the PDF at those places now +the height of the PDF is 1 over the area + + align:start position:0% +the height of the PDF is 1 over the area + + + align:start position:0% +the height of the PDF is 1 over the area +of s so this is the formula for + + align:start position:0% +of s so this is the formula for + + + align:start position:0% +of s so this is the formula for +calculating the probability of a certain + + align:start position:0% +calculating the probability of a certain + + + align:start position:0% +calculating the probability of a certain +set a let us now look at a specific + + align:start position:0% +set a let us now look at a specific + + + align:start position:0% +set a let us now look at a specific +example suppose that we have a uniform + + align:start position:0% +example suppose that we have a uniform + + + align:start position:0% +example suppose that we have a uniform +PDF over this particular set s this set + + align:start position:0% +PDF over this particular set s this set + + + align:start position:0% +PDF over this particular set s this set +has an area that is equal to 4 + + align:start position:0% +has an area that is equal to 4 + + + align:start position:0% +has an area that is equal to 4 +it consists of four unit rectangles and + + align:start position:0% +it consists of four unit rectangles and + + + align:start position:0% +it consists of four unit rectangles and +range next to each other so the height + + align:start position:0% +range next to each other so the height + + + align:start position:0% +range next to each other so the height +of the joint PDF in this example is + + align:start position:0% +of the joint PDF in this example is + + + align:start position:0% +of the joint PDF in this example is +going to be 1/4 it is 1/4 on that set + + align:start position:0% +going to be 1/4 it is 1/4 on that set + + + align:start position:0% +going to be 1/4 it is 1/4 on that set +but of course it's going to be zero + + align:start position:0% +but of course it's going to be zero + + + align:start position:0% +but of course it's going to be zero +outside that set we can now find the + + align:start position:0% +outside that set we can now find the + + + align:start position:0% +outside that set we can now find the +marginal PDF at some particular X so we + + align:start position:0% +marginal PDF at some particular X so we + + + align:start position:0% +marginal PDF at some particular X so we +can fix a particular value of x let's + + align:start position:0% +can fix a particular value of x let's + + + align:start position:0% +can fix a particular value of x let's +say this one to find the value of the + + align:start position:0% +say this one to find the value of the + + + align:start position:0% +say this one to find the value of the +marginal PDF we need to integrate over Y + + align:start position:0% +marginal PDF we need to integrate over Y + + + align:start position:0% +marginal PDF we need to integrate over Y +along that particular line and the + + align:start position:0% +along that particular line and the + + + align:start position:0% +along that particular line and the +integral is going to have a contribution + + align:start position:0% +integral is going to have a contribution + + + align:start position:0% +integral is going to have a contribution +only on that segment on that segment the + + align:start position:0% +only on that segment on that segment the + + + align:start position:0% +only on that segment on that segment the +value of the joint PDF is 1/4 and we're + + align:start position:0% +value of the joint PDF is 1/4 and we're + + + align:start position:0% +value of the joint PDF is 1/4 and we're +integrating over an interval that has a + + align:start position:0% +integrating over an interval that has a + + + align:start position:0% +integrating over an interval that has a +length of 1 so the integral is going to + + align:start position:0% +length of 1 so the integral is going to + + + align:start position:0% +length of 1 so the integral is going to +be equal to 1/4 but if X is somewhere + + align:start position:0% +be equal to 1/4 but if X is somewhere + + + align:start position:0% +be equal to 1/4 but if X is somewhere +around here as we integrate over that + + align:start position:0% +around here as we integrate over that + + + align:start position:0% +around here as we integrate over that +line we integrate a value of 1/4 the + + align:start position:0% +line we integrate a value of 1/4 the + + + align:start position:0% +line we integrate a value of 1/4 the +value of the PDF over an interval that + + align:start position:0% +value of the PDF over an interval that + + + align:start position:0% +value of the PDF over an interval that +has a length equal to 3 and so the + + align:start position:0% +has a length equal to 3 and so the + + + align:start position:0% +has a length equal to 3 and so the +result turns out to be 3/4 there is a + + align:start position:0% +result turns out to be 3/4 there is a + + + align:start position:0% +result turns out to be 3/4 there is a +similar calculation for the marginal PDF + + align:start position:0% +similar calculation for the marginal PDF + + + align:start position:0% +similar calculation for the marginal PDF +of y for any particular value of little + + align:start position:0% +of y for any particular value of little + + + align:start position:0% +of y for any particular value of little +Y to find the marginal PDF + + align:start position:0% +Y to find the marginal PDF + + + align:start position:0% +Y to find the marginal PDF +we integrate along this line the joint + + align:start position:0% +we integrate along this line the joint + + + align:start position:0% +we integrate along this line the joint +PDF the joint PDF is zero out here it's + + align:start position:0% +PDF the joint PDF is zero out here it's + + + align:start position:0% +PDF the joint PDF is zero out here it's +nonzero only on that interval and on + + align:start position:0% +nonzero only on that interval and on + + + align:start position:0% +nonzero only on that interval and on +that interval it has a value of + + align:start position:0% +that interval it has a value of + + + align:start position:0% +that interval it has a value of +one-fourth and the interval has a length + + align:start position:0% +one-fourth and the interval has a length + + + align:start position:0% +one-fourth and the interval has a length +of one so the integral is going to end + + align:start position:0% +of one so the integral is going to end + + + align:start position:0% +of one so the integral is going to end +up equal to one-fourth but if we were to + + align:start position:0% +up equal to one-fourth but if we were to + + + align:start position:0% +up equal to one-fourth but if we were to +take a line somewhere here we integrate + + align:start position:0% +take a line somewhere here we integrate + + + align:start position:0% +take a line somewhere here we integrate +the value of 1/4 over an interval of + + align:start position:0% +the value of 1/4 over an interval of + + + align:start position:0% +the value of 1/4 over an interval of +length 2 and so the result would be 1/2 + + align:start position:0% +length 2 and so the result would be 1/2 + + + align:start position:0% +length 2 and so the result would be 1/2 +so we have recovered from the joint PDF + + align:start position:0% +so we have recovered from the joint PDF + + + align:start position:0% +so we have recovered from the joint PDF +the marginal PDF of X and also the + + align:start position:0% +the marginal PDF of X and also the + + + align:start position:0% +the marginal PDF of X and also the +marginal PDF of Y \ No newline at end of file diff --git a/h9btrlN9JLk.txt b/h9btrlN9JLk.txt new file mode 100644 index 0000000000000000000000000000000000000000..007fd19e8a1a7d8f8bb9ae009679aa1388ea1b9f --- /dev/null +++ b/h9btrlN9JLk.txt @@ -0,0 +1,75 @@ +align:start position:0% + +all right so far hold the red ball for a + + align:start position:0% +all right so far hold the red ball for a + + + align:start position:0% +all right so far hold the red ball for a +moment you're going to start tossing it + + align:start position:0% +moment you're going to start tossing it + + + align:start position:0% +moment you're going to start tossing it +again but I'm going to add a blue ball + + align:start position:0% +again but I'm going to add a blue ball + + + align:start position:0% +again but I'm going to add a blue ball +in and I'm just going to eat all the + + align:start position:0% +in and I'm just going to eat all the + + + align:start position:0% +in and I'm just going to eat all the +balls man all right so this would be + + align:start position:0% +balls man all right so this would be + + + align:start position:0% +balls man all right so this would be +kind of distinct from the red ball then + + align:start position:0% +kind of distinct from the red ball then + + + align:start position:0% +kind of distinct from the red ball then +when you're ready to pass the blue ball + + align:start position:0% +when you're ready to pass the blue ball + + + align:start position:0% +when you're ready to pass the blue ball +and when you're ready to pass the red + + align:start position:0% +and when you're ready to pass the red + + + align:start position:0% +and when you're ready to pass the red +ball let's see if we can keep both going + + align:start position:0% +ball let's see if we can keep both going + + + align:start position:0% +ball let's see if we can keep both going +[Music] \ No newline at end of file diff --git a/hVYBgsi0JcM.txt b/hVYBgsi0JcM.txt new file mode 100644 index 0000000000000000000000000000000000000000..afa9580163a2e167d76824c15bd56352642056b9 --- /dev/null +++ b/hVYBgsi0JcM.txt @@ -0,0 +1,11995 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +and you can ask those questions right + + align:start position:0% +and you can ask those questions right + + + align:start position:0% +and you can ask those questions right +from the beginning so I would encourage + + align:start position:0% +from the beginning so I would encourage + + + align:start position:0% +from the beginning so I would encourage +you to just raise your hand in any world + + align:start position:0% +you to just raise your hand in any world + + + align:start position:0% +you to just raise your hand in any world +on the way so when I was your age I sort + + align:start position:0% +on the way so when I was your age I sort + + + align:start position:0% +on the way so when I was your age I sort +of wondered about why there were little + + align:start position:0% +of wondered about why there were little + + + align:start position:0% +of wondered about why there were little +kids in the world that didn't have clean + + align:start position:0% +kids in the world that didn't have clean + + + align:start position:0% +kids in the world that didn't have clean +water to drink and and that sort of + + align:start position:0% +water to drink and and that sort of + + + align:start position:0% +water to drink and and that sort of +bothered me and it was that kind of + + align:start position:0% +bothered me and it was that kind of + + + align:start position:0% +bothered me and it was that kind of +thing really they got me interested in + + align:start position:0% +thing really they got me interested in + + + align:start position:0% +thing really they got me interested in +engineering and got me interested in + + align:start position:0% +engineering and got me interested in + + + align:start position:0% +engineering and got me interested in +clean energy and it's hard to imagine + + align:start position:0% +clean energy and it's hard to imagine + + + align:start position:0% +clean energy and it's hard to imagine +like thirty years have gone by since + + align:start position:0% +like thirty years have gone by since + + + align:start position:0% +like thirty years have gone by since +that happened I mean you guys aren't + + align:start position:0% +that happened I mean you guys aren't + + + align:start position:0% +that happened I mean you guys aren't +even thirty years old that seems like + + align:start position:0% +even thirty years old that seems like + + + align:start position:0% +even thirty years old that seems like +forever so I'll tell you about Mt PV + + align:start position:0% +forever so I'll tell you about Mt PV + + + align:start position:0% +forever so I'll tell you about Mt PV +this is a clean energy technology that + + align:start position:0% +this is a clean energy technology that + + + align:start position:0% +this is a clean energy technology that +our startup company is developing to + + align:start position:0% +our startup company is developing to + + + align:start position:0% +our startup company is developing to +bring to market and and I'll also tell + + align:start position:0% +bring to market and and I'll also tell + + + align:start position:0% +bring to market and and I'll also tell +you some about my own personal journey + + align:start position:0% +you some about my own personal journey + + + align:start position:0% +you some about my own personal journey +in clean energy and happy to take it + + align:start position:0% +in clean energy and happy to take it + + + align:start position:0% +in clean energy and happy to take it +wherever you want to go so maybe maybe + + align:start position:0% +wherever you want to go so maybe maybe + + + align:start position:0% +wherever you want to go so maybe maybe +I'll do a couple of slides on sort of + + align:start position:0% +I'll do a couple of slides on sort of + + + align:start position:0% +I'll do a couple of slides on sort of +the technology and then then then you + + align:start position:0% +the technology and then then then you + + + align:start position:0% +the technology and then then then you +know where I am at the moment and and + + align:start position:0% +know where I am at the moment and and + + + align:start position:0% +know where I am at the moment and and +then how we got here and and and then we + + align:start position:0% +then how we got here and and and then we + + + align:start position:0% +then how we got here and and and then we +could go from there so our technology is + + align:start position:0% +could go from there so our technology is + + + align:start position:0% +could go from there so our technology is +called MTP V stands for micron gap + + align:start position:0% +called MTP V stands for micron gap + + + align:start position:0% +called MTP V stands for micron gap +thermal photovoltaics it draws on + + align:start position:0% +thermal photovoltaics it draws on + + + align:start position:0% +thermal photovoltaics it draws on +nanotechnology MEMS and photonics and + + align:start position:0% +nanotechnology MEMS and photonics and + + + align:start position:0% +nanotechnology MEMS and photonics and +what really motivates us is that we + + align:start position:0% +what really motivates us is that we + + + align:start position:0% +what really motivates us is that we +think that has the potential to change + + align:start position:0% +think that has the potential to change + + + align:start position:0% +think that has the potential to change +how we think about energy because it's a + + align:start position:0% +how we think about energy because it's a + + + align:start position:0% +how we think about energy because it's a +way of applying these very powerful + + align:start position:0% +way of applying these very powerful + + + align:start position:0% +way of applying these very powerful +techniques you know the whole the whole + + align:start position:0% +techniques you know the whole the whole + + + align:start position:0% +techniques you know the whole the whole +chip that we see in our iPhones and we + + align:start position:0% +chip that we see in our iPhones and we + + + align:start position:0% +chip that we see in our iPhones and we +see changing so many aspects of our + + align:start position:0% +see changing so many aspects of our + + + align:start position:0% +see changing so many aspects of our +socio-technical life if you will + + align:start position:0% +socio-technical life if you will + + + align:start position:0% +socio-technical life if you will +bringing these kinds of capabilities to + + align:start position:0% +bringing these kinds of capabilities to + + + align:start position:0% +bringing these kinds of capabilities to +bear on the energy world which in some + + align:start position:0% +bear on the energy world which in some + + + align:start position:0% +bear on the energy world which in some +ways is as you've been learning in this + + align:start position:0% +ways is as you've been learning in this + + + align:start position:0% +ways is as you've been learning in this +course is in some ways it's changed a + + align:start position:0% +course is in some ways it's changed a + + + align:start position:0% +course is in some ways it's changed a +lot and in some ways that hasn't changed + + align:start position:0% +lot and in some ways that hasn't changed + + + align:start position:0% +lot and in some ways that hasn't changed +for + + align:start position:0% +for + + + align:start position:0% +for +in the last hundred years we still make + + align:start position:0% +in the last hundred years we still make + + + align:start position:0% +in the last hundred years we still make +heat from things that we get from the + + align:start position:0% +heat from things that we get from the + + + align:start position:0% +heat from things that we get from the +ground and then we do things with that + + align:start position:0% +ground and then we do things with that + + + align:start position:0% +ground and then we do things with that +heat consume it as heat or turned into + + align:start position:0% +heat consume it as heat or turned into + + + align:start position:0% +heat consume it as heat or turned into +electricity etc our technology turns + + align:start position:0% +electricity etc our technology turns + + + align:start position:0% +electricity etc our technology turns +heat into electricity and so we start + + align:start position:0% +heat into electricity and so we start + + + align:start position:0% +heat into electricity and so we start +with photovoltaic cell you're all + + align:start position:0% +with photovoltaic cell you're all + + + align:start position:0% +with photovoltaic cell you're all +familiar with them you see them on + + align:start position:0% +familiar with them you see them on + + + align:start position:0% +familiar with them you see them on +buildings these days it wasn't that many + + align:start position:0% +buildings these days it wasn't that many + + + align:start position:0% +buildings these days it wasn't that many +years ago when folks really didn't even + + align:start position:0% +years ago when folks really didn't even + + + align:start position:0% +years ago when folks really didn't even +know what photovoltaic panels were + + align:start position:0% +know what photovoltaic panels were + + + align:start position:0% +know what photovoltaic panels were +because you didn't see him around it's + + align:start position:0% +because you didn't see him around it's + + + align:start position:0% +because you didn't see him around it's +quite remarkable in fact when I was just + + align:start position:0% +quite remarkable in fact when I was just + + + align:start position:0% +quite remarkable in fact when I was just +about getting ready to finish + + align:start position:0% +about getting ready to finish + + + align:start position:0% +about getting ready to finish +undergraduate work was just about the + + align:start position:0% +undergraduate work was just about the + + + align:start position:0% +undergraduate work was just about the +time that President Reagan took the + + align:start position:0% +time that President Reagan took the + + + align:start position:0% +time that President Reagan took the +solar panels off the White House now now + + align:start position:0% +solar panels off the White House now now + + + align:start position:0% +solar panels off the White House now now +they weren't they weren't solar electric + + align:start position:0% +they weren't they weren't solar electric + + + align:start position:0% +they weren't they weren't solar electric +panels they were just they were just hot + + align:start position:0% +panels they were just they were just hot + + + align:start position:0% +panels they were just they were just hot +water panels but clean energy wasn't it + + align:start position:0% +water panels but clean energy wasn't it + + + align:start position:0% +water panels but clean energy wasn't it +wasn't the primary focus of of too many + + align:start position:0% +wasn't the primary focus of of too many + + + align:start position:0% +wasn't the primary focus of of too many +folks at that point in time MIT actually + + align:start position:0% +folks at that point in time MIT actually + + + align:start position:0% +folks at that point in time MIT actually +in that timeframe had a solar house even + + align:start position:0% +in that timeframe had a solar house even + + + align:start position:0% +in that timeframe had a solar house even +sort of modern architecture lots of + + align:start position:0% +sort of modern architecture lots of + + + align:start position:0% +sort of modern architecture lots of +glass solar house that that later came + + align:start position:0% +glass solar house that that later came + + + align:start position:0% +glass solar house that that later came +down about 15 years later but now lots + + align:start position:0% +down about 15 years later but now lots + + + align:start position:0% +down about 15 years later but now lots +of things they're moving in that domain + + align:start position:0% +of things they're moving in that domain + + + align:start position:0% +of things they're moving in that domain +so we start with a photovoltaic cell + + align:start position:0% +so we start with a photovoltaic cell + + + align:start position:0% +so we start with a photovoltaic cell +you're familiar with the Sun bringing + + align:start position:0% +you're familiar with the Sun bringing + + + align:start position:0% +you're familiar with the Sun bringing +photons on the semiconductor material + + align:start position:0% +photons on the semiconductor material + + + align:start position:0% +photons on the semiconductor material +and making electricity there's another + + align:start position:0% +and making electricity there's another + + + align:start position:0% +and making electricity there's another +field called thermo photovoltaics or t + + align:start position:0% +field called thermo photovoltaics or t + + + align:start position:0% +field called thermo photovoltaics or t +PV where we have an intermediate body + + align:start position:0% +PV where we have an intermediate body + + + align:start position:0% +PV where we have an intermediate body +which receives the heat the heat can + + align:start position:0% +which receives the heat the heat can + + + align:start position:0% +which receives the heat the heat can +come from any conventional sources or + + align:start position:0% +come from any conventional sources or + + + align:start position:0% +come from any conventional sources or +solar and this this body at right now + + align:start position:0% +solar and this this body at right now + + + align:start position:0% +solar and this this body at right now +what we're doing is around a thousand + + align:start position:0% +what we're doing is around a thousand + + + align:start position:0% +what we're doing is around a thousand +degrees Celsius things start to glow red + + align:start position:0% +degrees Celsius things start to glow red + + + align:start position:0% +degrees Celsius things start to glow red +around 600 degrees Celsius it's very hot + + align:start position:0% +around 600 degrees Celsius it's very hot + + + align:start position:0% +around 600 degrees Celsius it's very hot +it radiates photons it glows red and and + + align:start position:0% +it radiates photons it glows red and and + + + align:start position:0% +it radiates photons it glows red and and +those photons and then convert + + align:start position:0% +those photons and then convert + + + align:start position:0% +those photons and then convert +electricity by photovoltaic cell so how + + align:start position:0% +electricity by photovoltaic cell so how + + + align:start position:0% +electricity by photovoltaic cell so how +many of you have heard of Planck's law + + align:start position:0% + + + + align:start position:0% + +okay so Planck's law was sort of the + + align:start position:0% +okay so Planck's law was sort of the + + + align:start position:0% +okay so Planck's law was sort of the +foundation of quantum mechanics and + + align:start position:0% +foundation of quantum mechanics and + + + align:start position:0% +foundation of quantum mechanics and +modern science in the twentieth century + + align:start position:0% +modern science in the twentieth century + + + align:start position:0% +modern science in the twentieth century +and and Planck's law tells you how many + + align:start position:0% +and and Planck's law tells you how many + + + align:start position:0% +and and Planck's law tells you how many +photons come off a heated surface + + align:start position:0% +photons come off a heated surface + + + align:start position:0% +photons come off a heated surface +and and what wavelength they are and so + + align:start position:0% +and and what wavelength they are and so + + + align:start position:0% +and and what wavelength they are and so +the photon flux the number of photons + + align:start position:0% +the photon flux the number of photons + + + align:start position:0% +the photon flux the number of photons +coming out off that surface is per + + align:start position:0% +coming out off that surface is per + + + align:start position:0% +coming out off that surface is per +square centimeters given by Planck's law + + align:start position:0% +square centimeters given by Planck's law + + + align:start position:0% +square centimeters given by Planck's law +and we represent that here 1x Planck's + + align:start position:0% +and we represent that here 1x Planck's + + + align:start position:0% +and we represent that here 1x Planck's +law and there were reasons that we + + align:start position:0% +law and there were reasons that we + + + align:start position:0% +law and there were reasons that we +thought that if you brought that real + + align:start position:0% +thought that if you brought that real + + + align:start position:0% +thought that if you brought that real +close you could do near-field coupling + + align:start position:0% +close you could do near-field coupling + + + align:start position:0% +close you could do near-field coupling +and you could exceed Planck's law and it + + align:start position:0% +and you could exceed Planck's law and it + + + align:start position:0% +and you could exceed Planck's law and it +was somewhat controversial in the + + align:start position:0% +was somewhat controversial in the + + + align:start position:0% +was somewhat controversial in the +beginning in fact in a meeting with + + align:start position:0% +beginning in fact in a meeting with + + + align:start position:0% +beginning in fact in a meeting with +Herman house who was a real powerhouse + + align:start position:0% +Herman house who was a real powerhouse + + + align:start position:0% +Herman house who was a real powerhouse +in electrical engineering and photonics + + align:start position:0% +in electrical engineering and photonics + + + align:start position:0% +in electrical engineering and photonics +fortunately passed away a few years ago + + align:start position:0% +fortunately passed away a few years ago + + + align:start position:0% +fortunately passed away a few years ago +the first time we came in his office + + align:start position:0% +the first time we came in his office + + + align:start position:0% +the first time we came in his office +with this he said forget it he said + + align:start position:0% +with this he said forget it he said + + + align:start position:0% +with this he said forget it he said +there's just there's no way to violate + + align:start position:0% +there's just there's no way to violate + + + align:start position:0% +there's just there's no way to violate +Planck's law and about an hour later he + + align:start position:0% +Planck's law and about an hour later he + + + align:start position:0% +Planck's law and about an hour later he +realized that we weren't really + + align:start position:0% +realized that we weren't really + + + align:start position:0% +realized that we weren't really +violating it that we were operating + + align:start position:0% +violating it that we were operating + + + align:start position:0% +violating it that we were operating +outside of the limits of applicability + + align:start position:0% +outside of the limits of applicability + + + align:start position:0% +outside of the limits of applicability +that Planck himself had put on the law + + align:start position:0% +that Planck himself had put on the law + + + align:start position:0% +that Planck himself had put on the law +Planck's law says that the the geometry + + align:start position:0% +Planck's law says that the the geometry + + + align:start position:0% +Planck's law says that the the geometry +of all the pieces of the system have to + + align:start position:0% +of all the pieces of the system have to + + + align:start position:0% +of all the pieces of the system have to +be large compared to the wavelength and + + align:start position:0% +be large compared to the wavelength and + + + align:start position:0% +be large compared to the wavelength and +one of the geometry metric piece of the + + align:start position:0% +one of the geometry metric piece of the + + + align:start position:0% +one of the geometry metric piece of the +system is the space between these two + + align:start position:0% +system is the space between these two + + + align:start position:0% +system is the space between these two +surfaces so literally the gap between + + align:start position:0% +surfaces so literally the gap between + + + align:start position:0% +surfaces so literally the gap between +the hot surface and the photovoltaic + + align:start position:0% +the hot surface and the photovoltaic + + + align:start position:0% +the hot surface and the photovoltaic +surface in Mt PV or micro gap thermo + + align:start position:0% +surface in Mt PV or micro gap thermo + + + align:start position:0% +surface in Mt PV or micro gap thermo +photovoltaic Swee put them very close + + align:start position:0% +photovoltaic Swee put them very close + + + align:start position:0% +photovoltaic Swee put them very close +together like 100 nanometers apart and + + align:start position:0% +together like 100 nanometers apart and + + + align:start position:0% +together like 100 nanometers apart and +or a tenth of a micron and and when you + + align:start position:0% +or a tenth of a micron and and when you + + + align:start position:0% +or a tenth of a micron and and when you +do that you get near field coupling and + + align:start position:0% +do that you get near field coupling and + + + align:start position:0% +do that you get near field coupling and +the photon flux and therefore the power + + align:start position:0% +the photon flux and therefore the power + + + align:start position:0% +the photon flux and therefore the power +out can dramatically go up by about an + + align:start position:0% +out can dramatically go up by about an + + + align:start position:0% +out can dramatically go up by about an +order of magnitude and so he said oh ok + + align:start position:0% +order of magnitude and so he said oh ok + + + align:start position:0% +order of magnitude and so he said oh ok +he said so you actually want to put the + + align:start position:0% +he said so you actually want to put the + + + align:start position:0% +he said so you actually want to put the +photovoltaic cell into the near field or + + align:start position:0% +photovoltaic cell into the near field or + + + align:start position:0% +photovoltaic cell into the near field or +evanescent field of this heated surface + + align:start position:0% +evanescent field of this heated surface + + + align:start position:0% +evanescent field of this heated surface +and he said yes exactly said ok well + + align:start position:0% +and he said yes exactly said ok well + + + align:start position:0% +and he said yes exactly said ok well +maybe you can do better than Planck's + + align:start position:0% +maybe you can do better than Planck's + + + align:start position:0% +maybe you can do better than Planck's +law and and so really this this is the + + align:start position:0% +law and and so really this this is the + + + align:start position:0% +law and and so really this this is the +field that we've been pioneering using + + align:start position:0% +field that we've been pioneering using + + + align:start position:0% +field that we've been pioneering using +this mechanism which basically derives + + align:start position:0% +this mechanism which basically derives + + + align:start position:0% +this mechanism which basically derives +from the fact that inside the hot body + + align:start position:0% +from the fact that inside the hot body + + + align:start position:0% +from the fact that inside the hot body +there are photons generated in every + + align:start position:0% +there are photons generated in every + + + align:start position:0% +there are photons generated in every +direction it's only the photons + + align:start position:0% +direction it's only the photons + + + align:start position:0% +direction it's only the photons +generated inside that come up to that + + align:start position:0% +generated inside that come up to that + + + align:start position:0% +generated inside that come up to that +surface normal to the surface or nearly + + align:start position:0% +surface normal to the surface or nearly + + + align:start position:0% +surface normal to the surface or nearly +normal to the surface + + align:start position:0% +normal to the surface + + + align:start position:0% +normal to the surface +that actually get out so in a hot body + + align:start position:0% +that actually get out so in a hot body + + + align:start position:0% +that actually get out so in a hot body +most of the photonic energy that's being + + align:start position:0% +most of the photonic energy that's being + + + align:start position:0% +most of the photonic energy that's being +generated all the time is trapped inside + + align:start position:0% +generated all the time is trapped inside + + + align:start position:0% +generated all the time is trapped inside +but if you bring a surface up close + + align:start position:0% +but if you bring a surface up close + + + align:start position:0% +but if you bring a surface up close +enough to it as those photons approach + + align:start position:0% +enough to it as those photons approach + + + align:start position:0% +enough to it as those photons approach +the surface they photon is as professor + + align:start position:0% +the surface they photon is as professor + + + align:start position:0% +the surface they photon is as professor +Haus pointed out actually has extent it + + align:start position:0% +Haus pointed out actually has extent it + + + align:start position:0% +Haus pointed out actually has extent it +has size of something on the order of + + align:start position:0% +has size of something on the order of + + + align:start position:0% +has size of something on the order of +the wavelength so we don't usually think + + align:start position:0% +the wavelength so we don't usually think + + + align:start position:0% +the wavelength so we don't usually think +of photons as having a size but they + + align:start position:0% +of photons as having a size but they + + + align:start position:0% +of photons as having a size but they +have an approximate size something like + + align:start position:0% +have an approximate size something like + + + align:start position:0% +have an approximate size something like +the wavelength the wavelength are + + align:start position:0% +the wavelength the wavelength are + + + align:start position:0% +the wavelength the wavelength are +working with is two microns the gap here + + align:start position:0% +working with is two microns the gap here + + + align:start position:0% +working with is two microns the gap here +is only 0.1 microns so this big two + + align:start position:0% +is only 0.1 microns so this big two + + + align:start position:0% +is only 0.1 microns so this big two +micron photon comes traveling up towards + + align:start position:0% +micron photon comes traveling up towards + + + align:start position:0% +micron photon comes traveling up towards +that surface and just goes right across + + align:start position:0% +that surface and just goes right across + + + align:start position:0% +that surface and just goes right across +this vacuum gap between the two surfaces + + align:start position:0% +this vacuum gap between the two surfaces + + + align:start position:0% +this vacuum gap between the two surfaces +enters affordable txl and then can + + align:start position:0% +enters affordable txl and then can + + + align:start position:0% +enters affordable txl and then can +become power so it's all the photons + + align:start position:0% +become power so it's all the photons + + + align:start position:0% +become power so it's all the photons +that are impinging upon the surface off + + align:start position:0% +that are impinging upon the surface off + + + align:start position:0% +that are impinging upon the surface off +normal that get into the photovoltaic + + align:start position:0% +normal that get into the photovoltaic + + + align:start position:0% +normal that get into the photovoltaic +cell here in our technology MT PV that + + align:start position:0% +cell here in our technology MT PV that + + + align:start position:0% +cell here in our technology MT PV that +do not get out of that hot body the trap + + align:start position:0% +do not get out of that hot body the trap + + + align:start position:0% +do not get out of that hot body the trap +side the hot body there and that's what + + align:start position:0% +side the hot body there and that's what + + + align:start position:0% +side the hot body there and that's what +causes this increase in power so why do + + align:start position:0% +causes this increase in power so why do + + + align:start position:0% +causes this increase in power so why do +we bother doing that we think that there + + align:start position:0% +we bother doing that we think that there + + + align:start position:0% +we bother doing that we think that there +are a number of places of application I + + align:start position:0% +are a number of places of application I + + + align:start position:0% +are a number of places of application I +think in the course you guys have + + align:start position:0% +think in the course you guys have + + + align:start position:0% +think in the course you guys have +contemplated that or about to complain a + + align:start position:0% +contemplated that or about to complain a + + + align:start position:0% +contemplated that or about to complain a +number of different sources of energy as + + align:start position:0% +number of different sources of energy as + + + align:start position:0% +number of different sources of energy as +well as uses of energy so one of the + + align:start position:0% +well as uses of energy so one of the + + + align:start position:0% +well as uses of energy so one of the +application domains is vehicles and + + align:start position:0% +application domains is vehicles and + + + align:start position:0% +application domains is vehicles and +we'll come back to this slide at the end + + align:start position:0% +we'll come back to this slide at the end + + + align:start position:0% +we'll come back to this slide at the end +to discuss in a little more detail the + + align:start position:0% +to discuss in a little more detail the + + + align:start position:0% +to discuss in a little more detail the +solar energy portable power industrial + + align:start position:0% +solar energy portable power industrial + + + align:start position:0% +solar energy portable power industrial +which is the first one that we're + + align:start position:0% +which is the first one that we're + + + align:start position:0% +which is the first one that we're +working on right now the other one not + + align:start position:0% +working on right now the other one not + + + align:start position:0% +working on right now the other one not +shown is building power co gen for a + + align:start position:0% +shown is building power co gen for a + + + align:start position:0% +shown is building power co gen for a +building like this so the first one is + + align:start position:0% +building like this so the first one is + + + align:start position:0% +building like this so the first one is +waste heat there is lots of waste heat + + align:start position:0% +waste heat there is lots of waste heat + + + align:start position:0% +waste heat there is lots of waste heat +in lots of places the the focus right + + align:start position:0% +in lots of places the the focus right + + + align:start position:0% +in lots of places the the focus right +now for our technology is industrial + + align:start position:0% +now for our technology is industrial + + + align:start position:0% +now for our technology is industrial +waste heat the kinds of things that you + + align:start position:0% +waste heat the kinds of things that you + + + align:start position:0% +waste heat the kinds of things that you +see in these pictures specifically a + + align:start position:0% +see in these pictures specifically a + + + align:start position:0% +see in these pictures specifically a +glass plan these are the basic modules + + align:start position:0% +glass plan these are the basic modules + + + align:start position:0% +glass plan these are the basic modules +these are the chips of which you saw a + + align:start position:0% +these are the chips of which you saw a + + + align:start position:0% +these are the chips of which you saw a +schematic a moment ago so there's the + + align:start position:0% +schematic a moment ago so there's the + + + align:start position:0% +schematic a moment ago so there's the +this is actually a chip stack each each + + align:start position:0% +this is actually a chip stack each each + + + align:start position:0% +this is actually a chip stack each each +one of these is a pair of chips the hot + + align:start position:0% +one of these is a pair of chips the hot + + + align:start position:0% +one of these is a pair of chips the hot +chip and then below it the cold + + align:start position:0% +chip and then below it the cold + + + align:start position:0% +chip and then below it the cold +affordable + + align:start position:0% +affordable + + + align:start position:0% +affordable +so we build them into arrays and then we + + align:start position:0% +so we build them into arrays and then we + + + align:start position:0% +so we build them into arrays and then we +take these modules and we build those + + align:start position:0% +take these modules and we build those + + + align:start position:0% +take these modules and we build those +into arrays like this where we have a + + align:start position:0% +into arrays like this where we have a + + + align:start position:0% +into arrays like this where we have a +housing on the outside and then the + + align:start position:0% +housing on the outside and then the + + + align:start position:0% +housing on the outside and then the +chips go on a mounting and control + + align:start position:0% +chips go on a mounting and control + + + align:start position:0% +chips go on a mounting and control +substructure if you will which is + + align:start position:0% +substructure if you will which is + + + align:start position:0% +substructure if you will which is +mounted inside of this hollow housing so + + align:start position:0% +mounted inside of this hollow housing so + + + align:start position:0% +mounted inside of this hollow housing so +the hollow housing protects from the + + align:start position:0% +the hollow housing protects from the + + + align:start position:0% +the hollow housing protects from the +outside combustion gases etc allows the + + align:start position:0% +outside combustion gases etc allows the + + + align:start position:0% +outside combustion gases etc allows the +heat to go through the surface into the + + align:start position:0% +heat to go through the surface into the + + + align:start position:0% +heat to go through the surface into the +chips makes electricity that's it it's a + + align:start position:0% +chips makes electricity that's it it's a + + + align:start position:0% +chips makes electricity that's it it's a +very modular technology and and that's + + align:start position:0% +very modular technology and and that's + + + align:start position:0% +very modular technology and and that's +one of the one of the promises of it + + align:start position:0% +one of the one of the promises of it + + + align:start position:0% +one of the one of the promises of it +that it can be deployed we call it kind + + align:start position:0% +that it can be deployed we call it kind + + + align:start position:0% +that it can be deployed we call it kind +of non-invasive and you've talked about + + align:start position:0% +of non-invasive and you've talked about + + + align:start position:0% +of non-invasive and you've talked about +disruptive technology some in the class + + align:start position:0% +disruptive technology some in the class + + + align:start position:0% +disruptive technology some in the class +which has become an important + + align:start position:0% +which has become an important + + + align:start position:0% +which has become an important +understanding in the business of + + align:start position:0% +understanding in the business of + + + align:start position:0% +understanding in the business of +bringing all technology and not even + + align:start position:0% +bringing all technology and not even + + + align:start position:0% +bringing all technology and not even +just pickup of products to market and + + align:start position:0% +just pickup of products to market and + + + align:start position:0% +just pickup of products to market and +the idea of disruptive technology is the + + align:start position:0% +the idea of disruptive technology is the + + + align:start position:0% +the idea of disruptive technology is the +new technology comes along and it's not + + align:start position:0% +new technology comes along and it's not + + + align:start position:0% +new technology comes along and it's not +very good technically compared to sort + + align:start position:0% +very good technically compared to sort + + + align:start position:0% +very good technically compared to sort +of the incumbents that are on the market + + align:start position:0% +of the incumbents that are on the market + + + align:start position:0% +of the incumbents that are on the market +but it finds a niche where it can + + align:start position:0% +but it finds a niche where it can + + + align:start position:0% +but it finds a niche where it can +perform often the niche is called non + + align:start position:0% +perform often the niche is called non + + + align:start position:0% +perform often the niche is called non +competition so developing a proc you + + align:start position:0% +competition so developing a proc you + + + align:start position:0% +competition so developing a proc you +look for a place where there is no + + align:start position:0% +look for a place where there is no + + + align:start position:0% +look for a place where there is no +competition and this is an example of a + + align:start position:0% +competition and this is an example of a + + + align:start position:0% +competition and this is an example of a +place where there is no competition this + + align:start position:0% +place where there is no competition this + + + align:start position:0% +place where there is no competition this +sits outside a coal mine coal mines + + align:start position:0% +sits outside a coal mine coal mines + + + align:start position:0% +sits outside a coal mine coal mines +nowadays they go down on the ground and + + align:start position:0% +nowadays they go down on the ground and + + + align:start position:0% +nowadays they go down on the ground and +then the coma and then at the front you + + align:start position:0% +then the coma and then at the front you + + + align:start position:0% +then the coma and then at the front you +know the digging front if you will the + + align:start position:0% +know the digging front if you will the + + + align:start position:0% +know the digging front if you will the +interface between the air and the mind + + align:start position:0% +interface between the air and the mind + + + align:start position:0% +interface between the air and the mind +and the coal that's still on the ground + + align:start position:0% +and the coal that's still on the ground + + + align:start position:0% +and the coal that's still on the ground +comes down and then proceeds + + align:start position:0% +comes down and then proceeds + + + align:start position:0% +comes down and then proceeds +horizontally and one of the issues with + + align:start position:0% +horizontally and one of the issues with + + + align:start position:0% +horizontally and one of the issues with +coal mines as who is there anybody that + + align:start position:0% +coal mines as who is there anybody that + + + align:start position:0% +coal mines as who is there anybody that +has not heard of a let's see how do we + + align:start position:0% +has not heard of a let's see how do we + + + align:start position:0% +has not heard of a let's see how do we +want to asset has anyone heard of a coal + + align:start position:0% +want to asset has anyone heard of a coal + + + align:start position:0% +want to asset has anyone heard of a coal +mine explosion raise your hand okay so + + align:start position:0% +mine explosion raise your hand okay so + + + align:start position:0% +mine explosion raise your hand okay so +most folks have heard of coal mine + + align:start position:0% +most folks have heard of coal mine + + + align:start position:0% +most folks have heard of coal mine +explosion so why the coal mines explode + + align:start position:0% +explosion so why the coal mines explode + + + align:start position:0% +explosion so why the coal mines explode +any guesses + + align:start position:0% + + + + align:start position:0% + +please + + align:start position:0% +please + + + align:start position:0% +please +yeah trapped methane exactly + + align:start position:0% +yeah trapped methane exactly + + + align:start position:0% +yeah trapped methane exactly +whenever you're digging up coal you also + + align:start position:0% +whenever you're digging up coal you also + + + align:start position:0% +whenever you're digging up coal you also +liberate trap nothing natural gas very + + align:start position:0% +liberate trap nothing natural gas very + + + align:start position:0% +liberate trap nothing natural gas very +explosive and so they go through lots of + + align:start position:0% +explosive and so they go through lots of + + + align:start position:0% +explosive and so they go through lots of +ways of controlling the methane content + + align:start position:0% +ways of controlling the methane content + + + align:start position:0% +ways of controlling the methane content +and air so that the coal mine doesn't + + align:start position:0% +and air so that the coal mine doesn't + + + align:start position:0% +and air so that the coal mine doesn't +blow up but they do blow up sometime and + + align:start position:0% +blow up but they do blow up sometime and + + + align:start position:0% +blow up but they do blow up sometime and +so what people have started to do is + + align:start position:0% +so what people have started to do is + + + align:start position:0% +so what people have started to do is +drill down in front of the coal mine + + align:start position:0% +drill down in front of the coal mine + + + align:start position:0% +drill down in front of the coal mine +this this vertical face that's coming + + align:start position:0% +this this vertical face that's coming + + + align:start position:0% +this this vertical face that's coming +horizontally under the ground they drill + + align:start position:0% +horizontally under the ground they drill + + + align:start position:0% +horizontally under the ground they drill +down into it like this and they liberate + + align:start position:0% +down into it like this and they liberate + + + align:start position:0% +down into it like this and they liberate +the methane in front of that and and + + align:start position:0% +the methane in front of that and and + + + align:start position:0% +the methane in front of that and and +then what do they do with the methane + + align:start position:0% +then what do they do with the methane + + + align:start position:0% +then what do they do with the methane +well this is what they do with the + + align:start position:0% +well this is what they do with the + + + align:start position:0% +well this is what they do with the +methane believe it or not often times I + + align:start position:0% +methane believe it or not often times I + + + align:start position:0% +methane believe it or not often times I +mean if it's big enough its if it's + + align:start position:0% +mean if it's big enough its if it's + + + align:start position:0% +mean if it's big enough its if it's +stable enough then they will actually + + align:start position:0% +stable enough then they will actually + + + align:start position:0% +stable enough then they will actually +you know feed it into a combined cycle + + align:start position:0% +you know feed it into a combined cycle + + + align:start position:0% +you know feed it into a combined cycle +or some type of combustion system to + + align:start position:0% +or some type of combustion system to + + + align:start position:0% +or some type of combustion system to +make electricity but first of all the + + align:start position:0% +make electricity but first of all the + + + align:start position:0% +make electricity but first of all the +coal mine front is moving and steam + + align:start position:0% +coal mine front is moving and steam + + + align:start position:0% +coal mine front is moving and steam +turbines don't like to be moved and so + + align:start position:0% +turbines don't like to be moved and so + + + align:start position:0% +turbines don't like to be moved and so +that's why you see this very portable + + align:start position:0% +that's why you see this very portable + + + align:start position:0% +that's why you see this very portable +looking infrastructure here that they + + align:start position:0% +looking infrastructure here that they + + + align:start position:0% +looking infrastructure here that they +actually move it as the coal mine is + + align:start position:0% +actually move it as the coal mine is + + + align:start position:0% +actually move it as the coal mine is +moving and what they need to do is they + + align:start position:0% +moving and what they need to do is they + + + align:start position:0% +moving and what they need to do is they +just need to destroy the methane so so + + align:start position:0% +just need to destroy the methane so so + + + align:start position:0% +just need to destroy the methane so so +here is methane being destroyed in that + + align:start position:0% +here is methane being destroyed in that + + + align:start position:0% +here is methane being destroyed in that +inner pipe there and and the idea is to + + align:start position:0% +inner pipe there and and the idea is to + + + align:start position:0% +inner pipe there and and the idea is to +just take panels like this and to run + + align:start position:0% +just take panels like this and to run + + + align:start position:0% +just take panels like this and to run +them down the middle of that tube and to + + align:start position:0% +them down the middle of that tube and to + + + align:start position:0% +them down the middle of that tube and to +turn that into electricity and you know + + align:start position:0% +turn that into electricity and you know + + + align:start position:0% +turn that into electricity and you know +so no one's really doing this right now + + align:start position:0% +so no one's really doing this right now + + + align:start position:0% +so no one's really doing this right now +because of some of the reasons cited you + + align:start position:0% +because of some of the reasons cited you + + + align:start position:0% +because of some of the reasons cited you +know you could do it with wood so maybe + + align:start position:0% +know you could do it with wood so maybe + + + align:start position:0% +know you could do it with wood so maybe +we should ask why so you guys some of + + align:start position:0% +we should ask why so you guys some of + + + align:start position:0% +we should ask why so you guys some of +you familiar with steam turbines or okay + + align:start position:0% +you familiar with steam turbines or okay + + + align:start position:0% +you familiar with steam turbines or okay +alright so you could imagine putting + + align:start position:0% +alright so you could imagine putting + + + align:start position:0% +alright so you could imagine putting +condensers in here gathering steam and + + align:start position:0% +condensers in here gathering steam and + + + align:start position:0% +condensers in here gathering steam and +running steam turbines in making + + align:start position:0% +running steam turbines in making + + + align:start position:0% +running steam turbines in making +electricity and but if the idea is if + + align:start position:0% +electricity and but if the idea is if + + + align:start position:0% +electricity and but if the idea is if +you had a module sort of like a + + align:start position:0% +you had a module sort of like a + + + align:start position:0% +you had a module sort of like a +photovoltaic module but made our high + + align:start position:0% +photovoltaic module but made our high + + + align:start position:0% +photovoltaic module but made our high +temperature materials that you could put + + align:start position:0% +temperature materials that you could put + + + align:start position:0% +temperature materials that you could put +in it easily move that would be + + align:start position:0% +in it easily move that would be + + + align:start position:0% +in it easily move that would be +preferable and and the reason that this + + align:start position:0% +preferable and and the reason that this + + + align:start position:0% +preferable and and the reason that this +is sitting here in this picture the way + + align:start position:0% +is sitting here in this picture the way + + + align:start position:0% +is sitting here in this picture the way +it is is because the steam turbines are + + align:start position:0% +it is is because the steam turbines are + + + align:start position:0% +it is is because the steam turbines are +not feasible now and so what we're going + + align:start position:0% +not feasible now and so what we're going + + + align:start position:0% +not feasible now and so what we're going +this this is an example of non + + align:start position:0% +this this is an example of non + + + align:start position:0% +this this is an example of non +competition in the energy space and + + align:start position:0% +competition in the energy space and + + + align:start position:0% +competition in the energy space and +clean energy space in particular because + + align:start position:0% +clean energy space in particular because + + + align:start position:0% +clean energy space in particular because +you know it would be a way of making + + align:start position:0% +you know it would be a way of making + + + align:start position:0% +you know it would be a way of making +electricity with zero net emissions + + align:start position:0% +electricity with zero net emissions + + + align:start position:0% +electricity with zero net emissions +relative to the status quo I mean this + + align:start position:0% +relative to the status quo I mean this + + + align:start position:0% +relative to the status quo I mean this +is the status quo so those emissions are + + align:start position:0% +is the status quo so those emissions are + + + align:start position:0% +is the status quo so those emissions are +going out anyways if some of the heat + + align:start position:0% +going out anyways if some of the heat + + + align:start position:0% +going out anyways if some of the heat +can make electricity that electricity's + + align:start position:0% +can make electricity that electricity's + + + align:start position:0% +can make electricity that electricity's +zero net emissions so this is an example + + align:start position:0% +zero net emissions so this is an example + + + align:start position:0% +zero net emissions so this is an example +of non competition we go after that we + + align:start position:0% +of non competition we go after that we + + + align:start position:0% +of non competition we go after that we +could not compete against GES gas + + align:start position:0% +could not compete against GES gas + + + align:start position:0% +could not compete against GES gas +turbines right now the performance of + + align:start position:0% +turbines right now the performance of + + + align:start position:0% +turbines right now the performance of +our units are not good enough to do that + + align:start position:0% +our units are not good enough to do that + + + align:start position:0% +our units are not good enough to do that +but they are good enough to do this in + + align:start position:0% +but they are good enough to do this in + + + align:start position:0% +but they are good enough to do this in +in the near term and just as the + + align:start position:0% +in the near term and just as the + + + align:start position:0% +in the near term and just as the +original integrated circuit chips when + + align:start position:0% +original integrated circuit chips when + + + align:start position:0% +original integrated circuit chips when +they first came out they didn't + + align:start position:0% +they first came out they didn't + + + align:start position:0% +they first came out they didn't +immediately displace tubes but they got + + align:start position:0% +immediately displace tubes but they got + + + align:start position:0% +immediately displace tubes but they got +better and they got better and I think + + align:start position:0% +better and they got better and I think + + + align:start position:0% +better and they got better and I think +Hyrum talked about the disruptive + + align:start position:0% +Hyrum talked about the disruptive + + + align:start position:0% +Hyrum talked about the disruptive +example of the Sony radio you know there + + align:start position:0% +example of the Sony radio you know there + + + align:start position:0% +example of the Sony radio you know there +were still tubes and radios for some + + align:start position:0% +were still tubes and radios for some + + + align:start position:0% +were still tubes and radios for some +amount of time after those chips were in + + align:start position:0% +amount of time after those chips were in + + + align:start position:0% +amount of time after those chips were in +those tiny little radios and so you + + align:start position:0% +those tiny little radios and so you + + + align:start position:0% +those tiny little radios and so you +could kind of view our chips as an + + align:start position:0% +could kind of view our chips as an + + + align:start position:0% +could kind of view our chips as an +analog to those chips and those + + align:start position:0% +analog to those chips and those + + + align:start position:0% +analog to those chips and those +transistors and this is an application + + align:start position:0% +transistors and this is an application + + + align:start position:0% +transistors and this is an application +to the transistor radio you know there + + align:start position:0% +to the transistor radio you know there + + + align:start position:0% +to the transistor radio you know there +the transistor radio had to be able to + + align:start position:0% +the transistor radio had to be able to + + + align:start position:0% +the transistor radio had to be able to +move into kids bedroom etc here it has + + align:start position:0% +move into kids bedroom etc here it has + + + align:start position:0% +move into kids bedroom etc here it has +to be able to move with the front of it + + align:start position:0% +to be able to move with the front of it + + + align:start position:0% +to be able to move with the front of it +yeah of a coal mine + + align:start position:0% +yeah of a coal mine + + + align:start position:0% +yeah of a coal mine +another application similar is + + align:start position:0% +another application similar is + + + align:start position:0% +another application similar is +combusting volatile organics as they're + + align:start position:0% +combusting volatile organics as they're + + + align:start position:0% +combusting volatile organics as they're +loaded on and off of ships so in the + + align:start position:0% +loaded on and off of ships so in the + + + align:start position:0% +loaded on and off of ships so in the +back here as a harbor this is done in + + align:start position:0% +back here as a harbor this is done in + + + align:start position:0% +back here as a harbor this is done in +Houston and the very back you can + + align:start position:0% +Houston and the very back you can + + + align:start position:0% +Houston and the very back you can +actually see a little tiny flare which + + align:start position:0% +actually see a little tiny flare which + + + align:start position:0% +actually see a little tiny flare which +basically a flame sticking out a pipe + + align:start position:0% +basically a flame sticking out a pipe + + + align:start position:0% +basically a flame sticking out a pipe +which is the older way of doing these + + align:start position:0% +which is the older way of doing these + + + align:start position:0% +which is the older way of doing these +things in which people have tried to + + align:start position:0% +things in which people have tried to + + + align:start position:0% +things in which people have tried to +eliminate because flaring of you know + + align:start position:0% +eliminate because flaring of you know + + + align:start position:0% +eliminate because flaring of you know +flaring of natural gas reduces the + + align:start position:0% +flaring of natural gas reduces the + + + align:start position:0% +flaring of natural gas reduces the +greenhouse impact by about a factor of + + align:start position:0% +greenhouse impact by about a factor of + + + align:start position:0% +greenhouse impact by about a factor of +20 so if you have natural gas and you + + align:start position:0% +20 so if you have natural gas and you + + + align:start position:0% +20 so if you have natural gas and you +just vent it to the atmosphere and you + + align:start position:0% +just vent it to the atmosphere and you + + + align:start position:0% +just vent it to the atmosphere and you +compare that with burning the natural + + align:start position:0% +compare that with burning the natural + + + align:start position:0% +compare that with burning the natural +gas before you vent it you reduce this + + align:start position:0% +gas before you vent it you reduce this + + + align:start position:0% +gas before you vent it you reduce this +global warming impact by a factor of 20 + + align:start position:0% +global warming impact by a factor of 20 + + + align:start position:0% +global warming impact by a factor of 20 +by burning it so in a way flares are a + + align:start position:0% +by burning it so in a way flares are a + + + align:start position:0% +by burning it so in a way flares are a +big advance on just venting natural gas + + align:start position:0% +big advance on just venting natural gas + + + align:start position:0% +big advance on just venting natural gas +but flares have their own pollution + + align:start position:0% +but flares have their own pollution + + + align:start position:0% +but flares have their own pollution +issues and so what has become prevalent + + align:start position:0% +issues and so what has become prevalent + + + align:start position:0% +issues and so what has become prevalent +particularly in the most developed + + align:start position:0% +particularly in the most developed + + + align:start position:0% +particularly in the most developed +countries at least enclosed flares so + + align:start position:0% +countries at least enclosed flares so + + + align:start position:0% +countries at least enclosed flares so +this is a stack basically and + + align:start position:0% +this is a stack basically and + + + align:start position:0% +this is a stack basically and +and it encloses a flare like this flame + + align:start position:0% +and it encloses a flare like this flame + + + align:start position:0% +and it encloses a flare like this flame +so as the ships are off are loaded here + + align:start position:0% +so as the ships are off are loaded here + + + align:start position:0% +so as the ships are off are loaded here +the volatile gases that fill the tanks + + align:start position:0% +the volatile gases that fill the tanks + + + align:start position:0% +the volatile gases that fill the tanks +before the liquid goes in gets pushed + + align:start position:0% +before the liquid goes in gets pushed + + + align:start position:0% +before the liquid goes in gets pushed +out and it has to go somewhere so it + + align:start position:0% +out and it has to go somewhere so it + + + align:start position:0% +out and it has to go somewhere so it +doesn't explode and where does it go it + + align:start position:0% +doesn't explode and where does it go it + + + align:start position:0% +doesn't explode and where does it go it +goes to this right here it gets burned + + align:start position:0% +goes to this right here it gets burned + + + align:start position:0% +goes to this right here it gets burned +and that he is just liberated and so we + + align:start position:0% +and that he is just liberated and so we + + + align:start position:0% +and that he is just liberated and so we +are working with a vendor that would put + + align:start position:0% +are working with a vendor that would put + + + align:start position:0% +are working with a vendor that would put +our panels right across this tube right + + align:start position:0% +our panels right across this tube right + + + align:start position:0% +our panels right across this tube right +in this flame to convert that heat into + + align:start position:0% +in this flame to convert that heat into + + + align:start position:0% +in this flame to convert that heat into +electricity so it's another example of + + align:start position:0% +electricity so it's another example of + + + align:start position:0% +electricity so it's another example of +of non consumption these things are + + align:start position:0% +of non consumption these things are + + + align:start position:0% +of non consumption these things are +running all the time and and and that + + align:start position:0% +running all the time and and and that + + + align:start position:0% +running all the time and and and that +heat is not being used because there's + + align:start position:0% +heat is not being used because there's + + + align:start position:0% +heat is not being used because there's +no good way to do it right now and this + + align:start position:0% +no good way to do it right now and this + + + align:start position:0% +no good way to do it right now and this +is just another example the same module + + align:start position:0% +is just another example the same module + + + align:start position:0% +is just another example the same module +that you saw bigger panels this is the + + align:start position:0% +that you saw bigger panels this is the + + + align:start position:0% +that you saw bigger panels this is the +kind of panel that might go into a glass + + align:start position:0% +kind of panel that might go into a glass + + + align:start position:0% +kind of panel that might go into a glass +factory which is depicted here so + + align:start position:0% +factory which is depicted here so + + + align:start position:0% +factory which is depicted here so +natural gas comes in here it burns it + + align:start position:0% +natural gas comes in here it burns it + + + align:start position:0% +natural gas comes in here it burns it +melts sand and lime in things which get + + align:start position:0% +melts sand and lime in things which get + + + align:start position:0% +melts sand and lime in things which get +pushed into this big furnace with + + align:start position:0% +pushed into this big furnace with + + + align:start position:0% +pushed into this big furnace with +bulldozers literally it's quite amazing + + align:start position:0% +bulldozers literally it's quite amazing + + + align:start position:0% +bulldozers literally it's quite amazing +and they melt it and it becomes like + + align:start position:0% +and they melt it and it becomes like + + + align:start position:0% +and they melt it and it becomes like +volcano lava sort of in here it's + + align:start position:0% +volcano lava sort of in here it's + + + align:start position:0% +volcano lava sort of in here it's +actually glass and then out the other + + align:start position:0% +actually glass and then out the other + + + align:start position:0% +actually glass and then out the other +end it flows down and becomes plate + + align:start position:0% +end it flows down and becomes plate + + + align:start position:0% +end it flows down and becomes plate +glass like for the windows up there etc + + align:start position:0% +glass like for the windows up there etc + + + align:start position:0% +glass like for the windows up there etc +and so this is the exhaust duct the + + align:start position:0% +and so this is the exhaust duct the + + + align:start position:0% +and so this is the exhaust duct the +exhaust comes up here and right now + + align:start position:0% +exhaust comes up here and right now + + + align:start position:0% +exhaust comes up here and right now +these these furnace the type a type of + + align:start position:0% +these these furnace the type a type of + + + align:start position:0% +these these furnace the type a type of +furnace called oxy fuel furnaces where + + align:start position:0% +furnace called oxy fuel furnaces where + + + align:start position:0% +furnace called oxy fuel furnaces where +oxygen is taken out of the air and put + + align:start position:0% +oxygen is taken out of the air and put + + + align:start position:0% +oxygen is taken out of the air and put +into the furnace + + align:start position:0% +into the furnace + + + align:start position:0% +into the furnace +they create the heat that heat just goes + + align:start position:0% +they create the heat that heat just goes + + + align:start position:0% +they create the heat that heat just goes +up the stacks our panels would go in + + align:start position:0% +up the stacks our panels would go in + + + align:start position:0% +up the stacks our panels would go in +there and convert that to electricity + + align:start position:0% +there and convert that to electricity + + + align:start position:0% +there and convert that to electricity +that's actually the first the first + + align:start position:0% +that's actually the first the first + + + align:start position:0% +that's actually the first the first +application that we have that we are + + align:start position:0% +application that we have that we are + + + align:start position:0% +application that we have that we are +working on developing so I'm thinking + + align:start position:0% +working on developing so I'm thinking + + + align:start position:0% +working on developing so I'm thinking +about pausing at some point and and I + + align:start position:0% +about pausing at some point and and I + + + align:start position:0% +about pausing at some point and and I +guess one question is how many of you + + align:start position:0% +guess one question is how many of you + + + align:start position:0% +guess one question is how many of you +are not electrical engineers okay + + align:start position:0% +are not electrical engineers okay + + + align:start position:0% +are not electrical engineers okay +okay how many of you are not chemical + + align:start position:0% +okay how many of you are not chemical + + + align:start position:0% +okay how many of you are not chemical +engineers okay and how many of you are + + align:start position:0% +engineers okay and how many of you are + + + align:start position:0% +engineers okay and how many of you are +not mechanical engineers how many of you + + align:start position:0% +not mechanical engineers how many of you + + + align:start position:0% +not mechanical engineers how many of you +are bio folks okay all right okay and I + + align:start position:0% +are bio folks okay all right okay and I + + + align:start position:0% +are bio folks okay all right okay and I +know we have some dust bins and Poli Sci + + align:start position:0% +know we have some dust bins and Poli Sci + + + align:start position:0% +know we have some dust bins and Poli Sci +folks and and ocean engineer for cetera + + align:start position:0% +folks and and ocean engineer for cetera + + + align:start position:0% +folks and and ocean engineer for cetera +so okay so this right here is an actual + + align:start position:0% +so okay so this right here is an actual + + + align:start position:0% +so okay so this right here is an actual +picture of the same kind of furnace that + + align:start position:0% +picture of the same kind of furnace that + + + align:start position:0% +picture of the same kind of furnace that +you saw actually the exhaust port of it + + align:start position:0% +you saw actually the exhaust port of it + + + align:start position:0% +you saw actually the exhaust port of it +and this is the same kind of housing + + align:start position:0% +and this is the same kind of housing + + + align:start position:0% +and this is the same kind of housing +that you saw and this is some initial + + align:start position:0% +that you saw and this is some initial + + + align:start position:0% +that you saw and this is some initial +testing that we were doing moving the + + align:start position:0% +testing that we were doing moving the + + + align:start position:0% +testing that we were doing moving the +panels in and out of this facility this + + align:start position:0% +panels in and out of this facility this + + + align:start position:0% +panels in and out of this facility this +is an earlier version before we came to + + align:start position:0% +is an earlier version before we came to + + + align:start position:0% +is an earlier version before we came to +this what we call product platform which + + align:start position:0% +this what we call product platform which + + + align:start position:0% +this what we call product platform which +is the basic architecture that we've + + align:start position:0% +is the basic architecture that we've + + + align:start position:0% +is the basic architecture that we've +been talking about to date sure sure + + align:start position:0% +been talking about to date sure sure + + + align:start position:0% +been talking about to date sure sure +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +I'd be happy to do that yeah I kind of + + align:start position:0% +I'd be happy to do that yeah I kind of + + + align:start position:0% +I'd be happy to do that yeah I kind of +got interested in this kind of market + + align:start position:0% +got interested in this kind of market + + + align:start position:0% +got interested in this kind of market +here and how many of you think you might + + align:start position:0% +here and how many of you think you might + + + align:start position:0% +here and how many of you think you might +someday start a company or be part of + + align:start position:0% +someday start a company or be part of + + + align:start position:0% +someday start a company or be part of +starting a company wow that's that's a + + align:start position:0% +starting a company wow that's that's a + + + align:start position:0% +starting a company wow that's that's a +lot that's that's more than well more + + align:start position:0% +lot that's that's more than well more + + + align:start position:0% +lot that's that's more than well more +than half the class okay + + align:start position:0% + + + + align:start position:0% + +so what are some of the ideas you're + + align:start position:0% +so what are some of the ideas you're + + + align:start position:0% +so what are some of the ideas you're +thinking about just to get a few + + align:start position:0% +thinking about just to get a few + + + align:start position:0% +thinking about just to get a few +examples on the table + + align:start position:0% +examples on the table + + + align:start position:0% +examples on the table +Samuel so the thermal fuels so building + + align:start position:0% +Samuel so the thermal fuels so building + + + align:start position:0% +Samuel so the thermal fuels so building +like liquid or gaseous fuels out of + + align:start position:0% +like liquid or gaseous fuels out of + + + align:start position:0% +like liquid or gaseous fuels out of +solar thermal energy or okay okay so the + + align:start position:0% +solar thermal energy or okay okay so the + + + align:start position:0% +solar thermal energy or okay okay so the +like artificial photosynthesis okay all + + align:start position:0% +like artificial photosynthesis okay all + + + align:start position:0% +like artificial photosynthesis okay all +right cool + + align:start position:0% +right cool + + + align:start position:0% +right cool +somebody else a lot of hands went up for + + align:start position:0% +somebody else a lot of hands went up for + + + align:start position:0% +somebody else a lot of hands went up for +starting companies including energy + + align:start position:0% +starting companies including energy + + + align:start position:0% +starting companies including energy +companies well come on + + align:start position:0% +companies well come on + + + align:start position:0% +companies well come on +yes max'll biotechnology okay can you + + align:start position:0% +yes max'll biotechnology okay can you + + + align:start position:0% +yes max'll biotechnology okay can you +say in in the energy context there are + + align:start position:0% +say in in the energy context there are + + + align:start position:0% +say in in the energy context there are +different than that in the energy + + align:start position:0% +different than that in the energy + + + align:start position:0% +different than that in the energy +probably not okay what what what realm + + align:start position:0% +probably not okay what what what realm + + + align:start position:0% +probably not okay what what what realm +medicine or okay okay + + align:start position:0% +medicine or okay okay + + + align:start position:0% +medicine or okay okay +okay someone else either energy or not + + align:start position:0% +okay someone else either energy or not + + + align:start position:0% +okay someone else either energy or not +energy let's see who else had their + + align:start position:0% +energy let's see who else had their + + + align:start position:0% +energy let's see who else had their +hands up engineers are so something + + align:start position:0% +hands up engineers are so something + + + align:start position:0% +hands up engineers are so something +engaging + + align:start position:0% + + + + align:start position:0% + +I love them I spend my whole life with + + align:start position:0% +I love them I spend my whole life with + + + align:start position:0% +I love them I spend my whole life with +them so what else even be not interested + + align:start position:0% +them so what else even be not interested + + + align:start position:0% +them so what else even be not interested +in it yourself something you know that + + align:start position:0% +in it yourself something you know that + + + align:start position:0% +in it yourself something you know that +somebody else might start Christopher so + + align:start position:0% +somebody else might start Christopher so + + + align:start position:0% +somebody else might start Christopher so +then that fertilizer would go into the + + align:start position:0% +then that fertilizer would go into the + + + align:start position:0% +then that fertilizer would go into the +food food production then that so that + + align:start position:0% +food food production then that so that + + + align:start position:0% +food food production then that so that +is a really cool solution to to having + + align:start position:0% +is a really cool solution to to having + + + align:start position:0% +is a really cool solution to to having +the ship you know build big grids and + + align:start position:0% +the ship you know build big grids and + + + align:start position:0% +the ship you know build big grids and +ship the power so there's wind in Iowa + + align:start position:0% +ship the power so there's wind in Iowa + + + align:start position:0% +ship the power so there's wind in Iowa +and there are farms in Iowa wow that's + + align:start position:0% +and there are farms in Iowa wow that's + + + align:start position:0% +and there are farms in Iowa wow that's +neat it's not somebody else all right + + align:start position:0% +neat it's not somebody else all right + + + align:start position:0% +neat it's not somebody else all right +let's see so who has not who was + + align:start position:0% +let's see so who has not who was + + + align:start position:0% +let's see so who has not who was +thinking who is not thinking about + + align:start position:0% +thinking who is not thinking about + + + align:start position:0% +thinking who is not thinking about +starting a business + + align:start position:0% + + + + align:start position:0% + +all right so do you mind if I just call + + align:start position:0% +all right so do you mind if I just call + + + align:start position:0% +all right so do you mind if I just call +in a couple of you to say what you're + + align:start position:0% +in a couple of you to say what you're + + + align:start position:0% +in a couple of you to say what you're +thinking about Latifah but you think you + + align:start position:0% +thinking about Latifah but you think you + + + align:start position:0% +thinking about Latifah but you think you +might start a business okay okay + + align:start position:0% +might start a business okay okay + + + align:start position:0% +might start a business okay okay +yes Scott okay that's important + + align:start position:0% +yes Scott okay that's important + + + align:start position:0% +yes Scott okay that's important +yes first name + + align:start position:0% + + + + align:start position:0% + +and actually understood how things work + + align:start position:0% +and actually understood how things work + + + align:start position:0% +and actually understood how things work +in reality they didn't at that point + + align:start position:0% +in reality they didn't at that point + + + align:start position:0% +in reality they didn't at that point +you're the idea that you thought that + + align:start position:0% +you're the idea that you thought that + + + align:start position:0% +you're the idea that you thought that +was good it wasn't make makes a lot of + + align:start position:0% +was good it wasn't make makes a lot of + + + align:start position:0% +was good it wasn't make makes a lot of +sense absolutely right + + align:start position:0% +sense absolutely right + + + align:start position:0% +sense absolutely right +it's the idea and everything else it + + align:start position:0% +it's the idea and everything else it + + + align:start position:0% +it's the idea and everything else it +takes to turn that into a product doing + + align:start position:0% +takes to turn that into a product doing + + + align:start position:0% +takes to turn that into a product doing +something useful for people in the real + + align:start position:0% +something useful for people in the real + + + align:start position:0% +something useful for people in the real +world okay + + align:start position:0% + + + + align:start position:0% + +one more input just to have a little + + align:start position:0% +one more input just to have a little + + + align:start position:0% +one more input just to have a little +collection that puts one more anyone + + align:start position:0% +collection that puts one more anyone + + + align:start position:0% +collection that puts one more anyone +want to jump in Columbus you thinking + + align:start position:0% +want to jump in Columbus you thinking + + + align:start position:0% +want to jump in Columbus you thinking +about what will you do what are you + + align:start position:0% +about what will you do what are you + + + align:start position:0% +about what will you do what are you +senior + + align:start position:0% + + + + align:start position:0% + +okay okay good so just based on the very + + align:start position:0% +okay okay good so just based on the very + + + align:start position:0% +okay okay good so just based on the very +little you know about our technology you + + align:start position:0% +little you know about our technology you + + + align:start position:0% +little you know about our technology you +know make an argument for starting which + + align:start position:0% +know make an argument for starting which + + + align:start position:0% +know make an argument for starting which +one you would started because one of the + + align:start position:0% +one you would started because one of the + + + align:start position:0% +one you would started because one of the +most difficult things in launching a + + align:start position:0% +most difficult things in launching a + + + align:start position:0% +most difficult things in launching a +business whether you're doing it as a + + align:start position:0% +business whether you're doing it as a + + + align:start position:0% +business whether you're doing it as a +startup or whether you're doing it in an + + align:start position:0% +startup or whether you're doing it in an + + + align:start position:0% +startup or whether you're doing it in an +existing large company is what market to + + align:start position:0% +existing large company is what market to + + + align:start position:0% +existing large company is what market to +go after first and you know there are + + align:start position:0% +go after first and you know there are + + + align:start position:0% +go after first and you know there are +advantages and disadvantages to + + align:start position:0% +advantages and disadvantages to + + + align:start position:0% +advantages and disadvantages to +different markets + + align:start position:0% +different markets + + + align:start position:0% +different markets +one of the advantage of doing something + + align:start position:0% +one of the advantage of doing something + + + align:start position:0% +one of the advantage of doing something +a large companies you may be able to go + + align:start position:0% +a large companies you may be able to go + + + align:start position:0% +a large companies you may be able to go +after more than one market at the same + + align:start position:0% +after more than one market at the same + + + align:start position:0% +after more than one market at the same +time but oftentimes not so so it's sort + + align:start position:0% +time but oftentimes not so so it's sort + + + align:start position:0% +time but oftentimes not so so it's sort +of like selecting a spouse right you + + align:start position:0% +of like selecting a spouse right you + + + align:start position:0% +of like selecting a spouse right you +know how do you you know there are lots + + align:start position:0% +know how do you you know there are lots + + + align:start position:0% +know how do you you know there are lots +of different interesting candidates in + + align:start position:0% +of different interesting candidates in + + + align:start position:0% +of different interesting candidates in +the world right and how do you narrow it + + align:start position:0% +the world right and how do you narrow it + + + align:start position:0% +the world right and how do you narrow it +down to you know a one particular person + + align:start position:0% +down to you know a one particular person + + + align:start position:0% +down to you know a one particular person +it can be a painful process and so this + + align:start position:0% +it can be a painful process and so this + + + align:start position:0% +it can be a painful process and so this +can be a painful process - so somebody + + align:start position:0% +can be a painful process - so somebody + + + align:start position:0% +can be a painful process - so somebody +say something about why you would or + + align:start position:0% +say something about why you would or + + + align:start position:0% +say something about why you would or +wouldn't choose one of these four as + + align:start position:0% +wouldn't choose one of these four as + + + align:start position:0% +wouldn't choose one of these four as +initial launch market yes + + align:start position:0% + + + + align:start position:0% + +lowest barrier to entry so what do you + + align:start position:0% +lowest barrier to entry so what do you + + + align:start position:0% +lowest barrier to entry so what do you +mean by buried entry so how might you + + align:start position:0% +mean by buried entry so how might you + + + align:start position:0% +mean by buried entry so how might you +address that + + align:start position:0% +address that + + + align:start position:0% +address that +oh did you write here yeah please go + + align:start position:0% +oh did you write here yeah please go + + + align:start position:0% +oh did you write here yeah please go +ahead + + align:start position:0% + + + + align:start position:0% + +yes seems like there's a lot of yep + + align:start position:0% + + + + align:start position:0% + +okay these are really these are really + + align:start position:0% +okay these are really these are really + + + align:start position:0% +okay these are really these are really +good inputs Charlotte + + align:start position:0% + + + + align:start position:0% + +they put me obviously Purdue's like use + + align:start position:0% +they put me obviously Purdue's like use + + + align:start position:0% +they put me obviously Purdue's like use +a lot of energy + + align:start position:0% + + + + align:start position:0% + +okay very interesting so we have low + + align:start position:0% +okay very interesting so we have low + + + align:start position:0% +okay very interesting so we have low +barriers to entry portable power + + align:start position:0% +barriers to entry portable power + + + align:start position:0% +barriers to entry portable power +industrial sector interesting terms of + + align:start position:0% +industrial sector interesting terms of + + + align:start position:0% +industrial sector interesting terms of +manufacturing I think personally there's + + align:start position:0% +manufacturing I think personally there's + + + align:start position:0% +manufacturing I think personally there's +too much focus just for startups just in + + align:start position:0% +too much focus just for startups just in + + + align:start position:0% +too much focus just for startups just in +technology per se but I don't personally + + align:start position:0% +technology per se but I don't personally + + + align:start position:0% +technology per se but I don't personally +see that meaning for example consulting + + align:start position:0% +see that meaning for example consulting + + + align:start position:0% +see that meaning for example consulting +firms advising how startups can secure I + + align:start position:0% +firms advising how startups can secure I + + + align:start position:0% +firms advising how startups can secure I +know the grants they're all starting to + + align:start position:0% +know the grants they're all starting to + + + align:start position:0% +know the grants they're all starting to +position themselves to take advantage of + + align:start position:0% +position themselves to take advantage of + + + align:start position:0% +position themselves to take advantage of +all existing policies related to + + align:start position:0% +all existing policies related to + + + align:start position:0% +all existing policies related to +interview some point that I think + + align:start position:0% +interview some point that I think + + + align:start position:0% +interview some point that I think +there's no third there are a lot of + + align:start position:0% +there's no third there are a lot of + + + align:start position:0% +there's no third there are a lot of +different areas that you can use + + align:start position:0% +different areas that you can use + + + align:start position:0% +different areas that you can use +knowledge so there's a lot more than + + align:start position:0% +knowledge so there's a lot more than + + + align:start position:0% +knowledge so there's a lot more than +just the technology right okay these are + + align:start position:0% +just the technology right okay these are + + + align:start position:0% +just the technology right okay these are +all really important points and as + + align:start position:0% +all really important points and as + + + align:start position:0% +all really important points and as +engineers that that may be one of the + + align:start position:0% +engineers that that may be one of the + + + align:start position:0% +engineers that that may be one of the +hardest ones to get and it sounds like + + align:start position:0% +hardest ones to get and it sounds like + + + align:start position:0% +hardest ones to get and it sounds like +you guys probably already have a very + + align:start position:0% +you guys probably already have a very + + + align:start position:0% +you guys probably already have a very +good sense of that the ecosystem that + + align:start position:0% +good sense of that the ecosystem that + + + align:start position:0% +good sense of that the ecosystem that +there's more than just the technology + + align:start position:0% +there's more than just the technology + + + align:start position:0% +there's more than just the technology +but oftentimes the technology's hard you + + align:start position:0% +but oftentimes the technology's hard you + + + align:start position:0% +but oftentimes the technology's hard you +know so it takes lots of your focus so + + align:start position:0% +know so it takes lots of your focus so + + + align:start position:0% +know so it takes lots of your focus so +and and and but then you've got to make + + align:start position:0% +and and and but then you've got to make + + + align:start position:0% +and and and but then you've got to make +all these other decisions so in our case + + align:start position:0% +all these other decisions so in our case + + + align:start position:0% +all these other decisions so in our case +we really struggled with portable power + + align:start position:0% +we really struggled with portable power + + + align:start position:0% +we really struggled with portable power +because it's small you know and so + + align:start position:0% +because it's small you know and so + + + align:start position:0% +because it's small you know and so +compared to the industrial industrial + + align:start position:0% +compared to the industrial industrial + + + align:start position:0% +compared to the industrial industrial +you need like more chips which requires + + align:start position:0% +you need like more chips which requires + + + align:start position:0% +you need like more chips which requires +more capital more manufacturing capacity + + align:start position:0% +more capital more manufacturing capacity + + + align:start position:0% +more capital more manufacturing capacity +you've got to deal with bigger vendors + + align:start position:0% +you've got to deal with bigger vendors + + + align:start position:0% +you've got to deal with bigger vendors +and there's more bureaucracy and + + align:start position:0% +and there's more bureaucracy and + + + align:start position:0% +and there's more bureaucracy and +everything else and so the portable + + align:start position:0% +everything else and so the portable + + + align:start position:0% +everything else and so the portable +power was very was very attractive to us + + align:start position:0% +power was very was very attractive to us + + + align:start position:0% +power was very was very attractive to us +we ended up going with industrial okay + + align:start position:0% +we ended up going with industrial okay + + + align:start position:0% +we ended up going with industrial okay +and so any guesses as to why we might + + align:start position:0% +and so any guesses as to why we might + + + align:start position:0% +and so any guesses as to why we might +have done that yes + + align:start position:0% + + + + align:start position:0% + +yep so that was definitely part of it + + align:start position:0% +yep so that was definitely part of it + + + align:start position:0% +yep so that was definitely part of it +performance how good a performance you + + align:start position:0% +performance how good a performance you + + + align:start position:0% +performance how good a performance you +know would you start with the technology + + align:start position:0% +know would you start with the technology + + + align:start position:0% +know would you start with the technology +is just new how good does the + + align:start position:0% +is just new how good does the + + + align:start position:0% +is just new how good does the +performance of the technology have to + + align:start position:0% +performance of the technology have to + + + align:start position:0% +performance of the technology have to +get before you can do you know X market + + align:start position:0% +get before you can do you know X market + + + align:start position:0% +get before you can do you know X market +and and and here we felt that it was was + + align:start position:0% +and and and here we felt that it was was + + + align:start position:0% +and and and here we felt that it was was +more stringent because here and I'll say + + align:start position:0% +more stringent because here and I'll say + + + align:start position:0% +more stringent because here and I'll say +we're gonna go into a laptop we had to + + align:start position:0% +we're gonna go into a laptop we had to + + + align:start position:0% +we're gonna go into a laptop we had to +compete with the with lithium-ion + + align:start position:0% +compete with the with lithium-ion + + + align:start position:0% +compete with the with lithium-ion +batteries that are in in laptops and so + + align:start position:0% +batteries that are in in laptops and so + + + align:start position:0% +batteries that are in in laptops and so +you know this kind of goes to technical + + align:start position:0% +you know this kind of goes to technical + + + align:start position:0% +you know this kind of goes to technical +details really but that that was a + + align:start position:0% +details really but that that was a + + + align:start position:0% +details really but that that was a +factor that we felt that no way you guys + + align:start position:0% +factor that we felt that no way you guys + + + align:start position:0% +factor that we felt that no way you guys +could know up for you all right sitting + + align:start position:0% +could know up for you all right sitting + + + align:start position:0% +could know up for you all right sitting +here but but we felt that it would have + + align:start position:0% +here but but we felt that it would have + + + align:start position:0% +here but but we felt that it would have +been harder to get that level of + + align:start position:0% +been harder to get that level of + + + align:start position:0% +been harder to get that level of +performance as opposed to the industrial + + align:start position:0% +performance as opposed to the industrial + + + align:start position:0% +performance as opposed to the industrial +situation where it just it basically + + align:start position:0% +situation where it just it basically + + + align:start position:0% +situation where it just it basically +it's it's economic it needs to be + + align:start position:0% +it's it's economic it needs to be + + + align:start position:0% +it's it's economic it needs to be +economically feasible but doesn't have + + align:start position:0% +economically feasible but doesn't have + + + align:start position:0% +economically feasible but doesn't have +to be any better than that + + align:start position:0% +to be any better than that + + + align:start position:0% +to be any better than that +and there's really no competition + + align:start position:0% +and there's really no competition + + + align:start position:0% +and there's really no competition +another thing was some of you guys + + align:start position:0% +another thing was some of you guys + + + align:start position:0% +another thing was some of you guys +mentioned related things and that is how + + align:start position:0% +mentioned related things and that is how + + + align:start position:0% +mentioned related things and that is how +tightly do you have to integrate with + + align:start position:0% +tightly do you have to integrate with + + + align:start position:0% +tightly do you have to integrate with +other companies with other technician + + align:start position:0% +other companies with other technician + + + align:start position:0% +other companies with other technician +technologies without applications and + + align:start position:0% +technologies without applications and + + + align:start position:0% +technologies without applications and +and we felt that in the industrial for + + align:start position:0% +and we felt that in the industrial for + + + align:start position:0% +and we felt that in the industrial for +example the heat source what kind of + + align:start position:0% +example the heat source what kind of + + + align:start position:0% +example the heat source what kind of +heat source are we going to use where + + align:start position:0% +heat source are we going to use where + + + align:start position:0% +heat source are we going to use where +are we going to actually get the heat + + align:start position:0% +are we going to actually get the heat + + + align:start position:0% +are we going to actually get the heat +here the heat would have to be produced + + align:start position:0% +here the heat would have to be produced + + + align:start position:0% +here the heat would have to be produced +in a very small combustion device a + + align:start position:0% +in a very small combustion device a + + + align:start position:0% +in a very small combustion device a +pretty high-tech combustion device and + + align:start position:0% +pretty high-tech combustion device and + + + align:start position:0% +pretty high-tech combustion device and +so we would need to very tightly couple + + align:start position:0% +so we would need to very tightly couple + + + align:start position:0% +so we would need to very tightly couple +with another another company to do that + + align:start position:0% +with another another company to do that + + + align:start position:0% +with another another company to do that +as well that the heat rejection safety + + align:start position:0% +as well that the heat rejection safety + + + align:start position:0% +as well that the heat rejection safety +FAA regulations etc whereas in the + + align:start position:0% +FAA regulations etc whereas in the + + + align:start position:0% +FAA regulations etc whereas in the +industrial space the heat was already + + align:start position:0% +industrial space the heat was already + + + align:start position:0% +industrial space the heat was already +there so it was just another piece of + + align:start position:0% +there so it was just another piece of + + + align:start position:0% +there so it was just another piece of +complexity that that we didn't that we + + align:start position:0% +complexity that that we didn't that we + + + align:start position:0% +complexity that that we didn't that we +didn't have to deal with okay so let's + + align:start position:0% +didn't have to deal with okay so let's + + + align:start position:0% +didn't have to deal with okay so let's +see let me that's about all I have with + + align:start position:0% +see let me that's about all I have with + + + align:start position:0% +see let me that's about all I have with +slides + + align:start position:0% +slides + + + align:start position:0% +slides +that's your life story my life story + + align:start position:0% +that's your life story my life story + + + align:start position:0% +that's your life story my life story +undergraduate kind of interested in this + + align:start position:0% +undergraduate kind of interested in this + + + align:start position:0% +undergraduate kind of interested in this +stuff too + + align:start position:0% +stuff too + + + align:start position:0% +stuff too +you know selling to glass makers yeah so + + align:start position:0% +you know selling to glass makers yeah so + + + align:start position:0% +you know selling to glass makers yeah so +my life story so you really want + + align:start position:0% +my life story so you really want + + + align:start position:0% +my life story so you really want +everybody I'll take a nap right now + + align:start position:0% +everybody I'll take a nap right now + + + align:start position:0% +everybody I'll take a nap right now +doesn't have to cover all aspects of + + align:start position:0% +doesn't have to cover all aspects of + + + align:start position:0% +doesn't have to cover all aspects of +your life no yeah so I mentioned the + + align:start position:0% +your life no yeah so I mentioned the + + + align:start position:0% +your life no yeah so I mentioned the +beginning what kind of triggered it + + align:start position:0% +beginning what kind of triggered it + + + align:start position:0% +beginning what kind of triggered it +right and I guess there were two things + + align:start position:0% +right and I guess there were two things + + + align:start position:0% +right and I guess there were two things +then there was an energy shock in like + + align:start position:0% +then there was an energy shock in like + + + align:start position:0% +then there was an energy shock in like +the in the 70s when I was a kid and then + + align:start position:0% +the in the 70s when I was a kid and then + + + align:start position:0% +the in the 70s when I was a kid and then +I was in late 70s in college and it + + align:start position:0% +I was in late 70s in college and it + + + align:start position:0% +I was in late 70s in college and it +looked like energy was really important + + align:start position:0% +looked like energy was really important + + + align:start position:0% +looked like energy was really important +so I guess you guys are sort of the fact + + align:start position:0% +so I guess you guys are sort of the fact + + + align:start position:0% +so I guess you guys are sort of the fact +that you're in this class the fact that + + align:start position:0% +that you're in this class the fact that + + + align:start position:0% +that you're in this class the fact that +this class exists and the fact that you + + align:start position:0% +this class exists and the fact that you + + + align:start position:0% +this class exists and the fact that you +guys are in this class you know means + + align:start position:0% +guys are in this class you know means + + + align:start position:0% +guys are in this class you know means +that Energy's gotten a lot more + + align:start position:0% +that Energy's gotten a lot more + + + align:start position:0% +that Energy's gotten a lot more +visibility now than it did say in the + + align:start position:0% +visibility now than it did say in the + + + align:start position:0% +visibility now than it did say in the +80s so at any rate I started what got me + + align:start position:0% +80s so at any rate I started what got me + + + align:start position:0% +80s so at any rate I started what got me +actually started was an article in The + + align:start position:0% +actually started was an article in The + + + align:start position:0% +actually started was an article in The +Boston Globe in 1978 in the summer I was + + align:start position:0% +Boston Globe in 1978 in the summer I was + + + align:start position:0% +Boston Globe in 1978 in the summer I was +sitting down the Cape my girlfriend + + align:start position:0% +sitting down the Cape my girlfriend + + + align:start position:0% +sitting down the Cape my girlfriend +later wife the B's cottage reading the + + align:start position:0% +later wife the B's cottage reading the + + + align:start position:0% +later wife the B's cottage reading the +Boston Sunday globe on a Sunday and + + align:start position:0% +Boston Sunday globe on a Sunday and + + + align:start position:0% +Boston Sunday globe on a Sunday and +there was an article it said kid in + + align:start position:0% +there was an article it said kid in + + + align:start position:0% +there was an article it said kid in +Texas gets a hundred miles per gallon + + align:start position:0% +Texas gets a hundred miles per gallon + + + align:start position:0% +Texas gets a hundred miles per gallon +from 68 Ford Galaxie 64 Galaxie was a + + align:start position:0% +from 68 Ford Galaxie 64 Galaxie was a + + + align:start position:0% +from 68 Ford Galaxie 64 Galaxie was a +big car that probably got like you know + + align:start position:0% +big car that probably got like you know + + + align:start position:0% +big car that probably got like you know +eight miles per gallon on a good day + + align:start position:0% +eight miles per gallon on a good day + + + align:start position:0% +eight miles per gallon on a good day +right hundred miles per gallon so could + + align:start position:0% +right hundred miles per gallon so could + + + align:start position:0% +right hundred miles per gallon so could +that be true so who thinks that it could + + align:start position:0% +that be true so who thinks that it could + + + align:start position:0% +that be true so who thinks that it could +be true who thinks that it could not be + + align:start position:0% +be true who thinks that it could not be + + + align:start position:0% +be true who thinks that it could not be +true and who's not sure okay I'm not + + align:start position:0% +true and who's not sure okay I'm not + + + align:start position:0% +true and who's not sure okay I'm not +sure okay now I mean in all the paths of + + align:start position:0% +sure okay now I mean in all the paths of + + + align:start position:0% +sure okay now I mean in all the paths of +hard to find the vehicle etc etc you + + align:start position:0% +hard to find the vehicle etc etc you + + + align:start position:0% +hard to find the vehicle etc etc you +know there only so many BTUs in the + + align:start position:0% +know there only so many BTUs in the + + + align:start position:0% +know there only so many BTUs in the +gallon of gas but any rate so it led me + + align:start position:0% +gallon of gas but any rate so it led me + + + align:start position:0% +gallon of gas but any rate so it led me +to the patent I was I was thinking about + + align:start position:0% +to the patent I was I was thinking about + + + align:start position:0% +to the patent I was I was thinking about +medical school I used to I studied at + + align:start position:0% +medical school I used to I studied at + + + align:start position:0% +medical school I used to I studied at +this school down the street the other + + align:start position:0% +this school down the street the other + + + align:start position:0% +this school down the street the other +end of mass M so I used to drive by this + + align:start position:0% +end of mass M so I used to drive by this + + + align:start position:0% +end of mass M so I used to drive by this +place you know I have three graduate + + align:start position:0% +place you know I have three graduate + + + align:start position:0% +place you know I have three graduate +degrees in this place now but the way I + + align:start position:0% +degrees in this place now but the way I + + + align:start position:0% +degrees in this place now but the way I +really discovered it was + + align:start position:0% +really discovered it was + + + align:start position:0% +really discovered it was +driving down math seven you know what I + + align:start position:0% +driving down math seven you know what I + + + align:start position:0% +driving down math seven you know what I +mean obviously I knew about MIT but I + + align:start position:0% +mean obviously I knew about MIT but I + + + align:start position:0% +mean obviously I knew about MIT but I +really didn't I really didn't understand + + align:start position:0% +really didn't I really didn't understand + + + align:start position:0% +really didn't I really didn't understand +what engineering was you know I thought + + align:start position:0% +what engineering was you know I thought + + + align:start position:0% +what engineering was you know I thought +if like you liked math and science and + + align:start position:0% +if like you liked math and science and + + + align:start position:0% +if like you liked math and science and +stuff like that well you could be a + + align:start position:0% +stuff like that well you could be a + + + align:start position:0% +stuff like that well you could be a +doctor you know so I figured well maybe + + align:start position:0% +doctor you know so I figured well maybe + + + align:start position:0% +doctor you know so I figured well maybe +that's what I'll do + + align:start position:0% +that's what I'll do + + + align:start position:0% +that's what I'll do +so I was a government major because I + + align:start position:0% +so I was a government major because I + + + align:start position:0% +so I was a government major because I +was interested in the kinds of things + + align:start position:0% +was interested in the kinds of things + + + align:start position:0% +was interested in the kinds of things +that you're talking about in this in + + align:start position:0% +that you're talking about in this in + + + align:start position:0% +that you're talking about in this in +this course but I really liked math and + + align:start position:0% +this course but I really liked math and + + + align:start position:0% +this course but I really liked math and +physics Oh science and in math and so I + + align:start position:0% +physics Oh science and in math and so I + + + align:start position:0% +physics Oh science and in math and so I +think well do medicine and and then I + + align:start position:0% +think well do medicine and and then I + + + align:start position:0% +think well do medicine and and then I +read this article you know and so then + + align:start position:0% +read this article you know and so then + + + align:start position:0% +read this article you know and so then +they kind of came together just like you + + align:start position:0% +they kind of came together just like you + + + align:start position:0% +they kind of came together just like you +guys are doing in this class you know + + align:start position:0% +guys are doing in this class you know + + + align:start position:0% +guys are doing in this class you know +you have technical backgrounds of + + align:start position:0% +you have technical backgrounds of + + + align:start position:0% +you have technical backgrounds of +various sorts and you hear learning + + align:start position:0% +various sorts and you hear learning + + + align:start position:0% +various sorts and you hear learning +about the whole the whole picture of + + align:start position:0% +about the whole the whole picture of + + + align:start position:0% +about the whole the whole picture of +energy which which really is I mean in + + align:start position:0% +energy which which really is I mean in + + + align:start position:0% +energy which which really is I mean in +some ways unfortunately much bigger than + + align:start position:0% +some ways unfortunately much bigger than + + + align:start position:0% +some ways unfortunately much bigger than +just the technology because it makes it + + align:start position:0% +just the technology because it makes it + + + align:start position:0% +just the technology because it makes it +much more complicated but in a way + + align:start position:0% +much more complicated but in a way + + + align:start position:0% +much more complicated but in a way +that's what makes it that much more + + align:start position:0% +that's what makes it that much more + + + align:start position:0% +that's what makes it that much more +important and so did early experiments + + align:start position:0% +important and so did early experiments + + + align:start position:0% +important and so did early experiments +in this realm found out about solar + + align:start position:0% +in this realm found out about solar + + + align:start position:0% +in this realm found out about solar +energy and photovoltaics + + align:start position:0% +energy and photovoltaics + + + align:start position:0% +energy and photovoltaics +came over here and Steve Santeria taught + + align:start position:0% +came over here and Steve Santeria taught + + + align:start position:0% +came over here and Steve Santeria taught +the class and microfabrication the + + align:start position:0% +the class and microfabrication the + + + align:start position:0% +the class and microfabrication the +interest in photovoltaics brought me + + align:start position:0% +interest in photovoltaics brought me + + + align:start position:0% +interest in photovoltaics brought me +there I ended up spending a semester + + align:start position:0% +there I ended up spending a semester + + + align:start position:0% +there I ended up spending a semester +here while I was an undergraduate down + + align:start position:0% +here while I was an undergraduate down + + + align:start position:0% +here while I was an undergraduate down +the street which if any of you are not + + align:start position:0% +the street which if any of you are not + + + align:start position:0% +the street which if any of you are not +seniors I highly recommend just get + + align:start position:0% +seniors I highly recommend just get + + + align:start position:0% +seniors I highly recommend just get +yourself down NASA take just one course + + align:start position:0% +yourself down NASA take just one course + + + align:start position:0% +yourself down NASA take just one course +at that other institution it's totally + + align:start position:0% +at that other institution it's totally + + + align:start position:0% +at that other institution it's totally +free it's totally easy it's a it's a + + align:start position:0% +free it's totally easy it's a it's a + + + align:start position:0% +free it's totally easy it's a it's a +very it's a very different world and + + align:start position:0% +very it's a very different world and + + + align:start position:0% +very it's a very different world and +you'll be glad that you did it you can + + align:start position:0% +you'll be glad that you did it you can + + + align:start position:0% +you'll be glad that you did it you can +you can write me for your money back if + + align:start position:0% +you can write me for your money back if + + + align:start position:0% +you can write me for your money back if +here if you don't if you don't think so + + align:start position:0% +here if you don't if you don't think so + + + align:start position:0% +here if you don't if you don't think so +afterwards any rate so I started my + + align:start position:0% +afterwards any rate so I started my + + + align:start position:0% +afterwards any rate so I started my +first company while I was a senior in + + align:start position:0% +first company while I was a senior in + + + align:start position:0% +first company while I was a senior in +college specifically to develop energy + + align:start position:0% +college specifically to develop energy + + + align:start position:0% +college specifically to develop energy +technology and it took probably 15 years + + align:start position:0% +technology and it took probably 15 years + + + align:start position:0% +technology and it took probably 15 years +to really do it directly which is this + + align:start position:0% +to really do it directly which is this + + + align:start position:0% +to really do it directly which is this +right here + + align:start position:0% +right here + + + align:start position:0% +right here +although along the way so from you know + + align:start position:0% +although along the way so from you know + + + align:start position:0% +although along the way so from you know +in the family garage tinkering with + + align:start position:0% +in the family garage tinkering with + + + align:start position:0% +in the family garage tinkering with +engines and trying to figure out can + + align:start position:0% +engines and trying to figure out can + + + align:start position:0% +engines and trying to figure out can +somebody really get a hundred miles per + + align:start position:0% +somebody really get a hundred miles per + + + align:start position:0% +somebody really get a hundred miles per +gallon and and and patient/family kind + + align:start position:0% +gallon and and and patient/family kind + + + align:start position:0% +gallon and and and patient/family kind +of dealing with all that and then right + + align:start position:0% +of dealing with all that and then right + + + align:start position:0% +of dealing with all that and then right +then in the beginning of the 80s + + align:start position:0% +then in the beginning of the 80s + + + align:start position:0% +then in the beginning of the 80s +difficult recession you know where do + + align:start position:0% +difficult recession you know where do + + + align:start position:0% +difficult recession you know where do +you get a job you really want to do + + align:start position:0% +you get a job you really want to do + + + align:start position:0% +you get a job you really want to do +clean energy there + + align:start position:0% +clean energy there + + + align:start position:0% +clean energy there +clean energy jobs and I went to work in + + align:start position:0% +clean energy jobs and I went to work in + + + align:start position:0% +clean energy jobs and I went to work in +the aircraft industry because I also + + align:start position:0% +the aircraft industry because I also + + + align:start position:0% +the aircraft industry because I also +taken Fred mcGarry's course here and + + align:start position:0% +taken Fred mcGarry's course here and + + + align:start position:0% +taken Fred mcGarry's course here and +composite materials because I was + + align:start position:0% +composite materials because I was + + + align:start position:0% +composite materials because I was +interested about materials for what why + + align:start position:0% +interested about materials for what why + + + align:start position:0% +interested about materials for what why +might you be interested in composite + + align:start position:0% +might you be interested in composite + + + align:start position:0% +might you be interested in composite +materials if you're interested in energy + + align:start position:0% +materials if you're interested in energy + + + align:start position:0% +materials if you're interested in energy +when I get it we got to get somebody + + align:start position:0% +when I get it we got to get somebody + + + align:start position:0% +when I get it we got to get somebody +else's young Mario thank you come on + + align:start position:0% +else's young Mario thank you come on + + + align:start position:0% +else's young Mario thank you come on +Kristin yeah exactly exactly right + + align:start position:0% +Kristin yeah exactly exactly right + + + align:start position:0% +Kristin yeah exactly exactly right +exactly yeah + + align:start position:0% +exactly yeah + + + align:start position:0% +exactly yeah +and and so they wanted to build + + align:start position:0% +and and so they wanted to build + + + align:start position:0% +and and so they wanted to build +lightweight helicopters and so later on + + align:start position:0% +lightweight helicopters and so later on + + + align:start position:0% +lightweight helicopters and so later on +I realized that you know like well I + + align:start position:0% +I realized that you know like well I + + + align:start position:0% +I realized that you know like well I +didn't it wasn't so clear at the time + + align:start position:0% +didn't it wasn't so clear at the time + + + align:start position:0% +didn't it wasn't so clear at the time +that I was really working on clean + + align:start position:0% +that I was really working on clean + + + align:start position:0% +that I was really working on clean +energy you know lightweight strong + + align:start position:0% +energy you know lightweight strong + + + align:start position:0% +energy you know lightweight strong +materials which are now going lots of + + align:start position:0% +materials which are now going lots of + + + align:start position:0% +materials which are now going lots of +airplanes and vehicles and I thought I + + align:start position:0% +airplanes and vehicles and I thought I + + + align:start position:0% +airplanes and vehicles and I thought I +was in the aircraft industry but I was + + align:start position:0% +was in the aircraft industry but I was + + + align:start position:0% +was in the aircraft industry but I was +really working pursuing my interest in + + align:start position:0% +really working pursuing my interest in + + + align:start position:0% +really working pursuing my interest in +in clean energy and then another stint + + align:start position:0% +in clean energy and then another stint + + + align:start position:0% +in clean energy and then another stint +with the company up the street might a + + align:start position:0% +with the company up the street might a + + + align:start position:0% +with the company up the street might a +corporation on the spin-out out of MIT + + align:start position:0% +corporation on the spin-out out of MIT + + + align:start position:0% +corporation on the spin-out out of MIT +well like a lab spung on either my team + + align:start position:0% +well like a lab spung on either my team + + + align:start position:0% +well like a lab spung on either my team +might or spun out of making that and + + align:start position:0% +might or spun out of making that and + + + align:start position:0% +might or spun out of making that and +when we started to explore some of these + + align:start position:0% +when we started to explore some of these + + + align:start position:0% +when we started to explore some of these +some of these concepts and but I really + + align:start position:0% +some of these concepts and but I really + + + align:start position:0% +some of these concepts and but I really +wanted to try to do things more directly + + align:start position:0% +wanted to try to do things more directly + + + align:start position:0% +wanted to try to do things more directly +and linked with sort of energy is the + + align:start position:0% +and linked with sort of energy is the + + + align:start position:0% +and linked with sort of energy is the +food piece that Christopher mentioned + + align:start position:0% +food piece that Christopher mentioned + + + align:start position:0% +food piece that Christopher mentioned +and sort of you know if the notion that + + align:start position:0% +and sort of you know if the notion that + + + align:start position:0% +and sort of you know if the notion that +if a home if a home is part of like like + + align:start position:0% +if a home if a home is part of like like + + + align:start position:0% +if a home if a home is part of like like +let's say what's an energy system in a + + align:start position:0% +let's say what's an energy system in a + + + align:start position:0% +let's say what's an energy system in a +home I know it's real easy but what's + + align:start position:0% +home I know it's real easy but what's + + + align:start position:0% +home I know it's real easy but what's +what's what's an energy system in a home + + align:start position:0% +what's what's an energy system in a home + + + align:start position:0% +what's what's an energy system in a home +that every home in the United States has + + align:start position:0% +that every home in the United States has + + + align:start position:0% +that every home in the United States has +yeah Jacob HVAC exactly so make making + + align:start position:0% +yeah Jacob HVAC exactly so make making + + + align:start position:0% +yeah Jacob HVAC exactly so make making +heat keep people warm the cold weather + + align:start position:0% +heat keep people warm the cold weather + + + align:start position:0% +heat keep people warm the cold weather +and when what's another energy system in + + align:start position:0% +and when what's another energy system in + + + align:start position:0% +and when what's another energy system in +the home oven okay what my table and run + + align:start position:0% +the home oven okay what my table and run + + + align:start position:0% +the home oven okay what my table and run +off of or electricity okay so then + + align:start position:0% +off of or electricity okay so then + + + align:start position:0% +off of or electricity okay so then +electricity is another energy system so + + align:start position:0% +electricity is another energy system so + + + align:start position:0% +electricity is another energy system so +you know one thought is so you know what + + align:start position:0% +you know one thought is so you know what + + + align:start position:0% +you know one thought is so you know what +if the foot off the foot if there was a + + align:start position:0% +if the foot off the foot if there was a + + + align:start position:0% +if the foot off the foot if there was a +food system in a home also going back to + + align:start position:0% +food system in a home also going back to + + + align:start position:0% +food system in a home also going back to +Chris to this point and so just the + + align:start position:0% +Chris to this point and so just the + + + align:start position:0% +Chris to this point and so just the +of the home as being sort of the energy + + align:start position:0% +of the home as being sort of the energy + + + align:start position:0% +of the home as being sort of the energy +energy central of your physical + + align:start position:0% +energy central of your physical + + + align:start position:0% +energy central of your physical +well-being whether it's in the developed + + align:start position:0% +well-being whether it's in the developed + + + align:start position:0% +well-being whether it's in the developed +world or developing countries even more + + align:start position:0% +world or developing countries even more + + + align:start position:0% +world or developing countries even more +important perhaps in developing + + align:start position:0% +important perhaps in developing + + + align:start position:0% +important perhaps in developing +countries any rate so it made me want to + + align:start position:0% +countries any rate so it made me want to + + + align:start position:0% +countries any rate so it made me want to +build a house and I built a house while + + align:start position:0% +build a house and I built a house while + + + align:start position:0% +build a house and I built a house while +I was working full-time and then built + + align:start position:0% +I was working full-time and then built + + + align:start position:0% +I was working full-time and then built +another one and so then I did that for + + align:start position:0% +another one and so then I did that for + + + align:start position:0% +another one and so then I did that for +about eight years and we were leaders in + + align:start position:0% +about eight years and we were leaders in + + + align:start position:0% +about eight years and we were leaders in +energy efficient housing no surprise and + + align:start position:0% +energy efficient housing no surprise and + + + align:start position:0% +energy efficient housing no surprise and +you know over the course of time we + + align:start position:0% +you know over the course of time we + + + align:start position:0% +you know over the course of time we +built some miles of roads and a hundred + + align:start position:0% +built some miles of roads and a hundred + + + align:start position:0% +built some miles of roads and a hundred +and fifty homes and then and then I went + + align:start position:0% +and fifty homes and then and then I went + + + align:start position:0% +and fifty homes and then and then I went +back to graduate school to more + + align:start position:0% +back to graduate school to more + + + align:start position:0% +back to graduate school to more +specifically concentrate directly on + + align:start position:0% +specifically concentrate directly on + + + align:start position:0% +specifically concentrate directly on +energy technology and the kinds of + + align:start position:0% +energy technology and the kinds of + + + align:start position:0% +energy technology and the kinds of +issues that talked about earlier and and + + align:start position:0% +issues that talked about earlier and and + + + align:start position:0% +issues that talked about earlier and and +that's what led MT PV with professors + + align:start position:0% +that's what led MT PV with professors + + + align:start position:0% +that's what led MT PV with professors +here and and then there's a laboratory + + align:start position:0% +here and and then there's a laboratory + + + align:start position:0% +here and and then there's a laboratory +across street grape a laboratory it used + + align:start position:0% +across street grape a laboratory it used + + + align:start position:0% +across street grape a laboratory it used +to be the M I used to be the MIT + + align:start position:0% +to be the M I used to be the MIT + + + align:start position:0% +to be the M I used to be the MIT +instrumentation lab and they they called + + align:start position:0% +instrumentation lab and they they called + + + align:start position:0% +instrumentation lab and they they called +me up and said we saw your resume and + + align:start position:0% +me up and said we saw your resume and + + + align:start position:0% +me up and said we saw your resume and +the course X resume book and you know + + align:start position:0% +the course X resume book and you know + + + align:start position:0% +the course X resume book and you know +and now this was in this was in 1996 an + + align:start position:0% +and now this was in this was in 1996 an + + + align:start position:0% +and now this was in this was in 1996 an +energy were so how important how hot a + + align:start position:0% +energy were so how important how hot a + + + align:start position:0% +energy were so how important how hot a +topic was energy in 1996 not for those + + align:start position:0% +topic was energy in 1996 not for those + + + align:start position:0% +topic was energy in 1996 not for those +of us that were working in the field and + + align:start position:0% +of us that were working in the field and + + + align:start position:0% +of us that were working in the field and +dedicated but I mean do you guys have + + align:start position:0% +dedicated but I mean do you guys have + + + align:start position:0% +dedicated but I mean do you guys have +any sense how old were you guys in 1996 + + align:start position:0% +any sense how old were you guys in 1996 + + + align:start position:0% +any sense how old were you guys in 1996 +just a couple of examples ball five six + + align:start position:0% +just a couple of examples ball five six + + + align:start position:0% +just a couple of examples ball five six +seven okay + + align:start position:0% +seven okay + + + align:start position:0% +seven okay +so wasn't on the top of you guys agenda + + align:start position:0% +so wasn't on the top of you guys agenda + + + align:start position:0% +so wasn't on the top of you guys agenda +right but do you have a sense of like + + align:start position:0% +right but do you have a sense of like + + + align:start position:0% +right but do you have a sense of like +how relevant it is today how much in the + + align:start position:0% +how relevant it is today how much in the + + + align:start position:0% +how relevant it is today how much in the +news it is today versus in nineteen + + align:start position:0% +news it is today versus in nineteen + + + align:start position:0% +news it is today versus in nineteen +ninety six more now or less now how many + + align:start position:0% +ninety six more now or less now how many + + + align:start position:0% +ninety six more now or less now how many +things more now than that okay yeah so + + align:start position:0% +things more now than that okay yeah so + + + align:start position:0% +things more now than that okay yeah so +so it certainly seems that way and but + + align:start position:0% +so it certainly seems that way and but + + + align:start position:0% +so it certainly seems that way and but +any rate there were folks over there + + align:start position:0% +any rate there were folks over there + + + align:start position:0% +any rate there were folks over there +that thought energy would be important + + align:start position:0% +that thought energy would be important + + + align:start position:0% +that thought energy would be important +and so we started developing this MT PV + + align:start position:0% +and so we started developing this MT PV + + + align:start position:0% +and so we started developing this MT PV +technology their first analysis for the + + align:start position:0% +technology their first analysis for the + + + align:start position:0% +technology their first analysis for the +visit that professor house mentioned + + align:start position:0% +visit that professor house mentioned + + + align:start position:0% +visit that professor house mentioned +earlier here on campus who once he + + align:start position:0% +earlier here on campus who once he + + + align:start position:0% +earlier here on campus who once he +realized that you actually could do + + align:start position:0% +realized that you actually could do + + + align:start position:0% +realized that you actually could do +better than Planck's law that we weren't + + align:start position:0% +better than Planck's law that we weren't + + + align:start position:0% +better than Planck's law that we weren't +by + + align:start position:0% +by + + + align:start position:0% +by +leading planck's law they were just + + align:start position:0% +leading planck's law they were just + + + align:start position:0% +leading planck's law they were just +operating outside of the limits that + + align:start position:0% +operating outside of the limits that + + + align:start position:0% +operating outside of the limits that +Planck himself put on his law he said + + align:start position:0% +Planck himself put on his law he said + + + align:start position:0% +Planck himself put on his law he said +okay go around the numbers you know so + + align:start position:0% +okay go around the numbers you know so + + + align:start position:0% +okay go around the numbers you know so +go back and crank through Maxwell's + + align:start position:0% +go back and crank through Maxwell's + + + align:start position:0% +go back and crank through Maxwell's +equations and do all that stuff and come + + align:start position:0% +equations and do all that stuff and come + + + align:start position:0% +equations and do all that stuff and come +back and tell me how much more how much + + align:start position:0% +back and tell me how much more how much + + + align:start position:0% +back and tell me how much more how much +better can you do that Planck's law and + + align:start position:0% +better can you do that Planck's law and + + + align:start position:0% +better can you do that Planck's law and +and so with a tremendous team at Draper + + align:start position:0% +and so with a tremendous team at Draper + + + align:start position:0% +and so with a tremendous team at Draper +laboratory many of who we still work + + align:start position:0% +laboratory many of who we still work + + + align:start position:0% +laboratory many of who we still work +with today we did that and then so this + + align:start position:0% +with today we did that and then so this + + + align:start position:0% +with today we did that and then so this +is part of one of you guys here + + align:start position:0% +is part of one of you guys here + + + align:start position:0% +is part of one of you guys here +mentioned starting in a larger company + + align:start position:0% +mentioned starting in a larger company + + + align:start position:0% +mentioned starting in a larger company +right you know what's it look like + + align:start position:0% +right you know what's it look like + + + align:start position:0% +right you know what's it look like +starting an energy technology in a + + align:start position:0% +starting an energy technology in a + + + align:start position:0% +starting an energy technology in a +start-up versus a larger company in the + + align:start position:0% +start-up versus a larger company in the + + + align:start position:0% +start-up versus a larger company in the +larger company there is management to + + align:start position:0% +larger company there is management to + + + align:start position:0% +larger company there is management to +deal with management does the resource + + align:start position:0% +deal with management does the resource + + + align:start position:0% +deal with management does the resource +allocation and hopefully which was the + + align:start position:0% +allocation and hopefully which was the + + + align:start position:0% +allocation and hopefully which was the +case for us they ask good questions + + align:start position:0% +case for us they ask good questions + + + align:start position:0% +case for us they ask good questions +you know first they said go convince + + align:start position:0% +you know first they said go convince + + + align:start position:0% +you know first they said go convince +professor house you know that you have + + align:start position:0% +professor house you know that you have + + + align:start position:0% +professor house you know that you have +it all right so when the analysis was + + align:start position:0% +it all right so when the analysis was + + + align:start position:0% +it all right so when the analysis was +done then they said ok now you know + + align:start position:0% +done then they said ok now you know + + + align:start position:0% +done then they said ok now you know +you're ready to design experiment start + + align:start position:0% +you're ready to design experiment start + + + align:start position:0% +you're ready to design experiment start +doing the experiments we built tiny + + align:start position:0% +doing the experiments we built tiny + + + align:start position:0% +doing the experiments we built tiny +chips 2 millimeters by 2 millimeters so + + align:start position:0% +chips 2 millimeters by 2 millimeters so + + + align:start position:0% +chips 2 millimeters by 2 millimeters so +smaller than you know half your baby + + align:start position:0% +smaller than you know half your baby + + + align:start position:0% +smaller than you know half your baby +fingernail and and gern off you know the + + align:start position:0% +fingernail and and gern off you know the + + + align:start position:0% +fingernail and and gern off you know the +effect was there as the theory as the + + align:start position:0% +effect was there as the theory as the + + + align:start position:0% +effect was there as the theory as the +analysis predicted we publish that in + + align:start position:0% +analysis predicted we publish that in + + + align:start position:0% +analysis predicted we publish that in +Applied Physics Letters the government + + align:start position:0% +Applied Physics Letters the government + + + align:start position:0% +Applied Physics Letters the government +got interested somebody mentioned + + align:start position:0% +got interested somebody mentioned + + + align:start position:0% +got interested somebody mentioned +government funding or whatnot that can + + align:start position:0% +government funding or whatnot that can + + + align:start position:0% +government funding or whatnot that can +be a very important part of energy + + align:start position:0% +be a very important part of energy + + + align:start position:0% +be a very important part of energy +technology because how is energy how is + + align:start position:0% +technology because how is energy how is + + + align:start position:0% +technology because how is energy how is +energy technology different than say + + align:start position:0% +energy technology different than say + + + align:start position:0% +energy technology different than say +software then say you know iPhone app + + align:start position:0% + + + + align:start position:0% + +oh boy huh you want to take a shot yeah + + align:start position:0% +oh boy huh you want to take a shot yeah + + + align:start position:0% +oh boy huh you want to take a shot yeah +yeah right right exactly yeah and so + + align:start position:0% +yeah right right exactly yeah and so + + + align:start position:0% +yeah right right exactly yeah and so +there was a recent book written called + + align:start position:0% +there was a recent book written called + + + align:start position:0% +there was a recent book written called +lean startup + + align:start position:0% +lean startup + + + align:start position:0% +lean startup +and so this the following is a basically + + align:start position:0% +and so this the following is a basically + + + align:start position:0% +and so this the following is a basically +a plug for the engineering field the + + align:start position:0% +a plug for the engineering field the + + + align:start position:0% +a plug for the engineering field the +plug for what many of you are doing so + + align:start position:0% +plug for what many of you are doing so + + + align:start position:0% +plug for what many of you are doing so +this book called lean startup and the + + align:start position:0% +this book called lean startup and the + + + align:start position:0% +this book called lean startup and the +folks at HBS and Sloan are very much + + align:start position:0% +folks at HBS and Sloan are very much + + + align:start position:0% +folks at HBS and Sloan are very much +aware of that etc but it turns out that + + align:start position:0% +aware of that etc but it turns out that + + + align:start position:0% +aware of that etc but it turns out that +it's been kind of a hit and it's almost + + align:start position:0% +it's been kind of a hit and it's almost + + + align:start position:0% +it's been kind of a hit and it's almost +sort of a craze and in the innovation + + align:start position:0% +sort of a craze and in the innovation + + + align:start position:0% +sort of a craze and in the innovation +world and but he says in it that he + + align:start position:0% +world and but he says in it that he + + + align:start position:0% +world and but he says in it that he +assumes that what they're trying to do + + align:start position:0% +assumes that what they're trying to do + + + align:start position:0% +assumes that what they're trying to do +can be done so in other words you're + + align:start position:0% +can be done so in other words you're + + + align:start position:0% +can be done so in other words you're +making an app for the iPhone you know + + align:start position:0% +making an app for the iPhone you know + + + align:start position:0% +making an app for the iPhone you know +you know that you can actually produce + + align:start position:0% +you know that you can actually produce + + + align:start position:0% +you know that you can actually produce +it it can actually do the thing do you + + align:start position:0% +it it can actually do the thing do you + + + align:start position:0% +it it can actually do the thing do you +do it this way for this market do you do + + align:start position:0% +do it this way for this market do you do + + + align:start position:0% +do it this way for this market do you do +it this way for this market and that's + + align:start position:0% +it this way for this market and that's + + + align:start position:0% +it this way for this market and that's +where that's where the the war gets lost + + align:start position:0% +where that's where the the war gets lost + + + align:start position:0% +where that's where the the war gets lost +or won in that world but here in energy + + align:start position:0% +or won in that world but here in energy + + + align:start position:0% +or won in that world but here in energy +it's it's really not that way because + + align:start position:0% +it's it's really not that way because + + + align:start position:0% +it's it's really not that way because +you know there's no guarantee that + + align:start position:0% +you know there's no guarantee that + + + align:start position:0% +you know there's no guarantee that +things can be done like we've seen + + align:start position:0% +things can be done like we've seen + + + align:start position:0% +things can be done like we've seen +billions of dollars go into the liquid + + align:start position:0% +billions of dollars go into the liquid + + + align:start position:0% +billions of dollars go into the liquid +biofuels which one you guys mentioned + + align:start position:0% +biofuels which one you guys mentioned + + + align:start position:0% +biofuels which one you guys mentioned +recently and it's turned out that it's + + align:start position:0% +recently and it's turned out that it's + + + align:start position:0% +recently and it's turned out that it's +very hard to do very hard to do so you + + align:start position:0% +very hard to do very hard to do so you + + + align:start position:0% +very hard to do very hard to do so you +know technically it was a technical + + align:start position:0% +know technically it was a technical + + + align:start position:0% +know technically it was a technical +impediment which is dramatically + + align:start position:0% +impediment which is dramatically + + + align:start position:0% +impediment which is dramatically +different than say if you're in the + + align:start position:0% +different than say if you're in the + + + align:start position:0% +different than say if you're in the +software world where you basically know + + align:start position:0% +software world where you basically know + + + align:start position:0% +software world where you basically know +that you can build what you want to + + align:start position:0% +that you can build what you want to + + + align:start position:0% +that you can build what you want to +build and so whether you're thinking + + align:start position:0% +build and so whether you're thinking + + + align:start position:0% +build and so whether you're thinking +about starting your own businesses or + + align:start position:0% +about starting your own businesses or + + + align:start position:0% +about starting your own businesses or +whether you're interacting with + + align:start position:0% +whether you're interacting with + + + align:start position:0% +whether you're interacting with +management and some big business you + + align:start position:0% +management and some big business you + + + align:start position:0% +management and some big business you +know that that understanding of applying + + align:start position:0% +know that that understanding of applying + + + align:start position:0% +know that that understanding of applying +the right the right questions you know + + align:start position:0% +the right the right questions you know + + + align:start position:0% +the right the right questions you know +and the right rules so if you're in an + + align:start position:0% +and the right rules so if you're in an + + + align:start position:0% +and the right rules so if you're in an +energy business you probably want the + + align:start position:0% +energy business you probably want the + + + align:start position:0% +energy business you probably want the +engineers to be more involved in + + align:start position:0% +engineers to be more involved in + + + align:start position:0% +engineers to be more involved in +management decisions than maybe if you + + align:start position:0% +management decisions than maybe if you + + + align:start position:0% +management decisions than maybe if you +were doing software something what you + + align:start position:0% +were doing software something what you + + + align:start position:0% +were doing software something what you +really need to know is you know it's + + align:start position:0% +really need to know is you know it's + + + align:start position:0% +really need to know is you know it's +it's the marketing people that need to + + align:start position:0% +it's the marketing people that need to + + + align:start position:0% +it's the marketing people that need to +drive + + align:start position:0% +drive + + + align:start position:0% +drive +that need to drive the process okay + + align:start position:0% + + + + align:start position:0% + +reactions more about his life story so + + align:start position:0% +reactions more about his life story so + + + align:start position:0% +reactions more about his life story so +we just a finished we develop we + + align:start position:0% +we just a finished we develop we + + + align:start position:0% +we just a finished we develop we +developed this for his about six year + + align:start position:0% +developed this for his about six year + + + align:start position:0% +developed this for his about six year +for excuse me we developed this for 10 + + align:start position:0% +for excuse me we developed this for 10 + + + align:start position:0% +for excuse me we developed this for 10 +years at Draper lab literally across the + + align:start position:0% +years at Draper lab literally across the + + + align:start position:0% +years at Draper lab literally across the +street + + align:start position:0% +street + + + align:start position:0% +street +it was about half internal and half + + align:start position:0% +it was about half internal and half + + + align:start position:0% +it was about half internal and half +government and from you know starting + + align:start position:0% +government and from you know starting + + + align:start position:0% +government and from you know starting +with just an idea like you guys have + + align:start position:0% +with just an idea like you guys have + + + align:start position:0% +with just an idea like you guys have +mentioned some ideas and then analysis + + align:start position:0% +mentioned some ideas and then analysis + + + align:start position:0% +mentioned some ideas and then analysis +and quickly moving on to actually + + align:start position:0% +and quickly moving on to actually + + + align:start position:0% +and quickly moving on to actually +building Hardware tiny hard with the + + align:start position:0% +building Hardware tiny hard with the + + + align:start position:0% +building Hardware tiny hard with the +scientific proof of concept + + align:start position:0% +scientific proof of concept + + + align:start position:0% +scientific proof of concept +demonstration hardware and and then + + align:start position:0% +demonstration hardware and and then + + + align:start position:0% +demonstration hardware and and then +scaling up to the kinds of panels and + + align:start position:0% +scaling up to the kinds of panels and + + + align:start position:0% +scaling up to the kinds of panels and +modules that you see us working on now + + align:start position:0% +modules that you see us working on now + + + align:start position:0% +modules that you see us working on now +the last five years of that work went on + + align:start position:0% +the last five years of that work went on + + + align:start position:0% +the last five years of that work went on +in in the startup mt pv corporation + + align:start position:0% +in in the startup mt pv corporation + + + align:start position:0% +in in the startup mt pv corporation +which got spun out of Draper I came back + + align:start position:0% +which got spun out of Draper I came back + + + align:start position:0% +which got spun out of Draper I came back +here for a year as a Sloan fellow blog + + align:start position:0% +here for a year as a Sloan fellow blog + + + align:start position:0% +here for a year as a Sloan fellow blog +for the snow fellows program and + + align:start position:0% +for the snow fellows program and + + + align:start position:0% +for the snow fellows program and +actually the first couple million + + align:start position:0% +actually the first couple million + + + align:start position:0% +actually the first couple million +dollars roughly invested in our country + + align:start position:0% +dollars roughly invested in our country + + + align:start position:0% +dollars roughly invested in our country +and our company was from fellow Sloan + + align:start position:0% +and our company was from fellow Sloan + + + align:start position:0% +and our company was from fellow Sloan +fellows which was pretty remarkable + + align:start position:0% + + + + align:start position:0% + +yes Draper labs involved as well d did + + align:start position:0% +yes Draper labs involved as well d did + + + align:start position:0% +yes Draper labs involved as well d did +they give you the IP or do they have the + + align:start position:0% +they give you the IP or do they have the + + + align:start position:0% +they give you the IP or do they have the +IP I actually had the IP here okay and + + align:start position:0% +IP I actually had the IP here okay and + + + align:start position:0% +IP I actually had the IP here okay and +so it went with me to there and then + + align:start position:0% +so it went with me to there and then + + + align:start position:0% +so it went with me to there and then +yeah that was kind of part of the + + align:start position:0% +yeah that was kind of part of the + + + align:start position:0% +yeah that was kind of part of the +original another important person that + + align:start position:0% +original another important person that + + + align:start position:0% +original another important person that +MIT whose name is Robert Rhines none of + + align:start position:0% +MIT whose name is Robert Rhines none of + + + align:start position:0% +MIT whose name is Robert Rhines none of +you probably had the pleasure of taking + + align:start position:0% +you probably had the pleasure of taking + + + align:start position:0% +you probably had the pleasure of taking +his course he kind of taught one of the + + align:start position:0% +his course he kind of taught one of the + + + align:start position:0% +his course he kind of taught one of the +first the first course poly for + + align:start position:0% +first the first course poly for + + + align:start position:0% +first the first course poly for +engineers in innovation now all you guys + + align:start position:0% +engineers in innovation now all you guys + + + align:start position:0% +engineers in innovation now all you guys +know about entrepreneurship and + + align:start position:0% +know about entrepreneurship and + + + align:start position:0% +know about entrepreneurship and +innovation some of you were smart enough + + align:start position:0% +innovation some of you were smart enough + + + align:start position:0% +innovation some of you were smart enough +to realize that you know + + align:start position:0% +to realize that you know + + + align:start position:0% +to realize that you know +entrepreneurship and innovation isn't + + align:start position:0% +entrepreneurship and innovation isn't + + + align:start position:0% +entrepreneurship and innovation isn't +right for everybody at every moment and + + align:start position:0% +right for everybody at every moment and + + + align:start position:0% +right for everybody at every moment and +and it can be very painful along the way + + align:start position:0% +and it can be very painful along the way + + + align:start position:0% +and it can be very painful along the way +and I'm happy to talk about some of that + + align:start position:0% +and I'm happy to talk about some of that + + + align:start position:0% +and I'm happy to talk about some of that +if you want and if you were smart you + + align:start position:0% +if you want and if you were smart you + + + align:start position:0% +if you want and if you were smart you +would ask about some of that if you want + + align:start position:0% +would ask about some of that if you want + + + align:start position:0% +would ask about some of that if you want +especially the half of you that are + + align:start position:0% +especially the half of you that are + + + align:start position:0% +especially the half of you that are +thinking about starting businesses and + + align:start position:0% +thinking about starting businesses and + + + align:start position:0% +thinking about starting businesses and +but at any rate Robert Rhines so he + + align:start position:0% +but at any rate Robert Rhines so he + + + align:start position:0% +but at any rate Robert Rhines so he +taught a course it was taught out of + + align:start position:0% +taught a course it was taught out of + + + align:start position:0% +taught a course it was taught out of +course six I'm not sure why + + align:start position:0% +course six I'm not sure why + + + align:start position:0% +course six I'm not sure why +like starting like 50 years ago on + + align:start position:0% +like starting like 50 years ago on + + + align:start position:0% +like starting like 50 years ago on +innovation and patents and I took that + + align:start position:0% +innovation and patents and I took that + + + align:start position:0% +innovation and patents and I took that +course and and he became a patent + + align:start position:0% +course and and he became a patent + + + align:start position:0% +course and and he became a patent +attorney for MTV beef corporation until + + align:start position:0% +attorney for MTV beef corporation until + + + align:start position:0% +attorney for MTV beef corporation until +he passed away a couple years ago so MIT + + align:start position:0% +he passed away a couple years ago so MIT + + + align:start position:0% +he passed away a couple years ago so MIT +is really all over this technology and I + + align:start position:0% +is really all over this technology and I + + + align:start position:0% +is really all over this technology and I +guess Hyrum said you know you should + + align:start position:0% +guess Hyrum said you know you should + + + align:start position:0% +guess Hyrum said you know you should +tell them that you think that you guys + + align:start position:0% +tell them that you think that you guys + + + align:start position:0% +tell them that you think that you guys +have the potential to get the 60% + + align:start position:0% +have the potential to get the 60% + + + align:start position:0% +have the potential to get the 60% +efficiency and like a megawatt per + + align:start position:0% +efficiency and like a megawatt per + + + align:start position:0% +efficiency and like a megawatt per +square meter you know and I hate talking + + align:start position:0% +square meter you know and I hate talking + + + align:start position:0% +square meter you know and I hate talking +about those things it really is what + + align:start position:0% +about those things it really is what + + + align:start position:0% +about those things it really is what +keeps us going you know I mean these + + align:start position:0% +keeps us going you know I mean these + + + align:start position:0% +keeps us going you know I mean these +initial niche markets they don't did + + align:start position:0% +initial niche markets they don't did + + + align:start position:0% +initial niche markets they don't did +they don't keep you going you know they + + align:start position:0% +they don't keep you going you know they + + + align:start position:0% +they don't keep you going you know they +keep you focused so you know what you + + align:start position:0% +keep you focused so you know what you + + + align:start position:0% +keep you focused so you know what you +need to do you know when you when you + + align:start position:0% +need to do you know when you when you + + + align:start position:0% +need to do you know when you when you +get up every day but they don't keep you + + align:start position:0% +get up every day but they don't keep you + + + align:start position:0% +get up every day but they don't keep you +going what keeps you going is a larger + + align:start position:0% +going what keeps you going is a larger + + + align:start position:0% +going what keeps you going is a larger +vision about something that it doesn't + + align:start position:0% +vision about something that it doesn't + + + align:start position:0% +vision about something that it doesn't +have to be as large as you know as + + align:start position:0% +have to be as large as you know as + + + align:start position:0% +have to be as large as you know as +producing 50% of the world's energy but + + align:start position:0% +producing 50% of the world's energy but + + + align:start position:0% +producing 50% of the world's energy but +it's a larger vision as to how what + + align:start position:0% +it's a larger vision as to how what + + + align:start position:0% +it's a larger vision as to how what +you're working on creates meaning you + + align:start position:0% +you're working on creates meaning you + + + align:start position:0% +you're working on creates meaning you +know and they hear you saying I hear in + + align:start position:0% +know and they hear you saying I hear in + + + align:start position:0% +know and they hear you saying I hear in +your narrative and that I hear from a + + align:start position:0% +your narrative and that I hear from a + + + align:start position:0% +your narrative and that I hear from a +lot of entrepreneurs in fact a lot of + + align:start position:0% +lot of entrepreneurs in fact a lot of + + + align:start position:0% +lot of entrepreneurs in fact a lot of +people but a lot of entrepreneurs in + + align:start position:0% +people but a lot of entrepreneurs in + + + align:start position:0% +people but a lot of entrepreneurs in +particular is your path has not been a + + align:start position:0% +particular is your path has not been a + + + align:start position:0% +particular is your path has not been a +straight line so and and if you sort of + + align:start position:0% +straight line so and and if you sort of + + + align:start position:0% +straight line so and and if you sort of +sit there sit out there and think I'm + + align:start position:0% +sit there sit out there and think I'm + + + align:start position:0% +sit there sit out there and think I'm +gonna do this that I'm gonna do this I'm + + align:start position:0% +gonna do this that I'm gonna do this I'm + + + align:start position:0% +gonna do this that I'm gonna do this I'm +gonna do that then I'm gonna do that + + align:start position:0% +gonna do that then I'm gonna do that + + + align:start position:0% +gonna do that then I'm gonna do that +that sort of work for Bill Gates but it + + align:start position:0% +that sort of work for Bill Gates but it + + + align:start position:0% +that sort of work for Bill Gates but it +doesn't work very often right it doesn't + + align:start position:0% +doesn't work very often right it doesn't + + + align:start position:0% +doesn't work very often right it doesn't +not an energy field that seems yeah is + + align:start position:0% +not an energy field that seems yeah is + + + align:start position:0% +not an energy field that seems yeah is +it possible there are some fields where + + align:start position:0% +it possible there are some fields where + + + align:start position:0% +it possible there are some fields where +it does sort of go more more linearly + + align:start position:0% +it does sort of go more more linearly + + + align:start position:0% +it does sort of go more more linearly +like you know like I don't know maybe + + align:start position:0% +like you know like I don't know maybe + + + align:start position:0% +like you know like I don't know maybe +biotech and drug discovery and something + + align:start position:0% +biotech and drug discovery and something + + + align:start position:0% +biotech and drug discovery and something +like what oh no I mean for individual + + align:start position:0% +like what oh no I mean for individual + + + align:start position:0% +like what oh no I mean for individual +careers for individual careers careers + + align:start position:0% +careers for individual careers careers + + + align:start position:0% +careers for individual careers careers +if you're gonna be an entrepreneur a lot + + align:start position:0% +if you're gonna be an entrepreneur a lot + + + align:start position:0% +if you're gonna be an entrepreneur a lot +of people you know I was with this + + align:start position:0% +of people you know I was with this + + + align:start position:0% +of people you know I was with this +startup and it failed and I worked with + + align:start position:0% +startup and it failed and I worked with + + + align:start position:0% +startup and it failed and I worked with +this company and then I did this and + + align:start position:0% +this company and then I did this and + + + align:start position:0% +this company and then I did this and +then three of us had this idea yeah and + + align:start position:0% +then three of us had this idea yeah and + + + align:start position:0% +then three of us had this idea yeah and +you don't sit here at 20 21 years of age + + align:start position:0% +you don't sit here at 20 21 years of age + + + align:start position:0% +you don't sit here at 20 21 years of age +and see that path true the path opens up + + align:start position:0% +and see that path true the path opens up + + + align:start position:0% +and see that path true the path opens up +in front of you + + align:start position:0% +in front of you + + + align:start position:0% +in front of you +yeah oftentimes true and it's why + + align:start position:0% +yeah oftentimes true and it's why + + + align:start position:0% +yeah oftentimes true and it's why +there's this a lot of merit in starting + + align:start position:0% +there's this a lot of merit in starting + + + align:start position:0% +there's this a lot of merit in starting +a career in in existing companies + + align:start position:0% +a career in in existing companies + + + align:start position:0% +a career in in existing companies +because as the young man pointed out you + + align:start position:0% +because as the young man pointed out you + + + align:start position:0% +because as the young man pointed out you +know you do get lots of experience and + + align:start position:0% +know you do get lots of experience and + + + align:start position:0% +know you do get lots of experience and +knowledge that addresses those kinds of + + align:start position:0% +knowledge that addresses those kinds of + + + align:start position:0% +knowledge that addresses those kinds of +dilemmas and risks + + align:start position:0% +dilemmas and risks + + + align:start position:0% +dilemmas and risks +etc give a little pain well I'll write + + align:start position:0% +etc give a little pain well I'll write + + + align:start position:0% +etc give a little pain well I'll write +my wife in to give you the pain yeah so + + align:start position:0% +my wife in to give you the pain yeah so + + + align:start position:0% +my wife in to give you the pain yeah so +when you're with startups and you're + + align:start position:0% +when you're with startups and you're + + + align:start position:0% +when you're with startups and you're +getting them funded yeah that can be + + align:start position:0% +getting them funded yeah that can be + + + align:start position:0% +getting them funded yeah that can be +challenging right so have any of you + + align:start position:0% +challenging right so have any of you + + + align:start position:0% +challenging right so have any of you +funded anything to date you know even + + align:start position:0% +funded anything to date you know even + + + align:start position:0% +funded anything to date you know even +like one more business when you were a + + align:start position:0% +like one more business when you were a + + + align:start position:0% +like one more business when you were a +kid do you bought the lawnmower yes + + align:start position:0% +kid do you bought the lawnmower yes + + + align:start position:0% +kid do you bought the lawnmower yes +woman oh yeah + + align:start position:0% + + + + align:start position:0% + +yeah so we're we are you in that process + + align:start position:0% +yeah so we're we are you in that process + + + align:start position:0% +yeah so we're we are you in that process +yeah in the fundraising process money's + + align:start position:0% +yeah in the fundraising process money's + + + align:start position:0% +yeah in the fundraising process money's +in the bank talking to yeah we're just + + align:start position:0% + + + + align:start position:0% + +congratulations that's a real big deal + + align:start position:0% +congratulations that's a real big deal + + + align:start position:0% +congratulations that's a real big deal +yeah and what are you doing in well + + align:start position:0% +yeah and what are you doing in well + + + align:start position:0% +yeah and what are you doing in well +that's it's an important point to be at + + align:start position:0% +that's it's an important point to be at + + + align:start position:0% +that's it's an important point to be at +the final to find a little legal details + + align:start position:0% +the final to find a little legal details + + + align:start position:0% +the final to find a little legal details +and the little words and everything else + + align:start position:0% +and the little words and everything else + + + align:start position:0% +and the little words and everything else +that can take a while it can take a + + align:start position:0% +that can take a while it can take a + + + align:start position:0% +that can take a while it can take a +while for the money to actually show up + + align:start position:0% +while for the money to actually show up + + + align:start position:0% +while for the money to actually show up +in the bank so so you can't count on + + align:start position:0% +in the bank so so you can't count on + + + align:start position:0% +in the bank so so you can't count on +until it's actually bit but it sounds + + align:start position:0% +until it's actually bit but it sounds + + + align:start position:0% +until it's actually bit but it sounds +like you guys are very close + + align:start position:0% +like you guys are very close + + + align:start position:0% +like you guys are very close +congratulations what what are you doing + + align:start position:0% + + + + align:start position:0% + +robotics League in which country thank + + align:start position:0% +robotics League in which country thank + + + align:start position:0% +robotics League in which country thank +you very cool Wow + + align:start position:0% +you very cool Wow + + + align:start position:0% +you very cool Wow +was there another hand yes + + align:start position:0% + + + + align:start position:0% + +excellent okay so you got two real + + align:start position:0% +excellent okay so you got two real + + + align:start position:0% +excellent okay so you got two real +entrepreneurs here you know pleasure + + align:start position:0% +entrepreneurs here you know pleasure + + + align:start position:0% +entrepreneurs here you know pleasure +speaking so to compromise between those + + align:start position:0% +speaking so to compromise between those + + + align:start position:0% +speaking so to compromise between those +who wanted that talk and those who + + align:start position:0% +who wanted that talk and those who + + + align:start position:0% +who wanted that talk and those who +wanted this talk I'll give you a little + + align:start position:0% +wanted this talk I'll give you a little + + + align:start position:0% +wanted this talk I'll give you a little +bit of what I would have tried to make + + align:start position:0% +bit of what I would have tried to make + + + align:start position:0% +bit of what I would have tried to make +an hour and a half out of if you had + + align:start position:0% +an hour and a half out of if you had + + + align:start position:0% +an hour and a half out of if you had +voted for economic development and green + + align:start position:0% +voted for economic development and green + + + align:start position:0% +voted for economic development and green +growth this story starts in 87 with the + + align:start position:0% +growth this story starts in 87 with the + + + align:start position:0% +growth this story starts in 87 with the +Brundtland report a commission chaired + + align:start position:0% +Brundtland report a commission chaired + + + align:start position:0% +Brundtland report a commission chaired +by Gro Harlem Brundtland a woman who was + + align:start position:0% +by Gro Harlem Brundtland a woman who was + + + align:start position:0% +by Gro Harlem Brundtland a woman who was +a former prime minister of norway that + + align:start position:0% +a former prime minister of norway that + + + align:start position:0% +a former prime minister of norway that +coined the phrase sustainable + + align:start position:0% +coined the phrase sustainable + + + align:start position:0% +coined the phrase sustainable +development and gave it the definition + + align:start position:0% +development and gave it the definition + + + align:start position:0% +development and gave it the definition +that you see there and in the first + + align:start position:0% +that you see there and in the first + + + align:start position:0% +that you see there and in the first +small bullet is sort of the economists + + align:start position:0% +small bullet is sort of the economists + + + align:start position:0% +small bullet is sort of the economists +interpretation and that is the economy + + align:start position:0% +interpretation and that is the economy + + + align:start position:0% +interpretation and that is the economy +as a certain set of assets intellectual + + align:start position:0% +as a certain set of assets intellectual + + + align:start position:0% +as a certain set of assets intellectual +capital and physical capital and in the + + align:start position:0% +capital and physical capital and in the + + + align:start position:0% +capital and physical capital and in the +environment and natural the natural + + align:start position:0% +environment and natural the natural + + + align:start position:0% +environment and natural the natural +world a set of stocks and the notion is + + align:start position:0% +world a set of stocks and the notion is + + + align:start position:0% +world a set of stocks and the notion is +you should pass on to be sustainable a + + align:start position:0% +you should pass on to be sustainable a + + + align:start position:0% +you should pass on to be sustainable a +set of stocks that are as desirable as + + align:start position:0% +set of stocks that are as desirable as + + + align:start position:0% +set of stocks that are as desirable as +the set you inherited the first + + align:start position:0% +the set you inherited the first + + + align:start position:0% +the set you inherited the first +president Bush called that stewardship + + align:start position:0% +president Bush called that stewardship + + + align:start position:0% +president Bush called that stewardship +since he was a Republican nobody used + + align:start position:0% +since he was a Republican nobody used + + + align:start position:0% +since he was a Republican nobody used +that term but but that's the concept + + align:start position:0% +that term but but that's the concept + + + align:start position:0% +that term but but that's the concept +that you have a certain set of assets so + + align:start position:0% +that you have a certain set of assets so + + + align:start position:0% +that you have a certain set of assets so +that you could say for instance that + + align:start position:0% +that you could say for instance that + + + align:start position:0% +that you could say for instance that +economic development in 19th century + + align:start position:0% +economic development in 19th century + + + align:start position:0% +economic development in 19th century +Britain was arguably sustainable right + + align:start position:0% +Britain was arguably sustainable right + + + align:start position:0% +Britain was arguably sustainable right +they burned all the coal the country was + + align:start position:0% +they burned all the coal the country was + + + align:start position:0% +they burned all the coal the country was +dirty as anything for decades but they + + align:start position:0% +dirty as anything for decades but they + + + align:start position:0% +dirty as anything for decades but they +came out of it with tangible capital + + align:start position:0% +came out of it with tangible capital + + + align:start position:0% +came out of it with tangible capital +intellectual capital a whole set of + + align:start position:0% +intellectual capital a whole set of + + + align:start position:0% +intellectual capital a whole set of +other assets that provided a standard of + + align:start position:0% +other assets that provided a standard of + + + align:start position:0% +other assets that provided a standard of +living + + align:start position:0% +living + + + align:start position:0% +living +Saudi Arabia is mostly spending the oil + + align:start position:0% +Saudi Arabia is mostly spending the oil + + + align:start position:0% +Saudi Arabia is mostly spending the oil +money on consumption so when the oil + + align:start position:0% +money on consumption so when the oil + + + align:start position:0% +money on consumption so when the oil +goes British British coal is long gone + + align:start position:0% +goes British British coal is long gone + + + align:start position:0% +goes British British coal is long gone +but Britain used it + + align:start position:0% +but Britain used it + + + align:start position:0% +but Britain used it +the issue is that when the Saudi oil is + + align:start position:0% +the issue is that when the Saudi oil is + + + align:start position:0% +the issue is that when the Saudi oil is +gone that generation is not going to + + align:start position:0% +gone that generation is not going to + + + align:start position:0% +gone that generation is not going to +have have the assets now it's a little + + align:start position:0% +have have the assets now it's a little + + + align:start position:0% +have have the assets now it's a little +vague right it doesn't distinguish + + align:start position:0% +vague right it doesn't distinguish + + + align:start position:0% +vague right it doesn't distinguish +between intellectual capital and species + + align:start position:0% +between intellectual capital and species + + + align:start position:0% +between intellectual capital and species +and it doesn't say anything about + + align:start position:0% +and it doesn't say anything about + + + align:start position:0% +and it doesn't say anything about +poverty and this question of their the + + align:start position:0% +poverty and this question of their the + + + align:start position:0% +poverty and this question of their the +future generations own needs I mean if + + align:start position:0% +future generations own needs I mean if + + + align:start position:0% +future generations own needs I mean if +the future generation wants to only play + + align:start position:0% +the future generation wants to only play + + + align:start position:0% +the future generation wants to only play +video games then wiping out the + + align:start position:0% +video games then wiping out the + + + align:start position:0% +video games then wiping out the +elephants won't matter but if future + + align:start position:0% +elephants won't matter but if future + + + align:start position:0% +elephants won't matter but if future +generations actually care a lot about + + align:start position:0% +generations actually care a lot about + + + align:start position:0% +generations actually care a lot about +the natural world then having great + + align:start position:0% +the natural world then having great + + + align:start position:0% +the natural world then having great +video games is not very important so if + + align:start position:0% +video games is not very important so if + + + align:start position:0% +video games is not very important so if +you don't know what their needs are it's + + align:start position:0% +you don't know what their needs are it's + + + align:start position:0% +you don't know what their needs are it's +a little tough and you know I was once + + align:start position:0% +a little tough and you know I was once + + + align:start position:0% +a little tough and you know I was once +interviewed and asked what I thought + + align:start position:0% +interviewed and asked what I thought + + + align:start position:0% +interviewed and asked what I thought +sustainable development met and I gave + + align:start position:0% +sustainable development met and I gave + + + align:start position:0% +sustainable development met and I gave +the Brundtland definition and they said + + align:start position:0% +the Brundtland definition and they said + + + align:start position:0% +the Brundtland definition and they said +is that all you mean and that's kind of + + align:start position:0% +is that all you mean and that's kind of + + + align:start position:0% +is that all you mean and that's kind of +narrow I said what do you mean said what + + align:start position:0% +narrow I said what do you mean said what + + + align:start position:0% +narrow I said what do you mean said what +about sustainable communities and + + align:start position:0% +about sustainable communities and + + + align:start position:0% +about sustainable communities and +sustainable lifestyles and sustainable + + align:start position:0% +sustainable lifestyles and sustainable + + + align:start position:0% +sustainable lifestyles and sustainable +it's gotten to mean sort of everything + + align:start position:0% +it's gotten to mean sort of everything + + + align:start position:0% +it's gotten to mean sort of everything +that's good and wholesome and green and + + align:start position:0% +that's good and wholesome and green and + + + align:start position:0% +that's good and wholesome and green and +a little vague but nonetheless start + + align:start position:0% +a little vague but nonetheless start + + + align:start position:0% +a little vague but nonetheless start +with the sustainable development notion + + align:start position:0% +with the sustainable development notion + + + align:start position:0% +with the sustainable development notion +the next big event was the 1992 + + align:start position:0% +the next big event was the 1992 + + + align:start position:0% +the next big event was the 1992 +conference on Environment Development + + align:start position:0% +conference on Environment Development + + + align:start position:0% +conference on Environment Development +this was the conference that led to the + + align:start position:0% +this was the conference that led to the + + + align:start position:0% +this was the conference that led to the +Framework Convention on Climate Change + + align:start position:0% +Framework Convention on Climate Change + + + align:start position:0% +Framework Convention on Climate Change +and really started that conversation the + + align:start position:0% +and really started that conversation the + + + align:start position:0% +and really started that conversation the +Kyoto Protocol and all of that that was + + align:start position:0% +Kyoto Protocol and all of that that was + + + align:start position:0% +Kyoto Protocol and all of that that was +a big deal + + align:start position:0% +a big deal + + + align:start position:0% +a big deal +172 governments participated a hundred + + align:start position:0% +172 governments participated a hundred + + + align:start position:0% +172 governments participated a hundred +and eight heads of state or Heads of + + align:start position:0% +and eight heads of state or Heads of + + + align:start position:0% +and eight heads of state or Heads of +Government went that's huge and what + + align:start position:0% +Government went that's huge and what + + + align:start position:0% +Government went that's huge and what +came out of it was a lot of paper but + + align:start position:0% +came out of it was a lot of paper but + + + align:start position:0% +came out of it was a lot of paper but +the Framework Convention on Climate + + align:start position:0% +the Framework Convention on Climate + + + align:start position:0% +the Framework Convention on Climate +Change which really structured all the + + align:start position:0% +Change which really structured all the + + + align:start position:0% +Change which really structured all the +subsequent debate so now we come to 20 + + align:start position:0% +subsequent debate so now we come to 20 + + + align:start position:0% +subsequent debate so now we come to 20 +years later and you've got this whole UN + + align:start position:0% +years later and you've got this whole UN + + + align:start position:0% +years later and you've got this whole UN +machinery and we ought to have a + + align:start position:0% +machinery and we ought to have a + + + align:start position:0% +machinery and we ought to have a +conference Rio +20 well if the headline + + align:start position:0% +conference Rio +20 well if the headline + + + align:start position:0% +conference Rio +20 well if the headline +was climate in 1992 the question is + + align:start position:0% +was climate in 1992 the question is + + + align:start position:0% +was climate in 1992 the question is +what's the headline now and that leads + + align:start position:0% +what's the headline now and that leads + + + align:start position:0% +what's the headline now and that leads +to the green growth discussion right so + + align:start position:0% +to the green growth discussion right so + + + align:start position:0% +to the green growth discussion right so +you began to get beginning a few years + + align:start position:0% +you began to get beginning a few years + + + align:start position:0% +you began to get beginning a few years +ago you began to see staff papers + + align:start position:0% +ago you began to see staff papers + + + align:start position:0% +ago you began to see staff papers +emerging talking about the green economy + + align:start position:0% +emerging talking about the green economy + + + align:start position:0% +emerging talking about the green economy +and green development and green growth + + align:start position:0% +and green development and green growth + + + align:start position:0% +and green development and green growth +now I have to say I've read a lot of + + align:start position:0% +now I have to say I've read a lot of + + + align:start position:0% +now I have to say I've read a lot of +this + + align:start position:0% +this + + + align:start position:0% +this +and the definition is not entirely clear + + align:start position:0% +and the definition is not entirely clear + + + align:start position:0% +and the definition is not entirely clear +it is described as a subset of + + align:start position:0% +it is described as a subset of + + + align:start position:0% +it is described as a subset of +sustainable development and it seems to + + align:start position:0% +sustainable development and it seems to + + + align:start position:0% +sustainable development and it seems to +be that subset of sustainable + + align:start position:0% +be that subset of sustainable + + + align:start position:0% +be that subset of sustainable +development strategies that doesn't + + align:start position:0% +development strategies that doesn't + + + align:start position:0% +development strategies that doesn't +involve degradation of the natural + + align:start position:0% +involve degradation of the natural + + + align:start position:0% +involve degradation of the natural +environment on the way all right so the + + align:start position:0% +environment on the way all right so the + + + align:start position:0% +environment on the way all right so the +British development wouldn't be might be + + align:start position:0% +British development wouldn't be might be + + + align:start position:0% +British development wouldn't be might be +sustainable because at the end of all + + align:start position:0% +sustainable because at the end of all + + + align:start position:0% +sustainable because at the end of all +that dirt they had high living standards + + align:start position:0% +that dirt they had high living standards + + + align:start position:0% +that dirt they had high living standards +in the prospect of higher living + + align:start position:0% +in the prospect of higher living + + + align:start position:0% +in the prospect of higher living +standards but not green because the + + align:start position:0% +standards but not green because the + + + align:start position:0% +standards but not green because the +environment was degraded rather + + align:start position:0% +environment was degraded rather + + + align:start position:0% +environment was degraded rather +substantially it recovered but it was + + align:start position:0% +substantially it recovered but it was + + + align:start position:0% +substantially it recovered but it was +degraded substantially in the process + + align:start position:0% +degraded substantially in the process + + + align:start position:0% +degraded substantially in the process +and I'm sure species were extinguished + + align:start position:0% +and I'm sure species were extinguished + + + align:start position:0% +and I'm sure species were extinguished +so maybe you could do fossil fuels and + + align:start position:0% +so maybe you could do fossil fuels and + + + align:start position:0% +so maybe you could do fossil fuels and +be green I think so + + align:start position:0% +be green I think so + + + align:start position:0% +be green I think so +but you know if you think about + + align:start position:0% +but you know if you think about + + + align:start position:0% +but you know if you think about +alternative ways of doing sustainable + + align:start position:0% +alternative ways of doing sustainable + + + align:start position:0% +alternative ways of doing sustainable +development there's another another part + + align:start position:0% +development there's another another part + + + align:start position:0% +development there's another another part +of the World Bank the World Bank the UN + + align:start position:0% +of the World Bank the World Bank the UN + + + align:start position:0% +of the World Bank the World Bank the UN +the OECD and others are talking about + + align:start position:0% +the OECD and others are talking about + + + align:start position:0% +the OECD and others are talking about +green economy if you go on the World + + align:start position:0% +green economy if you go on the World + + + align:start position:0% +green economy if you go on the World +Bank website and you look carefully you + + align:start position:0% +Bank website and you look carefully you + + + align:start position:0% +Bank website and you look carefully you +see papers on inclusive growth and that + + align:start position:0% +see papers on inclusive growth and that + + + align:start position:0% +see papers on inclusive growth and that +says well you have to be sustainable but + + align:start position:0% +says well you have to be sustainable but + + + align:start position:0% +says well you have to be sustainable but +you should focus on poverty green growth + + align:start position:0% +you should focus on poverty green growth + + + align:start position:0% +you should focus on poverty green growth +says you ought to be sustainable but you + + align:start position:0% +says you ought to be sustainable but you + + + align:start position:0% +says you ought to be sustainable but you +should focus on the environment okay + + align:start position:0% + + + + align:start position:0% + +where do you go from there + + align:start position:0% +where do you go from there + + + align:start position:0% +where do you go from there +well this is what is sort of the + + align:start position:0% +well this is what is sort of the + + + align:start position:0% +well this is what is sort of the +interesting thing particularly the UN + + align:start position:0% +interesting thing particularly the UN + + + align:start position:0% +interesting thing particularly the UN +now argues that if you make very large + + align:start position:0% +now argues that if you make very large + + + align:start position:0% +now argues that if you make very large +investments in going green growth of + + align:start position:0% +investments in going green growth of + + + align:start position:0% +investments in going green growth of +living standards will increase the + + align:start position:0% +living standards will increase the + + + align:start position:0% +living standards will increase the +phrase that's used is a new engine of + + align:start position:0% +phrase that's used is a new engine of + + + align:start position:0% +phrase that's used is a new engine of +growth now if you're a cynical economist + + align:start position:0% +growth now if you're a cynical economist + + + align:start position:0% +growth now if you're a cynical economist +you realize that not only does that mean + + align:start position:0% +you realize that not only does that mean + + + align:start position:0% +you realize that not only does that mean +there's a free lunch but one we'd all be + + align:start position:0% +there's a free lunch but one we'd all be + + + align:start position:0% +there's a free lunch but one we'd all be +paid to eat right going green will raise + + align:start position:0% +paid to eat right going green will raise + + + align:start position:0% +paid to eat right going green will raise +living standards after a very short + + align:start position:0% +living standards after a very short + + + align:start position:0% +living standards after a very short +period of time so what I want to do is + + align:start position:0% +period of time so what I want to do is + + + align:start position:0% +period of time so what I want to do is +talk a little bit about that you could + + align:start position:0% +talk a little bit about that you could + + + align:start position:0% +talk a little bit about that you could +imagine how I and others got engaged + + align:start position:0% +imagine how I and others got engaged + + + align:start position:0% +imagine how I and others got engaged +this was sort of very + + align:start position:0% +this was sort of very + + + align:start position:0% +this was sort of very +if you don't know this world the World + + align:start position:0% +if you don't know this world the World + + + align:start position:0% +if you don't know this world the World +Bank in the OECD and the UN have a lot + + align:start position:0% +Bank in the OECD and the UN have a lot + + + align:start position:0% +Bank in the OECD and the UN have a lot +of not to Unseld anybody but they have a + + align:start position:0% +of not to Unseld anybody but they have a + + + align:start position:0% +of not to Unseld anybody but they have a +lot of very smart people without much to + + align:start position:0% +lot of very smart people without much to + + + align:start position:0% +lot of very smart people without much to +do so a lot of papers generated and + + align:start position:0% +do so a lot of papers generated and + + + align:start position:0% +do so a lot of papers generated and +mostly people pay little attention to it + + align:start position:0% +mostly people pay little attention to it + + + align:start position:0% +mostly people pay little attention to it +but suddenly I'll get into specifics + + align:start position:0% +but suddenly I'll get into specifics + + + align:start position:0% +but suddenly I'll get into specifics +suddenly you have these organizations + + align:start position:0% +suddenly you have these organizations + + + align:start position:0% +suddenly you have these organizations +revving up for a big world conference + + align:start position:0% +revving up for a big world conference + + + align:start position:0% +revving up for a big world conference +talking about talking about massive + + align:start position:0% +talking about talking about massive + + + align:start position:0% +talking about talking about massive +changes in investment strategy and I'll + + align:start position:0% +changes in investment strategy and I'll + + + align:start position:0% +changes in investment strategy and I'll +give you I'll give you a sense of it so + + align:start position:0% +give you I'll give you a sense of it so + + + align:start position:0% +give you I'll give you a sense of it so +economists have begun to write about + + align:start position:0% +economists have begun to write about + + + align:start position:0% +economists have begun to write about +this what's on the reading list what's + + align:start position:0% +this what's on the reading list what's + + + align:start position:0% +this what's on the reading list what's +on this what's on stellar is a couple of + + align:start position:0% +on this what's on stellar is a couple of + + + align:start position:0% +on this what's on stellar is a couple of +of the shorter + + align:start position:0% +of the shorter + + + align:start position:0% +of the shorter +I think World Bank and I don't remember + + align:start position:0% +I think World Bank and I don't remember + + + align:start position:0% +I think World Bank and I don't remember +whether it's UN or OECD publications + + align:start position:0% +whether it's UN or OECD publications + + + align:start position:0% +whether it's UN or OECD publications +peace of mind commenting on this whole + + align:start position:0% +peace of mind commenting on this whole + + + align:start position:0% +peace of mind commenting on this whole +thing that's it'll be the introduction + + align:start position:0% +thing that's it'll be the introduction + + + align:start position:0% +thing that's it'll be the introduction +to a special issue of energy economics + + align:start position:0% +to a special issue of energy economics + + + align:start position:0% +to a special issue of energy economics +and then some other some other papers + + align:start position:0% +and then some other some other papers + + + align:start position:0% +and then some other some other papers +and I want to talk about about some of + + align:start position:0% +and I want to talk about about some of + + + align:start position:0% +and I want to talk about about some of +the some of the issues so let me talk + + align:start position:0% +the some of the issues so let me talk + + + align:start position:0% +the some of the issues so let me talk +about just some of the issues here one + + align:start position:0% +about just some of the issues here one + + + align:start position:0% +about just some of the issues here one +issue that everybody points out is + + align:start position:0% +issue that everybody points out is + + + align:start position:0% +issue that everybody points out is +absolutely right + + align:start position:0% +absolutely right + + + align:start position:0% +absolutely right +GDP doesn't pick this up GDP we talk + + align:start position:0% +GDP doesn't pick this up GDP we talk + + + align:start position:0% +GDP doesn't pick this up GDP we talk +about stocks and flows you have family + + align:start position:0% +about stocks and flows you have family + + + align:start position:0% +about stocks and flows you have family +silver you sell a family silver you have + + align:start position:0% +silver you sell a family silver you have + + + align:start position:0% +silver you sell a family silver you have +a party the party shows up in GDP the + + align:start position:0% +a party the party shows up in GDP the + + + align:start position:0% +a party the party shows up in GDP the +fact that somehow the Silver's out of + + align:start position:0% +fact that somehow the Silver's out of + + + align:start position:0% +fact that somehow the Silver's out of +your hands or shows up in sort of your + + align:start position:0% +your hands or shows up in sort of your + + + align:start position:0% +your hands or shows up in sort of your +consumption certainly if you burn down + + align:start position:0% +consumption certainly if you burn down + + + align:start position:0% +consumption certainly if you burn down +if you and there plenty of African + + align:start position:0% +if you and there plenty of African + + + align:start position:0% +if you and there plenty of African +countries plenty of other countries that + + align:start position:0% +countries plenty of other countries that + + + align:start position:0% +countries plenty of other countries that +have basically burned down New Hampshire + + align:start position:0% +have basically burned down New Hampshire + + + align:start position:0% +have basically burned down New Hampshire +did it Vermont did it you burn down the + + align:start position:0% +did it Vermont did it you burn down the + + + align:start position:0% +did it Vermont did it you burn down the +forest to fuel economic development + + align:start position:0% +forest to fuel economic development + + + align:start position:0% +forest to fuel economic development +there's a sense in which you're changing + + align:start position:0% +there's a sense in which you're changing + + + align:start position:0% +there's a sense in which you're changing +one asset to another certainly just + + align:start position:0% +one asset to another certainly just + + + align:start position:0% +one asset to another certainly just +looking at what gets produced under + + align:start position:0% +looking at what gets produced under + + + align:start position:0% +looking at what gets produced under +States the cost so if you look at net + + align:start position:0% +States the cost so if you look at net + + + align:start position:0% +States the cost so if you look at net +national product which gets depreciation + + align:start position:0% +national product which gets depreciation + + + align:start position:0% +national product which gets depreciation +of some assets it subtracts from gross + + align:start position:0% +of some assets it subtracts from gross + + + align:start position:0% +of some assets it subtracts from gross +national product it picks up some of + + align:start position:0% +national product it picks up some of + + + align:start position:0% +national product it picks up some of +this but you know properly measured + + align:start position:0% +this but you know properly measured + + + align:start position:0% +this but you know properly measured +you'd want to take into account the fact + + align:start position:0% +you'd want to take into account the fact + + + align:start position:0% +you'd want to take into account the fact +that what happened in nineteen + + align:start position:0% +that what happened in nineteen + + + align:start position:0% +that what happened in nineteen +century Britain was they paid for + + align:start position:0% +century Britain was they paid for + + + align:start position:0% +century Britain was they paid for +economic development in part by trashing + + align:start position:0% +economic development in part by trashing + + + align:start position:0% +economic development in part by trashing +the environment in part by killing + + align:start position:0% +the environment in part by killing + + + align:start position:0% +the environment in part by killing +people with the health effects of all + + align:start position:0% +people with the health effects of all + + + align:start position:0% +people with the health effects of all +that smoke and degrading the National + + align:start position:0% +that smoke and degrading the National + + + align:start position:0% +that smoke and degrading the National +Environment so you'd want to take that + + align:start position:0% +Environment so you'd want to take that + + + align:start position:0% +Environment so you'd want to take that +into account when you said what's income + + align:start position:0% +into account when you said what's income + + + align:start position:0% +into account when you said what's income +what are living standards really we + + align:start position:0% +what are living standards really we + + + align:start position:0% +what are living standards really we +don't know how to do that there's work + + align:start position:0% +don't know how to do that there's work + + + align:start position:0% +don't know how to do that there's work +at the UN there's work at the US but you + + align:start position:0% +at the UN there's work at the US but you + + + align:start position:0% +at the UN there's work at the US but you +know part of the green growth argument + + align:start position:0% +know part of the green growth argument + + + align:start position:0% +know part of the green growth argument +could be that what you want to measure + + align:start position:0% +could be that what you want to measure + + + align:start position:0% +could be that what you want to measure +is a GDP growth but growth in living + + align:start position:0% +is a GDP growth but growth in living + + + align:start position:0% +is a GDP growth but growth in living +standards taking into account all this + + align:start position:0% +standards taking into account all this + + + align:start position:0% +standards taking into account all this +other stuff taking into account changes + + align:start position:0% +other stuff taking into account changes + + + align:start position:0% +other stuff taking into account changes +in health taking into account changes in + + align:start position:0% +in health taking into account changes in + + + align:start position:0% +in health taking into account changes in +in the natural environment and so forth + + align:start position:0% +in the natural environment and so forth + + + align:start position:0% +in the natural environment and so forth +so you could say okay that's it that's a + + align:start position:0% +so you could say okay that's it that's a + + + align:start position:0% +so you could say okay that's it that's a +relevant point another relevant point is + + align:start position:0% +relevant point another relevant point is + + + align:start position:0% +relevant point another relevant point is +they talked about increasing investment + + align:start position:0% +they talked about increasing investment + + + align:start position:0% +they talked about increasing investment +taking 2% of world GDP and investing it + + align:start position:0% +taking 2% of world GDP and investing it + + + align:start position:0% +taking 2% of world GDP and investing it +in green things well if you make massive + + align:start position:0% +in green things well if you make massive + + + align:start position:0% +in green things well if you make massive +investments and they're not terrible + + align:start position:0% +investments and they're not terrible + + + align:start position:0% +investments and they're not terrible +they will eventually raise growth right + + align:start position:0% +they will eventually raise growth right + + + align:start position:0% +they will eventually raise growth right +so you're increasing that's up their + + align:start position:0% +so you're increasing that's up their + + + align:start position:0% +so you're increasing that's up their +numbers in my paper they don't matter + + align:start position:0% +numbers in my paper they don't matter + + + align:start position:0% +numbers in my paper they don't matter +but it's basically what the UN is saying + + align:start position:0% +but it's basically what the UN is saying + + + align:start position:0% +but it's basically what the UN is saying +is the world as a whole needs to make a + + align:start position:0% +is the world as a whole needs to make a + + + align:start position:0% +is the world as a whole needs to make a +massive increase in green investments if + + align:start position:0% +massive increase in green investments if + + + align:start position:0% +massive increase in green investments if +you do that you probably will raise + + align:start position:0% +you do that you probably will raise + + + align:start position:0% +you do that you probably will raise +growth that doesn't mean it's a good + + align:start position:0% +growth that doesn't mean it's a good + + + align:start position:0% +growth that doesn't mean it's a good +idea if you double the US capital + + align:start position:0% +idea if you double the US capital + + + align:start position:0% +idea if you double the US capital +formation you'd raise u.s. growth hey + + align:start position:0% +formation you'd raise u.s. growth hey + + + align:start position:0% +formation you'd raise u.s. growth hey +how do you do it B is it actually a good + + align:start position:0% +how do you do it B is it actually a good + + + align:start position:0% +how do you do it B is it actually a good +deal but the kicker here most of these + + align:start position:0% +deal but the kicker here most of these + + + align:start position:0% +deal but the kicker here most of these +models say here's how we raise growth we + + align:start position:0% +models say here's how we raise growth we + + + align:start position:0% +models say here's how we raise growth we +raise growth by reducing environmental + + align:start position:0% +raise growth by reducing environmental + + + align:start position:0% +raise growth by reducing environmental +limits on growth + + align:start position:0% +limits on growth + + + align:start position:0% +limits on growth +what would environmental limits be well + + align:start position:0% +what would environmental limits be well + + + align:start position:0% +what would environmental limits be well +in the limit everybody gets sick and + + align:start position:0% +in the limit everybody gets sick and + + + align:start position:0% +in the limit everybody gets sick and +production and productivity falls off so + + align:start position:0% +production and productivity falls off so + + + align:start position:0% +production and productivity falls off so +if you've ever tried to breathe in large + + align:start position:0% +if you've ever tried to breathe in large + + + align:start position:0% +if you've ever tried to breathe in large +Chinese cities you get a sense that + + align:start position:0% +Chinese cities you get a sense that + + + align:start position:0% +Chinese cities you get a sense that +there is some theoretical that this may + + align:start position:0% +there is some theoretical that this may + + + align:start position:0% +there is some theoretical that this may +be more than theory in some places at + + align:start position:0% +be more than theory in some places at + + + align:start position:0% +be more than theory in some places at +some times but globally + + align:start position:0% + + + + align:start position:0% + +probably not so two good points and one + + align:start position:0% +probably not so two good points and one + + + align:start position:0% +probably not so two good points and one +point that's sort of ok in theory the + + align:start position:0% +point that's sort of ok in theory the + + + align:start position:0% +point that's sort of ok in theory the +good points are in terms of going green + + align:start position:0% +good points are in terms of going green + + + align:start position:0% +good points are in terms of going green +that GDP growth isn't really a good + + align:start position:0% +that GDP growth isn't really a good + + + align:start position:0% +that GDP growth isn't really a good +measure of growth in standards of living + + align:start position:0% +measure of growth in standards of living + + + align:start position:0% +measure of growth in standards of living +it isn't a good measure of + + align:start position:0% +it isn't a good measure of + + + align:start position:0% +it isn't a good measure of +sustainability period sure increasing + + align:start position:0% +sustainability period sure increasing + + + align:start position:0% +sustainability period sure increasing +the rate of investment in green + + align:start position:0% +the rate of investment in green + + + align:start position:0% +the rate of investment in green +technologies and lots of other things + + align:start position:0% +technologies and lots of other things + + + align:start position:0% +technologies and lots of other things +will raise growth yep so would + + align:start position:0% +will raise growth yep so would + + + align:start position:0% +will raise growth yep so would +investment in railroad so it investment + + align:start position:0% +investment in railroad so it investment + + + align:start position:0% +investment in railroad so it investment +in highways so would investments in + + align:start position:0% +in highways so would investments in + + + align:start position:0% +in highways so would investments in +education but that's certainly true it + + align:start position:0% +education but that's certainly true it + + + align:start position:0% +education but that's certainly true it +is possible that one way going green + + align:start position:0% +is possible that one way going green + + + align:start position:0% +is possible that one way going green +increases economic growth is by sort of + + align:start position:0% +increases economic growth is by sort of + + + align:start position:0% +increases economic growth is by sort of +reducing environmental limits the soil + + align:start position:0% +reducing environmental limits the soil + + + align:start position:0% +reducing environmental limits the soil +is exhausted the people are sick etc etc + + align:start position:0% +is exhausted the people are sick etc etc + + + align:start position:0% +is exhausted the people are sick etc etc +the aquifers are depleted and you're + + align:start position:0% +the aquifers are depleted and you're + + + align:start position:0% +the aquifers are depleted and you're +stuck that is certainly possible and if + + align:start position:0% +stuck that is certainly possible and if + + + align:start position:0% +stuck that is certainly possible and if +you're really a pessimistic person you + + align:start position:0% +you're really a pessimistic person you + + + align:start position:0% +you're really a pessimistic person you +can look down the road and climate + + align:start position:0% +can look down the road and climate + + + align:start position:0% +can look down the road and climate +change is another set of mechanisms that + + align:start position:0% +change is another set of mechanisms that + + + align:start position:0% +change is another set of mechanisms that +could do this but is it globally + + align:start position:0% +could do this but is it globally + + + align:start position:0% +could do this but is it globally +quantitatively important in the near + + align:start position:0% +quantitatively important in the near + + + align:start position:0% +quantitatively important in the near +term no evidence ok more relevant points + + align:start position:0% +term no evidence ok more relevant points + + + align:start position:0% +term no evidence ok more relevant points +certainly in rich countries you can make + + align:start position:0% +certainly in rich countries you can make + + + align:start position:0% +certainly in rich countries you can make +the argument that yes we should be + + align:start position:0% +the argument that yes we should be + + + align:start position:0% +the argument that yes we should be +greener than we are particularly in this + + align:start position:0% +greener than we are particularly in this + + + align:start position:0% +greener than we are particularly in this +country if you think carbon dioxide does + + align:start position:0% +country if you think carbon dioxide does + + + align:start position:0% +country if you think carbon dioxide does +anything it probably makes sense to + + align:start position:0% +anything it probably makes sense to + + + align:start position:0% +anything it probably makes sense to +switch that understates the case to + + align:start position:0% +switch that understates the case to + + + align:start position:0% +switch that understates the case to +switch to less carbon intensive growth + + align:start position:0% +switch to less carbon intensive growth + + + align:start position:0% +switch to less carbon intensive growth +paths cut emissions conservation shift + + align:start position:0% +paths cut emissions conservation shift + + + align:start position:0% +paths cut emissions conservation shift +the natural gas the interesting question + + align:start position:0% +the natural gas the interesting question + + + align:start position:0% +the natural gas the interesting question +and the politically tricky question is + + align:start position:0% +and the politically tricky question is + + + align:start position:0% +and the politically tricky question is +in poor countries because the green + + align:start position:0% +in poor countries because the green + + + align:start position:0% +in poor countries because the green +growth story is a story not about the + + align:start position:0% +growth story is a story not about the + + + align:start position:0% +growth story is a story not about the +rich countries it's a story about mostly + + align:start position:0% +rich countries it's a story about mostly + + + align:start position:0% +rich countries it's a story about mostly +poor countries massive investments in + + align:start position:0% +poor countries massive investments in + + + align:start position:0% +poor countries massive investments in +going green in poor countries + + align:start position:0% +going green in poor countries + + + align:start position:0% +going green in poor countries +well massive investments in almost + + align:start position:0% +well massive investments in almost + + + align:start position:0% +well massive investments in almost +anything sensible in poor countries + + align:start position:0% +anything sensible in poor countries + + + align:start position:0% +anything sensible in poor countries +would be a good thing where does it come + + align:start position:0% +would be a good thing where does it come + + + align:start position:0% +would be a good thing where does it come +from + + align:start position:0% + + + + align:start position:0% + +probably doesn't come internally this is + + align:start position:0% +probably doesn't come internally this is + + + align:start position:0% +probably doesn't come internally this is +the climate problem revisited in a way + + align:start position:0% +the climate problem revisited in a way + + + align:start position:0% +the climate problem revisited in a way +probably doesn't come internally because + + align:start position:0% +probably doesn't come internally because + + + align:start position:0% +probably doesn't come internally because +they don't have it and they have other + + align:start position:0% +they don't have it and they have other + + + align:start position:0% +they don't have it and they have other +priorities you know again telling the + + align:start position:0% +priorities you know again telling the + + + align:start position:0% +priorities you know again telling the +Chinese not to use the coal while so + + align:start position:0% +Chinese not to use the coal while so + + + align:start position:0% +Chinese not to use the coal while so +many millions of people live in poverty + + align:start position:0% +many millions of people live in poverty + + + align:start position:0% +many millions of people live in poverty +is a tough point tough sale massive + + align:start position:0% +is a tough point tough sale massive + + + align:start position:0% +is a tough point tough sale massive +foreign aid + + align:start position:0% +foreign aid + + + align:start position:0% +foreign aid +well appropriating massive foreign aid + + align:start position:0% +well appropriating massive foreign aid + + + align:start position:0% +well appropriating massive foreign aid +again there's some numbers in my paper + + align:start position:0% +again there's some numbers in my paper + + + align:start position:0% +again there's some numbers in my paper +about a about four hundred billion a + + align:start position:0% +about a about four hundred billion a + + + align:start position:0% +about a about four hundred billion a +year from the US imagine walking into + + align:start position:0% +year from the US imagine walking into + + + align:start position:0% +year from the US imagine walking into +Congress and saying yes yes I know we + + align:start position:0% +Congress and saying yes yes I know we + + + align:start position:0% +Congress and saying yes yes I know we +have problems but we need to send four + + align:start position:0% +have problems but we need to send four + + + align:start position:0% +have problems but we need to send four +hundred billion a year in foreign aid + + align:start position:0% +hundred billion a year in foreign aid + + + align:start position:0% +hundred billion a year in foreign aid +you would not get a vote on the floor + + align:start position:0% +you would not get a vote on the floor + + + align:start position:0% +you would not get a vote on the floor +you would not get a vote in a committee + + align:start position:0% +you would not get a vote in a committee + + + align:start position:0% +you would not get a vote in a committee +and the other problem is the history + + align:start position:0% +and the other problem is the history + + + align:start position:0% +and the other problem is the history +says if you dump lots of foreign aid on + + align:start position:0% +says if you dump lots of foreign aid on + + + align:start position:0% +says if you dump lots of foreign aid on +countries that don't have good + + align:start position:0% +countries that don't have good + + + align:start position:0% +countries that don't have good +governance structures you don't get good + + align:start position:0% +governance structures you don't get good + + + align:start position:0% +governance structures you don't get good +results it gets stolen it gets wasted so + + align:start position:0% +results it gets stolen it gets wasted so + + + align:start position:0% +results it gets stolen it gets wasted so +that's not likely + + align:start position:0% +that's not likely + + + align:start position:0% +that's not likely +so without the aid how can you possibly + + align:start position:0% +so without the aid how can you possibly + + + align:start position:0% +so without the aid how can you possibly +say in Africa in particular where there + + align:start position:0% +say in Africa in particular where there + + + align:start position:0% +say in Africa in particular where there +is hydro potential where there is coal + + align:start position:0% +is hydro potential where there is coal + + + align:start position:0% +is hydro potential where there is coal +and where there is a lot of poverty why + + align:start position:0% +and where there is a lot of poverty why + + + align:start position:0% +and where there is a lot of poverty why +not use it now you can say you could say + + align:start position:0% +not use it now you can say you could say + + + align:start position:0% +not use it now you can say you could say +actually that's wrong you can say the + + align:start position:0% +actually that's wrong you can say the + + + align:start position:0% +actually that's wrong you can say the +equity issues are absolutely clear we + + align:start position:0% +equity issues are absolutely clear we + + + align:start position:0% +equity issues are absolutely clear we +talked about this and we talked about + + align:start position:0% +talked about this and we talked about + + + align:start position:0% +talked about this and we talked about +about climate change if I'm a poor + + align:start position:0% +about climate change if I'm a poor + + + align:start position:0% +about climate change if I'm a poor +country and you say to me we really need + + align:start position:0% +country and you say to me we really need + + + align:start position:0% +country and you say to me we really need +you to go green I would say to you you + + align:start position:0% +you to go green I would say to you you + + + align:start position:0% +you to go green I would say to you you +didn't you got rich you burned your coal + + align:start position:0% +didn't you got rich you burned your coal + + + align:start position:0% +didn't you got rich you burned your coal +you cut down your trees why can't I if + + align:start position:0% +you cut down your trees why can't I if + + + align:start position:0% +you cut down your trees why can't I if +you give me money how maybe I won't but + + align:start position:0% +you give me money how maybe I won't but + + + align:start position:0% +you give me money how maybe I won't but +maybe if you give me money I'll waste it + + align:start position:0% +maybe if you give me money I'll waste it + + + align:start position:0% +maybe if you give me money I'll waste it +it'll go to a bank account in + + align:start position:0% +it'll go to a bank account in + + + align:start position:0% +it'll go to a bank account in +Switzerland or the Cayman Islands or or + + align:start position:0% +Switzerland or the Cayman Islands or or + + + align:start position:0% +Switzerland or the Cayman Islands or or +you know it we hire my brother-in-law to + + align:start position:0% +you know it we hire my brother-in-law to + + + align:start position:0% +you know it we hire my brother-in-law to +build a dam so this is sort of a + + align:start position:0% +build a dam so this is sort of a + + + align:start position:0% +build a dam so this is sort of a +terrible thing now this is this is + + align:start position:0% +terrible thing now this is this is + + + align:start position:0% +terrible thing now this is this is +something that's sort of not on as the + + align:start position:0% +something that's sort of not on as the + + + align:start position:0% +something that's sort of not on as the +English say you there's just no way to + + align:start position:0% +English say you there's just no way to + + + align:start position:0% +English say you there's just no way to +to get it done without massive transfers + + align:start position:0% +to get it done without massive transfers + + + align:start position:0% +to get it done without massive transfers +of aid and there's no way to get the + + align:start position:0% +of aid and there's no way to get the + + + align:start position:0% +of aid and there's no way to get the +massive transfers of a done for + + align:start position:0% +massive transfers of a done for + + + align:start position:0% +massive transfers of a done for +I can tell in any case one point I do + + align:start position:0% +I can tell in any case one point I do + + + align:start position:0% +I can tell in any case one point I do +want to make though and that is while + + align:start position:0% +want to make though and that is while + + + align:start position:0% +want to make though and that is while +you're thinking about startups one of + + align:start position:0% +you're thinking about startups one of + + + align:start position:0% +you're thinking about startups one of +the really interesting opportunities + + align:start position:0% +the really interesting opportunities + + + align:start position:0% +the really interesting opportunities +globally + + align:start position:0% +globally + + + align:start position:0% +globally +is the large number of people who have + + align:start position:0% +is the large number of people who have + + + align:start position:0% +is the large number of people who have +no electricity period who are off-grid + + align:start position:0% +no electricity period who are off-grid + + + align:start position:0% +no electricity period who are off-grid +who are in rural areas and that's one of + + align:start position:0% +who are in rural areas and that's one of + + + align:start position:0% +who are in rural areas and that's one of +those interesting bottom of the pyramid + + align:start position:0% +those interesting bottom of the pyramid + + + align:start position:0% +those interesting bottom of the pyramid +opportunities that a lot of people have + + align:start position:0% +opportunities that a lot of people have + + + align:start position:0% +opportunities that a lot of people have +tried to crack because having lighting + + align:start position:0% +tried to crack because having lighting + + + align:start position:0% +tried to crack because having lighting +at night makes a huge difference it + + align:start position:0% +at night makes a huge difference it + + + align:start position:0% +at night makes a huge difference it +means kids can stay in school + + align:start position:0% +means kids can stay in school + + + align:start position:0% +means kids can stay in school +it means the family can work after after + + align:start position:0% +it means the family can work after after + + + align:start position:0% +it means the family can work after after +the Sun Goes Down at various things but + + align:start position:0% +the Sun Goes Down at various things but + + + align:start position:0% +the Sun Goes Down at various things but +in particular kids can study so and + + align:start position:0% +in particular kids can study so and + + + align:start position:0% +in particular kids can study so and +there are a lot of a lot of people have + + align:start position:0% +there are a lot of a lot of people have + + + align:start position:0% +there are a lot of a lot of people have +tried to crack that economically usually + + align:start position:0% +tried to crack that economically usually + + + align:start position:0% +tried to crack that economically usually +some version of solar plus storage + + align:start position:0% +some version of solar plus storage + + + align:start position:0% +some version of solar plus storage +deployed at the community level or solar + + align:start position:0% +deployed at the community level or solar + + + align:start position:0% +deployed at the community level or solar +lanterns that can be sold cheaply and + + align:start position:0% +lanterns that can be sold cheaply and + + + align:start position:0% +lanterns that can be sold cheaply and +charged in the daytime and used at night + + align:start position:0% +charged in the daytime and used at night + + + align:start position:0% +charged in the daytime and used at night +so there are lots of opportunities there + + align:start position:0% +so there are lots of opportunities there + + + align:start position:0% +so there are lots of opportunities there +it isn't massive it isn't massive the + + align:start position:0% +it isn't massive it isn't massive the + + + align:start position:0% +it isn't massive it isn't massive the +other thing to point out is one of the + + align:start position:0% +other thing to point out is one of the + + + align:start position:0% +other thing to point out is one of the +real tragedies here and one of the + + align:start position:0% +real tragedies here and one of the + + + align:start position:0% +real tragedies here and one of the +reasons why the whole green growth + + align:start position:0% +reasons why the whole green growth + + + align:start position:0% +reasons why the whole green growth +notion is is is compelling but painful + + align:start position:0% +notion is is is compelling but painful + + + align:start position:0% +notion is is is compelling but painful +and that is again there's a piece on + + align:start position:0% +and that is again there's a piece on + + + align:start position:0% +and that is again there's a piece on +stellar if you ask who's going to be + + align:start position:0% +stellar if you ask who's going to be + + + align:start position:0% +stellar if you ask who's going to be +harmed by climate change it's mostly the + + align:start position:0% +harmed by climate change it's mostly the + + + align:start position:0% +harmed by climate change it's mostly the +developing world right I mean we can + + align:start position:0% +developing world right I mean we can + + + align:start position:0% +developing world right I mean we can +afford to build a wall around Manhattan + + align:start position:0% +afford to build a wall around Manhattan + + + align:start position:0% +afford to build a wall around Manhattan +to deal with sea-level rise + + align:start position:0% +to deal with sea-level rise + + + align:start position:0% +to deal with sea-level rise +Bangladesh can't build a wall but of + + align:start position:0% +Bangladesh can't build a wall but of + + + align:start position:0% +Bangladesh can't build a wall but of +course the developing world is also + + align:start position:0% +course the developing world is also + + + align:start position:0% +course the developing world is also +driving climate change if you look the + + align:start position:0% +driving climate change if you look the + + + align:start position:0% +driving climate change if you look the +growth in emissions as we talked about + + align:start position:0% +growth in emissions as we talked about + + + align:start position:0% +growth in emissions as we talked about +on several occasions just no obvious fix + + align:start position:0% +on several occasions just no obvious fix + + + align:start position:0% +on several occasions just no obvious fix +so the green growth is trying to is is + + align:start position:0% +so the green growth is trying to is is + + + align:start position:0% +so the green growth is trying to is is +an attempt by a whole set of staff + + align:start position:0% +an attempt by a whole set of staff + + + align:start position:0% +an attempt by a whole set of staff +people to advocate for massive change in + + align:start position:0% +people to advocate for massive change in + + + align:start position:0% +people to advocate for massive change in +the way the world runs that's probably + + align:start position:0% +the way the world runs that's probably + + + align:start position:0% +the way the world runs that's probably +not going to work not going to work + + align:start position:0% +not going to work not going to work + + + align:start position:0% +not going to work not going to work +politically which is one reason why I + + align:start position:0% +politically which is one reason why I + + + align:start position:0% +politically which is one reason why I +didn't feel like doing an hour and a + + align:start position:0% +didn't feel like doing an hour and a + + + align:start position:0% +didn't feel like doing an hour and a +half on it because I think the I think + + align:start position:0% +half on it because I think the I think + + + align:start position:0% +half on it because I think the I think +the air is gone out there will be a cut + + align:start position:0% +the air is gone out there will be a cut + + + align:start position:0% +the air is gone out there will be a cut +a circus + + align:start position:0% +a circus + + + align:start position:0% +a circus +at in Rio they will probably be a + + align:start position:0% +at in Rio they will probably be a + + + align:start position:0% +at in Rio they will probably be a +hundred heads of state or government in + + align:start position:0% +hundred heads of state or government in + + + align:start position:0% +hundred heads of state or government in +Rio next next month + + align:start position:0% +Rio next next month + + + align:start position:0% +Rio next next month +I'm told hotel rooms go are going for + + align:start position:0% +I'm told hotel rooms go are going for + + + align:start position:0% +I'm told hotel rooms go are going for +thousands of dollars a night so it will + + align:start position:0% +thousands of dollars a night so it will + + + align:start position:0% +thousands of dollars a night so it will +be a big circus I'm told that the + + align:start position:0% +be a big circus I'm told that the + + + align:start position:0% +be a big circus I'm told that the +official US government position is that + + align:start position:0% +official US government position is that + + + align:start position:0% +official US government position is that +Rio should produce a clean five-page + + align:start position:0% +Rio should produce a clean five-page + + + align:start position:0% +Rio should produce a clean five-page +statement of principles and policies and + + align:start position:0% +statement of principles and policies and + + + align:start position:0% +statement of principles and policies and +that the current working draft is 260 + + align:start position:0% +that the current working draft is 260 + + + align:start position:0% +that the current working draft is 260 +pages long diplomats do this diplomats + + align:start position:0% +pages long diplomats do this diplomats + + + align:start position:0% +pages long diplomats do this diplomats +do this so so this is this is the the + + align:start position:0% +do this so so this is this is the the + + + align:start position:0% +do this so so this is this is the the +story of people trying to figure out + + align:start position:0% +story of people trying to figure out + + + align:start position:0% +story of people trying to figure out +what comes after the Framework + + align:start position:0% +what comes after the Framework + + + align:start position:0% +what comes after the Framework +Convention on Climate Change what comes + + align:start position:0% +Convention on Climate Change what comes + + + align:start position:0% +Convention on Climate Change what comes +after thinking about sustainability and + + align:start position:0% +after thinking about sustainability and + + + align:start position:0% +after thinking about sustainability and +the answer is or was a major push toward + + align:start position:0% +the answer is or was a major push toward + + + align:start position:0% +the answer is or was a major push toward +being green please really a serious + + align:start position:0% +being green please really a serious + + + align:start position:0% +being green please really a serious +major push I think it lacks intellectual + + align:start position:0% +major push I think it lacks intellectual + + + align:start position:0% +major push I think it lacks intellectual +foundation I think it lacks political + + align:start position:0% +foundation I think it lacks political + + + align:start position:0% +foundation I think it lacks political +foundation I think it will be much + + align:start position:0% +foundation I think it will be much + + + align:start position:0% +foundation I think it will be much +discussed at Rio and nothing will happen + + align:start position:0% +discussed at Rio and nothing will happen + + + align:start position:0% +discussed at Rio and nothing will happen +I do hate the last talk to be so cynical + + align:start position:0% +I do hate the last talk to be so cynical + + + align:start position:0% +I do hate the last talk to be so cynical +maybe will be helped hopeful next week + + align:start position:0% +maybe will be helped hopeful next week + + + align:start position:0% +maybe will be helped hopeful next week +when we hear your papers do you have + + align:start position:0% +when we hear your papers do you have + + + align:start position:0% +when we hear your papers do you have +questions or comments than any of this + + align:start position:0% +questions or comments than any of this + + + align:start position:0% +questions or comments than any of this +that's sort of the this is the current + + align:start position:0% +that's sort of the this is the current + + + align:start position:0% +that's sort of the this is the current +diplomatic state of play this is an + + align:start position:0% +diplomatic state of play this is an + + + align:start position:0% +diplomatic state of play this is an +attempt to do climate by the back door + + align:start position:0% +attempt to do climate by the back door + + + align:start position:0% +attempt to do climate by the back door +and call it green it isn't going to work + + align:start position:0% +and call it green it isn't going to work + + + align:start position:0% +and call it green it isn't going to work +sadly I think yeah Julian + + align:start position:0% + + + + align:start position:0% + +well you know diplomacy is a really + + align:start position:0% +well you know diplomacy is a really + + + align:start position:0% +well you know diplomacy is a really +strange process it's easy to mock right + + align:start position:0% +strange process it's easy to mock right + + + align:start position:0% +strange process it's easy to mock right +because particularly in climate there's + + align:start position:0% +because particularly in climate there's + + + align:start position:0% +because particularly in climate there's +this group of diplomats that like to get + + align:start position:0% +this group of diplomats that like to get + + + align:start position:0% +this group of diplomats that like to get +together every couple of years and talk + + align:start position:0% +together every couple of years and talk + + + align:start position:0% +together every couple of years and talk +and make progress but without government + + align:start position:0% +and make progress but without government + + + align:start position:0% +and make progress but without government +support it's all just talk given that + + align:start position:0% +support it's all just talk given that + + + align:start position:0% +support it's all just talk given that +the main problem the world sees right + + align:start position:0% +the main problem the world sees right + + + align:start position:0% +the main problem the world sees right +now is slow recovery from a deep + + align:start position:0% +now is slow recovery from a deep + + + align:start position:0% +now is slow recovery from a deep +recession and given the current state of + + align:start position:0% +recession and given the current state of + + + align:start position:0% +recession and given the current state of +politics in the US on climate + + align:start position:0% +politics in the US on climate + + + align:start position:0% +politics in the US on climate +I expect lovely prose to come out of + + align:start position:0% +I expect lovely prose to come out of + + + align:start position:0% +I expect lovely prose to come out of +this there might be agreement on + + align:start position:0% +this there might be agreement on + + + align:start position:0% +this there might be agreement on +something small they might get something + + align:start position:0% +something small they might get something + + + align:start position:0% +something small they might get something +on forests I give you my cynical lecture + + align:start position:0% +on forests I give you my cynical lecture + + + align:start position:0% +on forests I give you my cynical lecture +about forest protection sometime about + + align:start position:0% +about forest protection sometime about + + + align:start position:0% +about forest protection sometime about +as long as you don't affect if as long + + align:start position:0% +as long as you don't affect if as long + + + align:start position:0% +as long as you don't affect if as long +as you don't affect the demand for wood + + align:start position:0% +as you don't affect the demand for wood + + + align:start position:0% +as you don't affect the demand for wood +protecting this forest doesn't reduce + + align:start position:0% +protecting this forest doesn't reduce + + + align:start position:0% +protecting this forest doesn't reduce +the amount of wood cut but that's just + + align:start position:0% +the amount of wood cut but that's just + + + align:start position:0% +the amount of wood cut but that's just +just the economists I expect there will + + align:start position:0% +just the economists I expect there will + + + align:start position:0% +just the economists I expect there will +be some agreements I don't think they + + align:start position:0% +be some agreements I don't think they + + + align:start position:0% +be some agreements I don't think they +will be very important and as I say I + + align:start position:0% +will be very important and as I say I + + + align:start position:0% +will be very important and as I say I +expect a circus the folks in the + + align:start position:0% +expect a circus the folks in the + + + align:start position:0% +expect a circus the folks in the +diplomatic community would say that's + + align:start position:0% +diplomatic community would say that's + + + align:start position:0% +diplomatic community would say that's +too cynical even just talking with the + + align:start position:0% +too cynical even just talking with the + + + align:start position:0% +too cynical even just talking with the +whole world involved putting a spotlight + + align:start position:0% +whole world involved putting a spotlight + + + align:start position:0% +whole world involved putting a spotlight +on these issues keeping up pressure of + + align:start position:0% +on these issues keeping up pressure of + + + align:start position:0% +on these issues keeping up pressure of +some international kind on governments + + align:start position:0% +some international kind on governments + + + align:start position:0% +some international kind on governments +that don't want to act helps sort of the + + align:start position:0% +that don't want to act helps sort of the + + + align:start position:0% +that don't want to act helps sort of the +water on a stone view of the world you + + align:start position:0% +water on a stone view of the world you + + + align:start position:0% +water on a stone view of the world you +know that's what they do and every so + + align:start position:0% +know that's what they do and every so + + + align:start position:0% +know that's what they do and every so +often there'll be a chance you'll get + + align:start position:0% +often there'll be a chance you'll get + + + align:start position:0% +often there'll be a chance you'll get +the Montreal up you'll get the Montreal + + align:start position:0% +the Montreal up you'll get the Montreal + + + align:start position:0% +the Montreal up you'll get the Montreal +Protocol and ozone depleting gases + + align:start position:0% +Protocol and ozone depleting gases + + + align:start position:0% +Protocol and ozone depleting gases +because that process had started those + + align:start position:0% +because that process had started those + + + align:start position:0% +because that process had started those +meetings were being held new science + + align:start position:0% +meetings were being held new science + + + align:start position:0% +meetings were being held new science +came the structure was in place the + + align:start position:0% +came the structure was in place the + + + align:start position:0% +came the structure was in place the +support mobilized bang we got a very + + align:start position:0% +support mobilized bang we got a very + + + align:start position:0% +support mobilized bang we got a very +constructive international agreement it + + align:start position:0% +constructive international agreement it + + + align:start position:0% +constructive international agreement it +didn't going to happen here because the + + align:start position:0% +didn't going to happen here because the + + + align:start position:0% +didn't going to happen here because the +preconditions aren't there but the water + + align:start position:0% +preconditions aren't there but the water + + + align:start position:0% +preconditions aren't there but the water +will drip on the stone the water will + + align:start position:0% +will drip on the stone the water will + + + align:start position:0% +will drip on the stone the water will +drip on the stone Rory + + align:start position:0% +drip on the stone Rory + + + align:start position:0% +drip on the stone Rory +people's response he was saying ritual + + align:start position:0% +people's response he was saying ritual + + + align:start position:0% +people's response he was saying ritual +didn't follow a green birth path but + + align:start position:0% +didn't follow a green birth path but + + + align:start position:0% +didn't follow a green birth path but +they followed the greenish growth path + + align:start position:0% +they followed the greenish growth path + + + align:start position:0% +they followed the greenish growth path +available to them at the time with any + + align:start position:0% +available to them at the time with any + + + align:start position:0% +available to them at the time with any +economic then you could argue that you + + align:start position:0% +economic then you could argue that you + + + align:start position:0% +economic then you could argue that you +know Britain if they could have written + + align:start position:0% +know Britain if they could have written + + + align:start position:0% +know Britain if they could have written +wouldn't have covered all their cities + + align:start position:0% +wouldn't have covered all their cities + + + align:start position:0% +wouldn't have covered all their cities +and small yeah that's that's a decent + + align:start position:0% +and small yeah that's that's a decent + + + align:start position:0% +and small yeah that's that's a decent +debating point but you also say when did + + align:start position:0% +debating point but you also say when did + + + align:start position:0% +debating point but you also say when did +the rich world begin to take the + + align:start position:0% +the rich world begin to take the + + + align:start position:0% +the rich world begin to take the +environment seriously and when did it + + align:start position:0% +environment seriously and when did it + + + align:start position:0% +environment seriously and when did it +begin to have any impact on policy and + + align:start position:0% +begin to have any impact on policy and + + + align:start position:0% +begin to have any impact on policy and +that's sort of sixties seventies right + + align:start position:0% +that's sort of sixties seventies right + + + align:start position:0% +that's sort of sixties seventies right +you don't see much you don't see much + + align:start position:0% +you don't see much you don't see much + + + align:start position:0% +you don't see much you don't see much +conscious thinking about it the the big + + align:start position:0% +conscious thinking about it the the big + + + align:start position:0% +conscious thinking about it the the big +us event was DDT and Rachel Carson's + + align:start position:0% +us event was DDT and Rachel Carson's + + + align:start position:0% +us event was DDT and Rachel Carson's +Silent Spring which was do you remember + + align:start position:0% +Silent Spring which was do you remember + + + align:start position:0% +Silent Spring which was do you remember +5762 around there around there right + + align:start position:0% +5762 around there around there right + + + align:start position:0% +5762 around there around there right +birds were dying because DDT was making + + align:start position:0% +birds were dying because DDT was making + + + align:start position:0% +birds were dying because DDT was making +their shells too thin and they couldn't + + align:start position:0% +their shells too thin and they couldn't + + + align:start position:0% +their shells too thin and they couldn't +reproduce that was like oh my god our + + align:start position:0% +reproduce that was like oh my god our + + + align:start position:0% +reproduce that was like oh my god our +chemicals are actually doing something + + align:start position:0% +chemicals are actually doing something + + + align:start position:0% +chemicals are actually doing something +out there but you know to most people + + align:start position:0% +out there but you know to most people + + + align:start position:0% +out there but you know to most people +that are things through better living + + align:start position:0% +that are things through better living + + + align:start position:0% +that are things through better living +through chemistry so to argue that we + + align:start position:0% +through chemistry so to argue that we + + + align:start position:0% +through chemistry so to argue that we +were doing the best we could is to argue + + align:start position:0% +were doing the best we could is to argue + + + align:start position:0% +were doing the best we could is to argue +that we were doing it unconsciously now + + align:start position:0% +that we were doing it unconsciously now + + + align:start position:0% +that we were doing it unconsciously now +may be true but it's not that's not that + + align:start position:0% +may be true but it's not that's not that + + + align:start position:0% +may be true but it's not that's not that +persuasive it's good shot though + + align:start position:0% +persuasive it's good shot though + + + align:start position:0% +persuasive it's good shot though +anything else anything else on your + + align:start position:0% +anything else anything else on your + + + align:start position:0% +anything else anything else on your +minds feeling ready for the quiz on + + align:start position:0% +minds feeling ready for the quiz on + + + align:start position:0% +minds feeling ready for the quiz on +Wednesday you were brilliantly reviewed + + align:start position:0% +Wednesday you were brilliantly reviewed + + + align:start position:0% +Wednesday you were brilliantly reviewed +on on Friday ready to go ok off we go \ No newline at end of file diff --git a/htRqniQFm5g.txt b/htRqniQFm5g.txt new file mode 100644 index 0000000000000000000000000000000000000000..0a8123a375abf99e050a5701960b87f7cf1b376f --- /dev/null +++ b/htRqniQFm5g.txt @@ -0,0 +1,715 @@ +align:start position:0% + +I really want the students to feel + + align:start position:0% +I really want the students to feel + + + align:start position:0% +I really want the students to feel +actively participating in uh lectures + + align:start position:0% +actively participating in uh lectures + + + align:start position:0% +actively participating in uh lectures +and so the clickers definitely help I + + align:start position:0% +and so the clickers definitely help I + + + align:start position:0% +and so the clickers definitely help I +try to space them um every 5 to seven + + align:start position:0% +try to space them um every 5 to seven + + + align:start position:0% +try to space them um every 5 to seven +minutes that there's a clicker question + + align:start position:0% +minutes that there's a clicker question + + + align:start position:0% +minutes that there's a clicker question +and I know from teaching this uh a + + align:start position:0% +and I know from teaching this uh a + + + align:start position:0% +and I know from teaching this uh a +number of times now that some of the qu + + align:start position:0% +number of times now that some of the qu + + + align:start position:0% +number of times now that some of the qu +clicker questions they will pretty much + + align:start position:0% +clicker questions they will pretty much + + + align:start position:0% +clicker questions they will pretty much +all the students will get right and + + align:start position:0% +all the students will get right and + + + align:start position:0% +all the students will get right and +it'll be and they'll be all happy and + + align:start position:0% +it'll be and they'll be all happy and + + + align:start position:0% +it'll be and they'll be all happy and +feel good and then there are other ones + + align:start position:0% +feel good and then there are other ones + + + align:start position:0% +feel good and then there are other ones +that I ask on purpose because I know + + align:start position:0% +that I ask on purpose because I know + + + align:start position:0% +that I ask on purpose because I know +that these are questions that the + + align:start position:0% +that these are questions that the + + + align:start position:0% +that these are questions that the +students can really hang up on on exams + + align:start position:0% +students can really hang up on on exams + + + align:start position:0% +students can really hang up on on exams +they're tricky things and so I want them + + align:start position:0% +they're tricky things and so I want them + + + align:start position:0% +they're tricky things and so I want them +to make the mistake when it doesn't + + align:start position:0% +to make the mistake when it doesn't + + + align:start position:0% +to make the mistake when it doesn't +count in the clicker question so they + + align:start position:0% +count in the clicker question so they + + + align:start position:0% +count in the clicker question so they +get it right on the exam and so one + + align:start position:0% +get it right on the exam and so one + + + align:start position:0% +get it right on the exam and so one +thing that I will do um I'll often try + + align:start position:0% +thing that I will do um I'll often try + + + align:start position:0% +thing that I will do um I'll often try +to get them to tell if they got it right + + align:start position:0% +to get them to tell if they got it right + + + align:start position:0% +to get them to tell if they got it right +explain why so that's one thing I like + + align:start position:0% +explain why so that's one thing I like + + + align:start position:0% +explain why so that's one thing I like +to do and um I go around to different + + align:start position:0% +to do and um I go around to different + + + align:start position:0% +to do and um I go around to different +conferences and things and often we'll + + align:start position:0% +conferences and things and often we'll + + + align:start position:0% +conferences and things and often we'll +pick up free pens or you know free + + align:start position:0% +pick up free pens or you know free + + + align:start position:0% +pick up free pens or you know free +whatever rulers all sorts of stuff that + + align:start position:0% +whatever rulers all sorts of stuff that + + + align:start position:0% +whatever rulers all sorts of stuff that +people give out and so then I say if + + align:start position:0% +people give out and so then I say if + + + align:start position:0% +people give out and so then I say if +someone you know and they see that + + align:start position:0% +someone you know and they see that + + + align:start position:0% +someone you know and they see that +they've gotten it right so that makes + + align:start position:0% +they've gotten it right so that makes + + + align:start position:0% +they've gotten it right so that makes +them feel a little more confident before + + align:start position:0% +them feel a little more confident before + + + align:start position:0% +them feel a little more confident before +they speak in front of 350 people um and + + align:start position:0% +they speak in front of 350 people um and + + + align:start position:0% +they speak in front of 350 people um and +said okay I have this awesome little you + + align:start position:0% +said okay I have this awesome little you + + + align:start position:0% +said okay I have this awesome little you +know periodic table ruler thing who can + + align:start position:0% +know periodic table ruler thing who can + + + align:start position:0% +know periodic table ruler thing who can +tell me what the answer is and so then I + + align:start position:0% +tell me what the answer is and so then I + + + align:start position:0% +tell me what the answer is and so then I +have a TA go around with a microphone + + align:start position:0% +have a TA go around with a microphone + + + align:start position:0% +have a TA go around with a microphone +and that they say how how they thought + + align:start position:0% +and that they say how how they thought + + + align:start position:0% +and that they say how how they thought +about the problem what the answer is um + + align:start position:0% +about the problem what the answer is um + + + align:start position:0% +about the problem what the answer is um +and so just kind of encourag people to + + align:start position:0% +and so just kind of encourag people to + + + align:start position:0% +and so just kind of encourag people to +talk ask people to explain now that they + + align:start position:0% +talk ask people to explain now that they + + + align:start position:0% +talk ask people to explain now that they +know that the what the right answer is + + align:start position:0% +know that the what the right answer is + + + align:start position:0% +know that the what the right answer is +um if someone will explain why that is + + align:start position:0% +um if someone will explain why that is + + + align:start position:0% +um if someone will explain why that is +the right answer and I know it's a big + + align:start position:0% +the right answer and I know it's a big + + + align:start position:0% +the right answer and I know it's a big +class and people sometimes get nervous + + align:start position:0% +class and people sometimes get nervous + + + align:start position:0% +class and people sometimes get nervous +about talking so I I bribe people so + + align:start position:0% +about talking so I I bribe people so + + + align:start position:0% +about talking so I I bribe people so +today uh the person who answers why that + + align:start position:0% +today uh the person who answers why that + + + align:start position:0% +today uh the person who answers why that +is correct will get an MIT chemistry + + align:start position:0% +is correct will get an MIT chemistry + + + align:start position:0% +is correct will get an MIT chemistry +t-shirt all right um let's see for every + + align:start position:0% +t-shirt all right um let's see for every + + + align:start position:0% +t-shirt all right um let's see for every +if you're using five moles of N2 you're + + align:start position:0% +if you're using five moles of N2 you're + + + align:start position:0% +if you're using five moles of N2 you're +going to need 15 moles of uh hydrogen + + align:start position:0% +going to need 15 moles of uh hydrogen + + + align:start position:0% +going to need 15 moles of uh hydrogen +gas so since there's not enough hydrogen + + align:start position:0% +gas so since there's not enough hydrogen + + + align:start position:0% +gas so since there's not enough hydrogen +gas there's only 10 mes uh that means + + align:start position:0% +gas there's only 10 mes uh that means + + + align:start position:0% +gas there's only 10 mes uh that means +the hydrogen gas should be the liming + + align:start position:0% +the hydrogen gas should be the liming + + + align:start position:0% +the hydrogen gas should be the liming +reactant since you would need roughly 30 + + align:start position:0% +reactant since you would need roughly 30 + + + align:start position:0% +reactant since you would need roughly 30 +3.33 moles of N2 for it great and here + + align:start position:0% +3.33 moles of N2 for it great and here + + + align:start position:0% +3.33 moles of N2 for it great and here +is an MIT chemistry + + align:start position:0% + + + + align:start position:0% + +t-shirt other times if the clicker + + align:start position:0% +t-shirt other times if the clicker + + + align:start position:0% +t-shirt other times if the clicker +question you know it's like 50/50 in the + + align:start position:0% +question you know it's like 50/50 in the + + + align:start position:0% +question you know it's like 50/50 in the +answer then I won't tell them what's + + align:start position:0% +answer then I won't tell them what's + + + align:start position:0% +answer then I won't tell them what's +right and ask them to talk to their + + align:start position:0% +right and ask them to talk to their + + + align:start position:0% +right and ask them to talk to their +neighbor and and vote again um and + + align:start position:0% +neighbor and and vote again um and + + + align:start position:0% +neighbor and and vote again um and +sometimes I'll also you know have them + + align:start position:0% +sometimes I'll also you know have them + + + align:start position:0% +sometimes I'll also you know have them +you know talk to each other and then + + align:start position:0% +you know talk to each other and then + + + align:start position:0% +you know talk to each other and then +weigh in on something um and whenever + + align:start position:0% +weigh in on something um and whenever + + + align:start position:0% +weigh in on something um and whenever +we're going to do like a a demo I also I + + align:start position:0% +we're going to do like a a demo I also I + + + align:start position:0% +we're going to do like a a demo I also I +want them to think about what might + + align:start position:0% +want them to think about what might + + + align:start position:0% +want them to think about what might +happen and what what uh the + + align:start position:0% +happen and what what uh the + + + align:start position:0% +happen and what what uh the +possibilities are things like that and + + align:start position:0% +possibilities are things like that and + + + align:start position:0% +possibilities are things like that and +sometimes that'll be a clicker question + + align:start position:0% +sometimes that'll be a clicker question + + + align:start position:0% +sometimes that'll be a clicker question +ahead of time and then they're really + + align:start position:0% +ahead of time and then they're really + + + align:start position:0% +ahead of time and then they're really +ready and engage when they see the demo + + align:start position:0% +ready and engage when they see the demo + + + align:start position:0% +ready and engage when they see the demo +of what the answer is going to be um so + + align:start position:0% +of what the answer is going to be um so + + + align:start position:0% +of what the answer is going to be um so +those are some of of the things that I I + + align:start position:0% +those are some of of the things that I I + + + align:start position:0% +those are some of of the things that I I +can do another one of um the fun things + + align:start position:0% +can do another one of um the fun things + + + align:start position:0% +can do another one of um the fun things +that that I like when I'm talking about + + align:start position:0% +that that I like when I'm talking about + + + align:start position:0% +that that I like when I'm talking about +difference between thermodynamics and + + align:start position:0% +difference between thermodynamics and + + + align:start position:0% +difference between thermodynamics and +kinetics we can talk about how you know + + align:start position:0% +kinetics we can talk about how you know + + + align:start position:0% +kinetics we can talk about how you know +a a reaction might be thermodynamically + + align:start position:0% +a a reaction might be thermodynamically + + + align:start position:0% +a a reaction might be thermodynamically +favorable and so you know combustion of + + align:start position:0% +favorable and so you know combustion of + + + align:start position:0% +favorable and so you know combustion of +sugar thermodynamically favorable so + + align:start position:0% +sugar thermodynamically favorable so + + + align:start position:0% +sugar thermodynamically favorable so +I'll bring in some candy and we're we do + + align:start position:0% +I'll bring in some candy and we're we do + + + align:start position:0% +I'll bring in some candy and we're we do +like a demo in class and everyone has a + + align:start position:0% +like a demo in class and everyone has a + + + align:start position:0% +like a demo in class and everyone has a +candy it's like okay when you open it up + + align:start position:0% +candy it's like okay when you open it up + + + align:start position:0% +candy it's like okay when you open it up +to oxygen there should be CO2 release + + align:start position:0% +to oxygen there should be CO2 release + + + align:start position:0% +to oxygen there should be CO2 release +and so then we do the demo and and see + + align:start position:0% +and so then we do the demo and and see + + + align:start position:0% +and so then we do the demo and and see +that you know it's actually a slow + + align:start position:0% +that you know it's actually a slow + + + align:start position:0% +that you know it's actually a slow +reaction so we don't see the gas release + + align:start position:0% +reaction so we don't see the gas release + + + align:start position:0% +reaction so we don't see the gas release +um but you know ways where you know + + align:start position:0% +um but you know ways where you know + + + align:start position:0% +um but you know ways where you know +everyone in the class can have something + + align:start position:0% +everyone in the class can have something + + + align:start position:0% +everyone in the class can have something +that they do a demo with even if it's a + + align:start position:0% +that they do a demo with even if it's a + + + align:start position:0% +that they do a demo with even if it's a +little bit silly still there's that + + align:start position:0% +little bit silly still there's that + + + align:start position:0% +little bit silly still there's that +engagement then with the material \ No newline at end of file diff --git a/i4u7SZjoAs4.txt b/i4u7SZjoAs4.txt new file mode 100644 index 0000000000000000000000000000000000000000..a28007a422417965b5032ff8d3f42184f0e30f18 --- /dev/null +++ b/i4u7SZjoAs4.txt @@ -0,0 +1,443 @@ +align:start position:0% + +there's an important distinction to make + + align:start position:0% +there's an important distinction to make + + + align:start position:0% +there's an important distinction to make +between cause and effect when analyzing + + align:start position:0% +between cause and effect when analyzing + + + align:start position:0% +between cause and effect when analyzing +the motion of objects there are two very + + align:start position:0% +the motion of objects there are two very + + + align:start position:0% +the motion of objects there are two very +separate questions that we can ask the + + align:start position:0% +separate questions that we can ask the + + + align:start position:0% +separate questions that we can ask the +first is how does a particular object + + align:start position:0% +first is how does a particular object + + + align:start position:0% +first is how does a particular object +move this is a purely descriptive + + align:start position:0% +move this is a purely descriptive + + + align:start position:0% +move this is a purely descriptive +geometrical question that we're asking + + align:start position:0% +geometrical question that we're asking + + + align:start position:0% +geometrical question that we're asking +what does the geometry of the motion + + align:start position:0% +what does the geometry of the motion + + + align:start position:0% +what does the geometry of the motion +look like if we were to draw a + + align:start position:0% +look like if we were to draw a + + + align:start position:0% +look like if we were to draw a +trajectory as a function of time what's + + align:start position:0% +trajectory as a function of time what's + + + align:start position:0% +trajectory as a function of time what's +the shape of that trajectory the study + + align:start position:0% +the shape of that trajectory the study + + + align:start position:0% +the shape of that trajectory the study +of the geometry of motion of a + + align:start position:0% +of the geometry of motion of a + + + align:start position:0% +of the geometry of motion of a +trajectory is referred to as kinematics + + align:start position:0% +trajectory is referred to as kinematics + + + align:start position:0% +trajectory is referred to as kinematics +the second question we can ask is why + + align:start position:0% +the second question we can ask is why + + + align:start position:0% +the second question we can ask is why +does an object move the way it does why + + align:start position:0% +does an object move the way it does why + + + align:start position:0% +does an object move the way it does why +does the kinematic description of + + align:start position:0% +does the kinematic description of + + + align:start position:0% +does the kinematic description of +trajectory look the way it does this + + align:start position:0% +trajectory look the way it does this + + + align:start position:0% +trajectory look the way it does this +concerns what the causes are of the + + align:start position:0% +concerns what the causes are of the + + + align:start position:0% +concerns what the causes are of the +motion and of the changes in that motion + + align:start position:0% +motion and of the changes in that motion + + + align:start position:0% +motion and of the changes in that motion +the study of the cause behind the + + align:start position:0% +the study of the cause behind the + + + align:start position:0% +the study of the cause behind the +changes of motion is called dynamics + + align:start position:0% +changes of motion is called dynamics + + + align:start position:0% +changes of motion is called dynamics +Newton's second law of motion connects + + align:start position:0% +Newton's second law of motion connects + + + align:start position:0% +Newton's second law of motion connects +these two questions when we write F + + align:start position:0% +these two questions when we write F + + + align:start position:0% +these two questions when we write F +equals MA this is more than just a + + align:start position:0% +equals MA this is more than just a + + + align:start position:0% +equals MA this is more than just a +mathematical identity physically we're + + align:start position:0% +mathematical identity physically we're + + + align:start position:0% +mathematical identity physically we're +connecting two very different questions + + align:start position:0% +connecting two very different questions + + + align:start position:0% +connecting two very different questions +and we can symbolize that by dividing + + align:start position:0% +and we can symbolize that by dividing + + + align:start position:0% +and we can symbolize that by dividing +the equation into its two sides the + + align:start position:0% +the equation into its two sides the + + + align:start position:0% +the equation into its two sides the +right-hand side the MA side is + + align:start position:0% +right-hand side the MA side is + + + align:start position:0% +right-hand side the MA side is +essentially asking the question of how + + align:start position:0% +essentially asking the question of how + + + align:start position:0% +essentially asking the question of how +how does the object move what does that + + align:start position:0% +how does the object move what does that + + + align:start position:0% +how does the object move what does that +motion look like it's a description a + + align:start position:0% +motion look like it's a description a + + + align:start position:0% +motion look like it's a description a +geometric description of the object's + + align:start position:0% +geometric description of the object's + + + align:start position:0% +geometric description of the object's +motion the left-hand side of the + + align:start position:0% +motion the left-hand side of the + + + align:start position:0% +motion the left-hand side of the +equation where the forces are answers + + align:start position:0% +equation where the forces are answers + + + align:start position:0% +equation where the forces are answers +the question of why why does the object + + align:start position:0% +the question of why why does the object + + + align:start position:0% +the question of why why does the object +move the way it does what causes the + + align:start position:0% +move the way it does what causes the + + + align:start position:0% +move the way it does what causes the +motion to change these are very + + align:start position:0% +motion to change these are very + + + align:start position:0% +motion to change these are very +different conceptually + + align:start position:0% +different conceptually + + + align:start position:0% +different conceptually +and the remarkable thing about Newton's + + align:start position:0% +and the remarkable thing about Newton's + + + align:start position:0% +and the remarkable thing about Newton's +second law in fact one of Newton's + + align:start position:0% +second law in fact one of Newton's + + + align:start position:0% +second law in fact one of Newton's +signature accomplishments was to realize + + align:start position:0% +signature accomplishments was to realize + + + align:start position:0% +signature accomplishments was to realize +that these two questions can be + + align:start position:0% +that these two questions can be + + + align:start position:0% +that these two questions can be +connected in this way through Newton's + + align:start position:0% +connected in this way through Newton's + + + align:start position:0% +connected in this way through Newton's +second law of motion since these are + + align:start position:0% +second law of motion since these are + + + align:start position:0% +second law of motion since these are +very different issues we'll examine them + + align:start position:0% +very different issues we'll examine them + + + align:start position:0% +very different issues we'll examine them +separately in our course we'll begin + + align:start position:0% +separately in our course we'll begin + + + align:start position:0% +separately in our course we'll begin +this week by looking at kinematics in + + align:start position:0% +this week by looking at kinematics in + + + align:start position:0% +this week by looking at kinematics in +one in two dimensions basically learning + + align:start position:0% +one in two dimensions basically learning + + + align:start position:0% +one in two dimensions basically learning +how to describe the geometric motion of + + align:start position:0% +how to describe the geometric motion of + + + align:start position:0% +how to describe the geometric motion of +an object and its trajectory we'll + + align:start position:0% +an object and its trajectory we'll + + + align:start position:0% +an object and its trajectory we'll +follow that by discussing the dynamics + + align:start position:0% +follow that by discussing the dynamics + + + align:start position:0% +follow that by discussing the dynamics +of the motion examining why an object's + + align:start position:0% +of the motion examining why an object's + + + align:start position:0% +of the motion examining why an object's +motion changes when forces are applied + + align:start position:0% +motion changes when forces are applied + + + align:start position:0% +motion changes when forces are applied +through a discussion of Newton's laws + + align:start position:0% +through a discussion of Newton's laws + + + align:start position:0% +through a discussion of Newton's laws +and their applications \ No newline at end of file diff --git a/i81OpQJIH8U.txt b/i81OpQJIH8U.txt new file mode 100644 index 0000000000000000000000000000000000000000..7b1acff6be8563e961ec420bc56f94f8c1163016 --- /dev/null +++ b/i81OpQJIH8U.txt @@ -0,0 +1,1195 @@ +align:start position:0% + +let me demonstrate + + align:start position:0% +let me demonstrate + + + align:start position:0% +let me demonstrate +now with plain doing the integral that + + align:start position:0% +now with plain doing the integral that + + + align:start position:0% +now with plain doing the integral that +really the shape of this wave is moving + + align:start position:0% +really the shape of this wave is moving + + + align:start position:0% +really the shape of this wave is moving +with that + + align:start position:0% +with that + + + align:start position:0% +with that +velocity so in order to do that I + + align:start position:0% +velocity so in order to do that I + + + align:start position:0% +velocity so in order to do that I +basically have to do the + + align:start position:0% + + + + align:start position:0% + +integral um and of course if it's a + + align:start position:0% +integral um and of course if it's a + + + align:start position:0% +integral um and of course if it's a +general integral I cannot do it so I + + align:start position:0% +general integral I cannot do it so I + + + align:start position:0% +general integral I cannot do it so I +have to figure out enough about the + + align:start position:0% +have to figure out enough about the + + + align:start position:0% +have to figure out enough about the +integral so here it is we have s of x + + align:start position:0% +integral so here it is we have s of x + + + align:start position:0% +integral so here it is we have s of x +and t is integral DK F of + + align:start position:0% +and t is integral DK F of + + + align:start position:0% +and t is integral DK F of +k e to the I KX minus Omega of K + + align:start position:0% + + + + align:start position:0% + +T okay it's useful for us to look at + + align:start position:0% +T okay it's useful for us to look at + + + align:start position:0% +T okay it's useful for us to look at +this wave at time equals zero so that we + + align:start position:0% +this wave at time equals zero so that we + + + align:start position:0% +this wave at time equals zero so that we +later compare + + align:start position:0% +later compare + + + align:start position:0% +later compare +it with the result of the integral so f + + align:start position:0% +it with the result of the integral so f + + + align:start position:0% +it with the result of the integral so f +I at time equal Z is just + + align:start position:0% +I at time equal Z is just + + + align:start position:0% +I at time equal Z is just +DK 5 of + + align:start position:0% +DK 5 of + + + align:start position:0% +DK 5 of +k e to the I + + align:start position:0% + + + + align:start position:0% + +KX only thing you know is that five is + + align:start position:0% +KX only thing you know is that five is + + + align:start position:0% +KX only thing you know is that five is +picked around K KN you don't know more + + align:start position:0% +picked around K KN you don't know more + + + align:start position:0% +picked around K KN you don't know more +than that but you know that's s of X and + + align:start position:0% +than that but you know that's s of X and + + + align:start position:0% +than that but you know that's s of X and +time equal Z let's look at it later so + + align:start position:0% +time equal Z let's look at it later so + + + align:start position:0% +time equal Z let's look at it later so +we have this thing here and I cannot do + + align:start position:0% +we have this thing here and I cannot do + + + align:start position:0% +we have this thing here and I cannot do +the integral unless I do some + + align:start position:0% +the integral unless I do some + + + align:start position:0% +the integral unless I do some +approximations and I will approximate + + align:start position:0% +approximations and I will approximate + + + align:start position:0% +approximations and I will approximate +Omega Omega of + + align:start position:0% +Omega Omega of + + + align:start position:0% +Omega Omega of +K since we're anyway going to integrate + + align:start position:0% +K since we're anyway going to integrate + + + align:start position:0% +K since we're anyway going to integrate +around K KN let's do a tailor series is + + align:start position:0% +around K KN let's do a tailor series is + + + align:start position:0% +around K KN let's do a tailor series is +Omega of K + + align:start position:0% +Omega of K + + + align:start position:0% +Omega of K +KN plus K - K KN the derivative of Omega + + align:start position:0% +KN plus K - K KN the derivative of Omega + + + align:start position:0% +KN plus K - K KN the derivative of Omega +with respect to K at K + + align:start position:0% +with respect to K at K + + + align:start position:0% +with respect to K at K +KN plus order K - K KN s + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +let's do this + + align:start position:0% +let's do this + + + align:start position:0% +let's do this +here so if I've expanded + + align:start position:0% +here so if I've expanded + + + align:start position:0% +here so if I've expanded +omega as a function of K which is the + + align:start position:0% +omega as a function of K which is the + + + align:start position:0% +omega as a function of K which is the +only reasonable thing to do K's near K + + align:start position:0% +only reasonable thing to do K's near K + + + align:start position:0% +only reasonable thing to do K's near K +KN are the only ones that contribute so + + align:start position:0% +KN are the only ones that contribute so + + + align:start position:0% +KN are the only ones that contribute so +Omega of K may be an arbitrary function + + align:start position:0% +Omega of K may be an arbitrary function + + + align:start position:0% +Omega of K may be an arbitrary function +but it has a tailor expansion and + + align:start position:0% +but it has a tailor expansion and + + + align:start position:0% +but it has a tailor expansion and +certainly you've noticed that you get + + align:start position:0% +certainly you've noticed that you get + + + align:start position:0% +certainly you've noticed that you get +that derivative that somehow is part of + + align:start position:0% +that derivative that somehow is part of + + + align:start position:0% +that derivative that somehow is part of +the answer so that's certainly a + + align:start position:0% +the answer so that's certainly a + + + align:start position:0% +the answer so that's certainly a +bonus so now we have to plug this into + + align:start position:0% +bonus so now we have to plug this into + + + align:start position:0% +bonus so now we have to plug this into +the integral and this requires a little + + align:start position:0% +the integral and this requires a little + + + align:start position:0% +the integral and this requires a little +bit of vision because it suddenly seems + + align:start position:0% +bit of vision because it suddenly seems + + + align:start position:0% +bit of vision because it suddenly seems +it's going to get very messy but U if + + align:start position:0% +it's going to get very messy but U if + + + align:start position:0% +it's going to get very messy but U if +you look at it for a few seconds you can + + align:start position:0% +you look at it for a few seconds you can + + + align:start position:0% +you look at it for a few seconds you can +see what's going on so P of x and t so + + align:start position:0% +see what's going on so P of x and t so + + + align:start position:0% +see what's going on so P of x and t so +far + + align:start position:0% +far + + + align:start position:0% +far +DK five of K + + align:start position:0% +DK five of K + + + align:start position:0% +DK five of K +k e to the i k + + align:start position:0% +k e to the i k + + + align:start position:0% +k e to the i k +x so far so I'll split the + + align:start position:0% +x so far so I'll split the + + + align:start position:0% +x so far so I'll split the +exponential so as to have these things + + align:start position:0% +exponential so as to have these things + + + align:start position:0% +exponential so as to have these things +separate let's do this e to the minus I + + align:start position:0% +separate let's do this e to the minus I + + + align:start position:0% +separate let's do this e to the minus I +I should put Omega of K * T so I'll + + align:start position:0% +I should put Omega of K * T so I'll + + + align:start position:0% +I should put Omega of K * T so I'll +begin Omega of + + align:start position:0% +begin Omega of + + + align:start position:0% +begin Omega of +K * T that's a first Factor e to the + + align:start position:0% +K * T that's a first Factor e to the + + + align:start position:0% +K * T that's a first Factor e to the +minus I the same the second Factor + + align:start position:0% +minus I the same the second Factor + + + align:start position:0% +minus I the same the second Factor +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +k k d Omega d + + align:start position:0% +k k d Omega d + + + align:start position:0% +k k d Omega d +k k KN * + + align:start position:0% +k k KN * + + + align:start position:0% +k k KN * +T and the third factor is this one with + + align:start position:0% +T and the third factor is this one with + + + align:start position:0% +T and the third factor is this one with +a k e to the minus or should be e to the + + align:start position:0% +a k e to the minus or should be e to the + + + align:start position:0% +a k e to the minus or should be e to the +plus I K KN the Omega d + + align:start position:0% +plus I K KN the Omega d + + + align:start position:0% +plus I K KN the Omega d +k k not + + align:start position:0% +k k not + + + align:start position:0% +k k not +t plus or + + align:start position:0% +t plus or + + + align:start position:0% +t plus or +higher up so e to the + + align:start position:0% + + + + align:start position:0% + +negligible negligible until you need to + + align:start position:0% +negligible negligible until you need to + + + align:start position:0% +negligible negligible until you need to +figure out Distortion of wave packets + + align:start position:0% +figure out Distortion of wave packets + + + align:start position:0% +figure out Distortion of wave packets +we're going to see the wave pocket move + + align:start position:0% +we're going to see the wave pocket move + + + align:start position:0% +we're going to see the wave pocket move +if you want to see the Distortion you + + align:start position:0% +if you want to see the Distortion you + + + align:start position:0% +if you want to see the Distortion you +have to keep that next term we'll do + + align:start position:0% +have to keep that next term we'll do + + + align:start position:0% +have to keep that next term we'll do +that in a week from + + align:start position:0% +that in a week from + + + align:start position:0% +that in a week from +now okay so this is the integral and + + align:start position:0% +now okay so this is the integral and + + + align:start position:0% +now okay so this is the integral and +then you probably need to think a second + + align:start position:0% +then you probably need to think a second + + + align:start position:0% +then you probably need to think a second +second and you say look there's lots of + + align:start position:0% +second and you say look there's lots of + + + align:start position:0% +second and you say look there's lots of +things making it look like a difficult + + align:start position:0% +things making it look like a difficult + + + align:start position:0% +things making it look like a difficult +integral but it's not as difficult as it + + align:start position:0% +integral but it's not as difficult as it + + + align:start position:0% +integral but it's not as difficult as it +looks first I would say this + + align:start position:0% + + + + align:start position:0% + +Factor doesn't depend on + + align:start position:0% +Factor doesn't depend on + + + align:start position:0% +Factor doesn't depend on +K it's Omega evaluated at K not so this + + align:start position:0% +K it's Omega evaluated at K not so this + + + align:start position:0% +K it's Omega evaluated at K not so this +factor is just confusing me it's not + + align:start position:0% +factor is just confusing me it's not + + + align:start position:0% +factor is just confusing me it's not +doesn't belong in the + + align:start position:0% +doesn't belong in the + + + align:start position:0% +doesn't belong in the +integral this Factor two + + align:start position:0% + + + + align:start position:0% + +K not is not a function of K D Omega d k + + align:start position:0% +K not is not a function of K D Omega d k + + + align:start position:0% +K not is not a function of K D Omega d k +evaluated that K KN is not a function of + + align:start position:0% +evaluated that K KN is not a function of + + + align:start position:0% +evaluated that K KN is not a function of +K so this is not really in the integral + + align:start position:0% +K so this is not really in the integral + + + align:start position:0% +K so this is not really in the integral +this is negligible this is in the + + align:start position:0% +this is negligible this is in the + + + align:start position:0% +this is negligible this is in the +integral because it has a k and this is + + align:start position:0% +integral because it has a k and this is + + + align:start position:0% +integral because it has a k and this is +in the integral so let me put here e to + + align:start position:0% +in the integral so let me put here e to + + + align:start position:0% +in the integral so let me put here e to +the minus I Omega of k t e to the minus + + align:start position:0% +the minus I Omega of k t e to the minus + + + align:start position:0% +the minus I Omega of k t e to the minus +to the plus I K KN D Omega d + + align:start position:0% +to the plus I K KN D Omega d + + + align:start position:0% +to the plus I K KN D Omega d +k at K KN t o looks + + align:start position:0% +k at K KN t o looks + + + align:start position:0% +k at K KN t o looks +messy not bad + + align:start position:0% +messy not bad + + + align:start position:0% +messy not bad +DK and now I can put five of + + align:start position:0% + + + + align:start position:0% + +k e to the i + + align:start position:0% +k e to the i + + + align:start position:0% +k e to the i +k x minus these two + + align:start position:0% +k x minus these two + + + align:start position:0% +k x minus these two +exponentials D Omega d k k at K + + align:start position:0% +exponentials D Omega d k k at K + + + align:start position:0% +exponentials D Omega d k k at K +KN time + + align:start position:0% +KN time + + + align:start position:0% +KN time +T and I ignore this so far so + + align:start position:0% + + + + align:start position:0% + +good for this kind of + + align:start position:0% +good for this kind of + + + align:start position:0% +good for this kind of +wave we already get a very nice result + + align:start position:0% +wave we already get a very nice result + + + align:start position:0% +wave we already get a very nice result +because look at this + + align:start position:0% + + + + align:start position:0% + +thing this + + align:start position:0% +thing this + + + align:start position:0% +thing this +quantity can be written in terms of the + + align:start position:0% +quantity can be written in terms of the + + + align:start position:0% +quantity can be written in terms of the +wave function at time equals zero is of + + align:start position:0% +wave function at time equals zero is of + + + align:start position:0% +wave function at time equals zero is of +the same form a 5 K integrated with i k + + align:start position:0% +the same form a 5 K integrated with i k + + + align:start position:0% +the same form a 5 K integrated with i k +and some number that you call X which + + align:start position:0% +and some number that you call X which + + + align:start position:0% +and some number that you call X which +has been changed to + + align:start position:0% +has been changed to + + + align:start position:0% +has been changed to +this so to bring in this and to make it + + align:start position:0% +this so to bring in this and to make it + + + align:start position:0% +this so to bring in this and to make it +a little clearer and many times it's + + align:start position:0% +a little clearer and many times it's + + + align:start position:0% +a little clearer and many times it's +useful if you have a complex number it's + + align:start position:0% +useful if you have a complex number it's + + + align:start position:0% +useful if you have a complex number it's +a little hard to see the bump because + + align:start position:0% +a little hard to see the bump because + + + align:start position:0% +a little hard to see the bump because +maybe the bump is in the real part and + + align:start position:0% +maybe the bump is in the real part and + + + align:start position:0% +maybe the bump is in the real part and +not in the imaginary part or in the + + align:start position:0% +not in the imaginary part or in the + + + align:start position:0% +not in the imaginary part or in the +imaginary part and not in the real part + + align:start position:0% +imaginary part and not in the real part + + + align:start position:0% +imaginary part and not in the real part +so take the absolute value P of x and t + + align:start position:0% +so take the absolute value P of x and t + + + align:start position:0% +so take the absolute value P of x and t +absolute + + align:start position:0% +absolute + + + align:start position:0% +absolute +value and now you say Ah that's why this + + align:start position:0% +value and now you say Ah that's why this + + + align:start position:0% +value and now you say Ah that's why this +is a pure phase the absolute value of a + + align:start position:0% +is a pure phase the absolute value of a + + + align:start position:0% +is a pure phase the absolute value of a +pure phase is that so it's just the + + align:start position:0% +pure phase is that so it's just the + + + align:start position:0% +pure phase is that so it's just the +absolute value of this + + align:start position:0% +absolute value of this + + + align:start position:0% +absolute value of this +quantity which is the absolute value of + + align:start position:0% +quantity which is the absolute value of + + + align:start position:0% +quantity which is the absolute value of +P + + align:start position:0% +P + + + align:start position:0% +P +I at x - D Omega d k + + align:start position:0% +I at x - D Omega d k + + + align:start position:0% +I at x - D Omega d k +k + + align:start position:0% +k + + + align:start position:0% +k +t comma + + align:start position:0% + + + + align:start position:0% + +zero so look what we've + + align:start position:0% +zero so look what we've + + + align:start position:0% +zero so look what we've +proven the wave function the norm of the + + align:start position:0% +proven the wave function the norm of the + + + align:start position:0% +proven the wave function the norm of the +wave function or the wave should the + + align:start position:0% +wave function or the wave should the + + + align:start position:0% +wave function or the wave should the +norm of the + + align:start position:0% +norm of the + + + align:start position:0% +norm of the +wave at any time T looks like like the + + align:start position:0% +wave at any time T looks like like the + + + align:start position:0% +wave at any time T looks like like the +wave looked at time equals zero but just + + align:start position:0% +wave looked at time equals zero but just + + + align:start position:0% +wave looked at time equals zero but just +displaced a distance if there was a + + align:start position:0% +displaced a distance if there was a + + + align:start position:0% +displaced a distance if there was a +Peak at x equal + + align:start position:0% +Peak at x equal + + + align:start position:0% +Peak at x equal +0 at time equals z if a time equals z SI + + align:start position:0% +0 at time equals z if a time equals z SI + + + align:start position:0% +0 at time equals z if a time equals z SI +had a peak when X is equal to Z it will + + align:start position:0% +had a peak when X is equal to Z it will + + + align:start position:0% +had a peak when X is equal to Z it will +have a + + align:start position:0% +have a + + + align:start position:0% +have a +peak this function which is the wave + + align:start position:0% +peak this function which is the wave + + + align:start position:0% +peak this function which is the wave +function at time equals zero will have a + + align:start position:0% +function at time equals zero will have a + + + align:start position:0% +function at time equals zero will have a +peak when this thing is zero the + + align:start position:0% +peak when this thing is zero the + + + align:start position:0% +peak when this thing is zero the +argument and that corresponds to x + + align:start position:0% +argument and that corresponds to x + + + align:start position:0% +argument and that corresponds to x +equals to D Omega d k * T showing again + + align:start position:0% +equals to D Omega d k * T showing again + + + align:start position:0% +equals to D Omega d k * T showing again +that the wave has moved to the right by + + align:start position:0% +that the wave has moved to the right by + + + align:start position:0% +that the wave has moved to the right by +the Omega DK and times T so I've given + + align:start position:0% +the Omega DK and times T so I've given + + + align:start position:0% +the Omega DK and times T so I've given +two presentations basically of this uh + + align:start position:0% +two presentations basically of this uh + + + align:start position:0% +two presentations basically of this uh +very important result about wave packets + + align:start position:0% +very important result about wave packets + + + align:start position:0% +very important result about wave packets +that um we need to understand \ No newline at end of file diff --git a/j--zfB6AIpo.txt b/j--zfB6AIpo.txt new file mode 100644 index 0000000000000000000000000000000000000000..0dc854fba24b098c4ec74fc00edeb3da9e3d99ba --- /dev/null +++ b/j--zfB6AIpo.txt @@ -0,0 +1,4851 @@ +align:start position:0% + +and so now let's consider the spreading + + align:start position:0% +and so now let's consider the spreading + + + align:start position:0% +and so now let's consider the spreading +of infections disease indoors + + align:start position:0% +of infections disease indoors + + + align:start position:0% +of infections disease indoors +so the kendrick kermit models and + + align:start position:0% +so the kendrick kermit models and + + + align:start position:0% +so the kendrick kermit models and +various compartment models that we just + + align:start position:0% +various compartment models that we just + + + align:start position:0% +various compartment models that we just +described + + align:start position:0% +described + + + align:start position:0% +described +start from the assumption essentially of + + align:start position:0% +start from the assumption essentially of + + + align:start position:0% +start from the assumption essentially of +a well-mixed population where there's no + + align:start position:0% +a well-mixed population where there's no + + + align:start position:0% +a well-mixed population where there's no +spatial dependence no network dependence + + align:start position:0% +spatial dependence no network dependence + + + align:start position:0% +spatial dependence no network dependence +of connectivity of people with each + + align:start position:0% +of connectivity of people with each + + + align:start position:0% +of connectivity of people with each +other + + align:start position:0% +other + + + align:start position:0% +other +but rather sort of everyone is + + align:start position:0% +but rather sort of everyone is + + + align:start position:0% +but rather sort of everyone is +interacting with everyone in some sort + + align:start position:0% +interacting with everyone in some sort + + + align:start position:0% +interacting with everyone in some sort +of average sense + + align:start position:0% +of average sense + + + align:start position:0% +of average sense +so that philosophy has also been brought + + align:start position:0% +so that philosophy has also been brought + + + align:start position:0% +so that philosophy has also been brought +to bear on spreading events + + align:start position:0% +to bear on spreading events + + + align:start position:0% +to bear on spreading events +indoors where a little bit stronger + + align:start position:0% +indoors where a little bit stronger + + + align:start position:0% +indoors where a little bit stronger +assumption is made is that the + + align:start position:0% +assumption is made is that the + + + align:start position:0% +assumption is made is that the +transmission is occurring through + + align:start position:0% +transmission is occurring through + + + align:start position:0% +transmission is occurring through +the air and the air is well mixed so not + + align:start position:0% +the air and the air is well mixed so not + + + align:start position:0% +the air and the air is well mixed so not +only are the people well mixed in the + + align:start position:0% +only are the people well mixed in the + + + align:start position:0% +only are the people well mixed in the +sense that they can interact with each + + align:start position:0% +sense that they can interact with each + + + align:start position:0% +sense that they can interact with each +other you know regardless of their + + align:start position:0% +other you know regardless of their + + + align:start position:0% +other you know regardless of their +distance apart or anywhere placed in the + + align:start position:0% +distance apart or anywhere placed in the + + + align:start position:0% +distance apart or anywhere placed in the +room + + align:start position:0% +room + + + align:start position:0% +room +but the reason it's a valid + + align:start position:0% +but the reason it's a valid + + + align:start position:0% +but the reason it's a valid +approximation is because the air itself + + align:start position:0% +approximation is because the air itself + + + align:start position:0% +approximation is because the air itself +is well mixed and so we've already been + + align:start position:0% +is well mixed and so we've already been + + + align:start position:0% +is well mixed and so we've already been +talking about the + + align:start position:0% +talking about the + + + align:start position:0% +talking about the +air the well mixed area we've calculated + + align:start position:0% +air the well mixed area we've calculated + + + align:start position:0% +air the well mixed area we've calculated +a transmission rate + + align:start position:0% +a transmission rate + + + align:start position:0% +a transmission rate +now let's start to connect that to + + align:start position:0% +now let's start to connect that to + + + align:start position:0% +now let's start to connect that to +disease spreading + + align:start position:0% +disease spreading + + + align:start position:0% +disease spreading +so uh one concept there would be to + + align:start position:0% +so uh one concept there would be to + + + align:start position:0% +so uh one concept there would be to +consider + + align:start position:0% +consider + + + align:start position:0% +consider +that the initial number of infected + + align:start position:0% +that the initial number of infected + + + align:start position:0% +that the initial number of infected +people i zero + + align:start position:0% +people i zero + + + align:start position:0% +people i zero +enters a room or an indoor space + + align:start position:0% +enters a room or an indoor space + + + align:start position:0% +enters a room or an indoor space +with n persons including + + align:start position:0% +with n persons including + + + align:start position:0% +with n persons including +uh the infectors uh + + align:start position:0% + + + + align:start position:0% + +for a time tell so we now have + + align:start position:0% +for a time tell so we now have + + + align:start position:0% +for a time tell so we now have +introduced a finite time scale which is + + align:start position:0% +introduced a finite time scale which is + + + align:start position:0% +introduced a finite time scale which is +the time + + align:start position:0% +the time + + + align:start position:0% +the time +spent in the room so you have a room + + align:start position:0% +spent in the room so you have a room + + + align:start position:0% +spent in the room so you have a room +some people are in it and that we're + + align:start position:0% +some people are in it and that we're + + + align:start position:0% +some people are in it and that we're +imagining an infected person comes in + + align:start position:0% +imagining an infected person comes in + + + align:start position:0% +imagining an infected person comes in +and they spend a certain amount of time + + align:start position:0% +and they spend a certain amount of time + + + align:start position:0% +and they spend a certain amount of time +and then they leave and during that time + + align:start position:0% +and then they leave and during that time + + + align:start position:0% +and then they leave and during that time +we'd like to ask ourselves you know what + + align:start position:0% +we'd like to ask ourselves you know what + + + align:start position:0% +we'd like to ask ourselves you know what +what happened with all the other people + + align:start position:0% +what happened with all the other people + + + align:start position:0% +what happened with all the other people +how many people were infected + + align:start position:0% +how many people were infected + + + align:start position:0% +how many people were infected +okay so this tau kind of + + align:start position:0% +okay so this tau kind of + + + align:start position:0% +okay so this tau kind of +acts like the inverse of the removal + + align:start position:0% +acts like the inverse of the removal + + + align:start position:0% +acts like the inverse of the removal +rate + + align:start position:0% +rate + + + align:start position:0% +rate +but we also will assume + + align:start position:0% + + + + align:start position:0% + +that gamma tau is much less than one so + + align:start position:0% +that gamma tau is much less than one so + + + align:start position:0% +that gamma tau is much less than one so +if we think of gamma as the recovery + + align:start position:0% +if we think of gamma as the recovery + + + align:start position:0% +if we think of gamma as the recovery +rate + + align:start position:0% +rate + + + align:start position:0% +rate +or the death rate from the disease so + + align:start position:0% +or the death rate from the disease so + + + align:start position:0% +or the death rate from the disease so +that's the removal + + align:start position:0% +that's the removal + + + align:start position:0% +that's the removal +quantity at the population level + + align:start position:0% +quantity at the population level + + + align:start position:0% +quantity at the population level +then we're assuming the time spent in + + align:start position:0% +then we're assuming the time spent in + + + align:start position:0% +then we're assuming the time spent in +the room is small compared to that so in + + align:start position:0% +the room is small compared to that so in + + + align:start position:0% +the room is small compared to that so in +other words while you're in the room + + align:start position:0% +other words while you're in the room + + + align:start position:0% +other words while you're in the room +nobody's going to be recovering or dying + + align:start position:0% +nobody's going to be recovering or dying + + + align:start position:0% +nobody's going to be recovering or dying +we're just simply going to be + + align:start position:0% +we're just simply going to be + + + align:start position:0% +we're just simply going to be +transmitting the disease for a certain + + align:start position:0% +transmitting the disease for a certain + + + align:start position:0% +transmitting the disease for a certain +amount of time so the + + align:start position:0% +amount of time so the + + + align:start position:0% +amount of time so the +r is gone okay on the other hand + + align:start position:0% +r is gone okay on the other hand + + + align:start position:0% +r is gone okay on the other hand +we can also consider + + align:start position:0% + + + + align:start position:0% + +an exposed + + align:start position:0% + + + + align:start position:0% + +compartment of the population and or the + + align:start position:0% +compartment of the population and or the + + + align:start position:0% +compartment of the population and or the +group in the room + + align:start position:0% + + + + align:start position:0% + +so the exposed group is one which has + + align:start position:0% +so the exposed group is one which has + + + align:start position:0% +so the exposed group is one which has +essentially been exposed to + + align:start position:0% +essentially been exposed to + + + align:start position:0% +essentially been exposed to +the pathogen so let's say they've + + align:start position:0% +the pathogen so let's say they've + + + align:start position:0% +the pathogen so let's say they've +inhaled a critical quantity of the virus + + align:start position:0% +inhaled a critical quantity of the virus + + + align:start position:0% +inhaled a critical quantity of the virus +but they have not yet become themselves + + align:start position:0% +but they have not yet become themselves + + + align:start position:0% +but they have not yet become themselves +infectious so they are already exposed + + align:start position:0% +infectious so they are already exposed + + + align:start position:0% +infectious so they are already exposed +they are going to come down with the + + align:start position:0% +they are going to come down with the + + + align:start position:0% +they are going to come down with the +disease + + align:start position:0% +disease + + + align:start position:0% +disease +so they are going to be eventually + + align:start position:0% +so they are going to be eventually + + + align:start position:0% +so they are going to be eventually +you know symptomatic and potentially + + align:start position:0% +you know symptomatic and potentially + + + align:start position:0% +you know symptomatic and potentially +infectious but they may not be + + align:start position:0% +infectious but they may not be + + + align:start position:0% +infectious but they may not be +infectious yet + + align:start position:0% +infectious yet + + + align:start position:0% +infectious yet +um so the exposed group basically + + align:start position:0% +um so the exposed group basically + + + align:start position:0% +um so the exposed group basically +um has + + align:start position:0% +um has + + + align:start position:0% +um has +has has received + + align:start position:0% +has has received + + + align:start position:0% +has has received +the disease so it's been transmitted to + + align:start position:0% +the disease so it's been transmitted to + + + align:start position:0% +the disease so it's been transmitted to +them + + align:start position:0% +them + + + align:start position:0% +them +but is not yet + + align:start position:0% +but is not yet + + + align:start position:0% +but is not yet +themselves infectious + + align:start position:0% + + + + align:start position:0% + +okay so that's another uh sort of group + + align:start position:0% +okay so that's another uh sort of group + + + align:start position:0% +okay so that's another uh sort of group +that we want to think about + + align:start position:0% +that we want to think about + + + align:start position:0% +that we want to think about +so uh so they're um so they're not yes + + align:start position:0% +so uh so they're um so they're not yes + + + align:start position:0% +so uh so they're um so they're not yes +in other ways say they're not yet + + align:start position:0% +in other ways say they're not yet + + + align:start position:0% +in other ways say they're not yet +contagious okay so they're going to get + + align:start position:0% +contagious okay so they're going to get + + + align:start position:0% +contagious okay so they're going to get +sick but they're not contagious yet so i + + align:start position:0% +sick but they're not contagious yet so i + + + align:start position:0% +sick but they're not contagious yet so i +should put here contagious is another + + align:start position:0% +should put here contagious is another + + + align:start position:0% +should put here contagious is another +word we could think about using okay + + align:start position:0% +word we could think about using okay + + + align:start position:0% +word we could think about using okay +so we've gotten rid of r the recovered + + align:start position:0% +so we've gotten rid of r the recovered + + + align:start position:0% +so we've gotten rid of r the recovered +compartment but we've added e + + align:start position:0% +compartment but we've added e + + + align:start position:0% +compartment but we've added e +so instead of the scir model we have the + + align:start position:0% +so instead of the scir model we have the + + + align:start position:0% +so instead of the scir model we have the +sei + + align:start position:0% + + + + align:start position:0% + +model + + align:start position:0% +model + + + align:start position:0% +model +where we can write down the same kinds + + align:start position:0% +where we can write down the same kinds + + + align:start position:0% +where we can write down the same kinds +of equations as four + + align:start position:0% +of equations as four + + + align:start position:0% +of equations as four +d s dt is minus beta and i'll write beta + + align:start position:0% +d s dt is minus beta and i'll write beta + + + align:start position:0% +d s dt is minus beta and i'll write beta +of t + + align:start position:0% +of t + + + align:start position:0% +of t +s i because another complexity here as + + align:start position:0% +s i because another complexity here as + + + align:start position:0% +s i because another complexity here as +we know is that as soon as the infected + + align:start position:0% +we know is that as soon as the infected + + + align:start position:0% +we know is that as soon as the infected +person comes in + + align:start position:0% +person comes in + + + align:start position:0% +person comes in +if it's airborne transmission it takes + + align:start position:0% +if it's airborne transmission it takes + + + align:start position:0% +if it's airborne transmission it takes +time through the fluid mechanics that we + + align:start position:0% +time through the fluid mechanics that we + + + align:start position:0% +time through the fluid mechanics that we +were just describing + + align:start position:0% +were just describing + + + align:start position:0% +were just describing +for the concentration to build up so the + + align:start position:0% +for the concentration to build up so the + + + align:start position:0% +for the concentration to build up so the +transmission rate is not constant we've + + align:start position:0% +transmission rate is not constant we've + + + align:start position:0% +transmission rate is not constant we've +actually already calculated that + + align:start position:0% +actually already calculated that + + + align:start position:0% +actually already calculated that +transmission rate but it now enters this + + align:start position:0% +transmission rate but it now enters this + + + align:start position:0% +transmission rate but it now enters this +equation + + align:start position:0% +equation + + + align:start position:0% +equation +and when a person uh so this is now the + + align:start position:0% +and when a person uh so this is now the + + + align:start position:0% +and when a person uh so this is now the +tr the susceptible people + + align:start position:0% +tr the susceptible people + + + align:start position:0% +tr the susceptible people +are getting uh uh exposed + + align:start position:0% +are getting uh uh exposed + + + align:start position:0% +are getting uh uh exposed +and so when that sort of reaction + + align:start position:0% +and so when that sort of reaction + + + align:start position:0% +and so when that sort of reaction +happens if you will + + align:start position:0% +happens if you will + + + align:start position:0% +happens if you will +the exposed fraction then our population + + align:start position:0% +the exposed fraction then our population + + + align:start position:0% +the exposed fraction then our population +then grows + + align:start position:0% + + + + align:start position:0% + +and then there's a certain rate with + + align:start position:0% +and then there's a certain rate with + + + align:start position:0% +and then there's a certain rate with +which exposed people can become + + align:start position:0% +which exposed people can become + + + align:start position:0% +which exposed people can become +themselves infectious to others + + align:start position:0% +themselves infectious to others + + + align:start position:0% +themselves infectious to others +and that rate we'll call alpha so we can + + align:start position:0% +and that rate we'll call alpha so we can + + + align:start position:0% +and that rate we'll call alpha so we can +remove exposed people at a rate alpha + + align:start position:0% +remove exposed people at a rate alpha + + + align:start position:0% +remove exposed people at a rate alpha +and when they're removed they become + + align:start position:0% +and when they're removed they become + + + align:start position:0% +and when they're removed they become +infected people + + align:start position:0% +infected people + + + align:start position:0% +infected people +and so then the number of infections + + align:start position:0% +and so then the number of infections + + + align:start position:0% +and so then the number of infections +grows + + align:start position:0% +grows + + + align:start position:0% +grows +so this is a very closely related model + + align:start position:0% +so this is a very closely related model + + + align:start position:0% +so this is a very closely related model +that we could solve and in order to + + align:start position:0% +that we could solve and in order to + + + align:start position:0% +that we could solve and in order to +couple this + + align:start position:0% +couple this + + + align:start position:0% +couple this +to airborne disease spreading we need to + + align:start position:0% +to airborne disease spreading we need to + + + align:start position:0% +to airborne disease spreading we need to +go back to our + + align:start position:0% +go back to our + + + align:start position:0% +go back to our +model of the airborne pathogen so for + + align:start position:0% +model of the airborne pathogen so for + + + align:start position:0% +model of the airborne pathogen so for +example the virions per air volume which + + align:start position:0% +example the virions per air volume which + + + align:start position:0% +example the virions per air volume which +we called c + + align:start position:0% +we called c + + + align:start position:0% +we called c +and in fact i'll even write this as a dc + + align:start position:0% +and in fact i'll even write this as a dc + + + align:start position:0% +and in fact i'll even write this as a dc +dt with a partial derivative + + align:start position:0% +dt with a partial derivative + + + align:start position:0% +dt with a partial derivative +which is p which depends on the size + + align:start position:0% +which is p which depends on the size + + + align:start position:0% +which is p which depends on the size +r divided by actually this should be + + align:start position:0% +r divided by actually this should be + + + align:start position:0% +r divided by actually this should be +v minus + + align:start position:0% +v minus + + + align:start position:0% +v minus +lambda c of our c so that was the model + + align:start position:0% +lambda c of our c so that was the model + + + align:start position:0% +lambda c of our c so that was the model +we just talked about + + align:start position:0% +we just talked about + + + align:start position:0% +we just talked about +which we have to solve and then the beta + + align:start position:0% +which we have to solve and then the beta + + + align:start position:0% +which we have to solve and then the beta +of t is the breathing rate + + align:start position:0% +of t is the breathing rate + + + align:start position:0% +of t is the breathing rate +times the integral over all these sizes + + align:start position:0% +times the integral over all these sizes + + + align:start position:0% +times the integral over all these sizes +of uh c of r + + align:start position:0% +of uh c of r + + + align:start position:0% +of uh c of r +and t and then ci and of course there + + align:start position:0% +and t and then ci and of course there + + + align:start position:0% +and t and then ci and of course there +could be masks + + align:start position:0% +could be masks + + + align:start position:0% +could be masks +which might also be size dependent uh d + + align:start position:0% +which might also be size dependent uh d + + + align:start position:0% +which might also be size dependent uh d +r okay so + + align:start position:0% +r okay so + + + align:start position:0% +r okay so +we tie it together this way this kind of + + align:start position:0% +we tie it together this way this kind of + + + align:start position:0% +we tie it together this way this kind of +model + + align:start position:0% +model + + + align:start position:0% +model +which is typically uh run without + + align:start position:0% +which is typically uh run without + + + align:start position:0% +which is typically uh run without +accounting for the size dependence but + + align:start position:0% +accounting for the size dependence but + + + align:start position:0% +accounting for the size dependence but +that has been done by some authors as + + align:start position:0% +that has been done by some authors as + + + align:start position:0% +that has been done by some authors as +well + + align:start position:0% +well + + + align:start position:0% +well +generally falls into the category of + + align:start position:0% +generally falls into the category of + + + align:start position:0% +generally falls into the category of +wells riley models + + align:start position:0% + + + + align:start position:0% + +and i mention here that wells wells + + align:start position:0% +and i mention here that wells wells + + + align:start position:0% +and i mention here that wells wells +actually was a real pioneer here already + + align:start position:0% +actually was a real pioneer here already + + + align:start position:0% +actually was a real pioneer here already +starting the 1930s + + align:start position:0% +starting the 1930s + + + align:start position:0% +starting the 1930s +did careful studies of disease + + align:start position:0% +did careful studies of disease + + + align:start position:0% +did careful studies of disease +transmission especially for + + align:start position:0% +transmission especially for + + + align:start position:0% +transmission especially for +including for flu and other viral + + align:start position:0% +including for flu and other viral + + + align:start position:0% +including for flu and other viral +diseases and + + align:start position:0% +diseases and + + + align:start position:0% +diseases and +really what was one of the initial + + align:start position:0% +really what was one of the initial + + + align:start position:0% +really what was one of the initial +proponents of the idea of infectious + + align:start position:0% +proponents of the idea of infectious + + + align:start position:0% +proponents of the idea of infectious +air that there are particles suspended + + align:start position:0% +air that there are particles suspended + + + align:start position:0% +air that there are particles suspended +in the air which can become infectious + + align:start position:0% +in the air which can become infectious + + + align:start position:0% +in the air which can become infectious +he also was the one who pioneered the + + align:start position:0% +he also was the one who pioneered the + + + align:start position:0% +he also was the one who pioneered the +wells curve + + align:start position:0% +wells curve + + + align:start position:0% +wells curve +which explored evaporation versus + + align:start position:0% +which explored evaporation versus + + + align:start position:0% +which explored evaporation versus +settling + + align:start position:0% +settling + + + align:start position:0% +settling +and then around 1915 and in 1955 he + + align:start position:0% +and then around 1915 and in 1955 he + + + align:start position:0% +and then around 1915 and in 1955 he +introduced + + align:start position:0% +introduced + + + align:start position:0% +introduced +this kind of a model where he's taking + + align:start position:0% +this kind of a model where he's taking + + + align:start position:0% +this kind of a model where he's taking +into account the balance of the + + align:start position:0% +into account the balance of the + + + align:start position:0% +into account the balance of the +production rate p + + align:start position:0% +production rate p + + + align:start position:0% +production rate p +and then the ventilation rate in order + + align:start position:0% +and then the ventilation rate in order + + + align:start position:0% +and then the ventilation rate in order +to describe the buildup + + align:start position:0% +to describe the buildup + + + align:start position:0% +to describe the buildup +of the infectious droplets in the air + + align:start position:0% +of the infectious droplets in the air + + + align:start position:0% +of the infectious droplets in the air +and then the transmission is connected + + align:start position:0% +and then the transmission is connected + + + align:start position:0% +and then the transmission is connected +in this way uh here um + + align:start position:0% +in this way uh here um + + + align:start position:0% +in this way uh here um +and i should say that in wells riley + + align:start position:0% +and i should say that in wells riley + + + align:start position:0% +and i should say that in wells riley +modeling + + align:start position:0% +modeling + + + align:start position:0% +modeling +usually e is uh is ignored + + align:start position:0% +usually e is uh is ignored + + + align:start position:0% +usually e is uh is ignored +um and so uh + + align:start position:0% +um and so uh + + + align:start position:0% +um and so uh +we normally just go straight from s to + + align:start position:0% +we normally just go straight from s to + + + align:start position:0% +we normally just go straight from s to +i is so i'll say e is neglected + + align:start position:0% +i is so i'll say e is neglected + + + align:start position:0% +i is so i'll say e is neglected +and what that really means is that + + align:start position:0% +and what that really means is that + + + align:start position:0% +and what that really means is that +the incubation rate here this alpha + + align:start position:0% +the incubation rate here this alpha + + + align:start position:0% +the incubation rate here this alpha +is the incubation rate + + align:start position:0% +is the incubation rate + + + align:start position:0% +is the incubation rate +so it's the rate at which an exposed + + align:start position:0% +so it's the rate at which an exposed + + + align:start position:0% +so it's the rate at which an exposed +person becomes + + align:start position:0% +person becomes + + + align:start position:0% +person becomes +infectious or contagious that that + + align:start position:0% +infectious or contagious that that + + + align:start position:0% +infectious or contagious that that +alpha t is much less + + align:start position:0% +alpha t is much less + + + align:start position:0% +alpha t is much less +than one so it's essentially the wells + + align:start position:0% +than one so it's essentially the wells + + + align:start position:0% +than one so it's essentially the wells +rally model is sort of + + align:start position:0% +rally model is sort of + + + align:start position:0% +rally model is sort of +it's the slow incubation limit okay + + align:start position:0% +it's the slow incubation limit okay + + + align:start position:0% +it's the slow incubation limit okay +um but we've written down something more + + align:start position:0% +um but we've written down something more + + + align:start position:0% +um but we've written down something more +general here which does also allow for + + align:start position:0% +general here which does also allow for + + + align:start position:0% +general here which does also allow for +the possibility of exposed uh + + align:start position:0% +the possibility of exposed uh + + + align:start position:0% +the possibility of exposed uh +people that have not that could still be + + align:start position:0% +people that have not that could still be + + + align:start position:0% +people that have not that could still be +they could become infectious so we'll + + align:start position:0% +they could become infectious so we'll + + + align:start position:0% +they could become infectious so we'll +come back to that in just a moment + + align:start position:0% +come back to that in just a moment + + + align:start position:0% +come back to that in just a moment +so let's kind of summarize the results + + align:start position:0% +so let's kind of summarize the results + + + align:start position:0% +so let's kind of summarize the results +of + + align:start position:0% +of + + + align:start position:0% +of +the wells riley approach so + + align:start position:0% +the wells riley approach so + + + align:start position:0% +the wells riley approach so +we'll consider the slow incubation limit + + align:start position:0% + + + + align:start position:0% + +which is alpha tau much less than one + + align:start position:0% +which is alpha tau much less than one + + + align:start position:0% +which is alpha tau much less than one +and so in that case if there's slow + + align:start position:0% +and so in that case if there's slow + + + align:start position:0% +and so in that case if there's slow +incubation + + align:start position:0% +incubation + + + align:start position:0% +incubation +then you're not during the time of the + + align:start position:0% +then you're not during the time of the + + + align:start position:0% +then you're not during the time of the +expo of the infected person + + align:start position:0% +expo of the infected person + + + align:start position:0% +expo of the infected person +being in the room there's no time for + + align:start position:0% +being in the room there's no time for + + + align:start position:0% +being in the room there's no time for +new infected new people to become + + align:start position:0% +new infected new people to become + + + align:start position:0% +new infected new people to become +infectious so it's really just like a + + align:start position:0% +infectious so it's really just like a + + + align:start position:0% +infectious so it's really just like a +fixed source so it's essentially saying + + align:start position:0% +fixed source so it's essentially saying + + + align:start position:0% +fixed source so it's essentially saying +that i + + align:start position:0% +that i + + + align:start position:0% +that i +is equal to i0 which is a constant + + align:start position:0% +is equal to i0 which is a constant + + + align:start position:0% +is equal to i0 which is a constant +so even though the disease is being + + align:start position:0% +so even though the disease is being + + + align:start position:0% +so even though the disease is being +transmitted there's no kind of + + align:start position:0% +transmitted there's no kind of + + + align:start position:0% +transmitted there's no kind of +amplification effect because the people + + align:start position:0% +amplification effect because the people + + + align:start position:0% +amplification effect because the people +who have been exposed are no longer not + + align:start position:0% +who have been exposed are no longer not + + + align:start position:0% +who have been exposed are no longer not +able to themselves infect + + align:start position:0% +able to themselves infect + + + align:start position:0% +able to themselves infect +others because the incubation is too + + align:start position:0% +others because the incubation is too + + + align:start position:0% +others because the incubation is too +slow + + align:start position:0% +slow + + + align:start position:0% +slow +okay and this model um here + + align:start position:0% +okay and this model um here + + + align:start position:0% +okay and this model um here +uh where you sort of couple these + + align:start position:0% +uh where you sort of couple these + + + align:start position:0% +uh where you sort of couple these +equations with with + + align:start position:0% +equations with with + + + align:start position:0% +equations with with +uh the the um the the s + + align:start position:0% +uh the the um the the s + + + align:start position:0% +uh the the um the the s +i equations basically um that was done + + align:start position:0% +i equations basically um that was done + + + align:start position:0% +i equations basically um that was done +by + + align:start position:0% +by + + + align:start position:0% +by +uh gamma um + + align:start position:0% + + + + align:start position:0% + +gemaitoni and nucci + + align:start position:0% +gemaitoni and nucci + + + align:start position:0% +gemaitoni and nucci +in 1997. so you can see starting from + + align:start position:0% +in 1997. so you can see starting from + + + align:start position:0% +in 1997. so you can see starting from +wells you know we start to move towards + + align:start position:0% +wells you know we start to move towards + + + align:start position:0% +wells you know we start to move towards +this picture of actually coupling the + + align:start position:0% +this picture of actually coupling the + + + align:start position:0% +this picture of actually coupling the +dynamics of the pathogen + + align:start position:0% +dynamics of the pathogen + + + align:start position:0% +dynamics of the pathogen +to the transmission and there have been + + align:start position:0% +to the transmission and there have been + + + align:start position:0% +to the transmission and there have been +a number of models since then which have + + align:start position:0% +a number of models since then which have + + + align:start position:0% +a number of models since then which have +even taken into account some of these + + align:start position:0% +even taken into account some of these + + + align:start position:0% +even taken into account some of these +aspects of the different drop sizes + + align:start position:0% +aspects of the different drop sizes + + + align:start position:0% +aspects of the different drop sizes +and other effects that we've been + + align:start position:0% +and other effects that we've been + + + align:start position:0% +and other effects that we've been +discussing that were not initially + + align:start position:0% +discussing that were not initially + + + align:start position:0% +discussing that were not initially +considered + + align:start position:0% +considered + + + align:start position:0% +considered +by wells so okay so that's this + + align:start position:0% +by wells so okay so that's this + + + align:start position:0% +by wells so okay so that's this +so if we so the first thing to do + + align:start position:0% +so if we so the first thing to do + + + align:start position:0% +so if we so the first thing to do +is to deal with beta of t so how are we + + align:start position:0% +is to deal with beta of t so how are we + + + align:start position:0% +is to deal with beta of t so how are we +going to do that + + align:start position:0% +going to do that + + + align:start position:0% +going to do that +so if i put beta t on the other side if + + align:start position:0% +so if i put beta t on the other side if + + + align:start position:0% +so if i put beta t on the other side if +i kind of divide it down you can see + + align:start position:0% +i kind of divide it down you can see + + + align:start position:0% +i kind of divide it down you can see +that i really would like to define + + align:start position:0% +that i really would like to define + + + align:start position:0% +that i really would like to define +a new differential of a variable t + + align:start position:0% +a new differential of a variable t + + + align:start position:0% +a new differential of a variable t +hat which is beta of t + + align:start position:0% +hat which is beta of t + + + align:start position:0% +hat which is beta of t +times dt okay that's that would be my + + align:start position:0% +times dt okay that's that would be my + + + align:start position:0% +times dt okay that's that would be my +definition of a new + + align:start position:0% +definition of a new + + + align:start position:0% +definition of a new +new variable and so when i integrate + + align:start position:0% +new variable and so when i integrate + + + align:start position:0% +new variable and so when i integrate +this tells me that i should really + + align:start position:0% +this tells me that i should really + + + align:start position:0% +this tells me that i should really +switch + + align:start position:0% +switch + + + align:start position:0% +switch +to a new time variable which is not just + + align:start position:0% +to a new time variable which is not just + + + align:start position:0% +to a new time variable which is not just +t + + align:start position:0% +t + + + align:start position:0% +t +but it's the integral of beta + + align:start position:0% +but it's the integral of beta + + + align:start position:0% +but it's the integral of beta +dt so that's a time-like variable and + + align:start position:0% +dt so that's a time-like variable and + + + align:start position:0% +dt so that's a time-like variable and +once i do that i'm essentially + + align:start position:0% +once i do that i'm essentially + + + align:start position:0% +once i do that i'm essentially +sweeping this guy into the derivative + + align:start position:0% +sweeping this guy into the derivative + + + align:start position:0% +sweeping this guy into the derivative +there + + align:start position:0% +there + + + align:start position:0% +there +and if i also assume that i is roughly + + align:start position:0% +and if i also assume that i is roughly + + + align:start position:0% +and if i also assume that i is roughly +equal to i naught + + align:start position:0% +equal to i naught + + + align:start position:0% +equal to i naught +then what i have now is a much simpler + + align:start position:0% +then what i have now is a much simpler + + + align:start position:0% +then what i have now is a much simpler +equation here i go from this nonlinear + + align:start position:0% +equation here i go from this nonlinear + + + align:start position:0% +equation here i go from this nonlinear +equation with time dependent + + align:start position:0% +equation with time dependent + + + align:start position:0% +equation with time dependent +coefficients to something which is now + + align:start position:0% +coefficients to something which is now + + + align:start position:0% +coefficients to something which is now +linear and we have + + align:start position:0% +linear and we have + + + align:start position:0% +linear and we have +d s d t + + align:start position:0% +d s d t + + + align:start position:0% +d s d t +hat is is approximately equal to + + align:start position:0% +hat is is approximately equal to + + + align:start position:0% +hat is is approximately equal to +uh beta + + align:start position:0% + + + + align:start position:0% + +sorry it's is it's sorry is it probably + + align:start position:0% +sorry it's is it's sorry is it probably + + + align:start position:0% +sorry it's is it's sorry is it probably +it's + + align:start position:0% +it's + + + align:start position:0% +it's +right this is um + + align:start position:0% + + + + align:start position:0% + +sorry which is minus excuse me + + align:start position:0% +sorry which is minus excuse me + + + align:start position:0% +sorry which is minus excuse me +i zero + + align:start position:0% + + + + align:start position:0% + +s so again our i is roughly constant our + + align:start position:0% +s so again our i is roughly constant our + + + align:start position:0% +s so again our i is roughly constant our +beta got swept into the time + + align:start position:0% +beta got swept into the time + + + align:start position:0% +beta got swept into the time +so this is just kind of a simple + + align:start position:0% +so this is just kind of a simple + + + align:start position:0% +so this is just kind of a simple +exponential relaxation + + align:start position:0% +exponential relaxation + + + align:start position:0% +exponential relaxation +and the initial value is that s at time + + align:start position:0% +and the initial value is that s at time + + + align:start position:0% +and the initial value is that s at time +equals zero is + + align:start position:0% +equals zero is + + + align:start position:0% +equals zero is +n minus i zero so there are n people i + + align:start position:0% +n minus i zero so there are n people i + + + align:start position:0% +n minus i zero so there are n people i +zero of them are the initial affected + + align:start position:0% +zero of them are the initial affected + + + align:start position:0% +zero of them are the initial affected +ones and so + + align:start position:0% +ones and so + + + align:start position:0% +ones and so +this is a pretty easy equation to solve + + align:start position:0% +this is a pretty easy equation to solve + + + align:start position:0% +this is a pretty easy equation to solve +it's just an exponential relaxation + + align:start position:0% +it's just an exponential relaxation + + + align:start position:0% +it's just an exponential relaxation +which we've already seen a few times + + align:start position:0% +which we've already seen a few times + + + align:start position:0% +which we've already seen a few times +before + + align:start position:0% +before + + + align:start position:0% +before +and so the solution is that s is + + align:start position:0% +and so the solution is that s is + + + align:start position:0% +and so the solution is that s is +n minus i zero the initial value of s + + align:start position:0% +n minus i zero the initial value of s + + + align:start position:0% +n minus i zero the initial value of s +times e to the minus i zero t + + align:start position:0% +times e to the minus i zero t + + + align:start position:0% +times e to the minus i zero t +hat so it's i zero integral + + align:start position:0% +hat so it's i zero integral + + + align:start position:0% +hat so it's i zero integral +zero to t of beta dt + + align:start position:0% +zero to t of beta dt + + + align:start position:0% +zero to t of beta dt +okay and then we can also write + + align:start position:0% +okay and then we can also write + + + align:start position:0% +okay and then we can also write +so that that's the s and then the e is + + align:start position:0% +so that that's the s and then the e is + + + align:start position:0% +so that that's the s and then the e is +just if we have fast incubation + + align:start position:0% +just if we have fast incubation + + + align:start position:0% +just if we have fast incubation +um or sorry slow incubation this term is + + align:start position:0% +um or sorry slow incubation this term is + + + align:start position:0% +um or sorry slow incubation this term is +gone and we basically just have e + + align:start position:0% +gone and we basically just have e + + + align:start position:0% +gone and we basically just have e +is sort of uh just s and e have to add + + align:start position:0% +is sort of uh just s and e have to add + + + align:start position:0% +is sort of uh just s and e have to add +up to n + + align:start position:0% +up to n + + + align:start position:0% +up to n +basically and so we're left with e of t + + align:start position:0% +basically and so we're left with e of t + + + align:start position:0% +basically and so we're left with e of t +is n minus i and then 1 minus + + align:start position:0% +is n minus i and then 1 minus + + + align:start position:0% +is n minus i and then 1 minus +and let me actually write this quantity + + align:start position:0% +and let me actually write this quantity + + + align:start position:0% +and let me actually write this quantity +up here + + align:start position:0% +up here + + + align:start position:0% +up here +as q little q + + align:start position:0% +as q little q + + + align:start position:0% +as q little q +of t where + + align:start position:0% +of t where + + + align:start position:0% +of t where +little q of t is + + align:start position:0% +little q of t is + + + align:start position:0% +little q of t is +i zero times the time integral of beta + + align:start position:0% + + + + align:start position:0% + +dt + + align:start position:0% + + + + align:start position:0% + +and what is this q here this q + + align:start position:0% +and what is this q here this q + + + align:start position:0% +and what is this q here this q +can be thought of as the number of + + align:start position:0% +can be thought of as the number of + + + align:start position:0% +can be thought of as the number of +infection + + align:start position:0% +infection + + + align:start position:0% +infection +quanta per time that are released by the + + align:start position:0% +quanta per time that are released by the + + + align:start position:0% +quanta per time that are released by the +infectors because they're i zero + + align:start position:0% +infectors because they're i zero + + + align:start position:0% +infectors because they're i zero +infectors + + align:start position:0% +infectors + + + align:start position:0% +infectors +each one of them is infecting another + + align:start position:0% +each one of them is infecting another + + + align:start position:0% +each one of them is infecting another +individual person at a rate beta + + align:start position:0% +individual person at a rate beta + + + align:start position:0% +individual person at a rate beta +and that beta is time dependent so you + + align:start position:0% +and that beta is time dependent so you + + + align:start position:0% +and that beta is time dependent so you +have to integrate in time + + align:start position:0% +have to integrate in time + + + align:start position:0% +have to integrate in time +and so this is telling me the total + + align:start position:0% +and so this is telling me the total + + + align:start position:0% +and so this is telling me the total +number of people + + align:start position:0% +number of people + + + align:start position:0% +number of people +that would be infected by those in fact + + align:start position:0% +that would be infected by those in fact + + + align:start position:0% +that would be infected by those in fact +infected people + + align:start position:0% +infected people + + + align:start position:0% +infected people +if you weren't running into all of the + + align:start position:0% +if you weren't running into all of the + + + align:start position:0% +if you weren't running into all of the +limits that are described by this model + + align:start position:0% +limits that are described by this model + + + align:start position:0% +limits that are described by this model +so what is happening is that as someone + + align:start position:0% +so what is happening is that as someone + + + align:start position:0% +so what is happening is that as someone +gets + + align:start position:0% +gets + + + align:start position:0% +gets +exposed they can't be exposed again so + + align:start position:0% +exposed they can't be exposed again so + + + align:start position:0% +exposed they can't be exposed again so +there's some numbers there that are + + align:start position:0% +there's some numbers there that are + + + align:start position:0% +there's some numbers there that are +changing so you can't always you can't + + align:start position:0% +changing so you can't always you can't + + + align:start position:0% +changing so you can't always you can't +keep passing an infection quantum to + + align:start position:0% +keep passing an infection quantum to + + + align:start position:0% +keep passing an infection quantum to +somebody + + align:start position:0% +somebody + + + align:start position:0% +somebody +and have them get infected over and over + + align:start position:0% +and have them get infected over and over + + + align:start position:0% +and have them get infected over and over +so that doesn't happen + + align:start position:0% +so that doesn't happen + + + align:start position:0% +so that doesn't happen +but what this is measuring is somehow + + align:start position:0% +but what this is measuring is somehow + + + align:start position:0% +but what this is measuring is somehow +the number of times that somehow there's + + align:start position:0% +the number of times that somehow there's + + + align:start position:0% +the number of times that somehow there's +been an + + align:start position:0% +been an + + + align:start position:0% +been an +attempted infection uh you know or an + + align:start position:0% +attempted infection uh you know or an + + + align:start position:0% +attempted infection uh you know or an +expected infection if a person were + + align:start position:0% +expected infection if a person were + + + align:start position:0% +expected infection if a person were +susceptible + + align:start position:0% +susceptible + + + align:start position:0% +susceptible +okay so this q of t here is the um + + align:start position:0% +okay so this q of t here is the um + + + align:start position:0% +okay so this q of t here is the um +uh infection + + align:start position:0% +uh infection + + + align:start position:0% +uh infection +quanta as defined by wells + + align:start position:0% +quanta as defined by wells + + + align:start position:0% +quanta as defined by wells +uh transmitted + + align:start position:0% + + + + align:start position:0% + +in time t so up to time t + + align:start position:0% +in time t so up to time t + + + align:start position:0% +in time t so up to time t +they're i zero and vectors that number's + + align:start position:0% +they're i zero and vectors that number's + + + align:start position:0% +they're i zero and vectors that number's +not changing and they're basically the + + align:start position:0% +not changing and they're basically the + + + align:start position:0% +not changing and they're basically the +way + + align:start position:0% +way + + + align:start position:0% +way +you can think about this kind of + + align:start position:0% +you can think about this kind of + + + align:start position:0% +you can think about this kind of +airborne transmission is they're + + align:start position:0% +airborne transmission is they're + + + align:start position:0% +airborne transmission is they're +essentially spewing out + + align:start position:0% +essentially spewing out + + + align:start position:0% +essentially spewing out +infection quanta each one of them if it + + align:start position:0% +infection quanta each one of them if it + + + align:start position:0% +infection quanta each one of them if it +hits in a + + align:start position:0% +hits in a + + + align:start position:0% +hits in a +potentially susceptible person will + + align:start position:0% +potentially susceptible person will + + + align:start position:0% +potentially susceptible person will +infect them but the number of + + align:start position:0% +infect them but the number of + + + align:start position:0% +infect them but the number of +susceptible people is changing so it's + + align:start position:0% +susceptible people is changing so it's + + + align:start position:0% +susceptible people is changing so it's +not like you keep getting more + + align:start position:0% +not like you keep getting more + + + align:start position:0% +not like you keep getting more +infections eventually you run out of + + align:start position:0% +infections eventually you run out of + + + align:start position:0% +infections eventually you run out of +people and you can't keep infecting them + + align:start position:0% +people and you can't keep infecting them + + + align:start position:0% +people and you can't keep infecting them +but that's that's one way to think about + + align:start position:0% +but that's that's one way to think about + + + align:start position:0% +but that's that's one way to think about +this and we've already calculated + + align:start position:0% +this and we've already calculated + + + align:start position:0% +this and we've already calculated +um this concept of infection quanta in + + align:start position:0% +um this concept of infection quanta in + + + align:start position:0% +um this concept of infection quanta in +the context of the breathing we've + + align:start position:0% +the context of the breathing we've + + + align:start position:0% +the context of the breathing we've +we've uh we've defined a quantity which + + align:start position:0% +we've uh we've defined a quantity which + + + align:start position:0% +we've uh we've defined a quantity which +is the number of infection quanta + + align:start position:0% +is the number of infection quanta + + + align:start position:0% +is the number of infection quanta +per volume of exhaled breath we've also + + align:start position:0% +per volume of exhaled breath we've also + + + align:start position:0% +per volume of exhaled breath we've also +talked about the quantum emission rates + + align:start position:0% +talked about the quantum emission rates + + + align:start position:0% +talked about the quantum emission rates +for people and connected that back to + + align:start position:0% +for people and connected that back to + + + align:start position:0% +for people and connected that back to +the droplets + + align:start position:0% +the droplets + + + align:start position:0% +the droplets +and so here's how you see how that + + align:start position:0% +and so here's how you see how that + + + align:start position:0% +and so here's how you see how that +quantity enters into + + align:start position:0% +quantity enters into + + + align:start position:0% +quantity enters into +the disease spreading models + + align:start position:0% +the disease spreading models + + + align:start position:0% +the disease spreading models +and in fact we can sketch uh what + + align:start position:0% +and in fact we can sketch uh what + + + align:start position:0% +and in fact we can sketch uh what +happens with s and i here so basically + + align:start position:0% +happens with s and i here so basically + + + align:start position:0% +happens with s and i here so basically +if we we start with s for example starts + + align:start position:0% +if we we start with s for example starts + + + align:start position:0% +if we we start with s for example starts +at the value n minus i zero + + align:start position:0% +at the value n minus i zero + + + align:start position:0% +at the value n minus i zero +and as you go in time it decays + + align:start position:0% +and as you go in time it decays + + + align:start position:0% +and as you go in time it decays +uh well it the the decay rate is + + align:start position:0% +uh well it the the decay rate is + + + align:start position:0% +uh well it the the decay rate is +basically set by sort of the average + + align:start position:0% +basically set by sort of the average + + + align:start position:0% +basically set by sort of the average +beta + + align:start position:0% +beta + + + align:start position:0% +beta +uh so this is kind of like some kind of + + align:start position:0% +uh so this is kind of like some kind of + + + align:start position:0% +uh so this is kind of like some kind of +maybe if you're getting close to steady + + align:start position:0% +maybe if you're getting close to steady + + + align:start position:0% +maybe if you're getting close to steady +state then beta inverse is sort of what + + align:start position:0% +state then beta inverse is sort of what + + + align:start position:0% +state then beta inverse is sort of what +this time scale is + + align:start position:0% +this time scale is + + + align:start position:0% +this time scale is +but what's actually happening is you cut + + align:start position:0% +but what's actually happening is you cut + + + align:start position:0% +but what's actually happening is you cut +it off + + align:start position:0% +it off + + + align:start position:0% +it off +at a certain time tau so that's the time + + align:start position:0% +at a certain time tau so that's the time + + + align:start position:0% +at a certain time tau so that's the time +that you're in the room + + align:start position:0% +that you're in the room + + + align:start position:0% +that you're in the room +in that time the number of susceptible + + align:start position:0% +in that time the number of susceptible + + + align:start position:0% +in that time the number of susceptible +people has gone down + + align:start position:0% +people has gone down + + + align:start position:0% +people has gone down +and the number of + + align:start position:0% + + + + align:start position:0% + +exposed people goes up but then because + + align:start position:0% +exposed people goes up but then because + + + align:start position:0% +exposed people goes up but then because +the incubation rate is slow the exposed + + align:start position:0% +the incubation rate is slow the exposed + + + align:start position:0% +the incubation rate is slow the exposed +people + + align:start position:0% +people + + + align:start position:0% +people +never become infectious in this model so + + align:start position:0% +never become infectious in this model so + + + align:start position:0% +never become infectious in this model so +the number in factors + + align:start position:0% +the number in factors + + + align:start position:0% +the number in factors +is fixed and so + + align:start position:0% +is fixed and so + + + align:start position:0% +is fixed and so +um since we have slow in incubation and + + align:start position:0% +um since we have slow in incubation and + + + align:start position:0% +um since we have slow in incubation and +since the number and factor is fixed + + align:start position:0% +since the number and factor is fixed + + + align:start position:0% +since the number and factor is fixed +another way to look at this is notice + + align:start position:0% +another way to look at this is notice + + + align:start position:0% +another way to look at this is notice +this nonlinear equation which + + align:start position:0% +this nonlinear equation which + + + align:start position:0% +this nonlinear equation which +had s times i it became i zero times s + + align:start position:0% +had s times i it became i zero times s + + + align:start position:0% +had s times i it became i zero times s +so it became a linear response + + align:start position:0% +so it became a linear response + + + align:start position:0% +so it became a linear response +and so another way to think about this + + align:start position:0% +and so another way to think about this + + + align:start position:0% +and so another way to think about this +limit is this is the limit of linear + + align:start position:0% + + + + align:start position:0% + +linear response + + align:start position:0% + + + + align:start position:0% + +so the wells riley models are basically + + align:start position:0% +so the wells riley models are basically + + + align:start position:0% +so the wells riley models are basically +linear response + + align:start position:0% +linear response + + + align:start position:0% +linear response +models which are typically not taking + + align:start position:0% +models which are typically not taking + + + align:start position:0% +models which are typically not taking +into account + + align:start position:0% +into account + + + align:start position:0% +into account +a growth in the number of infectors + + align:start position:0% +a growth in the number of infectors + + + align:start position:0% +a growth in the number of infectors +which would lead to kind of an + + align:start position:0% +which would lead to kind of an + + + align:start position:0% +which would lead to kind of an +amplification of disease spreading in a + + align:start position:0% +amplification of disease spreading in a + + + align:start position:0% +amplification of disease spreading in a +room + + align:start position:0% +room + + + align:start position:0% +room +and that's often justified because the + + align:start position:0% +and that's often justified because the + + + align:start position:0% +and that's often justified because the +time someone spends in a room + + align:start position:0% +time someone spends in a room + + + align:start position:0% +time someone spends in a room +is often times a lot less than the + + align:start position:0% +is often times a lot less than the + + + align:start position:0% +is often times a lot less than the +incubation time which could be on the + + align:start position:0% +incubation time which could be on the + + + align:start position:0% +incubation time which could be on the +order of days + + align:start position:0% +order of days + + + align:start position:0% +order of days +people might only spend a few hours in + + align:start position:0% +people might only spend a few hours in + + + align:start position:0% +people might only spend a few hours in +the room on the other hand there are + + align:start position:0% +the room on the other hand there are + + + align:start position:0% +the room on the other hand there are +situations such as classrooms + + align:start position:0% +situations such as classrooms + + + align:start position:0% +situations such as classrooms +long-term care facilities and homes + + align:start position:0% +long-term care facilities and homes + + + align:start position:0% +long-term care facilities and homes +prisons + + align:start position:0% +prisons + + + align:start position:0% +prisons +workplaces where people are exposed to + + align:start position:0% +workplaces where people are exposed to + + + align:start position:0% +workplaces where people are exposed to +each other for days or weeks + + align:start position:0% +each other for days or weeks + + + align:start position:0% +each other for days or weeks +or months actually they may go home in + + align:start position:0% +or months actually they may go home in + + + align:start position:0% +or months actually they may go home in +between but there's a constant exposure + + align:start position:0% +between but there's a constant exposure + + + align:start position:0% +between but there's a constant exposure +and so uh you may need to worry about uh + + align:start position:0% +and so uh you may need to worry about uh + + + align:start position:0% +and so uh you may need to worry about uh +these + + align:start position:0% +these + + + align:start position:0% +these +other sorts of dynamics um even in an + + align:start position:0% +other sorts of dynamics um even in an + + + align:start position:0% +other sorts of dynamics um even in an +indoor setting actually so we'll come + + align:start position:0% +indoor setting actually so we'll come + + + align:start position:0% +indoor setting actually so we'll come +we'll come back to that + + align:start position:0% +we'll come back to that + + + align:start position:0% +we'll come back to that +now another important concept i'd like + + align:start position:0% +now another important concept i'd like + + + align:start position:0% +now another important concept i'd like +to get here is what is the early rate of + + align:start position:0% +to get here is what is the early rate of + + + align:start position:0% +to get here is what is the early rate of +infection + + align:start position:0% +infection + + + align:start position:0% +infection +uh so um you know this quantity here is + + align:start position:0% +uh so um you know this quantity here is + + + align:start position:0% +uh so um you know this quantity here is +q + + align:start position:0% +q + + + align:start position:0% +q +and then i wrote n minus 1 here that was + + align:start position:0% +and then i wrote n minus 1 here that was + + + align:start position:0% +and then i wrote n minus 1 here that was +the case actually more generally this + + align:start position:0% +the case actually more generally this + + + align:start position:0% +the case actually more generally this +should be n minus i zero because + + align:start position:0% +should be n minus i zero because + + + align:start position:0% +should be n minus i zero because +oftentimes we're thinking of one in + + align:start position:0% +oftentimes we're thinking of one in + + + align:start position:0% +oftentimes we're thinking of one in +factor so i kind of jump to that + + align:start position:0% +factor so i kind of jump to that + + + align:start position:0% +factor so i kind of jump to that +but more generally n minus i zero and + + align:start position:0% +but more generally n minus i zero and + + + align:start position:0% +but more generally n minus i zero and +this quantity here + + align:start position:0% +this quantity here + + + align:start position:0% +this quantity here +is also s zero that's the initial number + + align:start position:0% +is also s zero that's the initial number + + + align:start position:0% +is also s zero that's the initial number +of susceptible people okay so basically + + align:start position:0% +of susceptible people okay so basically + + + align:start position:0% +of susceptible people okay so basically +take the initial number susceptible + + align:start position:0% +take the initial number susceptible + + + align:start position:0% +take the initial number susceptible +and they slowly become exposed based on + + align:start position:0% +and they slowly become exposed based on + + + align:start position:0% +and they slowly become exposed based on +how many quanta + + align:start position:0% +how many quanta + + + align:start position:0% +how many quanta +you know they've consumed now + + align:start position:0% +you know they've consumed now + + + align:start position:0% +you know they've consumed now +the definition of quanta of infection + + align:start position:0% +the definition of quanta of infection + + + align:start position:0% +the definition of quanta of infection +often is tied to this equation this is + + align:start position:0% +often is tied to this equation this is + + + align:start position:0% +often is tied to this equation this is +essentially ills is the wells + + align:start position:0% +essentially ills is the wells + + + align:start position:0% +essentially ills is the wells +equation derived in 1955. + + align:start position:0% +equation derived in 1955. + + + align:start position:0% +equation derived in 1955. +and wells actually defined quanta from + + align:start position:0% +and wells actually defined quanta from + + + align:start position:0% +and wells actually defined quanta from +this he said + + align:start position:0% +this he said + + + align:start position:0% +this he said +that one quantum infection corresponds + + align:start position:0% +that one quantum infection corresponds + + + align:start position:0% +that one quantum infection corresponds +to a probability of transmission + + align:start position:0% +to a probability of transmission + + + align:start position:0% +to a probability of transmission +of 63 percent because + + align:start position:0% +of 63 percent because + + + align:start position:0% +of 63 percent because +one if you put q equals minus one + + align:start position:0% +one if you put q equals minus one + + + align:start position:0% +one if you put q equals minus one +one minus e to the minus one is 63 + + align:start position:0% +one minus e to the minus one is 63 + + + align:start position:0% +one minus e to the minus one is 63 +percent + + align:start position:0% +percent + + + align:start position:0% +percent +so basically he said a quantum so if + + align:start position:0% +so basically he said a quantum so if + + + align:start position:0% +so basically he said a quantum so if +someone asks you what is a quantum + + align:start position:0% +someone asks you what is a quantum + + + align:start position:0% +someone asks you what is a quantum +infection um a quantum + + align:start position:0% +infection um a quantum + + + align:start position:0% +infection um a quantum +is uh basically 63 chance + + align:start position:0% +is uh basically 63 chance + + + align:start position:0% +is uh basically 63 chance +of infection okay but the problem with + + align:start position:0% +of infection okay but the problem with + + + align:start position:0% +of infection okay but the problem with +that thinking though is that + + align:start position:0% +that thinking though is that + + + align:start position:0% +that thinking though is that +in some other situation where there's + + align:start position:0% +in some other situation where there's + + + align:start position:0% +in some other situation where there's +maybe incubation going on i might get + + align:start position:0% +maybe incubation going on i might get + + + align:start position:0% +maybe incubation going on i might get +more infected people so i can't just + + align:start position:0% +more infected people so i can't just + + + align:start position:0% +more infected people so i can't just +count the infected people in a room and + + align:start position:0% +count the infected people in a room and + + + align:start position:0% +count the infected people in a room and +assume that i'm getting a measure + + align:start position:0% +assume that i'm getting a measure + + + align:start position:0% +assume that i'm getting a measure +of infection quanta infection quanta + + align:start position:0% +of infection quanta infection quanta + + + align:start position:0% +of infection quanta infection quanta +actually are defined by beta + + align:start position:0% +actually are defined by beta + + + align:start position:0% +actually are defined by beta +that's an important thing so the effect + + align:start position:0% +that's an important thing so the effect + + + align:start position:0% +that's an important thing so the effect +so really what is beta it's actually the + + align:start position:0% +so really what is beta it's actually the + + + align:start position:0% +so really what is beta it's actually the +rate of infection quantum + + align:start position:0% +rate of infection quantum + + + align:start position:0% +rate of infection quantum +transfer from infectious to susceptible + + align:start position:0% +transfer from infectious to susceptible + + + align:start position:0% +transfer from infectious to susceptible +or + + align:start position:0% +or + + + align:start position:0% +or +sorry so it's s.i basically oh actually + + align:start position:0% +sorry so it's s.i basically oh actually + + + align:start position:0% +sorry so it's s.i basically oh actually +did i + + align:start position:0% +did i + + + align:start position:0% +did i +uh no that's correct yeah so it's it's + + align:start position:0% +uh no that's correct yeah so it's it's + + + align:start position:0% +uh no that's correct yeah so it's it's +it's the rate of basically becoming + + align:start position:0% +it's the rate of basically becoming + + + align:start position:0% +it's the rate of basically becoming +exposed excuse me so it's from + + align:start position:0% +exposed excuse me so it's from + + + align:start position:0% +exposed excuse me so it's from +susceptible to exposed so that rate is + + align:start position:0% +susceptible to exposed so that rate is + + + align:start position:0% +susceptible to exposed so that rate is +basically defines + + align:start position:0% +basically defines + + + align:start position:0% +basically defines +beta and that is giving you the rate of + + align:start position:0% +beta and that is giving you the rate of + + + align:start position:0% +beta and that is giving you the rate of +infection quantity transfer + + align:start position:0% +infection quantity transfer + + + align:start position:0% +infection quantity transfer +how many people actually get infected or + + align:start position:0% +how many people actually get infected or + + + align:start position:0% +how many people actually get infected or +exposed involve + + align:start position:0% +exposed involve + + + align:start position:0% +exposed involve +solving some set of equations like this + + align:start position:0% +solving some set of equations like this + + + align:start position:0% +solving some set of equations like this +which might not be the same as the wells + + align:start position:0% +which might not be the same as the wells + + + align:start position:0% +which might not be the same as the wells +riley model + + align:start position:0% +riley model + + + align:start position:0% +riley model +so that's an important thing to keep in + + align:start position:0% +so that's an important thing to keep in + + + align:start position:0% +so that's an important thing to keep in +mind and we'll come back to that so this + + align:start position:0% +mind and we'll come back to that so this + + + align:start position:0% +mind and we'll come back to that so this +is basically + + align:start position:0% + + + + align:start position:0% + +well's definition of a quantum + + align:start position:0% +well's definition of a quantum + + + align:start position:0% +well's definition of a quantum +is that basically there's a 63 chance + + align:start position:0% +is that basically there's a 63 chance + + + align:start position:0% +is that basically there's a 63 chance +that it's going to affect somebody but + + align:start position:0% +that it's going to affect somebody but + + + align:start position:0% +that it's going to affect somebody but +that's completely tied to this linear + + align:start position:0% +that's completely tied to this linear + + + align:start position:0% +that's completely tied to this linear +response exponential relaxation it's not + + align:start position:0% +response exponential relaxation it's not + + + align:start position:0% +response exponential relaxation it's not +really i don't think is the appropriate + + align:start position:0% +really i don't think is the appropriate + + + align:start position:0% +really i don't think is the appropriate +definition now another thing we can ask + + align:start position:0% +definition now another thing we can ask + + + align:start position:0% +definition now another thing we can ask +is + + align:start position:0% +is + + + align:start position:0% +is +what about at early times + + align:start position:0% + + + + align:start position:0% + +so and that would be the case where the + + align:start position:0% +so and that would be the case where the + + + align:start position:0% +so and that would be the case where the +expected number of quanta transferred + + align:start position:0% +expected number of quanta transferred + + + align:start position:0% +expected number of quanta transferred +is less than one so at early times you + + align:start position:0% +is less than one so at early times you + + + align:start position:0% +is less than one so at early times you +haven't really seen a lot of infection + + align:start position:0% +haven't really seen a lot of infection + + + align:start position:0% +haven't really seen a lot of infection +take place this will be very important + + align:start position:0% +take place this will be very important + + + align:start position:0% +take place this will be very important +for us + + align:start position:0% +for us + + + align:start position:0% +for us +because we're going to come to safety + + align:start position:0% +because we're going to come to safety + + + align:start position:0% +because we're going to come to safety +guidelines and in my opinion the right + + align:start position:0% +guidelines and in my opinion the right + + + align:start position:0% +guidelines and in my opinion the right +way to think about a safety guideline is + + align:start position:0% +way to think about a safety guideline is + + + align:start position:0% +way to think about a safety guideline is +you don't want + + align:start position:0% +you don't want + + + align:start position:0% +you don't want +one person to cause one or more + + align:start position:0% +one person to cause one or more + + + align:start position:0% +one person to cause one or more +infections you'd like + + align:start position:0% +infections you'd like + + + align:start position:0% +infections you'd like +the expectation to be that less than one + + align:start position:0% +the expectation to be that less than one + + + align:start position:0% +the expectation to be that less than one +person would get infected so this is + + align:start position:0% +person would get infected so this is + + + align:start position:0% +person would get infected so this is +this sort i'm calling early times here + + align:start position:0% +this sort i'm calling early times here + + + align:start position:0% +this sort i'm calling early times here +in the epidemiological model is actually + + align:start position:0% +in the epidemiological model is actually + + + align:start position:0% +in the epidemiological model is actually +very relevant for + + align:start position:0% +very relevant for + + + align:start position:0% +very relevant for +like a safety guideline because you + + align:start position:0% +like a safety guideline because you + + + align:start position:0% +like a safety guideline because you +don't want to deal with the case where + + align:start position:0% +don't want to deal with the case where + + + align:start position:0% +don't want to deal with the case where +this rampant infection you just want to + + align:start position:0% +this rampant infection you just want to + + + align:start position:0% +this rampant infection you just want to +say if an affected person comes in the + + align:start position:0% +say if an affected person comes in the + + + align:start position:0% +say if an affected person comes in the +room + + align:start position:0% +room + + + align:start position:0% +room +are they going to infect anybody else + + align:start position:0% +are they going to infect anybody else + + + align:start position:0% +are they going to infect anybody else +and you want that to be a low + + align:start position:0% +and you want that to be a low + + + align:start position:0% +and you want that to be a low +probability so we def + + align:start position:0% +probability so we def + + + align:start position:0% +probability so we def +this is a very relevant limit now if i + + align:start position:0% +this is a very relevant limit now if i + + + align:start position:0% +this is a very relevant limit now if i +take that limit here i can expand this + + align:start position:0% +take that limit here i can expand this + + + align:start position:0% +take that limit here i can expand this +exponential + + align:start position:0% +exponential + + + align:start position:0% +exponential +and i find that e of t at early times + + align:start position:0% +and i find that e of t at early times + + + align:start position:0% +and i find that e of t at early times +behaves like s 0 times q of t + + align:start position:0% +behaves like s 0 times q of t + + + align:start position:0% +behaves like s 0 times q of t +if s 0 is the number of susceptibles and + + align:start position:0% +if s 0 is the number of susceptibles and + + + align:start position:0% +if s 0 is the number of susceptibles and +more + + align:start position:0% +more + + + align:start position:0% +more +you know if i plug in what we have here + + align:start position:0% +you know if i plug in what we have here + + + align:start position:0% +you know if i plug in what we have here +that's n minus + + align:start position:0% +that's n minus + + + align:start position:0% +that's n minus +i zero times i zero times the integral + + align:start position:0% +i zero times i zero times the integral + + + align:start position:0% +i zero times i zero times the integral +in time of beta okay + + align:start position:0% +in time of beta okay + + + align:start position:0% +in time of beta okay +and so this is the expected number of + + align:start position:0% +and so this is the expected number of + + + align:start position:0% +and so this is the expected number of +people that will be infected + + align:start position:0% +people that will be infected + + + align:start position:0% +people that will be infected +by i zero infected people so the ratio + + align:start position:0% +by i zero infected people so the ratio + + + align:start position:0% +by i zero infected people so the ratio +of these two things is very important so + + align:start position:0% +of these two things is very important so + + + align:start position:0% +of these two things is very important so +if i look at e + + align:start position:0% +if i look at e + + + align:start position:0% +if i look at e +of of in time tau i should say we do + + align:start position:0% +of of in time tau i should say we do + + + align:start position:0% +of of in time tau i should say we do +this integral you know typically we want + + align:start position:0% +this integral you know typically we want + + + align:start position:0% +this integral you know typically we want +to go up to time + + align:start position:0% +to go up to time + + + align:start position:0% +to go up to time +tau which is the time that the person + + align:start position:0% +tau which is the time that the person + + + align:start position:0% +tau which is the time that the person +spends in the room and we divide by the + + align:start position:0% +spends in the room and we divide by the + + + align:start position:0% +spends in the room and we divide by the +initial number + + align:start position:0% +initial number + + + align:start position:0% +initial number +then that's basically telling us sort of + + align:start position:0% +then that's basically telling us sort of + + + align:start position:0% +then that's basically telling us sort of +what's the reproductive number of the + + align:start position:0% +what's the reproductive number of the + + + align:start position:0% +what's the reproductive number of the +room + + align:start position:0% +room + + + align:start position:0% +room +i zero people come in and the question + + align:start position:0% +i zero people come in and the question + + + align:start position:0% +i zero people come in and the question +is do more than i zero people come + + align:start position:0% +is do more than i zero people come + + + align:start position:0% +is do more than i zero people come +out that are infected so have you + + align:start position:0% +out that are infected so have you + + + align:start position:0% +out that are infected so have you +infected others okay so that's the ratio + + align:start position:0% +infected others okay so that's the ratio + + + align:start position:0% +infected others okay so that's the ratio +that you really care about + + align:start position:0% +that you really care about + + + align:start position:0% +that you really care about +and so i would call this the indoor + + align:start position:0% +and so i would call this the indoor + + + align:start position:0% +and so i would call this the indoor +reproductive number + + align:start position:0% +reproductive number + + + align:start position:0% +reproductive number +and in this case uh if there's um if we + + align:start position:0% +and in this case uh if there's um if we + + + align:start position:0% +and in this case uh if there's um if we +pick + + align:start position:0% +pick + + + align:start position:0% +pick +uh i zero equal to one then this is n + + align:start position:0% +uh i zero equal to one then this is n + + + align:start position:0% +uh i zero equal to one then this is n +minus one uh zero to tau + + align:start position:0% +minus one uh zero to tau + + + align:start position:0% +minus one uh zero to tau +uh beta dt + + align:start position:0% +uh beta dt + + + align:start position:0% +uh beta dt +so that's going to be an important thing + + align:start position:0% +so that's going to be an important thing + + + align:start position:0% +so that's going to be an important thing +which we'll come back to later which is + + align:start position:0% +which we'll come back to later which is + + + align:start position:0% +which we'll come back to later which is +the definition of kind of what makes a + + align:start position:0% +the definition of kind of what makes a + + + align:start position:0% +the definition of kind of what makes a +room actually + + align:start position:0% +room actually + + + align:start position:0% +room actually +safe well what we'd like to do is have + + align:start position:0% +safe well what we'd like to do is have + + + align:start position:0% +safe well what we'd like to do is have +this quantity + + align:start position:0% +this quantity + + + align:start position:0% +this quantity +be much less than one because i want to + + align:start position:0% +be much less than one because i want to + + + align:start position:0% +be much less than one because i want to +say if one in factor comes in the room + + align:start position:0% +say if one in factor comes in the room + + + align:start position:0% +say if one in factor comes in the room +and everybody is currently + + align:start position:0% +and everybody is currently + + + align:start position:0% +and everybody is currently +susceptible and healthy i want to make + + align:start position:0% +susceptible and healthy i want to make + + + align:start position:0% +susceptible and healthy i want to make +sure that + + align:start position:0% +sure that + + + align:start position:0% +sure that +less than one person actually gets + + align:start position:0% +less than one person actually gets + + + align:start position:0% +less than one person actually gets +infected and there'll be some tolerance + + align:start position:0% +infected and there'll be some tolerance + + + align:start position:0% +infected and there'll be some tolerance +maybe on how low i'd like that to be + + align:start position:0% +maybe on how low i'd like that to be + + + align:start position:0% +maybe on how low i'd like that to be +but that's a very important concept and + + align:start position:0% +but that's a very important concept and + + + align:start position:0% +but that's a very important concept and +here you see it comes out of the slow + + align:start position:0% +here you see it comes out of the slow + + + align:start position:0% +here you see it comes out of the slow +incubation limit + + align:start position:0% +incubation limit + + + align:start position:0% +incubation limit +what i'd like to show you next is that + + align:start position:0% +what i'd like to show you next is that + + + align:start position:0% +what i'd like to show you next is that +the very same + + align:start position:0% +the very same + + + align:start position:0% +the very same +indoor reproductive number actually + + align:start position:0% +indoor reproductive number actually + + + align:start position:0% +indoor reproductive number actually +occurs for any model + + align:start position:0% +occurs for any model + + + align:start position:0% +occurs for any model +including the opposite limit of fast + + align:start position:0% + + + + align:start position:0% + +incubation \ No newline at end of file diff --git a/j1c43B6ar3k.txt b/j1c43B6ar3k.txt new file mode 100644 index 0000000000000000000000000000000000000000..2c2134c0880f0b52ab6d235a41c97a3190797f1b --- /dev/null +++ b/j1c43B6ar3k.txt @@ -0,0 +1,1875 @@ +align:start position:0% + +in this video we'll look at an + + align:start position:0% +in this video we'll look at an + + + align:start position:0% +in this video we'll look at an +application of the probabilistic method + + align:start position:0% +application of the probabilistic method + + + align:start position:0% +application of the probabilistic method +to graph + + align:start position:0% +to graph + + + align:start position:0% +to graph +Theory an independent set in a graph is + + align:start position:0% +Theory an independent set in a graph is + + + align:start position:0% +Theory an independent set in a graph is +a subset of vertices with no two + + align:start position:0% +a subset of vertices with no two + + + align:start position:0% +a subset of vertices with no two +adjacent for example if the graph is + + align:start position:0% +adjacent for example if the graph is + + + align:start position:0% +adjacent for example if the graph is +this cycle on four vertices + + align:start position:0% +this cycle on four vertices + + + align:start position:0% +this cycle on four vertices +an example of an independent set would + + align:start position:0% +an example of an independent set would + + + align:start position:0% +an example of an independent set would +be two vertices like this and these two + + align:start position:0% +be two vertices like this and these two + + + align:start position:0% +be two vertices like this and these two +vertices do not uh none these two + + align:start position:0% +vertices do not uh none these two + + + align:start position:0% +vertices do not uh none these two +vertices are not adjacent to each + + align:start position:0% +vertices are not adjacent to each + + + align:start position:0% +vertices are not adjacent to each +other whereas had I chosen two vertices + + align:start position:0% +other whereas had I chosen two vertices + + + align:start position:0% +other whereas had I chosen two vertices +on the same Edge that would not be an + + align:start position:0% +on the same Edge that would not be an + + + align:start position:0% +on the same Edge that would not be an +independent + + align:start position:0% +independent + + + align:start position:0% +independent +set so important question in many in + + align:start position:0% +set so important question in many in + + + align:start position:0% +set so important question in many in +graph theory is given the graph what can + + align:start position:0% +graph theory is given the graph what can + + + align:start position:0% +graph theory is given the graph what can +you say about the size of its + + align:start position:0% +you say about the size of its + + + align:start position:0% +you say about the size of its +independent sets + + align:start position:0% +independent sets + + + align:start position:0% +independent sets +the following theorem due to Kon way + + align:start position:0% +the following theorem due to Kon way + + + align:start position:0% +the following theorem due to Kon way +says that every graph G contains a large + + align:start position:0% +says that every graph G contains a large + + + align:start position:0% +says that every graph G contains a large +independent set in the following sense + + align:start position:0% +independent set in the following sense + + + align:start position:0% +independent set in the following sense +contains an independent set of size at + + align:start position:0% +contains an independent set of size at + + + align:start position:0% +contains an independent set of size at +least the following quantity summing + + align:start position:0% +least the following quantity summing + + + align:start position:0% +least the following quantity summing +over o v among vertices in + + align:start position:0% +over o v among vertices in + + + align:start position:0% +over o v among vertices in +G one over the degree of V + + + align:start position:0% +G one over the degree of V + + + + align:start position:0% +G one over the degree of V + +one + + align:start position:0% +one + + + align:start position:0% +one +okay so this let let us prove this + + align:start position:0% +okay so this let let us prove this + + + align:start position:0% +okay so this let let us prove this +theorem first and then we'll see an + + align:start position:0% +theorem first and then we'll see an + + + align:start position:0% +theorem first and then we'll see an +application and some ways to interpret + + align:start position:0% +application and some ways to interpret + + + align:start position:0% +application and some ways to interpret +this + + align:start position:0% +this + + + align:start position:0% +this +result the proof of this theorem applies + + align:start position:0% +result the proof of this theorem applies + + + align:start position:0% +result the proof of this theorem applies +the probabilistic + + align:start position:0% +the probabilistic + + + align:start position:0% +the probabilistic +method okay so we are given this graph + + align:start position:0% +method okay so we are given this graph + + + align:start position:0% +method okay so we are given this graph +G and the first thing we'll do is + + align:start position:0% +G and the first thing we'll do is + + + align:start position:0% +G and the first thing we'll do is +order the vertices of + + align:start position:0% + + + + align:start position:0% + +g uniformly at random + + align:start position:0% + + + + align:start position:0% + +so consider a random permutation of the + + align:start position:0% +so consider a random permutation of the + + + align:start position:0% +so consider a random permutation of the +vertices of + + align:start position:0% +vertices of + + + align:start position:0% +vertices of +G and + + align:start position:0% +G and + + + align:start position:0% +G and +let's consider the set I of + + align:start position:0% +let's consider the set I of + + + align:start position:0% +let's consider the set I of +vertices def find as + + align:start position:0% +vertices def find as + + + align:start position:0% +vertices def find as +follows these are the vertices in G such + + align:start position:0% +follows these are the vertices in G such + + + align:start position:0% +follows these are the vertices in G such +that V + + align:start position:0% + + + + align:start position:0% + +appears before + + align:start position:0% + + + + align:start position:0% + +all its + + align:start position:0% + + + + align:start position:0% + +neighbors + + align:start position:0% +neighbors + + + align:start position:0% +neighbors +in the random + + align:start position:0% + + + + align:start position:0% + +ordering okay for example from the graph + + align:start position:0% +ordering okay for example from the graph + + + align:start position:0% +ordering okay for example from the graph +earlier had we ordered the + + align:start position:0% + + + + align:start position:0% + +vertices in this order so that's say + + align:start position:0% +vertices in this order so that's say + + + align:start position:0% +vertices in this order so that's say +some random ordering so let's order the + + align:start position:0% +some random ordering so let's order the + + + align:start position:0% +some random ordering so let's order the +vertices is 1 2 3 and four okay so the + + align:start position:0% +vertices is 1 2 3 and four okay so the + + + align:start position:0% +vertices is 1 2 3 and four okay so the +edges are 1 to 2 2 to + + align:start position:0% +edges are 1 to 2 2 to + + + align:start position:0% +edges are 1 to 2 2 to +4 3 to 4 and 1 to + + align:start position:0% +4 3 to 4 and 1 to + + + align:start position:0% +4 3 to 4 and 1 to +three what I would pick out is a set of + + align:start position:0% +three what I would pick out is a set of + + + align:start position:0% +three what I would pick out is a set of +vertices such + + align:start position:0% +vertices such + + + align:start position:0% +vertices such +that okay okay so let's see if each + + align:start position:0% +that okay okay so let's see if each + + + align:start position:0% +that okay okay so let's see if each +vertex would belong to I the first + + align:start position:0% +vertex would belong to I the first + + + align:start position:0% +vertex would belong to I the first +vertex appears before all of its + + align:start position:0% +vertex appears before all of its + + + align:start position:0% +vertex appears before all of its +neighbors so we put the first vertex in + + align:start position:0% +neighbors so we put the first vertex in + + + align:start position:0% +neighbors so we put the first vertex in +I the second ver vertex does not appear + + align:start position:0% +I the second ver vertex does not appear + + + align:start position:0% +I the second ver vertex does not appear +before one of its neighbors one so we do + + align:start position:0% +before one of its neighbors one so we do + + + align:start position:0% +before one of its neighbors one so we do +not put it in I and the third vertex + + align:start position:0% +not put it in I and the third vertex + + + align:start position:0% +not put it in I and the third vertex +here also does not appear before its + + align:start position:0% +here also does not appear before its + + + align:start position:0% +here also does not appear before its +neighbor and we don't put it in I and + + align:start position:0% +neighbor and we don't put it in I and + + + align:start position:0% +neighbor and we don't put it in I and +the fourth vertex likewise does not + + align:start position:0% +the fourth vertex likewise does not + + + align:start position:0% +the fourth vertex likewise does not +appear before all of its neighbors and + + align:start position:0% +appear before all of its neighbors and + + + align:start position:0% +appear before all of its neighbors and +we do not put it in is well so in this + + align:start position:0% +we do not put it in is well so in this + + + align:start position:0% +we do not put it in is well so in this +case this set picks up only the first + + align:start position:0% +case this set picks up only the first + + + align:start position:0% +case this set picks up only the first +vertex but in more complicated graphs it + + align:start position:0% +vertex but in more complicated graphs it + + + align:start position:0% +vertex but in more complicated graphs it +can pick up additional vertices + + align:start position:0% + + + + align:start position:0% + +I claim + + align:start position:0% + + + + align:start position:0% + +that I is + + align:start position:0% + + + + align:start position:0% + +always an independent + + align:start position:0% + + + + align:start position:0% + +set indeed it will be impossible to have + + align:start position:0% +set indeed it will be impossible to have + + + align:start position:0% +set indeed it will be impossible to have +two vertices in I that are adjacent to + + align:start position:0% +two vertices in I that are adjacent to + + + align:start position:0% +two vertices in I that are adjacent to +each other because one of them would + + align:start position:0% +each other because one of them would + + + align:start position:0% +each other because one of them would +appear before the other in the order and + + align:start position:0% +appear before the other in the order and + + + align:start position:0% +appear before the other in the order and +that would violate the condition on how + + align:start position:0% +that would violate the condition on how + + + align:start position:0% +that would violate the condition on how +we chose + + align:start position:0% + + + + align:start position:0% + +I next let's think about how large I is + + align:start position:0% +I next let's think about how large I is + + + align:start position:0% +I next let's think about how large I is +for + + align:start position:0% + + + + align:start position:0% + +every vertex V in + + align:start position:0% +every vertex V in + + + align:start position:0% +every vertex V in +G the + + align:start position:0% +G the + + + align:start position:0% +G the +probability that + + align:start position:0% +probability that + + + align:start position:0% +probability that +V is in I well this is the probability + + align:start position:0% +V is in I well this is the probability + + + align:start position:0% +V is in I well this is the probability +that b appears + + align:start position:0% + + + + align:start position:0% + +first + + align:start position:0% +first + + + align:start position:0% +first +among V and its + + align:start position:0% + + + + align:start position:0% + +neighbors well V has D subv the degree + + align:start position:0% +neighbors well V has D subv the degree + + + align:start position:0% +neighbors well V has D subv the degree +of V neighbors and all the ordering are + + align:start position:0% +of V neighbors and all the ordering are + + + align:start position:0% +of V neighbors and all the ordering are +chosen uniformly at random so this + + align:start position:0% +chosen uniformly at random so this + + + align:start position:0% +chosen uniformly at random so this +probability is 1 / the degree of v+ + + align:start position:0% +probability is 1 / the degree of v+ + + + align:start position:0% +probability is 1 / the degree of v+ +1 and thus by theine ity of expectations + + align:start position:0% +1 and thus by theine ity of expectations + + + align:start position:0% +1 and thus by theine ity of expectations +the expected size + + align:start position:0% +the expected size + + + align:start position:0% +the expected size +of this set I is equal to the sum + + align:start position:0% +of this set I is equal to the sum + + + align:start position:0% +of this set I is equal to the sum +over vertices V in + + align:start position:0% +over vertices V in + + + align:start position:0% +over vertices V in +G of the probability that this V Lies in + + align:start position:0% +G of the probability that this V Lies in + + + align:start position:0% +G of the probability that this V Lies in +I and we just computed this + + align:start position:0% + + + + align:start position:0% + +probability as + + align:start position:0% + + + + align:start position:0% + +such this is the expectation that's what + + align:start position:0% +such this is the expectation that's what + + + align:start position:0% +such this is the expectation that's what +happens on average + + align:start position:0% +happens on average + + + align:start position:0% +happens on average +therefore there must be some + + align:start position:0% +therefore there must be some + + + align:start position:0% +therefore there must be some +ordering that + + align:start position:0% +ordering that + + + align:start position:0% +ordering that +induces an I so there is some + + align:start position:0% +induces an I so there is some + + + align:start position:0% +induces an I so there is some +I with the size of I at + + align:start position:0% +I with the size of I at + + + align:start position:0% +I with the size of I at +least the quantity that we + + align:start position:0% +least the quantity that we + + + align:start position:0% +least the quantity that we +just + + align:start position:0% + + + + align:start position:0% + +produced okay so that finishes the proof + + align:start position:0% +produced okay so that finishes the proof + + + align:start position:0% +produced okay so that finishes the proof +of + + align:start position:0% + + + + align:start position:0% + +the Carol way + + align:start position:0% +the Carol way + + + align:start position:0% +the Carol way +theorem again it says the one the way + + align:start position:0% +theorem again it says the one the way + + + align:start position:0% +theorem again it says the one the way +they think about this theorem is that if + + align:start position:0% +they think about this theorem is that if + + + align:start position:0% +they think about this theorem is that if +you are given a graph G such that + + align:start position:0% +you are given a graph G such that + + + align:start position:0% +you are given a graph G such that +typically one does not have large + + align:start position:0% +typically one does not have large + + + align:start position:0% +typically one does not have large +degrees then it must contain a lot of + + align:start position:0% +degrees then it must contain a lot of + + + align:start position:0% +degrees then it must contain a lot of +inde a large independent + + align:start position:0% + + + + align:start position:0% + +set by considering the complement of + + align:start position:0% +set by considering the complement of + + + align:start position:0% +set by considering the complement of +this graph G + + align:start position:0% + + + + align:start position:0% + +by + + align:start position:0% + + + + align:start position:0% + +considering the graph complement the + + align:start position:0% +considering the graph complement the + + + align:start position:0% +considering the graph complement the +graph complement means that + + align:start position:0% +graph complement means that + + + align:start position:0% +graph complement means that +we switch flip the edge and non edges + + align:start position:0% +we switch flip the edge and non edges + + + align:start position:0% +we switch flip the edge and non edges +right so so this is a graph G and then + + align:start position:0% +right so so this is a graph G and then + + + align:start position:0% +right so so this is a graph G and then +this will be the complement of G so flip + + align:start position:0% +this will be the complement of G so flip + + + align:start position:0% +this will be the complement of G so flip +the edges and non-edges in + + align:start position:0% +the edges and non-edges in + + + align:start position:0% +the edges and non-edges in +G independent sets + + align:start position:0% +G independent sets + + + align:start position:0% +G independent sets +in G become + + align:start position:0% +in G become + + + align:start position:0% +in G become +Clicks in the complement the clicks are + + align:start position:0% +Clicks in the complement the clicks are + + + align:start position:0% +Clicks in the complement the clicks are +complete graphs with all the edges + + align:start position:0% +complete graphs with all the edges + + + align:start position:0% +complete graphs with all the edges +present okay and vice + + align:start position:0% +present okay and vice + + + align:start position:0% +present okay and vice +versa so we can read carway theorem for + + align:start position:0% +versa so we can read carway theorem for + + + align:start position:0% +versa so we can read carway theorem for +the complement of G to deduce the + + align:start position:0% +the complement of G to deduce the + + + align:start position:0% +the complement of G to deduce the +following + + align:start position:0% + + + + align:start position:0% + +corollary says that every + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +vertex graph G + + align:start position:0% + + + + align:start position:0% + +contains a + + align:start position:0% + + + + align:start position:0% + +click of + + align:start position:0% +click of + + + align:start position:0% +click of +on at + + align:start position:0% + + + + align:start position:0% + +least this many vertices + + align:start position:0% + + + + align:start position:0% + +okay so the expression inside the + + align:start position:0% +okay so the expression inside the + + + align:start position:0% +okay so the expression inside the +summation is the click of uh is the + + align:start position:0% +summation is the click of uh is the + + + align:start position:0% +summation is the click of uh is the +complement the degree in the + + align:start position:0% + + + + align:start position:0% + +complement + + align:start position:0% +complement + + + align:start position:0% +complement +okay let us derive a interesting + + align:start position:0% +okay let us derive a interesting + + + align:start position:0% +okay let us derive a interesting +corollary of uh of the scary and this + + align:start position:0% +corollary of uh of the scary and this + + + align:start position:0% +corollary of uh of the scary and this +turns out to be a pretty foundational + + align:start position:0% +turns out to be a pretty foundational + + + align:start position:0% +turns out to be a pretty foundational +result in graph Theory known as teron + + align:start position:0% + + + + align:start position:0% + +theorem ton themm says the + + align:start position:0% + + + + align:start position:0% + +following + + align:start position:0% +following + + + align:start position:0% +following +if an nver + + align:start position:0% + + + + align:start position:0% + +graph + + align:start position:0% + + + + align:start position:0% + +has more than the following number 1 + + align:start position:0% +has more than the following number 1 + + + align:start position:0% +has more than the following number 1 +minus 1/ r n^ 2 / 2 so it has more than + + align:start position:0% +minus 1/ r n^ 2 / 2 so it has more than + + + align:start position:0% +minus 1/ r n^ 2 / 2 so it has more than +this many + + align:start position:0% + + + + align:start position:0% + +edges + + align:start position:0% + + + + align:start position:0% + +then the + + align:start position:0% +then the + + + align:start position:0% +then the +graph + + align:start position:0% +graph + + + align:start position:0% +graph +contains a + + align:start position:0% + + + + align:start position:0% + +click + + align:start position:0% +click + + + align:start position:0% +click +on more than R + + align:start position:0% + + + + align:start position:0% + +vertices so tons theorem gives us some + + align:start position:0% +vertices so tons theorem gives us some + + + align:start position:0% +vertices so tons theorem gives us some +bound on + + align:start position:0% +bound on + + + align:start position:0% +bound on +the maximum number of edges that a graph + + align:start position:0% +the maximum number of edges that a graph + + + align:start position:0% +the maximum number of edges that a graph +can have if it doesn't have a large + + align:start position:0% + + + + align:start position:0% + +click and furthermore this bound here is + + align:start position:0% +click and furthermore this bound here is + + + align:start position:0% +click and furthermore this bound here is +best is best possible in the following + + align:start position:0% + + + + align:start position:0% + +sense and here let us restrict to the + + align:start position:0% +sense and here let us restrict to the + + + align:start position:0% +sense and here let us restrict to the +case when n is divisible by R when n's + + align:start position:0% +case when n is divisible by R when n's + + + align:start position:0% +case when n is divisible by R when n's +not divisible by R you need to do uh a + + align:start position:0% +not divisible by R you need to do uh a + + + align:start position:0% +not divisible by R you need to do uh a +similar construction turns out to be + + align:start position:0% +similar construction turns out to be + + + align:start position:0% +similar construction turns out to be +best possible and this bound is uh can + + align:start position:0% +best possible and this bound is uh can + + + align:start position:0% +best possible and this bound is uh can +be improved slightly but not by too + + align:start position:0% +be improved slightly but not by too + + + align:start position:0% +be improved slightly but not by too +much so here's the here's the example + + align:start position:0% +much so here's the here's the example + + + align:start position:0% +much so here's the here's the example +let us take the N vertices and split + + align:start position:0% +let us take the N vertices and split + + + align:start position:0% +let us take the N vertices and split +them + + align:start position:0% +them + + + align:start position:0% +them +into equal + + align:start position:0% + + + + align:start position:0% + +parts and there R parts so here in this + + align:start position:0% +parts and there R parts so here in this + + + align:start position:0% +parts and there R parts so here in this +illustration r equal to + + align:start position:0% + + + + align:start position:0% + +three and let's putting all the edges + + align:start position:0% +three and let's putting all the edges + + + align:start position:0% +three and let's putting all the edges +between + + align:start position:0% +between + + + align:start position:0% +between +Parts but no Edge within the part so + + align:start position:0% +Parts but no Edge within the part so + + + align:start position:0% +Parts but no Edge within the part so +this is called the + + align:start position:0% + + + + align:start position:0% + +complete R partite + + align:start position:0% + + + + align:start position:0% + +graph so you see that this graph here + + align:start position:0% +graph so you see that this graph here + + + align:start position:0% +graph so you see that this graph here +one can do a quick calculation to see + + align:start position:0% +one can do a quick calculation to see + + + align:start position:0% +one can do a quick calculation to see +that it has exactly this number 1 - 1 / + + align:start position:0% +that it has exactly this number 1 - 1 / + + + align:start position:0% +that it has exactly this number 1 - 1 / +R * n^ s over two + + align:start position:0% +R * n^ s over two + + + align:start position:0% +R * n^ s over two +edges on the other hand it does not + + align:start position:0% +edges on the other hand it does not + + + align:start position:0% +edges on the other hand it does not +contain a click on more than R vertices + + align:start position:0% +contain a click on more than R vertices + + + align:start position:0% +contain a click on more than R vertices +the biggest click you have comes from + + align:start position:0% +the biggest click you have comes from + + + align:start position:0% +the biggest click you have comes from +taking one vertex in each + + align:start position:0% +taking one vertex in each + + + align:start position:0% +taking one vertex in each +part so this is an example showing that + + align:start position:0% +part so this is an example showing that + + + align:start position:0% +part so this is an example showing that +the statement of Turon theorem is best + + align:start position:0% +the statement of Turon theorem is best + + + align:start position:0% +the statement of Turon theorem is best +possible let us prove Ton's theorem as a + + align:start position:0% +possible let us prove Ton's theorem as a + + + align:start position:0% +possible let us prove Ton's theorem as a +quick corollary of the earlier + + align:start position:0% +quick corollary of the earlier + + + align:start position:0% +quick corollary of the earlier +result so by the earlier + + align:start position:0% + + + + align:start position:0% + +corollary + + align:start position:0% +corollary + + + align:start position:0% +corollary +G has a + + align:start position:0% + + + + align:start position:0% + +click of size at least the sum over the + + align:start position:0% +click of size at least the sum over the + + + align:start position:0% +click of size at least the sum over the +vertices in + + align:start position:0% +vertices in + + + align:start position:0% +vertices in +G one over n minus the degree of v and + + align:start position:0% +G one over n minus the degree of v and + + + align:start position:0% +G one over n minus the degree of v and +here let us use the + + align:start position:0% + + + + align:start position:0% + +convexity so in this step let us use the + + align:start position:0% +convexity so in this step let us use the + + + align:start position:0% +convexity so in this step let us use the +convexity of the function sending X to 1 + + align:start position:0% +convexity of the function sending X to 1 + + + align:start position:0% +convexity of the function sending X to 1 +/ n minus X so this is a convex function + + align:start position:0% +/ n minus X so this is a convex function + + + align:start position:0% +/ n minus X so this is a convex function +which allows us to lower bound the sum + + align:start position:0% +which allows us to lower bound the sum + + + align:start position:0% +which allows us to lower bound the sum +by n Over N minus the average + + align:start position:0% +by n Over N minus the average + + + align:start position:0% +by n Over N minus the average +degree of + + align:start position:0% + + + + align:start position:0% + +G on the other hand if the graph has + + align:start position:0% +G on the other hand if the graph has + + + align:start position:0% +G on the other hand if the graph has +more than this many edges then the + + align:start position:0% +more than this many edges then the + + + align:start position:0% +more than this many edges then the +average degree is bigger than some + + align:start position:0% +average degree is bigger than some + + + align:start position:0% +average degree is bigger than some +corresponding quantity and putting this + + align:start position:0% +corresponding quantity and putting this + + + align:start position:0% +corresponding quantity and putting this +into the expression we can strict have a + + align:start position:0% +into the expression we can strict have a + + + align:start position:0% +into the expression we can strict have a +final expression is strictly bigger than + + align:start position:0% +final expression is strictly bigger than + + + align:start position:0% +final expression is strictly bigger than +n Over N - 1 - 1 / R * n and this + + align:start position:0% +n Over N - 1 - 1 / R * n and this + + + align:start position:0% +n Over N - 1 - 1 / R * n and this +quantity here equals to + + align:start position:0% +quantity here equals to + + + align:start position:0% +quantity here equals to +R okay so there's a strict equality sign + + align:start position:0% +R okay so there's a strict equality sign + + + align:start position:0% +R okay so there's a strict equality sign +here in particular G has a click of size + + align:start position:0% +here in particular G has a click of size + + + align:start position:0% +here in particular G has a click of size +strictly greater than R and that + + align:start position:0% +strictly greater than R and that + + + align:start position:0% +strictly greater than R and that +finishes the proof of Ton's + + align:start position:0% + + + + align:start position:0% + +theorem tons theorem is a important + + align:start position:0% +theorem tons theorem is a important + + + align:start position:0% +theorem tons theorem is a important +foundational result in graph Theory and + + align:start position:0% +foundational result in graph Theory and + + + align:start position:0% +foundational result in graph Theory and +it's a start of a subject that we now + + align:start position:0% +it's a start of a subject that we now + + + align:start position:0% +it's a start of a subject that we now +call extremal graph Theory + + align:start position:0% +call extremal graph Theory + + + align:start position:0% +call extremal graph Theory +concerning what can you say about a + + align:start position:0% +concerning what can you say about a + + + align:start position:0% +concerning what can you say about a +graph that has certain properties like + + align:start position:0% +graph that has certain properties like + + + align:start position:0% +graph that has certain properties like +not having a large click and this Pro + + align:start position:0% +not having a large click and this Pro + + + align:start position:0% +not having a large click and this Pro +that we just saw is a beautiful + + align:start position:0% +that we just saw is a beautiful + + + align:start position:0% +that we just saw is a beautiful +illustration of the probabilistic method + + align:start position:0% +illustration of the probabilistic method + + + align:start position:0% +illustration of the probabilistic method +two graph theory that allows us to prove + + align:start position:0% +two graph theory that allows us to prove + + + align:start position:0% +two graph theory that allows us to prove +this wonderful result tons theorem along + + align:start position:0% +this wonderful result tons theorem along + + + align:start position:0% +this wonderful result tons theorem along +with many other results that I hope that + + align:start position:0% +with many other results that I hope that + + + align:start position:0% +with many other results that I hope that +you'll learn in the future \ No newline at end of file diff --git a/juTnY6Wad84.txt b/juTnY6Wad84.txt new file mode 100644 index 0000000000000000000000000000000000000000..105d38a69d8dcb37fbaf1b6d5bc817adde89b09b --- /dev/null +++ b/juTnY6Wad84.txt @@ -0,0 +1,3242 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu so today I just like to + + align:start position:0% +ocw.mit.edu so today I just like to + + + align:start position:0% +ocw.mit.edu so today I just like to +cover in fair amount of detail how to + + align:start position:0% +cover in fair amount of detail how to + + + align:start position:0% +cover in fair amount of detail how to +how gather data and then analyze it for + + align:start position:0% +how gather data and then analyze it for + + + align:start position:0% +how gather data and then analyze it for +the elastic modulus experiment that + + align:start position:0% +the elastic modulus experiment that + + + align:start position:0% +the elastic modulus experiment that +we'll do and this parallels a pretty + + align:start position:0% +we'll do and this parallels a pretty + + + align:start position:0% +we'll do and this parallels a pretty +standard measurement that's done with + + align:start position:0% +standard measurement that's done with + + + align:start position:0% +standard measurement that's done with +standard AFM so what I'll do is kind of + + align:start position:0% +standard AFM so what I'll do is kind of + + + align:start position:0% +standard AFM so what I'll do is kind of +describe the two sides of it standard + + align:start position:0% +describe the two sides of it standard + + + align:start position:0% +describe the two sides of it standard +AFM and hours um and hopefully that'll + + align:start position:0% +AFM and hours um and hopefully that'll + + + align:start position:0% +AFM and hours um and hopefully that'll +make a little bit clear how our Force + + align:start position:0% +make a little bit clear how our Force + + + align:start position:0% +make a little bit clear how our Force +curves differ um and what what kind of + + align:start position:0% +curves differ um and what what kind of + + + align:start position:0% +curves differ um and what what kind of +information you're looking to get so + + align:start position:0% +information you're looking to get so + + + align:start position:0% +information you're looking to get so +uh those of you who used standard AFM + + align:start position:0% +uh those of you who used standard AFM + + + align:start position:0% +uh those of you who used standard AFM +know that a typical Force curve looks + + align:start position:0% +know that a typical Force curve looks + + + align:start position:0% +know that a typical Force curve looks +like + + align:start position:0% +like + + + align:start position:0% +like +this and I'll do the uh approach and + + align:start position:0% +this and I'll do the uh approach and + + + align:start position:0% +this and I'll do the uh approach and +retract sections in different + + align:start position:0% + + + + align:start position:0% + +colors and there may be also a small + + align:start position:0% +colors and there may be also a small + + + align:start position:0% +colors and there may be also a small +jump to contact + + align:start position:0% + + + + align:start position:0% + +here okay so that + + align:start position:0% +here okay so that + + + align:start position:0% +here okay so that +represents the approach out of contact + + align:start position:0% +represents the approach out of contact + + + align:start position:0% +represents the approach out of contact +and then the linear displacement of the + + align:start position:0% +and then the linear displacement of the + + + align:start position:0% +and then the linear displacement of the +can lever and this is the uh uh photo + + align:start position:0% +can lever and this is the uh uh photo + + + align:start position:0% +can lever and this is the uh uh photo +diode positional photo diode that will + + align:start position:0% +diode positional photo diode that will + + + align:start position:0% +diode positional photo diode that will +detect this the reflected spot okay so + + align:start position:0% +detect this the reflected spot okay so + + + align:start position:0% +detect this the reflected spot okay so +Standard Optical lever + + align:start position:0% +Standard Optical lever + + + align:start position:0% +Standard Optical lever +setup and uh if you look at what happens + + align:start position:0% +setup and uh if you look at what happens + + + align:start position:0% +setup and uh if you look at what happens +with substrates of different hardness + + align:start position:0% +with substrates of different hardness + + + align:start position:0% +with substrates of different hardness +you will just + + align:start position:0% +you will just + + + align:start position:0% +you will just +see the slope of this + + align:start position:0% + + + + align:start position:0% + +line so this is uh the readout will be + + align:start position:0% +line so this is uh the readout will be + + + align:start position:0% +line so this is uh the readout will be +in volts but + + align:start position:0% +in volts but + + + align:start position:0% +in volts but +typically this this axis is converted to + + align:start position:0% +typically this this axis is converted to + + + align:start position:0% +typically this this axis is converted to +Z which is pzo + + align:start position:0% +Z which is pzo + + + align:start position:0% +Z which is pzo +deflection or pzo + + align:start position:0% +deflection or pzo + + + align:start position:0% +deflection or pzo +motion and most software will do this + + align:start position:0% +motion and most software will do this + + + align:start position:0% +motion and most software will do this +automatically for you um but there's a + + align:start position:0% +automatically for you um but there's a + + + align:start position:0% +automatically for you um but there's a +there's a calibration going on there so + + align:start position:0% +there's a calibration going on there so + + + align:start position:0% +there's a calibration going on there so +you have to relate the pizo motion to + + align:start position:0% +you have to relate the pizo motion to + + + align:start position:0% +you have to relate the pizo motion to +whatever the voltage of the uh is being + + align:start position:0% +whatever the voltage of the uh is being + + + align:start position:0% +whatever the voltage of the uh is being +applied to the pzo or somehow being read + + align:start position:0% +applied to the pzo or somehow being read + + + align:start position:0% +applied to the pzo or somehow being read +into the AFM so the relationship between + + align:start position:0% +into the AFM so the relationship between + + + align:start position:0% +into the AFM so the relationship between +P motion to displacement of the of the + + align:start position:0% +P motion to displacement of the of the + + + align:start position:0% +P motion to displacement of the of the +spot on the photo diode + + align:start position:0% +spot on the photo diode + + + align:start position:0% +spot on the photo diode +it then gives you a conversion factor + + align:start position:0% +it then gives you a conversion factor + + + align:start position:0% +it then gives you a conversion factor +for basically nanometers per volt of + + align:start position:0% +for basically nanometers per volt of + + + align:start position:0% +for basically nanometers per volt of +displacement okay and that slope for + + align:start position:0% +displacement okay and that slope for + + + align:start position:0% +displacement okay and that slope for +different uh for different materials + + align:start position:0% +different uh for different materials + + + align:start position:0% +different uh for different materials +you'll see a different slope typically + + align:start position:0% +you'll see a different slope typically + + + align:start position:0% +you'll see a different slope typically +if you have a softer material uh the + + align:start position:0% +if you have a softer material uh the + + + align:start position:0% +if you have a softer material uh the +slope will get + + align:start position:0% +slope will get + + + align:start position:0% +slope will get +smaller something like this from the + + align:start position:0% +smaller something like this from the + + + align:start position:0% +smaller something like this from the +contact point I'm being a little bit + + align:start position:0% +contact point I'm being a little bit + + + align:start position:0% +contact point I'm being a little bit +quick about my drawing but the idea is + + align:start position:0% +quick about my drawing but the idea is + + + align:start position:0% +quick about my drawing but the idea is +simply that a material that's compliant + + align:start position:0% +simply that a material that's compliant + + + align:start position:0% +simply that a material that's compliant +that you're going to be indenting with + + align:start position:0% +that you're going to be indenting with + + + align:start position:0% +that you're going to be indenting with +the probe + + align:start position:0% +the probe + + + align:start position:0% +the probe +will uh as the stage moves it'll deflect + + align:start position:0% +will uh as the stage moves it'll deflect + + + align:start position:0% +will uh as the stage moves it'll deflect +the can lever less than it would if the + + align:start position:0% +the can lever less than it would if the + + + align:start position:0% +the can lever less than it would if the +material were hard so the difference + + align:start position:0% +material were hard so the difference + + + align:start position:0% +material were hard so the difference +between + + align:start position:0% +between + + + align:start position:0% +between +um the difference between the motion of + + align:start position:0% +um the difference between the motion of + + + align:start position:0% +um the difference between the motion of +the stage and uh the indentation of the + + align:start position:0% +the stage and uh the indentation of the + + + align:start position:0% +the stage and uh the indentation of the +can lever will give you the the actual + + align:start position:0% +can lever will give you the the actual + + + align:start position:0% +can lever will give you the the actual +distance through which the material has + + align:start position:0% +distance through which the material has + + + align:start position:0% +distance through which the material has +been indented okay does that make sense + + align:start position:0% +been indented okay does that make sense + + + align:start position:0% +been indented okay does that make sense +so let me say that again our first curve + + align:start position:0% +so let me say that again our first curve + + + align:start position:0% +so let me say that again our first curve +assuming we do this first first curve on + + align:start position:0% +assuming we do this first first curve on + + + align:start position:0% +assuming we do this first first curve on +a hard material is sort of a direct + + align:start position:0% +a hard material is sort of a direct + + + align:start position:0% +a hard material is sort of a direct +measure of the the mo movement of the + + align:start position:0% +measure of the the mo movement of the + + + align:start position:0% +measure of the the mo movement of the +stage okay if uh if we have an + + align:start position:0% +stage okay if uh if we have an + + + align:start position:0% +stage okay if uh if we have an +independent way of measuring the stage + + align:start position:0% +independent way of measuring the stage + + + align:start position:0% +independent way of measuring the stage +motion which again in a standard AFM + + align:start position:0% +motion which again in a standard AFM + + + align:start position:0% +motion which again in a standard AFM +typically you do you have a you have a + + align:start position:0% +typically you do you have a you have a + + + align:start position:0% +typically you do you have a you have a +pzo that is well calibrated and you have + + align:start position:0% +pzo that is well calibrated and you have + + + align:start position:0% +pzo that is well calibrated and you have +an independent measurement of stage + + align:start position:0% +an independent measurement of stage + + + align:start position:0% +an independent measurement of stage +motion then that's your kind of + + align:start position:0% +motion then that's your kind of + + + align:start position:0% +motion then that's your kind of +calibration factor for how much you're + + align:start position:0% +calibration factor for how much you're + + + align:start position:0% +calibration factor for how much you're +moving this uh sorry that's your + + align:start position:0% +moving this uh sorry that's your + + + align:start position:0% +moving this uh sorry that's your +calibration standard for how much you're + + align:start position:0% +calibration standard for how much you're + + + align:start position:0% +calibration standard for how much you're +moving the stage and then the cever + + align:start position:0% +moving the stage and then the cever + + + align:start position:0% +moving the stage and then the cever +deflection is a separate signal that + + align:start position:0% +deflection is a separate signal that + + + align:start position:0% +deflection is a separate signal that +you're comparing okay in our case you'll + + align:start position:0% +you're comparing okay in our case you'll + + + align:start position:0% +you're comparing okay in our case you'll +see that there's a subtle difference + + align:start position:0% +see that there's a subtle difference + + + align:start position:0% +see that there's a subtle difference +which is why I'm trying to emphasize + + align:start position:0% +which is why I'm trying to emphasize + + + align:start position:0% +which is why I'm trying to emphasize +this point okay and + + align:start position:0% +this point okay and + + + align:start position:0% +this point okay and +so uh in a very simple experiment what + + align:start position:0% +so uh in a very simple experiment what + + + align:start position:0% +so uh in a very simple experiment what +we just want to do is find out the + + align:start position:0% +we just want to do is find out the + + + align:start position:0% +we just want to do is find out the +amount by which the substrate is being + + align:start position:0% +amount by which the substrate is being + + + align:start position:0% +amount by which the substrate is being +indented by the AFM probe tip and that + + align:start position:0% +indented by the AFM probe tip and that + + + align:start position:0% +indented by the AFM probe tip and that +is simply the difference between how + + align:start position:0% +is simply the difference between how + + + align:start position:0% +is simply the difference between how +much the stage has moved and how much + + align:start position:0% +much the stage has moved and how much + + + align:start position:0% +much the stage has moved and how much +the can lever has + + align:start position:0% +the can lever has + + + align:start position:0% +the can lever has +bent distance uh the + + align:start position:0% +bent distance uh the + + + align:start position:0% +bent distance uh the +distance between those two okay so if we + + align:start position:0% +distance between those two okay so if we + + + align:start position:0% +distance between those two okay so if we +draw now the force + + align:start position:0% +draw now the force + + + align:start position:0% +draw now the force +curve that our AFM generates I'm just + + align:start position:0% +curve that our AFM generates I'm just + + + align:start position:0% +curve that our AFM generates I'm just +going to use the same color so red is + + align:start position:0% +going to use the same color so red is + + + align:start position:0% +going to use the same color so red is +going to be the approach we'll have some + + align:start position:0% +going to be the approach we'll have some + + + align:start position:0% +going to be the approach we'll have some +out of contact Section and I'm going to + + align:start position:0% +out of contact Section and I'm going to + + + align:start position:0% +out of contact Section and I'm going to +assume our bias is set as we like it to + + align:start position:0% +assume our bias is set as we like it to + + + align:start position:0% +assume our bias is set as we like it to +the middle of the uh of the S squared so + + align:start position:0% +the middle of the uh of the S squared so + + + align:start position:0% +the middle of the uh of the S squared so +we're going to start following the + + align:start position:0% +we're going to start following the + + + align:start position:0% +we're going to start following the +sinusoid + + align:start position:0% +sinusoid + + + align:start position:0% +sinusoid +okay and then as we retract we've seen + + align:start position:0% +okay and then as we retract we've seen + + + align:start position:0% +okay and then as we retract we've seen +that there's often times some sticking + + align:start position:0% +that there's often times some sticking + + + align:start position:0% +that there's often times some sticking +so we'll follow this curve back out + + align:start position:0% +so we'll follow this curve back out + + + align:start position:0% +so we'll follow this curve back out +again there's sometimes a little bit of + + align:start position:0% +again there's sometimes a little bit of + + + align:start position:0% +again there's sometimes a little bit of +hysteresis anyway we'll get back to + + align:start position:0% +hysteresis anyway we'll get back to + + + align:start position:0% +hysteresis anyway we'll get back to +somewhere and then we'll come back like + + align:start position:0% +somewhere and then we'll come back like + + + align:start position:0% +somewhere and then we'll come back like +this okay so if we + + align:start position:0% +this okay so if we + + + align:start position:0% +this okay so if we +now if we think carefully about this + + align:start position:0% +now if we think carefully about this + + + align:start position:0% +now if we think carefully about this +point of contact the equivalent to + + align:start position:0% +point of contact the equivalent to + + + align:start position:0% +point of contact the equivalent to +having a smaller slope on this uh in + + align:start position:0% +having a smaller slope on this uh in + + + align:start position:0% +having a smaller slope on this uh in +this situation the equivalent is to + + align:start position:0% +this situation the equivalent is to + + + align:start position:0% +this situation the equivalent is to +stretch out this sign squared to make + + align:start position:0% +stretch out this sign squared to make + + + align:start position:0% +stretch out this sign squared to make +the period of it longer and that + + align:start position:0% +the period of it longer and that + + + align:start position:0% +the period of it longer and that +actually if you look at just this + + align:start position:0% +actually if you look at just this + + + align:start position:0% +actually if you look at just this +contact point a smaller slope it will be + + align:start position:0% +contact point a smaller slope it will be + + + align:start position:0% +contact point a smaller slope it will be +exactly what you'll see so this Curve + + align:start position:0% +exactly what you'll see so this Curve + + + align:start position:0% +exactly what you'll see so this Curve +will start with a smaller slope and then + + align:start position:0% +will start with a smaller slope and then + + + align:start position:0% +will start with a smaller slope and then +it'll just have a much slower period + + align:start position:0% +it'll just have a much slower period + + + align:start position:0% +it'll just have a much slower period +okay so again comparing to this + + align:start position:0% +okay so again comparing to this + + + align:start position:0% +okay so again comparing to this +situation what we're going to be looking + + align:start position:0% +situation what we're going to be looking + + + align:start position:0% +situation what we're going to be looking +for is the difference between the stage + + align:start position:0% +for is the difference between the stage + + + align:start position:0% +for is the difference between the stage +movement and the amount that the C bends + + align:start position:0% +movement and the amount that the C bends + + + align:start position:0% +movement and the amount that the C bends +in order to determine how far we've + + align:start position:0% +in order to determine how far we've + + + align:start position:0% +in order to determine how far we've +indented our sample and that that + + align:start position:0% +indented our sample and that that + + + align:start position:0% +indented our sample and that that +distance will be what we'll use to + + align:start position:0% +distance will be what we'll use to + + + align:start position:0% +distance will be what we'll use to +calculate the elastic modulus of it and + + align:start position:0% +calculate the elastic modulus of it and + + + align:start position:0% +calculate the elastic modulus of it and +then and again there's a there's a + + align:start position:0% +then and again there's a there's a + + + align:start position:0% +then and again there's a there's a +subtle difference between these + + align:start position:0% +subtle difference between these + + + align:start position:0% +subtle difference between these +calculations because it's a little bit + + align:start position:0% +calculations because it's a little bit + + + align:start position:0% +calculations because it's a little bit +harder to interpret the numerical data + + align:start position:0% +harder to interpret the numerical data + + + align:start position:0% +harder to interpret the numerical data +out of this curve since it's nonlinear + + align:start position:0% +out of this curve since it's nonlinear + + + align:start position:0% +out of this curve since it's nonlinear +compared to this curve so the easiest + + align:start position:0% +compared to this curve so the easiest + + + align:start position:0% +compared to this curve so the easiest +way to do this experiment is to keep the + + align:start position:0% +way to do this experiment is to keep the + + + align:start position:0% +way to do this experiment is to keep the +bias the same between your + + align:start position:0% +bias the same between your + + + align:start position:0% +bias the same between your +measurements and to try to measure to a + + align:start position:0% +measurements and to try to measure to a + + + align:start position:0% +measurements and to try to measure to a +known point on the curve okay now we + + align:start position:0% +known point on the curve okay now we + + + align:start position:0% +known point on the curve okay now we +know uh we know the following we know + + align:start position:0% +know uh we know the following we know + + + align:start position:0% +know uh we know the following we know +that if we use a hard sample + + align:start position:0% +that if we use a hard sample + + + align:start position:0% +that if we use a hard sample +uh well no sample is infinitely hard um + + align:start position:0% +uh well no sample is infinitely hard um + + + align:start position:0% +uh well no sample is infinitely hard um +if we use a sample that is relatively + + align:start position:0% +if we use a sample that is relatively + + + align:start position:0% +if we use a sample that is relatively +hard compared to what the samples of + + align:start position:0% +hard compared to what the samples of + + + align:start position:0% +hard compared to what the samples of +interest that we're trying to measure + + align:start position:0% +interest that we're trying to measure + + + align:start position:0% +interest that we're trying to measure +which in this we're we're going to use + + align:start position:0% +which in this we're we're going to use + + + align:start position:0% +which in this we're we're going to use +silicon nitride um that is has the same + + align:start position:0% +silicon nitride um that is has the same + + + align:start position:0% +silicon nitride um that is has the same +hardness as our Canever material and + + align:start position:0% +hardness as our Canever material and + + + align:start position:0% +hardness as our Canever material and +it's going to indent very little + + align:start position:0% +it's going to indent very little + + + align:start position:0% +it's going to indent very little +compared to the polymer samples we're + + align:start position:0% +compared to the polymer samples we're + + + align:start position:0% +compared to the polymer samples we're +going to measure later so we'll we'll + + align:start position:0% +going to measure later so we'll we'll + + + align:start position:0% +going to measure later so we'll we'll +assume that that sample is ideally hard + + align:start position:0% +assume that that sample is ideally hard + + + align:start position:0% +assume that that sample is ideally hard +and does not indent at all and that'll + + align:start position:0% +and does not indent at all and that'll + + + align:start position:0% +and does not indent at all and that'll +provide us with that reference which we + + align:start position:0% +provide us with that reference which we + + + align:start position:0% +provide us with that reference which we +talked about here the the uh the stage + + align:start position:0% +talked about here the the uh the stage + + + align:start position:0% +talked about here the the uh the stage +motion okay so we want to be able to + + align:start position:0% +motion okay so we want to be able to + + + align:start position:0% +motion okay so we want to be able to +determine what + + align:start position:0% +determine what + + + align:start position:0% +determine what +uh what measurement along this axis of + + align:start position:0% +uh what measurement along this axis of + + + align:start position:0% +uh what measurement along this axis of +our + + align:start position:0% +our + + + align:start position:0% +our +output uh relates to certain nanometers + + align:start position:0% +output uh relates to certain nanometers + + + align:start position:0% +output uh relates to certain nanometers +of displacement of the stage okay so + + align:start position:0% +of displacement of the stage okay so + + + align:start position:0% +of displacement of the stage okay so +that first measurement on the hard + + align:start position:0% +that first measurement on the hard + + + align:start position:0% +that first measurement on the hard +sample will give us that and then once + + align:start position:0% +sample will give us that and then once + + + align:start position:0% +sample will give us that and then once +and then when we switch to measuring the + + align:start position:0% +and then when we switch to measuring the + + + align:start position:0% +and then when we switch to measuring the +software samples we can + + align:start position:0% +software samples we can + + + align:start position:0% +software samples we can +still use that same + + align:start position:0% +still use that same + + + align:start position:0% +still use that same +uh stage motion as a reference value and + + align:start position:0% +uh stage motion as a reference value and + + + align:start position:0% +uh stage motion as a reference value and +then we're simply measuring the can + + align:start position:0% +then we're simply measuring the can + + + align:start position:0% +then we're simply measuring the can +lever deflection right so in this again + + align:start position:0% +lever deflection right so in this again + + + align:start position:0% +lever deflection right so in this again +the difference is in this system we have + + align:start position:0% +the difference is in this system we have + + + align:start position:0% +the difference is in this system we have +only one thing that we can measure we + + align:start position:0% +only one thing that we can measure we + + + align:start position:0% +only one thing that we can measure we +don't have a calibrated pzo we don't + + align:start position:0% +don't have a calibrated pzo we don't + + + align:start position:0% +don't have a calibrated pzo we don't +have a reference to which we can say + + align:start position:0% +have a reference to which we can say + + + align:start position:0% +have a reference to which we can say +okay we know the stage is moving exactly + + align:start position:0% +okay we know the stage is moving exactly + + + align:start position:0% +okay we know the stage is moving exactly +this far but since we've done that once + + align:start position:0% +this far but since we've done that once + + + align:start position:0% +this far but since we've done that once +on the hard sample we can assume that + + align:start position:0% +on the hard sample we can assume that + + + align:start position:0% +on the hard sample we can assume that +that holds true throughout the other + + align:start position:0% +that holds true throughout the other + + + align:start position:0% +that holds true throughout the other +measurements and when we make the other + + align:start position:0% +measurements and when we make the other + + + align:start position:0% +measurements and when we make the other +measurements we can then measure the can + + align:start position:0% +measurements we can then measure the can + + + align:start position:0% +measurements we can then measure the can +lever deflection for the softer samples + + align:start position:0% +lever deflection for the softer samples + + + align:start position:0% +lever deflection for the softer samples +and compare that to the previous value + + align:start position:0% +and compare that to the previous value + + + align:start position:0% +and compare that to the previous value +and subtract it to get the + + align:start position:0% + + + + align:start position:0% + +indentation + + align:start position:0% +indentation + + + align:start position:0% +indentation +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so in order + + align:start position:0% +so in order + + + align:start position:0% +so in order +to uh in order to measure this in a + + align:start position:0% +to uh in order to measure this in a + + + align:start position:0% +to uh in order to measure this in a +known way the the the part about this + + align:start position:0% +known way the the the part about this + + + align:start position:0% +known way the the the part about this +calibration curve that we know we've + + align:start position:0% +calibration curve that we know we've + + + align:start position:0% +calibration curve that we know we've +discussed already a number of times is + + align:start position:0% +discussed already a number of times is + + + align:start position:0% +discussed already a number of times is +that this distance from Peak to + + align:start position:0% +that this distance from Peak to + + + align:start position:0% +that this distance from Peak to +trough + + align:start position:0% +trough + + + align:start position:0% +trough +okay that represents + + align:start position:0% +okay that represents + + + align:start position:0% +okay that represents +again when you're using the hard sample + + align:start position:0% +again when you're using the hard sample + + + align:start position:0% +again when you're using the hard sample +so I'm only talking about the case where + + align:start position:0% +so I'm only talking about the case where + + + align:start position:0% +so I'm only talking about the case where +the sample does not indent at all this + + align:start position:0% +the sample does not indent at all this + + + align:start position:0% +the sample does not indent at all this +represents a stage motion of 160 + + align:start position:0% +represents a stage motion of 160 + + + align:start position:0% +represents a stage motion of 160 +approximately 160 + + align:start position:0% +approximately 160 + + + align:start position:0% +approximately 160 +nanm uh which is a quarter of the laser + + align:start position:0% +nanm uh which is a quarter of the laser + + + align:start position:0% +nanm uh which is a quarter of the laser +wavelength and that's again remember + + align:start position:0% +wavelength and that's again remember + + + align:start position:0% +wavelength and that's again remember +this is only true at the fingers you + + align:start position:0% +this is only true at the fingers you + + + align:start position:0% +this is only true at the fingers you +have to make a correction for the tip + + align:start position:0% +have to make a correction for the tip + + + align:start position:0% +have to make a correction for the tip +location so once we know that this and + + align:start position:0% +location so once we know that this and + + + align:start position:0% +location so once we know that this and +then this is going to equal some number + + align:start position:0% +then this is going to equal some number + + + align:start position:0% +then this is going to equal some number +of volts so say this is two volts okay + + align:start position:0% +of volts so say this is two volts okay + + + align:start position:0% +of volts so say this is two volts okay +so now you have a calibration factor to + + align:start position:0% +so now you have a calibration factor to + + + align:start position:0% +so now you have a calibration factor to +convert the volts you see on the xaxis + + align:start position:0% +convert the volts you see on the xaxis + + + align:start position:0% +convert the volts you see on the xaxis +to nanometers of + + align:start position:0% +to nanometers of + + + align:start position:0% +to nanometers of +motion note that not always is it's not + + align:start position:0% +motion note that not always is it's not + + + align:start position:0% +motion note that not always is it's not +always going to be possible to measure + + align:start position:0% +always going to be possible to measure + + + align:start position:0% +always going to be possible to measure +it precisely by a peak in a trough so + + align:start position:0% +it precisely by a peak in a trough so + + + align:start position:0% +it precisely by a peak in a trough so +you can make + + align:start position:0% +you can make + + + align:start position:0% +you can make +other equal size seg take other equal + + align:start position:0% +other equal size seg take other equal + + + align:start position:0% +other equal size seg take other equal +size segments of the sin squar curve + + align:start position:0% +size segments of the sin squar curve + + + align:start position:0% +size segments of the sin squar curve +such as from midpoint to midpoint and + + align:start position:0% +such as from midpoint to midpoint and + + + align:start position:0% +such as from midpoint to midpoint and +you'll see that in reality when the S + + align:start position:0% +you'll see that in reality when the S + + + align:start position:0% +you'll see that in reality when the S +Square amplitudes varies because of the + + align:start position:0% +Square amplitudes varies because of the + + + align:start position:0% +Square amplitudes varies because of the +non idealities of the grading so you + + align:start position:0% +non idealities of the grading so you + + + align:start position:0% +non idealities of the grading so you +might you might be + + align:start position:0% +might you might be + + + align:start position:0% +might you might be +going one the first Fringe might be this + + align:start position:0% +going one the first Fringe might be this + + + align:start position:0% +going one the first Fringe might be this +High and the second Fringe might only be + + align:start position:0% +High and the second Fringe might only be + + + align:start position:0% +High and the second Fringe might only be +that high and so then it becomes a + + align:start position:0% +that high and so then it becomes a + + + align:start position:0% +that high and so then it becomes a +little bit harder so the key is to try + + align:start position:0% +little bit harder so the key is to try + + + align:start position:0% +little bit harder so the key is to try +to choose points where you know what + + align:start position:0% +to choose points where you know what + + + align:start position:0% +to choose points where you know what +that displacement value is peak and + + align:start position:0% +that displacement value is peak and + + + align:start position:0% +that displacement value is peak and +trough are really good but not always + + align:start position:0% +trough are really good but not always + + + align:start position:0% +trough are really good but not always +possible and especially if you're um if + + align:start position:0% +possible and especially if you're um if + + + align:start position:0% +possible and especially if you're um if +you're biased to the + + align:start position:0% +you're biased to the + + + align:start position:0% +you're biased to the +middle the next midpoint is actually a + + align:start position:0% +middle the next midpoint is actually a + + + align:start position:0% +middle the next midpoint is actually a +really good place and often times if you + + align:start position:0% +really good place and often times if you + + + align:start position:0% +really good place and often times if you +get the very nice clean curve for that + + align:start position:0% +get the very nice clean curve for that + + + align:start position:0% +get the very nice clean curve for that +first half wavelength or so okay + + align:start position:0% +first half wavelength or so okay + + + align:start position:0% +first half wavelength or so okay +um so I'm just draw this sort of as a + + align:start position:0% + + + + align:start position:0% + +closeup and you have um you have a + + align:start position:0% +closeup and you have um you have a + + + align:start position:0% +closeup and you have um you have a +picture of this in your lab manual again + + align:start position:0% +picture of this in your lab manual again + + + align:start position:0% +picture of this in your lab manual again +but I'm going to just go over it a + + align:start position:0% +but I'm going to just go over it a + + + align:start position:0% +but I'm going to just go over it a +little more + + align:start position:0% +little more + + + align:start position:0% +little more +carefully so I'm just drawing the first + + align:start position:0% + + + + align:start position:0% + +Fringe for a few different + + align:start position:0% + + + + align:start position:0% + +samples okay + + align:start position:0% + + + + align:start position:0% + +so the easiest calculation to make is + + align:start position:0% +so the easiest calculation to make is + + + align:start position:0% +so the easiest calculation to make is +basically to find the difference + + align:start position:0% +basically to find the difference + + + align:start position:0% +basically to find the difference +between this + + align:start position:0% +between this + + + align:start position:0% +between this +spacing sorry wrong + + align:start position:0% +spacing sorry wrong + + + align:start position:0% +spacing sorry wrong +color actually + + align:start position:0% + + + + align:start position:0% + +okay so as I mentioned before the purple + + align:start position:0% +okay so as I mentioned before the purple + + + align:start position:0% +okay so as I mentioned before the purple +curve is your reference the hard surface + + align:start position:0% +curve is your reference the hard surface + + + align:start position:0% +curve is your reference the hard surface +that represents the stage motion and + + align:start position:0% +that represents the stage motion and + + + align:start position:0% +that represents the stage motion and +then the red curve so now you'll see + + align:start position:0% +then the red curve so now you'll see + + + align:start position:0% +then the red curve so now you'll see +that you've had to make a larger stage + + align:start position:0% +that you've had to make a larger stage + + + align:start position:0% +that you've had to make a larger stage +motion to achieve the same can lever + + align:start position:0% +motion to achieve the same can lever + + + align:start position:0% +motion to achieve the same can lever +deflection okay + + align:start position:0% +deflection okay + + + align:start position:0% +deflection okay +so here we have to move the stage a + + align:start position:0% +so here we have to move the stage a + + + align:start position:0% +so here we have to move the stage a +certain amount and we've bent our can + + align:start position:0% +certain amount and we've bent our can + + + align:start position:0% +certain amount and we've bent our can +lever through 1/2 of its full cycle and + + align:start position:0% +lever through 1/2 of its full cycle and + + + align:start position:0% +lever through 1/2 of its full cycle and +here we have to move the stage this much + + align:start position:0% +here we have to move the stage this much + + + align:start position:0% +here we have to move the stage this much +further in order to bend the can lever + + align:start position:0% +further in order to bend the can lever + + + align:start position:0% +further in order to bend the can lever +to the same degree so that is that is + + align:start position:0% +to the same degree so that is that is + + + align:start position:0% +to the same degree so that is that is +the difference that we're looking for + + align:start position:0% +the difference that we're looking for + + + align:start position:0% +the difference that we're looking for +that's the indentation of the sample and + + align:start position:0% +that's the indentation of the sample and + + + align:start position:0% +that's the indentation of the sample and +the other uh numerical parameter you'll + + align:start position:0% +the other uh numerical parameter you'll + + + align:start position:0% +the other uh numerical parameter you'll +have to calculate is what is the force + + align:start position:0% +have to calculate is what is the force + + + align:start position:0% +have to calculate is what is the force +that you're applying with the can lever + + align:start position:0% +that you're applying with the can lever + + + align:start position:0% +that you're applying with the can lever +at that point and so again that that + + align:start position:0% +at that point and so again that that + + + align:start position:0% +at that point and so again that that +uh Lambda over 4 becomes the key key + + align:start position:0% +uh Lambda over 4 becomes the key key + + + align:start position:0% +uh Lambda over 4 becomes the key key +metric there because now you know that + + align:start position:0% +metric there because now you know that + + + align:start position:0% +metric there because now you know that +uh you've bent the can lever through a + + align:start position:0% +uh you've bent the can lever through a + + + align:start position:0% +uh you've bent the can lever through a +known known distance and if you know the + + align:start position:0% +known known distance and if you know the + + + align:start position:0% +known known distance and if you know the +spring constant you know the + + align:start position:0% +spring constant you know the + + + align:start position:0% +spring constant you know the +force so that I think is enough + + align:start position:0% +force so that I think is enough + + + align:start position:0% +force so that I think is enough +belaboring now we should get to actually + + align:start position:0% + + + + align:start position:0% + +measuring uh so now I'll I'll just talk + + align:start position:0% +measuring uh so now I'll I'll just talk + + + align:start position:0% +measuring uh so now I'll I'll just talk +about the Canever geometry correction + + align:start position:0% +about the Canever geometry correction + + + align:start position:0% +about the Canever geometry correction +factor that uh uh that plays into the + + align:start position:0% +factor that uh uh that plays into the + + + align:start position:0% +factor that uh uh that plays into the +numerical calculation of how much the + + align:start position:0% +numerical calculation of how much the + + + align:start position:0% +numerical calculation of how much the +can lever actually bends so uh whenever + + align:start position:0% +can lever actually bends so uh whenever + + + align:start position:0% +can lever actually bends so uh whenever +we talk about can lever bending we're + + align:start position:0% +we talk about can lever bending we're + + + align:start position:0% +we talk about can lever bending we're +always interested in what's going on at + + align:start position:0% +always interested in what's going on at + + + align:start position:0% +always interested in what's going on at +the tip um and in all of our can levers + + align:start position:0% +the tip um and in all of our can levers + + + align:start position:0% +the tip um and in all of our can levers +the in digitated fingers are located + + align:start position:0% +the in digitated fingers are located + + + align:start position:0% +the in digitated fingers are located +some distance + + align:start position:0% +some distance + + + align:start position:0% +some distance +away uh usually about halfway back + + align:start position:0% +away uh usually about halfway back + + + align:start position:0% +away uh usually about halfway back +towards the root of the can lever and so + + align:start position:0% +towards the root of the can lever and so + + + align:start position:0% +towards the root of the can lever and so +this is a little diagram of how the can + + align:start position:0% +this is a little diagram of how the can + + + align:start position:0% +this is a little diagram of how the can +lever is actually bending away from its + + align:start position:0% +lever is actually bending away from its + + + align:start position:0% +lever is actually bending away from its +equilibrium straight position and what + + align:start position:0% +equilibrium straight position and what + + + align:start position:0% +equilibrium straight position and what +you can see is that there's there's this + + align:start position:0% +you can see is that there's there's this + + + align:start position:0% +you can see is that there's there's this +is obviously exaggerated but there's a a + + align:start position:0% +is obviously exaggerated but there's a a + + + align:start position:0% +is obviously exaggerated but there's a a +certain curve to the can lever and the + + align:start position:0% +certain curve to the can lever and the + + + align:start position:0% +certain curve to the can lever and the +distance here that you + + align:start position:0% +distance here that you + + + align:start position:0% +distance here that you +see so this is this is the nominal + + align:start position:0% +see so this is this is the nominal + + + align:start position:0% +see so this is this is the nominal +deflection that you measure with the + + align:start position:0% +deflection that you measure with the + + + align:start position:0% +deflection that you measure with the +interdigitated grading right here okay + + align:start position:0% +interdigitated grading right here okay + + + align:start position:0% +interdigitated grading right here okay +this is uh we're going to call this Cai + + align:start position:0% +this is uh we're going to call this Cai + + + align:start position:0% +this is uh we're going to call this Cai +I think is the variable that's used for + + align:start position:0% +I think is the variable that's used for + + + align:start position:0% +I think is the variable that's used for +it in + + align:start position:0% +it in + + + align:start position:0% +it in +the in the lab manual + + align:start position:0% +the in the lab manual + + + align:start position:0% +the in the lab manual +um and that distance is different than + + align:start position:0% +um and that distance is different than + + + align:start position:0% +um and that distance is different than +the actual distance that the tip is + + align:start position:0% +the actual distance that the tip is + + + align:start position:0% +the actual distance that the tip is +moving so we we need a correction factor + + align:start position:0% +moving so we we need a correction factor + + + align:start position:0% +moving so we we need a correction factor +that accounts for this and says okay if + + align:start position:0% +that accounts for this and says okay if + + + align:start position:0% +that accounts for this and says okay if +we have a certain deflection here what's + + align:start position:0% +we have a certain deflection here what's + + + align:start position:0% +we have a certain deflection here what's +what's going to be the case here and for + + align:start position:0% +what's going to be the case here and for + + + align:start position:0% +what's going to be the case here and for +that there's there's two kind of one + + align:start position:0% +that there's there's two kind of one + + + align:start position:0% +that there's there's two kind of one +easy way and one slightly less easy way + + align:start position:0% +easy way and one slightly less easy way + + + align:start position:0% +easy way and one slightly less easy way +to do it um obviously the can lever does + + align:start position:0% +to do it um obviously the can lever does + + + align:start position:0% +to do it um obviously the can lever does +not stay a straight beam if you if it if + + align:start position:0% +not stay a straight beam if you if it if + + + align:start position:0% +not stay a straight beam if you if it if +it did you would just use a linear + + align:start position:0% +it did you would just use a linear + + + align:start position:0% +it did you would just use a linear +equation to fit it the actual true bent + + align:start position:0% +equation to fit it the actual true bent + + + align:start position:0% +equation to fit it the actual true bent +shape of the can lever is best + + align:start position:0% +shape of the can lever is best + + + align:start position:0% +shape of the can lever is best +represented by a third order equation + + align:start position:0% +represented by a third order equation + + + align:start position:0% +represented by a third order equation +and and it's described in your lab + + align:start position:0% +and and it's described in your lab + + + align:start position:0% +and and it's described in your lab +manual I'll show you the quadratic case + + align:start position:0% +manual I'll show you the quadratic case + + + align:start position:0% +manual I'll show you the quadratic case +cuz that's an easy way to um estimate it + + align:start position:0% +cuz that's an easy way to um estimate it + + + align:start position:0% +cuz that's an easy way to um estimate it +just kind of back of the envelope + + align:start position:0% +just kind of back of the envelope + + + align:start position:0% +just kind of back of the envelope +without having to get an exact number + + align:start position:0% +without having to get an exact number + + + align:start position:0% +without having to get an exact number +essentially + + align:start position:0% +essentially + + + align:start position:0% +essentially +um if you assume that the can lever + + align:start position:0% +um if you assume that the can lever + + + align:start position:0% +um if you assume that the can lever +assumes a quadratic shape then whatever + + align:start position:0% +assumes a quadratic shape then whatever + + + align:start position:0% +assumes a quadratic shape then whatever +distance you have here the ratio of this + + align:start position:0% +distance you have here the ratio of this + + + align:start position:0% +distance you have here the ratio of this +length to to this length um believe it's + + align:start position:0% +length to to this length um believe it's + + + align:start position:0% +length to to this length um believe it's +m in your lab manual let me just check + + align:start position:0% +m in your lab manual let me just check + + + align:start position:0% +m in your lab manual let me just check +what variables we + + align:start position:0% + + + + align:start position:0% + +use yeah + + align:start position:0% +use yeah + + + align:start position:0% +use yeah +so M + + align:start position:0% +so M + + + align:start position:0% +so M +ID is defined as the total + + align:start position:0% + + + + align:start position:0% + +length sorry the ID distance to the + + align:start position:0% +length sorry the ID distance to the + + + align:start position:0% +length sorry the ID distance to the +total length which is this is L + + align:start position:0% +total length which is this is L + + + align:start position:0% +total length which is this is L +ID here + + align:start position:0% +ID here + + + align:start position:0% +ID here +and LT is the total length of the can + + align:start position:0% +and LT is the total length of the can + + + align:start position:0% +and LT is the total length of the can +lver + + align:start position:0% + + + + align:start position:0% + +okay and you'll notice that this + + align:start position:0% +okay and you'll notice that this + + + align:start position:0% +okay and you'll notice that this +variable is a little bit uh poorly + + align:start position:0% +variable is a little bit uh poorly + + + align:start position:0% +variable is a little bit uh poorly +characterized because this defraction + + align:start position:0% +characterized because this defraction + + + align:start position:0% +characterized because this defraction +grading has a fairly long extent and you + + align:start position:0% +grading has a fairly long extent and you + + + align:start position:0% +grading has a fairly long extent and you +can position your laser beam in a number + + align:start position:0% +can position your laser beam in a number + + + align:start position:0% +can position your laser beam in a number +of different places on the defraction + + align:start position:0% +of different places on the defraction + + + align:start position:0% +of different places on the defraction +grading and still get + + align:start position:0% +grading and still get + + + align:start position:0% +grading and still get +valid defc modes so that's one of the + + align:start position:0% +valid defc modes so that's one of the + + + align:start position:0% +valid defc modes so that's one of the +main um main difficulties with making + + align:start position:0% +main um main difficulties with making + + + align:start position:0% +main um main difficulties with making +the measurement precise so you want to + + align:start position:0% +the measurement precise so you want to + + + align:start position:0% +the measurement precise so you want to +position that beam in a way that you can + + align:start position:0% +position that beam in a way that you can + + + align:start position:0% +position that beam in a way that you can +estimate its position best so if you + + align:start position:0% +estimate its position best so if you + + + align:start position:0% +estimate its position best so if you +choose one edge of the defraction + + align:start position:0% +choose one edge of the defraction + + + align:start position:0% +choose one edge of the defraction +grading that'll give you say maybe 20 + + align:start position:0% +grading that'll give you say maybe 20 + + + align:start position:0% +grading that'll give you say maybe 20 +Micron + + align:start position:0% +Micron + + + align:start position:0% +Micron +accuracy + + align:start position:0% +accuracy + + + align:start position:0% +accuracy +um + + align:start position:0% +um + + + align:start position:0% +um +so using that ratio if you just if you + + align:start position:0% +so using that ratio if you just if you + + + align:start position:0% +so using that ratio if you just if you +assume that the beam has a quadratic + + align:start position:0% +assume that the beam has a quadratic + + + align:start position:0% +assume that the beam has a quadratic +shape then you just take this ratio and + + align:start position:0% +shape then you just take this ratio and + + + align:start position:0% +shape then you just take this ratio and +square it to get the ratio + + align:start position:0% +square it to get the ratio + + + align:start position:0% +square it to get the ratio +of how far this is deflecting compared + + align:start position:0% +of how far this is deflecting compared + + + align:start position:0% +of how far this is deflecting compared +to the tip and if you want to be a + + align:start position:0% +to the tip and if you want to be a + + + align:start position:0% +to the tip and if you want to be a +little bit more precise you can use the + + align:start position:0% +little bit more precise you can use the + + + align:start position:0% +little bit more precise you can use the +uh equation given in um in the lab + + align:start position:0% +uh equation given in um in the lab + + + align:start position:0% +uh equation given in um in the lab +manual which is a slightly more + + align:start position:0% +manual which is a slightly more + + + align:start position:0% +manual which is a slightly more +complicated functional form but the + + align:start position:0% +complicated functional form but the + + + align:start position:0% +complicated functional form but the +essence of the + + align:start position:0% +essence of the + + + align:start position:0% +essence of the +uh of the correction is what I've + + align:start position:0% +uh of the correction is what I've + + + align:start position:0% +uh of the correction is what I've +described so does that uh does that make + + align:start position:0% +described so does that uh does that make + + + align:start position:0% +described so does that uh does that make +the issue + + align:start position:0% +the issue + + + align:start position:0% +the issue +clear good okay + + align:start position:0% + + + + align:start position:0% + +already + + align:start position:0% +already + + + align:start position:0% +already +done so now um we can get to + + align:start position:0% + + + + align:start position:0% + +measuring um the samples + + align:start position:0% + + + + align:start position:0% + +are let me just show the samples so the + + align:start position:0% +are let me just show the samples so the + + + align:start position:0% +are let me just show the samples so the +samples are in this box they're all kind + + align:start position:0% +samples are in this box they're all kind + + + align:start position:0% +samples are in this box they're all kind +of jammed together and uh if you try try + + align:start position:0% +of jammed together and uh if you try try + + + align:start position:0% +of jammed together and uh if you try try +to keep them spatially roughly where + + align:start position:0% +to keep them spatially roughly where + + + align:start position:0% +to keep them spatially roughly where +they are they won't get mixed + + align:start position:0% +they are they won't get mixed + + + align:start position:0% +they are they won't get mixed +up um in the middle there's just the + + align:start position:0% +up um in the middle there's just the + + + align:start position:0% +up um in the middle there's just the +bare silicon nitride and you'll see they + + align:start position:0% +bare silicon nitride and you'll see they + + + align:start position:0% +bare silicon nitride and you'll see they +just don't have any pdms on top and + + align:start position:0% +just don't have any pdms on top and + + + align:start position:0% +just don't have any pdms on top and +then uh this is I believe the soft pdms + + align:start position:0% +then uh this is I believe the soft pdms + + + align:start position:0% +then uh this is I believe the soft pdms +and this is the harder pdms but I can't + + align:start position:0% +and this is the harder pdms but I can't + + + align:start position:0% +and this is the harder pdms but I can't +remember exactly but just note which + + align:start position:0% +remember exactly but just note which + + + align:start position:0% +remember exactly but just note which +side you took your pdms from and + + align:start position:0% +side you took your pdms from and + + + align:start position:0% +side you took your pdms from and +everything should be okay I + + align:start position:0% +everything should be okay I + + + align:start position:0% +everything should be okay I +believe yeah I believe that's correct + + align:start position:0% +believe yeah I believe that's correct + + + align:start position:0% +believe yeah I believe that's correct +okay and then the can that we'll be + + align:start position:0% +okay and then the can that we'll be + + + align:start position:0% +okay and then the can that we'll be +using + + align:start position:0% +using + + + align:start position:0% +using +are well I I should be able to give you + + align:start position:0% +are well I I should be able to give you + + + align:start position:0% +are well I I should be able to give you +the right box again the labels are kind + + align:start position:0% +the right box again the labels are kind + + + align:start position:0% +the right box again the labels are kind +of fading but uh it's the shortest beams + + align:start position:0% +of fading but uh it's the shortest beams + + + align:start position:0% +of fading but uh it's the shortest beams +Imaging + + align:start position:0% +Imaging + + + align:start position:0% +Imaging +levers no here they are modulus levers + + align:start position:0% +levers no here they are modulus levers + + + align:start position:0% +levers no here they are modulus levers + + align:start position:0% + + + + align:start position:0% + +Micron so these will be these will be + + align:start position:0% +Micron so these will be these will be + + + align:start position:0% +Micron so these will be these will be +the same shape that you saw yesterday + + align:start position:0% +the same shape that you saw yesterday + + + align:start position:0% +the same shape that you saw yesterday +Long Middle beam short side beams but + + align:start position:0% +Long Middle beam short side beams but + + + align:start position:0% +Long Middle beam short side beams but +the whole thing is about 250 microns in + + align:start position:0% +the whole thing is about 250 microns in + + + align:start position:0% +the whole thing is about 250 microns in +length so uh there'll be more there'll + + align:start position:0% +length so uh there'll be more there'll + + + align:start position:0% +length so uh there'll be more there'll +be more angular aberration because the + + align:start position:0% +be more angular aberration because the + + + align:start position:0% +be more angular aberration because the +beams are shorter and so it presents its + + align:start position:0% +beams are shorter and so it presents its + + + align:start position:0% +beams are shorter and so it presents its +own little + + align:start position:0% +own little + + + align:start position:0% +own little +challenge which I guess we'll discover + + align:start position:0% +challenge which I guess we'll discover + + + align:start position:0% +challenge which I guess we'll discover +yes all right \ No newline at end of file diff --git a/jxxrwZtpHH0.txt b/jxxrwZtpHH0.txt new file mode 100644 index 0000000000000000000000000000000000000000..cae85216528a007f874400f4d9c9e92737ae1bf2 --- /dev/null +++ b/jxxrwZtpHH0.txt @@ -0,0 +1,505 @@ +In this problem, we will be +helping Romeo and Juliet meet + +up for a date. + +And in the process, also we'll +review some concepts in basic + +probability theory, including +sample spaces + +and probability laws. + +This problem, the basic setup +is that Romeo and Juliet are + +trying to meet up for a date. + +And let's say they're trying +to meet up for + +lunch tomorrow at noon. + +But they're not necessarily +punctual. + +So they may arrive on time with +a delay of 0, or they may + +actually be up to 1 hour late +and arrive at 1:00 PM. + +So the other thing that we +assume in this problem is that + +all pairs of arrival times-- so +the time that Romeo arrives + +paired with the time they +Juliet arrives-- + +all of these pairs are +equally likely. + +And I've put this in quotes, +because we haven't really + +specify exactly what +this means. + +And we'll come back to +that in a little bit. + +The last important thing is that +each person will wait for + +15 minutes for the other +person to arrive. + +If within that 15-minute +window the other person + +doesn't arrive, then they'll +give up and they'll end up not + +meeting up for lunch. + +So to solve this problem, let's +first try to set up a + +sample space and come up with a +probability law to describe + +this scenario. + +And let's actually start +with a simpler + +version of this problem. + +And instead of assuming that +they can arrive at any delay + +between 0 and 1 hour, let's +pretend instead that Romeo and + +Juliet can only arrive in +15-minute increments. + +So Romeo can arrive on time +with a delay 0, or be 15 + +minutes late, 30 minutes +late, 45 minutes + +late, or one hour late. + +But none of the other +times are possible. + +And the same thing for Juliet. + + + +Let's start out with just the +simple case first, because it + +helps us get the intuition for +the problem, and it's an + +easier case to analyze. + + + +So it's actually easy +to visualize this. + +It's a nice visual tool +to group this sample + +space into a grid. + +So the horizontal axis here +represents the arrival time of + +Romeo, and the vertical +axis represents the + +arrival time of Juliet. + +And so, for example, this point +here would represent + +Romeo arriving 15 minutes +late and Juliet + +arriving 30 minutes late. + +So this is our sample +space now. + +This is our omega. + +And now let's try to assign +a probability law. + +And we'll continue to assume +that all pairs of arrival + +times are equally likely. + +And now we can actually +specifically specify what this + +term means. + +And in particular, we'll be +invoking the discrete uniform + +law, which basically says that +all of these points, which are + +just outcomes in our +probabilistic experiment-- + +all of these outcomes +are equally likely. + +And so since there are 25 of +them, each one of these + +outcomes has a probability +of 1 over 25. + +So now we've specified our +sample space and our + +probability law. + +So now let's try to answer +the question, what is the + +probability that Romeo +and Juliet will meet + +up for their date? + +So all that amounts to now is +just identifying which of + +these 25 outcomes results in +Romeo and Juliet arriving + +within 15 minutes +of each other. + +So let's start with this one +that I've picked out. + +If Romeo arrives 15 minutes +late and Juliet arrives 30 + +minutes late, then they will +arrive within 15 minutes of + +each other. + +So this outcome does result in +the two of them meeting. + +And so we can actually highlight +all of these. + +And it turns out that these +outcomes that I'm highlighting + +result in the two them arriving +within 15 minutes of + +each other. + +So because each one has a +probability of 1 over 25, all + +we really need to do now +is just count how many + +outcomes there are. + +So there's 1, 2, 3, 4, 5, 6, +7, 8, 9, 10, 11, 12, 13. + +So the probability in the end +is for the discrete case. + +The discrete case-- + +I'm referring to the case where +we simplified it and + +considered only arrival times +with increments of 15 minutes. + +In this case, the probability +is 13 over 25. + +So now we have an idea of how +to solve this problem. + +It amounts to basically coming +up with a sample space, a + +probability law, and then +identifying the events of + +interest in calculating the +probability of that event. + +So now let's actually solve the +problem that we really are + +interested in, which is that +instead of confining Romeo and + +Juliet to arrive in only +15-minute minute increments, + +really, time is continuous, +and Romeo and Juliet can + +arrive at any time. + +So they don't necessarily have +to arrive 15 minutes late. + +Romeo could arrive 15 minutes +and 37 seconds late + +if he wanted to. + +So now our new sample space is +actually just, instead of only + +these 25 points in the grid, +it's this entire square. + +So any point within the square +could be a possible pair of + +meeting times between +Romeo and Juliet. + +So that is our new sample +space, our new omega. + +And now let's assign a +new probability law. + +And now, instead of being in the +discrete world, we're in + +the continuous world. + +And the analogy here +is to consider + +probabilities as areas. + +So the area of this entire +square is one. + +And that also corresponds to the +probability of omega, the + +sample space. + +And imagine just spreading +probability evenly across this + +square so that the probability +of any event-- + +which in this case +would just be any + +shape within this square-- + +is exactly equal to the +area of that shape. + +So now that is our new +sample space and our + +new probability law. + +So what we have to do now is +just to identify the event of + +interest, which is still the +event that Romeo and Juliet + +arrive within 15 minutes +of each other. + +So let's do that. + +If Romeo and Juliet arrive both +on time, then obviously + +they'll meet. + +And if Romeo's on time and +Juliet is 15 minutes late, + +then they will still meet. + +And in fact, any pairs of +meeting times between these + +would still work, because now +Romeo can be on time, and + +Juliet can arrive at any time +between 0 and 15 minutes late. + +But you notice that if Juliet is +even a tiny bit later than + +15 minutes, then they won't +end up meeting. + +So this segment here is part +of the event of interest. + +And similarly, this +segment here is + +also part of the event. + +And if you take this exercise +and extend it, you can + +actually verify that the event +of interest is this strip + +shape in the middle +of the square. + +Which, if you think about it, +makes sense, because you want + +the arrival times between Romeo +and Juliet to be close + +to each other, so you would be +expect it to be somewhere + +close to a diagonal +in this square. + +So now we have our event +of interest. + +We have our sample space and +our probability law. + +So all we have to do now is +just calculate what this + +probability is. + +And we've already said that +the probability in this + +probability law is just areas. + +So now it actually just boils +down to not a probability + +problem, but a problem +in geometry. + +So to calculate this area, you +can do it in lots of ways. + +One way is to calculate the area +of the square, which is + +1, and subtract the areas +of these two triangles. + +So let's do that. + +So in the continuous case, the +probability of meeting is + +going to be 1 minus the +area of this triangle. + +The base here is 3/4 and +3/4, so it's 1/2 + +times 3/4 times 3/4. + +That's the area of one +of these triangles. + +There's two of them, so +we'll multiply by two. + +And we end up with 1 +minus 9/16, or 7/16 + +as our final answer. + +So in this problem, we've +reviewed some basic concepts + +of probability, and that's +also helped us solve this + +problem of helping Romeo and +Juliet meet up for a date. + +And if you wanted to, you could +even extend this problem + +even further and turn +it on its head. + +And instead of calculating given +that they arrive within + +15 minutes of each other, what +is the probability that + +they'll meet, let's say that +Romeo really wants to meet up + +with Juliet, and he wants to +assure himself a least, say, a + +90% chance of meeting Juliet. + +Then you can ask, if he wants to +have at least a 90% chance + +of meeting her, how long should +he be willing to wait? + +And so that's the flip +side of the problem. + +And you can see that with just +some basic concepts of + +probability, you can answer +some already pretty + +interesting problems. + +So I hope this problem was +interesting, and we'll + +see you next time. \ No newline at end of file diff --git a/kIT2uMxYh6M.txt b/kIT2uMxYh6M.txt new file mode 100644 index 0000000000000000000000000000000000000000..ea48c8e026aaf9090f2d636ae8569013ccd56108 --- /dev/null +++ b/kIT2uMxYh6M.txt @@ -0,0 +1,1787 @@ +align:start position:0% + +so uh complex numbers are going to come + + align:start position:0% +so uh complex numbers are going to come + + + align:start position:0% +so uh complex numbers are going to come +in to today's video and let me show you + + align:start position:0% +in to today's video and let me show you + + + align:start position:0% +in to today's video and let me show you +why uh so I'm going to solve the problem + + align:start position:0% +why uh so I'm going to solve the problem + + + align:start position:0% +why uh so I'm going to solve the problem +the differential equation we know first + + align:start position:0% +the differential equation we know first + + + align:start position:0% +the differential equation we know first +order linear with a with a source term + + align:start position:0% +order linear with a with a source term + + + align:start position:0% +order linear with a with a source term +but now the source term has both the + + align:start position:0% +but now the source term has both the + + + align:start position:0% +but now the source term has both the +cosine and the sign and the sign you + + align:start position:0% +cosine and the sign and the sign you + + + align:start position:0% +cosine and the sign and the sign you +notice has this imaginary Square < TK of + + align:start position:0% +notice has this imaginary Square < TK of + + + align:start position:0% +notice has this imaginary Square < TK of +minus one involved so I'll I'll call + + align:start position:0% +minus one involved so I'll I'll call + + + align:start position:0% +minus one involved so I'll I'll call +this y complex with a little C because + + align:start position:0% +this y complex with a little C because + + + align:start position:0% +this y complex with a little C because +it's the answer is going to come out a + + align:start position:0% +it's the answer is going to come out a + + + align:start position:0% +it's the answer is going to come out a +complex number instead of a real number + + align:start position:0% +complex number instead of a real number + + + align:start position:0% +complex number instead of a real number +so last the previous lecture solved it + + align:start position:0% +so last the previous lecture solved it + + + align:start position:0% +so last the previous lecture solved it +with the cosine and now we're going to + + align:start position:0% +with the cosine and now we're going to + + + align:start position:0% +with the cosine and now we're going to +solve it with that combination and you + + align:start position:0% +solve it with that combination and you + + + align:start position:0% +solve it with that combination and you +may wonder why the reason is that Oiler + + align:start position:0% +may wonder why the reason is that Oiler + + + align:start position:0% +may wonder why the reason is that Oiler +left behind a fantastic + + align:start position:0% +left behind a fantastic + + + align:start position:0% +left behind a fantastic +formula for that the cosine plus I * the + + align:start position:0% +formula for that the cosine plus I * the + + + align:start position:0% +formula for that the cosine plus I * the +S of an angle equals the expon itial of + + align:start position:0% +S of an angle equals the expon itial of + + + align:start position:0% +S of an angle equals the expon itial of +the angle e to the I Omega T and the + + align:start position:0% +the angle e to the I Omega T and the + + + align:start position:0% +the angle e to the I Omega T and the +good part about that is which we saw + + align:start position:0% +good part about that is which we saw + + + align:start position:0% +good part about that is which we saw +earlier for exponentials that when the + + align:start position:0% +earlier for exponentials that when the + + + align:start position:0% +earlier for exponentials that when the +source term is an exponential the + + align:start position:0% +source term is an exponential the + + + align:start position:0% +source term is an exponential the +solution is an exponential so I look for + + align:start position:0% +solution is an exponential so I look for + + + align:start position:0% +solution is an exponential so I look for +a solution of this with that same e to + + align:start position:0% +a solution of this with that same e to + + + align:start position:0% +a solution of this with that same e to +the I Omega T and it's got some Factor + + align:start position:0% +the I Omega T and it's got some Factor + + + align:start position:0% +the I Omega T and it's got some Factor +capital Y that we have to find and we + + align:start position:0% +capital Y that we have to find and we + + + align:start position:0% +capital Y that we have to find and we +find that by substituting this into the + + align:start position:0% +find that by substituting this into the + + + align:start position:0% +find that by substituting this into the +equation and then we learn what this + + align:start position:0% +equation and then we learn what this + + + align:start position:0% +equation and then we learn what this +capital Y is so let me put that in the + + align:start position:0% +capital Y is so let me put that in the + + + align:start position:0% +capital Y is so let me put that in the +derivative the left side is so this is + + align:start position:0% +derivative the left side is so this is + + + align:start position:0% +derivative the left side is so this is +still going to be our complex solution + + align:start position:0% +still going to be our complex solution + + + align:start position:0% +still going to be our complex solution +it's still + + align:start position:0% +it's still + + + align:start position:0% +it's still +complex so I put this into the equation + + align:start position:0% +complex so I put this into the equation + + + align:start position:0% +complex so I put this into the equation +the derivative will be I Omega of course + + align:start position:0% +the derivative will be I Omega of course + + + align:start position:0% +the derivative will be I Omega of course +the derivative of the exponential brings + + align:start position:0% +the derivative of the exponential brings + + + align:start position:0% +the derivative of the exponential brings +down the N number there whatever it is I + + align:start position:0% +down the N number there whatever it is I + + + align:start position:0% +down the N number there whatever it is I +Omega y e to the I Omega + + align:start position:0% +Omega y e to the I Omega + + + align:start position:0% +Omega y e to the I Omega +T that's what we get for the derivative + + align:start position:0% +T that's what we get for the derivative + + + align:start position:0% +T that's what we get for the derivative +of this and now that should equal a + + align:start position:0% +of this and now that should equal a + + + align:start position:0% +of this and now that should equal a +times the + + align:start position:0% + + + + align:start position:0% + +function plus the source e to the I + + align:start position:0% +function plus the source e to the I + + + align:start position:0% +function plus the source e to the I +Omega + + align:start position:0% + + + + align:start position:0% + +T just as we did before with uh a real e + + align:start position:0% +T just as we did before with uh a real e + + + align:start position:0% +T just as we did before with uh a real e +to the St now it's s is I Omega okay and + + align:start position:0% +to the St now it's s is I Omega okay and + + + align:start position:0% +to the St now it's s is I Omega okay and +the beauty is we + + align:start position:0% +the beauty is we + + + align:start position:0% +the beauty is we +divide everything by e to the I Omega T + + align:start position:0% +divide everything by e to the I Omega T + + + align:start position:0% +divide everything by e to the I Omega T +and then we get a simple equation + + align:start position:0% + + + + align:start position:0% + +iega bring the A on the other side time + + align:start position:0% +iega bring the A on the other side time + + + align:start position:0% +iega bring the A on the other side time +Y is + + align:start position:0% +Y is + + + align:start position:0% +Y is +1 good so y we now know + + align:start position:0% +1 good so y we now know + + + align:start position:0% +1 good so y we now know +is 1/ I Omega minus + + align:start position:0% +is 1/ I Omega minus + + + align:start position:0% +is 1/ I Omega minus +a it involves the frequency Omega in the + + align:start position:0% +a it involves the frequency Omega in the + + + align:start position:0% +a it involves the frequency Omega in the +short first term and it involves the + + align:start position:0% +short first term and it involves the + + + align:start position:0% +short first term and it involves the +rate of growth the constant in the in + + align:start position:0% +rate of growth the constant in the in + + + align:start position:0% +rate of growth the constant in the in +the uh uh zero order term good that's + + align:start position:0% +the uh uh zero order term good that's + + + align:start position:0% +the uh uh zero order term good that's +our expression for capital Y now and if + + align:start position:0% +our expression for capital Y now and if + + + align:start position:0% +our expression for capital Y now and if +I put that in here I have the complex + + align:start position:0% +I put that in here I have the complex + + + align:start position:0% +I put that in here I have the complex +solution but my idea + + align:start position:0% +solution but my idea + + + align:start position:0% +solution but my idea +is to use this complex solution to find + + align:start position:0% +is to use this complex solution to find + + + align:start position:0% +is to use this complex solution to find +two real solutions that's really why I'm + + align:start position:0% +two real solutions that's really why I'm + + + align:start position:0% +two real solutions that's really why I'm +why I'm this video is about using this + + align:start position:0% +why I'm this video is about using this + + + align:start position:0% +why I'm this video is about using this +complex Source term to find the + + align:start position:0% +complex Source term to find the + + + align:start position:0% +complex Source term to find the +solutions for both that one and sin + + align:start position:0% +solutions for both that one and sin + + + align:start position:0% +solutions for both that one and sin +Omega T and the trick will be the way to + + align:start position:0% +Omega T and the trick will be the way to + + + align:start position:0% +Omega T and the trick will be the way to +do it will be I will take here's my + + align:start position:0% +do it will be I will take here's my + + + align:start position:0% +do it will be I will take here's my +complex solution I'll take the real + + align:start position:0% + + + + align:start position:0% + +part of this complex + + align:start position:0% +part of this complex + + + align:start position:0% +part of this complex +solution it will be the result match the + + align:start position:0% + + + + align:start position:0% + +cosine that's the real part of of of + + align:start position:0% +cosine that's the real part of of of + + + align:start position:0% +cosine that's the real part of of of +this expression which I now know and the + + align:start position:0% +this expression which I now know and the + + + align:start position:0% +this expression which I now know and the +imaginary part of of this same + + align:start position:0% +imaginary part of of this same + + + align:start position:0% +imaginary part of of this same +expression will give me the sign the + + align:start position:0% +expression will give me the sign the + + + align:start position:0% +expression will give me the sign the +output the response to the sign term so + + align:start position:0% +output the response to the sign term so + + + align:start position:0% +output the response to the sign term so +two problems solved one method but + + align:start position:0% +two problems solved one method but + + + align:start position:0% +two problems solved one method but +there's a step that I have to take I + + align:start position:0% +there's a step that I have to take I + + + align:start position:0% +there's a step that I have to take I +have to how do I find the real part of + + align:start position:0% +have to how do I find the real part of + + + align:start position:0% +have to how do I find the real part of +this + + align:start position:0% +this + + + align:start position:0% +this +expression real part's easy if the + + align:start position:0% +expression real part's easy if the + + + align:start position:0% +expression real part's easy if the +complex number is written a + i b the + + align:start position:0% +complex number is written a + i b the + + + align:start position:0% +complex number is written a + i b the +real part is a the imaginary part is B + + align:start position:0% +real part is a the imaginary part is B + + + align:start position:0% +real part is a the imaginary part is B +but I don't have it a plus I B I have it + + align:start position:0% +but I don't have it a plus I B I have it + + + align:start position:0% +but I don't have it a plus I B I have it +in this form and in a way it's a better + + align:start position:0% +in this form and in a way it's a better + + + align:start position:0% +in this form and in a way it's a better +form so now I have to think about and + + align:start position:0% +form so now I have to think about and + + + align:start position:0% +form so now I have to think about and +and why itself has this uh as this thing + + align:start position:0% +and why itself has this uh as this thing + + + align:start position:0% +and why itself has this uh as this thing +in the denominator so can I + + align:start position:0% +in the denominator so can I + + + align:start position:0% +in the denominator so can I +practice by taking the the by looking at + + align:start position:0% +practice by taking the the by looking at + + + align:start position:0% +practice by taking the the by looking at +this number I + + align:start position:0% +this number I + + + align:start position:0% +this number I +Omega I Omega minus + + align:start position:0% +Omega I Omega minus + + + align:start position:0% +Omega I Omega minus +a that's that's really the awkward + + align:start position:0% +a that's that's really the awkward + + + align:start position:0% +a that's that's really the awkward +quantity that I have to get into a good + + align:start position:0% +quantity that I have to get into a good + + + align:start position:0% +quantity that I have to get into a good +form and the form you want for complex + + align:start position:0% +form and the form you want for complex + + + align:start position:0% +form and the form you want for complex +numbers when you're going to multiply + + align:start position:0% +numbers when you're going to multiply + + + align:start position:0% +numbers when you're going to multiply +them is the polar form I want to put + + align:start position:0% +them is the polar form I want to put + + + align:start position:0% +them is the polar form I want to put +this in the form r e to the I Alpha + + align:start position:0% +this in the form r e to the I Alpha + + + align:start position:0% +this in the form r e to the I Alpha +so a a positive number the magnitude of + + align:start position:0% +so a a positive number the magnitude of + + + align:start position:0% +so a a positive number the magnitude of +this and the angle so I have to draw the + + align:start position:0% +this and the angle so I have to draw the + + + align:start position:0% +this and the angle so I have to draw the +complex plane I guess this is the first + + align:start position:0% +complex plane I guess this is the first + + + align:start position:0% +complex plane I guess this is the first +time in these lectures so there's the + + align:start position:0% +time in these lectures so there's the + + + align:start position:0% +time in these lectures so there's the +real axis here's the imaginary axis and + + align:start position:0% +real axis here's the imaginary axis and + + + align:start position:0% +real axis here's the imaginary axis and +here's a complex number I Omega minus a + + align:start position:0% +here's a complex number I Omega minus a + + + align:start position:0% +here's a complex number I Omega minus a +so in the imaginary Direction I go up + + align:start position:0% +so in the imaginary Direction I go up + + + align:start position:0% +so in the imaginary Direction I go up +Omega and in the real Direction I go + + align:start position:0% +Omega and in the real Direction I go + + + align:start position:0% +Omega and in the real Direction I go +minus a + + align:start position:0% +minus a + + + align:start position:0% +minus a +so here's my number this is up to I + + align:start position:0% +so here's my number this is up to I + + + align:start position:0% +so here's my number this is up to I +Omega and back to minus a and there is + + align:start position:0% +Omega and back to minus a and there is + + + align:start position:0% +Omega and back to minus a and there is +the number I Omega minus + + align:start position:0% +the number I Omega minus + + + align:start position:0% +the number I Omega minus +a + + align:start position:0% +a + + + align:start position:0% +a +and there's the angle + + align:start position:0% +and there's the angle + + + align:start position:0% +and there's the angle +Alpha and the length of that is the + + align:start position:0% +Alpha and the length of that is the + + + align:start position:0% +Alpha and the length of that is the +r so I have those two things to find + + align:start position:0% +r so I have those two things to find + + + align:start position:0% +r so I have those two things to find +that's called putting the number into + + align:start position:0% +that's called putting the number into + + + align:start position:0% +that's called putting the number into +its Polar form this is its re angular + + align:start position:0% +its Polar form this is its re angular + + + align:start position:0% +its Polar form this is its re angular +form uh real imaginary this is its + + align:start position:0% +form uh real imaginary this is its + + + align:start position:0% +form uh real imaginary this is its +magnitude and now what is the magnitude + + align:start position:0% +magnitude and now what is the magnitude + + + align:start position:0% +magnitude and now what is the magnitude +of that easy that's a right triangle + + align:start position:0% +of that easy that's a right triangle + + + align:start position:0% +of that easy that's a right triangle +with height that side is is is Omega + + align:start position:0% +with height that side is is is Omega + + + align:start position:0% +with height that side is is is Omega +this side is minus a I use Pythagoras to + + align:start position:0% +this side is minus a I use Pythagoras to + + + align:start position:0% +this side is minus a I use Pythagoras to +know that this R is the square T + + align:start position:0% +know that this R is the square T + + + align:start position:0% +know that this R is the square T +of a 2 + Omega s right + + align:start position:0% +of a 2 + Omega s right + + + align:start position:0% +of a 2 + Omega s right +that length squared the minus sign + + align:start position:0% +that length squared the minus sign + + + align:start position:0% +that length squared the minus sign +disappears that length squared Omega + + align:start position:0% +disappears that length squared Omega + + + align:start position:0% +disappears that length squared Omega +squar so that's the r now what about e + + align:start position:0% +squar so that's the r now what about e + + + align:start position:0% +squar so that's the r now what about e +to the I Alpha what's the angle e to the + + align:start position:0% +to the I Alpha what's the angle e to the + + + align:start position:0% +to the I Alpha what's the angle e to the +I Alpha uh the best I can say is I I + + align:start position:0% +I Alpha uh the best I can say is I I + + + align:start position:0% +I Alpha uh the best I can say is I I +know what I I know what that angle is I + + align:start position:0% +know what I I know what that angle is I + + + align:start position:0% +know what I I know what that angle is I +can only tell you it's tangent but let + + align:start position:0% +can only tell you it's tangent but let + + + align:start position:0% +can only tell you it's tangent but let +me just leave it as alpha alpha is the + + align:start position:0% +me just leave it as alpha alpha is the + + + align:start position:0% +me just leave it as alpha alpha is the +angle the the the tangent of this angle + + align:start position:0% +angle the the the tangent of this angle + + + align:start position:0% +angle the the the tangent of this angle +will be that that number over that + + align:start position:0% +will be that that number over that + + + align:start position:0% +will be that that number over that +number I'll leave it that way okay that + + align:start position:0% +number I'll leave it that way okay that + + + align:start position:0% +number I'll leave it that way okay that +so that's a key step a first step with + + align:start position:0% +so that's a key step a first step with + + + align:start position:0% +so that's a key step a first step with +complex numbers and in a later video + + align:start position:0% +complex numbers and in a later video + + + align:start position:0% +complex numbers and in a later video +will be devoted entirely to working with + + align:start position:0% +will be devoted entirely to working with + + + align:start position:0% +will be devoted entirely to working with +complex numbers so here you're getting a + + align:start position:0% +complex numbers so here you're getting a + + + align:start position:0% +complex numbers so here you're getting a +first look at it or you may have seen it + + align:start position:0% +first look at it or you may have seen it + + + align:start position:0% +first look at it or you may have seen it +before okay so now now I I had to divide + + align:start position:0% +before okay so now now I I had to divide + + + align:start position:0% +before okay so now now I I had to divide +by + + align:start position:0% +by + + + align:start position:0% +by +that that's why I like this form div in + + align:start position:0% +that that's why I like this form div in + + + align:start position:0% +that that's why I like this form div in +by it so now I'm ready for I'm ready to + + align:start position:0% +by it so now I'm ready for I'm ready to + + + align:start position:0% +by it so now I'm ready for I'm ready to +put in my + + align:start position:0% +put in my + + + align:start position:0% +put in my +complex y + + align:start position:0% +complex y + + + align:start position:0% +complex y +complex was this Y which was 1/ I Omega + + align:start position:0% +complex was this Y which was 1/ I Omega + + + align:start position:0% +complex was this Y which was 1/ I Omega +minus + + align:start position:0% +minus + + + align:start position:0% +minus +a and e to the I Omega T that's what we + + align:start position:0% +a and e to the I Omega T that's what we + + + align:start position:0% +a and e to the I Omega T that's what we +had but now I Omega minus a we have in + + align:start position:0% +had but now I Omega minus a we have in + + + align:start position:0% +had but now I Omega minus a we have in +this nicer form I can divide by that if + + align:start position:0% +this nicer form I can divide by that if + + + align:start position:0% +this nicer form I can divide by that if +I divide by that it'll be 1 over the < + + align:start position:0% +I divide by that it'll be 1 over the < + + + align:start position:0% +I divide by that it'll be 1 over the < +TK of a^ 2 + Omega + + align:start position:0% + + + + align:start position:0% + +2 time e to the I + + align:start position:0% +2 time e to the I + + + align:start position:0% +2 time e to the I +Alpha Oh e to the minus I Alpha when I + + align:start position:0% +Alpha Oh e to the minus I Alpha when I + + + align:start position:0% +Alpha Oh e to the minus I Alpha when I +divide by an + + align:start position:0% +divide by an + + + align:start position:0% +divide by an +exponent that exponent be exponential + + align:start position:0% +exponent that exponent be exponential + + + align:start position:0% +exponent that exponent be exponential +that exponent changes sign time e to the + + align:start position:0% +that exponent changes sign time e to the + + + align:start position:0% +that exponent changes sign time e to the +I Omega + + align:start position:0% + + + + align:start position:0% + +T are you good with + + align:start position:0% +T are you good with + + + align:start position:0% +T are you good with +that so this number + + align:start position:0% +that so this number + + + align:start position:0% +that so this number +produced both of those terms the + + align:start position:0% +produced both of those terms the + + + align:start position:0% +produced both of those terms the +magnitude part and the angle part and + + align:start position:0% +magnitude part and the angle part and + + + align:start position:0% +magnitude part and the angle part and +then this part was pure angle and that's + + align:start position:0% +then this part was pure angle and that's + + + align:start position:0% +then this part was pure angle and that's +my answer in a nicer form and here's + + align:start position:0% +my answer in a nicer form and here's + + + align:start position:0% +my answer in a nicer form and here's +even better form I combine these two e + + align:start position:0% +even better form I combine these two e + + + align:start position:0% +even better form I combine these two e +to the I something times when I multiply + + align:start position:0% +to the I something times when I multiply + + + align:start position:0% +to the I something times when I multiply +two + + align:start position:0% +two + + + align:start position:0% +two +exponentials I can put that as e to the + + align:start position:0% +exponentials I can put that as e to the + + + align:start position:0% +exponentials I can put that as e to the +I Omega T minus Alpha I just you see + + align:start position:0% +I Omega T minus Alpha I just you see + + + align:start position:0% +I Omega T minus Alpha I just you see +that it's has that factor e to the minus + + align:start position:0% +that it's has that factor e to the minus + + + align:start position:0% +that it's has that factor e to the minus +I Alpha as well as the e to the I Omega + + align:start position:0% +I Alpha as well as the e to the I Omega + + + align:start position:0% +I Alpha as well as the e to the I Omega +T + + align:start position:0% +T + + + align:start position:0% +T +now now I'm ready to take the real part + + align:start position:0% +now now I'm ready to take the real part + + + align:start position:0% +now now I'm ready to take the real part +and the imaginary part and that will + + align:start position:0% +and the imaginary part and that will + + + align:start position:0% +and the imaginary part and that will +give me my two solutions my two real + + align:start position:0% +give me my two solutions my two real + + + align:start position:0% +give me my two solutions my two real +solutions to the real equation so so + + align:start position:0% +solutions to the real equation so so + + + align:start position:0% +solutions to the real equation so so +take the real + + align:start position:0% + + + + align:start position:0% + +part and that's what I'll concentrate on + + align:start position:0% +part and that's what I'll concentrate on + + + align:start position:0% +part and that's what I'll concentrate on +the real + + align:start position:0% +the real + + + align:start position:0% +the real +part was is the original y t y real + + align:start position:0% +part was is the original y t y real + + + align:start position:0% +part was is the original y t y real +coming from the cosine the cosine of + + align:start position:0% +coming from the cosine the cosine of + + + align:start position:0% +coming from the cosine the cosine of +Omega T is the is is the case I'm + + align:start position:0% +Omega T is the is is the case I'm + + + align:start position:0% +Omega T is the is is the case I'm +redoing from what I had in an earlier + + align:start position:0% +redoing from what I had in an earlier + + + align:start position:0% +redoing from what I had in an earlier +lecture uh as a combination of signs and + + align:start position:0% +lecture uh as a combination of signs and + + + align:start position:0% +lecture uh as a combination of signs and +cosiness now we're going to see it more + + align:start position:0% +cosiness now we're going to see it more + + + align:start position:0% +cosiness now we're going to see it more +more beautifully so I'm ready to take + + align:start position:0% +more beautifully so I'm ready to take + + + align:start position:0% +more beautifully so I'm ready to take +the real part of that + + align:start position:0% +the real part of that + + + align:start position:0% +the real part of that +well this is a real number one over the + + align:start position:0% +well this is a real number one over the + + + align:start position:0% +well this is a real number one over the +< TK of a 2 + Omega + + align:start position:0% + + + + align:start position:0% + +2 and what is the real part of e to the + + align:start position:0% +2 and what is the real part of e to the + + + align:start position:0% +2 and what is the real part of e to the +I times an angle the real part of e to + + align:start position:0% +I times an angle the real part of e to + + + align:start position:0% +I times an angle the real part of e to +the I Theta is the cosign of theta the + + align:start position:0% +the I Theta is the cosign of theta the + + + align:start position:0% +the I Theta is the cosign of theta the +real part is the cosine that's we're + + align:start position:0% +real part is the cosine that's we're + + + align:start position:0% +real part is the cosine that's we're +using Oiler always using Oiler so it's + + align:start position:0% +using Oiler always using Oiler so it's + + + align:start position:0% +using Oiler always using Oiler so it's +just the + + align:start position:0% +just the + + + align:start position:0% +just the +cosine of Omega T minus + + align:start position:0% +cosine of Omega T minus + + + align:start position:0% +cosine of Omega T minus +Alpha and that's exactly what we ended + + align:start position:0% +Alpha and that's exactly what we ended + + + align:start position:0% +Alpha and that's exactly what we ended +up with with more + + align:start position:0% +up with with more + + + align:start position:0% +up with with more +work on in the previous + + align:start position:0% +work on in the previous + + + align:start position:0% +work on in the previous +lecture the magnitude this was called + + align:start position:0% +lecture the magnitude this was called + + + align:start position:0% +lecture the magnitude this was called +the gain this was the G part this is the + + align:start position:0% +the gain this was the G part this is the + + + align:start position:0% +the gain this was the G part this is the +G the gain the the + + align:start position:0% +G the gain the the + + + align:start position:0% +G the gain the the +the the the input was the size of cosine + + align:start position:0% +the the the input was the size of cosine + + + align:start position:0% +the the the input was the size of cosine +was size one it's it's increased or + + align:start position:0% +was size one it's it's increased or + + + align:start position:0% +was size one it's it's increased or +decreased by this factor and uh then the + + align:start position:0% +decreased by this factor and uh then the + + + align:start position:0% +decreased by this factor and uh then the +cosine is still here + + align:start position:0% + + + + align:start position:0% + +and Alpha you remember is the time + + align:start position:0% +and Alpha you remember is the time + + + align:start position:0% +and Alpha you remember is the time +lag we don't the input is a pure cosine + + align:start position:0% +lag we don't the input is a pure cosine + + + align:start position:0% +lag we don't the input is a pure cosine +but the output is a shifted cosine which + + align:start position:0% +but the output is a shifted cosine which + + + align:start position:0% +but the output is a shifted cosine which +is also a combination of cosine and S so + + align:start position:0% +is also a combination of cosine and S so + + + align:start position:0% +is also a combination of cosine and S so +there you've used complex numbers maybe + + align:start position:0% +there you've used complex numbers maybe + + + align:start position:0% +there you've used complex numbers maybe +the first time maybe not to get the nice + + align:start position:0% +the first time maybe not to get the nice + + + align:start position:0% +the first time maybe not to get the nice +form for for the answer and of course I + + align:start position:0% +form for for the answer and of course I + + + align:start position:0% +form for for the answer and of course I +could if the input was the S of Omega T + + align:start position:0% +could if the input was the S of Omega T + + + align:start position:0% +could if the input was the S of Omega T +then I would pay I would have the same + + align:start position:0% +then I would pay I would have the same + + + align:start position:0% +then I would pay I would have the same +thing that would be a + + align:start position:0% +thing that would be a + + + align:start position:0% +thing that would be a +sign so uh it it's really the important + + align:start position:0% +sign so uh it it's really the important + + + align:start position:0% +sign so uh it it's really the important +the physically important quantity is the + + align:start position:0% +the physically important quantity is the + + + align:start position:0% +the physically important quantity is the +gain and the phase lag good so that's + + align:start position:0% +gain and the phase lag good so that's + + + align:start position:0% +gain and the phase lag good so that's +the first use of complex numbers to get + + align:start position:0% +the first use of complex numbers to get + + + align:start position:0% +the first use of complex numbers to get +us back to uh an + + align:start position:0% +us back to uh an + + + align:start position:0% +us back to uh an +exponential after which the solution is + + align:start position:0% +exponential after which the solution is + + + align:start position:0% +exponential after which the solution is +easy okay I'll have more Source terms a + + align:start position:0% +easy okay I'll have more Source terms a + + + align:start position:0% +easy okay I'll have more Source terms a +few more and then I'll look at a look + + align:start position:0% +few more and then I'll look at a look + + + align:start position:0% +few more and then I'll look at a look +for a formula that applies for any + + align:start position:0% +for a formula that applies for any + + + align:start position:0% +for a formula that applies for any +Source + + align:start position:0% +Source + + + align:start position:0% +Source +term okay thank you \ No newline at end of file diff --git a/kZcGNN5cYCg.txt b/kZcGNN5cYCg.txt new file mode 100644 index 0000000000000000000000000000000000000000..468ba6c01d41495eef24dd4c108f5ae84c63287c --- /dev/null +++ b/kZcGNN5cYCg.txt @@ -0,0 +1,13291 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencare at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu so last time we were talking + + align:start position:0% +ocw.mit.edu so last time we were talking + + + align:start position:0% +ocw.mit.edu so last time we were talking +about the subleading one over mq lar in + + align:start position:0% +about the subleading one over mq lar in + + + align:start position:0% +about the subleading one over mq lar in +HQ hopefully more people remember that + + align:start position:0% +HQ hopefully more people remember that + + + align:start position:0% +HQ hopefully more people remember that +we have a makeup Le lecture today or it + + align:start position:0% +we have a makeup Le lecture today or it + + + align:start position:0% +we have a makeup Le lecture today or it +will not be stopped by the snow so today + + align:start position:0% +will not be stopped by the snow so today + + + align:start position:0% +will not be stopped by the snow so today +we're going to continue this discussion + + align:start position:0% +we're going to continue this discussion + + + align:start position:0% +we're going to continue this discussion +of power suppressed lonians and I'll + + align:start position:0% +of power suppressed lonians and I'll + + + align:start position:0% +of power suppressed lonians and I'll +explain to you why we think of these as + + align:start position:0% +explain to you why we think of these as + + + align:start position:0% +explain to you why we think of these as +giving power corrections to observables + + align:start position:0% +giving power corrections to observables + + + align:start position:0% +giving power corrections to observables +and we'll talk about a couple different + + align:start position:0% +and we'll talk about a couple different + + + align:start position:0% +and we'll talk about a couple different +observables where these specific + + align:start position:0% +observables where these specific + + + align:start position:0% +observables where these specific +operators are playing an important role + + align:start position:0% +operators are playing an important role + + + align:start position:0% +operators are playing an important role +and then we're going to turn to the + + align:start position:0% +and then we're going to turn to the + + + align:start position:0% +and then we're going to turn to the +topic of renormalons which is fun stuff + + align:start position:0% +topic of renormalons which is fun stuff + + + align:start position:0% +topic of renormalons which is fun stuff +how many people here people here know + + align:start position:0% +how many people here people here know + + + align:start position:0% +how many people here people here know +what a renormalon is + + align:start position:0% + + + + align:start position:0% + +yeah by the end of the lecture you'll + + align:start position:0% +yeah by the end of the lecture you'll + + + align:start position:0% +yeah by the end of the lecture you'll +all know whatever normal one + + align:start position:0% +all know whatever normal one + + + align:start position:0% +all know whatever normal one +is okay so this is where we left off we + + align:start position:0% +is okay so this is where we left off we + + + align:start position:0% +is okay so this is where we left off we +were talking about this symmetry + + align:start position:0% +were talking about this symmetry + + + align:start position:0% +were talking about this symmetry +reparameterization in variance and what + + align:start position:0% +reparameterization in variance and what + + + align:start position:0% +reparameterization in variance and what +we showed last time is that the Wilson + + align:start position:0% +we showed last time is that the Wilson + + + align:start position:0% +we showed last time is that the Wilson +coefficient of this operator is one to + + align:start position:0% +coefficient of this operator is one to + + + align:start position:0% +coefficient of this operator is one to +all orders in peration theory because of + + align:start position:0% +all orders in peration theory because of + + + align:start position:0% +all orders in peration theory because of +that symmetry the Wilson coefficient of + + align:start position:0% +that symmetry the Wilson coefficient of + + + align:start position:0% +that symmetry the Wilson coefficient of +this operator is not and I told you that + + align:start position:0% +this operator is not and I told you that + + + align:start position:0% +this operator is not and I told you that +at leading log order it would be given + + align:start position:0% +at leading log order it would be given + + + align:start position:0% +at leading log order it would be given +by some expression like this but in + + align:start position:0% +by some expression like this but in + + + align:start position:0% +by some expression like this but in +general this is is just the lowest order + + align:start position:0% +general this is is just the lowest order + + + align:start position:0% +general this is is just the lowest order +expression and it gets perturbatively + + align:start position:0% +expression and it gets perturbatively + + + align:start position:0% +expression and it gets perturbatively +corrected it's actually known at three + + align:start position:0% + + + + align:start position:0% + +Loops so let's + + align:start position:0% +Loops so let's + + + align:start position:0% +Loops so let's +continue we've talked about + + align:start position:0% +continue we've talked about + + + align:start position:0% +continue we've talked about +reparameterization invariance for the + + align:start position:0% +reparameterization invariance for the + + + align:start position:0% +reparameterization invariance for the +lran reparametrization invariance also + + align:start position:0% +lran reparametrization invariance also + + + align:start position:0% +lran reparametrization invariance also +has important consequences for operators + + align:start position:0% + + + + align:start position:0% + +so just like we wrote down subleading + + align:start position:0% +so just like we wrote down subleading + + + align:start position:0% +so just like we wrote down subleading +lrin we should also write subleading + + align:start position:0% +lrin we should also write subleading + + + align:start position:0% +lrin we should also write subleading +currents so there's 1/ mq suppress + + align:start position:0% +currents so there's 1/ mq suppress + + + align:start position:0% +currents so there's 1/ mq suppress +currents and if you look at those + + align:start position:0% +currents and if you look at those + + + align:start position:0% +currents and if you look at those +currents and you construct + + align:start position:0% +currents and you construct + + + align:start position:0% +currents and you construct +them then you find again that + + align:start position:0% +them then you find again that + + + align:start position:0% +them then you find again that +reparameterization and variance plays an + + align:start position:0% +reparameterization and variance plays an + + + align:start position:0% +reparameterization and variance plays an +important + + align:start position:0% +important + + + align:start position:0% +important +role and again there's relations between + + align:start position:0% +role and again there's relations between + + + align:start position:0% +role and again there's relations between +Wilson + + align:start position:0% + + + + align:start position:0% + +coefficients and what happens in this + + align:start position:0% +coefficients and what happens in this + + + align:start position:0% +coefficients and what happens in this +case is actually that the leading order + + align:start position:0% +case is actually that the leading order + + + align:start position:0% +case is actually that the leading order +operator had a Wilson + + align:start position:0% +operator had a Wilson + + + align:start position:0% +operator had a Wilson +coefficient the lowest order operator so + + align:start position:0% +coefficient the lowest order operator so + + + align:start position:0% +coefficient the lowest order operator so +the Wilson coefficients of The + + align:start position:0% +the Wilson coefficients of The + + + align:start position:0% +the Wilson coefficients of The +subleading Operators get related to that + + align:start position:0% +subleading Operators get related to that + + + align:start position:0% +subleading Operators get related to that +of the leading + + align:start position:0% + + + + align:start position:0% + +operator and I may give you a problem on + + align:start position:0% +operator and I may give you a problem on + + + align:start position:0% +operator and I may give you a problem on +that on your next problem set + + align:start position:0% +that on your next problem set + + + align:start position:0% +that on your next problem set +but haven't quite made up my mind + + align:start position:0% +but haven't quite made up my mind + + + align:start position:0% +but haven't quite made up my mind +yet so rather than go through that I + + align:start position:0% +yet so rather than go through that I + + + align:start position:0% +yet so rather than go through that I +want to talk about some observables + + align:start position:0% +want to talk about some observables + + + align:start position:0% +want to talk about some observables +where these operators play a + + align:start position:0% +where these operators play a + + + align:start position:0% +where these operators play a +role so we've seen one example of + + align:start position:0% +role so we've seen one example of + + + align:start position:0% +role so we've seen one example of +reparameterization in variance and I + + align:start position:0% +reparameterization in variance and I + + + align:start position:0% +reparameterization in variance and I +think from that one example you would be + + align:start position:0% +think from that one example you would be + + + align:start position:0% +think from that one example you would be +able to do other examples let's talk + + align:start position:0% +able to do other examples let's talk + + + align:start position:0% +able to do other examples let's talk +about masses these operators here + + align:start position:0% +about masses these operators here + + + align:start position:0% +about masses these operators here +actually have an impact on the masses of + + align:start position:0% +actually have an impact on the masses of + + + align:start position:0% +actually have an impact on the masses of +hadrons if we think about the mass of a + + align:start position:0% +hadrons if we think about the mass of a + + + align:start position:0% +hadrons if we think about the mass of a +heavy Meson + + align:start position:0% + + + + align:start position:0% + +H there's a heavy Quark in that heavy + + align:start position:0% +H there's a heavy Quark in that heavy + + + align:start position:0% +H there's a heavy Quark in that heavy +meeson + + align:start position:0% +meeson + + + align:start position:0% +meeson +and so we can pull out that heavy quark + + align:start position:0% +and so we can pull out that heavy quark + + + align:start position:0% +and so we can pull out that heavy quark +and then there's some + + align:start position:0% +and then there's some + + + align:start position:0% +and then there's some +remainder and we can characterize higher + + align:start position:0% +remainder and we can characterize higher + + + align:start position:0% +remainder and we can characterize higher +order terms in this + + align:start position:0% + + + + align:start position:0% + +formula so let me first explain what + + align:start position:0% +formula so let me first explain what + + + align:start position:0% +formula so let me first explain what +this Lambda bar is our lran here uh if + + align:start position:0% +this Lambda bar is our lran here uh if + + + align:start position:0% +this Lambda bar is our lran here uh if +we if we're working at lowest order in + + align:start position:0% +we if we're working at lowest order in + + + align:start position:0% +we if we're working at lowest order in +the theory our lran would be l0 of + + align:start position:0% + + + + align:start position:0% + +HQ Plus for the light quarks a basically + + align:start position:0% +HQ Plus for the light quarks a basically + + + align:start position:0% +HQ Plus for the light quarks a basically +just a qcd lran + + align:start position:0% + + + + align:start position:0% + +so for the light quarks and the + + align:start position:0% + + + + align:start position:0% + +gluons so for the heavy cork we have hqt + + align:start position:0% +gluons so for the heavy cork we have hqt + + + align:start position:0% +gluons so for the heavy cork we have hqt +and then there would be higher order + + align:start position:0% +and then there would be higher order + + + align:start position:0% +and then there would be higher order +terms that are 1 over M supressed which + + align:start position:0% +terms that are 1 over M supressed which + + + align:start position:0% +terms that are 1 over M supressed which +are the ones up + + align:start position:0% + + + + align:start position:0% + +there so the question is if we have this + + align:start position:0% +there so the question is if we have this + + + align:start position:0% +there so the question is if we have this +lran what is the mass of a a heavy uh + + align:start position:0% +lran what is the mass of a a heavy uh + + + align:start position:0% +lran what is the mass of a a heavy uh +State like the bmon or the dmon or the D + + align:start position:0% +State like the bmon or the dmon or the D + + + align:start position:0% +State like the bmon or the dmon or the D +star and we can characterize that by + + align:start position:0% +star and we can characterize that by + + + align:start position:0% +star and we can characterize that by +knowing the structure of the L + + align:start position:0% +knowing the structure of the L + + + align:start position:0% +knowing the structure of the L +so first of all what about this term + + align:start position:0% +so first of all what about this term + + + align:start position:0% +so first of all what about this term +with this Lambda bar that term actually + + align:start position:0% +with this Lambda bar that term actually + + + align:start position:0% +with this Lambda bar that term actually +comes from these these parts of the lran + + align:start position:0% +comes from these these parts of the lran + + + align:start position:0% +comes from these these parts of the lran +so if we take these parts of the lran we + + align:start position:0% +so if we take these parts of the lran we + + + align:start position:0% +so if we take these parts of the lran we +can calculate the + + align:start position:0% +can calculate the + + + align:start position:0% +can calculate the +hamiltonian let me call that + + align:start position:0% +hamiltonian let me call that + + + align:start position:0% +hamiltonian let me call that +h0 and the definition of this Lambda bar + + align:start position:0% +h0 and the definition of this Lambda bar + + + align:start position:0% +h0 and the definition of this Lambda bar +is the thing that you + + align:start position:0% + + + + align:start position:0% + +get by taking that hamiltonian and + + align:start position:0% +get by taking that hamiltonian and + + + align:start position:0% +get by taking that hamiltonian and +letting it act on the stage + + align:start position:0% + + + + align:start position:0% + +so you can think that this + + align:start position:0% +so you can think that this + + + align:start position:0% +so you can think that this +is if you like you can think that this + + align:start position:0% +is if you like you can think that this + + + align:start position:0% +is if you like you can think that this +state is just an IG state of the + + align:start position:0% +state is just an IG state of the + + + align:start position:0% +state is just an IG state of the +hamiltonian you get the + + align:start position:0% +hamiltonian you get the + + + align:start position:0% +hamiltonian you get the +energy but since the hamiltonian has no + + align:start position:0% +energy but since the hamiltonian has no + + + align:start position:0% +energy but since the hamiltonian has no +heavy quk mass in it what you're getting + + align:start position:0% +heavy quk mass in it what you're getting + + + align:start position:0% +heavy quk mass in it what you're getting +is some parameter which is traditionally + + align:start position:0% +is some parameter which is traditionally + + + align:start position:0% +is some parameter which is traditionally +called Lambda bar that doesn't have a + + align:start position:0% +called Lambda bar that doesn't have a + + + align:start position:0% +called Lambda bar that doesn't have a +heavy cork mass in + + align:start position:0% +heavy cork mass in + + + align:start position:0% +heavy cork mass in +it and so there's no heavy quk mass in + + align:start position:0% + + + + align:start position:0% + +here so it's independent of + + align:start position:0% +here so it's independent of + + + align:start position:0% +here so it's independent of +mq it's + + align:start position:0% +mq it's + + + align:start position:0% +mq it's +also independent of + + align:start position:0% +also independent of + + + align:start position:0% +also independent of +spin + + align:start position:0% +spin + + + align:start position:0% +spin +so and so B versus B Star and flavor B + + align:start position:0% +so and so B versus B Star and flavor B + + + align:start position:0% +so and so B versus B Star and flavor B +versus + + align:start position:0% +versus + + + align:start position:0% +versus +D so whether it's a b meeson d meeson as + + align:start position:0% +D so whether it's a b meeson d meeson as + + + align:start position:0% +D so whether it's a b meeson d meeson as +long as we're in this limit we're both + + align:start position:0% +long as we're in this limit we're both + + + align:start position:0% +long as we're in this limit we're both +the bottom mass and the charm Mass are + + align:start position:0% +the bottom mass and the charm Mass are + + + align:start position:0% +the bottom mass and the charm Mass are +heavy + + align:start position:0% + + + + align:start position:0% + +if we're thinking of this expansion then + + align:start position:0% +if we're thinking of this expansion then + + + align:start position:0% +if we're thinking of this expansion then +this is a universal thing just + + align:start position:0% +this is a universal thing just + + + align:start position:0% +this is a universal thing just +determined by these + + align:start position:0% +determined by these + + + align:start position:0% +determined by these +Lans it's traditionally called L the bar + + align:start position:0% +Lans it's traditionally called L the bar + + + align:start position:0% +Lans it's traditionally called L the bar +and it's telling you the if you think + + align:start position:0% +and it's telling you the if you think + + + align:start position:0% +and it's telling you the if you think +about this thing as having an order mq + + align:start position:0% +about this thing as having an order mq + + + align:start position:0% +about this thing as having an order mq +piece this is the order mq to the zero + + align:start position:0% +piece this is the order mq to the zero + + + align:start position:0% +piece this is the order mq to the zero +piece so the symmetry of the theory is + + align:start position:0% +piece so the symmetry of the theory is + + + align:start position:0% +piece so the symmetry of the theory is +telling us that this is a universal + + align:start position:0% + + + + align:start position:0% + +constant it does depend + + align:start position:0% +constant it does depend + + + align:start position:0% +constant it does depend +on the the state + + align:start position:0% +on the the state + + + align:start position:0% +on the the state +here and that state though that state + + align:start position:0% +here and that state though that state + + + align:start position:0% +here and that state though that state +could be connected to other states by + + align:start position:0% +could be connected to other states by + + + align:start position:0% +could be connected to other states by +spin Symmetry and flavor + + align:start position:0% +spin Symmetry and flavor + + + align:start position:0% +spin Symmetry and flavor +symmetry there was this quantum number + + align:start position:0% +symmetry there was this quantum number + + + align:start position:0% +symmetry there was this quantum number +we talked about last + + align:start position:0% + + + + align:start position:0% + +time which we called SL for the spin of + + align:start position:0% +time which we called SL for the spin of + + + align:start position:0% +time which we called SL for the spin of +the light degrees of freedom and then Pi + + align:start position:0% +the light degrees of freedom and then Pi + + + align:start position:0% +the light degrees of freedom and then Pi +for the parity of the light degrees of + + align:start position:0% +for the parity of the light degrees of + + + align:start position:0% +for the parity of the light degrees of +fre + + align:start position:0% + + + + align:start position:0% + +Freedom so it's the same within every + + align:start position:0% +Freedom so it's the same within every + + + align:start position:0% +Freedom so it's the same within every +multiplet that we get from a fixed SL + + align:start position:0% +multiplet that we get from a fixed SL + + + align:start position:0% +multiplet that we get from a fixed SL +Pi but there's a different value for + + align:start position:0% +Pi but there's a different value for + + + align:start position:0% +Pi but there's a different value for +each + + align:start position:0% + + + + align:start position:0% + +multipet so you'd have a different value + + align:start position:0% +multipet so you'd have a different value + + + align:start position:0% +multipet so you'd have a different value +of Lambda bar for the b d b star B then + + align:start position:0% +of Lambda bar for the b d b star B then + + + align:start position:0% +of Lambda bar for the b d b star B then +for the Lambda B and the Lambda C for + + align:start position:0% + + + + align:start position:0% + +example so that's this term we can also + + align:start position:0% +example so that's this term we can also + + + align:start position:0% +example so that's this term we can also +characterize what's going on with this + + align:start position:0% +characterize what's going on with this + + + align:start position:0% +characterize what's going on with this +term by using this lran here the + + align:start position:0% + + + + align:start position:0% + +L1 so at order 1 over mq we can figure + + align:start position:0% +L1 so at order 1 over mq we can figure + + + align:start position:0% +L1 so at order 1 over mq we can figure +out what kind of contributions to the + + align:start position:0% +out what kind of contributions to the + + + align:start position:0% +out what kind of contributions to the +mass we're + + align:start position:0% +mass we're + + + align:start position:0% +mass we're +getting H1 is just minus L1 you can + + align:start position:0% +getting H1 is just minus L1 you can + + + align:start position:0% +getting H1 is just minus L1 you can +think of it now perturbatively so that + + align:start position:0% +think of it now perturbatively so that + + + align:start position:0% +think of it now perturbatively so that +just Clips the sign of what we had + + align:start position:0% +just Clips the sign of what we had + + + align:start position:0% +just Clips the sign of what we had +before + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +and we get two parameters from taking + + align:start position:0% +and we get two parameters from taking + + + align:start position:0% +and we get two parameters from taking +Matrix elements + + align:start position:0% +Matrix elements + + + align:start position:0% +Matrix elements +here they get the following + + align:start position:0% + + + + align:start position:0% + +names and let me just do everything here + + align:start position:0% +names and let me just do everything here + + + align:start position:0% +names and let me just do everything here +in terms + + align:start position:0% +in terms + + + align:start position:0% +in terms +of it's not too it's not totally crucial + + align:start position:0% +of it's not too it's not totally crucial + + + align:start position:0% +of it's not too it's not totally crucial +but I'm going to + + align:start position:0% +but I'm going to + + + align:start position:0% +but I'm going to +it's a little easier to interpret + + align:start position:0% +it's a little easier to interpret + + + align:start position:0% +it's a little easier to interpret +certain things if we work in the rest + + align:start position:0% +certain things if we work in the rest + + + align:start position:0% +certain things if we work in the rest +frame so I'll just work in the rest + + align:start position:0% +frame so I'll just work in the rest + + + align:start position:0% +frame so I'll just work in the rest +frame so if you work in the rest frame + + align:start position:0% +frame so if you work in the rest frame + + + align:start position:0% +frame so if you work in the rest frame +you should just think of this as like + + align:start position:0% +you should just think of this as like + + + align:start position:0% +you should just think of this as like +giving some kind of measure of the + + align:start position:0% +giving some kind of measure of the + + + align:start position:0% +giving some kind of measure of the +kinetic energy that the the heavy cork + + align:start position:0% +kinetic energy that the the heavy cork + + + align:start position:0% +kinetic energy that the the heavy cork +gets wiggled by and that's called Lambda + + align:start position:0% +gets wiggled by and that's called Lambda + + + align:start position:0% +gets wiggled by and that's called Lambda +one this again is a matrix element that + + align:start position:0% +one this again is a matrix element that + + + align:start position:0% +one this again is a matrix element that +doesn't know about the heavy Quark mass + + align:start position:0% +doesn't know about the heavy Quark mass + + + align:start position:0% +doesn't know about the heavy Quark mass +and the heavy quk mass is an explicit mq + + align:start position:0% +and the heavy quk mass is an explicit mq + + + align:start position:0% +and the heavy quk mass is an explicit mq +so this guy has Dimension two if you + + align:start position:0% +so this guy has Dimension two if you + + + align:start position:0% +so this guy has Dimension two if you +work out the dimensions + + align:start position:0% + + + + align:start position:0% + +and then you can do the same for the + + align:start position:0% +and then you can do the same for the + + + align:start position:0% +and then you can do the same for the +other operator and here they have to + + align:start position:0% +other operator and here they have to + + + align:start position:0% +other operator and here they have to +think a little bit + + align:start position:0% +think a little bit + + + align:start position:0% +think a little bit +harder and if you think a little bit + + align:start position:0% +harder and if you think a little bit + + + align:start position:0% +harder and if you think a little bit +harder you can characterize how the co + + align:start position:0% +harder you can characterize how the co + + + align:start position:0% +harder you can characterize how the co +what the coefficients are for different + + align:start position:0% +what the coefficients are for different + + + align:start position:0% +what the coefficients are for different +spins so there's some Wilson + + align:start position:0% + + + + align:start position:0% + +coefficient and then we have this + + align:start position:0% +coefficient and then we have this + + + align:start position:0% +coefficient and then we have this +operator + + align:start position:0% + + + + align:start position:0% + +and this here is like sigma. + + align:start position:0% +and this here is like sigma. + + + align:start position:0% +and this here is like sigma. +B I told you that before and so you + + align:start position:0% +B I told you that before and so you + + + align:start position:0% +B I told you that before and so you +should think of what's going on here is + + align:start position:0% +should think of what's going on here is + + + align:start position:0% +should think of what's going on here is +you have Sigma which is giving the SQ + + align:start position:0% +you have Sigma which is giving the SQ + + + align:start position:0% +you have Sigma which is giving the SQ +and then you have a b field and then + + align:start position:0% +and then you have a b field and then + + + align:start position:0% +and then you have a b field and then +it's a question of what uh Vector could + + align:start position:0% +it's a question of what uh Vector could + + + align:start position:0% +it's a question of what uh Vector could +be left over that the B field can know + + align:start position:0% +be left over that the B field can know + + + align:start position:0% +be left over that the B field can know +about it's basically + + align:start position:0% +about it's basically + + + align:start position:0% +about it's basically +SL so + + align:start position:0% +SL so + + + align:start position:0% +SL so +this guy here is leading to the + + align:start position:0% +this guy here is leading to the + + + align:start position:0% +this guy here is leading to the +SQ and this guy here is leading to the + + align:start position:0% + + + + align:start position:0% + +SL and so that's where this SQ dosl + + align:start position:0% +SL and so that's where this SQ dosl + + + align:start position:0% +SL and so that's where this SQ dosl +comes + + align:start position:0% + + + + align:start position:0% + +from so you can think about other + + align:start position:0% +from so you can think about other + + + align:start position:0% +from so you can think about other +possibilities but you have to have the + + align:start position:0% +possibilities but you have to have the + + + align:start position:0% +possibilities but you have to have the +right symmetry structure under time + + align:start position:0% +right symmetry structure under time + + + align:start position:0% +right symmetry structure under time +reversal and parity and things like that + + align:start position:0% +reversal and parity and things like that + + + align:start position:0% +reversal and parity and things like that +and that forces you to use a spin here + + align:start position:0% +and that forces you to use a spin here + + + align:start position:0% +and that forces you to use a spin here +for the B and not something like the V + + align:start position:0% +for the B and not something like the V + + + align:start position:0% +for the B and not something like the V +so this SQ dosl is something that you + + align:start position:0% +so this SQ dosl is something that you + + + align:start position:0% +so this SQ dosl is something that you +can write out as remembering the + + align:start position:0% +can write out as remembering the + + + align:start position:0% +can write out as remembering the +definition of it and its relation to j + + align:start position:0% +definition of it and its relation to j + + + align:start position:0% +definition of it and its relation to j +s you can write out that factor like + + align:start position:0% +s you can write out that factor like + + + align:start position:0% +s you can write out that factor like +that and then we can derive here how + + align:start position:0% +that and then we can derive here how + + + align:start position:0% +that and then we can derive here how +this Lambda 2 contributes to the + + align:start position:0% +this Lambda 2 contributes to the + + + align:start position:0% +this Lambda 2 contributes to the +different states because we have a + + align:start position:0% +different states because we have a + + + align:start position:0% +different states because we have a +different contribution from for the B + + align:start position:0% +different contribution from for the B + + + align:start position:0% +different contribution from for the B +and the B star from the Lambda 2 guy + + align:start position:0% +and the B star from the Lambda 2 guy + + + align:start position:0% +and the B star from the Lambda 2 guy +because it was violating the spin + + align:start position:0% +because it was violating the spin + + + align:start position:0% +because it was violating the spin +symmetry + + align:start position:0% +symmetry + + + align:start position:0% +symmetry +so the lambo one guy is going to violate + + align:start position:0% +so the lambo one guy is going to violate + + + align:start position:0% +so the lambo one guy is going to violate +the flavor symmetry that's this one over + + align:start position:0% +the flavor symmetry that's this one over + + + align:start position:0% +the flavor symmetry that's this one over +mq and so charm quarks charm mesons and + + align:start position:0% +mq and so charm quarks charm mesons and + + + align:start position:0% +mq and so charm quarks charm mesons and +bottom mesons will get different + + align:start position:0% +bottom mesons will get different + + + align:start position:0% +bottom mesons will get different +contributions from that they have the + + align:start position:0% +contributions from that they have the + + + align:start position:0% +contributions from that they have the +same Lambda + + align:start position:0% +same Lambda + + + align:start position:0% +same Lambda +one but they have a different correction + + align:start position:0% +one but they have a different correction + + + align:start position:0% +one but they have a different correction +because it gets suppressed by a + + align:start position:0% +because it gets suppressed by a + + + align:start position:0% +because it gets suppressed by a +different + + align:start position:0% +different + + + align:start position:0% +different +factor and then again for the Lambda + + align:start position:0% + + + + align:start position:0% + +2 Lambda 2 is a little bit different + + align:start position:0% +2 Lambda 2 is a little bit different + + + align:start position:0% +2 Lambda 2 is a little bit different +because it actually has M dependence + + align:start position:0% + + + + align:start position:0% + +I didn't say that quite right + + align:start position:0% +I didn't say that quite right + + + align:start position:0% +I didn't say that quite right +so it actually has mq dependence because + + align:start position:0% +so it actually has mq dependence because + + + align:start position:0% +so it actually has mq dependence because +the coefficient here has mu dependence + + align:start position:0% +the coefficient here has mu dependence + + + align:start position:0% +the coefficient here has mu dependence +so this operator doesn't have any mq + + align:start position:0% +so this operator doesn't have any mq + + + align:start position:0% +so this operator doesn't have any mq +dependence but the coefficient does + + align:start position:0% +dependence but the coefficient does + + + align:start position:0% +dependence but the coefficient does +remember the MU dependence cancels and + + align:start position:0% +remember the MU dependence cancels and + + + align:start position:0% +remember the MU dependence cancels and +there's a leftover mq dependence to the + + align:start position:0% +there's a leftover mq dependence to the + + + align:start position:0% +there's a leftover mq dependence to the +Lambda 2 but it's logarithmic mq + + align:start position:0% + + + + align:start position:0% + +dependence if I Define it this way + + align:start position:0% +dependence if I Define it this way + + + align:start position:0% +dependence if I Define it this way +so that's why I wrote mq + + align:start position:0% + + + + align:start position:0% + +there so you could as we talked about + + align:start position:0% +there so you could as we talked about + + + align:start position:0% +there so you could as we talked about +last time you could sum up the logs the + + align:start position:0% +last time you could sum up the logs the + + + align:start position:0% +last time you could sum up the logs the +large logs and have this gu you could + + align:start position:0% +large logs and have this gu you could + + + align:start position:0% +large logs and have this gu you could +resum logs if you want so you could + + align:start position:0% +resum logs if you want so you could + + + align:start position:0% +resum logs if you want so you could +think of these as even resum logs inside + + align:start position:0% +think of these as even resum logs inside + + + align:start position:0% +think of these as even resum logs inside +this Lambda + + align:start position:0% + + + + align:start position:0% + +2 so if we ignore those logs where we + + align:start position:0% +2 so if we ignore those logs where we + + + align:start position:0% +2 so if we ignore those logs where we +imagine that we resum them and we just + + align:start position:0% +imagine that we resum them and we just + + + align:start position:0% +imagine that we resum them and we just +look at the remainder then we have + + align:start position:0% +look at the remainder then we have + + + align:start position:0% +look at the remainder then we have +expectations based on power counting for + + align:start position:0% +expectations based on power counting for + + + align:start position:0% +expectations based on power counting for +how big these things + + align:start position:0% +how big these things + + + align:start position:0% +how big these things +are and we just expect that they're both + + align:start position:0% +are and we just expect that they're both + + + align:start position:0% +are and we just expect that they're both +given by the dimension and the only + + align:start position:0% +given by the dimension and the only + + + align:start position:0% +given by the dimension and the only +dimensionful parameter around is Lambda + + align:start position:0% +dimensionful parameter around is Lambda + + + align:start position:0% +dimensionful parameter around is Lambda +qcd because the mqs can only occur in + + align:start position:0% +qcd because the mqs can only occur in + + + align:start position:0% +qcd because the mqs can only occur in +logarithms in the Wilson coefficient and + + align:start position:0% +logarithms in the Wilson coefficient and + + + align:start position:0% +logarithms in the Wilson coefficient and +nowhere + + align:start position:0% +nowhere + + + align:start position:0% +nowhere +else and these + + align:start position:0% +else and these + + + align:start position:0% +else and these +are non-perturbative + + align:start position:0% + + + + align:start position:0% + +parameters Lambda one Lambda bar is also + + align:start position:0% +parameters Lambda one Lambda bar is also + + + align:start position:0% +parameters Lambda one Lambda bar is also +perative + + align:start position:0% +perative + + + align:start position:0% +perative +parameter these ones have a little more + + align:start position:0% +parameter these ones have a little more + + + align:start position:0% +parameter these ones have a little more +Dynamics in + + align:start position:0% +Dynamics in + + + align:start position:0% +Dynamics in +them so then we could go out and write + + align:start position:0% +them so then we could go out and write + + + align:start position:0% +them so then we could go out and write +for our states the results by putting + + align:start position:0% +for our states the results by putting + + + align:start position:0% +for our states the results by putting +these things together so we'd have m + + align:start position:0% +these things together so we'd have m + + + align:start position:0% +these things together so we'd have m +capital B is M little B plus Lambda + + align:start position:0% +capital B is M little B plus Lambda + + + align:start position:0% +capital B is M little B plus Lambda +bar Lambda 1/ 2 m little B and if we go + + align:start position:0% +bar Lambda 1/ 2 m little B and if we go + + + align:start position:0% +bar Lambda 1/ 2 m little B and if we go +through the spin structure there we get + + align:start position:0% +through the spin structure there we get + + + align:start position:0% +through the spin structure there we get +a three + + align:start position:0% +a three + + + align:start position:0% +a three +halves and then Lambda 2 + + align:start position:0% +halves and then Lambda 2 + + + align:start position:0% +halves and then Lambda 2 +logarithmic MB dependence over + + align:start position:0% + + + + align:start position:0% + +MB so when we start with the F star the + + align:start position:0% +MB so when we start with the F star the + + + align:start position:0% +MB so when we start with the F star the +first three terms are the same and then + + align:start position:0% +first three terms are the same and then + + + align:start position:0% +first three terms are the same and then +this guy comes in with a + + align:start position:0% +this guy comes in with a + + + align:start position:0% +this guy comes in with a +plus and it's Lambda 2 + + align:start position:0% +plus and it's Lambda 2 + + + align:start position:0% +plus and it's Lambda 2 +MB over 2 + + align:start position:0% + + + + align:start position:0% + +MB and then the D + + align:start position:0% +MB and then the D + + + align:start position:0% +MB and then the D +states are similar + + align:start position:0% +states are similar + + + align:start position:0% +states are similar +M + + align:start position:0% +M + + + align:start position:0% +M +charm Lambda + + align:start position:0% +charm Lambda + + + align:start position:0% +charm Lambda +bar Lambda 1 over 2m + + align:start position:0% + + + + align:start position:0% + +charm and then these two terms + + align:start position:0% +charm and then these two terms + + + align:start position:0% +charm and then these two terms +again same spins so it's Lambda 2 and + + align:start position:0% +again same spins so it's Lambda 2 and + + + align:start position:0% +again same spins so it's Lambda 2 and +the only difference is now we're + + align:start position:0% +the only difference is now we're + + + align:start position:0% +the only difference is now we're +evaluating the Lambda 2 as logarithm + + align:start position:0% +evaluating the Lambda 2 as logarithm + + + align:start position:0% +evaluating the Lambda 2 as logarithm +charm + + align:start position:0% + + + + align:start position:0% + +dependence okay so there's some formulas + + align:start position:0% +dependence okay so there's some formulas + + + align:start position:0% +dependence okay so there's some formulas +that are correct actually including all + + align:start position:0% +that are correct actually including all + + + align:start position:0% +that are correct actually including all +the way up to 1 over M Corrections and + + align:start position:0% +the way up to 1 over M Corrections and + + + align:start position:0% +the way up to 1 over M Corrections and +you can see that there's still sort of a + + align:start position:0% +you can see that there's still sort of a + + + align:start position:0% +you can see that there's still sort of a +structure to these things this is a + + align:start position:0% +structure to these things this is a + + + align:start position:0% +structure to these things this is a +universal correction for all of them + + align:start position:0% +universal correction for all of them + + + align:start position:0% +universal correction for all of them +these Corrections are Universal between + + align:start position:0% +these Corrections are Universal between + + + align:start position:0% +these Corrections are Universal between +B and B Star and so the splitting + + align:start position:0% +B and B Star and so the splitting + + + align:start position:0% +B and B Star and so the splitting +between B and B Star is just given by + + align:start position:0% +between B and B Star is just given by + + + align:start position:0% +between B and B Star is just given by +this Lambda + + align:start position:0% +this Lambda + + + align:start position:0% +this Lambda +2 that's what causes the states to split + + align:start position:0% +2 that's what causes the states to split + + + align:start position:0% +2 that's what causes the states to split +so up to that level they're the same and + + align:start position:0% +so up to that level they're the same and + + + align:start position:0% +so up to that level they're the same and +that's why the B and B Star are very + + align:start position:0% +that's why the B and B Star are very + + + align:start position:0% +that's why the B and B Star are very +degenerate and the masses are very + + align:start position:0% +degenerate and the masses are very + + + align:start position:0% +degenerate and the masses are very +close so so you can form combinations to + + align:start position:0% +close so so you can form combinations to + + + align:start position:0% +close so so you can form combinations to +cancel things + + align:start position:0% +cancel things + + + align:start position:0% +cancel things +out so you can take a kind of spin + + align:start position:0% +out so you can take a kind of spin + + + align:start position:0% +out so you can take a kind of spin +averaged Mass where you take three * the + + align:start position:0% +averaged Mass where you take three * the + + + align:start position:0% +averaged Mass where you take three * the +vector plus the + + align:start position:0% +vector plus the + + + align:start position:0% +vector plus the +scalar IDE by four and if you do that + + align:start position:0% +scalar IDE by four and if you do that + + + align:start position:0% +scalar IDE by four and if you do that +then you're canceling out the Lambda + + align:start position:0% + + + + align:start position:0% + +2 and then you can also form differences + + align:start position:0% +2 and then you can also form differences + + + align:start position:0% +2 and then you can also form differences +so if you looked at MB star squ minus MB + + align:start position:0% +so if you looked at MB star squ minus MB + + + align:start position:0% +so if you looked at MB star squ minus MB +^2 then the only thing that's causing a + + align:start position:0% +^2 then the only thing that's causing a + + + align:start position:0% +^2 then the only thing that's causing a +difference + + align:start position:0% +difference + + + align:start position:0% +difference +is Lambda + + align:start position:0% +is Lambda + + + align:start position:0% +is Lambda +2 numerically this is 49 gv^ + + align:start position:0% +2 numerically this is 49 gv^ + + + align:start position:0% +2 numerically this is 49 gv^ +2 and from our formula up there it's 4 + + align:start position:0% +2 and from our formula up there it's 4 + + + align:start position:0% +2 and from our formula up there it's 4 +Lambda 2 of + + align:start position:0% +Lambda 2 of + + + align:start position:0% +Lambda 2 of +MB + + align:start position:0% +MB + + + align:start position:0% +MB +so something like four + + align:start position:0% +so something like four + + + align:start position:0% +so something like four +time12 GB ^2 + + align:start position:0% + + + + align:start position:0% + +so that's the value of this Lambda 2 is + + align:start position:0% +so that's the value of this Lambda 2 is + + + align:start position:0% +so that's the value of this Lambda 2 is +0.12g + + align:start position:0% +0.12g + + + align:start position:0% +0.12g +v^2 which is about Lambda qcd s so our + + align:start position:0% +v^2 which is about Lambda qcd s so our + + + align:start position:0% +v^2 which is about Lambda qcd s so our +dimensional analysis is + + align:start position:0% +dimensional analysis is + + + align:start position:0% +dimensional analysis is +working and then you can do the same + + align:start position:0% +working and then you can do the same + + + align:start position:0% +working and then you can do the same +thing for the + + align:start position:0% + + + + align:start position:0% + +dmon everything here Works beautifully + + align:start position:0% + + + + align:start position:0% + +actually oops + + align:start position:0% + + + + align:start position:0% + +extract the value of Lambda 2 and you + + align:start position:0% +extract the value of Lambda 2 and you + + + align:start position:0% +extract the value of Lambda 2 and you +see there's a slight + + align:start position:0% + + + + align:start position:0% + +difference because that difference can + + align:start position:0% +difference because that difference can + + + align:start position:0% +difference because that difference can +be attributed to the + + align:start position:0% +be attributed to the + + + align:start position:0% +be attributed to the +[Applause] + + align:start position:0% + + + + align:start position:0% + +logarithms so if you take Lambda 2 MB + + align:start position:0% +logarithms so if you take Lambda 2 MB + + + align:start position:0% +logarithms so if you take Lambda 2 MB +over + + align:start position:0% +over + + + align:start position:0% +over +Lambda 2 MC then the only thing that + + align:start position:0% +Lambda 2 MC then the only thing that + + + align:start position:0% +Lambda 2 MC then the only thing that +differs is the Wilson coefficient so + + align:start position:0% +differs is the Wilson coefficient so + + + align:start position:0% +differs is the Wilson coefficient so +that's something you can + + align:start position:0% +that's something you can + + + align:start position:0% +that's something you can +predict so + + align:start position:0% + + + + align:start position:0% + +experimentally if you take the ratio of + + align:start position:0% +experimentally if you take the ratio of + + + align:start position:0% +experimentally if you take the ratio of +those two things there you get a + + align:start position:0% +those two things there you get a + + + align:start position:0% +those two things there you get a +prediction like this + + align:start position:0% +prediction like this + + + align:start position:0% +prediction like this +one and if you plug in theory like + + align:start position:0% +one and if you plug in theory like + + + align:start position:0% +one and if you plug in theory like +leading log + + align:start position:0% +leading log + + + align:start position:0% +leading log +rge and you're getting alpha s of + + align:start position:0% +rge and you're getting alpha s of + + + align:start position:0% +rge and you're getting alpha s of +MB oh sorry try the + + align:start position:0% + + + + align:start position:0% + +numerator and this is + + align:start position:0% + + + + align:start position:0% + +1.17 so for that's for three Light + + align:start position:0% +1.17 so for that's for three Light + + + align:start position:0% +1.17 so for that's for three Light +Flavors which is the right thing to do + + align:start position:0% +Flavors which is the right thing to do + + + align:start position:0% +Flavors which is the right thing to do +for the beta function so it's not so + + align:start position:0% +for the beta function so it's not so + + + align:start position:0% +for the beta function so it's not so +bad for a leading log prediction that's + + align:start position:0% +bad for a leading log prediction that's + + + align:start position:0% +bad for a leading log prediction that's +kind of the accuracy you would + + align:start position:0% + + + + align:start position:0% + +expect all right so we're really + + align:start position:0% +expect all right so we're really + + + align:start position:0% +expect all right so we're really +understanding quite a bit from our + + align:start position:0% +understanding quite a bit from our + + + align:start position:0% +understanding quite a bit from our +construction of this effective theory + + align:start position:0% +construction of this effective theory + + + align:start position:0% +construction of this effective theory +about the states and even make + + align:start position:0% +about the states and even make + + + align:start position:0% +about the states and even make +predictions for the ratios of the MTH + + align:start position:0% +predictions for the ratios of the MTH + + + align:start position:0% +predictions for the ratios of the MTH +this divided by that is something + + align:start position:0% +this divided by that is something + + + align:start position:0% +this divided by that is something +perturbative which is I kind of + + align:start position:0% +perturbative which is I kind of + + + align:start position:0% +perturbative which is I kind of +non-trivial perturbative up to the order + + align:start position:0% +non-trivial perturbative up to the order + + + align:start position:0% +non-trivial perturbative up to the order +we were working there would be + + align:start position:0% +we were working there would be + + + align:start position:0% +we were working there would be +Corrections if we continued in our + + align:start position:0% +Corrections if we continued in our + + + align:start position:0% +Corrections if we continued in our +series here there could be some + + align:start position:0% +series here there could be some + + + align:start position:0% +series here there could be some +non-perturbative corrections but up to 1 + + align:start position:0% +non-perturbative corrections but up to 1 + + + align:start position:0% +non-perturbative corrections but up to 1 +over M the ratio of this to that which + + align:start position:0% +over M the ratio of this to that which + + + align:start position:0% +over M the ratio of this to that which +is what I wrote over there is + + align:start position:0% + + + + align:start position:0% + +perturbative all + + align:start position:0% +perturbative all + + + align:start position:0% +perturbative all +right so that's some phenomenology it's + + align:start position:0% +right so that's some phenomenology it's + + + align:start position:0% +right so that's some phenomenology it's +kind of Baseline phenomenology that we + + align:start position:0% +kind of Baseline phenomenology that we + + + align:start position:0% +kind of Baseline phenomenology that we +can do with the + + align:start position:0% +can do with the + + + align:start position:0% +can do with the +hamiltonian uh or with or Hamilton + + align:start position:0% +hamiltonian uh or with or Hamilton + + + align:start position:0% +hamiltonian uh or with or Hamilton +derived from our subleading + + align:start position:0% +derived from our subleading + + + align:start position:0% +derived from our subleading +lran there's other phenomenology that we + + align:start position:0% +lran there's other phenomenology that we + + + align:start position:0% +lran there's other phenomenology that we +can + + align:start position:0% +can + + + align:start position:0% +can +do and I'll mention some of the most + + align:start position:0% +do and I'll mention some of the most + + + align:start position:0% +do and I'll mention some of the most +important + + align:start position:0% + + + + align:start position:0% + +phenomenology there's another class of + + align:start position:0% +phenomenology there's another class of + + + align:start position:0% +phenomenology there's another class of +predictions that we can make where we + + align:start position:0% +predictions that we can make where we + + + align:start position:0% +predictions that we can make where we +have a lot of predictive power by using + + align:start position:0% +have a lot of predictive power by using + + + align:start position:0% +have a lot of predictive power by using +the effective Theory and I want to talk + + align:start position:0% +the effective Theory and I want to talk + + + align:start position:0% +the effective Theory and I want to talk +a little bit about that + + align:start position:0% + + + + align:start position:0% + +so you can look at semileptonic decays + + align:start position:0% +so you can look at semileptonic decays + + + align:start position:0% +so you can look at semileptonic decays +and there's two different types of + + align:start position:0% +and there's two different types of + + + align:start position:0% +and there's two different types of +semile leptonic decays that you can look + + align:start position:0% +semile leptonic decays that you can look + + + align:start position:0% +semile leptonic decays that you can look +at so-called exclusive decays and + + align:start position:0% +at so-called exclusive decays and + + + align:start position:0% +at so-called exclusive decays and +inclusive decays so exclusive is making + + align:start position:0% +inclusive decays so exclusive is making + + + align:start position:0% +inclusive decays so exclusive is making +transitions between the meeson states + + align:start position:0% +transitions between the meeson states + + + align:start position:0% +transitions between the meeson states +and inclusive is making a transition + + align:start position:0% +and inclusive is making a transition + + + align:start position:0% +and inclusive is making a transition +where you allow any charm State not just + + align:start position:0% +where you allow any charm State not just + + + align:start position:0% +where you allow any charm State not just +the lowest order ground state charm but + + align:start position:0% +the lowest order ground state charm but + + + align:start position:0% +the lowest order ground state charm but +you could have you could have in this + + align:start position:0% +you could have you could have in this + + + align:start position:0% +you could have you could have in this +state here XC you could have a D Pi or a + + align:start position:0% +state here XC you could have a D Pi or a + + + align:start position:0% +state here XC you could have a D Pi or a +d star Pi Pi or other things like that + + align:start position:0% +d star Pi Pi or other things like that + + + align:start position:0% +d star Pi Pi or other things like that +so it doesn't even have to be a single + + align:start position:0% +so it doesn't even have to be a single + + + align:start position:0% +so it doesn't even have to be a single +hadron + + align:start position:0% +hadron + + + align:start position:0% +hadron +state so exclusive refers to a + + align:start position:0% +state so exclusive refers to a + + + align:start position:0% +state so exclusive refers to a +particular Channel inclusive refers to a + + align:start position:0% +particular Channel inclusive refers to a + + + align:start position:0% +particular Channel inclusive refers to a +some overall + + align:start position:0% +some overall + + + align:start position:0% +some overall +channels so the theory between the in + + align:start position:0% +channels so the theory between the in + + + align:start position:0% +channels so the theory between the in +these two is quite different in this one + + align:start position:0% +these two is quite different in this one + + + align:start position:0% +these two is quite different in this one +you would have form + + align:start position:0% + + + + align:start position:0% + +factors for the current between the + + align:start position:0% +factors for the current between the + + + align:start position:0% +factors for the current between the +states and I already mentioned to you + + align:start position:0% +states and I already mentioned to you + + + align:start position:0% +states and I already mentioned to you +that heavy cork symmetry reduces the + + align:start position:0% +that heavy cork symmetry reduces the + + + align:start position:0% +that heavy cork symmetry reduces the +number of form factors you get the + + align:start position:0% +number of form factors you get the + + + align:start position:0% +number of form factors you get the +single is wise function + + align:start position:0% +single is wise function + + + align:start position:0% +single is wise function +and so heavy cork symmetry is very + + align:start position:0% +and so heavy cork symmetry is very + + + align:start position:0% +and so heavy cork symmetry is very +powerful + + align:start position:0% +powerful + + + align:start position:0% +powerful +here and you can actually also work out + + align:start position:0% +here and you can actually also work out + + + align:start position:0% +here and you can actually also work out +one of mq + + align:start position:0% +one of mq + + + align:start position:0% +one of mq +Corrections and people have done that + + align:start position:0% +Corrections and people have done that + + + align:start position:0% +Corrections and people have done that +and it turns out there aren't any so + + align:start position:0% +and it turns out there aren't any so + + + align:start position:0% +and it turns out there aren't any so +there's something called Luke's theorem + + align:start position:0% +there's something called Luke's theorem + + + align:start position:0% +there's something called Luke's theorem +which actually was a result derived I + + align:start position:0% +which actually was a result derived I + + + align:start position:0% +which actually was a result derived I +think when Luke was a graduate + + align:start position:0% +think when Luke was a graduate + + + align:start position:0% +think when Luke was a graduate +student that prove there was no one over + + align:start position:0% +student that prove there was no one over + + + align:start position:0% +student that prove there was no one over +mq Corrections + + align:start position:0% +mq Corrections + + + align:start position:0% +mq Corrections +here and then you can work out alpha s + + align:start position:0% +here and then you can work out alpha s + + + align:start position:0% +here and then you can work out alpha s +Corrections and so this this kind of you + + align:start position:0% +Corrections and so this this kind of you + + + align:start position:0% +Corrections and so this this kind of you +can just keep going people have worked + + align:start position:0% +can just keep going people have worked + + + align:start position:0% +can just keep going people have worked +out one of q s Corrections and this kind + + align:start position:0% +out one of q s Corrections and this kind + + + align:start position:0% +out one of q s Corrections and this kind +of formalism is used to measure VCB + + align:start position:0% +of formalism is used to measure VCB + + + align:start position:0% +of formalism is used to measure VCB +because these Decay rates would depend + + align:start position:0% +because these Decay rates would depend + + + align:start position:0% +because these Decay rates would depend +on VCB and that's kind of what you're + + align:start position:0% +on VCB and that's kind of what you're + + + align:start position:0% +on VCB and that's kind of what you're +after if you're doing this so you'd like + + align:start position:0% +after if you're doing this so you'd like + + + align:start position:0% +after if you're doing this so you'd like +to parameterize and figure out the the + + align:start position:0% +to parameterize and figure out the the + + + align:start position:0% +to parameterize and figure out the the +hydronic physics as much as possible and + + align:start position:0% +hydronic physics as much as possible and + + + align:start position:0% +hydronic physics as much as possible and +Aid the experiments in getting VCB and + + align:start position:0% +Aid the experiments in getting VCB and + + + align:start position:0% +Aid the experiments in getting VCB and +exactly this framework is used people + + align:start position:0% +exactly this framework is used people + + + align:start position:0% +exactly this framework is used people +nowadays what they do is the 1 over M + + align:start position:0% +nowadays what they do is the 1 over M + + + align:start position:0% +nowadays what they do is the 1 over M +q^2 Corrections need to be computed on + + align:start position:0% +q^2 Corrections need to be computed on + + + align:start position:0% +q^2 Corrections need to be computed on +on the lattice so latus qcd computes + + align:start position:0% +on the lattice so latus qcd computes + + + align:start position:0% +on the lattice so latus qcd computes +those Corrections the perturbative + + align:start position:0% +those Corrections the perturbative + + + align:start position:0% +those Corrections the perturbative +corrections need to be computed by + + align:start position:0% +corrections need to be computed by + + + align:start position:0% +corrections need to be computed by +Continuum people like me so those are + + align:start position:0% +Continuum people like me so those are + + + align:start position:0% +Continuum people like me so those are +computed and they put these things + + align:start position:0% +computed and they put these things + + + align:start position:0% +computed and they put these things +together to get VCB from these + + align:start position:0% +together to get VCB from these + + + align:start position:0% +together to get VCB from these +decays you could also do it with this + + align:start position:0% +decays you could also do it with this + + + align:start position:0% +decays you could also do it with this +inclusive + + align:start position:0% +inclusive + + + align:start position:0% +inclusive +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +guy and here it's more interesting + + align:start position:0% +guy and here it's more interesting + + + align:start position:0% +guy and here it's more interesting +because you can basically do everything + + align:start position:0% +because you can basically do everything + + + align:start position:0% +because you can basically do everything +with pen and + + align:start position:0% +with pen and + + + align:start position:0% +with pen and +paper so here you can use an operator + + align:start position:0% +paper so here you can use an operator + + + align:start position:0% +paper so here you can use an operator +product expansion + + align:start position:0% + + + + align:start position:0% + +op and actually + + align:start position:0% +op and actually + + + align:start position:0% +op and actually +HQ constrains the form of the operator + + align:start position:0% +HQ constrains the form of the operator + + + align:start position:0% +HQ constrains the form of the operator +product expansion as + + align:start position:0% + + + + align:start position:0% + +well and indeed when you work out the + + align:start position:0% +well and indeed when you work out the + + + align:start position:0% +well and indeed when you work out the +leading power Corrections + + align:start position:0% + + + + align:start position:0% + +they turn out to not + + align:start position:0% +they turn out to not + + + align:start position:0% +they turn out to not +enter until two orders down so again + + align:start position:0% +enter until two orders down so again + + + align:start position:0% +enter until two orders down so again +there's you're protected from first + + align:start position:0% +there's you're protected from first + + + align:start position:0% +there's you're protected from first +order Corrections and you just get + + align:start position:0% +order Corrections and you just get + + + align:start position:0% +order Corrections and you just get +Corrections that occur at 1/ NQ + + align:start position:0% +Corrections that occur at 1/ NQ + + + align:start position:0% +Corrections that occur at 1/ NQ +^2 and furthermore they depend only on + + align:start position:0% +^2 and furthermore they depend only on + + + align:start position:0% +^2 and furthermore they depend only on +the two parameters we already + + align:start position:0% + + + + align:start position:0% + +defined so it's not like you even get + + align:start position:0% +defined so it's not like you even get + + + align:start position:0% +defined so it's not like you even get +any new non-perturbative Matrix elements + + align:start position:0% +any new non-perturbative Matrix elements + + + align:start position:0% +any new non-perturbative Matrix elements +you just get the two we were talking + + align:start position:0% +you just get the two we were talking + + + align:start position:0% +you just get the two we were talking +over here with the + + align:start position:0% +over here with the + + + align:start position:0% +over here with the +masses okay okay so there's peration + + align:start position:0% +masses okay okay so there's peration + + + align:start position:0% +masses okay okay so there's peration +Corrections and there's power + + align:start position:0% +Corrections and there's power + + + align:start position:0% +Corrections and there's power +corrections but you're actually not even + + align:start position:0% +corrections but you're actually not even + + + align:start position:0% +corrections but you're actually not even +getting any new information relative to + + align:start position:0% +getting any new information relative to + + + align:start position:0% +getting any new information relative to +the + + align:start position:0% +the + + + align:start position:0% +the +masses any new Matrix + + align:start position:0% + + + + align:start position:0% + +elements okay so we'll talk a little bit + + align:start position:0% +elements okay so we'll talk a little bit + + + align:start position:0% +elements okay so we'll talk a little bit +more about this second one with the + + align:start position:0% + + + + align:start position:0% + +op there's a lot of work that's gone + + align:start position:0% +op there's a lot of work that's gone + + + align:start position:0% +op there's a lot of work that's gone +into this one both from the theory side + + align:start position:0% +into this one both from the theory side + + + align:start position:0% +into this one both from the theory side +as well as from + + align:start position:0% + + + + align:start position:0% + +experiment so when you think about the + + align:start position:0% +experiment so when you think about the + + + align:start position:0% +experiment so when you think about the +Decay rate for this bet to x sub c l new + + align:start position:0% +Decay rate for this bet to x sub c l new + + + align:start position:0% +Decay rate for this bet to x sub c l new +bar it's a doubly differential Decay + + align:start position:0% +bar it's a doubly differential Decay + + + align:start position:0% +bar it's a doubly differential Decay +rate in q^2 of the lepton pair so that's + + align:start position:0% +rate in q^2 of the lepton pair so that's + + + align:start position:0% +rate in q^2 of the lepton pair so that's +Q mu e is you can pick as a second + + align:start position:0% +Q mu e is you can pick as a second + + + align:start position:0% +Q mu e is you can pick as a second +variable and then you don't know the + + align:start position:0% +variable and then you don't know the + + + align:start position:0% +variable and then you don't know the +mass of the state x sub c because it + + align:start position:0% +mass of the state x sub c because it + + + align:start position:0% +mass of the state x sub c because it +could be different things it could be a + + align:start position:0% +could be different things it could be a + + + align:start position:0% +could be different things it could be a +d it could be a d star it could be a d + + align:start position:0% +d it could be a d star it could be a d + + + align:start position:0% +d it could be a d star it could be a d +pi + + align:start position:0% + + + + align:start position:0% + +so that's another variable so you have a + + align:start position:0% +so that's another variable so you have a + + + align:start position:0% +so that's another variable so you have a +triple differential spectrum and you can + + align:start position:0% +triple differential spectrum and you can + + + align:start position:0% +triple differential spectrum and you can +compute it with an operator product + + align:start position:0% + + + + align:start position:0% + +expansion I'm not going to go through + + align:start position:0% +expansion I'm not going to go through + + + align:start position:0% +expansion I'm not going to go through +the details of carrying out the operator + + align:start position:0% +the details of carrying out the operator + + + align:start position:0% +the details of carrying out the operator +prodct + + align:start position:0% +prodct + + + align:start position:0% +prodct +expansion if you want to do reading + + align:start position:0% +expansion if you want to do reading + + + align:start position:0% +expansion if you want to do reading +about that there's some supplemental + + align:start position:0% +about that there's some supplemental + + + align:start position:0% +about that there's some supplemental +reading that I haven't assigned to you + + align:start position:0% +reading that I haven't assigned to you + + + align:start position:0% +reading that I haven't assigned to you +where you can read about that in the + + align:start position:0% +where you can read about that in the + + + align:start position:0% +where you can read about that in the +book heavy Quark physics by manahar and + + align:start position:0% + + + + align:start position:0% + +wise so + + align:start position:0% +wise so + + + align:start position:0% +wise so +for our purposes here let's think of + + align:start position:0% +for our purposes here let's think of + + + align:start position:0% +for our purposes here let's think of +what operator product expansion + + align:start position:0% +what operator product expansion + + + align:start position:0% +what operator product expansion +means is simply that we want to carry + + align:start position:0% +means is simply that we want to carry + + + align:start position:0% +means is simply that we want to carry +out an + + align:start position:0% +out an + + + align:start position:0% +out an +expansion in Lambda qcd over mq + + align:start position:0% + + + + align:start position:0% + +and if you go into the details it + + align:start position:0% +and if you go into the details it + + + align:start position:0% +and if you go into the details it +actually there's an important role + + align:start position:0% +actually there's an important role + + + align:start position:0% +actually there's an important role +played by the fact that you're summing + + align:start position:0% +played by the fact that you're summing + + + align:start position:0% +played by the fact that you're summing +overall States and that's allowing you + + align:start position:0% +overall States and that's allowing you + + + align:start position:0% +overall States and that's allowing you +to connect a partonic calculations to + + align:start position:0% +to connect a partonic calculations to + + + align:start position:0% +to connect a partonic calculations to +hydronic calculations basically by + + align:start position:0% +hydronic calculations basically by + + + align:start position:0% +hydronic calculations basically by +probability conservation but I'm not + + align:start position:0% +probability conservation but I'm not + + + align:start position:0% +probability conservation but I'm not +going to go so much into + + align:start position:0% +going to go so much into + + + align:start position:0% +going to go so much into +that so when you do this operator + + align:start position:0% +that so when you do this operator + + + align:start position:0% +that so when you do this operator +product + + align:start position:0% +product + + + align:start position:0% +product +expansion you can think of it in terms + + align:start position:0% +expansion you can think of it in terms + + + align:start position:0% +expansion you can think of it in terms +of diagrams and usually draw these + + align:start position:0% +of diagrams and usually draw these + + + align:start position:0% +of diagrams and usually draw these +diagrams as forward + + align:start position:0% +diagrams as forward + + + align:start position:0% +diagrams as forward +diagrams so here's kind of the Matrix + + align:start position:0% +diagrams so here's kind of the Matrix + + + align:start position:0% +diagrams so here's kind of the Matrix +element + + align:start position:0% + + + + align:start position:0% + +squared Here's the final + + align:start position:0% + + + + align:start position:0% + +State here's the B Quark going in + + align:start position:0% +State here's the B Quark going in + + + align:start position:0% +State here's the B Quark going in +another B going out so that's like a + + align:start position:0% +another B going out so that's like a + + + align:start position:0% +another B going out so that's like a +matrix element + + align:start position:0% + + + + align:start position:0% + +squared amplitude squared and you think + + align:start position:0% +squared amplitude squared and you think + + + align:start position:0% +squared amplitude squared and you think +about doing an operator product + + align:start position:0% +about doing an operator product + + + align:start position:0% +about doing an operator product +expansion for that + + align:start position:0% +expansion for that + + + align:start position:0% +expansion for that +and you match onto operators in the + + align:start position:0% +and you match onto operators in the + + + align:start position:0% +and you match onto operators in the +effective + + align:start position:0% + + + + align:start position:0% + +Theory just to give you a schematic + + align:start position:0% +Theory just to give you a schematic + + + align:start position:0% +Theory just to give you a schematic +structure for those + + align:start position:0% + + + + align:start position:0% + +operators so there's a leading order + + align:start position:0% +operators so there's a leading order + + + align:start position:0% +operators so there's a leading order +operator there's a subleading order + + align:start position:0% +operator there's a subleading order + + + align:start position:0% +operator there's a subleading order +operator that has an extra coari + + align:start position:0% +operator that has an extra coari + + + align:start position:0% +operator that has an extra coari +derivative in it that's kind of what you + + align:start position:0% +derivative in it that's kind of what you + + + align:start position:0% +derivative in it that's kind of what you +would do and these and then you have + + align:start position:0% +would do and these and then you have + + + align:start position:0% +would do and these and then you have +Wilson coefficients the leading over + + align:start position:0% +Wilson coefficients the leading over + + + align:start position:0% +Wilson coefficients the leading over +operator here is just + + align:start position:0% +operator here is just + + + align:start position:0% +operator here is just +BB that's what it turns out to be this + + align:start position:0% +BB that's what it turns out to be this + + + align:start position:0% +BB that's what it turns out to be this +operator here would look familiar + + align:start position:0% +operator here would look familiar + + + align:start position:0% +operator here would look familiar +because it's D transverse + + align:start position:0% +because it's D transverse + + + align:start position:0% +because it's D transverse +squared so that's like our Lambda 1 + + align:start position:0% +squared so that's like our Lambda 1 + + + align:start position:0% +squared so that's like our Lambda 1 +operator and that's where the Lambda 1es + + align:start position:0% +operator and that's where the Lambda 1es + + + align:start position:0% +operator and that's where the Lambda 1es +are going to come from and then there + + align:start position:0% +are going to come from and then there + + + align:start position:0% +are going to come from and then there +would be a Lambda two term and I just + + align:start position:0% +would be a Lambda two term and I just + + + align:start position:0% +would be a Lambda two term and I just +didn't write + + align:start position:0% +didn't write + + + align:start position:0% +didn't write +it so there's a magnetic guy here too + + align:start position:0% + + + + align:start position:0% + +so when you look at the leading order + + align:start position:0% +so when you look at the leading order + + + align:start position:0% +so when you look at the leading order +operator bar Barb that counts the number + + align:start position:0% +operator bar Barb that counts the number + + + align:start position:0% +operator bar Barb that counts the number +of B + + align:start position:0% +of B + + + align:start position:0% +of B +quirks okay that's just a number + + align:start position:0% +quirks okay that's just a number + + + align:start position:0% +quirks okay that's just a number +operator so to all orders in peration + + align:start position:0% +operator so to all orders in peration + + + align:start position:0% +operator so to all orders in peration +theory + + align:start position:0% +theory + + + align:start position:0% +theory +BB is + + align:start position:0% + + + + align:start position:0% + +one + + align:start position:0% + + + + align:start position:0% + +y how do you cut + + align:start position:0% +y how do you cut + + + align:start position:0% +y how do you cut +these like you cut it like you're you're + + align:start position:0% +these like you cut it like you're you're + + + align:start position:0% +these like you cut it like you're you're +actually cut + + align:start position:0% + + + + align:start position:0% + +so you should think of actually looking + + align:start position:0% +so you should think of actually looking + + + align:start position:0% +so you should think of actually looking +so this is a charm + + align:start position:0% +so this is a charm + + + align:start position:0% +so this is a charm +Cork and so you would write down that + + align:start position:0% +Cork and so you would write down that + + + align:start position:0% +Cork and so you would write down that +propagator and then you have a large + + align:start position:0% +propagator and then you have a large + + + align:start position:0% +propagator and then you have a large +injection of momentum from the bork + + align:start position:0% +injection of momentum from the bork + + + align:start position:0% +injection of momentum from the bork +right use momentum conservation and + + align:start position:0% +right use momentum conservation and + + + align:start position:0% +right use momentum conservation and +expand the propagator thinking about the + + align:start position:0% +expand the propagator thinking about the + + + align:start position:0% +expand the propagator thinking about the +propagator if you like thinking about + + align:start position:0% +propagator if you like thinking about + + + align:start position:0% +propagator if you like thinking about +the this guy here + + align:start position:0% +the this guy here + + + align:start position:0% +the this guy here +having + + align:start position:0% +having + + + align:start position:0% +having +so you could write this guy's momentum + + align:start position:0% +so you could write this guy's momentum + + + align:start position:0% +so you could write this guy's momentum +as mbv plus + + align:start position:0% +as mbv plus + + + align:start position:0% +as mbv plus +K all right and you would EXP and + + align:start position:0% +K all right and you would EXP and + + + align:start position:0% +K all right and you would EXP and +K so at first order you just drop all + + align:start position:0% +K so at first order you just drop all + + + align:start position:0% +K so at first order you just drop all +the ks and that's basically giving you + + align:start position:0% +the ks and that's basically giving you + + + align:start position:0% +the ks and that's basically giving you +this term at second order you'd keep the + + align:start position:0% +this term at second order you'd keep the + + + align:start position:0% +this term at second order you'd keep the +ks and the K squ would be identified + + align:start position:0% +ks and the K squ would be identified + + + align:start position:0% +ks and the K squ would be identified +with this dt^ + + align:start position:0% +with this dt^ + + + align:start position:0% +with this dt^ +squ right but how do you cut the + + align:start position:0% +squ right but how do you cut the + + + align:start position:0% +squ right but how do you cut the +effective effective Theory diagram the + + align:start position:0% +effective effective Theory diagram the + + + align:start position:0% +effective effective Theory diagram the +it's already been it's already been cut + + align:start position:0% +it's already been it's already been cut + + + align:start position:0% +it's already been it's already been cut +if you like so these are just this is + + align:start position:0% +if you like so these are just this is + + + align:start position:0% +if you like so these are just this is +just a real thing and I've already taken + + align:start position:0% +just a real thing and I've already taken + + + align:start position:0% +just a real thing and I've already taken +the imaginary part so this is all + + align:start position:0% +the imaginary part so this is all + + + align:start position:0% +the imaginary part so this is all +real there's no cut to make in the + + align:start position:0% +real there's no cut to make in the + + + align:start position:0% +real there's no cut to make in the +effective Theory thing I'm integrating + + align:start position:0% +effective Theory thing I'm integrating + + + align:start position:0% +effective Theory thing I'm integrating +out here so this is good comment the + + align:start position:0% +out here so this is good comment the + + + align:start position:0% +out here so this is good comment the +thing I'm integrating out here is hard + + align:start position:0% +thing I'm integrating out here is hard + + + align:start position:0% +thing I'm integrating out here is hard +an off shell so when I go over to the + + align:start position:0% +an off shell so when I go over to the + + + align:start position:0% +an off shell so when I go over to the +effective Theory ofart and I get rid of + + align:start position:0% +effective Theory ofart and I get rid of + + + align:start position:0% +effective Theory ofart and I get rid of +the offshelf stuff I'm I'm being put on + + align:start position:0% +the offshelf stuff I'm I'm being put on + + + align:start position:0% +the offshelf stuff I'm I'm being put on +I have a real part here there's nothing + + align:start position:0% +I have a real part here there's nothing + + + align:start position:0% +I have a real part here there's nothing +to cut in the effective + + align:start position:0% +to cut in the effective + + + align:start position:0% +to cut in the effective +Theory sometimes as you know there are + + align:start position:0% +Theory sometimes as you know there are + + + align:start position:0% +Theory sometimes as you know there are +things to cut in the effective Theory + + align:start position:0% +things to cut in the effective Theory + + + align:start position:0% +things to cut in the effective Theory +but here there's nothing to cut on this + + align:start position:0% +but here there's nothing to cut on this + + + align:start position:0% +but here there's nothing to cut on this +side + + align:start position:0% + + + + align:start position:0% + +okay so this is one to all orders so + + align:start position:0% +okay so this is one to all orders so + + + align:start position:0% +okay so this is one to all orders so +that actually means that we don't even + + align:start position:0% +that actually means that we don't even + + + align:start position:0% +that actually means that we don't even +have a non a non-trivial matrix element + + align:start position:0% +have a non a non-trivial matrix element + + + align:start position:0% +have a non a non-trivial matrix element +here we just have a Wilson coefficient + + align:start position:0% +here we just have a Wilson coefficient + + + align:start position:0% +here we just have a Wilson coefficient +so everything in the first order term is + + align:start position:0% +so everything in the first order term is + + + align:start position:0% +so everything in the first order term is +completely + + align:start position:0% +completely + + + align:start position:0% +completely +calculable no + + align:start position:0% +calculable no + + + align:start position:0% +calculable no +non-perturbative + + align:start position:0% + + + + align:start position:0% + +parameter because of symmetry and this + + align:start position:0% +parameter because of symmetry and this + + + align:start position:0% +parameter because of symmetry and this +guy here is the power correction + + align:start position:0% + + + + align:start position:0% + +and if you look at what the Wilson + + align:start position:0% +and if you look at what the Wilson + + + align:start position:0% +and if you look at what the Wilson +coefficient is so it's a function of + + align:start position:0% +coefficient is so it's a function of + + + align:start position:0% +coefficient is so it's a function of +alpha + + align:start position:0% + + + + align:start position:0% + +s you could think of it like this if you + + align:start position:0% + + + + align:start position:0% + +want and all the kinematic variables + + align:start position:0% +want and all the kinematic variables + + + align:start position:0% +want and all the kinematic variables +like kinematic variables like these + + align:start position:0% +like kinematic variables like these + + + align:start position:0% +like kinematic variables like these +guys and it is equal to the free B Quark + + align:start position:0% + + + + align:start position:0% + +Decay including the loop Corrections of + + align:start position:0% +Decay including the loop Corrections of + + + align:start position:0% +Decay including the loop Corrections of +course so not only the tree level result + + align:start position:0% +course so not only the tree level result + + + align:start position:0% +course so not only the tree level result +but adding Loop corrections to the right + + align:start position:0% +but adding Loop corrections to the right + + + align:start position:0% +but adding Loop corrections to the right +hand side + + align:start position:0% +hand side + + + align:start position:0% +hand side +here if you add the loop Corrections and + + align:start position:0% +here if you add the loop Corrections and + + + align:start position:0% +here if you add the loop Corrections and +you drop all the K + + align:start position:0% +you drop all the K + + + align:start position:0% +you drop all the K +squares then you get the just the free B + + align:start position:0% +squares then you get the just the free B + + + align:start position:0% +squares then you get the just the free B +Decay no non-perturbative Matrix element + + align:start position:0% +Decay no non-perturbative Matrix element + + + align:start position:0% +Decay no non-perturbative Matrix element +so you can just calculate that first + + align:start position:0% +so you can just calculate that first + + + align:start position:0% +so you can just calculate that first +term order by order just doing a + + align:start position:0% +term order by order just doing a + + + align:start position:0% +term order by order just doing a +partonic calculation gives you the right + + align:start position:0% +partonic calculation gives you the right + + + align:start position:0% +partonic calculation gives you the right +thing to describe this + + align:start position:0% + + + + align:start position:0% + +Decay and the op is telling you that + + align:start position:0% +Decay and the op is telling you that + + + align:start position:0% +Decay and the op is telling you that +that formally is exactly the right thing + + align:start position:0% +that formally is exactly the right thing + + + align:start position:0% +that formally is exactly the right thing +even if you just started to do it it's + + align:start position:0% +even if you just started to do it it's + + + align:start position:0% +even if you just started to do it it's +actually technically the right thing to + + align:start position:0% +actually technically the right thing to + + + align:start position:0% +actually technically the right thing to +do here it wouldn't be the right thing + + align:start position:0% +do here it wouldn't be the right thing + + + align:start position:0% +do here it wouldn't be the right thing +to do for the exclusive + + align:start position:0% +to do for the exclusive + + + align:start position:0% +to do for the exclusive +decays but it is the right thing to do + + align:start position:0% +decays but it is the right thing to do + + + align:start position:0% +decays but it is the right thing to do +here for the inclusive + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +so what is the range of validity of this + + align:start position:0% +so what is the range of validity of this + + + align:start position:0% +so what is the range of validity of this +sort of is there any restrictions on + + align:start position:0% +sort of is there any restrictions on + + + align:start position:0% +sort of is there any restrictions on +this these kinematic variables and there + + align:start position:0% +this these kinematic variables and there + + + align:start position:0% +this these kinematic variables and there +is we're treating the kinematic + + align:start position:0% +is we're treating the kinematic + + + align:start position:0% +is we're treating the kinematic +variables as if they're + + align:start position:0% + + + + align:start position:0% + +hard and that means basically that we're + + align:start position:0% +hard and that means basically that we're + + + align:start position:0% +hard and that means basically that we're +thinking that they scale like powers of + + align:start position:0% +thinking that they scale like powers of + + + align:start position:0% +thinking that they scale like powers of +the heavy cork Mass + + align:start position:0% + + + + align:start position:0% + +so there can be regions of phase space + + align:start position:0% +so there can be regions of phase space + + + align:start position:0% +so there can be regions of phase space +where that wouldn't be true but as long + + align:start position:0% +where that wouldn't be true but as long + + + align:start position:0% +where that wouldn't be true but as long +as we stay away from those Corners + + align:start position:0% +as we stay away from those Corners + + + align:start position:0% +as we stay away from those Corners +edges then what I said is + + align:start position:0% + + + + align:start position:0% + +right and it's a little more powerful + + align:start position:0% +right and it's a little more powerful + + + align:start position:0% +right and it's a little more powerful +than than that + + align:start position:0% +than than that + + + align:start position:0% +than than that +so stay away from + + align:start position:0% + + + + align:start position:0% + +edges or + + align:start position:0% +edges or + + + align:start position:0% +edges or +there's another way of thinking about it + + align:start position:0% +there's another way of thinking about it + + + align:start position:0% +there's another way of thinking about it +and that is that you can integrate over + + align:start position:0% +and that is that you can integrate over + + + align:start position:0% +and that is that you can integrate over +regions of the D plane for the phase Bas + + align:start position:0% + + + + align:start position:0% + +variables that includes all the way up + + align:start position:0% +variables that includes all the way up + + + align:start position:0% +variables that includes all the way up +to the + + align:start position:0% +to the + + + align:start position:0% +to the +edges and as long as the size of your + + align:start position:0% +edges and as long as the size of your + + + align:start position:0% +edges and as long as the size of your +integration + + align:start position:0% + + + + align:start position:0% + +region is order mq then you're also fine + + align:start position:0% +region is order mq then you're also fine + + + align:start position:0% +region is order mq then you're also fine +so think of like some something with + + align:start position:0% +so think of like some something with + + + align:start position:0% +so think of like some something with +like MB 2 up here d mx^ s for example + + align:start position:0% +like MB 2 up here d mx^ s for example + + + align:start position:0% +like MB 2 up here d mx^ s for example +and you could doesn't have to be exactly + + align:start position:0% +and you could doesn't have to be exactly + + + align:start position:0% +and you could doesn't have to be exactly +MB squ it could be MB s over 2 MB s over + + align:start position:0% +MB squ it could be MB s over 2 MB s over + + + align:start position:0% +MB squ it could be MB s over 2 MB s over +4 something that you're counting is + + align:start position:0% +4 something that you're counting is + + + align:start position:0% +4 something that you're counting is +order MB squ and again you would be fine + + align:start position:0% +order MB squ and again you would be fine + + + align:start position:0% +order MB squ and again you would be fine +with doing this type of operator product + + align:start position:0% +with doing this type of operator product + + + align:start position:0% +with doing this type of operator product +expansion so what happens is if you + + align:start position:0% +expansion so what happens is if you + + + align:start position:0% +expansion so what happens is if you +restrict yourself to be close to the + + align:start position:0% +restrict yourself to be close to the + + + align:start position:0% +restrict yourself to be close to the +edges then restricting yourself to be + + align:start position:0% +edges then restricting yourself to be + + + align:start position:0% +edges then restricting yourself to be +close to the edges introduces new scales + + align:start position:0% +close to the edges introduces new scales + + + align:start position:0% +close to the edges introduces new scales +in the problem and if there's new scales + + align:start position:0% +in the problem and if there's new scales + + + align:start position:0% +in the problem and if there's new scales +in the problem just having a power + + align:start position:0% +in the problem just having a power + + + align:start position:0% +in the problem just having a power +counting that separates out Lambda qcd + + align:start position:0% +counting that separates out Lambda qcd + + + align:start position:0% +counting that separates out Lambda qcd +and MB would not be enough we'd have to + + align:start position:0% +and MB would not be enough we'd have to + + + align:start position:0% +and MB would not be enough we'd have to +do more + + align:start position:0% +do more + + + align:start position:0% +do more +detail uh and that there is actually + + align:start position:0% +detail uh and that there is actually + + + align:start position:0% +detail uh and that there is actually +some interesting things that happen + + align:start position:0% +some interesting things that happen + + + align:start position:0% +some interesting things that happen +there we may we probably will talk about + + align:start position:0% +there we may we probably will talk about + + + align:start position:0% +there we may we probably will talk about +at least one example later on when we + + align:start position:0% +at least one example later on when we + + + align:start position:0% +at least one example later on when we +talk + + align:start position:0% + + + + align:start position:0% + +about okay so I already said that + + align:start position:0% +about okay so I already said that + + + align:start position:0% +about okay so I already said that +there's a non-trivial fact happening at + + align:start position:0% +there's a non-trivial fact happening at + + + align:start position:0% +there's a non-trivial fact happening at +n while I already + + align:start position:0% +n while I already + + + align:start position:0% +n while I already +implied that there's no one over amb + + align:start position:0% +implied that there's no one over amb + + + align:start position:0% +implied that there's no one over amb +directions and so that's a important + + align:start position:0% +directions and so that's a important + + + align:start position:0% +directions and so that's a important +outcome from this result if you want to + + align:start position:0% +outcome from this result if you want to + + + align:start position:0% +outcome from this result if you want to +derive this you need the effective + + align:start position:0% +derive this you need the effective + + + align:start position:0% +derive this you need the effective +Theory you need that you basically need + + align:start position:0% +Theory you need that you basically need + + + align:start position:0% +Theory you need that you basically need +use the equation of motion to get that + + align:start position:0% +use the equation of motion to get that + + + align:start position:0% +use the equation of motion to get that +to be + + align:start position:0% + + + + align:start position:0% + +true and then so this is n nll in the + + align:start position:0% +true and then so this is n nll in the + + + align:start position:0% +true and then so this is n nll in the +power Corrections and then n + + align:start position:0% +power Corrections and then n + + + align:start position:0% +power Corrections and then n +nll as I said is just Lambda 1 and + + align:start position:0% +nll as I said is just Lambda 1 and + + + align:start position:0% +nll as I said is just Lambda 1 and +Lambda + + align:start position:0% + + + + align:start position:0% + +2 I'd order Lambda qcd squ over MB + + align:start position:0% + + + + align:start position:0% + +s so phenomenologically this is actually + + align:start position:0% +s so phenomenologically this is actually + + + align:start position:0% +s so phenomenologically this is actually +wildly successful this is as far as I + + align:start position:0% +wildly successful this is as far as I + + + align:start position:0% +wildly successful this is as far as I +know this is the case in qcd or in any + + align:start position:0% +know this is the case in qcd or in any + + + align:start position:0% +know this is the case in qcd or in any +Theory where people have actually + + align:start position:0% +Theory where people have actually + + + align:start position:0% +Theory where people have actually +carried out the operator product + + align:start position:0% +carried out the operator product + + + align:start position:0% +carried out the operator product +expansion in the most detail so people + + align:start position:0% +expansion in the most detail so people + + + align:start position:0% +expansion in the most detail so people +have gone up to 1 over mq 4th so they + + align:start position:0% +have gone up to 1 over mq 4th so they + + + align:start position:0% +have gone up to 1 over mq 4th so they +they've calculated at least two Loops + + align:start position:0% +they've calculated at least two Loops + + + align:start position:0% +they've calculated at least two Loops +for everything and maybe even three + + align:start position:0% +for everything and maybe even three + + + align:start position:0% +for everything and maybe even three +Loops for the NF pieces so and + + align:start position:0% +Loops for the NF pieces so and + + + align:start position:0% +Loops for the NF pieces so and +experimentally it's been explored you + + align:start position:0% +experimentally it's been explored you + + + align:start position:0% +experimentally it's been explored you +have this three to death you have this + + align:start position:0% +have this three to death you have this + + + align:start position:0% +have this three to death you have this +three these three variables and they've + + align:start position:0% +three these three variables and they've + + + align:start position:0% +three these three variables and they've +constructed of order 80 moments from + + align:start position:0% +constructed of order 80 moments from + + + align:start position:0% +constructed of order 80 moments from +these three different kinematic + + align:start position:0% +these three different kinematic + + + align:start position:0% +these three different kinematic +variables sliced and diced the C the + + align:start position:0% +variables sliced and diced the C the + + + align:start position:0% +variables sliced and diced the C the +Decay rate in all sorts of imag + + align:start position:0% +Decay rate in all sorts of imag + + + align:start position:0% +Decay rate in all sorts of imag +imaginative in crazy ways and they've + + align:start position:0% +imaginative in crazy ways and they've + + + align:start position:0% +imaginative in crazy ways and they've +really tested that this opu just works + + align:start position:0% +really tested that this opu just works + + + align:start position:0% +really tested that this opu just works +beautifully okay so you can think of + + align:start position:0% +beautifully okay so you can think of + + + align:start position:0% +beautifully okay so you can think of +that you're getting a consistent picture + + align:start position:0% +that you're getting a consistent picture + + + align:start position:0% +that you're getting a consistent picture +80 different observables just from a few + + align:start position:0% +80 different observables just from a few + + + align:start position:0% +80 different observables just from a few +simple predictions and your perturbative + + align:start position:0% +simple predictions and your perturbative + + + align:start position:0% +simple predictions and your perturbative +results + + align:start position:0% + + + + align:start position:0% + +you also get V + + align:start position:0% + + + + align:start position:0% + +VCB so everything fits together with the + + align:start position:0% +VCB so everything fits together with the + + + align:start position:0% +VCB so everything fits together with the +framework I've me I've discussed with + + align:start position:0% +framework I've me I've discussed with + + + align:start position:0% +framework I've me I've discussed with +you and you get a result for VCB which + + align:start position:0% +you and you get a result for VCB which + + + align:start position:0% +you and you get a result for VCB which +I'm not going to write down the + + align:start position:0% +I'm not going to write down the + + + align:start position:0% +I'm not going to write down the +board okay so that gives you I didn't go + + align:start position:0% +board okay so that gives you I didn't go + + + align:start position:0% +board okay so that gives you I didn't go +through the details I will give you some + + align:start position:0% +through the details I will give you some + + + align:start position:0% +through the details I will give you some +reading to learn more about this op if + + align:start position:0% +reading to learn more about this op if + + + align:start position:0% +reading to learn more about this op if +you're interested um and sort of sees + + align:start position:0% +you're interested um and sort of sees + + + align:start position:0% +you're interested um and sort of sees +how some of the things I mentioned like + + align:start position:0% +how some of the things I mentioned like + + + align:start position:0% +how some of the things I mentioned like +using the equation of motion how that + + align:start position:0% +using the equation of motion how that + + + align:start position:0% +using the equation of motion how that +actually works out it's all done very + + align:start position:0% +actually works out it's all done very + + + align:start position:0% +actually works out it's all done very +nicely in this book heavy quk physics + + align:start position:0% +nicely in this book heavy quk physics + + + align:start position:0% +nicely in this book heavy quk physics +but I just wanted to give you a flavor + + align:start position:0% +but I just wanted to give you a flavor + + + align:start position:0% +but I just wanted to give you a flavor +for kind of with this effective theory + + align:start position:0% +for kind of with this effective theory + + + align:start position:0% +for kind of with this effective theory +that there's something very useful you + + align:start position:0% +that there's something very useful you + + + align:start position:0% +that there's something very useful you +can do with it once you have it and in + + align:start position:0% +can do with it once you have it and in + + + align:start position:0% +can do with it once you have it and in +this case kind of the main + + align:start position:0% +this case kind of the main + + + align:start position:0% +this case kind of the main +phenomological thing that you're after + + align:start position:0% +phenomological thing that you're after + + + align:start position:0% +phenomological thing that you're after +is VCB and what I've described to you + + align:start position:0% +is VCB and what I've described to you + + + align:start position:0% +is VCB and what I've described to you +but you could also think about B decays + + align:start position:0% +but you could also think about B decays + + + align:start position:0% +but you could also think about B decays +where you're looking for new physics and + + align:start position:0% +where you're looking for new physics and + + + align:start position:0% +where you're looking for new physics and +again and you know if you can construct + + align:start position:0% +again and you know if you can construct + + + align:start position:0% +again and you know if you can construct +how the Decay rate is looking then you + + align:start position:0% +how the Decay rate is looking then you + + + align:start position:0% +how the Decay rate is looking then you +can have a hope of finding new physics + + align:start position:0% +can have a hope of finding new physics + + + align:start position:0% +can have a hope of finding new physics +and the coefficient of those Decay rates + + align:start position:0% +and the coefficient of those Decay rates + + + align:start position:0% +and the coefficient of those Decay rates +effectively in the Wilson coefficients + + align:start position:0% +effectively in the Wilson coefficients + + + align:start position:0% +effectively in the Wilson coefficients +of Decay + + align:start position:0% +of Decay + + + align:start position:0% +of Decay +rates okay so we're going to turn to + + align:start position:0% +rates okay so we're going to turn to + + + align:start position:0% +rates okay so we're going to turn to +something else but let me pause and see + + align:start position:0% +something else but let me pause and see + + + align:start position:0% +something else but let me pause and see +if there's any questions is this the + + align:start position:0% +if there's any questions is this the + + + align:start position:0% +if there's any questions is this the +best way to get + + align:start position:0% +best way to get + + + align:start position:0% +best way to get +VD the two are actually pretty + + align:start position:0% +VD the two are actually pretty + + + align:start position:0% +VD the two are actually pretty +competitive the exclusive and the + + align:start position:0% +competitive the exclusive and the + + + align:start position:0% +competitive the exclusive and the +inclusive um basically because the + + align:start position:0% +inclusive um basically because the + + + align:start position:0% +inclusive um basically because the +lattice is doing a good job of the + + align:start position:0% +lattice is doing a good job of the + + + align:start position:0% +lattice is doing a good job of the +Matrix elements that you need in the + + align:start position:0% +Matrix elements that you need in the + + + align:start position:0% +Matrix elements that you need in the +exclusive um and again you have a lot of + + align:start position:0% +exclusive um and again you have a lot of + + + align:start position:0% +exclusive um and again you have a lot of +kinematic information you can use from + + align:start position:0% +kinematic information you can use from + + + align:start position:0% +kinematic information you can use from +the experiment on the shape so they're + + align:start position:0% +the experiment on the shape so they're + + + align:start position:0% +the experiment on the shape so they're +pretty competitive + + align:start position:0% +pretty competitive + + + align:start position:0% +pretty competitive +actually they agree I think it's a the + + align:start position:0% +actually they agree I think it's a the + + + align:start position:0% +actually they agree I think it's a the +disagreement is at like kind of the 1.8 + + align:start position:0% +disagreement is at like kind of the 1.8 + + + align:start position:0% +disagreement is at like kind of the 1.8 +Sigma level so they + + align:start position:0% + + + + align:start position:0% + +agree there's a interesting story in VB + + align:start position:0% +agree there's a interesting story in VB + + + align:start position:0% +agree there's a interesting story in VB +so you could do the same kind of thing + + align:start position:0% +so you could do the same kind of thing + + + align:start position:0% +so you could do the same kind of thing +not for a charm Quark as we did here but + + align:start position:0% +not for a charm Quark as we did here but + + + align:start position:0% +not for a charm Quark as we did here but +for a light quark and then actually if + + align:start position:0% +for a light quark and then actually if + + + align:start position:0% +for a light quark and then actually if +you do B A pile new and you look at the + + align:start position:0% +you do B A pile new and you look at the + + + align:start position:0% +you do B A pile new and you look at the +inclusive version of that you can do the + + align:start position:0% +inclusive version of that you can do the + + + align:start position:0% +inclusive version of that you can do the +same type of op a little bit different + + align:start position:0% +same type of op a little bit different + + + align:start position:0% +same type of op a little bit different +actually but you can do an OP there as + + align:start position:0% +actually but you can do an OP there as + + + align:start position:0% +actually but you can do an OP there as +well then you go through and you get a v + + align:start position:0% +well then you go through and you get a v + + + align:start position:0% +well then you go through and you get a v +in the two different ways and the disre + + align:start position:0% +in the two different ways and the disre + + + align:start position:0% +in the two different ways and the disre +at the two and a half Sigma + + align:start position:0% +at the two and a half Sigma + + + align:start position:0% +at the two and a half Sigma +level maybe even yeah it fluctuates with + + align:start position:0% +level maybe even yeah it fluctuates with + + + align:start position:0% +level maybe even yeah it fluctuates with +time but on average it's two and a half + + align:start position:0% +time but on average it's two and a half + + + align:start position:0% +time but on average it's two and a half +Sigma so that's interesting there's not + + align:start position:0% +Sigma so that's interesting there's not + + + align:start position:0% +Sigma so that's interesting there's not +an understanding of what's going on + + align:start position:0% +an understanding of what's going on + + + align:start position:0% +an understanding of what's going on +there that's more interesting than than + + align:start position:0% +there that's more interesting than than + + + align:start position:0% +there that's more interesting than than +this one basically + + align:start position:0% +this one basically + + + align:start position:0% +this one basically +agrees okay so rather than go further + + align:start position:0% +agrees okay so rather than go further + + + align:start position:0% +agrees okay so rather than go further +into this I want to turn now to my + + align:start position:0% +into this I want to turn now to my + + + align:start position:0% +into this I want to turn now to my +promised topic to you to tell you about + + align:start position:0% +promised topic to you to tell you about + + + align:start position:0% +promised topic to you to tell you about +re normal + + align:start position:0% +re normal + + + align:start position:0% +re normal +LS actually re normal lines have + + align:start position:0% +LS actually re normal lines have + + + align:start position:0% +LS actually re normal lines have +something to do with power correction so + + align:start position:0% +something to do with power correction so + + + align:start position:0% +something to do with power correction so +it's not disconnected from what we've + + align:start position:0% +it's not disconnected from what we've + + + align:start position:0% +it's not disconnected from what we've +been talking + + align:start position:0% + + + + align:start position:0% + +about so what are the ideas here + + align:start position:0% + + + + align:start position:0% + +so we've already seen in our discussion + + align:start position:0% +so we've already seen in our discussion + + + align:start position:0% +so we've already seen in our discussion +of normalization that there is a freedom + + align:start position:0% +of normalization that there is a freedom + + + align:start position:0% +of normalization that there is a freedom +in defining the perturbative series and + + align:start position:0% +in defining the perturbative series and + + + align:start position:0% +in defining the perturbative series and +we kind of focused on the msar scheme as + + align:start position:0% +we kind of focused on the msar scheme as + + + align:start position:0% +we kind of focused on the msar scheme as +being the simplest + + align:start position:0% + + + + align:start position:0% + +thing but I told you about some + + align:start position:0% +thing but I told you about some + + + align:start position:0% +thing but I told you about some +subtleties with msar and now we're going + + align:start position:0% +subtleties with msar and now we're going + + + align:start position:0% +subtleties with msar and now we're going +to address one of them that's related to + + align:start position:0% +to address one of them that's related to + + + align:start position:0% +to address one of them that's related to +this thing called re normal on + + align:start position:0% + + + + align:start position:0% + +so we have some Freedom if you like in + + align:start position:0% +so we have some Freedom if you like in + + + align:start position:0% +so we have some Freedom if you like in +adjusting the cut offs and we had this + + align:start position:0% +adjusting the cut offs and we had this + + + align:start position:0% +adjusting the cut offs and we had this +cutoff mu and it was dividing up what + + align:start position:0% +cutoff mu and it was dividing up what + + + align:start position:0% +cutoff mu and it was dividing up what +was perturbative and + + align:start position:0% +was perturbative and + + + align:start position:0% +was perturbative and +non-perturbative in + + align:start position:0% + + + + align:start position:0% + +msar but we could have done something + + align:start position:0% +msar but we could have done something + + + align:start position:0% +msar but we could have done something +else we could have used a different type + + align:start position:0% +else we could have used a different type + + + align:start position:0% +else we could have used a different type +of cut off we could have used a + + align:start position:0% +of cut off we could have used a + + + align:start position:0% +of cut off we could have used a +wilsonian cut off and that would have + + align:start position:0% +wilsonian cut off and that would have + + + align:start position:0% +wilsonian cut off and that would have +divided up things a little bit + + align:start position:0% +divided up things a little bit + + + align:start position:0% +divided up things a little bit +differently and you should ask the + + align:start position:0% +differently and you should ask the + + + align:start position:0% +differently and you should ask the +question are they any possible way of + + align:start position:0% +question are they any possible way of + + + align:start position:0% +question are they any possible way of +dividing things up + + align:start position:0% + + + + align:start position:0% + +equivalent we've already saw when we + + align:start position:0% +equivalent we've already saw when we + + + align:start position:0% +equivalent we've already saw when we +were doing calc calculations that for + + align:start position:0% +were doing calc calculations that for + + + align:start position:0% +were doing calc calculations that for +the logarithms they were + + align:start position:0% +the logarithms they were + + + align:start position:0% +the logarithms they were +equivalent but it turns out + + align:start position:0% + + + + align:start position:0% + +that if you don't that the powers sort + + align:start position:0% +that if you don't that the powers sort + + + align:start position:0% +that if you don't that the powers sort +of the power separation uh of power + + align:start position:0% +of the power separation uh of power + + + align:start position:0% +of the power separation uh of power +divergences can actually have an impact + + align:start position:0% + + + + align:start position:0% + +and that's related to what re normal + + align:start position:0% +and that's related to what re normal + + + align:start position:0% +and that's related to what re normal +ones + + align:start position:0% + + + + align:start position:0% + +are and msar and dim rag basically + + align:start position:0% +are and msar and dim rag basically + + + align:start position:0% +are and msar and dim rag basically +avoids thinking about power Corrections + + align:start position:0% +avoids thinking about power Corrections + + + align:start position:0% +avoids thinking about power Corrections +you just set them to zero and so what + + align:start position:0% +you just set them to zero and so what + + + align:start position:0% +you just set them to zero and so what +can happen is in a m bar your Matrix + + align:start position:0% +can happen is in a m bar your Matrix + + + align:start position:0% +can happen is in a m bar your Matrix +elements are having a little bit too + + align:start position:0% +elements are having a little bit too + + + align:start position:0% +elements are having a little bit too +much UV physics and your Wilson + + align:start position:0% +much UV physics and your Wilson + + + align:start position:0% +much UV physics and your Wilson +coefficients are actually sensitive to + + align:start position:0% +coefficients are actually sensitive to + + + align:start position:0% +coefficients are actually sensitive to +the R they're not sense you don't really + + align:start position:0% +the R they're not sense you don't really + + + align:start position:0% +the R they're not sense you don't really +see it when you look at the coefficient + + align:start position:0% +see it when you look at the coefficient + + + align:start position:0% +see it when you look at the coefficient +you just see a number it looks pretty + + align:start position:0% +you just see a number it looks pretty + + + align:start position:0% +you just see a number it looks pretty +pretty good but there's actually an ASM + + align:start position:0% +pretty good but there's actually an ASM + + + align:start position:0% +pretty good but there's actually an ASM +totic structure to those Wilson + + align:start position:0% +totic structure to those Wilson + + + align:start position:0% +totic structure to those Wilson +coefficients that comes from high orders + + align:start position:0% +coefficients that comes from high orders + + + align:start position:0% +coefficients that comes from high orders +of peration theory there's things hiding + + align:start position:0% +of peration theory there's things hiding + + + align:start position:0% +of peration theory there's things hiding +there that's what this is going to this + + align:start position:0% +there that's what this is going to this + + + align:start position:0% +there that's what this is going to this +discussion is going to be + + align:start position:0% + + + + align:start position:0% + +about so if you do actually not make a + + align:start position:0% +about so if you do actually not make a + + + align:start position:0% +about so if you do actually not make a +good choice + + align:start position:0% + + + + align:start position:0% + +then it can be the case that when you go + + align:start position:0% +then it can be the case that when you go + + + align:start position:0% +then it can be the case that when you go +to higher orders in the perturbative + + align:start position:0% +to higher orders in the perturbative + + + align:start position:0% +to higher orders in the perturbative +expansion you get lousy + + align:start position:0% + + + + align:start position:0% + +convergence and that goes hand in hand + + align:start position:0% +convergence and that goes hand in hand + + + align:start position:0% +convergence and that goes hand in hand +actually + + align:start position:0% +actually + + + align:start position:0% +actually +with kind of another thing which is + + align:start position:0% +with kind of another thing which is + + + align:start position:0% +with kind of another thing which is +harder to visualize but I'll explain + + align:start position:0% +harder to visualize but I'll explain + + + align:start position:0% +harder to visualize but I'll explain +it and that is that you have trouble + + align:start position:0% +it and that is that you have trouble + + + align:start position:0% +it and that is that you have trouble +extra extracting the non- perative + + align:start position:0% + + + + align:start position:0% + +parameters and the reason that you're + + align:start position:0% +parameters and the reason that you're + + + align:start position:0% +parameters and the reason that you're +having trouble so you could think about + + align:start position:0% +having trouble so you could think about + + + align:start position:0% +having trouble so you could think about +doing some calculation like that op over + + align:start position:0% +doing some calculation like that op over + + + align:start position:0% +doing some calculation like that op over +there and you extract a value for Lambda + + align:start position:0% +there and you extract a value for Lambda + + + align:start position:0% +there and you extract a value for Lambda +1 from all your fits so these moments I + + align:start position:0% +1 from all your fits so these moments I + + + align:start position:0% +1 from all your fits so these moments I +was describing to you and then you go to + + align:start position:0% +was describing to you and then you go to + + + align:start position:0% +was describing to you and then you go to +one higher order in Alpha s and you + + align:start position:0% +one higher order in Alpha s and you + + + align:start position:0% +one higher order in Alpha s and you +extract another value and all of a + + align:start position:0% +extract another value and all of a + + + align:start position:0% +extract another value and all of a +sudden this guy changes by a factor of + + align:start position:0% +sudden this guy changes by a factor of + + + align:start position:0% +sudden this guy changes by a factor of +two and you wonder what's going on and + + align:start position:0% +two and you wonder what's going on and + + + align:start position:0% +two and you wonder what's going on and +you wonder well what what's nature + + align:start position:0% +you wonder well what what's nature + + + align:start position:0% +you wonder well what what's nature +telling me about the kinetic energy if I + + align:start position:0% +telling me about the kinetic energy if I + + + align:start position:0% +telling me about the kinetic energy if I +change the order of my peration theory + + align:start position:0% +change the order of my peration theory + + + align:start position:0% +change the order of my peration theory +and all of a sudden I'm extracting a + + align:start position:0% +and all of a sudden I'm extracting a + + + align:start position:0% +and all of a sudden I'm extracting a +factor of two different value for that + + align:start position:0% +factor of two different value for that + + + align:start position:0% +factor of two different value for that +Matrix element and that's related + + align:start position:0% +Matrix element and that's related + + + align:start position:0% +Matrix element and that's related +actually to this poor convergent the + + align:start position:0% +actually to this poor convergent the + + + align:start position:0% +actually to this poor convergent the +these things go hand in hand that + + align:start position:0% +these things go hand in hand that + + + align:start position:0% +these things go hand in hand that +there's poor if there's poor convergence + + align:start position:0% +there's poor if there's poor convergence + + + align:start position:0% +there's poor if there's poor convergence +in the series then when you extract + + align:start position:0% +in the series then when you extract + + + align:start position:0% +in the series then when you extract +Matrix elements um you can get different + + align:start position:0% +Matrix elements um you can get different + + + align:start position:0% +Matrix elements um you can get different +values phenom logically you can imagine + + align:start position:0% +values phenom logically you can imagine + + + align:start position:0% +values phenom logically you can imagine +how that would be related but it's + + align:start position:0% +how that would be related but it's + + + align:start position:0% +how that would be related but it's +physically related too it has to do with + + align:start position:0% +physically related too it has to do with + + + align:start position:0% +physically related too it has to do with +the fact that there's a poor convergence + + align:start position:0% +the fact that there's a poor convergence + + + align:start position:0% +the fact that there's a poor convergence +here because you haven't divided up the + + align:start position:0% +here because you haven't divided up the + + + align:start position:0% +here because you haven't divided up the +IR physics and the UV physics fully + + align:start position:0% +IR physics and the UV physics fully + + + align:start position:0% +IR physics and the UV physics fully +correctly and that's reflected in this + + align:start position:0% +correctly and that's reflected in this + + + align:start position:0% +correctly and that's reflected in this +inability to extract these guides in a + + align:start position:0% +inability to extract these guides in a + + + align:start position:0% +inability to extract these guides in a +convergent + + align:start position:0% + + + + align:start position:0% + +fashion and we can actually quantify + + align:start position:0% +fashion and we can actually quantify + + + align:start position:0% +fashion and we can actually quantify +that using something called renormalon + + align:start position:0% + + + + align:start position:0% + +techniques so one way of saying it + + align:start position:0% + + + + align:start position:0% + +is that if you make a poor choice you're + + align:start position:0% +is that if you make a poor choice you're + + + align:start position:0% +is that if you make a poor choice you're +plagued by something called re normal so + + align:start position:0% +plagued by something called re normal so + + + align:start position:0% +plagued by something called re normal so +they're actually something bad and you + + align:start position:0% +they're actually something bad and you + + + align:start position:0% +they're actually something bad and you +don't want + + align:start position:0% + + + + align:start position:0% + +them so what goes wrong is that the + + align:start position:0% +them so what goes wrong is that the + + + align:start position:0% +them so what goes wrong is that the +short + + align:start position:0% +short + + + align:start position:0% +short +distance coefficients + + align:start position:0% + + + + align:start position:0% + +have hidden power LW + + align:start position:0% + + + + align:start position:0% + +sensitivity to the IR you wanted these + + align:start position:0% +sensitivity to the IR you wanted these + + + align:start position:0% +sensitivity to the IR you wanted these +to be UV things but they're sensitive to + + align:start position:0% +to be UV things but they're sensitive to + + + align:start position:0% +to be UV things but they're sensitive to +the + + align:start position:0% +the + + + align:start position:0% +the +IR and it comes in dimensional + + align:start position:0% +IR and it comes in dimensional + + + align:start position:0% +IR and it comes in dimensional +legalization in in the powers we've been + + align:start position:0% +legalization in in the powers we've been + + + align:start position:0% +legalization in in the powers we've been +very careful about separating out + + align:start position:0% +very careful about separating out + + + align:start position:0% +very careful about separating out +logarithms but we weren't as careful + + align:start position:0% +logarithms but we weren't as careful + + + align:start position:0% +logarithms but we weren't as careful +about powers and it comes back to haunt + + align:start position:0% +about powers and it comes back to haunt + + + align:start position:0% +about powers and it comes back to haunt +us if we look carefully at the + + align:start position:0% + + + + align:start position:0% + +theory and there's a corresponding + + align:start position:0% +theory and there's a corresponding + + + align:start position:0% +theory and there's a corresponding +sensitivity the UV and the Matrix + + align:start position:0% +sensitivity the UV and the Matrix + + + align:start position:0% +sensitivity the UV and the Matrix +elements so let me give you an example + + align:start position:0% +elements so let me give you an example + + + align:start position:0% +elements so let me give you an example +that's not working through formalism but + + align:start position:0% +that's not working through formalism but + + + align:start position:0% +that's not working through formalism but +just + + align:start position:0% +just + + + align:start position:0% +just +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +numerics so let's look at B to u e bar + + align:start position:0% +numerics so let's look at B to u e bar + + + align:start position:0% +numerics so let's look at B to u e bar +new at lowest order the UPC is massive + + align:start position:0% +new at lowest order the UPC is massive + + + align:start position:0% +new at lowest order the UPC is massive +mass + + align:start position:0% +mass + + + align:start position:0% +mass +massless and we'll think about this + + align:start position:0% +massless and we'll think about this + + + align:start position:0% +massless and we'll think about this +like like we were talking about for the + + align:start position:0% +like like we were talking about for the + + + align:start position:0% +like like we were talking about for the +op for charm we'll think about it + + align:start position:0% +op for charm we'll think about it + + + align:start position:0% +op for charm we'll think about it +inclusively so we can actually just look + + align:start position:0% +inclusively so we can actually just look + + + align:start position:0% +inclusively so we can actually just look +at this and it makes physical sense the + + align:start position:0% +at this and it makes physical sense the + + + align:start position:0% +at this and it makes physical sense the +same thing that I told you about the + + align:start position:0% +same thing that I told you about the + + + align:start position:0% +same thing that I told you about the +charm case applies for the upcourt case + + align:start position:0% +charm case applies for the upcourt case + + + align:start position:0% +charm case applies for the upcourt case +the lowest order of prediction is just + + align:start position:0% +the lowest order of prediction is just + + + align:start position:0% +the lowest order of prediction is just +calculate this guy and include Loop + + align:start position:0% +calculate this guy and include Loop + + + align:start position:0% +calculate this guy and include Loop +Corrections the leading power prediction + + align:start position:0% +Corrections the leading power prediction + + + align:start position:0% +Corrections the leading power prediction +is the same story as for the + + align:start position:0% +is the same story as for the + + + align:start position:0% +is the same story as for the +charm so that means that physically it's + + align:start position:0% +charm so that means that physically it's + + + align:start position:0% +charm so that means that physically it's +relevant to think about this Decay + + align:start position:0% +relevant to think about this Decay + + + align:start position:0% +relevant to think about this Decay +rate so what does it look + + align:start position:0% +rate so what does it look + + + align:start position:0% +rate so what does it look +like there's some G + + align:start position:0% +like there's some G + + + align:start position:0% +like there's some G +fmy integrating out the W bz on there's + + align:start position:0% +fmy integrating out the W bz on there's + + + align:start position:0% +fmy integrating out the W bz on there's +some factors of + + align:start position:0% +some factors of + + + align:start position:0% +some factors of +Pi the mass + + align:start position:0% +Pi the mass + + + align:start position:0% +Pi the mass +dimensions of this guy are one geery + + align:start position:0% +dimensions of this guy are one geery + + + align:start position:0% +dimensions of this guy are one geery +squar is minus 4 so you need five powers + + align:start position:0% +squar is minus 4 so you need five powers + + + align:start position:0% +squar is minus 4 so you need five powers +and the thing that has the setting the + + align:start position:0% +and the thing that has the setting the + + + align:start position:0% +and the thing that has the setting the +mass Dimensions is MB so you get five + + align:start position:0% +mass Dimensions is MB so you get five + + + align:start position:0% +mass Dimensions is MB so you get five +powers of MB + + align:start position:0% + + + + align:start position:0% + +and if you look at the perturbative + + align:start position:0% +and if you look at the perturbative + + + align:start position:0% +and if you look at the perturbative +series and you set Mew equal + + align:start position:0% +series and you set Mew equal + + + align:start position:0% +series and you set Mew equal +MB this is what it looks + + align:start position:0% + + + + align:start position:0% + +like so Epsilon I'm just introducing + + align:start position:0% +like so Epsilon I'm just introducing + + + align:start position:0% +like so Epsilon I'm just introducing +something which is a counting + + align:start position:0% +something which is a counting + + + align:start position:0% +something which is a counting +parameter and it's one I could also make + + align:start position:0% +parameter and it's one I could also make + + + align:start position:0% +parameter and it's one I could also make +alpha s the counting parameter but I + + align:start position:0% +alpha s the counting parameter but I + + + align:start position:0% +alpha s the counting parameter but I +actually want to stick a number in for + + align:start position:0% +actually want to stick a number in for + + + align:start position:0% +actually want to stick a number in for +alpha s so alpha s is going to disappear + + align:start position:0% +alpha s so alpha s is going to disappear + + + align:start position:0% +alpha s so alpha s is going to disappear +in the next line and I'll just keep the + + align:start position:0% +in the next line and I'll just keep the + + + align:start position:0% +in the next line and I'll just keep the +Epsilon which is just telling me the + + align:start position:0% +Epsilon which is just telling me the + + + align:start position:0% +Epsilon which is just telling me the +contribution is coming from this + + align:start position:0% +contribution is coming from this + + + align:start position:0% +contribution is coming from this +order so you have some Choice here for + + align:start position:0% +order so you have some Choice here for + + + align:start position:0% +order so you have some Choice here for +what how you define the bork + + align:start position:0% +what how you define the bork + + + align:start position:0% +what how you define the bork +Mass okay you could use the pole Mass + + align:start position:0% +Mass okay you could use the pole Mass + + + align:start position:0% +Mass okay you could use the pole Mass +pole in the bort propagator or you could + + align:start position:0% +pole in the bort propagator or you could + + + align:start position:0% +pole in the bort propagator or you could +use the msar mass or you could use some + + align:start position:0% +use the msar mass or you could use some + + + align:start position:0% +use the msar mass or you could use some +other definition and it's raised to the + + align:start position:0% +other definition and it's raised to the + + + align:start position:0% +other definition and it's raised to the +fifth power so whatever definition you + + align:start position:0% +fifth power so whatever definition you + + + align:start position:0% +fifth power so whatever definition you +pick is going to it can be pretty + + align:start position:0% +pick is going to it can be pretty + + + align:start position:0% +pick is going to it can be pretty +sensitive to that so let's let me tell + + align:start position:0% +sensitive to that so let's let me tell + + + align:start position:0% +sensitive to that so let's let me tell +you what the results look like in two + + align:start position:0% +you what the results look like in two + + + align:start position:0% +you what the results look like in two +different in three different schemes for + + align:start position:0% +different in three different schemes for + + + align:start position:0% +different in three different schemes for +that + + align:start position:0% +that + + + align:start position:0% +that +mass so let's first do the pole scheme + + align:start position:0% +mass so let's first do the pole scheme + + + align:start position:0% +mass so let's first do the pole scheme +this is the + + align:start position:0% +this is the + + + align:start position:0% +this is the +same we have MD Pole to the fifth + + align:start position:0% +same we have MD Pole to the fifth + + + align:start position:0% +same we have MD Pole to the fifth +power and then we write out what this + + align:start position:0% +power and then we write out what this + + + align:start position:0% +power and then we write out what this +series looks like in that + + align:start position:0% + + + + align:start position:0% + +scheme you look like you're doing pretty + + align:start position:0% +scheme you look like you're doing pretty + + + align:start position:0% +scheme you look like you're doing pretty +good when you're at one Loop you went + + align:start position:0% +good when you're at one Loop you went + + + align:start position:0% +good when you're at one Loop you went +down by factor of five but then you go + + align:start position:0% +down by factor of five but then you go + + + align:start position:0% +down by factor of five but then you go +to two loops and you find that your + + align:start position:0% +to two loops and you find that your + + + align:start position:0% +to two loops and you find that your +correction at two Loops is pretty much + + align:start position:0% +correction at two Loops is pretty much + + + align:start position:0% +correction at two Loops is pretty much +the same size as your correction at one + + align:start position:0% + + + + align:start position:0% + +Loop so you say well let's use + + align:start position:0% + + + + align:start position:0% + +msar that changes the perturbative + + align:start position:0% +msar that changes the perturbative + + + align:start position:0% +msar that changes the perturbative +series + + align:start position:0% + + + + align:start position:0% + +and you maybe you think you're doing a + + align:start position:0% +and you maybe you think you're doing a + + + align:start position:0% +and you maybe you think you're doing a +little bit better because at least well + + align:start position:0% +little bit better because at least well + + + align:start position:0% +little bit better because at least well +but this guy got bigger and this guy's + + align:start position:0% +but this guy got bigger and this guy's + + + align:start position:0% +but this guy got bigger and this guy's +bigger than that guy so it's also not + + align:start position:0% +bigger than that guy so it's also not + + + align:start position:0% +bigger than that guy so it's also not +really + + align:start position:0% + + + + align:start position:0% + +working if the phenomenology is as + + align:start position:0% +working if the phenomenology is as + + + align:start position:0% +working if the phenomenology is as +accurate as I told you you must imagine + + align:start position:0% +accurate as I told you you must imagine + + + align:start position:0% +accurate as I told you you must imagine +that there is something that does work + + align:start position:0% +that there is something that does work + + + align:start position:0% +that there is something that does work +better than that + + align:start position:0% +better than that + + + align:start position:0% +better than that +indeed there + + align:start position:0% +indeed there + + + align:start position:0% +indeed there +is so there's other MTH schemes and + + align:start position:0% +is so there's other MTH schemes and + + + align:start position:0% +is so there's other MTH schemes and +I'll talk about one of them so + + align:start position:0% +I'll talk about one of them so + + + align:start position:0% +I'll talk about one of them so +continuing this + + align:start position:0% + + + + align:start position:0% + +table where we switch to something + + align:start position:0% +table where we switch to something + + + align:start position:0% +table where we switch to something +called a 1s mass now the series looks + + align:start position:0% +called a 1s mass now the series looks + + + align:start position:0% +called a 1s mass now the series looks +like that we're very happy or at least + + align:start position:0% +like that we're very happy or at least + + + align:start position:0% +like that we're very happy or at least +we're much happier than we were over + + align:start position:0% + + + + align:start position:0% + +here so what is what is the 1s Mass the + + align:start position:0% +here so what is what is the 1s Mass the + + + align:start position:0% +here so what is what is the 1s Mass the +1s mass is basically that you take half + + align:start position:0% +1s mass is basically that you take half + + + align:start position:0% +1s mass is basically that you take half +the perturbative mass for the Epsilon + + align:start position:0% +the perturbative mass for the Epsilon + + + align:start position:0% +the perturbative mass for the Epsilon +system so 1s + + align:start position:0% +system so 1s + + + align:start position:0% +system so 1s +mass + + align:start position:0% +mass + + + align:start position:0% +mass +is M BB bar system calculated + + align:start position:0% +is M BB bar system calculated + + + align:start position:0% +is M BB bar system calculated +perturbatively + + align:start position:0% +perturbatively + + + align:start position:0% +perturbatively +divided by + + align:start position:0% + + + + align:start position:0% + +two okay we'll talk more about why this + + align:start position:0% +two okay we'll talk more about why this + + + align:start position:0% +two okay we'll talk more about why this +is working in a + + align:start position:0% +is working in a + + + align:start position:0% +is working in a +minute let me also + + align:start position:0% +minute let me also + + + align:start position:0% +minute let me also +write down the conversion formulas + + align:start position:0% +write down the conversion formulas + + + align:start position:0% +write down the conversion formulas +because you calculate the Decay rate + + align:start position:0% +because you calculate the Decay rate + + + align:start position:0% +because you calculate the Decay rate +once and for all say you calculate the + + align:start position:0% +once and for all say you calculate the + + + align:start position:0% +once and for all say you calculate the +first line then you know how to convert + + align:start position:0% +first line then you know how to convert + + + align:start position:0% +first line then you know how to convert +between schemes and that's what's + + align:start position:0% +between schemes and that's what's + + + align:start position:0% +between schemes and that's what's +causing the perturbative series to + + align:start position:0% +causing the perturbative series to + + + align:start position:0% +causing the perturbative series to +differ so MB + + align:start position:0% +differ so MB + + + align:start position:0% +differ so MB +Pole is equal + + align:start position:0% +Pole is equal + + + align:start position:0% +Pole is equal +to MB + + align:start position:0% +to MB + + + align:start position:0% +to MB +msar and there's a series that relates + + align:start position:0% + + + + align:start position:0% + +them that looks like + + align:start position:0% + + + + align:start position:0% + +that and I could put in numbers here + + align:start position:0% + + + + align:start position:0% + +and so that's what's changing the + + align:start position:0% +and so that's what's changing the + + + align:start position:0% +and so that's what's changing the +numbers when I go from this line to this + + align:start position:0% +numbers when I go from this line to this + + + align:start position:0% +numbers when I go from this line to this +this line and + + align:start position:0% +this line and + + + align:start position:0% +this line and +basically kind of the five five powers + + align:start position:0% +basically kind of the five five powers + + + align:start position:0% +basically kind of the five five powers +of 009 that you get takes you from here + + align:start position:0% +of 009 that you get takes you from here + + + align:start position:0% +of 009 that you get takes you from here +to + + align:start position:0% + + + + align:start position:0% + +here we could also think about switching + + align:start position:0% +here we could also think about switching + + + align:start position:0% +here we could also think about switching +from the pole scheme to this mv1 s + + align:start position:0% +from the pole scheme to this mv1 s + + + align:start position:0% +from the pole scheme to this mv1 s +scheme + + align:start position:0% +scheme + + + align:start position:0% +scheme +have a different + + align:start position:0% + + + + align:start position:0% + +series it still doesn't look very + + align:start position:0% + + + + align:start position:0% + +convergent the numbers look small but + + align:start position:0% +convergent the numbers look small but + + + align:start position:0% +convergent the numbers look small but +this is supposed to be a six but this + + align:start position:0% +this is supposed to be a six but this + + + align:start position:0% +this is supposed to be a six but this +number here is bigger than that + + align:start position:0% +number here is bigger than that + + + align:start position:0% +number here is bigger than that +number but when I stick this series and + + align:start position:0% +number but when I stick this series and + + + align:start position:0% +number but when I stick this series and +take combine it together with this + + align:start position:0% +take combine it together with this + + + align:start position:0% +take combine it together with this +series for the pole mass then I get that + + align:start position:0% +series for the pole mass then I get that + + + align:start position:0% +series for the pole mass then I get that +series at the top of the board + + align:start position:0% +series at the top of the board + + + align:start position:0% +series at the top of the board +and what's the problem is not in the + + align:start position:0% +and what's the problem is not in the + + + align:start position:0% +and what's the problem is not in the +mb1s the problem is in the MB pole and + + align:start position:0% +mb1s the problem is in the MB pole and + + + align:start position:0% +mb1s the problem is in the MB pole and +the problem in the MB pole is being + + align:start position:0% +the problem in the MB pole is being + + + align:start position:0% +the problem in the MB pole is being +reflected in this series that relates + + align:start position:0% +reflected in this series that relates + + + align:start position:0% +reflected in this series that relates +them and it's poor + + align:start position:0% + + + + align:start position:0% + +convergence yeah so you calculate so you + + align:start position:0% +convergence yeah so you calculate so you + + + align:start position:0% +convergence yeah so you calculate so you +can think of calculating the coolon + + align:start position:0% +can think of calculating the coolon + + + align:start position:0% +can think of calculating the coolon +potential between B and B bar and that + + align:start position:0% +potential between B and B bar and that + + + align:start position:0% +potential between B and B bar and that +would give you Alphas corrections to + + align:start position:0% +would give you Alphas corrections to + + + align:start position:0% +would give you Alphas corrections to +just the mass so you have 2 MB plus Kum + + align:start position:0% +just the mass so you have 2 MB plus Kum + + + align:start position:0% +just the mass so you have 2 MB plus Kum +poti potential plus you know rad of + + align:start position:0% +poti potential plus you know rad of + + + align:start position:0% +poti potential plus you know rad of +Corrections to that and you keep + + align:start position:0% +Corrections to that and you keep + + + align:start position:0% +Corrections to that and you keep +dressing it up and just perturbatively + + align:start position:0% +dressing it up and just perturbatively + + + align:start position:0% +dressing it up and just perturbatively +calculate as if it was a Kon problem + + align:start position:0% +calculate as if it was a Kon problem + + + align:start position:0% +calculate as if it was a Kon problem +like QED problem the mass of the BB bar + + align:start position:0% +like QED problem the mass of the BB bar + + + align:start position:0% +like QED problem the mass of the BB bar +State and then you divide by + + align:start position:0% + + + + align:start position:0% + +two yeah just prend it's there's + + align:start position:0% +two yeah just prend it's there's + + + align:start position:0% +two yeah just prend it's there's +non-perturbative corrections to it but + + align:start position:0% +non-perturbative corrections to it but + + + align:start position:0% +non-perturbative corrections to it but +what we're extracting from it is a + + align:start position:0% +what we're extracting from it is a + + + align:start position:0% +what we're extracting from it is a +series okay I I'll explain more why it's + + align:start position:0% +series okay I I'll explain more why it's + + + align:start position:0% +series okay I I'll explain more why it's +going to work why this is like a + + align:start position:0% +going to work why this is like a + + + align:start position:0% +going to work why this is like a +reasonable Choice they'll come to that + + align:start position:0% +reasonable Choice they'll come to that + + + align:start position:0% +reasonable Choice they'll come to that +okay so the the lesson here is simply + + align:start position:0% +okay so the the lesson here is simply + + + align:start position:0% +okay so the the lesson here is simply +that the choice of mass + + align:start position:0% +that the choice of mass + + + align:start position:0% +that the choice of mass +scheme has a big impact on + + align:start position:0% +scheme has a big impact on + + + align:start position:0% +scheme has a big impact on +the Curative + + align:start position:0% + + + + align:start position:0% + +series and we haven't yet figured out + + align:start position:0% +series and we haven't yet figured out + + + align:start position:0% +series and we haven't yet figured out +why some things work and why some things + + align:start position:0% +why some things work and why some things + + + align:start position:0% +why some things work and why some things +don't but we will + + align:start position:0% + + + + align:start position:0% + +it's absolutely crucial to use the right + + align:start position:0% +it's absolutely crucial to use the right + + + align:start position:0% +it's absolutely crucial to use the right +one otherwise the predictions will not + + align:start position:0% +one otherwise the predictions will not + + + align:start position:0% +one otherwise the predictions will not +be + + align:start position:0% + + + + align:start position:0% + +good well physically we can actually + + align:start position:0% +good well physically we can actually + + + align:start position:0% +good well physically we can actually +argue right away why MB pole is no not + + align:start position:0% +argue right away why MB pole is no not + + + align:start position:0% +argue right away why MB pole is no not +so + + align:start position:0% + + + + align:start position:0% + +good and that's because physically there + + align:start position:0% +good and that's because physically there + + + align:start position:0% +good and that's because physically there +is no + + align:start position:0% + + + + align:start position:0% + +pole there's no pole in the Quark + + align:start position:0% +pole there's no pole in the Quark + + + align:start position:0% +pole there's no pole in the Quark +propagator + + align:start position:0% + + + + align:start position:0% + +and that is because of + + align:start position:0% + + + + align:start position:0% + +confinement so we use this notion of + + align:start position:0% +confinement so we use this notion of + + + align:start position:0% +confinement so we use this notion of +pole and a quark propagator when we're + + align:start position:0% +pole and a quark propagator when we're + + + align:start position:0% +pole and a quark propagator when we're +doing peration Theory but + + align:start position:0% +doing peration Theory but + + + align:start position:0% +doing peration Theory but +non-perturbatively it's not a well- + + align:start position:0% +non-perturbatively it's not a well- + + + align:start position:0% +non-perturbatively it's not a well- +defined notion or at least there doesn't + + align:start position:0% +defined notion or at least there doesn't + + + align:start position:0% +defined notion or at least there doesn't +ex really exist poles in court + + align:start position:0% +ex really exist poles in court + + + align:start position:0% +ex really exist poles in court +propagators + + align:start position:0% + + + + align:start position:0% + +so it's only + + align:start position:0% +so it's only + + + align:start position:0% +so it's only +perturbatively a good + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +notion so I'll say it's only + + align:start position:0% +notion so I'll say it's only + + + align:start position:0% +notion so I'll say it's only +perturbatively mean + + align:start position:0% +perturbatively mean + + + align:start position:0% +perturbatively mean +ful + + align:start position:0% +ful + + + align:start position:0% +ful +and in + + align:start position:0% + + + + align:start position:0% + +reality is + + align:start position:0% +reality is + + + align:start position:0% +reality is +ambiguous it's an ambiguous notion and + + align:start position:0% +ambiguous it's an ambiguous notion and + + + align:start position:0% +ambiguous it's an ambiguous notion and +you can think that the amount by which + + align:start position:0% +you can think that the amount by which + + + align:start position:0% +you can think that the amount by which +it's ambiguous is related to + + align:start position:0% +it's ambiguous is related to + + + align:start position:0% +it's ambiguous is related to +hadronization which is set by the scale + + align:start position:0% +hadronization which is set by the scale + + + align:start position:0% +hadronization which is set by the scale +Lambda + + align:start position:0% +Lambda + + + align:start position:0% +Lambda +qcd so there's an ambiguity in what you + + align:start position:0% +qcd so there's an ambiguity in what you + + + align:start position:0% +qcd so there's an ambiguity in what you +mean by a pole Mass physically due to + + align:start position:0% +mean by a pole Mass physically due to + + + align:start position:0% +mean by a pole Mass physically due to +non-perturbative + + align:start position:0% +non-perturbative + + + align:start position:0% +non-perturbative +effects now when we set up HQ we + + align:start position:0% +effects now when we set up HQ we + + + align:start position:0% +effects now when we set up HQ we +actually used + + align:start position:0% + + + + align:start position:0% + +pole so we're using a questionable + + align:start position:0% +pole so we're using a questionable + + + align:start position:0% +pole so we're using a questionable +physical + + align:start position:0% +physical + + + align:start position:0% +physical +parameter so when we did these phase + + align:start position:0% + + + + align:start position:0% + +redefinitions we were actually using the + + align:start position:0% +redefinitions we were actually using the + + + align:start position:0% +redefinitions we were actually using the +pole Mass scheme because we were + + align:start position:0% +pole Mass scheme because we were + + + align:start position:0% +pole Mass scheme because we were +expanding about Mass shell + + align:start position:0% + + + + align:start position:0% + +so if you were to do other things you + + align:start position:0% +so if you were to do other things you + + + align:start position:0% +so if you were to do other things you +can think about getting to other + + align:start position:0% +can think about getting to other + + + align:start position:0% +can think about getting to other +choices and implementing them in the + + align:start position:0% + + + + align:start position:0% + +hqet no problem with doing + + align:start position:0% +hqet no problem with doing + + + align:start position:0% +hqet no problem with doing +that but there does exist + + align:start position:0% +that but there does exist + + + align:start position:0% +that but there does exist +another + + align:start position:0% +another + + + align:start position:0% +another +operator that we sort of dropped without + + align:start position:0% +operator that we sort of dropped without + + + align:start position:0% +operator that we sort of dropped without +thinking too hard about + + align:start position:0% +thinking too hard about + + + align:start position:0% +thinking too hard about +it so if we switch to using a different + + align:start position:0% +it so if we switch to using a different + + + align:start position:0% +it so if we switch to using a different +Mass scheme there's some Delta M which + + align:start position:0% +Mass scheme there's some Delta M which + + + align:start position:0% +Mass scheme there's some Delta M which +you can think of as a series in alpha + + align:start position:0% + + + + align:start position:0% + +s which we wrote on the board moment + + align:start position:0% + + + + align:start position:0% + +ago and where that Delta M would show + + align:start position:0% +ago and where that Delta M would show + + + align:start position:0% +ago and where that Delta M would show +up is that you would have kind of an L + + align:start position:0% +up is that you would have kind of an L + + + align:start position:0% +up is that you would have kind of an L +Delta M operator which would just be + + align:start position:0% +Delta M operator which would just be + + + align:start position:0% +Delta M operator which would just be +exactly Delta M and then QV bar + + align:start position:0% + + + + align:start position:0% + +QV that would be left over when we + + align:start position:0% +QV that would be left over when we + + + align:start position:0% +QV that would be left over when we +cancel the masses in the lrin if You' + + align:start position:0% +cancel the masses in the lrin if You' + + + align:start position:0% +cancel the masses in the lrin if You' +like if you used it's one way of + + align:start position:0% +like if you used it's one way of + + + align:start position:0% +like if you used it's one way of +thinking about + + align:start position:0% + + + + align:start position:0% + +it so we have an extra term in the L + + align:start position:0% +it so we have an extra term in the L + + + align:start position:0% +it so we have an extra term in the L +HQ and now you can ask well if we have + + align:start position:0% +HQ and now you can ask well if we have + + + align:start position:0% +HQ and now you can ask well if we have +an extra term we better worry about + + align:start position:0% +an extra term we better worry about + + + align:start position:0% +an extra term we better worry about +power + + align:start position:0% +power + + + align:start position:0% +power +counting and it turns out that the way + + align:start position:0% +counting and it turns out that the way + + + align:start position:0% +counting and it turns out that the way +we can understand why msar wasn't + + align:start position:0% +we can understand why msar wasn't + + + align:start position:0% +we can understand why msar wasn't +working is related to power + + align:start position:0% + + + + align:start position:0% + +counting so in msar if you look at what + + align:start position:0% +counting so in msar if you look at what + + + align:start position:0% +counting so in msar if you look at what +Delta m + + align:start position:0% + + + + align:start position:0% + +is Delta m is MB bar itself times + + align:start position:0% +is Delta m is MB bar itself times + + + align:start position:0% +is Delta m is MB bar itself times +Alpha but by power counting you don't + + align:start position:0% +Alpha but by power counting you don't + + + align:start position:0% +Alpha but by power counting you don't +want something that's growing with MB in + + align:start position:0% +want something that's growing with MB in + + + align:start position:0% +want something that's growing with MB in +the + + align:start position:0% + + + + align:start position:0% + +lran MV bar is suppressed by Alpha so + + align:start position:0% +lran MV bar is suppressed by Alpha so + + + align:start position:0% +lran MV bar is suppressed by Alpha so +it's it's Alpha at MB that is providing + + align:start position:0% +it's it's Alpha at MB that is providing + + + align:start position:0% +it's it's Alpha at MB that is providing +suppression but that's only 0 2 and + + align:start position:0% +suppression but that's only 0 2 and + + + align:start position:0% +suppression but that's only 0 2 and +that's actually just not enough + + align:start position:0% +that's actually just not enough + + + align:start position:0% +that's actually just not enough +suppression to get rid of the the big MB + + align:start position:0% +suppression to get rid of the the big MB + + + align:start position:0% +suppression to get rid of the the big MB +here you don't get you go from 5 GV you + + align:start position:0% +here you don't get you go from 5 GV you + + + align:start position:0% +here you don't get you go from 5 GV you +know there's some number in front maybe + + align:start position:0% +know there's some number in front maybe + + + align:start position:0% +know there's some number in front maybe +you get down to one and a half 2 GV but + + align:start position:0% +you get down to one and a half 2 GV but + + + align:start position:0% +you get down to one and a half 2 GV but +you're not getting down to a small + + align:start position:0% +you're not getting down to a small + + + align:start position:0% +you're not getting down to a small +enough + + align:start position:0% + + + + align:start position:0% + +value so parametrically this is just not + + align:start position:0% +value so parametrically this is just not + + + align:start position:0% +value so parametrically this is just not +good both parametrically because it + + align:start position:0% +good both parametrically because it + + + align:start position:0% +good both parametrically because it +grows with + + align:start position:0% +grows with + + + align:start position:0% +grows with +MB and numerically + + align:start position:0% +MB and numerically + + + align:start position:0% +MB and numerically +it's too big it's + + align:start position:0% + + + + align:start position:0% + +not it's not order Lambda qcd which + + align:start position:0% +not it's not order Lambda qcd which + + + align:start position:0% +not it's not order Lambda qcd which +would be + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so parametrically and numerically Delta + + align:start position:0% +so parametrically and numerically Delta + + + align:start position:0% +so parametrically and numerically Delta +m is just too + + align:start position:0% +m is just too + + + align:start position:0% +m is just too +big for HQ power counting in this msar + + align:start position:0% + + + + align:start position:0% + +scheme you include an operator that + + align:start position:0% +scheme you include an operator that + + + align:start position:0% +scheme you include an operator that +affect L is on average larger and more + + align:start position:0% +affect L is on average larger and more + + + align:start position:0% +affect L is on average larger and more +important than your kinetic + + align:start position:0% +important than your kinetic + + + align:start position:0% +important than your kinetic +term because the v.d operator v.d is + + align:start position:0% +term because the v.d operator v.d is + + + align:start position:0% +term because the v.d operator v.d is +counting like Lambda qcd and it had v.d + + align:start position:0% +counting like Lambda qcd and it had v.d + + + align:start position:0% +counting like Lambda qcd and it had v.d +with two Q's now you have something + + align:start position:0% +with two Q's now you have something + + + align:start position:0% +with two Q's now you have something +Delta M with two q's and this if it's on + + align:start position:0% +Delta M with two q's and this if it's on + + + align:start position:0% +Delta M with two q's and this if it's on +average larger then you're you're messed + + align:start position:0% + + + + align:start position:0% + +up so that's why actually physically the + + align:start position:0% +up so that's why actually physically the + + + align:start position:0% +up so that's why actually physically the +M MB bar is not a good choice you can + + align:start position:0% +M MB bar is not a good choice you can + + + align:start position:0% +M MB bar is not a good choice you can +think about it from the effective Theory + + align:start position:0% +think about it from the effective Theory + + + align:start position:0% +think about it from the effective Theory +from that way MB bar is actually a mass + + align:start position:0% +from that way MB bar is actually a mass + + + align:start position:0% +from that way MB bar is actually a mass +that's you're supposed to think of it as + + align:start position:0% +that's you're supposed to think of it as + + + align:start position:0% +that's you're supposed to think of it as +a mass that Ed for high energy physics + + align:start position:0% +a mass that Ed for high energy physics + + + align:start position:0% +a mass that Ed for high energy physics +for physics really high energy above the + + align:start position:0% +for physics really high energy above the + + + align:start position:0% +for physics really high energy above the +bork Mass scale then it's a good + + align:start position:0% +bork Mass scale then it's a good + + + align:start position:0% +bork Mass scale then it's a good +parameter we're now doing physics below + + align:start position:0% +parameter we're now doing physics below + + + align:start position:0% +parameter we're now doing physics below +the B Quark Mass scale and this is just + + align:start position:0% +the B Quark Mass scale and this is just + + + align:start position:0% +the B Quark Mass scale and this is just +one way of seeing why it's not such a + + align:start position:0% +one way of seeing why it's not such a + + + align:start position:0% +one way of seeing why it's not such a +good parameter + + align:start position:0% +good parameter + + + align:start position:0% +good parameter +there because the perative corrections + + align:start position:0% +there because the perative corrections + + + align:start position:0% +there because the perative corrections +are just too + + align:start position:0% + + + + align:start position:0% + +big so what about this 1s + + align:start position:0% + + + + align:start position:0% + +Mass so here it turns out that if you + + align:start position:0% +Mass so here it turns out that if you + + + align:start position:0% +Mass so here it turns out that if you +calculate Delta + + align:start position:0% +calculate Delta + + + align:start position:0% +calculate Delta +M you get in the same way that you think + + align:start position:0% +M you get in the same way that you think + + + align:start position:0% +M you get in the same way that you think +about corrections to hydrogen being + + align:start position:0% +about corrections to hydrogen being + + + align:start position:0% +about corrections to hydrogen being +order Alpha squar you get mb1s Alpha squ + + align:start position:0% +order Alpha squar you get mb1s Alpha squ + + + align:start position:0% +order Alpha squar you get mb1s Alpha squ +and numerically that's small + + align:start position:0% +and numerically that's small + + + align:start position:0% +and numerically that's small +enough when you put the coefficient + + align:start position:0% +enough when you put the coefficient + + + align:start position:0% +enough when you put the coefficient +in so it still doesn't make us feel very + + align:start position:0% +in so it still doesn't make us feel very + + + align:start position:0% +in so it still doesn't make us feel very +good because it grows with MV but if I + + align:start position:0% +good because it grows with MV but if I + + + align:start position:0% +good because it grows with MV but if I +just care about numerics and I'm doing + + align:start position:0% +just care about numerics and I'm doing + + + align:start position:0% +just care about numerics and I'm doing +bork physics it works because the alpha + + align:start position:0% +bork physics it works because the alpha + + + align:start position:0% +bork physics it works because the alpha +squ is enough + + align:start position:0% +squ is enough + + + align:start position:0% +squ is enough +suppression that this is a good Mass + + align:start position:0% +suppression that this is a good Mass + + + align:start position:0% +suppression that this is a good Mass +scheme and that's why the privation + + align:start position:0% +scheme and that's why the privation + + + align:start position:0% +scheme and that's why the privation +theory treating this is order Lambda qcd + + align:start position:0% +theory treating this is order Lambda qcd + + + align:start position:0% +theory treating this is order Lambda qcd +numerically not + + align:start position:0% + + + + align:start position:0% + +parametrically is + + align:start position:0% + + + + align:start position:0% + +okay now that if that doesn't sit pretty + + align:start position:0% +okay now that if that doesn't sit pretty + + + align:start position:0% +okay now that if that doesn't sit pretty +with you you can do something even more + + align:start position:0% +with you you can do something even more + + + align:start position:0% +with you you can do something even more +fancy and we'll talk about one example + + align:start position:0% +fancy and we'll talk about one example + + + align:start position:0% +fancy and we'll talk about one example +of more fancy a little later on where + + align:start position:0% +of more fancy a little later on where + + + align:start position:0% +of more fancy a little later on where +you basically instead of having M show + + align:start position:0% +you basically instead of having M show + + + align:start position:0% +you basically instead of having M show +up there you have some parameter R and + + align:start position:0% +up there you have some parameter R and + + + align:start position:0% +up there you have some parameter R and +you + + align:start position:0% +you + + + align:start position:0% +you +have something that you can just + + align:start position:0% + + + + align:start position:0% + +pick and so you could pick a scheme here + + align:start position:0% +pick and so you could pick a scheme here + + + align:start position:0% +pick and so you could pick a scheme here +where R is a border L the qcd by however + + align:start position:0% +where R is a border L the qcd by however + + + align:start position:0% +where R is a border L the qcd by however +maybe you pick it to be 1 GV or 500 GV + + align:start position:0% +maybe you pick it to be 1 GV or 500 GV + + + align:start position:0% +maybe you pick it to be 1 GV or 500 GV +or whatever you 500 M or whatever you + + align:start position:0% +or whatever you 500 M or whatever you + + + align:start position:0% +or whatever you 500 M or whatever you +like so you can make up a scheme where + + align:start position:0% +like so you can make up a scheme where + + + align:start position:0% +like so you can make up a scheme where +this is true and then both pair + + align:start position:0% +this is true and then both pair + + + align:start position:0% +this is true and then both pair +parametrically and numerically you're + + align:start position:0% +parametrically and numerically you're + + + align:start position:0% +parametrically and numerically you're +okay and these schemes also work just as + + align:start position:0% +okay and these schemes also work just as + + + align:start position:0% +okay and these schemes also work just as +well as the 1s + + align:start position:0% + + + + align:start position:0% + +scheme so we can get more fancy and also + + align:start position:0% +scheme so we can get more fancy and also + + + align:start position:0% +scheme so we can get more fancy and also +satisfy our formal + + align:start position:0% + + + + align:start position:0% + +requirement all right so that's kind of + + align:start position:0% +requirement all right so that's kind of + + + align:start position:0% +requirement all right so that's kind of +phenomenological numbers and bit of + + align:start position:0% +phenomenological numbers and bit of + + + align:start position:0% +phenomenological numbers and bit of +physics let's come back to some + + align:start position:0% +physics let's come back to some + + + align:start position:0% +physics let's come back to some +mathematics and talk about what re + + align:start position:0% +mathematics and talk about what re + + + align:start position:0% +mathematics and talk about what re +normal ones are + + align:start position:0% + + + + align:start position:0% + +mathematically is there a mathematical + + align:start position:0% +mathematically is there a mathematical + + + align:start position:0% +mathematically is there a mathematical +way of character izing what's going + + align:start position:0% +way of character izing what's going + + + align:start position:0% +way of character izing what's going +wrong what if I didn't think about this + + align:start position:0% +wrong what if I didn't think about this + + + align:start position:0% +wrong what if I didn't think about this +physics could I do a calculation and be + + align:start position:0% +physics could I do a calculation and be + + + align:start position:0% +physics could I do a calculation and be +see that something's going wrong and the + + align:start position:0% +see that something's going wrong and the + + + align:start position:0% +see that something's going wrong and the +answer is + + align:start position:0% +answer is + + + align:start position:0% +answer is +yes so first I have to teach you a few + + align:start position:0% +yes so first I have to teach you a few + + + align:start position:0% +yes so first I have to teach you a few +things if you don't know them + + align:start position:0% +things if you don't know them + + + align:start position:0% +things if you don't know them +already about the astics of perturbative + + align:start position:0% +already about the astics of perturbative + + + align:start position:0% +already about the astics of perturbative +Series in Quantum field + + align:start position:0% +Series in Quantum field + + + align:start position:0% +Series in Quantum field +Theory and these are actually not + + align:start position:0% +Theory and these are actually not + + + align:start position:0% +Theory and these are actually not +convergent series + + align:start position:0% + + + + align:start position:0% + +so they are what are called ASM totic + + align:start position:0% + + + + align:start position:0% + +Series so what's the definition of an + + align:start position:0% +Series so what's the definition of an + + + align:start position:0% +Series so what's the definition of an +ASM totic + + align:start position:0% +ASM totic + + + align:start position:0% +ASM totic +Series so we'd say a function has an ASM + + align:start position:0% +Series so we'd say a function has an ASM + + + align:start position:0% +Series so we'd say a function has an ASM +totic + + align:start position:0% +totic + + + align:start position:0% +totic +series which + + align:start position:0% +series which + + + align:start position:0% +series which +is I'll write as follows sum + + align:start position:0% +is I'll write as follows sum + + + align:start position:0% +is I'll write as follows sum +coefficients and we'll just call the + + align:start position:0% +coefficients and we'll just call the + + + align:start position:0% +coefficients and we'll just call the +expansion parameter Alpha you can think + + align:start position:0% +expansion parameter Alpha you can think + + + align:start position:0% +expansion parameter Alpha you can think +of it as alpha s if you like but this is + + align:start position:0% +of it as alpha s if you like but this is + + + align:start position:0% +of it as alpha s if you like but this is +just math so you don't have to think + + align:start position:0% +just math so you don't have to think + + + align:start position:0% +just math so you don't have to think +about it as anything but the expansion + + align:start position:0% +about it as anything but the expansion + + + align:start position:0% +about it as anything but the expansion +parameter and we say that a function is + + align:start position:0% +parameter and we say that a function is + + + align:start position:0% +parameter and we say that a function is +has an ASM totic + + align:start position:0% +has an ASM totic + + + align:start position:0% +has an ASM totic +series if and only + + align:start position:0% +series if and only + + + align:start position:0% +series if and only +if the following is true F of alpha + + align:start position:0% +if the following is true F of alpha + + + align:start position:0% +if the following is true F of alpha +minus the partial sum up to some level + + align:start position:0% + + + + align:start position:0% + +n is less than kind of the next the + + align:start position:0% +n is less than kind of the next the + + + align:start position:0% +n is less than kind of the next the +scaling that you would get from the next + + align:start position:0% +scaling that you would get from the next + + + align:start position:0% +scaling that you would get from the next +term in the series which is n plus + + align:start position:0% + + + + align:start position:0% + +2 for + + align:start position:0% +2 for + + + align:start position:0% +2 for +some + + align:start position:0% +some + + + align:start position:0% +some +numbers k n + + + align:start position:0% + + + + align:start position:0% + +2 so that's actually a quite different + + align:start position:0% +2 so that's actually a quite different + + + align:start position:0% +2 so that's actually a quite different +definition than what you would have for + + align:start position:0% +definition than what you would have for + + + align:start position:0% +definition than what you would have for +convergent series for convergent series + + align:start position:0% +convergent series for convergent series + + + align:start position:0% +convergent series for convergent series +you would say that you could pick any + + align:start position:0% +you would say that you could pick any + + + align:start position:0% +you would say that you could pick any +Epsilon you like here and you could make + + align:start position:0% +Epsilon you like here and you could make + + + align:start position:0% +Epsilon you like here and you could make +the N big enough enough that this would + + align:start position:0% +the N big enough enough that this would + + + align:start position:0% +the N big enough enough that this would +get close to that here I'm just saying + + align:start position:0% +get close to that here I'm just saying + + + align:start position:0% +get close to that here I'm just saying +that it's less than this with some power + + align:start position:0% +that it's less than this with some power + + + align:start position:0% +that it's less than this with some power +of alpha so imagine that I pick Alpha to + + align:start position:0% +of alpha so imagine that I pick Alpha to + + + align:start position:0% +of alpha so imagine that I pick Alpha to +be 0.1 the thing is that this K here + + align:start position:0% +be 0.1 the thing is that this K here + + + align:start position:0% +be 0.1 the thing is that this K here +could still grow with n and that + + align:start position:0% +could still grow with n and that + + + align:start position:0% +could still grow with n and that +actually will happen so the truncation + + align:start position:0% +actually will happen so the truncation + + + align:start position:0% +actually will happen so the truncation +area in some sense is not being bounded + + align:start position:0% +area in some sense is not being bounded + + + align:start position:0% +area in some sense is not being bounded +in these ASM totic + + align:start position:0% + + + + align:start position:0% + +series and peration theory and Quantum + + align:start position:0% +series and peration theory and Quantum + + + align:start position:0% +series and peration theory and Quantum +field theory is generically of this + + align:start position:0% +field theory is generically of this + + + align:start position:0% +field theory is generically of this +structure and we'll show you some + + align:start position:0% +structure and we'll show you some + + + align:start position:0% +structure and we'll show you some +examples of + + align:start position:0% + + + + align:start position:0% + +that it's ASM totic rather than + + align:start position:0% + + + + align:start position:0% + +convergent so when you do a qfd + + align:start position:0% +convergent so when you do a qfd + + + align:start position:0% +convergent so when you do a qfd +calculation kind of typical result if + + align:start position:0% +calculation kind of typical result if + + + align:start position:0% +calculation kind of typical result if +you work out some + + align:start position:0% +you work out some + + + align:start position:0% +you work out some +astics is that you would have these FN + + align:start position:0% +astics is that you would have these FN + + + align:start position:0% +astics is that you would have these FN +coefficients that are some power of a + + align:start position:0% +coefficients that are some power of a + + + align:start position:0% +coefficients that are some power of a +and then times an N + + align:start position:0% + + + + align:start position:0% + +factorial and that's kind of how they're + + align:start position:0% +factorial and that's kind of how they're + + + align:start position:0% +factorial and that's kind of how they're +scaling as n is getting large you can + + align:start position:0% +scaling as n is getting large you can + + + align:start position:0% +scaling as n is getting large you can +think about the number of diagrams is + + align:start position:0% +think about the number of diagrams is + + + align:start position:0% +think about the number of diagrams is +just growing but even with even when + + align:start position:0% +just growing but even with even when + + + align:start position:0% +just growing but even with even when +diagrams are not growing you can get + + align:start position:0% +diagrams are not growing you can get + + + align:start position:0% +diagrams are not growing you can get +these n + + align:start position:0% + + + + align:start position:0% + +factorials so that means if you're + + align:start position:0% +factorials so that means if you're + + + align:start position:0% +factorials so that means if you're +fixing Alpha as some value of the + + align:start position:0% +fixing Alpha as some value of the + + + align:start position:0% +fixing Alpha as some value of the +parameter and no matter how small you + + align:start position:0% +parameter and no matter how small you + + + align:start position:0% +parameter and no matter how small you +take + + align:start position:0% +take + + + align:start position:0% +take +it at some order in pration theory + + align:start position:0% +it at some order in pration theory + + + align:start position:0% +it at some order in pration theory +you're basically running out of gas and + + align:start position:0% +you're basically running out of gas and + + + align:start position:0% +you're basically running out of gas and +your trunker truncation are you start + + align:start position:0% +your trunker truncation are you start + + + align:start position:0% +your trunker truncation are you start +to your prediction start to grow and + + align:start position:0% +to your prediction start to grow and + + + align:start position:0% +to your prediction start to grow and +diverge so the corresponding values of + + align:start position:0% +diverge so the corresponding values of + + + align:start position:0% +diverge so the corresponding values of +these KS if you had these FS that were + + align:start position:0% +these KS if you had these FS that were + + + align:start position:0% +these KS if you had these FS that were +of that form would be that the Ks are + + align:start position:0% +of that form would be that the Ks are + + + align:start position:0% +of that form would be that the Ks are +basically growing in the same + + align:start position:0% +basically growing in the same + + + align:start position:0% +basically growing in the same +way so you'd need larger and larger + + align:start position:0% +way so you'd need larger and larger + + + align:start position:0% +way so you'd need larger and larger +numbers in order to satisfy the + + align:start position:0% +numbers in order to satisfy the + + + align:start position:0% +numbers in order to satisfy the +definition of ASM totic over there and + + align:start position:0% +definition of ASM totic over there and + + + align:start position:0% +definition of ASM totic over there and +having these large numbers you're never + + align:start position:0% +having these large numbers you're never + + + align:start position:0% +having these large numbers you're never +able ble to satisfy + + align:start position:0% + + + + align:start position:0% + +convergent so the series has zero radius + + align:start position:0% +convergent so the series has zero radius + + + align:start position:0% +convergent so the series has zero radius +of + + align:start position:0% + + + + align:start position:0% + +convergence and then you wonder why have + + align:start position:0% +convergence and then you wonder why have + + + align:start position:0% +convergence and then you wonder why have +we been teaching you quum field + + align:start position:0% +we been teaching you quum field + + + align:start position:0% +we been teaching you quum field +Theory that's + + align:start position:0% +Theory that's + + + align:start position:0% +Theory that's +true so what do we know even though we + + align:start position:0% +true so what do we know even though we + + + align:start position:0% +true so what do we know even though we +the series are ASM totic we can still + + align:start position:0% +the series are ASM totic we can still + + + align:start position:0% +the series are ASM totic we can still +make use of + + align:start position:0% +make use of + + + align:start position:0% +make use of +them so so typically what happens is + + align:start position:0% +them so so typically what happens is + + + align:start position:0% +them so so typically what happens is +that the series will decrease for a + + align:start position:0% +that the series will decrease for a + + + align:start position:0% +that the series will decrease for a +while it'll look like it's convergent + + align:start position:0% +while it'll look like it's convergent + + + align:start position:0% +while it'll look like it's convergent +and then it'll start + + align:start position:0% +and then it'll start + + + align:start position:0% +and then it'll start +diverging and you can characterize + + align:start position:0% +diverging and you can characterize + + + align:start position:0% +diverging and you can characterize +where it starts to + + align:start position:0% +where it starts to + + + align:start position:0% +where it starts to +diverge and I'm not going to go through + + align:start position:0% +diverge and I'm not going to go through + + + align:start position:0% +diverge and I'm not going to go through +all the algebra but I'll just tell you + + align:start position:0% +all the algebra but I'll just tell you + + + align:start position:0% +all the algebra but I'll just tell you +some + + align:start position:0% + + + + align:start position:0% + +facts and so you can imagine that you're + + align:start position:0% +facts and so you can imagine that you're + + + align:start position:0% +facts and so you can imagine that you're +doing some perturbation theories and it + + align:start position:0% +doing some perturbation theories and it + + + align:start position:0% +doing some perturbation theories and it +looks like it's it's going well things + + align:start position:0% +looks like it's it's going well things + + + align:start position:0% +looks like it's it's going well things +are converging but then some things + + align:start position:0% +are converging but then some things + + + align:start position:0% +are converging but then some things +things don't start to go so well so + + align:start position:0% +things don't start to go so well so + + + align:start position:0% +things don't start to go so well so +think of what I'm plotting here as the + + align:start position:0% +think of what I'm plotting here as the + + + align:start position:0% +think of what I'm plotting here as the +partial sum of your privation + + align:start position:0% + + + + align:start position:0% + +theory at n + + align:start position:0% +theory at n + + + align:start position:0% +theory at n +order so I sum up all the corrections up + + align:start position:0% +order so I sum up all the corrections up + + + align:start position:0% +order so I sum up all the corrections up +to n so it's like the series that I was + + align:start position:0% +to n so it's like the series that I was + + + align:start position:0% +to n so it's like the series that I was +writing over here it's this + + align:start position:0% +writing over here it's this + + + align:start position:0% +writing over here it's this +thing now in PR per of QED P of qcd + + align:start position:0% +thing now in PR per of QED P of qcd + + + align:start position:0% +thing now in PR per of QED P of qcd +we're never really we're NE we're never + + align:start position:0% +we're never really we're NE we're never + + + align:start position:0% +we're never really we're NE we're never +uh getting more than a few terms so you + + align:start position:0% +uh getting more than a few terms so you + + + align:start position:0% +uh getting more than a few terms so you +could say well okay maybe I don't care + + align:start position:0% +could say well okay maybe I don't care + + + align:start position:0% +could say well okay maybe I don't care +so much about this and in QED that's + + align:start position:0% +so much about this and in QED that's + + + align:start position:0% +so much about this and in QED that's +actually the case you don't really care + + align:start position:0% +actually the case you don't really care + + + align:start position:0% +actually the case you don't really care +so much about that but in qcd actually + + align:start position:0% +so much about that but in qcd actually + + + align:start position:0% +so much about that but in qcd actually +the turnover happens already around + + align:start position:0% +the turnover happens already around + + + align:start position:0% +the turnover happens already around +three Loops so as soon as you start + + align:start position:0% +three Loops so as soon as you start + + + align:start position:0% +three Loops so as soon as you start +including two Loop Corrections this is + + align:start position:0% +including two Loop Corrections this is + + + align:start position:0% +including two Loop Corrections this is +something you have to care + + align:start position:0% + + + + align:start position:0% + +about now you can say well the best + + align:start position:0% +about now you can say well the best + + + align:start position:0% +about now you can say well the best +thing I can do is stop doing peration + + align:start position:0% +thing I can do is stop doing peration + + + align:start position:0% +thing I can do is stop doing peration +Theory at some end + + align:start position:0% +Theory at some end + + + align:start position:0% +Theory at some end +star because that's kind of where it + + align:start position:0% +star because that's kind of where it + + + align:start position:0% +star because that's kind of where it +looks the best like I'm I've gone to + + align:start position:0% +looks the best like I'm I've gone to + + + align:start position:0% +looks the best like I'm I've gone to +something and it and that actually is + + align:start position:0% +something and it and that actually is + + + align:start position:0% +something and it and that actually is +not such a bad thing and it turns out + + align:start position:0% +not such a bad thing and it turns out + + + align:start position:0% +not such a bad thing and it turns out +you can characterize actually the + + align:start position:0% +you can characterize actually the + + + align:start position:0% +you can characterize actually the +mistake you're making by stopping there + + align:start position:0% +mistake you're making by stopping there + + + align:start position:0% +mistake you're making by stopping there +and the mistake you're making by + + align:start position:0% +and the mistake you're making by + + + align:start position:0% +and the mistake you're making by +stopping + + align:start position:0% +stopping + + + align:start position:0% +stopping +there is of the following + + align:start position:0% + + + + align:start position:0% + +form + + align:start position:0% +form + + + align:start position:0% +form +so it's an + + align:start position:0% +so it's an + + + align:start position:0% +so it's an +exponential and one over + + align:start position:0% + + + + align:start position:0% + +Alpha so it would you would never be + + align:start position:0% +Alpha so it would you would never be + + + align:start position:0% +Alpha so it would you would never be +able to + + align:start position:0% +able to + + + align:start position:0% +able to +see the kind of the correction that you + + align:start position:0% +see the kind of the correction that you + + + align:start position:0% +see the kind of the correction that you +need to get to the correct value which + + align:start position:0% +need to get to the correct value which + + + align:start position:0% +need to get to the correct value which +I'm imagining is on the axis here in + + align:start position:0% +I'm imagining is on the axis here in + + + align:start position:0% +I'm imagining is on the axis here in +perturbation Theory because this doesn't + + align:start position:0% +perturbation Theory because this doesn't + + + align:start position:0% +perturbation Theory because this doesn't +have a perturbative expansion and I'll + + align:start position:0% +have a perturbative expansion and I'll + + + align:start position:0% +have a perturbative expansion and I'll +actually show you that kind of the the + + align:start position:0% +actually show you that kind of the the + + + align:start position:0% +actually show you that kind of the the +bad behavior here and this Gap are + + align:start position:0% +bad behavior here and this Gap are + + + align:start position:0% +bad behavior here and this Gap are +related to power Corrections and they're + + align:start position:0% +related to power Corrections and they're + + + align:start position:0% +related to power Corrections and they're +exactly related to this connection that + + align:start position:0% +exactly related to this connection that + + + align:start position:0% +exactly related to this connection that +I was telling you between perturbative + + align:start position:0% +I was telling you between perturbative + + + align:start position:0% +I was telling you between perturbative +Corrections and large order astics and + + align:start position:0% +Corrections and large order astics and + + + align:start position:0% +Corrections and large order astics and +power Corrections this type of + + align:start position:0% +power Corrections this type of + + + align:start position:0% +power Corrections this type of +exponential + + align:start position:0% +exponential + + + align:start position:0% +exponential +is something that we can relate to power + + align:start position:0% +is something that we can relate to power + + + align:start position:0% +is something that we can relate to power +Corrections and we'll see how that how + + align:start position:0% +Corrections and we'll see how that how + + + align:start position:0% +Corrections and we'll see how that how +that pans out Al though we might + + align:start position:0% +that pans out Al though we might + + + align:start position:0% +that pans out Al though we might +probably won't get there until next + + align:start position:0% +probably won't get there until next + + + align:start position:0% +probably won't get there until next +class okay so this is kind of a a + + align:start position:0% +class okay so this is kind of a a + + + align:start position:0% +class okay so this is kind of a a +Prelude and now we're going to go into + + align:start position:0% +Prelude and now we're going to go into + + + align:start position:0% +Prelude and now we're going to go into +more detail and it turns out in order to + + align:start position:0% +more detail and it turns out in order to + + + align:start position:0% +more detail and it turns out in order to +go into more detail here that much as + + align:start position:0% +go into more detail here that much as + + + align:start position:0% +go into more detail here that much as +you make 4 a transforms to explore + + align:start position:0% +you make 4 a transforms to explore + + + align:start position:0% +you make 4 a transforms to explore +another space we're going to do a + + align:start position:0% +another space we're going to do a + + + align:start position:0% +another space we're going to do a +transform to something called barell + + align:start position:0% +transform to something called barell + + + align:start position:0% +transform to something called barell +space + + align:start position:0% + + + + align:start position:0% + +so it turns out that when you have a + + align:start position:0% +so it turns out that when you have a + + + align:start position:0% +so it turns out that when you have a +Divergence series or an ASM totic + + align:start position:0% +Divergence series or an ASM totic + + + align:start position:0% +Divergence series or an ASM totic +series that you can there's still + + align:start position:0% +series that you can there's still + + + align:start position:0% +series that you can there's still +degrees of Divergence and we can + + align:start position:0% +degrees of Divergence and we can + + + align:start position:0% +degrees of Divergence and we can +classify how Divergent It Is by using + + align:start position:0% +classify how Divergent It Is by using + + + align:start position:0% +classify how Divergent It Is by using +something called a barell transform + + align:start position:0% + + + + align:start position:0% + +yeah we + + align:start position:0% +yeah we + + + align:start position:0% +yeah we +use + + align:start position:0% +use + + + align:start position:0% +use +be um so no it's not uh yeah so 1s Mass + + align:start position:0% +be um so no it's not uh yeah so 1s Mass + + + align:start position:0% +be um so no it's not uh yeah so 1s Mass +let's see yeah it it's not it's it is + + align:start position:0% +let's see yeah it it's not it's it is + + + align:start position:0% +let's see yeah it it's not it's it is +still ASM totic but it's it's in a way + + align:start position:0% +still ASM totic but it's it's in a way + + + align:start position:0% +still ASM totic but it's it's in a way +that I'll describe once we understand + + align:start position:0% +that I'll describe once we understand + + + align:start position:0% +that I'll describe once we understand +what this B barell is it's it's much + + align:start position:0% +what this B barell is it's it's much + + + align:start position:0% +what this B barell is it's it's much +less diverg + + align:start position:0% +less diverg + + + align:start position:0% +less diverg +than the other series than the pole + + align:start position:0% +than the other series than the pole + + + align:start position:0% +than the other series than the pole +series if you think about the pole + + align:start position:0% +series if you think about the pole + + + align:start position:0% +series if you think about the pole +series as being degree zero Divergent + + align:start position:0% +series as being degree zero Divergent + + + align:start position:0% +series as being degree zero Divergent +then this is like a few orders down less + + align:start position:0% +then this is like a few orders down less + + + align:start position:0% +then this is like a few orders down less +Divergent so once we Define less + + align:start position:0% +Divergent so once we Define less + + + align:start position:0% +Divergent so once we Define less +Divergent of a Divergent + + align:start position:0% +Divergent of a Divergent + + + align:start position:0% +Divergent of a Divergent +series then I'll be able to make that + + align:start position:0% +series then I'll be able to make that + + + align:start position:0% +series then I'll be able to make that +more + + align:start position:0% + + + + align:start position:0% + +precise it's a question of when power + + align:start position:0% +precise it's a question of when power + + + align:start position:0% +precise it's a question of when power +Corrections come in and if you look at + + align:start position:0% +Corrections come in and if you look at + + + align:start position:0% +Corrections come in and if you look at +like so physically the 1s mass is a + + align:start position:0% +like so physically the 1s mass is a + + + align:start position:0% +like so physically the 1s mass is a +physical thing for Upsilon State and if + + align:start position:0% +physical thing for Upsilon State and if + + + align:start position:0% +physical thing for Upsilon State and if +you look at how power Corrections come + + align:start position:0% +you look at how power Corrections come + + + align:start position:0% +you look at how power Corrections come +in then they're suppressed because + + align:start position:0% +in then they're suppressed because + + + align:start position:0% +in then they're suppressed because +there's an ambiguity between power + + align:start position:0% +there's an ambiguity between power + + + align:start position:0% +there's an ambiguity between power +Corrections and pertubation theory if + + align:start position:0% +Corrections and pertubation theory if + + + align:start position:0% +Corrections and pertubation theory if +the power Corrections are suppressed you + + align:start position:0% +the power Corrections are suppressed you + + + align:start position:0% +the power Corrections are suppressed you +have less ambiguity in the perturbation + + align:start position:0% +have less ambiguity in the perturbation + + + align:start position:0% +have less ambiguity in the perturbation +Theory that's another way of thinking + + align:start position:0% +Theory that's another way of thinking + + + align:start position:0% +Theory that's another way of thinking +about it about the answer to your + + align:start position:0% +about it about the answer to your + + + align:start position:0% +about it about the answer to your +question pushes + + align:start position:0% +question pushes + + + align:start position:0% +question pushes +up + + align:start position:0% +up + + + align:start position:0% +up +um it basically affects this + + align:start position:0% + + + + align:start position:0% + +a all right lots of good questions let's + + align:start position:0% +a all right lots of good questions let's + + + align:start position:0% +a all right lots of good questions let's +see how we get + + align:start position:0% +see how we get + + + align:start position:0% +see how we get +there so when I transform I'm going to + + align:start position:0% +there so when I transform I'm going to + + + align:start position:0% +there so when I transform I'm going to +call the transform function capital F + + align:start position:0% +call the transform function capital F + + + align:start position:0% +call the transform function capital F +and I'm going to call this argument B + + align:start position:0% +and I'm going to call this argument B + + + align:start position:0% +and I'm going to call this argument B +for Burell and so what's the definition + + align:start position:0% +for Burell and so what's the definition + + + align:start position:0% +for Burell and so what's the definition +of the Burell + + align:start position:0% +of the Burell + + + align:start position:0% +of the Burell +transform we're going to Define it as + + align:start position:0% +transform we're going to Define it as + + + align:start position:0% +transform we're going to Define it as +follows there's a first order + + align:start position:0% +follows there's a first order + + + align:start position:0% +follows there's a first order +term and I'm just going to put a Delta + + align:start position:0% +term and I'm just going to put a Delta + + + align:start position:0% +term and I'm just going to put a Delta +function there the real thing that + + align:start position:0% +function there the real thing that + + + align:start position:0% +function there the real thing that +matters is the series of terms that come + + align:start position:0% +matters is the series of terms that come + + + align:start position:0% +matters is the series of terms that come +next and instead of having F to the n + + align:start position:0% +next and instead of having F to the n + + + align:start position:0% +next and instead of having F to the n +Alpha to the N I'm going to divide by an + + align:start position:0% +Alpha to the N I'm going to divide by an + + + align:start position:0% +Alpha to the N I'm going to divide by an +extra n factorial and that's the + + align:start position:0% +extra n factorial and that's the + + + align:start position:0% +extra n factorial and that's the +definition of given a set of FS how I + + align:start position:0% +definition of given a set of FS how I + + + align:start position:0% +definition of given a set of FS how I +construct What's called the barell + + align:start position:0% +construct What's called the barell + + + align:start position:0% +construct What's called the barell +transform and because of the N factorial + + align:start position:0% +transform and because of the N factorial + + + align:start position:0% +transform and because of the N factorial +I get improved + + align:start position:0% + + + + align:start position:0% + +convergence so the N factorial is making + + align:start position:0% +convergence so the N factorial is making + + + align:start position:0% +convergence so the N factorial is making +it converge + + align:start position:0% + + + + align:start position:0% + +better so if there's a transform there + + align:start position:0% +better so if there's a transform there + + + align:start position:0% +better so if there's a transform there +should be an inverse + + align:start position:0% +should be an inverse + + + align:start position:0% +should be an inverse +transform so here's the inverse + + align:start position:0% +transform so here's the inverse + + + align:start position:0% +transform so here's the inverse +transform it's an integral from 0 to + + align:start position:0% +transform it's an integral from 0 to + + + align:start position:0% +transform it's an integral from 0 to +Infinity B over + + align:start position:0% +Infinity B over + + + align:start position:0% +Infinity B over +Alpha F of + + align:start position:0% + + + + align:start position:0% + +B that would give me back to the F so if + + align:start position:0% +B that would give me back to the F so if + + + align:start position:0% +B that would give me back to the F so if +you have a convergence + + align:start position:0% +you have a convergence + + + align:start position:0% +you have a convergence +series and you think of this transform + + align:start position:0% +series and you think of this transform + + + align:start position:0% +series and you think of this transform +then you just go back and forth and you + + align:start position:0% +then you just go back and forth and you + + + align:start position:0% +then you just go back and forth and you +get back the original the function that + + align:start position:0% +get back the original the function that + + + align:start position:0% +get back the original the function that +you started + + align:start position:0% + + + + align:start position:0% + +with so if you have some series that's + + align:start position:0% +with so if you have some series that's + + + align:start position:0% +with so if you have some series that's +like + + align:start position:0% +like + + + align:start position:0% +like +that you get + + align:start position:0% +that you get + + + align:start position:0% +that you get +back you can calculate that series and + + align:start position:0% +back you can calculate that series and + + + align:start position:0% +back you can calculate that series and +you get some f of alpha just before + + align:start position:0% +you get some f of alpha just before + + + align:start position:0% +you get some f of alpha just before +barell transforming if you do this + + align:start position:0% +barell transforming if you do this + + + align:start position:0% +barell transforming if you do this +barell transform then you calculate this + + align:start position:0% +barell transform then you calculate this + + + align:start position:0% +barell transform then you calculate this +integral you get + + align:start position:0% +integral you get + + + align:start position:0% +integral you get +back the + + align:start position:0% +back the + + + align:start position:0% +back the +same F of + + align:start position:0% +same F of + + + align:start position:0% +same F of +alpha from the inverse + + align:start position:0% + + + + align:start position:0% + +transform let me give you an example + + align:start position:0% +transform let me give you an example + + + align:start position:0% +transform let me give you an example +that shows you + + align:start position:0% +that shows you + + + align:start position:0% +that shows you +uh that if you have a Divergence series + + align:start position:0% +uh that if you have a Divergence series + + + align:start position:0% +uh that if you have a Divergence series +it's not too crazy to define the sum of + + align:start position:0% +it's not too crazy to define the sum of + + + align:start position:0% +it's not too crazy to define the sum of +the Divergence series by this by using + + align:start position:0% +the Divergence series by this by using + + + align:start position:0% +the Divergence series by this by using +these + + align:start position:0% +these + + + align:start position:0% +these +transforms so I claim that for a + + align:start position:0% +transforms so I claim that for a + + + align:start position:0% +transforms so I claim that for a +Divergence + + align:start position:0% +Divergence + + + align:start position:0% +Divergence +series where F of + + align:start position:0% +series where F of + + + align:start position:0% +series where F of +B and the inverse transform exist so if + + align:start position:0% +B and the inverse transform exist so if + + + align:start position:0% +B and the inverse transform exist so if +we start with a Divergence series but + + align:start position:0% +we start with a Divergence series but + + + align:start position:0% +we start with a Divergence series but +these things + + align:start position:0% + + + + align:start position:0% + +exist then we could just use this + + align:start position:0% +exist then we could just use this + + + align:start position:0% +exist then we could just use this +transform as a way of defining F of + + align:start position:0% + + + + align:start position:0% + +alpha so let me give you a simple + + align:start position:0% +alpha so let me give you a simple + + + align:start position:0% +alpha so let me give you a simple +example of that convince you that it's + + align:start position:0% +example of that convince you that it's + + + align:start position:0% +example of that convince you that it's +not such a bad thing to do so let's + + align:start position:0% +not such a bad thing to do so let's + + + align:start position:0% +not such a bad thing to do so let's +consider the following + + align:start position:0% + + + + align:start position:0% + +series just an alternating series but + + align:start position:0% +series just an alternating series but + + + align:start position:0% +series just an alternating series but +Alpha is a parameter greater than + + align:start position:0% +Alpha is a parameter greater than + + + align:start position:0% +Alpha is a parameter greater than +one that series doesn't + + align:start position:0% +one that series doesn't + + + align:start position:0% +one that series doesn't +converge of course for Alpha less than + + align:start position:0% +converge of course for Alpha less than + + + align:start position:0% +converge of course for Alpha less than +one it would converge + + align:start position:0% + + + + align:start position:0% + +and if I asked you what it should be you + + align:start position:0% +and if I asked you what it should be you + + + align:start position:0% +and if I asked you what it should be you +would say well I calculate for Alpha + + align:start position:0% +would say well I calculate for Alpha + + + align:start position:0% +would say well I calculate for Alpha +less than one I analytically continue + + align:start position:0% +less than one I analytically continue + + + align:start position:0% +less than one I analytically continue +and it's Alpha we at one plus + + align:start position:0% +and it's Alpha we at one plus + + + align:start position:0% +and it's Alpha we at one plus +Alpha well that's one way of getting + + align:start position:0% +Alpha well that's one way of getting + + + align:start position:0% +Alpha well that's one way of getting +there another way of getting there is + + align:start position:0% +there another way of getting there is + + + align:start position:0% +there another way of getting there is +using this Bal + + align:start position:0% +using this Bal + + + align:start position:0% +using this Bal +transform so if you calculate it here F + + align:start position:0% +transform so if you calculate it here F + + + align:start position:0% +transform so if you calculate it here F +of + + align:start position:0% + + + + align:start position:0% + +B you sum up 0 to Infinity minus B to + + align:start position:0% +B you sum up 0 to Infinity minus B to + + + align:start position:0% +B you sum up 0 to Infinity minus B to +the N once you put the minus one in + + align:start position:0% +the N once you put the minus one in + + + align:start position:0% +the N once you put the minus one in +there and there's an extra n factoral + + align:start position:0% +there and there's an extra n factoral + + + align:start position:0% +there and there's an extra n factoral +so that's eus B perfectly well behaved + + align:start position:0% +so that's eus B perfectly well behaved + + + align:start position:0% +so that's eus B perfectly well behaved +function and then you have to do an + + align:start position:0% +function and then you have to do an + + + align:start position:0% +function and then you have to do an +integral 0 to Infinity + + align:start position:0% +integral 0 to Infinity + + + align:start position:0% +integral 0 to Infinity +DB you have e Theus B over Alpha times + + align:start position:0% +DB you have e Theus B over Alpha times + + + align:start position:0% +DB you have e Theus B over Alpha times +the F of B which is eus + + align:start position:0% +the F of B which is eus + + + align:start position:0% +the F of B which is eus +B and that just gives you Alpha over 1 + + align:start position:0% +B and that just gives you Alpha over 1 + + + align:start position:0% +B and that just gives you Alpha over 1 +plus + + align:start position:0% + + + + align:start position:0% + +Alpha and this is a perfectly well- + + align:start position:0% +Alpha and this is a perfectly well- + + + align:start position:0% +Alpha and this is a perfectly well- +defined integral for large + + align:start position:0% +defined integral for large + + + align:start position:0% +defined integral for large +Alpha large Alpha's even making a bit + + align:start position:0% + + + + align:start position:0% + +better so the interval is perfectly well + + align:start position:0% +better so the interval is perfectly well + + + align:start position:0% +better so the interval is perfectly well +defined and we get an answer that we + + align:start position:0% + + + + align:start position:0% + +like Okay so this barel transform is a + + align:start position:0% +like Okay so this barel transform is a + + + align:start position:0% +like Okay so this barel transform is a +useful way of dealing with Divergent + + align:start position:0% +useful way of dealing with Divergent + + + align:start position:0% +useful way of dealing with Divergent +series + + align:start position:0% + + + + align:start position:0% + +the real question is what happens if the + + align:start position:0% +the real question is what happens if the + + + align:start position:0% +the real question is what happens if the +inverse transform doesn't + + align:start position:0% + + + + align:start position:0% + +exist that's what's going to be the + + align:start position:0% +exist that's what's going to be the + + + align:start position:0% +exist that's what's going to be the +thing that we're most interest most + + align:start position:0% +thing that we're most interest most + + + align:start position:0% +thing that we're most interest most +interested in + + align:start position:0% + + + + align:start position:0% + +so the F of B integral integral over the + + align:start position:0% +so the F of B integral integral over the + + + align:start position:0% +so the F of B integral integral over the +F of B doesn't + + align:start position:0% + + + + align:start position:0% + +exist then the integrand can tell us + + align:start position:0% +exist then the integrand can tell us + + + align:start position:0% +exist then the integrand can tell us +about the severity of the singularities + + align:start position:0% + + + + align:start position:0% + +I.E the severity of the + + align:start position:0% + + + + align:start position:0% + +Divergence and that's the real power of + + align:start position:0% +Divergence and that's the real power of + + + align:start position:0% +Divergence and that's the real power of +this barell + + align:start position:0% +this barell + + + align:start position:0% +this barell +method so let's do another example where + + align:start position:0% +method so let's do another example where + + + align:start position:0% +method so let's do another example where +actually things will diverge so let me + + align:start position:0% +actually things will diverge so let me + + + align:start position:0% +actually things will diverge so let me +take FN to be Aus + + align:start position:0% +take FN to be Aus + + + align:start position:0% +take FN to be Aus +n n + K + + align:start position:0% +n n + K + + + align:start position:0% +n n + K +factorial then if we do the transform of + + align:start position:0% +factorial then if we do the transform of + + + align:start position:0% +factorial then if we do the transform of +that do the series you can do + + align:start position:0% +that do the series you can do + + + align:start position:0% +that do the series you can do +it and there's only one piece of it that + + align:start position:0% +it and there's only one piece of it that + + + align:start position:0% +it and there's only one piece of it that +we care about so I'm just going to write + + align:start position:0% +we care about so I'm just going to write + + + align:start position:0% +we care about so I'm just going to write +that + + align:start position:0% + + + + align:start position:0% + +piece so there's this piece that has a + + align:start position:0% +piece so there's this piece that has a + + + align:start position:0% +piece so there's this piece that has a +kind of pole like + + align:start position:0% + + + + align:start position:0% + +structure and it has a pull at b equal a + + align:start position:0% +structure and it has a pull at b equal a + + + align:start position:0% +structure and it has a pull at b equal a +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +and what you say is you call this pole a + + align:start position:0% +and what you say is you call this pole a + + + align:start position:0% +and what you say is you call this pole a +renormalon this is the + + align:start position:0% + + + + align:start position:0% + +renormalon you call it a b equal a + + align:start position:0% + + + + align:start position:0% + +renormalon so you're characterizing the + + align:start position:0% +renormalon so you're characterizing the + + + align:start position:0% +renormalon so you're characterizing the +renormalon by where that pole + + align:start position:0% +renormalon by where that pole + + + align:start position:0% +renormalon by where that pole +is ver normal line is the flavor of a + + align:start position:0% +is ver normal line is the flavor of a + + + align:start position:0% +is ver normal line is the flavor of a +particle this has nothing to do to a + + align:start position:0% +particle this has nothing to do to a + + + align:start position:0% +particle this has nothing to do to a +particle usually you think of poles as + + align:start position:0% +particle usually you think of poles as + + + align:start position:0% +particle usually you think of poles as +having something to do with particles + + align:start position:0% +having something to do with particles + + + align:start position:0% +having something to do with particles +and that's where the name comes from let + + align:start position:0% +and that's where the name comes from let + + + align:start position:0% +and that's where the name comes from let +do it to Huff blame him + + align:start position:0% + + + + align:start position:0% + +so if a is less than zero your + + align:start position:0% +so if a is less than zero your + + + align:start position:0% +so if a is less than zero your +integration Contour is positive and the + + align:start position:0% +integration Contour is positive and the + + + align:start position:0% +integration Contour is positive and the +pole is on the other side so you don't + + align:start position:0% +pole is on the other side so you don't + + + align:start position:0% +pole is on the other side so you don't +have a problem the inverse transform + + align:start position:0% + + + + align:start position:0% + +exists these are called UV renormalons + + align:start position:0% +exists these are called UV renormalons + + + align:start position:0% +exists these are called UV renormalons +they still can guide the peration theory + + align:start position:0% +they still can guide the peration theory + + + align:start position:0% +they still can guide the peration theory +and they can be important for sort of + + align:start position:0% +and they can be important for sort of + + + align:start position:0% +and they can be important for sort of +thinking about why the privation theory + + align:start position:0% +thinking about why the privation theory + + + align:start position:0% +thinking about why the privation theory +is behaving the way it is but you can do + + align:start position:0% +is behaving the way it is but you can do + + + align:start position:0% +is behaving the way it is but you can do +the inverse + + align:start position:0% +the inverse + + + align:start position:0% +the inverse +transform the real ones that are kind of + + align:start position:0% +transform the real ones that are kind of + + + align:start position:0% +transform the real ones that are kind of +problematic IC are a greater than + + align:start position:0% +problematic IC are a greater than + + + align:start position:0% +problematic IC are a greater than +zero because then the pole is on the + + align:start position:0% +zero because then the pole is on the + + + align:start position:0% +zero because then the pole is on the +integration + + align:start position:0% +integration + + + align:start position:0% +integration +contour and we can't do the + + align:start position:0% + + + + align:start position:0% + +transform so we're integrating DB from0 + + align:start position:0% +transform so we're integrating DB from0 + + + align:start position:0% +transform so we're integrating DB from0 +to infinity and we just have a pole + + align:start position:0% +to infinity and we just have a pole + + + align:start position:0% +to infinity and we just have a pole +sitting on the axis and what do we do + + align:start position:0% + + + + align:start position:0% + +so you could think about characterizing + + align:start position:0% +so you could think about characterizing + + + align:start position:0% +so you could think about characterizing +how poorly behaved a peration theory is + + align:start position:0% +how poorly behaved a peration theory is + + + align:start position:0% +how poorly behaved a peration theory is +by looking at these poles and that's + + align:start position:0% +by looking at these poles and that's + + + align:start position:0% +by looking at these poles and that's +kind of what I meant by having some kind + + align:start position:0% +kind of what I meant by having some kind + + + align:start position:0% +kind of what I meant by having some kind +of notion of how Divergence a series is + + align:start position:0% +of notion of how Divergence a series is + + + align:start position:0% +of notion of how Divergence a series is +so you look in this br + + align:start position:0% +so you look in this br + + + align:start position:0% +so you look in this br +space and you look at + + align:start position:0% +space and you look at + + + align:start position:0% +space and you look at +the real axis and there's poles actually + + align:start position:0% +the real axis and there's poles actually + + + align:start position:0% +the real axis and there's poles actually +can be both on both + + align:start position:0% +can be both on both + + + align:start position:0% +can be both on both +sides the most severe pole is the one + + align:start position:0% +sides the most severe pole is the one + + + align:start position:0% +sides the most severe pole is the one +that's closest to the + + align:start position:0% + + + + align:start position:0% + +origin and that has the smallest value + + align:start position:0% +origin and that has the smallest value + + + align:start position:0% +origin and that has the smallest value +of B and you can see if you have a small + + align:start position:0% +of B and you can see if you have a small + + + align:start position:0% +of B and you can see if you have a small +value of B then you're multiplying here + + align:start position:0% +value of B then you're multiplying here + + + align:start position:0% +value of B then you're multiplying here +with some large numbers so if a was 0.1 + + align:start position:0% +with some large numbers so if a was 0.1 + + + align:start position:0% +with some large numbers so if a was 0.1 +you'd be multiplying by 10 to the + + align:start position:0% +you'd be multiplying by 10 to the + + + align:start position:0% +you'd be multiplying by 10 to the +N so these guys are more severe as you + + align:start position:0% +N so these guys are more severe as you + + + align:start position:0% +N so these guys are more severe as you +go to larger values you get additional + + align:start position:0% +go to larger values you get additional + + + align:start position:0% +go to larger values you get additional +suppression from this a to the N so if a + + align:start position:0% +suppression from this a to the N so if a + + + align:start position:0% +suppression from this a to the N so if a +was if you went all the way out to 100 + + align:start position:0% +was if you went all the way out to 100 + + + align:start position:0% +was if you went all the way out to 100 +then you'd have a one over 100 to the + + align:start position:0% +then you'd have a one over 100 to the + + + align:start position:0% +then you'd have a one over 100 to the +end that's good but factorial eventually + + align:start position:0% +end that's good but factorial eventually + + + align:start position:0% +end that's good but factorial eventually +wins so it's still Divergent but we + + align:start position:0% +wins so it's still Divergent but we + + + align:start position:0% +wins so it's still Divergent but we +looked like it was a lot better okay so + + align:start position:0% +looked like it was a lot better okay so + + + align:start position:0% +looked like it was a lot better okay so +you can characterize how severe that the + + align:start position:0% +you can characterize how severe that the + + + align:start position:0% +you can characterize how severe that the +series is diverging by the location of + + align:start position:0% +series is diverging by the location of + + + align:start position:0% +series is diverging by the location of +these + + align:start position:0% +these + + + align:start position:0% +these +poles and you can characterize the + + align:start position:0% +poles and you can characterize the + + + align:start position:0% +poles and you can characterize the +ambiguity + + align:start position:0% + + + + align:start position:0% + +in doing an integration by if you just + + align:start position:0% +in doing an integration by if you just + + + align:start position:0% +in doing an integration by if you just +think about one pole you can + + align:start position:0% +think about one pole you can + + + align:start position:0% +think about one pole you can +characterize the ambiguity so let's just + + align:start position:0% +characterize the ambiguity so let's just + + + align:start position:0% +characterize the ambiguity so let's just +imagine there's one pole you can + + align:start position:0% +imagine there's one pole you can + + + align:start position:0% +imagine there's one pole you can +characterize the ambiguity by going + + align:start position:0% +characterize the ambiguity by going + + + align:start position:0% +characterize the ambiguity by going +above or + + align:start position:0% +above or + + + align:start position:0% +above or +below so you know two possible ways of + + align:start position:0% +below so you know two possible ways of + + + align:start position:0% +below so you know two possible ways of +defining the intergal you don't know + + align:start position:0% +defining the intergal you don't know + + + align:start position:0% +defining the intergal you don't know +which to pick one is to go + + align:start position:0% + + + + align:start position:0% + +above others to go below + + align:start position:0% + + + + align:start position:0% + +and then you can think about what the + + align:start position:0% +and then you can think about what the + + + align:start position:0% +and then you can think about what the +ambiguity + + align:start position:0% +ambiguity + + + align:start position:0% +ambiguity +is and the + + align:start position:0% +is and the + + + align:start position:0% +is and the +ambiguity is the Contour + + align:start position:0% +ambiguity is the Contour + + + align:start position:0% +ambiguity is the Contour +one call this C1 this C2 the ambiguity + + align:start position:0% +one call this C1 this C2 the ambiguity + + + align:start position:0% +one call this C1 this C2 the ambiguity +is C1 minus + + align:start position:0% +is C1 minus + + + align:start position:0% +is C1 minus +C2 and that is circling the + + align:start position:0% + + + + align:start position:0% + +pole so you can look at the residue of + + align:start position:0% +pole so you can look at the residue of + + + align:start position:0% +pole so you can look at the residue of +the pole and that gives you the + + align:start position:0% +the pole and that gives you the + + + align:start position:0% +the pole and that gives you the +ambiguity + + align:start position:0% + + + + align:start position:0% + +so what we'll do next time is we'll look + + align:start position:0% +so what we'll do next time is we'll look + + + align:start position:0% +so what we'll do next time is we'll look +at an example in perturbative qcd we'll + + align:start position:0% +at an example in perturbative qcd we'll + + + align:start position:0% +at an example in perturbative qcd we'll +see that there's a series that has a re + + align:start position:0% +see that there's a series that has a re + + + align:start position:0% +see that there's a series that has a re +normal on and we'll find it and then + + align:start position:0% +normal on and we'll find it and then + + + align:start position:0% +normal on and we'll find it and then +we'll look at the residue and we'll find + + align:start position:0% +we'll look at the residue and we'll find + + + align:start position:0% +we'll look at the residue and we'll find +actually that it will get out pop out + + align:start position:0% +actually that it will get out pop out + + + align:start position:0% +actually that it will get out pop out +will pop Lambda qcd so we'll see we'll + + align:start position:0% +will pop Lambda qcd so we'll see we'll + + + align:start position:0% +will pop Lambda qcd so we'll see we'll +calculate for some perative series that + + align:start position:0% +calculate for some perative series that + + + align:start position:0% +calculate for some perative series that +the pole Mass really has an ambiguity of + + align:start position:0% +the pole Mass really has an ambiguity of + + + align:start position:0% +the pole Mass really has an ambiguity of +order Lambda qcd + + align:start position:0% +order Lambda qcd + + + align:start position:0% +order Lambda qcd +by using this technique of going around + + align:start position:0% +by using this technique of going around + + + align:start position:0% +by using this technique of going around +a residue of a + + align:start position:0% + + + + align:start position:0% + +pole when we say that the Bor is a 4GB + + align:start position:0% +pole when we say that the Bor is a 4GB + + + align:start position:0% +pole when we say that the Bor is a 4GB +Mass what's that mass yeah so if we if + + align:start position:0% +Mass what's that mass yeah so if we if + + + align:start position:0% +Mass what's that mass yeah so if we if +you say the bork has like 4.2 GV Mass + + align:start position:0% +you say the bork has like 4.2 GV Mass + + + align:start position:0% +you say the bork has like 4.2 GV Mass +that's the MS bar Mass if you say it has + + align:start position:0% +that's the MS bar Mass if you say it has + + + align:start position:0% +that's the MS bar Mass if you say it has +a + + align:start position:0% +a + + + align:start position:0% +a +4.73 GB Mass that's like the mb1s mass + + align:start position:0% +4.73 GB Mass that's like the mb1s mass + + + align:start position:0% +4.73 GB Mass that's like the mb1s mass +and if you look at how the PDG measures + + align:start position:0% +and if you look at how the PDG measures + + + align:start position:0% +and if you look at how the PDG measures +the bork Mass they measure it in one of + + align:start position:0% +the bork Mass they measure it in one of + + + align:start position:0% +the bork Mass they measure it in one of +these schemes that I'm telling you like + + align:start position:0% +these schemes that I'm telling you like + + + align:start position:0% +these schemes that I'm telling you like +the 1s scheme they quote a result for + + align:start position:0% +the 1s scheme they quote a result for + + + align:start position:0% +the 1s scheme they quote a result for +that you can convert between the 1s and + + align:start position:0% +that you can convert between the 1s and + + + align:start position:0% +that you can convert between the 1s and +M and the msar mass the msar mass is a + + align:start position:0% +M and the msar mass the msar mass is a + + + align:start position:0% +M and the msar mass the msar mass is a +perfectly well-defined quantity it + + align:start position:0% +perfectly well-defined quantity it + + + align:start position:0% +perfectly well-defined quantity it +doesn't actually have a + + align:start position:0% +doesn't actually have a + + + align:start position:0% +doesn't actually have a +renormalon okay that's not its problem + + align:start position:0% +renormalon okay that's not its problem + + + align:start position:0% +renormalon okay that's not its problem +the pole Mass has a renormalon the msar + + align:start position:0% +the pole Mass has a renormalon the msar + + + align:start position:0% +the pole Mass has a renormalon the msar +mass its problem is related to power + + align:start position:0% +mass its problem is related to power + + + align:start position:0% +mass its problem is related to power +counting in the low energy Theory it's a + + align:start position:0% +counting in the low energy Theory it's a + + + align:start position:0% +counting in the low energy Theory it's a +high it's a good mass for high energy + + align:start position:0% +high it's a good mass for high energy + + + align:start position:0% +high it's a good mass for high energy +physics it's a bad mass for low energy + + align:start position:0% +physics it's a bad mass for low energy + + + align:start position:0% +physics it's a bad mass for low energy +physics that's the problem with hemis + + align:start position:0% +physics that's the problem with hemis + + + align:start position:0% +physics that's the problem with hemis +bar it's not a it's not a technical + + align:start position:0% +bar it's not a it's not a technical + + + align:start position:0% +bar it's not a it's not a technical +problem that it has a the it + + align:start position:0% +problem that it has a the it + + + align:start position:0% +problem that it has a the it +severity of + + align:start position:0% +severity of + + + align:start position:0% +severity of +renormalon it it can have a higher + + align:start position:0% +renormalon it it can have a higher + + + align:start position:0% +renormalon it it can have a higher +weight of renormalon but it doesn't have + + align:start position:0% +weight of renormalon but it doesn't have + + + align:start position:0% +weight of renormalon but it doesn't have +the same severity of renormalon as the + + align:start position:0% +the same severity of renormalon as the + + + align:start position:0% +the same severity of renormalon as the +pole Mass the pole Mass basically has + + align:start position:0% +pole Mass the pole Mass basically has + + + align:start position:0% +pole Mass the pole Mass basically has +the most severe possible R normal line + + align:start position:0% +the most severe possible R normal line + + + align:start position:0% +the most severe possible R normal line +which is in some some units a half so + + align:start position:0% +which is in some some units a half so + + + align:start position:0% +which is in some some units a half so +there's an extra two to the nend we'll + + align:start position:0% +there's an extra two to the nend we'll + + + align:start position:0% +there's an extra two to the nend we'll +talk about that next + + align:start position:0% + + + + align:start position:0% + +time so basically it's the U equals a + + align:start position:0% +time so basically it's the U equals a + + + align:start position:0% +time so basically it's the U equals a +half for normal lines that really are + + align:start position:0% +half for normal lines that really are + + + align:start position:0% +half for normal lines that really are +causing a problem in perturbative QC + + align:start position:0% +causing a problem in perturbative QC + + + align:start position:0% +causing a problem in perturbative QC +they're the most important there's + + align:start position:0% +they're the most important there's + + + align:start position:0% +they're the most important there's +higher order ones even the even alpha s + + align:start position:0% +higher order ones even the even alpha s + + + align:start position:0% +higher order ones even the even alpha s +actually has a renormalon alpha s in the + + align:start position:0% +actually has a renormalon alpha s in the + + + align:start position:0% +actually has a renormalon alpha s in the +MS bar schem I + + align:start position:0% +MS bar schem I + + + align:start position:0% +MS bar schem I +suspect but but even up to five Loops + + align:start position:0% +suspect but but even up to five Loops + + + align:start position:0% +suspect but but even up to five Loops +you won't see it or it's very hard to + + align:start position:0% +you won't see it or it's very hard to + + + align:start position:0% +you won't see it or it's very hard to +see let's stop there \ No newline at end of file diff --git a/kjCQ2DUn55Y.txt b/kjCQ2DUn55Y.txt new file mode 100644 index 0000000000000000000000000000000000000000..e61301dd7955867e81fb9aae736a45d22fc13ee1 --- /dev/null +++ b/kjCQ2DUn55Y.txt @@ -0,0 +1,14336 @@ +align:start position:0% + +we're starting a new part of the course + + align:start position:0% +we're starting a new part of the course + + + align:start position:0% +we're starting a new part of the course +where we'll be dealing with uh + + align:start position:0% +where we'll be dealing with uh + + + align:start position:0% +where we'll be dealing with uh +industrial machine vision and um in + + align:start position:0% +industrial machine vision and um in + + + align:start position:0% +industrial machine vision and um in +particular we'll be looking at uh + + align:start position:0% +particular we'll be looking at uh + + + align:start position:0% +particular we'll be looking at uh +patterns on + + align:start position:0% +patterns on + + + align:start position:0% +patterns on +that and uh + + align:start position:0% +that and uh + + + align:start position:0% +that and uh +we'll start off with one by uh Bill + + align:start position:0% +we'll start off with one by uh Bill + + + align:start position:0% +we'll start off with one by uh Bill +silver at cognex so cognex is arguably + + align:start position:0% +silver at cognex so cognex is arguably + + + align:start position:0% +silver at cognex so cognex is arguably +the uh uh leading Machine Vision + + align:start position:0% +the uh uh leading Machine Vision + + + align:start position:0% +the uh uh leading Machine Vision +company and it's + + align:start position:0% +company and it's + + + align:start position:0% +company and it's +um an early starter uh I tried very hard + + align:start position:0% +um an early starter uh I tried very hard + + + align:start position:0% +um an early starter uh I tried very hard +to persuade him not to join a + + align:start position:0% +to persuade him not to join a + + + align:start position:0% +to persuade him not to join a +startup because U the success rate + + align:start position:0% +startup because U the success rate + + + align:start position:0% +startup because U the success rate +wasn't very high at the time and maybe + + align:start position:0% +wasn't very high at the time and maybe + + + align:start position:0% +wasn't very high at the time and maybe +still isn't anyway he joined anyway and + + align:start position:0% +still isn't anyway he joined anyway and + + + align:start position:0% +still isn't anyway he joined anyway and +he was he's their technical Guru and + + align:start position:0% +he was he's their technical Guru and + + + align:start position:0% +he was he's their technical Guru and +there's a bunch of pattern that describe + + align:start position:0% +there's a bunch of pattern that describe + + + align:start position:0% +there's a bunch of pattern that describe +uh what they did at this point uh you + + align:start position:0% +uh what they did at this point uh you + + + align:start position:0% +uh what they did at this point uh you +can't manufacture integrated circuits + + align:start position:0% +can't manufacture integrated circuits + + + align:start position:0% +can't manufacture integrated circuits +without Machine Vision they're uh needed + + align:start position:0% +without Machine Vision they're uh needed + + + align:start position:0% +without Machine Vision they're uh needed +all over the show for alignment and + + align:start position:0% +all over the show for alignment and + + + align:start position:0% +all over the show for alignment and +inspection uh and you can't uh + + align:start position:0% +inspection uh and you can't uh + + + align:start position:0% +inspection uh and you can't uh +manufacture Pharmaceuticals without + + align:start position:0% +manufacture Pharmaceuticals without + + + align:start position:0% +manufacture Pharmaceuticals without +Machine Vision you know for example + + align:start position:0% +Machine Vision you know for example + + + align:start position:0% +Machine Vision you know for example +there's a mandate that um + + align:start position:0% +there's a mandate that um + + + align:start position:0% +there's a mandate that um +the label should be + + align:start position:0% +the label should be + + + align:start position:0% +the label should be +readable + + align:start position:0% +readable + + + align:start position:0% +readable +so what's the uh language of the Mandate + + align:start position:0% +so what's the uh language of the Mandate + + + align:start position:0% +so what's the uh language of the Mandate +it's not you know most of the labels + + align:start position:0% +it's not you know most of the labels + + + align:start position:0% +it's not you know most of the labels +should be readable it says the Mandate + + align:start position:0% +should be readable it says the Mandate + + + align:start position:0% +should be readable it says the Mandate +the labels should be readable that means + + align:start position:0% +the labels should be readable that means + + + align:start position:0% +the labels should be readable that means +every single label has to be inspected + + align:start position:0% +every single label has to be inspected + + + align:start position:0% +every single label has to be inspected +well I don't think anyone wants people + + align:start position:0% +well I don't think anyone wants people + + + align:start position:0% +well I don't think anyone wants people +to do that so of course it's done using + + align:start position:0% +to do that so of course it's done using + + + align:start position:0% +to do that so of course it's done using +machine vision and uh those are the two + + align:start position:0% +machine vision and uh those are the two + + + align:start position:0% +machine vision and uh those are the two +areas that uh cognic managed to capture + + align:start position:0% +areas that uh cognic managed to capture + + + align:start position:0% +areas that uh cognic managed to capture +a large Market uh starting off with um + + align:start position:0% +a large Market uh starting off with um + + + align:start position:0% +a large Market uh starting off with um +uh integrated circuits mostly in Japan + + align:start position:0% +uh integrated circuits mostly in Japan + + + align:start position:0% +uh integrated circuits mostly in Japan +so most of their Market was there anyway + + align:start position:0% +so most of their Market was there anyway + + + align:start position:0% +so most of their Market was there anyway +let's dive into this pattern learn a + + align:start position:0% +let's dive into this pattern learn a + + + align:start position:0% +let's dive into this pattern learn a +little bit about uh patterns so first of + + align:start position:0% +little bit about uh patterns so first of + + + align:start position:0% +little bit about uh patterns so first of +all why patterns so uh the basic idea is + + align:start position:0% +all why patterns so uh the basic idea is + + + align:start position:0% +all why patterns so uh the basic idea is +that you come up with an idea to do + + align:start position:0% +that you come up with an idea to do + + + align:start position:0% +that you come up with an idea to do +something produce some chemical build + + align:start position:0% +something produce some chemical build + + + align:start position:0% +something produce some chemical build +some + + align:start position:0% +some + + + align:start position:0% +some +machine um and you set up to uh build + + align:start position:0% +machine um and you set up to uh build + + + align:start position:0% +machine um and you set up to uh build +such things and sell them and and your + + align:start position:0% +such things and sell them and and your + + + align:start position:0% +such things and sell them and and your +neighbor looks over and says oh that's + + align:start position:0% +neighbor looks over and says oh that's + + + align:start position:0% +neighbor looks over and says oh that's +nice you can make some money that way + + align:start position:0% +nice you can make some money that way + + + align:start position:0% +nice you can make some money that way +and basically competes with you without + + align:start position:0% +and basically competes with you without + + + align:start position:0% +and basically competes with you without +having put in the effort of actually + + align:start position:0% +having put in the effort of actually + + + align:start position:0% +having put in the effort of actually +coming up with the invention and so the + + align:start position:0% +coming up with the invention and so the + + + align:start position:0% +coming up with the invention and so the +whole idea of a patent is a kind of + + align:start position:0% +whole idea of a patent is a kind of + + + align:start position:0% +whole idea of a patent is a kind of +compromise whereby uh you get a limited + + align:start position:0% +compromise whereby uh you get a limited + + + align:start position:0% +compromise whereby uh you get a limited +Monopoly to use your invention in return + + align:start position:0% +Monopoly to use your invention in return + + + align:start position:0% +Monopoly to use your invention in return +for explaining exactly how it works so + + align:start position:0% +for explaining exactly how it works so + + + align:start position:0% +for explaining exactly how it works so +that after a certain amount of time + + align:start position:0% +that after a certain amount of time + + + align:start position:0% +that after a certain amount of time +anyone else can can build it so it's + + align:start position:0% +anyone else can can build it so it's + + + align:start position:0% +anyone else can can build it so it's +kind of a contract with Society where uh + + align:start position:0% +kind of a contract with Society where uh + + + align:start position:0% +kind of a contract with Society where uh +you get some benefit for a while and in + + align:start position:0% +you get some benefit for a while and in + + + align:start position:0% +you get some benefit for a while and in +return there's some benefit uh long term + + align:start position:0% +return there's some benefit uh long term + + + align:start position:0% +return there's some benefit uh long term +uh for + + align:start position:0% +uh for + + + align:start position:0% +uh for +society and this is how they get you to + + align:start position:0% +society and this is how they get you to + + + align:start position:0% +society and this is how they get you to +explain in detail how things work and + + align:start position:0% +explain in detail how things work and + + + align:start position:0% +explain in detail how things work and +you know there different opinions on + + align:start position:0% +you know there different opinions on + + + align:start position:0% +you know there different opinions on +various types of intellectual property + + align:start position:0% +various types of intellectual property + + + align:start position:0% +various types of intellectual property +um and we won't get into that uh there + + align:start position:0% +um and we won't get into that uh there + + + align:start position:0% +um and we won't get into that uh there +are obviously some benefits and some + + align:start position:0% +are obviously some benefits and some + + + align:start position:0% +are obviously some benefits and some +disadvantages uh to the + + align:start position:0% +disadvantages uh to the + + + align:start position:0% +disadvantages uh to the +and it's changed over the years there's + + align:start position:0% +and it's changed over the years there's + + + align:start position:0% +and it's changed over the years there's +a constant revision and it's remotely + + align:start position:0% +a constant revision and it's remotely + + + align:start position:0% +a constant revision and it's remotely +possible that some of the things I tell + + align:start position:0% +possible that some of the things I tell + + + align:start position:0% +possible that some of the things I tell +you are no longer true because they were + + align:start position:0% +you are no longer true because they were + + + align:start position:0% +you are no longer true because they were +true you know two years ago and + + align:start position:0% +true you know two years ago and + + + align:start position:0% +true you know two years ago and +whatever so let's look at what's there + + align:start position:0% +whatever so let's look at what's there + + + align:start position:0% +whatever so let's look at what's there +so first of all the the we'll get into + + align:start position:0% +so first of all the the we'll get into + + + align:start position:0% +so first of all the the we'll get into +the technical stuff later but sort of + + align:start position:0% +the technical stuff later but sort of + + + align:start position:0% +the technical stuff later but sort of +the structure of this and the metadata + + align:start position:0% +the structure of this and the metadata + + + align:start position:0% +the structure of this and the metadata +so obviously there's um the the number + + align:start position:0% +so obviously there's um the the number + + + align:start position:0% +so obviously there's um the the number +so at this point we're up to 6 million + + align:start position:0% +so at this point we're up to 6 million + + + align:start position:0% +so at this point we're up to 6 million +um + + align:start position:0% +um + + + align:start position:0% +um +I just got noticed that one of our x-ray + + align:start position:0% +I just got noticed that one of our x-ray + + + align:start position:0% +I just got noticed that one of our x-ray +patents got uh issued and it's in the 10 + + align:start position:0% +patents got uh issued and it's in the 10 + + + align:start position:0% +patents got uh issued and it's in the 10 +million range so since 2002 we've added + + align:start position:0% +million range so since 2002 we've added + + + align:start position:0% +million range so since 2002 we've added +a lot of patents and a lot of companies + + align:start position:0% +a lot of patents and a lot of companies + + + align:start position:0% +a lot of patents and a lot of companies +um large companies in particular file + + align:start position:0% +um large companies in particular file + + + align:start position:0% +um large companies in particular file +you know patents at an incredible rate + + align:start position:0% +you know patents at an incredible rate + + + align:start position:0% +you know patents at an incredible rate +and why is that well it's largely + + align:start position:0% +and why is that well it's largely + + + align:start position:0% +and why is that well it's largely +because they want sort of ammunition in + + align:start position:0% +because they want sort of ammunition in + + + align:start position:0% +because they want sort of ammunition in +a patent War so if say you IBM and you + + align:start position:0% +a patent War so if say you IBM and you + + + align:start position:0% +a patent War so if say you IBM and you +know there Microsoft + + align:start position:0% +know there Microsoft + + + align:start position:0% +know there Microsoft +uh you I hold 6,000 patents in my hand + + align:start position:0% +uh you I hold 6,000 patents in my hand + + + align:start position:0% +uh you I hold 6,000 patents in my hand +and if you promise not to sue me you can + + align:start position:0% +and if you promise not to sue me you can + + + align:start position:0% +and if you promise not to sue me you can +use that technology if I can use your + + align:start position:0% +use that technology if I can use your + + + align:start position:0% +use that technology if I can use your +8,000 patents that that kind of thing so + + align:start position:0% +8,000 patents that that kind of thing so + + + align:start position:0% +8,000 patents that that kind of thing so +uh you know patents can stand in the way + + align:start position:0% +uh you know patents can stand in the way + + + align:start position:0% +uh you know patents can stand in the way +of doing useful stuff they can also kind + + align:start position:0% +of doing useful stuff they can also kind + + + align:start position:0% +of doing useful stuff they can also kind +of sometimes prevent wasted money on + + align:start position:0% +of sometimes prevent wasted money on + + + align:start position:0% +of sometimes prevent wasted money on +litigation so here's uh the date of the + + align:start position:0% +litigation so here's uh the date of the + + + align:start position:0% +litigation so here's uh the date of the +patent uh we have a title apparatus and + + align:start position:0% +patent uh we have a title apparatus and + + + align:start position:0% +patent uh we have a title apparatus and +method for detecting and subpixel + + align:start position:0% +method for detecting and subpixel + + + align:start position:0% +method for detecting and subpixel +location of edges in a digital image so + + align:start position:0% +location of edges in a digital image so + + + align:start position:0% +location of edges in a digital image so +this is aimed at mostly sort of a + + align:start position:0% +this is aimed at mostly sort of a + + + align:start position:0% +this is aimed at mostly sort of a +conveyor belt world where you're looking + + align:start position:0% +conveyor belt world where you're looking + + + align:start position:0% +conveyor belt world where you're looking +down at things and you're measuring + + align:start position:0% +down at things and you're measuring + + + align:start position:0% +down at things and you're measuring +positions and attitudes and it's also + + align:start position:0% +positions and attitudes and it's also + + + align:start position:0% +positions and attitudes and it's also +aimed at integrated circuit world where + + align:start position:0% +aimed at integrated circuit world where + + + align:start position:0% +aimed at integrated circuit world where +you're largely dealing with um + + align:start position:0% +you're largely dealing with um + + + align:start position:0% +you're largely dealing with um +two-dimensional uh images so uh one of + + align:start position:0% +two-dimensional uh images so uh one of + + + align:start position:0% +two-dimensional uh images so uh one of +the things we know is that uh images + + align:start position:0% +the things we know is that uh images + + + align:start position:0% +the things we know is that uh images +often have large homogeneous regions of + + align:start position:0% +often have large homogeneous regions of + + + align:start position:0% +often have large homogeneous regions of +uniform intensity they aren't very + + align:start position:0% +uniform intensity they aren't very + + + align:start position:0% +uniform intensity they aren't very +interesting the interesting stuff is + + align:start position:0% +interesting the interesting stuff is + + + align:start position:0% +interesting the interesting stuff is +where there's a transition uh between + + align:start position:0% +where there's a transition uh between + + + align:start position:0% +where there's a transition uh between +different brightness levels and so uh + + align:start position:0% +different brightness levels and so uh + + + align:start position:0% +different brightness levels and so uh +edges are where it's at you can greatly + + align:start position:0% +edges are where it's at you can greatly + + + align:start position:0% +edges are where it's at you can greatly +reduce the um you know bits needed to + + align:start position:0% +reduce the um you know bits needed to + + + align:start position:0% +reduce the um you know bits needed to +describe something by just focusing uh + + align:start position:0% +describe something by just focusing uh + + + align:start position:0% +describe something by just focusing uh +on the edges so that's what this is + + align:start position:0% +on the edges so that's what this is + + + align:start position:0% +on the edges so that's what this is +about and it's about finding them to sub + + align:start position:0% +about and it's about finding them to sub + + + align:start position:0% +about and it's about finding them to sub +pixel accuracy that's very important + + align:start position:0% +pixel accuracy that's very important + + + align:start position:0% +pixel accuracy that's very important +because you can always get more accuracy + + align:start position:0% +because you can always get more accuracy + + + align:start position:0% +because you can always get more accuracy +by adding more more pixels you know + + align:start position:0% +by adding more more pixels you know + + + align:start position:0% +by adding more more pixels you know +instead of using a million pixel camera + + align:start position:0% +instead of using a million pixel camera + + + align:start position:0% +instead of using a million pixel camera +use 100 million pixel camera and you get + + align:start position:0% +use 100 million pixel camera and you get + + + align:start position:0% +use 100 million pixel camera and you get +10 times the accuracy and obviously uh + + align:start position:0% +10 times the accuracy and obviously uh + + + align:start position:0% +10 times the accuracy and obviously uh +that's expensive and also uh you know if + + align:start position:0% +that's expensive and also uh you know if + + + align:start position:0% +that's expensive and also uh you know if +you can do that in software uh for + + align:start position:0% +you can do that in software uh for + + + align:start position:0% +you can do that in software uh for +relatively low cost then that's a huge + + align:start position:0% +relatively low cost then that's a huge + + + align:start position:0% +relatively low cost then that's a huge +advantage or if you have that 100 + + align:start position:0% +advantage or if you have that 100 + + + align:start position:0% +advantage or if you have that 100 +million pixel camera you now have 10 + + align:start position:0% +million pixel camera you now have 10 + + + align:start position:0% +million pixel camera you now have 10 +times the resolution of whoever um else + + align:start position:0% +times the resolution of whoever um else + + + align:start position:0% +times the resolution of whoever um else +is working in that + + align:start position:0% +is working in that + + + align:start position:0% +is working in that +field um what accuracy can you achieve + + align:start position:0% +field um what accuracy can you achieve + + + align:start position:0% +field um what accuracy can you achieve +well it's fairly straightforward to get + + align:start position:0% +well it's fairly straightforward to get + + + align:start position:0% +well it's fairly straightforward to get +to a tenth of a pixel uh uh and at that + + align:start position:0% +to a tenth of a pixel uh uh and at that + + + align:start position:0% +to a tenth of a pixel uh uh and at that +point you start to see all kinds of + + align:start position:0% +point you start to see all kinds of + + + align:start position:0% +point you start to see all kinds of +problems that you didn't think of uh if + + align:start position:0% +problems that you didn't think of uh if + + + align:start position:0% +problems that you didn't think of uh if +you push it hard you can get to maybe a + + align:start position:0% +you push it hard you can get to maybe a + + + align:start position:0% +you push it hard you can get to maybe a +40th which is what what they claim and + + align:start position:0% +40th which is what what they claim and + + + align:start position:0% +40th which is what what they claim and +that's obviously huge you know two + + align:start position:0% +that's obviously huge you know two + + + align:start position:0% +that's obviously huge you know two +dimensionals that's a factor of 1,600 in + + align:start position:0% +dimensionals that's a factor of 1,600 in + + + align:start position:0% +dimensionals that's a factor of 1,600 in +terms of accuracy okay so that's what + + align:start position:0% +terms of accuracy okay so that's what + + + align:start position:0% +terms of accuracy okay so that's what +this is about and then the authors are + + align:start position:0% +this is about and then the authors are + + + align:start position:0% +this is about and then the authors are +listed and the assign is listed that is + + align:start position:0% +listed and the assign is listed that is + + + align:start position:0% +listed and the assign is listed that is +the authors don't necessarily get the + + align:start position:0% +the authors don't necessarily get the + + + align:start position:0% +the authors don't necessarily get the +benefit typically if you work at a + + align:start position:0% +benefit typically if you work at a + + + align:start position:0% +benefit typically if you work at a +company they make you sign over some + + align:start position:0% +company they make you sign over some + + + align:start position:0% +company they make you sign over some +piece of paper that says that uh + + align:start position:0% +piece of paper that says that uh + + + align:start position:0% +piece of paper that says that uh +whatever you invent is theirs and so on + + align:start position:0% +whatever you invent is theirs and so on + + + align:start position:0% +whatever you invent is theirs and so on +and uh I guess MIT wasn't that careful + + align:start position:0% +and uh I guess MIT wasn't that careful + + + align:start position:0% +and uh I guess MIT wasn't that careful +when I was hired uh and I don't think I + + align:start position:0% +when I was hired uh and I don't think I + + + align:start position:0% +when I was hired uh and I don't think I +ever signed that paper but didn't help + + align:start position:0% +ever signed that paper but didn't help + + + align:start position:0% +ever signed that paper but didn't help +me much anyway uh then we have the date + + align:start position:0% +me much anyway uh then we have the date + + + align:start position:0% +me much anyway uh then we have the date +filed and the fields of search so + + align:start position:0% +filed and the fields of search so + + + align:start position:0% +filed and the fields of search so +there's some numbers there that tell you + + align:start position:0% +there's some numbers there that tell you + + + align:start position:0% +there's some numbers there that tell you +you um what area this in those fields of + + align:start position:0% +you um what area this in those fields of + + + align:start position:0% +you um what area this in those fields of +search were established a long long time + + align:start position:0% +search were established a long long time + + + align:start position:0% +search were established a long long time +ago and so you know there isn't even + + align:start position:0% +ago and so you know there isn't even + + + align:start position:0% +ago and so you know there isn't even +something for computers it's sort of a + + align:start position:0% +something for computers it's sort of a + + + align:start position:0% +something for computers it's sort of a +subp part of electrical stuff uh if you + + align:start position:0% +subp part of electrical stuff uh if you + + + align:start position:0% +subp part of electrical stuff uh if you +into U rubber making the 10 categories + + align:start position:0% +into U rubber making the 10 categories + + + align:start position:0% +into U rubber making the 10 categories +for different types of rubber because + + align:start position:0% +for different types of rubber because + + + align:start position:0% +for different types of rubber because +that was so those categories are things + + align:start position:0% +that was so those categories are things + + + align:start position:0% +that was so those categories are things +that patent examiners know a lot about + + align:start position:0% +that patent examiners know a lot about + + + align:start position:0% +that patent examiners know a lot about +but they're not particularly + + align:start position:0% +but they're not particularly + + + align:start position:0% +but they're not particularly +interesting and what happens is that uh + + align:start position:0% +interesting and what happens is that uh + + + align:start position:0% +interesting and what happens is that uh +you submit this thing and it has to be + + align:start position:0% +you submit this thing and it has to be + + + align:start position:0% +you submit this thing and it has to be +in a form that's acceptable and there + + align:start position:0% +in a form that's acceptable and there + + + align:start position:0% +in a form that's acceptable and there +are lots of rules uh used to be you + + align:start position:0% +are lots of rules uh used to be you + + + align:start position:0% +are lots of rules uh used to be you +couldn't have any equations in there + + align:start position:0% +couldn't have any equations in there + + + align:start position:0% +couldn't have any equations in there +well this one has equations in it so + + align:start position:0% +well this one has equations in it so + + + align:start position:0% +well this one has equations in it so +that obviously is no longer the case uh + + align:start position:0% +that obviously is no longer the case uh + + + align:start position:0% +that obviously is no longer the case uh +you couldn't use gray levels had to be + + align:start position:0% +you couldn't use gray levels had to be + + + align:start position:0% +you couldn't use gray levels had to be +black and white line drawings and so the + + align:start position:0% +black and white line drawings and so the + + + align:start position:0% +black and white line drawings and so the +only way you could get something like + + align:start position:0% +only way you could get something like + + + align:start position:0% +only way you could get something like +gray levels was half tones you know dots + + align:start position:0% +gray levels was half tones you know dots + + + align:start position:0% +gray levels was half tones you know dots +with varying size dots and Dot spacing + + align:start position:0% +with varying size dots and Dot spacing + + + align:start position:0% +with varying size dots and Dot spacing +uh KF color uh the language is somewhat + + align:start position:0% +uh KF color uh the language is somewhat + + + align:start position:0% +uh KF color uh the language is somewhat +arcane + + align:start position:0% +arcane + + + align:start position:0% +arcane +uh there are particular terms that you + + align:start position:0% +uh there are particular terms that you + + + align:start position:0% +uh there are particular terms that you +come into again and again like plurality + + align:start position:0% +come into again and again like plurality + + + align:start position:0% +come into again and again like plurality +I can never pronounce that word it which + + align:start position:0% +I can never pronounce that word it which + + + align:start position:0% +I can never pronounce that word it which +means several and things like uh + + align:start position:0% +means several and things like uh + + + align:start position:0% +means several and things like uh +comprise so you know uh one way to say + + align:start position:0% +comprise so you know uh one way to say + + + align:start position:0% +comprise so you know uh one way to say +uh the apparatus contains certain things + + align:start position:0% +uh the apparatus contains certain things + + + align:start position:0% +uh the apparatus contains certain things +uh is to say that but that's not very + + align:start position:0% +uh is to say that but that's not very + + + align:start position:0% +uh is to say that but that's not very +accurate so comprise means there's at + + align:start position:0% +accurate so comprise means there's at + + + align:start position:0% +accurate so comprise means there's at +least one there may be more and so you + + align:start position:0% +least one there may be more and so you + + + align:start position:0% +least one there may be more and so you +know there it um patent lawyers uh make + + align:start position:0% +know there it um patent lawyers uh make + + + align:start position:0% +know there it um patent lawyers uh make +their money knowing this kind of + + align:start position:0% +their money knowing this kind of + + + align:start position:0% +their money knowing this kind of +stuff okay uh then we have uh references + + align:start position:0% +stuff okay uh then we have uh references + + + align:start position:0% +stuff okay uh then we have uh references +and there's a bunch of uh pattern listed + + align:start position:0% +and there's a bunch of uh pattern listed + + + align:start position:0% +and there's a bunch of uh pattern listed +along with their fields and the asterisk + + align:start position:0% +along with their fields and the asterisk + + + align:start position:0% +along with their fields and the asterisk +means they were added by The Examiner so + + align:start position:0% +means they were added by The Examiner so + + + align:start position:0% +means they were added by The Examiner so +it goes down and the examiner sits on it + + align:start position:0% +it goes down and the examiner sits on it + + + align:start position:0% +it goes down and the examiner sits on it +for a while and it used to be uh well it + + align:start position:0% +for a while and it used to be uh well it + + + align:start position:0% +for a while and it used to be uh well it +changed in history but in the '90s when + + align:start position:0% +changed in history but in the '90s when + + + align:start position:0% +changed in history but in the '90s when +this was submitted + + align:start position:0% +this was submitted + + + align:start position:0% +this was submitted +1996 uh there was a multi-year delay and + + align:start position:0% +1996 uh there was a multi-year delay and + + + align:start position:0% +1996 uh there was a multi-year delay and +at that point Congress uh changed the + + align:start position:0% +at that point Congress uh changed the + + + align:start position:0% +at that point Congress uh changed the +rules a little bit including charging + + align:start position:0% +rules a little bit including charging + + + align:start position:0% +rules a little bit including charging +you for that process and it speed it up + + align:start position:0% +you for that process and it speed it up + + + align:start position:0% +you for that process and it speed it up +a bit um and the patent examiner will + + align:start position:0% +a bit um and the patent examiner will + + + align:start position:0% +a bit um and the patent examiner will +add things that they think of you can + + align:start position:0% +add things that they think of you can + + + align:start position:0% +add things that they think of you can +see here that the inventors only thought + + align:start position:0% +see here that the inventors only thought + + + align:start position:0% +see here that the inventors only thought +of this one patent by well one of the + + align:start position:0% +of this one patent by well one of the + + + align:start position:0% +of this one patent by well one of the +inventors the sort of like you know when + + align:start position:0% +inventors the sort of like you know when + + + align:start position:0% +inventors the sort of like you know when +you write your technical paper they're + + align:start position:0% +you write your technical paper they're + + + align:start position:0% +you write your technical paper they're +probably going to be references to your + + align:start position:0% +probably going to be references to your + + + align:start position:0% +probably going to be references to your +own previous papers + + align:start position:0% +own previous papers + + + align:start position:0% +own previous papers +they didn't think of all these other + + align:start position:0% +they didn't think of all these other + + + align:start position:0% +they didn't think of all these other +people as being relevant and then + + align:start position:0% +people as being relevant and then + + + align:start position:0% +people as being relevant and then +there's more uh other Publications + + align:start position:0% +there's more uh other Publications + + + align:start position:0% +there's more uh other Publications +though you know to these people pattern + + align:start position:0% +though you know to these people pattern + + + align:start position:0% +though you know to these people pattern +are important technical papers aren't + + align:start position:0% +are important technical papers aren't + + + align:start position:0% +are important technical papers aren't +but they still listed because the author + + align:start position:0% +but they still listed because the author + + + align:start position:0% +but they still listed because the author +is from the scientific World in some + + align:start position:0% +is from the scientific World in some + + + align:start position:0% +is from the scientific World in some +sense and uh it doesn't it says list + + align:start position:0% +sense and uh it doesn't it says list + + + align:start position:0% +sense and uh it doesn't it says list +continue on the next page because there + + align:start position:0% +continue on the next page because there + + + align:start position:0% +continue on the next page because there +wasn't enough uh on the front page + + align:start position:0% +wasn't enough uh on the front page + + + align:start position:0% +wasn't enough uh on the front page +enough space on the front page to list + + align:start position:0% +enough space on the front page to list + + + align:start position:0% +enough space on the front page to list +all the papers that he wanted to refer + + align:start position:0% +all the papers that he wanted to refer + + + align:start position:0% +all the papers that he wanted to refer +to and and then there's the abstract and + + align:start position:0% +to and and then there's the abstract and + + + align:start position:0% +to and and then there's the abstract and +this pattern is kind of unusual in that + + align:start position:0% +this pattern is kind of unusual in that + + + align:start position:0% +this pattern is kind of unusual in that +um it's understandable it's detailed + + align:start position:0% +um it's understandable it's detailed + + + align:start position:0% +um it's understandable it's detailed +it's uh technical um there's not much + + align:start position:0% +it's uh technical um there's not much + + + align:start position:0% +it's uh technical um there's not much +and it's because it was written by an + + align:start position:0% +and it's because it was written by an + + + align:start position:0% +and it's because it was written by an +engineer mostly so uh if you read the + + align:start position:0% +engineer mostly so uh if you read the + + + align:start position:0% +engineer mostly so uh if you read the +abstract you get a pretty good idea of + + align:start position:0% +abstract you get a pretty good idea of + + + align:start position:0% +abstract you get a pretty good idea of +what it + + align:start position:0% +what it + + + align:start position:0% +what it +is um there's a figure uh this figure is + + align:start position:0% +is um there's a figure uh this figure is + + + align:start position:0% +is um there's a figure uh this figure is +chosen by the patent examiner out of the + + align:start position:0% +chosen by the patent examiner out of the + + + align:start position:0% +chosen by the patent examiner out of the +figures that are submitted with a patent + + align:start position:0% +figures that are submitted with a patent + + + align:start position:0% +figures that are submitted with a patent +uh as somehow most distinctive most uh + + align:start position:0% +uh as somehow most distinctive most uh + + + align:start position:0% +uh as somehow most distinctive most uh +likely to let you know what the patent + + align:start position:0% +likely to let you know what the patent + + + align:start position:0% +likely to let you know what the patent +is is all about so I'll uh we'll get + + align:start position:0% +is is all about so I'll uh we'll get + + + align:start position:0% +is is all about so I'll uh we'll get +back to the abstract later so let me go + + align:start position:0% +back to the abstract later so let me go + + + align:start position:0% +back to the abstract later so let me go +to the next page so here you can see a + + align:start position:0% +to the next page so here you can see a + + + align:start position:0% +to the next page so here you can see a +whole bunch of uh additional papers on + + align:start position:0% +whole bunch of uh additional papers on + + + align:start position:0% +whole bunch of uh additional papers on +edge detection of course Edge detection + + align:start position:0% +edge detection of course Edge detection + + + align:start position:0% +edge detection of course Edge detection +is an old Topic in Machine Vision uh it + + align:start position:0% +is an old Topic in Machine Vision uh it + + + align:start position:0% +is an old Topic in Machine Vision uh it +goes back uh to the 1950s if you can + + align:start position:0% +goes back uh to the 1950s if you can + + + align:start position:0% +goes back uh to the 1950s if you can +believe uh when people first started uh + + align:start position:0% +believe uh when people first started uh + + + align:start position:0% +believe uh when people first started uh +scanning in images + + align:start position:0% +scanning in images + + + align:start position:0% +scanning in images +and uh finding a need to somehow U + + align:start position:0% +and uh finding a need to somehow U + + + align:start position:0% +and uh finding a need to somehow U +compress the information um measure + + align:start position:0% +compress the information um measure + + + align:start position:0% +compress the information um measure +things and so on so um one of the early + + align:start position:0% +things and so on so um one of the early + + + align:start position:0% +things and so on so um one of the early +famous papers is by Roberts who was at + + align:start position:0% +famous papers is by Roberts who was at + + + align:start position:0% +famous papers is by Roberts who was at +Lincoln Labs uh + + align:start position:0% +Lincoln Labs uh + + + align:start position:0% +Lincoln Labs uh +1965 and I guess his his input device + + align:start position:0% +1965 and I guess his his input device + + + align:start position:0% +1965 and I guess his his input device +was a drum plotter so in those days one + + align:start position:0% +was a drum plotter so in those days one + + + align:start position:0% +was a drum plotter so in those days one +of the exciting output devices was a + + align:start position:0% +of the exciting output devices was a + + + align:start position:0% +of the exciting output devices was a +drum that rotated it and you had a a + + align:start position:0% +drum that rotated it and you had a a + + + align:start position:0% +drum that rotated it and you had a a +ballpoint pin and you could control uh + + align:start position:0% +ballpoint pin and you could control uh + + + align:start position:0% +ballpoint pin and you could control uh +its position and uh uh in some cases + + align:start position:0% +its position and uh uh in some cases + + + align:start position:0% +its position and uh uh in some cases +color that might might have multiple + + align:start position:0% +color that might might have multiple + + + align:start position:0% +color that might might have multiple +tips and you could make great plots of + + align:start position:0% +tips and you could make great plots of + + + align:start position:0% +tips and you could make great plots of +circuit + + align:start position:0% +circuit + + + align:start position:0% +circuit +diagrams uh PC board layouts and so on + + align:start position:0% +diagrams uh PC board layouts and so on + + + align:start position:0% +diagrams uh PC board layouts and so on +and so what he did was he replaced the + + align:start position:0% +and so what he did was he replaced the + + + align:start position:0% +and so what he did was he replaced the +pen with a photo detector vacuum tube + + align:start position:0% +pen with a photo detector vacuum tube + + + align:start position:0% +pen with a photo detector vacuum tube +photo detector and then he scanned his + + align:start position:0% +photo detector and then he scanned his + + + align:start position:0% +photo detector and then he scanned his +8x1 black and white + + align:start position:0% +8x1 black and white + + + align:start position:0% +8x1 black and white +glossy photographs and then he came back + + align:start position:0% +glossy photographs and then he came back + + + align:start position:0% +glossy photographs and then he came back +the next morning and looked at the data + + align:start position:0% +the next morning and looked at the data + + + align:start position:0% +the next morning and looked at the data +and uh he had a very simple Edge + + align:start position:0% +and uh he had a very simple Edge + + + align:start position:0% +and uh he had a very simple Edge +detector which was misleading in the + + align:start position:0% +detector which was misleading in the + + + align:start position:0% +detector which was misleading in the +sense that um he had a scanner that + + align:start position:0% +sense that um he had a scanner that + + + align:start position:0% +sense that um he had a scanner that +produced incredibly good images they you + + align:start position:0% +produced incredibly good images they you + + + align:start position:0% +produced incredibly good images they you +know because there was just a single uh + + align:start position:0% +know because there was just a single uh + + + align:start position:0% +know because there was just a single uh +detector he could afford to build a a + + align:start position:0% +detector he could afford to build a a + + + align:start position:0% +detector he could afford to build a a +12bit a2d uh he had much better quality + + align:start position:0% +12bit a2d uh he had much better quality + + + align:start position:0% +12bit a2d uh he had much better quality +images than we would get out of vidicons + + align:start position:0% +images than we would get out of vidicons + + + align:start position:0% +images than we would get out of vidicons +and other devices later and so his Edge + + align:start position:0% +and other devices later and so his Edge + + + align:start position:0% +and other devices later and so his Edge +detector which worked okay on his + + align:start position:0% +detector which worked okay on his + + + align:start position:0% +detector which worked okay on his +pictures you know wouldn't work for + + align:start position:0% +pictures you know wouldn't work for + + + align:start position:0% +pictures you know wouldn't work for +people on other pictures and so for a + + align:start position:0% +people on other pictures and so for a + + + align:start position:0% +people on other pictures and so for a +long time there was kind of a + + align:start position:0% +long time there was kind of a + + + align:start position:0% +long time there was kind of a +competition okay my Edge detector is + + align:start position:0% +competition okay my Edge detector is + + + align:start position:0% +competition okay my Edge detector is +more is better than yours and they all + + align:start position:0% +more is better than yours and they all + + + align:start position:0% +more is better than yours and they all +had + + align:start position:0% +had + + + align:start position:0% +had +names and I remember being at a + + align:start position:0% +names and I remember being at a + + + align:start position:0% +names and I remember being at a +conference and standing in the passage + + align:start position:0% +conference and standing in the passage + + + align:start position:0% +conference and standing in the passage +and you know trying to be social and + + align:start position:0% +and you know trying to be social and + + + align:start position:0% +and you know trying to be social and +chatting with this guy I'd never seen + + align:start position:0% +chatting with this guy I'd never seen + + + align:start position:0% +chatting with this guy I'd never seen +before and we got on to Edge detect + + align:start position:0% +before and we got on to Edge detect + + + align:start position:0% +before and we got on to Edge detect +and I said well you know it's too bad + + align:start position:0% +and I said well you know it's too bad + + + align:start position:0% +and I said well you know it's too bad +that all the edge detectors that have + + align:start position:0% +that all the edge detectors that have + + + align:start position:0% +that all the edge detectors that have +people's names on them are worthless + + align:start position:0% +people's names on them are worthless + + + align:start position:0% +people's names on them are worthless +well he was Irvin soel whose name is on + + align:start position:0% +well he was Irvin soel whose name is on + + + align:start position:0% +well he was Irvin soel whose name is on +one of the edge detectives and he's he's + + align:start position:0% +one of the edge detectives and he's he's + + + align:start position:0% +one of the edge detectives and he's he's +forgiven me since then but he's uh you + + align:start position:0% +forgiven me since then but he's uh you + + + align:start position:0% +forgiven me since then but he's uh you +know he's still trying to um claim his + + align:start position:0% +know he's still trying to um claim his + + + align:start position:0% +know he's still trying to um claim his +legacy and make sure that everyone knows + + align:start position:0% +legacy and make sure that everyone knows + + + align:start position:0% +legacy and make sure that everyone knows +that he invented that edge detector and + + align:start position:0% +that he invented that edge detector and + + + align:start position:0% +that he invented that edge detector and +he's he's blogging and whatever anyway + + align:start position:0% +he's he's blogging and whatever anyway + + + align:start position:0% +he's he's blogging and whatever anyway +so um those are some more papers + + align:start position:0% +so um those are some more papers + + + align:start position:0% +so um those are some more papers +and then we get to the + + align:start position:0% +and then we get to the + + + align:start position:0% +and then we get to the +figures so the top one is the Roberts + + align:start position:0% +figures so the top one is the Roberts + + + align:start position:0% +figures so the top one is the Roberts +cross Edge detector and you can see that + + align:start position:0% +cross Edge detector and you can see that + + + align:start position:0% +cross Edge detector and you can see that +it's sort of a directional derivative + + align:start position:0% +it's sort of a directional derivative + + + align:start position:0% +it's sort of a directional derivative +the left hand one is sort of a + + align:start position:0% +the left hand one is sort of a + + + align:start position:0% +the left hand one is sort of a +derivative in the 45 degree Direction + + align:start position:0% +derivative in the 45 degree Direction + + + align:start position:0% +derivative in the 45 degree Direction +and the right hand one is sort of in the + + align:start position:0% +and the right hand one is sort of in the + + + align:start position:0% +and the right hand one is sort of in the +135 degree Direction and uh you know why + + align:start position:0% +135 degree Direction and uh you know why + + + align:start position:0% +135 degree Direction and uh you know why +that well we'll talk about the + + align:start position:0% +that well we'll talk about the + + + align:start position:0% +that well we'll talk about the +advantages of that type of operator + + align:start position:0% +advantages of that type of operator + + + align:start position:0% +advantages of that type of operator +later and then so irin so Bell's + + align:start position:0% +later and then so irin so Bell's + + + align:start position:0% +later and then so irin so Bell's +operator is figure 1B uh which is um + + align:start position:0% +operator is figure 1B uh which is um + + + align:start position:0% +operator is figure 1B uh which is um +somewhat advantageous uh takes more + + align:start position:0% +somewhat advantageous uh takes more + + + align:start position:0% +somewhat advantageous uh takes more +computation uh is somewhat more + + align:start position:0% +computation uh is somewhat more + + + align:start position:0% +computation uh is somewhat more +resistant to noise is not as high + + align:start position:0% +resistant to noise is not as high + + + align:start position:0% +resistant to noise is not as high +resolution and so on and then um Bill + + align:start position:0% +resolution and so on and then um Bill + + + align:start position:0% +resolution and so on and then um Bill +Sila U having uh been to my classes uh + + align:start position:0% +Sila U having uh been to my classes uh + + + align:start position:0% +Sila U having uh been to my classes uh +was interested in hexagonal + + align:start position:0% +was interested in hexagonal + + + align:start position:0% +was interested in hexagonal +tessellations and so he proposed these + + align:start position:0% +tessellations and so he proposed these + + + align:start position:0% +tessellations and so he proposed these +alternate um operators uh which would + + align:start position:0% +alternate um operators uh which would + + + align:start position:0% +alternate um operators uh which would +work on a hexagonal grid un un + + align:start position:0% +work on a hexagonal grid un un + + + align:start position:0% +work on a hexagonal grid un un +fortunately you know no one ever built a + + align:start position:0% +fortunately you know no one ever built a + + + align:start position:0% +fortunately you know no one ever built a +hexagonal grid cameras uh uh they have + + align:start position:0% +hexagonal grid cameras uh uh they have + + + align:start position:0% +hexagonal grid cameras uh uh they have +some advantages in terms of uh + + align:start position:0% +some advantages in terms of uh + + + align:start position:0% +some advantages in terms of uh +resolution and rotational symmetry um + + align:start position:0% +resolution and rotational symmetry um + + + align:start position:0% +resolution and rotational symmetry um +but it's not a huge Advantage it's like + + align:start position:0% +but it's not a huge Advantage it's like + + + align:start position:0% +but it's not a huge Advantage it's like +um you know four over Pi so there's an + + align:start position:0% +um you know four over Pi so there's an + + + align:start position:0% +um you know four over Pi so there's an +advantage of some sort but it's not huge + + align:start position:0% +advantage of some sort but it's not huge + + + align:start position:0% +advantage of some sort but it's not huge +and so the extra trouble of working with + + align:start position:0% +and so the extra trouble of working with + + + align:start position:0% +and so the extra trouble of working with +a hexagonal grid apparently was too much + + align:start position:0% +a hexagonal grid apparently was too much + + + align:start position:0% +a hexagonal grid apparently was too much +for + + align:start position:0% +for + + + align:start position:0% +for +engineers uh this one here uh goes off + + align:start position:0% +engineers uh this one here uh goes off + + + align:start position:0% +engineers uh this one here uh goes off +in three different directions which is + + align:start position:0% +in three different directions which is + + + align:start position:0% +in three different directions which is +appropriate for hexagonal grid but of + + align:start position:0% +appropriate for hexagonal grid but of + + + align:start position:0% +appropriate for hexagonal grid but of +course that's redundant uh you know if + + align:start position:0% +course that's redundant uh you know if + + + align:start position:0% +course that's redundant uh you know if +you have the the uh DX and the Edy + + align:start position:0% +you have the the uh DX and the Edy + + + align:start position:0% +you have the the uh DX and the Edy +you've got everything so they two + + align:start position:0% +you've got everything so they two + + + align:start position:0% +you've got everything so they two +degrees of freedom to the brightness + + align:start position:0% +degrees of freedom to the brightness + + + align:start position:0% +degrees of freedom to the brightness +gradient you don't really need three + + align:start position:0% +gradient you don't really need three + + + align:start position:0% +gradient you don't really need three +numbers so he came up with this + + align:start position:0% +numbers so he came up with this + + + align:start position:0% +numbers so he came up with this +alternate pattern here where this one is + + align:start position:0% +alternate pattern here where this one is + + + align:start position:0% +alternate pattern here where this one is +estimating the derivative in the X + + align:start position:0% +estimating the derivative in the X + + + align:start position:0% +estimating the derivative in the X +Direction and this one in the y + + align:start position:0% +Direction and this one in the y + + + align:start position:0% +Direction and this one in the y +direction and the square root of three + + align:start position:0% +direction and the square root of three + + + align:start position:0% +direction and the square root of three +is because these cells are further apart + + align:start position:0% +is because these cells are further apart + + + align:start position:0% +is because these cells are further apart +than those cells so you have to + + align:start position:0% +than those cells so you have to + + + align:start position:0% +than those cells so you have to +compensate for + + align:start position:0% +compensate for + + + align:start position:0% +compensate for +that okay so a key step uh right up + + align:start position:0% +that okay so a key step uh right up + + + align:start position:0% +that okay so a key step uh right up +front is to convert from cartisian to + + align:start position:0% +front is to convert from cartisian to + + + align:start position:0% +front is to convert from cartisian to +Polar coordinates in that you want the + + align:start position:0% +Polar coordinates in that you want the + + + align:start position:0% +Polar coordinates in that you want the +magnitude of the gradient and its + + align:start position:0% +magnitude of the gradient and its + + + align:start position:0% +magnitude of the gradient and its +direction rather than the brightness + + align:start position:0% +direction rather than the brightness + + + align:start position:0% +direction rather than the brightness +gradient itself the X and Y components + + align:start position:0% +gradient itself the X and Y components + + + align:start position:0% +gradient itself the X and Y components +and so up there is a Formula you know + + align:start position:0% +and so up there is a Formula you know + + + align:start position:0% +and so up there is a Formula you know +you could take the square root of the + + align:start position:0% +you could take the square root of the + + + align:start position:0% +you could take the square root of the +sum of squares and you take the + + align:start position:0% +sum of squares and you take the + + + align:start position:0% +sum of squares and you take the +arctangent and part of that is sort of + + align:start position:0% +arctangent and part of that is sort of + + + align:start position:0% +arctangent and part of that is sort of +uh put out as a straw man which is like + + align:start position:0% +uh put out as a straw man which is like + + + align:start position:0% +uh put out as a straw man which is like +why on Earth would you do this this is + + align:start position:0% +why on Earth would you do this this is + + + align:start position:0% +why on Earth would you do this this is +very expensive now maybe today we + + align:start position:0% +very expensive now maybe today we + + + align:start position:0% +very expensive now maybe today we +wouldn't say that but but you know if + + align:start position:0% +wouldn't say that but but you know if + + + align:start position:0% +wouldn't say that but but you know if +you have 100 million pixels and you're + + align:start position:0% +you have 100 million pixels and you're + + + align:start position:0% +you have 100 million pixels and you're +trying to do things at 100 frames a + + align:start position:0% +trying to do things at 100 frames a + + + align:start position:0% +trying to do things at 100 frames a +second you still don't want to really + + align:start position:0% +second you still don't want to really + + + align:start position:0% +second you still don't want to really +take square roots and and Arc tangents + + align:start position:0% +take square roots and and Arc tangents + + + align:start position:0% +take square roots and and Arc tangents +actually square roots depending on where + + align:start position:0% +actually square roots depending on where + + + align:start position:0% +actually square roots depending on where +you grew up uh you would know you might + + align:start position:0% +you grew up uh you would know you might + + + align:start position:0% +you grew up uh you would know you might +know that square roots are as easy to + + align:start position:0% +know that square roots are as easy to + + + align:start position:0% +know that square roots are as easy to +calculate as divisions uh it's just a + + align:start position:0% +calculate as divisions uh it's just a + + + align:start position:0% +calculate as divisions uh it's just a +slight twiddle on the algorithm and + + align:start position:0% +slight twiddle on the algorithm and + + + align:start position:0% +slight twiddle on the algorithm and +unfortunately in the Western World we + + align:start position:0% +unfortunately in the Western World we + + + align:start position:0% +unfortunately in the Western World we +don't teach that so people think of + + align:start position:0% +don't teach that so people think of + + + align:start position:0% +don't teach that so people think of +square roots as these really nasty + + align:start position:0% +square roots as these really nasty + + + align:start position:0% +square roots as these really nasty +things so um but uh unfortunately the + + align:start position:0% +things so um but uh unfortunately the + + + align:start position:0% +things so um but uh unfortunately the +people who designed digital computers + + align:start position:0% +people who designed digital computers + + + align:start position:0% +people who designed digital computers +were also not from this other world and + + align:start position:0% +were also not from this other world and + + + align:start position:0% +were also not from this other world and +so for us uh square roots are more + + align:start position:0% +so for us uh square roots are more + + + align:start position:0% +so for us uh square roots are more +expensive than + + align:start position:0% +expensive than + + + align:start position:0% +expensive than +division anyway uh the argument in the + + align:start position:0% +division anyway uh the argument in the + + + align:start position:0% +division anyway uh the argument in the +in the patent is you know we can do it + + align:start position:0% +in the patent is you know we can do it + + + align:start position:0% +in the patent is you know we can do it +this way but uh it's expensive so let's + + align:start position:0% +this way but uh it's expensive so let's + + + align:start position:0% +this way but uh it's expensive so let's +find a better way of doing it then + + align:start position:0% +find a better way of doing it then + + + align:start position:0% +find a better way of doing it then +figure 2B is a alternate solution using + + align:start position:0% +figure 2B is a alternate solution using + + + align:start position:0% +figure 2B is a alternate solution using +lookup tables the idea there is that you + + align:start position:0% +lookup tables the idea there is that you + + + align:start position:0% +lookup tables the idea there is that you +encode the X and Y components of + + align:start position:0% +encode the X and Y components of + + + align:start position:0% +encode the X and Y components of +brightness uh in a small number of bits + + align:start position:0% +brightness uh in a small number of bits + + + align:start position:0% +brightness uh in a small number of bits +then you stick the bits together and + + align:start position:0% +then you stick the bits together and + + + align:start position:0% +then you stick the bits together and +that's the address of a lookup table and + + align:start position:0% +that's the address of a lookup table and + + + align:start position:0% +that's the address of a lookup table and +um creates a table index lookup table + + align:start position:0% +um creates a table index lookup table + + + align:start position:0% +um creates a table index lookup table +the lookup table gives you the magnitude + + align:start position:0% +the lookup table gives you the magnitude + + + align:start position:0% +the lookup table gives you the magnitude +and the direction and that's a great + + align:start position:0% +and the direction and that's a great + + + align:start position:0% +and the direction and that's a great +solution if uh arithmetic operations are + + align:start position:0% +solution if uh arithmetic operations are + + + align:start position:0% +solution if uh arithmetic operations are +expensive which is was true at the time + + align:start position:0% +expensive which is was true at the time + + + align:start position:0% +expensive which is was true at the time +and and if memory access isn't a problem + + align:start position:0% +and and if memory access isn't a problem + + + align:start position:0% +and and if memory access isn't a problem +then well things keep on changing so for + + align:start position:0% +then well things keep on changing so for + + + align:start position:0% +then well things keep on changing so for +a while + + align:start position:0% +a while + + + align:start position:0% +a while +there uh you know arithmetic operations + + align:start position:0% +there uh you know arithmetic operations + + + align:start position:0% +there uh you know arithmetic operations +became cheap because people just built + + align:start position:0% +became cheap because people just built + + + align:start position:0% +became cheap because people just built +uh 32x 32bit multiplies and you know be + + align:start position:0% +uh 32x 32bit multiplies and you know be + + + align:start position:0% +uh 32x 32bit multiplies and you know be +done with it and uh cash misses were a + + align:start position:0% +done with it and uh cash misses were a + + + align:start position:0% +done with it and uh cash misses were a +big deal so you didn't really want to + + align:start position:0% +big deal so you didn't really want to + + + align:start position:0% +big deal so you didn't really want to +use large lookup tables and so uh for + + align:start position:0% +use large lookup tables and so uh for + + + align:start position:0% +use large lookup tables and so uh for +that reason you might want to go back to + + align:start position:0% +that reason you might want to go back to + + + align:start position:0% +that reason you might want to go back to +a method that does a lot of arithmetic + + align:start position:0% +a method that does a lot of arithmetic + + + align:start position:0% +a method that does a lot of arithmetic +rather than have a large lookup table + + align:start position:0% +rather than have a large lookup table + + + align:start position:0% +rather than have a large lookup table +and that's changing again and so on so + + align:start position:0% +and that's changing again and so on so + + + align:start position:0% +and that's changing again and so on so +anyway at the time uh the idea of using + + align:start position:0% +anyway at the time uh the idea of using + + + align:start position:0% +anyway at the time uh the idea of using +the lookup table was uhu also not + + align:start position:0% +the lookup table was uhu also not + + + align:start position:0% +the lookup table was uhu also not +particularly attractive and so he came + + align:start position:0% +particularly attractive and so he came + + + align:start position:0% +particularly attractive and so he came +up with + + align:start position:0% +up with + + + align:start position:0% +up with +um this method Illustrated down here + + align:start position:0% +um this method Illustrated down here + + + align:start position:0% +um this method Illustrated down here +which we'll talk about called Cordic so + + align:start position:0% +which we'll talk about called Cordic so + + + align:start position:0% +which we'll talk about called Cordic so +Cordic is a way of estimating the uh + + align:start position:0% +Cordic is a way of estimating the uh + + + align:start position:0% +Cordic is a way of estimating the uh +magnitude and direction of a vector from + + align:start position:0% +magnitude and direction of a vector from + + + align:start position:0% +magnitude and direction of a vector from +its two coordinates and it was actually + + align:start position:0% +its two coordinates and it was actually + + + align:start position:0% +its two coordinates and it was actually +um pioneered in World War II uh you know + + align:start position:0% +um pioneered in World War II uh you know + + + align:start position:0% +um pioneered in World War II uh you know +you probably know that a lot of early + + align:start position:0% +you probably know that a lot of early + + + align:start position:0% +you probably know that a lot of early +Computing machineries were built for + + align:start position:0% +Computing machineries were built for + + + align:start position:0% +Computing machineries were built for +unpleasant purposes like war and you + + align:start position:0% +unpleasant purposes like war and you + + + align:start position:0% +unpleasant purposes like war and you +know making sure that you could aim your + + align:start position:0% +know making sure that you could aim your + + + align:start position:0% +know making sure that you could aim your +guns in the right direction and being + + align:start position:0% +guns in the right direction and being + + + align:start position:0% +guns in the right direction and being +able to compute Arc tangents and square + + align:start position:0% +able to compute Arc tangents and square + + + align:start position:0% +able to compute Arc tangents and square +roots was very important and so people + + align:start position:0% +roots was very important and so people + + + align:start position:0% +roots was very important and so people +came up with this method which is kind + + align:start position:0% +came up with this method which is kind + + + align:start position:0% +came up with this method which is kind +of a an iterative method that um rotates + + align:start position:0% +of a an iterative method that um rotates + + + align:start position:0% +of a an iterative method that um rotates +the coordinate system to bring it more + + align:start position:0% +the coordinate system to bring it more + + + align:start position:0% +the coordinate system to bring it more +into alignment with the brightness + + align:start position:0% +into alignment with the brightness + + + align:start position:0% +into alignment with the brightness +gradient Vector uh and at each step it + + align:start position:0% +gradient Vector uh and at each step it + + + align:start position:0% +gradient Vector uh and at each step it +reduces the uh error the difference and + + align:start position:0% +reduces the uh error the difference and + + + align:start position:0% +reduces the uh error the difference and +uh when you then add up all the results + + align:start position:0% +uh when you then add up all the results + + + align:start position:0% +uh when you then add up all the results +you can get the magnitude and the um uh + + align:start position:0% +you can get the magnitude and the um uh + + + align:start position:0% +you can get the magnitude and the um uh +Direction and amazingly you can do it + + align:start position:0% +Direction and amazingly you can do it + + + align:start position:0% +Direction and amazingly you can do it +without much arithmetic you only end up + + align:start position:0% +without much arithmetic you only end up + + + align:start position:0% +without much arithmetic you only end up +needing a shift which costs next to + + align:start position:0% +needing a shift which costs next to + + + align:start position:0% +needing a shift which costs next to +nothing adders and subtract us and an + + align:start position:0% +nothing adders and subtract us and an + + + align:start position:0% +nothing adders and subtract us and an +absolute value oper a so if you think + + align:start position:0% +absolute value oper a so if you think + + + align:start position:0% +absolute value oper a so if you think +about rotation you think of you know a + + align:start position:0% +about rotation you think of you know a + + + align:start position:0% +about rotation you think of you know a +matrix cosine Theta sin Theta minus sin + + align:start position:0% +matrix cosine Theta sin Theta minus sin + + + align:start position:0% +matrix cosine Theta sin Theta minus sin +Theta cosine Theta and multiplication so + + align:start position:0% +Theta cosine Theta and multiplication so + + + align:start position:0% +Theta cosine Theta and multiplication so +trigonometry that's expensive + + align:start position:0% +trigonometry that's expensive + + + align:start position:0% +trigonometry that's expensive +multiplication and addition expensive + + align:start position:0% +multiplication and addition expensive + + + align:start position:0% +multiplication and addition expensive +well um this is a method very cleverly + + align:start position:0% +well um this is a method very cleverly + + + align:start position:0% +well um this is a method very cleverly +designed to not do any of that and and + + align:start position:0% +designed to not do any of that and and + + + align:start position:0% +designed to not do any of that and and +um you know it can be implemented at low + + align:start position:0% +um you know it can be implemented at low + + + align:start position:0% +um you know it can be implemented at low +level so um you know in Intel + + align:start position:0% +level so um you know in Intel + + + align:start position:0% +level so um you know in Intel +architectures you have have an assembly + + align:start position:0% +architectures you have have an assembly + + + align:start position:0% +architectures you have have an assembly +language but you also have clever things + + align:start position:0% +language but you also have clever things + + + align:start position:0% +language but you also have clever things +you can do with uh instructions that + + align:start position:0% +you can do with uh instructions that + + + align:start position:0% +you can do with uh instructions that +access multiple bytes and so this can + + align:start position:0% +access multiple bytes and so this can + + + align:start position:0% +access multiple bytes and so this can +all be implemented extremely efficiently + + align:start position:0% +all be implemented extremely efficiently + + + align:start position:0% +all be implemented extremely efficiently +so that was the motivation for for + + align:start position:0% +so that was the motivation for for + + + align:start position:0% +so that was the motivation for for +that then + + align:start position:0% +that then + + + align:start position:0% +that then +um once we know the brightness gradient + + align:start position:0% +um once we know the brightness gradient + + + align:start position:0% +um once we know the brightness gradient +uh in magnitude and Direction one of the + + align:start position:0% +uh in magnitude and Direction one of the + + + align:start position:0% +uh in magnitude and Direction one of the +things we want to do is uh find the + + align:start position:0% +things we want to do is uh find the + + + align:start position:0% +things we want to do is uh find the +place where the gradient is large right + + align:start position:0% +place where the gradient is large right + + + align:start position:0% +place where the gradient is large right +that's where the edge is but uh we don't + + align:start position:0% +that's where the edge is but uh we don't + + + align:start position:0% +that's where the edge is but uh we don't +want to just take a local maximum + + align:start position:0% +want to just take a local maximum + + + align:start position:0% +want to just take a local maximum +because along and Edge the bradian going + + align:start position:0% +because along and Edge the bradian going + + + align:start position:0% +because along and Edge the bradian going +gradient is going to be large so that + + align:start position:0% +gradient is going to be large so that + + + align:start position:0% +gradient is going to be large so that +there'll be some places that are local + + align:start position:0% +there'll be some places that are local + + + align:start position:0% +there'll be some places that are local +Maxima but they're sort of meaningless + + align:start position:0% +Maxima but they're sort of meaningless + + + align:start position:0% +Maxima but they're sort of meaningless +they arbitary points along the edge what + + align:start position:0% +they arbitary points along the edge what + + + align:start position:0% +they arbitary points along the edge what +we really want is to look across the + + align:start position:0% +we really want is to look across the + + + align:start position:0% +we really want is to look across the +edge and take the maximum in that + + align:start position:0% +edge and take the maximum in that + + + align:start position:0% +edge and take the maximum in that +direction 1D not 2D and so we need the + + align:start position:0% +direction 1D not 2D and so we need the + + + align:start position:0% +direction 1D not 2D and so we need the +direction of the gradient so that we + + align:start position:0% +direction of the gradient so that we + + + align:start position:0% +direction of the gradient so that we +know which direction to search in and we + + align:start position:0% +know which direction to search in and we + + + align:start position:0% +know which direction to search in and we +need to have this uh maximum finding + + align:start position:0% +need to have this uh maximum finding + + + align:start position:0% +need to have this uh maximum finding +which is uh called non- maximum + + align:start position:0% +which is uh called non- maximum + + + align:start position:0% +which is uh called non- maximum +supression meaning we'll ignore stuff + + align:start position:0% +supression meaning we'll ignore stuff + + + align:start position:0% +supression meaning we'll ignore stuff +other than the maximum uh funny term for + + align:start position:0% +other than the maximum uh funny term for + + + align:start position:0% +other than the maximum uh funny term for +finding the maximum but that's what it + + align:start position:0% +finding the maximum but that's what it + + + align:start position:0% +finding the maximum but that's what it +was called and um since we're working on + + align:start position:0% +was called and um since we're working on + + + align:start position:0% +was called and um since we're working on +a discrete grid we have some + + align:start position:0% +a discrete grid we have some + + + align:start position:0% +a discrete grid we have some +limitations and uh you know on the + + align:start position:0% +limitations and uh you know on the + + + align:start position:0% +limitations and uh you know on the +particular on the Square grid we have to + + align:start position:0% +particular on the Square grid we have to + + + align:start position:0% +particular on the Square grid we have to +somehow decide to quantize the possible + + align:start position:0% +somehow decide to quantize the possible + + + align:start position:0% +somehow decide to quantize the possible +directions of the gradients I mean we + + align:start position:0% +directions of the gradients I mean we + + + align:start position:0% +directions of the gradients I mean we +compute the gradient Direction with high + + align:start position:0% +compute the gradient Direction with high + + + align:start position:0% +compute the gradient Direction with high +accuracy using any of the three methods + + align:start position:0% +accuracy using any of the three methods + + + align:start position:0% +accuracy using any of the three methods +we talked about but um then we're + + align:start position:0% +we talked about but um then we're + + + align:start position:0% +we talked about but um then we're +restricted to you know we only have + + align:start position:0% +restricted to you know we only have + + + align:start position:0% +restricted to you know we only have +those pixels so uh what do we do well uh + + align:start position:0% +those pixels so uh what do we do well uh + + + align:start position:0% +those pixels so uh what do we do well uh +we quantize it into these different + + align:start position:0% +we quantize it into these different + + + align:start position:0% +we quantize it into these different +directions and for purposes of finding + + align:start position:0% +directions and for purposes of finding + + + align:start position:0% +directions and for purposes of finding +the extremum we um pick one of eight + + align:start position:0% +the extremum we um pick one of eight + + + align:start position:0% +the extremum we um pick one of eight +possible Compass + + align:start position:0% +possible Compass + + + align:start position:0% +possible Compass +directions uh on the hexagonal grid you + + align:start position:0% +directions uh on the hexagonal grid you + + + align:start position:0% +directions uh on the hexagonal grid you +know we have six possible directions + + align:start position:0% +know we have six possible directions + + + align:start position:0% +know we have six possible directions +same + + align:start position:0% +same + + + align:start position:0% +same +idea um now if + + align:start position:0% +idea um now if + + + align:start position:0% +idea um now if +we want to we can + + align:start position:0% +we want to we can + + + align:start position:0% +we want to we can +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um look further a field so the previous + + align:start position:0% +um look further a field so the previous + + + align:start position:0% +um look further a field so the previous +figure was looking at a 3X3 area of the + + align:start position:0% +figure was looking at a 3X3 area of the + + + align:start position:0% +figure was looking at a 3X3 area of the +image so we just had U you know 3x3 uh + + align:start position:0% +image so we just had U you know 3x3 uh + + + align:start position:0% +image so we just had U you know 3x3 uh +values of gradient up there but if we + + align:start position:0% +values of gradient up there but if we + + + align:start position:0% +values of gradient up there but if we +not happy with that course quantization + + align:start position:0% +not happy with that course quantization + + + align:start position:0% +not happy with that course quantization +of direction we can go to 5x5 and now we + + align:start position:0% +of direction we can go to 5x5 and now we + + + align:start position:0% +of direction we can go to 5x5 and now we +have a larger range of directions so + + align:start position:0% +have a larger range of directions so + + + align:start position:0% +have a larger range of directions so +they talk about this but uh it's not + + align:start position:0% +they talk about this but uh it's not + + + align:start position:0% +they talk about this but uh it's not +what was actually + + align:start position:0% +what was actually + + + align:start position:0% +what was actually +implemented and of course you can go + + align:start position:0% +implemented and of course you can go + + + align:start position:0% +implemented and of course you can go +further okay so the next step is now + + align:start position:0% +further okay so the next step is now + + + align:start position:0% +further okay so the next step is now +we're looking along a certain direction + + align:start position:0% +we're looking along a certain direction + + + align:start position:0% +we're looking along a certain direction +in the image uh and we found the place + + align:start position:0% +in the image uh and we found the place + + + align:start position:0% +in the image uh and we found the place +where there's a + + align:start position:0% +where there's a + + + align:start position:0% +where there's a +extremum and uh now we'd like to know + + align:start position:0% +extremum and uh now we'd like to know + + + align:start position:0% +extremum and uh now we'd like to know +where the uh actual Peak is uh to sub + + align:start position:0% +where the uh actual Peak is uh to sub + + + align:start position:0% +where the uh actual Peak is uh to sub +pixel accuracy and so one thing we can + + align:start position:0% +pixel accuracy and so one thing we can + + + align:start position:0% +pixel accuracy and so one thing we can +do is figure uh 4 a uh those are the + + align:start position:0% +do is figure uh 4 a uh those are the + + + align:start position:0% +do is figure uh 4 a uh those are the +three values so imagine that zero is the + + align:start position:0% +three values so imagine that zero is the + + + align:start position:0% +three values so imagine that zero is the +pixel where you found the maximum and + + + align:start position:0% +pixel where you found the maximum and + + + + align:start position:0% +pixel where you found the maximum and + +one is one over and minus one is one + + align:start position:0% +one is one over and minus one is one + + + align:start position:0% +one is one over and minus one is one +over in the other direction and those + + align:start position:0% +over in the other direction and those + + + align:start position:0% +over in the other direction and those +don't need to be in the X Direction they + + align:start position:0% +don't need to be in the X Direction they + + + align:start position:0% +don't need to be in the X Direction they +could be in the diagonal direction or + + align:start position:0% +could be in the diagonal direction or + + + align:start position:0% +could be in the diagonal direction or +they could be up and down but three + + align:start position:0% +they could be up and down but three + + + align:start position:0% +they could be up and down but three +values anyway and uh we can fit a + + align:start position:0% +values anyway and uh we can fit a + + + align:start position:0% +values anyway and uh we can fit a +parabola to that um well that's the best + + align:start position:0% +parabola to that um well that's the best + + + align:start position:0% +parabola to that um well that's the best +we can do right we got three three + + align:start position:0% +we can do right we got three three + + + align:start position:0% +we can do right we got three three +numbers um we can only fit something + + align:start position:0% +numbers um we can only fit something + + + align:start position:0% +numbers um we can only fit something +with three degrees of freedom uh and so + + align:start position:0% +with three degrees of freedom uh and so + + + align:start position:0% +with three degrees of freedom uh and so +so ax^2 + BX + C we can fit that uh we + + align:start position:0% +so ax^2 + BX + C we can fit that uh we + + + align:start position:0% +so ax^2 + BX + C we can fit that uh we +we we could fit a cubic but it would be + + align:start position:0% +we we could fit a cubic but it would be + + + align:start position:0% +we we could fit a cubic but it would be +ambiguous because there' be one + + align:start position:0% +ambiguous because there' be one + + + align:start position:0% +ambiguous because there' be one +parameter that was uh you know hanging + + align:start position:0% +parameter that was uh you know hanging + + + align:start position:0% +parameter that was uh you know hanging +loose we could make it anything we want + + align:start position:0% +loose we could make it anything we want + + + align:start position:0% +loose we could make it anything we want +okay so we fit a parabola and we know + + align:start position:0% +okay so we fit a parabola and we know + + + align:start position:0% +okay so we fit a parabola and we know +how to find the peak of a parabola we + + align:start position:0% +how to find the peak of a parabola we + + + align:start position:0% +how to find the peak of a parabola we +just differentiate set the result equal + + align:start position:0% +just differentiate set the result equal + + + align:start position:0% +just differentiate set the result equal +to zero and there we are we find we can + + align:start position:0% +to zero and there we are we find we can + + + align:start position:0% +to zero and there we are we find we can +find the peak indicated by that dotted + + align:start position:0% +find the peak indicated by that dotted + + + align:start position:0% +find the peak indicated by that dotted +line um + + align:start position:0% +line um + + + align:start position:0% +line um +now um if if our model of the world is + + align:start position:0% +now um if if our model of the world is + + + align:start position:0% +now um if if our model of the world is +mandrian I.E we have patches of equal + + align:start position:0% +mandrian I.E we have patches of equal + + + align:start position:0% +mandrian I.E we have patches of equal +brightness with sharp edges between them + + align:start position:0% +brightness with sharp edges between them + + + align:start position:0% +brightness with sharp edges between them +then uh we know that um the brightness + + align:start position:0% +then uh we know that um the brightness + + + align:start position:0% +then uh we know that um the brightness +will be um constant in each patch and if + + align:start position:0% +will be um constant in each patch and if + + + align:start position:0% +will be um constant in each patch and if +the edge is very sharp we might expect a + + align:start position:0% +the edge is very sharp we might expect a + + + align:start position:0% +the edge is very sharp we might expect a +different uh local fitting which is + + align:start position:0% +different uh local fitting which is + + + align:start position:0% +different uh local fitting which is +shown on the right so up to the edge you + + align:start position:0% +shown on the right so up to the edge you + + + align:start position:0% +shown on the right so up to the edge you +know the brightness is increased the + + align:start position:0% +know the brightness is increased the + + + align:start position:0% +know the brightness is increased the +gradient is increasing and then it's + + align:start position:0% +gradient is increasing and then it's + + + align:start position:0% +gradient is increasing and then it's +going down and it might seem a little + + align:start position:0% +going down and it might seem a little + + + align:start position:0% +going down and it might seem a little +bit odd uh but uh that will give us a a + + align:start position:0% +bit odd uh but uh that will give us a a + + + align:start position:0% +bit odd uh but uh that will give us a a +different result and again we need um + + align:start position:0% +different result and again we need um + + + align:start position:0% +different result and again we need um +those three numbers to make that fit and + + align:start position:0% +those three numbers to make that fit and + + + align:start position:0% +those three numbers to make that fit and +we can find the peak you know find where + + align:start position:0% +we can find the peak you know find where + + + align:start position:0% +we can find the peak you know find where +those two uh lines intersect and we can + + align:start position:0% +those two uh lines intersect and we can + + + align:start position:0% +those two uh lines intersect and we can +find the uh dotted line in figure + + align:start position:0% +find the uh dotted line in figure + + + align:start position:0% +find the uh dotted line in figure +4B um and those two will generally be + + align:start position:0% +4B um and those two will generally be + + + align:start position:0% +4B um and those two will generally be +different so which one do we take which + + align:start position:0% +different so which one do we take which + + + align:start position:0% +different so which one do we take which +one is more accurate and so we we'll get + + align:start position:0% +one is more accurate and so we we'll get + + + align:start position:0% +one is more accurate and so we we'll get +to that in in a + + align:start position:0% +to that in in a + + + align:start position:0% +to that in in a +moment um then there's something they + + align:start position:0% +moment um then there's something they + + + align:start position:0% +moment um then there's something they +call the plane position interpolation so + + align:start position:0% +call the plane position interpolation so + + + align:start position:0% +call the plane position interpolation so +the idea is that when we found the + + align:start position:0% +the idea is that when we found the + + + align:start position:0% +the idea is that when we found the +extremum we quantize directions you know + + align:start position:0% +extremum we quantize directions you know + + + align:start position:0% +extremum we quantize directions you know +horizontal 45° vertical Etc U but the + + align:start position:0% +horizontal 45° vertical Etc U but the + + + align:start position:0% +horizontal 45° vertical Etc U but the +actual gradient we know uh to higher + + align:start position:0% +actual gradient we know uh to higher + + + align:start position:0% +actual gradient we know uh to higher +Precision we we know it's real direction + + align:start position:0% +Precision we we know it's real direction + + + align:start position:0% +Precision we we know it's real direction +to maybe eight bits of accuracy and so + + align:start position:0% +to maybe eight bits of accuracy and so + + + align:start position:0% +to maybe eight bits of accuracy and so +uh we what one step we can to form is to + + align:start position:0% +uh we what one step we can to form is to + + + align:start position:0% +uh we what one step we can to form is to +actually uh go in the gradient direction + + align:start position:0% +actually uh go in the gradient direction + + + align:start position:0% +actually uh go in the gradient direction +from the center pixel and find the place + + align:start position:0% +from the center pixel and find the place + + + align:start position:0% +from the center pixel and find the place +in that direction where the edge is so + + align:start position:0% +in that direction where the edge is so + + + align:start position:0% +in that direction where the edge is so +the uh the diagonal line is our + + align:start position:0% +the uh the diagonal line is our + + + align:start position:0% +the uh the diagonal line is our +quantized approximation of gradient + + align:start position:0% +quantized approximation of gradient + + + align:start position:0% +quantized approximation of gradient +Direction and we found at uh + + align:start position:0% +Direction and we found at uh + + + align:start position:0% +Direction and we found at uh +4113 we found uh its peak using the + + align:start position:0% +4113 we found uh its peak using the + + + align:start position:0% +4113 we found uh its peak using the +method of figure + + align:start position:0% +method of figure + + + align:start position:0% +method of figure +four in uh the arrow of 410 is the + + align:start position:0% +four in uh the arrow of 410 is the + + + align:start position:0% +four in uh the arrow of 410 is the +actual gradient Direction and now what + + align:start position:0% +actual gradient Direction and now what + + + align:start position:0% +actual gradient Direction and now what +we do is we draw a + + align:start position:0% +we do is we draw a + + + align:start position:0% +we do is we draw a +perpendicular uh to that gradient + + align:start position:0% +perpendicular uh to that gradient + + + align:start position:0% +perpendicular uh to that gradient +Direction and uh from going through 413 + + align:start position:0% +Direction and uh from going through 413 + + + align:start position:0% +Direction and uh from going through 413 +and we see where it intersects 4:15 so + + align:start position:0% +and we see where it intersects 4:15 so + + + align:start position:0% +and we see where it intersects 4:15 so +the idea is that um with the edge when + + align:start position:0% +the idea is that um with the edge when + + + align:start position:0% +the idea is that um with the edge when +we find an edge Point uh it's def its + + align:start position:0% +we find an edge Point uh it's def its + + + align:start position:0% +we find an edge Point uh it's def its +position is well defined in the + + align:start position:0% +position is well defined in the + + + align:start position:0% +position is well defined in the +direction of the gradient perpendicular + + align:start position:0% +direction of the gradient perpendicular + + + align:start position:0% +direction of the gradient perpendicular +to the edge but along the edge of course + + align:start position:0% +to the edge but along the edge of course + + + align:start position:0% +to the edge but along the edge of course +it isn't we could be anywhere on the + + align:start position:0% +it isn't we could be anywhere on the + + + align:start position:0% +it isn't we could be anywhere on the +edge so this is you know just like like + + align:start position:0% +edge so this is you know just like like + + + align:start position:0% +edge so this is you know just like like +our aperture problem Optical flow + + align:start position:0% +our aperture problem Optical flow + + + align:start position:0% +our aperture problem Optical flow +discussion uh and so which of those + + align:start position:0% +discussion uh and so which of those + + + align:start position:0% +discussion uh and so which of those +points do we take along the edge well + + align:start position:0% +points do we take along the edge well + + + align:start position:0% +points do we take along the edge well +one argument might be the further you + + align:start position:0% +one argument might be the further you + + + align:start position:0% +one argument might be the further you +get away from stuff that you really know + + align:start position:0% +get away from stuff that you really know + + + align:start position:0% +get away from stuff that you really know +the less accurate it's going to be so + + align:start position:0% +the less accurate it's going to be so + + + align:start position:0% +the less accurate it's going to be so +let's find the closest point right so so + + align:start position:0% +let's find the closest point right so so + + + align:start position:0% +let's find the closest point right so so +um we found an edge which point on the + + align:start position:0% +um we found an edge which point on the + + + align:start position:0% +um we found an edge which point on the +edge do we actually record in the output + + align:start position:0% +edge do we actually record in the output + + + align:start position:0% +edge do we actually record in the output +data well we pick the one that's as + + align:start position:0% +data well we pick the one that's as + + + align:start position:0% +data well we pick the one that's as +close as possible to gz Z and that's + + align:start position:0% +close as possible to gz Z and that's + + + align:start position:0% +close as possible to gz Z and that's +this point that we've constructed this + + align:start position:0% +this point that we've constructed this + + + align:start position:0% +this point that we've constructed this +way so uh that's that's that + + align:start position:0% +way so uh that's that's that + + + align:start position:0% +way so uh that's that's that +construction um so then uh we discover + + align:start position:0% +construction um so then uh we discover + + + align:start position:0% +construction um so then uh we discover +that we can get a pretty good sub pixel + + align:start position:0% +that we can get a pretty good sub pixel + + + align:start position:0% +that we can get a pretty good sub pixel +accuracy maybe a tenth of a pixel but uh + + align:start position:0% +accuracy maybe a tenth of a pixel but uh + + + align:start position:0% +accuracy maybe a tenth of a pixel but uh +to go further uh we need to take into + + align:start position:0% +to go further uh we need to take into + + + align:start position:0% +to go further uh we need to take into +account the fact that our constructions + + align:start position:0% +account the fact that our constructions + + + align:start position:0% +account the fact that our constructions +are you know based on some assumptions + + align:start position:0% +are you know based on some assumptions + + + align:start position:0% +are you know based on some assumptions +about how the brightness gr gradient + + align:start position:0% +about how the brightness gr gradient + + + align:start position:0% +about how the brightness gr gradient +varies with position and we have those + + align:start position:0% +varies with position and we have those + + + align:start position:0% +varies with position and we have those +two models and we could come up with + + align:start position:0% +two models and we could come up with + + + align:start position:0% +two models and we could come up with +some more and the the the real you know + + align:start position:0% +some more and the the the real you know + + + align:start position:0% +some more and the the the real you know +what is the real thing well the real + + align:start position:0% +what is the real thing well the real + + + align:start position:0% +what is the real thing well the real +thing is going to depend on properties + + align:start position:0% +thing is going to depend on properties + + + align:start position:0% +thing is going to depend on properties +of the Optics of the camera you're using + + align:start position:0% +of the Optics of the camera you're using + + + align:start position:0% +of the Optics of the camera you're using +it's going to depend on the fu factor of + + align:start position:0% +it's going to depend on the fu factor of + + + align:start position:0% +it's going to depend on the fu factor of +the chip that's sensing the image it's + + align:start position:0% +the chip that's sensing the image it's + + + align:start position:0% +the chip that's sensing the image it's +going to depend on how accurately in + + align:start position:0% +going to depend on how accurately in + + + align:start position:0% +going to depend on how accurately in +Focus the image is so it's uh The Edge + + align:start position:0% +Focus the image is so it's uh The Edge + + + align:start position:0% +Focus the image is so it's uh The Edge +transition of course is not a perfect + + align:start position:0% +transition of course is not a perfect + + + align:start position:0% +transition of course is not a perfect +step transition which is a good thing U + + align:start position:0% +step transition which is a good thing U + + + align:start position:0% +step transition which is a good thing U +but its actual shape is uh not you know + + align:start position:0% +but its actual shape is uh not you know + + + align:start position:0% +but its actual shape is uh not you know +something that you may be able to um + + align:start position:0% +something that you may be able to um + + + align:start position:0% +something that you may be able to um +predict ahead of time and it's the same + + align:start position:0% +predict ahead of time and it's the same + + + align:start position:0% +predict ahead of time and it's the same +for every possible camera and uh image + + align:start position:0% +for every possible camera and uh image + + + align:start position:0% +for every possible camera and uh image +situation that you can think of now if + + align:start position:0% +situation that you can think of now if + + + align:start position:0% +situation that you can think of now if +it doesn't fit those two models what + + align:start position:0% +it doesn't fit those two models what + + + align:start position:0% +it doesn't fit those two models what +happens we'll get the wrong answer but + + align:start position:0% +happens we'll get the wrong answer but + + + align:start position:0% +happens we'll get the wrong answer but +not hugely wrong so there's kind of a a + + align:start position:0% +not hugely wrong so there's kind of a a + + + align:start position:0% +not hugely wrong so there's kind of a a +bias introduced by our choice of uh that + + align:start position:0% +bias introduced by our choice of uh that + + + align:start position:0% +bias introduced by our choice of uh that +model and and uh we can calibrate out + + align:start position:0% +model and and uh we can calibrate out + + + align:start position:0% +model and and uh we can calibrate out +that bias and so that's what he's doing + + align:start position:0% +that bias and so that's what he's doing + + + align:start position:0% +that bias and so that's what he's doing +here so the these are exaggerated curves + + align:start position:0% +here so the these are exaggerated curves + + + align:start position:0% +here so the these are exaggerated curves +so s is the U one of them is the + + align:start position:0% +so s is the U one of them is the + + + align:start position:0% +so s is the U one of them is the +actually computed uh position based on + + align:start position:0% +actually computed uh position based on + + + align:start position:0% +actually computed uh position based on +our little Peak finding and Parabola + + align:start position:0% +our little Peak finding and Parabola + + + align:start position:0% +our little Peak finding and Parabola +fitting and S Prime is the actual Edge + + align:start position:0% +fitting and S Prime is the actual Edge + + + align:start position:0% +fitting and S Prime is the actual Edge +position and ideally you know be + + align:start position:0% +position and ideally you know be + + + align:start position:0% +position and ideally you know be +diagonal line if you plot those two and + + align:start position:0% +diagonal line if you plot those two and + + + align:start position:0% +diagonal line if you plot those two and +because of the factors I mentioned it's + + align:start position:0% +because of the factors I mentioned it's + + + align:start position:0% +because of the factors I mentioned it's +not a not a straight line it has a + + align:start position:0% +not a not a straight line it has a + + + align:start position:0% +not a not a straight line it has a +little bit of a bow to it uh and as I + + align:start position:0% +little bit of a bow to it uh and as I + + + align:start position:0% +little bit of a bow to it uh and as I +mentioned this is hugely exaggerated the + + align:start position:0% +mentioned this is hugely exaggerated the + + + align:start position:0% +mentioned this is hugely exaggerated the +bow is much less um but it shows that it + + align:start position:0% +bow is much less um but it shows that it + + + align:start position:0% +bow is much less um but it shows that it +might be three different shapes for + + align:start position:0% +might be three different shapes for + + + align:start position:0% +might be three different shapes for +three different cameras or Focus + + align:start position:0% +three different cameras or Focus + + + align:start position:0% +three different cameras or Focus +positions or you know phase of the moon + + align:start position:0% +positions or you know phase of the moon + + + align:start position:0% +positions or you know phase of the moon +whatever and so uh what do we do well um + + align:start position:0% +whatever and so uh what do we do well um + + + align:start position:0% +whatever and so uh what do we do well um +the think of this this is now just a + + align:start position:0% +the think of this this is now just a + + + align:start position:0% +the think of this this is now just a +correction on top of a correction so we + + align:start position:0% +correction on top of a correction so we + + + align:start position:0% +correction on top of a correction so we +don't need to be hugely sophisticated so + + align:start position:0% +don't need to be hugely sophisticated so + + + align:start position:0% +don't need to be hugely sophisticated so +he comes up with uh ways of removing + + align:start position:0% +he comes up with uh ways of removing + + + align:start position:0% +he comes up with uh ways of removing +that bias and in particular you can + + align:start position:0% +that bias and in particular you can + + + align:start position:0% +that bias and in particular you can +think of you know just powers of s um if + + align:start position:0% +think of you know just powers of s um if + + + align:start position:0% +think of you know just powers of s um if +you take s to the one then that's our + + align:start position:0% +you take s to the one then that's our + + + align:start position:0% +you take s to the one then that's our +diagonal line if you take s uh 1.1 then + + align:start position:0% +diagonal line if you take s uh 1.1 then + + + align:start position:0% +diagonal line if you take s uh 1.1 then +it's a little bowed down if you take s + + align:start position:0% +it's a little bowed down if you take s + + + align:start position:0% +it's a little bowed down if you take s +0.9 it's bowed a little bit the other + + align:start position:0% +0.9 it's bowed a little bit the other + + + align:start position:0% +0.9 it's bowed a little bit the other +way so that uh the idea here is that we + + align:start position:0% +way so that uh the idea here is that we + + + align:start position:0% +way so that uh the idea here is that we +can increase the accuracy even more by + + align:start position:0% +can increase the accuracy even more by + + + align:start position:0% +can increase the accuracy even more by +finding out for your particular Machine + + align:start position:0% +finding out for your particular Machine + + + align:start position:0% +finding out for your particular Machine +Vision system uh what what the S is that + + align:start position:0% +Vision system uh what what the S is that + + + align:start position:0% +Vision system uh what what the S is that +gives you the best + + align:start position:0% +gives you the best + + + align:start position:0% +gives you the best +fit and while we're there notice that + + align:start position:0% +fit and while we're there notice that + + + align:start position:0% +fit and while we're there notice that +when our gradient quantise gradient + + align:start position:0% +when our gradient quantise gradient + + + align:start position:0% +when our gradient quantise gradient +Direction happens to be diagonal + + align:start position:0% +Direction happens to be diagonal + + + align:start position:0% +Direction happens to be diagonal +45° then the points we've got are + + align:start position:0% +45° then the points we've got are + + + align:start position:0% +45° then the points we've got are +actually further apart but you know + + align:start position:0% +actually further apart but you know + + + align:start position:0% +actually further apart but you know +they're square root of two times as far + + align:start position:0% +they're square root of two times as far + + + align:start position:0% +they're square root of two times as far +apart as when we're horizontal and so + + align:start position:0% +apart as when we're horizontal and so + + + align:start position:0% +apart as when we're horizontal and so +you would imagine that the bias would be + + align:start position:0% +you would imagine that the bias would be + + + align:start position:0% +you would imagine that the bias would be +different and indeed it is and so + + align:start position:0% +different and indeed it is and so + + + align:start position:0% +different and indeed it is and so +another refinement of the pattern is + + align:start position:0% +another refinement of the pattern is + + + align:start position:0% +another refinement of the pattern is +that you make this bias depend on the uh + + align:start position:0% +that you make this bias depend on the uh + + + align:start position:0% +that you make this bias depend on the uh +gradient direction to get even higher + + align:start position:0% +gradient direction to get even higher + + + align:start position:0% +gradient direction to get even higher +accuracy + + align:start position:0% +accuracy + + + align:start position:0% +accuracy +so okay + + align:start position:0% +so okay + + + align:start position:0% +so okay +um and so this is the overall diagram of + + align:start position:0% +um and so this is the overall diagram of + + + align:start position:0% +um and so this is the overall diagram of +the whole thing so we start with the + + align:start position:0% +the whole thing so we start with the + + + align:start position:0% +the whole thing so we start with the +image we estimate the brightness + + align:start position:0% +image we estimate the brightness + + + align:start position:0% +image we estimate the brightness +gradient uh which we call E XE Y and he + + align:start position:0% +gradient uh which we call E XE Y and he + + + align:start position:0% +gradient uh which we call E XE Y and he +calls GX gy then we find the gradient + + align:start position:0% +calls GX gy then we find the gradient + + + align:start position:0% +calls GX gy then we find the gradient +magnitude and Direction g0 and G Theta + + align:start position:0% +magnitude and Direction g0 and G Theta + + + align:start position:0% +magnitude and Direction g0 and G Theta +uh then we um find the uh we do the non- + + align:start position:0% +uh then we um find the uh we do the non- + + + align:start position:0% +uh then we um find the uh we do the non- +maximum suppression and we find the + + align:start position:0% +maximum suppression and we find the + + + align:start position:0% +maximum suppression and we find the +neighbors we detect the peak uh in that + + align:start position:0% +neighbors we detect the peak uh in that + + + align:start position:0% +neighbors we detect the peak uh in that +direction and from that we get a + + align:start position:0% +direction and from that we get a + + + align:start position:0% +direction and from that we get a +position of the edge point and we still + + align:start position:0% +position of the edge point and we still + + + align:start position:0% +position of the edge point and we still +know the gradient there so we use that + + align:start position:0% +know the gradient there so we use that + + + align:start position:0% +know the gradient there so we use that +as well and then we interpolate using + + align:start position:0% +as well and then we interpolate using + + + align:start position:0% +as well and then we interpolate using +that Parabola or the triangle we + + align:start position:0% +that Parabola or the triangle we + + + align:start position:0% +that Parabola or the triangle we +compensate for the bias and we do that + + align:start position:0% +compensate for the bias and we do that + + + align:start position:0% +compensate for the bias and we do that +plain position in uh method that finds + + align:start position:0% +plain position in uh method that finds + + + align:start position:0% +plain position in uh method that finds +us the closest point to the maximum that + + align:start position:0% +us the closest point to the maximum that + + + align:start position:0% +us the closest point to the maximum that +H that is on the + + align:start position:0% +H that is on the + + + align:start position:0% +H that is on the +edge + + align:start position:0% +edge + + + align:start position:0% +edge +okay so um here's the pattern itself + + align:start position:0% +okay so um here's the pattern itself + + + align:start position:0% +okay so um here's the pattern itself +this this is of course part of the + + align:start position:0% +this this is of course part of the + + + align:start position:0% +this this is of course part of the +materials in the course so you can study + + align:start position:0% +materials in the course so you can study + + + align:start position:0% +materials in the course so you can study +this yourself and I'm not going to go + + align:start position:0% +this yourself and I'm not going to go + + + align:start position:0% +this yourself and I'm not going to go +through it word by word but just uh + + align:start position:0% +through it word by word but just uh + + + align:start position:0% +through it word by word but just uh +focus on the sections so it starts off + + align:start position:0% +focus on the sections so it starts off + + + align:start position:0% +focus on the sections so it starts off +as usual with the title and then the + + align:start position:0% +as usual with the title and then the + + + align:start position:0% +as usual with the title and then the +field of the invention you know is this + + align:start position:0% +field of the invention you know is this + + + align:start position:0% +field of the invention you know is this +about making rubber from coming out of + + align:start position:0% +about making rubber from coming out of + + + align:start position:0% +about making rubber from coming out of +trees or is this about Machine Vision so + + align:start position:0% +trees or is this about Machine Vision so + + + align:start position:0% +trees or is this about Machine Vision so +this very short uh uh this invention + + align:start position:0% +this very short uh uh this invention + + + align:start position:0% +this very short uh uh this invention +relates generally to Digital Image + + align:start position:0% +relates generally to Digital Image + + + align:start position:0% +relates generally to Digital Image +processing and particularly to Edge + + align:start position:0% +processing and particularly to Edge + + + align:start position:0% +processing and particularly to Edge +detection in digital images then we get + + align:start position:0% +detection in digital images then we get + + + align:start position:0% +detection in digital images then we get +to the + + align:start position:0% +to the + + + align:start position:0% +to the +background so the background is where + + align:start position:0% +background so the background is where + + + align:start position:0% +background so the background is where +you acknowledge that people have already + + align:start position:0% +you acknowledge that people have already + + + align:start position:0% +you acknowledge that people have already +done certain things so that's uh + + align:start position:0% +done certain things so that's uh + + + align:start position:0% +done certain things so that's uh +considered a prior art in in the + + align:start position:0% +considered a prior art in in the + + + align:start position:0% +considered a prior art in in the +terminology of patents and the the main + + align:start position:0% +terminology of patents and the the main + + + align:start position:0% +terminology of patents and the the main +point of this section from the point of + + align:start position:0% +point of this section from the point of + + + align:start position:0% +point of this section from the point of +view of the inventor is that you end + + align:start position:0% +view of the inventor is that you end + + + align:start position:0% +view of the inventor is that you end +with where you say uh therefore you need + + align:start position:0% +with where you say uh therefore you need + + + align:start position:0% +with where you say uh therefore you need +this thing I invented you know because + + align:start position:0% +this thing I invented you know because + + + align:start position:0% +this thing I invented you know because +all these other stuff it's great but it + + align:start position:0% +all these other stuff it's great but it + + + align:start position:0% +all these other stuff it's great but it +doesn't really solve the problem and so + + align:start position:0% +doesn't really solve the problem and so + + + align:start position:0% +doesn't really solve the problem and so +in this case what do they + + align:start position:0% +in this case what do they + + + align:start position:0% +in this case what do they +say uh consequently there is a need for + + align:start position:0% +say uh consequently there is a need for + + + align:start position:0% +say uh consequently there is a need for +an inexpensive Andor fast method of high + + align:start position:0% +an inexpensive Andor fast method of high + + + align:start position:0% +an inexpensive Andor fast method of high +accuracy sub pixel Edge detection so + + align:start position:0% +accuracy sub pixel Edge detection so + + + align:start position:0% +accuracy sub pixel Edge detection so +most of this discussion is about why do + + align:start position:0% +most of this discussion is about why do + + + align:start position:0% +most of this discussion is about why do +you want to detect edges why is that + + align:start position:0% +you want to detect edges why is that + + + align:start position:0% +you want to detect edges why is that +important problem and uh how have people + + align:start position:0% +important problem and uh how have people + + + align:start position:0% +important problem and uh how have people +been detecting ages you know there was + + align:start position:0% +been detecting ages you know there was + + + align:start position:0% +been detecting ages you know there was +uh Robert's gradient operator there was + + align:start position:0% +uh Robert's gradient operator there was + + + align:start position:0% +uh Robert's gradient operator there was +Irvin soel uh and so on and then it ends + + align:start position:0% +Irvin soel uh and so on and then it ends + + + align:start position:0% +Irvin soel uh and so on and then it ends +up with well all of those are too slow + + align:start position:0% +up with well all of those are too slow + + + align:start position:0% +up with well all of those are too slow +too inaccurate blah blah blah and here's + + align:start position:0% +too inaccurate blah blah blah and here's + + + align:start position:0% +too inaccurate blah blah blah and here's +you know here's why you need what I what + + align:start position:0% +you know here's why you need what I what + + + align:start position:0% +you know here's why you need what I what +I've got and then there's a summary of + + align:start position:0% +I've got and then there's a summary of + + + align:start position:0% +I've got and then there's a summary of +The Invention which is a short version + + align:start position:0% +The Invention which is a short version + + + align:start position:0% +The Invention which is a short version +of uh what it's all about um it the + + align:start position:0% +of uh what it's all about um it the + + + align:start position:0% +of uh what it's all about um it the +invention provides an apparatus and + + align:start position:0% +invention provides an apparatus and + + + align:start position:0% +invention provides an apparatus and +method for accurate subpal a detection + + align:start position:0% +method for accurate subpal a detection + + + align:start position:0% +method for accurate subpal a detection +so that's another thing about uh patents + + align:start position:0% +so that's another thing about uh patents + + + align:start position:0% +so that's another thing about uh patents +um originally the people who came up + + align:start position:0% +um originally the people who came up + + + align:start position:0% +um originally the people who came up +with the idea of patents uh the way it's + + align:start position:0% +with the idea of patents uh the way it's + + + align:start position:0% +with the idea of patents uh the way it's +written in our constitution um decided + + align:start position:0% +written in our constitution um decided + + + align:start position:0% +written in our constitution um decided +they didn't want to patent uh ideas uh + + align:start position:0% +they didn't want to patent uh ideas uh + + + align:start position:0% +they didn't want to patent uh ideas uh +abstract ideas they didn't want to + + align:start position:0% +abstract ideas they didn't want to + + + align:start position:0% +abstract ideas they didn't want to +patent mathematical formula and so um + + align:start position:0% +patent mathematical formula and so um + + + align:start position:0% +patent mathematical formula and so um +you know they they didn't know about + + align:start position:0% +you know they they didn't know about + + + align:start position:0% +you know they they didn't know about +programming but the uh Supreme Court + + align:start position:0% +programming but the uh Supreme Court + + + align:start position:0% +programming but the uh Supreme Court +later inter reinterpreted it to mean + + align:start position:0% +later inter reinterpreted it to mean + + + align:start position:0% +later inter reinterpreted it to mean +that you can't patent programs you know + + align:start position:0% +that you can't patent programs you know + + + align:start position:0% +that you can't patent programs you know +software is not patentable what that and + + align:start position:0% +software is not patentable what that and + + + align:start position:0% +software is not patentable what that and +so for a long time um people in Machine + + align:start position:0% +so for a long time um people in Machine + + + align:start position:0% +so for a long time um people in Machine +Vision uh weren't able to patent their + + align:start position:0% +Vision uh weren't able to patent their + + + align:start position:0% +Vision uh weren't able to patent their +stuff because it's basically software so + + align:start position:0% +stuff because it's basically software so + + + align:start position:0% +stuff because it's basically software so +then they came up with the idea well + + align:start position:0% +then they came up with the idea well + + + align:start position:0% +then they came up with the idea well +what if the software lives in some + + align:start position:0% +what if the software lives in some + + + align:start position:0% +what if the software lives in some +physical object you know you can patent + + align:start position:0% +physical object you know you can patent + + + align:start position:0% +physical object you know you can patent +that and so uh you know then they all + + align:start position:0% +that and so uh you know then they all + + + align:start position:0% +that and so uh you know then they all +this convoluted language to try and make + + align:start position:0% +this convoluted language to try and make + + + align:start position:0% +this convoluted language to try and make +it be a physical thing and uh then for a + + align:start position:0% +it be a physical thing and uh then for a + + + align:start position:0% +it be a physical thing and uh then for a +while what you did was uh because it was + + align:start position:0% +while what you did was uh because it was + + + align:start position:0% +while what you did was uh because it was +unclear how the Supreme Court would come + + align:start position:0% +unclear how the Supreme Court would come + + + align:start position:0% +unclear how the Supreme Court would come +down on this you you chose both so you + + align:start position:0% +down on this you you chose both so you + + + align:start position:0% +down on this you you chose both so you +basically you invented an apparatus a + + align:start position:0% +basically you invented an apparatus a + + + align:start position:0% +basically you invented an apparatus a +box that has you know an SD card with a + + align:start position:0% +box that has you know an SD card with a + + + align:start position:0% +box that has you know an SD card with a +program in it or whatever uh and the + + align:start position:0% +program in it or whatever uh and the + + + align:start position:0% +program in it or whatever uh and the +method separately and then if someday + + align:start position:0% +method separately and then if someday + + + align:start position:0% +method separately and then if someday +they decide that methods are not + + align:start position:0% +they decide that methods are not + + + align:start position:0% +they decide that methods are not +patentable uh then you're okay because + + align:start position:0% +patentable uh then you're okay because + + + align:start position:0% +patentable uh then you're okay because +you've still patented the apparatus so + + align:start position:0% +you've still patented the apparatus so + + + align:start position:0% +you've still patented the apparatus so +this meant that in many cases as here + + align:start position:0% +this meant that in many cases as here + + + align:start position:0% +this meant that in many cases as here +there twice as many claims at the end as + + align:start position:0% +there twice as many claims at the end as + + + align:start position:0% +there twice as many claims at the end as +really they need to be because they had + + align:start position:0% +really they need to be because they had + + + align:start position:0% +really they need to be because they had +to + + align:start position:0% +to + + + align:start position:0% +to +basically uh use the same language just + + align:start position:0% +basically uh use the same language just + + + align:start position:0% +basically uh use the same language just +with apparatus replaced with method and + + align:start position:0% +with apparatus replaced with method and + + + align:start position:0% +with apparatus replaced with method and +some other small changes so it's you + + align:start position:0% +some other small changes so it's you + + + align:start position:0% +some other small changes so it's you +know apparatus and + + align:start position:0% +know apparatus and + + + align:start position:0% +know apparatus and +Method there was a um case in uh so uh + + align:start position:0% +Method there was a um case in uh so uh + + + align:start position:0% +Method there was a um case in uh so uh +patent cases are litigated in various + + align:start position:0% +patent cases are litigated in various + + + align:start position:0% +patent cases are litigated in various +ways uh one one special one is uh import + + align:start position:0% +ways uh one one special one is uh import + + + align:start position:0% +ways uh one one special one is uh import +so if someone's trying to import + + align:start position:0% +so if someone's trying to import + + + align:start position:0% +so if someone's trying to import +something that you think violates your + + align:start position:0% +something that you think violates your + + + align:start position:0% +something that you think violates your +patent you can go to a particular patent + + align:start position:0% +patent you can go to a particular patent + + + align:start position:0% +patent you can go to a particular patent +Court which is in Washington and you can + + align:start position:0% +Court which is in Washington and you can + + + align:start position:0% +Court which is in Washington and you can +argue your case there and uh there was a + + align:start position:0% +argue your case there and uh there was a + + + align:start position:0% +argue your case there and uh there was a +case uh not related to this patent but a + + align:start position:0% +case uh not related to this patent but a + + + align:start position:0% +case uh not related to this patent but a +closely related patent and there's a + + align:start position:0% +closely related patent and there's a + + + align:start position:0% +closely related patent and there's a +company in Canada uh matrox which uh + + align:start position:0% +company in Canada uh matrox which uh + + + align:start position:0% +company in Canada uh matrox which uh +basically didn't build a machine but + + align:start position:0% +basically didn't build a machine but + + + align:start position:0% +basically didn't build a machine but +they had um software that implemented + + align:start position:0% +they had um software that implemented + + + align:start position:0% +they had um software that implemented +exactly what was in that pattern and so + + align:start position:0% +exactly what was in that pattern and so + + + align:start position:0% +exactly what was in that pattern and so +the expert Witnesses for the two sides + + align:start position:0% +the expert Witnesses for the two sides + + + align:start position:0% +the expert Witnesses for the two sides +got up and you know presented all their + + align:start position:0% +got up and you know presented all their + + + align:start position:0% +got up and you know presented all their +very hairy theories about how uh this + + align:start position:0% +very hairy theories about how uh this + + + align:start position:0% +very hairy theories about how uh this +might work and by the way the expert + + align:start position:0% +might work and by the way the expert + + + align:start position:0% +might work and by the way the expert +Witnesses get to look at your code so + + align:start position:0% +Witnesses get to look at your code so + + + align:start position:0% +Witnesses get to look at your code so +you know if you're trying to make an + + align:start position:0% +you know if you're trying to make an + + + align:start position:0% +you know if you're trying to make an +argument you don't want to show the + + align:start position:0% +argument you don't want to show the + + + align:start position:0% +argument you don't want to show the +other side the code but the expert + + align:start position:0% +other side the code but the expert + + + align:start position:0% +other side the code but the expert +witness for the other side can look at + + align:start position:0% +witness for the other side can look at + + + align:start position:0% +witness for the other side can look at +the code and so uh you put that person + + align:start position:0% +the code and so uh you put that person + + + align:start position:0% +the code and so uh you put that person +in a room where they can't copy things + + align:start position:0% +in a room where they can't copy things + + + align:start position:0% +in a room where they can't copy things +they're not allowed to bring their + + align:start position:0% +they're not allowed to bring their + + + align:start position:0% +they're not allowed to bring their +little us spe sticks with them and they + + align:start position:0% +little us spe sticks with them and they + + + align:start position:0% +little us spe sticks with them and they +can look at all of your code and so the + + align:start position:0% +can look at all of your code and so the + + + align:start position:0% +can look at all of your code and so the +ex and it was kind of pathetic because + + align:start position:0% +ex and it was kind of pathetic because + + + align:start position:0% +ex and it was kind of pathetic because +the expert Witnesses were being asked + + align:start position:0% +the expert Witnesses were being asked + + + align:start position:0% +the expert Witnesses were being asked +questions like well isn't finding a + + align:start position:0% +questions like well isn't finding a + + + align:start position:0% +questions like well isn't finding a +maximum of that function the same as + + align:start position:0% +maximum of that function the same as + + + align:start position:0% +maximum of that function the same as +finding the minimum of minus that + + align:start position:0% +finding the minimum of minus that + + + align:start position:0% +finding the minimum of minus that +function you know so and the judges just + + align:start position:0% +function you know so and the judges just + + + align:start position:0% +function you know so and the judges just +were completely out of their water and + + align:start position:0% +were completely out of their water and + + + align:start position:0% +were completely out of their water and +in the end fortunately the judges found + + align:start position:0% +in the end fortunately the judges found + + + align:start position:0% +in the end fortunately the judges found +the way out of it which was to say oh + + align:start position:0% +the way out of it which was to say oh + + + align:start position:0% +the way out of it which was to say oh +it's all software and that's not + + align:start position:0% +it's all software and that's not + + + align:start position:0% +it's all software and that's not +patentable so there were like three + + align:start position:0% +patentable so there were like three + + + align:start position:0% +patentable so there were like three +weeks of people discussing you know + + align:start position:0% +weeks of people discussing you know + + + align:start position:0% +weeks of people discussing you know +cubic uh uh interpolation and stuff like + + align:start position:0% +cubic uh uh interpolation and stuff like + + + align:start position:0% +cubic uh uh interpolation and stuff like +that and then in the end it was thrown + + align:start position:0% +that and then in the end it was thrown + + + align:start position:0% +that and then in the end it was thrown +out on the technicality if you like so + + align:start position:0% +out on the technicality if you like so + + + align:start position:0% +out on the technicality if you like so +anyway so uh that's part of that so the + + align:start position:0% +anyway so uh that's part of that so the + + + align:start position:0% +anyway so uh that's part of that so the +summary of The Invention now the in + + align:start position:0% +summary of The Invention now the in + + + align:start position:0% +summary of The Invention now the in +terms of patent + + align:start position:0% +terms of patent + + + align:start position:0% +terms of patent +litigation uh most of this is Irrelevant + + align:start position:0% +litigation uh most of this is Irrelevant + + + align:start position:0% +litigation uh most of this is Irrelevant +in the sense that that is the lawyers + + align:start position:0% +in the sense that that is the lawyers + + + align:start position:0% +in the sense that that is the lawyers +immediately go to the claims when we get + + align:start position:0% +immediately go to the claims when we get + + + align:start position:0% +immediately go to the claims when we get +to claims in a + + align:start position:0% +to claims in a + + + align:start position:0% +to claims in a +second okay so this is a unusually + + align:start position:0% +second okay so this is a unusually + + + align:start position:0% +second okay so this is a unusually +uh clear explanation of the method again + + align:start position:0% +uh clear explanation of the method again + + + align:start position:0% +uh clear explanation of the method again +you know part of what you want to do + + align:start position:0% +you know part of what you want to do + + + align:start position:0% +you know part of what you want to do +when writing a pattern is make it as + + align:start position:0% +when writing a pattern is make it as + + + align:start position:0% +when writing a pattern is make it as +broad as possible so you have a clear + + align:start position:0% +broad as possible so you have a clear + + + align:start position:0% +broad as possible so you have a clear +idea of how to do it but now uh someone + + align:start position:0% +idea of how to do it but now uh someone + + + align:start position:0% +idea of how to do it but now uh someone +else your your opponent is going to + + align:start position:0% +else your your opponent is going to + + + align:start position:0% +else your your opponent is going to +figure out a way of not doing things + + align:start position:0% +figure out a way of not doing things + + + align:start position:0% +figure out a way of not doing things +exactly the way you describe making some + + align:start position:0% +exactly the way you describe making some + + + align:start position:0% +exactly the way you describe making some +small change so he can say oh this isn't + + align:start position:0% +small change so he can say oh this isn't + + + align:start position:0% +small change so he can say oh this isn't +your patent because I did that instead + + align:start position:0% +your patent because I did that instead + + + align:start position:0% +your patent because I did that instead +of that so one of the jobs that you and + + align:start position:0% +of that so one of the jobs that you and + + + align:start position:0% +of that so one of the jobs that you and +your lawyer I have is to figure out you + + align:start position:0% +your lawyer I have is to figure out you + + + align:start position:0% +your lawyer I have is to figure out you +know all the ways of modifying it so + + align:start position:0% +know all the ways of modifying it so + + + align:start position:0% +know all the ways of modifying it so +that it's still sort of the same idea so + + align:start position:0% +that it's still sort of the same idea so + + + align:start position:0% +that it's still sort of the same idea so +probably things as an inventor you don't + + align:start position:0% +probably things as an inventor you don't + + + align:start position:0% +probably things as an inventor you don't +think of first because you just want to + + align:start position:0% +think of first because you just want to + + + align:start position:0% +think of first because you just want to +get it to work and to work well and now + + align:start position:0% +get it to work and to work well and now + + + align:start position:0% +get it to work and to work well and now +you've got to think about oh what if I + + align:start position:0% +you've got to think about oh what if I + + + align:start position:0% +you've got to think about oh what if I +replace ultraviolet with infrared what + + align:start position:0% +replace ultraviolet with infrared what + + + align:start position:0% +replace ultraviolet with infrared what +if I use sound instead of radio waves + + align:start position:0% +if I use sound instead of radio waves + + + align:start position:0% +if I use sound instead of radio waves +and so on and so as a result patents + + align:start position:0% +and so on and so as a result patents + + + align:start position:0% +and so on and so as a result patents +written by lawyers are almost impossible + + align:start position:0% +written by lawyers are almost impossible + + + align:start position:0% +written by lawyers are almost impossible +to read because they've generalized + + align:start position:0% +to read because they've generalized + + + align:start position:0% +to read because they've generalized +everything everything to such a large + + align:start position:0% +everything everything to such a large + + + align:start position:0% +everything everything to such a large +degree and so here uh Bill Sila refused + + align:start position:0% +degree and so here uh Bill Sila refused + + + align:start position:0% +degree and so here uh Bill Sila refused +to let them do that he just wrote it + + align:start position:0% +to let them do that he just wrote it + + + align:start position:0% +to let them do that he just wrote it +himself and it's you know it's clear + + align:start position:0% +himself and it's you know it's clear + + + align:start position:0% +himself and it's you know it's clear +instructions this is what you do and + + align:start position:0% +instructions this is what you do and + + + align:start position:0% +instructions this is what you do and +it's great it's uh very pleasant to read + + align:start position:0% +it's great it's uh very pleasant to read + + + align:start position:0% +it's great it's uh very pleasant to read +okay then we get to the figures and so + + align:start position:0% +okay then we get to the figures and so + + + align:start position:0% +okay then we get to the figures and so +there's a first of all a short section + + align:start position:0% +there's a first of all a short section + + + align:start position:0% +there's a first of all a short section +uh that lists all the figures and just + + align:start position:0% +uh that lists all the figures and just + + + align:start position:0% +uh that lists all the figures and just +gives them sort of names and then + + align:start position:0% +gives them sort of names and then + + + align:start position:0% +gives them sort of names and then +there's the detailed description of the + + align:start position:0% +there's the detailed description of the + + + align:start position:0% +there's the detailed description of the +drawings which is actually the detailed + + align:start position:0% +drawings which is actually the detailed + + + align:start position:0% +drawings which is actually the detailed +explanation of how the thing works + + align:start position:0% +explanation of how the thing works + + + align:start position:0% +explanation of how the thing works +uh and the other conventions for example + + align:start position:0% +uh and the other conventions for example + + + align:start position:0% +uh and the other conventions for example +uh all of the numbers that + + align:start position:0% +uh all of the numbers that + + + align:start position:0% +uh all of the numbers that +appear in bold phas refer to items in + + align:start position:0% +appear in bold phas refer to items in + + + align:start position:0% +appear in bold phas refer to items in +the figures and if they appear in more + + align:start position:0% +the figures and if they appear in more + + + align:start position:0% +the figures and if they appear in more +than one figure they better have the + + align:start position:0% +than one figure they better have the + + + align:start position:0% +than one figure they better have the +same number you know rules like that + + align:start position:0% +same number you know rules like that + + + align:start position:0% +same number you know rules like that +stuff can be rejected because you didn't + + align:start position:0% +stuff can be rejected because you didn't + + + align:start position:0% +stuff can be rejected because you didn't +follow uh the rules because your uh + + align:start position:0% +follow uh the rules because your uh + + + align:start position:0% +follow uh the rules because your uh +rectangular boxes aren't quite + + align:start position:0% +rectangular boxes aren't quite + + + align:start position:0% +rectangular boxes aren't quite +rectangular and also you know in one + + align:start position:0% +rectangular and also you know in one + + + align:start position:0% +rectangular and also you know in one +place you called uh the kernel 131 and + + align:start position:0% +place you called uh the kernel 131 and + + + align:start position:0% +place you called uh the kernel 131 and +in another place you called it 141 can't + + align:start position:0% +in another place you called it 141 can't + + + align:start position:0% +in another place you called it 141 can't +do that + + align:start position:0% + + + + align:start position:0% + +so uh and here's here's a formula uh for + + align:start position:0% +so uh and here's here's a formula uh for + + + align:start position:0% +so uh and here's here's a formula uh for +the cartisian to Polar conversion + + align:start position:0% +the cartisian to Polar conversion + + + align:start position:0% +the cartisian to Polar conversion +equation 1 a and 1 B which as I + + align:start position:0% +equation 1 a and 1 B which as I + + + align:start position:0% +equation 1 a and 1 B which as I +mentioned used to not be uh something + + align:start position:0% +mentioned used to not be uh something + + + align:start position:0% +mentioned used to not be uh something +that you'd see in + + align:start position:0% +that you'd see in + + + align:start position:0% +that you'd see in +patterns and you know really detailed + + align:start position:0% +patterns and you know really detailed + + + align:start position:0% +patterns and you know really detailed +we're only up to figure two at this + + align:start position:0% +we're only up to figure two at this + + + align:start position:0% +we're only up to figure two at this +point so they're giving really uh + + align:start position:0% +point so they're giving really uh + + + align:start position:0% +point so they're giving really uh +detailed explanations and we'll talk + + align:start position:0% +detailed explanations and we'll talk + + + align:start position:0% +detailed explanations and we'll talk +about some of that more formulas these + + align:start position:0% +about some of that more formulas these + + + align:start position:0% +about some of that more formulas these +are the formulas for finding the peaks + + align:start position:0% +are the formulas for finding the peaks + + + align:start position:0% +are the formulas for finding the peaks +in the one of the parabola in the top + + align:start position:0% +in the one of the parabola in the top + + + align:start position:0% +in the one of the parabola in the top +case and of the Triangular waveform in + + align:start position:0% +case and of the Triangular waveform in + + + align:start position:0% +case and of the Triangular waveform in +the second + + align:start position:0% +the second + + + align:start position:0% +the second +case um and this is the formula for the + + align:start position:0% +case um and this is the formula for the + + + align:start position:0% +case um and this is the formula for the +bias which is probably very hard to read + + align:start position:0% +bias which is probably very hard to read + + + align:start position:0% +bias which is probably very hard to read +but it's the absolute value of 2 s + + align:start position:0% +but it's the absolute value of 2 s + + + align:start position:0% +but it's the absolute value of 2 s +raised to the B uh where B is that thing + + align:start position:0% +raised to the B uh where B is that thing + + + align:start position:0% +raised to the B uh where B is that thing +that I said could be you know near one + + align:start position:0% +that I said could be you know near one + + + align:start position:0% +that I said could be you know near one +and it explicitly says it has to be + + align:start position:0% +and it explicitly says it has to be + + + align:start position:0% +and it explicitly says it has to be +bigger than minus one but other than + + align:start position:0% +bigger than minus one but other than + + + align:start position:0% +bigger than minus one but other than +that it can be any any value + + align:start position:0% +that it can be any any value + + + align:start position:0% +that it can be any any value +um tables let's see oh okay so now we + + align:start position:0% +um tables let's see oh okay so now we + + + align:start position:0% +um tables let's see oh okay so now we +get to the part that the lawyers will + + align:start position:0% +get to the part that the lawyers will + + + align:start position:0% +get to the part that the lawyers will +find the most interesting + + align:start position:0% +find the most interesting + + + align:start position:0% +find the most interesting +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um uh where is it uh starts up there + + align:start position:0% +um uh where is it uh starts up there + + + align:start position:0% +um uh where is it uh starts up there +okay what is claimed is and for some + + align:start position:0% +okay what is claimed is and for some + + + align:start position:0% +okay what is claimed is and for some +reason it's not a separate section it's + + align:start position:0% +reason it's not a separate section it's + + + align:start position:0% +reason it's not a separate section it's +just a convention the words what is + + align:start position:0% +just a convention the words what is + + + align:start position:0% +just a convention the words what is +claimed is appear and now you list the + + align:start position:0% +claimed is appear and now you list the + + + align:start position:0% +claimed is appear and now you list the +claims so those are the particular + + align:start position:0% +claims so those are the particular + + + align:start position:0% +claims so those are the particular +things that you think that you came up + + align:start position:0% +things that you think that you came up + + + align:start position:0% +things that you think that you came up +with and you want to protect and um uh + + align:start position:0% +with and you want to protect and um uh + + + align:start position:0% +with and you want to protect and um uh +the other side is probably going to + + align:start position:0% +the other side is probably going to + + + align:start position:0% +the other side is probably going to +argue that uh well actually it's obvious + + align:start position:0% +argue that uh well actually it's obvious + + + align:start position:0% +argue that uh well actually it's obvious +it was there and prior art whatever so + + align:start position:0% +it was there and prior art whatever so + + + align:start position:0% +it was there and prior art whatever so +so it starts off uh quite a long first + + align:start position:0% +so it starts off uh quite a long first + + + align:start position:0% +so it starts off uh quite a long first +claim and I'll read it out because we'll + + align:start position:0% +claim and I'll read it out because we'll + + + align:start position:0% +claim and I'll read it out because we'll +this is what we're actually going to + + align:start position:0% +this is what we're actually going to + + + align:start position:0% +this is what we're actually going to +study uh the algorithm for that + + align:start position:0% +study uh the algorithm for that + + + align:start position:0% +study uh the algorithm for that +um + + align:start position:0% +um + + + align:start position:0% +um +okay and an apparatus for that's claim + + align:start position:0% +okay and an apparatus for that's claim + + + align:start position:0% +okay and an apparatus for that's claim +one and claim 11 is going to be the same + + align:start position:0% +one and claim 11 is going to be the same + + + align:start position:0% +one and claim 11 is going to be the same +thing um sorry claim 21 is going to be + + align:start position:0% +thing um sorry claim 21 is going to be + + + align:start position:0% +thing um sorry claim 21 is going to be +the same thing which says a method for + + align:start position:0% +the same thing which says a method for + + + align:start position:0% +the same thing which says a method for +so this is apparatus 4 detection and sub + + align:start position:0% +so this is apparatus 4 detection and sub + + + align:start position:0% +so this is apparatus 4 detection and sub +pixel location of edges in a digital + + align:start position:0% +pixel location of edges in a digital + + + align:start position:0% +pixel location of edges in a digital +image said Digital Image including a + + align:start position:0% +image said Digital Image including a + + + align:start position:0% +image said Digital Image including a +plurality of pixel values each pixel + + align:start position:0% +plurality of pixel values each pixel + + + align:start position:0% +plurality of pixel values each pixel +value having been associated with + + align:start position:0% +value having been associated with + + + align:start position:0% +value having been associated with +respective pixel point on a regularly + + align:start position:0% +respective pixel point on a regularly + + + align:start position:0% +respective pixel point on a regularly +spaced pixel grid uh said apparatus + + align:start position:0% +spaced pixel grid uh said apparatus + + + align:start position:0% +spaced pixel grid uh said apparatus +comprising and compris in remember + + align:start position:0% +comprising and compris in remember + + + align:start position:0% +comprising and compris in remember +special term here in pattern language + + align:start position:0% +special term here in pattern language + + + align:start position:0% +special term here in pattern language +and then it lists uh uh three items for + + align:start position:0% +and then it lists uh uh three items for + + + align:start position:0% +and then it lists uh uh three items for +some reason they're all labeled uh well + + align:start position:0% +some reason they're all labeled uh well + + + align:start position:0% +some reason they're all labeled uh well +they all start with a so it looks like + + align:start position:0% +they all start with a so it looks like + + + align:start position:0% +they all start with a so it looks like +they're they're all labeled a but + + align:start position:0% +they're they're all labeled a but + + + align:start position:0% +they're they're all labeled a but +they're not so the first one is a + + align:start position:0% +they're not so the first one is a + + + align:start position:0% +they're not so the first one is a +gradient estimator for estimating + + align:start position:0% +gradient estimator for estimating + + + align:start position:0% +gradient estimator for estimating +gradient magnitude and gradient + + align:start position:0% +gradient magnitude and gradient + + + align:start position:0% +gradient magnitude and gradient +Direction at a purity of regularly + + align:start position:0% +Direction at a purity of regularly + + + align:start position:0% +Direction at a purity of regularly +spaced gradient points in said Digital + + align:start position:0% +spaced gradient points in said Digital + + + align:start position:0% +spaced gradient points in said Digital +Image so as to provide a plurality of + + align:start position:0% +Image so as to provide a plurality of + + + align:start position:0% +Image so as to provide a plurality of +estimates of gradient magnitude and + + align:start position:0% +estimates of gradient magnitude and + + + align:start position:0% +estimates of gradient magnitude and +gradient Direction each set estimate of + + align:start position:0% +gradient Direction each set estimate of + + + align:start position:0% +gradient Direction each set estimate of +gradient estimate and gradient Direction + + align:start position:0% +gradient estimate and gradient Direction + + + align:start position:0% +gradient estimate and gradient Direction +being associated with the respective + + align:start position:0% +being associated with the respective + + + align:start position:0% +being associated with the respective +gradient point on a regularly space uh + + align:start position:0% +gradient point on a regularly space uh + + + align:start position:0% +gradient point on a regularly space uh +gradient grid I mean you know um you + + align:start position:0% +gradient grid I mean you know um you + + + align:start position:0% +gradient grid I mean you know um you +wouldn't think that it'd be so difficult + + align:start position:0% +wouldn't think that it'd be so difficult + + + align:start position:0% +wouldn't think that it'd be so difficult +to talk about okay we're going to + + align:start position:0% +to talk about okay we're going to + + + align:start position:0% +to talk about okay we're going to +compute the image brightness gradient + + align:start position:0% +compute the image brightness gradient + + + align:start position:0% +compute the image brightness gradient +but there it is um and I suppose the + + align:start position:0% +but there it is um and I suppose the + + + align:start position:0% +but there it is um and I suppose the +idea is that you know to us it's obvious + + align:start position:0% +idea is that you know to us it's obvious + + + align:start position:0% +idea is that you know to us it's obvious +but um this is supposed to be um + + align:start position:0% +but um this is supposed to be um + + + align:start position:0% +but um this is supposed to be um +something that anyone uh could + + align:start position:0% +something that anyone uh could + + + align:start position:0% +something that anyone uh could +understand so that's one we're going to + + align:start position:0% +understand so that's one we're going to + + + align:start position:0% +understand so that's one we're going to +get the + + align:start position:0% +get the + + + align:start position:0% +get the +gradients and the second one is and oh + + align:start position:0% +gradients and the second one is and oh + + + align:start position:0% +gradients and the second one is and oh +and we're also going to get gradient + + align:start position:0% +and we're also going to get gradient + + + align:start position:0% +and we're also going to get gradient +magnitude and Direction so that that's + + align:start position:0% +magnitude and Direction so that that's + + + align:start position:0% +magnitude and Direction so that that's +the component one then component two is + + align:start position:0% +the component one then component two is + + + align:start position:0% +the component one then component two is +a peak detector Cooperative with said + + align:start position:0% +a peak detector Cooperative with said + + + align:start position:0% +a peak detector Cooperative with said +gradient estimate operating such that + + align:start position:0% +gradient estimate operating such that + + + align:start position:0% +gradient estimate operating such that +gradient Direction associated with each + + align:start position:0% +gradient Direction associated with each + + + align:start position:0% +gradient Direction associated with each +gradient point is used to select the + + align:start position:0% +gradient point is used to select the + + + align:start position:0% +gradient point is used to select the +respective set of neighboring gradient + + align:start position:0% +respective set of neighboring gradient + + + align:start position:0% +respective set of neighboring gradient +points so that's the quantization of the + + align:start position:0% +points so that's the quantization of the + + + align:start position:0% +points so that's the quantization of the +gradient Direction so we pick a certain + + align:start position:0% +gradient Direction so we pick a certain + + + align:start position:0% +gradient Direction so we pick a certain +set of uh certain direction and + + align:start position:0% +set of uh certain direction and + + + align:start position:0% +set of uh certain direction and +operating such that gradient magnitude + + align:start position:0% +operating such that gradient magnitude + + + align:start position:0% +operating such that gradient magnitude +associated with each gradient point is + + align:start position:0% +associated with each gradient point is + + + align:start position:0% +associated with each gradient point is +compared with each gradient magnitude of + + align:start position:0% +compared with each gradient magnitude of + + + align:start position:0% +compared with each gradient magnitude of +set respective set of neighboring + + align:start position:0% +set respective set of neighboring + + + align:start position:0% +set respective set of neighboring +gradient magnitudes as to determine + + align:start position:0% +gradient magnitudes as to determine + + + align:start position:0% +gradient magnitudes as to determine +which of set gradient magnitudes is a + + align:start position:0% +which of set gradient magnitudes is a + + + align:start position:0% +which of set gradient magnitudes is a +local maximum of gradient magnitude in + + align:start position:0% +local maximum of gradient magnitude in + + + align:start position:0% +local maximum of gradient magnitude in +appr appropriate said gradient Direction + + align:start position:0% +appr appropriate said gradient Direction + + + align:start position:0% +appr appropriate said gradient Direction +so that's you know in short words it's a + + align:start position:0% +so that's you know in short words it's a + + + align:start position:0% +so that's you know in short words it's a +non- maximum suppression in the quantize + + align:start position:0% +non- maximum suppression in the quantize + + + align:start position:0% +non- maximum suppression in the quantize +gradient Direction so that's two and + + align:start position:0% +gradient Direction so that's two and + + + align:start position:0% +gradient Direction so that's two and +then the third and last part is a Sub + + align:start position:0% +then the third and last part is a Sub + + + align:start position:0% +then the third and last part is a Sub +sub pixel + + align:start position:0% +sub pixel + + + align:start position:0% +sub pixel +interpolator cooperating with said peak + + align:start position:0% +interpolator cooperating with said peak + + + align:start position:0% +interpolator cooperating with said peak +detector operating such that said local + + align:start position:0% +detector operating such that said local + + + align:start position:0% +detector operating such that said local +maximum of gradient magnitude and a set + + align:start position:0% +maximum of gradient magnitude and a set + + + align:start position:0% +maximum of gradient magnitude and a set +of neighboring gradient magnitudes are + + align:start position:0% +of neighboring gradient magnitudes are + + + align:start position:0% +of neighboring gradient magnitudes are +used to determine an interpolated Edge + + align:start position:0% +used to determine an interpolated Edge + + + align:start position:0% +used to determine an interpolated Edge +position along a one one-dimensional + + align:start position:0% +position along a one one-dimensional + + + align:start position:0% +position along a one one-dimensional +gradient magnitude profile including a + + align:start position:0% +gradient magnitude profile including a + + + align:start position:0% +gradient magnitude profile including a +gradient Point associated with said + + align:start position:0% +gradient Point associated with said + + + align:start position:0% +gradient Point associated with said +local maximum of gradient magnitude and + + align:start position:0% +local maximum of gradient magnitude and + + + align:start position:0% +local maximum of gradient magnitude and +so on so that's the interpolation step + + align:start position:0% +so on so that's the interpolation step + + + align:start position:0% +so on so that's the interpolation step +where we fit the parabola and we find + + align:start position:0% +where we fit the parabola and we find + + + align:start position:0% +where we fit the parabola and we find +the peak of the parabola and that's all + + align:start position:0% +the peak of the parabola and that's all + + + align:start position:0% +the peak of the parabola and that's all +of claim one so so why do they need to + + align:start position:0% +of claim one so so why do they need to + + + align:start position:0% +of claim one so so why do they need to +be other claims well the thing is that + + align:start position:0% +be other claims well the thing is that + + + align:start position:0% +be other claims well the thing is that +someone might come along later and say + + align:start position:0% +someone might come along later and say + + + align:start position:0% +someone might come along later and say +well wait a minute uh we already + + align:start position:0% +well wait a minute uh we already + + + align:start position:0% +well wait a minute uh we already +invented that and so um your claim one + + align:start position:0% +invented that and so um your claim one + + + align:start position:0% +invented that and so um your claim one +is blown out of the water so what you + + align:start position:0% +is blown out of the water so what you + + + align:start position:0% +is blown out of the water so what you +then do is you specialize it further you + + align:start position:0% +then do is you specialize it further you + + + align:start position:0% +then do is you specialize it further you +uh add in other things that are in your + + align:start position:0% +uh add in other things that are in your + + + align:start position:0% +uh add in other things that are in your +specification uh and refine it more and + + align:start position:0% +specification uh and refine it more and + + + align:start position:0% +specification uh and refine it more and +more and more in the hope that if in + + align:start position:0% +more and more in the hope that if in + + + align:start position:0% +more and more in the hope that if in +litigation later on uh the early claims + + align:start position:0% +litigation later on uh the early claims + + + align:start position:0% +litigation later on uh the early claims +that are very broad are thrown out then + + align:start position:0% +that are very broad are thrown out then + + + align:start position:0% +that are very broad are thrown out then +the narrow ones will still stand so if + + align:start position:0% +the narrow ones will still stand so if + + + align:start position:0% +the narrow ones will still stand so if +they also violate all the other + + align:start position:0% +they also violate all the other + + + align:start position:0% +they also violate all the other +conditions then then you're good so in + + align:start position:0% +conditions then then you're good so in + + + align:start position:0% +conditions then then you're good so in +for example claim two so we have uh + + align:start position:0% +for example claim two so we have uh + + + align:start position:0% +for example claim two so we have uh +claim one further comprising a plane + + align:start position:0% +claim one further comprising a plane + + + align:start position:0% +claim one further comprising a plane +position uh so that last step that I + + align:start position:0% +position uh so that last step that I + + + align:start position:0% +position uh so that last step that I +described that plane position step where + + align:start position:0% +described that plane position step where + + + align:start position:0% +described that plane position step where +you intersect the uh gradient and + + align:start position:0% +you intersect the uh gradient and + + + align:start position:0% +you intersect the uh gradient and +another line uh that isn't in claim one + + align:start position:0% +another line uh that isn't in claim one + + + align:start position:0% +another line uh that isn't in claim one +so supposing that claim one gets thrown + + align:start position:0% +so supposing that claim one gets thrown + + + align:start position:0% +so supposing that claim one gets thrown +out then uh if you add if you using this + + align:start position:0% +out then uh if you add if you using this + + + align:start position:0% +out then uh if you add if you using this +plane position feature then you're going + + align:start position:0% +plane position feature then you're going + + + align:start position:0% +plane position feature then you're going +to violate claim to so that's a + + align:start position:0% +to violate claim to so that's a + + + align:start position:0% +to violate claim to so that's a +conditional claim and you know it goes + + align:start position:0% +conditional claim and you know it goes + + + align:start position:0% +conditional claim and you know it goes +on like that we won't obviously read + + align:start position:0% +on like that we won't obviously read + + + align:start position:0% +on like that we won't obviously read +through all of these uh claim three is + + align:start position:0% +through all of these uh claim three is + + + align:start position:0% +through all of these uh claim three is +the apparatus of claim two so claim two + + align:start position:0% +the apparatus of claim two so claim two + + + align:start position:0% +the apparatus of claim two so claim two +depends on one claim three depends on + + align:start position:0% +depends on one claim three depends on + + + align:start position:0% +depends on one claim three depends on +two which in turn depends on one and um + + align:start position:0% +two which in turn depends on one and um + + + align:start position:0% +two which in turn depends on one and um +and claim three as a gradient + + align:start position:0% +and claim three as a gradient + + + align:start position:0% +and claim three as a gradient +directional line so it's uh + + align:start position:0% +directional line so it's uh + + + align:start position:0% +directional line so it's uh +giving particular way of computing that + + align:start position:0% +giving particular way of computing that + + + align:start position:0% +giving particular way of computing that +plane position Point uh and then you + + align:start position:0% +plane position Point uh and then you + + + align:start position:0% +plane position Point uh and then you +know there's a whole bunch more + + align:start position:0% +know there's a whole bunch more + + + align:start position:0% +know there's a whole bunch more +obviously and they get uh more and more + + align:start position:0% +obviously and they get uh more and more + + + align:start position:0% +obviously and they get uh more and more +detailed so that you're protected in + + align:start position:0% +detailed so that you're protected in + + + align:start position:0% +detailed so that you're protected in +case it turns out that well claim one + + align:start position:0% +case it turns out that well claim one + + + align:start position:0% +case it turns out that well claim one +you know if you put together the + + align:start position:0% +you know if you put together the + + + align:start position:0% +you know if you put together the +writings of Roberts and Irvin soel it's + + align:start position:0% +writings of Roberts and Irvin soel it's + + + align:start position:0% +writings of Roberts and Irvin soel it's +there and so you need something else + + align:start position:0% +there and so you need something else + + + align:start position:0% +there and so you need something else +okay then let's see where does it get + + align:start position:0% +okay then let's see where does it get + + + align:start position:0% +okay then let's see where does it get +interesting again + + align:start position:0% +interesting again + + + align:start position:0% +interesting again +claim 11 uh starts all over again uh + + align:start position:0% +claim 11 uh starts all over again uh + + + align:start position:0% +claim 11 uh starts all over again uh +where claim one did with a change that + + align:start position:0% +where claim one did with a change that + + + align:start position:0% +where claim one did with a change that +this is a uh a function plus means claim + + align:start position:0% +this is a uh a function plus means claim + + + align:start position:0% +this is a uh a function plus means claim +so here instead of saying that you have + + align:start position:0% +so here instead of saying that you have + + + align:start position:0% +so here instead of saying that you have +an apparatus for gradient estimation + + align:start position:0% +an apparatus for gradient estimation + + + align:start position:0% +an apparatus for gradient estimation +gradient estimation means for estimating + + align:start position:0% +gradient estimation means for estimating + + + align:start position:0% +gradient estimation means for estimating +gradient magn Peak detection means for + + align:start position:0% +gradient magn Peak detection means for + + + align:start position:0% +gradient magn Peak detection means for +sub pixel interpolation means so it's + + align:start position:0% +sub pixel interpolation means so it's + + + align:start position:0% +sub pixel interpolation means so it's +not specific about whether it's + + align:start position:0% +not specific about whether it's + + + align:start position:0% +not specific about whether it's +apparatus or method or whatever and + + align:start position:0% +apparatus or method or whatever and + + + align:start position:0% +apparatus or method or whatever and +again this has to do with the history of + + align:start position:0% +again this has to do with the history of + + + align:start position:0% +again this has to do with the history of +patterns that uh they needed to do that + + align:start position:0% +patterns that uh they needed to do that + + + align:start position:0% +patterns that uh they needed to do that +and so everything's repeated so so we + + align:start position:0% +and so everything's repeated so so we + + + align:start position:0% +and so everything's repeated so so we +have claims 1 through 10 and then it's + + align:start position:0% +have claims 1 through 10 and then it's + + + align:start position:0% +have claims 1 through 10 and then it's +repeated in function plus means meth up + + align:start position:0% +repeated in function plus means meth up + + + align:start position:0% +repeated in function plus means meth up +to 21 and then at 21 everything is + + align:start position:0% +to 21 and then at 21 everything is + + + align:start position:0% +to 21 and then at 21 everything is +repeated with operators replaced with + + align:start position:0% +repeated with operators replaced with + + + align:start position:0% +repeated with operators replaced with +method so uh you know so you end up with + + align:start position:0% +method so uh you know so you end up with + + + align:start position:0% +method so uh you know so you end up with +a relatively simple problem and it ends + + align:start position:0% +a relatively simple problem and it ends + + + align:start position:0% +a relatively simple problem and it ends +up with uh 34 claims + + align:start position:0% +up with uh 34 claims + + + align:start position:0% +up with uh 34 claims +CLS 34 claims now these days they + + align:start position:0% +CLS 34 claims now these days they + + + align:start position:0% +CLS 34 claims now these days they +penalized you for that uh because you + + align:start position:0% +penalized you for that uh because you + + + align:start position:0% +penalized you for that uh because you +have to pay extra if you have more than + + align:start position:0% +have to pay extra if you have more than + + + align:start position:0% +have to pay extra if you have more than +20 claims so you know things change so + + align:start position:0% +20 claims so you know things change so + + + align:start position:0% +20 claims so you know things change so +for example at this + + align:start position:0% +for example at this + + + align:start position:0% +for example at this +time um let's + + align:start position:0% +time um let's + + + align:start position:0% +time um let's +see uh okay before this before this the + + align:start position:0% +see uh okay before this before this the + + + align:start position:0% +see uh okay before this before this the +rule was that uh your patent would uh be + + align:start position:0% +rule was that uh your patent would uh be + + + align:start position:0% +rule was that uh your patent would uh be +valid for 17 and a half years after it + + align:start position:0% +valid for 17 and a half years after it + + + align:start position:0% +valid for 17 and a half years after it +issued and that was different from the + + align:start position:0% +issued and that was different from the + + + align:start position:0% +issued and that was different from the +way the rest of the world did it and + + align:start position:0% +way the rest of the world did it and + + + align:start position:0% +way the rest of the world did it and +also it was kind of unfair because + + align:start position:0% +also it was kind of unfair because + + + align:start position:0% +also it was kind of unfair because +things could be delayed in the pattern + + align:start position:0% +things could be delayed in the pattern + + + align:start position:0% +things could be delayed in the pattern +process so something could issue 10 + + align:start position:0% +process so something could issue 10 + + + align:start position:0% +process so something could issue 10 +years after you submit it and then you + + align:start position:0% +years after you submit it and then you + + + align:start position:0% +years after you submit it and then you +like you get another 10 years just + + align:start position:0% +like you get another 10 years just + + + align:start position:0% +like you get another 10 years just +because of that delay and there were + + align:start position:0% +because of that delay and there were + + + align:start position:0% +because of that delay and there were +tricks of using that for example uh + + align:start position:0% +tricks of using that for example uh + + + align:start position:0% +tricks of using that for example uh +Jerome + + align:start position:0% +Jerome + + + align:start position:0% +Jerome +lemelson um claimed that he invented + + align:start position:0% +lemelson um claimed that he invented + + + align:start position:0% +lemelson um claimed that he invented +Machine Vision in + + align:start position:0% +Machine Vision in + + + align:start position:0% +Machine Vision in +1956 and he had a string of patents + + align:start position:0% +1956 and he had a string of patents + + + align:start position:0% +1956 and he had a string of patents +that U documented that and some of them + + align:start position:0% +that U documented that and some of them + + + align:start position:0% +that U documented that and some of them +were called submarine patterns because + + align:start position:0% +were called submarine patterns because + + + align:start position:0% +were called submarine patterns because +you didn't know they were in the + + align:start position:0% +you didn't know they were in the + + + align:start position:0% +you didn't know they were in the +pipeline uh but they depended on earlier + + align:start position:0% +pipeline uh but they depended on earlier + + + align:start position:0% +pipeline uh but they depended on earlier +patterns and so anyway so uh Congress + + align:start position:0% +patterns and so anyway so uh Congress + + + align:start position:0% +patterns and so anyway so uh Congress +decided to X that idea and so things + + align:start position:0% +decided to X that idea and so things + + + align:start position:0% +decided to X that idea and so things +changed and um I guess already at this + + align:start position:0% +changed and um I guess already at this + + + align:start position:0% +changed and um I guess already at this +point the U rule was 20 years after + + align:start position:0% +point the U rule was 20 years after + + + align:start position:0% +point the U rule was 20 years after +filing instead of 17 and a half after + + align:start position:0% +filing instead of 17 and a half after + + + align:start position:0% +filing instead of 17 and a half after +issue also they removed the + + align:start position:0% +issue also they removed the + + + align:start position:0% +issue also they removed the +rule uh that + + align:start position:0% +rule uh that + + + align:start position:0% +rule uh that +um you know who gets priority so suppose + + align:start position:0% +um you know who gets priority so suppose + + + align:start position:0% +um you know who gets priority so suppose +you think of some idea and someone else + + align:start position:0% +you think of some idea and someone else + + + align:start position:0% +you think of some idea and someone else +thinks of an idea and you submit uh + + align:start position:0% +thinks of an idea and you submit uh + + + align:start position:0% +thinks of an idea and you submit uh +patents and then you have these two + + align:start position:0% +patents and then you have these two + + + align:start position:0% +patents and then you have these two +conflicting patents who who gets the + + align:start position:0% +conflicting patents who who gets the + + + align:start position:0% +conflicting patents who who gets the +patent well it used to be that um + + align:start position:0% +patent well it used to be that um + + + align:start position:0% +patent well it used to be that um +whoever invented first and so in the old + + align:start position:0% +whoever invented first and so in the old + + + align:start position:0% +whoever invented first and so in the old +days all Engineers carried around books + + align:start position:0% +days all Engineers carried around books + + + align:start position:0% +days all Engineers carried around books +with squares in them and every page uh + + align:start position:0% +with squares in them and every page uh + + + align:start position:0% +with squares in them and every page uh +numbered and uh every day they would ask + + align:start position:0% +numbered and uh every day they would ask + + + align:start position:0% +numbered and uh every day they would ask +their buddies to sign page why well + + align:start position:0% +their buddies to sign page why well + + + align:start position:0% +their buddies to sign page why well +because that way you could document that + + align:start position:0% +because that way you could document that + + + align:start position:0% +because that way you could document that +you thought of this idea on April the 3 + + align:start position:0% +you thought of this idea on April the 3 + + + align:start position:0% +you thought of this idea on April the 3 +you know you didn't have it fully + + align:start position:0% +you know you didn't have it fully + + + align:start position:0% +you know you didn't have it fully +fleshed out but uh the pages were + + align:start position:0% +fleshed out but uh the pages were + + + align:start position:0% +fleshed out but uh the pages were +numbered so you couldn't cheat and tear + + align:start position:0% +numbered so you couldn't cheat and tear + + + align:start position:0% +numbered so you couldn't cheat and tear +out Pages or add pages and uh people's + + align:start position:0% +out Pages or add pages and uh people's + + + align:start position:0% +out Pages or add pages and uh people's +signature was on there saying that oh + + align:start position:0% +signature was on there saying that oh + + + align:start position:0% +signature was on there saying that oh +yeah I saw this he actually wrote this + + align:start position:0% +yeah I saw this he actually wrote this + + + align:start position:0% +yeah I saw this he actually wrote this +at that time and that was a giant pain + + align:start position:0% +at that time and that was a giant pain + + + align:start position:0% +at that time and that was a giant pain +because you know everything you did + + align:start position:0% +because you know everything you did + + + align:start position:0% +because you know everything you did +every time you thought of something you + + align:start position:0% +every time you thought of something you + + + align:start position:0% +every time you thought of something you +immediately had to write it down and so + + align:start position:0% +immediately had to write it down and so + + + align:start position:0% +immediately had to write it down and so +they decided no forget that that plus it + + align:start position:0% +they decided no forget that that plus it + + + align:start position:0% +they decided no forget that that plus it +was very hard to prove sometimes and so + + align:start position:0% +was very hard to prove sometimes and so + + + align:start position:0% +was very hard to prove sometimes and so +they the new rule is you know submission + + align:start position:0% +they the new rule is you know submission + + + align:start position:0% +they the new rule is you know submission +when you send it in that that's the date + + align:start position:0% +when you send it in that that's the date + + + align:start position:0% +when you send it in that that's the date +and if you if you take your time sending + + align:start position:0% +and if you if you take your time sending + + + align:start position:0% +and if you if you take your time sending +it in uh you know too too bad you lose + + align:start position:0% +it in uh you know too too bad you lose + + + align:start position:0% +it in uh you know too too bad you lose +so anyway okay so uh that's a typical + + align:start position:0% +so anyway okay so uh that's a typical + + + align:start position:0% +so anyway okay so uh that's a typical +pattern it's a relatively simple one uh + + align:start position:0% +pattern it's a relatively simple one uh + + + align:start position:0% +pattern it's a relatively simple one uh +but it has some interesting Machine + + align:start position:0% +but it has some interesting Machine + + + align:start position:0% +but it has some interesting Machine +Vision aspects which uh we'll talk about + + align:start position:0% +Vision aspects which uh we'll talk about + + + align:start position:0% +Vision aspects which uh we'll talk about +uh now + + align:start position:0% + + + + align:start position:0% + +okay so um we mentioned that in many + + align:start position:0% +okay so um we mentioned that in many + + + align:start position:0% +okay so um we mentioned that in many +cases images are um composed of patches + + align:start position:0% +cases images are um composed of patches + + + align:start position:0% +cases images are um composed of patches +that are pretty much uniform in + + align:start position:0% +that are pretty much uniform in + + + align:start position:0% +that are pretty much uniform in +brightness and uh the interesting stuff + + align:start position:0% +brightness and uh the interesting stuff + + + align:start position:0% +brightness and uh the interesting stuff +is at the Transitions and I mentioned + + align:start position:0% +is at the Transitions and I mentioned + + + align:start position:0% +is at the Transitions and I mentioned +that this uh Dutch artist uh Pete + + align:start position:0% +that this uh Dutch artist uh Pete + + + align:start position:0% +that this uh Dutch artist uh Pete +cornelus mandrian uh got rich by drawing + + align:start position:0% +cornelus mandrian uh got rich by drawing + + + align:start position:0% +cornelus mandrian uh got rich by drawing +you know things that just had + + align:start position:0% +you know things that just had + + + align:start position:0% +you know things that just had +rectangular patches of color and okay is + + align:start position:0% +rectangular patches of color and okay is + + + align:start position:0% +rectangular patches of color and okay is +it art I I don't know I I'm not in that + + align:start position:0% +it art I I don't know I I'm not in that + + + align:start position:0% +it art I I don't know I I'm not in that +field but anyway so I called is the + + align:start position:0% +field but anyway so I called is the + + + align:start position:0% +field but anyway so I called is the +mandrian model of the world and so in + + align:start position:0% +mandrian model of the world and so in + + + align:start position:0% +mandrian model of the world and so in +that model of the world um rather than + + align:start position:0% +that model of the world um rather than + + + align:start position:0% +that model of the world um rather than +have millions of pixels you can condense + + align:start position:0% +have millions of pixels you can condense + + + align:start position:0% +have millions of pixels you can condense +things down into just talking about the + + align:start position:0% +things down into just talking about the + + + align:start position:0% +things down into just talking about the +edges or if you want to find where + + align:start position:0% +edges or if you want to find where + + + align:start position:0% +edges or if you want to find where +something is on a conveyor belt uh you + + align:start position:0% +something is on a conveyor belt uh you + + + align:start position:0% +something is on a conveyor belt uh you +just need the edges if you're trying to + + align:start position:0% +just need the edges if you're trying to + + + align:start position:0% +just need the edges if you're trying to +line up different layers of an + + align:start position:0% +line up different layers of an + + + align:start position:0% +line up different layers of an +integrated circuit mask uh then you just + + align:start position:0% +integrated circuit mask uh then you just + + + align:start position:0% +integrated circuit mask uh then you just +need uh edges so um what what's an edge + + align:start position:0% +need uh edges so um what what's an edge + + + align:start position:0% +need uh edges so um what what's an edge +well uh and what what is an edge + + align:start position:0% +well uh and what what is an edge + + + align:start position:0% +well uh and what what is an edge +detector so again uh on use remarkably + + align:start position:0% +detector so again uh on use remarkably + + + align:start position:0% +detector so again uh on use remarkably +this is + + align:start position:0% + + + + align:start position:0% + +actually uh well pointed out here so + + align:start position:0% +actually uh well pointed out here so + + + align:start position:0% +actually uh well pointed out here so +Edge detection can be defined informally + + align:start position:0% +Edge detection can be defined informally + + + align:start position:0% +Edge detection can be defined informally +as a process for determining the + + align:start position:0% +as a process for determining the + + + align:start position:0% +as a process for determining the +location of boundaries between image + + align:start position:0% +location of boundaries between image + + + align:start position:0% +location of boundaries between image +regions that are different and roughly + + align:start position:0% +regions that are different and roughly + + + align:start position:0% +regions that are different and roughly +uniform in brightness so you know great + + align:start position:0% +uniform in brightness so you know great + + + align:start position:0% +uniform in brightness so you know great +and then uh in more detail uh an edge + + align:start position:0% +and then uh in more detail uh an edge + + + align:start position:0% +and then uh in more detail uh an edge +can be usefully defined as a point in an + + align:start position:0% +can be usefully defined as a point in an + + + align:start position:0% +can be usefully defined as a point in an +image where the image gradient magnitude + + align:start position:0% +image where the image gradient magnitude + + + align:start position:0% +image where the image gradient magnitude +reaches a local maximum in the image + + align:start position:0% +reaches a local maximum in the image + + + align:start position:0% +reaches a local maximum in the image +gradient dire Direction so that's that's + + align:start position:0% +gradient dire Direction so that's that's + + + align:start position:0% +gradient dire Direction so that's that's +our that's important it's not just the + + align:start position:0% +our that's important it's not just the + + + align:start position:0% +our that's important it's not just the +local maximum it's in that direction and + + align:start position:0% +local maximum it's in that direction and + + + align:start position:0% +local maximum it's in that direction and +by the way they mention another one + + align:start position:0% +by the way they mention another one + + + align:start position:0% +by the way they mention another one +which is where the second derivative of + + align:start position:0% +which is where the second derivative of + + + align:start position:0% +which is where the second derivative of +brightness crosses zero in the image + + align:start position:0% +brightness crosses zero in the image + + + align:start position:0% +brightness crosses zero in the image +gradient Direction so think about that + + align:start position:0% +gradient Direction so think about that + + + align:start position:0% +gradient Direction so think about that +and that makes sense so if the first + + align:start position:0% +and that makes sense so if the first + + + align:start position:0% +and that makes sense so if the first +derivative reaches a p a maximum how do + + align:start position:0% +derivative reaches a p a maximum how do + + + align:start position:0% +derivative reaches a p a maximum how do +you find the maximum well you + + align:start position:0% +you find the maximum well you + + + align:start position:0% +you find the maximum well you +differentiate one more time and set the + + align:start position:0% +differentiate one more time and set the + + + align:start position:0% +differentiate one more time and set the +result equal to zero so an alternate way + + align:start position:0% +result equal to zero so an alternate way + + + align:start position:0% +result equal to zero so an alternate way +of determining it where an edge is is to + + align:start position:0% +of determining it where an edge is is to + + + align:start position:0% +of determining it where an edge is is to +look at second derivatives and look at + + align:start position:0% +look at second derivatives and look at + + + align:start position:0% +look at second derivatives and look at +zero Crossings and and that's was used + + align:start position:0% +zero Crossings and and that's was used + + + align:start position:0% +zero Crossings and and that's was used +as well + + align:start position:0% +as well + + + align:start position:0% +as well +um and by the way then they mention + + align:start position:0% +um and by the way then they mention + + + align:start position:0% +um and by the way then they mention +multiscale now remember this is a while + + align:start position:0% +multiscale now remember this is a while + + + align:start position:0% +multiscale now remember this is a while +back but uh even then does it thus it is + + align:start position:0% +back but uh even then does it thus it is + + + align:start position:0% +back but uh even then does it thus it is +known in the art to perform Edge + + align:start position:0% +known in the art to perform Edge + + + align:start position:0% +known in the art to perform Edge +detection at a plurality of spatial + + align:start position:0% +detection at a plurality of spatial + + + align:start position:0% +detection at a plurality of spatial +frequencies or length scales as + + align:start position:0% +frequencies or length scales as + + + align:start position:0% +frequencies or length scales as +appropriate to the application so we're + + align:start position:0% +appropriate to the application so we're + + + align:start position:0% +appropriate to the application so we're +just going to pretend that we're working + + align:start position:0% +just going to pretend that we're working + + + align:start position:0% +just going to pretend that we're working +directly at the full resolution but + + align:start position:0% +directly at the full resolution but + + + align:start position:0% +directly at the full resolution but +imagine that for many applications + + align:start position:0% +imagine that for many applications + + + align:start position:0% +imagine that for many applications +uh you would not want to do that or you + + align:start position:0% +uh you would not want to do that or you + + + align:start position:0% +uh you would not want to do that or you +would want to work at multiple + + align:start position:0% +would want to work at multiple + + + align:start position:0% +would want to work at multiple +resolutions and so we're not going to + + align:start position:0% +resolutions and so we're not going to + + + align:start position:0% +resolutions and so we're not going to +for this pattern we're not going to get + + align:start position:0% +for this pattern we're not going to get + + + align:start position:0% +for this pattern we're not going to get +into that um and as they don't get into + + align:start position:0% +into that um and as they don't get into + + + align:start position:0% +into that um and as they don't get into +it so okay um + + align:start position:0% + + + + align:start position:0% + +so we have um an image transition so + + align:start position:0% +so we have um an image transition so + + + align:start position:0% +so we have um an image transition so +first of all you know here's an ideal + + align:start position:0% +first of all you know here's an ideal + + + align:start position:0% +first of all you know here's an ideal +Edge uh so this is a cross-section in + + align:start position:0% +Edge uh so this is a cross-section in + + + align:start position:0% +Edge uh so this is a cross-section in +the a cross The Edge uh it's a step + + align:start position:0% +the a cross The Edge uh it's a step + + + align:start position:0% +the a cross The Edge uh it's a step +function well it turns out actually + + align:start position:0% +function well it turns out actually + + + align:start position:0% +function well it turns out actually +that's not good uh that we don't want + + align:start position:0% +that's not good uh that we don't want + + + align:start position:0% +that's not good uh that we don't want +that we don't want infinite resolution + + align:start position:0% +that we don't want infinite resolution + + + align:start position:0% +that we don't want infinite resolution +that that seems kind of crazy because + + align:start position:0% +that that seems kind of crazy because + + + align:start position:0% +that that seems kind of crazy because +you think that the better the resolution + + align:start position:0% +you think that the better the resolution + + + align:start position:0% +you think that the better the resolution +you know the happier we should be well + + align:start position:0% +you know the happier we should be well + + + align:start position:0% +you know the happier we should be well +uh the problem is suppose we now image + + align:start position:0% +uh the problem is suppose we now image + + + align:start position:0% +uh the problem is suppose we now image +this onto a device that has discrete + + align:start position:0% + + + + align:start position:0% + +pixels so we're measuring uh the + + align:start position:0% +pixels so we're measuring uh the + + + align:start position:0% +pixels so we're measuring uh the +brightness at those + + align:start position:0% +brightness at those + + + align:start position:0% +brightness at those +points now can we tell where the edge is + + align:start position:0% +points now can we tell where the edge is + + + align:start position:0% +points now can we tell where the edge is +well suppose I move the edge a little + + align:start position:0% +well suppose I move the edge a little + + + align:start position:0% +well suppose I move the edge a little +bit uh nothing changes in terms of the + + align:start position:0% +bit uh nothing changes in terms of the + + + align:start position:0% +bit uh nothing changes in terms of the +brightness measurements of those points + + align:start position:0% +brightness measurements of those points + + + align:start position:0% +brightness measurements of those points +so actually I can In This Very idealized + + align:start position:0% +so actually I can In This Very idealized + + + align:start position:0% +so actually I can In This Very idealized +case I can move it a whole pixel width + + align:start position:0% +case I can move it a whole pixel width + + + align:start position:0% +case I can move it a whole pixel width +back and forth nothing changes so + + align:start position:0% +back and forth nothing changes so + + + align:start position:0% +back and forth nothing changes so +conversely that means I can't measure it + + align:start position:0% +conversely that means I can't measure it + + + align:start position:0% +conversely that means I can't measure it +where it is within the full pixel + + align:start position:0% +where it is within the full pixel + + + align:start position:0% +where it is within the full pixel +position so this is actually undesirable + + align:start position:0% +position so this is actually undesirable + + + align:start position:0% +position so this is actually undesirable +and basically uh this is a form of a + + align:start position:0% +and basically uh this is a form of a + + + align:start position:0% +and basically uh this is a form of a +iing so so we don't want a perfect step + + align:start position:0% +iing so so we don't want a perfect step + + + align:start position:0% +iing so so we don't want a perfect step +Edge we want something that's band + + align:start position:0% +Edge we want something that's band + + + align:start position:0% +Edge we want something that's band +limited so that when we sample it we're + + align:start position:0% +limited so that when we sample it we're + + + align:start position:0% +limited so that when we sample it we're +not introducing uh artificial frequency + + align:start position:0% +not introducing uh artificial frequency + + + align:start position:0% +not introducing uh artificial frequency +components which is you know one way of + + align:start position:0% +components which is you know one way of + + + align:start position:0% +components which is you know one way of +thinking about what what's going wrong + + align:start position:0% +thinking about what what's going wrong + + + align:start position:0% +thinking about what what's going wrong +here okay so we're looking for the for + + align:start position:0% +here okay so we're looking for the for + + + align:start position:0% +here okay so we're looking for the for +the edge and we've said that one method + + align:start position:0% +the edge and we've said that one method + + + align:start position:0% +the edge and we've said that one method +is to take the derivative and find the + + align:start position:0% +is to take the derivative and find the + + + align:start position:0% +is to take the derivative and find the +uh peak of the derivative + + align:start position:0% + + + + align:start position:0% + +and then we mentioned also that possibly + + align:start position:0% +and then we mentioned also that possibly + + + align:start position:0% +and then we mentioned also that possibly +you might want to take the second + + align:start position:0% + + + + align:start position:0% + +derivative and look for zero + + align:start position:0% + + + + align:start position:0% + +Crossing so this was actually a popular + + align:start position:0% +Crossing so this was actually a popular + + + align:start position:0% +Crossing so this was actually a popular +game for a while that we would be + + align:start position:0% +game for a while that we would be + + + align:start position:0% +game for a while that we would be +looking at second derivatives and in the + + align:start position:0% +looking at second derivatives and in the + + + align:start position:0% +looking at second derivatives and in the +case of images which are two-dimensional + + align:start position:0% +case of images which are two-dimensional + + + align:start position:0% +case of images which are two-dimensional +what's the generalization second + + align:start position:0% +what's the generalization second + + + align:start position:0% +what's the generalization second +derivative it's um + + align:start position:0% +derivative it's um + + + align:start position:0% +derivative it's um +lapasan so we instead of these Edge + + align:start position:0% +lapasan so we instead of these Edge + + + align:start position:0% +lapasan so we instead of these Edge +operators which give us an estimate of + + align:start position:0% +operators which give us an estimate of + + + align:start position:0% +operators which give us an estimate of +the brightness gradient we'll find um + + align:start position:0% +the brightness gradient we'll find um + + + align:start position:0% +the brightness gradient we'll find um +we'll take the lapasan and we find the + + align:start position:0% +we'll take the lapasan and we find the + + + align:start position:0% +we'll take the lapasan and we find the +zero Crossings and one of the appealing + + align:start position:0% +zero Crossings and one of the appealing + + + align:start position:0% +zero Crossings and one of the appealing +ideas about that was that um well zero + + align:start position:0% +ideas about that was that um well zero + + + align:start position:0% +ideas about that was that um well zero +Crossings are closed curves I mean it's + + align:start position:0% +Crossings are closed curves I mean it's + + + align:start position:0% +Crossings are closed curves I mean it's +like a contour map right so you have + + align:start position:0% +like a contour map right so you have + + + align:start position:0% +like a contour map right so you have +this we've talked about thinking of the + + align:start position:0% +this we've talked about thinking of the + + + align:start position:0% +this we've talked about thinking of the +image as a surface in 3D where height is + + align:start position:0% +image as a surface in 3D where height is + + + align:start position:0% +image as a surface in 3D where height is +brightness well then we can draw + + align:start position:0% +brightness well then we can draw + + + align:start position:0% +brightness well then we can draw +Contours isophotes certain level and uh + + align:start position:0% +Contours isophotes certain level and uh + + + align:start position:0% +Contours isophotes certain level and uh +we can draw the zero well not with + + align:start position:0% +we can draw the zero well not with + + + align:start position:0% +we can draw the zero well not with +images themselves but once we take the + + align:start position:0% +images themselves but once we take the + + + align:start position:0% +images themselves but once we take the +laian we'll have both positive and + + align:start position:0% +laian we'll have both positive and + + + align:start position:0% +laian we'll have both positive and +negative values and we can draw the + + align:start position:0% +negative values and we can draw the + + + align:start position:0% +negative values and we can draw the +Contour at zero while Contours are + + align:start position:0% +Contour at zero while Contours are + + + align:start position:0% +Contour at zero while Contours are +closed other than you know where they + + align:start position:0% +closed other than you know where they + + + align:start position:0% +closed other than you know where they +disappear off the edge of the image so + + align:start position:0% +disappear off the edge of the image so + + + align:start position:0% +disappear off the edge of the image so +that was very appealing because a lot of + + align:start position:0% +that was very appealing because a lot of + + + align:start position:0% +that was very appealing because a lot of +times other Edge detectors would sort of + + align:start position:0% +times other Edge detectors would sort of + + + align:start position:0% +times other Edge detectors would sort of +Peter out and then you wouldn't you know + + align:start position:0% +Peter out and then you wouldn't you know + + + align:start position:0% +Peter out and then you wouldn't you know +quite know where the edge was and so on + + align:start position:0% +quite know where the edge was and so on + + + align:start position:0% +quite know where the edge was and so on +so that was a interesting game for a + + align:start position:0% +so that was a interesting game for a + + + align:start position:0% +so that was a interesting game for a +while uh but it turns out that um you + + align:start position:0% +while uh but it turns out that um you + + + align:start position:0% +while uh but it turns out that um you +get worse uh performance in the presence + + align:start position:0% +get worse uh performance in the presence + + + align:start position:0% +get worse uh performance in the presence +of noise uh and we can discuss that in + + align:start position:0% +of noise uh and we can discuss that in + + + align:start position:0% +of noise uh and we can discuss that in +terms of convolution and so on but won't + + align:start position:0% +terms of convolution and so on but won't + + + align:start position:0% +terms of convolution and so on but won't +do that for the moment so second + + align:start position:0% +do that for the moment so second + + + align:start position:0% +do that for the moment so second +derivative and it's briefly mentioned in + + align:start position:0% +derivative and it's briefly mentioned in + + + align:start position:0% +derivative and it's briefly mentioned in +the pattern but it's not pursued uh and + + align:start position:0% +the pattern but it's not pursued uh and + + + align:start position:0% +the pattern but it's not pursued uh and +then what does that correspond to in the + + align:start position:0% + + + + align:start position:0% + +original um + + align:start position:0% +original um + + + align:start position:0% +original um +e so what we're really doing is looking + + align:start position:0% +e so what we're really doing is looking + + + align:start position:0% +e so what we're really doing is looking +for an inflection point what's an + + align:start position:0% +for an inflection point what's an + + + align:start position:0% +for an inflection point what's an +inflection point well imagine that + + align:start position:0% +inflection point well imagine that + + + align:start position:0% +inflection point well imagine that +you're driving along this curve uh + + align:start position:0% +you're driving along this curve uh + + + align:start position:0% +you're driving along this curve uh +you're turning left you're turning left + + align:start position:0% +you're turning left you're turning left + + + align:start position:0% +you're turning left you're turning left +you're turning left you're turning left + + align:start position:0% +you're turning left you're turning left + + + align:start position:0% +you're turning left you're turning left +oh now I'm turning right now I'm turning + + align:start position:0% +oh now I'm turning right now I'm turning + + + align:start position:0% +oh now I'm turning right now I'm turning +right so the inflection point is where + + align:start position:0% +right so the inflection point is where + + + align:start position:0% +right so the inflection point is where +you changing directions and in terms of + + align:start position:0% +you changing directions and in terms of + + + align:start position:0% +you changing directions and in terms of +derivatives it's the maximum of the + + align:start position:0% +derivatives it's the maximum of the + + + align:start position:0% +derivatives it's the maximum of the +derivative + + align:start position:0% +derivative + + + align:start position:0% +derivative +so those are uh different ways that we + + align:start position:0% +so those are uh different ways that we + + + align:start position:0% +so those are uh different ways that we +could Define + + align:start position:0% +could Define + + + align:start position:0% +could Define +um that we could Define uh where the + + align:start position:0% +um that we could Define uh where the + + + align:start position:0% +um that we could Define uh where the +edges okay so uh let's talk a little bit + + align:start position:0% +edges okay so uh let's talk a little bit + + + align:start position:0% +edges okay so uh let's talk a little bit +about the brightness gradient + + align:start position:0% +about the brightness gradient + + + align:start position:0% +about the brightness gradient +estimation so uh you saw in the figures + + align:start position:0% +estimation so uh you saw in the figures + + + align:start position:0% +estimation so uh you saw in the figures +there uh a number of operators + + align:start position:0% + + + + align:start position:0% + +so this was uh Larry Robert's idea and + + align:start position:0% +so this was uh Larry Robert's idea and + + + align:start position:0% +so this was uh Larry Robert's idea and +it's U very easy to compute very cheap + + align:start position:0% +it's U very easy to compute very cheap + + + align:start position:0% +it's U very easy to compute very cheap +to compute uh and uh but it's at 45 Dee + + align:start position:0% +to compute uh and uh but it's at 45 Dee + + + align:start position:0% +to compute uh and uh but it's at 45 Dee +angle so what what was the idea here + + align:start position:0% + + + + align:start position:0% + +so you know why not um operate in uh X + + align:start position:0% +so you know why not um operate in uh X + + + align:start position:0% +so you know why not um operate in uh X +and Y well uh it turns out that um this + + align:start position:0% +and Y well uh it turns out that um this + + + align:start position:0% +and Y well uh it turns out that um this +makes it possible to have the two + + align:start position:0% +makes it possible to have the two + + + align:start position:0% +makes it possible to have the two +operators referred to the same reference + + align:start position:0% +operators referred to the same reference + + + align:start position:0% +operators referred to the same reference +point so where where are we estimating + + align:start position:0% +point so where where are we estimating + + + align:start position:0% +point so where where are we estimating +the derivative well we might say okay uh + + align:start position:0% +the derivative well we might say okay uh + + + align:start position:0% +the derivative well we might say okay uh +I'm estimating the derivative here by + + align:start position:0% +I'm estimating the derivative here by + + + align:start position:0% +I'm estimating the derivative here by +taking the difference between this value + + align:start position:0% +taking the difference between this value + + + align:start position:0% +taking the difference between this value +and that and you know someone else might + + align:start position:0% +and that and you know someone else might + + + align:start position:0% +and that and you know someone else might +say well we estimating the derivative + + align:start position:0% +say well we estimating the derivative + + + align:start position:0% +say well we estimating the derivative +here because I'm taking the difference + + align:start position:0% +here because I'm taking the difference + + + align:start position:0% +here because I'm taking the difference +of the value here and the value there um + + align:start position:0% +of the value here and the value there um + + + align:start position:0% +of the value here and the value there um +and with see in a second that neither of + + align:start position:0% +and with see in a second that neither of + + + align:start position:0% +and with see in a second that neither of +those is well founded it's more uh + + align:start position:0% +those is well founded it's more uh + + + align:start position:0% +those is well founded it's more uh +reasonable to say I'm estimating the + + align:start position:0% +reasonable to say I'm estimating the + + + align:start position:0% +reasonable to say I'm estimating the +derivative there and the resistance to + + align:start position:0% +derivative there and the resistance to + + + align:start position:0% +derivative there and the resistance to +that of course is that's not a grid + + align:start position:0% +that of course is that's not a grid + + + align:start position:0% +that of course is that's not a grid +point so it's not a pixel it's halfway + + align:start position:0% +point so it's not a pixel it's halfway + + + align:start position:0% +point so it's not a pixel it's halfway +offset in pixels but but who cares maybe + + align:start position:0% +offset in pixels but but who cares maybe + + + align:start position:0% +offset in pixels but but who cares maybe +that's a good place to estimate the + + align:start position:0% +that's a good place to estimate the + + + align:start position:0% +that's a good place to estimate the +derivative then and so uh Robert used + + align:start position:0% +derivative then and so uh Robert used + + + align:start position:0% +derivative then and so uh Robert used +these two operators and then he he + + align:start position:0% + + + + align:start position:0% + +uh used the uh sum of squares and noted + + align:start position:0% +uh used the uh sum of squares and noted + + + align:start position:0% +uh used the uh sum of squares and noted +that conveniently um that's actually the + + align:start position:0% +that conveniently um that's actually the + + + align:start position:0% +that conveniently um that's actually the +same as if + + align:start position:0% + + + + align:start position:0% + +you'd computed the sum of squares of + + align:start position:0% +you'd computed the sum of squares of + + + align:start position:0% +you'd computed the sum of squares of +gradients in the original coordinate + + align:start position:0% +gradients in the original coordinate + + + align:start position:0% +gradients in the original coordinate +system right because if you do the 45° + + align:start position:0% +system right because if you do the 45° + + + align:start position:0% +system right because if you do the 45° +rotation cosine 45° sin 45° it's 1 / < + + align:start position:0% +rotation cosine 45° sin 45° it's 1 / < + + + align:start position:0% +rotation cosine 45° sin 45° it's 1 / < +TK of two um you get the same thing + + align:start position:0% +TK of two um you get the same thing + + + align:start position:0% +TK of two um you get the same thing +except for uh proportional it Factor + + align:start position:0% +except for uh proportional it Factor + + + align:start position:0% +except for uh proportional it Factor +right because these are further + + align:start position:0% +right because these are further + + + align:start position:0% +right because these are further +apart than the pixel spacing by squ otk + + align:start position:0% +apart than the pixel spacing by squ otk + + + align:start position:0% +apart than the pixel spacing by squ otk +of two so so these aren't the same but + + align:start position:0% +of two so so these aren't the same but + + + align:start position:0% +of two so so these aren't the same but +they're um related by some number uh + + align:start position:0% +they're um related by some number uh + + + align:start position:0% +they're um related by some number uh +they're proportional to one another okay + + align:start position:0% +they're proportional to one another okay + + + align:start position:0% +they're proportional to one another okay +so that uh so that uh is Robert's + + align:start position:0% +so that uh so that uh is Robert's + + + align:start position:0% +so that uh so that uh is Robert's +gradient and then we had Irving + + align:start position:0% +gradient and then we had Irving + + + align:start position:0% +gradient and then we had Irving +soell well let's + + align:start position:0% +soell well let's + + + align:start position:0% +soell well let's +uh let's first address this + + align:start position:0% +uh let's first address this + + + align:start position:0% +uh let's first address this +question about estimating the derivative + + align:start position:0% +question about estimating the derivative + + + align:start position:0% +question about estimating the derivative +and we may have done a little bit of + + align:start position:0% +and we may have done a little bit of + + + align:start position:0% +and we may have done a little bit of +this already but let's uh do it more + + align:start position:0% +this already but let's uh do it more + + + align:start position:0% +this already but let's uh do it more +carefully + + align:start position:0% +carefully + + + align:start position:0% +carefully +so we have this computational + + align:start position:0% +so we have this computational + + + align:start position:0% +so we have this computational +molecule for uh e of + + align:start position:0% +molecule for uh e of + + + align:start position:0% +molecule for uh e of +X and we know from Taylor series + + align:start position:0% + + + + align:start position:0% + +um and so now uh we can use that to + + align:start position:0% + + + + align:start position:0% + +um right so when we do that the F ofx + + align:start position:0% +um right so when we do that the F ofx + + + align:start position:0% +um right so when we do that the F ofx +cancels out and then we divide by Delta + + align:start position:0% +cancels out and then we divide by Delta + + + align:start position:0% +cancels out and then we divide by Delta +X so we get that's the part we want + + align:start position:0% +X so we get that's the part we want + + + align:start position:0% +X so we get that's the part we want +we're trying to estimate the derivative + + align:start position:0% +we're trying to estimate the derivative + + + align:start position:0% +we're trying to estimate the derivative +so that's perfect and then we divide by + + align:start position:0% +so that's perfect and then we divide by + + + align:start position:0% +so that's perfect and then we divide by +Delta X so we get Delta x + + align:start position:0% +Delta X so we get Delta x + + + align:start position:0% +Delta X so we get Delta x +[Music] + + align:start position:0% + + + + align:start position:0% + +or2 uh so this is the lowest order error + + align:start position:0% +or2 uh so this is the lowest order error + + + align:start position:0% +or2 uh so this is the lowest order error +terms so that's what we want and and + + align:start position:0% +terms so that's what we want and and + + + align:start position:0% +terms so that's what we want and and +that's the part we don't want and when + + align:start position:0% +that's the part we don't want and when + + + align:start position:0% +that's the part we don't want and when +we talk about how good a formula it is + + align:start position:0% +we talk about how good a formula it is + + + align:start position:0% +we talk about how good a formula it is +we'll be looking at two things one is + + align:start position:0% +we'll be looking at two things one is + + + align:start position:0% +we'll be looking at two things one is +the order of the lowest order error term + + align:start position:0% +the order of the lowest order error term + + + align:start position:0% +the order of the lowest order error term +which is here is second order and then + + align:start position:0% +which is here is second order and then + + + align:start position:0% +which is here is second order and then +the other one is the multiplier you know + + align:start position:0% +the other one is the multiplier you know + + + align:start position:0% +the other one is the multiplier you know +suppose we have two methods that have + + align:start position:0% +suppose we have two methods that have + + + align:start position:0% +suppose we have two methods that have +the same order of the lowest + + align:start position:0% +the same order of the lowest + + + align:start position:0% +the same order of the lowest +error term then we can compare them + + align:start position:0% +error term then we can compare them + + + align:start position:0% +error term then we can compare them +based on the size of this multiplier but + + align:start position:0% +based on the size of this multiplier but + + + align:start position:0% +based on the size of this multiplier but +the more important one first is the the + + align:start position:0% +the more important one first is the the + + + align:start position:0% +the more important one first is the the +order so this one's not very good + + align:start position:0% +order so this one's not very good + + + align:start position:0% +order so this one's not very good +because even uh it works perfectly on a + + align:start position:0% +because even uh it works perfectly on a + + + align:start position:0% +because even uh it works perfectly on a +straight line but even if there's a + + align:start position:0% +straight line but even if there's a + + + align:start position:0% +straight line but even if there's a +little bit of curvature to it it's going + + align:start position:0% +little bit of curvature to it it's going + + + align:start position:0% +little bit of curvature to it it's going +to get the wrong answer uh because of + + align:start position:0% +to get the wrong answer uh because of + + + align:start position:0% +to get the wrong answer uh because of +that so let's instead look at f ofx plus + + align:start position:0% +that so let's instead look at f ofx plus + + + align:start position:0% +that so let's instead look at f ofx plus +F ofx minus Delta + + align:start position:0% + + + + align:start position:0% + +X right so so here we said okay this + + align:start position:0% +X right so so here we said okay this + + + align:start position:0% +X right so so here we said okay this +this is our + + align:start position:0% +this is our + + + align:start position:0% +this is our +X and this is our X Plus Delta X and we + + align:start position:0% +X and this is our X Plus Delta X and we + + + align:start position:0% +X and this is our X Plus Delta X and we +obviously trying to get the derivative + + align:start position:0% +obviously trying to get the derivative + + + align:start position:0% +obviously trying to get the derivative +at at x uh now we're + + align:start position:0% + + + + align:start position:0% + +saying now we're saying okay this is X + + align:start position:0% +saying now we're saying okay this is X + + + align:start position:0% +saying now we're saying okay this is X +that's xus Delta X and we're trying to + + align:start position:0% +that's xus Delta X and we're trying to + + + align:start position:0% +that's xus Delta X and we're trying to +get the derivative there and if we go + + align:start position:0% +get the derivative there and if we go + + + align:start position:0% +get the derivative there and if we go +through the same arithmetic + + align:start position:0% + + + + align:start position:0% + +we uh get the same size error but this + + align:start position:0% +we uh get the same size error but this + + + align:start position:0% +we uh get the same size error but this +the sign is + + align:start position:0% +the sign is + + + align:start position:0% +the sign is +flipped so well what you might say is + + align:start position:0% +flipped so well what you might say is + + + align:start position:0% +flipped so well what you might say is +well Gee let's just average these two + + align:start position:0% +well Gee let's just average these two + + + align:start position:0% +well Gee let's just average these two +then we can get rid of that low order uh + + align:start position:0% +then we can get rid of that low order uh + + + align:start position:0% +then we can get rid of that low order uh +error + + align:start position:0% + + + + align:start position:0% + +term and then so if we average them + + align:start position:0% +term and then so if we average them + + + align:start position:0% +term and then so if we average them +which means the sum of the two divided + + align:start position:0% +which means the sum of the two divided + + + align:start position:0% +which means the sum of the two divided +the sum of these two divided by two then + + align:start position:0% +the sum of these two divided by two then + + + align:start position:0% +the sum of these two divided by two then +we just get F ofx that that's what we + + align:start position:0% +we just get F ofx that that's what we + + + align:start position:0% +we just get F ofx that that's what we +want and this cancels out well but then + + align:start position:0% +want and this cancels out well but then + + + align:start position:0% +want and this cancels out well but then +the higher order terms so we better fill + + align:start position:0% +the higher order terms so we better fill + + + align:start position:0% +the higher order terms so we better fill +in the higher order terms so here we got + + align:start position:0% +in the higher order terms so here we got + + + align:start position:0% +in the higher order terms so here we got +Delta x^2 / 6 F triple prime of + + align:start position:0% +Delta x^2 / 6 F triple prime of + + + align:start position:0% +Delta x^2 / 6 F triple prime of +X and + + align:start position:0% + + + + align:start position:0% + +um and so what we notice is that now uh + + align:start position:0% +um and so what we notice is that now uh + + + align:start position:0% +um and so what we notice is that now uh +we have a higher order error term which + + align:start position:0% +we have a higher order error term which + + + align:start position:0% +we have a higher order error term which +is desirable this so This formula will + + align:start position:0% +is desirable this so This formula will + + + align:start position:0% +is desirable this so This formula will +not just work for perfectly for a + + align:start position:0% +not just work for perfectly for a + + + align:start position:0% +not just work for perfectly for a +straight line but even if the straight + + align:start position:0% +straight line but even if the straight + + + align:start position:0% +straight line but even if the straight +line has a bit of curvature to it a + + align:start position:0% +line has a bit of curvature to it a + + + align:start position:0% +line has a bit of curvature to it a +second derivative as long as the third + + align:start position:0% +second derivative as long as the third + + + align:start position:0% +second derivative as long as the third +derivative isn't too large uh we will'll + + align:start position:0% +derivative isn't too large uh we will'll + + + align:start position:0% +derivative isn't too large uh we will'll +be okay so so what does averaging these + + align:start position:0% +be okay so so what does averaging these + + + align:start position:0% +be okay so so what does averaging these +two actually mean well it means that we + + align:start position:0% + + + + align:start position:0% + +that in effect we've Ed that + + align:start position:0% +that in effect we've Ed that + + + align:start position:0% +that in effect we've Ed that +operator right so + + align:start position:0% +operator right so + + + align:start position:0% +operator right so +um and you know that's a perfectly + + align:start position:0% +um and you know that's a perfectly + + + align:start position:0% +um and you know that's a perfectly +reasonable uh approximation to a + + align:start position:0% +reasonable uh approximation to a + + + align:start position:0% +reasonable uh approximation to a +derivative we're subtracting two things + + align:start position:0% +derivative we're subtracting two things + + + align:start position:0% +derivative we're subtracting two things +and we're dividing between the uh + + align:start position:0% +and we're dividing between the uh + + + align:start position:0% +and we're dividing between the uh +distance between where we've measured + + align:start position:0% +distance between where we've measured + + + align:start position:0% +distance between where we've measured +those those two + + align:start position:0% +those those two + + + align:start position:0% +those those two +things um + + align:start position:0% +things um + + + align:start position:0% +things um +okay and then you might say well um what + + align:start position:0% +okay and then you might say well um what + + + align:start position:0% +okay and then you might say well um what +if + + align:start position:0% +if + + + align:start position:0% +if +instead I sort of take this idea but now + + align:start position:0% +instead I sort of take this idea but now + + + align:start position:0% +instead I sort of take this idea but now +I'm saying I'm going to + + align:start position:0% + + + + align:start position:0% + +find I'm going to find an estimate of + + align:start position:0% +find I'm going to find an estimate of + + + align:start position:0% +find I'm going to find an estimate of +the derivative there and the objection + + align:start position:0% +the derivative there and the objection + + + align:start position:0% +the derivative there and the objection +would be well it's not a pixel position + + align:start position:0% +would be well it's not a pixel position + + + align:start position:0% +would be well it's not a pixel position +but that doesn't matter we can we can + + align:start position:0% +but that doesn't matter we can we can + + + align:start position:0% +but that doesn't matter we can we can +have even derivatives be offset by half + + align:start position:0% +have even derivatives be offset by half + + + align:start position:0% +have even derivatives be offset by half +a pixel as long as we just remember that + + align:start position:0% +a pixel as long as we just remember that + + + align:start position:0% +a pixel as long as we just remember that +that mentally that that's happened now I + + align:start position:0% +that mentally that that's happened now I + + + align:start position:0% +that mentally that that's happened now I +can go through and use tayor series blah + + align:start position:0% +can go through and use tayor series blah + + + align:start position:0% +can go through and use tayor series blah +blah blah but actually all I need to do + + align:start position:0% +blah blah but actually all I need to do + + + align:start position:0% +blah blah but actually all I need to do +is uh use this formula and divide Delta + + align:start position:0% +is uh use this formula and divide Delta + + + align:start position:0% +is uh use this formula and divide Delta +X by two right because this is the same + + align:start position:0% +X by two right because this is the same + + + align:start position:0% +X by two right because this is the same +thing with Delta x / 2 so in this case + + align:start position:0% +thing with Delta x / 2 so in this case + + + align:start position:0% +thing with Delta x / 2 so in this case +my formula is going to be f+ and then + + align:start position:0% +my formula is going to be f+ and then + + + align:start position:0% +my formula is going to be f+ and then +Delta X over 2^ 2 / + + align:start position:0% +Delta X over 2^ 2 / + + + align:start position:0% +Delta X over 2^ 2 / + + align:start position:0% + + + align:start position:0% +so now I have to compare two operators + + align:start position:0% +so now I have to compare two operators + + + align:start position:0% +so now I have to compare two operators +that have the same lowest order error + + align:start position:0% +that have the same lowest order error + + + align:start position:0% +that have the same lowest order error +term and now I look at the magnitude of + + align:start position:0% +term and now I look at the magnitude of + + + align:start position:0% +term and now I look at the magnitude of +the factor in front of the eror term and + + align:start position:0% +the factor in front of the eror term and + + + align:start position:0% +the factor in front of the eror term and +obviously this one is a quarter the size + + align:start position:0% +obviously this one is a quarter the size + + + align:start position:0% +obviously this one is a quarter the size +of that one right so so this one uh has + + align:start position:0% +of that one right so so this one uh has + + + align:start position:0% +of that one right so so this one uh has +an advantage in in uh that respect I can + + align:start position:0% +an advantage in in uh that respect I can + + + align:start position:0% +an advantage in in uh that respect I can +get a relatively high order error term + + align:start position:0% +get a relatively high order error term + + + align:start position:0% +get a relatively high order error term +and I can um have a a small multiplier + + align:start position:0% +and I can um have a a small multiplier + + + align:start position:0% +and I can um have a a small multiplier +so that the error is actually smaller + + align:start position:0% +so that the error is actually smaller + + + align:start position:0% +so that the error is actually smaller +and it makes sense I mean over here + + align:start position:0% +and it makes sense I mean over here + + + align:start position:0% +and it makes sense I mean over here +we're comparing things that are + + align:start position:0% +we're comparing things that are + + + align:start position:0% +we're comparing things that are +relatively far apart and seeing so + + align:start position:0% +relatively far apart and seeing so + + + align:start position:0% +relatively far apart and seeing so +obviously they'll be affected more by + + align:start position:0% +obviously they'll be affected more by + + + align:start position:0% +obviously they'll be affected more by +higher order derivatives than in this + + align:start position:0% +higher order derivatives than in this + + + align:start position:0% +higher order derivatives than in this +case where I'm + + align:start position:0% +case where I'm + + + align:start position:0% +case where I'm +uh looking at things that are close + + align:start position:0% +uh looking at things that are close + + + align:start position:0% +uh looking at things that are close +together okay uh + + align:start position:0% +together okay uh + + + align:start position:0% +together okay uh +um now that's fine for + + align:start position:0% +um now that's fine for + + + align:start position:0% +um now that's fine for +ex but how is this going to work with ey + + align:start position:0% +ex but how is this going to work with ey + + + align:start position:0% +ex but how is this going to work with ey +because if I uh + + align:start position:0% +because if I uh + + + align:start position:0% +because if I uh +take + + align:start position:0% +take + + + align:start position:0% +take +uh if I take that idea in both + + align:start position:0% +uh if I take that idea in both + + + align:start position:0% +uh if I take that idea in both +directions + + align:start position:0% + + + + align:start position:0% + +so so here's my ex + + align:start position:0% +so so here's my ex + + + align:start position:0% +so so here's my ex +operator and + + align:start position:0% +operator and + + + align:start position:0% +operator and +then you know there's a potential ey + + align:start position:0% +then you know there's a potential ey + + + align:start position:0% +then you know there's a potential ey +operator well that's not going to work + + align:start position:0% +operator well that's not going to work + + + align:start position:0% +operator well that's not going to work +because this one is a good estimate of + + align:start position:0% +because this one is a good estimate of + + + align:start position:0% +because this one is a good estimate of +the X derivative there and this one is a + + align:start position:0% +the X derivative there and this one is a + + + align:start position:0% +the X derivative there and this one is a +good estimate of the X derivative y + + align:start position:0% +good estimate of the X derivative y + + + align:start position:0% +good estimate of the X derivative y +derivative there and those aren't + + align:start position:0% +derivative there and those aren't + + + align:start position:0% +derivative there and those aren't +consistent and so uh what I do well one + + align:start position:0% +consistent and so uh what I do well one + + + align:start position:0% +consistent and so uh what I do well one +way to deal with it + + align:start position:0% +way to deal with it + + + align:start position:0% +way to deal with it +is is that + + align:start position:0% + + + + align:start position:0% + +right because these now um if I go + + align:start position:0% +right because these now um if I go + + + align:start position:0% +right because these now um if I go +through that Taylor series story these + + align:start position:0% +through that Taylor series story these + + + align:start position:0% +through that Taylor series story these +are good estimates of the X derivative + + align:start position:0% +are good estimates of the X derivative + + + align:start position:0% +are good estimates of the X derivative +here and this is a good estimate of the + + align:start position:0% +here and this is a good estimate of the + + + align:start position:0% +here and this is a good estimate of the +Y derivative here and oh those are the + + align:start position:0% +Y derivative here and oh those are the + + + align:start position:0% +Y derivative here and oh those are the +same point so so that's + + align:start position:0% +same point so so that's + + + align:start position:0% +same point so so that's +um that's how we get to that and when we + + align:start position:0% +um that's how we get to that and when we + + + align:start position:0% +um that's how we get to that and when we +talked about fixed Optical flow we + + align:start position:0% +talked about fixed Optical flow we + + + align:start position:0% +talked about fixed Optical flow we +already mentioned that that's the way uh + + align:start position:0% +already mentioned that that's the way uh + + + align:start position:0% +already mentioned that that's the way uh +you want to compute the derivatives and + + align:start position:0% +you want to compute the derivatives and + + + align:start position:0% +you want to compute the derivatives and +well there we needed uh not just just e + + align:start position:0% +well there we needed uh not just just e + + + align:start position:0% +well there we needed uh not just just e +x ey y e t uh we need not just ex X and + + align:start position:0% +x ey y e t uh we need not just ex X and + + + align:start position:0% +x ey y e t uh we need not just ex X and +e y but we needed e t and so + + align:start position:0% +e y but we needed e t and so + + + align:start position:0% +e y but we needed e t and so +there uh we're dealing with a whole + + align:start position:0% + + + + align:start position:0% + +Cube um and so for example to compute + + align:start position:0% +Cube um and so for example to compute + + + align:start position:0% +Cube um and so for example to compute +the derivative in the y + + align:start position:0% + + + + align:start position:0% + +direction we can do that + + align:start position:0% + + + + align:start position:0% + +okay and um you know under materials + + align:start position:0% +okay and um you know under materials + + + align:start position:0% +okay and um you know under materials +there's the detailed explanation of how + + align:start position:0% +there's the detailed explanation of how + + + align:start position:0% +there's the detailed explanation of how +to do um the fixed Optical flow and + + align:start position:0% +to do um the fixed Optical flow and + + + align:start position:0% +to do um the fixed Optical flow and +that's that's in there so that's um now + + align:start position:0% +that's that's in there so that's um now + + + align:start position:0% +that's that's in there so that's um now +story doesn't end there because now we + + align:start position:0% +story doesn't end there because now we + + + align:start position:0% +story doesn't end there because now we +might talk about efficiency and so for + + align:start position:0% +might talk about efficiency and so for + + + align:start position:0% +might talk about efficiency and so for +example um you know how much work are + + align:start position:0% +example um you know how much work are + + + align:start position:0% +example um you know how much work are +these operators well + + align:start position:0% +these operators well + + + align:start position:0% +these operators well +uh here we have um three we we can + + align:start position:0% +uh here we have um three we we can + + + align:start position:0% +uh here we have um three we we can +subtract these two that's one subtract + + align:start position:0% +subtract these two that's one subtract + + + align:start position:0% +subtract these two that's one subtract +those two that's two then we add them up + + align:start position:0% +those two that's two then we add them up + + + align:start position:0% +those two that's two then we add them up +so it's three operations for this and + + align:start position:0% +so it's three operations for this and + + + align:start position:0% +so it's three operations for this and +three operations for that but actually + + align:start position:0% +three operations for that but actually + + + align:start position:0% +three operations for that but actually +they + + align:start position:0% + + + + align:start position:0% + +share these sub + + align:start position:0% + + + + align:start position:0% + +computations right and this one's one + + align:start position:0% +computations right and this one's one + + + align:start position:0% +computations right and this one's one +operation and that one's one operation + + align:start position:0% +operation and that one's one operation + + + align:start position:0% +operation and that one's one operation +so 3 + 3 is 6 so one operation one + + align:start position:0% +so 3 + 3 is 6 so one operation one + + + align:start position:0% +so 3 + 3 is 6 so one operation one +operation and then we combine them we we + + align:start position:0% +operation and then we combine them we we + + + align:start position:0% +operation and then we combine them we we +add them to get uh e subx and we + + align:start position:0% +add them to get uh e subx and we + + + align:start position:0% +add them to get uh e subx and we +subtract them to get e sub y so that's + + align:start position:0% +subtract them to get e sub y so that's + + + align:start position:0% +subtract them to get e sub y so that's +one of plus one of so total of four + + align:start position:0% +one of plus one of so total of four + + + align:start position:0% +one of plus one of so total of four +ofs so uh by cleverly arranging the + + align:start position:0% +ofs so uh by cleverly arranging the + + + align:start position:0% +ofs so uh by cleverly arranging the +computation we can cut it back from six + + align:start position:0% +computation we can cut it back from six + + + align:start position:0% +computation we can cut it back from six +operations to four you might say who + + align:start position:0% +operations to four you might say who + + + align:start position:0% +operations to four you might say who +cares well the thing is you're doing + + align:start position:0% +cares well the thing is you're doing + + + align:start position:0% +cares well the thing is you're doing +this in in each of a few million pixels + + align:start position:0% +this in in each of a few million pixels + + + align:start position:0% +this in in each of a few million pixels +so this is one place where actually + + align:start position:0% +so this is one place where actually + + + align:start position:0% +so this is one place where actually +efficiency does does + + align:start position:0% +efficiency does does + + + align:start position:0% +efficiency does does +matter uh and I won't go through this I + + align:start position:0% +matter uh and I won't go through this I + + + align:start position:0% +matter uh and I won't go through this I +mean if you do this the obvious way it + + align:start position:0% +mean if you do this the obvious way it + + + align:start position:0% +mean if you do this the obvious way it +takes I don't know 21 Ops if you do this + + align:start position:0% +takes I don't know 21 Ops if you do this + + + align:start position:0% +takes I don't know 21 Ops if you do this +if you get exe T the obvious way you get + + align:start position:0% +if you get exe T the obvious way you get + + + align:start position:0% +if you get exe T the obvious way you get +21 Ops and I'll leave it to you to um + + align:start position:0% +21 Ops and I'll leave it to you to um + + + align:start position:0% +21 Ops and I'll leave it to you to um +you know and people sometimes U come up + + align:start position:0% +you know and people sometimes U come up + + + align:start position:0% +you know and people sometimes U come up +with surprising solutions that uh beat + + align:start position:0% +with surprising solutions that uh beat + + + align:start position:0% +with surprising solutions that uh beat +the obvious Solution by a significant + + align:start position:0% +the obvious Solution by a significant + + + align:start position:0% +the obvious Solution by a significant +factor okay and by the way there's + + align:start position:0% +factor okay and by the way there's + + + align:start position:0% +factor okay and by the way there's +robertt cross operator so you know he + + align:start position:0% +robertt cross operator so you know he + + + align:start position:0% +robertt cross operator so you know he +was way ahead of his + + align:start position:0% +was way ahead of his + + + align:start position:0% +was way ahead of his +time and uh what about irin soel so irin + + align:start position:0% +time and uh what about irin soel so irin + + + align:start position:0% +time and uh what about irin soel so irin +soel uh you know looked at this stuff + + align:start position:0% +soel uh you know looked at this stuff + + + align:start position:0% +soel uh you know looked at this stuff +and and this is this is where he got to + + align:start position:0% +and and this is this is where he got to + + + align:start position:0% +and and this is this is where he got to +he said well this is uh obviously a good + + align:start position:0% +he said well this is uh obviously a good + + + align:start position:0% +he said well this is uh obviously a good +way of doing it it's an estimate of the + + align:start position:0% +way of doing it it's an estimate of the + + + align:start position:0% +way of doing it it's an estimate of the +derivative at that pixel and it's not it + + align:start position:0% +derivative at that pixel and it's not it + + + align:start position:0% +derivative at that pixel and it's not it +doesn't have a low order error term but + + align:start position:0% +doesn't have a low order error term but + + + align:start position:0% +doesn't have a low order error term but +then he needed to do it in 2D so he + + align:start position:0% +then he needed to do it in 2D so he + + + align:start position:0% +then he needed to do it in 2D so he +replicated it but why did he replicate + + align:start position:0% +replicated it but why did he replicate + + + align:start position:0% +replicated it but why did he replicate +it a particular way he did well we can + + align:start position:0% +it a particular way he did well we can + + + align:start position:0% +it a particular way he did well we can +think of + + align:start position:0% +think of + + + align:start position:0% +think of +it in this + + align:start position:0% + + + + align:start position:0% + +way I'm leaving out the constants but + + align:start position:0% +way I'm leaving out the constants but + + + align:start position:0% +way I'm leaving out the constants but +basically we do an average so so this is + + align:start position:0% +basically we do an average so so this is + + + align:start position:0% +basically we do an average so so this is +a convolution so that's the underlying + + align:start position:0% +a convolution so that's the underlying + + + align:start position:0% +a convolution so that's the underlying +operator and now we're going to smooth + + align:start position:0% +operator and now we're going to smooth + + + align:start position:0% +operator and now we're going to smooth +it by doing an average over a four a 2X + + align:start position:0% +it by doing an average over a four a 2X + + + align:start position:0% +it by doing an average over a four a 2X +two block right which is which + + align:start position:0% +two block right which is which + + + align:start position:0% +two block right which is which +corresponds to convolution with this and + + align:start position:0% +corresponds to convolution with this and + + + align:start position:0% +corresponds to convolution with this and +you know if you like we can put in one + + align:start position:0% +you know if you like we can put in one + + + align:start position:0% +you know if you like we can put in one +over + + align:start position:0% + + + + align:start position:0% + +four um not concerned about those + + align:start position:0% +four um not concerned about those + + + align:start position:0% +four um not concerned about those +multipliers at the moment um okay and + + align:start position:0% +multipliers at the moment um okay and + + + align:start position:0% +multipliers at the moment um okay and +what what what do we get well uh + + align:start position:0% +what what what do we get well uh + + + align:start position:0% +what what what do we get well uh +hopefully you remember something about + + align:start position:0% +hopefully you remember something about + + + align:start position:0% +hopefully you remember something about +convolution so we flip one of these well + + align:start position:0% +convolution so we flip one of these well + + + align:start position:0% +convolution so we flip one of these well +that doesn't do anything to this because + + align:start position:0% +that doesn't do anything to this because + + + align:start position:0% +that doesn't do anything to this because +it's symmetrical and then we shift it + + align:start position:0% +it's symmetrical and then we shift it + + + align:start position:0% +it's symmetrical and then we shift it +over the other one so uh the first + + align:start position:0% +over the other one so uh the first + + + align:start position:0% +over the other one so uh the first +position where we get some something non + + align:start position:0% +position where we get some something non + + + align:start position:0% +position where we get some something non +zero is when we have it in this + + align:start position:0% +zero is when we have it in this + + + align:start position:0% +zero is when we have it in this +position and what do we get we get minus + + align:start position:0% +position and what do we get we get minus + + + align:start position:0% +position and what do we get we get minus +one so then I take you know so this + + align:start position:0% +one so then I take you know so this + + + align:start position:0% +one so then I take you know so this +operator and move it one to the right + + align:start position:0% +operator and move it one to the right + + + align:start position:0% +operator and move it one to the right +now it's overlapping in two places I get + + align:start position:0% +now it's overlapping in two places I get + + + align:start position:0% +now it's overlapping in two places I get +minus one * 1 is -1 plus + 1 * 1 that's + + align:start position:0% +minus one * 1 is -1 plus + 1 * 1 that's + + + align:start position:0% +minus one * 1 is -1 plus + 1 * 1 that's +zero I shift it over one more + + align:start position:0% +zero I shift it over one more + + + align:start position:0% +zero I shift it over one more +time now it's only overlapping over here + + align:start position:0% +time now it's only overlapping over here + + + align:start position:0% +time now it's only overlapping over here +and I get uh Plus + + align:start position:0% +and I get uh Plus + + + align:start position:0% +and I get uh Plus +one okay then I move it one row down and + + align:start position:0% +one okay then I move it one row down and + + + align:start position:0% +one okay then I move it one row down and +now I line it up over here and I get 1 + + align:start position:0% +now I line it up over here and I get 1 + + + align:start position:0% +now I line it up over here and I get 1 +one * -1 - one that's Min + + align:start position:0% +one * -1 - one that's Min + + + align:start position:0% +one * -1 - one that's Min +-2 I shifted one to the right they all + + align:start position:0% +-2 I shifted one to the right they all + + + align:start position:0% +-2 I shifted one to the right they all +cancel out zero shifted one to the right + + align:start position:0% +cancel out zero shifted one to the right + + + align:start position:0% +cancel out zero shifted one to the right +I get 1 one * 1 1 is + + + align:start position:0% +I get 1 one * 1 1 is + + + + align:start position:0% +I get 1 one * 1 1 is + +2 uh shift it down one more I get min - + + align:start position:0% +2 uh shift it down one more I get min - + + + align:start position:0% +2 uh shift it down one more I get min - +one 0 + + + align:start position:0% +one 0 + + + + align:start position:0% +one 0 + +one and there's uh uran so Bell's uh X + + align:start position:0% +one and there's uh uran so Bell's uh X + + + align:start position:0% +one and there's uh uran so Bell's uh X +operated same in the y direction so we + + align:start position:0% +operated same in the y direction so we + + + align:start position:0% +operated same in the y direction so we +can think of um it as uh just a way of + + align:start position:0% +can think of um it as uh just a way of + + + align:start position:0% +can think of um it as uh just a way of +um smoothing and smoothing has the + + align:start position:0% +um smoothing and smoothing has the + + + align:start position:0% +um smoothing and smoothing has the +effect of reducing noise so uh + + align:start position:0% +effect of reducing noise so uh + + + align:start position:0% +effect of reducing noise so uh +unfortunately also has the effect of + + align:start position:0% +unfortunately also has the effect of + + + align:start position:0% +unfortunately also has the effect of +blurring things making them so there's a + + align:start position:0% +blurring things making them so there's a + + + align:start position:0% +blurring things making them so there's a +trade-off obviously uh we can um reduce + + align:start position:0% +trade-off obviously uh we can um reduce + + + align:start position:0% +trade-off obviously uh we can um reduce +the edge uh gradient at the same time as + + align:start position:0% +the edge uh gradient at the same time as + + + align:start position:0% +the edge uh gradient at the same time as +we're cutting down on the noise and uh + + align:start position:0% +we're cutting down on the noise and uh + + + align:start position:0% +we're cutting down on the noise and uh +so Iran soell managed + + align:start position:0% +so Iran soell managed + + + align:start position:0% +so Iran soell managed +to uh avoid the half pixel offset + + align:start position:0% +to uh avoid the half pixel offset + + + align:start position:0% +to uh avoid the half pixel offset +Problem by having two operators Each of + + align:start position:0% +Problem by having two operators Each of + + + align:start position:0% +Problem by having two operators Each of +which is half pixel offset and when you + + align:start position:0% +which is half pixel offset and when you + + + align:start position:0% +which is half pixel offset and when you +convolve them together you get zero or + + align:start position:0% +convolve them together you get zero or + + + align:start position:0% +convolve them together you get zero or +one or minus one offset + + align:start position:0% +one or minus one offset + + + align:start position:0% +one or minus one offset +so okay so that's like the very front + + align:start position:0% +so okay so that's like the very front + + + align:start position:0% +so okay so that's like the very front +end of um of this + + align:start position:0% +end of um of this + + + align:start position:0% +end of um of this +operation uh and you know they discuss + + align:start position:0% +operation uh and you know they discuss + + + align:start position:0% +operation uh and you know they discuss +but they don't say you should use this + + align:start position:0% +but they don't say you should use this + + + align:start position:0% +but they don't say you should use this +or that they just give various uh + + align:start position:0% +or that they just give various uh + + + align:start position:0% +or that they just give various uh +formulas and uh um the preferred one so + + align:start position:0% +formulas and uh um the preferred one so + + + align:start position:0% +formulas and uh um the preferred one so +a lot of times it also say the preferred + + align:start position:0% +a lot of times it also say the preferred + + + align:start position:0% +a lot of times it also say the preferred +implementation and that's kind of a + + align:start position:0% +implementation and that's kind of a + + + align:start position:0% +implementation and that's kind of a +tricky one because later on if someone + + align:start position:0% +tricky one because later on if someone + + + align:start position:0% +tricky one because later on if someone +says oh but I didn't Implement your + + align:start position:0% +says oh but I didn't Implement your + + + align:start position:0% +says oh but I didn't Implement your +preferred implementation you know the + + align:start position:0% +preferred implementation you know the + + + align:start position:0% +preferred implementation you know the +lawyer will say well you're talking + + align:start position:0% +lawyer will say well you're talking + + + align:start position:0% +lawyer will say well you're talking +about an exemplary implementation not + + align:start position:0% +about an exemplary implementation not + + + align:start position:0% +about an exemplary implementation not +what's claimed in the pattern what's + + align:start position:0% +what's claimed in the pattern what's + + + align:start position:0% +what's claimed in the pattern what's +claimed in the pattern is in the claims + + align:start position:0% +claimed in the pattern is in the claims + + + align:start position:0% +claimed in the pattern is in the claims +what you say in in the specification is + + align:start position:0% +what you say in in the specification is + + + align:start position:0% +what you say in in the specification is +just a way for somebody to implement + + align:start position:0% +just a way for somebody to implement + + + align:start position:0% +just a way for somebody to implement +this and just because us doesn't + + align:start position:0% +this and just because us doesn't + + + align:start position:0% +this and just because us doesn't +implement it exactly the same way it's + + align:start position:0% +implement it exactly the same way it's + + + align:start position:0% +implement it exactly the same way it's +irrelevant what's relevant is whether it + + align:start position:0% +irrelevant what's relevant is whether it + + + align:start position:0% +irrelevant what's relevant is whether it +violates infringes on the + + align:start position:0% +violates infringes on the + + + align:start position:0% +violates infringes on the +claims and so a lot of times there'll be + + align:start position:0% +claims and so a lot of times there'll be + + + align:start position:0% +claims and so a lot of times there'll be +verbiage about in a preferred + + align:start position:0% +verbiage about in a preferred + + + align:start position:0% +verbiage about in a preferred +implementation the gain is 10 or + + align:start position:0% +implementation the gain is 10 or + + + align:start position:0% +implementation the gain is 10 or +whatever so if your gain is 11 that + + align:start position:0% +whatever so if your gain is 11 that + + + align:start position:0% +whatever so if your gain is 11 that +doesn't excuse you because the important + + align:start position:0% +doesn't excuse you because the important + + + align:start position:0% +doesn't excuse you because the important +part is whether the claims cover it or + + align:start position:0% +part is whether the claims cover it or + + + align:start position:0% +part is whether the claims cover it or +not okay so that's the very front end + + align:start position:0% +not okay so that's the very front end + + + align:start position:0% +not okay so that's the very front end +and then we're going toh talk about + + align:start position:0% +and then we're going toh talk about + + + align:start position:0% +and then we're going toh talk about +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um The Next + + align:start position:0% + + + + align:start position:0% + +Step uh so the next step is the + + align:start position:0% +Step uh so the next step is the + + + align:start position:0% +Step uh so the next step is the +conversion from uh + + align:start position:0% + + + + align:start position:0% + +cartisian to Polar coordinates for the + + align:start position:0% +cartisian to Polar coordinates for the + + + align:start position:0% +cartisian to Polar coordinates for the +um uh brightness gradient and um we'll + + align:start position:0% +um uh brightness gradient and um we'll + + + align:start position:0% +um uh brightness gradient and um we'll +do this mostly next time but + + align:start position:0% + + + + align:start position:0% + +for programming people we'll call it uh + + align:start position:0% +for programming people we'll call it uh + + + align:start position:0% +for programming people we'll call it uh +A1 two of those two arguments and the + + align:start position:0% +A1 two of those two arguments and the + + + align:start position:0% +A1 two of those two arguments and the +reason is that we don't want to have + + align:start position:0% +reason is that we don't want to have + + + align:start position:0% +reason is that we don't want to have +division by zero which we can avoid by + + align:start position:0% +division by zero which we can avoid by + + + align:start position:0% +division by zero which we can avoid by +using the two argument version of + + align:start position:0% +using the two argument version of + + + align:start position:0% +using the two argument version of +A1 okay so uh now we have a bra gradient + + align:start position:0% +A1 okay so uh now we have a bra gradient + + + align:start position:0% +A1 okay so uh now we have a bra gradient +magnitude and we have a direction and + + align:start position:0% +magnitude and we have a direction and + + + align:start position:0% +magnitude and we have a direction and +the next step is to quantize the + + align:start position:0% +the next step is to quantize the + + + align:start position:0% +the next step is to quantize the +direction so what we're trying to find + + align:start position:0% +direction so what we're trying to find + + + align:start position:0% +direction so what we're trying to find +is uh maximum in the direction across + + align:start position:0% +is uh maximum in the direction across + + + align:start position:0% +is uh maximum in the direction across +the Edge so suppose The Edge is running + + align:start position:0% +the Edge so suppose The Edge is running + + + align:start position:0% +the Edge so suppose The Edge is running +um this way brightness E1 E2 then we + + align:start position:0% +um this way brightness E1 E2 then we + + + align:start position:0% +um this way brightness E1 E2 then we +want to scan across the edge and look + + align:start position:0% +want to scan across the edge and look + + + align:start position:0% +want to scan across the edge and look +for uh + + align:start position:0% + + + + align:start position:0% + +maximum + + align:start position:0% +maximum + + + align:start position:0% +maximum +EO and the direction is given + + align:start position:0% +EO and the direction is given + + + align:start position:0% +EO and the direction is given +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +by E Theta so that's why we need e Theta + + align:start position:0% +by E Theta so that's why we need e Theta + + + align:start position:0% +by E Theta so that's why we need e Theta +and E + + align:start position:0% +and E + + + align:start position:0% +and E +and unfortunately we don't have points + + align:start position:0% +and unfortunately we don't have points + + + align:start position:0% +and unfortunately we don't have points +in all places in the plane only on this + + align:start position:0% +in all places in the plane only on this + + + align:start position:0% +in all places in the plane only on this +grid so we can only deal with uh easily + + align:start position:0% +grid so we can only deal with uh easily + + + align:start position:0% +grid so we can only deal with uh easily +deal with quantized directions so we got + + align:start position:0% +deal with quantized directions so we got + + + align:start position:0% +deal with quantized directions so we got +you know Compass directions uh eight + + align:start position:0% +you know Compass directions uh eight + + + align:start position:0% +you know Compass directions uh eight +possible uh + + align:start position:0% +possible uh + + + align:start position:0% +possible uh +directions and uh we're looking for a + + align:start position:0% +directions and uh we're looking for a + + + align:start position:0% +directions and uh we're looking for a +maximum and now on a different grid we + + align:start position:0% +maximum and now on a different grid we + + + align:start position:0% +maximum and now on a different grid we +would have different quantization but we + + align:start position:0% +would have different quantization but we + + + align:start position:0% +would have different quantization but we +would still have a + + align:start position:0% +would still have a + + + align:start position:0% +would still have a +problem okay so the center one is going + + align:start position:0% +problem okay so the center one is going + + + align:start position:0% +problem okay so the center one is going +to be uh uh + + align:start position:0% +to be uh uh + + + align:start position:0% +to be uh uh +g0 and then so suppose this is + + align:start position:0% +g0 and then so suppose this is + + + align:start position:0% +g0 and then so suppose this is +our this is our quanti gradient + + align:start position:0% +our this is our quanti gradient + + + align:start position:0% +our this is our quanti gradient +Direction and then we'll call the + + align:start position:0% +Direction and then we'll call the + + + align:start position:0% +Direction and then we'll call the +gradient here G+ and the gradient there + + align:start position:0% +gradient here G+ and the gradient there + + + align:start position:0% +gradient here G+ and the gradient there +G + + align:start position:0% + + + + align:start position:0% + +minus and so we have those three values + + align:start position:0% +minus and so we have those three values + + + align:start position:0% +minus and so we have those three values +and um clearly you know the center pixel + + align:start position:0% +and um clearly you know the center pixel + + + align:start position:0% +and um clearly you know the center pixel +is an important one it's it's on the + + align:start position:0% +is an important one it's it's on the + + + align:start position:0% +is an important one it's it's on the +edge + + align:start position:0% +edge + + + align:start position:0% +edge +but quantized to pixel position so so it + + align:start position:0% +but quantized to pixel position so so it + + + align:start position:0% +but quantized to pixel position so so it +doesn't give us sub pixel accuracy so + + align:start position:0% +doesn't give us sub pixel accuracy so + + + align:start position:0% +doesn't give us sub pixel accuracy so +now uh we um first of all we + + align:start position:0% +now uh we um first of all we + + + align:start position:0% +now uh we um first of all we +uh keep + + align:start position:0% +uh keep + + + align:start position:0% +uh keep +only + + align:start position:0% + + + + align:start position:0% + +if so we step through the + + align:start position:0% +if so we step through the + + + align:start position:0% +if so we step through the +image and we ignore non + + align:start position:0% +image and we ignore non + + + align:start position:0% +image and we ignore non +Maxima and um now what we actually want + + align:start position:0% +Maxima and um now what we actually want + + + align:start position:0% +Maxima and um now what we actually want +is something that is + + align:start position:0% + + + + align:start position:0% + +asymmetrical okay so it could happen + + align:start position:0% +asymmetrical okay so it could happen + + + align:start position:0% +asymmetrical okay so it could happen +that g0 is equal to G+ or equal to G + + align:start position:0% +that g0 is equal to G+ or equal to G + + + align:start position:0% +that g0 is equal to G+ or equal to G +minus and we could say well that means + + align:start position:0% +minus and we could say well that means + + + align:start position:0% +minus and we could say well that means +it's not a maximum and just throw it out + + align:start position:0% +it's not a maximum and just throw it out + + + align:start position:0% +it's not a maximum and just throw it out +but of course that's wrong because you + + align:start position:0% +but of course that's wrong because you + + + align:start position:0% +but of course that's wrong because you +you know we have to keep one of those + + align:start position:0% +you know we have to keep one of those + + + align:start position:0% +you know we have to keep one of those +two points but we don't to keep both + + align:start position:0% +two points but we don't to keep both + + + align:start position:0% +two points but we don't to keep both +because then we have two points on the + + align:start position:0% +because then we have two points on the + + + align:start position:0% +because then we have two points on the +edge that are on quote on the edge that + + align:start position:0% +edge that are on quote on the edge that + + + align:start position:0% +edge that are on quote on the edge that +are a pixelart so that's no good either + + align:start position:0% +are a pixelart so that's no good either + + + align:start position:0% +are a pixelart so that's no good either +so we have to have a tie breaker so it's + + align:start position:0% +so we have to have a tie breaker so it's + + + align:start position:0% +so we have to have a tie breaker so it's +important that + + align:start position:0% +important that + + + align:start position:0% +important that +uh this condition is asymmetrical I mean + + align:start position:0% +uh this condition is asymmetrical I mean + + + align:start position:0% +uh this condition is asymmetrical I mean +we can make it asymmetrical the other + + align:start position:0% +we can make it asymmetrical the other + + + align:start position:0% +we can make it asymmetrical the other +way that'll also work but but we need to + + align:start position:0% +way that'll also work but but we need to + + + align:start position:0% +way that'll also work but but we need to +have a way of dealing with a case where + + align:start position:0% +have a way of dealing with a case where + + + align:start position:0% +have a way of dealing with a case where +g0 is equal to G Plus or equal to G + + align:start position:0% +g0 is equal to G Plus or equal to G + + + align:start position:0% +g0 is equal to G Plus or equal to G +minus okay and then + + align:start position:0% +minus okay and then + + + align:start position:0% +minus okay and then +uh we're trying to find the peak now you + + align:start position:0% +uh we're trying to find the peak now you + + + align:start position:0% +uh we're trying to find the peak now you +know how does the curve go well we don't + + align:start position:0% +know how does the curve go well we don't + + + align:start position:0% +know how does the curve go well we don't +know but uh we can imagine various kinds + + align:start position:0% +know but uh we can imagine various kinds + + + align:start position:0% +know but uh we can imagine various kinds +of uh it's not a very good Parabola + + align:start position:0% +of uh it's not a very good Parabola + + + align:start position:0% +of uh it's not a very good Parabola +but okay so we have + + align:start position:0% + + + + align:start position:0% + +uh is our Parabola we take its + + align:start position:0% + + + + align:start position:0% + +derivative and there's the peak + + align:start position:0% +derivative and there's the peak + + + align:start position:0% +derivative and there's the peak +and um in terms of uh these quantities + + align:start position:0% + + + + align:start position:0% + +here you know if you go through and + + align:start position:0% +here you know if you go through and + + + align:start position:0% +here you know if you go through and +substitute if you fit a b and + + align:start position:0% +substitute if you fit a b and + + + align:start position:0% +substitute if you fit a b and +c then uh you you get this formula and + + align:start position:0% +c then uh you you get this formula and + + + align:start position:0% +c then uh you you get this formula and +um well here I've used + + align:start position:0% +um well here I've used + + + align:start position:0% +um well here I've used +x uh here I'm using + + align:start position:0% +x uh here I'm using + + + align:start position:0% +x uh here I'm using +S and we can show importantly + + align:start position:0% + + + + align:start position:0% + +that uh s computed this way is a half is + + align:start position:0% +that uh s computed this way is a half is + + + align:start position:0% +that uh s computed this way is a half is +limited in magnitude to + + align:start position:0% +limited in magnitude to + + + align:start position:0% +limited in magnitude to +half uh why is that well if it was let's + + align:start position:0% +half uh why is that well if it was let's + + + align:start position:0% +half uh why is that well if it was let's +say 3/4 that would mean that uh we'd be + + align:start position:0% +say 3/4 that would mean that uh we'd be + + + align:start position:0% +say 3/4 that would mean that uh we'd be +closer to this point and then this + + align:start position:0% +closer to this point and then this + + + align:start position:0% +closer to this point and then this +should be the maximum so you can + + align:start position:0% +should be the maximum so you can + + + align:start position:0% +should be the maximum so you can +actually show that can't happen so if at + + align:start position:0% +actually show that can't happen so if at + + + align:start position:0% +actually show that can't happen so if at +that's it's a range of solutions + + align:start position:0% +that's it's a range of solutions + + + align:start position:0% +that's it's a range of solutions +provided g0 is the maximum and you can + + align:start position:0% +provided g0 is the maximum and you can + + + align:start position:0% +provided g0 is the maximum and you can +sort of understand what's going on here + + align:start position:0% +sort of understand what's going on here + + + align:start position:0% +sort of understand what's going on here +so if G+ is the same as G + + align:start position:0% +so if G+ is the same as G + + + align:start position:0% +so if G+ is the same as G +minus s is zero that's you know we're + + align:start position:0% +minus s is zero that's you know we're + + + align:start position:0% +minus s is zero that's you know we're +right we have a balanced Parabola we we + + align:start position:0% +right we have a balanced Parabola we we + + + align:start position:0% +right we have a balanced Parabola we we +have this + + align:start position:0% + + + + align:start position:0% + +situation right and and in this case you + + align:start position:0% +situation right and and in this case you + + + align:start position:0% +situation right and and in this case you +know of course you would say oh that's + + align:start position:0% +know of course you would say oh that's + + + align:start position:0% +know of course you would say oh that's +it right if these two are the same and + + align:start position:0% +it right if these two are the same and + + + align:start position:0% +it right if these two are the same and +then it gets shifted the more there's a + + align:start position:0% +then it gets shifted the more there's a + + + align:start position:0% +then it gets shifted the more there's a +difference between the two + + align:start position:0% +difference between the two + + + align:start position:0% +difference between the two +sides um and how much does it get + + align:start position:0% +sides um and how much does it get + + + align:start position:0% +sides um and how much does it get +shifted by well we look at the second + + align:start position:0% +shifted by well we look at the second + + + align:start position:0% +shifted by well we look at the second +derivative which is uh this difference + + align:start position:0% +derivative which is uh this difference + + + align:start position:0% +derivative which is uh this difference +here well it's not the second derivative + + align:start position:0% +here well it's not the second derivative + + + align:start position:0% +here well it's not the second derivative +but proportional to the second + + align:start position:0% +but proportional to the second + + + align:start position:0% +but proportional to the second +derivative so we're looking at the + + align:start position:0% +derivative so we're looking at the + + + align:start position:0% +derivative so we're looking at the +average of G+ and G minus and comparing + + align:start position:0% +average of G+ and G minus and comparing + + + align:start position:0% +average of G+ and G minus and comparing +it to this point and the larger that + + align:start position:0% +it to this point and the larger that + + + align:start position:0% +it to this point and the larger that +difference is the higher the second + + align:start position:0% +difference is the higher the second + + + align:start position:0% +difference is the higher the second +derivative so it it just corresponds to + + align:start position:0% +derivative so it it just corresponds to + + + align:start position:0% +derivative so it it just corresponds to +you know b as the first derivative a is + + align:start position:0% +you know b as the first derivative a is + + + align:start position:0% +you know b as the first derivative a is +the second + + align:start position:0% +the second + + + align:start position:0% +the second +derivative okay so that's uh one way of + + align:start position:0% +derivative okay so that's uh one way of + + + align:start position:0% +derivative okay so that's uh one way of +getting the sub pixel accuracy and then + + align:start position:0% +getting the sub pixel accuracy and then + + + align:start position:0% +getting the sub pixel accuracy and then +the other way they mention is uh the + + align:start position:0% +the other way they mention is uh the + + + align:start position:0% +the other way they mention is uh the +Little Triangle model and that just + + align:start position:0% +Little Triangle model and that just + + + align:start position:0% +Little Triangle model and that just +seems weird but um for some reason there + + align:start position:0% +seems weird but um for some reason there + + + align:start position:0% +seems weird but um for some reason there +circumstances where it's a pretty good + + align:start position:0% +circumstances where it's a pretty good + + + align:start position:0% +circumstances where it's a pretty good +model + + align:start position:0% + + + + align:start position:0% + +so again we have g0 G+ G + + align:start position:0% + + + + align:start position:0% + +minus um let's see + + align:start position:0% + + + + align:start position:0% + +so so um again with three measurements + + align:start position:0% +so so um again with three measurements + + + align:start position:0% +so so um again with three measurements +we have just enough information to fit + + align:start position:0% +we have just enough information to fit + + + align:start position:0% +we have just enough information to fit +this model the Assumption of the model + + align:start position:0% +this model the Assumption of the model + + + align:start position:0% +this model the Assumption of the model +is that the slopes of the two lines are + + align:start position:0% +is that the slopes of the two lines are + + + align:start position:0% +is that the slopes of the two lines are +the same + + align:start position:0% +the same + + + align:start position:0% +the same +uh and then we just need to Vertical + + align:start position:0% +uh and then we just need to Vertical + + + align:start position:0% +uh and then we just need to Vertical +position and horizontal position and in + + align:start position:0% +position and horizontal position and in + + + align:start position:0% +position and horizontal position and in +this case s comes out to + + align:start position:0% +this case s comes out to + + + align:start position:0% +this case s comes out to +[Music] + + align:start position:0% + + + + align:start position:0% + +be okay and again that formula is in the + + align:start position:0% +be okay and again that formula is in the + + + align:start position:0% +be okay and again that formula is in the +in the pattern and it's pretty easy to + + align:start position:0% +in the pattern and it's pretty easy to + + + align:start position:0% +in the pattern and it's pretty easy to +to + + align:start position:0% + + + + align:start position:0% + +derive um okay so this we'll talk about + + align:start position:0% +derive um okay so this we'll talk about + + + align:start position:0% +derive um okay so this we'll talk about +this uh pattern some more um but there's + + align:start position:0% +this uh pattern some more um but there's + + + align:start position:0% +this uh pattern some more um but there's +some interesting um you know technical + + align:start position:0% +some interesting um you know technical + + + align:start position:0% +some interesting um you know technical +uh issues uh aside from + + align:start position:0% +uh issues uh aside from + + + align:start position:0% +uh issues uh aside from +the uh from the uh patent + + align:start position:0% +the uh from the uh patent + + + align:start position:0% +the uh from the uh patent +patentes uh that we'll get to uh you + + align:start position:0% +patentes uh that we'll get to uh you + + + align:start position:0% +patentes uh that we'll get to uh you +know for + + align:start position:0% +know for + + + align:start position:0% +know for +example uh one reason an edge might not + + align:start position:0% +example uh one reason an edge might not + + + align:start position:0% +example uh one reason an edge might not +be a unit step Edge is because of + + align:start position:0% +be a unit step Edge is because of + + + align:start position:0% +be a unit step Edge is because of +defocus and so the question is you know + + align:start position:0% +defocus and so the question is you know + + + align:start position:0% +defocus and so the question is you know +what is the shape of that curve because + + align:start position:0% +what is the shape of that curve because + + + align:start position:0% +what is the shape of that curve because +this whole business here we're just + + align:start position:0% +this whole business here we're just + + + align:start position:0% +this whole business here we're just +making we're making up stuff we're + + align:start position:0% +making we're making up stuff we're + + + align:start position:0% +making we're making up stuff we're +saying oh maybe it's a parabola or maybe + + align:start position:0% +saying oh maybe it's a parabola or maybe + + + align:start position:0% +saying oh maybe it's a parabola or maybe +it's a triangle uh well can't we just + + align:start position:0% +it's a triangle uh well can't we just + + + align:start position:0% +it's a triangle uh well can't we just +figure out exactly what it is uh + + align:start position:0% +figure out exactly what it is uh + + + align:start position:0% +figure out exactly what it is uh +particularly in the case of defocus we + + align:start position:0% +particularly in the case of defocus we + + + align:start position:0% +particularly in the case of defocus we +should be able to figure out just what + + align:start position:0% +should be able to figure out just what + + + align:start position:0% +should be able to figure out just what +obviously it's not going to be a step + + align:start position:0% +obviously it's not going to be a step + + + align:start position:0% +obviously it's not going to be a step +Edge anymore it's going to be smeared + + align:start position:0% +Edge anymore it's going to be smeared + + + align:start position:0% +Edge anymore it's going to be smeared +out because it's blurred it's out of + + align:start position:0% +out because it's blurred it's out of + + + align:start position:0% +out because it's blurred it's out of +focus but what what is that so we'll + + align:start position:0% +focus but what what is that so we'll + + + align:start position:0% +focus but what what is that so we'll +talk about that and um see how that + + align:start position:0% +talk about that and um see how that + + + align:start position:0% +talk about that and um see how that +affects our uh method of covering the + + align:start position:0% +affects our uh method of covering the + + + align:start position:0% +affects our uh method of covering the +actual Edge position and then we'll uh + + align:start position:0% +actual Edge position and then we'll uh + + + align:start position:0% +actual Edge position and then we'll uh +talk about some alternatives to what's + + align:start position:0% +talk about some alternatives to what's + + + align:start position:0% +talk about some alternatives to what's +in the patent um in + + align:start position:0% +in the patent um in + + + align:start position:0% +in the patent um in +particular uh you know this quantization + + align:start position:0% +particular uh you know this quantization + + + align:start position:0% +particular uh you know this quantization +of gradient direction is kind of + + align:start position:0% +of gradient direction is kind of + + + align:start position:0% +of gradient direction is kind of +problematic uh particularly on the + + align:start position:0% +problematic uh particularly on the + + + align:start position:0% +problematic uh particularly on the +Square grid where we only got eight + + align:start position:0% +Square grid where we only got eight + + + align:start position:0% +Square grid where we only got eight +directions and so we'll talk about other + + align:start position:0% +directions and so we'll talk about other + + + align:start position:0% +directions and so we'll talk about other +ways of uh proceeding that do not have + + align:start position:0% +ways of uh proceeding that do not have + + + align:start position:0% +ways of uh proceeding that do not have +that very Co quantization you know like + + align:start position:0% +that very Co quantization you know like + + + align:start position:0% +that very Co quantization you know like +here we're finding a maximum in that + + align:start position:0% +here we're finding a maximum in that + + + align:start position:0% +here we're finding a maximum in that +direction direction or in this direction + + align:start position:0% +direction direction or in this direction + + + align:start position:0% +direction direction or in this direction +but uh if the gradient is actually in + + align:start position:0% +but uh if the gradient is actually in + + + align:start position:0% +but uh if the gradient is actually in +between you know it's not anyway so so + + align:start position:0% +between you know it's not anyway so so + + + align:start position:0% +between you know it's not anyway so so +there's there's more and it seems like a + + align:start position:0% +there's there's more and it seems like a + + + align:start position:0% +there's there's more and it seems like a +very simple problem but uh it shows how + + align:start position:0% +very simple problem but uh it shows how + + + align:start position:0% +very simple problem but uh it shows how +if you want really good performance uh + + align:start position:0% +if you want really good performance uh + + + align:start position:0% +if you want really good performance uh +there are a lot of details to figure out + + align:start position:0% +there are a lot of details to figure out + + + align:start position:0% +there are a lot of details to figure out +like this business about you know what's + + align:start position:0% +like this business about you know what's + + + align:start position:0% +like this business about you know what's +a good way to compute the derivatives so + + align:start position:0% +a good way to compute the derivatives so + + + align:start position:0% +a good way to compute the derivatives so +okay \ No newline at end of file diff --git a/kpzzA_koPuk.txt b/kpzzA_koPuk.txt new file mode 100644 index 0000000000000000000000000000000000000000..6328c538dfbc026a6d03c4f6b91965562fe89e27 --- /dev/null +++ b/kpzzA_koPuk.txt @@ -0,0 +1,12280 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT + + align:start position:0% +hundreds of MIT courses visit MIT + + + align:start position:0% +hundreds of MIT courses visit MIT +opencourseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu today there are more + + align:start position:0% +ocw.mit.edu today there are more + + + align:start position:0% +ocw.mit.edu today there are more +lectur and we uh um + + align:start position:0% +lectur and we uh um + + + align:start position:0% +lectur and we uh um +um I uh guest + + align:start position:0% +um I uh guest + + + align:start position:0% +um I uh guest +lectures uh one will be on the + + align:start position:0% +lectures uh one will be on the + + + align:start position:0% +lectures uh one will be on the +reliability of the materials at high + + align:start position:0% +reliability of the materials at high + + + align:start position:0% +reliability of the materials at high +temperature + + align:start position:0% +temperature + + + align:start position:0% +temperature +this last + + align:start position:0% +this last + + + align:start position:0% +this last +lecture also have to J Around schedule + + align:start position:0% +lecture also have to J Around schedule + + + align:start position:0% +lecture also have to J Around schedule +everybody so instead of what uh I will + + align:start position:0% +everybody so instead of what uh I will + + + align:start position:0% +everybody so instead of what uh I will +do is the next Friday uh we'll be + + align:start position:0% +do is the next Friday uh we'll be + + + align:start position:0% +do is the next Friday uh we'll be +talking about the reliability of the + + align:start position:0% +talking about the reliability of the + + + align:start position:0% +talking about the reliability of the +materials um this is Professor + + align:start position:0% +materials um this is Professor + + + align:start position:0% +materials um this is Professor +Christoper in the mat + + align:start position:0% + + + + align:start position:0% + +research in this long + + align:start position:0% +research in this long + + + align:start position:0% +research in this long +time I could + + align:start position:0% +time I could + + + align:start position:0% +time I could +get and uh uh then uh on on the week + + align:start position:0% +get and uh uh then uh on on the week + + + align:start position:0% +get and uh uh then uh on on the week +after next week uh we will have Dr Avan + + align:start position:0% +after next week uh we will have Dr Avan + + + align:start position:0% +after next week uh we will have Dr Avan +sonov talk about selective surface it's + + align:start position:0% +sonov talk about selective surface it's + + + align:start position:0% +sonov talk about selective surface it's +being working on several + + align:start position:0% +being working on several + + + align:start position:0% +being working on several +phot and uh so working the spectral + + align:start position:0% +phot and uh so working the spectral + + + align:start position:0% +phot and uh so working the spectral +control + + align:start position:0% +control + + + align:start position:0% +control +area help you again better talk than + + align:start position:0% +area help you again better talk than + + + align:start position:0% +area help you again better talk than +me and then say the final lecture uh we + + align:start position:0% +me and then say the final lecture uh we + + + align:start position:0% +me and then say the final lecture uh we +will be um um uh talking come back a + + align:start position:0% +will be um um uh talking come back a + + + align:start position:0% +will be um um uh talking come back a +little bit to talk about how we combine + + align:start position:0% +little bit to talk about how we combine + + + align:start position:0% +little bit to talk about how we combine +selected surface + + align:start position:0% +selected surface + + + align:start position:0% +selected surface +with and with uh also + + align:start position:0% +with and with uh also + + + align:start position:0% +with and with uh also +phot so we have learned thcs we have + + align:start position:0% +phot so we have learned thcs we have + + + align:start position:0% +phot so we have learned thcs we have +learned uh phot + + align:start position:0% +learned uh phot + + + align:start position:0% +learned uh phot +also uh so that's a solar solid state + + align:start position:0% +also uh so that's a solar solid state + + + align:start position:0% +also uh so that's a solar solid state +solar thermal energy + + align:start position:0% +solar thermal energy + + + align:start position:0% +solar thermal energy +conversion and uh today uh what I want + + align:start position:0% +conversion and uh today uh what I want + + + align:start position:0% +conversion and uh today uh what I want +to cover is the mechanical uh energy + + align:start position:0% +to cover is the mechanical uh energy + + + align:start position:0% +to cover is the mechanical uh energy +conversion solar uh to Electric solar + + align:start position:0% +conversion solar uh to Electric solar + + + align:start position:0% +conversion solar uh to Electric solar +mechanic + + align:start position:0% +mechanic + + + align:start position:0% +mechanic +is uh so let's uh uh recall what I was + + align:start position:0% +is uh so let's uh uh recall what I was + + + align:start position:0% +is uh so let's uh uh recall what I was +talking uh in the last previous lecture + + align:start position:0% +talking uh in the last previous lecture + + + align:start position:0% +talking uh in the last previous lecture +we talked about black body rision we + + align:start position:0% +we talked about black body rision we + + + align:start position:0% +we talked about black body rision we +mentioned a little bit on the the Earth + + align:start position:0% +mentioned a little bit on the the Earth + + + align:start position:0% +mentioned a little bit on the the Earth +motion and uh how we usually test uh + + align:start position:0% +motion and uh how we usually test uh + + + align:start position:0% +motion and uh how we usually test uh +solar Spectrum uh am01 + + align:start position:0% +solar Spectrum uh am01 + + + align:start position:0% +solar Spectrum uh am01 +m1.5 Etc and then um we Define r + + align:start position:0% +m1.5 Etc and then um we Define r + + + align:start position:0% +m1.5 Etc and then um we Define r +property those definition many different + + align:start position:0% +property those definition many different + + + align:start position:0% +property those definition many different +definitions as I said uh I don't expect + + align:start position:0% +definitions as I said uh I don't expect + + + align:start position:0% +definitions as I said uh I don't expect +they you remember all those details the + + align:start position:0% +they you remember all those details the + + + align:start position:0% +they you remember all those details the +the point is for spectral control it's + + align:start position:0% +the point is for spectral control it's + + + align:start position:0% +the point is for spectral control it's +very important to understand the wence + + align:start position:0% +very important to understand the wence + + + align:start position:0% +very important to understand the wence +dependence of the properties and then + + align:start position:0% +dependence of the properties and then + + + align:start position:0% +dependence of the properties and then +with that we discuss the uh maximum + + align:start position:0% +with that we discuss the uh maximum + + + align:start position:0% +with that we discuss the uh maximum +efficiency of solar thermal engines and + + align:start position:0% +efficiency of solar thermal engines and + + + align:start position:0% +efficiency of solar thermal engines and +maximum achievable + + align:start position:0% +maximum achievable + + + align:start position:0% +maximum achievable +temperature and uh again say emphasiz + + align:start position:0% +temperature and uh again say emphasiz + + + align:start position:0% +temperature and uh again say emphasiz +the selective surface but and we don't + + align:start position:0% +the selective surface but and we don't + + + align:start position:0% +the selective surface but and we don't +know you don't know how to do it yet but + + align:start position:0% +know you don't know how to do it yet but + + + align:start position:0% +know you don't know how to do it yet but +it's + + align:start position:0% + + + + align:start position:0% + +important so uh in today's uh uh lecture + + align:start position:0% +important so uh in today's uh uh lecture + + + align:start position:0% +important so uh in today's uh uh lecture +as I said I want to cover uh really the + + align:start position:0% +as I said I want to cover uh really the + + + align:start position:0% +as I said I want to cover uh really the +solar theral mechanical part and what + + align:start position:0% +solar theral mechanical part and what + + + align:start position:0% +solar theral mechanical part and what +will start with is the hot water system + + align:start position:0% +will start with is the hot water system + + + align:start position:0% +will start with is the hot water system +solar hot water and uh then we'll talk + + align:start position:0% +solar hot water and uh then we'll talk + + + align:start position:0% +solar hot water and uh then we'll talk +about the to bring up to a higher + + align:start position:0% +about the to bring up to a higher + + + align:start position:0% +about the to bring up to a higher +temperature we'll talk about the uh + + align:start position:0% +temperature we'll talk about the uh + + + align:start position:0% +temperature we'll talk about the uh +solar + + align:start position:0% +solar + + + align:start position:0% +solar +concentration and uh we talk about the + + align:start position:0% +concentration and uh we talk about the + + + align:start position:0% +concentration and uh we talk about the +maximum how much you can concentrate + + align:start position:0% +maximum how much you can concentrate + + + align:start position:0% +maximum how much you can concentrate +this solar radiation and then uh we look + + align:start position:0% +this solar radiation and then uh we look + + + align:start position:0% +this solar radiation and then uh we look +at how you could in Practical uh uh to + + align:start position:0% +at how you could in Practical uh uh to + + + align:start position:0% +at how you could in Practical uh uh to +do different ways of + + align:start position:0% +do different ways of + + + align:start position:0% +do different ways of +concentration and to do concentration + + align:start position:0% +concentration and to do concentration + + + align:start position:0% +concentration and to do concentration +you'll need to track the sun that's one + + align:start position:0% +you'll need to track the sun that's one + + + align:start position:0% +you'll need to track the sun that's one +of the problem Challenge and so I'll + + align:start position:0% +of the problem Challenge and so I'll + + + align:start position:0% +of the problem Challenge and so I'll +talk a little bit tracking long tracking + + align:start position:0% +talk a little bit tracking long tracking + + + align:start position:0% +talk a little bit tracking long tracking +and then I'll go to sort mechan if I + + align:start position:0% +and then I'll go to sort mechan if I + + + align:start position:0% +and then I'll go to sort mechan if I +have enough time I'll start a little bit + + align:start position:0% +have enough time I'll start a little bit + + + align:start position:0% +have enough time I'll start a little bit +I give you a preview of what control the + + align:start position:0% +I give you a preview of what control the + + + align:start position:0% +I give you a preview of what control the +surface properties + + align:start position:0% +surface properties + + + align:start position:0% +surface properties +uhne + + align:start position:0% +uhne + + + align:start position:0% +uhne +W + + align:start position:0% +W + + + align:start position:0% +W +um so s how water right uh it's very M + + align:start position:0% +um so s how water right uh it's very M + + + align:start position:0% +um so s how water right uh it's very M +but I I really appreciate this as + + align:start position:0% +but I I really appreciate this as + + + align:start position:0% +but I I really appreciate this as +probably mentioned before when I was a + + align:start position:0% +probably mentioned before when I was a + + + align:start position:0% +probably mentioned before when I was a +kid uh I grew up in China didn't have + + align:start position:0% +kid uh I grew up in China didn't have + + + align:start position:0% +kid uh I grew up in China didn't have +chance to take a half shower and now + + align:start position:0% +chance to take a half shower and now + + + align:start position:0% +chance to take a half shower and now +when I go back to my parents this in + + align:start position:0% +when I go back to my parents this in + + + align:start position:0% +when I go back to my parents this in +China and and they use solar + + align:start position:0% +China and and they use solar + + + align:start position:0% +China and and they use solar +power uh uh concept of course is very + + align:start position:0% +power uh uh concept of course is very + + + align:start position:0% +power uh uh concept of course is very +simple uh solar collector you absorb the + + align:start position:0% +simple uh solar collector you absorb the + + + align:start position:0% +simple uh solar collector you absorb the +solar radiation and you heat up the + + align:start position:0% +solar radiation and you heat up the + + + align:start position:0% +solar radiation and you heat up the +water um very simple concept right and + + align:start position:0% +water um very simple concept right and + + + align:start position:0% +water um very simple concept right and +also uh I want to give you a very simple + + align:start position:0% +also uh I want to give you a very simple + + + align:start position:0% +also uh I want to give you a very simple +uh backup Im so if you're mechanical + + align:start position:0% +uh backup Im so if you're mechanical + + + align:start position:0% +uh backup Im so if you're mechanical +engineer this will be pretty easy but uh + + align:start position:0% +engineer this will be pretty easy but uh + + + align:start position:0% +engineer this will be pretty easy but uh +I did this for the preparation of the + + align:start position:0% +I did this for the preparation of the + + + align:start position:0% +I did this for the preparation of the +class also out of my own curiosity uh + + align:start position:0% +class also out of my own curiosity uh + + + align:start position:0% +class also out of my own curiosity uh +first year from materal this probably a + + align:start position:0% +first year from materal this probably a + + + align:start position:0% +first year from materal this probably a +little bit more more uh say not not very + + align:start position:0% +little bit more more uh say not not very + + + align:start position:0% +little bit more more uh say not not very +familiar with you but uh it's a simple + + align:start position:0% +familiar with you but uh it's a simple + + + align:start position:0% +familiar with you but uh it's a simple +energy balance so what I want to ask is + + align:start position:0% +energy balance so what I want to ask is + + + align:start position:0% +energy balance so what I want to ask is +how much if I want to put in my uh own + + align:start position:0% +how much if I want to put in my uh own + + + align:start position:0% +how much if I want to put in my uh own +house uh how what's the area I live + + align:start position:0% +house uh how what's the area I live + + + align:start position:0% +house uh how what's the area I live +right solar H water and uh typical + + align:start position:0% +right solar H water and uh typical + + + align:start position:0% +right solar H water and uh typical +household uh water tank is about 80 + + align:start position:0% +household uh water tank is about 80 + + + align:start position:0% +household uh water tank is about 80 +gallon it's pretty it's a larger house + + align:start position:0% +gallon it's pretty it's a larger house + + + align:start position:0% +gallon it's pretty it's a larger house +if you have smaller so ring from 40 to + + align:start position:0% +if you have smaller so ring from 40 to + + + align:start position:0% +if you have smaller so ring from 40 to +100 gon I guess and uh if I take a St + + align:start position:0% +100 gon I guess and uh if I take a St + + + align:start position:0% +100 gon I guess and uh if I take a St +temperature of water at + + align:start position:0% +temperature of water at + + + align:start position:0% +temperature of water at +15° and I want to keep the water tank at + + align:start position:0% +15° and I want to keep the water tank at + + + align:start position:0% +15° and I want to keep the water tank at +60° C so during a day right let's + + align:start position:0% +60° C so during a day right let's + + + align:start position:0% +60° C so during a day right let's +suppose I deplete all the hot water + + align:start position:0% +suppose I deplete all the hot water + + + align:start position:0% +suppose I deplete all the hot water +during the night and uh I want to store + + align:start position:0% +during the night and uh I want to store + + + align:start position:0% +during the night and uh I want to store +80 during day I want to heat up the + + align:start position:0% +80 during day I want to heat up the + + + align:start position:0% +80 during day I want to heat up the +water from 15° to uh to + + align:start position:0% +water from 15° to uh to + + + align:start position:0% +water from 15° to uh to +60° and uh it's a it's a so so you you + + align:start position:0% +60° and uh it's a it's a so so you you + + + align:start position:0% +60° and uh it's a it's a so so you you +you want to say how much what's this + + align:start position:0% +you want to say how much what's this + + + align:start position:0% +you want to say how much what's this +solar surface area how water surface + + align:start position:0% +solar surface area how water surface + + + align:start position:0% +solar surface area how water surface +area you want and it's simple energy + + align:start position:0% +area you want and it's simple energy + + + align:start position:0% +area you want and it's simple energy +balance right during the day how much + + align:start position:0% +balance right during the day how much + + + align:start position:0% +balance right during the day how much +solar radiation reset and then of course + + align:start position:0% +solar radiation reset and then of course + + + align:start position:0% +solar radiation reset and then of course +you consider efficiency of the + + align:start position:0% +you consider efficiency of the + + + align:start position:0% +you consider efficiency of the +absorber and then that balance the to + + align:start position:0% +absorber and then that balance the to + + + align:start position:0% +absorber and then that balance the to +heat up this much water how much energy + + align:start position:0% +heat up this much water how much energy + + + align:start position:0% +heat up this much water how much energy +you need so you do that energy balance + + align:start position:0% +you need so you do that energy balance + + + align:start position:0% +you need so you do that energy balance +the the area that what I want the solar + + align:start position:0% +the the area that what I want the solar + + + align:start position:0% +the the area that what I want the solar +radiation uh + + align:start position:0% +radiation uh + + + align:start position:0% +radiation uh +insulation uh and uh time of the day + + align:start position:0% +insulation uh and uh time of the day + + + align:start position:0% +insulation uh and uh time of the day +efficiency and equals the uh heat + + align:start position:0% +efficiency and equals the uh heat + + + align:start position:0% +efficiency and equals the uh heat +capacity that's stored in the hot water + + align:start position:0% +capacity that's stored in the hot water + + + align:start position:0% +capacity that's stored in the hot water +so I put in those lbers typically when + + align:start position:0% +so I put in those lbers typically when + + + align:start position:0% +so I put in those lbers typically when +people calculate uh you can see it's a + + align:start position:0% +people calculate uh you can see it's a + + + align:start position:0% +people calculate uh you can see it's a +little bit + + align:start position:0% +little bit + + + align:start position:0% +little bit +optimistic if you live in Boston you + + align:start position:0% +optimistic if you live in Boston you + + + align:start position:0% +optimistic if you live in Boston you +don't get a s wat okay and uh I took a a + + align:start position:0% +don't get a s wat okay and uh I took a a + + + align:start position:0% +don't get a s wat okay and uh I took a a +standard calculation sou one 5.5 hour so + + align:start position:0% +standard calculation sou one 5.5 hour so + + + align:start position:0% +standard calculation sou one 5.5 hour so +that's a average say uh uh the whole day + + align:start position:0% +that's a average say uh uh the whole day + + + align:start position:0% +that's a average say uh uh the whole day +average typical that's what people take + + align:start position:0% +average typical that's what people take + + + align:start position:0% +average typical that's what people take +when they test the solar cell s when + + align:start position:0% +when they test the solar cell s when + + + align:start position:0% +when they test the solar cell s when +they calculate solar cell output and + + align:start position:0% +they calculate solar cell output and + + + align:start position:0% +they calculate solar cell output and +efficiency of SAR thermal hot water + + align:start position:0% +efficiency of SAR thermal hot water + + + align:start position:0% +efficiency of SAR thermal hot water +system uh ranging from I'll tell you how + + align:start position:0% +system uh ranging from I'll tell you how + + + align:start position:0% +system uh ranging from I'll tell you how +to estimate efficiency but I take a + + align:start position:0% +to estimate efficiency but I take a + + + align:start position:0% +to estimate efficiency but I take a +typical L + + align:start position:0% +typical L + + + align:start position:0% +typical L +60% okay so I need a 5 + + align:start position:0% +60% okay so I need a 5 + + + align:start position:0% +60% okay so I need a 5 +m + + align:start position:0% +m + + + align:start position:0% +m +here and uh uh in China I know it's very + + align:start position:0% +here and uh uh in China I know it's very + + + align:start position:0% +here and uh uh in China I know it's very +cheap and typically people install + + align:start position:0% +cheap and typically people install + + + align:start position:0% +cheap and typically people install +somewhere 1.5 2 meters so it's a lot + + align:start position:0% +somewhere 1.5 2 meters so it's a lot + + + align:start position:0% +somewhere 1.5 2 meters so it's a lot +very big tank most people live in + + align:start position:0% +very big tank most people live in + + + align:start position:0% +very big tank most people live in +apartment and they use less + + align:start position:0% + + + + align:start position:0% + +water okay uh in terms solar hot water + + align:start position:0% +water okay uh in terms solar hot water + + + align:start position:0% +water okay uh in terms solar hot water +there different form form uh format uh + + align:start position:0% +there different form form uh format uh + + + align:start position:0% +there different form form uh format uh +one uh of the format is a flat + + align:start position:0% +one uh of the format is a flat + + + align:start position:0% +one uh of the format is a flat +panel right so here we have what we have + + align:start position:0% +panel right so here we have what we have + + + align:start position:0% +panel right so here we have what we have +is the absorber + + align:start position:0% +is the absorber + + + align:start position:0% +is the absorber +that's uh uh typically is a frequency + + align:start position:0% +that's uh uh typically is a frequency + + + align:start position:0% +that's uh uh typically is a frequency +selected meaning they absorb solar + + align:start position:0% +selected meaning they absorb solar + + + align:start position:0% +selected meaning they absorb solar +radiation but do not or you want Reit a + + align:start position:0% +radiation but do not or you want Reit a + + + align:start position:0% +radiation but do not or you want Reit a +very small amount of theral emission + + align:start position:0% +very small amount of theral emission + + + align:start position:0% +very small amount of theral emission +when it hits up and so you can say the + + align:start position:0% +when it hits up and so you can say the + + + align:start position:0% +when it hits up and so you can say the +back side is insulation and this is + + align:start position:0% +back side is insulation and this is + + + align:start position:0% +back side is insulation and this is +absorber tube could be on top or on the + + align:start position:0% +absorber tube could be on top or on the + + + align:start position:0% +absorber tube could be on top or on the +bottom and typically they do not so in + + align:start position:0% +bottom and typically they do not so in + + + align:start position:0% +bottom and typically they do not so in +between is the + + align:start position:0% +between is the + + + align:start position:0% +between is the +air okay and uh uh uh the tank could be + + align:start position:0% +air okay and uh uh uh the tank could be + + + align:start position:0% +air okay and uh uh uh the tank could be +on the top of theber itself so in that + + align:start position:0% +on the top of theber itself so in that + + + align:start position:0% +on the top of theber itself so in that +case uh you don't put a tank uh in the + + align:start position:0% +case uh you don't put a tank uh in the + + + align:start position:0% +case uh you don't put a tank uh in the +basement and uh you can use the gravity + + align:start position:0% +basement and uh you can use the gravity + + + align:start position:0% +basement and uh you can use the gravity +of the water uh to drive the water flow + + align:start position:0% +of the water uh to drive the water flow + + + align:start position:0% +of the water uh to drive the water flow +to drive the hot water down let say the + + align:start position:0% +to drive the hot water down let say the + + + align:start position:0% +to drive the hot water down let say the +problem is your water flu rate is lot + + align:start position:0% +problem is your water flu rate is lot + + + align:start position:0% +problem is your water flu rate is lot +depends on how high you put the tank so + + align:start position:0% +depends on how high you put the tank so + + + align:start position:0% +depends on how high you put the tank so +if you live a low low buildings uh your + + align:start position:0% +if you live a low low buildings uh your + + + align:start position:0% +if you live a low low buildings uh your +uh your pressure is + + align:start position:0% +uh your pressure is + + + align:start position:0% +uh your pressure is +no uh + + align:start position:0% +no uh + + + align:start position:0% +no uh +and uh this is the example clearly war + + align:start position:0% +and uh this is the example clearly war + + + align:start position:0% +and uh this is the example clearly war +tank is not on the roof it's in the + + align:start position:0% +tank is not on the roof it's in the + + + align:start position:0% +tank is not on the roof it's in the +basement and in that case you use a pump + + align:start position:0% +basement and in that case you use a pump + + + align:start position:0% +basement and in that case you use a pump +to pump the water so it's a pressurized + + align:start position:0% +to pump the water so it's a pressurized + + + align:start position:0% +to pump the water so it's a pressurized +system so they're pressurized and this + + align:start position:0% +system so they're pressurized and this + + + align:start position:0% +system so they're pressurized and this +one is uh uh not force force system just + + align:start position:0% +one is uh uh not force force system just + + + align:start position:0% +one is uh uh not force force system just +natural and the one that's uh uh uh what + + align:start position:0% +natural and the one that's uh uh uh what + + + align:start position:0% +natural and the one that's uh uh uh what +I thought really uh interesting is this + + align:start position:0% +I thought really uh interesting is this + + + align:start position:0% +I thought really uh interesting is this +uh vacuum system + + align:start position:0% +uh vacuum system + + + align:start position:0% +uh vacuum system +and uh uh this is a this is a prominant + + align:start position:0% +and uh uh this is a this is a prominant + + + align:start position:0% +and uh uh this is a this is a prominant +used in China and uh uh it's a glass so + + align:start position:0% +used in China and uh uh it's a glass so + + + align:start position:0% +used in China and uh uh it's a glass so +it's a double layer glass inside uh is a + + align:start position:0% +it's a double layer glass inside uh is a + + + align:start position:0% +it's a double layer glass inside uh is a +black Co what looks black is actually + + align:start position:0% +black Co what looks black is actually + + + align:start position:0% +black Co what looks black is actually +inside outside is another glass clear + + align:start position:0% +inside outside is another glass clear + + + align:start position:0% +inside outside is another glass clear +glass so it's a circular and the inside + + align:start position:0% +glass so it's a circular and the inside + + + align:start position:0% +glass so it's a circular and the inside +glass is First Co with Selective + + align:start position:0% +glass is First Co with Selective + + + align:start position:0% +glass is First Co with Selective +surface and then you see all you + + align:start position:0% +surface and then you see all you + + + align:start position:0% +surface and then you see all you +evacuate it you see on the other side so + + align:start position:0% +evacuate it you see on the other side so + + + align:start position:0% +evacuate it you see on the other side so +it's a it's a it's a H jacket and uh in + + align:start position:0% +it's a it's a it's a H jacket and uh in + + + align:start position:0% +it's a it's a it's a H jacket and uh in +on this side because the vacuum so it + + align:start position:0% +on this side because the vacuum so it + + + align:start position:0% +on this side because the vacuum so it +has a g um the G what what does g do is + + align:start position:0% +has a g um the G what what does g do is + + + align:start position:0% +has a g um the G what what does g do is +say the + + align:start position:0% +say the + + + align:start position:0% +say the +evaporation is actually collected by + + align:start position:0% +evaporation is actually collected by + + + align:start position:0% +evaporation is actually collected by +this metal reactive is whatever + + align:start position:0% +this metal reactive is whatever + + + align:start position:0% +this metal reactive is whatever +evaporates and uh uh uh so you you would + + align:start position:0% +evaporates and uh uh uh so you you would + + + align:start position:0% +evaporates and uh uh uh so you you would +imagine so putting vacuum under s how + + align:start position:0% +imagine so putting vacuum under s how + + + align:start position:0% +imagine so putting vacuum under s how +long last and I actually with the Su of + + align:start position:0% +long last and I actually with the Su of + + + align:start position:0% +long last and I actually with the Su of +this I say uh the + + align:start position:0% +this I say uh the + + + align:start position:0% +this I say uh the +the + + align:start position:0% +the + + + align:start position:0% +the +Father the father of this technology in + + align:start position:0% +Father the father of this technology in + + + align:start position:0% +Father the father of this technology in +China and he said that he put this stuff + + align:start position:0% +China and he said that he put this stuff + + + align:start position:0% +China and he said that he put this stuff +early in the 90s in in chinua he from + + align:start position:0% +early in the 90s in in chinua he from + + + align:start position:0% +early in the 90s in in chinua he from +chinua University and uh and still + + align:start position:0% +chinua University and uh and still + + + align:start position:0% +chinua University and uh and still +working so after 20 years and that's uh + + align:start position:0% +working so after 20 years and that's uh + + + align:start position:0% +working so after 20 years and that's uh +considerable considerable because if you + + align:start position:0% +considerable considerable because if you + + + align:start position:0% +considerable considerable because if you +think about in my house I bought a TV I + + align:start position:0% +think about in my house I bought a TV I + + + align:start position:0% +think about in my house I bought a TV I +remember I first uh my first T is still + + align:start position:0% +remember I first uh my first T is still + + + align:start position:0% +remember I first uh my first T is still +working about more than 20 years and + + align:start position:0% +working about more than 20 years and + + + align:start position:0% +working about more than 20 years and +that's a CR it's a vacuum technology + + align:start position:0% +that's a CR it's a vacuum technology + + + align:start position:0% +that's a CR it's a vacuum technology +right see the screen of the TV uh say + + align:start position:0% +right see the screen of the TV uh say + + + align:start position:0% +right see the screen of the TV uh say +the uh tax R inside is actually Ultra + + align:start position:0% +the uh tax R inside is actually Ultra + + + align:start position:0% +the uh tax R inside is actually Ultra +hyd so uh the vacuum is pretty high and + + align:start position:0% +hyd so uh the vacuum is pretty high and + + + align:start position:0% +hyd so uh the vacuum is pretty high and +you can uh uh do a calculation find why + + align:start position:0% +you can uh uh do a calculation find why + + + align:start position:0% +you can uh uh do a calculation find why +if the vacuum is too low the air + + align:start position:0% +if the vacuum is too low the air + + + align:start position:0% +if the vacuum is too low the air +conduction Mak too much + + align:start position:0% +conduction Mak too much + + + align:start position:0% +conduction Mak too much +here and so this is a Evacuate the + + align:start position:0% +here and so this is a Evacuate the + + + align:start position:0% +here and so this is a Evacuate the +tube uh that glass this glass is really + + align:start position:0% +tube uh that glass this glass is really + + + align:start position:0% +tube uh that glass this glass is really +cheap I with the say the manufacturing + + align:start position:0% +cheap I with the say the manufacturing + + + align:start position:0% +cheap I with the say the manufacturing +s and uh uh the whole tube is about this + + align:start position:0% +s and uh uh the whole tube is about this + + + align:start position:0% +s and uh uh the whole tube is about this +Tye uh the diameter is a 50 mm and the + + align:start position:0% +Tye uh the diameter is a 50 mm and the + + + align:start position:0% +Tye uh the diameter is a 50 mm and the +manufacturer the double glass tube is + + align:start position:0% +manufacturer the double glass tube is + + + align:start position:0% +manufacturer the double glass tube is +about $1.5 per tube so really + + align:start position:0% +about $1.5 per tube so really + + + align:start position:0% +about $1.5 per tube so really +cheap uh this one is a little more + + align:start position:0% +cheap uh this one is a little more + + + align:start position:0% +cheap uh this one is a little more +expensive uh it's not a glass glass and + + align:start position:0% +expensive uh it's not a glass glass and + + + align:start position:0% +expensive uh it's not a glass glass and +what it has is a metal + + align:start position:0% +what it has is a metal + + + align:start position:0% +what it has is a metal +absorber uh so it's a uh + + align:start position:0% +absorber uh so it's a uh + + + align:start position:0% +absorber uh so it's a uh +it could be a copper or aluminum again + + align:start position:0% +it could be a copper or aluminum again + + + align:start position:0% +it could be a copper or aluminum again +this is a cost right this is really the + + align:start position:0% +this is a cost right this is really the + + + align:start position:0% +this is a cost right this is really the +see the cost is a Cru here and uh this + + align:start position:0% +see the cost is a Cru here and uh this + + + align:start position:0% +see the cost is a Cru here and uh this +is selective absorptive codent + + align:start position:0% +is selective absorptive codent + + + align:start position:0% +is selective absorptive codent +again and uh so what it does is this is + + align:start position:0% +again and uh so what it does is this is + + + align:start position:0% +again and uh so what it does is this is +a heat pipe so the heat absorb conducts + + align:start position:0% +a heat pipe so the heat absorb conducts + + + align:start position:0% +a heat pipe so the heat absorb conducts +to the heat heat pipe so heat pipe is + + align:start position:0% +to the heat heat pipe so heat pipe is + + + align:start position:0% +to the heat heat pipe so heat pipe is +diameter is not this big that's too much + + align:start position:0% +diameter is not this big that's too much + + + align:start position:0% +diameter is not this big that's too much +copper right it's a small diameter pipe + + align:start position:0% +copper right it's a small diameter pipe + + + align:start position:0% +copper right it's a small diameter pipe +and so the heat is evaporate the liquid + + align:start position:0% +and so the heat is evaporate the liquid + + + align:start position:0% +and so the heat is evaporate the liquid +inside the pipe heat pipe and on this + + align:start position:0% +inside the pipe heat pipe and on this + + + align:start position:0% +inside the pipe heat pipe and on this +side you have Force water heat exchanger + + align:start position:0% +side you have Force water heat exchanger + + + align:start position:0% +side you have Force water heat exchanger +Force water take the heat + + align:start position:0% + + + + align:start position:0% + +away so this is a uh the uh one of the + + align:start position:0% +away so this is a uh the uh one of the + + + align:start position:0% +away so this is a uh the uh one of the +chip form + + align:start position:0% +chip form + + + align:start position:0% +chip form +unpressurized um uh so what it has is + + align:start position:0% +unpressurized um uh so what it has is + + + align:start position:0% +unpressurized um uh so what it has is +the Double Glass layer you fill the + + align:start position:0% +the Double Glass layer you fill the + + + align:start position:0% +the Double Glass layer you fill the +glass in inside glass with water I go + + align:start position:0% +glass in inside glass with water I go + + + align:start position:0% +glass in inside glass with water I go +back here + + align:start position:0% +back here + + + align:start position:0% +back here +inside right this is empty so you fill + + align:start position:0% +inside right this is empty so you fill + + + align:start position:0% +inside right this is empty so you fill +with water and when it heats up natural + + align:start position:0% +with water and when it heats up natural + + + align:start position:0% +with water and when it heats up natural +convention so the hot water goes up here + + align:start position:0% +convention so the hot water goes up here + + + align:start position:0% +convention so the hot water goes up here +and the cold water flows down so there's + + align:start position:0% +and the cold water flows down so there's + + + align:start position:0% +and the cold water flows down so there's +no it's a passive system no no pump at + + align:start position:0% +no it's a passive system no no pump at + + + align:start position:0% +no it's a passive system no no pump at +all and you put on the roof and uh then + + align:start position:0% +all and you put on the roof and uh then + + + align:start position:0% +all and you put on the roof and uh then +you can take a shower uh so that's a a + + align:start position:0% +you can take a shower uh so that's a a + + + align:start position:0% +you can take a shower uh so that's a a +typical family uh in China probably + + align:start position:0% +typical family uh in China probably + + + align:start position:0% +typical family uh in China probably +isuse about 15 to + + align:start position:0% +isuse about 15 to + + + align:start position:0% +isuse about 15 to +uh and this one is a force pressure + + align:start position:0% +uh and this one is a force pressure + + + align:start position:0% +uh and this one is a force pressure +right you put a separate tank you put a + + align:start position:0% +right you put a separate tank you put a + + + align:start position:0% +right you put a separate tank you put a +pump on through and force at the + + align:start position:0% +pump on through and force at the + + + align:start position:0% +pump on through and force at the +end okay so that's the uh uh how the + + align:start position:0% +end okay so that's the uh uh how the + + + align:start position:0% +end okay so that's the uh uh how the +what the system looks like again out of + + align:start position:0% +what the system looks like again out of + + + align:start position:0% +what the system looks like again out of +my own curiosity I say okay I'm going to + + align:start position:0% +my own curiosity I say okay I'm going to + + + align:start position:0% +my own curiosity I say okay I'm going to +estimate what's the efficiency uh of the + + align:start position:0% +estimate what's the efficiency uh of the + + + align:start position:0% +estimate what's the efficiency uh of the +system flat panel and the vacuum systems + + align:start position:0% +system flat panel and the vacuum systems + + + align:start position:0% +system flat panel and the vacuum systems +so this is a vacum a model for vacum + + align:start position:0% +so this is a vacum a model for vacum + + + align:start position:0% +so this is a vacum a model for vacum +system where I have a cylinder in inside + + align:start position:0% +system where I have a cylinder in inside + + + align:start position:0% +system where I have a cylinder in inside +is a cylinder inner cylinder so this + + align:start position:0% +is a cylinder inner cylinder so this + + + align:start position:0% +is a cylinder inner cylinder so this +cylinder uh there is one uh so actually + + align:start position:0% +cylinder uh there is one uh so actually + + + align:start position:0% +cylinder uh there is one uh so actually +this is a self tracking right no matter + + align:start position:0% +this is a self tracking right no matter + + + align:start position:0% +this is a self tracking right no matter +what Sun direction is the there's always + + align:start position:0% +what Sun direction is the there's always + + + align:start position:0% +what Sun direction is the there's always +side wall uh is is facing the + + align:start position:0% +side wall uh is is facing the + + + align:start position:0% +side wall uh is is facing the +perpendicular to this side so this is a + + align:start position:0% +perpendicular to this side so this is a + + + align:start position:0% +perpendicular to this side so this is a +have this does have some Advantage there + + align:start position:0% +have this does have some Advantage there + + + align:start position:0% +have this does have some Advantage there +in fact there's a uh startup company + + align:start position:0% +in fact there's a uh startup company + + + align:start position:0% +in fact there's a uh startup company +called cindra + + align:start position:0% +called cindra + + + align:start position:0% +called cindra +and they are putting solar + + align:start position:0% +and they are putting solar + + + align:start position:0% +and they are putting solar +cells like this so Circle along the + + align:start position:0% +cells like this so Circle along the + + + align:start position:0% +cells like this so Circle along the +circle of the + + align:start position:0% +circle of the + + + align:start position:0% +circle of the +cylinder and + + align:start position:0% +cylinder and + + + align:start position:0% +cylinder and +uh uh it's vacuum in between so uh + + align:start position:0% +uh uh it's vacuum in between so uh + + + align:start position:0% +uh uh it's vacuum in between so uh +incoming solar radiation uh is just the + + align:start position:0% +incoming solar radiation uh is just the + + + align:start position:0% +incoming solar radiation uh is just the +cross-section area uh that's I come the + + align:start position:0% +cross-section area uh that's I come the + + + align:start position:0% +cross-section area uh that's I come the +outer diameter and say the uh the um uh + + align:start position:0% +outer diameter and say the uh the um uh + + + align:start position:0% +outer diameter and say the uh the um uh +insulation solar insulation + + align:start position:0% +insulation solar insulation + + + align:start position:0% +insulation solar insulation +so absorbed how much is absorbed uh in + + align:start position:0% +so absorbed how much is absorbed uh in + + + align:start position:0% +so absorbed how much is absorbed uh in +terms of absorption the first thing you + + align:start position:0% +terms of absorption the first thing you + + + align:start position:0% +terms of absorption the first thing you +have to go through is the outer glass + + align:start position:0% +have to go through is the outer glass + + + align:start position:0% +have to go through is the outer glass +layer so that's a + + align:start position:0% +layer so that's a + + + align:start position:0% +layer so that's a +transmissivity p and + + align:start position:0% +transmissivity p and + + + align:start position:0% +transmissivity p and +then uh inside uh the surface is absorb + + align:start position:0% +then uh inside uh the surface is absorb + + + align:start position:0% +then uh inside uh the surface is absorb +Alpha is the absorptivity so that's + + align:start position:0% +Alpha is the absorptivity so that's + + + align:start position:0% +Alpha is the absorptivity so that's +absorptivity to solar + + align:start position:0% + + + + align:start position:0% + +radiation now this is a disadvantage + + align:start position:0% +radiation now this is a disadvantage + + + align:start position:0% +radiation now this is a disadvantage +here the radiation lws + + align:start position:0% +here the radiation lws + + + align:start position:0% +here the radiation lws +right uh radiation loss because the + + align:start position:0% +right uh radiation loss because the + + + align:start position:0% +right uh radiation loss because the +whole inner tube is absor uh is heated + + align:start position:0% +whole inner tube is absor uh is heated + + + align:start position:0% +whole inner tube is absor uh is heated +up so the surface area is actually the + + align:start position:0% +up so the surface area is actually the + + + align:start position:0% +up so the surface area is actually the +pi times the inner diameter is not just + + align:start position:0% +pi times the inner diameter is not just + + + align:start position:0% +pi times the inner diameter is not just +the cross-section flat compared to Flat + + align:start position:0% +the cross-section flat compared to Flat + + + align:start position:0% +the cross-section flat compared to Flat +is only uh uh the the flat area now is + + align:start position:0% +is only uh uh the the flat area now is + + + align:start position:0% +is only uh uh the the flat area now is +the whole surface area and then that's + + align:start position:0% +the whole surface area and then that's + + + align:start position:0% +the whole surface area and then that's +theity and uh I do a BL body uh simple + + align:start position:0% +theity and uh I do a BL body uh simple + + + align:start position:0% +theity and uh I do a BL body uh simple +BL body calculation the uh surface so + + align:start position:0% +BL body calculation the uh surface so + + + align:start position:0% +BL body calculation the uh surface so +what I did not consider is multiple + + align:start position:0% +what I did not consider is multiple + + + align:start position:0% +what I did not consider is multiple +reflection this surface emission I just + + align:start position:0% +reflection this surface emission I just + + + align:start position:0% +reflection this surface emission I just +say okay everything goes to the + + align:start position:0% +say okay everything goes to the + + + align:start position:0% +say okay everything goes to the +environment and in reality the some of + + align:start position:0% +environment and in reality the some of + + + align:start position:0% +environment and in reality the some of +this cannot go in fact the glass we TR + + align:start position:0% +this cannot go in fact the glass we TR + + + align:start position:0% +this cannot go in fact the glass we TR +some of the radiation + + align:start position:0% +some of the radiation + + + align:start position:0% +some of the radiation +back reflection and also uh the uh + + align:start position:0% +back reflection and also uh the uh + + + align:start position:0% +back reflection and also uh the uh +glasses non transparent in certain W + + align:start position:0% +glasses non transparent in certain W + + + align:start position:0% +glasses non transparent in certain W +range so with that I can say this is the + + align:start position:0% +range so with that I can say this is the + + + align:start position:0% +range so with that I can say this is the +absorbed radiation min + + align:start position:0% +absorbed radiation min + + + align:start position:0% +absorbed radiation min +the that differen is what I actually get + + align:start position:0% +the that differen is what I actually get + + + align:start position:0% +the that differen is what I actually get +into the hard time and then divided by + + align:start position:0% +into the hard time and then divided by + + + align:start position:0% +into the hard time and then divided by +what comes in so have my efficiency so + + align:start position:0% +what comes in so have my efficiency so + + + align:start position:0% +what comes in so have my efficiency so +this is a simple again backup envelope + + align:start position:0% +this is a simple again backup envelope + + + align:start position:0% +this is a simple again backup envelope +okay for + + align:start position:0% +okay for + + + align:start position:0% +okay for +fun yes question so the tube is pretty + + align:start position:0% +fun yes question so the tube is pretty + + + align:start position:0% +fun yes question so the tube is pretty +large I think the only half the total + + align:start position:0% +large I think the only half the total + + + align:start position:0% +large I think the only half the total +surface that's + + align:start position:0% + + + + align:start position:0% + +that's 100 right this cross-section area + + align:start position:0% +that's 100 right this cross-section area + + + align:start position:0% +that's 100 right this cross-section area +but the emission is pi D so that's a + + align:start position:0% +but the emission is pi D so that's a + + + align:start position:0% +but the emission is pi D so that's a +disadvantage + + align:start position:0% + + + + align:start position:0% + +okay and so that's that that's analy + + align:start position:0% +okay and so that's that that's analy + + + align:start position:0% +okay and so that's that that's analy +I'll show you the curve later on now I'm + + align:start position:0% +I'll show you the curve later on now I'm + + + align:start position:0% +I'll show you the curve later on now I'm +going to look at the hot water flat + + align:start position:0% +going to look at the hot water flat + + + align:start position:0% +going to look at the hot water flat +panel type so our flat panel type in + + align:start position:0% +panel type so our flat panel type in + + + align:start position:0% +panel type so our flat panel type in +between the + + align:start position:0% +between the + + + align:start position:0% +between the +air I was actually curious whether + + align:start position:0% +air I was actually curious whether + + + align:start position:0% +air I was actually curious whether +people use double glaze uh windows on + + align:start position:0% +people use double glaze uh windows on + + + align:start position:0% +people use double glaze uh windows on +here or not and what I found since they + + align:start position:0% +here or not and what I found since they + + + align:start position:0% +here or not and what I found since they +do not use it so it's just a uh uh one + + align:start position:0% +do not use it so it's just a uh uh one + + + align:start position:0% +do not use it so it's just a uh uh one +layer of glass so this is the + + align:start position:0% +layer of glass so this is the + + + align:start position:0% +layer of glass so this is the +air and uh selective surface uh and of + + align:start position:0% +air and uh selective surface uh and of + + + align:start position:0% +air and uh selective surface uh and of +course what you think about heat + + align:start position:0% +course what you think about heat + + + align:start position:0% +course what you think about heat +transfer this absorb solar radiation and + + align:start position:0% +transfer this absorb solar radiation and + + + align:start position:0% +transfer this absorb solar radiation and +then will conduct through the air + + align:start position:0% +then will conduct through the air + + + align:start position:0% +then will conduct through the air +conduct through glass and outside is + + align:start position:0% +conduct through glass and outside is + + + align:start position:0% +conduct through glass and outside is +electrial convetion so you have the + + align:start position:0% +electrial convetion so you have the + + + align:start position:0% +electrial convetion so you have the +uh uh resistance in series conduction + + align:start position:0% +uh uh resistance in series conduction + + + align:start position:0% +uh uh resistance in series conduction +air conduction resistance glass + + align:start position:0% +air conduction resistance glass + + + align:start position:0% +air conduction resistance glass +resistance convetion resistance so + + align:start position:0% +resistance convetion resistance so + + + align:start position:0% +resistance convetion resistance so +that's one part of the heat uh through + + align:start position:0% +that's one part of the heat uh through + + + align:start position:0% +that's one part of the heat uh through +conduction and conention and back side + + align:start position:0% +conduction and conention and back side + + + align:start position:0% +conduction and conention and back side +the thermal insulation can still leak he + + align:start position:0% +the thermal insulation can still leak he + + + align:start position:0% +the thermal insulation can still leak he +so back side I have a conduction and + + align:start position:0% +so back side I have a conduction and + + + align:start position:0% +so back side I have a conduction and +then I have re radiation goes through + + align:start position:0% +then I have re radiation goes through + + + align:start position:0% +then I have re radiation goes through +directly so I have three parts for the + + align:start position:0% +directly so I have three parts for the + + + align:start position:0% +directly so I have three parts for the +heat transfer and this is a my simple + + align:start position:0% +heat transfer and this is a my simple + + + align:start position:0% +heat transfer and this is a my simple +circuit the solar radiation come to this + + align:start position:0% +circuit the solar radiation come to this + + + align:start position:0% +circuit the solar radiation come to this +electon surface the energy now one part + + align:start position:0% +electon surface the energy now one part + + + align:start position:0% +electon surface the energy now one part +is go directly through radiation and the + + align:start position:0% +is go directly through radiation and the + + + align:start position:0% +is go directly through radiation and the +other part goes through the air glass uh + + align:start position:0% +other part goes through the air glass uh + + + align:start position:0% +other part goes through the air glass uh +conention outside and then the backside + + align:start position:0% +conention outside and then the backside + + + align:start position:0% +conention outside and then the backside +the + + align:start position:0% +the + + + align:start position:0% +the +insulation + + align:start position:0% +insulation + + + align:start position:0% +insulation +okay and they I put a resistance because + + align:start position:0% +okay and they I put a resistance because + + + align:start position:0% +okay and they I put a resistance because +I this is a something if you're not the + + align:start position:0% +I this is a something if you're not the + + + align:start position:0% +I this is a something if you're not the +mechanic or engineer didn't take heat + + align:start position:0% +mechanic or engineer didn't take heat + + + align:start position:0% +mechanic or engineer didn't take heat +transfer before this is probably n famar + + align:start position:0% +transfer before this is probably n famar + + + align:start position:0% +transfer before this is probably n famar +but this is similar like a circuit + + align:start position:0% +but this is similar like a circuit + + + align:start position:0% +but this is similar like a circuit +okay thermal resistance uh you you do + + align:start position:0% +okay thermal resistance uh you you do + + + align:start position:0% +okay thermal resistance uh you you do +the resistance calculation for air the + + align:start position:0% +the resistance calculation for air the + + + align:start position:0% +the resistance calculation for air the +thickness divide by thermal conductivity + + align:start position:0% +thickness divide by thermal conductivity + + + align:start position:0% +thickness divide by thermal conductivity +so the Gap thickness divide by + + align:start position:0% +so the Gap thickness divide by + + + align:start position:0% +so the Gap thickness divide by +conductivity divide by area and they say + + align:start position:0% +conductivity divide by area and they say + + + align:start position:0% +conductivity divide by area and they say +if you do that why don't you use th + + align:start position:0% +if you do that why don't you use th + + + align:start position:0% +if you do that why don't you use th +thicker and the problem is once you two + + align:start position:0% +thicker and the problem is once you two + + + align:start position:0% +thicker and the problem is once you two +th there start circulation convection + + align:start position:0% +th there start circulation convection + + + align:start position:0% +th there start circulation convection +start to happen so you look at the + + align:start position:0% +start to happen so you look at the + + + align:start position:0% +start to happen so you look at the +Double pan window in the typical window + + align:start position:0% +Double pan window in the typical window + + + align:start position:0% +Double pan window in the typical window +that thickness is not not it's a few + + align:start position:0% +that thickness is not not it's a few + + + align:start position:0% +that thickness is not not it's a few +millimet thickness so you don't use to + + align:start position:0% +millimet thickness so you don't use to + + + align:start position:0% +millimet thickness so you don't use to +th here so here I took a 10 10 mm and + + align:start position:0% +th here so here I took a 10 10 mm and + + + align:start position:0% +th here so here I took a 10 10 mm and +then say glass uh glass is a a few weeks + + align:start position:0% +then say glass uh glass is a a few weeks + + + align:start position:0% +then say glass uh glass is a a few weeks +ago there was a talk somebody is going + + align:start position:0% +ago there was a talk somebody is going + + + align:start position:0% +ago there was a talk somebody is going +to install a flat panel system in one of + + align:start position:0% +to install a flat panel system in one of + + + align:start position:0% +to install a flat panel system in one of +the MIT building MIT I don't know uhuh + + align:start position:0% +the MIT building MIT I don't know uhuh + + + align:start position:0% +the MIT building MIT I don't know uhuh +Ash okay I was surprised that uh the + + align:start position:0% +Ash okay I was surprised that uh the + + + align:start position:0% +Ash okay I was surprised that uh the +cost per was just a surprise for me + + align:start position:0% +cost per was just a surprise for me + + + align:start position:0% +cost per was just a surprise for me +because that's like a 13 15 year return + + align:start position:0% +because that's like a 13 15 year return + + + align:start position:0% +because that's like a 13 15 year return +uh uh I don't not understand why but I + + align:start position:0% +uh uh I don't not understand why but I + + + align:start position:0% +uh uh I don't not understand why but I +say it looks like they use a very uh + + align:start position:0% +say it looks like they use a very uh + + + align:start position:0% +say it looks like they use a very uh +very tough glass this is a steel uh + + align:start position:0% +very tough glass this is a steel uh + + + align:start position:0% +very tough glass this is a steel uh +what's the glass L you you you you + + align:start position:0% +what's the glass L you you you you + + + align:start position:0% +what's the glass L you you you you +harden the glass you can walk on it so + + align:start position:0% +harden the glass you can walk on it so + + + align:start position:0% +harden the glass you can walk on it so +uh but anyway but glass resistance very + + align:start position:0% +uh but anyway but glass resistance very + + + align:start position:0% +uh but anyway but glass resistance very +small really air resistance contion + + align:start position:0% +small really air resistance contion + + + align:start position:0% +small really air resistance contion +resistance those are the resistance that + + align:start position:0% +resistance those are the resistance that + + + align:start position:0% +resistance those are the resistance that +cost the toor that's this side the + + align:start position:0% +cost the toor that's this side the + + + align:start position:0% +cost the toor that's this side the +resistant and then the insulation + + align:start position:0% +resistant and then the insulation + + + align:start position:0% +resistant and then the insulation +resistance the back side so I put all + + align:start position:0% +resistance the back side so I put all + + + align:start position:0% +resistance the back side so I put all +this L together and did the energy uh + + align:start position:0% +this L together and did the energy uh + + + align:start position:0% +this L together and did the energy uh +loss again considering all the radiation + + align:start position:0% +loss again considering all the radiation + + + align:start position:0% +loss again considering all the radiation +so I have radiation loss I have the + + align:start position:0% +so I have radiation loss I have the + + + align:start position:0% +so I have radiation loss I have the +conduction + + align:start position:0% +conduction + + + align:start position:0% +conduction +loss the conduction conversion + + align:start position:0% +loss the conduction conversion + + + align:start position:0% +loss the conduction conversion +loss and with this loss I can again go + + align:start position:0% +loss and with this loss I can again go + + + align:start position:0% +loss and with this loss I can again go +calculate how much energy comes in + + align:start position:0% +calculate how much energy comes in + + + align:start position:0% +calculate how much energy comes in +absorb Mon's loss divide by what comes + + align:start position:0% +absorb Mon's loss divide by what comes + + + align:start position:0% +absorb Mon's loss divide by what comes +in and that's what I + + align:start position:0% +in and that's what I + + + align:start position:0% +in and that's what I +have okay uh those numbers I assume for + + align:start position:0% +have okay uh those numbers I assume for + + + align:start position:0% +have okay uh those numbers I assume for +example uh in the next graph I assume + + align:start position:0% +example uh in the next graph I assume + + + align:start position:0% +example uh in the next graph I assume +95% absorption 5% emission this is what + + align:start position:0% +95% absorption 5% emission this is what + + + align:start position:0% +95% absorption 5% emission this is what +the industry can do so we have a + + align:start position:0% +the industry can do so we have a + + + align:start position:0% +the industry can do so we have a +researching a group on selective surface + + align:start position:0% +researching a group on selective surface + + + align:start position:0% +researching a group on selective surface +always I say how we can do better + + align:start position:0% +always I say how we can do better + + + align:start position:0% +always I say how we can do better +industry can do that at the meters per + + align:start position:0% +industry can do that at the meters per + + + align:start position:0% +industry can do that at the meters per +second okay select the surface 95% + + align:start position:0% +second okay select the surface 95% + + + align:start position:0% +second okay select the surface 95% +absorption 5% emission um and this hot + + align:start position:0% +absorption 5% emission um and this hot + + + align:start position:0% +absorption 5% emission um and this hot +water is of course the typical + + align:start position:0% +water is of course the typical + + + align:start position:0% +water is of course the typical +operational temperature is about 70 uh + + align:start position:0% +operational temperature is about 70 uh + + + align:start position:0% +operational temperature is about 70 uh +80° so they do not operate at very high + + align:start position:0% +80° so they do not operate at very high + + + align:start position:0% +80° so they do not operate at very high +temperatures and when you go to higher + + align:start position:0% +temperatures and when you go to higher + + + align:start position:0% +temperatures and when you go to higher +temperature if you can go 500 Degrees + + align:start position:0% +temperature if you can go 500 Degrees + + + align:start position:0% +temperature if you can go 500 Degrees +still keep this uh you will be the best + + align:start position:0% +still keep this uh you will be the best + + + align:start position:0% +still keep this uh you will be the best +in the world it's very hard to do + + align:start position:0% +in the world it's very hard to do + + + align:start position:0% +in the world it's very hard to do +that okay that's that's the uh uh curve + + align:start position:0% +that okay that's that's the uh uh curve + + + align:start position:0% +that okay that's that's the uh uh curve +I have that's the vacuum + + align:start position:0% +I have that's the vacuum + + + align:start position:0% +I have that's the vacuum +system and this is the flat panel + + align:start position:0% +system and this is the flat panel + + + align:start position:0% +system and this is the flat panel +system and efficiency uh depends of + + align:start position:0% +system and efficiency uh depends of + + + align:start position:0% +system and efficiency uh depends of +course the temperature of the water + + align:start position:0% +course the temperature of the water + + + align:start position:0% +course the temperature of the water +essentially the temperature of the + + align:start position:0% +essentially the temperature of the + + + align:start position:0% +essentially the temperature of the +selective surface + + align:start position:0% +selective surface + + + align:start position:0% +selective surface +there and uh I went to a web and I found + + align:start position:0% +there and uh I went to a web and I found + + + align:start position:0% +there and uh I went to a web and I found +this depends on who you which website + + align:start position:0% +this depends on who you which website + + + align:start position:0% +this depends on who you which website +they looking people have different + + align:start position:0% +they looking people have different + + + align:start position:0% +they looking people have different +curves but I found the one that uh I + + align:start position:0% +curves but I found the one that uh I + + + align:start position:0% +curves but I found the one that uh I +thought closer to what I have um so uh + + align:start position:0% +thought closer to what I have um so uh + + + align:start position:0% +thought closer to what I have um so uh +this is this is a one company see that's + + align:start position:0% +this is this is a one company see that's + + + align:start position:0% +this is this is a one company see that's +a vacuum system that compared to flat + + align:start position:0% +a vacuum system that compared to flat + + + align:start position:0% +a vacuum system that compared to flat +panel flat panel goes to almost zero I + + align:start position:0% +panel flat panel goes to almost zero I + + + align:start position:0% +panel flat panel goes to almost zero I +don't believe that that's probably too + + align:start position:0% +don't believe that that's probably too + + + align:start position:0% +don't believe that that's probably too +small + + align:start position:0% +small + + + align:start position:0% +small +okay so uh but uh solar + + align:start position:0% +okay so uh but uh solar + + + align:start position:0% +okay so uh but uh solar +thermal is a efficiency compare of + + align:start position:0% +thermal is a efficiency compare of + + + align:start position:0% +thermal is a efficiency compare of +course the photo + + align:start position:0% +course the photo + + + align:start position:0% +course the photo +voltage is many times better and uh uh + + align:start position:0% +voltage is many times better and uh uh + + + align:start position:0% +voltage is many times better and uh uh +so in terms of if you look at what has + + align:start position:0% +so in terms of if you look at what has + + + align:start position:0% +so in terms of if you look at what has +been + + align:start position:0% +been + + + align:start position:0% +been +use is uh this is a chart I got from + + align:start position:0% +use is uh this is a chart I got from + + + align:start position:0% +use is uh this is a chart I got from +this uh uh publication + + align:start position:0% +this uh uh publication + + + align:start position:0% +this uh uh publication +it's uh and here is this side is solar + + align:start position:0% +it's uh and here is this side is solar + + + align:start position:0% +it's uh and here is this side is solar +thermal that's it's compare all the + + align:start position:0% +thermal that's it's compare all the + + + align:start position:0% +thermal that's it's compare all the +Renewables solar thermal here is a wind + + align:start position:0% +Renewables solar thermal here is a wind + + + align:start position:0% +Renewables solar thermal here is a wind +here's geothermal photo voltak solar + + align:start position:0% +here's geothermal photo voltak solar + + + align:start position:0% +here's geothermal photo voltak solar +thermal power plant ocean tile power + + align:start position:0% +thermal power plant ocean tile power + + + align:start position:0% +thermal power plant ocean tile power +power and uh uh you you find out that uh + + align:start position:0% +power and uh uh you you find out that uh + + + align:start position:0% +power and uh uh you you find out that uh +uh total capacity and the red is + + align:start position:0% +uh total capacity and the red is + + + align:start position:0% +uh total capacity and the red is +actually produced energy so so you can + + align:start position:0% +actually produced energy so so you can + + + align:start position:0% +actually produced energy so so you can +see the solar + + align:start position:0% +see the solar + + + align:start position:0% +see the solar +thermal is + + align:start position:0% +thermal is + + + align:start position:0% +thermal is +actually a pretty large part of how + + align:start position:0% +actually a pretty large part of how + + + align:start position:0% +actually a pretty large part of how +people are currently using renewable + + align:start position:0% +people are currently using renewable + + + align:start position:0% +people are currently using renewable +energy okay just heating up heating uh + + align:start position:0% +energy okay just heating up heating uh + + + align:start position:0% +energy okay just heating up heating uh +heating up the hot hot water + + align:start position:0% +heating up the hot hot water + + + align:start position:0% +heating up the hot hot water +meaning and this is a this is in terms + + align:start position:0% +meaning and this is a this is in terms + + + align:start position:0% +meaning and this is a this is in terms +of + + align:start position:0% +of + + + align:start position:0% +of +Technology uh uh vactive tube uh is + + align:start position:0% +Technology uh uh vactive tube uh is + + + align:start position:0% +Technology uh uh vactive tube uh is +dominant because China really China use + + align:start position:0% +dominant because China really China use + + + align:start position:0% +dominant because China really China use +it + + align:start position:0% +it + + + align:start position:0% +it +and uh uh flat panel + + align:start position:0% +and uh uh flat panel + + + align:start position:0% +and uh uh flat panel +32% uh unaz The Collector uh and air + + align:start position:0% +32% uh unaz The Collector uh and air + + + align:start position:0% +32% uh unaz The Collector uh and air +collector so this is this is the where + + align:start position:0% +collector so this is this is the where + + + align:start position:0% +collector so this is this is the where +it's being used you can see the channel + + align:start position:0% +it's being used you can see the channel + + + align:start position:0% +it's being used you can see the channel +is off the chart + + align:start position:0% +is off the chart + + + align:start position:0% +is off the chart +here it has about 100 million square + + align:start position:0% +here it has about 100 million square + + + align:start position:0% +here it has about 100 million square +meter + + align:start position:0% +meter + + + align:start position:0% +meter +inall I don't understand way why we + + align:start position:0% +inall I don't understand way why we + + + align:start position:0% +inall I don't understand way why we +don't use the here and but I did say I I + + align:start position:0% +don't use the here and but I did say I I + + + align:start position:0% +don't use the here and but I did say I I +think I say Hawaii now has legislation + + align:start position:0% +think I say Hawaii now has legislation + + + align:start position:0% +think I say Hawaii now has legislation +if you have uh new house being built a + + align:start position:0% +if you have uh new house being built a + + + align:start position:0% +if you have uh new house being built a +new house built you have to put in hot + + align:start position:0% +new house built you have to put in hot + + + align:start position:0% +new house built you have to put in hot +water system can your from right you can + + align:start position:0% +water system can your from right you can + + + align:start position:0% +water system can your from right you can +go back + + align:start position:0% + + + + align:start position:0% + +check + + align:start position:0% +check + + + align:start position:0% +check +uh so um I was once talking to every + + align:start position:0% +uh so um I was once talking to every + + + align:start position:0% +uh so um I was once talking to every +time I have a chance I was asking people + + align:start position:0% +time I have a chance I was asking people + + + align:start position:0% +time I have a chance I was asking people +why and also price gets very high that's + + align:start position:0% +why and also price gets very high that's + + + align:start position:0% +why and also price gets very high that's +uh uh probably um uh because in China + + align:start position:0% +uh uh probably um uh because in China + + + align:start position:0% +uh uh probably um uh because in China +you can Ty household $300 they put that + + align:start position:0% +you can Ty household $300 they put that + + + align:start position:0% +you can Ty household $300 they put that +for + + align:start position:0% + + + + align:start position:0% + +system okay so that's solar thermal now + + align:start position:0% +system okay so that's solar thermal now + + + align:start position:0% +system okay so that's solar thermal now +we want to go to higher temperature + + align:start position:0% +we want to go to higher temperature + + + align:start position:0% +we want to go to higher temperature +right solar thermal is 80° + + align:start position:0% +right solar thermal is 80° + + + align:start position:0% +right solar thermal is 80° +100° and uh you want now go to uh higher + + align:start position:0% +100° and uh you want now go to uh higher + + + align:start position:0% +100° and uh you want now go to uh higher +temperature and to have to get the + + align:start position:0% +temperature and to have to get the + + + align:start position:0% +temperature and to have to get the +higher temperature uh you need a + + align:start position:0% +higher temperature uh you need a + + + align:start position:0% +higher temperature uh you need a +concentration and now uh we need to look + + align:start position:0% +concentration and now uh we need to look + + + align:start position:0% +concentration and now uh we need to look +at the uh the concentration let me + + align:start position:0% +at the uh the concentration let me + + + align:start position:0% +at the uh the concentration let me +remind you I showed this before uh the + + align:start position:0% +remind you I showed this before uh the + + + align:start position:0% +remind you I showed this before uh the +uh the Earth + + align:start position:0% +uh the Earth + + + align:start position:0% +uh the Earth +itself uh see on the uh see the orbital + + align:start position:0% +itself uh see on the uh see the orbital + + + align:start position:0% +itself uh see on the uh see the orbital +is not just a perpendicular of this + + align:start position:0% +is not just a perpendicular of this + + + align:start position:0% +is not just a perpendicular of this +plant there's a + + align:start position:0% +plant there's a + + + align:start position:0% +plant there's a +23.5 CH of the Earth right so on this + + align:start position:0% +23.5 CH of the Earth right so on this + + + align:start position:0% +23.5 CH of the Earth right so on this +side this is til on this side the same + + align:start position:0% +side this is til on this side the same + + + align:start position:0% +side this is til on this side the same +til that til is fix that's why we have + + align:start position:0% +til that til is fix that's why we have + + + align:start position:0% +til that til is fix that's why we have +summer and uh up uh the r direction we + + align:start position:0% +summer and uh up uh the r direction we + + + align:start position:0% +summer and uh up uh the r direction we +have a summer and uh uh winter okay and + + align:start position:0% +have a summer and uh uh winter okay and + + + align:start position:0% +have a summer and uh uh winter okay and +the uh degree suspended of the Sun by + + align:start position:0% +the uh degree suspended of the Sun by + + + align:start position:0% +the uh degree suspended of the Sun by +say if you view from Earth the degree is + + align:start position:0% +say if you view from Earth the degree is + + + align:start position:0% +say if you view from Earth the degree is +35 32 uh second so that's uh um + + align:start position:0% +35 32 uh second so that's uh um + + + align:start position:0% +35 32 uh second so that's uh um +um that's about the0 + + align:start position:0% +um that's about the0 + + + align:start position:0% +um that's about the0 +five I forgot point about 4.5 + + align:start position:0% +five I forgot point about 4.5 + + + align:start position:0% +five I forgot point about 4.5 +degree + + align:start position:0% +degree + + + align:start position:0% +degree +okay and now uh the question I want to + + align:start position:0% +okay and now uh the question I want to + + + align:start position:0% +okay and now uh the question I want to +ask first is if you do concentration how + + align:start position:0% +ask first is if you do concentration how + + + align:start position:0% +ask first is if you do concentration how +much you can + + align:start position:0% + + + + align:start position:0% + +get what's the maximum concentration + + align:start position:0% +get what's the maximum concentration + + + align:start position:0% +get what's the maximum concentration +right uh so we can look at the + + align:start position:0% +right uh so we can look at the + + + align:start position:0% +right uh so we can look at the +theoretically um what's the limit the + + align:start position:0% +theoretically um what's the limit the + + + align:start position:0% +theoretically um what's the limit the +maximum seric limit is I + + align:start position:0% +maximum seric limit is I + + + align:start position:0% +maximum seric limit is I +cannot heat up object harder than this + + align:start position:0% +cannot heat up object harder than this + + + align:start position:0% +cannot heat up object harder than this +s right + + align:start position:0% + + + + align:start position:0% + +and now so that that you all agree but + + align:start position:0% +and now so that that you all agree but + + + align:start position:0% +and now so that that you all agree but +if I ask you can I + + align:start position:0% +if I ask you can I + + + align:start position:0% +if I ask you can I +concentrate radiation even with + + align:start position:0% +concentrate radiation even with + + + align:start position:0% +concentrate radiation even with +intensity harder than the Sun not not + + align:start position:0% +intensity harder than the Sun not not + + + align:start position:0% +intensity harder than the Sun not not +harder the intensity higher than the + + align:start position:0% + + + + align:start position:0% + +sun is that crazy or + + align:start position:0% +sun is that crazy or + + + align:start position:0% +sun is that crazy or +not + + align:start position:0% +not + + + align:start position:0% +not +huh okay you'll see it + + align:start position:0% +huh okay you'll see it + + + align:start position:0% +huh okay you'll see it +later okay so first we let's look at the + + align:start position:0% +later okay so first we let's look at the + + + align:start position:0% +later okay so first we let's look at the +first just energy balance if I think + + align:start position:0% +first just energy balance if I think + + + align:start position:0% +first just energy balance if I think +about the + + align:start position:0% +about the + + + align:start position:0% +about the +spherical uh radius from the sunand + + align:start position:0% +spherical uh radius from the sunand + + + align:start position:0% +spherical uh radius from the sunand +right and the area of the sphere times + + align:start position:0% +right and the area of the sphere times + + + align:start position:0% +right and the area of the sphere times +the energy + + align:start position:0% +the energy + + + align:start position:0% +the energy +flux and uh uh area of the uh see uh is + + align:start position:0% +flux and uh uh area of the uh see uh is + + + align:start position:0% +flux and uh uh area of the uh see uh is +a constant the once the energy leave the + + align:start position:0% +a constant the once the energy leave the + + + align:start position:0% +a constant the once the energy leave the +surface the larger you draw Circle the + + align:start position:0% +surface the larger you draw Circle the + + + align:start position:0% +surface the larger you draw Circle the +less is your intensity so the intensity + + align:start position:0% +less is your intensity so the intensity + + + align:start position:0% +less is your intensity so the intensity +of the this Earth think of circle here + + align:start position:0% +of the this Earth think of circle here + + + align:start position:0% +of the this Earth think of circle here +that is a capital r 4 pi r squ times + + align:start position:0% +that is a capital r 4 pi r squ times + + + align:start position:0% +that is a capital r 4 pi r squ times +whatever insulation outside the Earth's + + align:start position:0% +whatever insulation outside the Earth's + + + align:start position:0% +whatever insulation outside the Earth's +atmosphere right so this is + + align:start position:0% +atmosphere right so this is + + + align:start position:0% +atmosphere right so this is +the insulation outside the earth + + align:start position:0% +the insulation outside the earth + + + align:start position:0% +the insulation outside the earth +atmosphere this is the uh intensity on + + align:start position:0% +atmosphere this is the uh intensity on + + + align:start position:0% +atmosphere this is the uh intensity on +the surface of the S radius of the sand + + align:start position:0% +the surface of the S radius of the sand + + + align:start position:0% +the surface of the S radius of the sand +so that's energy balance conserve always + + align:start position:0% +so that's energy balance conserve always + + + align:start position:0% +so that's energy balance conserve always +of course you see oh there's something + + align:start position:0% +of course you see oh there's something + + + align:start position:0% +of course you see oh there's something +in between scatter a little bit light + + align:start position:0% +in between scatter a little bit light + + + align:start position:0% +in between scatter a little bit light +consuming uh uh the space is pretty much + + align:start position:0% +consuming uh uh the space is pretty much + + + align:start position:0% +consuming uh uh the space is pretty much +all + + align:start position:0% +all + + + align:start position:0% +all +empty right so now let me + + align:start position:0% +empty right so now let me + + + align:start position:0% +empty right so now let me +concentrate if I concentrate this + + align:start position:0% +concentrate if I concentrate this + + + align:start position:0% +concentrate if I concentrate this +concentration ratio and this intensity + + align:start position:0% +concentration ratio and this intensity + + + align:start position:0% +concentration ratio and this intensity +on the earth uh surface the Earth of the + + align:start position:0% +on the earth uh surface the Earth of the + + + align:start position:0% +on the earth uh surface the Earth of the +the Earth in + + align:start position:0% +the Earth in + + + align:start position:0% +the Earth in +solution and uh this is the energy I put + + align:start position:0% +solution and uh this is the energy I put + + + align:start position:0% +solution and uh this is the energy I put +in onto object that receive this + + align:start position:0% +in onto object that receive this + + + align:start position:0% +in onto object that receive this +concentr light right so energy balance + + align:start position:0% +concentr light right so energy balance + + + align:start position:0% +concentr light right so energy balance +will tell me + + align:start position:0% +will tell me + + + align:start position:0% +will tell me +in this case again uh this the object + + align:start position:0% +in this case again uh this the object + + + align:start position:0% +in this case again uh this the object +should be black body + + align:start position:0% +should be black body + + + align:start position:0% +should be black body +actually because you want to absorb + + align:start position:0% +actually because you want to absorb + + + align:start position:0% +actually because you want to absorb +every drop of solar + + align:start position:0% +every drop of solar + + + align:start position:0% +every drop of solar +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +radiation and because you you absorb the + + align:start position:0% +radiation and because you you absorb the + + + align:start position:0% +radiation and because you you absorb the +solar radiation you also rate so you + + align:start position:0% +solar radiation you also rate so you + + + align:start position:0% +solar radiation you also rate so you +want to absorb maximum you also rate Max + + align:start position:0% +want to absorb maximum you also rate Max + + + align:start position:0% +want to absorb maximum you also rate Max +maximum so it's black body so actually I + + align:start position:0% +maximum so it's black body so actually I + + + align:start position:0% +maximum so it's black body so actually I +put a say the energy absorb the balance + + align:start position:0% +put a say the energy absorb the balance + + + align:start position:0% +put a say the energy absorb the balance +the energy radiated I do perfect + + align:start position:0% +the energy radiated I do perfect + + + align:start position:0% +the energy radiated I do perfect +insulation so this is per unit area + + align:start position:0% +insulation so this is per unit area + + + align:start position:0% +insulation so this is per unit area +based this is per unit area based so + + align:start position:0% +based this is per unit area based so + + + align:start position:0% +based this is per unit area based so +that's the energy balance for the object + + align:start position:0% +that's the energy balance for the object + + + align:start position:0% +that's the energy balance for the object +that receive the concentrated + + align:start position:0% +that receive the concentrated + + + align:start position:0% +that receive the concentrated +light and of course as I said my + + align:start position:0% +light and of course as I said my + + + align:start position:0% +light and of course as I said my +condition is that this object cannot be + + align:start position:0% +condition is that this object cannot be + + + align:start position:0% +condition is that this object cannot be +harder than the + + align:start position:0% +harder than the + + + align:start position:0% +harder than the +seven + + align:start position:0% +seven + + + align:start position:0% +seven +right so so this is the uh concentration + + align:start position:0% +right so so this is the uh concentration + + + align:start position:0% +right so so this is the uh concentration +and uh from here I get my maximum + + align:start position:0% +and uh from here I get my maximum + + + align:start position:0% +and uh from here I get my maximum +concentration + + align:start position:0% +concentration + + + align:start position:0% +concentration +happens when this equal and that's the + + align:start position:0% +happens when this equal and that's the + + + align:start position:0% +happens when this equal and that's the +solar flux intensity divid by whatever + + align:start position:0% +solar flux intensity divid by whatever + + + align:start position:0% +solar flux intensity divid by whatever +in in Earth so that's R over small R + + align:start position:0% +in in Earth so that's R over small R + + + align:start position:0% +in in Earth so that's R over small R +based on my energy balance and if you + + align:start position:0% +based on my energy balance and if you + + + align:start position:0% +based on my energy balance and if you +look at R small R and this Thea here is + + align:start position:0% +look at R small R and this Thea here is + + + align:start position:0% +look at R small R and this Thea here is +a half angle sustain to Earth so that's + + align:start position:0% +a half angle sustain to Earth so that's + + + align:start position:0% +a half angle sustain to Earth so that's +a sin Theta Square so that's my maximum + + align:start position:0% +a sin Theta Square so that's my maximum + + + align:start position:0% +a sin Theta Square so that's my maximum +concentration and uh if you plug in the + + align:start position:0% +concentration and uh if you plug in the + + + align:start position:0% +concentration and uh if you plug in the +lumber I said 2 Theta this is 32 second + + align:start position:0% +lumber I said 2 Theta this is 32 second + + + align:start position:0% +lumber I said 2 Theta this is 32 second +so plug in lber that's about + + align:start position:0% +so plug in lber that's about + + + align:start position:0% +so plug in lber that's about +46 100 thousand times it's the maximum + + align:start position:0% +46 100 thousand times it's the maximum + + + align:start position:0% +46 100 thousand times it's the maximum +you can + + align:start position:0% +you can + + + align:start position:0% +you can +get it's not the maximum people actually + + align:start position:0% +get it's not the maximum people actually + + + align:start position:0% +get it's not the maximum people actually +have achieved higher than this + + align:start position:0% + + + + align:start position:0% + +one + + align:start position:0% +one + + + align:start position:0% +one +okay this is a + + align:start position:0% +okay this is a + + + align:start position:0% +okay this is a +because the emission inside the + + align:start position:0% +because the emission inside the + + + align:start position:0% +because the emission inside the +object is is uh + + align:start position:0% +object is is uh + + + align:start position:0% +object is is uh +proportional I have one mistake here + + align:start position:0% +proportional I have one mistake here + + + align:start position:0% +proportional I have one mistake here +should be proportional to n Square not + + align:start position:0% +should be proportional to n Square not + + + align:start position:0% +should be proportional to n Square not +proportional to + + align:start position:0% +proportional to + + + align:start position:0% +proportional to +n okay so the mission inside object + + align:start position:0% +n okay so the mission inside object + + + align:start position:0% +n okay so the mission inside object +proportional n + + align:start position:0% +proportional n + + + align:start position:0% +proportional n +Square so so if I have a a medium like a + + align:start position:0% +Square so so if I have a a medium like a + + + align:start position:0% +Square so so if I have a a medium like a +water or glass right the inst intensity + + align:start position:0% +water or glass right the inst intensity + + + align:start position:0% +water or glass right the inst intensity +inside could be higher than the + + align:start position:0% +inside could be higher than the + + + align:start position:0% +inside could be higher than the +vacuum black body intensity and square + + align:start position:0% +vacuum black body intensity and square + + + align:start position:0% +vacuum black body intensity and square +and glass is uh two uh 1.5 so square is + + align:start position:0% +and glass is uh two uh 1.5 so square is + + + align:start position:0% +and glass is uh two uh 1.5 so square is +2.25 and uh uh if you use silicon the N + + align:start position:0% +2.25 and uh uh if you use silicon the N + + + align:start position:0% +2.25 and uh uh if you use silicon the N +is about 3.5 the square is about + + align:start position:0% +is about 3.5 the square is about + + + align:start position:0% +is about 3.5 the square is about +10 right so um if you do that again your + + align:start position:0% +10 right so um if you do that again your + + + align:start position:0% +10 right so um if you do that again your +limit is the temperature limit is not + + align:start position:0% +limit is the temperature limit is not + + + align:start position:0% +limit is the temperature limit is not +the intensity limit your temperature of + + align:start position:0% +the intensity limit your temperature of + + + align:start position:0% +the intensity limit your temperature of +the concentrated surface cannot be + + align:start position:0% +the concentrated surface cannot be + + + align:start position:0% +the concentrated surface cannot be +higher than the temperature of the Sun + + align:start position:0% +higher than the temperature of the Sun + + + align:start position:0% +higher than the temperature of the Sun +you do that you can your maximum is n² + + align:start position:0% +you do that you can your maximum is n² + + + align:start position:0% +you do that you can your maximum is n² +sin Theta + + align:start position:0% +sin Theta + + + align:start position:0% +sin Theta +squ okay so that's higher than the + + align:start position:0% +squ okay so that's higher than the + + + align:start position:0% +squ okay so that's higher than the +previous one and indeed this was + + align:start position:0% +previous one and indeed this was + + + align:start position:0% +previous one and indeed this was +achieved in the lab uh this is Roland uh + + align:start position:0% +achieved in the lab uh this is Roland uh + + + align:start position:0% +achieved in the lab uh this is Roland uh +Winston uh they have talk about this + + align:start position:0% +Winston uh they have talk about this + + + align:start position:0% +Winston uh they have talk about this +more detail this is a compound with the + + align:start position:0% +more detail this is a compound with the + + + align:start position:0% +more detail this is a compound with the +focus and non focus and they have shied + + align:start position:0% + + + + align:start position:0% + +56 okay + + align:start position:0% +56 okay + + + align:start position:0% +56 okay +so that's the um from the second low + + align:start position:0% +so that's the um from the second low + + + align:start position:0% +so that's the um from the second low +perspective your absolute upper limit + + align:start position:0% +perspective your absolute upper limit + + + align:start position:0% +perspective your absolute upper limit +and now let's see how we can get there + + align:start position:0% +and now let's see how we can get there + + + align:start position:0% +and now let's see how we can get there +okay and uh you think I'm going to use a + + align:start position:0% +okay and uh you think I'm going to use a + + + align:start position:0% +okay and uh you think I'm going to use a +lens and this lens if I think about the + + align:start position:0% +lens and this lens if I think about the + + + align:start position:0% +lens and this lens if I think about the +lens okay so uh all all all parabolic 12 + + align:start position:0% +lens okay so uh all all all parabolic 12 + + + align:start position:0% +lens okay so uh all all all parabolic 12 +right we know that you have parel comes + + align:start position:0% +right we know that you have parel comes + + + align:start position:0% +right we know that you have parel comes +in it Focus one point so that's the the + + align:start position:0% +in it Focus one point so that's the the + + + align:start position:0% +in it Focus one point so that's the the +question is what's the concentration + + align:start position:0% +question is what's the concentration + + + align:start position:0% +question is what's the concentration +limit if you those are the image + + align:start position:0% +limit if you those are the image + + + align:start position:0% +limit if you those are the image +formation right using a lens using a uh + + align:start position:0% +formation right using a lens using a uh + + + align:start position:0% +formation right using a lens using a uh +uh using a lens or using a uh parabolic + + align:start position:0% +uh using a lens or using a uh parabolic + + + align:start position:0% +uh using a lens or using a uh parabolic +12 you have a focal point that's a focal + + align:start position:0% +12 you have a focal point that's a focal + + + align:start position:0% +12 you have a focal point that's a focal +point this is the image so image forming + + align:start position:0% +point this is the image so image forming + + + align:start position:0% +point this is the image so image forming +of and remember the sign sustain angle + + align:start position:0% +of and remember the sign sustain angle + + + align:start position:0% +of and remember the sign sustain angle +that's the K right even though we say + + align:start position:0% +that's the K right even though we say + + + align:start position:0% +that's the K right even though we say +solar radiation is a parel light but + + align:start position:0% +solar radiation is a parel light but + + + align:start position:0% +solar radiation is a parel light but +when you want to do Focus you want to uh + + align:start position:0% +when you want to do Focus you want to uh + + + align:start position:0% +when you want to do Focus you want to uh +uh that that angle becomes important + + align:start position:0% +uh that that angle becomes important + + + align:start position:0% +uh that that angle becomes important +because previously you already say so + + align:start position:0% +because previously you already say so + + + align:start position:0% +because previously you already say so +what I want to say uh think about is if + + align:start position:0% +what I want to say uh think about is if + + + align:start position:0% +what I want to say uh think about is if +I have either l or parabolic control uh + + align:start position:0% +I have either l or parabolic control uh + + + align:start position:0% +I have either l or parabolic control uh +uh say the uh opening here is + + align:start position:0% +uh say the uh opening here is + + + align:start position:0% +uh say the uh opening here is +D and the uh forus uh uh here is a small + + align:start position:0% +D and the uh forus uh uh here is a small + + + align:start position:0% +D and the uh forus uh uh here is a small +d one is Big D the other is small D and + + align:start position:0% +d one is Big D the other is small D and + + + align:start position:0% +d one is Big D the other is small D and +I want to find the + + align:start position:0% +I want to find the + + + align:start position:0% +I want to find the +ratio okay let's look at it so if I do + + align:start position:0% +ratio okay let's look at it so if I do + + + align:start position:0% +ratio okay let's look at it so if I do +2D uh this one is a flat right flat + + align:start position:0% +2D uh this one is a flat right flat + + + align:start position:0% +2D uh this one is a flat right flat +panel is if you do a tube you you have a + + align:start position:0% +panel is if you do a tube you you have a + + + align:start position:0% +panel is if you do a tube you you have a +different result but the here I'm a flat + + align:start position:0% +different result but the here I'm a flat + + + align:start position:0% +different result but the here I'm a flat +panel and this is the half of + + align:start position:0% +panel and this is the half of + + + align:start position:0% +panel and this is the half of +it and uh uh now I look at the uh this + + align:start position:0% +it and uh uh now I look at the uh this + + + align:start position:0% +it and uh uh now I look at the uh this +is a this is a vertical perpendicular + + align:start position:0% +is a this is a vertical perpendicular + + + align:start position:0% +is a this is a vertical perpendicular +line here so R * sin Theta here is 2 + + align:start position:0% +line here so R * sin Theta here is 2 + + + align:start position:0% +line here so R * sin Theta here is 2 +Theta so this is really if you think + + align:start position:0% +Theta so this is really if you think + + + align:start position:0% +Theta so this is really if you think +about parall line comes in this way and + + align:start position:0% +about parall line comes in this way and + + + align:start position:0% +about parall line comes in this way and +that's my reflection here and this one + + align:start position:0% +that's my reflection here and this one + + + align:start position:0% +that's my reflection here and this one +is my uh this line reflection so that's + + align:start position:0% +is my uh this line reflection so that's + + + align:start position:0% +is my uh this line reflection so that's +the uh uh edge of the uh solar cor there + + align:start position:0% +the uh uh edge of the uh solar cor there + + + align:start position:0% +the uh uh edge of the uh solar cor there +and so R * sin Theta gives me this + + align:start position:0% +and so R * sin Theta gives me this + + + align:start position:0% +and so R * sin Theta gives me this +one right perpendicular line and d/2 so + + align:start position:0% +one right perpendicular line and d/2 so + + + align:start position:0% +one right perpendicular line and d/2 so +that's here times this is a five and + + align:start position:0% +that's here times this is a five and + + + align:start position:0% +that's here times this is a five and +here is a five so here is also five so D + + align:start position:0% +here is a five so here is also five so D + + + align:start position:0% +here is a five so here is also five so D +over 2 * cosine 5 is all G me this SE + + align:start position:0% +over 2 * cosine 5 is all G me this SE + + + align:start position:0% +over 2 * cosine 5 is all G me this SE +segment so I have a equation geometry + + align:start position:0% +segment so I have a equation geometry + + + align:start position:0% +segment so I have a equation geometry +here geometrical + + align:start position:0% + + + + align:start position:0% + +relation and then I + + align:start position:0% +relation and then I + + + align:start position:0% +relation and then I +have this R and this R is about the same + + align:start position:0% +have this R and this R is about the same + + + align:start position:0% +have this R and this R is about the same +so R * sin Theta gives me + + align:start position:0% +so R * sin Theta gives me + + + align:start position:0% +so R * sin Theta gives me +d/2 right the open in + + align:start position:0% +d/2 right the open in + + + align:start position:0% +d/2 right the open in +there and then I have from here I can + + align:start position:0% +there and then I have from here I can + + + align:start position:0% +there and then I have from here I can +get my relation how much Focus I get + + align:start position:0% +get my relation how much Focus I get + + + align:start position:0% +get my relation how much Focus I get +capital D over small D I have sin 25 / 2 + + align:start position:0% +capital D over small D I have sin 25 / 2 + + + align:start position:0% +capital D over small D I have sin 25 / 2 +sin Theta so this is the uh maximum you + + align:start position:0% +sin Theta so this is the uh maximum you + + + align:start position:0% +sin Theta so this is the uh maximum you +will get uh this is the concentration + + align:start position:0% +will get uh this is the concentration + + + align:start position:0% +will get uh this is the concentration +you get and you will see the maximum + + align:start position:0% +you get and you will see the maximum + + + align:start position:0% +you get and you will see the maximum +happens is sin 25 = + + align:start position:0% +happens is sin 25 = + + + align:start position:0% +happens is sin 25 = +1 right so 45° + + align:start position:0% +1 right so 45° + + + align:start position:0% +1 right so 45° +so when 5 = 45° + + align:start position:0% +so when 5 = 45° + + + align:start position:0% +so when 5 = 45° +here I have the + + align:start position:0% +here I have the + + + align:start position:0% +here I have the +maximum and that + + align:start position:0% +maximum and that + + + align:start position:0% +maximum and that +maximum is 2 sin Theta that's + + align:start position:0% +maximum is 2 sin Theta that's + + + align:start position:0% +maximum is 2 sin Theta that's +107 my calculation maybe you can go back + + align:start position:0% +107 my calculation maybe you can go back + + + align:start position:0% +107 my calculation maybe you can go back +to + + align:start position:0% +to + + + align:start position:0% +to +check + + align:start position:0% +check + + + align:start position:0% +check +and if you use 3D X symmetric you square + + align:start position:0% +and if you use 3D X symmetric you square + + + align:start position:0% +and if you use 3D X symmetric you square +that and that's 4 sin th + + align:start position:0% +that and that's 4 sin th + + + align:start position:0% +that and that's 4 sin th +for the problem is now you can say this + + align:start position:0% +for the problem is now you can say this + + + align:start position:0% +for the problem is now you can say this +is a factor of four smaller than the + + align:start position:0% +is a factor of four smaller than the + + + align:start position:0% +is a factor of four smaller than the +limit right thermodynamic is 1/ + + align:start position:0% +limit right thermodynamic is 1/ + + + align:start position:0% +limit right thermodynamic is 1/ +Sina here if you form an + + align:start position:0% +Sina here if you form an + + + align:start position:0% +Sina here if you form an +image your limit is a factor of force + + align:start position:0% + + + + align:start position:0% + +more and how you can reach that maximum + + align:start position:0% + + + + align:start position:0% + +limit okay so image Optics + + align:start position:0% +limit okay so image Optics + + + align:start position:0% +limit okay so image Optics +it's a little bit too constraint you + + align:start position:0% +it's a little bit too constraint you + + + align:start position:0% +it's a little bit too constraint you +ideally you want everything goes to one + + align:start position:0% +ideally you want everything goes to one + + + align:start position:0% +ideally you want everything goes to one +point right and you want to form an + + align:start position:0% +point right and you want to form an + + + align:start position:0% +point right and you want to form an +image so this is a uh here there's + + align:start position:0% +image so this is a uh here there's + + + align:start position:0% +image so this is a uh here there's +another slides that I just copied from + + align:start position:0% +another slides that I just copied from + + + align:start position:0% +another slides that I just copied from +Winston's book and uh uh if you have if + + align:start position:0% +Winston's book and uh uh if you have if + + + align:start position:0% +Winston's book and uh uh if you have if +you want to focus on the cylinder that's + + align:start position:0% +you want to focus on the cylinder that's + + + align:start position:0% +you want to focus on the cylinder that's +one or Pi smaller uh than the previous + + align:start position:0% + + + + align:start position:0% + +slide now uh + + align:start position:0% +slide now uh + + + align:start position:0% +slide now uh +there's another way to do it that's a + + align:start position:0% +there's another way to do it that's a + + + align:start position:0% +there's another way to do it that's a +long image method this is a uh Rand + + align:start position:0% +long image method this is a uh Rand + + + align:start position:0% +long image method this is a uh Rand +winance baby and uh uh if you read uh + + align:start position:0% +winance baby and uh uh if you read uh + + + align:start position:0% +winance baby and uh uh if you read uh +his rational is starting from this one + + align:start position:0% +his rational is starting from this one + + + align:start position:0% +his rational is starting from this one +over + + align:start position:0% +over + + + align:start position:0% +over +four how you can get to the maximum sum + + align:start position:0% +four how you can get to the maximum sum + + + align:start position:0% +four how you can get to the maximum sum +damic limit and here is one way there's + + align:start position:0% +damic limit and here is one way there's + + + align:start position:0% +damic limit and here is one way there's +no simple mathematic in terms of the + + align:start position:0% +no simple mathematic in terms of the + + + align:start position:0% +no simple mathematic in terms of the +shape of the concentrator but this is + + align:start position:0% +shape of the concentrator but this is + + + align:start position:0% +shape of the concentrator but this is +how uh he would explain so this is where + + align:start position:0% +how uh he would explain so this is where + + + align:start position:0% +how uh he would explain so this is where +the area you want to Flat this is a flat + + align:start position:0% +the area you want to Flat this is a flat + + + align:start position:0% +the area you want to Flat this is a flat +plate example you want to focus on a + + align:start position:0% +plate example you want to focus on a + + + align:start position:0% +plate example you want to focus on a +flat plate B Prime to + + align:start position:0% +flat plate B Prime to + + + align:start position:0% +flat plate B Prime to +D okay and uh uh this is the angle of + + align:start position:0% +D okay and uh uh this is the angle of + + + align:start position:0% +D okay and uh uh this is the angle of +incidence right so that's the maximum + + align:start position:0% +incidence right so that's the maximum + + + align:start position:0% +incidence right so that's the maximum +angle uh let's suppose uh this is the + + align:start position:0% +angle uh let's suppose uh this is the + + + align:start position:0% +angle uh let's suppose uh this is the +maximum angle that you accept the + + align:start position:0% +maximum angle that you accept the + + + align:start position:0% +maximum angle that you accept the +radiation coming + + align:start position:0% +radiation coming + + + align:start position:0% +radiation coming +in right if you have another angle + + align:start position:0% +in right if you have another angle + + + align:start position:0% +in right if you have another angle +higher than this it will uh not get in + + align:start position:0% +higher than this it will uh not get in + + + align:start position:0% +higher than this it will uh not get in +you will be blocked so uh if you this is + + align:start position:0% +you will be blocked so uh if you this is + + + align:start position:0% +you will be blocked so uh if you this is +the maximum angle so you take a string + + align:start position:0% +the maximum angle so you take a string + + + align:start position:0% +the maximum angle so you take a string +here at this point you take a + + align:start position:0% +here at this point you take a + + + align:start position:0% +here at this point you take a +strand uh this is the opening uh num a + + align:start position:0% +strand uh this is the opening uh num a + + + align:start position:0% +strand uh this is the opening uh num a +so you draw you keep this string fix + + align:start position:0% +so you draw you keep this string fix + + + align:start position:0% +so you draw you keep this string fix +lens fixed and you draw the curve down + + align:start position:0% +lens fixed and you draw the curve down + + + align:start position:0% +lens fixed and you draw the curve down +so this one will slide so the angle of + + align:start position:0% +so this one will slide so the angle of + + + align:start position:0% +so this one will slide so the angle of +incidence equals + + align:start position:0% +incidence equals + + + align:start position:0% +incidence equals +reflection that's what what is following + + align:start position:0% +reflection that's what what is following + + + align:start position:0% +reflection that's what what is following +this surface gives the surface such that + + align:start position:0% +this surface gives the surface such that + + + align:start position:0% +this surface gives the surface such that +the angle of incidence equals angle + + align:start position:0% +the angle of incidence equals angle + + + align:start position:0% +the angle of incidence equals angle +reflection of course is a specular + + align:start position:0% +reflection of course is a specular + + + align:start position:0% +reflection of course is a specular +surface that's being + + align:start position:0% +surface that's being + + + align:start position:0% +surface that's being +assumed and at the limit this one when + + align:start position:0% +assumed and at the limit this one when + + + align:start position:0% +assumed and at the limit this one when +is here the refle angle to the goes to D + + align:start position:0% +is here the refle angle to the goes to D + + + align:start position:0% +is here the refle angle to the goes to D +Prime okay so that's the image surface + + align:start position:0% +Prime okay so that's the image surface + + + align:start position:0% +Prime okay so that's the image surface +this is the image method it + + align:start position:0% +this is the image method it + + + align:start position:0% +this is the image method it +developed and now we can check where + + align:start position:0% +developed and now we can check where + + + align:start position:0% +developed and now we can check where +this one gets to maximum or + + align:start position:0% +this one gets to maximum or + + + align:start position:0% +this one gets to maximum or +not so this again simple + + align:start position:0% +not so this again simple + + + align:start position:0% +not so this again simple +geometry I have + + align:start position:0% +geometry I have + + + align:start position:0% +geometry I have +AC this section plus a b Prime that's + + align:start position:0% +AC this section plus a b Prime that's + + + align:start position:0% +AC this section plus a b Prime that's +the Str length right and the other limit + + align:start position:0% +the Str length right and the other limit + + + align:start position:0% +the Str length right and the other limit +so this is The Edge you look at the edge + + align:start position:0% +so this is The Edge you look at the edge + + + align:start position:0% +so this is The Edge you look at the edge +only a prime to B plus b b + + align:start position:0% +only a prime to B plus b b + + + align:start position:0% +only a prime to B plus b b +Prime + + align:start position:0% +Prime + + + align:start position:0% +Prime +right so this is the Str length this is + + align:start position:0% +right so this is the Str length this is + + + align:start position:0% +right so this is the Str length this is +the Str l + + align:start position:0% +the Str l + + + align:start position:0% +the Str l +and the same + + align:start position:0% +and the same + + + align:start position:0% +and the same +string so it's actually very convenient + + align:start position:0% +string so it's actually very convenient + + + align:start position:0% +string so it's actually very convenient +simple way to do uh the uh the geometry + + align:start position:0% +simple way to do uh the uh the geometry + + + align:start position:0% +simple way to do uh the uh the geometry +Al the surface is harder to express + + align:start position:0% +Al the surface is harder to express + + + align:start position:0% +Al the surface is harder to express +analytically and uh you know uh see the + + align:start position:0% +analytically and uh you know uh see the + + + align:start position:0% +analytically and uh you know uh see the +symmetry A B prime a prime B from + + align:start position:0% +symmetry A B prime a prime B from + + + align:start position:0% +symmetry A B prime a prime B from +symmetry they equal so you get rid of + + align:start position:0% +symmetry they equal so you get rid of + + + align:start position:0% +symmetry they equal so you get rid of +two variable in the above + + align:start position:0% +two variable in the above + + + align:start position:0% +two variable in the above +equation and your a + + align:start position:0% +equation and your a + + + align:start position:0% +equation and your a +uh + + align:start position:0% +uh + + + align:start position:0% +uh +is uh your AC is this one time + + align:start position:0% +is uh your AC is this one time + + + align:start position:0% +is uh your AC is this one time +Sina so a a prime time sin + + align:start position:0% +Sina so a a prime time sin + + + align:start position:0% +Sina so a a prime time sin +Theta and your concentration then is 1/ + + align:start position:0% +Theta and your concentration then is 1/ + + + align:start position:0% +Theta and your concentration then is 1/ +Sina remember before + + align:start position:0% +Sina remember before + + + align:start position:0% +Sina remember before +is say sin 25 over 2 Sina now you got + + align:start position:0% +is say sin 25 over 2 Sina now you got + + + align:start position:0% +is say sin 25 over 2 Sina now you got +rid of that factor of two in the two + + align:start position:0% +rid of that factor of two in the two + + + align:start position:0% +rid of that factor of two in the two +dimensional geometry + + align:start position:0% +dimensional geometry + + + align:start position:0% +dimensional geometry +and you go to 3D you actually + + align:start position:0% +and you go to 3D you actually + + + align:start position:0% +and you go to 3D you actually +reach 1 sin Theta squ so if you put your + + align:start position:0% +reach 1 sin Theta squ so if you put your + + + align:start position:0% +reach 1 sin Theta squ so if you put your +Theta angle of acceptance right if you + + align:start position:0% +Theta angle of acceptance right if you + + + align:start position:0% +Theta angle of acceptance right if you +just say I only accepted the solar com + + align:start position:0% +just say I only accepted the solar com + + + align:start position:0% +just say I only accepted the solar com +Theta + + align:start position:0% +Theta + + + align:start position:0% +Theta +s when when that that's your maximum you + + align:start position:0% +s when when that that's your maximum you + + + align:start position:0% +s when when that that's your maximum you +have to accept the all solar within that + + align:start position:0% +have to accept the all solar within that + + + align:start position:0% +have to accept the all solar within that +20 uh 32 R right + + align:start position:0% +20 uh 32 R right + + + align:start position:0% +20 uh 32 R right +second so that's a maximum there but + + align:start position:0% +second so that's a maximum there but + + + align:start position:0% +second so that's a maximum there but +this is a conent because say If you + + align:start position:0% +this is a conent because say If you + + + align:start position:0% +this is a conent because say If you +think about uh Your Design you don't + + align:start position:0% +think about uh Your Design you don't + + + align:start position:0% +think about uh Your Design you don't +need that high concentration but you + + align:start position:0% +need that high concentration but you + + + align:start position:0% +need that high concentration but you +want a large angle acceptance + + align:start position:0% +want a large angle acceptance + + + align:start position:0% +want a large angle acceptance +particularly when you have also street + + align:start position:0% +particularly when you have also street + + + align:start position:0% +particularly when you have also street +light right you if you think about you + + align:start position:0% +light right you if you think about you + + + align:start position:0% +light right you if you think about you +don't always have parallel light you + + align:start position:0% +don't always have parallel light you + + + align:start position:0% +don't always have parallel light you +also have the scatter light and then uh + + align:start position:0% +also have the scatter light and then uh + + + align:start position:0% +also have the scatter light and then uh +typically people take a 820 depends on + + align:start position:0% +typically people take a 820 depends on + + + align:start position:0% +typically people take a 820 depends on +where you live and so scalar light is a + + align:start position:0% +where you live and so scalar light is a + + + align:start position:0% +where you live and so scalar light is a +actually approximate isotropic in all + + align:start position:0% +actually approximate isotropic in all + + + align:start position:0% +actually approximate isotropic in all +directions so tracking if you track only + + align:start position:0% +directions so tracking if you track only + + + align:start position:0% +directions so tracking if you track only +the solar + + align:start position:0% +the solar + + + align:start position:0% +the solar +part right maximum concentration + + align:start position:0% +part right maximum concentration + + + align:start position:0% +part right maximum concentration +anything that beyond that angle you + + align:start position:0% +anything that beyond that angle you + + + align:start position:0% +anything that beyond that angle you +can't C capture it so that's 80 that 20% + + align:start position:0% +can't C capture it so that's 80 that 20% + + + align:start position:0% +can't C capture it so that's 80 that 20% +is + + align:start position:0% + + + + align:start position:0% + +gone and so with this this is the other + + align:start position:0% +gone and so with this this is the other + + + align:start position:0% +gone and so with this this is the other +examples and if you read the paper it's + + align:start position:0% +examples and if you read the paper it's + + + align:start position:0% +examples and if you read the paper it's +interesting uh uh uh this is when you + + align:start position:0% +interesting uh uh uh this is when you + + + align:start position:0% +interesting uh uh uh this is when you +concentrate + + align:start position:0% +concentrate + + + align:start position:0% +concentrate +to a + + align:start position:0% +to a + + + align:start position:0% +to a +cylinder using the same string rule you + + align:start position:0% +cylinder using the same string rule you + + + align:start position:0% +cylinder using the same string rule you +can you can draw this and in fact those + + align:start position:0% +can you can draw this and in fact those + + + align:start position:0% +can you can draw this and in fact those +curves shows different acceptance angle + + align:start position:0% +curves shows different acceptance angle + + + align:start position:0% +curves shows different acceptance angle +Theta uh and the concentration + + align:start position:0% +Theta uh and the concentration + + + align:start position:0% +Theta uh and the concentration +ratio and also the height of the height + + align:start position:0% +ratio and also the height of the height + + + align:start position:0% +ratio and also the height of the height +versus aperture so uh the uh this High + + align:start position:0% +versus aperture so uh the uh this High + + + align:start position:0% +versus aperture so uh the uh this High +aperture right and if you look at it if + + align:start position:0% +aperture right and if you look at it if + + + align:start position:0% +aperture right and if you look at it if +you want three times + + align:start position:0% +you want three times + + + align:start position:0% +you want three times +concentration that's about 21° and + + align:start position:0% +concentration that's about 21° and + + + align:start position:0% +concentration that's about 21° and +height aperature is about 2 to + + align:start position:0% + + + + align:start position:0% + +1 and also what's + + align:start position:0% +1 and also what's + + + align:start position:0% +1 and also what's +important is you can never make a + + align:start position:0% +important is you can never make a + + + align:start position:0% +important is you can never make a +perfect surface + + align:start position:0% +perfect surface + + + align:start position:0% +perfect surface +reflector so every time the lights light + + align:start position:0% +reflector so every time the lights light + + + align:start position:0% +reflector so every time the lights light +bounce once you lost a fraction of light + + align:start position:0% +bounce once you lost a fraction of light + + + align:start position:0% +bounce once you lost a fraction of light +right so this surface is lever perfectly + + align:start position:0% +right so this surface is lever perfectly + + + align:start position:0% +right so this surface is lever perfectly +reflecting 100% reflecting + + align:start position:0% +reflecting 100% reflecting + + + align:start position:0% +reflecting 100% reflecting +so you want to minimize that number of + + align:start position:0% +so you want to minimize that number of + + + align:start position:0% +so you want to minimize that number of +BNS because every time BNS it's absorb a + + align:start position:0% +BNS because every time BNS it's absorb a + + + align:start position:0% +BNS because every time BNS it's absorb a +fraction of it and when say aluminum is + + align:start position:0% +fraction of it and when say aluminum is + + + align:start position:0% +fraction of it and when say aluminum is +you can get about 97% reflection but + + align:start position:0% +you can get about 97% reflection but + + + align:start position:0% +you can get about 97% reflection but +that's 3% if you have 10 bounces 97 10 + + align:start position:0% +that's 3% if you have 10 bounces 97 10 + + + align:start position:0% +that's 3% if you have 10 bounces 97 10 +to power you'll get small L right so you + + align:start position:0% +to power you'll get small L right so you + + + align:start position:0% +to power you'll get small L right so you +want to minimize so he this this is the + + align:start position:0% +want to minimize so he this this is the + + + align:start position:0% +want to minimize so he this this is the +the average L of bums is he + + align:start position:0% +the average L of bums is he + + + align:start position:0% +the average L of bums is he +calculated uh for for this geometries + + align:start position:0% +calculated uh for for this geometries + + + align:start position:0% +calculated uh for for this geometries +okay so that's the this is the + + align:start position:0% +okay so that's the this is the + + + align:start position:0% +okay so that's the this is the +concentration right now you concentrate + + align:start position:0% +concentration right now you concentrate + + + align:start position:0% +concentration right now you concentrate +it particular when you go to higher + + align:start position:0% +it particular when you go to higher + + + align:start position:0% +it particular when you go to higher +concentration you have to track + + align:start position:0% +concentration you have to track + + + align:start position:0% +concentration you have to track +it because the the only certain angle is + + align:start position:0% +it because the the only certain angle is + + + align:start position:0% +it because the the only certain angle is +accepted right so you have to go track + + align:start position:0% +accepted right so you have to go track + + + align:start position:0% +accepted right so you have to go track +it so let's think + + align:start position:0% +it so let's think + + + align:start position:0% +it so let's think +about how we uh with + + align:start position:0% +about how we uh with + + + align:start position:0% +about how we uh with +the uh TI uh how you should do track + + align:start position:0% +the uh TI uh how you should do track + + + align:start position:0% +the uh TI uh how you should do track +right again think about the + + align:start position:0% +right again think about the + + + align:start position:0% +right again think about the +Earth has this + + align:start position:0% +Earth has this + + + align:start position:0% +Earth has this +23.5 degree til and in fact I haven't + + align:start position:0% +23.5 degree til and in fact I haven't + + + align:start position:0% +23.5 degree til and in fact I haven't +figur out all this a little bit detail + + align:start position:0% +figur out all this a little bit detail + + + align:start position:0% +figur out all this a little bit detail +in the earth's motion yet that tell 23.5 + + align:start position:0% +in the earth's motion yet that tell 23.5 + + + align:start position:0% +in the earth's motion yet that tell 23.5 +is the average L which it turns out the + + align:start position:0% +is the average L which it turns out the + + + align:start position:0% +is the average L which it turns out the +Earth is actually wble a little bit so + + align:start position:0% +Earth is actually wble a little bit so + + + align:start position:0% +Earth is actually wble a little bit so +it's wble that wobble happens between 22 + + align:start position:0% +it's wble that wobble happens between 22 + + + align:start position:0% +it's wble that wobble happens between 22 +to 24.5 + + align:start position:0% +to 24.5 + + + align:start position:0% +to 24.5 +okay and this will be important when you + + align:start position:0% +okay and this will be important when you + + + align:start position:0% +okay and this will be important when you +do the uh High concentration + + align:start position:0% +do the uh High concentration + + + align:start position:0% +do the uh High concentration +ratios and the acceptance angle so uh if + + align:start position:0% +ratios and the acceptance angle so uh if + + + align:start position:0% +ratios and the acceptance angle so uh if +you think about so that's what I I + + align:start position:0% +you think about so that's what I I + + + align:start position:0% +you think about so that's what I I +listed uh think in the + + align:start position:0% +listed uh think in the + + + align:start position:0% +listed uh think in the +summer right Northern + + align:start position:0% + + + + align:start position:0% + +Hemisphere and in the + + align:start position:0% +Hemisphere and in the + + + align:start position:0% +Hemisphere and in the +winter I come from uh so winter thousand + + align:start position:0% +winter I come from uh so winter thousand + + + align:start position:0% +winter I come from uh so winter thousand +hamere get there share of the + + align:start position:0% + + + + align:start position:0% + +sunlight + + align:start position:0% +sunlight + + + align:start position:0% +sunlight +and now let's think about the why of + + align:start position:0% +and now let's think about the why of + + + align:start position:0% +and now let's think about the why of +course it's easy to think why you need + + align:start position:0% +course it's easy to think why you need + + + align:start position:0% +course it's easy to think why you need +the tracking so I Lear say your + + align:start position:0% +the tracking so I Lear say your + + + align:start position:0% +the tracking so I Lear say your +radiation come in + + align:start position:0% +radiation come in + + + align:start position:0% +radiation come in +perpendicularly and when you come at the + + align:start position:0% +perpendicularly and when you come at the + + + align:start position:0% +perpendicularly and when you come at the +angle the mod energy you get is time + + align:start position:0% +angle the mod energy you get is time + + + align:start position:0% +angle the mod energy you get is time +Sina so you don't get all the energy you + + align:start position:0% +Sina so you don't get all the energy you + + + align:start position:0% +Sina so you don't get all the energy you +could get if you if you make this plate + + align:start position:0% +could get if you if you make this plate + + + align:start position:0% +could get if you if you make this plate +perpendicular to the re direction + + align:start position:0% + + + + align:start position:0% + +right but the uh uh the + + align:start position:0% +right but the uh uh the + + + align:start position:0% +right but the uh uh the +insulation not only just a s theeta + + align:start position:0% +insulation not only just a s theeta + + + align:start position:0% +insulation not only just a s theeta +change you also if you think about the + + align:start position:0% +change you also if you think about the + + + align:start position:0% +change you also if you think about the +the Pence through the atmosphere + + align:start position:0% +the Pence through the atmosphere + + + align:start position:0% +the Pence through the atmosphere +right different angle of incidence the + + align:start position:0% +right different angle of incidence the + + + align:start position:0% +right different angle of incidence the +Pence going through the + + align:start position:0% +Pence going through the + + + align:start position:0% +Pence going through the +atmosphere changes called 1/ cosine + + align:start position:0% +atmosphere changes called 1/ cosine + + + align:start position:0% +atmosphere changes called 1/ cosine +Theta sickness cosine Theta Direction + + align:start position:0% +Theta sickness cosine Theta Direction + + + align:start position:0% +Theta sickness cosine Theta Direction +relation so uh so you uh your + + align:start position:0% +relation so uh so you uh your + + + align:start position:0% +relation so uh so you uh your +insulation also changes and if you + + align:start position:0% +insulation also changes and if you + + + align:start position:0% +insulation also changes and if you +combine all this together uh uh those + + align:start position:0% +combine all this together uh uh those + + + align:start position:0% +combine all this together uh uh those +are some of the places people measure + + align:start position:0% +are some of the places people measure + + + align:start position:0% +are some of the places people measure +per square meter how much energy comes + + align:start position:0% +per square meter how much energy comes + + + align:start position:0% +per square meter how much energy comes +in and uh uh so this is like low than + + align:start position:0% +in and uh uh so this is like low than + + + align:start position:0% +in and uh uh so this is like low than +netive + + align:start position:0% +netive + + + align:start position:0% +netive +45° uh anybody remember Boston + + align:start position:0% + + + + align:start position:0% + +mag I was I thought I was going to check + + align:start position:0% +mag I was I thought I was going to check + + + align:start position:0% +mag I was I thought I was going to check +but I + + align:start position:0% +but I + + + align:start position:0% +but I +forgot + + align:start position:0% +forgot + + + align:start position:0% +forgot +okay so we're close on this L you can + + align:start position:0% +okay so we're close on this L you can + + + align:start position:0% +okay so we're close on this L you can +say this a not very + + align:start position:0% +say this a not very + + + align:start position:0% +say this a not very +good solution so my calculation was too + + align:start position:0% +good solution so my calculation was too + + + align:start position:0% +good solution so my calculation was too +optimistic I need about 78 square me for + + align:start position:0% +optimistic I need about 78 square me for + + + align:start position:0% +optimistic I need about 78 square me for +my hos + + align:start position:0% +my hos + + + align:start position:0% +my hos +okay so how which direction is should + + align:start position:0% +okay so how which direction is should + + + align:start position:0% +okay so how which direction is should +track right if you have a solar power + + align:start position:0% +track right if you have a solar power + + + align:start position:0% +track right if you have a solar power +water or solar panel should oriented the + + align:start position:0% +water or solar panel should oriented the + + + align:start position:0% +water or solar panel should oriented the +South + + align:start position:0% +South + + + align:start position:0% +South +loss East + + align:start position:0% +loss East + + + align:start position:0% +loss East +West right so uh of course this is a + + align:start position:0% +West right so uh of course this is a + + + align:start position:0% +West right so uh of course this is a +this is the East West uh this is the + + align:start position:0% +this is the East West uh this is the + + + align:start position:0% +this is the East West uh this is the +rotation the angle rotation is uh East + + align:start position:0% +rotation the angle rotation is uh East + + + align:start position:0% +rotation the angle rotation is uh East +West Direction so of course if you do + + align:start position:0% +West Direction so of course if you do + + + align:start position:0% +West Direction so of course if you do +Only One X tracking you want the maximum + + align:start position:0% +Only One X tracking you want the maximum + + + align:start position:0% +Only One X tracking you want the maximum +the amount of energy received the your + + align:start position:0% +the amount of energy received the your + + + align:start position:0% +the amount of energy received the your +solar Cale area or your aperture then + + align:start position:0% +solar Cale area or your aperture then + + + align:start position:0% +solar Cale area or your aperture then +you want to do the uh AIS in the south + + align:start position:0% +you want to do the uh AIS in the south + + + align:start position:0% +you want to do the uh AIS in the south +north Direction and then your rotation + + align:start position:0% +north Direction and then your rotation + + + align:start position:0% +north Direction and then your rotation +is the uh uh so that it's a East West + + align:start position:0% +is the uh uh so that it's a East West + + + align:start position:0% +is the uh uh so that it's a East West +direction right and then say in the + + align:start position:0% +direction right and then say in the + + + align:start position:0% +direction right and then say in the +other + + align:start position:0% +other + + + align:start position:0% +other +direction you remember the the Earth is + + align:start position:0% +direction you remember the the Earth is + + + align:start position:0% +direction you remember the the Earth is +say uh the the Tilt right during the + + align:start position:0% +say uh the the Tilt right during the + + + align:start position:0% +say uh the the Tilt right during the +summer and the winter that degree will + + align:start position:0% +summer and the winter that degree will + + + align:start position:0% +summer and the winter that degree will +go from go + + align:start position:0% +go from go + + + align:start position:0% +go from go +back + + align:start position:0% +back + + + align:start position:0% +back +here right so this angle F fits the uh + + align:start position:0% +here right so this angle F fits the uh + + + align:start position:0% +here right so this angle F fits the uh +your solar cell here this on the summer + + align:start position:0% +your solar cell here this on the summer + + + align:start position:0% +your solar cell here this on the summer +and then when you go to the uh winter + + align:start position:0% +and then when you go to the uh winter + + + align:start position:0% +and then when you go to the uh winter +side this side right your anle change so + + align:start position:0% +side this side right your anle change so + + + align:start position:0% +side this side right your anle change so +the uh uh so ideally you want to track + + align:start position:0% +the uh uh so ideally you want to track + + + align:start position:0% +the uh uh so ideally you want to track +both directions + + align:start position:0% + + + + align:start position:0% + +okay there is one uh case people have + + align:start position:0% +okay there is one uh case people have + + + align:start position:0% +okay there is one uh case people have +done + + align:start position:0% +done + + + align:start position:0% +done +before uh that uh uh I think it's + + align:start position:0% +before uh that uh uh I think it's + + + align:start position:0% +before uh that uh uh I think it's +interesting where you do not me + + align:start position:0% +interesting where you do not me + + + align:start position:0% +interesting where you do not me +tracking or you do seasonal adjustment + + align:start position:0% +tracking or you do seasonal adjustment + + + align:start position:0% +tracking or you do seasonal adjustment +and this is just when you have a low + + align:start position:0% +and this is just when you have a low + + + align:start position:0% +and this is just when you have a low +concentration and they people use the v + + align:start position:0% +concentration and they people use the v + + + align:start position:0% +concentration and they people use the v +v sh so uh this are the uh you put a + + align:start position:0% +v sh so uh this are the uh you put a + + + align:start position:0% +v sh so uh this are the uh you put a +solar cell here those surfaces are + + align:start position:0% +solar cell here those surfaces are + + + align:start position:0% +solar cell here those surfaces are +reflecting surfaces is a wave + + align:start position:0% +reflecting surfaces is a wave + + + align:start position:0% +reflecting surfaces is a wave +group okay and uh now if you orent those + + align:start position:0% +group okay and uh now if you orent those + + + align:start position:0% +group okay and uh now if you orent those +way in the uh East West direction if you + + align:start position:0% +way in the uh East West direction if you + + + align:start position:0% +way in the uh East West direction if you +think about East West Direction those + + align:start position:0% +think about East West Direction those + + + align:start position:0% +think about East West Direction those +groups in the east west so I you you you + + align:start position:0% +groups in the east west so I you you you + + + align:start position:0% +groups in the east west so I you you you +you will use this one means you can the + + align:start position:0% +you will use this one means you can the + + + align:start position:0% +you will use this one means you can the +light here you don't need to put the + + align:start position:0% +light here you don't need to put the + + + align:start position:0% +light here you don't need to put the +solar cell so you can actually increase + + align:start position:0% +solar cell so you can actually increase + + + align:start position:0% +solar cell so you can actually increase +the flux here by a factor of two you use + + align:start position:0% +the flux here by a factor of two you use + + + align:start position:0% +the flux here by a factor of two you use +a less two times less of + + align:start position:0% +a less two times less of + + + align:start position:0% +a less two times less of +area so uh uh the the typically for this + + align:start position:0% +area so uh uh the the typically for this + + + align:start position:0% +area so uh uh the the typically for this +geometry uh this Grove + + align:start position:0% +geometry uh this Grove + + + align:start position:0% +geometry uh this Grove +geometry uh uh you have you can get that + + align:start position:0% +geometry uh uh you have you can get that + + + align:start position:0% +geometry uh uh you have you can get that +say concentration ratio is uh 2.5 to + + align:start position:0% +say concentration ratio is uh 2.5 to + + + align:start position:0% +say concentration ratio is uh 2.5 to +three times so you can operate in that + + align:start position:0% +three times so you can operate in that + + + align:start position:0% +three times so you can operate in that +range low concentration R range and then + + align:start position:0% +range low concentration R range and then + + + align:start position:0% +range low concentration R range and then +if you do will do a little bit what you + + align:start position:0% +if you do will do a little bit what you + + + align:start position:0% +if you do will do a little bit what you +need here is a seasonal change because + + align:start position:0% +need here is a seasonal change because + + + align:start position:0% +need here is a seasonal change because +the acceptance angle in the uh South + + align:start position:0% +the acceptance angle in the uh South + + + align:start position:0% +the acceptance angle in the uh South +North Direction uh will change so uh um + + align:start position:0% +North Direction uh will change so uh um + + + align:start position:0% +North Direction uh will change so uh um +but there are also people now developing + + align:start position:0% +but there are also people now developing + + + align:start position:0% +but there are also people now developing +this Mo I was check and there people + + align:start position:0% +this Mo I was check and there people + + + align:start position:0% +this Mo I was check and there people +actually do tracking littleit tracking + + align:start position:0% +actually do tracking littleit tracking + + + align:start position:0% +actually do tracking littleit tracking +so there are even people doing South + + align:start position:0% +so there are even people doing South + + + align:start position:0% +so there are even people doing South +North Direction tracking but in the in + + align:start position:0% +North Direction tracking but in the in + + + align:start position:0% +North Direction tracking but in the in +theory so for those low concentration + + align:start position:0% +theory so for those low concentration + + + align:start position:0% +theory so for those low concentration +looks like you put it in Direction you + + align:start position:0% +looks like you put it in Direction you + + + align:start position:0% +looks like you put it in Direction you +still don't capture that s Theta right + + align:start position:0% +still don't capture that s Theta right + + + align:start position:0% +still don't capture that s Theta right +the sort of insulation that that's still + + align:start position:0% +the sort of insulation that that's still + + + align:start position:0% +the sort of insulation that that's still +will change because your angle coming at + + align:start position:0% +will change because your angle coming at + + + align:start position:0% +will change because your angle coming at +an angle your your projected area you're + + align:start position:0% +an angle your your projected area you're + + + align:start position:0% +an angle your your projected area you're +not tracking uh perpendicular there but + + align:start position:0% +not tracking uh perpendicular there but + + + align:start position:0% +not tracking uh perpendicular there but +you you use less in this case you if you + + align:start position:0% +you you use less in this case you if you + + + align:start position:0% +you you use less in this case you if you +do this concentration you use two or + + align:start position:0% +do this concentration you use two or + + + align:start position:0% +do this concentration you use two or +three times less solar + + align:start position:0% +three times less solar + + + align:start position:0% +three times less solar +shell so you cut a + + align:start position:0% + + + + align:start position:0% + +cost okay + + align:start position:0% +cost okay + + + align:start position:0% +cost okay +so this is the uh uh what we uh talked + + align:start position:0% +so this is the uh uh what we uh talked + + + align:start position:0% +so this is the uh uh what we uh talked +about is the uh concentration and + + align:start position:0% +about is the uh concentration and + + + align:start position:0% +about is the uh concentration and +tracking and uh uh I uh in terms of PV + + align:start position:0% +tracking and uh uh I uh in terms of PV + + + align:start position:0% +tracking and uh uh I uh in terms of PV +people do s concentrated P there are + + align:start position:0% +people do s concentrated P there are + + + align:start position:0% +people do s concentrated P there are +there's effort uh there are some uh uh + + align:start position:0% +there's effort uh there are some uh uh + + + align:start position:0% +there's effort uh there are some uh uh +company startup company I'm not sure how + + align:start position:0% +company startup company I'm not sure how + + + align:start position:0% +company startup company I'm not sure how +successful they they have been in + + align:start position:0% +successful they they have been in + + + align:start position:0% +successful they they have been in +deploying uh this is particularly when + + align:start position:0% +deploying uh this is particularly when + + + align:start position:0% +deploying uh this is particularly when +when you think about the high efficient + + align:start position:0% +when you think about the high efficient + + + align:start position:0% +when you think about the high efficient +solar cells like gum asite the maximum + + align:start position:0% +solar cells like gum asite the maximum + + + align:start position:0% +solar cells like gum asite the maximum +here you can get about + + align:start position:0% +here you can get about + + + align:start position:0% +here you can get about +40% right that's very expensive so what + + align:start position:0% +40% right that's very expensive so what + + + align:start position:0% +40% right that's very expensive so what +you want is use a high concentration + + align:start position:0% +you want is use a high concentration + + + align:start position:0% +you want is use a high concentration +ratio to reduce the cost uh per unit + + align:start position:0% +ratio to reduce the cost uh per unit + + + align:start position:0% +ratio to reduce the cost uh per unit +area say s of incoming + + align:start position:0% +area say s of incoming + + + align:start position:0% +area say s of incoming +cost and uh uh but say the um I'm not + + align:start position:0% +cost and uh uh but say the um I'm not + + + align:start position:0% +cost and uh uh but say the um I'm not +sure how successful they are + + align:start position:0% +sure how successful they are + + + align:start position:0% +sure how successful they are +commercially and uh I know one of the + + align:start position:0% +commercially and uh I know one of the + + + align:start position:0% +commercially and uh I know one of the +problem is actually the ke transfer is a + + align:start position:0% +problem is actually the ke transfer is a + + + align:start position:0% +problem is actually the ke transfer is a +problem and the other is it's very I I + + align:start position:0% +problem and the other is it's very I I + + + align:start position:0% +problem and the other is it's very I I +think it's very important to keep the + + align:start position:0% +think it's very important to keep the + + + align:start position:0% +think it's very important to keep the +light the uniform so uh if the higher + + align:start position:0% +light the uniform so uh if the higher + + + align:start position:0% +light the uniform so uh if the higher +the concentration you have the if your + + align:start position:0% +the concentration you have the if your + + + align:start position:0% +the concentration you have the if your +tracking is lot accurate your light goes + + align:start position:0% +tracking is lot accurate your light goes + + + align:start position:0% +tracking is lot accurate your light goes +off the + + align:start position:0% +off the + + + align:start position:0% +off the +your then uh uh so you're screwed so + + align:start position:0% +your then uh uh so you're screwed so + + + align:start position:0% +your then uh uh so you're screwed so +that's the the tracking accuracy becomes + + align:start position:0% +that's the the tracking accuracy becomes + + + align:start position:0% +that's the the tracking accuracy becomes +very + + align:start position:0% +very + + + align:start position:0% +very +important uh now I'm going to shift next + + align:start position:0% +important uh now I'm going to shift next + + + align:start position:0% +important uh now I'm going to shift next +to the uh solar uh the uh uh energy + + align:start position:0% +to the uh solar uh the uh uh energy + + + align:start position:0% +to the uh solar uh the uh uh energy +conversion system and uh uh the sort of + + align:start position:0% +conversion system and uh uh the sort of + + + align:start position:0% +conversion system and uh uh the sort of +mechanical uh energy conversion and one + + align:start position:0% +mechanical uh energy conversion and one + + + align:start position:0% +mechanical uh energy conversion and one +uh the most popular in use is the 12 so + + align:start position:0% +uh the most popular in use is the 12 so + + + align:start position:0% +uh the most popular in use is the 12 so +uh the absorber is a tube and you + + align:start position:0% +uh the absorber is a tube and you + + + align:start position:0% +uh the absorber is a tube and you +concentrate the light and uh uh or so + + align:start position:0% +concentrate the light and uh uh or so + + + align:start position:0% +concentrate the light and uh uh or so +this concentration could be either by + + align:start position:0% +this concentration could be either by + + + align:start position:0% +this concentration could be either by +parabolic + + align:start position:0% +parabolic + + + align:start position:0% +parabolic +mirrors uh all the frale uh arrays in + + align:start position:0% +mirrors uh all the frale uh arrays in + + + align:start position:0% +mirrors uh all the frale uh arrays in +this FR now so you can see the the + + align:start position:0% +this FR now so you can see the the + + + align:start position:0% +this FR now so you can see the the +mirror is individually adjusted so this + + align:start position:0% +mirror is individually adjusted so this + + + align:start position:0% +mirror is individually adjusted so this +is not part one uh say parabolic but the + + align:start position:0% +is not part one uh say parabolic but the + + + align:start position:0% +is not part one uh say parabolic but the +angle of each mirror is adjusted so that + + align:start position:0% +angle of each mirror is adjusted so that + + + align:start position:0% +angle of each mirror is adjusted so that +the light Focus to the pipe + + align:start position:0% + + + + align:start position:0% + +there it's called the FR but I think the + + align:start position:0% +there it's called the FR but I think the + + + align:start position:0% +there it's called the FR but I think the +FR is I my understand FR + + align:start position:0% +FR is I my understand FR + + + align:start position:0% +FR is I my understand FR +is real object that's a defraction side + + align:start position:0% +is real object that's a defraction side + + + align:start position:0% +is real object that's a defraction side +but anyway um and this is a u a dish + + align:start position:0% +but anyway um and this is a u a dish + + + align:start position:0% +but anyway um and this is a u a dish +where you concentrate uh to uh you track + + align:start position:0% +where you concentrate uh to uh you track + + + align:start position:0% +where you concentrate uh to uh you track +2D uh here you could the uh just do 1D + + align:start position:0% +2D uh here you could the uh just do 1D + + + align:start position:0% +2D uh here you could the uh just do 1D +da packing or uh I'm not sure people do + + align:start position:0% +da packing or uh I'm not sure people do + + + align:start position:0% +da packing or uh I'm not sure people do +a season adjustment or not and here you + + align:start position:0% +a season adjustment or not and here you + + + align:start position:0% +a season adjustment or not and here you +do uh you need a 2d tracking is a dish + + align:start position:0% + + + + align:start position:0% + +structure or you do Tower you have was a + + align:start position:0% +structure or you do Tower you have was a + + + align:start position:0% +structure or you do Tower you have was a +uh station of the mirror reflecting uh + + align:start position:0% +uh station of the mirror reflecting uh + + + align:start position:0% +uh station of the mirror reflecting uh +and and uh uh uh to the + + align:start position:0% +and and uh uh uh to the + + + align:start position:0% +and and uh uh uh to the +Tower and 12 is the most uh uh commonly + + align:start position:0% +Tower and 12 is the most uh uh commonly + + + align:start position:0% +Tower and 12 is the most uh uh commonly +use look at the more Char structure + + align:start position:0% +use look at the more Char structure + + + align:start position:0% +use look at the more Char structure +where you have a parabolic mirror and + + align:start position:0% +where you have a parabolic mirror and + + + align:start position:0% +where you have a parabolic mirror and +you have the uh pipe inside in the focal + + align:start position:0% + + + + align:start position:0% + +plant and this is + + align:start position:0% +plant and this is + + + align:start position:0% +plant and this is +a a typ uh pipe the solar collector pipe + + align:start position:0% +a a typ uh pipe the solar collector pipe + + + align:start position:0% +a a typ uh pipe the solar collector pipe +again it's a vacuum so the vacuum is a + + align:start position:0% +again it's a vacuum so the vacuum is a + + + align:start position:0% +again it's a vacuum so the vacuum is a +pretty uh High vacuum here 10us 3 + + align:start position:0% +pretty uh High vacuum here 10us 3 + + + align:start position:0% +pretty uh High vacuum here 10us 3 +m right and uh uh the uh you can imagine + + align:start position:0% +m right and uh uh the uh you can imagine + + + align:start position:0% +m right and uh uh the uh you can imagine +the challenge because the pipe itself is + + align:start position:0% +the challenge because the pipe itself is + + + align:start position:0% +the challenge because the pipe itself is +a steel pipe uh steel pipe and then + + align:start position:0% +a steel pipe uh steel pipe and then + + + align:start position:0% +a steel pipe uh steel pipe and then +outside is coated with Selective + + align:start position:0% +outside is coated with Selective + + + align:start position:0% +outside is coated with Selective +resolver so um this is a um typically + + align:start position:0% +resolver so um this is a um typically + + + align:start position:0% +resolver so um this is a um typically +you can you can see the absorptance is + + align:start position:0% +you can you can see the absorptance is + + + align:start position:0% +you can you can see the absorptance is +larger than 95 emittance is less than + + align:start position:0% +larger than 95 emittance is less than + + + align:start position:0% +larger than 95 emittance is less than +14% at 400° + + align:start position:0% +14% at 400° + + + align:start position:0% +14% at 400° +in and the outer clear glass is also + + align:start position:0% +in and the outer clear glass is also + + + align:start position:0% +in and the outer clear glass is also +coated and say uh so that so it's enter + + align:start position:0% +coated and say uh so that so it's enter + + + align:start position:0% +coated and say uh so that so it's enter +reflection coding so the transmission + + align:start position:0% +reflection coding so the transmission + + + align:start position:0% +reflection coding so the transmission +Tiber glass Transmissions about + + align:start position:0% +Tiber glass Transmissions about + + + align:start position:0% +Tiber glass Transmissions about +93% now get to + + align:start position:0% +93% now get to + + + align:start position:0% +93% now get to +96% and uh um the um what's + + align:start position:0% +96% and uh um the um what's + + + align:start position:0% +96% and uh um the um what's +if you look at this what's important how + + align:start position:0% +if you look at this what's important how + + + align:start position:0% +if you look at this what's important how +you make the Cale here right high + + align:start position:0% +you make the Cale here right high + + + align:start position:0% +you make the Cale here right high +temperature Cale is really say you have + + align:start position:0% +temperature Cale is really say you have + + + align:start position:0% +temperature Cale is really say you have +a tube 100 met long and thermal + + align:start position:0% +a tube 100 met long and thermal + + + align:start position:0% +a tube 100 met long and thermal +expansion and seale that's those are + + align:start position:0% +expansion and seale that's those are + + + align:start position:0% +expansion and seale that's those are +really critical + + align:start position:0% + + + + align:start position:0% + +Technologies so uh temp 12 plan got the + + align:start position:0% +Technologies so uh temp 12 plan got the + + + align:start position:0% +Technologies so uh temp 12 plan got the +collectors you have the uh steam + + align:start position:0% +collectors you have the uh steam + + + align:start position:0% +collectors you have the uh steam +turbine and you + + align:start position:0% +turbine and you + + + align:start position:0% +turbine and you +also uh have very often you have to have + + align:start position:0% +also uh have very often you have to have + + + align:start position:0% +also uh have very often you have to have +the gas fire so you have to code + + align:start position:0% +the gas fire so you have to code + + + align:start position:0% +the gas fire so you have to code +generation what what what do you what do + + align:start position:0% +generation what what what do you what do + + + align:start position:0% +generation what what what do you what do +you do in the light or what happens if + + align:start position:0% +you do in the light or what happens if + + + align:start position:0% +you do in the light or what happens if +you have clouds + + align:start position:0% +you have clouds + + + align:start position:0% +you have clouds +coming that's actually big heit + + align:start position:0% +coming that's actually big heit + + + align:start position:0% +coming that's actually big heit +there particular for p SAR theral + + align:start position:0% +there particular for p SAR theral + + + align:start position:0% +there particular for p SAR theral +actually slight better because theral + + align:start position:0% +actually slight better because theral + + + align:start position:0% +actually slight better because theral +inertia thermal ke capacity damping that + + align:start position:0% +inertia thermal ke capacity damping that + + + align:start position:0% +inertia thermal ke capacity damping that +that's that's one of the that solar Thal + + align:start position:0% +that's that's one of the that solar Thal + + + align:start position:0% +that's that's one of the that solar Thal +has and uh uh you could also do uh uh + + align:start position:0% +has and uh uh you could also do uh uh + + + align:start position:0% +has and uh uh you could also do uh uh +some uh storage I'm not sure here has + + align:start position:0% +some uh storage I'm not sure here has + + + align:start position:0% +some uh storage I'm not sure here has +storage uh but you could you could do uh + + align:start position:0% +storage uh but you could you could do uh + + + align:start position:0% +storage uh but you could you could do uh +storage and the solar stal plant here + + align:start position:0% +storage and the solar stal plant here + + + align:start position:0% +storage and the solar stal plant here +the fluid itself you can see is a close + + align:start position:0% +the fluid itself you can see is a close + + + align:start position:0% +the fluid itself you can see is a close +loop the fluid through the pipe is close + + align:start position:0% +loop the fluid through the pipe is close + + + align:start position:0% +loop the fluid through the pipe is close +well steam generation steam turbine + + align:start position:0% +well steam generation steam turbine + + + align:start position:0% +well steam generation steam turbine +typic is the water based steam turbine + + align:start position:0% +typic is the water based steam turbine + + + align:start position:0% +typic is the water based steam turbine +so that's the this is the other loop the + + align:start position:0% +so that's the this is the other loop the + + + align:start position:0% +so that's the this is the other loop the +steam Lo here and in fact the in the + + align:start position:0% +steam Lo here and in fact the in the + + + align:start position:0% +steam Lo here and in fact the in the +pipe they use oil and the oil is one + + align:start position:0% +pipe they use oil and the oil is one + + + align:start position:0% +pipe they use oil and the oil is one +problem you can't go to too high + + align:start position:0% +problem you can't go to too high + + + align:start position:0% +problem you can't go to too high +temperature you go to too high + + align:start position:0% +temperature you go to too high + + + align:start position:0% +temperature you go to too high +temperature you + + align:start position:0% +temperature you + + + align:start position:0% +temperature you +decompos and uh uh so the uh oil has a + + align:start position:0% +decompos and uh uh so the uh oil has a + + + align:start position:0% +decompos and uh uh so the uh oil has a +stability this this is a steel area + + align:start position:0% +stability this this is a steel area + + + align:start position:0% +stability this this is a steel area +where people doing research stability + + align:start position:0% +where people doing research stability + + + align:start position:0% +where people doing research stability +problem and how you can develop higher + + align:start position:0% +problem and how you can develop higher + + + align:start position:0% +problem and how you can develop higher +temperature oils you can you can get to + + align:start position:0% +temperature oils you can you can get to + + + align:start position:0% +temperature oils you can you can get to +higher temperature but the your oil will + + align:start position:0% + + + + align:start position:0% + +not okay and this is another just a + + align:start position:0% +not okay and this is another just a + + + align:start position:0% +not okay and this is another just a +picture + + align:start position:0% +picture + + + align:start position:0% +picture +here uh the TP uh they if you look at + + align:start position:0% +here uh the TP uh they if you look at + + + align:start position:0% +here uh the TP uh they if you look at +the + + align:start position:0% +the + + + align:start position:0% +the +install uh uh the uh typical installed + + align:start position:0% +install uh uh the uh typical installed + + + align:start position:0% +install uh uh the uh typical installed +and typical size of the plant is around + + align:start position:0% +and typical size of the plant is around + + + align:start position:0% +and typical size of the plant is around + + align:start position:0% + + + align:start position:0% +m 100 megawatt is small uh in terms of + + align:start position:0% +m 100 megawatt is small uh in terms of + + + align:start position:0% +m 100 megawatt is small uh in terms of +if you compare with + + align:start position:0% +if you compare with + + + align:start position:0% +if you compare with +coire right kire plant typically one + + align:start position:0% +coire right kire plant typically one + + + align:start position:0% +coire right kire plant typically one +steam turbine there is one + + align:start position:0% +steam turbine there is one + + + align:start position:0% +steam turbine there is one +gwatt + + align:start position:0% + + + + align:start position:0% + +okay and uh this is too small uh you can + + align:start position:0% +okay and uh this is too small uh you can + + + align:start position:0% +okay and uh this is too small uh you can +read uh your hand out but so those are + + align:start position:0% +read uh your hand out but so those are + + + align:start position:0% +read uh your hand out but so those are +examples and what I want to point out + + align:start position:0% +examples and what I want to point out + + + align:start position:0% +examples and what I want to point out +here are the concentration here it's + + align:start position:0% +here are the concentration here it's + + + align:start position:0% +here are the concentration here it's +typically uh those concentration is + + align:start position:0% +typically uh those concentration is + + + align:start position:0% +typically uh those concentration is +between 60 to 80 uh + + align:start position:0% +between 60 to 80 uh + + + align:start position:0% +between 60 to 80 uh +that's um the concentration + + align:start position:0% +that's um the concentration + + + align:start position:0% +that's um the concentration +ratio and you look at the cost of the + + align:start position:0% +ratio and you look at the cost of the + + + align:start position:0% +ratio and you look at the cost of the +solar theral this are the uh one case + + align:start position:0% +solar theral this are the uh one case + + + align:start position:0% +solar theral this are the uh one case +where different generation 30 + + align:start position:0% +where different generation 30 + + + align:start position:0% +where different generation 30 +megawatt uh this is a US dollar megawatt + + align:start position:0% +megawatt uh this is a US dollar megawatt + + + align:start position:0% +megawatt uh this is a US dollar megawatt +hour so if you do kilowatt hour you + + align:start position:0% +hour so if you do kilowatt hour you + + + align:start position:0% +hour so if you do kilowatt hour you +divide it by thousand so that's about 90 + + align:start position:0% +divide it by thousand so that's about 90 + + + align:start position:0% +divide it by thousand so that's about 90 +Cent 19 cents per kilowatt hour cold + + align:start position:0% +Cent 19 cents per kilowatt hour cold + + + align:start position:0% +Cent 19 cents per kilowatt hour cold +fire is about 5 + + align:start position:0% + + + + align:start position:0% + +cents power power PL so here is 16 cents + + align:start position:0% +cents power power PL so here is 16 cents + + + align:start position:0% +cents power power PL so here is 16 cents +and there's some projecting you scale up + + align:start position:0% +and there's some projecting you scale up + + + align:start position:0% +and there's some projecting you scale up +that will go down to 10 + + align:start position:0% + + + + align:start position:0% + +cents the efficiency again I'm not + + align:start position:0% +cents the efficiency again I'm not + + + align:start position:0% +cents the efficiency again I'm not +expecting to read it I'm just let me + + align:start position:0% +expecting to read it I'm just let me + + + align:start position:0% +expecting to read it I'm just let me +just quoted uh uh the view efficiency + + align:start position:0% +just quoted uh uh the view efficiency + + + align:start position:0% +just quoted uh uh the view efficiency +lambers uh uh the collector efficiency + + align:start position:0% +lambers uh uh the collector efficiency + + + align:start position:0% +lambers uh uh the collector efficiency +here is uh + + align:start position:0% +here is uh + + + align:start position:0% +here is uh +50% receiver efficiency + + align:start position:0% +50% receiver efficiency + + + align:start position:0% +50% receiver efficiency +82% and the cycle that's steam turine + + align:start position:0% +82% and the cycle that's steam turine + + + align:start position:0% +82% and the cycle that's steam turine +cycle efficiency here uh + + align:start position:0% +cycle efficiency here uh + + + align:start position:0% +cycle efficiency here uh +45% right uh see right now is + + align:start position:0% +45% right uh see right now is + + + align:start position:0% +45% right uh see right now is +38% so at the end if you combine all + + align:start position:0% +38% so at the end if you combine all + + + align:start position:0% +38% so at the end if you combine all +this efficiency here this is about uh + + align:start position:0% +this efficiency here this is about uh + + + align:start position:0% +this efficiency here this is about uh +between 13 to + + align:start position:0% + + + + align:start position:0% + +17% the collection + + align:start position:0% +17% the collection + + + align:start position:0% +17% the collection +efficiency is not + + align:start position:0% +efficiency is not + + + align:start position:0% +efficiency is not +good collector efficiency here is only + + align:start position:0% +good collector efficiency here is only + + + align:start position:0% +good collector efficiency here is only +about + + align:start position:0% +about + + + align:start position:0% +about +50% you lost a lot of + + align:start position:0% +50% you lost a lot of + + + align:start position:0% +50% you lost a lot of +light in the collection so there you + + align:start position:0% +light in the collection so there you + + + align:start position:0% +light in the collection so there you +want to minimize the Lum of reflection + + align:start position:0% +want to minimize the Lum of reflection + + + align:start position:0% +want to minimize the Lum of reflection +the other problem is your streight light + + align:start position:0% +the other problem is your streight light + + + align:start position:0% +the other problem is your streight light +right if you design High concentration + + align:start position:0% +right if you design High concentration + + + align:start position:0% +right if you design High concentration +if it's not parallel you don't fall into + + align:start position:0% +if it's not parallel you don't fall into + + + align:start position:0% +if it's not parallel you don't fall into +the focal point + + align:start position:0% + + + + align:start position:0% + +uh interesting to look at the cost uh + + align:start position:0% +uh interesting to look at the cost uh + + + align:start position:0% +uh interesting to look at the cost uh +the cost here uh the uh uh uh if you + + align:start position:0% +the cost here uh the uh uh uh if you + + + align:start position:0% +the cost here uh the uh uh uh if you +look at here we have 58 that's the + + align:start position:0% +look at here we have 58 that's the + + + align:start position:0% +look at here we have 58 that's the +collection system 58 and structure this + + align:start position:0% +collection system 58 and structure this + + + align:start position:0% +collection system 58 and structure this +is a uh this is this one uh the um does + + align:start position:0% +is a uh this is this one uh the um does + + + align:start position:0% +is a uh this is this one uh the um does +not include the uh the engine so you + + align:start position:0% +not include the uh the engine so you + + + align:start position:0% +not include the uh the engine so you +have the Storage seral storage is here + + align:start position:0% +have the Storage seral storage is here + + + align:start position:0% +have the Storage seral storage is here +and uh uh we have 14% is the power block + + align:start position:0% +and uh uh we have 14% is the power block + + + align:start position:0% +and uh uh we have 14% is the power block +I do not know what exactly is + + align:start position:0% +I do not know what exactly is + + + align:start position:0% +I do not know what exactly is +that okay and uh now here is the um so + + align:start position:0% +that okay and uh now here is the um so + + + align:start position:0% +that okay and uh now here is the um so +this is the + + align:start position:0% +this is the + + + align:start position:0% +this is the +parabolic and + + align:start position:0% +parabolic and + + + align:start position:0% +parabolic and +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh again this is a break down different + + align:start position:0% +uh again this is a break down different + + + align:start position:0% +uh again this is a break down different +materials the cost + + align:start position:0% +materials the cost + + + align:start position:0% +materials the cost +structure and uh so that's the uh + + align:start position:0% +structure and uh so that's the uh + + + align:start position:0% +structure and uh so that's the uh +I thought I was trying to find out I + + align:start position:0% +I thought I was trying to find out I + + + align:start position:0% +I thought I was trying to find out I +thought I saw it before where is the + + align:start position:0% +thought I saw it before where is the + + + align:start position:0% +thought I saw it before where is the +uh + + align:start position:0% +uh + + + align:start position:0% +uh +cycle huh oh okay yeah okay so that's + + align:start position:0% +cycle huh oh okay yeah okay so that's + + + align:start position:0% +cycle huh oh okay yeah okay so that's +that's where it is yeah so cycle the + + align:start position:0% +that's where it is yeah so cycle the + + + align:start position:0% +that's where it is yeah so cycle the +cycle itself is not + + align:start position:0% + + + + align:start position:0% + +the uh yeah this is yeah this is so the + + align:start position:0% +the uh yeah this is yeah this is so the + + + align:start position:0% +the uh yeah this is yeah this is so the +the first one is the the overall the + + align:start position:0% +the first one is the the overall the + + + align:start position:0% +the first one is the the overall the +bottom one is the uh field + + align:start position:0% + + + + align:start position:0% + +component so the uh uh cycle itself is + + align:start position:0% +component so the uh uh cycle itself is + + + align:start position:0% +component so the uh uh cycle itself is +not big top the uh + + align:start position:0% +not big top the uh + + + align:start position:0% +not big top the uh +collector look at I think was + + align:start position:0% +collector look at I think was + + + align:start position:0% +collector look at I think was +interesting look at this here metal + + align:start position:0% +interesting look at this here metal + + + align:start position:0% +interesting look at this here metal +support structure + + align:start position:0% + + + + align:start position:0% + +29% right this is a big big stuff there + + align:start position:0% +29% right this is a big big stuff there + + + align:start position:0% +29% right this is a big big stuff there +the steel is use a lot of + + align:start position:0% +the steel is use a lot of + + + align:start position:0% +the steel is use a lot of +Steel and uh + + align:start position:0% +Steel and uh + + + align:start position:0% +Steel and uh +receiver 20% mural 9% Mass support is + + align:start position:0% +receiver 20% mural 9% Mass support is + + + align:start position:0% +receiver 20% mural 9% Mass support is +the big + + align:start position:0% + + + + align:start position:0% + +one so if you can cut that cost that's + + align:start position:0% +one so if you can cut that cost that's + + + align:start position:0% +one so if you can cut that cost that's +good the + + align:start position:0% +good the + + + align:start position:0% +good the +engine the engine is + + align:start position:0% +engine the engine is + + + align:start position:0% +engine the engine is +here 14 that's + + align:start position:0% +here 14 that's + + + align:start position:0% +here 14 that's +L compared to the the solar + + align:start position:0% +L compared to the the solar + + + align:start position:0% +L compared to the the solar +side okay so uh if you were in Jacob Car + + align:start position:0% +side okay so uh if you were in Jacob Car + + + align:start position:0% +side okay so uh if you were in Jacob Car +Talk a few weeks ago he give much he + + align:start position:0% +Talk a few weeks ago he give much he + + + align:start position:0% +Talk a few weeks ago he give much he +does a lot of the K St so you have + + align:start position:0% +does a lot of the K St so you have + + + align:start position:0% +does a lot of the K St so you have +mirors uh uh trag sign each one and + + align:start position:0% +mirors uh uh trag sign each one and + + + align:start position:0% +mirors uh uh trag sign each one and +reflect to the power the center there so + + align:start position:0% +reflect to the power the center there so + + + align:start position:0% +reflect to the power the center there so +it's like a big two big array of MIRS + + align:start position:0% +it's like a big two big array of MIRS + + + align:start position:0% +it's like a big two big array of MIRS +reflecting the + + align:start position:0% +reflecting the + + + align:start position:0% +reflecting the +light so the how the uh solar + + align:start position:0% +light so the how the uh solar + + + align:start position:0% +light so the how the uh solar +tower and uh uh what's interesting is + + align:start position:0% +tower and uh uh what's interesting is + + + align:start position:0% +tower and uh uh what's interesting is +this is what I learned from Jacob party + + align:start position:0% +this is what I learned from Jacob party + + + align:start position:0% +this is what I learned from Jacob party +is that the uh the fber size and he he + + align:start position:0% +is that the uh the fber size and he he + + + align:start position:0% +is that the uh the fber size and he he +put a question mark but I think the fber + + align:start position:0% +put a question mark but I think the fber + + + align:start position:0% +put a question mark but I think the fber +size is actually smaller than 12 the + + align:start position:0% +size is actually smaller than 12 the + + + align:start position:0% +size is actually smaller than 12 the +tower you don't want to build too + + align:start position:0% +tower you don't want to build too + + + align:start position:0% +tower you don't want to build too +big + + align:start position:0% +big + + + align:start position:0% +big +okay and uh L because but the + + align:start position:0% +okay and uh L because but the + + + align:start position:0% +okay and uh L because but the +temperature is much higher so the color + + align:start position:0% +temperature is much higher so the color + + + align:start position:0% +temperature is much higher so the color +efficiency should be higher and uh + + align:start position:0% +efficiency should be higher and uh + + + align:start position:0% +efficiency should be higher and uh +the problem is focer focus and he showed + + align:start position:0% +the problem is focer focus and he showed + + + align:start position:0% +the problem is focer focus and he showed +some very interesting + + align:start position:0% +some very interesting + + + align:start position:0% +some very interesting +pictures you don't always hit your + + align:start position:0% +pictures you don't always hit your + + + align:start position:0% +pictures you don't always hit your +target you have a lot of missing light + + align:start position:0% +target you have a lot of missing light + + + align:start position:0% +target you have a lot of missing light +like so if you look at around the uh the + + align:start position:0% +like so if you look at around the uh the + + + align:start position:0% +like so if you look at around the uh the +focal point you see lot of white light + + align:start position:0% +focal point you see lot of white light + + + align:start position:0% +focal point you see lot of white light +that's miss the + + align:start position:0% +that's miss the + + + align:start position:0% +that's miss the +scatter and so this is the absorber uh + + align:start position:0% +scatter and so this is the absorber uh + + + align:start position:0% +scatter and so this is the absorber uh +to uh different absorber uh ways to + + align:start position:0% +to uh different absorber uh ways to + + + align:start position:0% +to uh different absorber uh ways to +absorb the + + align:start position:0% +absorb the + + + align:start position:0% +absorb the +radiation and uh + + align:start position:0% +radiation and uh + + + align:start position:0% +radiation and uh +what uh in this Cas is so uh I showed I + + align:start position:0% +what uh in this Cas is so uh I showed I + + + align:start position:0% +what uh in this Cas is so uh I showed I +think in the last + + align:start position:0% +think in the last + + + align:start position:0% +think in the last +lecture once you get to higher + + align:start position:0% +lecture once you get to higher + + + align:start position:0% +lecture once you get to higher +concentration your absorption + + align:start position:0% +concentration your absorption + + + align:start position:0% +concentration your absorption +absorptivity is more important the + + align:start position:0% +absorptivity is more important the + + + align:start position:0% +absorptivity is more important the +emissivity is less + + align:start position:0% +emissivity is less + + + align:start position:0% +emissivity is less +important okay so uh this uh I think + + align:start position:0% +important okay so uh this uh I think + + + align:start position:0% +important okay so uh this uh I think +those are pretty uh it's not uh really + + align:start position:0% +those are pretty uh it's not uh really + + + align:start position:0% +those are pretty uh it's not uh really +spectral controlled + + align:start position:0% + + + + align:start position:0% + +surfaces uh there really not I think + + align:start position:0% +surfaces uh there really not I think + + + align:start position:0% +surfaces uh there really not I think +they only one or two span probably has + + align:start position:0% +they only one or two span probably has + + + align:start position:0% +they only one or two span probably has +but in us there The crimer Junction + + align:start position:0% +but in us there The crimer Junction + + + align:start position:0% +but in us there The crimer Junction +mostly is 12 but it does have a uh Power + + align:start position:0% +mostly is 12 but it does have a uh Power + + + align:start position:0% +mostly is 12 but it does have a uh Power +System uh and uh uh so here it gives you + + align:start position:0% +System uh and uh uh so here it gives you + + + align:start position:0% +System uh and uh uh so here it gives you +some uh in terms of the cost uh the + + align:start position:0% +some uh in terms of the cost uh the + + + align:start position:0% +some uh in terms of the cost uh the +field itself + + align:start position:0% +field itself + + + align:start position:0% +field itself +40% power is uh uh 14% people storage 11 + + align:start position:0% +40% power is uh uh 14% people storage 11 + + + align:start position:0% +40% power is uh uh 14% people storage 11 +and the engine is + + align:start position:0% +and the engine is + + + align:start position:0% +and the engine is +32 and uh so uh the uh this is the + + align:start position:0% +32 and uh so uh the uh this is the + + + align:start position:0% +32 and uh so uh the uh this is the +uh here is a structure reflector + + align:start position:0% +uh here is a structure reflector + + + align:start position:0% +uh here is a structure reflector +structure t% reflector + + align:start position:0% +structure t% reflector + + + align:start position:0% +structure t% reflector +36% uh Drive is drive for the packing is + + align:start position:0% +36% uh Drive is drive for the packing is + + + align:start position:0% +36% uh Drive is drive for the packing is +30% and the foundation so that's the + + align:start position:0% +30% and the foundation so that's the + + + align:start position:0% +30% and the foundation so that's the +packing system + + align:start position:0% + + + + align:start position:0% + +itself okay the uh car efficiency uh the + + align:start position:0% +itself okay the uh car efficiency uh the + + + align:start position:0% +itself okay the uh car efficiency uh the +this from the buper here is not much + + align:start position:0% +this from the buper here is not much + + + align:start position:0% +this from the buper here is not much +better uh than the uh uh no this one is + + align:start position:0% +better uh than the uh uh no this one is + + + align:start position:0% +better uh than the uh uh no this one is +not power I think sorry for that this + + align:start position:0% +not power I think sorry for that this + + + align:start position:0% +not power I think sorry for that this +one is not power this is still power I + + align:start position:0% +one is not power this is still power I + + + align:start position:0% +one is not power this is still power I +so I was going to this + + align:start position:0% +so I was going to this + + + align:start position:0% +so I was going to this +one okay uh the uh other form of the + + align:start position:0% +one okay uh the uh other form of the + + + align:start position:0% +one okay uh the uh other form of the +generator is a + + align:start position:0% +generator is a + + + align:start position:0% +generator is a +dish so this you you make smaller this + + align:start position:0% +dish so this you you make smaller this + + + align:start position:0% +dish so this you you make smaller this +one is say 2D say track + + align:start position:0% +one is say 2D say track + + + align:start position:0% +one is say 2D say track +and uh uh the problem is the generator + + align:start position:0% +and uh uh the problem is the generator + + + align:start position:0% +and uh uh the problem is the generator +here so you have the how you can make a + + align:start position:0% +here so you have the how you can make a + + + align:start position:0% +here so you have the how you can make a +small power G and here uh there a + + align:start position:0% +small power G and here uh there a + + + align:start position:0% +small power G and here uh there a +stering mechanical system so stering + + align:start position:0% +stering mechanical system so stering + + + align:start position:0% +stering mechanical system so stering +engine and if your mechanic engineer + + align:start position:0% +engine and if your mechanic engineer + + + align:start position:0% +engine and if your mechanic engineer +student here the second year they always + + align:start position:0% +student here the second year they always + + + align:start position:0% +student here the second year they always +build the a sterning engine it's a + + align:start position:0% +build the a sterning engine it's a + + + align:start position:0% +build the a sterning engine it's a +burner Benz is the sterning engine uh + + align:start position:0% +burner Benz is the sterning engine uh + + + align:start position:0% +burner Benz is the sterning engine uh +but so uh it's so the stting engine is + + align:start position:0% +but so uh it's so the stting engine is + + + align:start position:0% +but so uh it's so the stting engine is +very different from internal combust + + align:start position:0% +very different from internal combust + + + align:start position:0% +very different from internal combust +engine that's used in the car you can + + align:start position:0% +engine that's used in the car you can + + + align:start position:0% +engine that's used in the car you can +heat up uh one side of this turning + + align:start position:0% +heat up uh one side of this turning + + + align:start position:0% +heat up uh one side of this turning +engine and uh uh from external so + + align:start position:0% +engine and uh uh from external so + + + align:start position:0% +engine and uh uh from external so +external heating uh and then you + + align:start position:0% +external heating uh and then you + + + align:start position:0% +external heating uh and then you +generate the mechanical motion uh to + + align:start position:0% +generate the mechanical motion uh to + + + align:start position:0% +generate the mechanical motion uh to +drive uh to den power the cost is much + + align:start position:0% +drive uh to den power the cost is much + + + align:start position:0% +drive uh to den power the cost is much +higher I + + align:start position:0% +higher I + + + align:start position:0% +higher I +learned uh so uh I do not know anybody + + align:start position:0% +learned uh so uh I do not know anybody + + + align:start position:0% +learned uh so uh I do not know anybody +has is using this it's not + + align:start position:0% +has is using this it's not + + + align:start position:0% +has is using this it's not +mature the most mature is the 12 + + align:start position:0% + + + + align:start position:0% + +okay and + + align:start position:0% +okay and + + + align:start position:0% +okay and +uh so this uh we have an efficiency + + align:start position:0% +uh so this uh we have an efficiency + + + align:start position:0% +uh so this uh we have an efficiency +number + + align:start position:0% + + + + align:start position:0% + +here right here is + + align:start position:0% +here right here is + + + align:start position:0% +here right here is +the + + align:start position:0% +the + + + align:start position:0% +the +efficiency this efficiency is the + + align:start position:0% +efficiency this efficiency is the + + + align:start position:0% +efficiency this efficiency is the +uh I look this I don't it's a pretty + + align:start position:0% +uh I look this I don't it's a pretty + + + align:start position:0% +uh I look this I don't it's a pretty +high + + align:start position:0% + + + + align:start position:0% + +efficiency that's see uh but I I can't + + align:start position:0% +efficiency that's see uh but I I can't + + + align:start position:0% +efficiency that's see uh but I I can't +believe this number is 29 30% + + align:start position:0% + + + + align:start position:0% + +39 and so this is the + + align:start position:0% +39 and so this is the + + + align:start position:0% +39 and so this is the +stting and uh that's that's all I have + + align:start position:0% +stting and uh that's that's all I have + + + align:start position:0% +stting and uh that's that's all I have +in terms of the Thal mechanical + + align:start position:0% +in terms of the Thal mechanical + + + align:start position:0% +in terms of the Thal mechanical +systems any questions + + align:start position:0% + + + + align:start position:0% + +if not I will go back so this is a big + + align:start position:0% +if not I will go back so this is a big + + + align:start position:0% +if not I will go back so this is a big +stuff and I'll go back to uh it's a it's + + align:start position:0% +stuff and I'll go back to uh it's a it's + + + align:start position:0% +stuff and I'll go back to uh it's a it's +a it's simp + + align:start position:0% + + + + align:start position:0% + +question I think the the last two uh + + align:start position:0% +question I think the the last two uh + + + align:start position:0% +question I think the the last two uh +well at least it's stting I don't think + + align:start position:0% +well at least it's stting I don't think + + + align:start position:0% +well at least it's stting I don't think +this mature enough to about dollar per + + align:start position:0% +this mature enough to about dollar per + + + align:start position:0% +this mature enough to about dollar per +wat and some I don't have exact L ask + + align:start position:0% +wat and some I don't have exact L ask + + + align:start position:0% +wat and some I don't have exact L ask +the people around this is 10 times more + + align:start position:0% +the people around this is 10 times more + + + align:start position:0% +the people around this is 10 times more +expensive than uh + + align:start position:0% + + + + align:start position:0% + +but uh the hel + + align:start position:0% +but uh the hel + + + align:start position:0% +but uh the hel +St uh I have not looked at how many + + align:start position:0% +St uh I have not looked at how many + + + align:start position:0% +St uh I have not looked at how many +deployment let's say there was there was + + align:start position:0% +deployment let's say there was there was + + + align:start position:0% +deployment let's say there was there was +one running together with the I think + + align:start position:0% +one running together with the I think + + + align:start position:0% +one running together with the I think +the primier junction the the 12 + + align:start position:0% + + + + align:start position:0% + +system so uh what I want to do in the + + align:start position:0% +system so uh what I want to do in the + + + align:start position:0% +system so uh what I want to do in the +rest of the time now it's coming back to + + align:start position:0% +rest of the time now it's coming back to + + + align:start position:0% +rest of the time now it's coming back to +we have too many simple hand we stuff + + align:start position:0% +we have too many simple hand we stuff + + + align:start position:0% +we have too many simple hand we stuff +now now I want to come back to a little + + align:start position:0% +now now I want to come back to a little + + + align:start position:0% +now now I want to come back to a little +bit more uh math and the math the reason + + align:start position:0% +bit more uh math and the math the reason + + + align:start position:0% +bit more uh math and the math the reason +we want to do Le is what what are you + + align:start position:0% +we want to do Le is what what are you + + + align:start position:0% +we want to do Le is what what are you +going to say is a selective + + align:start position:0% +going to say is a selective + + + align:start position:0% +going to say is a selective +surface and it's important to have the + + align:start position:0% +surface and it's important to have the + + + align:start position:0% +surface and it's important to have the +in the case of concentrating parabolic + + align:start position:0% +in the case of concentrating parabolic + + + align:start position:0% +in the case of concentrating parabolic +miror it's important to have less + + align:start position:0% +miror it's important to have less + + + align:start position:0% +miror it's important to have less +reflection each reflection you lose very + + align:start position:0% +reflection each reflection you lose very + + + align:start position:0% +reflection each reflection you lose very +small amount of energy so you want a + + align:start position:0% +small amount of energy so you want a + + + align:start position:0% +small amount of energy so you want a +high reflectivity you want the high + + align:start position:0% +high reflectivity you want the high + + + align:start position:0% +high reflectivity you want the high +transmissivity going through glass and + + align:start position:0% +transmissivity going through glass and + + + align:start position:0% +transmissivity going through glass and +once you get onto the surface you absorb + + align:start position:0% +once you get onto the surface you absorb + + + align:start position:0% +once you get onto the surface you absorb +solar radiation you want to spectr + + align:start position:0% +solar radiation you want to spectr + + + align:start position:0% +solar radiation you want to spectr +absorb the solar radiation but do not + + align:start position:0% +absorb the solar radiation but do not + + + align:start position:0% +absorb the solar radiation but do not +radiate so now we this is in terms of + + align:start position:0% +radiate so now we this is in terms of + + + align:start position:0% +radiate so now we this is in terms of +Technology some of the key Technologies + + align:start position:0% +Technology some of the key Technologies + + + align:start position:0% +Technology some of the key Technologies +and for those technology now you have to + + align:start position:0% +and for those technology now you have to + + + align:start position:0% +and for those technology now you have to +come back to the basics how you can + + align:start position:0% +come back to the basics how you can + + + align:start position:0% +come back to the basics how you can +develop further understand what what + + align:start position:0% +develop further understand what what + + + align:start position:0% +develop further understand what what +people have and develop further so the + + align:start position:0% +people have and develop further so the + + + align:start position:0% +people have and develop further so the +basic is + + align:start position:0% +basic is + + + align:start position:0% +basic is +Max and uh I'm not going to spend much + + align:start position:0% +Max and uh I'm not going to spend much + + + align:start position:0% +Max and uh I'm not going to spend much +time on the max equation if you + + align:start position:0% +time on the max equation if you + + + align:start position:0% +time on the max equation if you +want to really learn you you should take + + align:start position:0% +want to really learn you you should take + + + align:start position:0% +want to really learn you you should take +a course right but you all heard about + + align:start position:0% +a course right but you all heard about + + + align:start position:0% +a course right but you all heard about +Max equations it's so set of four + + align:start position:0% +Max equations it's so set of four + + + align:start position:0% +Max equations it's so set of four +equations for electric field for + + align:start position:0% +equations for electric field for + + + align:start position:0% +equations for electric field for +magnetic field Edge and displacement and + + align:start position:0% +magnetic field Edge and displacement and + + + align:start position:0% +magnetic field Edge and displacement and +magnetic + + align:start position:0% +magnetic + + + align:start position:0% +magnetic +induction right so uh I give you the + + align:start position:0% +induction right so uh I give you the + + + align:start position:0% +induction right so uh I give you the +definitions of those symol electric + + align:start position:0% +definitions of those symol electric + + + align:start position:0% +definitions of those symol electric +field magnetic field displacement and J + + align:start position:0% +field magnetic field displacement and J + + + align:start position:0% +field magnetic field displacement and J +is the current and they conceal relation + + align:start position:0% +is the current and they conceal relation + + + align:start position:0% +is the current and they conceal relation +related placement to electric field + + align:start position:0% +related placement to electric field + + + align:start position:0% +related placement to electric field +magnetic induction to magnetic field and + + align:start position:0% +magnetic induction to magnetic field and + + + align:start position:0% +magnetic induction to magnetic field and +those constants are the material + + align:start position:0% +those constants are the material + + + align:start position:0% +those constants are the material +properties electri permitivity magnetic + + align:start position:0% +properties electri permitivity magnetic + + + align:start position:0% +properties electri permitivity magnetic +perity okay + + align:start position:0% + + + + align:start position:0% + +Max and uh it's a wave + + align:start position:0% +Max and uh it's a wave + + + align:start position:0% +Max and uh it's a wave +equation to describe electromagnetic + + align:start position:0% +equation to describe electromagnetic + + + align:start position:0% +equation to describe electromagnetic +waves so if you go to solve those + + align:start position:0% +waves so if you go to solve those + + + align:start position:0% +waves so if you go to solve those +waves and uh because that's important + + align:start position:0% +waves and uh because that's important + + + align:start position:0% +waves and uh because that's important +what's important I say when you do the + + align:start position:0% +what's important I say when you do the + + + align:start position:0% +what's important I say when you do the +particularly selective surface very + + align:start position:0% +particularly selective surface very + + + align:start position:0% +particularly selective surface very +often in terms of the base on + + align:start position:0% +often in terms of the base on + + + align:start position:0% +often in terms of the base on +controlling the face of those + + align:start position:0% +controlling the face of those + + + align:start position:0% +controlling the face of those +waves okay so if you look at a a simple + + align:start position:0% +waves okay so if you look at a a simple + + + align:start position:0% +waves okay so if you look at a a simple +solution a way has a directional + + align:start position:0% +solution a way has a directional + + + align:start position:0% +solution a way has a directional +propagation V + + align:start position:0% +propagation V + + + align:start position:0% +propagation V +vector and it's electromagnetic field so + + align:start position:0% +vector and it's electromagnetic field so + + + align:start position:0% +vector and it's electromagnetic field so +electric field magnetic field turns out + + align:start position:0% +electric field magnetic field turns out + + + align:start position:0% +electric field magnetic field turns out +the solution tells you they are + + align:start position:0% +the solution tells you they are + + + align:start position:0% +the solution tells you they are +perpendicular to each other + + align:start position:0% +perpendicular to each other + + + align:start position:0% +perpendicular to each other +and in fact they form a right hand rule + + align:start position:0% +and in fact they form a right hand rule + + + align:start position:0% +and in fact they form a right hand rule +so you go from electric field to + + align:start position:0% +so you go from electric field to + + + align:start position:0% +so you go from electric field to +magnetic field some point to the point + + align:start position:0% +magnetic field some point to the point + + + align:start position:0% +magnetic field some point to the point +pointing uh the propagation + + align:start position:0% +pointing uh the propagation + + + align:start position:0% +pointing uh the propagation +Direction and uh uh to describe a wave + + align:start position:0% +Direction and uh uh to describe a wave + + + align:start position:0% +Direction and uh uh to describe a wave +uh wave we have wav length and pure in + + align:start position:0% +uh wave we have wav length and pure in + + + align:start position:0% +uh wave we have wav length and pure in +time pure the inverse is frequency + + align:start position:0% +time pure the inverse is frequency + + + align:start position:0% +time pure the inverse is frequency +angular frequency is 2 pi * per uh say + + align:start position:0% +angular frequency is 2 pi * per uh say + + + align:start position:0% +angular frequency is 2 pi * per uh say +uh uh uh 2 pi times + + align:start position:0% +uh uh uh 2 pi times + + + align:start position:0% +uh uh uh 2 pi times +frequency wave Vector has + + align:start position:0% +frequency wave Vector has + + + align:start position:0% +frequency wave Vector has +Direction but also has the it's the + + align:start position:0% +Direction but also has the it's the + + + align:start position:0% +Direction but also has the it's the +inverse of wavelength so wave L is one + + align:start position:0% +inverse of wavelength so wave L is one + + + align:start position:0% +inverse of wavelength so wave L is one +over Lambda 2 pi over wave Lambda give + + align:start position:0% +over Lambda 2 pi over wave Lambda give + + + align:start position:0% +over Lambda 2 pi over wave Lambda give +you the magnitude of the wave vector and + + align:start position:0% +you the magnitude of the wave vector and + + + align:start position:0% +you the magnitude of the wave vector and +the direction of the wave Vector is the + + align:start position:0% +the direction of the wave Vector is the + + + align:start position:0% +the direction of the wave Vector is the +UN Vector here and then if you uh solve + + align:start position:0% +UN Vector here and then if you uh solve + + + align:start position:0% +UN Vector here and then if you uh solve +the equation uh turn turns out at the + + align:start position:0% +the equation uh turn turns out at the + + + align:start position:0% +the equation uh turn turns out at the +end Theon and mu combined give you the + + align:start position:0% +end Theon and mu combined give you the + + + align:start position:0% +end Theon and mu combined give you the +uh fractal index of the material this is + + align:start position:0% +uh fractal index of the material this is + + + align:start position:0% +uh fractal index of the material this is +a property you can look at the different + + align:start position:0% +a property you can look at the different + + + align:start position:0% +a property you can look at the different +materials many times people have + + align:start position:0% +materials many times people have + + + align:start position:0% +materials many times people have +measured it's a sometimes it's called uh + + align:start position:0% +measured it's a sometimes it's called uh + + + align:start position:0% +measured it's a sometimes it's called uh +the uh object constant but it's not a + + align:start position:0% +the uh object constant but it's not a + + + align:start position:0% +the uh object constant but it's not a +constant it's a frequency dependent body + + align:start position:0% +constant it's a frequency dependent body + + + align:start position:0% +constant it's a frequency dependent body +okay so you have the real part and + + align:start position:0% +okay so you have the real part and + + + align:start position:0% +okay so you have the real part and +imagine + + align:start position:0% + + + + align:start position:0% + +part and uh uh since it's a wave So the + + align:start position:0% +part and uh uh since it's a wave So the + + + align:start position:0% +part and uh uh since it's a wave So the +plan wave simplest solution of this wave + + align:start position:0% +plan wave simplest solution of this wave + + + align:start position:0% +plan wave simplest solution of this wave +is electric field is a function of + + align:start position:0% +is electric field is a function of + + + align:start position:0% +is electric field is a function of +location time this is the direction it's + + align:start position:0% +location time this is the direction it's + + + align:start position:0% +location time this is the direction it's +a vector direction of the + + align:start position:0% +a vector direction of the + + + align:start position:0% +a vector direction of the +field right and uh uh the V Vector uh + + align:start position:0% +field right and uh uh the V Vector uh + + + align:start position:0% +field right and uh uh the V Vector uh +frequency complex ref + + align:start position:0% +frequency complex ref + + + align:start position:0% +frequency complex ref +index so that's your solution for + + align:start position:0% +index so that's your solution for + + + align:start position:0% +index so that's your solution for +electric field similarly for magnetic + + align:start position:0% +electric field similarly for magnetic + + + align:start position:0% +electric field similarly for magnetic +field and this two e and H perpendicular + + align:start position:0% +field and this two e and H perpendicular + + + align:start position:0% +field and this two e and H perpendicular +to each + + align:start position:0% +to each + + + align:start position:0% +to each +other and so that's your plan with + + align:start position:0% +other and so that's your plan with + + + align:start position:0% +other and so that's your plan with +solution this one you can subtitute back + + align:start position:0% +solution this one you can subtitute back + + + align:start position:0% +solution this one you can subtitute back +into max equation you find this satisfi + + align:start position:0% +into max equation you find this satisfi + + + align:start position:0% +into max equation you find this satisfi +Max + + align:start position:0% +Max + + + align:start position:0% +Max +equation okay and then so this is the + + align:start position:0% +equation okay and then so this is the + + + align:start position:0% +equation okay and then so this is the +field what's the energy energy is the + + align:start position:0% +field what's the energy energy is the + + + align:start position:0% +field what's the energy energy is the +product of e and H and particular this + + align:start position:0% +product of e and H and particular this + + + align:start position:0% +product of e and H and particular this +time a average this is time dependent + + align:start position:0% +time a average this is time dependent + + + align:start position:0% +time a average this is time dependent +but to do time average you can simply + + align:start position:0% +but to do time average you can simply + + + align:start position:0% +but to do time average you can simply +calculate the E cross H complex + + align:start position:0% +calculate the E cross H complex + + + align:start position:0% +calculate the E cross H complex +conjugated if you do complex con you see + + align:start position:0% +conjugated if you do complex con you see + + + align:start position:0% +conjugated if you do complex con you see +this I Omega T can there's no time there + + align:start position:0% +this I Omega T can there's no time there + + + align:start position:0% +this I Omega T can there's no time there +okay so that's + + align:start position:0% +okay so that's + + + align:start position:0% +okay so that's +poting and if I do + + align:start position:0% +poting and if I do + + + align:start position:0% +poting and if I do +that I will get for a propagation in + + align:start position:0% +that I will get for a propagation in + + + align:start position:0% +that I will get for a propagation in +homogeneous medium the pointing Vector + + align:start position:0% +homogeneous medium the pointing Vector + + + align:start position:0% +homogeneous medium the pointing Vector +is the real part of the refractive index + + align:start position:0% +is the real part of the refractive index + + + align:start position:0% +is the real part of the refractive index +mu c0 exponential decay + + align:start position:0% +mu c0 exponential decay + + + align:start position:0% +mu c0 exponential decay +function so this exponential decay + + align:start position:0% +function so this exponential decay + + + align:start position:0% +function so this exponential decay +that's the problem silicon we said right + + align:start position:0% +that's the problem silicon we said right + + + align:start position:0% +that's the problem silicon we said right +silicon fot will takes that Alpha is a + + align:start position:0% +silicon fot will takes that Alpha is a + + + align:start position:0% +silicon fot will takes that Alpha is a +problem is too + + align:start position:0% +problem is too + + + align:start position:0% +problem is too +small okay we have to use a very thick + + align:start position:0% +small okay we have to use a very thick + + + align:start position:0% +small okay we have to use a very thick +one to absorb and this Alpha is the + + align:start position:0% +one to absorb and this Alpha is the + + + align:start position:0% +one to absorb and this Alpha is the +absorption coefficient we we mentioned + + align:start position:0% +absorption coefficient we we mentioned + + + align:start position:0% +absorption coefficient we we mentioned +before and that's relate to the me part + + align:start position:0% +before and that's relate to the me part + + + align:start position:0% +before and that's relate to the me part +of the complex refractive index + + align:start position:0% + + + + align:start position:0% + +Extinction okay so this is a this is the + + align:start position:0% +Extinction okay so this is a this is the + + + align:start position:0% +Extinction okay so this is a this is the +uh uh uh see plan inside one medium now + + align:start position:0% +uh uh uh see plan inside one medium now + + + align:start position:0% +uh uh uh see plan inside one medium now +what I can control is really you with + + align:start position:0% +what I can control is really you with + + + align:start position:0% +what I can control is really you with +the interface to control so you got the + + align:start position:0% +the interface to control so you got the + + + align:start position:0% +the interface to control so you got the +interfaces when you have a light comes + + align:start position:0% +interfaces when you have a light comes + + + align:start position:0% +interfaces when you have a light comes +in reflection refraction right High + + align:start position:0% +in reflection refraction right High + + + align:start position:0% +in reflection refraction right High +School you will learn + + align:start position:0% +School you will learn + + + align:start position:0% +School you will learn +that and uh uh it because the light can + + align:start position:0% +that and uh uh it because the light can + + + align:start position:0% +that and uh uh it because the light can +actually have two uh uh say you + + align:start position:0% +actually have two uh uh say you + + + align:start position:0% +actually have two uh uh say you +decompose into two directions it's a + + align:start position:0% +decompose into two directions it's a + + + align:start position:0% +decompose into two directions it's a +transverse way two directions one is + + align:start position:0% +transverse way two directions one is + + + align:start position:0% +transverse way two directions one is +your electric field is in the plan of + + align:start position:0% +your electric field is in the plan of + + + align:start position:0% +your electric field is in the plan of +incident so direction of coming Norm + + align:start position:0% +incident so direction of coming Norm + + + align:start position:0% +incident so direction of coming Norm +from the plan of + + align:start position:0% +from the plan of + + + align:start position:0% +from the plan of +incidence right so if your electric + + align:start position:0% +incidence right so if your electric + + + align:start position:0% +incidence right so if your electric +field is withing the + + align:start position:0% +field is withing the + + + align:start position:0% +field is withing the +plan uh all your uh electric field is in + + align:start position:0% +plan uh all your uh electric field is in + + + align:start position:0% +plan uh all your uh electric field is in +the other direction so we + + align:start position:0% +the other direction so we + + + align:start position:0% +the other direction so we +have the uh uh electric field if it's in + + align:start position:0% +have the uh uh electric field if it's in + + + align:start position:0% +have the uh uh electric field if it's in +the plan of + + align:start position:0% +the plan of + + + align:start position:0% +the plan of +incidence the magnetic field is + + align:start position:0% +incidence the magnetic field is + + + align:start position:0% +incidence the magnetic field is +perpendicular right it's always + + align:start position:0% +perpendicular right it's always + + + align:start position:0% +perpendicular right it's always +perpendicular to electric field so will + + align:start position:0% +perpendicular to electric field so will + + + align:start position:0% +perpendicular to electric field so will +be in the perpendicular plan so that's + + align:start position:0% +be in the perpendicular plan so that's + + + align:start position:0% +be in the perpendicular plan so that's +the uh in this case we have transverse + + align:start position:0% +the uh in this case we have transverse + + + align:start position:0% +the uh in this case we have transverse +magnetic wave or parallel if that's for + + align:start position:0% +magnetic wave or parallel if that's for + + + align:start position:0% +magnetic wave or parallel if that's for +electric field different + + align:start position:0% +electric field different + + + align:start position:0% +electric field different +LS I always I can't remember this I + + align:start position:0% +LS I always I can't remember this I + + + align:start position:0% +LS I always I can't remember this I +always just say TM then I say transverse + + align:start position:0% + + + + align:start position:0% + +magnetic that's more + + align:start position:0% +magnetic that's more + + + align:start position:0% +magnetic that's more +intuitive okay H field okay that's the + + align:start position:0% +intuitive okay H field okay that's the + + + align:start position:0% +intuitive okay H field okay that's the +if we if the magnetic field is a PL + + align:start position:0% +if we if the magnetic field is a PL + + + align:start position:0% +if we if the magnetic field is a PL +incidence then electric field is + + align:start position:0% +incidence then electric field is + + + align:start position:0% +incidence then electric field is +perpendicular that's T it's + + align:start position:0% +perpendicular that's T it's + + + align:start position:0% +perpendicular that's T it's +perpendicular and + + align:start position:0% +perpendicular and + + + align:start position:0% +perpendicular and +S so you have Expressions when you have + + align:start position:0% +S so you have Expressions when you have + + + align:start position:0% +S so you have Expressions when you have +look at the calculate the interface you + + align:start position:0% +look at the calculate the interface you + + + align:start position:0% +look at the calculate the interface you +have to calculate for both solar + + align:start position:0% +have to calculate for both solar + + + align:start position:0% +have to calculate for both solar +radiation is a typical combination of + + align:start position:0% +radiation is a typical combination of + + + align:start position:0% +radiation is a typical combination of +5050 we see we calculate we say oh you + + align:start position:0% +5050 we see we calculate we say oh you + + + align:start position:0% +5050 we see we calculate we say oh you +say there a 50 te 50 + + align:start position:0% + + + + align:start position:0% + +TM okay now what happens first thing is + + align:start position:0% +TM okay now what happens first thing is + + + align:start position:0% +TM okay now what happens first thing is +reflection if you have a smooth surface + + align:start position:0% +reflection if you have a smooth surface + + + align:start position:0% +reflection if you have a smooth surface +right angle of incidence equal angle + + align:start position:0% +right angle of incidence equal angle + + + align:start position:0% +right angle of incidence equal angle +reflection so that's a reflection Rule + + align:start position:0% +reflection so that's a reflection Rule + + + align:start position:0% +reflection so that's a reflection Rule +and then reflection is the angle change + + align:start position:0% +and then reflection is the angle change + + + align:start position:0% +and then reflection is the angle change +depends based on the refractive + + align:start position:0% + + + + align:start position:0% + +index and then you can actually + + align:start position:0% +index and then you can actually + + + align:start position:0% +index and then you can actually +calculate the + + align:start position:0% +calculate the + + + align:start position:0% +calculate the +magnitude of the field reflected and + + align:start position:0% +magnitude of the field reflected and + + + align:start position:0% +magnitude of the field reflected and +refractive and again this I I'm giving + + align:start position:0% +refractive and again this I I'm giving + + + align:start position:0% +refractive and again this I I'm giving +you the solution the point that I want + + align:start position:0% +you the solution the point that I want + + + align:start position:0% +you the solution the point that I want +to tell you those could be + + align:start position:0% +to tell you those could be + + + align:start position:0% +to tell you those could be +calculated okay and if you want to uh + + align:start position:0% +calculated okay and if you want to uh + + + align:start position:0% +calculated okay and if you want to uh +learn how to calculate you got you need + + align:start position:0% +learn how to calculate you got you need + + + align:start position:0% +learn how to calculate you got you need +to take a course or pick up the book + + align:start position:0% +to take a course or pick up the book + + + align:start position:0% +to take a course or pick up the book +read it yourself but it depends on what + + align:start position:0% +read it yourself but it depends on what + + + align:start position:0% +read it yourself but it depends on what +it depends on is the refractive index of + + align:start position:0% +it depends on is the refractive index of + + + align:start position:0% +it depends on is the refractive index of +the material on both + + align:start position:0% + + + + align:start position:0% + +sides and so you need to know the + + align:start position:0% +sides and so you need to know the + + + align:start position:0% +sides and so you need to know the +property very often although you think + + align:start position:0% +property very often although you think + + + align:start position:0% +property very often although you think +people should list it you go when you + + align:start position:0% +people should list it you go when you + + + align:start position:0% +people should list it you go when you +need it you don't find it that's one and + + align:start position:0% +need it you don't find it that's one and + + + align:start position:0% +need it you don't find it that's one and +even people list it you do solar seral + + align:start position:0% +even people list it you do solar seral + + + align:start position:0% +even people list it you do solar seral +you want high temperature you don't find + + align:start position:0% +you want high temperature you don't find + + + align:start position:0% +you want high temperature you don't find +it okay so there are lot of things you + + align:start position:0% +it okay so there are lot of things you + + + align:start position:0% +it okay so there are lot of things you +can do find them that's a when we when + + align:start position:0% +can do find them that's a when we when + + + align:start position:0% +can do find them that's a when we when +we do the uh we want to design the first + + align:start position:0% +we do the uh we want to design the first + + + align:start position:0% +we do the uh we want to design the first +Serv let's design let's deposit a film + + align:start position:0% +Serv let's design let's deposit a film + + + align:start position:0% +Serv let's design let's deposit a film +and try to measure + + align:start position:0% +and try to measure + + + align:start position:0% +and try to measure +properties right so those are they just + + align:start position:0% +properties right so those are they just + + + align:start position:0% +properties right so those are they just +the feel the reflection and the energy + + align:start position:0% +the feel the reflection and the energy + + + align:start position:0% +the feel the reflection and the energy +that's reflectivity transm it so you do + + align:start position:0% +that's reflectivity transm it so you do + + + align:start position:0% +that's reflectivity transm it so you do +reflection coefficient Square you get + + align:start position:0% +reflection coefficient Square you get + + + align:start position:0% +reflection coefficient Square you get +reflectivity transmissivity you have to + + align:start position:0% +reflectivity transmissivity you have to + + + align:start position:0% +reflectivity transmissivity you have to +plug in the uh some factors in the front + + align:start position:0% +plug in the uh some factors in the front + + + align:start position:0% +plug in the uh some factors in the front +but again those are all depends on the + + align:start position:0% +but again those are all depends on the + + + align:start position:0% +but again those are all depends on the +complex refractive + + align:start position:0% +complex refractive + + + align:start position:0% +complex refractive +index so the final one just one + + align:start position:0% +index so the final one just one + + + align:start position:0% +index so the final one just one +example where uh it's a calculation + + align:start position:0% +example where uh it's a calculation + + + align:start position:0% +example where uh it's a calculation +given the refractor index is between + + align:start position:0% +given the refractor index is between + + + align:start position:0% +given the refractor index is between +vacuum or air which is one and say + + align:start position:0% +vacuum or air which is one and say + + + align:start position:0% +vacuum or air which is one and say +dialectric took constant gold I also + + align:start position:0% +dialectric took constant gold I also + + + align:start position:0% +dialectric took constant gold I also +took a constant but remember it's not a + + align:start position:0% +took a constant but remember it's not a + + + align:start position:0% +took a constant but remember it's not a +constant it's a wence dependent so each + + align:start position:0% +constant it's a wence dependent so each + + + align:start position:0% +constant it's a wence dependent so each +wav length this can change but here is + + align:start position:0% +wav length this can change but here is + + + align:start position:0% +wav length this can change but here is +calculating only the angle + + align:start position:0% +calculating only the angle + + + align:start position:0% +calculating only the angle +dependence so if it's Dil so and CA is + + align:start position:0% +dependence so if it's Dil so and CA is + + + align:start position:0% +dependence so if it's Dil so and CA is +is say zero and uh here is for the T + + align:start position:0% +is say zero and uh here is for the T + + + align:start position:0% +is say zero and uh here is for the T +wave transverse electric and here is for + + align:start position:0% +wave transverse electric and here is for + + + align:start position:0% +wave transverse electric and here is for +the uh TM transe + + align:start position:0% +the uh TM transe + + + align:start position:0% +the uh TM transe +magnetic and then what's interesting is + + align:start position:0% +magnetic and then what's interesting is + + + align:start position:0% +magnetic and then what's interesting is +this Bristal angle and they're certain + + align:start position:0% +this Bristal angle and they're certain + + + align:start position:0% +this Bristal angle and they're certain +so that's how people make the polarized + + align:start position:0% +so that's how people make the polarized + + + align:start position:0% +so that's how people make the polarized +uh glas + + align:start position:0% +uh glas + + + align:start position:0% +uh glas +codings uh and uh you you can choose the + + align:start position:0% +codings uh and uh you you can choose the + + + align:start position:0% +codings uh and uh you you can choose the +polarization there certain angle you can + + align:start position:0% +polarization there certain angle you can + + + align:start position:0% +polarization there certain angle you can +get as a no reflection at a + + align:start position:0% +get as a no reflection at a + + + align:start position:0% +get as a no reflection at a +g go is a very good reflector you you + + align:start position:0% +g go is a very good reflector you you + + + align:start position:0% +g go is a very good reflector you you +look at that right reflectivity is + + align:start position:0% +look at that right reflectivity is + + + align:start position:0% +look at that right reflectivity is +almost close to one + + align:start position:0% +almost close to one + + + align:start position:0% +almost close to one +so when people do selective surface + + align:start position:0% +so when people do selective surface + + + align:start position:0% +so when people do selective surface +varable they start with aluminum metal + + align:start position:0% +varable they start with aluminum metal + + + align:start position:0% +varable they start with aluminum metal +it's good reflection in the + + align:start position:0% +it's good reflection in the + + + align:start position:0% +it's good reflection in the +infrared the problem is reflect up to + + align:start position:0% +infrared the problem is reflect up to + + + align:start position:0% +infrared the problem is reflect up to +about 2 micr or5 micr or4 m but you + + align:start position:0% +about 2 micr or5 micr or4 m but you + + + align:start position:0% +about 2 micr or5 micr or4 m but you +don't want to uh you do you do not want + + align:start position:0% +don't want to uh you do you do not want + + + align:start position:0% +don't want to uh you do you do not want +to uh reflect the solar radiation you + + align:start position:0% +to uh reflect the solar radiation you + + + align:start position:0% +to uh reflect the solar radiation you +want to absorb it so you try to put + + align:start position:0% +want to absorb it so you try to put + + + align:start position:0% +want to absorb it so you try to put +materials on the surface to absorb to + + align:start position:0% +materials on the surface to absorb to + + + align:start position:0% +materials on the surface to absorb to +make them absorb between the solar + + align:start position:0% +make them absorb between the solar + + + align:start position:0% +make them absorb between the solar +radiation up to 2 Micron and then you + + align:start position:0% +radiation up to 2 Micron and then you + + + align:start position:0% +radiation up to 2 Micron and then you +still keep the old say infr is very + + align:start position:0% +still keep the old say infr is very + + + align:start position:0% +still keep the old say infr is very +reflecting which is good because that + + align:start position:0% +reflecting which is good because that + + + align:start position:0% +reflecting which is good because that +means emissivity is + + align:start position:0% +means emissivity is + + + align:start position:0% +means emissivity is +small so people have developed like I + + align:start position:0% +small so people have developed like I + + + align:start position:0% +small so people have developed like I +said let's say the different coding even + + align:start position:0% +said let's say the different coding even + + + align:start position:0% +said let's say the different coding even +for the solar theral uh uh solar hot + + align:start position:0% +for the solar theral uh uh solar hot + + + align:start position:0% +for the solar theral uh uh solar hot +water I said very cheap right $1.5 per + + align:start position:0% +water I said very cheap right $1.5 per + + + align:start position:0% +water I said very cheap right $1.5 per +two you will you go through the factory + + align:start position:0% +two you will you go through the factory + + + align:start position:0% +two you will you go through the factory +you will see their vacuum deol I saw one + + align:start position:0% +you will see their vacuum deol I saw one + + + align:start position:0% +you will see their vacuum deol I saw one +vacuum deposition is it's about 100 m n + + align:start position:0% +vacuum deposition is it's about 100 m n + + + align:start position:0% +vacuum deposition is it's about 100 m n +continuously uh dep deposit in different + + align:start position:0% +continuously uh dep deposit in different + + + align:start position:0% +continuously uh dep deposit in different +layers and do it at that low cost it's + + align:start position:0% +layers and do it at that low cost it's + + + align:start position:0% +layers and do it at that low cost it's +amazing + + align:start position:0% +amazing + + + align:start position:0% +amazing +okay okay so I'll stop here \ No newline at end of file diff --git a/mBdrvfytLDQ.txt b/mBdrvfytLDQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..b0fa27b2eee4ed7efc75d99db256048d5a11594f --- /dev/null +++ b/mBdrvfytLDQ.txt @@ -0,0 +1,14811 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +I'm going to talk about alternate + + align:start position:0% +I'm going to talk about alternate + + + align:start position:0% +I'm going to talk about alternate +consensus mechanisms and there's a bunch + + align:start position:0% +consensus mechanisms and there's a bunch + + + align:start position:0% +consensus mechanisms and there's a bunch +of them and sort of some of them are + + align:start position:0% +of them and sort of some of them are + + + align:start position:0% +of them and sort of some of them are +berry and some proof work some of them + + align:start position:0% +berry and some proof work some of them + + + align:start position:0% +berry and some proof work some of them +are proved mistake all these different + + align:start position:0% +are proved mistake all these different + + + align:start position:0% +are proved mistake all these different +things so unique node lists this is + + align:start position:0% +things so unique node lists this is + + + align:start position:0% +things so unique node lists this is +something that ripple and stellar use + + align:start position:0% +something that ripple and stellar use + + + align:start position:0% +something that ripple and stellar use +I'm not sure if there's others proof of + + align:start position:0% +I'm not sure if there's others proof of + + + align:start position:0% +I'm not sure if there's others proof of +stake is like this huge research topic + + align:start position:0% +stake is like this huge research topic + + + align:start position:0% +stake is like this huge research topic +that lots of things fall under there's + + align:start position:0% +that lots of things fall under there's + + + align:start position:0% +that lots of things fall under there's +lots of variants one of them I'll talk + + align:start position:0% +lots of variants one of them I'll talk + + + align:start position:0% +lots of variants one of them I'll talk +about is delegated proof of stake proof + + align:start position:0% +about is delegated proof of stake proof + + + align:start position:0% +about is delegated proof of stake proof +of space is an interesting thing that is + + align:start position:0% +of space is an interesting thing that is + + + align:start position:0% +of space is an interesting thing that is +basically a form of proof of work that + + align:start position:0% +basically a form of proof of work that + + + align:start position:0% +basically a form of proof of work that +doesn't use CPU as much there's the idea + + align:start position:0% +doesn't use CPU as much there's the idea + + + align:start position:0% +doesn't use CPU as much there's the idea +of directed acyclic graphs which iota is + + align:start position:0% +of directed acyclic graphs which iota is + + + align:start position:0% +of directed acyclic graphs which iota is +a great example of and then one that I + + align:start position:0% +a great example of and then one that I + + + align:start position:0% +a great example of and then one that I +sort of came up with a few years ago and + + align:start position:0% +sort of came up with a few years ago and + + + align:start position:0% +sort of came up with a few years ago and +it's kind of fun proof of Idol which is + + align:start position:0% +it's kind of fun proof of Idol which is + + + align:start position:0% +it's kind of fun proof of Idol which is +sort of chilling but silly - so okay and + + align:start position:0% +sort of chilling but silly - so okay and + + + align:start position:0% +sort of chilling but silly - so okay and +so sort of disclaimer I'm okay with + + align:start position:0% +so sort of disclaimer I'm okay with + + + align:start position:0% +so sort of disclaimer I'm okay with +proof of work so like I think if you if + + align:start position:0% +proof of work so like I think if you if + + + align:start position:0% +proof of work so like I think if you if +you were at the class on Monday it's a + + align:start position:0% +you were at the class on Monday it's a + + + align:start position:0% +you were at the class on Monday it's a +great sort of segue into this we're + + align:start position:0% +great sort of segue into this we're + + + align:start position:0% +great sort of segue into this we're +clearly proof of work has I don't if you + + align:start position:0% +clearly proof of work has I don't if you + + + align:start position:0% +clearly proof of work has I don't if you +want to call it problems but like it's + + align:start position:0% +want to call it problems but like it's + + + align:start position:0% +want to call it problems but like it's +kind of crazy right the all the stuff + + align:start position:0% +kind of crazy right the all the stuff + + + align:start position:0% +kind of crazy right the all the stuff +David was saying on Monday it's not in + + align:start position:0% +David was saying on Monday it's not in + + + align:start position:0% +David was saying on Monday it's not in +egalitarian you know and I think in the + + align:start position:0% +egalitarian you know and I think in the + + + align:start position:0% +egalitarian you know and I think in the +Satoshi white paper he sort of says one + + align:start position:0% +Satoshi white paper he sort of says one + + + align:start position:0% +Satoshi white paper he sort of says one +CPU one vote well that's not really how + + align:start position:0% +CPU one vote well that's not really how + + + align:start position:0% +CPU one vote well that's not really how +it works + + align:start position:0% +it works + + + align:start position:0% +it works +there's even if you define CPU maybe you + + align:start position:0% +there's even if you define CPU maybe you + + + align:start position:0% +there's even if you define CPU maybe you +have your own CPU someone else has a + + align:start position:0% +have your own CPU someone else has a + + + align:start position:0% +have your own CPU someone else has a +different CPU and there's you know that + + align:start position:0% +different CPU and there's you know that + + + align:start position:0% +different CPU and there's you know that +huge industry of building all these + + align:start position:0% +huge industry of building all these + + + align:start position:0% +huge industry of building all these +chips so there's a lot of issues with + + align:start position:0% +chips so there's a lot of issues with + + + align:start position:0% +chips so there's a lot of issues with +River work it's certainly not ideal + + align:start position:0% +River work it's certainly not ideal + + + align:start position:0% +River work it's certainly not ideal +that's probably not why most people + + align:start position:0% +that's probably not why most people + + + align:start position:0% +that's probably not why most people +don't like it so I generally in academia + + align:start position:0% +don't like it so I generally in academia + + + align:start position:0% +don't like it so I generally in academia +in a lot of business places people don't + + align:start position:0% +in a lot of business places people don't + + + align:start position:0% +in a lot of business places people don't +like the Bitcoin proof work mechanism + + align:start position:0% +like the Bitcoin proof work mechanism + + + align:start position:0% +like the Bitcoin proof work mechanism +not everyone but but it's a pretty wide + + align:start position:0% +not everyone but but it's a pretty wide + + + align:start position:0% +not everyone but but it's a pretty wide +spread like oh Bitcoin is bad because it + + align:start position:0% +spread like oh Bitcoin is bad because it + + + align:start position:0% +spread like oh Bitcoin is bad because it +uses as much electricity as Denmark or + + align:start position:0% +uses as much electricity as Denmark or + + + align:start position:0% +uses as much electricity as Denmark or +something and I think that's the sort of + + align:start position:0% +something and I think that's the sort of + + + align:start position:0% +something and I think that's the sort of +early I don't like it because it uses + + align:start position:0% +early I don't like it because it uses + + + align:start position:0% +early I don't like it because it uses +electricity there's other reasons not to + + align:start position:0% +electricity there's other reasons not to + + + align:start position:0% +electricity there's other reasons not to +like + + align:start position:0% +like + + + align:start position:0% +like +which I think you have to go into much + + align:start position:0% +which I think you have to go into much + + + align:start position:0% +which I think you have to go into much +more depth like with David's talk + + align:start position:0% +more depth like with David's talk + + + align:start position:0% +more depth like with David's talk +yesterday sure it uses a lot of + + align:start position:0% +yesterday sure it uses a lot of + + + align:start position:0% +yesterday sure it uses a lot of +electricity but it also uses a lot of + + align:start position:0% +electricity but it also uses a lot of + + + align:start position:0% +electricity but it also uses a lot of +fabrication plants and it uses all these + + align:start position:0% +fabrication plants and it uses all these + + + align:start position:0% +fabrication plants and it uses all these +other sort of distribution networks so + + align:start position:0% +other sort of distribution networks so + + + align:start position:0% +other sort of distribution networks so +anyway I get that there's a lot of you + + align:start position:0% +anyway I get that there's a lot of you + + + align:start position:0% +anyway I get that there's a lot of you +know one of the first things with + + align:start position:0% +know one of the first things with + + + align:start position:0% +know one of the first things with +Bitcoin is okay how can we improve upon + + align:start position:0% +Bitcoin is okay how can we improve upon + + + align:start position:0% +Bitcoin is okay how can we improve upon +this how can we get rid of this huge + + align:start position:0% +this how can we get rid of this huge + + + align:start position:0% +this how can we get rid of this huge +energy sink on the other hand I'm sort + + align:start position:0% +energy sink on the other hand I'm sort + + + align:start position:0% +energy sink on the other hand I'm sort +of okay with it right like i-i've been + + align:start position:0% +of okay with it right like i-i've been + + + align:start position:0% +of okay with it right like i-i've been +the first thing that I thought about + + align:start position:0% +the first thing that I thought about + + + align:start position:0% +the first thing that I thought about +Bitcoin is wow this is gonna be huge is + + align:start position:0% +Bitcoin is wow this is gonna be huge is + + + align:start position:0% +Bitcoin is wow this is gonna be huge is +it gonna take a lot of electricity but + + align:start position:0% +it gonna take a lot of electricity but + + + align:start position:0% +it gonna take a lot of electricity but +it's kind of cool that it works that way + + align:start position:0% +it's kind of cool that it works that way + + + align:start position:0% +it's kind of cool that it works that way +so I'm sort of okay with people you know + + align:start position:0% +so I'm sort of okay with people you know + + + align:start position:0% +so I'm sort of okay with people you know +if like to me like you can't really get + + align:start position:0% +if like to me like you can't really get + + + align:start position:0% +if like to me like you can't really get +mad at people doing things you think are + + align:start position:0% +mad at people doing things you think are + + + align:start position:0% +mad at people doing things you think are +stupid because you'll just get mad all + + align:start position:0% +stupid because you'll just get mad all + + + align:start position:0% +stupid because you'll just get mad all +the time like people mined gold people + + align:start position:0% +the time like people mined gold people + + + align:start position:0% +the time like people mined gold people +spend billions of dollars on diamonds I + + align:start position:0% +spend billions of dollars on diamonds I + + + align:start position:0% +spend billions of dollars on diamonds I +think diamonds are really stupid but hey + + align:start position:0% +think diamonds are really stupid but hey + + + align:start position:0% +think diamonds are really stupid but hey +you want to dig up diamonds and yeah + + align:start position:0% +you want to dig up diamonds and yeah + + + align:start position:0% +you want to dig up diamonds and yeah +there's entire cultural areas that I + + align:start position:0% +there's entire cultural areas that I + + + align:start position:0% +there's entire cultural areas that I +just have no interest in okay + + align:start position:0% +just have no interest in okay + + + align:start position:0% +just have no interest in okay +okay so I'll try to explain these other + + align:start position:0% +okay so I'll try to explain these other + + + align:start position:0% +okay so I'll try to explain these other +methods in a neutral way but I do have + + align:start position:0% +methods in a neutral way but I do have + + + align:start position:0% +methods in a neutral way but I do have +my own sort of biases where I think like + + align:start position:0% +my own sort of biases where I think like + + + align:start position:0% +my own sort of biases where I think like +hey prove work pretty much works I think + + align:start position:0% +hey prove work pretty much works I think + + + align:start position:0% +hey prove work pretty much works I think +it's a cool system and I'm somewhat + + align:start position:0% +it's a cool system and I'm somewhat + + + align:start position:0% +it's a cool system and I'm somewhat +skeptical of various different + + align:start position:0% +skeptical of various different + + + align:start position:0% +skeptical of various different +algorithms and mechanisms here and so + + align:start position:0% +algorithms and mechanisms here and so + + + align:start position:0% +algorithms and mechanisms here and so +I'm you know I'm and also I'm most + + align:start position:0% +I'm you know I'm and also I'm most + + + align:start position:0% +I'm you know I'm and also I'm most +familiar with the proof of work system + + align:start position:0% +familiar with the proof of work system + + + align:start position:0% +familiar with the proof of work system +and all the sort of intricacies of it so + + align:start position:0% +and all the sort of intricacies of it so + + + align:start position:0% +and all the sort of intricacies of it so +like with David's talk yesterday like + + align:start position:0% +like with David's talk yesterday like + + + align:start position:0% +like with David's talk yesterday like +there's some new stuff but I sort of + + align:start position:0% +there's some new stuff but I sort of + + + align:start position:0% +there's some new stuff but I sort of +knew because I talked to these people + + align:start position:0% +knew because I talked to these people + + + align:start position:0% +knew because I talked to these people +for a long time I'm like this is how + + align:start position:0% +for a long time I'm like this is how + + + align:start position:0% +for a long time I'm like this is how +this system works proof of stake I've + + align:start position:0% +this system works proof of stake I've + + + align:start position:0% +this system works proof of stake I've +seen it implemented in altcoins + + align:start position:0% +seen it implemented in altcoins + + + align:start position:0% +seen it implemented in altcoins +but I haven't followed them that closely + + align:start position:0% +but I haven't followed them that closely + + + align:start position:0% +but I haven't followed them that closely +so I don't know as intimately like what + + align:start position:0% +so I don't know as intimately like what + + + align:start position:0% +so I don't know as intimately like what +goes wrong and all the weird details + + align:start position:0% +goes wrong and all the weird details + + + align:start position:0% +goes wrong and all the weird details +anyway okay so the first one UNL or + + align:start position:0% +anyway okay so the first one UNL or + + + align:start position:0% +anyway okay so the first one UNL or +unique node list this is essentially the + + align:start position:0% +unique node list this is essentially the + + + align:start position:0% +unique node list this is essentially the +consensus mechanism used by ripple and + + align:start position:0% +consensus mechanism used by ripple and + + + align:start position:0% +consensus mechanism used by ripple and +seller for history ripple started 2013 + + align:start position:0% +seller for history ripple started 2013 + + + align:start position:0% +seller for history ripple started 2013 +they know 2011 I don't know it was + + align:start position:0% +they know 2011 I don't know it was + + + align:start position:0% +they know 2011 I don't know it was +awhile ago + + align:start position:0% + + + + align:start position:0% + +20:13 okay but the comp well the so + + align:start position:0% +20:13 okay but the comp well the so + + + align:start position:0% +20:13 okay but the comp well the so +actually the ripple eyed the the name + + align:start position:0% +actually the ripple eyed the the name + + + align:start position:0% +actually the ripple eyed the the name +ripple and the idea of sort of these + + align:start position:0% +ripple and the idea of sort of these + + + align:start position:0% +ripple and the idea of sort of these +debt obligations through this network + + align:start position:0% +debt obligations through this network + + + align:start position:0% +debt obligations through this network +was actually predates bitcoin and then + + align:start position:0% +was actually predates bitcoin and then + + + align:start position:0% +was actually predates bitcoin and then +jedd McCaleb started the company he's + + align:start position:0% +jedd McCaleb started the company he's + + + align:start position:0% +jedd McCaleb started the company he's +also the guy who started mount GOx + + align:start position:0% +also the guy who started mount GOx + + + align:start position:0% +also the guy who started mount GOx +so he started mount Cox I believe in + + align:start position:0% +so he started mount Cox I believe in + + + align:start position:0% +so he started mount Cox I believe in +2011 or 10 late 2010 sold it to Mark + + align:start position:0% +2011 or 10 late 2010 sold it to Mark + + + align:start position:0% +2011 or 10 late 2010 sold it to Mark +Karr fellas started Ripple + + align:start position:0% +Karr fellas started Ripple + + + align:start position:0% +Karr fellas started Ripple +hired a bunch of people sort of got + + align:start position:0% +hired a bunch of people sort of got + + + align:start position:0% +hired a bunch of people sort of got +fired from ripple a lot of bad everyone + + align:start position:0% +fired from ripple a lot of bad everyone + + + align:start position:0% +fired from ripple a lot of bad everyone +fighting because like you know it was + + align:start position:0% +fighting because like you know it was + + + align:start position:0% +fighting because like you know it was +all these people who used to play Magic + + align:start position:0% +all these people who used to play Magic + + + align:start position:0% +all these people who used to play Magic +the Gathering and like we're friends and + + align:start position:0% +the Gathering and like we're friends and + + + align:start position:0% +the Gathering and like we're friends and +now they're not friends anymore and it + + align:start position:0% +now they're not friends anymore and it + + + align:start position:0% +now they're not friends anymore and it +sucks and then he started stellar which + + align:start position:0% +sucks and then he started stellar which + + + align:start position:0% +sucks and then he started stellar which +he called secret Bitcoin project and I + + align:start position:0% +he called secret Bitcoin project and I + + + align:start position:0% +he called secret Bitcoin project and I +was thinking of joining it but he + + align:start position:0% +was thinking of joining it but he + + + align:start position:0% +was thinking of joining it but he +wouldn't tell me what it was and and I + + align:start position:0% +wouldn't tell me what it was and and I + + + align:start position:0% +wouldn't tell me what it was and and I +also it was like I knew that other + + align:start position:0% +also it was like I knew that other + + + align:start position:0% +also it was like I knew that other +people knew what it was like my friends + + align:start position:0% +people knew what it was like my friends + + + align:start position:0% +people knew what it was like my friends +and if they weren't telling me because + + align:start position:0% +and if they weren't telling me because + + + align:start position:0% +and if they weren't telling me because +they're not supposed to it was like well + + align:start position:0% +they're not supposed to it was like well + + + align:start position:0% +they're not supposed to it was like well +it must not be that cool because nobody + + align:start position:0% +it must not be that cool because nobody + + + align:start position:0% +it must not be that cool because nobody +can actually keep a secret if it's + + align:start position:0% +can actually keep a secret if it's + + + align:start position:0% +can actually keep a secret if it's +really cool so so that was my sort of + + align:start position:0% +really cool so so that was my sort of + + + align:start position:0% +really cool so so that was my sort of +like I'll just go work somewhere else + + align:start position:0% +like I'll just go work somewhere else + + + align:start position:0% +like I'll just go work somewhere else +and steller was more or less a copy of + + align:start position:0% +and steller was more or less a copy of + + + align:start position:0% +and steller was more or less a copy of +the ripple code which was open source so + + align:start position:0% +the ripple code which was open source so + + + align:start position:0% +the ripple code which was open source so +it was totally fun to do this and then + + align:start position:0% +it was totally fun to do this and then + + + align:start position:0% +it was totally fun to do this and then +it sort of diverged and they added their + + align:start position:0% +it sort of diverged and they added their + + + align:start position:0% +it sort of diverged and they added their +own their own sort of different parts of + + align:start position:0% +own their own sort of different parts of + + + align:start position:0% +own their own sort of different parts of +the consensus algorithm than ripple did + + align:start position:0% +the consensus algorithm than ripple did + + + align:start position:0% +the consensus algorithm than ripple did +so it's a count basis somewhat like + + align:start position:0% +so it's a count basis somewhat like + + + align:start position:0% +so it's a count basis somewhat like +aetherium transactions have sort of + + align:start position:0% +aetherium transactions have sort of + + + align:start position:0% +aetherium transactions have sort of +senders receivers what's interesting is + + align:start position:0% +senders receivers what's interesting is + + + align:start position:0% +senders receivers what's interesting is +in the stellar case and possibly rippled + + align:start position:0% +in the stellar case and possibly rippled + + + align:start position:0% +in the stellar case and possibly rippled +there's a minimum balance so I actually + + align:start position:0% +there's a minimum balance so I actually + + + align:start position:0% +there's a minimum balance so I actually +had some stellar last year up until last + + align:start position:0% +had some stellar last year up until last + + + align:start position:0% +had some stellar last year up until last +year because I went to the sort of + + align:start position:0% +year because I went to the sort of + + + align:start position:0% +year because I went to the sort of +initial release party and they gave out + + align:start position:0% +initial release party and they gave out + + + align:start position:0% +initial release party and they gave out +stellar and I had I had some and it was + + align:start position:0% +stellar and I had I had some and it was + + + align:start position:0% +stellar and I had I had some and it was +like then it wasn't much but then last + + align:start position:0% +like then it wasn't much but then last + + + align:start position:0% +like then it wasn't much but then last +year I looked it was like oh this is + + align:start position:0% +year I looked it was like oh this is + + + align:start position:0% +year I looked it was like oh this is +like 200 bucks worth I'll sell it and I + + align:start position:0% +like 200 bucks worth I'll sell it and I + + + align:start position:0% +like 200 bucks worth I'll sell it and I +sold it got some bitcoins but it was + + align:start position:0% +sold it got some bitcoins but it was + + + align:start position:0% +sold it got some bitcoins but it was +weird because they enforced a minimum + + align:start position:0% +weird because they enforced a minimum + + + align:start position:0% +weird because they enforced a minimum +balance which seems like weird to me + + align:start position:0% +balance which seems like weird to me + + + align:start position:0% +balance which seems like weird to me +because you you had to retain some + + align:start position:0% +because you you had to retain some + + + align:start position:0% +because you you had to retain some +number of stellar + + align:start position:0% +number of stellar + + + align:start position:0% +number of stellar +units in every account which to me seems + + align:start position:0% +units in every account which to me seems + + + align:start position:0% +units in every account which to me seems +like sort of weird because that means + + align:start position:0% +like sort of weird because that means + + + align:start position:0% +like sort of weird because that means +like those accounts those the sellers + + align:start position:0% +like those accounts those the sellers + + + align:start position:0% +like those accounts those the sellers +haven't really there they're sort of + + align:start position:0% +haven't really there they're sort of + + + align:start position:0% +haven't really there they're sort of +gone in a way in that if you open a new + + align:start position:0% +gone in a way in that if you open a new + + + align:start position:0% +gone in a way in that if you open a new +account and it must have 50 stellar in + + align:start position:0% +account and it must have 50 stellar in + + + align:start position:0% +account and it must have 50 stellar in +it forever will still are effectively + + align:start position:0% +it forever will still are effectively + + + align:start position:0% +it forever will still are effectively +destroyed it just seemed like I mean + + align:start position:0% +destroyed it just seemed like I mean + + + align:start position:0% +destroyed it just seemed like I mean +which is a fine thing to do it's sort of + + align:start position:0% +which is a fine thing to do it's sort of + + + align:start position:0% +which is a fine thing to do it's sort of +a transaction fee but from a computer + + align:start position:0% +a transaction fee but from a computer + + + align:start position:0% +a transaction fee but from a computer +science like database standpoint it's + + align:start position:0% +science like database standpoint it's + + + align:start position:0% +science like database standpoint it's +like why not just have it cost money to + + align:start position:0% +like why not just have it cost money to + + + align:start position:0% +like why not just have it cost money to +create a new account instead of have it + + align:start position:0% + + + + align:start position:0% + +so so these are sort of you know just + + align:start position:0% +so so these are sort of you know just + + + align:start position:0% +so so these are sort of you know just +interacting with it's like so there's no + + align:start position:0% +interacting with it's like so there's no + + + align:start position:0% +interacting with it's like so there's no +work but the idea is that nodes sign + + align:start position:0% +work but the idea is that nodes sign + + + align:start position:0% +work but the idea is that nodes sign +transactions that they've seen every one + + align:start position:0% +transactions that they've seen every one + + + align:start position:0% +transactions that they've seen every one +sort of makes blocks and you sign them + + align:start position:0% +sort of makes blocks and you sign them + + + align:start position:0% +sort of makes blocks and you sign them +so you've got some kind of identity your + + align:start position:0% +so you've got some kind of identity your + + + align:start position:0% +so you've got some kind of identity your +node has a key when you when you start a + + align:start position:0% +node has a key when you when you start a + + + align:start position:0% +node has a key when you when you start a +new node you've got a public key private + + align:start position:0% +new node you've got a public key private + + + align:start position:0% +new node you've got a public key private +key pair you can sign off on + + align:start position:0% +key pair you can sign off on + + + align:start position:0% +key pair you can sign off on +transactions this is not the case in + + align:start position:0% +transactions this is not the case in + + + align:start position:0% +transactions this is not the case in +Bitcoin right in Bitcoin you have a full + + align:start position:0% +Bitcoin right in Bitcoin you have a full + + + align:start position:0% +Bitcoin right in Bitcoin you have a full +node your full node might have a wallet + + align:start position:0% +node your full node might have a wallet + + + align:start position:0% +node your full node might have a wallet +associated with it with public keys and + + align:start position:0% +associated with it with public keys and + + + align:start position:0% +associated with it with public keys and +private keys but the node itself does + + align:start position:0% +private keys but the node itself does + + + align:start position:0% +private keys but the node itself does +not possibly in the future there's bit + + align:start position:0% +not possibly in the future there's bit + + + align:start position:0% +not possibly in the future there's bit +150 I believe which the idea is to have + + align:start position:0% +150 I believe which the idea is to have + + + align:start position:0% +150 I believe which the idea is to have +encrypted communications between nodes + + align:start position:0% +encrypted communications between nodes + + + align:start position:0% +encrypted communications between nodes +which would have some kind of + + align:start position:0% +which would have some kind of + + + align:start position:0% +which would have some kind of +authentication + + align:start position:0% +authentication + + + align:start position:0% +authentication +there's 115 bit 151 one I might have + + align:start position:0% +there's 115 bit 151 one I might have + + + align:start position:0% +there's 115 bit 151 one I might have +them backwards 151 I believe is just + + align:start position:0% +them backwards 151 I believe is just + + + align:start position:0% +them backwards 151 I believe is just +encryption so for privacy sort of + + align:start position:0% +encryption so for privacy sort of + + + align:start position:0% +encryption so for privacy sort of +confidentiality and then bit 150 is for + + align:start position:0% +confidentiality and then bit 150 is for + + + align:start position:0% +confidentiality and then bit 150 is for +authenticity so you connect to a node + + align:start position:0% +authenticity so you connect to a node + + + align:start position:0% +authenticity so you connect to a node +you were like oh this is the same node + + align:start position:0% +you were like oh this is the same node + + + align:start position:0% +you were like oh this is the same node +at the same IP address that I connected + + align:start position:0% +at the same IP address that I connected + + + align:start position:0% +at the same IP address that I connected +to before they're not implemented yet + + align:start position:0% +to before they're not implemented yet + + + align:start position:0% +to before they're not implemented yet +that I'm aware of so right now in + + align:start position:0% +that I'm aware of so right now in + + + align:start position:0% +that I'm aware of so right now in +Bitcoin when you connect to people you + + align:start position:0% +Bitcoin when you connect to people you + + + align:start position:0% +Bitcoin when you connect to people you +sort of just use their IP address you + + align:start position:0% +sort of just use their IP address you + + + align:start position:0% +sort of just use their IP address you +don't really know who they are there's + + align:start position:0% +don't really know who they are there's + + + align:start position:0% +don't really know who they are there's +no authentication there but in these in + + align:start position:0% +no authentication there but in these in + + + align:start position:0% +no authentication there but in these in +ripple and seller you do know okay I'm + + align:start position:0% +ripple and seller you do know okay I'm + + + align:start position:0% +ripple and seller you do know okay I'm +connecting this node it's got a key it's + + align:start position:0% +connecting this node it's got a key it's + + + align:start position:0% +connecting this node it's got a key it's +got an ID in it so to sync instead of + + align:start position:0% +got an ID in it so to sync instead of + + + align:start position:0% +got an ID in it so to sync instead of +verifying all the work you verify the + + align:start position:0% +verifying all the work you verify the + + + align:start position:0% +verifying all the work you verify the +signatures on blocks and the question is + + align:start position:0% +signatures on blocks and the question is + + + align:start position:0% +signatures on blocks and the question is +whose signatures right so if you assume + + align:start position:0% +whose signatures right so if you assume + + + align:start position:0% +whose signatures right so if you assume +okay well if we have a majority that's + + align:start position:0% +okay well if we have a majority that's + + + align:start position:0% +okay well if we have a majority that's +honest and is not trying to you know + + align:start position:0% +honest and is not trying to you know + + + align:start position:0% +honest and is not trying to you know +create transactions that are invalid or + + align:start position:0% +create transactions that are invalid or + + + align:start position:0% +create transactions that are invalid or +something + + align:start position:0% +something + + + align:start position:0% +something +that then it might work but majority is + + align:start position:0% +that then it might work but majority is + + + align:start position:0% +that then it might work but majority is +hard to define when you're subject to + + align:start position:0% +hard to define when you're subject to + + + align:start position:0% +hard to define when you're subject to +civil attacks right the obvious attack + + align:start position:0% +civil attacks right the obvious attack + + + align:start position:0% +civil attacks right the obvious attack +is I just make thousands of nodes or + + align:start position:0% +is I just make thousands of nodes or + + + align:start position:0% +is I just make thousands of nodes or +maybe these nodes don't even really + + align:start position:0% +maybe these nodes don't even really + + + align:start position:0% +maybe these nodes don't even really +exist I just make thousands of key pairs + + align:start position:0% +exist I just make thousands of key pairs + + + align:start position:0% +exist I just make thousands of key pairs +have them pretend to be nodes in my own + + align:start position:0% +have them pretend to be nodes in my own + + + align:start position:0% +have them pretend to be nodes in my own +sort of sub network and they all endorse + + align:start position:0% +sort of sub network and they all endorse + + + align:start position:0% +sort of sub network and they all endorse +blocks that are different than the rest + + align:start position:0% +blocks that are different than the rest + + + align:start position:0% +blocks that are different than the rest +of the network is endorsed it so + + align:start position:0% +of the network is endorsed it so + + + align:start position:0% +of the network is endorsed it so +majority is the tricky part how do you + + align:start position:0% +majority is the tricky part how do you + + + align:start position:0% +majority is the tricky part how do you +know who is the majority with you don't + + align:start position:0% +know who is the majority with you don't + + + align:start position:0% +know who is the majority with you don't +know who these people are you need some + + align:start position:0% +know who these people are you need some + + + align:start position:0% +know who these people are you need some +kind of way to identify humans or + + align:start position:0% +kind of way to identify humans or + + + align:start position:0% +kind of way to identify humans or +computers even and this is a problem + + align:start position:0% +computers even and this is a problem + + + align:start position:0% +computers even and this is a problem +akin to certificate authorities and I + + align:start position:0% +akin to certificate authorities and I + + + align:start position:0% +akin to certificate authorities and I +just wanted to sort of so they a lot of + + align:start position:0% +just wanted to sort of so they a lot of + + + align:start position:0% +just wanted to sort of so they a lot of +the problems that you see in like block + + align:start position:0% +the problems that you see in like block + + + align:start position:0% +the problems that you see in like block +chaining Bitcoin these kind of things + + align:start position:0% +chaining Bitcoin these kind of things + + + align:start position:0% +chaining Bitcoin these kind of things +are not exactly new problems and have + + align:start position:0% +are not exactly new problems and have + + + align:start position:0% +are not exactly new problems and have +sort of already been quote-unquote + + align:start position:0% +sort of already been quote-unquote + + + align:start position:0% +sort of already been quote-unquote +solved so does everyone you know how + + align:start position:0% +solved so does everyone you know how + + + align:start position:0% +solved so does everyone you know how +ca'se work or do people have some idea + + align:start position:0% +ca'se work or do people have some idea + + + align:start position:0% +ca'se work or do people have some idea +or who's like what's a CA okay so it's + + align:start position:0% +or who's like what's a CA okay so it's + + + align:start position:0% +or who's like what's a CA okay so it's +kind of interesting um I can give a + + align:start position:0% +kind of interesting um I can give a + + + align:start position:0% +kind of interesting um I can give a +little demo + + align:start position:0% + + + + align:start position:0% + +yes no this doesn't work hold on okay so + + align:start position:0% +yes no this doesn't work hold on okay so + + + align:start position:0% +yes no this doesn't work hold on okay so +if you have a computer I don't know + + align:start position:0% +if you have a computer I don't know + + + align:start position:0% +if you have a computer I don't know +where that isn't Windows but I think in + + align:start position:0% +where that isn't Windows but I think in + + + align:start position:0% +where that isn't Windows but I think in +Mac and Linux it's in the same place you + + align:start position:0% +Mac and Linux it's in the same place you + + + align:start position:0% +Mac and Linux it's in the same place you +go to act and then shoot I forget where + + align:start position:0% +go to act and then shoot I forget where + + + align:start position:0% +go to act and then shoot I forget where +it is where yeah where's the + + align:start position:0% +it is where yeah where's the + + + align:start position:0% +it is where yeah where's the +certificates sir + + align:start position:0% +certificates sir + + + align:start position:0% +certificates sir +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +there it is okay so in your computer and + + align:start position:0% +there it is okay so in your computer and + + + align:start position:0% +there it is okay so in your computer and +whether you have Linux or Mac you've got + + align:start position:0% +whether you have Linux or Mac you've got + + + align:start position:0% +whether you have Linux or Mac you've got +a folder somewhere ET c /c h + + align:start position:0% +a folder somewhere ET c /c h + + + align:start position:0% +a folder somewhere ET c /c h +certificates something like that in Mac + + align:start position:0% +certificates something like that in Mac + + + align:start position:0% +certificates something like that in Mac +as well and oh no that's not it + + align:start position:0% +as well and oh no that's not it + + + align:start position:0% +as well and oh no that's not it +where are they wait wait wait what is in + + align:start position:0% +where are they wait wait wait what is in + + + align:start position:0% +where are they wait wait wait what is in +update dot d and then there's nothing + + align:start position:0% +update dot d and then there's nothing + + + align:start position:0% +update dot d and then there's nothing +there hold on I need to find this is + + align:start position:0% +there hold on I need to find this is + + + align:start position:0% +there hold on I need to find this is +kind of cool + + align:start position:0% + + + + align:start position:0% + +we are X ah + + align:start position:0% +we are X ah + + + align:start position:0% +we are X ah +SSL yeah there we go + + align:start position:0% +SSL yeah there we go + + + align:start position:0% +SSL yeah there we go +okay so sorry ET c / ssl and then you've + + align:start position:0% +okay so sorry ET c / ssl and then you've + + + align:start position:0% +okay so sorry ET c / ssl and then you've +got certs and this folder has a bunch of + + align:start position:0% +got certs and this folder has a bunch of + + + align:start position:0% +got certs and this folder has a bunch of +sirs I trust all of these entities well + + align:start position:0% +sirs I trust all of these entities well + + + align:start position:0% +sirs I trust all of these entities well +my computer does and by extension my + + align:start position:0% +my computer does and by extension my + + + align:start position:0% +my computer does and by extension my +browser's and my computer which is crazy + + align:start position:0% +browser's and my computer which is crazy + + + align:start position:0% +browser's and my computer which is crazy +because Turk just really trusts turkey + + align:start position:0% + + + + align:start position:0% + +but there's okay stop there another + + align:start position:0% +but there's okay stop there another + + + align:start position:0% +but there's okay stop there another +let's Netherlands somewhere there's a + + align:start position:0% +let's Netherlands somewhere there's a + + + align:start position:0% +let's Netherlands somewhere there's a +bunch of you know things you've never + + align:start position:0% +bunch of you know things you've never + + + align:start position:0% +bunch of you know things you've never +heard of Hellenic academic and research + + align:start position:0% +heard of Hellenic academic and research + + + align:start position:0% +heard of Hellenic academic and research +institutions Hong Kong post Hong Kong + + align:start position:0% +institutions Hong Kong post Hong Kong + + + align:start position:0% +institutions Hong Kong post Hong Kong +post office seems trustworthy yeah so + + align:start position:0% +post office seems trustworthy yeah so + + + align:start position:0% +post office seems trustworthy yeah so +there's a lot of and then like CNN I see + + align:start position:0% +there's a lot of and then like CNN I see + + + align:start position:0% +there's a lot of and then like CNN I see +is one which is like is that still in + + align:start position:0% +is one which is like is that still in + + + align:start position:0% +is one which is like is that still in +here maybe maybe they got rid of it and + + align:start position:0% +here maybe maybe they got rid of it and + + + align:start position:0% +here maybe maybe they got rid of it and +then some of them are just have these + + align:start position:0% +then some of them are just have these + + + align:start position:0% +then some of them are just have these +numbers and you don't even know you have + + align:start position:0% +numbers and you don't even know you have + + + align:start position:0% +numbers and you don't even know you have +to go in yeah trying to internet Network + + align:start position:0% +to go in yeah trying to internet Network + + + align:start position:0% +to go in yeah trying to internet Network +Information Center Evy certificates + + align:start position:0% +Information Center Evy certificates + + + align:start position:0% +Information Center Evy certificates +route I I don't I actually really don't + + align:start position:0% +route I I don't I actually really don't + + + align:start position:0% +route I I don't I actually really don't +trust them to endorse there we go + + align:start position:0% +trust them to endorse there we go + + + align:start position:0% +trust them to endorse there we go +okay it's gone solved it solve the + + align:start position:0% +okay it's gone solved it solve the + + + align:start position:0% +okay it's gone solved it solve the +distributed internet trust problems but + + align:start position:0% +distributed internet trust problems but + + + align:start position:0% +distributed internet trust problems but +oh yeah well I might get I might get + + align:start position:0% +oh yeah well I might get I might get + + + align:start position:0% +oh yeah well I might get I might get +invalid certificate errors for some + + align:start position:0% +invalid certificate errors for some + + + align:start position:0% +invalid certificate errors for some +Chinese sites now I don't go to many + + align:start position:0% +Chinese sites now I don't go to many + + + align:start position:0% +Chinese sites now I don't go to many +Chinese um anyway so so that's the the + + align:start position:0% +Chinese um anyway so so that's the the + + + align:start position:0% +Chinese um anyway so so that's the the +basic idea of certificate authorities + + align:start position:0% +basic idea of certificate authorities + + + align:start position:0% +basic idea of certificate authorities +and this started in like mid-90s when + + align:start position:0% +and this started in like mid-90s when + + + align:start position:0% +and this started in like mid-90s when +they wanted to make public key + + align:start position:0% +they wanted to make public key + + + align:start position:0% +they wanted to make public key +infrastructure for secure websites one + + align:start position:0% +infrastructure for secure websites one + + + align:start position:0% +infrastructure for secure websites one +of the problems is how do you know like + + align:start position:0% +of the problems is how do you know like + + + align:start position:0% +of the problems is how do you know like +so you've got oh we didn't talk about + + align:start position:0% +so you've got oh we didn't talk about + + + align:start position:0% +so you've got oh we didn't talk about +diffie-hellman or maybe I mentioned it + + align:start position:0% +diffie-hellman or maybe I mentioned it + + + align:start position:0% +diffie-hellman or maybe I mentioned it +but you've got you know public keys + + align:start position:0% +but you've got you know public keys + + + align:start position:0% +but you've got you know public keys +private keys you've got a ways to do + + align:start position:0% +private keys you've got a ways to do + + + align:start position:0% +private keys you've got a ways to do +signatures diffie-hellman is a way to do + + align:start position:0% +signatures diffie-hellman is a way to do + + + align:start position:0% +signatures diffie-hellman is a way to do +key exchange so you can have you know if + + align:start position:0% +key exchange so you can have you know if + + + align:start position:0% +key exchange so you can have you know if +I know your public key and I give you my + + align:start position:0% +I know your public key and I give you my + + + align:start position:0% +I know your public key and I give you my +public key we can form a third basically + + align:start position:0% +public key we can form a third basically + + + align:start position:0% +public key we can form a third basically +key that we can then use for encryption + + align:start position:0% +key that we can then use for encryption + + + align:start position:0% +key that we can then use for encryption +and secure messaging this also works but + + align:start position:0% +and secure messaging this also works but + + + align:start position:0% +and secure messaging this also works but +how do you know given a key who is on + + align:start position:0% +how do you know given a key who is on + + + align:start position:0% +how do you know given a key who is on +the other end so that's the idea of + + align:start position:0% +the other end so that's the idea of + + + align:start position:0% +the other end so that's the idea of +certificate authorities you have this + + align:start position:0% +certificate authorities you have this + + + align:start position:0% +certificate authorities you have this +sort of root of trust and these + + align:start position:0% +sort of root of trust and these + + + align:start position:0% +sort of root of trust and these +certificate authorities sign + + align:start position:0% +certificate authorities sign + + + align:start position:0% +certificate authorities sign +certificates in websites and let you + + align:start position:0% +certificates in websites and let you + + + align:start position:0% +certificates in websites and let you +know oh this is the person who you think + + align:start position:0% +know oh this is the person who you think + + + align:start position:0% +know oh this is the person who you think +it is so for example Google secure + + align:start position:0% +it is so for example Google secure + + + align:start position:0% +it is so for example Google secure +connection really how do I know verified + + align:start position:0% +connection really how do I know verified + + + align:start position:0% +connection really how do I know verified +by Google trust well Google has verified + + align:start position:0% +by Google trust well Google has verified + + + align:start position:0% +by Google trust well Google has verified +that Google is trustworthy which is + + align:start position:0% +that Google is trustworthy which is + + + align:start position:0% +that Google is trustworthy which is +somewhat circular but but no that's sort + + align:start position:0% +somewhat circular but but no that's sort + + + align:start position:0% +somewhat circular but but no that's sort +of how it works yeah so Google Google + + align:start position:0% +of how it works yeah so Google Google + + + align:start position:0% +of how it works yeah so Google Google +trust Services is a certificate + + align:start position:0% +trust Services is a certificate + + + align:start position:0% +trust Services is a certificate +authority they ultimately yeah and they + + align:start position:0% +authority they ultimately yeah and they + + + align:start position:0% +authority they ultimately yeah and they +signed off their own certificate for + + align:start position:0% +signed off their own certificate for + + + align:start position:0% +signed off their own certificate for +their own website that's maybe not the + + align:start position:0% +their own website that's maybe not the + + + align:start position:0% +their own website that's maybe not the +best example there's other what okay The + + align:start position:0% +best example there's other what okay The + + + align:start position:0% +best example there's other what okay The +New York Times they are certified by + + align:start position:0% +New York Times they are certified by + + + align:start position:0% +New York Times they are certified by +Comodo CA who also has had like Komodos + + align:start position:0% +Comodo CA who also has had like Komodos + + + align:start position:0% +Comodo CA who also has had like Komodos +gotten in a lot of trouble for signing + + align:start position:0% +gotten in a lot of trouble for signing + + + align:start position:0% +gotten in a lot of trouble for signing +the wrong things so yeah New York Times + + align:start position:0% +the wrong things so yeah New York Times + + + align:start position:0% +the wrong things so yeah New York Times +does not have an EB cert does I think + + align:start position:0% +does not have an EB cert does I think + + + align:start position:0% +does not have an EB cert does I think +Washington Post does so there's also + + align:start position:0% +Washington Post does so there's also + + + align:start position:0% +Washington Post does so there's also +Evie certs where like you've got now the + + align:start position:0% +Evie certs where like you've got now the + + + align:start position:0% +Evie certs where like you've got now the +Washington Post WP company LLC that's + + align:start position:0% +Washington Post WP company LLC that's + + + align:start position:0% +Washington Post WP company LLC that's +like an extended validation certain C a + + align:start position:0% +like an extended validation certain C a + + + align:start position:0% +like an extended validation certain C a +is saying we didn't just check that they + + align:start position:0% +is saying we didn't just check that they + + + align:start position:0% +is saying we didn't just check that they +had an IP address + + align:start position:0% +had an IP address + + + align:start position:0% +had an IP address +we actually checked that they had some + + align:start position:0% +we actually checked that they had some + + + align:start position:0% +we actually checked that they had some +kind of legal corporate entity and they + + align:start position:0% +kind of legal corporate entity and they + + + align:start position:0% +kind of legal corporate entity and they +sent it on their letterhead and we I + + align:start position:0% +sent it on their letterhead and we I + + + align:start position:0% +sent it on their letterhead and we I +don't know emailed someone in Delaware + + align:start position:0% +don't know emailed someone in Delaware + + + align:start position:0% +don't know emailed someone in Delaware +to make sure they actually had a company + + align:start position:0% +to make sure they actually had a company + + + align:start position:0% +to make sure they actually had a company +and this is verified by interest okay so + + align:start position:0% +and this is verified by interest okay so + + + align:start position:0% +and this is verified by interest okay so +in trust Komodo those are all gonna be + + align:start position:0% +in trust Komodo those are all gonna be + + + align:start position:0% +in trust Komodo those are all gonna be +in here + + align:start position:0% +in here + + + align:start position:0% +in here +yeah there's Komodo so you've got these + + align:start position:0% +yeah there's Komodo so you've got these + + + align:start position:0% +yeah there's Komodo so you've got these +companies called CAS that have some kind + + align:start position:0% +companies called CAS that have some kind + + + align:start position:0% +companies called CAS that have some kind +of agreement with each other there's + + align:start position:0% +of agreement with each other there's + + + align:start position:0% +of agreement with each other there's +sort of these standards where you make + + align:start position:0% +sort of these standards where you make + + + align:start position:0% +sort of these standards where you make +some kind of standards where okay don't + + align:start position:0% +some kind of standards where okay don't + + + align:start position:0% +some kind of standards where okay don't +sign the wrong thing if you do we're + + align:start position:0% +sign the wrong thing if you do we're + + + align:start position:0% +sign the wrong thing if you do we're +gonna delete you and then they all sort + + align:start position:0% +gonna delete you and then they all sort + + + align:start position:0% +gonna delete you and then they all sort +of endorse entities identity usually for + + align:start position:0% +of endorse entities identity usually for + + + align:start position:0% +of endorse entities identity usually for +companies there's also stuff now let's + + align:start position:0% +companies there's also stuff now let's + + + align:start position:0% +companies there's also stuff now let's +encrypt which does it for free and + + align:start position:0% +encrypt which does it for free and + + + align:start position:0% +encrypt which does it for free and +without really into in endorsing + + align:start position:0% +without really into in endorsing + + + align:start position:0% +without really into in endorsing +anything this whole thing was kind of + + align:start position:0% +anything this whole thing was kind of + + + align:start position:0% +anything this whole thing was kind of +sort of felt like it was like the big + + align:start position:0% +sort of felt like it was like the big + + + align:start position:0% +sort of felt like it was like the big +scam of like the late 90s because they + + align:start position:0% +scam of like the late 90s because they + + + align:start position:0% +scam of like the late 90s because they +made billions of dollars but then again + + align:start position:0% +made billions of dollars but then again + + + align:start position:0% +made billions of dollars but then again +we got you know boo boo two out of it + + align:start position:0% +we got you know boo boo two out of it + + + align:start position:0% +we got you know boo boo two out of it +right + + align:start position:0% +right + + + align:start position:0% +right +so yeah Lubuntu was funded by Mark + + align:start position:0% +so yeah Lubuntu was funded by Mark + + + align:start position:0% +so yeah Lubuntu was funded by Mark +Shuttleworth who started this one I + + align:start position:0% +Shuttleworth who started this one I + + + align:start position:0% +Shuttleworth who started this one I +believe and made a couple hundred + + align:start position:0% +believe and made a couple hundred + + + align:start position:0% +believe and made a couple hundred +million Orbitz had some fun you know + + align:start position:0% +million Orbitz had some fun you know + + + align:start position:0% +million Orbitz had some fun you know +eccentric millionaires are what fund a + + align:start position:0% +eccentric millionaires are what fund a + + + align:start position:0% +eccentric millionaires are what fund a +lot of Technology Development and we got + + align:start position:0% +lot of Technology Development and we got + + + align:start position:0% +lot of Technology Development and we got +them so ca's are a lot of the people who + + align:start position:0% +them so ca's are a lot of the people who + + + align:start position:0% +them so ca's are a lot of the people who +work on Bitcoin and these systems feel + + align:start position:0% +work on Bitcoin and these systems feel + + + align:start position:0% +work on Bitcoin and these systems feel +that like the current it's called x.509 + + align:start position:0% +that like the current it's called x.509 + + + align:start position:0% +that like the current it's called x.509 +it's like the whole the name of this + + align:start position:0% +it's like the whole the name of this + + + align:start position:0% +it's like the whole the name of this +whole system with these certificate + + align:start position:0% +whole system with these certificate + + + align:start position:0% +whole system with these certificate +authorities and I also sort of feel this + + align:start position:0% +authorities and I also sort of feel this + + + align:start position:0% +authorities and I also sort of feel this +is a suboptimal solution in that there's + + align:start position:0% +is a suboptimal solution in that there's + + + align:start position:0% +is a suboptimal solution in that there's +a lot of problems with certificates + + align:start position:0% +a lot of problems with certificates + + + align:start position:0% +a lot of problems with certificates +being signed inappropriately it's it + + align:start position:0% +being signed inappropriately it's it + + + align:start position:0% +being signed inappropriately it's it +works in a way but it's like not great + + align:start position:0% +works in a way but it's like not great + + + align:start position:0% +works in a way but it's like not great +so this is a problem so the problem that + + align:start position:0% +so this is a problem so the problem that + + + align:start position:0% +so this is a problem so the problem that +these systems like rippln know I have to + + align:start position:0% +these systems like rippln know I have to + + + align:start position:0% +these systems like rippln know I have to +deal with are in some ways similar to + + align:start position:0% +deal with are in some ways similar to + + + align:start position:0% +deal with are in some ways similar to +the the problem that is solved by CA so + + align:start position:0% +the the problem that is solved by CA so + + + align:start position:0% +the the problem that is solved by CA so +what they do is they say we have a + + align:start position:0% +what they do is they say we have a + + + align:start position:0% +what they do is they say we have a +unique node list we're not actually + + align:start position:0% +unique node list we're not actually + + + align:start position:0% +unique node list we're not actually +endorsing an identity from you know + + align:start position:0% +endorsing an identity from you know + + + align:start position:0% +endorsing an identity from you know +here's a public key here's a human + + align:start position:0% +here's a public key here's a human + + + align:start position:0% +here's a public key here's a human +company you know here human name + + align:start position:0% +company you know here human name + + + align:start position:0% +company you know here human name +or a company name or something like that + + align:start position:0% +or a company name or something like that + + + align:start position:0% +or a company name or something like that +it's we're just saying that they're + + align:start position:0% +it's we're just saying that they're + + + align:start position:0% +it's we're just saying that they're +unique so it's it's more limited than a + + align:start position:0% +unique so it's it's more limited than a + + + align:start position:0% +unique so it's it's more limited than a +certificate authority it's just saying + + align:start position:0% +certificate authority it's just saying + + + align:start position:0% +certificate authority it's just saying +we're certifying that these two keys + + align:start position:0% +we're certifying that these two keys + + + align:start position:0% +we're certifying that these two keys +belong to different people or different + + align:start position:0% +belong to different people or different + + + align:start position:0% +belong to different people or different +companies which seems easier than the + + align:start position:0% +companies which seems easier than the + + + align:start position:0% +companies which seems easier than the +job of the CA right the CA has to verify + + align:start position:0% +job of the CA right the CA has to verify + + + align:start position:0% +job of the CA right the CA has to verify +that like the Washington Post is + + align:start position:0% +that like the Washington Post is + + + align:start position:0% +that like the Washington Post is +actually the washing you know the key + + align:start position:0% +actually the washing you know the key + + + align:start position:0% +actually the washing you know the key +whoever's presenting a public key is + + align:start position:0% +whoever's presenting a public key is + + + align:start position:0% +whoever's presenting a public key is +actually the Washington Post + + align:start position:0% +actually the Washington Post + + + align:start position:0% +actually the Washington Post +so the actual certificate is just + + align:start position:0% +so the actual certificate is just + + + align:start position:0% +so the actual certificate is just +basically here's the pump key here's the + + align:start position:0% +basically here's the pump key here's the + + + align:start position:0% +basically here's the pump key here's the +name and then the CA science and you can + + align:start position:0% +name and then the CA science and you can + + + align:start position:0% +name and then the CA science and you can +look at those and stuff okay so for + + align:start position:0% +look at those and stuff okay so for + + + align:start position:0% +look at those and stuff okay so for +synchronization you wait for a majority + + align:start position:0% +synchronization you wait for a majority + + + align:start position:0% +synchronization you wait for a majority +of nodes in your unique node list to + + align:start position:0% +of nodes in your unique node list to + + + align:start position:0% +of nodes in your unique node list to +sign and if they've signed accept so + + align:start position:0% +sign and if they've signed accept so + + + align:start position:0% +sign and if they've signed accept so +there's some recent papers from Ripple + + align:start position:0% +there's some recent papers from Ripple + + + align:start position:0% +there's some recent papers from Ripple +and in order to really get consensus you + + align:start position:0% +and in order to really get consensus you + + + align:start position:0% +and in order to really get consensus you +need basically a 90 percent overlap in + + align:start position:0% +need basically a 90 percent overlap in + + + align:start position:0% +need basically a 90 percent overlap in +your unique node list so if I have a + + align:start position:0% +your unique node list so if I have a + + + align:start position:0% +your unique node list so if I have a +unique node list of Alice and Bob and + + align:start position:0% +unique node list of Alice and Bob and + + + align:start position:0% +unique node list of Alice and Bob and +Carol and you have a unique node list of + + align:start position:0% +Carol and you have a unique node list of + + + align:start position:0% +Carol and you have a unique node list of +Carol and Dave and we might diverge we + + align:start position:0% +Carol and Dave and we might diverge we + + + align:start position:0% +Carol and Dave and we might diverge we +might not agree on the same sort of + + align:start position:0% +might not agree on the same sort of + + + align:start position:0% +might not agree on the same sort of +chain of transactions because we've got + + align:start position:0% +chain of transactions because we've got + + + align:start position:0% +chain of transactions because we've got +different people that were looking at + + align:start position:0% +different people that were looking at + + + align:start position:0% +different people that were looking at +their signatures + + align:start position:0% +their signatures + + + align:start position:0% +their signatures +we may also with them may all be unique + + align:start position:0% +we may also with them may all be unique + + + align:start position:0% +we may also with them may all be unique +but if we have different unique people + + align:start position:0% +but if we have different unique people + + + align:start position:0% +but if we have different unique people +we're looking to it might not converge + + align:start position:0% +we're looking to it might not converge + + + align:start position:0% +we're looking to it might not converge +so there's they have a newer paper that + + align:start position:0% +so there's they have a newer paper that + + + align:start position:0% +so there's they have a newer paper that +reduces that to 60% ish where the + + align:start position:0% +reduces that to 60% ish where the + + + align:start position:0% +reduces that to 60% ish where the +overlap of what unique nodes everyone + + align:start position:0% +overlap of what unique nodes everyone + + + align:start position:0% +overlap of what unique nodes everyone +needs to look at is not as large but + + align:start position:0% +needs to look at is not as large but + + + align:start position:0% +needs to look at is not as large but +still quite large and then the real + + align:start position:0% +still quite large and then the real + + + align:start position:0% +still quite large and then the real +question is okay well who provides the + + align:start position:0% +question is okay well who provides the + + + align:start position:0% +question is okay well who provides the +unique node list because how you know + + align:start position:0% +unique node list because how you know + + + align:start position:0% +unique node list because how you know +that's not really a job I can do maybe + + align:start position:0% +that's not really a job I can do maybe + + + align:start position:0% +that's not really a job I can do maybe +it is in a way if I know you and like we + + align:start position:0% +it is in a way if I know you and like we + + + align:start position:0% +it is in a way if I know you and like we +do some kind of web of trust thing where + + align:start position:0% +do some kind of web of trust thing where + + + align:start position:0% +do some kind of web of trust thing where +I'm like oh what's your ripple nodes + + align:start position:0% +I'm like oh what's your ripple nodes + + + align:start position:0% +I'm like oh what's your ripple nodes +bump key okay cool I know you and what's + + align:start position:0% +bump key okay cool I know you and what's + + + align:start position:0% +bump key okay cool I know you and what's +your ripple knows Bucky we meet in + + align:start position:0% +your ripple knows Bucky we meet in + + + align:start position:0% +your ripple knows Bucky we meet in +person we sign each other's pub keys we + + align:start position:0% +person we sign each other's pub keys we + + + align:start position:0% +person we sign each other's pub keys we +do the whole PGP kind of thing which you + + align:start position:0% +do the whole PGP kind of thing which you + + + align:start position:0% +do the whole PGP kind of thing which you +know I do and the Bitcoin people + + align:start position:0% +know I do and the Bitcoin people + + + align:start position:0% +know I do and the Bitcoin people +actually do this so if I go to so I've + + align:start position:0% +actually do this so if I go to so I've + + + align:start position:0% +actually do this so if I go to so I've +got like a bunch of keys and everyone + + align:start position:0% +got like a bunch of keys and everyone + + + align:start position:0% +got like a bunch of keys and everyone +signed them and there's like your child + + align:start position:0% +signed them and there's like your child + + + align:start position:0% +signed them and there's like your child +and Kylie and you know all these Bitcoin + + align:start position:0% +and Kylie and you know all these Bitcoin + + + align:start position:0% +and Kylie and you know all these Bitcoin +people and I'm signing their keys and + + align:start position:0% +people and I'm signing their keys and + + + align:start position:0% +people and I'm signing their keys and +they've signed my keys because we meet + + align:start position:0% +they've signed my keys because we meet + + + align:start position:0% +they've signed my keys because we meet +in person and do that kind of thing so + + align:start position:0% +in person and do that kind of thing so + + + align:start position:0% +in person and do that kind of thing so +we've established not just the unique + + align:start position:0% +we've established not just the unique + + + align:start position:0% +we've established not just the unique +node list but we've you know done a CA + + align:start position:0% +node list but we've you know done a CA + + + align:start position:0% +node list but we've you know done a CA +free validation of each other's keys you + + align:start position:0% +free validation of each other's keys you + + + align:start position:0% +free validation of each other's keys you +just meet in person read each other's + + align:start position:0% +just meet in person read each other's + + + align:start position:0% +just meet in person read each other's +keys off so you can do that in practice + + align:start position:0% +keys off so you can do that in practice + + + align:start position:0% +keys off so you can do that in practice +it's really nerdy and no one does that + + align:start position:0% +it's really nerdy and no one does that + + + align:start position:0% +it's really nerdy and no one does that +and and it would be cool if we could get + + align:start position:0% +and and it would be cool if we could get + + + align:start position:0% +and and it would be cool if we could get +it to be you know easier and maybe + + align:start position:0% +it to be you know easier and maybe + + + align:start position:0% +it to be you know easier and maybe +cooler somehow but uh it's been a battle + + align:start position:0% +cooler somehow but uh it's been a battle + + + align:start position:0% +cooler somehow but uh it's been a battle +so who provides the UNL it's probably + + align:start position:0% +so who provides the UNL it's probably + + + align:start position:0% +so who provides the UNL it's probably +kind of obvious well the ripple company + + align:start position:0% +kind of obvious well the ripple company + + + align:start position:0% +kind of obvious well the ripple company +provides the UNL right so when you + + align:start position:0% +provides the UNL right so when you + + + align:start position:0% +provides the UNL right so when you +download a triple it has a list of + + align:start position:0% +download a triple it has a list of + + + align:start position:0% +download a triple it has a list of +unique nodes those are essentially + + align:start position:0% +unique nodes those are essentially + + + align:start position:0% +unique nodes those are essentially +de-facto + + align:start position:0% +de-facto + + + align:start position:0% +de-facto +the the nodes that run ripple and at the + + align:start position:0% +the the nodes that run ripple and at the + + + align:start position:0% +the the nodes that run ripple and at the +current time they're basically those + + align:start position:0% +current time they're basically those + + + align:start position:0% +current time they're basically those +nodes are run by the ripple corporation + + align:start position:0% +nodes are run by the ripple corporation + + + align:start position:0% +nodes are run by the ripple corporation +so a ripple apps stellar + + align:start position:0% +so a ripple apps stellar + + + align:start position:0% +so a ripple apps stellar +similarly like it it comes with a + + align:start position:0% +similarly like it it comes with a + + + align:start position:0% +similarly like it it comes with a +default UNL sort of acts like the ca's + + align:start position:0% +default UNL sort of acts like the ca's + + + align:start position:0% +default UNL sort of acts like the ca's +right it's sort of how when you start + + align:start position:0% +right it's sort of how when you start + + + align:start position:0% +right it's sort of how when you start +your computer you've got this this comes + + align:start position:0% +your computer you've got this this comes + + + align:start position:0% +your computer you've got this this comes +with your OS and you don't really have a + + align:start position:0% +with your OS and you don't really have a + + + align:start position:0% +with your OS and you don't really have a +choice + + align:start position:0% +choice + + + align:start position:0% +choice +in practice you can I just deleted the + + align:start position:0% +in practice you can I just deleted the + + + align:start position:0% +in practice you can I just deleted the +CNNIC one but nobody looks at this stuff + + align:start position:0% +CNNIC one but nobody looks at this stuff + + + align:start position:0% +CNNIC one but nobody looks at this stuff +everyone just goes with the default so + + align:start position:0% +everyone just goes with the default so + + + align:start position:0% +everyone just goes with the default so +that's the problem centralization wife + + align:start position:0% +that's the problem centralization wife + + + align:start position:0% +that's the problem centralization wife +yes + + align:start position:0% + + + + align:start position:0% + +in ripples at least like a year to go + + align:start position:0% +in ripples at least like a year to go + + + align:start position:0% +in ripples at least like a year to go +they may have changed that I know I + + align:start position:0% +they may have changed that I know I + + + align:start position:0% +they may have changed that I know I +think they're trying to but um in + + align:start position:0% +think they're trying to but um in + + + align:start position:0% +think they're trying to but um in +ripples case yeah they ran their own + + align:start position:0% +ripples case yeah they ran their own + + + align:start position:0% +ripples case yeah they ran their own +triple notes they may have some III but + + align:start position:0% +triple notes they may have some III but + + + align:start position:0% +triple notes they may have some III but +they may now but I know that two years + + align:start position:0% +they may now but I know that two years + + + align:start position:0% +they may now but I know that two years +ago it was just ripple or you know + + align:start position:0% +ago it was just ripple or you know + + + align:start position:0% +ago it was just ripple or you know +majority ripple they basically because + + align:start position:0% +majority ripple they basically because + + + align:start position:0% +majority ripple they basically because +they also put in things like they can + + align:start position:0% +they also put in things like they can + + + align:start position:0% +they also put in things like they can +sort of freeze funds because ripple got + + align:start position:0% +sort of freeze funds because ripple got + + + align:start position:0% +sort of freeze funds because ripple got +in trouble with Vinson and they part of + + align:start position:0% +in trouble with Vinson and they part of + + + align:start position:0% +in trouble with Vinson and they part of +the things they modified their code to + + align:start position:0% +the things they modified their code to + + + align:start position:0% +the things they modified their code to +be able to like freeze people's funds if + + align:start position:0% +be able to like freeze people's funds if + + + align:start position:0% +be able to like freeze people's funds if +they did something bad that's definitely + + align:start position:0% +they did something bad that's definitely + + + align:start position:0% +they did something bad that's definitely +not something that the Bitcoin + + align:start position:0% +not something that the Bitcoin + + + align:start position:0% +not something that the Bitcoin +developers or even like the etherium + + align:start position:0% +developers or even like the etherium + + + align:start position:0% +developers or even like the etherium +foundation not it's not as direct anyway + + align:start position:0% +foundation not it's not as direct anyway + + + align:start position:0% +foundation not it's not as direct anyway +the Hearing Foundation sort of did + + align:start position:0% +the Hearing Foundation sort of did + + + align:start position:0% +the Hearing Foundation sort of did +freeze funds and move them against the + + align:start position:0% +freeze funds and move them against the + + + align:start position:0% +freeze funds and move them against the +rules of the system in the case of the + + align:start position:0% +rules of the system in the case of the + + + align:start position:0% +rules of the system in the case of the +Dow but that was in a lot of ways with + + align:start position:0% +Dow but that was in a lot of ways with + + + align:start position:0% +Dow but that was in a lot of ways with +support of a lot of the people running a + + align:start position:0% +support of a lot of the people running a + + + align:start position:0% +support of a lot of the people running a +theory with ripple or they can do it + + align:start position:0% +theory with ripple or they can do it + + + align:start position:0% +theory with ripple or they can do it +sort of enough you know without much + + align:start position:0% +sort of enough you know without much + + + align:start position:0% +sort of enough you know without much +brouhaha they just sort of freeze these + + align:start position:0% +brouhaha they just sort of freeze these + + + align:start position:0% +brouhaha they just sort of freeze these +funds so it's fast there's no work + + align:start position:0% +funds so it's fast there's no work + + + align:start position:0% +funds so it's fast there's no work +involved there's no worry about + + align:start position:0% +involved there's no worry about + + + align:start position:0% +involved there's no worry about +propagating blocks and miners getting + + align:start position:0% +propagating blocks and miners getting + + + align:start position:0% +propagating blocks and miners getting +advantages but there's also known + + align:start position:0% +advantages but there's also known + + + align:start position:0% +advantages but there's also known +identities and so it's sort of more + + align:start position:0% +identities and so it's sort of more + + + align:start position:0% +identities and so it's sort of more +susceptible to subpoenas and things like + + align:start position:0% +susceptible to subpoenas and things like + + + align:start position:0% +susceptible to subpoenas and things like +that all the coins in in these cases all + + align:start position:0% +that all the coins in in these cases all + + + align:start position:0% +that all the coins in in these cases all +the coins existed at the Genesis block + + align:start position:0% +the coins existed at the Genesis block + + + align:start position:0% +the coins existed at the Genesis block +so in the case of ripple I think is a + + align:start position:0% +so in the case of ripple I think is a + + + align:start position:0% +so in the case of ripple I think is a +hundred billion or something and they + + align:start position:0% +hundred billion or something and they + + + align:start position:0% +hundred billion or something and they +just started with all the coins and sort + + align:start position:0% +just started with all the coins and sort + + + align:start position:0% +just started with all the coins and sort +of distributive distributed them as they + + align:start position:0% +of distributive distributed them as they + + + align:start position:0% +of distributive distributed them as they +saw fit + + align:start position:0% +saw fit + + + align:start position:0% +saw fit +same same with stellar stellar had this + + align:start position:0% +same same with stellar stellar had this + + + align:start position:0% +same same with stellar stellar had this +thing where they this party and they + + align:start position:0% +thing where they this party and they + + + align:start position:0% +thing where they this party and they +would give them away if you signed up on + + align:start position:0% +would give them away if you signed up on + + + align:start position:0% +would give them away if you signed up on +Facebook really interesting article + + align:start position:0% +Facebook really interesting article + + + align:start position:0% +Facebook really interesting article +about people in Manila getting thousands + + align:start position:0% +about people in Manila getting thousands + + + align:start position:0% +about people in Manila getting thousands +of used SIM cards from the US + + align:start position:0% +of used SIM cards from the US + + + align:start position:0% +of used SIM cards from the US +registering for new Facebook accounts + + align:start position:0% +registering for new Facebook accounts + + + align:start position:0% +registering for new Facebook accounts +selling those Facebook accounts to + + align:start position:0% +selling those Facebook accounts to + + + align:start position:0% +selling those Facebook accounts to +people in China the people in China then + + align:start position:0% +people in China the people in China then + + + align:start position:0% +people in China the people in China then +registering with stellar as unique + + align:start position:0% +registering with stellar as unique + + + align:start position:0% +registering with stellar as unique +people to get more sellers when you + + align:start position:0% +people to get more sellers when you + + + align:start position:0% +people to get more sellers when you +incentivize things weird things happen + + align:start position:0% +incentivize things weird things happen + + + align:start position:0% +incentivize things weird things happen +be it either giant warehouses full of + + align:start position:0% +be it either giant warehouses full of + + + align:start position:0% +be it either giant warehouses full of +sha-256 chips or giant warehouses full + + align:start position:0% +sha-256 chips or giant warehouses full + + + align:start position:0% +sha-256 chips or giant warehouses full +of you know 20 year old girls in vanilla + + align:start position:0% +of you know 20 year old girls in vanilla + + + align:start position:0% +of you know 20 year old girls in vanilla +putting SIM cards and cell phones all + + align:start position:0% +putting SIM cards and cell phones all + + + align:start position:0% +putting SIM cards and cell phones all +day yeah I should link to that articles + + align:start position:0% +day yeah I should link to that articles + + + align:start position:0% +day yeah I should link to that articles +related so anyway so this is seller 1 + + align:start position:0% +related so anyway so this is seller 1 + + + align:start position:0% +related so anyway so this is seller 1 +and stellar also had this thing where + + align:start position:0% +and stellar also had this thing where + + + align:start position:0% +and stellar also had this thing where +they were gonna give 20% of the seller + + align:start position:0% +they were gonna give 20% of the seller + + + align:start position:0% +they were gonna give 20% of the seller +to people who held Bitcoin sort of an + + align:start position:0% +to people who held Bitcoin sort of an + + + align:start position:0% +to people who held Bitcoin sort of an +airdrop it didn't I didn't get any from + + align:start position:0% +airdrop it didn't I didn't get any from + + + align:start position:0% +airdrop it didn't I didn't get any from +that it wasn't I was I was sort of + + align:start position:0% +that it wasn't I was I was sort of + + + align:start position:0% +that it wasn't I was I was sort of +hoping I'm like hey cool airdrop I have + + align:start position:0% +hoping I'm like hey cool airdrop I have + + + align:start position:0% +hoping I'm like hey cool airdrop I have +a Bitcoin I'll get some seller I didn't + + align:start position:0% +a Bitcoin I'll get some seller I didn't + + + align:start position:0% +a Bitcoin I'll get some seller I didn't +because you basically had to kytc with + + align:start position:0% +because you basically had to kytc with + + + align:start position:0% +because you basically had to kytc with +them they said okay you know send in + + align:start position:0% +them they said okay you know send in + + + align:start position:0% +them they said okay you know send in +your you know I don't know if it was a + + align:start position:0% +your you know I don't know if it was a + + + align:start position:0% +your you know I don't know if it was a +social security number but send in your + + align:start position:0% +social security number but send in your + + + align:start position:0% +social security number but send in your +documents and prove that you know you + + align:start position:0% +documents and prove that you know you + + + align:start position:0% +documents and prove that you know you +have these bitcoins and we will credit + + align:start position:0% +have these bitcoins and we will credit + + + align:start position:0% +have these bitcoins and we will credit +some stellar to the same keys and yeah + + align:start position:0% +some stellar to the same keys and yeah + + + align:start position:0% +some stellar to the same keys and yeah +some people did some people got some + + align:start position:0% +some people did some people got some + + + align:start position:0% +some people did some people got some +stellar that way but yeah so anyway yeah + + align:start position:0% + + + + align:start position:0% + +we'll put that in stellar is a different + + align:start position:0% +we'll put that in stellar is a different + + + align:start position:0% +we'll put that in stellar is a different +you know it's similar software they + + align:start position:0% +you know it's similar software they + + + align:start position:0% +you know it's similar software they +certainly argue about how different they + + align:start position:0% +certainly argue about how different they + + + align:start position:0% +certainly argue about how different they +are stellar had a bog in 2015 I believe + + align:start position:0% +are stellar had a bog in 2015 I believe + + + align:start position:0% +are stellar had a bog in 2015 I believe +where the sort of consensus broke and + + align:start position:0% +where the sort of consensus broke and + + + align:start position:0% +where the sort of consensus broke and +then they said oh it's ripples codes + + align:start position:0% +then they said oh it's ripples codes + + + align:start position:0% +then they said oh it's ripples codes +fault you know this is this is a fault + + align:start position:0% +fault you know this is this is a fault + + + align:start position:0% +fault you know this is this is a fault +with all this code base and then ripple + + align:start position:0% +with all this code base and then ripple + + + align:start position:0% +with all this code base and then ripple +said no no it's because you changed it + + align:start position:0% +said no no it's because you changed it + + + align:start position:0% +said no no it's because you changed it +you don't know what you're doing + + align:start position:0% + + + + align:start position:0% + +yeah there's a minimum account balance + + align:start position:0% + + + + align:start position:0% + +yeah I mean it's a lot though there's + + align:start position:0% +yeah I mean it's a lot though there's + + + align:start position:0% +yeah I mean it's a lot though there's +hundreds of bit so there's enough + + align:start position:0% +hundreds of bit so there's enough + + + align:start position:0% +hundreds of bit so there's enough +forever I mean there's a lot of coins + + align:start position:0% +forever I mean there's a lot of coins + + + align:start position:0% +forever I mean there's a lot of coins +but yeah I guess the egg but the idea is + + align:start position:0% +but yeah I guess the egg but the idea is + + + align:start position:0% +but yeah I guess the egg but the idea is +not that you have UT EXO's like in + + align:start position:0% +not that you have UT EXO's like in + + + align:start position:0% +not that you have UT EXO's like in +Bitcoin and you sort of make new + + align:start position:0% +Bitcoin and you sort of make new + + + align:start position:0% +Bitcoin and you sort of make new +addresses you shine the edgy is you have + + align:start position:0% +addresses you shine the edgy is you have + + + align:start position:0% +addresses you shine the edgy is you have +an address you keep that forever so why + + align:start position:0% +an address you keep that forever so why + + + align:start position:0% +an address you keep that forever so why +would you have multiple different + + align:start position:0% +would you have multiple different + + + align:start position:0% +would you have multiple different +addresses that kind of thing anyway so + + align:start position:0% +addresses that kind of thing anyway so + + + align:start position:0% +addresses that kind of thing anyway so +it's a pretty different system in some + + align:start position:0% +it's a pretty different system in some + + + align:start position:0% +it's a pretty different system in some +ways you could argue it's one of the + + align:start position:0% +ways you could argue it's one of the + + + align:start position:0% +ways you could argue it's one of the +first I SEOs gripple because it's pretty + + align:start position:0% +first I SEOs gripple because it's pretty + + + align:start position:0% +first I SEOs gripple because it's pretty +early they just came up with all their + + align:start position:0% +early they just came up with all their + + + align:start position:0% +early they just came up with all their +coins and sort of gave them out and then + + align:start position:0% +coins and sort of gave them out and then + + + align:start position:0% +coins and sort of gave them out and then +started selling them and that's they + + align:start position:0% +started selling them and that's they + + + align:start position:0% +started selling them and that's they +continued to do that to this day stellar + + align:start position:0% +continued to do that to this day stellar + + + align:start position:0% +continued to do that to this day stellar +is a non-profit which is also sort of + + align:start position:0% +is a non-profit which is also sort of + + + align:start position:0% +is a non-profit which is also sort of +weird because if you make like a billion + + align:start position:0% +weird because if you make like a billion + + + align:start position:0% +weird because if you make like a billion +dollars off of something that really a + + align:start position:0% +dollars off of something that really a + + + align:start position:0% +dollars off of something that really a +non-profit I don't know you didn't the + + align:start position:0% +non-profit I don't know you didn't the + + + align:start position:0% +non-profit I don't know you didn't the +organization didn't directly make the + + align:start position:0% +organization didn't directly make the + + + align:start position:0% +organization didn't directly make the +money and then pay it to the employees + + align:start position:0% +money and then pay it to the employees + + + align:start position:0% +money and then pay it to the employees +or anything but the people who have all + + align:start position:0% +or anything but the people who have all + + + align:start position:0% +or anything but the people who have all +the stellar tokens made a lot of money + + align:start position:0% +the stellar tokens made a lot of money + + + align:start position:0% +the stellar tokens made a lot of money +interesting sort of ways to do it so I + + align:start position:0% +interesting sort of ways to do it so I + + + align:start position:0% +interesting sort of ways to do it so I +would I mean sort of they I think both + + align:start position:0% +would I mean sort of they I think both + + + align:start position:0% +would I mean sort of they I think both +ripple and stellar argue that that it's + + align:start position:0% +ripple and stellar argue that that it's + + + align:start position:0% +ripple and stellar argue that that it's +decentralized distributed but I think a + + align:start position:0% +decentralized distributed but I think a + + + align:start position:0% +decentralized distributed but I think a +lot of people say well maybe to some + + align:start position:0% +lot of people say well maybe to some + + + align:start position:0% +lot of people say well maybe to some +extent but on the spectrum of like + + align:start position:0% +extent but on the spectrum of like + + + align:start position:0% +extent but on the spectrum of like +completely decentralized versus you know + + align:start position:0% +completely decentralized versus you know + + + align:start position:0% +completely decentralized versus you know +one server handles at all it's it's a + + align:start position:0% +one server handles at all it's it's a + + + align:start position:0% +one server handles at all it's it's a +lot further on the centralize side and + + align:start position:0% +lot further on the centralize side and + + + align:start position:0% +lot further on the centralize side and +you know Bitcoin is also kind of + + align:start position:0% +you know Bitcoin is also kind of + + + align:start position:0% +you know Bitcoin is also kind of +centralized to like we were talking + + align:start position:0% +centralized to like we were talking + + + align:start position:0% +centralized to like we were talking +about on Monday but I would I would + + align:start position:0% +about on Monday but I would I would + + + align:start position:0% +about on Monday but I would I would +argue these are more so yeah any + + align:start position:0% +argue these are more so yeah any + + + align:start position:0% +argue these are more so yeah any +questions about riffle stellar pretty + + align:start position:0% +questions about riffle stellar pretty + + + align:start position:0% +questions about riffle stellar pretty +fun okay + + align:start position:0% +fun okay + + + align:start position:0% +fun okay +the next the big one proof of stake so + + align:start position:0% +the next the big one proof of stake so + + + align:start position:0% +the next the big one proof of stake so +this is we've mentioned a little bit its + + align:start position:0% +this is we've mentioned a little bit its + + + align:start position:0% +this is we've mentioned a little bit its +popular alternative where people really + + align:start position:0% +popular alternative where people really + + + align:start position:0% +popular alternative where people really +don't like the proof work stuff + + align:start position:0% +don't like the proof work stuff + + + align:start position:0% +don't like the proof work stuff +so instead of proving work have the + + align:start position:0% +so instead of proving work have the + + + align:start position:0% +so instead of proving work have the +people who hold coins sign the blocks so + + align:start position:0% +people who hold coins sign the blocks so + + + align:start position:0% +people who hold coins sign the blocks so +you don't really that sort of bootstraps + + align:start position:0% +you don't really that sort of bootstraps + + + align:start position:0% +you don't really that sort of bootstraps +in a way your unique node list or your + + align:start position:0% +in a way your unique node list or your + + + align:start position:0% +in a way your unique node list or your +list of who's who well you don't really + + align:start position:0% +list of who's who well you don't really + + + align:start position:0% +list of who's who well you don't really +care who they are but if they have coins + + align:start position:0% +care who they are but if they have coins + + + align:start position:0% +care who they are but if they have coins +you + + align:start position:0% +you + + + align:start position:0% +you +already if you already have a set of who + + align:start position:0% +already if you already have a set of who + + + align:start position:0% +already if you already have a set of who +owns what coins you can use that to say + + align:start position:0% +owns what coins you can use that to say + + + align:start position:0% +owns what coins you can use that to say +okay well the people who own coins now + + align:start position:0% +okay well the people who own coins now + + + align:start position:0% +okay well the people who own coins now +sign and they presumably have incentives + + align:start position:0% +sign and they presumably have incentives + + + align:start position:0% +sign and they presumably have incentives +not to destroy the network they have + + align:start position:0% +not to destroy the network they have + + + align:start position:0% +not to destroy the network they have +coins in um so if you have a given + + align:start position:0% +coins in um so if you have a given + + + align:start position:0% +coins in um so if you have a given +Genesis block with some kind of initial + + align:start position:0% +Genesis block with some kind of initial + + + align:start position:0% +Genesis block with some kind of initial +distribution you can make it + + align:start position:0% +distribution you can make it + + + align:start position:0% +distribution you can make it +deterministic I can say I'm just gonna + + align:start position:0% +deterministic I can say I'm just gonna + + + align:start position:0% +deterministic I can say I'm just gonna +go with whatever has the most stake + + align:start position:0% +go with whatever has the most stake + + + align:start position:0% +go with whatever has the most stake +whichever you know whoever that's the + + align:start position:0% +whichever you know whoever that's the + + + align:start position:0% +whichever you know whoever that's the +most coins signing off on the next block + + align:start position:0% +most coins signing off on the next block + + + align:start position:0% +most coins signing off on the next block +and you know given two or three + + align:start position:0% +and you know given two or three + + + align:start position:0% +and you know given two or three +different histories you can see okay + + align:start position:0% +different histories you can see okay + + + align:start position:0% +different histories you can see okay +from the start which has the mo you know + + align:start position:0% +from the start which has the mo you know + + + align:start position:0% +from the start which has the mo you know +most total stake signing off on these + + align:start position:0% +most total stake signing off on these + + + align:start position:0% +most total stake signing off on these +things so that seems pretty cool here's + + align:start position:0% +things so that seems pretty cool here's + + + align:start position:0% +things so that seems pretty cool here's +some issues stake grinding so for + + align:start position:0% +some issues stake grinding so for + + + align:start position:0% +some issues stake grinding so for +example let's say you have a system + + align:start position:0% +example let's say you have a system + + + align:start position:0% +example let's say you have a system +where the signer of the next block is + + align:start position:0% +where the signer of the next block is + + + align:start position:0% +where the signer of the next block is +determined by the public key nearest to + + align:start position:0% +determined by the public key nearest to + + + align:start position:0% +determined by the public key nearest to +the previous block hash so for example + + align:start position:0% +the previous block hash so for example + + + align:start position:0% +the previous block hash so for example +okay I'm looking at the current block + + align:start position:0% +okay I'm looking at the current block + + + align:start position:0% +okay I'm looking at the current block +hash who gets to sign next well + + align:start position:0% +hash who gets to sign next well + + + align:start position:0% +hash who gets to sign next well +whoever's key is closest use X or you + + align:start position:0% +whoever's key is closest use X or you + + + align:start position:0% +whoever's key is closest use X or you +know just treat the hash as a number and + + align:start position:0% +know just treat the hash as a number and + + + align:start position:0% +know just treat the hash as a number and +treat the pub key as a number and see + + align:start position:0% +treat the pub key as a number and see + + + align:start position:0% +treat the pub key as a number and see +which is closest you can do that but the + + align:start position:0% +which is closest you can do that but the + + + align:start position:0% +which is closest you can do that but the +problem is if the next hash is + + align:start position:0% +problem is if the next hash is + + + align:start position:0% +problem is if the next hash is +determined by the current signer that + + align:start position:0% +determined by the current signer that + + + align:start position:0% +determined by the current signer that +current signer can sort of make a new + + align:start position:0% +current signer can sort of make a new + + + align:start position:0% +current signer can sort of make a new +signature each time and try to make sure + + align:start position:0% +signature each time and try to make sure + + + align:start position:0% +signature each time and try to make sure +that the block after is also going to be + + align:start position:0% +that the block after is also going to be + + + align:start position:0% +that the block after is also going to be +one where they are again the next signer + + align:start position:0% +one where they are again the next signer + + + align:start position:0% +one where they are again the next signer +and they can make you know a couple + + align:start position:0% +and they can make you know a couple + + + align:start position:0% +and they can make you know a couple +hundred different accounts with their + + align:start position:0% +hundred different accounts with their + + + align:start position:0% +hundred different accounts with their +keys and then keep grinding steak and + + align:start position:0% +keys and then keep grinding steak and + + + align:start position:0% +keys and then keep grinding steak and +this would allow this basically means + + align:start position:0% +this would allow this basically means + + + align:start position:0% +this would allow this basically means +that it turns into proof of work because + + align:start position:0% +that it turns into proof of work because + + + align:start position:0% +that it turns into proof of work because +if you can influence who's going to be + + align:start position:0% +if you can influence who's going to be + + + align:start position:0% +if you can influence who's going to be +the next block signer yourself by keep + + align:start position:0% +the next block signer yourself by keep + + + align:start position:0% +the next block signer yourself by keep +Trump you know keep trying different + + align:start position:0% +Trump you know keep trying different + + + align:start position:0% +Trump you know keep trying different +ways to sign okay but it's basically + + align:start position:0% +ways to sign okay but it's basically + + + align:start position:0% +ways to sign okay but it's basically +proof of work what instead of hashing + + align:start position:0% +proof of work what instead of hashing + + + align:start position:0% +proof of work what instead of hashing +you're signing and then this has + + align:start position:0% +you're signing and then this has + + + align:start position:0% +you're signing and then this has +happened in many altcoins one that I + + align:start position:0% +happened in many altcoins one that I + + + align:start position:0% +happened in many altcoins one that I +think was kind of interesting was NXT + + align:start position:0% +think was kind of interesting was NXT + + + align:start position:0% +think was kind of interesting was NXT +which is the people who made later when + + align:start position:0% +which is the people who made later when + + + align:start position:0% +which is the people who made later when +they said okay well we have a + + align:start position:0% +they said okay well we have a + + + align:start position:0% +they said okay well we have a +deterministic signature scheme and so + + align:start position:0% +deterministic signature scheme and so + + + align:start position:0% +deterministic signature scheme and so +this can't happen right given a message + + align:start position:0% +this can't happen right given a message + + + align:start position:0% +this can't happen right given a message +and the public key sorry give it a + + align:start position:0% +and the public key sorry give it a + + + align:start position:0% +and the public key sorry give it a +message in a private key there's only + + align:start position:0% +message in a private key there's only + + + align:start position:0% +message in a private key there's only +one signature that can be produce + + align:start position:0% +one signature that can be produce + + + align:start position:0% +one signature that can be produce +and this is true like so Bitcoin uses + + align:start position:0% +and this is true like so Bitcoin uses + + + align:start position:0% +and this is true like so Bitcoin uses +this + + align:start position:0% +this + + + align:start position:0% +this +it's called RFC 679 basically then the + + align:start position:0% +it's called RFC 679 basically then the + + + align:start position:0% +it's called RFC 679 basically then the +random nonce can be deterministically + + align:start position:0% +random nonce can be deterministically + + + align:start position:0% +random nonce can be deterministically +created from your private key and + + align:start position:0% +created from your private key and + + + align:start position:0% +created from your private key and +message oh the problem is I don't they + + align:start position:0% +message oh the problem is I don't they + + + align:start position:0% +message oh the problem is I don't they +realized probably not but you can't + + align:start position:0% +realized probably not but you can't + + + align:start position:0% +realized probably not but you can't +enforce this you don't you know it's a + + align:start position:0% +enforce this you don't you know it's a + + + align:start position:0% +enforce this you don't you know it's a +it's a policy that says okay I'm going + + align:start position:0% +it's a policy that says okay I'm going + + + align:start position:0% +it's a policy that says okay I'm going +to make a deterministic signature but + + align:start position:0% +to make a deterministic signature but + + + align:start position:0% +to make a deterministic signature but +given a signature you can't tell if + + align:start position:0% +given a signature you can't tell if + + + align:start position:0% +given a signature you can't tell if +someone did this or not right so it's + + align:start position:0% +someone did this or not right so it's + + + align:start position:0% +someone did this or not right so it's +it's up to you to obey this rule but you + + align:start position:0% +it's up to you to obey this rule but you + + + align:start position:0% +it's up to you to obey this rule but you +can't verify that anyone did it so that + + align:start position:0% +can't verify that anyone did it so that + + + align:start position:0% +can't verify that anyone did it so that +one also quickly devolved into proof of + + align:start position:0% +one also quickly devolved into proof of + + + align:start position:0% +one also quickly devolved into proof of +work and in a tricky way because a lot + + align:start position:0% +work and in a tricky way because a lot + + + align:start position:0% +work and in a tricky way because a lot +of people read the documentation said + + align:start position:0% +of people read the documentation said + + + align:start position:0% +of people read the documentation said +okay well there is no way to keep + + align:start position:0% +okay well there is no way to keep + + + align:start position:0% +okay well there is no way to keep +signing you know you their function that + + align:start position:0% +signing you know you their function that + + + align:start position:0% +signing you know you their function that +they wrote there's only one way to sign + + align:start position:0% +they wrote there's only one way to sign + + + align:start position:0% +they wrote there's only one way to sign +you know when you sign a message with + + align:start position:0% +you know when you sign a message with + + + align:start position:0% +you know when you sign a message with +the public key you get a single + + align:start position:0% +the public key you get a single + + + align:start position:0% +the public key you get a single +signature but people who knew how that + + align:start position:0% +signature but people who knew how that + + + align:start position:0% +signature but people who knew how that +worked under the hood said oh I can + + align:start position:0% +worked under the hood said oh I can + + + align:start position:0% +worked under the hood said oh I can +change this code it will still be + + align:start position:0% +change this code it will still be + + + align:start position:0% +change this code it will still be +accepted as a valid signature even + + align:start position:0% +accepted as a valid signature even + + + align:start position:0% +accepted as a valid signature even +though I'm using a different signing + + align:start position:0% +though I'm using a different signing + + + align:start position:0% +though I'm using a different signing +scheme so this is one issue state crime + + align:start position:0% +scheme so this is one issue state crime + + + align:start position:0% +scheme so this is one issue state crime +Nick that's there's ways to get around + + align:start position:0% +Nick that's there's ways to get around + + + align:start position:0% +Nick that's there's ways to get around +it so let's say you make it + + align:start position:0% +it so let's say you make it + + + align:start position:0% +it so let's say you make it +deterministic you have some way to + + align:start position:0% +deterministic you have some way to + + + align:start position:0% +deterministic you have some way to +enforce that a signer can only create + + align:start position:0% +enforce that a signer can only create + + + align:start position:0% +enforce that a signer can only create +one message there are certain signature + + align:start position:0% +one message there are certain signature + + + align:start position:0% +one message there are certain signature +schemes where you can verifiably make + + align:start position:0% +schemes where you can verifiably make + + + align:start position:0% +schemes where you can verifiably make +sure that a single key can only make a + + align:start position:0% +sure that a single key can only make a + + + align:start position:0% +sure that a single key can only make a +signal signature on a message other ways + + align:start position:0% +signal signature on a message other ways + + + align:start position:0% +signal signature on a message other ways +to do it is to say have this big lead + + align:start position:0% +to do it is to say have this big lead + + + align:start position:0% +to do it is to say have this big lead +time where the people who are signing + + align:start position:0% +time where the people who are signing + + + align:start position:0% +time where the people who are signing +the next block are determined by entropy + + align:start position:0% +the next block are determined by entropy + + + align:start position:0% +the next block are determined by entropy +created days or weeks ago so it's hard + + align:start position:0% +created days or weeks ago so it's hard + + + align:start position:0% +created days or weeks ago so it's hard +to know what's going to happen in a week + + align:start position:0% +to know what's going to happen in a week + + + align:start position:0% +to know what's going to happen in a week +because it's you know a long period of + + align:start position:0% +because it's you know a long period of + + + align:start position:0% +because it's you know a long period of +times worth of entropy going into it + + align:start position:0% +times worth of entropy going into it + + + align:start position:0% +times worth of entropy going into it +okay there's another issue with prove + + align:start position:0% +okay there's another issue with prove + + + align:start position:0% +okay there's another issue with prove +mistake call nothing at stake so yeah so + + align:start position:0% +mistake call nothing at stake so yeah so + + + align:start position:0% +mistake call nothing at stake so yeah so +improve of work this happens right this + + align:start position:0% +improve of work this happens right this + + + align:start position:0% +improve of work this happens right this +happens just by accident where okay + + align:start position:0% +happens just by accident where okay + + + align:start position:0% +happens just by accident where okay +there's a block and then two people are + + align:start position:0% +there's a block and then two people are + + + align:start position:0% +there's a block and then two people are +minding on top of it oh they both got + + align:start position:0% +minding on top of it oh they both got + + + align:start position:0% +minding on top of it oh they both got +this + + align:start position:0% +this + + + align:start position:0% +this +and then sometimes even this that's + + align:start position:0% +and then sometimes even this that's + + + align:start position:0% +and then sometimes even this that's +almost never happens in Bitcoin but + + align:start position:0% +almost never happens in Bitcoin but + + + align:start position:0% +almost never happens in Bitcoin but +where you just randomly get + + align:start position:0% +where you just randomly get + + + align:start position:0% +where you just randomly get +to sort of split chains coming out at + + align:start position:0% +to sort of split chains coming out at + + + align:start position:0% +to sort of split chains coming out at +the same time but then this happens + + align:start position:0% +the same time but then this happens + + + align:start position:0% +the same time but then this happens +right someone builds on this one okay + + align:start position:0% +right someone builds on this one okay + + + align:start position:0% +right someone builds on this one okay +you get rid of those two and that's just + + align:start position:0% +you get rid of those two and that's just + + + align:start position:0% +you get rid of those two and that's just +because you know this is a random + + align:start position:0% +because you know this is a random + + + align:start position:0% +because you know this is a random +process you can mine on whichever you + + align:start position:0% +process you can mine on whichever you + + + align:start position:0% +process you can mine on whichever you +want one of those was gonna happen first + + align:start position:0% +want one of those was gonna happen first + + + align:start position:0% +want one of those was gonna happen first +you can lie on both you can split your + + align:start position:0% +you can lie on both you can split your + + + align:start position:0% +you can lie on both you can split your +hash power if you have a billion hashes + + align:start position:0% +hash power if you have a billion hashes + + + align:start position:0% +hash power if you have a billion hashes +per second you could say well I'll do + + align:start position:0% +per second you could say well I'll do + + + align:start position:0% +per second you could say well I'll do +500 million here and 500 million here + + align:start position:0% +500 million here and 500 million here + + + align:start position:0% +500 million here and 500 million here +you can equivocate it's sort of + + align:start position:0% +you can equivocate it's sort of + + + align:start position:0% +you can equivocate it's sort of +equivocation that way but one of them + + align:start position:0% +equivocation that way but one of them + + + align:start position:0% +equivocation that way but one of them +will finish first with you know very + + align:start position:0% +will finish first with you know very + + + align:start position:0% +will finish first with you know very +high probability so eventually this + + align:start position:0% +high probability so eventually this + + + align:start position:0% +high probability so eventually this +happens and then everyone just starts + + align:start position:0% +happens and then everyone just starts + + + align:start position:0% +happens and then everyone just starts +building off this zero zero three broom + + align:start position:0% +building off this zero zero three broom + + + align:start position:0% +building off this zero zero three broom +stake so this happens also notice so + + align:start position:0% +stake so this happens also notice so + + + align:start position:0% +stake so this happens also notice so +this happens but then this happens and + + align:start position:0% +this happens but then this happens and + + + align:start position:0% +this happens but then this happens and +then this happens and then it just keeps + + align:start position:0% +then this happens and then it just keeps + + + align:start position:0% +then this happens and then it just keeps +going because why not sign both right I + + align:start position:0% +going because why not sign both right I + + + align:start position:0% +going because why not sign both right I +don't I don't know which one's gonna win + + align:start position:0% +don't I don't know which one's gonna win + + + align:start position:0% +don't I don't know which one's gonna win +right as a proof of stake sort of minor + + align:start position:0% +right as a proof of stake sort of minor + + + align:start position:0% +right as a proof of stake sort of minor +or Staker I don't really know which + + align:start position:0% +or Staker I don't really know which + + + align:start position:0% +or Staker I don't really know which +one's gonna win which is the same case + + align:start position:0% +one's gonna win which is the same case + + + align:start position:0% +one's gonna win which is the same case +improve work improve work I just flip a + + align:start position:0% +improve work improve work I just flip a + + + align:start position:0% +improve work improve work I just flip a +coin and pick right I don't know what's + + align:start position:0% +coin and pick right I don't know what's + + + align:start position:0% +coin and pick right I don't know what's +gonna win I think in Bitcoin the default + + align:start position:0% +gonna win I think in Bitcoin the default + + + align:start position:0% +gonna win I think in Bitcoin the default +is go with the one I saw first because + + align:start position:0% +is go with the one I saw first because + + + align:start position:0% +is go with the one I saw first because +maybe whatever it doesn't matter who + + align:start position:0% +maybe whatever it doesn't matter who + + + align:start position:0% +maybe whatever it doesn't matter who +wins right if I basically I win + + align:start position:0% +wins right if I basically I win + + + align:start position:0% +wins right if I basically I win +whichever I pick if I'm the next one + + align:start position:0% +whichever I pick if I'm the next one + + + align:start position:0% +whichever I pick if I'm the next one +making block I went but what I don't + + align:start position:0% +making block I went but what I don't + + + align:start position:0% +making block I went but what I don't +want is I don't want to be this zero + + align:start position:0% +want is I don't want to be this zero + + + align:start position:0% +want is I don't want to be this zero +this uh what I don't want to be in proof + + align:start position:0% +this uh what I don't want to be in proof + + + align:start position:0% +this uh what I don't want to be in proof +of work is I don't want to be OA wait + + align:start position:0% +of work is I don't want to be OA wait + + + align:start position:0% +of work is I don't want to be OA wait +right I don't want to be the last one to + + align:start position:0% +right I don't want to be the last one to + + + align:start position:0% +right I don't want to be the last one to +make a block and then something else + + align:start position:0% +make a block and then something else + + + align:start position:0% +make a block and then something else +comes out here so if I see you know I'd + + align:start position:0% +comes out here so if I see you know I'd + + + align:start position:0% +comes out here so if I see you know I'd +rather be Oh Oh F - but you don't know + + align:start position:0% +rather be Oh Oh F - but you don't know + + + align:start position:0% +rather be Oh Oh F - but you don't know +here right so you just pick one okay + + align:start position:0% +here right so you just pick one okay + + + align:start position:0% +here right so you just pick one okay +well um improve mistake you don't have + + align:start position:0% +well um improve mistake you don't have + + + align:start position:0% +well um improve mistake you don't have +to worry about that I'll just build both + + align:start position:0% +to worry about that I'll just build both + + + align:start position:0% +to worry about that I'll just build both +right it takes me no work to sign so I + + align:start position:0% +right it takes me no work to sign so I + + + align:start position:0% +right it takes me no work to sign so I +just sign off on both of them and make + + align:start position:0% +just sign off on both of them and make + + + align:start position:0% +just sign off on both of them and make +parallel chain and then everyone just + + align:start position:0% +parallel chain and then everyone just + + + align:start position:0% +parallel chain and then everyone just +keeps doing that because if I pick one + + align:start position:0% +keeps doing that because if I pick one + + + align:start position:0% +keeps doing that because if I pick one +I might be wrong if I pick both I can't + + align:start position:0% +I might be wrong if I pick both I can't + + + align:start position:0% +I might be wrong if I pick both I can't +be wrong so this is a problem called + + align:start position:0% +be wrong so this is a problem called + + + align:start position:0% +be wrong so this is a problem called +nothing at stake like you have no risk + + align:start position:0% +nothing at stake like you have no risk + + + align:start position:0% +nothing at stake like you have no risk +here you're not actually doing any work + + align:start position:0% +here you're not actually doing any work + + + align:start position:0% +here you're not actually doing any work +might as well just keep going yeah + + align:start position:0% +might as well just keep going yeah + + + align:start position:0% +might as well just keep going yeah +faced with two blocks one I'm both so + + align:start position:0% +faced with two blocks one I'm both so + + + align:start position:0% +faced with two blocks one I'm both so +the mitigations one of the ideas early + + align:start position:0% +the mitigations one of the ideas early + + + align:start position:0% +the mitigations one of the ideas early +in aetherium was okay this thing called + + align:start position:0% +in aetherium was okay this thing called + + + align:start position:0% +in aetherium was okay this thing called +slasher where if you can prove that a + + align:start position:0% +slasher where if you can prove that a + + + align:start position:0% +slasher where if you can prove that a +signature from a different chain you + + align:start position:0% +signature from a different chain you + + + align:start position:0% +signature from a different chain you +know so the idea is on chain oo a3 wait + + align:start position:0% +know so the idea is on chain oo a3 wait + + + align:start position:0% +know so the idea is on chain oo a3 wait +sorry on this chain you say hey look + + align:start position:0% +sorry on this chain you say hey look + + + align:start position:0% +sorry on this chain you say hey look +this guy equivocated you set it off on + + align:start position:0% +this guy equivocated you set it off on + + + align:start position:0% +this guy equivocated you set it off on +two blocks one of which one of which + + align:start position:0% +two blocks one of which one of which + + + align:start position:0% +two blocks one of which one of which +exists in my history that I can point to + + align:start position:0% +exists in my history that I can point to + + + align:start position:0% +exists in my history that I can point to +one of which doesn't exist in my history + + align:start position:0% +one of which doesn't exist in my history + + + align:start position:0% +one of which doesn't exist in my history +but I can provide that signature I can + + align:start position:0% +but I can provide that signature I can + + + align:start position:0% +but I can provide that signature I can +say look here's two signatures at the + + align:start position:0% +say look here's two signatures at the + + + align:start position:0% +say look here's two signatures at the +same block height but from the same + + align:start position:0% +same block height but from the same + + + align:start position:0% +same block height but from the same +person what they're signing different + + align:start position:0% +person what they're signing different + + + align:start position:0% +person what they're signing different +things + + align:start position:0% +things + + + align:start position:0% +things +let's not invalidate this block but + + align:start position:0% +let's not invalidate this block but + + + align:start position:0% +let's not invalidate this block but +let's take all the rewards from the + + align:start position:0% +let's take all the rewards from the + + + align:start position:0% +let's take all the rewards from the +person who signed okay so yeah this is + + align:start position:0% +person who signed okay so yeah this is + + + align:start position:0% +person who signed okay so yeah this is +called flasher I believe in aetherium + + align:start position:0% +called flasher I believe in aetherium + + + align:start position:0% +called flasher I believe in aetherium +like 2014 dude they were sort of saying + + align:start position:0% +like 2014 dude they were sort of saying + + + align:start position:0% +like 2014 dude they were sort of saying +hey we're gonna do a prove mistake and + + align:start position:0% +hey we're gonna do a prove mistake and + + + align:start position:0% +hey we're gonna do a prove mistake and +then they sort of tried all these things + + align:start position:0% +then they sort of tried all these things + + + align:start position:0% +then they sort of tried all these things +and sort of oh it's kind of it's not + + align:start position:0% +and sort of oh it's kind of it's not + + + align:start position:0% +and sort of oh it's kind of it's not +trivial let's start with proof of work + + align:start position:0% +trivial let's start with proof of work + + + align:start position:0% +trivial let's start with proof of work +and then we'll move to proof mistake + + align:start position:0% +and then we'll move to proof mistake + + + align:start position:0% +and then we'll move to proof mistake +later and that's currently their plan so + + align:start position:0% +later and that's currently their plan so + + + align:start position:0% +later and that's currently their plan so +this was one of their early algorithms + + align:start position:0% +this was one of their early algorithms + + + align:start position:0% +this was one of their early algorithms +their early ideas there's also issues + + align:start position:0% +their early ideas there's also issues + + + align:start position:0% +their early ideas there's also issues +with the mitigation because maybe maybe + + align:start position:0% +with the mitigation because maybe maybe + + + align:start position:0% +with the mitigation because maybe maybe +it's hard to get this proof into the + + align:start position:0% +it's hard to get this proof into the + + + align:start position:0% +it's hard to get this proof into the +blockchain because the the miners or + + align:start position:0% +blockchain because the the miners or + + + align:start position:0% +blockchain because the the miners or +thus takers are the ones who determine + + align:start position:0% +thus takers are the ones who determine + + + align:start position:0% +thus takers are the ones who determine +what gets in and what doesn't and so + + align:start position:0% +what gets in and what doesn't and so + + + align:start position:0% +what gets in and what doesn't and so +they certainly could say look if you + + align:start position:0% +they certainly could say look if you + + + align:start position:0% +they certainly could say look if you +provide so it's the this is if the + + align:start position:0% +provide so it's the this is if the + + + align:start position:0% +provide so it's the this is if the +person who created this block then sees + + align:start position:0% +person who created this block then sees + + + align:start position:0% +person who created this block then sees +in this block that there is a slasher + + align:start position:0% +in this block that there is a slasher + + + align:start position:0% +in this block that there is a slasher +proof where hey I just now proved that + + align:start position:0% +proof where hey I just now proved that + + + align:start position:0% +proof where hey I just now proved that +you equivocated and destroy your account + + align:start position:0% +you equivocated and destroy your account + + + align:start position:0% +you equivocated and destroy your account +well the person who signed this doesn't + + align:start position:0% +well the person who signed this doesn't + + + align:start position:0% +well the person who signed this doesn't +build on this and instead Forks off and + + align:start position:0% +build on this and instead Forks off and + + + align:start position:0% +build on this and instead Forks off and +builds their own right why would I + + align:start position:0% +builds their own right why would I + + + align:start position:0% +builds their own right why would I +continue to mine on a chain where I just + + align:start position:0% +continue to mine on a chain where I just + + + align:start position:0% +continue to mine on a chain where I just +lost all my money so there's there's all + + align:start position:0% +lost all my money so there's there's all + + + align:start position:0% +lost all my money so there's there's all +sorts of weird you know + + align:start position:0% +sorts of weird you know + + + align:start position:0% +sorts of weird you know +and there's mitigation through that so + + align:start position:0% +and there's mitigation through that so + + + align:start position:0% +and there's mitigation through that so +it's a little bit whack-a-mole where + + align:start position:0% +it's a little bit whack-a-mole where + + + align:start position:0% +it's a little bit whack-a-mole where +there's all these weird problems and you + + align:start position:0% +there's all these weird problems and you + + + align:start position:0% +there's all these weird problems and you +have to sort of try to fix them and then + + align:start position:0% +have to sort of try to fix them and then + + + align:start position:0% +have to sort of try to fix them and then +fixing them introduces new weird things + + align:start position:0% +fixing them introduces new weird things + + + align:start position:0% +fixing them introduces new weird things +so there's a lot of people working on it + + align:start position:0% +so there's a lot of people working on it + + + align:start position:0% +so there's a lot of people working on it +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +long range of taxes is another big one + + align:start position:0% +long range of taxes is another big one + + + align:start position:0% +long range of taxes is another big one +let's say you go back to the Genesis + + align:start position:0% +let's say you go back to the Genesis + + + align:start position:0% +let's say you go back to the Genesis +block and you rewrite history in Bitcoin + + align:start position:0% +block and you rewrite history in Bitcoin + + + align:start position:0% +block and you rewrite history in Bitcoin +you can also do this it's just really + + align:start position:0% +you can also do this it's just really + + + align:start position:0% +you can also do this it's just really +hard right you could say I'm gonna get a + + align:start position:0% +hard right you could say I'm gonna get a + + + align:start position:0% +hard right you could say I'm gonna get a +bunch of miners rewrite all nine years + + align:start position:0% +bunch of miners rewrite all nine years + + + align:start position:0% +bunch of miners rewrite all nine years +of bitcoins blocks and we know exactly + + align:start position:0% +of bitcoins blocks and we know exactly + + + align:start position:0% +of bitcoins blocks and we know exactly +how long that will take + + align:start position:0% +how long that will take + + + align:start position:0% +how long that will take +there's a simple has a nice graph of it + + align:start position:0% +there's a simple has a nice graph of it + + + align:start position:0% +there's a simple has a nice graph of it +I think and sometimes it's not very long + + align:start position:0% +I think and sometimes it's not very long + + + align:start position:0% +I think and sometimes it's not very long +sometimes it's actually pretty easy to + + align:start position:0% +sometimes it's actually pretty easy to + + + align:start position:0% +sometimes it's actually pretty easy to +do that hash ray this wait yes Bitcoin + + align:start position:0% +do that hash ray this wait yes Bitcoin + + + align:start position:0% +do that hash ray this wait yes Bitcoin +network proof of work equivalent days + + align:start position:0% +network proof of work equivalent days + + + align:start position:0% +network proof of work equivalent days +that's this year this is since the + + align:start position:0% +that's this year this is since the + + + align:start position:0% +that's this year this is since the +beginning where what this means is okay + + align:start position:0% +beginning where what this means is okay + + + align:start position:0% +beginning where what this means is okay +given the current hash rate in Bitcoin + + align:start position:0% +given the current hash rate in Bitcoin + + + align:start position:0% +given the current hash rate in Bitcoin +how long would it take to rewrite the + + align:start position:0% +how long would it take to rewrite the + + + align:start position:0% +how long would it take to rewrite the +entire history of Bitcoin because the + + align:start position:0% +entire history of Bitcoin because the + + + align:start position:0% +entire history of Bitcoin because the +hash rate goes up right and sometimes it + + align:start position:0% +hash rate goes up right and sometimes it + + + align:start position:0% +hash rate goes up right and sometimes it +goes up in so this is the all-time hash + + align:start position:0% +goes up in so this is the all-time hash + + + align:start position:0% +goes up in so this is the all-time hash +rate it basically always looks like this + + align:start position:0% +rate it basically always looks like this + + + align:start position:0% +rate it basically always looks like this +because it's exponential so if you look + + align:start position:0% +because it's exponential so if you look + + + align:start position:0% +because it's exponential so if you look +at it three years ago pretty much the + + align:start position:0% +at it three years ago pretty much the + + + align:start position:0% +at it three years ago pretty much the +same the and then this is a log chart so + + align:start position:0% +same the and then this is a log chart so + + + align:start position:0% +same the and then this is a log chart so +this actually does show some interesting + + align:start position:0% +this actually does show some interesting + + + align:start position:0% +this actually does show some interesting +like detail where okay this is when the + + align:start position:0% +like detail where okay this is when the + + + align:start position:0% +like detail where okay this is when the +GPUs came out this is when nothing much + + align:start position:0% +GPUs came out this is when nothing much + + + align:start position:0% +GPUs came out this is when nothing much +happened in 2012 this is when Asics came + + align:start position:0% +happened in 2012 this is when Asics came + + + align:start position:0% +happened in 2012 this is when Asics came +out and then sort of keeps going up and + + align:start position:0% +out and then sort of keeps going up and + + + align:start position:0% +out and then sort of keeps going up and +this is log scale where each number is + + align:start position:0% +this is log scale where each number is + + + align:start position:0% +this is log scale where each number is +so big but so when you have these really + + align:start position:0% +so big but so when you have these really + + + align:start position:0% +so big but so when you have these really +sharp up ticks like in mid-2010 the + + align:start position:0% +sharp up ticks like in mid-2010 the + + + align:start position:0% +sharp up ticks like in mid-2010 the +current power of the network is so high + + align:start position:0% +current power of the network is so high + + + align:start position:0% +current power of the network is so high +that's probably corresponds to this the + + align:start position:0% +that's probably corresponds to this the + + + align:start position:0% +that's probably corresponds to this the +lowest point there because that's the + + align:start position:0% +lowest point there because that's the + + + align:start position:0% +lowest point there because that's the +steepest slope where I don't know what + + align:start position:0% +steepest slope where I don't know what + + + align:start position:0% +steepest slope where I don't know what +this is a week you could rewrite the + + align:start position:0% +this is a week you could rewrite the + + + align:start position:0% +this is a week you could rewrite the +entire history of Bitcoin in a week and + + align:start position:0% +entire history of Bitcoin in a week and + + + align:start position:0% +entire history of Bitcoin in a week and +destroy + + align:start position:0% +destroy + + + align:start position:0% +destroy +everyone's currency you know and have + + align:start position:0% +everyone's currency you know and have + + + align:start position:0% +everyone's currency you know and have +all the coins herself if you had enough + + align:start position:0% +all the coins herself if you had enough + + + align:start position:0% +all the coins herself if you had enough +power and under your control you + + align:start position:0% +power and under your control you + + + align:start position:0% +power and under your control you +probably do so and today it sits at + + align:start position:0% +probably do so and today it sits at + + + align:start position:0% +probably do so and today it sits at +around 200 a little less than 200 so a + + align:start position:0% +around 200 a little less than 200 so a + + + align:start position:0% +around 200 a little less than 200 so a +little over six months where if you + + align:start position:0% +little over six months where if you + + + align:start position:0% +little over six months where if you +devoted all the current hash power you + + align:start position:0% +devoted all the current hash power you + + + align:start position:0% +devoted all the current hash power you +could rewrite all the previous history + + align:start position:0% +could rewrite all the previous history + + + align:start position:0% +could rewrite all the previous history +still six months it's a lot and it's + + align:start position:0% +still six months it's a lot and it's + + + align:start position:0% +still six months it's a lot and it's +interesting how this changes this is I + + align:start position:0% +interesting how this changes this is I + + + align:start position:0% +interesting how this changes this is I +guess when the Asics first came out so + + align:start position:0% +guess when the Asics first came out so + + + align:start position:0% +guess when the Asics first came out so +that is an issue in proof of work that + + align:start position:0% +that is an issue in proof of work that + + + align:start position:0% +that is an issue in proof of work that +can happen it's not clear what would + + align:start position:0% +can happen it's not clear what would + + + align:start position:0% +can happen it's not clear what would +happen would the Bitcoin software like + + align:start position:0% +happen would the Bitcoin software like + + + align:start position:0% +happen would the Bitcoin software like +the software at least in theory the idea + + align:start position:0% +the software at least in theory the idea + + + align:start position:0% +the software at least in theory the idea +is if something like that happens where + + align:start position:0% +is if something like that happens where + + + align:start position:0% +is if something like that happens where +there's a reorg that spans nine years + + align:start position:0% +there's a reorg that spans nine years + + + align:start position:0% +there's a reorg that spans nine years +well you know you know extend this out + + align:start position:0% +well you know you know extend this out + + + align:start position:0% +well you know you know extend this out +to 500,000 say okay all the stuff you've + + align:start position:0% +to 500,000 say okay all the stuff you've + + + align:start position:0% +to 500,000 say okay all the stuff you've +been dealing with the last nine years + + align:start position:0% +been dealing with the last nine years + + + align:start position:0% +been dealing with the last nine years +it's out we've got this new history now + + align:start position:0% +it's out we've got this new history now + + + align:start position:0% +it's out we've got this new history now +with one person holding all the money + + align:start position:0% +with one person holding all the money + + + align:start position:0% +with one person holding all the money +presumably the software will do that + + align:start position:0% +presumably the software will do that + + + align:start position:0% +presumably the software will do that +probably or oral does crash or something + + align:start position:0% +probably or oral does crash or something + + + align:start position:0% +probably or oral does crash or something +it's sort of seen as like well if + + align:start position:0% +it's sort of seen as like well if + + + align:start position:0% +it's sort of seen as like well if +there's a reorg that spans also you know + + align:start position:0% +there's a reorg that spans also you know + + + align:start position:0% +there's a reorg that spans also you know +weeks or months like the whole system's + + align:start position:0% +weeks or months like the whole system's + + + align:start position:0% +weeks or months like the whole system's +broken kind of but probably you know so + + align:start position:0% +broken kind of but probably you know so + + + align:start position:0% +broken kind of but probably you know so +this is this is an issue for Bitcoin but + + align:start position:0% +this is this is an issue for Bitcoin but + + + align:start position:0% +this is this is an issue for Bitcoin but +it's it's a big issue in prove mistake + + align:start position:0% +it's it's a big issue in prove mistake + + + align:start position:0% +it's it's a big issue in prove mistake +because it seems possibly more feasible + + align:start position:0% +because it seems possibly more feasible + + + align:start position:0% +because it seems possibly more feasible +right in in Bitcoin there have been + + align:start position:0% +right in in Bitcoin there have been + + + align:start position:0% +right in in Bitcoin there have been +times it's like whoa a week yeah that's + + align:start position:0% +times it's like whoa a week yeah that's + + + align:start position:0% +times it's like whoa a week yeah that's +beautiful whereas right now it's like + + align:start position:0% +beautiful whereas right now it's like + + + align:start position:0% +beautiful whereas right now it's like +okay it would take all the hash power in + + align:start position:0% +okay it would take all the hash power in + + + align:start position:0% +okay it would take all the hash power in +existence maybe seven or eight months so + + align:start position:0% +existence maybe seven or eight months so + + + align:start position:0% +existence maybe seven or eight months so +that means that Bitcoin would just halt + + align:start position:0% +that means that Bitcoin would just halt + + + align:start position:0% +that means that Bitcoin would just halt +for seven months and then you'd see this + + align:start position:0% +for seven months and then you'd see this + + + align:start position:0% +for seven months and then you'd see this +reorge happen it seems and also you'd + + align:start position:0% +reorge happen it seems and also you'd + + + align:start position:0% +reorge happen it seems and also you'd +need you it assumes 51% of the miners + + align:start position:0% +need you it assumes 51% of the miners + + + align:start position:0% +need you it assumes 51% of the miners +are doing this however approves take it + + align:start position:0% +are doing this however approves take it + + + align:start position:0% +are doing this however approves take it +might not be that expensive especially + + align:start position:0% +might not be that expensive especially + + + align:start position:0% +might not be that expensive especially +if you can get old keys so if you've got + + align:start position:0% +if you can get old keys so if you've got + + + align:start position:0% +if you can get old keys so if you've got +the keys from the Genesis block in your + + align:start position:0% +the keys from the Genesis block in your + + + align:start position:0% +the keys from the Genesis block in your +occurrence in this proof of State + + align:start position:0% +occurrence in this proof of State + + + align:start position:0% +occurrence in this proof of State +currency you can rewrite a history from + + align:start position:0% +currency you can rewrite a history from + + + align:start position:0% +currency you can rewrite a history from +those with different transactions + + align:start position:0% +those with different transactions + + + align:start position:0% +those with different transactions +so yeah so a lot of times the solution + + align:start position:0% +so yeah so a lot of times the solution + + + align:start position:0% +so yeah so a lot of times the solution +is okay well delete all keys and assume + + align:start position:0% +is okay well delete all keys and assume + + + align:start position:0% +is okay well delete all keys and assume +50% honest that's tricky because old + + align:start position:0% +50% honest that's tricky because old + + + align:start position:0% +50% honest that's tricky because old +keys can be sold and people have been I + + align:start position:0% +keys can be sold and people have been I + + + align:start position:0% +keys can be sold and people have been I +know that people have asked like hey can + + align:start position:0% +know that people have asked like hey can + + + align:start position:0% +know that people have asked like hey can +I buy your old aetherium keys why do you + + align:start position:0% +I buy your old aetherium keys why do you + + + align:start position:0% +I buy your old aetherium keys why do you +want these + + align:start position:0% +want these + + + align:start position:0% +want these +well mistake happens they might be worth + + align:start position:0% +well mistake happens they might be worth + + + align:start position:0% +well mistake happens they might be worth +something currently proof of you know + + align:start position:0% +something currently proof of you know + + + align:start position:0% +something currently proof of you know +currently if you have keys that are for + + align:start position:0% +currently if you have keys that are for + + + align:start position:0% +currently if you have keys that are for +addresses or accounts that don't have + + align:start position:0% +addresses or accounts that don't have + + + align:start position:0% +addresses or accounts that don't have +any money anymore + + align:start position:0% +any money anymore + + + align:start position:0% +any money anymore +it's not very useful but possibly can be + + align:start position:0% +it's not very useful but possibly can be + + + align:start position:0% +it's not very useful but possibly can be +sold yeah so you checkpoint it so + + align:start position:0% +sold yeah so you checkpoint it so + + + align:start position:0% +sold yeah so you checkpoint it so +basically to prevent long-range attacks + + align:start position:0% +basically to prevent long-range attacks + + + align:start position:0% +basically to prevent long-range attacks +the developers usually in github will + + align:start position:0% +the developers usually in github will + + + align:start position:0% +the developers usually in github will +just say okay well the the block height + + align:start position:0% +just say okay well the the block height + + + align:start position:0% +just say okay well the the block height +Nina the block hash here is this and so + + align:start position:0% +Nina the block hash here is this and so + + + align:start position:0% +Nina the block hash here is this and so +you can tree or debuff for that but then + + align:start position:0% +you can tree or debuff for that but then + + + align:start position:0% +you can tree or debuff for that but then +what's the mechanism for that if it's + + align:start position:0% +what's the mechanism for that if it's + + + align:start position:0% +what's the mechanism for that if it's +the developers just sort of sticking in + + align:start position:0% +the developers just sort of sticking in + + + align:start position:0% +the developers just sort of sticking in +a checkpoint that's not really + + align:start position:0% +a checkpoint that's not really + + + align:start position:0% +a checkpoint that's not really +decentralized + + align:start position:0% + + + + align:start position:0% + +okay well that's even more sort of not + + align:start position:0% +okay well that's even more sort of not + + + align:start position:0% +okay well that's even more sort of not +very decentralized if you've now got a + + align:start position:0% +very decentralized if you've now got a + + + align:start position:0% +very decentralized if you've now got a +you know a pub key hard-coded into the + + align:start position:0% +you know a pub key hard-coded into the + + + align:start position:0% +you know a pub key hard-coded into the +code which then calls out to somewhere + + align:start position:0% +code which then calls out to somewhere + + + align:start position:0% +code which then calls out to somewhere +and says okay what what's the correct + + align:start position:0% +and says okay what what's the correct + + + align:start position:0% +and says okay what what's the correct +block to be on and then that key signs + + align:start position:0% +block to be on and then that key signs + + + align:start position:0% +block to be on and then that key signs +something so go here okay + + align:start position:0% +something so go here okay + + + align:start position:0% +something so go here okay +that's yeah that's pretty centralized so + + align:start position:0% +that's yeah that's pretty centralized so + + + align:start position:0% +that's yeah that's pretty centralized so +these this is this is one that I think + + align:start position:0% +these this is this is one that I think + + + align:start position:0% +these this is this is one that I think +is it's hard right because and before + + align:start position:0% +is it's hard right because and before + + + align:start position:0% +is it's hard right because and before +these things happen it's easy to + + align:start position:0% +these things happen it's easy to + + + align:start position:0% +these things happen it's easy to +businesses like this is crazy that's + + align:start position:0% +businesses like this is crazy that's + + + align:start position:0% +businesses like this is crazy that's +never gonna happen + + align:start position:0% +never gonna happen + + + align:start position:0% +never gonna happen +who's gonna go back and you know buy up + + align:start position:0% +who's gonna go back and you know buy up + + + align:start position:0% +who's gonna go back and you know buy up +all these old keys that people were + + align:start position:0% +all these old keys that people were + + + align:start position:0% +all these old keys that people were +supposed to have deleted people probably + + align:start position:0% +supposed to have deleted people probably + + + align:start position:0% +supposed to have deleted people probably +did delete them you know you can't + + align:start position:0% +did delete them you know you can't + + + align:start position:0% +did delete them you know you can't +assume if they haven't and even if they + + align:start position:0% +assume if they haven't and even if they + + + align:start position:0% +assume if they haven't and even if they +did and you made this big reorder well + + align:start position:0% +did and you made this big reorder well + + + align:start position:0% +did and you made this big reorder well +everyone would know in practice that + + align:start position:0% +everyone would know in practice that + + + align:start position:0% +everyone would know in practice that +that's not the right chain similar to + + align:start position:0% +that's not the right chain similar to + + + align:start position:0% +that's not the right chain similar to +our if there's a nine year block reorg + + align:start position:0% +our if there's a nine year block reorg + + + align:start position:0% +our if there's a nine year block reorg +and bitcoin everyone would know okay + + align:start position:0% +and bitcoin everyone would know okay + + + align:start position:0% +and bitcoin everyone would know okay +come on we we all knew what the blocks + + align:start position:0% +come on we we all knew what the blocks + + + align:start position:0% +come on we we all knew what the blocks +were well yesterday you can't just tell + + align:start position:0% +were well yesterday you can't just tell + + + align:start position:0% +were well yesterday you can't just tell +me there's this entirely new history + + align:start position:0% +me there's this entirely new history + + + align:start position:0% +me there's this entirely new history +today and in practice that's probably + + align:start position:0% +today and in practice that's probably + + + align:start position:0% +today and in practice that's probably +true right if there was a nine year + + align:start position:0% +true right if there was a nine year + + + align:start position:0% +true right if there was a nine year +block reorg and Bitcoin I probably + + align:start position:0% +block reorg and Bitcoin I probably + + + align:start position:0% +block reorg and Bitcoin I probably +people wouldn't deal you know would just + + align:start position:0% +people wouldn't deal you know would just + + + align:start position:0% +people wouldn't deal you know would just +ignore it + + align:start position:0% +ignore it + + + align:start position:0% +ignore it +similarly in these systems probably they + + align:start position:0% +similarly in these systems probably they + + + align:start position:0% +similarly in these systems probably they +would ignore it but it's it's harder to + + align:start position:0% +would ignore it but it's it's harder to + + + align:start position:0% +would ignore it but it's it's harder to +it's harder to reason about in these + + align:start position:0% +it's harder to reason about in these + + + align:start position:0% +it's harder to reason about in these +systems I think but anyway so proves + + align:start position:0% +systems I think but anyway so proves + + + align:start position:0% +systems I think but anyway so proves +take there is a bunch of coins that use + + align:start position:0% +take there is a bunch of coins that use + + + align:start position:0% +take there is a bunch of coins that use +it in a lot of cases they sort of have + + align:start position:0% +it in a lot of cases they sort of have + + + align:start position:0% +it in a lot of cases they sort of have +centralization that sort of hidden in + + align:start position:0% +centralization that sort of hidden in + + + align:start position:0% +centralization that sort of hidden in +certain ways I like the term Greg + + align:start position:0% +certain ways I like the term Greg + + + align:start position:0% +certain ways I like the term Greg +Maxwell came up called trust laundering + + align:start position:0% +Maxwell came up called trust laundering + + + align:start position:0% +Maxwell came up called trust laundering +it's not money laundering it's stress + + align:start position:0% +it's not money laundering it's stress + + + align:start position:0% +it's not money laundering it's stress +laundering like you you sort of move + + align:start position:0% +laundering like you you sort of move + + + align:start position:0% +laundering like you you sort of move +where you're trusting and trying to hide + + align:start position:0% +where you're trusting and trying to hide + + + align:start position:0% +where you're trusting and trying to hide +it + + align:start position:0% + + + + align:start position:0% + +yeah so so a very common pat this also + + align:start position:0% +yeah so so a very common pat this also + + + align:start position:0% +yeah so so a very common pat this also +deals with okay who gets the initial + + align:start position:0% +deals with okay who gets the initial + + + align:start position:0% +deals with okay who gets the initial +coins because they have an enormous + + align:start position:0% +coins because they have an enormous + + + align:start position:0% +coins because they have an enormous +power over the system so very common for + + align:start position:0% +power over the system so very common for + + + align:start position:0% +power over the system so very common for +alt coins less so now I think was start + + align:start position:0% +alt coins less so now I think was start + + + align:start position:0% +alt coins less so now I think was start +with proof of work then transition to + + align:start position:0% +with proof of work then transition to + + + align:start position:0% +with proof of work then transition to +proof mistake they still do they still + + align:start position:0% +proof mistake they still do they still + + + align:start position:0% +proof mistake they still do they still +not as much right so you just do er c20 + + align:start position:0% +not as much right so you just do er c20 + + + align:start position:0% +not as much right so you just do er c20 +yeah but you it used to be like + + align:start position:0% +yeah but you it used to be like + + + align:start position:0% +yeah but you it used to be like +2014-2015 a lot of the coins would be + + align:start position:0% +2014-2015 a lot of the coins would be + + + align:start position:0% +2014-2015 a lot of the coins would be +okay proof-of-work for the first month + + align:start position:0% +okay proof-of-work for the first month + + + align:start position:0% +okay proof-of-work for the first month +two months whatever it was with some + + align:start position:0% +two months whatever it was with some + + + align:start position:0% +two months whatever it was with some +weird algorithm and comodo gravity well + + align:start position:0% +weird algorithm and comodo gravity well + + + align:start position:0% +weird algorithm and comodo gravity well +and all sorts of weird stuff and then it + + align:start position:0% +and all sorts of weird stuff and then it + + + align:start position:0% +and all sorts of weird stuff and then it +would switch in a certain point to proof + + align:start position:0% +would switch in a certain point to proof + + + align:start position:0% +would switch in a certain point to proof +of steak so that proof work period + + align:start position:0% +of steak so that proof work period + + + align:start position:0% +of steak so that proof work period +builds out the list of who owns what in + + align:start position:0% +builds out the list of who owns what in + + + align:start position:0% +builds out the list of who owns what in +a sort of provable way and then from + + align:start position:0% +a sort of provable way and then from + + + align:start position:0% +a sort of provable way and then from +there you can use proof of steak because + + align:start position:0% +there you can use proof of steak because + + + align:start position:0% +there you can use proof of steak because +you've got a fairly hopefully fairly + + align:start position:0% +you've got a fairly hopefully fairly + + + align:start position:0% +you've got a fairly hopefully fairly +well distributed set of who owns one ya + + align:start position:0% +well distributed set of who owns one ya + + + align:start position:0% +well distributed set of who owns one ya +know something still do this and some + + align:start position:0% +know something still do this and some + + + align:start position:0% +know something still do this and some +things have hybrid where you still have + + align:start position:0% +things have hybrid where you still have + + + align:start position:0% +things have hybrid where you still have +to do work each block but depending on + + align:start position:0% +to do work each block but depending on + + + align:start position:0% +to do work each block but depending on +how much steak you have depending on how + + align:start position:0% +how much steak you have depending on how + + + align:start position:0% +how much steak you have depending on how +many coins you have you have to do less + + align:start position:0% +many coins you have you have to do less + + + align:start position:0% +many coins you have you have to do less +work i think d cred is something like + + align:start position:0% +work i think d cred is something like + + + align:start position:0% +work i think d cred is something like +that that actually can make sense + + align:start position:0% +that that actually can make sense + + + align:start position:0% +that that actually can make sense +because you still got work and you could + + align:start position:0% +because you still got work and you could + + + align:start position:0% +because you still got work and you could +mix them in ways that sort of negate + + align:start position:0% +mix them in ways that sort of negate + + + align:start position:0% +mix them in ways that sort of negate +some of the downsides of both + + align:start position:0% + + + + align:start position:0% + +distributed there no sorry delegated + + align:start position:0% +distributed there no sorry delegated + + + align:start position:0% +distributed there no sorry delegated +proof of steak + + align:start position:0% +proof of steak + + + align:start position:0% +proof of steak +well signing requires you to actually do + + align:start position:0% +well signing requires you to actually do + + + align:start position:0% +well signing requires you to actually do +something and be online so in a lot of + + align:start position:0% +something and be online so in a lot of + + + align:start position:0% +something and be online so in a lot of +proof of state currencies very few + + align:start position:0% +proof of state currencies very few + + + align:start position:0% +proof of state currencies very few +people actually stake because they don't + + align:start position:0% +people actually stake because they don't + + + align:start position:0% +people actually stake because they don't +care and they leave money on the table + + align:start position:0% +care and they leave money on the table + + + align:start position:0% +care and they leave money on the table +sure but like they don't want to run + + align:start position:0% +sure but like they don't want to run + + + align:start position:0% +sure but like they don't want to run +their own node they don't want to deal + + align:start position:0% +their own node they don't want to deal + + + align:start position:0% +their own node they don't want to deal +with this stuff they just buy that keep + + align:start position:0% +with this stuff they just buy that keep + + + align:start position:0% +with this stuff they just buy that keep +it on exchange or maybe keep it on their + + align:start position:0% +it on exchange or maybe keep it on their + + + align:start position:0% +it on exchange or maybe keep it on their +own computer so instead you can endorse + + align:start position:0% +own computer so instead you can endorse + + + align:start position:0% +own computer so instead you can endorse +a leader by signing with your coins and + + align:start position:0% +a leader by signing with your coins and + + + align:start position:0% +a leader by signing with your coins and +saying hey I'm not going to actually + + align:start position:0% +saying hey I'm not going to actually + + + align:start position:0% +saying hey I'm not going to actually +sign off on blocks but I'll sign off on + + align:start position:0% +sign off on blocks but I'll sign off on + + + align:start position:0% +sign off on blocks but I'll sign off on +a different key who now can sign on my + + align:start position:0% +a different key who now can sign on my + + + align:start position:0% +a different key who now can sign on my +behalf and so this can be called like + + align:start position:0% +behalf and so this can be called like + + + align:start position:0% +behalf and so this can be called like +super nodes master nodes and then is it + + align:start position:0% +super nodes master nodes and then is it + + + align:start position:0% +super nodes master nodes and then is it +peer to peer or is a client server is + + align:start position:0% +peer to peer or is a client server is + + + align:start position:0% +peer to peer or is a client server is +what sort of it becomes so the the + + align:start position:0% +what sort of it becomes so the the + + + align:start position:0% +what sort of it becomes so the the +current one that's pretty popular is + + align:start position:0% +current one that's pretty popular is + + + align:start position:0% +current one that's pretty popular is +called yose where I think they're doing + + align:start position:0% +called yose where I think they're doing + + + align:start position:0% +called yose where I think they're doing +this kind of thing and they're like well + + align:start position:0% +this kind of thing and they're like well + + + align:start position:0% +this kind of thing and they're like well +there's twenty twenty computers that run + + align:start position:0% +there's twenty twenty computers that run + + + align:start position:0% +there's twenty twenty computers that run +the network and you can endorse one of + + align:start position:0% +the network and you can endorse one of + + + align:start position:0% +the network and you can endorse one of +them and they'll give you some kind of + + align:start position:0% +them and they'll give you some kind of + + + align:start position:0% +them and they'll give you some kind of +profit back or something and you need + + align:start position:0% +profit back or something and you need + + + align:start position:0% +profit back or something and you need +like a million dollars to run one of + + align:start position:0% +like a million dollars to run one of + + + align:start position:0% +like a million dollars to run one of +these computers because it's gonna be + + align:start position:0% +these computers because it's gonna be + + + align:start position:0% +these computers because it's gonna be +super powerful and do free transactions + + align:start position:0% +super powerful and do free transactions + + + align:start position:0% +super powerful and do free transactions +that way so this gets pretty far into + + align:start position:0% +that way so this gets pretty far into + + + align:start position:0% +that way so this gets pretty far into +client-server territory where you're not + + align:start position:0% +client-server territory where you're not + + + align:start position:0% +client-server territory where you're not +up here + + align:start position:0% +up here + + + align:start position:0% +up here +you're just the client and you ask them + + align:start position:0% +you're just the client and you ask them + + + align:start position:0% +you're just the client and you ask them +what's going on + + align:start position:0% +what's going on + + + align:start position:0% +what's going on +which in many cases works right that's + + align:start position:0% +which in many cases works right that's + + + align:start position:0% +which in many cases works right that's +but then again it's not quite as + + align:start position:0% +but then again it's not quite as + + + align:start position:0% +but then again it's not quite as +interesting because that sort of the + + align:start position:0% +interesting because that sort of the + + + align:start position:0% +interesting because that sort of the +system we already have the banks so but + + align:start position:0% +system we already have the banks so but + + + align:start position:0% +system we already have the banks so but +in a lot of cases yeah that's what + + align:start position:0% +in a lot of cases yeah that's what + + + align:start position:0% +in a lot of cases yeah that's what +people want + + align:start position:0% +people want + + + align:start position:0% +people want +I sort of joke that I should just make + + align:start position:0% +I sort of joke that I should just make + + + align:start position:0% +I sort of joke that I should just make +one called central coin where there's + + align:start position:0% +one called central coin where there's + + + align:start position:0% +one called central coin where there's +just a nice server and it just keeps + + align:start position:0% +just a nice server and it just keeps + + + align:start position:0% +just a nice server and it just keeps +track of who owns what and then like + + align:start position:0% +track of who owns what and then like + + + align:start position:0% +track of who owns what and then like +have a nice ego and people will use it + + align:start position:0% + + + + align:start position:0% + +anyway so that's distributed proof + + align:start position:0% +anyway so that's distributed proof + + + align:start position:0% +anyway so that's distributed proof +mistake + + align:start position:0% +mistake + + + align:start position:0% +mistake +okay so broomstick in general it's hard + + align:start position:0% +okay so broomstick in general it's hard + + + align:start position:0% +okay so broomstick in general it's hard +to resolve conflicts using only the + + align:start position:0% +to resolve conflicts using only the + + + align:start position:0% +to resolve conflicts using only the +system itself proof work has this really + + align:start position:0% +system itself proof work has this really + + + align:start position:0% +system itself proof work has this really +nice property where it's taking + + align:start position:0% +nice property where it's taking + + + align:start position:0% +nice property where it's taking +something from the external world be it + + align:start position:0% +something from the external world be it + + + align:start position:0% +something from the external world be it +you know CPU time get chips and using + + align:start position:0% +you know CPU time get chips and using + + + align:start position:0% +you know CPU time get chips and using +that to sort of get a sort of dead + + align:start position:0% +that to sort of get a sort of dead + + + align:start position:0% +that to sort of get a sort of dead +reckoning on the system itself that's + + align:start position:0% +reckoning on the system itself that's + + + align:start position:0% +reckoning on the system itself that's +nice + + align:start position:0% +nice + + + align:start position:0% +nice +proof mistake the really difficult part + + align:start position:0% +proof mistake the really difficult part + + + align:start position:0% +proof mistake the really difficult part +is it's a closed system you're trying to + + align:start position:0% +is it's a closed system you're trying to + + + align:start position:0% +is it's a closed system you're trying to +resolve conflicts within the system + + align:start position:0% +resolve conflicts within the system + + + align:start position:0% +resolve conflicts within the system +using no external data that's really + + align:start position:0% +using no external data that's really + + + align:start position:0% +using no external data that's really +hard + + align:start position:0% +hard + + + align:start position:0% +hard +another problem people complain about is + + align:start position:0% +another problem people complain about is + + + align:start position:0% +another problem people complain about is +that the rich get richer I you know + + align:start position:0% +that the rich get richer I you know + + + align:start position:0% +that the rich get richer I you know +agree it's a problem kind of sucks but + + align:start position:0% +agree it's a problem kind of sucks but + + + align:start position:0% +agree it's a problem kind of sucks but +you know a broom work is the same I + + align:start position:0% +you know a broom work is the same I + + + align:start position:0% +you know a broom work is the same I +don't feel like any of these systems + + align:start position:0% +don't feel like any of these systems + + + align:start position:0% +don't feel like any of these systems +will change the inherent sort of Pareto + + align:start position:0% +will change the inherent sort of Pareto + + + align:start position:0% +will change the inherent sort of Pareto +distribution of wealth in the universe + + align:start position:0% +distribution of wealth in the universe + + + align:start position:0% +distribution of wealth in the universe +that just seems to be how things work be + + align:start position:0% +that just seems to be how things work be + + + align:start position:0% +that just seems to be how things work be +cool if everyone had the same on the + + align:start position:0% +cool if everyone had the same on the + + + align:start position:0% +cool if everyone had the same on the +money I guess maybe but I don't think + + align:start position:0% +money I guess maybe but I don't think + + + align:start position:0% +money I guess maybe but I don't think +yeah and then it relies on different + + align:start position:0% +yeah and then it relies on different + + + align:start position:0% +yeah and then it relies on different +assumptions so the assumption in bitcoin + + align:start position:0% +assumptions so the assumption in bitcoin + + + align:start position:0% +assumptions so the assumption in bitcoin +is like 51% of miners can destroy the + + align:start position:0% +is like 51% of miners can destroy the + + + align:start position:0% +is like 51% of miners can destroy the +system so in some cases people say well + + align:start position:0% +system so in some cases people say well + + + align:start position:0% +system so in some cases people say well +you assume 51% honest in Bitcoin kind of + + align:start position:0% +you assume 51% honest in Bitcoin kind of + + + align:start position:0% +you assume 51% honest in Bitcoin kind of +it's more like 51% rational in Bitcoin + + align:start position:0% +it's more like 51% rational in Bitcoin + + + align:start position:0% +it's more like 51% rational in Bitcoin +you you could have miners with 51% + + align:start position:0% +you you could have miners with 51% + + + align:start position:0% +you you could have miners with 51% +attacked the system but they make more + + align:start position:0% +attacked the system but they make more + + + align:start position:0% +attacked the system but they make more +money by doing the right thing um so + + align:start position:0% +money by doing the right thing um so + + + align:start position:0% +money by doing the right thing um so +there are certain cases in prove mistake + + align:start position:0% +there are certain cases in prove mistake + + + align:start position:0% +there are certain cases in prove mistake +where honesty is not as profitable and + + align:start position:0% +where honesty is not as profitable and + + + align:start position:0% +where honesty is not as profitable and +if honesty is not profitable well maybe + + align:start position:0% +if honesty is not profitable well maybe + + + align:start position:0% +if honesty is not profitable well maybe +there's a lot more incentive to be not + + align:start position:0% +there's a lot more incentive to be not + + + align:start position:0% +there's a lot more incentive to be not +honest in the terms of the system + + align:start position:0% +honest in the terms of the system + + + align:start position:0% +honest in the terms of the system +whereas a Bitcoin it's like you've got + + align:start position:0% +whereas a Bitcoin it's like you've got + + + align:start position:0% +whereas a Bitcoin it's like you've got +this nice system where it seems like the + + align:start position:0% +this nice system where it seems like the + + + align:start position:0% +this nice system where it seems like the +honesty is not just enforced by people + + align:start position:0% +honesty is not just enforced by people + + + align:start position:0% +honesty is not just enforced by people +trying to be nice it's enforced by + + align:start position:0% +trying to be nice it's enforced by + + + align:start position:0% +trying to be nice it's enforced by +people being greedy which is seems more + + align:start position:0% +people being greedy which is seems more + + + align:start position:0% +people being greedy which is seems more +common than + + align:start position:0% +common than + + + align:start position:0% +common than +being nice in the world so there's tons + + align:start position:0% +being nice in the world so there's tons + + + align:start position:0% +being nice in the world so there's tons +of research and prove mistakes um that's + + align:start position:0% +of research and prove mistakes um that's + + + align:start position:0% +of research and prove mistakes um that's +pretty interesting but if ever I'm not + + align:start position:0% +pretty interesting but if ever I'm not + + + align:start position:0% +pretty interesting but if ever I'm not +super hopeful but the thing is it works + + align:start position:0% +super hopeful but the thing is it works + + + align:start position:0% +super hopeful but the thing is it works +until it doesn't and so it's it's really + + align:start position:0% +until it doesn't and so it's it's really + + + align:start position:0% +until it doesn't and so it's it's really +hard to show security like under what + + align:start position:0% +hard to show security like under what + + + align:start position:0% +hard to show security like under what +different attacks so you what I would + + align:start position:0% +different attacks so you what I would + + + align:start position:0% +different attacks so you what I would +worry about is you've got this proof + + align:start position:0% +worry about is you've got this proof + + + align:start position:0% +worry about is you've got this proof +mistake system seems to be working and + + align:start position:0% +mistake system seems to be working and + + + align:start position:0% +mistake system seems to be working and +then something weird happens and it's + + align:start position:0% +then something weird happens and it's + + + align:start position:0% +then something weird happens and it's +sort of revealed as oh actually this was + + align:start position:0% +sort of revealed as oh actually this was + + + align:start position:0% +sort of revealed as oh actually this was +a lot more centralized than it seemed to + + align:start position:0% +a lot more centralized than it seemed to + + + align:start position:0% +a lot more centralized than it seemed to +be which is also a worry improving any + + align:start position:0% +be which is also a worry improving any + + + align:start position:0% +be which is also a worry improving any +questions proved mistake yes a lot of + + align:start position:0% +questions proved mistake yes a lot of + + + align:start position:0% +questions proved mistake yes a lot of +coins the majority of the coins are held + + align:start position:0% +coins the majority of the coins are held + + + align:start position:0% +coins the majority of the coins are held +on different exchanges and so that means + + align:start position:0% +on different exchanges and so that means + + + align:start position:0% +on different exchanges and so that means +the exchanges would possibly be able to + + align:start position:0% +the exchanges would possibly be able to + + + align:start position:0% +the exchanges would possibly be able to +then stake and get some kind of revenue + + align:start position:0% + + + + align:start position:0% + +yes yeah and so that that's also an + + align:start position:0% +yes yeah and so that that's also an + + + align:start position:0% +yes yeah and so that that's also an +issue that there's all different sort of + + align:start position:0% +issue that there's all different sort of + + + align:start position:0% +issue that there's all different sort of +ways to mitigate and you know you can + + align:start position:0% +ways to mitigate and you know you can + + + align:start position:0% +ways to mitigate and you know you can +say oh I'm in an exchange but I get to + + align:start position:0% +say oh I'm in an exchange but I get to + + + align:start position:0% +say oh I'm in an exchange but I get to +sign and sort of delegate my stake to + + align:start position:0% +sign and sort of delegate my stake to + + + align:start position:0% +sign and sort of delegate my stake to +someone else and then I get some kind of + + align:start position:0% +someone else and then I get some kind of + + + align:start position:0% +someone else and then I get some kind of +revenue sharing from that but yeah it's + + align:start position:0% +revenue sharing from that but yeah it's + + + align:start position:0% +revenue sharing from that but yeah it's +also tricky how do you incentivize it in + + align:start position:0% +also tricky how do you incentivize it in + + + align:start position:0% +also tricky how do you incentivize it in +terms of how much new coins get issued + + align:start position:0% +terms of how much new coins get issued + + + align:start position:0% +terms of how much new coins get issued +to the people staking if it's zero then + + align:start position:0% +to the people staking if it's zero then + + + align:start position:0% +to the people staking if it's zero then +there's no real incentive to do it you + + align:start position:0% +there's no real incentive to do it you + + + align:start position:0% +there's no real incentive to do it you +could have a lot of different change + + align:start position:0% +could have a lot of different change + + + align:start position:0% +could have a lot of different change +boards if it's very high then it's like + + align:start position:0% +boards if it's very high then it's like + + + align:start position:0% +boards if it's very high then it's like +very you know Genie Genie net curve goes + + align:start position:0% +very you know Genie Genie net curve goes + + + align:start position:0% +very you know Genie Genie net curve goes +way crazy because the rich really get + + align:start position:0% +way crazy because the rich really get + + + align:start position:0% +way crazy because the rich really get +Richard because the more coins you have + + align:start position:0% +Richard because the more coins you have + + + align:start position:0% +Richard because the more coins you have +you have like an enormous amount of + + align:start position:0% +you have like an enormous amount of + + + align:start position:0% +you have like an enormous amount of +revenue so you sort of need a balance + + align:start position:0% +revenue so you sort of need a balance + + + align:start position:0% +revenue so you sort of need a balance +there that's also a bit difficult + + align:start position:0% +there that's also a bit difficult + + + align:start position:0% +there that's also a bit difficult +economically that's also a problem and + + align:start position:0% +economically that's also a problem and + + + align:start position:0% +economically that's also a problem and +proof-of-work I feel like one of the big + + align:start position:0% +proof-of-work I feel like one of the big + + + align:start position:0% +proof-of-work I feel like one of the big +issues with Bitcoin is half the coins + + align:start position:0% +issues with Bitcoin is half the coins + + + align:start position:0% +issues with Bitcoin is half the coins +came out in the first four years we're + + align:start position:0% +came out in the first four years we're + + + align:start position:0% +came out in the first four years we're +like hardly everyone anyone was aware of + + align:start position:0% +like hardly everyone anyone was aware of + + + align:start position:0% +like hardly everyone anyone was aware of +it and that makes people not want to + + align:start position:0% +it and that makes people not want to + + + align:start position:0% +it and that makes people not want to +adopt the system because it's like well + + align:start position:0% +adopt the system because it's like well + + + align:start position:0% +adopt the system because it's like well +wait you guys just got all this coin for + + align:start position:0% +wait you guys just got all this coin for + + + align:start position:0% +wait you guys just got all this coin for +basically free use like running your + + align:start position:0% +basically free use like running your + + + align:start position:0% +basically free use like running your +computer in like 2011 I'm not gonna be + + align:start position:0% +computer in like 2011 I'm not gonna be + + + align:start position:0% +computer in like 2011 I'm not gonna be +part of that system so I sort of feel + + align:start position:0% +part of that system so I sort of feel + + + align:start position:0% +part of that system so I sort of feel +like it would been nicer if it was more + + align:start position:0% +like it would been nicer if it was more + + + align:start position:0% +like it would been nicer if it was more +of an s-curve and less of a log curve + + align:start position:0% +of an s-curve and less of a log curve + + + align:start position:0% +of an s-curve and less of a log curve +because then maybe it would like ramp up + + align:start position:0% +because then maybe it would like ramp up + + + align:start position:0% +because then maybe it would like ramp up +in like 2015 and then lots of points + + align:start position:0% +in like 2015 and then lots of points + + + align:start position:0% +in like 2015 and then lots of points +were coming out but anyway that's so + + align:start position:0% +were coming out but anyway that's so + + + align:start position:0% +were coming out but anyway that's so +like a ripple or stellar sort of an + + align:start position:0% +like a ripple or stellar sort of an + + + align:start position:0% +like a ripple or stellar sort of an +extreme case of that where all the coins + + align:start position:0% +extreme case of that where all the coins + + + align:start position:0% +extreme case of that where all the coins +were initially Kate you know made by one + + align:start position:0% +were initially Kate you know made by one + + + align:start position:0% +were initially Kate you know made by one +entity and so to me I'm like I don't + + align:start position:0% +entity and so to me I'm like I don't + + + align:start position:0% +entity and so to me I'm like I don't +want these like that's that's your money + + align:start position:0% +want these like that's that's your money + + + align:start position:0% +want these like that's that's your money +like you just made it up yourself + + align:start position:0% +like you just made it up yourself + + + align:start position:0% +like you just made it up yourself +there's sort of a like I don't know it + + align:start position:0% +there's sort of a like I don't know it + + + align:start position:0% +there's sort of a like I don't know it +just feels like kids being like I have a + + align:start position:0% +just feels like kids being like I have a + + + align:start position:0% +just feels like kids being like I have a +bazillion dollars and I write a + + align:start position:0% +bazillion dollars and I write a + + + align:start position:0% +bazillion dollars and I write a +bazillion dollars it's like okay well + + align:start position:0% +bazillion dollars it's like okay well + + + align:start position:0% +bazillion dollars it's like okay well +you just wrote that like I don't not + + align:start position:0% +you just wrote that like I don't not + + + align:start position:0% +you just wrote that like I don't not +gonna honor that anyway okay so Bruce + + align:start position:0% +gonna honor that anyway okay so Bruce + + + align:start position:0% +gonna honor that anyway okay so Bruce +take kind of interesting proof of space + + align:start position:0% +take kind of interesting proof of space + + + align:start position:0% +take kind of interesting proof of space +there's a bunch of ideas here some of + + align:start position:0% +there's a bunch of ideas here some of + + + align:start position:0% +there's a bunch of ideas here some of +them space coins basements was some + + align:start position:0% +them space coins basements was some + + + align:start position:0% +them space coins basements was some +people here I know Bram Cohen who is the + + align:start position:0% +people here I know Bram Cohen who is the + + + align:start position:0% +people here I know Bram Cohen who is the +author of BitTorrent right he made + + align:start position:0% +author of BitTorrent right he made + + + align:start position:0% +author of BitTorrent right he made +BitTorrent whatever and + + align:start position:0% + + + + align:start position:0% + +he's now working on some of these kind + + align:start position:0% +he's now working on some of these kind + + + align:start position:0% +he's now working on some of these kind +of things he's working on a proof of + + align:start position:0% +of things he's working on a proof of + + + align:start position:0% +of things he's working on a proof of +space coin called Chia and the idea is + + align:start position:0% +space coin called Chia and the idea is + + + align:start position:0% +space coin called Chia and the idea is +you know it's still similar to proven + + align:start position:0% +you know it's still similar to proven + + + align:start position:0% +you know it's still similar to proven +work but you're using some kind of + + align:start position:0% +work but you're using some kind of + + + align:start position:0% +work but you're using some kind of +memory or storage space rather than your + + align:start position:0% +memory or storage space rather than your + + + align:start position:0% +memory or storage space rather than your +CPU and the idea is the benefit as well + + align:start position:0% +CPU and the idea is the benefit as well + + + align:start position:0% +CPU and the idea is the benefit as well +maybe it doesn't use as much electricity + + align:start position:0% +maybe it doesn't use as much electricity + + + align:start position:0% +maybe it doesn't use as much electricity +and also from talking to Bram with his + + align:start position:0% +and also from talking to Bram with his + + + align:start position:0% +and also from talking to Bram with his +he's saying there's much more sort of + + align:start position:0% +he's saying there's much more sort of + + + align:start position:0% +he's saying there's much more sort of +dead storage space than dead CPU so + + align:start position:0% +dead storage space than dead CPU so + + + align:start position:0% +dead storage space than dead CPU so +every computer has a CPU but like see if + + align:start position:0% +every computer has a CPU but like see if + + + align:start position:0% +every computer has a CPU but like see if +you hear is not that powerful it can't + + align:start position:0% +you hear is not that powerful it can't + + + align:start position:0% +you hear is not that powerful it can't +really compete with Asics but lots of + + align:start position:0% +really compete with Asics but lots of + + + align:start position:0% +really compete with Asics but lots of +people have empty hard drive space and + + align:start position:0% +people have empty hard drive space and + + + align:start position:0% +people have empty hard drive space and +you might have a terabyte of empty hard + + align:start position:0% +you might have a terabyte of empty hard + + + align:start position:0% +you might have a terabyte of empty hard +drive space and you know 1 terabytes as + + align:start position:0% +drive space and you know 1 terabytes as + + + align:start position:0% +drive space and you know 1 terabytes as +good as another + + align:start position:0% +good as another + + + align:start position:0% +good as another +and it's also empty is what you need + + align:start position:0% +and it's also empty is what you need + + + align:start position:0% +and it's also empty is what you need +because you need to fill in space for + + align:start position:0% +because you need to fill in space for + + + align:start position:0% +because you need to fill in space for +these systems and so if you're like well + + align:start position:0% +these systems and so if you're like well + + + align:start position:0% +these systems and so if you're like well +I'm AWS I've got you know tons of hard + + align:start position:0% +I'm AWS I've got you know tons of hard + + + align:start position:0% +I'm AWS I've got you know tons of hard +drives right but people are using them + + align:start position:0% +drives right but people are using them + + + align:start position:0% +drives right but people are using them +so you're not able to then just like + + align:start position:0% +so you're not able to then just like + + + align:start position:0% +so you're not able to then just like +fill it in for these kind of systems + + align:start position:0% +fill it in for these kind of systems + + + align:start position:0% +fill it in for these kind of systems +well to some extent they do have a lot + + align:start position:0% +well to some extent they do have a lot + + + align:start position:0% +well to some extent they do have a lot +of slack and we can probably do but + + align:start position:0% +of slack and we can probably do but + + + align:start position:0% +of slack and we can probably do but +several ideas some are pretty cool so + + align:start position:0% +several ideas some are pretty cool so + + + align:start position:0% +several ideas some are pretty cool so +one example that this is sort of an + + align:start position:0% +one example that this is sort of an + + + align:start position:0% +one example that this is sort of an +example idea it's not fully fleshed out + + align:start position:0% +example idea it's not fully fleshed out + + + align:start position:0% +example idea it's not fully fleshed out +but to give you an idea so you buy a 10 + + align:start position:0% +but to give you an idea so you buy a 10 + + + align:start position:0% +but to give you an idea so you buy a 10 +terabyte drive ok you pre-compute 100 + + align:start position:0% +terabyte drive ok you pre-compute 100 + + + align:start position:0% +terabyte drive ok you pre-compute 100 +billion key pairs and this takes a long + + align:start position:0% +billion key pairs and this takes a long + + + align:start position:0% +billion key pairs and this takes a long +time and this is work right you're doing + + align:start position:0% +time and this is work right you're doing + + + align:start position:0% +time and this is work right you're doing +100 billion computations of coming up + + align:start position:0% +100 billion computations of coming up + + + align:start position:0% +100 billion computations of coming up +with a random private key multiplying by + + align:start position:0% +with a random private key multiplying by + + + align:start position:0% +with a random private key multiplying by +GE getting the pub key and you store it + + align:start position:0% +GE getting the pub key and you store it + + + align:start position:0% +GE getting the pub key and you store it +in a key value store like a database + + align:start position:0% +in a key value store like a database + + + align:start position:0% +in a key value store like a database +level DB or something on your hard drive + + align:start position:0% +level DB or something on your hard drive + + + align:start position:0% +level DB or something on your hard drive +and the key is the bump key and the + + align:start position:0% +and the key is the bump key and the + + + align:start position:0% +and the key is the bump key and the +value is the private key so you remember + + align:start position:0% +value is the private key so you remember + + + align:start position:0% +value is the private key so you remember +your key pairs but you've sorted it in a + + align:start position:0% +your key pairs but you've sorted it in a + + + align:start position:0% +your key pairs but you've sorted it in a +way so that you can quickly go through + + align:start position:0% +way so that you can quickly go through + + + align:start position:0% +way so that you can quickly go through +the pump keys alright so you have like + + align:start position:0% +the pump keys alright so you have like + + + align:start position:0% +the pump keys alright so you have like +logins search time some kind of binary + + align:start position:0% +logins search time some kind of binary + + + align:start position:0% +logins search time some kind of binary +tree whatever it is in your database and + + align:start position:0% +tree whatever it is in your database and + + + align:start position:0% +tree whatever it is in your database and +so then the idea is to create the next + + align:start position:0% +so then the idea is to create the next + + + align:start position:0% +so then the idea is to create the next +block you want the key closest to the + + align:start position:0% +block you want the key closest to the + + + align:start position:0% +block you want the key closest to the +current block hash consign so a valid + + align:start position:0% +current block hash consign so a valid + + + align:start position:0% +current block hash consign so a valid +proof of work you have some threshold + + align:start position:0% +proof of work you have some threshold + + + align:start position:0% +proof of work you have some threshold +maybe a valid proof of work is whoever + + align:start position:0% +maybe a valid proof of work is whoever + + + align:start position:0% +maybe a valid proof of work is whoever +you know whoever's got a key that's very + + align:start position:0% +you know whoever's got a key that's very + + + align:start position:0% +you know whoever's got a key that's very +close to this they're able to sign and + + align:start position:0% +close to this they're able to sign and + + + align:start position:0% +close to this they're able to sign and +those keys do not exist + + align:start position:0% +those keys do not exist + + + align:start position:0% +those keys do not exist +the network prior to the signing + + align:start position:0% +the network prior to the signing + + + align:start position:0% +the network prior to the signing +procedure they exist just hidden on + + align:start position:0% +procedure they exist just hidden on + + + align:start position:0% +procedure they exist just hidden on +people's hard drives and so the idea is + + align:start position:0% +people's hard drives and so the idea is + + + align:start position:0% +people's hard drives and so the idea is +you could just try to keep computing + + align:start position:0% +you could just try to keep computing + + + align:start position:0% +you could just try to keep computing +keys till you find one and then sign + + align:start position:0% +keys till you find one and then sign + + + align:start position:0% +keys till you find one and then sign +with it and that would just make it + + align:start position:0% +with it and that would just make it + + + align:start position:0% +with it and that would just make it +completely proof-of-work + + align:start position:0% +completely proof-of-work + + + align:start position:0% +completely proof-of-work +so it is performed and then you can use + + align:start position:0% +so it is performed and then you can use + + + align:start position:0% +so it is performed and then you can use +that free computed proof of work later + + align:start position:0% +that free computed proof of work later + + + align:start position:0% +that free computed proof of work later +on and possibly multiple times in + + align:start position:0% +on and possibly multiple times in + + + align:start position:0% +on and possibly multiple times in +practice it's not going to be multiple + + align:start position:0% +practice it's not going to be multiple + + + align:start position:0% +practice it's not going to be multiple +times because you've got 100 billion and + + align:start position:0% +times because you've got 100 billion and + + + align:start position:0% +times because you've got 100 billion and +you're never gonna like use the same key + + align:start position:0% +you're never gonna like use the same key + + + align:start position:0% +you're never gonna like use the same key +twice the idea is everyone knows this + + align:start position:0% +twice the idea is everyone knows this + + + align:start position:0% +twice the idea is everyone knows this +right so you have trillions quadrillions + + align:start position:0% +right so you have trillions quadrillions + + + align:start position:0% +right so you have trillions quadrillions +however many keys out there that + + align:start position:0% +however many keys out there that + + + align:start position:0% +however many keys out there that +everyone is generated and every block + + align:start position:0% +everyone is generated and every block + + + align:start position:0% +everyone is generated and every block +that comes out someone will say ah I've + + align:start position:0% +that comes out someone will say ah I've + + + align:start position:0% +that comes out someone will say ah I've +I you know was lucky and I made a key + + align:start position:0% +I you know was lucky and I made a key + + + align:start position:0% +I you know was lucky and I made a key +that can now sign the next block + + align:start position:0% +that can now sign the next block + + + align:start position:0% +that can now sign the next block +so it's work but it's amortized over + + align:start position:0% +so it's work but it's amortized over + + + align:start position:0% +so it's work but it's amortized over +weeks months years and it's basically + + align:start position:0% +weeks months years and it's basically + + + align:start position:0% +weeks months years and it's basically +how fast you know how big is your + + align:start position:0% +how fast you know how big is your + + + align:start position:0% +how fast you know how big is your +storage if you have a lot of storage you + + align:start position:0% +storage if you have a lot of storage you + + + align:start position:0% +storage if you have a lot of storage you +can pre-compute a lot of this stuff and + + align:start position:0% +can pre-compute a lot of this stuff and + + + align:start position:0% +can pre-compute a lot of this stuff and +then use it so it's kind of a cool + + align:start position:0% +then use it so it's kind of a cool + + + align:start position:0% +then use it so it's kind of a cool +system we'll see there's sort of other + + align:start position:0% +system we'll see there's sort of other + + + align:start position:0% +system we'll see there's sort of other +asterisks is that it actually gets a + + align:start position:0% +asterisks is that it actually gets a + + + align:start position:0% +asterisks is that it actually gets a +little more a little more complex + + align:start position:0% +little more a little more complex + + + align:start position:0% +little more a little more complex +because you need some timing mechanisms + + align:start position:0% +because you need some timing mechanisms + + + align:start position:0% +because you need some timing mechanisms +as well but I think it's it's a cool + + align:start position:0% +as well but I think it's it's a cool + + + align:start position:0% +as well but I think it's it's a cool +idea + + align:start position:0% + + + + align:start position:0% + +hard drives then maybe get more + + align:start position:0% +hard drives then maybe get more + + + align:start position:0% +hard drives then maybe get more +expensive instead of graphics cards + + align:start position:0% +expensive instead of graphics cards + + + align:start position:0% +expensive instead of graphics cards +getting more expensive I don't know but + + align:start position:0% +getting more expensive I don't know but + + + align:start position:0% +getting more expensive I don't know but +the idea is like yeah you use the work + + align:start position:0% +the idea is like yeah you use the work + + + align:start position:0% +the idea is like yeah you use the work +but later on so any questions about that + + align:start position:0% +but later on so any questions about that + + + align:start position:0% +but later on so any questions about that +one cool there's there's a spaceman it's + + align:start position:0% +one cool there's there's a spaceman it's + + + align:start position:0% +one cool there's there's a spaceman it's +a cool paper about how to do this + + align:start position:0% +a cool paper about how to do this + + + align:start position:0% +a cool paper about how to do this +cryptographically and then she is + + align:start position:0% +cryptographically and then she is + + + align:start position:0% +cryptographically and then she is +another one doing this kind of idea I + + align:start position:0% +another one doing this kind of idea I + + + align:start position:0% +another one doing this kind of idea I +sort of like it because it doesn't + + align:start position:0% +sort of like it because it doesn't + + + align:start position:0% +sort of like it because it doesn't +really change the assumptions of proof + + align:start position:0% +really change the assumptions of proof + + + align:start position:0% +really change the assumptions of proof +of work right it's it is still a form of + + align:start position:0% +of work right it's it is still a form of + + + align:start position:0% +of work right it's it is still a form of +proof of work but instead of burning + + align:start position:0% +proof of work but instead of burning + + + align:start position:0% +proof of work but instead of burning +electricity you're using hard drives you + + align:start position:0% +electricity you're using hard drives you + + + align:start position:0% +electricity you're using hard drives you +sort of already have that right like + + align:start position:0% +sort of already have that right like + + + align:start position:0% +sort of already have that right like +there's server farms where they're just + + align:start position:0% +there's server farms where they're just + + + align:start position:0% +there's server farms where they're just +storage farms and they just have tons of + + align:start position:0% +storage farms and they just have tons of + + + align:start position:0% +storage farms and they just have tons of +hard drives so that's already a thing + + align:start position:0% + + + + align:start position:0% + +I guess I guess the idea is the economy + + align:start position:0% +I guess I guess the idea is the economy + + + align:start position:0% +I guess I guess the idea is the economy +the the economies of scale are not quite + + align:start position:0% +the the economies of scale are not quite + + + align:start position:0% +the the economies of scale are not quite +as bad in that hard drives are already + + align:start position:0% +as bad in that hard drives are already + + + align:start position:0% +as bad in that hard drives are already +basically optimal at doing this and if + + align:start position:0% +basically optimal at doing this and if + + + align:start position:0% +basically optimal at doing this and if +you can make a system that's better at + + align:start position:0% +you can make a system that's better at + + + align:start position:0% +you can make a system that's better at +doing this you've just made a better + + align:start position:0% +doing this you've just made a better + + + align:start position:0% +doing this you've just made a better +hard drive which hey great you made a + + align:start position:0% +hard drive which hey great you made a + + + align:start position:0% +hard drive which hey great you made a +better hard drive everyone can use it + + align:start position:0% +better hard drive everyone can use it + + + align:start position:0% +better hard drive everyone can use it +so I guess the idea is it's not as + + align:start position:0% +so I guess the idea is it's not as + + + align:start position:0% +so I guess the idea is it's not as +specific cuz it's just hey store a bunch + + align:start position:0% +specific cuz it's just hey store a bunch + + + align:start position:0% +specific cuz it's just hey store a bunch +of data and then see quickly through it + + align:start position:0% +of data and then see quickly through it + + + align:start position:0% +of data and then see quickly through it +so okay once you generate this you okay + + align:start position:0% +so okay once you generate this you okay + + + align:start position:0% +so okay once you generate this you okay +generating this is compute pop right you + + align:start position:0% +generating this is compute pop right you + + + align:start position:0% +generating this is compute pop right you +need to populate your tent area bright + + align:start position:0% +need to populate your tent area bright + + + align:start position:0% +need to populate your tent area bright +right but that might only take a few + + align:start position:0% +right but that might only take a few + + + align:start position:0% +right but that might only take a few +hours right to make a hundred billion + + align:start position:0% +hours right to make a hundred billion + + + align:start position:0% +hours right to make a hundred billion +key pairs guessing less than a day right + + align:start position:0% +key pairs guessing less than a day right + + + align:start position:0% +key pairs guessing less than a day right +yeah and so and you can do that in + + align:start position:0% +yeah and so and you can do that in + + + align:start position:0% +yeah and so and you can do that in +parallel so you make it and then once + + align:start position:0% +parallel so you make it and then once + + + align:start position:0% +parallel so you make it and then once +you've made it you leave it there and + + align:start position:0% +you've made it you leave it there and + + + align:start position:0% +you've made it you leave it there and +then you're gonna be able to mine with + + align:start position:0% +then you're gonna be able to mine with + + + align:start position:0% +then you're gonna be able to mine with +that forever something you're gonna I + + align:start position:0% +that forever something you're gonna I + + + align:start position:0% +that forever something you're gonna I +think the the hard drive cost is much + + align:start position:0% +think the the hard drive cost is much + + + align:start position:0% +think the the hard drive cost is much +higher than the cost to fill it right + + align:start position:0% +higher than the cost to fill it right + + + align:start position:0% +higher than the cost to fill it right +because a 10 terabyte hard drives gonna + + align:start position:0% +because a 10 terabyte hard drives gonna + + + align:start position:0% +because a 10 terabyte hard drives gonna +be like 200 bucks but you and you can + + align:start position:0% +be like 200 bucks but you and you can + + + align:start position:0% +be like 200 bucks but you and you can +fill with it with a cheap CPU you can + + align:start position:0% +fill with it with a cheap CPU you can + + + align:start position:0% +fill with it with a cheap CPU you can +fill a 10 carbohydrate I have 10 + + align:start position:0% +fill a 10 carbohydrate I have 10 + + + align:start position:0% +fill a 10 carbohydrate I have 10 +terabyte hard drive every few hours so I + + align:start position:0% +terabyte hard drive every few hours so I + + + align:start position:0% +terabyte hard drive every few hours so I +think that like so yeah the the CPU is a + + align:start position:0% +think that like so yeah the the CPU is a + + + align:start position:0% +think that like so yeah the the CPU is a +is a factor but I think it's gonna be + + align:start position:0% +is a factor but I think it's gonna be + + + align:start position:0% +is a factor but I think it's gonna be +smaller than + + align:start position:0% + + + + align:start position:0% + +yeah this is just a seek right + + align:start position:0% +yeah this is just a seek right + + + align:start position:0% +yeah this is just a seek right +and this any even a crummy hard drive + + align:start position:0% +and this any even a crummy hard drive + + + align:start position:0% +and this any even a crummy hard drive +you just read through your binary + + align:start position:0% +you just read through your binary + + + align:start position:0% +you just read through your binary +trainer like Oh found it so you look at + + align:start position:0% +trainer like Oh found it so you look at + + + align:start position:0% +trainer like Oh found it so you look at +okay here's the current block - what do + + align:start position:0% +okay here's the current block - what do + + + align:start position:0% +okay here's the current block - what do +I have that's close + + align:start position:0% +I have that's close + + + align:start position:0% +I have that's close +seek - that on my drive nope not gonna + + align:start position:0% +seek - that on my drive nope not gonna + + + align:start position:0% +seek - that on my drive nope not gonna +win this one okay let someone else do it + + align:start position:0% +win this one okay let someone else do it + + + align:start position:0% +win this one okay let someone else do it +or you know you see can you find it hey + + align:start position:0% +or you know you see can you find it hey + + + align:start position:0% +or you know you see can you find it hey +cool I can find yeah so there so that's + + align:start position:0% +cool I can find yeah so there so that's + + + align:start position:0% +cool I can find yeah so there so that's +in Chia they sort of add this time + + align:start position:0% +in Chia they sort of add this time + + + align:start position:0% +in Chia they sort of add this time +component which I'm not 100% clear on + + align:start position:0% +component which I'm not 100% clear on + + + align:start position:0% +component which I'm not 100% clear on +how it works it's changed a little bit + + align:start position:0% +how it works it's changed a little bit + + + align:start position:0% +how it works it's changed a little bit +but you want so the the idea of a time + + align:start position:0% +but you want so the the idea of a time + + + align:start position:0% +but you want so the the idea of a time +beacon is you want some function that + + align:start position:0% +beacon is you want some function that + + + align:start position:0% +beacon is you want some function that +cannot be parallelized so that if you + + align:start position:0% +cannot be parallelized so that if you + + + align:start position:0% +cannot be parallelized so that if you +have 100 computers doing it it's not + + align:start position:0% +have 100 computers doing it it's not + + + align:start position:0% +have 100 computers doing it it's not +going to be any faster than one computer + + align:start position:0% +going to be any faster than one computer + + + align:start position:0% +going to be any faster than one computer +doing it so basically whoever's got the + + align:start position:0% +doing it so basically whoever's got the + + + align:start position:0% +doing it so basically whoever's got the +fastest single CPU will always win this + + align:start position:0% +fastest single CPU will always win this + + + align:start position:0% +fastest single CPU will always win this +and that can be sort of a time beacon + + align:start position:0% +and that can be sort of a time beacon + + + align:start position:0% +and that can be sort of a time beacon +for these space things + + align:start position:0% + + + + align:start position:0% + +I mean if you have like tons of hard + + align:start position:0% +I mean if you have like tons of hard + + + align:start position:0% +I mean if you have like tons of hard +drives and you want it like you know + + align:start position:0% +drives and you want it like you know + + + align:start position:0% +drives and you want it like you know +tons of key values and you just want to + + align:start position:0% +tons of key values and you just want to + + + align:start position:0% +tons of key values and you just want to +find one or find the closest match like + + align:start position:0% +find one or find the closest match like + + + align:start position:0% +find one or find the closest match like +you can do that in log n time even over + + align:start position:0% +you can do that in log n time even over + + + align:start position:0% +you can do that in log n time even over +a whole data center like you know Google + + align:start position:0% +a whole data center like you know Google + + + align:start position:0% +a whole data center like you know Google +like you just search and it's like hey + + align:start position:0% +like you just search and it's like hey + + + align:start position:0% +like you just search and it's like hey +it comes up in like a fraction of a + + align:start position:0% +it comes up in like a fraction of a + + + align:start position:0% +it comes up in like a fraction of a +second so that's that's doable it's you + + align:start position:0% +second so that's that's doable it's you + + + align:start position:0% +second so that's that's doable it's you +know you need so you need good software + + align:start position:0% +know you need so you need good software + + + align:start position:0% +know you need so you need good software +and you need like a good infrastructure + + align:start position:0% +and you need like a good infrastructure + + + align:start position:0% +and you need like a good infrastructure +to do it but I think it's doable + + align:start position:0% +to do it but I think it's doable + + + align:start position:0% +to do it but I think it's doable +it scales pretty well I think but yeah + + align:start position:0% +it scales pretty well I think but yeah + + + align:start position:0% +it scales pretty well I think but yeah +it has the same issues where like you + + align:start position:0% +it has the same issues where like you + + + align:start position:0% +it has the same issues where like you +just end up with people buying a whole + + align:start position:0% +just end up with people buying a whole + + + align:start position:0% +just end up with people buying a whole +bunch of hard drives and like what are + + align:start position:0% +bunch of hard drives and like what are + + + align:start position:0% +bunch of hard drives and like what are +the economies of scale there there's + + align:start position:0% +the economies of scale there there's + + + align:start position:0% +the economies of scale there there's +arguments that it might be better than + + align:start position:0% +arguments that it might be better than + + + align:start position:0% +arguments that it might be better than +the economies of scale with like Asics + + align:start position:0% +the economies of scale with like Asics + + + align:start position:0% +the economies of scale with like Asics +that we've heard about on Monday maybe + + align:start position:0% +that we've heard about on Monday maybe + + + align:start position:0% +that we've heard about on Monday maybe +not I don't know most will see if this + + align:start position:0% +not I don't know most will see if this + + + align:start position:0% +not I don't know most will see if this +takes off I don't it's like fairly new + + align:start position:0% +takes off I don't it's like fairly new + + + align:start position:0% +takes off I don't it's like fairly new +it's it's an idea that's been talked + + align:start position:0% +it's it's an idea that's been talked + + + align:start position:0% +it's it's an idea that's been talked +about for a few years but + + align:start position:0% + + + + align:start position:0% + +okay well so there's there's different + + align:start position:0% +okay well so there's there's different + + + align:start position:0% +okay well so there's there's different +it seems like it it seems like one of + + align:start position:0% +it seems like it it seems like one of + + + align:start position:0% +it seems like it it seems like one of +the more interesting sort of there's + + align:start position:0% +the more interesting sort of there's + + + align:start position:0% +the more interesting sort of there's +school math and cool crypto involved + + align:start position:0% +school math and cool crypto involved + + + align:start position:0% +school math and cool crypto involved +okay so work but amortized so perennial + + align:start position:0% +okay so work but amortized so perennial + + + align:start position:0% +okay so work but amortized so perennial +MIT favorite iota they use a just + + align:start position:0% +MIT favorite iota they use a just + + + align:start position:0% +MIT favorite iota they use a just +directed acyclic graph and now a chain + + align:start position:0% +directed acyclic graph and now a chain + + + align:start position:0% +directed acyclic graph and now a chain +is also a - you know dag because it's + + align:start position:0% +is also a - you know dag because it's + + + align:start position:0% +is also a - you know dag because it's +directed there's no cycles and it's a + + align:start position:0% +directed there's no cycles and it's a + + + align:start position:0% +directed there's no cycles and it's a +graph but it's a pretty simple one but + + align:start position:0% +graph but it's a pretty simple one but + + + align:start position:0% +graph but it's a pretty simple one but +the idea is have multiple multiple + + align:start position:0% +the idea is have multiple multiple + + + align:start position:0% +the idea is have multiple multiple +parents right so if you have a block + + align:start position:0% +parents right so if you have a block + + + align:start position:0% +parents right so if you have a block +instead of just pointing to one you + + align:start position:0% +instead of just pointing to one you + + + align:start position:0% +instead of just pointing to one you +could say well now this can happen in + + align:start position:0% +could say well now this can happen in + + + align:start position:0% +could say well now this can happen in +Bitcoin right well you've got two blocks + + align:start position:0% +Bitcoin right well you've got two blocks + + + align:start position:0% +Bitcoin right well you've got two blocks +postponing the same thing but this + + align:start position:0% +postponing the same thing but this + + + align:start position:0% +postponing the same thing but this +cannot happen in big where are you + + align:start position:0% +cannot happen in big where are you + + + align:start position:0% +cannot happen in big where are you +saying oh I'm coming off and I'm + + align:start position:0% +saying oh I'm coming off and I'm + + + align:start position:0% +saying oh I'm coming off and I'm +referring to both of these but in a + + align:start position:0% +referring to both of these but in a + + + align:start position:0% +referring to both of these but in a +directed acyclic graph you can do that + + align:start position:0% +directed acyclic graph you can do that + + + align:start position:0% +directed acyclic graph you can do that +so if p.m. actually does this I think + + align:start position:0% +so if p.m. actually does this I think + + + align:start position:0% +so if p.m. actually does this I think +Joe Joe when I was mentioning that and + + align:start position:0% +Joe Joe when I was mentioning that and + + + align:start position:0% +Joe Joe when I was mentioning that and +so what happens is you sort of endorse + + align:start position:0% +so what happens is you sort of endorse + + + align:start position:0% +so what happens is you sort of endorse +one as the correct one and one is the + + align:start position:0% +one as the correct one and one is the + + + align:start position:0% +one as the correct one and one is the +uncle so you're saying no this is the + + align:start position:0% +uncle so you're saying no this is the + + + align:start position:0% +uncle so you're saying no this is the +real one but I also saw this one and + + align:start position:0% +real one but I also saw this one and + + + align:start position:0% +real one but I also saw this one and +give this one a little bit of money + + align:start position:0% +give this one a little bit of money + + + align:start position:0% +give this one a little bit of money +right maybe not the whole reward they + + align:start position:0% +right maybe not the whole reward they + + + align:start position:0% +right maybe not the whole reward they +were hoping for but they get something + + align:start position:0% +were hoping for but they get something + + + align:start position:0% +were hoping for but they get something +and so then something like iota says + + align:start position:0% +and so then something like iota says + + + align:start position:0% +and so then something like iota says +okay we have lots and every node points + + align:start position:0% +okay we have lots and every node points + + + align:start position:0% +okay we have lots and every node points +to two previous and so you get this + + align:start position:0% +to two previous and so you get this + + + align:start position:0% +to two previous and so you get this +whole map they can even point to + + align:start position:0% +whole map they can even point to + + + align:start position:0% +whole map they can even point to +different heights so I can point to here + + align:start position:0% +different heights so I can point to here + + + align:start position:0% +different heights so I can point to here +and here I don't really know why you do + + align:start position:0% +and here I don't really know why you do + + + align:start position:0% +and here I don't really know why you do +this I guess so there's some ways it can + + align:start position:0% +this I guess so there's some ways it can + + + align:start position:0% +this I guess so there's some ways it can +reduce latency right so one of the + + align:start position:0% +reduce latency right so one of the + + + align:start position:0% +reduce latency right so one of the +trade-offs in bitcoin is 10 minute block + + align:start position:0% +trade-offs in bitcoin is 10 minute block + + + align:start position:0% +trade-offs in bitcoin is 10 minute block +time seems fairly arbitrary it's kind of + + align:start position:0% +time seems fairly arbitrary it's kind of + + + align:start position:0% +time seems fairly arbitrary it's kind of +slow latency people don't like late in + + align:start position:0% +slow latency people don't like late in + + + align:start position:0% +slow latency people don't like late in +these latency because they have to wait + + align:start position:0% +these latency because they have to wait + + + align:start position:0% +these latency because they have to wait +fine the more important metric I think + + align:start position:0% +fine the more important metric I think + + + align:start position:0% +fine the more important metric I think +is that it leads to minor centralization + + align:start position:0% +is that it leads to minor centralization + + + align:start position:0% +is that it leads to minor centralization +and minor pools because if there's only + + align:start position:0% +and minor pools because if there's only + + + align:start position:0% +and minor pools because if there's only +one hundred forty four blocks a day + + align:start position:0% +one hundred forty four blocks a day + + + align:start position:0% +one hundred forty four blocks a day +which like in Bitcoin if you have a + + align:start position:0% +which like in Bitcoin if you have a + + + align:start position:0% +which like in Bitcoin if you have a +million of the hash power of the network + + align:start position:0% +million of the hash power of the network + + + align:start position:0% +million of the hash power of the network +you're just never going to find anything + + align:start position:0% +you're just never going to find anything + + + align:start position:0% +you're just never going to find anything +right if you're just mining on your own + + align:start position:0% +right if you're just mining on your own + + + align:start position:0% +right if you're just mining on your own +over the course of a year you're + + align:start position:0% +over the course of a year you're + + + align:start position:0% +over the course of a year you're +probably not going to find a single + + align:start position:0% +probably not going to find a single + + + align:start position:0% +probably not going to find a single +block and you'll avoid all of that + + align:start position:0% +block and you'll avoid all of that + + + align:start position:0% +block and you'll avoid all of that +effort so instead you join a pool and + + align:start position:0% +effort so instead you join a pool and + + + align:start position:0% +effort so instead you join a pool and +try to you know pool with other people + + align:start position:0% +try to you know pool with other people + + + align:start position:0% +try to you know pool with other people +to distribute those rewards however if + + align:start position:0% +to distribute those rewards however if + + + align:start position:0% +to distribute those rewards however if +there's like an aetherium block every 15 + + align:start position:0% +there's like an aetherium block every 15 + + + align:start position:0% +there's like an aetherium block every 15 +seconds and there's you know millions of + + align:start position:0% +seconds and there's you know millions of + + + align:start position:0% +seconds and there's you know millions of +blocks that come out if you have a + + align:start position:0% +blocks that come out if you have a + + + align:start position:0% +blocks that come out if you have a +millionth of the hash power you might + + align:start position:0% +millionth of the hash power you might + + + align:start position:0% +millionth of the hash power you might +find a block the blocks have smaller + + align:start position:0% +find a block the blocks have smaller + + + align:start position:0% +find a block the blocks have smaller +rewards but it's like you know chopping + + align:start position:0% +rewards but it's like you know chopping + + + align:start position:0% +rewards but it's like you know chopping +it up more finally is a nice way to do + + align:start position:0% +it up more finally is a nice way to do + + + align:start position:0% +it up more finally is a nice way to do +it so like pee to pool which you work on + + align:start position:0% +it so like pee to pool which you work on + + + align:start position:0% +it so like pee to pool which you work on +it's a sort of way to try to make that + + align:start position:0% +it's a sort of way to try to make that + + + align:start position:0% +it's a sort of way to try to make that +and it's important to get it more + + align:start position:0% +and it's important to get it more + + + align:start position:0% +and it's important to get it more +decentralized but it's hard yeah yeah + + align:start position:0% +decentralized but it's hard yeah yeah + + + align:start position:0% +decentralized but it's hard yeah yeah +yeah pee to pool sort of does this and + + align:start position:0% +yeah pee to pool sort of does this and + + + align:start position:0% +yeah pee to pool sort of does this and +as a layer on top so it could help Lane + + align:start position:0% +as a layer on top so it could help Lane + + + align:start position:0% +as a layer on top so it could help Lane +see and then it could help reduce the + + align:start position:0% +see and then it could help reduce the + + + align:start position:0% +see and then it could help reduce the +amount of orphans in the blocks in the + + align:start position:0% +amount of orphans in the blocks in the + + + align:start position:0% +amount of orphans in the blocks in the +block chain which then helps minor + + align:start position:0% +block chain which then helps minor + + + align:start position:0% +block chain which then helps minor +centralization so that does it is there + + align:start position:0% +centralization so that does it is there + + + align:start position:0% +centralization so that does it is there +are interesting ideas for it but it + + align:start position:0% +are interesting ideas for it but it + + + align:start position:0% +are interesting ideas for it but it +doesn't help scalability at all right it + + align:start position:0% +doesn't help scalability at all right it + + + align:start position:0% +doesn't help scalability at all right it +actually hurts scalability because now I + + align:start position:0% +actually hurts scalability because now I + + + align:start position:0% +actually hurts scalability because now I +have to keep track of all these things + + align:start position:0% +have to keep track of all these things + + + align:start position:0% +have to keep track of all these things +instead of just one chain and I'm gonna + + align:start position:0% +instead of just one chain and I'm gonna + + + align:start position:0% +instead of just one chain and I'm gonna +have to keep track of all the data + + align:start position:0% +have to keep track of all the data + + + align:start position:0% +have to keep track of all the data +anyway if I've got the UT Exocet I can't + + align:start position:0% +anyway if I've got the UT Exocet I can't + + + align:start position:0% +anyway if I've got the UT Exocet I can't +just ignore parts of it so doesn't help + + align:start position:0% +just ignore parts of it so doesn't help + + + align:start position:0% +just ignore parts of it so doesn't help +fail ability at all and in the case of + + align:start position:0% +fail ability at all and in the case of + + + align:start position:0% +fail ability at all and in the case of +iota their custom ternary hash functions + + align:start position:0% +iota their custom ternary hash functions + + + align:start position:0% +iota their custom ternary hash functions +also don't help much either so that was + + align:start position:0% +also don't help much either so that was + + + align:start position:0% +also don't help much either so that was +what we wrote about last year they made + + align:start position:0% +what we wrote about last year they made + + + align:start position:0% +what we wrote about last year they made +all their own weird stuff so there there + + align:start position:0% +all their own weird stuff so there there + + + align:start position:0% +all their own weird stuff so there there +are interesting ideas between directed + + align:start position:0% +are interesting ideas between directed + + + align:start position:0% +are interesting ideas between directed +acyclic graphs but it feels like when + + align:start position:0% +acyclic graphs but it feels like when + + + align:start position:0% +acyclic graphs but it feels like when +they when they say hey this is more + + align:start position:0% +they when they say hey this is more + + + align:start position:0% +they when they say hey this is more +scalable I get very suspicious because + + align:start position:0% +scalable I get very suspicious because + + + align:start position:0% +scalable I get very suspicious because +like it doesn't seem to help scalability + + align:start position:0% +like it doesn't seem to help scalability + + + align:start position:0% +like it doesn't seem to help scalability +it does possibly help some other things + + align:start position:0% + + + + align:start position:0% + +so also in the case in iota the idea is + + align:start position:0% +so also in the case in iota the idea is + + + align:start position:0% +so also in the case in iota the idea is +well they don't call it this but it's + + align:start position:0% +well they don't call it this but it's + + + align:start position:0% +well they don't call it this but it's +it's the equivalent of saying every + + align:start position:0% +it's the equivalent of saying every + + + align:start position:0% +it's the equivalent of saying every +block must have one and only one + + align:start position:0% +block must have one and only one + + + align:start position:0% +block must have one and only one +transaction the transactions themselves + + align:start position:0% +transaction the transactions themselves + + + align:start position:0% +transaction the transactions themselves +have proof work on them + + align:start position:0% +have proof work on them + + + align:start position:0% +have proof work on them +and they point to each other which + + align:start position:0% +and they point to each other which + + + align:start position:0% +and they point to each other which +basically is the same as you know blocks + + align:start position:0% +basically is the same as you know blocks + + + align:start position:0% +basically is the same as you know blocks +have one transaction and you do the work + + align:start position:0% +have one transaction and you do the work + + + align:start position:0% +have one transaction and you do the work +yourself instead of paying a miner to do + + align:start position:0% +yourself instead of paying a miner to do + + + align:start position:0% +yourself instead of paying a miner to do +it I think that's not a great deal and + + align:start position:0% +it I think that's not a great deal and + + + align:start position:0% +it I think that's not a great deal and +they say that that means there's no fees + + align:start position:0% +they say that that means there's no fees + + + align:start position:0% +they say that that means there's no fees +I think it's kind of there's still fees + + align:start position:0% +I think it's kind of there's still fees + + + align:start position:0% +I think it's kind of there's still fees +because you're just doing the work + + align:start position:0% +because you're just doing the work + + + align:start position:0% +because you're just doing the work +yourself + + align:start position:0% +yourself + + + align:start position:0% +yourself +I think that's equivalent to saying + + align:start position:0% +I think that's equivalent to saying + + + align:start position:0% +I think that's equivalent to saying +there is a refrigerator at Home Depot + + align:start position:0% +there is a refrigerator at Home Depot + + + align:start position:0% +there is a refrigerator at Home Depot +that doesn't use electricity so hey it's + + align:start position:0% +that doesn't use electricity so hey it's + + + align:start position:0% +that doesn't use electricity so hey it's +electricity free but there's a crank on + + align:start position:0% +electricity free but there's a crank on + + + align:start position:0% +electricity free but there's a crank on +the back and you have to crank it to + + align:start position:0% +the back and you have to crank it to + + + align:start position:0% +the back and you have to crank it to +make the refrigerator cold yeah you + + align:start position:0% +make the refrigerator cold yeah you + + + align:start position:0% +make the refrigerator cold yeah you +could make a refrigerator that way I + + align:start position:0% +could make a refrigerator that way I + + + align:start position:0% +could make a refrigerator that way I +don't think people would want it you're + + align:start position:0% +don't think people would want it you're + + + align:start position:0% +don't think people would want it you're +still doing the work you just have to + + align:start position:0% +still doing the work you just have to + + + align:start position:0% +still doing the work you just have to +crank it instead of plugging it in so + + align:start position:0% +crank it instead of plugging it in so + + + align:start position:0% +crank it instead of plugging it in so +the idea of like you don't have to pay + + align:start position:0% +the idea of like you don't have to pay + + + align:start position:0% +the idea of like you don't have to pay +miners a fee to get into a block cuz you + + align:start position:0% +miners a fee to get into a block cuz you + + + align:start position:0% +miners a fee to get into a block cuz you +just mind the block yourself or in this + + align:start position:0% +just mind the block yourself or in this + + + align:start position:0% +just mind the block yourself or in this +case you mind the transaction yourself + + align:start position:0% +case you mind the transaction yourself + + + align:start position:0% +case you mind the transaction yourself +doesn't see my usable anyway so I Otis + + align:start position:0% +doesn't see my usable anyway so I Otis + + + align:start position:0% +doesn't see my usable anyway so I Otis +fun there we've talked about them a + + align:start position:0% +fun there we've talked about them a + + + align:start position:0% +fun there we've talked about them a +while ago okay last one that's fun a + + align:start position:0% +while ago okay last one that's fun a + + + align:start position:0% +while ago okay last one that's fun a +group of idle an old idea that I wrote + + align:start position:0% +group of idle an old idea that I wrote + + + align:start position:0% +group of idle an old idea that I wrote +up four years ago almost it probably + + align:start position:0% +up four years ago almost it probably + + + align:start position:0% +up four years ago almost it probably +doesn't actually work that well but a + + align:start position:0% +doesn't actually work that well but a + + + align:start position:0% +doesn't actually work that well but a +lot of these things don't work that even + + align:start position:0% +lot of these things don't work that even + + + align:start position:0% +lot of these things don't work that even +if it works it would just move the Cox + + align:start position:0% +if it works it would just move the Cox + + + align:start position:0% +if it works it would just move the Cox +from up x2 capex but what you do is you + + align:start position:0% +from up x2 capex but what you do is you + + + align:start position:0% +from up x2 capex but what you do is you +prove that you're not mining and you get + + align:start position:0% +prove that you're not mining and you get + + + align:start position:0% +prove that you're not mining and you get +paid and the other fun thing about this + + align:start position:0% +paid and the other fun thing about this + + + align:start position:0% +paid and the other fun thing about this +is it sort of led to some of the ideas + + align:start position:0% +is it sort of led to some of the ideas + + + align:start position:0% +is it sort of led to some of the ideas +in Lightning Network so the idea is in + + align:start position:0% +in Lightning Network so the idea is in + + + align:start position:0% +in Lightning Network so the idea is in +Bitcoin the difficulty adjusts so the + + align:start position:0% +Bitcoin the difficulty adjusts so the + + + align:start position:0% +Bitcoin the difficulty adjusts so the +blocks come out every ten minutes right + + align:start position:0% +blocks come out every ten minutes right + + + align:start position:0% +blocks come out every ten minutes right +every two thousand sixteen blocks you + + align:start position:0% +every two thousand sixteen blocks you + + + align:start position:0% +every two thousand sixteen blocks you +look at the timestamps adjust the + + align:start position:0% +look at the timestamps adjust the + + + align:start position:0% +look at the timestamps adjust the +difficulty so new miners coming in make + + align:start position:0% +difficulty so new miners coming in make + + + align:start position:0% +difficulty so new miners coming in make +it harder for the existing miners so if + + align:start position:0% +it harder for the existing miners so if + + + align:start position:0% +it harder for the existing miners so if +you're a miner you really don't want + + align:start position:0% +you're a miner you really don't want + + + align:start position:0% +you're a miner you really don't want +anyone else to start joining this + + align:start position:0% +anyone else to start joining this + + + align:start position:0% +anyone else to start joining this +network in mining you really like it as + + align:start position:0% +network in mining you really like it as + + + align:start position:0% +network in mining you really like it as +it is so if you you have the first Asics + + align:start position:0% +it is so if you you have the first Asics + + + align:start position:0% +it is so if you you have the first Asics +you're good + + align:start position:0% +you're good + + + align:start position:0% +you're good +and you don't want everyone to come in + + align:start position:0% +and you don't want everyone to come in + + + align:start position:0% +and you don't want everyone to come in +and this is why so many people by mining + + align:start position:0% +and this is why so many people by mining + + + align:start position:0% +and this is why so many people by mining +equipment and lose money because they + + align:start position:0% +equipment and lose money because they + + + align:start position:0% +equipment and lose money because they +look at the current difficulty and they + + align:start position:0% +look at the current difficulty and they + + + align:start position:0% +look at the current difficulty and they +say hey here's this device here's how + + align:start position:0% +say hey here's this device here's how + + + align:start position:0% +say hey here's this device here's how +much electricity uses how many coins it + + align:start position:0% +much electricity uses how many coins it + + + align:start position:0% +much electricity uses how many coins it +generates this is profitable I'm gonna + + align:start position:0% +generates this is profitable I'm gonna + + + align:start position:0% +generates this is profitable I'm gonna +buy this thing and what they don't + + align:start position:0% +buy this thing and what they don't + + + align:start position:0% +buy this thing and what they don't +realize this is by the time they + + align:start position:0% +realize this is by the time they + + + align:start position:0% +realize this is by the time they +actually get it or maybe a few weeks + + align:start position:0% +actually get it or maybe a few weeks + + + align:start position:0% +actually get it or maybe a few weeks +later the difficulty is like doubled and + + align:start position:0% +later the difficulty is like doubled and + + + align:start position:0% +later the difficulty is like doubled and +now it's making half as many coins for + + align:start position:0% +now it's making half as many coins for + + + align:start position:0% +now it's making half as many coins for +the exact same amount electricity so + + align:start position:0% +the exact same amount electricity so + + + align:start position:0% +the exact same amount electricity so +yeah and that's a fairly unique property + + align:start position:0% +yeah and that's a fairly unique property + + + align:start position:0% +yeah and that's a fairly unique property +of Bitcoin that's not the case and say + + align:start position:0% +of Bitcoin that's not the case and say + + + align:start position:0% +of Bitcoin that's not the case and say +gold mining or other extractive + + align:start position:0% +gold mining or other extractive + + + align:start position:0% +gold mining or other extractive +industries there's some kind of curve in + + align:start position:0% +industries there's some kind of curve in + + + align:start position:0% +industries there's some kind of curve in +in gold mining where if you pay twice as + + align:start position:0% +in gold mining where if you pay twice as + + + align:start position:0% +in gold mining where if you pay twice as +much money to like have twice as many + + align:start position:0% +much money to like have twice as many + + + align:start position:0% +much money to like have twice as many +people dig holes and mine gold you won't + + align:start position:0% +people dig holes and mine gold you won't + + + align:start position:0% +people dig holes and mine gold you won't +get twice as much gold maybe you only + + align:start position:0% +get twice as much gold maybe you only + + + align:start position:0% +get twice as much gold maybe you only +get 10% more gold but you will get some + + align:start position:0% +get 10% more gold but you will get some + + + align:start position:0% +get 10% more gold but you will get some +more right and if you you know drill for + + align:start position:0% +more right and if you you know drill for + + + align:start position:0% +more right and if you you know drill for +oil + + align:start position:0% +oil + + + align:start position:0% +oil +you pay twice as much you'll get some + + align:start position:0% +you pay twice as much you'll get some + + + align:start position:0% +you pay twice as much you'll get some +more but yeah in Bitcoin two times the + + align:start position:0% +more but yeah in Bitcoin two times the + + + align:start position:0% +more but yeah in Bitcoin two times the +mining leads to 1x the coins mind right + + align:start position:0% +mining leads to 1x the coins mind right + + + align:start position:0% +mining leads to 1x the coins mind right +there is zero marginal product product + + align:start position:0% +there is zero marginal product product + + + align:start position:0% +there is zero marginal product product +of labor in this system which is weird + + align:start position:0% +of labor in this system which is weird + + + align:start position:0% +of labor in this system which is weird +and counterintuitive and like doesn't + + align:start position:0% +and counterintuitive and like doesn't + + + align:start position:0% +and counterintuitive and like doesn't +really exist in normal life + + align:start position:0% +really exist in normal life + + + align:start position:0% +really exist in normal life +most things like if you know most things + + align:start position:0% +most things like if you know most things + + + align:start position:0% +most things like if you know most things +have some kind of sublinear curve where + + align:start position:0% +have some kind of sublinear curve where + + + align:start position:0% +have some kind of sublinear curve where +yeah the first low-hanging fruit you + + align:start position:0% +yeah the first low-hanging fruit you + + + align:start position:0% +yeah the first low-hanging fruit you +know if you're mining coal and you start + + align:start position:0% +know if you're mining coal and you start + + + align:start position:0% +know if you're mining coal and you start +in Pittsburgh and it's just sitting + + align:start position:0% +in Pittsburgh and it's just sitting + + + align:start position:0% +in Pittsburgh and it's just sitting +there on the hill and you're like hey + + align:start position:0% +there on the hill and you're like hey + + + align:start position:0% +there on the hill and you're like hey +that was easy and then eventually you + + align:start position:0% +that was easy and then eventually you + + + align:start position:0% +that was easy and then eventually you +have to start you know open pit mines + + align:start position:0% +have to start you know open pit mines + + + align:start position:0% +have to start you know open pit mines +and digging holes and it's expensive and + + align:start position:0% +and digging holes and it's expensive and + + + align:start position:0% +and digging holes and it's expensive and +you you know don't get as good but you + + align:start position:0% +you you know don't get as good but you + + + align:start position:0% +you you know don't get as good but you +still if you double your effort you're + + align:start position:0% +still if you double your effort you're + + + align:start position:0% +still if you double your effort you're +gonna get some extra stuff out then + + align:start position:0% +gonna get some extra stuff out then + + + align:start position:0% +gonna get some extra stuff out then +again there might be cases and I'm sure + + align:start position:0% +again there might be cases and I'm sure + + + align:start position:0% +again there might be cases and I'm sure +in economics where like eventually goes + + align:start position:0% +in economics where like eventually goes + + + align:start position:0% +in economics where like eventually goes +negative where if you continue adding + + align:start position:0% +negative where if you continue adding + + + align:start position:0% +negative where if you continue adding +two members to an organization + + align:start position:0% +two members to an organization + + + align:start position:0% +two members to an organization +eventually they're just like deadweight + + align:start position:0% +eventually they're just like deadweight + + + align:start position:0% +eventually they're just like deadweight +it may make it less efficient or + + align:start position:0% +it may make it less efficient or + + + align:start position:0% +it may make it less efficient or +something but in a Bitcoin it doesn't + + align:start position:0% +something but in a Bitcoin it doesn't + + + align:start position:0% +something but in a Bitcoin it doesn't +matter how much you mind you always get + + align:start position:0% +matter how much you mind you always get + + + align:start position:0% +matter how much you mind you always get +the same number of coins so the the + + align:start position:0% +the same number of coins so the the + + + align:start position:0% +the same number of coins so the the +obvious thing there is well we should + + align:start position:0% +obvious thing there is well we should + + + align:start position:0% +obvious thing there is well we should +all just stop mining and then we'll have + + align:start position:0% +all just stop mining and then we'll have + + + align:start position:0% +all just stop mining and then we'll have +zero electricity usage and we'll still + + align:start position:0% +zero electricity usage and we'll still + + + align:start position:0% +zero electricity usage and we'll still +get the same + + align:start position:0% + + + + align:start position:0% + +yeah however good the science is you + + align:start position:0% +yeah however good the science is you + + + align:start position:0% +yeah however good the science is you +just get one developer so okay so let's + + align:start position:0% +just get one developer so okay so let's + + + align:start position:0% +just get one developer so okay so let's +say there's two miners and let's focus + + align:start position:0% +say there's two miners and let's focus + + + align:start position:0% +say there's two miners and let's focus +more and each mining with two gigawatts + + align:start position:0% +more and each mining with two gigawatts + + + align:start position:0% +more and each mining with two gigawatts +and they both think we'll wait if we + + align:start position:0% +and they both think we'll wait if we + + + align:start position:0% +and they both think we'll wait if we +both turned our mining down five percent + + align:start position:0% +both turned our mining down five percent + + + align:start position:0% +both turned our mining down five percent +we'd still get the same amount of coins + + align:start position:0% +we'd still get the same amount of coins + + + align:start position:0% +we'd still get the same amount of coins +but we'd be using five percent less + + align:start position:0% +but we'd be using five percent less + + + align:start position:0% +but we'd be using five percent less +electricity we should have a meeting + + align:start position:0% +electricity we should have a meeting + + + align:start position:0% +electricity we should have a meeting +maybe some kind of cartel so this is + + align:start position:0% +maybe some kind of cartel so this is + + + align:start position:0% +maybe some kind of cartel so this is +sort of OPEC right this is a car this is + + align:start position:0% +sort of OPEC right this is a car this is + + + align:start position:0% +sort of OPEC right this is a car this is +a classic cartel if we all restrict our + + align:start position:0% +a classic cartel if we all restrict our + + + align:start position:0% +a classic cartel if we all restrict our +output we can raise prices and reduce + + align:start position:0% +output we can raise prices and reduce + + + align:start position:0% +output we can raise prices and reduce +our costs in Bitcoin it's like the + + align:start position:0% +our costs in Bitcoin it's like the + + + align:start position:0% +our costs in Bitcoin it's like the +perfect cartel environment because if we + + align:start position:0% +perfect cartel environment because if we + + + align:start position:0% +perfect cartel environment because if we +all reduce our output we get the same + + align:start position:0% +all reduce our output we get the same + + + align:start position:0% +all reduce our output we get the same +output sort of right if we all if we all + + align:start position:0% +output sort of right if we all if we all + + + align:start position:0% +output sort of right if we all if we all +turn down mining 50% we all still get + + align:start position:0% +turn down mining 50% we all still get + + + align:start position:0% +turn down mining 50% we all still get +the same number of coins the network + + align:start position:0% +the same number of coins the network + + + align:start position:0% +the same number of coins the network +still works fine maybe nobody even knows + + align:start position:0% +still works fine maybe nobody even knows + + + align:start position:0% +still works fine maybe nobody even knows +we're doing this this is like ideal of + + align:start position:0% +we're doing this this is like ideal of + + + align:start position:0% +we're doing this this is like ideal of +Part L scenario problem for cartels + + align:start position:0% +Part L scenario problem for cartels + + + align:start position:0% +Part L scenario problem for cartels +generally is that cartels are hard to + + align:start position:0% +generally is that cartels are hard to + + + align:start position:0% +generally is that cartels are hard to +maintain especially when there's not a + + align:start position:0% +maintain especially when there's not a + + + align:start position:0% +maintain especially when there's not a +lot of trust because there's so much + + align:start position:0% +lot of trust because there's so much + + + align:start position:0% +lot of trust because there's so much +profit in defecting and like going + + align:start position:0% +profit in defecting and like going + + + align:start position:0% +profit in defecting and like going +against the rules a good bit of the + + align:start position:0% +against the rules a good bit of the + + + align:start position:0% +against the rules a good bit of the +cartel and OPEC has this all the time + + align:start position:0% +cartel and OPEC has this all the time + + + align:start position:0% +cartel and OPEC has this all the time +where one of the OPEC countries says no + + align:start position:0% +where one of the OPEC countries says no + + + align:start position:0% +where one of the OPEC countries says no +we're just gonna pump a bunch of oil and + + align:start position:0% +we're just gonna pump a bunch of oil and + + + align:start position:0% +we're just gonna pump a bunch of oil and +sell it because everyone else reducing + + align:start position:0% +sell it because everyone else reducing + + + align:start position:0% +sell it because everyone else reducing +their output raises the prices and now + + align:start position:0% +their output raises the prices and now + + + align:start position:0% +their output raises the prices and now +we can sell more with high prices so in + + align:start position:0% +we can sell more with high prices so in + + + align:start position:0% +we can sell more with high prices so in +this kind of system if all the miners + + align:start position:0% +this kind of system if all the miners + + + align:start position:0% +this kind of system if all the miners +said hey let's all turn down 50% the one + + align:start position:0% +said hey let's all turn down 50% the one + + + align:start position:0% +said hey let's all turn down 50% the one +miner who then mines at full blast is + + align:start position:0% +miner who then mines at full blast is + + + align:start position:0% +miner who then mines at full blast is +gonna make a lot of coins so this is the + + align:start position:0% +gonna make a lot of coins so this is the + + + align:start position:0% +gonna make a lot of coins so this is the +problem in Bitcoin nobody trusts anyone + + align:start position:0% +problem in Bitcoin nobody trusts anyone + + + align:start position:0% +problem in Bitcoin nobody trusts anyone +right so the solution here is trustless + + align:start position:0% +right so the solution here is trustless + + + align:start position:0% +right so the solution here is trustless +collusion and I in the papers like well + + align:start position:0% +collusion and I in the papers like well + + + align:start position:0% +collusion and I in the papers like well +is a collusion or cooperation it was + + align:start position:0% +is a collusion or cooperation it was + + + align:start position:0% +is a collusion or cooperation it was +sort of mean the same thing and close in + + align:start position:0% +sort of mean the same thing and close in + + + align:start position:0% +sort of mean the same thing and close in +just a bad word for cooperation + + align:start position:0% +just a bad word for cooperation + + + align:start position:0% +just a bad word for cooperation +cooperation is good okay so the basic + + align:start position:0% +cooperation is good okay so the basic + + + align:start position:0% +cooperation is good okay so the basic +system is a pay Alice pays Bob not to + + align:start position:0% +system is a pay Alice pays Bob not to + + + align:start position:0% +system is a pay Alice pays Bob not to +mine so first the thing Alice needs to + + align:start position:0% +mine so first the thing Alice needs to + + + align:start position:0% +mine so first the thing Alice needs to +prove that Bob can mine because + + align:start position:0% +prove that Bob can mine because + + + align:start position:0% +prove that Bob can mine because +she doesn't want to pay Bob but if Bob + + align:start position:0% +she doesn't want to pay Bob but if Bob + + + align:start position:0% +she doesn't want to pay Bob but if Bob +doesn't have any mining capacity that + + align:start position:0% +doesn't have any mining capacity that + + + align:start position:0% +doesn't have any mining capacity that +he's taking offline + + align:start position:0% +he's taking offline + + + align:start position:0% +he's taking offline +she only wants to pay Bob for you know + + align:start position:0% +she only wants to pay Bob for you know + + + align:start position:0% +she only wants to pay Bob for you know +having the ability to mine and then not + + align:start position:0% +having the ability to mine and then not + + + align:start position:0% +having the ability to mine and then not +doing it + + align:start position:0% +doing it + + + align:start position:0% +doing it +so a posts a block header and a + + align:start position:0% +so a posts a block header and a + + + align:start position:0% +so a posts a block header and a +specified time and says okay be mine for + + align:start position:0% +specified time and says okay be mine for + + + align:start position:0% +specified time and says okay be mine for +10 seconds and give me like your hundred + + align:start position:0% +10 seconds and give me like your hundred + + + align:start position:0% +10 seconds and give me like your hundred +best shots right so you can so in + + align:start position:0% +best shots right so you can so in + + + align:start position:0% +best shots right so you can so in +Bitcoin you have this like fixed + + align:start position:0% +Bitcoin you have this like fixed + + + align:start position:0% +Bitcoin you have this like fixed +difficulty and you just say okay + + align:start position:0% +difficulty and you just say okay + + + align:start position:0% +difficulty and you just say okay +anything above anything's right below + + align:start position:0% +anything above anything's right below + + + align:start position:0% +anything above anything's right below +this block hash is valid but you could + + align:start position:0% +this block hash is valid but you could + + + align:start position:0% +this block hash is valid but you could +make one where you say hey give me your + + align:start position:0% +make one where you say hey give me your + + + align:start position:0% +make one where you say hey give me your +best hundred and I can then extrapolate + + align:start position:0% +best hundred and I can then extrapolate + + + align:start position:0% +best hundred and I can then extrapolate +or you know interpret from that what + + align:start position:0% +or you know interpret from that what + + + align:start position:0% +or you know interpret from that what +your hash rate is you can get pretty + + align:start position:0% +your hash rate is you can get pretty + + + align:start position:0% +your hash rate is you can get pretty +accurate in them so they have to do some + + align:start position:0% +accurate in them so they have to do some + + + align:start position:0% +accurate in them so they have to do some +work right Bob does some work but for a + + align:start position:0% +work right Bob does some work but for a + + + align:start position:0% +work right Bob does some work but for a +brief period and I don't know ten + + align:start position:0% +brief period and I don't know ten + + + align:start position:0% +brief period and I don't know ten +seconds you don't you don't want latency + + align:start position:0% +seconds you don't you don't want latency + + + align:start position:0% +seconds you don't you don't want latency +to be an issue so maybe 10 seconds maybe + + align:start position:0% +to be an issue so maybe 10 seconds maybe + + + align:start position:0% +to be an issue so maybe 10 seconds maybe +a minute whatever some some small amount + + align:start position:0% +a minute whatever some some small amount + + + align:start position:0% +a minute whatever some some small amount +of work to prove that they have the + + align:start position:0% +of work to prove that they have the + + + align:start position:0% +of work to prove that they have the +capability to do the work they respond + + align:start position:0% +capability to do the work they respond + + + align:start position:0% +capability to do the work they respond +with that analysis validates that says + + align:start position:0% +with that analysis validates that says + + + align:start position:0% +with that analysis validates that says +okay + + align:start position:0% +okay + + + align:start position:0% +okay +you've got X amount of work capacity + + align:start position:0% +you've got X amount of work capacity + + + align:start position:0% +you've got X amount of work capacity +Allison creates a - of - multi-sig + + align:start position:0% +Allison creates a - of - multi-sig + + + align:start position:0% +Allison creates a - of - multi-sig +transaction and sends one Bitcoin to + + align:start position:0% +transaction and sends one Bitcoin to + + + align:start position:0% +transaction and sends one Bitcoin to +this address and builds two transactions + + align:start position:0% +this address and builds two transactions + + + align:start position:0% +this address and builds two transactions +with Bob this is sort of like how like + + align:start position:0% +with Bob this is sort of like how like + + + align:start position:0% +with Bob this is sort of like how like +net network looks lightening channels + + align:start position:0% +net network looks lightening channels + + + align:start position:0% +net network looks lightening channels +but this predates it by a year - the + + align:start position:0% +but this predates it by a year - the + + + align:start position:0% +but this predates it by a year - the +idea is you've got this funding and then + + align:start position:0% +idea is you've got this funding and then + + + align:start position:0% +idea is you've got this funding and then +you've got two transactions they're both + + align:start position:0% +you've got two transactions they're both + + + align:start position:0% +you've got two transactions they're both +signed by both parties and held by both + + align:start position:0% +signed by both parties and held by both + + + align:start position:0% +signed by both parties and held by both +parties although in practice the one + + align:start position:0% +parties although in practice the one + + + align:start position:0% +parties although in practice the one +that pays out to Alice Bob doesn't + + align:start position:0% +that pays out to Alice Bob doesn't + + + align:start position:0% +that pays out to Alice Bob doesn't +really need to store he doesn't like it + + align:start position:0% +really need to store he doesn't like it + + + align:start position:0% +really need to store he doesn't like it +and the one that pays out to Bob Alice + + align:start position:0% +and the one that pays out to Bob Alice + + + align:start position:0% +and the one that pays out to Bob Alice +doesn't need a store but the idea is + + align:start position:0% +doesn't need a store but the idea is + + + align:start position:0% +doesn't need a store but the idea is +they have conflicting lock times so in + + align:start position:0% +they have conflicting lock times so in + + + align:start position:0% +they have conflicting lock times so in +the in the transaction header you can + + align:start position:0% +the in the transaction header you can + + + align:start position:0% +the in the transaction header you can +have a lock time say okay this + + align:start position:0% +have a lock time say okay this + + + align:start position:0% +have a lock time say okay this +transaction is only valid after this + + align:start position:0% +transaction is only valid after this + + + align:start position:0% +transaction is only valid after this +point so the one that pays Alice is + + align:start position:0% +point so the one that pays Alice is + + + align:start position:0% +point so the one that pays Alice is +height plus 144 so the current height of + + align:start position:0% +height plus 144 so the current height of + + + align:start position:0% +height plus 144 so the current height of +the blockchain plus 144 well that should + + align:start position:0% +the blockchain plus 144 well that should + + + align:start position:0% +the blockchain plus 144 well that should +take about a day right if blocks come + + align:start position:0% +take about a day right if blocks come + + + align:start position:0% +take about a day right if blocks come +out every 10 minutes 144 blocks is one + + align:start position:0% +out every 10 minutes 144 blocks is one + + + align:start position:0% +out every 10 minutes 144 blocks is one +day for Bob Bob gets the coin with the + + align:start position:0% +day for Bob Bob gets the coin with the + + + align:start position:0% +day for Bob Bob gets the coin with the +current lock time plus 24 hours so in + + align:start position:0% +current lock time plus 24 hours so in + + + align:start position:0% +current lock time plus 24 hours so in +Bitcoin you can specify either unix time + + align:start position:0% +Bitcoin you can specify either unix time + + + align:start position:0% +Bitcoin you can specify either unix time +or block height and I think everything + + align:start position:0% +or block height and I think everything + + + align:start position:0% +or block height and I think everything +above 500 million is a time everything + + align:start position:0% +above 500 million is a time everything + + + align:start position:0% +above 500 million is a time everything +below 500 million is interpretive and + + align:start position:0% +below 500 million is interpretive and + + + align:start position:0% +below 500 million is interpretive and +the height + + align:start position:0% +the height + + + align:start position:0% +the height +which means the full system runs out in + + align:start position:0% +which means the full system runs out in + + + align:start position:0% +which means the full system runs out in +like a couple thousand years so so that + + align:start position:0% +like a couple thousand years so so that + + + align:start position:0% +like a couple thousand years so so that +this is a race right there's two + + align:start position:0% +this is a race right there's two + + + align:start position:0% +this is a race right there's two +transactions one of them can be + + align:start position:0% +transactions one of them can be + + + align:start position:0% +transactions one of them can be +broadcast first + + align:start position:0% +broadcast first + + + align:start position:0% +broadcast first +depending on how fast blocks come out so + + align:start position:0% +depending on how fast blocks come out so + + + align:start position:0% +depending on how fast blocks come out so +if Fox come out very quickly this will + + align:start position:0% +if Fox come out very quickly this will + + + align:start position:0% +if Fox come out very quickly this will +be valid first 144 blocks maybe it only + + align:start position:0% +be valid first 144 blocks maybe it only + + + align:start position:0% +be valid first 144 blocks maybe it only +takes 20 hours and these hundred + + align:start position:0% +takes 20 hours and these hundred + + + align:start position:0% +takes 20 hours and these hundred +forty-four blocks have come out and + + align:start position:0% +forty-four blocks have come out and + + + align:start position:0% +forty-four blocks have come out and +Alice can post this transaction and get + + align:start position:0% +Alice can post this transaction and get + + + align:start position:0% +Alice can post this transaction and get +all of our money back yet her one coin + + align:start position:0% +all of our money back yet her one coin + + + align:start position:0% +all of our money back yet her one coin +back + + align:start position:0% +back + + + align:start position:0% +back +however if blocks come out slowly and + + align:start position:0% +however if blocks come out slowly and + + + align:start position:0% +however if blocks come out slowly and +after 24 hours only a hundred and twenty + + align:start position:0% +after 24 hours only a hundred and twenty + + + align:start position:0% +after 24 hours only a hundred and twenty +blocks have come out + + align:start position:0% +blocks have come out + + + align:start position:0% +blocks have come out +Bob can post this transaction first and + + align:start position:0% +Bob can post this transaction first and + + + align:start position:0% +Bob can post this transaction first and +it will be valid and confirmed and Bob + + align:start position:0% +it will be valid and confirmed and Bob + + + align:start position:0% +it will be valid and confirmed and Bob +gets the coin so now Bob's incentives + + align:start position:0% +gets the coin so now Bob's incentives + + + align:start position:0% +gets the coin so now Bob's incentives +are well I I'd like a hundred forty four + + align:start position:0% +are well I I'd like a hundred forty four + + + align:start position:0% +are well I I'd like a hundred forty four +blocks to take longer than 24 hours + + align:start position:0% +blocks to take longer than 24 hours + + + align:start position:0% +blocks to take longer than 24 hours +because then I'll get this coin and Bob + + align:start position:0% +because then I'll get this coin and Bob + + + align:start position:0% +because then I'll get this coin and Bob +has the means to influence this right + + align:start position:0% +has the means to influence this right + + + align:start position:0% +has the means to influence this right +Bob's a minor so Bob can say well I'll + + align:start position:0% +Bob's a minor so Bob can say well I'll + + + align:start position:0% +Bob's a minor so Bob can say well I'll +just mined less and if I mine such that + + align:start position:0% +just mined less and if I mine such that + + + align:start position:0% +just mined less and if I mine such that +it you know in 24 hours only 130 blocks + + align:start position:0% +it you know in 24 hours only 130 blocks + + + align:start position:0% +it you know in 24 hours only 130 blocks +come out I get the coin cool right if + + align:start position:0% +come out I get the coin cool right if + + + align:start position:0% +come out I get the coin cool right if +blocks them up fast on the other hand + + align:start position:0% +blocks them up fast on the other hand + + + align:start position:0% +blocks them up fast on the other hand +Alex yes their money back so alice has + + align:start position:0% +Alex yes their money back so alice has + + + align:start position:0% +Alex yes their money back so alice has +no real risk here that Bob will run away + + align:start position:0% +no real risk here that Bob will run away + + + align:start position:0% +no real risk here that Bob will run away +with the money without doing his part of + + align:start position:0% +with the money without doing his part of + + + align:start position:0% +with the money without doing his part of +the job so Bob can slow down his mining + + align:start position:0% +the job so Bob can slow down his mining + + + align:start position:0% +the job so Bob can slow down his mining +in order to get the bounty coins if + + align:start position:0% +in order to get the bounty coins if + + + align:start position:0% +in order to get the bounty coins if +Alice sort of estimates incorrectly how + + align:start position:0% +Alice sort of estimates incorrectly how + + + align:start position:0% +Alice sort of estimates incorrectly how +much profitability bob has Bob just + + align:start position:0% +much profitability bob has Bob just + + + align:start position:0% +much profitability bob has Bob just +doesn't do you know just Bob just keeps + + align:start position:0% +doesn't do you know just Bob just keeps + + + align:start position:0% +doesn't do you know just Bob just keeps +mining Alice gets their money back the + + align:start position:0% +mining Alice gets their money back the + + + align:start position:0% +mining Alice gets their money back the +this collusion didn't occur at very + + align:start position:0% +this collusion didn't occur at very + + + align:start position:0% +this collusion didn't occur at very +little cost right Bob had to prove a + + align:start position:0% +little cost right Bob had to prove a + + + align:start position:0% +little cost right Bob had to prove a +little bit there's some coordination + + align:start position:0% +little bit there's some coordination + + + align:start position:0% +little bit there's some coordination +costs but like basically nobody loses + + align:start position:0% +costs but like basically nobody loses + + + align:start position:0% +costs but like basically nobody loses +the money so Alice can put whatever + + align:start position:0% +the money so Alice can put whatever + + + align:start position:0% +the money so Alice can put whatever +bounty she thinks is you know beneficial + + align:start position:0% +bounty she thinks is you know beneficial + + + align:start position:0% +bounty she thinks is you know beneficial +to her okay I'll pay you three coins not + + align:start position:0% +to her okay I'll pay you three coins not + + + align:start position:0% +to her okay I'll pay you three coins not +to mine as much and you can chop this up + + align:start position:0% +to mine as much and you can chop this up + + + align:start position:0% +to mine as much and you can chop this up +you can have like a lot of different + + align:start position:0% +you can have like a lot of different + + + align:start position:0% +you can have like a lot of different +smaller transactions and sort of make a + + align:start position:0% +smaller transactions and sort of make a + + + align:start position:0% +smaller transactions and sort of make a +curve a lot you know if you mind a lot + + align:start position:0% +curve a lot you know if you mind a lot + + + align:start position:0% +curve a lot you know if you mind a lot +less I'll tell you more things like that + + align:start position:0% + + + + align:start position:0% + +yeah so that's the idea of I'm improving + + align:start position:0% +yeah so that's the idea of I'm improving + + + align:start position:0% +yeah so that's the idea of I'm improving +vital it doesn't all the product it + + align:start position:0% +vital it doesn't all the product it + + + align:start position:0% +vital it doesn't all the product it +feels like it might happen to some + + align:start position:0% +feels like it might happen to some + + + align:start position:0% +feels like it might happen to some +extent like long term it feels sort of + + align:start position:0% +extent like long term it feels sort of + + + align:start position:0% +extent like long term it feels sort of +like you know nuclear weapons where like + + align:start position:0% +like you know nuclear weapons where like + + + align:start position:0% +like you know nuclear weapons where like +everyone's got + + align:start position:0% +everyone's got + + + align:start position:0% +everyone's got +but like they don't really use them they + + align:start position:0% +but like they don't really use them they + + + align:start position:0% +but like they don't really use them they +just sort of threaten so it feels like + + align:start position:0% +just sort of threaten so it feels like + + + align:start position:0% +just sort of threaten so it feels like +mining could be that kind of thing where + + align:start position:0% +mining could be that kind of thing where + + + align:start position:0% +mining could be that kind of thing where +well we've all got all this mining + + align:start position:0% +well we've all got all this mining + + + align:start position:0% +well we've all got all this mining +capacity but we just sort of threatened + + align:start position:0% +capacity but we just sort of threatened + + + align:start position:0% +capacity but we just sort of threatened +each other with it and we don't really + + align:start position:0% +each other with it and we don't really + + + align:start position:0% +each other with it and we don't really +mind uh because the mining is actually + + align:start position:0% +mind uh because the mining is actually + + + align:start position:0% +mind uh because the mining is actually +really expensive and it's just a threat + + align:start position:0% +really expensive and it's just a threat + + + align:start position:0% +really expensive and it's just a threat +of mining that you need and and if + + align:start position:0% +of mining that you need and and if + + + align:start position:0% +of mining that you need and and if +someone tries to do say a 51% attack and + + align:start position:0% +someone tries to do say a 51% attack and + + + align:start position:0% +someone tries to do say a 51% attack and +reorg the existing mining infrastructure + + align:start position:0% +reorg the existing mining infrastructure + + + align:start position:0% +reorg the existing mining infrastructure +can spin up and say oh no you thought + + align:start position:0% +can spin up and say oh no you thought + + + align:start position:0% +can spin up and say oh no you thought +you were 51% you are actually 5.1 + + align:start position:0% +you were 51% you are actually 5.1 + + + align:start position:0% +you were 51% you are actually 5.1 +percent and we're 90 percent offline we + + align:start position:0% +percent and we're 90 percent offline we + + + align:start position:0% +percent and we're 90 percent offline we +all come back online and and reaaargh + + align:start position:0% +all come back online and and reaaargh + + + align:start position:0% +all come back online and and reaaargh +you out it's an interesting I mean I + + align:start position:0% +you out it's an interesting I mean I + + + align:start position:0% +you out it's an interesting I mean I +think it's a kind of a fun idea in + + align:start position:0% +think it's a kind of a fun idea in + + + align:start position:0% +think it's a kind of a fun idea in +practice it doesn't work now because + + align:start position:0% +practice it doesn't work now because + + + align:start position:0% +practice it doesn't work now because +it's mostly capex so this doesn't help + + align:start position:0% +it's mostly capex so this doesn't help + + + align:start position:0% +it's mostly capex so this doesn't help +if your main constraint is building the + + align:start position:0% +if your main constraint is building the + + + align:start position:0% +if your main constraint is building the +chips which it sounds like it still is + + align:start position:0% +chips which it sounds like it still is + + + align:start position:0% +chips which it sounds like it still is +like from David's talk on Monday right + + align:start position:0% +like from David's talk on Monday right + + + align:start position:0% +like from David's talk on Monday right +yeah you need to get electricity sure + + align:start position:0% +yeah you need to get electricity sure + + + align:start position:0% +yeah you need to get electricity sure +but also a really big problem is getting + + align:start position:0% +but also a really big problem is getting + + + align:start position:0% +but also a really big problem is getting +a supply of all these chips and so and + + align:start position:0% +a supply of all these chips and so and + + + align:start position:0% +a supply of all these chips and so and +this would just exacerbate that this + + align:start position:0% +this would just exacerbate that this + + + align:start position:0% +this would just exacerbate that this +would make it so that I don't even need + + align:start position:0% +would make it so that I don't even need + + + align:start position:0% +would make it so that I don't even need +electricity I just get the chips I don't + + align:start position:0% +electricity I just get the chips I don't + + + align:start position:0% +electricity I just get the chips I don't +really care how much I'm paying + + align:start position:0% +really care how much I'm paying + + + align:start position:0% +really care how much I'm paying +electricity because most of the time my + + align:start position:0% +electricity because most of the time my + + + align:start position:0% +electricity because most of the time my +chips it off I just need to occasionally + + align:start position:0% +chips it off I just need to occasionally + + + align:start position:0% +chips it off I just need to occasionally +prove I have them and have the ability + + align:start position:0% +prove I have them and have the ability + + + align:start position:0% +prove I have them and have the ability +to mine with them so it wouldn't solve + + align:start position:0% +to mine with them so it wouldn't solve + + + align:start position:0% +to mine with them so it wouldn't solve +the problem of proof work in terms of + + align:start position:0% +the problem of proof work in terms of + + + align:start position:0% +the problem of proof work in terms of +people spending tons of money on it + + align:start position:0% +people spending tons of money on it + + + align:start position:0% +people spending tons of money on it +but it would move it towards okay less + + align:start position:0% +but it would move it towards okay less + + + align:start position:0% +but it would move it towards okay less +electricity usage more fabrication plant + + align:start position:0% +electricity usage more fabrication plant + + + align:start position:0% +electricity usage more fabrication plant +usage is that a good thing I don't I + + align:start position:0% +usage is that a good thing I don't I + + + align:start position:0% +usage is that a good thing I don't I +don't know my in certain cases it may be + + align:start position:0% +don't know my in certain cases it may be + + + align:start position:0% +don't know my in certain cases it may be +that it saves people money it may be + + align:start position:0% +that it saves people money it may be + + + align:start position:0% +that it saves people money it may be +that like hey if we can collude in this + + align:start position:0% +that like hey if we can collude in this + + + align:start position:0% +that like hey if we can collude in this +way it actually we save money and then + + align:start position:0% +way it actually we save money and then + + + align:start position:0% +way it actually we save money and then +we can we can use it to build more hash + + align:start position:0% +we can we can use it to build more hash + + + align:start position:0% +we can we can use it to build more hash +power so this might happen I'm not as + + align:start position:0% +power so this might happen I'm not as + + + align:start position:0% +power so this might happen I'm not as +convinced I was sort of convinced like + + align:start position:0% +convinced I was sort of convinced like + + + align:start position:0% +convinced I was sort of convinced like +in 2014 I'm like oh I think this is + + align:start position:0% +in 2014 I'm like oh I think this is + + + align:start position:0% +in 2014 I'm like oh I think this is +gonna happen I also thought that it + + align:start position:0% +gonna happen I also thought that it + + + align:start position:0% +gonna happen I also thought that it +would become predominantly effects in + + align:start position:0% +would become predominantly effects in + + + align:start position:0% +would become predominantly effects in +like 2015 or 16 and it just did not even + + align:start position:0% +like 2015 or 16 and it just did not even + + + align:start position:0% +like 2015 or 16 and it just did not even +close so who knows okay so in general + + align:start position:0% +close so who knows okay so in general + + + align:start position:0% +close so who knows okay so in general +lots of new ideas out there proven work + + align:start position:0% +lots of new ideas out there proven work + + + align:start position:0% +lots of new ideas out there proven work +does seem to work + + align:start position:0% +does seem to work + + + align:start position:0% +does seem to work +but I think one of the big issues is + + align:start position:0% +but I think one of the big issues is + + + align:start position:0% +but I think one of the big issues is +it's not really compatible with the sort + + align:start position:0% +it's not really compatible with the sort + + + align:start position:0% +it's not really compatible with the sort +of Kurzweil Roddenberry future idea I + + align:start position:0% +of Kurzweil Roddenberry future idea I + + + align:start position:0% +of Kurzweil Roddenberry future idea I +don't know if anyone read like Ray + + align:start position:0% +don't know if anyone read like Ray + + + align:start position:0% +don't know if anyone read like Ray +Kurzweil like age of spiritual machines + + align:start position:0% +Kurzweil like age of spiritual machines + + + align:start position:0% +Kurzweil like age of spiritual machines +there's it's sort of like this future II + + align:start position:0% +there's it's sort of like this future II + + + align:start position:0% +there's it's sort of like this future II +like AI is gonna make everything great + + align:start position:0% +like AI is gonna make everything great + + + align:start position:0% +like AI is gonna make everything great +and we're all gonna live forever and + + align:start position:0% +and we're all gonna live forever and + + + align:start position:0% +and we're all gonna live forever and +computers are gonna be like our best + + align:start position:0% +computers are gonna be like our best + + + align:start position:0% +computers are gonna be like our best +friends and we're gonna take over the + + align:start position:0% +friends and we're gonna take over the + + + align:start position:0% +friends and we're gonna take over the +universe and Gene Roddenberry of Star + + align:start position:0% +universe and Gene Roddenberry of Star + + + align:start position:0% +universe and Gene Roddenberry of Star +Trek is is sort of a popular not quite + + align:start position:0% +Trek is is sort of a popular not quite + + + align:start position:0% +Trek is is sort of a popular not quite +as crazy maybe justice crazy view of + + align:start position:0% +as crazy maybe justice crazy view of + + + align:start position:0% +as crazy maybe justice crazy view of +that we're like we're all gonna you know + + align:start position:0% +that we're like we're all gonna you know + + + align:start position:0% +that we're like we're all gonna you know +in Star Trek they don't have money they + + align:start position:0% +in Star Trek they don't have money they + + + align:start position:0% +in Star Trek they don't have money they +just sort of explore the universe and + + align:start position:0% +just sort of explore the universe and + + + align:start position:0% +just sort of explore the universe and +make the world a better place and stuff + + align:start position:0% +make the world a better place and stuff + + + align:start position:0% +make the world a better place and stuff +like that and it's like cool and there's + + align:start position:0% +like that and it's like cool and there's + + + align:start position:0% +like that and it's like cool and there's +a lot of people who are into technology + + align:start position:0% +a lot of people who are into technology + + + align:start position:0% +a lot of people who are into technology +in research who are you know maybe not + + align:start position:0% +in research who are you know maybe not + + + align:start position:0% +in research who are you know maybe not +consciously but identify with these + + align:start position:0% +consciously but identify with these + + + align:start position:0% +consciously but identify with these +ideas that like yeah we're making the + + align:start position:0% +ideas that like yeah we're making the + + + align:start position:0% +ideas that like yeah we're making the +world a better place we're making + + align:start position:0% +world a better place we're making + + + align:start position:0% +world a better place we're making +computers are gonna help people and it's + + align:start position:0% +computers are gonna help people and it's + + + align:start position:0% +computers are gonna help people and it's +gonna be great and I think one of the + + align:start position:0% +gonna be great and I think one of the + + + align:start position:0% +gonna be great and I think one of the +issues with Bitcoin and proof-of-work is + + align:start position:0% +issues with Bitcoin and proof-of-work is + + + align:start position:0% +issues with Bitcoin and proof-of-work is +it doesn't fit into that right it's sort + + align:start position:0% +it doesn't fit into that right it's sort + + + align:start position:0% +it doesn't fit into that right it's sort +of dystopian in a way and then it's like + + align:start position:0% +of dystopian in a way and then it's like + + + align:start position:0% +of dystopian in a way and then it's like +wait we're gonna have like giant server + + align:start position:0% +wait we're gonna have like giant server + + + align:start position:0% +wait we're gonna have like giant server +farms performing sha-256 for the next 50 + + align:start position:0% +farms performing sha-256 for the next 50 + + + align:start position:0% +farms performing sha-256 for the next 50 +years like how what does how does how + + align:start position:0% +years like how what does how does how + + + align:start position:0% +years like how what does how does how +does the benevolent AI fit into this + + align:start position:0% +does the benevolent AI fit into this + + + align:start position:0% +does the benevolent AI fit into this +system so so that's one of the reasons + + align:start position:0% +system so so that's one of the reasons + + + align:start position:0% +system so so that's one of the reasons +people like I the prove vital idea was + + align:start position:0% +people like I the prove vital idea was + + + align:start position:0% +people like I the prove vital idea was +my I was at University of Virginia and I + + align:start position:0% +my I was at University of Virginia and I + + + align:start position:0% +my I was at University of Virginia and I +Miche a lot who's now at Northeastern he + + align:start position:0% +Miche a lot who's now at Northeastern he + + + align:start position:0% +Miche a lot who's now at Northeastern he +was like I hate Bitcoin because the + + align:start position:0% +was like I hate Bitcoin because the + + + align:start position:0% +was like I hate Bitcoin because the +whole point of sha-256 is that you can't + + align:start position:0% +whole point of sha-256 is that you can't + + + align:start position:0% +whole point of sha-256 is that you can't +find collisions that was the design like + + align:start position:0% +find collisions that was the design like + + + align:start position:0% +find collisions that was the design like +there's no you know collision resistant + + align:start position:0% +there's no you know collision resistant + + + align:start position:0% +there's no you know collision resistant +hash function and now you've built this + + align:start position:0% +hash function and now you've built this + + + align:start position:0% +hash function and now you've built this +giant system which the whole point of + + align:start position:0% +giant system which the whole point of + + + align:start position:0% +giant system which the whole point of +the system is to find collisions like ah + + align:start position:0% +the system is to find collisions like ah + + + align:start position:0% +the system is to find collisions like ah +like that's the opposite of what it was + + align:start position:0% +like that's the opposite of what it was + + + align:start position:0% +like that's the opposite of what it was +supposed to be and so it was just sort + + align:start position:0% +supposed to be and so it was just sort + + + align:start position:0% +supposed to be and so it was just sort +of like in elegant and ugly and that was + + align:start position:0% +of like in elegant and ugly and that was + + + align:start position:0% +of like in elegant and ugly and that was +why I'm like well maybe you don't really + + align:start position:0% +why I'm like well maybe you don't really + + + align:start position:0% +why I'm like well maybe you don't really +have to mind that much and so I wrote + + align:start position:0% +have to mind that much and so I wrote + + + align:start position:0% +have to mind that much and so I wrote +this thing about broom life but anyway + + align:start position:0% +this thing about broom life but anyway + + + align:start position:0% +this thing about broom life but anyway +that's one of the issues that people + + align:start position:0% +that's one of the issues that people + + + align:start position:0% +that's one of the issues that people +have with proof work and that's I think + + align:start position:0% +have with proof work and that's I think + + + align:start position:0% +have with proof work and that's I think +one of the big you know motivating + + align:start position:0% +one of the big you know motivating + + + align:start position:0% +one of the big you know motivating +factors for all this other research into + + align:start position:0% +factors for all this other research into + + + align:start position:0% +factors for all this other research into +different consensus algorithms and + + align:start position:0% +different consensus algorithms and + + + align:start position:0% +different consensus algorithms and +further research is required + + align:start position:0% +further research is required + + + align:start position:0% +further research is required +maybe the interesting thing is a lot of + + align:start position:0% +maybe the interesting thing is a lot of + + + align:start position:0% +maybe the interesting thing is a lot of +the people doing proof of work are fine + + align:start position:0% +the people doing proof of work are fine + + + align:start position:0% +the people doing proof of work are fine +with it + + align:start position:0% +with it + + + align:start position:0% +with it +right so like David Monday he's not + + align:start position:0% +right so like David Monday he's not + + + align:start position:0% +right so like David Monday he's not +interested in mistake haha despite the + + align:start position:0% +interested in mistake haha despite the + + + align:start position:0% +interested in mistake haha despite the +proof of work you know ecosystem being + + align:start position:0% +proof of work you know ecosystem being + + + align:start position:0% +proof of work you know ecosystem being +so crazy he's just like no this is what + + align:start position:0% +so crazy he's just like no this is what + + + align:start position:0% +so crazy he's just like no this is what +I'm doing so none of the miners are + + align:start position:0% +I'm doing so none of the miners are + + + align:start position:0% +I'm doing so none of the miners are +interest I mean you know miners their + + align:start position:0% +interest I mean you know miners their + + + align:start position:0% +interest I mean you know miners their +job is to mine so they're usually not + + align:start position:0% +job is to mine so they're usually not + + + align:start position:0% +job is to mine so they're usually not +interested in proof of steak and and + + align:start position:0% +interested in proof of steak and and + + + align:start position:0% +interested in proof of steak and and +then Bitcoin in general a lot of it's + + align:start position:0% +then Bitcoin in general a lot of it's + + + align:start position:0% +then Bitcoin in general a lot of it's +like no this seems to work we're okay + + align:start position:0% +like no this seems to work we're okay + + + align:start position:0% +like no this seems to work we're okay +with it this is the cost we're willing + + align:start position:0% +with it this is the cost we're willing + + + align:start position:0% +with it this is the cost we're willing +to bear but other people want to do + + align:start position:0% +to bear but other people want to do + + + align:start position:0% +to bear but other people want to do +other systems so further research is + + align:start position:0% +other systems so further research is + + + align:start position:0% +other systems so further research is +required or not but it's happening + + align:start position:0% +required or not but it's happening + + + align:start position:0% +required or not but it's happening +there's tons of research into different + + align:start position:0% +there's tons of research into different + + + align:start position:0% +there's tons of research into different +consensus mechanisms I would say an + + align:start position:0% +consensus mechanisms I would say an + + + align:start position:0% +consensus mechanisms I would say an +academic research that's like the + + align:start position:0% +academic research that's like the + + + align:start position:0% +academic research that's like the +biggest thing what I would like to see + + align:start position:0% +biggest thing what I would like to see + + + align:start position:0% +biggest thing what I would like to see +more of is more academic research in + + align:start position:0% +more of is more academic research in + + + align:start position:0% +more of is more academic research in +proof-of-work + + align:start position:0% +proof-of-work + + + align:start position:0% +proof-of-work +because there's a little bit but there's + + align:start position:0% +because there's a little bit but there's + + + align:start position:0% +because there's a little bit but there's +all sorts of interesting things with + + align:start position:0% +all sorts of interesting things with + + + align:start position:0% +all sorts of interesting things with +proof-of-work where it's like oh you + + align:start position:0% +proof-of-work where it's like oh you + + + align:start position:0% +proof-of-work where it's like oh you +know something like prove vital or + + align:start position:0% +know something like prove vital or + + + align:start position:0% +know something like prove vital or +something like the stuff David was + + align:start position:0% +something like the stuff David was + + + align:start position:0% +something like the stuff David was +talking about on Monday like there's not + + align:start position:0% +talking about on Monday like there's not + + + align:start position:0% +talking about on Monday like there's not +much economics research into this and I + + align:start position:0% +much economics research into this and I + + + align:start position:0% +much economics research into this and I +think it's a really interesting question + + align:start position:0% +think it's a really interesting question + + + align:start position:0% +think it's a really interesting question +where you've got like hey I've got a + + align:start position:0% +where you've got like hey I've got a + + + align:start position:0% +where you've got like hey I've got a +device that prints money and I want to + + align:start position:0% +device that prints money and I want to + + + align:start position:0% +device that prints money and I want to +sell it to you like how does that work + + align:start position:0% +sell it to you like how does that work + + + align:start position:0% +sell it to you like how does that work +in terms of economics like how much + + align:start position:0% +in terms of economics like how much + + + align:start position:0% +in terms of economics like how much +should I sell it for how much should I + + align:start position:0% +should I sell it for how much should I + + + align:start position:0% +should I sell it for how much should I +buy it for things like that um so + + align:start position:0% +buy it for things like that um so + + + align:start position:0% +buy it for things like that um so +there's a lot of new research into new + + align:start position:0% +there's a lot of new research into new + + + align:start position:0% +there's a lot of new research into new +proof of stake different consensus or + + align:start position:0% +proof of stake different consensus or + + + align:start position:0% +proof of stake different consensus or +mechanisms economics that way and not as + + align:start position:0% +mechanisms economics that way and not as + + + align:start position:0% +mechanisms economics that way and not as +much into new forms or how proof of work + + align:start position:0% +much into new forms or how proof of work + + + align:start position:0% +much into new forms or how proof of work +works which i think is actually really + + align:start position:0% +works which i think is actually really + + + align:start position:0% +works which i think is actually really +interesting \ No newline at end of file diff --git a/mJMS4mvNAag.txt b/mJMS4mvNAag.txt new file mode 100644 index 0000000000000000000000000000000000000000..69ca4490001a71cff9e202798565ce576117ae42 --- /dev/null +++ b/mJMS4mvNAag.txt @@ -0,0 +1,2787 @@ +align:start position:0% + +two other types of sampling devices i + + align:start position:0% +two other types of sampling devices i + + + align:start position:0% +two other types of sampling devices i +just want to mention here because it's a + + align:start position:0% +just want to mention here because it's a + + + align:start position:0% +just want to mention here because it's a +good place to do it + + align:start position:0% +good place to do it + + + align:start position:0% +good place to do it +an awful lot of the focus here is the + + align:start position:0% +an awful lot of the focus here is the + + + align:start position:0% +an awful lot of the focus here is the +sampling on of volatile organic + + align:start position:0% +sampling on of volatile organic + + + align:start position:0% +sampling on of volatile organic +compounds + + align:start position:0% +compounds + + + align:start position:0% +compounds +the vocs tce pce the solvents + + align:start position:0% +the vocs tce pce the solvents + + + align:start position:0% +the vocs tce pce the solvents +and so um when you pump a well to sample + + align:start position:0% +and so um when you pump a well to sample + + + align:start position:0% +and so um when you pump a well to sample +it + + align:start position:0% +it + + + align:start position:0% +it +and you got to purge that water right i + + align:start position:0% +and you got to purge that water right i + + + align:start position:0% +and you got to purge that water right i +was telling you about + + align:start position:0% +was telling you about + + + align:start position:0% +was telling you about +you end up with water that contains + + align:start position:0% +you end up with water that contains + + + align:start position:0% +you end up with water that contains +these contaminants and they're a + + align:start position:0% +these contaminants and they're a + + + align:start position:0% +these contaminants and they're a +hazardous waste in themselves so you + + align:start position:0% +hazardous waste in themselves so you + + + align:start position:0% +hazardous waste in themselves so you +can't just dump them on the ground + + align:start position:0% +can't just dump them on the ground + + + align:start position:0% +can't just dump them on the ground +so you usually have to containerize them + + align:start position:0% +so you usually have to containerize them + + + align:start position:0% +so you usually have to containerize them +bring them to a treatment plant and have + + align:start position:0% +bring them to a treatment plant and have + + + align:start position:0% +bring them to a treatment plant and have +them treated so this is your purge water + + align:start position:0% +them treated so this is your purge water + + + align:start position:0% +them treated so this is your purge water +so the objective is to try to come up + + align:start position:0% +so the objective is to try to come up + + + align:start position:0% +so the objective is to try to come up +with ways of sampling + + align:start position:0% +with ways of sampling + + + align:start position:0% +with ways of sampling +um wells without having to pump water + + align:start position:0% +um wells without having to pump water + + + align:start position:0% +um wells without having to pump water +out of them + + align:start position:0% +out of them + + + align:start position:0% +out of them +sort of passive sampling would it be + + align:start position:0% +sort of passive sampling would it be + + + align:start position:0% +sort of passive sampling would it be +nice if you could lower something down + + align:start position:0% +nice if you could lower something down + + + align:start position:0% +nice if you could lower something down +on those well screens + + align:start position:0% +on those well screens + + + align:start position:0% +on those well screens +let it sit there for a while and then + + align:start position:0% +let it sit there for a while and then + + + align:start position:0% +let it sit there for a while and then +pull it out and not have to actually + + align:start position:0% +pull it out and not have to actually + + + align:start position:0% +pull it out and not have to actually +purge any water out so + + align:start position:0% +purge any water out so + + + align:start position:0% +purge any water out so +folks have been coming up with things + + align:start position:0% +folks have been coming up with things + + + align:start position:0% +folks have been coming up with things +called the fusion devices let me step + + align:start position:0% +called the fusion devices let me step + + + align:start position:0% +called the fusion devices let me step +over here + + align:start position:0% +over here + + + align:start position:0% +over here +this is an example of one of these uh + + align:start position:0% +this is an example of one of these uh + + + align:start position:0% +this is an example of one of these uh +that's been sitting in this well since + + align:start position:0% +that's been sitting in this well since + + + align:start position:0% +that's been sitting in this well since +the last time i came and did a filter + + align:start position:0% +the last time i came and did a filter + + + align:start position:0% +the last time i came and did a filter +probably in + + align:start position:0% +probably in + + + align:start position:0% +probably in +a year ago it's like i opened up and i + + align:start position:0% +a year ago it's like i opened up and i + + + align:start position:0% +a year ago it's like i opened up and i +went huh + + align:start position:0% +went huh + + + align:start position:0% +went huh +so what we've done is we've actually + + align:start position:0% +so what we've done is we've actually + + + align:start position:0% +so what we've done is we've actually +hung a sampling device i'm gonna have + + align:start position:0% +hung a sampling device i'm gonna have + + + align:start position:0% +hung a sampling device i'm gonna have +someone just hold on to that it's a + + align:start position:0% +someone just hold on to that it's a + + + align:start position:0% +someone just hold on to that it's a +little + + align:start position:0% +little + + + align:start position:0% +little +we'll see if i can't do this in some + + align:start position:0% +we'll see if i can't do this in some + + + align:start position:0% +we'll see if i can't do this in some +sort of a rational way + + align:start position:0% + + + + align:start position:0% + +we have a sampling device hanging on the + + align:start position:0% +we have a sampling device hanging on the + + + align:start position:0% +we have a sampling device hanging on the +bottom of this i hope + + align:start position:0% +bottom of this i hope + + + align:start position:0% +bottom of this i hope +um and um the theory is this + + align:start position:0% +um and um the theory is this + + + align:start position:0% +um and um the theory is this +um the well screen is down there there + + align:start position:0% +um the well screen is down there there + + + align:start position:0% +um the well screen is down there there +it is it is an alley at the bottom i was + + align:start position:0% +it is it is an alley at the bottom i was + + + align:start position:0% +it is it is an alley at the bottom i was +kind of worried there for a minute + + align:start position:0% +kind of worried there for a minute + + + align:start position:0% +kind of worried there for a minute +it's just it's a fake one just hanging + + align:start position:0% +it's just it's a fake one just hanging + + + align:start position:0% +it's just it's a fake one just hanging +down there this would normally be + + align:start position:0% +down there this would normally be + + + align:start position:0% +down there this would normally be +hanging down on the well screen + + align:start position:0% +hanging down on the well screen + + + align:start position:0% +hanging down on the well screen +okay the idea being that the well screen + + align:start position:0% +okay the idea being that the well screen + + + align:start position:0% +okay the idea being that the well screen +is an open to the aquifer + + align:start position:0% +is an open to the aquifer + + + align:start position:0% +is an open to the aquifer +because the interior of the well is + + align:start position:0% +because the interior of the well is + + + align:start position:0% +because the interior of the well is +infinitely permeable compared to the + + align:start position:0% +infinitely permeable compared to the + + + align:start position:0% +infinitely permeable compared to the +aquifers an open hole + + align:start position:0% +aquifers an open hole + + + align:start position:0% +aquifers an open hole +groundwater if you look at freezing + + align:start position:0% +groundwater if you look at freezing + + + align:start position:0% +groundwater if you look at freezing +cherry page 279 i think it is + + align:start position:0% +cherry page 279 i think it is + + + align:start position:0% +cherry page 279 i think it is +there's actually a diagon that shows + + align:start position:0% +there's actually a diagon that shows + + + align:start position:0% +there's actually a diagon that shows +that flow lines at least in theory would + + align:start position:0% +that flow lines at least in theory would + + + align:start position:0% +that flow lines at least in theory would +converge in a well pass through the well + + align:start position:0% +converge in a well pass through the well + + + align:start position:0% +converge in a well pass through the well +and go out so the well would constantly + + align:start position:0% +and go out so the well would constantly + + + align:start position:0% +and go out so the well would constantly +be flushing itself out naturally + + align:start position:0% +be flushing itself out naturally + + + align:start position:0% +be flushing itself out naturally +because it's slowed of an infinitely + + align:start position:0% +because it's slowed of an infinitely + + + align:start position:0% +because it's slowed of an infinitely +permeable piece of the aquifer right + + align:start position:0% +permeable piece of the aquifer right + + + align:start position:0% +permeable piece of the aquifer right +there so it's like a lens it would focus + + align:start position:0% +there so it's like a lens it would focus + + + align:start position:0% +there so it's like a lens it would focus +flow through itself + + align:start position:0% +flow through itself + + + align:start position:0% +flow through itself +so you so in theory the water in the + + align:start position:0% +so you so in theory the water in the + + + align:start position:0% +so you so in theory the water in the +screen + + align:start position:0% +screen + + + align:start position:0% +screen +always represents the water in the + + align:start position:0% +always represents the water in the + + + align:start position:0% +always represents the water in the +aquifer adjacent to the screen because + + align:start position:0% +aquifer adjacent to the screen because + + + align:start position:0% +aquifer adjacent to the screen because +it naturally purges itself + + align:start position:0% +it naturally purges itself + + + align:start position:0% +it naturally purges itself +so what you do is you hang some sort of + + align:start position:0% +so what you do is you hang some sort of + + + align:start position:0% +so what you do is you hang some sort of +a diffusion device down there + + align:start position:0% +a diffusion device down there + + + align:start position:0% +a diffusion device down there +to be able to to sample that water and + + align:start position:0% +to be able to to sample that water and + + + align:start position:0% +to be able to to sample that water and +what this is is just a polyethylene bag + + align:start position:0% +what this is is just a polyethylene bag + + + align:start position:0% +what this is is just a polyethylene bag +filled with distilled water so it's + + align:start position:0% +filled with distilled water so it's + + + align:start position:0% +filled with distilled water so it's +organic free distilled water + + align:start position:0% +organic free distilled water + + + align:start position:0% +organic free distilled water +it's just regular polyethylene sandwich + + align:start position:0% +it's just regular polyethylene sandwich + + + align:start position:0% +it's just regular polyethylene sandwich +bag stuff + + align:start position:0% +bag stuff + + + align:start position:0% +bag stuff +we buy in tubes but sandwich bag and you + + align:start position:0% +we buy in tubes but sandwich bag and you + + + align:start position:0% +we buy in tubes but sandwich bag and you +fill it with di water and you lower it + + align:start position:0% +fill it with di water and you lower it + + + align:start position:0% +fill it with di water and you lower it +down to the screen this thing's bathed + + align:start position:0% +down to the screen this thing's bathed + + + align:start position:0% +down to the screen this thing's bathed +with the water going by that contains + + align:start position:0% +with the water going by that contains + + + align:start position:0% +with the water going by that contains +the solvents + + align:start position:0% +the solvents + + + align:start position:0% +the solvents +and it turns out that polyethylene is + + align:start position:0% +and it turns out that polyethylene is + + + align:start position:0% +and it turns out that polyethylene is +permeable to solvent that's why you + + align:start position:0% +permeable to solvent that's why you + + + align:start position:0% +permeable to solvent that's why you +don't sample it in plastic bottles + + align:start position:0% +don't sample it in plastic bottles + + + align:start position:0% +don't sample it in plastic bottles +you sample it in glass bottles so what + + align:start position:0% +you sample it in glass bottles so what + + + align:start position:0% +you sample it in glass bottles so what +happens is you just by diffusion + + align:start position:0% +happens is you just by diffusion + + + align:start position:0% +happens is you just by diffusion +you get you know henry's law you get + + align:start position:0% +you get you know henry's law you get + + + align:start position:0% +you get you know henry's law you get +diffusion of the solvents into here + + align:start position:0% +diffusion of the solvents into here + + + align:start position:0% +diffusion of the solvents into here +until it reaches equilibrium with the + + align:start position:0% +until it reaches equilibrium with the + + + align:start position:0% +until it reaches equilibrium with the +water on the outside + + align:start position:0% +water on the outside + + + align:start position:0% +water on the outside +so if you leave it in there long enough + + align:start position:0% +so if you leave it in there long enough + + + align:start position:0% +so if you leave it in there long enough +you can just pull this out + + align:start position:0% +you can just pull this out + + + align:start position:0% +you can just pull this out +and take this and sample it and then + + align:start position:0% +and take this and sample it and then + + + align:start position:0% +and take this and sample it and then +you've sampled your well you haven't you + + align:start position:0% +you've sampled your well you haven't you + + + align:start position:0% +you've sampled your well you haven't you +don't have to actually + + align:start position:0% +don't have to actually + + + align:start position:0% +don't have to actually +pump the well does it make sense so it's + + align:start position:0% +pump the well does it make sense so it's + + + align:start position:0% +pump the well does it make sense so it's +called a passive diffusion bag + + align:start position:0% +called a passive diffusion bag + + + align:start position:0% +called a passive diffusion bag +sampling um and uh it's being uh tested + + align:start position:0% +sampling um and uh it's being uh tested + + + align:start position:0% +sampling um and uh it's being uh tested +and it's actually being used in a number + + align:start position:0% +and it's actually being used in a number + + + align:start position:0% +and it's actually being used in a number +of places now for + + align:start position:0% +of places now for + + + align:start position:0% +of places now for +for the long-term uh monitoring program + + align:start position:0% +for the long-term uh monitoring program + + + align:start position:0% +for the long-term uh monitoring program +at uh again just for solvents + + align:start position:0% +at uh again just for solvents + + + align:start position:0% +at uh again just for solvents +things like nitrate and phosphate won't + + align:start position:0% +things like nitrate and phosphate won't + + + align:start position:0% +things like nitrate and phosphate won't +go through this but solvents will + + align:start position:0% +go through this but solvents will + + + align:start position:0% +go through this but solvents will +and usually that's what they're stuck + + align:start position:0% +and usually that's what they're stuck + + + align:start position:0% +and usually that's what they're stuck +monitoring for is solvents + + align:start position:0% +monitoring for is solvents + + + align:start position:0% +monitoring for is solvents +for these long-term programs so that's + + align:start position:0% +for these long-term programs so that's + + + align:start position:0% +for these long-term programs so that's +all there is to that this one's just it + + align:start position:0% +all there is to that this one's just it + + + align:start position:0% +all there is to that this one's just it +isn't even in the screen it's just a + + align:start position:0% +isn't even in the screen it's just a + + + align:start position:0% +isn't even in the screen it's just a +dummy one + + align:start position:0% +dummy one + + + align:start position:0% +dummy one +one of the first rules of there's a + + align:start position:0% +one of the first rules of there's a + + + align:start position:0% +one of the first rules of there's a +device called the baler which is + + align:start position:0% +device called the baler which is + + + align:start position:0% +device called the baler which is +basically a very narrow bucket that you + + align:start position:0% +basically a very narrow bucket that you + + + align:start position:0% +basically a very narrow bucket that you +could put down a well and take a sample + + align:start position:0% +could put down a well and take a sample + + + align:start position:0% +could put down a well and take a sample +with + + align:start position:0% +with + + + align:start position:0% +with +manually one of the first rules is tie + + align:start position:0% +manually one of the first rules is tie + + + align:start position:0% +manually one of the first rules is tie +the end of the rope to your wrist + + align:start position:0% +the end of the rope to your wrist + + + align:start position:0% +the end of the rope to your wrist +before you start to lower the other + + align:start position:0% +before you start to lower the other + + + align:start position:0% +before you start to lower the other +thing too is that the other thing too is + + align:start position:0% +thing too is that the other thing too is + + + align:start position:0% +thing too is that the other thing too is +that um + + align:start position:0% +that um + + + align:start position:0% +that um +all pens have a special homing device + + align:start position:0% +all pens have a special homing device + + + align:start position:0% +all pens have a special homing device +and sharpies and pens that can go down a + + align:start position:0% +and sharpies and pens that can go down a + + + align:start position:0% +and sharpies and pens that can go down a +two inch hole from any distance + + align:start position:0% +two inch hole from any distance + + + align:start position:0% +two inch hole from any distance +if you bend over right we've all + + align:start position:0% + + + + align:start position:0% + +we've all experienced that however + + align:start position:0% +we've all experienced that however + + + align:start position:0% +we've all experienced that however +happily and there's another rule that uh + + align:start position:0% +happily and there's another rule that uh + + + align:start position:0% +happily and there's another rule that uh +no matter how large a hazardous waste + + align:start position:0% +no matter how large a hazardous waste + + + align:start position:0% +no matter how large a hazardous waste +site you or or how small rather a + + align:start position:0% +site you or or how small rather a + + + align:start position:0% +site you or or how small rather a +hazardous waste site you work on + + align:start position:0% +hazardous waste site you work on + + + align:start position:0% +hazardous waste site you work on +it will be on the edge of two + + align:start position:0% +it will be on the edge of two + + + align:start position:0% +it will be on the edge of two +topographic that's right + + align:start position:0% +topographic that's right + + + align:start position:0% +topographic that's right +the topographic maps are this big and + + align:start position:0% +the topographic maps are this big and + + + align:start position:0% +the topographic maps are this big and +your site is that big it's gonna be + + align:start position:0% +your site is that big it's gonna be + + + align:start position:0% +your site is that big it's gonna be +right on the edge + + align:start position:0% +right on the edge + + + align:start position:0% +right on the edge +usually in the corner of four + + align:start position:0% + + + + align:start position:0% + +i'm just gonna tighten these up while + + align:start position:0% +i'm just gonna tighten these up while + + + align:start position:0% +i'm just gonna tighten these up while +i'm here we don't have too much problems + + align:start position:0% +i'm here we don't have too much problems + + + align:start position:0% +i'm here we don't have too much problems +with vandalism but + + align:start position:0% +with vandalism but + + + align:start position:0% +with vandalism but +we don't we don't take our chances too + + align:start position:0% +we don't we don't take our chances too + + + align:start position:0% +we don't we don't take our chances too +much um + + align:start position:0% +much um + + + align:start position:0% +much um +let me just check my hand out here see + + align:start position:0% +let me just check my hand out here see + + + align:start position:0% +let me just check my hand out here see +if there's anything else i wanted to + + align:start position:0% +if there's anything else i wanted to + + + align:start position:0% +if there's anything else i wanted to +bring up oh yeah there is + + align:start position:0% + + + + align:start position:0% + +candy corn i mentioned that these uh + + align:start position:0% +candy corn i mentioned that these uh + + + align:start position:0% +candy corn i mentioned that these uh +i mentioned that these diffusion + + align:start position:0% +i mentioned that these diffusion + + + align:start position:0% +i mentioned that these diffusion +samplers don't work for anything but the + + align:start position:0% +samplers don't work for anything but the + + + align:start position:0% +samplers don't work for anything but the +volatile organics which will go through + + align:start position:0% +volatile organics which will go through + + + align:start position:0% +volatile organics which will go through +the plastic + + align:start position:0% +the plastic + + + align:start position:0% +the plastic +uh and of course there's a great + + align:start position:0% +uh and of course there's a great + + + align:start position:0% +uh and of course there's a great +interest in could could diffusion + + align:start position:0% +interest in could could diffusion + + + align:start position:0% +interest in could could diffusion +sampling be used for + + align:start position:0% +sampling be used for + + + align:start position:0% +sampling be used for +could other types of membranes be useful + + align:start position:0% +could other types of membranes be useful + + + align:start position:0% +could other types of membranes be useful +for sampling say metals + + align:start position:0% +for sampling say metals + + + align:start position:0% +for sampling say metals +or things that won't go through + + align:start position:0% +or things that won't go through + + + align:start position:0% +or things that won't go through +polyethylene and there's a number of + + align:start position:0% +polyethylene and there's a number of + + + align:start position:0% +polyethylene and there's a number of +folks experimenting with this right now + + align:start position:0% +folks experimenting with this right now + + + align:start position:0% +folks experimenting with this right now +this is a a a pretty new type of + + align:start position:0% +this is a a a pretty new type of + + + align:start position:0% +this is a a a pretty new type of +diffusion sampler someone's come up with + + align:start position:0% +diffusion sampler someone's come up with + + + align:start position:0% +diffusion sampler someone's come up with +this is porous polyethylene it doesn't + + align:start position:0% +this is porous polyethylene it doesn't + + + align:start position:0% +this is porous polyethylene it doesn't +look very porous + + align:start position:0% +look very porous + + + align:start position:0% +look very porous +but it's actually made up of little + + align:start position:0% +but it's actually made up of little + + + align:start position:0% +but it's actually made up of little +beads of polyethylene that have been + + align:start position:0% +beads of polyethylene that have been + + + align:start position:0% +beads of polyethylene that have been +squished together + + align:start position:0% +squished together + + + align:start position:0% +squished together +and it's actually the material how many + + align:start position:0% +and it's actually the material how many + + + align:start position:0% +and it's actually the material how many +of you have a fish aquarium and you have + + align:start position:0% +of you have a fish aquarium and you have + + + align:start position:0% +of you have a fish aquarium and you have +a fish aquarium and you have a little + + align:start position:0% +a fish aquarium and you have a little + + + align:start position:0% +a fish aquarium and you have a little +diffuser + + align:start position:0% +diffuser + + + align:start position:0% +diffuser +that bubbles and it's a little white + + align:start position:0% +that bubbles and it's a little white + + + align:start position:0% +that bubbles and it's a little white +tube like this sometimes this is really + + align:start position:0% +tube like this sometimes this is really + + + align:start position:0% +tube like this sometimes this is really +uh + + align:start position:0% +uh + + + align:start position:0% +uh +it's just a porous polyethylene with + + align:start position:0% +it's just a porous polyethylene with + + + align:start position:0% +it's just a porous polyethylene with +large pores + + align:start position:0% +large pores + + + align:start position:0% +large pores +and so um what you do is you fill this + + align:start position:0% +and so um what you do is you fill this + + + align:start position:0% +and so um what you do is you fill this +with distilled water just like the other + + align:start position:0% +with distilled water just like the other + + + align:start position:0% +with distilled water just like the other +sampler + + align:start position:0% +sampler + + + align:start position:0% +sampler +and of course you shut these little + + align:start position:0% +and of course you shut these little + + + align:start position:0% +and of course you shut these little +valves and you lower it down in your + + align:start position:0% +valves and you lower it down in your + + + align:start position:0% +valves and you lower it down in your +screen + + align:start position:0% +screen + + + align:start position:0% +screen +and it turns out that even our + + align:start position:0% +and it turns out that even our + + + align:start position:0% +and it turns out that even our +inorganics will go through this metals + + align:start position:0% +inorganics will go through this metals + + + align:start position:0% +inorganics will go through this metals +and large large organic molecules and in + + align:start position:0% +and large large organic molecules and in + + + align:start position:0% +and large large organic molecules and in +particular we're testing it right now + + align:start position:0% +particular we're testing it right now + + + align:start position:0% +particular we're testing it right now +looking for explosives compounds + + align:start position:0% +looking for explosives compounds + + + align:start position:0% +looking for explosives compounds +we have an experiment we're running up + + align:start position:0% +we have an experiment we're running up + + + align:start position:0% +we have an experiment we're running up +on the base where we're seeing if we + + align:start position:0% +on the base where we're seeing if we + + + align:start position:0% +on the base where we're seeing if we +can't + + align:start position:0% +can't + + + align:start position:0% +can't +again they have the problem of having to + + align:start position:0% +again they have the problem of having to + + + align:start position:0% +again they have the problem of having to +pump up this water and then having to + + align:start position:0% +pump up this water and then having to + + + align:start position:0% +pump up this water and then having to +treat it + + align:start position:0% +treat it + + + align:start position:0% +treat it +uh and also uh anytime you start to + + align:start position:0% +uh and also uh anytime you start to + + + align:start position:0% +uh and also uh anytime you start to +bring pumps out you have to have a truck + + align:start position:0% +bring pumps out you have to have a truck + + + align:start position:0% +bring pumps out you have to have a truck +and they're they're hoping to get to the + + align:start position:0% +and they're they're hoping to get to the + + + align:start position:0% +and they're they're hoping to get to the +point where a guy with a backpack + + align:start position:0% +point where a guy with a backpack + + + align:start position:0% +point where a guy with a backpack +will have a bunch of these he'll run out + + align:start position:0% +will have a bunch of these he'll run out + + + align:start position:0% +will have a bunch of these he'll run out +or she'll run out + + align:start position:0% +or she'll run out + + + align:start position:0% +or she'll run out +you know pull out the old one fill the + + align:start position:0% +you know pull out the old one fill the + + + align:start position:0% +you know pull out the old one fill the +bottles put the new ones down and leave + + align:start position:0% +bottles put the new ones down and leave + + + align:start position:0% +bottles put the new ones down and leave +and it could just be a person on foot + + align:start position:0% +and it could just be a person on foot + + + align:start position:0% +and it could just be a person on foot +doing sampling + + align:start position:0% +doing sampling + + + align:start position:0% +doing sampling +so we're experimenting to see whether we + + align:start position:0% +so we're experimenting to see whether we + + + align:start position:0% +so we're experimenting to see whether we +can do long-term monitoring of + + align:start position:0% +can do long-term monitoring of + + + align:start position:0% +can do long-term monitoring of +other compounds like like uh the uh + + align:start position:0% +other compounds like like uh the uh + + + align:start position:0% +other compounds like like uh the uh +aromatic explosive compounds or + + align:start position:0% +aromatic explosive compounds or + + + align:start position:0% +aromatic explosive compounds or +perchlorate + + align:start position:0% +perchlorate + + + align:start position:0% +perchlorate +you know using these kinds of devices so + + align:start position:0% +you know using these kinds of devices so + + + align:start position:0% +you know using these kinds of devices so +uh that hasn't uh + + align:start position:0% +uh that hasn't uh + + + align:start position:0% +uh that hasn't uh +they work in the lab but uh everything + + align:start position:0% +they work in the lab but uh everything + + + align:start position:0% +they work in the lab but uh everything +has to be tried in the field + + align:start position:0% +has to be tried in the field + + + align:start position:0% +has to be tried in the field +yeah is there any way you can put a + + align:start position:0% +yeah is there any way you can put a + + + align:start position:0% +yeah is there any way you can put a +material in there that would act like a + + align:start position:0% +material in there that would act like a + + + align:start position:0% +material in there that would act like a +magnet + + align:start position:0% +magnet + + + align:start position:0% +magnet +for the crap um actually that + + align:start position:0% +for the crap um actually that + + + align:start position:0% +for the crap um actually that +the whole idea comes from exactly that + + align:start position:0% +the whole idea comes from exactly that + + + align:start position:0% +the whole idea comes from exactly that +um they've used um + + align:start position:0% +um they've used um + + + align:start position:0% +um they've used um +have you ever done this eric you know + + align:start position:0% +have you ever done this eric you know + + + align:start position:0% +have you ever done this eric you know +they + + align:start position:0% +they + + + align:start position:0% +they +they uh when they're looking for things + + align:start position:0% +they uh when they're looking for things + + + align:start position:0% +they uh when they're looking for things +like pcbs and rivers + + align:start position:0% +like pcbs and rivers + + + align:start position:0% +like pcbs and rivers +they have these um i feel what they call + + align:start position:0% +they have these um i feel what they call + + + align:start position:0% +they have these um i feel what they call +them + + align:start position:0% +them + + + align:start position:0% +them +do you remember huh where they put the + + align:start position:0% +do you remember huh where they put the + + + align:start position:0% +do you remember huh where they put the +little things on with the with the uh + + align:start position:0% +little things on with the with the uh + + + align:start position:0% +little things on with the with the uh +the lipids and it + + align:start position:0% +the lipids and it + + + align:start position:0% +the lipids and it +it absorbs the uh + + align:start position:0% + + + + align:start position:0% + +i don't remember the name of it people + + align:start position:0% +i don't remember the name of it people + + + align:start position:0% +i don't remember the name of it people +have done this they actually have a + + align:start position:0% +have done this they actually have a + + + align:start position:0% +have done this they actually have a +chamber filled with a particular + + align:start position:0% +chamber filled with a particular + + + align:start position:0% +chamber filled with a particular +material + + align:start position:0% +material + + + align:start position:0% +material +that absorbs a contaminant of interest + + align:start position:0% +that absorbs a contaminant of interest + + + align:start position:0% +that absorbs a contaminant of interest +and they've done that a lot in streams + + align:start position:0% +and they've done that a lot in streams + + + align:start position:0% +and they've done that a lot in streams +looking for pcbs and stuff like + + align:start position:0% +looking for pcbs and stuff like + + + align:start position:0% +looking for pcbs and stuff like +permeable bags yeah semi-permeable bags + + align:start position:0% +permeable bags yeah semi-permeable bags + + + align:start position:0% +permeable bags yeah semi-permeable bags +uh or they have blocks of material that + + align:start position:0% +uh or they have blocks of material that + + + align:start position:0% +uh or they have blocks of material that +will + + align:start position:0% +will + + + align:start position:0% +will +eventually store the contaminants in is + + align:start position:0% +eventually store the contaminants in is + + + align:start position:0% +eventually store the contaminants in is +that you can actually clean up + + align:start position:0% +that you can actually clean up + + + align:start position:0% +that you can actually clean up +uh the quantities are just too tiny yeah + + align:start position:0% +uh the quantities are just too tiny yeah + + + align:start position:0% +uh the quantities are just too tiny yeah +it's more for sampling + + align:start position:0% +it's more for sampling + + + align:start position:0% +it's more for sampling +i mean now the way they clean up the + + align:start position:0% +i mean now the way they clean up the + + + align:start position:0% +i mean now the way they clean up the +water is to run it through activated + + align:start position:0% +water is to run it through activated + + + align:start position:0% +water is to run it through activated +carbon + + align:start position:0% +carbon + + + align:start position:0% +carbon +they have big huge carbon vessels they + + align:start position:0% +they have big huge carbon vessels they + + + align:start position:0% +they have big huge carbon vessels they +pump up the contaminated water and they + + align:start position:0% +pump up the contaminated water and they + + + align:start position:0% +pump up the contaminated water and they +run it through activated carbon and soar + + align:start position:0% +run it through activated carbon and soar + + + align:start position:0% +run it through activated carbon and soar +about so yeah on that scale + + align:start position:0% +about so yeah on that scale + + + align:start position:0% +about so yeah on that scale +but that's on the scale of you know + + align:start position:0% +but that's on the scale of you know + + + align:start position:0% +but that's on the scale of you know +massive buildings not + + align:start position:0% +massive buildings not + + + align:start position:0% +massive buildings not +well at a time okay + + align:start position:0% +well at a time okay + + + align:start position:0% +well at a time okay +all right yeah if the suction pump works + + align:start position:0% +all right yeah if the suction pump works + + + align:start position:0% +all right yeah if the suction pump works +so well why do you go to the trouble of + + align:start position:0% +so well why do you go to the trouble of + + + align:start position:0% +so well why do you go to the trouble of +getting a + + align:start position:0% +getting a + + + align:start position:0% +getting a +really complicated pump that comes + + align:start position:0% +really complicated pump that comes + + + align:start position:0% +really complicated pump that comes +because at the top of the hill the + + align:start position:0% +because at the top of the hill the + + + align:start position:0% +because at the top of the hill the +suction pot won't work anymore + + align:start position:0% +suction pot won't work anymore + + + align:start position:0% +suction pot won't work anymore +how far can you lift water + + align:start position:0% +how far can you lift water + + + align:start position:0% +how far can you lift water +33 theoretically right + + align:start position:0% +33 theoretically right + + + align:start position:0% +33 theoretically right +well just also because it's hard to pull + + align:start position:0% +well just also because it's hard to pull + + + align:start position:0% +well just also because it's hard to pull +a perfect vacuum you can lift water with + + align:start position:0% +a perfect vacuum you can lift water with + + + align:start position:0% +a perfect vacuum you can lift water with +a suction pump uh + + align:start position:0% +a suction pump uh + + + align:start position:0% +a suction pump uh +basically uh at sea level here about + + align:start position:0% +basically uh at sea level here about + + + align:start position:0% +basically uh at sea level here about +theoretically about 32 feet + + align:start position:0% +theoretically about 32 feet + + + align:start position:0% +theoretically about 32 feet +practically most pumps have a hard time + + align:start position:0% +practically most pumps have a hard time + + + align:start position:0% +practically most pumps have a hard time +after about 29. our peristal + + align:start position:0% +after about 29. our peristal + + + align:start position:0% +after about 29. our peristal +we actually ran an experiment here one + + align:start position:0% +we actually ran an experiment here one + + + align:start position:0% +we actually ran an experiment here one +time we got a big tall ladder + + align:start position:0% +time we got a big tall ladder + + + align:start position:0% +time we got a big tall ladder +and uh we uh took the peristellic pump + + align:start position:0% +and uh we uh took the peristellic pump + + + align:start position:0% +and uh we uh took the peristellic pump +and we just walked up the ladder and we + + align:start position:0% +and we just walked up the ladder and we + + + align:start position:0% +and we just walked up the ladder and we +walked it up until it wouldn't pump + + align:start position:0% +walked it up until it wouldn't pump + + + align:start position:0% +walked it up until it wouldn't pump +anymore + + align:start position:0% +anymore + + + align:start position:0% +anymore +and it was about 29 29 feet it just + + align:start position:0% +and it was about 29 29 feet it just + + + align:start position:0% +and it was about 29 29 feet it just +couldn't produce enough of a pull + + align:start position:0% +couldn't produce enough of a pull + + + align:start position:0% +couldn't produce enough of a pull +once you get beyond that you're pulling + + align:start position:0% +once you get beyond that you're pulling + + + align:start position:0% +once you get beyond that you're pulling +a perfect vacuum like a barometer + + align:start position:0% +a perfect vacuum like a barometer + + + align:start position:0% +a perfect vacuum like a barometer +so then you need to put something down + + align:start position:0% +so then you need to put something down + + + align:start position:0% +so then you need to put something down +the hole and push the water out + + align:start position:0% +the hole and push the water out + + + align:start position:0% +the hole and push the water out +you actually will vaporize the water + + align:start position:0% +you actually will vaporize the water + + + align:start position:0% +you actually will vaporize the water +yeah the water will just boil + + align:start position:0% +yeah the water will just boil + + + align:start position:0% +yeah the water will just boil +yeah but you can't get that perfect to + + align:start position:0% +yeah but you can't get that perfect to + + + align:start position:0% +yeah but you can't get that perfect to +vacuum it's really hard to do so + + align:start position:0% +vacuum it's really hard to do so + + + align:start position:0% +vacuum it's really hard to do so +for example we didn't do it today but + + align:start position:0% +for example we didn't do it today but + + + align:start position:0% +for example we didn't do it today but +when you walk up on the hill instead of + + align:start position:0% +when you walk up on the hill instead of + + + align:start position:0% +when you walk up on the hill instead of +multi levels like that you see clusters + + align:start position:0% +multi levels like that you see clusters + + + align:start position:0% +multi levels like that you see clusters +of 10 wells + + align:start position:0% +of 10 wells + + + align:start position:0% +of 10 wells +and there are devices that will go down + + align:start position:0% +and there are devices that will go down + + + align:start position:0% +and there are devices that will go down +smaller diameter + + align:start position:0% +smaller diameter + + + align:start position:0% +smaller diameter +multi-level samples we found that + + align:start position:0% +multi-level samples we found that + + + align:start position:0% +multi-level samples we found that +they're um + + align:start position:0% +they're um + + + align:start position:0% +they're um +they're prone to being plugged by little + + align:start position:0% +they're prone to being plugged by little + + + align:start position:0% +they're prone to being plugged by little +pieces of grit + + align:start position:0% +pieces of grit + + + align:start position:0% +pieces of grit +you know in other words they look great + + align:start position:0% +you know in other words they look great + + + align:start position:0% +you know in other words they look great +on paper and they just never work for a + + align:start position:0% +on paper and they just never work for a + + + align:start position:0% +on paper and they just never work for a +very long time + + align:start position:0% +very long time + + + align:start position:0% +very long time +so we just when we're when we're below + + align:start position:0% +so we just when we're when we're below + + + align:start position:0% +so we just when we're when we're below +suck when we're too deep to water to use + + align:start position:0% +suck when we're too deep to water to use + + + align:start position:0% +suck when we're too deep to water to use +a multi-level sampler we just put in + + align:start position:0% +a multi-level sampler we just put in + + + align:start position:0% +a multi-level sampler we just put in +clusters of wells you just live with + + align:start position:0% +clusters of wells you just live with + + + align:start position:0% +clusters of wells you just live with +that limitation one of the things to + + align:start position:0% +that limitation one of the things to + + + align:start position:0% +that limitation one of the things to +kind of get a feel for too is + + align:start position:0% +kind of get a feel for too is + + + align:start position:0% +kind of get a feel for too is +as you watch all this is how much + + align:start position:0% +as you watch all this is how much + + + align:start position:0% +as you watch all this is how much +planning has gone into being able to do + + align:start position:0% +planning has gone into being able to do + + + align:start position:0% +planning has gone into being able to do +this efficiently + + align:start position:0% +this efficiently + + + align:start position:0% +this efficiently +you know there's an awful lot of detail + + align:start position:0% +you know there's an awful lot of detail + + + align:start position:0% +you know there's an awful lot of detail +required to do field work + + align:start position:0% +required to do field work + + + align:start position:0% +required to do field work +and these folks are these folks are + + align:start position:0% +and these folks are these folks are + + + align:start position:0% +and these folks are these folks are +whizzes headed i mean + + align:start position:0% +whizzes headed i mean + + + align:start position:0% +whizzes headed i mean +they've done it a lot and they've really + + align:start position:0% +they've done it a lot and they've really + + + align:start position:0% +they've done it a lot and they've really +worked out a routine but um + + align:start position:0% +worked out a routine but um + + + align:start position:0% +worked out a routine but um +field work requires a lot of careful + + align:start position:0% +field work requires a lot of careful + + + align:start position:0% +field work requires a lot of careful +work and a lot of attention to detail + + align:start position:0% +work and a lot of attention to detail + + + align:start position:0% +work and a lot of attention to detail +and you know + + align:start position:0% +and you know + + + align:start position:0% +and you know +things like bungee cords on you know + + align:start position:0% +things like bungee cords on you know + + + align:start position:0% +things like bungee cords on you know +spools so they don't run + + align:start position:0% +spools so they don't run + + + align:start position:0% +spools so they don't run +loose and all that kind of stuff it just + + align:start position:0% +loose and all that kind of stuff it just + + + align:start position:0% +loose and all that kind of stuff it just +um it takes a lot of time to develop + + align:start position:0% +um it takes a lot of time to develop + + + align:start position:0% +um it takes a lot of time to develop +those techniques so that you can do this + + align:start position:0% +those techniques so that you can do this + + + align:start position:0% +those techniques so that you can do this +quickly and efficiently + + align:start position:0% +quickly and efficiently + + + align:start position:0% +quickly and efficiently +we'll see a real good example of that in + + align:start position:0% +we'll see a real good example of that in + + + align:start position:0% +we'll see a real good example of that in +a minute let's + + align:start position:0% +a minute let's + + + align:start position:0% +a minute let's +discover their contamination and then + + align:start position:0% +discover their contamination and then + + + align:start position:0% +discover their contamination and then +the uh cleanup of the + + align:start position:0% +the uh cleanup of the + + + align:start position:0% +the uh cleanup of the +most of the plumes is is a it's it's the + + align:start position:0% +most of the plumes is is a it's it's the + + + align:start position:0% +most of the plumes is is a it's it's the +military's version of superfund it does + + align:start position:0% +military's version of superfund it does + + + align:start position:0% +military's version of superfund it does +fall into the superfund laws + + align:start position:0% +fall into the superfund laws + + + align:start position:0% +fall into the superfund laws +but it's not it's it's uh it's the + + align:start position:0% +but it's not it's it's uh it's the + + + align:start position:0% +but it's not it's it's uh it's the +military's cleanup program + + align:start position:0% +military's cleanup program + + + align:start position:0% +military's cleanup program +um and then uh the impact area the stuff + + align:start position:0% +um and then uh the impact area the stuff + + + align:start position:0% +um and then uh the impact area the stuff +with explosives and + + align:start position:0% +with explosives and + + + align:start position:0% +with explosives and +perchlorate is actually uh different + + align:start position:0% +perchlorate is actually uh different + + + align:start position:0% +perchlorate is actually uh different +that's under the safe drinking water act + + align:start position:0% +that's under the safe drinking water act + + + align:start position:0% +that's under the safe drinking water act +because it's considered present activity + + align:start position:0% +because it's considered present activity + + + align:start position:0% +because it's considered present activity +so it doesn't superfund's only clean up + + align:start position:0% +so it doesn't superfund's only clean up + + + align:start position:0% +so it doesn't superfund's only clean up +of old stuff and that's considered a + + align:start position:0% +of old stuff and that's considered a + + + align:start position:0% +of old stuff and that's considered a +present day activity + + align:start position:0% +present day activity + + + align:start position:0% +present day activity +so that's actually being regulated + + align:start position:0% +so that's actually being regulated + + + align:start position:0% +so that's actually being regulated +underneath the clean drinking water act + + align:start position:0% +underneath the clean drinking water act + + + align:start position:0% +underneath the clean drinking water act +so there's multiple and it's all dod + + align:start position:0% +so there's multiple and it's all dod + + + align:start position:0% +so there's multiple and it's all dod +money except for the usgs research money + + align:start position:0% +money except for the usgs research money + + + align:start position:0% +money except for the usgs research money +it's all + + align:start position:0% +it's all + + + align:start position:0% +it's all +department of defense money they think + + align:start position:0% +department of defense money they think + + + align:start position:0% +department of defense money they think +they're going to spend about 1.5 billion + + align:start position:0% +they're going to spend about 1.5 billion + + + align:start position:0% +they're going to spend about 1.5 billion +before they're finished + + align:start position:0% +before they're finished + + + align:start position:0% +before they're finished +which sounds like a lot but in the + + align:start position:0% +which sounds like a lot but in the + + + align:start position:0% +which sounds like a lot but in the +scheme of things + + align:start position:0% +scheme of things + + + align:start position:0% +scheme of things +percent of a big dig yeah one \ No newline at end of file diff --git a/mNGVkKeMUtc.txt b/mNGVkKeMUtc.txt new file mode 100644 index 0000000000000000000000000000000000000000..97a090567342573304a2dccde6ecef5a9d2e40ef --- /dev/null +++ b/mNGVkKeMUtc.txt @@ -0,0 +1,3718 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: OK. + +Today we're going to finish +up with Markov chains. + +And the last topic will be +dynamic programming. + +I'm not going to say an awful +lot about dynamic programming. + +It's a topic that was enormously +important in + +research for probably 20 +years from 1960 until + +about 1980, or 1990. + +And it seemed as if half the +Ph.D. theses done in the + +control area and the +operations research + +were in this area. + +Suddenly, everything seemed +to be done, could be done. + +And strangely enough, not +many people seem to + +know about it anymore. + +It's an enormously useful +algorithm for solving an awful + +lot of different problems. + +It's quite a simple algorithm. + +You don't need the full power +of Markov chains in order to + +understand it. + +So I do want to at least talk +about it a little bit. + +And we will use what we've done +so far with Markov chains + +in order to understand it. + +I want to start out today by +reviewing a little bit of what + +we did last time about +eigenvalues and eigenvectors. + +This was a somewhat awkward +topic to talk about, because + +you people have very different +backgrounds in linear algebra. + +Some of you have a very strong +background, some of you have + +almost no background. + +So it was a lot of material for +those of you who know very + +little about linear algebra. + +And probably somewhat boring +for those of you + +use it all the time. + +At any rate, if you don't know +anything about it, linear + +algebra is a topic that you +ought to understand for almost + +anything you do. + +If you've gotten to this point +without having to study it, + +it's very strange. + +So you should probably take +some extra time out, not + +because you need it so +much for this course. + +We won't use it enormously +in many of the + +things we do later. + +But you will use it so many +times in the future that you + +ought to just sit down, not to +learn abstract linear algebra, + +which is very useful also, but +just to learn how to use the + +topic of solving linear +equations. + +Being able to express them +in terms of matrices. + +Being able to use the +eigenvalues and eigenvectors, + +and matrices as a way of +understanding these things. + +So I want to say a little more +about that today, which is why + +I've called this a review +plus of eigenvalues and + +eigenvectors. + +It's a review of the topics +we did last time, but it's + +looking at it in a somewhat +different way. + +So let's proceed with that. + +We said that the determinant of +an M by M matrix is given + +by this strange formula. + +The determinant of a is the sum +over all permutations of + +the integers 1 to M of the +product from i equals 1 to M + +of the matrix element +a sub i mu of i. + +Mu of i is the permutation of +the number i. i is between one + +and M, and mu of i is a +permutation of that. + +Now if you look at the matrix, +which has the form, which is + +block upper diagonal. + +In other words, there's a matrix +here, a square matrix a + +sub t, which is a transient +matrix. + +There's a recurrent matrix here, +and there's some way of + +getting from the transient +states to + +the recurring states. + +And this is the general form +that a unit chain has to have. + +There are a bunch of transient +states, there are a bunch of + +recurring states. + +And the interesting thing here +is that the determinant of a + +is exactly the determinant +of a sub t times the + +determinant a sub r. + +I'm calling this a instead of +the transition matrix p + +because I want to replace a by +p minus lambda i, so I can + +talk about the eigenvalues +of p. + +So when I do that replacement +here, if I know that the + +determinant of a is this product +of determinants, then + +the determinant of p minus +lambda i is the determinant of + +pt minus lambda it, where it is +just a crazy way of saying + +a diagonal matrix. + +A diagonal t by t matrix, +because this is a t by t + +matrix, also. + +i sub r is an r by r matrix, +where this is a square r by r + +matrix also. + +Now, why is it that this +determinant is equal to this + +product of determinants here? + +Well, before explaining why this +is true, why do you care? + +Well, because we know that if +we have a recurring matrix + +here, we know that it has-- + +I mean, we know a great +deal about it. + +We know that any square matrix, +r by r matrix has r + +different eigenvalues. + +Some of them might be repeated, +but they're always r + +eigenvalues. + +This matrix here has +t eigenvalues. + +OK. + +This matrix here, we know has +r plus t eigenvalues. + +You look at this formula here +and you say aha, I can take + +all the eigenvalues here, add +them to all the eigenvalues + +here, and I have every one +of the eigenvalues here. + +In other words, if I want to +find all of the eigenvalues of + +p, all I have to do is define +the eigenvalues of p sub t, + +add them to the eigenvalues of +p sub r, and I'm all done. + +So that really has simplified +things a good deal. + +And it also really says +explicitly that if you + +understand how to deal with +recurrent Markov chains, you + +really know everything. + +Well, you also have to know how +to deal with a transient + +chain, but the main part of it +is dealing with this chain. + +This has little r different +eigenvalues, and all of those + +are eigenvalues, excuse me, +p sub r has little r + +eigenvalues. + +They're given by the roots +of this determinant here. + +And all of those +are roots here. + +OK, so why is this true? + +Well, the reason for it is that +this product up here, + +look at this. + +We're taking the sum over +all permutations. + +But which one of those +permutations can be non-zero? + +If I start out by saying that a +sub t is t by t, then I know + +that this might be anything. + +These have to be zeroes here. + +If I choose some permutation of +down here, of sum i, which + +is greater than t. + +In other words, if I choose +mu o i to be some + +element over here. + +If I choose mu of i to be less +than our equal to t, and i to + +be greater than t, +what happens? + +I get a term which +is equal to zero. + +That term in this +product is zero. + +And none of those products +can be zero. + +So the only way I can get non +zeros here is when I'm dealing + +with an i which is less +than or equal to t. + +Namely an i here. + +I have to choose a mu of +i, a column which is + +less than t, also. + +If I'm dealing with an i which +is greater than t, namely and + +i up here, then, well, it +looks like I can choose + +anything there. + +But look. + +I've already used up all of +these columns here by the five + +by the non-zero terms here. + +So I can't do anything +but use a smaller i, + +smaller than t up here. + +So when I look at the +permutations that are non + +zero, the only permutations that +are non zero are those + +where mu of i is less than t if +i less than t, and mu of i + +is less than or equal to t if i +is less than or equal to t. + +And mu of i is greater than +t if i is greater than t. + +Now, how does that show that +this is equal here? + +Well, let's look at +that a little bit. + +I didn't even try to do it on +the slide because the notation + +is kind of horrifying. + +But let's try to write this +the following way. + +Determinant of a is equal to the +sum, and now I'll write it + +as a sum over mu of 1 up to t. + +And the sum over mu of t +plus 1 up to, well, t + +plus r, let's say. + +OK, so here I have all of +the permutations of the + +numbers 1 to t. + +And here I have all the +permutations of the + +numbers t plus 1 up. + +And for all of those, +I'm going to + +ignore this plus minus. + +You can sort that out +for yourselves. + +And then I have a product +from i equals 1 to t. + +And then a product from i +equals t plus 1 up to m. + +Excuse me. + +i sub i, mu of i times +product of a of i. + +Mu of i for i equals t plus +1 up to t plus r. + +OK? + +So I'm separating this product +here into a product first of + +the terms i less than or equal +to t, and then for the terms i + +greater than t. + +For every permutation I choose +using the i's that are less + +than or equal to t, I can choose +any of the permutation + +using mu of i greater than +t that I choose to use. + +So this breaks up in this way. + +I have this sum, I +have this sum. + +I have these two products, so +I can break this up as a sum + +over mu of 1 to t of plus minus +product from i equals 1 + +to t of ai, mu of i times the +sum over mu of t plus 1 up to + +t plus r ai mu of i. + +Product. + +OK. + +So I've separated that into +two different terms. + +STUDENT: T equals [INAUDIBLE]. + +PROFESSOR: What? + +STUDENT: T plus r +equals big m? + +PROFESSOR: T plus +r is big m, yes. + +Because I have t terms here, +and I have r terms here. + +OK, so the interesting thing +here is having this non-zero + +term here doesn't make +any difference here. + +I mean, this is more +straightforward if you have a + +block diagonal matrix. + +It's clear that the eigenvalues +of a block + +diagonal matrix are going to be +the eigenvalues of 1 plus + +the eigenvalues of the other. + +Here we have the eigenvalues +of this, and the + +eigenvalues is this. + +And what's surprising is that as +far as the eigenvalues are + +concerned, this has nothing +whatsoever to do with it. + +OK. + +The only thing that this has +to do with it is it says + +something about the sums of this +matrix here, because the + +sums of these rows are +now less than 1. + +They all have to be, some of +them, at least, have to be + +less than or equal to 1. + +Because you do have this way of +getting from the transient + +elements to the non transient +elements. + +But it's very surprising that +these elements, which are + +critically important, because +those are the things that get + +you from the transition states +to the recurrent states have + +nothing to do in the eigenvalues +whatsoever. + +I don't know why. + +I can't give you any insights +about that, but + +that's the way it is. + +That's an interesting thing, +because if you take this + +transition matrix, and you keep +at and a sub r fixed, and + +you play any kind of funny game +you want to with those + +terms going from the transient +states to the non transient + +states, it won't change +any eigenvalues. + +Don't know why it doesn't. + +OK, so where do we +go with that? + +Well, that's what it says. + +The eigenvalues of p, or the t +eigenvalues of pt, and the r + +eigenvalues of PR. + +It also tells you something +about simple eigenvalues, and + +these crazy eigenvalues, which +don't have enough eigenvectors + +to go along with them. + +Because it tells you that a +piece of r has all of its + +eigenvectors, and a piece of t +has all of its eigenvectors. + +Then you don't have any of this +crazy [INAUDIBLE] form + +thing, or anything. + +OK If pi is a left eigenvector +of this recurrent matrix, then + +if you look at the vector, +starting was zeros, and then I + +guess I should really say, well, +if pi sub 1 up to pi sub + +r as a left eigenvalue of this r +by r matrix, then if I start + +out with t zeroes, and then +put in pi 1 to pi r, this + +vector here has to be a left +eigenvector of all of p. + +Why is that? + +Well, if I look at a vector, +which starts out with zeroes, + +and then has this eigenvector +pi, and I multiply that vector + +by this matrix here, I'm +taking these terms, + +multiplying them by the columns +of this matrix, these + +zeros knock out all of +these elements here. + +These zeroes knock out all +of these elements. + +So I start out with zeroes +everywhere here. + +That's what this says. + +And then when I'm dealing with +this part of the matrix, the + +zeros knock out all of this, and +I just have pi multiplying + +piece of r. + +So if I have an eigenvalue +lambda, it says I have the + +eigenvalue lambda times a +vector zero times pi. + +It says that if I have an +eigenvector, a left + +eigenvector of this recurrent +matrix, then that turns into, + +if you put some zeroes up in +front of, it turns into an + +eigenvector of the +whole matrix. + +If we look at the eigenvalue 1, +which is the most important + +thing this, is the thing that +gives you the steady state + +factor, this is sort +of obvious. + +Because the steady state +vector is where you go + +eventually, and eventually where +you go is you have to be + +in one of these recurrent +states, eventually. + +And the probabilities within +the recurrent set of states + +are the same as the +probabilities if you didn't + +have this transient +states at all. + +so this is all sort of obvious, +as far as the steady + +state factor pi. + +But it's a little less obvious +as far as the other vectors. + +The left eigenvectors, +a piece of t, I don't + +understand them at all. + +They aren't the same as the left +eigenvectors of, well, + +the left eigenvectors of the +eigenvalues of p sub t. + +I didn't say this right here. + +The left eigenvectors of p +corresponding to the left + +eigenvectors of p sub t. + +I don't understand how they +work, and I don't understand + +anything you can derive +from them. + +They're just kind of crazy +things, which are what they + +happen to be. + +And I don't care about them. + +I don't know anything +to do with them. + +But these other eigenvectors +are very useful. + +OK. + +We can extend this to as many +different recurrent sets of + +states as you choose. + +Here I'm doing it with a Markov +chain, which has two + +different sets of recurrent +states. + +They might be periodic, they +might be ergodic, it doesn't + +make any difference. + +So the matrix p has these +transient states up here. + +Here we have those transition +states would just go to each + +other, where the transition +probabilities starting with + +the transient state and going +to a transition state. + +Here we have the transitions, +which go from transient states + +to this first set of +recurrent states. + +Here we have the transitions, +which go from a transient + +state to the second state +of recurrent states. + +OK. + +The same way as before, the +determinant of this whole + +thing here, and this +determinant, the roots of that + +are in fact the eigenvalues of +p, are the product of the + +determinant of pt minus lambda +it times the product of this, + +times this determinant here. + +This has little t eigenvalues. + +This has little r eigenvalues. + +This has little r prime +eigenvalues, and if you add up + +t plus little r plus little +r prime, what do you get? + +You get jM, excuse me, capital +M, which is the total number + +of states in the Markov chain. + +So the eigenvalues here are +exactly the eigenvalues here + +plus the eigenvalues here, plus +the eigenvalues here. + +And you can find the +eigenvectors, the left + +eigenvectors for these +states in exactly + +the same way as before. + +OK. + +Yeah? + +STUDENT: So again, the +eigenvalues can be repeated + +both within t, r, r prime, +and in between the-- + +PROFESSOR: Yes. + +STUDENT: There's nothing +that says [INAUDIBLE]. + +PROFESSOR: No. + +There's nothing that says they +can't, except you can always + +find the left eigenvectors, +anyway, of this are, in fact, + +these things in the form. + +If pi is a left eigenvector of p +sub r, then zero followed by + +pi followed by zero. + +In other words, little t zeros +followed by r, followed by the + +eigenvector pi, followed by +little r prime zeroes here, + +this has to be a left +eigenvector of t. + +So this tells you something +about whether you're going to + +have a Jordan form or not, +one of these really + +ugly things in it. + +And it tells you that +in many cases, you + +just can't have them. + +If you have them, they're +usually tied up with this + +matrix here. + +OK, so that, I don't know. + +Was this useful? + +Does this clarify anything? + +Or if it doesn't, +it's too bad. + +OK. + +So now we want to start +talking about rewards. + +Some people call these costs. + +If you're an optimist, +you call it rewards. + +If you're a pessimist, +you call it costs. + +They're both the same thing. + +If you're dealing with rewards, +you maximize them. + +If you're dealing with costs, +you minimize them. + +So mathematically, who cares? + +OK, so suppose that each state +i of a Markov chain is + +associated with a given +reward, or a sub i. + +In other words, you think of +this Markov chain, which is + +running along. + +You go from one state to +another over time. + +And while this is happening, +you're pocketing some reward + +all the time. + +OK. + +You invest in a stock. + +Strangely enough, these +particular stocks we're + +thinking about here I this +Markov property. + +Stocks really don't have a +Markov property, but we'll + +assume they do. + +And since they have this Markov +property, you win for a + +while, and you lose +for a while. + +You win for a while, you +lose for a while. + +But we have something +extra, other than + +just the Markov chains. + +We can analyze this whole +situation, knowing how Markov + +chains behave. + +There's not much left besides +that, but there are an + +extraordinary number of +applications of this idea, and + +dynamic programming +is one of them. + +Because that's just one +added extension beyond + +this idea of rewards. + +OK. + +The random variable x of n. + +That's a random quantity. + +It's the state at time n. + +And the random reward of time n +is then the random variable + +r of xn that maps xn equals +i into ri for each i. + +This is the same idea of taking +one random variable, + +which is a function of another +random variable. + +The one random variable takes +on the values one up to + +capital M. + +And then the other random +variable takes on a value + +which is determined by the state +that you happen to be + +in, which is this +random states. + +So specifying our sub i +specifies what the set of + +rewards are, what the reward +is in each given state. + +Again, we have this awful +problem, which I wish we could + +avoid in Markov chains, of using +the same word state to + +talk about the set of +different states. + +And also to talk about +the random state + +at any given time. + +But hopefully by now you're +used to that. + +In our discussion here, the only +thing we're going to talk + +about are expected rewards. + +Now, you know that expected +rewards, or expectations are a + +little more generally than you +would think they would be, + +because you're going to take the +expected value of any sort + +of crazy thing. + +If you want to talk about any +event, you can take the + +indicator function of that +event, and find the expected + +value of that indicator +function. + +And that's just the probability +of that event. + +So by understanding how to deal +with expectations, you + +really have the capability +of finding distribution + +functions, or anything else +you want to find. + +OK. + +But anyway, since we're +interested only in expected + +rewards, the expected reward at +time n, given that x zero + +is i is the expected value of r +of xn given x zero equals i, + +which is the sum over j of the +reward you get if you're in + +state j at time n times p sub +ij, super n, which we've + +talked about ad nauseum for the +last four lectures now. + +And this is the probability that +the state at time n is j, + +given that the state +at time zero is i. + +So you can just automatically +find the expected + +value of r of xn. + +And it's by that formula. + +Now, recall that this quantity +here is not all that simple. + +This is the ij element of the +product of the matrix, of the + +nth product of the matrix p. + +But, so what? + +We can at least write a nice +formula for it now. + +The expected aggregate reward +over the n steps from m to m + +plus n minus 1. + +What is m doing in here? + +It's just reminding us that +Markov chains are + +homogeneous over time. + +So, when I talk about the +aggregate reward from time m + +the m plus n minus 1, it's the +same as the aggregate reward + +from time 0 up to +time n minus 1. + +The expected values +are the same. + +The actual sample functions +are different. + +OK, so if I try to calculate +this aggregate reward + +conditional on xm equals i, +mainly conditional on starting + +in state i, then this expected +aggregate reward, I use that + +as a symbol for it, is the +expected value of r of xm, + +given xm equals i. + +What is that? + +Well, that's ri. + +I mean, given that xm +is equal to i, this + +isn't random anymore. + +It's just the source sub i. + +Plus the expected value of r of +xm plus 1, which is the sum + +over j, of pij times r sub j. + +That's the time m plus 1 given +that you're in state i at time + +m, and so forth, up until time +n minus 1, where the expected + +reward, then, is +a piece of ij. + +Probability of being in state j +at time n minus 1 given that + +you started off in state i +at time 0 times r sub j. + +And since expectations add, we +have this nice, convenient + +formula here. + +We're doing something I normally +hate doing, which is + +building up a lot of notation, +and then using that notation + +to write extremely complicated +formulas in a way that looks + +very simple. + +And therefore you will get some +sense of what we're doing + +is very simple. + +These quantities in +here, again, are + +not all that simple. + +But at least we can write +it in a simple way. + +And since we can write it in a +simple way, it turns out we + +can do some nice +things with it. + +OK. + +So where do we go from +all of this? + +We have just said that the +expected reward we get, + +expected aggregate reward over n +steps, namely from m up to m + +plus n minus 1. + +We're assuming that if we start +at time m, we pick up a + +reward at time n. + +I mean, that's just an +arbitrary decision. + +We might as well do that, +because otherwise we just have + +one more transition matrix +sitting here. + +OK, so we start at time m. + +We pick up a reward, which +is conditional on the + +state we start in. + +And then we look at the expected +reward for time m and + +time m plus 1, m plus 2, +up to m plus n minus 1. + +Since we started at +m, we're picking + +up n different rewards. + +We have to stop at time +m plus n minus 1. + +OK, so that's this expected +aggregate reward. + +Why do I care about expected +aggregate reward? + +Because the rewards at any time +n are sort of trivial. + +What we're are interested +in is how does this + +build up over time? + +You start to invest +in a stock. + +You don't much care what +it's worth at time 10. + +You care how it grows. + +You care about its value when +you want to sell it, and you + +don't know when you're going to +sell it, most of the time. + +So you're really interested +in these aggregate + +rewards that you. + +You'll see when we get to +dynamic programming what + +you're interested +in that, also. + +OK. + +If the Markov chain is an +ergotic unit chain, then + +successive terms of this +expression tend to a steady + +state gain per step. + +In other words, these terms here +, when n gets very large, + +if I run this process for very +long time, what happens to p + +sub ij to n minus 1? + +This tends towards the steady +state vector pi sub j. + +And it doesn't matter +where we started. + +The only thing of importance +is where we end up. + +It doesn't matter how +high this is. + +So we have a sum over j, of +pi sub j times r sub j. + +After a very long time, the +expected gain per step is just + +a sum of pi j times +our r sub j. + +That's what's important +after a long time. + +And that's independent of +the starting state. + +So what we have here is a big, +messy transient, which is a + +sum of a whole bunch +of things. + +And then eventually it just +settles down, and every extra + +step you do, you just pick up +an extra factor of g as an + +extra reward. + +The reward might, of course, be +negative, like in the stock + +market over the last 10 years, +or up until the last year or + +so, who was negative +for a long time. + +But that doesn't make +any difference. + +This is just a number, and +this is independent of + +starting state. + +And p sub in can be viewed a +transient ni, which is all + +this stuff at the beginning. + +The sum of all these terms at +the beginning plus something + +that settles down over a +long period of time. + +How to calculate that transient, +how to combine it + +with the steady state gain. + +Then those talk a great +deal about that. + +What we're trying to do today +is to talk about dynamic + +programming without going into +all of this terrible mess + +about dealing rewards +words in a very + +systematic and simple way. + +You can read about that later. + +What we're aiming at is to talk +about dynamic programming + +a little bit, and then get +off to other things. + +OK. + +So anyway, we have a transient, +plus we have a + +steady state gain. + +The transient is important. + +And it's particularly important +if g equals zero. + +Namely if your average gain per +step is nothing, then what + +you're primarily interested in +is how valuable is it to start + +in a particular state? + +If you start in one state versus +another state, you + +might get a great deal of reward +in this one state, + +whereas you make a loss +in some other state. + +So it's important to know which +state is worth being in. + +So that's the next thing +we try to look at. + +How does the state +affect things? + +This brings us to one example +which is particularly useful. + +And along with being a useful +example, well, it's a nice + +illustration of Markov +rewards. + +It's also something which +you often want to find. + +And when we start talking about +renewal processes, you + +will find that this idea here +is a nice connection between + +Markov chains and +renewal series. + +So it's important for a whole +bunch of different reasons. + +OK. + +Suppose for some arbitrary +unit chain, namely we're + +saying one set of recurring +states. + +We want to find the expected +number of steps, starting from + +a given state i, until +some particular + +state 1 is first entered. + +So you start at one state. + +There's this other state +way over here. + +This state is recurrent, so +presumably, eventually you're + +going to enter it. + +And you want to find out, what's +the expected time that + +it takes to get to that +particular state? + +OK? + +If you're a Ph.D. student, you +have this Markov chain of + +doing your research. + +And at some point, you're going +to get a Ph.D. So we can + +think of this as the first pass +each time to your first + +Ph.D. I mean, if you want to +get more Ph.D.'s, fine, but + +that's probably a different +Markov chain. + +OK. + +So anyway, that's the problem +we're trying to solve here. + +We can view this problem +as a reward problem. + +We have to go through a number +of steps if we want to view it + +as a reward problem. + +The first one, first step is to +assign one unit of reward + +to each successive state until +you enter state 1. + +So you're bombing through this +Markov chain, a frog jumping + +from lily pad to lily pad. + +And finally, the frog +gets to the lily pad + +with the food on it. + +And the frog wants to know, is +it going to start before he + +gets to this lily pad +with the food on it? + +So, if we're trying to find +the expected time to get + +there, here what we're really +interested in is a cost, + +because the frog is in +danger of starving. + +Or on the other hand, there +might be a snake lying under + +this one lily pad. + +And then he's getting a reward +for staying alive. + +You can look at these things +whichever way you want to. + +OK. + +We're going to assign one unit +of reward to successive state + +until state 1 is entered. + +1 is just an arbitrary state +that we've selected. + +That's where the snake is +underneath a lily pad, or + +that's where the food is, +or what have you. + +Now, there's something +else we have to do. + +Because if we're starting out at +some arbitrary state i, and + +we're trying to look for the +first time that we enter state + +1, what do you do after +you enter state 1? + +Well eventually, normally you're +going to go away from + +state 1, and you're +going to start + +picking up rewards again. + +You don't want that to happen. + +So you do something we do all +the time when we're dealing + +with Markov chains, which is +we start with one Markov + +chain, and we say, to solve this +problem I'm interested + +in, I've got to change +the Markov chain. + +So how are we going +to change it? + +We're going to change it to say, +once we get in state 1, + +we're going to stay +there forever. + +Or in other words, the frog gets +eaten by the snake, and + +therefore its remains always +stay at that one lily pad. + +So we change the Markov +chain again. + +The frog can't jump anymore. + +And the way we change it is +to change the transition + +probabilities out of state 1 +to p sub 1, 1, namely the + +probability given you're in +state 1, of going back to + +state 1 in the next transition +is equal to 1. + +So whenever you get +to state 1, you + +just stay there forever. + +We're going to say r1 equal to +zero, namely the reward you + +get in state 1 will be zero. + +So you keep getting rewards +until you go to state 1. + +And then when you go to state +1, you don't get any reward. + +You don't get any reward from +any time after that. + +So in fact, we've converted +the problem. + +We've converted the Markov chain +to be able to solve the + +problem that we want to solve. + +Now, how do we know that we +haven't changed the problem in + +some awful way? + +I mean, any time you start out +with a Markov chain and you + +modify it, and you solve a +problem for the modified + +chain, you have to really think +through whether you + +changed the problem that +you started to solve. + +Well, think of any sample path +which starts in some state i, + +which is not equal to 1. + +Think of the sample path +as going forever. + +In the original Markov chain, +that sample path at some + +point, presumably, is going +to get to state 1. + +After it gets to state 1, we +don't care what happens, + +because we then know how long +it's taken to get to state 1. + +And after it gets to state +1, the transition + +probabilities change. + +We don't care about that. + +So for every sample path, the +time that it takes the first + +pass each time to state 1 is the +same in the modify chain + +as it is in the actual chain. + +The transition probabilities are +the same up until the time + +when you first get to state 1. + +So for first pass each time +problems, it doesn't make any + +difference what you do after +you get to state 1. + +So to make the problem easy, +we're going to set these + +transition probabilities in +state 1 to 1, and we're going + +to set the reward +equal to zero. + +What do you call a state which +has p sub i, i equal to 1? + +You call it a trapping state. + +It's a trapping state because +once you get there, + +you can't get out. + +And since we started out with +a unit chain, and since + +presumably state 1 is a +recurrent state in that unit + +chain, eventually you're going +to get to state 1. + +But once you get there, +you can't get out. + +So what you've done is you've +turned the unit chain into + +another unit chain where the +recurrent set of states has + +only this one state, +state 1 in it. + +So it's a trapping state. + +Everything eventually +leads to state 1. + +All roads lead to Rome, but it's +not obvious that they're + +leading to Rome. + +And all of these states +eventually lead to state 1, + +but not for quite a +while sometimes. + +OK. + +So the probability of an initial +segment until 1 is + +entered is unchanged, and +expected first pass each time + +is unchanged. + +OK. + +A modified Markov chain is now +an ergotic unit chain. + +It has a single recurrent +state. + +State 1 is a trapping +state, we call it. + +ri is equal to 1 for i unequal +to 1, and r1 is equal to zero. + +This says that a state 1 is +first entered at time l, and + +the aggregate reward from 0 to +n is l for all m greater than + +or equal to l. + +In other words, after you get +to the trapping state, you + +stay there, and you don't +pick up any more + +reward from then on. + +One of the things that's +maddening about problems like + +this, at least that's maddening +for me, because I + +can't keep those things +straight, is the difference + +between n and n plus 1, +or n and n minus 1. + +There's always that strange +thing, we've started at time + +m, we get reward at time m. + +So if we're looking at m +transitions, as we go from m + +the m plus n minus 1. + +And that's just life. + +If you try to do it in a +different way, you wind up + +with a similar problem. + +You can't avoid it. + +OK, so what we're trying to find +is the expected value of + +v sub i of n, and the limit as n +goes to infinity, we'll just + +call that v sub i without +the n on it. + +And what we want to do is to +calculate this expected time + +until we first enter +state one. + +We want to calculate that for +all of the other states i. + +Well fortunately, there's a +sneaky way to calculate this. + +For most of these problems, +there's a sneaky way to + +calculate these limits. + +And you don't have to worry +about the limit. + +So the next thing I'm going to +do is to explain what this + +sneaky way is. + +You will see the same sneaky +method done about 100 times + +from now on until the +end of course. + +We use it all the time. + +And each time we do it, we'll +get a better sense of what it + +really amounts to. + +So for each state unequal to +the trapping state, let's + +start out by assuming that +we start at time + +zero, and state i. + +In other words, what this means +is first we're going to + +assume that x sub 0 equals +i for some given i. + +We're going to go through +whatever we're going to go + +through, then we'll go back +and assume that x sub 0 is + +some other i. + +And we don't have to worry about +that, because i is just + +a generic state. + +So we'll do it for everything +at once. + +There's a unit reward +at time 0. + +r sub i is equal to 1. + +So we start out at time +zero and state i. + +We pick up our reward of 1, and +then we go on from there + +to see how much longer it +takes to get to state 1. + +In addition to this unit reward +at time zero, which + +means it's already taken us one +unit of time to get the + +state 1, given that x sub 1 +equals j, namely, given that + +we go from state i to state j, +the remaining expected reward + +is v sub j. + +In other words, if it's times +0, I'm in some state i. + +Given that I go to some stage +j, the next unit of time, + +what's the remaining accepted +expected time they + +get to state 1? + +The remaining expected time is +just v sub j, because that's + +the expected time. + +I mean, if v sub j is something +where it's very hard + +to get to state 1, then +we really lost out. + +If it's something which is +closer to state 1 in some + +sense, then we've gained. + +But what we wind up with is the +expected time to get to + +state 1 from state i is one. + +That's the instant reward that +we get, or the instant cost + +that we pay, plus each of +the possible states + +we might get to. + +There's a cost to go, or +reward to go from that + +particular j. + +So this is the formula +we have to solve. + +What's this mean? + +It means we have to solve +this formula for all i. + +If I solve it for all i, and +I've solved this for all i, + +then that's the linear equation +in the variables v + +sub 1 up to v linear equations +in i equals 2, up to m. + +We also have decided that +v sub 1 is equal to 0. + +In other words, if we start out +in state 1, you expect the + +time to get to state 1 is 0. + +We're already there. + +OK. + +So we have to solve these +linear equations. + +And if your philosophy on +solving linear equations is + +that of, I shouldn't say a +computer scientist because I + +don't want to indicate that they +are any different from + +any of the rest of us, but for +many people, your philosophy + +of solving linear equations +is to try to solve it. + +If you can't solve it, it +doesn't have any solution. + +And if you're happy with +doing that, fine. + +Some people would rather spend +10 hours asking whether in + +general it has any solution, +rather than spending five + +minutes solving it. + +So either way, this expected +first passage time, we've just + +stated what it is. + +Starting in state i, it's 1 plus +the time to go for any + +other state you happen +to go to. + +If we put this in vector form, +you put things in vector form + +because you want to spend two +hours finding the general + +solution, rather than five +minutes solving the problem. + +If you have 1,000 states, then +it works the other way. + +It takes you multiple hours to +work it out by hand, and it + +takes you five minutes by +looking at the equation. + +So sometimes you win, and +sometimes you lose by looking + +at the general solution. + +If you look at this as a vector +solution, the vector v + +where v1 is equal to zero, and +the other v's are unknowns, is + +the vector r, the +vector r is 0. + +0 reward in state 1. + +Unit reward in all other states, +because we're trying + +to get to this end. + +And then we have the matrix +here, t times v. + +So we want to solve this set of +linear equations, and what + +do we know about this set +of linear equations? + +We have an ergotic unit chain. + +We know that p has +an eigenvalue, + +which is equal to 1. + +We know that's a simple +eigenvalue. + +So that in fact, when we write +v equals r plus pv as zero + +equals r plus p minus +i times v. + +And we try to ask whether +v has any + +solution, what's the answer? + +Well, this matrix here has +an eigenvalue of 1. + +Since it has an eigenvalue of +one, and since it's a simple + +eigenvalue, there's a space of +solutions to this equation. + +The space of solutions is the +vector of all ones and the + +vector of all anything else. + +In other words, it's a vector of +v times any constant alpha. + +Now we've stuck this in here, +so now we want to find out + +what's the set of +solutions now. + +We observe v plus alpha e also +satisfies this equation if we + +found another solution. + +So if we found a solution, we +have a one dimensional family + +of solutions. + +Well, since this eigenvalue is a +simple eigenvalue, the space + +of vectors for which r is equal +to p minus i times v as + +a one dimensional space, and +therefore there has to be a + +unique solution to +this question. + +OK. + +So in fact, in only 15 minutes, +we've solved the + +problem in general, so that you +can deal with matrices of + +1,000 states, as opposed +to two states. + +And you still have +the same answer. + +OK. + +So this equation has a simple +solution, which says that you + +can program your computer to +solve this set of linear + +equations, and you're bound +to get an answer. + +And the answer will tell you +how long it takes to get to + +this particular state. + +OK. + +Let's go one to aggregate +rewards with a final reward. + +Starting to sound like-- yes? + +STUDENT: I'm sorry, for the +last example, how are we + +guaranteed that it's ergotic? + +Like, I possible you enter a +loop somewhere that can never + +go to your trapping +state, right? + +PROFESSOR: But I can't do that +because there always has to be + +a way of getting to the trapping +state, because + +there's only one recurrent +state. + +All these other states +are transient now. + +STUDENT: No, but I mean-- + +OK, like, let's say you +start off with a + +general Markov chain. + +PROFESSOR: Oh, I start off with +a general Markov chain? + +You're absolutely right. + +Then there might be no way of +getting from some starting + +state to state 1, and therefore, +the amount of time + +that it takes you to get from +that state to the starting + +state is going to be infinite. + +You can't get there. + +So in fact, what you have to do +with a problem like this is + +to look at it first, and say, +are you in fact dealing with a + +unit chain? + +Or do you have multiple +recurrent sets? + +If you have multiple recurrent +sets, then the expected time + +to get into one of the recurrent +states, starting + +from either a transient state, +or from some other recurrent + +set is infinite. + +I mean, just like this business +we were going through + +at the beginning. + +What you would like to do is not +have to go through a lot + +of calculation when you have, or +a lot of thinking when you + +have multiple recurrent +sets of states. + +You just know what +happens there. + +There's no way to get from this +recurrent set to this + +recurrent set. + +So that's the end of it. + +STUDENT: OK. + +So like it works when you have +the unit chain, and then you + +choose your trapping state to +be one instance [INAUDIBLE]. + +PROFESSOR: Yes. + +OK. + +Good. + +Now, yes? + +STUDENT: The previous equation +is true for any reward. + +But it's not necessary-- + +PROFESSOR: Yeah, it is true for +any set of rewards, yes. + +Although what the interpretation +would be of any + +set of rewards is if you +have to sort that out. + +But yes. + +For any r that you choose, +there's going to be one unique + +solution, so long as one is +actually a trapping state, and + +everything else leads to one. + +OK, so why do I want to +put a-- ah, good. + +STUDENT: I feel like there's a +lot of the rewards that are + +designed for it, designed with +respect to being in a + +particular state. + +PROFESSOR: Yes. + +STUDENT: But if the rewards are +actually in transition, so + +for example, if you go from i to +j, there are going to be a + +different number from j to j. + +How do you deal with that? + +PROFESSOR: How do I +deal with that? + +Well, then let's talk +about that. + +And in fact, it's fairly simple +so long as you're only + +talking about expected +rewards. + +Because if I have a reward +associated with-- + +if I have a reward rij, which is +the reward for transition i + +to j, then if I take the sum of +rij times p summed over j, + +what this gives me is the +expected reward associated + +with state j, with state i. + +Now, you have to be a little bit +careful with this because + +before we've been picking up +this reward as soon as we get + +to state i, and here suddenly +we have a slightly different + +situation where you have a +reward associated with state i + +but you don't pick it up +until the next set. + +So this is where this problem +of i or i plus 1 comes in. + +And you guys can do that much +better than I can, because at + +my age I start out with an age +of 60 and an age of 61 is the + +same thing. + +I mean, these are-- + +OK. + +So anyway, the point of it is, +if you have rewards associated + +with transitions you can always +convert that to rewards + +associated with states. + +Oh, I didn't really +get to this. + +What I've been trying to say +now for a while is that + +sometimes, for some reason or +other, after you go through + +and end steps of this Markov +chain, when you get to the + +end, you want to consider some +particularly large reward for + +having gotten to the end, or +some particularly large cost + +of getting to the end, or +something which depends on the + +state that you happen +to be in. + +So we will assign some final +reward which in general can be + +different from the reward that +we're picking up at each of + +the other states. + +We're going to do this +in a particular way. + +You would think that what we +would want to do is, if we + +went through in steps, we would +associate this final + +reward with the n-th step. + +We're going to do it +a different way. + +We're going to go through n +steps, and then the final + +reward is what happens on +the state after that. + +So we're really turning the +problem of looking at n steps + +into a problem of looking +at n plus 1 steps. + +Why do we do that? + +Completely arbitrary. + +It turns out to be convenient +when we talk about dynamic + +programming, and you'll see +why in just a minute. + +So this extra final state is +just an arbitrary thing that + +you add, and we'll see +the main purpose for + +it in just a minute. + +OK. + +So we're going to now look at +what in principle is a much + +more complicated situation than +what we were looking at + +before, but you still have this +basic mark off condition + +which is making things +simple for you. + +So the idea is, you're looking +at a discrete time situation. + +Things happen in steps. + +There's a finite set of states +which don't change over time. + +At each unit of time, you're +going to be in one of the set + +of m states, and at each time l, +there's some decision maker + +sitting around who looks +at the state that + +you're in at time l. + +And the decision maker says I +have a choice between what + +reward I'm going to pick up +at this time and what the + +transition probabilities are for +going to the next state. + +OK, so it's kind of a +complicated thing. + +It's the same thing that +you face all the time. + +I mean, in the stock market for +example, you see that one + +stock is doing poorly, +so you have a choice. + +Should I sell it, eat my losses, +or should I keep on + +going and hope it'll +turnaround? + +If you're doing a thesis, you +have the even worse problem. + +You go for three months without +getting the result + +that you need, and you say, +well, I don't have a thesis. + +I can't say something +about this. + +Should I go on for one more +month, or should I can it and + +go on to another topic? + +OK, it's exactly the +same situation. + +So this is really a very broad +set of situations. + +The only thing that makes it +really different from real + +life is this Markov property +sitting there and the fact + +that you actually understand +what the rewards are and you + +can predict them in advance. + +You can't predict what state +you're going to be in, but you + +know that if you're in a +particular state, you know + +what your choices are in the +future as well as now, and all + +you have to do at each unit of +time is to make this choice + +between various different +things. + +You see an interesting +example of that here. + +If you look at this Markov chain +here, it's a two state + +Markov chain. + +And what's the steady +state probability of + +being in state one? + +Anybody? + +It's a half, yes. + +Why is it a half, and +why don't you have + +to solve for this? + +Why can you look at it +and say it's a half? + +Because it's completely +symmetric. + +0.99 here, 0.99 here, 0.01 +here, 0.01 here. + +These rewards here had nothing +to do with the + +Markov chain itself. + +The Markov chain is symmetric +between states one and two, + +and therefore, the steady state +probabilities have to be + +one half each. + +So here's something where, if +you happen to be in state two, + +you're going to stay +there typically + +for a very long time. + +And while you're studying there +for a very long time, + +you're going to be picking up +rewards one unit of reward + +every unit of time. + +You work for some very stable +employer who pays you very + +little, and that's a +situation you have. + +You're sitting here, you have +a job but you're not making + +much, but still you're making +something, and you have a lot + +of job security. + +Now, we have a different choice +when we're sitting here + +with a job in state two, we can, +for example, you can go + +to the cash register and take +all the money out of it and + +disappear from the company. + +I don't advocate doing +that, except, + +it's one of your choices. + +So you pick up a big reward of +50, and then for a long period + +of time you go back to this +state over here and you make + +nothing in reward for a +long period of time + +while you're in jail. + +And then eventually you pop back +here, and if we assume + +the judicial system is such +that it has no memory, + +[INAUDIBLE] + +you can cut into the cash +register, and, well, OK. + +So anyway, this decision two, +you're looking for instant + +gratification here. + +You're getting a big reward all +at once, but by getting a + +big reward with probability +one, you're going back to + +state zero. + +From state zero, it takes a long +time to get back to the + +point where you can get a big +reward again, so you wonder, + +is it better to use this policy +or is it better to use + +this policy? + +Now, there are two basic ways +to look at this problem. + +I think it's important to +understand what they are + +before we go further. + +One of the ways is to say, OK, +let's suppose that I work out + +which is the best policy +and I use it forever. + +Namely, I use this policy +forever or I + +use this policy forever. + +And if I use this policy +forever, I can pretty easily + +work out what the steady state +probabilities of these two + +states are. + +I can then work out what my +expected gain is per unit time + +and I can compare +this with that. + +And who thinks that this is +going to be better than that + +and who thinks that this is +going to be better than that? + +Well, you can work +it out easily. + +It's kind of interesting because +the steady state gain + +here and here are very +close to the same. + +It turns out that this is just +a smidgen better than this, + +only by a very small amount. + +OK. + +See, what happens here is that +here, you tend to go for about + +100 steps here. + +So you pick up every reward of +about 100 if you use this very + +simple minded analysis. + +Then for 100 steps, you're +sitting here, you're getting + +no reward, so you think we ought +to get every reward of + +one half on the average, +and that's exactly + +what you do get here. + +And here, you get this big +reward of 50, but then you go + +over here and you spend 100 +units of time in purgatory and + +then you get back again, you get +another reward of 50 and + +then spend hundreds units +of time in purgatory. + +So again, you're getting pretty +close to a half of a + +unit of reward, but it turns +out, when you work it out, + +that here is just a smidgen. + +It's 1% less than a half, so +this is not as good as that. + +But suppose that you have +a shorter time horizon. + +Suppose you don't want to wait +for 1,000 steps to see what's + +going on, so you don't want +to look at the average. + +Suppose this was a +gambling game. + +You have your choice of these +two gambling options, and + +suppose you're only going to be +playing for a short time. + +Suppose you're going +to be only playing + +for one unit of time. + +You can only play for one unit +of time and then you have to + +stop, you have to go home, you +have to go back to work, or + +something else. + +And you happen to be sitting +in state two. + +What do you want to do +if you only have one + +unit of time to play. + +Well, obviously, you want to get +the reward of 50, because + +delayed gratification doesn't +work here, because you don't + +get any opportunity for that +gratification later. + +So you pick up the big +reward at first. + +So when you have this problem of +playing for a finite amount + +of time, whatever kind of +situation you're in, what you + +would like to do is say, for +this finite amount of time + +that I'm going to play, what's +my best strategy then? + +Dynamic programming is the +problem, which is the + +algorithm which finds out what +the best thing to do is + +dynamically. + +Namely, if you're going to stop +in 10 steps, stop in 100 + +steps, stop in one step, it +tells you what to do under all + +of those circumstances. + +And the stationary policy tells +you what to do if you're + +going to play forever. + +But in a situation like this +where things happen rather + +slowly, it might not be the +relevant thing to deal with. + +A lot of the notes deal with +comparing the stationary + +policy with this +dynamic policy. + +And I'm not going to do that +here because, well, we have + +too many other interesting +things that we + +want to deal with. + +So we're just going to skip +all of that stuff about + +stationary policies. + +You don't have to bother to +read it unless you're + +interested in it. + +I mean, if you're interested in +it, by all means, read it. + +It's a very interesting topic. + +It's not all that interesting +to find out what the best + +stationary policy is. + +That's kind of simple. + +What's the interesting topic +is what's the comparison + +between the dynamic policy and +the stationary policy. + +But all we're going to do +is worry about what the + +dynamic policy is. + +That seems like a hard problem, +and someone by the + +name of Bellman figured out what +the optimal solution to + +that dynamic policy was. + +And it turned out to be a +trivially simple algorithm, + +and Bellman became +famous forever. + +One of the things I want to +point out to you, again, I + +keep coming back to this because +you people are just + +starting a research career. + +Everyone in this class, given +the formulation of this + +dynamic programming problem, +could develop and would + +develop, I'm pretty sure, the +dynamic programming algorithm. + +Developing the algorithm, +understanding what the problem + +is is a trivial matter. + +Why is Bellman famous? + +Because he formulated +the problem. + +He said, aha, this dynamic +problem is interesting. + +I don't have to go through +the stationary problem. + +And in fact, my sense from +reading his book and from + +reading things he's written is +that he couldn't have solved + +the stationary problem because +he didn't understand + +probability that well. + +But he did understand how to +formulate what this really + +important problem was +and he solved it. + +So, all the more credit to him, +but when you're doing + +research, the time you spend +on formulating the right + +problem is far more important +than the time you spend + +solving it. + +If you start out with the right +problem, the solution is + +trivial and you're all done. + +It's hard to formulate the right +problem, and you learn + +to formulate the problem not +by playing all of this + +calculating things, but by +setting back and thinking + +about the problem and trying +to look at things in a more + +general way. + +So just another plug. + +I've been saying this, I will +probably say it every three or + +four lectures throughout +the term. + +OK. + +So let's go back and look +at what the problem is. + +We haven't quite formulated +it yet. + +We're going to assume this +process of random transitions + +combined with decisions based +on the current state. + +In other words, in this decision +maker, the decision + +maker at each unit of time sees +what state you're in at + +this unit of time. + +And seeing what state you're in +at this given unit of time, + +the decision maker has a choice +between how much reward + +is to be taken and along with +how much reward is to be + +taken, what the transition +probabilities are + +for the next state. + +If you rob the cash register, +your transition probabilities + +are going to be very different +than if you don't + +rob the cash register. + +By robbing the cash register, +your transition probabilities + +go into a rather high transition +probability that + +you're going to be caught. + +OK, so you don't want that. + +So you can't avoid the problem +of having the rewards at a + +given time locked into what the +transition probabilities + +are for going to the next state, +and that's the essence + +of this problem. + +OK. + +So, the decision maker observers +the state and + +chooses one of a finite +set of alternatives. + +Each alternative consists of +recurrent reward which we'll + +call r sub j of k, the +alternative is k, and a set of + +transition probabilities. + +pjl of k, one less than or +equal to a l less than or + +equal to m for going +to the next state. + +OK, the notation here is +horrifying, but the idea is + +very simple. + +I mean, once you get used to the +notation, there's nothing + +complicated here at all. + +OK, so in this example here, +well, we already + +talked about that. + +We're going to start +out at time m. + +We're going to make a decision +at time m, pick up the + +associated reward for that +decision, and pick the + +transition probabilities that +we're going to use at that + +time m, and then go on +to the next state. + +We're going to continue doing +this until time m + +plus n minus 1. + +Mainly, we're going to do this +for n steps of time. + +After the n-th decision-- + +you make the n-th decision +at m plus n minus t-- + +there's a final transition +based on that decision. + +The final transition is based +on that decision, but the + +final reward is fixed +ahead of time. + +You know what the final reward +is going to be, which happens + +at time m plus n. + +So the things which are variable +is how much reward do + +you get at each of these first +n time units, and what + +probabilities you choose for +going through the next state. + +Is this still a Markov chain? + +Is this still Markov? + +You can talk about this +for a long time. + +You can think about it for +a long time because this + +decision maker might or +might not be Markov. + +What is Markov is the transition +probabilities that + +are taking place in +each unit of time. + +After I make a decision, the +transition probabilities are + +fixed for that decision and +that initial state and had + +nothing to do with the decisions +that had been made + +before that or the states you've +been in before that. + +The Markov condition says that +what happens in the next unit + +of time is a function simply +of those transition + +probabilities that +had been chosen. + +We will see that when we look at +the algorithm, and then you + +can sort out for yourselves +whether there's something + +dishonest here or not. + +Turns out there isn't, but to +Bellman's credit he did sort + +out correctly that this worked, +and many people for a + +long time did not +think it worked. + +So the objective of dynamic +programming is both to + +determine the optimal decision +at each time and to determine + +the expected reward for each +starting state and for each + +number and steps. + +As one might suspect, now here's +the first thing that + +Bellman did. + +He said, here, I have +this problem. + +I want to find out what happens +after 1,000 steps. + +How do I solve the problem? + +Well, anybody with any sense +will tell you don't solve the + +problem with 1,000 +steps first. + +Solve the problem with one step +first, and then see if + +you find out anything from it +and then maybe you can solve + +the problem with two steps and +then maybe something nice will + +happen, or maybe it won't. + +When we do this, it'll turn +out that what we're really + +doing is we're starting at the +end and working our way back, + +and this algorithm is due to +Richard Bellman, as I said. + +And he was the one who sorted +out how it worked. + +So what is the algorithm? + +We're going to start out making +a decision at time 1. + +So we're going to +start at time n. + +We're going to start +in a given state i. + +You make a decision, decision +k at time m. + +This provides a reward at time +m, and the selected transition + +probabilities lead to a +final expected reward. + +These are these final rewards +which occur at time n plus 1. + +It's nice to have that n because +it's what let's us + +generalize the problem. + +So this was another clever +thing that went on here. + +So the expected optimal +aggregate reward for a one + +step problem is the sum of the +reward that you get at time m + +plus this final reward you get +at time n plus 1, and you're + +maximizing over the different +policies you have + +available to you. + +So it looks like a trivial +problem, but the optimal + +reward with a one step +problem is just this. + +OK, next you want to consider +the two step problem. + +What's the maximum expected +reward starting at xm equals i + +with decisions at times +m and n plus 1. + +You make two decisions. + +Now, before, we just made +one decision at time m. + +Now we make a decision at time +m and at time n plus 1, and + +finally we pick up a final +reward at time n plus 2. + +Knowing what that final reward +is going to be is going to + +affect the decision you make at +time n plus 1, but it's a + +fixed reward which is a +function of the state. + +You can adjust the transition +probabilities of getting to + +those different rewards. + +The key to dynamic programming +is an optimal decision at time + +n plus 1 can be selected based +only on the state j + +at time n plus 1. + +This decision, given that you're +in state j at time n + +plus 1, is optimal independent +of what you did before that, + +which is why we're starting +out looking at what we're + +going to do with time n plus 1 +before we even worry about + +what we're going to +do with time n. + +So, whatever decision you made +at time n, you observe what + +state you're at time n plus +1 and the maximal expected + +reward over times n plus 1 and +n plus 2, given that you + +happen to be in state j is just +maximal over k as the + +reward you're going to get by +choosing policy k and the + +expected value of the final +reward you get if you're using + +this policy k. + +This is just dj* of 1 and +u as you just found. + +In other words, you have the +same situation at time n plus + +1 as you have at time n. + +Well, surprisingly, you've just +solved the whole problem. + +So we've seen that what we +should do at time n plus 1 is + +do this maximization. + +So the optimal reward, aggregate +reward over times m, + +n plus 1, and n plus 2 is what +we get maximizing over our + +choice at time m of the reward +we get at time m plus the + +decision plus the transition +probabilities which we've + +decided on which get us to this +reward at time n plus 1 + +and n plus 2. + +We found out what the reward +is for times n plus 1 and n + +plus 2 together. + +That's the reward to go, And +we know what that is, so we + +have this same formula +we used before. + +Why do we want to look at +these final rewards now? + +Well, you can view this as a +final reward in state m. + +It's the final reward which +tells you what you get both + +from state n plus +1 and n plus 2. + +And, going quickly, if we look +at playing this game for three + +steps, the optimal reward for +the three step game is the + +immediate reward optimized over +k plus the rewards at n + +plus 1, n plus 2, and n plus 3, +which we've already found. + +And in general, the optimal +reward at time n-- + +when you play the game for n +steps, the optimal reward is + +maximum here. + +So, all you do in the algorithm +is, for each value + +of n when you start with n +equal to 1, you solve the + +problem for all states and you +maximize over all policies you + +have a choice over, and then you +go on to the next larger + +value of n, you solve the +problem for all states and you + +keep on going. + +If you don't have many +states, it's easy. + +If you have 100,000 states, it's +kind of tedious to run + +the algorithm. + +Today it's not bad, but today +we look at problems with + +millions and millions of states +or billions of states, + +and no matter how fast +computation gets, the + +ingenuity people to invent +harder problems always makes + +it hard to solve +these problems. + +So anyway, that's the dynamic +programming algorithm. + +And next time, we're going to +start on renewal processes. \ No newline at end of file diff --git a/m_G3z-C1C2g.txt b/m_G3z-C1C2g.txt new file mode 100644 index 0000000000000000000000000000000000000000..8fbcda97fe73c573f9db2d5c049c9f19c453fee3 --- /dev/null +++ b/m_G3z-C1C2g.txt @@ -0,0 +1,156 @@ +Two's complement representation is a way of +representing both positive and negative numbers + +in binary. + +Let's take a look at an example of a positive +number represented in two's complement in + +order to begin understanding how this representation +works. + +If we look at the number, 001000, the way +that we determine the value of this two's + +complement number is as follows. + +Each bit represents a power of 2, with the +right most bit representing 2<sup>0</sup>, + +the next bit is 2<sup>1</sup>, then 2<sup>2</sup>, +2<sup>3</sup>, 2<sup>4</sup>, and finally + +-2<sup>5</sup>. + +Having the most significant bit represent +a negative power of 2 rather than a positive + +power allows us to express both positive and +negative numbers with our notation. + +If your number has a 0 in a certain position, +then the power of 2 associated with that position + +is not present in your number. + +If the number has a 1, then that tells us +that the corresponding power of 2 makes up + +part of the number's value. + +To figure out the value of the number 001000, +we see that there is a single 1 which is in + +the 2<sup>3</sup> position. + +So this number is equal to 2<sup>3</sup> which +equals 8. + +Note that if I wanted to represent the same +number 8 using a larger number of binary bits, + +I would simply add some leading zeroes to +my positive number. + +For example, the number 8 represented in 8-bits +two's complement is the same as the 6-bit + +representation but with 2 additional leading +zeroes. + +Now let's try a negative number. + +Negative numbers in 2's complement representation +always have a 1 in their most significant + +bit (MSB). + +What is the value of 101100? + +We apply the same logic as before, now we +have a 1 in bit positions 2, 3, and 5. + +That means that this number is equal to -2<sup>5</sup> ++ 2<sup>3</sup> + 2<sup>2</sup> which equals + +-32 + 8 + 4 = -20. + +In the case of negative numbers, if we wanted +to represent the same value, -20 using more + +bits, one would simply need to append leading +1's to the number to end up with the same + +value. + +For example, -20, using 8 bits is 11101100. + +Let's check that this is correct. + +This number is equal to -2<sup>7</sup> + 2<sup>6</sup> ++ 2<sup>5</sup> + 2<sup>3</sup> + 2<sup>2</sup> + +which is equal to -128 + 64 + 32 + 8 + 4 which +is -128 + 108 and that is equal to -20. + +Let's take a look at the range of numbers +that can be represented using N-bit 2's complement. + +Let's begin with our example of 6-bits. + +The largest positive number in that case is +0 followed by five 1's (011111) which is equal + +to 2<sup>0</sup> + 2<sup>1</sup> + 2<sup>2</sup> ++ 2<sup>3</sup> + 2<sup>4</sup> which is equal + +to 1 + 2 + 4 + 8 + 16 which equals 31 which +is also equal to 2<sup>5</sup>-1. + +The most negative number using 6 bits is 1 +followed by five 0's (100000) which equals + +-2<sup>5</sup> with no positive component +added to the number and that is equal to -32. + +So in general for N-bits, the 2's complement +number can range from -2<sup>N-1</sup> through + +2<sup>N-1</sup>-1. + +An easy way of converting between positive +and negative 2's complement numbers is by + +flipping all the bits and adding 1. + +For example, earlier we calculated that 101100 += -20. + +If I take this number and flip all of the +bits, I get 010011. + +I then add 1 to that, which results in 010100. + +This number is = 2<sup>2</sup> + 2<sup>4</sup> += 4 + 16 = 20. + +This tells us that our original number 101100 +was equal to -20. + +The same methodology can be applied in reverse. + +If you start with a positive number 20 = 010100, +and you flip all the bits and add 1, you get + +101011 + 1 = 101100. + +This brings us back to our original number +which is -20. + +So to easily determine the value of a negative +2's complement number, one flips all the bits + +and adds 1 to find the corresponding positive +number, say X, which in turn means that your + +original negative number had a value of -X. \ No newline at end of file diff --git a/n9gSOBwauRw.txt b/n9gSOBwauRw.txt new file mode 100644 index 0000000000000000000000000000000000000000..27584134f85f18dda5729fce3faa7570baffb748 --- /dev/null +++ b/n9gSOBwauRw.txt @@ -0,0 +1,1915 @@ +align:start position:0% + +welcome back to recitation in this video + + align:start position:0% +welcome back to recitation in this video + + + align:start position:0% +welcome back to recitation in this video +I want us to work on the following + + align:start position:0% +I want us to work on the following + + + align:start position:0% +I want us to work on the following +problem which is to show that this this + + align:start position:0% +problem which is to show that this this + + + align:start position:0% +problem which is to show that this this +Vector field is not conservative uh and + + align:start position:0% +Vector field is not conservative uh and + + + align:start position:0% +Vector field is not conservative uh and +the vector field is min - y i + XJ all + + align:start position:0% +the vector field is min - y i + XJ all + + + align:start position:0% +the vector field is min - y i + XJ all +divided x^2 + y^2 so you can think about + + align:start position:0% +divided x^2 + y^2 so you can think about + + + align:start position:0% +divided x^2 + y^2 so you can think about +this in two separate components if you + + align:start position:0% +this in two separate components if you + + + align:start position:0% +this in two separate components if you +need to as Min - y / x^2 + y^2 I Plus X + + align:start position:0% +need to as Min - y / x^2 + y^2 I Plus X + + + align:start position:0% +need to as Min - y / x^2 + y^2 I Plus X +over x^2 + y^2 J so that's really that's + + align:start position:0% +over x^2 + y^2 J so that's really that's + + + align:start position:0% +over x^2 + y^2 J so that's really that's +exactly the same thing so your object is + + align:start position:0% +exactly the same thing so your object is + + + align:start position:0% +exactly the same thing so your object is +to show that this Vector field is not + + align:start position:0% +to show that this Vector field is not + + + align:start position:0% +to show that this Vector field is not +conservative and why don't you work on + + align:start position:0% +conservative and why don't you work on + + + align:start position:0% +conservative and why don't you work on +that for a while pause the video and + + align:start position:0% +that for a while pause the video and + + + align:start position:0% +that for a while pause the video and +then when you're ready to see my + + align:start position:0% +then when you're ready to see my + + + align:start position:0% +then when you're ready to see my +solution you can bring the video back + + align:start position:0% + + + + align:start position:0% + +up so welcome back well maybe some of + + align:start position:0% +up so welcome back well maybe some of + + + align:start position:0% +up so welcome back well maybe some of +you thought I had a typo in this problem + + align:start position:0% +you thought I had a typo in this problem + + + align:start position:0% +you thought I had a typo in this problem +initially and I wanted you to show it in + + align:start position:0% +initially and I wanted you to show it in + + + align:start position:0% +initially and I wanted you to show it in +fact was conservative but but it + + align:start position:0% +fact was conservative but but it + + + align:start position:0% +fact was conservative but but it +actually is not a conservative Vector + + align:start position:0% +actually is not a conservative Vector + + + align:start position:0% +actually is not a conservative Vector +field and let me explain how we can show + + align:start position:0% +field and let me explain how we can show + + + align:start position:0% +field and let me explain how we can show +it's not conservative and why probably + + align:start position:0% +it's not conservative and why probably + + + align:start position:0% +it's not conservative and why probably +what you did initially uh to try and + + align:start position:0% +what you did initially uh to try and + + + align:start position:0% +what you did initially uh to try and +show it what show it was not didn't work + + align:start position:0% +show it what show it was not didn't work + + + align:start position:0% +show it what show it was not didn't work +so maybe that wording was a little + + align:start position:0% +so maybe that wording was a little + + + align:start position:0% +so maybe that wording was a little +confusing but let me take you through it + + align:start position:0% +confusing but let me take you through it + + + align:start position:0% +confusing but let me take you through it +so the first thing I would imagine you + + align:start position:0% +so the first thing I would imagine you + + + align:start position:0% +so the first thing I would imagine you +tried is you looked at M suby and N subx + + align:start position:0% +tried is you looked at M suby and N subx + + + align:start position:0% +tried is you looked at M suby and N subx +so m in this case is- y/ x^2 + y^2 and N + + align:start position:0% +so m in this case is- y/ x^2 + y^2 and N + + + align:start position:0% +so m in this case is- y/ x^2 + y^2 and N +in this case capital N in this case case + + align:start position:0% +in this case capital N in this case case + + + align:start position:0% +in this case capital N in this case case +is x / x^2 + y^2 so if you work that out + + align:start position:0% +is x / x^2 + y^2 so if you work that out + + + align:start position:0% +is x / x^2 + y^2 so if you work that out +you probably did or maybe you didn't and + + align:start position:0% +you probably did or maybe you didn't and + + + align:start position:0% +you probably did or maybe you didn't and +I'll just show you m sub y let me just + + align:start position:0% +I'll just show you m sub y let me just + + + align:start position:0% +I'll just show you m sub y let me just +double check is y^2 - + + align:start position:0% +double check is y^2 - + + + align:start position:0% +double check is y^2 - +x^2 over x^2 + y^2 I think with an extra + + align:start position:0% +x^2 over x^2 + y^2 I think with an extra + + + align:start position:0% +x^2 over x^2 + y^2 I think with an extra +squared on it + + align:start position:0% +squared on it + + + align:start position:0% +squared on it +yep and that's also equal to n + + align:start position:0% +yep and that's also equal to n + + + align:start position:0% +yep and that's also equal to n +subx right so what you know so far what + + align:start position:0% +subx right so what you know so far what + + + align:start position:0% +subx right so what you know so far what +you might have thought immediately was + + align:start position:0% +you might have thought immediately was + + + align:start position:0% +you might have thought immediately was +well N subx - M suby is the curl of f + + align:start position:0% +well N subx - M suby is the curl of f + + + align:start position:0% +well N subx - M suby is the curl of f +and that's equal to zero and therefore + + align:start position:0% +and that's equal to zero and therefore + + + align:start position:0% +and that's equal to zero and therefore +this Vector field is is conservative but + + align:start position:0% +this Vector field is is conservative but + + + align:start position:0% +this Vector field is is conservative but +the problem is the theorem you were + + align:start position:0% +the problem is the theorem you were + + + align:start position:0% +the problem is the theorem you were +thinking about referencing doesn't hold + + align:start position:0% +thinking about referencing doesn't hold + + + align:start position:0% +thinking about referencing doesn't hold +and the reason is because there are two + + align:start position:0% +and the reason is because there are two + + + align:start position:0% +and the reason is because there are two +hypotheses in that theorem and one is + + align:start position:0% +hypotheses in that theorem and one is + + + align:start position:0% +hypotheses in that theorem and one is +that uh if I if I Define this Vector + + align:start position:0% +that uh if I if I Define this Vector + + + align:start position:0% +that uh if I if I Define this Vector +field if I call it capital F the vector + + align:start position:0% +field if I call it capital F the vector + + + align:start position:0% +field if I call it capital F the vector +field or the theorem is that capital + + align:start position:0% +field or the theorem is that capital + + + align:start position:0% +field or the theorem is that capital +F defined + + align:start position:0% + + + + align:start position:0% + +everywhere and + + align:start position:0% +everywhere and + + + align:start position:0% +everywhere and +curl of + + align:start position:0% +curl of + + + align:start position:0% +curl of +f equal to zero + + align:start position:0% +f equal to zero + + + align:start position:0% +f equal to zero +implies F + + align:start position:0% + + + + align:start position:0% + +conservative okay so that's what that's + + align:start position:0% +conservative okay so that's what that's + + + align:start position:0% +conservative okay so that's what that's +the theorem you might have been trying + + align:start position:0% +the theorem you might have been trying + + + align:start position:0% +the theorem you might have been trying +to use you see from this the curl of f + + align:start position:0% +to use you see from this the curl of f + + + align:start position:0% +to use you see from this the curl of f +equals zero but the problem is the first + + align:start position:0% +equals zero but the problem is the first + + + align:start position:0% +equals zero but the problem is the first +part of this statement that F being + + align:start position:0% +part of this statement that F being + + + align:start position:0% +part of this statement that F being +defined everywhere is not true in fact + + align:start position:0% +defined everywhere is not true in fact + + + align:start position:0% +defined everywhere is not true in fact +there is one place in R2 where this + + align:start position:0% +there is one place in R2 where this + + + align:start position:0% +there is one place in R2 where this +Vector field is not defined and that is + + align:start position:0% +Vector field is not defined and that is + + + align:start position:0% +Vector field is not defined and that is +when X is zero and Y is zero because at + + align:start position:0% +when X is zero and Y is zero because at + + + align:start position:0% +when X is zero and Y is zero because at +that point Point obviously the + + align:start position:0% +that point Point obviously the + + + align:start position:0% +that point Point obviously the +denominator is zero and we run into + + align:start position:0% +denominator is zero and we run into + + + align:start position:0% +denominator is zero and we run into +trouble so you cannot use this theorem + + align:start position:0% +trouble so you cannot use this theorem + + + align:start position:0% +trouble so you cannot use this theorem +to say f is conservative because it's + + align:start position:0% +to say f is conservative because it's + + + align:start position:0% +to say f is conservative because it's +not defined everywhere or it's I should + + align:start position:0% +not defined everywhere or it's I should + + + align:start position:0% +not defined everywhere or it's I should +be careful I say that there is somewhere + + align:start position:0% +be careful I say that there is somewhere + + + align:start position:0% +be careful I say that there is somewhere +that it is not defined right so even + + align:start position:0% +that it is not defined right so even + + + align:start position:0% +that it is not defined right so even +though the curl of f equals z the first + + align:start position:0% +though the curl of f equals z the first + + + align:start position:0% +though the curl of f equals z the first +part of the statement is not true so you + + align:start position:0% +part of the statement is not true so you + + + align:start position:0% +part of the statement is not true so you +cannot get anything out of this theorem + + align:start position:0% +cannot get anything out of this theorem + + + align:start position:0% +cannot get anything out of this theorem +so so knowing the curl of f equals z + + align:start position:0% +so so knowing the curl of f equals z + + + align:start position:0% +so so knowing the curl of f equals z +doesn't tell you whether it's + + align:start position:0% +doesn't tell you whether it's + + + align:start position:0% +doesn't tell you whether it's +conservative or not okay so now what I'm + + align:start position:0% +conservative or not okay so now what I'm + + + align:start position:0% +conservative or not okay so now what I'm +going to do is I'm going to show I I + + align:start position:0% +going to do is I'm going to show I I + + + align:start position:0% +going to do is I'm going to show I I +told you we want to show it's not + + align:start position:0% +told you we want to show it's not + + + align:start position:0% +told you we want to show it's not +conservative I'm going to show you how + + align:start position:0% +conservative I'm going to show you how + + + align:start position:0% +conservative I'm going to show you how +we can show that and what we're going to + + align:start position:0% +we can show that and what we're going to + + + align:start position:0% +we can show that and what we're going to +do is we're going to find a a loop a + + align:start position:0% +do is we're going to find a a loop a + + + align:start position:0% +do is we're going to find a a loop a +closed loop so a closed curve in R2 that + + align:start position:0% +closed loop so a closed curve in R2 that + + + align:start position:0% +closed loop so a closed curve in R2 that +when I integrate this Vector field over + + align:start position:0% +when I integrate this Vector field over + + + align:start position:0% +when I integrate this Vector field over +that closed curve I don't get zero and + + align:start position:0% +that closed curve I don't get zero and + + + align:start position:0% +that closed curve I don't get zero and +then we would know that the that the + + align:start position:0% +then we would know that the that the + + + align:start position:0% +then we would know that the that the +vector field is not conservative so + + align:start position:0% +vector field is not conservative so + + + align:start position:0% +vector field is not conservative so +that's what we're going to do so let me + + align:start position:0% +that's what we're going to do so let me + + + align:start position:0% +that's what we're going to do so let me +uh let me write down what I'm let me + + align:start position:0% +uh let me write down what I'm let me + + + align:start position:0% +uh let me write down what I'm let me +write it out explicitly and then we'll + + align:start position:0% +write it out explicitly and then we'll + + + align:start position:0% +write it out explicitly and then we'll +figure out the curve we want and then + + align:start position:0% +figure out the curve we want and then + + + align:start position:0% +figure out the curve we want and then +we'll parameterize the curve of + + align:start position:0% +we'll parameterize the curve of + + + align:start position:0% +we'll parameterize the curve of +appropriately so I'm going to show for + + align:start position:0% +appropriately so I'm going to show for + + + align:start position:0% +appropriately so I'm going to show for +some closed curve I'm going to pick my + + align:start position:0% +some closed curve I'm going to pick my + + + align:start position:0% +some closed curve I'm going to pick my +curve and I'm going to integrate over + + align:start position:0% +curve and I'm going to integrate over + + + align:start position:0% +curve and I'm going to integrate over +the closed curve and I'm going to + + align:start position:0% +the closed curve and I'm going to + + + align:start position:0% +the closed curve and I'm going to +integrate this - y /x^2 + y^ 2 + + align:start position:0% +integrate this - y /x^2 + y^ 2 + + + align:start position:0% +integrate this - y /x^2 + y^ 2 +DX + x over x^2 + y^2 Dy and I'm going + + align:start position:0% +DX + x over x^2 + y^2 Dy and I'm going + + + align:start position:0% +DX + x over x^2 + y^2 Dy and I'm going +to show that if I pick a certain curve + + align:start position:0% +to show that if I pick a certain curve + + + align:start position:0% +to show that if I pick a certain curve +I'm going to get something that's not + + align:start position:0% +I'm going to get something that's not + + + align:start position:0% +I'm going to get something that's not +equal to zero okay and the curve I'm + + align:start position:0% +equal to zero okay and the curve I'm + + + align:start position:0% +equal to zero okay and the curve I'm +going to pick is the unit Circle so + + align:start position:0% +going to pick is the unit Circle so + + + align:start position:0% +going to pick is the unit Circle so +we're going to let C be the unit + + align:start position:0% + + + + align:start position:0% + +circle let c equal I'll just write the + + align:start position:0% +circle let c equal I'll just write the + + + align:start position:0% +circle let c equal I'll just write the +unit + + align:start position:0% +unit + + + align:start position:0% +unit +circle but how can I parameterize the + + align:start position:0% +circle but how can I parameterize the + + + align:start position:0% +circle but how can I parameterize the +unit circle easily I can parameterize + + align:start position:0% +unit circle easily I can parameterize + + + align:start position:0% +unit circle easily I can parameterize +the unit circle easily by x equal to + + align:start position:0% +the unit circle easily by x equal to + + + align:start position:0% +the unit circle easily by x equal to +cosine Theta and y equal to sin Theta + + align:start position:0% +cosine Theta and y equal to sin Theta + + + align:start position:0% +cosine Theta and y equal to sin Theta +right so let me do that and why am I + + align:start position:0% +right so let me do that and why am I + + + align:start position:0% +right so let me do that and why am I +picking the unit circle we'll see why + + align:start position:0% +picking the unit circle we'll see why + + + align:start position:0% +picking the unit circle we'll see why +that is in a second so we're going to + + align:start position:0% +that is in a second so we're going to + + + align:start position:0% +that is in a second so we're going to +let xal cosine Theta and y = sin + + align:start position:0% +let xal cosine Theta and y = sin + + + align:start position:0% +let xal cosine Theta and y = sin +Theta right and so now we know what goes + + align:start position:0% +Theta right and so now we know what goes + + + align:start position:0% +Theta right and so now we know what goes +here and we know what goes here by the + + align:start position:0% +here and we know what goes here by the + + + align:start position:0% +here and we know what goes here by the +way what is x^2 + y^2 it's cosine s thet + + align:start position:0% +way what is x^2 + y^2 it's cosine s thet + + + align:start position:0% +way what is x^2 + y^2 it's cosine s thet +plus sin s thet which is equal to 1 this + + align:start position:0% +plus sin s thet which is equal to 1 this + + + align:start position:0% +plus sin s thet which is equal to 1 this +is exactly the square of the radius and + + align:start position:0% +is exactly the square of the radius and + + + align:start position:0% +is exactly the square of the radius and +since we're on the unit circle that's + + align:start position:0% +since we're on the unit circle that's + + + align:start position:0% +since we're on the unit circle that's +one that's why I picked the unit circle + + align:start position:0% +one that's why I picked the unit circle + + + align:start position:0% +one that's why I picked the unit circle +because I didn't want I wanted the + + align:start position:0% +because I didn't want I wanted the + + + align:start position:0% +because I didn't want I wanted the +denominator to be very simple so I've + + align:start position:0% +denominator to be very simple so I've + + + align:start position:0% +denominator to be very simple so I've +got the x's and the Y's now what's + + align:start position:0% +got the x's and the Y's now what's + + + align:start position:0% +got the x's and the Y's now what's +DX DX is going to be equal to minus sin + + align:start position:0% +DX DX is going to be equal to minus sin + + + align:start position:0% +DX DX is going to be equal to minus sin +Theta D Theta + + align:start position:0% +Theta D Theta + + + align:start position:0% +Theta D Theta +and what's Dy I'll just write it right + + align:start position:0% +and what's Dy I'll just write it right + + + align:start position:0% +and what's Dy I'll just write it right +underneath here Dy is going to equal + + align:start position:0% +underneath here Dy is going to equal + + + align:start position:0% +underneath here Dy is going to equal +cine Theta D + + align:start position:0% +cine Theta D + + + align:start position:0% +cine Theta D +Theta right so let me let me uh just + + align:start position:0% +Theta right so let me let me uh just + + + align:start position:0% +Theta right so let me let me uh just +point out again what we were doing here + + align:start position:0% +point out again what we were doing here + + + align:start position:0% +point out again what we were doing here +we want to parameterize the unit circle + + align:start position:0% +we want to parameterize the unit circle + + + align:start position:0% +we want to parameterize the unit circle +I chose to parameterize it in Theta + + align:start position:0% +I chose to parameterize it in Theta + + + align:start position:0% +I chose to parameterize it in Theta +which I haven't told you what my bounds + + align:start position:0% +which I haven't told you what my bounds + + + align:start position:0% +which I haven't told you what my bounds +are yet but I've done everything else I + + align:start position:0% +are yet but I've done everything else I + + + align:start position:0% +are yet but I've done everything else I +needed to know what X and Y were and + + align:start position:0% +needed to know what X and Y were and + + + align:start position:0% +needed to know what X and Y were and +also what DX and Dy were and so now I + + align:start position:0% +also what DX and Dy were and so now I + + + align:start position:0% +also what DX and Dy were and so now I +can start substituting in okay so let's + + align:start position:0% +can start substituting in okay so let's + + + align:start position:0% +can start substituting in okay so let's +let's figure out what I get when I start + + align:start position:0% +let's figure out what I get when I start + + + align:start position:0% +let's figure out what I get when I start +substituting in so I'm integrating now + + align:start position:0% +substituting in so I'm integrating now + + + align:start position:0% +substituting in so I'm integrating now +again I said I didn't mention the bounds + + align:start position:0% +again I said I didn't mention the bounds + + + align:start position:0% +again I said I didn't mention the bounds +what are the bounds on Theta to get the + + align:start position:0% +what are the bounds on Theta to get the + + + align:start position:0% +what are the bounds on Theta to get the +whole unit circle I'm just going to + + align:start position:0% +whole unit circle I'm just going to + + + align:start position:0% +whole unit circle I'm just going to +integrate from 0 to 2 pi okay so I + + align:start position:0% +integrate from 0 to 2 pi okay so I + + + align:start position:0% +integrate from 0 to 2 pi okay so I +integrate from 0 to 2 pi that takes me + + align:start position:0% +integrate from 0 to 2 pi that takes me + + + align:start position:0% +integrate from 0 to 2 pi that takes me +all the way around the + + align:start position:0% +all the way around the + + + align:start position:0% +all the way around the +circle minus y is Nega sin Theta this + + align:start position:0% +circle minus y is Nega sin Theta this + + + align:start position:0% +circle minus y is Nega sin Theta this +part is one as I mentioned earlier and + + align:start position:0% +part is one as I mentioned earlier and + + + align:start position:0% +part is one as I mentioned earlier and +then DX is minus sin Theta D Theta so I + + align:start position:0% +then DX is minus sin Theta D Theta so I + + + align:start position:0% +then DX is minus sin Theta D Theta so I +have a minus sin Theta * a minus sin + + align:start position:0% +have a minus sin Theta * a minus sin + + + align:start position:0% +have a minus sin Theta * a minus sin +Theta that's going to give me a s^ 2 + + align:start position:0% +Theta that's going to give me a s^ 2 + + + align:start position:0% +Theta that's going to give me a s^ 2 +Theta D + + align:start position:0% +Theta D + + + align:start position:0% +Theta D +Theta and then this term the second term + + align:start position:0% +Theta and then this term the second term + + + align:start position:0% +Theta and then this term the second term +when I integrate over the curve I'm + + align:start position:0% +when I integrate over the curve I'm + + + align:start position:0% +when I integrate over the curve I'm +going to just rewrite another one here + + align:start position:0% +going to just rewrite another one here + + + align:start position:0% +going to just rewrite another one here +separately momentarily X is cosine + + align:start position:0% +separately momentarily X is cosine + + + align:start position:0% +separately momentarily X is cosine +Theta x^2 + y^2 is 1 and Dy is cosine + + align:start position:0% +Theta x^2 + y^2 is 1 and Dy is cosine + + + align:start position:0% +Theta x^2 + y^2 is 1 and Dy is cosine +Theta D Theta so I get cosine 2 Theta D + + align:start position:0% +Theta D Theta so I get cosine 2 Theta D + + + align:start position:0% +Theta D Theta so I get cosine 2 Theta D +Theta all + + align:start position:0% + + + + align:start position:0% + +right now here we are if I tried to + + align:start position:0% +right now here we are if I tried to + + + align:start position:0% +right now here we are if I tried to +integrate both of these separately it + + align:start position:0% +integrate both of these separately it + + + align:start position:0% +integrate both of these separately it +would take potentially a very long time + + align:start position:0% +would take potentially a very long time + + + align:start position:0% +would take potentially a very long time +and be kind of annoying but if you + + align:start position:0% +and be kind of annoying but if you + + + align:start position:0% +and be kind of annoying but if you +notice because I can I can add these + + align:start position:0% +notice because I can I can add these + + + align:start position:0% +notice because I can I can add these +integrals I can add over over they have + + align:start position:0% +integrals I can add over over they have + + + align:start position:0% +integrals I can add over over they have +the same bounds so I can put them back + + align:start position:0% +the same bounds so I can put them back + + + align:start position:0% +the same bounds so I can put them back +together right sin squ theta plus cosine + + align:start position:0% +together right sin squ theta plus cosine + + + align:start position:0% +together right sin squ theta plus cosine +squ Theta always equals one that's a + + align:start position:0% +squ Theta always equals one that's a + + + align:start position:0% +squ Theta always equals one that's a +trig identity that's good to know so + + align:start position:0% +trig identity that's good to know so + + + align:start position:0% +trig identity that's good to know so +this in fact is equal to the integral + + align:start position:0% +this in fact is equal to the integral + + + align:start position:0% +this in fact is equal to the integral +from 0 to 2 pi of D + + align:start position:0% +from 0 to 2 pi of D + + + align:start position:0% +from 0 to 2 pi of D +Theta so let me come back one more time + + align:start position:0% +Theta so let me come back one more time + + + align:start position:0% +Theta so let me come back one more time +and and make sure we understand we're + + align:start position:0% +and and make sure we understand we're + + + align:start position:0% +and and make sure we understand we're +integrating from 0 2 pi sin th D theta + + align:start position:0% +integrating from 0 2 pi sin th D theta + + + align:start position:0% +integrating from 0 2 pi sin th D theta +plus cosine th D Theta that's just sin + + align:start position:0% +plus cosine th D Theta that's just sin + + + align:start position:0% +plus cosine th D Theta that's just sin +th plus cosine thet D Theta so that's + + align:start position:0% +th plus cosine thet D Theta so that's + + + align:start position:0% +th plus cosine thet D Theta so that's +one so 1 time D Theta but what is this + + align:start position:0% +one so 1 time D Theta but what is this + + + align:start position:0% +one so 1 time D Theta but what is this +well this integral from 0 to 2 pi of D + + align:start position:0% +well this integral from 0 to 2 pi of D + + + align:start position:0% +well this integral from 0 to 2 pi of D +Theta is Theta evaluated at 2 pi and Zer + + align:start position:0% +Theta is Theta evaluated at 2 pi and Zer + + + align:start position:0% +Theta is Theta evaluated at 2 pi and Zer +I actually get 2 pi which is in + + align:start position:0% +I actually get 2 pi which is in + + + align:start position:0% +I actually get 2 pi which is in +particular not equal to zero right so + + align:start position:0% +particular not equal to zero right so + + + align:start position:0% +particular not equal to zero right so +that actually shows you that this Vector + + align:start position:0% +that actually shows you that this Vector + + + align:start position:0% +that actually shows you that this Vector +field is not conservative now why does + + align:start position:0% +field is not conservative now why does + + + align:start position:0% +field is not conservative now why does +this make sense this makes sense because + + align:start position:0% +this make sense this makes sense because + + + align:start position:0% +this make sense this makes sense because +if I really think about what I'm doing + + align:start position:0% +if I really think about what I'm doing + + + align:start position:0% +if I really think about what I'm doing +if you actually this is the place where + + align:start position:0% +if you actually this is the place where + + + align:start position:0% +if you actually this is the place where +maybe it'll ultimately make the most + + align:start position:0% +maybe it'll ultimately make the most + + + align:start position:0% +maybe it'll ultimately make the most +sense what you're doing is you're + + align:start position:0% +sense what you're doing is you're + + + align:start position:0% +sense what you're doing is you're +looking at how Theta changes as you go + + align:start position:0% +looking at how Theta changes as you go + + + align:start position:0% +looking at how Theta changes as you go +all the way around the origin once and + + align:start position:0% +all the way around the origin once and + + + align:start position:0% +all the way around the origin once and +Theta changes by 2 pi if you go all the + + align:start position:0% +Theta changes by 2 pi if you go all the + + + align:start position:0% +Theta changes by 2 pi if you go all the +way around one time the Theta value + + align:start position:0% +way around one time the Theta value + + + align:start position:0% +way around one time the Theta value +starts at zero and then goes up to 2 pi + + align:start position:0% +starts at zero and then goes up to 2 pi + + + align:start position:0% +starts at zero and then goes up to 2 pi +and so that's exactly where this 2 pi is + + align:start position:0% +and so that's exactly where this 2 pi is + + + align:start position:0% +and so that's exactly where this 2 pi is +coming from so that actually is + + align:start position:0% +coming from so that actually is + + + align:start position:0% +coming from so that actually is +ultimately how you were going to be able + + align:start position:0% +ultimately how you were going to be able + + + align:start position:0% +ultimately how you were going to be able +to show that this Vector field is not + + align:start position:0% +to show that this Vector field is not + + + align:start position:0% +to show that this Vector field is not +conservative so let me go back and just + + align:start position:0% +conservative so let me go back and just + + + align:start position:0% +conservative so let me go back and just +remind you where we came + + align:start position:0% +remind you where we came + + + align:start position:0% +remind you where we came +from we started off with a vector + + align:start position:0% +from we started off with a vector + + + align:start position:0% +from we started off with a vector +field and we wanted to know if it was + + align:start position:0% +field and we wanted to know if it was + + + align:start position:0% +field and we wanted to know if it was +not + + align:start position:0% +not + + + align:start position:0% +not +conservative we wanted to show sorry it + + align:start position:0% +conservative we wanted to show sorry it + + + align:start position:0% +conservative we wanted to show sorry it +was not conservative so the first thing + + align:start position:0% +was not conservative so the first thing + + + align:start position:0% +was not conservative so the first thing +you might want to check which maybe you + + align:start position:0% +you might want to check which maybe you + + + align:start position:0% +you might want to check which maybe you +did was if the curl was zero and in fact + + align:start position:0% +did was if the curl was zero and in fact + + + align:start position:0% +did was if the curl was zero and in fact +the curl is zero and so maybe you + + align:start position:0% +the curl is zero and so maybe you + + + align:start position:0% +the curl is zero and so maybe you +thought well she might have done + + align:start position:0% +thought well she might have done + + + align:start position:0% +thought well she might have done +something wrong or she might have + + align:start position:0% +something wrong or she might have + + + align:start position:0% +something wrong or she might have +written something wrong but we can't + + align:start position:0% +written something wrong but we can't + + + align:start position:0% +written something wrong but we can't +actually appeal to the theorem you want + + align:start position:0% +actually appeal to the theorem you want + + + align:start position:0% +actually appeal to the theorem you want +to appeal to to make any conclusion + + align:start position:0% +to appeal to to make any conclusion + + + align:start position:0% +to appeal to to make any conclusion +about the vector field because the + + align:start position:0% +about the vector field because the + + + align:start position:0% +about the vector field because the +vector field in our example is not + + align:start position:0% +vector field in our example is not + + + align:start position:0% +vector field in our example is not +defined for every value uh of XY so for + + align:start position:0% +defined for every value uh of XY so for + + + align:start position:0% +defined for every value uh of XY so for +every value in the XY plane we cannot + + align:start position:0% +every value in the XY plane we cannot + + + align:start position:0% +every value in the XY plane we cannot +Define f there's one value for which we + + align:start position:0% +Define f there's one value for which we + + + align:start position:0% +Define f there's one value for which we +cannot Define f okay and so we cannot + + align:start position:0% +cannot Define f okay and so we cannot + + + align:start position:0% +cannot Define f okay and so we cannot +say that if the curl is zero then the + + align:start position:0% +say that if the curl is zero then the + + + align:start position:0% +say that if the curl is zero then the +then the vector field is conservative we + + align:start position:0% +then the vector field is conservative we + + + align:start position:0% +then the vector field is conservative we +can't draw any conclusion from this + + align:start position:0% +can't draw any conclusion from this + + + align:start position:0% +can't draw any conclusion from this +theorem so then we had to actually find + + align:start position:0% +theorem so then we had to actually find + + + align:start position:0% +theorem so then we had to actually find +a way to show it was not conservative + + align:start position:0% +a way to show it was not conservative + + + align:start position:0% +a way to show it was not conservative +without looking at the curl and that + + align:start position:0% +without looking at the curl and that + + + align:start position:0% +without looking at the curl and that +amounts to showing there is a closed + + align:start position:0% +amounts to showing there is a closed + + + align:start position:0% +amounts to showing there is a closed +curve that when I integrate over that + + align:start position:0% +curve that when I integrate over that + + + align:start position:0% +curve that when I integrate over that +closed curve when I look at what the + + align:start position:0% +closed curve when I look at what the + + + align:start position:0% +closed curve when I look at what the +vector field does over that closed curve + + align:start position:0% +vector field does over that closed curve + + + align:start position:0% +vector field does over that closed curve +I get something non zero and we picked + + align:start position:0% +I get something non zero and we picked + + + align:start position:0% +I get something non zero and we picked +an easy example this is actually what + + align:start position:0% +an easy example this is actually what + + + align:start position:0% +an easy example this is actually what +what the integral will look like over + + align:start position:0% +what the integral will look like over + + + align:start position:0% +what the integral will look like over +the closed curve in X and Y we let our + + align:start position:0% +the closed curve in X and Y we let our + + + align:start position:0% +the closed curve in X and Y we let our +closed curve be the unit circle then we + + align:start position:0% +closed curve be the unit circle then we + + + align:start position:0% +closed curve be the unit circle then we +parameterized in Theta and we see that + + align:start position:0% +parameterized in Theta and we see that + + + align:start position:0% +parameterized in Theta and we see that +actually what this Vector field is doing + + align:start position:0% +actually what this Vector field is doing + + + align:start position:0% +actually what this Vector field is doing +is it's it's looking at what is what is + + align:start position:0% +is it's it's looking at what is what is + + + align:start position:0% +is it's it's looking at what is what is +D Theta it's finding out what D Theta is + + align:start position:0% +D Theta it's finding out what D Theta is + + + align:start position:0% +D Theta it's finding out what D Theta is +and so we we find out the integral from + + align:start position:0% +and so we we find out the integral from + + + align:start position:0% +and so we we find out the integral from +0 to 2 pi of D Theta is obviously not + + align:start position:0% +0 to 2 pi of D Theta is obviously not + + + align:start position:0% +0 to 2 pi of D Theta is obviously not +zero and that gives us the vector field + + align:start position:0% +zero and that gives us the vector field + + + align:start position:0% +zero and that gives us the vector field +is not conservative so that's where all + + align:start position:0% +is not conservative so that's where all + + + align:start position:0% +is not conservative so that's where all +stop \ No newline at end of file diff --git a/nvXRJIBOREc.txt b/nvXRJIBOREc.txt new file mode 100644 index 0000000000000000000000000000000000000000..933ea3b774d4293b3787072f578b2561849b10c0 --- /dev/null +++ b/nvXRJIBOREc.txt @@ -0,0 +1,6491 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +well ok I'm happy to be back and I'm + + align:start position:0% +well ok I'm happy to be back and I'm + + + align:start position:0% +well ok I'm happy to be back and I'm +really happy about the project proposals + + align:start position:0% +really happy about the project proposals + + + align:start position:0% +really happy about the project proposals +that are coming in + + align:start position:0% +that are coming in + + + align:start position:0% +that are coming in +this is like ok this is a really a good + + align:start position:0% +this is like ok this is a really a good + + + align:start position:0% +this is like ok this is a really a good +part of the course and so keep them + + align:start position:0% +part of the course and so keep them + + + align:start position:0% +part of the course and so keep them +coming if and and I happy to give + + align:start position:0% +coming if and and I happy to give + + + align:start position:0% +coming if and and I happy to give +whatever feedback I can on those + + align:start position:0% +whatever feedback I can on those + + + align:start position:0% +whatever feedback I can on those +proposals and do make a start there + + align:start position:0% +proposals and do make a start there + + + align:start position:0% +proposals and do make a start there +they're really good and if if some are + + align:start position:0% +they're really good and if if some are + + + align:start position:0% +they're really good and if if some are +completed before the end of the semester + + align:start position:0% +completed before the end of the semester + + + align:start position:0% +completed before the end of the semester +and we can give produce a chance offer + + align:start position:0% +and we can give produce a chance offer + + + align:start position:0% +and we can give produce a chance offer +you a chance to report on them that's + + align:start position:0% +you a chance to report on them that's + + + align:start position:0% +you a chance to report on them that's +that's good too so well done with those + + align:start position:0% +that's good too so well done with those + + + align:start position:0% +that's good too so well done with those +proposals so while I'm today I'm jumping + + align:start position:0% +proposals so while I'm today I'm jumping + + + align:start position:0% +proposals so while I'm today I'm jumping +to part six + + align:start position:0% +to part six + + + align:start position:0% +to part six +so part six and part seven are + + align:start position:0% +so part six and part seven are + + + align:start position:0% +so part six and part seven are +optimization which is the fundamental + + align:start position:0% +optimization which is the fundamental + + + align:start position:0% +optimization which is the fundamental +algorithm that goes into deep learning + + align:start position:0% +algorithm that goes into deep learning + + + align:start position:0% +algorithm that goes into deep learning +so we've got to start with optimization + + align:start position:0% +so we've got to start with optimization + + + align:start position:0% +so we've got to start with optimization +everybody has to get that picture and + + align:start position:0% +everybody has to get that picture and + + + align:start position:0% +everybody has to get that picture and +then part seven will be the structure of + + align:start position:0% +then part seven will be the structure of + + + align:start position:0% +then part seven will be the structure of +CNN's convolutional neural nets and all + + align:start position:0% +CNN's convolutional neural nets and all + + + align:start position:0% +CNN's convolutional neural nets and all +that all kinds of applications and so + + align:start position:0% +that all kinds of applications and so + + + align:start position:0% +that all kinds of applications and so +can we start with optimization so first + + align:start position:0% +can we start with optimization so first + + + align:start position:0% +can we start with optimization so first +could I like get the basic facts about + + align:start position:0% +could I like get the basic facts about + + + align:start position:0% +could I like get the basic facts about +three terms of a Taylor series so that's + + align:start position:0% +three terms of a Taylor series so that's + + + align:start position:0% +three terms of a Taylor series so that's +typical it's seldom that we would go up + + align:start position:0% +typical it's seldom that we would go up + + + align:start position:0% +typical it's seldom that we would go up +to third derivatives in optimization so + + align:start position:0% +to third derivatives in optimization so + + + align:start position:0% +to third derivatives in optimization so +that's the most useful approximation to + + align:start position:0% +that's the most useful approximation to + + + align:start position:0% +that's the most useful approximation to +a function everybody recognizes it here + + align:start position:0% +a function everybody recognizes it here + + + align:start position:0% +a function everybody recognizes it here +I'm thinking of f as just one function + + align:start position:0% +I'm thinking of f as just one function + + + align:start position:0% +I'm thinking of f as just one function +and X as just one variable but but now I + + align:start position:0% +and X as just one variable but but now I + + + align:start position:0% +and X as just one variable but but now I +really want to go to + + align:start position:0% +really want to go to + + + align:start position:0% +really want to go to +more variables so what do I have to + + align:start position:0% +more variables so what do I have to + + + align:start position:0% +more variables so what do I have to +change if f is a function of more + + align:start position:0% +change if f is a function of more + + + align:start position:0% +change if f is a function of more +variables so now now I'm thinking of X + + align:start position:0% +variables so now now I'm thinking of X + + + align:start position:0% +variables so now now I'm thinking of X +as well no let me see yeah I want n + + align:start position:0% +as well no let me see yeah I want n + + + align:start position:0% +as well no let me see yeah I want n +variables here X is X 1 up to xn so what + + align:start position:0% +variables here X is X 1 up to xn so what + + + align:start position:0% +variables here X is X 1 up to xn so what +it would just to get the words straight + + align:start position:0% +it would just to get the words straight + + + align:start position:0% +it would just to get the words straight +so we can begin on optimization so what + + align:start position:0% +so we can begin on optimization so what + + + align:start position:0% +so we can begin on optimization so what +will be the similar step so the function + + align:start position:0% +will be the similar step so the function + + + align:start position:0% +will be the similar step so the function +f at X remember X is n variables okay + + align:start position:0% +f at X remember X is n variables okay + + + align:start position:0% +f at X remember X is n variables okay +now what do I have Delta X so what + + align:start position:0% +now what do I have Delta X so what + + + align:start position:0% +now what do I have Delta X so what +what's the point about Delta X now it's + + align:start position:0% +what's the point about Delta X now it's + + + align:start position:0% +what's the point about Delta X now it's +a vector Delta X 1 to Delta X n and what + + align:start position:0% +a vector Delta X 1 to Delta X n and what + + + align:start position:0% +a vector Delta X 1 to Delta X n and what +about the derivative of F it's a vector + + align:start position:0% +about the derivative of F it's a vector + + + align:start position:0% +about the derivative of F it's a vector +to the derivative of F with respect to X + + align:start position:0% +to the derivative of F with respect to X + + + align:start position:0% +to the derivative of F with respect to X +1 the derivative of F with respect X 2 + + align:start position:0% +1 the derivative of F with respect X 2 + + + align:start position:0% +1 the derivative of F with respect X 2 +and so on so what do I have what do I + + align:start position:0% +and so on so what do I have what do I + + + align:start position:0% +and so on so what do I have what do I +have to change about that I now those + + align:start position:0% +have to change about that I now those + + + align:start position:0% +have to change about that I now those +guys are vectors so it's their dot + + align:start position:0% +guys are vectors so it's their dot + + + align:start position:0% +guys are vectors so it's their dot +product so it's Delta X transpose that + + align:start position:0% +product so it's Delta X transpose that + + + align:start position:0% +product so it's Delta X transpose that +vector times this DF DX so what's the so + + align:start position:0% +vector times this DF DX so what's the so + + + align:start position:0% +vector times this DF DX so what's the so +this now I'm replacing this by all the + + align:start position:0% +this now I'm replacing this by all the + + + align:start position:0% +this now I'm replacing this by all the +derivatives and the it's the gradient so + + align:start position:0% +derivatives and the it's the gradient so + + + align:start position:0% +derivatives and the it's the gradient so +the gradient of F at X is the + + align:start position:0% +the gradient of F at X is the + + + align:start position:0% +the gradient of F at X is the +derivatives let's see it's essential to + + align:start position:0% +derivatives let's see it's essential to + + + align:start position:0% +derivatives let's see it's essential to +get the notation straight here yeah so + + align:start position:0% +get the notation straight here yeah so + + + align:start position:0% +get the notation straight here yeah so +it'll be the partial derivatives of the + + align:start position:0% +it'll be the partial derivatives of the + + + align:start position:0% +it'll be the partial derivatives of the +function f so grad F is the partial + + align:start position:0% +function f so grad F is the partial + + + align:start position:0% +function f so grad F is the partial +derivatives of F with respect to X 1 + + align:start position:0% +derivatives of F with respect to X 1 + + + align:start position:0% +derivatives of F with respect to X 1 +down to partial derivative the strike to + + align:start position:0% +down to partial derivative the strike to + + + align:start position:0% +down to partial derivative the strike to +exam okay good that's the linear term + + align:start position:0% +exam okay good that's the linear term + + + align:start position:0% +exam okay good that's the linear term +and now what's the quadratic term 1/2 + + align:start position:0% +and now what's the quadratic term 1/2 + + + align:start position:0% +and now what's the quadratic term 1/2 +now Delta X isn't a scalar anymore it's + + align:start position:0% +now Delta X isn't a scalar anymore it's + + + align:start position:0% +now Delta X isn't a scalar anymore it's +a vector so I'm going to have Delta X + + align:start position:0% +a vector so I'm going to have Delta X + + + align:start position:0% +a vector so I'm going to have Delta X +transpose and a Delta X and what goes in + + align:start position:0% +transpose and a Delta X and what goes in + + + align:start position:0% +transpose and a Delta X and what goes in +between is the second derivatives but + + align:start position:0% +between is the second derivatives but + + + align:start position:0% +between is the second derivatives but +I've got a function of n variables and + + align:start position:0% +I've got a function of n variables and + + + align:start position:0% +I've got a function of n variables and +so what does this mmm so now I have a + + align:start position:0% +so what does this mmm so now I have a + + + align:start position:0% +so what does this mmm so now I have a +matrix of second derivatives right and + + align:start position:0% +matrix of second derivatives right and + + + align:start position:0% +matrix of second derivatives right and +I'll call it H this is the matrix of + + align:start position:0% +I'll call it H this is the matrix of + + + align:start position:0% +I'll call it H this is the matrix of +second derivatives h JK is the second + + align:start position:0% +second derivatives h JK is the second + + + align:start position:0% +second derivatives h JK is the second +derivative of F with respect to XJ and + + align:start position:0% +derivative of F with respect to XJ and + + + align:start position:0% +derivative of F with respect to XJ and +XK and what's the name for this guy the + + align:start position:0% +XK and what's the name for this guy the + + + align:start position:0% +XK and what's the name for this guy the +Hessian Hessian matrix how the Hessians + + align:start position:0% +Hessian Hessian matrix how the Hessians + + + align:start position:0% +Hessian Hessian matrix how the Hessians +got into this picture I don't know the + + align:start position:0% +got into this picture I don't know the + + + align:start position:0% +got into this picture I don't know the +only Hessians I know are the ones who + + align:start position:0% +only Hessians I know are the ones who + + + align:start position:0% +only Hessians I know are the ones who +fought in the Revolutionary War for + + align:start position:0% +fought in the Revolutionary War for + + + align:start position:0% +fought in the Revolutionary War for +somebody who which side were they on I + + align:start position:0% +somebody who which side were they on I + + + align:start position:0% +somebody who which side were they on I +think maybe the wrong side the French + + align:start position:0% +think maybe the wrong side the French + + + align:start position:0% +think maybe the wrong side the French +were on our side and yeah anyway Hessian + + align:start position:0% +were on our side and yeah anyway Hessian + + + align:start position:0% +were on our side and yeah anyway Hessian +matrix and what what are the facts about + + align:start position:0% +matrix and what what are the facts about + + + align:start position:0% +matrix and what what are the facts about +that matrix well the first fact is that + + align:start position:0% +that matrix well the first fact is that + + + align:start position:0% +that matrix well the first fact is that +it's them and the key fact is it's + + align:start position:0% +it's them and the key fact is it's + + + align:start position:0% +it's them and the key fact is it's +symmetric ok and again that's an + + align:start position:0% +symmetric ok and again that's an + + + align:start position:0% +symmetric ok and again that's an +approximation so and everybody involved + + align:start position:0% +approximation so and everybody involved + + + align:start position:0% +approximation so and everybody involved +recognizes that if we have a fun if n is + + align:start position:0% +recognizes that if we have a fun if n is + + + align:start position:0% +recognizes that if we have a fun if n is +very large and we have a function of + + align:start position:0% +very large and we have a function of + + + align:start position:0% +very large and we have a function of +many variables then we had n derivatives + + align:start position:0% +many variables then we had n derivatives + + + align:start position:0% +many variables then we had n derivatives +to compute here and about 1/2 and + + align:start position:0% +to compute here and about 1/2 and + + + align:start position:0% +to compute here and about 1/2 and +squared derivatives using the the half + + align:start position:0% +squared derivatives using the the half + + + align:start position:0% +squared derivatives using the the half +comes from the symmetry but the key + + align:start position:0% +comes from the symmetry but the key + + + align:start position:0% +comes from the symmetry but the key +point is the N squared variables + + align:start position:0% +point is the N squared variables + + + align:start position:0% +point is the N squared variables +derivatives to compute there so + + align:start position:0% +derivatives to compute there so + + + align:start position:0% +derivatives to compute there so +computing the gradient is feasible if n + + align:start position:0% +computing the gradient is feasible if n + + + align:start position:0% +computing the gradient is feasible if n +is small or moderately large actually + + align:start position:0% +is small or moderately large actually + + + align:start position:0% +is small or moderately large actually +you by using autumn + + align:start position:0% +you by using autumn + + + align:start position:0% +you by using autumn +differentiation the key idea of back + + align:start position:0% +differentiation the key idea of back + + + align:start position:0% +differentiation the key idea of back +propagation back prop you can get you + + align:start position:0% +propagation back prop you can get you + + + align:start position:0% +propagation back prop you can get you +can do you can speed up the computation + + align:start position:0% +can do you can speed up the computation + + + align:start position:0% +can do you can speed up the computation +of derivatives quite amazingly but still + + align:start position:0% +of derivatives quite amazingly but still + + + align:start position:0% +of derivatives quite amazingly but still +for the size of deep learning problems + + align:start position:0% +for the size of deep learning problems + + + align:start position:0% +for the size of deep learning problems +as that's that's how to reach okay so + + align:start position:0% +as that's that's how to reach okay so + + + align:start position:0% +as that's that's how to reach okay so +that's the picture and then I will want + + align:start position:0% +that's the picture and then I will want + + + align:start position:0% +that's the picture and then I will want +to solve use this to solve equations let + + align:start position:0% +to solve use this to solve equations let + + + align:start position:0% +to solve use this to solve equations let +me there's a parallel picture for us + + align:start position:0% +me there's a parallel picture for us + + + align:start position:0% +me there's a parallel picture for us +vector F so now this is a vector + + align:start position:0% +vector F so now this is a vector + + + align:start position:0% +vector F so now this is a vector +function this is F 1 of X up to f of X + + align:start position:0% +function this is F 1 of X up to f of X + + + align:start position:0% +function this is F 1 of X up to f of X +and X is X 1 to X n so I have n + + align:start position:0% +and X is X 1 to X n so I have n + + + align:start position:0% +and X is X 1 to X n so I have n +functions of n variables and functions + + align:start position:0% +functions of n variables and functions + + + align:start position:0% +functions of n variables and functions +of n variables well that's exactly what + + align:start position:0% +of n variables well that's exactly what + + + align:start position:0% +of n variables well that's exactly what +I have in the gradient that's think of + + align:start position:0% +I have in the gradient that's think of + + + align:start position:0% +I have in the gradient that's think of +these two is parallel the parallel being + + align:start position:0% +these two is parallel the parallel being + + + align:start position:0% +these two is parallel the parallel being +s is corresponds to the gradient of F n + + align:start position:0% +s is corresponds to the gradient of F n + + + align:start position:0% +s is corresponds to the gradient of F n +functions of n variables ok ok so now + + align:start position:0% +functions of n variables ok ok so now + + + align:start position:0% +functions of n variables ok ok so now +maybe what I'm after here is to solve F + + align:start position:0% +maybe what I'm after here is to solve F + + + align:start position:0% +maybe what I'm after here is to solve F +equals 0 so I'm going to think about the + + align:start position:0% +equals 0 so I'm going to think about the + + + align:start position:0% +equals 0 so I'm going to think about the +the F at X plus Delta X so it starts + + align:start position:0% +the F at X plus Delta X so it starts + + + align:start position:0% +the F at X plus Delta X so it starts +with f of X and then we have the + + align:start position:0% +with f of X and then we have the + + + align:start position:0% +with f of X and then we have the +correction times the matrix of first + + align:start position:0% +correction times the matrix of first + + + align:start position:0% +correction times the matrix of first +derivatives and what's the name for that + + align:start position:0% + + + + align:start position:0% + +matrix of first derivatives + + align:start position:0% +matrix of first derivatives + + + align:start position:0% +matrix of first derivatives +well if I'm just given n functions and I + + align:start position:0% +well if I'm just given n functions and I + + + align:start position:0% +well if I'm just given n functions and I +yeah what am i what am i after here I'm + + align:start position:0% +yeah what am i what am i after here I'm + + + align:start position:0% +yeah what am i what am i after here I'm +looking for the Jacobian so hair will go + + align:start position:0% +looking for the Jacobian so hair will go + + + align:start position:0% +looking for the Jacobian so hair will go +the Jacobian J this is the Jacobian + + align:start position:0% +the Jacobian J this is the Jacobian + + + align:start position:0% +the Jacobian J this is the Jacobian +named after Jacobi Jacobian matrix and + + align:start position:0% +named after Jacobi Jacobian matrix and + + + align:start position:0% +named after Jacobi Jacobian matrix and +what are its entries J the JK entry is + + align:start position:0% +what are its entries J the JK entry is + + + align:start position:0% +what are its entries J the JK entry is +the derivative of the Jayce function + + align:start position:0% +the derivative of the Jayce function + + + align:start position:0% +the derivative of the Jayce function +with respect to the case very okay and + + align:start position:0% +with respect to the case very okay and + + + align:start position:0% +with respect to the case very okay and +I'm stopping a first-order there okay so + + align:start position:0% +I'm stopping a first-order there okay so + + + align:start position:0% +I'm stopping a first-order there okay so +these are those sort of like facts of + + align:start position:0% +these are those sort of like facts of + + + align:start position:0% +these are those sort of like facts of +calculus facts of 1802 you could say + + align:start position:0% +calculus facts of 1802 you could say + + + align:start position:0% +calculus facts of 1802 you could say +multivariable calculus that's the point + + align:start position:0% +multivariable calculus that's the point + + + align:start position:0% +multivariable calculus that's the point +notice that we're we're doing just like + + align:start position:0% +notice that we're we're doing just like + + + align:start position:0% +notice that we're we're doing just like +the first half of 1802 just different + + align:start position:0% +the first half of 1802 just different + + + align:start position:0% +the first half of 1802 just different +differential calculus derivatives Taylor + + align:start position:0% +differential calculus derivatives Taylor + + + align:start position:0% +differential calculus derivatives Taylor +series we're not doing multiple + + align:start position:0% +series we're not doing multiple + + + align:start position:0% +series we're not doing multiple +integrals that's not part of our world + + align:start position:0% +integrals that's not part of our world + + + align:start position:0% +integrals that's not part of our world +here okay so that's the background now I + + align:start position:0% +here okay so that's the background now I + + + align:start position:0% +here okay so that's the background now I +want to look at optimization okay okay + + align:start position:0% +want to look at optimization okay okay + + + align:start position:0% +want to look at optimization okay okay +so over here I want to optimize well + + align:start position:0% +so over here I want to optimize well + + + align:start position:0% +so over here I want to optimize well +over here let me try to minimize f of X + + align:start position:0% +over here let me try to minimize f of X + + + align:start position:0% +over here let me try to minimize f of X +and I'll be in the vector case here and + + align:start position:0% +and I'll be in the vector case here and + + + align:start position:0% +and I'll be in the vector case here and +over here + + align:start position:0% + + + + align:start position:0% + +I want to solve F equals zero and of + + align:start position:0% +I want to solve F equals zero and of + + + align:start position:0% +I want to solve F equals zero and of +course that means that means F of one + + align:start position:0% +course that means that means F of one + + + align:start position:0% +course that means that means F of one +equal to zero all the way along to F N + + align:start position:0% +equal to zero all the way along to F N + + + align:start position:0% +equal to zero all the way along to F N +equals zero here I have n equations let + + align:start position:0% +equals zero here I have n equations let + + + align:start position:0% +equals zero here I have n equations let +me start with that one and I'll start + + align:start position:0% +me start with that one and I'll start + + + align:start position:0% +me start with that one and I'll start +with Newton's method Newton the best to + + align:start position:0% +with Newton's method Newton the best to + + + align:start position:0% +with Newton's method Newton the best to +solve these n equations in n unknowns + + align:start position:0% +solve these n equations in n unknowns + + + align:start position:0% +solve these n equations in n unknowns +okay so Newton which is often not + + align:start position:0% +okay so Newton which is often not + + + align:start position:0% +okay so Newton which is often not +presented in 1802 that's a crime because + + align:start position:0% +presented in 1802 that's a crime because + + + align:start position:0% +presented in 1802 that's a crime because +that's the that's the big application of + + align:start position:0% + + + + align:start position:0% + +gradients in jacobians okay so I'm + + align:start position:0% +gradients in jacobians okay so I'm + + + align:start position:0% +gradients in jacobians okay so I'm +trying to solve n equations in n + + align:start position:0% +trying to solve n equations in n + + + align:start position:0% +trying to solve n equations in n +unknowns and so I want F at X plus Delta + + align:start position:0% +unknowns and so I want F at X plus Delta + + + align:start position:0% +unknowns and so I want F at X plus Delta +X to be zero right so I want f of X plus + + align:start position:0% +X to be zero right so I want f of X plus + + + align:start position:0% +X to be zero right so I want f of X plus +Delta X to be zero so so f of X plus + + align:start position:0% +Delta X to be zero so so f of X plus + + + align:start position:0% +Delta X to be zero so so f of X plus +Delta X is I'm putting in a zero I'm + + align:start position:0% +Delta X is I'm putting in a zero I'm + + + align:start position:0% +Delta X is I'm putting in a zero I'm +just copying that equation is f at where + + align:start position:0% +just copying that equation is f at where + + + align:start position:0% +just copying that equation is f at where +I am X let's let me use K for the case + + align:start position:0% +I am X let's let me use K for the case + + + align:start position:0% +I am X let's let me use K for the case +iteration so I'm at a point XK I want to + + align:start position:0% +iteration so I'm at a point XK I want to + + + align:start position:0% +iteration so I'm at a point XK I want to +get to a point XK plus one and so I've 0 + + align:start position:0% +get to a point XK plus one and so I've 0 + + + align:start position:0% +get to a point XK plus one and so I've 0 +is f of X plus J at that point times + + align:start position:0% +is f of X plus J at that point times + + + align:start position:0% +is f of X plus J at that point times +Delta X which is XK plus one minus XK + + align:start position:0% + + + + align:start position:0% + +good that's Newton's method of course a + + align:start position:0% +good that's Newton's method of course a + + + align:start position:0% +good that's Newton's method of course a +zero isn't quite true well zero will be + + align:start position:0% +zero isn't quite true well zero will be + + + align:start position:0% +zero isn't quite true well zero will be +true for the for the if I'm constructing + + align:start position:0% +true for the for the if I'm constructing + + + align:start position:0% +true for the for the if I'm constructing +XK plus one here I'm constructing XK + + align:start position:0% +XK plus one here I'm constructing XK + + + align:start position:0% +XK plus one here I'm constructing XK +plus one okay so let me just rewrite + + align:start position:0% +plus one okay so let me just rewrite + + + align:start position:0% +plus one okay so let me just rewrite +that knife and we've got Newton's method + + align:start position:0% +that knife and we've got Newton's method + + + align:start position:0% +that knife and we've got Newton's method +so we're looking for this + + align:start position:0% +so we're looking for this + + + align:start position:0% +so we're looking for this +change XK plus one minus XK I'll put it + + align:start position:0% +change XK plus one minus XK I'll put it + + + align:start position:0% +change XK plus one minus XK I'll put it +on this side s plus XK so that's this + + align:start position:0% +on this side s plus XK so that's this + + + align:start position:0% +on this side s plus XK so that's this +now I have to invert that and put it on + + align:start position:0% +now I have to invert that and put it on + + + align:start position:0% +now I have to invert that and put it on +the other side of the equation so + + align:start position:0% +the other side of the equation so + + + align:start position:0% +the other side of the equation so +that'll go with a minus this guy will be + + align:start position:0% +that'll go with a minus this guy will be + + + align:start position:0% +that'll go with a minus this guy will be +inverted and F at XK that's Newton's + + align:start position:0% +inverted and F at XK that's Newton's + + + align:start position:0% +inverted and F at XK that's Newton's +method natural let me just repeat that + + align:start position:0% +method natural let me just repeat that + + + align:start position:0% +method natural let me just repeat that +you see where the XK plus 1 minus XK is + + align:start position:0% +you see where the XK plus 1 minus XK is + + + align:start position:0% +you see where the XK plus 1 minus XK is +city right and I moved FX K to the other + + align:start position:0% +city right and I moved FX K to the other + + + align:start position:0% +city right and I moved FX K to the other +side with a minus sign and then I + + align:start position:0% +side with a minus sign and then I + + + align:start position:0% +side with a minus sign and then I +multiply through by J inverse so I got + + align:start position:0% +multiply through by J inverse so I got + + + align:start position:0% +multiply through by J inverse so I got +that + + align:start position:0% +that + + + align:start position:0% +that +so that's Newton's method for a system + + align:start position:0% +so that's Newton's method for a system + + + align:start position:0% +so that's Newton's method for a system +of equations but over there I'm going to + + align:start position:0% +of equations but over there I'm going to + + + align:start position:0% +of equations but over there I'm going to +write down Newton's method for + + align:start position:0% +write down Newton's method for + + + align:start position:0% +write down Newton's method for +minimizing a function this is such basic + + align:start position:0% +minimizing a function this is such basic + + + align:start position:0% +minimizing a function this is such basic +stuff that we have to begin here let me + + align:start position:0% +stuff that we have to begin here let me + + + align:start position:0% +stuff that we have to begin here let me +even begin with a with a extremely + + align:start position:0% +even begin with a with a extremely + + + align:start position:0% +even begin with a with a extremely +straightforward example of Newton's + + align:start position:0% +straightforward example of Newton's + + + align:start position:0% +straightforward example of Newton's +method here suppose my function I + + align:start position:0% +method here suppose my function I + + + align:start position:0% +method here suppose my function I +suppose I've only got one function + + align:start position:0% +suppose I've only got one function + + + align:start position:0% +suppose I've only got one function +actually suppose I only have one + + align:start position:0% +actually suppose I only have one + + + align:start position:0% +actually suppose I only have one +function so so I'm so suppose my + + align:start position:0% +function so so I'm so suppose my + + + align:start position:0% +function so so I'm so suppose my +function is x squared minus 9 and I want + + align:start position:0% +function is x squared minus 9 and I want + + + align:start position:0% +function is x squared minus 9 and I want +to solve f of X equals 0 I want to find + + align:start position:0% +to solve f of X equals 0 I want to find + + + align:start position:0% +to solve f of X equals 0 I want to find +this square root of 9 okay so what what + + align:start position:0% +this square root of 9 okay so what what + + + align:start position:0% +this square root of 9 okay so what what +is Newton's method for it we just should + + align:start position:0% +is Newton's method for it we just should + + + align:start position:0% +is Newton's method for it we just should +see my point is just to see how Newton's + + align:start position:0% +see my point is just to see how Newton's + + + align:start position:0% +see my point is just to see how Newton's +method is written and then rewrite it a + + align:start position:0% +method is written and then rewrite it a + + + align:start position:0% +method is written and then rewrite it a +little bit so that we see there + + align:start position:0% +little bit so that we see there + + + align:start position:0% +little bit so that we see there +convergence okay so so of course the + + align:start position:0% +convergence okay so so of course the + + + align:start position:0% +convergence okay so so of course the +Jacobian is 2x so Newton's method says + + align:start position:0% +Jacobian is 2x so Newton's method says + + + align:start position:0% +Jacobian is 2x so Newton's method says +that XK plus 1 I'm just going to copy + + align:start position:0% +that XK plus 1 I'm just going to copy + + + align:start position:0% +that XK plus 1 I'm just going to copy +that + + align:start position:0% + + + + align:start position:0% + +minus 1 over 2 XK + + align:start position:0% +minus 1 over 2 XK + + + align:start position:0% +minus 1 over 2 XK +right that's the derivative times F at X + + align:start position:0% +right that's the derivative times F at X + + + align:start position:0% +right that's the derivative times F at X +K which is XK squared minus 9 okay + + align:start position:0% +K which is XK squared minus 9 okay + + + align:start position:0% +K which is XK squared minus 9 okay +we followed the formula we that this + + align:start position:0% +we followed the formula we that this + + + align:start position:0% +we followed the formula we that this +determines XK plus 1 and let's let's + + align:start position:0% +determines XK plus 1 and let's let's + + + align:start position:0% +determines XK plus 1 and let's let's +simplify it so here I have XK - that + + align:start position:0% +simplify it so here I have XK - that + + + align:start position:0% +simplify it so here I have XK - that +looks like a half of XK so I think I + + align:start position:0% +looks like a half of XK so I think I + + + align:start position:0% +looks like a half of XK so I think I +have a half of XK and then this times + + align:start position:0% +have a half of XK and then this times + + + align:start position:0% +have a half of XK and then this times +this is 9 halves of one over X K is that + + align:start position:0% +this is 9 halves of one over X K is that + + + align:start position:0% +this is 9 halves of one over X K is that +right half of XK from this stuff and + + align:start position:0% +right half of XK from this stuff and + + + align:start position:0% +right half of XK from this stuff and +plus nine halves of one over X here ok + + align:start position:0% + + + + align:start position:0% + +can I just like check that I know the + + align:start position:0% +can I just like check that I know the + + + align:start position:0% +can I just like check that I know the +answer is three can I be sure that I get + + align:start position:0% +answer is three can I be sure that I get + + + align:start position:0% +answer is three can I be sure that I get +the right answer 3 so this was that if + + align:start position:0% +the right answer 3 so this was that if + + + align:start position:0% +the right answer 3 so this was that if +if XK was exactly three then of course I + + align:start position:0% +if XK was exactly three then of course I + + + align:start position:0% +if XK was exactly three then of course I +expect XK plus 1 to stay at 3 so do what + + align:start position:0% +expect XK plus 1 to stay at 3 so do what + + + align:start position:0% +expect XK plus 1 to stay at 3 so do what +does that happen so half of three and + + align:start position:0% +does that happen so half of three and + + + align:start position:0% +does that happen so half of three and +nine halves of one serve what's that + + align:start position:0% +nine halves of one serve what's that + + + align:start position:0% +nine halves of one serve what's that +half of three and nine halves of + + align:start position:0% +half of three and nine halves of + + + align:start position:0% +half of three and nine halves of +one-third okay that's that's three + + align:start position:0% +one-third okay that's that's three + + + align:start position:0% +one-third okay that's that's three +halves and three halves at six halves + + align:start position:0% +halves and three halves at six halves + + + align:start position:0% +halves and three halves at six halves +and that's three okay okay so we've + + align:start position:0% +and that's three okay okay so we've + + + align:start position:0% +and that's three okay okay so we've +checked that the method is consistent + + align:start position:0% +checked that the method is consistent + + + align:start position:0% +checked that the method is consistent +which just means we kept the algebra + + align:start position:0% +which just means we kept the algebra + + + align:start position:0% +which just means we kept the algebra +straight but then the really important + + align:start position:0% +straight but then the really important + + + align:start position:0% +straight but then the really important +point about Newton's method is this is + + align:start position:0% +point about Newton's method is this is + + + align:start position:0% +point about Newton's method is this is +to discover how fast it converges so now + + align:start position:0% +to discover how fast it converges so now + + + align:start position:0% +to discover how fast it converges so now +let me dou XK plus one minus three so + + align:start position:0% +let me dou XK plus one minus three so + + + align:start position:0% +let me dou XK plus one minus three so +now I'm looking at the error which is I + + align:start position:0% +now I'm looking at the error which is I + + + align:start position:0% +now I'm looking at the error which is I +hope approaching zero + + align:start position:0% +hope approaching zero + + + align:start position:0% +hope approaching zero +is it approaching zero how quickly is it + + align:start position:0% +is it approaching zero how quickly is it + + + align:start position:0% +is it approaching zero how quickly is it +approaching zero these are the + + align:start position:0% +approaching zero these are the + + + align:start position:0% +approaching zero these are the +fundamental questions of optimization so + + align:start position:0% +fundamental questions of optimization so + + + align:start position:0% +fundamental questions of optimization so +I'm going to subtract three from both + + align:start position:0% +I'm going to subtract three from both + + + align:start position:0% +I'm going to subtract three from both +sides + + align:start position:0% +sides + + + align:start position:0% +sides +somehow okay from here I guess I'm gonna + + align:start position:0% +somehow okay from here I guess I'm gonna + + + align:start position:0% +somehow okay from here I guess I'm gonna +subtract three can I just so I was just + + align:start position:0% +subtract three can I just so I was just + + + align:start position:0% +subtract three can I just so I was just +checking that it was correct okay now so + + align:start position:0% +checking that it was correct okay now so + + + align:start position:0% +checking that it was correct okay now so +XK plus one minus three I'm gonna + + align:start position:0% +XK plus one minus three I'm gonna + + + align:start position:0% +XK plus one minus three I'm gonna +subtract three from both sides I'm gonna + + align:start position:0% +subtract three from both sides I'm gonna + + + align:start position:0% +subtract three from both sides I'm gonna +subtract three there and then I hope + + align:start position:0% +subtract three there and then I hope + + + align:start position:0% +subtract three there and then I hope +that that's that box is what goes down + + align:start position:0% +that that's that box is what goes down + + + align:start position:0% +that that's that box is what goes down +here right subtracted three from both + + align:start position:0% +here right subtracted three from both + + + align:start position:0% +here right subtracted three from both +sides so I'm looking at I'm hoping it + + align:start position:0% +sides so I'm looking at I'm hoping it + + + align:start position:0% +sides so I'm looking at I'm hoping it +goes now hoping things go to zero okay + + align:start position:0% +goes now hoping things go to zero okay + + + align:start position:0% +goes now hoping things go to zero okay +so what do I have there let me factor + + align:start position:0% +so what do I have there let me factor + + + align:start position:0% +so what do I have there let me factor +out the 1 over X K so what do I have + + align:start position:0% +out the 1 over X K so what do I have + + + align:start position:0% +out the 1 over X K so what do I have +then left one over X K so there's a 9 + + align:start position:0% +then left one over X K so there's a 9 + + + align:start position:0% +then left one over X K so there's a 9 +halves from there one over X K so I + + align:start position:0% +halves from there one over X K so I + + + align:start position:0% +halves from there one over X K so I +really have 1/2 of X K squared because + + align:start position:0% +really have 1/2 of X K squared because + + + align:start position:0% +really have 1/2 of X K squared because +I've divided by n X K and this minus 3 I + + align:start position:0% +I've divided by n X K and this minus 3 I + + + align:start position:0% +I've divided by n X K and this minus 3 I +better put minus 3 X K cause I'm + + align:start position:0% +better put minus 3 X K cause I'm + + + align:start position:0% +better put minus 3 X K cause I'm +dividing by X K I claim that that's okay + + align:start position:0% +dividing by X K I claim that that's okay + + + align:start position:0% +dividing by X K I claim that that's okay +now I've got it + + align:start position:0% + + + + align:start position:0% + +and let's see let me take out the 2 to + + align:start position:0% +and let's see let me take out the 2 to + + + align:start position:0% +and let's see let me take out the 2 to +forget these twos and make that a 6 so I + + align:start position:0% +forget these twos and make that a 6 so I + + + align:start position:0% +forget these twos and make that a 6 so I +have 1 over 2 X K times 9 plus X K + + align:start position:0% +have 1 over 2 X K times 9 plus X K + + + align:start position:0% +have 1 over 2 X K times 9 plus X K +squared minus 6 anything good about that + + align:start position:0% +squared minus 6 anything good about that + + + align:start position:0% +squared minus 6 anything good about that +we hope so week we hope that that is + + align:start position:0% +we hope so week we hope that that is + + + align:start position:0% +we hope so week we hope that that is +something attractive so this is again + + align:start position:0% +something attractive so this is again + + + align:start position:0% +something attractive so this is again +this is the error at step K plus 1 and + + align:start position:0% +this is the error at step K plus 1 and + + + align:start position:0% +this is the error at step K plus 1 and +it's 1 over 2 X K times this thing in + + align:start position:0% +it's 1 over 2 X K times this thing in + + + align:start position:0% +it's 1 over 2 X K times this thing in +brackets 9 plus X K squared minus 6x k + + align:start position:0% +brackets 9 plus X K squared minus 6x k + + + align:start position:0% +brackets 9 plus X K squared minus 6x k +and we recognize that as X K minus 3 + + align:start position:0% +and we recognize that as X K minus 3 + + + align:start position:0% +and we recognize that as X K minus 3 +squared + + align:start position:0% +squared + + + align:start position:0% +squared +XK squared minus six of them plus 9 + + align:start position:0% +XK squared minus six of them plus 9 + + + align:start position:0% +XK squared minus six of them plus 9 +that's XK minus 3 squared okay that was + + align:start position:0% +that's XK minus 3 squared okay that was + + + align:start position:0% +that's XK minus 3 squared okay that was +the goal of course that's the goal that + + align:start position:0% +the goal of course that's the goal that + + + align:start position:0% +the goal of course that's the goal that +shows why Newton's method is fantastic + + align:start position:0% +shows why Newton's method is fantastic + + + align:start position:0% +shows why Newton's method is fantastic +if you can execute it if you can start + + align:start position:0% +if you can execute it if you can start + + + align:start position:0% +if you can execute it if you can start +near enough notice that so that's that's + + align:start position:0% +near enough notice that so that's that's + + + align:start position:0% +near enough notice that so that's that's +so how do I describe this this great + + align:start position:0% +so how do I describe this this great + + + align:start position:0% +so how do I describe this this great +equation it says that the error is + + align:start position:0% +equation it says that the error is + + + align:start position:0% +equation it says that the error is +squared at every step + + align:start position:0% +squared at every step + + + align:start position:0% +squared at every step +squared at every step so if I'm + + align:start position:0% +squared at every step so if I'm + + + align:start position:0% +squared at every step so if I'm +converging to a limit it will satisfy + + align:start position:0% +converging to a limit it will satisfy + + + align:start position:0% +converging to a limit it will satisfy +that it'll be 3 or I guess minus 3 is + + align:start position:0% +that it'll be 3 or I guess minus 3 is + + + align:start position:0% +that it'll be 3 or I guess minus 3 is +that possible + + align:start position:0% +that possible + + + align:start position:0% +that possible +yeah minus 3 is another solution here so + + align:start position:0% +yeah minus 3 is another solution here so + + + align:start position:0% +yeah minus 3 is another solution here so +we're so we've got two solutions the + + align:start position:0% +we're so we've got two solutions the + + + align:start position:0% +we're so we've got two solutions the +Newton's method could converge to 3 am i + + align:start position:0% +Newton's method could converge to 3 am i + + + align:start position:0% +Newton's method could converge to 3 am i +right it could converge to minus 3 so I + + align:start position:0% +right it could converge to minus 3 so I + + + align:start position:0% +right it could converge to minus 3 so I +could I'd have a similar equation sort + + align:start position:0% +could I'd have a similar equation sort + + + align:start position:0% +could I'd have a similar equation sort +of centered at minus 3 or what does it + + align:start position:0% +of centered at minus 3 or what does it + + + align:start position:0% +of centered at minus 3 or what does it +always do one of those it could blow up + + align:start position:0% +always do one of those it could blow up + + + align:start position:0% +always do one of those it could blow up +it could so that so those are there are + + align:start position:0% +it could so that so those are there are + + + align:start position:0% +it could so that so those are there are +sort of regions of Attraction there are + + align:start position:0% +sort of regions of Attraction there are + + + align:start position:0% +sort of regions of Attraction there are +all the starting points that approach 3 + + align:start position:0% +all the starting points that approach 3 + + + align:start position:0% +all the starting points that approach 3 +and the whole point of that equation is + + align:start position:0% +and the whole point of that equation is + + + align:start position:0% +and the whole point of that equation is +with quadratic convergence the error + + align:start position:0% +with quadratic convergence the error + + + align:start position:0% +with quadratic convergence the error +being squared at every step it seems in + + align:start position:0% +being squared at every step it seems in + + + align:start position:0% +being squared at every step it seems in +on three then there's a whole all these + + align:start position:0% +on three then there's a whole all these + + + align:start position:0% +on three then there's a whole all these +starting points that would would go to + + align:start position:0% +starting points that would would go to + + + align:start position:0% +starting points that would would go to +minus 3 and then their their starting + + align:start position:0% +minus 3 and then their their starting + + + align:start position:0% +minus 3 and then their their starting +points that would blow up so and and + + align:start position:0% +points that would blow up so and and + + + align:start position:0% +points that would blow up so and and +those may be for this very simple + + align:start position:0% +those may be for this very simple + + + align:start position:0% +those may be for this very simple +problem that the picture is not too + + align:start position:0% +problem that the picture is not too + + + align:start position:0% +problem that the picture is not too +difficult to sort out those three + + align:start position:0% +difficult to sort out those three + + + align:start position:0% +difficult to sort out those three +regions but if we had and this is + + align:start position:0% +regions but if we had and this is + + + align:start position:0% +regions but if we had and this is +allowing for a vector + + align:start position:0% + + + + align:start position:0% + +two equations or n equations then we're + + align:start position:0% +two equations or n equations then we're + + + align:start position:0% +two equations or n equations then we're +in n variables and is really you get + + align:start position:0% +in n variables and is really you get + + + align:start position:0% +in n variables and is really you get +beautiful pictures you get some some of + + align:start position:0% +beautiful pictures you get some some of + + + align:start position:0% +beautiful pictures you get some some of +the type of pictures that gave gave rise + + align:start position:0% +the type of pictures that gave gave rise + + + align:start position:0% +the type of pictures that gave gave rise +to these books on fractals the picture + + align:start position:0% +to these books on fractals the picture + + + align:start position:0% +to these books on fractals the picture +books on fractals - for these basins of + + align:start position:0% +books on fractals - for these basins of + + + align:start position:0% +books on fractals - for these basins of +attraction does the does the starting + + align:start position:0% +attraction does the does the starting + + + align:start position:0% +attraction does the does the starting +point lead you to one of the solutions + + align:start position:0% +point lead you to one of the solutions + + + align:start position:0% +point lead you to one of the solutions +or does it lead you to infinity here it + + align:start position:0% +or does it lead you to infinity here it + + + align:start position:0% +or does it lead you to infinity here it +that would be interesting to just draw + + align:start position:0% +that would be interesting to just draw + + + align:start position:0% +that would be interesting to just draw +it for this okay but the the essential + + align:start position:0% +it for this okay but the the essential + + + align:start position:0% +it for this okay but the the essential +point is they're quadratic convergence + + align:start position:0% +point is they're quadratic convergence + + + align:start position:0% +point is they're quadratic convergence +if it's close enough you see that it has + + align:start position:0% +if it's close enough you see that it has + + + align:start position:0% +if it's close enough you see that it has +to be close if if X K is if X 0 is + + align:start position:0% +to be close if if X K is if X 0 is + + + align:start position:0% +to be close if if X K is if X 0 is +pretty near 3 then this is about + + align:start position:0% +pretty near 3 then this is about + + + align:start position:0% +pretty near 3 then this is about +one-sixth of that and there'll be a good + + align:start position:0% +one-sixth of that and there'll be a good + + + align:start position:0% +one-sixth of that and there'll be a good +region of Attraction in this case okay + + align:start position:0% +region of Attraction in this case okay + + + align:start position:0% +region of Attraction in this case okay +so that's that's Newton's method for + + align:start position:0% + + + + align:start position:0% + +equations and now I want to do Newton's + + align:start position:0% +equations and now I want to do Newton's + + + align:start position:0% +equations and now I want to do Newton's +method + + align:start position:0% +method + + + align:start position:0% +method +I just want to convert all those words + + align:start position:0% +I just want to convert all those words + + + align:start position:0% +I just want to convert all those words +over to Newton's method for optimization + + align:start position:0% +over to Newton's method for optimization + + + align:start position:0% +over to Newton's method for optimization +so remember the these boards were + + align:start position:0% +so remember the these boards were + + + align:start position:0% +so remember the these boards were +solving F equals 0 + + align:start position:0% +solving F equals 0 + + + align:start position:0% +solving F equals 0 +this board is minimizing capital F and + + align:start position:0% +this board is minimizing capital F and + + + align:start position:0% +this board is minimizing capital F and +what's the connection between them well + + align:start position:0% +what's the connection between them well + + + align:start position:0% +what's the connection between them well +of course when we this corresponds to + + align:start position:0% +of course when we this corresponds to + + + align:start position:0% +of course when we this corresponds to +solving the gradient at a minimum if I'm + + align:start position:0% +solving the gradient at a minimum if I'm + + + align:start position:0% +solving the gradient at a minimum if I'm +minimizing I'm finding a point where all + + align:start position:0% +minimizing I'm finding a point where all + + + align:start position:0% +minimizing I'm finding a point where all +the first derivatives are zero so so + + align:start position:0% +the first derivatives are zero so so + + + align:start position:0% +the first derivatives are zero so so +that'll be the match between these that + + align:start position:0% +that'll be the match between these that + + + align:start position:0% +that'll be the match between these that +that this right F in this picture is the + + align:start position:0% +that this right F in this picture is the + + + align:start position:0% +that this right F in this picture is the +small F in that picture + + align:start position:0% +small F in that picture + + + align:start position:0% +small F in that picture +ok now I guess here I have and this is + + align:start position:0% +ok now I guess here I have and this is + + + align:start position:0% +ok now I guess here I have and this is +sort of the heart of our applications to + + align:start position:0% +sort of the heart of our applications to + + + align:start position:0% +sort of the heart of our applications to +deep learning we have very complicated + + align:start position:0% +deep learning we have very complicated + + + align:start position:0% +deep learning we have very complicated +loss functions to minimize functions of + + align:start position:0% +loss functions to minimize functions of + + + align:start position:0% +loss functions to minimize functions of +thousands or hundred + + align:start position:0% +thousands or hundred + + + align:start position:0% +thousands or hundred +thousands of variable okay so that means + + align:start position:0% +thousands of variable okay so that means + + + align:start position:0% +thousands of variable okay so that means +that we would like to use Newton's + + align:start position:0% +that we would like to use Newton's + + + align:start position:0% +that we would like to use Newton's +method but often we can't let me so let + + align:start position:0% +method but often we can't let me so let + + + align:start position:0% +method but often we can't let me so let +me so I need to to put down here two + + align:start position:0% +me so I need to to put down here two + + + align:start position:0% +me so I need to to put down here two +methods one that doesn't involve those + + align:start position:0% +methods one that doesn't involve those + + + align:start position:0% +methods one that doesn't involve those +high second derivatives and one a + + align:start position:0% +high second derivatives and one a + + + align:start position:0% +high second derivatives and one a +Newton's that does so so so first so + + align:start position:0% +Newton's that does so so so first so + + + align:start position:0% +Newton's that does so so so first so +first I'll write down a method that does + + align:start position:0% +first I'll write down a method that does + + + align:start position:0% +first I'll write down a method that does +not involve so so method one and this + + align:start position:0% +not involve so so method one and this + + + align:start position:0% +not involve so so method one and this +will be steepest descent and what is + + align:start position:0% +will be steepest descent and what is + + + align:start position:0% +will be steepest descent and what is +that that says that XK plus one the new + + align:start position:0% +that that says that XK plus one the new + + + align:start position:0% +that that says that XK plus one the new +X is the old X minus my steepest descent + + align:start position:0% +X is the old X minus my steepest descent + + + align:start position:0% +X is the old X minus my steepest descent +means that I move in the steepest + + align:start position:0% +means that I move in the steepest + + + align:start position:0% +means that I move in the steepest +direction which is the direction of the + + align:start position:0% +direction which is the direction of the + + + align:start position:0% +direction which is the direction of the +gradient of F I move some distance and I + + align:start position:0% +gradient of F I move some distance and I + + + align:start position:0% +gradient of F I move some distance and I +better have freedom to decide what that + + align:start position:0% +better have freedom to decide what that + + + align:start position:0% +better have freedom to decide what that +distance should be so this is a step + + align:start position:0% +distance should be so this is a step + + + align:start position:0% +distance should be so this is a step +size yes or in the language of deep + + align:start position:0% +size yes or in the language of deep + + + align:start position:0% +size yes or in the language of deep +learning it's often called the learning + + align:start position:0% +learning it's often called the learning + + + align:start position:0% +learning it's often called the learning +rate learning rate okay so is that that + + align:start position:0% +rate learning rate okay so is that that + + + align:start position:0% +rate learning rate okay so is that that +so and it's natural to choose SK we're + + align:start position:0% +so and it's natural to choose SK we're + + + align:start position:0% +so and it's natural to choose SK we're +going along do you see where what this + + align:start position:0% +going along do you see where what this + + + align:start position:0% +going along do you see where what this +right hand side looks like I'm at a + + align:start position:0% +right hand side looks like I'm at a + + + align:start position:0% +right hand side looks like I'm at a +point in n dimensions they were all it + + align:start position:0% +point in n dimensions they were all it + + + align:start position:0% +point in n dimensions they were all it +were in n dimensions here we have + + align:start position:0% +were in n dimensions here we have + + + align:start position:0% +were in n dimensions here we have +functions of n variables there's a + + align:start position:0% +functions of n variables there's a + + + align:start position:0% +functions of n variables there's a +vector there's a direction to move down + + align:start position:0% +vector there's a direction to move down + + + align:start position:0% +vector there's a direction to move down +the steepest slope of the of the graph + + align:start position:0% +the steepest slope of the of the graph + + + align:start position:0% +the steepest slope of the of the graph +and here's a distance to move and we + + align:start position:0% +and here's a distance to move and we + + + align:start position:0% +and here's a distance to move and we +will stop we'll have to get off this + + align:start position:0% +will stop we'll have to get off this + + + align:start position:0% +will stop we'll have to get off this +step normally if we if we stay on it a + + align:start position:0% +step normally if we if we stay on it a + + + align:start position:0% +step normally if we if we stay on it a +little sway it'll swing back it'll take + + align:start position:0% +little sway it'll swing back it'll take + + + align:start position:0% +little sway it'll swing back it'll take +us off to infinity + + align:start position:0% +us off to infinity + + + align:start position:0% +us off to infinity +wait the the you would like to choose SK + + align:start position:0% +wait the the you would like to choose SK + + + align:start position:0% +wait the the you would like to choose SK +so that you minimize capital F you take + + align:start position:0% +so that you minimize capital F you take + + + align:start position:0% +so that you minimize capital F you take +the point on this line so this is I'm + + align:start position:0% +the point on this line so this is I'm + + + align:start position:0% +the point on this line so this is I'm +this is a line in our in a direction in + + align:start position:0% +this is a line in our in a direction in + + + align:start position:0% +this is a line in our in a direction in +RN and for all the points on that line + + align:start position:0% +RN and for all the points on that line + + + align:start position:0% +RN and for all the points on that line +in that direction F has some value and + + align:start position:0% +in that direction F has some value and + + + align:start position:0% +in that direction F has some value and +what you expect is that initially + + align:start position:0% +what you expect is that initially + + + align:start position:0% +what you expect is that initially +because you chose it sensibly the value + + align:start position:0% +because you chose it sensibly the value + + + align:start position:0% +because you chose it sensibly the value +of F will drop but then at a certain + + align:start position:0% +of F will drop but then at a certain + + + align:start position:0% +of F will drop but then at a certain +point it'll it'll turn turn back on you + + align:start position:0% +point it'll it'll turn turn back on you + + + align:start position:0% +point it'll it'll turn turn back on you +and increase so that would be the + + align:start position:0% +and increase so that would be the + + + align:start position:0% +and increase so that would be the +natural stopping point and that would I + + align:start position:0% +natural stopping point and that would I + + + align:start position:0% +natural stopping point and that would I +would call that an exact line search so + + align:start position:0% +would call that an exact line search so + + + align:start position:0% +would call that an exact line search so +exact line search would be exact line + + align:start position:0% +exact line search would be exact line + + + align:start position:0% +exact line search would be exact line +search is the best sense of course that + + align:start position:0% +search is the best sense of course that + + + align:start position:0% +search is the best sense of course that +would take time to to compute and you + + align:start position:0% +would take time to to compute and you + + + align:start position:0% +would take time to to compute and you +probably in deep learning that's time + + align:start position:0% +probably in deep learning that's time + + + align:start position:0% +probably in deep learning that's time +you can't afford so you fix the learning + + align:start position:0% +you can't afford so you fix the learning + + + align:start position:0% +you can't afford so you fix the learning +rate s maybe you choose point o1 to be + + align:start position:0% +rate s maybe you choose point o1 to be + + + align:start position:0% +rate s maybe you choose point o1 to be +pretty safe okay so that's method one + + align:start position:0% +pretty safe okay so that's method one + + + align:start position:0% +pretty safe okay so that's method one +steepest descent now a method two will + + align:start position:0% +steepest descent now a method two will + + + align:start position:0% +steepest descent now a method two will +be Newton's method so now we have XK + + align:start position:0% +be Newton's method so now we have XK + + + align:start position:0% +be Newton's method so now we have XK +plus one my two XK minus something times + + align:start position:0% +plus one my two XK minus something times + + + align:start position:0% +plus one my two XK minus something times +Delta F + + align:start position:0% + + + + align:start position:0% + +and now I'm going to do the right thing + + align:start position:0% +and now I'm going to do the right thing + + + align:start position:0% +and now I'm going to do the right thing +I'm gonna live right here and the right + + align:start position:0% +I'm gonna live right here and the right + + + align:start position:0% +I'm gonna live right here and the right +thing is the Hessian the second + + align:start position:0% +thing is the Hessian the second + + + align:start position:0% +thing is the Hessian the second +derivative that's what this is this was + + align:start position:0% +derivative that's what this is this was + + + align:start position:0% +derivative that's what this is this was +cheap we just took the direction and and + + align:start position:0% +cheap we just took the direction and and + + + align:start position:0% +cheap we just took the direction and and +went along it now we're getting really + + align:start position:0% +went along it now we're getting really + + + align:start position:0% +went along it now we're getting really +the right direction by using the second + + align:start position:0% +the right direction by using the second + + + align:start position:0% +the right direction by using the second +derivative so that's H inverse okay and + + align:start position:0% +derivative so that's H inverse okay and + + + align:start position:0% +derivative so that's H inverse okay and +what I've done is to is to set that to + + align:start position:0% +what I've done is to is to set that to + + + align:start position:0% +what I've done is to is to set that to +zero so that would be do you see thats + + align:start position:0% +zero so that would be do you see thats + + + align:start position:0% +zero so that would be do you see thats +Newton's method + + align:start position:0% +Newton's method + + + align:start position:0% +Newton's method +it's totally parallel to this guy + + align:start position:0% +it's totally parallel to this guy + + + align:start position:0% +it's totally parallel to this guy +actually I'm really happy to have these + + align:start position:0% +actually I'm really happy to have these + + + align:start position:0% +actually I'm really happy to have these +two on the board parallel to each other + + align:start position:0% +two on the board parallel to each other + + + align:start position:0% +two on the board parallel to each other +because you have to kind of keep + + align:start position:0% +because you have to kind of keep + + + align:start position:0% +because you have to kind of keep +straight are you solving equations or + + align:start position:0% +straight are you solving equations or + + + align:start position:0% +straight are you solving equations or +are you minimizing functions and you're + + align:start position:0% +are you minimizing functions and you're + + + align:start position:0% +are you minimizing functions and you're +using different letters in the two + + align:start position:0% +using different letters in the two + + + align:start position:0% +using different letters in the two +problems but now you see how they match + + align:start position:0% +problems but now you see how they match + + + align:start position:0% +problems but now you see how they match +the Jacobian of so so again the matches + + align:start position:0% +the Jacobian of so so again the matches + + + align:start position:0% +the Jacobian of so so again the matches +think of F as the gradient of F that's + + align:start position:0% +think of F as the gradient of F that's + + + align:start position:0% +think of F as the gradient of F that's +that's the way you should think of it so + + align:start position:0% +that's the way you should think of it so + + + align:start position:0% +that's the way you should think of it so +the Jacobian for of the gradient is the + + align:start position:0% +the Jacobian for of the gradient is the + + + align:start position:0% +the Jacobian for of the gradient is the +Hessian the Jacobian of the gradient is + + align:start position:0% +Hessian the Jacobian of the gradient is + + + align:start position:0% +Hessian the Jacobian of the gradient is +the Hessian and that makes sense because + + align:start position:0% +the Hessian and that makes sense because + + + align:start position:0% +the Hessian and that makes sense because +we take the first derivative of the + + align:start position:0% +we take the first derivative of the + + + align:start position:0% +we take the first derivative of the +first derivative is the second + + align:start position:0% +first derivative is the second + + + align:start position:0% +first derivative is the second +derivative only we're doing matrix y so + + align:start position:0% +derivative only we're doing matrix y so + + + align:start position:0% +derivative only we're doing matrix y so +that's so the Jacobian of the gradient + + align:start position:0% +that's so the Jacobian of the gradient + + + align:start position:0% +that's so the Jacobian of the gradient +we're doing a vector matrix sentence + + align:start position:0% +we're doing a vector matrix sentence + + + align:start position:0% +we're doing a vector matrix sentence +instead of a scalar sentence the + + align:start position:0% +instead of a scalar sentence the + + + align:start position:0% +instead of a scalar sentence the +Jacobian of the gradient is a Hessian + + align:start position:0% +Jacobian of the gradient is a Hessian + + + align:start position:0% +Jacobian of the gradient is a Hessian +yep right okay so that's what I wanted + + align:start position:0% +yep right okay so that's what I wanted + + + align:start position:0% +yep right okay so that's what I wanted +to start with just to get those basic + + align:start position:0% +to start with just to get those basic + + + align:start position:0% +to start with just to get those basic +facts down and so the basic facts were + + align:start position:0% +facts down and so the basic facts were + + + align:start position:0% +facts down and so the basic facts were +the were the three term Taylor series + + align:start position:0% +the were the three term Taylor series + + + align:start position:0% +the were the three term Taylor series +and then the basic algorithms followed + + align:start position:0% +and then the basic algorithms followed + + + align:start position:0% +and then the basic algorithms followed +naturally from it by setting the + + align:start position:0% +naturally from it by setting the + + + align:start position:0% +naturally from it by setting the +FF at the new point to zero if that's + + align:start position:0% +FF at the new point to zero if that's + + + align:start position:0% +FF at the new point to zero if that's +what you were solving or by assume he + + align:start position:0% +what you were solving or by assume he + + + align:start position:0% +what you were solving or by assume he +had right good good good good okay now + + align:start position:0% +had right good good good good okay now + + + align:start position:0% +had right good good good good okay now +what now we have to think about solving + + align:start position:0% +what now we have to think about solving + + + align:start position:0% +what now we have to think about solving +these problems + + align:start position:0% +these problems + + + align:start position:0% +these problems +studying do they converge what rate do + + align:start position:0% +studying do they converge what rate do + + + align:start position:0% +studying do they converge what rate do +they converge well that's the rate of + + align:start position:0% +they converge well that's the rate of + + + align:start position:0% +they converge well that's the rate of +convergence is like what I why I took + + align:start position:0% +convergence is like what I why I took + + + align:start position:0% +convergence is like what I why I took +this separated off this example so the + + align:start position:0% +this separated off this example so the + + + align:start position:0% +this separated off this example so the +convergence rate for Newton's method + + align:start position:0% +convergence rate for Newton's method + + + align:start position:0% +convergence rate for Newton's method +will be quadratic the error gets squared + + align:start position:0% +will be quadratic the error gets squared + + + align:start position:0% +will be quadratic the error gets squared +and of course that means super fast + + align:start position:0% +and of course that means super fast + + + align:start position:0% +and of course that means super fast +convergence if you start close enough + + align:start position:0% +convergence if you start close enough + + + align:start position:0% +convergence if you start close enough +the rate of convergence for a steepest + + align:start position:0% +the rate of convergence for a steepest + + + align:start position:0% +the rate of convergence for a steepest +descent is of course not you're not + + align:start position:0% +descent is of course not you're not + + + align:start position:0% +descent is of course not you're not +squaring errors here because you're + + align:start position:0% +squaring errors here because you're + + + align:start position:0% +squaring errors here because you're +you're just taking some number instead + + align:start position:0% +you're just taking some number instead + + + align:start position:0% +you're just taking some number instead +of the inverse of the correct matrix so + + align:start position:0% +of the inverse of the correct matrix so + + + align:start position:0% +of the inverse of the correct matrix so +you you can't expect SuperSpeed so a + + align:start position:0% +you you can't expect SuperSpeed so a + + + align:start position:0% +you you can't expect SuperSpeed so a +linear rate of convergence would be + + align:start position:0% +linear rate of convergence would be + + + align:start position:0% +linear rate of convergence would be +right you expect that the error to you + + align:start position:0% +right you expect that the error to you + + + align:start position:0% +right you expect that the error to you +would like to know that the error is + + align:start position:0% +would like to know that the error is + + + align:start position:0% +would like to know that the error is +multiplied by said every step by some + + align:start position:0% +multiplied by said every step by some + + + align:start position:0% +multiplied by said every step by some +constant below one that would be a + + align:start position:0% +constant below one that would be a + + + align:start position:0% +constant below one that would be a +linear rate where compared to be + + align:start position:0% +linear rate where compared to be + + + align:start position:0% +linear rate where compared to be +multiplied by being squared at every + + align:start position:0% +multiplied by being squared at every + + + align:start position:0% +multiplied by being squared at every +step and so this will be our our basic + + align:start position:0% +step and so this will be our our basic + + + align:start position:0% +step and so this will be our our basic +this is the basic formula for for + + align:start position:0% +this is the basic formula for for + + + align:start position:0% +this is the basic formula for for +large-scale for really large-scale + + align:start position:0% +large-scale for really large-scale + + + align:start position:0% +large-scale for really large-scale +problems and there are methods of course + + align:start position:0% +problems and there are methods of course + + + align:start position:0% +problems and there are methods of course +people are going to come up with methods + + align:start position:0% +people are going to come up with methods + + + align:start position:0% +people are going to come up with methods +that they're sort of a cheap Newton's + + align:start position:0% +that they're sort of a cheap Newton's + + + align:start position:0% +that they're sort of a cheap Newton's +method Levenberg Marquardt and it's in + + align:start position:0% +method Levenberg Marquardt and it's in + + + align:start position:0% +method Levenberg Marquardt and it's in +the notes at the end of this section at + + align:start position:0% +the notes at the end of this section at + + + align:start position:0% +the notes at the end of this section at +the end of the six point for that we'll + + align:start position:0% +the end of the six point for that we'll + + + align:start position:0% +the end of the six point for that we'll +get to + + align:start position:0% +get to + + + align:start position:0% +get to +so Levenberg Marquardt is a sort of + + align:start position:0% +so Levenberg Marquardt is a sort of + + + align:start position:0% +so Levenberg Marquardt is a sort of +cheap man's Newton's Newton's method it + + align:start position:0% +cheap man's Newton's Newton's method it + + + align:start position:0% +cheap man's Newton's Newton's method it +does not compute to Hessian but it can + + align:start position:0% +does not compute to Hessian but it can + + + align:start position:0% +does not compute to Hessian but it can +but it says okay I owe i from the + + align:start position:0% +but it says okay I owe i from the + + + align:start position:0% +but it says okay I owe i from the +gradient I can see a + + align:start position:0% +gradient I can see a + + + align:start position:0% +gradient I can see a +sort of one term in the Hesse you know + + align:start position:0% +sort of one term in the Hesse you know + + + align:start position:0% +sort of one term in the Hesse you know +so it grabs that term but it's not fully + + align:start position:0% +so it grabs that term but it's not fully + + + align:start position:0% +so it grabs that term but it's not fully +fully second-order okay so now we're now + + align:start position:0% +fully second-order okay so now we're now + + + align:start position:0% +fully second-order okay so now we're now +we have to think about problems and I + + align:start position:0% +we have to think about problems and I + + + align:start position:0% +we have to think about problems and I +guess the whole the the message here is + + align:start position:0% +guess the whole the the message here is + + + align:start position:0% +guess the whole the the message here is +and our starting point has to be + + align:start position:0% +and our starting point has to be + + + align:start position:0% +and our starting point has to be +convexity convexity is the key word for + + align:start position:0% +convexity convexity is the key word for + + + align:start position:0% +convexity convexity is the key word for +this for these for these problems for + + align:start position:0% +this for these for these problems for + + + align:start position:0% +this for these for these problems for +the function that we want to minimize if + + align:start position:0% +the function that we want to minimize if + + + align:start position:0% +the function that we want to minimize if +that's a convex function well first of + + align:start position:0% +that's a convex function well first of + + + align:start position:0% +that's a convex function well first of +all the convex function is likely to + + align:start position:0% +all the convex function is likely to + + + align:start position:0% +all the convex function is likely to +have one minimum and the picture that's + + align:start position:0% +have one minimum and the picture that's + + + align:start position:0% +have one minimum and the picture that's +in our mind of steepest descent this + + align:start position:0% +in our mind of steepest descent this + + + align:start position:0% +in our mind of steepest descent this +picture of a bowl a bowl is the graph of + + align:start position:0% +picture of a bowl a bowl is the graph of + + + align:start position:0% +picture of a bowl a bowl is the graph of +a convex function so that so I'm turning + + align:start position:0% +a convex function so that so I'm turning + + + align:start position:0% +a convex function so that so I'm turning +to convexity now I'll leave that board + + align:start position:0% +to convexity now I'll leave that board + + + align:start position:0% +to convexity now I'll leave that board +there because that's pretty crucial and + + align:start position:0% +there because that's pretty crucial and + + + align:start position:0% +there because that's pretty crucial and +speak about the idea of convexity convex + + align:start position:0% +speak about the idea of convexity convex + + + align:start position:0% +speak about the idea of convexity convex +function convex set so let's call the + + align:start position:0% +function convex set so let's call the + + + align:start position:0% +function convex set so let's call the +function f of X and typical convex set + + align:start position:0% +function f of X and typical convex set + + + align:start position:0% +function f of X and typical convex set +will be i'll call it k okay so we just + + align:start position:0% +will be i'll call it k okay so we just + + + align:start position:0% +will be i'll call it k okay so we just +want to remember what does that word can + + align:start position:0% +want to remember what does that word can + + + align:start position:0% +want to remember what does that word can +convex mean and how do you know if you + + align:start position:0% +convex mean and how do you know if you + + + align:start position:0% +convex mean and how do you know if you +have a convex function or a convex set + + align:start position:0% +have a convex function or a convex set + + + align:start position:0% +have a convex function or a convex set +okay let me start with convex set so + + align:start position:0% +okay let me start with convex set so + + + align:start position:0% +okay let me start with convex set so +it's a because here's my general problem + + align:start position:0% +it's a because here's my general problem + + + align:start position:0% +it's a because here's my general problem +my convex minimization which you hope to + + align:start position:0% +my convex minimization which you hope to + + + align:start position:0% +my convex minimization which you hope to +have an in many applications you do have + + align:start position:0% +have an in many applications you do have + + + align:start position:0% +have an in many applications you do have +so you minimize a convex function for + + align:start position:0% +so you minimize a convex function for + + + align:start position:0% +so you minimize a convex function for +points in a convex set so that's like + + align:start position:0% +points in a convex set so that's like + + + align:start position:0% +points in a convex set so that's like +the ideal situation that's the ideal + + align:start position:0% +the ideal situation that's the ideal + + + align:start position:0% +the ideal situation that's the ideal +situation okay get something + + align:start position:0% +situation okay get something + + + align:start position:0% +situation okay get something +inside something powerful convexity the + + align:start position:0% +inside something powerful convexity the + + + align:start position:0% +inside something powerful convexity the +function is convex and so let me draw + + align:start position:0% +function is convex and so let me draw + + + align:start position:0% +function is convex and so let me draw +our convex function with the graph + + align:start position:0% +our convex function with the graph + + + align:start position:0% +our convex function with the graph +ok so I'll draw our convex function say + + align:start position:0% +ok so I'll draw our convex function say + + + align:start position:0% +ok so I'll draw our convex function say +Bowl so that's a graph of f of X and + + align:start position:0% +Bowl so that's a graph of f of X and + + + align:start position:0% +Bowl so that's a graph of f of X and +then so here are the X's with X 1 and X + + align:start position:0% +then so here are the X's with X 1 and X + + + align:start position:0% +then so here are the X's with X 1 and X +2 in the base and the graph of f of X 1 + + align:start position:0% +2 in the base and the graph of f of X 1 + + + align:start position:0% +2 in the base and the graph of f of X 1 +X 2 up here okay actually I'm over there + + align:start position:0% +X 2 up here okay actually I'm over there + + + align:start position:0% +X 2 up here okay actually I'm over there +I should be calling this function f I + + align:start position:0% +I should be calling this function f I + + + align:start position:0% +I should be calling this function f I +think is that right yeah little F would + + align:start position:0% +think is that right yeah little F would + + + align:start position:0% +think is that right yeah little F would +be there graining of this guy yeah I + + align:start position:0% +be there graining of this guy yeah I + + + align:start position:0% +be there graining of this guy yeah I +think so okay so so what now I'm + + align:start position:0% +think so okay so so what now I'm + + + align:start position:0% +think so okay so so what now I'm +minimizing over X in over certain X's + + align:start position:0% +minimizing over X in over certain X's + + + align:start position:0% +minimizing over X in over certain X's +not all X's I might be minimizing for + + align:start position:0% +not all X's I might be minimizing for + + + align:start position:0% +not all X's I might be minimizing for +example K might be the set where ax + + align:start position:0% +example K might be the set where ax + + + align:start position:0% +example K might be the set where ax +equals B K might be in that case a + + align:start position:0% +equals B K might be in that case a + + + align:start position:0% +equals B K might be in that case a +substrate or a shifted subspace when I + + align:start position:0% +substrate or a shifted subspace when I + + + align:start position:0% +substrate or a shifted subspace when I +said subspace but then 1806 is reminding + + align:start position:0% +said subspace but then 1806 is reminding + + + align:start position:0% +said subspace but then 1806 is reminding +me in my mind that I only have a + + align:start position:0% +me in my mind that I only have a + + + align:start position:0% +me in my mind that I only have a +subspace when V is 0 but I have a you + + align:start position:0% +subspace when V is 0 but I have a you + + + align:start position:0% +subspace when V is 0 but I have a you +know the word for a subspace that sort + + align:start position:0% +know the word for a subspace that sort + + + align:start position:0% +know the word for a subspace that sort +of moved over a fine so I'll just put + + align:start position:0% +of moved over a fine so I'll just put + + + align:start position:0% +of moved over a fine so I'll just put +that word down a bunch of words to learn + + align:start position:0% +that word down a bunch of words to learn + + + align:start position:0% +that word down a bunch of words to learn +for this topic but okay so it's a it's + + align:start position:0% +for this topic but okay so it's a it's + + + align:start position:0% +for this topic but okay so it's a it's +like a plane but not necessarily through + + align:start position:0% +like a plane but not necessarily through + + + align:start position:0% +like a plane but not necessarily through +the origin if B is 0 it doesn't go + + align:start position:0% +the origin if B is 0 it doesn't go + + + align:start position:0% +the origin if B is 0 it doesn't go +through if B is not ok anyway or I have + + align:start position:0% +through if B is not ok anyway or I have + + + align:start position:0% +through if B is not ok anyway or I have +some other convex set let me just put + + align:start position:0% +some other convex set let me just put + + + align:start position:0% +some other convex set let me just put +this + + align:start position:0% +this + + + align:start position:0% +this +like said K in the base and did I make + + align:start position:0% +like said K in the base and did I make + + + align:start position:0% +like said K in the base and did I make +it convex I think pretty good luckily I + + align:start position:0% +it convex I think pretty good luckily I + + + align:start position:0% +it convex I think pretty good luckily I +did so now what well the convex sets the + + align:start position:0% +did so now what well the convex sets the + + + align:start position:0% +did so now what well the convex sets the +the constraint so this is the constraint + + align:start position:0% +the constraint so this is the constraint + + + align:start position:0% +the constraint so this is the constraint +set constraint is that X must be X is in + + align:start position:0% +set constraint is that X must be X is in + + + align:start position:0% +set constraint is that X must be X is in +the set K okay and I drew it as a convex + + align:start position:0% +the set K okay and I drew it as a convex + + + align:start position:0% +the set K okay and I drew it as a convex +blob here was an example where it's a + + align:start position:0% +blob here was an example where it's a + + + align:start position:0% +blob here was an example where it's a +flat not a blob but a flat flat plane + + align:start position:0% +flat not a blob but a flat flat plane + + + align:start position:0% +flat not a blob but a flat flat plane +but what does let me come back to what + + align:start position:0% +but what does let me come back to what + + + align:start position:0% +but what does let me come back to what +does convex mean what what's a convex + + align:start position:0% +does convex mean what what's a convex + + + align:start position:0% +does convex mean what what's a convex +set + + align:start position:0% +set + + + align:start position:0% +set +yeah let's we have to do that should + + align:start position:0% +yeah let's we have to do that should + + + align:start position:0% +yeah let's we have to do that should +have done that before + + align:start position:0% + + + + align:start position:0% + +in the in the notes I had the fun of + + align:start position:0% +in the in the notes I had the fun of + + + align:start position:0% +in the in the notes I had the fun of +figuring out if I took two if I took a + + align:start position:0% +figuring out if I took two if I took a + + + align:start position:0% +figuring out if I took two if I took a +triangle is that a convex set let's just + + align:start position:0% +triangle is that a convex set let's just + + + align:start position:0% +triangle is that a convex set let's just +be sure so what's a convex set that is a + + align:start position:0% +be sure so what's a convex set that is a + + + align:start position:0% +be sure so what's a convex set that is a +convex set because if I take any two + + align:start position:0% +convex set because if I take any two + + + align:start position:0% +convex set because if I take any two +points in the set and draw the line + + align:start position:0% +points in the set and draw the line + + + align:start position:0% +points in the set and draw the line +between them it stays in this set so + + align:start position:0% +between them it stays in this set so + + + align:start position:0% +between them it stays in this set so +that's convexity any edge line from x1 + + align:start position:0% +that's convexity any edge line from x1 + + + align:start position:0% +that's convexity any edge line from x1 +to x2 stays in in the set okay good so + + align:start position:0% +to x2 stays in in the set okay good so + + + align:start position:0% +to x2 stays in in the set okay good so +here's my little exercise to myself what + + align:start position:0% +here's my little exercise to myself what + + + align:start position:0% +here's my little exercise to myself what +if I took the union of two triangles all + + align:start position:0% +if I took the union of two triangles all + + + align:start position:0% +if I took the union of two triangles all +I want to get you to do is this sort of + + align:start position:0% +I want to get you to do is this sort of + + + align:start position:0% +I want to get you to do is this sort of +thing visualize convex and not convex + + align:start position:0% +thing visualize convex and not convex + + + align:start position:0% +thing visualize convex and not convex +possibilities suppose I have two one + + align:start position:0% +possibilities suppose I have two one + + + align:start position:0% +possibilities suppose I have two one +triangle even if it was obtuse that's + + align:start position:0% +triangle even if it was obtuse that's + + + align:start position:0% +triangle even if it was obtuse that's +still convex right + + align:start position:0% +still convex right + + + align:start position:0% +still convex right +no problem but now what if I put those + + align:start position:0% +no problem but now what if I put those + + + align:start position:0% +no problem but now what if I put those +two triangles together take their union + + align:start position:0% +two triangles together take their union + + + align:start position:0% +two triangles together take their union +well if I take them sitting with a big + + align:start position:0% +well if I take them sitting with a big + + + align:start position:0% +well if I take them sitting with a big +gap between like I've lost I mean I've + + align:start position:0% +gap between like I've lost I mean I've + + + align:start position:0% +gap between like I've lost I mean I've +never had a chance that way because if I + + align:start position:0% +never had a chance that way because if I + + + align:start position:0% +never had a chance that way because if I +took one of my if it was the union of + + align:start position:0% +took one of my if it was the union of + + + align:start position:0% +took one of my if it was the union of +these two well you know what I'm gonna + + align:start position:0% +these two well you know what I'm gonna + + + align:start position:0% +these two well you know what I'm gonna +say if I took that point in that point + + align:start position:0% +say if I took that point in that point + + + align:start position:0% +say if I took that point in that point +of course it goes outside stupid all + + align:start position:0% +of course it goes outside stupid all + + + align:start position:0% +of course it goes outside stupid all +right what about a but what if the + + align:start position:0% +right what about a but what if the + + + align:start position:0% +right what about a but what if the +triangles what if what if that triangle + + align:start position:0% +triangles what if what if that triangle + + + align:start position:0% +triangles what if what if that triangle +that lower triangle kind of overlaps the + + align:start position:0% +that lower triangle kind of overlaps the + + + align:start position:0% +that lower triangle kind of overlaps the +upper triangle is that a convex set + + align:start position:0% +upper triangle is that a convex set + + + align:start position:0% +upper triangle is that a convex set +you're everybody's right saying no why + + align:start position:0% +you're everybody's right saying no why + + + align:start position:0% +you're everybody's right saying no why +how do I see that the union of those two + + align:start position:0% +how do I see that the union of those two + + + align:start position:0% +how do I see that the union of those two +triangles is not a convex set guys you + + align:start position:0% +triangles is not a convex set guys you + + + align:start position:0% +triangles is not a convex set guys you +tell me where to pick two points where + + align:start position:0% +tell me where to pick two points where + + + align:start position:0% +tell me where to pick two points where +the line goes out well I take one from + + align:start position:0% +the line goes out well I take one from + + + align:start position:0% +the line goes out well I take one from +that corner and one from that corner and + + align:start position:0% +that corner and one from that corner and + + + align:start position:0% +that corner and one from that corner and +the line between them went outside + + align:start position:0% +the line between them went outside + + + align:start position:0% +the line between them went outside +so you Union is usually not convex well + + align:start position:0% +so you Union is usually not convex well + + + align:start position:0% +so you Union is usually not convex well +if I think of the union of two sets my + + align:start position:0% +if I think of the union of two sets my + + + align:start position:0% +if I think of the union of two sets my +mind actually automatically goes to the + + align:start position:0% +mind actually automatically goes to the + + + align:start position:0% +mind actually automatically goes to the +the other corresponding possibility + + align:start position:0% +the other corresponding possibility + + + align:start position:0% +the other corresponding possibility +which is the intersection of the two + + align:start position:0% +which is the intersection of the two + + + align:start position:0% +which is the intersection of the two +sets so if I take the intersection of + + align:start position:0% +sets so if I take the intersection of + + + align:start position:0% +sets so if I take the intersection of +the two sets now what's the deal with + + align:start position:0% +the two sets now what's the deal with + + + align:start position:0% +the two sets now what's the deal with +that + + align:start position:0% +that + + + align:start position:0% +that +what was the when I had two triangles + + align:start position:0% +what was the when I had two triangles + + + align:start position:0% +what was the when I had two triangles +two separated triangles what what can we + + align:start position:0% +two separated triangles what what can we + + + align:start position:0% +two separated triangles what what can we +say about the intersection of those two + + align:start position:0% +say about the intersection of those two + + + align:start position:0% +say about the intersection of those two +triangles it's empty so shall we regard + + align:start position:0% +triangles it's empty so shall we regard + + + align:start position:0% +triangles it's empty so shall we regard +the empty set as a convex set yes isn't + + align:start position:0% +the empty set as a convex set yes isn't + + + align:start position:0% +the empty set as a convex set yes isn't +it it's vacuous so it hasn't got any + + align:start position:0% +it it's vacuous so it hasn't got any + + + align:start position:0% +it it's vacuous so it hasn't got any +problems right + + align:start position:0% +problems right + + + align:start position:0% +problems right +okay but now is the intersection is + + align:start position:0% +okay but now is the intersection is + + + align:start position:0% +okay but now is the intersection is +always convex if I'm assuming the two + + align:start position:0% +always convex if I'm assuming the two + + + align:start position:0% +always convex if I'm assuming the two +sets that we start with are now that's + + align:start position:0% +sets that we start with are now that's + + + align:start position:0% +sets that we start with are now that's +an important fact that the intersection + + align:start position:0% +an important fact that the intersection + + + align:start position:0% +an important fact that the intersection +of convex sets let's just draw a picture + + align:start position:0% +of convex sets let's just draw a picture + + + align:start position:0% +of convex sets let's just draw a picture +that shows an example so what's the + + align:start position:0% +that shows an example so what's the + + + align:start position:0% +that shows an example so what's the +intersection just this part and it's + + align:start position:0% +intersection just this part and it's + + + align:start position:0% +intersection just this part and it's +convex okay can you give me a little + + align:start position:0% +convex okay can you give me a little + + + align:start position:0% +convex okay can you give me a little +proof that the intersection is convex so + + align:start position:0% +proof that the intersection is convex so + + + align:start position:0% +proof that the intersection is convex so +I take two points in the intersection + + align:start position:0% +I take two points in the intersection + + + align:start position:0% +I take two points in the intersection +let me start the proof to test if + + align:start position:0% +let me start the proof to test if + + + align:start position:0% +let me start the proof to test if +something's convex how do you test it + + align:start position:0% +something's convex how do you test it + + + align:start position:0% +something's convex how do you test it +you take two points in the set in the + + align:start position:0% +you take two points in the set in the + + + align:start position:0% +you take two points in the set in the +intersection and you want to show that + + align:start position:0% +intersection and you want to show that + + + align:start position:0% +intersection and you want to show that +the line between them is in the + + align:start position:0% +the line between them is in the + + + align:start position:0% +the line between them is in the +intersection okay why is that so take + + align:start position:0% +intersection okay why is that so take + + + align:start position:0% +intersection okay why is that so take +two points take x1 in the intersection + + align:start position:0% +two points take x1 in the intersection + + + align:start position:0% +two points take x1 in the intersection +of we've got two sets here and that's + + align:start position:0% +of we've got two sets here and that's + + + align:start position:0% +of we've got two sets here and that's +the symbol for intersection and we've + + align:start position:0% +the symbol for intersection and we've + + + align:start position:0% +the symbol for intersection and we've +got another point in the intersection + + align:start position:0% +got another point in the intersection + + + align:start position:0% +got another point in the intersection +and now we want to look at the line + + align:start position:0% +and now we want to look at the line + + + align:start position:0% +and now we want to look at the line +between them the line from x1 to x2 + + align:start position:0% +between them the line from x1 to x2 + + + align:start position:0% +between them the line from x1 to x2 +what's the deal with that one is that + + align:start position:0% +what's the deal with that one is that + + + align:start position:0% +what's the deal with that one is that +fully in x1 in k1 + + align:start position:0% +fully in x1 in k1 + + + align:start position:0% +fully in x1 in k1 +why is it fully in k1 this we took two + + align:start position:0% +why is it fully in k1 this we took two + + + align:start position:0% +why is it fully in k1 this we took two +points in the intersection I'm looking + + align:start position:0% +points in the intersection I'm looking + + + align:start position:0% +points in the intersection I'm looking +at the line between them and I'm asking + + align:start position:0% +at the line between them and I'm asking + + + align:start position:0% +at the line between them and I'm asking +is it in the first set k1 and the answer + + align:start position:0% +is it in the first set k1 and the answer + + + align:start position:0% +is it in the first set k1 and the answer +is yes + + align:start position:0% +is yes + + + align:start position:0% +is yes +because those points were in k1 and k1 + + align:start position:0% +because those points were in k1 and k1 + + + align:start position:0% +because those points were in k1 and k1 +is convex and is that line between them + + align:start position:0% +is convex and is that line between them + + + align:start position:0% +is convex and is that line between them +in k2 yes same reason the X the two + + align:start position:0% +in k2 yes same reason the X the two + + + align:start position:0% +in k2 yes same reason the X the two +endpoints were in k2 so the line between + + align:start position:0% +endpoints were in k2 so the line between + + + align:start position:0% +endpoints were in k2 so the line between +them is in k tube so the intersection of + + align:start position:0% +them is in k tube so the intersection of + + + align:start position:0% +them is in k tube so the intersection of +convex sets is always convex the + + align:start position:0% +convex sets is always convex the + + + align:start position:0% +convex sets is always convex the +intersection of convex + + align:start position:0% + + + + align:start position:0% + +it's good so you'll see in the notes + + align:start position:0% +it's good so you'll see in the notes + + + align:start position:0% +it's good so you'll see in the notes +these possibilities with two triangles + + align:start position:0% +these possibilities with two triangles + + + align:start position:0% +these possibilities with two triangles +there's sometimes you can you can take + + align:start position:0% +there's sometimes you can you can take + + + align:start position:0% +there's sometimes you can you can take +the Union but not very often + + align:start position:0% +the Union but not very often + + + align:start position:0% +the Union but not very often +okay now what's what's the next thing I + + align:start position:0% +okay now what's what's the next thing I + + + align:start position:0% +okay now what's what's the next thing I +have to do convex functions we got + + align:start position:0% +have to do convex functions we got + + + align:start position:0% +have to do convex functions we got +convex sets what are convex functions + + align:start position:0% +convex sets what are convex functions + + + align:start position:0% +convex sets what are convex functions +then we're good right because this is + + align:start position:0% +then we're good right because this is + + + align:start position:0% +then we're good right because this is +our this is our prototype of a problem + + align:start position:0% +our this is our prototype of a problem + + + align:start position:0% +our this is our prototype of a problem +and I now want to know what it means to + + align:start position:0% +and I now want to know what it means to + + + align:start position:0% +and I now want to know what it means to +be for that F to be a confident I'm + + align:start position:0% +be for that F to be a confident I'm + + + align:start position:0% +be for that F to be a confident I'm +sorry I now know what it means for the + + align:start position:0% +sorry I now know what it means for the + + + align:start position:0% +sorry I now know what it means for the +said K to be convex set but now I have + + align:start position:0% +said K to be convex set but now I have + + + align:start position:0% +said K to be convex set but now I have +to look at the other often more + + align:start position:0% +to look at the other often more + + + align:start position:0% +to look at the other often more +important part of the problem what's the + + align:start position:0% +important part of the problem what's the + + + align:start position:0% +important part of the problem what's the +function I'm minimizing and I'm looking + + align:start position:0% +function I'm minimizing and I'm looking + + + align:start position:0% +function I'm minimizing and I'm looking +for functions with this kind of a + + align:start position:0% +for functions with this kind of a + + + align:start position:0% +for functions with this kind of a +picture okay + + align:start position:0% +picture okay + + + align:start position:0% +picture okay +the coolest way is to connect the + + align:start position:0% +the coolest way is to connect the + + + align:start position:0% +the coolest way is to connect the +definition of a convex function to the + + align:start position:0% +definition of a convex function to the + + + align:start position:0% +definition of a convex function to the +definition of a convex set this is + + align:start position:0% +definition of a convex set this is + + + align:start position:0% +definition of a convex set this is +really the nicest way it's a little + + align:start position:0% +really the nicest way it's a little + + + align:start position:0% +really the nicest way it's a little +quick it just switches by you but tell + + align:start position:0% +quick it just switches by you but tell + + + align:start position:0% +quick it just switches by you but tell +me do you see a convex set in that + + align:start position:0% +me do you see a convex set in that + + + align:start position:0% +me do you see a convex set in that +picture you see a convex set in that + + align:start position:0% +picture you see a convex set in that + + + align:start position:0% +picture you see a convex set in that +picture that's the picture of a graph of + + align:start position:0% +picture that's the picture of a graph of + + + align:start position:0% +picture that's the picture of a graph of +a convex function it's a picture of a + + align:start position:0% +a convex function it's a picture of a + + + align:start position:0% +a convex function it's a picture of a +bowl is are the points on that surface + + align:start position:0% +bowl is are the points on that surface + + + align:start position:0% +bowl is are the points on that surface +is that a convex set no certainly not + + align:start position:0% +is that a convex set no certainly not + + + align:start position:0% +is that a convex set no certainly not +no but where is a convex set to be found + + align:start position:0% +no but where is a convex set to be found + + + align:start position:0% +no but where is a convex set to be found +here in that picture yes yes the points + + align:start position:0% +here in that picture yes yes the points + + + align:start position:0% +here in that picture yes yes the points +on and above the bowl the in inside the + + align:start position:0% +on and above the bowl the in inside the + + + align:start position:0% +on and above the bowl the in inside the +bowl we could say these points so convex + + align:start position:0% +bowl we could say these points so convex + + + align:start position:0% +bowl we could say these points so convex +function me yes a functions convex when + + align:start position:0% +function me yes a functions convex when + + + align:start position:0% +function me yes a functions convex when +the points on and above the graph + + align:start position:0% + + + + align:start position:0% + +our our convex set yeah this is you + + align:start position:0% +our our convex set yeah this is you + + + align:start position:0% +our our convex set yeah this is you +could say okay math my mathematicians + + align:start position:0% +could say okay math my mathematicians + + + align:start position:0% +could say okay math my mathematicians +are just being lazy having got one + + align:start position:0% +are just being lazy having got one + + + align:start position:0% +are just being lazy having got one +definition straight for a convex said + + align:start position:0% +definition straight for a convex said + + + align:start position:0% +definition straight for a convex said +now they're just using that to give an + + align:start position:0% +now they're just using that to give an + + + align:start position:0% +now they're just using that to give an +easy definition of a convex function + + align:start position:0% +easy definition of a convex function + + + align:start position:0% +easy definition of a convex function +actually it's quite useful for functions + + align:start position:0% +actually it's quite useful for functions + + + align:start position:0% +actually it's quite useful for functions +that could maybe equal infinity sort of + + align:start position:0% +that could maybe equal infinity sort of + + + align:start position:0% +that could maybe equal infinity sort of +general generalized functions but it's + + align:start position:0% +general generalized functions but it's + + + align:start position:0% +general generalized functions but it's +not the quickest way to tell if the + + align:start position:0% +not the quickest way to tell if the + + + align:start position:0% +not the quickest way to tell if the +function is convex it's not our usual + + align:start position:0% +function is convex it's not our usual + + + align:start position:0% +function is convex it's not our usual +test for convex function so now I want + + align:start position:0% +test for convex function so now I want + + + align:start position:0% +test for convex function so now I want +to give such a test okay so now I + + align:start position:0% +to give such a test okay so now I + + + align:start position:0% +to give such a test okay so now I +definition of convex function smooth + + align:start position:0% +definition of convex function smooth + + + align:start position:0% +definition of convex function smooth +yeah yeah the the this fact don't rush + + align:start position:0% +yeah yeah the the this fact don't rush + + + align:start position:0% +yeah yeah the the this fact don't rush +in Russia off away from it from the from + + align:start position:0% +in Russia off away from it from the from + + + align:start position:0% +in Russia off away from it from the from +the definition of a convex function as + + align:start position:0% +the definition of a convex function as + + + align:start position:0% +the definition of a convex function as +having a convex set above its graph + + align:start position:0% +having a convex set above its graph + + + align:start position:0% +having a convex set above its graph +there's a really official French name + + align:start position:0% +there's a really official French name + + + align:start position:0% +there's a really official French name +for that said above the graph is the + + align:start position:0% +for that said above the graph is the + + + align:start position:0% +for that said above the graph is the +epigraph okay because why do I come back + + align:start position:0% +epigraph okay because why do I come back + + + align:start position:0% +epigraph okay because why do I come back +to that for a minute because I would + + align:start position:0% +to that for a minute because I would + + + align:start position:0% +to that for a minute because I would +like to think about two functions F 1 + + align:start position:0% +like to think about two functions F 1 + + + align:start position:0% +like to think about two functions F 1 +and F 2 out of two functions I can + + align:start position:0% +and F 2 out of two functions I can + + + align:start position:0% +and F 2 out of two functions I can +always create the minimum or the maximum + + align:start position:0% +always create the minimum or the maximum + + + align:start position:0% +always create the minimum or the maximum +so I suppose I have two convex functions + + align:start position:0% +so I suppose I have two convex functions + + + align:start position:0% +so I suppose I have two convex functions +convex functions F 1 and F 2 + + align:start position:0% + + + + align:start position:0% + +okay then I could choose the minimum I + + align:start position:0% +okay then I could choose the minimum I + + + align:start position:0% +okay then I could choose the minimum I +could choose my new function shall i + + align:start position:0% +could choose my new function shall i + + + align:start position:0% +could choose my new function shall i +call it little m for minimum M of X is + + align:start position:0% +call it little m for minimum M of X is + + + align:start position:0% +call it little m for minimum M of X is +the minimum of f1 and f2 and I could + + align:start position:0% +the minimum of f1 and f2 and I could + + + align:start position:0% +the minimum of f1 and f2 and I could +choose a maximum function which would be + + align:start position:0% +choose a maximum function which would be + + + align:start position:0% +choose a maximum function which would be +the maximum of f1 of X and f2 of X at + + align:start position:0% +the maximum of f1 of X and f2 of X at + + + align:start position:0% +the maximum of f1 of X and f2 of X at +the same point X if I it's just a + + align:start position:0% +the same point X if I it's just a + + + align:start position:0% +the same point X if I it's just a +natural thing okay I have two functions + + align:start position:0% +natural thing okay I have two functions + + + align:start position:0% +natural thing okay I have two functions +I've got a bowl and I've got another + + align:start position:0% +I've got a bowl and I've got another + + + align:start position:0% +I've got a bowl and I've got another +bowl and suppose they're both convex so + + align:start position:0% +bowl and suppose they're both convex so + + + align:start position:0% +bowl and suppose they're both convex so +I'm just stretching you the thing here + + align:start position:0% +I'm just stretching you the thing here + + + align:start position:0% +I'm just stretching you the thing here +if I've got I've got the graphs of two + + align:start position:0% +if I've got I've got the graphs of two + + + align:start position:0% +if I've got I've got the graphs of two +convex functions and I would like to + + align:start position:0% +convex functions and I would like to + + + align:start position:0% +convex functions and I would like to +consider the minimum of those two + + align:start position:0% +consider the minimum of those two + + + align:start position:0% +consider the minimum of those two +functions and also the maximum of those + + align:start position:0% +functions and also the maximum of those + + + align:start position:0% +functions and also the maximum of those +two functions I believe you know life is + + align:start position:0% +two functions I believe you know life is + + + align:start position:0% +two functions I believe you know life is +good one of these will be convex and the + + align:start position:0% +good one of these will be convex and the + + + align:start position:0% +good one of these will be convex and the +other won't and can you identify which + + align:start position:0% +other won't and can you identify which + + + align:start position:0% +other won't and can you identify which +one is convex and which one is not + + align:start position:0% +one is convex and which one is not + + + align:start position:0% +one is convex and which one is not +convex what about the minimum is that a + + align:start position:0% +convex what about the minimum is that a + + + align:start position:0% +convex what about the minimum is that a +convex function so just look at the + + align:start position:0% +convex function so just look at the + + + align:start position:0% +convex function so just look at the +graph what does the minimum look like + + align:start position:0% +graph what does the minimum look like + + + align:start position:0% +graph what does the minimum look like +the minimum is this guy until they meet + + align:start position:0% +the minimum is this guy until they meet + + + align:start position:0% +the minimum is this guy until they meet +somehow on some surface and then this + + align:start position:0% +somehow on some surface and then this + + + align:start position:0% +somehow on some surface and then this +guy is that convex we have like one + + align:start position:0% +guy is that convex we have like one + + + align:start position:0% +guy is that convex we have like one +minute to answer that question + + align:start position:0% +minute to answer that question + + + align:start position:0% +minute to answer that question +absolutely no it's got this bad kink in + + align:start position:0% +absolutely no it's got this bad kink in + + + align:start position:0% +absolutely no it's got this bad kink in +it what about the maximum of the two + + align:start position:0% +it what about the maximum of the two + + + align:start position:0% +it what about the maximum of the two +functions so the maximum is the one that + + align:start position:0% +functions so the maximum is the one that + + + align:start position:0% +functions so the maximum is the one that +it's above all the all the points that + + align:start position:0% +it's above all the all the points that + + + align:start position:0% +it's above all the all the points that +are or things that are above or on on + + align:start position:0% +are or things that are above or on on + + + align:start position:0% +are or things that are above or on on +the there there's the there's the + + align:start position:0% +the there there's the there's the + + + align:start position:0% +the there there's the there's the +maximum function that was the minimum + + align:start position:0% +maximum function that was the minimum + + + align:start position:0% +maximum function that was the minimum +function it had a kink the maximum + + align:start position:0% +function it had a kink the maximum + + + align:start position:0% +function it had a kink the maximum +function is like that and it is convex + + align:start position:0% +function is like that and it is convex + + + align:start position:0% +function is like that and it is convex +so maximum yes + + align:start position:0% +so maximum yes + + + align:start position:0% +so maximum yes +minimum know and we could max if we + + align:start position:0% +minimum know and we could max if we + + + align:start position:0% +minimum know and we could max if we +could have a maximum of 1500 functions + + align:start position:0% +could have a maximum of 1500 functions + + + align:start position:0% +could have a maximum of 1500 functions +if the 1500 functions are all convex the + + align:start position:0% +if the 1500 functions are all convex the + + + align:start position:0% +if the 1500 functions are all convex the +maximum will be because it's the part + + align:start position:0% +maximum will be because it's the part + + + align:start position:0% +maximum will be because it's the part +way above everybody everybody's graph + + align:start position:0% +way above everybody everybody's graph + + + align:start position:0% +way above everybody everybody's graph +and that would be the graph of the + + align:start position:0% +and that would be the graph of the + + + align:start position:0% +and that would be the graph of the +maximum okay good + + align:start position:0% +maximum okay good + + + align:start position:0% +maximum okay good +and now finally let me just say how do + + align:start position:0% +and now finally let me just say how do + + + align:start position:0% +and now finally let me just say how do +you know whether a function is convex + + align:start position:0% +you know whether a function is convex + + + align:start position:0% +you know whether a function is convex +how to test out of Chester + + align:start position:0% + + + + align:start position:0% + +okay so let me take just a function of + + align:start position:0% +okay so let me take just a function of + + + align:start position:0% +okay so let me take just a function of +one variable what's what's the test you + + align:start position:0% +one variable what's what's the test you + + + align:start position:0% +one variable what's what's the test you +learn in calculus freshman calculus + + align:start position:0% +learn in calculus freshman calculus + + + align:start position:0% +learn in calculus freshman calculus +actually just show that this is a convex + + align:start position:0% +actually just show that this is a convex + + + align:start position:0% +actually just show that this is a convex +function what's what's the test for that + + align:start position:0% +function what's what's the test for that + + + align:start position:0% +function what's what's the test for that +second derivative should be positive or + + align:start position:0% +second derivative should be positive or + + + align:start position:0% +second derivative should be positive or +possibly zero so second derivative + + align:start position:0% + + + + align:start position:0% + +greater equals zero everywhere + + align:start position:0% +greater equals zero everywhere + + + align:start position:0% +greater equals zero everywhere +that's this convex okay final question + + align:start position:0% +that's this convex okay final question + + + align:start position:0% +that's this convex okay final question +suppose F is a vector so this is a + + align:start position:0% +suppose F is a vector so this is a + + + align:start position:0% +suppose F is a vector so this is a +vector and so I have n functions of n + + align:start position:0% +vector and so I have n functions of n + + + align:start position:0% +vector and so I have n functions of n +variable no I don't have one + + align:start position:0% +variable no I don't have one + + + align:start position:0% +variable no I don't have one +sorry I've got one function but I'm in n + + align:start position:0% +sorry I've got one function but I'm in n + + + align:start position:0% +sorry I've got one function but I'm in n +variables so so this was just one that + + align:start position:0% +variables so so this was just one that + + + align:start position:0% +variables so so this was just one that +what's the test for convexity yes so it + + align:start position:0% +what's the test for convexity yes so it + + + align:start position:0% +what's the test for convexity yes so it +would be passed for example by x1 + + align:start position:0% +would be passed for example by x1 + + + align:start position:0% +would be passed for example by x1 +squared plus x2 squared would it be + + align:start position:0% +squared plus x2 squared would it be + + + align:start position:0% +squared plus x2 squared would it be +passed by so here would be the question + + align:start position:0% +passed by so here would be the question + + + align:start position:0% +passed by so here would be the question +would it be passed by X transpose some + + align:start position:0% +would it be passed by X transpose some + + + align:start position:0% +would it be passed by X transpose some +symmetric matrix F that would be a + + align:start position:0% +symmetric matrix F that would be a + + + align:start position:0% +symmetric matrix F that would be a +quadratic the pure quadratic would it be + + align:start position:0% +quadratic the pure quadratic would it be + + + align:start position:0% +quadratic the pure quadratic would it be +convex + + align:start position:0% +convex + + + align:start position:0% +convex +what would be the test it's got I'm + + align:start position:0% +what would be the test it's got I'm + + + align:start position:0% +what would be the test it's got I'm +looking for an n-dimensional equivalent + + align:start position:0% +looking for an n-dimensional equivalent + + + align:start position:0% +looking for an n-dimensional equivalent +of positive second derivative the + + align:start position:0% +of positive second derivative the + + + align:start position:0% +of positive second derivative the +n-dimensional equivalent of positive + + align:start position:0% +n-dimensional equivalent of positive + + + align:start position:0% +n-dimensional equivalent of positive +second derivative is convexity and we + + align:start position:0% +second derivative is convexity and we + + + align:start position:0% +second derivative is convexity and we +want it we have to recognize what's the + + align:start position:0% +want it we have to recognize what's the + + + align:start position:0% +want it we have to recognize what's the +test so I could apply it to this + + align:start position:0% +test so I could apply it to this + + + align:start position:0% +test so I could apply it to this +function or I could apply it to any + + align:start position:0% +function or I could apply it to any + + + align:start position:0% +function or I could apply it to any +function of n variables okay what's the + + align:start position:0% +function of n variables okay what's the + + + align:start position:0% +function of n variables okay what's the +test here here I have a matrix instead + + align:start position:0% +test here here I have a matrix instead + + + align:start position:0% +test here here I have a matrix instead +of a number so what's what's a good + + align:start position:0% +of a number so what's what's a good + + + align:start position:0% +of a number so what's what's a good +requirement going to be x out yeah + + align:start position:0% +requirement going to be x out yeah + + + align:start position:0% +requirement going to be x out yeah +positive definite or semi definite or + + align:start position:0% +positive definite or semi definite or + + + align:start position:0% +positive definite or semi definite or +semi definite just as here yeah so the + + align:start position:0% +semi definite just as here yeah so the + + + align:start position:0% +semi definite just as here yeah so the +test is positive semi definite yes yes + + align:start position:0% +test is positive semi definite yes yes + + + align:start position:0% +test is positive semi definite yes yes +and here the Hessian is actually that is + + align:start position:0% +and here the Hessian is actually that is + + + align:start position:0% +and here the Hessian is actually that is +because the second derivatives will + + align:start position:0% +because the second derivatives will + + + align:start position:0% +because the second derivatives will +produce output 1/2 in there the second + + align:start position:0% +produce output 1/2 in there the second + + + align:start position:0% +produce output 1/2 in there the second +derivatives will produce s equal the + + align:start position:0% +derivatives will produce s equal the + + + align:start position:0% +derivatives will produce s equal the +Hessian H so this here the S so positive + + align:start position:0% +Hessian H so this here the S so positive + + + align:start position:0% +Hessian H so this here the S so positive +semi definite Hessian in general second + + align:start position:0% +semi definite Hessian in general second + + + align:start position:0% +semi definite Hessian in general second +derivative matrix for for a quadratic + + align:start position:0% +derivative matrix for for a quadratic + + + align:start position:0% +derivative matrix for for a quadratic +okay so so those it's convex problems + + align:start position:0% +okay so so those it's convex problems + + + align:start position:0% +okay so so those it's convex problems +that where we're going to get farther + + align:start position:0% +that where we're going to get farther + + + align:start position:0% +that where we're going to get farther +with we run into no saddle points we run + + align:start position:0% +with we run into no saddle points we run + + + align:start position:0% +with we run into no saddle points we run +into no local minimum once we found the + + align:start position:0% +into no local minimum once we found the + + + align:start position:0% +into no local minimum once we found the +minimum it's the global minimum these + + align:start position:0% +minimum it's the global minimum these + + + align:start position:0% +minimum it's the global minimum these +are the good problems okay again happy + + align:start position:0% +are the good problems okay again happy + + + align:start position:0% +are the good problems okay again happy +to see you today and I look forward to + + align:start position:0% +to see you today and I look forward to + + + align:start position:0% +to see you today and I look forward to +Wednesday \ No newline at end of file diff --git a/ol1COj0LACs.txt b/ol1COj0LACs.txt new file mode 100644 index 0000000000000000000000000000000000000000..2ce183eebbdd5ea77769a1d72753e2f25050f2f1 --- /dev/null +++ b/ol1COj0LACs.txt @@ -0,0 +1,699 @@ +align:start position:0% + +today we'd like to explore the idea of + + align:start position:0% +today we'd like to explore the idea of + + + align:start position:0% +today we'd like to explore the idea of +the center of mass or the center of + + align:start position:0% +the center of mass or the center of + + + align:start position:0% +the center of mass or the center of +gravity of a rigid object for instance + + align:start position:0% +gravity of a rigid object for instance + + + align:start position:0% +gravity of a rigid object for instance +take this rod and if I try to balance it + + align:start position:0% +take this rod and if I try to balance it + + + align:start position:0% +take this rod and if I try to balance it +on my finger at a certain point in that + + align:start position:0% +on my finger at a certain point in that + + + align:start position:0% +on my finger at a certain point in that +Rod I'm balancing it via the + + align:start position:0% +Rod I'm balancing it via the + + + align:start position:0% +Rod I'm balancing it via the +gravitational force and this point is + + align:start position:0% +gravitational force and this point is + + + align:start position:0% +gravitational force and this point is +often referred to as the center of + + align:start position:0% +often referred to as the center of + + + align:start position:0% +often referred to as the center of +gravity of the rod now if we were in + + align:start position:0% +gravity of the rod now if we were in + + + align:start position:0% +gravity of the rod now if we were in +empty space with no gravitational field + + align:start position:0% +empty space with no gravitational field + + + align:start position:0% +empty space with no gravitational field +then center of gravity doesn't make any + + align:start position:0% +then center of gravity doesn't make any + + + align:start position:0% +then center of gravity doesn't make any +sense but this point still coincides + + align:start position:0% +sense but this point still coincides + + + align:start position:0% +sense but this point still coincides +with what we call the center of mass of + + align:start position:0% +with what we call the center of mass of + + + align:start position:0% +with what we call the center of mass of +the object and now I'd like to Define + + align:start position:0% +the object and now I'd like to Define + + + align:start position:0% +the object and now I'd like to Define +Center of mass so let's consider our + + align:start position:0% +Center of mass so let's consider our + + + align:start position:0% +Center of mass so let's consider our +rigid body and we'll just describe it as + + align:start position:0% +rigid body and we'll just describe it as + + + align:start position:0% +rigid body and we'll just describe it as +some object we'll make it + + align:start position:0% +some object we'll make it + + + align:start position:0% +some object we'll make it +idealized and that there's going to be + + align:start position:0% +idealized and that there's going to be + + + align:start position:0% +idealized and that there's going to be +trying to find some point in this object + + align:start position:0% +trying to find some point in this object + + + align:start position:0% +trying to find some point in this object +and we'll identify that point as the + + align:start position:0% +and we'll identify that point as the + + + align:start position:0% +and we'll identify that point as the +center of mass now let's imagine that + + align:start position:0% +center of mass now let's imagine that + + + align:start position:0% +center of mass now let's imagine that +this rigid body is made up of a bunch of + + align:start position:0% +this rigid body is made up of a bunch of + + + align:start position:0% +this rigid body is made up of a bunch of +little pieces so we have MJ and this J + + align:start position:0% +little pieces so we have MJ and this J + + + align:start position:0% +little pieces so we have MJ and this J +piece is located from the center of mass + + align:start position:0% +piece is located from the center of mass + + + align:start position:0% +piece is located from the center of mass +a vector + + align:start position:0% +a vector + + + align:start position:0% +a vector +RCM now what we want to Def how we want + + align:start position:0% +RCM now what we want to Def how we want + + + align:start position:0% +RCM now what we want to Def how we want +to Define this particular point is that + + align:start position:0% +to Define this particular point is that + + + align:start position:0% +to Define this particular point is that +when we make the sum from Jal 1 to n + + align:start position:0% +when we make the sum from Jal 1 to n + + + align:start position:0% +when we make the sum from Jal 1 to n +over every single point in this body + + align:start position:0% +over every single point in this body + + + align:start position:0% +over every single point in this body +then that will be zero and this will be + + align:start position:0% +then that will be zero and this will be + + + align:start position:0% +then that will be zero and this will be +the + + align:start position:0% +the + + + align:start position:0% +the +definition of the Cent of mass that when + + align:start position:0% +definition of the Cent of mass that when + + + align:start position:0% +definition of the Cent of mass that when +you add + + align:start position:0% +you add + + + align:start position:0% +you add +up the position Vector with respect to + + align:start position:0% +up the position Vector with respect to + + + align:start position:0% +up the position Vector with respect to +this point weighted by the mass and you + + align:start position:0% +this point weighted by the mass and you + + + align:start position:0% +this point weighted by the mass and you +add up all of those vectors you'll get + + align:start position:0% +add up all of those vectors you'll get + + + align:start position:0% +add up all of those vectors you'll get +zero now if you don't know where the + + align:start position:0% +zero now if you don't know where the + + + align:start position:0% +zero now if you don't know where the +center of mass is then this is difficult + + align:start position:0% +center of mass is then this is difficult + + + align:start position:0% +center of mass is then this is difficult +to calculate so let's find a way where + + align:start position:0% +to calculate so let's find a way where + + + align:start position:0% +to calculate so let's find a way where +you choose an arbitrary point and let's + + align:start position:0% +you choose an arbitrary point and let's + + + align:start position:0% +you choose an arbitrary point and let's +write that arbitrary Point say over here + + align:start position:0% +write that arbitrary Point say over here + + + align:start position:0% +write that arbitrary Point say over here +um we'll write it like this s and we'll + + align:start position:0% +um we'll write it like this s and we'll + + + align:start position:0% +um we'll write it like this s and we'll +treat that is our origin and I'll draw a + + align:start position:0% +treat that is our origin and I'll draw a + + + align:start position:0% +treat that is our origin and I'll draw a +vector + + align:start position:0% +vector + + + align:start position:0% +vector +rsj and here I'll draw the vector R + + align:start position:0% +rsj and here I'll draw the vector R + + + align:start position:0% +rsj and here I'll draw the vector R +cm and now what we have from our Vector + + align:start position:0% +cm and now what we have from our Vector + + + align:start position:0% +cm and now what we have from our Vector +relationship is that the vector + + align:start position:0% +relationship is that the vector + + + align:start position:0% +relationship is that the vector +rsj equals the vector RCM and that's + + align:start position:0% +rsj equals the vector RCM and that's + + + align:start position:0% +rsj equals the vector RCM and that's +what I want to find plus the vector R CM + + align:start position:0% +what I want to find plus the vector R CM + + + align:start position:0% +what I want to find plus the vector R CM +J and now let's add up um multiply each + + align:start position:0% +J and now let's add up um multiply each + + + align:start position:0% +J and now let's add up um multiply each +of these by the mass and make a sum so + + align:start position:0% +of these by the mass and make a sum so + + + align:start position:0% +of these by the mass and make a sum so +we have + + align:start position:0% +we have + + + align:start position:0% +we have +MJ R + + align:start position:0% +MJ R + + + align:start position:0% +MJ R +SJ equals the sum of + + align:start position:0% +SJ equals the sum of + + + align:start position:0% +SJ equals the sum of +MJ now the vector + + align:start position:0% +MJ now the vector + + + align:start position:0% +MJ now the vector +RCM this Vector no matter where we + + align:start position:0% +RCM this Vector no matter where we + + + align:start position:0% +RCM this Vector no matter where we +picked a point in this object this + + align:start position:0% +picked a point in this object this + + + align:start position:0% +picked a point in this object this +Vector is always the same and that's why + + align:start position:0% +Vector is always the same and that's why + + + align:start position:0% +Vector is always the same and that's why +I pull it out of the sum and over here I + + align:start position:0% +I pull it out of the sum and over here I + + + align:start position:0% +I pull it out of the sum and over here I +have the sum from J goes from 1 to n j 1 + + align:start position:0% +have the sum from J goes from 1 to n j 1 + + + align:start position:0% +have the sum from J goes from 1 to n j 1 +to n of MJ R CM J now recall this is + + align:start position:0% +to n of MJ R CM J now recall this is + + + align:start position:0% +to n of MJ R CM J now recall this is +precisely how we Define the center of + + align:start position:0% +precisely how we Define the center of + + + align:start position:0% +precisely how we Define the center of +mass point that this is zero and so we + + align:start position:0% +mass point that this is zero and so we + + + align:start position:0% +mass point that this is zero and so we +can now conclude that the center of mass + + align:start position:0% +can now conclude that the center of mass + + + align:start position:0% +can now conclude that the center of mass +so you pick an arbitrary point and if + + align:start position:0% +so you pick an arbitrary point and if + + + align:start position:0% +so you pick an arbitrary point and if +you want to find that Vector to the + + align:start position:0% +you want to find that Vector to the + + + align:start position:0% +you want to find that Vector to the +center of mass what you do is you make + + align:start position:0% +center of mass what you do is you make + + + align:start position:0% +center of mass what you do is you make +the sum from J goes from one to n of MJ + + align:start position:0% +the sum from J goes from one to n of MJ + + + align:start position:0% +the sum from J goes from one to n of MJ +R SJ and you divide that by J goes from + + align:start position:0% +R SJ and you divide that by J goes from + + + align:start position:0% +R SJ and you divide that by J goes from +1 to n + + align:start position:0% +1 to n + + + align:start position:0% +1 to n +MJ and this is what we call the center + + align:start position:0% +MJ and this is what we call the center + + + align:start position:0% +MJ and this is what we call the center +of mass so conceptually the center of + + align:start position:0% +of mass so conceptually the center of + + + align:start position:0% +of mass so conceptually the center of +mass is the point in the object where if + + align:start position:0% +mass is the point in the object where if + + + align:start position:0% +mass is the point in the object where if +you take a vector to any of the Little + + align:start position:0% +you take a vector to any of the Little + + + align:start position:0% +you take a vector to any of the Little +Mass elements and you weight it by the + + align:start position:0% +Mass elements and you weight it by the + + + align:start position:0% +Mass elements and you weight it by the +mass element and you add them up you get + + align:start position:0% +mass element and you add them up you get + + + align:start position:0% +mass element and you add them up you get +zero if you wanted to calculate the + + align:start position:0% +zero if you wanted to calculate the + + + align:start position:0% +zero if you wanted to calculate the +center of mass about any point you + + align:start position:0% +center of mass about any point you + + + align:start position:0% +center of mass about any point you +choose a point s you draw the vector + + align:start position:0% +choose a point s you draw the vector + + + align:start position:0% +choose a point s you draw the vector +from s to the object you sum up those + + align:start position:0% +from s to the object you sum up those + + + align:start position:0% +from s to the object you sum up those +vectors we see by our vector triangle + + align:start position:0% +vectors we see by our vector triangle + + + align:start position:0% +vectors we see by our vector triangle +rule that we can now calculate that + + align:start position:0% +rule that we can now calculate that + + + align:start position:0% +rule that we can now calculate that +Center of mass vector by this + + align:start position:0% +Center of mass vector by this + + + align:start position:0% +Center of mass vector by this +equation um and now let's just rewrite + + align:start position:0% +equation um and now let's just rewrite + + + align:start position:0% +equation um and now let's just rewrite +this because this is the total + + align:start position:0% +this because this is the total + + + align:start position:0% +this because this is the total +mass and what we see is that our + + align:start position:0% +mass and what we see is that our + + + align:start position:0% +mass and what we see is that our +cm equals J goes from 1 to n MJ R SJ + + align:start position:0% +cm equals J goes from 1 to n MJ R SJ + + + align:start position:0% +cm equals J goes from 1 to n MJ R SJ +divided by the total mass \ No newline at end of file diff --git a/ozjMIKustF4.txt b/ozjMIKustF4.txt new file mode 100644 index 0000000000000000000000000000000000000000..9b9a8e9d2d2e98146e1548d5154398f266129bf5 --- /dev/null +++ b/ozjMIKustF4.txt @@ -0,0 +1,11555 @@ +align:start position:0% + +I thought I would start by maybe the + + align:start position:0% +I thought I would start by maybe the + + + align:start position:0% +I thought I would start by maybe the +most uh outstanding example uh in this + + align:start position:0% +most uh outstanding example uh in this + + + align:start position:0% +most uh outstanding example uh in this +direction of linear programming. So + + align:start position:0% +direction of linear programming. So + + + align:start position:0% +direction of linear programming. So +linear programming it's an whole area + + align:start position:0% +linear programming it's an whole area + + + align:start position:0% +linear programming it's an whole area +it's linear algebra with inequalities. + + align:start position:0% +it's linear algebra with inequalities. + + + align:start position:0% +it's linear algebra with inequalities. +That's what it really is about. And um + + align:start position:0% +That's what it really is about. And um + + + align:start position:0% +That's what it really is about. And um +the whole area just sprang into + + align:start position:0% +the whole area just sprang into + + + align:start position:0% +the whole area just sprang into +existence after World War II or in the + + align:start position:0% +existence after World War II or in the + + + align:start position:0% +existence after World War II or in the +in the developments of World War II. Uh + + align:start position:0% +in the developments of World War II. Uh + + + align:start position:0% +in the developments of World War II. Uh +I guess the name the most famous name in + + align:start position:0% +I guess the name the most famous name in + + + align:start position:0% +I guess the name the most famous name in +linear programming is uh Danig who + + align:start position:0% +linear programming is uh Danig who + + + align:start position:0% +linear programming is uh Danig who +created this uh simplex method. pretty + + align:start position:0% +created this uh simplex method. pretty + + + align:start position:0% +created this uh simplex method. pretty +unusual for a method to + + align:start position:0% +unusual for a method to + + + align:start position:0% +unusual for a method to +um + + align:start position:0% +um + + + align:start position:0% +um +survive fundamentally unchanged for such + + align:start position:0% +survive fundamentally unchanged for such + + + align:start position:0% +survive fundamentally unchanged for such +a long time. That the that the first + + align:start position:0% +a long time. That the that the first + + + align:start position:0% +a long time. That the that the first +method suggested to solve linear + + align:start position:0% +method suggested to solve linear + + + align:start position:0% +method suggested to solve linear +programs should turn out to have such a + + align:start position:0% +programs should turn out to have such a + + + align:start position:0% +programs should turn out to have such a +a long life and still still very alive + + align:start position:0% +a long life and still still very alive + + + align:start position:0% +a long life and still still very alive +uh with competition now from uh a + + align:start position:0% +uh with competition now from uh a + + + align:start position:0% +uh with competition now from uh a +different a different class of methods. + + align:start position:0% +different a different class of methods. + + + align:start position:0% +different a different class of methods. +But uh I hope you'll feel that this + + align:start position:0% +But uh I hope you'll feel that this + + + align:start position:0% +But uh I hope you'll feel that this +subject is kind of fun. Uh I'm picking + + align:start position:0% +subject is kind of fun. Uh I'm picking + + + align:start position:0% +subject is kind of fun. Uh I'm picking +linear programming. Well, I'm just + + align:start position:0% +linear programming. Well, I'm just + + + align:start position:0% +linear programming. Well, I'm just +creating an example here uh to show what + + align:start position:0% +creating an example here uh to show what + + + align:start position:0% +creating an example here uh to show what +duality is about. Um and then the second + + align:start position:0% +duality is about. Um and then the second + + + align:start position:0% +duality is about. Um and then the second +lecture this afternoon, please stay for + + align:start position:0% +lecture this afternoon, please stay for + + + align:start position:0% +lecture this afternoon, please stay for +part of it if possible. Uh it's about + + align:start position:0% +part of it if possible. Uh it's about + + + align:start position:0% +part of it if possible. Uh it's about +some integer programming problems. Uh + + align:start position:0% +some integer programming problems. Uh + + + align:start position:0% +some integer programming problems. Uh +like the marriage problem. Marriage + + align:start position:0% +like the marriage problem. Marriage + + + align:start position:0% +like the marriage problem. Marriage +usually have an integer number of + + align:start position:0% +usually have an integer number of + + + align:start position:0% +usually have an integer number of +marriages. Uh and in fact this problem + + align:start position:0% +marriages. Uh and in fact this problem + + + align:start position:0% +marriages. Uh and in fact this problem +is highly moral. You have either zero or + + align:start position:0% +is highly moral. You have either zero or + + + align:start position:0% +is highly moral. You have either zero or +one uh marriages and and how many are + + align:start position:0% +one uh marriages and and how many are + + + align:start position:0% +one uh marriages and and how many are +possible and so on. And the network flow + + align:start position:0% +possible and so on. And the network flow + + + align:start position:0% +possible and so on. And the network flow +problem, maximal flow problem. Uh so + + align:start position:0% +problem, maximal flow problem. Uh so + + + align:start position:0% +problem, maximal flow problem. Uh so +that's the second lecture. This will be + + align:start position:0% +that's the second lecture. This will be + + + align:start position:0% +that's the second lecture. This will be +uh linear algebra as I + + align:start position:0% +uh linear algebra as I + + + align:start position:0% +uh linear algebra as I +said let let me see what are the so + + align:start position:0% +said let let me see what are the so + + + align:start position:0% +said let let me see what are the so +what's the primal + + align:start position:0% + + + + align:start position:0% + +problem the unknown is + + align:start position:0% +problem the unknown is + + + align:start position:0% +problem the unknown is +x so we minimize the + + align:start position:0% + + + + align:start position:0% + +cost which is cranspose + + align:start position:0% +cost which is cranspose + + + align:start position:0% +cost which is cranspose +x you see the linearity the cost depends + + align:start position:0% +x you see the linearity the cost depends + + + align:start position:0% +x you see the linearity the cost depends +linearly X1 up to XN might be the + + align:start position:0% +linearly X1 up to XN might be the + + + align:start position:0% +linearly X1 up to XN might be the +uh + + align:start position:0% +uh + + + align:start position:0% +uh +amounts of N different materials that we + + align:start position:0% +amounts of N different materials that we + + + align:start position:0% +amounts of N different materials that we +have to buy and um C's would be the + + align:start position:0% +have to buy and um C's would be the + + + align:start position:0% +have to buy and um C's would be the +costs per the unit costs of those + + align:start position:0% +costs per the unit costs of those + + + align:start position:0% +costs per the unit costs of those +materials. So if we buy N materials in + + align:start position:0% +materials. So if we buy N materials in + + + align:start position:0% +materials. So if we buy N materials in +these amounts at these costs that's our + + align:start position:0% +these amounts at these costs that's our + + + align:start position:0% +these amounts at these costs that's our +total cost. What are the constraints? + + align:start position:0% +total cost. What are the constraints? + + + align:start position:0% +total cost. What are the constraints? +The constraints are the constraints are + + align:start position:0% +The constraints are the constraints are + + + align:start position:0% +The constraints are the constraints are +one here's the key constraint is that + + align:start position:0% +one here's the key constraint is that + + + align:start position:0% +one here's the key constraint is that +the the vector x all the components have + + align:start position:0% +the the vector x all the components have + + + align:start position:0% +the the vector x all the components have +to be non- + + align:start position:0% +to be non- + + + align:start position:0% +to be non- +negative. We can't use negative amounts + + align:start position:0% +negative. We can't use negative amounts + + + align:start position:0% +negative. We can't use negative amounts +of + + align:start position:0% +of + + + align:start position:0% +of +materials. And the other constraint is + + align:start position:0% +materials. And the other constraint is + + + align:start position:0% +materials. And the other constraint is +that we have to satisfy some + + align:start position:0% +that we have to satisfy some + + + align:start position:0% +that we have to satisfy some +requirements and those will be expressed + + align:start position:0% +requirements and those will be expressed + + + align:start position:0% +requirements and those will be expressed +by ax= + + align:start position:0% +by ax= + + + align:start position:0% +by ax= +b. So there you go. We've here's our + + align:start position:0% +b. So there you go. We've here's our + + + align:start position:0% +b. So there you go. We've here's our +friend ax= b appearing again. And now + + align:start position:0% +friend ax= b appearing again. And now + + + align:start position:0% +friend ax= b appearing again. And now +notice with + + align:start position:0% +notice with + + + align:start position:0% +notice with +m with few + + align:start position:0% +m with few + + + align:start position:0% +m with few +equations. So + + align:start position:0% +equations. So + + + align:start position:0% +equations. So +hopefully many solutions. We we're + + align:start position:0% +hopefully many solutions. We we're + + + align:start position:0% +hopefully many solutions. We we're +expecting lots of + + align:start position:0% +expecting lots of + + + align:start position:0% +expecting lots of +solutions if we + + align:start position:0% +solutions if we + + + align:start position:0% +solutions if we +have more unknowns than + + align:start position:0% +have more unknowns than + + + align:start position:0% +have more unknowns than +equations. But we're of course looking + + align:start position:0% +equations. But we're of course looking + + + align:start position:0% +equations. But we're of course looking +for non-gative solutions. Well then the + + align:start position:0% +for non-gative solutions. Well then the + + + align:start position:0% +for non-gative solutions. Well then the +question is are there any? That's + + align:start position:0% +question is are there any? That's + + + align:start position:0% +question is are there any? That's +already a question. Are there any + + align:start position:0% +already a question. Are there any + + + align:start position:0% +already a question. Are there any +vectors X that that that are solve the + + align:start position:0% +vectors X that that that are solve the + + + align:start position:0% +vectors X that that that are solve the +constraints? This is called feasible. If + + align:start position:0% +constraints? This is called feasible. If + + + align:start position:0% +constraints? This is called feasible. If +an X that satisfy the constraints is + + align:start position:0% +an X that satisfy the constraints is + + + align:start position:0% +an X that satisfy the constraints is +called + + align:start position:0% + + + + align:start position:0% + +feasible feasible X and then among the + + align:start position:0% +feasible feasible X and then among the + + + align:start position:0% +feasible feasible X and then among the +feasible X's, we're looking to minimize + + align:start position:0% +feasible X's, we're looking to minimize + + + align:start position:0% +feasible X's, we're looking to minimize +the cost. So that used the inputs A, B, + + align:start position:0% +the cost. So that used the inputs A, B, + + + align:start position:0% +the cost. So that used the inputs A, B, +and + + align:start position:0% +and + + + align:start position:0% +and +C. And it's pretty straightforward. you + + align:start position:0% +C. And it's pretty straightforward. you + + + align:start position:0% +C. And it's pretty straightforward. you +can see the type of problem that that + + align:start position:0% +can see the type of problem that that + + + align:start position:0% +can see the type of problem that that +comes in. The cost is linear, the + + align:start position:0% +comes in. The cost is linear, the + + + align:start position:0% +comes in. The cost is linear, the +constraints are linear and there's this + + align:start position:0% +constraints are linear and there's this + + + align:start position:0% +constraints are linear and there's this +inequality constraint. Okay. + + align:start position:0% +inequality constraint. Okay. + + + align:start position:0% +inequality constraint. Okay. +Now I want to talk about the jewel + + align:start position:0% +Now I want to talk about the jewel + + + align:start position:0% +Now I want to talk about the jewel +problem and the point is that + + align:start position:0% +problem and the point is that + + + align:start position:0% +problem and the point is that +in + + align:start position:0% +in + + + align:start position:0% +in +throughout this subject of + + align:start position:0% + + + + align:start position:0% + +optimization + + align:start position:0% +optimization + + + align:start position:0% +optimization +there's a twin problem that uses the + + align:start position:0% +there's a twin problem that uses the + + + align:start position:0% +there's a twin problem that uses the +same inputs ABC and in what looks a + + align:start position:0% +same inputs ABC and in what looks a + + + align:start position:0% +same inputs ABC and in what looks a +completely different + + align:start position:0% +completely different + + + align:start position:0% +completely different +way and yet their two are closely + + align:start position:0% +way and yet their two are closely + + + align:start position:0% +way and yet their two are closely +related. It's it's this is one of the + + align:start position:0% +related. It's it's this is one of the + + + align:start position:0% +related. It's it's this is one of the +more subtle aspects + + align:start position:0% +more subtle aspects + + + align:start position:0% +more subtle aspects +of linear programming and all of + + align:start position:0% +of linear programming and all of + + + align:start position:0% +of linear programming and all of +optimization is this presence of dual + + align:start position:0% +optimization is this presence of dual + + + align:start position:0% +optimization is this presence of dual +variables. Well, + + align:start position:0% +variables. Well, + + + align:start position:0% +variables. Well, +actually that theme of variables x's and + + align:start position:0% +actually that theme of variables x's and + + + align:start position:0% +actually that theme of variables x's and +y's has been fundamental in this whole + + align:start position:0% +y's has been fundamental in this whole + + + align:start position:0% +y's has been fundamental in this whole +from the start of these lectures. We are + + align:start position:0% +from the start of these lectures. We are + + + align:start position:0% +from the start of these lectures. We are +our are you remember in our network flow + + align:start position:0% +our are you remember in our network flow + + + align:start position:0% +our are you remember in our network flow +problems we had potentials U and + + align:start position:0% +problems we had potentials U and + + + align:start position:0% +problems we had potentials U and +currents W and there was a certain + + align:start position:0% +currents W and there was a certain + + + align:start position:0% +currents W and there was a certain +duality between + + align:start position:0% +duality between + + + align:start position:0% +duality between +those and in fact we had M M n + + align:start position:0% +those and in fact we had M M n + + + align:start position:0% +those and in fact we had M M n +potentials and M + + align:start position:0% +potentials and M + + + align:start position:0% +potentials and M +currents nodes and M edges. Oh actually + + align:start position:0% +currents nodes and M edges. Oh actually + + + align:start position:0% +currents nodes and M edges. Oh actually +graphs are with nodes and edges are + + align:start position:0% +graphs are with nodes and edges are + + + align:start position:0% +graphs are with nodes and edges are +going to be central in the uh second + + align:start position:0% +going to be central in the uh second + + + align:start position:0% +going to be central in the uh second +lecture today. + + align:start position:0% +lecture today. + + + align:start position:0% +lecture today. +So we want aren't totally it's not + + align:start position:0% +So we want aren't totally it's not + + + align:start position:0% +So we want aren't totally it's not +totally news to us that uh that there's + + align:start position:0% +totally news to us that uh that there's + + + align:start position:0% +totally news to us that uh that there's +some reverse problem which turns out to + + align:start position:0% +some reverse problem which turns out to + + + align:start position:0% +some reverse problem which turns out to +be a + + align:start position:0% +be a + + + align:start position:0% +be a +maximization also linear problem of + + align:start position:0% +maximization also linear problem of + + + align:start position:0% +maximization also linear problem of +course and now it'll be the b transpose + + align:start position:0% +course and now it'll be the b transpose + + + align:start position:0% +course and now it'll be the b transpose +y so the b that was in the constraint is + + align:start position:0% +y so the b that was in the constraint is + + + align:start position:0% +y so the b that was in the constraint is +now popping into the + + align:start position:0% +now popping into the + + + align:start position:0% +now popping into the +cost if I call this + + align:start position:0% +cost if I call this + + + align:start position:0% +cost if I call this +cost or whatever income come + + align:start position:0% +cost or whatever income come + + + align:start position:0% +cost or whatever income come +maybe and what are the constraints on + + align:start position:0% +maybe and what are the constraints on + + + align:start position:0% +maybe and what are the constraints on +this? Uh well, not to anybody's + + align:start position:0% +this? Uh well, not to anybody's + + + align:start position:0% +this? Uh well, not to anybody's +surprise, arpose is going to show up and + + align:start position:0% +surprise, arpose is going to show up and + + + align:start position:0% +surprise, arpose is going to show up and +this vector c is going to show up on the + + align:start position:0% +this vector c is going to show up on the + + + align:start position:0% +this vector c is going to show up on the +right hand side. So it'll be a transpose + + align:start position:0% +right hand side. So it'll be a transpose + + + align:start position:0% +right hand side. So it'll be a transpose +y equals + + align:start position:0% +y equals + + + align:start position:0% +y equals +c. Okay, have I got that right? Or do I + + align:start position:0% +c. Okay, have I got that right? Or do I + + + align:start position:0% +c. Okay, have I got that right? Or do I +want greater than or equal? I bet I want + + align:start position:0% +want greater than or equal? I bet I want + + + align:start position:0% +want greater than or equal? I bet I want +greater than or + + align:start position:0% +greater than or + + + align:start position:0% +greater than or +equal here. If here I Yeah, I I better + + align:start position:0% +equal here. If here I Yeah, I I better + + + align:start position:0% +equal here. If here I Yeah, I I better +just check. Do I want less or equal or + + align:start position:0% +just check. Do I want less or equal or + + + align:start position:0% +just check. Do I want less or equal or +greater equal? I think I want less or + + align:start position:0% +greater equal? I think I want less or + + + align:start position:0% +greater equal? I think I want less or +equal + + align:start position:0% +equal + + + align:start position:0% +equal +because not surprisingly the uh we had a + + align:start position:0% +because not surprisingly the uh we had a + + + align:start position:0% +because not surprisingly the uh we had a +greater than or equal in in in the + + align:start position:0% +greater than or equal in in in the + + + align:start position:0% +greater than or equal in in in the +primal problem. Well, less or equal + + align:start position:0% +primal problem. Well, less or equal + + + align:start position:0% +primal problem. Well, less or equal +shows up here. But the main point is a + + align:start position:0% +shows up here. But the main point is a + + + align:start position:0% +shows up here. But the main point is a +transpose shows up again. So we really + + align:start position:0% +transpose shows up again. So we really + + + align:start position:0% +transpose shows up again. So we really +uh I could stretch our little + + align:start position:0% +uh I could stretch our little + + + align:start position:0% +uh I could stretch our little +framework. Why do I say little? our + + align:start position:0% +framework. Why do I say little? our + + + align:start position:0% +framework. Why do I say little? our +framework of uh three steps to include + + align:start position:0% +framework of uh three steps to include + + + align:start position:0% +framework of uh three steps to include +linear programming. Shall I do that? Uh + + align:start position:0% +linear programming. Shall I do that? Uh + + + align:start position:0% +linear programming. Shall I do that? Uh +and + + align:start position:0% +and + + + align:start position:0% +and +then well so let me make some comments + + align:start position:0% +then well so let me make some comments + + + align:start position:0% +then well so let me make some comments +about this and and and do that. Yeah. + + align:start position:0% +about this and and and do that. Yeah. + + + align:start position:0% +about this and and and do that. Yeah. +Yeah. How are the X's? Well, at the + + align:start position:0% +Yeah. How are the X's? Well, at the + + + align:start position:0% +Yeah. How are the X's? Well, at the +moment, these are two independent + + align:start position:0% +moment, these are two independent + + + align:start position:0% +moment, these are two independent +problems that I mean I I could hide the + + align:start position:0% +problems that I mean I I could hide the + + + align:start position:0% +problems that I mean I I could hide the +dual problem, never tell it, never tell + + align:start position:0% +dual problem, never tell it, never tell + + + align:start position:0% +dual problem, never tell it, never tell +you about it and just discuss the + + align:start position:0% +you about it and just discuss the + + + align:start position:0% +you about it and just discuss the +primal, how to solve that. + + align:start position:0% +primal, how to solve that. + + + align:start position:0% +primal, how to solve that. +I am revealing that there's a second + + align:start position:0% +I am revealing that there's a second + + + align:start position:0% +I am revealing that there's a second +problem which if I had five lectures on + + align:start position:0% +problem which if I had five lectures on + + + align:start position:0% +problem which if I had five lectures on +linear programming I probably wouldn't + + align:start position:0% +linear programming I probably wouldn't + + + align:start position:0% +linear programming I probably wouldn't +reveal so early that there's a second + + align:start position:0% +reveal so early that there's a second + + + align:start position:0% +reveal so early that there's a second +problem hiding around with the same + + align:start position:0% +problem hiding around with the same + + + align:start position:0% +problem hiding around with the same +inputs and also another linear program + + align:start position:0% +inputs and also another linear program + + + align:start position:0% +inputs and also another linear program +this is that's a linear programming + + align:start position:0% +this is that's a linear programming + + + align:start position:0% +this is that's a linear programming +problem too linear programming is linear + + align:start position:0% +problem too linear programming is linear + + + align:start position:0% +problem too linear programming is linear +costs linear equality and inequality + + align:start position:0% +costs linear equality and inequality + + + align:start position:0% +costs linear equality and inequality +constraints however I I can play I can + + align:start position:0% +constraints however I I can play I can + + + align:start position:0% +constraints however I I can play I can +massage one problem to fit another one. + + align:start position:0% +massage one problem to fit another one. + + + align:start position:0% +massage one problem to fit another one. +I could uh I could uh I could have ax + + align:start position:0% +I could uh I could uh I could have ax + + + align:start position:0% +I could uh I could uh I could have ax +less or equal b there and play with it + + align:start position:0% +less or equal b there and play with it + + + align:start position:0% +less or equal b there and play with it +and and and introduce some slack + + align:start position:0% +and and and introduce some slack + + + align:start position:0% +and and and introduce some slack +unknowns to make up the equality sign + + align:start position:0% +unknowns to make up the equality sign + + + align:start position:0% +unknowns to make up the equality sign +and they would have to be non- negative + + align:start position:0% +and they would have to be non- negative + + + align:start position:0% +and they would have to be non- negative +and put them add them to the x's. + + align:start position:0% +and put them add them to the x's. + + + align:start position:0% +and put them add them to the x's. +All I want to say is that the pre this + + align:start position:0% +All I want to say is that the pre this + + + align:start position:0% +All I want to say is that the pre this +fits the general form, but others that + + align:start position:0% +fits the general form, but others that + + + align:start position:0% +fits the general form, but others that +don't look like they quite fit do as + + align:start position:0% +don't look like they quite fit do as + + + align:start position:0% +don't look like they quite fit do as +long as they have + + align:start position:0% +long as they have + + + align:start position:0% +long as they have +linear + + align:start position:0% +linear + + + align:start position:0% +linear +costs and linear equations and + + align:start position:0% +costs and linear equations and + + + align:start position:0% +costs and linear equations and +inequalities. + + align:start position:0% +inequalities. + + + align:start position:0% +inequalities. +Condition on why like no condition on + + align:start position:0% +Condition on why like no condition on + + + align:start position:0% +Condition on why like no condition on +why. Yeah, it's it's it's interesting. + + align:start position:0% +why. Yeah, it's it's it's interesting. + + + align:start position:0% +why. Yeah, it's it's it's interesting. +Uh uh that's why you saw me goof and + + align:start position:0% +Uh uh that's why you saw me goof and + + + align:start position:0% +Uh uh that's why you saw me goof and +correct. I have to think every time. + + align:start position:0% +correct. I have to think every time. + + + align:start position:0% +correct. I have to think every time. +Okay. Is there a condition? Let me let + + align:start position:0% +Okay. Is there a condition? Let me let + + + align:start position:0% +Okay. Is there a condition? Let me let +me tell you about duality. So + + align:start position:0% + + + + align:start position:0% + +duality. So I'm really jumping here to + + align:start position:0% +duality. So I'm really jumping here to + + + align:start position:0% +duality. So I'm really jumping here to +the heart of the of the underlying math + + align:start position:0% +the heart of the of the underlying math + + + align:start position:0% +the heart of the of the underlying math +says that the maximum in the dual + + align:start position:0% +says that the maximum in the dual + + + align:start position:0% +says that the maximum in the dual +problem equals the minimum in the + + align:start position:0% +problem equals the minimum in the + + + align:start position:0% +problem equals the minimum in the +primal. that the answer to this problem + + align:start position:0% +primal. that the answer to this problem + + + align:start position:0% +primal. that the answer to this problem +the the the maximum whatever is the min + + align:start position:0% +the the the maximum whatever is the min + + + align:start position:0% +the the the maximum whatever is the min +is equal to the minimum cost. So that uh + + align:start position:0% +is equal to the minimum cost. So that uh + + + align:start position:0% +is equal to the minimum cost. So that uh +um in a way this is a big help because + + align:start position:0% +um in a way this is a big help because + + + align:start position:0% +um in a way this is a big help because +it tells us when to stop. If we have a + + align:start position:0% +it tells us when to stop. If we have a + + + align:start position:0% +it tells us when to stop. If we have a +suppose we have an algorithm that + + align:start position:0% +suppose we have an algorithm that + + + align:start position:0% +suppose we have an algorithm that +gradually finds better and better x's. + + align:start position:0% +gradually finds better and better x's. + + + align:start position:0% +gradually finds better and better x's. +This is what you really do in reality. + + align:start position:0% +This is what you really do in reality. + + + align:start position:0% +This is what you really do in reality. +You you get a approximate x and you say + + align:start position:0% +You you get a approximate x and you say + + + align:start position:0% +You you get a approximate x and you say +is that the best I can do? You look + + align:start position:0% +is that the best I can do? You look + + + align:start position:0% +is that the best I can do? You look +around it as calculus always does. You + + align:start position:0% +around it as calculus always does. You + + + align:start position:0% +around it as calculus always does. You +say I can go off I can change that x to + + align:start position:0% +say I can go off I can change that x to + + + align:start position:0% +say I can go off I can change that x to +to in to reduce the + + align:start position:0% +to in to reduce the + + + align:start position:0% +to in to reduce the +cost. And so you go that way and then + + align:start position:0% +cost. And so you go that way and then + + + align:start position:0% +cost. And so you go that way and then +you don't know when to stop. Well, + + align:start position:0% +you don't know when to stop. Well, + + + align:start position:0% +you don't know when to stop. Well, +there's several ways to know when to + + align:start position:0% +there's several ways to know when to + + + align:start position:0% +there's several ways to know when to +stop. One way is when you get to a point + + align:start position:0% +stop. One way is when you get to a point + + + align:start position:0% +stop. One way is when you get to a point +x star let's say let's call let's call y + + align:start position:0% +x star let's say let's call let's call y + + + align:start position:0% +x star let's say let's call let's call y +star the winner here and + + align:start position:0% +star the winner here and + + + align:start position:0% +star the winner here and +xar the winner here. So I'll sort of + + align:start position:0% +xar the winner here. So I'll sort of + + + align:start position:0% +xar the winner here. So I'll sort of +introduce the notation star for the + + align:start position:0% +introduce the notation star for the + + + align:start position:0% +introduce the notation star for the +optimizer the best then. So one way to + + align:start position:0% +optimizer the best then. So one way to + + + align:start position:0% +optimizer the best then. So one way to +stop is to get to some xstar. You don't + + align:start position:0% +stop is to get to some xstar. You don't + + + align:start position:0% +stop is to get to some xstar. You don't +know that it's xstar yet. You look + + align:start position:0% +know that it's xstar yet. You look + + + align:start position:0% +know that it's xstar yet. You look +around but every way you look is worse. + + align:start position:0% +around but every way you look is worse. + + + align:start position:0% +around but every way you look is worse. +You mean equality? Uh yes. Yeah. This is + + align:start position:0% +You mean equality? Uh yes. Yeah. This is + + + align:start position:0% +You mean equality? Uh yes. Yeah. This is +the this is the minimum C. So I mean + + align:start position:0% +the this is the minimum C. So I mean + + + align:start position:0% +the this is the minimum C. So I mean +that at the E this is this says the + + align:start position:0% +that at the E this is this says the + + + align:start position:0% +that at the E this is this says the +the this quantity that you're trying to + + align:start position:0% +the this quantity that you're trying to + + + align:start position:0% +the this quantity that you're trying to +maximize when you do it equals this + + align:start position:0% +maximize when you do it equals this + + + align:start position:0% +maximize when you do it equals this +quantity that in this other problem + + align:start position:0% +quantity that in this other problem + + + align:start position:0% +quantity that in this other problem +you're trying to minimize. Well, you are + + align:start position:0% +you're trying to minimize. Well, you are + + + align:start position:0% +you're trying to minimize. Well, you are +naturally asking yourself, what's the + + align:start position:0% +naturally asking yourself, what's the + + + align:start position:0% +naturally asking yourself, what's the +relation between these problems? So, let + + align:start position:0% +relation between these problems? So, let + + + align:start position:0% +relation between these problems? So, let +me prove right away weak + + align:start position:0% +me prove right away weak + + + align:start position:0% +me prove right away weak +duality. + + align:start position:0% +duality. + + + align:start position:0% +duality. +We what's what's always easy in these + + align:start position:0% + + + + align:start position:0% + +problems is to show that the + + align:start position:0% +problems is to show that the + + + align:start position:0% +problems is to show that the +maximum is is always below the + + align:start position:0% + + + + align:start position:0% + +minimum. Maximum in one problem. That + + align:start position:0% +minimum. Maximum in one problem. That + + + align:start position:0% +minimum. Maximum in one problem. That +that looks goofy, right? Max less or + + align:start position:0% +that looks goofy, right? Max less or + + + align:start position:0% +that looks goofy, right? Max less or +equal min. But this is the maximum in + + align:start position:0% +equal min. But this is the maximum in + + + align:start position:0% +equal min. But this is the maximum in +the + + align:start position:0% +the + + + align:start position:0% +the +jewel is always less or equal to minimum + + align:start position:0% +jewel is always less or equal to minimum + + + align:start position:0% +jewel is always less or equal to minimum +in the primal. We can show that right + + align:start position:0% +in the primal. We can show that right + + + align:start position:0% +in the primal. We can show that right +off the bat just from taking two two + + align:start position:0% +off the bat just from taking two two + + + align:start position:0% +off the bat just from taking two two +steps will do it. But those are + + align:start position:0% +steps will do it. But those are + + + align:start position:0% +steps will do it. But those are +different problems. So not too + + align:start position:0% +different problems. So not too + + + align:start position:0% +different problems. So not too +surprising. And then + + align:start position:0% +surprising. And then + + + align:start position:0% +surprising. And then +um and then the the serious duality + + align:start position:0% +um and then the the serious duality + + + align:start position:0% +um and then the the serious duality +thing is that actually when you push + + align:start position:0% +thing is that actually when you push + + + align:start position:0% +thing is that actually when you push +this quantity you're trying to maximize + + align:start position:0% +this quantity you're trying to maximize + + + align:start position:0% +this quantity you're trying to maximize +as high as it'll go and you pull this + + align:start position:0% +as high as it'll go and you pull this + + + align:start position:0% +as high as it'll go and you pull this +quantity you're trying to minimize this + + align:start position:0% +quantity you're trying to minimize this + + + align:start position:0% +quantity you're trying to minimize this +cost down as low as it'll go. They meet + + align:start position:0% +cost down as low as it'll go. They meet + + + align:start position:0% +cost down as low as it'll go. They meet +and then you know you've got the answer + + align:start position:0% +and then you know you've got the answer + + + align:start position:0% +and then you know you've got the answer +because they + + align:start position:0% +because they + + + align:start position:0% +because they +can't pass each other according to this + + align:start position:0% +can't pass each other according to this + + + align:start position:0% +can't pass each other according to this +symbol. Let me just prove that. So the + + align:start position:0% +symbol. Let me just prove that. So the + + + align:start position:0% +symbol. Let me just prove that. So the +maximum in the duel for for any so this + + align:start position:0% +maximum in the duel for for any so this + + + align:start position:0% +maximum in the duel for for any so this +take any x I want to show that this + + align:start position:0% +take any x I want to show that this + + + align:start position:0% +take any x I want to show that this +quantity cranspose x is I I want to show + + align:start position:0% +quantity cranspose x is I I want to show + + + align:start position:0% +quantity cranspose x is I I want to show +that cranspose x is + + align:start position:0% +that cranspose x is + + + align:start position:0% +that cranspose x is +always less or equal b branspose y for + + align:start position:0% +always less or equal b branspose y for + + + align:start position:0% +always less or equal b branspose y for +for any for any allowable x for this is + + align:start position:0% +for any for any allowable x for this is + + + align:start position:0% +for any for any allowable x for this is +for any allowable x and y. So, + + align:start position:0% +for any allowable x and y. So, + + + align:start position:0% +for any allowable x and y. So, +uh, no. Yes. Maybe no. Maybe. Yes. Let's + + align:start position:0% +uh, no. Yes. Maybe no. Maybe. Yes. Let's + + + align:start position:0% +uh, no. Yes. Maybe no. Maybe. Yes. Let's +see. What is it? I'm I I just got them + + align:start position:0% +see. What is it? I'm I I just got them + + + align:start position:0% +see. What is it? I'm I I just got them +reversed here. The thing I'm maximizing, + + align:start position:0% +reversed here. The thing I'm maximizing, + + + align:start position:0% +reversed here. The thing I'm maximizing, +right? Thank you. The thing I'm + + align:start position:0% + + + + align:start position:0% + +maximizing, take that off the videape. + + align:start position:0% +maximizing, take that off the videape. + + + align:start position:0% +maximizing, take that off the videape. +Okay. B is branspose Y. That's the + + align:start position:0% +Okay. B is branspose Y. That's the + + + align:start position:0% +Okay. B is branspose Y. That's the +quantity that I'm maximizing. So, I push + + align:start position:0% +quantity that I'm maximizing. So, I push + + + align:start position:0% +quantity that I'm maximizing. So, I push +that up. But it doesn't matter. any Y + + align:start position:0% +that up. But it doesn't matter. any Y + + + align:start position:0% +that up. But it doesn't matter. any Y +that's acceptable will be + + align:start position:0% +that's acceptable will be + + + align:start position:0% +that's acceptable will be +below in the cost of any X that's + + align:start position:0% +below in the cost of any X that's + + + align:start position:0% +below in the cost of any X that's +acceptable. + + align:start position:0% +acceptable. + + + align:start position:0% +acceptable. +Thanks. And now that's for for any + + align:start position:0% +Thanks. And now that's for for any + + + align:start position:0% +Thanks. And now that's for for any +acceptable any shall I use the right + + align:start position:0% +acceptable any shall I use the right + + + align:start position:0% +acceptable any shall I use the right +word + + align:start position:0% + + + + align:start position:0% + +feasible X and + + align:start position:0% + + + + align:start position:0% + +Y. Any feasible X and Y this will work. + + align:start position:0% +Y. Any feasible X and Y this will work. + + + align:start position:0% +Y. Any feasible X and Y this will work. +Okay. Can we just take that step? Let's + + align:start position:0% +Okay. Can we just take that step? Let's + + + align:start position:0% +Okay. Can we just take that step? Let's +see if if if y is + + align:start position:0% +see if if if y is + + + align:start position:0% +see if if if y is +feasible + + align:start position:0% + + + + align:start position:0% + +then let's see ax is b right if x is + + align:start position:0% +then let's see ax is b right if x is + + + align:start position:0% +then let's see ax is b right if x is +feasible ax is b right so I know that so + + align:start position:0% +feasible ax is b right so I know that so + + + align:start position:0% +feasible ax is b right so I know that so +now I'm I'm going to connect those + + align:start position:0% +now I'm I'm going to connect those + + + align:start position:0% +now I'm I'm going to connect those +problems if if x is feasible then ax is + + align:start position:0% +problems if if x is feasible then ax is + + + align:start position:0% +problems if if x is feasible then ax is +b so this is a x transpose y right + + align:start position:0% +b so this is a x transpose y right + + + align:start position:0% +b so this is a x transpose y right +because b is + + align:start position:0% +because b is + + + align:start position:0% +because b is +ax + + align:start position:0% +ax + + + align:start position:0% +ax +Okay, now what am I going to + + align:start position:0% + + + + align:start position:0% + +do? Well, anytime I see + + align:start position:0% +do? Well, anytime I see + + + align:start position:0% +do? Well, anytime I see +axrpose like like one idea in my + + align:start position:0% +axrpose like like one idea in my + + + align:start position:0% +axrpose like like one idea in my +head, write it as xrpose move the + + align:start position:0% +head, write it as xrpose move the + + + align:start position:0% +head, write it as xrpose move the +parenthesis. Write it as + + align:start position:0% +parenthesis. Write it as + + + align:start position:0% +parenthesis. Write it as +xrpose a transpose y and move the + + align:start position:0% +xrpose a transpose y and move the + + + align:start position:0% +xrpose a transpose y and move the +parenthesis so that I'm looking at a + + align:start position:0% +parenthesis so that I'm looking at a + + + align:start position:0% +parenthesis so that I'm looking at a +transpose. Was that a transpose? What + + align:start position:0% +transpose. Was that a transpose? What + + + align:start position:0% +transpose. Was that a transpose? What +did I have + + align:start position:0% + + + + align:start position:0% + +there? Why? Yes, it is. Thanks. + + align:start position:0% +there? Why? Yes, it is. Thanks. + + + align:start position:0% +there? Why? Yes, it is. Thanks. +Okay, that's the key step. So simple for + + align:start position:0% +Okay, that's the key step. So simple for + + + align:start position:0% +Okay, that's the key step. So simple for +matrices corresponds to integration by + + align:start position:0% +matrices corresponds to integration by + + + align:start position:0% +matrices corresponds to integration by +parts in continuum problems that we met + + align:start position:0% +parts in continuum problems that we met + + + align:start position:0% +parts in continuum problems that we met +for a while. Okay. And now why is this? + + align:start position:0% +for a while. Okay. And now why is this? + + + align:start position:0% +for a while. Okay. And now why is this? +So that's okay, + + align:start position:0% +So that's okay, + + + align:start position:0% +So that's okay, +right? Actually, was that an even and + + align:start position:0% +right? Actually, was that an even and + + + align:start position:0% +right? Actually, was that an even and +equal? No, that was right. That okay. + + align:start position:0% +equal? No, that was right. That okay. + + + align:start position:0% +equal? No, that was right. That okay. +Oh, that was even an equal sign, wasn't + + align:start position:0% +Oh, that was even an equal sign, wasn't + + + align:start position:0% +Oh, that was even an equal sign, wasn't +it? That was even an equal sign because + + align:start position:0% +it? That was even an equal sign because + + + align:start position:0% +it? That was even an equal sign because +ax was exactly b. Okay, now I'm ready + + align:start position:0% +ax was exactly b. Okay, now I'm ready + + + align:start position:0% +ax was exactly b. Okay, now I'm ready +for the step that this is less or equal + + align:start position:0% +for the step that this is less or equal + + + align:start position:0% +for the step that this is less or equal +this. Now, why is + + align:start position:0% +this. Now, why is + + + align:start position:0% +this. Now, why is +that? Because a transpose + + align:start position:0% +that? Because a transpose + + + align:start position:0% +that? Because a transpose +y, you don't mind what order this inner + + align:start position:0% +y, you don't mind what order this inner + + + align:start position:0% +y, you don't mind what order this inner +product comes in. Those are just two + + align:start position:0% +product comes in. Those are just two + + + align:start position:0% +product comes in. Those are just two +vectors. I I I'm happy to write + + align:start position:0% +vectors. I I I'm happy to write + + + align:start position:0% +vectors. I I I'm happy to write +xranspose c if you if you would like. + + align:start position:0% +xranspose c if you if you would like. + + + align:start position:0% +xranspose c if you if you would like. +Let me write it there as xrpose c which + + align:start position:0% +Let me write it there as xrpose c which + + + align:start position:0% +Let me write it there as xrpose c which +is the same as cranspose x. It's just + + align:start position:0% +is the same as cranspose x. It's just + + + align:start position:0% +is the same as cranspose x. It's just +just uh the dotproduct doesn't matter. + + align:start position:0% +just uh the dotproduct doesn't matter. + + + align:start position:0% +just uh the dotproduct doesn't matter. +Okay, here here's the key step then + + align:start position:0% +Okay, here here's the key step then + + + align:start position:0% +Okay, here here's the key step then +obviously and why is that + + align:start position:0% +obviously and why is that + + + align:start position:0% +obviously and why is that +true? Well, first of all, a transpose y + + align:start position:0% +true? Well, first of all, a transpose y + + + align:start position:0% +true? Well, first of all, a transpose y +we have to it's beautiful how all the + + align:start position:0% +we have to it's beautiful how all the + + + align:start position:0% +we have to it's beautiful how all the +requirements come in. A transpose Y is + + align:start position:0% +requirements come in. A transpose Y is + + + align:start position:0% +requirements come in. A transpose Y is +less or equal to C. So does that make + + align:start position:0% +less or equal to C. So does that make + + + align:start position:0% +less or equal to C. So does that make +this true right away? If A transpose Y + + align:start position:0% +this true right away? If A transpose Y + + + align:start position:0% +this true right away? If A transpose Y +is less or equal C, not right away. I + + align:start position:0% +is less or equal C, not right away. I + + + align:start position:0% +is less or equal C, not right away. I +need to know that I'm multiplying these + + align:start position:0% +need to know that I'm multiplying these + + + align:start position:0% +need to know that I'm multiplying these +this inequality a transpose Y less or + + align:start position:0% +this inequality a transpose Y less or + + + align:start position:0% +this inequality a transpose Y less or +equal C by positive + + align:start position:0% +equal C by positive + + + align:start position:0% +equal C by positive +numbers. If you take an inequality + + align:start position:0% +numbers. If you take an inequality + + + align:start position:0% +numbers. If you take an inequality +multiply by a negative number, it + + align:start position:0% +multiply by a negative number, it + + + align:start position:0% +multiply by a negative number, it +reverses it. But that's exactly where + + align:start position:0% +reverses it. But that's exactly where + + + align:start position:0% +reverses it. But that's exactly where +this comes in. + + align:start position:0% +this comes in. + + + align:start position:0% +this comes in. +So, oh, and in a way, yeah, more than in + + align:start position:0% +So, oh, and in a way, yeah, more than in + + + align:start position:0% +So, oh, and in a way, yeah, more than in +a way. Here we can + + align:start position:0% +a way. Here we can + + + align:start position:0% +a way. Here we can +see is that all + + align:start position:0% +see is that all + + + align:start position:0% +see is that all +right? So that so that any feasible one + + align:start position:0% +right? So that so that any feasible one + + + align:start position:0% +right? So that so that any feasible one +matched was less any any feasible Y gave + + align:start position:0% +matched was less any any feasible Y gave + + + align:start position:0% +matched was less any any feasible Y gave +a brppose Y that was smaller than or + + align:start position:0% +a brppose Y that was smaller than or + + + align:start position:0% +a brppose Y that was smaller than or +equal to cranspose X. Now our point is + + align:start position:0% +equal to cranspose X. Now our point is + + + align:start position:0% +equal to cranspose X. Now our point is +that so that's the easy step. I mean + + align:start position:0% +that so that's the easy step. I mean + + + align:start position:0% +that so that's the easy step. I mean +right that just a and there was a + + align:start position:0% +right that just a and there was a + + + align:start position:0% +right that just a and there was a +corresponding + + align:start position:0% +corresponding + + + align:start position:0% +corresponding +uh easy step when we were doing + + align:start position:0% +uh easy step when we were doing + + + align:start position:0% +uh easy step when we were doing +minimizing potential energy. There was a + + align:start position:0% +minimizing potential energy. There was a + + + align:start position:0% +minimizing potential energy. There was a +something called a complimentary energy + + align:start position:0% +something called a complimentary energy + + + align:start position:0% +something called a complimentary energy +that involved the the flows the or the + + align:start position:0% +that involved the the flows the or the + + + align:start position:0% +that involved the the flows the or the +uh or + + align:start position:0% +uh or + + + align:start position:0% +uh or +the stresses whatever that dual variable + + align:start position:0% +the stresses whatever that dual variable + + + align:start position:0% +the stresses whatever that dual variable +was and we could have found a weak + + align:start position:0% +was and we could have found a weak + + + align:start position:0% +was and we could have found a weak +duality and then + + align:start position:0% +duality and then + + + align:start position:0% +duality and then +ultimately equality. So, so I proved + + align:start position:0% +ultimately equality. So, so I proved + + + align:start position:0% +ultimately equality. So, so I proved +like you'll see that often to un to + + align:start position:0% +like you'll see that often to un to + + + align:start position:0% +like you'll see that often to un to +prove this that in one direction it's + + align:start position:0% +prove this that in one direction it's + + + align:start position:0% +prove this that in one direction it's +it's easy. That's the direction we took + + align:start position:0% +it's easy. That's the direction we took + + + align:start position:0% +it's easy. That's the direction we took +and but now to get equality is not so + + align:start position:0% +and but now to get equality is not so + + + align:start position:0% +and but now to get equality is not so +easy. But actually when would equality + + align:start position:0% +easy. But actually when would equality + + + align:start position:0% +easy. But actually when would equality +hold. So now this this actually not only + + align:start position:0% +hold. So now this this actually not only + + + align:start position:0% +hold. So now this this actually not only +gives us a easy argument but also gives + + align:start position:0% +gives us a easy argument but also gives + + + align:start position:0% +gives us a easy argument but also gives +us a condition for optimality. + + align:start position:0% + + + + align:start position:0% + +When + + align:start position:0% +When + + + align:start position:0% +When +are when these equal? When Well, we + + align:start position:0% +are when these equal? When Well, we + + + align:start position:0% +are when these equal? When Well, we +since we have all the equal sign, I only + + align:start position:0% +since we have all the equal sign, I only + + + align:start position:0% +since we have all the equal sign, I only +have to ask right there. When does Well, + + align:start position:0% +have to ask right there. When does Well, + + + align:start position:0% +have to ask right there. When does Well, +it's when they're equal when they're + + align:start position:0% +it's when they're equal when they're + + + align:start position:0% +it's when they're equal when they're +equal, I guess. Uh + + align:start position:0% +equal, I guess. Uh + + + align:start position:0% +equal, I guess. Uh +Xrpose. So, but when will equality hold? + + align:start position:0% +Xrpose. So, but when will equality hold? + + + align:start position:0% +Xrpose. So, but when will equality hold? +Xrpose times, now I'm just going to put + + align:start position:0% +Xrpose times, now I'm just going to put + + + align:start position:0% +Xrpose times, now I'm just going to put +them on the same side of the equation. + + align:start position:0% +them on the same side of the equation. + + + align:start position:0% +them on the same side of the equation. +time c - a transpose y has to be what? + + align:start position:0% +time c - a transpose y has to be what? + + + align:start position:0% +time c - a transpose y has to be what? +Well, right. It it's always greater or + + align:start position:0% +Well, right. It it's always greater or + + + align:start position:0% +Well, right. It it's always greater or +equal + + align:start position:0% +equal + + + align:start position:0% +equal +zero from feasibility. But to get + + align:start position:0% +zero from feasibility. But to get + + + align:start position:0% +zero from feasibility. But to get +equality so this is to get to hit to to + + align:start position:0% +equality so this is to get to hit to to + + + align:start position:0% +equality so this is to get to hit to to +get + + align:start position:0% +get + + + align:start position:0% +get +equality equal + + align:start position:0% +equality equal + + + align:start position:0% +equality equal +sign to be optimal. So that that was a + + align:start position:0% +sign to be optimal. So that that was a + + + align:start position:0% +sign to be optimal. So that that was a +important word in there optimality that + + align:start position:0% +important word in there optimality that + + + align:start position:0% +important word in there optimality that +meant what's the condition like + + align:start position:0% +meant what's the condition like + + + align:start position:0% +meant what's the condition like +derivative equals zero in this in this + + align:start position:0% +derivative equals zero in this in this + + + align:start position:0% +derivative equals zero in this in this +world. + + align:start position:0% +world. + + + align:start position:0% +world. +Well, it's this it's just that this has + + align:start position:0% +Well, it's this it's just that this has + + + align:start position:0% +Well, it's this it's just that this has +to be equal zero, + + align:start position:0% +to be equal zero, + + + align:start position:0% +to be equal zero, +right? I just I mean I'm just looking at + + align:start position:0% +right? I just I mean I'm just looking at + + + align:start position:0% +right? I just I mean I'm just looking at +the only place there was any question + + align:start position:0% +the only place there was any question + + + align:start position:0% +the only place there was any question +and saying if we want + + align:start position:0% +and saying if we want + + + align:start position:0% +and saying if we want +equality then we got to have equality at + + align:start position:0% +equality then we got to have equality at + + + align:start position:0% +equality then we got to have equality at +that step. So this lesser equal followed + + align:start position:0% +that step. So this lesser equal followed + + + align:start position:0% +that step. So this lesser equal followed +immediately for any x and + + align:start position:0% +immediately for any x and + + + align:start position:0% +immediately for any x and +y. Equality is only going to happen at + + align:start position:0% +y. Equality is only going to happen at + + + align:start position:0% +y. Equality is only going to happen at +the best ones. So maybe I should put the + + align:start position:0% +the best ones. So maybe I should put the + + + align:start position:0% +the best ones. So maybe I should put the +star xar transpose c minus ar transpose + + align:start position:0% +star xar transpose c minus ar transpose + + + align:start position:0% +star xar transpose c minus ar transpose +y star. That's how we recognize the + + align:start position:0% +y star. That's how we recognize the + + + align:start position:0% +y star. That's how we recognize the +winner. And and do you see what's going + + align:start position:0% +winner. And and do you see what's going + + + align:start position:0% +winner. And and do you see what's going +on here? This is a dotproduct of two + + align:start position:0% +on here? This is a dotproduct of two + + + align:start position:0% +on here? This is a dotproduct of two +vectors. And what's the deal with those + + align:start position:0% +vectors. And what's the deal with those + + + align:start position:0% +vectors. And what's the deal with those +vectors? What do we know about those + + align:start position:0% +vectors? What do we know about those + + + align:start position:0% +vectors? What do we know about those +vectors? + + align:start position:0% +vectors? + + + align:start position:0% +vectors? +Well, they're orthogonal. But then each + + align:start position:0% +Well, they're orthogonal. But then each + + + align:start position:0% +Well, they're orthogonal. But then each +of those + + align:start position:0% +of those + + + align:start position:0% +of those +vectors is non- negative. The x is non- + + align:start position:0% +vectors is non- negative. The x is non- + + + align:start position:0% +vectors is non- negative. The x is non- +negative and the c minus arpose y is + + align:start position:0% +negative and the c minus arpose y is + + + align:start position:0% +negative and the c minus arpose y is +non- negative. So when could + + align:start position:0% +non- negative. So when could + + + align:start position:0% +non- negative. So when could +two non- negative vectors be + + align:start position:0% +two non- negative vectors be + + + align:start position:0% +two non- negative vectors be +orthogonal? If I have a couple of + + align:start position:0% +orthogonal? If I have a couple of + + + align:start position:0% +orthogonal? If I have a couple of +vectors there's some sort of a + + align:start position:0% +vectors there's some sort of a + + + align:start position:0% +vectors there's some sort of a +complimentary condition. If if x is a is + + align:start position:0% +complimentary condition. If if x is a is + + + align:start position:0% +complimentary condition. If if x is a is +actually positive then x i sorry if if + + align:start position:0% +actually positive then x i sorry if if + + + align:start position:0% +actually positive then x i sorry if if +if a particular component of x is + + align:start position:0% +if a particular component of x is + + + align:start position:0% +if a particular component of x is +actually positive then the i component + + align:start position:0% +actually positive then the i component + + + align:start position:0% +actually positive then the i component +of this guy has to be + + align:start position:0% +of this guy has to be + + + align:start position:0% +of this guy has to be +zero. + + align:start position:0% +zero. + + + align:start position:0% +zero. +I similarly if if if we h if we if our + + align:start position:0% +I similarly if if if we h if we if our + + + align:start position:0% +I similarly if if if we h if we if our +arpose y is strictly below c on some + + align:start position:0% +arpose y is strictly below c on some + + + align:start position:0% +arpose y is strictly below c on some +component then the corresponding x has + + align:start position:0% +component then the corresponding x has + + + align:start position:0% +component then the corresponding x has +to be zero. It's um it's really neat + + align:start position:0% +to be zero. It's um it's really neat + + + align:start position:0% +to be zero. It's um it's really neat +neat stuff. In a way, these X's are like + + align:start position:0% +neat stuff. In a way, these X's are like + + + align:start position:0% +neat stuff. In a way, these X's are like +lrange multipliers for these. And + + align:start position:0% +lrange multipliers for these. And + + + align:start position:0% +lrange multipliers for these. And +somehow this this uh business of + + align:start position:0% +somehow this this uh business of + + + align:start position:0% +somehow this this uh business of +uh this is somehow + + align:start position:0% +uh this is somehow + + + align:start position:0% +uh this is somehow +uh um yeah, it's well, I don't know what + + align:start position:0% +uh um yeah, it's well, I don't know what + + + align:start position:0% +uh um yeah, it's well, I don't know what +words to use. uh there's this but this + + align:start position:0% +words to use. uh there's this but this + + + align:start position:0% +words to use. uh there's this but this +is a typical feature showing up in + + align:start position:0% +is a typical feature showing up in + + + align:start position:0% +is a typical feature showing up in +linear programming that that connects + + align:start position:0% +linear programming that that connects + + + align:start position:0% +linear programming that that connects +the x's and the y's at the + + align:start position:0% + + + + align:start position:0% + +winner. So what I'm doing so + + align:start position:0% +winner. So what I'm doing so + + + align:start position:0% +winner. So what I'm doing so +far is pure algebra, right? I'm asking + + align:start position:0% +far is pure algebra, right? I'm asking + + + align:start position:0% +far is pure algebra, right? I'm asking +you I've asked you now for these minutes + + align:start position:0% +you I've asked you now for these minutes + + + align:start position:0% +you I've asked you now for these minutes +to + + align:start position:0% +to + + + align:start position:0% +to +just accept this these two problems the + + align:start position:0% +just accept this these two problems the + + + align:start position:0% +just accept this these two problems the +primal and the + + align:start position:0% + + + + align:start position:0% + +dual as as announced. + + align:start position:0% +dual as as announced. + + + align:start position:0% +dual as as announced. +Then + + align:start position:0% +Then + + + align:start position:0% +Then +to verify that sure enough by accepting + + align:start position:0% +to verify that sure enough by accepting + + + align:start position:0% +to verify that sure enough by accepting +those we got weak duality and then + + align:start position:0% +those we got weak duality and then + + + align:start position:0% +those we got weak duality and then +identify the one place where equality + + align:start position:0% +identify the one place where equality + + + align:start position:0% +identify the one place where equality +has to hold to + + align:start position:0% +has to hold to + + + align:start position:0% +has to hold to +get + + align:start position:0% +get + + + align:start position:0% +get +duality. + + align:start position:0% +duality. + + + align:start position:0% +duality. +I I haven't given you any help up to now + + align:start position:0% +I I haven't given you any help up to now + + + align:start position:0% +I I haven't given you any help up to now +with examples. So it's time for me to + + align:start position:0% +with examples. So it's time for me to + + + align:start position:0% +with examples. So it's time for me to +turn to an example so you see what kind + + align:start position:0% +turn to an example so you see what kind + + + align:start position:0% +turn to an example so you see what kind +of questions these are and and uh uh so + + align:start position:0% +of questions these are and and uh uh so + + + align:start position:0% +of questions these are and and uh uh so +I'm uh well this these four le last four + + align:start position:0% +I'm uh well this these four le last four + + + align:start position:0% +I'm uh well this these four le last four +lectures are really coming back from the + + align:start position:0% +lectures are really coming back from the + + + align:start position:0% +lectures are really coming back from the +uh applied math book introduction to + + align:start position:0% +uh applied math book introduction to + + + align:start position:0% +uh applied math book introduction to +applied math + + align:start position:0% + + + + align:start position:0% + +uh chapter + + align:start position:0% + + + + align:start position:0% + +7 chapter + + align:start position:0% +7 chapter + + + align:start position:0% +7 chapter +Seven, seven and 8 really is where the + + align:start position:0% +Seven, seven and 8 really is where the + + + align:start position:0% +Seven, seven and 8 really is where the +last lectures are going to come from. + + align:start position:0% +last lectures are going to come from. + + + align:start position:0% +last lectures are going to come from. +And + + align:start position:0% + + + + align:start position:0% + +uh including the + + align:start position:0% +uh including the + + + align:start position:0% +uh including the +um marriage problem and the and the uh + + align:start position:0% +um marriage problem and the and the uh + + + align:start position:0% +um marriage problem and the and the uh +other special network problems that that + + align:start position:0% +other special network problems that that + + + align:start position:0% +other special network problems that that +are following this afternoon. Uh but for + + align:start position:0% +are following this afternoon. Uh but for + + + align:start position:0% +are following this afternoon. Uh but for +an example I'm going to turn to my + + align:start position:0% +an example I'm going to turn to my + + + align:start position:0% +an example I'm going to turn to my +linear algebra book so that you have a + + align:start position:0% +linear algebra book so that you have a + + + align:start position:0% +linear algebra book so that you have a +sort of independent example. Uh + + align:start position:0% +sort of independent example. Uh + + + align:start position:0% +sort of independent example. Uh +uh this is one where well this is so now + + align:start position:0% +uh this is one where well this is so now + + + align:start position:0% +uh this is one where well this is so now +I'm going to this + + align:start position:0% + + + + align:start position:0% + +example. So can I describe the example + + align:start position:0% +example. So can I describe the example + + + align:start position:0% +example. So can I describe the example +and and you'll see it as and then see it + + align:start position:0% +and and you'll see it as and then see it + + + align:start position:0% +and and you'll see it as and then see it +as a linear programming problem. + + align:start position:0% +as a linear programming problem. + + + align:start position:0% +as a linear programming problem. +Okay. So we've + + align:start position:0% +Okay. So we've + + + align:start position:0% +Okay. So we've +got we so the problem is four homework + + align:start position:0% +got we so the problem is four homework + + + align:start position:0% +got we so the problem is four homework +problems. Well, if I write that up + + align:start position:0% +problems. Well, if I write that up + + + align:start position:0% +problems. Well, if I write that up +there, it'll you won't realize this is + + align:start position:0% +there, it'll you won't realize this is + + + align:start position:0% +there, it'll you won't realize this is +example. This isn't the homework. These + + align:start position:0% +example. This isn't the homework. These + + + align:start position:0% +example. This isn't the homework. These +are not the homework. I'm not going to + + align:start position:0% +are not the homework. I'm not going to + + + align:start position:0% +are not the homework. I'm not going to +say the homework problems. This is just + + align:start position:0% +say the homework problems. This is just + + + align:start position:0% +say the homework problems. This is just +there are four imaginary homework + + align:start position:0% +there are four imaginary homework + + + align:start position:0% +there are four imaginary homework +problems + + align:start position:0% +problems + + + align:start position:0% +problems +uh at minimum + + align:start position:0% +uh at minimum + + + align:start position:0% +uh at minimum +cost. + + align:start position:0% +cost. + + + align:start position:0% +cost. +Okay. So what are the rules? We've got + + align:start position:0% +Okay. So what are the rules? We've got + + + align:start position:0% +Okay. So what are the rules? We've got +uh three x's three. So + + align:start position:0% +uh three x's three. So + + + align:start position:0% +uh three x's three. So +x1 is the work is the work done by a PhD + + align:start position:0% +x1 is the work is the work done by a PhD + + + align:start position:0% +x1 is the work is the work done by a PhD +on these problems. X2 is the number of + + align:start position:0% +on these problems. X2 is the number of + + + align:start position:0% +on these problems. X2 is the number of +hours spent by + + align:start position:0% +hours spent by + + + align:start position:0% +hours spent by +um uh a grad + + align:start position:0% + + + + align:start position:0% + +student and x3 will be the number of + + align:start position:0% +student and x3 will be the number of + + + align:start position:0% +student and x3 will be the number of +hours spent on the problem by a uh + + align:start position:0% +hours spent on the problem by a uh + + + align:start position:0% +hours spent on the problem by a uh +computer. + + align:start position:0% + + + + align:start position:0% + +Okay, so we can solve these problems by + + align:start position:0% +Okay, so we can solve these problems by + + + align:start position:0% +Okay, so we can solve these problems by +any combination of number of hours. So + + align:start position:0% +any combination of number of hours. So + + + align:start position:0% +any combination of number of hours. So +now I have to tell you how much those + + align:start position:0% +now I have to tell you how much those + + + align:start position:0% +now I have to tell you how much those +cost. And actually I used numbers that + + align:start position:0% +cost. And actually I used numbers that + + + align:start position:0% +cost. And actually I used numbers that +were unrealistically small, but let's + + align:start position:0% +were unrealistically small, but let's + + + align:start position:0% +were unrealistically small, but let's +stay with them. So, this is the cost is + + align:start position:0% +stay with them. So, this is the cost is + + + align:start position:0% +stay with them. So, this is the cost is +$5 an hour for the PhD, $3 an hour. + + align:start position:0% +$5 an hour for the PhD, $3 an hour. + + + align:start position:0% +$5 an hour for the PhD, $3 an hour. +Well, that's unrealistically large, most + + align:start position:0% +Well, that's unrealistically large, most + + + align:start position:0% +Well, that's unrealistically large, most +grad students would say, and uh $8 an + + align:start position:0% +grad students would say, and uh $8 an + + + align:start position:0% +grad students would say, and uh $8 an +hour for the + + align:start position:0% +hour for the + + + align:start position:0% +hour for the +computer. + + align:start position:0% +computer. + + + align:start position:0% +computer. +Okay. And + + align:start position:0% +Okay. And + + + align:start position:0% +Okay. And +then how fast can they solve the + + align:start position:0% +then how fast can they solve the + + + align:start position:0% +then how fast can they solve the +problems is another question. The PhD + + align:start position:0% +problems is another question. The PhD + + + align:start position:0% +problems is another question. The PhD +can solve one problem per hour. + + align:start position:0% +can solve one problem per hour. + + + align:start position:0% +can solve one problem per hour. +The this guy is equally fast, one + + align:start position:0% +The this guy is equally fast, one + + + align:start position:0% +The this guy is equally fast, one +problem per hour, and the computer is + + align:start position:0% +problem per hour, and the computer is + + + align:start position:0% +problem per hour, and the computer is +twice as fast. It can solve two problems + + align:start position:0% +twice as fast. It can solve two problems + + + align:start position:0% +twice as fast. It can solve two problems +per + + align:start position:0% +per + + + align:start position:0% +per +hour. + + align:start position:0% +hour. + + + align:start position:0% +hour. +Okay. Okay. Now, I've told you + + align:start position:0% +Okay. Okay. Now, I've told you + + + align:start position:0% +Okay. Okay. Now, I've told you +everything about the primal + + align:start position:0% +everything about the primal + + + align:start position:0% +everything about the primal +problem and can we state it as a linear + + align:start position:0% +problem and can we state it as a linear + + + align:start position:0% +problem and can we state it as a linear +program? + + align:start position:0% + + + + align:start position:0% + +So what's the cost? Total cost is the So + + align:start position:0% +So what's the cost? Total cost is the So + + + align:start position:0% +So what's the cost? Total cost is the So +we + + align:start position:0% + + + + align:start position:0% + +minimized we minimize the cost which is + + align:start position:0% +minimized we minimize the cost which is + + + align:start position:0% +minimized we minimize the cost which is +what? Well, this is $5 an hour for X1 + + align:start position:0% +what? Well, this is $5 an hour for X1 + + + align:start position:0% +what? Well, this is $5 an hour for X1 +hours and the grad student spent it + + align:start position:0% +hours and the grad student spent it + + + align:start position:0% +hours and the grad student spent it +costs $3 an hour for X2 hours and the + + align:start position:0% +costs $3 an hour for X2 hours and the + + + align:start position:0% +costs $3 an hour for X2 hours and the +computer costs $8 an hour for X3 hours. + + align:start position:0% + + + + align:start position:0% + +Good. So our cost is + + align:start position:0% +Good. So our cost is + + + align:start position:0% +Good. So our cost is +linear and that's linear cost is quite + + align:start position:0% +linear and that's linear cost is quite + + + align:start position:0% +linear and that's linear cost is quite +reasonable. You know we're assuming then + + align:start position:0% +reasonable. You know we're assuming then + + + align:start position:0% +reasonable. You know we're assuming then +no efficiency of scale. Right? If we had + + align:start position:0% +no efficiency of scale. Right? If we had + + + align:start position:0% +no efficiency of scale. Right? If we had +a 100 problems the computer might be + + align:start position:0% +a 100 problems the computer might be + + + align:start position:0% +a 100 problems the computer might be +able to you know we could write a better + + align:start position:0% +able to you know we could write a better + + + align:start position:0% +able to you know we could write a better +program and solve them more efficiently + + align:start position:0% +program and solve them more efficiently + + + align:start position:0% +program and solve them more efficiently +or even the grad student might speed up + + align:start position:0% +or even the grad student might speed up + + + align:start position:0% +or even the grad student might speed up +or slow down or whatever. But right now + + align:start position:0% +or slow down or whatever. But right now + + + align:start position:0% +or slow down or whatever. But right now +linear. Okay. What's the constraint? + + align:start position:0% +linear. Okay. What's the constraint? + + + align:start position:0% +linear. Okay. What's the constraint? +Well, the constraints are that + + align:start position:0% +Well, the constraints are that + + + align:start position:0% +Well, the constraints are that +they they can't work a negative number + + align:start position:0% +they they can't work a negative number + + + align:start position:0% +they they can't work a negative number +of hours and and interfere here. So So + + align:start position:0% +of hours and and interfere here. So So + + + align:start position:0% +of hours and and interfere here. So So +x1, x2, and x3 are all all greater equal + + align:start position:0% +x1, x2, and x3 are all all greater equal + + + align:start position:0% +x1, x2, and x3 are all all greater equal +to zero. Right? Okay. But now what's the + + align:start position:0% +to zero. Right? Okay. But now what's the + + + align:start position:0% +to zero. Right? Okay. But now what's the +constraint about getting the four + + align:start position:0% +constraint about getting the four + + + align:start position:0% +constraint about getting the four +problems solved? + + align:start position:0% + + + + align:start position:0% + +All right. See, so I just want to get + + align:start position:0% +All right. See, so I just want to get + + + align:start position:0% +All right. See, so I just want to get +four problems solved. So if + + align:start position:0% +four problems solved. So if + + + align:start position:0% +four problems solved. So if +this + + align:start position:0% +this + + + align:start position:0% +this +person works for x1 hours and is able to + + align:start position:0% +person works for x1 hours and is able to + + + align:start position:0% +person works for x1 hours and is able to +solve one problem per hour, I think + + align:start position:0% +solve one problem per hour, I think + + + align:start position:0% +solve one problem per hour, I think +here's the constraint that x1 + x2 + 2 + + align:start position:0% +here's the constraint that x1 + x2 + 2 + + + align:start position:0% +here's the constraint that x1 + x2 + 2 +x3's four. This is the number of + + align:start position:0% +x3's four. This is the number of + + + align:start position:0% +x3's four. This is the number of +problems solved. This is this is an + + align:start position:0% +problems solved. This is this is an + + + align:start position:0% +problems solved. This is this is an +equation of the number of + + align:start position:0% + + + + align:start position:0% + +problems + + align:start position:0% + + + + align:start position:0% + +solved. So this one works x1 hours + + align:start position:0% +solved. So this one works x1 hours + + + align:start position:0% +solved. So this one works x1 hours +solves one problem per hour total x1 + + align:start position:0% +solves one problem per hour total x1 + + + align:start position:0% +solves one problem per hour total x1 +problems x2 problems. This the computer + + align:start position:0% +problems x2 problems. This the computer + + + align:start position:0% +problems x2 problems. This the computer +works x3 hours but because it solves two + + align:start position:0% +works x3 hours but because it solves two + + + align:start position:0% +works x3 hours but because it solves two +problems an hour the number of problems + + align:start position:0% +problems an hour the number of problems + + + align:start position:0% +problems an hour the number of problems +it solves in x3 hours is 2x3. Is that + + align:start position:0% +it solves in x3 hours is 2x3. Is that + + + align:start position:0% +it solves in x3 hours is 2x3. Is that +okay? So that our matrix then has only + + align:start position:0% +okay? So that our matrix then has only + + + align:start position:0% +okay? So that our matrix then has only +one + + align:start position:0% +one + + + align:start position:0% +one +row. It's the matrix 11 one two. M is + + align:start position:0% +row. It's the matrix 11 one two. M is + + + align:start position:0% +row. It's the matrix 11 one two. M is +one one one constraint and n is + + align:start position:0% + + + + align:start position:0% + +three. And you're not allowed to solve + + align:start position:0% +three. And you're not allowed to solve + + + align:start position:0% +three. And you're not allowed to solve +the problem on the fly here. You have to + + align:start position:0% +the problem on the fly here. You have to + + + align:start position:0% +the problem on the fly here. You have to +listen to linear programming as as we + + align:start position:0% +listen to linear programming as as we + + + align:start position:0% +listen to linear programming as as we +go. Okay. + + align:start position:0% + + + + align:start position:0% + +It it it fits this framework that that + + align:start position:0% +It it it fits this framework that that + + + align:start position:0% +It it it fits this framework that that +first of all there are many many + + align:start position:0% +first of all there are many many + + + align:start position:0% +first of all there are many many +solutions many many feasible points + + align:start position:0% +solutions many many feasible points + + + align:start position:0% +solutions many many feasible points +feasible point is a is a is a vector x + + align:start position:0% +feasible point is a is a is a vector x + + + align:start position:0% +feasible point is a is a is a vector x +that's non- negative required and that's + + align:start position:0% +that's non- negative required and that's + + + align:start position:0% +that's non- negative required and that's +satisfies the the one equation we got + + align:start position:0% +satisfies the the one equation we got + + + align:start position:0% +satisfies the the one equation we got +three x's let me draw the feasible set + + align:start position:0% +three x's let me draw the feasible set + + + align:start position:0% +three x's let me draw the feasible set +so this is coming from introduction to + + align:start position:0% +so this is coming from introduction to + + + align:start position:0% +so this is coming from introduction to +applied math and here's a picture of the + + align:start position:0% +applied math and here's a picture of the + + + align:start position:0% +applied math and here's a picture of the +feasible set this is x1 one direction. + + align:start position:0% +feasible set this is x1 one direction. + + + align:start position:0% +feasible set this is x1 one direction. +This is the x2 direction. This is the x3 + + align:start position:0% +This is the x2 direction. This is the x3 + + + align:start position:0% +This is the x2 direction. This is the x3 +direction. And I'm sort of imagining the + + align:start position:0% +direction. And I'm sort of imagining the + + + align:start position:0% +direction. And I'm sort of imagining the +positive octant. Do you you two uh + + align:start position:0% +positive octant. Do you you two uh + + + align:start position:0% +positive octant. Do you you two uh +so so what is that? What's that equation + + align:start position:0% +so so what is that? What's that equation + + + align:start position:0% +so so what is that? What's that equation +give me in my + + align:start position:0% +give me in my + + + align:start position:0% +give me in my +picture? If I graph the if I graph the + + align:start position:0% +picture? If I graph the if I graph the + + + align:start position:0% +picture? If I graph the if I graph the +points that solve that equation, I get a + + align:start position:0% +points that solve that equation, I get a + + + align:start position:0% +points that solve that equation, I get a +plane. I get a plane. That's a that's a + + align:start position:0% +plane. I get a plane. That's a that's a + + + align:start position:0% +plane. I get a plane. That's a that's a +linear equation gives me a plane + + align:start position:0% +linear equation gives me a plane + + + align:start position:0% +linear equation gives me a plane +and but so that + + align:start position:0% +and but so that + + + align:start position:0% +and but so that +plane of course goes infinitely far I + + align:start position:0% +plane of course goes infinitely far I + + + align:start position:0% +plane of course goes infinitely far I +mean regular plane but I'm only + + align:start position:0% +mean regular plane but I'm only + + + align:start position:0% +mean regular plane but I'm only +interested uh allowed to look at the + + align:start position:0% +interested uh allowed to look at the + + + align:start position:0% +interested uh allowed to look at the +part of the plane that's in the in this + + align:start position:0% +part of the plane that's in the in this + + + align:start position:0% +part of the plane that's in the in this +positive octant. So, I'm seeing sort of + + align:start position:0% +positive octant. So, I'm seeing sort of + + + align:start position:0% +positive octant. So, I'm seeing sort of +a plane + + align:start position:0% +a plane + + + align:start position:0% +a plane +that Well, actually, we could figure out + + align:start position:0% +that Well, actually, we could figure out + + + align:start position:0% +that Well, actually, we could figure out +what these corners + + align:start position:0% + + + + align:start position:0% + +are. You see, this is the plane. This + + align:start position:0% +are. You see, this is the plane. This + + + align:start position:0% +are. You see, this is the plane. This +this plane is there, but + + align:start position:0% +this plane is there, but + + + align:start position:0% +this plane is there, but +it's we're only keeping the part that's + + align:start position:0% +it's we're only keeping the part that's + + + align:start position:0% +it's we're only keeping the part that's +that's a + + align:start position:0% +that's a + + + align:start position:0% +that's a +feasible, right? The we're only keeping + + align:start position:0% +feasible, right? The we're only keeping + + + align:start position:0% +feasible, right? The we're only keeping +the points that are So, what is this + + align:start position:0% +the points that are So, what is this + + + align:start position:0% +the points that are So, what is this +point here? + + align:start position:0% +point here? + + + align:start position:0% +point here? +That's that's the point x1 + + align:start position:0% +That's that's the point x1 + + + align:start position:0% +That's that's the point x1 +equal four, right? Yeah, x1 is four and + + align:start position:0% +equal four, right? Yeah, x1 is four and + + + align:start position:0% +equal four, right? Yeah, x1 is four and +the other x's are zero. So that's the + + align:start position:0% +the other x's are zero. So that's the + + + align:start position:0% +the other x's are zero. So that's the +point x if I wrote it write it as a + + align:start position:0% +point x if I wrote it write it as a + + + align:start position:0% +point x if I wrote it write it as a +vector 4 0 0. That's a corner. May maybe + + align:start position:0% +vector 4 0 0. That's a corner. May maybe + + + align:start position:0% +vector 4 0 0. That's a corner. May maybe +I call that corner + + align:start position:0% +I call that corner + + + align:start position:0% +I call that corner +P. And what's this corner Q? This is the + + align:start position:0% +P. And what's this corner Q? This is the + + + align:start position:0% +P. And what's this corner Q? This is the +point also four. So it would be the + + align:start position:0% +point also four. So it would be the + + + align:start position:0% +point also four. So it would be the +point + + align:start position:0% +point + + + align:start position:0% +point +040 where all the work all four problems + + align:start position:0% +040 where all the work all four problems + + + align:start position:0% +040 where all the work all four problems +are being solved by the grad student and + + align:start position:0% +are being solved by the grad student and + + + align:start position:0% +are being solved by the grad student and +then this point up here say r has + + align:start position:0% +then this point up here say r has + + + align:start position:0% +then this point up here say r has +coordinates 0 0 because + + align:start position:0% +coordinates 0 0 because + + + align:start position:0% +coordinates 0 0 because +it's and then two because then the + + align:start position:0% +it's and then two because then the + + + align:start position:0% +it's and then two because then the +computer would work two + + align:start position:0% + + + + align:start position:0% + +hours now and any mixture in between the + + align:start position:0% +hours now and any mixture in between the + + + align:start position:0% +hours now and any mixture in between the +the triangle in between is any mixture + + align:start position:0% +the triangle in between is any mixture + + + align:start position:0% +the triangle in between is any mixture +where where they're all + + align:start position:0% +where where they're all + + + align:start position:0% +where where they're all +working. Well, the point is that not + + align:start position:0% +working. Well, the point is that not + + + align:start position:0% +working. Well, the point is that not +that at the at the I'm looking for the + + align:start position:0% +that at the at the I'm looking for the + + + align:start position:0% +that at the at the I'm looking for the +X-ar now the best the + + align:start position:0% +X-ar now the best the + + + align:start position:0% +X-ar now the best the +cheapest the cheapest who who should do + + align:start position:0% +cheapest the cheapest who who should do + + + align:start position:0% +cheapest the cheapest who who should do +this work here and the can the point + + align:start position:0% +this work here and the can the point + + + align:start position:0% +this work here and the can the point +will be that one of these corners is the + + align:start position:0% +will be that one of these corners is the + + + align:start position:0% +will be that one of these corners is the +winner that that if I and I'll think why + + align:start position:0% +winner that that if I and I'll think why + + + align:start position:0% +winner that that if I and I'll think why +but but let me emphasize that point the + + align:start position:0% +but but let me emphasize that point the + + + align:start position:0% +but but let me emphasize that point the +winner is at a + + align:start position:0% +winner is at a + + + align:start position:0% +winner is at a +corner the winner is at a + + align:start position:0% +corner the winner is at a + + + align:start position:0% +corner the winner is at a +corner. So let me think. So what does + + align:start position:0% +corner. So let me think. So what does + + + align:start position:0% +corner. So let me think. So what does +that mean in ordinary words? That means + + align:start position:0% +that mean in ordinary words? That means + + + align:start position:0% +that mean in ordinary words? That means +that the winner only one of these + + align:start position:0% +that the winner only one of these + + + align:start position:0% +that the winner only one of these +x's at the optimal + + align:start position:0% +x's at the optimal + + + align:start position:0% +x's at the optimal +xstar is not is working is not + + align:start position:0% +xstar is not is working is not + + + align:start position:0% +xstar is not is working is not +zero. If if and I only need like one x + + align:start position:0% +zero. If if and I only need like one x + + + align:start position:0% +zero. If if and I only need like one x +to to adjust because I only have one + + align:start position:0% +to to adjust because I only have one + + + align:start position:0% +to to adjust because I only have one +equation. So so so a corner. Let me sort + + align:start position:0% +equation. So so so a corner. Let me sort + + + align:start position:0% +equation. So so so a corner. Let me sort +of say what a corner + + align:start position:0% + + + + align:start position:0% + +is. Corner is I have + + align:start position:0% +is. Corner is I have + + + align:start position:0% +is. Corner is I have +m + + align:start position:0% + + + + align:start position:0% + +nonzero x's and that and that gives me + + align:start position:0% +nonzero x's and that and that gives me + + + align:start position:0% +nonzero x's and that and that gives me +enough to solve the m equations ax= + + align:start position:0% +enough to solve the m equations ax= + + + align:start position:0% +enough to solve the m equations ax= +b and the n minus + + align:start position:0% +b and the n minus + + + align:start position:0% +b and the n minus +m zero + + align:start position:0% + + + + align:start position:0% + +x's because I'm at a corner. So + + align:start position:0% +x's because I'm at a corner. So + + + align:start position:0% +x's because I'm at a corner. So +that's it's vi we can visualize this + + align:start position:0% +that's it's vi we can visualize this + + + align:start position:0% +that's it's vi we can visualize this +thing in this 3D picture the + + align:start position:0% +thing in this 3D picture the + + + align:start position:0% +thing in this 3D picture the +visualization gets quite + + align:start position:0% +visualization gets quite + + + align:start position:0% +visualization gets quite +um + + align:start position:0% +um + + + align:start position:0% +um +harder in so in m and n dimensions in so + + align:start position:0% +harder in so in m and n dimensions in so + + + align:start position:0% +harder in so in m and n dimensions in so +my point was that the + + align:start position:0% + + + + align:start position:0% + +winner + + align:start position:0% +winner + + + align:start position:0% +winner +xar is a corner some corner + + align:start position:0% +xar is a corner some corner + + + align:start position:0% +xar is a corner some corner +But the thing is, so you might think, + + align:start position:0% +But the thing is, so you might think, + + + align:start position:0% +But the thing is, so you might think, +okay, just try all the + + align:start position:0% +okay, just try all the + + + align:start position:0% +okay, just try all the +corners. Evaluate the cost at every + + align:start position:0% +corners. Evaluate the cost at every + + + align:start position:0% +corners. Evaluate the cost at every +corner once you know the winner is a + + align:start position:0% +corner once you know the winner is a + + + align:start position:0% +corner once you know the winner is a +corner. And but the thing is there are + + align:start position:0% +corner. And but the thing is there are + + + align:start position:0% +corner. And but the thing is there are +too many corners. The number of corners + + align:start position:0% +too many corners. The number of corners + + + align:start position:0% +too many corners. The number of corners +is n choose m or something which is a + + align:start position:0% +is n choose m or something which is a + + + align:start position:0% +is n choose m or something which is a +very big number fast. It's three here. + + align:start position:0% +very big number fast. It's three here. + + + align:start position:0% +very big number fast. It's three here. +So there are three corners and we can + + align:start position:0% +So there are three corners and we can + + + align:start position:0% +So there are three corners and we can +check them all but generally you have to + + align:start position:0% +check them all but generally you have to + + + align:start position:0% +check them all but generally you have to +imagine so are you imagining + + align:start position:0% +imagine so are you imagining + + + align:start position:0% +imagine so are you imagining +n-dimensional space like this where n + + align:start position:0% +n-dimensional space like this where n + + + align:start position:0% +n-dimensional space like this where n +was three and then what do the + + align:start position:0% +was three and then what do the + + + align:start position:0% +was three and then what do the +constraints give + + align:start position:0% +constraints give + + + align:start position:0% +constraints give +us? So so think of n dimensional space + + align:start position:0% +us? So so think of n dimensional space + + + align:start position:0% +us? So so think of n dimensional space +x1 to xn and then we have m + + align:start position:0% + + + + align:start position:0% + +equations. The m equations what do they + + align:start position:0% +equations. The m equations what do they + + + align:start position:0% +equations. The m equations what do they +give in this space? Well, every equation + + align:start position:0% +give in this space? Well, every equation + + + align:start position:0% +give in this space? Well, every equation +is linear, so it's a plane. So, I've got + + align:start position:0% +is linear, so it's a plane. So, I've got + + + align:start position:0% +is linear, so it's a plane. So, I've got +m + + align:start position:0% +m + + + align:start position:0% +m +planes. And so, I've got this octant. + + align:start position:0% +planes. And so, I've got this octant. + + + align:start position:0% +planes. And so, I've got this octant. +I've got this octant positive direction + + align:start position:0% +I've got this octant positive direction + + + align:start position:0% +I've got this octant positive direction +in n dimensional space. I I don't know + + align:start position:0% +in n dimensional space. I I don't know + + + align:start position:0% +in n dimensional space. I I don't know +why I'm saying this because I can't + + align:start position:0% +why I'm saying this because I can't + + + align:start position:0% +why I'm saying this because I can't +visualize it either, but except it's + + align:start position:0% +visualize it either, but except it's + + + align:start position:0% +visualize it either, but except it's +it's sort of important to realize that + + align:start position:0% +it's sort of important to realize that + + + align:start position:0% +it's sort of important to realize that +the feasible set + + align:start position:0% +the feasible set + + + align:start position:0% +the feasible set +is a polyhedrin. It's it's hadn't got + + align:start position:0% +is a polyhedrin. It's it's hadn't got + + + align:start position:0% +is a polyhedrin. It's it's hadn't got +any curved + + align:start position:0% +any curved + + + align:start position:0% +any curved +boundaries. Everything is either they're + + align:start position:0% +boundaries. Everything is either they're + + + align:start position:0% +boundaries. Everything is either they're +the base planes which chop out the + + align:start position:0% +the base planes which chop out the + + + align:start position:0% +the base planes which chop out the +uh coming from x greater equal z chop + + align:start position:0% +uh coming from x greater equal z chop + + + align:start position:0% +uh coming from x greater equal z chop +out the positive part or the constraint + + align:start position:0% +out the positive part or the constraint + + + align:start position:0% +out the positive part or the constraint +planes coming from the m constraints + + align:start position:0% +planes coming from the m constraints + + + align:start position:0% +planes coming from the m constraints +that cut through in some way. So you got + + align:start position:0% +that cut through in some way. So you got + + + align:start position:0% +that cut through in some way. So you got +somehow a + + align:start position:0% +somehow a + + + align:start position:0% +somehow a +region that's created out of m plus n + + align:start position:0% +region that's created out of m plus n + + + align:start position:0% +region that's created out of m plus n +planes. It's a it's a but + + align:start position:0% +planes. It's a it's a but + + + align:start position:0% +planes. It's a it's a but +it's can be quite + + align:start position:0% +it's can be quite + + + align:start position:0% +it's can be quite +complicated. N plus n is pretty big + + align:start position:0% +complicated. N plus n is pretty big + + + align:start position:0% +complicated. N plus n is pretty big +number. You just you're you're uh say we + + align:start position:0% +number. You just you're you're uh say we + + + align:start position:0% +number. You just you're you're uh say we +have oh I mean this wouldn't be big. 20 + + align:start position:0% +have oh I mean this wouldn't be big. 20 + + + align:start position:0% +have oh I mean this wouldn't be big. 20 +equations 10 constraints. So we're in 20 + + align:start position:0% +equations 10 constraints. So we're in 20 + + + align:start position:0% +equations 10 constraints. So we're in 20 +dimensional space. We've got 30 planes + + align:start position:0% +dimensional space. We've got 30 planes + + + align:start position:0% +dimensional space. We've got 30 planes +all woofing through. And you can see + + align:start position:0% +all woofing through. And you can see + + + align:start position:0% +all woofing through. And you can see +that the feasible set could be empty. + + align:start position:0% +that the feasible set could be empty. + + + align:start position:0% +that the feasible set could be empty. +For example, how could I how could I + + align:start position:0% +For example, how could I how could I + + + align:start position:0% +For example, how could I how could I +change this pro? How could + + align:start position:0% +change this pro? How could + + + align:start position:0% +change this pro? How could +I create a problem where the where there + + align:start position:0% +I create a problem where the where there + + + align:start position:0% +I create a problem where the where there +were no feasible x's out of this + + align:start position:0% +were no feasible x's out of this + + + align:start position:0% +were no feasible x's out of this +example? Well, I could make that four a + + align:start position:0% +example? Well, I could make that four a + + + align:start position:0% +example? Well, I could make that four a +minus4. If I made that four a minus4, + + align:start position:0% +minus4. If I made that four a minus4, + + + align:start position:0% +minus4. If I made that four a minus4, +then there wouldn't be any non- negative + + align:start position:0% +then there wouldn't be any non- negative + + + align:start position:0% +then there wouldn't be any non- negative +x's that would solve with a minus4. But + + align:start position:0% +x's that would solve with a minus4. But + + + align:start position:0% +x's that would solve with a minus4. But +of course the problem with with minus4 + + align:start position:0% +of course the problem with with minus4 + + + align:start position:0% +of course the problem with with minus4 +homeworks to + + align:start position:0% +homeworks to + + + align:start position:0% +homeworks to +do well often I have no homeworks but I + + align:start position:0% +do well often I have no homeworks but I + + + align:start position:0% +do well often I have no homeworks but I +never assign negative number of homework + + align:start position:0% +never assign negative number of homework + + + align:start position:0% +never assign negative number of homework +problems. So + + align:start position:0% + + + + align:start position:0% + +anyway okay which is the + + align:start position:0% +anyway okay which is the + + + align:start position:0% +anyway okay which is the +winner but which is the best point? + + align:start position:0% +winner but which is the best point? + + + align:start position:0% +winner but which is the best point? +Well, in this case, I could just check + + align:start position:0% +Well, in this case, I could just check + + + align:start position:0% +Well, in this case, I could just check +the cost at every at every corner, + + align:start position:0% +the cost at every at every corner, + + + align:start position:0% +the cost at every at every corner, +right? Oh, I and I have to say, why is + + align:start position:0% +right? Oh, I and I have to say, why is + + + align:start position:0% +right? Oh, I and I have to say, why is +the winner at a + + align:start position:0% +the winner at a + + + align:start position:0% +the winner at a +corner? The fact that the winner is at a + + align:start position:0% +corner? The fact that the winner is at a + + + align:start position:0% +corner? The fact that the winner is at a +corner is is a big + + align:start position:0% +corner is is a big + + + align:start position:0% +corner is is a big +help. And it somehow depends on + + align:start position:0% +help. And it somehow depends on + + + align:start position:0% +help. And it somehow depends on +linearity. You know, if we have a linear + + align:start position:0% +linearity. You know, if we have a linear + + + align:start position:0% +linearity. You know, if we have a linear +function, you know, + + align:start position:0% +function, you know, + + + align:start position:0% +function, you know, +you if it's increasing, it continues to + + align:start position:0% +you if it's increasing, it continues to + + + align:start position:0% +you if it's increasing, it continues to +increase until you bump up against + + align:start position:0% +increase until you bump up against + + + align:start position:0% +increase until you bump up against +the constraint. or continues to decrease + + align:start position:0% +the constraint. or continues to decrease + + + align:start position:0% +the constraint. or continues to decrease +if we're trying to make something + + align:start position:0% +if we're trying to make something + + + align:start position:0% +if we're trying to make something +decrease like like suppose you said well + + align:start position:0% +decrease like like suppose you said well + + + align:start position:0% +decrease like like suppose you said well +maybe that's the winner in the middle + + align:start position:0% +maybe that's the winner in the middle + + + align:start position:0% +maybe that's the winner in the middle +there all three working away well but if + + align:start position:0% +there all three working away well but if + + + align:start position:0% +there all three working away well but if +I discover that to move from around from + + align:start position:0% +I discover that to move from around from + + + align:start position:0% +I discover that to move from around from +there in some direction is better then + + align:start position:0% +there in some direction is better then + + + align:start position:0% +there in some direction is better then +more is better more is better more is + + align:start position:0% +more is better more is better more is + + + align:start position:0% +more is better more is better more is +better until finally maybe I just make + + align:start position:0% +better until finally maybe I just make + + + align:start position:0% +better until finally maybe I just make +it + + align:start position:0% +it + + + align:start position:0% +it +hit an edge at that point it can't So + + align:start position:0% +hit an edge at that point it can't So + + + align:start position:0% +hit an edge at that point it can't So +it's not legal to go further because an + + align:start position:0% +it's not legal to go further because an + + + align:start position:0% +it's not legal to go further because an +x would get negative. So at that point I + + align:start position:0% +x would get negative. So at that point I + + + align:start position:0% +x would get negative. So at that point I +uh look again. Okay. But now my point is + + align:start position:0% +uh look again. Okay. But now my point is + + + align:start position:0% +uh look again. Okay. But now my point is +that we only have to consider corners. + + align:start position:0% +that we only have to consider corners. + + + align:start position:0% +that we only have to consider corners. +And why is that? + + align:start position:0% +And why is that? + + + align:start position:0% +And why is that? +Suppose that to one of the edges and + + align:start position:0% +Suppose that to one of the edges and + + + align:start position:0% +Suppose that to one of the edges and +it's the same reason. That's right. A + + align:start position:0% +it's the same reason. That's right. A + + + align:start position:0% +it's the same reason. That's right. A +drive to a corner. That's the that's a + + align:start position:0% +drive to a corner. That's the that's a + + + align:start position:0% +drive to a corner. That's the that's a +fundamental reasoning. Yeah. What one + + align:start position:0% +fundamental reasoning. Yeah. What one + + + align:start position:0% +fundamental reasoning. Yeah. What one +way to see it + + align:start position:0% +way to see it + + + align:start position:0% +way to see it +is is now to think of these + + align:start position:0% +is is now to think of these + + + align:start position:0% +is is now to think of these +costs if we got the so this is a good + + align:start position:0% +costs if we got the so this is a good + + + align:start position:0% +costs if we got the so this is a good +way to see it not only that it's at a + + align:start position:0% +way to see it not only that it's at a + + + align:start position:0% +way to see it not only that it's at a +corner but but what what picks out that + + align:start position:0% +corner but but what what picks out that + + + align:start position:0% +corner but but what what picks out that +corner so the cost suppose I'm trying to + + align:start position:0% +corner so the cost suppose I'm trying to + + + align:start position:0% +corner so the cost suppose I'm trying to +do this job for a total cost of a + + align:start position:0% +do this job for a total cost of a + + + align:start position:0% +do this job for a total cost of a +million dollars it's not going to cost + + align:start position:0% +million dollars it's not going to cost + + + align:start position:0% +million dollars it's not going to cost +me a million dollars for these uh very + + align:start position:0% +me a million dollars for these uh very + + + align:start position:0% +me a million dollars for these uh very +uh parts monious uh workers and only + + align:start position:0% +uh parts monious uh workers and only + + + align:start position:0% +uh parts monious uh workers and only +four homework problems. But suppose I + + align:start position:0% +four homework problems. But suppose I + + + align:start position:0% +four homework problems. But suppose I +look at the equation 5x1 + 3x2 + 8 + + align:start position:0% +look at the equation 5x1 + 3x2 + 8 + + + align:start position:0% +look at the equation 5x1 + 3x2 + 8 +x3. Oh, I don't even know if I could + + align:start position:0% +x3. Oh, I don't even know if I could + + + align:start position:0% +x3. Oh, I don't even know if I could +spend a million + + align:start position:0% +spend a million + + + align:start position:0% +spend a million +dollar. Yes, I could. Could I? + + align:start position:0% +dollar. Yes, I could. Could I? + + + align:start position:0% +dollar. Yes, I could. Could I? +That's bad. I don't Well, I don't even + + align:start position:0% +That's bad. I don't Well, I don't even + + + align:start position:0% +That's bad. I don't Well, I don't even +know. But anyway, suppose I look at the + + align:start position:0% +know. But anyway, suppose I look at the + + + align:start position:0% +know. But anyway, suppose I look at the +x's that solve the that give me a cost + + align:start position:0% +x's that solve the that give me a cost + + + align:start position:0% +x's that solve the that give me a cost +of a million dollars. + + align:start position:0% +of a million dollars. + + + align:start position:0% +of a million dollars. +Yeah. I I I don't think I could spend a + + align:start position:0% +Yeah. I I I don't think I could spend a + + + align:start position:0% +Yeah. I I I don't think I could spend a +million. Not feasible. They're not + + align:start position:0% +million. Not feasible. They're not + + + align:start position:0% +million. Not feasible. They're not +feasible. Right. If you think of it that + + align:start position:0% +feasible. Right. If you think of it that + + + align:start position:0% +feasible. Right. If you think of it that +as another plane. Yes. Exactly. That's + + align:start position:0% +as another plane. Yes. Exactly. That's + + + align:start position:0% +as another plane. Yes. Exactly. That's +what I want to do. Moving in. That's + + align:start position:0% +what I want to do. Moving in. That's + + + align:start position:0% +what I want to do. Moving in. That's +right. You hit a corner. Exactly. + + align:start position:0% +right. You hit a corner. Exactly. + + + align:start position:0% +right. You hit a corner. Exactly. +Exactly. Right. So, if I tried to spend + + align:start position:0% +Exactly. Right. So, if I tried to spend + + + align:start position:0% +Exactly. Right. So, if I tried to spend +a million dollars, that would if I look + + align:start position:0% +a million dollars, that would if I look + + + align:start position:0% +a million dollars, that would if I look +at the + + align:start position:0% + + + + align:start position:0% + +equals a million. That's off here + + align:start position:0% +equals a million. That's off here + + + align:start position:0% +equals a million. That's off here +somewhere. Well, okay. I'll reduce + + align:start position:0% +somewhere. Well, okay. I'll reduce + + + align:start position:0% +somewhere. Well, okay. I'll reduce +that. Let's see. What am I trying to do? + + align:start position:0% +that. Let's see. What am I trying to do? + + + align:start position:0% +that. Let's see. What am I trying to do? +Minimum cost. + + align:start position:0% +Minimum cost. + + + align:start position:0% +Minimum cost. +Why don't I start at zero and move up? + + align:start position:0% +Why don't I start at zero and move up? + + + align:start position:0% +Why don't I start at zero and move up? +That'd be smarter, right? Okay. So, let + + align:start position:0% +That'd be smarter, right? Okay. So, let + + + align:start position:0% +That'd be smarter, right? Okay. So, let +me take the plane equals + + align:start position:0% +me take the plane equals + + + align:start position:0% +me take the plane equals +zero. That's a plane, right? It's + + align:start position:0% +zero. That's a plane, right? It's + + + align:start position:0% +zero. That's a plane, right? It's +through the origin, but I don't think it + + align:start position:0% +through the origin, but I don't think it + + + align:start position:0% +through the origin, but I don't think it +would touch the feasible set. I can't + + align:start position:0% +would touch the feasible set. I can't + + + align:start position:0% +would touch the feasible set. I can't +get my problem solved for zero, right? I + + align:start position:0% +get my problem solved for zero, right? I + + + align:start position:0% +get my problem solved for zero, right? I +mean, somebody's going to have to work + + align:start position:0% +mean, somebody's going to have to work + + + align:start position:0% +mean, somebody's going to have to work +and get paid here. Yeah. So, the this + + align:start position:0% +and get paid here. Yeah. So, the this + + + align:start position:0% +and get paid here. Yeah. So, the this +plane would like, are you imagining this + + align:start position:0% +plane would like, are you imagining this + + + align:start position:0% +plane would like, are you imagining this +as kind of the the it's a plane now. + + align:start position:0% +as kind of the the it's a plane now. + + + align:start position:0% +as kind of the the it's a plane now. +It's not a tetrahedrin. That's just a + + align:start position:0% +It's not a tetrahedrin. That's just a + + + align:start position:0% +It's not a tetrahedrin. That's just a +plane. And this plane would lie + + align:start position:0% +plane. And this plane would lie + + + align:start position:0% +plane. And this plane would lie +somewhere behind it, not touching. But + + align:start position:0% +somewhere behind it, not touching. But + + + align:start position:0% +somewhere behind it, not touching. But +then Bob says, if I move if I increase + + align:start position:0% +then Bob says, if I move if I increase + + + align:start position:0% +then Bob says, if I move if I increase +this to one, it'll move up. It'll move + + align:start position:0% +this to one, it'll move up. It'll move + + + align:start position:0% +this to one, it'll move up. It'll move +parallel to itself, of course, because + + align:start position:0% +parallel to itself, of course, because + + + align:start position:0% +parallel to itself, of course, because +I'm just changing the right hand side. + + align:start position:0% +I'm just changing the right hand side. + + + align:start position:0% +I'm just changing the right hand side. +But still, I can't get them solved for$1 + + align:start position:0% +But still, I can't get them solved for$1 + + + align:start position:0% +But still, I can't get them solved for$1 +up to$ two dollars and so on. The plane + + align:start position:0% +up to$ two dollars and so on. The plane + + + align:start position:0% +up to$ two dollars and so on. The plane +is moving. You see this plane, this cost + + align:start position:0% +is moving. You see this plane, this cost + + + align:start position:0% +is moving. You see this plane, this cost +plane sort of + + align:start position:0% +plane sort of + + + align:start position:0% +plane sort of +moving toward the feasible set, but but + + align:start position:0% +moving toward the feasible set, but but + + + align:start position:0% +moving toward the feasible set, but but +not touching it at $2. There's nobody. I + + align:start position:0% +not touching it at $2. There's nobody. I + + + align:start position:0% +not touching it at $2. There's nobody. I +can't do it for + + align:start position:0% +can't do it for + + + align:start position:0% +can't do it for +$2. And then finally, it touches the + + align:start position:0% +$2. And then finally, it touches the + + + align:start position:0% +$2. And then finally, it touches the +feasible set. And of course it touches + + align:start position:0% +feasible set. And of course it touches + + + align:start position:0% +feasible set. And of course it touches +out a corner. That's the minimum cost. + + align:start position:0% +out a corner. That's the minimum cost. + + + align:start position:0% +out a corner. That's the minimum cost. +So the cost is I can't do it for cost + + align:start position:0% +So the cost is I can't do it for cost + + + align:start position:0% +So the cost is I can't do it for cost +zero. I can't do it for cost one. I + + align:start position:0% +zero. I can't do it for cost one. I + + + align:start position:0% +zero. I can't do it for cost one. I +can't do it for cost two. I move that + + align:start position:0% +can't do it for cost two. I move that + + + align:start position:0% +can't do it for cost two. I move that +plane up and if finally I can do it. And + + align:start position:0% +plane up and if finally I can do it. And + + + align:start position:0% +plane up and if finally I can do it. And +a plane moving forward will hit + + align:start position:0% +a plane moving forward will hit + + + align:start position:0% +a plane moving forward will hit +a + + align:start position:0% +a + + + align:start position:0% +a +polyhedrin at a corner. That's that's + + align:start position:0% +polyhedrin at a corner. That's that's + + + align:start position:0% +polyhedrin at a corner. That's that's +the geometric way to visualize the re + + align:start position:0% +the geometric way to visualize the re + + + align:start position:0% +the geometric way to visualize the re +the reason why the winner is a + + align:start position:0% + + + + align:start position:0% + +corner. So I just + + align:start position:0% +corner. So I just + + + align:start position:0% +corner. So I just +[Music] + + align:start position:0% + + + + align:start position:0% + +ah what would happen then? It could hit + + align:start position:0% +ah what would happen then? It could hit + + + align:start position:0% +ah what would happen then? It could hit +the whole thing. Right. + + align:start position:0% +the whole thing. Right. + + + align:start position:0% +the whole thing. Right. +Right. So that would mean that any of + + align:start position:0% +Right. So that would mean that any of + + + align:start position:0% +Right. So that would mean that any of +these plans would work. So if I adjusted + + align:start position:0% +these plans would work. So if I adjusted + + + align:start position:0% +these plans would work. So if I adjusted +that if I adjusted these costs to be one + + align:start position:0% +that if I adjusted these costs to be one + + + align:start position:0% +that if I adjusted these costs to be one +one and + + align:start position:0% +one and + + + align:start position:0% +one and +two suppose I suppose I exactly you're + + align:start position:0% +two suppose I suppose I exactly you're + + + align:start position:0% +two suppose I suppose I exactly you're +you're picking out a degenerate case + + align:start position:0% +you're picking out a degenerate case + + + align:start position:0% +you're picking out a degenerate case +uh that if if if the PhD and grad + + align:start position:0% +uh that if if if the PhD and grad + + + align:start position:0% +uh that if if if the PhD and grad +student charge $1 an hour and the + + align:start position:0% +student charge $1 an hour and the + + + align:start position:0% +student charge $1 an hour and the +computer $2 an hour and they solve them + + align:start position:0% +computer $2 an hour and they solve them + + + align:start position:0% +computer $2 an hour and they solve them +exactly in proportion to their cost + + align:start position:0% +exactly in proportion to their cost + + + align:start position:0% +exactly in proportion to their cost +which would + + align:start position:0% +which would + + + align:start position:0% +which would +be imagine able then as you say uh this + + align:start position:0% +be imagine able then as you say uh this + + + align:start position:0% +be imagine able then as you say uh this +plane would be parallel to this and it + + align:start position:0% +plane would be parallel to this and it + + + align:start position:0% +plane would be parallel to this and it +would boom it would hit the whole + + align:start position:0% +would boom it would hit the whole + + + align:start position:0% +would boom it would hit the whole +feasible set all at once and that would + + align:start position:0% +feasible set all at once and that would + + + align:start position:0% +feasible set all at once and that would +mean that in that degenerate case not + + align:start position:0% +mean that in that degenerate case not + + + align:start position:0% +mean that in that degenerate case not +only are the corners winners but even + + align:start position:0% +only are the corners winners but even + + + align:start position:0% +only are the corners winners but even +everything in between but still it's + + align:start position:0% +everything in between but still it's + + + align:start position:0% +everything in between but still it's +true that the winner is a corner well + + align:start position:0% +true that the winner is a corner well + + + align:start position:0% +true that the winner is a corner well +but not the only winner. Yeah. Yeah. So + + align:start position:0% +but not the only winner. Yeah. Yeah. So + + + align:start position:0% +but not the only winner. Yeah. Yeah. So +it's it's like a line a lines Yeah. It's + + align:start position:0% +it's it's like a line a lines Yeah. It's + + + align:start position:0% +it's it's like a line a lines Yeah. It's +like it's like uh I mean we're dealing + + align:start position:0% +like it's like uh I mean we're dealing + + + align:start position:0% +like it's like uh I mean we're dealing +with linear equations here. It's like + + align:start position:0% +with linear equations here. It's like + + + align:start position:0% +with linear equations here. It's like +that case would be like you know + + align:start position:0% +that case would be like you know + + + align:start position:0% +that case would be like you know +optimize when you're what's the maximum + + align:start position:0% +optimize when you're what's the maximum + + + align:start position:0% +optimize when you're what's the maximum +of that horizontal function. + + align:start position:0% +of that horizontal function. + + + align:start position:0% +of that horizontal function. +Well the maximum is whatever that height + + align:start position:0% +Well the maximum is whatever that height + + + align:start position:0% +Well the maximum is whatever that height +is but it's satisfied at it's all the + + align:start position:0% +is but it's satisfied at it's all the + + + align:start position:0% +is but it's satisfied at it's all the +all the points are just as good. So but + + align:start position:0% +all the points are just as good. So but + + + align:start position:0% +all the points are just as good. So but +of course you you know that that's uh a + + align:start position:0% +of course you you know that that's uh a + + + align:start position:0% +of course you you know that that's uh a +special special case. So typically when + + align:start position:0% +special special case. So typically when + + + align:start position:0% +special special case. So typically when +a bunch of planes when planes move + + align:start position:0% +a bunch of planes when planes move + + + align:start position:0% +a bunch of planes when planes move +parallel to theirel to themselves + + align:start position:0% +parallel to theirel to themselves + + + align:start position:0% +parallel to theirel to themselves +they'll hit a corner first but there + + align:start position:0% +they'll hit a corner first but there + + + align:start position:0% +they'll hit a corner first but there +would be degenerate cases where it could + + align:start position:0% +would be degenerate cases where it could + + + align:start position:0% +would be degenerate cases where it could +hit a whole edge at once or even a whole + + align:start position:0% +hit a whole edge at once or even a whole + + + align:start position:0% +hit a whole edge at once or even a whole +flat face at once. Oh, that Yeah. Yeah. + + align:start position:0% +flat face at once. Oh, that Yeah. Yeah. + + + align:start position:0% +flat face at once. Oh, that Yeah. Yeah. +So, there are degenerate cases always + + align:start position:0% +So, there are degenerate cases always + + + align:start position:0% +So, there are degenerate cases always +possible just like the feasible set + + align:start position:0% +possible just like the feasible set + + + align:start position:0% +possible just like the feasible set +might be empty. There might be nobody + + align:start position:0% +might be empty. There might be nobody + + + align:start position:0% +might be empty. There might be nobody +that solves the equation if if I had a + + align:start position:0% +that solves the equation if if I had a + + + align:start position:0% +that solves the equation if if I had a +minus4 here, but I don't. Yeah. So, this + + align:start position:0% +minus4 here, but I don't. Yeah. So, this + + + align:start position:0% +minus4 here, but I don't. Yeah. So, this +will be a perfectly non- + + align:start position:0% +will be a perfectly non- + + + align:start position:0% +will be a perfectly non- +degenerate completely normal case of + + align:start position:0% +degenerate completely normal case of + + + align:start position:0% +degenerate completely normal case of +linear programming. And and let's see, I + + align:start position:0% +linear programming. And and let's see, I + + + align:start position:0% +linear programming. And and let's see, I +was going to emphasize this. So where + + align:start position:0% +was going to emphasize this. So where + + + align:start position:0% +was going to emphasize this. So where +who uses linear programming + + align:start position:0% +who uses linear programming + + + align:start position:0% +who uses linear programming +uh management I mean this is like a + + align:start position:0% +uh management I mean this is like a + + + align:start position:0% +uh management I mean this is like a +major application of of uh mathematics + + align:start position:0% +major application of of uh mathematics + + + align:start position:0% +major application of of uh mathematics +in uh management planning management + + align:start position:0% +in uh management planning management + + + align:start position:0% +in uh management planning management +science I guess is the right + + align:start position:0% +science I guess is the right + + + align:start position:0% +science I guess is the right +description. Uh so there's a uh but but + + align:start position:0% +description. Uh so there's a uh but but + + + align:start position:0% +description. Uh so there's a uh but but +also in our science + + align:start position:0% +also in our science + + + align:start position:0% +also in our science +uh the big the big uh requirement is the + + align:start position:0% +uh the big the big uh requirement is the + + + align:start position:0% +uh the big the big uh requirement is the +linearity here and of course lots of + + align:start position:0% +linearity here and of course lots of + + + align:start position:0% +linearity here and of course lots of +problems are not linear and then we have + + align:start position:0% +problems are not linear and then we have + + + align:start position:0% +problems are not linear and then we have +to escape from those requirements. Maybe + + align:start position:0% +to escape from those requirements. Maybe + + + align:start position:0% +to escape from those requirements. Maybe +I mention what is quadratic + + align:start position:0% +I mention what is quadratic + + + align:start position:0% +I mention what is quadratic +programming. What is quadratic + + align:start position:0% +programming. What is quadratic + + + align:start position:0% +programming. What is quadratic +programming? quadratic programming I'll + + align:start position:0% +programming? quadratic programming I'll + + + align:start position:0% +programming? quadratic programming I'll +include a quadratic factor like xrpose + + align:start position:0% +include a quadratic factor like xrpose + + + align:start position:0% +include a quadratic factor like xrpose +kx in the + + align:start position:0% +kx in the + + + align:start position:0% +kx in the +cost. So then I'm minimizing a quadratic + + align:start position:0% +cost. So then I'm minimizing a quadratic + + + align:start position:0% +cost. So then I'm minimizing a quadratic +subject to linear equations and + + align:start position:0% +subject to linear equations and + + + align:start position:0% +subject to linear equations and +constraints. So that's a case of + + align:start position:0% +constraints. So that's a case of + + + align:start position:0% +constraints. So that's a case of +quadratic programming much closer to the + + align:start position:0% +quadratic programming much closer to the + + + align:start position:0% +quadratic programming much closer to the +rest of this course. If I throw away + + align:start position:0% +rest of this course. If I throw away + + + align:start position:0% +rest of this course. If I throw away +those constraints then I'm right at the + + align:start position:0% +those constraints then I'm right at the + + + align:start position:0% +those constraints then I'm right at the +rest of this course. Minimizing a + + align:start position:0% +rest of this course. Minimizing a + + + align:start position:0% +rest of this course. Minimizing a +quadratic with linear constraints is + + align:start position:0% +quadratic with linear constraints is + + + align:start position:0% +quadratic with linear constraints is +exactly what we might have. Minimize + + align:start position:0% +exactly what we might have. Minimize + + + align:start position:0% +exactly what we might have. Minimize +that energy subject to Kirkoff's current + + align:start position:0% +that energy subject to Kirkoff's current + + + align:start position:0% +that energy subject to Kirkoff's current +law or something like that. Uh or uh um + + align:start position:0% +law or something like that. Uh or uh um + + + align:start position:0% +law or something like that. Uh or uh um +the subject to the balance equation. So, + + align:start position:0% +the subject to the balance equation. So, + + + align:start position:0% +the subject to the balance equation. So, +so this is + + align:start position:0% +so this is + + + align:start position:0% +so this is +that this is the next step after linear + + align:start position:0% +that this is the next step after linear + + + align:start position:0% +that this is the next step after linear +programming would be quadratic + + align:start position:0% +programming would be quadratic + + + align:start position:0% +programming would be quadratic +programming and there would be a duel + + align:start position:0% +programming and there would be a duel + + + align:start position:0% +programming and there would be a duel +for that too and it would be another + + align:start position:0% +for that too and it would be another + + + align:start position:0% +for that too and it would be another +quadratic program but uh the real + + align:start position:0% +quadratic program but uh the real + + + align:start position:0% +quadratic program but uh the real +starting point here is linear + + align:start position:0% +starting point here is linear + + + align:start position:0% +starting point here is linear +programming and then this and that + + align:start position:0% +programming and then this and that + + + align:start position:0% +programming and then this and that +simplifies the the theory because it + + align:start position:0% +simplifies the the theory because it + + + align:start position:0% +simplifies the the theory because it +because we know the winner's at a + + align:start position:0% +because we know the winner's at a + + + align:start position:0% +because we know the winner's at a +corner. Okay. Now, which which corner + + align:start position:0% +corner. Okay. Now, which which corner + + + align:start position:0% +corner. Okay. Now, which which corner +does win? + + align:start position:0% +does win? + + + align:start position:0% +does win? +The grad student, right? Because the + + align:start position:0% +The grad student, right? Because the + + + align:start position:0% +The grad student, right? Because the +three corners are I could figure out the + + align:start position:0% +three corners are I could figure out the + + + align:start position:0% +three corners are I could figure out the +cost. Here are the PhDs doing all the + + align:start position:0% +cost. Here are the PhDs doing all the + + + align:start position:0% +cost. Here are the PhDs doing all the +work, solving all four problems, working + + align:start position:0% +work, solving all four problems, working + + + align:start position:0% +work, solving all four problems, working +four hours for 20 + + align:start position:0% + + + + align:start position:0% + +bucks. Here, the grad student is doing + + align:start position:0% +bucks. Here, the grad student is doing + + + align:start position:0% +bucks. Here, the grad student is doing +all the work, working four hours, $3 an + + align:start position:0% +all the work, working four hours, $3 an + + + align:start position:0% +all the work, working four hours, $3 an +hour for 12. Here the computer is doing + + align:start position:0% +hour for 12. Here the computer is doing + + + align:start position:0% +hour for 12. Here the computer is doing +all the work. Only has to work two + + align:start position:0% +all the work. Only has to work two + + + align:start position:0% +all the work. Only has to work two +hours, but its cost is $8 an hour. So + + align:start position:0% +hours, but its cost is $8 an hour. So + + + align:start position:0% +hours, but its cost is $8 an hour. So +this is $16 also. So + + align:start position:0% +this is $16 also. So + + + align:start position:0% +this is $16 also. So +16. Is that right? Yeah. 16 20 or 12. So + + align:start position:0% +16. Is that right? Yeah. 16 20 or 12. So + + + align:start position:0% +16. Is that right? Yeah. 16 20 or 12. So +the winner is the optimum is there the + + align:start position:0% +the winner is the optimum is there the + + + align:start position:0% +the winner is the optimum is there the +grad + + align:start position:0% +grad + + + align:start position:0% +grad +student. All right. + + align:start position:0% +student. All right. + + + align:start position:0% +student. All right. +Now but that was this was a small + + align:start position:0% +Now but that was this was a small + + + align:start position:0% +Now but that was this was a small +problem where we could check all the + + align:start position:0% +problem where we could check all the + + + align:start position:0% +problem where we could check all the +corners and my point was can't do that + + align:start position:0% +corners and my point was can't do that + + + align:start position:0% +corners and my point was can't do that +usually. So now I speak about the + + align:start position:0% +usually. So now I speak about the + + + align:start position:0% +usually. So now I speak about the +simplex + + align:start position:0% +simplex + + + align:start position:0% +simplex +method which + + align:start position:0% +method which + + + align:start position:0% +method which +um starts at some + + align:start position:0% +um starts at some + + + align:start position:0% +um starts at some +corner but I I need some preliminary + + align:start position:0% +corner but I I need some preliminary + + + align:start position:0% +corner but I I need some preliminary +method to find a corner. Suppose I start + + align:start position:0% +method to find a corner. Suppose I start + + + align:start position:0% +method to find a corner. Suppose I start +at corner P. So + + align:start position:0% +at corner P. So + + + align:start position:0% +at corner P. So +start and the idea of the simplex method + + align:start position:0% +start and the idea of the simplex method + + + align:start position:0% +start and the idea of the simplex method +will + + align:start position:0% +will + + + align:start position:0% +will +be to move uh to another corner, a + + align:start position:0% +be to move uh to another corner, a + + + align:start position:0% +be to move uh to another corner, a +neighboring + + align:start position:0% +neighboring + + + align:start position:0% +neighboring +corner. What's a neighboring corner on a + + align:start position:0% +corner. What's a neighboring corner on a + + + align:start position:0% +corner. What's a neighboring corner on a +on a on a one of these highdimensional + + align:start position:0% +on a on a one of these highdimensional + + + align:start position:0% +on a on a one of these highdimensional +deals? + + align:start position:0% +deals? + + + align:start position:0% +deals? +A neighboring corner + + align:start position:0% +A neighboring corner + + + align:start position:0% +A neighboring corner +means one of the + + align:start position:0% +means one of the + + + align:start position:0% +means one of the +x's becomes one of the x's that was + + align:start position:0% +x's becomes one of the x's that was + + + align:start position:0% +x's becomes one of the x's that was +zero. Well, look, here you go. Here's + + align:start position:0% +zero. Well, look, here you go. Here's + + + align:start position:0% +zero. Well, look, here you go. Here's +the x at this corner. What happens if I + + align:start position:0% +the x at this corner. What happens if I + + + align:start position:0% +the x at this corner. What happens if I +move to that + + align:start position:0% +move to that + + + align:start position:0% +move to that +corner? This + + align:start position:0% +corner? This + + + align:start position:0% +corner? This +x one, some x drops to zero and some + + align:start position:0% +x one, some x drops to zero and some + + + align:start position:0% +x one, some x drops to zero and some +other x enters. You could + + align:start position:0% +other x enters. You could + + + align:start position:0% +other x enters. You could +say x1 leaves the basis is when I travel + + align:start position:0% +say x1 leaves the basis is when I travel + + + align:start position:0% +say x1 leaves the basis is when I travel +up + + align:start position:0% + + + + align:start position:0% + +here and x2 x3 rather enters the + + align:start position:0% +here and x2 x3 rather enters the + + + align:start position:0% +here and x2 x3 rather enters the +basis. I'm using that word basis pretty + + align:start position:0% +basis. I'm using that word basis pretty + + + align:start position:0% +basis. I'm using that word basis pretty +freely. X1 enter leaves leaves the + + align:start position:0% +freely. X1 enter leaves leaves the + + + align:start position:0% +freely. X1 enter leaves leaves the +solution becomes zero and a different + + align:start position:0% +solution becomes zero and a different + + + align:start position:0% +solution becomes zero and a different +one X3 enters the + + align:start position:0% +one X3 enters the + + + align:start position:0% +one X3 enters the +solution becomes non zero and the cost + + align:start position:0% +solution becomes non zero and the cost + + + align:start position:0% +solution becomes non zero and the cost +is reduced went from $20 down to + + align:start position:0% +is reduced went from $20 down to + + + align:start position:0% +is reduced went from $20 down to +16 okay then I look around from this + + align:start position:0% + + + + align:start position:0% + +corner which way shall I go I go along + + align:start position:0% +corner which way shall I go I go along + + + align:start position:0% +corner which way shall I go I go along +an edge to the next corner so I could go + + align:start position:0% +an edge to the next corner so I could go + + + align:start position:0% +an edge to the next corner so I could go +along this edge + + align:start position:0% +along this edge + + + align:start position:0% +along this edge +or along this edge. So I compute which + + align:start position:0% +or along this edge. So I compute which + + + align:start position:0% +or along this edge. So I compute which +way is the best way to go. Well, when I + + align:start position:0% +way is the best way to go. Well, when I + + + align:start position:0% +way is the best way to go. Well, when I +go this way, my computations are going + + align:start position:0% +go this way, my computations are going + + + align:start position:0% +go this way, my computations are going +to show I'm worse. It costs + + align:start position:0% +to show I'm worse. It costs + + + align:start position:0% +to show I'm worse. It costs +more. When I go this way, it costs less. + + align:start position:0% +more. When I go this way, it costs less. + + + align:start position:0% +more. When I go this way, it costs less. +I'm reducing the cost. So, of course, + + align:start position:0% +I'm reducing the cost. So, of course, + + + align:start position:0% +I'm reducing the cost. So, of course, +I'll go that way until I can't go any + + align:start position:0% +I'll go that way until I can't go any + + + align:start position:0% +I'll go that way until I can't go any +further because I'm reducing reducing. + + align:start position:0% +further because I'm reducing reducing. + + + align:start position:0% +further because I'm reducing reducing. +The more work the grad student does, the + + align:start position:0% +The more work the grad student does, the + + + align:start position:0% +The more work the grad student does, the +more work that's taken away from the + + align:start position:0% +more work that's taken away from the + + + align:start position:0% +more work that's taken away from the +computer and given to the grad student, + + align:start position:0% +computer and given to the grad student, + + + align:start position:0% +computer and given to the grad student, +much cheaper, the more as I travel down + + align:start position:0% +much cheaper, the more as I travel down + + + align:start position:0% +much cheaper, the more as I travel down +here, I'm giving more and more work to + + align:start position:0% +here, I'm giving more and more work to + + + align:start position:0% +here, I'm giving more and more work to +the grad student until I reach that + + align:start position:0% +the grad student until I reach that + + + align:start position:0% +the grad student until I reach that +point when I can't take away any more + + align:start position:0% +point when I can't take away any more + + + align:start position:0% +point when I can't take away any more +work from the computer. The computer is + + align:start position:0% +work from the computer. The computer is + + + align:start position:0% +work from the computer. The computer is +is no longer doing anything. It's + + align:start position:0% +is no longer doing anything. It's + + + align:start position:0% +is no longer doing anything. It's +dropped to zero. + + align:start position:0% +dropped to zero. + + + align:start position:0% +dropped to zero. +So in this case the entering variable + + align:start position:0% +So in this case the entering variable + + + align:start position:0% +So in this case the entering variable +was the grad student number two and the + + align:start position:0% +was the grad student number two and the + + + align:start position:0% +was the grad student number two and the +leaving variable was the computer number + + align:start position:0% +leaving variable was the computer number + + + align:start position:0% +leaving variable was the computer number +three and it left to the point of + + align:start position:0% +three and it left to the point of + + + align:start position:0% +three and it left to the point of +dropping to zero. The grad student moved + + align:start position:0% +dropping to zero. The grad student moved + + + align:start position:0% +dropping to zero. The grad student moved +up from zero to something whatever it + + align:start position:0% +up from zero to something whatever it + + + align:start position:0% +up from zero to something whatever it +whatever something it took to to satisfy + + align:start position:0% +whatever something it took to to satisfy + + + align:start position:0% +whatever something it took to to satisfy +the constraint and I am at a new corner. + + align:start position:0% +the constraint and I am at a new corner. + + + align:start position:0% +the constraint and I am at a new corner. +Now I look around from that corner and + + align:start position:0% +Now I look around from that corner and + + + align:start position:0% +Now I look around from that corner and +the simplex method of course doesn't + + align:start position:0% +the simplex method of course doesn't + + + align:start position:0% +the simplex method of course doesn't +know it's got to xstar. So it would look + + align:start position:0% +know it's got to xstar. So it would look + + + align:start position:0% +know it's got to xstar. So it would look +around it would say there are two ways I + + align:start position:0% +around it would say there are two ways I + + + align:start position:0% +around it would say there are two ways I +can move from + + align:start position:0% +can move from + + + align:start position:0% +can move from +here but they + + align:start position:0% +here but they + + + align:start position:0% +here but they +both mean a cost increase. So I must be + + align:start position:0% +both mean a cost increase. So I must be + + + align:start position:0% +both mean a cost increase. So I must be +at the winner. So that's the that's the + + align:start position:0% +at the winner. So that's the that's the + + + align:start position:0% +at the winner. So that's the that's the +idea of the simplex method. Start + + align:start position:0% +idea of the simplex method. Start + + + align:start position:0% +idea of the simplex method. Start +somewhere. Start at some corner. + + align:start position:0% +somewhere. Start at some corner. + + + align:start position:0% +somewhere. Start at some corner. +move travel along + + align:start position:0% +move travel along + + + align:start position:0% +move travel along +edges reducing the cost every + + align:start position:0% +edges reducing the cost every + + + align:start position:0% +edges reducing the cost every +time and until you get to an edge where + + align:start position:0% +time and until you get to an edge where + + + align:start position:0% +time and until you get to an edge where +you can't the cost cannot be reduced and + + align:start position:0% +you can't the cost cannot be reduced and + + + align:start position:0% +you can't the cost cannot be reduced and +then that's that's that's Xar the + + align:start position:0% +then that's that's that's Xar the + + + align:start position:0% +then that's that's that's Xar the +winner. So that's the simplex method. + + align:start position:0% +winner. So that's the simplex method. + + + align:start position:0% +winner. So that's the simplex method. +Now I have to tell + + align:start position:0% +Now I have to tell + + + align:start position:0% +Now I have to tell +you how the simplex method chooses the + + align:start position:0% +you how the simplex method chooses the + + + align:start position:0% +you how the simplex method chooses the +edge to travel on, right? because in a + + align:start position:0% +edge to travel on, right? because in a + + + align:start position:0% +edge to travel on, right? because in a +big + + align:start position:0% +big + + + align:start position:0% +big +problem I'll be at a corner whole bunch + + align:start position:0% +problem I'll be at a corner whole bunch + + + align:start position:0% +problem I'll be at a corner whole bunch +of edges a whole bunch of possible + + align:start position:0% +of edges a whole bunch of possible + + + align:start position:0% +of edges a whole bunch of possible +entering variables whole bunch of x's + + align:start position:0% +entering variables whole bunch of x's + + + align:start position:0% +entering variables whole bunch of x's +that are willing to work and uh the + + align:start position:0% +that are willing to work and uh the + + + align:start position:0% +that are willing to work and uh the +simplex and and some of those will mean + + align:start position:0% +simplex and and some of those will mean + + + align:start position:0% +simplex and and some of those will mean +higher cost so I won't go those ways and + + align:start position:0% +higher cost so I won't go those ways and + + + align:start position:0% +higher cost so I won't go those ways and +some will mean lower cost so I will pick + + align:start position:0% +some will mean lower cost so I will pick + + + align:start position:0% +some will mean lower cost so I will pick +out which one which way to go which new + + align:start position:0% +out which one which way to go which new + + + align:start position:0% +out which one which way to go which new +x should enter and then I have to go + + align:start position:0% +x should enter and then I have to go + + + align:start position:0% +x should enter and then I have to go +along that edge + + align:start position:0% +along that edge + + + align:start position:0% +along that edge +until I come to that corner to that next + + align:start position:0% +until I come to that corner to that next + + + align:start position:0% +until I come to that corner to that next +corner and then I do it again. So that's + + align:start position:0% +corner and then I do it again. So that's + + + align:start position:0% +corner and then I do it again. So that's +the that's the + + align:start position:0% +the that's the + + + align:start position:0% +the that's the +algorithm. Repeatedly you're at a + + align:start position:0% +algorithm. Repeatedly you're at a + + + align:start position:0% +algorithm. Repeatedly you're at a +corner, you test + + align:start position:0% +corner, you test + + + align:start position:0% +corner, you test +directions, you travel on the direction + + align:start position:0% +directions, you travel on the direction + + + align:start position:0% +directions, you travel on the direction +where the like steepest descent, the + + align:start position:0% +where the like steepest descent, the + + + align:start position:0% +where the like steepest descent, the +cost goes down fastest per step along + + align:start position:0% +cost goes down fastest per step along + + + align:start position:0% +cost goes down fastest per step along +that edge and then you get to the next + + align:start position:0% +that edge and then you get to the next + + + align:start position:0% +that edge and then you get to the next +corner and you do it again. Is that a + + align:start position:0% +corner and you do it again. Is that a + + + align:start position:0% +corner and you do it again. Is that a +picture of Yeah. How do you know? + + align:start position:0% +picture of Yeah. How do you know? + + + align:start position:0% +picture of Yeah. How do you know? +How do you know that you're not just at + + align:start position:0% +How do you know that you're not just at + + + align:start position:0% +How do you know that you're not just at +a local minimum? Very good question. + + align:start position:0% +a local minimum? Very good question. + + + align:start position:0% +a local minimum? Very good question. +It's it's because of this linearity. + + align:start position:0% +It's it's because of this linearity. + + + align:start position:0% +It's it's because of this linearity. +It's it's be from these linear equations + + align:start position:0% +It's it's be from these linear equations + + + align:start position:0% +It's it's be from these linear equations +and linear constraints you can't you you + + align:start position:0% +and linear constraints you can't you you + + + align:start position:0% +and linear constraints you can't you you +you can't get in uh trapped. But uh and + + align:start position:0% +you can't get in uh trapped. But uh and + + + align:start position:0% +you can't get in uh trapped. But uh and +similarly if I had this quadratic one + + align:start position:0% +similarly if I had this quadratic one + + + align:start position:0% +similarly if I had this quadratic one +and was positive definite I couldn't get + + align:start position:0% +and was positive definite I couldn't get + + + align:start position:0% +and was positive definite I couldn't get +trapped. But absolutely local minima and + + align:start position:0% +trapped. But absolutely local minima and + + + align:start position:0% +trapped. But absolutely local minima and +so on are the are the you know they're + + align:start position:0% +so on are the are the you know they're + + + align:start position:0% +so on are the are the you know they're +the big challenge in in minimization + + align:start position:0% +the big challenge in in minimization + + + align:start position:0% +the big challenge in in minimization +problems in general. You give me a + + align:start position:0% +problems in general. You give me a + + + align:start position:0% +problems in general. You give me a +function a cost function. See most cost + + align:start position:0% +function a cost function. See most cost + + + align:start position:0% +function a cost function. See most cost +functions aren't linear. You give me a + + align:start position:0% +functions aren't linear. You give me a + + + align:start position:0% +functions aren't linear. You give me a +cost function of f + + align:start position:0% +cost function of f + + + align:start position:0% +cost function of f +of 100 variables that you allow me to + + align:start position:0% +of 100 variables that you allow me to + + + align:start position:0% +of 100 variables that you allow me to +play with. And uh how do I how do you + + align:start position:0% +play with. And uh how do I how do you + + + align:start position:0% +play with. And uh how do I how do you +minimize a function of 100 variables? + + align:start position:0% +minimize a function of 100 variables? + + + align:start position:0% +minimize a function of 100 variables? +Boy, that's the that's the zillion + + align:start position:0% +Boy, that's the that's the zillion + + + align:start position:0% +Boy, that's the that's the zillion +dollar question. And if that function + + align:start position:0% +dollar question. And if that function + + + align:start position:0% +dollar question. And if that function +is + + align:start position:0% +is + + + align:start position:0% +is +convex, then you so if the function is + + align:start position:0% +convex, then you so if the function is + + + align:start position:0% +convex, then you so if the function is +shaped like this, maybe with wiggles, + + align:start position:0% +shaped like this, maybe with wiggles, + + + align:start position:0% +shaped like this, maybe with wiggles, +but still convex, then you know there's + + align:start position:0% +but still convex, then you know there's + + + align:start position:0% +but still convex, then you know there's +only one minimum and the problem is much + + align:start position:0% +only one minimum and the problem is much + + + align:start position:0% +only one minimum and the problem is much +easier. If the function is quite + + align:start position:0% +easier. If the function is quite + + + align:start position:0% +easier. If the function is quite +general, it loops like a golf course. + + align:start position:0% +general, it loops like a golf course. + + + align:start position:0% +general, it loops like a golf course. +its graph is some surface with ups and + + align:start position:0% +its graph is some surface with ups and + + + align:start position:0% +its graph is some surface with ups and +downs and ups and downs. Then when you + + align:start position:0% +downs and ups and downs. Then when you + + + align:start position:0% +downs and ups and downs. Then when you +find a local minimum, you + + align:start position:0% +find a local minimum, you + + + align:start position:0% +find a local minimum, you +gota you can't just look around in a + + align:start position:0% +gota you can't just look around in a + + + align:start position:0% +gota you can't just look around in a +local minimum cuz everything looks + + align:start position:0% +local minimum cuz everything looks + + + align:start position:0% +local minimum cuz everything looks +upwards. But at some other point there's + + align:start position:0% +upwards. But at some other point there's + + + align:start position:0% +upwards. But at some other point there's +a there's a thing much further down and + + align:start position:0% +a there's a thing much further down and + + + align:start position:0% +a there's a thing much further down and +and a whole lot of ideas have gone in to + + align:start position:0% +and a whole lot of ideas have gone in to + + + align:start position:0% +and a whole lot of ideas have gone in to +this subject. And I guess there are a + + align:start position:0% +this subject. And I guess there are a + + + align:start position:0% +this subject. And I guess there are a +lot more to + + align:start position:0% +lot more to + + + align:start position:0% +lot more to +come because you somehow have to jog + + align:start position:0% +come because you somehow have to jog + + + align:start position:0% +come because you somehow have to jog +that that possible local + + align:start position:0% +that that possible local + + + align:start position:0% +that that possible local +minimum, you know, enough to get out of + + align:start position:0% +minimum, you know, enough to get out of + + + align:start position:0% +minimum, you know, enough to get out of +that little well and on with the + + align:start position:0% +that little well and on with the + + + align:start position:0% +that little well and on with the +job. But + + align:start position:0% +job. But + + + align:start position:0% +job. But +uh how much do you jog by? And you don't + + align:start position:0% +uh how much do you jog by? And you don't + + + align:start position:0% +uh how much do you jog by? And you don't +want if you spend all your time worrying + + align:start position:0% +want if you spend all your time worrying + + + align:start position:0% +want if you spend all your time worrying +about this, you won't find that logo + + align:start position:0% +about this, you won't find that logo + + + align:start position:0% +about this, you won't find that logo +minimum in the first place. It's + + align:start position:0% +minimum in the first place. It's + + + align:start position:0% +minimum in the first place. It's +fascinating. + + align:start position:0% +fascinating. + + + align:start position:0% +fascinating. +Now, okay, one comment here and I not + + align:start position:0% +Now, okay, one comment here and I not + + + align:start position:0% +Now, okay, one comment here and I not +wasn't planning and and don't have time + + align:start position:0% +wasn't planning and and don't have time + + + align:start position:0% +wasn't planning and and don't have time +to develop interior point methods, but + + align:start position:0% +to develop interior point methods, but + + + align:start position:0% +to develop interior point methods, but +just so you you could guess what that + + align:start position:0% +just so you you could guess what that + + + align:start position:0% +just so you you could guess what that +means. That means that we we travel in + + align:start position:0% +means. That means that we we travel in + + + align:start position:0% +means. That means that we we travel in +the interior. We find a point. So + + align:start position:0% +the interior. We find a point. So + + + align:start position:0% +the interior. We find a point. So +interior interior is interior of this + + align:start position:0% +interior interior is interior of this + + + align:start position:0% +interior interior is interior of this +feasible set. Find some place that + + align:start position:0% +feasible set. Find some place that + + + align:start position:0% +feasible set. Find some place that +solves the + + align:start position:0% +solves the + + + align:start position:0% +solves the +equation. Don't worry about the number + + align:start position:0% +equation. Don't worry about the number + + + align:start position:0% +equation. Don't worry about the number +of zeros and nonzeros. This this had to + + align:start position:0% +of zeros and nonzeros. This this had to + + + align:start position:0% +of zeros and nonzeros. This this had to +do with + + align:start position:0% +do with + + + align:start position:0% +do with +corners. Find a point. Find a direction + + align:start position:0% +corners. Find a point. Find a direction + + + align:start position:0% +corners. Find a point. Find a direction +is better. Travel in + + align:start position:0% +is better. Travel in + + + align:start position:0% +is better. Travel in +it. Decide when to stop and probably + + align:start position:0% +it. Decide when to stop and probably + + + align:start position:0% +it. Decide when to stop and probably +stop short of the + + align:start position:0% +stop short of the + + + align:start position:0% +stop short of the +boundary. Then you're still inside. + + align:start position:0% +boundary. Then you're still inside. + + + align:start position:0% +boundary. Then you're still inside. +Calculus still operates so to speak. + + align:start position:0% +Calculus still operates so to speak. + + + align:start position:0% +Calculus still operates so to speak. +Look around, find another point, travel + + align:start position:0% +Look around, find another point, travel + + + align:start position:0% +Look around, find another point, travel +for a while, find another point, and + + align:start position:0% +for a while, find another point, and + + + align:start position:0% +for a while, find another point, and +eventually in infinite many steps reach + + align:start position:0% +eventually in infinite many steps reach + + + align:start position:0% +eventually in infinite many steps reach +the winner. I mean, because you're + + align:start position:0% +the winner. I mean, because you're + + + align:start position:0% +the winner. I mean, because you're +always stopping short but getting closer + + align:start position:0% +always stopping short but getting closer + + + align:start position:0% +always stopping short but getting closer +and closer. But of course, in reality, + + align:start position:0% +and closer. But of course, in reality, + + + align:start position:0% +and closer. But of course, in reality, +we are happy to get within 10 to the + + align:start position:0% +we are happy to get within 10 to the + + + align:start position:0% +we are happy to get within 10 to the +minus something of the winner and and + + align:start position:0% +minus something of the winner and and + + + align:start position:0% +minus something of the winner and and +that's okay, too. So that's that's + + align:start position:0% +that's okay, too. So that's that's + + + align:start position:0% +that's okay, too. So that's that's +iterative. And this is a finite + + align:start position:0% +iterative. And this is a finite + + + align:start position:0% +iterative. And this is a finite +algorithm, right? Can't take well, we + + align:start position:0% +algorithm, right? Can't take well, we + + + align:start position:0% +algorithm, right? Can't take well, we +know it's finite because the darn thing + + align:start position:0% +know it's finite because the darn thing + + + align:start position:0% +know it's finite because the darn thing +has only a finite number of + + align:start position:0% +has only a finite number of + + + align:start position:0% +has only a finite number of +corners, finite number of edges. And + + align:start position:0% +corners, finite number of edges. And + + + align:start position:0% +corners, finite number of edges. And +we're not going to go backwards on an + + align:start position:0% +we're not going to go backwards on an + + + align:start position:0% +we're not going to go backwards on an +edge because as we saw, if forward on if + + align:start position:0% +edge because as we saw, if forward on if + + + align:start position:0% +edge because as we saw, if forward on if +we went forward on an edge, that was + + align:start position:0% +we went forward on an edge, that was + + + align:start position:0% +we went forward on an edge, that was +because it improved the cost, reduced + + align:start position:0% +because it improved the cost, reduced + + + align:start position:0% +because it improved the cost, reduced +the cost, and we'll never travel + + align:start position:0% +the cost, and we'll never travel + + + align:start position:0% +the cost, and we'll never travel +backward on that edge. So it's got to be + + align:start position:0% +backward on that edge. So it's got to be + + + align:start position:0% +backward on that edge. So it's got to be +finite. But the number of edges is + + align:start position:0% +finite. But the number of edges is + + + align:start position:0% +finite. But the number of edges is +exponentially large for M&N. And so + + align:start position:0% +exponentially large for M&N. And so + + + align:start position:0% +exponentially large for M&N. And so +there's a big I mean the big the theory + + align:start position:0% +there's a big I mean the big the theory + + + align:start position:0% +there's a big I mean the big the theory +of the simplex method is does it + + align:start position:0% +of the simplex method is does it + + + align:start position:0% +of the simplex method is does it +actually take exponentially long as M&N + + align:start position:0% +actually take exponentially long as M&N + + + align:start position:0% +actually take exponentially long as M&N +increases + + align:start position:0% +increases + + + align:start position:0% +increases +or can it be done in polomial time? This + + align:start position:0% +or can it be done in polomial time? This + + + align:start position:0% +or can it be done in polomial time? This +is the one the the most important pro + + align:start position:0% +is the one the the most important pro + + + align:start position:0% +is the one the the most important pro +problem where it was quite unclear even + + align:start position:0% +problem where it was quite unclear even + + + align:start position:0% +problem where it was quite unclear even +to experts whether + + align:start position:0% +to experts whether + + + align:start position:0% +to experts whether +um it whether it can be done in polomial + + align:start position:0% +um it whether it can be done in polomial + + + align:start position:0% +um it whether it can be done in polomial +time meaning a power of m and + + align:start position:0% +time meaning a power of m and + + + align:start position:0% +time meaning a power of m and +n or whether the n whether it grows like + + align:start position:0% +n or whether the n whether it grows like + + + align:start position:0% +n or whether the n whether it grows like +the number of corners which + + align:start position:0% +the number of corners which + + + align:start position:0% +the number of corners which +is m n choose m and and grows + + align:start position:0% +is m n choose m and and grows + + + align:start position:0% +is m n choose m and and grows +exponentially. Well, here's the answer + + align:start position:0% +exponentially. Well, here's the answer + + + align:start position:0% +exponentially. Well, here's the answer +to a quick report on that. The simplex + + align:start position:0% +to a quick report on that. The simplex + + + align:start position:0% +to a quick report on that. The simplex +method can in really hooked up cases + + align:start position:0% +method can in really hooked up cases + + + align:start position:0% +method can in really hooked up cases +take exponentially long. So if I + + align:start position:0% +take exponentially long. So if I + + + align:start position:0% +take exponentially long. So if I +describe the simplex the the clear + + align:start position:0% +describe the simplex the the clear + + + align:start position:0% +describe the simplex the the clear +straightforward simplex method although + + align:start position:0% +straightforward simplex method although + + + align:start position:0% +straightforward simplex method although +it's average cost and it's used all the + + align:start position:0% +it's average cost and it's used all the + + + align:start position:0% +it's average cost and it's used all the +time. So of course it doesn't take + + align:start position:0% +time. So of course it doesn't take + + + align:start position:0% +time. So of course it doesn't take +exponentially long or or we wouldn't use + + align:start position:0% +exponentially long or or we wouldn't use + + + align:start position:0% +exponentially long or or we wouldn't use +it. + + align:start position:0% +it. + + + align:start position:0% +it. +But its worst cost in in a in a extreme + + align:start position:0% +But its worst cost in in a in a extreme + + + align:start position:0% +But its worst cost in in a in a extreme +example could be + + align:start position:0% +example could be + + + align:start position:0% +example could be +exponential. We we could travel along + + align:start position:0% +exponential. We we could travel along + + + align:start position:0% +exponential. We we could travel along +exponential number of edges before we + + align:start position:0% +exponential number of edges before we + + + align:start position:0% +exponential number of edges before we +finally settled on the winner. And you + + align:start position:0% +finally settled on the winner. And you + + + align:start position:0% +finally settled on the winner. And you +see because traveling on an edge the co + + align:start position:0% +see because traveling on an edge the co + + + align:start position:0% +see because traveling on an edge the co +the cost the computing cost is is the + + align:start position:0% +the cost the computing cost is is the + + + align:start position:0% +the cost the computing cost is is the +same however long the edge. So anyway uh + + align:start position:0% +same however long the edge. So anyway uh + + + align:start position:0% +same however long the edge. So anyway uh +but the but average costs are uh + + align:start position:0% +but the but average costs are uh + + + align:start position:0% +but the but average costs are uh +polomial. So a lot of people and a guy + + align:start position:0% +polomial. So a lot of people and a guy + + + align:start position:0% +polomial. So a lot of people and a guy +at MIT is uh looking at this problem + + align:start position:0% +at MIT is uh looking at this problem + + + align:start position:0% +at MIT is uh looking at this problem +again and found another way of + + align:start position:0% +again and found another way of + + + align:start position:0% +again and found another way of +describing average costs and and uh + + align:start position:0% +describing average costs and and uh + + + align:start position:0% +describing average costs and and uh +showing that that's polomial and then + + align:start position:0% +showing that that's polomial and then + + + align:start position:0% +showing that that's polomial and then +there is a + + align:start position:0% + + + + align:start position:0% + +polomial algorithm for linear + + align:start position:0% +polomial algorithm for linear + + + align:start position:0% +polomial algorithm for linear +programming. You have + + align:start position:0% +programming. You have + + + align:start position:0% +programming. You have +to twist the simplex method to make it + + align:start position:0% +to twist the simplex method to make it + + + align:start position:0% +to twist the simplex method to make it +polomial but you can do it. So there is + + align:start position:0% +polomial but you can do it. So there is + + + align:start position:0% +polomial but you can do it. So there is +a polomial algorithm but most people + + align:start position:0% +a polomial algorithm but most people + + + align:start position:0% +a polomial algorithm but most people +happy with a simplex method which is + + align:start position:0% +happy with a simplex method which is + + + align:start position:0% +happy with a simplex method which is +polomial in all practical cases. So this + + align:start position:0% +polomial in all practical cases. So this + + + align:start position:0% +polomial in all practical cases. So this +is this is polomial actually this is + + align:start position:0% +is this is polomial actually this is + + + align:start position:0% +is this is polomial actually this is +polomial 2 in getting arbitrary getting + + align:start position:0% +polomial 2 in getting arbitrary getting + + + align:start position:0% +polomial 2 in getting arbitrary getting +within given epsilon in polomial time. + + align:start position:0% +within given epsilon in polomial time. + + + align:start position:0% +within given epsilon in polomial time. +Can I mention the name of the guy who uh + + align:start position:0% +Can I mention the name of the guy who uh + + + align:start position:0% +Can I mention the name of the guy who uh +guy + + align:start position:0% + + + + align:start position:0% + +carer who + + align:start position:0% +carer who + + + align:start position:0% +carer who +uh + + align:start position:0% + + + + align:start position:0% + +uh proposed I mean he he threw a + + align:start position:0% +uh proposed I mean he he threw a + + + align:start position:0% +uh proposed I mean he he threw a +bombshell into this wellestablished + + align:start position:0% +bombshell into this wellestablished + + + align:start position:0% +bombshell into this wellestablished +theory um by discovering a method that + + align:start position:0% +theory um by discovering a method that + + + align:start position:0% +theory um by discovering a method that +that he for which he claimed high high + + align:start position:0% +that he for which he claimed high high + + + align:start position:0% +that he for which he claimed high high +efficiency. So he's in his presentation + + align:start position:0% +efficiency. So he's in his presentation + + + align:start position:0% +efficiency. So he's in his presentation +of his new method it was beating the + + align:start position:0% +of his new method it was beating the + + + align:start position:0% +of his new method it was beating the +simplex method which I mean there is a + + align:start position:0% +simplex method which I mean there is a + + + align:start position:0% +simplex method which I mean there is a +serious revolution in a important + + align:start position:0% +serious revolution in a important + + + align:start position:0% +serious revolution in a important +scientific subject because th this is + + align:start position:0% +scientific subject because th this is + + + align:start position:0% +scientific subject because th this is +these calculations are done a lot. uh + + align:start position:0% +these calculations are done a lot. uh + + + align:start position:0% +these calculations are done a lot. uh +then well much more of course that led + + align:start position:0% +then well much more of course that led + + + align:start position:0% +then well much more of course that led +to many discussions much much further + + align:start position:0% +to many discussions much much further + + + align:start position:0% +to many discussions much much further +work to understand the theory behind it + + align:start position:0% +work to understand the theory behind it + + + align:start position:0% +work to understand the theory behind it +and now uh I think probably in reality + + align:start position:0% +and now uh I think probably in reality + + + align:start position:0% +and now uh I think probably in reality +most people most codes would just + + align:start position:0% +most people most codes would just + + + align:start position:0% +most people most codes would just +quickly use the simplex method but uh + + align:start position:0% +quickly use the simplex method but uh + + + align:start position:0% +quickly use the simplex method but uh +interior methods are definitely + + align:start position:0% +interior methods are definitely + + + align:start position:0% +interior methods are definitely +competitive as always this will be + + align:start position:0% +competitive as always this will be + + + align:start position:0% +competitive as always this will be +better in some problems this will be + + align:start position:0% +better in some problems this will be + + + align:start position:0% +better in some problems this will be +better in other problems + + align:start position:0% +better in other problems + + + align:start position:0% +better in other problems +Okay, so I've done everything except to + + align:start position:0% +Okay, so I've done everything except to + + + align:start position:0% +Okay, so I've done everything except to +explain the simplex + + align:start position:0% +explain the simplex + + + align:start position:0% +explain the simplex +method. Uh, and I haven't explained this + + align:start position:0% +method. Uh, and I haven't explained this + + + align:start position:0% +method. Uh, and I haven't explained this +interior point sort of there's a + + align:start position:0% +interior point sort of there's a + + + align:start position:0% +interior point sort of there's a +penalty. Uh, anyway, there's a penalty + + align:start position:0% +penalty. Uh, anyway, there's a penalty + + + align:start position:0% +penalty. Uh, anyway, there's a penalty +as you get near the border. So, you it + + align:start position:0% +as you get near the border. So, you it + + + align:start position:0% +as you get near the border. So, you it +stops you short and then you look again. + + align:start position:0% +stops you short and then you look again. + + + align:start position:0% +stops you short and then you look again. +I could try to explain that simplex + + align:start position:0% +I could try to explain that simplex + + + align:start position:0% +I could try to explain that simplex +method since we've got to this point in + + align:start position:0% +method since we've got to this point in + + + align:start position:0% +method since we've got to this point in +a few minutes. Let's can I take these + + align:start position:0% +a few minutes. Let's can I take these + + + align:start position:0% +a few minutes. Let's can I take these +few minutes to to uh describe how the + + align:start position:0% +few minutes to to uh describe how the + + + align:start position:0% +few minutes to to uh describe how the +simplex method works. Oh, and I haven't + + align:start position:0% +simplex method works. Oh, and I haven't + + + align:start position:0% +simplex method works. Oh, and I haven't +done duality. I haven't looked at the + + align:start position:0% +done duality. I haven't looked at the + + + align:start position:0% +done duality. I haven't looked at the +and this is I want to do I haven't + + align:start position:0% +and this is I want to do I haven't + + + align:start position:0% +and this is I want to do I haven't +looked at the dual + + align:start position:0% +looked at the dual + + + align:start position:0% +looked at the dual +problem. So, what's the dual problem in + + align:start position:0% +problem. So, what's the dual problem in + + + align:start position:0% +problem. So, what's the dual problem in +this particular case? B is just the + + align:start position:0% +this particular case? B is just the + + + align:start position:0% +this particular case? B is just the +number four. I think there's only one + + align:start position:0% +number four. I think there's only one + + + align:start position:0% +number four. I think there's only one +Y. And what's the constraint in the dual + + align:start position:0% +Y. And what's the constraint in the dual + + + align:start position:0% +Y. And what's the constraint in the dual +problem? A transpose Y less or equal C. + + align:start position:0% +problem? A transpose Y less or equal C. + + + align:start position:0% +problem? A transpose Y less or equal C. +A was + + align:start position:0% +A was + + + align:start position:0% +A was +112. So that's now transpose is 112. + + align:start position:0% +112. So that's now transpose is 112. + + + align:start position:0% +112. So that's now transpose is 112. +1 2 multiplying y is less than or equal + + align:start position:0% +1 2 multiplying y is less than or equal + + + align:start position:0% +1 2 multiplying y is less than or equal +to what are the + + align:start position:0% +to what are the + + + align:start position:0% +to what are the +costs five 3 and 8. Yeah, I'd rather + + align:start position:0% +costs five 3 and 8. Yeah, I'd rather + + + align:start position:0% +costs five 3 and 8. Yeah, I'd rather +tell you about the dual problem. + + align:start position:0% + + + + align:start position:0% + +Okay. Okay. So, that says y less or + + align:start position:0% +Okay. Okay. So, that says y less or + + + align:start position:0% +Okay. Okay. So, that says y less or +equal 5, y less or equal 3, 2 y less or + + align:start position:0% +equal 5, y less or equal 3, 2 y less or + + + align:start position:0% +equal 5, y less or equal 3, 2 y less or +equal + + align:start position:0% +equal + + + align:start position:0% +equal +8, and what's the biggest y? Oh, you + + align:start position:0% +8, and what's the biggest y? Oh, you + + + align:start position:0% +8, and what's the biggest y? Oh, you +could tell me the + + align:start position:0% +could tell me the + + + align:start position:0% +could tell me the +answer. We could solve that dual + + align:start position:0% +answer. We could solve that dual + + + align:start position:0% +answer. We could solve that dual +problem. I want to maximize 4 + + align:start position:0% +problem. I want to maximize 4 + + + align:start position:0% +problem. I want to maximize 4 +Y where Y has to be less or equal 5 also + + align:start position:0% +Y where Y has to be less or equal 5 also + + + align:start position:0% +Y where Y has to be less or equal 5 also +less or equal 3 and 2 Y less or equal 8. + + align:start position:0% +less or equal 3 and 2 Y less or equal 8. + + + align:start position:0% +less or equal 3 and 2 Y less or equal 8. +So what's the smallest Y? + + align:start position:0% + + + + align:start position:0% + +Y the largest Y. Yes, the largest Y + + align:start position:0% +Y the largest Y. Yes, the largest Y + + + align:start position:0% +Y the largest Y. Yes, the largest Y +possible + + align:start position:0% +possible + + + align:start position:0% +possible +is no. But but the y has to solve all + + align:start position:0% +is no. But but the y has to solve all + + + align:start position:0% +is no. But but the y has to solve all +three of these conditions. + + align:start position:0% +three of these conditions. + + + align:start position:0% +three of these conditions. +It's three, right? The y has to be less + + align:start position:0% +It's three, right? The y has to be less + + + align:start position:0% +It's three, right? The y has to be less +equal five. The y has to be less. + + align:start position:0% +equal five. The y has to be less. + + + align:start position:0% +equal five. The y has to be less. +Essentially, I have a cheater who's + + align:start position:0% +Essentially, I have a cheater who's + + + align:start position:0% +Essentially, I have a cheater who's +compu compare competing with the PhD for + + align:start position:0% +compu compare competing with the PhD for + + + align:start position:0% +compu compare competing with the PhD for +the + + align:start position:0% +the + + + align:start position:0% +the +money. But he has to also compete with + + align:start position:0% +money. But he has to also compete with + + + align:start position:0% +money. But he has to also compete with +the grad student for the money. And the + + align:start position:0% +the grad student for the money. And the + + + align:start position:0% +the grad student for the money. And the +grad student because he's cheaper is + + align:start position:0% +grad student because he's cheaper is + + + align:start position:0% +grad student because he's cheaper is +going to the cheater has to reduce his + + align:start position:0% +going to the cheater has to reduce his + + + align:start position:0% +going to the cheater has to reduce his +rate because he has to beat the grad + + align:start position:0% +rate because he has to beat the grad + + + align:start position:0% +rate because he has to beat the grad +student. and he has to also beat what + + align:start position:0% +student. and he has to also beat what + + + align:start position:0% +student. and he has to also beat what +the computer is charging. So this + + align:start position:0% +the computer is charging. So this + + + align:start position:0% +the computer is charging. So this +cheater, if I allow me to use that word, + + align:start position:0% +cheater, if I allow me to use that word, + + + align:start position:0% +cheater, if I allow me to use that word, +is is a coming in and saying, "I'll + + align:start position:0% +is is a coming in and saying, "I'll + + + align:start position:0% +is is a coming in and saying, "I'll +solve the problems for you. Pay + + align:start position:0% + + + + align:start position:0% + +me." And he's going to solve four + + align:start position:0% +me." And he's going to solve four + + + align:start position:0% +me." And he's going to solve four +problems. And he wants to set his rate + + align:start position:0% +problems. And he wants to set his rate + + + align:start position:0% +problems. And he wants to set his rate +as high as he + + align:start position:0% +as high as he + + + align:start position:0% +as high as he +can, but he can't set the rate above + + align:start position:0% +can, but he can't set the rate above + + + align:start position:0% +can, but he can't set the rate above +what he's competing with. + + align:start position:0% +what he's competing with. + + + align:start position:0% +what he's competing with. +and he's competing among other things + + align:start position:0% +and he's competing among other things + + + align:start position:0% +and he's competing among other things +with the grad student. So the cheater + + align:start position:0% +with the grad student. So the cheater + + + align:start position:0% +with the grad student. So the cheater +can't set his rate per problem. He he + + align:start position:0% +can't set his rate per problem. He he + + + align:start position:0% +can't set his rate per problem. He he +charges a rate per problem, not per hour + + align:start position:0% +charges a rate per problem, not per hour + + + align:start position:0% +charges a rate per problem, not per hour +because he's just looking up the + + align:start position:0% +because he's just looking up the + + + align:start position:0% +because he's just looking up the +answers. Only takes him two seconds. But + + align:start position:0% +answers. Only takes him two seconds. But + + + align:start position:0% +answers. Only takes him two seconds. But +per + + align:start position:0% +per + + + align:start position:0% +per +problem he has + + align:start position:0% +problem he has + + + align:start position:0% +problem he has +to has to uh beat or match. Yeah. Like + + align:start position:0% +to has to uh beat or match. Yeah. Like + + + align:start position:0% +to has to uh beat or match. Yeah. Like +like auto sales here. He has to match + + align:start position:0% +like auto sales here. He has to match + + + align:start position:0% +like auto sales here. He has to match +what the other guys will do. And the + + align:start position:0% +what the other guys will do. And the + + + align:start position:0% +what the other guys will do. And the +other + + align:start position:0% +other + + + align:start position:0% +other +guys will will solve so many this it's + + align:start position:0% +guys will will solve so many this it's + + + align:start position:0% +guys will will solve so many this it's +the computer solves a problem solves + + align:start position:0% +the computer solves a problem solves + + + align:start position:0% +the computer solves a problem solves +charges $4 a problem, + + align:start position:0% +charges $4 a problem, + + + align:start position:0% +charges $4 a problem, +right? Cuz the computer charges $8 an + + align:start position:0% +right? Cuz the computer charges $8 an + + + align:start position:0% +right? Cuz the computer charges $8 an +hour but solves two problems. So the + + align:start position:0% +hour but solves two problems. So the + + + align:start position:0% +hour but solves two problems. So the +computer is really solving charging $4 a + + align:start position:0% +computer is really solving charging $4 a + + + align:start position:0% +computer is really solving charging $4 a +problem. So the cheater can't charge + + align:start position:0% +problem. So the cheater can't charge + + + align:start position:0% +problem. So the cheater can't charge +more than four, but the grad student is + + align:start position:0% +more than four, but the grad student is + + + align:start position:0% +more than four, but the grad student is +only charging $3 a problem. So what's + + align:start position:0% +only charging $3 a problem. So what's + + + align:start position:0% +only charging $3 a problem. So what's +the minimum the maximum here? What's the + + align:start position:0% +the minimum the maximum here? What's the + + + align:start position:0% +the minimum the maximum here? What's the +what's the + + align:start position:0% + + + + align:start position:0% + +yar? The y star is how much can the + + align:start position:0% +yar? The y star is how much can the + + + align:start position:0% +yar? The y star is how much can the +cheater charge + + align:start position:0% +cheater charge + + + align:start position:0% +cheater charge +three. The the maximum is y equal three. + + align:start position:0% +three. The the maximum is y equal three. + + + align:start position:0% +three. The the maximum is y equal three. +This this is the tight + + align:start position:0% +This this is the tight + + + align:start position:0% +This this is the tight +constraint. And the maximum is 12. And + + align:start position:0% +constraint. And the maximum is 12. And + + + align:start position:0% +constraint. And the maximum is 12. And +that's what of course the grad + + align:start position:0% +that's what of course the grad + + + align:start position:0% +that's what of course the grad +student charged. He + + align:start position:0% +student charged. He + + + align:start position:0% +student charged. He +charged it took the grad student 4 hours + + align:start position:0% +charged it took the grad student 4 hours + + + align:start position:0% +charged it took the grad student 4 hours +where I took the cheater 4 seconds but + + align:start position:0% +where I took the cheater 4 seconds but + + + align:start position:0% +where I took the cheater 4 seconds but +the grad student the the the cost was + + align:start position:0% +the grad student the the the cost was + + + align:start position:0% +the grad student the the the cost was +the same. So that this was 12= + + align:start position:0% + + + + align:start position:0% + +12 and + + align:start position:0% +12 and + + + align:start position:0% +12 and +um and we could even see that it was + + align:start position:0% +um and we could even see that it was + + + align:start position:0% +um and we could even see that it was +optimal. Do you see why it's optimal? + + align:start position:0% +optimal. Do you see why it's optimal? + + + align:start position:0% +optimal. Do you see why it's optimal? +Which of these + + align:start position:0% +Which of these + + + align:start position:0% +Which of these +inequalities? Yeah. Do you see why you + + align:start position:0% +inequalities? Yeah. Do you see why you + + + align:start position:0% +inequalities? Yeah. Do you see why you +see the winning Xstar? You remember XAR + + align:start position:0% +see the winning Xstar? You remember XAR + + + align:start position:0% +see the winning Xstar? You remember XAR +is 040. Only the only the grad student + + align:start position:0% +is 040. Only the only the grad student + + + align:start position:0% +is 040. Only the only the grad student +works. So two components of X are zero + + align:start position:0% +works. So two components of X are zero + + + align:start position:0% +works. So two components of X are zero +and in those two components the com the + + align:start position:0% +and in those two components the com the + + + align:start position:0% +and in those two components the com the +cheater + + align:start position:0% +cheater + + + align:start position:0% +cheater +uh has + + align:start position:0% +uh has + + + align:start position:0% +uh has +inequalities but in the component which + + align:start position:0% +inequalities but in the component which + + + align:start position:0% +inequalities but in the component which +matches the grad student in X the + + align:start position:0% +matches the grad student in X the + + + align:start position:0% +matches the grad student in X the +cheater has equalities. + + align:start position:0% +cheater has equalities. + + + align:start position:0% +cheater has equalities. +You see it's it's just a beautiful + + align:start position:0% +You see it's it's just a beautiful + + + align:start position:0% +You see it's it's just a beautiful +subject this complimentarity of the two + + align:start position:0% +subject this complimentarity of the two + + + align:start position:0% +subject this complimentarity of the two +problems and it gives there it it it + + align:start position:0% +problems and it gives there it it it + + + align:start position:0% +problems and it gives there it it it +this because this is a theme through all + + align:start position:0% +this because this is a theme through all + + + align:start position:0% +this because this is a theme through all +of optimization. The best algorithms are + + align:start position:0% +of optimization. The best algorithms are + + + align:start position:0% +of optimization. The best algorithms are +called primal jewel algorithms. They pay + + align:start position:0% +called primal jewel algorithms. They pay + + + align:start position:0% +called primal jewel algorithms. They pay +attention to both problems at once and + + align:start position:0% +attention to both problems at once and + + + align:start position:0% +attention to both problems at once and +uh p and and solve faster. Okay. So we + + align:start position:0% +uh p and and solve faster. Okay. So we + + + align:start position:0% +uh p and and solve faster. Okay. So we +saw the the dual problem there and you + + align:start position:0% +saw the the dual problem there and you + + + align:start position:0% +saw the the dual problem there and you +saw how it came out of the blue. I mean + + align:start position:0% +saw how it came out of the blue. I mean + + + align:start position:0% +saw how it came out of the blue. I mean +somebody was prepared to do the same job + + align:start position:0% +somebody was prepared to do the same job + + + align:start position:0% +somebody was prepared to do the same job +and wanted to maximum income from that + + align:start position:0% +and wanted to maximum income from that + + + align:start position:0% +and wanted to maximum income from that +and uh but constrained by the the + + align:start position:0% +and uh but constrained by the the + + + align:start position:0% +and uh but constrained by the the +inequality + + align:start position:0% +inequality + + + align:start position:0% +inequality +uh the max equal the min. + + align:start position:0% + + + + align:start position:0% + +So that's the duality in in this + + align:start position:0% +So that's the duality in in this + + + align:start position:0% +So that's the duality in in this +example. I I could + + align:start position:0% +example. I I could + + + align:start position:0% +example. I I could +uh yeah maybe I'll since since time's + + align:start position:0% +uh yeah maybe I'll since since time's + + + align:start position:0% +uh yeah maybe I'll since since time's +really up on this + + align:start position:0% +really up on this + + + align:start position:0% +really up on this +lecture I don't know whether to describe + + align:start position:0% +lecture I don't know whether to describe + + + align:start position:0% +lecture I don't know whether to describe +maybe I'll start by des maybe I'll just + + align:start position:0% +maybe I'll start by des maybe I'll just + + + align:start position:0% +maybe I'll start by des maybe I'll just +quickly describe how does the simplex + + align:start position:0% +quickly describe how does the simplex + + + align:start position:0% +quickly describe how does the simplex +method operate. Yeah because I already + + align:start position:0% +method operate. Yeah because I already + + + align:start position:0% +method operate. Yeah because I already +have in words. So let me just repeat + + align:start position:0% +have in words. So let me just repeat + + + align:start position:0% +have in words. So let me just repeat +those words. How does the simplex method + + align:start position:0% +those words. How does the simplex method + + + align:start position:0% +those words. How does the simplex method +work? Okay, we're at a corner. + + align:start position:0% + + + + align:start position:0% + +Okay, now you might + + align:start position:0% +Okay, now you might + + + align:start position:0% +Okay, now you might +think it's natural to think, okay, I'm + + align:start position:0% +think it's natural to think, okay, I'm + + + align:start position:0% +think it's natural to think, okay, I'm +going to travel to another corner and + + align:start position:0% +going to travel to another corner and + + + align:start position:0% +going to travel to another corner and +I've got two edges to choose + + align:start position:0% +I've got two edges to choose + + + align:start position:0% +I've got two edges to choose +from. And you might think, okay, the + + align:start position:0% +from. And you might think, okay, the + + + align:start position:0% +from. And you might think, okay, the +natural thing is figure out the other + + align:start position:0% +natural thing is figure out the other + + + align:start position:0% +natural thing is figure out the other +corners, their costs, and choose the + + align:start position:0% +corners, their costs, and choose the + + + align:start position:0% +corners, their costs, and choose the +lowest. That sounds totally reasonable, + + align:start position:0% +lowest. That sounds totally reasonable, + + + align:start position:0% +lowest. That sounds totally reasonable, +but it takes time. to figure out where + + align:start position:0% +but it takes time. to figure out where + + + align:start position:0% +but it takes time. to figure out where +this corner is means solving a system of + + align:start position:0% +this corner is means solving a system of + + + align:start position:0% +this corner is means solving a system of +equations. So the simplex method doesn't + + align:start position:0% +equations. So the simplex method doesn't + + + align:start position:0% +equations. So the simplex method doesn't +do that. It computes the sort of + + align:start position:0% +do that. It computes the sort of + + + align:start position:0% +do that. It computes the sort of +steepness of the + + align:start position:0% +steepness of the + + + align:start position:0% +steepness of the +descent. If I if we let the if we let + + align:start position:0% +descent. If I if we let the if we let + + + align:start position:0% +descent. If I if we let the if we let +the grad student in to work for an hour, + + align:start position:0% +the grad student in to work for an hour, + + + align:start position:0% +the grad student in to work for an hour, +how much will that reduce the cost? If + + align:start position:0% +how much will that reduce the cost? If + + + align:start position:0% +how much will that reduce the cost? If +we let the computer in to work for an + + align:start position:0% +we let the computer in to work for an + + + align:start position:0% +we let the computer in to work for an +hour, how much will that reduce the + + align:start position:0% +hour, how much will that reduce the + + + align:start position:0% +hour, how much will that reduce the +cost? We're we're figuring out the not + + align:start position:0% +cost? We're we're figuring out the not + + + align:start position:0% +cost? We're we're figuring out the not +knowing the length of the edge cuz we + + align:start position:0% +knowing the length of the edge cuz we + + + align:start position:0% +knowing the length of the edge cuz we +don't know where the next corner is. + + align:start position:0% +don't know where the next corner is. + + + align:start position:0% +don't know where the next corner is. +We're figuring out we're doing local + + align:start position:0% +We're figuring out we're doing local + + + align:start position:0% +We're figuring out we're doing local +problem around this corner. We're + + align:start position:0% +problem around this corner. We're + + + align:start position:0% +problem around this corner. We're +looking for the steepest descent. That's + + align:start position:0% +looking for the steepest descent. That's + + + align:start position:0% +looking for the steepest descent. That's +that's the steepest descent is the first + + align:start position:0% +that's the steepest descent is the first + + + align:start position:0% +that's the steepest descent is the first +idea in in + + align:start position:0% +idea in in + + + align:start position:0% +idea in in +minimization. Go + + align:start position:0% +minimization. Go + + + align:start position:0% +minimization. Go +downhill. Go downhill as steeply as + + align:start position:0% +downhill. Go downhill as steeply as + + + align:start position:0% +downhill. Go downhill as steeply as +possible. Now it can happen and it + + align:start position:0% +possible. Now it can happen and it + + + align:start position:0% +possible. Now it can happen and it +actually does here that that the + + align:start position:0% +actually does here that that the + + + align:start position:0% +actually does here that that the +steepest descent is actually along this + + align:start position:0% +steepest descent is actually along this + + + align:start position:0% +steepest descent is actually along this +edge but the edge so then you say okay + + align:start position:0% +edge but the edge so then you say okay + + + align:start position:0% +edge but the edge so then you say okay +I'll take that edge so that's the + + align:start position:0% +I'll take that edge so that's the + + + align:start position:0% +I'll take that edge so that's the +decision which the which the simplex + + align:start position:0% +decision which the which the simplex + + + align:start position:0% +decision which the which the simplex +method makes which way is + + align:start position:0% +method makes which way is + + + align:start position:0% +method makes which way is +steepest once it's that tells us which + + align:start position:0% +steepest once it's that tells us which + + + align:start position:0% +steepest once it's that tells us which +corner it's which that tells us which + + align:start position:0% +corner it's which that tells us which + + + align:start position:0% +corner it's which that tells us which +new guy is coming into the picture then + + align:start position:0% +new guy is coming into the picture then + + + align:start position:0% +new guy is coming into the picture then +It solves the system ax= b to find out + + align:start position:0% +It solves the system ax= b to find out + + + align:start position:0% +It solves the system ax= b to find out +where that corner is and it has and and + + align:start position:0% +where that corner is and it has and and + + + align:start position:0% +where that corner is and it has and and +somebody it's because it's a corner + + align:start position:0% +somebody it's because it's a corner + + + align:start position:0% +somebody it's because it's a corner +somebody has to stop working. Okay. So + + align:start position:0% +somebody has to stop working. Okay. So + + + align:start position:0% +somebody has to stop working. Okay. So +it travels along there. So there I've + + align:start position:0% +it travels along there. So there I've + + + align:start position:0% +it travels along there. So there I've +described the simplex method without + + align:start position:0% +described the simplex method without + + + align:start position:0% +described the simplex method without +giving you the algebra of how it does it + + align:start position:0% +giving you the algebra of how it does it + + + align:start position:0% +giving you the algebra of how it does it +but we're talking linear equations here. + + align:start position:0% +but we're talking linear equations here. + + + align:start position:0% +but we're talking linear equations here. +It it it's at a it's at a corner. It's + + align:start position:0% +It it it's at a it's at a corner. It's + + + align:start position:0% +It it it's at a it's at a corner. It's +wondering, okay, who which X shall I let + + align:start position:0% +wondering, okay, who which X shall I let + + + align:start position:0% +wondering, okay, who which X shall I let +in? Which shall be the entering + + align:start position:0% +in? Which shall be the entering + + + align:start position:0% +in? Which shall be the entering +variable? Okay, so it it says I've got a + + align:start position:0% +variable? Okay, so it it says I've got a + + + align:start position:0% +variable? Okay, so it it says I've got a +choice of edges and in each along each + + align:start position:0% +choice of edges and in each along each + + + align:start position:0% +choice of edges and in each along each +edge, it can figure out + + align:start position:0% +edge, it can figure out + + + align:start position:0% +edge, it can figure out +locally what + + align:start position:0% +locally what + + + align:start position:0% +locally what +the reduction in cost would be if we let + + align:start position:0% +the reduction in cost would be if we let + + + align:start position:0% +the reduction in cost would be if we let +these in, say, for unit + + align:start position:0% + + + + align:start position:0% + +amount. and then it chooses the one that + + align:start position:0% +amount. and then it chooses the one that + + + align:start position:0% +amount. and then it chooses the one that +looks the best, the steepest. But just + + align:start position:0% +looks the best, the steepest. But just + + + align:start position:0% +looks the best, the steepest. But just +as in steepest + + align:start position:0% +as in steepest + + + align:start position:0% +as in steepest +ascent, that doesn't mean it's going to + + align:start position:0% +ascent, that doesn't mean it's going to + + + align:start position:0% +ascent, that doesn't mean it's going to +hit the winner, cuz this one could be + + align:start position:0% +hit the winner, cuz this one could be + + + align:start position:0% +hit the winner, cuz this one could be +steepest but shorter. And and and it + + align:start position:0% +steepest but shorter. And and and it + + + align:start position:0% +steepest but shorter. And and and it +very likely is that the it doesn't mean + + align:start position:0% +very likely is that the it doesn't mean + + + align:start position:0% +very likely is that the it doesn't mean +the steepest one is probably not the + + align:start position:0% +the steepest one is probably not the + + + align:start position:0% +the steepest one is probably not the +right one, but it's downhill anyway. So + + align:start position:0% +right one, but it's downhill anyway. So + + + align:start position:0% +right one, but it's downhill anyway. So +you go downhill to this point, and then + + align:start position:0% +you go downhill to this point, and then + + + align:start position:0% +you go downhill to this point, and then +again, you apply the simplex method. You + + align:start position:0% +again, you apply the simplex method. You + + + align:start position:0% +again, you apply the simplex method. You +look around here. Well, this way it's + + align:start position:0% +look around here. Well, this way it's + + + align:start position:0% +look around here. Well, this way it's +descending. This way it's not even + + align:start position:0% +descending. This way it's not even + + + align:start position:0% +descending. This way it's not even +descending. So, of course, the steepest + + align:start position:0% +descending. So, of course, the steepest + + + align:start position:0% +descending. So, of course, the steepest +is this way. Travel along here. So, the + + align:start position:0% +is this way. Travel along here. So, the + + + align:start position:0% +is this way. Travel along here. So, the +cost is at every every simplex step + + align:start position:0% +cost is at every every simplex step + + + align:start position:0% +cost is at every every simplex step +you've got you've got linear equations + + align:start position:0% +you've got you've got linear equations + + + align:start position:0% +you've got you've got linear equations +to + + align:start position:0% +to + + + align:start position:0% +to +solve. That's so that's why you the cost + + align:start position:0% +solve. That's so that's why you the cost + + + align:start position:0% +solve. That's so that's why you the cost +depends on the number of equations and + + align:start position:0% +depends on the number of equations and + + + align:start position:0% +depends on the number of equations and +then it depends on the number of steps + + align:start position:0% +then it depends on the number of steps + + + align:start position:0% +then it depends on the number of steps +you take. And the point is that then of + + align:start position:0% +you take. And the point is that then of + + + align:start position:0% +you take. And the point is that then of +course this cost per the cost here which + + align:start position:0% +course this cost per the cost here which + + + align:start position:0% +course this cost per the cost here which +is significant is still polomial right + + align:start position:0% +is significant is still polomial right + + + align:start position:0% +is significant is still polomial right +we have only n m equations here so but + + align:start position:0% +we have only n m equations here so but + + + align:start position:0% +we have only n m equations here so but +that's the in reality that's significant + + align:start position:0% +that's the in reality that's significant + + + align:start position:0% +that's the in reality that's significant +part of the cost is solving those + + align:start position:0% +part of the cost is solving those + + + align:start position:0% +part of the cost is solving those +equations and then how many steps it + + align:start position:0% +equations and then how many steps it + + + align:start position:0% +equations and then how many steps it +takes can be exponentially large but in + + align:start position:0% +takes can be exponentially large but in + + + align:start position:0% +takes can be exponentially large but in +reality is not. So there's the simplex + + align:start position:0% +reality is not. So there's the simplex + + + align:start position:0% +reality is not. So there's the simplex +method for linear programming and there + + align:start position:0% +method for linear programming and there + + + align:start position:0% +method for linear programming and there +so that's the practical side and the the + + align:start position:0% +so that's the practical side and the the + + + align:start position:0% +so that's the practical side and the the +basic side tells us the winner's a + + align:start position:0% +basic side tells us the winner's a + + + align:start position:0% +basic side tells us the winner's a +corner and at the winning corner the + + align:start position:0% +corner and at the winning corner the + + + align:start position:0% +corner and at the winning corner the +uh the max equals the min. + + align:start position:0% + + + + align:start position:0% + +That's that's sort of my uh shot at + + align:start position:0% +That's that's sort of my uh shot at + + + align:start position:0% +That's that's sort of my uh shot at +linear programming here. And what what's + + align:start position:0% +linear programming here. And what what's + + + align:start position:0% +linear programming here. And what what's +to be remembered? Well, first of all, + + align:start position:0% +to be remembered? Well, first of all, + + + align:start position:0% +to be remembered? Well, first of all, +it's it's u described more fully in the + + align:start position:0% +it's it's u described more fully in the + + + align:start position:0% +it's it's u described more fully in the +applied math book. + + align:start position:0% +applied math book. + + + align:start position:0% +applied math book. +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +Um so you could look there for uh + + align:start position:0% +Um so you could look there for uh + + + align:start position:0% +Um so you could look there for uh +details of the method and some more + + align:start position:0% +details of the method and some more + + + align:start position:0% +details of the method and some more +mention of the excitement which came + + align:start position:0% +mention of the excitement which came + + + align:start position:0% +mention of the excitement which came +with Carmarker's ideas. I can remember + + align:start position:0% +with Carmarker's ideas. I can remember + + + align:start position:0% +with Carmarker's ideas. I can remember +going to a meeting in Boston standing + + align:start position:0% +going to a meeting in Boston standing + + + align:start position:0% +going to a meeting in Boston standing +room only in a Boston hotel when he + + align:start position:0% +room only in a Boston hotel when he + + + align:start position:0% +room only in a Boston hotel when he +first announced his results. Is he an + + align:start position:0% +first announced his results. Is he an + + + align:start position:0% +first announced his results. Is he an +MIT professor? + + align:start position:0% +MIT professor? + + + align:start position:0% +MIT professor? +Uh no. Where was he at that time? And he + + align:start position:0% +Uh no. Where was he at that time? And he + + + align:start position:0% +Uh no. Where was he at that time? And he +he actually did come to visit MIT for a + + align:start position:0% +he actually did come to visit MIT for a + + + align:start position:0% +he actually did come to visit MIT for a +year after that. Uh but his courses were + + align:start position:0% +year after that. Uh but his courses were + + + align:start position:0% +year after that. Uh but his courses were +not successful. Uh he he and so he I'm + + align:start position:0% +not successful. Uh he he and so he I'm + + + align:start position:0% +not successful. Uh he he and so he I'm +sure he wasn't that happy because nobody + + align:start position:0% +sure he wasn't that happy because nobody + + + align:start position:0% +sure he wasn't that happy because nobody +wants to give a class with one person or + + align:start position:0% +wants to give a class with one person or + + + align:start position:0% +wants to give a class with one person or +something. Uh and that's what it + + align:start position:0% +something. Uh and that's what it + + + align:start position:0% +something. Uh and that's what it +happened I think. So then he went to + + align:start position:0% +happened I think. So then he went to + + + align:start position:0% +happened I think. So then he went to +AT&T. So he's been at AT&T quite a + + align:start position:0% +AT&T. So he's been at AT&T quite a + + + align:start position:0% +AT&T. So he's been at AT&T quite a +while. My impression is perhaps he's + + align:start position:0% +while. My impression is perhaps he's + + + align:start position:0% +while. My impression is perhaps he's +he's uh left that was quite a while ago + + align:start position:0% +he's uh left that was quite a while ago + + + align:start position:0% +he's uh left that was quite a while ago +and I think probably he's moved on but + + align:start position:0% +and I think probably he's moved on but + + + align:start position:0% +and I think probably he's moved on but +I'm not 100% sure. Uh but that that was + + align:start position:0% +I'm not 100% sure. Uh but that that was + + + align:start position:0% +I'm not 100% sure. Uh but that that was +at the time where the question was could + + align:start position:0% +at the time where the question was could + + + align:start position:0% +at the time where the question was could +you patent this? I mean you know this + + align:start position:0% +you patent this? I mean you know this + + + align:start position:0% +you patent this? I mean you know this +meeting in the Boston hotel was all the + + align:start position:0% +meeting in the Boston hotel was all the + + + align:start position:0% +meeting in the Boston hotel was all the +newspapers were all there and + + align:start position:0% +newspapers were all there and + + + align:start position:0% +newspapers were all there and +everything. It was big news and uh that + + align:start position:0% +everything. It was big news and uh that + + + align:start position:0% +everything. It was big news and uh that +was at the time first time + + align:start position:0% +was at the time first time + + + align:start position:0% +was at the time first time +when I think he did patent it by of + + align:start position:0% +when I think he did patent it by of + + + align:start position:0% +when I think he did patent it by of +course patent you can't patent an + + align:start position:0% +course patent you can't patent an + + + align:start position:0% +course patent you can't patent an +algorithm which is what the simplex + + align:start position:0% +algorithm which is what the simplex + + + align:start position:0% +algorithm which is what the simplex +method is but somehow the lawyers + + align:start position:0% +method is but somehow the lawyers + + + align:start position:0% +method is but somehow the lawyers +created a way you could patent the mach + + align:start position:0% +created a way you could patent the mach + + + align:start position:0% +created a way you could patent the mach +the apparatus which would execute the + + align:start position:0% +the apparatus which would execute the + + + align:start position:0% +the apparatus which would execute the +algorithm which was of course just a + + align:start position:0% +algorithm which was of course just a + + + align:start position:0% +algorithm which was of course just a +computer but + + align:start position:0% +computer but + + + align:start position:0% +computer but +um it now it's a standard thing that + + align:start position:0% +um it now it's a standard thing that + + + align:start position:0% +um it now it's a standard thing that +stuff gets patented and this set that + + align:start position:0% +stuff gets patented and this set that + + + align:start position:0% +stuff gets patented and this set that +precedent. Uh I don't know about the + + align:start position:0% +precedent. Uh I don't know about the + + + align:start position:0% +precedent. Uh I don't know about the +things here at the lab. Uh but in + + align:start position:0% +things here at the lab. Uh but in + + + align:start position:0% +things here at the lab. Uh but in +engineer math guys don't we're not + + align:start position:0% +engineer math guys don't we're not + + + align:start position:0% +engineer math guys don't we're not +business enough to do it but uh all my + + align:start position:0% +business enough to do it but uh all my + + + align:start position:0% +business enough to do it but uh all my +friends in the wavelet world um patent + + align:start position:0% +friends in the wavelet world um patent + + + align:start position:0% +friends in the wavelet world um patent +algorithms. I mean the companies + + align:start position:0% +algorithms. I mean the companies + + + align:start position:0% +algorithms. I mean the companies +involved patent those ideas uh and uh + + align:start position:0% +involved patent those ideas uh and uh + + + align:start position:0% +involved patent those ideas uh and uh +and uh it's now an established part of + + align:start position:0% +and uh it's now an established part of + + + align:start position:0% +and uh it's now an established part of +life. Well, I'll pick up again at 3:30 + + align:start position:0% +life. Well, I'll pick up again at 3:30 + + + align:start position:0% +life. Well, I'll pick up again at 3:30 +if you like. Okay, good. Thanks. \ No newline at end of file diff --git a/pQ10vZKnttA.txt b/pQ10vZKnttA.txt new file mode 100644 index 0000000000000000000000000000000000000000..a6f847769e8a63c03b5e3d5e2756ead779bd293f --- /dev/null +++ b/pQ10vZKnttA.txt @@ -0,0 +1,3504 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: So, good afternoon. + +Our subject for all of today +and some part of Monday + +is coherence in +free-level systems. + +And what I want to +show you are there + +are certain fundamentally +new and, to some extent, + +surprising processes +which are possible when + +you have three levels +and not only two. + +Because when you +have three levels, + +you have one excited +state which is + +coupled to two ground states. + +And that gives us the +possibility of interference. + +And actually, all +the special things + +I will tell you about +three-level system + +are related to interference. + +Certain phenomena will +constructively interfere. + +Other will +destructively interfere. + +And that leads to a number +of important effects. + +The first effect you +want to talk about + +is the possibility +of dark states, + +that there are +superposition states which + +are bombarded with two laser +beams, and they're not excited. + +Because the amplitudes to go to +the excited state destructively + +interfere. + +When you have a +state which is dark, + +which cannot absorb the light, +then you already understand + +the possibility of doing +lasing without inversion. + +Because if a lot of the +population is in a dark state, + +you don't have to invert +excited and ground state. + +Because the dark +state doesn't count. + +Lasing without inversion is +a little bit more intricate + +than this, but just +kind of the idea, + +the notion of a dark +state helps you already + +to anticipate why something +like lasing with inversion + +may be possible. + +The dark state is only dark +in a very narrow frequency + +interval of the two lasers. + +So if you're a very +narrow resonance, + +then you have a very +narrow resonance + +where something goes dark. + +But if something goes +dark, it's not absorbing. + +And therefore you have +electromagnetically + +induced transparency, which +is a very, very sharp feature + +in frequency space. + +And when you have very, very +sharp features in frequency, + +you can change the +group velocity of light, + +because if transmission and +absorption index of refraction + +changes a functional +frequency very, + +very sharply, you have huge +effects on propagation lights. + +So kind of all of these +different subjects which + +I want to go through are +different perspectives, + +but you will find +similar physics. + +It's just we look +at interference. + +We look at dark states +in various ways. + +And each of them has +created a cottage industry + +and a subfield of itself. + +So I started to +remind you that you're + +very familiar with the dark +state in the situation where + +we have optical pumping. + +If you have two ground +states in an excited state, + +and you switch only one +laser, sooner or later you + +will just pump all the +atoms into the state f + +and the state f is +dark, and vice versa. + +So what I want to show you now +is that even if both lasers are + +on, then no matter in what kind +of state or superposition state + +you have the atoms, +the atoms see + +light, which is +ready to excite them. + +But there is-- and this is +what I want to show you now-- + +a coherent superposition state, +which is still the dark state. + +So the last thing I did on +Monday, I wrote down for you + +our Hamiltonian, +which is nothing + +else in the well-known dipole +Hamiltonian in the rotating + +wave approximation. + +And what is important now +is that we have pathways + +with Rabi frequency +omega 1 and omega 2. + +And we have one laser fields. + +The photons are +created, annihilated + +by the a operator, and +the second laser field, + +where the operator +is C and C dega. + +So there are two ways how +we go to the excited state. + +We can couple from the ground +state f to the excited state + +and from the ground state +to g to the excited state. + +So when you shine +on the light, atoms + +may be in some initial state. + +They will sort of spontaneously +emit but scatter light. + +But then after some +transient, the state + +which is stable against further +illumination, is a dark state. + +That's like optical pumping. + +So you will optically pump +into the following state, + +which I write down for you. + +And then we can inspect that +indeed it is a dark state. + +It is a coherent superposition +of the two ground states. + +And the coefficient +involves the Rabi frequency, + +omega 2 of laser 2, +omega 1 of laser 1. + +And we just normalize it by +taking the quadrature some + +of the two Rabi frequencies. + +So this state is +indeed a dark state. + +So let me show that +to you by looking + +what happens when we +expose it to this operator. + +This operator v +in the Hamiltonian + +is the operator which couples +the atoms to light, which + +couples the atom to +the excited state + +and this causes +spontaneous emission. + +So what I want to show +you that is a dark state, + +since if you take this operator, +apply it to the dark state + +and ask, is there +any possibility + +how you can excite, how you can +excite to the excited state? + +And the answer is, +it will be zero. + +The dark state has a +component on-- the dark state + +has one component in f, and +it has one component in g. + +How did I want to do that? + +Sometimes it's easier +to say it in words + +than to write down +a long equation. + +The light atom interaction +couples the component + +of the ground state +to the excited state + +with Rabi frequency omega 1 +and the state f with omega 2. + +However, in the construction +of the dark state, + +I've made sure that the +amplitude of the component g + +is omega 2. + +So therefore when we +apply this operator, + +we have omega 1 from the +operator and omega 2 here. + +And here we also get +omega 1 and omega 2. + +And this minus sign means +the two effects cancel. + +So therefore, I've +shown you that even + +though in its full frame with +second quantization, photon + +operators and all this, +this coupling is identically + +0 and therefore we +have a dark state. + +So this phenomenon of +having a dark state + +and populating the dark +state by light scattering, + +you have spontaneous +emission into the dark state + +until the scattering light +staggering stops and no matter + +what the initial +state of the atom + +bar where the dark state +is now 100% populated. + +This is called coherent +population trapping. + +Let me mention that +this coherent population + +trapping can be some good +thing if you want to pump atoms + +into a certain state and then +they stop scattering light. + +They're not heated up anymore. + +But sometimes you want the +atoms to scatter light. + +For instance, in current +laser cooling experiments + +with molecules, +there is a problem + +that the multiplicity of the +angular momentum states, which + +are suitable for laser +cooling in molecules + +is such that you always +have a dark state. + +So if you irradiate the +atoms with laser light, + +they will not be on +a cycling transition. + +The cycling +transition will stop. + +So you have to play +additional tricks. + +One is to apply a +transverse magnetic field + +that the axis of the laser and +the quantization axis given + +by the magnetic field are +in two different directions. + +And then once the atom is +pumped into a dark state, + +it will actually precess, Zeeman +precess out of the dark state. + +Or magneto-optical +traps for molecules + +use a magnetic field gradient, +which is rapidly switched, + +because when you are +in a dark state for one + +value of the magnetic field, you +just change the sign quickly. + +And then the atoms are no +longer in the dark state + +for the new situation +you've created. + +So in other words, to have +these wonderful dark state, + +which is a major +intellectual accomplishment + +and eventually was exploited +in many experiments, + +for a number of experiments +it's a real nuisance. + +And you have to +find ways around it + +to make sure that the atoms are +not stopping scattering light + +and don't stop scattering light. + +I gave you the simple +example that the dark state + +exists for resonant excitation. + +But as you can immediately +show, the dark state + +also exists for +detuning of resonance. + +The only thing which is +important as long as the two + +lasers fulfill the two +photon resonance condition. + +So you want the difference +between the two lasers + +is the energy difference +between the two states. + +Also remember if you +have two lasers which + +are very different in power-- so +let's say one Rabi frequency is + +much smaller than the other one. + +So then the dark state, +the superposition + +which is the dark +state, the dark state + +is now predominantly which one? + +The state with the +stronger coupling + +or with the weaker coupling? + +Well, it's the state +with the weaker coupling. + +The dark state has +always a larger amplitude + +in the state for which +the coupling is weaker. + +And that of course +immediately makes a connection + +to optical pumping. + +For instance, if omega 1 +the Rabi frequency is 0, + +then the dark state +is what we started out + +with a trivial +example, is a state g. + +So you see that actually +what I taught you + +about coherent +population trapping + +is nothing else than +extension of the concept + +of optical pumping. + +OK, so we've talked +about the dark state + +as a superposition +of state g and f. + +But if you have a +two-dimensional Hilbert + +space given by two +ground states g and f, + +we can now find a new basis. + +We have defined the dark state. + +But now we can get +the orthogonal state, + +which is the bright state. + +It has a plus sign here and it +has the omega 1 and omega 2, + +the Rabi frequencies reversed. + +So this state is now orthogonal. + +And you can now visualize the +preparation of the dark state + +as follows. + +We have the dark state. + +We have the bright state. + +The bright state, as you +can immediately verify, + +is strongly coupled by the laser +field to the excited state. + +So we have an excited state. + +The laser fields-- well, its +two laser fields strongly + +couple the bright state +to the excited state. + +And then spontaneous emission-- +two photon lights scattering-- + +can take you back to +either of the two states. + +But now you see that the +concept of optical pumping, + +which I started out +with a trivial example, + +is now applying in the +new basis to the bright + +and to the dark state. + +And what happens is you +would, by optical pumping, + +populate the dark state +and completely pump out + +the bright state. + +Just as a side remark, there +are lots of subtleties. + +Most of them you will +probably see by yourself + +by just inspecting the results. + +But if you may +ask yourself, what + +happens when the +Raman resonance is not + +made, when the difference +between the two lasers + +is not exactly the +difference between the two? + +Well, then what you have +is you have a superposition + +of ground and excited state. + +So we have the two +ground states g and f. + +But the two laser +fields have a phase + +which evolves different from +the phase between g and f. + +And suddenly, what you +have is relative-- I mean, + +everything is relative to +the laser field, so to speak. + +This plus sign turns +into a minus sign. + +So therefore, if you have +pumped into the dark state, + +but now the frequency +difference of the two lasers + +is slightly different from the +frequency difference between g + +and f, this mean in +essence that as time + +goes by, with the frequency, +with the detuning away + +from the two photon resonance, +the dark state will now + +precess into the bright state. + +And it is only for +the Raman resonance, + +when it is exactly met, that you +have a long-lived dark state, + +a dark state which is a 2 +eigenstate of this Hamiltonian. + +Yes? + +AUDIENCE: Would +the precession also + +change omega 1 into omega 2? + +PROFESSOR: No, we have +defined omega 1 and omega 2 + +as the Rabi frequencies +of the two lasers. + +Omega 1 is a Rabi frequency +of the laser which + +talks to, I think, the state g. + +And omega two is +the Rabi frequency + +of the laser which +talks to the state f. + +So this doesn't change. + +I'm just sort of telling you how +you may want to think about it, + +that if you put in all of +the temporal phase factors, + +on resonance, at least in +some dressed atom picture, + +all the phase factors are 0. + +Because the e to the i omega +t of the atomic wave function + +is compensated by the +light atom coupling. + +And therefore phase +factors just disappear, + +and the state is stationary. + +But if you write down what +happens as a function of time + +to the state, and you couple +it as a function of time + +to the laser field, +you will find out + +that there is an +evolving relative phase + +between the light field +and the atomic state. + +And the essence of that +is that with these, there + +will be a beat node at which +the dark state becomes bright + +and the bright +state becomes dark. + +OK. + +One important application +of the dark state + +is the STIRAP technique. + +STIRAP is adiabetic +population transfer. + +So STIRAP stands for +stimulated-- what is the r? + +Stimulated Rapid +Adiabetic Passage? + +AUDIENCE: I've seen +both rapid and Raman. + +PROFESSOR: So we +have two choices. + +It's both Raman and rapid. + +A is adiabetic, p is passage. + +And STI is stimulated, +because it's + +a coherent stimulated process. + +The idea is the following. + +With this concept +of a dark state, + +I can immediately +explain to you how, + +by changing the intensities +of the laser beams, + +you can make an adiabetic +transfer from one state + +g to the other state f. + +And this is important because +in many atomic physics + +experiments, you +start with one state + +and then you want to +prepare another state. + +You always have the option of +having some suitable pi pulse + +and going from one +state to the next. + +But the pi pulse has +to be exactly pi. + +You have to be careful +what the intensity + +and duration of your pulse is. + +But if you can adiabetically +go from one stage + +to the other one, +this is terribly + +robust against pretty +much everything. + +And I want to now use the +concept of the dark state + +to tell you how this +population transfer works. + +But before I even get +into any explanation, + +the picture is the following. + +The dark state-- if you +change laser parameters, + +you can change which +state is the dark state. + +I gave you the simple example +if one laser beam is on, + +the state g is the dark state. + +If the other laser beam is on, +the state f is the dark state. + +So if you switch one laser +beam off and the other one on, + +you've changed the +definition of the dark state. + +And as I want to show you is the +dark state, if we can set it up + +in the situation that the dark +state is the absolute ground + +state of the system, and you +know when you change parameters + +of your Hamiltonian, +adiabeticity + +tells you that you always +stay in the ground state. + +See now, even +without any equations + +you understand what adiabetic +population transfer is. + +But let's work it out. + +So we want to understand-- and +this is our adiabetic process-- + +what happens when the laser +parameters, omega 1 and omega + +2, change slowly. + +So for pedagogical +reasons, I will + +drop all the assumptions +I'm making now, + +but let me make them. + +So let's discuss +degenerate states first. + +So g and f are degenerate. + +And let me also discuss +blue-detuned light. + +And you will see +in a moment why. + +So that would mean that-- and +let's set up the situation. + +We have the state g, f, and e. + +We have a green laser beam +and an orange laser beam. + +And we know already, from +what we have just learned, + +that this should be +transformed into-- + +and let me just be +more specific here. + +I said I want to use +blue-detuned light. + +So now we do what +we just learned. + +We express things as the dark +state and the bright state. + +And here we have +the excited state. + +And the beauty of degeneracy +is that dark state + +and bright state are +superposition states, + +but since they're +superposition states + +of two states with +the same energy, + +I can draw them without +twisting my hand + +or doing sort of a double line. + +Anyway, but now what +happens is the following. + +The bright state is +coupled to the excited + +state by the two laser fields. + +And the question is, +what is the energy + +of the bright state +relative to the dark state? + +Well, if I have a +blue-detuned laser beam, + +I get an ac-Stark shift, +which increases the energy. + +So therefore, the state +which sees the light, which + +scatters photon-- +scattering photon + +means there is an +excited state admixture. + +An excited state admixture means +there's an ac-Stark effect. + +And the ac-Stark +effect is positive. + +So therefore, the dark state +is-- the uncoupled state + +is the lowest state in +the ground state manifold. + +And even if you would +not generalize it + +to multiple levels and all that, +if there is one dark state, + +it's not upshifted by +the ac-Stark effect. + +Whereas every state +which sees the light + +is upshifted by +the ac-Stark effect + +which provides a blue shift. + +So the dark state is the +lowest quantum state. + +So therefore, we can now +use the general concept + +in quantum mechanics of +adiabetic state transfer + +to achieve a perfect 100% +transfer from one ground + +state to the other one by +tailoring as a function of time + +our laser fields as follows. + +We start out in a situation +where the only beam which is on + +is-- I want to change that to +orange-- is the orange laser. + +And when the orange laser is +on, then the dark state is g. + +Then we ramp down +the orange laser. + +But we ramp up the green laser. + +And we have the situation +that initially g + +and eventually f +is the dark state. + +So this is a picture behind +the rapid adiabetic passage + +from state g to f. + +I want to point out that the +application of the two laser + +pulse, first orange +and then green + +is called the +counter-intuitive sequence. + +Because if you ask +yourself the problem, + +you're starting out +in state g and you + +want to go over to +state f, which laser + +would you first switch +on if you're in state g? + +Well, if you want to +get out of state g, + +you would say first +the green laser + +to go up and then the +orange laser to go down. + +So what I just said, first +the green and then the orange + +is called the +intuitive sequence. + +But STIRAP works with the +counter-intuitive sequence. + +OK. + +Any questions? + +Yes? + +AUDIENCE: So what's the +intuition we have with this? + +PROFESSOR: Well, I +gave you the intuition. + +I said, you want to +have a dark state. + +The dark state is +the ground state, + +the lowest state +of the manifold. + +So you want to first make sure +that g is the ground state. + +And then you turn +opposite your Hamiltonian, + +and eventually f is +the ground state. + +And this is exactly +the situation. + +f is the ground state +with the green light on. + +I've given you the +intuitive picture. + +Now I will actually +come back to that. + +There is the kind +of-- it's called + +the magic of the +adiabetic state transfer + +that if you always +stay in the dark state, + +if you always stay +in the dark state, + +you never populate +the excited state. + +So it looks like +magic that you can + +go from the ground +state to the final state + +without having ever any +population in the excited + +state. + +And of course, can that be true? + +No, because there is +no coupling direct. + +So somehow in this picture +of adiabetic transfer always + +staying in the dark and never +populating the excited state, + +maybe we have +over-emphasized something. + +We need a little bit +of excited state, + +otherwise we cannot go there, +because our Hamiltonian does + +not allow the direct +path from g to f. + +So a lot of people +think that STIRAP + +is a method where you +can go from g to f + +without going through +the excited state. + +I have many, many +people talking about it. + +So I want to discuss it +in the next few minutes + +and to some extent demystify it. + +But since you're asking me-- now +in a black and white picture, + +STIRAP is the way. + +I'm correcting +myself in a moment, + +but STIRAP is a way +where you can go directly + +without going through +the excited state. + +And this is done by the +counter-intuitive sequence + +where you just want to keep +atoms in the dark state, + +whereas the intuitive sequence +is really based on the fact you + +want to take population here, +put population here and the + +stimulate it down. + +And this is not what +STIRAP is about. + +Other questions? + +Yes? + +AUDIENCE: So if there +is very strong coupling + +to a fourth state from the +excited state, because you need + +to-- the population needs to +travel through the excited + +state in STIRAP, it's possible +to spoil the whole process. + +PROFESSOR: We will +talk about it. + +And actually in the next +minute, I want to sort of simply + +calculate how many photons are +emitted during the passage. + +And if you now say the photons +have a branching ratio, + +this could be a branching +ratio to you fourth state. + +But by just calculating what is +the time integrated population + +in the excited state +multiplied with gamma, + +this is the amount +of photons scattered. + +And you can say if you try to +do a STIRAP with the bosons + +then condensate, every time +you scatter, you heat up, + +you reach momentum states +outside the condensate. + +And those momentum states +are your fourth state. + +So actually, by discussing how +much light scattering happens + +in this transfer, +I will pretty much + +talk indirectly about +how much population + +is going into a fourth state. + +So that's what you want +to understand now-- + +how true is the magic of the +dark state transfer where + +we can go from one +state to the next + +without ever going +through the excited state. + +Yes? + +AUDIENCE: So are the two laser +frequencies the same for that? + +PROFESSOR: Yes. + +I actually assumed that-- I +come to that in a second-- + +that the two states +are degenerate. + +And for all this +dark state busyness, + +we have to fulfill +the Raman resonance. + +So if the two states +are degenerate, + +then the two laser beams. + +AUDIENCE: So then +what's the meaning + +of increasing one of them? + +We are satisfied-- + +PROFESSOR: OK. + +One possibility is that +this is an m equals 0 state. + +This is an m equals +minus 1 state. + +This is m equals plus 1. + +And this is sigma plus. + +And this is sigma +minus radiation. + +So yes, and this +was actually very + +important for the whole +discussion of three level + +coherence that this level can +only talk to the green laser, + +this level can only talk +with the orange laser. + +And we have two ways +to accomplish it. + +One is by frequency difference. + +But if you don't have +a frequency difference, + +we need polarization +selection rules. + +Yes? + +AUDIENCE: It's sort +of a silly question. + +In this particular case, if +I have all my atoms in g, + +can I turn on the green laser? + +Can I optically pump +everything to f? + +Right? + +And so in this +particular case, is there + +an advantage of doing STIRAP +as opposed to optical pumping? + +PROFESSOR: Yes there is, +and we'll talk about that. + +There is a difference between +transferring population or only + +transferring an amplitude. + +And so it depends what you want. + +If all you want is to +get the atoms from g + +to f and you don't care how they +are heated up, so that's OK. + +But the STIRAP process +is a stimulated process, + +so you have momentum k and +here you have the momentum k2. + +So you take the atoms +from an initial state + +and put them in a very +well-defined momentum state. + +So a PEC in one state +after STIRAP transfer + +is in another +state, maybe if you + +have the lasers in a +counter-propagating way + +back to zero momentum. + +Whereas if you do +optical pumping, which + +involves spontaneous +emission, then you always + +have dissipation. + +You create entropy. + +And because spontaneous +emission goes into many modes, + +you have many different recoils, +and eventually your final state + +is no longer a single state. + +It has many different +momentum states involved. + +So that's why we've been talking +here about a coherent transfer, + +sort of assuming +that optical pumping + +with spontaneous emission +and the many modes involved + +is not what you want +because of heating. + +OK, so lots of +interesting questions. + +First, let's now drop all +the assumptions we've made. + +So what happens when we +change from blue detuning + +to red detuning? + +Well, for blue detuning, +we use the argument + +that adiabetically we +stay in the ground state, + +but for red detuning +it's a higher state, + +and we adiabetically +stay in the higher state. + +Same thing. + +What happens if f and +g are not degenerate? + +Well, the argument +is the following. + +It's the same result, and I +can quickly show that to you + +by saying use the +dressed state basis. + +You have the state g with Na +and Nb photons in laser beams. + +Let me be consistent. + +I call the operators +c and Na and Nc. + +And if you now look +at the state f, + +which has one photon less +here and one photon more here, + +those two states are degenerate. + +So I was just +showing the situation + +if g and f are not +degenerate, here + +we have a laser beam +with Na photons. + +Here we have a laser +beam with Nc photons. + +If we include the photons +in our description, + +we have a degeneracy. + +And that's what matters. + +But what is relevant +of course is + +you have this degeneracy +only when the energy + +difference between g and +f is the energy frequency + +difference between +the two laser beams. + +So it is essential, and +you see that again here, + +that the two photon +Raman resonance + +condition has to be made. + +So we've talked all the +assumptions so we know you can, + +in a general system +you can transfer + +between two hyperfine states. + +You can use red or +blue detuned laser. + +Everything is robust. + +OK. + +So STIRAP goes by the +name dark state transfer. + +And what I want +to address now is, + +what is the magic +which is going on? + +How can we transfer +from state g to state f + +without going to +the excited state? + +And the answer is-- +I gave it already + +to you-- it's not possible, +because the only couplings we + +have are the two couplings +which I've shown. + +But-- and this is sort of the +gist you should carry away. + +Since the whole transfer +is a coherent process-- + +and I will be more +exact in a moment-- + +we are not building +up population + +in the excited state. + +We're just building +up a small amplitude. + +And the population is the +small amplitude squared. + +It's, so to speak, +epsilon squared. + +And so you win one +power of epsilon, + +one power of the +small amplitude, + +if you do a coherent +transfer, as compared + +to incoherent +transfer, which relies + +on shuffling over population. + +And I want to show you +now how this pans out. + +Jenny? + +AUDIENCE: But in the limit +of infinitely adiabetic, + +infinitely slow, you still +would have the transfer happen + +without ever going into +the excited state, right? + +PROFESSOR: Well, I will show you +that the integrated population + +in the excited state goes as +one over the transfer time. + +So if you allow an infinite +amount for the transfer, + +you can make the population +[INAUDIBLE] slow. + +But ultimately, what +I also want to show + +you is that how much you +put into the excited state + +depends-- and I think this +is a very satisfying result + +for me-- depends +on your resources. + +It depends on your laser power. + +if you have infinite +laser power, + +you can keep the population +infinitesimally small. + +And if you have infinite time. + +But if you go to the lab and +do an experiment and say, + +I want to be done +in 24 hours, well + +this defines your time budget. + +And the strongest laser +you have in the laboratory + +defines your laser power budget. + +And given those two resources, +there is a small amount. + +And I want to give you +an estimate for that. + +And then we have to discuss, +is that small amount, + +which we get in STIRAP, +does that really + +stand out over other methods +to transfer population? + +And the answer will +be interesting. + +So let me just say, no. + +Excited state is needed +as a stepping stone. + +I want to give you +a quantitative touch + +without doing too much math. + +So let me just write down +Schrodinger's equation. + +We have the three amplitudes, +the three states involved, + +e, g, f. + +Schrodinger's equation gives +us the time derivative. + +c dot f. + +Since we assumed in the +dressed state picture, + +we can assume everything +is degenerate. + +But now we have couplings. + +And the only couplings +are-- and this + +is what I was emphasizing-- +between ground and excited + +state with the Rabi frequency +omega 1 and between the state f + +and the excited state with +Rabi frequency omega 2. + +So the important part +is-- I can write it down, + +but the third equation is +the one I want to focus, + +that you can only build up +population in the final state + +by transferring with +a Rabi frequency omega + +two population from +the excited state. + +So let me just assume +that Rabi frequency omega + +1 equals omega 2 +equals omega Rabi. + +Let's have a symmetric situation +so I can now completely focus + +how can you get from the excited +state to the final state, + +but how you get from +the ground state, + +from the state g to the excited +state is fairly symmetric here. + +OK, so what we want is we want +that at the end of the transfer + +time, t transfer, +the final state + +amplitude is on the order of 1. + +This would be 100% +percent transfer. + +So therefore, just looking +at the differential equation + +above, that means +that this here has + +to be 1 divided by +the transfer time. + +So therefore, we find that +for this adiabetic transfer, + +the excited state +amplitude has to be-- + +and I neglect factors +on the order of 2 + +now-- has to be 1 over the Rabi +frequency times the transfer + +time. + +So the probability to +be in the excited state + +is the amplitude squared. + +And if you are asking, which I +think is a practical question + +and I suggest to use this +as a figure of merit, + +when we discuss how well, how +perfectly we have transferred + +population, we can +now ask, what is + +the probability of +spontaneous emission? + +P spontaneous is the probability +to be in the excited state + +times gamma +integrated over time. + +So what we obtain +for that is yes, + +it's proportionate to gamma. + +But we have the excited +state amplitude squared. + +We've multiplied with +the transfer time. + +So therefore, what we +have in the denominator + +is the laser power +or the Rabi frequency + +squared times the transfer time. + +So therefore, this +probability to go + +to a spontaneous emission, +which is also the integrated + +probability of having +populated the excited state, + +it goes to 0 in the case that +you have infinite laser power + +or that you're +infinitely patient. + +So one question is, how long +can the transfer time be? + +And this is actually +setting an limit to it. + +We're talking about +a coherent transfer. + +So the transfer time +has to be smaller + +than the coherence +time of your system. + +For instance, we do that +all the time in my lab. + +If you go from on sublevel +to another sublevel, + +and we have magnetic field +noise, if the magnetic field + +noise is destroying the phase +relationship between the two + +hyperfine states, then +the coherent transfer + +gets interrupted, and +then eventually we + +are no longer talking +about the amplitude. + +We are talking about population +in the excited state. + +OK, so we have this result, +which at least demystifies what + +many people say-- +actually I've heard + +truly experienced researchers +in the field to say, + +we can do the transfer +without ever populating + +the excited state. + +So the truth is what I +just derived for you. + +But now we want to +compare it to what + +would happen if you use +an incoherent picture. + +If you use an +incoherent picture, + +let's assume we +would use a pi pulse, + +put all the population +in the excited state, + +and then we would +stimulate it down. + +So we have a pi pulse. + +So we build our population. + +And then we use a +second pi pulse. + +Well, we would then have about +unity population in the excited + +state. + +It would emit light +at a rate gamma. + +And it would take the time of +the inverse Rabi frequency, + +the Rabi period, to +stimulate it down. + +Now you can say, what +happens if-- maybe that's + +dumb to have a pi pulse and +put all the population in, take + +a pi over 20 pulse, put a little +bit population in, stimulate it + +down. + +The next batch, the next +batch, the next batch, but you + +get exactly the same result, +because each population which + +you've put into +the excited state + +had to wait for a Rabi +period to be stimulated down. + +So therefore in the +incoherent picture, + +if you sort of transfer +batches of population, + +you realize that the probability +for spontaneous emission + +or for populating a four state +is independent of the transfer + +time, because it cancels out. + +If you do small +pieces of population, + +you have a smaller +rate of emission, + +but you integrate for longer +and the two temporal factors + +cancel out. + +And now you realize that +the coherent transfer + +is more favorable by another +power of omega Rabi times t + +transfer in the denominator. + +So that's why people +prefer STIRAP. + +Questions about that? + +Can you suggest +another method how + +we could transfer population +from one state to the next? + +I gave you two examples. + +One was this magic, or not so +magic, dark state transfer. + +The other one is +a method where we + +put population, stimulated it +down, next batch of population, + +stimulate it down. + +What is another process which we +can do to transfer population? + +AUDIENCE: Landau-Zener? + +PROFESSOR: Pardon? + +AUDIENCE: Landau-Zener? + +PROFESSOR: Landau-Zener? + +Actually, the STIRAP +is a Landau-Zener. + +The dark state is +always the lowest state. + +There is a crossing +sort of in between, + +but it's an avoided crossing. + +Actually, in a way, you +may want to think about it. + +The STIRAP is actually +a Landau-Zener transfer + +between where the lower +state is a dark state, + +the upper state +is a bright state. + +Will? + +AUDIENCE: I still +have a question. + +So Landau-Zener [INAUDIBLE] +But the STIRAP scheme + +is sensitive to the +run-on resonance. + +PROFESSOR: Absolutely it is. + +AUDIENCE: So how robust is +it against small violations + +[INAUDIBLE]? + +PROFESSOR: Well, I gave +you already the hint + +when I discussed that if you +are detuned from the Raman + +resonance, this detuning, +at the detuning frequency + +would be between dark +and bright state. + +So this picture what is +dark and what is bright + +is scrambled up by that. + +So in other words, +as long as you're + +inverse detuning is smaller than +the transfer time, you're OK. + +Because the dark state +is the dark state. + +But if during the transfer +time you turn the dark state + +into a bright state, +you've completely + +messed up the scheme. + +So in other words, I know people +in this hallway, in my group + +want to STIRAP transfer +between molecules. + +And we have to +stabilize our lasers. + +So we have automatically +little bit laser fluctuations. + +But if you do the +transfer in a millisecond, + +it is sufficient to have the +laser frequency under control + +at the kilohertz level. + +So that's a requirement. + +But back to my question. + +We have discussed sort +of an incoherent transfer + +and we've discussed STIRAP. + +Can you suggest +another method how + +you can go from one +count state to the next? + +AUDIENCE: We talked +about optical pumping. + +PROFESSOR: Optical pumping? + +Yes, but optical +pumping means we + +really go with +spontaneous emission. + +And then we have 100% +spontaneous emission. + +So we want a process where +we go from one momentum state + +to another momentum state. + +Well-- + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Yes. + +Optical pumping is a +two-photon process. + +Actually, everything's a +two-photon process here. + +But optical pumping +is actually a process + +where we have a Raman +to photon transition. + +The first leg is stimulated. + +The second one is spontaneous. + +But I would suggest now +what [INAUDIBLE] said, + +let's have a two photon +Raman transition. + +So we want to go from state g +to state f with two photon Raman + +transition. + +Let's assume we have +a detuning delta. + +So now, do you have +any expectations + +whether these-- we +can do a pi pulse. + +Two photon Raman transition is +a two photon Rabi frequency. + +I'll remind you +in a second of it. + +And if you do a +pi pulse in that, + +we have half a Rabi +oscillation, which + +takes us from cg to f and +we have 100% transfer. + +So do you have an +expectation if this Raman + +process how will it turn out +to be in our figure of merit, + +how many photons are +emitted from the excited + +state during the transfer? + +Will it be the same as STIRAP? + +Will it be the same as +in population transfer? + +Will it be something else? + +AUDIENCE: You have to scale. + +PROFESSOR: It will +scale with the detuning, + +but-- OK, what I will do is +actually-- I will in a moment + +say, OK. + +We have a certain laser. + +What I'm going to say? + +We have to compare +apples with apples. + +And here we have the +detuning as a parameter. + +And what I want to +replace is I will-- + +what will replace the +detuning by the time it + +takes to do the pi pulse. + +So the detuning is +determined by the condition + +that we want to do the transfer +in the same time as the STIRAP. + +So this will eliminate +the detuning. + +So we want to use +the same resources. + +Our resources are +time and laser power. + +And we want to use our resources +of time and laser power + +in the same way for the +two photon transition. + +So the question is +what happens to-- what + +is the answer to the question, +how much excited state is + +involved in the two photon Raman +process as compared to STIRAP? + +Do you have an expectation? + +Who of you is doing +STIRAP in the laboratory? + +A few people, yeah. + +Actually, I know that +99-- my observation + +is that 99% of the people +say STIRAP is special + +because it's a dark +state transfer. + +And when I started to confront +famous people in the field + +and say the two photon Raman +process does exactly the same, + +they were completely surprised. + +Anyway I want to show +you in one equation + +that the two photon +Raman process has + +exactly the same integrated +population in the excited + +state, and therefore it is as +good-- the two photon Raman + +process performs exactly as +well as the so-called dark state + +transfer, where you never go +through the excited state. + +And this for me +completely demystifies it, + +because the two +photon Raman process + +has in common with the STIRAP +that everything is coherent. + +And if everything +is coherent, it + +means we are not +building a population. + +We are only building up +amplitude in the excited state. + +So let me just show +you in one equation + +that indeed it works +out in that way. + +It's also a nice way +to quickly recapitulate + +what we learned in +the previous chapter + +about two photon transitions. + +So the two photon Rabi +frequency is nothing else + +than the product of the two +Rabi frequencies divided + +by the detuning. + +And of course as-- if you +use studied larger and larger + +detuning as you said, +everything will slow down. + +But we know that +the transfer time + +will be the inverse of the +two photon Rabi frequency. + +And this is delta +over omega square. + +So therefore, we will eliminate +delta from our equations + +by replacing it by +the time it will + +take to perform a pi pulse +between the two ground states. + +OK, so what is the probability +to be in the excited state? + +Well, we've done the theory +of the ac-Stark effect. + +We have beaten perturbation +theory to death. + +You know the first +order admixture + +is omega Rabi over delta +and the probability + +is omega Rabi squared +over delta squared. + +So therefore, the probability +to spontaneously emit a photon + +is omega Rabi squared over delta +squared times gamma times t + +transfer. + +And this is nothing else than +gamma divided by omega Rabi + +squared times t transfer. + +So if you use a Raman pulse +to transfer the population + +coherently, the +integrated population + +of the excited state, which is a +measure for heating and measure + +for winding up in the +wrong state, emission + +to a false state is inversely +proportional to your laser + +power and inversely +proportional to the time + +you can afford to +do the transfer. + +Exactly the same as for STIRAP. + +And the limit to the +transfer time in both cases + +is set by the coherence time. + +Try to tell people who do +STIRAP that a two photon Raman + +pulse would do exactly +the same as STIRAP, + +at least in populating +the excited state. + +They will be surprised. + +Because here, you explicitly +go through the excited state. + +We don't have a +counter-intuitive sequence. + +We switch on both +lasers simultaneously. + +But I think this for me +illustrates or completely + +demystifies what people have +said about the dark state + +transfer and the STIRAP process. + +Any question? + +Cody? + +AUDIENCE: Why do +people use STIRAP? + +What's the advantage? + +PROFESSOR: Well, why are you +using Landau-Zener sweeps when + +you go from one hyperfine +state to the next, + +and why don't you use a pi +pulse with your f generator, + +because it's more robust. + +AUDIENCE: [INAUDIBLE]. + +As you said [INAUDIBLE]. + +PROFESSOR: But similar, +if you detune-- + +if you detune your-- the +condition is the same. + +If you have your two Raman +laser and you detune them, + +you no longer have +resonant Rabi oscillations. + +You have off-resonant +Rabi oscillations. + +And you will find if you want +to do the transfer in half + +a period, you have to +make sure that you don't + +get one cycle of +the beat node or one + +cycle of the detuning +in your transfer time. + +So the condition for the +frequency stability for the two + +photon Raman and +the STIRAP I think + +are pretty exactly identical. + +So I think it's pretty +much the robustness. + +And you have to decide what +you need and what you want. + +For instance, if you have laser +beam and the laser beam has + +an inhomogeneous profile, +you cannot meet the pi pulse + +condition for the atoms in +the middle and at the edge + +of your laser beam. + +But in STIRAP you just +provide plenty of extra power + +and then everything is robust +against the laser beam profile. + +So there are clearly +advantages like that. + +But all what I point +out is the advantage + +is not the population +of the excited state. + +It's the same. + +Questions? + +OK. + +So this is dark +state and STIRAP. + +Our next topic is lasing +or gain without inversion. + +So in other words, +I want to show you + +what was actually rather +recent accomplishment + +that this common belief that you +need population in the excited + +state, which is larger +in the ground state, + +for optical gain and +lasing is not true. + +Well, it's true for +two level system, + +but it's not true when you +have more than two levels. + +And I discuss it here for the +case of a three-level system. + +And this is really insight which +came as recent as in the '80s. + +One reference is the person +who pioneered a lot of work + +on three-level systems and +provided a lot of insight + +was Steve Harris at Stanford. + +And this was a paper +in the late '80s which + +enunciated the +possibility of having + +lasing without inversion. + +And when you are a +graduate student like me, + +who was educated earlier, +you say, gee whiz. + +That's not what I +learned in class. + +But of course it's +often the small sprint. + +It's the assumption +for two-level system. + +So the secret behind +lasing without inversion + +is that you can have +cancellation of absorption + +by interference. + +In other words, this belief +that you need inversion + +comes that you want that +the stimulated emission is + +stronger than the absorption. + +But if you have a three-level +system, you have to be careful. + +We have interference effect. + +And what I want to show you is +that we can create a situation + +where we have destructive +interference for absorption, + +but we don't have +destructive interference + +for stimulated emission. + +So therefore, we can now +afford to have more population + +in the ground state, because +the absorption out of the ground + +state does not have to be +suppressed by minimizing + +the population in +the ground state. + +We have an interference effect, +which suppresses absorption + +from the ground +state population. + +And therefore, the +ground state population + +can be larger than in +a two-level system. + +I could simply tell you +you can hide population + +in the dark state, +end of discussion, + +and you get the basic idea. + +But the concept of +lasing without inversion + +is richer than that. + +It's connected to the dark +state, but there is more to it. + +So that's why I want to spend +the rest of today's class + +in discussing this concept. + +So I want to discuss it in +the simplest possible scheme. + +So I want to discuss +first the simple system. + +In the end, this +is not the system + +in which it has +been accomplished. + +But I think what you +realize is I draw you + +up a very simple scheme. + +I make all assumptions, +and there is maybe + +no atomic, no suitable atom +where you can realize it. + +But then I will do what I've +done so often in this class. + +I turn around and say, but if +you go to a tri-state basis, + +we can exactly engineer that. + +So in other words, if you +need a certain level scheme + +and you don't get it, you +can just take another level, + +put it there with a strong +laser as a virtual level, + +and you get the level +scheme you want. + +And in a dress +state description, + +you have exactly +the idealized level + +scheme I'm presenting to you. + +So therefore with +that justification, + +let me just try to give +you the simple scheme where + +you can understand +this absorption + +cancellation by interference. + +I mean, later in +the end, we want + +to use lambda systems +with two stable ground + +state, two hyperfine states. + +That's how all the +research is done. + +But now I assume +we have a V system. + +So we have two excited states +and we have one ground state. + +And I want to assume that by +coupling through radiation, + +spontaneous emission, +those excited states + +couple to the same continuum. + +I want to say that this is +an important assumption. + +If you have two states, +hyperfine states, + +n equals plus 1, +n equals minus 1, + +which would emit photons +of different circular + +polarization, no. + +They are not coupling +to the same continuum. + +They would be distinguishable, +and then certain interference + +effects will not happen. + +So eventually, the magic +of quantum interference + +comes if it is absolutely +indistinguishable + +which excited state +has emitted the photon. + +So we have to really be-- +set up something like this. + +So it must be fundamentally +impossible to distinguish + +photons emitted through +one state or the other. + +So we know already if +we treat the system, + +we couple the atoms +to the continuum. + +That means in the +end, that those states + +acquire a certain width. + +And yes, this is a situation +we want to discuss. + +So what we have set +up now is a situation + +where we have, with +these two states, two + +indistinguishable paths +to scatter photons. + +So let's say we take +the ground state + +and we shine laser light on it. + +It's a two photon process. + +A photon goes in, +a photon comes out. + +And we can now go +through excited state 1, + +through excited state out +then a photon comes out + +and eventually we have now the +coupled through this two photon + +process the ground state +to continuum of modes. + +But those two processes +to go through e1 and e2 + +are indistinguishable. + +So I will give you +immediately an expression + +where in perturbation theory, +we are not adding intensities. + +We are adding the +two amplitudes. + +It's like a +double-slit experiment. + +Or in other words, the +situation I want to discuss now + +is the following. + +We have all of the population +in the ground state. + +We have the two excited states. + +And our laser is +tuned in between. + +And now we can scatter light. + +We've talked about really +scattering and such. + +And you know that for an +infinitely heavy atom, + +the emitted radiation is a delta +function at the incident light. + +And you will not +know, you can never + +know which excited state was +involved in the scattering. + +So we assume that +we have excited + +state-- which one +is the lower one? + +I think e1. + +This is e2. + +And our laser beam is detuned. + +We have a detuning of delta +1 and delta 2 respectively. + +So now we have to add amplitudes +when we do perturbation theory. + +So in second order +perturbation theory, + +for the light +scattering, if you want + +to derive Fermi's golden rule as +we have done a number of times + +here, you remember, +the critical part-- + +I'm not writing down the whole +expression-- the critical part + +is sort of a product of two +matrix element or two photon + +matrix element which takes +us from the ground state + +through the light atom +coupling to the excited state. + +And then from the excited state +why are the coupling eventually + +back to the ground state, which +is now a continuum of modes. + +And we sum over +all possible modes. + +And what we have here is +the detuning denominator. + +Well, if you want to +do a little bit better, + +I'm just mentioning +here for completeness, + +we want to add the +imaginary part. + +That's more placeholder for a +command I want to make later. + +It's not really essential. + +But the new thing I +want to discuss now + +is that since we have two +excited states and not one, + +we have to sum over +the two excited states, + +and it's a coherent sum. + +So if I detune between-- if +my laser detuning is tuned + +in between, then +delta 1 is positive + +and delta 2 is negative. + +So therefore, we do a sum +here with opposite signs. + +And if I can neglect the +gamma, assuming the gamma + +is small or much smaller +than the detuning, + +then I'm just adding up two +numbers with opposite sign. + +And depending now on the matrix +element, if they're identical + +I get a cancellation if +I'm detuning half between. + +But even if the matrix +element are different, + +I will always find a +detuning where the sum is 0. + +So to the extent that I can +neglect the imaginary part, + +the gamma in the denominator, +I have now this situation + +that this is 0. + +It vanishes for a certain +laser frequency, omega 0, + +tuned between the +levels e1 and e2. + +And what I've assumed here is +that the detunings are larger + +than the decay widths, and +therefore I can neglect that. + +Any questions about that? + +So OK. + +Very trivially, +two excited states + +which are indistinguishable. + +It's the modern +version of Feynman's + +double-slit experiment. + +We add up the amplitudes +and by necessity, we get 0. + +But that sounds so trivial, +but it took a Steve Harris, + +some genius person to +invent it, to realize + +that when we have light at omega +0, it would be absorbed by e1. + +It would be absorbed by e2. + +But it is not absorbed +in the situation + +we have with e1 and e2. + +But now we have to make the +connection that the statement + +that we need inversion +for lasing was related + +to absorption, but now we +have cancelled absorption. + +So now what we want +to do is we want + +to create a situation +where we have lasing. + +We want to put population +into the excited state. + +But the population +in this excited state + +will be much, much smaller than +the population in the ground + +state. + +So you're not even +close to inversion. + +So let me draw the diagram. + +We have lots and lots +and lots and lots + +of population in +the ground state. + +We have 0 population in e1. + +And in e2, we just +have a little bit. + +And now you would say, well, +you don't have inversion. + +How can you get lasing? + +But if we have now a cavity +at frequency omega 0, + +then you can say the Lorentzian +profile of the excited state e2 + +overlaps with omega 0. + +So at least you have some +possibility for the excited + +state e2 to decay +into the cavity mode. + +And therefore, a very weak +field in the cavity mode + +will be amplified by +stimulated emission + +without suffering +any absorption. + +So therefore it will be +amplified and we have gain. + +So if you have a +cavity at omega 0, + +we have gain because we have +some stimulated emission + +at omega 0 but no absorption. + +Of course, if you +would tune your cavity + +to be in a resonance +with e2, you + +would have more +stimulated emission, + +but you would have +much more absorption + +and you would not be able to +get a net gain for a small probe + +field. + +So you would not have lasing. + +So you can say that what +we have achieved here + +in a three-level system, +we have accomplished + +destructive interference +for absorption. + +But the way how we've put +population just in e2, + +we have not any +destructive interference + +for the stimulated gain. + +So we have tweaked on +the lasing equation, + +on the laser equation +the absorption part, + +but not the stimulated +emission part by interference + +in a three-level system. + +So how can this be realized? + +Let me just give you the +first possible realization + +and then I think we should stop. + +We could, in +principle, realize it + +with hydrogen and a +DC electric field. + +Remember, hydrogen has the +1s level, has the 2s level, + +and the 2p state. + +And you all had a nice, little +nice homework assignment + +that when you have a DC field, +you actually couple 2s and 2p. + +And if your DC field is +stronger than the Lamb shift, + +you actually create +a superposition + +of 2s and 2p states. + +And now, if you tune your +laser right in between, + +you have a dark resonance. + +So the situation +is if I would now + +plot the absorption +versus frequency, + +you would find that if you're in +resonance with the upper state + +you absorb, but then +even in between, + +there is this notch where +you have zero absorption. + +So for this simple +case with hydrogen + +in a DC electric field, +the dark resonance + +occurs when you +have equal detuning. + +You have an equal detuning +for the atom with respect + +to the two states. + +And I like to sort of connect +it to classical physics. + +You know that +absorption is related. + +When you absorb, you +have light scattering. + +The photons are +not disappearing. + +They're just scattered +into other modes. + +That's what absorption is about. + +And classically, +light scattering + +comes because you have an +oscillating dipole moment. + +But what happens is if you have +this coherent superposition + +and you're right in between, +you have a positive detuning + +with one harmonic oscillator +and a negative detuning + +with the other +harmonic oscillator. + +So if you drive an harmonic +oscillator-- and this is one + +and this is the other-- +with positive detuning, + +with red detuning, +the dipole moment + +is in phase with +the electric field. + +In the other case, +it's out of phase. + +So now you have the +two excited states + +and you're driving two equal +but opposite dipole moments + +in those two states. + +And therefore, the two +dipole moments add up to 0. + +Therefore the laser, just +using our understanding + +of a simple harmonic +oscillator, is not + +creating any dipole moment. + +Therefore, we're not +scattering any light + +and therefore we're not +absorbing any light. + +So this is how you can now +realize in the hydrogen atom + +using DC magnetic field and +creating this level structure, + +you can create lasing +without inversion. + +But I will tell you +on Wednesday-- no, + +today is Wednesday-- +next Monday, + +next week that we +don't have to deal + +with the difficulties +of hydrogen atoms + +in the laboratory. + +We can just use our +favorite alkalize + +and dress the alkalize +up with laser beams + +and eventually create +the same situation + +with an atom which +is experimentally + +much simpler to address. + +Any questions? + +OK, one more week to go. + +See you on Monday. \ No newline at end of file diff --git a/qE0eHhe6muY.txt b/qE0eHhe6muY.txt new file mode 100644 index 0000000000000000000000000000000000000000..d4f658d74aab983917650fb11ad554dde515ebce --- /dev/null +++ b/qE0eHhe6muY.txt @@ -0,0 +1,251 @@ +align:start position:0% + +let's take a quick look of how to set + + align:start position:0% +let's take a quick look of how to set + + + align:start position:0% +let's take a quick look of how to set +your scanner settings that is to set it + + align:start position:0% +your scanner settings that is to set it + + + align:start position:0% +your scanner settings that is to set it +for a particular DPI so what you do is + + align:start position:0% +for a particular DPI so what you do is + + + align:start position:0% +for a particular DPI so what you do is +you first take a preview at least on my + + align:start position:0% +you first take a preview at least on my + + + align:start position:0% +you first take a preview at least on my +scanner this is the software that I see + + align:start position:0% +scanner this is the software that I see + + + align:start position:0% +scanner this is the software that I see +yours might be different but the idea is + + align:start position:0% +yours might be different but the idea is + + + align:start position:0% +yours might be different but the idea is +the same so we get a preview this is + + align:start position:0% +the same so we get a preview this is + + + align:start position:0% +the same so we get a preview this is +what what my screen looks like and what + + align:start position:0% +what what my screen looks like and what + + + align:start position:0% +what what my screen looks like and what +I decided to do is scan only this + + align:start position:0% +I decided to do is scan only this + + + align:start position:0% +I decided to do is scan only this +particular portion to get final images + + align:start position:0% +particular portion to get final images + + + align:start position:0% +particular portion to get final images +of this particular device so I did that + + align:start position:0% +of this particular device so I did that + + + align:start position:0% +of this particular device so I did that +that's how it looks and when I press + + align:start position:0% +that's how it looks and when I press + + + align:start position:0% +that's how it looks and when I press +scan I am asked whether I want to save + + align:start position:0% +scan I am asked whether I want to save + + + align:start position:0% +scan I am asked whether I want to save +it and I didn't intend to save it at 72 + + align:start position:0% +it and I didn't intend to save it at 72 + + + align:start position:0% +it and I didn't intend to save it at 72 +DPI that's the first scan that I decided + + align:start position:0% +DPI that's the first scan that I decided + + + align:start position:0% +DPI that's the first scan that I decided +to take and then I went through a whole + + align:start position:0% +to take and then I went through a whole + + + align:start position:0% +to take and then I went through a whole +series of various scans and let's look + + align:start position:0% +series of various scans and let's look + + + align:start position:0% +series of various scans and let's look +at them all together the various scans + + align:start position:0% +at them all together the various scans + + + align:start position:0% +at them all together the various scans +were 72 DPI 324 hundred up to 60 400 DPI + + align:start position:0% +were 72 DPI 324 hundred up to 60 400 DPI + + + align:start position:0% +were 72 DPI 324 hundred up to 60 400 DPI +and let's see the difference here it is + + align:start position:0% +and let's see the difference here it is + + + align:start position:0% +and let's see the difference here it is +slightly enlarged sort of trying to keep + + align:start position:0% +slightly enlarged sort of trying to keep + + + align:start position:0% +slightly enlarged sort of trying to keep +the same visuals for you to compare I'm + + align:start position:0% +the same visuals for you to compare I'm + + + align:start position:0% +the same visuals for you to compare I'm +starting to see that the 72 DPI is + + align:start position:0% +starting to see that the 72 DPI is + + + align:start position:0% +starting to see that the 72 DPI is +definitely losing clarity the others + + align:start position:0% +definitely losing clarity the others + + + align:start position:0% +definitely losing clarity the others +look okay and as we increase the images + + align:start position:0% +look okay and as we increase the images + + + align:start position:0% +look okay and as we increase the images +more so we're starting to see this one + + align:start position:0% +more so we're starting to see this one + + + align:start position:0% +more so we're starting to see this one +breaking down and it's starting to + + align:start position:0% +breaking down and it's starting to + + + align:start position:0% +breaking down and it's starting to +really show up as we increase the image + + align:start position:0% +really show up as we increase the image + + + align:start position:0% +really show up as we increase the image +size so you see as you increase the + + align:start position:0% +size so you see as you increase the + + + align:start position:0% +size so you see as you increase the +resolution you get more clarity in the + + align:start position:0% +resolution you get more clarity in the + + + align:start position:0% +resolution you get more clarity in the +image you're getting more information + + align:start position:0% +image you're getting more information + + + align:start position:0% +image you're getting more information +for the most part \ No newline at end of file diff --git a/qK_sOYUyUtQ.txt b/qK_sOYUyUtQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..5abc6883e0c5ff766d03fd5e4f12064a4cda0fe0 --- /dev/null +++ b/qK_sOYUyUtQ.txt @@ -0,0 +1,10667 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT + + align:start position:0% +hundreds of MIT courses visit MIT + + + align:start position:0% +hundreds of MIT courses visit MIT +opencourseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu engine we talk about solar + + align:start position:0% +ocw.mit.edu engine we talk about solar + + + align:start position:0% +ocw.mit.edu engine we talk about solar +sales so in the uh rest of this course + + align:start position:0% +sales so in the uh rest of this course + + + align:start position:0% +sales so in the uh rest of this course +not shifting our attention to solar they + + align:start position:0% +not shifting our attention to solar they + + + align:start position:0% +not shifting our attention to solar they +will combine in solar to this engin and + + align:start position:0% +will combine in solar to this engin and + + + align:start position:0% +will combine in solar to this engin and +particularly solar ther electric and + + align:start position:0% +particularly solar ther electric and + + + align:start position:0% +particularly solar ther electric and +solar + + align:start position:0% +solar + + + align:start position:0% +solar +th and uh uh so the uh here uh what's + + align:start position:0% +th and uh uh so the uh here uh what's + + + align:start position:0% +th and uh uh so the uh here uh what's +important is not a person really have a + + align:start position:0% +important is not a person really have a + + + align:start position:0% +important is not a person really have a +system perspective you find out the + + align:start position:0% +system perspective you find out the + + + align:start position:0% +system perspective you find out the +spectral control is really crucial for + + align:start position:0% +spectral control is really crucial for + + + align:start position:0% +spectral control is really crucial for +the overall system efficiency if you + + align:start position:0% +the overall system efficiency if you + + + align:start position:0% +the overall system efficiency if you +want to achieve + + align:start position:0% +want to achieve + + + align:start position:0% +want to achieve +an so let's review the three modes of e + + align:start position:0% +an so let's review the three modes of e + + + align:start position:0% +an so let's review the three modes of e +this is the first class uh for some + + align:start position:0% +this is the first class uh for some + + + align:start position:0% +this is the first class uh for some +mechanical engineer this is very simple + + align:start position:0% +mechanical engineer this is very simple + + + align:start position:0% +mechanical engineer this is very simple +but you come from other field this + + align:start position:0% +but you come from other field this + + + align:start position:0% +but you come from other field this +probably familiar but see we know there + + align:start position:0% +probably familiar but see we know there + + + align:start position:0% +probably familiar but see we know there +are mod of conduction ration and + + align:start position:0% +are mod of conduction ration and + + + align:start position:0% +are mod of conduction ration and +conduction is by the + + align:start position:0% +conduction is by the + + + align:start position:0% +conduction is by the +conductivity trans rate that's the power + + align:start position:0% +conductivity trans rate that's the power + + + align:start position:0% +conductivity trans rate that's the power +proportion to the r and conver con we + + align:start position:0% +proportion to the r and conver con we + + + align:start position:0% +proportion to the r and conver con we +usually characterize with the + + align:start position:0% +usually characterize with the + + + align:start position:0% +usually characterize with the +coefficient H proportional to the + + align:start position:0% +coefficient H proportional to the + + + align:start position:0% +coefficient H proportional to the +difference between the wall and the + + align:start position:0% +difference between the wall and the + + + align:start position:0% +difference between the wall and the +fluids which is the away from the + + align:start position:0% +fluids which is the away from the + + + align:start position:0% +fluids which is the away from the +surface and ELC con po con and then uh + + align:start position:0% +surface and ELC con po con and then uh + + + align:start position:0% +surface and ELC con po con and then uh +theral radiation we talk about step + + align:start position:0% +theral radiation we talk about step + + + align:start position:0% +theral radiation we talk about step +ement for black body radiation and we + + align:start position:0% +ement for black body radiation and we + + + align:start position:0% +ement for black body radiation and we +calculate the transer ration transer + + align:start position:0% +calculate the transer ration transer + + + align:start position:0% +calculate the transer ration transer +between surfaces in terms of view factor + + align:start position:0% +between surfaces in terms of view factor + + + align:start position:0% +between surfaces in terms of view factor +and + + align:start position:0% +and + + + align:start position:0% +and +invasivity uh which will go more into + + align:start position:0% +invasivity uh which will go more into + + + align:start position:0% +invasivity uh which will go more into +into more detail since we're talking + + align:start position:0% +into more detail since we're talking + + + align:start position:0% +into more detail since we're talking +more now on the uh radiation + + align:start position:0% +more now on the uh radiation + + + align:start position:0% +more now on the uh radiation +part uh so the uh uh thermal radiation + + align:start position:0% +part uh so the uh uh thermal radiation + + + align:start position:0% +part uh so the uh uh thermal radiation +PL slw is usually considered the maximum + + align:start position:0% +PL slw is usually considered the maximum + + + align:start position:0% +PL slw is usually considered the maximum +and uh uh uh we Define the intensity as + + align:start position:0% +and uh uh uh we Define the intensity as + + + align:start position:0% +and uh uh uh we Define the intensity as +the uh Power leaving the surface in + + align:start position:0% +the uh Power leaving the surface in + + + align:start position:0% +the uh Power leaving the surface in +certain direction so that's intensity + + align:start position:0% +certain direction so that's intensity + + + align:start position:0% +certain direction so that's intensity +different from power so this is the + + align:start position:0% +different from power so this is the + + + align:start position:0% +different from power so this is the +power in this direction that will by + + align:start position:0% +power in this direction that will by + + + align:start position:0% +power in this direction that will by +solid angle as power in this direction + + align:start position:0% +solid angle as power in this direction + + + align:start position:0% +solid angle as power in this direction +perit Sol angle per unit area nor the + + align:start position:0% +perit Sol angle per unit area nor the + + + align:start position:0% +perit Sol angle per unit area nor the +directional propagation for un mov so + + align:start position:0% +directional propagation for un mov so + + + align:start position:0% +directional propagation for un mov so +that's the uh intensity so this is what + + align:start position:0% +that's the uh intensity so this is what + + + align:start position:0% +that's the uh intensity so this is what +we mean by intensity uh it's propagating + + align:start position:0% +we mean by intensity uh it's propagating + + + align:start position:0% +we mean by intensity uh it's propagating +in this direction and when we think + + align:start position:0% +in this direction and when we think + + + align:start position:0% +in this direction and when we think +about the uh area this is the area not + + align:start position:0% +about the uh area this is the area not + + + align:start position:0% +about the uh area this is the area not +this area but the area projected into + + align:start position:0% +this area but the area projected into + + + align:start position:0% +this area but the area projected into +direction of propagation so b a + + align:start position:0% +direction of propagation so b a + + + align:start position:0% +direction of propagation so b a +perpendicular has coine when + + align:start position:0% +perpendicular has coine when + + + align:start position:0% +perpendicular has coine when +that and Sol angle is the measure of the + + align:start position:0% +that and Sol angle is the measure of the + + + align:start position:0% +that and Sol angle is the measure of the +angle in space so if you think about 2D + + align:start position:0% +angle in space so if you think about 2D + + + align:start position:0% +angle in space so if you think about 2D +we use a polar angle right and and the + + align:start position:0% +we use a polar angle right and and the + + + align:start position:0% +we use a polar angle right and and the +polar angle is the aride radius or solid + + align:start position:0% +polar angle is the aride radius or solid + + + align:start position:0% +polar angle is the aride radius or solid +angle is the area perpendicular to the + + align:start position:0% +angle is the area perpendicular to the + + + align:start position:0% +angle is the area perpendicular to the +direction a + + align:start position:0% +direction a + + + align:start position:0% +direction a +here r² so if you take a sphere in space + + align:start position:0% +here r² so if you take a sphere in space + + + align:start position:0% +here r² so if you take a sphere in space +that's 4 pi r s your solid angle is 4 Pi + + align:start position:0% +that's 4 pi r s your solid angle is 4 Pi + + + align:start position:0% +that's 4 pi r s your solid angle is 4 Pi +in 2D polar angle the ma is 2 right so + + align:start position:0% +in 2D polar angle the ma is 2 right so + + + align:start position:0% +in 2D polar angle the ma is 2 right so +the solid angle is space angle and if we + + align:start position:0% +the solid angle is space angle and if we + + + align:start position:0% +the solid angle is space angle and if we +do uh into AAL + + align:start position:0% +do uh into AAL + + + align:start position:0% +do uh into AAL +coordinate and then as M direction to + + align:start position:0% +coordinate and then as M direction to + + + align:start position:0% +coordinate and then as M direction to +the five then you can show that this is + + align:start position:0% +the five then you can show that this is + + + align:start position:0% +the five then you can show that this is +a + + align:start position:0% +a + + + align:start position:0% +a +s So Sol angle really including + + align:start position:0% +s So Sol angle really including + + + align:start position:0% +s So Sol angle really including +both so that's the uh definition in + + align:start position:0% +both so that's the uh definition in + + + align:start position:0% +both so that's the uh definition in +terms of + + align:start position:0% +terms of + + + align:start position:0% +terms of +intensity and uh when we want to + + align:start position:0% +intensity and uh when we want to + + + align:start position:0% +intensity and uh when we want to +calculate so intensity is the user + + align:start position:0% +calculate so intensity is the user + + + align:start position:0% +calculate so intensity is the user +starting point in fact uh it will be + + align:start position:0% +starting point in fact uh it will be + + + align:start position:0% +starting point in fact uh it will be +really interesting you go back read PL + + align:start position:0% +really interesting you go back read PL + + + align:start position:0% +really interesting you go back read PL +slw he have very interesting discussions + + align:start position:0% +slw he have very interesting discussions + + + align:start position:0% +slw he have very interesting discussions +very careful interesting discussion + + align:start position:0% + + + + align:start position:0% + +about the immedate total immediate power + + align:start position:0% +about the immedate total immediate power + + + align:start position:0% +about the immedate total immediate power +of a Surface normalized by surface area + + align:start position:0% +of a Surface normalized by surface area + + + align:start position:0% +of a Surface normalized by surface area +that's they call the enive power so now + + align:start position:0% +that's they call the enive power so now + + + align:start position:0% +that's they call the enive power so now +if you look at we normalize theive power + + align:start position:0% +if you look at we normalize theive power + + + align:start position:0% +if you look at we normalize theive power +so power equals intensity times the area + + align:start position:0% +so power equals intensity times the area + + + align:start position:0% +so power equals intensity times the area +a is perpendicular to the in Direction + + align:start position:0% +a is perpendicular to the in Direction + + + align:start position:0% +a is perpendicular to the in Direction +so I have coine and D Omega integration + + align:start position:0% +so I have coine and D Omega integration + + + align:start position:0% +so I have coine and D Omega integration +so this is Ste per unit wavelength so + + align:start position:0% +so this is Ste per unit wavelength so + + + align:start position:0% +so this is Ste per unit wavelength so +that's + + align:start position:0% +that's + + + align:start position:0% +that's +the theive power and for black body + + align:start position:0% +the theive power and for black body + + + align:start position:0% +the theive power and for black body +radiation the intensity is isotopic it's + + align:start position:0% +radiation the intensity is isotopic it's + + + align:start position:0% +radiation the intensity is isotopic it's +the same in all directions so it's + + align:start position:0% +the same in all directions so it's + + + align:start position:0% +the same in all directions so it's +independent of Direction you can take + + align:start position:0% +independent of Direction you can take + + + align:start position:0% +independent of Direction you can take +this out body and then you have cosine + + align:start position:0% +this out body and then you have cosine + + + align:start position:0% +this out body and then you have cosine +Theta and Sina Thea so you go to do the + + align:start position:0% +Theta and Sina Thea so you go to do the + + + align:start position:0% +Theta and Sina Thea so you go to do the +integration and if we think about the + + align:start position:0% +integration and if we think about the + + + align:start position:0% +integration and if we think about the +integration Theta is from Z to 2 pi + + align:start position:0% +integration Theta is from Z to 2 pi + + + align:start position:0% +integration Theta is from Z to 2 pi +right that's 90° and five is as M polar + + align:start position:0% +right that's 90° and five is as M polar + + + align:start position:0% +right that's 90° and five is as M polar +say coordinate the coordinate that's 2 + + align:start position:0% +say coordinate the coordinate that's 2 + + + align:start position:0% +say coordinate the coordinate that's 2 +pi so if you do the integration find the + + align:start position:0% +pi so if you do the integration find the + + + align:start position:0% +pi so if you do the integration find the +intensity for body radiation or + + align:start position:0% +intensity for body radiation or + + + align:start position:0% +intensity for body radiation or +isotropic radiation then intensity and + + align:start position:0% +isotropic radiation then intensity and + + + align:start position:0% +isotropic radiation then intensity and +power + + align:start position:0% +power + + + align:start position:0% +power +is relationship + + align:start position:0% +is relationship + + + align:start position:0% +is relationship +so that's the uh uh the uh M power and B + + align:start position:0% +so that's the uh uh the uh M power and B + + + align:start position:0% +so that's the uh uh the uh M power and B +law of black body radiation could be + + align:start position:0% +law of black body radiation could be + + + align:start position:0% +law of black body radiation could be +either written uh in the uh intensity + + align:start position:0% +either written uh in the uh intensity + + + align:start position:0% +either written uh in the uh intensity +form or in the powerful I apologize I + + align:start position:0% +form or in the powerful I apologize I + + + align:start position:0% +form or in the powerful I apologize I +had Miss C Square in my previous first + + align:start position:0% +had Miss C Square in my previous first + + + align:start position:0% +had Miss C Square in my previous first +lecture if you go back to the not we add + + align:start position:0% +lecture if you go back to the not we add + + + align:start position:0% +lecture if you go back to the not we add +that so that's the uh um intensity and + + align:start position:0% +that so that's the uh um intensity and + + + align:start position:0% +that so that's the uh um intensity and +Power + + align:start position:0% +Power + + + align:start position:0% +Power +and uh uh so this is what we talked + + align:start position:0% +and uh uh so this is what we talked + + + align:start position:0% +and uh uh so this is what we talked +pretty much what we talked before and if + + align:start position:0% +pretty much what we talked before and if + + + align:start position:0% +pretty much what we talked before and if +you PL PL the body radiation curve as a + + align:start position:0% +you PL PL the body radiation curve as a + + + align:start position:0% +you PL PL the body radiation curve as a +function of + + align:start position:0% +function of + + + align:start position:0% +function of +wavelength uh usually is use a unit of + + align:start position:0% +wavelength uh usually is use a unit of + + + align:start position:0% +wavelength uh usually is use a unit of +micro unit micrometer and you find + + align:start position:0% +micro unit micrometer and you find + + + align:start position:0% +micro unit micrometer and you find +out shift as you go to higher + + align:start position:0% +out shift as you go to higher + + + align:start position:0% +out shift as you go to higher +temperature the sh toor + + align:start position:0% +temperature the sh toor + + + align:start position:0% +temperature the sh toor +so this is a with + + align:start position:0% +so this is a with + + + align:start position:0% +so this is a with +displacement where this happens is the + + align:start position:0% +displacement where this happens is the + + + align:start position:0% +displacement where this happens is the +maximum radiation + + align:start position:0% +maximum radiation + + + align:start position:0% +maximum radiation +say where Ma happens temperature is + + align:start position:0% +say where Ma happens temperature is + + + align:start position:0% +say where Ma happens temperature is +about 3,000 that's the number you + + align:start position:0% +about 3,000 that's the number you + + + align:start position:0% +about 3,000 that's the number you +remember and the solar temperature s + + align:start position:0% +remember and the solar temperature s + + + align:start position:0% +remember and the solar temperature s +temperature fact about 6,000 so that's + + align:start position:0% +temperature fact about 6,000 so that's + + + align:start position:0% +temperature fact about 6,000 so that's +why our is5 + + align:start position:0% + + + + align:start position:0% + +the evolution work really well here and + + align:start position:0% +the evolution work really well here and + + + align:start position:0% +the evolution work really well here and +we have not that so it's interesting + + align:start position:0% +we have not that so it's interesting + + + align:start position:0% +we have not that so it's interesting +that the human adapt the sensitivity to + + align:start position:0% +that the human adapt the sensitivity to + + + align:start position:0% +that the human adapt the sensitivity to +the sun right not not night night they + + align:start position:0% +the sun right not not night night they + + + align:start position:0% +the sun right not not night night they +probably sleeping so um if you think + + align:start position:0% +probably sleeping so um if you think + + + align:start position:0% +probably sleeping so um if you think +about the emission everybody has is 10 + + align:start position:0% +about the emission everybody has is 10 + + + align:start position:0% +about the emission everybody has is 10 +right uh because + + align:start position:0% +right uh because + + + align:start position:0% +right uh because +300° around + + align:start position:0% +300° around + + + align:start position:0% +300° around +M so + + align:start position:0% +M so + + + align:start position:0% +M so +uh uh so uh the if you do integrate all + + align:start position:0% +uh uh so uh the if you do integrate all + + + align:start position:0% +uh uh so uh the if you do integrate all +energy uh in + + align:start position:0% +energy uh in + + + align:start position:0% +energy uh in +this you get St St + + align:start position:0% + + + + align:start position:0% + +concept so this is pretty much what we + + align:start position:0% +concept so this is pretty much what we + + + align:start position:0% +concept so this is pretty much what we +review and now uh I want to PL this uh + + align:start position:0% +review and now uh I want to PL this uh + + + align:start position:0% +review and now uh I want to PL this uh +into a more convenient form black body + + align:start position:0% +into a more convenient form black body + + + align:start position:0% +into a more convenient form black body +radiation because it's a function of two + + align:start position:0% +radiation because it's a function of two + + + align:start position:0% +radiation because it's a function of two +parameters + + align:start position:0% +parameters + + + align:start position:0% +parameters +wavelength and temperature but if I + + align:start position:0% +wavelength and temperature but if I + + + align:start position:0% +wavelength and temperature but if I +normalize + + align:start position:0% +normalize + + + align:start position:0% +normalize +this power by temperature F power I + + align:start position:0% +this power by temperature F power I + + + align:start position:0% +this power by temperature F power I +change it to + + align:start position:0% +change it to + + + align:start position:0% +change it to +smaller change so if I if I L temp face + + align:start position:0% +smaller change so if I if I L temp face + + + align:start position:0% +smaller change so if I if I L temp face +power you find out this temperature face + + align:start position:0% +power you find out this temperature face + + + align:start position:0% +power you find out this temperature face +power combined with Lambda here is + + align:start position:0% +power combined with Lambda here is + + + align:start position:0% +power combined with Lambda here is +combined with Lambda T so now I only I + + align:start position:0% +combined with Lambda T so now I only I + + + align:start position:0% +combined with Lambda T so now I only I +think about Lambda t as one parameter + + align:start position:0% +think about Lambda t as one parameter + + + align:start position:0% +think about Lambda t as one parameter +so this sh this curve + + align:start position:0% +so this sh this curve + + + align:start position:0% +so this sh this curve +now F power is really + + align:start position:0% +now F power is really + + + align:start position:0% +now F power is really +function T so I can have a universal + + align:start position:0% +function T so I can have a universal + + + align:start position:0% +function T so I can have a universal +curve rather than a say each temperature + + align:start position:0% +curve rather than a say each temperature + + + align:start position:0% +curve rather than a say each temperature +I have different Body + + align:start position:0% +I have different Body + + + align:start position:0% +I have different Body +Curve and in fact if you take your + + align:start position:0% +Curve and in fact if you take your + + + align:start position:0% +Curve and in fact if you take your +maximum now Lambda T you can say if you + + align:start position:0% +maximum now Lambda T you can say if you + + + align:start position:0% +maximum now Lambda T you can say if you +this x you find out where maximum is + + align:start position:0% +this x you find out where maximum is + + + align:start position:0% +this x you find out where maximum is +that's WIS displacement when got this by + + align:start position:0% +that's WIS displacement when got this by + + + align:start position:0% +that's WIS displacement when got this by +experiment and in fact you say that wi + + align:start position:0% +experiment and in fact you say that wi + + + align:start position:0% +experiment and in fact you say that wi +had over price too and but this is from + + align:start position:0% +had over price too and but this is from + + + align:start position:0% +had over price too and but this is from +F Theory you can derive + + align:start position:0% +F Theory you can derive + + + align:start position:0% +F Theory you can derive +the okay so now uh see uh this function + + align:start position:0% +the okay so now uh see uh this function + + + align:start position:0% +the okay so now uh see uh this function +we can also calculate uh the fraction of + + align:start position:0% +we can also calculate uh the fraction of + + + align:start position:0% +we can also calculate uh the fraction of +energy this is a very convenient + + align:start position:0% +energy this is a very convenient + + + align:start position:0% +energy this is a very convenient +particularly in the old days even now + + align:start position:0% +particularly in the old days even now + + + align:start position:0% +particularly in the old days even now +for me it's every time I want see how + + align:start position:0% +for me it's every time I want see how + + + align:start position:0% +for me it's every time I want see how +much energy in certain wav L from this + + align:start position:0% +much energy in certain wav L from this + + + align:start position:0% +much energy in certain wav L from this +side I take this function and look at + + align:start position:0% +side I take this function and look at + + + align:start position:0% +side I take this function and look at +table much faster so um uh this is the + + align:start position:0% +table much faster so um uh this is the + + + align:start position:0% +table much faster so um uh this is the +fraction of + + align:start position:0% +fraction of + + + align:start position:0% +fraction of +energy between zero to Lambda that's the + + align:start position:0% +energy between zero to Lambda that's the + + + align:start position:0% +energy between zero to Lambda that's the +uh + + align:start position:0% +uh + + + align:start position:0% +uh +integrate between Z to Lambda + + align:start position:0% +integrate between Z to Lambda + + + align:start position:0% +integrate between Z to Lambda +and of course using this function we can + + align:start position:0% +and of course using this function we can + + + align:start position:0% +and of course using this function we can +say that eventually we could write this + + align:start position:0% +say that eventually we could write this + + + align:start position:0% +say that eventually we could write this +into Lambda t f power of um this is + + align:start position:0% +into Lambda t f power of um this is + + + align:start position:0% +into Lambda t f power of um this is +force so there should be another T here + + align:start position:0% +force so there should be another T here + + + align:start position:0% +force so there should be another T here +and then say t + + align:start position:0% +and then say t + + + align:start position:0% +and then say t +t here the fth power here is nor F power + + align:start position:0% +t here the fth power here is nor F power + + + align:start position:0% +t here the fth power here is nor F power +here only four power because this is the + + align:start position:0% +here only four power because this is the + + + align:start position:0% +here only four power because this is the +toal that's + + align:start position:0% +toal that's + + + align:start position:0% +toal that's +step + + align:start position:0% +step + + + align:start position:0% +step +so uh after I write this you can say I + + align:start position:0% +so uh after I write this you can say I + + + align:start position:0% +so uh after I write this you can say I +can do this integration this function is + + align:start position:0% +can do this integration this function is + + + align:start position:0% +can do this integration this function is +a function this integral is a function + + align:start position:0% +a function this integral is a function + + + align:start position:0% +a function this integral is a function +of LDA T only here is t l l t so it's + + align:start position:0% +of LDA T only here is t l l t so it's + + + align:start position:0% +of LDA T only here is t l l t so it's +LDA T only again so by doing this I have + + align:start position:0% +LDA T only again so by doing this I have + + + align:start position:0% +LDA T only again so by doing this I have +a universal function uh that contains + + align:start position:0% +a universal function uh that contains + + + align:start position:0% +a universal function uh that contains +this is the fraction of energy with the + + align:start position:0% +this is the fraction of energy with the + + + align:start position:0% +this is the fraction of energy with the +w between zero and LDA for any + + align:start position:0% +w between zero and LDA for any + + + align:start position:0% +w between zero and LDA for any +temperature T right so if you give me a + + align:start position:0% +temperature T right so if you give me a + + + align:start position:0% +temperature T right so if you give me a +temperature I I look at the wance I do + + align:start position:0% +temperature I I look at the wance I do + + + align:start position:0% +temperature I I look at the wance I do +the multiplication I go to check the + + align:start position:0% +the multiplication I go to check the + + + align:start position:0% +the multiplication I go to check the +table and usually quickly you find out + + align:start position:0% +table and usually quickly you find out + + + align:start position:0% +table and usually quickly you find out +so that's the this is the integral + + align:start position:0% +so that's the this is the integral + + + align:start position:0% +so that's the this is the integral +that's the small + + align:start position:0% +that's the small + + + align:start position:0% +that's the small +F that's here and as a function of L T + + align:start position:0% +F that's here and as a function of L T + + + align:start position:0% +F that's here and as a function of L T +Lambda T is written in micro K and here + + align:start position:0% +Lambda T is written in micro K and here + + + align:start position:0% +Lambda T is written in micro K and here +is the integral so that's the fraction + + align:start position:0% +is the integral so that's the fraction + + + align:start position:0% +is the integral so that's the fraction +of energy between zero and lamb t Okay + + align:start position:0% +of energy between zero and lamb t Okay + + + align:start position:0% +of energy between zero and lamb t Okay +so uh uh you can quickly uh do an + + align:start position:0% +so uh uh you can quickly uh do an + + + align:start position:0% +so uh uh you can quickly uh do an +exercise again let me take a solar + + align:start position:0% +exercise again let me take a solar + + + align:start position:0% +exercise again let me take a solar +energy uh the sign as 6 6,000 K right A + + align:start position:0% +energy uh the sign as 6 6,000 K right A + + + align:start position:0% +energy uh the sign as 6 6,000 K right A +cicon B Gap is about 1.1 Micron so 6,000 + + align:start position:0% +cicon B Gap is about 1.1 Micron so 6,000 + + + align:start position:0% +cicon B Gap is about 1.1 Micron so 6,000 +* 1.1 66 right 6600 so + + align:start position:0% +* 1.1 66 right 6600 so + + + align:start position:0% +* 1.1 66 right 6600 so +6600 uh if you look at this curve here + + align:start position:0% +6600 uh if you look at this curve here + + + align:start position:0% +6600 uh if you look at this curve here +this is L SK it's harder to rate so + + align:start position:0% +this is L SK it's harder to rate so + + + align:start position:0% +this is L SK it's harder to rate so +properly + + align:start position:0% +properly + + + align:start position:0% +properly +75% so uh the other said 25% of the Sol + + align:start position:0% +75% so uh the other said 25% of the Sol + + + align:start position:0% +75% so uh the other said 25% of the Sol +energy beyond the bank below the bank + + align:start position:0% +energy beyond the bank below the bank + + + align:start position:0% +energy beyond the bank below the bank +Gap we number is not used at all so + + align:start position:0% +Gap we number is not used at all so + + + align:start position:0% +Gap we number is not used at all so +that's the case of when you use a + + align:start position:0% +that's the case of when you use a + + + align:start position:0% +that's the case of when you use a +photoex there's a b Gap and the photons + + align:start position:0% +photoex there's a b Gap and the photons + + + align:start position:0% +photoex there's a b Gap and the photons +below the back Gap does not elect not + + align:start position:0% +below the back Gap does not elect not + + + align:start position:0% +below the back Gap does not elect not +inside elect so that part is completely + + align:start position:0% +inside elect so that part is completely + + + align:start position:0% +inside elect so that part is completely +gone + + align:start position:0% +gone + + + align:start position:0% +gone +right and in fact you can also think for + + align:start position:0% +right and in fact you can also think for + + + align:start position:0% +right and in fact you can also think for +that part it's better even just a f out + + align:start position:0% +that part it's better even just a f out + + + align:start position:0% +that part it's better even just a f out +if you can do it cheaply why because if + + align:start position:0% +if you can do it cheaply why because if + + + align:start position:0% +if you can do it cheaply why because if +you uh your solar C absorb it you will + + align:start position:0% +you uh your solar C absorb it you will + + + align:start position:0% +you uh your solar C absorb it you will +hit up the solar cell and usually solar + + align:start position:0% +hit up the solar cell and usually solar + + + align:start position:0% +hit up the solar cell and usually solar +cell hits up the efficiency + + align:start position:0% + + + + align:start position:0% + +drw okay so that's the FL body now let's + + align:start position:0% +drw okay so that's the FL body now let's + + + align:start position:0% +drw okay so that's the FL body now let's +look at the S itself uh and Earth so the + + align:start position:0% +look at the S itself uh and Earth so the + + + align:start position:0% +look at the S itself uh and Earth so the +uh distance uh diameter of this s is 1.4 + + align:start position:0% +uh distance uh diameter of this s is 1.4 + + + align:start position:0% +uh distance uh diameter of this s is 1.4 +the L about 1 billion meter + + align:start position:0% + + + + align:start position:0% + +remember uh diameter of the + + align:start position:0% +remember uh diameter of the + + + align:start position:0% +remember uh diameter of the +earth right that's 12 minute 13 minut uh + + align:start position:0% +earth right that's 12 minute 13 minut uh + + + align:start position:0% +earth right that's 12 minute 13 minut uh +M and the distance is close to uh what + + align:start position:0% +M and the distance is close to uh what + + + align:start position:0% +M and the distance is close to uh what +is it 10 today 11 10 to 12 is there for + + align:start position:0% +is it 10 today 11 10 to 12 is there for + + + align:start position:0% +is it 10 today 11 10 to 12 is there for +10 to 12 for + + align:start position:0% + + + + align:start position:0% + +distance so 1.5 the 11 power so that's + + align:start position:0% +distance so 1.5 the 11 power so that's + + + align:start position:0% +distance so 1.5 the 11 power so that's +distance and you look at the solar um of + + align:start position:0% +distance and you look at the solar um of + + + align:start position:0% +distance and you look at the solar um of +course the orbital changes the distance + + align:start position:0% +course the orbital changes the distance + + + align:start position:0% +course the orbital changes the distance +between the Sun and the Earth SL change + + align:start position:0% +between the Sun and the Earth SL change + + + align:start position:0% +between the Sun and the Earth SL change +right but uh you see + + align:start position:0% +right but uh you see + + + align:start position:0% +right but uh you see +that this this might be high school know + + align:start position:0% +that this this might be high school know + + + align:start position:0% +that this this might be high school know +for you but some of you may not aware of + + align:start position:0% +for you but some of you may not aware of + + + align:start position:0% +for you but some of you may not aware of +this actually in uh June and July the + + align:start position:0% +this actually in uh June and July the + + + align:start position:0% +this actually in uh June and July the +solar flux is lowest + + align:start position:0% +solar flux is lowest + + + align:start position:0% +solar flux is lowest +right uh the from the uh distance July + + align:start position:0% +right uh the from the uh distance July + + + align:start position:0% +right uh the from the uh distance July +you see here and uh it's away from the + + align:start position:0% +you see here and uh it's away from the + + + align:start position:0% +you see here and uh it's away from the +sun right not the thought this this is + + align:start position:0% +sun right not the thought this this is + + + align:start position:0% +sun right not the thought this this is +the + + align:start position:0% +the + + + align:start position:0% +the +thought so the U uh we have the lowest + + align:start position:0% +thought so the U uh we have the lowest + + + align:start position:0% +thought so the U uh we have the lowest +flux but we have the + + align:start position:0% +flux but we have the + + + align:start position:0% +flux but we have the +summer right and uh the reason is not du + + align:start position:0% +summer right and uh the reason is not du + + + align:start position:0% +summer right and uh the reason is not du +to the + + align:start position:0% +to the + + + align:start position:0% +to the +distance is because the Earth + + align:start position:0% +distance is because the Earth + + + align:start position:0% +distance is because the Earth +is wobbling a little bit right when you + + align:start position:0% +is wobbling a little bit right when you + + + align:start position:0% +is wobbling a little bit right when you +surround the sand you look at that the + + align:start position:0% +surround the sand you look at that the + + + align:start position:0% +surround the sand you look at that the +uh the the Earth's axis is not + + align:start position:0% +uh the the Earth's axis is not + + + align:start position:0% +uh the the Earth's axis is not +perpendicular to the plan of + + align:start position:0% +perpendicular to the plan of + + + align:start position:0% +perpendicular to the plan of +rotation and uh uh it's has it has a 24 + + align:start position:0% +rotation and uh uh it's has it has a 24 + + + align:start position:0% +rotation and uh uh it's has it has a 24 +Dee + + align:start position:0% + + + + align:start position:0% + +of2 so this is + + align:start position:0% + + + + align:start position:0% + +the about 22 + + align:start position:0% + + + + align:start position:0% + +23.5 from the uh + + align:start position:0% +23.5 from the uh + + + align:start position:0% +23.5 from the uh +theal Direction so this is the Lal + + align:start position:0% +theal Direction so this is the Lal + + + align:start position:0% +theal Direction so this is the Lal +Direction and because of that uh on each + + align:start position:0% +Direction and because of that uh on each + + + align:start position:0% +Direction and because of that uh on each +side here the sou atmosphere + + align:start position:0% +side here the sou atmosphere + + + align:start position:0% +side here the sou atmosphere +is and here + + align:start position:0% + + + + align:start position:0% + +atmosphere okay so that's the uh the + + align:start position:0% +atmosphere okay so that's the uh the + + + align:start position:0% +atmosphere okay so that's the uh the +telting and this actually create the + + align:start position:0% +telting and this actually create the + + + align:start position:0% +telting and this actually create the +problem par when you want to track this + + align:start position:0% +problem par when you want to track this + + + align:start position:0% +problem par when you want to track this +time and say some people do uh when you + + align:start position:0% +time and say some people do uh when you + + + align:start position:0% +time and say some people do uh when you +use concentration you have to track you + + align:start position:0% +use concentration you have to track you + + + align:start position:0% +use concentration you have to track you +you maximum you want to maximize your + + align:start position:0% +you maximum you want to maximize your + + + align:start position:0% +you maximum you want to maximize your +intercepting eror and so that's the the + + align:start position:0% +intercepting eror and so that's the the + + + align:start position:0% +intercepting eror and so that's the the +tracking you have to comp the rotation + + align:start position:0% + + + + align:start position:0% + +of so uh here is the uh black body + + align:start position:0% +of so uh here is the uh black body + + + align:start position:0% +of so uh here is the uh black body +radiation coming from the reaching the + + align:start position:0% +radiation coming from the reaching the + + + align:start position:0% +radiation coming from the reaching the +Earth surface it's out outside + + align:start position:0% +Earth surface it's out outside + + + align:start position:0% +Earth surface it's out outside +atmosphere and it's close to 58 + + align:start position:0% +atmosphere and it's close to 58 + + + align:start position:0% +atmosphere and it's close to 58 +different people have side different + + align:start position:0% +different people have side different + + + align:start position:0% +different people have side different +numbers I later on I'll show you if I + + align:start position:0% +numbers I later on I'll show you if I + + + align:start position:0% +numbers I later on I'll show you if I +use a + + align:start position:0% +use a + + + align:start position:0% +use a +5777 k i get a overall constant very + + align:start position:0% +5777 k i get a overall constant very + + + align:start position:0% +5777 k i get a overall constant very +close to solar constant so this is the + + align:start position:0% +close to solar constant so this is the + + + align:start position:0% +close to solar constant so this is the +uh it's very close to BL body + + align:start position:0% + + + + align:start position:0% + +overall and of course when the sand + + align:start position:0% +overall and of course when the sand + + + align:start position:0% +overall and of course when the sand +comes through the atmosphere you have a + + align:start position:0% +comes through the atmosphere you have a + + + align:start position:0% +comes through the atmosphere you have a +lot of things happening uh the solar + + align:start position:0% +lot of things happening uh the solar + + + align:start position:0% +lot of things happening uh the solar +radiation coming in uh you will be + + align:start position:0% +radiation coming in uh you will be + + + align:start position:0% +radiation coming in uh you will be +reflected by the atmosphere the clouds + + align:start position:0% +reflected by the atmosphere the clouds + + + align:start position:0% +reflected by the atmosphere the clouds +can scatter like to all directions some + + align:start position:0% +can scatter like to all directions some + + + align:start position:0% +can scatter like to all directions some +will go back back and the atmosphere + + align:start position:0% +will go back back and the atmosphere + + + align:start position:0% +will go back back and the atmosphere +itself will absorb the solar radiation + + align:start position:0% +itself will absorb the solar radiation + + + align:start position:0% +itself will absorb the solar radiation +depends on what molecular species those + + align:start position:0% +depends on what molecular species those + + + align:start position:0% +depends on what molecular species those +are the vibrational modes of the + + align:start position:0% +are the vibrational modes of the + + + align:start position:0% +are the vibrational modes of the +molecules uh typically of the micr range + + align:start position:0% +molecules uh typically of the micr range + + + align:start position:0% +molecules uh typically of the micr range +so depends on what kind molec you have + + align:start position:0% +so depends on what kind molec you have + + + align:start position:0% +so depends on what kind molec you have +different absortion band so if the + + align:start position:0% +different absortion band so if the + + + align:start position:0% +different absortion band so if the +molecules are absorbing + + align:start position:0% +molecules are absorbing + + + align:start position:0% +molecules are absorbing +or those Moes then say those those phon + + align:start position:0% +or those Moes then say those those phon + + + align:start position:0% +or those Moes then say those those phon +reach the surface it's up the mo + + align:start position:0% +reach the surface it's up the mo + + + align:start position:0% +reach the surface it's up the mo +directly but there are transparency with + + align:start position:0% +directly but there are transparency with + + + align:start position:0% +directly but there are transparency with +those again this is pretty lucky for us + + align:start position:0% +those again this is pretty lucky for us + + + align:start position:0% +those again this is pretty lucky for us +right if everything is just absor by + + align:start position:0% +right if everything is just absor by + + + align:start position:0% +right if everything is just absor by +Moes we don't do have direct sunl and we + + align:start position:0% +Moes we don't do have direct sunl and we + + + align:start position:0% +Moes we don't do have direct sunl and we +will do so uh and of course the also + + align:start position:0% +will do so uh and of course the also + + + align:start position:0% +will do so uh and of course the also +surface you have the Reflection from the + + align:start position:0% +surface you have the Reflection from the + + + align:start position:0% +surface you have the Reflection from the +surface of the Earth so when you put a + + align:start position:0% +surface of the Earth so when you put a + + + align:start position:0% +surface of the Earth so when you put a +solar panel there uh you have direct + + align:start position:0% +solar panel there uh you have direct + + + align:start position:0% +solar panel there uh you have direct +knif you also have scatter knife from + + align:start position:0% +knif you also have scatter knife from + + + align:start position:0% +knif you also have scatter knife from +the atmosphere and from the + + align:start position:0% + + + + align:start position:0% + +ground okay so this is a uh + + align:start position:0% +ground okay so this is a uh + + + align:start position:0% +ground okay so this is a uh +uh to characterize solar cell right + + align:start position:0% +uh to characterize solar cell right + + + align:start position:0% +uh to characterize solar cell right +people have to compare orange to Orange + + align:start position:0% +people have to compare orange to Orange + + + align:start position:0% +people have to compare orange to Orange +uh so they are standard in terms of the + + align:start position:0% +uh so they are standard in terms of the + + + align:start position:0% +uh so they are standard in terms of the +what you should compare and uh this s + + align:start position:0% +what you should compare and uh this s + + + align:start position:0% +what you should compare and uh this s +Spectrum by the air mass right which is + + align:start position:0% +Spectrum by the air mass right which is + + + align:start position:0% +Spectrum by the air mass right which is +the ratio of the P of air of air Trav + + align:start position:0% +the ratio of the P of air of air Trav + + + align:start position:0% +the ratio of the P of air of air Trav +through uh to the shortest possible pop + + align:start position:0% +through uh to the shortest possible pop + + + align:start position:0% +through uh to the shortest possible pop +so you buy + + align:start position:0% +so you buy + + + align:start position:0% +so you buy +uh uh the outside atmosphere is + + align:start position:0% +uh uh the outside atmosphere is + + + align:start position:0% +uh uh the outside atmosphere is +am0 and then am1 air mass one ERS when + + align:start position:0% +am0 and then am1 air mass one ERS when + + + align:start position:0% +am0 and then am1 air mass one ERS when +the sun is directly over + + align:start position:0% +the sun is directly over + + + align:start position:0% +the sun is directly over +here okay and in 1.5 or when the sun ra + + align:start position:0% +here okay and in 1.5 or when the sun ra + + + align:start position:0% +here okay and in 1.5 or when the sun ra +power through roughly 50% power through + + align:start position:0% +power through roughly 50% power through + + + align:start position:0% +power through roughly 50% power through +50% more of the atmosphere than when the + + align:start position:0% +50% more of the atmosphere than when the + + + align:start position:0% +50% more of the atmosphere than when the +sun is directly overhead so at the angle + + align:start position:0% +sun is directly overhead so at the angle + + + align:start position:0% +sun is directly overhead so at the angle +right there's say the Pence of the sound + + align:start position:0% +right there's say the Pence of the sound + + + align:start position:0% +right there's say the Pence of the sound +will be longer and you can imagine + + align:start position:0% +will be longer and you can imagine + + + align:start position:0% +will be longer and you can imagine +because the longer Pence the uh Spectrum + + align:start position:0% +because the longer Pence the uh Spectrum + + + align:start position:0% +because the longer Pence the uh Spectrum +our solar radiation reaching the surface + + align:start position:0% +our solar radiation reaching the surface + + + align:start position:0% +our solar radiation reaching the surface +will be different because the absorption + + align:start position:0% +will be different because the absorption + + + align:start position:0% +will be different because the absorption +of the atmosphere and SC process right + + align:start position:0% +of the atmosphere and SC process right + + + align:start position:0% +of the atmosphere and SC process right +so uh you look at say 1.5 the angular + + align:start position:0% +so uh you look at say 1.5 the angular + + + align:start position:0% +so uh you look at say 1.5 the angular +relation the actual distance is 1/ coine + + align:start position:0% +relation the actual distance is 1/ coine + + + align:start position:0% +relation the actual distance is 1/ coine +th so cosine 48.2 gives 1.5 so this is + + align:start position:0% +th so cosine 48.2 gives 1.5 so this is + + + align:start position:0% +th so cosine 48.2 gives 1.5 so this is +what offers + + align:start position:0% +what offers + + + align:start position:0% +what offers +1.5 in angle the angle away from the + + align:start position:0% +1.5 in angle the angle away from the + + + align:start position:0% +1.5 in angle the angle away from the +perpendicular is + + align:start position:0% + + + + align:start position:0% + +48.2 okay so that's the uh uh but there + + align:start position:0% +48.2 okay so that's the uh uh but there + + + align:start position:0% +48.2 okay so that's the uh uh but there +are also U different uh depends on + + align:start position:0% +are also U different uh depends on + + + align:start position:0% +are also U different uh depends on +whether the solar radiation we measure + + align:start position:0% +whether the solar radiation we measure + + + align:start position:0% +whether the solar radiation we measure +is directly coming from the + + align:start position:0% +is directly coming from the + + + align:start position:0% +is directly coming from the +or there are also scattered diffuse SL + + align:start position:0% +or there are also scattered diffuse SL + + + align:start position:0% +or there are also scattered diffuse SL +so + + align:start position:0% +so + + + align:start position:0% +so +there m 1.5 there different + + align:start position:0% +there m 1.5 there different + + + align:start position:0% +there m 1.5 there different +m1.5 mention before m z is the uh + + align:start position:0% +m1.5 mention before m z is the uh + + + align:start position:0% +m1.5 mention before m z is the uh +spectrum of the uh radiation outside the + + align:start position:0% +spectrum of the uh radiation outside the + + + align:start position:0% +spectrum of the uh radiation outside the +atmosphere And1 is direcly + + align:start position:0% +atmosphere And1 is direcly + + + align:start position:0% +atmosphere And1 is direcly +uh + + align:start position:0% +uh + + + align:start position:0% +uh +dir and + + align:start position:0% +dir and + + + align:start position:0% +dir and +1.5 has a uh 1.5 Global G and 1.5 + + align:start position:0% +1.5 has a uh 1.5 Global G and 1.5 + + + align:start position:0% +1.5 has a uh 1.5 Global G and 1.5 +direct ccum s so the uh uh the direct + + align:start position:0% +direct ccum s so the uh uh the direct + + + align:start position:0% +direct ccum s so the uh uh the direct +one is really considering a small cor of + + align:start position:0% +one is really considering a small cor of + + + align:start position:0% +one is really considering a small cor of +solar + + align:start position:0% +solar + + + align:start position:0% +solar +radiation and this cor is confined to uh + + align:start position:0% +radiation and this cor is confined to uh + + + align:start position:0% +radiation and this cor is confined to uh +2.5 degre let's say here 2.5 half + + align:start position:0% +2.5 degre let's say here 2.5 half + + + align:start position:0% +2.5 degre let's say here 2.5 half +2.5 the Sun and and so this is uh the uh + + align:start position:0% +2.5 the Sun and and so this is uh the uh + + + align:start position:0% +2.5 the Sun and and so this is uh the uh +m.5 and then um m + + align:start position:0% +m.5 and then um m + + + align:start position:0% +m.5 and then um m +1.5g is the radiation from the sun sky + + align:start position:0% +1.5g is the radiation from the sun sky + + + align:start position:0% +1.5g is the radiation from the sun sky +reflecting out the ground and so in this + + align:start position:0% +reflecting out the ground and so in this + + + align:start position:0% +reflecting out the ground and so in this +case the Z is 1.5 is 40 + + align:start position:0% +case the Z is 1.5 is 40 + + + align:start position:0% +case the Z is 1.5 is 40 +48.2 but also the panel itself okay is + + align:start position:0% +48.2 but also the panel itself okay is + + + align:start position:0% +48.2 but also the panel itself okay is +tiled at the angle 37 so it's not + + align:start position:0% +tiled at the angle 37 so it's not + + + align:start position:0% +tiled at the angle 37 so it's not +perpect + + align:start position:0% +perpect + + + align:start position:0% +perpect +incidence from the sand to the Sol pan + + align:start position:0% +incidence from the sand to the Sol pan + + + align:start position:0% +incidence from the sand to the Sol pan +right here is 37 so the angle really + + align:start position:0% +right here is 37 so the angle really + + + align:start position:0% +right here is 37 so the angle really +incidence Ang of incidence is + + align:start position:0% + + + + align:start position:0% + +11.2 and so people + + align:start position:0% +11.2 and so people + + + align:start position:0% +11.2 and so people +1.5 for solar + + align:start position:0% + + + + align:start position:0% + +cells okay so that's a this is just a + + align:start position:0% +cells okay so that's a this is just a + + + align:start position:0% +cells okay so that's a this is just a +proit illustration uh 1.5 + + align:start position:0% +proit illustration uh 1.5 + + + align:start position:0% +proit illustration uh 1.5 +is 4 not + + align:start position:0% +is 4 not + + + align:start position:0% +is 4 not +481 48.2 + + align:start position:0% + + + + align:start position:0% + +right and uh so the global includ + + align:start position:0% +right and uh so the global includ + + + align:start position:0% +right and uh so the global includ +scatter light + + align:start position:0% +scatter light + + + align:start position:0% +scatter light +and also the panel is + + align:start position:0% +and also the panel is + + + align:start position:0% +and also the panel is +11.1 away from the normal incident + + align:start position:0% + + + + align:start position:0% + +okay so if you look at the uh + + align:start position:0% +okay so if you look at the uh + + + align:start position:0% +okay so if you look at the uh +Spectrum right this is how the different + + align:start position:0% +Spectrum right this is how the different + + + align:start position:0% +Spectrum right this is how the different +gaps in the atmosphere + + align:start position:0% +gaps in the atmosphere + + + align:start position:0% +gaps in the atmosphere +absorbs and water is actually really the + + align:start position:0% +absorbs and water is actually really the + + + align:start position:0% +absorbs and water is actually really the +uh absorption is the + + align:start position:0% +uh absorption is the + + + align:start position:0% +uh absorption is the +worst okay so this is the water + + align:start position:0% +worst okay so this is the water + + + align:start position:0% +worst okay so this is the water +absorption stum different W carbon + + align:start position:0% +absorption stum different W carbon + + + align:start position:0% +absorption stum different W carbon +dioxide here is 10 uh uh Micron right + + align:start position:0% +dioxide here is 10 uh uh Micron right + + + align:start position:0% +dioxide here is 10 uh uh Micron right +that's about Micron carbon dioxide this + + align:start position:0% +that's about Micron carbon dioxide this + + + align:start position:0% +that's about Micron carbon dioxide this +B is what people wear most because you + + align:start position:0% +B is what people wear most because you + + + align:start position:0% +B is what people wear most because you +increase carbon dioxide the 10 Micron + + align:start position:0% +increase carbon dioxide the 10 Micron + + + align:start position:0% +increase carbon dioxide the 10 Micron +radiation from the earth cannot + + align:start position:0% +radiation from the earth cannot + + + align:start position:0% +radiation from the earth cannot +escape and uh in fact if you combine all + + align:start position:0% +escape and uh in fact if you combine all + + + align:start position:0% +escape and uh in fact if you combine all +this let's say the Earth warms a little + + align:start position:0% +this let's say the Earth warms a little + + + align:start position:0% +this let's say the Earth warms a little +bit + + align:start position:0% +bit + + + align:start position:0% +bit +more right and this there more water + + align:start position:0% +more right and this there more water + + + align:start position:0% +more right and this there more water +evaporate from the + + align:start position:0% +evaporate from the + + + align:start position:0% +evaporate from the +ocean and and more water will more + + align:start position:0% +ocean and and more water will more + + + align:start position:0% +ocean and and more water will more +radiation so there is + + align:start position:0% +radiation so there is + + + align:start position:0% +radiation so there is +a that's why it's very complex problem + + align:start position:0% +a that's why it's very complex problem + + + align:start position:0% +a that's why it's very complex problem +and + + align:start position:0% +and + + + align:start position:0% +and +meate + + align:start position:0% +meate + + + align:start position:0% +meate +oide Scatter is the scatter is the most + + align:start position:0% +oide Scatter is the scatter is the most + + + align:start position:0% +oide Scatter is the scatter is the most +severe in the blue region and that's why + + align:start position:0% +severe in the blue region and that's why + + + align:start position:0% +severe in the blue region and that's why +the sky is blue it's the uh scatter + + align:start position:0% +the sky is blue it's the uh scatter + + + align:start position:0% +the sky is blue it's the uh scatter +proportional we got four power frequency + + align:start position:0% +proportional we got four power frequency + + + align:start position:0% +proportional we got four power frequency +four power so the equ scatter more SK + + align:start position:0% +four power so the equ scatter more SK + + + align:start position:0% +four power so the equ scatter more SK +you don't look at only scatter you + + align:start position:0% +you don't look at only scatter you + + + align:start position:0% +you don't look at only scatter you +direct so that's the solar Spectrum so + + align:start position:0% +direct so that's the solar Spectrum so + + + align:start position:0% +direct so that's the solar Spectrum so +of the absortion + + align:start position:0% +of the absortion + + + align:start position:0% +of the absortion +characteristics andh here + + align:start position:0% +characteristics andh here + + + align:start position:0% +characteristics andh here +is the spectral so outside the Earth you + + align:start position:0% +is the spectral so outside the Earth you + + + align:start position:0% +is the spectral so outside the Earth you +can say the blue curve here right and uh + + align:start position:0% +can say the blue curve here right and uh + + + align:start position:0% +can say the blue curve here right and uh +I say when they uh releasing those + + align:start position:0% +I say when they uh releasing those + + + align:start position:0% +I say when they uh releasing those +through the + + align:start position:0% +through the + + + align:start position:0% +through the +atmosphere the absorption bands + + align:start position:0% +atmosphere the absorption bands + + + align:start position:0% +atmosphere the absorption bands +different absorption + + align:start position:0% +different absorption + + + align:start position:0% +different absorption +bands here s Ki in and the is diminish + + align:start position:0% +bands here s Ki in and the is diminish + + + align:start position:0% +bands here s Ki in and the is diminish +when you reach the Earth + + align:start position:0% + + + + align:start position:0% + +surface and if you integrate all the Sol + + align:start position:0% +surface and if you integrate all the Sol + + + align:start position:0% +surface and if you integrate all the Sol +radiation + + align:start position:0% +radiation + + + align:start position:0% +radiation +here and you get the tot radiation + + align:start position:0% +here and you get the tot radiation + + + align:start position:0% +here and you get the tot radiation +energy in the + + align:start position:0% +energy in the + + + align:start position:0% +energy in the +Spectrum that's outside the atmosphere + + align:start position:0% +Spectrum that's outside the atmosphere + + + align:start position:0% +Spectrum that's outside the atmosphere +is + + align:start position:0% +is + + + align:start position:0% +is +1366 me Square so you go through uh say + + align:start position:0% +1366 me Square so you go through uh say + + + align:start position:0% +1366 me Square so you go through uh say +probably I think + + align:start position:0% +probably I think + + + align:start position:0% +probably I think +Professor Al Al he has a startup company + + align:start position:0% +Professor Al Al he has a startup company + + + align:start position:0% +Professor Al Al he has a startup company + + align:start position:0% + + + + align:start position:0% + +and uh this is a + + align:start position:0% +and uh this is a + + + align:start position:0% +and uh this is a +see 577 + + align:start position:0% +see 577 + + + align:start position:0% +see 577 +K so that's about the S now let's talk + + align:start position:0% +K so that's about the S now let's talk + + + align:start position:0% +K so that's about the S now let's talk +about the surface itself and I'm giving + + align:start position:0% +about the surface itself and I'm giving + + + align:start position:0% +about the surface itself and I'm giving +you the next few slides are definitions + + align:start position:0% +you the next few slides are definitions + + + align:start position:0% +you the next few slides are definitions +and the key point I want to you don't + + align:start position:0% +and the key point I want to you don't + + + align:start position:0% +and the key point I want to you don't +you not uh you don't need to know all + + align:start position:0% +you not uh you don't need to know all + + + align:start position:0% +you not uh you don't need to know all +the details but the key point is the + + align:start position:0% +the details but the key point is the + + + align:start position:0% +the details but the key point is the +surface properties + + align:start position:0% +surface properties + + + align:start position:0% +surface properties +radiation surface property is spectral + + align:start position:0% +radiation surface property is spectral + + + align:start position:0% +radiation surface property is spectral +dependent depends on + + align:start position:0% +dependent depends on + + + align:start position:0% +dependent depends on +wav also directional dependent so this + + align:start position:0% +wav also directional dependent so this + + + align:start position:0% +wav also directional dependent so this +particular lat will talk a lot on + + align:start position:0% +particular lat will talk a lot on + + + align:start position:0% +particular lat will talk a lot on +selective surface that's the spectal + + align:start position:0% +selective surface that's the spectal + + + align:start position:0% +selective surface that's the spectal +dependence and in fact also Direction + + align:start position:0% +dependence and in fact also Direction + + + align:start position:0% +dependence and in fact also Direction +can control spectral and directional + + align:start position:0% +can control spectral and directional + + + align:start position:0% +can control spectral and directional +property of the surfaces so uh uh the + + align:start position:0% +property of the surfaces so uh uh the + + + align:start position:0% +property of the surfaces so uh uh the +appreciation I want you to have is those + + align:start position:0% +appreciation I want you to have is those + + + align:start position:0% +appreciation I want you to have is those +uh uh you can start is the basic + + align:start position:0% +uh uh you can start is the basic + + + align:start position:0% +uh uh you can start is the basic +property like when I look at theity of a + + align:start position:0% +property like when I look at theity of a + + + align:start position:0% +property like when I look at theity of a +surface I can look at different + + align:start position:0% +surface I can look at different + + + align:start position:0% +surface I can look at different +direction and different wav how it's + + align:start position:0% +direction and different wav how it's + + + align:start position:0% +direction and different wav how it's +emitting uh the emission characteristics + + align:start position:0% +emitting uh the emission characteristics + + + align:start position:0% +emitting uh the emission characteristics +so this is the light coming the + + align:start position:0% +so this is the light coming the + + + align:start position:0% +so this is the light coming the +intensity immediate in certain direction + + align:start position:0% +intensity immediate in certain direction + + + align:start position:0% +intensity immediate in certain direction +and then normaliz to the intensity + + align:start position:0% +and then normaliz to the intensity + + + align:start position:0% +and then normaliz to the intensity +that's usually consider that as the + + align:start position:0% +that's usually consider that as the + + + align:start position:0% +that's usually consider that as the +maximum right so this normalization is + + align:start position:0% +maximum right so this normalization is + + + align:start position:0% +maximum right so this normalization is +the uh rational which I put a + + align:start position:0% +the uh rational which I put a + + + align:start position:0% +the uh rational which I put a +prime a rotation wise and the Spectrum + + align:start position:0% +prime a rotation wise and the Spectrum + + + align:start position:0% +prime a rotation wise and the Spectrum +which I put a Lambda so directional + + align:start position:0% +which I put a Lambda so directional + + + align:start position:0% +which I put a Lambda so directional +spectral + + align:start position:0% +spectral + + + align:start position:0% +spectral +emissivity and it's a function of the + + align:start position:0% +emissivity and it's a function of the + + + align:start position:0% +emissivity and it's a function of the +temperature of the surface the material + + align:start position:0% +temperature of the surface the material + + + align:start position:0% +temperature of the surface the material +temperature depends on temperature + + align:start position:0% +temperature depends on temperature + + + align:start position:0% +temperature depends on temperature +depends on material and also depends on + + align:start position:0% +depends on material and also depends on + + + align:start position:0% +depends on material and also depends on +Surface finish right how we that's how + + align:start position:0% +Surface finish right how we that's how + + + align:start position:0% +Surface finish right how we that's how +we + + align:start position:0% +we + + + align:start position:0% +we +control the uh prop this you can have p + + align:start position:0% +control the uh prop this you can have p + + + align:start position:0% +control the uh prop this you can have p +of aluminum which is very shiny no imity + + align:start position:0% +of aluminum which is very shiny no imity + + + align:start position:0% +of aluminum which is very shiny no imity +but you rough it then your imity will + + align:start position:0% +but you rough it then your imity will + + + align:start position:0% +but you rough it then your imity will +change uh into much higher + + align:start position:0% +change uh into much higher + + + align:start position:0% +change uh into much higher +values so that's a spectral directional + + align:start position:0% +values so that's a spectral directional + + + align:start position:0% +values so that's a spectral directional +spectral and then you also now you you + + align:start position:0% +spectral and then you also now you you + + + align:start position:0% +spectral and then you also now you you +integrate all the energy so this is + + align:start position:0% +integrate all the energy so this is + + + align:start position:0% +integrate all the energy so this is +intensity here I'm talking about the + + align:start position:0% +intensity here I'm talking about the + + + align:start position:0% +intensity here I'm talking about the +energy now because + + align:start position:0% +energy now because + + + align:start position:0% +energy now because +it's dire if I integrate the energy + + align:start position:0% +it's dire if I integrate the energy + + + align:start position:0% +it's dire if I integrate the energy +going leave the surface but still at a + + align:start position:0% +going leave the surface but still at a + + + align:start position:0% +going leave the surface but still at a +certain W interval only at a certain + + align:start position:0% +certain W interval only at a certain + + + align:start position:0% +certain W interval only at a certain +wance then I get the hand that's + + align:start position:0% +wance then I get the hand that's + + + align:start position:0% +wance then I get the hand that's +over + + align:start position:0% +over + + + align:start position:0% +over +and and you can you can calculate you + + align:start position:0% +and and you can you can calculate you + + + align:start position:0% +and and you can you can calculate you +can calculate from here to here if you + + align:start position:0% +can calculate from here to here if you + + + align:start position:0% +can calculate from here to here if you +know if you know this you know + + align:start position:0% +know if you know this you know + + + align:start position:0% +know if you know this you know +everything okay we just want to go + + align:start position:0% +everything okay we just want to go + + + align:start position:0% +everything okay we just want to go +through the uh the concept and then uh + + align:start position:0% +through the uh the concept and then uh + + + align:start position:0% +through the uh the concept and then uh +you can also say in this + + align:start position:0% +you can also say in this + + + align:start position:0% +you can also say in this +dire you integrate the all Spectrum so + + align:start position:0% +dire you integrate the all Spectrum so + + + align:start position:0% +dire you integrate the all Spectrum so +we call that total total means all the + + align:start position:0% +we call that total total means all the + + + align:start position:0% +we call that total total means all the +w h means all the angle so you have + + align:start position:0% +w h means all the angle so you have + + + align:start position:0% +w h means all the angle so you have +Direction total and then + + align:start position:0% +Direction total and then + + + align:start position:0% +Direction total and then +for + + align:start position:0% + + + + align:start position:0% + +course L you look at + + align:start position:0% + + + + align:start position:0% + +table that's the all Direction + + align:start position:0% +table that's the all Direction + + + align:start position:0% +table that's the all Direction +all okay so those are the uh + + align:start position:0% +all okay so those are the uh + + + align:start position:0% +all okay so those are the uh +definitions and a surface when we see + + align:start position:0% +definitions and a surface when we see + + + align:start position:0% +definitions and a surface when we see +how good it's in terms of the emission + + align:start position:0% +how good it's in terms of the emission + + + align:start position:0% +how good it's in terms of the emission +characteristics if it goes or em in all + + align:start position:0% +characteristics if it goes or em in all + + + align:start position:0% +characteristics if it goes or em in all +Direction + + align:start position:0% +Direction + + + align:start position:0% +Direction +isotropically okay intensity is same in + + align:start position:0% +isotropically okay intensity is same in + + + align:start position:0% +isotropically okay intensity is same in +all Direction body is one example a + + align:start position:0% +all Direction body is one example a + + + align:start position:0% +all Direction body is one example a +diffusing those is + + align:start position:0% +diffusing those is + + + align:start position:0% +diffusing those is +dire and if the emission is independent + + align:start position:0% +dire and if the emission is independent + + + align:start position:0% +dire and if the emission is independent +of w + + align:start position:0% +of w + + + align:start position:0% +of w +so the directional emity is same as if + + align:start position:0% +so the directional emity is same as if + + + align:start position:0% +so the directional emity is same as if +you integrate all W in the same + + align:start position:0% +you integrate all W in the same + + + align:start position:0% +you integrate all W in the same +direction so that's the G independent + + align:start position:0% +direction so that's the G independent + + + align:start position:0% +direction so that's the G independent +means + + align:start position:0% +means + + + align:start position:0% +means +inde diffuse means is so diffuse gr + + align:start position:0% +inde diffuse means is so diffuse gr + + + align:start position:0% +inde diffuse means is so diffuse gr +means the so if it's diffuse gr then all + + align:start position:0% +means the so if it's diffuse gr then all + + + align:start position:0% +means the so if it's diffuse gr then all +direction is the same and all those + + align:start position:0% +direction is the same and all those + + + align:start position:0% +direction is the same and all those +imity are the same but fundamentally you + + align:start position:0% +imity are the same but fundamentally you + + + align:start position:0% +imity are the same but fundamentally you +can start from here and write relation + + align:start position:0% +can start from here and write relation + + + align:start position:0% +can start from here and write relation +between all properties you all other + + align:start position:0% +between all properties you all other + + + align:start position:0% +between all properties you all other +property + + align:start position:0% +property + + + align:start position:0% +property +this but this one doesn't always equal + + align:start position:0% +this but this one doesn't always equal + + + align:start position:0% +this but this one doesn't always equal +the + + align:start position:0% +the + + + align:start position:0% +the +okay so that's the uh + + align:start position:0% +okay so that's the uh + + + align:start position:0% +okay so that's the uh +emissivity and uh uh the reverse of + + align:start position:0% +emissivity and uh uh the reverse of + + + align:start position:0% +emissivity and uh uh the reverse of +emission is absorption right so if light + + align:start position:0% +emission is absorption right so if light + + + align:start position:0% +emission is absorption right so if light +comes + + align:start position:0% +comes + + + align:start position:0% +comes +in and th radiation of light and then + + align:start position:0% +in and th radiation of light and then + + + align:start position:0% +in and th radiation of light and then +the + + align:start position:0% +the + + + align:start position:0% +the +power + + align:start position:0% +power + + + align:start position:0% +power +really I think I + + align:start position:0% +really I think I + + + align:start position:0% +really I think I +probably small form how much com in and + + align:start position:0% +probably small form how much com in and + + + align:start position:0% +probably small form how much com in and +the power absorb in this the fraction of + + align:start position:0% +the power absorb in this the fraction of + + + align:start position:0% +the power absorb in this the fraction of +the power that's being absorbed in this + + align:start position:0% +the power that's being absorbed in this + + + align:start position:0% +the power that's being absorbed in this +small that's the absor absor and again + + align:start position:0% +small that's the absor absor and again + + + align:start position:0% +small that's the absor absor and again +uh here we have coming from a certain + + align:start position:0% +uh here we have coming from a certain + + + align:start position:0% +uh here we have coming from a certain +direction that's Prime and at a specific + + align:start position:0% +direction that's Prime and at a specific + + + align:start position:0% +direction that's Prime and at a specific +w l that's + + align:start position:0% +w l that's + + + align:start position:0% +w l that's +Lambda okay so we D Define directional + + align:start position:0% +Lambda okay so we D Define directional + + + align:start position:0% +Lambda okay so we D Define directional +spectrum and then you do the same thing + + align:start position:0% +spectrum and then you do the same thing + + + align:start position:0% +spectrum and then you do the same thing +you integrate all angle of incidence + + align:start position:0% +you integrate all angle of incidence + + + align:start position:0% +you integrate all angle of incidence +they absorb + + align:start position:0% + + + + align:start position:0% + +as and then the same direction integrate + + align:start position:0% +as and then the same direction integrate + + + align:start position:0% +as and then the same direction integrate +all W or you integrate both W and dire + + align:start position:0% +all W or you integrate both W and dire + + + align:start position:0% +all W or you integrate both W and dire +same + + align:start position:0% +same + + + align:start position:0% +same +analogous to emission except now the + + align:start position:0% +analogous to emission except now the + + + align:start position:0% +analogous to emission except now the +reference is what comes + + align:start position:0% +reference is what comes + + + align:start position:0% +reference is what comes +in but uh let me just make one comment + + align:start position:0% +in but uh let me just make one comment + + + align:start position:0% +in but uh let me just make one comment +here uh although what comes in the the + + align:start position:0% +here uh although what comes in the the + + + align:start position:0% +here uh although what comes in the the +uh overall spectrum of so for example + + align:start position:0% +uh overall spectrum of so for example + + + align:start position:0% +uh overall spectrum of so for example +solar coming to the surface depends on + + align:start position:0% +solar coming to the surface depends on + + + align:start position:0% +solar coming to the surface depends on +temperature of + + align:start position:0% +temperature of + + + align:start position:0% +temperature of +the right but the spectal here doesn't + + align:start position:0% +the right but the spectal here doesn't + + + align:start position:0% +the right but the spectal here doesn't +depend on temperature I can have the + + align:start position:0% +depend on temperature I can have the + + + align:start position:0% +depend on temperature I can have the +surface thism come to the surface or + + align:start position:0% +surface thism come to the surface or + + + align:start position:0% +surface thism come to the surface or +this later being come to the surface + + align:start position:0% +this later being come to the surface + + + align:start position:0% +this later being come to the surface +that's my + + align:start position:0% +that's my + + + align:start position:0% +that's my +intens right and this temperature is + + align:start position:0% +intens right and this temperature is + + + align:start position:0% +intens right and this temperature is +really the temperature of the + + align:start position:0% +really the temperature of the + + + align:start position:0% +really the temperature of the +material it's not the temperature of the + + align:start position:0% +material it's not the temperature of the + + + align:start position:0% +material it's not the temperature of the +source so this is the absorptivity and + + align:start position:0% +source so this is the absorptivity and + + + align:start position:0% +source so this is the absorptivity and +then + + align:start position:0% +then + + + align:start position:0% +then +the is very important second second La + + align:start position:0% +the is very important second second La + + + align:start position:0% +the is very important second second La +relation for imity and + + align:start position:0% +relation for imity and + + + align:start position:0% +relation for imity and +absorptivity as courage possible + + align:start position:0% +absorptivity as courage possible + + + align:start position:0% +absorptivity as courage possible +okay the + + align:start position:0% +okay the + + + align:start position:0% +okay the +C this is the same of the object + + align:start position:0% +C this is the same of the object + + + align:start position:0% +C this is the same of the object +theal spect + + align:start position:0% + + + + align:start position:0% + +abity spect + + align:start position:0% +abity spect + + + align:start position:0% +abity spect +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +AB black body + + align:start position:0% +AB black body + + + align:start position:0% +AB black body +radiation is not second the Cal SL is + + align:start position:0% +radiation is not second the Cal SL is + + + align:start position:0% +radiation is not second the Cal SL is +equ the max the SL + + align:start position:0% +equ the max the SL + + + align:start position:0% +equ the max the SL +I mean PL slow you can break it peral + + align:start position:0% +I mean PL slow you can break it peral + + + align:start position:0% +I mean PL slow you can break it peral +slow you cannot break + + align:start position:0% + + + + align:start position:0% + +it fundamental + + align:start position:0% +it fundamental + + + align:start position:0% +it fundamental +but remember I'm putting down again it's + + align:start position:0% +but remember I'm putting down again it's + + + align:start position:0% +but remember I'm putting down again it's +the rational + + align:start position:0% +the rational + + + align:start position:0% +the rational +spectal I don't mean the other property + + align:start position:0% +spectal I don't mean the other property + + + align:start position:0% +spectal I don't mean the other property +are the same now if you have a diffus + + align:start position:0% +are the same now if you have a diffus + + + align:start position:0% +are the same now if you have a diffus +surface diffuse Emer diffuse absorber + + align:start position:0% +surface diffuse Emer diffuse absorber + + + align:start position:0% +surface diffuse Emer diffuse absorber +this is fine then then all the other + + align:start position:0% +this is fine then then all the other + + + align:start position:0% +this is fine then then all the other +property higher level properties are + + align:start position:0% +property higher level properties are + + + align:start position:0% +property higher level properties are +also equal but in general they are not + + align:start position:0% +also equal but in general they are not + + + align:start position:0% +also equal but in general they are not +equal for higher order it's only at this + + align:start position:0% +equal for higher order it's only at this + + + align:start position:0% +equal for higher order it's only at this +fundamental + + align:start position:0% + + + + align:start position:0% + +level so uh uh like I said the message + + align:start position:0% +level so uh uh like I said the message + + + align:start position:0% +level so uh uh like I said the message +is depend on M and angle and if you + + align:start position:0% +is depend on M and angle and if you + + + align:start position:0% +is depend on M and angle and if you +think about the reflectivity + + align:start position:0% +think about the reflectivity + + + align:start position:0% +think about the reflectivity +transmissivity so you have a piece of + + align:start position:0% +transmissivity so you have a piece of + + + align:start position:0% +transmissivity so you have a piece of +glass right your light comes in you have + + align:start position:0% +glass right your light comes in you have + + + align:start position:0% +glass right your light comes in you have +reflection and light can go through of + + align:start position:0% +reflection and light can go through of + + + align:start position:0% +reflection and light can go through of +course there also bling here inside and + + align:start position:0% +course there also bling here inside and + + + align:start position:0% +course there also bling here inside and +the light comes see the reflectivity is + + align:start position:0% +the light comes see the reflectivity is + + + align:start position:0% +the light comes see the reflectivity is +us more complicated because you can go + + align:start position:0% +us more complicated because you can go + + + align:start position:0% +us more complicated because you can go +other directions you can go uh one light + + align:start position:0% +other directions you can go uh one light + + + align:start position:0% +other directions you can go uh one light +comes to a surface and this is a Val + + align:start position:0% +comes to a surface and this is a Val + + + align:start position:0% +comes to a surface and this is a Val +smooth but you can go diffusely to all + + align:start position:0% +smooth but you can go diffusely to all + + + align:start position:0% +smooth but you can go diffusely to all +other directions so uh then we have to + + align:start position:0% +other directions so uh then we have to + + + align:start position:0% +other directions so uh then we have to +say incoming is One Direction out is + + align:start position:0% +say incoming is One Direction out is + + + align:start position:0% +say incoming is One Direction out is +other so the fundamental definition is + + align:start position:0% +other so the fundamental definition is + + + align:start position:0% +other so the fundamental definition is +actually by + + align:start position:0% +actually by + + + align:start position:0% +actually by +Direction what comes in what goes + + align:start position:0% +Direction what comes in what goes + + + align:start position:0% +Direction what comes in what goes +out the intensity so you have two angle + + align:start position:0% +out the intensity so you have two angle + + + align:start position:0% +out the intensity so you have two angle +angle of incid the other is angle of + + align:start position:0% +angle of incid the other is angle of + + + align:start position:0% +angle of incid the other is angle of +reflection that's a by directional + + align:start position:0% +reflection that's a by directional + + + align:start position:0% +reflection that's a by directional +reflectivity but say now if you + + align:start position:0% +reflectivity but say now if you + + + align:start position:0% +reflectivity but say now if you +integrate the all reflected the + + align:start position:0% +integrate the all reflected the + + + align:start position:0% +integrate the all reflected the +intensity you got the uh say the uh uh + + align:start position:0% +intensity you got the uh say the uh uh + + + align:start position:0% +intensity you got the uh say the uh uh +the rational when I say the rational + + align:start position:0% +the rational when I say the rational + + + align:start position:0% +the rational when I say the rational +spectral so that's coming in all Ang so + + align:start position:0% +spectral so that's coming in all Ang so + + + align:start position:0% +spectral so that's coming in all Ang so +here when I do + + align:start position:0% +here when I do + + + align:start position:0% +here when I do +bational notation I have two + + align:start position:0% +bational notation I have two + + + align:start position:0% +bational notation I have two +Prim okay + + align:start position:0% +Prim okay + + + align:start position:0% +Prim okay +and when I integrate all angle of + + align:start position:0% +and when I integrate all angle of + + + align:start position:0% +and when I integrate all angle of +reflection I get direction of spectral + + align:start position:0% +reflection I get direction of spectral + + + align:start position:0% +reflection I get direction of spectral +so this Direction only means incoming + + align:start position:0% +so this Direction only means incoming + + + align:start position:0% +so this Direction only means incoming +because I integr the reflection over all + + align:start position:0% +because I integr the reflection over all + + + align:start position:0% +because I integr the reflection over all +angle already and then I have so this + + align:start position:0% +angle already and then I have so this + + + align:start position:0% +angle already and then I have so this +now from here I can do the rest similar + + align:start position:0% +now from here I can do the rest similar + + + align:start position:0% +now from here I can do the rest similar +as I did for imity and up so in fact + + align:start position:0% +as I did for imity and up so in fact + + + align:start position:0% +as I did for imity and up so in fact +there are eight you can start more + + align:start position:0% +there are eight you can start more + + + align:start position:0% +there are eight you can start more +fundamental andine all those other + + align:start position:0% +fundamental andine all those other + + + align:start position:0% +fundamental andine all those other +properties and you can do the same for + + align:start position:0% +properties and you can do the same for + + + align:start position:0% +properties and you can do the same for +transmissivity okay uh by directional + + align:start position:0% +transmissivity okay uh by directional + + + align:start position:0% +transmissivity okay uh by directional +transmissivity and then Bally the + + align:start position:0% +transmissivity and then Bally the + + + align:start position:0% +transmissivity and then Bally the +overall transmitted light and uh that's + + align:start position:0% +overall transmitted light and uh that's + + + align:start position:0% +overall transmitted light and uh that's +One + + align:start position:0% + + + + align:start position:0% + +Direction now enery will tell us if I + + align:start position:0% +Direction now enery will tell us if I + + + align:start position:0% +Direction now enery will tell us if I +think about the light comes in right and + + align:start position:0% +think about the light comes in right and + + + align:start position:0% +think about the light comes in right and +it's either reflected that's the + + align:start position:0% +it's either reflected that's the + + + align:start position:0% +it's either reflected that's the +reflection of all + + align:start position:0% +reflection of all + + + align:start position:0% +reflection of all +angle in that one angle and absorb it + + align:start position:0% +angle in that one angle and absorb it + + + align:start position:0% +angle in that one angle and absorb it +inside the material or transmit it to + + align:start position:0% +inside the material or transmit it to + + + align:start position:0% +inside the material or transmit it to +the other + + align:start position:0% +the other + + + align:start position:0% +the other +side so that's energy that's first law + + align:start position:0% +side so that's energy that's first law + + + align:start position:0% +side so that's energy that's first law +so in those relations I've told you the + + align:start position:0% +so in those relations I've told you the + + + align:start position:0% +so in those relations I've told you the +first law and second can violate in any + + align:start position:0% +first law and second can violate in any + + + align:start position:0% +first law and second can violate in any +of + + align:start position:0% +of + + + align:start position:0% +of +right so uh ifuse reflector so sign to + + align:start position:0% +right so uh ifuse reflector so sign to + + + align:start position:0% +right so uh ifuse reflector so sign to +the uh what we talk about is when one + + align:start position:0% +the uh what we talk about is when one + + + align:start position:0% +the uh what we talk about is when one +light comes in uh the reflect like go + + align:start position:0% +light comes in uh the reflect like go + + + align:start position:0% +light comes in uh the reflect like go +all directions a really bad say surface + + align:start position:0% +all directions a really bad say surface + + + align:start position:0% +all directions a really bad say surface +u in the sense of light goes all + + align:start position:0% +u in the sense of light goes all + + + align:start position:0% +u in the sense of light goes all +Direction but in fact a lot of time you + + align:start position:0% +Direction but in fact a lot of time you + + + align:start position:0% +Direction but in fact a lot of time you +do want this uh particularly in some + + align:start position:0% +do want this uh particularly in some + + + align:start position:0% +do want this uh particularly in some +illumination case right you actually + + align:start position:0% +illumination case right you actually + + + align:start position:0% +illumination case right you actually +want the diffuse slide to make the room + + align:start position:0% +want the diffuse slide to make the room + + + align:start position:0% +want the diffuse slide to make the room +feel + + align:start position:0% +feel + + + align:start position:0% +feel +comfortable and uh uh so GRE is w and + + align:start position:0% +comfortable and uh uh so GRE is w and + + + align:start position:0% +comfortable and uh uh so GRE is w and +diffuse reflector is both isotropic and + + align:start position:0% +diffuse reflector is both isotropic and + + + align:start position:0% +diffuse reflector is both isotropic and +frequeny + + align:start position:0% +frequeny + + + align:start position:0% +frequeny +independent so if you some of you to the + + align:start position:0% +independent so if you some of you to the + + + align:start position:0% +independent so if you some of you to the +other learn diffuse + + align:start position:0% +other learn diffuse + + + align:start position:0% +other learn diffuse +surface means diffusive re emitter and + + align:start position:0% +surface means diffusive re emitter and + + + align:start position:0% +surface means diffusive re emitter and +diffusive reflector so it means both we + + align:start position:0% +diffusive reflector so it means both we + + + align:start position:0% +diffusive reflector so it means both we +have come back to diff + + align:start position:0% + + + + align:start position:0% + +here okay lot of definitions we're not + + align:start position:0% +here okay lot of definitions we're not + + + align:start position:0% +here okay lot of definitions we're not +going to use much I just want to uh make + + align:start position:0% +going to use much I just want to uh make + + + align:start position:0% +going to use much I just want to uh make +you aware that the surface properties of + + align:start position:0% +you aware that the surface properties of + + + align:start position:0% +you aware that the surface properties of +frequency dependence dependent and + + align:start position:0% +frequency dependence dependent and + + + align:start position:0% +frequency dependence dependent and +Direction dep + + align:start position:0% +Direction dep + + + align:start position:0% +Direction dep +and now there's another key concept when + + align:start position:0% +and now there's another key concept when + + + align:start position:0% +and now there's another key concept when +I want to + + align:start position:0% +I want to + + + align:start position:0% +I want to +calculate how much ration those if I + + align:start position:0% +calculate how much ration those if I + + + align:start position:0% +calculate how much ration those if I +have how + + align:start position:0% +have how + + + align:start position:0% +have how +many how much of my ration get to you + + align:start position:0% +many how much of my ration get to you + + + align:start position:0% +many how much of my ration get to you +right so that's the uh concept of view + + align:start position:0% +right so that's the uh concept of view + + + align:start position:0% +right so that's the uh concept of view +Factor if I have one surface here + + align:start position:0% +Factor if I have one surface here + + + align:start position:0% +Factor if I have one surface here +another surface here okay view factor is + + align:start position:0% +another surface here okay view factor is + + + align:start position:0% +another surface here okay view factor is +Define the power leaving + + align:start position:0% +Define the power leaving + + + align:start position:0% +Define the power leaving +this + + align:start position:0% +this + + + align:start position:0% +this +surface okay that's the total power of + + align:start position:0% +surface okay that's the total power of + + + align:start position:0% +surface okay that's the total power of +this surface and intercept it by the + + align:start position:0% +this surface and intercept it by the + + + align:start position:0% +this surface and intercept it by the +surface I didn't say uh absorbed by the + + align:start position:0% +surface I didn't say uh absorbed by the + + + align:start position:0% +surface I didn't say uh absorbed by the +OU surface just reaching the OU Surface + + align:start position:0% +OU surface just reaching the OU Surface + + + align:start position:0% +OU surface just reaching the OU Surface +after reach you could reflect it + + align:start position:0% +after reach you could reflect it + + + align:start position:0% +after reach you could reflect it +transmit it that's the uh that's not + + align:start position:0% +transmit it that's the uh that's not + + + align:start position:0% +transmit it that's the uh that's not +including the part say the view Factor + + align:start position:0% +including the part say the view Factor + + + align:start position:0% +including the part say the view Factor +just say defraction reach okay so that + + align:start position:0% +just say defraction reach okay so that + + + align:start position:0% +just say defraction reach okay so that +gives you way of if you think about the + + align:start position:0% +gives you way of if you think about the + + + align:start position:0% +gives you way of if you think about the +P reflectivity transmissivity that's + + align:start position:0% +P reflectivity transmissivity that's + + + align:start position:0% +P reflectivity transmissivity that's +near the surface this just say how much + + align:start position:0% +near the surface this just say how much + + + align:start position:0% +near the surface this just say how much +to that + + align:start position:0% +to that + + + align:start position:0% +to that +surface and uh if I uh use this + + align:start position:0% +surface and uh if I uh use this + + + align:start position:0% +surface and uh if I uh use this +definition uh the power leaving the + + align:start position:0% +definition uh the power leaving the + + + align:start position:0% +definition uh the power leaving the +surface uh here is the uh I uh EI so + + align:start position:0% +surface uh here is the uh I uh EI so + + + align:start position:0% +surface uh here is the uh I uh EI so +that's the + + align:start position:0% +that's the + + + align:start position:0% +that's the +uh have multi pi + + align:start position:0% +uh have multi pi + + + align:start position:0% +uh have multi pi +I + + align:start position:0% +I + + + align:start position:0% +I +think so that's because the intensity Pi + + align:start position:0% +think so that's because the intensity Pi + + + align:start position:0% +think so that's because the intensity Pi +the diffuse surface give me the to + + align:start position:0% +the diffuse surface give me the to + + + align:start position:0% +the diffuse surface give me the to +radiation even the surface and then this + + align:start position:0% +radiation even the surface and then this + + + align:start position:0% +radiation even the surface and then this +is the radiation if I go back to + + align:start position:0% +is the radiation if I go back to + + + align:start position:0% +is the radiation if I go back to +definition of intensity so this is the + + align:start position:0% +definition of intensity so this is the + + + align:start position:0% +definition of intensity so this is the +power in the corn times the solid angle + + align:start position:0% +power in the corn times the solid angle + + + align:start position:0% +power in the corn times the solid angle +that this area d a + + align:start position:0% +that this area d a + + + align:start position:0% +that this area d a +suspended with respect to this this this + + align:start position:0% +suspended with respect to this this this + + + align:start position:0% +suspended with respect to this this this +uh uh Point here so that's d a cosine + + align:start position:0% +uh uh Point here so that's d a cosine + + + align:start position:0% +uh uh Point here so that's d a cosine +Theta that's the normal area and IDE by + + align:start position:0% +Theta that's the normal area and IDE by + + + align:start position:0% +Theta that's the normal area and IDE by +r² that's the distance between the two + + align:start position:0% +r² that's the distance between the two + + + align:start position:0% +r² that's the distance between the two +surfaces and this is what's the power in + + align:start position:0% +surfaces and this is what's the power in + + + align:start position:0% +surfaces and this is what's the power in +this form and reaching that + + align:start position:0% +this form and reaching that + + + align:start position:0% +this form and reaching that +area + + align:start position:0% +area + + + align:start position:0% +area +so this with this definition I have + + align:start position:0% +so this with this definition I have + + + align:start position:0% +so this with this definition I have +uh + + align:start position:0% + + + + align:start position:0% + +think check that so I have a + + align:start position:0% + + + + align:start position:0% + +R A so that's a differential small area + + align:start position:0% +R A so that's a differential small area + + + align:start position:0% +R A so that's a differential small area +two + + align:start position:0% + + + + align:start position:0% + +surfaces anybody + + align:start position:0% + + + + align:start position:0% + +remember + + align:start position:0% +remember + + + align:start position:0% +remember +okay if I integrate the both + + align:start position:0% +okay if I integrate the both + + + align:start position:0% +okay if I integrate the both +surfaces I got a toal the surface is + + align:start position:0% +surfaces I got a toal the surface is + + + align:start position:0% +surfaces I got a toal the surface is +uniformly immedi right and uh that's the + + align:start position:0% +uniformly immedi right and uh that's the + + + align:start position:0% +uniformly immedi right and uh that's the +view Factor those kind of view Factor + + align:start position:0% +view Factor those kind of view Factor + + + align:start position:0% +view Factor those kind of view Factor +again you can look for + + align:start position:0% +again you can look for + + + align:start position:0% +again you can look for +tables one way to is go to do this + + align:start position:0% +tables one way to is go to do this + + + align:start position:0% +tables one way to is go to do this +calculation but a lot of standard + + align:start position:0% +calculation but a lot of standard + + + align:start position:0% +calculation but a lot of standard +geometry people have done the + + align:start position:0% +geometry people have done the + + + align:start position:0% +geometry people have done the +calculation so it's + + align:start position:0% + + + + align:start position:0% + +calculated and the Assumption I made is + + align:start position:0% +calculated and the Assumption I made is + + + align:start position:0% +calculated and the Assumption I made is +that over this surface the radiation is + + align:start position:0% +that over this surface the radiation is + + + align:start position:0% +that over this surface the radiation is +diffus so I said I have a pi I and then + + align:start position:0% +diffus so I said I have a pi I and then + + + align:start position:0% +diffus so I said I have a pi I and then +ration even the surface the whole + + align:start position:0% +ration even the surface the whole + + + align:start position:0% +ration even the surface the whole +surface is uniform so that's the + + align:start position:0% +surface is uniform so that's the + + + align:start position:0% +surface is uniform so that's the +Assumption making and I said you can + + align:start position:0% +Assumption making and I said you can + + + align:start position:0% +Assumption making and I said you can +look at the tables but there are also + + align:start position:0% +look at the tables but there are also + + + align:start position:0% +look at the tables but there are also +relationship if you look at the + + align:start position:0% +relationship if you look at the + + + align:start position:0% +relationship if you look at the +definition very symetric right so the uh + + align:start position:0% +definition very symetric right so the uh + + + align:start position:0% +definition very symetric right so the uh +from this you will see the reciprocity + + align:start position:0% +from this you will see the reciprocity + + + align:start position:0% +from this you will see the reciprocity +relation from view factor from a to J is + + align:start position:0% +relation from view factor from a to J is + + + align:start position:0% +relation from view factor from a to J is +times the area I I and and equals from J + + align:start position:0% +times the area I I and and equals from J + + + align:start position:0% +times the area I I and and equals from J +to I area + + align:start position:0% +to I area + + + align:start position:0% +to I area +J that's a re + + align:start position:0% +J that's a re + + + align:start position:0% +J that's a re +relation and if you do the + + align:start position:0% +relation and if you do the + + + align:start position:0% +relation and if you do the +toal we have and then the summation + + align:start position:0% +toal we have and then the summation + + + align:start position:0% +toal we have and then the summation +summation is basically the energy + + align:start position:0% +summation is basically the energy + + + align:start position:0% +summation is basically the energy +balance the energy leing surface I will + + align:start position:0% +balance the energy leing surface I will + + + align:start position:0% +balance the energy leing surface I will +reach J combine I plus k then it's the + + align:start position:0% +reach J combine I plus k then it's the + + + align:start position:0% +reach J combine I plus k then it's the +same as Le i j and Le + + align:start position:0% +same as Le i j and Le + + + align:start position:0% +same as Le i j and Le +I + + align:start position:0% +I + + + align:start position:0% +I +first first one okay so with those + + align:start position:0% +first first one okay so with those + + + align:start position:0% +first first one okay so with those +relation The View factors most time you + + align:start position:0% +relation The View factors most time you + + + align:start position:0% +relation The View factors most time you +can for simple geometry you can find it + + align:start position:0% +can for simple geometry you can find it + + + align:start position:0% +can for simple geometry you can find it +from table or you talk this relation + + align:start position:0% +from table or you talk this relation + + + align:start position:0% +from table or you talk this relation +than doing those + + align:start position:0% + + + + align:start position:0% + +complicated let's go to look at the + + align:start position:0% +complicated let's go to look at the + + + align:start position:0% +complicated let's go to look at the +Earth right so uh the Earth and Sun + + align:start position:0% +Earth right so uh the Earth and Sun + + + align:start position:0% +Earth right so uh the Earth and Sun +because they are so far part essentially + + align:start position:0% +because they are so far part essentially + + + align:start position:0% +because they are so far part essentially +I can f a very small surface to each + + align:start position:0% +I can f a very small surface to each + + + align:start position:0% +I can f a very small surface to each +other so D area and rather than look at + + align:start position:0% +other so D area and rather than look at + + + align:start position:0% +other so D area and rather than look at +the curvature because when I look at + + align:start position:0% +the curvature because when I look at + + + align:start position:0% +the curvature because when I look at +curvature each point will be different + + align:start position:0% +curvature each point will be different + + + align:start position:0% +curvature each point will be different +angle wise perpendicular surface and in + + align:start position:0% +angle wise perpendicular surface and in + + + align:start position:0% +angle wise perpendicular surface and in +fact you can just this at a disc and + + align:start position:0% +fact you can just this at a disc and + + + align:start position:0% +fact you can just this at a disc and +this at a disc this + + align:start position:0% +this at a disc this + + + align:start position:0% +this at a disc this +equivalent okay the dis area which + + align:start position:0% +equivalent okay the dis area which + + + align:start position:0% +equivalent okay the dis area which +p² + + align:start position:0% +p² + + + align:start position:0% +p² +4 and then I look at the view factor + + align:start position:0% +4 and then I look at the view factor + + + align:start position:0% +4 and then I look at the view factor +from the Sun to the + + align:start position:0% +from the Sun to the + + + align:start position:0% +from the Sun to the +Earth is the Earth's areaid by the + + align:start position:0% +Earth is the Earth's areaid by the + + + align:start position:0% +Earth is the Earth's areaid by the +distance + + align:start position:0% +distance + + + align:start position:0% +distance +so very + + align:start position:0% +so very + + + align:start position:0% +so very +small and from Earth to the Sun so how + + align:start position:0% +small and from Earth to the Sun so how + + + align:start position:0% +small and from Earth to the Sun so how +much radiation even Earth which the sun + + align:start position:0% +much radiation even Earth which the sun + + + align:start position:0% +much radiation even Earth which the sun +that's the fraction right this is the + + align:start position:0% +that's the fraction right this is the + + + align:start position:0% +that's the fraction right this is the +fraction ration even reach the Earth + + align:start position:0% +fraction ration even reach the Earth + + + align:start position:0% +fraction ration even reach the Earth +that's here there is the reverse and + + align:start position:0% +that's here there is the reverse and + + + align:start position:0% +that's here there is the reverse and +because the side crosssection area is + + align:start position:0% +because the side crosssection area is + + + align:start position:0% +because the side crosssection area is +larger the vi + + align:start position:0% +larger the vi + + + align:start position:0% +larger the vi +from Earth to is larger fraction more + + align:start position:0% +from Earth to is larger fraction more + + + align:start position:0% +from Earth to is larger fraction more +here right so that's the uh Rel first + + align:start position:0% +here right so that's the uh Rel first + + + align:start position:0% +here right so that's the uh Rel first +you go to check the reciprocity is + + align:start position:0% +you go to check the reciprocity is + + + align:start position:0% +you go to check the reciprocity is +sfy okay now I want to + + align:start position:0% +sfy okay now I want to + + + align:start position:0% +sfy okay now I want to +calculate the Sol + + align:start position:0% +calculate the Sol + + + align:start position:0% +calculate the Sol +concept okay I said + + align:start position:0% +concept okay I said + + + align:start position:0% +concept okay I said +1366 I want to check radiation uh + + align:start position:0% +1366 I want to check radiation uh + + + align:start position:0% +1366 I want to check radiation uh +reaching the Earth + + align:start position:0% +reaching the Earth + + + align:start position:0% +reaching the Earth +from the Sun so this is the uh black + + align:start position:0% +from the Sun so this is the uh black + + + align:start position:0% +from the Sun so this is the uh black +body uh from the + + align:start position:0% +body uh from the + + + align:start position:0% +body uh from the +Sun by approximate as the blood body + + align:start position:0% +Sun by approximate as the blood body + + + align:start position:0% +Sun by approximate as the blood body +times the surface area the dis area + + align:start position:0% +times the surface area the dis area + + + align:start position:0% +times the surface area the dis area +as times the view factor from Sun to the + + align:start position:0% +as times the view factor from Sun to the + + + align:start position:0% +as times the view factor from Sun to the +Earth right so that's the total + + align:start position:0% +Earth right so that's the total + + + align:start position:0% +Earth right so that's the total +radiation from the Sun reaching the + + align:start position:0% +radiation from the Sun reaching the + + + align:start position:0% +radiation from the Sun reaching the +Earth intercepted by Earth + + align:start position:0% + + + + align:start position:0% + +and I can use the reciprocity to have a + + align:start position:0% +and I can use the reciprocity to have a + + + align:start position:0% +and I can use the reciprocity to have a +per area right because as s s e as s s + + align:start position:0% +per area right because as s s e as s s + + + align:start position:0% +per area right because as s s e as s s +e a earth f s so when I do per unit area + + align:start position:0% +e a earth f s so when I do per unit area + + + align:start position:0% +e a earth f s so when I do per unit area +I normalize I use reciprocity I will + + align:start position:0% +I normalize I use reciprocity I will + + + align:start position:0% +I normalize I use reciprocity I will +actually write this as the sign emissive + + align:start position:0% +actually write this as the sign emissive + + + align:start position:0% +actually write this as the sign emissive +Power Times the Earth to s + + align:start position:0% +Power Times the Earth to s + + + align:start position:0% +Power Times the Earth to s +to Earth but the area gives me + + align:start position:0% + + + + align:start position:0% + +Earth I + + align:start position:0% +Earth I + + + align:start position:0% +Earth I +forgot this number so this is + + align:start position:0% +forgot this number so this is + + + align:start position:0% +forgot this number so this is +stus + + align:start position:0% +stus + + + align:start position:0% +stus +IUS 8 temper power that's + + align:start position:0% +IUS 8 temper power that's + + + align:start position:0% +IUS 8 temper power that's +5.67 8 + + align:start position:0% +5.67 8 + + + align:start position:0% +5.67 8 +57 tempure + + align:start position:0% +57 tempure + + + align:start position:0% +57 tempure +times this Factor here 679 I did a + + align:start position:0% +times this Factor here 679 I did a + + + align:start position:0% +times this Factor here 679 I did a +calculation what I got is + + align:start position:0% +calculation what I got is + + + align:start position:0% +calculation what I got is +1365 pretty close Okay and Sor constant + + align:start position:0% +1365 pretty close Okay and Sor constant + + + align:start position:0% +1365 pretty close Okay and Sor constant +that you integrate is not exactly FL + + align:start position:0% +that you integrate is not exactly FL + + + align:start position:0% +that you integrate is not exactly FL +body so this is why some equivalent + + align:start position:0% +body so this is why some equivalent + + + align:start position:0% +body so this is why some equivalent + + align:start position:0% + + + align:start position:0% +okay right is + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + + align:start position:0% + +okay now now let's look at so that's the + + align:start position:0% +okay now now let's look at so that's the + + + align:start position:0% +okay now now let's look at so that's the +energy coming from the Sun to the + + align:start position:0% +energy coming from the Sun to the + + + align:start position:0% +energy coming from the Sun to the +Earth what's the maximum efficiency I + + align:start position:0% +Earth what's the maximum efficiency I + + + align:start position:0% +Earth what's the maximum efficiency I +potentially can get what's my best + + align:start position:0% +potentially can get what's my best + + + align:start position:0% +potentially can get what's my best +luck if I can convert the solar energy + + align:start position:0% +luck if I can convert the solar energy + + + align:start position:0% +luck if I can convert the solar energy +into uh into mechanical or electrical + + align:start position:0% +into uh into mechanical or electrical + + + align:start position:0% +into uh into mechanical or electrical +energy uh they maximum using C + + align:start position:0% +energy uh they maximum using C + + + align:start position:0% +energy uh they maximum using C +Thal engine right Thal engine of course + + align:start position:0% +Thal engine right Thal engine of course + + + align:start position:0% +Thal engine right Thal engine of course +is limited by the P SL no the car car + + align:start position:0% +is limited by the P SL no the car car + + + align:start position:0% +is limited by the P SL no the car car +efficiency so you can always say it's + + align:start position:0% +efficiency so you can always say it's + + + align:start position:0% +efficiency so you can always say it's +the Earth temperature and sand + + align:start position:0% +the Earth temperature and sand + + + align:start position:0% +the Earth temperature and sand +temperature you drive power efficiency + + align:start position:0% +temperature you drive power efficiency + + + align:start position:0% +temperature you drive power efficiency +between the + + align:start position:0% +between the + + + align:start position:0% +between the +two and uh you will get one + + align:start position:0% +two and uh you will get one + + + align:start position:0% +two and uh you will get one + + align:start position:0% + + + align:start position:0% +5777 which is about + + align:start position:0% +5777 which is about + + + align:start position:0% +5777 which is about +90% that's that's upper absolute + + align:start position:0% +90% that's that's upper absolute + + + align:start position:0% +90% that's that's upper absolute +absolute possible suppos you can somehow + + align:start position:0% +absolute possible suppos you can somehow + + + align:start position:0% +absolute possible suppos you can somehow +into same dire right of course we can't + + align:start position:0% +into same dire right of course we can't + + + align:start position:0% +into same dire right of course we can't +put the anything in contact with + + align:start position:0% +put the anything in contact with + + + align:start position:0% +put the anything in contact with +s and so let's dream up this + + align:start position:0% +s and so let's dream up this + + + align:start position:0% +s and so let's dream up this +process I have a body of + + align:start position:0% +process I have a body of + + + align:start position:0% +process I have a body of +this very close to my + + align:start position:0% +this very close to my + + + align:start position:0% +this very close to my +absorver right see the this is the uh uh + + align:start position:0% +absorver right see the this is the uh uh + + + align:start position:0% +absorver right see the this is the uh uh +I very close because reality can be + + align:start position:0% +I very close because reality can be + + + align:start position:0% +I very close because reality can be +close but I can focus it Focus the solar + + align:start position:0% +close but I can focus it Focus the solar + + + align:start position:0% +close but I can focus it Focus the solar +radiation and uh it turns out that if + + align:start position:0% +radiation and uh it turns out that if + + + align:start position:0% +radiation and uh it turns out that if +you do the + + align:start position:0% +you do the + + + align:start position:0% +you do the +focus and the + + align:start position:0% +focus and the + + + align:start position:0% +focus and the +uh the maximum you can get is something + + align:start position:0% +uh the maximum you can get is something + + + align:start position:0% +uh the maximum you can get is something +like gu solar temperature so uh the body + + align:start position:0% +like gu solar temperature so uh the body + + + align:start position:0% +like gu solar temperature so uh the body +at the S and I if I all the solaration + + align:start position:0% +at the S and I if I all the solaration + + + align:start position:0% +at the S and I if I all the solaration +so here is also + + align:start position:0% +so here is also + + + align:start position:0% +so here is also +body and then say I at this temperature + + align:start position:0% +body and then say I at this temperature + + + align:start position:0% +body and then say I at this temperature +T and then I put the engine in between + + align:start position:0% +T and then I put the engine in between + + + align:start position:0% +T and then I put the engine in between +this absorber and the and the output and + + align:start position:0% +this absorber and the and the output and + + + align:start position:0% +this absorber and the and the output and +I can imagine this engine is perfect + + align:start position:0% +I can imagine this engine is perfect + + + align:start position:0% +I can imagine this engine is perfect +car so what would be the + + align:start position:0% +car so what would be the + + + align:start position:0% +car so what would be the +efficiency of such a uh + + align:start position:0% + + + + align:start position:0% + +this and first I want to see how much + + align:start position:0% +this and first I want to see how much + + + align:start position:0% +this and first I want to see how much +heat can go from the sand to + + align:start position:0% +heat can go from the sand to + + + align:start position:0% +heat can go from the sand to +this right here I'm doing two black body + + align:start position:0% +this right here I'm doing two black body + + + align:start position:0% +this right here I'm doing two black body +so black body radiation is + + align:start position:0% +so black body radiation is + + + align:start position:0% +so black body radiation is +from4 power you can see now I don't have + + align:start position:0% +from4 power you can see now I don't have + + + align:start position:0% +from4 power you can see now I don't have +this very small view right I'm just + + align:start position:0% +this very small view right I'm just + + + align:start position:0% +this very small view right I'm just +doing two parallel + + align:start position:0% +doing two parallel + + + align:start position:0% +doing two parallel +plates Okay so Sigma G4 area + + align:start position:0% +plates Okay so Sigma G4 area + + + align:start position:0% +plates Okay so Sigma G4 area +is no area difference anymore Sigma G4 + + align:start position:0% +is no area difference anymore Sigma G4 + + + align:start position:0% +is no area difference anymore Sigma G4 +powerus this radiation now the absorber + + align:start position:0% +powerus this radiation now the absorber + + + align:start position:0% +powerus this radiation now the absorber +will radiated back + + align:start position:0% + + + + align:start position:0% + +so so that's the the heat transfer from + + align:start position:0% +so so that's the the heat transfer from + + + align:start position:0% +so so that's the the heat transfer from +the sand to this + + align:start position:0% +the sand to this + + + align:start position:0% +the sand to this +absorver okay maximum you can + + align:start position:0% +absorver okay maximum you can + + + align:start position:0% +absorver okay maximum you can +get and + + align:start position:0% +get and + + + align:start position:0% +get and +the so that means the thermal + + align:start position:0% +the so that means the thermal + + + align:start position:0% +the so that means the thermal +efficiency right what comes in the Solar + + align:start position:0% +efficiency right what comes in the Solar + + + align:start position:0% +efficiency right what comes in the Solar +is Sigma t for power and the am of that + + align:start position:0% +is Sigma t for power and the am of that + + + align:start position:0% +is Sigma t for power and the am of that +actually is + + align:start position:0% + + + + align:start position:0% + +T4 + + align:start position:0% +T4 + + + align:start position:0% +T4 +efficiency is the + + align:start position:0% +efficiency is the + + + align:start position:0% +efficiency is the +onece + + align:start position:0% + + + + align:start position:0% + +power so the high the temperature is + + align:start position:0% +power so the high the temperature is + + + align:start position:0% +power so the high the temperature is +absorber the is no is + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% + + + + align:start position:0% + +and the + + align:start position:0% +and the + + + align:start position:0% +and the +efficiency is + + align:start position:0% +efficiency is + + + align:start position:0% +efficiency is +here okay and in fact as a move on you + + align:start position:0% +here okay and in fact as a move on you + + + align:start position:0% +here okay and in fact as a move on you +should ask questions because what the + + align:start position:0% +should ask questions because what the + + + align:start position:0% +should ask questions because what the +question is what if I use selective + + align:start position:0% + + + + align:start position:0% + +surface why you put a FL body here + + align:start position:0% +surface why you put a FL body here + + + align:start position:0% +surface why you put a FL body here +and this will be related to what kind of + + align:start position:0% +and this will be related to what kind of + + + align:start position:0% +and this will be related to what kind of +concentration how you concentrate + + align:start position:0% +concentration how you concentrate + + + align:start position:0% +concentration how you concentrate +because here I'm really putting the + + align:start position:0% +because here I'm really putting the + + + align:start position:0% +because here I'm really putting the +maximum temperature really like this is + + align:start position:0% +maximum temperature really like this is + + + align:start position:0% +maximum temperature really like this is +the this black body they facing each + + align:start position:0% +the this black body they facing each + + + align:start position:0% +the this black body they facing each +other right and that will require you + + align:start position:0% +other right and that will require you + + + align:start position:0% +other right and that will require you +put your maximum + + align:start position:0% +put your maximum + + + align:start position:0% +put your maximum +concentration and in the case of Maximum + + align:start position:0% +concentration and in the case of Maximum + + + align:start position:0% +concentration and in the case of Maximum +concentration the EM the the emission of + + align:start position:0% +concentration the EM the the emission of + + + align:start position:0% +concentration the EM the the emission of +this surface becomes uh + + align:start position:0% +this surface becomes uh + + + align:start position:0% +this surface becomes uh +not important it's really the absorption + + align:start position:0% +not important it's really the absorption + + + align:start position:0% +not important it's really the absorption +that's most important absorption the + + align:start position:0% +that's most important absorption the + + + align:start position:0% +that's most important absorption the +higher the better the FAS is why you get + + align:start position:0% +higher the better the FAS is why you get + + + align:start position:0% +higher the better the FAS is why you get +body that's + + align:start position:0% + + + + align:start position:0% + +why so now I have a theral efficiency I + + align:start position:0% +why so now I have a theral efficiency I + + + align:start position:0% +why so now I have a theral efficiency I +have col efficiency and the product of + + align:start position:0% +have col efficiency and the product of + + + align:start position:0% +have col efficiency and the product of +the two gives me the + + align:start position:0% +the two gives me the + + + align:start position:0% +the two gives me the +maximum they combin efficiency so this + + align:start position:0% +maximum they combin efficiency so this + + + align:start position:0% +maximum they combin efficiency so this +is the theral efficiency this is the col + + align:start position:0% +is the theral efficiency this is the col + + + align:start position:0% +is the theral efficiency this is the col +efficiency of course col efficiency you + + align:start position:0% +efficiency of course col efficiency you + + + align:start position:0% +efficiency of course col efficiency you +want to operate your engine as high + + align:start position:0% +want to operate your engine as high + + + align:start position:0% +want to operate your engine as high +temperature as possible the thermal + + align:start position:0% +temperature as possible the thermal + + + align:start position:0% +temperature as possible the thermal +efficiency as you operate the higher + + align:start position:0% +efficiency as you operate the higher + + + align:start position:0% +efficiency as you operate the higher +temperature radiation L + + align:start position:0% +temperature radiation L + + + align:start position:0% +temperature radiation L +increase so you have a + + align:start position:0% +increase so you have a + + + align:start position:0% +increase so you have a +Max this is the maximum efficiency you + + align:start position:0% +Max this is the maximum efficiency you + + + align:start position:0% +Max this is the maximum efficiency you +can get about + + align:start position:0% +can get about + + + align:start position:0% +can get about +85% efficiency out of the Sun and this + + align:start position:0% +85% efficiency out of the Sun and this + + + align:start position:0% +85% efficiency out of the Sun and this +happens around + + align:start position:0% + + + + align:start position:0% + +2450 when you + + align:start position:0% + + + + align:start position:0% + +have interesting is actually there's a + + align:start position:0% +have interesting is actually there's a + + + align:start position:0% +have interesting is actually there's a +pretty wide range the efficiency this + + align:start position:0% +pretty wide range the efficiency this + + + align:start position:0% +pretty wide range the efficiency this +this is this is actually really + + align:start position:0% +this is this is actually really + + + align:start position:0% +this is this is actually really +good pretty flat relative + + align:start position:0% +good pretty flat relative + + + align:start position:0% +good pretty flat relative +flat okay and so if you operate if you + + align:start position:0% +flat okay and so if you operate if you + + + align:start position:0% +flat okay and so if you operate if you +think about here is only about de here + + align:start position:0% +think about here is only about de here + + + align:start position:0% +think about here is only about de here +is full + + align:start position:0% +is full + + + align:start position:0% +is full +be and this is + + align:start position:0% +be and this is + + + align:start position:0% +be and this is +70% right pretty good if you get and we + + align:start position:0% +70% right pretty good if you get and we + + + align:start position:0% +70% right pretty good if you get and we +know the sour of the core plant is only + + align:start position:0% +know the sour of the core plant is only + + + align:start position:0% +know the sour of the core plant is only +40% the combined that's the cold buring + + align:start position:0% +40% the combined that's the cold buring + + + align:start position:0% +40% the combined that's the cold buring +PL coal PL is about + + align:start position:0% +PL coal PL is about + + + align:start position:0% +PL coal PL is about +40% and if you combine gas turbine and + + align:start position:0% +40% and if you combine gas turbine and + + + align:start position:0% +40% and if you combine gas turbine and +combine cycle combine gas turbine with + + align:start position:0% +combine cycle combine gas turbine with + + + align:start position:0% +combine cycle combine gas turbine with +steam turbine so you you burn uh fuels + + align:start position:0% +steam turbine so you you burn uh fuels + + + align:start position:0% +steam turbine so you you burn uh fuels +you generally hot gas and gas uh profile + + align:start position:0% +you generally hot gas and gas uh profile + + + align:start position:0% +you generally hot gas and gas uh profile +turbine uh say gas turbine and exhaust + + align:start position:0% +turbine uh say gas turbine and exhaust + + + align:start position:0% +turbine uh say gas turbine and exhaust +gener steam steam steam driver steam + + align:start position:0% +gener steam steam steam driver steam + + + align:start position:0% +gener steam steam steam driver steam +turine that combined by + + align:start position:0% +turine that combined by + + + align:start position:0% +turine that combined by +6% that's best that's you can do the uh + + align:start position:0% +6% that's best that's you can do the uh + + + align:start position:0% +6% that's best that's you can do the uh +the fuels and internal combustion engine + + align:start position:0% +the fuels and internal combustion engine + + + align:start position:0% +the fuels and internal combustion engine +the car is about 25 to + + align:start position:0% +the car is about 25 to + + + align:start position:0% +the car is about 25 to +30% so that's the uh so uh so this is a + + align:start position:0% +30% so that's the uh so uh so this is a + + + align:start position:0% +30% so that's the uh so uh so this is a +pretty optim value here so if you put + + align:start position:0% +pretty optim value here so if you put + + + align:start position:0% +pretty optim value here so if you put +your solar if you put a server engine + + align:start position:0% +your solar if you put a server engine + + + align:start position:0% +your solar if you put a server engine +between the using he from the sun right + + align:start position:0% +between the using he from the sun right + + + align:start position:0% +between the using he from the sun right +but of course there are many + + align:start position:0% + + + + align:start position:0% + +limitation + + align:start position:0% +limitation + + + align:start position:0% +limitation +okay now uh the next question I want to + + align:start position:0% +okay now uh the next question I want to + + + align:start position:0% +okay now uh the next question I want to +ask + + align:start position:0% +ask + + + align:start position:0% +ask +is if I put a material here under this + + align:start position:0% +is if I put a material here under this + + + align:start position:0% +is if I put a material here under this +how far I can get what's the + + align:start position:0% + + + + align:start position:0% + +okay and uh I can imagine a case where + + align:start position:0% +okay and uh I can imagine a case where + + + align:start position:0% +okay and uh I can imagine a case where +it could potentially get to very high + + align:start position:0% +it could potentially get to very high + + + align:start position:0% +it could potentially get to very high +temperature and this is a this radiation + + align:start position:0% +temperature and this is a this radiation + + + align:start position:0% +temperature and this is a this radiation +comes in you will be up FL now I don't + + align:start position:0% +comes in you will be up FL now I don't + + + align:start position:0% +comes in you will be up FL now I don't +think about the direction let me just + + align:start position:0% +think about the direction let me just + + + align:start position:0% +think about the direction let me just +say all Direction same and again this + + align:start position:0% +say all Direction same and again this + + + align:start position:0% +say all Direction same and again this +because of that maybe you have ways to + + align:start position:0% +because of that maybe you have ways to + + + align:start position:0% +because of that maybe you have ways to +do better I don't know yet so Rel I'm + + align:start position:0% +do better I don't know yet so Rel I'm + + + align:start position:0% +do better I don't know yet so Rel I'm +see is absorptivity of the surface is + + align:start position:0% +see is absorptivity of the surface is + + + align:start position:0% +see is absorptivity of the surface is +the function of + + align:start position:0% +the function of + + + align:start position:0% +the function of +Lambda and then also uh the emission you + + align:start position:0% +Lambda and then also uh the emission you + + + align:start position:0% +Lambda and then also uh the emission you +will radiate right so absorption if I do + + align:start position:0% +will radiate right so absorption if I do + + + align:start position:0% +will radiate right so absorption if I do +the r + + align:start position:0% +the r + + + align:start position:0% +the r +i + + align:start position:0% + + + + align:start position:0% + +absor at least if I say the rational the + + align:start position:0% +absor at least if I say the rational the + + + align:start position:0% +absor at least if I say the rational the +same so it's all diffus you can imagine + + align:start position:0% +same so it's all diffus you can imagine + + + align:start position:0% +same so it's all diffus you can imagine +that + + align:start position:0% +that + + + align:start position:0% +that +okay so when I do + + align:start position:0% +okay so when I do + + + align:start position:0% +okay so when I do +this uh uh I will + + align:start position:0% +this uh uh I will + + + align:start position:0% +this uh uh I will +have the absorbed energy this is the uh + + align:start position:0% +have the absorbed energy this is the uh + + + align:start position:0% +have the absorbed energy this is the uh +you can see this is the Spectrum from + + align:start position:0% +you can see this is the Spectrum from + + + align:start position:0% +you can see this is the Spectrum from +the and times + + align:start position:0% +the and times + + + align:start position:0% +the and times +absity clear I angle right and + + align:start position:0% +absity clear I angle right and + + + align:start position:0% +absity clear I angle right and +integrated over D + + align:start position:0% +integrated over D + + + align:start position:0% +integrated over D +Lambda so that's all the energy comes in + + align:start position:0% +Lambda so that's all the energy comes in + + + align:start position:0% +Lambda so that's all the energy comes in +and then uh this is the + + align:start position:0% +and then uh this is the + + + align:start position:0% +and then uh this is the +energy that is + + align:start position:0% +energy that is + + + align:start position:0% +energy that is +reated one is the surface + + align:start position:0% +reated one is the surface + + + align:start position:0% +reated one is the surface +radiation body emission this body + + align:start position:0% +radiation body emission this body + + + align:start position:0% +radiation body emission this body +emission but also the ambient + + align:start position:0% +emission but also the ambient + + + align:start position:0% +emission but also the ambient +is you have change here and ambient so + + align:start position:0% +is you have change here and ambient so + + + align:start position:0% +is you have change here and ambient so +uh this is the relation to the ENT T + + align:start position:0% +uh this is the relation to the ENT T + + + align:start position:0% +uh this is the relation to the ENT T +should not be t + + align:start position:0% + + + + align:start position:0% + +and here I have + + align:start position:0% +and here I have + + + align:start position:0% +and here I have +contion as I said this may not be I + + align:start position:0% +contion as I said this may not be I + + + align:start position:0% +contion as I said this may not be I +think this probably is not the maximum + + align:start position:0% +think this probably is not the maximum + + + align:start position:0% +think this probably is not the maximum +well as I talk I'm just making comments + + align:start position:0% +well as I talk I'm just making comments + + + align:start position:0% +well as I talk I'm just making comments +uh because ration from the sun is in a + + align:start position:0% +uh because ration from the sun is in a + + + align:start position:0% +uh because ration from the sun is in a +very small angle right it's almost lower + + align:start position:0% +very small angle right it's almost lower + + + align:start position:0% +very small angle right it's almost lower +in you see lower + + align:start position:0% +in you see lower + + + align:start position:0% +in you see lower +incidence and when I write + + align:start position:0% +incidence and when I write + + + align:start position:0% +incidence and when I write +this and writing the + + align:start position:0% +this and writing the + + + align:start position:0% +this and writing the +emissivity + + align:start position:0% +emissivity + + + align:start position:0% +emissivity +isotop I could potentially design + + align:start position:0% +isotop I could potentially design + + + align:start position:0% +isotop I could potentially design +surface emission only also in the same + + align:start position:0% +surface emission only also in the same + + + align:start position:0% +surface emission only also in the same +angle where the same then I have to do + + align:start position:0% +angle where the same then I have to do + + + align:start position:0% +angle where the same then I have to do +angular integration that uh probably go + + align:start position:0% +angular integration that uh probably go + + + align:start position:0% +angular integration that uh probably go +even higher temperature than this if I + + align:start position:0% +even higher temperature than this if I + + + align:start position:0% +even higher temperature than this if I +just make that + + align:start position:0% +just make that + + + align:start position:0% +just make that +guess + + align:start position:0% + + + + align:start position:0% + +okay so uh once they uh uh terms of the + + align:start position:0% +okay so uh once they uh uh terms of the + + + align:start position:0% +okay so uh once they uh uh terms of the +um how I the spectral characteristics + + align:start position:0% +um how I the spectral characteristics + + + align:start position:0% +um how I the spectral characteristics +right so if you look at this is the + + align:start position:0% +right so if you look at this is the + + + align:start position:0% +right so if you look at this is the +radiation from the Sun and this might be + + align:start position:0% +radiation from the Sun and this might be + + + align:start position:0% +radiation from the Sun and this might be +the radiation emission from the + + align:start position:0% +the radiation emission from the + + + align:start position:0% +the radiation emission from the +surface + + align:start position:0% +surface + + + align:start position:0% +surface +and at each wav length right so you can + + align:start position:0% +and at each wav length right so you can + + + align:start position:0% +and at each wav length right so you can +design your selective surface + + align:start position:0% +design your selective surface + + + align:start position:0% +design your selective surface +IDE you can design if you could okay + + align:start position:0% +IDE you can design if you could okay + + + align:start position:0% +IDE you can design if you could okay +seriously uh no seriously + + align:start position:0% +seriously uh no seriously + + + align:start position:0% +seriously uh no seriously +not but it's hard to do but let's just + + align:start position:0% +not but it's hard to do but let's just + + + align:start position:0% +not but it's hard to do but let's just +say imagine I have I have that magic + + align:start position:0% +say imagine I have I have that magic + + + align:start position:0% +say imagine I have I have that magic +surface that I have a sharp cut off so + + align:start position:0% +surface that I have a sharp cut off so + + + align:start position:0% +surface that I have a sharp cut off so +below certain mment all the radiation is + + align:start position:0% +below certain mment all the radiation is + + + align:start position:0% +below certain mment all the radiation is +absorbed so that could be the + + align:start position:0% +absorbed so that could be the + + + align:start position:0% +absorbed so that could be the +solaration right and then uh beyond that + + align:start position:0% +solaration right and then uh beyond that + + + align:start position:0% +solaration right and then uh beyond that +all radiation is + + align:start position:0% +all radiation is + + + align:start position:0% +all radiation is +rejected so that's the spectral idea one + + align:start position:0% +rejected so that's the spectral idea one + + + align:start position:0% +rejected so that's the spectral idea one +z uh spectral properties select + + align:start position:0% +z uh spectral properties select + + + align:start position:0% +z uh spectral properties select +surface and uh so if this selective + + align:start position:0% +surface and uh so if this selective + + + align:start position:0% +surface and uh so if this selective +surface is one zero and I can look at if + + align:start position:0% +surface is one zero and I can look at if + + + align:start position:0% +surface is one zero and I can look at if +I design The Selective equivalence here + + align:start position:0% +I design The Selective equivalence here + + + align:start position:0% +I design The Selective equivalence here +if you look at it right this FL body + + align:start position:0% +if you look at it right this FL body + + + align:start position:0% +if you look at it right this FL body +from emission reduces rapidly so if I + + align:start position:0% +from emission reduces rapidly so if I + + + align:start position:0% +from emission reduces rapidly so if I +make my here this will be Cal and now I + + align:start position:0% +make my here this will be Cal and now I + + + align:start position:0% +make my here this will be Cal and now I +have to remind you of + + align:start position:0% +have to remind you of + + + align:start position:0% +have to remind you of +calope when I say this + + align:start position:0% +calope when I say this + + + align:start position:0% +calope when I say this +spectrum this absortion one I also mean + + align:start position:0% +spectrum this absortion one I also mean + + + align:start position:0% +spectrum this absortion one I also mean +the + + align:start position:0% +the + + + align:start position:0% +the +emission is also one right I can't + + align:start position:0% +emission is also one right I can't + + + align:start position:0% +emission is also one right I can't +violate that so this radiation will be + + align:start position:0% +violate that so this radiation will be + + + align:start position:0% +violate that so this radiation will be +going out this blue in this region will + + align:start position:0% +going out this blue in this region will + + + align:start position:0% +going out this blue in this region will +Beed if I absorb + + align:start position:0% +Beed if I absorb + + + align:start position:0% +Beed if I absorb +everything uh from this + + align:start position:0% +everything uh from this + + + align:start position:0% +everything uh from this +side that's the second what tells me so + + align:start position:0% +side that's the second what tells me so + + + align:start position:0% +side that's the second what tells me so +uh if I have I change this W you can say + + align:start position:0% +uh if I have I change this W you can say + + + align:start position:0% +uh if I have I change this W you can say +now I make the W + + align:start position:0% +now I make the W + + + align:start position:0% +now I make the W +shorter there's less emission from the + + align:start position:0% +shorter there's less emission from the + + + align:start position:0% +shorter there's less emission from the +blue curve because here is almost zero + + align:start position:0% +blue curve because here is almost zero + + + align:start position:0% +blue curve because here is almost zero +but there's still a fraction of the S + + align:start position:0% +but there's still a fraction of the S + + + align:start position:0% +but there's still a fraction of the S +radiation that comes in + + align:start position:0% +radiation that comes in + + + align:start position:0% +radiation that comes in +absorb right so I want do my energy + + align:start position:0% +absorb right so I want do my energy + + + align:start position:0% +absorb right so I want do my energy +balance say what's the maximum + + align:start position:0% +balance say what's the maximum + + + align:start position:0% +balance say what's the maximum +temperature I can get just with a flat + + align:start position:0% +temperature I can get just with a flat + + + align:start position:0% +temperature I can get just with a flat +surface one + + align:start position:0% +surface one + + + align:start position:0% +surface one +side okay so Cal to one and I do rather + + align:start position:0% +side okay so Cal to one and I do rather + + + align:start position:0% +side okay so Cal to one and I do rather +than do BL body back from here I was + + align:start position:0% +than do BL body back from here I was + + + align:start position:0% +than do BL body back from here I was +trying to do this by by hand and then + + align:start position:0% +trying to do this by by hand and then + + + align:start position:0% +trying to do this by by hand and then +later on I found I still couldn't solve + + align:start position:0% +later on I found I still couldn't solve + + + align:start position:0% +later on I found I still couldn't solve +the equation + + align:start position:0% + + + + align:start position:0% + +I lat so here is the uh uh the + + align:start position:0% +I lat so here is the uh uh the + + + align:start position:0% +I lat so here is the uh uh the +Rel from the and I see absortion one + + align:start position:0% +Rel from the and I see absortion one + + + align:start position:0% +Rel from the and I see absortion one +between Z Lambda so this is white PS + + align:start position:0% +between Z Lambda so this is white PS + + + align:start position:0% +between Z Lambda so this is white PS +what comes to from the sunand so view + + align:start position:0% +what comes to from the sunand so view + + + align:start position:0% +what comes to from the sunand so view +factor from sunand to Earth surface the + + align:start position:0% +factor from sunand to Earth surface the + + + align:start position:0% +factor from sunand to Earth surface the +surface area of the + + align:start position:0% +surface area of the + + + align:start position:0% +surface area of the +sand of theand Lambda that's what comes + + align:start position:0% +sand of theand Lambda that's what comes + + + align:start position:0% +sand of theand Lambda that's what comes +to surface and this is the + + align:start position:0% +to surface and this is the + + + align:start position:0% +to surface and this is the +emion uh reling out from this surface so + + align:start position:0% +emion uh reling out from this surface so + + + align:start position:0% +emion uh reling out from this surface so +I'm assuming this surface is the in the + + align:start position:0% +I'm assuming this surface is the in the + + + align:start position:0% +I'm assuming this surface is the in the +side directly right there's no angle + + align:start position:0% +side directly right there's no angle + + + align:start position:0% +side directly right there's no angle +CH and uhing out and emission to + + align:start position:0% + + + + align:start position:0% + +the okay and of course say I use this + + align:start position:0% +the okay and of course say I use this + + + align:start position:0% +the okay and of course say I use this +trick before this area time VI factor is + + align:start position:0% +trick before this area time VI factor is + + + align:start position:0% +trick before this area time VI factor is +same area on the factor from to so that + + align:start position:0% +same area on the factor from to so that + + + align:start position:0% +same area on the factor from to so that +I can cancel the area so independent of + + align:start position:0% +I can cancel the area so independent of + + + align:start position:0% +I can cancel the area so independent of +area + + align:start position:0% +area + + + align:start position:0% +area +here + + align:start position:0% +here + + + align:start position:0% +here +right I can cancel the area and uh + + align:start position:0% +right I can cancel the area and uh + + + align:start position:0% +right I can cancel the area and uh +that's why I was doing the universal + + align:start position:0% +that's why I was doing the universal + + + align:start position:0% +that's why I was doing the universal +black Body Curve so if I do my Universal + + align:start position:0% +black Body Curve so if I do my Universal + + + align:start position:0% +black Body Curve so if I do my Universal +black Body Curve this is the uh relation + + align:start position:0% +black Body Curve this is the uh relation + + + align:start position:0% +black Body Curve this is the uh relation +between the same tempu any we to same + + align:start position:0% +between the same tempu any we to same + + + align:start position:0% +between the same tempu any we to same +temp power this is the function I want + + align:start position:0% +temp power this is the function I want + + + align:start position:0% +temp power this is the function I want +to find the time temperature I thought I + + align:start position:0% +to find the time temperature I thought I + + + align:start position:0% +to find the time temperature I thought I +could do this by hand again function is + + align:start position:0% +could do this by hand again function is + + + align:start position:0% +could do this by hand again function is +not I + + align:start position:0% + + + + align:start position:0% + +have so but this is definitely solvable + + align:start position:0% +have so but this is definitely solvable + + + align:start position:0% +have so but this is definitely solvable +you can go to solve the equation you can + + align:start position:0% +you can go to solve the equation you can + + + align:start position:0% +you can go to solve the equation you can +even take the real Spectrum to solve it + + align:start position:0% +even take the real Spectrum to solve it + + + align:start position:0% +even take the real Spectrum to solve it +rather than doing BL body Spectrum as + + align:start position:0% +rather than doing BL body Spectrum as + + + align:start position:0% +rather than doing BL body Spectrum as +I'm doing here I I've written down in + + align:start position:0% +I'm doing here I I've written down in + + + align:start position:0% +I'm doing here I I've written down in +fact that's what K has done uh uh this + + align:start position:0% +fact that's what K has done uh uh this + + + align:start position:0% +fact that's what K has done uh uh this +is the curve a z + + align:start position:0% +is the curve a z + + + align:start position:0% +is the curve a z +condition and if you choose your wance + + align:start position:0% +condition and if you choose your wance + + + align:start position:0% +condition and if you choose your wance +it's interesting that the shorter the + + align:start position:0% +it's interesting that the shorter the + + + align:start position:0% +it's interesting that the shorter the +wance you choose the higher the + + align:start position:0% +wance you choose the higher the + + + align:start position:0% +wance you choose the higher the +temperature you + + align:start position:0% +temperature you + + + align:start position:0% +temperature you +get that's because the loss is smaller + + align:start position:0% +get that's because the loss is smaller + + + align:start position:0% +get that's because the loss is smaller +right you look at it you go to Shi to + + align:start position:0% +right you look at it you go to Shi to + + + align:start position:0% +right you look at it you go to Shi to +small W you absorb the radiation but you + + align:start position:0% +small W you absorb the radiation but you + + + align:start position:0% +small W you absorb the radiation but you +lose very small because this curve once + + align:start position:0% +lose very small because this curve once + + + align:start position:0% +lose very small because this curve once +you go to very short this curve is + + align:start position:0% +you go to very short this curve is + + + align:start position:0% +you go to very short this curve is +always below + + align:start position:0% +always below + + + align:start position:0% +always below +the Cur of the + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +reun and so your uh uh isn't this + + align:start position:0% +reun and so your uh uh isn't this + + + align:start position:0% +reun and so your uh uh isn't this +amazing if you have that surface + + align:start position:0% +amazing if you have that surface + + + align:start position:0% +amazing if you have that surface +here + + align:start position:0% + + + + align:start position:0% + +my water + + align:start position:0% + + + + align:start position:0% + +yes no and no + + align:start position:0% +yes no and no + + + align:start position:0% +yes no and no +let's say no Optical treatment no + + align:start position:0% +let's say no Optical treatment no + + + align:start position:0% +let's say no Optical treatment no +filters it's definitely not + + align:start position:0% +filters it's definitely not + + + align:start position:0% +filters it's definitely not +600 no no 81 it's 81 yes I I what is + + align:start position:0% +600 no no 81 it's 81 yes I I what is + + + align:start position:0% +600 no no 81 it's 81 yes I I what is +that is is a flat panel flat panel yeah + + align:start position:0% +that is is a flat panel flat panel yeah + + + align:start position:0% +that is is a flat panel flat panel yeah +flat panel you got a lot of losses first + + align:start position:0% +flat panel you got a lot of losses first + + + align:start position:0% +flat panel you got a lot of losses first +the services is not bad the actually + + align:start position:0% +the services is not bad the actually + + + align:start position:0% +the services is not bad the actually +industry has done pretty good job and uh + + align:start position:0% +industry has done pretty good job and uh + + + align:start position:0% +industry has done pretty good job and uh +you can + + align:start position:0% +you can + + + align:start position:0% +you can +buy uh I this is part of the that we + + align:start position:0% +buy uh I this is part of the that we + + + align:start position:0% +buy uh I this is part of the that we +talk later you can I uh commercial this + + align:start position:0% +talk later you can I uh commercial this + + + align:start position:0% +talk later you can I uh commercial this +hot water uh surfaces have 95% + + align:start position:0% +hot water uh surfaces have 95% + + + align:start position:0% +hot water uh surfaces have 95% +of + + align:start position:0% +of + + + align:start position:0% +of +5% not sh we have example later and not + + align:start position:0% +5% not sh we have example later and not + + + align:start position:0% +5% not sh we have example later and not +flat panel it's not a vacum you take a + + align:start position:0% +flat panel it's not a vacum you take a + + + align:start position:0% +flat panel it's not a vacum you take a +vacuum tube that that CH use you put on + + align:start position:0% +vacuum tube that that CH use you put on + + + align:start position:0% +vacuum tube that that CH use you put on +sun it go to + + align:start position:0% +sun it go to + + + align:start position:0% +sun it go to +200° right uh that's you don't have + + align:start position:0% +200° right uh that's you don't have + + + align:start position:0% +200° right uh that's you don't have +water inside just dry right + + align:start position:0% + + + + align:start position:0% + +okay yeah so this is the uh uh the I + + align:start position:0% +okay yeah so this is the uh uh the I + + + align:start position:0% +okay yeah so this is the uh uh the I +guess the point + + align:start position:0% +guess the point + + + align:start position:0% +guess the point +is if you can design right in here is if + + align:start position:0% +is if you can design right in here is if + + + align:start position:0% +is if you can design right in here is if +you recall for a thermal engine 8 + + align:start position:0% +you recall for a thermal engine 8 + + + align:start position:0% +you recall for a thermal engine 8 +85% efficieny range or 70 + + align:start position:0% +85% efficieny range or 70 + + + align:start position:0% +85% efficieny range or 70 +85 right you need a thousand to 4,000 + + align:start position:0% +85 right you need a thousand to 4,000 + + + align:start position:0% +85 right you need a thousand to 4,000 +temperature + + align:start position:0% +temperature + + + align:start position:0% +temperature +R and here it doesn't seem to be that + + align:start position:0% +R and here it doesn't seem to be that + + + align:start position:0% +R and here it doesn't seem to be that +hard right if you got that surface of + + align:start position:0% +hard right if you got that surface of + + + align:start position:0% +hard right if you got that surface of +course that's really IDE + + align:start position:0% + + + + align:start position:0% + +surface with one Sun + + align:start position:0% + + + + align:start position:0% + +black and here is another example 1.5 + + align:start position:0% +black and here is another example 1.5 + + + align:start position:0% +black and here is another example 1.5 +that's Earth and again + + align:start position:0% + + + + align:start position:0% + +okay now uh but those IDE situation + + align:start position:0% +okay now uh but those IDE situation + + + align:start position:0% +okay now uh but those IDE situation +could do almost this doesn't give you + + align:start position:0% +could do almost this doesn't give you + + + align:start position:0% +could do almost this doesn't give you +any + + align:start position:0% +any + + + align:start position:0% +any +power right what we did is just + + align:start position:0% +power right what we did is just + + + align:start position:0% +power right what we did is just +say is com in equals to the L no power + + align:start position:0% +say is com in equals to the L no power + + + align:start position:0% +say is com in equals to the L no power +right so now let's look at the more + + align:start position:0% +right so now let's look at the more + + + align:start position:0% +right so now let's look at the more +realistic case where uh this is still + + align:start position:0% +realistic case where uh this is still + + + align:start position:0% +realistic case where uh this is still +the surface right here but I I don't uh + + align:start position:0% +the surface right here but I I don't uh + + + align:start position:0% +the surface right here but I I don't uh +uh + + align:start position:0% +uh + + + align:start position:0% +uh +optimize the temperature trying to reach + + align:start position:0% +optimize the temperature trying to reach + + + align:start position:0% +optimize the temperature trying to reach +maximum temperature I try to say given a + + align:start position:0% +maximum temperature I try to say given a + + + align:start position:0% +maximum temperature I try to say given a +temperature of + + align:start position:0% +temperature of + + + align:start position:0% +temperature of +operation once the uh I choose the the + + align:start position:0% +operation once the uh I choose the the + + + align:start position:0% +operation once the uh I choose the the +wance so the the way I choose wance if I + + align:start position:0% +wance so the the way I choose wance if I + + + align:start position:0% +wance so the the way I choose wance if I +see this is the curve here the coming in + + align:start position:0% +see this is the curve here the coming in + + + align:start position:0% +see this is the curve here the coming in +from the Sun and at this the body at + + align:start position:0% +from the Sun and at this the body at + + + align:start position:0% +from the Sun and at this the body at +this temperature the black body + + align:start position:0% +this temperature the black body + + + align:start position:0% +this temperature the black body +intersect the uh solar radiation at this + + align:start position:0% +intersect the uh solar radiation at this + + + align:start position:0% +intersect the uh solar radiation at this +temperature this W so I cut out this + + align:start position:0% +temperature this W so I cut out this + + + align:start position:0% +temperature this W so I cut out this +point and below this W I have one about + + align:start position:0% +point and below this W I have one about + + + align:start position:0% +point and below this W I have one about +I have + + align:start position:0% +I have + + + align:start position:0% +I have +zero so the difference from the previous + + align:start position:0% +zero so the difference from the previous + + + align:start position:0% +zero so the difference from the previous +discussion is previously I see at each w + + align:start position:0% +discussion is previously I see at each w + + + align:start position:0% +discussion is previously I see at each w +l was maximum temperature and here is I + + align:start position:0% +l was maximum temperature and here is I + + + align:start position:0% +l was maximum temperature and here is I +give a temperature I choose my wave + + align:start position:0% +give a temperature I choose my wave + + + align:start position:0% +give a temperature I choose my wave +length Okay and then I say if I operate + + align:start position:0% +length Okay and then I say if I operate + + + align:start position:0% +length Okay and then I say if I operate +the heat engine + + align:start position:0% +the heat engine + + + align:start position:0% +the heat engine +at this + + align:start position:0% +at this + + + align:start position:0% +at this +temperature what's the efficiency I can + + align:start position:0% +temperature what's the efficiency I can + + + align:start position:0% +temperature what's the efficiency I can +get + + align:start position:0% +get + + + align:start position:0% +get +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and so this is the uh the same picture + + align:start position:0% +and so this is the uh the same picture + + + align:start position:0% +and so this is the uh the same picture +here than this + + align:start position:0% +here than this + + + align:start position:0% +here than this +just work together say I'm at one + + align:start position:0% +just work together say I'm at one + + + align:start position:0% +just work together say I'm at one +side okay again like what I said um now + + align:start position:0% +side okay again like what I said um now + + + align:start position:0% +side okay again like what I said um now +in this case the thermal + + align:start position:0% +in this case the thermal + + + align:start position:0% +in this case the thermal +efficiency is uh what comes in the total + + align:start position:0% +efficiency is uh what comes in the total + + + align:start position:0% +efficiency is uh what comes in the total +and then this part is lost the blue c + + align:start position:0% +and then this part is lost the blue c + + + align:start position:0% +and then this part is lost the blue c +part is + + align:start position:0% +part is + + + align:start position:0% +part is +lost right so if I + + align:start position:0% +lost right so if I + + + align:start position:0% +lost right so if I +calculate the thermal + + align:start position:0% +calculate the thermal + + + align:start position:0% +calculate the thermal +efficiency and this is this is the king + + align:start position:0% +efficiency and this is this is the king + + + align:start position:0% +efficiency and this is this is the king +calculation and as you uh here is the + + align:start position:0% +calculation and as you uh here is the + + + align:start position:0% +calculation and as you uh here is the +thermal efficiency so uh + + align:start position:0% +thermal efficiency so uh + + + align:start position:0% +thermal efficiency so uh +the loss + + align:start position:0% +the loss + + + align:start position:0% +the loss +is this is the larger the blue the + + align:start position:0% +is this is the larger the blue the + + + align:start position:0% +is this is the larger the blue the +purple area + + align:start position:0% +purple area + + + align:start position:0% +purple area +is area this is A9 High Thal efficiency + + align:start position:0% +is area this is A9 High Thal efficiency + + + align:start position:0% +is area this is A9 High Thal efficiency +so + + align:start position:0% +so + + + align:start position:0% +so +naturally if you want to have a good + + align:start position:0% +naturally if you want to have a good + + + align:start position:0% +naturally if you want to have a good +theral efficiency you want to re out + + align:start position:0% +theral efficiency you want to re out + + + align:start position:0% +theral efficiency you want to re out +here so you want to operate again at a + + align:start position:0% +here so you want to operate again at a + + + align:start position:0% +here so you want to operate again at a +low temperature you go to low + + align:start position:0% +low temperature you go to low + + + align:start position:0% +low temperature you go to low +temperature like K so that's the but of + + align:start position:0% +temperature like K so that's the but of + + + align:start position:0% +temperature like K so that's the but of +course you get zero power efficiency so + + align:start position:0% +course you get zero power efficiency so + + + align:start position:0% +course you get zero power efficiency so +you still got a + + align:start position:0% +you still got a + + + align:start position:0% +you still got a +optim right so you or you multiply this + + align:start position:0% +optim right so you or you multiply this + + + align:start position:0% +optim right so you or you multiply this +to the C + + align:start position:0% +to the C + + + align:start position:0% +to the C +efficiency and this is the transition + + align:start position:0% +efficiency and this is the transition + + + align:start position:0% +efficiency and this is the transition +wavelength uh + + align:start position:0% +wavelength uh + + + align:start position:0% +wavelength uh +uh and uh so this is in this case what + + align:start position:0% +uh and uh so this is in this case what + + + align:start position:0% +uh and uh so this is in this case what +you have is + + align:start position:0% +you have is + + + align:start position:0% +you have is +05 so still pretty ideal right pretty + + align:start position:0% +05 so still pretty ideal right pretty + + + align:start position:0% +05 so still pretty ideal right pretty +good very good you can get even half of + + align:start position:0% +good very good you can get even half of + + + align:start position:0% +good very good you can get even half of +that okay because 50% let's assume you + + align:start position:0% +that okay because 50% let's assume you + + + align:start position:0% +that okay because 50% let's assume you +have a cal engine right engine operate + + align:start position:0% +have a cal engine right engine operate + + + align:start position:0% +have a cal engine right engine operate +between in this case let's say here is + + align:start position:0% +between in this case let's say here is + + + align:start position:0% +between in this case let's say here is +50% the car engine operate + + align:start position:0% +50% the car engine operate + + + align:start position:0% +50% the car engine operate +800 to room + + align:start position:0% + + + + align:start position:0% + +temperature okay and of course you if + + align:start position:0% +temperature okay and of course you if + + + align:start position:0% +temperature okay and of course you if +you have a real efficiency l l power so + + align:start position:0% +you have a real efficiency l l power so + + + align:start position:0% +you have a real efficiency l l power so +uh um likely you shifted + + align:start position:0% + + + + align:start position:0% + +to this is actually a new selective + + align:start position:0% +to this is actually a new selective + + + align:start position:0% +to this is actually a new selective +surface this selective surface is from s + + align:start position:0% +surface this selective surface is from s + + + align:start position:0% +surface this selective surface is from s +select this is + + align:start position:0% +select this is + + + align:start position:0% +select this is +theity the in the + + align:start position:0% +theity the in the + + + align:start position:0% +theity the in the +solion and in the + + align:start position:0% +solion and in the + + + align:start position:0% +solion and in the +IR problem is nobody could make this + + align:start position:0% +IR problem is nobody could make this + + + align:start position:0% +IR problem is nobody could make this +really + + align:start position:0% +really + + + align:start position:0% +really +sh okay it's a trans the transition the + + align:start position:0% +sh okay it's a trans the transition the + + + align:start position:0% +sh okay it's a trans the transition the +sharper the + + align:start position:0% +sharper the + + + align:start position:0% +sharper the +better + + align:start position:0% +better + + + align:start position:0% +better +and so if you use this surface to do the + + align:start position:0% +and so if you use this surface to do the + + + align:start position:0% +and so if you use this surface to do the +calculation real surface to do + + align:start position:0% +calculation real surface to do + + + align:start position:0% +calculation real surface to do +calculation and again uh assuming a Col + + align:start position:0% +calculation and again uh assuming a Col + + + align:start position:0% +calculation and again uh assuming a Col +efficiency so here is the system + + align:start position:0% +efficiency so here is the system + + + align:start position:0% +efficiency so here is the system +efficiency + + align:start position:0% +efficiency + + + align:start position:0% +efficiency +now becomes um about + + align:start position:0% +now becomes um about + + + align:start position:0% +now becomes um about +30% and it operate you you want to + + align:start position:0% +30% and it operate you you want to + + + align:start position:0% +30% and it operate you you want to +operate that high + + align:start position:0% +operate that high + + + align:start position:0% +operate that high +temperature see here the op is actually + + align:start position:0% +temperature see here the op is actually + + + align:start position:0% +temperature see here the op is actually +low temperature except you need a + + align:start position:0% +low temperature except you need a + + + align:start position:0% +low temperature except you need a +device converter that work as a car + + align:start position:0% +device converter that work as a car + + + align:start position:0% +device converter that work as a car +efficiency here right if you recall the + + align:start position:0% +efficiency here right if you recall the + + + align:start position:0% +efficiency here right if you recall the +solar cell sh say sh quiser paper right + + align:start position:0% +solar cell sh say sh quiser paper right + + + align:start position:0% +solar cell sh say sh quiser paper right +Sher liit for simpler Junction solar + + align:start position:0% +Sher liit for simpler Junction solar + + + align:start position:0% +Sher liit for simpler Junction solar +cell silicon solar cell Max efficient is + + align:start position:0% +cell silicon solar cell Max efficient is + + + align:start position:0% +cell silicon solar cell Max efficient is +about + + align:start position:0% + + + + align:start position:0% + +28% now look at this yeah this is very + + align:start position:0% + + + + align:start position:0% + +good and uh of + + align:start position:0% +good and uh of + + + align:start position:0% +good and uh of +course solar + + align:start position:0% +course solar + + + align:start position:0% +course solar +cell is also all + + align:start position:0% +cell is also all + + + align:start position:0% +cell is also all +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +surface is limited by this + + align:start position:0% + + + + align:start position:0% + +efficiency what discussing except the + + align:start position:0% +efficiency what discussing except the + + + align:start position:0% +efficiency what discussing except the +emission no not this one sorry the + + align:start position:0% +emission no not this one sorry the + + + align:start position:0% +emission no not this one sorry the +emission solar cell do not have + + align:start position:0% +emission solar cell do not have + + + align:start position:0% +emission solar cell do not have +reemission + + align:start position:0% +reemission + + + align:start position:0% +reemission +problem so it's a matter of the what's + + align:start position:0% +problem so it's a matter of the what's + + + align:start position:0% +problem so it's a matter of the what's +about the B Gap times the the car + + align:start position:0% +about the B Gap times the the car + + + align:start position:0% +about the B Gap times the the car +efficiency limit of solar shell + + align:start position:0% +efficiency limit of solar shell + + + align:start position:0% +efficiency limit of solar shell +is uh the Sol shell is of itself operate + + align:start position:0% +is uh the Sol shell is of itself operate + + + align:start position:0% +is uh the Sol shell is of itself operate +no temperature so thec + + align:start position:0% + + + + align:start position:0% + +and if you do it turns out that if you + + align:start position:0% +and if you do it turns out that if you + + + align:start position:0% +and if you do it turns out that if you +do INF multi Junction solar cell the + + align:start position:0% +do INF multi Junction solar cell the + + + align:start position:0% +do INF multi Junction solar cell the +maximum efficiency is still that + + align:start position:0% +maximum efficiency is still that + + + align:start position:0% +maximum efficiency is still that +85% same + + align:start position:0% + + + + align:start position:0% + +oper okay so uh those were the previous + + align:start position:0% +oper okay so uh those were the previous + + + align:start position:0% +oper okay so uh those were the previous +discussion were done for the + + align:start position:0% +discussion were done for the + + + align:start position:0% +discussion were done for the +concentration inverse one right one Sun + + align:start position:0% +concentration inverse one right one Sun + + + align:start position:0% +concentration inverse one right one Sun +condition and you can add other + + align:start position:0% +condition and you can add other + + + align:start position:0% +condition and you can add other +concentrations and uh uh the uh kind of + + align:start position:0% +concentrations and uh uh the uh kind of + + + align:start position:0% +concentrations and uh uh the uh kind of +absorbers and uh uh this is a uh we + + align:start position:0% + + + + align:start position:0% + +have body + + align:start position:0% +have body + + + align:start position:0% +have body +absor + + align:start position:0% + + + + align:start position:0% + +different and uh that's the temperature + + align:start position:0% +different and uh that's the temperature + + + align:start position:0% +different and uh that's the temperature +of operation here is the uh + + align:start position:0% +of operation here is the uh + + + align:start position:0% +of operation here is the uh +efficiency and now you use a more + + align:start position:0% +efficiency and now you use a more + + + align:start position:0% +efficiency and now you use a more +realistic uh AB over + + align:start position:0% +realistic uh AB over + + + align:start position:0% +realistic uh AB over +uh the body is this overall Spectrum but + + align:start position:0% +uh the body is this overall Spectrum but + + + align:start position:0% +uh the body is this overall Spectrum but +see here is selective absorber that's + + align:start position:0% +see here is selective absorber that's + + + align:start position:0% +see here is selective absorber that's +you get a higher + + align:start position:0% +you get a higher + + + align:start position:0% +you get a higher +efficiency and if you compare this two + + align:start position:0% +efficiency and if you compare this two + + + align:start position:0% +efficiency and if you compare this two +you also operate to higher + + align:start position:0% +you also operate to higher + + + align:start position:0% +you also operate to higher +temperature so here you got to operate + + align:start position:0% +temperature so here you got to operate + + + align:start position:0% +temperature so here you got to operate +to higher temperature if your + + align:start position:0% +to higher temperature if your + + + align:start position:0% +to higher temperature if your +selectivity is good you can push to a + + align:start position:0% +selectivity is good you can push to a + + + align:start position:0% +selectivity is good you can push to a +higher temperature because stivity is + + align:start position:0% +higher temperature because stivity is + + + align:start position:0% +higher temperature because stivity is +not good spectrum is not good black body + + align:start position:0% +not good spectrum is not good black body + + + align:start position:0% +not good spectrum is not good black body +you don't want to operate the high + + align:start position:0% +you don't want to operate the high + + + align:start position:0% +you don't want to operate the high +temper low + + align:start position:0% +temper low + + + align:start position:0% +temper low +tempure so the Thal engine is always the + + align:start position:0% +tempure so the Thal engine is always the + + + align:start position:0% +tempure so the Thal engine is always the +fight between the losing by + + align:start position:0% +fight between the losing by + + + align:start position:0% +fight between the losing by +radiation and the col Li the theral + + align:start position:0% +radiation and the col Li the theral + + + align:start position:0% +radiation and the col Li the theral +engine want to operate a higher + + align:start position:0% +engine want to operate a higher + + + align:start position:0% +engine want to operate a higher +temperature your surface don't want oper + + align:start position:0% + + + + align:start position:0% + +higher and now if you go back to even + + align:start position:0% +higher and now if you go back to even + + + align:start position:0% +higher and now if you go back to even +the idea absorber idea absorber means + + align:start position:0% +the idea absorber idea absorber means + + + align:start position:0% +the idea absorber idea absorber means +and zero stivity spect right push to + + align:start position:0% +and zero stivity spect right push to + + + align:start position:0% +and zero stivity spect right push to +higher and higher temperature depends + + align:start position:0% +higher and higher temperature depends + + + align:start position:0% +higher and higher temperature depends +your + + align:start position:0% + + + + align:start position:0% + +concentration + + align:start position:0% +concentration + + + align:start position:0% +concentration +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so those were + + align:start position:0% + + + + align:start position:0% + +um you + + align:start position:0% +um you + + + align:start position:0% +um you +can + + align:start position:0% +can + + + align:start position:0% +can +control you can get + + align:start position:0% +control you can get + + + align:start position:0% +control you can get +high right so that's say uh spectral + + align:start position:0% +high right so that's say uh spectral + + + align:start position:0% +high right so that's say uh spectral +control is really a crial + + align:start position:0% +control is really a crial + + + align:start position:0% +control is really a crial +problem + + align:start position:0% +problem + + + align:start position:0% +problem +and + + align:start position:0% +and + + + align:start position:0% +and +know Energy resour Center we have two + + align:start position:0% +know Energy resour Center we have two + + + align:start position:0% +know Energy resour Center we have two +parts one is look at the the is really + + align:start position:0% +parts one is look at the the is really + + + align:start position:0% +parts one is look at the the is really +look at the spect control and in fact + + align:start position:0% +look at the spect control and in fact + + + align:start position:0% +look at the spect control and in fact +later on we talk more to + + align:start position:0% +later on we talk more to + + + align:start position:0% +later on we talk more to +C and uh uh you realize that you you're + + align:start position:0% +C and uh uh you realize that you you're + + + align:start position:0% +C and uh uh you realize that you you're +transforming one difficult + + align:start position:0% +transforming one difficult + + + align:start position:0% +transforming one difficult +another in solar cell the difficulty is + + align:start position:0% +another in solar cell the difficulty is + + + align:start position:0% +another in solar cell the difficulty is +single cell is limited to sh that's so + + align:start position:0% +single cell is limited to sh that's so + + + align:start position:0% +single cell is limited to sh that's so +you try to do multi- juning scale which + + align:start position:0% +you try to do multi- juning scale which + + + align:start position:0% +you try to do multi- juning scale which +people have reached about + + align:start position:0% +people have reached about + + + align:start position:0% +people have reached about +41% three Junction but say infinite + + align:start position:0% +41% three Junction but say infinite + + + align:start position:0% +41% three Junction but say infinite +Junction get to + + align:start position:0% +Junction get to + + + align:start position:0% +Junction get to +85% right so but the growing material to + + align:start position:0% +85% right so but the growing material to + + + align:start position:0% +85% right so but the growing material to +more than Street Junction is + + align:start position:0% +more than Street Junction is + + + align:start position:0% +more than Street Junction is +very and uh uh now transform one problem + + align:start position:0% +very and uh uh now transform one problem + + + align:start position:0% +very and uh uh now transform one problem +into one this difficulty into another + + align:start position:0% +into one this difficulty into another + + + align:start position:0% +into one this difficulty into another +difficulty if I can have a selective + + align:start position:0% +difficulty if I can have a selective + + + align:start position:0% +difficulty if I can have a selective +surface right really the idea how work + + align:start position:0% +surface right really the idea how work + + + align:start position:0% +surface right really the idea how work +at a high temperature then + + align:start position:0% +at a high temperature then + + + align:start position:0% +at a high temperature then +I even with single + + align:start position:0% +I even with single + + + align:start position:0% +I even with single +JS so uh um but of course this has now a + + align:start position:0% +JS so uh um but of course this has now a + + + align:start position:0% +JS so uh um but of course this has now a +lot of engineering + + align:start position:0% +lot of engineering + + + align:start position:0% +lot of engineering +aspect because let suppose when I have + + align:start position:0% +aspect because let suppose when I have + + + align:start position:0% +aspect because let suppose when I have +this IDE surface right stive surface + + align:start position:0% +this IDE surface right stive surface + + + align:start position:0% +this IDE surface right stive surface +abity on the other side you can hardly + + align:start position:0% +abity on the other side you can hardly + + + align:start position:0% +abity on the other side you can hardly +design circuit really zero so this lose + + align:start position:0% +design circuit really zero so this lose + + + align:start position:0% +design circuit really zero so this lose +ration and also you have to hold it + + align:start position:0% +ration and also you have to hold it + + + align:start position:0% +ration and also you have to hold it +somehow de + + align:start position:0% +somehow de + + + align:start position:0% +somehow de +2000° you have to hold it and of course + + align:start position:0% +2000° you have to hold it and of course + + + align:start position:0% +2000° you have to hold it and of course +you can use let say a suspension you can + + align:start position:0% +you can use let say a suspension you can + + + align:start position:0% +you can use let say a suspension you can +use about this is actually the if you do + + align:start position:0% +use about this is actually the if you do + + + align:start position:0% +use about this is actually the if you do +this solar + + align:start position:0% +this solar + + + align:start position:0% +this solar +in this is the one advantage I consider + + align:start position:0% +in this is the one advantage I consider + + + align:start position:0% +in this is the one advantage I consider +Soler if you do + + align:start position:0% +Soler if you do + + + align:start position:0% +Soler if you do +with a combustion + + align:start position:0% +with a combustion + + + align:start position:0% +with a combustion +chamber you has to Gas contact or a very + + align:start position:0% +chamber you has to Gas contact or a very + + + align:start position:0% +chamber you has to Gas contact or a very +sturdy structure right at least in the + + align:start position:0% +sturdy structure right at least in the + + + align:start position:0% +sturdy structure right at least in the +case of sun what comes in let's suppose + + align:start position:0% +case of sun what comes in let's suppose + + + align:start position:0% +case of sun what comes in let's suppose +this + + align:start position:0% +this + + + align:start position:0% +this +chamber what comes in the pH can go + + align:start position:0% +chamber what comes in the pH can go + + + align:start position:0% +chamber what comes in the pH can go +through the + + align:start position:0% +through the + + + align:start position:0% +through the +glass right then you have much less the + + align:start position:0% +glass right then you have much less the + + + align:start position:0% +glass right then you have much less the +in terms of the complexity dealing with + + align:start position:0% +in terms of the complexity dealing with + + + align:start position:0% +in terms of the complexity dealing with +the top gas the F contact I can you can + + align:start position:0% +the top gas the F contact I can you can + + + align:start position:0% +the top gas the F contact I can you can +use a really say very small string to + + align:start position:0% +use a really say very small string to + + + align:start position:0% +use a really say very small string to +suspend the + + align:start position:0% +suspend the + + + align:start position:0% +suspend the +surface so that's that's one I view + + align:start position:0% +surface so that's that's one I view + + + align:start position:0% +surface so that's that's one I view +which is probably better if you do the + + align:start position:0% +which is probably better if you do the + + + align:start position:0% +which is probably better if you do the +solar compared to + + align:start position:0% +solar compared to + + + align:start position:0% +solar compared to +Thermal so here is the suspension and of + + align:start position:0% +Thermal so here is the suspension and of + + + align:start position:0% +Thermal so here is the suspension and of +course if you have suspension then you + + align:start position:0% +course if you have suspension then you + + + align:start position:0% +course if you have suspension then you +have P loss they have to come for other + + align:start position:0% +have P loss they have to come for other + + + align:start position:0% +have P loss they have to come for other +P loss suspension and other emission + + align:start position:0% +P loss suspension and other emission + + + align:start position:0% +P loss suspension and other emission +losses and so it's say then become + + align:start position:0% +losses and so it's say then become + + + align:start position:0% +losses and so it's say then become +careful engineering problem that's why + + align:start position:0% +careful engineering problem that's why + + + align:start position:0% +careful engineering problem that's why +at the end now you work on + + align:start position:0% + + + + align:start position:0% + +the you have to go back to B conduction + + align:start position:0% + + + + align:start position:0% + +de factor for + + align:start position:0% + + + + align:start position:0% + +your any questions \ No newline at end of file diff --git a/qqtEQsBjh28.txt b/qqtEQsBjh28.txt new file mode 100644 index 0000000000000000000000000000000000000000..ab78d05182f952b9a1b8e2eae8c473abb4c0243b --- /dev/null +++ b/qqtEQsBjh28.txt @@ -0,0 +1,17224 @@ +align:start position:0% + +we're starting to talk about + + align:start position:0% +we're starting to talk about + + + align:start position:0% +we're starting to talk about +what determines + + align:start position:0% +what determines + + + align:start position:0% +what determines +brightness in an image + + align:start position:0% +brightness in an image + + + align:start position:0% +brightness in an image +and how we can + + align:start position:0% +and how we can + + + align:start position:0% +and how we can +exploit that + + align:start position:0% +exploit that + + + align:start position:0% +exploit that +and we introduced + + align:start position:0% +and we introduced + + + align:start position:0% +and we introduced +the idea of a gradient space + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +why well because + + align:start position:0% +why well because + + + align:start position:0% +why well because +brightness is going to depend on the + + align:start position:0% +brightness is going to depend on the + + + align:start position:0% +brightness is going to depend on the +illumination obviously + + align:start position:0% +illumination obviously + + + align:start position:0% +illumination obviously +and it's going to depend on the geometry + + align:start position:0% +and it's going to depend on the geometry + + + align:start position:0% +and it's going to depend on the geometry +of the situation + + align:start position:0% +of the situation + + + align:start position:0% +of the situation +including + + align:start position:0% +including + + + align:start position:0% +including +surface orientation + + align:start position:0% +surface orientation + + + align:start position:0% +surface orientation +obviously the amount of light falling on + + align:start position:0% +obviously the amount of light falling on + + + align:start position:0% +obviously the amount of light falling on +the surface will + + align:start position:0% +the surface will + + + align:start position:0% +the surface will +per unit area will depend on its + + align:start position:0% +per unit area will depend on its + + + align:start position:0% +per unit area will depend on its +orientation and then different types of + + align:start position:0% +orientation and then different types of + + + align:start position:0% +orientation and then different types of +surfaces will reflect that light in + + align:start position:0% +surfaces will reflect that light in + + + align:start position:0% +surfaces will reflect that light in +different ways + + align:start position:0% +different ways + + + align:start position:0% +different ways +in any case + + align:start position:0% +in any case + + + align:start position:0% +in any case +we expect that + + align:start position:0% +we expect that + + + align:start position:0% +we expect that +the brightness we observe in an image is + + align:start position:0% +the brightness we observe in an image is + + + align:start position:0% +the brightness we observe in an image is +going to depend on the surface + + align:start position:0% +going to depend on the surface + + + align:start position:0% +going to depend on the surface +orientation + + align:start position:0% +orientation + + + align:start position:0% +orientation +of the corresponding patch on an on an + + align:start position:0% +of the corresponding patch on an on an + + + align:start position:0% +of the corresponding patch on an on an +object + + align:start position:0% +object + + + align:start position:0% +object +and so we need to talk about the + + align:start position:0% +and so we need to talk about the + + + align:start position:0% +and so we need to talk about the +orientation of the patch and we had unit + + align:start position:0% +orientation of the patch and we had unit + + + align:start position:0% +orientation of the patch and we had unit +normals and then we had p and q + + align:start position:0% + + + + align:start position:0% + +well these are just convenient + + align:start position:0% +well these are just convenient + + + align:start position:0% +well these are just convenient +shorthands + + align:start position:0% + + + + align:start position:0% + +for those + + align:start position:0% +for those + + + align:start position:0% +for those +slopes in in the image + + align:start position:0% + + + + align:start position:0% + +slopes on the surface so those are + + align:start position:0% +slopes on the surface so those are + + + align:start position:0% +slopes on the surface so those are +derivatives of height rather than + + align:start position:0% +derivatives of height rather than + + + align:start position:0% +derivatives of height rather than +derivatives of brightness + + align:start position:0% +derivatives of brightness + + + align:start position:0% +derivatives of brightness +and then um + + align:start position:0% +and then um + + + align:start position:0% +and then um +since we were busy with photometric + + align:start position:0% +since we were busy with photometric + + + align:start position:0% +since we were busy with photometric +stereo and we just + + align:start position:0% +stereo and we just + + + align:start position:0% +stereo and we just +talked a bit about + + align:start position:0% +talked a bit about + + + align:start position:0% +talked a bit about +lambertian surfaces + + align:start position:0% + + + + align:start position:0% + +which have the property that their + + align:start position:0% +which have the property that their + + + align:start position:0% +which have the property that their +brightness + + align:start position:0% +brightness + + + align:start position:0% +brightness +depends on the cosine of the incident + + align:start position:0% +depends on the cosine of the incident + + + align:start position:0% +depends on the cosine of the incident +angle + + align:start position:0% +angle + + + align:start position:0% +angle +and it does not depend on the viewing + + align:start position:0% +and it does not depend on the viewing + + + align:start position:0% +and it does not depend on the viewing +direction so + + align:start position:0% +direction so + + + align:start position:0% +direction so +a surface of that type + + align:start position:0% +a surface of that type + + + align:start position:0% +a surface of that type +will appear pretty much equally bright + + align:start position:0% +will appear pretty much equally bright + + + align:start position:0% +will appear pretty much equally bright +from + + align:start position:0% +from + + + align:start position:0% +from +uh all viewing points that you might + + align:start position:0% +uh all viewing points that you might + + + align:start position:0% +uh all viewing points that you might +have + + align:start position:0% +have + + + align:start position:0% +have +which is fairly common + + align:start position:0% +which is fairly common + + + align:start position:0% +which is fairly common +for material uh on on our human scale + + align:start position:0% +for material uh on on our human scale + + + align:start position:0% +for material uh on on our human scale +so what what determines how surfaces + + align:start position:0% +so what what determines how surfaces + + + align:start position:0% +so what what determines how surfaces +reflect light + + align:start position:0% +reflect light + + + align:start position:0% +reflect light +well we get into that but largely it's a + + align:start position:0% +well we get into that but largely it's a + + + align:start position:0% +well we get into that but largely it's a +microstructure you know + + align:start position:0% +microstructure you know + + + align:start position:0% +microstructure you know +photons get into the fibers in my paper + + align:start position:0% +photons get into the fibers in my paper + + + align:start position:0% +photons get into the fibers in my paper +they bounce around they come back out + + align:start position:0% +they bounce around they come back out + + + align:start position:0% +they bounce around they come back out +again in a different direction + + align:start position:0% +again in a different direction + + + align:start position:0% +again in a different direction +and that's what determines how bright + + align:start position:0% +and that's what determines how bright + + + align:start position:0% +and that's what determines how bright +the surface will appear from a certain + + align:start position:0% +the surface will appear from a certain + + + align:start position:0% +the surface will appear from a certain +direction + + align:start position:0% +direction + + + align:start position:0% +direction +and + + align:start position:0% +and + + + align:start position:0% +and +so a lot depends on the imaging + + align:start position:0% +so a lot depends on the imaging + + + align:start position:0% +so a lot depends on the imaging +situation if i'm looking at the moon + + align:start position:0% +situation if i'm looking at the moon + + + align:start position:0% +situation if i'm looking at the moon +what constitute + + align:start position:0% +what constitute + + + align:start position:0% +what constitute +microstructure + + align:start position:0% +microstructure + + + align:start position:0% +microstructure +are you know craters uh not fibers of + + align:start position:0% +are you know craters uh not fibers of + + + align:start position:0% +are you know craters uh not fibers of +paper + + align:start position:0% +paper + + + align:start position:0% +paper +so as we'll discuss later + + align:start position:0% + + + + align:start position:0% + +lambertian surfaces or near lambertian + + align:start position:0% +lambertian surfaces or near lambertian + + + align:start position:0% +lambertian surfaces or near lambertian +surfaces are fairly common in our world + + align:start position:0% +surfaces are fairly common in our world + + + align:start position:0% +surfaces are fairly common in our world +a lot of matte surfaces are pretty good + + align:start position:0% +a lot of matte surfaces are pretty good + + + align:start position:0% +a lot of matte surfaces are pretty good +approximations + + align:start position:0% +approximations + + + align:start position:0% +approximations +snow and whatever + + align:start position:0% +snow and whatever + + + align:start position:0% +snow and whatever +but they don't necessarily + + align:start position:0% +but they don't necessarily + + + align:start position:0% +but they don't necessarily +apply when we go to microscopic scale or + + align:start position:0% +apply when we go to microscopic scale or + + + align:start position:0% +apply when we go to microscopic scale or +to + + align:start position:0% +to + + + align:start position:0% +to +a cosmic scale so + + align:start position:0% +a cosmic scale so + + + align:start position:0% +a cosmic scale so +anyway so + + align:start position:0% +anyway so + + + align:start position:0% +anyway so +lambertian is a handy + + align:start position:0% + + + + align:start position:0% + +approximation for some surfaces and + + align:start position:0% +approximation for some surfaces and + + + align:start position:0% +approximation for some surfaces and +we can + + align:start position:0% +we can + + + align:start position:0% +we can +address it in different ways when if we + + align:start position:0% +address it in different ways when if we + + + align:start position:0% +address it in different ways when if we +expand out that n dot s + + align:start position:0% +expand out that n dot s + + + align:start position:0% +expand out that n dot s +you may remember we got + + align:start position:0% + + + + align:start position:0% + +something like this which is linear in p + + align:start position:0% +something like this which is linear in p + + + align:start position:0% +something like this which is linear in p +and q so that's the good part + + align:start position:0% +and q so that's the good part + + + align:start position:0% +and q so that's the good part +but then unfortunately we divide by this + + align:start position:0% +but then unfortunately we divide by this + + + align:start position:0% +but then unfortunately we divide by this +term here which is uh + + align:start position:0% +term here which is uh + + + align:start position:0% +term here which is uh +not linear in p and q + + align:start position:0% +not linear in p and q + + + align:start position:0% +not linear in p and q +and there's also + + align:start position:0% + + + + align:start position:0% + +uh this term although we don't + + align:start position:0% +uh this term although we don't + + + align:start position:0% +uh this term although we don't +worry too much about that because that's + + align:start position:0% +worry too much about that because that's + + + align:start position:0% +worry too much about that because that's +a constant if the light source is + + align:start position:0% +a constant if the light source is + + + align:start position:0% +a constant if the light source is +somewhere as defined by psqs + + align:start position:0% +somewhere as defined by psqs + + + align:start position:0% +somewhere as defined by psqs +then that's a constant and i'm going to + + align:start position:0% +then that's a constant and i'm going to + + + align:start position:0% +then that's a constant and i'm going to +get tired of writing that so i'm just + + align:start position:0% +get tired of writing that so i'm just + + + align:start position:0% +get tired of writing that so i'm just +going to + + align:start position:0% +going to + + + align:start position:0% +going to +introduce + + align:start position:0% +introduce + + + align:start position:0% +introduce +a constant rs + + align:start position:0% +a constant rs + + + align:start position:0% +a constant rs +to represent it + + align:start position:0% +to represent it + + + align:start position:0% +to represent it +and then we went through the business of + + align:start position:0% +and then we went through the business of + + + align:start position:0% +and then we went through the business of +what are the isophotes well that's where + + align:start position:0% +what are the isophotes well that's where + + + align:start position:0% +what are the isophotes well that's where +this expression is constant and we can + + align:start position:0% +this expression is constant and we can + + + align:start position:0% +this expression is constant and we can +get rid of the square root by squaring + + align:start position:0% +get rid of the square root by squaring + + + align:start position:0% +get rid of the square root by squaring +and if we do that we end up with an + + align:start position:0% +and if we do that we end up with an + + + align:start position:0% +and if we do that we end up with an +expression which is uh second order in p + + align:start position:0% +expression which is uh second order in p + + + align:start position:0% +expression which is uh second order in p +and q so it's got + + align:start position:0% +and q so it's got + + + align:start position:0% +and q so it's got +p s p squared q squared p q p and q and + + align:start position:0% +p s p squared q squared p q p and q and + + + align:start position:0% +p s p squared q squared p q p and q and +constants and plotting those + + align:start position:0% +constants and plotting those + + + align:start position:0% +constants and plotting those +gives us conic sections and in + + align:start position:0% +gives us conic sections and in + + + align:start position:0% +gives us conic sections and in +particular + + align:start position:0% + + + + align:start position:0% + +we end up with a diagram like this + + align:start position:0% + + + + align:start position:0% + +and what is this + + align:start position:0% +and what is this + + + align:start position:0% +and what is this +well this says if you tell me what the + + align:start position:0% +well this says if you tell me what the + + + align:start position:0% +well this says if you tell me what the +surface orientation is i can tell you + + align:start position:0% +surface orientation is i can tell you + + + align:start position:0% +surface orientation is i can tell you +how bright it's supposed to look + + align:start position:0% +how bright it's supposed to look + + + align:start position:0% +how bright it's supposed to look +so um + + align:start position:0% +so um + + + align:start position:0% +so um +again uh imagine a terrain + + align:start position:0% +again uh imagine a terrain + + + align:start position:0% +again uh imagine a terrain +built above the floor + + align:start position:0% +built above the floor + + + align:start position:0% +built above the floor +and i don't know x-axis to the right and + + align:start position:0% +and i don't know x-axis to the right and + + + align:start position:0% +and i don't know x-axis to the right and +y-axis forward + + align:start position:0% +y-axis forward + + + align:start position:0% +y-axis forward +then i can + + align:start position:0% +then i can + + + align:start position:0% +then i can +take the derivative in the x-direction + + align:start position:0% +take the derivative in the x-direction + + + align:start position:0% +take the derivative in the x-direction +that's p + + align:start position:0% +that's p + + + align:start position:0% +that's p +and i can take the derivative in the y + + align:start position:0% +and i can take the derivative in the y + + + align:start position:0% +and i can take the derivative in the y +direction that's q + + align:start position:0% +direction that's q + + + align:start position:0% +direction that's q +and those define the orientation locally + + align:start position:0% +and those define the orientation locally + + + align:start position:0% +and those define the orientation locally +of that surface of course it might be + + align:start position:0% +of that surface of course it might be + + + align:start position:0% +of that surface of course it might be +different p and q somewhere else + + align:start position:0% +different p and q somewhere else + + + align:start position:0% +different p and q somewhere else +and that defines a point in this plane + + align:start position:0% +and that defines a point in this plane + + + align:start position:0% +and that defines a point in this plane +and i can go to that point and say + + align:start position:0% +and i can go to that point and say + + + align:start position:0% +and i can go to that point and say +you know what is the value of this + + align:start position:0% +you know what is the value of this + + + align:start position:0% +you know what is the value of this +function there and that + + align:start position:0% +function there and that + + + align:start position:0% +function there and that +will be the brightness + + align:start position:0% +will be the brightness + + + align:start position:0% +will be the brightness +and this is you know obviously handy in + + align:start position:0% +and this is you know obviously handy in + + + align:start position:0% +and this is you know obviously handy in +graphics because we can + + align:start position:0% +graphics because we can + + + align:start position:0% +graphics because we can +have + + align:start position:0% +have + + + align:start position:0% +have +surface models we can determine not just + + align:start position:0% +surface models we can determine not just + + + align:start position:0% +surface models we can determine not just +their + + align:start position:0% +their + + + align:start position:0% +their +z position their depth but also these + + align:start position:0% +z position their depth but also these + + + align:start position:0% +z position their depth but also these +derivatives + + align:start position:0% +derivatives + + + align:start position:0% +derivatives +surface orientation + + align:start position:0% +surface orientation + + + align:start position:0% +surface orientation +and then we go to this diagram which + + align:start position:0% +and then we go to this diagram which + + + align:start position:0% +and then we go to this diagram which +could be perhaps a lookup table in the + + align:start position:0% +could be perhaps a lookup table in the + + + align:start position:0% +could be perhaps a lookup table in the +computer and we just look up the + + align:start position:0% +computer and we just look up the + + + align:start position:0% +computer and we just look up the +appropriate gray level to paint at that + + align:start position:0% +appropriate gray level to paint at that + + + align:start position:0% +appropriate gray level to paint at that +point in the image + + align:start position:0% +point in the image + + + align:start position:0% +point in the image +that's the forward problem and we're + + align:start position:0% +that's the forward problem and we're + + + align:start position:0% +that's the forward problem and we're +dealing with the inverse problem so our + + align:start position:0% +dealing with the inverse problem so our + + + align:start position:0% +dealing with the inverse problem so our +problem is okay i have measured the + + align:start position:0% +problem is okay i have measured the + + + align:start position:0% +problem is okay i have measured the +brightness of + + align:start position:0% +brightness of + + + align:start position:0% +brightness of +e equals e1 + + align:start position:0% +e equals e1 + + + align:start position:0% +e equals e1 +what can you tell me about the surface + + align:start position:0% +what can you tell me about the surface + + + align:start position:0% +what can you tell me about the surface +orientation + + align:start position:0% +orientation + + + align:start position:0% +orientation +well it's confined to + + align:start position:0% +well it's confined to + + + align:start position:0% +well it's confined to +that curve + + align:start position:0% +that curve + + + align:start position:0% +that curve +it's unfortunately not going to tell me + + align:start position:0% +it's unfortunately not going to tell me + + + align:start position:0% +it's unfortunately not going to tell me +uniquely what the surface orientation is + + align:start position:0% +uniquely what the surface orientation is + + + align:start position:0% +uniquely what the surface orientation is +but it's restricted now to + + align:start position:0% +but it's restricted now to + + + align:start position:0% +but it's restricted now to +a great deal + + align:start position:0% + + + + align:start position:0% + +and so i need additional information + + align:start position:0% +and so i need additional information + + + align:start position:0% +and so i need additional information +and there are various ways of getting + + align:start position:0% +and there are various ways of getting + + + align:start position:0% +and there are various ways of getting +additional information one is to say + + align:start position:0% +additional information one is to say + + + align:start position:0% +additional information one is to say +well most objects in the world aren't + + align:start position:0% +well most objects in the world aren't + + + align:start position:0% +well most objects in the world aren't +sort of haphazard + + align:start position:0% +sort of haphazard + + + align:start position:0% +sort of haphazard +collections of blobs in three space but + + align:start position:0% +collections of blobs in three space but + + + align:start position:0% +collections of blobs in three space but +they hang together you know objects are + + align:start position:0% +they hang together you know objects are + + + align:start position:0% +they hang together you know objects are +solid they have surfaces + + align:start position:0% +solid they have surfaces + + + align:start position:0% +solid they have surfaces +neighboring points tend to often have + + align:start position:0% +neighboring points tend to often have + + + align:start position:0% +neighboring points tend to often have +similar properties + + align:start position:0% +similar properties + + + align:start position:0% +similar properties +you know different parts of this table + + align:start position:0% +you know different parts of this table + + + align:start position:0% +you know different parts of this table +have pretty much the same surface + + align:start position:0% +have pretty much the same surface + + + align:start position:0% +have pretty much the same surface +orientation until you get to the edge + + align:start position:0% +orientation until you get to the edge + + + align:start position:0% +orientation until you get to the edge +but that's a hard + + align:start position:0% +but that's a hard + + + align:start position:0% +but that's a hard +constraint to implement we'll get to + + align:start position:0% +constraint to implement we'll get to + + + align:start position:0% +constraint to implement we'll get to +that later + + align:start position:0% +that later + + + align:start position:0% +that later +a much easier idea is + + align:start position:0% +a much easier idea is + + + align:start position:0% +a much easier idea is +well if i illuminate the surface + + align:start position:0% +well if i illuminate the surface + + + align:start position:0% +well if i illuminate the surface +differently i'll get a different map + + align:start position:0% +differently i'll get a different map + + + align:start position:0% +differently i'll get a different map +and + + align:start position:0% +and + + + align:start position:0% +and +i'll get a constraint on that number so + + align:start position:0% +i'll get a constraint on that number so + + + align:start position:0% +i'll get a constraint on that number so +for example suppose i move the light + + align:start position:0% +for example suppose i move the light + + + align:start position:0% +for example suppose i move the light +source from there to over here + + align:start position:0% + + + + align:start position:0% + +and then i draw the same diagram + + align:start position:0% + + + + align:start position:0% + +and now i measure the brightness in that + + align:start position:0% +and now i measure the brightness in that + + + align:start position:0% +and now i measure the brightness in that +second image under different + + align:start position:0% +second image under different + + + align:start position:0% +second image under different +illumination + + align:start position:0% +illumination + + + align:start position:0% +illumination +and let's suppose it comes out to be i + + align:start position:0% +and let's suppose it comes out to be i + + + align:start position:0% +and let's suppose it comes out to be i +don't know this this one here + + align:start position:0% +don't know this this one here + + + align:start position:0% +don't know this this one here +well then i know that the surface + + align:start position:0% +well then i know that the surface + + + align:start position:0% +well then i know that the surface +orientation is where those um two curves + + align:start position:0% +orientation is where those um two curves + + + align:start position:0% +orientation is where those um two curves +intersect + + align:start position:0% +intersect + + + align:start position:0% +intersect +so that's phenomena exterior done in in + + align:start position:0% +so that's phenomena exterior done in in + + + align:start position:0% +so that's phenomena exterior done in in +the graphical way we we've done it + + align:start position:0% +the graphical way we we've done it + + + align:start position:0% +the graphical way we we've done it +before in an algebraic way + + align:start position:0% +before in an algebraic way + + + align:start position:0% +before in an algebraic way +of course that algebraic way + + align:start position:0% +of course that algebraic way + + + align:start position:0% +of course that algebraic way +only worked if we had lambertian + + align:start position:0% +only worked if we had lambertian + + + align:start position:0% +only worked if we had lambertian +surfaces + + align:start position:0% +surfaces + + + align:start position:0% +surfaces +this is going to work for any surface as + + align:start position:0% +this is going to work for any surface as + + + align:start position:0% +this is going to work for any surface as +long as you can draw + + align:start position:0% +long as you can draw + + + align:start position:0% +long as you can draw +this diagram which is called a + + align:start position:0% +this diagram which is called a + + + align:start position:0% +this diagram which is called a +reflectance map + + align:start position:0% + + + + align:start position:0% + +so the reflectance map basically + + align:start position:0% +so the reflectance map basically + + + align:start position:0% +so the reflectance map basically +is a diagram that shows you for every + + align:start position:0% +is a diagram that shows you for every + + + align:start position:0% +is a diagram that shows you for every +orientation how bright that surface will + + align:start position:0% +orientation how bright that surface will + + + align:start position:0% +orientation how bright that surface will +look for that orientation + + align:start position:0% +look for that orientation + + + align:start position:0% +look for that orientation +okay now + + align:start position:0% + + + + align:start position:0% + +we've talked a lot about lambertian + + align:start position:0% +we've talked a lot about lambertian + + + align:start position:0% +we've talked a lot about lambertian +surfaces and that's mostly because + + align:start position:0% +surfaces and that's mostly because + + + align:start position:0% +surfaces and that's mostly because +they allow us to write down the + + align:start position:0% +they allow us to write down the + + + align:start position:0% +they allow us to write down the +equations and solve them but real + + align:start position:0% +equations and solve them but real + + + align:start position:0% +equations and solve them but real +surfaces aren't perfectly lumberjane + + align:start position:0% +surfaces aren't perfectly lumberjane + + + align:start position:0% +surfaces aren't perfectly lumberjane +and some are dramatically non-version so + + align:start position:0% +and some are dramatically non-version so + + + align:start position:0% +and some are dramatically non-version so +what do we do in that case + + align:start position:0% +what do we do in that case + + + align:start position:0% +what do we do in that case +well it's pretty easy to + + align:start position:0% +well it's pretty easy to + + + align:start position:0% +well it's pretty easy to +imagine we can create a diagram like + + align:start position:0% +imagine we can create a diagram like + + + align:start position:0% +imagine we can create a diagram like +this and use that + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +we can + + align:start position:0% +we can + + + align:start position:0% +we can +perhaps think about building a lookup + + align:start position:0% +perhaps think about building a lookup + + + align:start position:0% +perhaps think about building a lookup +table + + align:start position:0% +table + + + align:start position:0% +table +now this is sort of going the wrong way + + align:start position:0% +now this is sort of going the wrong way + + + align:start position:0% +now this is sort of going the wrong way +here + + align:start position:0% +here + + + align:start position:0% +here +if you've got p and q + + align:start position:0% +if you've got p and q + + + align:start position:0% +if you've got p and q +you can look up what the brightness + + align:start position:0% +you can look up what the brightness + + + align:start position:0% +you can look up what the brightness +should be we need a table that goes in + + align:start position:0% +should be we need a table that goes in + + + align:start position:0% +should be we need a table that goes in +the opposite direction so + + align:start position:0% +the opposite direction so + + + align:start position:0% +the opposite direction so +let's think about how to do that so one + + align:start position:0% +let's think about how to do that so one + + + align:start position:0% +let's think about how to do that so one +way + + align:start position:0% +way + + + align:start position:0% +way +is to + + align:start position:0% +is to + + + align:start position:0% +is to +let's first + + align:start position:0% +let's first + + + align:start position:0% +let's first +say non-line version + + align:start position:0% + + + + align:start position:0% + +uh one one way + + align:start position:0% +uh one one way + + + align:start position:0% +uh one one way +is to take a surface element + + align:start position:0% +is to take a surface element + + + align:start position:0% +is to take a surface element +and + + align:start position:0% +and + + + align:start position:0% +and +look at it under different lighting + + align:start position:0% +look at it under different lighting + + + align:start position:0% +look at it under different lighting +conditions and record + + align:start position:0% +conditions and record + + + align:start position:0% +conditions and record +what you see and then repeat that for + + align:start position:0% +what you see and then repeat that for + + + align:start position:0% +what you see and then repeat that for +different orientations + + align:start position:0% +different orientations + + + align:start position:0% +different orientations +and you can do that it's going to get + + align:start position:0% +and you can do that it's going to get + + + align:start position:0% +and you can do that it's going to get +pretty tedious because you have to + + align:start position:0% +pretty tedious because you have to + + + align:start position:0% +pretty tedious because you have to +basically explore this whole space + + align:start position:0% +basically explore this whole space + + + align:start position:0% +basically explore this whole space +and every + + align:start position:0% +and every + + + align:start position:0% +and every +cell in the space in your lookup table + + align:start position:0% +cell in the space in your lookup table + + + align:start position:0% +cell in the space in your lookup table +is going to + + align:start position:0% +is going to + + + align:start position:0% +is going to +require that you reorient that + + align:start position:0% +require that you reorient that + + + align:start position:0% +require that you reorient that +piece + + align:start position:0% +piece + + + align:start position:0% +piece +because you can automate that and have + + align:start position:0% +because you can automate that and have + + + align:start position:0% +because you can automate that and have +some + + align:start position:0% +some + + + align:start position:0% +some +robot do the calibration for you + + align:start position:0% +robot do the calibration for you + + + align:start position:0% +robot do the calibration for you +but it's uh an alternative that's often + + align:start position:0% +but it's uh an alternative that's often + + + align:start position:0% +but it's uh an alternative that's often +easier is to use a calibration object of + + align:start position:0% +easier is to use a calibration object of + + + align:start position:0% +easier is to use a calibration object of +known shape and you know what better + + align:start position:0% +known shape and you know what better + + + align:start position:0% +known shape and you know what better +than a sphere + + align:start position:0% +than a sphere + + + align:start position:0% +than a sphere +partly because it's very easy to make a + + align:start position:0% +partly because it's very easy to make a + + + align:start position:0% +partly because it's very easy to make a +sphere + + align:start position:0% +sphere + + + align:start position:0% +sphere +and what do we do well um + + align:start position:0% +and what do we do well um + + + align:start position:0% +and what do we do well um +we take an image + + align:start position:0% +we take an image + + + align:start position:0% +we take an image +first we'll have it lit up from all + + align:start position:0% +first we'll have it lit up from all + + + align:start position:0% +first we'll have it lit up from all +sides + + align:start position:0% +sides + + + align:start position:0% +sides +and + + align:start position:0% +and + + + align:start position:0% +and +the sphere of course will image as a + + align:start position:0% +the sphere of course will image as a + + + align:start position:0% +the sphere of course will image as a +circle + + align:start position:0% + + + + align:start position:0% + +and presumably + + align:start position:0% +and presumably + + + align:start position:0% +and presumably +uh the brightness inside the circle is + + align:start position:0% +uh the brightness inside the circle is + + + align:start position:0% +uh the brightness inside the circle is +going to be much larger than outside so + + align:start position:0% +going to be much larger than outside so + + + align:start position:0% +going to be much larger than outside so +we should be able to uh distinguish the + + align:start position:0% +we should be able to uh distinguish the + + + align:start position:0% +we should be able to uh distinguish the +two and and fit a + + align:start position:0% +two and and fit a + + + align:start position:0% +two and and fit a +circle to this + + align:start position:0% +circle to this + + + align:start position:0% +circle to this +so we take this image and then we fit a + + align:start position:0% +so we take this image and then we fit a + + + align:start position:0% +so we take this image and then we fit a +circle and what does that mean that + + align:start position:0% +circle and what does that mean that + + + align:start position:0% +circle and what does that mean that +means we find estimates for the center + + align:start position:0% +means we find estimates for the center + + + align:start position:0% +means we find estimates for the center +and the radius + + align:start position:0% +and the radius + + + align:start position:0% +and the radius +such that all points within that are + + align:start position:0% +such that all points within that are + + + align:start position:0% +such that all points within that are +bright and all points out are + + align:start position:0% +bright and all points out are + + + align:start position:0% +bright and all points out are +not and you know you can do some + + align:start position:0% +not and you know you can do some + + + align:start position:0% +not and you know you can do some +subtle clever things + + align:start position:0% +subtle clever things + + + align:start position:0% +subtle clever things +to make that accurate to sub pixels and + + align:start position:0% +to make that accurate to sub pixels and + + + align:start position:0% +to make that accurate to sub pixels and +so on but we won't talk about that now + + align:start position:0% +so on but we won't talk about that now + + + align:start position:0% +so on but we won't talk about that now +okay so what good is that well + + align:start position:0% +okay so what good is that well + + + align:start position:0% +okay so what good is that well +for a sphere we have a very convenient + + align:start position:0% +for a sphere we have a very convenient + + + align:start position:0% +for a sphere we have a very convenient +relationship + + align:start position:0% +relationship + + + align:start position:0% +relationship +if we draw a point from the center of + + align:start position:0% +if we draw a point from the center of + + + align:start position:0% +if we draw a point from the center of +the sphere + + align:start position:0% +the sphere + + + align:start position:0% +the sphere +to the surface + + align:start position:0% +to the surface + + + align:start position:0% +to the surface +and then we at that point on the surface + + align:start position:0% +and then we at that point on the surface + + + align:start position:0% +and then we at that point on the surface +draw a unit vector + + align:start position:0% +draw a unit vector + + + align:start position:0% +draw a unit vector +uh guess what those are parallel so and + + align:start position:0% +uh guess what those are parallel so and + + + align:start position:0% +uh guess what those are parallel so and +you know that's a unique property of the + + align:start position:0% +you know that's a unique property of the + + + align:start position:0% +you know that's a unique property of the +sphere so it makes it really easy to + + align:start position:0% +sphere so it makes it really easy to + + + align:start position:0% +sphere so it makes it really easy to +know what the surface orientation is + + align:start position:0% +know what the surface orientation is + + + align:start position:0% +know what the surface orientation is +because we just connect the center of + + align:start position:0% +because we just connect the center of + + + align:start position:0% +because we just connect the center of +the sphere to the point on the surface + + align:start position:0% +the sphere to the point on the surface + + + align:start position:0% +the sphere to the point on the surface +you're interested in and there's your + + align:start position:0% +you're interested in and there's your + + + align:start position:0% +you're interested in and there's your +and of course this doesn't quite apply + + align:start position:0% +and of course this doesn't quite apply + + + align:start position:0% +and of course this doesn't quite apply +to the earth because it's not a sphere + + align:start position:0% +to the earth because it's not a sphere + + + align:start position:0% +to the earth because it's not a sphere +so + + align:start position:0% +so + + + align:start position:0% +so +need to modify that slightly + + align:start position:0% +need to modify that slightly + + + align:start position:0% +need to modify that slightly +and that's why there are several + + align:start position:0% +and that's why there are several + + + align:start position:0% +and that's why there are several +different definitions of latitude + + align:start position:0% +different definitions of latitude + + + align:start position:0% +different definitions of latitude +depending on whether you're talking + + align:start position:0% +depending on whether you're talking + + + align:start position:0% +depending on whether you're talking +about the local surface normal or the + + align:start position:0% +about the local surface normal or the + + + align:start position:0% +about the local surface normal or the +vector from the center of the earth + + align:start position:0% +vector from the center of the earth + + + align:start position:0% +vector from the center of the earth +and usually we take the local surface + + align:start position:0% +and usually we take the local surface + + + align:start position:0% +and usually we take the local surface +normal + + align:start position:0% +normal + + + align:start position:0% +normal +as the definition for + + align:start position:0% +as the definition for + + + align:start position:0% +as the definition for +the angle that's latitude okay so now + + align:start position:0% +the angle that's latitude okay so now + + + align:start position:0% +the angle that's latitude okay so now +what well you know we we could be a + + align:start position:0% +what well you know we we could be a + + + align:start position:0% +what well you know we we could be a +little bit more precise here + + align:start position:0% +little bit more precise here + + + align:start position:0% +little bit more precise here +um so we have um + + align:start position:0% +um so we have um + + + align:start position:0% +um so we have um +for every point in this image now + + align:start position:0% +for every point in this image now + + + align:start position:0% +for every point in this image now +uh let's let's call this point x y + + align:start position:0% +uh let's let's call this point x y + + + align:start position:0% +uh let's let's call this point x y +uh we can calculate what the surface + + align:start position:0% +uh we can calculate what the surface + + + align:start position:0% +uh we can calculate what the surface +orientation is and how do we do this + + align:start position:0% +orientation is and how do we do this + + + align:start position:0% +orientation is and how do we do this +well let's start with a cross section + + align:start position:0% + + + + align:start position:0% + +so this is + + align:start position:0% +so this is + + + align:start position:0% +so this is +you know here we're looking down on the + + align:start position:0% +you know here we're looking down on the + + + align:start position:0% +you know here we're looking down on the +sphere + + align:start position:0% +sphere + + + align:start position:0% +sphere +now we're looking + + align:start position:0% +now we're looking + + + align:start position:0% +now we're looking +sideways across it and i don't know the + + align:start position:0% +sideways across it and i don't know the + + + align:start position:0% +sideways across it and i don't know the +camera is + + align:start position:0% +camera is + + + align:start position:0% +camera is +way up there + + align:start position:0% +way up there + + + align:start position:0% +way up there +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so the surface normal is + + align:start position:0% +so the surface normal is + + + align:start position:0% +so the surface normal is +parallel to this + + align:start position:0% + + + + align:start position:0% + +right it's just well this is the point x + + align:start position:0% +right it's just well this is the point x + + + align:start position:0% +right it's just well this is the point x +naught y naught z naught + + align:start position:0% +naught y naught z naught + + + align:start position:0% +naught y naught z naught +and + + align:start position:0% +and + + + align:start position:0% +and +this is the point x y z + + align:start position:0% +this is the point x y z + + + align:start position:0% +this is the point x y z +and so um + + align:start position:0% +and so um + + + align:start position:0% +and so um +that's the surface normal so all we + + align:start position:0% +that's the surface normal so all we + + + align:start position:0% +that's the surface normal so all we +really need is a formula for + + align:start position:0% +really need is a formula for + + + align:start position:0% +really need is a formula for +z minus xenos + + align:start position:0% +z minus xenos + + + align:start position:0% +z minus xenos +we we're measuring + + align:start position:0% +we we're measuring + + + align:start position:0% +we we're measuring +x and y in the image plane so we know + + align:start position:0% +x and y in the image plane so we know + + + align:start position:0% +x and y in the image plane so we know +those + + align:start position:0% +those + + + align:start position:0% +those +we can't measure the depth + + align:start position:0% +we can't measure the depth + + + align:start position:0% +we can't measure the depth +so we have to calculate that and of + + align:start position:0% +so we have to calculate that and of + + + align:start position:0% +so we have to calculate that and of +course + + align:start position:0% +course + + + align:start position:0% +course +it's just going to be + + align:start position:0% +it's just going to be + + + align:start position:0% +it's just going to be +r 0 squared + + align:start position:0% + + + + align:start position:0% + +where's that come from well it just + + align:start position:0% +where's that come from well it just + + + align:start position:0% +where's that come from well it just +comes from the formula for sphere which + + align:start position:0% +comes from the formula for sphere which + + + align:start position:0% +comes from the formula for sphere which +is that the + + align:start position:0% +is that the + + + align:start position:0% +is that the +radius vector has a fixed size + + align:start position:0% +radius vector has a fixed size + + + align:start position:0% +radius vector has a fixed size +uh x minus x naught squared plus y minus + + align:start position:0% +uh x minus x naught squared plus y minus + + + align:start position:0% +uh x minus x naught squared plus y minus +y naught squared plus z minus z naught + + align:start position:0% +y naught squared plus z minus z naught + + + align:start position:0% +y naught squared plus z minus z naught +squared is r squared okay so having that + + align:start position:0% +squared is r squared okay so having that + + + align:start position:0% +squared is r squared okay so having that +uh we can then compute uh p and q + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +that comes from the formula we had last + + align:start position:0% +that comes from the formula we had last + + + align:start position:0% +that comes from the formula we had last +time last time we showed how to compute + + align:start position:0% +time last time we showed how to compute + + + align:start position:0% +time last time we showed how to compute +n from p and q and we also said you can + + align:start position:0% +n from p and q and we also said you can + + + align:start position:0% +n from p and q and we also said you can +go the other way + + align:start position:0% +go the other way + + + align:start position:0% +go the other way +if you're given p and q you can compute + + align:start position:0% +if you're given p and q you can compute + + + align:start position:0% +if you're given p and q you can compute +n and so that's where that comes from + + align:start position:0% +n and so that's where that comes from + + + align:start position:0% +n and so that's where that comes from +and you'll notice that + + align:start position:0% +and you'll notice that + + + align:start position:0% +and you'll notice that +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +oh sorry i think this is plus let's see + + align:start position:0% +oh sorry i think this is plus let's see + + + align:start position:0% +oh sorry i think this is plus let's see +if we go to the right of the center the + + align:start position:0% +if we go to the right of the center the + + + align:start position:0% +if we go to the right of the center the +the vector tilts to the right so it's + + align:start position:0% +the vector tilts to the right so it's + + + align:start position:0% +the vector tilts to the right so it's +plus sorry + + align:start position:0% + + + + align:start position:0% + +okay so for every + + align:start position:0% +okay so for every + + + align:start position:0% +okay so for every +pixel + + align:start position:0% +pixel + + + align:start position:0% +pixel +we can + + align:start position:0% +we can + + + align:start position:0% +we can +we know the orientation of the surface + + align:start position:0% +we know the orientation of the surface + + + align:start position:0% +we know the orientation of the surface +p and q and then we take a picture + + align:start position:0% +p and q and then we take a picture + + + align:start position:0% +p and q and then we take a picture +and + + align:start position:0% +and + + + align:start position:0% +and +we get a map + + align:start position:0% +we get a map + + + align:start position:0% +we get a map +under different lighting conditions so + + align:start position:0% +under different lighting conditions so + + + align:start position:0% +under different lighting conditions so +under one lighting conditions we get one + + align:start position:0% +under one lighting conditions we get one + + + align:start position:0% +under one lighting conditions we get one +e1 and another one we get e2 and let's + + align:start position:0% +e1 and another one we get e2 and let's + + + align:start position:0% +e1 and another one we get e2 and let's +suppose we take three + + align:start position:0% +suppose we take three + + + align:start position:0% +suppose we take three +so we we developed this numerical + + align:start position:0% +so we we developed this numerical + + + align:start position:0% +so we we developed this numerical +mapping from surface orientation uh to + + align:start position:0% +mapping from surface orientation uh to + + + align:start position:0% +mapping from surface orientation uh to +brightness in three pictures taken under + + align:start position:0% +brightness in three pictures taken under + + + align:start position:0% +brightness in three pictures taken under +different lighting conditions so we're + + align:start position:0% +different lighting conditions so we're + + + align:start position:0% +different lighting conditions so we're +treating pixels completely independently + + align:start position:0% +treating pixels completely independently + + + align:start position:0% +treating pixels completely independently +you know just think of a single point + + align:start position:0% +you know just think of a single point + + + align:start position:0% +you know just think of a single point +that we're imaging and a single pixel + + align:start position:0% +that we're imaging and a single pixel + + + align:start position:0% +that we're imaging and a single pixel +that's imaging because we repeat that at + + align:start position:0% +that's imaging because we repeat that at + + + align:start position:0% +that's imaging because we repeat that at +all the others + + align:start position:0% +all the others + + + align:start position:0% +all the others +okay so now + + align:start position:0% +okay so now + + + align:start position:0% +okay so now +that's going the wrong way + + align:start position:0% +that's going the wrong way + + + align:start position:0% +that's going the wrong way +we really want to go the other way + + align:start position:0% +we really want to go the other way + + + align:start position:0% +we really want to go the other way +we want + + align:start position:0% +we want + + + align:start position:0% +we want +to use this information + + align:start position:0% +to use this information + + + align:start position:0% +to use this information +so that when we then later take + + align:start position:0% +so that when we then later take + + + align:start position:0% +so that when we then later take +three images of the of an object + + align:start position:0% +three images of the of an object + + + align:start position:0% +three images of the of an object +under the three lighting conditions + + align:start position:0% +under the three lighting conditions + + + align:start position:0% +under the three lighting conditions +we can go to some sort of table or some + + align:start position:0% +we can go to some sort of table or some + + + align:start position:0% +we can go to some sort of table or some +calculation that gives us p and q so so + + align:start position:0% +calculation that gives us p and q so so + + + align:start position:0% +calculation that gives us p and q so so +we want to + + align:start position:0% +we want to + + + align:start position:0% +we want to +go that way + + align:start position:0% +go that way + + + align:start position:0% +go that way +and in terms of implementation + + align:start position:0% +and in terms of implementation + + + align:start position:0% +and in terms of implementation +you know + + align:start position:0% +you know + + + align:start position:0% +you know +we left lambertian behind lambertian's + + align:start position:0% +we left lambertian behind lambertian's + + + align:start position:0% +we left lambertian behind lambertian's +nice and analytic you can invert it and + + align:start position:0% +nice and analytic you can invert it and + + + align:start position:0% +nice and analytic you can invert it and +do all sorts of stuff but once we've + + align:start position:0% +do all sorts of stuff but once we've + + + align:start position:0% +do all sorts of stuff but once we've +decided that we want to be completely + + align:start position:0% +decided that we want to be completely + + + align:start position:0% +decided that we want to be completely +general then we can't depend on + + align:start position:0% +general then we can't depend on + + + align:start position:0% +general then we can't depend on +analytically inverting things so let's + + align:start position:0% +analytically inverting things so let's + + + align:start position:0% +analytically inverting things so let's +use a numerical table + + align:start position:0% + + + + align:start position:0% + +and so this is a three-dimensional array + + align:start position:0% +and so this is a three-dimensional array + + + align:start position:0% +and so this is a three-dimensional array +in the computer + + align:start position:0% +in the computer + + + align:start position:0% +in the computer +and you know each each little voxel here + + align:start position:0% +and you know each each little voxel here + + + align:start position:0% +and you know each each little voxel here +is one entry + + align:start position:0% +is one entry + + + align:start position:0% +is one entry +and what is what is in that box well + + align:start position:0% +and what is what is in that box well + + + align:start position:0% +and what is what is in that box well +each of these little boxes has + + align:start position:0% +each of these little boxes has + + + align:start position:0% +each of these little boxes has +uh p and q + + align:start position:0% +uh p and q + + + align:start position:0% +uh p and q +so what i would do is i would make the + + align:start position:0% +so what i would do is i would make the + + + align:start position:0% +so what i would do is i would make the +measurement + + align:start position:0% +measurement + + + align:start position:0% +measurement +in three image situation situations use + + align:start position:0% +in three image situation situations use + + + align:start position:0% +in three image situation situations use +them i quantize them to + + align:start position:0% +them i quantize them to + + + align:start position:0% +them i quantize them to +the discrete + + align:start position:0% +the discrete + + + align:start position:0% +the discrete +intervals of this + + align:start position:0% +intervals of this + + + align:start position:0% +intervals of this +lookup table + + align:start position:0% +lookup table + + + align:start position:0% +lookup table +i go to that place and it tells me what + + align:start position:0% +i go to that place and it tells me what + + + align:start position:0% +i go to that place and it tells me what +the surface orientation is + + align:start position:0% +the surface orientation is + + + align:start position:0% +the surface orientation is +so so that's what i'd like but how do + + align:start position:0% +so so that's what i'd like but how do + + + align:start position:0% +so so that's what i'd like but how do +how do i build that + + align:start position:0% + + + + align:start position:0% + +right so so is that clear i mean you can + + align:start position:0% +right so so is that clear i mean you can + + + align:start position:0% +right so so is that clear i mean you can +see how computationally trivial this is + + align:start position:0% +see how computationally trivial this is + + + align:start position:0% +see how computationally trivial this is +it costs you nothing just about to + + align:start position:0% +it costs you nothing just about to + + + align:start position:0% +it costs you nothing just about to +interpret these images there's no + + align:start position:0% +interpret these images there's no + + + align:start position:0% +interpret these images there's no +complicated iteration or anything it's + + align:start position:0% +complicated iteration or anything it's + + + align:start position:0% +complicated iteration or anything it's +just a table lookup is + + align:start position:0% +just a table lookup is + + + align:start position:0% +just a table lookup is +hard to imagine anything cheaper than + + align:start position:0% +hard to imagine anything cheaper than + + + align:start position:0% +hard to imagine anything cheaper than +that so if i can build this table i'll + + align:start position:0% +that so if i can build this table i'll + + + align:start position:0% +that so if i can build this table i'll +have a very efficient method for + + align:start position:0% +have a very efficient method for + + + align:start position:0% +have a very efficient method for +getting the shape well not quite we will + + align:start position:0% +getting the shape well not quite we will + + + align:start position:0% +getting the shape well not quite we will +get local surface orientations we still + + align:start position:0% +get local surface orientations we still + + + align:start position:0% +get local surface orientations we still +have to talk about how to patch that + + align:start position:0% +have to talk about how to patch that + + + align:start position:0% +have to talk about how to patch that +together + + align:start position:0% +together + + + align:start position:0% +together +into shape but for the moment + + align:start position:0% +into shape but for the moment + + + align:start position:0% +into shape but for the moment +we're just going to get surface + + align:start position:0% +we're just going to get surface + + + align:start position:0% +we're just going to get surface +orientation + + align:start position:0% +orientation + + + align:start position:0% +orientation +okay now what i'm doing then is i'm + + align:start position:0% +okay now what i'm doing then is i'm + + + align:start position:0% +okay now what i'm doing then is i'm +running over this calibration image + + align:start position:0% +running over this calibration image + + + align:start position:0% +running over this calibration image +and at every pixel + + align:start position:0% +and at every pixel + + + align:start position:0% +and at every pixel +i'm looking i'm computing uh p and q + + align:start position:0% +i'm looking i'm computing uh p and q + + + align:start position:0% +i'm looking i'm computing uh p and q +and i'm uh measuring e1 e2 in e3 and i + + align:start position:0% +and i'm uh measuring e1 e2 in e3 and i + + + align:start position:0% +and i'm uh measuring e1 e2 in e3 and i +use that to put something into this + + align:start position:0% +use that to put something into this + + + align:start position:0% +use that to put something into this +table + + align:start position:0% +table + + + align:start position:0% +table +so i can quantize my e1 e2 e3 + + align:start position:0% +so i can quantize my e1 e2 e3 + + + align:start position:0% +so i can quantize my e1 e2 e3 +that gives me the index into this 3d + + align:start position:0% +that gives me the index into this 3d + + + align:start position:0% +that gives me the index into this 3d +array and i write the p and q there and + + align:start position:0% +array and i write the p and q there and + + + align:start position:0% +array and i write the p and q there and +and i do this for every pixel + + align:start position:0% +and i do this for every pixel + + + align:start position:0% +and i do this for every pixel +and you know there might be + + align:start position:0% +and you know there might be + + + align:start position:0% +and you know there might be +some overlap because uh i can't + + align:start position:0% +some overlap because uh i can't + + + align:start position:0% +some overlap because uh i can't +represent the table with infinite + + align:start position:0% +represent the table with infinite + + + align:start position:0% +represent the table with infinite +precision + + align:start position:0% +precision + + + align:start position:0% +precision +um i'll have to make some sort of + + align:start position:0% +um i'll have to make some sort of + + + align:start position:0% +um i'll have to make some sort of +compromise where i say okay i'm gonna + + align:start position:0% +compromise where i say okay i'm gonna + + + align:start position:0% +compromise where i say okay i'm gonna +quantize quantize + + align:start position:0% +quantize quantize + + + align:start position:0% +quantize quantize +let's suppose i quantized 200 different + + align:start position:0% +let's suppose i quantized 200 different + + + align:start position:0% +let's suppose i quantized 200 different +values that means the lookup table will + + align:start position:0% +values that means the lookup table will + + + align:start position:0% +values that means the lookup table will +be uh what a million entries so that + + align:start position:0% +be uh what a million entries so that + + + align:start position:0% +be uh what a million entries so that +that's + + align:start position:0% +that's + + + align:start position:0% +that's +you know + + align:start position:0% +you know + + + align:start position:0% +you know +it's a lot in terms of cash size and so + + align:start position:0% +it's a lot in terms of cash size and so + + + align:start position:0% +it's a lot in terms of cash size and so +on but + + align:start position:0% +on but + + + align:start position:0% +on but +it's a reasonable value whereas let's + + align:start position:0% +it's a reasonable value whereas let's + + + align:start position:0% +it's a reasonable value whereas let's +say + + align:start position:0% +say + + + align:start position:0% +say +a petabyte lookup table probably + + align:start position:0% +a petabyte lookup table probably + + + align:start position:0% +a petabyte lookup table probably +wouldn't be very satisfactory + + align:start position:0% +wouldn't be very satisfactory + + + align:start position:0% +wouldn't be very satisfactory +but in any case that means we need to + + align:start position:0% +but in any case that means we need to + + + align:start position:0% +but in any case that means we need to +quantize and we might need to quantize + + align:start position:0% +quantize and we might need to quantize + + + align:start position:0% +quantize and we might need to quantize +um fairly costly like 100 + + align:start position:0% +um fairly costly like 100 + + + align:start position:0% +um fairly costly like 100 +and that means that some of these points + + align:start position:0% +and that means that some of these points + + + align:start position:0% +and that means that some of these points +may produce the same + + align:start position:0% +may produce the same + + + align:start position:0% +may produce the same +they happen to produce the same rounded + + align:start position:0% +they happen to produce the same rounded + + + align:start position:0% +they happen to produce the same rounded +off values and so they'll be writing on + + align:start position:0% +off values and so they'll be writing on + + + align:start position:0% +off values and so they'll be writing on +top of each other + + align:start position:0% +top of each other + + + align:start position:0% +top of each other +so that's one issue and how do you deal + + align:start position:0% +so that's one issue and how do you deal + + + align:start position:0% +so that's one issue and how do you deal +with that well one way is to average + + align:start position:0% +with that well one way is to average + + + align:start position:0% +with that well one way is to average +them + + align:start position:0% +them + + + align:start position:0% +them +because presumably they're slightly + + align:start position:0% +because presumably they're slightly + + + align:start position:0% +because presumably they're slightly +different p and q's and by combining + + align:start position:0% +different p and q's and by combining + + + align:start position:0% +different p and q's and by combining +them in some weighted fashion we can get + + align:start position:0% +them in some weighted fashion we can get + + + align:start position:0% +them in some weighted fashion we can get +higher accuracy + + align:start position:0% +higher accuracy + + + align:start position:0% +higher accuracy +but a more serious problem is + + align:start position:0% +but a more serious problem is + + + align:start position:0% +but a more serious problem is +there could be cells here that never get + + align:start position:0% +there could be cells here that never get + + + align:start position:0% +there could be cells here that never get +touched that never get filled in + + align:start position:0% +touched that never get filled in + + + align:start position:0% +touched that never get filled in +and there are a couple of reasons for + + align:start position:0% +and there are a couple of reasons for + + + align:start position:0% +and there are a couple of reasons for +that one is just the nature of you know + + align:start position:0% +that one is just the nature of you know + + + align:start position:0% +that one is just the nature of you know +these numerical quantization effects but + + align:start position:0% +these numerical quantization effects but + + + align:start position:0% +these numerical quantization effects but +there's a more basic one which is + + align:start position:0% +there's a more basic one which is + + + align:start position:0% +there's a more basic one which is +p and q + + align:start position:0% +p and q + + + align:start position:0% +p and q +gradient space is a two-dimensional + + align:start position:0% +gradient space is a two-dimensional + + + align:start position:0% +gradient space is a two-dimensional +space + + align:start position:0% +space + + + align:start position:0% +space +and we're mapping it here into a + + align:start position:0% +and we're mapping it here into a + + + align:start position:0% +and we're mapping it here into a +three-dimensional space + + align:start position:0% +three-dimensional space + + + align:start position:0% +three-dimensional space +so + + align:start position:0% +so + + + align:start position:0% +so +we're not actually filling that space at + + align:start position:0% +we're not actually filling that space at + + + align:start position:0% +we're not actually filling that space at +all + + align:start position:0% +all + + + align:start position:0% +all +right + + align:start position:0% +right + + + align:start position:0% +right +so what do we get well we get a surface + + align:start position:0% +so what do we get well we get a surface + + + align:start position:0% +so what do we get well we get a surface +in that space + + align:start position:0% +in that space + + + align:start position:0% +in that space +so + + align:start position:0% +so + + + align:start position:0% +so +if we ignore the quantization for the + + align:start position:0% +if we ignore the quantization for the + + + align:start position:0% +if we ignore the quantization for the +moment + + align:start position:0% + + + + align:start position:0% + +you know + + align:start position:0% +you know + + + align:start position:0% +you know +we're not filling that space we're + + align:start position:0% +we're not filling that space we're + + + align:start position:0% +we're not filling that space we're +getting + + align:start position:0% +getting + + + align:start position:0% +getting +some surface and you know if you like + + align:start position:0% +some surface and you know if you like + + + align:start position:0% +some surface and you know if you like +you can + + align:start position:0% + + + + align:start position:0% + +address points on that surface using p + + align:start position:0% +address points on that surface using p + + + align:start position:0% +address points on that surface using p +and q + + align:start position:0% + + + + align:start position:0% + +so that's + + align:start position:0% +so that's + + + align:start position:0% +so that's +point number one so that means that + + align:start position:0% +point number one so that means that + + + align:start position:0% +point number one so that means that +later on + + align:start position:0% +later on + + + align:start position:0% +later on +if i find some combination of e1 e2 and + + align:start position:0% +if i find some combination of e1 e2 and + + + align:start position:0% +if i find some combination of e1 e2 and +e3 it's quite possible that it won't + + align:start position:0% +e3 it's quite possible that it won't + + + align:start position:0% +e3 it's quite possible that it won't +happen to be on that surface and you + + align:start position:0% +happen to be on that surface and you + + + align:start position:0% +happen to be on that surface and you +know then that means the lookup table's + + align:start position:0% +know then that means the lookup table's + + + align:start position:0% +know then that means the lookup table's +not giving me an answer + + align:start position:0% +not giving me an answer + + + align:start position:0% +not giving me an answer +so so what's what's with that well if + + align:start position:0% +so so what's what's with that well if + + + align:start position:0% +so so what's what's with that well if +you remember when we went from two + + align:start position:0% +you remember when we went from two + + + align:start position:0% +you remember when we went from two +images to three + + align:start position:0% +images to three + + + align:start position:0% +images to three +uh we introduced the albedo + + align:start position:0% + + + + align:start position:0% + +so that was one case we're making a + + align:start position:0% +so that was one case we're making a + + + align:start position:0% +so that was one case we're making a +problem more complicated made it easier + + align:start position:0% +problem more complicated made it easier + + + align:start position:0% +problem more complicated made it easier +right we before we only had two unknowns + + align:start position:0% +right we before we only had two unknowns + + + align:start position:0% +right we before we only had two unknowns +p and q and we ended up with a quadratic + + align:start position:0% +p and q and we ended up with a quadratic + + + align:start position:0% +p and q and we ended up with a quadratic +so we had two solutions and we said oh + + align:start position:0% +so we had two solutions and we said oh + + + align:start position:0% +so we had two solutions and we said oh +you know ambiguity let's add a third + + align:start position:0% +you know ambiguity let's add a third + + + align:start position:0% +you know ambiguity let's add a third +unknown and then suddenly we get linear + + align:start position:0% +unknown and then suddenly we get linear + + + align:start position:0% +unknown and then suddenly we get linear +equations unique answer + + align:start position:0% +equations unique answer + + + align:start position:0% +equations unique answer +well + + align:start position:0% +well + + + align:start position:0% +well +this would apply here as well so our + + align:start position:0% +this would apply here as well so our + + + align:start position:0% +this would apply here as well so our +calibration object of course is made + + align:start position:0% +calibration object of course is made + + + align:start position:0% +calibration object of course is made +with one particular albedo perhaps we + + align:start position:0% +with one particular albedo perhaps we + + + align:start position:0% +with one particular albedo perhaps we +painted it white and so its albedo is + + align:start position:0% +painted it white and so its albedo is + + + align:start position:0% +painted it white and so its albedo is +basically one + + align:start position:0% +basically one + + + align:start position:0% +basically one +but + + align:start position:0% +but + + + align:start position:0% +but +suppose we also want to deal with cal + + align:start position:0% +suppose we also want to deal with cal + + + align:start position:0% +suppose we also want to deal with cal +with similar objects where not all the + + align:start position:0% +with similar objects where not all the + + + align:start position:0% +with similar objects where not all the +light is reflected + + align:start position:0% +light is reflected + + + align:start position:0% +light is reflected +and so how do we do that well it's very + + align:start position:0% +and so how do we do that well it's very + + + align:start position:0% +and so how do we do that well it's very +easy because rho albedo + + align:start position:0% +easy because rho albedo + + + align:start position:0% +easy because rho albedo +linearly scales e1 e2 e3 + + align:start position:0% +linearly scales e1 e2 e3 + + + align:start position:0% +linearly scales e1 e2 e3 +and so that means that + + align:start position:0% +and so that means that + + + align:start position:0% +and so that means that +anything on array out here + + align:start position:0% +anything on array out here + + + align:start position:0% +anything on array out here +is connected and you know rho + + align:start position:0% +is connected and you know rho + + + align:start position:0% +is connected and you know rho +row is zero on this end and one on that + + align:start position:0% +row is zero on this end and one on that + + + align:start position:0% +row is zero on this end and one on that +end + + align:start position:0% +end + + + align:start position:0% +end +so suppose we've painted our sphere nice + + align:start position:0% +so suppose we've painted our sphere nice + + + align:start position:0% +so suppose we've painted our sphere nice +and white and we made these measurements + + align:start position:0% +and white and we made these measurements + + + align:start position:0% +and white and we made these measurements +then we've defined that uh that shape + + align:start position:0% +then we've defined that uh that shape + + + align:start position:0% +then we've defined that uh that shape +that + + align:start position:0% +that + + + align:start position:0% +that +surface in the space + + align:start position:0% +surface in the space + + + align:start position:0% +surface in the space +and now + + align:start position:0% +and now + + + align:start position:0% +and now +that's for rho equal to one and we can + + align:start position:0% +that's for rho equal to one and we can + + + align:start position:0% +that's for rho equal to one and we can +because it's perfectly linear + + align:start position:0% +because it's perfectly linear + + + align:start position:0% +because it's perfectly linear +for other rows we can just + + align:start position:0% +for other rows we can just + + + align:start position:0% +for other rows we can just +generate those + + align:start position:0% +generate those + + + align:start position:0% +generate those +so + + align:start position:0% +so + + + align:start position:0% +so +when we place + + align:start position:0% +when we place + + + align:start position:0% +when we place +an entry in the lookup table up here + + align:start position:0% +an entry in the lookup table up here + + + align:start position:0% +an entry in the lookup table up here +we can just say okay for now we scan + + align:start position:0% +we can just say okay for now we scan + + + align:start position:0% +we can just say okay for now we scan +along this line and + + align:start position:0% +along this line and + + + align:start position:0% +along this line and +we fill in + + align:start position:0% +we fill in + + + align:start position:0% +we fill in +all of those cubes and now instead of + + align:start position:0% +all of those cubes and now instead of + + + align:start position:0% +all of those cubes and now instead of +just writing uh + + align:start position:0% +just writing uh + + + align:start position:0% +just writing uh +p and q + + align:start position:0% +p and q + + + align:start position:0% +p and q +we write p q and row in there + + align:start position:0% +we write p q and row in there + + + align:start position:0% +we write p q and row in there +so it's a three to three lookup table + + align:start position:0% +so it's a three to three lookup table + + + align:start position:0% +so it's a three to three lookup table +now three dimensions to three dimensions + + align:start position:0% +now three dimensions to three dimensions + + + align:start position:0% +now three dimensions to three dimensions +and you know in a in a real situation + + align:start position:0% +and you know in a in a real situation + + + align:start position:0% +and you know in a in a real situation +maybe you know that the object is + + align:start position:0% +maybe you know that the object is + + + align:start position:0% +maybe you know that the object is +supposed to be a certain color and so + + align:start position:0% +supposed to be a certain color and so + + + align:start position:0% +supposed to be a certain color and so +having a + + align:start position:0% +having a + + + align:start position:0% +having a +value different value of row + + align:start position:0% +value different value of row + + + align:start position:0% +value different value of row +is uh not really acceptable it indicates + + align:start position:0% +is uh not really acceptable it indicates + + + align:start position:0% +is uh not really acceptable it indicates +there's something wrong and that can be + + align:start position:0% +there's something wrong and that can be + + + align:start position:0% +there's something wrong and that can be +pretty useful like you know there's a + + align:start position:0% +pretty useful like you know there's a + + + align:start position:0% +pretty useful like you know there's a +smudge on the surface + + align:start position:0% +smudge on the surface + + + align:start position:0% +smudge on the surface +or it's not actually the surface you + + align:start position:0% +or it's not actually the surface you + + + align:start position:0% +or it's not actually the surface you +were told it was + + align:start position:0% +were told it was + + + align:start position:0% +were told it was +so uh it's like a check + + align:start position:0% +so uh it's like a check + + + align:start position:0% +so uh it's like a check +an error condition that you can check + + align:start position:0% +an error condition that you can check + + + align:start position:0% +an error condition that you can check +for + + align:start position:0% + + + + align:start position:0% + +or for example suppose that + + align:start position:0% +or for example suppose that + + + align:start position:0% +or for example suppose that +there's something blocking one of the + + align:start position:0% +there's something blocking one of the + + + align:start position:0% +there's something blocking one of the +three light sources + + align:start position:0% +three light sources + + + align:start position:0% +three light sources +casting a shadow well that means that + + align:start position:0% +casting a shadow well that means that + + + align:start position:0% +casting a shadow well that means that +one of these e1 e2 e2e3s is going to be + + align:start position:0% +one of these e1 e2 e2e3s is going to be + + + align:start position:0% +one of these e1 e2 e2e3s is going to be +relatively small + + align:start position:0% +relatively small + + + align:start position:0% +relatively small +and so you'll be + + align:start position:0% +and so you'll be + + + align:start position:0% +and so you'll be +away from the surface + + align:start position:0% +away from the surface + + + align:start position:0% +away from the surface +and + + align:start position:0% +and + + + align:start position:0% +and +if if you're using this method you can + + align:start position:0% +if if you're using this method you can + + + align:start position:0% +if if you're using this method you can +pick that up and say oh this + + align:start position:0% +pick that up and say oh this + + + align:start position:0% +pick that up and say oh this +i don't know what p and q is here but + + align:start position:0% +i don't know what p and q is here but + + + align:start position:0% +i don't know what p and q is here but +there's something weird going on + + align:start position:0% +there's something weird going on + + + align:start position:0% +there's something weird going on +or + + align:start position:0% +or + + + align:start position:0% +or +i know if you remember the slides but + + align:start position:0% +i know if you remember the slides but + + + align:start position:0% +i know if you remember the slides but +one of the other things that can happen + + align:start position:0% +one of the other things that can happen + + + align:start position:0% +one of the other things that can happen +is that + + align:start position:0% +is that + + + align:start position:0% +is that +if + + align:start position:0% +if + + + align:start position:0% +if +highly reflective surfaces are close to + + align:start position:0% +highly reflective surfaces are close to + + + align:start position:0% +highly reflective surfaces are close to +each other there'll be interflection and + + align:start position:0% +each other there'll be interflection and + + + align:start position:0% +each other there'll be interflection and +we will have brightnesses that are + + align:start position:0% +we will have brightnesses that are + + + align:start position:0% +we will have brightnesses that are +abnormally high + + align:start position:0% +abnormally high + + + align:start position:0% +abnormally high +and will actually be outside this + + align:start position:0% +and will actually be outside this + + + align:start position:0% +and will actually be outside this +surface + + align:start position:0% +surface + + + align:start position:0% +surface +and again we can say okay + + align:start position:0% +and again we can say okay + + + align:start position:0% +and again we can say okay +my method doesn't tell me what the + + align:start position:0% +my method doesn't tell me what the + + + align:start position:0% +my method doesn't tell me what the +surface orientation is but there's + + align:start position:0% +surface orientation is but there's + + + align:start position:0% +surface orientation is but there's +something going on here and so um i'm + + align:start position:0% +something going on here and so um i'm + + + align:start position:0% +something going on here and so um i'm +not going to make that part of the + + align:start position:0% +not going to make that part of the + + + align:start position:0% +not going to make that part of the +surface i'm going to use that to break + + align:start position:0% +surface i'm going to use that to break + + + align:start position:0% +surface i'm going to use that to break +up uh the image into parts that hang + + align:start position:0% +up uh the image into parts that hang + + + align:start position:0% +up uh the image into parts that hang +together and parts that don't so in the + + align:start position:0% +together and parts that don't so in the + + + align:start position:0% +together and parts that don't so in the +case of those overlapping donuts this is + + align:start position:0% +case of those overlapping donuts this is + + + align:start position:0% +case of those overlapping donuts this is +a way to segment it + + align:start position:0% +a way to segment it + + + align:start position:0% +a way to segment it +into + + align:start position:0% +into + + + align:start position:0% +into +you know you start off the image is one + + align:start position:0% +you know you start off the image is one + + + align:start position:0% +you know you start off the image is one +thing it's just e of x and y + + align:start position:0% +thing it's just e of x and y + + + align:start position:0% +thing it's just e of x and y +but you know that it's an image of + + align:start position:0% +but you know that it's an image of + + + align:start position:0% +but you know that it's an image of +multiple objects and so segmentation is + + align:start position:0% +multiple objects and so segmentation is + + + align:start position:0% +multiple objects and so segmentation is +a big problem + + align:start position:0% +a big problem + + + align:start position:0% +a big problem +and if we use these methods we can + + align:start position:0% +and if we use these methods we can + + + align:start position:0% +and if we use these methods we can +segment on on cast shadows where one + + align:start position:0% +segment on on cast shadows where one + + + align:start position:0% +segment on on cast shadows where one +donut casts a shadow on another and we + + align:start position:0% +donut casts a shadow on another and we + + + align:start position:0% +donut casts a shadow on another and we +can segment on areas of high + + align:start position:0% +can segment on areas of high + + + align:start position:0% +can segment on areas of high +interflection which is where they touch + + align:start position:0% +interflection which is where they touch + + + align:start position:0% +interflection which is where they touch +and so + + align:start position:0% +and so + + + align:start position:0% +and so +what looks like a drawback can actually + + align:start position:0% +what looks like a drawback can actually + + + align:start position:0% +what looks like a drawback can actually +be + + align:start position:0% +be + + + align:start position:0% +be +helpful + + align:start position:0% +helpful + + + align:start position:0% +helpful +now this still doesn't guarantee that + + align:start position:0% +now this still doesn't guarantee that + + + align:start position:0% +now this still doesn't guarantee that +we'll have filled in all of the voxels + + align:start position:0% +we'll have filled in all of the voxels + + + align:start position:0% +we'll have filled in all of the voxels +in this three-dimensional space + + align:start position:0% +in this three-dimensional space + + + align:start position:0% +in this three-dimensional space +so actually + + align:start position:0% +so actually + + + align:start position:0% +so actually +um + + align:start position:0% +um + + + align:start position:0% +um +there's a customary way of solving this + + align:start position:0% +there's a customary way of solving this + + + align:start position:0% +there's a customary way of solving this +kind of problem which is + + align:start position:0% +kind of problem which is + + + align:start position:0% +kind of problem which is +to go the other direction so what we did + + align:start position:0% +to go the other direction so what we did + + + align:start position:0% +to go the other direction so what we did +was we went to the image and we said + + align:start position:0% +was we went to the image and we said + + + align:start position:0% +was we went to the image and we said +okay + + align:start position:0% +okay + + + align:start position:0% +okay +for that pixel we get p and q and we + + align:start position:0% +for that pixel we get p and q and we + + + align:start position:0% +for that pixel we get p and q and we +measure e1 e2 3 then we put that in this + + align:start position:0% +measure e1 e2 3 then we put that in this + + + align:start position:0% +measure e1 e2 3 then we put that in this +table + + align:start position:0% +table + + + align:start position:0% +table +the other way is to systematically step + + align:start position:0% +the other way is to systematically step + + + align:start position:0% +the other way is to systematically step +through the table rather than step + + align:start position:0% +through the table rather than step + + + align:start position:0% +through the table rather than step +through the pixels and then for each of + + align:start position:0% +through the pixels and then for each of + + + align:start position:0% +through the pixels and then for each of +these voxels find the corresponding + + align:start position:0% +these voxels find the corresponding + + + align:start position:0% +these voxels find the corresponding +thing over there + + align:start position:0% +thing over there + + + align:start position:0% +thing over there +and that way you can be assured that you + + align:start position:0% +and that way you can be assured that you + + + align:start position:0% +and that way you can be assured that you +filled in the table + + align:start position:0% +filled in the table + + + align:start position:0% +filled in the table +this this way it's sort of you're + + align:start position:0% +this this way it's sort of you're + + + align:start position:0% +this this way it's sort of you're +projecting in a non-linear way from + + align:start position:0% +projecting in a non-linear way from + + + align:start position:0% +projecting in a non-linear way from +lattice or cubic lattice onto this + + align:start position:0% +lattice or cubic lattice onto this + + + align:start position:0% +lattice or cubic lattice onto this +curvilinear space and there's no + + align:start position:0% +curvilinear space and there's no + + + align:start position:0% +curvilinear space and there's no +guarantee that you won't have overlaps + + align:start position:0% +guarantee that you won't have overlaps + + + align:start position:0% +guarantee that you won't have overlaps +and yet you will fill everything in + + align:start position:0% +and yet you will fill everything in + + + align:start position:0% +and yet you will fill everything in +so but that's you know fairly boring so + + align:start position:0% +so but that's you know fairly boring so + + + align:start position:0% +so but that's you know fairly boring so +i won't talk about that + + align:start position:0% +i won't talk about that + + + align:start position:0% +i won't talk about that +now i was going to talk about lambert's + + align:start position:0% +now i was going to talk about lambert's + + + align:start position:0% +now i was going to talk about lambert's +lunch paper + + align:start position:0% +lunch paper + + + align:start position:0% +lunch paper +and explain exactly why + + align:start position:0% +and explain exactly why + + + align:start position:0% +and explain exactly why +when you cannot see the fatty spot the + + align:start position:0% +when you cannot see the fatty spot the + + + align:start position:0% +when you cannot see the fatty spot the +illumination from the left and the right + + align:start position:0% +illumination from the left and the right + + + align:start position:0% +illumination from the left and the right +is equal + + align:start position:0% +is equal + + + align:start position:0% +is equal +but i'm hoping you'll believe me it's + + align:start position:0% +but i'm hoping you'll believe me it's + + + align:start position:0% +but i'm hoping you'll believe me it's +it's just a page of uh fairly boring + + align:start position:0% +it's just a page of uh fairly boring + + + align:start position:0% +it's just a page of uh fairly boring +algebra so + + align:start position:0% +algebra so + + + align:start position:0% +algebra so +maybe we'll turn it into a homework + + align:start position:0% +maybe we'll turn it into a homework + + + align:start position:0% +maybe we'll turn it into a homework +problem or something so + + align:start position:0% +problem or something so + + + align:start position:0% +problem or something so +anyway that was uh + + align:start position:0% +anyway that was uh + + + align:start position:0% +anyway that was uh +lambert's uh instrument for discovering + + align:start position:0% +lambert's uh instrument for discovering + + + align:start position:0% +lambert's uh instrument for discovering +a lot of things about photometry so + + align:start position:0% +a lot of things about photometry so + + + align:start position:0% +a lot of things about photometry so +let's uh get a little more serious about + + align:start position:0% +let's uh get a little more serious about + + + align:start position:0% +let's uh get a little more serious about +photometry + + align:start position:0% +photometry + + + align:start position:0% +photometry +you know we + + align:start position:0% +you know we + + + align:start position:0% +you know we +we use these terms like brightness and + + align:start position:0% +we use these terms like brightness and + + + align:start position:0% +we use these terms like brightness and +intensity + + align:start position:0% +intensity + + + align:start position:0% +intensity +rather loosely and it's good to + + align:start position:0% + + + + align:start position:0% + +make them precise + + align:start position:0% + + + + align:start position:0% + +so the first term is irradiance + + align:start position:0% + + + + align:start position:0% + +and it's a you know + + align:start position:0% +and it's a you know + + + align:start position:0% +and it's a you know +the most trivial concept you can + + align:start position:0% +the most trivial concept you can + + + align:start position:0% +the most trivial concept you can +imagine here's a patch of the surface of + + align:start position:0% +imagine here's a patch of the surface of + + + align:start position:0% +imagine here's a patch of the surface of +area delta a + + align:start position:0% +area delta a + + + align:start position:0% +area delta a +and here's some light source + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +there's a + + align:start position:0% + + + + align:start position:0% + +bit of the power emitted by the light + + align:start position:0% +bit of the power emitted by the light + + + align:start position:0% +bit of the power emitted by the light +source which + + align:start position:0% +source which + + + align:start position:0% +source which +is intercepted by the surface + + align:start position:0% +is intercepted by the surface + + + align:start position:0% +is intercepted by the surface +and + + align:start position:0% + + + + align:start position:0% + +the irradiance is just the power per + + align:start position:0% +the irradiance is just the power per + + + align:start position:0% +the irradiance is just the power per +unit area + + align:start position:0% + + + + align:start position:0% + +and in terms of you know it's watts per + + align:start position:0% +and in terms of you know it's watts per + + + align:start position:0% +and in terms of you know it's watts per +square meter if you like + + align:start position:0% +square meter if you like + + + align:start position:0% +square meter if you like +and just for reference + + align:start position:0% +and just for reference + + + align:start position:0% +and just for reference +noonday sun in washington dc is + + align:start position:0% +noonday sun in washington dc is + + + align:start position:0% +noonday sun in washington dc is +supposedly + + align:start position:0% +supposedly + + + align:start position:0% +supposedly +one kilowatt per square meter + + align:start position:0% +one kilowatt per square meter + + + align:start position:0% +one kilowatt per square meter +and you know what what does that mean + + align:start position:0% +and you know what what does that mean + + + align:start position:0% +and you know what what does that mean +well it's it's not a very precise value + + align:start position:0% +well it's it's not a very precise value + + + align:start position:0% +well it's it's not a very precise value +because it'll depend on the state of the + + align:start position:0% +because it'll depend on the state of the + + + align:start position:0% +because it'll depend on the state of the +atmosphere and the time of year and + + align:start position:0% +atmosphere and the time of year and + + + align:start position:0% +atmosphere and the time of year and +what is what are you measuring are you + + align:start position:0% +what is what are you measuring are you + + + align:start position:0% +what is what are you measuring are you +measuring only visible light uh are you + + align:start position:0% +measuring only visible light uh are you + + + align:start position:0% +measuring only visible light uh are you +measuring near infrared as well and so + + align:start position:0% +measuring near infrared as well and so + + + align:start position:0% +measuring near infrared as well and so +on but roughly speaking that's a useful + + align:start position:0% +on but roughly speaking that's a useful + + + align:start position:0% +on but roughly speaking that's a useful +number to know because from that we can + + align:start position:0% +number to know because from that we can + + + align:start position:0% +number to know because from that we can +calculate things like uh suppose you + + align:start position:0% +calculate things like uh suppose you + + + align:start position:0% +calculate things like uh suppose you +have an image sensor that's four microns + + align:start position:0% +have an image sensor that's four microns + + + align:start position:0% +have an image sensor that's four microns +by four microns what energy falls on + + align:start position:0% +by four microns what energy falls on + + + align:start position:0% +by four microns what energy falls on +that + + align:start position:0% +that + + + align:start position:0% +that +and then you put that image sensor + + align:start position:0% +and then you put that image sensor + + + align:start position:0% +and then you put that image sensor +behind the lens which attenuates even + + align:start position:0% +behind the lens which attenuates even + + + align:start position:0% +behind the lens which attenuates even +more you know how much comes out so it's + + align:start position:0% +more you know how much comes out so it's + + + align:start position:0% +more you know how much comes out so it's +a very simple concept + + align:start position:0% +a very simple concept + + + align:start position:0% +a very simple concept +and unfortunately it's not terribly + + align:start position:0% +and unfortunately it's not terribly + + + align:start position:0% +and unfortunately it's not terribly +useful for us because we have an imaging + + align:start position:0% +useful for us because we have an imaging + + + align:start position:0% +useful for us because we have an imaging +system we're not exposing the sensor + + align:start position:0% +system we're not exposing the sensor + + + align:start position:0% +system we're not exposing the sensor +directly to the illumination well if we + + align:start position:0% +directly to the illumination well if we + + + align:start position:0% +directly to the illumination well if we +did we wouldn't learn anything about + + align:start position:0% +did we wouldn't learn anything about + + + align:start position:0% +did we wouldn't learn anything about +the environment + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +you might say well what we're interested + + align:start position:0% +you might say well what we're interested + + + align:start position:0% +you might say well what we're interested +in is how much light comes off so we + + align:start position:0% +in is how much light comes off so we + + + align:start position:0% +in is how much light comes off so we +could have + + align:start position:0% +could have + + + align:start position:0% +could have +perhaps a + + align:start position:0% +perhaps a + + + align:start position:0% +perhaps a +complementary + + align:start position:0% + + + + align:start position:0% + +idea where + + align:start position:0% +idea where + + + align:start position:0% +idea where +you know we have a give a name to this + + align:start position:0% +you know we have a give a name to this + + + align:start position:0% +you know we have a give a name to this +quantity + + align:start position:0% +quantity + + + align:start position:0% +quantity +uh where + + align:start position:0% + + + + align:start position:0% + +we take the power that's emitted divided + + align:start position:0% +we take the power that's emitted divided + + + align:start position:0% +we take the power that's emitted divided +by the area + + align:start position:0% +by the area + + + align:start position:0% +by the area +trouble is + + align:start position:0% +trouble is + + + align:start position:0% +trouble is +you know that could be going anywhere + + align:start position:0% + + + + align:start position:0% + +and and there is terminology for this + + align:start position:0% +and and there is terminology for this + + + align:start position:0% +and and there is terminology for this +quantity but since it's useless to us + + align:start position:0% +quantity but since it's useless to us + + + align:start position:0% +quantity but since it's useless to us +we're not going to bother with it so um + + align:start position:0% +we're not going to bother with it so um + + + align:start position:0% +we're not going to bother with it so um +i mean this is obviously useful if + + align:start position:0% +i mean this is obviously useful if + + + align:start position:0% +i mean this is obviously useful if +you're worrying about you know heat + + align:start position:0% +you're worrying about you know heat + + + align:start position:0% +you're worrying about you know heat +exchange like + + align:start position:0% +exchange like + + + align:start position:0% +exchange like +how do i keep my satellite cool enough + + align:start position:0% +how do i keep my satellite cool enough + + + align:start position:0% +how do i keep my satellite cool enough +given that the sun is illuminating it on + + align:start position:0% +given that the sun is illuminating it on + + + align:start position:0% +given that the sun is illuminating it on +one side and there's + + align:start position:0% +one side and there's + + + align:start position:0% +one side and there's +heat going off in into + + align:start position:0% +heat going off in into + + + align:start position:0% +heat going off in into +black space in another direction and so + + align:start position:0% +black space in another direction and so + + + align:start position:0% +black space in another direction and so +on but it's not useful for us because + + align:start position:0% +on but it's not useful for us because + + + align:start position:0% +on but it's not useful for us because +we're we're not intercepting all of this + + align:start position:0% +we're we're not intercepting all of this + + + align:start position:0% +we're we're not intercepting all of this +we're over here + + align:start position:0% +we're over here + + + align:start position:0% +we're over here +uh intercepting a tiny part of that and + + align:start position:0% +uh intercepting a tiny part of that and + + + align:start position:0% +uh intercepting a tiny part of that and +therefore it matters that this radiation + + align:start position:0% +therefore it matters that this radiation + + + align:start position:0% +therefore it matters that this radiation +is not + + align:start position:0% +is not + + + align:start position:0% +is not +isotropic it's not + + align:start position:0% +isotropic it's not + + + align:start position:0% +isotropic it's not +going in all directions equally + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +we don't want that + + align:start position:0% + + + + align:start position:0% + +so then + + align:start position:0% +so then + + + align:start position:0% +so then +you know many textbooks will use this + + align:start position:0% +you know many textbooks will use this + + + align:start position:0% +you know many textbooks will use this +term + + align:start position:0% +term + + + align:start position:0% +term +intensity and we often talk about + + align:start position:0% +intensity and we often talk about + + + align:start position:0% +intensity and we often talk about +well i try not to talk about image + + align:start position:0% +well i try not to talk about image + + + align:start position:0% +well i try not to talk about image +intensity because it's really wrong + + align:start position:0% +intensity because it's really wrong + + + align:start position:0% +intensity because it's really wrong +the intensity has a technical it's a + + align:start position:0% +the intensity has a technical it's a + + + align:start position:0% +the intensity has a technical it's a +technical term that has a meaning and + + align:start position:0% +technical term that has a meaning and + + + align:start position:0% +technical term that has a meaning and +what is it well it's + + align:start position:0% +what is it well it's + + + align:start position:0% +what is it well it's +useful for point source to talk about + + align:start position:0% +useful for point source to talk about + + + align:start position:0% +useful for point source to talk about +how much radiation is going off into a + + align:start position:0% +how much radiation is going off into a + + + align:start position:0% +how much radiation is going off into a +certain direction so here's a point + + align:start position:0% +certain direction so here's a point + + + align:start position:0% +certain direction so here's a point +source i don't know star a light bulb + + align:start position:0% +source i don't know star a light bulb + + + align:start position:0% +source i don't know star a light bulb +and + + align:start position:0% +and + + + align:start position:0% +and +we're measuring how much power is going + + align:start position:0% +we're measuring how much power is going + + + align:start position:0% +we're measuring how much power is going +in a certain direction + + align:start position:0% + + + + align:start position:0% + +uh well we need to normalize that + + align:start position:0% +uh well we need to normalize that + + + align:start position:0% +uh well we need to normalize that +right we need to + + align:start position:0% +right we need to + + + align:start position:0% +right we need to +take this cone of possible directions + + align:start position:0% +take this cone of possible directions + + + align:start position:0% +take this cone of possible directions +and somehow measure how big it is + + align:start position:0% +and somehow measure how big it is + + + align:start position:0% +and somehow measure how big it is +so it's + + align:start position:0% + + + + align:start position:0% + +so we have to + + align:start position:0% +so we have to + + + align:start position:0% +so we have to +define this + + align:start position:0% +define this + + + align:start position:0% +define this +measure which is called the solid angle + + align:start position:0% +measure which is called the solid angle + + + align:start position:0% +measure which is called the solid angle +and the units of which are + + align:start position:0% +and the units of which are + + + align:start position:0% +and the units of which are +stair radians + + align:start position:0% +stair radians + + + align:start position:0% +stair radians +and in in case you haven't come across + + align:start position:0% +and in in case you haven't come across + + + align:start position:0% +and in in case you haven't come across +it before + + align:start position:0% +it before + + + align:start position:0% +it before +it's very simple + + align:start position:0% +it's very simple + + + align:start position:0% +it's very simple +so in the plane in 2d + + align:start position:0% + + + + align:start position:0% + +you know the preferred way of talking + + align:start position:0% +you know the preferred way of talking + + + align:start position:0% +you know the preferred way of talking +about angles + + align:start position:0% +about angles + + + align:start position:0% +about angles +is in terms of radians and + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +you know it's what you get by cutting + + align:start position:0% +you know it's what you get by cutting + + + align:start position:0% +you know it's what you get by cutting +that + + align:start position:0% +that + + + align:start position:0% +that +circle + + align:start position:0% +circle + + + align:start position:0% +circle +with that angle and looking at the + + align:start position:0% +with that angle and looking at the + + + align:start position:0% +with that angle and looking at the +length of the arc of the circle and + + align:start position:0% +length of the arc of the circle and + + + align:start position:0% +length of the arc of the circle and +dividing by the radius so we all know + + align:start position:0% +dividing by the radius so we all know + + + align:start position:0% +dividing by the radius so we all know +how to do that + + align:start position:0% +how to do that + + + align:start position:0% +how to do that +well this is very similar + + align:start position:0% +well this is very similar + + + align:start position:0% +well this is very similar +in that + + align:start position:0% + + + + align:start position:0% + +in that we + + align:start position:0% +in that we + + + align:start position:0% +in that we +take this cone of possible directions in + + align:start position:0% +take this cone of possible directions in + + + align:start position:0% +take this cone of possible directions in +three space now instead of in two space + + align:start position:0% +three space now instead of in two space + + + align:start position:0% +three space now instead of in two space +and we cut it with a circle + + align:start position:0% +and we cut it with a circle + + + align:start position:0% +and we cut it with a circle +and we imagine we're at the center of a + + align:start position:0% +and we imagine we're at the center of a + + + align:start position:0% +and we imagine we're at the center of a +sphere we're at the center of the sphere + + align:start position:0% +sphere we're at the center of the sphere + + + align:start position:0% +sphere we're at the center of the sphere +we're cutting it and we get a certain + + align:start position:0% +we're cutting it and we get a certain + + + align:start position:0% +we're cutting it and we get a certain +area + + align:start position:0% +area + + + align:start position:0% +area +and now to normalize it we need to + + align:start position:0% +and now to normalize it we need to + + + align:start position:0% +and now to normalize it we need to +divide by r squared because this area + + align:start position:0% +divide by r squared because this area + + + align:start position:0% +divide by r squared because this area +will grow with radius square you know + + align:start position:0% +will grow with radius square you know + + + align:start position:0% +will grow with radius square you know +radius squared rather than radius and so + + align:start position:0% +radius squared rather than radius and so + + + align:start position:0% +radius squared rather than radius and so +that's the definition of solid angle so + + align:start position:0% +that's the definition of solid angle so + + + align:start position:0% +that's the definition of solid angle so +this allows us to talk about + + align:start position:0% +this allows us to talk about + + + align:start position:0% +this allows us to talk about +a set of directions it doesn't have to + + align:start position:0% +a set of directions it doesn't have to + + + align:start position:0% +a set of directions it doesn't have to +be a right circular cone could be any + + align:start position:0% +be a right circular cone could be any + + + align:start position:0% +be a right circular cone could be any +shape and i could have something like + + align:start position:0% +shape and i could have something like + + + align:start position:0% +shape and i could have something like +this + + align:start position:0% +this + + + align:start position:0% +this +all that matters is what this area is on + + align:start position:0% +all that matters is what this area is on + + + align:start position:0% +all that matters is what this area is on +the sphere + + align:start position:0% +the sphere + + + align:start position:0% +the sphere +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +you know radians we go from zero to two + + align:start position:0% +you know radians we go from zero to two + + + align:start position:0% +you know radians we go from zero to two +pi + + align:start position:0% +pi + + + align:start position:0% +pi +so what's the corresponding thing for + + align:start position:0% +so what's the corresponding thing for + + + align:start position:0% +so what's the corresponding thing for +stair radians + + align:start position:0% + + + + align:start position:0% + +so if i want to talk about all possible + + align:start position:0% +so if i want to talk about all possible + + + align:start position:0% +so if i want to talk about all possible +directions around me + + align:start position:0% +directions around me + + + align:start position:0% +directions around me +how many stir radians is that + + align:start position:0% + + + + align:start position:0% + +what's the surface area of a sphere + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +four pi r squared and so + + align:start position:0% +four pi r squared and so + + + align:start position:0% +four pi r squared and so +thank you and so uh it's four pi right + + align:start position:0% +thank you and so uh it's four pi right + + + align:start position:0% +thank you and so uh it's four pi right +so this uh you know there we go here we + + align:start position:0% +so this uh you know there we go here we + + + align:start position:0% +so this uh you know there we go here we +go zero to two pi and this goes up to + + align:start position:0% +go zero to two pi and this goes up to + + + align:start position:0% +go zero to two pi and this goes up to +four pi so the the + + align:start position:0% +four pi so the the + + + align:start position:0% +four pi so the the +set of all possible directions around me + + align:start position:0% +set of all possible directions around me + + + align:start position:0% +set of all possible directions around me +so if i'm radiating energy it could go + + align:start position:0% +so if i'm radiating energy it could go + + + align:start position:0% +so if i'm radiating energy it could go +into a solid angle of four pi + + align:start position:0% +into a solid angle of four pi + + + align:start position:0% +into a solid angle of four pi +uh if i'm for example only worrying + + align:start position:0% +uh if i'm for example only worrying + + + align:start position:0% +uh if i'm for example only worrying +about light coming from the sky + + align:start position:0% +about light coming from the sky + + + align:start position:0% +about light coming from the sky +that's a hemisphere so that's obviously + + align:start position:0% +that's a hemisphere so that's obviously + + + align:start position:0% +that's a hemisphere so that's obviously +two pi still radians so + + align:start position:0% +two pi still radians so + + + align:start position:0% +two pi still radians so +there's just one more little subtle + + align:start position:0% +there's just one more little subtle + + + align:start position:0% +there's just one more little subtle +thing that's kind of handy which is + + align:start position:0% +thing that's kind of handy which is + + + align:start position:0% +thing that's kind of handy which is +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +if that surface area is inclined + + align:start position:0% +if that surface area is inclined + + + align:start position:0% +if that surface area is inclined +relative to the + + align:start position:0% +relative to the + + + align:start position:0% +relative to the +direction to the center of the sphere + + align:start position:0% +direction to the center of the sphere + + + align:start position:0% +direction to the center of the sphere +in that case + + align:start position:0% + + + + align:start position:0% + +so this is just another manifestation of + + align:start position:0% +so this is just another manifestation of + + + align:start position:0% +so this is just another manifestation of +that + + align:start position:0% +that + + + align:start position:0% +that +um foreshortening phenomenon and this is + + align:start position:0% +um foreshortening phenomenon and this is + + + align:start position:0% +um foreshortening phenomenon and this is +sometimes handy because we will have + + align:start position:0% +sometimes handy because we will have + + + align:start position:0% +sometimes handy because we will have +cases where there is an inclination for + + align:start position:0% +cases where there is an inclination for + + + align:start position:0% +cases where there is an inclination for +example now we're going to be talking + + align:start position:0% +example now we're going to be talking + + + align:start position:0% +example now we're going to be talking +about cameras and the lens is going to + + align:start position:0% +about cameras and the lens is going to + + + align:start position:0% +about cameras and the lens is going to +be tilted relative to a subject that's + + align:start position:0% +be tilted relative to a subject that's + + + align:start position:0% +be tilted relative to a subject that's +off-center and so we'll need to account + + align:start position:0% +off-center and so we'll need to account + + + align:start position:0% +off-center and so we'll need to account +for that and and that's obviously and + + align:start position:0% +for that and and that's obviously and + + + align:start position:0% +for that and and that's obviously and +why is that well because + + align:start position:0% +why is that well because + + + align:start position:0% +why is that well because +this area at an angle is equivalent + + align:start position:0% +this area at an angle is equivalent + + + align:start position:0% +this area at an angle is equivalent +to an area that's at right angle to the + + align:start position:0% +to an area that's at right angle to the + + + align:start position:0% +to an area that's at right angle to the +axis and the ratio of these two lines to + + align:start position:0% +axis and the ratio of these two lines to + + + align:start position:0% +axis and the ratio of these two lines to +each other is cosine theta + + align:start position:0% +each other is cosine theta + + + align:start position:0% +each other is cosine theta +and that also is the ratio of the two + + align:start position:0% +and that also is the ratio of the two + + + align:start position:0% +and that also is the ratio of the two +areas so + + align:start position:0% +areas so + + + align:start position:0% +areas so +okay so now we know how to calculate uh + + align:start position:0% +okay so now we know how to calculate uh + + + align:start position:0% +okay so now we know how to calculate uh +solid angles + + align:start position:0% +solid angles + + + align:start position:0% +solid angles +very handy concept we go back to + + align:start position:0% +very handy concept we go back to + + + align:start position:0% +very handy concept we go back to +intensity and intensity + + align:start position:0% +intensity and intensity + + + align:start position:0% +intensity and intensity +i + + align:start position:0% +i + + + align:start position:0% +i +is defined as a power + + align:start position:0% +is defined as a power + + + align:start position:0% +is defined as a power +for solid angle and you can see that + + align:start position:0% +for solid angle and you can see that + + + align:start position:0% +for solid angle and you can see that +it's independent of distance so if i go + + align:start position:0% +it's independent of distance so if i go + + + align:start position:0% +it's independent of distance so if i go +further out you know it will cover a + + align:start position:0% +further out you know it will cover a + + + align:start position:0% +further out you know it will cover a +larger area but we're assuming that + + align:start position:0% +larger area but we're assuming that + + + align:start position:0% +larger area but we're assuming that +there's no loss so the power going into + + align:start position:0% +there's no loss so the power going into + + + align:start position:0% +there's no loss so the power going into +that cone is the same the further out i + + align:start position:0% +that cone is the same the further out i + + + align:start position:0% +that cone is the same the further out i +go + + align:start position:0% +go + + + align:start position:0% +go +and so + + align:start position:0% +and so + + + align:start position:0% +and so +that's a useful quantity and it's a way + + align:start position:0% +that's a useful quantity and it's a way + + + align:start position:0% +that's a useful quantity and it's a way +of describing you know how um distant + + align:start position:0% +of describing you know how um distant + + + align:start position:0% +of describing you know how um distant +point source might + + align:start position:0% +point source might + + + align:start position:0% +point source might +um act and usually in machine vision + + align:start position:0% +um act and usually in machine vision + + + align:start position:0% +um act and usually in machine vision +that's not the case we're dealing with + + align:start position:0% +that's not the case we're dealing with + + + align:start position:0% +that's not the case we're dealing with +we're dealing mostly with continuous + + align:start position:0% +we're dealing mostly with continuous + + + align:start position:0% +we're dealing mostly with continuous +surfaces + + align:start position:0% +surfaces + + + align:start position:0% +surfaces +and you know we could imagine breaking + + align:start position:0% +and you know we could imagine breaking + + + align:start position:0% +and you know we could imagine breaking +them up into an array of point sources + + align:start position:0% +them up into an array of point sources + + + align:start position:0% +them up into an array of point sources +but + + align:start position:0% +but + + + align:start position:0% +but +that + + align:start position:0% +that + + + align:start position:0% +that +it isn't usually done and it's not very + + align:start position:0% +it isn't usually done and it's not very + + + align:start position:0% +it isn't usually done and it's not very +helpful + + align:start position:0% +helpful + + + align:start position:0% +helpful +okay so intensity + + align:start position:0% +okay so intensity + + + align:start position:0% +okay so intensity +so + + align:start position:0% +so + + + align:start position:0% +so +if you use that word in your homework + + align:start position:0% +if you use that word in your homework + + + align:start position:0% +if you use that word in your homework +problems you will + + align:start position:0% +problems you will + + + align:start position:0% +problems you will +flunk the course + + align:start position:0% +flunk the course + + + align:start position:0% +flunk the course +just just kidding + + align:start position:0% +just just kidding + + + align:start position:0% +just just kidding +since all the textbooks use intensities + + align:start position:0% +since all the textbooks use intensities + + + align:start position:0% +since all the textbooks use intensities +unfortunately + + align:start position:0% +unfortunately + + + align:start position:0% +unfortunately +we have to accept that + + align:start position:0% +we have to accept that + + + align:start position:0% +we have to accept that +that is an alternate term for something + + align:start position:0% +that is an alternate term for something + + + align:start position:0% +that is an alternate term for something +else which we'll talk about next so the + + align:start position:0% +else which we'll talk about next so the + + + align:start position:0% +else which we'll talk about next so the +the true meaning of intensity is this + + align:start position:0% +the true meaning of intensity is this + + + align:start position:0% +the true meaning of intensity is this +and it's all and it's never something + + align:start position:0% +and it's all and it's never something + + + align:start position:0% +and it's all and it's never something +that people in machine vision consider + + align:start position:0% +that people in machine vision consider + + + align:start position:0% +that people in machine vision consider +unless they're doing things like trying + + align:start position:0% +unless they're doing things like trying + + + align:start position:0% +unless they're doing things like trying +to reconstruct the center of our galaxy + + align:start position:0% +to reconstruct the center of our galaxy + + + align:start position:0% +to reconstruct the center of our galaxy +and finding you know what that black + + align:start position:0% +and finding you know what that black + + + align:start position:0% +and finding you know what that black +hole looks like + + align:start position:0% +hole looks like + + + align:start position:0% +hole looks like +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so what is it that we want well uh we + + align:start position:0% +so what is it that we want well uh we + + + align:start position:0% +so what is it that we want well uh we +kind of had it here + + align:start position:0% +kind of had it here + + + align:start position:0% +kind of had it here +we we don't want to know the whole + + align:start position:0% +we we don't want to know the whole + + + align:start position:0% +we we don't want to know the whole +power coming off the surface we're only + + align:start position:0% +power coming off the surface we're only + + + align:start position:0% +power coming off the surface we're only +interested in what reaches the observer + + align:start position:0% +interested in what reaches the observer + + + align:start position:0% +interested in what reaches the observer +or the camera and so we introduced this + + align:start position:0% +or the camera and so we introduced this + + + align:start position:0% +or the camera and so we introduced this +idea of radians + + align:start position:0% + + + + align:start position:0% + +which is power + + align:start position:0% +which is power + + + align:start position:0% +which is power +per unit area per unit solid angle + + align:start position:0% +per unit area per unit solid angle + + + align:start position:0% +per unit area per unit solid angle +right so we have a little part of the + + align:start position:0% +right so we have a little part of the + + + align:start position:0% +right so we have a little part of the +surface here + + align:start position:0% +surface here + + + align:start position:0% +surface here +with an area + + align:start position:0% +with an area + + + align:start position:0% +with an area +and we have a person or a camera + + align:start position:0% +and we have a person or a camera + + + align:start position:0% +and we have a person or a camera +over here and this is a solid angle + + align:start position:0% +over here and this is a solid angle + + + align:start position:0% +over here and this is a solid angle +delta omega and there's some power + + align:start position:0% +delta omega and there's some power + + + align:start position:0% +delta omega and there's some power +delta p going that way and that's + + align:start position:0% +delta p going that way and that's + + + align:start position:0% +delta p going that way and that's +obviously much more what what we want + + align:start position:0% +obviously much more what what we want + + + align:start position:0% +obviously much more what what we want +because that's that's what we're + + align:start position:0% +because that's that's what we're + + + align:start position:0% +because that's that's what we're +measuring + + align:start position:0% +measuring + + + align:start position:0% +measuring +it's uh + + align:start position:0% +it's uh + + + align:start position:0% +it's uh +in in the image this power will be + + align:start position:0% +in in the image this power will be + + + align:start position:0% +in in the image this power will be +projected onto a certain area and uh + + align:start position:0% +projected onto a certain area and uh + + + align:start position:0% +projected onto a certain area and uh +our senses are measuring uh power + + align:start position:0% +our senses are measuring uh power + + + align:start position:0% +our senses are measuring uh power +basically + + align:start position:0% +basically + + + align:start position:0% +basically +which which by the way is is unfortunate + + align:start position:0% +which which by the way is is unfortunate + + + align:start position:0% +which which by the way is is unfortunate +it'd be great if they measure the + + align:start position:0% +it'd be great if they measure the + + + align:start position:0% +it'd be great if they measure the +electric field + + align:start position:0% +electric field + + + align:start position:0% +electric field +but + + align:start position:0% +but + + + align:start position:0% +but +instead measuring the absolute value + + align:start position:0% +instead measuring the absolute value + + + align:start position:0% +instead measuring the absolute value +squared of the electric field + + align:start position:0% +squared of the electric field + + + align:start position:0% +squared of the electric field +and so amongst other things we know that + + align:start position:0% +and so amongst other things we know that + + + align:start position:0% +and so amongst other things we know that +quantity can never be negative + + align:start position:0% +quantity can never be negative + + + align:start position:0% +quantity can never be negative +and so we can't do any phase imaging + + align:start position:0% +and so we can't do any phase imaging + + + align:start position:0% +and so we can't do any phase imaging +with our usual + + align:start position:0% +with our usual + + + align:start position:0% +with our usual +cameras + + align:start position:0% +cameras + + + align:start position:0% +cameras +and there's some there would be some + + align:start position:0% +and there's some there would be some + + + align:start position:0% +and there's some there would be some +real advantages to that but we we can't + + align:start position:0% +real advantages to that but we we can't + + + align:start position:0% +real advantages to that but we we can't +do that okay + + align:start position:0% +do that okay + + + align:start position:0% +do that okay +um + + align:start position:0% +um + + + align:start position:0% +um +so that's radiance and it's a power per + + align:start position:0% +so that's radiance and it's a power per + + + align:start position:0% +so that's radiance and it's a power per +unit area per unit solid angle or + + align:start position:0% +unit area per unit solid angle or + + + align:start position:0% +unit area per unit solid angle or +in terms of uh + + align:start position:0% +in terms of uh + + + align:start position:0% +in terms of uh +units it's watts + + align:start position:0% +units it's watts + + + align:start position:0% +units it's watts +per square meter per uh solid angle + + align:start position:0% +per square meter per uh solid angle + + + align:start position:0% +per square meter per uh solid angle +still radiant + + align:start position:0% +still radiant + + + align:start position:0% +still radiant +now if you're a mechanical engineer and + + align:start position:0% +now if you're a mechanical engineer and + + + align:start position:0% +now if you're a mechanical engineer and +you do dimensional analysis + + align:start position:0% +you do dimensional analysis + + + align:start position:0% +you do dimensional analysis +that's kind of a nuisance because the + + align:start position:0% +that's kind of a nuisance because the + + + align:start position:0% +that's kind of a nuisance because the +radians like radiance doesn't have you + + align:start position:0% +radians like radiance doesn't have you + + + align:start position:0% +radians like radiance doesn't have you +know units like meters per kilogram per + + align:start position:0% +know units like meters per kilogram per + + + align:start position:0% +know units like meters per kilogram per +second or something they're just ratios + + align:start position:0% +second or something they're just ratios + + + align:start position:0% +second or something they're just ratios +and so that clever trick mechanical + + align:start position:0% +and so that clever trick mechanical + + + align:start position:0% +and so that clever trick mechanical +engineers use to guess at the answer by + + align:start position:0% +engineers use to guess at the answer by + + + align:start position:0% +engineers use to guess at the answer by +just matching dimensions it doesn't + + align:start position:0% +just matching dimensions it doesn't + + + align:start position:0% +just matching dimensions it doesn't +quite work because you have these + + align:start position:0% +quite work because you have these + + + align:start position:0% +quite work because you have these +quantities that + + align:start position:0% +quantities that + + + align:start position:0% +quantities that +are dimensionless so + + align:start position:0% +are dimensionless so + + + align:start position:0% +are dimensionless so +okay + + align:start position:0% + + + + align:start position:0% + +so what to do next well what we what i + + align:start position:0% +so what to do next well what we what i + + + align:start position:0% +so what to do next well what we what i +want to do next is to + + align:start position:0% +want to do next is to + + + align:start position:0% +want to do next is to +relate + + align:start position:0% + + + + align:start position:0% + +brightness out there to brightness in + + align:start position:0% +brightness out there to brightness in + + + align:start position:0% +brightness out there to brightness in +the camera + + align:start position:0% +the camera + + + align:start position:0% +the camera +and so i'm using this term brightness in + + align:start position:0% +and so i'm using this term brightness in + + + align:start position:0% +and so i'm using this term brightness in +a very loose way + + align:start position:0% +a very loose way + + + align:start position:0% +a very loose way +and we'll justify in a little while + + align:start position:0% +and we'll justify in a little while + + + align:start position:0% +and we'll justify in a little while +while we why that's acceptable so in a + + align:start position:0% +while we why that's acceptable so in a + + + align:start position:0% +while we why that's acceptable so in a +way we can talk about + + align:start position:0% + + + + align:start position:0% + +a brightness of a surface + + align:start position:0% +a brightness of a surface + + + align:start position:0% +a brightness of a surface +in terms of radiance + + align:start position:0% +in terms of radiance + + + align:start position:0% +in terms of radiance +this is how bright it's going to appear + + align:start position:0% +this is how bright it's going to appear + + + align:start position:0% +this is how bright it's going to appear +then in the image plane + + align:start position:0% +then in the image plane + + + align:start position:0% +then in the image plane +we can talk about the brightness we + + align:start position:0% +we can talk about the brightness we + + + align:start position:0% +we can talk about the brightness we +measure as as irradiance so notice that + + align:start position:0% +measure as as irradiance so notice that + + + align:start position:0% +measure as as irradiance so notice that +before i talked about light falling on + + align:start position:0% +before i talked about light falling on + + + align:start position:0% +before i talked about light falling on +an object in the world but the same + + align:start position:0% +an object in the world but the same + + + align:start position:0% +an object in the world but the same +concept of course applies in the image + + align:start position:0% +concept of course applies in the image + + + align:start position:0% +concept of course applies in the image +plane i've got these little areas that + + align:start position:0% +plane i've got these little areas that + + + align:start position:0% +plane i've got these little areas that +are light sensitive and what are they + + align:start position:0% +are light sensitive and what are they + + + align:start position:0% +are light sensitive and what are they +measuring they're measuring irradiance + + align:start position:0% +measuring they're measuring irradiance + + + align:start position:0% +measuring they're measuring irradiance +well they're actually measuring energy + + align:start position:0% +well they're actually measuring energy + + + align:start position:0% +well they're actually measuring energy +over a certain time but of course energy + + align:start position:0% +over a certain time but of course energy + + + align:start position:0% +over a certain time but of course energy +of a certain time is the same as power + + align:start position:0% +of a certain time is the same as power + + + align:start position:0% +of a certain time is the same as power +so they're measuring measuring power + + align:start position:0% +so they're measuring measuring power + + + align:start position:0% +so they're measuring measuring power +okay so i want to relate those two and + + align:start position:0% +okay so i want to relate those two and + + + align:start position:0% +okay so i want to relate those two and +what we're going to end up showing is + + align:start position:0% +what we're going to end up showing is + + + align:start position:0% +what we're going to end up showing is +that they're + + align:start position:0% +that they're + + + align:start position:0% +that they're +proportional to each other and therefore + + align:start position:0% +proportional to each other and therefore + + + align:start position:0% +proportional to each other and therefore +we can be sloppy we can call both of + + align:start position:0% +we can be sloppy we can call both of + + + align:start position:0% +we can be sloppy we can call both of +them brightness as people actually + + align:start position:0% +them brightness as people actually + + + align:start position:0% +them brightness as people actually +usually do and so we we you know once + + align:start position:0% +usually do and so we we you know once + + + align:start position:0% +usually do and so we we you know once +we've defined the being careful about + + align:start position:0% +we've defined the being careful about + + + align:start position:0% +we've defined the being careful about +the terminology + + align:start position:0% +the terminology + + + align:start position:0% +the terminology +we can justify being sloppy about the + + align:start position:0% +we can justify being sloppy about the + + + align:start position:0% +we can justify being sloppy about the +terminology + + align:start position:0% +terminology + + + align:start position:0% +terminology +okay so uh for this to be + + align:start position:0% +okay so uh for this to be + + + align:start position:0% +okay so uh for this to be +meaningful we need uh finite aperture so + + align:start position:0% +meaningful we need uh finite aperture so + + + align:start position:0% +meaningful we need uh finite aperture so +so far we've talked about pinhole model + + align:start position:0% +so far we've talked about pinhole model + + + align:start position:0% +so far we've talked about pinhole model +and the pinhole model + + align:start position:0% +and the pinhole model + + + align:start position:0% +and the pinhole model +gives us + + align:start position:0% +gives us + + + align:start position:0% +gives us +perspective projection and it's very + + align:start position:0% +perspective projection and it's very + + + align:start position:0% +perspective projection and it's very +useful for that but we know that um + + align:start position:0% +useful for that but we know that um + + + align:start position:0% +useful for that but we know that um +in terms of image the + + align:start position:0% +in terms of image the + + + align:start position:0% +in terms of image the +measurement is problematic you know if + + align:start position:0% +measurement is problematic you know if + + + align:start position:0% +measurement is problematic you know if +we make the pinhole too large the image + + align:start position:0% +we make the pinhole too large the image + + + align:start position:0% +we make the pinhole too large the image +is going to be blurred + + align:start position:0% +is going to be blurred + + + align:start position:0% +is going to be blurred +and if we make the pinhole too small we + + align:start position:0% +and if we make the pinhole too small we + + + align:start position:0% +and if we make the pinhole too small we +don't have enough photons to count and + + align:start position:0% +don't have enough photons to count and + + + align:start position:0% +don't have enough photons to count and +also there'll be fractions so if you + + align:start position:0% +also there'll be fractions so if you + + + align:start position:0% +also there'll be fractions so if you +make it small enough it'll appear just + + align:start position:0% +make it small enough it'll appear just + + + align:start position:0% +make it small enough it'll appear just +like a isotropic source that's radiating + + align:start position:0% +like a isotropic source that's radiating + + + align:start position:0% +like a isotropic source that's radiating +into two pi still radians okay so i + + align:start position:0% +into two pi still radians okay so i + + + align:start position:0% +into two pi still radians okay so i +don't know if anyone else uh thought + + align:start position:0% +don't know if anyone else uh thought + + + align:start position:0% +don't know if anyone else uh thought +about this but + + align:start position:0% +about this but + + + align:start position:0% +about this but +in + + align:start position:0% +in + + + align:start position:0% +in +notation of infinitesimals it is sort of + + align:start position:0% +notation of infinitesimals it is sort of + + + align:start position:0% +notation of infinitesimals it is sort of +customary to do that + + align:start position:0% +customary to do that + + + align:start position:0% +customary to do that +right because you're dividing by two + + align:start position:0% +right because you're dividing by two + + + align:start position:0% +right because you're dividing by two +infinite decimals so this should be + + align:start position:0% +infinite decimals so this should be + + + align:start position:0% +infinite decimals so this should be +i don't know two infinite decimals a + + align:start position:0% +i don't know two infinite decimals a + + + align:start position:0% +i don't know two infinite decimals a +product of two infinitesimals + + align:start position:0% +product of two infinitesimals + + + align:start position:0% +product of two infinitesimals +now fortunately we're not going to + + align:start position:0% +now fortunately we're not going to + + + align:start position:0% +now fortunately we're not going to +uh get too perturbed by that but that's + + align:start position:0% +uh get too perturbed by that but that's + + + align:start position:0% +uh get too perturbed by that but that's +a good observation + + align:start position:0% +a good observation + + + align:start position:0% +a good observation +and and you know i guess + + align:start position:0% +and and you know i guess + + + align:start position:0% +and and you know i guess +in textbooks + + align:start position:0% +in textbooks + + + align:start position:0% +in textbooks +that'll be the notation + + align:start position:0% +that'll be the notation + + + align:start position:0% +that'll be the notation +and then and then you have someone else + + align:start position:0% +and then and then you have someone else + + + align:start position:0% +and then and then you have someone else +saying + + align:start position:0% +saying + + + align:start position:0% +saying +oh what do you mean it's del squared p + + align:start position:0% +oh what do you mean it's del squared p + + + align:start position:0% +oh what do you mean it's del squared p +that's the power going there what is + + align:start position:0% +that's the power going there what is + + + align:start position:0% +that's the power going there what is +that why is it squared so i i didn't + + align:start position:0% +that why is it squared so i i didn't + + + align:start position:0% +that why is it squared so i i didn't +want to go there so + + align:start position:0% +want to go there so + + + align:start position:0% +want to go there so +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh + + align:start position:0% +uh + + + align:start position:0% +uh +lenses + + align:start position:0% +lenses + + + align:start position:0% +lenses +so what we're going to do is + + align:start position:0% +so what we're going to do is + + + align:start position:0% +so what we're going to do is +invent this device + + align:start position:0% +invent this device + + + align:start position:0% +invent this device +that has the property that it provides + + align:start position:0% +that has the property that it provides + + + align:start position:0% +that has the property that it provides +the same projection as the pinhole but + + align:start position:0% +the same projection as the pinhole but + + + align:start position:0% +the same projection as the pinhole but +has a huge advantage that it actually + + align:start position:0% +has a huge advantage that it actually + + + align:start position:0% +has a huge advantage that it actually +gives you a finite number of photons + + align:start position:0% +gives you a finite number of photons + + + align:start position:0% +gives you a finite number of photons +and there there'll be you know a penalty + + align:start position:0% +and there there'll be you know a penalty + + + align:start position:0% +and there there'll be you know a penalty +which is it only works at a certain + + align:start position:0% +which is it only works at a certain + + + align:start position:0% +which is it only works at a certain +focal uh length it only works at a + + align:start position:0% +focal uh length it only works at a + + + align:start position:0% +focal uh length it only works at a +certain distance + + align:start position:0% +certain distance + + + align:start position:0% +certain distance +but let's uh so let's talk about lenses + + align:start position:0% +but let's uh so let's talk about lenses + + + align:start position:0% +but let's uh so let's talk about lenses +ideal uh thin lenses + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +gauss already showed that + + align:start position:0% +gauss already showed that + + + align:start position:0% +gauss already showed that +there's no such thing + + align:start position:0% +there's no such thing + + + align:start position:0% +there's no such thing +you cannot make a perfect lens + + align:start position:0% +you cannot make a perfect lens + + + align:start position:0% +you cannot make a perfect lens +and but + + align:start position:0% +and but + + + align:start position:0% +and but +you can become you can come incredibly + + align:start position:0% +you can become you can come incredibly + + + align:start position:0% +you can become you can come incredibly +close to making this ideal object so let + + align:start position:0% +close to making this ideal object so let + + + align:start position:0% +close to making this ideal object so let +me um + + align:start position:0% +me um + + + align:start position:0% +me um +the three rules + + align:start position:0% + + + + align:start position:0% + +so uh of course you know that you know + + align:start position:0% +so uh of course you know that you know + + + align:start position:0% +so uh of course you know that you know +lenses are made of glass transparent + + align:start position:0% +lenses are made of glass transparent + + + align:start position:0% +lenses are made of glass transparent +material they have a refractive index + + align:start position:0% +material they have a refractive index + + + align:start position:0% +material they have a refractive index +that's different from air and so + + align:start position:0% +that's different from air and so + + + align:start position:0% +that's different from air and so +light rays are deflected when they hit + + align:start position:0% +light rays are deflected when they hit + + + align:start position:0% +light rays are deflected when they hit +the surface and that simple lenses are + + align:start position:0% +the surface and that simple lenses are + + + align:start position:0% +the surface and that simple lenses are +made with spherical surfaces + + align:start position:0% +made with spherical surfaces + + + align:start position:0% +made with spherical surfaces +particularly easy to grind uh you can + + align:start position:0% +particularly easy to grind uh you can + + + align:start position:0% +particularly easy to grind uh you can +plonk uh you know epoxy 100 of them onto + + align:start position:0% +plonk uh you know epoxy 100 of them onto + + + align:start position:0% +plonk uh you know epoxy 100 of them onto +a sphere and grind them all at once + + align:start position:0% +a sphere and grind them all at once + + + align:start position:0% +a sphere and grind them all at once +because you they all have spherical + + align:start position:0% +because you they all have spherical + + + align:start position:0% +because you they all have spherical +surfaces fancier lenses are aspherical + + align:start position:0% +surfaces fancier lenses are aspherical + + + align:start position:0% +surfaces fancier lenses are aspherical +and they're obviously much harder to + + align:start position:0% +and they're obviously much harder to + + + align:start position:0% +and they're obviously much harder to +make and more expensive but the simple + + align:start position:0% +make and more expensive but the simple + + + align:start position:0% +make and more expensive but the simple +ones are there but for us what's + + align:start position:0% +ones are there but for us what's + + + align:start position:0% +ones are there but for us what's +important is the following so rule + + align:start position:0% +important is the following so rule + + + align:start position:0% +important is the following so rule +number one + + align:start position:0% +number one + + + align:start position:0% +number one +so rule number one is a central ray + + align:start position:0% +so rule number one is a central ray + + + align:start position:0% +so rule number one is a central ray +undeflected + + align:start position:0% + + + + align:start position:0% + +so what does that mean it means that if + + align:start position:0% +so what does that mean it means that if + + + align:start position:0% +so what does that mean it means that if +you have a ray of light going through + + align:start position:0% +you have a ray of light going through + + + align:start position:0% +you have a ray of light going through +the center of the lens it comes out + + align:start position:0% +the center of the lens it comes out + + + align:start position:0% +the center of the lens it comes out +traveling in the same direction on the + + align:start position:0% +traveling in the same direction on the + + + align:start position:0% +traveling in the same direction on the +other side + + align:start position:0% +other side + + + align:start position:0% +other side +and not just that ray but any ray that + + align:start position:0% +and not just that ray but any ray that + + + align:start position:0% +and not just that ray but any ray that +goes through the center + + align:start position:0% +goes through the center + + + align:start position:0% +goes through the center +and + + align:start position:0% +and + + + align:start position:0% +and +since time is reversible it works the + + align:start position:0% +since time is reversible it works the + + + align:start position:0% +since time is reversible it works the +other way around as well so + + align:start position:0% +other way around as well so + + + align:start position:0% +other way around as well so +we'll just show arrays going in one + + align:start position:0% +we'll just show arrays going in one + + + align:start position:0% +we'll just show arrays going in one +direction + + align:start position:0% +direction + + + align:start position:0% +direction +and so that's a pretty remarkable + + align:start position:0% +and so that's a pretty remarkable + + + align:start position:0% +and so that's a pretty remarkable +property and why is that important well + + align:start position:0% +property and why is that important well + + + align:start position:0% +property and why is that important well +because that gives us perspective + + align:start position:0% +because that gives us perspective + + + align:start position:0% +because that gives us perspective +projection that means that in terms of + + align:start position:0% +projection that means that in terms of + + + align:start position:0% +projection that means that in terms of +projection this is acting just like our + + align:start position:0% +projection this is acting just like our + + + align:start position:0% +projection this is acting just like our +pinhole so + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +number two is a + + align:start position:0% +number two is a + + + align:start position:0% +number two is a +ray from + + align:start position:0% +ray from + + + align:start position:0% +ray from +focal center + + align:start position:0% + + + + align:start position:0% + +emerges + + align:start position:0% +emerges + + + align:start position:0% +emerges +parallel + + align:start position:0% +parallel + + + align:start position:0% +parallel +to optical axis + + align:start position:0% + + + + align:start position:0% + +so so what is that + + align:start position:0% +so so what is that + + + align:start position:0% +so so what is that +well uh lenses have a focal length + + align:start position:0% +well uh lenses have a focal length + + + align:start position:0% +well uh lenses have a focal length +and let's call that f0 + + align:start position:0% +and let's call that f0 + + + align:start position:0% +and let's call that f0 +so i can define a point here that's one + + align:start position:0% +so i can define a point here that's one + + + align:start position:0% +so i can define a point here that's one +focal length away from the lens and what + + align:start position:0% +focal length away from the lens and what + + + align:start position:0% +focal length away from the lens and what +this rule is saying that if + + align:start position:0% +this rule is saying that if + + + align:start position:0% +this rule is saying that if +i take any ray + + align:start position:0% +i take any ray + + + align:start position:0% +i take any ray +coming from that + + align:start position:0% +coming from that + + + align:start position:0% +coming from that +focal center + + align:start position:0% +focal center + + + align:start position:0% +focal center +and i see what it does after it comes + + align:start position:0% +and i see what it does after it comes + + + align:start position:0% +and i see what it does after it comes +through the lens is going to be parallel + + align:start position:0% +through the lens is going to be parallel + + + align:start position:0% +through the lens is going to be parallel +to the optical axis and again of course + + align:start position:0% +to the optical axis and again of course + + + align:start position:0% +to the optical axis and again of course +not just that ray but + + align:start position:0% +not just that ray but + + + align:start position:0% +not just that ray but +you know any + + align:start position:0% +you know any + + + align:start position:0% +you know any +any array + + align:start position:0% + + + + align:start position:0% + +and then rule number three is + + align:start position:0% +and then rule number three is + + + align:start position:0% +and then rule number three is +well it's really the same thing + + align:start position:0% +well it's really the same thing + + + align:start position:0% +well it's really the same thing +parallel array + + align:start position:0% +parallel array + + + align:start position:0% +parallel array +goes + + align:start position:0% +goes + + + align:start position:0% +goes +through + + align:start position:0% + + + + align:start position:0% + +focal center + + align:start position:0% + + + + align:start position:0% + +so if i have a parallel array coming in + + align:start position:0% +so if i have a parallel array coming in + + + align:start position:0% +so if i have a parallel array coming in +from the right + + align:start position:0% +from the right + + + align:start position:0% +from the right +it's going to go through + + align:start position:0% + + + + align:start position:0% + +it's starting to look a bit messy but so + + align:start position:0% +it's starting to look a bit messy but so + + + align:start position:0% +it's starting to look a bit messy but so +you can see that if you have a bundle of + + align:start position:0% +you can see that if you have a bundle of + + + align:start position:0% +you can see that if you have a bundle of +parallel rays coming in from the right + + align:start position:0% +parallel rays coming in from the right + + + align:start position:0% +parallel rays coming in from the right +they're all going to go through that + + align:start position:0% +they're all going to go through that + + + align:start position:0% +they're all going to go through that +point + + align:start position:0% +point + + + align:start position:0% +point +that's what that's where they are + + align:start position:0% +that's what that's where they are + + + align:start position:0% +that's what that's where they are +in focus + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +from that diagram + + align:start position:0% + + + + align:start position:0% + +we can use + + align:start position:0% + + + + align:start position:0% + +similar triangles + + align:start position:0% +similar triangles + + + align:start position:0% +similar triangles +to + + align:start position:0% +to + + + align:start position:0% +to +get the lens formula and + + align:start position:0% +get the lens formula and + + + align:start position:0% +get the lens formula and +i'm not going to go through it's kind of + + align:start position:0% +i'm not going to go through it's kind of + + + align:start position:0% +i'm not going to go through it's kind of +boring algebra + + align:start position:0% +boring algebra + + + align:start position:0% +boring algebra +again possibly suitable for homework + + align:start position:0% +again possibly suitable for homework + + + align:start position:0% +again possibly suitable for homework +problem + + align:start position:0% +problem + + + align:start position:0% +problem +but at least i'll draw the diagram so + + align:start position:0% +but at least i'll draw the diagram so + + + align:start position:0% +but at least i'll draw the diagram so +so we have these two special points + + align:start position:0% +so we have these two special points + + + align:start position:0% +so we have these two special points +one of which is one focal length ahead + + align:start position:0% +one of which is one focal length ahead + + + align:start position:0% +one of which is one focal length ahead +and one is one focal length behind and + + align:start position:0% +and one is one focal length behind and + + + align:start position:0% +and one is one focal length behind and +we have a central array + + align:start position:0% +we have a central array + + + align:start position:0% +we have a central array +and let's see so then + + align:start position:0% + + + + align:start position:0% + +that's parallel + + align:start position:0% +that's parallel + + + align:start position:0% +that's parallel +and it's going to go through here + + align:start position:0% + + + + align:start position:0% + +notice how that didn't hit the lens + + align:start position:0% +notice how that didn't hit the lens + + + align:start position:0% +notice how that didn't hit the lens +that's because the simple model doesn't + + align:start position:0% +that's because the simple model doesn't + + + align:start position:0% +that's because the simple model doesn't +have an idea of the diameter of the lens + + align:start position:0% +have an idea of the diameter of the lens + + + align:start position:0% +have an idea of the diameter of the lens +it's + + align:start position:0% +it's + + + align:start position:0% +it's +it's what happens in this plane it + + align:start position:0% +it's what happens in this plane it + + + align:start position:0% +it's what happens in this plane it +doesn't it doesn't + + align:start position:0% +doesn't it doesn't + + + align:start position:0% +doesn't it doesn't +you know + + align:start position:0% +you know + + + align:start position:0% +you know +i can get a larger lens to do that if i + + align:start position:0% +i can get a larger lens to do that if i + + + align:start position:0% +i can get a larger lens to do that if i +want to + + align:start position:0% +want to + + + align:start position:0% +want to +okay and then + + align:start position:0% + + + + align:start position:0% + +um and so + + align:start position:0% + + + + align:start position:0% + +what this lens does + + align:start position:0% +what this lens does + + + align:start position:0% +what this lens does +is kind of remarkable namely it takes + + align:start position:0% +is kind of remarkable namely it takes + + + align:start position:0% +is kind of remarkable namely it takes +all of the rays that come from + + align:start position:0% +all of the rays that come from + + + align:start position:0% +all of the rays that come from +this point up here + + align:start position:0% +this point up here + + + align:start position:0% +this point up here +and it magically brings them back + + align:start position:0% +and it magically brings them back + + + align:start position:0% +and it magically brings them back +together again over here + + align:start position:0% +together again over here + + + align:start position:0% +together again over here +so so that's the good news the bad news + + align:start position:0% +so so that's the good news the bad news + + + align:start position:0% +so so that's the good news the bad news +is that if i move this in depth if i go + + align:start position:0% +is that if i move this in depth if i go + + + align:start position:0% +is that if i move this in depth if i go +over here it'll no longer be focused in + + align:start position:0% +over here it'll no longer be focused in + + + align:start position:0% +over here it'll no longer be focused in +this plane it'll be focused in a + + align:start position:0% +this plane it'll be focused in a + + + align:start position:0% +this plane it'll be focused in a +different plane we didn't have that with + + align:start position:0% +different plane we didn't have that with + + + align:start position:0% +different plane we didn't have that with +a pinhole we didn't say anything about + + align:start position:0% +a pinhole we didn't say anything about + + + align:start position:0% +a pinhole we didn't say anything about +you know focus or length or whatever + + align:start position:0% +you know focus or length or whatever + + + align:start position:0% +you know focus or length or whatever +so the the upside is that we are now + + align:start position:0% +so the the upside is that we are now + + + align:start position:0% +so the the upside is that we are now +bringing a significant number of + + align:start position:0% +bringing a significant number of + + + align:start position:0% +bringing a significant number of +photons + + align:start position:0% +photons + + + align:start position:0% +photons +together in order to make a good + + align:start position:0% +together in order to make a good + + + align:start position:0% +together in order to make a good +measurement the downside is + + align:start position:0% +measurement the downside is + + + align:start position:0% +measurement the downside is +we have this penalty that things can be + + align:start position:0% +we have this penalty that things can be + + + align:start position:0% +we have this penalty that things can be +in and out of focus + + align:start position:0% +in and out of focus + + + align:start position:0% +in and out of focus +okay + + align:start position:0% +okay + + + align:start position:0% +okay +then what + + align:start position:0% +then what + + + align:start position:0% +then what +what you can do with this is uh + + align:start position:0% +what you can do with this is uh + + + align:start position:0% +what you can do with this is uh +draw similar triangles and you get three + + align:start position:0% +draw similar triangles and you get three + + + align:start position:0% +draw similar triangles and you get three +equations + + align:start position:0% +equations + + + align:start position:0% +equations +and if you put them together just the + + align:start position:0% +and if you put them together just the + + + align:start position:0% +and if you put them together just the +right way + + align:start position:0% + + + + align:start position:0% + +and again + + align:start position:0% +and again + + + align:start position:0% +and again +it's you know + + align:start position:0% +it's you know + + + align:start position:0% +it's you know +a page of fairly boring algebra i don't + + align:start position:0% +a page of fairly boring algebra i don't + + + align:start position:0% +a page of fairly boring algebra i don't +really want to do that + + align:start position:0% +really want to do that + + + align:start position:0% +really want to do that +and also you know you should know that + + align:start position:0% +and also you know you should know that + + + align:start position:0% +and also you know you should know that +from physics but + + align:start position:0% +from physics but + + + align:start position:0% +from physics but +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +what else + + align:start position:0% +what else + + + align:start position:0% +what else +so + + align:start position:0% +so + + + align:start position:0% +so +as i think i mentioned before we can + + align:start position:0% +as i think i mentioned before we can + + + align:start position:0% +as i think i mentioned before we can +think of the lens as this amazing analog + + align:start position:0% +think of the lens as this amazing analog + + + align:start position:0% +think of the lens as this amazing analog +computer + + align:start position:0% +computer + + + align:start position:0% +computer +because you know rays come in from this + + align:start position:0% +because you know rays come in from this + + + align:start position:0% +because you know rays come in from this +side going in every which direction and + + align:start position:0% +side going in every which direction and + + + align:start position:0% +side going in every which direction and +it magically figures out where to send + + align:start position:0% +it magically figures out where to send + + + align:start position:0% +it magically figures out where to send +them to + + align:start position:0% +them to + + + align:start position:0% +them to +um you know i don't think we really + + align:start position:0% +um you know i don't think we really + + + align:start position:0% +um you know i don't think we really +appreciate how amazing this is because + + align:start position:0% +appreciate how amazing this is because + + + align:start position:0% +appreciate how amazing this is because +you know we all use lenses since we were + + align:start position:0% +you know we all use lenses since we were + + + align:start position:0% +you know we all use lenses since we were +very small and we just accept that you + + align:start position:0% +very small and we just accept that you + + + align:start position:0% +very small and we just accept that you +know you can + + align:start position:0% +know you can + + + align:start position:0% +know you can +do things with them that depend on this + + align:start position:0% +do things with them that depend on this + + + align:start position:0% +do things with them that depend on this +property + + align:start position:0% +property + + + align:start position:0% +property +now this is a planar diagram + + align:start position:0% +now this is a planar diagram + + + align:start position:0% +now this is a planar diagram +but this applies in 3d as well which + + align:start position:0% +but this applies in 3d as well which + + + align:start position:0% +but this applies in 3d as well which +makes it even more amazing because now + + align:start position:0% +makes it even more amazing because now + + + align:start position:0% +makes it even more amazing because now +uh the rays coming from this point + + align:start position:0% +uh the rays coming from this point + + + align:start position:0% +uh the rays coming from this point +occupy a whole solid angle you know one + + align:start position:0% +occupy a whole solid angle you know one + + + align:start position:0% +occupy a whole solid angle you know one +of them is going to come out of the + + align:start position:0% +of them is going to come out of the + + + align:start position:0% +of them is going to come out of the +board and it's going to hit the lens + + align:start position:0% +board and it's going to hit the lens + + + align:start position:0% +board and it's going to hit the lens +over here and magically that part of the + + align:start position:0% +over here and magically that part of the + + + align:start position:0% +over here and magically that part of the +lens will redirect it to to be over + + align:start position:0% +lens will redirect it to to be over + + + align:start position:0% +lens will redirect it to to be over +there so + + align:start position:0% +there so + + + align:start position:0% +there so +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +i mentioned that actually you can't make + + align:start position:0% +i mentioned that actually you can't make + + + align:start position:0% +i mentioned that actually you can't make +a perfect ideal lens + + align:start position:0% +a perfect ideal lens + + + align:start position:0% +a perfect ideal lens +and + + align:start position:0% +and + + + align:start position:0% +and +that's connected to this property that + + align:start position:0% +that's connected to this property that + + + align:start position:0% +that's connected to this property that +um + + align:start position:0% +um + + + align:start position:0% +um +each part of the surface of the lens + + align:start position:0% +each part of the surface of the lens + + + align:start position:0% +each part of the surface of the lens +has to somehow + + align:start position:0% +has to somehow + + + align:start position:0% +has to somehow +deal with rays coming from a whole solid + + align:start position:0% +deal with rays coming from a whole solid + + + align:start position:0% +deal with rays coming from a whole solid +angle of possible directions and so you + + align:start position:0% +angle of possible directions and so you + + + align:start position:0% +angle of possible directions and so you +can't optimize it for one particular + + align:start position:0% +can't optimize it for one particular + + + align:start position:0% +can't optimize it for one particular +direction + + align:start position:0% +direction + + + align:start position:0% +direction +nevertheless by combining different + + align:start position:0% +nevertheless by combining different + + + align:start position:0% +nevertheless by combining different +lenses + + align:start position:0% +lenses + + + align:start position:0% +lenses +you can get + + align:start position:0% +you can get + + + align:start position:0% +you can get +you know very good performance very + + align:start position:0% +you know very good performance very + + + align:start position:0% +you know very good performance very +accurate performance + + align:start position:0% +accurate performance + + + align:start position:0% +accurate performance +and they're trade-offs between different + + align:start position:0% +and they're trade-offs between different + + + align:start position:0% +and they're trade-offs between different +kinds of defects + + align:start position:0% +kinds of defects + + + align:start position:0% +kinds of defects +one of which is radial distortion + + align:start position:0% +one of which is radial distortion + + + align:start position:0% +one of which is radial distortion +so um + + align:start position:0% +so um + + + align:start position:0% +so um +if you + + align:start position:0% +if you + + + align:start position:0% +if you +think of an image + + align:start position:0% +think of an image + + + align:start position:0% +think of an image +and particularly you know think of a + + align:start position:0% +and particularly you know think of a + + + align:start position:0% +and particularly you know think of a +fisheye lens image where + + align:start position:0% +fisheye lens image where + + + align:start position:0% +fisheye lens image where +more than 90 degrees of the world is + + align:start position:0% +more than 90 degrees of the world is + + + align:start position:0% +more than 90 degrees of the world is +image perhaps as much as 180 degrees + + align:start position:0% +image perhaps as much as 180 degrees + + + align:start position:0% +image perhaps as much as 180 degrees +well in order to bring that into the + + align:start position:0% +well in order to bring that into the + + + align:start position:0% +well in order to bring that into the +plane you have to kind of squash the + + align:start position:0% +plane you have to kind of squash the + + + align:start position:0% +plane you have to kind of squash the +outer parts and so in terms of the image + + align:start position:0% +outer parts and so in terms of the image + + + align:start position:0% +outer parts and so in terms of the image +what's happening is that the distance + + align:start position:0% +what's happening is that the distance + + + align:start position:0% +what's happening is that the distance +from the center of the image is + + align:start position:0% +from the center of the image is + + + align:start position:0% +from the center of the image is +distorted and is made smaller than it + + align:start position:0% +distorted and is made smaller than it + + + align:start position:0% +distorted and is made smaller than it +would be with perspective projection + + align:start position:0% +would be with perspective projection + + + align:start position:0% +would be with perspective projection +and that's the only way you can get you + + align:start position:0% +and that's the only way you can get you + + + align:start position:0% +and that's the only way you can get you +know a large angle + + align:start position:0% +know a large angle + + + align:start position:0% +know a large angle +in a wide angle lens or fisheye lens + + align:start position:0% +in a wide angle lens or fisheye lens + + + align:start position:0% +in a wide angle lens or fisheye lens +and that type of + + align:start position:0% +and that type of + + + align:start position:0% +and that type of +distortion is actually inherent in in + + align:start position:0% +distortion is actually inherent in in + + + align:start position:0% +distortion is actually inherent in in +lenses and we're not very sensitive to + + align:start position:0% +lenses and we're not very sensitive to + + + align:start position:0% +lenses and we're not very sensitive to +it if it's relatively small and so + + align:start position:0% +it if it's relatively small and so + + + align:start position:0% +it if it's relatively small and so +oftentimes lenses are designed + + align:start position:0% +oftentimes lenses are designed + + + align:start position:0% +oftentimes lenses are designed +such that + + align:start position:0% +such that + + + align:start position:0% +such that +they will suppress certain defects at + + align:start position:0% +they will suppress certain defects at + + + align:start position:0% +they will suppress certain defects at +the cost of increasing + + align:start position:0% +the cost of increasing + + + align:start position:0% +the cost of increasing +radial distortion and that's why when we + + align:start position:0% +radial distortion and that's why when we + + + align:start position:0% +radial distortion and that's why when we +talked about + + align:start position:0% +talked about + + + align:start position:0% +talked about +calibration i mentioned that + + align:start position:0% +calibration i mentioned that + + + align:start position:0% +calibration i mentioned that +unfortunately with real lenses we need + + align:start position:0% +unfortunately with real lenses we need + + + align:start position:0% +unfortunately with real lenses we need +to not just find the + + align:start position:0% +to not just find the + + + align:start position:0% +to not just find the +principal point principal distance and + + align:start position:0% +principal point principal distance and + + + align:start position:0% +principal point principal distance and +the principal point but we may also need + + align:start position:0% +the principal point but we may also need + + + align:start position:0% +the principal point but we may also need +to talk about + + align:start position:0% +to talk about + + + align:start position:0% +to talk about +radial distortion + + align:start position:0% +radial distortion + + + align:start position:0% +radial distortion +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +now we're ready to put it together to + + align:start position:0% +now we're ready to put it together to + + + align:start position:0% +now we're ready to put it together to +see + + align:start position:0% +see + + + align:start position:0% +see +what + + align:start position:0% +what + + + align:start position:0% +what +the irradiance in the image is + + align:start position:0% +the irradiance in the image is + + + align:start position:0% +the irradiance in the image is +given a + + align:start position:0% +given a + + + align:start position:0% +given a +object radiance out in the world + + align:start position:0% +object radiance out in the world + + + align:start position:0% +object radiance out in the world +so we'll draw a diagram of a simple + + align:start position:0% +so we'll draw a diagram of a simple + + + align:start position:0% +so we'll draw a diagram of a simple +imaging system that includes a lens + + align:start position:0% + + + + align:start position:0% + +now you know biological vision systems + + align:start position:0% +now you know biological vision systems + + + align:start position:0% +now you know biological vision systems +don't have flat image planes + + align:start position:0% +don't have flat image planes + + + align:start position:0% +don't have flat image planes +but + + align:start position:0% +but + + + align:start position:0% +but +all of our cameras do and it'd be kind + + align:start position:0% +all of our cameras do and it'd be kind + + + align:start position:0% +all of our cameras do and it'd be kind +of + + align:start position:0% +of + + + align:start position:0% +of +people people have built cameras with + + align:start position:0% +people people have built cameras with + + + align:start position:0% +people people have built cameras with +curved uh + + align:start position:0% +curved uh + + + align:start position:0% +curved uh +retinas but it's hard and it doesn't + + align:start position:0% +retinas but it's hard and it doesn't + + + align:start position:0% +retinas but it's hard and it doesn't +seem to serve any particular purpose so + + align:start position:0% +seem to serve any particular purpose so + + + align:start position:0% +seem to serve any particular purpose so +let's assume as usual that we have a + + align:start position:0% +let's assume as usual that we have a + + + align:start position:0% +let's assume as usual that we have a +planar + + align:start position:0% +planar + + + align:start position:0% +planar +image + + align:start position:0% +image + + + align:start position:0% +image +plane + + align:start position:0% + + + + align:start position:0% + +okay so then + + align:start position:0% + + + + align:start position:0% + +there's a lens + + align:start position:0% +there's a lens + + + align:start position:0% +there's a lens +and there's an object + + align:start position:0% +and there's an object + + + align:start position:0% +and there's an object +let's pick something + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +i'm calling the distance from the lens + + align:start position:0% +i'm calling the distance from the lens + + + align:start position:0% +i'm calling the distance from the lens +to the image plane f + + align:start position:0% +to the image plane f + + + align:start position:0% +to the image plane f +as opposed to f0 + + align:start position:0% +as opposed to f0 + + + align:start position:0% +as opposed to f0 +why is that well i've i'm using f0 to + + align:start position:0% +why is that well i've i'm using f0 to + + + align:start position:0% +why is that well i've i'm using f0 to +denote the focal length which is a fixed + + align:start position:0% +denote the focal length which is a fixed + + + align:start position:0% +denote the focal length which is a fixed +property of the lens and because of this + + align:start position:0% +property of the lens and because of this + + + align:start position:0% +property of the lens and because of this +formula over here we know that for + + align:start position:0% +formula over here we know that for + + + align:start position:0% +formula over here we know that for +things to be in focus they have to + + align:start position:0% +things to be in focus they have to + + + align:start position:0% +things to be in focus they have to +actually be further away from the lens + + align:start position:0% +actually be further away from the lens + + + align:start position:0% +actually be further away from the lens +than f + + align:start position:0% +than f + + + align:start position:0% +than f +and so + + align:start position:0% +and so + + + align:start position:0% +and so +then f0 and so this is going to be a + + align:start position:0% +then f0 and so this is going to be a + + + align:start position:0% +then f0 and so this is going to be a +little bit larger than f0 depending on + + align:start position:0% +little bit larger than f0 depending on + + + align:start position:0% +little bit larger than f0 depending on +the magnification well the way i've + + align:start position:0% +the magnification well the way i've + + + align:start position:0% +the magnification well the way i've +drawn it actually it's going to be a lot + + align:start position:0% +drawn it actually it's going to be a lot + + + align:start position:0% +drawn it actually it's going to be a lot +larger than f0 but + + align:start position:0% +larger than f0 but + + + align:start position:0% +larger than f0 but +okay so then + + align:start position:0% +okay so then + + + align:start position:0% +okay so then +we said that the central arrays are + + align:start position:0% +we said that the central arrays are + + + align:start position:0% +we said that the central arrays are +undeflected so the rays going into the + + align:start position:0% +undeflected so the rays going into the + + + align:start position:0% +undeflected so the rays going into the +lens here come out in the same direction + + align:start position:0% +lens here come out in the same direction + + + align:start position:0% +lens here come out in the same direction +and therefore + + align:start position:0% +and therefore + + + align:start position:0% +and therefore +a couple of things one of them is that + + align:start position:0% +a couple of things one of them is that + + + align:start position:0% +a couple of things one of them is that +suppose there is a very narrow cone of + + align:start position:0% +suppose there is a very narrow cone of + + + align:start position:0% +suppose there is a very narrow cone of +directions i can assign an angle to this + + align:start position:0% +directions i can assign an angle to this + + + align:start position:0% +directions i can assign an angle to this +that it makes with respect to the + + align:start position:0% +that it makes with respect to the + + + align:start position:0% +that it makes with respect to the +optical axis and that angle is going to + + align:start position:0% +optical axis and that angle is going to + + + align:start position:0% +optical axis and that angle is going to +be the same on the two sides + + align:start position:0% +be the same on the two sides + + + align:start position:0% +be the same on the two sides +and the other thing i can say is that + + align:start position:0% +and the other thing i can say is that + + + align:start position:0% +and the other thing i can say is that +these cones of directions have the same + + align:start position:0% +these cones of directions have the same + + + align:start position:0% +these cones of directions have the same +solid angle because they're the same + + align:start position:0% +solid angle because they're the same + + + align:start position:0% +solid angle because they're the same +rays just turned around + + align:start position:0% +rays just turned around + + + align:start position:0% +rays just turned around +okay + + align:start position:0% +okay + + + align:start position:0% +okay +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +there's a small patch in the image + + align:start position:0% +there's a small patch in the image + + + align:start position:0% +there's a small patch in the image +that's being illuminated i'll call that + + align:start position:0% +that's being illuminated i'll call that + + + align:start position:0% +that's being illuminated i'll call that +delta i + + align:start position:0% +delta i + + + align:start position:0% +delta i +and there's a small patch on the object + + align:start position:0% +and there's a small patch on the object + + + align:start position:0% +and there's a small patch on the object +that's being illuminated and + + align:start position:0% +that's being illuminated and + + + align:start position:0% +that's being illuminated and +we're going to see how much power coming + + align:start position:0% +we're going to see how much power coming + + + align:start position:0% +we're going to see how much power coming +off + + align:start position:0% +off + + + align:start position:0% +off +that patch ends up in this patch that + + align:start position:0% +that patch ends up in this patch that + + + align:start position:0% +that patch ends up in this patch that +that's + + align:start position:0% +that's + + + align:start position:0% +that's +that's the kind of thing we'll be + + align:start position:0% +that's the kind of thing we'll be + + + align:start position:0% +that's the kind of thing we'll be +looking at + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but first + + align:start position:0% +but first + + + align:start position:0% +but first +let's equate + + align:start position:0% +let's equate + + + align:start position:0% +let's equate +those um + + align:start position:0% +those um + + + align:start position:0% +those um +two solid angles + + align:start position:0% +two solid angles + + + align:start position:0% +two solid angles +i'm trying to relate these two areas + + align:start position:0% +i'm trying to relate these two areas + + + align:start position:0% +i'm trying to relate these two areas +then in order to do that i need to take + + align:start position:0% +then in order to do that i need to take + + + align:start position:0% +then in order to do that i need to take +into account the foreshortening + + align:start position:0% +into account the foreshortening + + + align:start position:0% +into account the foreshortening +so there's a unit vector on the surface + + align:start position:0% +so there's a unit vector on the surface + + + align:start position:0% +so there's a unit vector on the surface +of the object + + align:start position:0% +of the object + + + align:start position:0% +of the object +and what's well this also is + + align:start position:0% +and what's well this also is + + + align:start position:0% +and what's well this also is +not + + align:start position:0% +not + + + align:start position:0% +not +immune to that effect because the light + + align:start position:0% +immune to that effect because the light + + + align:start position:0% +immune to that effect because the light +is not coming in perpendicular to the + + align:start position:0% +is not coming in perpendicular to the + + + align:start position:0% +is not coming in perpendicular to the +image sensor the light is coming in at + + align:start position:0% +image sensor the light is coming in at + + + align:start position:0% +image sensor the light is coming in at +an angle + + align:start position:0% +an angle + + + align:start position:0% +an angle +right if i draw a surface normal to the + + align:start position:0% +right if i draw a surface normal to the + + + align:start position:0% +right if i draw a surface normal to the +image plane + + align:start position:0% +image plane + + + align:start position:0% +image plane +then + + align:start position:0% +then + + + align:start position:0% +then +it's not the center of this cone of b of + + align:start position:0% +it's not the center of this cone of b of + + + align:start position:0% +it's not the center of this cone of b of +rays + + align:start position:0% +rays + + + align:start position:0% +rays +and what is the angle + + align:start position:0% +and what is the angle + + + align:start position:0% +and what is the angle +between the surface normal to the image + + align:start position:0% +between the surface normal to the image + + + align:start position:0% +between the surface normal to the image +plane and the incoming + + align:start position:0% +plane and the incoming + + + align:start position:0% +plane and the incoming +rays here + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +remember that diagram + + align:start position:0% +remember that diagram + + + align:start position:0% +remember that diagram +uh where + + align:start position:0% +uh where + + + align:start position:0% +uh where +you know put these angles are the same + + align:start position:0% +you know put these angles are the same + + + align:start position:0% +you know put these angles are the same +and these angles are the same so over + + align:start position:0% +and these angles are the same so over + + + align:start position:0% +and these angles are the same so over +here + + align:start position:0% +here + + + align:start position:0% +here +this angle and that angle are the same + + align:start position:0% +this angle and that angle are the same + + + align:start position:0% +this angle and that angle are the same +so that alpha affects the + + align:start position:0% +so that alpha affects the + + + align:start position:0% +so that alpha affects the +incident light onto the image sensor as + + align:start position:0% +incident light onto the image sensor as + + + align:start position:0% +incident light onto the image sensor as +well + + align:start position:0% +well + + + align:start position:0% +well +okay so now i can write down i can use + + align:start position:0% +okay so now i can write down i can use + + + align:start position:0% +okay so now i can write down i can use +that formula i had for solid angle + + align:start position:0% + + + + align:start position:0% + +so on on this side the area is delta i + + align:start position:0% +so on on this side the area is delta i + + + align:start position:0% +so on on this side the area is delta i +and then there's a foreshortening effect + + align:start position:0% +and then there's a foreshortening effect + + + align:start position:0% +and then there's a foreshortening effect +cosine alpha + + align:start position:0% +cosine alpha + + + align:start position:0% +cosine alpha +and then i have to divide by the + + align:start position:0% +and then i have to divide by the + + + align:start position:0% +and then i have to divide by the +distance squared + + align:start position:0% +distance squared + + + align:start position:0% +distance squared +so that's + + align:start position:0% +so that's + + + align:start position:0% +so that's +f squared + + align:start position:0% +f squared + + + align:start position:0% +f squared +or + + align:start position:0% +or + + + align:start position:0% +or +maybe + + align:start position:0% +maybe + + + align:start position:0% +maybe +not + + align:start position:0% +not + + + align:start position:0% +not +it's bigger than f squared right + + align:start position:0% +it's bigger than f squared right + + + align:start position:0% +it's bigger than f squared right +so + + align:start position:0% +so + + + align:start position:0% +so +it's + + align:start position:0% +it's + + + align:start position:0% +it's +f secant alpha squared + + align:start position:0% +f secant alpha squared + + + align:start position:0% +f secant alpha squared +here's the + + align:start position:0% +here's the + + + align:start position:0% +here's the +so this part is f + + align:start position:0% +so this part is f + + + align:start position:0% +so this part is f +this is alpha and i'm measuring uh this + + align:start position:0% +this is alpha and i'm measuring uh this + + + align:start position:0% +this is alpha and i'm measuring uh this +length + + align:start position:0% + + + + align:start position:0% + +right so + + align:start position:0% +right so + + + align:start position:0% +right so +you can imagine if i draw this further + + align:start position:0% +you can imagine if i draw this further + + + align:start position:0% +you can imagine if i draw this further +out then that's going to become even + + align:start position:0% +out then that's going to become even + + + align:start position:0% +out then that's going to become even +more obvious + + align:start position:0% +more obvious + + + align:start position:0% +more obvious +okay and now that + + align:start position:0% +okay and now that + + + align:start position:0% +okay and now that +since we said that the central rays are + + align:start position:0% +since we said that the central rays are + + + align:start position:0% +since we said that the central rays are +undeflected this cone of directions is + + align:start position:0% +undeflected this cone of directions is + + + align:start position:0% +undeflected this cone of directions is +the same as that cone of direction so i + + align:start position:0% +the same as that cone of direction so i + + + align:start position:0% +the same as that cone of direction so i +can just equate that to + + align:start position:0% + + + + align:start position:0% + +and it's the same thing on the other + + align:start position:0% +and it's the same thing on the other + + + align:start position:0% +and it's the same thing on the other +side + + align:start position:0% + + + + align:start position:0% + +okay and fortunately those secants + + align:start position:0% +okay and fortunately those secants + + + align:start position:0% +okay and fortunately those secants +cancel out + + align:start position:0% +cancel out + + + align:start position:0% +cancel out +so + + align:start position:0% +so + + + align:start position:0% +so +let's see i want delta o over delta i or + + align:start position:0% +let's see i want delta o over delta i or + + + align:start position:0% +let's see i want delta o over delta i or +do i want the other way around + + align:start position:0% + + + + align:start position:0% + +okay so that's half of the story that + + align:start position:0% +okay so that's half of the story that + + + align:start position:0% +okay so that's half of the story that +we're making good progress here + + align:start position:0% +we're making good progress here + + + align:start position:0% +we're making good progress here +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and that's important because + + align:start position:0% +and that's important because + + + align:start position:0% +and that's important because +you know the the total energy coming off + + align:start position:0% +you know the the total energy coming off + + + align:start position:0% +you know the the total energy coming off +that patch depends on how big it is and + + align:start position:0% +that patch depends on how big it is and + + + align:start position:0% +that patch depends on how big it is and +then that energy gets concentrated into + + align:start position:0% +then that energy gets concentrated into + + + align:start position:0% +then that energy gets concentrated into +that smaller patch in the image and + + align:start position:0% +that smaller patch in the image and + + + align:start position:0% +that smaller patch in the image and +so the irradiance in the image is going + + align:start position:0% +so the irradiance in the image is going + + + align:start position:0% +so the irradiance in the image is going +to be + + align:start position:0% +to be + + + align:start position:0% +to be +whatever power ends up here divided by + + align:start position:0% +whatever power ends up here divided by + + + align:start position:0% +whatever power ends up here divided by +this area delta i + + align:start position:0% +this area delta i + + + align:start position:0% +this area delta i +and so we'll be able to relate + + align:start position:0% +and so we'll be able to relate + + + align:start position:0% +and so we'll be able to relate +the radians over there to the irradiance + + align:start position:0% +the radians over there to the irradiance + + + align:start position:0% +the radians over there to the irradiance +over here and this is what we measure + + align:start position:0% +over here and this is what we measure + + + align:start position:0% +over here and this is what we measure +it's the irradiance there okay so now + + align:start position:0% +it's the irradiance there okay so now + + + align:start position:0% +it's the irradiance there okay so now +we have to think about + + align:start position:0% +we have to think about + + + align:start position:0% +we have to think about +how much of the light from that patch on + + align:start position:0% +how much of the light from that patch on + + + align:start position:0% +how much of the light from that patch on +the surface + + align:start position:0% +the surface + + + align:start position:0% +the surface +actually is going to be concentrated + + align:start position:0% + + + + align:start position:0% + +into that + + align:start position:0% +into that + + + align:start position:0% +into that +image + + align:start position:0% + + + + align:start position:0% + +right so + + align:start position:0% +right so + + + align:start position:0% +right so +the good news is that because + + align:start position:0% +the good news is that because + + + align:start position:0% +the good news is that because +the lens focuses the rays + + align:start position:0% +the lens focuses the rays + + + align:start position:0% +the lens focuses the rays +all i need to know really is + + align:start position:0% +all i need to know really is + + + align:start position:0% +all i need to know really is +the solid angle that the lens occupies + + align:start position:0% +the solid angle that the lens occupies + + + align:start position:0% +the solid angle that the lens occupies +when viewed from the object right so i + + align:start position:0% +when viewed from the object right so i + + + align:start position:0% +when viewed from the object right so i +need to know what the solid angle is + + align:start position:0% +need to know what the solid angle is + + + align:start position:0% +need to know what the solid angle is +because + + align:start position:0% +because + + + align:start position:0% +because +the rays that come out the other side + + align:start position:0% +the rays that come out the other side + + + align:start position:0% +the rays that come out the other side +all get concentrated into the + + align:start position:0% +all get concentrated into the + + + align:start position:0% +all get concentrated into the +corresponding patch + + align:start position:0% + + + + align:start position:0% + +if things are in focus + + align:start position:0% +if things are in focus + + + align:start position:0% +if things are in focus +the light that comes off this patch and + + align:start position:0% +the light that comes off this patch and + + + align:start position:0% +the light that comes off this patch and +goes through the lens is all + + align:start position:0% +goes through the lens is all + + + align:start position:0% +goes through the lens is all +concentrated into this area in the image + + align:start position:0% +concentrated into this area in the image + + + align:start position:0% +concentrated into this area in the image +and conversely + + align:start position:0% +and conversely + + + align:start position:0% +and conversely +light coming from anywhere else + + align:start position:0% +light coming from anywhere else + + + align:start position:0% +light coming from anywhere else +has no effect on on this it's image + + align:start position:0% +has no effect on on this it's image + + + align:start position:0% +has no effect on on this it's image +somewhere else so so there's a direct + + align:start position:0% +somewhere else so so there's a direct + + + align:start position:0% +somewhere else so so there's a direct +match between + + align:start position:0% +match between + + + align:start position:0% +match between +the + + align:start position:0% +the + + + align:start position:0% +the +power coming off here that makes it + + align:start position:0% +power coming off here that makes it + + + align:start position:0% +power coming off here that makes it +through the lens + + align:start position:0% +through the lens + + + align:start position:0% +through the lens +and the power that's delivered to that + + align:start position:0% +and the power that's delivered to that + + + align:start position:0% +and the power that's delivered to that +small area in the image okay so what is + + align:start position:0% +small area in the image okay so what is + + + align:start position:0% +small area in the image okay so what is +this well + + align:start position:0% +this well + + + align:start position:0% +this well +it's the area of the lens let's suppose + + align:start position:0% +it's the area of the lens let's suppose + + + align:start position:0% +it's the area of the lens let's suppose +the lens has a diameter d + + align:start position:0% +the lens has a diameter d + + + align:start position:0% +the lens has a diameter d +so it's a four pi squared and then + + align:start position:0% +so it's a four pi squared and then + + + align:start position:0% +so it's a four pi squared and then +there's a for shortening effect there's + + align:start position:0% +there's a for shortening effect there's + + + align:start position:0% +there's a for shortening effect there's +an angle + + align:start position:0% +an angle + + + align:start position:0% +an angle +which we drew as alpha + + align:start position:0% + + + + align:start position:0% + +and then we have to divide by the + + align:start position:0% +and then we have to divide by the + + + align:start position:0% +and then we have to divide by the +distance squared + + align:start position:0% +distance squared + + + align:start position:0% +distance squared +and that again is + + align:start position:0% +and that again is + + + align:start position:0% +and that again is +f + + align:start position:0% +f + + + align:start position:0% +f +secant alpha squared + + align:start position:0% + + + + align:start position:0% + +so so that's the solid angle + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +typically that's actually quite small + + align:start position:0% +typically that's actually quite small + + + align:start position:0% +typically that's actually quite small +and so we + + align:start position:0% +and so we + + + align:start position:0% +and so we +typically only gather up a relatively + + align:start position:0% +typically only gather up a relatively + + + align:start position:0% +typically only gather up a relatively +small fraction of the uh + + align:start position:0% + + + + align:start position:0% + +oh sorry not f z + + align:start position:0% + + + + align:start position:0% + +and now this time the cosines and + + align:start position:0% +and now this time the cosines and + + + align:start position:0% +and now this time the cosines and +secants don't cancel out unfortunately + + align:start position:0% +secants don't cancel out unfortunately + + + align:start position:0% +secants don't cancel out unfortunately +and and we get that + + align:start position:0% +and and we get that + + + align:start position:0% +and and we get that +okay so almost done + + align:start position:0% +okay so almost done + + + align:start position:0% +okay so almost done +so the uh + + align:start position:0% +so the uh + + + align:start position:0% +so the uh +power delivered to that small area in + + align:start position:0% +power delivered to that small area in + + + align:start position:0% +power delivered to that small area in +the image + + align:start position:0% +the image + + + align:start position:0% +the image +is the radiance of the surface times its + + align:start position:0% +is the radiance of the surface times its + + + align:start position:0% +is the radiance of the surface times its +area + + align:start position:0% +area + + + align:start position:0% +area +times the + + align:start position:0% +times the + + + align:start position:0% +times the +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +solid angle times cosine theta and + + align:start position:0% +solid angle times cosine theta and + + + align:start position:0% +solid angle times cosine theta and +that's going to be l + + align:start position:0% +that's going to be l + + + align:start position:0% +that's going to be l +delta + + align:start position:0% +delta + + + align:start position:0% +delta +o pi over 4 + + align:start position:0% +o pi over 4 + + + align:start position:0% +o pi over 4 +d over z squared + + align:start position:0% + + + + align:start position:0% + +so that's the total power we're + + align:start position:0% +so that's the total power we're + + + align:start position:0% +so that's the total power we're +delivering and it's concentrated into an + + align:start position:0% +delivering and it's concentrated into an + + + align:start position:0% +delivering and it's concentrated into an +area delta i so the power per unit area + + align:start position:0% +area delta i so the power per unit area + + + align:start position:0% +area delta i so the power per unit area +is we just divide through by + + align:start position:0% +is we just divide through by + + + align:start position:0% +is we just divide through by +delta i and that's that's what we + + align:start position:0% +delta i and that's that's what we + + + align:start position:0% +delta i and that's that's what we +actually measure + + align:start position:0% + + + + align:start position:0% + +so that's the + + align:start position:0% +so that's the + + + align:start position:0% +so that's the +conclusion of that + + align:start position:0% +conclusion of that + + + align:start position:0% +conclusion of that +so let's let's study that a little bit + + align:start position:0% +so let's let's study that a little bit + + + align:start position:0% +so let's let's study that a little bit +carefully + + align:start position:0% + + + + align:start position:0% + +let's look at this d over d over f + + align:start position:0% +let's look at this d over d over f + + + align:start position:0% +let's look at this d over d over f +what is that + + align:start position:0% + + + + align:start position:0% + +or + + align:start position:0% +or + + + align:start position:0% +or +maybe f over d looks more familiar + + align:start position:0% + + + + align:start position:0% + +i guess the + + align:start position:0% +i guess the + + + align:start position:0% +i guess the +no amateur photographers here + + align:start position:0% +no amateur photographers here + + + align:start position:0% +no amateur photographers here +that's the f-stop + + align:start position:0% +that's the f-stop + + + align:start position:0% +that's the f-stop +that tells you how + + align:start position:0% +that tells you how + + + align:start position:0% +that tells you how +open your aperture is + + align:start position:0% +open your aperture is + + + align:start position:0% +open your aperture is +is + + align:start position:0% +is + + + align:start position:0% +is +f l d + + align:start position:0% +f l d + + + align:start position:0% +f l d +and so + + align:start position:0% +and so + + + align:start position:0% +and so +you know typically + + align:start position:0% +you know typically + + + align:start position:0% +you know typically +slrs will have a maximum + + align:start position:0% +slrs will have a maximum + + + align:start position:0% +slrs will have a maximum +opening of maybe i don't know 1.8 for + + align:start position:0% +opening of maybe i don't know 1.8 for + + + align:start position:0% +opening of maybe i don't know 1.8 for +that ratio and you can stop it down to i + + align:start position:0% +that ratio and you can stop it down to i + + + align:start position:0% +that ratio and you can stop it down to i +don't know 22 let's say + + align:start position:0% +don't know 22 let's say + + + align:start position:0% +don't know 22 let's say +and so obviously the square of that + + align:start position:0% +and so obviously the square of that + + + align:start position:0% +and so obviously the square of that +controls how much light you get and + + align:start position:0% +controls how much light you get and + + + align:start position:0% +controls how much light you get and +that's one way of controlling the + + align:start position:0% +that's one way of controlling the + + + align:start position:0% +that's one way of controlling the +exposure the other one is is time + + align:start position:0% +exposure the other one is is time + + + align:start position:0% +exposure the other one is is time +and so often there are trade-offs + + align:start position:0% +and so often there are trade-offs + + + align:start position:0% +and so often there are trade-offs +between + + align:start position:0% +between + + + align:start position:0% +between +using the + + align:start position:0% +using the + + + align:start position:0% +using the +aperture opening + + align:start position:0% +aperture opening + + + align:start position:0% +aperture opening +versus using time you know for example + + align:start position:0% +versus using time you know for example + + + align:start position:0% +versus using time you know for example +if you want + + align:start position:0% +if you want + + + align:start position:0% +if you want +a lot of depth of field + + align:start position:0% +a lot of depth of field + + + align:start position:0% +a lot of depth of field +then + + align:start position:0% +then + + + align:start position:0% +then +you can achieve that by + + align:start position:0% +you can achieve that by + + + align:start position:0% +you can achieve that by +making the aperture very small now + + align:start position:0% +making the aperture very small now + + + align:start position:0% +making the aperture very small now +approaching a pinhole + + align:start position:0% +approaching a pinhole + + + align:start position:0% +approaching a pinhole +but the cost is you need a longer + + align:start position:0% +but the cost is you need a longer + + + align:start position:0% +but the cost is you need a longer +exposure so if things are moving that's + + align:start position:0% +exposure so if things are moving that's + + + align:start position:0% +exposure so if things are moving that's +not going to work conversely if you want + + align:start position:0% +not going to work conversely if you want + + + align:start position:0% +not going to work conversely if you want +to + + align:start position:0% +to + + + align:start position:0% +to +you know have a great portrait and you + + align:start position:0% +you know have a great portrait and you + + + align:start position:0% +you know have a great portrait and you +want to wash out the background out of + + align:start position:0% +want to wash out the background out of + + + align:start position:0% +want to wash out the background out of +focus + + align:start position:0% +focus + + + align:start position:0% +focus +then you go the other direction you open + + align:start position:0% +then you go the other direction you open + + + align:start position:0% +then you go the other direction you open +the lens very wide so that + + align:start position:0% +the lens very wide so that + + + align:start position:0% +the lens very wide so that +it only has a narrow + + align:start position:0% +it only has a narrow + + + align:start position:0% +it only has a narrow +field of depth + + align:start position:0% +field of depth + + + align:start position:0% +field of depth +and uh then use a very short exposure + + align:start position:0% +and uh then use a very short exposure + + + align:start position:0% +and uh then use a very short exposure +anyway so so that anyway that quantity + + align:start position:0% +anyway so so that anyway that quantity + + + align:start position:0% +anyway so so that anyway that quantity +is one that's well known to people + + align:start position:0% +is one that's well known to people + + + align:start position:0% +is one that's well known to people +working with cameras and it's uh + + align:start position:0% +working with cameras and it's uh + + + align:start position:0% +working with cameras and it's uh +intuitive that + + align:start position:0% +intuitive that + + + align:start position:0% +intuitive that +the + + align:start position:0% +the + + + align:start position:0% +the +image irradiance goes as the inverse + + align:start position:0% +image irradiance goes as the inverse + + + align:start position:0% +image irradiance goes as the inverse +square of the f-stop + + align:start position:0% +square of the f-stop + + + align:start position:0% +square of the f-stop +and that's why the f-stops are usually + + align:start position:0% +and that's why the f-stops are usually + + + align:start position:0% +and that's why the f-stops are usually +done in square roots of two so it goes 1 + + align:start position:0% +done in square roots of two so it goes 1 + + + align:start position:0% +done in square roots of two so it goes 1 +1.4 2 2.8 + + align:start position:0% +1.4 2 2.8 + + + align:start position:0% +1.4 2 2.8 + + align:start position:0% + + + align:start position:0% +5.6 8 11 16 22 32 + + align:start position:0% +5.6 8 11 16 22 32 + + + align:start position:0% +5.6 8 11 16 22 32 +and those are steps of square root of 2 + + align:start position:0% +and those are steps of square root of 2 + + + align:start position:0% +and those are steps of square root of 2 +in size of the aperture which give you + + align:start position:0% +in size of the aperture which give you + + + align:start position:0% +in size of the aperture which give you +uh steps of two in uh exposure + + align:start position:0% +uh steps of two in uh exposure + + + align:start position:0% +uh steps of two in uh exposure +okay so that's that so that's you know + + align:start position:0% +okay so that's that so that's you know + + + align:start position:0% +okay so that's that so that's you know +kind of intuitive and not particularly + + align:start position:0% +kind of intuitive and not particularly + + + align:start position:0% +kind of intuitive and not particularly +interesting + + align:start position:0% +interesting + + + align:start position:0% +interesting +uh the pi over four uh who cares it's + + align:start position:0% +uh the pi over four uh who cares it's + + + align:start position:0% +uh the pi over four uh who cares it's +just a constant we're not too excited + + align:start position:0% +just a constant we're not too excited + + + align:start position:0% +just a constant we're not too excited +about that + + align:start position:0% +about that + + + align:start position:0% +about that +what's what's really exciting though is + + align:start position:0% +what's what's really exciting though is + + + align:start position:0% +what's what's really exciting though is +that the thing we measure + + align:start position:0% +that the thing we measure + + + align:start position:0% +that the thing we measure +e + + align:start position:0% +e + + + align:start position:0% +e +image irradiance + + align:start position:0% +image irradiance + + + align:start position:0% +image irradiance +is proportional to l the thing we're + + align:start position:0% +is proportional to l the thing we're + + + align:start position:0% +is proportional to l the thing we're +interested in out in the world the + + align:start position:0% +interested in out in the world the + + + align:start position:0% +interested in out in the world the +radiance + + align:start position:0% +radiance + + + align:start position:0% +radiance +so that's why we can be sloppy about + + align:start position:0% +so that's why we can be sloppy about + + + align:start position:0% +so that's why we can be sloppy about +talking about brightness because the + + align:start position:0% +talking about brightness because the + + + align:start position:0% +talking about brightness because the +brightness of the surface + + align:start position:0% +brightness of the surface + + + align:start position:0% +brightness of the surface +radiance is proportional to the + + align:start position:0% +radiance is proportional to the + + + align:start position:0% +radiance is proportional to the +brightness in the image irradiance so + + align:start position:0% +brightness in the image irradiance so + + + align:start position:0% +brightness in the image irradiance so +you know we're measuring brightness in + + align:start position:0% +you know we're measuring brightness in + + + align:start position:0% +you know we're measuring brightness in +the image and that has a meaning beyond + + align:start position:0% +the image and that has a meaning beyond + + + align:start position:0% +the image and that has a meaning beyond +just power per unit area in the image + + align:start position:0% +just power per unit area in the image + + + align:start position:0% +just power per unit area in the image +plane but it has a meaning out there in + + align:start position:0% +plane but it has a meaning out there in + + + align:start position:0% +plane but it has a meaning out there in +terms of how much that object is + + align:start position:0% +terms of how much that object is + + + align:start position:0% +terms of how much that object is +radiating + + align:start position:0% +radiating + + + align:start position:0% +radiating +and the remaining part is this uh + + align:start position:0% +and the remaining part is this uh + + + align:start position:0% +and the remaining part is this uh +annoying thing here + + align:start position:0% +annoying thing here + + + align:start position:0% +annoying thing here +um cosine to the fourth of alpha + + align:start position:0% +um cosine to the fourth of alpha + + + align:start position:0% +um cosine to the fourth of alpha +what does that do well it means that the + + align:start position:0% +what does that do well it means that the + + + align:start position:0% +what does that do well it means that the +brightness is dropping off as we go off + + align:start position:0% +brightness is dropping off as we go off + + + align:start position:0% +brightness is dropping off as we go off +axis so if you have a + + align:start position:0% + + + + align:start position:0% + +part of the image that's way out on in + + align:start position:0% +part of the image that's way out on in + + + align:start position:0% +part of the image that's way out on in +the corner here + + align:start position:0% +the corner here + + + align:start position:0% +the corner here +it's going to receive less + + align:start position:0% +it's going to receive less + + + align:start position:0% +it's going to receive less +power per unit area + + align:start position:0% +power per unit area + + + align:start position:0% +power per unit area +than something in the middle of the + + align:start position:0% +than something in the middle of the + + + align:start position:0% +than something in the middle of the +image + + align:start position:0% +image + + + align:start position:0% +image +and that means that + + align:start position:0% +and that means that + + + align:start position:0% +and that means that +you need to take that into account now + + align:start position:0% +you need to take that into account now + + + align:start position:0% +you need to take that into account now +unfortunately for small alpha cosine to + + align:start position:0% +unfortunately for small alpha cosine to + + + align:start position:0% +unfortunately for small alpha cosine to +the fourth alpha is as close to one as + + align:start position:0% +the fourth alpha is as close to one as + + + align:start position:0% +the fourth alpha is as close to one as +you can get + + align:start position:0% +you can get + + + align:start position:0% +you can get +and so + + align:start position:0% +and so + + + align:start position:0% +and so +as long as alpha is small you can + + align:start position:0% +as long as alpha is small you can + + + align:start position:0% +as long as alpha is small you can +completely ignore this + + align:start position:0% +completely ignore this + + + align:start position:0% +completely ignore this +so when does alpha get big well it only + + align:start position:0% +so when does alpha get big well it only + + + align:start position:0% +so when does alpha get big well it only +really gets big when you have a wide + + align:start position:0% +really gets big when you have a wide + + + align:start position:0% +really gets big when you have a wide +angle lens + + align:start position:0% +angle lens + + + align:start position:0% +angle lens +when you're taking in a large + + align:start position:0% +when you're taking in a large + + + align:start position:0% +when you're taking in a large +solid angle of the world + + align:start position:0% +solid angle of the world + + + align:start position:0% +solid angle of the world +and then + + align:start position:0% +and then + + + align:start position:0% +and then +you know alpha maybe + + align:start position:0% +you know alpha maybe + + + align:start position:0% +you know alpha maybe +20 30 40 degrees + + align:start position:0% +20 30 40 degrees + + + align:start position:0% +20 30 40 degrees +and then it starts to + + align:start position:0% +and then it starts to + + + align:start position:0% +and then it starts to +matter because cosine + + align:start position:0% +matter because cosine + + + align:start position:0% +matter because cosine +of 40 degrees is not any more close to + + align:start position:0% +of 40 degrees is not any more close to + + + align:start position:0% +of 40 degrees is not any more close to +one + + align:start position:0% +one + + + align:start position:0% +one +fortunately it's a fixed thing so you + + align:start position:0% +fortunately it's a fixed thing so you + + + align:start position:0% +fortunately it's a fixed thing so you +can compensate for it + + align:start position:0% +can compensate for it + + + align:start position:0% +can compensate for it +and in fact + + align:start position:0% +and in fact + + + align:start position:0% +and in fact +you know if you buy a + + align:start position:0% +you know if you buy a + + + align:start position:0% +you know if you buy a +dslr + + align:start position:0% +dslr + + + align:start position:0% +dslr +part of the magic that happens that + + align:start position:0% +part of the magic that happens that + + + align:start position:0% +part of the magic that happens that +you're not allowed to see or understand + + align:start position:0% +you're not allowed to see or understand + + + align:start position:0% +you're not allowed to see or understand +is to compensate for this + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +also we're not very sensitive to this + + align:start position:0% +also we're not very sensitive to this + + + align:start position:0% +also we're not very sensitive to this +effect so if you have an image + + align:start position:0% +effect so if you have an image + + + align:start position:0% +effect so if you have an image +that sort of slowly gets darker towards + + align:start position:0% +that sort of slowly gets darker towards + + + align:start position:0% +that sort of slowly gets darker towards +the edge + + align:start position:0% +the edge + + + align:start position:0% +the edge +you really have to focus on it to to + + align:start position:0% +you really have to focus on it to to + + + align:start position:0% +you really have to focus on it to to +notice it so + + align:start position:0% + + + + align:start position:0% + +when i was much younger i was very keen + + align:start position:0% +when i was much younger i was very keen + + + align:start position:0% +when i was much younger i was very keen +to have a telephoto lens but i couldn't + + align:start position:0% +to have a telephoto lens but i couldn't + + + align:start position:0% +to have a telephoto lens but i couldn't +afford a telephoto lens and then i saw + + align:start position:0% +afford a telephoto lens and then i saw + + + align:start position:0% +afford a telephoto lens and then i saw +uh advertisement for + + align:start position:0% +uh advertisement for + + + align:start position:0% +uh advertisement for +a russian uh casa dioptic uh telephoto + + align:start position:0% +a russian uh casa dioptic uh telephoto + + + align:start position:0% +a russian uh casa dioptic uh telephoto +lens + + align:start position:0% +lens + + + align:start position:0% +lens +and you know + + align:start position:0% +and you know + + + align:start position:0% +and you know +having worked in telescopes that rang a + + align:start position:0% +having worked in telescopes that rang a + + + align:start position:0% +having worked in telescopes that rang a +bell + + align:start position:0% +bell + + + align:start position:0% +bell +and i could afford that once i got it + + align:start position:0% +and i could afford that once i got it + + + align:start position:0% +and i could afford that once i got it +and it was quite nice and then i looked + + align:start position:0% +and it was quite nice and then i looked + + + align:start position:0% +and it was quite nice and then i looked +at + + align:start position:0% +at + + + align:start position:0% +at +those days we used slides and projected + + align:start position:0% +those days we used slides and projected + + + align:start position:0% +those days we used slides and projected +them on the wall so i'm looking at this + + align:start position:0% +them on the wall so i'm looking at this + + + align:start position:0% +them on the wall so i'm looking at this +slide of + + align:start position:0% +slide of + + + align:start position:0% +slide of +predatory bird that i took looking up in + + align:start position:0% +predatory bird that i took looking up in + + + align:start position:0% +predatory bird that i took looking up in +the tree and the sky background behind + + align:start position:0% +the tree and the sky background behind + + + align:start position:0% +the tree and the sky background behind +it and this guy behind the bird is white + + align:start position:0% +it and this guy behind the bird is white + + + align:start position:0% +it and this guy behind the bird is white +and i'm like okay this is odd + + align:start position:0% +and i'm like okay this is odd + + + align:start position:0% +and i'm like okay this is odd +and strangely in the corners the sky is + + align:start position:0% +and strangely in the corners the sky is + + + align:start position:0% +and strangely in the corners the sky is +blue + + align:start position:0% +blue + + + align:start position:0% +blue +and you know so what's going on there + + align:start position:0% +and you know so what's going on there + + + align:start position:0% +and you know so what's going on there +well what's going on is that this lens + + align:start position:0% +well what's going on is that this lens + + + align:start position:0% +well what's going on is that this lens +was cheap in part because it had a rapid + + align:start position:0% +was cheap in part because it had a rapid + + + align:start position:0% +was cheap in part because it had a rapid +drop off + + align:start position:0% +drop off + + + align:start position:0% +drop off +in brightness with the angle perhaps + + align:start position:0% +in brightness with the angle perhaps + + + align:start position:0% +in brightness with the angle perhaps +even worse than this + + align:start position:0% +even worse than this + + + align:start position:0% +even worse than this +and + + align:start position:0% +and + + + align:start position:0% +and +so the corners were not illuminated as + + align:start position:0% +so the corners were not illuminated as + + + align:start position:0% +so the corners were not illuminated as +well as the center + + align:start position:0% +well as the center + + + align:start position:0% +well as the center +and in the center there was enough light + + align:start position:0% +and in the center there was enough light + + + align:start position:0% +and in the center there was enough light +so that these um the colors were over + + align:start position:0% +so that these um the colors were over + + + align:start position:0% +so that these um the colors were over +saturated so + + align:start position:0% +saturated so + + + align:start position:0% +saturated so +you know not only + + align:start position:0% +you know not only + + + align:start position:0% +you know not only +did i get the um + + align:start position:0% +did i get the um + + + align:start position:0% +did i get the um +the green and the red channels + + align:start position:0% +the green and the red channels + + + align:start position:0% +the green and the red channels +overexposed but i even got the blue + + align:start position:0% +overexposed but i even got the blue + + + align:start position:0% +overexposed but i even got the blue +channel overexposed so it just looked + + align:start position:0% +channel overexposed so it just looked + + + align:start position:0% +channel overexposed so it just looked +white it you know it had + + align:start position:0% +white it you know it had + + + align:start position:0% +white it you know it had +more than the maximum intensity that the + + align:start position:0% +more than the maximum intensity that the + + + align:start position:0% +more than the maximum intensity that the +film could handle + + align:start position:0% +film could handle + + + align:start position:0% +film could handle +in all three channels anyway so + + align:start position:0% +in all three channels anyway so + + + align:start position:0% +in all three channels anyway so +this comes up a lot in other situations + + align:start position:0% +this comes up a lot in other situations + + + align:start position:0% +this comes up a lot in other situations +in x-ray imaging + + align:start position:0% +in x-ray imaging + + + align:start position:0% +in x-ray imaging +it's slightly different it's cosine + + align:start position:0% +it's slightly different it's cosine + + + align:start position:0% +it's slightly different it's cosine +cubed + + align:start position:0% +cubed + + + align:start position:0% +cubed +but it's something that people often + + align:start position:0% +but it's something that people often + + + align:start position:0% +but it's something that people often +forget about and as i said you can kind + + align:start position:0% +forget about and as i said you can kind + + + align:start position:0% +forget about and as i said you can kind +of forget about it because it's + + align:start position:0% +of forget about it because it's + + + align:start position:0% +of forget about it because it's +something you can compensate for + + align:start position:0% +something you can compensate for + + + align:start position:0% +something you can compensate for +you just in your image processing chain + + align:start position:0% +you just in your image processing chain + + + align:start position:0% +you just in your image processing chain +it doesn't change from image to image + + align:start position:0% +it doesn't change from image to image + + + align:start position:0% +it doesn't change from image to image +unless you change the lens and + + align:start position:0% +unless you change the lens and + + + align:start position:0% +unless you change the lens and +and the uh + + align:start position:0% +and the uh + + + align:start position:0% +and the uh +yeah okay + + align:start position:0% +yeah okay + + + align:start position:0% +yeah okay +so + + align:start position:0% +so + + + align:start position:0% +so +so that this formula is uh central + + align:start position:0% +so that this formula is uh central + + + align:start position:0% +so that this formula is uh central +um not because we're going to play a lot + + align:start position:0% +um not because we're going to play a lot + + + align:start position:0% +um not because we're going to play a lot +with it but just because + + align:start position:0% +with it but just because + + + align:start position:0% +with it but just because +it justifies uh this whole idea of + + align:start position:0% +it justifies uh this whole idea of + + + align:start position:0% +it justifies uh this whole idea of +talking about brightness + + align:start position:0% +talking about brightness + + + align:start position:0% +talking about brightness +and measuring it using gray levels in + + align:start position:0% +and measuring it using gray levels in + + + align:start position:0% +and measuring it using gray levels in +the image and + + align:start position:0% +the image and + + + align:start position:0% +the image and +thinking that that has something to do + + align:start position:0% +thinking that that has something to do + + + align:start position:0% +thinking that that has something to do +with + + align:start position:0% +with + + + align:start position:0% +with +what's out in the real world + + align:start position:0% +what's out in the real world + + + align:start position:0% +what's out in the real world +okay uh + + align:start position:0% +okay uh + + + align:start position:0% +okay uh +so that that + + align:start position:0% +so that that + + + align:start position:0% +so that that +that's our + + align:start position:0% +that's our + + + align:start position:0% +that's our +description of what the camera does in + + align:start position:0% +description of what the camera does in + + + align:start position:0% +description of what the camera does in +terms of brightness so this is the + + align:start position:0% +terms of brightness so this is the + + + align:start position:0% +terms of brightness so this is the +counterpart to + + align:start position:0% +counterpart to + + + align:start position:0% +counterpart to +what it does in terms of position which + + align:start position:0% +what it does in terms of position which + + + align:start position:0% +what it does in terms of position which +was the perspective projection equation + + align:start position:0% +was the perspective projection equation + + + align:start position:0% +was the perspective projection equation +which of course was trivial in + + align:start position:0% +which of course was trivial in + + + align:start position:0% +which of course was trivial in +comparison but those are the two key + + align:start position:0% +comparison but those are the two key + + + align:start position:0% +comparison but those are the two key +uh you know cornerstones of + + align:start position:0% +uh you know cornerstones of + + + align:start position:0% +uh you know cornerstones of +understanding of cameras + + align:start position:0% +understanding of cameras + + + align:start position:0% +understanding of cameras +okay so now that we know what it is + + align:start position:0% +okay so now that we know what it is + + + align:start position:0% +okay so now that we know what it is +we're measuring + + align:start position:0% +we're measuring + + + align:start position:0% +we're measuring +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +well we already knew it was the power + + align:start position:0% +well we already knew it was the power + + + align:start position:0% +well we already knew it was the power +per unit area we're measuring but now we + + align:start position:0% +per unit area we're measuring but now we + + + align:start position:0% +per unit area we're measuring but now we +also know that that corresponds to + + align:start position:0% + + + + align:start position:0% + +radians in the world + + align:start position:0% +radians in the world + + + align:start position:0% +radians in the world +we need to try and understand what + + align:start position:0% +we need to try and understand what + + + align:start position:0% +we need to try and understand what +determines the radians in the world and + + align:start position:0% +determines the radians in the world and + + + align:start position:0% +determines the radians in the world and +we already mentioned it depends on the + + align:start position:0% +we already mentioned it depends on the + + + align:start position:0% +we already mentioned it depends on the +illumination it depends on the material + + align:start position:0% +illumination it depends on the material + + + align:start position:0% +illumination it depends on the material +it depends on orientation so let's try + + align:start position:0% +it depends on orientation so let's try + + + align:start position:0% +it depends on orientation so let's try +and make that a little bit clearer + + align:start position:0% +and make that a little bit clearer + + + align:start position:0% +and make that a little bit clearer +and + + align:start position:0% + + + + align:start position:0% + +and talk about the + + align:start position:0% +and talk about the + + + align:start position:0% +and talk about the +bi-directional reflectance distribution + + align:start position:0% +bi-directional reflectance distribution + + + align:start position:0% +bi-directional reflectance distribution +function + + align:start position:0% +function + + + align:start position:0% +function +so let me tell you that until + + align:start position:0% +so let me tell you that until + + + align:start position:0% +so let me tell you that until +i don't know the the 80s + + align:start position:0% +i don't know the the 80s + + + align:start position:0% +i don't know the the 80s +this field was a complete mess and there + + align:start position:0% +this field was a complete mess and there + + + align:start position:0% +this field was a complete mess and there +were dozens of different terms all + + align:start position:0% +were dozens of different terms all + + + align:start position:0% +were dozens of different terms all +competing for attention some of whom had + + align:start position:0% +competing for attention some of whom had + + + align:start position:0% +competing for attention some of whom had +famous people's names on them and some + + align:start position:0% +famous people's names on them and some + + + align:start position:0% +famous people's names on them and some +didn't and + + align:start position:0% +didn't and + + + align:start position:0% +didn't and +and then + + align:start position:0% +and then + + + align:start position:0% +and then +the national bureau of standards stepped + + align:start position:0% +the national bureau of standards stepped + + + align:start position:0% +the national bureau of standards stepped +in and a brilliant man named + + align:start position:0% +in and a brilliant man named + + + align:start position:0% +in and a brilliant man named +nicodemus + + align:start position:0% +nicodemus + + + align:start position:0% +nicodemus +cleaned it up + + align:start position:0% +cleaned it up + + + align:start position:0% +cleaned it up +and + + align:start position:0% +and + + + align:start position:0% +and +who knows maybe the last thing the + + align:start position:0% +who knows maybe the last thing the + + + align:start position:0% +who knows maybe the last thing the +national bureau standard did that was + + align:start position:0% +national bureau standard did that was + + + align:start position:0% +national bureau standard did that was +very interesting but it was a very + + align:start position:0% +very interesting but it was a very + + + align:start position:0% +very interesting but it was a very +powerful effect on imaging + + align:start position:0% +powerful effect on imaging + + + align:start position:0% +powerful effect on imaging +not just optical but x-ray as well and + + align:start position:0% +not just optical but x-ray as well and + + + align:start position:0% +not just optical but x-ray as well and +so what is this well + + align:start position:0% +so what is this well + + + align:start position:0% +so what is this well +the idea is that + + align:start position:0% +the idea is that + + + align:start position:0% +the idea is that +we have light coming in + + align:start position:0% +we have light coming in + + + align:start position:0% +we have light coming in +and we have light going out + + align:start position:0% +and we have light going out + + + align:start position:0% +and we have light going out +and + + align:start position:0% +and + + + align:start position:0% +and +you know crudely speaking when we talk + + align:start position:0% +you know crudely speaking when we talk + + + align:start position:0% +you know crudely speaking when we talk +about reflectance the ratio of those two + + align:start position:0% +about reflectance the ratio of those two + + + align:start position:0% +about reflectance the ratio of those two +things is reflectance right so so + + align:start position:0% +things is reflectance right so so + + + align:start position:0% +things is reflectance right so so +cruelly speaking + + align:start position:0% +cruelly speaking + + + align:start position:0% +cruelly speaking +something that's white reflects all of + + align:start position:0% +something that's white reflects all of + + + align:start position:0% +something that's white reflects all of +the light coming in something that's + + align:start position:0% +the light coming in something that's + + + align:start position:0% +the light coming in something that's +black reflects none of it + + align:start position:0% +black reflects none of it + + + align:start position:0% +black reflects none of it +but you know where is that light going + + align:start position:0% +but you know where is that light going + + + align:start position:0% +but you know where is that light going +so it's not as simple as just saying oh + + align:start position:0% +so it's not as simple as just saying oh + + + align:start position:0% +so it's not as simple as just saying oh +reflectance is 0.3 + + align:start position:0% +reflectance is 0.3 + + + align:start position:0% +reflectance is 0.3 +it's more nuanced and and that's what + + align:start position:0% +it's more nuanced and and that's what + + + align:start position:0% +it's more nuanced and and that's what +this is about so this basically + + align:start position:0% +this is about so this basically + + + align:start position:0% +this is about so this basically +is a quantity + + align:start position:0% + + + + align:start position:0% + +that depends on the incident and the + + align:start position:0% +that depends on the incident and the + + + align:start position:0% +that depends on the incident and the +emitted direction and it tells you + + align:start position:0% +emitted direction and it tells you + + + align:start position:0% +emitted direction and it tells you +how bright the surface will appear so so + + align:start position:0% +how bright the surface will appear so so + + + align:start position:0% +how bright the surface will appear so so +let's uh look at it so we have a patch + + align:start position:0% +let's uh look at it so we have a patch + + + align:start position:0% +let's uh look at it so we have a patch +of the surface a usual diagram + + align:start position:0% +of the surface a usual diagram + + + align:start position:0% +of the surface a usual diagram +should have a rubber stamp for that + + align:start position:0% +should have a rubber stamp for that + + + align:start position:0% +should have a rubber stamp for that +and + + align:start position:0% +and + + + align:start position:0% +and +we have light coming in + + align:start position:0% +we have light coming in + + + align:start position:0% +we have light coming in +and we have light going out + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +how how bright the surface will appear + + align:start position:0% +how how bright the surface will appear + + + align:start position:0% +how how bright the surface will appear +its radiance will depend on those angles + + align:start position:0% +its radiance will depend on those angles + + + align:start position:0% +its radiance will depend on those angles +but more + + align:start position:0% +but more + + + align:start position:0% +but more +uh because this is in 3d + + align:start position:0% +uh because this is in 3d + + + align:start position:0% +uh because this is in 3d +i've drawn it on a plane but it's of + + align:start position:0% +i've drawn it on a plane but it's of + + + align:start position:0% +i've drawn it on a plane but it's of +course really in 3d so i really need to + + align:start position:0% +course really in 3d so i really need to + + + align:start position:0% +course really in 3d so i really need to +talk about the directions of these two + + align:start position:0% +talk about the directions of these two + + + align:start position:0% +talk about the directions of these two +rays + + align:start position:0% +rays + + + align:start position:0% +rays +in more detail than just saying they + + align:start position:0% +in more detail than just saying they + + + align:start position:0% +in more detail than just saying they +make an angle with the surface normal + + align:start position:0% +make an angle with the surface normal + + + align:start position:0% +make an angle with the surface normal +and so how do i talk about + + align:start position:0% +and so how do i talk about + + + align:start position:0% +and so how do i talk about +directions well we've already been + + align:start position:0% +directions well we've already been + + + align:start position:0% +directions well we've already been +through this unit vectors + + align:start position:0% +through this unit vectors + + + align:start position:0% +through this unit vectors +points on the sphere + + align:start position:0% + + + + align:start position:0% + +latitude longitude + + align:start position:0% + + + + align:start position:0% + +so in this field it's customary to use + + align:start position:0% +so in this field it's customary to use + + + align:start position:0% +so in this field it's customary to use +um + + align:start position:0% +um + + + align:start position:0% +um +these angles + + align:start position:0% +these angles + + + align:start position:0% +these angles +so let's suppose that + + align:start position:0% +so let's suppose that + + + align:start position:0% +so let's suppose that +this line down this curve down here is + + align:start position:0% +this line down this curve down here is + + + align:start position:0% +this line down this curve down here is +is in the surface and i've constructed + + align:start position:0% +is in the surface and i've constructed + + + align:start position:0% +is in the surface and i've constructed +the hemisphere above it + + align:start position:0% +the hemisphere above it + + + align:start position:0% +the hemisphere above it +and this is called the polar angle + + align:start position:0% + + + + align:start position:0% + +also called cold latitude + + align:start position:0% +also called cold latitude + + + align:start position:0% +also called cold latitude +why because it's 90 degrees minus + + align:start position:0% +why because it's 90 degrees minus + + + align:start position:0% +why because it's 90 degrees minus +latitude + + align:start position:0% +latitude + + + align:start position:0% +latitude +and this is called azimuth + + align:start position:0% +and this is called azimuth + + + align:start position:0% +and this is called azimuth +azimuth angle + + align:start position:0% +azimuth angle + + + align:start position:0% +azimuth angle +so + + align:start position:0% +so + + + align:start position:0% +so +to specify the direction of light coming + + align:start position:0% +to specify the direction of light coming + + + align:start position:0% +to specify the direction of light coming +in or light going out i need two angles + + align:start position:0% +in or light going out i need two angles + + + align:start position:0% +in or light going out i need two angles +polar angle and azimuth + + align:start position:0% +polar angle and azimuth + + + align:start position:0% +polar angle and azimuth +and so here i've only shown + + align:start position:0% +and so here i've only shown + + + align:start position:0% +and so here i've only shown +the polar angle + + align:start position:0% +the polar angle + + + align:start position:0% +the polar angle +and to draw the azimuth i'd have to + + align:start position:0% +and to draw the azimuth i'd have to + + + align:start position:0% +and to draw the azimuth i'd have to +project this down into the plane of the + + align:start position:0% +project this down into the plane of the + + + align:start position:0% +project this down into the plane of the +surface + + align:start position:0% + + + + align:start position:0% + +and then look at + + align:start position:0% +and then look at + + + align:start position:0% +and then look at +the direction of those lines + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +then + + align:start position:0% +then + + + align:start position:0% +then +since the brightness + + align:start position:0% +since the brightness + + + align:start position:0% +since the brightness +is going to depend on all of those + + align:start position:0% +is going to depend on all of those + + + align:start position:0% +is going to depend on all of those +i can write it as some function like + + align:start position:0% +i can write it as some function like + + + align:start position:0% +i can write it as some function like +this and + + align:start position:0% +this and + + + align:start position:0% +this and +the official terminology is that's the + + align:start position:0% +the official terminology is that's the + + + align:start position:0% +the official terminology is that's the +bi-directional reflectance distribution + + align:start position:0% +bi-directional reflectance distribution + + + align:start position:0% +bi-directional reflectance distribution +function + + align:start position:0% + + + + align:start position:0% + +and as we said uh reflectance should be + + align:start position:0% +and as we said uh reflectance should be + + + align:start position:0% +and as we said uh reflectance should be +you know power going out divided by + + align:start position:0% +you know power going out divided by + + + align:start position:0% +you know power going out divided by +power going in + + align:start position:0% +power going in + + + align:start position:0% +power going in +and so that's that's what this is you + + align:start position:0% +and so that's that's what this is you + + + align:start position:0% +and so that's that's what this is you +know clean and formalized so what we've + + align:start position:0% +know clean and formalized so what we've + + + align:start position:0% +know clean and formalized so what we've +got is it's the radiance you know how + + align:start position:0% +got is it's the radiance you know how + + + align:start position:0% +got is it's the radiance you know how +bright the object will appear when + + align:start position:0% +bright the object will appear when + + + align:start position:0% +bright the object will appear when +viewed from this position + + align:start position:0% +viewed from this position + + + align:start position:0% +viewed from this position +divided by how much energy i'm putting + + align:start position:0% +divided by how much energy i'm putting + + + align:start position:0% +divided by how much energy i'm putting +in from the source direction + + align:start position:0% +in from the source direction + + + align:start position:0% +in from the source direction +so so this is + + align:start position:0% +so so this is + + + align:start position:0% +so so this is +finally + + align:start position:0% +finally + + + align:start position:0% +finally +a sense uh definition of reflectance + + align:start position:0% +a sense uh definition of reflectance + + + align:start position:0% +a sense uh definition of reflectance +that actually works + + align:start position:0% +that actually works + + + align:start position:0% +that actually works +right good because the other definition + + align:start position:0% +right good because the other definition + + + align:start position:0% +right good because the other definition +of just saying oh it's 0.3 or something + + align:start position:0% +of just saying oh it's 0.3 or something + + + align:start position:0% +of just saying oh it's 0.3 or something +doesn't unfortunately this is much more + + align:start position:0% +doesn't unfortunately this is much more + + + align:start position:0% +doesn't unfortunately this is much more +complicated but + + align:start position:0% +complicated but + + + align:start position:0% +complicated but +but any other definition of reflectance + + align:start position:0% +but any other definition of reflectance + + + align:start position:0% +but any other definition of reflectance +can be based on this basically it's an + + align:start position:0% +can be based on this basically it's an + + + align:start position:0% +can be based on this basically it's an +integral of this + + align:start position:0% +integral of this + + + align:start position:0% +integral of this +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so um + + align:start position:0% +so um + + + align:start position:0% +so um +well there are lots of questions that + + align:start position:0% +well there are lots of questions that + + + align:start position:0% +well there are lots of questions that +immediately come up one of them is you + + align:start position:0% +immediately come up one of them is you + + + align:start position:0% +immediately come up one of them is you +know how on earth + + align:start position:0% +know how on earth + + + align:start position:0% +know how on earth +do you measure this thing + + align:start position:0% +do you measure this thing + + + align:start position:0% +do you measure this thing +well + + align:start position:0% +well + + + align:start position:0% +well +one way you can do it is + + align:start position:0% +one way you can do it is + + + align:start position:0% +one way you can do it is +you know put the light source in a + + align:start position:0% +you know put the light source in a + + + align:start position:0% +you know put the light source in a +certain position put your camera in a + + align:start position:0% +certain position put your camera in a + + + align:start position:0% +certain position put your camera in a +certain position + + align:start position:0% +certain position + + + align:start position:0% +certain position +take a measurement then move your camera + + align:start position:0% +take a measurement then move your camera + + + align:start position:0% +take a measurement then move your camera +blah blah blah + + align:start position:0% +blah blah blah + + + align:start position:0% +blah blah blah +move your light source + + align:start position:0% +move your light source + + + align:start position:0% +move your light source +but you're exploring a four-dimensional + + align:start position:0% +but you're exploring a four-dimensional + + + align:start position:0% +but you're exploring a four-dimensional +space so that's pretty expensive + + align:start position:0% +space so that's pretty expensive + + + align:start position:0% +space so that's pretty expensive +nevertheless it's done and one one + + align:start position:0% +nevertheless it's done and one one + + + align:start position:0% +nevertheless it's done and one one +method is using goniometers + + align:start position:0% +method is using goniometers + + + align:start position:0% +method is using goniometers +but just a fancy way of saying + + align:start position:0% +but just a fancy way of saying + + + align:start position:0% +but just a fancy way of saying +angle measurement devices + + align:start position:0% +angle measurement devices + + + align:start position:0% +angle measurement devices +so + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +what i'm trying to draw here is + + align:start position:0% +what i'm trying to draw here is + + + align:start position:0% +what i'm trying to draw here is +something that will rotate about this + + align:start position:0% +something that will rotate about this + + + align:start position:0% +something that will rotate about this +vertical axis + + align:start position:0% +vertical axis + + + align:start position:0% +vertical axis +and then has a + + align:start position:0% +and then has a + + + align:start position:0% +and then has a +an arc + + align:start position:0% +an arc + + + align:start position:0% +an arc +along which the apparatus can move + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +the first rotation corresponds to the + + align:start position:0% +the first rotation corresponds to the + + + align:start position:0% +the first rotation corresponds to the +azimuth angle + + align:start position:0% +azimuth angle + + + align:start position:0% +azimuth angle +and the second movement corresponds to + + align:start position:0% +and the second movement corresponds to + + + align:start position:0% +and the second movement corresponds to +the polar angle so the pole would be up + + align:start position:0% +the polar angle so the pole would be up + + + align:start position:0% +the polar angle so the pole would be up +here i can + + align:start position:0% +here i can + + + align:start position:0% +here i can +and so we can mount the light sensor on + + align:start position:0% +and so we can mount the light sensor on + + + align:start position:0% +and so we can mount the light sensor on +one of these + + align:start position:0% +one of these + + + align:start position:0% +one of these +then we get a second one and we mount + + align:start position:0% +then we get a second one and we mount + + + align:start position:0% +then we get a second one and we mount +the light source on it as well + + align:start position:0% +the light source on it as well + + + align:start position:0% +the light source on it as well +and uh + + align:start position:0% + + + + align:start position:0% + +then we make measurements well you'll + + align:start position:0% +then we make measurements well you'll + + + align:start position:0% +then we make measurements well you'll +get you know tired of it pretty soon + + align:start position:0% +get you know tired of it pretty soon + + + align:start position:0% +get you know tired of it pretty soon +because you're exploring this four + + align:start position:0% +because you're exploring this four + + + align:start position:0% +because you're exploring this four +dimensional space and even if you sample + + align:start position:0% +dimensional space and even if you sample + + + align:start position:0% +dimensional space and even if you sample +it pretty coarsely like you know one in + + align:start position:0% +it pretty coarsely like you know one in + + + align:start position:0% +it pretty coarsely like you know one in +ten you're not talking about 10 000 + + align:start position:0% +ten you're not talking about 10 000 + + + align:start position:0% +ten you're not talking about 10 000 +measurements + + align:start position:0% +measurements + + + align:start position:0% +measurements +but of course you can automate it you + + align:start position:0% +but of course you can automate it you + + + align:start position:0% +but of course you can automate it you +can you know build a + + align:start position:0% +can you know build a + + + align:start position:0% +can you know build a +robotic device that + + align:start position:0% +robotic device that + + + align:start position:0% +robotic device that +mechanically moves this and you know go + + align:start position:0% +mechanically moves this and you know go + + + align:start position:0% +mechanically moves this and you know go +away for the weekend and it'll do these + + align:start position:0% +away for the weekend and it'll do these + + + align:start position:0% +away for the weekend and it'll do these +measurements for you + + align:start position:0% + + + + align:start position:0% + +if you're in a hurry as people in + + align:start position:0% + + + + align:start position:0% + +movie making are + + align:start position:0% +movie making are + + + align:start position:0% +movie making are +you can have many light sources that you + + align:start position:0% +you can have many light sources that you + + + align:start position:0% +you can have many light sources that you +can turn on and off so you could + + align:start position:0% +can turn on and off so you could + + + align:start position:0% +can turn on and off so you could +construct + + align:start position:0% +construct + + + align:start position:0% +construct +maybe a whole sphere or maybe a + + align:start position:0% +maybe a whole sphere or maybe a + + + align:start position:0% +maybe a whole sphere or maybe a +hemisphere + + align:start position:0% +hemisphere + + + align:start position:0% +hemisphere +and you distribute light sources all + + align:start position:0% +and you distribute light sources all + + + align:start position:0% +and you distribute light sources all +over the + + align:start position:0% + + + + align:start position:0% + +surface that can be individually + + align:start position:0% +surface that can be individually + + + align:start position:0% +surface that can be individually +controlled + + align:start position:0% +controlled + + + align:start position:0% +controlled +and then if you want to so that takes + + align:start position:0% +and then if you want to so that takes + + + align:start position:0% +and then if you want to so that takes +care of two of the angles + + align:start position:0% +care of two of the angles + + + align:start position:0% +care of two of the angles +so right so by picking + + align:start position:0% +so right so by picking + + + align:start position:0% +so right so by picking +by turning on one of these light sources + + align:start position:0% +by turning on one of these light sources + + + align:start position:0% +by turning on one of these light sources +you've controlled one of the goniometers + + align:start position:0% +you've controlled one of the goniometers + + + align:start position:0% +you've controlled one of the goniometers +to position the light source and then + + align:start position:0% +to position the light source and then + + + align:start position:0% +to position the light source and then +you can have light sensors or perhaps + + align:start position:0% +you can have light sensors or perhaps + + + align:start position:0% +you can have light sensors or perhaps +even cameras + + align:start position:0% +even cameras + + + align:start position:0% +even cameras +interspersed + + align:start position:0% + + + + align:start position:0% + +and now you can do all of your + + align:start position:0% +and now you can do all of your + + + align:start position:0% +and now you can do all of your +measurements very quickly + + align:start position:0% +measurements very quickly + + + align:start position:0% +measurements very quickly +because you just + + align:start position:0% +because you just + + + align:start position:0% +because you just +flash one source at a time + + align:start position:0% +flash one source at a time + + + align:start position:0% +flash one source at a time +and take pictures and then + + align:start position:0% +and take pictures and then + + + align:start position:0% +and take pictures and then +process the images you get + + align:start position:0% +process the images you get + + + align:start position:0% +process the images you get +to + + align:start position:0% +to + + + align:start position:0% +to +then why would you want to do this well + + align:start position:0% +then why would you want to do this well + + + align:start position:0% +then why would you want to do this well +suppose you want to realistically + + align:start position:0% +suppose you want to realistically + + + align:start position:0% +suppose you want to realistically +model how someone's skin reflects light + + align:start position:0% +model how someone's skin reflects light + + + align:start position:0% +model how someone's skin reflects light +well you could try and build some + + align:start position:0% +well you could try and build some + + + align:start position:0% +well you could try and build some +mathematical model but who knows how + + align:start position:0% +mathematical model but who knows how + + + align:start position:0% +mathematical model but who knows how +good that is the better way is just to + + align:start position:0% +good that is the better way is just to + + + align:start position:0% +good that is the better way is just to +measure it and + + align:start position:0% +measure it and + + + align:start position:0% +measure it and +so that's something people do you don't + + align:start position:0% +so that's something people do you don't + + + align:start position:0% +so that's something people do you don't +want to approximate it with i don't know + + align:start position:0% +want to approximate it with i don't know + + + align:start position:0% +want to approximate it with i don't know +lambertian or some other well-known + + align:start position:0% +lambertian or some other well-known + + + align:start position:0% +lambertian or some other well-known +model you you want the real thing and so + + align:start position:0% +model you you want the real thing and so + + + align:start position:0% +model you you want the real thing and so +uh you you can do this + + align:start position:0% +uh you you can do this + + + align:start position:0% +uh you you can do this +um + + align:start position:0% +um + + + align:start position:0% +um +so that's part of the story of this + + align:start position:0% +so that's part of the story of this + + + align:start position:0% +so that's part of the story of this +four-dimensional space the next part is + + align:start position:0% +four-dimensional space the next part is + + + align:start position:0% +four-dimensional space the next part is +that well in most cases it's not + + align:start position:0% +that well in most cases it's not + + + align:start position:0% +that well in most cases it's not +four-dimensional + + align:start position:0% +four-dimensional + + + align:start position:0% +four-dimensional +okay and i think if you + + align:start position:0% +okay and i think if you + + + align:start position:0% +okay and i think if you +look at this diagram + + align:start position:0% +look at this diagram + + + align:start position:0% +look at this diagram +you can see that what really matters + + align:start position:0% +you can see that what really matters + + + align:start position:0% +you can see that what really matters +is + + align:start position:0% +is + + + align:start position:0% +is +the angle between these two azimuth + + align:start position:0% +the angle between these two azimuth + + + align:start position:0% +the angle between these two azimuth +lines + + align:start position:0% + + + + align:start position:0% + +so this is a general formula that + + align:start position:0% +so this is a general formula that + + + align:start position:0% +so this is a general formula that +applies to any surface + + align:start position:0% +applies to any surface + + + align:start position:0% +applies to any surface +but for many surfaces what really only + + align:start position:0% +but for many surfaces what really only + + + align:start position:0% +but for many surfaces what really only +matters is the difference between these + + align:start position:0% +matters is the difference between these + + + align:start position:0% +matters is the difference between these +two angles and what type of surfaces are + + align:start position:0% +two angles and what type of surfaces are + + + align:start position:0% +two angles and what type of surfaces are +those well those are surfaces where if + + align:start position:0% +those well those are surfaces where if + + + align:start position:0% +those well those are surfaces where if +you rotate them in the plane + + align:start position:0% +you rotate them in the plane + + + align:start position:0% +you rotate them in the plane +you know perpend if you rotate them + + align:start position:0% +you know perpend if you rotate them + + + align:start position:0% +you know perpend if you rotate them +about their surface normal they don't + + align:start position:0% +about their surface normal they don't + + + align:start position:0% +about their surface normal they don't +change brightness + + align:start position:0% +change brightness + + + align:start position:0% +change brightness +so + + align:start position:0% +so + + + align:start position:0% +so +that you know it's pretty pretty much + + align:start position:0% +that you know it's pretty pretty much + + + align:start position:0% +that you know it's pretty pretty much +true of this thing and it's pretty much + + align:start position:0% +true of this thing and it's pretty much + + + align:start position:0% +true of this thing and it's pretty much +true of of lots of things like you know + + align:start position:0% +true of of lots of things like you know + + + align:start position:0% +true of of lots of things like you know +wood and + + align:start position:0% +wood and + + + align:start position:0% +wood and +um this floor and so on so that's a + + align:start position:0% +um this floor and so on so that's a + + + align:start position:0% +um this floor and so on so that's a +dramatic improvement because now you've + + align:start position:0% +dramatic improvement because now you've + + + align:start position:0% +dramatic improvement because now you've +got a 3d lookup table to fill in instead + + align:start position:0% +got a 3d lookup table to fill in instead + + + align:start position:0% +got a 3d lookup table to fill in instead +of 4d + + align:start position:0% +of 4d + + + align:start position:0% +of 4d +so + + align:start position:0% + + + + align:start position:0% + +what kind of materials are there that do + + align:start position:0% +what kind of materials are there that do + + + align:start position:0% +what kind of materials are there that do +not + + align:start position:0% +not + + + align:start position:0% +not +satisfy this + + align:start position:0% +satisfy this + + + align:start position:0% +satisfy this +what materials + + align:start position:0% +what materials + + + align:start position:0% +what materials +require that we take the full + + align:start position:0% +require that we take the full + + + align:start position:0% +require that we take the full +four dimensions into account where + + align:start position:0% + + + + align:start position:0% + +you know and think about it is there a + + align:start position:0% +you know and think about it is there a + + + align:start position:0% +you know and think about it is there a +surface where if you look at it and you + + align:start position:0% +surface where if you look at it and you + + + align:start position:0% +surface where if you look at it and you +rotate it in the plane of the surface it + + align:start position:0% +rotate it in the plane of the surface it + + + align:start position:0% +rotate it in the plane of the surface it +changes appearance can you think of + + align:start position:0% +changes appearance can you think of + + + align:start position:0% +changes appearance can you think of +something like that + + align:start position:0% + + + + align:start position:0% + +something that's iridescent + + align:start position:0% +something that's iridescent + + + align:start position:0% +something that's iridescent +why because an iridescent material has + + align:start position:0% +why because an iridescent material has + + + align:start position:0% +why because an iridescent material has +microstructure that's oriented + + align:start position:0% +microstructure that's oriented + + + align:start position:0% +microstructure that's oriented +and you know like a hummingbird's + + align:start position:0% +and you know like a hummingbird's + + + align:start position:0% +and you know like a hummingbird's +neck + + align:start position:0% +neck + + + align:start position:0% +neck +the feathers are lined up + + align:start position:0% +the feathers are lined up + + + align:start position:0% +the feathers are lined up +it produces the color not by pigment but + + align:start position:0% +it produces the color not by pigment but + + + align:start position:0% +it produces the color not by pigment but +by + + align:start position:0% +by + + + align:start position:0% +by +interference and so if the + + align:start position:0% +interference and so if the + + + align:start position:0% +interference and so if the +microstructure you know with my fingers + + align:start position:0% +microstructure you know with my fingers + + + align:start position:0% +microstructure you know with my fingers +and then i rotate that microstructure + + align:start position:0% +and then i rotate that microstructure + + + align:start position:0% +and then i rotate that microstructure +it'll diffract light differently so the + + align:start position:0% +it'll diffract light differently so the + + + align:start position:0% +it'll diffract light differently so the +the uh our ruby hummingbirds if you look + + align:start position:0% +the uh our ruby hummingbirds if you look + + + align:start position:0% +the uh our ruby hummingbirds if you look +at the neck of the male from the wrong + + align:start position:0% +at the neck of the male from the wrong + + + align:start position:0% +at the neck of the male from the wrong +angle it looks black + + align:start position:0% +angle it looks black + + + align:start position:0% +angle it looks black +why because it's reflecting all of the + + align:start position:0% +why because it's reflecting all of the + + + align:start position:0% +why because it's reflecting all of the +light in one direction and it's and it's + + align:start position:0% +light in one direction and it's and it's + + + align:start position:0% +light in one direction and it's and it's +only the red so so that's an example of + + align:start position:0% +only the red so so that's an example of + + + align:start position:0% +only the red so so that's an example of +something where unfortunately you need + + align:start position:0% +something where unfortunately you need + + + align:start position:0% +something where unfortunately you need +the full + + align:start position:0% +the full + + + align:start position:0% +the full +the full model you can't + + align:start position:0% +the full model you can't + + + align:start position:0% +the full model you can't +reduce + + align:start position:0% +reduce + + + align:start position:0% +reduce +and you uh use this so and the other + + align:start position:0% +and you uh use this so and the other + + + align:start position:0% +and you uh use this so and the other +examples like the + + align:start position:0% +examples like the + + + align:start position:0% +examples like the +semi-precious stones called tiger eye or + + align:start position:0% +semi-precious stones called tiger eye or + + + align:start position:0% +semi-precious stones called tiger eye or +various other things they're basically + + align:start position:0% +various other things they're basically + + + align:start position:0% +various other things they're basically +very fancy forms of asbestos and you + + align:start position:0% +very fancy forms of asbestos and you + + + align:start position:0% +very fancy forms of asbestos and you +people don't people don't call them that + + align:start position:0% +people don't people don't call them that + + + align:start position:0% +people don't people don't call them that +because you know as soon as you say + + align:start position:0% +because you know as soon as you say + + + align:start position:0% +because you know as soon as you say +asbestos + + align:start position:0% +asbestos + + + align:start position:0% +asbestos +lawyers come and so on but it's + + align:start position:0% +lawyers come and so on but it's + + + align:start position:0% +lawyers come and so on but it's +basically + + align:start position:0% +basically + + + align:start position:0% +basically +just as asbestos it has a microstructure + + align:start position:0% +just as asbestos it has a microstructure + + + align:start position:0% +just as asbestos it has a microstructure +that's very linear and very tightly + + align:start position:0% +that's very linear and very tightly + + + align:start position:0% +that's very linear and very tightly +packed on the scale of the wavelength of + + align:start position:0% +packed on the scale of the wavelength of + + + align:start position:0% +packed on the scale of the wavelength of +light and so it has a very different + + align:start position:0% +light and so it has a very different + + + align:start position:0% +light and so it has a very different +appearance as you rotate it which gives + + align:start position:0% +appearance as you rotate it which gives + + + align:start position:0% +appearance as you rotate it which gives +it its appeal as a piece of jewelry + + align:start position:0% +it its appeal as a piece of jewelry + + + align:start position:0% +it its appeal as a piece of jewelry +then you know some people have + + align:start position:0% +then you know some people have + + + align:start position:0% +then you know some people have +very straight black hair that's very + + align:start position:0% +very straight black hair that's very + + + align:start position:0% +very straight black hair that's very +parallel + + align:start position:0% +parallel + + + align:start position:0% +parallel +and that will have the same effect where + + align:start position:0% +and that will have the same effect where + + + align:start position:0% +and that will have the same effect where +because they're all parallel they'll + + align:start position:0% +because they're all parallel they'll + + + align:start position:0% +because they're all parallel they'll +reflect light in a certain way and so as + + align:start position:0% +reflect light in a certain way and so as + + + align:start position:0% +reflect light in a certain way and so as +their head rotates the sheen on the on + + align:start position:0% +their head rotates the sheen on the on + + + align:start position:0% +their head rotates the sheen on the on +that hair will will move and so it + + align:start position:0% +that hair will will move and so it + + + align:start position:0% +that hair will will move and so it +you need the full four-dimensional model + + align:start position:0% +you need the full four-dimensional model + + + align:start position:0% +you need the full four-dimensional model +for that whereas for a lot of things + + align:start position:0% +for that whereas for a lot of things + + + align:start position:0% +for that whereas for a lot of things +like paper and snow and you know + + align:start position:0% +like paper and snow and you know + + + align:start position:0% +like paper and snow and you know +strawberries + + align:start position:0% +strawberries + + + align:start position:0% +strawberries +the three-dimensional + + align:start position:0% +the three-dimensional + + + align:start position:0% +the three-dimensional +model is is + + align:start position:0% +model is is + + + align:start position:0% +model is is +so + + align:start position:0% +so + + + align:start position:0% +so +what else do we know about this + + align:start position:0% +what else do we know about this + + + align:start position:0% +what else do we know about this +bi-directional reflectance function well + + align:start position:0% +bi-directional reflectance function well + + + align:start position:0% +bi-directional reflectance function well +there's an important property + + align:start position:0% +there's an important property + + + align:start position:0% +there's an important property +due to helmholtz + + align:start position:0% + + + + align:start position:0% + +called the helmholtz reciprocity + + align:start position:0% +called the helmholtz reciprocity + + + align:start position:0% +called the helmholtz reciprocity +now helmholtz of course lived a long + + align:start position:0% +now helmholtz of course lived a long + + + align:start position:0% +now helmholtz of course lived a long +long time ago but long before nicodemus + + align:start position:0% +long time ago but long before nicodemus + + + align:start position:0% +long time ago but long before nicodemus +of the national bureau of standards so + + align:start position:0% +of the national bureau of standards so + + + align:start position:0% +of the national bureau of standards so +how could he have come up with a + + align:start position:0% +how could he have come up with a + + + align:start position:0% +how could he have come up with a +property of the bi-directional + + align:start position:0% +property of the bi-directional + + + align:start position:0% +property of the bi-directional +reflectance distribution function well + + align:start position:0% +reflectance distribution function well + + + align:start position:0% +reflectance distribution function well +he didn't call it that but he had the + + align:start position:0% +he didn't call it that but he had the + + + align:start position:0% +he didn't call it that but he had the +basic idea which was you know basically + + align:start position:0% +basic idea which was you know basically + + + align:start position:0% +basic idea which was you know basically +second law of thermodynamics + + align:start position:0% + + + + align:start position:0% + +so suppose we have two objects at + + align:start position:0% +so suppose we have two objects at + + + align:start position:0% +so suppose we have two objects at +different temperatures + + align:start position:0% +different temperatures + + + align:start position:0% +different temperatures +and there's an object patched down here + + align:start position:0% +and there's an object patched down here + + + align:start position:0% +and there's an object patched down here +and so there's radiation coming from one + + align:start position:0% +and so there's radiation coming from one + + + align:start position:0% +and so there's radiation coming from one +and going to the other + + align:start position:0% +and going to the other + + + align:start position:0% +and going to the other +and reciprocally there'll be radiation + + align:start position:0% +and reciprocally there'll be radiation + + + align:start position:0% +and reciprocally there'll be radiation +coming from t the object at temperature + + align:start position:0% +coming from t the object at temperature + + + align:start position:0% +coming from t the object at temperature +t2 and + + align:start position:0% +t2 and + + + align:start position:0% +t2 and +arriving at t1 + + align:start position:0% +arriving at t1 + + + align:start position:0% +arriving at t1 +and + + align:start position:0% +and + + + align:start position:0% +and +it takes a little bit of hand waving but + + align:start position:0% +it takes a little bit of hand waving but + + + align:start position:0% +it takes a little bit of hand waving but +basically what it's saying is if it's + + align:start position:0% +basically what it's saying is if it's + + + align:start position:0% +basically what it's saying is if it's +not a reciprocal + + align:start position:0% +not a reciprocal + + + align:start position:0% +not a reciprocal +then + + align:start position:0% +then + + + align:start position:0% +then +then there will be energy transfer from + + align:start position:0% +then there will be energy transfer from + + + align:start position:0% +then there will be energy transfer from +the colder object to the hotter object + + align:start position:0% +the colder object to the hotter object + + + align:start position:0% +the colder object to the hotter object +which we know doesn't happen + + align:start position:0% + + + + align:start position:0% + +so what this is saying if you + + align:start position:0% +so what this is saying if you + + + align:start position:0% +so what this is saying if you +interchange + + align:start position:0% + + + + align:start position:0% + +if you interchange incident and emitted + + align:start position:0% +if you interchange incident and emitted + + + align:start position:0% +if you interchange incident and emitted +you should get the same value for your + + align:start position:0% +you should get the same value for your + + + align:start position:0% +you should get the same value for your +bi-directional + + align:start position:0% +bi-directional + + + align:start position:0% +bi-directional +so there's a symmetry + + align:start position:0% +so there's a symmetry + + + align:start position:0% +so there's a symmetry +which in a way helps you in the data + + align:start position:0% +which in a way helps you in the data + + + align:start position:0% +which in a way helps you in the data +collection because there's half of the + + align:start position:0% +collection because there's half of the + + + align:start position:0% +collection because there's half of the +data you don't have to collect + + align:start position:0% + + + + align:start position:0% + +by the way it reminds me of + + align:start position:0% +by the way it reminds me of + + + align:start position:0% +by the way it reminds me of +when i was a student here + + align:start position:0% +when i was a student here + + + align:start position:0% +when i was a student here +there was a famous professor called + + align:start position:0% +there was a famous professor called + + + align:start position:0% +there was a famous professor called +letrin and he jerome litwin + + align:start position:0% +letrin and he jerome litwin + + + align:start position:0% +letrin and he jerome litwin +came up with a paper + + align:start position:0% +came up with a paper + + + align:start position:0% +came up with a paper +called what the frog's eye tells the + + align:start position:0% +called what the frog's eye tells the + + + align:start position:0% +called what the frog's eye tells the +frog's brain which was one of the early + + align:start position:0% +frog's brain which was one of the early + + + align:start position:0% +frog's brain which was one of the early +attempts to try and understand how + + align:start position:0% +attempts to try and understand how + + + align:start position:0% +attempts to try and understand how +neurons work and how image processing + + align:start position:0% +neurons work and how image processing + + + align:start position:0% +neurons work and how image processing +might work and so on + + align:start position:0% +might work and so on + + + align:start position:0% +might work and so on +and you know everyone wanted to hear his + + align:start position:0% +and you know everyone wanted to hear his + + + align:start position:0% +and you know everyone wanted to hear his +talk and he was talking about color and + + align:start position:0% +talk and he was talking about color and + + + align:start position:0% +talk and he was talking about color and +i was way back in the room and as + + align:start position:0% +i was way back in the room and as + + + align:start position:0% +i was way back in the room and as +as a student i was really intimidated by + + align:start position:0% +as a student i was really intimidated by + + + align:start position:0% +as a student i was really intimidated by +these people but i just had to ask and + + align:start position:0% +these people but i just had to ask and + + + align:start position:0% +these people but i just had to ask and +so + + align:start position:0% +so + + + align:start position:0% +so +i stuck up my hand and i asked him some + + align:start position:0% +i stuck up my hand and i asked him some + + + align:start position:0% +i stuck up my hand and i asked him some +question i + + align:start position:0% +question i + + + align:start position:0% +question i +at this point don't even remember what + + align:start position:0% +at this point don't even remember what + + + align:start position:0% +at this point don't even remember what +it was and he stared at me for about + + align:start position:0% +it was and he stared at me for about + + + align:start position:0% +it was and he stared at me for about +five seconds and then he said + + align:start position:0% +five seconds and then he said + + + align:start position:0% +five seconds and then he said +well if you had read the original book + + align:start position:0% +well if you had read the original book + + + align:start position:0% +well if you had read the original book +by helmholtz + + align:start position:0% +by helmholtz + + + align:start position:0% +by helmholtz +the + + align:start position:0% +the + + + align:start position:0% +the +book by helmholtz in the original german + + align:start position:0% +book by helmholtz in the original german + + + align:start position:0% +book by helmholtz in the original german +version you would know blah blah blah + + align:start position:0% +version you would know blah blah blah + + + align:start position:0% +version you would know blah blah blah +and i'm like oh my god i really + + align:start position:0% +and i'm like oh my god i really + + + align:start position:0% +and i'm like oh my god i really +killed my career here because + + align:start position:0% +killed my career here because + + + align:start position:0% +killed my career here because +and then years later i was thinking + + align:start position:0% +and then years later i was thinking + + + align:start position:0% +and then years later i was thinking +about that same problem and i realized + + align:start position:0% +about that same problem and i realized + + + align:start position:0% +about that same problem and i realized +that he was just using a wonderful + + align:start position:0% +that he was just using a wonderful + + + align:start position:0% +that he was just using a wonderful +debating technique + + align:start position:0% +debating technique + + + align:start position:0% +debating technique +because he had no idea what the answer + + align:start position:0% +because he had no idea what the answer + + + align:start position:0% +because he had no idea what the answer +was but he certainly put me in my place + + align:start position:0% +was but he certainly put me in my place + + + align:start position:0% +was but he certainly put me in my place +and you know and some of these people + + align:start position:0% +and you know and some of these people + + + align:start position:0% +and you know and some of these people +went to schools where they taught you + + align:start position:0% +went to schools where they taught you + + + align:start position:0% +went to schools where they taught you +how to debate i didn't so i i was i was + + align:start position:0% +how to debate i didn't so i i was i was + + + align:start position:0% +how to debate i didn't so i i was i was +just flabbergasted anyway helmholtz so + + align:start position:0% +just flabbergasted anyway helmholtz so + + + align:start position:0% +just flabbergasted anyway helmholtz so +that was how i'm all there + + align:start position:0% +that was how i'm all there + + + align:start position:0% +that was how i'm all there +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so next time what we're going to do is + + align:start position:0% +so next time what we're going to do is + + + align:start position:0% +so next time what we're going to do is +um apply this to + + align:start position:0% +um apply this to + + + align:start position:0% +um apply this to +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +look at different types of + + align:start position:0% +look at different types of + + + align:start position:0% +look at different types of +surface material models of course using + + align:start position:0% +surface material models of course using + + + align:start position:0% +surface material models of course using +lambertian again + + align:start position:0% +lambertian again + + + align:start position:0% +lambertian again +and also some new ones that apply to + + align:start position:0% +and also some new ones that apply to + + + align:start position:0% +and also some new ones that apply to +the moon and rocky planets in our solar + + align:start position:0% +the moon and rocky planets in our solar + + + align:start position:0% +the moon and rocky planets in our solar +system and that uh enable us to + + align:start position:0% +system and that uh enable us to + + + align:start position:0% +system and that uh enable us to +determine their uh surface shade + + align:start position:0% +determine their uh surface shade + + + align:start position:0% +determine their uh surface shade +okay and i guess there you there was an + + align:start position:0% +okay and i guess there you there was an + + + align:start position:0% +okay and i guess there you there was an +extension right + + align:start position:0% +extension right + + + align:start position:0% +extension right +so make sure you keep up to date on + + align:start position:0% +so make sure you keep up to date on + + + align:start position:0% +so make sure you keep up to date on +what's on piazza because there was an + + align:start position:0% +what's on piazza because there was an + + + align:start position:0% +what's on piazza because there was an +extension on the homework problem and + + align:start position:0% +extension on the homework problem and + + + align:start position:0% +extension on the homework problem and +other good stuff happening there \ No newline at end of file diff --git a/r1yb4-JvZhU.txt b/r1yb4-JvZhU.txt new file mode 100644 index 0000000000000000000000000000000000000000..3066deb7acddc81f5040bc8eea5fc6fc3bf7a766 --- /dev/null +++ b/r1yb4-JvZhU.txt @@ -0,0 +1,1531 @@ +align:start position:0% + +Today we're speaking with Liz Scheler, + + align:start position:0% +Today we're speaking with Liz Scheler, + + + align:start position:0% +Today we're speaking with Liz Scheler, +the secretary treasurer of the AFL CIO. + + align:start position:0% +the secretary treasurer of the AFL CIO. + + + align:start position:0% +the secretary treasurer of the AFL CIO. +Liz is not only the chief financial + + align:start position:0% +Liz is not only the chief financial + + + align:start position:0% +Liz is not only the chief financial +officer for the AFL CIO, she has a + + align:start position:0% +officer for the AFL CIO, she has a + + + align:start position:0% +officer for the AFL CIO, she has a +special interest and responsibility in + + align:start position:0% +special interest and responsibility in + + + align:start position:0% +special interest and responsibility in +working with young people to introduce + + align:start position:0% +working with young people to introduce + + + align:start position:0% +working with young people to introduce +the labor movement to them and to learn + + align:start position:0% +the labor movement to them and to learn + + + align:start position:0% +the labor movement to them and to learn +from them about what they would like to + + align:start position:0% +from them about what they would like to + + + align:start position:0% +from them about what they would like to +see the labor movement of the future + + align:start position:0% +see the labor movement of the future + + + align:start position:0% +see the labor movement of the future +look like. + + align:start position:0% + + + + align:start position:0% + +So, I'm the secretary treasurer, uh, + + align:start position:0% +So, I'm the secretary treasurer, uh, + + + align:start position:0% +So, I'm the secretary treasurer, uh, +which is the chief financial officer of + + align:start position:0% +which is the chief financial officer of + + + align:start position:0% +which is the chief financial officer of +the AFL CIO. Uh, we have 57 affiliated + + align:start position:0% +the AFL CIO. Uh, we have 57 affiliated + + + align:start position:0% +the AFL CIO. Uh, we have 57 affiliated +unions, and I actually came up through + + align:start position:0% +unions, and I actually came up through + + + align:start position:0% +unions, and I actually came up through +one of those unions, the International + + align:start position:0% +one of those unions, the International + + + align:start position:0% +one of those unions, the International +Brotherhood of Electrical Workers, as a + + align:start position:0% +Brotherhood of Electrical Workers, as a + + + align:start position:0% +Brotherhood of Electrical Workers, as a +rank and file member. Um, and my + + align:start position:0% +rank and file member. Um, and my + + + align:start position:0% +rank and file member. Um, and my +responsibilities here are to manage the + + align:start position:0% +responsibilities here are to manage the + + + align:start position:0% +responsibilities here are to manage the +money and make sure that we're using the + + align:start position:0% +money and make sure that we're using the + + + align:start position:0% +money and make sure that we're using the +DE's money wisely and building program. + + align:start position:0% +DE's money wisely and building program. + + + align:start position:0% +DE's money wisely and building program. +um making sure that our finances are in + + align:start position:0% +um making sure that our finances are in + + + align:start position:0% +um making sure that our finances are in +order. But in addition to that finance + + align:start position:0% +order. But in addition to that finance + + + align:start position:0% +order. But in addition to that finance +hat, I also uh work to engage, educate, + + align:start position:0% +hat, I also uh work to engage, educate, + + + align:start position:0% +hat, I also uh work to engage, educate, +mobilize young people in our movement. + + align:start position:0% +mobilize young people in our movement. + + + align:start position:0% +mobilize young people in our movement. +Uh I'm particularly focused as a woman + + align:start position:0% +Uh I'm particularly focused as a woman + + + align:start position:0% +Uh I'm particularly focused as a woman +officer and making sure that we are um + + align:start position:0% +officer and making sure that we are um + + + align:start position:0% +officer and making sure that we are um +engaging women in our labor movement and + + align:start position:0% +engaging women in our labor movement and + + + align:start position:0% +engaging women in our labor movement and +really speaking out on issues that + + align:start position:0% +really speaking out on issues that + + + align:start position:0% +really speaking out on issues that +affect women in the workplace. And then + + align:start position:0% +affect women in the workplace. And then + + + align:start position:0% +affect women in the workplace. And then +sort of in terms of innovation, what can + + align:start position:0% +sort of in terms of innovation, what can + + + align:start position:0% +sort of in terms of innovation, what can +we be doing uh as a labor movement to + + align:start position:0% +we be doing uh as a labor movement to + + + align:start position:0% +we be doing uh as a labor movement to +change as the workplace changes and + + align:start position:0% +change as the workplace changes and + + + align:start position:0% +change as the workplace changes and +evolves? And that can include anything + + align:start position:0% +evolves? And that can include anything + + + align:start position:0% +evolves? And that can include anything +from workforce development and training + + align:start position:0% +from workforce development and training + + + align:start position:0% +from workforce development and training +to issues around the ondemand economy. + + align:start position:0% +to issues around the ondemand economy. + + + align:start position:0% +to issues around the ondemand economy. +Um there's so much happening in the + + align:start position:0% +Um there's so much happening in the + + + align:start position:0% +Um there's so much happening in the +world of work. + + align:start position:0% + + + + align:start position:0% + +Well, the young people in the labor + + align:start position:0% +Well, the young people in the labor + + + align:start position:0% +Well, the young people in the labor +movement, uh, I was a young person when + + align:start position:0% +movement, uh, I was a young person when + + + align:start position:0% +movement, uh, I was a young person when +I first started in my union at 23 years + + align:start position:0% +I first started in my union at 23 years + + + align:start position:0% +I first started in my union at 23 years +old, often feel that they don't have as + + align:start position:0% +old, often feel that they don't have as + + + align:start position:0% +old, often feel that they don't have as +much of a voice in our labor movement. + + align:start position:0% +much of a voice in our labor movement. + + + align:start position:0% +much of a voice in our labor movement. +And I wanted to figure out a way to + + align:start position:0% +And I wanted to figure out a way to + + + align:start position:0% +And I wanted to figure out a way to +change that and make their ideas and + + align:start position:0% +change that and make their ideas and + + + align:start position:0% +change that and make their ideas and +opinions and thoughts and approaches um, + + align:start position:0% +opinions and thoughts and approaches um, + + + align:start position:0% +opinions and thoughts and approaches um, +woven into the fabric of what we do + + align:start position:0% +woven into the fabric of what we do + + + align:start position:0% +woven into the fabric of what we do +every day. So, we started a young worker + + align:start position:0% +every day. So, we started a young worker + + + align:start position:0% +every day. So, we started a young worker +program we call Next Up about six years + + align:start position:0% +program we call Next Up about six years + + + align:start position:0% +program we call Next Up about six years +ago. And the intent was to figure out + + align:start position:0% +ago. And the intent was to figure out + + + align:start position:0% +ago. And the intent was to figure out +ways to get young people engaged in + + align:start position:0% +ways to get young people engaged in + + + align:start position:0% +ways to get young people engaged in +their their own unions, but also making + + align:start position:0% +their their own unions, but also making + + + align:start position:0% +their their own unions, but also making +connections with young people outside + + align:start position:0% +connections with young people outside + + + align:start position:0% +connections with young people outside +the labor movement so that we're all + + align:start position:0% +the labor movement so that we're all + + + align:start position:0% +the labor movement so that we're all +working together to advance the + + align:start position:0% +working together to advance the + + + align:start position:0% +working together to advance the +interests of young people in this + + align:start position:0% +interests of young people in this + + + align:start position:0% +interests of young people in this +economy. And we've been um building + + align:start position:0% +economy. And we've been um building + + + align:start position:0% +economy. And we've been um building +young worker groups all across the + + align:start position:0% +young worker groups all across the + + + align:start position:0% +young worker groups all across the +country through our AFL CIO structure. + + align:start position:0% +country through our AFL CIO structure. + + + align:start position:0% +country through our AFL CIO structure. +So, in most major cities and pretty much + + align:start position:0% +So, in most major cities and pretty much + + + align:start position:0% +So, in most major cities and pretty much +every state, we have a young worker + + align:start position:0% +every state, we have a young worker + + + align:start position:0% +every state, we have a young worker +group uh that's giving voice to young + + align:start position:0% +group uh that's giving voice to young + + + align:start position:0% +group uh that's giving voice to young +people. Uh they're leading in politics, + + align:start position:0% +people. Uh they're leading in politics, + + + align:start position:0% +people. Uh they're leading in politics, +in legislation, + + align:start position:0% +in legislation, + + + align:start position:0% +in legislation, +uh in organizing, and really being a + + align:start position:0% +uh in organizing, and really being a + + + align:start position:0% +uh in organizing, and really being a +voice and a presence for the labor + + align:start position:0% +voice and a presence for the labor + + + align:start position:0% +voice and a presence for the labor +movement in their local communities. I'm + + align:start position:0% +movement in their local communities. I'm + + + align:start position:0% +movement in their local communities. I'm +really proud of the work they've done to + + align:start position:0% +really proud of the work they've done to + + + align:start position:0% +really proud of the work they've done to +put together a young worker economic + + align:start position:0% +put together a young worker economic + + + align:start position:0% +put together a young worker economic +platform so that they can hold + + align:start position:0% +platform so that they can hold + + + align:start position:0% +platform so that they can hold +politicians accountable on the issues + + align:start position:0% +politicians accountable on the issues + + + align:start position:0% +politicians accountable on the issues +that matter to young people in the + + align:start position:0% +that matter to young people in the + + + align:start position:0% +that matter to young people in the +economy. And of course, front and center + + align:start position:0% +economy. And of course, front and center + + + align:start position:0% +economy. And of course, front and center +is job opportunities. Making sure that + + align:start position:0% +is job opportunities. Making sure that + + + align:start position:0% +is job opportunities. Making sure that +when people graduate from high school or + + align:start position:0% +when people graduate from high school or + + + align:start position:0% +when people graduate from high school or +even graduate from college that we have + + align:start position:0% +even graduate from college that we have + + + align:start position:0% +even graduate from college that we have +good jobs waiting for them. And often we + + align:start position:0% +good jobs waiting for them. And often we + + + align:start position:0% +good jobs waiting for them. And often we +know young people are grappling with a + + align:start position:0% +know young people are grappling with a + + + align:start position:0% +know young people are grappling with a +lot of student loan debt when they've + + align:start position:0% +lot of student loan debt when they've + + + align:start position:0% +lot of student loan debt when they've +gone through college. And how are our + + align:start position:0% +gone through college. And how are our + + + align:start position:0% +gone through college. And how are our +elected officials responding to that? + + align:start position:0% +elected officials responding to that? + + + align:start position:0% +elected officials responding to that? +And really connecting the labor movement + + align:start position:0% +And really connecting the labor movement + + + align:start position:0% +And really connecting the labor movement +to the issues that matter to young + + align:start position:0% +to the issues that matter to young + + + align:start position:0% +to the issues that matter to young +people. + + align:start position:0% + + + + align:start position:0% + +Well, the course is a a real opportunity + + align:start position:0% +Well, the course is a a real opportunity + + + align:start position:0% +Well, the course is a a real opportunity +for young people to connect on what is + + align:start position:0% +for young people to connect on what is + + + align:start position:0% +for young people to connect on what is +the future of work going to look like? + + align:start position:0% +the future of work going to look like? + + + align:start position:0% +the future of work going to look like? +What are we doing + + align:start position:0% +What are we doing + + + align:start position:0% +What are we doing +as working people to influence that? And + + align:start position:0% +as working people to influence that? And + + + align:start position:0% +as working people to influence that? And +in the labor movement, of course, front + + align:start position:0% +in the labor movement, of course, front + + + align:start position:0% +in the labor movement, of course, front +and center is collective bargaining. And + + align:start position:0% +and center is collective bargaining. And + + + align:start position:0% +and center is collective bargaining. And +how can we strengthen collective + + align:start position:0% +how can we strengthen collective + + + align:start position:0% +how can we strengthen collective +bargaining and how does the role of + + align:start position:0% +bargaining and how does the role of + + + align:start position:0% +bargaining and how does the role of +collective bargaining um influence uh + + align:start position:0% +collective bargaining um influence uh + + + align:start position:0% +collective bargaining um influence uh +work in general? And we know uh the + + align:start position:0% +work in general? And we know uh the + + + align:start position:0% +work in general? And we know uh the +unionized workforce has been shrinking, + + align:start position:0% +unionized workforce has been shrinking, + + + align:start position:0% +unionized workforce has been shrinking, +but in a time of the greatest inequality + + align:start position:0% +but in a time of the greatest inequality + + + align:start position:0% +but in a time of the greatest inequality +we've seen, it's more important than + + align:start position:0% +we've seen, it's more important than + + + align:start position:0% +we've seen, it's more important than +ever that we grow the labor movement and + + align:start position:0% +ever that we grow the labor movement and + + + align:start position:0% +ever that we grow the labor movement and +and get our fair share of that growth uh + + align:start position:0% +and get our fair share of that growth uh + + + align:start position:0% +and get our fair share of that growth uh +in the economy. And so I think for young + + align:start position:0% +in the economy. And so I think for young + + + align:start position:0% +in the economy. And so I think for young +people who are looking at what can I do + + align:start position:0% +people who are looking at what can I do + + + align:start position:0% +people who are looking at what can I do +to influence, what can I do to help um + + align:start position:0% +to influence, what can I do to help um + + + align:start position:0% +to influence, what can I do to help um +taking a course like this, educating + + align:start position:0% +taking a course like this, educating + + + align:start position:0% +taking a course like this, educating +themselves, but then also taking that + + align:start position:0% +themselves, but then also taking that + + + align:start position:0% +themselves, but then also taking that +education and moving it into action. And + + align:start position:0% +education and moving it into action. And + + + align:start position:0% +education and moving it into action. And +I think when I talk to young people, + + align:start position:0% +I think when I talk to young people, + + + align:start position:0% +I think when I talk to young people, +they often feel powerless and um don't + + align:start position:0% +they often feel powerless and um don't + + + align:start position:0% +they often feel powerless and um don't +see the labor movement as a vehicle for + + align:start position:0% +see the labor movement as a vehicle for + + + align:start position:0% +see the labor movement as a vehicle for +that kind of action. And so I think uh + + align:start position:0% +that kind of action. And so I think uh + + + align:start position:0% +that kind of action. And so I think uh +the message is that yeah, there there + + align:start position:0% +the message is that yeah, there there + + + align:start position:0% +the message is that yeah, there there +are opportunities. There are places you + + align:start position:0% +are opportunities. There are places you + + + align:start position:0% +are opportunities. There are places you +can go uh to exert your power and um the + + align:start position:0% +can go uh to exert your power and um the + + + align:start position:0% +can go uh to exert your power and um the +power of coming together and the power + + align:start position:0% +power of coming together and the power + + + align:start position:0% +power of coming together and the power +of collective action. Nowhere is that + + align:start position:0% +of collective action. Nowhere is that + + + align:start position:0% +of collective action. Nowhere is that +better on display than with the labor + + align:start position:0% +better on display than with the labor + + + align:start position:0% +better on display than with the labor +movement. + + align:start position:0% + + + + align:start position:0% + +Young people in the labor movement have + + align:start position:0% +Young people in the labor movement have + + + align:start position:0% +Young people in the labor movement have +a a very unique perspective. Um they + + align:start position:0% +a a very unique perspective. Um they + + + align:start position:0% +a a very unique perspective. Um they +often are some of the only young people + + align:start position:0% +often are some of the only young people + + + align:start position:0% +often are some of the only young people +in their peer group that have a decent + + align:start position:0% +in their peer group that have a decent + + + align:start position:0% +in their peer group that have a decent +job that pays benefits. Um that gives + + align:start position:0% +job that pays benefits. Um that gives + + + align:start position:0% +job that pays benefits. Um that gives +them the training they need without + + align:start position:0% +them the training they need without + + + align:start position:0% +them the training they need without +going into debt. Um, so I think that + + align:start position:0% +going into debt. Um, so I think that + + + align:start position:0% +going into debt. Um, so I think that +they can do um a service to other young + + align:start position:0% +they can do um a service to other young + + + align:start position:0% +they can do um a service to other young +people who may not know those + + align:start position:0% +people who may not know those + + + align:start position:0% +people who may not know those +opportunities exist by lifting up um the + + align:start position:0% +opportunities exist by lifting up um the + + + align:start position:0% +opportunities exist by lifting up um the +possibilities of what the labor movement + + align:start position:0% +possibilities of what the labor movement + + + align:start position:0% +possibilities of what the labor movement +can offer. Um they also have a unique + + align:start position:0% +can offer. Um they also have a unique + + + align:start position:0% +can offer. Um they also have a unique +perspective on what's happening in the + + align:start position:0% +perspective on what's happening in the + + + align:start position:0% +perspective on what's happening in the +economy. Uh as we know this generation + + align:start position:0% +economy. Uh as we know this generation + + + align:start position:0% +economy. Uh as we know this generation +has suffered disproportionately with the + + align:start position:0% +has suffered disproportionately with the + + + align:start position:0% +has suffered disproportionately with the +lack of opportunity. um the economy, the + + align:start position:0% +lack of opportunity. um the economy, the + + + align:start position:0% +lack of opportunity. um the economy, the +unemployment numbers have hit them, I + + align:start position:0% +unemployment numbers have hit them, I + + + align:start position:0% +unemployment numbers have hit them, I +think, at double the rate of of the + + align:start position:0% +think, at double the rate of of the + + + align:start position:0% +think, at double the rate of of the +average uh who's out of work. Um and you + + align:start position:0% +average uh who's out of work. Um and you + + + align:start position:0% +average uh who's out of work. Um and you +know, we want to come together as a + + align:start position:0% +know, we want to come together as a + + + align:start position:0% +know, we want to come together as a +society to figure out what kind of jobs + + align:start position:0% +society to figure out what kind of jobs + + + align:start position:0% +society to figure out what kind of jobs +do we want to see in this country as we + + align:start position:0% +do we want to see in this country as we + + + align:start position:0% +do we want to see in this country as we +go forward in the future. Do we want low + + align:start position:0% +go forward in the future. Do we want low + + + align:start position:0% +go forward in the future. Do we want low +road, low-wage jobs or do we want + + align:start position:0% +road, low-wage jobs or do we want + + + align:start position:0% +road, low-wage jobs or do we want +opportunities to really um support your + + align:start position:0% +opportunities to really um support your + + + align:start position:0% +opportunities to really um support your +family and put food on the table? And I + + align:start position:0% +family and put food on the table? And I + + + align:start position:0% +family and put food on the table? And I +think young people are feeling that so + + align:start position:0% +think young people are feeling that so + + + align:start position:0% +think young people are feeling that so +acutely. Um and so they have ideas and + + align:start position:0% +acutely. Um and so they have ideas and + + + align:start position:0% +acutely. Um and so they have ideas and +thoughts to share on how we can rebuild + + align:start position:0% +thoughts to share on how we can rebuild + + + align:start position:0% +thoughts to share on how we can rebuild +the economy. So I think that this is a + + align:start position:0% +the economy. So I think that this is a + + + align:start position:0% +the economy. So I think that this is a +great opportunity to bring people + + align:start position:0% +great opportunity to bring people + + + align:start position:0% +great opportunity to bring people +together um have their voices heard um + + align:start position:0% +together um have their voices heard um + + + align:start position:0% +together um have their voices heard um +make sure that um we're getting our + + align:start position:0% +make sure that um we're getting our + + + align:start position:0% +make sure that um we're getting our +politicians attention on this because + + align:start position:0% +politicians attention on this because + + + align:start position:0% +politicians attention on this because +those elected officials are the ones + + align:start position:0% +those elected officials are the ones + + + align:start position:0% +those elected officials are the ones +that write the rules um and pass the + + align:start position:0% +that write the rules um and pass the + + + align:start position:0% +that write the rules um and pass the +policies. And so if we're going to + + align:start position:0% +policies. And so if we're going to + + + align:start position:0% +policies. And so if we're going to +rewrite the rules of the economy, we + + align:start position:0% +rewrite the rules of the economy, we + + + align:start position:0% +rewrite the rules of the economy, we +need to get more and more young voices + + align:start position:0% +need to get more and more young voices + + + align:start position:0% +need to get more and more young voices +in that + + align:start position:0% + + + + align:start position:0% + +conversation. I think there is so much + + align:start position:0% +conversation. I think there is so much + + + align:start position:0% +conversation. I think there is so much +opportunity at this moment in time as of + + align:start position:0% +opportunity at this moment in time as of + + + align:start position:0% +opportunity at this moment in time as of +course the workplace is changing and + + align:start position:0% +course the workplace is changing and + + + align:start position:0% +course the workplace is changing and +evolving. Um so is the labor movement + + align:start position:0% +evolving. Um so is the labor movement + + + align:start position:0% +evolving. Um so is the labor movement +and so is the progressive infrastructure + + align:start position:0% +and so is the progressive infrastructure + + + align:start position:0% +and so is the progressive infrastructure +in the country. And I think the message + + align:start position:0% +in the country. And I think the message + + + align:start position:0% +in the country. And I think the message +is that we don't just have to sit back + + align:start position:0% +is that we don't just have to sit back + + + align:start position:0% +is that we don't just have to sit back +and wait for change to happen. and and + + align:start position:0% +and wait for change to happen. and and + + + align:start position:0% +and wait for change to happen. and and +feel like we can't be a part of that + + align:start position:0% +feel like we can't be a part of that + + + align:start position:0% +feel like we can't be a part of that +change. Um I think it's important that + + align:start position:0% +change. Um I think it's important that + + + align:start position:0% +change. Um I think it's important that +you see the labor movement as a vehicle + + align:start position:0% +you see the labor movement as a vehicle + + + align:start position:0% +you see the labor movement as a vehicle +for that possibility of of bringing + + align:start position:0% +for that possibility of of bringing + + + align:start position:0% +for that possibility of of bringing +people's voice to get voices together + + align:start position:0% +people's voice to get voices together + + + align:start position:0% +people's voice to get voices together +and as an institution + + align:start position:0% +and as an institution + + + align:start position:0% +and as an institution +um we can do that but we can't do it + + align:start position:0% +um we can do that but we can't do it + + + align:start position:0% +um we can do that but we can't do it +alone. We need to be working together in + + align:start position:0% +alone. We need to be working together in + + + align:start position:0% +alone. We need to be working together in +collaboration and in partnership with + + align:start position:0% +collaboration and in partnership with + + + align:start position:0% +collaboration and in partnership with +all kinds of organizations and the more + + align:start position:0% +all kinds of organizations and the more + + + align:start position:0% +all kinds of organizations and the more +people we bring together the more + + align:start position:0% +people we bring together the more + + + align:start position:0% +people we bring together the more +powerful our voices are. So I think for + + align:start position:0% +powerful our voices are. So I think for + + + align:start position:0% +powerful our voices are. So I think for +young people who are looking for an + + align:start position:0% +young people who are looking for an + + + align:start position:0% +young people who are looking for an +avenue and a way to make change + + align:start position:0% +avenue and a way to make change + + + align:start position:0% +avenue and a way to make change +certainly look to the labor movement but + + align:start position:0% +certainly look to the labor movement but + + + align:start position:0% +certainly look to the labor movement but +look in your communities uh look at all + + align:start position:0% +look in your communities uh look at all + + + align:start position:0% +look in your communities uh look at all +the the different organizations that are + + align:start position:0% +the the different organizations that are + + + align:start position:0% +the the different organizations that are +uh lifting up voices in different ways. + + align:start position:0% +uh lifting up voices in different ways. + + + align:start position:0% +uh lifting up voices in different ways. +Um look at your local businesses for + + align:start position:0% +Um look at your local businesses for + + + align:start position:0% +Um look at your local businesses for +example. We often think that labor and + + align:start position:0% +example. We often think that labor and + + + align:start position:0% +example. We often think that labor and +management are at odds with each other. + + align:start position:0% +management are at odds with each other. + + + align:start position:0% +management are at odds with each other. +But could we be more powerful if we were + + align:start position:0% +But could we be more powerful if we were + + + align:start position:0% +But could we be more powerful if we were +working together uh in collaboration on + + align:start position:0% +working together uh in collaboration on + + + align:start position:0% +working together uh in collaboration on +the things that matter to um creating + + align:start position:0% +the things that matter to um creating + + + align:start position:0% +the things that matter to um creating +better jobs uh high road high wage jobs. + + align:start position:0% +better jobs uh high road high wage jobs. + + + align:start position:0% +better jobs uh high road high wage jobs. +Um and so I think that young people will + + align:start position:0% +Um and so I think that young people will + + + align:start position:0% +Um and so I think that young people will +play an integral and important role in + + align:start position:0% +play an integral and important role in + + + align:start position:0% +play an integral and important role in +making that happen. \ No newline at end of file diff --git a/roATER6-1yI.txt b/roATER6-1yI.txt new file mode 100644 index 0000000000000000000000000000000000000000..b052f0b58704ae50ee4637b95b790f906754e5ea --- /dev/null +++ b/roATER6-1yI.txt @@ -0,0 +1,9203 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +okay so let's get started I understand + + align:start position:0% +okay so let's get started I understand + + + align:start position:0% +okay so let's get started I understand +to wire myself have you okay so hmm so + + align:start position:0% +to wire myself have you okay so hmm so + + + align:start position:0% +to wire myself have you okay so hmm so +before we get into the into the to the + + align:start position:0% +before we get into the into the to the + + + align:start position:0% +before we get into the into the to the +PowerPoint here so basically what I'm + + align:start position:0% +PowerPoint here so basically what I'm + + + align:start position:0% +PowerPoint here so basically what I'm +doing is is I'm picking up from the + + align:start position:0% +doing is is I'm picking up from the + + + align:start position:0% +doing is is I'm picking up from the +point where we left last time we were + + align:start position:0% +point where we left last time we were + + + align:start position:0% +point where we left last time we were +discussing waves and what I would like + + align:start position:0% +discussing waves and what I would like + + + align:start position:0% +discussing waves and what I would like +to do now is derive wave equation + + align:start position:0% +to do now is derive wave equation + + + align:start position:0% +to do now is derive wave equation +basically for a mathematical form that + + align:start position:0% +basically for a mathematical form that + + + align:start position:0% +basically for a mathematical form that +there may that allows that should allow + + align:start position:0% +there may that allows that should allow + + + align:start position:0% +there may that allows that should allow +us to predict different kinds of waves + + align:start position:0% +us to predict different kinds of waves + + + align:start position:0% +us to predict different kinds of waves +of waves not the way all right so what + + align:start position:0% +of waves not the way all right so what + + + align:start position:0% +of waves not the way all right so what +what we start with here I felt with a + + align:start position:0% +what we start with here I felt with a + + + align:start position:0% +what we start with here I felt with a +general function C of an argument at so + + align:start position:0% +general function C of an argument at so + + + align:start position:0% +general function C of an argument at so +for those of you who are not not fluent + + align:start position:0% +for those of you who are not not fluent + + + align:start position:0% +for those of you who are not not fluent +in the Greek this is C this is hat okay + + align:start position:0% +in the Greek this is C this is hat okay + + + align:start position:0% +in the Greek this is C this is hat okay +and and these are at the moment this + + align:start position:0% +and and these are at the moment this + + + align:start position:0% +and and these are at the moment this +don't necessarily have the physical + + align:start position:0% +don't necessarily have the physical + + + align:start position:0% +don't necessarily have the physical +meaning but in order to produce a wave + + align:start position:0% +meaning but in order to produce a wave + + + align:start position:0% +meaning but in order to produce a wave +out of this function what I can do is I + + align:start position:0% +out of this function what I can do is I + + + align:start position:0% +out of this function what I can do is I +can write it as C or F of Z comma T + + align:start position:0% + + + + align:start position:0% + +equals C of Z minus CT okay now why is + + align:start position:0% +equals C of Z minus CT okay now why is + + + align:start position:0% +equals C of Z minus CT okay now why is +that a wave if you first of all Z now + + align:start position:0% +that a wave if you first of all Z now + + + align:start position:0% +that a wave if you first of all Z now +has become a special coordinate T usual + + align:start position:0% +has become a special coordinate T usual + + + align:start position:0% +has become a special coordinate T usual +is time so if you actually hide time so + + align:start position:0% +is time so if you actually hide time so + + + align:start position:0% +is time so if you actually hide time so +now time is 0 or time is a constant or + + align:start position:0% +now time is 0 or time is a constant or + + + align:start position:0% +now time is 0 or time is a constant or +something like that then you actually + + align:start position:0% +something like that then you actually + + + align:start position:0% +something like that then you actually +have basically the same argument but if + + align:start position:0% +have basically the same argument but if + + + align:start position:0% +have basically the same argument but if +you allow time to increase then you can + + align:start position:0% +you allow time to increase then you can + + + align:start position:0% +you allow time to increase then you can +see that it the time increase will have + + align:start position:0% +see that it the time increase will have + + + align:start position:0% +see that it the time increase will have +the effect of sliding the + + align:start position:0% +the effect of sliding the + + + align:start position:0% +the effect of sliding the +the same say along the special axis so + + align:start position:0% +the same say along the special axis so + + + align:start position:0% +the same say along the special axis so +for example if let's say let's take this + + align:start position:0% +for example if let's say let's take this + + + align:start position:0% +for example if let's say let's take this +as our reference point here the first + + align:start position:0% +as our reference point here the first + + + align:start position:0% +as our reference point here the first +peak after you advanced I'm a little + + align:start position:0% +peak after you advanced I'm a little + + + align:start position:0% +peak after you advanced I'm a little +further then this point has moved fast + + align:start position:0% +further then this point has moved fast + + + align:start position:0% +further then this point has moved fast +has moved to the right and how much is + + align:start position:0% +has moved to the right and how much is + + + align:start position:0% +has moved to the right and how much is +this distance well anybody this is easy + + align:start position:0% +this distance well anybody this is easy + + + align:start position:0% +this distance well anybody this is easy +I just I'm just trying to see if the + + align:start position:0% +I just I'm just trying to see if the + + + align:start position:0% +I just I'm just trying to see if the +people in Boston working up + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +nobody's awakened boss so this distance + + align:start position:0% +nobody's awakened boss so this distance + + + align:start position:0% +nobody's awakened boss so this distance +equals city right because if I if I set + + align:start position:0% +equals city right because if I if I set + + + align:start position:0% +equals city right because if I if I set +the argument of of this function to zero + + align:start position:0% +the argument of of this function to zero + + + align:start position:0% +the argument of of this function to zero +then basically recover my original + + align:start position:0% +then basically recover my original + + + align:start position:0% +then basically recover my original +function so so basically as a advance + + align:start position:0% +function so so basically as a advance + + + align:start position:0% +function so so basically as a advance +time the effect is that this waveform + + align:start position:0% +time the effect is that this waveform + + + align:start position:0% +time the effect is that this waveform +moves to the right okay so now what we + + align:start position:0% +moves to the right okay so now what we + + + align:start position:0% +moves to the right okay so now what we +do is and at the moment there is no + + align:start position:0% +do is and at the moment there is no + + + align:start position:0% +do is and at the moment there is no +obvious motivation for why I'm going to + + align:start position:0% +obvious motivation for why I'm going to + + + align:start position:0% +obvious motivation for why I'm going to +do what I'm about to do but please take + + align:start position:0% +do what I'm about to do but please take + + + align:start position:0% +do what I'm about to do but please take +my word for it for a while I'm going to + + align:start position:0% +my word for it for a while I'm going to + + + align:start position:0% +my word for it for a while I'm going to +take two partial derivatives I'm going + + align:start position:0% +take two partial derivatives I'm going + + + align:start position:0% +take two partial derivatives I'm going +to take DF DZ and they have the team + + align:start position:0% +to take DF DZ and they have the team + + + align:start position:0% +to take DF DZ and they have the team +okay the FD z equals basically C prime + + align:start position:0% +okay the FD z equals basically C prime + + + align:start position:0% +okay the FD z equals basically C prime +were C Prime I used C prime is simply to + + align:start position:0% +were C Prime I used C prime is simply to + + + align:start position:0% +were C Prime I used C prime is simply to +denote the derivative of C with respect + + align:start position:0% +denote the derivative of C with respect + + + align:start position:0% +denote the derivative of C with respect +to its mysterious argument so that's + + align:start position:0% +to its mysterious argument so that's + + + align:start position:0% +to its mysterious argument so that's +very easy what about the F DT + + align:start position:0% + + + + align:start position:0% + +that's right I have to apply the chain + + align:start position:0% +that's right I have to apply the chain + + + align:start position:0% +that's right I have to apply the chain +rule because there is a multiplicative + + align:start position:0% +rule because there is a multiplicative + + + align:start position:0% +rule because there is a multiplicative +argument inside so this is going to be + + align:start position:0% +argument inside so this is going to be + + + align:start position:0% +argument inside so this is going to be +minus C times C Prime + + align:start position:0% +minus C times C Prime + + + align:start position:0% +minus C times C Prime +so because C prime appears in both in + + align:start position:0% +so because C prime appears in both in + + + align:start position:0% +so because C prime appears in both in +both places over here I can combine + + align:start position:0% +both places over here I can combine + + + align:start position:0% +both places over here I can combine +these equations and say the F of D Z + + align:start position:0% + + + + align:start position:0% + +equals minus 1 over C be our bitting + + align:start position:0% +equals minus 1 over C be our bitting + + + align:start position:0% +equals minus 1 over C be our bitting +okay what is a partial differential + + align:start position:0% +okay what is a partial differential + + + align:start position:0% +okay what is a partial differential +equation and you might say well what I + + align:start position:0% +equation and you might say well what I + + + align:start position:0% +equation and you might say well what I +did is a little bit stupid right because + + align:start position:0% +did is a little bit stupid right because + + + align:start position:0% +did is a little bit stupid right because +I had a relatively simple expression for + + align:start position:0% +I had a relatively simple expression for + + + align:start position:0% +I had a relatively simple expression for +the wave I actually had the wave just in + + align:start position:0% +the wave I actually had the wave just in + + + align:start position:0% +the wave I actually had the wave just in +front of me and what I did was I wrote a + + align:start position:0% +front of me and what I did was I wrote a + + + align:start position:0% +front of me and what I did was I wrote a +partial differential equation could but + + align:start position:0% +partial differential equation could but + + + align:start position:0% +partial differential equation could but +the benefit of doing that is of course + + align:start position:0% +the benefit of doing that is of course + + + align:start position:0% +the benefit of doing that is of course +that the wave that they wrote here is a + + align:start position:0% +that the wave that they wrote here is a + + + align:start position:0% +that the wave that they wrote here is a +very special very limited kind of wave + + align:start position:0% +very special very limited kind of wave + + + align:start position:0% +very special very limited kind of wave +that propagates without change in shape + + align:start position:0% +that propagates without change in shape + + + align:start position:0% +that propagates without change in shape +without anything fancy happening we know + + align:start position:0% +without anything fancy happening we know + + + align:start position:0% +without anything fancy happening we know +from experience for example in real life + + align:start position:0% +from experience for example in real life + + + align:start position:0% +from experience for example in real life +if you have ever seen water waves water + + align:start position:0% +if you have ever seen water waves water + + + align:start position:0% +if you have ever seen water waves water +waves they don't quite propagate like + + align:start position:0% +waves they don't quite propagate like + + + align:start position:0% +waves they don't quite propagate like +this they change shape in all kinds of + + align:start position:0% +this they change shape in all kinds of + + + align:start position:0% +this they change shape in all kinds of +complicated ways so even even though I + + align:start position:0% +complicated ways so even even though I + + + align:start position:0% +complicated ways so even even though I +derived this equation from that simple + + align:start position:0% +derived this equation from that simple + + + align:start position:0% +derived this equation from that simple +set we will see in a little bit later + + align:start position:0% +set we will see in a little bit later + + + align:start position:0% +set we will see in a little bit later +that this equation actually can describe + + align:start position:0% +that this equation actually can describe + + + align:start position:0% +that this equation actually can describe +much more general wave we're not quite + + align:start position:0% +much more general wave we're not quite + + + align:start position:0% +much more general wave we're not quite +done yet because the question that I + + align:start position:0% +done yet because the question that I + + + align:start position:0% +done yet because the question that I +derived here applies for a wave moving + + align:start position:0% +derived here applies for a wave moving + + + align:start position:0% +derived here applies for a wave moving +to the right + + align:start position:0% +to the right + + + align:start position:0% +to the right +I can equally well consider a wave that + + align:start position:0% +I can equally well consider a wave that + + + align:start position:0% +I can equally well consider a wave that +is moving to the left and in this case + + align:start position:0% +is moving to the left and in this case + + + align:start position:0% +is moving to the left and in this case +what I would have to do is I would have + + align:start position:0% +what I would have to do is I would have + + + align:start position:0% +what I would have to do is I would have +to write F of Z comma T equals C of Z + + align:start position:0% +to write F of Z comma T equals C of Z + + + align:start position:0% +to write F of Z comma T equals C of Z +plus city a little bit of thought will + + align:start position:0% +plus city a little bit of thought will + + + align:start position:0% +plus city a little bit of thought will +convention out that if you advance time + + align:start position:0% +convention out that if you advance time + + + align:start position:0% +convention out that if you advance time +then the way we will have actually to + + align:start position:0% +then the way we will have actually to + + + align:start position:0% +then the way we will have actually to +move to the left towards negative Z in + + align:start position:0% +move to the left towards negative Z in + + + align:start position:0% +move to the left towards negative Z in +order to maintain its argument and if I + + align:start position:0% +order to maintain its argument and if I + + + align:start position:0% +order to maintain its argument and if I +do the same game now we can simply again + + align:start position:0% +do the same game now we can simply again + + + align:start position:0% +do the same game now we can simply again +I can write DF be Z equals C prime that + + align:start position:0% +I can write DF be Z equals C prime that + + + align:start position:0% +I can write DF be Z equals C prime that +did not change this time the F DT was + + align:start position:0% +did not change this time the F DT was + + + align:start position:0% +did not change this time the F DT was +Plus C C Prime + + align:start position:0% +Plus C C Prime + + + align:start position:0% +Plus C C Prime +now have another partial differential + + align:start position:0% +now have another partial differential + + + align:start position:0% +now have another partial differential +partial differential equation we have DZ + + align:start position:0% +partial differential equation we have DZ + + + align:start position:0% +partial differential equation we have DZ +equals 1 over c DF DT ok let me put back + + align:start position:0% +equals 1 over c DF DT ok let me put back + + + align:start position:0% +equals 1 over c DF DT ok let me put back +the question so this is a wave going to + + align:start position:0% +the question so this is a wave going to + + + align:start position:0% +the question so this is a wave going to +the left backwards and had another + + align:start position:0% +the left backwards and had another + + + align:start position:0% +the left backwards and had another +equation VFD Z equals minus 1 over C the + + align:start position:0% +equation VFD Z equals minus 1 over C the + + + align:start position:0% +equation VFD Z equals minus 1 over C the +DT that is a way of going to the right + + align:start position:0% + + + + align:start position:0% + +ok you can see very easily that if you + + align:start position:0% +ok you can see very easily that if you + + + align:start position:0% +ok you can see very easily that if you +take a second derivative of these + + align:start position:0% +take a second derivative of these + + + align:start position:0% +take a second derivative of these +equations you would actually just go + + align:start position:0% +equations you would actually just go + + + align:start position:0% +equations you would actually just go +back to the first one if you do the + + align:start position:0% +back to the first one if you do the + + + align:start position:0% +back to the first one if you do the +second derivative d square F this is + + align:start position:0% +second derivative d square F this is + + + align:start position:0% +second derivative d square F this is +square we will pick up an extra minus + + align:start position:0% +square we will pick up an extra minus + + + align:start position:0% +square we will pick up an extra minus +sign from the same equation that you + + align:start position:0% +sign from the same equation that you + + + align:start position:0% +sign from the same equation that you +will find that it is 1 over C Square D + + align:start position:0% +will find that it is 1 over C Square D + + + align:start position:0% +will find that it is 1 over C Square D +square F DT square you can do the same + + align:start position:0% +square F DT square you can do the same + + + align:start position:0% +square F DT square you can do the same +in this equation there's no sign here to + + align:start position:0% +in this equation there's no sign here to + + + align:start position:0% +in this equation there's no sign here to +begin with that is 1 over C Square D + + align:start position:0% +begin with that is 1 over C Square D + + + align:start position:0% +begin with that is 1 over C Square D +square F DT square so basically this + + align:start position:0% +square F DT square so basically this + + + align:start position:0% +square F DT square so basically this +single equation + + align:start position:0% + + + + align:start position:0% + +the single equation can describe both + + align:start position:0% +the single equation can describe both + + + align:start position:0% +the single equation can describe both +forward and backward and propagating + + align:start position:0% +forward and backward and propagating + + + align:start position:0% +forward and backward and propagating +waves and this equation actually it's a + + align:start position:0% +waves and this equation actually it's a + + + align:start position:0% +waves and this equation actually it's a +three-dimensional version of this one + + align:start position:0% +three-dimensional version of this one + + + align:start position:0% +three-dimensional version of this one +but its three-dimensional version it is + + align:start position:0% +but its three-dimensional version it is + + + align:start position:0% +but its three-dimensional version it is +it has the name Helmholtz wave equation + + align:start position:0% +it has the name Helmholtz wave equation + + + align:start position:0% +it has the name Helmholtz wave equation +and because of Helmholtz it's a little + + align:start position:0% +and because of Helmholtz it's a little + + + align:start position:0% +and because of Helmholtz it's a little +bit difficult to pronounce actually + + align:start position:0% +bit difficult to pronounce actually + + + align:start position:0% +bit difficult to pronounce actually +that's not the reason but the legend is + + align:start position:0% +that's not the reason but the legend is + + + align:start position:0% +that's not the reason but the legend is +anyway it's a very commonly encountered + + align:start position:0% +anyway it's a very commonly encountered + + + align:start position:0% +anyway it's a very commonly encountered +wave equation + + align:start position:0% +wave equation + + + align:start position:0% +wave equation +so typically we simply omit Helmholtz + + align:start position:0% +so typically we simply omit Helmholtz + + + align:start position:0% +so typically we simply omit Helmholtz +and we say wave equation now why we + + align:start position:0% +and we say wave equation now why we + + + align:start position:0% +and we say wave equation now why we +might want to distinguish this as + + align:start position:0% +might want to distinguish this as + + + align:start position:0% +might want to distinguish this as +opposed to are there other wave equation + + align:start position:0% +opposed to are there other wave equation + + + align:start position:0% +opposed to are there other wave equation +yes there is the Schrodinger equation + + align:start position:0% +yes there is the Schrodinger equation + + + align:start position:0% +yes there is the Schrodinger equation +that is the klein-gordon equation that + + align:start position:0% +that is the klein-gordon equation that + + + align:start position:0% +that is the klein-gordon equation that +is the for those of you who do fluid + + align:start position:0% +is the for those of you who do fluid + + + align:start position:0% +is the for those of you who do fluid +mechanics there is a quarter deck the + + align:start position:0% +mechanics there is a quarter deck the + + + align:start position:0% +mechanics there is a quarter deck the +bridge equation also known as kdv + + align:start position:0% +bridge equation also known as kdv + + + align:start position:0% +bridge equation also known as kdv +there's a bunch of different wave + + align:start position:0% +there's a bunch of different wave + + + align:start position:0% +there's a bunch of different wave +equations so we need to we need some way + + align:start position:0% +equations so we need to we need some way + + + align:start position:0% +equations so we need to we need some way +to discriminate nevertheless the other + + align:start position:0% +to discriminate nevertheless the other + + + align:start position:0% +to discriminate nevertheless the other +wave equations they are referred with + + align:start position:0% +wave equations they are referred with + + + align:start position:0% +wave equations they are referred with +their name so when you wanna refer to so + + align:start position:0% +their name so when you wanna refer to so + + + align:start position:0% +their name so when you wanna refer to so +I think it is a question you say + + align:start position:0% +I think it is a question you say + + + align:start position:0% +I think it is a question you say +Salonika this equation when by + + align:start position:0% +Salonika this equation when by + + + align:start position:0% +Salonika this equation when by +convention when you say wave equation + + align:start position:0% +convention when you say wave equation + + + align:start position:0% +convention when you say wave equation +you mean this one so the Helmholtz okay + + align:start position:0% +you mean this one so the Helmholtz okay + + + align:start position:0% +you mean this one so the Helmholtz okay +but it's all very nice but and it's + + align:start position:0% +but it's all very nice but and it's + + + align:start position:0% +but it's all very nice but and it's +actually done on your slides so there's + + align:start position:0% +actually done on your slides so there's + + + align:start position:0% +actually done on your slides so there's +no reason to to to organize over what I + + align:start position:0% +no reason to to to organize over what I + + + align:start position:0% +no reason to to to organize over what I +did over here what I would like to + + align:start position:0% +did over here what I would like to + + + align:start position:0% +did over here what I would like to +remind you before I move on is for the + + align:start position:0% +remind you before I move on is for the + + + align:start position:0% +remind you before I move on is for the +simple case of a first of all but you + + align:start position:0% +simple case of a first of all but you + + + align:start position:0% +simple case of a first of all but you +can imagine that this is a very general + + align:start position:0% +can imagine that this is a very general + + + align:start position:0% +can imagine that this is a very general +kind of solution because what is see + + align:start position:0% +kind of solution because what is see + + + align:start position:0% +kind of solution because what is see +after all I put up this this strange + + align:start position:0% +after all I put up this this strange + + + align:start position:0% +after all I put up this this strange +shape over here I didn't say where it + + align:start position:0% +shape over here I didn't say where it + + + align:start position:0% +shape over here I didn't say where it +came from so for that matter if someone + + align:start position:0% +came from so for that matter if someone + + + align:start position:0% +came from so for that matter if someone +gives you the wave equation how can you + + align:start position:0% +gives you the wave equation how can you + + + align:start position:0% +gives you the wave equation how can you +go ahead and solve it well we're not + + align:start position:0% +go ahead and solve it well we're not + + + align:start position:0% +go ahead and solve it well we're not +going to do this in great detail here + + align:start position:0% +going to do this in great detail here + + + align:start position:0% +going to do this in great detail here +this is a little bit beside the scope of + + align:start position:0% +this is a little bit beside the scope of + + + align:start position:0% +this is a little bit beside the scope of +the + + align:start position:0% +the + + + align:start position:0% +the +but generally if you need to solve the + + align:start position:0% +but generally if you need to solve the + + + align:start position:0% +but generally if you need to solve the +partial differential like this one you + + align:start position:0% +partial differential like this one you + + + align:start position:0% +partial differential like this one you +need additional information you need the + + align:start position:0% +need additional information you need the + + + align:start position:0% +need additional information you need the +initial conditions how did the wave + + align:start position:0% +initial conditions how did the wave + + + align:start position:0% +initial conditions how did the wave +start at time equal to zero and you also + + align:start position:0% +start at time equal to zero and you also + + + align:start position:0% +start at time equal to zero and you also +need the boundary condition so what + + align:start position:0% +need the boundary condition so what + + + align:start position:0% +need the boundary condition so what +happens to the wave has it expands + + align:start position:0% +happens to the wave has it expands + + + align:start position:0% +happens to the wave has it expands +sometimes the boundary condition is at + + align:start position:0% +sometimes the boundary condition is at + + + align:start position:0% +sometimes the boundary condition is at +infinity maybe the wave is not bounded + + align:start position:0% +infinity maybe the wave is not bounded + + + align:start position:0% +infinity maybe the wave is not bounded +it can propagate outwards all the way + + align:start position:0% +it can propagate outwards all the way + + + align:start position:0% +it can propagate outwards all the way +and that's a good example of what + + align:start position:0% +and that's a good example of what + + + align:start position:0% +and that's a good example of what +happens if you are you know flying with + + align:start position:0% +happens if you are you know flying with + + + align:start position:0% +happens if you are you know flying with +a helicopter on top of the ocean and you + + align:start position:0% +a helicopter on top of the ocean and you + + + align:start position:0% +a helicopter on top of the ocean and you +drop I don't know you drop a stone into + + align:start position:0% +drop I don't know you drop a stone into + + + align:start position:0% +drop I don't know you drop a stone into +the surface of the ocean then the wave + + align:start position:0% +the surface of the ocean then the wave + + + align:start position:0% +the surface of the ocean then the wave +that you generate the wave you that you + + align:start position:0% +that you generate the wave you that you + + + align:start position:0% +that you generate the wave you that you +generate to a good approximation you can + + align:start position:0% +generate to a good approximation you can + + + align:start position:0% +generate to a good approximation you can +use infinite boundary conditions right + + align:start position:0% +use infinite boundary conditions right + + + align:start position:0% +use infinite boundary conditions right +because the ocean is not quite infinite + + align:start position:0% +because the ocean is not quite infinite + + + align:start position:0% +because the ocean is not quite infinite +but very large if if you generate in a + + align:start position:0% +but very large if if you generate in a + + + align:start position:0% +but very large if if you generate in a +wave in a small channel then you might + + align:start position:0% +wave in a small channel then you might + + + align:start position:0% +wave in a small channel then you might +have to include boundary conditions + + align:start position:0% +have to include boundary conditions + + + align:start position:0% +have to include boundary conditions +right because the wave will be confined + + align:start position:0% +right because the wave will be confined + + + align:start position:0% +right because the wave will be confined +by the walls of the channel and we will + + align:start position:0% +by the walls of the channel and we will + + + align:start position:0% +by the walls of the channel and we will +see later that this is actually quite + + align:start position:0% +see later that this is actually quite + + + align:start position:0% +see later that this is actually quite +commonly the case in optics we don't + + align:start position:0% +commonly the case in optics we don't + + + align:start position:0% +commonly the case in optics we don't +call them channels we call them wave + + align:start position:0% +call them channels we call them wave + + + align:start position:0% +call them channels we call them wave +guides but but the boundary conditions + + align:start position:0% +guides but but the boundary conditions + + + align:start position:0% +guides but but the boundary conditions +can actually significantly alter the + + align:start position:0% +can actually significantly alter the + + + align:start position:0% +can actually significantly alter the +shape of the wave so what I mean here is + + align:start position:0% +shape of the wave so what I mean here is + + + align:start position:0% +shape of the wave so what I mean here is +just a resort to give you an idea a what + + align:start position:0% +just a resort to give you an idea a what + + + align:start position:0% +just a resort to give you an idea a what +a called solved nothing interesting + + align:start position:0% +a called solved nothing interesting + + + align:start position:0% +a called solved nothing interesting +happens here but this is actually a + + align:start position:0% +happens here but this is actually a + + + align:start position:0% +happens here but this is actually a +solution of the wave equation with a + + align:start position:0% +solution of the wave equation with a + + + align:start position:0% +solution of the wave equation with a +particular initial condition where at + + align:start position:0% +particular initial condition where at + + + align:start position:0% +particular initial condition where at +time equals 0 the wave is a sinusoid so + + align:start position:0% +time equals 0 the wave is a sinusoid so + + + align:start position:0% +time equals 0 the wave is a sinusoid so +so I basically said I said that this is + + align:start position:0% +so I basically said I said that this is + + + align:start position:0% +so I basically said I said that this is +my equation and I say that F of Z at T + + align:start position:0% +my equation and I say that F of Z at T + + + align:start position:0% +my equation and I say that F of Z at T +equals 0 equals some sinusoid with + + align:start position:0% +equals 0 equals some sinusoid with + + + align:start position:0% +equals 0 equals some sinusoid with +amplitude a and a wave number K + + align:start position:0% +amplitude a and a wave number K + + + align:start position:0% +amplitude a and a wave number K +if that is the case then all by + + align:start position:0% +if that is the case then all by + + + align:start position:0% +if that is the case then all by +inspection I don't have to do anything + + align:start position:0% +inspection I don't have to do anything + + + align:start position:0% +inspection I don't have to do anything +very important and what I did not write + + align:start position:0% +very important and what I did not write + + + align:start position:0% +very important and what I did not write +down but it is implied is that the + + align:start position:0% +down but it is implied is that the + + + align:start position:0% +down but it is implied is that the +boundary conditions are free so this + + align:start position:0% +boundary conditions are free so this + + + align:start position:0% +boundary conditions are free so this +wave is free to go as far as it pleases + + align:start position:0% +wave is free to go as far as it pleases + + + align:start position:0% +wave is free to go as far as it pleases +without any special constraints so if + + align:start position:0% +without any special constraints so if + + + align:start position:0% +without any special constraints so if +that is the case then then you can write + + align:start position:0% +that is the case then then you can write + + + align:start position:0% +that is the case then then you can write +the solution almost by inspection f of Z + + align:start position:0% +the solution almost by inspection f of Z + + + align:start position:0% +the solution almost by inspection f of Z +comma T equals a cosine KZ by K Z minus + + align:start position:0% +comma T equals a cosine KZ by K Z minus + + + align:start position:0% +comma T equals a cosine KZ by K Z minus +CT and you can see by inspection here + + align:start position:0% +CT and you can see by inspection here + + + align:start position:0% +CT and you can see by inspection here +that because of the way I wrote it this + + align:start position:0% +that because of the way I wrote it this + + + align:start position:0% +that because of the way I wrote it this +actually satisfies both of the partial + + align:start position:0% +actually satisfies both of the partial + + + align:start position:0% +actually satisfies both of the partial +differential equation the wave equation + + align:start position:0% +differential equation the wave equation + + + align:start position:0% +differential equation the wave equation +and the boundary condition so therefore + + align:start position:0% +and the boundary condition so therefore + + + align:start position:0% +and the boundary condition so therefore +this is a proper solution of the of the + + align:start position:0% +this is a proper solution of the of the + + + align:start position:0% +this is a proper solution of the of the +wave equation in fact I only wrote half + + align:start position:0% +wave equation in fact I only wrote half + + + align:start position:0% +wave equation in fact I only wrote half +of it the wave remember can go forwards + + align:start position:0% +of it the wave remember can go forwards + + + align:start position:0% +of it the wave remember can go forwards +it can go backward so to cover both + + align:start position:0% +it can go backward so to cover both + + + align:start position:0% +it can go backward so to cover both +cases I actually write the solution this + + align:start position:0% +cases I actually write the solution this + + + align:start position:0% +cases I actually write the solution this +way with a data that I have here + + align:start position:0% +way with a data that I have here + + + align:start position:0% +way with a data that I have here +actually I don't have enough to specify + + align:start position:0% +actually I don't have enough to specify + + + align:start position:0% +actually I don't have enough to specify +actually in principle the wave can go + + align:start position:0% +actually in principle the wave can go + + + align:start position:0% +actually in principle the wave can go +both ways I would have to apply to give + + align:start position:0% +both ways I would have to apply to give + + + align:start position:0% +both ways I would have to apply to give +you additional information to know which + + align:start position:0% +you additional information to know which + + + align:start position:0% +you additional information to know which +actually happened the other thing that I + + align:start position:0% +actually happened the other thing that I + + + align:start position:0% +actually happened the other thing that I +wanted to point out which is not really + + align:start position:0% +wanted to point out which is not really + + + align:start position:0% +wanted to point out which is not really +difficult but if X I'm getting used to + + align:start position:0% +difficult but if X I'm getting used to + + + align:start position:0% +difficult but if X I'm getting used to +is the various terms that appear inside + + align:start position:0% +is the various terms that appear inside + + + align:start position:0% +is the various terms that appear inside +this equation over here so the terms + + align:start position:0% +this equation over here so the terms + + + align:start position:0% +this equation over here so the terms +that we've been very familiar with is + + align:start position:0% +that we've been very familiar with is + + + align:start position:0% +that we've been very familiar with is +the wavelength there's another over + + align:start position:0% +the wavelength there's another over + + + align:start position:0% +the wavelength there's another over +those crazy Greek symbols that called + + align:start position:0% +those crazy Greek symbols that called + + + align:start position:0% +those crazy Greek symbols that called +lambda and the wavelength is related to + + align:start position:0% +lambda and the wavelength is related to + + + align:start position:0% +lambda and the wavelength is related to +the quantity that we have over here as 2 + + align:start position:0% +the quantity that we have over here as 2 + + + align:start position:0% +the quantity that we have over here as 2 +PI over lambda equals K so lambda is the + + align:start position:0% +PI over lambda equals K so lambda is the + + + align:start position:0% +PI over lambda equals K so lambda is the +wavelength as I said K is known as the + + align:start position:0% +wavelength as I said K is known as the + + + align:start position:0% +wavelength as I said K is known as the +wave number so so the relationship that + + align:start position:0% +wave number so so the relationship that + + + align:start position:0% +wave number so so the relationship that +they have that they have is if you think + + align:start position:0% +they have that they have is if you think + + + align:start position:0% +they have that they have is if you think +of the wavelength as a period which it + + align:start position:0% +of the wavelength as a period which it + + + align:start position:0% +of the wavelength as a period which it +is the period of the wave in the space + + align:start position:0% +is the period of the wave in the space + + + align:start position:0% +is the period of the wave in the space +domain then K would actually be + + align:start position:0% +domain then K would actually be + + + align:start position:0% +domain then K would actually be +the angular frequency but we call it + + align:start position:0% +the angular frequency but we call it + + + align:start position:0% +the angular frequency but we call it +wave number to keep them separated okay + + align:start position:0% +wave number to keep them separated okay + + + align:start position:0% +wave number to keep them separated okay +equivalently you can define the actual + + align:start position:0% +equivalently you can define the actual + + + align:start position:0% +equivalently you can define the actual +angular frequency of the wave usually + + align:start position:0% +angular frequency of the wave usually + + + align:start position:0% +angular frequency of the wave usually +this goes by the symbol Omega and from + + align:start position:0% +this goes by the symbol Omega and from + + + align:start position:0% +this goes by the symbol Omega and from +this equation over here very simply you + + align:start position:0% +this equation over here very simply you + + + align:start position:0% +this equation over here very simply you +can see that if you wanted to write it + + align:start position:0% +can see that if you wanted to write it + + + align:start position:0% +can see that if you wanted to write it +in the form a cosine KZ minus Omega T + + align:start position:0% +in the form a cosine KZ minus Omega T + + + align:start position:0% +in the form a cosine KZ minus Omega T +then clearly Omega is the angular + + align:start position:0% +then clearly Omega is the angular + + + align:start position:0% +then clearly Omega is the angular +frequency and be comparing the two + + align:start position:0% +frequency and be comparing the two + + + align:start position:0% +frequency and be comparing the two +equations you can see that Omega equals + + align:start position:0% +equations you can see that Omega equals + + + align:start position:0% +equations you can see that Omega equals +KC so the angular frequency of n is + + align:start position:0% +KC so the angular frequency of n is + + + align:start position:0% +KC so the angular frequency of n is +related to the spatial frequency the + + align:start position:0% +related to the spatial frequency the + + + align:start position:0% +related to the spatial frequency the +wave number and the and the frequency + + align:start position:0% +wave number and the and the frequency + + + align:start position:0% +wave number and the and the frequency +and the and the I'm sorry and the speed + + align:start position:0% +and the and the I'm sorry and the speed + + + align:start position:0% +and the and the I'm sorry and the speed +over the wave and of course this is + + align:start position:0% +over the wave and of course this is + + + align:start position:0% +over the wave and of course this is +nothing new because we've seen this + + align:start position:0% +nothing new because we've seen this + + + align:start position:0% +nothing new because we've seen this +equation before but we saw it in this + + align:start position:0% +equation before but we saw it in this + + + align:start position:0% +equation before but we saw it in this +guide and that's why I'm going through + + align:start position:0% +guide and that's why I'm going through + + + align:start position:0% +guide and that's why I'm going through +this because all the symbols they can be + + align:start position:0% +this because all the symbols they can be + + + align:start position:0% +this because all the symbols they can be +played around with quite a bit so this + + align:start position:0% +played around with quite a bit so this + + + align:start position:0% +played around with quite a bit so this +equation I can rewrite and the very + + align:start position:0% +equation I can rewrite and the very + + + align:start position:0% +equation I can rewrite and the very +light is like this so Omega is the + + align:start position:0% +light is like this so Omega is the + + + align:start position:0% +light is like this so Omega is the +angular frequency we also have the plane + + align:start position:0% +angular frequency we also have the plane + + + align:start position:0% +angular frequency we also have the plane +so to speak frequency nu which is + + align:start position:0% +so to speak frequency nu which is + + + align:start position:0% +so to speak frequency nu which is +related as Omega over 2 pi okay + + align:start position:0% +related as Omega over 2 pi okay + + + align:start position:0% +related as Omega over 2 pi okay +one of them goes full the radiance + + align:start position:0% +one of them goes full the radiance + + + align:start position:0% +one of them goes full the radiance +I mean I'm sorry is better than in full + + align:start position:0% +I mean I'm sorry is better than in full + + + align:start position:0% +I mean I'm sorry is better than in full +radians per second this is Omega nu is + + align:start position:0% +radians per second this is Omega nu is + + + align:start position:0% +radians per second this is Omega nu is +measured in health simply inverse + + align:start position:0% +measured in health simply inverse + + + align:start position:0% +measured in health simply inverse +seconds okay pleasure + + align:start position:0% +seconds okay pleasure + + + align:start position:0% +seconds okay pleasure +so so I can substitute in this equation + + align:start position:0% +so so I can substitute in this equation + + + align:start position:0% +so so I can substitute in this equation +Omega is 2 pi times nu K according to my + + align:start position:0% +Omega is 2 pi times nu K according to my + + + align:start position:0% +Omega is 2 pi times nu K according to my +question over here is 2 pi upon lambda + + align:start position:0% +question over here is 2 pi upon lambda + + + align:start position:0% +question over here is 2 pi upon lambda +and C is C so the two PI's cancel here + + align:start position:0% + + + + align:start position:0% + +the to pass cancel here and I end up + + align:start position:0% +the to pass cancel here and I end up + + + align:start position:0% +the to pass cancel here and I end up +with the question C equals lambda nu + + align:start position:0% +with the question C equals lambda nu + + + align:start position:0% +with the question C equals lambda nu +which I think of what are they seen a + + align:start position:0% +which I think of what are they seen a + + + align:start position:0% +which I think of what are they seen a +couple of times before who call it the + + align:start position:0% +couple of times before who call it the + + + align:start position:0% +couple of times before who call it the +dispersion relation of the wave okay so + + align:start position:0% +dispersion relation of the wave okay so + + + align:start position:0% +dispersion relation of the wave okay so +this is how all this come about + + align:start position:0% +this is how all this come about + + + align:start position:0% +this is how all this come about +I haven't said anything new + + align:start position:0% +I haven't said anything new + + + align:start position:0% +I haven't said anything new +about this I'm just trying to point out + + align:start position:0% +about this I'm just trying to point out + + + align:start position:0% +about this I'm just trying to point out +the different ways that this equation + + align:start position:0% +the different ways that this equation + + + align:start position:0% +the different ways that this equation +can Menace asthma can manifest itself + + align:start position:0% +can Menace asthma can manifest itself + + + align:start position:0% +can Menace asthma can manifest itself +okay and the other two terms that we + + align:start position:0% +okay and the other two terms that we + + + align:start position:0% +okay and the other two terms that we +encountered last time and I wanted to + + align:start position:0% +encountered last time and I wanted to + + + align:start position:0% +encountered last time and I wanted to +remind you one is the amplitude of the + + align:start position:0% +remind you one is the amplitude of the + + + align:start position:0% +remind you one is the amplitude of the +wave this is this constant a over here + + align:start position:0% +wave this is this constant a over here + + + align:start position:0% +wave this is this constant a over here +for some reason in the slide that I + + align:start position:0% +for some reason in the slide that I + + + align:start position:0% +for some reason in the slide that I +decided to call it a knot anyway it is + + align:start position:0% +decided to call it a knot anyway it is + + + align:start position:0% +decided to call it a knot anyway it is +the same thing and also we said last + + align:start position:0% +the same thing and also we said last + + + align:start position:0% +the same thing and also we said last +time that in general the wave can also + + align:start position:0% +time that in general the wave can also + + + align:start position:0% +time that in general the wave can also +have a phase delay so in here i can also + + align:start position:0% +have a phase delay so in here i can also + + + align:start position:0% +have a phase delay so in here i can also +add the constant plus fee which does not + + align:start position:0% +add the constant plus fee which does not + + + align:start position:0% +add the constant plus fee which does not +really do anything by itself all it does + + align:start position:0% +really do anything by itself all it does + + + align:start position:0% +really do anything by itself all it does +if you wish is equivalently it shifts + + align:start position:0% +if you wish is equivalently it shifts + + + align:start position:0% +if you wish is equivalently it shifts +the time origin so that's a relatively + + align:start position:0% +the time origin so that's a relatively + + + align:start position:0% +the time origin so that's a relatively +trivial thing because after all i am + + align:start position:0% +trivial thing because after all i am + + + align:start position:0% +trivial thing because after all i am +free to start my clock whenever I want + + align:start position:0% +free to start my clock whenever I want + + + align:start position:0% +free to start my clock whenever I want +if I have a wave that never changes I + + align:start position:0% +if I have a wave that never changes I + + + align:start position:0% +if I have a wave that never changes I +can start my clock whenever one so it + + align:start position:0% +can start my clock whenever one so it + + + align:start position:0% +can start my clock whenever one so it +doesn't really make a big difference but + + align:start position:0% +doesn't really make a big difference but + + + align:start position:0% +doesn't really make a big difference but +we saw last time that if you have two + + align:start position:0% +we saw last time that if you have two + + + align:start position:0% +we saw last time that if you have two +waves that are as we said interfering so + + align:start position:0% +waves that are as we said interfering so + + + align:start position:0% +waves that are as we said interfering so +there are simultaneously happening so to + + align:start position:0% +there are simultaneously happening so to + + + align:start position:0% +there are simultaneously happening so to +speak then relatively the relative phase + + align:start position:0% +speak then relatively the relative phase + + + align:start position:0% +speak then relatively the relative phase +delay between the two can actually be + + align:start position:0% +delay between the two can actually be + + + align:start position:0% +delay between the two can actually be +quite significant and I will play this + + align:start position:0% +quite significant and I will play this + + + align:start position:0% +quite significant and I will play this +movie again in this case the two waves + + align:start position:0% +movie again in this case the two waves + + + align:start position:0% +movie again in this case the two waves +are actually they have the same phase + + align:start position:0% +are actually they have the same phase + + + align:start position:0% +are actually they have the same phase +between them in other words they if you + + align:start position:0% +between them in other words they if you + + + align:start position:0% +between them in other words they if you +look at the center they're both + + align:start position:0% +look at the center they're both + + + align:start position:0% +look at the center they're both +simultaneously bright for simultaneously + + align:start position:0% +simultaneously bright for simultaneously + + + align:start position:0% +simultaneously bright for simultaneously +dark whereas in the other case it's the + + align:start position:0% +dark whereas in the other case it's the + + + align:start position:0% +dark whereas in the other case it's the +other way round they're off by PI so + + align:start position:0% +other way round they're off by PI so + + + align:start position:0% +other way round they're off by PI so +when one is maximum the other is minimum + + align:start position:0% +when one is maximum the other is minimum + + + align:start position:0% +when one is maximum the other is minimum +I think it is worth playing this one + + align:start position:0% + + + + align:start position:0% + +this also has the interesting fact that + + align:start position:0% +this also has the interesting fact that + + + align:start position:0% +this also has the interesting fact that +it can happen in hypnotized you so for + + align:start position:0% +it can happen in hypnotized you so for + + + align:start position:0% +it can happen in hypnotized you so for +those of you who are in Boston are not + + align:start position:0% +those of you who are in Boston are not + + + align:start position:0% +those of you who are in Boston are not +fully awake yet yes oh so when you are + + align:start position:0% +fully awake yet yes oh so when you are + + + align:start position:0% +fully awake yet yes oh so when you are +requesting you to push the button + + align:start position:0% + + + + align:start position:0% + +so far dampen our two weeks travel in + + align:start position:0% +so far dampen our two weeks travel in + + + align:start position:0% +so far dampen our two weeks travel in +the opposite direction they have a sim + + align:start position:0% +the opposite direction they have a sim + + + align:start position:0% +the opposite direction they have a sim +amplitude but perfect cancel each other + + align:start position:0% +amplitude but perfect cancel each other + + + align:start position:0% +amplitude but perfect cancel each other +so in this case where does the energy go + + align:start position:0% +so in this case where does the energy go + + + align:start position:0% +so in this case where does the energy go +not quite cancel each other right + + align:start position:0% +not quite cancel each other right + + + align:start position:0% +not quite cancel each other right +so as we will see I will actually do + + align:start position:0% +so as we will see I will actually do + + + align:start position:0% +so as we will see I will actually do +this in a second it's called the + + align:start position:0% +this in a second it's called the + + + align:start position:0% +this in a second it's called the +standing wave so you will see that they + + align:start position:0% +standing wave so you will see that they + + + align:start position:0% +standing wave so you will see that they +don't quite cancel they they just + + align:start position:0% +don't quite cancel they they just + + + align:start position:0% +don't quite cancel they they just +produce it well what is called the + + align:start position:0% +produce it well what is called the + + + align:start position:0% +produce it well what is called the +standing wave so I will get to your + + align:start position:0% +standing wave so I will get to your + + + align:start position:0% +standing wave so I will get to your +question and maybe I think is actually + + align:start position:0% +question and maybe I think is actually + + + align:start position:0% +question and maybe I think is actually +coming up now yeah so give me a second I + + align:start position:0% +coming up now yeah so give me a second I + + + align:start position:0% +coming up now yeah so give me a second I +will get to your question okay + + align:start position:0% + + + + align:start position:0% + +so that is a standing wave so like your + + align:start position:0% +so that is a standing wave so like your + + + align:start position:0% +so that is a standing wave so like your +colleague asked over here suppose that + + align:start position:0% +colleague asked over here suppose that + + + align:start position:0% +colleague asked over here suppose that +you have a superposition of two waves + + align:start position:0% +you have a superposition of two waves + + + align:start position:0% +you have a superposition of two waves +now both are solutions to the wave + + align:start position:0% +now both are solutions to the wave + + + align:start position:0% +now both are solutions to the wave +equation now by the by its looks I don't + + align:start position:0% +equation now by the by its looks I don't + + + align:start position:0% +equation now by the by its looks I don't +want to do the proof here it is it takes + + align:start position:0% +want to do the proof here it is it takes + + + align:start position:0% +want to do the proof here it is it takes +three lines but by its looks this is a + + align:start position:0% +three lines but by its looks this is a + + + align:start position:0% +three lines but by its looks this is a +linear differential equation so + + align:start position:0% +linear differential equation so + + + align:start position:0% +linear differential equation so +basically it means that if you know one + + align:start position:0% +basically it means that if you know one + + + align:start position:0% +basically it means that if you know one +solution you know another solution and + + align:start position:0% +solution you know another solution and + + + align:start position:0% +solution you know another solution and +then you add these two solutions after + + align:start position:0% +then you add these two solutions after + + + align:start position:0% +then you add these two solutions after +multiplying by arbitrary constants the + + align:start position:0% +multiplying by arbitrary constants the + + + align:start position:0% +multiplying by arbitrary constants the +result from the addition is still a + + align:start position:0% +result from the addition is still a + + + align:start position:0% +result from the addition is still a +solution to this equation very + + align:start position:0% +solution to this equation very + + + align:start position:0% +solution to this equation very +fundamental property of that we use + + align:start position:0% +fundamental property of that we use + + + align:start position:0% +fundamental property of that we use +again and again later in the class so + + align:start position:0% +again and again later in the class so + + + align:start position:0% +again and again later in the class so +that said suppose that I pick two + + align:start position:0% +that said suppose that I pick two + + + align:start position:0% +that said suppose that I pick two +solutions that they already saw one of + + align:start position:0% +solutions that they already saw one of + + + align:start position:0% +solutions that they already saw one of +them is a forward propagating wave the + + align:start position:0% +them is a forward propagating wave the + + + align:start position:0% +them is a forward propagating wave the +other is a backward propagating wave so + + align:start position:0% +other is a backward propagating wave so + + + align:start position:0% +other is a backward propagating wave so +here they are + + align:start position:0% +here they are + + + align:start position:0% +here they are +the one with the minus is propagating + + align:start position:0% +the one with the minus is propagating + + + align:start position:0% +the one with the minus is propagating +form work the one with the plus is + + align:start position:0% +form work the one with the plus is + + + align:start position:0% +form work the one with the plus is +propagating backward so your colleague + + align:start position:0% +propagating backward so your colleague + + + align:start position:0% +propagating backward so your colleague +here asked what will happen if I + + align:start position:0% +here asked what will happen if I + + + align:start position:0% +here asked what will happen if I +superimpose them so one of them is going + + align:start position:0% +superimpose them so one of them is going + + + align:start position:0% +superimpose them so one of them is going +to the right one is to the left are they + + align:start position:0% +to the right one is to the left are they + + + align:start position:0% +to the right one is to the left are they +gonna cancel what are they gonna do okay + + align:start position:0% +gonna cancel what are they gonna do okay + + + align:start position:0% +gonna cancel what are they gonna do okay +so this is a computational so perhaps + + align:start position:0% +so this is a computational so perhaps + + + align:start position:0% +so this is a computational so perhaps +you should not trust it after all + + align:start position:0% +you should not trust it after all + + + align:start position:0% +you should not trust it after all +what is this but anyway this is what I + + align:start position:0% +what is this but anyway this is what I + + + align:start position:0% +what is this but anyway this is what I +got in MATLAB when I simulated this okay + + align:start position:0% +got in MATLAB when I simulated this okay + + + align:start position:0% +got in MATLAB when I simulated this okay +let me play this again so this is the + + align:start position:0% +let me play this again so this is the + + + align:start position:0% +let me play this again so this is the +result of the two waves + + align:start position:0% +result of the two waves + + + align:start position:0% +result of the two waves +okay I pushed the button I did not let a + + align:start position:0% +okay I pushed the button I did not let a + + + align:start position:0% +okay I pushed the button I did not let a +movie again I revealed the derivation + + align:start position:0% +movie again I revealed the derivation + + + align:start position:0% +movie again I revealed the derivation +but that's quite okay okay so I will + + align:start position:0% +but that's quite okay okay so I will + + + align:start position:0% +but that's quite okay okay so I will +actually meant to do this on the one the + + align:start position:0% +actually meant to do this on the one the + + + align:start position:0% +actually meant to do this on the one the +free hand here + + align:start position:0% +free hand here + + + align:start position:0% +free hand here +okay nevermind ignore what you see on + + align:start position:0% +okay nevermind ignore what you see on + + + align:start position:0% +okay nevermind ignore what you see on +the on there slide then just watch the + + align:start position:0% +the on there slide then just watch the + + + align:start position:0% +the on there slide then just watch the +the whiteboard mmm I guess I can call it + + align:start position:0% +the whiteboard mmm I guess I can call it + + + align:start position:0% +the whiteboard mmm I guess I can call it +white board can't I and it is a + + align:start position:0% +white board can't I and it is a + + + align:start position:0% +white board can't I and it is a +whiteboard + + align:start position:0% +whiteboard + + + align:start position:0% +whiteboard +okay okay so so here the two waves + + align:start position:0% +okay okay so so here the two waves + + + align:start position:0% +okay okay so so here the two waves +so I actually omitted the should have + + align:start position:0% +so I actually omitted the should have + + + align:start position:0% +so I actually omitted the should have +said that not only are the + + align:start position:0% +said that not only are the + + + align:start position:0% +said that not only are the +counter-propagating but also I pick them + + align:start position:0% +counter-propagating but also I pick them + + + align:start position:0% +counter-propagating but also I pick them +both to be harmonic waves so that well + + align:start position:0% +both to be harmonic waves so that well + + + align:start position:0% +both to be harmonic waves so that well +so that would who can do the math easily + + align:start position:0% +so that would who can do the math easily + + + align:start position:0% +so that would who can do the math easily +okay so let's write this out so we + + align:start position:0% +okay so let's write this out so we + + + align:start position:0% +okay so let's write this out so we +picked the exact the identical amplitude + + align:start position:0% +picked the exact the identical amplitude + + + align:start position:0% +picked the exact the identical amplitude +so one of them will be written as did + + align:start position:0% +so one of them will be written as did + + + align:start position:0% +so one of them will be written as did +you say Onizuka failure okay + + align:start position:0% + + + + align:start position:0% + +okay now for sim for generality I don't + + align:start position:0% +okay now for sim for generality I don't + + + align:start position:0% +okay now for sim for generality I don't +really have to but for generality I also + + align:start position:0% +really have to but for generality I also + + + align:start position:0% +really have to but for generality I also +added the face face delay fee to the + + align:start position:0% +added the face face delay fee to the + + + align:start position:0% +added the face face delay fee to the +first wave so this one is forward and + + align:start position:0% +first wave so this one is forward and + + + align:start position:0% +first wave so this one is forward and +then I have the other one which looks + + align:start position:0% +then I have the other one which looks + + + align:start position:0% +then I have the other one which looks +very similar except for this devious + + align:start position:0% +very similar except for this devious + + + align:start position:0% +very similar except for this devious +minus sign that goes backward okay and + + align:start position:0% +minus sign that goes backward okay and + + + align:start position:0% +minus sign that goes backward okay and +the superposition principle says that + + align:start position:0% +the superposition principle says that + + + align:start position:0% +the superposition principle says that +they can simply add the two waves and + + align:start position:0% +they can simply add the two waves and + + + align:start position:0% +they can simply add the two waves and +the summation is still a solution to the + + align:start position:0% +the summation is still a solution to the + + + align:start position:0% +the summation is still a solution to the +wave equation therefore still a valid + + align:start position:0% +wave equation therefore still a valid + + + align:start position:0% +wave equation therefore still a valid +wave okay so what is the result so now I + + align:start position:0% +wave okay so what is the result so now I + + + align:start position:0% +wave okay so what is the result so now I +don't know how how to tell you to the + + align:start position:0% +don't know how how to tell you to the + + + align:start position:0% +don't know how how to tell you to the +memories + + align:start position:0% +memories + + + align:start position:0% +memories +most people look it up in books of + + align:start position:0% +most people look it up in books of + + + align:start position:0% +most people look it up in books of +trigonometry I have a certain mnemonic + + align:start position:0% +trigonometry I have a certain mnemonic + + + align:start position:0% +trigonometry I have a certain mnemonic +for it but I will not tell you but + + align:start position:0% +for it but I will not tell you but + + + align:start position:0% +for it but I will not tell you but +anyway so there's a remedy monitor says + + align:start position:0% +anyway so there's a remedy monitor says + + + align:start position:0% +anyway so there's a remedy monitor says +if you have the sum of two cosines + + align:start position:0% +if you have the sum of two cosines + + + align:start position:0% +if you have the sum of two cosines +equals now this is a mathematical + + align:start position:0% +equals now this is a mathematical + + + align:start position:0% +equals now this is a mathematical +property so there's no intuition to be + + align:start position:0% +property so there's no intuition to be + + + align:start position:0% +property so there's no intuition to be +derived here this is this is obtained by + + align:start position:0% +derived here this is this is obtained by + + + align:start position:0% +derived here this is this is obtained by +trigonometric manipulation equals twice + + align:start position:0% +trigonometric manipulation equals twice + + + align:start position:0% +trigonometric manipulation equals twice +cosine a plus B over 2 cosine a minus B + + align:start position:0% +cosine a plus B over 2 cosine a minus B + + + align:start position:0% +cosine a plus B over 2 cosine a minus B +over 2 okay so I never remember this one + + align:start position:0% +over 2 okay so I never remember this one + + + align:start position:0% +over 2 okay so I never remember this one +I will tell you actually I am my + + align:start position:0% +I will tell you actually I am my + + + align:start position:0% +I will tell you actually I am my +mnemonic is not is not that in strange + + align:start position:0% +mnemonic is not is not that in strange + + + align:start position:0% +mnemonic is not is not that in strange +all I remember is that if you have + + align:start position:0% +all I remember is that if you have + + + align:start position:0% +all I remember is that if you have +cosine of a plus of two things + + align:start position:0% +cosine of a plus of two things + + + align:start position:0% +cosine of a plus of two things +it equals let me write it in your own + + align:start position:0% +it equals let me write it in your own + + + align:start position:0% +it equals let me write it in your own +linkage so cosine of two things + + align:start position:0% + + + + align:start position:0% + +it has a minus sign here and sign or two + + align:start position:0% +it has a minus sign here and sign or two + + + align:start position:0% +it has a minus sign here and sign or two +things + + align:start position:0% + + + + align:start position:0% + +okay these two I have memorized and you + + align:start position:0% +okay these two I have memorized and you + + + align:start position:0% +okay these two I have memorized and you +can see very easily that from this two + + align:start position:0% +can see very easily that from this two + + + align:start position:0% +can see very easily that from this two +you can obtain the question we said + + align:start position:0% +you can obtain the question we said + + + align:start position:0% +you can obtain the question we said +before because for example you can write + + align:start position:0% +before because for example you can write + + + align:start position:0% +before because for example you can write +cosine alpha plus that plus minus beta + + align:start position:0% +cosine alpha plus that plus minus beta + + + align:start position:0% +cosine alpha plus that plus minus beta +equals cosine alpha cosine beta minus + + align:start position:0% +equals cosine alpha cosine beta minus + + + align:start position:0% +equals cosine alpha cosine beta minus +plus sine alpha sine beta okay so if you + + align:start position:0% +plus sine alpha sine beta okay so if you + + + align:start position:0% +plus sine alpha sine beta okay so if you +add the term with a plus and the time + + align:start position:0% +add the term with a plus and the time + + + align:start position:0% +add the term with a plus and the time +with a minus the sine terms of a polite + + align:start position:0% +with a minus the sine terms of a polite + + + align:start position:0% +with a minus the sine terms of a polite +and you end up with with a identity that + + align:start position:0% +and you end up with with a identity that + + + align:start position:0% +and you end up with with a identity that +they're before so this is Magne monic + + align:start position:0% +they're before so this is Magne monic + + + align:start position:0% +they're before so this is Magne monic +for remember this one we will not have + + align:start position:0% +for remember this one we will not have + + + align:start position:0% +for remember this one we will not have +to do this too often because the only + + align:start position:0% +to do this too often because the only + + + align:start position:0% +to do this too often because the only +last time if you remember who introduced + + align:start position:0% +last time if you remember who introduced + + + align:start position:0% +last time if you remember who introduced +phasers going to reduce the complex + + align:start position:0% +phasers going to reduce the complex + + + align:start position:0% +phasers going to reduce the complex +notation for waves so now we don't have + + align:start position:0% +notation for waves so now we don't have + + + align:start position:0% +notation for waves so now we don't have +to deal with this trigonometry very + + align:start position:0% +to deal with this trigonometry very + + + align:start position:0% +to deal with this trigonometry very +often in this case there's no way out + + align:start position:0% +often in this case there's no way out + + + align:start position:0% +often in this case there's no way out +because well actually there's a way out + + align:start position:0% +because well actually there's a way out + + + align:start position:0% +because well actually there's a way out +but it is simpler to do it okay right so + + align:start position:0% +but it is simpler to do it okay right so + + + align:start position:0% +but it is simpler to do it okay right so +now I have basically a equals KZ minus + + align:start position:0% +now I have basically a equals KZ minus + + + align:start position:0% +now I have basically a equals KZ minus +Omega T plus V B equals KZ plus Omega T + + align:start position:0% +Omega T plus V B equals KZ plus Omega T + + + align:start position:0% +Omega T plus V B equals KZ plus Omega T +plus V so if you apply my formula here + + align:start position:0% +plus V so if you apply my formula here + + + align:start position:0% +plus V so if you apply my formula here +you will find that the wave actually + + align:start position:0% +you will find that the wave actually + + + align:start position:0% +you will find that the wave actually +okay the amplitude is the same I pick up + + align:start position:0% +okay the amplitude is the same I pick up + + + align:start position:0% +okay the amplitude is the same I pick up +a factor of 2 so it is 2 and then I have + + align:start position:0% +a factor of 2 so it is 2 and then I have + + + align:start position:0% +a factor of 2 so it is 2 and then I have +the cosine of the sum so if I sum the + + align:start position:0% +the cosine of the sum so if I sum the + + + align:start position:0% +the cosine of the sum so if I sum the +two the time param will disappear so + + align:start position:0% +two the time param will disappear so + + + align:start position:0% +two the time param will disappear so +we'll have cosine and that is well you + + align:start position:0% +we'll have cosine and that is well you + + + align:start position:0% +we'll have cosine and that is well you +get twice of it but there's a factor of + + align:start position:0% +get twice of it but there's a factor of + + + align:start position:0% +get twice of it but there's a factor of +2 years of the console will be cosine + + align:start position:0% +2 years of the console will be cosine + + + align:start position:0% +2 years of the console will be cosine +cosine KZ plus V and if I subtract the + + align:start position:0% +cosine KZ plus V and if I subtract the + + + align:start position:0% +cosine KZ plus V and if I subtract the +two then actually the special terms and + + align:start position:0% +two then actually the special terms and + + + align:start position:0% +two then actually the special terms and +the phase will disappear and I will get + + align:start position:0% +the phase will disappear and I will get + + + align:start position:0% +the phase will disappear and I will get +a cosine Omega T okay now do I believe + + align:start position:0% +a cosine Omega T okay now do I believe + + + align:start position:0% +a cosine Omega T okay now do I believe +MATLAB I think I should believe MATLAB + + align:start position:0% +MATLAB I think I should believe MATLAB + + + align:start position:0% +MATLAB I think I should believe MATLAB +because let's see what did MATLAB saw + + align:start position:0% +because let's see what did MATLAB saw + + + align:start position:0% +because let's see what did MATLAB saw +here time is frozen so you see basically + + align:start position:0% +here time is frozen so you see basically + + + align:start position:0% +here time is frozen so you see basically +the same term where this has been + + align:start position:0% +the same term where this has been + + + align:start position:0% +the same term where this has been +replaced by constant because the first + + align:start position:0% +replaced by constant because the first + + + align:start position:0% +replaced by constant because the first +time so indeed this looks like a + + align:start position:0% +time so indeed this looks like a + + + align:start position:0% +time so indeed this looks like a +sinusoid of the same frequency as we had + + align:start position:0% +sinusoid of the same frequency as we had + + + align:start position:0% +sinusoid of the same frequency as we had +before + + align:start position:0% +before + + + align:start position:0% +before +and actually of course you have no way + + align:start position:0% +and actually of course you have no way + + + align:start position:0% +and actually of course you have no way +of knowing that but the waves that they + + align:start position:0% +of knowing that but the waves that they + + + align:start position:0% +of knowing that but the waves that they +entered had an amplitude that was half + + align:start position:0% +entered had an amplitude that was half + + + align:start position:0% +entered had an amplitude that was half +of this so basically the factor of two + + align:start position:0% +of this so basically the factor of two + + + align:start position:0% +of this so basically the factor of two +was also reproduced by my simulation + + align:start position:0% +was also reproduced by my simulation + + + align:start position:0% +was also reproduced by my simulation +okay now if I play the movie again it is + + align:start position:0% +okay now if I play the movie again it is + + + align:start position:0% +okay now if I play the movie again it is +basically like and freezing time okay so + + align:start position:0% +basically like and freezing time okay so + + + align:start position:0% +basically like and freezing time okay so +here I have unfrozen time and you see + + align:start position:0% +here I have unfrozen time and you see + + + align:start position:0% +here I have unfrozen time and you see +that I get a sinusoidal variation in the + + align:start position:0% +that I get a sinusoidal variation in the + + + align:start position:0% +that I get a sinusoidal variation in the +time domain so therefore that's my term + + align:start position:0% +time domain so therefore that's my term + + + align:start position:0% +time domain so therefore that's my term +cosine Omega T here so basically the + + align:start position:0% +cosine Omega T here so basically the + + + align:start position:0% +cosine Omega T here so basically the +MATLAB simulation is correct we were + + align:start position:0% +MATLAB simulation is correct we were + + + align:start position:0% +MATLAB simulation is correct we were +very happy okay so now then let me come + + align:start position:0% +very happy okay so now then let me come + + + align:start position:0% +very happy okay so now then let me come +to your question we have what happens to + + align:start position:0% +to your question we have what happens to + + + align:start position:0% +to your question we have what happens to +the wave when the when it vanishes right + + align:start position:0% +the wave when the when it vanishes right + + + align:start position:0% +the wave when the when it vanishes right +first of all it doesn't really value Sri + + align:start position:0% +first of all it doesn't really value Sri + + + align:start position:0% +first of all it doesn't really value Sri +I don't know how to do + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that look like at some point the wave + + align:start position:0% +so that look like at some point the wave + + + align:start position:0% +so that look like at some point the wave +vanishes and then it reappears okay + + align:start position:0% +vanishes and then it reappears okay + + + align:start position:0% +vanishes and then it reappears okay +there's a little bit annoying that it + + align:start position:0% +there's a little bit annoying that it + + + align:start position:0% +there's a little bit annoying that it +vanishes but in electromagnetic waves + + align:start position:0% +vanishes but in electromagnetic waves + + + align:start position:0% +vanishes but in electromagnetic waves +and usually in other kinds of waves we + + align:start position:0% +and usually in other kinds of waves we + + + align:start position:0% +and usually in other kinds of waves we +won't worry about the instantaneous + + align:start position:0% +won't worry about the instantaneous + + + align:start position:0% +won't worry about the instantaneous +energy we'll worry about the average + + align:start position:0% +energy we'll worry about the average + + + align:start position:0% +energy we'll worry about the average +energy so what you can see here is that + + align:start position:0% +energy so what you can see here is that + + + align:start position:0% +energy so what you can see here is that +the average energy is actually concerned + + align:start position:0% +the average energy is actually concerned + + + align:start position:0% +the average energy is actually concerned +because as the wave oscillates from a + + align:start position:0% +because as the wave oscillates from a + + + align:start position:0% +because as the wave oscillates from a +maximum to a minimum its average energy + + align:start position:0% +maximum to a minimum its average energy + + + align:start position:0% +maximum to a minimum its average energy +remains the same + + align:start position:0% +remains the same + + + align:start position:0% +remains the same +now you might ask well what happens in + + align:start position:0% +now you might ask well what happens in + + + align:start position:0% +now you might ask well what happens in +between I mean you know what happens + + align:start position:0% +between I mean you know what happens + + + align:start position:0% +between I mean you know what happens +when the when this wave has gone to zero + + align:start position:0% +when the when this wave has gone to zero + + + align:start position:0% +when the when this wave has gone to zero +again a will a central cause of + + align:start position:0% +again a will a central cause of + + + align:start position:0% +again a will a central cause of +electromagnetic waves they well the what + + align:start position:0% +electromagnetic waves they well the what + + + align:start position:0% +electromagnetic waves they well the what +we have done here is we have basically + + align:start position:0% +we have done here is we have basically + + + align:start position:0% +we have done here is we have basically +launched two waves that are moving in + + align:start position:0% +launched two waves that are moving in + + + align:start position:0% +launched two waves that are moving in +opposite direction today so who is + + align:start position:0% +opposite direction today so who is + + + align:start position:0% +opposite direction today so who is +providing the energy well if you are + + align:start position:0% +providing the energy well if you are + + + align:start position:0% +providing the energy well if you are +providing the energy on one end and + + align:start position:0% +providing the energy on one end and + + + align:start position:0% +providing the energy on one end and +someone else is providing the energy on + + align:start position:0% +someone else is providing the energy on + + + align:start position:0% +someone else is providing the energy on +the other end so what happens when what + + align:start position:0% +the other end so what happens when what + + + align:start position:0% +the other end so what happens when what +happens when the two waves cancel is + + align:start position:0% +happens when the two waves cancel is + + + align:start position:0% +happens when the two waves cancel is +that the energy is actually stored in + + align:start position:0% +that the energy is actually stored in + + + align:start position:0% +that the energy is actually stored in +another place which does not show up in + + align:start position:0% +another place which does not show up in + + + align:start position:0% +another place which does not show up in +this equation that's one way to to think + + align:start position:0% +this equation that's one way to to think + + + align:start position:0% +this equation that's one way to to think +about if you if you remember when I saw + + align:start position:0% +about if you if you remember when I saw + + + align:start position:0% +about if you if you remember when I saw +actually you don't remember because you + + align:start position:0% +actually you don't remember because you + + + align:start position:0% +actually you don't remember because you +were not in the class one week ago but a + + align:start position:0% +were not in the class one week ago but a + + + align:start position:0% +were not in the class one week ago but a +certain example of a simple harmonic + + align:start position:0% +certain example of a simple harmonic + + + align:start position:0% +certain example of a simple harmonic +oscillator right so simple harmonic + + align:start position:0% +oscillator right so simple harmonic + + + align:start position:0% +oscillator right so simple harmonic +oscillator goes from zero velocity + + align:start position:0% +oscillator goes from zero velocity + + + align:start position:0% +oscillator goes from zero velocity +maximum potential energy to the edge + + align:start position:0% +maximum potential energy to the edge + + + align:start position:0% +maximum potential energy to the edge +where the velocity now is employed to + + align:start position:0% +where the velocity now is employed to + + + align:start position:0% +where the velocity now is employed to +the left position where the velocity is + + align:start position:0% +the left position where the velocity is + + + align:start position:0% +the left position where the velocity is +maximum and the potential energy has + + align:start position:0% +maximum and the potential energy has + + + align:start position:0% +maximum and the potential energy has +become zero right at the last position + + align:start position:0% +become zero right at the last position + + + align:start position:0% +become zero right at the last position +so the same kind of thing the kinetic + + align:start position:0% +so the same kind of thing the kinetic + + + align:start position:0% +so the same kind of thing the kinetic +energy disappears well what happens to + + align:start position:0% +energy disappears well what happens to + + + align:start position:0% +energy disappears well what happens to +it it has become potential but is very + + align:start position:0% +it it has become potential but is very + + + align:start position:0% +it it has become potential but is very +similar to this the energy has become + + align:start position:0% +similar to this the energy has become + + + align:start position:0% +similar to this the energy has become +potential energy and you don't see it + + align:start position:0% +potential energy and you don't see it + + + align:start position:0% +potential energy and you don't see it +here yeah + + align:start position:0% +here yeah + + + align:start position:0% +here yeah +okay maybe your follow up on the + + align:start position:0% +okay maybe your follow up on the + + + align:start position:0% +okay maybe your follow up on the +question so now let's assume the two we + + align:start position:0% +question so now let's assume the two we + + + align:start position:0% +question so now let's assume the two we +were traveling along the same direction + + align:start position:0% +were traveling along the same direction + + + align:start position:0% +were traveling along the same direction +and that they are out of phase by PI so + + align:start position:0% +and that they are out of phase by PI so + + + align:start position:0% +and that they are out of phase by PI so +music in this case they be a perfect + + align:start position:0% +music in this case they be a perfect + + + align:start position:0% +music in this case they be a perfect +cuts on each other other so where does + + align:start position:0% +cuts on each other other so where does + + + align:start position:0% +cuts on each other other so where does +energy go just for your information the + + align:start position:0% +energy go just for your information the + + + align:start position:0% +energy go just for your information the +previous answer I get is such Simula not + + align:start position:0% +previous answer I get is such Simula not + + + align:start position:0% +previous answer I get is such Simula not +happen in the first place but just not + + align:start position:0% +happen in the first place but just not + + + align:start position:0% +happen in the first place but just not +comfortable with this answer so I would + + align:start position:0% +comfortable with this answer so I would + + + align:start position:0% +comfortable with this answer so I would +like to know your comments well either + + align:start position:0% +like to know your comments well either + + + align:start position:0% +like to know your comments well either +the wave started by phase shift it's + + align:start position:0% +the wave started by phase shift it's + + + align:start position:0% +the wave started by phase shift it's +equivalent to that not having launched + + align:start position:0% +equivalent to that not having launched + + + align:start position:0% +equivalent to that not having launched +anyway the Tollan whoever launched the + + align:start position:0% +anyway the Tollan whoever launched the + + + align:start position:0% +anyway the Tollan whoever launched the +two waves basically cancelled his own + + align:start position:0% +two waves basically cancelled his own + + + align:start position:0% +two waves basically cancelled his own +action so if you think about it + + align:start position:0% +action so if you think about it + + + align:start position:0% +action so if you think about it +physically what happened ray first of + + align:start position:0% +physically what happened ray first of + + + align:start position:0% +physically what happened ray first of +all had the two waves been launched at + + align:start position:0% +all had the two waves been launched at + + + align:start position:0% +all had the two waves been launched at +infinity or at the finite time so for + + align:start position:0% +infinity or at the finite time so for + + + align:start position:0% +infinity or at the finite time so for +example now and lunch and wave and a Z + + align:start position:0% +example now and lunch and wave and a Z + + + align:start position:0% +example now and lunch and wave and a Z +equals zero and this is a way of + + align:start position:0% +equals zero and this is a way of + + + align:start position:0% +equals zero and this is a way of +traveling through the day as to the + + align:start position:0% +traveling through the day as to the + + + align:start position:0% +traveling through the day as to the +positive direction and continuously now + + align:start position:0% +positive direction and continuously now + + + align:start position:0% +positive direction and continuously now +I'm not sure another wave and as M + + align:start position:0% +I'm not sure another wave and as M + + + align:start position:0% +I'm not sure another wave and as M +equals of a number years that equals + + align:start position:0% +equals of a number years that equals + + + align:start position:0% +equals of a number years that equals +minus ten but this show it is we've only + + align:start position:0% +minus ten but this show it is we've only + + + align:start position:0% +minus ten but this show it is we've only +last for three period for example so as + + align:start position:0% +last for three period for example so as + + + align:start position:0% +last for three period for example so as +this way this way of travelling into a + + align:start position:0% +this way this way of travelling into a + + + align:start position:0% +this way this way of travelling into a +positive direction it's going to cancel + + align:start position:0% +positive direction it's going to cancel + + + align:start position:0% +positive direction it's going to cancel +three periods our previous wheel right + + align:start position:0% + + + + align:start position:0% + +now a bit more complicated because what + + align:start position:0% +now a bit more complicated because what + + + align:start position:0% +now a bit more complicated because what +happens to the edges of the wave are you + + align:start position:0% +happens to the edges of the wave are you + + + align:start position:0% +happens to the edges of the wave are you +multiplying by by a boxcar function what + + align:start position:0% +multiplying by by a boxcar function what + + + align:start position:0% +multiplying by by a boxcar function what +happens later right + + align:start position:0% + + + + align:start position:0% + +it's not you're not given enough + + align:start position:0% +it's not you're not given enough + + + align:start position:0% +it's not you're not given enough +information to answer the question right + + align:start position:0% +information to answer the question right + + + align:start position:0% +information to answer the question right +you just tell me that three periods + + align:start position:0% +you just tell me that three periods + + + align:start position:0% +you just tell me that three periods +cancelled but then what happens later + + align:start position:0% +cancelled but then what happens later + + + align:start position:0% +cancelled but then what happens later +did you just stop the wave or it's not + + align:start position:0% +did you just stop the wave or it's not + + + align:start position:0% +did you just stop the wave or it's not +understand or sucia yeah that's right + + align:start position:0% +understand or sucia yeah that's right + + + align:start position:0% +understand or sucia yeah that's right +I'll check yeah thanks the questions are + + align:start position:0% +I'll check yeah thanks the questions are + + + align:start position:0% +I'll check yeah thanks the questions are +defined again so I cannot answer it but + + align:start position:0% +defined again so I cannot answer it but + + + align:start position:0% +defined again so I cannot answer it but +but I can tell you this suppose that I + + align:start position:0% +but I can tell you this suppose that I + + + align:start position:0% +but I can tell you this suppose that I +launched a wave at some time and then a + + align:start position:0% +launched a wave at some time and then a + + + align:start position:0% +launched a wave at some time and then a +certain time later I launched the same + + align:start position:0% +certain time later I launched the same + + + align:start position:0% +certain time later I launched the same +way with PI phase shift rate so there's + + align:start position:0% +way with PI phase shift rate so there's + + + align:start position:0% +way with PI phase shift rate so there's +no doubt that they would - waves at this + + align:start position:0% +no doubt that they would - waves at this + + + align:start position:0% +no doubt that they would - waves at this +point will cancel so what happened to + + align:start position:0% +point will cancel so what happened to + + + align:start position:0% +point will cancel so what happened to +the - the energy well it is equivalent + + align:start position:0% +the - the energy well it is equivalent + + + align:start position:0% +the - the energy well it is equivalent +to thinking that they did not really + + align:start position:0% +to thinking that they did not really + + + align:start position:0% +to thinking that they did not really +lose launched a second wave with a PI + + align:start position:0% +lose launched a second wave with a PI + + + align:start position:0% +lose launched a second wave with a PI +phase shift but they actually turned off + + align:start position:0% +phase shift but they actually turned off + + + align:start position:0% +phase shift but they actually turned off +the sweeps that was producing my first + + align:start position:0% +the sweeps that was producing my first + + + align:start position:0% +the sweeps that was producing my first +wave in the first place okay so with + + align:start position:0% +wave in the first place okay so with + + + align:start position:0% +wave in the first place okay so with +there might be a transient or something + + align:start position:0% +there might be a transient or something + + + align:start position:0% +there might be a transient or something +like that but in effect I've just + + align:start position:0% +like that but in effect I've just + + + align:start position:0% +like that but in effect I've just +canceled the wave so simply stop the + + align:start position:0% +canceled the wave so simply stop the + + + align:start position:0% +canceled the wave so simply stop the +flow of energy right I mean that that's + + align:start position:0% +flow of energy right I mean that that's + + + align:start position:0% +flow of energy right I mean that that's +not something that would be happy with + + align:start position:0% +not something that would be happy with + + + align:start position:0% +not something that would be happy with +this answer or discuss this + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +nothing today Eliza actually this is + + align:start position:0% +nothing today Eliza actually this is + + + align:start position:0% +nothing today Eliza actually this is +interesting there they brought up energy + + align:start position:0% +interesting there they brought up energy + + + align:start position:0% +interesting there they brought up energy +in the standing waves the energy is + + align:start position:0% +in the standing waves the energy is + + + align:start position:0% +in the standing waves the energy is +actually not going anywhere right + + align:start position:0% +actually not going anywhere right + + + align:start position:0% +actually not going anywhere right +because depends well that's one way to + + align:start position:0% +because depends well that's one way to + + + align:start position:0% +because depends well that's one way to +think about it it's not going anywhere + + align:start position:0% +think about it it's not going anywhere + + + align:start position:0% +think about it it's not going anywhere +or you can think about it in the way + + align:start position:0% +or you can think about it in the way + + + align:start position:0% +or you can think about it in the way +that the Energy's going back and forth + + align:start position:0% +that the Energy's going back and forth + + + align:start position:0% +that the Energy's going back and forth +right so it's yeah okay + + align:start position:0% + + + + align:start position:0% + +well actually I did not know Fraser in + + align:start position:0% +well actually I did not know Fraser in + + + align:start position:0% +well actually I did not know Fraser in +last time you do that okay + + align:start position:0% + + + + align:start position:0% + +right so so yes I pulled the first one a + + align:start position:0% +right so so yes I pulled the first one a + + + align:start position:0% +right so so yes I pulled the first one a +few minutes ago I was talking about the + + align:start position:0% +few minutes ago I was talking about the + + + align:start position:0% +few minutes ago I was talking about the +difficulty of trigonometry and I said + + align:start position:0% +difficulty of trigonometry and I said + + + align:start position:0% +difficulty of trigonometry and I said +that's why I introduced phaser last time + + align:start position:0% +that's why I introduced phaser last time + + + align:start position:0% +that's why I introduced phaser last time +I was mistaken I had not introduced any + + align:start position:0% +I was mistaken I had not introduced any + + + align:start position:0% +I was mistaken I had not introduced any +phasers last time I'm introducing + + align:start position:0% +phasers last time I'm introducing + + + align:start position:0% +phasers last time I'm introducing +phasers now and illusion of course that + + align:start position:0% +phasers now and illusion of course that + + + align:start position:0% +phasers now and illusion of course that +were introduced in phases because we + + align:start position:0% +were introduced in phases because we + + + align:start position:0% +were introduced in phases because we +don't want to have to remember + + align:start position:0% +don't want to have to remember + + + align:start position:0% +don't want to have to remember +complicated identities like this one + + align:start position:0% +complicated identities like this one + + + align:start position:0% +complicated identities like this one +okay anyway another point that I would + + align:start position:0% +okay anyway another point that I would + + + align:start position:0% +okay anyway another point that I would +like to bring up before I move on to + + align:start position:0% +like to bring up before I move on to + + + align:start position:0% +like to bring up before I move on to +phasers is that the way that I'm showing + + align:start position:0% +phasers is that the way that I'm showing + + + align:start position:0% +phasers is that the way that I'm showing +here is actually very different than the + + align:start position:0% +here is actually very different than the + + + align:start position:0% +here is actually very different than the +travelling wave that led us to the wave + + align:start position:0% +travelling wave that led us to the wave + + + align:start position:0% +travelling wave that led us to the wave +equation you agree with that that looks + + align:start position:0% +equation you agree with that that looks + + + align:start position:0% +equation you agree with that that looks +very different both in the way it + + align:start position:0% +very different both in the way it + + + align:start position:0% +very different both in the way it +behaves with time and space and the way + + align:start position:0% +behaves with time and space and the way + + + align:start position:0% +behaves with time and space and the way +it looks like an equation yet it still + + align:start position:0% +it looks like an equation yet it still + + + align:start position:0% +it looks like an equation yet it still +originated from the same wave equation + + align:start position:0% +originated from the same wave equation + + + align:start position:0% +originated from the same wave equation +so this is actually the power of partial + + align:start position:0% +so this is actually the power of partial + + + align:start position:0% +so this is actually the power of partial +differential equations and superposition + + align:start position:0% +differential equations and superposition + + + align:start position:0% +differential equations and superposition +that I took two solutions of my partial + + align:start position:0% +that I took two solutions of my partial + + + align:start position:0% +that I took two solutions of my partial +differential equation that were not + + align:start position:0% +differential equation that were not + + + align:start position:0% +differential equation that were not +particularly interesting I superimpose + + align:start position:0% +particularly interesting I superimpose + + + align:start position:0% +particularly interesting I superimpose +them and then a new value and then I + + align:start position:0% +them and then a new value and then I + + + align:start position:0% +them and then a new value and then I +created another solution which is still + + align:start position:0% +created another solution which is still + + + align:start position:0% +created another solution which is still +a very valid wave but we have totally + + align:start position:0% +a very valid wave but we have totally + + + align:start position:0% +a very valid wave but we have totally +different it is a stationary wave it has + + align:start position:0% +different it is a stationary wave it has + + + align:start position:0% +different it is a stationary wave it has +this oscillation and so on and so forth + + align:start position:0% +this oscillation and so on and so forth + + + align:start position:0% +this oscillation and so on and so forth +so that is why we bother to write this + + align:start position:0% +so that is why we bother to write this + + + align:start position:0% +so that is why we bother to write this +partial differential equation because it + + align:start position:0% +partial differential equation because it + + + align:start position:0% +partial differential equation because it +allows us to generate a much richer set + + align:start position:0% +allows us to generate a much richer set + + + align:start position:0% +allows us to generate a much richer set +of waves that of course very importantly + + align:start position:0% +of waves that of course very importantly + + + align:start position:0% +of waves that of course very importantly +practice standing waves happen all the + + align:start position:0% +practice standing waves happen all the + + + align:start position:0% +practice standing waves happen all the +time + + align:start position:0% +time + + + align:start position:0% +time +okay so now let's go to phasers okay so + + align:start position:0% +okay so now let's go to phasers okay so + + + align:start position:0% +okay so now let's go to phasers okay so +just like before I wrote two waves that + + align:start position:0% +just like before I wrote two waves that + + + align:start position:0% +just like before I wrote two waves that +were propagating in opposite direction + + align:start position:0% +were propagating in opposite direction + + + align:start position:0% +were propagating in opposite direction +now what I'm going to do is I'm going to + + align:start position:0% +now what I'm going to do is I'm going to + + + align:start position:0% +now what I'm going to do is I'm going to +write two waves that are phase shifted + + align:start position:0% +write two waves that are phase shifted + + + align:start position:0% +write two waves that are phase shifted +by PI over two one of them is cosine KZ + + align:start position:0% +by PI over two one of them is cosine KZ + + + align:start position:0% +by PI over two one of them is cosine KZ +minus Omega T plus V okay + + align:start position:0% +minus Omega T plus V okay + + + align:start position:0% +minus Omega T plus V okay +and the other is phase shifted by PI + + align:start position:0% +and the other is phase shifted by PI + + + align:start position:0% +and the other is phase shifted by PI +over 2 which means instead of the cosine + + align:start position:0% +over 2 which means instead of the cosine + + + align:start position:0% +over 2 which means instead of the cosine +that is a sign + + align:start position:0% + + + + align:start position:0% + +okay both are very valid solutions to + + align:start position:0% +okay both are very valid solutions to + + + align:start position:0% +okay both are very valid solutions to +the wave equation with different initial + + align:start position:0% +the wave equation with different initial + + + align:start position:0% +the wave equation with different initial +conditions but that doesn't bother us + + align:start position:0% +conditions but that doesn't bother us + + + align:start position:0% +conditions but that doesn't bother us +they're still valid solution therefore + + align:start position:0% +they're still valid solution therefore + + + align:start position:0% +they're still valid solution therefore +the superposition is also a solution and + + align:start position:0% +the superposition is also a solution and + + + align:start position:0% +the superposition is also a solution and +I said before that when you do a linear + + align:start position:0% +I said before that when you do a linear + + + align:start position:0% +I said before that when you do a linear +superposition you can also multiply the + + align:start position:0% +superposition you can also multiply the + + + align:start position:0% +superposition you can also multiply the +waves by arbitrary constants I said this + + align:start position:0% +waves by arbitrary constants I said this + + + align:start position:0% +waves by arbitrary constants I said this +little bit fast but I hope that remember + + align:start position:0% +little bit fast but I hope that remember + + + align:start position:0% +little bit fast but I hope that remember +that I said in fact in this class we + + align:start position:0% +that I said in fact in this class we + + + align:start position:0% +that I said in fact in this class we +have evidence of what I said and what is + + align:start position:0% +have evidence of what I said and what is + + + align:start position:0% +have evidence of what I said and what is +MA say and go back to the video and see + + align:start position:0% +MA say and go back to the video and see + + + align:start position:0% +MA say and go back to the video and see +if I said it and I did okay + + align:start position:0% +if I said it and I did okay + + + align:start position:0% +if I said it and I did okay +so I will pick a very particular + + align:start position:0% +so I will pick a very particular + + + align:start position:0% +so I will pick a very particular +constant which may sound like a crazy + + align:start position:0% +constant which may sound like a crazy + + + align:start position:0% +constant which may sound like a crazy +choice but I would pick it and that's + + align:start position:0% +choice but I would pick it and that's + + + align:start position:0% +choice but I would pick it and that's +the imaginary constant I've also known + + align:start position:0% +the imaginary constant I've also known + + + align:start position:0% +the imaginary constant I've also known +as one of the two square roots of minus + + align:start position:0% +as one of the two square roots of minus + + + align:start position:0% +as one of the two square roots of minus +one okay what is this now so the first + + align:start position:0% +one okay what is this now so the first + + + align:start position:0% +one okay what is this now so the first +confession that I will make is that it + + align:start position:0% +confession that I will make is that it + + + align:start position:0% +confession that I will make is that it +is not physical anymore there's no such + + align:start position:0% +is not physical anymore there's no such + + + align:start position:0% +is not physical anymore there's no such +thing as a complex wave the wave that we + + align:start position:0% +thing as a complex wave the wave that we + + + align:start position:0% +thing as a complex wave the wave that we +see around us are real they can be + + align:start position:0% +see around us are real they can be + + + align:start position:0% +see around us are real they can be +measured by instruments such as + + align:start position:0% +measured by instruments such as + + + align:start position:0% +measured by instruments such as +oscilloscopes cameras know what else the + + align:start position:0% +oscilloscopes cameras know what else the + + + align:start position:0% +oscilloscopes cameras know what else the +real the as far as I know nobody has + + align:start position:0% +real the as far as I know nobody has + + + align:start position:0% +real the as far as I know nobody has +ever measured anything complex however + + align:start position:0% +ever measured anything complex however + + + align:start position:0% +ever measured anything complex however +what I'm doing here is mathematically + + align:start position:0% +what I'm doing here is mathematically + + + align:start position:0% +what I'm doing here is mathematically +correct even if it has no physical + + align:start position:0% +correct even if it has no physical + + + align:start position:0% +correct even if it has no physical +meaning and it turns out it provides a + + align:start position:0% +meaning and it turns out it provides a + + + align:start position:0% +meaning and it turns out it provides a +huge mathematical convenience so I'm + + align:start position:0% +huge mathematical convenience so I'm + + + align:start position:0% +huge mathematical convenience so I'm +justified in doing it as long as I + + align:start position:0% +justified in doing it as long as I + + + align:start position:0% +justified in doing it as long as I +remember what is the physics that is + + align:start position:0% +remember what is the physics that is + + + align:start position:0% +remember what is the physics that is +behind and the physics that is behind it + + align:start position:0% +behind and the physics that is behind it + + + align:start position:0% +behind and the physics that is behind it +is that every time I see a wave like + + align:start position:0% +is that every time I see a wave like + + + align:start position:0% +is that every time I see a wave like +this I have to remember that the + + align:start position:0% +this I have to remember that the + + + align:start position:0% +this I have to remember that the +physical quantity is the real part okay + + align:start position:0% +physical quantity is the real part okay + + + align:start position:0% +physical quantity is the real part okay +so the physical wave the one that they + + align:start position:0% +so the physical wave the one that they + + + align:start position:0% +so the physical wave the one that they +can actually measure observe generate + + align:start position:0% +can actually measure observe generate + + + align:start position:0% +can actually measure observe generate +with you know natural means is the real + + align:start position:0% +with you know natural means is the real + + + align:start position:0% +with you know natural means is the real +part the imaginary part is something + + align:start position:0% +part the imaginary part is something + + + align:start position:0% +part the imaginary part is something +that I added for mathematical + + align:start position:0% +that I added for mathematical + + + align:start position:0% +that I added for mathematical +convenience and originality is because I + + align:start position:0% +convenience and originality is because I + + + align:start position:0% +convenience and originality is because I +forget whose formula is called the MOI + + align:start position:0% +forget whose formula is called the MOI + + + align:start position:0% +forget whose formula is called the MOI +world + + align:start position:0% + + + + align:start position:0% + +anyway one of those friends de moivre + + align:start position:0% +anyway one of those friends de moivre + + + align:start position:0% +anyway one of those friends de moivre +yeah the Moapa yeah okay I go to travel + + align:start position:0% +yeah the Moapa yeah okay I go to travel + + + align:start position:0% +yeah the Moapa yeah okay I go to travel +so the mother then if I remember + + align:start position:0% +so the mother then if I remember + + + align:start position:0% +so the mother then if I remember +correctly the scariest family the mother + + align:start position:0% +correctly the scariest family the mother + + + align:start position:0% +correctly the scariest family the mother +says that this thing here is a complex + + align:start position:0% +says that this thing here is a complex + + + align:start position:0% +says that this thing here is a complex +exponential okay no that's very nice + + align:start position:0% +exponential okay no that's very nice + + + align:start position:0% +exponential okay no that's very nice +because for example if you have to + + align:start position:0% +because for example if you have to + + + align:start position:0% +because for example if you have to +multiply two cosines it's a big pain + + align:start position:0% +multiply two cosines it's a big pain + + + align:start position:0% +multiply two cosines it's a big pain +that you have to remember the trick to + + align:start position:0% +that you have to remember the trick to + + + align:start position:0% +that you have to remember the trick to +multiply two Exponential's it is trivial + + align:start position:0% +multiply two Exponential's it is trivial + + + align:start position:0% +multiply two Exponential's it is trivial +you just add their faces I mean they're + + align:start position:0% +you just add their faces I mean they're + + + align:start position:0% +you just add their faces I mean they're +their exponent so so a lot of a lot of + + align:start position:0% +their exponent so so a lot of a lot of + + + align:start position:0% +their exponent so so a lot of a lot of +convenience is to be to be expected so + + align:start position:0% +convenience is to be to be expected so + + + align:start position:0% +convenience is to be to be expected so +this representation it comes with + + align:start position:0% +this representation it comes with + + + align:start position:0% +this representation it comes with +different names which sometimes used + + align:start position:0% +different names which sometimes used + + + align:start position:0% +different names which sometimes used +confusingly in an interchangeable way so + + align:start position:0% +confusingly in an interchangeable way so + + + align:start position:0% +confusingly in an interchangeable way so +some people call this a phaser notation + + align:start position:0% +some people call this a phaser notation + + + align:start position:0% +some people call this a phaser notation +I prefer to call this the complex + + align:start position:0% +I prefer to call this the complex + + + align:start position:0% +I prefer to call this the complex +representation of the wave it becomes a + + align:start position:0% +representation of the wave it becomes a + + + align:start position:0% +representation of the wave it becomes a +phaser when we drop I'm going to do + + align:start position:0% +phaser when we drop I'm going to do + + + align:start position:0% +phaser when we drop I'm going to do +something nasty here okay remember that + + align:start position:0% +something nasty here okay remember that + + + align:start position:0% +something nasty here okay remember that +I can i this is a product right so + + align:start position:0% +I can i this is a product right so + + + align:start position:0% +I can i this is a product right so +Canada says e to the i kz e to the minus + + align:start position:0% +Canada says e to the i kz e to the minus + + + align:start position:0% +Canada says e to the i kz e to the minus +I Omega T e to the I Ching okay if you + + align:start position:0% +I Omega T e to the I Ching okay if you + + + align:start position:0% +I Omega T e to the I Ching okay if you +recall during the beginnings of the + + align:start position:0% +recall during the beginnings of the + + + align:start position:0% +recall during the beginnings of the +class we saw that the wave length in a + + align:start position:0% +class we saw that the wave length in a + + + align:start position:0% +class we saw that the wave length in a +medium changes but there is a property + + align:start position:0% +medium changes but there is a property + + + align:start position:0% +medium changes but there is a property +of the wave that does not change that + + align:start position:0% +of the wave that does not change that + + + align:start position:0% +of the wave that does not change that +property if you recall is the temporal + + align:start position:0% +property if you recall is the temporal + + + align:start position:0% +property if you recall is the temporal +frequency Omega or new it's related by 2 + + align:start position:0% +frequency Omega or new it's related by 2 + + + align:start position:0% +frequency Omega or new it's related by 2 +pi okay that is true in linear media of + + align:start position:0% +pi okay that is true in linear media of + + + align:start position:0% +pi okay that is true in linear media of +course there is a class of optics called + + align:start position:0% +course there is a class of optics called + + + align:start position:0% +course there is a class of optics called +nonlinear where actually the frequency + + align:start position:0% +nonlinear where actually the frequency + + + align:start position:0% +nonlinear where actually the frequency +in changes can double or even + + align:start position:0% +in changes can double or even + + + align:start position:0% +in changes can double or even +or fancy things can happen to it but in + + align:start position:0% +or fancy things can happen to it but in + + + align:start position:0% +or fancy things can happen to it but in +this class we don't deal with this + + align:start position:0% +this class we don't deal with this + + + align:start position:0% +this class we don't deal with this +complicated things we'll just deal with + + align:start position:0% +complicated things we'll just deal with + + + align:start position:0% +complicated things we'll just deal with +linear optics so in linear optics the + + align:start position:0% +linear optics so in linear optics the + + + align:start position:0% +linear optics so in linear optics the +temporal frequency of the light no + + align:start position:0% +temporal frequency of the light no + + + align:start position:0% +temporal frequency of the light no +matter what happens to the light even if + + align:start position:0% +matter what happens to the light even if + + + align:start position:0% +matter what happens to the light even if +it goes through glass and reflects and + + align:start position:0% +it goes through glass and reflects and + + + align:start position:0% +it goes through glass and reflects and +all kinds of things that important + + align:start position:0% +all kinds of things that important + + + align:start position:0% +all kinds of things that important +frequency remains the same so when we + + align:start position:0% +frequency remains the same so when we + + + align:start position:0% +frequency remains the same so when we +deal with optical waves of a single + + align:start position:0% +deal with optical waves of a single + + + align:start position:0% +deal with optical waves of a single +frequency that is the corner is fixed + + align:start position:0% +frequency that is the corner is fixed + + + align:start position:0% +frequency that is the corner is fixed +and the medium is linear then this term + + align:start position:0% +and the medium is linear then this term + + + align:start position:0% +and the medium is linear then this term +is actually super full we don't have to + + align:start position:0% +is actually super full we don't have to + + + align:start position:0% +is actually super full we don't have to +remind ourselves that the light goes + + align:start position:0% +remind ourselves that the light goes + + + align:start position:0% +remind ourselves that the light goes +like e to the minus Omega T it does but + + align:start position:0% +like e to the minus Omega T it does but + + + align:start position:0% +like e to the minus Omega T it does but +we don't have to write it because if we + + align:start position:0% +we don't have to write it because if we + + + align:start position:0% +we don't have to write it because if we +keep writing it it clattered is our + + align:start position:0% +keep writing it it clattered is our + + + align:start position:0% +keep writing it it clattered is our +equation so we simply drop it okay drop + + align:start position:0% +equation so we simply drop it okay drop + + + align:start position:0% +equation so we simply drop it okay drop +it very important to remember we allowed + + align:start position:0% +it very important to remember we allowed + + + align:start position:0% +it very important to remember we allowed +to drop it if we know that we have a + + align:start position:0% +to drop it if we know that we have a + + + align:start position:0% +to drop it if we know that we have a +single color in our system a single + + align:start position:0% +single color in our system a single + + + align:start position:0% +single color in our system a single +frequency if there is multiple + + align:start position:0% +frequency if there is multiple + + + align:start position:0% +frequency if there is multiple +frequencies we cannot do that anymore + + align:start position:0% +frequencies we cannot do that anymore + + + align:start position:0% +frequencies we cannot do that anymore +right because then this these + + align:start position:0% +right because then this these + + + align:start position:0% +right because then this these +frequencies have to adapt in a certain + + align:start position:0% +frequencies have to adapt in a certain + + + align:start position:0% +frequencies have to adapt in a certain +way and we have to keep track of their + + align:start position:0% +way and we have to keep track of their + + + align:start position:0% +way and we have to keep track of their +relative phases so okay so we can only + + align:start position:0% +relative phases so okay so we can only + + + align:start position:0% +relative phases so okay so we can only +drop this term if we two conditions if + + align:start position:0% +drop this term if we two conditions if + + + align:start position:0% +drop this term if we two conditions if +you know that we have a linear medium + + align:start position:0% +you know that we have a linear medium + + + align:start position:0% +you know that we have a linear medium +and a single frequency light propagating + + align:start position:0% +and a single frequency light propagating + + + align:start position:0% +and a single frequency light propagating +in that medium okay so in my terminology + + align:start position:0% +in that medium okay so in my terminology + + + align:start position:0% +in that medium okay so in my terminology +at least after we drop this term then it + + align:start position:0% +at least after we drop this term then it + + + align:start position:0% +at least after we drop this term then it +becomes a phasor so what is left e to + + align:start position:0% +becomes a phasor so what is left e to + + + align:start position:0% +becomes a phasor so what is left e to +the ikj plus five that I call a phasor + + align:start position:0% +the ikj plus five that I call a phasor + + + align:start position:0% +the ikj plus five that I call a phasor +and you notice what happened there is I + + align:start position:0% +and you notice what happened there is I + + + align:start position:0% +and you notice what happened there is I +only left the spatial dependency of the + + align:start position:0% +only left the spatial dependency of the + + + align:start position:0% +only left the spatial dependency of the +wave plus the phase delay the temporal + + align:start position:0% +wave plus the phase delay the temporal + + + align:start position:0% +wave plus the phase delay the temporal +variation is it's hidden it is not gone + + align:start position:0% +variation is it's hidden it is not gone + + + align:start position:0% +variation is it's hidden it is not gone +it is just hidden okay okay now let's + + align:start position:0% +it is just hidden okay okay now let's + + + align:start position:0% +it is just hidden okay okay now let's +see this in action so what I'm going to + + align:start position:0% +see this in action so what I'm going to + + + align:start position:0% +see this in action so what I'm going to +do is I'm going to derive the standing + + align:start position:0% +do is I'm going to derive the standing + + + align:start position:0% +do is I'm going to derive the standing +wave but using the phasor so you can see + + align:start position:0% +wave but using the phasor so you can see + + + align:start position:0% +wave but using the phasor so you can see +how nice and simple it comes out and we + + align:start position:0% +how nice and simple it comes out and we + + + align:start position:0% +how nice and simple it comes out and we +don't have to agonize over it but before + + align:start position:0% +don't have to agonize over it but before + + + align:start position:0% +don't have to agonize over it but before +I do it I actually have to solve a + + align:start position:0% +I do it I actually have to solve a + + + align:start position:0% +I do it I actually have to solve a +little problem the problem is that I did + + align:start position:0% +little problem the problem is that I did + + + align:start position:0% +little problem the problem is that I did +this very nice derivation for the phasor + + align:start position:0% +this very nice derivation for the phasor + + + align:start position:0% +this very nice derivation for the phasor +of the forward propagating wave what + + align:start position:0% +of the forward propagating wave what + + + align:start position:0% +of the forward propagating wave what +about the phasor for the backward + + align:start position:0% +about the phasor for the backward + + + align:start position:0% +about the phasor for the backward +propagating wave okay + + align:start position:0% +propagating wave okay + + + align:start position:0% +propagating wave okay +the backward propagating wave would be + + align:start position:0% +the backward propagating wave would be + + + align:start position:0% +the backward propagating wave would be +something of this sort so this will + + align:start position:0% +something of this sort so this will + + + align:start position:0% +something of this sort so this will +always forward a canal would let me + + align:start position:0% +always forward a canal would let me + + + align:start position:0% +always forward a canal would let me +write the backward I think I have enough + + align:start position:0% +write the backward I think I have enough + + + align:start position:0% +write the backward I think I have enough +space here so I can do it okay + + align:start position:0% +space here so I can do it okay + + + align:start position:0% +space here so I can do it okay +so the backward of this would be + + align:start position:0% +so the backward of this would be + + + align:start position:0% +so the backward of this would be +something of the sort of the form cosine + + align:start position:0% +something of the sort of the form cosine + + + align:start position:0% +something of the sort of the form cosine +KZ plus Omega T last fee then it is very + + align:start position:0% +KZ plus Omega T last fee then it is very + + + align:start position:0% +KZ plus Omega T last fee then it is very +inconvenient because the way I got the + + align:start position:0% +inconvenient because the way I got the + + + align:start position:0% +inconvenient because the way I got the +failure is a got rid of the term of the + + align:start position:0% +failure is a got rid of the term of the + + + align:start position:0% +failure is a got rid of the term of the +form e to the minus Omega T if I add the + + align:start position:0% +form e to the minus Omega T if I add the + + + align:start position:0% +form e to the minus Omega T if I add the +imaginary part here I don't have a term + + align:start position:0% +imaginary part here I don't have a term + + + align:start position:0% +imaginary part here I don't have a term +e to the minus Omega T some stock but I + + align:start position:0% +e to the minus Omega T some stock but I + + + align:start position:0% +e to the minus Omega T some stock but I +can do some mathematical trickery now + + align:start position:0% +can do some mathematical trickery now + + + align:start position:0% +can do some mathematical trickery now +this is sure tickly but it works the + + align:start position:0% +this is sure tickly but it works the + + + align:start position:0% +this is sure tickly but it works the +trick is the following we know that the + + align:start position:0% +trick is the following we know that the + + + align:start position:0% +trick is the following we know that the +cosine is an even function so this is + + align:start position:0% +cosine is an even function so this is + + + align:start position:0% +cosine is an even function so this is +actually identical I can replace it with + + align:start position:0% +actually identical I can replace it with + + + align:start position:0% +actually identical I can replace it with +in other words with the cosine of the + + align:start position:0% +in other words with the cosine of the + + + align:start position:0% +in other words with the cosine of the +negative element not harm done it is + + align:start position:0% +negative element not harm done it is + + + align:start position:0% +negative element not harm done it is +ticular backward propagating wave + + align:start position:0% +ticular backward propagating wave + + + align:start position:0% +ticular backward propagating wave +nothing has changed is the same equation + + align:start position:0% +nothing has changed is the same equation + + + align:start position:0% +nothing has changed is the same equation +now according to my good principle here + + align:start position:0% +now according to my good principle here + + + align:start position:0% +now according to my good principle here +I + + align:start position:0% + + + + align:start position:0% + +that is not the same as before right + + align:start position:0% +that is not the same as before right + + + align:start position:0% +that is not the same as before right +because the sine is an odd function but + + align:start position:0% +because the sine is an odd function but + + + align:start position:0% +because the sine is an odd function but +this is a non-physical term anyway I + + align:start position:0% +this is a non-physical term anyway I + + + align:start position:0% +this is a non-physical term anyway I +just put it there for mathematical + + align:start position:0% +just put it there for mathematical + + + align:start position:0% +just put it there for mathematical +convenience so don't particularly care + + align:start position:0% +convenience so don't particularly care + + + align:start position:0% +convenience so don't particularly care +I'm very happy because the real part is + + align:start position:0% +I'm very happy because the real part is + + + align:start position:0% +I'm very happy because the real part is +the same as I started with what + + align:start position:0% +the same as I started with what + + + align:start position:0% +the same as I started with what +imaginary part does as long as + + align:start position:0% +imaginary part does as long as + + + align:start position:0% +imaginary part does as long as +mathematically convenient I couldn't + + align:start position:0% +mathematically convenient I couldn't + + + align:start position:0% +mathematically convenient I couldn't +care less right okay so that gives me + + align:start position:0% +care less right okay so that gives me + + + align:start position:0% +care less right okay so that gives me +the license to write this now this of + + align:start position:0% +the license to write this now this of + + + align:start position:0% +the license to write this now this of +course equals e to the minus I K Z minus + + align:start position:0% +course equals e to the minus I K Z minus + + + align:start position:0% +course equals e to the minus I K Z minus +I Omega t minus V now very happy because + + align:start position:0% +I Omega t minus V now very happy because + + + align:start position:0% +I Omega t minus V now very happy because +I did get a term it was a minus I Omega + + align:start position:0% +I did get a term it was a minus I Omega + + + align:start position:0% +I did get a term it was a minus I Omega +T in the phase of this exponential and + + align:start position:0% +T in the phase of this exponential and + + + align:start position:0% +T in the phase of this exponential and +therefore I can drop it to produce my + + align:start position:0% +therefore I can drop it to produce my + + + align:start position:0% +therefore I can drop it to produce my +fashion so the lesser then is that the + + align:start position:0% +fashion so the lesser then is that the + + + align:start position:0% +fashion so the lesser then is that the +phase or for the backward wave is e to + + align:start position:0% +phase or for the backward wave is e to + + + align:start position:0% +phase or for the backward wave is e to +the minus I K is e minus IV in other + + align:start position:0% +the minus I K is e minus IV in other + + + align:start position:0% +the minus I K is e minus IV in other +words if I give you a forward propagated + + align:start position:0% +words if I give you a forward propagated + + + align:start position:0% +words if I give you a forward propagated +wave and you compute its phasor and then + + align:start position:0% +wave and you compute its phasor and then + + + align:start position:0% +wave and you compute its phasor and then +I ask you well what is the phasor for + + align:start position:0% +I ask you well what is the phasor for + + + align:start position:0% +I ask you well what is the phasor for +the backward propagating wave well all + + align:start position:0% +the backward propagating wave well all + + + align:start position:0% +the backward propagating wave well all +you do is you flip the sign on the + + align:start position:0% +you do is you flip the sign on the + + + align:start position:0% +you do is you flip the sign on the +exponent okay fine so in order to have + + align:start position:0% +exponent okay fine so in order to have + + + align:start position:0% +exponent okay fine so in order to have +this can will produce whoa what did this + + align:start position:0% +this can will produce whoa what did this + + + align:start position:0% +this can will produce whoa what did this +come to I think this is an old all the + + align:start position:0% +come to I think this is an old all the + + + align:start position:0% +come to I think this is an old all the +paper from some previous lecture but + + align:start position:0% +paper from some previous lecture but + + + align:start position:0% +paper from some previous lecture but +anyway then we ignore this I have to + + align:start position:0% +anyway then we ignore this I have to + + + align:start position:0% +anyway then we ignore this I have to +remember class for in you five for less + + align:start position:0% +remember class for in you five for less + + + align:start position:0% +remember class for in you five for less +than okay okay so what I will do now let + + align:start position:0% +than okay okay so what I will do now let + + + align:start position:0% +than okay okay so what I will do now let +me reproduce the standing wave so the + + align:start position:0% +me reproduce the standing wave so the + + + align:start position:0% +me reproduce the standing wave so the +standing wave is using the phasers now + + align:start position:0% +standing wave is using the phasers now + + + align:start position:0% +standing wave is using the phasers now +is e to the ikj plus fin that is the + + align:start position:0% +is e to the ikj plus fin that is the + + + align:start position:0% +is e to the ikj plus fin that is the +forward wave plus e to the minus I K is + + align:start position:0% +forward wave plus e to the minus I K is + + + align:start position:0% +forward wave plus e to the minus I K is +e - I think that is the backward wave + + align:start position:0% +e - I think that is the backward wave + + + align:start position:0% +e - I think that is the backward wave +can you deliver that well yes actually + + align:start position:0% +can you deliver that well yes actually + + + align:start position:0% +can you deliver that well yes actually +because again the more ever says that if + + align:start position:0% +because again the more ever says that if + + + align:start position:0% +because again the more ever says that if +you add two Exponential's of this form + + align:start position:0% +you add two Exponential's of this form + + + align:start position:0% +you add two Exponential's of this form +notice they have the same phase within a + + align:start position:0% +notice they have the same phase within a + + + align:start position:0% +notice they have the same phase within a +minus sign I will simply get two eyes + + align:start position:0% +minus sign I will simply get two eyes + + + align:start position:0% +minus sign I will simply get two eyes +cosine is Z plus V so I got my my thing + + align:start position:0% +cosine is Z plus V so I got my my thing + + + align:start position:0% +cosine is Z plus V so I got my my thing +here not quite though because the + + align:start position:0% +here not quite though because the + + + align:start position:0% +here not quite though because the +standing wave it had the cosine Omega T + + align:start position:0% +standing wave it had the cosine Omega T + + + align:start position:0% +standing wave it had the cosine Omega T +term what happened to this cosine Omega + + align:start position:0% +term what happened to this cosine Omega + + + align:start position:0% +term what happened to this cosine Omega +T what happened to the cosine Omega T + + align:start position:0% +T what happened to the cosine Omega T + + + align:start position:0% +T what happened to the cosine Omega T +well remember we neglected and e to the + + align:start position:0% +well remember we neglected and e to the + + + align:start position:0% +well remember we neglected and e to the +minus I Omega T you didn't really + + align:start position:0% +minus I Omega T you didn't really + + + align:start position:0% +minus I Omega T you didn't really +neglect it we hit it because we didn't + + align:start position:0% +neglect it we hit it because we didn't + + + align:start position:0% +neglect it we hit it because we didn't +want to carry it when you arrived the + + align:start position:0% +want to carry it when you arrived the + + + align:start position:0% +want to carry it when you arrived the +question well if I did if first of all + + align:start position:0% +question well if I did if first of all + + + align:start position:0% +question well if I did if first of all +if I don't care about that important + + align:start position:0% +if I don't care about that important + + + align:start position:0% +if I don't care about that important +variation I don't really have to do any + + align:start position:0% +variation I don't really have to do any + + + align:start position:0% +variation I don't really have to do any +anything I'm done but if I want to put + + align:start position:0% +anything I'm done but if I want to put + + + align:start position:0% +anything I'm done but if I want to put +that important variation back in what I + + align:start position:0% +that important variation back in what I + + + align:start position:0% +that important variation back in what I +have to do is I have to put back what I + + align:start position:0% +have to do is I have to put back what I + + + align:start position:0% +have to do is I have to put back what I +took + + align:start position:0% +took + + + align:start position:0% +took +when did not belong to me and what did + + align:start position:0% +when did not belong to me and what did + + + align:start position:0% +when did not belong to me and what did +not belong to me is did this e to the + + align:start position:0% +not belong to me is did this e to the + + + align:start position:0% +not belong to me is did this e to the +minus I Omega T okay I put it back now + + align:start position:0% +minus I Omega T okay I put it back now + + + align:start position:0% +minus I Omega T okay I put it back now +that is still not a physical wave + + align:start position:0% +that is still not a physical wave + + + align:start position:0% +that is still not a physical wave +because it is complex how can I find the + + align:start position:0% +because it is complex how can I find the + + + align:start position:0% +because it is complex how can I find the +actual physical way when I have to take + + align:start position:0% +actual physical way when I have to take + + + align:start position:0% +actual physical way when I have to take +its real part the real part is easy here + + align:start position:0% +its real part the real part is easy here + + + align:start position:0% +its real part the real part is easy here +because the only complex thing is this + + align:start position:0% +because the only complex thing is this + + + align:start position:0% +because the only complex thing is this +exponential so if I take the real part + + align:start position:0% +exponential so if I take the real part + + + align:start position:0% +exponential so if I take the real part +of this of all of this now it would + + align:start position:0% +of this of all of this now it would + + + align:start position:0% +of this of all of this now it would +simply be 2 cosine KZ plus V cosine + + align:start position:0% +simply be 2 cosine KZ plus V cosine + + + align:start position:0% +simply be 2 cosine KZ plus V cosine +Omega T and I'm done I've actually + + align:start position:0% +Omega T and I'm done I've actually + + + align:start position:0% +Omega T and I'm done I've actually +reproduced my standing way + + align:start position:0% + + + + align:start position:0% + +any questions + + align:start position:0% + + + + align:start position:0% + +we're almost done here so I have about + + align:start position:0% +we're almost done here so I have about + + + align:start position:0% +we're almost done here so I have about +three minutes or so I think I will use + + align:start position:0% +three minutes or so I think I will use + + + align:start position:0% +three minutes or so I think I will use +them to finish up this lecture so can + + align:start position:0% +them to finish up this lecture so can + + + align:start position:0% +them to finish up this lecture so can +move on bigger and better things + + align:start position:0% +move on bigger and better things + + + align:start position:0% +move on bigger and better things +the question that I wrote before is the + + align:start position:0% +the question that I wrote before is the + + + align:start position:0% +the question that I wrote before is the +one-dimensional wave equation because + + align:start position:0% +one-dimensional wave equation because + + + align:start position:0% +one-dimensional wave equation because +the waves that I've written they can + + align:start position:0% +the waves that I've written they can + + + align:start position:0% +the waves that I've written they can +only go down one special axis right Z + + align:start position:0% +only go down one special axis right Z + + + align:start position:0% +only go down one special axis right Z +the more generalized + + align:start position:0% +the more generalized + + + align:start position:0% +the more generalized +of course situation is three dimensional + + align:start position:0% +of course situation is three dimensional + + + align:start position:0% +of course situation is three dimensional +waves and what you see here is the + + align:start position:0% +waves and what you see here is the + + + align:start position:0% +waves and what you see here is the +generalized three-dimensional wave + + align:start position:0% +generalized three-dimensional wave + + + align:start position:0% +generalized three-dimensional wave +equation which of course I will not + + align:start position:0% +equation which of course I will not + + + align:start position:0% +equation which of course I will not +derive but it can be pretty easily + + align:start position:0% +derive but it can be pretty easily + + + align:start position:0% +derive but it can be pretty easily +derived we using the same arguments that + + align:start position:0% +derived we using the same arguments that + + + align:start position:0% +derived we using the same arguments that +would it before except you have to kind + + align:start position:0% +would it before except you have to kind + + + align:start position:0% +would it before except you have to kind +of generalize them if you dimension and + + align:start position:0% +of generalize them if you dimension and + + + align:start position:0% +of generalize them if you dimension and +this produces things that we've seen + + align:start position:0% +this produces things that we've seen + + + align:start position:0% +this produces things that we've seen +before in geometrical optics for example + + align:start position:0% +before in geometrical optics for example + + + align:start position:0% +before in geometrical optics for example +the plane wave except now you see the + + align:start position:0% +the plane wave except now you see the + + + align:start position:0% +the plane wave except now you see the +wave description it is you have + + align:start position:0% +wave description it is you have + + + align:start position:0% +wave description it is you have +alternating was positive and negative + + align:start position:0% +alternating was positive and negative + + + align:start position:0% +alternating was positive and negative +how do you call those peaks and traps + + align:start position:0% +how do you call those peaks and traps + + + align:start position:0% +how do you call those peaks and traps +which are propagating along an arbitrary + + align:start position:0% +which are propagating along an arbitrary + + + align:start position:0% +which are propagating along an arbitrary +Ally now they can go in any angle in 3d + + align:start position:0% +Ally now they can go in any angle in 3d + + + align:start position:0% +Ally now they can go in any angle in 3d +space right this particular so you see + + align:start position:0% +space right this particular so you see + + + align:start position:0% +space right this particular so you see +just a cross-section here or you can + + align:start position:0% +just a cross-section here or you can + + + align:start position:0% +just a cross-section here or you can +have a spherical wave which you saw it + + align:start position:0% +have a spherical wave which you saw it + + + align:start position:0% +have a spherical wave which you saw it +before it starts at a given point and + + align:start position:0% +before it starts at a given point and + + + align:start position:0% +before it starts at a given point and +then radiates outward that's a spherical + + align:start position:0% +then radiates outward that's a spherical + + + align:start position:0% +then radiates outward that's a spherical +wave well we're not quite finished yet + + align:start position:0% +wave well we're not quite finished yet + + + align:start position:0% +wave well we're not quite finished yet +but I think we're almost out of time so + + align:start position:0% +but I think we're almost out of time so + + + align:start position:0% +but I think we're almost out of time so +I think I'll stop here we can still + + align:start position:0% +I think I'll stop here we can still + + + align:start position:0% +I think I'll stop here we can still +continue next time are there any + + align:start position:0% +continue next time are there any + + + align:start position:0% +continue next time are there any +questions + + align:start position:0% + + + + align:start position:0% + +there's no homework due on Wednesday so + + align:start position:0% +there's no homework due on Wednesday so + + + align:start position:0% +there's no homework due on Wednesday so +what I would like to do you have a + + align:start position:0% +what I would like to do you have a + + + align:start position:0% +what I would like to do you have a +question oh yeah there's a question + + align:start position:0% +question oh yeah there's a question + + + align:start position:0% +question oh yeah there's a question +right how is the wave equation + + align:start position:0% +right how is the wave equation + + + align:start position:0% +right how is the wave equation +intuitively different from simple + + align:start position:0% +intuitively different from simple + + + align:start position:0% +intuitively different from simple +harmonic oscillator like the variation + + align:start position:0% +harmonic oscillator like the variation + + + align:start position:0% +harmonic oscillator like the variation +in space depends on the variation on + + align:start position:0% +in space depends on the variation on + + + align:start position:0% +in space depends on the variation on +time + + align:start position:0% +time + + + align:start position:0% +time +so that's coupling okay yeah the + + align:start position:0% +so that's coupling okay yeah the + + + align:start position:0% +so that's coupling okay yeah the +mathematical answer of course is varies + + align:start position:0% +mathematical answer of course is varies + + + align:start position:0% +mathematical answer of course is varies +if they simply have more nicosia later + + align:start position:0% +if they simply have more nicosia later + + + align:start position:0% +if they simply have more nicosia later +is an ordinary differential equation + + align:start position:0% +is an ordinary differential equation + + + align:start position:0% +is an ordinary differential equation +this is a partial differential equation + + align:start position:0% +this is a partial differential equation + + + align:start position:0% +this is a partial differential equation +but let me let me think how to formulate + + align:start position:0% +but let me let me think how to formulate + + + align:start position:0% +but let me let me think how to formulate +the physical answer okay so the physical + + align:start position:0% +the physical answer okay so the physical + + + align:start position:0% +the physical answer okay so the physical +answer is that the the harmonic + + align:start position:0% +answer is that the the harmonic + + + align:start position:0% +answer is that the the harmonic +oscillator is a single particle whose + + align:start position:0% +oscillator is a single particle whose + + + align:start position:0% +oscillator is a single particle whose +position you track as a function of time + + align:start position:0% +position you track as a function of time + + + align:start position:0% +position you track as a function of time +right a wave is a distributed physical + + align:start position:0% +right a wave is a distributed physical + + + align:start position:0% +right a wave is a distributed physical +system so you can think of a way in this + + align:start position:0% +system so you can think of a way in this + + + align:start position:0% +system so you can think of a way in this +case for example you can interpret the + + align:start position:0% +case for example you can interpret the + + + align:start position:0% +case for example you can interpret the +physical meaning of these black and + + align:start position:0% +physical meaning of these black and + + + align:start position:0% +physical meaning of these black and +white stripes as particles which are + + align:start position:0% +white stripes as particles which are + + + align:start position:0% +white stripes as particles which are +moving for example the perfectly that is + + align:start position:0% +moving for example the perfectly that is + + + align:start position:0% +moving for example the perfectly that is +on the white stripe is moving up the + + align:start position:0% +on the white stripe is moving up the + + + align:start position:0% +on the white stripe is moving up the +particle in the black stripe is moving + + align:start position:0% +particle in the black stripe is moving + + + align:start position:0% +particle in the black stripe is moving +down right whereas if I play the wave + + align:start position:0% +down right whereas if I play the wave + + + align:start position:0% +down right whereas if I play the wave +again what you will see that the part it + + align:start position:0% +again what you will see that the part it + + + align:start position:0% +again what you will see that the part it +is I can home because a Tooting like + + align:start position:0% +is I can home because a Tooting like + + + align:start position:0% +is I can home because a Tooting like +coordinated motion right because you + + align:start position:0% +coordinated motion right because you + + + align:start position:0% +coordinated motion right because you +have particles that were down then they + + align:start position:0% +have particles that were down then they + + + align:start position:0% +have particles that were down then they +go up then they go down again but they + + align:start position:0% +go up then they go down again but they + + + align:start position:0% +go up then they go down again but they +go out in a coordinated motion + + align:start position:0% +go out in a coordinated motion + + + align:start position:0% +go out in a coordinated motion +throughout the entire plane how do they + + align:start position:0% +throughout the entire plane how do they + + + align:start position:0% +throughout the entire plane how do they +know well there is a physical system + + align:start position:0% +know well there is a physical system + + + align:start position:0% +know well there is a physical system +associated with it for example this + + align:start position:0% +associated with it for example this + + + align:start position:0% +associated with it for example this +could be a membrane with the sound wave + + align:start position:0% +could be a membrane with the sound wave + + + align:start position:0% +could be a membrane with the sound wave +propagating on e3 and now the reason the + + align:start position:0% +propagating on e3 and now the reason the + + + align:start position:0% +propagating on e3 and now the reason the +particles are connected that the + + align:start position:0% +particles are connected that the + + + align:start position:0% +particles are connected that the +executes the coordinated motion is + + align:start position:0% +executes the coordinated motion is + + + align:start position:0% +executes the coordinated motion is +because of the entire atomic you know + + align:start position:0% +because of the entire atomic you know + + + align:start position:0% +because of the entire atomic you know +forces between the membrane particle if + + align:start position:0% +forces between the membrane particle if + + + align:start position:0% +forces between the membrane particle if +it is an electromagnetic wave then it is + + align:start position:0% +it is an electromagnetic wave then it is + + + align:start position:0% +it is an electromagnetic wave then it is +a field that is that is distributed and + + align:start position:0% +a field that is that is distributed and + + + align:start position:0% +a field that is that is distributed and +of course it knows to be connected + + align:start position:0% +of course it knows to be connected + + + align:start position:0% +of course it knows to be connected +because of Maxwell's equation right you + + align:start position:0% +because of Maxwell's equation right you + + + align:start position:0% +because of Maxwell's equation right you +know that things like charge + + align:start position:0% +know that things like charge + + + align:start position:0% +know that things like charge +conservation and so on that force it to + + align:start position:0% +conservation and so on that force it to + + + align:start position:0% +conservation and so on that force it to +act this way so a wave is actually + + align:start position:0% +act this way so a wave is actually + + + align:start position:0% +act this way so a wave is actually +distributed system where the physics + + align:start position:0% +distributed system where the physics + + + align:start position:0% +distributed system where the physics +force an extended + + align:start position:0% +force an extended + + + align:start position:0% +force an extended +systems particles or fields or you know + + align:start position:0% +systems particles or fields or you know + + + align:start position:0% +systems particles or fields or you know +whatever the case may be to execute the + + align:start position:0% +whatever the case may be to execute the + + + align:start position:0% +whatever the case may be to execute the +coordinated motion that's the difference + + align:start position:0% +coordinated motion that's the difference + + + align:start position:0% +coordinated motion that's the difference +between they simply have no notion it + + align:start position:0% +between they simply have no notion it + + + align:start position:0% +between they simply have no notion it +over you just have one particle now you + + align:start position:0% +over you just have one particle now you + + + align:start position:0% +over you just have one particle now you +can go from one to the other imagine you + + align:start position:0% +can go from one to the other imagine you + + + align:start position:0% +can go from one to the other imagine you +take a single harmonic oscillator that's + + align:start position:0% +take a single harmonic oscillator that's + + + align:start position:0% +take a single harmonic oscillator that's +a good one so let me let me draw it here + + align:start position:0% +a good one so let me let me draw it here + + + align:start position:0% +a good one so let me let me draw it here +well we're actually going backwards now + + align:start position:0% +well we're actually going backwards now + + + align:start position:0% +well we're actually going backwards now +in in the knowledge that they use in the + + align:start position:0% +in in the knowledge that they use in the + + + align:start position:0% +in in the knowledge that they use in the +path so you take a simple harmonic + + align:start position:0% +path so you take a simple harmonic + + + align:start position:0% +path so you take a simple harmonic +oscillator here it is right at the + + align:start position:0% +oscillator here it is right at the + + + align:start position:0% +oscillator here it is right at the +pendulum right this is a simple harmonic + + align:start position:0% +pendulum right this is a simple harmonic + + + align:start position:0% +pendulum right this is a simple harmonic +oscillator then you couple it with the + + align:start position:0% +oscillator then you couple it with the + + + align:start position:0% +oscillator then you couple it with the +second pendulum how do you cut they're + + align:start position:0% +second pendulum how do you cut they're + + + align:start position:0% +second pendulum how do you cut they're +not traveled at the moment but you can + + align:start position:0% +not traveled at the moment but you can + + + align:start position:0% +not traveled at the moment but you can +couple them for example by connecting + + align:start position:0% +couple them for example by connecting + + + align:start position:0% +couple them for example by connecting +the spring in between right but there's + + align:start position:0% +the spring in between right but there's + + + align:start position:0% +the spring in between right but there's +not quite a wave but you can see now + + align:start position:0% +not quite a wave but you can see now + + + align:start position:0% +not quite a wave but you can see now +that because I coupled them if I kick + + align:start position:0% +that because I coupled them if I kick + + + align:start position:0% +that because I coupled them if I kick +one of these it will also cause the + + align:start position:0% +one of these it will also cause the + + + align:start position:0% +one of these it will also cause the +other one to move right so they program + + align:start position:0% +other one to move right so they program + + + align:start position:0% +other one to move right so they program +coordinated well now let me generalize + + align:start position:0% +coordinated well now let me generalize + + + align:start position:0% +coordinated well now let me generalize +imagine that they have a bunch of + + align:start position:0% +imagine that they have a bunch of + + + align:start position:0% +imagine that they have a bunch of +harmonic oscillators and in fact I can + + align:start position:0% +harmonic oscillators and in fact I can + + + align:start position:0% +harmonic oscillators and in fact I can +make an infinite and a couple them now + + align:start position:0% +make an infinite and a couple them now + + + align:start position:0% +make an infinite and a couple them now +in fact the system will become wave-like + + align:start position:0% +in fact the system will become wave-like + + + align:start position:0% +in fact the system will become wave-like +in the sense that if you kick it at one + + align:start position:0% +in the sense that if you kick it at one + + + align:start position:0% +in the sense that if you kick it at one +end okay let's say not at infinity let's + + align:start position:0% +end okay let's say not at infinity let's + + + align:start position:0% +end okay let's say not at infinity let's +say it starts actually here and then it + + align:start position:0% +say it starts actually here and then it + + + align:start position:0% +say it starts actually here and then it +goes to infinity so if you kick it at + + align:start position:0% +goes to infinity so if you kick it at + + + align:start position:0% +goes to infinity so if you kick it at +one end then the disturbance will + + align:start position:0% +one end then the disturbance will + + + align:start position:0% +one end then the disturbance will +actually propagate very similar to a + + align:start position:0% +actually propagate very similar to a + + + align:start position:0% +actually propagate very similar to a +wave it's a discrete wave but silly wave + + align:start position:0% +wave it's a discrete wave but silly wave + + + align:start position:0% +wave it's a discrete wave but silly wave +so you can go from one to the other by + + align:start position:0% +so you can go from one to the other by + + + align:start position:0% +so you can go from one to the other by +introducing the kind of a coordination + + align:start position:0% +introducing the kind of a coordination + + + align:start position:0% +introducing the kind of a coordination +mechanisms which is the coupling here + + align:start position:0% +mechanisms which is the coupling here + + + align:start position:0% +mechanisms which is the coupling here +does the coordination + + align:start position:0% + + + + align:start position:0% + +another question we can stay here + + align:start position:0% +another question we can stay here + + + align:start position:0% +another question we can stay here +actually nobody claimed the classroom + + align:start position:0% +actually nobody claimed the classroom + + + align:start position:0% +actually nobody claimed the classroom +say they here there so we have more + + align:start position:0% +say they here there so we have more + + + align:start position:0% +say they here there so we have more +questions we'll be happy to stay in + + align:start position:0% +questions we'll be happy to stay in + + + align:start position:0% +questions we'll be happy to stay in +answer them + + align:start position:0% + + + + align:start position:0% + +but about the Pfizer's is it clear the + + align:start position:0% +but about the Pfizer's is it clear the + + + align:start position:0% +but about the Pfizer's is it clear the +phasers I realized the phasers when I + + align:start position:0% +phasers I realized the phasers when I + + + align:start position:0% +phasers I realized the phasers when I +was your age you went over the student I + + align:start position:0% +was your age you went over the student I + + + align:start position:0% +was your age you went over the student I +was also very upset by phasers because + + align:start position:0% +was also very upset by phasers because + + + align:start position:0% +was also very upset by phasers because +they they look very much like + + align:start position:0% +they they look very much like + + + align:start position:0% +they they look very much like +mathematical tickity I mean I'm trying + + align:start position:0% +mathematical tickity I mean I'm trying + + + align:start position:0% +mathematical tickity I mean I'm trying +to find my I guess that's one benefit of + + align:start position:0% +to find my I guess that's one benefit of + + + align:start position:0% +to find my I guess that's one benefit of +this over the whiteboard that they have + + align:start position:0% +this over the whiteboard that they have + + + align:start position:0% +this over the whiteboard that they have +a history of what they do but yet but + + align:start position:0% +a history of what they do but yet but + + + align:start position:0% +a history of what they do but yet but +the phasers they look very much like a + + align:start position:0% +the phasers they look very much like a + + + align:start position:0% +the phasers they look very much like a +mathematical pre-k I mean just look like + + align:start position:0% +mathematical pre-k I mean just look like + + + align:start position:0% +mathematical pre-k I mean just look like +someone pulled it out of the Hat but but + + align:start position:0% +someone pulled it out of the Hat but but + + + align:start position:0% +someone pulled it out of the Hat but but +the only reason to justify it in your + + align:start position:0% +the only reason to justify it in your + + + align:start position:0% +the only reason to justify it in your +mind is that it provides huge + + align:start position:0% +mind is that it provides huge + + + align:start position:0% +mind is that it provides huge +mathematical convenience now this looks + + align:start position:0% +mathematical convenience now this looks + + + align:start position:0% +mathematical convenience now this looks +like a trivial thing I mean the + + align:start position:0% +like a trivial thing I mean the + + + align:start position:0% +like a trivial thing I mean the +derivation of the standing wave was + + align:start position:0% +derivation of the standing wave was + + + align:start position:0% +derivation of the standing wave was +maybe four lines with trigonometry two + + align:start position:0% +maybe four lines with trigonometry two + + + align:start position:0% +maybe four lines with trigonometry two +lines with the complex exponential so + + align:start position:0% +lines with the complex exponential so + + + align:start position:0% +lines with the complex exponential so +okay why mess with complex numbers well + + align:start position:0% +okay why mess with complex numbers well + + + align:start position:0% +okay why mess with complex numbers well +try superposition if you have like you + + align:start position:0% +try superposition if you have like you + + + align:start position:0% +try superposition if you have like you +know several waves superimposed or if + + align:start position:0% +know several waves superimposed or if + + + align:start position:0% +know several waves superimposed or if +you have an integral a continuum of + + align:start position:0% +you have an integral a continuum of + + + align:start position:0% +you have an integral a continuum of +superimposed waves which will see very + + align:start position:0% +superimposed waves which will see very + + + align:start position:0% +superimposed waves which will see very +soon like fully eternal formulas on + + align:start position:0% +soon like fully eternal formulas on + + + align:start position:0% +soon like fully eternal formulas on +written as formula extremely + + align:start position:0% +written as formula extremely + + + align:start position:0% +written as formula extremely +inconvenient if you write them as cosine + + align:start position:0% +inconvenient if you write them as cosine + + + align:start position:0% +inconvenient if you write them as cosine +transform big mess the kratom is full of + + align:start position:0% +transform big mess the kratom is full of + + + align:start position:0% +transform big mess the kratom is full of +complex Exponential's is actually very + + align:start position:0% +complex Exponential's is actually very + + + align:start position:0% +complex Exponential's is actually very +simple to do the math which is it is a + + align:start position:0% +simple to do the math which is it is a + + + align:start position:0% +simple to do the math which is it is a +it is a very very time-saving tool + + align:start position:0% +it is a very very time-saving tool + + + align:start position:0% +it is a very very time-saving tool +basically a lot of strange than that it + + align:start position:0% +basically a lot of strange than that it + + + align:start position:0% +basically a lot of strange than that it +gives leads to some insights that the + + align:start position:0% +gives leads to some insights that the + + + align:start position:0% +gives leads to some insights that the +real numbers do not give you that's an + + align:start position:0% +real numbers do not give you that's an + + + align:start position:0% +real numbers do not give you that's an +additional convenience but having + + align:start position:0% +additional convenience but having + + + align:start position:0% +additional convenience but having +Google's appreciated later for now it is + + align:start position:0% +Google's appreciated later for now it is + + + align:start position:0% +Google's appreciated later for now it is +simply the mathematical convenience that + + align:start position:0% +simply the mathematical convenience that + + + align:start position:0% +simply the mathematical convenience that +drives this mathematical wizardry yeah + + align:start position:0% + + + + align:start position:0% + +yeah he's saying instead when the + + align:start position:0% +yeah he's saying instead when the + + + align:start position:0% +yeah he's saying instead when the +angular frequency in the temporal + + align:start position:0% +angular frequency in the temporal + + + align:start position:0% +angular frequency in the temporal +frequency are different or it's the same + + align:start position:0% +frequency are different or it's the same + + + align:start position:0% +frequency are different or it's the same +because you initially defined Omega as + + align:start position:0% +because you initially defined Omega as + + + align:start position:0% +because you initially defined Omega as +angular frequency i confuse those myself + + align:start position:0% +angular frequency i confuse those myself + + + align:start position:0% +angular frequency i confuse those myself +usually the terms usually knew this only + + align:start position:0% +usually the terms usually knew this only + + + align:start position:0% +usually the terms usually knew this only +know is called the frequency and it is + + align:start position:0% +know is called the frequency and it is + + + align:start position:0% +know is called the frequency and it is +measured in Hertz a 2 pi nu is measured + + align:start position:0% +measured in Hertz a 2 pi nu is measured + + + align:start position:0% +measured in Hertz a 2 pi nu is measured +in radians per second and this is + + align:start position:0% +in radians per second and this is + + + align:start position:0% +in radians per second and this is +defined what about angular frequency + + align:start position:0% +defined what about angular frequency + + + align:start position:0% +defined what about angular frequency +isn't it yeah + + align:start position:0% + + + + align:start position:0% + +Oh as opposed to what else and guess I'd + + align:start position:0% +Oh as opposed to what else and guess I'd + + + align:start position:0% +Oh as opposed to what else and guess I'd +understand the question + + align:start position:0% + + + + align:start position:0% + +yeah what I mean is that that for + + align:start position:0% +yeah what I mean is that that for + + + align:start position:0% +yeah what I mean is that that for +example take the propagating wave the + + align:start position:0% +example take the propagating wave the + + + align:start position:0% +example take the propagating wave the +propagating wave is e to the I we say + + align:start position:0% +propagating wave is e to the I we say + + + align:start position:0% +propagating wave is e to the I we say +forwarded KZ minus Omega T the standing + + align:start position:0% +forwarded KZ minus Omega T the standing + + + align:start position:0% +forwarded KZ minus Omega T the standing +wave is cosine KZ e to the minus I Omega + + align:start position:0% +wave is cosine KZ e to the minus I Omega + + + align:start position:0% +wave is cosine KZ e to the minus I Omega +T I'll go I'll go + + align:start position:0% +T I'll go I'll go + + + align:start position:0% +T I'll go I'll go +I'll step ahead a bit and write + + align:start position:0% +I'll step ahead a bit and write + + + align:start position:0% +I'll step ahead a bit and write +something awful + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +this is actually a wave it is what we'll + + align:start position:0% +this is actually a wave it is what we'll + + + align:start position:0% +this is actually a wave it is what we'll +see later it is called a diffraction + + align:start position:0% +see later it is called a diffraction + + + align:start position:0% +see later it is called a diffraction +integral and if you can see it is + + align:start position:0% +integral and if you can see it is + + + align:start position:0% +integral and if you can see it is +nothing even though it looks really + + align:start position:0% +nothing even though it looks really + + + align:start position:0% +nothing even though it looks really +complicated it is just a superposition + + align:start position:0% +complicated it is just a superposition + + + align:start position:0% +complicated it is just a superposition +right because the integral is a + + align:start position:0% +right because the integral is a + + + align:start position:0% +right because the integral is a +summation and then what I have here is a + + align:start position:0% +summation and then what I have here is a + + + align:start position:0% +summation and then what I have here is a +phaser and I put a lot a lot of these + + align:start position:0% +phaser and I put a lot a lot of these + + + align:start position:0% +phaser and I put a lot a lot of these +values together what they all share is + + align:start position:0% +values together what they all share is + + + align:start position:0% +values together what they all share is +is this pyramid to the I minus I Omega T + + align:start position:0% +is this pyramid to the I minus I Omega T + + + align:start position:0% +is this pyramid to the I minus I Omega T +okay so I could actually to be strictly + + align:start position:0% +okay so I could actually to be strictly + + + align:start position:0% +okay so I could actually to be strictly +correct there should really carry this + + align:start position:0% +correct there should really carry this + + + align:start position:0% +correct there should really carry this +term I'm not really allowed to drop it + + align:start position:0% +term I'm not really allowed to drop it + + + align:start position:0% +term I'm not really allowed to drop it +but because this is the same always I + + align:start position:0% +but because this is the same always I + + + align:start position:0% +but because this is the same always I +might as well just as well not writing + + align:start position:0% +might as well just as well not writing + + + align:start position:0% +might as well just as well not writing +so it basically saves me writing and + + align:start position:0% +so it basically saves me writing and + + + align:start position:0% +so it basically saves me writing and +also confusion because as you know the + + align:start position:0% +also confusion because as you know the + + + align:start position:0% +also confusion because as you know the +more things you write the more likely + + align:start position:0% +more things you write the more likely + + + align:start position:0% +more things you write the more likely +you are to make mistakes so a typically + + align:start position:0% +you are to make mistakes so a typically + + + align:start position:0% +you are to make mistakes so a typically +you know it is typical in these + + align:start position:0% +you know it is typical in these + + + align:start position:0% +you know it is typical in these +derivations if you don't need something + + align:start position:0% +derivations if you don't need something + + + align:start position:0% +derivations if you don't need something +you drop it right because if you start + + align:start position:0% +you drop it right because if you start + + + align:start position:0% +you drop it right because if you start +carrying it around it it involves + + align:start position:0% +carrying it around it it involves + + + align:start position:0% +carrying it around it it involves +mistakes so that's why I would drop them + + align:start position:0% + + + + align:start position:0% + +so I can just as well say that if I have + + align:start position:0% +so I can just as well say that if I have + + + align:start position:0% +so I can just as well say that if I have +a propagating wave I can just write it + + align:start position:0% +a propagating wave I can just write it + + + align:start position:0% +a propagating wave I can just write it +as e to the ikj that's a propagating + + align:start position:0% +as e to the ikj that's a propagating + + + align:start position:0% +as e to the ikj that's a propagating +wave have a standing wave I can just as + + align:start position:0% +wave have a standing wave I can just as + + + align:start position:0% +wave have a standing wave I can just as +well write it cosine KZ okay they - + + align:start position:0% +well write it cosine KZ okay they - + + + align:start position:0% +well write it cosine KZ okay they - +there - I Omega T is included right if I + + align:start position:0% +there - I Omega T is included right if I + + + align:start position:0% +there - I Omega T is included right if I +have this diffraction integral I can + + align:start position:0% +have this diffraction integral I can + + + align:start position:0% +have this diffraction integral I can +just write it without this term but + + align:start position:0% +just write it without this term but + + + align:start position:0% +just write it without this term but +again the time is implicit if I have to + + align:start position:0% +again the time is implicit if I have to + + + align:start position:0% +again the time is implicit if I have to +figure out what is the temporal + + align:start position:0% +figure out what is the temporal + + + align:start position:0% +figure out what is the temporal +variation of the way I have to put it + + align:start position:0% +variation of the way I have to put it + + + align:start position:0% +variation of the way I have to put it +back in and again I cannot do it if I + + align:start position:0% +back in and again I cannot do it if I + + + align:start position:0% +back in and again I cannot do it if I +have two waves of different frequencies + + align:start position:0% +have two waves of different frequencies + + + align:start position:0% +have two waves of different frequencies +if I have e to the I Omega let me write + + align:start position:0% +if I have e to the I Omega let me write + + + align:start position:0% +if I have e to the I Omega let me write +- let me write another superposition get + + align:start position:0% +- let me write another superposition get + + + align:start position:0% +- let me write another superposition get +to the I k1 Z minus Omega 1 T plus e to + + align:start position:0% +to the I k1 Z minus Omega 1 T plus e to + + + align:start position:0% +to the I k1 Z minus Omega 1 T plus e to +the I a - Z minus Omega 2 T that's still + + align:start position:0% +the I a - Z minus Omega 2 T that's still + + + align:start position:0% +the I a - Z minus Omega 2 T that's still +a valid superposition provided that the + + align:start position:0% +a valid superposition provided that the + + + align:start position:0% +a valid superposition provided that the +ratios of these you know K 1 over Omega + + align:start position:0% +ratios of these you know K 1 over Omega + + + align:start position:0% +ratios of these you know K 1 over Omega +1 equal see a 2 Omega 2 equal C still + + align:start position:0% +1 equal see a 2 Omega 2 equal C still + + + align:start position:0% +1 equal see a 2 Omega 2 equal C still +valid superposition I'm not violating it + + align:start position:0% +valid superposition I'm not violating it + + + align:start position:0% +valid superposition I'm not violating it +but I cannot do the phaser trick anymore + + align:start position:0% +but I cannot do the phaser trick anymore + + + align:start position:0% +but I cannot do the phaser trick anymore +right I have to keep the + + align:start position:0% +right I have to keep the + + + align:start position:0% +right I have to keep the +it was I am I get it terms or I will + + align:start position:0% +it was I am I get it terms or I will + + + align:start position:0% +it was I am I get it terms or I will +make a mistake there's one more case + + align:start position:0% +make a mistake there's one more case + + + align:start position:0% +make a mistake there's one more case +when if you produce any kind of + + align:start position:0% +when if you produce any kind of + + + align:start position:0% +when if you produce any kind of +non-linearity we will say later and + + align:start position:0% +non-linearity we will say later and + + + align:start position:0% +non-linearity we will say later and +again where we're going a little bit + + align:start position:0% +again where we're going a little bit + + + align:start position:0% +again where we're going a little bit +ahead I'm in trouble + + align:start position:0% +ahead I'm in trouble + + + align:start position:0% +ahead I'm in trouble +these are from the police okay we'll see + + align:start position:0% +these are from the police okay we'll see + + + align:start position:0% +these are from the police okay we'll see +little bit later when we try to compute + + align:start position:0% +little bit later when we try to compute + + + align:start position:0% +little bit later when we try to compute +the flux of electromagnetic energy the + + align:start position:0% +the flux of electromagnetic energy the + + + align:start position:0% +the flux of electromagnetic energy the +something called the pointing vector + + align:start position:0% +something called the pointing vector + + + align:start position:0% +something called the pointing vector +which is defined as the electric field + + align:start position:0% +which is defined as the electric field + + + align:start position:0% +which is defined as the electric field +cross with the magnetic field okay if + + align:start position:0% +cross with the magnetic field okay if + + + align:start position:0% +cross with the magnetic field okay if +you try to write the expression for the + + align:start position:0% +you try to write the expression for the + + + align:start position:0% +you try to write the expression for the +pointing vector + + align:start position:0% +pointing vector + + + align:start position:0% +pointing vector +you cannot just multiply the phasers the + + align:start position:0% +you cannot just multiply the phasers the + + + align:start position:0% +you cannot just multiply the phasers the +electric and the magnetic field because + + align:start position:0% +electric and the magnetic field because + + + align:start position:0% +electric and the magnetic field because +it's a product so you can use phasers + + align:start position:0% +it's a product so you can use phasers + + + align:start position:0% +it's a product so you can use phasers +only when you have linear operations + + align:start position:0% +only when you have linear operations + + + align:start position:0% +only when you have linear operations +such as a distance ray or integrals in + + align:start position:0% +such as a distance ray or integrals in + + + align:start position:0% +such as a distance ray or integrals in +this case you can't we will see what you + + align:start position:0% +this case you can't we will see what you + + + align:start position:0% +this case you can't we will see what you +do in this case you do a temporal + + align:start position:0% +do in this case you do a temporal + + + align:start position:0% +do in this case you do a temporal +average but but there is a shoe if you a + + align:start position:0% +average but but there is a shoe if you a + + + align:start position:0% +average but but there is a shoe if you a +cases where one has to be careful with + + align:start position:0% +cases where one has to be careful with + + + align:start position:0% +cases where one has to be careful with +this phaser \ No newline at end of file diff --git a/ruRaCsL9tpQ.txt b/ruRaCsL9tpQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..c13632aca553f15bcc0e8fa77cfb2f26549703c5 --- /dev/null +++ b/ruRaCsL9tpQ.txt @@ -0,0 +1,12155 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Common License your support + + align:start position:0% +a Creative Common License your support + + + align:start position:0% +a Creative Common License your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT Open Courseware + + align:start position:0% +of MIT courses visit MIT Open Courseware + + + align:start position:0% +of MIT courses visit MIT Open Courseware +at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +what I want to do today + + align:start position:0% +what I want to do today + + + align:start position:0% +what I want to do today +is look ahead and talk a little bit + + align:start position:0% +is look ahead and talk a little bit + + + align:start position:0% +is look ahead and talk a little bit +about where the grid's going this is + + align:start position:0% +about where the grid's going this is + + + align:start position:0% +about where the grid's going this is +going to be based largely on that future + + align:start position:0% +going to be based largely on that future + + + align:start position:0% +going to be based largely on that future +of the electric grid study that uh a + + align:start position:0% +of the electric grid study that uh a + + + align:start position:0% +of the electric grid study that uh a +bunch of us did you'll see in the Jocow + + align:start position:0% +bunch of us did you'll see in the Jocow + + + align:start position:0% +bunch of us did you'll see in the Jocow +paper a fair amount of overlap and an + + align:start position:0% +paper a fair amount of overlap and an + + + align:start position:0% +paper a fair amount of overlap and an +awful lot of agreement although his + + align:start position:0% +awful lot of agreement although his + + + align:start position:0% +awful lot of agreement although his +emphasis is a bit different so let me + + align:start position:0% +emphasis is a bit different so let me + + + align:start position:0% +emphasis is a bit different so let me +start + + align:start position:0% +start + + + align:start position:0% +start +with what the system looks like now + + align:start position:0% +with what the system looks like now + + + align:start position:0% +with what the system looks like now +that's a picture of um line losses in in + + align:start position:0% +that's a picture of um line losses in in + + + align:start position:0% +that's a picture of um line losses in in +transmission and distribution right + + align:start position:0% +transmission and distribution right + + + align:start position:0% +transmission and distribution right +that's heat basically waste heat and + + align:start position:0% +that's heat basically waste heat and + + + align:start position:0% +that's heat basically waste heat and +that's gone down sharply over time uh it + + align:start position:0% +that's gone down sharply over time uh it + + + align:start position:0% +that's gone down sharply over time uh it +floats around + + align:start position:0% +floats around + + + align:start position:0% +floats around +67% these appear to be in line with line + + align:start position:0% +67% these appear to be in line with line + + + align:start position:0% +67% these appear to be in line with line +losses in other developed countries if + + align:start position:0% +losses in other developed countries if + + + align:start position:0% +losses in other developed countries if +you take a if you make allowance for + + align:start position:0% +you take a if you make allowance for + + + align:start position:0% +you take a if you make allowance for +density it they're higher in Canada and + + align:start position:0% +density it they're higher in Canada and + + + align:start position:0% +density it they're higher in Canada and +Australia they're lower in Germany and + + align:start position:0% +Australia they're lower in Germany and + + + align:start position:0% +Australia they're lower in Germany and +France because it's more compact + + align:start position:0% +France because it's more compact + + + align:start position:0% +France because it's more compact +countries but but you can put us all + + align:start position:0% +countries but but you can put us all + + + align:start position:0% +countries but but you can put us all +more or less on a line um reliability is + + align:start position:0% +more or less on a line um reliability is + + + align:start position:0% +more or less on a line um reliability is +a little tougher you might ask the + + align:start position:0% +a little tougher you might ask the + + + align:start position:0% +a little tougher you might ask the +question is the US system more or less + + align:start position:0% +question is the US system more or less + + + align:start position:0% +question is the US system more or less +reliable than systems elsewhere and the + + align:start position:0% +reliable than systems elsewhere and the + + + align:start position:0% +reliable than systems elsewhere and the +answer is we don't know because u data + + align:start position:0% +answer is we don't know because u data + + + align:start position:0% +answer is we don't know because u data +on reliability and other aspects of + + align:start position:0% +on reliability and other aspects of + + + align:start position:0% +on reliability and other aspects of +performance are terrible in the US + + align:start position:0% +performance are terrible in the US + + + align:start position:0% +performance are terrible in the US +you might ask why that + + align:start position:0% +you might ask why that + + + align:start position:0% +you might ask why that +is i'll suggest an + + align:start position:0% +is i'll suggest an + + + align:start position:0% +is i'll suggest an +answer and it has to do with the + + align:start position:0% +answer and it has to do with the + + + align:start position:0% +answer and it has to do with the +structure of regulation right if I + + align:start position:0% +structure of regulation right if I + + + align:start position:0% +structure of regulation right if I +measure if I use a standard definition + + align:start position:0% +measure if I use a standard definition + + + align:start position:0% +measure if I use a standard definition +of an + + align:start position:0% +of an + + + align:start position:0% +of an +outage and I measure how often my + + align:start position:0% +outage and I measure how often my + + + align:start position:0% +outage and I measure how often my +customers don't have power how many + + align:start position:0% +customers don't have power how many + + + align:start position:0% +customers don't have power how many +outages how long they last and you do + + align:start position:0% +outages how long they last and you do + + + align:start position:0% +outages how long they last and you do +the same and I'm above you in + + align:start position:0% +the same and I'm above you in + + + align:start position:0% +the same and I'm above you in +outages people yell at me if nobody + + align:start position:0% +outages people yell at me if nobody + + + align:start position:0% +outages people yell at me if nobody +knows nobody yells at + + align:start position:0% +knows nobody yells at + + + align:start position:0% +knows nobody yells at +me these things are just not measured in + + align:start position:0% +me these things are just not measured in + + + align:start position:0% +me these things are just not measured in +the US i mean they're measured in some + + align:start position:0% +the US i mean they're measured in some + + + align:start position:0% +the US i mean they're measured in some +states they're not reported in some + + align:start position:0% +states they're not reported in some + + + align:start position:0% +states they're not reported in some +states where they're measured and + + align:start position:0% +states where they're measured and + + + align:start position:0% +states where they're measured and +different definitions are used all over + + align:start position:0% +different definitions are used all over + + + align:start position:0% +different definitions are used all over +the country there is now a standard IE + + align:start position:0% +the country there is now a standard IE + + + align:start position:0% +the country there is now a standard IE +definition for outages and it's + + align:start position:0% +definition for outages and it's + + + align:start position:0% +definition for outages and it's +spreading slowly but even then it it's + + align:start position:0% +spreading slowly but even then it it's + + + align:start position:0% +spreading slowly but even then it it's +not reported in lots of places so we + + align:start position:0% +not reported in lots of places so we + + + align:start position:0% +not reported in lots of places so we +cannot tell if the system is more or + + align:start position:0% +cannot tell if the system is more or + + + align:start position:0% +cannot tell if the system is more or +less reliable than it was in 1930 which + + align:start position:0% +less reliable than it was in 1930 which + + + align:start position:0% +less reliable than it was in 1930 which +is bizarre but there's more um so I'm + + align:start position:0% +is bizarre but there's more um so I'm + + + align:start position:0% +is bizarre but there's more um so I'm +going to talk about most of the terrain + + align:start position:0% +going to talk about most of the terrain + + + align:start position:0% +going to talk about most of the terrain +we covered in in the future of the grid + + align:start position:0% +we covered in in the future of the grid + + + align:start position:0% +we covered in in the future of the grid +we focused on 2030 because at the speed + + align:start position:0% +we focused on 2030 because at the speed + + + align:start position:0% +we focused on 2030 because at the speed +at which things + + align:start position:0% +at which things + + + align:start position:0% +at which things +change the grid in 2030 will be + + align:start position:0% +change the grid in 2030 will be + + + align:start position:0% +change the grid in 2030 will be +dominated by technologies we know today + + align:start position:0% +dominated by technologies we know today + + + align:start position:0% +dominated by technologies we know today +not necessarily technologies in + + align:start position:0% +not necessarily technologies in + + + align:start position:0% +not necessarily technologies in +widespread use but stuff we know stuff + + align:start position:0% +widespread use but stuff we know stuff + + + align:start position:0% +widespread use but stuff we know stuff +we don't know that's invented tomorrow + + align:start position:0% +we don't know that's invented tomorrow + + + align:start position:0% +we don't know that's invented tomorrow +is unlikely to penetrate by then so we + + align:start position:0% +is unlikely to penetrate by then so we + + + align:start position:0% +is unlikely to penetrate by then so we +said what are the big challenges and + + align:start position:0% +said what are the big challenges and + + + align:start position:0% +said what are the big challenges and +opportunities and these are the ones we + + align:start position:0% +opportunities and these are the ones we + + + align:start position:0% +opportunities and these are the ones we +focused + + align:start position:0% +focused + + + align:start position:0% +focused +on there are a bunch of new technologies + + align:start position:0% +on there are a bunch of new technologies + + + align:start position:0% +on there are a bunch of new technologies +will they get developed and used + + align:start position:0% +will they get developed and used + + + align:start position:0% +will they get developed and used +properly there'll be more largecale wind + + align:start position:0% +properly there'll be more largecale wind + + + align:start position:0% +properly there'll be more largecale wind +and + + align:start position:0% +and + + + align:start position:0% +and +solar I'll talk about the issues that + + align:start position:0% +solar I'll talk about the issues that + + + align:start position:0% +solar I'll talk about the issues that +raises there'll be more electric + + align:start position:0% +raises there'll be more electric + + + align:start position:0% +raises there'll be more electric +vehicles how many more nobody knows but + + align:start position:0% +vehicles how many more nobody knows but + + + align:start position:0% +vehicles how many more nobody knows but +more and in some places a fair amount + + align:start position:0% +more and in some places a fair amount + + + align:start position:0% +more and in some places a fair amount +There'll be more distributed generation + + align:start position:0% +There'll be more distributed generation + + + align:start position:0% +There'll be more distributed generation +rooftop solar on various kinds of roofs + + align:start position:0% +rooftop solar on various kinds of roofs + + + align:start position:0% +rooftop solar on various kinds of roofs +um and some distributed + + align:start position:0% +um and some distributed + + + align:start position:0% +um and some distributed +wind and the system will be more reliant + + align:start position:0% +wind and the system will be more reliant + + + align:start position:0% +wind and the system will be more reliant +on communications and computation which + + align:start position:0% +on communications and computation which + + + align:start position:0% +on communications and computation which +means there'll be more of an issue of + + align:start position:0% +means there'll be more of an issue of + + + align:start position:0% +means there'll be more of an issue of +cyber + + align:start position:0% +cyber + + + align:start position:0% +cyber +security and an issue of information + + align:start position:0% +security and an issue of information + + + align:start position:0% +security and an issue of information +privacy + + align:start position:0% +privacy + + + align:start position:0% +privacy +people will know every 15 minutes how + + align:start position:0% +people will know every 15 minutes how + + + align:start position:0% +people will know every 15 minutes how +much electricity you're using and you + + align:start position:0% +much electricity you're using and you + + + align:start position:0% +much electricity you're using and you +might not want everybody to know + + align:start position:0% +might not want everybody to know + + + align:start position:0% +might not want everybody to know +that so to remind you of some of the + + align:start position:0% +that so to remind you of some of the + + + align:start position:0% +that so to remind you of some of the +constraints I talked last time um last + + align:start position:0% +constraints I talked last time um last + + + align:start position:0% +constraints I talked last time um last +Wednesday about uh the state federal + + align:start position:0% +Wednesday about uh the state federal + + + align:start position:0% +Wednesday about uh the state federal +divide + + align:start position:0% +divide + + + align:start position:0% +divide +states are + + align:start position:0% +states are + + + align:start position:0% +states are +important um there's not much evidence + + align:start position:0% +important um there's not much evidence + + + align:start position:0% +important um there's not much evidence +not much + + align:start position:0% +not much + + + align:start position:0% +not much +appetite after the California debacle + + align:start position:0% +appetite after the California debacle + + + align:start position:0% +appetite after the California debacle +and after the layman uh crisis and the + + align:start position:0% +and after the layman uh crisis and the + + + align:start position:0% +and after the layman uh crisis and the +the whole crisis um not much appetite + + align:start position:0% +the whole crisis um not much appetite + + + align:start position:0% +the whole crisis um not much appetite +for + + align:start position:0% +for + + + align:start position:0% +for +reform very diverse system municipal + + align:start position:0% +reform very diverse system municipal + + + align:start position:0% +reform very diverse system municipal +utilities co-ops big utilities little + + align:start position:0% +utilities co-ops big utilities little + + + align:start position:0% +utilities co-ops big utilities little +utilities vertically integrated in some + + align:start position:0% +utilities vertically integrated in some + + + align:start position:0% +utilities vertically integrated in some +places federally owned in other + + align:start position:0% +places federally owned in other + + + align:start position:0% +places federally owned in other +places there's not much growth + + align:start position:0% +places there's not much growth + + + align:start position:0% +places there's not much growth +expected 7/10 of a percentage point a + + align:start position:0% +expected 7/10 of a percentage point a + + + align:start position:0% +expected 7/10 of a percentage point a +year is the standard case forecast out + + align:start position:0% +year is the standard case forecast out + + + align:start position:0% +year is the standard case forecast out +to + + align:start position:0% +to + + + align:start position:0% +to +2035 and very durable assets this is + + align:start position:0% +2035 and very durable assets this is + + + align:start position:0% +2035 and very durable assets this is +actually a number I had it last year the + + align:start position:0% +actually a number I had it last year the + + + align:start position:0% +actually a number I had it last year the +forecast number has doubled since last + + align:start position:0% +forecast number has doubled since last + + + align:start position:0% +forecast number has doubled since last +year but it's still low + + align:start position:0% +year but it's still low + + + align:start position:0% +year but it's still low +um + + align:start position:0% +um + + + align:start position:0% +um +h anybody care to guess what fraction of + + align:start position:0% +h anybody care to guess what fraction of + + + align:start position:0% +h anybody care to guess what fraction of +2000 what fraction of say let's say 2010 + + align:start position:0% +2000 what fraction of say let's say 2010 + + + align:start position:0% +2000 what fraction of say let's say 2010 +capacity will be retired by 2035 + + align:start position:0% +capacity will be retired by 2035 + + + align:start position:0% +capacity will be retired by 2035 +1% well now you're + + align:start position:0% +1% well now you're + + + align:start position:0% +1% well now you're +reaching no it's higher than that it's + + align:start position:0% +reaching no it's higher than that it's + + + align:start position:0% +reaching no it's higher than that it's +higher than that + + align:start position:0% +higher than that + + + align:start position:0% +higher than that +almost 7% last year it was three and a + + align:start position:0% +almost 7% last year it was three and a + + + align:start position:0% +almost 7% last year it was three and a +half last year the estimate was three + + align:start position:0% +half last year the estimate was three + + + align:start position:0% +half last year the estimate was three +and a half% the difference is mainly + + align:start position:0% +and a half% the difference is mainly + + + align:start position:0% +and a half% the difference is mainly +environmental retirements and really + + align:start position:0% +environmental retirements and really + + + align:start position:0% +environmental retirements and really +cheap gas so the notion is because of + + align:start position:0% +cheap gas so the notion is because of + + + align:start position:0% +cheap gas so the notion is because of +really cheap gas and tight tighter + + align:start position:0% +really cheap gas and tight tighter + + + align:start position:0% +really cheap gas and tight tighter +environmental policy 7% of capacity will + + align:start position:0% +environmental policy 7% of capacity will + + + align:start position:0% +environmental policy 7% of capacity will +be retired that's not a lot of turnover + + align:start position:0% +be retired that's not a lot of turnover + + + align:start position:0% +be retired that's not a lot of turnover +in 25 + + align:start position:0% +in 25 + + + align:start position:0% +in 25 +years that's not a lot of turnover so + + align:start position:0% +years that's not a lot of turnover so + + + align:start position:0% +years that's not a lot of turnover so +the generating fleet's going to look a + + align:start position:0% +the generating fleet's going to look a + + + align:start position:0% +the generating fleet's going to look a +lot like it does now a lot like it does + + align:start position:0% +lot like it does now a lot like it does + + + align:start position:0% +lot like it does now a lot like it does +now andrew you said this is for a base + + align:start position:0% +now andrew you said this is for a base + + + align:start position:0% +now andrew you said this is for a base +case assumption like that uh yeah so it + + align:start position:0% +case assumption like that uh yeah so it + + + align:start position:0% +case assumption like that uh yeah so it +has no assumption about like + + align:start position:0% +has no assumption about like + + + align:start position:0% +has no assumption about like +environmental regulation or something + + align:start position:0% +environmental regulation or something + + + align:start position:0% +environmental regulation or something +like that or No this is EIA the Energy + + align:start position:0% +like that or No this is EIA the Energy + + + align:start position:0% +like that or No this is EIA the Energy +Information Administration and their + + align:start position:0% +Information Administration and their + + + align:start position:0% +Information Administration and their +base case assumes no change in current + + align:start position:0% +base case assumes no change in current + + + align:start position:0% +base case assumes no change in current +policy + + align:start position:0% +policy + + + align:start position:0% +policy +so one of the things it used to assume + + align:start position:0% +so one of the things it used to assume + + + align:start position:0% +so one of the things it used to assume +in fact it does assume it assumes that + + align:start position:0% +in fact it does assume it assumes that + + + align:start position:0% +in fact it does assume it assumes that +current renewable subsidies which have + + align:start position:0% +current renewable subsidies which have + + + align:start position:0% +current renewable subsidies which have +you know you don't laws don't have + + align:start position:0% +you know you don't laws don't have + + + align:start position:0% +you know you don't laws don't have +infinite lifetimes the law expires at + + align:start position:0% +infinite lifetimes the law expires at + + + align:start position:0% +infinite lifetimes the law expires at +some point it assumes it expires so + + align:start position:0% +some point it assumes it expires so + + + align:start position:0% +some point it assumes it expires so +it'll be a little light on renewables + + align:start position:0% +it'll be a little light on renewables + + + align:start position:0% +it'll be a little light on renewables +they'll run some other cases they're not + + align:start position:0% +they'll run some other cases they're not + + + align:start position:0% +they'll run some other cases they're not +out yet uh you know assuming more + + align:start position:0% +out yet uh you know assuming more + + + align:start position:0% +out yet uh you know assuming more +renewables assuming higher prices and + + align:start position:0% +renewables assuming higher prices and + + + align:start position:0% +renewables assuming higher prices and +lower prices but that's the base case + + align:start position:0% +lower prices but that's the base case + + + align:start position:0% +lower prices but that's the base case +okay so not much turnover the argument + + align:start position:0% +okay so not much turnover the argument + + + align:start position:0% +okay so not much turnover the argument +is that we have made is that uh the grid + + align:start position:0% +is that we have made is that uh the grid + + + align:start position:0% +is that we have made is that uh the grid +does have these challenges and + + align:start position:0% +does have these challenges and + + + align:start position:0% +does have these challenges and +opportunities the turnover is slow uh if + + align:start position:0% +opportunities the turnover is slow uh if + + + align:start position:0% +opportunities the turnover is slow uh if +you want to get anything done in 2035 + + align:start position:0% +you want to get anything done in 2035 + + + align:start position:0% +you want to get anything done in 2035 +you got to start now um a little bit + + align:start position:0% +you got to start now um a little bit + + + align:start position:0% +you got to start now um a little bit +about the smart + + align:start position:0% +about the smart + + + align:start position:0% +about the smart +grid and it's not a term I like because + + align:start position:0% +grid and it's not a term I like because + + + align:start position:0% +grid and it's not a term I like because +it + + align:start position:0% +it + + + align:start position:0% +it +means different things to different + + align:start position:0% +means different things to different + + + align:start position:0% +means different things to different +people and here are four + + align:start position:0% +people and here are four + + + align:start position:0% +people and here are four +examples right this is the National + + align:start position:0% +examples right this is the National + + + align:start position:0% +examples right this is the National +Institute of Standards and Technologies + + align:start position:0% +Institute of Standards and Technologies + + + align:start position:0% +Institute of Standards and Technologies +favorite diagram because and it stresses + + align:start position:0% +favorite diagram because and it stresses + + + align:start position:0% +favorite diagram because and it stresses +that the grid in the future will have + + align:start position:0% +that the grid in the future will have + + + align:start position:0% +that the grid in the future will have +this flow of power of course but lots of + + align:start position:0% +this flow of power of course but lots of + + + align:start position:0% +this flow of power of course but lots of +flows of data and why did they stress + + align:start position:0% +flows of data and why did they stress + + + align:start position:0% +flows of data and why did they stress +that view because they're doing this + + align:start position:0% +that view because they're doing this + + + align:start position:0% +that view because they're doing this +interface + + align:start position:0% +interface + + + align:start position:0% +interface +standards they're doing standard setting + + align:start position:0% +standards they're doing standard setting + + + align:start position:0% +standards they're doing standard setting +for all of those flows that's a big deal + + align:start position:0% +for all of those flows that's a big deal + + + align:start position:0% +for all of those flows that's a big deal +um this is EPRI over here the Electric + + align:start position:0% +um this is EPRI over here the Electric + + + align:start position:0% +um this is EPRI over here the Electric +Power Research Institute uh EPR's view + + align:start position:0% +Power Research Institute uh EPR's view + + + align:start position:0% +Power Research Institute uh EPR's view +of the smart grid has to do with things + + align:start position:0% +of the smart grid has to do with things + + + align:start position:0% +of the smart grid has to do with things +that go that happen around the user so + + align:start position:0% +that go that happen around the user so + + + align:start position:0% +that go that happen around the user so +there's some focus some automation of + + align:start position:0% +there's some focus some automation of + + + align:start position:0% +there's some focus some automation of +the distribution system and plug-in + + align:start position:0% +the distribution system and plug-in + + + align:start position:0% +the distribution system and plug-in +hybrids and smart smart refrigerators + + align:start position:0% +hybrids and smart smart refrigerators + + + align:start position:0% +hybrids and smart smart refrigerators +and rooftop solar they focus on your + + align:start position:0% +and rooftop solar they focus on your + + + align:start position:0% +and rooftop solar they focus on your +house this is somebody in + + align:start position:0% +house this is somebody in + + + align:start position:0% +house this is somebody in +nature and in nature they focus on micro + + align:start position:0% +nature and in nature they focus on micro + + + align:start position:0% +nature and in nature they focus on micro +grids uh or in this picture they focus + + align:start position:0% +grids uh or in this picture they focus + + + align:start position:0% +grids uh or in this picture they focus +on micro grids which we can talk about + + align:start position:0% +on micro grids which we can talk about + + + align:start position:0% +on micro grids which we can talk about +if you want to but is not something that + + align:start position:0% +if you want to but is not something that + + + align:start position:0% +if you want to but is not something that +uh we think is going to be a big deal + + align:start position:0% +uh we think is going to be a big deal + + + align:start position:0% +uh we think is going to be a big deal +and this is the department of energy + + align:start position:0% +and this is the department of energy + + + align:start position:0% +and this is the department of energy +which has it all which has it all so as + + align:start position:0% +which has it all which has it all so as + + + align:start position:0% +which has it all which has it all so as +the title says I + + align:start position:0% +the title says I + + + align:start position:0% +the title says I +guess my view is that smart is a u a + + align:start position:0% +guess my view is that smart is a u a + + + align:start position:0% +guess my view is that smart is a u a +means not an end right you don't care + + align:start position:0% +means not an end right you don't care + + + align:start position:0% +means not an end right you don't care +how smart the grid is what you care is + + align:start position:0% +how smart the grid is what you care is + + + align:start position:0% +how smart the grid is what you care is +what's it what's its performance and + + align:start position:0% +what's it what's its performance and + + + align:start position:0% +what's it what's its performance and +what's its cost it will get smarter but + + align:start position:0% +what's its cost it will get smarter but + + + align:start position:0% +what's its cost it will get smarter but +that's not the objective that's the + + align:start position:0% +that's not the objective that's the + + + align:start position:0% +that's not the objective that's the +that's the means + + align:start position:0% +that's the means + + + align:start position:0% +that's the means +so I went through some of the challenges + + align:start position:0% +so I went through some of the challenges + + + align:start position:0% +so I went through some of the challenges +and constraints we focused on a bunch of + + align:start position:0% +and constraints we focused on a bunch of + + + align:start position:0% +and constraints we focused on a bunch of +policy areas so let me talk first + + align:start position:0% +policy areas so let me talk first + + + align:start position:0% +policy areas so let me talk first +about + + align:start position:0% +about + + + align:start position:0% +about +technology here i immediately get out of + + align:start position:0% +technology here i immediately get out of + + + align:start position:0% +technology here i immediately get out of +my depth but I will do what I can um + + align:start position:0% +my depth but I will do what I can um + + + align:start position:0% +my depth but I will do what I can um +there's really a lot of interesting + + align:start position:0% +there's really a lot of interesting + + + align:start position:0% +there's really a lot of interesting +stuff i'm going to talk about phaser + + align:start position:0% +stuff i'm going to talk about phaser + + + align:start position:0% +stuff i'm going to talk about phaser +measurement units + + align:start position:0% +measurement units + + + align:start position:0% +measurement units +um in in a few minutes flexible AC + + align:start position:0% +um in in a few minutes flexible AC + + + align:start position:0% +um in in a few minutes flexible AC +transmission + + align:start position:0% +transmission + + + align:start position:0% +transmission +systems let you vary the characteristics + + align:start position:0% +systems let you vary the characteristics + + + align:start position:0% +systems let you vary the characteristics +of lines so that you can to some extent + + align:start position:0% +of lines so that you can to some extent + + + align:start position:0% +of lines so that you can to some extent +control + + align:start position:0% +control + + + align:start position:0% +control +flows i told you last time that electric + + align:start position:0% +flows i told you last time that electric + + + align:start position:0% +flows i told you last time that electric +power networks are not really like sort + + align:start position:0% +power networks are not really like sort + + + align:start position:0% +power networks are not really like sort +of old style telephone systems or water + + align:start position:0% +of old style telephone systems or water + + + align:start position:0% +of old style telephone systems or water +systems you don't do valves you can sort + + align:start position:0% +systems you don't do valves you can sort + + + align:start position:0% +systems you don't do valves you can sort +of do valves new sensor technologies let + + align:start position:0% +of do valves new sensor technologies let + + + align:start position:0% +of do valves new sensor technologies let +you know the state of the lines so that + + align:start position:0% +you know the state of the lines so that + + + align:start position:0% +you know the state of the lines so that +on a hot day you'd put less electricity + + align:start position:0% +on a hot day you'd put less electricity + + + align:start position:0% +on a hot day you'd put less electricity +through them because you can see they're + + align:start position:0% +through them because you can see they're + + + align:start position:0% +through them because you can see they're +sagging and there are a bunch of well + + align:start position:0% +sagging and there are a bunch of well + + + align:start position:0% +sagging and there are a bunch of well +that's dynamic line rating systems deal + + align:start position:0% +that's dynamic line rating systems deal + + + align:start position:0% +that's dynamic line rating systems deal +with automating the u uh readings from + + align:start position:0% +with automating the u uh readings from + + + align:start position:0% +with automating the u uh readings from +these sensors energy storage I'll talk + + align:start position:0% +these sensors energy storage I'll talk + + + align:start position:0% +these sensors energy storage I'll talk +about and a bunch of a bunch of uh uh + + align:start position:0% +about and a bunch of a bunch of uh uh + + + align:start position:0% +about and a bunch of a bunch of uh uh +other + + align:start position:0% +other + + + align:start position:0% +other +technologies farther on down toward the + + align:start position:0% +technologies farther on down toward the + + + align:start position:0% +technologies farther on down toward the +customers the low voltage stuff there's + + align:start position:0% +customers the low voltage stuff there's + + + align:start position:0% +customers the low voltage stuff there's +a lot of automation at the substation + + align:start position:0% +a lot of automation at the substation + + + align:start position:0% +a lot of automation at the substation +that's possible quicker detection of + + align:start position:0% +that's possible quicker detection of + + + align:start position:0% +that's possible quicker detection of +outages + + align:start position:0% +outages + + + align:start position:0% +outages +uh optimization of the volt VAR + + align:start position:0% +uh optimization of the volt VAR + + + align:start position:0% +uh optimization of the volt VAR +optimization controls enables you to + + align:start position:0% +optimization controls enables you to + + + align:start position:0% +optimization controls enables you to +control voltage levels particularly on + + align:start position:0% +control voltage levels particularly on + + + align:start position:0% +control voltage levels particularly on +long lines more accurately + + align:start position:0% +long lines more accurately + + + align:start position:0% +long lines more accurately +um conservation voltage reduction lets + + align:start position:0% +um conservation voltage reduction lets + + + align:start position:0% +um conservation voltage reduction lets +you reduce voltage on the whole system + + align:start position:0% +you reduce voltage on the whole system + + + align:start position:0% +you reduce voltage on the whole system +just a little bit to save a lot of + + align:start position:0% +just a little bit to save a lot of + + + align:start position:0% +just a little bit to save a lot of +energy you now there are places where + + align:start position:0% +energy you now there are places where + + + align:start position:0% +energy you now there are places where +the voltage is above the requirement + + align:start position:0% +the voltage is above the requirement + + + align:start position:0% +the voltage is above the requirement +because you can't properly control it so + + align:start position:0% +because you can't properly control it so + + + align:start position:0% +because you can't properly control it so +it ends and you have to keep it above + + align:start position:0% +it ends and you have to keep it above + + + align:start position:0% +it ends and you have to keep it above +you have to keep it within a certain + + align:start position:0% +you have to keep it within a certain + + + align:start position:0% +you have to keep it within a certain +bound everywhere if you can control + + align:start position:0% +bound everywhere if you can control + + + align:start position:0% +bound everywhere if you can control +better you can reduce it everywhere + + align:start position:0% +better you can reduce it everywhere + + + align:start position:0% +better you can reduce it everywhere +automated fault detection is really + + align:start position:0% +automated fault detection is really + + + align:start position:0% +automated fault detection is really +quite um uh quite interesting the + + align:start position:0% +quite um uh quite interesting the + + + align:start position:0% +quite um uh quite interesting the +interesting part is automatic + + align:start position:0% +interesting part is automatic + + + align:start position:0% +interesting part is automatic +restoration advanced metering systems + + align:start position:0% +restoration advanced metering systems + + + align:start position:0% +restoration advanced metering systems +are very important and I will talk about + + align:start position:0% +are very important and I will talk about + + + align:start position:0% +are very important and I will talk about +those and of course this all comes + + align:start position:0% +those and of course this all comes + + + align:start position:0% +those and of course this all comes +together where you control the grid and + + align:start position:0% +together where you control the grid and + + + align:start position:0% +together where you control the grid and +I'm going to talk about particularly + + align:start position:0% +I'm going to talk about particularly + + + align:start position:0% +I'm going to talk about particularly +using these meters in a little while and + + align:start position:0% +using these meters in a little while and + + + align:start position:0% +using these meters in a little while and +right now making the control center work + + align:start position:0% +right now making the control center work + + + align:start position:0% +right now making the control center work +so here's if it works if it + + align:start position:0% +so here's if it works if it + + + align:start position:0% +so here's if it works if it +works my favorite + + align:start position:0% + + + + align:start position:0% + +movie all right + + align:start position:0% + + + + align:start position:0% + +i've played this a million times in a + + align:start position:0% +i've played this a million times in a + + + align:start position:0% +i've played this a million times in a +million places and it's never been this + + align:start position:0% +million places and it's never been this + + + align:start position:0% +million places and it's never been this +bad let me tell you what you would have + + align:start position:0% +bad let me tell you what you would have + + + align:start position:0% +bad let me tell you what you would have +seen if this had worked + + align:start position:0% + + + + align:start position:0% + +um what you would see this is the result + + align:start position:0% +um what you would see this is the result + + + align:start position:0% +um what you would see this is the result +of an outage in southern Florida in + + align:start position:0% +of an outage in southern Florida in + + + align:start position:0% +of an outage in southern Florida in +2008 and what you're seeing those red + + align:start position:0% +2008 and what you're seeing those red + + + align:start position:0% +2008 and what you're seeing those red +dots are phaser measurement units that + + align:start position:0% +dots are phaser measurement units that + + + align:start position:0% +dots are phaser measurement units that +describe this that pick up the state of + + align:start position:0% +describe this that pick up the state of + + + align:start position:0% +describe this that pick up the state of +the system in terms of frequency and + + align:start position:0% +the system in terms of frequency and + + + align:start position:0% +the system in terms of frequency and +phase angle uh of voltage and current + + align:start position:0% +phase angle uh of voltage and current + + + align:start position:0% +phase angle uh of voltage and current +um many times a second + + align:start position:0% +um many times a second + + + align:start position:0% +um many times a second +timestamped so that in principle they + + align:start position:0% +timestamped so that in principle they + + + align:start position:0% +timestamped so that in principle they +give a picture of the state of the whole + + align:start position:0% +give a picture of the state of the whole + + + align:start position:0% +give a picture of the state of the whole +system instant by instant which we do + + align:start position:0% +system instant by instant which we do + + + align:start position:0% +system instant by instant which we do +not now have the red dots are where the + + align:start position:0% +not now have the red dots are where the + + + align:start position:0% +not now have the red dots are where the +measurements are made the spaghetti + + align:start position:0% +measurements are made the spaghetti + + + align:start position:0% +measurements are made the spaghetti +chart on the left is the readings from + + align:start position:0% +chart on the left is the readings from + + + align:start position:0% +chart on the left is the readings from +individual ones and the folks at + + align:start position:0% +individual ones and the folks at + + + align:start position:0% +individual ones and the folks at +Virginia Tech who invented the measuring + + align:start position:0% +Virginia Tech who invented the measuring + + + align:start position:0% +Virginia Tech who invented the measuring +systems + + align:start position:0% +systems + + + align:start position:0% +systems +um have basically interpolated and + + align:start position:0% +um have basically interpolated and + + + align:start position:0% +um have basically interpolated and +extrapolated + + align:start position:0% +extrapolated + + + align:start position:0% +extrapolated +um to to put together a picture of the + + align:start position:0% +um to to put together a picture of the + + + align:start position:0% +um to to put together a picture of the +whole + + align:start position:0% +whole + + + align:start position:0% +whole +system what's interesting here there are + + align:start position:0% +system what's interesting here there are + + + align:start position:0% +system what's interesting here there are +a couple things interesting here + + align:start position:0% +a couple things interesting here + + + align:start position:0% +a couple things interesting here +first of all and I won't hurt your eyes + + align:start position:0% +first of all and I won't hurt your eyes + + + align:start position:0% +first of all and I won't hurt your eyes +by playing it + + align:start position:0% +by playing it + + + align:start position:0% +by playing it +again what's interesting here is one the + + align:start position:0% +again what's interesting here is one the + + + align:start position:0% +again what's interesting here is one the +geographic extent so something happens + + align:start position:0% +geographic extent so something happens + + + align:start position:0% +geographic extent so something happens +in Florida and the frequency is + + align:start position:0% +in Florida and the frequency is + + + align:start position:0% +in Florida and the frequency is +distortion most durably is in northern + + align:start position:0% +distortion most durably is in northern + + + align:start position:0% +distortion most durably is in northern +Minnesota or Canada you may be able to + + align:start position:0% +Minnesota or Canada you may be able to + + + align:start position:0% +Minnesota or Canada you may be able to +see that the second is it happens fast + + align:start position:0% +see that the second is it happens fast + + + align:start position:0% +see that the second is it happens fast +this is 25 seconds so here's where it + + align:start position:0% +this is 25 seconds so here's where it + + + align:start position:0% +this is 25 seconds so here's where it +goes out boom it is happening there are + + align:start position:0% +goes out boom it is happening there are + + + align:start position:0% +goes out boom it is happening there are +things all around the country all around + + align:start position:0% +things all around the country all around + + + align:start position:0% +things all around the country all around +the eastern interconnect and most + + align:start position:0% +the eastern interconnect and most + + + align:start position:0% +the eastern interconnect and most +durably up there in northern + + align:start position:0% +durably up there in northern + + + align:start position:0% +durably up there in northern +Minnesota um so it's fast there's a lot + + align:start position:0% +Minnesota um so it's fast there's a lot + + + align:start position:0% +Minnesota um so it's fast there's a lot +of data um you couldn't react to it as a + + align:start position:0% +of data um you couldn't react to it as a + + + align:start position:0% +of data um you couldn't react to it as a +human yeah sorry what is the red and + + align:start position:0% +human yeah sorry what is the red and + + + align:start position:0% +human yeah sorry what is the red and +blue like different well it's Let me see + + align:start position:0% +blue like different well it's Let me see + + + align:start position:0% +blue like different well it's Let me see +if I can freeze it i can't see the the + + align:start position:0% +if I can freeze it i can't see the the + + + align:start position:0% +if I can freeze it i can't see the the +axis on the right + + align:start position:0% +axis on the right + + + align:start position:0% +axis on the right +it's the extent of the departure let me + + align:start position:0% + + + + align:start position:0% + +just It doesn't want to stop + + align:start position:0% +just It doesn't want to stop + + + align:start position:0% +just It doesn't want to stop +um red red means I think that it's uh uh + + align:start position:0% +um red red means I think that it's uh uh + + + align:start position:0% +um red red means I think that it's uh uh +yeah it means it's faster than 60 cycles + + align:start position:0% +yeah it means it's faster than 60 cycles + + + align:start position:0% +yeah it means it's faster than 60 cycles +a second the frequency locally is is is + + align:start position:0% +a second the frequency locally is is is + + + align:start position:0% +a second the frequency locally is is is +higher uh blue means it's slower so + + align:start position:0% +higher uh blue means it's slower so + + + align:start position:0% +higher uh blue means it's slower so +you're getting a you're getting a a + + align:start position:0% +you're getting a you're getting a a + + + align:start position:0% +you're getting a you're getting a a +pattern a distortion slight distortion + + align:start position:0% +pattern a distortion slight distortion + + + align:start position:0% +pattern a distortion slight distortion +in system frequency now I in this case + + align:start position:0% +in system frequency now I in this case + + + align:start position:0% +in system frequency now I in this case +nothing terrible happened right black + + align:start position:0% +nothing terrible happened right black + + + align:start position:0% +nothing terrible happened right black +blackout happened in Florida boom + + align:start position:0% +blackout happened in Florida boom + + + align:start position:0% +blackout happened in Florida boom +disturbance propagates throughout the + + align:start position:0% +disturbance propagates throughout the + + + align:start position:0% +disturbance propagates throughout the +whole eastern interconnect within a + + align:start position:0% +whole eastern interconnect within a + + + align:start position:0% +whole eastern interconnect within a +matter of seconds + + align:start position:0% +matter of seconds + + + align:start position:0% +matter of seconds +so a nobody could respond to that and + + align:start position:0% +so a nobody could respond to that and + + + align:start position:0% +so a nobody could respond to that and +nobody looking at the the data on the + + align:start position:0% +nobody looking at the the data on the + + + align:start position:0% +nobody looking at the the data on the +graph on the left or the map on the + + align:start position:0% +graph on the left or the map on the + + + align:start position:0% +graph on the left or the map on the +right + + align:start position:0% +right + + + align:start position:0% +right +um + + align:start position:0% +um + + + align:start position:0% +um +uh could sort of think through what to + + align:start position:0% +uh could sort of think through what to + + + align:start position:0% +uh could sort of think through what to +do in time if there were something + + align:start position:0% +do in time if there were something + + + align:start position:0% +do in time if there were something +serious that's just too fast with so + + align:start position:0% +serious that's just too fast with so + + + align:start position:0% +serious that's just too fast with so +much data + + align:start position:0% +much data + + + align:start position:0% +much data +so the great thing about these these + + align:start position:0% +so the great thing about these these + + + align:start position:0% +so the great thing about these these +units is they they give control systems + + align:start position:0% +units is they they give control systems + + + align:start position:0% +units is they they give control systems +control centers a picture of the grid + + align:start position:0% +control centers a picture of the grid + + + align:start position:0% +control centers a picture of the grid +over wide scale that has never existed + + align:start position:0% +over wide scale that has never existed + + + align:start position:0% +over wide scale that has never existed +before in real time lots of data this is + + align:start position:0% +before in real time lots of data this is + + + align:start position:0% +before in real time lots of data this is +just one one aspect of it frequency + + align:start position:0% +just one one aspect of it frequency + + + align:start position:0% +just one one aspect of it frequency +frequency distortion + + align:start position:0% +frequency distortion + + + align:start position:0% +frequency distortion +but nobody knows what to do with it + + align:start position:0% +but nobody knows what to do with it + + + align:start position:0% +but nobody knows what to do with it +there's another picture that isn't a + + align:start position:0% +there's another picture that isn't a + + + align:start position:0% +there's another picture that isn't a +movie which says if you look before the + + align:start position:0% +movie which says if you look before the + + + align:start position:0% +movie which says if you look before the +200 when was the last big blackout + + align:start position:0% +200 when was the last big blackout + + + align:start position:0% +200 when was the last big blackout +2008 you you see um you see a um uh a + + align:start position:0% +2008 you you see um you see a um uh a + + + align:start position:0% +2008 you you see um you see a um uh a +phase angle change near Cleveland over a + + align:start position:0% +phase angle change near Cleveland over a + + + align:start position:0% +phase angle change near Cleveland over a +period of about 30 seconds and then it + + align:start position:0% +period of about 30 seconds and then it + + + align:start position:0% +period of about 30 seconds and then it +breaks + + align:start position:0% +breaks + + + align:start position:0% +breaks +so if you actually knew what that angle + + align:start position:0% +so if you actually knew what that angle + + + align:start position:0% +so if you actually knew what that angle +should be and measured it and had um had + + align:start position:0% +should be and measured it and had um had + + + align:start position:0% +should be and measured it and had um had +a monitoring system you might have been + + align:start position:0% +a monitoring system you might have been + + + align:start position:0% +a monitoring system you might have been +able to tell that the system was about + + align:start position:0% +able to tell that the system was about + + + align:start position:0% +able to tell that the system was about +to + + align:start position:0% +to + + + align:start position:0% +to +break but + + align:start position:0% +break but + + + align:start position:0% +break but +um not everybody that has one of these + + align:start position:0% +um not everybody that has one of these + + + align:start position:0% +um not everybody that has one of these +units actually shares data in real time + + align:start position:0% +units actually shares data in real time + + + align:start position:0% +units actually shares data in real time +we don't have control systems to use the + + align:start position:0% +we don't have control systems to use the + + + align:start position:0% +we don't have control systems to use the +data in real time the federal government + + align:start position:0% +data in real time the federal government + + + align:start position:0% +data in real time the federal government +has subsidized putting these boxes out + + align:start position:0% +has subsidized putting these boxes out + + + align:start position:0% +has subsidized putting these boxes out +there to measure the system but we don't + + align:start position:0% +there to measure the system but we don't + + + align:start position:0% +there to measure the system but we don't +have + + align:start position:0% +have + + + align:start position:0% +have +uh the ability to respond i mean you're + + align:start position:0% +uh the ability to respond i mean you're + + + align:start position:0% +uh the ability to respond i mean you're +sitting there in a control room you see + + align:start position:0% +sitting there in a control room you see + + + align:start position:0% +sitting there in a control room you see +this thing is this a problem is it not a + + align:start position:0% +this thing is this a problem is it not a + + + align:start position:0% +this thing is this a problem is it not a +problem all of a sudden frequencies are + + align:start position:0% +problem all of a sudden frequencies are + + + align:start position:0% +problem all of a sudden frequencies are +changing throughout the Eastern + + align:start position:0% +changing throughout the Eastern + + + align:start position:0% +changing throughout the Eastern +Interconnect do I need to isolate New + + align:start position:0% +Interconnect do I need to isolate New + + + align:start position:0% +Interconnect do I need to isolate New +England to avoid a blackout up here well + + align:start position:0% +England to avoid a blackout up here well + + + align:start position:0% +England to avoid a blackout up here well +the answer it turns out was no + + align:start position:0% +the answer it turns out was no + + + align:start position:0% +the answer it turns out was no +but without a lot of automation you + + align:start position:0% +but without a lot of automation you + + + align:start position:0% +but without a lot of automation you +wouldn't be and a good model of the + + align:start position:0% +wouldn't be and a good model of the + + + align:start position:0% +wouldn't be and a good model of the +system you wouldn't be able to know that + + align:start position:0% +system you wouldn't be able to know that + + + align:start position:0% +system you wouldn't be able to know that +um so + + align:start position:0% + + + + align:start position:0% + +uh moving right + + align:start position:0% + + + + align:start position:0% + +along so you see you see the issue + + align:start position:0% +along so you see you see the issue + + + align:start position:0% +along so you see you see the issue +that we've got this incredible source of + + align:start position:0% +that we've got this incredible source of + + + align:start position:0% +that we've got this incredible source of +real time data with no ability to use it + + align:start position:0% +real time data with no ability to use it + + + align:start position:0% +real time data with no ability to use it +and not much sharing and your tax + + align:start position:0% +and not much sharing and your tax + + + align:start position:0% +and not much sharing and your tax +dollars have produced it it's terrific + + align:start position:0% +dollars have produced it it's terrific + + + align:start position:0% +dollars have produced it it's terrific +but um we don't know how to use it + + align:start position:0% +but um we don't know how to use it + + + align:start position:0% +but um we don't know how to use it +i mentioned these devices that control + + align:start position:0% +i mentioned these devices that control + + + align:start position:0% +i mentioned these devices that control +control the transmission system and + + align:start position:0% +control the transmission system and + + + align:start position:0% +control the transmission system and +enhance capacity they're + + align:start position:0% +enhance capacity they're + + + align:start position:0% +enhance capacity they're +expensive the ideal way to use them + + align:start position:0% +expensive the ideal way to use them + + + align:start position:0% +expensive the ideal way to use them +would be to use this data from phaser + + align:start position:0% +would be to use this data from phaser + + + align:start position:0% +would be to use this data from phaser +measurement units through an automated + + align:start position:0% +measurement units through an automated + + + align:start position:0% +measurement units through an automated +control system to modify line + + align:start position:0% +control system to modify line + + + align:start position:0% +control system to modify line +characteristics we've got we've got the + + align:start position:0% +characteristics we've got we've got the + + + align:start position:0% +characteristics we've got we've got the +fax devices we've got the phaser + + align:start position:0% +fax devices we've got the phaser + + + align:start position:0% +fax devices we've got the phaser +measurement units we do not have any + + align:start position:0% +measurement units we do not have any + + + align:start position:0% +measurement units we do not have any +system to link them + + align:start position:0% +system to link them + + + align:start position:0% +system to link them +so we think that's sort of a a useful + + align:start position:0% +so we think that's sort of a a useful + + + align:start position:0% +so we think that's sort of a a useful +useful thing to do since the boxes are + + align:start position:0% +useful thing to do since the boxes are + + + align:start position:0% +useful thing to do since the boxes are +out there it's also the case that there + + align:start position:0% +out there it's also the case that there + + + align:start position:0% +out there it's also the case that there +are a lot of so-called smart grid uh + + align:start position:0% +are a lot of so-called smart grid uh + + + align:start position:0% +are a lot of so-called smart grid uh +technologies going in at the + + align:start position:0% +technologies going in at the + + + align:start position:0% +technologies going in at the +distribution level your tax dollars or + + align:start position:0% +distribution level your tax dollars or + + + align:start position:0% +distribution level your tax dollars or +rather the deficits you will fund uh + + align:start position:0% +rather the deficits you will fund uh + + + align:start position:0% +rather the deficits you will fund uh +later on uh have funded putting out a + + align:start position:0% +later on uh have funded putting out a + + + align:start position:0% +later on uh have funded putting out a +lot of very smart boxes in distribution + + align:start position:0% +lot of very smart boxes in distribution + + + align:start position:0% +lot of very smart boxes in distribution +systems but what they do hasn't yet been + + align:start position:0% +systems but what they do hasn't yet been + + + align:start position:0% +systems but what they do hasn't yet been +published so it's a little unclear arra + + align:start position:0% +published so it's a little unclear arra + + + align:start position:0% +published so it's a little unclear arra +is the stimulus stimulus + + align:start position:0% +is the stimulus stimulus + + + align:start position:0% +is the stimulus stimulus +legislation so we need more + + align:start position:0% +legislation so we need more + + + align:start position:0% +legislation so we need more +R&D it's pretty cheap + + align:start position:0% +R&D it's pretty cheap + + + align:start position:0% +R&D it's pretty cheap +R&D we need computational tools to use + + align:start position:0% +R&D we need computational tools to use + + + align:start position:0% +R&D we need computational tools to use +these these uh uh all this data should + + align:start position:0% +these these uh uh all this data should + + + align:start position:0% +these these uh uh all this data should +have impressed you with how closely + + align:start position:0% +have impressed you with how closely + + + align:start position:0% +have impressed you with how closely +coupled that whole eastern interconnect + + align:start position:0% +coupled that whole eastern interconnect + + + align:start position:0% +coupled that whole eastern interconnect +is that from Florida to Minnesota very + + align:start position:0% +is that from Florida to Minnesota very + + + align:start position:0% +is that from Florida to Minnesota very +quickly a disturbance propagates that + + align:start position:0% +quickly a disturbance propagates that + + + align:start position:0% +quickly a disturbance propagates that +means if you think about it um + + align:start position:0% +means if you think about it um + + + align:start position:0% +means if you think about it um +particularly if you think about + + align:start position:0% +particularly if you think about + + + align:start position:0% +particularly if you think about +renewables which I'll come to in a + + align:start position:0% +renewables which I'll come to in a + + + align:start position:0% +renewables which I'll come to in a +second you need to be able to plan at + + align:start position:0% +second you need to be able to plan at + + + align:start position:0% +second you need to be able to plan at +the level of at that level at the level + + align:start position:0% +the level of at that level at the level + + + align:start position:0% +the level of at that level at the level +of the eastern system the western system + + align:start position:0% +of the eastern system the western system + + + align:start position:0% +of the eastern system the western system +is simpler texas is simpler the eastern + + align:start position:0% +is simpler texas is simpler the eastern + + + align:start position:0% +is simpler texas is simpler the eastern +system is the big one we can't begin to + + align:start position:0% +system is the big one we can't begin to + + + align:start position:0% +system is the big one we can't begin to +plan + + align:start position:0% +plan + + + align:start position:0% +plan +that it's the dimensionality is too high + + align:start position:0% +that it's the dimensionality is too high + + + align:start position:0% +that it's the dimensionality is too high +for current techniques um and just to + + align:start position:0% +for current techniques um and just to + + + align:start position:0% +for current techniques um and just to +get to things I will come to in a little + + align:start position:0% +get to things I will come to in a little + + + align:start position:0% +get to things I will come to in a little +while + + align:start position:0% +while + + + align:start position:0% +while +um there's a lot of focus on preventing + + align:start position:0% +um there's a lot of focus on preventing + + + align:start position:0% +um there's a lot of focus on preventing +cyber attacks there's very little effort + + align:start position:0% +cyber attacks there's very little effort + + + align:start position:0% +cyber attacks there's very little effort +on what do you do when you get when one + + align:start position:0% +on what do you do when you get when one + + + align:start position:0% +on what do you do when you get when one +succeeds but one will + + align:start position:0% +succeeds but one will + + + align:start position:0% +succeeds but one will +succeed and um we need to understand + + align:start position:0% +succeed and um we need to understand + + + align:start position:0% +succeed and um we need to understand +more about uh + + align:start position:0% +more about uh + + + align:start position:0% +more about uh +automated uh about uh dynamic pricing + + align:start position:0% +automated uh about uh dynamic pricing + + + align:start position:0% +automated uh about uh dynamic pricing +i'll come to + + align:start position:0% +i'll come to + + + align:start position:0% +i'll come to +it this is a troublesome thing + + align:start position:0% +it this is a troublesome thing + + + align:start position:0% +it this is a troublesome thing +there are technologies that have been + + align:start position:0% +there are technologies that have been + + + align:start position:0% +there are technologies that have been +standard in Scandinavia for 20 years + + align:start position:0% +standard in Scandinavia for 20 years + + + align:start position:0% +standard in Scandinavia for 20 years +that are required in India that can't be + + align:start position:0% +that are required in India that can't be + + + align:start position:0% +that are required in India that can't be +sold in this country because no utility + + align:start position:0% +sold in this country because no utility + + + align:start position:0% +sold in this country because no utility +is ever seen it + + align:start position:0% +is ever seen it + + + align:start position:0% +is ever seen it +work the level of risk aversion is kind + + align:start position:0% +work the level of risk aversion is kind + + + align:start position:0% +work the level of risk aversion is kind +of breathtaking and it's like why don't + + align:start position:0% +of breathtaking and it's like why don't + + + align:start position:0% +of breathtaking and it's like why don't +we measure things because if we put it + + align:start position:0% +we measure things because if we put it + + + align:start position:0% +we measure things because if we put it +in and it's new and it doesn't work the + + align:start position:0% +in and it's new and it doesn't work the + + + align:start position:0% +in and it's new and it doesn't work the +utility gets hammered the utility + + align:start position:0% +utility gets hammered the utility + + + align:start position:0% +utility gets hammered the utility +management get gets hammered the + + align:start position:0% +management get gets hammered the + + + align:start position:0% +management get gets hammered the +stockholders get punished and the + + align:start position:0% +stockholders get punished and the + + + align:start position:0% +stockholders get punished and the +regulator gets punished if you put it in + + align:start position:0% +regulator gets punished if you put it in + + + align:start position:0% +regulator gets punished if you put it in +and it works everybody yawns so this the + + align:start position:0% +and it works everybody yawns so this the + + + align:start position:0% +and it works everybody yawns so this the +regulatory system here in particular is + + align:start position:0% +regulatory system here in particular is + + + align:start position:0% +regulatory system here in particular is +biased against innovation in a way + + align:start position:0% +biased against innovation in a way + + + align:start position:0% +biased against innovation in a way +that's um hard to fix because it's + + align:start position:0% +that's um hard to fix because it's + + + align:start position:0% +that's um hard to fix because it's +political it's not technical it's + + align:start position:0% +political it's not technical it's + + + align:start position:0% +political it's not technical it's +political okay what about + + align:start position:0% +political okay what about + + + align:start position:0% +political okay what about +renewables well there's going to be more + + align:start position:0% +renewables well there's going to be more + + + align:start position:0% +renewables well there's going to be more +wind and solar this is renewable + + align:start position:0% +wind and solar this is renewable + + + align:start position:0% +wind and solar this is renewable +generation in the US up to 2007 + + align:start position:0% +generation in the US up to 2007 + + + align:start position:0% +generation in the US up to 2007 +you'll see the the big story is the big + + align:start position:0% +you'll see the the big story is the big + + + align:start position:0% +you'll see the the big story is the big +growth story is wind uh wood is very + + align:start position:0% +growth story is wind uh wood is very + + + align:start position:0% +growth story is wind uh wood is very +important a lot of that is waste from uh + + align:start position:0% +important a lot of that is waste from uh + + + align:start position:0% +important a lot of that is waste from uh +lumber mills that they just use it to + + align:start position:0% +lumber mills that they just use it to + + + align:start position:0% +lumber mills that they just use it to +generate power some of them sell to the + + align:start position:0% +generate power some of them sell to the + + + align:start position:0% +generate power some of them sell to the +grid some of them + + align:start position:0% +grid some of them + + + align:start position:0% +grid some of them +don't maine a few years ago passed a + + align:start position:0% +don't maine a few years ago passed a + + + align:start position:0% +don't maine a few years ago passed a +requirement for renewable generation did + + align:start position:0% +requirement for renewable generation did + + + align:start position:0% +requirement for renewable generation did +the numbers realize they had already met + + align:start position:0% +the numbers realize they had already met + + + align:start position:0% +the numbers realize they had already met +the requirement because of all the + + align:start position:0% +the requirement because of all the + + + align:start position:0% +the requirement because of all the +lumber mills um you'll see solar here uh + + align:start position:0% +lumber mills um you'll see solar here uh + + + align:start position:0% +lumber mills um you'll see solar here uh +solar's in the data but it's too small + + align:start position:0% +solar's in the data but it's too small + + + align:start position:0% +solar's in the data but it's too small +to see in the picture so um since 2007 + + align:start position:0% +to see in the picture so um since 2007 + + + align:start position:0% +to see in the picture so um since 2007 +you see this peaks at about what do you + + align:start position:0% +you see this peaks at about what do you + + + align:start position:0% +you see this peaks at about what do you +figure 100,000 it's 173,000 in + + align:start position:0% +figure 100,000 it's 173,000 in + + + align:start position:0% +figure 100,000 it's 173,000 in +2010 over half of that was wind so you + + align:start position:0% +2010 over half of that was wind so you + + + align:start position:0% +2010 over half of that was wind so you +see the wind wind has continued to drive + + align:start position:0% +see the wind wind has continued to drive + + + align:start position:0% +see the wind wind has continued to drive +the growth through 2010 so that's + + align:start position:0% +the growth through 2010 so that's + + + align:start position:0% +the growth through 2010 so that's +renewables in the US there are a lot of + + align:start position:0% +renewables in the US there are a lot of + + + align:start position:0% +renewables in the US there are a lot of +policies oh that's + + align:start position:0% +policies oh that's + + + align:start position:0% +policies oh that's +Europe um this is putting aside hydro um + + align:start position:0% +Europe um this is putting aside hydro um + + + align:start position:0% +Europe um this is putting aside hydro um +we were way ahead of Europe around 1990 + + align:start position:0% +we were way ahead of Europe around 1990 + + + align:start position:0% +we were way ahead of Europe around 1990 +we've stayed pretty constant as a + + align:start position:0% +we've stayed pretty constant as a + + + align:start position:0% +we've stayed pretty constant as a +percentage of total generation europe is + + align:start position:0% +percentage of total generation europe is + + + align:start position:0% +percentage of total generation europe is +shot up and the European goal the EU + + align:start position:0% +shot up and the European goal the EU + + + align:start position:0% +shot up and the European goal the EU +goal is well 20% of all energy from + + align:start position:0% +goal is well 20% of all energy from + + + align:start position:0% +goal is well 20% of all energy from +renewables so 35% of electricity from + + align:start position:0% +renewables so 35% of electricity from + + + align:start position:0% +renewables so 35% of electricity from +renewables by + + align:start position:0% +renewables by + + + align:start position:0% +renewables by +2020 very very ambitious + + align:start position:0% +2020 very very ambitious + + + align:start position:0% +2020 very very ambitious +um there's well you see Maine this is + + align:start position:0% +um there's well you see Maine this is + + + align:start position:0% +um there's well you see Maine this is +2007 non-hydro renewable generation as a + + align:start position:0% +2007 non-hydro renewable generation as a + + + align:start position:0% +2007 non-hydro renewable generation as a +percentage of the state total maine + + align:start position:0% +percentage of the state total maine + + + align:start position:0% +percentage of the state total maine +leads because of all the wood uh + + align:start position:0% +leads because of all the wood uh + + + align:start position:0% +leads because of all the wood uh +California pretty high mostly geothermal + + align:start position:0% +California pretty high mostly geothermal + + + align:start position:0% +California pretty high mostly geothermal +but wind and solar coming and + + align:start position:0% +but wind and solar coming and + + + align:start position:0% +but wind and solar coming and +Texas just an absolute generation uh + + align:start position:0% +Texas just an absolute generation uh + + + align:start position:0% +Texas just an absolute generation uh +with a lot of wind a lot of wind the um + + align:start position:0% +with a lot of wind a lot of wind the um + + + align:start position:0% +with a lot of wind a lot of wind the um +this is a policy + + align:start position:0% +this is a policy + + + align:start position:0% +this is a policy +map it shows you the 29 states and the + + align:start position:0% +map it shows you the 29 states and the + + + align:start position:0% +map it shows you the 29 states and the +District of Columbombia have renewable + + align:start position:0% +District of Columbombia have renewable + + + align:start position:0% +District of Columbombia have renewable +portfolio + + align:start position:0% +portfolio + + + align:start position:0% +portfolio +standards those are state laws that + + align:start position:0% +standards those are state laws that + + + align:start position:0% +standards those are state laws that +require generally that require if you + + align:start position:0% +require generally that require if you + + + align:start position:0% +require generally that require if you +sell electricity at retail X% of that + + align:start position:0% +sell electricity at retail X% of that + + + align:start position:0% +sell electricity at retail X% of that +has to be + + align:start position:0% +has to be + + + align:start position:0% +has to be +renewable usually much more detail you + + align:start position:0% +renewable usually much more detail you + + + align:start position:0% +renewable usually much more detail you +know um New Jersey has a requirement for + + align:start position:0% +know um New Jersey has a requirement for + + + align:start position:0% +know um New Jersey has a requirement for +offshore instate wind north Carolina has + + align:start position:0% +offshore instate wind north Carolina has + + + align:start position:0% +offshore instate wind north Carolina has +a requirement for electricity produced + + align:start position:0% +a requirement for electricity produced + + + align:start position:0% +a requirement for electricity produced +from um I think it's poultry waste maybe + + align:start position:0% +from um I think it's poultry waste maybe + + + align:start position:0% +from um I think it's poultry waste maybe +a separate one for swine waste um + + align:start position:0% +a separate one for swine waste um + + + align:start position:0% +a separate one for swine waste um +uh and they all vary rhode Island has + + align:start position:0% +uh and they all vary rhode Island has + + + align:start position:0% +uh and they all vary rhode Island has +three different levels of + + align:start position:0% +three different levels of + + + align:start position:0% +three different levels of +requirement so there's a lot of + + align:start position:0% +requirement so there's a lot of + + + align:start position:0% +requirement so there's a lot of +push for u renewables they're called + + align:start position:0% +push for u renewables they're called + + + align:start position:0% +push for u renewables they're called +renewable portfolio standards because + + align:start position:0% +renewable portfolio standards because + + + align:start position:0% +renewable portfolio standards because +the notion is in your portfolio of + + align:start position:0% +the notion is in your portfolio of + + + align:start position:0% +the notion is in your portfolio of +generation so much of it has to be + + align:start position:0% +generation so much of it has to be + + + align:start position:0% +generation so much of it has to be +renewable um and we can talk about how + + align:start position:0% +renewable um and we can talk about how + + + align:start position:0% +renewable um and we can talk about how +these work but well they're they're all + + align:start position:0% +these work but well they're they're all + + + align:start position:0% +these work but well they're they're all +different but um you don't + + align:start position:0% +different but um you don't + + + align:start position:0% +different but um you don't +necessarily have to be physically + + align:start position:0% +necessarily have to be physically + + + align:start position:0% +necessarily have to be physically +connected to a renewable generator but + + align:start position:0% +connected to a renewable generator but + + + align:start position:0% +connected to a renewable generator but +you have to make a purchase that amounts + + align:start position:0% +you have to make a purchase that amounts + + + align:start position:0% +you have to make a purchase that amounts +to encouraging that much + + align:start position:0% +to encouraging that much + + + align:start position:0% +to encouraging that much +generation + + align:start position:0% +generation + + + align:start position:0% +generation +um okay i I I used to be able to say + + align:start position:0% +um okay i I I used to be able to say + + + align:start position:0% +um okay i I I used to be able to say +that every state but Arkansas subsidized + + align:start position:0% +that every state but Arkansas subsidized + + + align:start position:0% +that every state but Arkansas subsidized +renewables but Arkansas put in a subsidy + + align:start position:0% +renewables but Arkansas put in a subsidy + + + align:start position:0% +renewables but Arkansas put in a subsidy +in 2010 so every state subsidizes + + align:start position:0% +in 2010 so every state subsidizes + + + align:start position:0% +in 2010 so every state subsidizes +renewables now + + align:start position:0% +renewables now + + + align:start position:0% +renewables now +um now here's issue one issue one is + + align:start position:0% +um now here's issue one issue one is + + + align:start position:0% +um now here's issue one issue one is +here's where the wind is there's a lot + + align:start position:0% +here's where the wind is there's a lot + + + align:start position:0% +here's where the wind is there's a lot +of good wind offshore and in the Great + + align:start position:0% +of good wind offshore and in the Great + + + align:start position:0% +of good wind offshore and in the Great +Lakes + + align:start position:0% +Lakes + + + align:start position:0% +Lakes +but offshore is expensive + + align:start position:0% +but offshore is expensive + + + align:start position:0% +but offshore is expensive +the good onshore wind tends to be in the + + align:start position:0% +the good onshore wind tends to be in the + + + align:start position:0% +the good onshore wind tends to be in the +middle of the + + align:start position:0% +middle of the + + + align:start position:0% +middle of the +country people tend not to be in the + + align:start position:0% +country people tend not to be in the + + + align:start position:0% +country people tend not to be in the +middle of the + + align:start position:0% +middle of the + + + align:start position:0% +middle of the +country so if you're going to use that + + align:start position:0% +country so if you're going to use that + + + align:start position:0% +country so if you're going to use that +you're going to have to build + + align:start position:0% +you're going to have to build + + + align:start position:0% +you're going to have to build +transmission and that transmission is + + align:start position:0% +transmission and that transmission is + + + align:start position:0% +transmission and that transmission is +going to have to cross state + + align:start position:0% +going to have to cross state + + + align:start position:0% +going to have to cross state +lines right i mean there's a lot of wind + + align:start position:0% +lines right i mean there's a lot of wind + + + align:start position:0% +lines right i mean there's a lot of wind +in North Dakota there are not a lot of + + align:start position:0% +in North Dakota there are not a lot of + + + align:start position:0% +in North Dakota there are not a lot of +people in North Dakota despite the shale + + align:start position:0% +people in North Dakota despite the shale + + + align:start position:0% +people in North Dakota despite the shale +boom uh if you're going to use that wind + + align:start position:0% +boom uh if you're going to use that wind + + + align:start position:0% +boom uh if you're going to use that wind +you're probably going to have to go from + + align:start position:0% +you're probably going to have to go from + + + align:start position:0% +you're probably going to have to go from +North Dakota or at least to Minneapolis + + align:start position:0% +North Dakota or at least to Minneapolis + + + align:start position:0% +North Dakota or at least to Minneapolis +and maybe down to Chicago uh which is a + + align:start position:0% +and maybe down to Chicago uh which is a + + + align:start position:0% +and maybe down to Chicago uh which is a +problem even in New England this is an + + align:start position:0% +problem even in New England this is an + + + align:start position:0% +problem even in New England this is an +impossible map but it shows you where + + align:start position:0% +impossible map but it shows you where + + + align:start position:0% +impossible map but it shows you where +the wind is in New England up here + + align:start position:0% +the wind is in New England up here + + + align:start position:0% +the wind is in New England up here +that's offshore this is where the load + + align:start position:0% +that's offshore this is where the load + + + align:start position:0% +that's offshore this is where the load +is in um Massachusetts and and Rhode + + align:start position:0% +is in um Massachusetts and and Rhode + + + align:start position:0% +is in um Massachusetts and and Rhode +Island and Connecticut uh to get wind + + align:start position:0% +Island and Connecticut uh to get wind + + + align:start position:0% +Island and Connecticut uh to get wind +from northern Maine down here you've got + + align:start position:0% +from northern Maine down here you've got + + + align:start position:0% +from northern Maine down here you've got +to cross state + + align:start position:0% +to cross state + + + align:start position:0% +to cross state +lines + + align:start position:0% +lines + + + align:start position:0% +lines +the problem is states approve power + + align:start position:0% +the problem is states approve power + + + align:start position:0% +the problem is states approve power +lines and states can block power lines + + align:start position:0% +lines and states can block power lines + + + align:start position:0% +lines and states can block power lines +so my favorite is there was a proposal + + align:start position:0% +so my favorite is there was a proposal + + + align:start position:0% +so my favorite is there was a proposal +from uh Southern California Edison to + + align:start position:0% +from uh Southern California Edison to + + + align:start position:0% +from uh Southern California Edison to +build a line into Arizona to connect to + + align:start position:0% +build a line into Arizona to connect to + + + align:start position:0% +build a line into Arizona to connect to +some cheap generation and take the power + + align:start position:0% +some cheap generation and take the power + + + align:start position:0% +some cheap generation and take the power +to Los Angeles and the Arizona + + align:start position:0% +to Los Angeles and the Arizona + + + align:start position:0% +to Los Angeles and the Arizona +Commission vetoed + + align:start position:0% +Commission vetoed + + + align:start position:0% +Commission vetoed +it and one commissioner said "That's a + + align:start position:0% +it and one commissioner said "That's a + + + align:start position:0% +it and one commissioner said "That's a +230,000 230 mile straw sucking energy + + align:start position:0% +230,000 230 mile straw sucking energy + + + align:start position:0% +230,000 230 mile straw sucking energy +out of Arizona we won't do + + align:start position:0% +out of Arizona we won't do + + + align:start position:0% +out of Arizona we won't do +it." Okay each state can block it if it + + align:start position:0% +it." Okay each state can block it if it + + + align:start position:0% +it." Okay each state can block it if it +crosses federally owned land which is I + + align:start position:0% +crosses federally owned land which is I + + + align:start position:0% +crosses federally owned land which is I +think a third of the land in the country + + align:start position:0% +think a third of the land in the country + + + align:start position:0% +think a third of the land in the country +the federal agency can block it nobody + + align:start position:0% +the federal agency can block it nobody + + + align:start position:0% +the federal agency can block it nobody +can say + + align:start position:0% +can say + + + align:start position:0% +can say +yes we can build gas pipelines because + + align:start position:0% +yes we can build gas pipelines because + + + align:start position:0% +yes we can build gas pipelines because +those are federally federally done um uh + + align:start position:0% +those are federally federally done um uh + + + align:start position:0% +those are federally federally done um uh +the FK approves gas pipelines there is + + align:start position:0% +the FK approves gas pipelines there is + + + align:start position:0% +the FK approves gas pipelines there is +no such approval for power lines well if + + align:start position:0% +no such approval for power lines well if + + + align:start position:0% +no such approval for power lines well if +you're going to do renewables there has + + align:start position:0% +you're going to do renewables there has + + + align:start position:0% +you're going to do renewables there has +to + + align:start position:0% +to + + + align:start position:0% +to +be so one of our recommendations is to + + align:start position:0% +be so one of our recommendations is to + + + align:start position:0% +be so one of our recommendations is to +change that + + align:start position:0% +change that + + + align:start position:0% +change that +law um this is not necessarily popular + + align:start position:0% +law um this is not necessarily popular + + + align:start position:0% +law um this is not necessarily popular +at the state + + align:start position:0% +at the state + + + align:start position:0% +at the state +level because as I said there's a lot of + + align:start position:0% +level because as I said there's a lot of + + + align:start position:0% +level because as I said there's a lot of +holding of power by the states but if + + align:start position:0% +holding of power by the states but if + + + align:start position:0% +holding of power by the states but if +you want to build renew you want to use + + align:start position:0% +you want to build renew you want to use + + + align:start position:0% +you want to build renew you want to use +renewables that come + + align:start position:0% +renewables that come + + + align:start position:0% +renewables that come +from remote + + align:start position:0% +from remote + + + align:start position:0% +from remote +areas you + + align:start position:0% + + + + align:start position:0% + +u need to have somebody who can say + + align:start position:0% +u need to have somebody who can say + + + align:start position:0% +u need to have somebody who can say +yes okay so far questions on any of + + align:start position:0% +yes okay so far questions on any of + + + align:start position:0% +yes okay so far questions on any of +this okay that's one issue with + + align:start position:0% +this okay that's one issue with + + + align:start position:0% +this okay that's one issue with +renewables the other issue with + + align:start position:0% +renewables the other issue with + + + align:start position:0% +renewables the other issue with +renewables + + align:start position:0% +renewables + + + align:start position:0% +renewables +is the fact that you can't dispatch them + + align:start position:0% +is the fact that you can't dispatch them + + + align:start position:0% +is the fact that you can't dispatch them +you can't control them this is + + align:start position:0% +you can't control them this is + + + align:start position:0% +you can't control them this is +um that's the output from a photovoltaic + + align:start position:0% +um that's the output from a photovoltaic + + + align:start position:0% +um that's the output from a photovoltaic +plant solar cells on a partly cloudy day + + align:start position:0% +plant solar cells on a partly cloudy day + + + align:start position:0% +plant solar cells on a partly cloudy day +the output can change very rapidly in a + + align:start position:0% +the output can change very rapidly in a + + + align:start position:0% +the output can change very rapidly in a +matter of seconds there is no inertia in + + align:start position:0% +matter of seconds there is no inertia in + + + align:start position:0% +matter of seconds there is no inertia in +the + + align:start position:0% +the + + + align:start position:0% +the +system no inertia in the system now if + + align:start position:0% +system no inertia in the system now if + + + align:start position:0% +system no inertia in the system now if +you have a bunch of them spread out + + align:start position:0% +you have a bunch of them spread out + + + align:start position:0% +you have a bunch of them spread out +geographically this problem is reduced + + align:start position:0% +geographically this problem is reduced + + + align:start position:0% +geographically this problem is reduced +but it's not eliminated right because + + align:start position:0% +but it's not eliminated right because + + + align:start position:0% +but it's not eliminated right because +sometimes a whole state will be + + align:start position:0% +sometimes a whole state will be + + + align:start position:0% +sometimes a whole state will be +cloudy so that's a that's a that's a + + align:start position:0% +cloudy so that's a that's a that's a + + + align:start position:0% +cloudy so that's a that's a that's a +real issue and and the no inertia means + + align:start position:0% +real issue and and the no inertia means + + + align:start position:0% +real issue and and the no inertia means +if you think about + + align:start position:0% + + + + align:start position:0% + +the way power systems currently operate + + align:start position:0% +the way power systems currently operate + + + align:start position:0% +the way power systems currently operate +there's a lot of rotating metal in these + + align:start position:0% +there's a lot of rotating metal in these + + + align:start position:0% +there's a lot of rotating metal in these +in generators and turbines and such but + + align:start position:0% +in generators and turbines and such but + + + align:start position:0% +in generators and turbines and such but +particularly in generators so if all of + + align:start position:0% +particularly in generators so if all of + + + align:start position:0% +particularly in generators so if all of +a sudden 5,000 people turn on the lights + + align:start position:0% +a sudden 5,000 people turn on the lights + + + align:start position:0% +a sudden 5,000 people turn on the lights +that's a big increase in load but the + + align:start position:0% +that's a big increase in load but the + + + align:start position:0% +that's a big increase in load but the +system has what you call ride through + + align:start position:0% +system has what you call ride through + + + align:start position:0% +system has what you call ride through +capability you know you've got all this + + align:start position:0% +capability you know you've got all this + + + align:start position:0% +capability you know you've got all this +inertia going through going in the + + align:start position:0% +inertia going through going in the + + + align:start position:0% +inertia going through going in the +generators it just carries carries you + + align:start position:0% +generators it just carries carries you + + + align:start position:0% +generators it just carries carries you +through bumps well there's no inertia + + align:start position:0% +through bumps well there's no inertia + + + align:start position:0% +through bumps well there's no inertia +here there's nothing carrying you + + align:start position:0% +here there's nothing carrying you + + + align:start position:0% +here there's nothing carrying you +through bumps and there's no real + + align:start position:0% +through bumps and there's no real + + + align:start position:0% +through bumps and there's no real +inertia in wind + + align:start position:0% +inertia in wind + + + align:start position:0% +inertia in wind +turbines not a serious problem at all + + align:start position:0% +turbines not a serious problem at all + + + align:start position:0% +turbines not a serious problem at all +yet but as you look down the road to a + + align:start position:0% +yet but as you look down the road to a + + + align:start position:0% +yet but as you look down the road to a +lot of it potentially it is + + align:start position:0% +lot of it potentially it is + + + align:start position:0% +lot of it potentially it is +wind this is total output of wind in + + align:start position:0% +wind this is total output of wind in + + + align:start position:0% +wind this is total output of wind in +California the the top line and the + + align:start position:0% +California the the top line and the + + + align:start position:0% +California the the top line and the +bottom line are individual + + align:start position:0% +bottom line are individual + + + align:start position:0% +bottom line are individual +facilities a and the the axis these + + align:start position:0% +facilities a and the the axis these + + + align:start position:0% +facilities a and the the axis these +are well this is a whole day right so + + align:start position:0% +are well this is a whole day right so + + + align:start position:0% +are well this is a whole day right so +it's 10 seconds 10 seconds sampling + + align:start position:0% +it's 10 seconds 10 seconds sampling + + + align:start position:0% +it's 10 seconds 10 seconds sampling +these are hours and this is sort of + + align:start position:0% +these are hours and this is sort of + + + align:start position:0% +these are hours and this is sort of +characteristic of wind wind ramps not + + align:start position:0% +characteristic of wind wind ramps not + + + align:start position:0% +characteristic of wind wind ramps not +minutes or seconds really but with + + align:start position:0% +minutes or seconds really but with + + + align:start position:0% +minutes or seconds really but with +except for maybe some individual + + align:start position:0% +except for maybe some individual + + + align:start position:0% +except for maybe some individual +windmill it gets a gust but over any + + align:start position:0% +windmill it gets a gust but over any + + + align:start position:0% +windmill it gets a gust but over any +reasonable area it can ramp in the + + align:start position:0% +reasonable area it can ramp in the + + + align:start position:0% +reasonable area it can ramp in the +course of hours from nothing to a lot or + + align:start position:0% +course of hours from nothing to a lot or + + + align:start position:0% +course of hours from nothing to a lot or +from a lot to nothing both of those are + + align:start position:0% +from a lot to nothing both of those are + + + align:start position:0% +from a lot to nothing both of those are +problems + + align:start position:0% +problems + + + align:start position:0% +problems +this is the most discouraging graph I've + + align:start position:0% +this is the most discouraging graph I've + + + align:start position:0% +this is the most discouraging graph I've +seen on + + align:start position:0% +seen on + + + align:start position:0% +seen on +wind this is um a week in July 2006 when + + align:start position:0% +wind this is um a week in July 2006 when + + + align:start position:0% +wind this is um a week in July 2006 when +it was very hot in California and the + + align:start position:0% +it was very hot in California and the + + + align:start position:0% +it was very hot in California and the +green is wind generation so you'll + + align:start position:0% +green is wind generation so you'll + + + align:start position:0% +green is wind generation so you'll +notice that + + align:start position:0% +notice that + + + align:start position:0% +notice that +uh has wind capacity of 2600 megawws + + align:start position:0% +uh has wind capacity of 2600 megawws + + + align:start position:0% +uh has wind capacity of 2600 megawws +that week it ne wind never produced more + + align:start position:0% +that week it ne wind never produced more + + + align:start position:0% +that week it ne wind never produced more +than a + + align:start position:0% +than a + + + align:start position:0% +than a +thousand but and it varies over the + + align:start position:0% +thousand but and it varies over the + + + align:start position:0% +thousand but and it varies over the +course of a day + + align:start position:0% +course of a day + + + align:start position:0% +course of a day +substantially but here's the kicker the + + align:start position:0% +substantially but here's the kicker the + + + align:start position:0% +substantially but here's the kicker the +red dots are the times of the system + + align:start position:0% +red dots are the times of the system + + + align:start position:0% +red dots are the times of the system +peak the red dots is are when the system + + align:start position:0% +peak the red dots is are when the system + + + align:start position:0% +peak the red dots is are when the system +really needed + + align:start position:0% +really needed + + + align:start position:0% +really needed +power late afternoon on a in a very hot + + align:start position:0% +power late afternoon on a in a very hot + + + align:start position:0% +power late afternoon on a in a very hot +week when it's really hot the wind tends + + align:start position:0% +week when it's really hot the wind tends + + + align:start position:0% +week when it's really hot the wind tends +not to blow that much + + align:start position:0% +not to blow that much + + + align:start position:0% +not to blow that much +so not only is there a lot of variation + + align:start position:0% +so not only is there a lot of variation + + + align:start position:0% +so not only is there a lot of variation +that the system has to respond to but at + + align:start position:0% +that the system has to respond to but at + + + align:start position:0% +that the system has to respond to but at +least in this case the peak out the the + + align:start position:0% +least in this case the peak out the the + + + align:start position:0% +least in this case the peak out the the +output at peak was tiny relative to + + align:start position:0% +output at peak was tiny relative to + + + align:start position:0% +output at peak was tiny relative to +capacity so windforms tend to have + + align:start position:0% +capacity so windforms tend to have + + + align:start position:0% +capacity so windforms tend to have +capacity factors 20s and 30s that is to + + align:start position:0% +capacity factors 20s and 30s that is to + + + align:start position:0% +capacity factors 20s and 30s that is to +say about 20 to 30% of nominal capacity + + align:start position:0% +say about 20 to 30% of nominal capacity + + + align:start position:0% +say about 20 to 30% of nominal capacity +you know if you ran at 2600 megawws 24 + + align:start position:0% +you know if you ran at 2600 megawws 24 + + + align:start position:0% +you know if you ran at 2600 megawws 24 +hours a day you'd get X what you + + align:start position:0% +hours a day you'd get X what you + + + align:start position:0% +hours a day you'd get X what you +actually get overx is the capacity + + align:start position:0% +actually get overx is the capacity + + + align:start position:0% +actually get overx is the capacity +factor and it tends they tend to be 20 + + align:start position:0% +factor and it tends they tend to be 20 + + + align:start position:0% +factor and it tends they tend to be 20 +30% solar not so much at + + align:start position:0% +30% solar not so much at + + + align:start position:0% +30% solar not so much at +night um so that's the other problem + + align:start position:0% +night um so that's the other problem + + + align:start position:0% +night um so that's the other problem +with renewables that um you can't + + align:start position:0% +with renewables that um you can't + + + align:start position:0% +with renewables that um you can't +dispatch them they're variable variable + + align:start position:0% +dispatch them they're variable variable + + + align:start position:0% +dispatch them they're variable variable +energy resources as the phrase goes this + + align:start position:0% +energy resources as the phrase goes this + + + align:start position:0% +energy resources as the phrase goes this +is another terrific picture this is + + align:start position:0% +is another terrific picture this is + + + align:start position:0% +is another terrific picture this is +Bonavville this is the Pacific + + align:start position:0% +Bonavville this is the Pacific + + + align:start position:0% +Bonavville this is the Pacific +Northwest and uh this is over the course + + align:start position:0% +Northwest and uh this is over the course + + + align:start position:0% +Northwest and uh this is over the course +of uh 2009 + + align:start position:0% +of uh 2009 + + + align:start position:0% +of uh 2009 +um early December 2009 saturday + + align:start position:0% +um early December 2009 saturday + + + align:start position:0% +um early December 2009 saturday +night wind output goes from nothing to + + align:start position:0% +night wind output goes from nothing to + + + align:start position:0% +night wind output goes from nothing to +around 2,000 + + align:start position:0% +around 2,000 + + + align:start position:0% +around 2,000 +megawws holds during the day Sunday + + align:start position:0% +megawws holds during the day Sunday + + + align:start position:0% +megawws holds during the day Sunday +Sunday is not a high demand day and then + + align:start position:0% +Sunday is not a high demand day and then + + + align:start position:0% +Sunday is not a high demand day and then +just as you're coming into Monday ramps + + align:start position:0% +just as you're coming into Monday ramps + + + align:start position:0% +just as you're coming into Monday ramps +down to zero by Monday night + + align:start position:0% +down to zero by Monday night + + + align:start position:0% +down to zero by Monday night +now we are told that Bonavville handled + + align:start position:0% +now we are told that Bonavville handled + + + align:start position:0% +now we are told that Bonavville handled +that bonavville handled that by backing + + align:start position:0% +that bonavville handled that by backing + + + align:start position:0% +that bonavville handled that by backing +off everything they could possibly back + + align:start position:0% +off everything they could possibly back + + + align:start position:0% +off everything they could possibly back +off and then bringing everything they + + align:start position:0% +off and then bringing everything they + + + align:start position:0% +off and then bringing everything they +could possibly bring up back + + align:start position:0% +could possibly bring up back + + + align:start position:0% +could possibly bring up back +online not + + align:start position:0% +online not + + + align:start position:0% +online not +easy double it and the system wouldn't + + align:start position:0% +easy double it and the system wouldn't + + + align:start position:0% +easy double it and the system wouldn't +have been able to handle + + align:start position:0% +have been able to handle + + + align:start position:0% +have been able to handle +it probably + + align:start position:0% + + + + align:start position:0% + +so wind output solar output are more + + align:start position:0% +so wind output solar output are more + + + align:start position:0% +so wind output solar output are more +variable than demand and you can't + + align:start position:0% +variable than demand and you can't + + + align:start position:0% +variable than demand and you can't +predict them as well there's a lot of + + align:start position:0% +predict them as well there's a lot of + + + align:start position:0% +predict them as well there's a lot of +work on predicting these + + align:start position:0% +work on predicting these + + + align:start position:0% +work on predicting these +things there has not been a lot of + + align:start position:0% +things there has not been a lot of + + + align:start position:0% +things there has not been a lot of +research on forecasting wind at 50 meter + + align:start position:0% +research on forecasting wind at 50 meter + + + align:start position:0% +research on forecasting wind at 50 meter +heights has not been a subject of much + + align:start position:0% +heights has not been a subject of much + + + align:start position:0% +heights has not been a subject of much +interest in meteorology until recently + + align:start position:0% +interest in meteorology until recently + + + align:start position:0% +interest in meteorology until recently +it's very interesting now hard to get + + align:start position:0% +it's very interesting now hard to get + + + align:start position:0% +it's very interesting now hard to get +data not a lot of weather stations at 50 + + align:start position:0% +data not a lot of weather stations at 50 + + + align:start position:0% +data not a lot of weather stations at 50 +meters um there are a lot of other + + align:start position:0% +meters um there are a lot of other + + + align:start position:0% +meters um there are a lot of other +changes + + align:start position:0% +changes + + + align:start position:0% +changes +and thinking about how you reconfigure + + align:start position:0% +and thinking about how you reconfigure + + + align:start position:0% +and thinking about how you reconfigure +the system the interesting thing from + + align:start position:0% +the system the interesting thing from + + + align:start position:0% +the system the interesting thing from +the point of view of the of market + + align:start position:0% +the point of view of the of market + + + align:start position:0% +the point of view of the of market +design is you don't just need capacity + + align:start position:0% +design is you don't just need capacity + + + align:start position:0% +design is you don't just need capacity +in a power system what you need now is + + align:start position:0% +in a power system what you need now is + + + align:start position:0% +in a power system what you need now is +capacity that can ramp can go up fast + + align:start position:0% +capacity that can ramp can go up fast + + + align:start position:0% +capacity that can ramp can go up fast +down fast + + align:start position:0% +down fast + + + align:start position:0% +down fast +um the current market design doesn't + + align:start position:0% +um the current market design doesn't + + + align:start position:0% +um the current market design doesn't +provide incentives for building that + + align:start position:0% +provide incentives for building that + + + align:start position:0% +provide incentives for building that +kind of + + align:start position:0% +kind of + + + align:start position:0% +kind of +capacity or for making it available so + + align:start position:0% +capacity or for making it available so + + + align:start position:0% +capacity or for making it available so +again as you go forward + + align:start position:0% +again as you go forward + + + align:start position:0% +again as you go forward +uh it's going to be important to figure + + align:start position:0% +uh it's going to be important to figure + + + align:start position:0% +uh it's going to be important to figure +out how to do this how do we make the + + align:start position:0% +out how to do this how do we make the + + + align:start position:0% +out how to do this how do we make the +system more flexible so it can respond + + align:start position:0% +system more flexible so it can respond + + + align:start position:0% +system more flexible so it can respond +to wind and + + align:start position:0% +to wind and + + + align:start position:0% +to wind and +solar at higher levels of penetration + + align:start position:0% +solar at higher levels of penetration + + + align:start position:0% +solar at higher levels of penetration +now one answer that everybody has is + + align:start position:0% +now one answer that everybody has is + + + align:start position:0% +now one answer that everybody has is +storage and here's from a recent report + + align:start position:0% +storage and here's from a recent report + + + align:start position:0% +storage and here's from a recent report +on storage + + align:start position:0% +on storage + + + align:start position:0% +on storage +technologies there are lots of storage + + align:start position:0% +technologies there are lots of storage + + + align:start position:0% +technologies there are lots of storage +technologies lots of + + align:start position:0% +technologies lots of + + + align:start position:0% +technologies lots of +them the ones in widespread use are pump + + align:start position:0% +them the ones in widespread use are pump + + + align:start position:0% +them the ones in widespread use are pump +storage and pump storage is terrific i + + align:start position:0% +storage and pump storage is terrific i + + + align:start position:0% +storage and pump storage is terrific i +was not perfect there's a roundtrip loss + + align:start position:0% +was not perfect there's a roundtrip loss + + + align:start position:0% +was not perfect there's a roundtrip loss +you pump water uphill you run it down + + align:start position:0% +you pump water uphill you run it down + + + align:start position:0% +you pump water uphill you run it down +through a turbine it's great you can + + align:start position:0% +through a turbine it's great you can + + + align:start position:0% +through a turbine it's great you can +start it fast not seconds but pretty + + align:start position:0% +start it fast not seconds but pretty + + + align:start position:0% +start it fast not seconds but pretty +fast you can stop it pretty fast not + + align:start position:0% +fast you can stop it pretty fast not + + + align:start position:0% +fast you can stop it pretty fast not +instantly you got a lot of rotating + + align:start position:0% +instantly you got a lot of rotating + + + align:start position:0% +instantly you got a lot of rotating +metal but you can stop it pretty fast um + + align:start position:0% +metal but you can stop it pretty fast um + + + align:start position:0% +metal but you can stop it pretty fast um +uh but you can't build it there's one in + + align:start position:0% +uh but you can't build it there's one in + + + align:start position:0% +uh but you can't build it there's one in +New England nobody imagines we'll ever + + align:start position:0% +New England nobody imagines we'll ever + + + align:start position:0% +New England nobody imagines we'll ever +be able to build another one it's the + + align:start position:0% +be able to build another one it's the + + + align:start position:0% +be able to build another one it's the +problem of building dams you can't build + + align:start position:0% +problem of building dams you can't build + + + align:start position:0% +problem of building dams you can't build +dams so this is a technology that's in + + align:start position:0% +dams so this is a technology that's in + + + align:start position:0% +dams so this is a technology that's in +some use you could build more of it this + + align:start position:0% +some use you could build more of it this + + + align:start position:0% +some use you could build more of it this +is compressed air + + align:start position:0% + + + + align:start position:0% + +um mostly in a cavern of one kind or + + align:start position:0% +um mostly in a cavern of one kind or + + + align:start position:0% +um mostly in a cavern of one kind or +another put a lot of air in under + + align:start position:0% +another put a lot of air in under + + + align:start position:0% +another put a lot of air in under +pressure drive a turbine when it when it + + align:start position:0% +pressure drive a turbine when it when it + + + align:start position:0% +pressure drive a turbine when it when it +comes out you can do that there are + + align:start position:0% +comes out you can do that there are + + + align:start position:0% +comes out you can do that there are +about three of them I think in the world + + align:start position:0% +about three of them I think in the world + + + align:start position:0% +about three of them I think in the world +and then there are all these batteries + + align:start position:0% +and then there are all these batteries + + + align:start position:0% +and then there are all these batteries +all and cap super capacitors which are + + align:start position:0% +all and cap super capacitors which are + + + align:start position:0% +all and cap super capacitors which are +kind of cute and + + align:start position:0% +kind of cute and + + + align:start position:0% +kind of cute and +flywheels and you know they work these + + align:start position:0% +flywheels and you know they work these + + + align:start position:0% +flywheels and you know they work these +are known technologies we can build + + align:start position:0% +are known technologies we can build + + + align:start position:0% +are known technologies we can build +these are these are sort of neat these + + align:start position:0% +these are these are sort of neat these + + + align:start position:0% +these are these are sort of neat these +are uh batteries that + + align:start position:0% +are uh batteries that + + + align:start position:0% +are uh batteries that +are that basically work off uh either + + align:start position:0% +are that basically work off uh either + + + align:start position:0% +are that basically work off uh either +liquid cathodes or or anodess and things + + align:start position:0% +liquid cathodes or or anodess and things + + + align:start position:0% +liquid cathodes or or anodess and things +flow and it's great stuff and um but + + align:start position:0% +flow and it's great stuff and um but + + + align:start position:0% +flow and it's great stuff and um but +they're all really + + align:start position:0% +they're all really + + + align:start position:0% +they're all really +expensive at + + align:start position:0% +expensive at + + + align:start position:0% +expensive at +scale this you can sort of afford if you + + align:start position:0% +scale this you can sort of afford if you + + + align:start position:0% +scale this you can sort of afford if you +can build it this is is okay where you + + align:start position:0% +can build it this is is okay where you + + + align:start position:0% +can build it this is is okay where you +have a suitable site not great but it's + + align:start position:0% +have a suitable site not great but it's + + + align:start position:0% +have a suitable site not great but it's +okay and all this other stuff is + + align:start position:0% +okay and all this other stuff is + + + align:start position:0% +okay and all this other stuff is +expensive so it's very hard + + align:start position:0% +expensive so it's very hard + + + align:start position:0% +expensive so it's very hard +uh right this is + + align:start position:0% +uh right this is + + + align:start position:0% +uh right this is +the this is the holy grail in electric + + align:start position:0% +the this is the holy grail in electric + + + align:start position:0% +the this is the holy grail in electric +power + + align:start position:0% +power + + + align:start position:0% +power +research if you could do cheap grid + + align:start position:0% +research if you could do cheap grid + + + align:start position:0% +research if you could do cheap grid +level storage solar and wind would not + + align:start position:0% +level storage solar and wind would not + + + align:start position:0% +level storage solar and wind would not +be a + + align:start position:0% + + + + align:start position:0% + +problem but with technologies we now + + align:start position:0% +problem but with technologies we now + + + align:start position:0% +problem but with technologies we now +know you + + align:start position:0% +know you + + + align:start position:0% +know you +can't this stuff just does not look to + + align:start position:0% +can't this stuff just does not look to + + + align:start position:0% +can't this stuff just does not look to +have the prospect of becoming cheap + + align:start position:0% +have the prospect of becoming cheap + + + align:start position:0% +have the prospect of becoming cheap +enough to deploy at scale by + + align:start position:0% + + + + align:start position:0% + +2030 could you do it sure could you + + align:start position:0% +2030 could you do it sure could you + + + align:start position:0% +2030 could you do it sure could you +afford it probably + + align:start position:0% +afford it probably + + + align:start position:0% +afford it probably +not + + align:start position:0% +not + + + align:start position:0% +not +okay question so + + align:start position:0% +okay question so + + + align:start position:0% +okay question so +far it's kind of a + + align:start position:0% +far it's kind of a + + + align:start position:0% +far it's kind of a +downer but there we are you know I mean + + align:start position:0% +downer but there we are you know I mean + + + align:start position:0% +downer but there we are you know I mean +it is what it is + + align:start position:0% + + + + align:start position:0% + +so a and now the third thing they're + + align:start position:0% +so a and now the third thing they're + + + align:start position:0% +so a and now the third thing they're +remote they're intermittent and they're + + align:start position:0% +remote they're intermittent and they're + + + align:start position:0% +remote they're intermittent and they're +expensive so what do you do uh you can + + align:start position:0% +expensive so what do you do uh you can + + + align:start position:0% +expensive so what do you do uh you can +do R&D we've done some + + align:start position:0% +do R&D we've done some + + + align:start position:0% +do R&D we've done some +uh you could do more easily + + align:start position:0% +uh you could do more easily + + + align:start position:0% +uh you could do more easily +there is an interesting question + + align:start position:0% +there is an interesting question + + + align:start position:0% +there is an interesting question +of should you bring renewables on by + + align:start position:0% +of should you bring renewables on by + + + align:start position:0% +of should you bring renewables on by +subsidizing them or should you bring + + align:start position:0% +subsidizing them or should you bring + + + align:start position:0% +subsidizing them or should you bring +renewables on by taxing what you don't + + align:start position:0% +renewables on by taxing what you don't + + + align:start position:0% +renewables on by taxing what you don't +like which is possibly coal or carbon or + + align:start position:0% +like which is possibly coal or carbon or + + + align:start position:0% +like which is possibly coal or carbon or +oil or some + + align:start position:0% +oil or some + + + align:start position:0% +oil or some +mixture um there are carbon taxes in + + align:start position:0% +mixture um there are carbon taxes in + + + align:start position:0% +mixture um there are carbon taxes in +various places in the world not that + + align:start position:0% +various places in the world not that + + + align:start position:0% +various places in the world not that +many + + align:start position:0% +many + + + align:start position:0% +many +um what the US has done at the state + + align:start position:0% +um what the US has done at the state + + + align:start position:0% +um what the US has done at the state +level we've had these these + + align:start position:0% +level we've had these these + + + align:start position:0% +level we've had these these +requirements what the Europeans have + + align:start position:0% +requirements what the Europeans have + + + align:start position:0% +requirements what the Europeans have +done is to basically pay + + align:start position:0% +done is to basically pay + + + align:start position:0% +done is to basically pay +prices right so if you put up a solar + + align:start position:0% +prices right so if you put up a solar + + + align:start position:0% +prices right so if you put up a solar +farm in Germany your revenue per + + align:start position:0% +farm in Germany your revenue per + + + align:start position:0% +farm in Germany your revenue per +kilowatt hour is guaranteed for 20 + + align:start position:0% +kilowatt hour is guaranteed for 20 + + + align:start position:0% +kilowatt hour is guaranteed for 20 +years in the US you got to find a + + align:start position:0% +years in the US you got to find a + + + align:start position:0% +years in the US you got to find a +utility that wants to deal with you for + + align:start position:0% +utility that wants to deal with you for + + + align:start position:0% +utility that wants to deal with you for +the fact that you're + + align:start position:0% +the fact that you're + + + align:start position:0% +the fact that you're +renewable + + align:start position:0% +renewable + + + align:start position:0% +renewable +Um one argument is why do we do it that + + align:start position:0% +Um one argument is why do we do it that + + + align:start position:0% +Um one argument is why do we do it that +way in the US there are lots of problems + + align:start position:0% +way in the US there are lots of problems + + + align:start position:0% +way in the US there are lots of problems +with it because the cost is + + align:start position:0% +with it because the cost is + + + align:start position:0% +with it because the cost is +hidden it hides the cost I think is the + + align:start position:0% +hidden it hides the cost I think is the + + + align:start position:0% +hidden it hides the cost I think is the +main reason it hides the cost in Germany + + align:start position:0% +main reason it hides the cost in Germany + + + align:start position:0% +main reason it hides the cost in Germany +I mean you know there's a price it's + + align:start position:0% +I mean you know there's a price it's + + + align:start position:0% +I mean you know there's a price it's +posted in Spain there's a price it's + + align:start position:0% +posted in Spain there's a price it's + + + align:start position:0% +posted in Spain there's a price it's +posted in the US how much does solar and + + align:start position:0% +posted in the US how much does solar and + + + align:start position:0% +posted in the US how much does solar and +wind add to our electric bills we don't + + align:start position:0% +wind add to our electric bills we don't + + + align:start position:0% +wind add to our electric bills we don't +have a clue cuz there's you know there's + + align:start position:0% +have a clue cuz there's you know there's + + + align:start position:0% +have a clue cuz there's you know there's +a there are deals done but they're not + + align:start position:0% +a there are deals done but they're not + + + align:start position:0% +a there are deals done but they're not +typically public so we don't know the + + align:start position:0% +typically public so we don't know the + + + align:start position:0% +typically public so we don't know the +the fact that you may or may not have + + align:start position:0% +the fact that you may or may not have + + + align:start position:0% +the fact that you may or may not have +followed that that onshore + + align:start position:0% +followed that that onshore + + + align:start position:0% +followed that that onshore +wind was um that the the Cape Wind you + + align:start position:0% +wind was um that the the Cape Wind you + + + align:start position:0% +wind was um that the the Cape Wind you +all remember Cape Wind this pro this + + align:start position:0% +all remember Cape Wind this pro this + + + align:start position:0% +all remember Cape Wind this pro this +project to build a a bunch of wind mills + + align:start position:0% +project to build a a bunch of wind mills + + + align:start position:0% +project to build a a bunch of wind mills +off Cape Cod hugely controversial + + align:start position:0% +off Cape Cod hugely controversial + + + align:start position:0% +off Cape Cod hugely controversial +um also + + align:start position:0% +um also + + + align:start position:0% +um also +expensive people were shocked that the + + align:start position:0% +expensive people were shocked that the + + + align:start position:0% +expensive people were shocked that the +price to be paid for that electricity + + align:start position:0% +price to be paid for that electricity + + + align:start position:0% +price to be paid for that electricity +was three times the going wholesale rate + + align:start position:0% +was three times the going wholesale rate + + + align:start position:0% +was three times the going wholesale rate +shocked well you're building windmills + + align:start position:0% +shocked well you're building windmills + + + align:start position:0% +shocked well you're building windmills +offshore with in this in the ocean with + + align:start position:0% +offshore with in this in the ocean with + + + align:start position:0% +offshore with in this in the ocean with +transmission and gas is really + + align:start position:0% +transmission and gas is really + + + align:start position:0% +transmission and gas is really +cheap people were shocked because they + + align:start position:0% +cheap people were shocked because they + + + align:start position:0% +cheap people were shocked because they +had there were a number of interviews + + align:start position:0% +had there were a number of interviews + + + align:start position:0% +had there were a number of interviews +people said "Well the wind is + + align:start position:0% +people said "Well the wind is + + + align:start position:0% +people said "Well the wind is +free." Okay the wind is free um so we we + + align:start position:0% +free." Okay the wind is free um so we we + + + align:start position:0% +free." Okay the wind is free um so we we +do this this um uh the other thing we do + + align:start position:0% +do this this um uh the other thing we do + + + align:start position:0% +do this this um uh the other thing we do +is tax breaks um and tax + + align:start position:0% +is tax breaks um and tax + + + align:start position:0% +is tax breaks um and tax +breaks give you this pattern this is + + align:start position:0% +breaks give you this pattern this is + + + align:start position:0% +breaks give you this pattern this is +wind additions in megawws over + + align:start position:0% +wind additions in megawws over + + + align:start position:0% +wind additions in megawws over +time and you might ask why it looks like + + align:start position:0% +time and you might ask why it looks like + + + align:start position:0% +time and you might ask why it looks like +that + + align:start position:0% +that + + + align:start position:0% +that +okay whenever you see weird business + + align:start position:0% +okay whenever you see weird business + + + align:start position:0% +okay whenever you see weird business +conduct the first thing you might want + + align:start position:0% +conduct the first thing you might want + + + align:start position:0% +conduct the first thing you might want +to look at is tax policy + + align:start position:0% +to look at is tax policy + + + align:start position:0% +to look at is tax policy +these are the years in which either the + + align:start position:0% +these are the years in which either the + + + align:start position:0% +these are the years in which either the +tax subsidy was absent or in which it + + align:start position:0% +tax subsidy was absent or in which it + + + align:start position:0% +tax subsidy was absent or in which it +wasn't clear it was going to be + + align:start position:0% +wasn't clear it was going to be + + + align:start position:0% +wasn't clear it was going to be +renewed and when that happens people + + align:start position:0% +renewed and when that happens people + + + align:start position:0% +renewed and when that happens people +stop and of course if you want to build + + align:start position:0% +stop and of course if you want to build + + + align:start position:0% +stop and of course if you want to build +a wind industry that's + + align:start position:0% +a wind industry that's + + + align:start position:0% +a wind industry that's +insane because it means you can't ever + + align:start position:0% +insane because it means you can't ever + + + align:start position:0% +insane because it means you can't ever +gear up for production because next year + + align:start position:0% +gear up for production because next year + + + align:start position:0% +gear up for production because next year +you might not have any orders uh it's + + align:start position:0% +you might not have any orders uh it's + + + align:start position:0% +you might not have any orders uh it's +also a little problem with using t we + + align:start position:0% +also a little problem with using t we + + + align:start position:0% +also a little problem with using t we +use tax breaks too because that hides + + align:start position:0% +use tax breaks too because that hides + + + align:start position:0% +use tax breaks too because that hides +the cost + + align:start position:0% +the cost + + + align:start position:0% +the cost +right you can cut revenue and subsidize + + align:start position:0% +right you can cut revenue and subsidize + + + align:start position:0% +right you can cut revenue and subsidize +renewable + + align:start position:0% +renewable + + + align:start position:0% +renewable +power cut taxes and subsidize renewable + + align:start position:0% +power cut taxes and subsidize renewable + + + align:start position:0% +power cut taxes and subsidize renewable +power in one fell swoop just that's just + + align:start position:0% +power in one fell swoop just that's just + + + align:start position:0% +power in one fell swoop just that's just +fabulous um but of course if the firm + + align:start position:0% +fabulous um but of course if the firm + + + align:start position:0% +fabulous um but of course if the firm +doesn't have any profits it can't use a + + align:start position:0% +doesn't have any profits it can't use a + + + align:start position:0% +doesn't have any profits it can't use a +profits tax + + align:start position:0% +profits tax + + + align:start position:0% +profits tax +break and a lot of money is wasted + + align:start position:0% +break and a lot of money is wasted + + + align:start position:0% +break and a lot of money is wasted +making that + + align:start position:0% +making that + + + align:start position:0% +making that +work + + align:start position:0% + + + + align:start position:0% + +so we also don't enforce much so we have + + align:start position:0% +so we also don't enforce much so we have + + + align:start position:0% +so we also don't enforce much so we have +probably the worst possible + + align:start position:0% +probably the worst possible + + + align:start position:0% +probably the worst possible +uh policy mix and uh the only + + align:start position:0% +uh policy mix and uh the only + + + align:start position:0% +uh policy mix and uh the only +explanation I've ever heard is that it's + + align:start position:0% +explanation I've ever heard is that it's + + + align:start position:0% +explanation I've ever heard is that it's +perfectly designed to hide the + + align:start position:0% +perfectly designed to hide the + + + align:start position:0% +perfectly designed to hide the +costs the tax breaks who knows how much + + align:start position:0% +costs the tax breaks who knows how much + + + align:start position:0% +costs the tax breaks who knows how much +we spend i mean you + + align:start position:0% +we spend i mean you + + + align:start position:0% +we spend i mean you +can it can be found out but not easily + + align:start position:0% +can it can be found out but not easily + + + align:start position:0% +can it can be found out but not easily +how much does it add to the cost of + + align:start position:0% +how much does it add to the cost of + + + align:start position:0% +how much does it add to the cost of +power well it doesn't it adds to your + + align:start position:0% +power well it doesn't it adds to your + + + align:start position:0% +power well it doesn't it adds to your +income taxes + + align:start position:0% +income taxes + + + align:start position:0% +income taxes +uh what about these renewable standards + + align:start position:0% +uh what about these renewable standards + + + align:start position:0% +uh what about these renewable standards +what do they add to the cost of power + + align:start position:0% +what do they add to the cost of power + + + align:start position:0% +what do they add to the cost of power +well hard to know bunches of deals + + align:start position:0% +well hard to know bunches of deals + + + align:start position:0% +well hard to know bunches of deals +bunches of + + align:start position:0% +bunches of + + + align:start position:0% +bunches of +contracts not ever really + + align:start position:0% +contracts not ever really + + + align:start position:0% +contracts not ever really +reported so we hide the cost pretty + + align:start position:0% +reported so we hide the cost pretty + + + align:start position:0% +reported so we hide the cost pretty +well um a carbon tax would be a much + + align:start position:0% +well um a carbon tax would be a much + + + align:start position:0% +well um a carbon tax would be a much +better approach + + align:start position:0% +better approach + + + align:start position:0% +better approach +um I should tell you this is actually I + + align:start position:0% +um I should tell you this is actually I + + + align:start position:0% +um I should tell you this is actually I +find this fascinating but the latest + + align:start position:0% +find this fascinating but the latest + + + align:start position:0% +find this fascinating but the latest +word from Washington is that the carbon + + align:start position:0% +word from Washington is that the carbon + + + align:start position:0% +word from Washington is that the carbon +tax is coming + + align:start position:0% +tax is coming + + + align:start position:0% +tax is coming +back remember capp trade the climate + + align:start position:0% +back remember capp trade the climate + + + align:start position:0% +back remember capp trade the climate +bill that we were going to have because + + align:start position:0% +bill that we were going to have because + + + align:start position:0% +bill that we were going to have because +both candidates in the last presidential + + align:start position:0% +both candidates in the last presidential + + + align:start position:0% +both candidates in the last presidential +election supported having a cap and + + align:start position:0% +election supported having a cap and + + + align:start position:0% +election supported having a cap and +trade program which went down to defeat + + align:start position:0% +trade program which went down to defeat + + + align:start position:0% +trade program which went down to defeat +as cap and + + align:start position:0% +as cap and + + + align:start position:0% +as cap and +tax well there now serious serious uh + + align:start position:0% +tax well there now serious serious uh + + + align:start position:0% +tax well there now serious serious uh +work going on in Washington as far as I + + align:start position:0% +work going on in Washington as far as I + + + align:start position:0% +work going on in Washington as far as I +can tell on both sides of the aisle + + align:start position:0% +can tell on both sides of the aisle + + + align:start position:0% +can tell on both sides of the aisle +preparing carbon tax + + align:start position:0% +preparing carbon tax + + + align:start position:0% +preparing carbon tax +bills they don't mention + + align:start position:0% +bills they don't mention + + + align:start position:0% +bills they don't mention +climate turns out it's okay to tax + + align:start position:0% +climate turns out it's okay to tax + + + align:start position:0% +climate turns out it's okay to tax +carbon if you don't mention climate you + + align:start position:0% +carbon if you don't mention climate you + + + align:start position:0% +carbon if you don't mention climate you +mention + + align:start position:0% +mention + + + align:start position:0% +mention +revenue energy + + align:start position:0% +revenue energy + + + align:start position:0% +revenue energy +self-sufficiency so we're going to have + + align:start position:0% +self-sufficiency so we're going to have + + + align:start position:0% +self-sufficiency so we're going to have +a carbon tax to we may have a carbon tax + + align:start position:0% +a carbon tax to we may have a carbon tax + + + align:start position:0% +a carbon tax to we may have a carbon tax +to raise revenue without the word + + align:start position:0% +to raise revenue without the word + + + align:start position:0% +to raise revenue without the word +climate being uttered in the debate it's + + align:start position:0% +climate being uttered in the debate it's + + + align:start position:0% +climate being uttered in the debate it's +fabulous stuff anyway that's + + align:start position:0% +fabulous stuff anyway that's + + + align:start position:0% +fabulous stuff anyway that's +renewables questions comments + + align:start position:0% + + + + align:start position:0% + +reactions you're not terminally + + align:start position:0% +reactions you're not terminally + + + align:start position:0% +reactions you're not terminally +depressed by all + + align:start position:0% +depressed by all + + + align:start position:0% +depressed by all +that okay all right i'll I'll depress + + align:start position:0% +that okay all right i'll I'll depress + + + align:start position:0% +that okay all right i'll I'll depress +you some more let's talk about + + align:start position:0% +you some more let's talk about + + + align:start position:0% +you some more let's talk about +prices + + align:start position:0% +prices + + + align:start position:0% +prices +um prices don't reflect the nature of + + align:start position:0% +um prices don't reflect the nature of + + + align:start position:0% +um prices don't reflect the nature of +actual + + align:start position:0% +actual + + + align:start position:0% +actual +costs demand varies over time you saw + + align:start position:0% +costs demand varies over time you saw + + + align:start position:0% +costs demand varies over time you saw +last time a supply curve that says + + align:start position:0% +last time a supply curve that says + + + align:start position:0% +last time a supply curve that says +prices vary over + + align:start position:0% +prices vary over + + + align:start position:0% +prices vary over +time this is these are average these are + + align:start position:0% +time this is these are average these are + + + align:start position:0% +time this is these are average these are +daily average prices over 2010 in the + + align:start position:0% +daily average prices over 2010 in the + + + align:start position:0% +daily average prices over 2010 in the +PJM market area that began is + + align:start position:0% +PJM market area that began is + + + align:start position:0% +PJM market area that began is +Pennsylvania Jersey Maryland it's now + + align:start position:0% +Pennsylvania Jersey Maryland it's now + + + align:start position:0% +Pennsylvania Jersey Maryland it's now +broader it's the biggest electricity + + align:start position:0% +broader it's the biggest electricity + + + align:start position:0% +broader it's the biggest electricity +market in the country and you notice a + + align:start position:0% +market in the country and you notice a + + + align:start position:0% +market in the country and you notice a +bunch of things you notice they vary you + + align:start position:0% +bunch of things you notice they vary you + + + align:start position:0% +bunch of things you notice they vary you +can sort of see a seasonal pattern they + + align:start position:0% +can sort of see a seasonal pattern they + + + align:start position:0% +can sort of see a seasonal pattern they +tend to be a little higher in the summer + + align:start position:0% +tend to be a little higher in the summer + + + align:start position:0% +tend to be a little higher in the summer +on average than they are other times of + + align:start position:0% +on average than they are other times of + + + align:start position:0% +on average than they are other times of +the year + + align:start position:0% +the year + + + align:start position:0% +the year +not that much higher because other times + + align:start position:0% +not that much higher because other times + + + align:start position:0% +not that much higher because other times +of the year you do your maintenance so + + align:start position:0% +of the year you do your maintenance so + + + align:start position:0% +of the year you do your maintenance so +the supply curve shifts when you take + + align:start position:0% +the supply curve shifts when you take + + + align:start position:0% +the supply curve shifts when you take +units off to maintain them this must + + align:start position:0% +units off to maintain them this must + + + align:start position:0% +units off to maintain them this must +have been a particularly hot day who + + align:start position:0% +have been a particularly hot day who + + + align:start position:0% +have been a particularly hot day who +knows what happened here in + + align:start position:0% +knows what happened here in + + + align:start position:0% +knows what happened here in +December a unit went off so the point + + align:start position:0% +December a unit went off so the point + + + align:start position:0% +December a unit went off so the point +here is you'd have kind of a hard time + + align:start position:0% +here is you'd have kind of a hard time + + + align:start position:0% +here is you'd have kind of a hard time +you could predict this maybe uh that + + align:start position:0% +you could predict this maybe uh that + + + align:start position:0% +you could predict this maybe uh that +yeah it tends to be lower in the spring + + align:start position:0% +yeah it tends to be lower in the spring + + + align:start position:0% +yeah it tends to be lower in the spring +and maybe what the hell is that but + + align:start position:0% +and maybe what the hell is that but + + + align:start position:0% +and maybe what the hell is that but +you'd predict a basically a summer peak + + align:start position:0% +you'd predict a basically a summer peak + + + align:start position:0% +you'd predict a basically a summer peak +in prices but you'd miss a lot you'd + + align:start position:0% +in prices but you'd miss a lot you'd + + + align:start position:0% +in prices but you'd miss a lot you'd +miss a lot of the variation uh you're + + align:start position:0% +miss a lot of the variation uh you're + + + align:start position:0% +miss a lot of the variation uh you're +talking down from $20 a megawatt hour up + + align:start position:0% +talking down from $20 a megawatt hour up + + + align:start position:0% +talking down from $20 a megawatt hour up +to 120 and this is not if we deveraged + + align:start position:0% +to 120 and this is not if we deveraged + + + align:start position:0% +to 120 and this is not if we deveraged +and didn't do daily averages you'd get + + align:start position:0% +and didn't do daily averages you'd get + + + align:start position:0% +and didn't do daily averages you'd get +more of a spread than that you can get + + align:start position:0% +more of a spread than that you can get + + + align:start position:0% +more of a spread than that you can get +several orders of magnitude spread in + + align:start position:0% +several orders of magnitude spread in + + + align:start position:0% +several orders of magnitude spread in +marginal cost of electricity you do not + + align:start position:0% +marginal cost of electricity you do not + + + align:start position:0% +marginal cost of electricity you do not +see that at home if you looked at the + + align:start position:0% +see that at home if you looked at the + + + align:start position:0% +see that at home if you looked at the +daily level it's even more striking this + + align:start position:0% +daily level it's even more striking this + + + align:start position:0% +daily level it's even more striking this +is a couple of days in 2010 by hour and + + align:start position:0% +is a couple of days in 2010 by hour and + + + align:start position:0% +is a couple of days in 2010 by hour and +um you see on whatever whichever of the + + align:start position:0% +um you see on whatever whichever of the + + + align:start position:0% +um you see on whatever whichever of the +two days this is uh you got you had your + + align:start position:0% +two days this is uh you got you had your + + + align:start position:0% +two days this is uh you got you had your +morning peak and you had your afternoon + + align:start position:0% +morning peak and you had your afternoon + + + align:start position:0% +morning peak and you had your afternoon +peak um okay you could kind of predict + + align:start position:0% +peak um okay you could kind of predict + + + align:start position:0% +peak um okay you could kind of predict +that i have no idea what happened on + + align:start position:0% +that i have no idea what happened on + + + align:start position:0% +that i have no idea what happened on +this day this is like one or two in the + + align:start position:0% +this day this is like one or two in the + + + align:start position:0% +this day this is like one or two in the +afternoon the prices shoot up well and + + align:start position:0% +afternoon the prices shoot up well and + + + align:start position:0% +afternoon the prices shoot up well and +that's real that's the cost of + + align:start position:0% +that's real that's the cost of + + + align:start position:0% +that's real that's the cost of +generating electricity at the margin + + align:start position:0% +generating electricity at the margin + + + align:start position:0% +generating electricity at the margin +that's a marginal cost and it's at $300 + + align:start position:0% +that's a marginal cost and it's at $300 + + + align:start position:0% +that's a marginal cost and it's at $300 +a megawatt hour they they've put pulled + + align:start position:0% +a megawatt hour they they've put pulled + + + align:start position:0% +a megawatt hour they they've put pulled +all the old dirty diesels out and turned + + align:start position:0% +all the old dirty diesels out and turned + + + align:start position:0% +all the old dirty diesels out and turned +them + + align:start position:0% +them + + + align:start position:0% +them +on for an hour or two so you can't + + align:start position:0% +on for an hour or two so you can't + + + align:start position:0% +on for an hour or two so you can't +forecast that you don't pay that small + + align:start position:0% +forecast that you don't pay that small + + + align:start position:0% +forecast that you don't pay that small +commercial and residential users don't + + align:start position:0% +commercial and residential users don't + + + align:start position:0% +commercial and residential users don't +see that variation in cost oranges get + + align:start position:0% +see that variation in cost oranges get + + + align:start position:0% +see that variation in cost oranges get +more expensive at wholesale they're more + + align:start position:0% +more expensive at wholesale they're more + + + align:start position:0% +more expensive at wholesale they're more +expensive at retail power gets more + + align:start position:0% +expensive at retail power gets more + + + align:start position:0% +expensive at retail power gets more +expensive at wholesale nothing + + align:start position:0% +expensive at wholesale nothing + + + align:start position:0% +expensive at wholesale nothing +happens um + + align:start position:0% +happens um + + + align:start position:0% +happens um +now it could happen i mentioned earlier + + align:start position:0% +now it could happen i mentioned earlier + + + align:start position:0% +now it could happen i mentioned earlier +advanced meters what advanced meters do + + align:start position:0% +advanced meters what advanced meters do + + + align:start position:0% +advanced meters what advanced meters do +is advanced meters basically record + + align:start position:0% +is advanced meters basically record + + + align:start position:0% +is advanced meters basically record +usage at short at short intervals say 15 + + align:start position:0% +usage at short at short intervals say 15 + + + align:start position:0% +usage at short at short intervals say 15 +minutes can receive price signals can + + align:start position:0% +minutes can receive price signals can + + + align:start position:0% +minutes can receive price signals can +send 15minute or even finer usage + + align:start position:0% +send 15minute or even finer usage + + + align:start position:0% +send 15minute or even finer usage +information to the + + align:start position:0% +information to the + + + align:start position:0% +information to the +utility so you could use these and there + + align:start position:0% +utility so you could use these and there + + + align:start position:0% +utility so you could use these and there +are millions of them around the country + + align:start position:0% +are millions of them around the country + + + align:start position:0% +are millions of them around the country +you could use them to charge those + + align:start position:0% +you could use them to charge those + + + align:start position:0% +you could use them to charge those +prices + + align:start position:0% + + + + align:start position:0% + +um you can imagine exactly uh how + + align:start position:0% +um you can imagine exactly uh how + + + align:start position:0% +um you can imagine exactly uh how +popular that would + + align:start position:0% +popular that would + + + align:start position:0% +popular that would +be you know you come home one day and oh + + align:start position:0% +be you know you come home one day and oh + + + align:start position:0% +be you know you come home one day and oh +by the way you've just spent a jillion + + align:start position:0% +by the way you've just spent a jillion + + + align:start position:0% +by the way you've just spent a jillion +dollars for electricity because + + align:start position:0% +dollars for electricity because + + + align:start position:0% +dollars for electricity because +something + + align:start position:0% +something + + + align:start position:0% +something +happened + + align:start position:0% +happened + + + align:start position:0% +happened +so these meters they're required in + + align:start position:0% +so these meters they're required in + + + align:start position:0% +so these meters they're required in +California they're required in several + + align:start position:0% +California they're required in several + + + align:start position:0% +California they're required in several +other + + align:start position:0% +other + + + align:start position:0% +other +states everywhere + + align:start position:0% +states everywhere + + + align:start position:0% +states everywhere +um federal tax dollars your federal tax + + align:start position:0% +um federal tax dollars your federal tax + + + align:start position:0% +um federal tax dollars your federal tax +dollars have paid for millions of + + align:start position:0% +dollars have paid for millions of + + + align:start position:0% +dollars have paid for millions of +them but they're not being + + align:start position:0% +them but they're not being + + + align:start position:0% +them but they're not being +used they're very smart meters that are + + align:start position:0% +used they're very smart meters that are + + + align:start position:0% +used they're very smart meters that are +going to go slowly insane not using any + + align:start position:0% +going to go slowly insane not using any + + + align:start position:0% +going to go slowly insane not using any +of that intelligence um they're not + + align:start position:0% +of that intelligence um they're not + + + align:start position:0% +of that intelligence um they're not +being used for pricing they're not being + + align:start position:0% +being used for pricing they're not being + + + align:start position:0% +being used for pricing they're not being +used for measuring every 15 seconds + + align:start position:0% +used for measuring every 15 seconds + + + align:start position:0% +used for measuring every 15 seconds +because or 15 minutes because who cares + + align:start position:0% +because or 15 minutes because who cares + + + align:start position:0% +because or 15 minutes because who cares +the price is the same + + align:start position:0% +the price is the same + + + align:start position:0% +the price is the same +so the one thing everybody's convinced + + align:start position:0% +so the one thing everybody's convinced + + + align:start position:0% +so the one thing everybody's convinced +of is if you just cut people over to + + align:start position:0% +of is if you just cut people over to + + + align:start position:0% +of is if you just cut people over to +pricing like that there would be riots + + align:start position:0% +pricing like that there would be riots + + + align:start position:0% +pricing like that there would be riots +in the street because people would have + + align:start position:0% +in the street because people would have + + + align:start position:0% +in the street because people would have +nasty surprises and people don't like + + align:start position:0% +nasty surprises and people don't like + + + align:start position:0% +nasty surprises and people don't like +nasty surprises you go away for a week + + align:start position:0% +nasty surprises you go away for a week + + + align:start position:0% +nasty surprises you go away for a week +it's a heat wave you forgot to turn off + + align:start position:0% +it's a heat wave you forgot to turn off + + + align:start position:0% +it's a heat wave you forgot to turn off +your air turn down your air conditioner + + align:start position:0% +your air turn down your air conditioner + + + align:start position:0% +your air turn down your air conditioner +boom $3,000 electricity bill you don't + + align:start position:0% +boom $3,000 electricity bill you don't + + + align:start position:0% +boom $3,000 electricity bill you don't +like that too much so it seems clear to + + align:start position:0% +like that too much so it seems clear to + + + align:start position:0% +like that too much so it seems clear to +most of us that the only way this works + + align:start position:0% +most of us that the only way this works + + + align:start position:0% +most of us that the only way this works +is if you can have simple automated + + align:start position:0% +is if you can have simple automated + + + align:start position:0% +is if you can have simple automated +response simple automated + + align:start position:0% + + + + align:start position:0% + +response the main issue is going to be + + align:start position:0% +response the main issue is going to be + + + align:start position:0% +response the main issue is going to be +air conditioning and and heating but + + align:start position:0% +air conditioning and and heating but + + + align:start position:0% +air conditioning and and heating but +even so um you you might like some + + align:start position:0% +even so um you you might like some + + + align:start position:0% +even so um you you might like some +signal that says uh don't don't do your + + align:start position:0% +signal that says uh don't don't do your + + + align:start position:0% +signal that says uh don't don't do your +uh uh uh close at 5 in the afternoon uh + + align:start position:0% +uh uh uh close at 5 in the afternoon uh + + + align:start position:0% +uh uh uh close at 5 in the afternoon uh +something that says to you electricity + + align:start position:0% +something that says to you electricity + + + align:start position:0% +something that says to you electricity +is really expensive right now and for + + align:start position:0% +is really expensive right now and for + + + align:start position:0% +is really expensive right now and for +some things it's got to be automated + + align:start position:0% +some things it's got to be automated + + + align:start position:0% +some things it's got to be automated +the flip side of all this price + + align:start position:0% +the flip side of all this price + + + align:start position:0% +the flip side of all this price +variation is a change in uh in load + + align:start position:0% +variation is a change in uh in load + + + align:start position:0% +variation is a change in uh in load +duration curves you recall this is these + + align:start position:0% +duration curves you recall this is these + + + align:start position:0% +duration curves you recall this is these +curves you get by stacking the power + + align:start position:0% +curves you get by stacking the power + + + align:start position:0% +curves you get by stacking the power +cons by measuring power consumption each + + align:start position:0% +cons by measuring power consumption each + + + align:start position:0% +cons by measuring power consumption each +hour and then graphing first the the + + align:start position:0% +hour and then graphing first the the + + + align:start position:0% +hour and then graphing first the the +hour with the highest use then second + + align:start position:0% +hour with the highest use then second + + + align:start position:0% +hour with the highest use then second +highest and so on down to the lowest + + align:start position:0% +highest and so on down to the lowest + + + align:start position:0% +highest and so on down to the lowest +these are um load duration curves for + + align:start position:0% +these are um load duration curves for + + + align:start position:0% +these are um load duration curves for +New York + + align:start position:0% +New York + + + align:start position:0% +New York +um rescaled so that that the peak is + + align:start position:0% +um rescaled so that that the peak is + + + align:start position:0% +um rescaled so that that the peak is +equal to one and averaged over 198084 + + align:start position:0% +equal to one and averaged over 198084 + + + align:start position:0% +equal to one and averaged over 198084 +and 2005 to + + align:start position:0% +and 2005 to + + + align:start position:0% +and 2005 to +2009 okay you notice they change it + + align:start position:0% +2009 okay you notice they change it + + + align:start position:0% +2009 okay you notice they change it +changes shape it changes shape kind of + + align:start position:0% +changes shape it changes shape kind of + + + align:start position:0% +changes shape it changes shape kind of +dramatically in 80 to 84 what this 21% + + align:start position:0% +dramatically in 80 to 84 what this 21% + + + align:start position:0% +dramatically in 80 to 84 what this 21% +is if you just size the system to meet + + align:start position:0% +is if you just size the system to meet + + + align:start position:0% +is if you just size the system to meet +peak demand exactly 21% of your capacity + + align:start position:0% +peak demand exactly 21% of your capacity + + + align:start position:0% +peak demand exactly 21% of your capacity +would be used fewer than a thousand of + + align:start position:0% +would be used fewer than a thousand of + + + align:start position:0% +would be used fewer than a thousand of +the 8760 hours in the year that's a lot + + align:start position:0% +the 8760 hours in the year that's a lot + + + align:start position:0% +the 8760 hours in the year that's a lot +of idle + + align:start position:0% +of idle + + + align:start position:0% +of idle +capital but it gets worse 2005 to 2009 + + align:start position:0% +capital but it gets worse 2005 to 2009 + + + align:start position:0% +capital but it gets worse 2005 to 2009 +that curve is peakier technical term uh + + align:start position:0% +that curve is peakier technical term uh + + + align:start position:0% +that curve is peakier technical term uh +it has a sharper peak and over a third + + align:start position:0% +it has a sharper peak and over a third + + + align:start position:0% +it has a sharper peak and over a third +of your + + align:start position:0% +of your + + + align:start position:0% +of your +capacity was used only a thousand hours + + align:start position:0% +capacity was used only a thousand hours + + + align:start position:0% +capacity was used only a thousand hours +a less than a thousand hours a + + align:start position:0% +a less than a thousand hours a + + + align:start position:0% +a less than a thousand hours a +year so why + + align:start position:0% +year so why + + + align:start position:0% +year so why +well the data are what the data are + + align:start position:0% +well the data are what the data are + + + align:start position:0% +well the data are what the data are +there are two explanations that people + + align:start position:0% +there are two explanations that people + + + align:start position:0% +there are two explanations that people +have the first is air + + align:start position:0% +have the first is air + + + align:start position:0% +have the first is air +conditioning because more more central + + align:start position:0% +conditioning because more more central + + + align:start position:0% +conditioning because more more central +air conditioning in particular means + + align:start position:0% +air conditioning in particular means + + + align:start position:0% +air conditioning in particular means +more load on hot summer days and hot + + align:start position:0% +more load on hot summer days and hot + + + align:start position:0% +more load on hot summer days and hot +summer days are the system peaks so more + + align:start position:0% +summer days are the system peaks so more + + + align:start position:0% +summer days are the system peaks so more +more air conditioning you know every + + align:start position:0% +more air conditioning you know every + + + align:start position:0% +more air conditioning you know every +every unit in the state is on at these + + align:start position:0% +every unit in the state is on at these + + + align:start position:0% +every unit in the state is on at these +peak times and there are more units in + + align:start position:0% +peak times and there are more units in + + + align:start position:0% +peak times and there are more units in +the + + align:start position:0% +the + + + align:start position:0% +the +state um the other is that it's + + align:start position:0% +state um the other is that it's + + + align:start position:0% +state um the other is that it's +interesting if you look at the numbers + + align:start position:0% +interesting if you look at the numbers + + + align:start position:0% +interesting if you look at the numbers +in the 50s industrial load was about + + align:start position:0% +in the 50s industrial load was about + + + align:start position:0% +in the 50s industrial load was about +half of electricity usage about half and + + align:start position:0% +half of electricity usage about half and + + + align:start position:0% +half of electricity usage about half and +that tends not to be seasonal and it + + align:start position:0% +that tends not to be seasonal and it + + + align:start position:0% +that tends not to be seasonal and it +also tends to run at night a lot it's + + align:start position:0% +also tends to run at night a lot it's + + + align:start position:0% +also tends to run at night a lot it's +now down to about 28% + + align:start position:0% +now down to about 28% + + + align:start position:0% +now down to about 28% +nationally so you know if it if it if + + align:start position:0% +nationally so you know if it if it if + + + align:start position:0% +nationally so you know if it if it if +it's all industrial load that runs 24 + + align:start position:0% +it's all industrial load that runs 24 + + + align:start position:0% +it's all industrial load that runs 24 +hours a day this thing is flat + + align:start position:0% +hours a day this thing is flat + + + align:start position:0% +hours a day this thing is flat +but as you get less of that this back + + align:start position:0% +but as you get less of that this back + + + align:start position:0% +but as you get less of that this back +end falls off and the top end goes uh + + align:start position:0% +end falls off and the top end goes uh + + + align:start position:0% +end falls off and the top end goes uh +comparatively higher now you know + + align:start position:0% +comparatively higher now you know + + + align:start position:0% +comparatively higher now you know +everybody's got an air conditioner but + + align:start position:0% +everybody's got an air conditioner but + + + align:start position:0% +everybody's got an air conditioner but +what happens when you have an + + align:start position:0% +what happens when you have an + + + align:start position:0% +what happens when you have an +appreciable number of electric + + align:start position:0% +appreciable number of electric + + + align:start position:0% +appreciable number of electric +vehicles and everybody comes home from + + align:start position:0% +vehicles and everybody comes home from + + + align:start position:0% +vehicles and everybody comes home from +work and plugs them in so plug-in + + align:start position:0% +work and plugs them in so plug-in + + + align:start position:0% +work and plugs them in so plug-in +electric charged at sort of high + + align:start position:0% +electric charged at sort of high + + + align:start position:0% +electric charged at sort of high +capacity is a house + + align:start position:0% +capacity is a house + + + align:start position:0% +capacity is a house +i mean it it's comparable in terms of in + + align:start position:0% +i mean it it's comparable in terms of in + + + align:start position:0% +i mean it it's comparable in terms of in +terms of load + + align:start position:0% +terms of load + + + align:start position:0% +terms of load +uh so electric vehicles in areas where + + align:start position:0% +uh so electric vehicles in areas where + + + align:start position:0% +uh so electric vehicles in areas where +they h where they penetrate have the + + align:start position:0% +they h where they penetrate have the + + + align:start position:0% +they h where they penetrate have the +ability to make this problem a lot worse + + align:start position:0% +ability to make this problem a lot worse + + + align:start position:0% +ability to make this problem a lot worse +and the reason it's a problem is you got + + align:start position:0% +and the reason it's a problem is you got + + + align:start position:0% +and the reason it's a problem is you got +to pay for all that + + align:start position:0% +to pay for all that + + + align:start position:0% +to pay for all that +capacity that's capital sitting there + + align:start position:0% +capacity that's capital sitting there + + + align:start position:0% +capacity that's capital sitting there +that has to get paid for so rates go up + + align:start position:0% +that has to get paid for so rates go up + + + align:start position:0% +that has to get paid for so rates go up +so electric vehicles could have a + + align:start position:0% +so electric vehicles could have a + + + align:start position:0% +so electric vehicles could have a +disproportionate impact if they spread + + align:start position:0% +disproportionate impact if they spread + + + align:start position:0% +disproportionate impact if they spread +on + + align:start position:0% +on + + + align:start position:0% +on +rates i I personally don't think they're + + align:start position:0% +rates i I personally don't think they're + + + align:start position:0% +rates i I personally don't think they're +going to spread that much they're going + + align:start position:0% +going to spread that much they're going + + + align:start position:0% +going to spread that much they're going +to have great penetration by 2030 i'd + + align:start position:0% +to have great penetration by 2030 i'd + + + align:start position:0% +to have great penetration by 2030 i'd +love to be wrong uh but in some + + align:start position:0% +love to be wrong uh but in some + + + align:start position:0% +love to be wrong uh but in some +areas Southern California they expect us + + align:start position:0% +areas Southern California they expect us + + + align:start position:0% +areas Southern California they expect us +probably Cambridge i mean who knows but + + align:start position:0% +probably Cambridge i mean who knows but + + + align:start position:0% +probably Cambridge i mean who knows but +well except for batteries in cold + + align:start position:0% +well except for batteries in cold + + + align:start position:0% +well except for batteries in cold +weather but but but um Southern + + align:start position:0% +weather but but but um Southern + + + align:start position:0% +weather but but but um Southern +California + + align:start position:0% +California + + + align:start position:0% +California +Edison monitors automobile purchases in + + align:start position:0% +Edison monitors automobile purchases in + + + align:start position:0% +Edison monitors automobile purchases in +Beverly Hills and Brentwood and various + + align:start position:0% +Beverly Hills and Brentwood and various + + + align:start position:0% +Beverly Hills and Brentwood and various +other rich areas in Southern California + + align:start position:0% +other rich areas in Southern California + + + align:start position:0% +other rich areas in Southern California +in PaloAlto I'm told you can see parades + + align:start position:0% +in PaloAlto I'm told you can see parades + + + align:start position:0% +in PaloAlto I'm told you can see parades +of Teslas every so often um so um there + + align:start position:0% +of Teslas every so often um so um there + + + align:start position:0% +of Teslas every so often um so um there +are some areas that will have uh a lot + + align:start position:0% +are some areas that will have uh a lot + + + align:start position:0% +are some areas that will have uh a lot +of electric vehicles and the obvious + + align:start position:0% +of electric vehicles and the obvious + + + align:start position:0% +of electric vehicles and the obvious +thing to do is if you take it to work + + align:start position:0% +thing to do is if you take it to work + + + align:start position:0% +thing to do is if you take it to work +you plug it in when you come home and + + align:start position:0% +you plug it in when you come home and + + + align:start position:0% +you plug it in when you come home and +that's exactly when the system peaks + + align:start position:0% +that's exactly when the system peaks + + + align:start position:0% +that's exactly when the system peaks +that's exactly when the system peaks so + + align:start position:0% +that's exactly when the system peaks so + + + align:start position:0% +that's exactly when the system peaks so +it could make this worse so if you can + + align:start position:0% +it could make this worse so if you can + + + align:start position:0% +it could make this worse so if you can +move loads off peak move charging to the + + align:start position:0% +move loads off peak move charging to the + + + align:start position:0% +move loads off peak move charging to the +middle of the night + + align:start position:0% +middle of the night + + + align:start position:0% +middle of the night +um have people dry their clothes at + + align:start position:0% +um have people dry their clothes at + + + align:start position:0% +um have people dry their clothes at +night + + align:start position:0% +night + + + align:start position:0% +night +um uh run the air conditioner as I'm + + align:start position:0% +um uh run the air conditioner as I'm + + + align:start position:0% +um uh run the air conditioner as I'm +told Walmart does really hard at 5 and + + align:start position:0% +told Walmart does really hard at 5 and + + + align:start position:0% +told Walmart does really hard at 5 and +6:00 in the morning and then back it off + + align:start position:0% +6:00 in the morning and then back it off + + + align:start position:0% +6:00 in the morning and then back it off +during the day and run it hard at noon + + align:start position:0% +during the day and run it hard at noon + + + align:start position:0% +during the day and run it hard at noon +and back it off in the afternoon um uh + + align:start position:0% +and back it off in the afternoon um uh + + + align:start position:0% +and back it off in the afternoon um uh +you could flatten the + + align:start position:0% +you could flatten the + + + align:start position:0% +you could flatten the +curve but and there are programs in + + align:start position:0% +curve but and there are programs in + + + align:start position:0% +curve but and there are programs in +which demand demand responds to peak + + align:start position:0% +which demand demand responds to peak + + + align:start position:0% +which demand demand responds to peak +conditions there's something like 2 + + align:start position:0% +conditions there's something like 2 + + + align:start position:0% +conditions there's something like 2 +million air conditioners in Florida that + + align:start position:0% +million air conditioners in Florida that + + + align:start position:0% +million air conditioners in Florida that +are centrally + + align:start position:0% +are centrally + + + align:start position:0% +are centrally +controlled and the utilities are allowed + + align:start position:0% +controlled and the utilities are allowed + + + align:start position:0% +controlled and the utilities are allowed +to basically turn them well turn them up + + align:start position:0% +to basically turn them well turn them up + + + align:start position:0% +to basically turn them well turn them up +in terms of + + align:start position:0% +in terms of + + + align:start position:0% +in terms of +temperature in system emergencies + + align:start position:0% +temperature in system emergencies + + + align:start position:0% +temperature in system emergencies +or system stress periods not every + + align:start position:0% +or system stress periods not every + + + align:start position:0% +or system stress periods not every +day but in principle right pricing can + + align:start position:0% +day but in principle right pricing can + + + align:start position:0% +day but in principle right pricing can +can take care of this if you can make + + align:start position:0% +can take care of this if you can make + + + align:start position:0% +can take care of this if you can make +this electricity really expensive in + + align:start position:0% +this electricity really expensive in + + + align:start position:0% +this electricity really expensive in +those hours you bring that peak down use + + align:start position:0% +those hours you bring that peak down use + + + align:start position:0% +those hours you bring that peak down use +capacity more more effectively + + align:start position:0% +capacity more more effectively + + + align:start position:0% +capacity more more effectively +um deal with electric vehicles i mean + + align:start position:0% +um deal with electric vehicles i mean + + + align:start position:0% +um deal with electric vehicles i mean +some people have said + + align:start position:0% +some people have said + + + align:start position:0% +some people have said +well you really shouldn't allow people + + align:start position:0% +well you really shouldn't allow people + + + align:start position:0% +well you really shouldn't allow people +to charge their electric vehicles at 5 + + align:start position:0% +to charge their electric vehicles at 5 + + + align:start position:0% +to charge their electric vehicles at 5 +in the afternoon + + align:start position:0% +in the afternoon + + + align:start position:0% +in the afternoon +that is not politically possible can you + + align:start position:0% +that is not politically possible can you + + + align:start position:0% +that is not politically possible can you +imagine being told you can't refuel your + + align:start position:0% +imagine being told you can't refuel your + + + align:start position:0% +imagine being told you can't refuel your +vehicle and go out in the evening no + + align:start position:0% +vehicle and go out in the evening no + + + align:start position:0% +vehicle and go out in the evening no +that's not going to happen if you can't + + align:start position:0% +that's not going to happen if you can't + + + align:start position:0% +that's not going to happen if you can't +make it a rule then maybe you have to + + align:start position:0% +make it a rule then maybe you have to + + + align:start position:0% +make it a rule then maybe you have to +make it expensive well how do you make + + align:start position:0% +make it expensive well how do you make + + + align:start position:0% +make it expensive well how do you make +it expensive well you use price the + + align:start position:0% +it expensive well you use price the + + + align:start position:0% +it expensive well you use price the +technology is out there you just have to + + align:start position:0% +technology is out there you just have to + + + align:start position:0% +technology is out there you just have to +do it so we think this is actually + + align:start position:0% +do it so we think this is actually + + + align:start position:0% +do it so we think this is actually +important we also think this is going to + + align:start position:0% +important we also think this is going to + + + align:start position:0% +important we also think this is going to +happen + + align:start position:0% +happen + + + align:start position:0% +happen +um but there has to be some way to make + + align:start position:0% +um but there has to be some way to make + + + align:start position:0% +um but there has to be some way to make +it easy for + + align:start position:0% +it easy for + + + align:start position:0% +it easy for +households you know the Department of + + align:start position:0% +households you know the Department of + + + align:start position:0% +households you know the Department of +Energy some few years ago put out a + + align:start position:0% +Energy some few years ago put out a + + + align:start position:0% +Energy some few years ago put out a +brochure in which it talked about new + + align:start position:0% +brochure in which it talked about new + + + align:start position:0% +brochure in which it talked about new +technology will let every household be + + align:start position:0% +technology will let every household be + + + align:start position:0% +technology will let every household be +an active participant in the electricity + + align:start position:0% +an active participant in the electricity + + + align:start position:0% +an active participant in the electricity +market electricity is about 2% of the + + align:start position:0% +market electricity is about 2% of the + + + align:start position:0% +market electricity is about 2% of the +average household budget milk is + + align:start position:0% +average household budget milk is + + + align:start position:0% +average household budget milk is +probably more important the notion that + + align:start position:0% +probably more important the notion that + + + align:start position:0% +probably more important the notion that +people actually want to sit around and + + align:start position:0% +people actually want to sit around and + + + align:start position:0% +people actually want to sit around and +look at electricity prices all day + + align:start position:0% +look at electricity prices all day + + + align:start position:0% +look at electricity prices all day +that's nutty um but you got to if you + + align:start position:0% +that's nutty um but you got to if you + + + align:start position:0% +that's nutty um but you got to if you +want to have them respond they have to + + align:start position:0% +want to have them respond they have to + + + align:start position:0% +want to have them respond they have to +be able to automate the response and + + align:start position:0% +be able to automate the response and + + + align:start position:0% +be able to automate the response and +that technology is just a lot of people + + align:start position:0% +that technology is just a lot of people + + + align:start position:0% +that technology is just a lot of people +playing in it but it's it's not it's not + + align:start position:0% +playing in it but it's it's not it's not + + + align:start position:0% +playing in it but it's it's not it's not +there yet people like Cisco drool at + + align:start position:0% +there yet people like Cisco drool at + + + align:start position:0% +there yet people like Cisco drool at +this as you can imagine cisco has hired + + align:start position:0% +this as you can imagine cisco has hired + + + align:start position:0% +this as you can imagine cisco has hired +people from electric utilities cisco is + + align:start position:0% +people from electric utilities cisco is + + + align:start position:0% +people from electric utilities cisco is +talking to appliance makers cisco sees + + align:start position:0% +talking to appliance makers cisco sees + + + align:start position:0% +talking to appliance makers cisco sees +this as a future um but we're not there + + align:start position:0% +this as a future um but we're not there + + + align:start position:0% +this as a future um but we're not there +yet uh as I say there are a lot of these + + align:start position:0% +yet uh as I say there are a lot of these + + + align:start position:0% +yet uh as I say there are a lot of these +meters out your tax dollars have paid + + align:start position:0% +meters out your tax dollars have paid + + + align:start position:0% +meters out your tax dollars have paid +for millions of meters that are going + + align:start position:0% +for millions of meters that are going + + + align:start position:0% +for millions of meters that are going +slowly insane not using their + + align:start position:0% +slowly insane not using their + + + align:start position:0% +slowly insane not using their +intelligence so we actually think that + + align:start position:0% +intelligence so we actually think that + + + align:start position:0% +intelligence so we actually think that +it's pretty + + align:start position:0% +it's pretty + + + align:start position:0% +it's pretty +important to begin running sensible + + align:start position:0% +important to begin running sensible + + + align:start position:0% +important to begin running sensible +experiments and sharing data so that we + + align:start position:0% +experiments and sharing data so that we + + + align:start position:0% +experiments and sharing data so that we +can actually deal with this issue using + + align:start position:0% +can actually deal with this issue using + + + align:start position:0% +can actually deal with this issue using +the technology we have + + align:start position:0% +the technology we have + + + align:start position:0% +the technology we have +um questions + + align:start position:0% +um questions + + + align:start position:0% +um questions +here okay let me talk about distributed + + align:start position:0% +here okay let me talk about distributed + + + align:start position:0% +here okay let me talk about distributed +generation this is this is a pure + + align:start position:0% +generation this is this is a pure + + + align:start position:0% +generation this is this is a pure +economic issue and if you think about it + + align:start position:0% +economic issue and if you think about it + + + align:start position:0% +economic issue and if you think about it +for a little while it's a really easy + + align:start position:0% +for a little while it's a really easy + + + align:start position:0% +for a little while it's a really easy +economic issue but it's politically + + align:start position:0% +economic issue but it's politically + + + align:start position:0% +economic issue but it's politically +impossible + + align:start position:0% +impossible + + + align:start position:0% +impossible +so there are + + align:start position:0% +so there are + + + align:start position:0% +so there are +subsidies for distributed + + align:start position:0% +subsidies for distributed + + + align:start position:0% +subsidies for distributed +generation rooftop solar california + + align:start position:0% +generation rooftop solar california + + + align:start position:0% +generation rooftop solar california +talks about a million solar roofs + + align:start position:0% +talks about a million solar roofs + + + align:start position:0% +talks about a million solar roofs +everybody loves it um except of course + + align:start position:0% +everybody loves it um except of course + + + align:start position:0% +everybody loves it um except of course +the utilities and the utilities don't + + align:start position:0% +the utilities and the utilities don't + + + align:start position:0% +the utilities and the utilities don't +like it for the two reasons one reason + + align:start position:0% +like it for the two reasons one reason + + + align:start position:0% +like it for the two reasons one reason +is the grid isn't designed to have power + + align:start position:0% +is the grid isn't designed to have power + + + align:start position:0% +is the grid isn't designed to have power +generated out on the + + align:start position:0% +generated out on the + + + align:start position:0% +generated out on the +edge particularly the distribution + + align:start position:0% +edge particularly the distribution + + + align:start position:0% +edge particularly the distribution +system the simplest example is + + align:start position:0% +system the simplest example is + + + align:start position:0% +system the simplest example is +this suppose the utility needs to work + + align:start position:0% +this suppose the utility needs to work + + + align:start position:0% +this suppose the utility needs to work +on a power line + + align:start position:0% +on a power line + + + align:start position:0% +on a power line +um connecting to your house what do they + + align:start position:0% +um connecting to your house what do they + + + align:start position:0% +um connecting to your house what do they +do now they go to the substation that + + align:start position:0% +do now they go to the substation that + + + align:start position:0% +do now they go to the substation that +feeds your house and they turn off that + + align:start position:0% +feeds your house and they turn off that + + + align:start position:0% +feeds your house and they turn off that +circuit okay suppose every house in your + + align:start position:0% +circuit okay suppose every house in your + + + align:start position:0% +circuit okay suppose every house in your +neighborhood has a solar roof generating + + align:start position:0% +neighborhood has a solar roof generating + + + align:start position:0% +neighborhood has a solar roof generating +power + + align:start position:0% +power + + + align:start position:0% +power +well without those roofs you turn off + + align:start position:0% +well without those roofs you turn off + + + align:start position:0% +well without those roofs you turn off +the substation the linemen can go work + + align:start position:0% +the substation the linemen can go work + + + align:start position:0% +the substation the linemen can go work +on the line it's safe the line's + + align:start position:0% +on the line it's safe the line's + + + align:start position:0% +on the line it's safe the line's +dead if everybody's got a generator you + + align:start position:0% +dead if everybody's got a generator you + + + align:start position:0% +dead if everybody's got a generator you +have to make sure they're all + + align:start position:0% +have to make sure they're all + + + align:start position:0% +have to make sure they're all +disconnected and as a former dean of + + align:start position:0% +disconnected and as a former dean of + + + align:start position:0% +disconnected and as a former dean of +engineering said let's say let's say + + align:start position:0% +engineering said let's say let's say + + + align:start position:0% +engineering said let's say let's say +there are 200 of them on the line what's + + align:start position:0% +there are 200 of them on the line what's + + + align:start position:0% +there are 200 of them on the line what's +the probability that all of them + + align:start position:0% +the probability that all of them + + + align:start position:0% +the probability that all of them +disconnect properly oo that's zero uh + + align:start position:0% +disconnect properly oo that's zero uh + + + align:start position:0% +disconnect properly oo that's zero uh +close to it + + align:start position:0% +close to it + + + align:start position:0% +close to it +so that's an issue that's troublesome + + align:start position:0% +so that's an issue that's troublesome + + + align:start position:0% +so that's an issue that's troublesome +not impossible there are standards being + + align:start position:0% +not impossible there are standards being + + + align:start position:0% +not impossible there are standards being +developed there are technologies being + + align:start position:0% +developed there are technologies being + + + align:start position:0% +developed there are technologies being +developed that requires + + align:start position:0% +developed that requires + + + align:start position:0% +developed that requires +investment the policy problem is + + align:start position:0% +investment the policy problem is + + + align:start position:0% +investment the policy problem is +trickier shouldn't be but it is so it + + align:start position:0% +trickier shouldn't be but it is so it + + + align:start position:0% +trickier shouldn't be but it is so it +goes like this um I get an electric bill + + align:start position:0% +goes like this um I get an electric bill + + + align:start position:0% +goes like this um I get an electric bill +from NSAR the electric bill has two + + align:start position:0% +from NSAR the electric bill has two + + + align:start position:0% +from NSAR the electric bill has two +components + + align:start position:0% +components + + + align:start position:0% +components +my kilowatt hour consumption times an + + align:start position:0% +my kilowatt hour consumption times an + + + align:start position:0% +my kilowatt hour consumption times an +energy charge which is roughly what they + + align:start position:0% +energy charge which is roughly what they + + + align:start position:0% +energy charge which is roughly what they +pay for electricity on the + + align:start position:0% +pay for electricity on the + + + align:start position:0% +pay for electricity on the +market and the kilowatt hours I consume + + align:start position:0% +market and the kilowatt hours I consume + + + align:start position:0% +market and the kilowatt hours I consume +times a capacity charge what's + + align:start position:0% +times a capacity charge what's + + + align:start position:0% +times a capacity charge what's +that well that's the way they recover + + align:start position:0% +that well that's the way they recover + + + align:start position:0% +that well that's the way they recover +the fixed cost of the wires + + align:start position:0% + + + + align:start position:0% + +so if I put a solar roof + + align:start position:0% +so if I put a solar roof + + + align:start position:0% +so if I put a solar roof +on I save the energy charge which the + + align:start position:0% +on I save the energy charge which the + + + align:start position:0% +on I save the energy charge which the +utility also saves and I save the + + align:start position:0% +utility also saves and I save the + + + align:start position:0% +utility also saves and I save the +capacity charge which they don't + + align:start position:0% +capacity charge which they don't + + + align:start position:0% +capacity charge which they don't +save so on the one hand there's an extra + + align:start position:0% +save so on the one hand there's an extra + + + align:start position:0% +save so on the one hand there's an extra +subsidy + + align:start position:0% +subsidy + + + align:start position:0% +subsidy +there right in addition to whatever + + align:start position:0% +there right in addition to whatever + + + align:start position:0% +there right in addition to whatever +other subsidies I get for putting a + + align:start position:0% +other subsidies I get for putting a + + + align:start position:0% +other subsidies I get for putting a +solar roof on there's an extra subsidy i + + align:start position:0% +solar roof on there's an extra subsidy i + + + align:start position:0% +solar roof on there's an extra subsidy i +get this this elucory extra reduction in + + align:start position:0% +get this this elucory extra reduction in + + + align:start position:0% +get this this elucory extra reduction in +my electric bill doesn't correspond to + + align:start position:0% +my electric bill doesn't correspond to + + + align:start position:0% +my electric bill doesn't correspond to +anybody's cost reductions the costs are + + align:start position:0% +anybody's cost reductions the costs are + + + align:start position:0% +anybody's cost reductions the costs are +still there the wires are still there + + align:start position:0% +still there the wires are still there + + + align:start position:0% +still there the wires are still there +but I get a cut okay that gives me an + + align:start position:0% +but I get a cut okay that gives me an + + + align:start position:0% +but I get a cut okay that gives me an +extra incentive to install a solar roof + + align:start position:0% +extra incentive to install a solar roof + + + align:start position:0% +extra incentive to install a solar roof +what about the + + align:start position:0% +what about the + + + align:start position:0% +what about the +utility well it gives the utility every + + align:start position:0% +utility well it gives the utility every + + + align:start position:0% +utility well it gives the utility every +incentive to make it hard for me to + + align:start position:0% +incentive to make it hard for me to + + + align:start position:0% +incentive to make it hard for me to +install a solar roof it's money out of + + align:start position:0% +install a solar roof it's money out of + + + align:start position:0% +install a solar roof it's money out of +their pocket + + align:start position:0% +their pocket + + + align:start position:0% +their pocket +it's money they don't get to cover the + + align:start position:0% +it's money they don't get to cover the + + + align:start position:0% +it's money they don't get to cover the +fixed cost of the + + align:start position:0% +fixed cost of the + + + align:start position:0% +fixed cost of the +wires so I have a strong incentive a + + align:start position:0% +wires so I have a strong incentive a + + + align:start position:0% +wires so I have a strong incentive a +stronger incentive to put up a solar + + align:start position:0% +stronger incentive to put up a solar + + + align:start position:0% +stronger incentive to put up a solar +roof and they have a strong incentive to + + align:start position:0% +roof and they have a strong incentive to + + + align:start position:0% +roof and they have a strong incentive to +resist my putting up a solar roof this + + align:start position:0% +resist my putting up a solar roof this + + + align:start position:0% +resist my putting up a solar roof this +is not a great + + align:start position:0% +is not a great + + + align:start position:0% +is not a great +policy if you care about solar roofs the + + align:start position:0% +policy if you care about solar roofs the + + + align:start position:0% +policy if you care about solar roofs the +fix is is straightforward conceptually + + align:start position:0% + + + + align:start position:0% + +that there ought to be a fixed + + align:start position:0% +that there ought to be a fixed + + + align:start position:0% +that there ought to be a fixed +charge X dollars a month that doesn't + + align:start position:0% +charge X dollars a month that doesn't + + + align:start position:0% +charge X dollars a month that doesn't +change with how much electricity I + + align:start position:0% +change with how much electricity I + + + align:start position:0% +change with how much electricity I +consume and one way to convince yourself + + align:start position:0% +consume and one way to convince yourself + + + align:start position:0% +consume and one way to convince yourself +that makes sense is suppose I install + + align:start position:0% +that makes sense is suppose I install + + + align:start position:0% +that makes sense is suppose I install +not a solar roof but I install a diesel + + align:start position:0% +not a solar roof but I install a diesel + + + align:start position:0% +not a solar roof but I install a diesel +generator in my basement and the diesel + + align:start position:0% +generator in my basement and the diesel + + + align:start position:0% +generator in my basement and the diesel +generator which I I vent the exhaust + + align:start position:0% +generator which I I vent the exhaust + + + align:start position:0% +generator which I I vent the exhaust +into my neighbor's yard so it doesn't + + align:start position:0% +into my neighbor's yard so it doesn't + + + align:start position:0% +into my neighbor's yard so it doesn't +bother me so the diesel generator covers + + align:start position:0% +bother me so the diesel generator covers + + + align:start position:0% +bother me so the diesel generator covers +all of my electric needs when it runs + + align:start position:0% +all of my electric needs when it runs + + + align:start position:0% +all of my electric needs when it runs +but I still connect to the grid for + + align:start position:0% +but I still connect to the grid for + + + align:start position:0% +but I still connect to the grid for +backup now if you're only charging me + + align:start position:0% +backup now if you're only charging me + + + align:start position:0% +backup now if you're only charging me +for the kilowatt hours I consume I'm + + align:start position:0% +for the kilowatt hours I consume I'm + + + align:start position:0% +for the kilowatt hours I consume I'm +getting the backup for + + align:start position:0% +getting the backup for + + + align:start position:0% +getting the backup for +free that doesn't make + + align:start position:0% +free that doesn't make + + + align:start position:0% +free that doesn't make +sense so there ought to be a fixed + + align:start position:0% +sense so there ought to be a fixed + + + align:start position:0% +sense so there ought to be a fixed +charge it could vary with your maximum + + align:start position:0% +charge it could vary with your maximum + + + align:start position:0% +charge it could vary with your maximum +consumption it could vary with in Spain + + align:start position:0% +consumption it could vary with in Spain + + + align:start position:0% +consumption it could vary with in Spain +you contract for a certain maximum + + align:start position:0% +you contract for a certain maximum + + + align:start position:0% +you contract for a certain maximum +uh your charge varies with that if you + + align:start position:0% +uh your charge varies with that if you + + + align:start position:0% +uh your charge varies with that if you +ever exceed that maximum it cuts you off + + align:start position:0% +ever exceed that maximum it cuts you off + + + align:start position:0% +ever exceed that maximum it cuts you off +very clever system um so you know I I + + align:start position:0% +very clever system um so you know I I + + + align:start position:0% +very clever system um so you know I I +would contract for backup i'd pay for it + + align:start position:0% +would contract for backup i'd pay for it + + + align:start position:0% +would contract for backup i'd pay for it +if the generator went out I'd pay a + + align:start position:0% +if the generator went out I'd pay a + + + align:start position:0% +if the generator went out I'd pay a +charge i I' I'd pay for the power if the + + align:start position:0% +charge i I' I'd pay for the power if the + + + align:start position:0% +charge i I' I'd pay for the power if the +generator doesn't go out I still pay for + + align:start position:0% +generator doesn't go out I still pay for + + + align:start position:0% +generator doesn't go out I still pay for +my share of the wires that I have to + + align:start position:0% +my share of the wires that I have to + + + align:start position:0% +my share of the wires that I have to +have connecting now I will tell you we + + align:start position:0% +have connecting now I will tell you we + + + align:start position:0% +have connecting now I will tell you we +have made this presentation i've made + + align:start position:0% +have made this presentation i've made + + + align:start position:0% +have made this presentation i've made +this presentation others have made this + + align:start position:0% +this presentation others have made this + + + align:start position:0% +this presentation others have made this +presentation the state level the federal + + align:start position:0% +presentation the state level the federal + + + align:start position:0% +presentation the state level the federal +level utilities users everybody nods and + + align:start position:0% +level utilities users everybody nods and + + + align:start position:0% +level utilities users everybody nods and +says "Yeah of course but we can't do + + align:start position:0% +says "Yeah of course but we can't do + + + align:start position:0% +says "Yeah of course but we can't do +that how could we do that?" I'm the the + + align:start position:0% +that how could we do that?" I'm the the + + + align:start position:0% +that how could we do that?" I'm the the +usual argument is "Well it would be + + align:start position:0% +usual argument is "Well it would be + + + align:start position:0% +usual argument is "Well it would be +unfair to poor people." Well it would be + + align:start position:0% +unfair to poor people." Well it would be + + + align:start position:0% +unfair to poor people." Well it would be +unfair to poor people for everybody to + + align:start position:0% +unfair to poor people for everybody to + + + align:start position:0% +unfair to poor people for everybody to +pay the same + + align:start position:0% +pay the same + + + align:start position:0% +pay the same +charge but why would everybody pay the + + align:start position:0% +charge but why would everybody pay the + + + align:start position:0% +charge but why would everybody pay the +same charge oh but you'd then have to + + align:start position:0% +same charge oh but you'd then have to + + + align:start position:0% +same charge oh but you'd then have to +discriminate + + align:start position:0% +discriminate + + + align:start position:0% +discriminate +well shouldn't people who have used a + + align:start position:0% +well shouldn't people who have used a + + + align:start position:0% +well shouldn't people who have used a +lot of electricity and have the capacity + + align:start position:0% +lot of electricity and have the capacity + + + align:start position:0% +lot of electricity and have the capacity +to use a lot of electricity pay more + + align:start position:0% +to use a lot of electricity pay more + + + align:start position:0% +to use a lot of electricity pay more +than those who don't isn't that fair + + align:start position:0% +than those who don't isn't that fair + + + align:start position:0% +than those who don't isn't that fair +well no that's too hard so this is a + + align:start position:0% +well no that's too hard so this is a + + + align:start position:0% +well no that's too hard so this is a +this is a a recommendation that as far + + align:start position:0% +this is a a recommendation that as far + + + align:start position:0% +this is a a recommendation that as far +as we can tell has been floating around + + align:start position:0% +as we can tell has been floating around + + + align:start position:0% +as we can tell has been floating around +for 20 years and more which may or may + + align:start position:0% +for 20 years and more which may or may + + + align:start position:0% +for 20 years and more which may or may +not get adopted + + align:start position:0% +not get adopted + + + align:start position:0% +not get adopted +anywhere so finally let me do cyber + + align:start position:0% + + + + align:start position:0% + +security no clear + + align:start position:0% +security no clear + + + align:start position:0% +security no clear +authority so here's a picture from NIST + + align:start position:0% +authority so here's a picture from NIST + + + align:start position:0% +authority so here's a picture from NIST +that is sort of what the grid will look + + align:start position:0% +that is sort of what the grid will look + + + align:start position:0% +that is sort of what the grid will look +like the road map for the smart grid + + align:start position:0% +like the road map for the smart grid + + + align:start position:0% +like the road map for the smart grid +interoperability standards this is what + + align:start position:0% +interoperability standards this is what + + + align:start position:0% +interoperability standards this is what +what they're working off or a cartoon of + + align:start position:0% +what they're working off or a cartoon of + + + align:start position:0% +what they're working off or a cartoon of +what they're working off in generating + + align:start position:0% +what they're working off in generating + + + align:start position:0% +what they're working off in generating +standards and every one of those lines + + align:start position:0% +standards and every one of those lines + + + align:start position:0% +standards and every one of those lines +is a communication line they're + + align:start position:0% +is a communication line they're + + + align:start position:0% +is a communication line they're +computation in various places there's + + align:start position:0% +computation in various places there's + + + align:start position:0% +computation in various places there's +communication along those lines and you + + align:start position:0% +communication along those lines and you + + + align:start position:0% +communication along those lines and you +know some of them are thousands of + + align:start position:0% +know some of them are thousands of + + + align:start position:0% +know some of them are thousands of +pieces of equipment some of them down + + align:start position:0% +pieces of equipment some of them down + + + align:start position:0% +pieces of equipment some of them down +here in households are millions of + + align:start position:0% +here in households are millions of + + + align:start position:0% +here in households are millions of +pieces of equipment they all have to + + align:start position:0% +pieces of equipment they all have to + + + align:start position:0% +pieces of equipment they all have to +interoperate they all + + align:start position:0% +interoperate they all + + + align:start position:0% +interoperate they all +talk the standard setting problem is + + align:start position:0% +talk the standard setting problem is + + + align:start position:0% +talk the standard setting problem is +hard enough but the fact + + align:start position:0% +hard enough but the fact + + + align:start position:0% +hard enough but the fact +is they're all talking that means there + + align:start position:0% +is they're all talking that means there + + + align:start position:0% +is they're all talking that means there +all these channels that can be hacked + + align:start position:0% +all these channels that can be hacked + + + align:start position:0% +all these channels that can be hacked +can have failures can be sabotaged + + align:start position:0% +can have failures can be sabotaged + + + align:start position:0% +can have failures can be sabotaged +there was a great demonstration a couple + + align:start position:0% +there was a great demonstration a couple + + + align:start position:0% +there was a great demonstration a couple +of years ago + + align:start position:0% +of years ago + + + align:start position:0% +of years ago +um done for for purposes of a video uh a + + align:start position:0% +um done for for purposes of a video uh a + + + align:start position:0% +um done for for purposes of a video uh a +small + + align:start position:0% +small + + + align:start position:0% +small +turbine oh that is a diesel a small + + align:start position:0% +turbine oh that is a diesel a small + + + align:start position:0% +turbine oh that is a diesel a small +diesel generator was run and um they + + align:start position:0% +diesel generator was run and um they + + + align:start position:0% +diesel generator was run and um they +purposely hacked the control + + align:start position:0% +purposely hacked the control + + + align:start position:0% +purposely hacked the control +system and caused the generator to + + align:start position:0% +system and caused the generator to + + + align:start position:0% +system and caused the generator to +connect to the grid out of phase the + + align:start position:0% +connect to the grid out of phase the + + + align:start position:0% +connect to the grid out of phase the +generator blew up now that's a hack that + + align:start position:0% +generator blew up now that's a hack that + + + align:start position:0% +generator blew up now that's a hack that +can take you take out a large piece of + + align:start position:0% +can take you take out a large piece of + + + align:start position:0% +can take you take out a large piece of +equipment and that's not like + + align:start position:0% +equipment and that's not like + + + align:start position:0% +equipment and that's not like +days that could be months to fix or + + align:start position:0% +days that could be months to fix or + + + align:start position:0% +days that could be months to fix or +years so it's a it's a serious issue + + align:start position:0% +years so it's a it's a serious issue + + + align:start position:0% +years so it's a it's a serious issue +um most + + align:start position:0% +um most + + + align:start position:0% +um most +people are aware of + + align:start position:0% +people are aware of + + + align:start position:0% +people are aware of +it but the response the governmental + + align:start position:0% +it but the response the governmental + + + align:start position:0% +it but the response the governmental +response is is quite fragmented at the + + align:start position:0% +response is is quite fragmented at the + + + align:start position:0% +response is is quite fragmented at the +federal level + + align:start position:0% +federal level + + + align:start position:0% +federal level +there are standards there's some + + align:start position:0% +there are standards there's some + + + align:start position:0% +there are standards there's some +compliance some regulation each state + + align:start position:0% +compliance some regulation each state + + + align:start position:0% +compliance some regulation each state +regulates cyber security in its + + align:start position:0% +regulates cyber security in its + + + align:start position:0% +regulates cyber security in its +state and I remember talking to one of + + align:start position:0% +state and I remember talking to one of + + + align:start position:0% +state and I remember talking to one of +the commissioners from Ohio and he said + + align:start position:0% +the commissioners from Ohio and he said + + + align:start position:0% +the commissioners from Ohio and he said +"Oh we have workshops we're getting all + + align:start position:0% +"Oh we have workshops we're getting all + + + align:start position:0% +"Oh we have workshops we're getting all +these guys to do standards this is + + align:start position:0% +these guys to do standards this is + + + align:start position:0% +these guys to do standards this is +fabulous." I said "What about the + + align:start position:0% +fabulous." I said "What about the + + + align:start position:0% +fabulous." I said "What about the +municipal utilities and the co-ops in + + align:start position:0% +municipal utilities and the co-ops in + + + align:start position:0% +municipal utilities and the co-ops in +Ohio?" + + align:start position:0% +Ohio?" + + + align:start position:0% +Ohio?" +"Oh well we invite them to come there's + + align:start position:0% +"Oh well we invite them to come there's + + + align:start position:0% +"Oh well we invite them to come there's +no jurisdiction + + align:start position:0% +no jurisdiction + + + align:start position:0% +no jurisdiction +they're connected to the + + align:start position:0% +they're connected to the + + + align:start position:0% +they're connected to the +grid so no development uh or + + align:start position:0% +grid so no development uh or + + + align:start position:0% +grid so no development uh or +coordination of standards for + + align:start position:0% +coordination of standards for + + + align:start position:0% +coordination of standards for +distribution systems those are regulated + + align:start position:0% +distribution systems those are regulated + + + align:start position:0% +distribution systems those are regulated +by the states or not at + + align:start position:0% +by the states or not at + + + align:start position:0% +by the states or not at +all um and nobody deals with the whole + + align:start position:0% +all um and nobody deals with the whole + + + align:start position:0% +all um and nobody deals with the whole +grid so you know it's pretty simple it's + + align:start position:0% +grid so you know it's pretty simple it's + + + align:start position:0% +grid so you know it's pretty simple it's +a simple + + align:start position:0% +a simple + + + align:start position:0% +a simple +recommendation somebody ought to be in + + align:start position:0% +recommendation somebody ought to be in + + + align:start position:0% +recommendation somebody ought to be in +charge there are people in charge of + + align:start position:0% +charge there are people in charge of + + + align:start position:0% +charge there are people in charge of +cyber sec the Department of Homeland + + align:start position:0% +cyber sec the Department of Homeland + + + align:start position:0% +cyber sec the Department of Homeland +Security has a chart that shows who's in + + align:start position:0% +Security has a chart that shows who's in + + + align:start position:0% +Security has a chart that shows who's in +charge of what and it it goes industry + + align:start position:0% +charge of what and it it goes industry + + + align:start position:0% +charge of what and it it goes industry +by industry usually a match of agencies + + align:start position:0% +by industry usually a match of agencies + + + align:start position:0% +by industry usually a match of agencies +nobody's in charge in electricity the + + align:start position:0% +nobody's in charge in electricity the + + + align:start position:0% +nobody's in charge in electricity the +latest the latest uh statement from the + + align:start position:0% +latest the latest uh statement from the + + + align:start position:0% +latest the latest uh statement from the +administration is the Department of + + align:start position:0% +administration is the Department of + + + align:start position:0% +administration is the Department of +Homeland Security and the Department of + + align:start position:0% +Homeland Security and the Department of + + + align:start position:0% +Homeland Security and the Department of +Energy will coordinate on this + + align:start position:0% +Energy will coordinate on this + + + align:start position:0% +Energy will coordinate on this +subject now you don't have to have spent + + align:start position:0% +subject now you don't have to have spent + + + align:start position:0% +subject now you don't have to have spent +too much time in organizations to + + align:start position:0% +too much time in organizations to + + + align:start position:0% +too much time in organizations to +realize that means nobody's in charge + + align:start position:0% +realize that means nobody's in charge + + + align:start position:0% +realize that means nobody's in charge +um everybody this is a recommendation + + align:start position:0% +um everybody this is a recommendation + + + align:start position:0% +um everybody this is a recommendation +that everybody agrees + + align:start position:0% +that everybody agrees + + + align:start position:0% +that everybody agrees +with but there's violent disagreement + + align:start position:0% +with but there's violent disagreement + + + align:start position:0% +with but there's violent disagreement +over who gets + + align:start position:0% +over who gets + + + align:start position:0% +over who gets +it the administration has said it ought + + align:start position:0% +it the administration has said it ought + + + align:start position:0% +it the administration has said it ought +to be the Department of Homeland + + align:start position:0% +to be the Department of Homeland + + + align:start position:0% +to be the Department of Homeland +Security the relevant folks in Congress + + align:start position:0% +Security the relevant folks in Congress + + + align:start position:0% +Security the relevant folks in Congress +say it should be the Department of + + align:start position:0% +say it should be the Department of + + + align:start position:0% +say it should be the Department of +Energy that current compromise that says + + align:start position:0% +Energy that current compromise that says + + + align:start position:0% +Energy that current compromise that says +let them play nicely together is uh uh + + align:start position:0% +let them play nicely together is uh uh + + + align:start position:0% +let them play nicely together is uh uh +something that no one thinks no one + + align:start position:0% +something that no one thinks no one + + + align:start position:0% +something that no one thinks no one +outside the beltway thinks can possibly + + align:start position:0% +outside the beltway thinks can possibly + + + align:start position:0% +outside the beltway thinks can possibly +work so this is a look of at the future + + align:start position:0% +work so this is a look of at the future + + + align:start position:0% +work so this is a look of at the future +of the grid + + align:start position:0% +of the grid + + + align:start position:0% +of the grid +um it's it's interesting i we did this + + align:start position:0% +um it's it's interesting i we did this + + + align:start position:0% +um it's it's interesting i we did this +study for two + + align:start position:0% +study for two + + + align:start position:0% +study for two +reasons one because we got very tired of + + align:start position:0% +reasons one because we got very tired of + + + align:start position:0% +reasons one because we got very tired of +hearing that we have a third world grid + + align:start position:0% +hearing that we have a third world grid + + + align:start position:0% +hearing that we have a third world grid +and it's all broken and we're all going + + align:start position:0% +and it's all broken and we're all going + + + align:start position:0% +and it's all broken and we're all going +to die + + align:start position:0% +to die + + + align:start position:0% +to die +uh that seemed a little + + align:start position:0% +uh that seemed a little + + + align:start position:0% +uh that seemed a little +extreme and then this stuff about how + + align:start position:0% +extreme and then this stuff about how + + + align:start position:0% +extreme and then this stuff about how +smart grids are going to transform our + + align:start position:0% +smart grids are going to transform our + + + align:start position:0% +smart grids are going to transform our +lives like the internet has transformed + + align:start position:0% +lives like the internet has transformed + + + align:start position:0% +lives like the internet has transformed +our lives and we're all going to be + + align:start position:0% +our lives and we're all going to be + + + align:start position:0% +our lives and we're all going to be +active participants in the electricity + + align:start position:0% +active participants in the electricity + + + align:start position:0% +active participants in the electricity +market and that sounded even dumber uh + + align:start position:0% +market and that sounded even dumber uh + + + align:start position:0% +market and that sounded even dumber uh +we thought it might be worthwhile + + align:start position:0% +we thought it might be worthwhile + + + align:start position:0% +we thought it might be worthwhile +getting some economists and engineers to + + align:start position:0% +getting some economists and engineers to + + + align:start position:0% +getting some economists and engineers to +actually look at the grid uh the + + align:start position:0% +actually look at the grid uh the + + + align:start position:0% +actually look at the grid uh the +conclusion we have is yeah I mean you + + align:start position:0% +conclusion we have is yeah I mean you + + + align:start position:0% +conclusion we have is yeah I mean you +can there's a there's a way forward um + + align:start position:0% +can there's a there's a way forward um + + + align:start position:0% +can there's a there's a way forward um +uh we're not in crisis the they're real + + align:start position:0% +uh we're not in crisis the they're real + + + align:start position:0% +uh we're not in crisis the they're real +opportunities they're not transformative + + align:start position:0% +opportunities they're not transformative + + + align:start position:0% +opportunities they're not transformative +but they're real opportunities but there + + align:start position:0% +but they're real opportunities but there + + + align:start position:0% +but they're real opportunities but there +are problems uh we need to do + + align:start position:0% +are problems uh we need to do + + + align:start position:0% +are problems uh we need to do +relatively inexpensive R&D i mean this + + align:start position:0% +relatively inexpensive R&D i mean this + + + align:start position:0% +relatively inexpensive R&D i mean this +is software development algorithm + + align:start position:0% +is software development algorithm + + + align:start position:0% +is software development algorithm +development it's not nuclear power um we + + align:start position:0% +development it's not nuclear power um we + + + align:start position:0% +development it's not nuclear power um we +need to be smarter about citing + + align:start position:0% +need to be smarter about citing + + + align:start position:0% +need to be smarter about citing +transmission lines we need to move + + align:start position:0% +transmission lines we need to move + + + align:start position:0% +transmission lines we need to move +toward getting retail prices right um we + + align:start position:0% +toward getting retail prices right um we + + + align:start position:0% +toward getting retail prices right um we +need to deal with network costs + + align:start position:0% +need to deal with network costs + + + align:start position:0% +need to deal with network costs +appropriately and we need to deal with + + align:start position:0% +appropriately and we need to deal with + + + align:start position:0% +appropriately and we need to deal with +cyber security if that all happens you + + align:start position:0% +cyber security if that all happens you + + + align:start position:0% +cyber security if that all happens you +will live happily ever after questions + + align:start position:0% + + + + align:start position:0% + +yeah Matthew earlier in lecture you + + align:start position:0% +yeah Matthew earlier in lecture you + + + align:start position:0% +yeah Matthew earlier in lecture you +talked about how the bill for uh for the + + align:start position:0% +talked about how the bill for uh for the + + + align:start position:0% +talked about how the bill for uh for the +carbon tax mentions nothing about the + + align:start position:0% +carbon tax mentions nothing about the + + + align:start position:0% +carbon tax mentions nothing about the +environment what would happen if it said + + align:start position:0% +environment what would happen if it said + + + align:start position:0% +environment what would happen if it said +"Hey this is good for the environment + + align:start position:0% +"Hey this is good for the environment + + + align:start position:0% +"Hey this is good for the environment +too." As part of I think the + + align:start position:0% +too." As part of I think the + + + align:start position:0% +too." As part of I think the +environmental well it's not a bill yet + + align:start position:0% +environmental well it's not a bill yet + + + align:start position:0% +environmental well it's not a bill yet +uh there's no point in introducing a + + align:start position:0% +uh there's no point in introducing a + + + align:start position:0% +uh there's no point in introducing a +bill into this Congress um there will be + + align:start position:0% +bill into this Congress um there will be + + + align:start position:0% +bill into this Congress um there will be +it is expected the expectation + + align:start position:0% +it is expected the expectation + + + align:start position:0% +it is expected the expectation +is that after the + + align:start position:0% +is that after the + + + align:start position:0% +is that after the +election when there's some hope of + + align:start position:0% +election when there's some hope of + + + align:start position:0% +election when there's some hope of +people actually working together for a + + align:start position:0% +people actually working together for a + + + align:start position:0% +people actually working together for a +short window that proposals for a carbon + + align:start position:0% +short window that proposals for a carbon + + + align:start position:0% +short window that proposals for a carbon +tax are going to come leaping out of the + + align:start position:0% +tax are going to come leaping out of the + + + align:start position:0% +tax are going to come leaping out of the +closet and those proposals will talk + + align:start position:0% +closet and those proposals will talk + + + align:start position:0% +closet and those proposals will talk +about + + align:start position:0% +about + + + align:start position:0% +about +revenue and the environmentalists will + + align:start position:0% +revenue and the environmentalists will + + + align:start position:0% +revenue and the environmentalists will +be relatively quiet + + align:start position:0% +be relatively quiet + + + align:start position:0% +be relatively quiet +because if the environmentalists talk + + align:start position:0% +because if the environmentalists talk + + + align:start position:0% +because if the environmentalists talk +about climate the Republicans who have + + align:start position:0% +about climate the Republicans who have + + + align:start position:0% +about climate the Republicans who have +said there is no such thing as climate + + align:start position:0% +said there is no such thing as climate + + + align:start position:0% +said there is no such thing as climate +will be backed into a + + align:start position:0% +will be backed into a + + + align:start position:0% +will be backed into a +corner even though you know some of them + + align:start position:0% +corner even though you know some of them + + + align:start position:0% +corner even though you know some of them +have had to deny climate + + align:start position:0% +have had to deny climate + + + align:start position:0% +have had to deny climate +change to be in line with the leadership + + align:start position:0% +change to be in line with the leadership + + + align:start position:0% +change to be in line with the leadership +even though they actually are capable of + + align:start position:0% +even though they actually are capable of + + + align:start position:0% +even though they actually are capable of +words of more than one syllable so um + + align:start position:0% +words of more than one syllable so um + + + align:start position:0% +words of more than one syllable so um +some of those folks would be pushed to + + align:start position:0% +some of those folks would be pushed to + + + align:start position:0% +some of those folks would be pushed to +opposition if you don't mention climate + + align:start position:0% +opposition if you don't mention climate + + + align:start position:0% +opposition if you don't mention climate +they can quietly say "Yeah it's good for + + align:start position:0% +they can quietly say "Yeah it's good for + + + align:start position:0% +they can quietly say "Yeah it's good for +the climate." and vote for it i don't + + align:start position:0% +the climate." and vote for it i don't + + + align:start position:0% +the climate." and vote for it i don't +know if it's going to happen it's It's a + + align:start position:0% +know if it's going to happen it's It's a + + + align:start position:0% +know if it's going to happen it's It's a +cocktail party conversation but it + + align:start position:0% +cocktail party conversation but it + + + align:start position:0% +cocktail party conversation but it +appears to be a fairly serious cocktail + + align:start position:0% +appears to be a fairly serious cocktail + + + align:start position:0% +appears to be a fairly serious cocktail +party conversation anything else yeah + + align:start position:0% +party conversation anything else yeah + + + align:start position:0% +party conversation anything else yeah +what are you going to be presenting + + align:start position:0% +what are you going to be presenting + + + align:start position:0% +what are you going to be presenting +tomorrow in DC uh I'll be presenting a + + align:start position:0% +tomorrow in DC uh I'll be presenting a + + + align:start position:0% +tomorrow in DC uh I'll be presenting a +longer version of this to a + + align:start position:0% +longer version of this to a + + + align:start position:0% +longer version of this to a +uh and a + + align:start position:0% +uh and a + + + align:start position:0% +uh and a +somewhat different version but close to + + align:start position:0% +somewhat different version but close to + + + align:start position:0% +somewhat different version but close to +it to a group of uh large electricity + + align:start position:0% +it to a group of uh large electricity + + + align:start position:0% +it to a group of uh large electricity +users and I'm very interested in what + + align:start position:0% +users and I'm very interested in what + + + align:start position:0% +users and I'm very interested in what +they're going to have to say uh we've + + align:start position:0% +they're going to have to say uh we've + + + align:start position:0% +they're going to have to say uh we've +talked to state commissioners we've + + align:start position:0% +talked to state commissioners we've + + + align:start position:0% +talked to state commissioners we've +talked to the federal regulators + + align:start position:0% +talked to the federal regulators + + + align:start position:0% +talked to the federal regulators +um we've talked to congressional + + align:start position:0% +um we've talked to congressional + + + align:start position:0% +um we've talked to congressional +staff this is the first conversation + + align:start position:0% +staff this is the first conversation + + + align:start position:0% +staff this is the first conversation +I've had with consumers so I'm looking + + align:start position:0% +I've had with consumers so I'm looking + + + align:start position:0% +I've had with consumers so I'm looking +forward to it big industrials + + align:start position:0% +forward to it big industrials + + + align:start position:0% +forward to it big industrials +the problem with cyber security that + + align:start position:0% +the problem with cyber security that + + + align:start position:0% +the problem with cyber security that +nobody wants to deal with it or + + align:start position:0% +nobody wants to deal with it or + + + align:start position:0% +nobody wants to deal with it or +everybody wants everybody wants to deal + + align:start position:0% +everybody wants everybody wants to deal + + + align:start position:0% +everybody wants everybody wants to deal +with it yeah + + align:start position:0% +with it yeah + + + align:start position:0% +with it yeah +um you um you know the problem is that + + align:start position:0% +um you um you know the problem is that + + + align:start position:0% +um you um you know the problem is that +the Department of Homeland Security has + + align:start position:0% +the Department of Homeland Security has + + + align:start position:0% +the Department of Homeland Security has +no expertise in power systems and the + + align:start position:0% +no expertise in power systems and the + + + align:start position:0% +no expertise in power systems and the +Department of Energy has no expertise in + + align:start position:0% +Department of Energy has no expertise in + + + align:start position:0% +Department of Energy has no expertise in +cyber security so so whoever gets it has + + align:start position:0% +cyber security so so whoever gets it has + + + align:start position:0% +cyber security so so whoever gets it has +to staff up well staffing up is fun uh + + align:start position:0% +to staff up well staffing up is fun uh + + + align:start position:0% +to staff up well staffing up is fun uh +you add you add headcounts you add + + align:start position:0% +you add you add headcounts you add + + + align:start position:0% +you add you add headcounts you add +people you add payroll you add prestige + + align:start position:0% +people you add payroll you add prestige + + + align:start position:0% +people you add payroll you add prestige +so whoever does it gets to staff up uh + + align:start position:0% +so whoever does it gets to staff up uh + + + align:start position:0% +so whoever does it gets to staff up uh +if you split it then you've got sort of + + align:start position:0% +if you split it then you've got sort of + + + align:start position:0% +if you split it then you've got sort of +dueling staffs you know you don't + + align:start position:0% +dueling staffs you know you don't + + + align:start position:0% +dueling staffs you know you don't +understand anything about electricity oh + + align:start position:0% +understand anything about electricity oh + + + align:start position:0% +understand anything about electricity oh +yeah but you don't understand about + + align:start position:0% +yeah but you don't understand about + + + align:start position:0% +yeah but you don't understand about +security i mean come on um so that + + align:start position:0% +security i mean come on um so that + + + align:start position:0% +security i mean come on um so that +doesn't work so no everybody wants Well + + align:start position:0% +doesn't work so no everybody wants Well + + + align:start position:0% +doesn't work so no everybody wants Well +both people want it and at some point I + + align:start position:0% +both people want it and at some point I + + + align:start position:0% +both people want it and at some point I +assume one of them will be declared the + + align:start position:0% +assume one of them will be declared the + + + align:start position:0% +assume one of them will be declared the +winner but not + + align:start position:0% +winner but not + + + align:start position:0% +winner but not +soon anything + + align:start position:0% +soon anything + + + align:start position:0% +soon anything +else okay see you Wednesday \ No newline at end of file diff --git a/suHTm7R7kfQ.txt b/suHTm7R7kfQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..9ed4574885310d2ec45b016118721b4526074180 --- /dev/null +++ b/suHTm7R7kfQ.txt @@ -0,0 +1,182 @@ +In this lecture, +we'll discuss how + +analytics and, in +particular, optimization + +is used in online dating. + +Specifically, we'll discuss the +story of the company eHarmony + +that uses optimization +to maximize + +the probability of +a successful match + +between compatible adults. + +The goal of eHarmony is to +take a scientific approach + +to love and marriage and +offer it to the masses + +through an online +dating website focused + +on long term relationships. + +Indicators of +success for eHarmony + +include the fact that nearly +4% of U.S. marriages in 2012 + +are a result of eHarmony. + +Furthermore, the company +has generated, by 2009, + +over $1 billion in revenue. + +How is eHarmony different? + +Unlike other online +dating websites, + +eHarmony does not have users +browse other users' profiles. + +Instead, eHarmony uses +a compatibility score + +between two people and uses +optimization algorithms + +to determine the +user's best matches. + +How does eHarmony compute +the compatibility score? + +The score is based on +29 different dimensions + +of personality including +character, emotions, values, + +traits, etc. + +The calculation involves +a 436 questionnaire. + +The matches must +meet at least 25 + +out of 29 compatibility areas. + +The graph from eHarmony's +website shown in this slide + +describes one such question +regarding character. + +Let us discuss the +history of the company. + +The founder of the company +is Dr. Neil Clark Warren, + +a clinical psychologist who +counseled couples and began + +to see that many marriages +ended in divorce because couples + +were not initially compatible. + +Warren has written many +relationship books. + +Finding the Love of your +Life, The Triumphant Marriage, + +Learning to Live with the Love +of Your Life and Loving It, + +Finding Commitment, +and many others. + +In the late 1990s, +after more than 35 years + +of work as a clinical +psychologist and marriage + +counselor, Warren decided +to test his theory + +that certain characteristics can +predict compatibility and lead + +to more satisfying +relationships. + +After three years +of research Warren + +developed a model +of compatibility + +that is now the basis of the +company's matching system. + +The service launched its +matching service for singles + +in 2000. + +Since then, the company has +had about 33 million members, + +and as of 2008, +about 15,000 people + +take the eHarmony +questionnaire each day. + +Interested users may fill +out the compatibility quiz, + +but in order to +see matches members + +must pay a membership +fee to eHarmony. + +What is a distinguishing +characteristic of eHarmony? + +While eHarmony was not the +first online dating website + +and faced serious +competition, there + +is a key difference from +other dating websites. + +eHarmony takes a quantitative +optimization approach + +to matchmaking +rather than letting + +users browse their website. + +In this lecture, +we'll explore some + +of the analytics eHarmony uses. \ No newline at end of file diff --git a/t9zBeCrLYE4.txt b/t9zBeCrLYE4.txt new file mode 100644 index 0000000000000000000000000000000000000000..66f31cef8cb012c2560ff0b6a4bad3f3c9b77c34 --- /dev/null +++ b/t9zBeCrLYE4.txt @@ -0,0 +1,214 @@ +EMILY: He basically just +said five minute + +presentation on the topic. + +And then the day we were +doing it, he was like, + +this is very important. + +This is serious stuff. + +And we're like, oh. + +Oops. + +[MUSIC PLAYING] + +GUEST SPEAKER: Science isn't +just about doing experiments. + +The students have to learn +to talk about them too. + +Why? + +Because one day, any one +of them might win this. + +JOHN DOLHUN: You will be giving +oral presentations in + +this course. + +And they start next Friday. + +Seven of you will be +going next Friday. + +And seven of you will be going +the following week. + +So you'll be preparing a five +minute oral delivery on some + +aspect that we'll +assign to you. + +GUEST SPEAKER: Let's see how +the first group does. + +JOHN DOLHUN: Now today we're +going to go through seven of + +your presentations. + +This is serious business. + +You get scored for this. + +EMILY: My topic was solvent +choices and techniques for + +single crystal determination. + +[INTERPOSING VOICES] + +FRED: It's like a mathematical +puzzle. + +Any questions? + +JOHN DOLHUN: Could you show +us your spectrum and your + +interpretation of the peaks? + +JASON: Dr. Dolhun was very +disappointed in a lot of + +people's presentations. + +People would conclude, and then +they would ask if there + +are any questions. + +And Dr. Dolhun would be the +first one on there. + +He's like, yeah. + +And he spits out the question he +gave them in the beginning. + +JOHN DOLHUN: Your topic +was solvent choices. + +Your topic was vacuum +distillation problems. + +So can you draw a grid +on the board? + +It came out as crystals. + +How much of those solutions +did you use? + +So could you tell us some +of the problems? + +You have all those. + +Show us which solvents you +actually went through. + +EMILY: Um. + +FRED: Um. + +JASON: Um. + +DAN: Um. + +ROO-RA: Um. + +PAUL: Um. + +IKE: I'm sorry. + +I thought I was supposed +to do the NMR. + +GUEST SPEAKER: What happened? + +EMILY: Professor Dolhun didn't +tell us beforehand to focus + +more on our results from +our experiments. + +So he was disappointed. + +FRED: I wasn't too sure what +the instructions were. + +So now that I know that he +wanted us to analyze our own + +data, I definitely would have +done that a lot more. + +It was mostly improvised. + +I didn't prepare that much +because I was out with friends + +last night. + +PAUL: I did everything right. + +It just wasn't a great +presentation. + +ANTHONY: I'm glad I didn't go +today, because it was nice to + +see what he wanted. + +I guess there was +some confusion. + +But now I know exactly +what he wants. + +So I can give it to +him next week. + +PHIL: It was clear who put time +into the talk and clear + +who didn't. + +EMILY: Next week the people +going will do a lot better. + +GUEST SPEAKER: Emily's right. + +They do. + +And Dr. Dolhun is impressed. + +The students really +turned it around. + +JOHN DOLHUN: So these were +actually very, very good. + +Very well done. + +I'm very, very happy. + +JASON: I didn't do so well. + +Oh my gosh, did I +talk too fast? + +I need to take a public +speaking class next. + +JULIE: I did say that, yeah. + +[MUSIC PLAYING] \ No newline at end of file diff --git a/tTUT7YuSMoc.txt b/tTUT7YuSMoc.txt new file mode 100644 index 0000000000000000000000000000000000000000..cf11c718229afa35855b096c7075ae9d4a719d57 --- /dev/null +++ b/tTUT7YuSMoc.txt @@ -0,0 +1,6971 @@ +align:start position:0% + +this is a topic that's sometimes called + + align:start position:0% +this is a topic that's sometimes called + + + align:start position:0% +this is a topic that's sometimes called +calculus of variations that's sort of + + align:start position:0% +calculus of variations that's sort of + + + align:start position:0% +calculus of variations that's sort of +the classic name for + + align:start position:0% + + + + align:start position:0% + +it and it cookie are you causing + + align:start position:0% + + + + align:start position:0% + +trouble + + align:start position:0% +trouble + + + align:start position:0% +trouble +okay calcul variations but all it really + + align:start position:0% +okay calcul variations but all it really + + + align:start position:0% +okay calcul variations but all it really +is is the same idea of derivatives where + + align:start position:0% +is is the same idea of derivatives where + + + align:start position:0% +is is the same idea of derivatives where +uh you know so we're going to have um f + + align:start position:0% +uh you know so we're going to have um f + + + align:start position:0% +uh you know so we're going to have um f +of + + align:start position:0% +of + + + align:start position:0% +of +U uh you know plus du minus F of U + + align:start position:0% +U uh you know plus du minus F of U + + + align:start position:0% +U uh you know plus du minus F of U +that's our + + align:start position:0% +that's our + + + align:start position:0% +that's our +DF is going to be I'm going to call it + + align:start position:0% +DF is going to be I'm going to call it + + + align:start position:0% +DF is going to be I'm going to call it +FR Prime of U + + align:start position:0% +FR Prime of U + + + align:start position:0% +FR Prime of U +du right that's it's the same + + align:start position:0% +du right that's it's the same + + + align:start position:0% +du right that's it's the same +formula it's um except that + + align:start position:0% +formula it's um except that + + + align:start position:0% +formula it's um except that +now where um + + align:start position:0% +now where um + + + align:start position:0% +now where um +U is in a vector + + align:start position:0% + + + + align:start position:0% + +space of + + align:start position:0% + + + + align:start position:0% + +functions and usually F and and usually + + align:start position:0% +functions and usually F and and usually + + + align:start position:0% +functions and usually F and and usually +f is a + + align:start position:0% +f is a + + + align:start position:0% +f is a +scalar F of U is just a real number okay + + align:start position:0% +scalar F of U is just a real number okay + + + align:start position:0% +scalar F of U is just a real number okay +so we're going to take a function map it + + align:start position:0% +so we're going to take a function map it + + + align:start position:0% +so we're going to take a function map it +to real number and this is one of the + + align:start position:0% +to real number and this is one of the + + + align:start position:0% +to real number and this is one of the +things when I teach 1806 I come back to + + align:start position:0% +things when I teach 1806 I come back to + + + align:start position:0% +things when I teach 1806 I come back to +periodically that you know vectors are + + align:start position:0% +periodically that you know vectors are + + + align:start position:0% +periodically that you know vectors are +not just column vectors they even + + align:start position:0% +not just column vectors they even + + + align:start position:0% +not just column vectors they even +matrices you can even think of functions + + align:start position:0% +matrices you can even think of functions + + + align:start position:0% +matrices you can even think of functions +as as a vector because you can take two + + align:start position:0% +as as a vector because you can take two + + + align:start position:0% +as as a vector because you can take two +functions you can add them you can take + + align:start position:0% +functions you can add them you can take + + + align:start position:0% +functions you can add them you can take +two and get another function you can + + align:start position:0% +two and get another function you can + + + align:start position:0% +two and get another function you can +take two functions and multiply a + + align:start position:0% +take two functions and multiply a + + + align:start position:0% +take two functions and multiply a +function multiply by two and get another + + align:start position:0% +function multiply by two and get another + + + align:start position:0% +function multiply by two and get another +function and so a lot of the things you + + align:start position:0% +function and so a lot of the things you + + + align:start position:0% +function and so a lot of the things you +can do linear algebra for column vectors + + align:start position:0% +can do linear algebra for column vectors + + + align:start position:0% +can do linear algebra for column vectors +you can do for functions right you can + + align:start position:0% +you can do for functions right you can + + + align:start position:0% +you can do for functions right you can +talk about linear operators on functions + + align:start position:0% +talk about linear operators on functions + + + align:start position:0% +talk about linear operators on functions +like a derivative is a linear operator + + align:start position:0% +like a derivative is a linear operator + + + align:start position:0% +like a derivative is a linear operator +on function you can talk about + + align:start position:0% +on function you can talk about + + + align:start position:0% +on function you can talk about +orthogonal functions and dot products of + + align:start position:0% +orthogonal functions and dot products of + + + align:start position:0% +orthogonal functions and dot products of +functions and Graham Schmidt on + + align:start position:0% +functions and Graham Schmidt on + + + align:start position:0% +functions and Graham Schmidt on +functions and igen functions if you do + + align:start position:0% +functions and igen functions if you do + + + align:start position:0% +functions and igen functions if you do +quantum mechanics you do lots of things + + align:start position:0% +quantum mechanics you do lots of things + + + align:start position:0% +quantum mechanics you do lots of things +with Ian functions right so you know + + align:start position:0% +with Ian functions right so you know + + + align:start position:0% +with Ian functions right so you know +it's the + + align:start position:0% +it's the + + + align:start position:0% +it's the +same all the the same kind of Concepts + + align:start position:0% +same all the the same kind of Concepts + + + align:start position:0% +same all the the same kind of Concepts +you have to be a little bit careful with + + align:start position:0% +you have to be a little bit careful with + + + align:start position:0% +you have to be a little bit careful with +functions they can do crazy things that + + align:start position:0% +functions they can do crazy things that + + + align:start position:0% +functions they can do crazy things that +column vectors can't like they can + + align:start position:0% +column vectors can't like they can + + + align:start position:0% +column vectors can't like they can +oscillate infinitely fast they can blow + + align:start position:0% +oscillate infinitely fast they can blow + + + align:start position:0% +oscillate infinitely fast they can blow +up or do things like that so if you want + + align:start position:0% +up or do things like that so if you want + + + align:start position:0% +up or do things like that so if you want +to do rigorous math with functions you + + align:start position:0% +to do rigorous math with functions you + + + align:start position:0% +to do rigorous math with functions you +spend a lot of time kind of nailing down + + align:start position:0% +spend a lot of time kind of nailing down + + + align:start position:0% +spend a lot of time kind of nailing down +the space of functions that are not + + align:start position:0% +the space of functions that are not + + + align:start position:0% +the space of functions that are not +terribly behaved um I'm not I'm not + + align:start position:0% +terribly behaved um I'm not I'm not + + + align:start position:0% +terribly behaved um I'm not I'm not +going to do that I'm not I'm just going + + align:start position:0% +going to do that I'm not I'm just going + + + align:start position:0% +going to do that I'm not I'm just going +to be kind of implicitly I'm gonna write + + align:start position:0% +to be kind of implicitly I'm gonna write + + + align:start position:0% +to be kind of implicitly I'm gonna write +down an integral + + align:start position:0% +down an integral + + + align:start position:0% +down an integral +functions of a function I'm going to + + align:start position:0% +functions of a function I'm going to + + + align:start position:0% +functions of a function I'm going to +implicitly assume that we're dealing + + align:start position:0% +implicitly assume that we're dealing + + + align:start position:0% +implicitly assume that we're dealing +with functions where that integral is + + align:start position:0% +with functions where that integral is + + + align:start position:0% +with functions where that integral is +defined so you know that's things like + + align:start position:0% +defined so you know that's things like + + + align:start position:0% +defined so you know that's things like +that right so so for let me just do an + + align:start position:0% +that right so so for let me just do an + + + align:start position:0% +that right so so for let me just do an +example right so let's do um U of + + align:start position:0% +example right so let's do um U of + + + align:start position:0% +example right so let's do um U of +X is a + + align:start position:0% +X is a + + + align:start position:0% +X is a +function you know from you know 0 to one + + align:start position:0% +function you know from you know 0 to one + + + align:start position:0% +function you know from you know 0 to one +right X is in 0 to + + align:start position:0% + + + + align:start position:0% + +one to real numbers right it's just it + + align:start position:0% +one to real numbers right it's just it + + + align:start position:0% +one to real numbers right it's just it +just here's uh here's uh x = 0 x = 1 and + + align:start position:0% +just here's uh here's uh x = 0 x = 1 and + + + align:start position:0% +just here's uh here's uh x = 0 x = 1 and +U is some function right U of + + align:start position:0% + + + + align:start position:0% + +X + + align:start position:0% +X + + + align:start position:0% +X +right right and let's suppose that F of + + align:start position:0% +right right and let's suppose that F of + + + align:start position:0% +right right and let's suppose that F of +U I need to write down something that + + align:start position:0% +U I need to write down something that + + + align:start position:0% +U I need to write down something that +that takes in a function and gives me a + + align:start position:0% +that takes in a function and gives me a + + + align:start position:0% +that takes in a function and gives me a +number and there are a few ways to do + + align:start position:0% +number and there are a few ways to do + + + align:start position:0% +number and there are a few ways to do +that but the one that I want to deal + + align:start position:0% +that but the one that I want to deal + + + align:start position:0% +that but the one that I want to deal +with is uh is just + + align:start position:0% +with is uh is just + + + align:start position:0% +with is uh is just +integral 0 to 1 of say sine of U of + + align:start position:0% +integral 0 to 1 of say sine of U of + + + align:start position:0% +integral 0 to 1 of say sine of U of +X DX let's just start with right that + + align:start position:0% +X DX let's just start with right that + + + align:start position:0% +X DX let's just start with right that +takes in a function gives me a number + + align:start position:0% +takes in a function gives me a number + + + align:start position:0% +takes in a function gives me a number +technically it doesn't work for all + + align:start position:0% +technically it doesn't work for all + + + align:start position:0% +technically it doesn't work for all +functions right you could have functions + + align:start position:0% +functions right you could have functions + + + align:start position:0% +functions right you could have functions +where + + align:start position:0% +where + + + align:start position:0% +where +this where where this this integral + + align:start position:0% +this where where this this integral + + + align:start position:0% +this where where this this integral +doesn't exist or something like that so + + align:start position:0% +doesn't exist or something like that so + + + align:start position:0% +doesn't exist or something like that so +implicitly I'm limiting myself to the + + align:start position:0% +implicitly I'm limiting myself to the + + + align:start position:0% +implicitly I'm limiting myself to the +space of functions where the integrals + + align:start position:0% +space of functions where the integrals + + + align:start position:0% +space of functions where the integrals +work + + align:start position:0% +work + + + align:start position:0% +work +right and what I want to do is find out + + align:start position:0% +right and what I want to do is find out + + + align:start position:0% +right and what I want to do is find out +what is + + align:start position:0% +what is + + + align:start position:0% +what is +the what is the the gradient of f right + + align:start position:0% +the what is the the gradient of f right + + + align:start position:0% +the what is the the gradient of f right +what is and what is fed + + align:start position:0% +what is and what is fed + + + align:start position:0% +what is and what is fed +also right with respect to U of course + + align:start position:0% +also right with respect to U of course + + + align:start position:0% +also right with respect to U of course +right now with respect to a function and + + align:start position:0% +right now with respect to a function and + + + align:start position:0% +right now with respect to a function and +it's going to be exactly the same + + align:start position:0% +it's going to be exactly the same + + + align:start position:0% +it's going to be exactly the same +definition for to take a derivative I to + + align:start position:0% +definition for to take a derivative I to + + + align:start position:0% +definition for to take a derivative I to +take a derivative I just need to + + align:start position:0% +take a derivative I just need to + + + align:start position:0% +take a derivative I just need to +linearize you need to ask how does f + + align:start position:0% +linearize you need to ask how does f + + + align:start position:0% +linearize you need to ask how does f +change for a small change in the input + + align:start position:0% +change for a small change in the input + + + align:start position:0% +change for a small change in the input +right linearize it and then to get one + + align:start position:0% +right linearize it and then to get one + + + align:start position:0% +right linearize it and then to get one +step further to get a gradient I'm going + + align:start position:0% +step further to get a gradient I'm going + + + align:start position:0% +step further to get a gradient I'm going +to need a DOT product but Let's do let's + + align:start position:0% +to need a DOT product but Let's do let's + + + align:start position:0% +to need a DOT product but Let's do let's +before we do the the + + align:start position:0% +before we do the the + + + align:start position:0% +before we do the the +um the the gradient and the dot product + + align:start position:0% +um the the gradient and the dot product + + + align:start position:0% +um the the gradient and the dot product +let's just linearize right + + align:start position:0% + + + + align:start position:0% + +so right so so we're going to take + + align:start position:0% +so right so so we're going to take + + + align:start position:0% +so right so so we're going to take +DF we take F of U remember U is a + + align:start position:0% +DF we take F of U remember U is a + + + align:start position:0% +DF we take F of U remember U is a +function by the way this is sometimes + + align:start position:0% +function by the way this is sometimes + + + align:start position:0% +function by the way this is sometimes +called a functional + + align:start position:0% + + + + align:start position:0% + +uh it's something that takes in a a + + align:start position:0% +uh it's something that takes in a a + + + align:start position:0% +uh it's something that takes in a a +function and gives you a number um but + + align:start position:0% +function and gives you a number um but + + + align:start position:0% +function and gives you a number um but +sorry and I'm and here I need to F of U + + align:start position:0% +sorry and I'm and here I need to F of U + + + align:start position:0% +sorry and I'm and here I need to F of U +plus + + align:start position:0% +plus + + + align:start position:0% +plus +du minus F of U and the key thing to + + align:start position:0% +du minus F of U and the key thing to + + + align:start position:0% +du minus F of U and the key thing to +remember is that this is a + + align:start position:0% + + + + align:start position:0% + +function U of + + align:start position:0% +function U of + + + align:start position:0% +function U of +X that's a terrible X and this du + + align:start position:0% + + + + align:start position:0% + +here this is also a function think of it + + align:start position:0% +here this is also a function think of it + + + align:start position:0% +here this is also a function think of it +as a small + + align:start position:0% + + + + align:start position:0% + +function uh du of X right and as I said + + align:start position:0% +function uh du of X right and as I said + + + align:start position:0% +function uh du of X right and as I said +last last lecture to get some notion of + + align:start position:0% +last last lecture to get some notion of + + + align:start position:0% +last last lecture to get some notion of +small we're going to need a Norm of a + + align:start position:0% +small we're going to need a Norm of a + + + align:start position:0% +small we're going to need a Norm of a +function but pretty soon I have dot + + align:start position:0% +function but pretty soon I have dot + + + align:start position:0% +function but pretty soon I have dot +products of functions so I'll have Norms + + align:start position:0% +products of functions so I'll have Norms + + + align:start position:0% +products of functions so I'll have Norms +as well so let me sweep sweep that under + + align:start position:0% +as well so let me sweep sweep that under + + + align:start position:0% +as well so let me sweep sweep that under +the rug but it's just like a little + + align:start position:0% +the rug but it's just like a little + + + align:start position:0% +the rug but it's just like a little +peration right so you're taking you're + + align:start position:0% +peration right so you're taking you're + + + align:start position:0% +peration right so you're taking you're +taking you know U of + + align:start position:0% +taking you know U of + + + align:start position:0% +taking you know U of +x uh U of X and you're adding you know + + align:start position:0% +x uh U of X and you're adding you know + + + align:start position:0% +x uh U of X and you're adding you know +some arbitrary little change to this + + align:start position:0% +some arbitrary little change to this + + + align:start position:0% +some arbitrary little change to this +this is a u plus du of + + align:start position:0% +this is a u plus du of + + + align:start position:0% +this is a u plus du of +X right so you're going to change change + + align:start position:0% +X right so you're going to change change + + + align:start position:0% +X right so you're going to change change +that function by a little bit anywhere + + align:start position:0% +that function by a little bit anywhere + + + align:start position:0% +that function by a little bit anywhere +want but it has to be small and then we + + align:start position:0% +want but it has to be small and then we + + + align:start position:0% +want but it has to be small and then we +so we can drop terms that are go like du + + align:start position:0% + + + + align:start position:0% + +^2 and so what is this so this is + + align:start position:0% +^2 and so what is this so this is + + + align:start position:0% +^2 and so what is this so this is +integral from 0 to one I said f was s of + + align:start position:0% +integral from 0 to one I said f was s of + + + align:start position:0% +integral from 0 to one I said f was s of +U of X DX so this is looks like s of U + + align:start position:0% +U of X DX so this is looks like s of U + + + align:start position:0% +U of X DX so this is looks like s of U +of X Plus du of + + align:start position:0% +of X Plus du of + + + align:start position:0% +of X Plus du of +x minus sin of + + align:start position:0% +x minus sin of + + + align:start position:0% +x minus sin of +X DX I'm just plugging that into my f my + + align:start position:0% +X DX I'm just plugging that into my f my + + + align:start position:0% +X DX I'm just plugging that into my f my +f was integral sin + + align:start position:0% +f was integral sin + + + align:start position:0% +f was integral sin +U right and I'm going to ask how much + + align:start position:0% +U right and I'm going to ask how much + + + align:start position:0% +U right and I'm going to ask how much +does that integral change for a small + + align:start position:0% +does that integral change for a small + + + align:start position:0% +does that integral change for a small +change in U and I need want to linearize + + align:start position:0% +change in U and I need want to linearize + + + align:start position:0% +change in U and I need want to linearize +it right so I want to write this as drop + + align:start position:0% +it right so I want to write this as drop + + + align:start position:0% +it right so I want to write this as drop +every ter term that goes like du ^2 or + + align:start position:0% +every ter term that goes like du ^2 or + + + align:start position:0% +every ter term that goes like du ^2 or +higher so of course the point is all I + + align:start position:0% +higher so of course the point is all I + + + align:start position:0% +higher so of course the point is all I +need to do is linearize this linearize + + align:start position:0% +need to do is linearize this linearize + + + align:start position:0% +need to do is linearize this linearize +the + + align:start position:0% +the + + + align:start position:0% +the +integrand + + align:start position:0% + + + + align:start position:0% + +right that thing s oops sorry and this + + align:start position:0% +right that thing s oops sorry and this + + + align:start position:0% +right that thing s oops sorry and this +is not s of X this is s of U of + + align:start position:0% + + + + align:start position:0% + +X right okay so I want to I want to + + align:start position:0% +X right okay so I want to I want to + + + align:start position:0% +X right okay so I want to I want to +linearize this what is sign so + + align:start position:0% +linearize this what is sign so + + + align:start position:0% +linearize this what is sign so +s s of of U plus + + align:start position:0% +s s of of U plus + + + align:start position:0% +s s of of U plus +du right that's equal + + align:start position:0% +du right that's equal + + + align:start position:0% +du right that's equal +to sine of + + align:start position:0% +to sine of + + + align:start position:0% +to sine of +U Plus plus the derivative which is + + align:start position:0% +U Plus plus the derivative which is + + + align:start position:0% +U Plus plus the derivative which is +cosine of U * + + align:start position:0% + + + + align:start position:0% + +du right this is just because this is Du + + align:start position:0% +du right this is just because this is Du + + + align:start position:0% +du right this is just because this is Du +of du is a function but du of X is just + + align:start position:0% +of du is a function but du of X is just + + + align:start position:0% +of du is a function but du of X is just +a number right at each X I have a small + + align:start position:0% +a number right at each X I have a small + + + align:start position:0% +a number right at each X I have a small +change in U of X so this is just + + align:start position:0% +change in U of X so this is just + + + align:start position:0% +change in U of X so this is just +ordinary you know + + align:start position:0% + + + + align:start position:0% + +1801 right linearization or from from + + align:start position:0% +1801 right linearization or from from + + + align:start position:0% +1801 right linearization or from from +lecture lecture one of this class right + + align:start position:0% +lecture lecture one of this class right + + + align:start position:0% +lecture lecture one of this class right +so if or this could be a you know yeah + + align:start position:0% +so if or this could be a you know yeah + + + align:start position:0% +so if or this could be a you know yeah +anyway so this is just a number ordinary + + align:start position:0% +anyway so this is just a number ordinary + + + align:start position:0% +anyway so this is just a number ordinary +linearization and then of course this + + align:start position:0% +linearization and then of course this + + + align:start position:0% +linearization and then of course this +term + + align:start position:0% +term + + + align:start position:0% +term +here cancels that + + align:start position:0% +here cancels that + + + align:start position:0% +here cancels that +term right so what this is + + align:start position:0% +term right so what this is + + + align:start position:0% +term right so what this is +is integral 0 to 1 of what's left cosine + + align:start position:0% +is integral 0 to 1 of what's left cosine + + + align:start position:0% +is integral 0 to 1 of what's left cosine +of U of + + align:start position:0% +of U of + + + align:start position:0% +of U of +X du + + align:start position:0% +X du + + + align:start position:0% +X du +DX and this is exactly a this is a + + align:start position:0% +DX and this is exactly a this is a + + + align:start position:0% +DX and this is exactly a this is a +linear operator this is fime + + align:start position:0% +linear operator this is fime + + + align:start position:0% +linear operator this is fime +of + + align:start position:0% + + + + align:start position:0% + +U adding on du right so sorry again I + + align:start position:0% +U adding on du right so sorry again I + + + align:start position:0% +U adding on du right so sorry again I +should put a du of X + + align:start position:0% +should put a du of X + + + align:start position:0% +should put a du of X +here is that is that clear if I plug in + + align:start position:0% +here is that is that clear if I plug in + + + align:start position:0% +here is that is that clear if I plug in +any function here any change in my my U + + align:start position:0% +any function here any change in my my U + + + align:start position:0% +any function here any change in my my U +this is clearly linear in that like if I + + align:start position:0% +this is clearly linear in that like if I + + + align:start position:0% +this is clearly linear in that like if I +double this it doubles the integral like + + align:start position:0% +double this it doubles the integral like + + + align:start position:0% +double this it doubles the integral like +if I add two things here it adds two + + align:start position:0% +if I add two things here it adds two + + + align:start position:0% +if I add two things here it adds two +things in the integral so this is this + + align:start position:0% +things in the integral so this is this + + + align:start position:0% +things in the integral so this is this +this is a linear operator this is we're + + align:start position:0% +this is a linear operator this is we're + + + align:start position:0% +this is a linear operator this is we're +done + + align:start position:0% + + + + align:start position:0% + +from that takes du in and it gives you + + align:start position:0% +from that takes du in and it gives you + + + align:start position:0% +from that takes du in and it gives you +out a a + + align:start position:0% +out a a + + + align:start position:0% +out a a +number right this is my + + align:start position:0% +number right this is my + + + align:start position:0% +number right this is my +DF so so so so you know once you get + + align:start position:0% +DF so so so so you know once you get + + + align:start position:0% +DF so so so so you know once you get +used to this as being you know the + + align:start position:0% +used to this as being you know the + + + align:start position:0% +used to this as being you know the +definition of a derivative right you can + + align:start position:0% +definition of a derivative right you can + + + align:start position:0% +definition of a derivative right you can +always fall back on this when U is some + + align:start position:0% +always fall back on this when U is some + + + align:start position:0% +always fall back on this when U is some +crazy object Matrix function whatever as + + align:start position:0% +crazy object Matrix function whatever as + + + align:start position:0% +crazy object Matrix function whatever as +long as it's a vector space or + + align:start position:0% +long as it's a vector space or + + + align:start position:0% +long as it's a vector space or +technically a Bono bace it has to have a + + align:start position:0% +technically a Bono bace it has to have a + + + align:start position:0% +technically a Bono bace it has to have a +norm um then then you can Define the + + align:start position:0% +norm um then then you can Define the + + + align:start position:0% +norm um then then you can Define the +derivative as the linear operator that + + align:start position:0% +derivative as the linear operator that + + + align:start position:0% +derivative as the linear operator that +gives you the first order change + + align:start position:0% +gives you the first order change + + + align:start position:0% +gives you the first order change +right so as I you know I said + + align:start position:0% +right so as I you know I said + + + align:start position:0% +right so as I you know I said +technically you know we're dropping + + align:start position:0% +technically you know we're dropping + + + align:start position:0% +technically you know we're dropping +terms of you know little little o of du + + align:start position:0% +terms of you know little little o of du + + + align:start position:0% +terms of you know little little o of du +right terms that go to zero faster than + + align:start position:0% +right terms that go to zero faster than + + + align:start position:0% +right terms that go to zero faster than +du here so I have to make that precise + + align:start position:0% +du here so I have to make that precise + + + align:start position:0% +du here so I have to make that precise +you need to have a norm but anyway this + + align:start position:0% +you need to have a norm but anyway this + + + align:start position:0% +you need to have a norm but anyway this +is a function that takes a vector by + + align:start position:0% +is a function that takes a vector by + + + align:start position:0% +is a function that takes a vector by +function I'm thinking of it as a vector + + align:start position:0% +function I'm thinking of it as a vector + + + align:start position:0% +function I'm thinking of it as a vector +space Vector in it gives you out a + + align:start position:0% +space Vector in it gives you out a + + + align:start position:0% +space Vector in it gives you out a +scalar so I should be able to write that + + align:start position:0% +scalar so I should be able to write that + + + align:start position:0% +scalar so I should be able to write that +linear operator this linear form as a + + align:start position:0% +linear operator this linear form as a + + + align:start position:0% +linear operator this linear form as a +DOT product with something so for that + + align:start position:0% +DOT product with something so for that + + + align:start position:0% +DOT product with something so for that +also I want a DOT product which will + + align:start position:0% +also I want a DOT product which will + + + align:start position:0% +also I want a DOT product which will +give me a norm so let's let's just + + align:start position:0% +give me a norm so let's let's just + + + align:start position:0% +give me a norm so let's let's just +remind you hopefully you've seen this + + align:start position:0% +remind you hopefully you've seen this + + + align:start position:0% +remind you hopefully you've seen this +before in 1806 or some other linear + + align:start position:0% +before in 1806 or some other linear + + + align:start position:0% +before in 1806 or some other linear +algebra dot products of + + align:start position:0% + + + + align:start position:0% + +functions + + align:start position:0% +functions + + + align:start position:0% +functions +right so + + align:start position:0% + + + + align:start position:0% + +yes yeah well if it's if it's if if if + + align:start position:0% +yes yeah well if it's if it's if if if + + + align:start position:0% +yes yeah well if it's if it's if if if +if the output is a scaler right yes yes + + align:start position:0% +if the output is a scaler right yes yes + + + align:start position:0% +if the output is a scaler right yes yes +so this is this is exactly a something + + align:start position:0% +so this is this is exactly a something + + + align:start position:0% +so this is this is exactly a something +in the Dual space physicists would call + + align:start position:0% +in the Dual space physicists would call + + + align:start position:0% +in the Dual space physicists would call +this a + + align:start position:0% + + + + align:start position:0% + +Braun + + align:start position:0% + + + + align:start position:0% + +yeah this is a measure that because that + + align:start position:0% +yeah this is a measure that because that + + + align:start position:0% +yeah this is a measure that because that +that exactly this is the density of that + + align:start position:0% +that exactly this is the density of that + + + align:start position:0% +that exactly this is the density of that +measure yeah absolutely this this takes + + align:start position:0% +measure yeah absolutely this this takes + + + align:start position:0% +measure yeah absolutely this this takes +the measure of that function exactly yep + + align:start position:0% +the measure of that function exactly yep + + + align:start position:0% +the measure of that function exactly yep +so there all sorts of you know you can + + align:start position:0% +so there all sorts of you know you can + + + align:start position:0% +so there all sorts of you know you can +think of this as a linear form or + + align:start position:0% +think of this as a linear form or + + + align:start position:0% +think of this as a linear form or +something in the Dual space or a coor + + align:start position:0% +something in the Dual space or a coor + + + align:start position:0% +something in the Dual space or a coor +this Vector space right um but I want to + + align:start position:0% +this Vector space right um but I want to + + + align:start position:0% +this Vector space right um but I want to +say a little bit informal in terms of + + align:start position:0% +say a little bit informal in terms of + + + align:start position:0% +say a little bit informal in terms of +those abstractions here and as I said + + align:start position:0% +those abstractions here and as I said + + + align:start position:0% +those abstractions here and as I said +you know technically speaking we have to + + align:start position:0% +you know technically speaking we have to + + + align:start position:0% +you know technically speaking we have to +restrict ourselves to not all possible + + align:start position:0% +restrict ourselves to not all possible + + + align:start position:0% +restrict ourselves to not all possible +functions here they have to be functions + + align:start position:0% +functions here they have to be functions + + + align:start position:0% +functions here they have to be functions +where this integral is defined so they + + align:start position:0% +where this integral is defined so they + + + align:start position:0% +where this integral is defined so they +can't be functions that blow up or or + + align:start position:0% +can't be functions that blow up or or + + + align:start position:0% +can't be functions that blow up or or +not measurable or you know something + + align:start position:0% +not measurable or you know something + + + align:start position:0% +not measurable or you know something +like that right um but know that that's + + align:start position:0% +like that right um but know that that's + + + align:start position:0% +like that right um but know that that's +something that pure mathematicians worry + + align:start position:0% +something that pure mathematicians worry + + + align:start position:0% +something that pure mathematicians worry +about that physicists and Engineers + + align:start position:0% +about that physicists and Engineers + + + align:start position:0% +about that physicists and Engineers +don't because you know the the functions + + align:start position:0% +don't because you know the the functions + + + align:start position:0% +don't because you know the the functions +basically if this is a physical context + + align:start position:0% +basically if this is a physical context + + + align:start position:0% +basically if this is a physical context +implicitly you're dealing with functions + + align:start position:0% +implicitly you're dealing with functions + + + align:start position:0% +implicitly you're dealing with functions +where these things are defined like you + + align:start position:0% +where these things are defined like you + + + align:start position:0% +where these things are defined like you +you only really worry about ruling out + + align:start position:0% +you only really worry about ruling out + + + align:start position:0% +you only really worry about ruling out +those crazy functions if you're if + + align:start position:0% +those crazy functions if you're if + + + align:start position:0% +those crazy functions if you're if +you're doing pure math that's unored + + align:start position:0% +you're doing pure math that's unored + + + align:start position:0% +you're doing pure math that's unored +from reality um so okay so dotp of + + align:start position:0% +from reality um so okay so dotp of + + + align:start position:0% +from reality um so okay so dotp of +functions so so you know if you take a + + align:start position:0% +functions so so you know if you take a + + + align:start position:0% +functions so so you know if you take a +DOT product of two column vectors the + + align:start position:0% +DOT product of two column vectors the + + + align:start position:0% +DOT product of two column vectors the +standard there are many dot products but + + align:start position:0% +standard there are many dot products but + + + align:start position:0% +standard there are many dot products but +the standard one the ukian one is you + + align:start position:0% +the standard one the ukian one is you + + + align:start position:0% +the standard one the ukian one is you +just multiply the components and add + + align:start position:0% +just multiply the components and add + + + align:start position:0% +just multiply the components and add +them up so if you think of of two + + align:start position:0% +them up so if you think of of two + + + align:start position:0% +them up so if you think of of two +functions you know U of X and V ofx you + + align:start position:0% +functions you know U of X and V ofx you + + + align:start position:0% +functions you know U of X and V ofx you +know on you know X in uh 0 to + + align:start position:0% + + + + align:start position:0% + +one then then the the sort of the ukian + + align:start position:0% +one then then the the sort of the ukian + + + align:start position:0% +one then then the the sort of the ukian +dot + + align:start position:0% +dot + + + align:start position:0% +dot +product the sort of the obvious dot + + align:start position:0% +product the sort of the obvious dot + + + align:start position:0% +product the sort of the obvious dot +product the idian inner + + align:start position:0% + + + + align:start position:0% + +product right should be to multiply the + + align:start position:0% +product right should be to multiply the + + + align:start position:0% +product right should be to multiply the +components and add them up so the + + align:start position:0% +components and add them up so the + + + align:start position:0% +components and add them up so the +components if you think of these as + + align:start position:0% +components if you think of these as + + + align:start position:0% +components if you think of these as +column vectors they're like infinite + + align:start position:0% +column vectors they're like infinite + + + align:start position:0% +column vectors they're like infinite +dimensional column vectors the + + align:start position:0% +dimensional column vectors the + + + align:start position:0% +dimensional column vectors the +components are the values at each point + + align:start position:0% +components are the values at each point + + + align:start position:0% +components are the values at each point +so multiply you want basically what you + + align:start position:0% +so multiply you want basically what you + + + align:start position:0% +so multiply you want basically what you +want to do is multiply U of x * V ofx + + align:start position:0% +want to do is multiply U of x * V ofx + + + align:start position:0% +want to do is multiply U of x * V ofx +and add that up for all the X's and the + + align:start position:0% +and add that up for all the X's and the + + + align:start position:0% +and add that up for all the X's and the +analog of adding it up is an + + align:start position:0% + + + + align:start position:0% + +integral that's our U + + align:start position:0% +integral that's our U + + + align:start position:0% +integral that's our U +Dov so we can and and then of course + + align:start position:0% +Dov so we can and and then of course + + + align:start position:0% +Dov so we can and and then of course +this is not the only possible do product + + align:start position:0% +this is not the only possible do product + + + align:start position:0% +this is not the only possible do product +this is the most obvious one the first + + align:start position:0% +this is the most obvious one the first + + + align:start position:0% +this is the most obvious one the first +one that you typically reach for right + + align:start position:0% +one that you typically reach for right + + + align:start position:0% +one that you typically reach for right +so once you have a DOT product then of + + align:start position:0% +so once you have a DOT product then of + + + align:start position:0% +so once you have a DOT product then of +course we have a + + align:start position:0% +course we have a + + + align:start position:0% +course we have a +norm so if you want the norm of U that's + + align:start position:0% +norm so if you want the norm of U that's + + + align:start position:0% +norm so if you want the norm of U that's +the just the square root of the integral + + align:start position:0% +the just the square root of the integral + + + align:start position:0% +the just the square root of the integral +from 0 to 1 of U of x x s + + align:start position:0% +from 0 to 1 of U of x x s + + + align:start position:0% +from 0 to 1 of U of x x s +DX I guess I don't need absolute values + + align:start position:0% +DX I guess I don't need absolute values + + + align:start position:0% +DX I guess I don't need absolute values +here because everything is real right + + align:start position:0% +here because everything is real right + + + align:start position:0% +here because everything is real right +now if if they were complex I'd be + + align:start position:0% +now if if they were complex I'd be + + + align:start position:0% +now if if they were complex I'd be +putting complex conjugates over one of + + align:start position:0% +putting complex conjugates over one of + + + align:start position:0% +putting complex conjugates over one of +these + + align:start position:0% +these + + + align:start position:0% +these +but um so let let me remove my absolute + + align:start position:0% +but um so let let me remove my absolute + + + align:start position:0% +but um so let let me remove my absolute +values there just for I don't need them + + align:start position:0% +values there just for I don't need them + + + align:start position:0% +values there just for I don't need them +right so and this is the and and once we + + align:start position:0% +right so and this is the and and once we + + + align:start position:0% +right so and this is the and and once we +have the norm then then that's the the + + align:start position:0% +have the norm then then that's the the + + + align:start position:0% +have the norm then then that's the the +precise sense in which we're dropping + + align:start position:0% +precise sense in which we're dropping + + + align:start position:0% +precise sense in which we're dropping +terms that go like du^ 2 right so so + + align:start position:0% +terms that go like du^ 2 right so so + + + align:start position:0% +terms that go like du^ 2 right so so +we're going to drop drop terms that go + + align:start position:0% +we're going to drop drop terms that go + + + align:start position:0% +we're going to drop drop terms that go +like the norm of du^ 2 and higher or + + align:start position:0% +like the norm of du^ 2 and higher or + + + align:start position:0% +like the norm of du^ 2 and higher or +actually anything higher than linear + + align:start position:0% +actually anything higher than linear + + + align:start position:0% +actually anything higher than linear +right and once you have + + align:start position:0% + + + + align:start position:0% + +this now we can compute we can find the + + align:start position:0% + + + + align:start position:0% + +gradient right because what what was our + + align:start position:0% +gradient right because what what was our + + + align:start position:0% +gradient right because what what was our +DF right + + align:start position:0% + + + + align:start position:0% + +DF which was um fimed of + + align:start position:0% +DF which was um fimed of + + + align:start position:0% +DF which was um fimed of +U + + align:start position:0% +U + + + align:start position:0% +U +acting on + + align:start position:0% + + + + align:start position:0% + +du right we said that was integral from + + align:start position:0% +du right we said that was integral from + + + align:start position:0% +du right we said that was integral from +0 to + + align:start position:0% +0 to + + + align:start position:0% +0 to +one of of what it cosine of U of + + align:start position:0% +one of of what it cosine of U of + + + align:start position:0% +one of of what it cosine of U of +X time du of + + align:start position:0% +X time du of + + + align:start position:0% +X time du of +X + + align:start position:0% +X + + + align:start position:0% +X +DX right we want to think of this just + + align:start position:0% +DX right we want to think of this just + + + align:start position:0% +DX right we want to think of this just +our generic definition of the + + align:start position:0% +our generic definition of the + + + align:start position:0% +our generic definition of the +gradient is when you have something that + + align:start position:0% +gradient is when you have something that + + + align:start position:0% +gradient is when you have something that +takes a vector in scalar out the first + + align:start position:0% +takes a vector in scalar out the first + + + align:start position:0% +takes a vector in scalar out the first +derivative had better be the dotproduct + + align:start position:0% +derivative had better be the dotproduct + + + align:start position:0% +derivative had better be the dotproduct +of the + + align:start position:0% +of the + + + align:start position:0% +of the +gradient with + + align:start position:0% +gradient with + + + align:start position:0% +gradient with +du and if we just just by + + align:start position:0% + + + + align:start position:0% + +inspection right this is here this is + + align:start position:0% +inspection right this is here this is + + + align:start position:0% +inspection right this is here this is +our definition of a DOT + + align:start position:0% +our definition of a DOT + + + align:start position:0% +our definition of a DOT +product so what is the + + align:start position:0% + + + + align:start position:0% + +gradient it's what what would I take the + + align:start position:0% +gradient it's what what would I take the + + + align:start position:0% +gradient it's what what would I take the +dot product with the U to of to get to + + align:start position:0% +dot product with the U to of to get to + + + align:start position:0% +dot product with the U to of to get to +get + + align:start position:0% + + + + align:start position:0% + +this Co of + + align:start position:0% +this Co of + + + align:start position:0% +this Co of +U exactly it's it's so it's a function + + align:start position:0% +U exactly it's it's so it's a function + + + align:start position:0% +U exactly it's it's so it's a function +it's just cosine of U of + + align:start position:0% + + + + align:start position:0% + +X by the way in this this context this + + align:start position:0% +X by the way in this this context this + + + align:start position:0% +X by the way in this this context this +is this this this this is called this is + + align:start position:0% +is this this this this is called this is + + + align:start position:0% +is this this this this is called this is +sometimes also called a fret + + align:start position:0% + + + + align:start position:0% + +derivative + + align:start position:0% +derivative + + + align:start position:0% +derivative +right uh I mean foret derivative + + align:start position:0% +right uh I mean foret derivative + + + align:start position:0% +right uh I mean foret derivative +technically refers just to this General + + align:start position:0% +technically refers just to this General + + + align:start position:0% +technically refers just to this General +notion of you have any any Bon space the + + align:start position:0% +notion of you have any any Bon space the + + + align:start position:0% +notion of you have any any Bon space the +Fret derivative is the linear operator + + align:start position:0% +Fret derivative is the linear operator + + + align:start position:0% +Fret derivative is the linear operator +that does this but most often you see + + align:start position:0% +that does this but most often you see + + + align:start position:0% +that does this but most often you see +this coming up in in the in the context + + align:start position:0% +this coming up in in the in the context + + + align:start position:0% +this coming up in in the in the context +of vector spaces of functions that's + + align:start position:0% +of vector spaces of functions that's + + + align:start position:0% +of vector spaces of functions that's +where they use that terminology for + + align:start position:0% +where they use that terminology for + + + align:start position:0% +where they use that terminology for +everything else people just say the + + align:start position:0% +everything else people just say the + + + align:start position:0% +everything else people just say the +derivative right it really is just the + + align:start position:0% +derivative right it really is just the + + + align:start position:0% +derivative right it really is just the +derivative but you know um that's it + + align:start position:0% +derivative but you know um that's it + + + align:start position:0% +derivative but you know um that's it +right this is a gradient so let's do a + + align:start position:0% +right this is a gradient so let's do a + + + align:start position:0% +right this is a gradient so let's do a +more complicated case + + align:start position:0% +more complicated case + + + align:start position:0% +more complicated case +case so let's do another + + align:start position:0% + + + + align:start position:0% + +example or a tricky + + align:start position:0% + + + + align:start position:0% + +example + + align:start position:0% +example + + + align:start position:0% +example +right suppose that + + align:start position:0% +right suppose that + + + align:start position:0% +right suppose that +um + + align:start position:0% +um + + + align:start position:0% +um +suppose + + align:start position:0% +suppose + + + align:start position:0% +suppose +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um that uh + + align:start position:0% +um that uh + + + align:start position:0% +um that uh +F of U so we still going to be functions + + align:start position:0% +F of U so we still going to be functions + + + align:start position:0% +F of U so we still going to be functions +from 0 to one + + align:start position:0% +from 0 to one + + + align:start position:0% +from 0 to one +okay suppose it's the integral from 0 to + + align:start position:0% +okay suppose it's the integral from 0 to + + + align:start position:0% +okay suppose it's the integral from 0 to +1 of the square root of 1 + U Prim of x^ + + align:start position:0% +1 of the square root of 1 + U Prim of x^ + + + align:start position:0% +1 of the square root of 1 + U Prim of x^ +squar DX where this is just the the you + + align:start position:0% +squar DX where this is just the the you + + + align:start position:0% +squar DX where this is just the the you +know the derivative the + + align:start position:0% + + + + align:start position:0% + +the know the ordinary du DX 1801 + + align:start position:0% +the know the ordinary du DX 1801 + + + align:start position:0% +the know the ordinary du DX 1801 +derivative + + align:start position:0% +derivative + + + align:start position:0% +derivative +right so this takes a function in gives + + align:start position:0% +right so this takes a function in gives + + + align:start position:0% +right so this takes a function in gives +you a number out clearly we have to + + align:start position:0% +you a number out clearly we have to + + + align:start position:0% +you a number out clearly we have to +restrict ourselves to differentiable + + align:start position:0% +restrict ourselves to differentiable + + + align:start position:0% +restrict ourselves to differentiable +functions now right + + align:start position:0% +functions now right + + + align:start position:0% +functions now right +um and uh and what is this do anyone + + align:start position:0% +um and uh and what is this do anyone + + + align:start position:0% +um and uh and what is this do anyone +recognize this can you + + align:start position:0% +recognize this can you + + + align:start position:0% +recognize this can you +describe what this quantity is + + align:start position:0% +describe what this quantity is + + + align:start position:0% +describe what this quantity is +geometrically so if I have a function U + + align:start position:0% +geometrically so if I have a function U + + + align:start position:0% +geometrically so if I have a function U +of + + align:start position:0% +of + + + align:start position:0% +of +X right it goes that that + + align:start position:0% +X right it goes that that + + + align:start position:0% +X right it goes that that +here's here's U of + + align:start position:0% +here's here's U of + + + align:start position:0% +here's here's U of +X what is this quantity that I've just + + align:start position:0% +X what is this quantity that I've just + + + align:start position:0% +X what is this quantity that I've just +computed here from from a from fresh + + align:start position:0% +computed here from from a from fresh + + + align:start position:0% +computed here from from a from fresh +first year calculus there's a there's an + + align:start position:0% +first year calculus there's a there's an + + + align:start position:0% +first year calculus there's a there's an +important name of this + + align:start position:0% +important name of this + + + align:start position:0% +important name of this +yeah it's the length it's the Arc Length + + align:start position:0% +yeah it's the length it's the Arc Length + + + align:start position:0% +yeah it's the length it's the Arc Length +right it's the length of the + + align:start position:0% + + + + align:start position:0% + +curve the arc length of the of U of x + + align:start position:0% +curve the arc length of the of U of x + + + align:start position:0% +curve the arc length of the of U of x +from you know xal 0 to xal 1 right + + align:start position:0% +from you know xal 0 to xal 1 right + + + align:start position:0% +from you know xal 0 to xal 1 right +that's that's what this quantity is if + + align:start position:0% +that's that's what this quantity is if + + + align:start position:0% +that's that's what this quantity is if +you if you multiply through by DX this + + align:start position:0% +you if you multiply through by DX this + + + align:start position:0% +you if you multiply through by DX this +is basically square root of dx2 plus d + + align:start position:0% +is basically square root of dx2 plus d + + + align:start position:0% +is basically square root of dx2 plus d +y^2 right it's if you each if you take + + align:start position:0% +y^2 right it's if you each if you take + + + align:start position:0% +y^2 right it's if you each if you take +each little line segment here it's like + + align:start position:0% +each little line segment here it's like + + + align:start position:0% +each little line segment here it's like +the length of that little line segment + + align:start position:0% +the length of that little line segment + + + align:start position:0% +the length of that little line segment +you're adding them up okay so now let's + + align:start position:0% +you're adding them up okay so now let's + + + align:start position:0% +you're adding them up okay so now let's +think about the + + align:start position:0% +think about the + + + align:start position:0% +think about the +derivative okay so now let's take + + align:start position:0% +derivative okay so now let's take + + + align:start position:0% +derivative okay so now let's take +F of U and we're going to add a little + + align:start position:0% +F of U and we're going to add a little + + + align:start position:0% +F of U and we're going to add a little +change + + align:start position:0% + + + + align:start position:0% + +du right subtract F of U it's it's + + align:start position:0% +du right subtract F of U it's it's + + + align:start position:0% +du right subtract F of U it's it's +always good to just fall back on the the + + align:start position:0% +always good to just fall back on the the + + + align:start position:0% +always good to just fall back on the the +definition the most basic + + align:start position:0% +definition the most basic + + + align:start position:0% +definition the most basic +definition uh if we're if we're in doubt + + align:start position:0% +definition uh if we're if we're in doubt + + + align:start position:0% +definition uh if we're if we're in doubt +of what to + + align:start position:0% +of what to + + + align:start position:0% +of what to +do right we're going to just add a + + align:start position:0% +do right we're going to just add a + + + align:start position:0% +do right we're going to just add a +little + + align:start position:0% +little + + + align:start position:0% +little +change + + align:start position:0% +change + + + align:start position:0% +change +and what's this going to be so let's + + align:start position:0% +and what's this going to be so let's + + + align:start position:0% +and what's this going to be so let's +just it's it's the integral of from 0 to + + align:start position:0% +just it's it's the integral of from 0 to + + + align:start position:0% +just it's it's the integral of from 0 to +1 square root of 1 + U + + + align:start position:0% +1 square root of 1 + U + + + + align:start position:0% +1 square root of 1 + U + +du primed squared minus theare < TK of 1 + + align:start position:0% +du primed squared minus theare < TK of 1 + + + align:start position:0% +du primed squared minus theare < TK of 1 ++ U Prime + + align:start position:0% ++ U Prime + + + align:start position:0% ++ U Prime +squar so again we just + + align:start position:0% +squar so again we just + + + align:start position:0% +squar so again we just +think so now we have we have to tailor + + align:start position:0% +think so now we have we have to tailor + + + align:start position:0% +think so now we have we have to tailor +expand this we have to assume that du is + + align:start position:0% +expand this we have to assume that du is + + + align:start position:0% +expand this we have to assume that du is +now a differentiable thing and its + + align:start position:0% +now a differentiable thing and its + + + align:start position:0% +now a differentiable thing and its +derivative is getting smaller and + + align:start position:0% +derivative is getting smaller and + + + align:start position:0% +derivative is getting smaller and +smaller as well so I can do this this + + align:start position:0% +smaller as well so I can do this this + + + align:start position:0% +smaller as well so I can do this this +kind + + align:start position:0% +kind + + + align:start position:0% +kind +of uh you know expansion first order + + align:start position:0% +of uh you know expansion first order + + + align:start position:0% +of uh you know expansion first order +expansion so what is this so well it's + + align:start position:0% +expansion so what is this so well it's + + + align:start position:0% +expansion so what is this so well it's +it's the if I have let's see if I have + + align:start position:0% +it's the if I have let's see if I have + + + align:start position:0% +it's the if I have let's see if I have +like 1 plus um uh like uh uh um let's + + align:start position:0% +like 1 plus um uh like uh uh um let's + + + align:start position:0% +like 1 plus um uh like uh uh um let's +say V uh plus DV squared what's the + + align:start position:0% +say V uh plus DV squared what's the + + + align:start position:0% +say V uh plus DV squared what's the +tailor expansion of that that's that's + + align:start position:0% +tailor expansion of that that's that's + + + align:start position:0% +tailor expansion of that that's that's +where 1 + v^2 that's the first term + + align:start position:0% +where 1 + v^2 that's the first term + + + align:start position:0% +where 1 + v^2 that's the first term +right and the second term is the + + align:start position:0% +right and the second term is the + + + align:start position:0% +right and the second term is the +derivative with respect to V which ends + + align:start position:0% +derivative with respect to V which ends + + + align:start position:0% +derivative with respect to V which ends +up being v/ 1 + v^ 2 * DV I kind of went + + align:start position:0% +up being v/ 1 + v^ 2 * DV I kind of went + + + align:start position:0% +up being v/ 1 + v^ 2 * DV I kind of went +this through that a little bit this is + + align:start position:0% +this through that a little bit this is + + + align:start position:0% +this through that a little bit this is +but this is just 1801 this is just 1801 + + align:start position:0% +but this is just 1801 this is just 1801 + + + align:start position:0% +but this is just 1801 this is just 1801 +right so plus right this + + align:start position:0% +right so plus right this + + + align:start position:0% +right so plus right this +is this this is this function for DV + + align:start position:0% +is this this is this function for DV + + + align:start position:0% +is this this is this function for DV +equals z this is the derivative of this + + align:start position:0% +equals z this is the derivative of this + + + align:start position:0% +equals z this is the derivative of this +right so when you take the derivative of + + align:start position:0% +right so when you take the derivative of + + + align:start position:0% +right so when you take the derivative of +the square root it's 12 one over the + + align:start position:0% +the square root it's 12 one over the + + + align:start position:0% +the square root it's 12 one over the +square root right but then there's a + + align:start position:0% +square root right but then there's a + + + align:start position:0% +square root right but then there's a +derivative of this which gives you a 2v + + align:start position:0% +derivative of this which gives you a 2v + + + align:start position:0% +derivative of this which gives you a 2v +on top so the two cancels the one half + + align:start position:0% +on top so the two cancels the one half + + + align:start position:0% +on top so the two cancels the one half +so this just so just from uh um + + align:start position:0% +so this just so just from uh um + + + align:start position:0% +so this just so just from uh um +calculus expanding everything to first + + align:start position:0% +calculus expanding everything to first + + + align:start position:0% +calculus expanding everything to first +order in Du and also du Prime so + + align:start position:0% +order in Du and also du Prime so + + + align:start position:0% +order in Du and also du Prime so +dropping anything that goes like + + align:start position:0% +dropping anything that goes like + + + align:start position:0% +dropping anything that goes like +anything with a du whether you take a + + align:start position:0% +anything with a du whether you take a + + + align:start position:0% +anything with a du whether you take a +derivative or not squared we're going to + + align:start position:0% +derivative or not squared we're going to + + + align:start position:0% +derivative or not squared we're going to +just drop this is the + + align:start position:0% +just drop this is the + + + align:start position:0% +just drop this is the +integral of the of that second term + + align:start position:0% +integral of the of that second term + + + align:start position:0% +integral of the of that second term +which is + + align:start position:0% +which is + + + align:start position:0% +which is +U over squ < TK of 1 + U ^ + + align:start position:0% +U over squ < TK of 1 + U ^ + + + align:start position:0% +U over squ < TK of 1 + U ^ +2 time + + align:start position:0% +2 time + + + align:start position:0% +2 time +sorry and du that's + + align:start position:0% +sorry and du that's + + + align:start position:0% +sorry and du that's +primed + + align:start position:0% + + + + align:start position:0% + +right divided uh times + + align:start position:0% +right divided uh times + + + align:start position:0% +right divided uh times +du + + align:start position:0% +du + + + align:start position:0% +du +primed + + align:start position:0% +primed + + + align:start position:0% +primed +DX + + align:start position:0% +DX + + + align:start position:0% +DX +right so this is a this is a linear + + align:start position:0% + + + + align:start position:0% + +operator but it's acting + + align:start position:0% +operator but it's acting + + + align:start position:0% +operator but it's acting +on du primed not on du per se right I + + align:start position:0% +on du primed not on du per se right I + + + align:start position:0% +on du primed not on du per se right I +mean we I mean the derivative is is a + + align:start position:0% +mean we I mean the derivative is is a + + + align:start position:0% +mean we I mean the derivative is is a +linear operator on du but I'd like to + + align:start position:0% +linear operator on du but I'd like to + + + align:start position:0% +linear operator on du but I'd like to +write it explicit directly in terms of + + align:start position:0% +write it explicit directly in terms of + + + align:start position:0% +write it explicit directly in terms of +du right because I'd like to write it + + align:start position:0% +du right because I'd like to write it + + + align:start position:0% +du right because I'd like to write it +eventually as a take a gradient write it + + align:start position:0% +eventually as a take a gradient write it + + + align:start position:0% +eventually as a take a gradient write it +as a do product of something with the so + + align:start position:0% +as a do product of something with the so + + + align:start position:0% +as a do product of something with the so +I really want to do is write this as a + + align:start position:0% +I really want to do is write this as a + + + align:start position:0% +I really want to do is write this as a +do product of a + + align:start position:0% + + + + align:start position:0% + +gradient do du and + + align:start position:0% +gradient do du and + + + align:start position:0% +gradient do du and +somehow I have to get a du and not a du + + align:start position:0% +somehow I have to get a du and not a du + + + align:start position:0% +somehow I have to get a du and not a du +Prim so we just saw this in the first + + align:start position:0% +Prim so we just saw this in the first + + + align:start position:0% +Prim so we just saw this in the first +hour if you have an integral and you + + align:start position:0% +hour if you have an integral and you + + + align:start position:0% +hour if you have an integral and you +have a term that has a derivative and + + align:start position:0% +have a term that has a derivative and + + + align:start position:0% +have a term that has a derivative and +you don't want the derivative what do + + align:start position:0% +you don't want the derivative what do + + + align:start position:0% +you don't want the derivative what do +you + + align:start position:0% +you + + + align:start position:0% +you +do what can you do in in first year + + align:start position:0% +do what can you do in in first year + + + align:start position:0% +do what can you do in in first year +calculus to get rid of a derivative on a + + align:start position:0% +calculus to get rid of a derivative on a + + + align:start position:0% +calculus to get rid of a derivative on a +term in an + + align:start position:0% +term in an + + + align:start position:0% +term in an +integral integrate by + + align:start position:0% + + + + align:start position:0% + +parts + + align:start position:0% +parts + + + align:start position:0% +parts +right so what do we do + + align:start position:0% +right so what do we do + + + align:start position:0% +right so what do we do +so so that whole thing let's see + + align:start position:0% + + + + align:start position:0% + +DF there is a boundary term that looks + + align:start position:0% +DF there is a boundary term that looks + + + align:start position:0% +DF there is a boundary term that looks +like U Prime over < TK of 1 + U Prime + + align:start position:0% +like U Prime over < TK of 1 + U Prime + + + align:start position:0% +like U Prime over < TK of 1 + U Prime +sared Times uh du at the boundaries + + align:start position:0% +sared Times uh du at the boundaries + + + align:start position:0% +sared Times uh du at the boundaries +01 and then you have a minus sign and an + + align:start position:0% +01 and then you have a minus sign and an + + + align:start position:0% +01 and then you have a minus sign and an +integral uh from 0 to one of of we take + + align:start position:0% +integral uh from 0 to one of of we take + + + align:start position:0% +integral uh from 0 to one of of we take +this whole + + align:start position:0% + + + + align:start position:0% + +thing + + align:start position:0% +thing + + + align:start position:0% +thing +Prime du and then times DX right all the + + align:start position:0% +Prime du and then times DX right all the + + + align:start position:0% +Prime du and then times DX right all the +U's and duus are functions of + + align:start position:0% + + + + align:start position:0% + +X so to go further Ian this is it this + + align:start position:0% +X so to go further Ian this is it this + + + align:start position:0% +X so to go further Ian this is it this +is the linear operator right you know + + align:start position:0% +is the linear operator right you know + + + align:start position:0% +is the linear operator right you know +this this is this is now our this is our + + align:start position:0% +this this is this is now our this is our + + + align:start position:0% +this this is this is now our this is our +our f Prime of U acting on + + align:start position:0% +our f Prime of U acting on + + + align:start position:0% +our f Prime of U acting on +du this is a linear operator acting on + + align:start position:0% +du this is a linear operator acting on + + + align:start position:0% +du this is a linear operator acting on +du and there's no du primes here this is + + align:start position:0% +du and there's no du primes here this is + + + align:start position:0% +du and there's no du primes here this is +nice but it has these these boundary + + align:start position:0% +nice but it has these these boundary + + + align:start position:0% +nice but it has these these boundary +terms are kind of annoying right but + + align:start position:0% +terms are kind of annoying right but + + + align:start position:0% +terms are kind of annoying right but +usually in context where I'm interested + + align:start position:0% +usually in context where I'm interested + + + align:start position:0% +usually in context where I'm interested +in this I'm actually going to set some + + align:start position:0% +in this I'm actually going to set some + + + align:start position:0% +in this I'm actually going to set some +boundary conditions so in particular + + align:start position:0% +boundary conditions so in particular + + + align:start position:0% +boundary conditions so in particular +suppose I want to + + align:start position:0% +suppose I want to + + + align:start position:0% +suppose I want to +fix the end points of my U right and I + + align:start position:0% +fix the end points of my U right and I + + + align:start position:0% +fix the end points of my U right and I +want to + + align:start position:0% +want to + + + align:start position:0% +want to +find the curve that has the minimum + + align:start position:0% +find the curve that has the minimum + + + align:start position:0% +find the curve that has the minimum +distance from one point to another of + + align:start position:0% +distance from one point to another of + + + align:start position:0% +distance from one point to another of +course that's going to be a straight + + align:start position:0% +course that's going to be a straight + + + align:start position:0% +course that's going to be a straight +line right but suppose I didn't know + + align:start position:0% +line right but suppose I didn't know + + + align:start position:0% +line right but suppose I didn't know +that right so this is this is a simple + + align:start position:0% +that right so this is this is a simple + + + align:start position:0% +that right so this is this is a simple +problem where you know the solution + + align:start position:0% +problem where you know the solution + + + align:start position:0% +problem where you know the solution +ahead of time but the more complicated + + align:start position:0% +ahead of time but the more complicated + + + align:start position:0% +ahead of time but the more complicated +things you won't know that right right + + align:start position:0% +things you won't know that right right + + + align:start position:0% +things you won't know that right right +so so I want to suppose we want to + + align:start position:0% + + + + align:start position:0% + +fix uh to uh fix uh let's just even say + + align:start position:0% +fix uh to uh fix uh let's just even say + + + align:start position:0% +fix uh to uh fix uh let's just even say +U of 0al U of 1al 0 just even for + + align:start position:0% +U of 0al U of 1al 0 just even for + + + align:start position:0% +U of 0al U of 1al 0 just even for +simplic + + align:start position:0% + + + + align:start position:0% + +right and so that's and now we want to + + align:start position:0% +right and so that's and now we want to + + + align:start position:0% +right and so that's and now we want to +find uh find uh the U that + + align:start position:0% + + + + align:start position:0% + +minimizes the Arc + + align:start position:0% +minimizes the Arc + + + align:start position:0% +minimizes the Arc +Length F of + + align:start position:0% +Length F of + + + align:start position:0% +Length F of +U right we know probably it's a straight + + align:start position:0% +U right we know probably it's a straight + + + align:start position:0% +U right we know probably it's a straight +line from from one point to the other + + align:start position:0% +line from from one point to the other + + + align:start position:0% +line from from one point to the other +right but let's pretend we don't know + + align:start position:0% +right but let's pretend we don't know + + + align:start position:0% +right but let's pretend we don't know +that so so what we want if you want to + + align:start position:0% +that so so what we want if you want to + + + align:start position:0% +that so so what we want if you want to +minimize something what you want is for + + align:start position:0% +minimize something what you want is for + + + align:start position:0% +minimize something what you want is for +the gradient to be + + align:start position:0% +the gradient to be + + + align:start position:0% +the gradient to be +zero right so we're we're going to need + + align:start position:0% +zero right so we're we're going to need + + + align:start position:0% +zero right so we're we're going to need +to take a gradient set it equal to zero + + align:start position:0% +to take a gradient set it equal to zero + + + align:start position:0% +to take a gradient set it equal to zero +in a + + align:start position:0% +in a + + + align:start position:0% +in a +minute + + align:start position:0% +minute + + + align:start position:0% +minute +but if we fix the end + + align:start position:0% + + + + align:start position:0% + +points we're going to want du also at + + align:start position:0% +points we're going to want du also at + + + align:start position:0% +points we're going to want du also at +Zer or one to be + + align:start position:0% +Zer or one to be + + + align:start position:0% +Zer or one to be +zero right if we fix them at zero + + align:start position:0% +zero right if we fix them at zero + + + align:start position:0% +zero right if we fix them at zero +because if if we start with with Vector + + align:start position:0% +because if if we start with with Vector + + + align:start position:0% +because if if we start with with Vector +space of you know use that are zero at + + align:start position:0% +space of you know use that are zero at + + + align:start position:0% +space of you know use that are zero at +the end points and we want to look at + + align:start position:0% +the end points and we want to look at + + + align:start position:0% +the end points and we want to look at +not all possible perturbations but + + align:start position:0% +not all possible perturbations but + + + align:start position:0% +not all possible perturbations but +perations to keep those end fixed but if + + align:start position:0% +perations to keep those end fixed but if + + + align:start position:0% +perations to keep those end fixed but if +I keep or if I kept the ends fixed at + + align:start position:0% +I keep or if I kept the ends fixed at + + + align:start position:0% +I keep or if I kept the ends fixed at +some other point still I would want to + + align:start position:0% +some other point still I would want to + + + align:start position:0% +some other point still I would want to +look at not all possible + + align:start position:0% +look at not all possible + + + align:start position:0% +look at not all possible +perations Right I'd want to put look at + + align:start position:0% +perations Right I'd want to put look at + + + align:start position:0% +perations Right I'd want to put look at +the perturbations that keep the ends + + align:start position:0% +the perturbations that keep the ends + + + align:start position:0% +the perturbations that keep the ends +fixed so the U is zero at the ends so + + align:start position:0% +fixed so the U is zero at the ends so + + + align:start position:0% +fixed so the U is zero at the ends so +this is this + + align:start position:0% +this is this + + + align:start position:0% +this is this +keeps the end points + + align:start position:0% + + + + align:start position:0% + +fixed right and then what happens is + + align:start position:0% +fixed right and then what happens is + + + align:start position:0% +fixed right and then what happens is +that that boundary term + + align:start position:0% +that that boundary term + + + align:start position:0% +that that boundary term +disappears + + align:start position:0% +disappears + + + align:start position:0% +disappears +right our our what was it U Prim over > + + align:start position:0% +right our our what was it U Prim over > + + + align:start position:0% +right our our what was it U Prim over > +1 + U Prime 2 + + align:start position:0% +1 + U Prime 2 + + + align:start position:0% +1 + U Prime 2 +du taken at 01 this is now just + + align:start position:0% +du taken at 01 this is now just + + + align:start position:0% +du taken at 01 this is now just +zero right because you fixed the end + + align:start position:0% +zero right because you fixed the end + + + align:start position:0% +zero right because you fixed the end +points so + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +DF is just integral 0 to 1 of U Prime + + align:start position:0% +DF is just integral 0 to 1 of U Prime + + + align:start position:0% +DF is just integral 0 to 1 of U Prime +over < TK 1 + U Prime s Prime Times du + + align:start position:0% +over < TK 1 + U Prime s Prime Times du + + + align:start position:0% +over < TK 1 + U Prime s Prime Times du +DX so our + + align:start position:0% + + + + align:start position:0% + +gradient is + + align:start position:0% +gradient is + + + align:start position:0% +gradient is +just this thing here right it's the + + align:start position:0% +just this thing here right it's the + + + align:start position:0% +just this thing here right it's the +thing we're taking with the dotproduct + + align:start position:0% +thing we're taking with the dotproduct + + + align:start position:0% +thing we're taking with the dotproduct +of du with to get the solution so it's + + align:start position:0% +of du with to get the solution so it's + + + align:start position:0% +of du with to get the solution so it's +just U Prim over < TK 1 + U Prime + + align:start position:0% +just U Prim over < TK 1 + U Prime + + + align:start position:0% +just U Prim over < TK 1 + U Prime +SAR + + align:start position:0% +SAR + + + align:start position:0% +SAR +Prime doeses everyone see that so this + + align:start position:0% +Prime doeses everyone see that so this + + + align:start position:0% +Prime doeses everyone see that so this +is this this is this DF had better be + + align:start position:0% +is this this is this DF had better be + + + align:start position:0% +is this this is this DF had better be +the dotproduct of grad f with with DOT + + align:start position:0% +the dotproduct of grad f with with DOT + + + align:start position:0% +the dotproduct of grad f with with DOT +gr u i integrated by Parts I turned my U + + align:start position:0% +gr u i integrated by Parts I turned my U + + + align:start position:0% +gr u i integrated by Parts I turned my U +primed into a du I set boundary + + align:start position:0% +primed into a du I set boundary + + + align:start position:0% +primed into a du I set boundary +conditions to fix the boundar so the + + align:start position:0% +conditions to fix the boundar so the + + + align:start position:0% +conditions to fix the boundar so the +boundary terms disappeared what I have + + align:start position:0% +boundary terms disappeared what I have + + + align:start position:0% +boundary terms disappeared what I have +left is just is just a dotproduct + + align:start position:0% +left is just is just a dotproduct + + + align:start position:0% +left is just is just a dotproduct +of this with du so I can think of this + + align:start position:0% +of this with du so I can think of this + + + align:start position:0% +of this with du so I can think of this +as the gradient right and if you're at a + + align:start position:0% +as the gradient right and if you're at a + + + align:start position:0% +as the gradient right and if you're at a +minimum it's the same for the same + + align:start position:0% +minimum it's the same for the same + + + align:start position:0% +minimum it's the same for the same +reason as in 1801 and 1802 and so forth + + align:start position:0% +reason as in 1801 and 1802 and so forth + + + align:start position:0% +reason as in 1801 and 1802 and so forth +at a minimum the R has to be zero + + align:start position:0% +at a minimum the R has to be zero + + + align:start position:0% +at a minimum the R has to be zero +because if it's not zero you could move + + align:start position:0% +because if it's not zero you could move + + + align:start position:0% +because if it's not zero you could move +in that direction and make it bigger or + + align:start position:0% +in that direction and make it bigger or + + + align:start position:0% +in that direction and make it bigger or +move in the opposite of that direction + + align:start position:0% +move in the opposite of that direction + + + align:start position:0% +move in the opposite of that direction +and make it + + align:start position:0% + + + + align:start position:0% + +smaller so this has to equal zero at a + + align:start position:0% + + + + align:start position:0% + +minimum right and so now let's just I + + align:start position:0% +minimum right and so now let's just I + + + align:start position:0% +minimum right and so now let's just I +need to work out okay now it's a little + + align:start position:0% +need to work out okay now it's a little + + + align:start position:0% +need to work out okay now it's a little +bit of a calculus exercise right what is + + align:start position:0% +bit of a calculus exercise right what is + + + align:start position:0% +bit of a calculus exercise right what is +the the derivative of this of this + + align:start position:0% +the the derivative of this of this + + + align:start position:0% +the the derivative of this of this +thing okay so now it's quotient rule + + align:start position:0% +thing okay so now it's quotient rule + + + align:start position:0% +thing okay so now it's quotient rule +right so this is going to be + + align:start position:0% +right so this is going to be + + + align:start position:0% +right so this is going to be +quotient rule right so on the in the + + align:start position:0% +quotient rule right so on the in the + + + align:start position:0% +quotient rule right so on the in the +quotient rule on the bottom you get that + + align:start position:0% +quotient rule on the bottom you get that + + + align:start position:0% +quotient rule on the bottom you get that +denominator squared so you get 1 + U + + align:start position:0% +denominator squared so you get 1 + U + + + align:start position:0% +denominator squared so you get 1 + U +Prim squar the square root squared on + + align:start position:0% +Prim squar the square root squared on + + + align:start position:0% +Prim squar the square root squared on +the top you get the derivative of the + + align:start position:0% +the top you get the derivative of the + + + align:start position:0% +the top you get the derivative of the +top which is uble primed times the + + align:start position:0% +top which is uble primed times the + + + align:start position:0% +top which is uble primed times the +bottom Square < TK of 1 + U + + align:start position:0% +bottom Square < TK of 1 + U + + + align:start position:0% +bottom Square < TK of 1 + U +primed uh + + align:start position:0% + + + + align:start position:0% + +squared um and then minus + + align:start position:0% +squared um and then minus + + + align:start position:0% +squared um and then minus +uh the + + align:start position:0% +uh the + + + align:start position:0% +uh the +top times the derivative of the bottom + + align:start position:0% +top times the derivative of the bottom + + + align:start position:0% +top times the derivative of the bottom +and we just did that the Der the + + align:start position:0% +and we just did that the Der the + + + align:start position:0% +and we just did that the Der the +derivative that square root is in fact U + + align:start position:0% +derivative that square root is in fact U + + + align:start position:0% +derivative that square root is in fact U +Prim over < TK of 1 + U Prim squar I + + align:start position:0% + + + + align:start position:0% + +think did I make hopefully I'm not + + align:start position:0% +think did I make hopefully I'm not + + + align:start position:0% +think did I make hopefully I'm not +making any any mistakes here okay so now + + align:start position:0% +making any any mistakes here okay so now + + + align:start position:0% +making any any mistakes here okay so now +if I want to put this over let's let's + + align:start position:0% +if I want to put this over let's let's + + + align:start position:0% +if I want to put this over let's let's +simplify this a little bit this is 1 + U + + align:start position:0% +simplify this a little bit this is 1 + U + + + align:start position:0% +simplify this a little bit this is 1 + U +Prime s I'm just going to put I'm going + + align:start position:0% +Prime s I'm just going to put I'm going + + + align:start position:0% +Prime s I'm just going to put I'm going +to put a three halves on the bottom so + + align:start position:0% +to put a three halves on the bottom so + + + align:start position:0% +to put a three halves on the bottom so +I'm going to pull this term and put it + + align:start position:0% +I'm going to pull this term and put it + + + align:start position:0% +I'm going to pull this term and put it +on the bottom so I'm just going to + + align:start position:0% +on the bottom so I'm just going to + + + align:start position:0% +on the bottom so I'm just going to +multiply and divide by by that square + + align:start position:0% +multiply and divide by by that square + + + align:start position:0% +multiply and divide by by that square +root and what you get is a u Prime * 1 + + + align:start position:0% +root and what you get is a u Prime * 1 + + + + align:start position:0% +root and what you get is a u Prime * 1 + +U Prime + + align:start position:0% +U Prime + + + align:start position:0% +U Prime +s minus U Prime + + align:start position:0% + + + + align:start position:0% + +squ I'm just simplifying this a little + + align:start position:0% + + + + align:start position:0% + +bit the second one no that's because + + align:start position:0% +bit the second one no that's because + + + align:start position:0% +bit the second one no that's because +this came from U Prime * U + + align:start position:0% +this came from U Prime * U + + + align:start position:0% +this came from U Prime * U +Prime this one is + + align:start position:0% + + + + align:start position:0% + +Urie + + align:start position:0% +Urie + + + align:start position:0% +Urie +there that came from this square root I + + align:start position:0% +there that came from this square root I + + + align:start position:0% +there that came from this square root I +multiplied the top and the Bottom by + + align:start position:0% +multiplied the top and the Bottom by + + + align:start position:0% +multiplied the top and the Bottom by +sare of 1 plus u Prime + + align:start position:0% +sare of 1 plus u Prime + + + align:start position:0% +sare of 1 plus u Prime +squ the second term what + + align:start position:0% + + + + align:start position:0% + +that so this term are we talking about + + align:start position:0% +that so this term are we talking about + + + align:start position:0% +that so this term are we talking about +the right term and the left + + align:start position:0% +the right term and the left + + + align:start position:0% +the right term and the left +terms this one + + align:start position:0% +terms this one + + + align:start position:0% +terms this one +here + + align:start position:0% + + + + align:start position:0% + +sorry what is this your T saying this + + align:start position:0% +sorry what is this your T saying this + + + align:start position:0% +sorry what is this your T saying this +term is wrong did I make a + + align:start position:0% +term is wrong did I make a + + + align:start position:0% +term is wrong did I make a +mistake so was this term + + align:start position:0% + + + + align:start position:0% + +correct oh yes thank you oh good good + + align:start position:0% +correct oh yes thank you oh good good + + + align:start position:0% +correct oh yes thank you oh good good +yeah because that's going to screw + + align:start position:0% +yeah because that's going to screw + + + align:start position:0% +yeah because that's going to screw +things up okay + + align:start position:0% +things up okay + + + align:start position:0% +things up okay +so um yeah yes okay so good sorry yes + + align:start position:0% +so um yeah yes okay so good sorry yes + + + align:start position:0% +so um yeah yes okay so good sorry yes +you're right the top is not even that + + align:start position:0% +you're right the top is not even that + + + align:start position:0% +you're right the top is not even that +it's it's u double primed good okay I I + + align:start position:0% +it's it's u double primed good okay I I + + + align:start position:0% +it's it's u double primed good okay I I +knew something was supposed to cancel + + align:start position:0% +knew something was supposed to cancel + + + align:start position:0% +knew something was supposed to cancel +here good it's actually U Prime Time U + + align:start position:0% +here good it's actually U Prime Time U + + + align:start position:0% +here good it's actually U Prime Time U +primed right okay good because it's the + + align:start position:0% +primed right okay good because it's the + + + align:start position:0% +primed right okay good because it's the +derivative of the U prime squar it gives + + align:start position:0% +derivative of the U prime squar it gives + + + align:start position:0% +derivative of the U prime squar it gives +you a two U Prime U primed the two + + align:start position:0% +you a two U Prime U primed the two + + + align:start position:0% +you a two U Prime U primed the two +cancel the D from the square root good + + align:start position:0% +cancel the D from the square root good + + + align:start position:0% +cancel the D from the square root good +I'm good I'm missing a u Prime there ah + + align:start position:0% +I'm good I'm missing a u Prime there ah + + + align:start position:0% +I'm good I'm missing a u Prime there ah +that good I knew it was supposed to + + align:start position:0% +that good I knew it was supposed to + + + align:start position:0% +that good I knew it was supposed to +simplify I was a worried a little + + align:start position:0% +simplify I was a worried a little + + + align:start position:0% +simplify I was a worried a little +worried about that so now this term + + align:start position:0% +worried about that so now this term + + + align:start position:0% +worried about that so now this term +cancels this + + align:start position:0% +cancels this + + + align:start position:0% +cancels this +term and what you get is just U Prim + + align:start position:0% +term and what you get is just U Prim + + + align:start position:0% +term and what you get is just U Prim +over 1 + U Prime squ to the three halfes + + align:start position:0% +over 1 + U Prime squ to the three halfes + + + align:start position:0% +over 1 + U Prime squ to the three halfes +and this is supposed to equal zero be + + align:start position:0% +and this is supposed to equal zero be + + + align:start position:0% +and this is supposed to equal zero be +said so the only way you can zero is If + + align:start position:0% +said so the only way you can zero is If + + + align:start position:0% +said so the only way you can zero is If +U Prim equals + + align:start position:0% + + + + align:start position:0% + +z and that's a straight + + align:start position:0% + + + + align:start position:0% + +line right so what we just derived is + + align:start position:0% +line right so what we just derived is + + + align:start position:0% +line right so what we just derived is +that the shortest distance between two + + align:start position:0% +that the shortest distance between two + + + align:start position:0% +that the shortest distance between two +points is a straight line of course you + + align:start position:0% +points is a straight line of course you + + + align:start position:0% +points is a straight line of course you +knew that right um but let's do a + + align:start position:0% + + + + align:start position:0% + +generalization okay so let's say F of + + align:start position:0% +generalization okay so let's say F of + + + align:start position:0% +generalization okay so let's say F of +U is an + + align:start position:0% +U is an + + + align:start position:0% +U is an +integral right from A to B right of some + + align:start position:0% +integral right from A to B right of some + + + align:start position:0% +integral right from A to B right of some +other function let's call it capital f + + align:start position:0% +other function let's call it capital f + + + align:start position:0% +other function let's call it capital f +right of Depends it may depend on U it + + align:start position:0% +right of Depends it may depend on U it + + + align:start position:0% +right of Depends it may depend on U it +may depend on U prime it may depend on + + align:start position:0% + + + + align:start position:0% + +X right this is a + + align:start position:0% +X right this is a + + + align:start position:0% +X right this is a +functional and then what is + + align:start position:0% + + + + align:start position:0% + +DF so + + align:start position:0% +DF so + + + align:start position:0% +DF so +DF is is you know F of U plus du minus F + + align:start position:0% +DF is is you know F of U plus du minus F + + + align:start position:0% +DF is is you know F of U plus du minus F +of U right so now what what are we going + + align:start position:0% +of U right so now what what are we going + + + align:start position:0% +of U right so now what what are we going +to have + + align:start position:0% +to have + + + align:start position:0% +to have +so there is going to be a term that + + align:start position:0% +so there is going to be a term that + + + align:start position:0% +so there is going to be a term that +looks + + align:start position:0% +looks + + + align:start position:0% +looks +like uh partial + + align:start position:0% +like uh partial + + + align:start position:0% +like uh partial +F partial + + align:start position:0% +F partial + + + align:start position:0% +F partial +U right this is an ordinary 01 partial + + align:start position:0% +U right this is an ordinary 01 partial + + + align:start position:0% +U right this is an ordinary 01 partial +derivative I'm assuming you as a number + + align:start position:0% +derivative I'm assuming you as a number + + + align:start position:0% +derivative I'm assuming you as a number +I guess it could be a vector or + + align:start position:0% +I guess it could be a vector or + + + align:start position:0% +I guess it could be a vector or +something like that but let's just keep + + align:start position:0% +something like that but let's just keep + + + align:start position:0% +something like that but let's just keep +it simple times + + align:start position:0% + + + + align:start position:0% + +du there's also a term that looks like + + align:start position:0% +du there's also a term that looks like + + + align:start position:0% +du there's also a term that looks like +partial + + align:start position:0% +partial + + + align:start position:0% +partial +f + + align:start position:0% +f + + + align:start position:0% +f +partial U primed time duu + + align:start position:0% + + + + align:start position:0% + +primed DX right + + align:start position:0% +primed DX right + + + align:start position:0% +primed DX right +and this sometimes confuses people it's + + align:start position:0% +and this sometimes confuses people it's + + + align:start position:0% +and this sometimes confuses people it's +like how can I if I take derivative to U + + align:start position:0% +like how can I if I take derivative to U + + + align:start position:0% +like how can I if I take derivative to U +keeping U Prime fixed because obviously + + align:start position:0% +keeping U Prime fixed because obviously + + + align:start position:0% +keeping U Prime fixed because obviously +U and U are related it really means the + + align:start position:0% +U and U are related it really means the + + + align:start position:0% +U and U are related it really means the +derivative of f with respect to the + + align:start position:0% +derivative of f with respect to the + + + align:start position:0% +derivative of f with respect to the +first argument right right this is the + + align:start position:0% +first argument right right this is the + + + align:start position:0% +first argument right right this is the +Der respect to the second argument right + + align:start position:0% +Der respect to the second argument right + + + align:start position:0% +Der respect to the second argument right +and then you plug in U and U Prime + + align:start position:0% +and then you plug in U and U Prime + + + align:start position:0% +and then you plug in U and U Prime +afterwards right so it's just it's just + + align:start position:0% +afterwards right so it's just it's just + + + align:start position:0% +afterwards right so it's just it's just +you're doing exactly the same and you're + + align:start position:0% +you're doing exactly the same and you're + + + align:start position:0% +you're doing exactly the same and you're +doing much like like this in homework + + align:start position:0% +doing much like like this in homework + + + align:start position:0% +doing much like like this in homework +but I'm skipping a couple of steps here + + align:start position:0% +but I'm skipping a couple of steps here + + + align:start position:0% +but I'm skipping a couple of steps here +but right that this change there's + + align:start position:0% +but right that this change there's + + + align:start position:0% +but right that this change there's +there's a change that comes from the + + align:start position:0% +there's a change that comes from the + + + align:start position:0% +there's a change that comes from the +first term like we did on the first + + align:start position:0% +first term like we did on the first + + + align:start position:0% +first term like we did on the first +example a sign of U there's a change + + align:start position:0% +example a sign of U there's a change + + + align:start position:0% +example a sign of U there's a change +that comes from the second term like in + + align:start position:0% +that comes from the second term like in + + + align:start position:0% +that comes from the second term like in +the second example right and you have to + + align:start position:0% +the second example right and you have to + + + align:start position:0% +the second example right and you have to +add them up + + align:start position:0% +add them up + + + align:start position:0% +add them up +but now you integrate by + + align:start position:0% + + + + align:start position:0% + +parts right and on the on this on the um + + align:start position:0% +parts right and on the on this on the um + + + align:start position:0% +parts right and on the on this on the um +the DU Prim Prime term because we don't + + align:start position:0% +the DU Prim Prime term because we don't + + + align:start position:0% +the DU Prim Prime term because we don't +like having du primes and so you get a + + align:start position:0% +like having du primes and so you get a + + + align:start position:0% +like having du primes and so you get a +partial F partial U Prim Time + + align:start position:0% +partial F partial U Prim Time + + + align:start position:0% +partial F partial U Prim Time +du at a B and then we have a plus an + + align:start position:0% +du at a B and then we have a plus an + + + align:start position:0% +du at a B and then we have a plus an +integral A to + + align:start position:0% +integral A to + + + align:start position:0% +integral A to +B and then there is a term that looks + + align:start position:0% +B and then there is a term that looks + + + align:start position:0% +B and then there is a term that looks +like DF du and there's another term that + + align:start position:0% +like DF du and there's another term that + + + align:start position:0% +like DF du and there's another term that +looks like with a minus sign + + align:start position:0% +looks like with a minus sign + + + align:start position:0% +looks like with a minus sign +DF duu primed + + align:start position:0% +DF duu primed + + + align:start position:0% +DF duu primed +primed + + align:start position:0% +primed + + + align:start position:0% +primed +multiplying du * DX again du is D my + + align:start position:0% +multiplying du * DX again du is D my + + + align:start position:0% +multiplying du * DX again du is D my +small change it's a du of X right I'm + + align:start position:0% +small change it's a du of X right I'm + + + align:start position:0% +small change it's a du of X right I'm +just suppressing all those and this + + align:start position:0% +just suppressing all those and this + + + align:start position:0% +just suppressing all those and this +term we're going to set to zero uh if + + align:start position:0% +term we're going to set to zero uh if + + + align:start position:0% +term we're going to set to zero uh if +the end points are + + align:start position:0% + + + + align:start position:0% + +fixed uh of you are fixed so if we keep + + align:start position:0% +fixed uh of you are fixed so if we keep + + + align:start position:0% +fixed uh of you are fixed so if we keep +youu fixed at the end points then we're + + align:start position:0% +youu fixed at the end points then we're + + + align:start position:0% +youu fixed at the end points then we're +going to only allow changes duus that + + align:start position:0% +going to only allow changes duus that + + + align:start position:0% +going to only allow changes duus that +are arbitrary functions but at the Z end + + align:start position:0% +are arbitrary functions but at the Z end + + + align:start position:0% +are arbitrary functions but at the Z end +points have to be zero and so what you + + align:start position:0% +points have to be zero and so what you + + + align:start position:0% +points have to be zero and so what you +get is this term here is the + + align:start position:0% + + + + align:start position:0% + +gradient this is a gr F right this is a + + align:start position:0% +gradient this is a gr F right this is a + + + align:start position:0% +gradient this is a gr F right this is a +DOT product with with the and so I can + + align:start position:0% +DOT product with with the and so I can + + + align:start position:0% +DOT product with with the and so I can +write this out so this is uh so grad f + + align:start position:0% +write this out so this is uh so grad f + + + align:start position:0% +write this out so this is uh so grad f +is + + align:start position:0% +is + + + align:start position:0% +is +DF du minus DF du + + align:start position:0% +DF du minus DF du + + + align:start position:0% +DF du minus DF du +primed + + align:start position:0% +primed + + + align:start position:0% +primed +primed and we set this equal to zero uh + + align:start position:0% +primed and we set this equal to zero uh + + + align:start position:0% +primed and we set this equal to zero uh +at an extremum at a minimum and + + align:start position:0% +at an extremum at a minimum and + + + align:start position:0% +at an extremum at a minimum and +maximum and the + + align:start position:0% +maximum and the + + + align:start position:0% +maximum and the +result this this is this is we set this + + align:start position:0% +result this this is this is we set this + + + align:start position:0% +result this this is this is we set this +equal to zero this is some differential + + align:start position:0% +equal to zero this is some differential + + + align:start position:0% +equal to zero this is some differential +equation is + + align:start position:0% + + + + align:start position:0% + +it + + align:start position:0% +it + + + align:start position:0% +it +equation in u + + align:start position:0% + + + + align:start position:0% + +right and involves and it's actually a + + align:start position:0% +right and involves and it's actually a + + + align:start position:0% +right and involves and it's actually a +second + + align:start position:0% +second + + + align:start position:0% +second +order right because the you start out + + align:start position:0% +order right because the you start out + + + align:start position:0% +order right because the you start out +with u and U primed in your F but when I + + align:start position:0% +with u and U primed in your F but when I + + + align:start position:0% +with u and U primed in your F but when I +take this derivative here I'm going to + + align:start position:0% +take this derivative here I'm going to + + + align:start position:0% +take this derivative here I'm going to +get some you double primed terms does + + align:start position:0% +get some you double primed terms does + + + align:start position:0% +get some you double primed terms does +anyone know the name of this + + align:start position:0% +anyone know the name of this + + + align:start position:0% +anyone know the name of this +differential equation has anyone seen + + align:start position:0% +differential equation has anyone seen + + + align:start position:0% +differential equation has anyone seen +this + + align:start position:0% +this + + + align:start position:0% +this +before orrange equations so these These + + align:start position:0% +before orrange equations so these These + + + align:start position:0% +before orrange equations so these These +are exactly the oil lrange equations + + align:start position:0% +are exactly the oil lrange equations + + + align:start position:0% +are exactly the oil lrange equations +where did you see oil lrange equations + + align:start position:0% +where did you see oil lrange equations + + + align:start position:0% +where did you see oil lrange equations +before + + align:start position:0% +before + + + align:start position:0% +before +optimal control optimal + + align:start position:0% + + + + align:start position:0% + +control right you're also famously see + + align:start position:0% +control right you're also famously see + + + align:start position:0% +control right you're also famously see +them in advanced mechanics uh like 806 + + align:start position:0% +them in advanced mechanics uh like 806 + + + align:start position:0% +them in advanced mechanics uh like 806 +or 808 I know what the number is these + + align:start position:0% +or 808 I know what the number is these + + + align:start position:0% +or 808 I know what the number is these +days um where where this is a there's + + align:start position:0% +days um where where this is a there's + + + align:start position:0% +days um where where this is a there's +something called the least action + + align:start position:0% +something called the least action + + + align:start position:0% +something called the least action +principle and you you can write down the + + align:start position:0% +principle and you you can write down the + + + align:start position:0% +principle and you you can write down the +the equations of motion as minimizing + + align:start position:0% +the equations of motion as minimizing + + + align:start position:0% +the equations of motion as minimizing +some integral and you get these these + + align:start position:0% +some integral and you get these these + + + align:start position:0% +some integral and you get these these +oil instead of Newton's Laws you get a + + align:start position:0% +oil instead of Newton's Laws you get a + + + align:start position:0% +oil instead of Newton's Laws you get a +as a different way of getting Newton's + + align:start position:0% +as a different way of getting Newton's + + + align:start position:0% +as a different way of getting Newton's +Law laws you get these oil L equations + + align:start position:0% +Law laws you get these oil L equations + + + align:start position:0% +Law laws you get these oil L equations +they're really nice because they let you + + align:start position:0% +they're really nice because they let you + + + align:start position:0% +they're really nice because they let you +write down basically Newton's laws in + + align:start position:0% +write down basically Newton's laws in + + + align:start position:0% +write down basically Newton's laws in +like really weird coordinate systems uh + + align:start position:0% +like really weird coordinate systems uh + + + align:start position:0% +like really weird coordinate systems uh +pretty easily um yeah so there's a a + + align:start position:0% +pretty easily um yeah so there's a a + + + align:start position:0% +pretty easily um yeah so there's a a +famous example of of the o l Grange + + align:start position:0% +famous example of of the o l Grange + + + align:start position:0% +famous example of of the o l Grange +equation that everyone gives um which is + + align:start position:0% +equation that everyone gives um which is + + + align:start position:0% +equation that everyone gives um which is +called the bistone problem has anyone + + align:start position:0% +called the bistone problem has anyone + + + align:start position:0% +called the bistone problem has anyone +heard of the bistone problem we have one + + align:start position:0% +heard of the bistone problem we have one + + + align:start position:0% +heard of the bistone problem we have one +person a couple people right so this is + + align:start position:0% +person a couple people right so this is + + + align:start position:0% +person a couple people right so this is +a famous problem from I think the 18th + + align:start position:0% +a famous problem from I think the 18th + + + align:start position:0% +a famous problem from I think the 18th +century right so suppose you have a mass + + align:start position:0% +century right so suppose you have a mass + + + align:start position:0% +century right so suppose you have a mass +falling down a + + align:start position:0% +falling down a + + + align:start position:0% +falling down a +slope you know sliding down a curve with + + align:start position:0% +slope you know sliding down a curve with + + + align:start position:0% +slope you know sliding down a curve with +with gravity right so it's it's going + + align:start position:0% +with gravity right so it's it's going + + + align:start position:0% +with gravity right so it's it's going +down this curve like a ramp right with + + align:start position:0% +down this curve like a ramp right with + + + align:start position:0% +down this curve like a ramp right with +no friction right just slides down and + + align:start position:0% +no friction right just slides down and + + + align:start position:0% +no friction right just slides down and +you're going starting here you're ending + + align:start position:0% +you're going starting here you're ending + + + align:start position:0% +you're going starting here you're ending +up here and the question is what shape + + align:start position:0% +up here and the question is what shape + + + align:start position:0% +up here and the question is what shape +should this ramp be to get down as + + align:start position:0% +should this ramp be to get down as + + + align:start position:0% +should this ramp be to get down as +quickly as possible should it be a + + align:start position:0% +quickly as possible should it be a + + + align:start position:0% +quickly as possible should it be a +straight ramp well or should be like + + align:start position:0% +straight ramp well or should be like + + + align:start position:0% +straight ramp well or should be like +this you can pretty easily see this + + align:start position:0% +this you can pretty easily see this + + + align:start position:0% +this you can pretty easily see this +shouldn't be like this because then you + + align:start position:0% +shouldn't be like this because then you + + + align:start position:0% +shouldn't be like this because then you +start it'll start out going very very + + align:start position:0% +start it'll start out going very very + + + align:start position:0% +start it'll start out going very very +slowly and then go right a straight ramp + + align:start position:0% +slowly and then go right a straight ramp + + + align:start position:0% +slowly and then go right a straight ramp +or you can go should go down very sleep + + align:start position:0% +or you can go should go down very sleep + + + align:start position:0% +or you can go should go down very sleep +steeply and then flatten out right if it + + align:start position:0% +steeply and then flatten out right if it + + + align:start position:0% +steeply and then flatten out right if it +goes down very steeply it'll get going + + align:start position:0% +goes down very steeply it'll get going + + + align:start position:0% +goes down very steeply it'll get going +up getting a good head of speed pretty + + align:start position:0% +up getting a good head of speed pretty + + + align:start position:0% +up getting a good head of speed pretty +quickly but then it has a longer + + align:start position:0% +quickly but then it has a longer + + + align:start position:0% +quickly but then it has a longer +distance right the straight line would + + align:start position:0% +distance right the straight line would + + + align:start position:0% +distance right the straight line would +be the shortest distance but it's not + + align:start position:0% +be the shortest distance but it's not + + + align:start position:0% +be the shortest distance but it's not +the highest speed and so it was a famous + + align:start position:0% +the highest speed and so it was a famous + + + align:start position:0% +the highest speed and so it was a famous +problem to find called the bistone + + align:start position:0% +problem to find called the bistone + + + align:start position:0% +problem to find called the bistone +problem to find the curve that the of + + align:start position:0% +problem to find the curve that the of + + + align:start position:0% +problem to find the curve that the of +this ramp that minimizes the time and + + align:start position:0% +this ramp that minimizes the time and + + + align:start position:0% +this ramp that minimizes the time and +it's exactly an integral you can write + + align:start position:0% +it's exactly an integral you can write + + + align:start position:0% +it's exactly an integral you can write +down this and you write down a + + align:start position:0% +down this and you write down a + + + align:start position:0% +down this and you write down a +differential equation you can solve it + + align:start position:0% +differential equation you can solve it + + + align:start position:0% +differential equation you can solve it +to get this curve unfortunately the + + align:start position:0% +to get this curve unfortunately the + + + align:start position:0% +to get this curve unfortunately the +differential equation you get is is + + align:start position:0% +differential equation you get is is + + + align:start position:0% +differential equation you get is is +rather nasty it is in close form but + + align:start position:0% +rather nasty it is in close form but + + + align:start position:0% +rather nasty it is in close form but +like it's you know it's not nothing I + + align:start position:0% +like it's you know it's not nothing I + + + align:start position:0% +like it's you know it's not nothing I +would ever assign as a homework problem + + align:start position:0% +would ever assign as a homework problem + + + align:start position:0% +would ever assign as a homework problem +in 1803 for example right so turns out + + align:start position:0% +in 1803 for example right so turns out + + + align:start position:0% +in 1803 for example right so turns out +the the minimum shaped curve is called a + + align:start position:0% +the the minimum shaped curve is called a + + + align:start position:0% +the the minimum shaped curve is called a +cycloid it's like a it's the curve that + + align:start position:0% +cycloid it's like a it's the curve that + + + align:start position:0% +cycloid it's like a it's the curve that +if you like if you have a wheel rolling + + align:start position:0% +if you like if you have a wheel rolling + + + align:start position:0% +if you like if you have a wheel rolling +and you attach a a a pen to one spot in + + align:start position:0% +and you attach a a a pen to one spot in + + + align:start position:0% +and you attach a a a pen to one spot in +the reel on the wheel and as it rolls + + align:start position:0% +the reel on the wheel and as it rolls + + + align:start position:0% +the reel on the wheel and as it rolls +you mark out like the curve that that + + align:start position:0% +you mark out like the curve that that + + + align:start position:0% +you mark out like the curve that that +wheel traces out that's that's the + + align:start position:0% +wheel traces out that's that's the + + + align:start position:0% +wheel traces out that's that's the +that's the shape that you get um so it's + + align:start position:0% +that's the shape that you get um so it's + + + align:start position:0% +that's the shape that you get um so it's +a famous so I'll even write that down is + + align:start position:0% +a famous so I'll even write that down is + + + align:start position:0% +a famous so I'll even write that down is +it a + + align:start position:0% +it a + + + align:start position:0% +it a +Google uh + + align:start position:0% +Google uh + + + align:start position:0% +Google uh +example uh + + align:start position:0% +example uh + + + align:start position:0% +example uh +Google the brachistochrone problem + + align:start position:0% +Google the brachistochrone problem + + + align:start position:0% +Google the brachistochrone problem +braist + + align:start position:0% +braist + + + align:start position:0% +braist +toone + + align:start position:0% +toone + + + align:start position:0% +toone +problem that's another that's one + + align:start position:0% +problem that's another that's one + + + align:start position:0% +problem that's another that's one +example uh another example would be uh + + align:start position:0% +example uh another example would be uh + + + align:start position:0% +example uh another example would be uh +Google the um the um the principle of + + align:start position:0% +Google the um the um the principle of + + + align:start position:0% +Google the um the um the principle of +least action + + align:start position:0% + + + + align:start position:0% + +that's that's how you get the oil the gr + + align:start position:0% +that's that's how you get the oil the gr + + + align:start position:0% +that's that's how you get the oil the gr +equations in mechanics um so great + + align:start position:0% +equations in mechanics um so great + + + align:start position:0% +equations in mechanics um so great +example so but it lets you turn these + + align:start position:0% +example so but it lets you turn these + + + align:start position:0% +example so but it lets you turn these +things into differen equations right but + + align:start position:0% +things into differen equations right but + + + align:start position:0% +things into differen equations right but +what you're really doing is just taking + + align:start position:0% +what you're really doing is just taking + + + align:start position:0% +what you're really doing is just taking +the gradient in set an equal to zero and + + align:start position:0% +the gradient in set an equal to zero and + + + align:start position:0% +the gradient in set an equal to zero and +it just it's just you have to understand + + align:start position:0% +it just it's just you have to understand + + + align:start position:0% +it just it's just you have to understand +okay functions are a kind of vector I + + align:start position:0% +okay functions are a kind of vector I + + + align:start position:0% +okay functions are a kind of vector I +can still talk about linear operators on + + align:start position:0% +can still talk about linear operators on + + + align:start position:0% +can still talk about linear operators on +functions I can talk about dot products + + align:start position:0% +functions I can talk about dot products + + + align:start position:0% +functions I can talk about dot products +of functions so this this linear + + align:start position:0% +of functions so this this linear + + + align:start position:0% +of functions so this this linear +operator is exactly for the change I can + + align:start position:0% +operator is exactly for the change I can + + + align:start position:0% +operator is exactly for the change I can +take the the derivative just is the + + align:start position:0% +take the the derivative just is the + + + align:start position:0% +take the the derivative just is the +linearized change in the output in this + + align:start position:0% +linearized change in the output in this + + + align:start position:0% +linearized change in the output in this +integral and if I do a little bit of + + align:start position:0% +integral and if I do a little bit of + + + align:start position:0% +integral and if I do a little bit of +algebra with the integration by parts I + + align:start position:0% +algebra with the integration by parts I + + + align:start position:0% +algebra with the integration by parts I +can write that as an integral of + + align:start position:0% +can write that as an integral of + + + align:start position:0% +can write that as an integral of +something times du that's that's a DOT + + align:start position:0% +something times du that's that's a DOT + + + align:start position:0% +something times du that's that's a DOT +product and it generalized sense so this + + align:start position:0% +product and it generalized sense so this + + + align:start position:0% +product and it generalized sense so this +thing is a generalized gradient um so um + + align:start position:0% +thing is a generalized gradient um so um + + + align:start position:0% +thing is a generalized gradient um so um +that that you you set equal to zero if + + align:start position:0% +that that you you set equal to zero if + + + align:start position:0% +that that you you set equal to zero if +you want a minimum or + + align:start position:0% +you want a minimum or + + + align:start position:0% +you want a minimum or +maximum any + + align:start position:0% +maximum any + + + align:start position:0% +maximum any +questions right so there's and I'll put + + align:start position:0% +questions right so there's and I'll put + + + align:start position:0% +questions right so there's and I'll put +up some references as well on both the + + align:start position:0% +up some references as well on both the + + + align:start position:0% +up some references as well on both the +um what Frank talked about uh there + + align:start position:0% +um what Frank talked about uh there + + + align:start position:0% +um what Frank talked about uh there +there's we have some uh some Pap there's + + align:start position:0% +there's we have some uh some Pap there's + + + align:start position:0% +there's we have some uh some Pap there's +some papers and other reviews and and + + align:start position:0% +some papers and other reviews and and + + + align:start position:0% +some papers and other reviews and and +things on adjoint methods for Odes and + + align:start position:0% +things on adjoint methods for Odes and + + + align:start position:0% +things on adjoint methods for Odes and +there's lots of uh papers and books on C + + align:start position:0% +there's lots of uh papers and books on C + + + align:start position:0% +there's lots of uh papers and books on C +this or Grange equations and the the + + align:start position:0% +this or Grange equations and the the + + + align:start position:0% +this or Grange equations and the the +traditional topic for deriving these or + + align:start position:0% +traditional topic for deriving these or + + + align:start position:0% +traditional topic for deriving these or +Grange equations is is calculus of + + align:start position:0% +Grange equations is is calculus of + + + align:start position:0% +Grange equations is is calculus of +variations that's what it's called or + + align:start position:0% +variations that's what it's called or + + + align:start position:0% +variations that's what it's called or +variational calculus um um but it really + + align:start position:0% +variational calculus um um but it really + + + align:start position:0% +variational calculus um um but it really +is just taking the once we've now that + + align:start position:0% +is just taking the once we've now that + + + align:start position:0% +is just taking the once we've now that +we've generalized a notion of derivative + + align:start position:0% +we've generalized a notion of derivative + + + align:start position:0% +we've generalized a notion of derivative +it's just it's it's it's the same notion + + align:start position:0% +it's just it's it's it's the same notion + + + align:start position:0% +it's just it's it's it's the same notion +it's not it's nothing really new it's + + align:start position:0% +it's not it's nothing really new it's + + + align:start position:0% +it's not it's nothing really new it's +just applied to a new Vector space + + align:start position:0% +just applied to a new Vector space + + + align:start position:0% +just applied to a new Vector space +there's a beautiful beautiful book by + + align:start position:0% +there's a beautiful beautiful book by + + + align:start position:0% +there's a beautiful beautiful book by +gelfond and shiloff that I'll put up a + + align:start position:0% +gelfond and shiloff that I'll put up a + + + align:start position:0% +gelfond and shiloff that I'll put up a +link to on calculus of variations I + + align:start position:0% +link to on calculus of variations I + + + align:start position:0% +link to on calculus of variations I +really like it it's like it's one of + + align:start position:0% +really like it it's like it's one of + + + align:start position:0% +really like it it's like it's one of +those things that starts out chapter one + + align:start position:0% +those things that starts out chapter one + + + align:start position:0% +those things that starts out chapter one +is accessible to a freshman and then you + + align:start position:0% +is accessible to a freshman and then you + + + align:start position:0% +is accessible to a freshman and then you +know gets more and more advanced as it + + align:start position:0% +know gets more and more advanced as it + + + align:start position:0% +know gets more and more advanced as it +goes along but uh it's a me a very very + + align:start position:0% +goes along but uh it's a me a very very + + + align:start position:0% +goes along but uh it's a me a very very +slim book like you know 150 Pages or + + align:start position:0% +slim book like you know 150 Pages or + + + align:start position:0% +slim book like you know 150 Pages or +something like + + align:start position:0% + + + + align:start position:0% + +that \ No newline at end of file diff --git a/v_VmhyueJNQ.txt b/v_VmhyueJNQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..3514278ccd8e2a732d2dec45d3bbdc4664c10378 --- /dev/null +++ b/v_VmhyueJNQ.txt @@ -0,0 +1,8155 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +ocw.mit.edu uh we + + align:start position:0% +ocw.mit.edu uh we + + + align:start position:0% +ocw.mit.edu uh we +have few more slides from last time to + + align:start position:0% +have few more slides from last time to + + + align:start position:0% +have few more slides from last time to +finish up because of the problems I had + + align:start position:0% +finish up because of the problems I had + + + align:start position:0% +finish up because of the problems I had +with the computer we have a class + + align:start position:0% +with the computer we have a class + + + align:start position:0% +with the computer we have a class +wednesday with a quiz and Friday as most + + align:start position:0% +wednesday with a quiz and Friday as most + + + align:start position:0% +wednesday with a quiz and Friday as most +of you know there's it's a student + + align:start position:0% +of you know there's it's a student + + + align:start position:0% +of you know there's it's a student +holiday I would encourage all of you to + + align:start position:0% +holiday I would encourage all of you to + + + align:start position:0% +holiday I would encourage all of you to +go to the career fair especially if + + align:start position:0% +go to the career fair especially if + + + align:start position:0% +go to the career fair especially if +you've not been to one before even if + + align:start position:0% +you've not been to one before even if + + + align:start position:0% +you've not been to one before even if +you're you fully expect to go to medical + + align:start position:0% +you're you fully expect to go to medical + + + align:start position:0% +you're you fully expect to go to medical +school or something like that you never + + align:start position:0% +school or something like that you never + + + align:start position:0% +school or something like that you never +know you should know what's out + + align:start position:0% + + + + align:start position:0% + +there + + align:start position:0% + + + + align:start position:0% + +all right we started talking about the + + align:start position:0% +all right we started talking about the + + + align:start position:0% +all right we started talking about the +ethology of geese last time and we + + align:start position:0% +ethology of geese last time and we + + + align:start position:0% +ethology of geese last time and we +saw we saw a video + + align:start position:0% +saw we saw a video + + + align:start position:0% +saw we saw a video +of where you could see Conor Lawrence + + align:start position:0% +of where you could see Conor Lawrence + + + align:start position:0% +of where you could see Conor Lawrence +and some of his uh his early work + + align:start position:0% +and some of his uh his early work + + + align:start position:0% +and some of his uh his early work +discovering + + align:start position:0% +discovering + + + align:start position:0% +discovering +imprinting they showed the work he had + + align:start position:0% +imprinting they showed the work he had + + + align:start position:0% +imprinting they showed the work he had +done with + + align:start position:0% +done with + + + align:start position:0% +done with +Geese U and then later work on social + + align:start position:0% +Geese U and then later work on social + + + align:start position:0% +Geese U and then later work on social +behavior of geese and the role of early + + align:start position:0% +behavior of geese and the role of early + + + align:start position:0% +behavior of geese and the role of early +experience and + + align:start position:0% + + + + align:start position:0% + +learning what was the what was the + + align:start position:0% +learning what was the what was the + + + align:start position:0% +learning what was the what was the +answer to this question is the response + + align:start position:0% +answer to this question is the response + + + align:start position:0% +answer to this question is the response +of geese to an aerial Predator innate + + align:start position:0% +of geese to an aerial Predator innate + + + align:start position:0% +of geese to an aerial Predator innate +you know in the video you saw this + + align:start position:0% +you know in the video you saw this + + + align:start position:0% +you know in the video you saw this +uh bird shape that they Glide it was + + align:start position:0% +uh bird shape that they Glide it was + + + align:start position:0% +uh bird shape that they Glide it was +actually made to look quite a bit like a + + align:start position:0% +actually made to look quite a bit like a + + + align:start position:0% +actually made to look quite a bit like a +bird for that video but you can use a + + align:start position:0% +bird for that video but you can use a + + + align:start position:0% +bird for that video but you can use a +silhouette and they glided above the + + align:start position:0% +silhouette and they glided above the + + + align:start position:0% +silhouette and they glided above the +bird and the birds show it a mobbing + + align:start position:0% +bird and the birds show it a mobbing + + + align:start position:0% +bird and the birds show it a mobbing +reaction uh they forget about their + + align:start position:0% +reaction uh they forget about their + + + align:start position:0% +reaction uh they forget about their +individual squabbles and whatever they + + align:start position:0% +individual squabbles and whatever they + + + align:start position:0% +individual squabbles and whatever they +had been doing and they + + align:start position:0% +had been doing and they + + + align:start position:0% +had been doing and they +all pretty much do the same thing and + + align:start position:0% +all pretty much do the same thing and + + + align:start position:0% +all pretty much do the same thing and +they protect their young and so + + align:start position:0% +they protect their young and so + + + align:start position:0% +they protect their young and so +forth is that an innate response what + + align:start position:0% +forth is that an innate response what + + + align:start position:0% +forth is that an innate response what +did we + + align:start position:0% + + + + align:start position:0% + +say do they have an innate response to + + align:start position:0% +say do they have an innate response to + + + align:start position:0% +say do they have an innate response to +to the shape of a hawk as opposed to a + + align:start position:0% +to the shape of a hawk as opposed to a + + + align:start position:0% +to the shape of a hawk as opposed to a +goose + + align:start position:0% + + + + align:start position:0% + +Hawk shapes short neck longer tail + + align:start position:0% +Hawk shapes short neck longer tail + + + align:start position:0% +Hawk shapes short neck longer tail +theose shape or duck shape long neck + + align:start position:0% +theose shape or duck shape long neck + + + align:start position:0% +theose shape or duck shape long neck +shorter + + align:start position:0% +shorter + + + align:start position:0% +shorter +tail so they make a very different + + align:start position:0% +tail so they make a very different + + + align:start position:0% +tail so they make a very different +silhouette when they're when it's + + align:start position:0% +silhouette when they're when it's + + + align:start position:0% +silhouette when they're when it's +moving is that an innate + + align:start position:0% +moving is that an innate + + + align:start position:0% +moving is that an innate +response there's still some claims in + + align:start position:0% +response there's still some claims in + + + align:start position:0% +response there's still some claims in +the literature that in perhaps some + + align:start position:0% +the literature that in perhaps some + + + align:start position:0% +the literature that in perhaps some +birds it is innate and it's clear that + + align:start position:0% +birds it is innate and it's clear that + + + align:start position:0% +birds it is innate and it's clear that +there are some innate responses they to + + align:start position:0% +there are some innate responses they to + + + align:start position:0% +there are some innate responses they to +overhead + + align:start position:0% +overhead + + + align:start position:0% +overhead +movement but the precise shape they're + + align:start position:0% +movement but the precise shape they're + + + align:start position:0% +movement but the precise shape they're +responding to is it's probably not + + align:start position:0% +responding to is it's probably not + + + align:start position:0% +responding to is it's probably not +innate that doesn't mean that birds + + align:start position:0% +innate that doesn't mean that birds + + + align:start position:0% +innate that doesn't mean that birds +don't have many innate responses to + + align:start position:0% +don't have many innate responses to + + + align:start position:0% +don't have many innate responses to +specific visual configurations because + + align:start position:0% +specific visual configurations because + + + align:start position:0% +specific visual configurations because +they certainly + + align:start position:0% +they certainly + + + align:start position:0% +they certainly +do migrating birds for example can + + align:start position:0% +do migrating birds for example can + + + align:start position:0% +do migrating birds for example can +respond to the pattern patterns of the + + align:start position:0% +respond to the pattern patterns of the + + + align:start position:0% +respond to the pattern patterns of the +Stars + + align:start position:0% +Stars + + + align:start position:0% +Stars +but + + align:start position:0% +but + + + align:start position:0% +but +uh in this case they're responding to + + align:start position:0% +uh in this case they're responding to + + + align:start position:0% +uh in this case they're responding to +slow overhead movement and the species + + align:start position:0% +slow overhead movement and the species + + + align:start position:0% +slow overhead movement and the species +may differ a little bit into the details + + align:start position:0% +may differ a little bit into the details + + + align:start position:0% +may differ a little bit into the details +of the movement they respond best + + align:start position:0% +of the movement they respond best + + + align:start position:0% +of the movement they respond best +to but that doesn't mean it doesn't + + align:start position:0% +to but that doesn't mean it doesn't + + + align:start position:0% +to but that doesn't mean it doesn't +change with experience they do depending + + align:start position:0% +change with experience they do depending + + + align:start position:0% +change with experience they do depending +on their experience they can + + align:start position:0% +on their experience they can + + + align:start position:0% +on their experience they can +change + + align:start position:0% +change + + + align:start position:0% +change +uh so let's that was this + + align:start position:0% +uh so let's that was this + + + align:start position:0% +uh so let's that was this +discussion + + align:start position:0% +discussion + + + align:start position:0% +discussion +and this is the paper that did that a + + align:start position:0% +and this is the paper that did that a + + + align:start position:0% +and this is the paper that did that a +very nice analysis of the whole Haw + + align:start position:0% +very nice analysis of the whole Haw + + + align:start position:0% +very nice analysis of the whole Haw +Goose story because of + + align:start position:0% +Goose story because of + + + align:start position:0% +Goose story because of +the some of the early work of Timber and + + align:start position:0% +the some of the early work of Timber and + + + align:start position:0% +the some of the early work of Timber and +Lawrence some of which they did + + align:start position:0% +Lawrence some of which they did + + + align:start position:0% +Lawrence some of which they did +together uh before World War II where + + align:start position:0% +together uh before World War II where + + + align:start position:0% +together uh before World War II where +they met and spent a summer together + + align:start position:0% +they met and spent a summer together + + + align:start position:0% +they met and spent a summer together +working on this and other + + align:start position:0% + + + + align:start position:0% + +problems + + align:start position:0% + + + + align:start position:0% + +let's talk a little bit about + + align:start position:0% +let's talk a little bit about + + + align:start position:0% +let's talk a little bit about +human instincts or fixed action + + align:start position:0% + + + + align:start position:0% + +patterns we know that yawning can be + + align:start position:0% +patterns we know that yawning can be + + + align:start position:0% +patterns we know that yawning can be +considered a human fixed action + + align:start position:0% +considered a human fixed action + + + align:start position:0% +considered a human fixed action +pattern tends to be triggered by the + + align:start position:0% +pattern tends to be triggered by the + + + align:start position:0% +pattern tends to be triggered by the +yawning in other people it seems to have + + align:start position:0% +yawning in other people it seems to have + + + align:start position:0% +yawning in other people it seems to have +some kind of social meaning it doesn't + + align:start position:0% +some kind of social meaning it doesn't + + + align:start position:0% +some kind of social meaning it doesn't +only mean that you feel tired in fact it + + align:start position:0% +only mean that you feel tired in fact it + + + align:start position:0% +only mean that you feel tired in fact it +has other meanings as well + + align:start position:0% +has other meanings as well + + + align:start position:0% +has other meanings as well +and there's still some things about it + + align:start position:0% +and there's still some things about it + + + align:start position:0% +and there's still some things about it +we don't fully understand but we do know + + align:start position:0% +we don't fully understand but we do know + + + align:start position:0% +we don't fully understand but we do know +it's + + align:start position:0% + + + + align:start position:0% + +inbuilt um these are other other + + align:start position:0% +inbuilt um these are other other + + + align:start position:0% +inbuilt um these are other other +examples first of all expressions of + + align:start position:0% +examples first of all expressions of + + + align:start position:0% +examples first of all expressions of +emotion that was the work remember of + + align:start position:0% +emotion that was the work remember of + + + align:start position:0% +emotion that was the work remember of +irus iel iisf felt where he studied + + align:start position:0% +irus iel iisf felt where he studied + + + align:start position:0% +irus iel iisf felt where he studied +emotional + + align:start position:0% +emotional + + + align:start position:0% +emotional +expressions in blind and deaf people + + align:start position:0% +expressions in blind and deaf people + + + align:start position:0% +expressions in blind and deaf people +people born blind and deaf found that + + align:start position:0% +people born blind and deaf found that + + + align:start position:0% +people born blind and deaf found that +they were the same as in normally cited + + align:start position:0% +they were the same as in normally cited + + + align:start position:0% +they were the same as in normally cited +and hearing people and he also studied + + align:start position:0% +and hearing people and he also studied + + + align:start position:0% +and hearing people and he also studied +across cultures he went to cultures that + + align:start position:0% +across cultures he went to cultures that + + + align:start position:0% +across cultures he went to cultures that +had never seen + + align:start position:0% +had never seen + + + align:start position:0% +had never seen +Western Expressions at all and uh people + + align:start position:0% +Western Expressions at all and uh people + + + align:start position:0% +Western Expressions at all and uh people +in those cultures + + align:start position:0% +in those cultures + + + align:start position:0% +in those cultures +U made all the very same types of + + align:start position:0% +U made all the very same types of + + + align:start position:0% +U made all the very same types of +Expressions that you see + + align:start position:0% +Expressions that you see + + + align:start position:0% +Expressions that you see +in and uh what we call the more + + align:start position:0% +in and uh what we call the more + + + align:start position:0% +in and uh what we call the more +developed culture + + align:start position:0% + + + + align:start position:0% + +walking is an instinct but don't we + + align:start position:0% +walking is an instinct but don't we + + + align:start position:0% +walking is an instinct but don't we +teach our children to walk we always say + + align:start position:0% +teach our children to walk we always say + + + align:start position:0% +teach our children to walk we always say +that oh I've been teaching my child to + + align:start position:0% +that oh I've been teaching my child to + + + align:start position:0% +that oh I've been teaching my child to +walk and he finally did + + align:start position:0% +walk and he finally did + + + align:start position:0% +walk and he finally did +it he was a little bit slow to + + align:start position:0% +it he was a little bit slow to + + + align:start position:0% +it he was a little bit slow to +learn is this an accurate way of + + align:start position:0% +learn is this an accurate way of + + + align:start position:0% +learn is this an accurate way of +talking + + align:start position:0% +talking + + + align:start position:0% +talking +somebody + + align:start position:0% +somebody + + + align:start position:0% +somebody +no because walking is instinctive + + align:start position:0% +no because walking is instinctive + + + align:start position:0% +no because walking is instinctive +Behavior the child + + align:start position:0% +Behavior the child + + + align:start position:0% +Behavior the child +walks learn he he starts walking because + + align:start position:0% +walks learn he he starts walking because + + + align:start position:0% +walks learn he he starts walking because +his nervous system has reached a state + + align:start position:0% +his nervous system has reached a state + + + align:start position:0% +his nervous system has reached a state +of maturity where the circuits + + align:start position:0% +of maturity where the circuits + + + align:start position:0% +of maturity where the circuits +underlying walking are mature enough + + align:start position:0% +underlying walking are mature enough + + + align:start position:0% +underlying walking are mature enough +they're spinal circuits primarily also + + align:start position:0% +they're spinal circuits primarily also + + + align:start position:0% +they're spinal circuits primarily also +hindbrain that you need to B you need + + align:start position:0% +hindbrain that you need to B you need + + + align:start position:0% +hindbrain that you need to B you need +the balance of the V system and so forth + + align:start position:0% +the balance of the V system and so forth + + + align:start position:0% +the balance of the V system and so forth +which is a hindbrain + + align:start position:0% +which is a hindbrain + + + align:start position:0% +which is a hindbrain +sense uh + + align:start position:0% + + + + align:start position:0% + +but it's distinctive movement then I + + align:start position:0% +but it's distinctive movement then I + + + align:start position:0% +but it's distinctive movement then I +said that iblink and swallowing are + + align:start position:0% +said that iblink and swallowing are + + + align:start position:0% +said that iblink and swallowing are +actually fixed action patterns though + + align:start position:0% +actually fixed action patterns though + + + align:start position:0% +actually fixed action patterns though +they're normally called + + align:start position:0% +they're normally called + + + align:start position:0% +they're normally called +reflexes so what would why would they be + + align:start position:0% +reflexes so what would why would they be + + + align:start position:0% +reflexes so what would why would they be +called fixed action patterns or not + + align:start position:0% +called fixed action patterns or not + + + align:start position:0% +called fixed action patterns or not +reflexes what what do they need to be a + + align:start position:0% +reflexes what what do they need to be a + + + align:start position:0% +reflexes what what do they need to be a +fixed action pattern and not a + + align:start position:0% +fixed action pattern and not a + + + align:start position:0% +fixed action pattern and not a +reflex that could be on the quiz on + + align:start position:0% +reflex that could be on the quiz on + + + align:start position:0% +reflex that could be on the quiz on +St there's got to be a difference + + align:start position:0% +St there's got to be a difference + + + align:start position:0% +St there's got to be a difference +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +yes okay there's some motivation which + + align:start position:0% +yes okay there's some motivation which + + + align:start position:0% +yes okay there's some motivation which +builds up over time so the longer you go + + align:start position:0% +builds up over time so the longer you go + + + align:start position:0% +builds up over time so the longer you go +okay without an eye blank or without + + align:start position:0% +okay without an eye blank or without + + + align:start position:0% +okay without an eye blank or without +swallowing the more likely you are to do + + align:start position:0% +swallowing the more likely you are to do + + + align:start position:0% +swallowing the more likely you are to do +it and we + + align:start position:0% +it and we + + + align:start position:0% +it and we +do we you it's difficult to go too long + + align:start position:0% +do we you it's difficult to go too long + + + align:start position:0% +do we you it's difficult to go too long +without blinking your eyes I mean + + align:start position:0% +without blinking your eyes I mean + + + align:start position:0% +without blinking your eyes I mean +there's clear function of that you need + + align:start position:0% +there's clear function of that you need + + + align:start position:0% +there's clear function of that you need +need to lubricate the + + align:start position:0% + + + + align:start position:0% + +corneas and we can stare at each other + + align:start position:0% +corneas and we can stare at each other + + + align:start position:0% +corneas and we can stare at each other +and see who blinks + + align:start position:0% +and see who blinks + + + align:start position:0% +and see who blinks +first but in fact the motivation to + + align:start position:0% +first but in fact the motivation to + + + align:start position:0% +first but in fact the motivation to +Blink gets the motivation goes up and up + + align:start position:0% +Blink gets the motivation goes up and up + + + align:start position:0% +Blink gets the motivation goes up and up +and up until until the threshold for + + align:start position:0% +and up until until the threshold for + + + align:start position:0% +and up until until the threshold for +eliciting that + + align:start position:0% +eliciting that + + + align:start position:0% +eliciting that +response becomes very low and almost + + align:start position:0% +response becomes very low and almost + + + align:start position:0% +response becomes very low and almost +anything can cause + + align:start position:0% +anything can cause + + + align:start position:0% +anything can cause +it of course we blink our eyes to + + align:start position:0% +it of course we blink our eyes to + + + align:start position:0% +it of course we blink our eyes to +protect our corneas not just from trying + + align:start position:0% +protect our corneas not just from trying + + + align:start position:0% +protect our corneas not just from trying +but from other things too if you puff + + align:start position:0% +but from other things too if you puff + + + align:start position:0% +but from other things too if you puff +air on it that's the one that's normally + + align:start position:0% +air on it that's the one that's normally + + + align:start position:0% +air on it that's the one that's normally +called a reflex any Touch of Coria will + + align:start position:0% +called a reflex any Touch of Coria will + + + align:start position:0% +called a reflex any Touch of Coria will +elicit but it also fits all the + + align:start position:0% +elicit but it also fits all the + + + align:start position:0% +elicit but it also fits all the +characteristics of an instinctive + + align:start position:0% +characteristics of an instinctive + + + align:start position:0% +characteristics of an instinctive +movement the fixed action + + align:start position:0% +movement the fixed action + + + align:start position:0% +movement the fixed action +pattern okay it doesn't normally respond + + align:start position:0% +pattern okay it doesn't normally respond + + + align:start position:0% +pattern okay it doesn't normally respond +to a sensory trigger but it will occur + + align:start position:0% +to a sensory trigger but it will occur + + + align:start position:0% +to a sensory trigger but it will occur +with almost no trigger with very little + + align:start position:0% +with almost no trigger with very little + + + align:start position:0% +with almost no trigger with very little +trigger um after enough time has passed + + align:start position:0% +trigger um after enough time has passed + + + align:start position:0% +trigger um after enough time has passed +the same is true for swallowing we don't + + align:start position:0% +the same is true for swallowing we don't + + + align:start position:0% +the same is true for swallowing we don't +swallow as often as we blink our eyes + + align:start position:0% +swallow as often as we blink our eyes + + + align:start position:0% +swallow as often as we blink our eyes +but it it still has many of the + + align:start position:0% +but it it still has many of the + + + align:start position:0% +but it it still has many of the +characteristics of a fixed action + + align:start position:0% +characteristics of a fixed action + + + align:start position:0% +characteristics of a fixed action +pattern okay and that we discussed a + + align:start position:0% +pattern okay and that we discussed a + + + align:start position:0% +pattern okay and that we discussed a +little bit here + + align:start position:0% +little bit here + + + align:start position:0% +little bit here +um so now let's go to another term + + align:start position:0% +um so now let's go to another term + + + align:start position:0% +um so now let's go to another term +common in + + align:start position:0% +common in + + + align:start position:0% +common in +ethology uh the concept of a supernormal + + align:start position:0% +ethology uh the concept of a supernormal + + + align:start position:0% +ethology uh the concept of a supernormal +stimulus we say such a stimulus acts as + + align:start position:0% +stimulus we say such a stimulus acts as + + + align:start position:0% +stimulus we say such a stimulus acts as +a Rel leer of a fixed action + + align:start position:0% + + + + align:start position:0% + +pattern uh and I'm asking here for a + + align:start position:0% +pattern uh and I'm asking here for a + + + align:start position:0% +pattern uh and I'm asking here for a +fixed action pattern in haing Gull + + align:start position:0% +fixed action pattern in haing Gull + + + align:start position:0% +fixed action pattern in haing Gull +chicks but you can think of supern + + align:start position:0% +chicks but you can think of supern + + + align:start position:0% +chicks but you can think of supern +normal other kinds of supernormal + + align:start position:0% +normal other kinds of supernormal + + + align:start position:0% +normal other kinds of supernormal +stimuli for other + + align:start position:0% +stimuli for other + + + align:start position:0% +stimuli for other +animals + + align:start position:0% +animals + + + align:start position:0% +animals +so in the case of hering GS they have + + align:start position:0% +so in the case of hering GS they have + + + align:start position:0% +so in the case of hering GS they have +this conspicuous red orange spot pretty + + align:start position:0% +this conspicuous red orange spot pretty + + + align:start position:0% +this conspicuous red orange spot pretty +conspicuous you can see it there in the + + align:start position:0% +conspicuous you can see it there in the + + + align:start position:0% +conspicuous you can see it there in the +go that orange spot spot it seen better + + align:start position:0% +go that orange spot spot it seen better + + + align:start position:0% +go that orange spot spot it seen better +from + + align:start position:0% +from + + + align:start position:0% +from +below + + align:start position:0% +below + + + align:start position:0% +below +uh and chicks G chicks respond to that + + align:start position:0% +uh and chicks G chicks respond to that + + + align:start position:0% +uh and chicks G chicks respond to that +spot when the the their parent is over + + align:start position:0% +spot when the the their parent is over + + + align:start position:0% +spot when the the their parent is over +them and + + align:start position:0% +them and + + + align:start position:0% +them and +moving + + align:start position:0% +moving + + + align:start position:0% +moving +uh you can get an even stronger gaping + + align:start position:0% +uh you can get an even stronger gaping + + + align:start position:0% +uh you can get an even stronger gaping +response just + + align:start position:0% +response just + + + align:start position:0% +response just +by painting an orange out on a yellow + + align:start position:0% +by painting an orange out on a yellow + + + align:start position:0% +by painting an orange out on a yellow +pencil and moving it a lot you're can to + + align:start position:0% +pencil and moving it a lot you're can to + + + align:start position:0% +pencil and moving it a lot you're can to +get a stronger response you can make it + + align:start position:0% +get a stronger response you can make it + + + align:start position:0% +get a stronger response you can make it +a supernormal + + align:start position:0% +a supernormal + + + align:start position:0% +a supernormal +stimulus by making it more prominent by + + align:start position:0% +stimulus by making it more prominent by + + + align:start position:0% +stimulus by making it more prominent by +more + + align:start position:0% +more + + + align:start position:0% +more +movement uh you can have perhaps greater + + align:start position:0% +movement uh you can have perhaps greater + + + align:start position:0% +movement uh you can have perhaps greater +contrast but you can elicit that + + align:start position:0% +contrast but you can elicit that + + + align:start position:0% +contrast but you can elicit that +response even more and when you it you + + align:start position:0% +response even more and when you it you + + + align:start position:0% +response even more and when you it you +create a stronger response than + + align:start position:0% +create a stronger response than + + + align:start position:0% +create a stronger response than +normal with a slightly different + + align:start position:0% +normal with a slightly different + + + align:start position:0% +normal with a slightly different +stimulus than we call it a supernormal + + align:start position:0% +stimulus than we call it a supernormal + + + align:start position:0% +stimulus than we call it a supernormal +stimulus + + align:start position:0% +stimulus + + + align:start position:0% +stimulus +another early Discovery by ethologist + + align:start position:0% +another early Discovery by ethologist + + + align:start position:0% +another early Discovery by ethologist +was the supernormal stimulus in G gulls + + align:start position:0% +was the supernormal stimulus in G gulls + + + align:start position:0% +was the supernormal stimulus in G gulls +to uh an egg that's rolled away from the + + align:start position:0% +to uh an egg that's rolled away from the + + + align:start position:0% +to uh an egg that's rolled away from the +nest like a hering gull a nest on + + align:start position:0% +nest like a hering gull a nest on + + + align:start position:0% +nest like a hering gull a nest on +Shore an egg that rolls away from the + + align:start position:0% +Shore an egg that rolls away from the + + + align:start position:0% +Shore an egg that rolls away from the +other + + align:start position:0% +other + + + align:start position:0% +other +eggs uh the bird reaches out + + align:start position:0% +eggs uh the bird reaches out + + + align:start position:0% +eggs uh the bird reaches out +and you know hooks his beak around it + + align:start position:0% +and you know hooks his beak around it + + + align:start position:0% +and you know hooks his beak around it +and pulls it back into the nest by + + align:start position:0% +and pulls it back into the nest by + + + align:start position:0% +and pulls it back into the nest by +Rolling the egg back into the nest and + + align:start position:0% +Rolling the egg back into the nest and + + + align:start position:0% +Rolling the egg back into the nest and +if you make an egg larger than + + align:start position:0% +if you make an egg larger than + + + align:start position:0% +if you make an egg larger than +normal he responds more strongly shows + + align:start position:0% +normal he responds more strongly shows + + + align:start position:0% +normal he responds more strongly shows +more vigorous egg rolling serves as a + + align:start position:0% +more vigorous egg rolling serves as a + + + align:start position:0% +more vigorous egg rolling serves as a +supernormal + + align:start position:0% + + + + align:start position:0% + +stimulus so then I want some examples in + + align:start position:0% +stimulus so then I want some examples in + + + align:start position:0% +stimulus so then I want some examples in +humans can you think of any supernormal + + align:start position:0% +humans can you think of any supernormal + + + align:start position:0% +humans can you think of any supernormal +stimuli in humans we actually use this + + align:start position:0% +stimuli in humans we actually use this + + + align:start position:0% +stimuli in humans we actually use this +in + + align:start position:0% +in + + + align:start position:0% +in +advertising and in social behavior let's + + align:start position:0% +advertising and in social behavior let's + + + align:start position:0% +advertising and in social behavior let's +start with Foods + + align:start position:0% +start with Foods + + + align:start position:0% +start with Foods +foods that are especially sweet and high + + align:start position:0% +foods that are especially sweet and high + + + align:start position:0% +foods that are especially sweet and high +in + + align:start position:0% +in + + + align:start position:0% +in +fats uh serve as super normal stimuli we + + align:start position:0% +fats uh serve as super normal stimuli we + + + align:start position:0% +fats uh serve as super normal stimuli we +have an instinctive + + align:start position:0% +have an instinctive + + + align:start position:0% +have an instinctive +preference for sweeter and fatter + + align:start position:0% + + + + align:start position:0% + +Foods U at least most of us + + align:start position:0% +Foods U at least most of us + + + align:start position:0% +Foods U at least most of us +do and I put in here beware of + + align:start position:0% +do and I put in here beware of + + + align:start position:0% +do and I put in here beware of +restaurants because there's a simple + + align:start position:0% +restaurants because there's a simple + + + align:start position:0% +restaurants because there's a simple +reason why I say beware in restaurants + + align:start position:0% +reason why I say beware in restaurants + + + align:start position:0% +reason why I say beware in restaurants +the restaurant owner is in business he + + align:start position:0% +the restaurant owner is in business he + + + align:start position:0% +the restaurant owner is in business he +wants to sell more food he wants to sell + + align:start position:0% +wants to sell more food he wants to sell + + + align:start position:0% +wants to sell more food he wants to sell +food that attracts + + align:start position:0% +food that attracts + + + align:start position:0% +food that attracts +people and the same is true of + + align:start position:0% +people and the same is true of + + + align:start position:0% +people and the same is true of +supermarkets I say beware of + + align:start position:0% +supermarkets I say beware of + + + align:start position:0% +supermarkets I say beware of +supermarkets too I always read the label + + align:start position:0% +supermarkets too I always read the label + + + align:start position:0% +supermarkets too I always read the label +for example when I buy a jam I read all + + align:start position:0% +for example when I buy a jam I read all + + + align:start position:0% +for example when I buy a jam I read all +these different jams they're lined up + + align:start position:0% +these different jams they're lined up + + + align:start position:0% +these different jams they're lined up +all along the Shelf I read calories per + + align:start position:0% +all along the Shelf I read calories per + + + align:start position:0% +all along the Shelf I read calories per +tablespoon 50 + + align:start position:0% +tablespoon 50 + + + align:start position:0% +tablespoon 50 +everyone and then you read the details + + align:start position:0% +everyone and then you read the details + + + align:start position:0% +everyone and then you read the details +and you find out why they've + + align:start position:0% +and you find out why they've + + + align:start position:0% +and you find out why they've +added high fructose corn syrup to it one + + align:start position:0% +added high fructose corn syrup to it one + + + align:start position:0% +added high fructose corn syrup to it one +of the most common ingredients on the + + align:start position:0% +of the most common ingredients on the + + + align:start position:0% +of the most common ingredients on the +American in the American Supermarket is + + align:start position:0% +American in the American Supermarket is + + + align:start position:0% +American in the American Supermarket is +high fructose corn syrup why because + + align:start position:0% +high fructose corn syrup why because + + + align:start position:0% +high fructose corn syrup why because +it's sweet and because people like it + + align:start position:0% +it's sweet and because people like it + + + align:start position:0% +it's sweet and because people like it +better when it's + + align:start position:0% +better when it's + + + align:start position:0% +better when it's +sweet and because I'm diabetic I don't + + align:start position:0% +sweet and because I'm diabetic I don't + + + align:start position:0% +sweet and because I'm diabetic I don't +want the 50 calories I want it to be + + align:start position:0% +want the 50 calories I want it to be + + + align:start position:0% +want the 50 calories I want it to be +natural I don't want artificial + + align:start position:0% +natural I don't want artificial + + + align:start position:0% +natural I don't want artificial +sweetener + + align:start position:0% + + + + align:start position:0% + +either so I prefer to make the jam + + align:start position:0% +either so I prefer to make the jam + + + align:start position:0% +either so I prefer to make the jam +myself or find one that doesn't add that + + align:start position:0% +myself or find one that doesn't add that + + + align:start position:0% +myself or find one that doesn't add that +they even will say all natural on it + + align:start position:0% +they even will say all natural on it + + + align:start position:0% +they even will say all natural on it +sometimes and they'll still add sugar + + align:start position:0% +sometimes and they'll still add sugar + + + align:start position:0% +sometimes and they'll still add sugar +they say well Sugar's + + align:start position:0% + + + + align:start position:0% + +natural + + align:start position:0% +natural + + + align:start position:0% +natural +anyway it's because it's instinctive + + align:start position:0% +anyway it's because it's instinctive + + + align:start position:0% +anyway it's because it's instinctive +that it's used to make more + + align:start position:0% + + + + align:start position:0% + +money think of the stimuli in sexual + + align:start position:0% +money think of the stimuli in sexual + + + align:start position:0% +money think of the stimuli in sexual +attraction we call it the post Bo effect + + align:start position:0% +attraction we call it the post Bo effect + + + align:start position:0% +attraction we call it the post Bo effect +in + + align:start position:0% + + + + align:start position:0% + +advertising when they adverti cars or + + align:start position:0% +advertising when they adverti cars or + + + align:start position:0% +advertising when they adverti cars or +other products they often use a + + align:start position:0% +other products they often use a + + + align:start position:0% +other products they often use a +beautiful woman in the + + align:start position:0% +beautiful woman in the + + + align:start position:0% +beautiful woman in the +ad you know why just to attract + + align:start position:0% +ad you know why just to attract + + + align:start position:0% +ad you know why just to attract +attention they're trying to sell it okay + + align:start position:0% +attention they're trying to sell it okay + + + align:start position:0% +attention they're trying to sell it okay +they put them on posters even if they + + align:start position:0% +they put them on posters even if they + + + align:start position:0% +they put them on posters even if they +have nothing to do with the product that + + align:start position:0% +have nothing to do with the product that + + + align:start position:0% +have nothing to do with the product that +they're actually + + align:start position:0% + + + + align:start position:0% + +advertising with a beautiful smile that + + align:start position:0% +advertising with a beautiful smile that + + + align:start position:0% +advertising with a beautiful smile that +helps too we have an instinct response + + align:start position:0% +helps too we have an instinct response + + + align:start position:0% +helps too we have an instinct response +to + + align:start position:0% +to + + + align:start position:0% +to +that what about enhancements of + + align:start position:0% +that what about enhancements of + + + align:start position:0% +that what about enhancements of +appearance how is male appearance been + + align:start position:0% +appearance how is male appearance been + + + align:start position:0% +appearance how is male appearance been +enhanced in men of course we exaggerate + + align:start position:0% +enhanced in men of course we exaggerate + + + align:start position:0% +enhanced in men of course we exaggerate +shoulder withth we we create suits we + + align:start position:0% +shoulder withth we we create suits we + + + align:start position:0% +shoulder withth we we create suits we +put shoulder pads in I mean men already + + align:start position:0% +put shoulder pads in I mean men already + + + align:start position:0% +put shoulder pads in I mean men already +have broader shoulders than women on + + align:start position:0% +have broader shoulders than women on + + + align:start position:0% +have broader shoulders than women on +average you know but to enhance that we + + align:start position:0% +average you know but to enhance that we + + + align:start position:0% +average you know but to enhance that we +add shoulder + + align:start position:0% + + + + align:start position:0% + +pit + + align:start position:0% +pit + + + align:start position:0% +pit +uh + + align:start position:0% +uh + + + align:start position:0% +uh +in medieval costumes it was common to + + align:start position:0% +in medieval costumes it was common to + + + align:start position:0% +in medieval costumes it was common to +enhance the penis area by uh putting + + align:start position:0% +enhance the penis area by uh putting + + + align:start position:0% +enhance the penis area by uh putting +this cow often in a different color than + + align:start position:0% +this cow often in a different color than + + + align:start position:0% +this cow often in a different color than +you see it in Shakespearean place if + + align:start position:0% +you see it in Shakespearean place if + + + align:start position:0% +you see it in Shakespearean place if +they have period + + align:start position:0% +they have period + + + align:start position:0% +they have period +costumes um + + align:start position:0% +costumes um + + + align:start position:0% +costumes um +and primitive tribes you often see for + + align:start position:0% +and primitive tribes you often see for + + + align:start position:0% +and primitive tribes you often see for +example many of them use this sometimes + + align:start position:0% +example many of them use this sometimes + + + align:start position:0% +example many of them use this sometimes +the only clothing they wear is a peanut + + align:start position:0% +the only clothing they wear is a peanut + + + align:start position:0% +the only clothing they wear is a peanut +sheath their males enh hand the whole + + align:start position:0% +sheath their males enh hand the whole + + + align:start position:0% +sheath their males enh hand the whole +appearance usually of an erect + + align:start position:0% +appearance usually of an erect + + + align:start position:0% +appearance usually of an erect +piece but it's just part of the TR part + + align:start position:0% +piece but it's just part of the TR part + + + align:start position:0% +piece but it's just part of the TR part +of the + + align:start position:0% +of the + + + align:start position:0% +of the +costume so another enhancement it's + + align:start position:0% +costume so another enhancement it's + + + align:start position:0% +costume so another enhancement it's +creating a kind of supernormal stimulus + + align:start position:0% +creating a kind of supernormal stimulus + + + align:start position:0% +creating a kind of supernormal stimulus +female it's even easier to think of + + align:start position:0% +female it's even easier to think of + + + align:start position:0% +female it's even easier to think of +these things the the ways to hip ratio + + align:start position:0% +these things the the ways to hip ratio + + + align:start position:0% +these things the the ways to hip ratio +we have men have a natural response to + + align:start position:0% +we have men have a natural response to + + + align:start position:0% +we have men have a natural response to +young women with a certain waste to hip + + align:start position:0% +young women with a certain waste to hip + + + align:start position:0% +young women with a certain waste to hip +ratio we'll talk about that when we talk + + align:start position:0% +ratio we'll talk about that when we talk + + + align:start position:0% +ratio we'll talk about that when we talk +about research in + + align:start position:0% +about research in + + + align:start position:0% +about research in +sociobiology okay but girdles and + + align:start position:0% +sociobiology okay but girdles and + + + align:start position:0% +sociobiology okay but girdles and +bustles were invented in order to + + align:start position:0% +bustles were invented in order to + + + align:start position:0% +bustles were invented in order to +enhance that of course breast prominence + + align:start position:0% +enhance that of course breast prominence + + + align:start position:0% +enhance that of course breast prominence +that's still pretty common especially in + + align:start position:0% +that's still pretty common especially in + + + align:start position:0% +that's still pretty common especially in +young uh in girls you see it in high + + align:start position:0% +young uh in girls you see it in high + + + align:start position:0% +young uh in girls you see it in high +school but it + + align:start position:0% +school but it + + + align:start position:0% +school but it +occurs almost everywhere in Men Women of + + align:start position:0% +occurs almost everywhere in Men Women of + + + align:start position:0% +occurs almost everywhere in Men Women of +different ages think of other aspects + + align:start position:0% +different ages think of other aspects + + + align:start position:0% +different ages think of other aspects +lip color why is lip color enhanced why + + align:start position:0% +lip color why is lip color enhanced why + + + align:start position:0% +lip color why is lip color enhanced why +do women wear lips again in fact they + + align:start position:0% +do women wear lips again in fact they + + + align:start position:0% +do women wear lips again in fact they +enlarge the lips + + align:start position:0% +enlarge the lips + + + align:start position:0% +enlarge the lips +sometimes what is that related + + align:start position:0% +sometimes what is that related + + + align:start position:0% +sometimes what is that related +to you don't know you do it right some + + align:start position:0% +to you don't know you do it right some + + + align:start position:0% +to you don't know you do it right some +of you + + align:start position:0% +of you + + + align:start position:0% +of you +do you know why often we you know you + + align:start position:0% +do you know why often we you know you + + + align:start position:0% +do you know why often we you know you +don't have to know why when it comes to + + align:start position:0% +don't have to know why when it comes to + + + align:start position:0% +don't have to know why when it comes to +instincts you don't have to know why + + align:start position:0% +instincts you don't have to know why + + + align:start position:0% +instincts you don't have to know why +it's built in you don't have to know + + align:start position:0% +it's built in you don't have to know + + + align:start position:0% +it's built in you don't have to know +where it came from well in sexual + + align:start position:0% +where it came from well in sexual + + + align:start position:0% +where it came from well in sexual +arousal the lips become redder and + + align:start position:0% +arousal the lips become redder and + + + align:start position:0% +arousal the lips become redder and +larger + + align:start position:0% + + + + align:start position:0% + +so it elicits this response especially + + align:start position:0% +so it elicits this response especially + + + align:start position:0% +so it elicits this response especially +from the opposite sex all + + align:start position:0% +from the opposite sex all + + + align:start position:0% +from the opposite sex all +right + + align:start position:0% + + + + align:start position:0% + +uh why would shoulder sze be enhanced in + + align:start position:0% +uh why would shoulder sze be enhanced in + + + align:start position:0% +uh why would shoulder sze be enhanced in +women I can think of one possibility + + align:start position:0% +women I can think of one possibility + + + align:start position:0% +women I can think of one possibility +that would fit what we've been saying + + align:start position:0% +that would fit what we've been saying + + + align:start position:0% +that would fit what we've been saying +and one is simply that the hour + + align:start position:0% +and one is simply that the hour + + + align:start position:0% +and one is simply that the hour +hourglass + + align:start position:0% + + + + align:start position:0% + +shape it's not just waste to hip ratio + + align:start position:0% +shape it's not just waste to hip ratio + + + align:start position:0% +shape it's not just waste to hip ratio +but it's the whole enhancement of a + + align:start position:0% +but it's the whole enhancement of a + + + align:start position:0% +but it's the whole enhancement of a +narrow waist by make the shoulders a + + align:start position:0% +narrow waist by make the shoulders a + + + align:start position:0% +narrow waist by make the shoulders a +little wider but I think there's other + + align:start position:0% +little wider but I think there's other + + + align:start position:0% +little wider but I think there's other +reasons in modern culture in fact it's + + align:start position:0% +reasons in modern culture in fact it's + + + align:start position:0% +reasons in modern culture in fact it's +become much more common in modern + + align:start position:0% +become much more common in modern + + + align:start position:0% +become much more common in modern +culture than it was in many years ago + + align:start position:0% +culture than it was in many years ago + + + align:start position:0% +culture than it was in many years ago +and that is that + + align:start position:0% +and that is that + + + align:start position:0% +and that is that +women want to defeminize their parents + + align:start position:0% +women want to defeminize their parents + + + align:start position:0% +women want to defeminize their parents +somewhat they want to be more like men + + align:start position:0% +somewhat they want to be more like men + + + align:start position:0% +somewhat they want to be more like men +uh now we don't think of it that way + + align:start position:0% +uh now we don't think of it that way + + + align:start position:0% +uh now we don't think of it that way +away so much but certainly when women + + align:start position:0% +away so much but certainly when women + + + align:start position:0% +away so much but certainly when women +first begin to enter the business World + + align:start position:0% +first begin to enter the business World + + + align:start position:0% +first begin to enter the business World +a lot + + align:start position:0% +a lot + + + align:start position:0% +a lot +more when did women really enter the + + align:start position:0% +more when did women really enter the + + + align:start position:0% +more when did women really enter the +world of business and the world of + + align:start position:0% +world of business and the world of + + + align:start position:0% +world of business and the world of +Labor during the + + align:start position:0% +Labor during the + + + align:start position:0% +Labor during the +wars when all the men were going out to + + align:start position:0% +wars when all the men were going out to + + + align:start position:0% +wars when all the men were going out to +war the cult the economy would have + + align:start position:0% +war the cult the economy would have + + + align:start position:0% +war the cult the economy would have +fallen + + align:start position:0% +fallen + + + align:start position:0% +fallen +apart so older men that were not going + + align:start position:0% +apart so older men that were not going + + + align:start position:0% +apart so older men that were not going +to the war they needed help so when + + align:start position:0% +to the war they needed help so when + + + align:start position:0% +to the war they needed help so when +women came + + align:start position:0% +women came + + + align:start position:0% +women came +in and took over a lot of those + + align:start position:0% +in and took over a lot of those + + + align:start position:0% +in and took over a lot of those +jobs but now of course women are at + + align:start position:0% +jobs but now of course women are at + + + align:start position:0% +jobs but now of course women are at +every level in business including right + + align:start position:0% +every level in business including right + + + align:start position:0% +every level in business including right +up to the top uh but it's still fairly + + align:start position:0% +up to the top uh but it's still fairly + + + align:start position:0% +up to the top uh but it's still fairly +common for a business + + align:start position:0% +common for a business + + + align:start position:0% +common for a business +woman to wear suits that look like male + + align:start position:0% +woman to wear suits that look like male + + + align:start position:0% +woman to wear suits that look like male +suits all right well anyway that's a + + align:start position:0% +suits all right well anyway that's a + + + align:start position:0% +suits all right well anyway that's a +somewhat separate reason it has nothing + + align:start position:0% +somewhat separate reason it has nothing + + + align:start position:0% +somewhat separate reason it has nothing +to do with super normal stimuli it has + + align:start position:0% +to do with super normal stimuli it has + + + align:start position:0% +to do with super normal stimuli it has +to do with the kind of imitation + + align:start position:0% +to do with the kind of imitation + + + align:start position:0% +to do with the kind of imitation +okay then Scott in the your textbook + + align:start position:0% +okay then Scott in the your textbook + + + align:start position:0% +okay then Scott in the your textbook +he's talking about controlling Behavior + + align:start position:0% +he's talking about controlling Behavior + + + align:start position:0% +he's talking about controlling Behavior +the role of the nervous + + align:start position:0% +the role of the nervous + + + align:start position:0% +the role of the nervous +system and uh I would like you to at + + align:start position:0% +system and uh I would like you to at + + + align:start position:0% +system and uh I would like you to at +least know simple definitions of neurons + + align:start position:0% +least know simple definitions of neurons + + + align:start position:0% +least know simple definitions of neurons +in the nervous systems so we can talk + + align:start position:0% +in the nervous systems so we can talk + + + align:start position:0% +in the nervous systems so we can talk +more easily about it so I'm asking you + + align:start position:0% +more easily about it so I'm asking you + + + align:start position:0% +more easily about it so I'm asking you +for definitions of a primary sensory + + align:start position:0% +for definitions of a primary sensory + + + align:start position:0% +for definitions of a primary sensory +neuron a secondary sensory neuron a + + align:start position:0% +neuron a secondary sensory neuron a + + + align:start position:0% +neuron a secondary sensory neuron a +motor neuron an inter neuron how do we + + align:start position:0% +motor neuron an inter neuron how do we + + + align:start position:0% +motor neuron an inter neuron how do we +Define those things you should all know + + align:start position:0% +Define those things you should all know + + + align:start position:0% +Define those things you should all know +you've all had 901 + + align:start position:0% +you've all had 901 + + + align:start position:0% +you've all had 901 +right or you're taking it + + align:start position:0% + + + + align:start position:0% + +now but maybe you didn't learn it + + align:start position:0% +now but maybe you didn't learn it + + + align:start position:0% +now but maybe you didn't learn it +because they're not always so attentive + + align:start position:0% +because they're not always so attentive + + + align:start position:0% +because they're not always so attentive +to neuroanatomical details as I + + align:start position:0% +to neuroanatomical details as I + + + align:start position:0% +to neuroanatomical details as I +am so let me give you some + + align:start position:0% +am so let me give you some + + + align:start position:0% +am so let me give you some +definitions a primary sensory neuron is + + align:start position:0% +definitions a primary sensory neuron is + + + align:start position:0% +definitions a primary sensory neuron is +a neuron with a cell body outside the + + align:start position:0% +a neuron with a cell body outside the + + + align:start position:0% +a neuron with a cell body outside the +brain or spinal cord outside the central + + align:start position:0% +brain or spinal cord outside the central + + + align:start position:0% +brain or spinal cord outside the central +the central nervous system is brain and + + align:start position:0% +the central nervous system is brain and + + + align:start position:0% +the central nervous system is brain and +spinal cord the peripheral nervous + + align:start position:0% +spinal cord the peripheral nervous + + + align:start position:0% +spinal cord the peripheral nervous +system are outside peripheral nervous + + align:start position:0% +system are outside peripheral nervous + + + align:start position:0% +system are outside peripheral nervous +system or the nerves going to our skin + + align:start position:0% +system or the nerves going to our skin + + + align:start position:0% +system or the nerves going to our skin +and + + align:start position:0% +and + + + align:start position:0% +and +muscle okay so the primary sensory + + align:start position:0% +muscle okay so the primary sensory + + + align:start position:0% +muscle okay so the primary sensory +neuron has the cell body outside in + + align:start position:0% +neuron has the cell body outside in + + + align:start position:0% +neuron has the cell body outside in +primitive animals it's in the surface + + align:start position:0% +primitive animals it's in the surface + + + align:start position:0% +primitive animals it's in the surface +epithelium in us it's in a ganglion near + + align:start position:0% +epithelium in us it's in a ganglion near + + + align:start position:0% +epithelium in us it's in a ganglion near +the central nervous system with a + + align:start position:0% +the central nervous system with a + + + align:start position:0% +the central nervous system with a +peripheral axon going out to the + + align:start position:0% +peripheral axon going out to the + + + align:start position:0% +peripheral axon going out to the +periphery okay + + align:start position:0% + + + + align:start position:0% + +we have them in a little bit different + + align:start position:0% +we have them in a little bit different + + + align:start position:0% +we have them in a little bit different +shape for the skin of the body and let + + align:start position:0% +shape for the skin of the body and let + + + align:start position:0% +shape for the skin of the body and let +say the auditory or the factory + + align:start position:0% +say the auditory or the factory + + + align:start position:0% +say the auditory or the factory +system but all these systems have a + + align:start position:0% +system but all these systems have a + + + align:start position:0% +system but all these systems have a +primary sensory neuron what is a + + align:start position:0% +primary sensory neuron what is a + + + align:start position:0% +primary sensory neuron what is a +secondary sensory neuron well the neuron + + align:start position:0% +secondary sensory neuron well the neuron + + + align:start position:0% +secondary sensory neuron well the neuron +that those neurons synapse with or + + align:start position:0% +that those neurons synapse with or + + + align:start position:0% +that those neurons synapse with or +contact and transmit their activity to + + align:start position:0% +contact and transmit their activity to + + + align:start position:0% +contact and transmit their activity to +they're in the central nervous system + + align:start position:0% +they're in the central nervous system + + + align:start position:0% +they're in the central nervous system +but they're the ones + + align:start position:0% +but they're the ones + + + align:start position:0% +but they're the ones +contacted so we talk about the clear + + align:start position:0% +contacted so we talk about the clear + + + align:start position:0% +contacted so we talk about the clear +nuclei for example they get input from + + align:start position:0% +nuclei for example they get input from + + + align:start position:0% +nuclei for example they get input from +the auditory + + align:start position:0% + + + + align:start position:0% + +nerve the trigeminal nuclei in the hind + + align:start position:0% +nerve the trigeminal nuclei in the hind + + + align:start position:0% +nerve the trigeminal nuclei in the hind +frame getting input from the skin of the + + align:start position:0% + + + + align:start position:0% + +face okay what's a motor + + align:start position:0% +face okay what's a motor + + + align:start position:0% +face okay what's a motor +neuron where's it cell + + align:start position:0% +neuron where's it cell + + + align:start position:0% +neuron where's it cell +body where's the cell body of a neuron + + align:start position:0% +body where's the cell body of a neuron + + + align:start position:0% +body where's the cell body of a neuron +inating a + + align:start position:0% +inating a + + + align:start position:0% +inating a +muscle I was going to say + + align:start position:0% +muscle I was going to say + + + align:start position:0% +muscle I was going to say +no it isn't it's in the central nervous + + align:start position:0% +no it isn't it's in the central nervous + + + align:start position:0% +no it isn't it's in the central nervous +system any neuron in the central nervous + + align:start position:0% +system any neuron in the central nervous + + + align:start position:0% +system any neuron in the central nervous +system with a a nerve fiber and axon + + align:start position:0% +system with a a nerve fiber and axon + + + align:start position:0% +system with a a nerve fiber and axon +leaving the central nervous + + align:start position:0% +leaving the central nervous + + + align:start position:0% +leaving the central nervous +system is a motor + + align:start position:0% +system is a motor + + + align:start position:0% +system is a motor +neuron okay if it's an alpha motor + + align:start position:0% +neuron okay if it's an alpha motor + + + align:start position:0% +neuron okay if it's an alpha motor +neuron it's contacting a strided muscle + + align:start position:0% +neuron it's contacting a strided muscle + + + align:start position:0% +neuron it's contacting a strided muscle +cell so most of them are like that but + + align:start position:0% +cell so most of them are like that but + + + align:start position:0% +cell so most of them are like that but +then there are also neurons like that + + align:start position:0% +then there are also neurons like that + + + align:start position:0% +then there are also neurons like that +that contact a cell in a ganglion these + + align:start position:0% +that contact a cell in a ganglion these + + + align:start position:0% +that contact a cell in a ganglion these +are the out automic nervous system cells + + align:start position:0% +are the out automic nervous system cells + + + align:start position:0% +are the out automic nervous system cells +there you have a preganglionic motor + + align:start position:0% +there you have a preganglionic motor + + + align:start position:0% +there you have a preganglionic motor +neuron and then the ganglionic motor + + align:start position:0% +neuron and then the ganglionic motor + + + align:start position:0% +neuron and then the ganglionic motor +neuron + + align:start position:0% +neuron + + + align:start position:0% +neuron +okay uh what are all the other neurons + + align:start position:0% +okay uh what are all the other neurons + + + align:start position:0% +okay uh what are all the other neurons +we have the primary sensory secondary + + align:start position:0% +we have the primary sensory secondary + + + align:start position:0% +we have the primary sensory secondary +sensory and motor neuron what are those + + align:start position:0% +sensory and motor neuron what are those + + + align:start position:0% +sensory and motor neuron what are those +enormous numbers of neurons in + + align:start position:0% +enormous numbers of neurons in + + + align:start position:0% +enormous numbers of neurons in +between the general term is they're + + align:start position:0% +between the general term is they're + + + align:start position:0% +between the general term is they're +interneurons but in in the and at the + + align:start position:0% +interneurons but in in the and at the + + + align:start position:0% +interneurons but in in the and at the +field of neuron Anatomy usually the + + align:start position:0% +field of neuron Anatomy usually the + + + align:start position:0% +field of neuron Anatomy usually the +interneuron is a small axon a short axon + + align:start position:0% +interneuron is a small axon a short axon + + + align:start position:0% +interneuron is a small axon a short axon +cell and but really all the long axon + + align:start position:0% +cell and but really all the long axon + + + align:start position:0% +cell and but really all the long axon +cells and the short axon neurons are all + + align:start position:0% +cells and the short axon neurons are all + + + align:start position:0% +cells and the short axon neurons are all +interneurons okay this just a diagram + + align:start position:0% +interneurons okay this just a diagram + + + align:start position:0% +interneurons okay this just a diagram +that summarizes all those things I just + + align:start position:0% +that summarizes all those things I just + + + align:start position:0% +that summarizes all those things I just +told + + align:start position:0% +told + + + align:start position:0% +told +you some of you learn best if I describe + + align:start position:0% +you some of you learn best if I describe + + + align:start position:0% +you some of you learn best if I describe +it all verbally some of you have more + + align:start position:0% +it all verbally some of you have more + + + align:start position:0% +it all verbally some of you have more +trouble with that but you see a picture + + align:start position:0% +trouble with that but you see a picture + + + align:start position:0% +trouble with that but you see a picture +like that and it's all obvious okay U my + + align:start position:0% +like that and it's all obvious okay U my + + + align:start position:0% +like that and it's all obvious okay U my +in the left screen the colors a lot + + align:start position:0% +in the left screen the colors a lot + + + align:start position:0% +in the left screen the colors a lot +better because I used green to describe + + align:start position:0% +better because I used green to describe + + + align:start position:0% +better because I used green to describe +the uh some of those cells with I've got + + align:start position:0% +the uh some of those cells with I've got + + + align:start position:0% +the uh some of those cells with I've got +pointers going to them so there's the + + align:start position:0% +pointers going to them so there's the + + + align:start position:0% +pointers going to them so there's the +primary sensory neuron you see where the + + align:start position:0% +primary sensory neuron you see where the + + + align:start position:0% +primary sensory neuron you see where the +cell body is there everything within + + align:start position:0% +cell body is there everything within + + + align:start position:0% +cell body is there everything within +those two lines is the central nervous + + align:start position:0% +those two lines is the central nervous + + + align:start position:0% +those two lines is the central nervous +system like the spinal cord but could be + + align:start position:0% +system like the spinal cord but could be + + + align:start position:0% +system like the spinal cord but could be +in the brain too and there's the motor + + align:start position:0% +in the brain too and there's the motor + + + align:start position:0% +in the brain too and there's the motor +neuron with an Aon going to the muscle + + align:start position:0% + + + + align:start position:0% + +cell so I colored the motor neurons in + + align:start position:0% +cell so I colored the motor neurons in + + + align:start position:0% +cell so I colored the motor neurons in +I've colored the primary sensory neurons + + align:start position:0% +I've colored the primary sensory neurons + + + align:start position:0% +I've colored the primary sensory neurons +secondary Sensory + + align:start position:0% +secondary Sensory + + + align:start position:0% +secondary Sensory +neurons well in the book I'm writing I + + align:start position:0% +neurons well in the book I'm writing I + + + align:start position:0% +neurons well in the book I'm writing I +color them Green in the initial diagram + + align:start position:0% +color them Green in the initial diagram + + + align:start position:0% +color them Green in the initial diagram +but I didn't color them green here all + + align:start position:0% +but I didn't color them green here all + + + align:start position:0% +but I didn't color them green here all +right so what are the major + + align:start position:0% +right so what are the major + + + align:start position:0% +right so what are the major +specializations of + + align:start position:0% +specializations of + + + align:start position:0% +specializations of +neurons that govern how we sense how we + + align:start position:0% +neurons that govern how we sense how we + + + align:start position:0% +neurons that govern how we sense how we +move how we think + + align:start position:0% +move how we think + + + align:start position:0% +move how we think +everything what are how are those cells + + align:start position:0% +everything what are how are those cells + + + align:start position:0% +everything what are how are those cells +different from other cells + + align:start position:0% +different from other cells + + + align:start position:0% +different from other cells +how are they different from liver cells + + align:start position:0% +how are they different from liver cells + + + align:start position:0% +how are they different from liver cells +and kidney cells and skin cells and so + + align:start position:0% +and kidney cells and skin cells and so + + + align:start position:0% +and kidney cells and skin cells and so +forth + + align:start position:0% + + + + align:start position:0% + +yes okay that's a big one that's a + + align:start position:0% +yes okay that's a big one that's a + + + align:start position:0% +yes okay that's a big one that's a +specialization of a neuron they can + + align:start position:0% +specialization of a neuron they can + + + align:start position:0% +specialization of a neuron they can +transmit what we call Action potentials + + align:start position:0% +transmit what we call Action potentials + + + align:start position:0% +transmit what we call Action potentials +over long distances down axons because + + align:start position:0% +over long distances down axons because + + + align:start position:0% +over long distances down axons because +the axon is a specialized memor U uh + + align:start position:0% +the axon is a specialized memor U uh + + + align:start position:0% +the axon is a specialized memor U uh +property of the neuron membrane of the + + align:start position:0% +property of the neuron membrane of the + + + align:start position:0% +property of the neuron membrane of the +axon now they have many processes that + + align:start position:0% +axon now they have many processes that + + + align:start position:0% +axon now they have many processes that +don't + + align:start position:0% +don't + + + align:start position:0% +don't +action potentials but they still respond + + align:start position:0% +action potentials but they still respond + + + align:start position:0% +action potentials but they still respond +to input so the general property here is + + align:start position:0% +to input so the general property here is + + + align:start position:0% +to input so the general property here is +this first one we call it irritability + + align:start position:0% +this first one we call it irritability + + + align:start position:0% +this first one we call it irritability +they respond to + + align:start position:0% +they respond to + + + align:start position:0% +they respond to +stimulation and the response spre + + align:start position:0% +stimulation and the response spre + + + align:start position:0% +stimulation and the response spre +spreads okay even if it's not an action + + align:start position:0% +spreads okay even if it's not an action + + + align:start position:0% +spreads okay even if it's not an action +potential you still get that + + align:start position:0% +potential you still get that + + + align:start position:0% +potential you still get that +spread well if you could record from + + align:start position:0% +spread well if you could record from + + + align:start position:0% +spread well if you could record from +cells in a leaf and you might find + + align:start position:0% +cells in a leaf and you might find + + + align:start position:0% +cells in a leaf and you might find +potentials across the membrane and it + + align:start position:0% +potentials across the membrane and it + + + align:start position:0% +potentials across the membrane and it +might respond to stimulation and spread + + align:start position:0% +might respond to stimulation and spread + + + align:start position:0% +might respond to stimulation and spread +but they're rarely like action + + align:start position:0% +but they're rarely like action + + + align:start position:0% +but they're rarely like action +potentials + + align:start position:0% + + + + align:start position:0% + +okay that's the so we call the response + + align:start position:0% +okay that's the so we call the response + + + align:start position:0% +okay that's the so we call the response +to a stimulus either mechanical or + + align:start position:0% + + + + align:start position:0% + +chemical that's being irritable or + + align:start position:0% +chemical that's being irritable or + + + align:start position:0% +chemical that's being irritable or +responsive to the outside world outside + + align:start position:0% +responsive to the outside world outside + + + align:start position:0% +responsive to the outside world outside +the cell conduction is that spread of + + align:start position:0% +the cell conduction is that spread of + + + align:start position:0% +the cell conduction is that spread of +the potential + + align:start position:0% +the potential + + + align:start position:0% +the potential +where they have that extra + + align:start position:0% +where they have that extra + + + align:start position:0% +where they have that extra +specialization in the aone it begins at + + align:start position:0% +specialization in the aone it begins at + + + align:start position:0% +specialization in the aone it begins at +a little place right near the cell body + + align:start position:0% +a little place right near the cell body + + + align:start position:0% +a little place right near the cell body +usually near the beginning of the axon + + align:start position:0% +usually near the beginning of the axon + + + align:start position:0% +usually near the beginning of the axon +the axon hilic and the ACT that's where + + align:start position:0% +the axon hilic and the ACT that's where + + + align:start position:0% +the axon hilic and the ACT that's where +the action potentials initiated how is + + align:start position:0% +the action potentials initiated how is + + + align:start position:0% +the action potentials initiated how is +it different from the other potentials + + align:start position:0% +it different from the other potentials + + + align:start position:0% +it different from the other potentials +well it spreads from once it's triggered + + align:start position:0% +well it spreads from once it's triggered + + + align:start position:0% +well it spreads from once it's triggered +it goes all the way down the ax + + align:start position:0% +it goes all the way down the ax + + + align:start position:0% +it goes all the way down the ax +sign unless something unusual happens to + + align:start position:0% +sign unless something unusual happens to + + + align:start position:0% +sign unless something unusual happens to +block it it goes all the way down to the + + align:start position:0% +block it it goes all the way down to the + + + align:start position:0% +block it it goes all the way down to the +xon endings and + + align:start position:0% +xon endings and + + + align:start position:0% +xon endings and +there there's + + align:start position:0% +there there's + + + align:start position:0% +there there's +are it can transmit its response to + + align:start position:0% +are it can transmit its response to + + + align:start position:0% +are it can transmit its response to +other + + align:start position:0% +other + + + align:start position:0% +other +cells at these contacts with other cells + + align:start position:0% +cells at these contacts with other cells + + + align:start position:0% +cells at these contacts with other cells +we call that we call those contacts + + align:start position:0% +we call that we call those contacts + + + align:start position:0% +we call that we call those contacts +synapses most of them are chemical + + align:start position:0% +synapses most of them are chemical + + + align:start position:0% +synapses most of them are chemical +synapses and they cause the release of a + + align:start position:0% +synapses and they cause the release of a + + + align:start position:0% +synapses and they cause the release of a +chemical substance a neurotransmitter + + align:start position:0% +chemical substance a neurotransmitter + + + align:start position:0% +chemical substance a neurotransmitter +that affects the next cell okay so these + + align:start position:0% +that affects the next cell okay so these + + + align:start position:0% +that affects the next cell okay so these +are the major specializations of nerve + + align:start position:0% +are the major specializations of nerve + + + align:start position:0% +are the major specializations of nerve +cells + + align:start position:0% +cells + + + align:start position:0% +cells +compared with any other cells in the + + align:start position:0% + + + + align:start position:0% + +body so let's talk + + align:start position:0% +body so let's talk + + + align:start position:0% +body so let's talk +about these how these some of the things + + align:start position:0% +about these how these some of the things + + + align:start position:0% +about these how these some of the things +these nervous system cells + + align:start position:0% +these nervous system cells + + + align:start position:0% +these nervous system cells +do we'll talk about an example used by + + align:start position:0% +do we'll talk about an example used by + + + align:start position:0% +do we'll talk about an example used by +Scott in his book he talks about the + + align:start position:0% +Scott in his book he talks about the + + + align:start position:0% +Scott in his book he talks about the +wandering spider as a spider that + + align:start position:0% +wandering spider as a spider that + + + align:start position:0% +wandering spider as a spider that +doesn't make a web but it still hunts + + align:start position:0% +doesn't make a web but it still hunts + + + align:start position:0% +doesn't make a web but it still hunts +insect + + align:start position:0% +insect + + + align:start position:0% +insect +prey how does it catch without a + + align:start position:0% + + + + align:start position:0% + +whb it's got a lot of + + align:start position:0% +whb it's got a lot of + + + align:start position:0% +whb it's got a lot of +eyes so you would think it's using its + + align:start position:0% +eyes so you would think it's using its + + + align:start position:0% +eyes so you would think it's using its +eyes but you can blind them or block + + align:start position:0% +eyes but you can blind them or block + + + align:start position:0% +eyes but you can blind them or block +their eyes you can temporarily blind + + align:start position:0% +their eyes you can temporarily blind + + + align:start position:0% +their eyes you can temporarily blind +them just by covering their eyes with + + align:start position:0% + + + + align:start position:0% + +something and they still catch + + align:start position:0% +something and they still catch + + + align:start position:0% +something and they still catch +flies how do they do + + align:start position:0% +flies how do they do + + + align:start position:0% +flies how do they do +it yes a lot of + + align:start position:0% +it yes a lot of + + + align:start position:0% +it yes a lot of +a little hairs + + align:start position:0% + + + + align:start position:0% + +right disturbances yeah you're + + align:start position:0% +right disturbances yeah you're + + + align:start position:0% +right disturbances yeah you're +describing the uh a pattern of + + align:start position:0% +describing the uh a pattern of + + + align:start position:0% +describing the uh a pattern of +disturbance in the air around a moving + + align:start position:0% +disturbance in the air around a moving + + + align:start position:0% +disturbance in the air around a moving +insect + + align:start position:0% +insect + + + align:start position:0% +insect +exactly okay and this little spider is + + align:start position:0% +exactly okay and this little spider is + + + align:start position:0% +exactly okay and this little spider is +has these little sensory hairs very + + align:start position:0% +has these little sensory hairs very + + + align:start position:0% +has these little sensory hairs very +interesting because each hair when it + + align:start position:0% +interesting because each hair when it + + + align:start position:0% +interesting because each hair when it +bends there are at least four afen + + align:start position:0% +bends there are at least four afen + + + align:start position:0% +bends there are at least four afen +Sensory neurons or called afen sensory + + align:start position:0% +Sensory neurons or called afen sensory + + + align:start position:0% +Sensory neurons or called afen sensory +processes attached to that hair uh so + + align:start position:0% +processes attached to that hair uh so + + + align:start position:0% +processes attached to that hair uh so +when the hair bends one way one cell + + align:start position:0% +when the hair bends one way one cell + + + align:start position:0% +when the hair bends one way one cell +responds the most it bends another way + + align:start position:0% +responds the most it bends another way + + + align:start position:0% +responds the most it bends another way +the opposite way another cell responds + + align:start position:0% +the opposite way another cell responds + + + align:start position:0% +the opposite way another cell responds +and so forth so in four different + + align:start position:0% +and so forth so in four different + + + align:start position:0% +and so forth so in four different +directions and depending on its response + + align:start position:0% +directions and depending on its response + + + align:start position:0% +directions and depending on its response +that one hair uh you can tell basically + + align:start position:0% +that one hair uh you can tell basically + + + align:start position:0% +that one hair uh you can tell basically +where the the direction of air current + + align:start position:0% +where the the direction of air current + + + align:start position:0% +where the the direction of air current +stimulating the + + align:start position:0% +stimulating the + + + align:start position:0% +stimulating the +hair and it's it seems to be born with + + align:start position:0% +hair and it's it seems to be born with + + + align:start position:0% +hair and it's it seems to be born with +the ability to use the pattern of + + align:start position:0% +the ability to use the pattern of + + + align:start position:0% +the ability to use the pattern of +responses and all + + align:start position:0% +responses and all + + + align:start position:0% +responses and all +those uh hairs covering its body and + + align:start position:0% +those uh hairs covering its body and + + + align:start position:0% +those uh hairs covering its body and +there's there's lots of them over 100 + + align:start position:0% +there's there's lots of them over 100 + + + align:start position:0% +there's there's lots of them over 100 +and + + align:start position:0% +and + + + align:start position:0% +and +uh that it will it can actually leap + + align:start position:0% +uh that it will it can actually leap + + + align:start position:0% +uh that it will it can actually leap +into the air and grab insects up to 20 + + align:start position:0% +into the air and grab insects up to 20 + + + align:start position:0% +into the air and grab insects up to 20 +cm a way they can detect things and it + + align:start position:0% +cm a way they can detect things and it + + + align:start position:0% +cm a way they can detect things and it +can leap several centimeters so you can + + align:start position:0% +can leap several centimeters so you can + + + align:start position:0% +can leap several centimeters so you can +tell when the insect's approaching when + + align:start position:0% +tell when the insect's approaching when + + + align:start position:0% +tell when the insect's approaching when +it gets close so at times it's leap so + + align:start position:0% +it gets close so at times it's leap so + + + align:start position:0% +it gets close so at times it's leap so +it's when it's close + + align:start position:0% +it's when it's close + + + align:start position:0% +it's when it's close +enough and it can catch the + + align:start position:0% + + + + align:start position:0% + +insect very interesting he's got a nice + + align:start position:0% +insect very interesting he's got a nice + + + align:start position:0% +insect very interesting he's got a nice +description there's a Box covering two + + align:start position:0% +description there's a Box covering two + + + align:start position:0% +description there's a Box covering two +pages there and they even have some + + align:start position:0% +pages there and they even have some + + + align:start position:0% +pages there and they even have some +neurophysiological results where they're + + align:start position:0% +neurophysiological results where they're + + + align:start position:0% +neurophysiological results where they're +recording from um some some of the + + align:start position:0% +recording from um some some of the + + + align:start position:0% +recording from um some some of the +neurons responsive to those + + align:start position:0% + + + + align:start position:0% + +hairs and of course other other kinds of + + align:start position:0% +hairs and of course other other kinds of + + + align:start position:0% +hairs and of course other other kinds of +spiders have other kinds of + + align:start position:0% +spiders have other kinds of + + + align:start position:0% +spiders have other kinds of +specializations usually they're + + align:start position:0% +specializations usually they're + + + align:start position:0% +specializations usually they're +responding to vibrations in the web when + + align:start position:0% +responding to vibrations in the web when + + + align:start position:0% +responding to vibrations in the web when +something is caught in their web but + + align:start position:0% +something is caught in their web but + + + align:start position:0% +something is caught in their web but +these webless spiders have other + + align:start position:0% + + + + align:start position:0% + +means so let's talk a little bit about + + align:start position:0% +means so let's talk a little bit about + + + align:start position:0% +means so let's talk a little bit about +the + + align:start position:0% +the + + + align:start position:0% +the +toad frogs and toads have very + + align:start position:0% +toad frogs and toads have very + + + align:start position:0% +toad frogs and toads have very +specialized system for catching prey + + align:start position:0% +specialized system for catching prey + + + align:start position:0% +specialized system for catching prey +they also catch insects like that + + align:start position:0% +they also catch insects like that + + + align:start position:0% +they also catch insects like that +spider but here the specializations are + + align:start position:0% +spider but here the specializations are + + + align:start position:0% +spider but here the specializations are +in its visual system + + align:start position:0% +in its visual system + + + align:start position:0% +in its visual system +okay there are cells in the retina that + + align:start position:0% +okay there are cells in the retina that + + + align:start position:0% +okay there are cells in the retina that +are specifically tuned to respond to a + + align:start position:0% +are specifically tuned to respond to a + + + align:start position:0% +are specifically tuned to respond to a +small usually + + align:start position:0% +small usually + + + align:start position:0% +small usually +darker an little stimulus in the visual + + align:start position:0% +darker an little stimulus in the visual + + + align:start position:0% +darker an little stimulus in the visual +darker than the rest of the field like a + + align:start position:0% +darker than the rest of the field like a + + + align:start position:0% +darker than the rest of the field like a +fly okay or another small + + align:start position:0% +fly okay or another small + + + align:start position:0% +fly okay or another small +insect and these cells respond best when + + align:start position:0% +insect and these cells respond best when + + + align:start position:0% +insect and these cells respond best when +a fly like stimulus is moving so just a + + align:start position:0% +a fly like stimulus is moving so just a + + + align:start position:0% +a fly like stimulus is moving so just a +little spot will stimulate those those + + align:start position:0% +little spot will stimulate those those + + + align:start position:0% +little spot will stimulate those those +cells as long as it's + + align:start position:0% + + + + align:start position:0% + +moving now those are in the retina the + + align:start position:0% +moving now those are in the retina the + + + align:start position:0% +moving now those are in the retina the +retina is not enough to let the to cause + + align:start position:0% +retina is not enough to let the to cause + + + align:start position:0% +retina is not enough to let the to cause +the Frog to catch him where does the + + align:start position:0% +the Frog to catch him where does the + + + align:start position:0% +the Frog to catch him where does the +information go it goes down the optic + + align:start position:0% +information go it goes down the optic + + + align:start position:0% +information go it goes down the optic +nerve and to the opposite side of the + + align:start position:0% +nerve and to the opposite side of the + + + align:start position:0% +nerve and to the opposite side of the +roof of the midbrain the optic lobe of + + align:start position:0% +roof of the midbrain the optic lobe of + + + align:start position:0% +roof of the midbrain the optic lobe of +the + + align:start position:0% +the + + + align:start position:0% +the +midbrain okay or the optic tectum tectum + + align:start position:0% +midbrain okay or the optic tectum tectum + + + align:start position:0% +midbrain okay or the optic tectum tectum +just means roof the roof of the mid + + align:start position:0% +just means roof the roof of the mid + + + align:start position:0% +just means roof the roof of the mid +brain on the opposite side gets that + + align:start position:0% + + + + align:start position:0% + +input okay and what do we know about the + + align:start position:0% +input okay and what do we know about the + + + align:start position:0% +input okay and what do we know about the +way the retina Maps sends its + + align:start position:0% +way the retina Maps sends its + + + align:start position:0% +way the retina Maps sends its +fibers to the midbrain tecton well we + + align:start position:0% +fibers to the midbrain tecton well we + + + align:start position:0% +fibers to the midbrain tecton well we +know it forms an organized map so one + + align:start position:0% +know it forms an organized map so one + + + align:start position:0% +know it forms an organized map so one +part of the retina projects to one part + + align:start position:0% +part of the retina projects to one part + + + align:start position:0% +part of the retina projects to one part +of that optic lobe another part of the + + align:start position:0% +of that optic lobe another part of the + + + align:start position:0% +of that optic lobe another part of the +retina projects to another part so it + + align:start position:0% +retina projects to another part so it + + + align:start position:0% +retina projects to another part so it +forms a map of the retina in the brain + + align:start position:0% +forms a map of the retina in the brain + + + align:start position:0% +forms a map of the retina in the brain +okay we have that in our mid brain + + align:start position:0% +okay we have that in our mid brain + + + align:start position:0% +okay we have that in our mid brain +too as well as other parts of our visual + + align:start position:0% +too as well as other parts of our visual + + + align:start position:0% +too as well as other parts of our visual +system but in the Frog the dominant part + + align:start position:0% +system but in the Frog the dominant part + + + align:start position:0% +system but in the Frog the dominant part +by far and the only really important + + align:start position:0% +by far and the only really important + + + align:start position:0% +by far and the only really important +part part for this preat is there in the + + align:start position:0% + + + + align:start position:0% + +midbrain okay so what if if you're you + + align:start position:0% +midbrain okay so what if if you're you + + + align:start position:0% +midbrain okay so what if if you're you +using there are stimuli other what else + + align:start position:0% +using there are stimuli other what else + + + align:start position:0% +using there are stimuli other what else +does do frogs and toads eat besides + + align:start position:0% + + + + align:start position:0% + +flies don't you ever have pet frogs and + + align:start position:0% +flies don't you ever have pet frogs and + + + align:start position:0% +flies don't you ever have pet frogs and +toads worms right they love worms as + + align:start position:0% +toads worms right they love worms as + + + align:start position:0% +toads worms right they love worms as +much as they love life okay what + + align:start position:0% +much as they love life okay what + + + align:start position:0% +much as they love life okay what +characterizes a worm well it's got to be + + align:start position:0% +characterizes a worm well it's got to be + + + align:start position:0% +characterizes a worm well it's got to be +moving and longer than it is wide okay + + align:start position:0% +moving and longer than it is wide okay + + + align:start position:0% +moving and longer than it is wide okay +so if you have even if you make + + align:start position:0% +so if you have even if you make + + + align:start position:0% +so if you have even if you make +artificial stimuli and show them to the + + align:start position:0% +artificial stimuli and show them to the + + + align:start position:0% +artificial stimuli and show them to the +Frog and this has been done by say + + align:start position:0% +Frog and this has been done by say + + + align:start position:0% +Frog and this has been done by say +placing the frog or the toad in the + + align:start position:0% +placing the frog or the toad in the + + + align:start position:0% +placing the frog or the toad in the +center of a turntable and you put the + + align:start position:0% +center of a turntable and you put the + + + align:start position:0% +center of a turntable and you put the +stimuli on the platter and you rotate it + + align:start position:0% +stimuli on the platter and you rotate it + + + align:start position:0% +stimuli on the platter and you rotate it +around him and you can put little black + + align:start position:0% +around him and you can put little black + + + align:start position:0% +around him and you can put little black +spots and you'll see that the Frog keeps + + align:start position:0% +spots and you'll see that the Frog keeps + + + align:start position:0% +spots and you'll see that the Frog keeps +making these orany movements towards it + + align:start position:0% +making these orany movements towards it + + + align:start position:0% +making these orany movements towards it +well if you put an elongated wormlike + + align:start position:0% +well if you put an elongated wormlike + + + align:start position:0% +well if you put an elongated wormlike +object he does the same thing and the if + + align:start position:0% +object he does the same thing and the if + + + align:start position:0% +object he does the same thing and the if +you make it longer and longer he + + align:start position:0% +you make it longer and longer he + + + align:start position:0% +you make it longer and longer he +responds more and + + align:start position:0% +responds more and + + + align:start position:0% +responds more and +more + + align:start position:0% +more + + + align:start position:0% +more +okay what if you do the opposite you + + align:start position:0% +okay what if you do the opposite you + + + align:start position:0% +okay what if you do the opposite you +make it wider and + + align:start position:0% + + + + align:start position:0% + +wider he responds less and less okay and + + align:start position:0% +wider he responds less and less okay and + + + align:start position:0% +wider he responds less and less okay and +if you start say with a square object + + align:start position:0% +if you start say with a square object + + + align:start position:0% +if you start say with a square object +when it's little he does resp respond + + align:start position:0% +when it's little he does resp respond + + + align:start position:0% +when it's little he does resp respond +more and more but then it reaches a + + align:start position:0% +more and more but then it reaches a + + + align:start position:0% +more and more but then it reaches a +certain side and rapidly responds less + + align:start position:0% +certain side and rapidly responds less + + + align:start position:0% +certain side and rapidly responds less +and less and it gets really big and he + + align:start position:0% +and less and it gets really big and he + + + align:start position:0% +and less and it gets really big and he +this whole response changes he starts + + align:start position:0% +this whole response changes he starts + + + align:start position:0% +this whole response changes he starts +crouching it starts being dangerous to + + align:start position:0% +crouching it starts being dangerous to + + + align:start position:0% +crouching it starts being dangerous to +him these are all built in responses in + + align:start position:0% +him these are all built in responses in + + + align:start position:0% +him these are all built in responses in +NE response of frogs and + + align:start position:0% +NE response of frogs and + + + align:start position:0% +NE response of frogs and +toads + + align:start position:0% + + + + align:start position:0% + +Okay so we've already talked about wear + + align:start position:0% +Okay so we've already talked about wear + + + align:start position:0% +Okay so we've already talked about wear +in the central nervous system of a toad + + align:start position:0% +in the central nervous system of a toad + + + align:start position:0% +in the central nervous system of a toad +and we could say the same thing about + + align:start position:0% +and we could say the same thing about + + + align:start position:0% +and we could say the same thing about +frogs um that input from the retina is + + align:start position:0% +frogs um that input from the retina is + + + align:start position:0% +frogs um that input from the retina is +going so here I'm asking well where in + + align:start position:0% +going so here I'm asking well where in + + + align:start position:0% +going so here I'm asking well where in +the central nervous system of a toad + + align:start position:0% +the central nervous system of a toad + + + align:start position:0% +the central nervous system of a toad +could the electrical stimulus elicit a + + align:start position:0% +could the electrical stimulus elicit a + + + align:start position:0% +could the electrical stimulus elicit a +pre catching fixed action pattern well + + align:start position:0% +pre catching fixed action pattern well + + + align:start position:0% +pre catching fixed action pattern well +you could put an electrode in there you + + align:start position:0% +you could put an electrode in there you + + + align:start position:0% +you could put an electrode in there you +anesthetize the Frog and imp plant the + + align:start position:0% +anesthetize the Frog and imp plant the + + + align:start position:0% +anesthetize the Frog and imp plant the +electrode you know let him wake up + + align:start position:0% +electrode you know let him wake up + + + align:start position:0% +electrode you know let him wake up +recover from the surgery now just a + + align:start position:0% +recover from the surgery now just a + + + align:start position:0% +recover from the surgery now just a +little electrical stimulus stimulus in + + align:start position:0% +little electrical stimulus stimulus in + + + align:start position:0% +little electrical stimulus stimulus in +one part of that tectum that midbrain + + align:start position:0% +one part of that tectum that midbrain + + + align:start position:0% +one part of that tectum that midbrain +surface will elicit those turning + + align:start position:0% +surface will elicit those turning + + + align:start position:0% +surface will elicit those turning +movements that we were just talking + + align:start position:0% +movements that we were just talking + + + align:start position:0% +movements that we were just talking +about so they can be elicit elicited + + align:start position:0% + + + + align:start position:0% + +electrically the only problem is when + + align:start position:0% +electrically the only problem is when + + + align:start position:0% +electrically the only problem is when +you elicit them electrically he never + + align:start position:0% +you elicit them electrically he never + + + align:start position:0% +you elicit them electrically he never +follows through what does a normal frog + + align:start position:0% +follows through what does a normal frog + + + align:start position:0% +follows through what does a normal frog +do he's following the + + align:start position:0% + + + + align:start position:0% + +worm + + align:start position:0% +worm + + + align:start position:0% +worm +then what does he do to get + + align:start position:0% +then what does he do to get + + + align:start position:0% +then what does he do to get +it flips his tongue out tongue comes out + + align:start position:0% +it flips his tongue out tongue comes out + + + align:start position:0% +it flips his tongue out tongue comes out +like a like a little like a dart okay + + align:start position:0% +like a like a little like a dart okay + + + align:start position:0% +like a like a little like a dart okay +and the thong tongue is sticky at the + + align:start position:0% +and the thong tongue is sticky at the + + + align:start position:0% +and the thong tongue is sticky at the +end + + align:start position:0% +end + + + align:start position:0% +end +so flat he gets it pulls it back same + + align:start position:0% +so flat he gets it pulls it back same + + + align:start position:0% +so flat he gets it pulls it back same +for a fly for the fly it's he's tuned to + + align:start position:0% +for a fly for the fly it's he's tuned to + + + align:start position:0% +for a fly for the fly it's he's tuned to +wait until the fly lights if it wasn't + + align:start position:0% +wait until the fly lights if it wasn't + + + align:start position:0% +wait until the fly lights if it wasn't +moving he will never try to get it but + + align:start position:0% +moving he will never try to get it but + + + align:start position:0% +moving he will never try to get it but +if it was moving and + + align:start position:0% +if it was moving and + + + align:start position:0% +if it was moving and +stops see the Frog will just sit there + + align:start position:0% +stops see the Frog will just sit there + + + align:start position:0% +stops see the Frog will just sit there +and watch it move but if it light lights + + align:start position:0% +and watch it move but if it light lights + + + align:start position:0% +and watch it move but if it light lights +then you'll get the pre catching + + align:start position:0% +then you'll get the pre catching + + + align:start position:0% +then you'll get the pre catching +response if it's within range he does + + align:start position:0% +response if it's within range he does + + + align:start position:0% +response if it's within range he does +have enough depth Vision to know whether + + align:start position:0% +have enough depth Vision to know whether + + + align:start position:0% +have enough depth Vision to know whether +it's in range of his tongue when you + + align:start position:0% +it's in range of his tongue when you + + + align:start position:0% +it's in range of his tongue when you +stimulate it electrically you never get + + align:start position:0% +stimulate it electrically you never get + + + align:start position:0% +stimulate it electrically you never get +the tongue flate tongue flip + + align:start position:0% +the tongue flate tongue flip + + + align:start position:0% +the tongue flate tongue flip +why give me a reason I can stimulate + + align:start position:0% +why give me a reason I can stimulate + + + align:start position:0% +why give me a reason I can stimulate +repeatedly + + align:start position:0% +repeatedly + + + align:start position:0% +repeatedly +I can stimulate the Turning movements he + + align:start position:0% +I can stimulate the Turning movements he + + + align:start position:0% +I can stimulate the Turning movements he +keeps reorienting there are different + + align:start position:0% +keeps reorienting there are different + + + align:start position:0% +keeps reorienting there are different +positions in the field every time I + + align:start position:0% +positions in the field every time I + + + align:start position:0% +positions in the field every time I +stimulate the midbrain why does he never + + align:start position:0% +stimulate the midbrain why does he never + + + align:start position:0% +stimulate the midbrain why does he never +flip his + + align:start position:0% +flip his + + + align:start position:0% +flip his +tongue isn't that all built + + align:start position:0% +tongue isn't that all built + + + align:start position:0% +tongue isn't that all built +in isn't it part of the same fixed + + align:start position:0% +in isn't it part of the same fixed + + + align:start position:0% +in isn't it part of the same fixed +action pattern Well normally yes because + + align:start position:0% +action pattern Well normally yes because + + + align:start position:0% +action pattern Well normally yes because +normally of course just + + align:start position:0% +normally of course just + + + align:start position:0% +normally of course just +think when he turns this is a frog wheel + + align:start position:0% +think when he turns this is a frog wheel + + + align:start position:0% +think when he turns this is a frog wheel +out in an electrode he turns okay that + + align:start position:0% +out in an electrode he turns okay that + + + align:start position:0% +out in an electrode he turns okay that +stimulus is moving across his tectum it + + align:start position:0% +stimulus is moving across his tectum it + + + align:start position:0% +stimulus is moving across his tectum it +always he always brings it so the + + align:start position:0% +always he always brings it so the + + + align:start position:0% +always he always brings it so the +stimulus that's in front of it so he's + + align:start position:0% +stimulus that's in front of it so he's + + + align:start position:0% +stimulus that's in front of it so he's +aligned so he can make the tongue flip + + align:start position:0% +aligned so he can make the tongue flip + + + align:start position:0% +aligned so he can make the tongue flip +response now it's always up in the front + + align:start position:0% +response now it's always up in the front + + + align:start position:0% +response now it's always up in the front +of the + + align:start position:0% +of the + + + align:start position:0% +of the +tectum that's the part of the tectum + + align:start position:0% +tectum that's the part of the tectum + + + align:start position:0% +tectum that's the part of the tectum +where which if you stimulate you can + + align:start position:0% +where which if you stimulate you can + + + align:start position:0% +where which if you stimulate you can +also get the tong + + align:start position:0% +also get the tong + + + align:start position:0% +also get the tong +flick but with just one electrode in the + + align:start position:0% +flick but with just one electrode in the + + + align:start position:0% +flick but with just one electrode in the +middle of the tectum you'll never get it + + align:start position:0% +middle of the tectum you'll never get it + + + align:start position:0% +middle of the tectum you'll never get it +because we can't imitate with a fixed + + align:start position:0% +because we can't imitate with a fixed + + + align:start position:0% +because we can't imitate with a fixed +electrode we can't IM imitate the whole + + align:start position:0% +electrode we can't IM imitate the whole + + + align:start position:0% +electrode we can't IM imitate the whole +normal stimulus + + align:start position:0% +normal stimulus + + + align:start position:0% +normal stimulus +sequence then here I say what would + + align:start position:0% +sequence then here I say what would + + + align:start position:0% +sequence then here I say what would +change if an electrode were moved a + + align:start position:0% +change if an electrode were moved a + + + align:start position:0% +change if an electrode were moved a +short distance well he would just change + + align:start position:0% +short distance well he would just change + + + align:start position:0% +short distance well he would just change +the position he's orienting towards so + + align:start position:0% +the position he's orienting towards so + + + align:start position:0% +the position he's orienting towards so +you put it way in the back of the tectum + + align:start position:0% +you put it way in the back of the tectum + + + align:start position:0% +you put it way in the back of the tectum +you would make these bigger orienting + + align:start position:0% +you would make these bigger orienting + + + align:start position:0% +you would make these bigger orienting +movements to put it closer to the front + + align:start position:0% +movements to put it closer to the front + + + align:start position:0% +movements to put it closer to the front +and make short orienting + + align:start position:0% +and make short orienting + + + align:start position:0% +and make short orienting +movements if you place it closer to the + + align:start position:0% +movements if you place it closer to the + + + align:start position:0% +movements if you place it closer to the +midline he orients upward you place it + + align:start position:0% +midline he orients upward you place it + + + align:start position:0% +midline he orients upward you place it +further out laterally he orients to the + + align:start position:0% +further out laterally he orients to the + + + align:start position:0% +further out laterally he orients to the +side and + + align:start position:0% +side and + + + align:start position:0% +side and +downward + + align:start position:0% +downward + + + align:start position:0% +downward +well the map we have of the retina in + + align:start position:0% +well the map we have of the retina in + + + align:start position:0% +well the map we have of the retina in +our midbrain is the same as that map in + + align:start position:0% +our midbrain is the same as that map in + + + align:start position:0% +our midbrain is the same as that map in +the + + align:start position:0% +the + + + align:start position:0% +the +Frog it's conserved across all the + + align:start position:0% +Frog it's conserved across all the + + + align:start position:0% +Frog it's conserved across all the +vertebrates the relative size of + + align:start position:0% +vertebrates the relative size of + + + align:start position:0% +vertebrates the relative size of +structures changes a + + align:start position:0% +structures changes a + + + align:start position:0% +structures changes a +lot okay but the existence of these + + align:start position:0% +lot okay but the existence of these + + + align:start position:0% +lot okay but the existence of these +structures + + align:start position:0% +structures + + + align:start position:0% +structures +is the same throughout the vertebraes + + align:start position:0% +is the same throughout the vertebraes + + + align:start position:0% +is the same throughout the vertebraes +and that's true for all these structures + + align:start position:0% +and that's true for all these structures + + + align:start position:0% +and that's true for all these structures +of the spinal cord and brain stem that + + align:start position:0% +of the spinal cord and brain stem that + + + align:start position:0% +of the spinal cord and brain stem that +control these fixed action + + align:start position:0% +control these fixed action + + + align:start position:0% +control these fixed action +patterns okay another concept here we + + align:start position:0% +patterns okay another concept here we + + + align:start position:0% +patterns okay another concept here we +talked about what a motor neuron is if + + align:start position:0% +talked about what a motor neuron is if + + + align:start position:0% +talked about what a motor neuron is if +the motor neurons stimulated you get a + + align:start position:0% +the motor neurons stimulated you get a + + + align:start position:0% +the motor neurons stimulated you get a +muscle twitch + + align:start position:0% +muscle twitch + + + align:start position:0% +muscle twitch +okay a group of motor neurons are + + align:start position:0% +okay a group of motor neurons are + + + align:start position:0% +okay a group of motor neurons are +stimulated you can get more movement if + + align:start position:0% +stimulated you can get more movement if + + + align:start position:0% +stimulated you can get more movement if +I stimulate all the motor neurons uh in + + align:start position:0% +I stimulate all the motor neurons uh in + + + align:start position:0% +I stimulate all the motor neurons uh in +the cord I can get suddenly rigidity if + + align:start position:0% +the cord I can get suddenly rigidity if + + + align:start position:0% +the cord I can get suddenly rigidity if +I'm stimulating saying the motor R is + + align:start position:0% +I'm stimulating saying the motor R is + + + align:start position:0% +I'm stimulating saying the motor R is +controlling my hand but if I'm + + align:start position:0% +controlling my hand but if I'm + + + align:start position:0% +controlling my hand but if I'm +stimulating just one group of them I can + + align:start position:0% +stimulating just one group of them I can + + + align:start position:0% +stimulating just one group of them I can +get flexion of the hand I stimulate + + align:start position:0% +get flexion of the hand I stimulate + + + align:start position:0% +get flexion of the hand I stimulate +another group I can get well this would + + align:start position:0% +another group I can get well this would + + + align:start position:0% +another group I can get well this would +be extension this would be flexion okay + + align:start position:0% +be extension this would be flexion okay + + + align:start position:0% +be extension this would be flexion okay +so I could elicit + + align:start position:0% +so I could elicit + + + align:start position:0% +so I could elicit +grasping what about a command + + align:start position:0% +grasping what about a command + + + align:start position:0% +grasping what about a command +neuron it has a different meaning also + + align:start position:0% +neuron it has a different meaning also + + + align:start position:0% +neuron it has a different meaning also +very important in studying the control + + align:start position:0% +very important in studying the control + + + align:start position:0% +very important in studying the control +of these movements in fixed action + + align:start position:0% +of these movements in fixed action + + + align:start position:0% +of these movements in fixed action +patterns what is a command + + align:start position:0% + + + + align:start position:0% + +neuron it's a term used + + align:start position:0% +neuron it's a term used + + + align:start position:0% +neuron it's a term used +in in + + align:start position:0% + + + + align:start position:0% + +neuroethology to describe a neuron that + + align:start position:0% +neuroethology to describe a neuron that + + + align:start position:0% +neuroethology to describe a neuron that +you can identify usually it's a neuron + + align:start position:0% +you can identify usually it's a neuron + + + align:start position:0% +you can identify usually it's a neuron +you can identify the same neuron in one + + align:start position:0% +you can identify the same neuron in one + + + align:start position:0% +you can identify the same neuron in one +member of the species to another + + align:start position:0% +member of the species to another + + + align:start position:0% +member of the species to another +sometimes they even have different color + + align:start position:0% +sometimes they even have different color + + + align:start position:0% +sometimes they even have different color +pigments okay + + align:start position:0% +pigments okay + + + align:start position:0% +pigments okay +it's a neuron where if you stimulate + + align:start position:0% +it's a neuron where if you stimulate + + + align:start position:0% +it's a neuron where if you stimulate +that one neuron you stimulate a whole + + align:start position:0% +that one neuron you stimulate a whole + + + align:start position:0% +that one neuron you stimulate a whole +pattern of movement okay you get a + + align:start position:0% +pattern of movement okay you get a + + + align:start position:0% +pattern of movement okay you get a +behavior from one + + align:start position:0% +behavior from one + + + align:start position:0% +behavior from one +neuron you stimulate a command neuron in + + align:start position:0% +neuron you stimulate a command neuron in + + + align:start position:0% +neuron you stimulate a command neuron in +a crayfish you can Elis if you're in the + + align:start position:0% +a crayfish you can Elis if you're in the + + + align:start position:0% +a crayfish you can Elis if you're in the +right place you stimulate the right + + align:start position:0% +right place you stimulate the right + + + align:start position:0% +right place you stimulate the right +command neuron you can get a tail flip + + align:start position:0% +command neuron you can get a tail flip + + + align:start position:0% +command neuron you can get a tail flip +response the animal will + + align:start position:0% +response the animal will + + + align:start position:0% +response the animal will +escape as if escaping from a + + align:start position:0% + + + + align:start position:0% + +predator + + align:start position:0% +predator + + + align:start position:0% +predator +mammals in vertebrates in general don't + + align:start position:0% +mammals in vertebrates in general don't + + + align:start position:0% +mammals in vertebrates in general don't +have it's harder to find the command + + align:start position:0% +have it's harder to find the command + + + align:start position:0% +have it's harder to find the command +neuron there are a few very large + + align:start position:0% +neuron there are a few very large + + + align:start position:0% +neuron there are a few very large +neurons that you can identify say across + + align:start position:0% +neurons that you can identify say across + + + align:start position:0% +neurons that you can identify say across +fish and + + align:start position:0% +fish and + + + align:start position:0% +fish and +amphibians um there's very giant cells + + align:start position:0% +amphibians um there's very giant cells + + + align:start position:0% +amphibians um there's very giant cells +in the hind brand they call the moer + + align:start position:0% +in the hind brand they call the moer + + + align:start position:0% +in the hind brand they call the moer +cells that can elicit rapid Escape + + align:start position:0% +cells that can elicit rapid Escape + + + align:start position:0% +cells that can elicit rapid Escape +responses they're like command neurons + + align:start position:0% +responses they're like command neurons + + + align:start position:0% +responses they're like command neurons +but otherwise it's usually these are in + + align:start position:0% +but otherwise it's usually these are in + + + align:start position:0% +but otherwise it's usually these are in +insects and other in + + align:start position:0% + + + + align:start position:0% + +vertebrates all right that's the + + align:start position:0% +vertebrates all right that's the + + + align:start position:0% +vertebrates all right that's the +difference between a command neuron and + + align:start position:0% +difference between a command neuron and + + + align:start position:0% +difference between a command neuron and +a motor neuron in a vertebrate you have + + align:start position:0% +a motor neuron in a vertebrate you have + + + align:start position:0% +a motor neuron in a vertebrate you have +groups of neurons though that act as + + align:start position:0% +groups of neurons though that act as + + + align:start position:0% +groups of neurons though that act as +command command groups of neurons which + + align:start position:0% +command command groups of neurons which + + + align:start position:0% +command command groups of neurons which +when stimulated can elicit a whole + + align:start position:0% +when stimulated can elicit a whole + + + align:start position:0% +when stimulated can elicit a whole +sequence of + + align:start position:0% +sequence of + + + align:start position:0% +sequence of +movements for example in the cotle part + + align:start position:0% +movements for example in the cotle part + + + align:start position:0% +movements for example in the cotle part +of the + + align:start position:0% +of the + + + align:start position:0% +of the +midbrain below the optic tectum below in + + align:start position:0% +midbrain below the optic tectum below in + + + align:start position:0% +midbrain below the optic tectum below in +fact the auditory tectum it's in the + + align:start position:0% +fact the auditory tectum it's in the + + + align:start position:0% +fact the auditory tectum it's in the +coddle midbrain there's an area there + + align:start position:0% +coddle midbrain there's an area there + + + align:start position:0% +coddle midbrain there's an area there +which when + + align:start position:0% +which when + + + align:start position:0% +which when +activated elicits + + align:start position:0% +activated elicits + + + align:start position:0% +activated elicits +Locomotion okay you get the right place + + align:start position:0% +Locomotion okay you get the right place + + + align:start position:0% +Locomotion okay you get the right place +you stimulate + + align:start position:0% +you stimulate + + + align:start position:0% +you stimulate +with enough activation you can get rapid + + align:start position:0% +with enough activation you can get rapid + + + align:start position:0% +with enough activation you can get rapid +running movements there are similar + + align:start position:0% +running movements there are similar + + + align:start position:0% +running movements there are similar +groups of neurons in for further forward + + align:start position:0% +groups of neurons in for further forward + + + align:start position:0% +groups of neurons in for further forward +in an area we call the + + align:start position:0% +in an area we call the + + + align:start position:0% +in an area we call the +subthalamus parts of the subthalamus get + + align:start position:0% +subthalamus parts of the subthalamus get + + + align:start position:0% +subthalamus parts of the subthalamus get +direct visual impul from the + + align:start position:0% +direct visual impul from the + + + align:start position:0% +direct visual impul from the +retina okay and more + + align:start position:0% +retina okay and more + + + align:start position:0% +retina okay and more +immediately they can activate these + + align:start position:0% +immediately they can activate these + + + align:start position:0% +immediately they can activate these +neurons that connect seem to connect + + align:start position:0% +neurons that connect seem to connect + + + align:start position:0% +neurons that connect seem to connect +directly to that midbrain Center because + + align:start position:0% +directly to that midbrain Center because + + + align:start position:0% +directly to that midbrain Center because +they also elicit rapid running + + align:start position:0% +they also elicit rapid running + + + align:start position:0% +they also elicit rapid running +movements usually involved in Escape + + align:start position:0% +movements usually involved in Escape + + + align:start position:0% +movements usually involved in Escape +Behavior that's a kind of command neuron + + align:start position:0% +Behavior that's a kind of command neuron + + + align:start position:0% +Behavior that's a kind of command neuron +group it's just that we can't identify + + align:start position:0% +group it's just that we can't identify + + + align:start position:0% +group it's just that we can't identify +the single neuron so if I say command + + align:start position:0% +the single neuron so if I say command + + + align:start position:0% +the single neuron so if I say command +neuron I'm almost always talking about + + align:start position:0% +neuron I'm almost always talking about + + + align:start position:0% +neuron I'm almost always talking about +invertebrate animals + + align:start position:0% +invertebrate animals + + + align:start position:0% +invertebrate animals +okay where we can actually identify the + + align:start position:0% +okay where we can actually identify the + + + align:start position:0% +okay where we can actually identify the +same cell from animal to + + align:start position:0% + + + + align:start position:0% + +animal okay so let's talk + + align:start position:0% +animal okay so let's talk + + + align:start position:0% +animal okay so let's talk +about the giant axon what is the main + + align:start position:0% +about the giant axon what is the main + + + align:start position:0% +about the giant axon what is the main +advantage of a giant axon in the + + align:start position:0% +advantage of a giant axon in the + + + align:start position:0% +advantage of a giant axon in the +triggering of an escape + + align:start position:0% +triggering of an escape + + + align:start position:0% +triggering of an escape +response you get you see giant axons in + + align:start position:0% +response you get you see giant axons in + + + align:start position:0% +response you get you see giant axons in +Squid it was the discovery of giant + + align:start position:0% +Squid it was the discovery of giant + + + align:start position:0% +Squid it was the discovery of giant +axons + + align:start position:0% +axons + + + align:start position:0% +axons +in + + align:start position:0% +in + + + align:start position:0% +in +squid that led + + align:start position:0% +squid that led + + + align:start position:0% +squid that led +to the detailed physiology of the action + + align:start position:0% +to the detailed physiology of the action + + + align:start position:0% +to the detailed physiology of the action +potential for the first + + align:start position:0% +potential for the first + + + align:start position:0% +potential for the first +time because this + + align:start position:0% +time because this + + + align:start position:0% +time because this +was before micro electrodes were + + align:start position:0% +was before micro electrodes were + + + align:start position:0% +was before micro electrodes were +perfected they could get a tiny wire + + align:start position:0% +perfected they could get a tiny wire + + + align:start position:0% +perfected they could get a tiny wire +inside that giant axon they were up to 1 + + align:start position:0% +inside that giant axon they were up to 1 + + + align:start position:0% +inside that giant axon they were up to 1 +millimeter in diameter okay in a squid + + align:start position:0% +millimeter in diameter okay in a squid + + + align:start position:0% +millimeter in diameter okay in a squid +so it enabled detailed study of the + + align:start position:0% +so it enabled detailed study of the + + + align:start position:0% +so it enabled detailed study of the +physiology of the action potential in + + align:start position:0% +physiology of the action potential in + + + align:start position:0% +physiology of the action potential in +the giant + + align:start position:0% +the giant + + + align:start position:0% +the giant +accent but why would the squid have + + align:start position:0% +accent but why would the squid have + + + align:start position:0% +accent but why would the squid have +giant accents they're they use a lot of + + align:start position:0% +giant accents they're they use a lot of + + + align:start position:0% +giant accents they're they use a lot of +energy if all their accents were like + + align:start position:0% +energy if all their accents were like + + + align:start position:0% +energy if all their accents were like +that you know they'd be gigantic + + align:start position:0% +that you know they'd be gigantic + + + align:start position:0% +that you know they'd be gigantic +animals okay some of them are pretty + + align:start position:0% +animals okay some of them are pretty + + + align:start position:0% +animals okay some of them are pretty +large but they're not gigantic and some + + align:start position:0% +large but they're not gigantic and some + + + align:start position:0% +large but they're not gigantic and some +of them are small too but all of them + + align:start position:0% +of them are small too but all of them + + + align:start position:0% +of them are small too but all of them +have these giant accents + + align:start position:0% +have these giant accents + + + align:start position:0% +have these giant accents +why what's the advantage of making + + align:start position:0% +why what's the advantage of making + + + align:start position:0% +why what's the advantage of making +Aon larger in + + align:start position:0% + + + + align:start position:0% + +diameter yeah one word speed rapid + + align:start position:0% +diameter yeah one word speed rapid + + + align:start position:0% +diameter yeah one word speed rapid +conduction + + align:start position:0% + + + + align:start position:0% + +okay that's why giant axon + + align:start position:0% +okay that's why giant axon + + + align:start position:0% +okay that's why giant axon +evolved because axonal conduction speed + + align:start position:0% +evolved because axonal conduction speed + + + align:start position:0% +evolved because axonal conduction speed +depends first of all on the diameter of + + align:start position:0% +depends first of all on the diameter of + + + align:start position:0% +depends first of all on the diameter of +the X of the X the xon so you get faster + + align:start position:0% +the X of the X the xon so you get faster + + + align:start position:0% +the X of the X the xon so you get faster +condu uction of the action + + align:start position:0% + + + + align:start position:0% + +potential well we have rapid conduction + + align:start position:0% +potential well we have rapid conduction + + + align:start position:0% +potential well we have rapid conduction +too and we don't have giant accents we + + align:start position:0% +too and we don't have giant accents we + + + align:start position:0% +too and we don't have giant accents we +do have some accents larger than others + + align:start position:0% +do have some accents larger than others + + + align:start position:0% +do have some accents larger than others +and they do conduct more rapidly but + + align:start position:0% +and they do conduct more rapidly but + + + align:start position:0% +and they do conduct more rapidly but +they're nowhere near the size of the + + align:start position:0% +they're nowhere near the size of the + + + align:start position:0% +they're nowhere near the size of the +squid and yet we get + + align:start position:0% +squid and yet we get + + + align:start position:0% +squid and yet we get +conduction that's just as fast as in the + + align:start position:0% +conduction that's just as fast as in the + + + align:start position:0% +conduction that's just as fast as in the +squid probably faster I can't remember + + align:start position:0% +squid probably faster I can't remember + + + align:start position:0% +squid probably faster I can't remember +the exact speed of conduction in in a + + align:start position:0% +the exact speed of conduction in in a + + + align:start position:0% +the exact speed of conduction in in a +giant but I + + align:start position:0% +giant but I + + + align:start position:0% +giant but I +know the long axons down to our spinal + + align:start position:0% +know the long axons down to our spinal + + + align:start position:0% +know the long axons down to our spinal +cord are very rapidly + + align:start position:0% +cord are very rapidly + + + align:start position:0% +cord are very rapidly +conducting the reason + + align:start position:0% +conducting the reason + + + align:start position:0% +conducting the reason +is the evolution of the myin + + align:start position:0% +is the evolution of the myin + + + align:start position:0% +is the evolution of the myin +sheath + + align:start position:0% +sheath + + + align:start position:0% +sheath +okay myelin is when the axon is + + align:start position:0% +okay myelin is when the axon is + + + align:start position:0% +okay myelin is when the axon is +wrapped around and around by the + + align:start position:0% +wrapped around and around by the + + + align:start position:0% +wrapped around and around by the +membrane of a gal cell that sort of + + align:start position:0% +membrane of a gal cell that sort of + + + align:start position:0% +membrane of a gal cell that sort of +insulates the axon from the ionic + + align:start position:0% +insulates the axon from the ionic + + + align:start position:0% +insulates the axon from the ionic +potential IAL that normally are involved + + align:start position:0% +potential IAL that normally are involved + + + align:start position:0% +potential IAL that normally are involved +in the action potential well if you + + align:start position:0% +in the action potential well if you + + + align:start position:0% +in the action potential well if you +insulated the whole axon like that you + + align:start position:0% +insulated the whole axon like that you + + + align:start position:0% +insulated the whole axon like that you +wouldn't get any action potentials at + + align:start position:0% +wouldn't get any action potentials at + + + align:start position:0% +wouldn't get any action potentials at +all so this is why it gets first of + + align:start position:0% +all so this is why it gets first of + + + align:start position:0% +all so this is why it gets first of +all deal with the rate of spread of + + align:start position:0% +all deal with the rate of spread of + + + align:start position:0% +all deal with the rate of spread of +current down an + + align:start position:0% +current down an + + + align:start position:0% +current down an +accent for all you + + align:start position:0% +accent for all you + + + align:start position:0% +accent for all you +Engineers this should make sense to you + + align:start position:0% +Engineers this should make sense to you + + + align:start position:0% +Engineers this should make sense to you +if you're not Engineers well be patient + + align:start position:0% +if you're not Engineers well be patient + + + align:start position:0% +if you're not Engineers well be patient +you've studied basic physics and + + align:start position:0% +you've studied basic physics and + + + align:start position:0% +you've studied basic physics and +math the rate of passive spread of + + align:start position:0% +math the rate of passive spread of + + + align:start position:0% +math the rate of passive spread of +current down the center of an axent okay + + align:start position:0% +current down the center of an axent okay + + + align:start position:0% +current down the center of an axent okay +is proportional to the reciprocal of + + align:start position:0% +is proportional to the reciprocal of + + + align:start position:0% +is proportional to the reciprocal of +this product + + align:start position:0% +this product + + + align:start position:0% +this product +the the radius of the of the + + align:start position:0% +the the radius of the of the + + + align:start position:0% +the the radius of the of the +axon okay sorry the resistance of the + + align:start position:0% +axon okay sorry the resistance of the + + + align:start position:0% +axon okay sorry the resistance of the +axon down the cylinder which can be + + align:start position:0% +axon down the cylinder which can be + + + align:start position:0% +axon down the cylinder which can be +measured okay and the capacitance of the + + align:start position:0% +measured okay and the capacitance of the + + + align:start position:0% +measured okay and the capacitance of the +membrane okay you can increase the of + + align:start position:0% +membrane okay you can increase the of + + + align:start position:0% +membrane okay you can increase the of +capacitance with + + align:start position:0% +capacitance with + + + align:start position:0% +capacitance with +milon you can decrease the resistance + + align:start position:0% +milon you can decrease the resistance + + + align:start position:0% +milon you can decrease the resistance +simply by making the axon bigger around + + align:start position:0% + + + + align:start position:0% + +okay I point out here that down here + + align:start position:0% +okay I point out here that down here + + + align:start position:0% +okay I point out here that down here +that the resistance decreases in + + align:start position:0% +that the resistance decreases in + + + align:start position:0% +that the resistance decreases in +proportion to the square of the diameter + + align:start position:0% +proportion to the square of the diameter + + + align:start position:0% +proportion to the square of the diameter +of the axon and the capacitance + + align:start position:0% +of the axon and the capacitance + + + align:start position:0% +of the axon and the capacitance +increases in proportion to the + + align:start position:0% +increases in proportion to the + + + align:start position:0% +increases in proportion to the +diameter so then how does the action + + align:start position:0% +diameter so then how does the action + + + align:start position:0% +diameter so then how does the action +potential move we know that the myin + + align:start position:0% +potential move we know that the myin + + + align:start position:0% +potential move we know that the myin +makes that passive + + align:start position:0% +makes that passive + + + align:start position:0% +makes that passive +conduction the passive spread of current + + align:start position:0% +conduction the passive spread of current + + + align:start position:0% +conduction the passive spread of current +the kind of spread you get in the cell + + align:start position:0% +the kind of spread you get in the cell + + + align:start position:0% +the kind of spread you get in the cell +body where you touch the cell in one + + align:start position:0% +body where you touch the cell in one + + + align:start position:0% +body where you touch the cell in one +place stimulate it in one place it does + + align:start position:0% +place stimulate it in one place it does + + + align:start position:0% +place stimulate it in one place it does +spread to the rest of the + + align:start position:0% +spread to the rest of the + + + align:start position:0% +spread to the rest of the +cell but not it's not an action + + align:start position:0% +cell but not it's not an action + + + align:start position:0% +cell but not it's not an action +potential in fact it get detrimental it + + align:start position:0% +potential in fact it get detrimental it + + + align:start position:0% +potential in fact it get detrimental it +gets weaker the further you get from + + align:start position:0% +gets weaker the further you get from + + + align:start position:0% +gets weaker the further you get from +where you stimulate the same is true in + + align:start position:0% +where you stimulate the same is true in + + + align:start position:0% +where you stimulate the same is true in +those all those little processes of the + + align:start position:0% +those all those little processes of the + + + align:start position:0% +those all those little processes of the +cell we call dendrites it spreads + + align:start position:0% +cell we call dendrites it spreads + + + align:start position:0% +cell we call dendrites it spreads +passively + + align:start position:0% +passively + + + align:start position:0% +passively +okay just if you diagram myON here's a + + align:start position:0% +okay just if you diagram myON here's a + + + align:start position:0% +okay just if you diagram myON here's a +greatly enlarged axon this long cylinder + + align:start position:0% +greatly enlarged axon this long cylinder + + + align:start position:0% +greatly enlarged axon this long cylinder +that's the axon + + align:start position:0% +that's the axon + + + align:start position:0% +that's the axon +membrane the way the myin forms + + align:start position:0% +membrane the way the myin forms + + + align:start position:0% +membrane the way the myin forms +is let + + align:start position:0% +is let + + + align:start position:0% +is let +me let's say this is a peripheral axon + + align:start position:0% +me let's say this is a peripheral axon + + + align:start position:0% +me let's say this is a peripheral axon +in our + + align:start position:0% +in our + + + align:start position:0% +in our +leg + + align:start position:0% +leg + + + align:start position:0% +leg +okay we'll draw this cell body forming + + align:start position:0% +okay we'll draw this cell body forming + + + align:start position:0% +okay we'll draw this cell body forming +that here's the nucleus + + align:start position:0% +that here's the nucleus + + + align:start position:0% +that here's the nucleus +that cell has its membrane is wrapped + + align:start position:0% +that cell has its membrane is wrapped + + + align:start position:0% +that cell has its membrane is wrapped +round and round and round this portion + + align:start position:0% +round and round and round this portion + + + align:start position:0% +round and round and round this portion +of the axon this is a cross-section + + align:start position:0% +of the axon this is a cross-section + + + align:start position:0% +of the axon this is a cross-section +okay and then there's another cell + + align:start position:0% +okay and then there's another cell + + + align:start position:0% +okay and then there's another cell +wrapping its membrane here another one + + align:start position:0% +wrapping its membrane here another one + + + align:start position:0% +wrapping its membrane here another one +here wrapping its membrane these cells + + align:start position:0% +here wrapping its membrane these cells + + + align:start position:0% +here wrapping its membrane these cells +are called Schwan cells they're in the + + align:start position:0% +are called Schwan cells they're in the + + + align:start position:0% +are called Schwan cells they're in the +periphery if this was in the central + + align:start position:0% +periphery if this was in the central + + + align:start position:0% +periphery if this was in the central +nervous system in the brain say where we + + align:start position:0% +nervous system in the brain say where we + + + align:start position:0% +nervous system in the brain say where we +also have a lot of myin same in the + + align:start position:0% +also have a lot of myin same in the + + + align:start position:0% +also have a lot of myin same in the +spinal cord then there would be a cell + + align:start position:0% +spinal cord then there would be a cell + + + align:start position:0% +spinal cord then there would be a cell +up here forming myin and and + + align:start position:0% + + + + align:start position:0% + +uh like this here's the and it would + + align:start position:0% +uh like this here's the and it would + + + align:start position:0% +uh like this here's the and it would +have these + + align:start position:0% + + + + align:start position:0% + +branches spreading + + align:start position:0% + + + + align:start position:0% + +down and wrapping the membrane round and + + align:start position:0% +down and wrapping the membrane round and + + + align:start position:0% +down and wrapping the membrane round and +round and + + align:start position:0% +round and + + + align:start position:0% +round and +around the + + align:start position:0% +around the + + + align:start position:0% +around the +AEL so the same cell here can Ming a + + align:start position:0% +AEL so the same cell here can Ming a + + + align:start position:0% +AEL so the same cell here can Ming a +whole bunch of ax + + align:start position:0% +whole bunch of ax + + + align:start position:0% +whole bunch of ax +okay that's anodite in the brain so the + + align:start position:0% +okay that's anodite in the brain so the + + + align:start position:0% +okay that's anodite in the brain so the +same thing is accomplished these cells + + align:start position:0% +same thing is accomplished these cells + + + align:start position:0% +same thing is accomplished these cells +are wrapping + + align:start position:0% +are wrapping + + + align:start position:0% +are wrapping +their insulating the accent okay so how + + align:start position:0% +their insulating the accent okay so how + + + align:start position:0% +their insulating the accent okay so how +does that + + align:start position:0% +does that + + + align:start position:0% +does that +help okay if the action action potential + + align:start position:0% +help okay if the action action potential + + + align:start position:0% +help okay if the action action potential +say is triggered + + align:start position:0% + + + + align:start position:0% + +here we know that + + align:start position:0% +here we know that + + + align:start position:0% +here we know that +the the this depolarization of the + + align:start position:0% +the the this depolarization of the + + + align:start position:0% +the the this depolarization of the +membrane spreads very very + + align:start position:0% +membrane spreads very very + + + align:start position:0% +membrane spreads very very +fast down the + + align:start position:0% +fast down the + + + align:start position:0% +fast down the +axon no action potential until you get + + align:start position:0% +axon no action potential until you get + + + align:start position:0% +axon no action potential until you get +to the next node here where there's no + + align:start position:0% +to the next node here where there's no + + + align:start position:0% +to the next node here where there's no +mile it triggers an action potential + + align:start position:0% +mile it triggers an action potential + + + align:start position:0% +mile it triggers an action potential +there then that spreads decrementally + + align:start position:0% +there then that spreads decrementally + + + align:start position:0% +there then that spreads decrementally +down to the next node the spread is + + align:start position:0% +down to the next node the spread is + + + align:start position:0% +down to the next node the spread is +extremely rapid with a large diameter + + align:start position:0% +extremely rapid with a large diameter + + + align:start position:0% +extremely rapid with a large diameter +and with the insulated membrane it keeps + + align:start position:0% +and with the insulated membrane it keeps + + + align:start position:0% +and with the insulated membrane it keeps +triggering the action potential and Noe + + align:start position:0% +triggering the action potential and Noe + + + align:start position:0% +triggering the action potential and Noe +after Noe after Noe that's called + + align:start position:0% +after Noe after Noe that's called + + + align:start position:0% +after Noe after Noe that's called +saltatory conduction jumping conduction + + align:start position:0% +saltatory conduction jumping conduction + + + align:start position:0% +saltatory conduction jumping conduction +and it just + + align:start position:0% +and it just + + + align:start position:0% +and it just +goes and it goes very very fast without + + align:start position:0% +goes and it goes very very fast without + + + align:start position:0% +goes and it goes very very fast without +making the axon so + + align:start position:0% +making the axon so + + + align:start position:0% +making the axon so +gigantic so that's how it + + align:start position:0% +gigantic so that's how it + + + align:start position:0% +gigantic so that's how it +happens and + + align:start position:0% +happens and + + + align:start position:0% +happens and +uh that's the end of the class and + + align:start position:0% +uh that's the end of the class and + + + align:start position:0% +uh that's the end of the class and +we'll talk about motivational States + + align:start position:0% +we'll talk about motivational States + + + align:start position:0% +we'll talk about motivational States +next + + align:start position:0% + + + + align:start position:0% + +time + + align:start position:0% + + + + align:start position:0% + +okay \ No newline at end of file diff --git a/vuS8mlpRn_0.txt b/vuS8mlpRn_0.txt new file mode 100644 index 0000000000000000000000000000000000000000..247a1f84a8e17e90627f28121431f53d975bcd46 --- /dev/null +++ b/vuS8mlpRn_0.txt @@ -0,0 +1,11824 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +Okay, let's start. + + align:start position:0% +Okay, let's start. + + + align:start position:0% +Okay, let's start. +So + + align:start position:0% +So + + + align:start position:0% +So +we are back to calculating + + align:start position:0% +we are back to calculating + + + align:start position:0% +we are back to calculating +partition functions for ising models. So + + align:start position:0% +partition functions for ising models. So + + + align:start position:0% +partition functions for ising models. So +again some in general hyper cubic latis + + align:start position:0% +again some in general hyper cubic latis + + + align:start position:0% +again some in general hyper cubic latis +where you have variables zigma i being + + align:start position:0% +where you have variables zigma i being + + + align:start position:0% +where you have variables zigma i being +minus + one at each side with a tendency + + align:start position:0% +minus + one at each side with a tendency + + + align:start position:0% +minus + one at each side with a tendency +to be parallel. And our task is to + + align:start position:0% +to be parallel. And our task is to + + + align:start position:0% +to be parallel. And our task is to +calculate a partition function + + align:start position:0% +calculate a partition function + + + align:start position:0% +calculate a partition function +which for n sides amounts to summing + + align:start position:0% +which for n sides amounts to summing + + + align:start position:0% +which for n sides amounts to summing +over 2 to the n binary configurations + + align:start position:0% +over 2 to the n binary configurations + + + align:start position:0% +over 2 to the n binary configurations +of a weight that favors + + align:start position:0% +of a weight that favors + + + align:start position:0% +of a weight that favors +near neighbors to be in the same state + + align:start position:0% +near neighbors to be in the same state + + + align:start position:0% +near neighbors to be in the same state +with a strength k. + + align:start position:0% +with a strength k. + + + align:start position:0% +with a strength k. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So the procedure that we are going to + + align:start position:0% +So the procedure that we are going to + + + align:start position:0% +So the procedure that we are going to +follow is this high temperature + + align:start position:0% +follow is this high temperature + + + align:start position:0% +follow is this high temperature +expansion that is writing this as + + align:start position:0% +expansion that is writing this as + + + align:start position:0% +expansion that is writing this as +hyperbolic cosine of K 1 + T standing + + align:start position:0% +hyperbolic cosine of K 1 + T standing + + + align:start position:0% +hyperbolic cosine of K 1 + T standing +for tangent K + + align:start position:0% + + + + align:start position:0% + +zigma I zigma J + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +then as we + + align:start position:0% +then as we + + + align:start position:0% +then as we +discussed actually this I would have to + + align:start position:0% +discussed actually this I would have to + + + align:start position:0% +discussed actually this I would have to +write as a product + + align:start position:0% +write as a product + + + align:start position:0% +write as a product +over all bonds + + align:start position:0% +over all bonds + + + align:start position:0% +over all bonds +and + + align:start position:0% +and + + + align:start position:0% +and +then essentially to each bond on this + + align:start position:0% +then essentially to each bond on this + + + align:start position:0% +then essentially to each bond on this +latice + + align:start position:0% +latice + + + align:start position:0% +latice +I would have to either assign one or t + + align:start position:0% +I would have to either assign one or t + + + align:start position:0% +I would have to either assign one or t +sigma i sigma j binary choice now move + + align:start position:0% +sigma i sigma j binary choice now move + + + align:start position:0% +sigma i sigma j binary choice now move +to bonds + + align:start position:0% +to bonds + + + align:start position:0% +to bonds +and then we saw that + + align:start position:0% + + + + align:start position:0% + +in order to make sure that following the + + align:start position:0% +in order to make sure that following the + + + align:start position:0% +in order to make sure that following the +summation over sigma these factors + + align:start position:0% +summation over sigma these factors + + + align:start position:0% +summation over sigma these factors +survive. We have to make sure that we + + align:start position:0% +survive. We have to make sure that we + + + align:start position:0% +survive. We have to make sure that we +construct graphs where out of each side + + align:start position:0% +construct graphs where out of each side + + + align:start position:0% +construct graphs where out of each side +go out an even number of bonds and we + + align:start position:0% +go out an even number of bonds and we + + + align:start position:0% +go out an even number of bonds and we +rewrote the whole thing as 2 to the n k + + align:start position:0% +rewrote the whole thing as 2 to the n k + + + align:start position:0% +rewrote the whole thing as 2 to the n k +to the number of bonds which for a hyper + + align:start position:0% +to the number of bonds which for a hyper + + + align:start position:0% +to the number of bonds which for a hyper +cubic latis is dn. + + align:start position:0% +cubic latis is dn. + + + align:start position:0% +cubic latis is dn. +And then we had a sum + + align:start position:0% +And then we had a sum + + + align:start position:0% +And then we had a sum +over graphs + + align:start position:0% +over graphs + + + align:start position:0% +over graphs +where we had an even number of bonds per + + align:start position:0% +where we had an even number of bonds per + + + align:start position:0% +where we had an even number of bonds per +site + + align:start position:0% +site + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +and the contribution of the graph + + align:start position:0% +and the contribution of the graph + + + align:start position:0% +and the contribution of the graph +was basically t + + align:start position:0% +was basically t + + + align:start position:0% +was basically t +to the power of the number of bonds. + + align:start position:0% + + + + align:start position:0% + +So I'm going to call this sum over here + + align:start position:0% +So I'm going to call this sum over here + + + align:start position:0% +So I'm going to call this sum over here +s + + align:start position:0% +s + + + align:start position:0% +s +after all the interesting part of the + + align:start position:0% +after all the interesting part of the + + + align:start position:0% +after all the interesting part of the +problem is captured in this factor s + + align:start position:0% +problem is captured in this factor s + + + align:start position:0% +problem is captured in this factor s +these 2 to the n cos k to the power of + + align:start position:0% +these 2 to the n cos k to the power of + + + align:start position:0% +these 2 to the n cos k to the power of +dn are perfectly well behaved analytical + + align:start position:0% +dn are perfectly well behaved analytical + + + align:start position:0% +dn are perfectly well behaved analytical +functions we are looking for something + + align:start position:0% +functions we are looking for something + + + align:start position:0% +functions we are looking for something +that is singular + + align:start position:0% +that is singular + + + align:start position:0% +that is singular +so this s + + align:start position:0% +so this s + + + align:start position:0% +so this s +I can either pick one from all of the + + align:start position:0% +I can either pick one from all of the + + + align:start position:0% +I can either pick one from all of the +factors. So to the lowest order in t I + + align:start position:0% +factors. So to the lowest order in t I + + + align:start position:0% +factors. So to the lowest order in t I +would have to put 2 one + + align:start position:0% +would have to put 2 one + + + align:start position:0% +would have to put 2 one +and then we saw that the next order + + align:start position:0% +and then we saw that the next order + + + align:start position:0% +and then we saw that the next order +correction would be something like a + + align:start position:0% +correction would be something like a + + + align:start position:0% +correction would be something like a +square would be this t to the 4th and + + align:start position:0% +square would be this t to the 4th and + + + align:start position:0% +square would be this t to the 4th and +then objects that are more complicated + + align:start position:0% +then objects that are more complicated + + + align:start position:0% +then objects that are more complicated +versions + + align:start position:0% +versions + + + align:start position:0% +versions +and I can write all of those as a sum + + align:start position:0% +and I can write all of those as a sum + + + align:start position:0% +and I can write all of those as a sum +over kind of graphs that I can draw on + + align:start position:0% +over kind of graphs that I can draw on + + + align:start position:0% +over kind of graphs that I can draw on +the latice by going around than making a + + align:start position:0% +the latice by going around than making a + + + align:start position:0% +the latice by going around than making a +loop. + + align:start position:0% +loop. + + + align:start position:0% +loop. +But then I will have graphs + + align:start position:0% +But then I will have graphs + + + align:start position:0% +But then I will have graphs +that will be composed of two loops for + + align:start position:0% +that will be composed of two loops for + + + align:start position:0% +that will be composed of two loops for +example + + align:start position:0% +example + + + align:start position:0% +example +that are disconnected. + + align:start position:0% +that are disconnected. + + + align:start position:0% +that are disconnected. +Since this can be translated all over + + align:start position:0% +Since this can be translated all over + + + align:start position:0% +Since this can be translated all over +the place, this would have a factor of n + + align:start position:0% +the place, this would have a factor of n + + + align:start position:0% +the place, this would have a factor of n +for a latis that is large for getting + + align:start position:0% +for a latis that is large for getting + + + align:start position:0% +for a latis that is large for getting +side effects and edge effects. This + + align:start position:0% +side effects and edge effects. This + + + align:start position:0% +side effects and edge effects. This +would have a contribution once I slide + + align:start position:0% +would have a contribution once I slide + + + align:start position:0% +would have a contribution once I slide +these two with respect to each other + + align:start position:0% +these two with respect to each other + + + align:start position:0% +these two with respect to each other +that is of the order of n squ and then I + + align:start position:0% +that is of the order of n squ and then I + + + align:start position:0% +that is of the order of n squ and then I +would have things that were would be + + align:start position:0% +would have things that were would be + + + align:start position:0% +would have things that were would be +three loops and so forth. + + align:start position:0% + + + + align:start position:0% + +Now based on what we have seen before, + + align:start position:0% +Now based on what we have seen before, + + + align:start position:0% +Now based on what we have seen before, +it is very tempting + + align:start position:0% +it is very tempting + + + align:start position:0% +it is very tempting +to + + align:start position:0% +to + + + align:start position:0% +to +somehow exponentiate this sum + + align:start position:0% +somehow exponentiate this sum + + + align:start position:0% +somehow exponentiate this sum +and write it as exponential + + align:start position:0% +and write it as exponential + + + align:start position:0% +and write it as exponential +of the sum over objects that have a + + align:start position:0% +of the sum over objects that have a + + + align:start position:0% +of the sum over objects that have a +single loop. + + align:start position:0% + + + + align:start position:0% + +And I will call this new sum actually s + + align:start position:0% +And I will call this new sum actually s + + + align:start position:0% +And I will call this new sum actually s +prime + + align:start position:0% + + + + align:start position:0% + +for reasons to become apparent because + + align:start position:0% +for reasons to become apparent because + + + align:start position:0% +for reasons to become apparent because +if I start to expand this exponential + + align:start position:0% +if I start to expand this exponential + + + align:start position:0% +if I start to expand this exponential +what do I get? I will certainly start to + + align:start position:0% +what do I get? I will certainly start to + + + align:start position:0% +what do I get? I will certainly start to +get one. Then I will have the sum over + + align:start position:0% +get one. Then I will have the sum over + + + align:start position:0% +get one. Then I will have the sum over +single loop graphs plus 12 whatever is + + align:start position:0% +single loop graphs plus 12 whatever is + + + align:start position:0% +single loop graphs plus 12 whatever is +in the numerator or in the exponent over + + align:start position:0% +in the numerator or in the exponent over + + + align:start position:0% +in the numerator or in the exponent over +here squared 1 / 3 factorial + + align:start position:0% +here squared 1 / 3 factorial + + + align:start position:0% +here squared 1 / 3 factorial +whatever is in the exponent which is + + align:start position:0% +whatever is in the exponent which is + + + align:start position:0% +whatever is in the exponent which is +this sum cubed and so forth. + + align:start position:0% + + + + align:start position:0% + +And + + align:start position:0% +And + + + align:start position:0% +And +if I were to expand + + align:start position:0% +if I were to expand + + + align:start position:0% +if I were to expand +this thing that is something squared, I + + align:start position:0% +this thing that is something squared, I + + + align:start position:0% +this thing that is something squared, I +will certainly get terms in it that + + align:start position:0% +will certainly get terms in it that + + + align:start position:0% +will certainly get terms in it that +would correspond to two of the terms in + + align:start position:0% +would correspond to two of the terms in + + + align:start position:0% +would correspond to two of the terms in +the sum. Here I would get things that + + align:start position:0% +the sum. Here I would get things that + + + align:start position:0% +the sum. Here I would get things that +would correspond to three of the terms + + align:start position:0% +would correspond to three of the terms + + + align:start position:0% +would correspond to three of the terms +in the sum and the combinatorial factors + + align:start position:0% +in the sum and the combinatorial factors + + + align:start position:0% +in the sum and the combinatorial factors +would certainly work out to get rid of + + align:start position:0% +would certainly work out to get rid of + + + align:start position:0% +would certainly work out to get rid of +the two and the six etc. depending on + + align:start position:0% +the two and the six etc. depending on + + + align:start position:0% +the two and the six etc. depending on +let's say I have loop a b or c I could + + align:start position:0% +let's say I have loop a b or c I could + + + align:start position:0% +let's say I have loop a b or c I could +pick a from the first uh uh sum here b + + align:start position:0% +pick a from the first uh uh sum here b + + + align:start position:0% +pick a from the first uh uh sum here b +from the second c from the third or any + + align:start position:0% +from the second c from the third or any + + + align:start position:0% +from the second c from the third or any +permutation thereof that would amount to + + align:start position:0% +permutation thereof that would amount to + + + align:start position:0% +permutation thereof that would amount to +c I would have a factor of c ab c but + + align:start position:0% +c I would have a factor of c ab c but + + + align:start position:0% +c I would have a factor of c ab c but +s definitely is not equal to s prime + + align:start position:0% +s definitely is not equal to s prime + + + align:start position:0% +s definitely is not equal to s prime +because immediately we see that once I + + align:start position:0% +because immediately we see that once I + + + align:start position:0% +because immediately we see that once I +square this term a + b squared in + + align:start position:0% +square this term a + b squared in + + + align:start position:0% +square this term a + b squared in +addition to a squ a b I will also get a + + align:start position:0% +addition to a squ a b I will also get a + + + align:start position:0% +addition to a squ a b I will also get a +squ and b square which corresponds to + + align:start position:0% +squ and b square which corresponds to + + + align:start position:0% +squ and b square which corresponds to +objects such as this + + align:start position:0% +objects such as this + + + align:start position:0% +objects such as this +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +1/2 + + align:start position:0% +1/2 + + + align:start position:0% +1/2 +of the same graph repeated twice + + align:start position:0% + + + + align:start position:0% + +right it is the a² term that is + + align:start position:0% +right it is the a² term that is + + + align:start position:0% +right it is the a² term that is +appearing in this s + + align:start position:0% +appearing in this s + + + align:start position:0% +appearing in this s +and this clearly has no analog Here in + + align:start position:0% +and this clearly has no analog Here in + + + align:start position:0% +and this clearly has no analog Here in +my sum s I emphasize that in the sum s + + align:start position:0% +my sum s I emphasize that in the sum s + + + align:start position:0% +my sum s I emphasize that in the sum s +each bond can occur either zero or one + + align:start position:0% +each bond can occur either zero or one + + + align:start position:0% +each bond can occur either zero or one +time. + + align:start position:0% +time. + + + align:start position:0% +time. +Whereas if I exponentiate this you can + + align:start position:0% +Whereas if I exponentiate this you can + + + align:start position:0% +Whereas if I exponentiate this you can +see that s prime certainly contains + + align:start position:0% +see that s prime certainly contains + + + align:start position:0% +see that s prime certainly contains +things that potentially are repeated + + align:start position:0% +things that potentially are repeated + + + align:start position:0% +things that potentially are repeated +twice. As I go further I could have + + align:start position:0% +twice. As I go further I could have + + + align:start position:0% +twice. As I go further I could have +multiple times. + + align:start position:0% +multiple times. + + + align:start position:0% +multiple times. +Also when I square this term I could + + align:start position:0% +Also when I square this term I could + + + align:start position:0% +Also when I square this term I could +potentially get + + align:start position:0% +potentially get + + + align:start position:0% +potentially get +one factor + + align:start position:0% +one factor + + + align:start position:0% +one factor +from one another factor which is also a + + align:start position:0% +from one another factor which is also a + + + align:start position:0% +from one another factor which is also a +loop from the second terms the second + + align:start position:0% +loop from the second terms the second + + + align:start position:0% +loop from the second terms the second +term in this product of two brackets + + align:start position:0% +term in this product of two brackets + + + align:start position:0% +term in this product of two brackets +which once I multiply them happen to + + align:start position:0% +which once I multiply them happen to + + + align:start position:0% +which once I multiply them happen to +overlap and share something. Okay. + + align:start position:0% +overlap and share something. Okay. + + + align:start position:0% +overlap and share something. Okay. +All right. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% + + + + align:start position:0% + +very roughly and handwavingly + + align:start position:0% +very roughly and handwavingly + + + align:start position:0% +very roughly and handwavingly +the thing is that S has loops + + align:start position:0% +the thing is that S has loops + + + align:start position:0% +the thing is that S has loops +that avoid each other don't intersect + + align:start position:0% +that avoid each other don't intersect + + + align:start position:0% +that avoid each other don't intersect +whereas S prime has loops that + + align:start position:0% +whereas S prime has loops that + + + align:start position:0% +whereas S prime has loops that +intersect. So very naively s is sum + + align:start position:0% +intersect. So very naively s is sum + + + align:start position:0% +intersect. So very naively s is sum +over if you like a gas + + align:start position:0% +over if you like a gas + + + align:start position:0% +over if you like a gas +of non-intersecting loops. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +Whereas s prime + + align:start position:0% +Whereas s prime + + + align:start position:0% +Whereas s prime +is a sum over gas of what I could call + + align:start position:0% +is a sum over gas of what I could call + + + align:start position:0% +is a sum over gas of what I could call +phantom loops. They're kind of like + + align:start position:0% +phantom loops. They're kind of like + + + align:start position:0% +phantom loops. They're kind of like +ghosts. they can go through each other. + + align:start position:0% +ghosts. they can go through each other. + + + align:start position:0% +ghosts. they can go through each other. +Okay. + + align:start position:0% + + + + align:start position:0% + +All right. + + align:start position:0% +All right. + + + align:start position:0% +All right. +So + + align:start position:0% +So + + + align:start position:0% +So +that's one of a number of problems. + + align:start position:0% +that's one of a number of problems. + + + align:start position:0% +that's one of a number of problems. +Now in this lecture we are going to + + align:start position:0% +Now in this lecture we are going to + + + align:start position:0% +Now in this lecture we are going to +ignore this difference between S and S + + align:start position:0% +ignore this difference between S and S + + + align:start position:0% +ignore this difference between S and S +prime and calculate S prime which + + align:start position:0% +prime and calculate S prime which + + + align:start position:0% +prime and calculate S prime which +therefore we will not be doing the right + + align:start position:0% +therefore we will not be doing the right + + + align:start position:0% +therefore we will not be doing the right +job. + + align:start position:0% +job. + + + align:start position:0% +job. +And this is one example of where I'm not + + align:start position:0% +And this is one example of where I'm not + + + align:start position:0% +And this is one example of where I'm not +doing a right job. And as I go through + + align:start position:0% +doing a right job. And as I go through + + + align:start position:0% +doing a right job. And as I go through +the calculation, you may want to figure + + align:start position:0% +the calculation, you may want to figure + + + align:start position:0% +the calculation, you may want to figure +out also other places where I don't + + align:start position:0% +out also other places where I don't + + + align:start position:0% +out also other places where I don't +correctly reproduce the sum s in order + + align:start position:0% +correctly reproduce the sum s in order + + + align:start position:0% +correctly reproduce the sum s in order +to ultimately be able to make a + + align:start position:0% +to ultimately be able to make a + + + align:start position:0% +to ultimately be able to make a +calculation and see what it comes to. + + align:start position:0% +calculation and see what it comes to. + + + align:start position:0% +calculation and see what it comes to. +Now, next lecture we will try to correct + + align:start position:0% +Now, next lecture we will try to correct + + + align:start position:0% +Now, next lecture we will try to correct +all of those errors. So you better keep + + align:start position:0% +all of those errors. So you better keep + + + align:start position:0% +all of those errors. So you better keep +track of all of those errors. Make sure + + align:start position:0% +track of all of those errors. Make sure + + + align:start position:0% +track of all of those errors. Make sure +that I am doing everything right. + + align:start position:0% +that I am doing everything right. + + + align:start position:0% +that I am doing everything right. +I think + + align:start position:0% + + + + align:start position:0% + +seems good. + + align:start position:0% +seems good. + + + align:start position:0% +seems good. +All right. + + align:start position:0% + + + + align:start position:0% + +So, + + align:start position:0% + + + + align:start position:0% + +let's go and take a look at this S + + align:start position:0% +let's go and take a look at this S + + + align:start position:0% +let's go and take a look at this S +prime. + + align:start position:0% +prime. + + + align:start position:0% +prime. +So s prime + + align:start position:0% +So s prime + + + align:start position:0% +So s prime +actually + + align:start position:0% +actually + + + align:start position:0% +actually +log of s prime + + align:start position:0% +log of s prime + + + align:start position:0% +log of s prime +is a sum + + align:start position:0% +is a sum + + + align:start position:0% +is a sum +over graphs that I can draw on the + + align:start position:0% +over graphs that I can draw on the + + + align:start position:0% +over graphs that I can draw on the +latice + + align:start position:0% +latice + + + align:start position:0% +latice +and since I could exponentiate that + + align:start position:0% +and since I could exponentiate that + + + align:start position:0% +and since I could exponentiate that +there was no problem in the + + align:start position:0% +there was no problem in the + + + align:start position:0% +there was no problem in the +exponentiation involved over here. + + align:start position:0% +exponentiation involved over here. + + + align:start position:0% +exponentiation involved over here. +Essentially I have to for calculating + + align:start position:0% +Essentially I have to for calculating + + + align:start position:0% +Essentially I have to for calculating +the log just calculate this singly + + align:start position:0% +the log just calculate this singly + + + align:start position:0% +the log just calculate this singly +connected loops and you can see that + + align:start position:0% +connected loops and you can see that + + + align:start position:0% +connected loops and you can see that +that will work out fine as far as + + align:start position:0% +that will work out fine as far as + + + align:start position:0% +that will work out fine as far as +extensivity is concerned because I could + + align:start position:0% +extensivity is concerned because I could + + + align:start position:0% +extensivity is concerned because I could +translate each one of these figures of + + align:start position:0% +translate each one of these figures of + + + align:start position:0% +translate each one of these figures of +the loops over the latis and get the + + align:start position:0% +the loops over the latis and get the + + + align:start position:0% +the loops over the latis and get the +factor of n. So this is clearly + + align:start position:0% +factor of n. So this is clearly + + + align:start position:0% +factor of n. So this is clearly +something that is uh okay. + + align:start position:0% + + + + align:start position:0% + +Now since I'm already making this + + align:start position:0% +Now since I'm already making this + + + align:start position:0% +Now since I'm already making this +mistake of forgetting about the + + align:start position:0% +mistake of forgetting about the + + + align:start position:0% +mistake of forgetting about the +intersections between loops, I'm going + + align:start position:0% +intersections between loops, I'm going + + + align:start position:0% +intersections between loops, I'm going +to make another assumption + + align:start position:0% + + + + align:start position:0% + +that is in this + + align:start position:0% + + + + align:start position:0% + +sum of single loops + + align:start position:0% +sum of single loops + + + align:start position:0% +sum of single loops +I already include things where the uh + + align:start position:0% +I already include things where the uh + + + align:start position:0% +I already include things where the uh +single loop is allowed to intersect + + align:start position:0% +single loop is allowed to intersect + + + align:start position:0% +single loop is allowed to intersect +itself. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +For example, + + align:start position:0% +For example, + + + align:start position:0% +For example, +I'm going to allow + + align:start position:0% +I'm going to allow + + + align:start position:0% +I'm going to allow +as a single loop entity something that + + align:start position:0% +as a single loop entity something that + + + align:start position:0% +as a single loop entity something that +is like this + + align:start position:0% +is like this + + + align:start position:0% +is like this +where this particular bond + + align:start position:0% +where this particular bond + + + align:start position:0% +where this particular bond +will give a factor of t ^2. Clearly, I + + align:start position:0% +will give a factor of t ^2. Clearly, I + + + align:start position:0% +will give a factor of t ^2. Clearly, I +should not include this in the correct + + align:start position:0% +should not include this in the correct + + + align:start position:0% +should not include this in the correct +sum. But since I'm ignoring + + align:start position:0% +sum. But since I'm ignoring + + + align:start position:0% +sum. But since I'm ignoring +intersections among the different loops + + align:start position:0% +intersections among the different loops + + + align:start position:0% +intersections among the different loops +and I'm making it phantom, let's make it + + align:start position:0% +and I'm making it phantom, let's make it + + + align:start position:0% +and I'm making it phantom, let's make it +also phantom with respect to itself. + + align:start position:0% +also phantom with respect to itself. + + + align:start position:0% +also phantom with respect to itself. +Allow it to intersect itself also. It's + + align:start position:0% +Allow it to intersect itself also. It's + + + align:start position:0% +Allow it to intersect itself also. It's +in the same spirit of the mistake that + + align:start position:0% +in the same spirit of the mistake that + + + align:start position:0% +in the same spirit of the mistake that +we are going to do. + + align:start position:0% +we are going to do. + + + align:start position:0% +we are going to do. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So now what do we have? We can write + + align:start position:0% +So now what do we have? We can write + + + align:start position:0% +So now what do we have? We can write +that log of S prime + + align:start position:0% + + + + align:start position:0% + +is this sum over + + align:start position:0% +is this sum over + + + align:start position:0% +is this sum over +loops + + align:start position:0% +loops + + + align:start position:0% +loops +of length L + + align:start position:0% +of length L + + + align:start position:0% +of length L +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +and then multiply it by T to the L right + + align:start position:0% +and then multiply it by T to the L right + + + align:start position:0% +and then multiply it by T to the L right +so basically I say that I can draw loops + + align:start position:0% +so basically I say that I can draw loops + + + align:start position:0% +so basically I say that I can draw loops +let's say of size four loops of light + + align:start position:0% +let's say of size four loops of light + + + align:start position:0% +let's say of size four loops of light +size six etc each one of them I have to + + align:start position:0% +size six etc each one of them I have to + + + align:start position:0% +size six etc each one of them I have to +multip multiply by T the L. Uh, of + + align:start position:0% +multip multiply by T the L. Uh, of + + + align:start position:0% +multip multiply by T the L. Uh, of +course I have to multiply with the + + align:start position:0% +course I have to multiply with the + + + align:start position:0% +course I have to multiply with the +number of loops + + align:start position:0% + + + + align:start position:0% + +of length L. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +And this I'm going to write slightly + + align:start position:0% +And this I'm going to write slightly + + + align:start position:0% +And this I'm going to write slightly +differently. + + align:start position:0% +differently. + + + align:start position:0% +differently. +So I'm going to say that log of s prime + + align:start position:0% +So I'm going to say that log of s prime + + + align:start position:0% +So I'm going to say that log of s prime +is sum over this length of the loop. + + align:start position:0% +is sum over this length of the loop. + + + align:start position:0% +is sum over this length of the loop. +All loops of length l are going to + + align:start position:0% +All loops of length l are going to + + + align:start position:0% +All loops of length l are going to +contribute a factor of t to the l. + + align:start position:0% +contribute a factor of t to the l. + + + align:start position:0% +contribute a factor of t to the l. +And I'm going to + + align:start position:0% +And I'm going to + + + align:start position:0% +And I'm going to +count + + align:start position:0% +count + + + align:start position:0% +count +the loops of length l that start and end + + align:start position:0% +the loops of length l that start and end + + + align:start position:0% +the loops of length l that start and end +at the origin. And I'll give that a + + align:start position:0% +at the origin. And I'll give that a + + + align:start position:0% +at the origin. And I'll give that a +symbol WL0 0. Actually very soon I will + + align:start position:0% +symbol WL0 0. Actually very soon I will + + + align:start position:0% +symbol WL0 0. Actually very soon I will +introduce a generalization of this. So + + align:start position:0% +introduce a generalization of this. So + + + align:start position:0% +introduce a generalization of this. So +let me write the definition. + + align:start position:0% + + + + align:start position:0% + +I define a matrix + + align:start position:0% +I define a matrix + + + align:start position:0% +I define a matrix +that is indexed by two sides of the + + align:start position:0% +that is indexed by two sides of the + + + align:start position:0% +that is indexed by two sides of the +latice + + align:start position:0% +latice + + + align:start position:0% +latice +and counts the number of walks that I + + align:start position:0% +and counts the number of walks that I + + + align:start position:0% +and counts the number of walks that I +can have from one to the other from I to + + align:start position:0% +can have from one to the other from I to + + + align:start position:0% +can have from one to the other from I to +J in L steps. So this is number + + align:start position:0% +J in L steps. So this is number + + + align:start position:0% +J in L steps. So this is number +of walks + + align:start position:0% +of walks + + + align:start position:0% +of walks +of length + + align:start position:0% +of length + + + align:start position:0% +of length +L from + + align:start position:0% +L from + + + align:start position:0% +L from +I to J. + + align:start position:0% +I to J. + + + align:start position:0% +I to J. +Okay. + + align:start position:0% + + + + align:start position:0% + +So what am I doing here? + + align:start position:0% + + + + align:start position:0% + +Since I'm looking at single loop + + align:start position:0% +Since I'm looking at single loop + + + align:start position:0% +Since I'm looking at single loop +objects, + + align:start position:0% +objects, + + + align:start position:0% +objects, +I want to sum over let's say all terms + + align:start position:0% +I want to sum over let's say all terms + + + align:start position:0% +I want to sum over let's say all terms +that contribute + + align:start position:0% +that contribute + + + align:start position:0% +that contribute +in this case t to the 4. It's obvious + + align:start position:0% +in this case t to the 4. It's obvious + + + align:start position:0% +in this case t to the 4. It's obvious +because it's really just one shape. It's + + align:start position:0% +because it's really just one shape. It's + + + align:start position:0% +because it's really just one shape. It's +a square. But this square I could have + + align:start position:0% +a square. But this square I could have + + + align:start position:0% +a square. But this square I could have +started at anywhere on the latice. + + align:start position:0% +started at anywhere on the latice. + + + align:start position:0% +started at anywhere on the latice. +And this slight factor + + align:start position:0% +And this slight factor + + + align:start position:0% +And this slight factor +which captures the extensivity + + align:start position:0% +which captures the extensivity + + + align:start position:0% +which captures the extensivity +I'll take outside because I expect this + + align:start position:0% +I'll take outside because I expect this + + + align:start position:0% +I'll take outside because I expect this +log of s to be extensive. It should be + + align:start position:0% +log of s to be extensive. It should be + + + align:start position:0% +log of s to be extensive. It should be +proportional to n. So one part of it is + + align:start position:0% +proportional to n. So one part of it is + + + align:start position:0% +proportional to n. So one part of it is +essentially where I start to draw this + + align:start position:0% +essentially where I start to draw this + + + align:start position:0% +essentially where I start to draw this +loop. So I say that I always start with + + align:start position:0% +loop. So I say that I always start with + + + align:start position:0% +loop. So I say that I always start with +the loops that I uh have at point zero. + + align:start position:0% +the loops that I uh have at point zero. + + + align:start position:0% +the loops that I uh have at point zero. +then I want to come back to it to to + + align:start position:0% +then I want to come back to it to to + + + align:start position:0% +then I want to come back to it to to +myself. So I indicate that the end point + + align:start position:0% +myself. So I indicate that the end point + + + align:start position:0% +myself. So I indicate that the end point +should also be zero. + + align:start position:0% +should also be zero. + + + align:start position:0% +should also be zero. +And if I want to get a term here, this + + align:start position:0% +And if I want to get a term here, this + + + align:start position:0% +And if I want to get a term here, this +is a term that is t to the 4th. I need + + align:start position:0% +is a term that is t to the 4th. I need + + + align:start position:0% +is a term that is t to the 4th. I need +to know how many of such blocks I have? + + align:start position:0% +to know how many of such blocks I have? + + + align:start position:0% +to know how many of such blocks I have? +Yes. Um are you allowing the loop to + + align:start position:0% +Yes. Um are you allowing the loop to + + + align:start position:0% +Yes. Um are you allowing the loop to +intersect itself in this case or not? In + + align:start position:0% +intersect itself in this case or not? In + + + align:start position:0% +intersect itself in this case or not? In +this case, yes. I will also when I'm + + align:start position:0% +this case, yes. I will also when I'm + + + align:start position:0% +this case, yes. I will also when I'm +calculating anything to do with S prime + + align:start position:0% +calculating anything to do with S prime + + + align:start position:0% +calculating anything to do with S prime +I allow intersection. So if you're + + align:start position:0% +I allow intersection. So if you're + + + align:start position:0% +I allow intersection. So if you're +asking whether I'm allowing something + + align:start position:0% +asking whether I'm allowing something + + + align:start position:0% +asking whether I'm allowing something +like this the answer is yes. Okay. Yeah. + + align:start position:0% +like this the answer is yes. Okay. Yeah. + + + align:start position:0% +like this the answer is yes. Okay. Yeah. +And are we assuming infinitely large + + align:start position:0% +And are we assuming infinitely large + + + align:start position:0% +And are we assuming infinitely large +system so that yes that's right. So that + + align:start position:0% +system so that yes that's right. So that + + + align:start position:0% +system so that yes that's right. So that +the edge effects you don't have to worry + + align:start position:0% +the edge effects you don't have to worry + + + align:start position:0% +the edge effects you don't have to worry +about. Or alternatively you can imagine + + align:start position:0% +about. Or alternatively you can imagine + + + align:start position:0% +about. Or alternatively you can imagine +that you have periodic boundary + + align:start position:0% +that you have periodic boundary + + + align:start position:0% +that you have periodic boundary +conditions and with periodic boundary + + align:start position:0% +conditions and with periodic boundary + + + align:start position:0% +conditions and with periodic boundary +condition you can still slide it all + + align:start position:0% +condition you can still slide it all + + + align:start position:0% +condition you can still slide it all +over the place. + + align:start position:0% +over the place. + + + align:start position:0% +over the place. +Okay. But clearly then the maximal size + + align:start position:0% +Okay. But clearly then the maximal size + + + align:start position:0% +Okay. But clearly then the maximal size +of these loops etc will be determined + + align:start position:0% +of these loops etc will be determined + + + align:start position:0% +of these loops etc will be determined +potentially by the size of the letter. + + align:start position:0% +potentially by the size of the letter. + + + align:start position:0% +potentially by the size of the letter. +Now this is not entirely correct + + align:start position:0% +Now this is not entirely correct + + + align:start position:0% +Now this is not entirely correct +because there is an overounting + + align:start position:0% +because there is an overounting + + + align:start position:0% +because there is an overounting +this one square that I have drawn over + + align:start position:0% +this one square that I have drawn over + + + align:start position:0% +this one square that I have drawn over +here. + + align:start position:0% +here. + + + align:start position:0% +here. +I could have started from this point + + align:start position:0% +I could have started from this point + + + align:start position:0% +I could have started from this point +this point this point and essentially + + align:start position:0% +this point this point and essentially + + + align:start position:0% +this point this point and essentially +for something that has length L I would + + align:start position:0% +for something that has length L I would + + + align:start position:0% +for something that has length L I would +have had L possible + + align:start position:0% +have had L possible + + + align:start position:0% +have had L possible +starting point. So in order to avoid the + + align:start position:0% +starting point. So in order to avoid the + + + align:start position:0% +starting point. So in order to avoid the +overounting I have to divide by L. + + align:start position:0% +overounting I have to divide by L. + + + align:start position:0% +overounting I have to divide by L. +And in fact I could have started walking + + align:start position:0% +And in fact I could have started walking + + + align:start position:0% +And in fact I could have started walking +along this direction or alternatively I + + align:start position:0% +along this direction or alternatively I + + + align:start position:0% +along this direction or alternatively I +could have gone in the clockwise + + align:start position:0% +could have gone in the clockwise + + + align:start position:0% +could have gone in the clockwise +direction. So there's two orientations + + align:start position:0% +direction. So there's two orientations + + + align:start position:0% +direction. So there's two orientations +to the walk that will take me from the + + align:start position:0% +to the walk that will take me from the + + + align:start position:0% +to the walk that will take me from the +origin back to the origin in L steps. + + align:start position:0% +origin back to the origin in L steps. + + + align:start position:0% +origin back to the origin in L steps. +And not to do the over counting I have + + align:start position:0% +And not to do the over counting I have + + + align:start position:0% +And not to do the over counting I have +to divide by 2 L. + + align:start position:0% +to divide by 2 L. + + + align:start position:0% +to divide by 2 L. +Yes. Um if we allow um walking over + + align:start position:0% +Yes. Um if we allow um walking over + + + align:start position:0% +Yes. Um if we allow um walking over +ourselves, yes, is it always a + + align:start position:0% +ourselves, yes, is it always a + + + align:start position:0% +ourselves, yes, is it always a +degeneracy of 2L in a sense? You can you + + align:start position:0% +degeneracy of 2L in a sense? You can you + + + align:start position:0% +degeneracy of 2L in a sense? You can you +can go and do the calculation etc to + + align:start position:0% +can go and do the calculation etc to + + + align:start position:0% +can go and do the calculation etc to +convince yourself that even for + + align:start position:0% +convince yourself that even for + + + align:start position:0% +convince yourself that even for +something as convoluted as that + + align:start position:0% +something as convoluted as that + + + align:start position:0% +something as convoluted as that +you can it is true. + + align:start position:0% + + + + align:start position:0% + +Okay. So this is what we want to to + + align:start position:0% +Okay. So this is what we want to to + + + align:start position:0% +Okay. So this is what we want to to +calculate. + + align:start position:0% +calculate. + + + align:start position:0% +calculate. +uh well it turns out that this entity + + align:start position:0% +uh well it turns out that this entity + + + align:start position:0% +uh well it turns out that this entity +actually shows up somewhere else also. + + align:start position:0% +actually shows up somewhere else also. + + + align:start position:0% +actually shows up somewhere else also. +So let me tell you why I wanted to write + + align:start position:0% +So let me tell you why I wanted to write + + + align:start position:0% +So let me tell you why I wanted to write +a more general thing. Another quantity + + align:start position:0% +a more general thing. Another quantity + + + align:start position:0% +a more general thing. Another quantity +that I can try to calculate is the spin + + align:start position:0% +that I can try to calculate is the spin + + + align:start position:0% +that I can try to calculate is the spin +spin correlation. I can pick spin zero + + align:start position:0% +spin correlation. I can pick spin zero + + + align:start position:0% +spin correlation. I can pick spin zero +here and say spin r here some other + + align:start position:0% +here and say spin r here some other + + + align:start position:0% +here and say spin r here some other +location + + align:start position:0% +location + + + align:start position:0% +location +and I want to calculate what is the + + align:start position:0% +and I want to calculate what is the + + + align:start position:0% +and I want to calculate what is the +correlation between these two spins. + + align:start position:0% +correlation between these two spins. + + + align:start position:0% +correlation between these two spins. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So how do I have to do that for the + + align:start position:0% +So how do I have to do that for the + + + align:start position:0% +So how do I have to do that for the +model? I have to essentially sum over + + align:start position:0% +model? I have to essentially sum over + + + align:start position:0% +model? I have to essentially sum over +all configurations + + align:start position:0% +all configurations + + + align:start position:0% +all configurations +with an additional factor of zigma 0 + + align:start position:0% +with an additional factor of zigma 0 + + + align:start position:0% +with an additional factor of zigma 0 +sigma r of this weight e to the k sum + + align:start position:0% +sigma r of this weight e to the k sum + + + align:start position:0% +sigma r of this weight e to the k sum +over i j s zigma i zigma j appropriately + + align:start position:0% +over i j s zigma i zigma j appropriately + + + align:start position:0% +over i j s zigma i zigma j appropriately +normalized of course by the partition + + align:start position:0% +normalized of course by the partition + + + align:start position:0% +normalized of course by the partition +function + + align:start position:0% + + + + align:start position:0% + +and I can make the same transformation + + align:start position:0% +and I can make the same transformation + + + align:start position:0% +and I can make the same transformation +that I have on the first line of these + + align:start position:0% +that I have on the first line of these + + + align:start position:0% +that I have on the first line of these +exponential factors + + align:start position:0% +exponential factors + + + align:start position:0% +exponential factors +to write this as a sum over zigma i. + + align:start position:0% +to write this as a sum over zigma i. + + + align:start position:0% +to write this as a sum over zigma i. +I have zigma 0 s zigma r and then + + align:start position:0% +I have zigma 0 s zigma r and then + + + align:start position:0% +I have zigma 0 s zigma r and then +product over all bonds of these factors + + align:start position:0% +product over all bonds of these factors + + + align:start position:0% +product over all bonds of these factors +of 1 + t sigma i sigma j. the factors of + + align:start position:0% +of 1 + t sigma i sigma j. the factors of + + + align:start position:0% +of 1 + t sigma i sigma j. the factors of +2 to the n k will cancel out between the + + align:start position:0% +2 to the n k will cancel out between the + + + align:start position:0% +2 to the n k will cancel out between the +numerator and the denominator and + + align:start position:0% +numerator and the denominator and + + + align:start position:0% +numerator and the denominator and +basically I will get + + align:start position:0% +basically I will get + + + align:start position:0% +basically I will get +the same thing. + + align:start position:0% +the same thing. + + + align:start position:0% +the same thing. +Now of course the denominator + + align:start position:0% +Now of course the denominator + + + align:start position:0% +Now of course the denominator +is the partition function. It is the sum + + align:start position:0% +is the partition function. It is the sum + + + align:start position:0% +is the partition function. It is the sum +s that we are after. + + align:start position:0% +s that we are after. + + + align:start position:0% +s that we are after. +But we can also and we've seen this + + align:start position:0% +But we can also and we've seen this + + + align:start position:0% +But we can also and we've seen this +already how to do this express the sum + + align:start position:0% +already how to do this express the sum + + + align:start position:0% +already how to do this express the sum +in the numerator graphically. And the + + align:start position:0% +in the numerator graphically. And the + + + align:start position:0% +in the numerator graphically. And the +difference between the numerator and the + + align:start position:0% +difference between the numerator and the + + + align:start position:0% +difference between the numerator and the +denominator is that I have an additional + + align:start position:0% +denominator is that I have an additional + + + align:start position:0% +denominator is that I have an additional +zigma sitting here and additional zigma + + align:start position:0% +zigma sitting here and additional zigma + + + align:start position:0% +zigma sitting here and additional zigma +sitting there that if left by themselves + + align:start position:0% +sitting there that if left by themselves + + + align:start position:0% +sitting there that if left by themselves +will average out to zero. So I need to + + align:start position:0% +will average out to zero. So I need to + + + align:start position:0% +will average out to zero. So I need to +connect them by paths that are composed + + align:start position:0% +connect them by paths that are composed + + + align:start position:0% +connect them by paths that are composed +of factors of t sigma sigma originating + + align:start position:0% +of factors of t sigma sigma originating + + + align:start position:0% +of factors of t sigma sigma originating +on one and ending on the other. + + align:start position:0% +on one and ending on the other. + + + align:start position:0% +on one and ending on the other. +Right? + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% + + + + align:start position:0% + +in the same sense that what is appearing + + align:start position:0% +in the same sense that what is appearing + + + align:start position:0% +in the same sense that what is appearing +in the denominator is a sum that + + align:start position:0% +in the denominator is a sum that + + + align:start position:0% +in the denominator is a sum that +involves these loops. + + align:start position:0% +involves these loops. + + + align:start position:0% +involves these loops. +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +The first term that appears in the + + align:start position:0% +The first term that appears in the + + + align:start position:0% +The first term that appears in the +numerator + + align:start position:0% +numerator + + + align:start position:0% +numerator +is a path that connects zero to r + + align:start position:0% +is a path that connects zero to r + + + align:start position:0% +is a path that connects zero to r +through some combination of these + + align:start position:0% +through some combination of these + + + align:start position:0% +through some combination of these +factors of t. And then I have to sum + + align:start position:0% +factors of t. And then I have to sum + + + align:start position:0% +factors of t. And then I have to sum +over all possible ways of doing that. + + align:start position:0% +over all possible ways of doing that. + + + align:start position:0% +over all possible ways of doing that. +But then I could certainly have graphs + + align:start position:0% +But then I could certainly have graphs + + + align:start position:0% +But then I could certainly have graphs +that involves the same thing and a loop. + + align:start position:0% +that involves the same thing and a loop. + + + align:start position:0% +that involves the same thing and a loop. +There is nothing that is against that or + + align:start position:0% +There is nothing that is against that or + + + align:start position:0% +There is nothing that is against that or +the same thing and two loops + + align:start position:0% +the same thing and two loops + + + align:start position:0% +the same thing and two loops +and so forth. + + align:start position:0% +and so forth. + + + align:start position:0% +and so forth. +And you can see that as long as and only + + align:start position:0% +And you can see that as long as and only + + + align:start position:0% +And you can see that as long as and only +as long as I treat these as phantom + + align:start position:0% +as long as I treat these as phantom + + + align:start position:0% +as long as I treat these as phantom +objects that can pass through each + + align:start position:0% +objects that can pass through each + + + align:start position:0% +objects that can pass through each +other, + + align:start position:0% +other, + + + align:start position:0% +other, +I can factor out this term and the rest + + align:start position:0% +I can factor out this term and the rest + + + align:start position:0% +I can factor out this term and the rest +of 1 + 1 loop + 2 loop etc. is exactly + + align:start position:0% +of 1 + 1 loop + 2 loop etc. is exactly + + + align:start position:0% +of 1 + 1 loop + 2 loop etc. is exactly +what I have in the denominator. + + align:start position:0% +what I have in the denominator. + + + align:start position:0% +what I have in the denominator. +So we see that under + + align:start position:0% +So we see that under + + + align:start position:0% +So we see that under +the + + align:start position:0% +the + + + align:start position:0% +the +assumption of phantomness + + align:start position:0% +assumption of phantomness + + + align:start position:0% +assumption of phantomness +if phantom + + align:start position:0% + + + + align:start position:0% + +then this becomes really just the sum + + align:start position:0% +then this becomes really just the sum + + + align:start position:0% +then this becomes really just the sum +over all + + align:start position:0% +over all + + + align:start position:0% +over all +paths that go from 0 to r. + + align:start position:0% +paths that go from 0 to r. + + + align:start position:0% +paths that go from 0 to r. +And of course the contribution of each + + align:start position:0% +And of course the contribution of each + + + align:start position:0% +And of course the contribution of each +path is how many factors of t I have + + align:start position:0% +path is how many factors of t I have + + + align:start position:0% +path is how many factors of t I have +right. + + align:start position:0% +right. + + + align:start position:0% +right. +So I have to have a sum over the length + + align:start position:0% +So I have to have a sum over the length + + + align:start position:0% +So I have to have a sum over the length +of this path L. Paths of length L will + + align:start position:0% +of this path L. Paths of length L will + + + align:start position:0% +of this path L. Paths of length L will +contribute a factor of T to the L. + + align:start position:0% +contribute a factor of T to the L. + + + align:start position:0% +contribute a factor of T to the L. +But there are potentially multiple ways + + align:start position:0% +But there are potentially multiple ways + + + align:start position:0% +But there are potentially multiple ways +to go from I to R in L steps. + + align:start position:0% +to go from I to R in L steps. + + + align:start position:0% +to go from I to R in L steps. +How many ways? That's precisely what I + + align:start position:0% +How many ways? That's precisely what I + + + align:start position:0% +How many ways? That's precisely what I +call this zero w + + align:start position:0% +call this zero w + + + align:start position:0% +call this zero w +of lr. + + align:start position:0% + + + + align:start position:0% + +Yes. Why does it graph that goes from + + align:start position:0% +Yes. Why does it graph that goes from + + + align:start position:0% +Yes. Why does it graph that goes from +zero to r in three different ways? Does + + align:start position:0% +zero to r in three different ways? Does + + + align:start position:0% +zero to r in three different ways? Does +that + + align:start position:0% +that + + + align:start position:0% +that +can have + + align:start position:0% +can have + + + align:start position:0% +can have +okay? So you want to have to go from + + align:start position:0% +okay? So you want to have to go from + + + align:start position:0% +okay? So you want to have to go from +zero to R, you want to have a single + + align:start position:0% +zero to R, you want to have a single + + + align:start position:0% +zero to R, you want to have a single +path and then you want that path + + align:start position:0% +path and then you want that path + + + align:start position:0% +path and then you want that path +to do something like this. Yeah, that's + + align:start position:0% +to do something like this. Yeah, that's + + + align:start position:0% +to do something like this. Yeah, that's +that doesn't very difficult. That's + + align:start position:0% +that doesn't very difficult. That's + + + align:start position:0% +that doesn't very difficult. That's +fine. If I ignore the phantomness + + align:start position:0% +fine. If I ignore the phantomness + + + align:start position:0% +fine. If I ignore the phantomness +condition, this is the same as this + + align:start position:0% +condition, this is the same as this + + + align:start position:0% +condition, this is the same as this +multiplied by this, + + align:start position:0% +multiplied by this, + + + align:start position:0% +multiplied by this, +which is a term that appears in the + + align:start position:0% +which is a term that appears in the + + + align:start position:0% +which is a term that appears in the +denominator and cancels out. + + align:start position:0% +denominator and cancels out. + + + align:start position:0% +denominator and cancels out. +But you're assuming that you have the + + align:start position:0% +But you're assuming that you have the + + + align:start position:0% +But you're assuming that you have the +factor condition. + + align:start position:0% +factor condition. + + + align:start position:0% +factor condition. +So this is completely normal. Doesn't + + align:start position:0% +So this is completely normal. Doesn't + + + align:start position:0% +So this is completely normal. Doesn't +matter. + + align:start position:0% + + + + align:start position:0% + +I'm not sure I understand your question. + + align:start position:0% +I'm not sure I understand your question. + + + align:start position:0% +I'm not sure I understand your question. +You say that even without the phantom + + align:start position:0% +You say that even without the phantom + + + align:start position:0% +You say that even without the phantom +condition, this graph exists. The + + align:start position:0% +condition, this graph exists. The + + + align:start position:0% +condition, this graph exists. The +phantom condition, yes, this graph is + + align:start position:0% +phantom condition, yes, this graph is + + + align:start position:0% +phantom condition, yes, this graph is +perfectly normal. + + align:start position:0% +perfectly normal. + + + align:start position:0% +perfectly normal. +Even without the random phantom + + align:start position:0% +Even without the random phantom + + + align:start position:0% +Even without the random phantom +condition, this is an acceptable graph. + + align:start position:0% + + + + align:start position:0% + +Yeah. Right. So + + align:start position:0% + + + + align:start position:0% + +okay. + + align:start position:0% +okay. + + + align:start position:0% +okay. +Um yeah. So what does what does + + align:start position:0% +Um yeah. So what does what does + + + align:start position:0% +Um yeah. So what does what does +phantomness + + align:start position:0% +phantomness + + + align:start position:0% +phantomness +mean? Like why why then we can simplify + + align:start position:0% +mean? Like why why then we can simplify + + + align:start position:0% +mean? Like why why then we can simplify +to only uh consider pass? Okay. Because + + align:start position:0% +to only uh consider pass? Okay. Because + + + align:start position:0% +to only uh consider pass? Okay. Because +uh + + align:start position:0% + + + + align:start position:0% + +let's say I were to take this as a check + + align:start position:0% +let's say I were to take this as a check + + + align:start position:0% +let's say I were to take this as a check +and multiply it by the denominator. + + align:start position:0% +and multiply it by the denominator. + + + align:start position:0% +and multiply it by the denominator. +The question is would I generate the + + align:start position:0% +The question is would I generate the + + + align:start position:0% +The question is would I generate the +series that is in the numerator. Okay. + + align:start position:0% +series that is in the numerator. Okay. + + + align:start position:0% +series that is in the numerator. Okay. +So if I take this object that I have + + align:start position:0% +So if I take this object that I have + + + align:start position:0% +So if I take this object that I have +said is the answer, I have to multiply + + align:start position:0% +said is the answer, I have to multiply + + + align:start position:0% +said is the answer, I have to multiply +it by this object + + align:start position:0% + + + + align:start position:0% + +and make sure that it introduces + + align:start position:0% +and make sure that it introduces + + + align:start position:0% +and make sure that it introduces +correctly the numerator. The question is + + align:start position:0% +correctly the numerator. The question is + + + align:start position:0% +correctly the numerator. The question is +when does it I mean certainly when I + + align:start position:0% +when does it I mean certainly when I + + + align:start position:0% +when does it I mean certainly when I +multiply this by this I will get the + + align:start position:0% +multiply this by this I will get the + + + align:start position:0% +multiply this by this I will get the +possibility of having a graph such as + + align:start position:0% +possibility of having a graph such as + + + align:start position:0% +possibility of having a graph such as +this and from here I can have a loop + + align:start position:0% +this and from here I can have a loop + + + align:start position:0% +this and from here I can have a loop +such as this and the two of them would + + align:start position:0% +such as this and the two of them would + + + align:start position:0% +such as this and the two of them would +share a bond such as that. + + align:start position:0% +share a bond such as that. + + + align:start position:0% +share a bond such as that. +So in the realizing model that is not + + align:start position:0% +So in the realizing model that is not + + + align:start position:0% +So in the realizing model that is not +allowed. So that's the phantomness + + align:start position:0% +allowed. So that's the phantomness + + + align:start position:0% +allowed. So that's the phantomness +condition that allows me to factor these + + align:start position:0% +condition that allows me to factor these + + + align:start position:0% +condition that allows me to factor these +things. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +All right. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% +So + + + align:start position:0% +So +we see that + + align:start position:0% +we see that + + + align:start position:0% +we see that +if I have this quantity that I have + + align:start position:0% +if I have this quantity that I have + + + align:start position:0% +if I have this quantity that I have +written in red + + align:start position:0% +written in red + + + align:start position:0% +written in red +then I can calculate both correlation + + align:start position:0% +then I can calculate both correlation + + + align:start position:0% +then I can calculate both correlation +functions + + align:start position:0% +functions + + + align:start position:0% +functions +as well as the free energy log of the + + align:start position:0% +as well as the free energy log of the + + + align:start position:0% +as well as the free energy log of the +partition function within this + + align:start position:0% +partition function within this + + + align:start position:0% +partition function within this +phantomness uh assumption. + + align:start position:0% +phantomness uh assumption. + + + align:start position:0% +phantomness uh assumption. +So the question is can I calculate that + + align:start position:0% +So the question is can I calculate that + + + align:start position:0% +So the question is can I calculate that +and the answer is that calculating + + align:start position:0% +and the answer is that calculating + + + align:start position:0% +and the answer is that calculating +number of random walks is one of the + + align:start position:0% +number of random walks is one of the + + + align:start position:0% +number of random walks is one of the +most basic things that one does in + + align:start position:0% +most basic things that one does in + + + align:start position:0% +most basic things that one does in +statistical physics and easily + + align:start position:0% +statistical physics and easily + + + align:start position:0% +statistical physics and easily +accomplished + + align:start position:0% +accomplished + + + align:start position:0% +accomplished +uh as follows. + + align:start position:0% +uh as follows. + + + align:start position:0% +uh as follows. +Basically I say that okay let's say that + + align:start position:0% +Basically I say that okay let's say that + + + align:start position:0% +Basically I say that okay let's say that +I start from zero + + align:start position:0% + + + + align:start position:0% + +actually does yeah let's do it zero and + + align:start position:0% +actually does yeah let's do it zero and + + + align:start position:0% +actually does yeah let's do it zero and +r + + align:start position:0% +r + + + align:start position:0% +r +and let's say that I have looked at all + + align:start position:0% +and let's say that I have looked at all + + + align:start position:0% +and let's say that I have looked at all +possible paths + + align:start position:0% + + + + align:start position:0% + +that have ls + + align:start position:0% +that have ls + + + align:start position:0% +that have ls +and end up over here. + + align:start position:0% +and end up over here. + + + align:start position:0% +and end up over here. +So this is step one, step two, step + + align:start position:0% +So this is step one, step two, step + + + align:start position:0% +So this is step one, step two, step +number three. And the last one, step L, + + align:start position:0% +number three. And the last one, step L, + + + align:start position:0% +number three. And the last one, step L, +I have purposely drawn as a dotted line. + + align:start position:0% +I have purposely drawn as a dotted line. + + + align:start position:0% +I have purposely drawn as a dotted line. +Maybe I will pull this point further + + align:start position:0% +Maybe I will pull this point further + + + align:start position:0% +Maybe I will pull this point further +down to emphasize + + align:start position:0% +down to emphasize + + + align:start position:0% +down to emphasize +that this is the last one. This is L + + align:start position:0% +that this is the last one. This is L + + + align:start position:0% +that this is the last one. This is L +minus one is the previous one. + + align:start position:0% +minus one is the previous one. + + + align:start position:0% +minus one is the previous one. +So I can certainly state that the number + + align:start position:0% +So I can certainly state that the number + + + align:start position:0% +So I can certainly state that the number +of walks + + align:start position:0% + + + + align:start position:0% + +from zero + + align:start position:0% +from zero + + + align:start position:0% +from zero +to R in L steps. + + align:start position:0% + + + + align:start position:0% + +Well, any walk that got to R in L steps + + align:start position:0% +Well, any walk that got to R in L steps + + + align:start position:0% +Well, any walk that got to R in L steps +at the L minus one step had to be + + align:start position:0% +at the L minus one step had to be + + + align:start position:0% +at the L minus one step had to be +somewhere. Okay. So what I do is I do a + + align:start position:0% +somewhere. Okay. So what I do is I do a + + + align:start position:0% +somewhere. Okay. So what I do is I do a +number of walks + + align:start position:0% + + + + align:start position:0% + +from + + align:start position:0% +from + + + align:start position:0% +from +0 to R prime. + + align:start position:0% +0 to R prime. + + + align:start position:0% +0 to R prime. +I'll call this point R prime + + align:start position:0% +I'll call this point R prime + + + align:start position:0% +I'll call this point R prime +in L minus one steps. + + align:start position:0% + + + + align:start position:0% + +and then times number of ways or number + + align:start position:0% +and then times number of ways or number + + + align:start position:0% +and then times number of ways or number +of walks + + align:start position:0% +of walks + + + align:start position:0% +of walks +from + + align:start position:0% +from + + + align:start position:0% +from +R prime to R in one step. + + align:start position:0% + + + + align:start position:0% + +So before I reach my destination in the + + align:start position:0% +So before I reach my destination in the + + + align:start position:0% +So before I reach my destination in the +previous step I had to have been + + align:start position:0% +previous step I had to have been + + + align:start position:0% +previous step I had to have been +somewhere + + align:start position:0% +somewhere + + + align:start position:0% +somewhere +I sum over all possible B places where + + align:start position:0% +I sum over all possible B places where + + + align:start position:0% +I sum over all possible B places where +that somewhere has to be + + align:start position:0% +that somewhere has to be + + + align:start position:0% +that somewhere has to be +and then I have to make sure that I can + + align:start position:0% +and then I have to make sure that I can + + + align:start position:0% +and then I have to make sure that I can +reach from that somewhere in one step to + + align:start position:0% +reach from that somewhere in one step to + + + align:start position:0% +reach from that somewhere in one step to +my destination. That's all that sums. + + align:start position:0% +my destination. That's all that sums. + + + align:start position:0% +my destination. That's all that sums. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Now I can convert that to mathematics. + + align:start position:0% +Now I can convert that to mathematics. + + + align:start position:0% +Now I can convert that to mathematics. +This quantity is start from zero, take L + + align:start position:0% +This quantity is start from zero, take L + + + align:start position:0% +This quantity is start from zero, take L +steps, arrive at R. By definition, + + align:start position:0% +steps, arrive at R. By definition, + + + align:start position:0% +steps, arrive at R. By definition, +that's the number. + + align:start position:0% +that's the number. + + + align:start position:0% +that's the number. +And what it says is that this should be + + align:start position:0% +And what it says is that this should be + + + align:start position:0% +And what it says is that this should be +a sum over R prime. + + align:start position:0% +a sum over R prime. + + + align:start position:0% +a sum over R prime. +Start from zero, take L minus one steps, + + align:start position:0% +Start from zero, take L minus one steps, + + + align:start position:0% +Start from zero, take L minus one steps, +arrive at R prime. + + align:start position:0% +arrive at R prime. + + + align:start position:0% +arrive at R prime. +Start from R prime. Take one step. + + align:start position:0% +Start from R prime. Take one step. + + + align:start position:0% +Start from R prime. Take one step. +Arrive at your destination R. Sum over R + + align:start position:0% +Arrive at your destination R. Sum over R + + + align:start position:0% +Arrive at your destination R. Sum over R +prime. + + align:start position:0% +prime. + + + align:start position:0% +prime. +Okay. + + align:start position:0% + + + + align:start position:0% + +Now these are N byN matrices that are + + align:start position:0% +Now these are N byN matrices that are + + + align:start position:0% +Now these are N byN matrices that are +labeled by L. Right? + + align:start position:0% +labeled by L. Right? + + + align:start position:0% +labeled by L. Right? +So these being N byN matrices. + + align:start position:0% +So these being N byN matrices. + + + align:start position:0% +So these being N byN matrices. +This summation over R prime is clearly a + + align:start position:0% +This summation over R prime is clearly a + + + align:start position:0% +This summation over R prime is clearly a +matrix multiplication. + + align:start position:0% +matrix multiplication. + + + align:start position:0% +matrix multiplication. +Right? So what that says is that summing + + align:start position:0% +Right? So what that says is that summing + + + align:start position:0% +Right? So what that says is that summing +over R prime tells you that that is W 1 + + align:start position:0% +over R prime tells you that that is W 1 + + + align:start position:0% +over R prime tells you that that is W 1 +W of L minus one Z + + align:start position:0% +W of L minus one Z + + + align:start position:0% +W of L minus one Z +and that is true for any pair of + + align:start position:0% +and that is true for any pair of + + + align:start position:0% +and that is true for any pair of +elements starting and final point. So + + align:start position:0% +elements starting and final point. So + + + align:start position:0% +elements starting and final point. So +basically quite generically we see that + + align:start position:0% +basically quite generically we see that + + + align:start position:0% +basically quite generically we see that +W the matrix that corresponds to the + + align:start position:0% +W the matrix that corresponds to the + + + align:start position:0% +W the matrix that corresponds to the +count for L steps is obtained from the + + align:start position:0% +count for L steps is obtained from the + + + align:start position:0% +count for L steps is obtained from the +matrix that corresponds to the count for + + align:start position:0% +matrix that corresponds to the count for + + + align:start position:0% +matrix that corresponds to the count for +one step multiplying that of L minus one + + align:start position:0% +one step multiplying that of L minus one + + + align:start position:0% +one step multiplying that of L minus one +steps + + align:start position:0% +steps + + + align:start position:0% +steps +and clearly I can keep going WLUS1 + + align:start position:0% +and clearly I can keep going WLUS1 + + + align:start position:0% +and clearly I can keep going WLUS1 +I can write as W1 W of LUS2 two + + align:start position:0% +I can write as W1 W of LUS2 two + + + align:start position:0% +I can write as W1 W of LUS2 two +and so forth. + + align:start position:0% +and so forth. + + + align:start position:0% +and so forth. +And ultimately the answer is none other + + align:start position:0% +And ultimately the answer is none other + + + align:start position:0% +And ultimately the answer is none other +than the entity that corresponds to one + + align:start position:0% +than the entity that corresponds to one + + + align:start position:0% +than the entity that corresponds to one +step raised to the L power. + + align:start position:0% +step raised to the L power. + + + align:start position:0% +step raised to the L power. +And just to make things easier on my + + align:start position:0% +And just to make things easier on my + + + align:start position:0% +And just to make things easier on my +writing, I will indicate this as T + + align:start position:0% +writing, I will indicate this as T + + + align:start position:0% +writing, I will indicate this as T +where T stands for this matrix + + align:start position:0% +where T stands for this matrix + + + align:start position:0% +where T stands for this matrix +for one set. Okay. + + align:start position:0% + + + + align:start position:0% + +This condition + + align:start position:0% +This condition + + + align:start position:0% +This condition +over here that I said in words that + + align:start position:0% +over here that I said in words that + + + align:start position:0% +over here that I said in words that +allows me to write this in D this nice + + align:start position:0% +allows me to write this in D this nice + + + align:start position:0% +allows me to write this in D this nice +matrix form is uh called the marovian + + align:start position:0% +matrix form is uh called the marovian + + + align:start position:0% +matrix form is uh called the marovian +condition. + + align:start position:0% + + + + align:start position:0% + +The kind of walks that I have been + + align:start position:0% +The kind of walks that I have been + + + align:start position:0% +The kind of walks that I have been +telling you + + align:start position:0% +telling you + + + align:start position:0% +telling you +are marovian in the sense that they only + + align:start position:0% +are marovian in the sense that they only + + + align:start position:0% +are marovian in the sense that they only +depend on where you came from at the + + align:start position:0% +depend on where you came from at the + + + align:start position:0% +depend on where you came from at the +last step. They don't have memory of + + align:start position:0% +last step. They don't have memory of + + + align:start position:0% +last step. They don't have memory of +where you had been before. And that's + + align:start position:0% +where you had been before. And that's + + + align:start position:0% +where you had been before. And that's +what enables us to do this. And that's + + align:start position:0% +what enables us to do this. And that's + + + align:start position:0% +what enables us to do this. And that's +why I had to do the phantom condition + + align:start position:0% +why I had to do the phantom condition + + + align:start position:0% +why I had to do the phantom condition +because if I really wanted to say that + + align:start position:0% +because if I really wanted to say that + + + align:start position:0% +because if I really wanted to say that +something like this has to be excluded + + align:start position:0% +something like this has to be excluded + + + align:start position:0% +something like this has to be excluded +then the walk must keep memory of every + + align:start position:0% +then the walk must keep memory of every + + + align:start position:0% +then the walk must keep memory of every +place that it had been before right and + + align:start position:0% +place that it had been before right and + + + align:start position:0% +place that it had been before right and +then it would be non-M marovian and I + + align:start position:0% +then it would be non-M marovian and I + + + align:start position:0% +then it would be non-M marovian and I +wouldn't have been able to do this nice + + align:start position:0% +wouldn't have been able to do this nice + + + align:start position:0% +wouldn't have been able to do this nice +calculation that's why I had to do this + + align:start position:0% +calculation that's why I had to do this + + + align:start position:0% +calculation that's why I had to do this +phantomness assumption so that I forgot + + align:start position:0% +phantomness assumption so that I forgot + + + align:start position:0% +phantomness assumption so that I forgot +the memory of where my walk was + + align:start position:0% +the memory of where my walk was + + + align:start position:0% +the memory of where my walk was +previously. + + align:start position:0% +previously. + + + align:start position:0% +previously. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Now, + + align:start position:0% +Now, + + + align:start position:0% +Now, +yeah. Question. Nope. + + align:start position:0% +yeah. Question. Nope. + + + align:start position:0% +yeah. Question. Nope. +So, + + align:start position:0% +So, + + + align:start position:0% +So, +this matrix uh + + align:start position:0% + + + + align:start position:0% + +where you can go in one step is really + + align:start position:0% +where you can go in one step is really + + + align:start position:0% +where you can go in one step is really +the matrix of who is connected to whom, + + align:start position:0% +the matrix of who is connected to whom, + + + align:start position:0% +the matrix of who is connected to whom, +right? So this is this tells you the + + align:start position:0% +right? So this is this tells you the + + + align:start position:0% +right? So this is this tells you the +connectivity, + + align:start position:0% + + + + align:start position:0% + +right? + + align:start position:0% +right? + + + align:start position:0% +right? +So for example, + + align:start position:0% +So for example, + + + align:start position:0% +So for example, +if I'm dealing with a 2D square latice, + + align:start position:0% + + + + align:start position:0% + +the sides on my latice are labeled by X + + align:start position:0% +the sides on my latice are labeled by X + + + align:start position:0% +the sides on my latice are labeled by X +and Y. + + align:start position:0% +and Y. + + + align:start position:0% +and Y. +And I can ask + + align:start position:0% +And I can ask + + + align:start position:0% +And I can ask +where can I go in one step + + align:start position:0% +where can I go in one step + + + align:start position:0% +where can I go in one step +if I start from X and Y. + + align:start position:0% +if I start from X and Y. + + + align:start position:0% +if I start from X and Y. +And the answer is that either X stays + + align:start position:0% +And the answer is that either X stays + + + align:start position:0% +And the answer is that either X stays +the same and Y shifts by one + + align:start position:0% + + + + align:start position:0% + +or Y stays the same + + align:start position:0% +or Y stays the same + + + align:start position:0% +or Y stays the same +and X shifts by one. + + align:start position:0% + + + + align:start position:0% + +These are the four nonzero elements + + align:start position:0% +These are the four nonzero elements + + + align:start position:0% +These are the four nonzero elements +of the matrix that allows you to go on + + align:start position:0% +of the matrix that allows you to go on + + + align:start position:0% +of the matrix that allows you to go on +the square latice either up, down, right + + align:start position:0% +the square latice either up, down, right + + + align:start position:0% +the square latice either up, down, right +or left and the corresponding things + + align:start position:0% +or left and the corresponding things + + + align:start position:0% +or left and the corresponding things +that you would have for the cube or + + align:start position:0% +that you would have for the cube or + + + align:start position:0% +that you would have for the cube or +whatever latice. + + align:start position:0% +whatever latice. + + + align:start position:0% +whatever latice. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Now you look at this and you can see + + align:start position:0% +Now you look at this and you can see + + + align:start position:0% +Now you look at this and you can see +that what I have imposed clearly is such + + align:start position:0% +that what I have imposed clearly is such + + + align:start position:0% +that what I have imposed clearly is such +that + + align:start position:0% +that + + + align:start position:0% +that +for a latis where every site looks like + + align:start position:0% +for a latis where every site looks like + + + align:start position:0% +for a latis where every site looks like +every equivalent site this is really a + + align:start position:0% +every equivalent site this is really a + + + align:start position:0% +every equivalent site this is really a +function only of the separation between + + align:start position:0% +function only of the separation between + + + align:start position:0% +function only of the separation between +the two points. + + align:start position:0% +the two points. + + + align:start position:0% +the two points. +It's an n² by it's an n byn matrix. It + + align:start position:0% +It's an n² by it's an n byn matrix. It + + + align:start position:0% +It's an n² by it's an n byn matrix. It +has n squ elements, but the elements + + align:start position:0% +has n squ elements, but the elements + + + align:start position:0% +has n squ elements, but the elements +really are essentially one column that + + align:start position:0% +really are essentially one column that + + + align:start position:0% +really are essentially one column that +gets shifted as you go further and + + align:start position:0% +gets shifted as you go further and + + + align:start position:0% +gets shifted as you go further and +further down in a very specific way. + + align:start position:0% + + + + align:start position:0% + +And + + align:start position:0% +And + + + align:start position:0% +And +whenever you have a matrix such as this, + + align:start position:0% +whenever you have a matrix such as this, + + + align:start position:0% +whenever you have a matrix such as this, +translational symmetry implies that you + + align:start position:0% +translational symmetry implies that you + + + align:start position:0% +translational symmetry implies that you +can diagonalize it by four uh + + align:start position:0% +can diagonalize it by four uh + + + align:start position:0% +can diagonalize it by four uh +transformation. + + align:start position:0% + + + + align:start position:0% + +And what do I mean by that? That is I + + align:start position:0% +And what do I mean by that? That is I + + + align:start position:0% +And what do I mean by that? That is I +can uh define a vector Q + + align:start position:0% +can uh define a vector Q + + + align:start position:0% +can uh define a vector Q +such that its various components + + align:start position:0% +such that its various components + + + align:start position:0% +such that its various components +are things like E to the I Q dot R in + + align:start position:0% +are things like E to the I Q dot R in + + + align:start position:0% +are things like E to the I Q dot R in +whatever dimension. Let's normalize it + + align:start position:0% +whatever dimension. Let's normalize it + + + align:start position:0% +whatever dimension. Let's normalize it +by square root of N. + + align:start position:0% +by square root of N. + + + align:start position:0% +by square root of N. +And I should be sure that that is an + + align:start position:0% +And I should be sure that that is an + + + align:start position:0% +And I should be sure that that is an +igen uh vector. So basically my + + align:start position:0% +igen uh vector. So basically my + + + align:start position:0% +igen uh vector. So basically my +statement is that if I take the matrix T + + align:start position:0% +statement is that if I take the matrix T + + + align:start position:0% +statement is that if I take the matrix T +act on Q + + align:start position:0% + + + + align:start position:0% + +then I should get uh some value + + align:start position:0% +then I should get uh some value + + + align:start position:0% +then I should get uh some value +in the vector back + + align:start position:0% +in the vector back + + + align:start position:0% +in the vector back +and let's take check that for the case + + align:start position:0% +and let's take check that for the case + + + align:start position:0% +and let's take check that for the case +of the 2D system. So for the 2D system + + align:start position:0% +of the 2D system. So for the 2D system + + + align:start position:0% +of the 2D system. So for the 2D system +if I say that x + + align:start position:0% +if I say that x + + + align:start position:0% +if I say that x +uh + + align:start position:0% +uh + + + align:start position:0% +uh +y t + + align:start position:0% +y t + + + align:start position:0% +y t +qx q y + + align:start position:0% +qx q y + + + align:start position:0% +qx q y +what is it? Well, that is x y t x prime + + align:start position:0% +what is it? Well, that is x y t x prime + + + align:start position:0% +what is it? Well, that is x y t x prime +yprime the entity that I have calculated + + align:start position:0% +yprime the entity that I have calculated + + + align:start position:0% +yprime the entity that I have calculated +here x prime y prime qx qy and of course + + align:start position:0% +here x prime y prime qx qy and of course + + + align:start position:0% +here x prime y prime qx qy and of course +I have a sum over x prime and y prime + + align:start position:0% +I have a sum over x prime and y prime + + + align:start position:0% +I have a sum over x prime and y prime +that's the matrix product + + align:start position:0% +that's the matrix product + + + align:start position:0% +that's the matrix product +and so again remember + + align:start position:0% +and so again remember + + + align:start position:0% +and so again remember +uh this entity is simply e to the i qx x + + align:start position:0% +uh this entity is simply e to the i qx x + + + align:start position:0% +uh this entity is simply e to the i qx x +prime + QY Y prime uh divided by square + + align:start position:0% +prime + QY Y prime uh divided by square + + + align:start position:0% +prime + QY Y prime uh divided by square +roo<unk> of N. + + align:start position:0% +roo<unk> of N. + + + align:start position:0% +roo<unk> of N. +And because this is a set of delta + + align:start position:0% +And because this is a set of delta + + + align:start position:0% +And because this is a set of delta +functions, + + align:start position:0% +functions, + + + align:start position:0% +functions, +what does it do? It basically sets X + + align:start position:0% +what does it do? It basically sets X + + + align:start position:0% +what does it do? It basically sets X +prime either to X + one or X -1, Y prime + + align:start position:0% +prime either to X + one or X -1, Y prime + + + align:start position:0% +prime either to X + one or X -1, Y prime +either to Y or Y -1, Y - one. You can + + align:start position:0% +either to Y or Y -1, Y - one. You can + + + align:start position:0% +either to Y or Y -1, Y - one. You can +see that you always get back your e to + + align:start position:0% +see that you always get back your e to + + + align:start position:0% +see that you always get back your e to +the i qx x + i q y + + align:start position:0% +the i qx x + i q y + + + align:start position:0% +the i qx x + i q y +with a factor of root n. So essentially + + align:start position:0% +with a factor of root n. So essentially + + + align:start position:0% +with a factor of root n. So essentially +that by the delta functions just changes + + align:start position:0% +that by the delta functions just changes + + + align:start position:0% +that by the delta functions just changes +the x primes to x at the cost of the + + align:start position:0% +the x primes to x at the cost of the + + + align:start position:0% +the x primes to x at the cost of the +different shifts that you have to do + + align:start position:0% +different shifts that you have to do + + + align:start position:0% +different shifts that you have to do +over there. Which means that you will + + align:start position:0% +over there. Which means that you will + + + align:start position:0% +over there. Which means that you will +get a factor of e to the i qx eus iqx + + align:start position:0% +get a factor of e to the i qx eus iqx + + + align:start position:0% +get a factor of e to the i qx eus iqx +with qy not changing or e to the i q y + + align:start position:0% +with qy not changing or e to the i q y + + + align:start position:0% +with qy not changing or e to the i q y +and e to the minus i qy with the x + + align:start position:0% +and e to the minus i qy with the x + + + align:start position:0% +and e to the minus i qy with the x +component not changing. So this is the + + align:start position:0% +component not changing. So this is the + + + align:start position:0% +component not changing. So this is the +standard thing that you have seen is + + align:start position:0% +standard thing that you have seen is + + + align:start position:0% +standard thing that you have seen is +none other than 2 cosine of qx plus + + align:start position:0% +none other than 2 cosine of qx plus + + + align:start position:0% +none other than 2 cosine of qx plus +cosine of qy. + + align:start position:0% +cosine of qy. + + + align:start position:0% +cosine of qy. +And so we can see that quite generally + + align:start position:0% +And so we can see that quite generally + + + align:start position:0% +And so we can see that quite generally +in the D-dimensional hyper cube + + align:start position:0% + + + + align:start position:0% + +my T of Q is going to be the sum over + + align:start position:0% +my T of Q is going to be the sum over + + + align:start position:0% +my T of Q is going to be the sum over +all D components of these factors of + + align:start position:0% +all D components of these factors of + + + align:start position:0% +all D components of these factors of +cosine of Q alpha and that's about it. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +So why did I bother + + align:start position:0% +So why did I bother + + + align:start position:0% +So why did I bother +to do this diagonalization? + + align:start position:0% +to do this diagonalization? + + + align:start position:0% +to do this diagonalization? +The answer is that that now allows me to + + align:start position:0% +The answer is that that now allows me to + + + align:start position:0% +The answer is that that now allows me to +calculate everything that I want. So for + + align:start position:0% +calculate everything that I want. So for + + + align:start position:0% +calculate everything that I want. So for +example + + align:start position:0% +example + + + align:start position:0% +example +uh I know that uh + + align:start position:0% +uh I know that uh + + + align:start position:0% +uh I know that uh +this quantity that I'm interested in + + align:start position:0% +this quantity that I'm interested in + + + align:start position:0% +this quantity that I'm interested in +zigma 0 sigma r + + align:start position:0% +zigma 0 sigma r + + + align:start position:0% +zigma 0 sigma r +is going to be a sum over l + + align:start position:0% + + + + align:start position:0% + +t to the l + + align:start position:0% +t to the l + + + align:start position:0% +t to the l +then zero + + align:start position:0% +then zero + + + align:start position:0% +then zero +wl is t to the l * Right. + + align:start position:0% + + + + align:start position:0% + +Now this small T I can take inside here + + align:start position:0% +Now this small T I can take inside here + + + align:start position:0% +Now this small T I can take inside here +and do it like this. + + align:start position:0% +and do it like this. + + + align:start position:0% +and do it like this. +And if I want I can write this as the + + align:start position:0% +And if I want I can write this as the + + + align:start position:0% +And if I want I can write this as the +zero arch component of a sum over L t + + align:start position:0% +zero arch component of a sum over L t + + + align:start position:0% +zero arch component of a sum over L t +raised to the power of L. + + align:start position:0% + + + + align:start position:0% + +So it's a new matrix + + align:start position:0% +So it's a new matrix + + + align:start position:0% +So it's a new matrix +which is essentially sum over L small T + + align:start position:0% +which is essentially sum over L small T + + + align:start position:0% +which is essentially sum over L small T +* this connectivity matrix to the L + + align:start position:0% +* this connectivity matrix to the L + + + align:start position:0% +* this connectivity matrix to the L +power. + + align:start position:0% +power. + + + align:start position:0% +power. +This is a geometric series. We can + + align:start position:0% +This is a geometric series. We can + + + align:start position:0% +This is a geometric series. We can +immediately do the geometric series. The + + align:start position:0% +immediately do the geometric series. The + + + align:start position:0% +immediately do the geometric series. The +answer is 0 1 / 1 - tt + + align:start position:0% +answer is 0 1 / 1 - tt + + + align:start position:0% +answer is 0 1 / 1 - tt +going all the way to R. + + align:start position:0% +going all the way to R. + + + align:start position:0% +going all the way to R. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +And + + align:start position:0% +And + + + align:start position:0% +And +the reason I did this diagonalization + + align:start position:0% +the reason I did this diagonalization + + + align:start position:0% +the reason I did this diagonalization +is so that I can calculate this matrix + + align:start position:0% +is so that I can calculate this matrix + + + align:start position:0% +is so that I can calculate this matrix +element + + align:start position:0% +element + + + align:start position:0% +element +because I don't really want to invert a + + align:start position:0% +because I don't really want to invert a + + + align:start position:0% +because I don't really want to invert a +whole matrix + + align:start position:0% +whole matrix + + + align:start position:0% +whole matrix +but I can certainly invert the matrix + + align:start position:0% +but I can certainly invert the matrix + + + align:start position:0% +but I can certainly invert the matrix +when it is in the diagonal basis because + + align:start position:0% +when it is in the diagonal basis because + + + align:start position:0% +when it is in the diagonal basis because +all I have to do is to invert pure + + align:start position:0% +all I have to do is to invert pure + + + align:start position:0% +all I have to do is to invert pure +numbers. + + align:start position:0% +numbers. + + + align:start position:0% +numbers. +So what is done is to go to the FIA + + align:start position:0% +So what is done is to go to the FIA + + + align:start position:0% +So what is done is to go to the FIA +basis + + align:start position:0% +basis + + + align:start position:0% +basis +and rotate to the f FIA basis. Calculate + + align:start position:0% +and rotate to the f FIA basis. Calculate + + + align:start position:0% +and rotate to the f FIA basis. Calculate +this + + align:start position:0% + + + + align:start position:0% + +it is diagonal in this basis. I have QR + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and so what is that? These are these + + align:start position:0% +and so what is that? These are these + + + align:start position:0% +and so what is that? These are these +exponentials here evaluated at the + + align:start position:0% +exponentials here evaluated at the + + + align:start position:0% +exponentials here evaluated at the +origin. So it's just 1 / roo<unk> n. + + align:start position:0% +origin. So it's just 1 / roo<unk> n. + + + align:start position:0% +origin. So it's just 1 / roo<unk> n. +This is 1 /<unk> n. + + align:start position:0% +This is 1 /<unk> n. + + + align:start position:0% +This is 1 /<unk> n. +This is e to the i q dot r / roo<unk> n. + + align:start position:0% +This is e to the i q dot r / roo<unk> n. + + + align:start position:0% +This is e to the i q dot r / roo<unk> n. +This is just the value that I have + + align:start position:0% +This is just the value that I have + + + align:start position:0% +This is just the value that I have +calculated over here. + + align:start position:0% +calculated over here. + + + align:start position:0% +calculated over here. +So this entity + + align:start position:0% +So this entity + + + align:start position:0% +So this entity +is none other than + + align:start position:0% +is none other than + + + align:start position:0% +is none other than +a sum over q + + align:start position:0% +a sum over q + + + align:start position:0% +a sum over q +e to the i q dot r / n two factors of + + align:start position:0% +e to the i q dot r / n two factors of + + + align:start position:0% +e to the i q dot r / n two factors of +square root of n + + align:start position:0% +square root of n + + + align:start position:0% +square root of n +1 / 1 - t well actually let's write it + + align:start position:0% +1 / 1 - t well actually let's write it + + + align:start position:0% +1 / 1 - t well actually let's write it +2t sum over alpha cosine of q alpha + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +And then of course I'm interested in big + + align:start position:0% +And then of course I'm interested in big + + + align:start position:0% +And then of course I'm interested in big +systems. + + align:start position:0% +systems. + + + align:start position:0% +systems. +I replace the sum over Q with an + + align:start position:0% +I replace the sum over Q with an + + + align:start position:0% +I replace the sum over Q with an +integral over Q + + align:start position:0% +integral over Q + + + align:start position:0% +integral over Q +2 pi to the D density of states. + + align:start position:0% +2 pi to the D density of states. + + + align:start position:0% +2 pi to the D density of states. +In going from there to there there is a + + align:start position:0% +In going from there to there there is a + + + align:start position:0% +In going from there to there there is a +factor of volume. The way that I have + + align:start position:0% +factor of volume. The way that I have + + + align:start position:0% +factor of volume. The way that I have +set the unit of length in my system, the + + align:start position:0% +set the unit of length in my system, the + + + align:start position:0% +set the unit of length in my system, the +volume is actually the number of + + align:start position:0% +volume is actually the number of + + + align:start position:0% +volume is actually the number of +particles that I have. So that factor of + + align:start position:0% +particles that I have. So that factor of + + + align:start position:0% +particles that I have. So that factor of +n disappears and all I need to do is + + align:start position:0% +n disappears and all I need to do is + + + align:start position:0% +n disappears and all I need to do is +evaluate this factor of 1 - 2t s alpha + + align:start position:0% +evaluate this factor of 1 - 2t s alpha + + + align:start position:0% +evaluate this factor of 1 - 2t s alpha +cosine of q + + align:start position:0% +cosine of q + + + align:start position:0% +cosine of q +integrated over q + + align:start position:0% +integrated over q + + + align:start position:0% +integrated over q +fully trans. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Yes. So I notic that you have a sum over + + align:start position:0% +Yes. So I notic that you have a sum over + + + align:start position:0% +Yes. So I notic that you have a sum over +Q but then you also have a sum over + + align:start position:0% +Q but then you also have a sum over + + + align:start position:0% +Q but then you also have a sum over +alpha of Q alpha. Is there a + + align:start position:0% +alpha of Q alpha. Is there a + + + align:start position:0% +alpha of Q alpha. Is there a +relationship between the Q and the Q + + align:start position:0% +relationship between the Q and the Q + + + align:start position:0% +relationship between the Q and the Q +alpha or not? Okay. So that goes back + + align:start position:0% +alpha or not? Okay. So that goes back + + + align:start position:0% +alpha or not? Okay. So that goes back +here. So when I had two dimensions I had + + align:start position:0% +here. So when I had two dimensions I had + + + align:start position:0% +here. So when I had two dimensions I had +qx and qy right and so I labeled rather + + align:start position:0% +qx and qy right and so I labeled rather + + + align:start position:0% +qx and qy right and so I labeled rather +than x and y with q1 and q2. So the + + align:start position:0% +than x and y with q1 and q2. So the + + + align:start position:0% +than x and y with q1 and q2. So the +index alpha is just the number of + + align:start position:0% +index alpha is just the number of + + + align:start position:0% +index alpha is just the number of +spatial dimension. If you like this is + + align:start position:0% +spatial dimension. If you like this is + + + align:start position:0% +spatial dimension. If you like this is +also dq1, dq2, + + align:start position:0% +also dq1, dq2, + + + align:start position:0% +also dq1, dq2, +dqd. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +All right. So, we are down here. + + align:start position:0% + + + + align:start position:0% + +Uh let's proceed. + + align:start position:0% +Uh let's proceed. + + + align:start position:0% +Uh let's proceed. +So what is going to happen? + + align:start position:0% + + + + align:start position:0% + +So suppose I'm picking two sides zero + + align:start position:0% +So suppose I'm picking two sides zero + + + align:start position:0% +So suppose I'm picking two sides zero +and r let's say both along the x + + align:start position:0% +and r let's say both along the x + + + align:start position:0% +and r let's say both along the x +direction + + align:start position:0% +direction + + + align:start position:0% +direction +some particular distance apart let's say + + align:start position:0% +some particular distance apart let's say + + + align:start position:0% +some particular distance apart let's say +7 8 apart. + + align:start position:0% +7 8 apart. + + + align:start position:0% +7 8 apart. +So in order to evaluate this I would + + align:start position:0% +So in order to evaluate this I would + + + align:start position:0% +So in order to evaluate this I would +have an integral if this is the x + + align:start position:0% +have an integral if this is the x + + + align:start position:0% +have an integral if this is the x +direction of something like e to the i + + align:start position:0% +direction of something like e to the i + + + align:start position:0% +direction of something like e to the i +qx * r. + + align:start position:0% + + + + align:start position:0% + +Now when I integrate over qx the + + align:start position:0% +Now when I integrate over qx the + + + align:start position:0% +Now when I integrate over qx the +integral of e to the i qx * r would go + + align:start position:0% +integral of e to the i qx * r would go + + + align:start position:0% +integral of e to the i qx * r would go +go to zero. + + align:start position:0% +go to zero. + + + align:start position:0% +go to zero. +The only way that it won't go to zero is + + align:start position:0% +The only way that it won't go to zero is + + + align:start position:0% +The only way that it won't go to zero is +from the expansion of what is in the + + align:start position:0% +from the expansion of what is in the + + + align:start position:0% +from the expansion of what is in the +denominator. + + align:start position:0% +denominator. + + + align:start position:0% +denominator. +I should bring on enough factors of e to + + align:start position:0% +I should bring on enough factors of e to + + + align:start position:0% +I should bring on enough factors of e to +the minus iqx which certainly exist in + + align:start position:0% +the minus iqx which certainly exist in + + + align:start position:0% +the minus iqx which certainly exist in +these cosine factors + + align:start position:0% +these cosine factors + + + align:start position:0% +these cosine factors +to get rid of that. So essentially the + + align:start position:0% +to get rid of that. So essentially the + + + align:start position:0% +to get rid of that. So essentially the +mathematical procedure that is over here + + align:start position:0% +mathematical procedure that is over here + + + align:start position:0% +mathematical procedure that is over here +is to bring in sufficient factors of e + + align:start position:0% +is to bring in sufficient factors of e + + + align:start position:0% +is to bring in sufficient factors of e +to the minus i q dot r to eliminate that + + align:start position:0% +to the minus i q dot r to eliminate that + + + align:start position:0% +to the minus i q dot r to eliminate that +and the number of ways that you're going + + align:start position:0% +and the number of ways that you're going + + + align:start position:0% +and the number of ways that you're going +to do that is precisely another way of + + align:start position:0% +to do that is precisely another way of + + + align:start position:0% +to do that is precisely another way of +capturing this entity + + align:start position:0% +capturing this entity + + + align:start position:0% +capturing this entity +which means that clearly + + align:start position:0% +which means that clearly + + + align:start position:0% +which means that clearly +if I'm + + align:start position:0% +if I'm + + + align:start position:0% +if I'm +uh looking at something like this and I + + align:start position:0% +uh looking at something like this and I + + + align:start position:0% +uh looking at something like this and I +mean the limit that t goes to be very + + align:start position:0% +mean the limit that t goes to be very + + + align:start position:0% +mean the limit that t goes to be very +very small so that the lowest order in t + + align:start position:0% +very small so that the lowest order in t + + + align:start position:0% +very small so that the lowest order in t +contributes the lowest order t would be + + align:start position:0% +contributes the lowest order t would be + + + align:start position:0% +contributes the lowest order t would be +the shortest path that correspond uh + + align:start position:0% +the shortest path that correspond uh + + + align:start position:0% +the shortest path that correspond uh +that joins these two points so it is + + align:start position:0% +that joins these two points so it is + + + align:start position:0% +that joins these two points so it is +like connecting these two points with a + + align:start position:0% +like connecting these two points with a + + + align:start position:0% +like connecting these two points with a +string that is very tight + + align:start position:0% +string that is very tight + + + align:start position:0% +string that is very tight +so that the what I'm saying is that the + + align:start position:0% +so that the what I'm saying is that the + + + align:start position:0% +so that the what I'm saying is that the +limit as t goes to zero of something + + align:start position:0% +limit as t goes to zero of something + + + align:start position:0% +limit as t goes to zero of something +like zigma 0 s zigma R is going to be + + align:start position:0% +like zigma 0 s zigma R is going to be + + + align:start position:0% +like zigma 0 s zigma R is going to be +proportional to actually is going to be + + align:start position:0% +proportional to actually is going to be + + + align:start position:0% +proportional to actually is going to be +identical to T to the uh minimum + + align:start position:0% +identical to T to the uh minimum + + + align:start position:0% +identical to T to the uh minimum +distance + + align:start position:0% +distance + + + align:start position:0% +distance +between zero and R. + + align:start position:0% +between zero and R. + + + align:start position:0% +between zero and R. +Actually I should say proportional is in + + align:start position:0% +Actually I should say proportional is in + + + align:start position:0% +Actually I should say proportional is in +fact more correct + + align:start position:0% +fact more correct + + + align:start position:0% +fact more correct +because there could be multiple shortest + + align:start position:0% +because there could be multiple shortest + + + align:start position:0% +because there could be multiple shortest +path that go between two points. + + align:start position:0% +path that go between two points. + + + align:start position:0% +path that go between two points. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Now + + align:start position:0% +Now + + + align:start position:0% +Now +this makes sense. There's kind of an + + align:start position:0% +this makes sense. There's kind of an + + + align:start position:0% +this makes sense. There's kind of an +exponential + + align:start position:0% +exponential + + + align:start position:0% +exponential +essentially I start with the high + + align:start position:0% +essentially I start with the high + + + align:start position:0% +essentially I start with the high +temperature limit where the two things + + align:start position:0% +temperature limit where the two things + + + align:start position:0% +temperature limit where the two things +don't know anything about each other. So + + align:start position:0% +don't know anything about each other. So + + + align:start position:0% +don't know anything about each other. So +sigma 0 s zigma r is going to be zero. + + align:start position:0% +sigma 0 s zigma r is going to be zero. + + + align:start position:0% +sigma 0 s zigma r is going to be zero. +So anything that is beyond zero has to + + align:start position:0% +So anything that is beyond zero has to + + + align:start position:0% +So anything that is beyond zero has to +come from some way in which the + + align:start position:0% +come from some way in which the + + + align:start position:0% +come from some way in which the +information about the state of this site + + align:start position:0% +information about the state of this site + + + align:start position:0% +information about the state of this site +was conveyed all the way over here and + + align:start position:0% +was conveyed all the way over here and + + + align:start position:0% +was conveyed all the way over here and +it is done through passing one bond at a + + align:start position:0% +it is done through passing one bond at a + + + align:start position:0% +it is done through passing one bond at a +time and in some sense the fidelity of + + align:start position:0% +time and in some sense the fidelity of + + + align:start position:0% +time and in some sense the fidelity of +each one of those transformations is + + align:start position:0% +each one of those transformations is + + + align:start position:0% +each one of those transformations is +proportional to t. + + align:start position:0% +proportional to t. + + + align:start position:0% +proportional to t. +Now, as t becomes larger, + + align:start position:0% +Now, as t becomes larger, + + + align:start position:0% +Now, as t becomes larger, +you are going to be willing to pay the + + align:start position:0% +you are going to be willing to pay the + + + align:start position:0% +you are going to be willing to pay the +costs of paths that go from zero to r in + + align:start position:0% +costs of paths that go from zero to r in + + + align:start position:0% +costs of paths that go from zero to r in +slightly more + + align:start position:0% +slightly more + + + align:start position:0% +slightly more +disordered way. So, your string that was + + align:start position:0% +disordered way. So, your string that was + + + align:start position:0% +disordered way. So, your string that was +tight becomes kind of loose and floppy. + + align:start position:0% +tight becomes kind of loose and floppy. + + + align:start position:0% +tight becomes kind of loose and floppy. +And why does that become the case? + + align:start position:0% +And why does that become the case? + + + align:start position:0% +And why does that become the case? +Because now although these paths are + + align:start position:0% +Because now although these paths are + + + align:start position:0% +Because now although these paths are +longer and carry more factors of this t + + align:start position:0% +longer and carry more factors of this t + + + align:start position:0% +longer and carry more factors of this t +that is small they're just so many of + + align:start position:0% +that is small they're just so many of + + + align:start position:0% +that is small they're just so many of +them that the entropy the number of + + align:start position:0% +them that the entropy the number of + + + align:start position:0% +them that the entropy the number of +these paths starts to dominate. + + align:start position:0% +these paths starts to dominate. + + + align:start position:0% +these paths starts to dominate. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So very roughly you can state the + + align:start position:0% +So very roughly you can state the + + + align:start position:0% +So very roughly you can state the +competition between them as follows that + + align:start position:0% +competition between them as follows that + + + align:start position:0% +competition between them as follows that +the contribution of a path of length L + + align:start position:0% +the contribution of a path of length L + + + align:start position:0% +the contribution of a path of length L +decays like T to the L but the number of + + align:start position:0% +decays like T to the L but the number of + + + align:start position:0% +decays like T to the L but the number of +paths roughly grows like 2D to the power + + align:start position:0% +paths roughly grows like 2D to the power + + + align:start position:0% +paths roughly grows like 2D to the power +of L. + + align:start position:0% +of L. + + + align:start position:0% +of L. +Since we have this phantomness + + align:start position:0% +Since we have this phantomness + + + align:start position:0% +Since we have this phantomness +character, if I'm sitting at a + + align:start position:0% +character, if I'm sitting at a + + + align:start position:0% +character, if I'm sitting at a +particular site, I can go up, down, + + align:start position:0% +particular site, I can go up, down, + + + align:start position:0% +particular site, I can go up, down, +right, left. So at each step, I have in + + align:start position:0% +right, left. So at each step, I have in + + + align:start position:0% +right, left. So at each step, I have in +two dimensions a choice of four. In + + align:start position:0% +two dimensions a choice of four. In + + + align:start position:0% +two dimensions a choice of four. In +three dimensions, a choice of six, in + + align:start position:0% +three dimensions, a choice of six, in + + + align:start position:0% +three dimensions, a choice of six, in +Dimensions, a choice of 2D. + + align:start position:0% +Dimensions, a choice of 2D. + + + align:start position:0% +Dimensions, a choice of 2D. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So you can see that this is + + align:start position:0% +So you can see that this is + + + align:start position:0% +So you can see that this is +exponentially small. This is + + align:start position:0% +exponentially small. This is + + + align:start position:0% +exponentially small. This is +exponentially large. So they kind of + + align:start position:0% +exponentially large. So they kind of + + + align:start position:0% +exponentially large. So they kind of +balance each other. And the balance is + + align:start position:0% +balance each other. And the balance is + + + align:start position:0% +balance each other. And the balance is +something like E to the minus L over + + align:start position:0% +something like E to the minus L over + + + align:start position:0% +something like E to the minus L over +some typical L that will contribute. + + align:start position:0% +some typical L that will contribute. + + + align:start position:0% +some typical L that will contribute. +And clearly the typical L is going to be + + align:start position:0% +And clearly the typical L is going to be + + + align:start position:0% +And clearly the typical L is going to be +finite as long as 2DT + + align:start position:0% +finite as long as 2DT + + + align:start position:0% +finite as long as 2DT +is less than one. So you can see that + + align:start position:0% +is less than one. So you can see that + + + align:start position:0% +is less than one. So you can see that +something strange has to happen at a + + align:start position:0% +something strange has to happen at a + + + align:start position:0% +something strange has to happen at a +value where TC is such that 2DTC is + + align:start position:0% +value where TC is such that 2DTC is + + + align:start position:0% +value where TC is such that 2DTC is +equal to 1. At that point, the cost of + + align:start position:0% +equal to 1. At that point, the cost of + + + align:start position:0% +equal to 1. At that point, the cost of +making your paths longer + + align:start position:0% +making your paths longer + + + align:start position:0% +making your paths longer +is more than made up by the increase in + + align:start position:0% +is more than made up by the increase in + + + align:start position:0% +is more than made up by the increase in +the number of paths that you can have. + + align:start position:0% +the number of paths that you can have. + + + align:start position:0% +the number of paths that you can have. +The entropies starts to win. + + align:start position:0% +The entropies starts to win. + + + align:start position:0% +The entropies starts to win. +And you can see that precisely that + + align:start position:0% +And you can see that precisely that + + + align:start position:0% +And you can see that precisely that +condition tells me whether or not this + + align:start position:0% +condition tells me whether or not this + + + align:start position:0% +condition tells me whether or not this +integral exists, + + align:start position:0% +integral exists, + + + align:start position:0% +integral exists, +right? Because + + align:start position:0% +right? Because + + + align:start position:0% +right? Because +one point of this integral where the + + align:start position:0% +one point of this integral where the + + + align:start position:0% +one point of this integral where the +integrant is largest + + align:start position:0% +integrant is largest + + + align:start position:0% +integrant is largest +is when Q goes to zero. And you can see + + align:start position:0% +is when Q goes to zero. And you can see + + + align:start position:0% +is when Q goes to zero. And you can see +that as Q goes to zero the value in the + + align:start position:0% +that as Q goes to zero the value in the + + + align:start position:0% +that as Q goes to zero the value in the +denominator is 1 minus 2T. + + align:start position:0% +denominator is 1 minus 2T. + + + align:start position:0% +denominator is 1 minus 2T. +So there is precisely a pole when this + + align:start position:0% +So there is precisely a pole when this + + + align:start position:0% +So there is precisely a pole when this +condition takes place. + + align:start position:0% +condition takes place. + + + align:start position:0% +condition takes place. +And if I'm interested in seeing what is + + align:start position:0% +And if I'm interested in seeing what is + + + align:start position:0% +And if I'm interested in seeing what is +happening + + align:start position:0% +happening + + + align:start position:0% +happening +when I'm in the vicinity of that + + align:start position:0% +when I'm in the vicinity of that + + + align:start position:0% +when I'm in the vicinity of that +transition right before these paths + + align:start position:0% +transition right before these paths + + + align:start position:0% +transition right before these paths +become very large what I can do is I can + + align:start position:0% +become very large what I can do is I can + + + align:start position:0% +become very large what I can do is I can +start exploring what is happening in the + + align:start position:0% +start exploring what is happening in the + + + align:start position:0% +start exploring what is happening in the +vicinity of that pole. + + align:start position:0% +vicinity of that pole. + + + align:start position:0% +vicinity of that pole. +So 1 - 2D sum over alpha cosine of Q + + align:start position:0% +So 1 - 2D sum over alpha cosine of Q + + + align:start position:0% +So 1 - 2D sum over alpha cosine of Q +alpha + + align:start position:0% +alpha + + + align:start position:0% +alpha +how does it behave each cosine I can + + align:start position:0% +how does it behave each cosine I can + + + align:start position:0% +how does it behave each cosine I can +start expanding around it q going to + + align:start position:0% +start expanding around it q going to + + + align:start position:0% +start expanding around it q going to +zero as 1 - q ^2 / 2 so you can see that + + align:start position:0% +zero as 1 - q ^2 / 2 so you can see that + + + align:start position:0% +zero as 1 - q ^2 / 2 so you can see that +this is going to be 1 - 2d + + align:start position:0% + + + + align:start position:0% + +and then I would have + t q ^2 because I + + align:start position:0% +and then I would have + t q ^2 because I + + + align:start position:0% +and then I would have + t q ^2 because I +will have q1 2 + q2 2 ^ 2 + QD. So this + + align:start position:0% +will have q1 2 + q2 2 ^ 2 + QD. So this + + + align:start position:0% +will have q1 2 + q2 2 ^ 2 + QD. So this +Q ^2 is the sum of all the Q's. And then + + align:start position:0% +Q ^2 is the sum of all the Q's. And then + + + align:start position:0% +Q ^2 is the sum of all the Q's. And then +I will have higher order terms order of + + align:start position:0% +I will have higher order terms order of + + + align:start position:0% +I will have higher order terms order of +Q to the 4th and so forth. + + align:start position:0% +Q to the 4th and so forth. + + + align:start position:0% +Q to the 4th and so forth. +Okay. + + align:start position:0% + + + + align:start position:0% + +So if I'm looking in the vicinity of T + + align:start position:0% +So if I'm looking in the vicinity of T + + + align:start position:0% +So if I'm looking in the vicinity of T +going to TC, + + align:start position:0% +going to TC, + + + align:start position:0% +going to TC, +this is roughly TC + + align:start position:0% +this is roughly TC + + + align:start position:0% +this is roughly TC +Q ^2. This is something that goes to + + align:start position:0% +Q ^2. This is something that goes to + + + align:start position:0% +Q ^2. This is something that goes to +zero. + + align:start position:0% +zero. + + + align:start position:0% +zero. +And once I factor out the TC, I can + + align:start position:0% +And once I factor out the TC, I can + + + align:start position:0% +And once I factor out the TC, I can +define a length squared in this fashion. + + align:start position:0% +define a length squared in this fashion. + + + align:start position:0% +define a length squared in this fashion. +Inverse length squared. Okay, you can + + align:start position:0% +Inverse length squared. Okay, you can + + + align:start position:0% +Inverse length squared. Okay, you can +see that this inverse + + align:start position:0% +see that this inverse + + + align:start position:0% +see that this inverse +length squar + + align:start position:0% +length squar + + + align:start position:0% +length squar +is going to be uh 1 / tc 1 - 2d which is + + align:start position:0% +is going to be uh 1 / tc 1 - 2d which is + + + align:start position:0% +is going to be uh 1 / tc 1 - 2d which is +1 / tc + + align:start position:0% +1 / tc + + + align:start position:0% +1 / tc +* t. + + align:start position:0% +* t. + + + align:start position:0% +* t. +So you can see that this is none other + + align:start position:0% +So you can see that this is none other + + + align:start position:0% +So you can see that this is none other +than tc minus t. + + align:start position:0% +than tc minus t. + + + align:start position:0% +than tc minus t. +Okay. + + align:start position:0% + + + + align:start position:0% + +And if I'm looking at the vicinity of + + align:start position:0% +And if I'm looking at the vicinity of + + + align:start position:0% +And if I'm looking at the vicinity of +that point, I find that the correlation + + align:start position:0% +that point, I find that the correlation + + + align:start position:0% +that point, I find that the correlation +between zigma 0 sigma r is approximately + + align:start position:0% +between zigma 0 sigma r is approximately + + + align:start position:0% +between zigma 0 sigma r is approximately +the integral ddq 2<unk>i to the d for a + + align:start position:0% +the integral ddq 2<unk>i to the d for a + + + align:start position:0% +the integral ddq 2<unk>i to the d for a +transform + + align:start position:0% +transform + + + align:start position:0% +transform +of the denominator that I said is + + align:start position:0% +of the denominator that I said is + + + align:start position:0% +of the denominator that I said is +approximately 1 / t cc * q ^2 + cus 2. + + align:start position:0% +approximately 1 / t cc * q ^2 + cus 2. + + + align:start position:0% +approximately 1 / t cc * q ^2 + cus 2. +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +we've seen this before, right? + + align:start position:0% +we've seen this before, right? + + + align:start position:0% +we've seen this before, right? +we evaluated this fia transform when we + + align:start position:0% +we evaluated this fia transform when we + + + align:start position:0% +we evaluated this fia transform when we +were doing uh Land of Ginsburg. So this + + align:start position:0% +were doing uh Land of Ginsburg. So this + + + align:start position:0% +were doing uh Land of Ginsburg. So this +is something + + align:start position:0% +is something + + + align:start position:0% +is something +that + + align:start position:0% +that + + + align:start position:0% +that +uh goes when you are looking at + + align:start position:0% +uh goes when you are looking at + + + align:start position:0% +uh goes when you are looking at +distances that are much less than this + + align:start position:0% +distances that are much less than this + + + align:start position:0% +distances that are much less than this +correlation length as the kulum power + + align:start position:0% +correlation length as the kulum power + + + align:start position:0% +correlation length as the kulum power +law. + + align:start position:0% +law. + + + align:start position:0% +law. +When you are looking at distances that + + align:start position:0% +When you are looking at distances that + + + align:start position:0% +When you are looking at distances that +are much larger than the correlation + + align:start position:0% +are much larger than the correlation + + + align:start position:0% +are much larger than the correlation +length, you get the exponential decay + + align:start position:0% +length, you get the exponential decay + + + align:start position:0% +length, you get the exponential decay +with this r -1 / 2 factor. + + align:start position:0% +with this r -1 / 2 factor. + + + align:start position:0% +with this r -1 / 2 factor. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So what we find + + align:start position:0% +So what we find + + + align:start position:0% +So what we find +is that the correlation of these phantom + + align:start position:0% +is that the correlation of these phantom + + + align:start position:0% +is that the correlation of these phantom +loops + + align:start position:0% +loops + + + align:start position:0% +loops +is precisely the correlation that we had + + align:start position:0% +is precisely the correlation that we had + + + align:start position:0% +is precisely the correlation that we had +seen for the Gaussian model. In fact, it + + align:start position:0% +seen for the Gaussian model. In fact, it + + + align:start position:0% +seen for the Gaussian model. In fact, it +has a correlation length that diverges + + align:start position:0% +has a correlation length that diverges + + + align:start position:0% +has a correlation length that diverges +in precisely the same way that we had + + align:start position:0% +in precisely the same way that we had + + + align:start position:0% +in precisely the same way that we had +seen for the Gaussian model with a + + align:start position:0% +seen for the Gaussian model with a + + + align:start position:0% +seen for the Gaussian model with a +square root singularity. So this is our + + align:start position:0% +square root singularity. So this is our + + + align:start position:0% +square root singularity. So this is our +usual mu = to 1/2 type of uh behavior + + align:start position:0% +usual mu = to 1/2 type of uh behavior + + + align:start position:0% +usual mu = to 1/2 type of uh behavior +that we are seeing + + align:start position:0% +that we are seeing + + + align:start position:0% +that we are seeing +and somehow + + align:start position:0% +and somehow + + + align:start position:0% +and somehow +by all of these root + + align:start position:0% +by all of these root + + + align:start position:0% +by all of these root +we reproduced uh some property of the + + align:start position:0% +we reproduced uh some property of the + + + align:start position:0% +we reproduced uh some property of the +Gaussian model. + + align:start position:0% +Gaussian model. + + + align:start position:0% +Gaussian model. +In fact, + + align:start position:0% +In fact, + + + align:start position:0% +In fact, +it's a little bit more than that because + + align:start position:0% +it's a little bit more than that because + + + align:start position:0% +it's a little bit more than that because +we can go back and look at what we had + + align:start position:0% +we can go back and look at what we had + + + align:start position:0% +we can go back and look at what we had +here for the free energy. + + align:start position:0% +here for the free energy. + + + align:start position:0% +here for the free energy. +So let's erase the things that pertain + + align:start position:0% +So let's erase the things that pertain + + + align:start position:0% +So let's erase the things that pertain +to the correlation length + + align:start position:0% + + + + align:start position:0% + +and correlations + + align:start position:0% + + + + align:start position:0% + +and focus on a calculation + + align:start position:0% +and focus on a calculation + + + align:start position:0% +and focus on a calculation +that we kind of left in the middle + + align:start position:0% + + + + align:start position:0% + +over here. + + align:start position:0% +over here. + + + align:start position:0% +over here. +So what do we have? We have that log of + + align:start position:0% +So what do we have? We have that log of + + + align:start position:0% +So what do we have? We have that log of +s prime the intensive part + + align:start position:0% +s prime the intensive part + + + align:start position:0% +s prime the intensive part +is a sum over the length of these loops + + align:start position:0% +is a sum over the length of these loops + + + align:start position:0% +is a sum over the length of these loops +that start + + align:start position:0% +that start + + + align:start position:0% +that start +and end at the origin. + + align:start position:0% +and end at the origin. + + + align:start position:0% +and end at the origin. +And the contribution of a loop of length + + align:start position:0% +And the contribution of a loop of length + + + align:start position:0% +And the contribution of a loop of length +L is small T to the L. And since WL is + + align:start position:0% +L is small T to the L. And since WL is + + + align:start position:0% +L is small T to the L. And since WL is +the connectivity matrix to the L power, + + align:start position:0% +the connectivity matrix to the L power, + + + align:start position:0% +the connectivity matrix to the L power, +it's really like looking at the matrix + + align:start position:0% +it's really like looking at the matrix + + + align:start position:0% +it's really like looking at the matrix +element of this entity. + + align:start position:0% + + + + align:start position:0% + +And of course, there is this degeneracy + + align:start position:0% +And of course, there is this degeneracy + + + align:start position:0% +And of course, there is this degeneracy +factor of 2 L and I can write this as 12 + + align:start position:0% +factor of 2 L and I can write this as 12 + + + align:start position:0% +factor of 2 L and I can write this as 12 +a sum over L. Well, let's do it this + + align:start position:0% +a sum over L. Well, let's do it this + + + align:start position:0% +a sum over L. Well, let's do it this +way. the zero zero element + + align:start position:0% +way. the zero zero element + + + align:start position:0% +way. the zero zero element +of uh one + + align:start position:0% +of uh one + + + align:start position:0% +of uh one +uh oops sum over l tt to the l + + align:start position:0% +uh oops sum over l tt to the l + + + align:start position:0% +uh oops sum over l tt to the l +/ l. + + align:start position:0% +/ l. + + + align:start position:0% +/ l. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +And what is this? + + align:start position:0% +And what is this? + + + align:start position:0% +And what is this? +This is in fact the expansion the series + + align:start position:0% +This is in fact the expansion the series + + + align:start position:0% +This is in fact the expansion the series +expansion of minus log of 1 minus tt. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So + + align:start position:0% + + + + align:start position:0% + +I can again + + align:start position:0% +I can again + + + align:start position:0% +I can again +go to the FIA basis write this as minus + + align:start position:0% +go to the FIA basis write this as minus + + + align:start position:0% +go to the FIA basis write this as minus + + align:start position:0% + + + align:start position:0% +sum / q 0 q + + align:start position:0% +sum / q 0 q + + + align:start position:0% +sum / q 0 q +uh + + align:start position:0% +uh + + + align:start position:0% +uh +log of 1 - t the value t of q and then + + align:start position:0% +log of 1 - t the value t of q and then + + + align:start position:0% +log of 1 - t the value t of q and then +uh q0. + + align:start position:0% +uh q0. + + + align:start position:0% +uh q0. +Each one of these is just a factor of 1 + + align:start position:0% +Each one of these is just a factor of 1 + + + align:start position:0% +Each one of these is just a factor of 1 +/ square<unk> of n. + + align:start position:0% + + + + align:start position:0% + +The sum over q goes over to n integral / + + align:start position:0% +The sum over q goes over to n integral / + + + align:start position:0% +The sum over q goes over to n integral / +q. So this simply becomes - 12 + + align:start position:0% +q. So this simply becomes - 12 + + + align:start position:0% +q. So this simply becomes - 12 +uh integral / q + + align:start position:0% +uh integral / q + + + align:start position:0% +uh integral / q +2 pi to the d log of + + align:start position:0% +2 pi to the d log of + + + align:start position:0% +2 pi to the d log of +1 - t this sum / alpha cosine of q alpha + + align:start position:0% +1 - t this sum / alpha cosine of q alpha + + + align:start position:0% +1 - t this sum / alpha cosine of q alpha +e the 2 that we had over here. + + align:start position:0% +e the 2 that we had over here. + + + align:start position:0% +e the 2 that we had over here. +Okay. + + align:start position:0% + + + + align:start position:0% + +And again if I go to this limit where + + align:start position:0% +And again if I go to this limit where + + + align:start position:0% +And again if I go to this limit where +I'm close to TC the critical value of + + align:start position:0% +I'm close to TC the critical value of + + + align:start position:0% +I'm close to TC the critical value of +this T + + align:start position:0% +this T + + + align:start position:0% +this T +and focus on the behavior as Q goes to + + align:start position:0% +and focus on the behavior as Q goes to + + + align:start position:0% +and focus on the behavior as Q goes to +zero this is going to be something that + + align:start position:0% +zero this is going to be something that + + + align:start position:0% +zero this is going to be something that +has this Q ^2 + C to the minus2 type of + + align:start position:0% +has this Q ^2 + C to the minus2 type of + + + align:start position:0% +has this Q ^2 + C to the minus2 type of +singularity + + align:start position:0% +singularity + + + align:start position:0% +singularity +and again this is a kind of integral + + align:start position:0% +and again this is a kind of integral + + + align:start position:0% +and again this is a kind of integral +that we saw in connection with the + + align:start position:0% +that we saw in connection with the + + + align:start position:0% +that we saw in connection with the +Gaussian model and we know the kind of + + align:start position:0% +Gaussian model and we know the kind of + + + align:start position:0% +Gaussian model and we know the kind of +singularities it gives. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +But why did we end up with the Gaussian + + align:start position:0% +But why did we end up with the Gaussian + + + align:start position:0% +But why did we end up with the Gaussian +model? + + align:start position:0% +model? + + + align:start position:0% +model? +Okay. Let's work backward. + + align:start position:0% +Okay. Let's work backward. + + + align:start position:0% +Okay. Let's work backward. +That is typically + + align:start position:0% +That is typically + + + align:start position:0% +That is typically +when we are doing some kind of a + + align:start position:0% +when we are doing some kind of a + + + align:start position:0% +when we are doing some kind of a +partition function of a Gaussian model. + + align:start position:0% +partition function of a Gaussian model. + + + align:start position:0% +partition function of a Gaussian model. +Let's say we have some integral + + align:start position:0% +Let's say we have some integral + + + align:start position:0% +Let's say we have some integral +over some variables fi. + + align:start position:0% +over some variables fi. + + + align:start position:0% +over some variables fi. +Let's say we put them on the sides of a + + align:start position:0% +Let's say we put them on the sides of a + + + align:start position:0% +Let's say we put them on the sides of a +latis and we have e to the minus 5 i + + align:start position:0% +latis and we have e to the minus 5 i + + + align:start position:0% +latis and we have e to the minus 5 i +some matrix m i j 5 j over two sum over + + align:start position:0% +some matrix m i j 5 j over two sum over + + + align:start position:0% +some matrix m i j 5 j over two sum over +i and j implicit over there. + + align:start position:0% +i and j implicit over there. + + + align:start position:0% +i and j implicit over there. +What was the answer then? And the answer + + align:start position:0% +What was the answer then? And the answer + + + align:start position:0% +What was the answer then? And the answer +was typically proportional to 1 / the + + align:start position:0% +was typically proportional to 1 / the + + + align:start position:0% +was typically proportional to 1 / the +determinant of this matrix to the 1/2 + + align:start position:0% +determinant of this matrix to the 1/2 + + + align:start position:0% +determinant of this matrix to the 1/2 +which if I exponentiated it would be + + align:start position:0% +which if I exponentiated it would be + + + align:start position:0% +which if I exponentiated it would be +exponential of min - one + + align:start position:0% +exponential of min - one + + + align:start position:0% +exponential of min - one +uh logarithm of the determinant of this + + align:start position:0% +uh logarithm of the determinant of this + + + align:start position:0% +uh logarithm of the determinant of this +matrix. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So that's the general result and we see + + align:start position:0% +So that's the general result and we see + + + align:start position:0% +So that's the general result and we see +that the result for our log of S prime + + align:start position:0% +that the result for our log of S prime + + + align:start position:0% +that the result for our log of S prime +is indeed the form of a 12 - 1/2 the log + + align:start position:0% +is indeed the form of a 12 - 1/2 the log + + + align:start position:0% +is indeed the form of a 12 - 1/2 the log +of something + + align:start position:0% +of something + + + align:start position:0% +of something +and indeed uh this sum over Q + + align:start position:0% +and indeed uh this sum over Q + + + align:start position:0% +and indeed uh this sum over Q +corresponds to summing over the + + align:start position:0% +corresponds to summing over the + + + align:start position:0% +corresponds to summing over the +different values and if I were to + + align:start position:0% +different values and if I were to + + + align:start position:0% +different values and if I were to +express + + align:start position:0% +express + + + align:start position:0% +express +M in terms of the product of its igen + + align:start position:0% +M in terms of the product of its igen + + + align:start position:0% +M in terms of the product of its igen +values it would be precisely that. + + align:start position:0% +values it would be precisely that. + + + align:start position:0% +values it would be precisely that. +So you can see that actually + + align:start position:0% +So you can see that actually + + + align:start position:0% +So you can see that actually +what we have calculated + + align:start position:0% +what we have calculated + + + align:start position:0% +what we have calculated +by comparison of these two things + + align:start position:0% +by comparison of these two things + + + align:start position:0% +by comparison of these two things +corresponds to a matrix MIG + + align:start position:0% +corresponds to a matrix MIG + + + align:start position:0% +corresponds to a matrix MIG +which is delta J + + align:start position:0% + + + + align:start position:0% + +minus T * this uh single step + + align:start position:0% +minus T * this uh single step + + + align:start position:0% +minus T * this uh single step +connectivity matrix that I had before. + + align:start position:0% +connectivity matrix that I had before. + + + align:start position:0% +connectivity matrix that I had before. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So indeed the partition function that I + + align:start position:0% +So indeed the partition function that I + + + align:start position:0% +So indeed the partition function that I +calculated that I called Zp prime or S + + align:start position:0% +calculated that I called Zp prime or S + + + align:start position:0% +calculated that I called Zp prime or S +prime + + align:start position:0% +prime + + + align:start position:0% +prime +corresponds to doing the following. + + align:start position:0% +corresponds to doing the following. + + + align:start position:0% +corresponds to doing the following. +Doing an integral + + align:start position:0% +Doing an integral + + + align:start position:0% +Doing an integral +over 5 I + + align:start position:0% + + + + align:start position:0% + +from the delta J. Essentially for each + + align:start position:0% +from the delta J. Essentially for each + + + align:start position:0% +from the delta J. Essentially for each +fi I would have a factor of min - 5 i^2 + + align:start position:0% +fi I would have a factor of min - 5 i^2 + + + align:start position:0% +fi I would have a factor of min - 5 i^2 +/ 2. So essentially I have to do this + + align:start position:0% +/ 2. So essentially I have to do this + + + align:start position:0% +/ 2. So essentially I have to do this +and then from here once it exponentiated + + align:start position:0% +and then from here once it exponentiated + + + align:start position:0% +and then from here once it exponentiated +I will get a factor of e to the sum over + + align:start position:0% +I will get a factor of e to the sum over + + + align:start position:0% +I will get a factor of e to the sum over +uh i j + + align:start position:0% +uh i j + + + align:start position:0% +uh i j +uh this t uh 5 i j. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So you can see that I started + + align:start position:0% + + + + align:start position:0% + +calculating + + align:start position:0% + + + + align:start position:0% + +ing variables on this lattice. + + align:start position:0% +ing variables on this lattice. + + + align:start position:0% +ing variables on this lattice. +The result that I calculated for these + + align:start position:0% +The result that I calculated for these + + + align:start position:0% +The result that I calculated for these +phantom walks is actually identical if I + + align:start position:0% +phantom walks is actually identical if I + + + align:start position:0% +phantom walks is actually identical if I +had replaced the icing variables with + + align:start position:0% +had replaced the icing variables with + + + align:start position:0% +had replaced the icing variables with +just quantities that I integrate all + + align:start position:0% +just quantities that I integrate all + + + align:start position:0% +just quantities that I integrate all +over the place provided that I weigh + + align:start position:0% +over the place provided that I weigh + + + align:start position:0% +over the place provided that I weigh +them with this factor. + + align:start position:0% +them with this factor. + + + align:start position:0% +them with this factor. +So really the difference between the + + align:start position:0% +So really the difference between the + + + align:start position:0% +So really the difference between the +icing and what I have done here can be + + align:start position:0% +icing and what I have done here can be + + + align:start position:0% +icing and what I have done here can be +captured by putting a weight for the + + align:start position:0% +captured by putting a weight for the + + + align:start position:0% +captured by putting a weight for the +inter integration per site. + + align:start position:0% +inter integration per site. + + + align:start position:0% +inter integration per site. +So if I really want to do izing + + align:start position:0% +So if I really want to do izing + + + align:start position:0% +So if I really want to do izing +the weight that I want to do for the + + align:start position:0% +the weight that I want to do for the + + + align:start position:0% +the weight that I want to do for the +icing actually let's do it this way for + + align:start position:0% +icing actually let's do it this way for + + + align:start position:0% +icing actually let's do it this way for +phi + + align:start position:0% +phi + + + align:start position:0% +phi +has to have a delta function at minus1 + + align:start position:0% +has to have a delta function at minus1 + + + align:start position:0% +has to have a delta function at minus1 +and a delta function at + one + + align:start position:0% +and a delta function at + one + + + align:start position:0% +and a delta function at + one +right rather than doing that I have + + align:start position:0% +right rather than doing that I have + + + align:start position:0% +right rather than doing that I have +calculated a w that corresponds to + + align:start position:0% +calculated a w that corresponds to + + + align:start position:0% +calculated a w that corresponds to +Gaussian + + align:start position:0% + + + + align:start position:0% + +where the weight for each phi is + + align:start position:0% +where the weight for each phi is + + + align:start position:0% +where the weight for each phi is +basically a Gaussian weight. + + align:start position:0% + + + + align:start position:0% + +And if I really wanted to do the Lando + + align:start position:0% +And if I really wanted to do the Lando + + + align:start position:0% +And if I really wanted to do the Lando +Ginsburg, all I would need to do is to + + align:start position:0% +Ginsburg, all I would need to do is to + + + align:start position:0% +Ginsburg, all I would need to do is to +add here a pi to the 4th. + + align:start position:0% +add here a pi to the 4th. + + + align:start position:0% +add here a pi to the 4th. +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +the problem with this Gaussian, the + + align:start position:0% +the problem with this Gaussian, the + + + align:start position:0% +the problem with this Gaussian, the +phantom system that I have + + align:start position:0% +phantom system that I have + + + align:start position:0% +phantom system that I have +is the same problem that we had with the + + align:start position:0% +is the same problem that we had with the + + + align:start position:0% +is the same problem that we had with the +Gaussian model. + + align:start position:0% +Gaussian model. + + + align:start position:0% +Gaussian model. +It only gives me one side of the phase + + align:start position:0% +It only gives me one side of the phase + + + align:start position:0% +It only gives me one side of the phase +transition + + align:start position:0% +transition + + + align:start position:0% +transition +because you see that I did all of these + + align:start position:0% +because you see that I did all of these + + + align:start position:0% +because you see that I did all of these +calculations. + + align:start position:0% +calculations. + + + align:start position:0% +calculations. +All of these calculations were + + align:start position:0% +All of these calculations were + + + align:start position:0% +All of these calculations were +consistent as long as I was dealing with + + align:start position:0% +consistent as long as I was dealing with + + + align:start position:0% +consistent as long as I was dealing with +T that was less than TC. + + align:start position:0% +T that was less than TC. + + + align:start position:0% +T that was less than TC. +Right? + + align:start position:0% +Right? + + + align:start position:0% +Right? +Once I go to T that is greater than TC, + + align:start position:0% +Once I go to T that is greater than TC, + + + align:start position:0% +Once I go to T that is greater than TC, +then this denominator that I had became + + align:start position:0% +then this denominator that I had became + + + align:start position:0% +then this denominator that I had became +negative. It just doesn't make sense. + + align:start position:0% +negative. It just doesn't make sense. + + + align:start position:0% +negative. It just doesn't make sense. +correlations negative don't make sense. + + align:start position:0% +correlations negative don't make sense. + + + align:start position:0% +correlations negative don't make sense. +the log the argument that I have to + + align:start position:0% +the log the argument that I have to + + + align:start position:0% +the log the argument that I have to +calculate here if T is below is larger + + align:start position:0% +calculate here if T is below is larger + + + align:start position:0% +calculate here if T is below is larger +than 2D uh one over 2D then it doesn't + + align:start position:0% +than 2D uh one over 2D then it doesn't + + + align:start position:0% +than 2D uh one over 2D then it doesn't +make sense + + align:start position:0% +make sense + + + align:start position:0% +make sense +and of course the reason the whole + + align:start position:0% +and of course the reason the whole + + + align:start position:0% +and of course the reason the whole +theory doesn't make sense is kind of + + align:start position:0% +theory doesn't make sense is kind of + + + align:start position:0% +theory doesn't make sense is kind of +related to the uh instability that we + + align:start position:0% +related to the uh instability that we + + + align:start position:0% +related to the uh instability that we +have in the Gaussian model essentially + + align:start position:0% +have in the Gaussian model essentially + + + align:start position:0% +have in the Gaussian model essentially +in the Gaussian model also when t + + align:start position:0% +in the Gaussian model also when t + + + align:start position:0% +in the Gaussian model also when t +becomes large enough this pi squar is + + align:start position:0% +becomes large enough this pi squar is + + + align:start position:0% +becomes large enough this pi squar is +not enough + + align:start position:0% +not enough + + + align:start position:0% +not enough +to remove the instability that you have + + align:start position:0% +to remove the instability that you have + + + align:start position:0% +to remove the instability that you have +for the largest value physically. What + + align:start position:0% +for the largest value physically. What + + + align:start position:0% +for the largest value physically. What +that means is that we started with this + + align:start position:0% +that means is that we started with this + + + align:start position:0% +that means is that we started with this +taut string and as we approached the + + align:start position:0% +taut string and as we approached the + + + align:start position:0% +taut string and as we approached the +transition the string became more + + align:start position:0% +transition the string became more + + + align:start position:0% +transition the string became more +flexible + + align:start position:0% +flexible + + + align:start position:0% +flexible +and in principle what this instability + + align:start position:0% +and in principle what this instability + + + align:start position:0% +and in principle what this instability +is telling me is that you go below the + + align:start position:0% +is telling me is that you go below the + + + align:start position:0% +is telling me is that you go below the +transition + + align:start position:0% +transition + + + align:start position:0% +transition +oops t greater than tc and uh the string + + align:start position:0% +oops t greater than tc and uh the string + + + align:start position:0% +oops t greater than tc and uh the string +becomes something that can go over and + + align:start position:0% +becomes something that can go over and + + + align:start position:0% +becomes something that can go over and +over itself as many times and gain entry + + align:start position:0% +over itself as many times and gain entry + + + align:start position:0% +over itself as many times and gain entry +Py further and further. So it will keep + + align:start position:0% +Py further and further. So it will keep + + + align:start position:0% +Py further and further. So it will keep +going forever. There is nothing to stop + + align:start position:0% +going forever. There is nothing to stop + + + align:start position:0% +going forever. There is nothing to stop +it. So the phantomness condition the + + align:start position:0% +it. So the phantomness condition the + + + align:start position:0% +it. So the phantomness condition the +cost that you pay for it is that once + + align:start position:0% +cost that you pay for it is that once + + + align:start position:0% +cost that you pay for it is that once +you go beyond the transition you + + align:start position:0% +you go beyond the transition you + + + align:start position:0% +you go beyond the transition you +essentially overwhelm yourself. There's + + align:start position:0% +essentially overwhelm yourself. There's + + + align:start position:0% +essentially overwhelm yourself. There's +just so much that is going on. There is + + align:start position:0% +just so much that is going on. There is + + + align:start position:0% +just so much that is going on. There is +nothing that you can do. + + align:start position:0% +nothing that you can do. + + + align:start position:0% +nothing that you can do. +So, + + align:start position:0% + + + + align:start position:0% + +so that's the story. + + align:start position:0% +so that's the story. + + + align:start position:0% +so that's the story. +Now, let's try to finally understand + + align:start position:0% +Now, let's try to finally understand + + + align:start position:0% +Now, let's try to finally understand +some of the things that we + + align:start position:0% +some of the things that we + + + align:start position:0% +some of the things that we +had before like this upper critical + + align:start position:0% +had before like this upper critical + + + align:start position:0% +had before like this upper critical +dimension of four, where did it come + + align:start position:0% +dimension of four, where did it come + + + align:start position:0% +dimension of four, where did it come +from etc. We are in now in the position + + align:start position:0% +from etc. We are in now in the position + + + align:start position:0% +from etc. We are in now in the position +to do things and understand things. + + align:start position:0% +to do things and understand things. + + + align:start position:0% +to do things and understand things. +First thing to note is let's try to + + align:start position:0% +First thing to note is let's try to + + + align:start position:0% +First thing to note is let's try to +understand + + align:start position:0% +understand + + + align:start position:0% +understand +what uh this exponent uh + + align:start position:0% +what uh this exponent uh + + + align:start position:0% +what uh this exponent uh +new = to 12 means. + + align:start position:0% +new = to 12 means. + + + align:start position:0% +new = to 12 means. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So we said that + + align:start position:0% +So we said that + + + align:start position:0% +So we said that +if I think about + + align:start position:0% + + + + align:start position:0% + +having + + align:start position:0% +having + + + align:start position:0% +having +information about my site at the origin + + align:start position:0% +information about my site at the origin + + + align:start position:0% +information about my site at the origin +that has to propagate so that further + + align:start position:0% +that has to propagate so that further + + + align:start position:0% +that has to propagate so that further +and further neighbors start to know + + align:start position:0% +and further neighbors start to know + + + align:start position:0% +and further neighbors start to know +what the information was at site zigma + + align:start position:0% +what the information was at site zigma + + + align:start position:0% +what the information was at site zigma +zero + + align:start position:0% +zero + + + align:start position:0% +zero +that that information can come through + + align:start position:0% +that that information can come through + + + align:start position:0% +that that information can come through +these paths. + + align:start position:0% +these paths. + + + align:start position:0% +these paths. +that fluctuate, go different distances + + align:start position:0% +that fluctuate, go different distances + + + align:start position:0% +that fluctuate, go different distances +and eventually let's say reach a + + align:start position:0% +and eventually let's say reach a + + + align:start position:0% +and eventually let's say reach a +boundary that is at size R. + + align:start position:0% + + + + align:start position:0% + +As we said, the contribution of each + + align:start position:0% +As we said, the contribution of each + + + align:start position:0% +As we said, the contribution of each +path + + align:start position:0% +path + + + align:start position:0% +path +decays exponentially, + + align:start position:0% +decays exponentially, + + + align:start position:0% +decays exponentially, +but the number of paths grows + + align:start position:0% +but the number of paths grows + + + align:start position:0% +but the number of paths grows +exponentially. + + align:start position:0% + + + + align:start position:0% + +And so for a particular t + + align:start position:0% +And so for a particular t + + + align:start position:0% +And so for a particular t +that is smaller than the critical value + + align:start position:0% +that is smaller than the critical value + + + align:start position:0% +that is smaller than the critical value +I can roughly say that this falls off + + align:start position:0% +I can roughly say that this falls off + + + align:start position:0% +I can roughly say that this falls off +like this. So that there is a + + align:start position:0% +like this. So that there is a + + + align:start position:0% +like this. So that there is a +characteristic length LB bar. + + align:start position:0% +characteristic length LB bar. + + + align:start position:0% +characteristic length LB bar. +This characteristic LB bar is going to + + align:start position:0% +This characteristic LB bar is going to + + + align:start position:0% +This characteristic LB bar is going to +be minus 1 / log of 2dt + + align:start position:0% + + + + align:start position:0% + +and 2dt I can write as 2dc + t minus tc + + align:start position:0% + + + + align:start position:0% + +2dc is by construction one. So this is + + align:start position:0% +2dc is by construction one. So this is + + + align:start position:0% +2dc is by construction one. So this is +-1 / log of 1 + something like 2D which + + align:start position:0% +-1 / log of 1 + something like 2D which + + + align:start position:0% +-1 / log of 1 + something like 2D which +is 1 / t minus tc t minus tc over tc. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Now log of 1 plus a small number. So if + + align:start position:0% +Now log of 1 plus a small number. So if + + + align:start position:0% +Now log of 1 plus a small number. So if +I my t goes and approaches tc + + align:start position:0% +I my t goes and approaches tc + + + align:start position:0% +I my t goes and approaches tc +this log will behave like what I have + + align:start position:0% +this log will behave like what I have + + + align:start position:0% +this log will behave like what I have +over here. So you can see that this + + align:start position:0% +over here. So you can see that this + + + align:start position:0% +over here. So you can see that this +diverges as t minus t c to the minus one + + align:start position:0% +diverges as t minus t c to the minus one + + + align:start position:0% +diverges as t minus t c to the minus one +power. + + align:start position:0% + + + + align:start position:0% + +I want it I guess to be correct tc minus + + align:start position:0% +I want it I guess to be correct tc minus + + + align:start position:0% +I want it I guess to be correct tc minus +t because t is less than tc. + + align:start position:0% +t because t is less than tc. + + + align:start position:0% +t because t is less than tc. +But the point is that the divergence is + + align:start position:0% +But the point is that the divergence is + + + align:start position:0% +But the point is that the divergence is +linear. + + align:start position:0% +linear. + + + align:start position:0% +linear. +As I approach TC, + + align:start position:0% +As I approach TC, + + + align:start position:0% +As I approach TC, +the length of these paths will grow + + align:start position:0% +the length of these paths will grow + + + align:start position:0% +the length of these paths will grow +inversely to how close I am. + + align:start position:0% +inversely to how close I am. + + + align:start position:0% +inversely to how close I am. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Now, what are these paths? + + align:start position:0% +Now, what are these paths? + + + align:start position:0% +Now, what are these paths? +I start from the origin + + align:start position:0% +I start from the origin + + + align:start position:0% +I start from the origin +and I randomly take steps. + + align:start position:0% +and I randomly take steps. + + + align:start position:0% +and I randomly take steps. +And I've said that the typical steps + + align:start position:0% +And I've said that the typical steps + + + align:start position:0% +And I've said that the typical steps +that I will get will roughly have length + + align:start position:0% +that I will get will roughly have length + + + align:start position:0% +that I will get will roughly have length +LB bar. + + align:start position:0% +LB bar. + + + align:start position:0% +LB bar. +How far have these paths carried the + + align:start position:0% +How far have these paths carried the + + + align:start position:0% +How far have these paths carried the +information? + + align:start position:0% +information? + + + align:start position:0% +information? +These are random blocks. So the distance + + align:start position:0% +These are random blocks. So the distance + + + align:start position:0% +These are random blocks. So the distance +over which they have managed to carry + + align:start position:0% +over which they have managed to carry + + + align:start position:0% +over which they have managed to carry +the information C + + align:start position:0% +the information C + + + align:start position:0% +the information C +is going to be like the square root of + + align:start position:0% +is going to be like the square root of + + + align:start position:0% +is going to be like the square root of +the length of these walks. + + align:start position:0% +the length of these walks. + + + align:start position:0% +the length of these walks. +And since the length of the box grows + + align:start position:0% +And since the length of the box grows + + + align:start position:0% +And since the length of the box grows +like t minus t c this goes like t c + + align:start position:0% +like t minus t c this goes like t c + + + align:start position:0% +like t minus t c this goes like t c +minus t to the minus one/2 power. + + align:start position:0% +minus t to the minus one/2 power. + + + align:start position:0% +minus t to the minus one/2 power. +So the exponent new of 12 that we have + + align:start position:0% +So the exponent new of 12 that we have + + + align:start position:0% +So the exponent new of 12 that we have +been thinking about is none other than + + align:start position:0% +been thinking about is none other than + + + align:start position:0% +been thinking about is none other than +the 1/2 that you have for random walks. + + align:start position:0% +the 1/2 that you have for random walks. + + + align:start position:0% +the 1/2 that you have for random walks. +Once you realize that what is going on + + align:start position:0% +Once you realize that what is going on + + + align:start position:0% +Once you realize that what is going on +is that the length of the paths that + + align:start position:0% +is that the length of the paths that + + + align:start position:0% +is that the length of the paths that +carry information + + align:start position:0% +carry information + + + align:start position:0% +carry information +essentially diverges + + align:start position:0% +essentially diverges + + + align:start position:0% +essentially diverges +linearly on approaching this. + + align:start position:0% +linearly on approaching this. + + + align:start position:0% +linearly on approaching this. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So that's one understanding. + + align:start position:0% + + + + align:start position:0% + +Now you would say that okay + + align:start position:0% +Now you would say that okay + + + align:start position:0% +Now you would say that okay +this is the Gaussian picture. + + align:start position:0% +this is the Gaussian picture. + + + align:start position:0% +this is the Gaussian picture. +Now I know that when we calculated + + align:start position:0% +Now I know that when we calculated + + + align:start position:0% +Now I know that when we calculated +things to order of epsilon we found that + + align:start position:0% +things to order of epsilon we found that + + + align:start position:0% +things to order of epsilon we found that +mu was 12 plus something + + align:start position:0% +mu was 12 plus something + + + align:start position:0% +mu was 12 plus something +it became larger. + + align:start position:0% + + + + align:start position:0% + +So what does that mean? Well if you have + + align:start position:0% +So what does that mean? Well if you have + + + align:start position:0% +So what does that mean? Well if you have +these paths + + align:start position:0% +these paths + + + align:start position:0% +these paths +and the paths + + align:start position:0% +and the paths + + + align:start position:0% +and the paths +cannot cross each other. It comes here. + + align:start position:0% +cannot cross each other. It comes here. + + + align:start position:0% +cannot cross each other. It comes here. +it has to go further away + + align:start position:0% +it has to go further away + + + align:start position:0% +it has to go further away +because they are really non-fantom + + align:start position:0% +because they are really non-fantom + + + align:start position:0% +because they are really non-fantom +then they will swell. + + align:start position:0% +then they will swell. + + + align:start position:0% +then they will swell. +So the exponent new that you expect to + + align:start position:0% +So the exponent new that you expect to + + + align:start position:0% +So the exponent new that you expect to +get will be larger than 1/2. So that's + + align:start position:0% +get will be larger than 1/2. So that's + + + align:start position:0% +get will be larger than 1/2. So that's +what's captured here. + + align:start position:0% + + + + align:start position:0% + +Well, how can I really try to capture + + align:start position:0% +Well, how can I really try to capture + + + align:start position:0% +Well, how can I really try to capture +that + + align:start position:0% +that + + + align:start position:0% +that +uh more mathematically? + + align:start position:0% +uh more mathematically? + + + align:start position:0% +uh more mathematically? +Well, I say that in the calculations + + align:start position:0% +Well, I say that in the calculations + + + align:start position:0% +Well, I say that in the calculations +that I did, let's say when I was + + align:start position:0% +that I did, let's say when I was + + + align:start position:0% +that I did, let's say when I was +calculating the correlation function + + align:start position:0% +calculating the correlation function + + + align:start position:0% +calculating the correlation function +zigma 0 sigma r, in the approximation of + + align:start position:0% +zigma 0 sigma r, in the approximation of + + + align:start position:0% +zigma 0 sigma r, in the approximation of +phantomness, I included all paths that + + align:start position:0% +phantomness, I included all paths that + + + align:start position:0% +phantomness, I included all paths that +went from zero to r. + + align:start position:0% +went from zero to r. + + + align:start position:0% +went from zero to r. +Among those there were paths that were + + align:start position:0% +Among those there were paths that were + + + align:start position:0% +Among those there were paths that were +crossing themselves. So I really have to + + align:start position:0% +crossing themselves. So I really have to + + + align:start position:0% +crossing themselves. So I really have to +subtract from that a path that comes and + + align:start position:0% +subtract from that a path that comes and + + + align:start position:0% +subtract from that a path that comes and +crosses itself. So I have to subtract + + align:start position:0% +crosses itself. So I have to subtract + + + align:start position:0% +crosses itself. So I have to subtract +that. + + align:start position:0% + + + + align:start position:0% + +I also had this condition that I had the + + align:start position:0% +I also had this condition that I had the + + + align:start position:0% +I also had this condition that I had the +numerator and the denominator that I + + align:start position:0% +numerator and the denominator that I + + + align:start position:0% +numerator and the denominator that I +cancelled each other which really means + + align:start position:0% +cancelled each other which really means + + + align:start position:0% +cancelled each other which really means +that I have to subtract the possibility + + align:start position:0% +that I have to subtract the possibility + + + align:start position:0% +that I have to subtract the possibility +of my path intersecting with another + + align:start position:0% +of my path intersecting with another + + + align:start position:0% +of my path intersecting with another +loop that is over here. + + align:start position:0% + + + + align:start position:0% + +Okay. And we can try to incorporate + + align:start position:0% +Okay. And we can try to incorporate + + + align:start position:0% +Okay. And we can try to incorporate +these as corrections. + + align:start position:0% + + + + align:start position:0% + +But we've already done that because if I + + align:start position:0% +But we've already done that because if I + + + align:start position:0% +But we've already done that because if I +fa transformed this object, I saw that + + align:start position:0% +fa transformed this object, I saw that + + + align:start position:0% +fa transformed this object, I saw that +it is this 1 / q ^2 + k ^2. And then we + + align:start position:0% +it is this 1 / q ^2 + k ^2. And then we + + + align:start position:0% +it is this 1 / q ^2 + k ^2. And then we +were calculating this u perturbative + + align:start position:0% +were calculating this u perturbative + + + align:start position:0% +were calculating this u perturbative +corrections and we had diagrams that + + align:start position:0% +corrections and we had diagrams that + + + align:start position:0% +corrections and we had diagrams that +kind of looked uh like this. + + align:start position:0% +kind of looked uh like this. + + + align:start position:0% +kind of looked uh like this. +Oops. I guess I want to first draw the + + align:start position:0% +Oops. I guess I want to first draw the + + + align:start position:0% +Oops. I guess I want to first draw the +other diagram. + + align:start position:0% + + + + align:start position:0% + +And then we had a diagram that was like + + align:start position:0% +And then we had a diagram that was like + + + align:start position:0% +And then we had a diagram that was like +this. + + align:start position:0% +this. + + + align:start position:0% +this. +Remember when we were doing these pi to + + align:start position:0% +Remember when we were doing these pi to + + + align:start position:0% +Remember when we were doing these pi to +the 4th calculations, + + align:start position:0% +the 4th calculations, + + + align:start position:0% +the 4th calculations, +the corrections that we had for the + + align:start position:0% +the corrections that we had for the + + + align:start position:0% +the corrections that we had for the +propagator which was related to the + + align:start position:0% +propagator which was related to the + + + align:start position:0% +propagator which was related to the +point correlation function were + + align:start position:0% +point correlation function were + + + align:start position:0% +point correlation function were +precisely these diagrams + + align:start position:0% +precisely these diagrams + + + align:start position:0% +precisely these diagrams +where we were essentially subtracting + + align:start position:0% +where we were essentially subtracting + + + align:start position:0% +where we were essentially subtracting +factors that were set by u. + + align:start position:0% +factors that were set by u. + + + align:start position:0% +factors that were set by u. +Of course, the value of U could be + + align:start position:0% +Of course, the value of U could be + + + align:start position:0% +Of course, the value of U could be +anything. And you can see that there is + + align:start position:0% +anything. And you can see that there is + + + align:start position:0% +anything. And you can see that there is +really one to one correspondence. + + align:start position:0% +really one to one correspondence. + + + align:start position:0% +really one to one correspondence. +Any of the diagrams that you had before + + align:start position:0% +Any of the diagrams that you had before + + + align:start position:0% +Any of the diagrams that you had before +really captures a picture of one of + + align:start position:0% +really captures a picture of one of + + + align:start position:0% +really captures a picture of one of +these paths trying to cross itself that + + align:start position:0% +these paths trying to cross itself that + + + align:start position:0% +these paths trying to cross itself that +you have to subtract + + align:start position:0% +you have to subtract + + + align:start position:0% +you have to subtract +and you can sort of put a one to one + + align:start position:0% +and you can sort of put a one to one + + + align:start position:0% +and you can sort of put a one to one +mathematical correspondence between what + + align:start position:0% +mathematical correspondence between what + + + align:start position:0% +mathematical correspondence between what +is going on here. Yeah. So, why can't we + + align:start position:0% +is going on here. Yeah. So, why can't we + + + align:start position:0% +is going on here. Yeah. So, why can't we +have the path in the first correction + + align:start position:0% +have the path in the first correction + + + align:start position:0% +have the path in the first correction +you drew? Because it aren't we allowed + + align:start position:0% +you drew? Because it aren't we allowed + + + align:start position:0% +you drew? Because it aren't we allowed +to have four um bonds that attach to one + + align:start position:0% +to have four um bonds that attach to one + + + align:start position:0% +to have four um bonds that attach to one +site when we're doing the original + + align:start position:0% +site when we're doing the original + + + align:start position:0% +site when we're doing the original +expansion. Okay. So, I told you at the + + align:start position:0% +expansion. Okay. So, I told you at the + + + align:start position:0% +expansion. Okay. So, I told you at the +beginning that you should keep track of + + align:start position:0% +beginning that you should keep track of + + + align:start position:0% +beginning that you should keep track of +all of my mistakes and that's a very + + align:start position:0% +all of my mistakes and that's a very + + + align:start position:0% +all of my mistakes and that's a very +subtle thing. So what you are asking is + + align:start position:0% +subtle thing. So what you are asking is + + + align:start position:0% +subtle thing. So what you are asking is +in the original Ising model I can draw + + align:start position:0% +in the original Ising model I can draw + + + align:start position:0% +in the original Ising model I can draw +perfectly okay a graph such as this that + + align:start position:0% +perfectly okay a graph such as this that + + + align:start position:0% +perfectly okay a graph such as this that +has an intersection such as this as we + + align:start position:0% +has an intersection such as this as we + + + align:start position:0% +has an intersection such as this as we +will show next time. So bear with me in + + align:start position:0% +will show next time. So bear with me in + + + align:start position:0% +will show next time. So bear with me in +calculating things via the phantom + + align:start position:0% +calculating things via the phantom + + + align:start position:0% +calculating things via the phantom +condition this is counted three times as + + align:start position:0% +condition this is counted three times as + + + align:start position:0% +condition this is counted three times as +much as it should. So I have to subtract + + align:start position:0% +much as it should. So I have to subtract + + + align:start position:0% +much as it should. So I have to subtract +that because a walk that comes here can + + align:start position:0% +that because a walk that comes here can + + + align:start position:0% +that because a walk that comes here can +either go forward up or down. There is + + align:start position:0% +either go forward up or down. There is + + + align:start position:0% +either go forward up or down. There is +some degeneracy there that essentially + + align:start position:0% +some degeneracy there that essentially + + + align:start position:0% +some degeneracy there that essentially +this has done an overounting that is + + align:start position:0% +this has done an overounting that is + + + align:start position:0% +this has done an overounting that is +important and I have to correct for when + + align:start position:0% +important and I have to correct for when + + + align:start position:0% +important and I have to correct for when +I do things more carefully next time. + + align:start position:0% +I do things more carefully next time. + + + align:start position:0% +I do things more carefully next time. +Yes. Um when we did the Gaussian model + + align:start position:0% +Yes. Um when we did the Gaussian model + + + align:start position:0% +Yes. Um when we did the Gaussian model +we never had to put any sort of + + align:start position:0% +we never had to put any sort of + + + align:start position:0% +we never had to put any sort of +requirement on the lattice being a + + align:start position:0% +requirement on the lattice being a + + + align:start position:0% +requirement on the lattice being a +square lattice. No. Did we have didn't + + align:start position:0% +square lattice. No. Did we have didn't + + + align:start position:0% +square lattice. No. Did we have didn't +we have to do that here when we did + + align:start position:0% +we have to do that here when we did + + + align:start position:0% +we have to do that here when we did +these random walks? No, I only use the + + align:start position:0% +these random walks? No, I only use the + + + align:start position:0% +these random walks? No, I only use the +square condition + + align:start position:0% +square condition + + + align:start position:0% +square condition +or hyper cube condition in order to be + + align:start position:0% +or hyper cube condition in order to be + + + align:start position:0% +or hyper cube condition in order to be +able to write this in general dimension. + + align:start position:0% +able to write this in general dimension. + + + align:start position:0% +able to write this in general dimension. +I could very well have done triangular + + align:start position:0% +I could very well have done triangular + + + align:start position:0% +I could very well have done triangular +FCC or any other latis. The expression + + align:start position:0% +FCC or any other latis. The expression + + + align:start position:0% +FCC or any other latis. The expression +here would have been more complicated. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +All right. + + align:start position:0% + + + + align:start position:0% + +So, + + align:start position:0% +So, + + + align:start position:0% +So, +so finally we can also ask + + align:start position:0% +so finally we can also ask + + + align:start position:0% +so finally we can also ask +well + + align:start position:0% +well + + + align:start position:0% +well +we have a field from reormalization + + align:start position:0% +we have a field from reormalization + + + align:start position:0% +we have a field from reormalization +group etc that the uh Gaussian exponents + + align:start position:0% +group etc that the uh Gaussian exponents + + + align:start position:0% +group etc that the uh Gaussian exponents +like mu= to 1/2 are in fact good + + align:start position:0% +like mu= to 1/2 are in fact good + + + align:start position:0% +like mu= to 1/2 are in fact good +provided that you are in sufficiently + + align:start position:0% +provided that you are in sufficiently + + + align:start position:0% +provided that you are in sufficiently +high dimension if you are above four + + align:start position:0% +high dimension if you are above four + + + align:start position:0% +high dimension if you are above four +dimensions + + align:start position:0% +dimensions + + + align:start position:0% +dimensions +where do you see that occurring in this + + align:start position:0% +where do you see that occurring in this + + + align:start position:0% +where do you see that occurring in this +picture. + + align:start position:0% +picture. + + + align:start position:0% +picture. +The answer is as follows. + + align:start position:0% + + + + align:start position:0% + +So basically + + align:start position:0% +So basically + + + align:start position:0% +So basically +I have ignored + + align:start position:0% +I have ignored + + + align:start position:0% +I have ignored +the possibility + + align:start position:0% +the possibility + + + align:start position:0% +the possibility +of intersections. + + align:start position:0% +of intersections. + + + align:start position:0% +of intersections. +So + + align:start position:0% +So + + + align:start position:0% +So +let's see when that condition is roughly + + align:start position:0% +let's see when that condition is roughly + + + align:start position:0% +let's see when that condition is roughly +good. + + align:start position:0% +good. + + + align:start position:0% +good. +The kind of entities that I have as I + + align:start position:0% +The kind of entities that I have as I + + + align:start position:0% +The kind of entities that I have as I +get closer and closer to TC in the + + align:start position:0% +get closer and closer to TC in the + + + align:start position:0% +get closer and closer to TC in the +phantom case are these random walks. + + align:start position:0% +phantom case are these random walks. + + + align:start position:0% +phantom case are these random walks. +And we said that the characteristic of a + + align:start position:0% +And we said that the characteristic of a + + + align:start position:0% +And we said that the characteristic of a +random walk is that if I have something + + align:start position:0% +random walk is that if I have something + + + align:start position:0% +random walk is that if I have something +that carries L steps + + align:start position:0% +that carries L steps + + + align:start position:0% +that carries L steps +that the typical size in space + + align:start position:0% +that the typical size in space + + + align:start position:0% +that the typical size in space +that it will grow + + align:start position:0% +that it will grow + + + align:start position:0% +that it will grow +scales like L to the 12, + + align:start position:0% +scales like L to the 12, + + + align:start position:0% +scales like L to the 12, +right? + + align:start position:0% + + + + align:start position:0% + +So we can + + align:start position:0% +So we can + + + align:start position:0% +So we can +recast this as a dimension. + + align:start position:0% +recast this as a dimension. + + + align:start position:0% +recast this as a dimension. +Basically we are used to say linear + + align:start position:0% +Basically we are used to say linear + + + align:start position:0% +Basically we are used to say linear +objects + + align:start position:0% +objects + + + align:start position:0% +objects +having a uh + + align:start position:0% +having a uh + + + align:start position:0% +having a uh +mass + + align:start position:0% +mass + + + align:start position:0% +mass +that grows + + align:start position:0% +that grows + + + align:start position:0% +that grows +u + + align:start position:0% + + + + align:start position:0% + +what do I want to do? + + align:start position:0% +what do I want to do? + + + align:start position:0% +what do I want to do? +Let's say that I have a hyper cube + + align:start position:0% + + + + align:start position:0% + +of size L. + + align:start position:0% +of size L. + + + align:start position:0% +of size L. +Okay, + + align:start position:0% + + + + align:start position:0% + +let's actually call it size R. Okay, + + align:start position:0% +let's actually call it size R. Okay, + + + align:start position:0% +let's actually call it size R. Okay, +then the mass of this or the number of + + align:start position:0% +then the mass of this or the number of + + + align:start position:0% +then the mass of this or the number of +elements that constitute this object + + align:start position:0% +elements that constitute this object + + + align:start position:0% +elements that constitute this object +grow like R to the D. + + align:start position:0% +grow like R to the D. + + + align:start position:0% +grow like R to the D. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So if I take my random walk and think of + + align:start position:0% +So if I take my random walk and think of + + + align:start position:0% +So if I take my random walk and think of +it as something in which every step has + + align:start position:0% +it as something in which every step has + + + align:start position:0% +it as something in which every step has +unit mass, you would say that the L is + + align:start position:0% +unit mass, you would say that the L is + + + align:start position:0% +unit mass, you would say that the L is +proportional to mass. + + align:start position:0% +proportional to mass. + + + align:start position:0% +proportional to mass. +So that the radius grows like the number + + align:start position:0% +So that the radius grows like the number + + + align:start position:0% +So that the radius grows like the number +of elements to the 1/2 power or the mass + + align:start position:0% +of elements to the 1/2 power or the mass + + + align:start position:0% +of elements to the 1/2 power or the mass +to the 1/2 power. So you would say that + + align:start position:0% +to the 1/2 power. So you would say that + + + align:start position:0% +to the 1/2 power. So you would say that +the random walk + + align:start position:0% +the random walk + + + align:start position:0% +the random walk +if I want to force it in terms of a + + align:start position:0% +if I want to force it in terms of a + + + align:start position:0% +if I want to force it in terms of a +relationship between mass and radius + + align:start position:0% +relationship between mass and radius + + + align:start position:0% +relationship between mass and radius +that mass goes like radius squared. + + align:start position:0% +that mass goes like radius squared. + + + align:start position:0% +that mass goes like radius squared. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So in that sense you can say that a + + align:start position:0% +So in that sense you can say that a + + + align:start position:0% +So in that sense you can say that a +random walk + + align:start position:0% +random walk + + + align:start position:0% +random walk +has a fractal or housedorf dimension + + align:start position:0% + + + + align:start position:0% + +of two. + + align:start position:0% +of two. + + + align:start position:0% +of two. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So if you kind of + + align:start position:0% +So if you kind of + + + align:start position:0% +So if you kind of +are very very blind you would say that + + align:start position:0% +are very very blind you would say that + + + align:start position:0% +are very very blind you would say that +uh this is like a random walk. It's a + + align:start position:0% +uh this is like a random walk. It's a + + + align:start position:0% +uh this is like a random walk. It's a +two-dimensional thing. It's a page. + + align:start position:0% +two-dimensional thing. It's a page. + + + align:start position:0% +two-dimensional thing. It's a page. +Right? + + align:start position:0% +Right? + + + align:start position:0% +Right? +So now the question is + + align:start position:0% +So now the question is + + + align:start position:0% +So now the question is +if I have two geometrical entities, + + align:start position:0% +if I have two geometrical entities, + + + align:start position:0% +if I have two geometrical entities, +will they intersect? + + align:start position:0% +will they intersect? + + + align:start position:0% +will they intersect? +So if I have a plane and a line in three + + align:start position:0% +So if I have a plane and a line in three + + + align:start position:0% +So if I have a plane and a line in three +dimensions, they will barely intersect. + + align:start position:0% +dimensions, they will barely intersect. + + + align:start position:0% +dimensions, they will barely intersect. +In four dimensions, they won't + + align:start position:0% +In four dimensions, they won't + + + align:start position:0% +In four dimensions, they won't +intersect. + + align:start position:0% +intersect. + + + align:start position:0% +intersect. +If I have two surfaces that are + + align:start position:0% +If I have two surfaces that are + + + align:start position:0% +If I have two surfaces that are +two-dimensional, in three dimensions + + align:start position:0% +two-dimensional, in three dimensions + + + align:start position:0% +two-dimensional, in three dimensions +they intersect in a line in four + + align:start position:0% +they intersect in a line in four + + + align:start position:0% +they intersect in a line in four +dimensions they would intersect in a + + align:start position:0% +dimensions they would intersect in a + + + align:start position:0% +dimensions they would intersect in a +point and in five dimensions they won't + + align:start position:0% +point and in five dimensions they won't + + + align:start position:0% +point and in five dimensions they won't +generically intersect like two lines + + align:start position:0% +generically intersect like two lines + + + align:start position:0% +generically intersect like two lines +generically don't intersect in three + + align:start position:0% +generically don't intersect in three + + + align:start position:0% +generically don't intersect in three +dimensions. + + align:start position:0% +dimensions. + + + align:start position:0% +dimensions. +So if you ask + + align:start position:0% +So if you ask + + + align:start position:0% +So if you ask +how bad is it that I ignored + + align:start position:0% +how bad is it that I ignored + + + align:start position:0% +how bad is it that I ignored +the intersection of objects that are + + align:start position:0% +the intersection of objects that are + + + align:start position:0% +the intersection of objects that are +inherently + + align:start position:0% +inherently + + + align:start position:0% +inherently +random walky + + align:start position:0% +random walky + + + align:start position:0% +random walky +in sufficiently high dimensions. + + align:start position:0% +in sufficiently high dimensions. + + + align:start position:0% +in sufficiently high dimensions. +I would say the answer geometrically + + align:start position:0% +I would say the answer geometrically + + + align:start position:0% +I would say the answer geometrically +would be intersection + + align:start position:0% +would be intersection + + + align:start position:0% +would be intersection +is generic + + align:start position:0% +is generic + + + align:start position:0% +is generic +if D is less than 2DF which is four. + + align:start position:0% +if D is less than 2DF which is four. + + + align:start position:0% +if D is less than 2DF which is four. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So we made a very drastic assumption + + align:start position:0% +So we made a very drastic assumption + + + align:start position:0% +So we made a very drastic assumption +but as long as we are above four + + align:start position:0% +but as long as we are above four + + + align:start position:0% +but as long as we are above four +dimension + + align:start position:0% +dimension + + + align:start position:0% +dimension +it's okay. I mean there's so much space + + align:start position:0% +it's okay. I mean there's so much space + + + align:start position:0% +it's okay. I mean there's so much space +around + + align:start position:0% +around + + + align:start position:0% +around +that statistically + + align:start position:0% +that statistically + + + align:start position:0% +that statistically +these intersections these non-fantomness + + align:start position:0% +these intersections these non-fantomness + + + align:start position:0% +these intersections these non-fantomness +is so entropically constraining that it + + align:start position:0% +is so entropically constraining that it + + + align:start position:0% +is so entropically constraining that it +never happens. You can ignore it and the + + align:start position:0% +never happens. You can ignore it and the + + + align:start position:0% +never happens. You can ignore it and the +results are okay. But you go to four + + align:start position:0% +results are okay. But you go to four + + + align:start position:0% +results are okay. But you go to four +dimensions and below + + align:start position:0% +dimensions and below + + + align:start position:0% +dimensions and below +you can't ignore it because generically + + align:start position:0% +you can't ignore it because generically + + + align:start position:0% +you can't ignore it because generically +these things will intersect with each + + align:start position:0% +these things will intersect with each + + + align:start position:0% +these things will intersect with each +other. That's why these diagrams are + + align:start position:0% +other. That's why these diagrams are + + + align:start position:0% +other. That's why these diagrams are +going to blow up on you and give you + + align:start position:0% +going to blow up on you and give you + + + align:start position:0% +going to blow up on you and give you +some important contribution that would + + align:start position:0% +some important contribution that would + + + align:start position:0% +some important contribution that would +swell and give you a value of new that + + align:start position:0% +swell and give you a value of new that + + + align:start position:0% +swell and give you a value of new that +is larger than the 1/2 that we have for + + align:start position:0% +is larger than the 1/2 that we have for + + + align:start position:0% +is larger than the 1/2 that we have for +random box. + + align:start position:0% +random box. + + + align:start position:0% +random box. +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +so that's the essence of where the + + align:start position:0% +so that's the essence of where the + + + align:start position:0% +so that's the essence of where the +Gaussian model was. Why we get new + + align:start position:0% +Gaussian model was. Why we get new + + + align:start position:0% +Gaussian model was. Why we get new +equals to 1/2, why we get news that are + + align:start position:0% +equals to 1/2, why we get news that are + + + align:start position:0% +equals to 1/2, why we get news that are +larger than 1/2. what the meaning of + + align:start position:0% +larger than 1/2. what the meaning of + + + align:start position:0% +larger than 1/2. what the meaning of +these diagrams is, what four dimensions + + align:start position:0% +these diagrams is, what four dimensions + + + align:start position:0% +these diagrams is, what four dimensions +is special, all of it really just comes + + align:start position:0% +is special, all of it really just comes + + + align:start position:0% +is special, all of it really just comes +down to central limit theorem and + + align:start position:0% +down to central limit theorem and + + + align:start position:0% +down to central limit theorem and +knowing that the sum of a large number + + align:start position:0% +knowing that the sum of a large number + + + align:start position:0% +knowing that the sum of a large number +of variables has a square root of n type + + align:start position:0% +of variables has a square root of n type + + + align:start position:0% +of variables has a square root of n type +of variance and fluctuations and it's + + align:start position:0% +of variance and fluctuations and it's + + + align:start position:0% +of variance and fluctuations and it's +all captured by that. + + align:start position:0% +all captured by that. + + + align:start position:0% +all captured by that. +So, but we wanted to really solve the + + align:start position:0% +So, but we wanted to really solve the + + + align:start position:0% +So, but we wanted to really solve the +model exactly. It turns out that we can + + align:start position:0% +model exactly. It turns out that we can + + + align:start position:0% +model exactly. It turns out that we can +make the conditions + + align:start position:0% +make the conditions + + + align:start position:0% +make the conditions +that were very hard to implement in + + align:start position:0% +that were very hard to implement in + + + align:start position:0% +that were very hard to implement in +general dimensions to work out correctly + + align:start position:0% +general dimensions to work out correctly + + + align:start position:0% +general dimensions to work out correctly +in two dimensions. + + align:start position:0% +in two dimensions. + + + align:start position:0% +in two dimensions. +And so next lecture we'll show you what + + align:start position:0% +And so next lecture we'll show you what + + + align:start position:0% +And so next lecture we'll show you what +these mistakes are, how to avoid them, + + align:start position:0% +these mistakes are, how to avoid them, + + + align:start position:0% +these mistakes are, how to avoid them, +and how to get the exact value of this + + align:start position:0% +and how to get the exact value of this + + + align:start position:0% +and how to get the exact value of this +sum in two dimensions. \ No newline at end of file diff --git a/vxOO8cIn398.txt b/vxOO8cIn398.txt new file mode 100644 index 0000000000000000000000000000000000000000..15201f4d0cfb9d6773babc5f03692bed2b88b121 --- /dev/null +++ b/vxOO8cIn398.txt @@ -0,0 +1,11507 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +so first some review + + align:start position:0% +so first some review + + + align:start position:0% +so first some review +um last time we were doing unlockable + + align:start position:0% +um last time we were doing unlockable + + + align:start position:0% +um last time we were doing unlockable +and I was you know trying to convince + + align:start position:0% +and I was you know trying to convince + + + align:start position:0% +and I was you know trying to convince +you that it's useful to think of words + + align:start position:0% +you that it's useful to think of words + + + align:start position:0% +you that it's useful to think of words +at least some words as consisting of + + align:start position:0% +at least some words as consisting of + + + align:start position:0% +at least some words as consisting of +multiple Parts we're calling these parts + + align:start position:0% +multiple Parts we're calling these parts + + + align:start position:0% +multiple Parts we're calling these parts +morphemes + + align:start position:0% +morphemes + + + align:start position:0% +morphemes +um and that there's this process of + + align:start position:0% +um and that there's this process of + + + align:start position:0% +um and that there's this process of +combining morphemes we called it merge + + align:start position:0% +combining morphemes we called it merge + + + align:start position:0% +combining morphemes we called it merge +where you take two things two morphemes + + align:start position:0% +where you take two things two morphemes + + + align:start position:0% +where you take two things two morphemes +not necessarily two morphemes two things + + align:start position:0% +not necessarily two morphemes two things + + + align:start position:0% +not necessarily two morphemes two things +and you put them together and you make a + + align:start position:0% +and you put them together and you make a + + + align:start position:0% +and you put them together and you make a +new thing so you can take a morpheme + + align:start position:0% +new thing so you can take a morpheme + + + align:start position:0% +new thing so you can take a morpheme +like un and a morpheme-like lock and you + + align:start position:0% +like un and a morpheme-like lock and you + + + align:start position:0% +like un and a morpheme-like lock and you +can put them together to make a verb + + align:start position:0% +can put them together to make a verb + + + align:start position:0% +can put them together to make a verb +unlock + + align:start position:0% + + + + align:start position:0% + +um and so I just corrected myself + + align:start position:0% +um and so I just corrected myself + + + align:start position:0% +um and so I just corrected myself +sometimes the two things you take are + + align:start position:0% +sometimes the two things you take are + + + align:start position:0% +sometimes the two things you take are +morphemes but sometimes they are the + + align:start position:0% +morphemes but sometimes they are the + + + align:start position:0% +morphemes but sometimes they are the +results of previous instances of merge + + align:start position:0% +results of previous instances of merge + + + align:start position:0% +results of previous instances of merge +so you can also take this thing unlock + + align:start position:0% +so you can also take this thing unlock + + + align:start position:0% +so you can also take this thing unlock +that you've made as a result of merging + + align:start position:0% +that you've made as a result of merging + + + align:start position:0% +that you've made as a result of merging +on unlock and merge that with a bull to + + align:start position:0% +on unlock and merge that with a bull to + + + align:start position:0% +on unlock and merge that with a bull to +get you unlockable yeah that procedure + + align:start position:0% +get you unlockable yeah that procedure + + + align:start position:0% +get you unlockable yeah that procedure +that I just ran through is what gives + + align:start position:0% +that I just ran through is what gives + + + align:start position:0% +that I just ran through is what gives +you the tree on the left so the trees + + align:start position:0% +you the tree on the left so the trees + + + align:start position:0% +you the tree on the left so the trees +there are meant to be representations of + + align:start position:0% +there are meant to be representations of + + + align:start position:0% +there are meant to be representations of +the order in which you did things yeah + + align:start position:0% +the order in which you did things yeah + + + align:start position:0% +the order in which you did things yeah +so the the uh the tree on the left is a + + align:start position:0% +so the the uh the tree on the left is a + + + align:start position:0% +so the the uh the tree on the left is a +representation of of uh two merge + + align:start position:0% +representation of of uh two merge + + + align:start position:0% +representation of of uh two merge +operations first merging on with lock + + align:start position:0% +operations first merging on with lock + + + align:start position:0% +operations first merging on with lock +and then merging able with unlock giving + + align:start position:0% +and then merging able with unlock giving + + + align:start position:0% +and then merging able with unlock giving +you an adjective that means uh + + align:start position:0% +you an adjective that means uh + + + align:start position:0% +you an adjective that means uh +you know a functioning lock able to be + + align:start position:0% +you know a functioning lock able to be + + + align:start position:0% +you know a functioning lock able to be +unlocked this is all the stuff we went + + align:start position:0% +unlocked this is all the stuff we went + + + align:start position:0% +unlocked this is all the stuff we went +through last time + + align:start position:0% +through last time + + + align:start position:0% +through last time +and this is why the word unlockable is + + align:start position:0% +and this is why the word unlockable is + + + align:start position:0% +and this is why the word unlockable is +ambiguous because well there are two + + align:start position:0% +ambiguous because well there are two + + + align:start position:0% +ambiguous because well there are two +ways that you can assemble it and the + + align:start position:0% +ways that you can assemble it and the + + + align:start position:0% +ways that you can assemble it and the +two ways give you different + + align:start position:0% +two ways give you different + + + align:start position:0% +two ways give you different +interpretations + + align:start position:0% +interpretations + + + align:start position:0% +interpretations +are there any questions about any of + + align:start position:0% +are there any questions about any of + + + align:start position:0% +are there any questions about any of +that this is all stuff we did last time + + align:start position:0% + + + + align:start position:0% + +so that's that's what we were doing with + + align:start position:0% +so that's that's what we were doing with + + + align:start position:0% +so that's that's what we were doing with +unlockable and then we also said and we + + align:start position:0% +unlockable and then we also said and we + + + align:start position:0% +unlockable and then we also said and we +talked about this a little bit there + + align:start position:0% +talked about this a little bit there + + + align:start position:0% +talked about this a little bit there +need to be some statements about what's + + align:start position:0% +need to be some statements about what's + + + align:start position:0% +need to be some statements about what's +called allomorphy so sometimes you don't + + align:start position:0% +called allomorphy so sometimes you don't + + + align:start position:0% +called allomorphy so sometimes you don't +just peacefully put morphemes next to + + align:start position:0% +just peacefully put morphemes next to + + + align:start position:0% +just peacefully put morphemes next to +each other they change as a result of + + align:start position:0% +each other they change as a result of + + + align:start position:0% +each other they change as a result of +being next to another morpheme the + + align:start position:0% +being next to another morpheme the + + + align:start position:0% +being next to another morpheme the +result is what's called alamorphy so a + + align:start position:0% +result is what's called alamorphy so a + + + align:start position:0% +result is what's called alamorphy so a +morpheme can have allomorphs different + + align:start position:0% +morpheme can have allomorphs different + + + align:start position:0% +morpheme can have allomorphs different +forms that it has depending on its + + align:start position:0% +forms that it has depending on its + + + align:start position:0% +forms that it has depending on its +environment + + align:start position:0% +environment + + + align:start position:0% +environment +sometimes our statements of alamorphy + + align:start position:0% +sometimes our statements of alamorphy + + + align:start position:0% +sometimes our statements of alamorphy +will have to be very specific to the + + align:start position:0% +will have to be very specific to the + + + align:start position:0% +will have to be very specific to the +morphemes in question so you know we'll + + align:start position:0% +morphemes in question so you know we'll + + + align:start position:0% +morphemes in question so you know we'll +say that when you you merge go together + + align:start position:0% +say that when you you merge go together + + + align:start position:0% +say that when you you merge go together +with past tense that the result is went + + align:start position:0% +with past tense that the result is went + + + align:start position:0% +with past tense that the result is went +and that's not the result of a general + + align:start position:0% +and that's not the result of a general + + + align:start position:0% +and that's not the result of a general +process that's something you just have + + align:start position:0% +process that's something you just have + + + align:start position:0% +process that's something you just have +to look up when you look up the word Go + + align:start position:0% +to look up when you look up the word Go + + + align:start position:0% +to look up when you look up the word Go +in English yeah + + align:start position:0% +in English yeah + + + align:start position:0% +in English yeah +um or that when you add IDI to something + + align:start position:0% +um or that when you add IDI to something + + + align:start position:0% +um or that when you add IDI to something +ending in ick like electric that the k + + align:start position:0% +ending in ick like electric that the k + + + align:start position:0% +ending in ick like electric that the k +sound at the end of ick will be + + align:start position:0% +sound at the end of ick will be + + + align:start position:0% +sound at the end of ick will be +pronounced like an S you get electricity + + align:start position:0% +pronounced like an S you get electricity + + + align:start position:0% +pronounced like an S you get electricity +and not electricity + + align:start position:0% +and not electricity + + + align:start position:0% +and not electricity +so sometimes these are statements about + + align:start position:0% +so sometimes these are statements about + + + align:start position:0% +so sometimes these are statements about +particular morphemes and what they do + + align:start position:0% +particular morphemes and what they do + + + align:start position:0% +particular morphemes and what they do +when they combine + + align:start position:0% +when they combine + + + align:start position:0% +when they combine +other times we'll be able to do + + align:start position:0% +other times we'll be able to do + + + align:start position:0% +other times we'll be able to do +allomorphy via more general rules so we + + align:start position:0% +allomorphy via more general rules so we + + + align:start position:0% +allomorphy via more general rules so we +didn't spend some time talking about + + align:start position:0% +didn't spend some time talking about + + + align:start position:0% +didn't spend some time talking about +polish + + align:start position:0% +polish + + + align:start position:0% +polish +where we convinced ourselves that it's + + align:start position:0% +where we convinced ourselves that it's + + + align:start position:0% +where we convinced ourselves that it's +useful to think that polish has a + + align:start position:0% +useful to think that polish has a + + + align:start position:0% +useful to think that polish has a +general rule which we'll Circle back and + + align:start position:0% +general rule which we'll Circle back and + + + align:start position:0% +general rule which we'll Circle back and +talk about more uh later on a general + + align:start position:0% +talk about more uh later on a general + + + align:start position:0% +talk about more uh later on a general +rule that says that if you have a g at + + align:start position:0% +rule that says that if you have a g at + + + align:start position:0% +rule that says that if you have a g at +the end of a word it becomes a k so in + + align:start position:0% +the end of a word it becomes a k so in + + + align:start position:0% +the end of a word it becomes a k so in +Polish uh uh there are various words + + align:start position:0% +Polish uh uh there are various words + + + align:start position:0% +Polish uh uh there are various words +that when you pronounce them they seem + + align:start position:0% +that when you pronounce them they seem + + + align:start position:0% +that when you pronounce them they seem +to end in K and then we saw that if you + + align:start position:0% +to end in K and then we saw that if you + + + align:start position:0% +to end in K and then we saw that if you +add a suffix so that the K is no longer + + align:start position:0% +add a suffix so that the K is no longer + + + align:start position:0% +add a suffix so that the K is no longer +at the end of a word sometimes it really + + align:start position:0% +at the end of a word sometimes it really + + + align:start position:0% +at the end of a word sometimes it really +was a K in which case it stays okay but + + align:start position:0% +was a K in which case it stays okay but + + + align:start position:0% +was a K in which case it stays okay but +sometimes it was a g concealing itself + + align:start position:0% +sometimes it was a g concealing itself + + + align:start position:0% +sometimes it was a g concealing itself +as a k and it reveals its true self as a + + align:start position:0% +as a k and it reveals its true self as a + + + align:start position:0% +as a k and it reveals its true self as a +g when you add a suffix yep + + align:start position:0% +g when you add a suffix yep + + + align:start position:0% +g when you add a suffix yep +crash course in Polish now you know as + + align:start position:0% +crash course in Polish now you know as + + + align:start position:0% +crash course in Polish now you know as +much about polish as I do which is not + + align:start position:0% +much about polish as I do which is not + + + align:start position:0% +much about polish as I do which is not +any this is all reviewed does this all + + align:start position:0% +any this is all reviewed does this all + + + align:start position:0% +any this is all reviewed does this all +make sense no questions okay + + align:start position:0% +make sense no questions okay + + + align:start position:0% +make sense no questions okay +all right so one of the things that we + + align:start position:0% +all right so one of the things that we + + + align:start position:0% +all right so one of the things that we +did several times in fact I casually did + + align:start position:0% +did several times in fact I casually did + + + align:start position:0% +did several times in fact I casually did +it on the last slide was to use words + + align:start position:0% +it on the last slide was to use words + + + align:start position:0% +it on the last slide was to use words +like noun and adjective and um I thought + + align:start position:0% +like noun and adjective and um I thought + + + align:start position:0% +like noun and adjective and um I thought +we should just take a second to talk + + align:start position:0% +we should just take a second to talk + + + align:start position:0% +we should just take a second to talk +about what we mean when we say words + + align:start position:0% +about what we mean when we say words + + + align:start position:0% +about what we mean when we say words +like that + + align:start position:0% +like that + + + align:start position:0% +like that +um I bet that a lot of you were taught + + align:start position:0% +um I bet that a lot of you were taught + + + align:start position:0% +um I bet that a lot of you were taught +what nouns and adjectives are but it's + + align:start position:0% +what nouns and adjectives are but it's + + + align:start position:0% +what nouns and adjectives are but it's +possible that some of you were not and I + + align:start position:0% +possible that some of you were not and I + + + align:start position:0% +possible that some of you were not and I +know that some of you are not native + + align:start position:0% +know that some of you are not native + + + align:start position:0% +know that some of you are not native +speakers of English and this might not + + align:start position:0% +speakers of English and this might not + + + align:start position:0% +speakers of English and this might not +be high on my list of words to learn if + + align:start position:0% +be high on my list of words to learn if + + + align:start position:0% +be high on my list of words to learn if +I were learning another language + + align:start position:0% +I were learning another language + + + align:start position:0% +I were learning another language +um wow my power chord has turned into a + + align:start position:0% +um wow my power chord has turned into a + + + align:start position:0% +um wow my power chord has turned into a +pretzel this is pretty impressive I + + align:start position:0% +pretzel this is pretty impressive I + + + align:start position:0% +pretzel this is pretty impressive I +didn't know they did that + + align:start position:0% +didn't know they did that + + + align:start position:0% +didn't know they did that +um + + align:start position:0% +um + + + align:start position:0% +um +so uh I wanted to just talk briefly + + align:start position:0% +so uh I wanted to just talk briefly + + + align:start position:0% +so uh I wanted to just talk briefly +about that before we go any further into + + align:start position:0% +about that before we go any further into + + + align:start position:0% +about that before we go any further into +into morphology uh what's a noun + + align:start position:0% +into morphology uh what's a noun + + + align:start position:0% +into morphology uh what's a noun +you guys maybe some of you were taught + + align:start position:0% +you guys maybe some of you were taught + + + align:start position:0% +you guys maybe some of you were taught +what a noun is yes + + align:start position:0% +what a noun is yes + + + align:start position:0% +what a noun is yes +an object or a thing yeah anybody else + + align:start position:0% +an object or a thing yeah anybody else + + + align:start position:0% +an object or a thing yeah anybody else +taught things like that about what nouns + + align:start position:0% +taught things like that about what nouns + + + align:start position:0% +taught things like that about what nouns +are yeah yes + + align:start position:0% + + + + align:start position:0% + +a signifier of a particular matter I I + + align:start position:0% +a signifier of a particular matter I I + + + align:start position:0% +a signifier of a particular matter I I +like that that's a very classy + + align:start position:0% +like that that's a very classy + + + align:start position:0% +like that that's a very classy +definition yes + + align:start position:0% + + + + align:start position:0% + +yeah so I was taught that a person + + align:start position:0% +yeah so I was taught that a person + + + align:start position:0% +yeah so I was taught that a person +actually I was taught a person place or + + align:start position:0% +actually I was taught a person place or + + + align:start position:0% +actually I was taught a person place or +thing yeah yeah and then later I learned + + align:start position:0% +thing yeah yeah and then later I learned + + + align:start position:0% +thing yeah yeah and then later I learned +that you know kids today were learning + + align:start position:0% +that you know kids today were learning + + + align:start position:0% +that you know kids today were learning +that it was also idea I guess on the + + align:start position:0% +that it was also idea I guess on the + + + align:start position:0% +that it was also idea I guess on the +idea that ideas are not things which I + + align:start position:0% +idea that ideas are not things which I + + + align:start position:0% +idea that ideas are not things which I +guess I guess they're not so these are + + align:start position:0% +guess I guess they're not so these are + + + align:start position:0% +guess I guess they're not so these are +all definitions of noun that um make + + align:start position:0% +all definitions of noun that um make + + + align:start position:0% +all definitions of noun that um make +reference to the kinds of things that + + align:start position:0% +reference to the kinds of things that + + + align:start position:0% +reference to the kinds of things that +nouns mean right so that they they refer + + align:start position:0% +nouns mean right so that they they refer + + + align:start position:0% +nouns mean right so that they they refer +to uh people or ideas or things or yeah + + align:start position:0% +to uh people or ideas or things or yeah + + + align:start position:0% +to uh people or ideas or things or yeah +that's what nouns are and that's fine if + + align:start position:0% +that's what nouns are and that's fine if + + + align:start position:0% +that's what nouns are and that's fine if +that works for you uh that's uh that + + align:start position:0% +that works for you uh that's uh that + + + align:start position:0% +that works for you uh that's uh that +might be the best way for you to think + + align:start position:0% +might be the best way for you to think + + + align:start position:0% +might be the best way for you to think +about nouns + + align:start position:0% +about nouns + + + align:start position:0% +about nouns +um here's another way of thinking about + + align:start position:0% +um here's another way of thinking about + + + align:start position:0% +um here's another way of thinking about +it which you can use if you want to if + + align:start position:0% +it which you can use if you want to if + + + align:start position:0% +it which you can use if you want to if +you're ever confused about whether + + align:start position:0% +you're ever confused about whether + + + align:start position:0% +you're ever confused about whether +something is a noun or not if you find + + align:start position:0% +something is a noun or not if you find + + + align:start position:0% +something is a noun or not if you find +yourself you know as you go further in + + align:start position:0% +yourself you know as you go further in + + + align:start position:0% +yourself you know as you go further in +linguistics every so often you will yeah + + align:start position:0% +linguistics every so often you will yeah + + + align:start position:0% +linguistics every so often you will yeah +part of the point of higher education is + + align:start position:0% +part of the point of higher education is + + + align:start position:0% +part of the point of higher education is +to make you like doubt yourself and be + + align:start position:0% +to make you like doubt yourself and be + + + align:start position:0% +to make you like doubt yourself and be +unhappy things that you were sure that + + align:start position:0% +unhappy things that you were sure that + + + align:start position:0% +unhappy things that you were sure that +you understood all of a sudden you're + + align:start position:0% +you understood all of a sudden you're + + + align:start position:0% +you understood all of a sudden you're +like wait do I really deeply understand + + align:start position:0% +like wait do I really deeply understand + + + align:start position:0% +like wait do I really deeply understand +that and uh um it's meant to undermine + + align:start position:0% +that and uh um it's meant to undermine + + + align:start position:0% +that and uh um it's meant to undermine +your emotional security basically that's + + align:start position:0% +your emotional security basically that's + + + align:start position:0% +your emotional security basically that's +that's what education is for + + align:start position:0% +that's what education is for + + + align:start position:0% +that's what education is for +um so here's another way of thinking + + align:start position:0% +um so here's another way of thinking + + + align:start position:0% +um so here's another way of thinking +about what nouns are + + align:start position:0% +about what nouns are + + + align:start position:0% +about what nouns are +um if you're making a sentence let's say + + align:start position:0% +um if you're making a sentence let's say + + + align:start position:0% +um if you're making a sentence let's say +putting a sentence together is like + + align:start position:0% +putting a sentence together is like + + + align:start position:0% +putting a sentence together is like +putting together any other complicated + + align:start position:0% +putting together any other complicated + + + align:start position:0% +putting together any other complicated +thing with lots of Parts take your + + align:start position:0% +thing with lots of Parts take your + + + align:start position:0% +thing with lots of Parts take your +favorite example of that a jigsaw puzzle + + align:start position:0% +favorite example of that a jigsaw puzzle + + + align:start position:0% +favorite example of that a jigsaw puzzle +or a model airplane or whatever or Ikea + + align:start position:0% +or a model airplane or whatever or Ikea + + + align:start position:0% +or a model airplane or whatever or Ikea +furniture if you've ever assembled that + + align:start position:0% +furniture if you've ever assembled that + + + align:start position:0% +furniture if you've ever assembled that +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +um if you're ever assembling things like + + align:start position:0% +um if you're ever assembling things like + + + align:start position:0% +um if you're ever assembling things like +that + + align:start position:0% +that + + + align:start position:0% +that +um you know they have different parts + + align:start position:0% +um you know they have different parts + + + align:start position:0% +um you know they have different parts +with different shapes that go in + + align:start position:0% +with different shapes that go in + + + align:start position:0% +with different shapes that go in +different places right if you're making + + align:start position:0% +different places right if you're making + + + align:start position:0% +different places right if you're making +a model airplane there are the wheels + + align:start position:0% +a model airplane there are the wheels + + + align:start position:0% +a model airplane there are the wheels +and the wheels go well where the wheels + + align:start position:0% +and the wheels go well where the wheels + + + align:start position:0% +and the wheels go well where the wheels +go you know if you're making an Ikea + + align:start position:0% +go you know if you're making an Ikea + + + align:start position:0% +go you know if you're making an Ikea +chair there are uh you know various you + + align:start position:0% +chair there are uh you know various you + + + align:start position:0% +chair there are uh you know various you +know boards but then there are also + + align:start position:0% +know boards but then there are also + + + align:start position:0% +know boards but then there are also +screws and they're right there are + + align:start position:0% +screws and they're right there are + + + align:start position:0% +screws and they're right there are +things that you're supposed to put in + + align:start position:0% +things that you're supposed to put in + + + align:start position:0% +things that you're supposed to put in +particular places + + align:start position:0% +particular places + + + align:start position:0% +particular places +um and you could name those things by + + align:start position:0% +um and you could name those things by + + + align:start position:0% +um and you could name those things by +their shapes right so you could talk + + align:start position:0% +their shapes right so you could talk + + + align:start position:0% +their shapes right so you could talk +about the wheel on an airplane or the + + align:start position:0% +about the wheel on an airplane or the + + + align:start position:0% +about the wheel on an airplane or the +the uh The Edge piece on a jigsaw puzzle + + align:start position:0% +the uh The Edge piece on a jigsaw puzzle + + + align:start position:0% +the uh The Edge piece on a jigsaw puzzle +and you can also kind of name them by + + align:start position:0% +and you can also kind of name them by + + + align:start position:0% +and you can also kind of name them by +their by their functions you know if you + + align:start position:0% +their by their functions you know if you + + + align:start position:0% +their by their functions you know if you +were weren't sure what an edge piece was + + align:start position:0% +were weren't sure what an edge piece was + + + align:start position:0% +were weren't sure what an edge piece was +well it would be you know the piece that + + align:start position:0% +well it would be you know the piece that + + + align:start position:0% +well it would be you know the piece that +goes on the edge of the jigsaw puzzle + + align:start position:0% +goes on the edge of the jigsaw puzzle + + + align:start position:0% +goes on the edge of the jigsaw puzzle +the one that goes on the outside + + align:start position:0% +the one that goes on the outside + + + align:start position:0% +the one that goes on the outside +and I guess kind of similarly + + align:start position:0% +and I guess kind of similarly + + + align:start position:0% +and I guess kind of similarly +noun when we say that something is a + + align:start position:0% +noun when we say that something is a + + + align:start position:0% +noun when we say that something is a +noun what we mean is that it's something + + align:start position:0% +noun what we mean is that it's something + + + align:start position:0% +noun what we mean is that it's something +that goes where nouns go you know kind + + align:start position:0% +that goes where nouns go you know kind + + + align:start position:0% +that goes where nouns go you know kind +of like an edge piece is a piece that + + align:start position:0% +of like an edge piece is a piece that + + + align:start position:0% +of like an edge piece is a piece that +goes on the edge right so if you're + + align:start position:0% +goes on the edge right so if you're + + + align:start position:0% +goes on the edge right so if you're +putting a sentence together there are + + align:start position:0% +putting a sentence together there are + + + align:start position:0% +putting a sentence together there are +parts of the sentence where nouns belong + + align:start position:0% +parts of the sentence where nouns belong + + + align:start position:0% +parts of the sentence where nouns belong +and noun is just a name for the class of + + align:start position:0% +and noun is just a name for the class of + + + align:start position:0% +and noun is just a name for the class of +things that can go in those places + + align:start position:0% +things that can go in those places + + + align:start position:0% +things that can go in those places +so I mean for example + + align:start position:0% +so I mean for example + + + align:start position:0% +so I mean for example +if you can grammatically finish a + + align:start position:0% +if you can grammatically finish a + + + align:start position:0% +if you can grammatically finish a +sentence with a single word a sentence + + align:start position:0% +sentence with a single word a sentence + + + align:start position:0% +sentence with a single word a sentence +like we are talking about blank or we + + align:start position:0% +like we are talking about blank or we + + + align:start position:0% +like we are talking about blank or we +are talking about V blank + + align:start position:0% +are talking about V blank + + + align:start position:0% +are talking about V blank +then it's a noun + + align:start position:0% +then it's a noun + + + align:start position:0% +then it's a noun +and I'm saying this partly as a + + align:start position:0% +and I'm saying this partly as a + + + align:start position:0% +and I'm saying this partly as a +challenge try to show me that I'm wrong + + align:start position:0% +challenge try to show me that I'm wrong + + + align:start position:0% +challenge try to show me that I'm wrong +yes + + align:start position:0% + + + + align:start position:0% + +you don't you're right so we are talking + + align:start position:0% +you don't you're right so we are talking + + + align:start position:0% +you don't you're right so we are talking +about him so him gets to count as a noun + + align:start position:0% +about him so him gets to count as a noun + + + align:start position:0% +about him so him gets to count as a noun +and we would want pronouns to be a + + align:start position:0% +and we would want pronouns to be a + + + align:start position:0% +and we would want pronouns to be a +particular subspecies of noun + + align:start position:0% +particular subspecies of noun + + + align:start position:0% +particular subspecies of noun +um that might not be such a bad result + + align:start position:0% +um that might not be such a bad result + + + align:start position:0% +um that might not be such a bad result +yes + + align:start position:0% + + + + align:start position:0% + +yeah so we're talking about Mary uh Mary + + align:start position:0% +yeah so we're talking about Mary uh Mary + + + align:start position:0% +yeah so we're talking about Mary uh Mary +would be a noun and that's probably + + align:start position:0% +would be a noun and that's probably + + + align:start position:0% +would be a noun and that's probably +right Mary should probably be a noun yes + + align:start position:0% + + + + align:start position:0% + +it's a gerund yeah so this is one of the + + align:start position:0% +it's a gerund yeah so this is one of the + + + align:start position:0% +it's a gerund yeah so this is one of the +places where you're supposed to be + + align:start position:0% +places where you're supposed to be + + + align:start position:0% +places where you're supposed to be +filled with emotional angst wait running + + align:start position:0% +filled with emotional angst wait running + + + align:start position:0% +filled with emotional angst wait running +it's got run in it that looks like a + + align:start position:0% +it's got run in it that looks like a + + + align:start position:0% +it's got run in it that looks like a +verb but it's a verb that's been + + align:start position:0% +verb but it's a verb that's been + + + align:start position:0% +verb but it's a verb that's been +converted into a noun so that we can put + + align:start position:0% +converted into a noun so that we can put + + + align:start position:0% +converted into a noun so that we can put +it in this sentence that's what a gerund + + align:start position:0% +it in this sentence that's what a gerund + + + align:start position:0% +it in this sentence that's what a gerund +is it's a name for a verb that's been + + align:start position:0% +is it's a name for a verb that's been + + + align:start position:0% +is it's a name for a verb that's been +turned into a noun + + align:start position:0% +turned into a noun + + + align:start position:0% +turned into a noun +yeah good point + + align:start position:0% +yeah good point + + + align:start position:0% +yeah good point +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +okay so I invite you to try to come up + + align:start position:0% +okay so I invite you to try to come up + + + align:start position:0% +okay so I invite you to try to come up +with sentences like this for your for + + align:start position:0% +with sentences like this for your for + + + align:start position:0% +with sentences like this for your for +your favorite parts of speech here's + + align:start position:0% +your favorite parts of speech here's + + + align:start position:0% +your favorite parts of speech here's +another one uh if you can grammatically + + align:start position:0% +another one uh if you can grammatically + + + align:start position:0% +another one uh if you can grammatically +finish a sentence like I consider her + + align:start position:0% +finish a sentence like I consider her + + + align:start position:0% +finish a sentence like I consider her +blank + + align:start position:0% +blank + + + align:start position:0% +blank +and the result is a sentence that means + + align:start position:0% +and the result is a sentence that means + + + align:start position:0% +and the result is a sentence that means +I think that she is blank + + align:start position:0% +I think that she is blank + + + align:start position:0% +I think that she is blank +so I consider her tall or brilliant or + + align:start position:0% +so I consider her tall or brilliant or + + + align:start position:0% +so I consider her tall or brilliant or +whatever + + align:start position:0% +whatever + + + align:start position:0% +whatever +then that's an adjective the thing + + align:start position:0% +then that's an adjective the thing + + + align:start position:0% +then that's an adjective the thing +that's in the blank + + align:start position:0% + + + + align:start position:0% + +sometimes the sentences will not make a + + align:start position:0% +sometimes the sentences will not make a + + + align:start position:0% +sometimes the sentences will not make a +whole lot of sense right so I consider + + align:start position:0% +whole lot of sense right so I consider + + + align:start position:0% +whole lot of sense right so I consider +her autumnal + + align:start position:0% +her autumnal + + + align:start position:0% +her autumnal +um it's not clear what that means but + + align:start position:0% +um it's not clear what that means but + + + align:start position:0% +um it's not clear what that means but +it's if you compare it with I consider + + align:start position:0% +it's if you compare it with I consider + + + align:start position:0% +it's if you compare it with I consider +her run + + align:start position:0% +her run + + + align:start position:0% +her run +so I consider her run just makes no + + align:start position:0% +so I consider her run just makes no + + + align:start position:0% +so I consider her run just makes no +sense at all whereas I consider her + + align:start position:0% +sense at all whereas I consider her + + + align:start position:0% +sense at all whereas I consider her +autumnal I sound deeply poetic I guess + + align:start position:0% +autumnal I sound deeply poetic I guess + + + align:start position:0% +autumnal I sound deeply poetic I guess +and you wonder what I mean by that yeah + + align:start position:0% +and you wonder what I mean by that yeah + + + align:start position:0% +and you wonder what I mean by that yeah +yeah but so autumnal is an adjective run + + align:start position:0% +yeah but so autumnal is an adjective run + + + align:start position:0% +yeah but so autumnal is an adjective run +is not an adjective + + align:start position:0% +is not an adjective + + + align:start position:0% +is not an adjective +and I have this bit about that it has to + + align:start position:0% +and I have this bit about that it has to + + + align:start position:0% +and I have this bit about that it has to +mean I think she is blank because you + + align:start position:0% +mean I think she is blank because you + + + align:start position:0% +mean I think she is blank because you +know you can say things like I consider + + align:start position:0% +know you can say things like I consider + + + align:start position:0% +know you can say things like I consider +her often + + align:start position:0% +her often + + + align:start position:0% +her often +that means I think about her often often + + align:start position:0% +that means I think about her often often + + + align:start position:0% +that means I think about her often often +is not an adjective because if I say I + + align:start position:0% +is not an adjective because if I say I + + + align:start position:0% +is not an adjective because if I say I +consider her often I don't mean I think + + align:start position:0% +consider her often I don't mean I think + + + align:start position:0% +consider her often I don't mean I think +that she is often + + align:start position:0% +that she is often + + + align:start position:0% +that she is often +that's not what that means so so often + + align:start position:0% +that's not what that means so so often + + + align:start position:0% +that's not what that means so so often +is not an adjective it's an adverb + + align:start position:0% +is not an adjective it's an adverb + + + align:start position:0% +is not an adjective it's an adverb +actually + + align:start position:0% +actually + + + align:start position:0% +actually +I'm not going to make you go through + + align:start position:0% +I'm not going to make you go through + + + align:start position:0% +I'm not going to make you go through +this for all the parts of speech but + + align:start position:0% +this for all the parts of speech but + + + align:start position:0% +this for all the parts of speech but +this is an interesting exercise yes + + align:start position:0% + + + + align:start position:0% + +uh-huh + + align:start position:0% + + + + align:start position:0% + +I consider her coming + + align:start position:0% + + + + align:start position:0% + +I'm full of doubt and angst + + align:start position:0% + + + + align:start position:0% + +so there is a parse of that I consider + + align:start position:0% +so there is a parse of that I consider + + + align:start position:0% +so there is a parse of that I consider +her coming which means I am thinking + + align:start position:0% +her coming which means I am thinking + + + align:start position:0% +her coming which means I am thinking +about the fact that she is coming + + align:start position:0% +about the fact that she is coming + + + align:start position:0% +about the fact that she is coming +you can mean that I think + + align:start position:0% +you can mean that I think + + + align:start position:0% +you can mean that I think +I consider her + + align:start position:0% +I consider her + + + align:start position:0% +I consider her +can it mean I can I believe that she is + + align:start position:0% +can it mean I can I believe that she is + + + align:start position:0% +can it mean I can I believe that she is +coming + + align:start position:0% + + + + align:start position:0% + +I know there are other English speakers + + align:start position:0% +I know there are other English speakers + + + align:start position:0% +I know there are other English speakers +in this room what do you guys think yes + + align:start position:0% + + + + align:start position:0% + +exactly oh + + align:start position:0% +exactly oh + + + align:start position:0% +exactly oh +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +yeah so um but I think + + align:start position:0% +yeah so um but I think + + + align:start position:0% +yeah so um but I think +uh I'm sorry what's your name is it + + align:start position:0% +uh I'm sorry what's your name is it + + + align:start position:0% +uh I'm sorry what's your name is it +Ivana no + + align:start position:0% +Ivana no + + + align:start position:0% +Ivana no +sorry what is your what is your name the + + align:start position:0% +sorry what is your what is your name the + + + align:start position:0% +sorry what is your what is your name the +you were you were asking about I + + align:start position:0% +you were you were asking about I + + + align:start position:0% +you were you were asking about I +consider her coming just a second ago + + align:start position:0% +consider her coming just a second ago + + + align:start position:0% +consider her coming just a second ago +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +sorry Vlada okay I got you wrong sorry + + align:start position:0% +sorry Vlada okay I got you wrong sorry + + + align:start position:0% +sorry Vlada okay I got you wrong sorry +uh Vlad is asking about whether it's + + align:start position:0% +uh Vlad is asking about whether it's + + + align:start position:0% +uh Vlad is asking about whether it's +possible to have a formula coming + + align:start position:0% +possible to have a formula coming + + + align:start position:0% +possible to have a formula coming +as an adjective here + + align:start position:0% +as an adjective here + + + align:start position:0% +as an adjective here +forms like coming can be adjectives + + align:start position:0% +forms like coming can be adjectives + + + align:start position:0% +forms like coming can be adjectives +um so you can say things like the coming + + align:start position:0% +um so you can say things like the coming + + + align:start position:0% +um so you can say things like the coming +Century right where coming is being used + + align:start position:0% +Century right where coming is being used + + + align:start position:0% +Century right where coming is being used +as an adjective so I said a second ago + + align:start position:0% +as an adjective so I said a second ago + + + align:start position:0% +as an adjective so I said a second ago +um running can be a noun right we're + + align:start position:0% +um running can be a noun right we're + + + align:start position:0% +um running can be a noun right we're +talking about running + + align:start position:0% +talking about running + + + align:start position:0% +talking about running +um this is one of many tricky things + + align:start position:0% +um this is one of many tricky things + + + align:start position:0% +um this is one of many tricky things +about English forms of verbs that end in + + align:start position:0% +about English forms of verbs that end in + + + align:start position:0% +about English forms of verbs that end in +ing can be nouns and then we call them + + align:start position:0% +ing can be nouns and then we call them + + + align:start position:0% +ing can be nouns and then we call them +gerunds they can also be participles uh + + align:start position:0% +gerunds they can also be participles uh + + + align:start position:0% +gerunds they can also be participles uh +and then we call them adjectives + + align:start position:0% +and then we call them adjectives + + + align:start position:0% +and then we call them adjectives +um sorry they can they can also be + + align:start position:0% +um sorry they can they can also be + + + align:start position:0% +um sorry they can they can also be +adjectives and then we call them + + align:start position:0% +adjectives and then we call them + + + align:start position:0% +adjectives and then we call them +participles let me do that again ing if + + align:start position:0% +participles let me do that again ing if + + + align:start position:0% +participles let me do that again ing if +you add it to a noun there's an ing that + + align:start position:0% +you add it to a noun there's an ing that + + + align:start position:0% +you add it to a noun there's an ing that +you add to a noun that makes it into a + + align:start position:0% +you add to a noun that makes it into a + + + align:start position:0% +you add to a noun that makes it into a +sorry there's an ing that you add to a + + align:start position:0% +sorry there's an ing that you add to a + + + align:start position:0% +sorry there's an ing that you add to a +verb that makes it into a noun yeah + + align:start position:0% +verb that makes it into a noun yeah + + + align:start position:0% +verb that makes it into a noun yeah +that's the that's when it's adjourned + + align:start position:0% +that's the that's when it's adjourned + + + align:start position:0% +that's the that's when it's adjourned +like in uh we're talking about running + + align:start position:0% +like in uh we're talking about running + + + align:start position:0% +like in uh we're talking about running +there's an ing that you add to a verb + + align:start position:0% +there's an ing that you add to a verb + + + align:start position:0% +there's an ing that you add to a verb +that makes it into an adjective and + + align:start position:0% +that makes it into an adjective and + + + align:start position:0% +that makes it into an adjective and +that's a present participle that's the + + align:start position:0% +that's a present participle that's the + + + align:start position:0% +that's a present participle that's the +kind of thing Vlada is asking about so + + align:start position:0% +kind of thing Vlada is asking about so + + + align:start position:0% +kind of thing Vlada is asking about so +the coming Century or a running man + + align:start position:0% +the coming Century or a running man + + + align:start position:0% +the coming Century or a running man +those Runnings are those ing verbs are + + align:start position:0% +those Runnings are those ing verbs are + + + align:start position:0% +those Runnings are those ing verbs are +are adjectives they're participles sort + + align:start position:0% +are adjectives they're participles sort + + + align:start position:0% +are adjectives they're participles sort +of of like if we go back to un we + + align:start position:0% +of of like if we go back to un we + + + align:start position:0% +of of like if we go back to un we +convinced ourselves that un has a couple + + align:start position:0% +convinced ourselves that un has a couple + + + align:start position:0% +convinced ourselves that un has a couple +different forms + + align:start position:0% +different forms + + + align:start position:0% +different forms +that it can attach either to an + + align:start position:0% +that it can attach either to an + + + align:start position:0% +that it can attach either to an +adjective or to a verb right with + + align:start position:0% +adjective or to a verb right with + + + align:start position:0% +adjective or to a verb right with +slightly different meanings similarly + + align:start position:0% +slightly different meanings similarly + + + align:start position:0% +slightly different meanings similarly +ing + + align:start position:0% +ing + + + align:start position:0% +ing +has several different guises it can be a + + align:start position:0% +has several different guises it can be a + + + align:start position:0% +has several different guises it can be a +couple different things yeah English + + align:start position:0% +couple different things yeah English + + + align:start position:0% +couple different things yeah English +really needs more morphemes we have + + align:start position:0% +really needs more morphemes we have + + + align:start position:0% +really needs more morphemes we have +several morphemes that are pronounced + + align:start position:0% +several morphemes that are pronounced + + + align:start position:0% +several morphemes that are pronounced +the same way + + align:start position:0% +the same way + + + align:start position:0% +the same way +not every language does that there are + + align:start position:0% +not every language does that there are + + + align:start position:0% +not every language does that there are +plenty of languages that have just + + align:start position:0% +plenty of languages that have just + + + align:start position:0% +plenty of languages that have just +different forms for gerunds and + + align:start position:0% +different forms for gerunds and + + + align:start position:0% +different forms for gerunds and +participles + + align:start position:0% + + + + align:start position:0% + +okay all right so this has just been an + + align:start position:0% +okay all right so this has just been an + + + align:start position:0% +okay all right so this has just been an +exercise in trying to convince ourselves + + align:start position:0% +exercise in trying to convince ourselves + + + align:start position:0% +exercise in trying to convince ourselves +that we know what we're talking about + + align:start position:0% +that we know what we're talking about + + + align:start position:0% +that we know what we're talking about +when we're talking about things like + + align:start position:0% +when we're talking about things like + + + align:start position:0% +when we're talking about things like +nouns and adjectives and like I say I + + align:start position:0% +nouns and adjectives and like I say I + + + align:start position:0% +nouns and adjectives and like I say I +won't make you do this for every part of + + align:start position:0% +won't make you do this for every part of + + + align:start position:0% +won't make you do this for every part of +speech but if you uh want to annoy your + + align:start position:0% +speech but if you uh want to annoy your + + + align:start position:0% +speech but if you uh want to annoy your +friends back in the dorm + + align:start position:0% +friends back in the dorm + + + align:start position:0% +friends back in the dorm +um uh trying to come up with sentences + + align:start position:0% +um uh trying to come up with sentences + + + align:start position:0% +um uh trying to come up with sentences +like this might be an interesting + + align:start position:0% +like this might be an interesting + + + align:start position:0% +like this might be an interesting +exercise yeah + + align:start position:0% +exercise yeah + + + align:start position:0% +exercise yeah +interesting for me maybe not for them + + align:start position:0% +interesting for me maybe not for them + + + align:start position:0% +interesting for me maybe not for them +okay questions about any of that + + align:start position:0% +okay questions about any of that + + + align:start position:0% +okay questions about any of that +this has just been so that if anybody + + align:start position:0% +this has just been so that if anybody + + + align:start position:0% +this has just been so that if anybody +heard all this talk about nouns and + + align:start position:0% +heard all this talk about nouns and + + + align:start position:0% +heard all this talk about nouns and +adjectives and was wondering what the + + align:start position:0% +adjectives and was wondering what the + + + align:start position:0% +adjectives and was wondering what the +heck are we talking about exactly that + + align:start position:0% +heck are we talking about exactly that + + + align:start position:0% +heck are we talking about exactly that +is what we were talking about exactly + + align:start position:0% +is what we were talking about exactly + + + align:start position:0% +is what we were talking about exactly +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh so we've been talking now about + + align:start position:0% +uh so we've been talking now about + + + align:start position:0% +uh so we've been talking now about +morphology for a little while + + align:start position:0% +morphology for a little while + + + align:start position:0% +morphology for a little while +um and we have mostly been talking about + + align:start position:0% +um and we have mostly been talking about + + + align:start position:0% +um and we have mostly been talking about +uh language specific properties so we've + + align:start position:0% +uh language specific properties so we've + + + align:start position:0% +uh language specific properties so we've +been saying uh a morpheme with a given + + align:start position:0% +been saying uh a morpheme with a given + + + align:start position:0% +been saying uh a morpheme with a given +meaning is pronounced differently in + + align:start position:0% +meaning is pronounced differently in + + + align:start position:0% +meaning is pronounced differently in +different languages so we started with + + align:start position:0% +different languages so we started with + + + align:start position:0% +different languages so we started with +cats we convinced ourselves that if we + + align:start position:0% +cats we convinced ourselves that if we + + + align:start position:0% +cats we convinced ourselves that if we +wanted to look for things that were + + align:start position:0% +wanted to look for things that were + + + align:start position:0% +wanted to look for things that were +Universal about language uh + + align:start position:0% +Universal about language uh + + + align:start position:0% +Universal about language uh +you know figuring out that the word for + + align:start position:0% +you know figuring out that the word for + + + align:start position:0% +you know figuring out that the word for +cat is Cat that's clearly not Universal + + align:start position:0% +cat is Cat that's clearly not Universal + + + align:start position:0% +cat is Cat that's clearly not Universal +every language has a different word for + + align:start position:0% +every language has a different word for + + + align:start position:0% +every language has a different word for +cat + + align:start position:0% +cat + + + align:start position:0% +cat +um so morphemes with a different meaning + + align:start position:0% +um so morphemes with a different meaning + + + align:start position:0% +um so morphemes with a different meaning +can be pronounced differently in + + align:start position:0% +can be pronounced differently in + + + align:start position:0% +can be pronounced differently in +different languages + + align:start position:0% + + + + align:start position:0% + +morphemes can be various types they can + + align:start position:0% +morphemes can be various types they can + + + align:start position:0% +morphemes can be various types they can +be prefixes or suffixes or infixes or + + align:start position:0% +be prefixes or suffixes or infixes or + + + align:start position:0% +be prefixes or suffixes or infixes or +other things so those here are three + + align:start position:0% +other things so those here are three + + + align:start position:0% +other things so those here are three +verbs in English + + align:start position:0% +verbs in English + + + align:start position:0% +verbs in English +that all mean danced they all have + + align:start position:0% +that all mean danced they all have + + + align:start position:0% +that all mean danced they all have +consist of a verb along with another + + align:start position:0% +consist of a verb along with another + + + align:start position:0% +consist of a verb along with another +morpheme that indicates past tense that + + align:start position:0% +morpheme that indicates past tense that + + + align:start position:0% +morpheme that indicates past tense that +morpheme is a suffix in English but it's + + align:start position:0% +morpheme is a suffix in English but it's + + + align:start position:0% +morpheme is a suffix in English but it's +a prefix in lardel and it's an infix in + + align:start position:0% +a prefix in lardel and it's an infix in + + + align:start position:0% +a prefix in lardel and it's an infix in +Tagalog + + align:start position:0% +Tagalog + + + align:start position:0% +Tagalog +um and morphemes can be bound or free + + align:start position:0% +um and morphemes can be bound or free + + + align:start position:0% +um and morphemes can be bound or free +um so here are some sort of new examples + + align:start position:0% +um so here are some sort of new examples + + + align:start position:0% +um so here are some sort of new examples +of that + + align:start position:0% +of that + + + align:start position:0% +of that +um this is again a point of + + align:start position:0% +um this is again a point of + + + align:start position:0% +um this is again a point of +cross-linguistic variation so in English + + align:start position:0% +cross-linguistic variation so in English + + + align:start position:0% +cross-linguistic variation so in English +a phrase like in my hand consists of + + align:start position:0% +a phrase like in my hand consists of + + + align:start position:0% +a phrase like in my hand consists of +three words three free morphemes but in + + align:start position:0% +three words three free morphemes but in + + + align:start position:0% +three words three free morphemes but in +Turkish uh it consists of a root plus + + align:start position:0% +Turkish uh it consists of a root plus + + + align:start position:0% +Turkish uh it consists of a root plus +two bound morphemes so there's the word + + align:start position:0% +two bound morphemes so there's the word + + + align:start position:0% +two bound morphemes so there's the word +for and for hand to which you are adding + + align:start position:0% +for and for hand to which you are adding + + + align:start position:0% +for and for hand to which you are adding +suffixes that mean things like my and in + + align:start position:0% +suffixes that mean things like my and in + + + align:start position:0% +suffixes that mean things like my and in +anybody here speak Turkish quote is this + + align:start position:0% +anybody here speak Turkish quote is this + + + align:start position:0% +anybody here speak Turkish quote is this +true am I lying okay good + + align:start position:0% +true am I lying okay good + + + align:start position:0% +true am I lying okay good +um uh similarly in English a sentence + + align:start position:0% +um uh similarly in English a sentence + + + align:start position:0% +um uh similarly in English a sentence +like I bought a bed consists of four + + align:start position:0% +like I bought a bed consists of four + + + align:start position:0% +like I bought a bed consists of four +freestanding words in Mohawk it consists + + align:start position:0% +freestanding words in Mohawk it consists + + + align:start position:0% +freestanding words in Mohawk it consists +of one word uh so there's a verb by that + + align:start position:0% +of one word uh so there's a verb by that + + + align:start position:0% +of one word uh so there's a verb by that +is combining with various things + + align:start position:0% +is combining with various things + + + align:start position:0% +is combining with various things +including a morpheme that means bed so + + align:start position:0% +including a morpheme that means bed so + + + align:start position:0% +including a morpheme that means bed so +if the object becomes part of this long + + align:start position:0% +if the object becomes part of this long + + + align:start position:0% +if the object becomes part of this long +verb yeah + + align:start position:0% +verb yeah + + + align:start position:0% +verb yeah +anybody here speak mohawk + + align:start position:0% +anybody here speak mohawk + + + align:start position:0% +anybody here speak mohawk +okay good so please just believe me yeah + + align:start position:0% +okay good so please just believe me yeah + + + align:start position:0% +okay good so please just believe me yeah +this is how this is how Mohawk works + + align:start position:0% +this is how this is how Mohawk works + + + align:start position:0% +this is how this is how Mohawk works +this is a process called noun + + align:start position:0% +this is a process called noun + + + align:start position:0% +this is a process called noun +incorporation it's not obligatory in + + align:start position:0% +incorporation it's not obligatory in + + + align:start position:0% +incorporation it's not obligatory in +Mohawk but it's an option that you have + + align:start position:0% +Mohawk but it's an option that you have + + + align:start position:0% +Mohawk but it's an option that you have +okay so languages can vary with respect + + align:start position:0% +okay so languages can vary with respect + + + align:start position:0% +okay so languages can vary with respect +to uh uh how their morphemes are + + align:start position:0% +to uh uh how their morphemes are + + + align:start position:0% +to uh uh how their morphemes are +pronounced uh whether they're prefixes + + align:start position:0% +pronounced uh whether they're prefixes + + + align:start position:0% +pronounced uh whether they're prefixes +or suffixes or other things and whether + + align:start position:0% +or suffixes or other things and whether + + + align:start position:0% +or suffixes or other things and whether +they are boundary yeah + + align:start position:0% +they are boundary yeah + + + align:start position:0% +they are boundary yeah +um + + align:start position:0% +um + + + align:start position:0% +um +languages are sometimes informally + + align:start position:0% +languages are sometimes informally + + + align:start position:0% +languages are sometimes informally +classified by How likely their morphemes + + align:start position:0% +classified by How likely their morphemes + + + align:start position:0% +classified by How likely their morphemes +are to be bound and + + align:start position:0% +are to be bound and + + + align:start position:0% +are to be bound and +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um + + align:start position:0% +um + + + align:start position:0% +um +when I say that they're informally + + align:start position:0% +when I say that they're informally + + + align:start position:0% +when I say that they're informally +classified in this way what I mean is + + align:start position:0% +classified in this way what I mean is + + + align:start position:0% +classified in this way what I mean is +it's it's probably hopeless to try to + + align:start position:0% +it's it's probably hopeless to try to + + + align:start position:0% +it's it's probably hopeless to try to +tightly Define what this means but this + + align:start position:0% +tightly Define what this means but this + + + align:start position:0% +tightly Define what this means but this +is a quick and dirty classification that + + align:start position:0% +is a quick and dirty classification that + + + align:start position:0% +is a quick and dirty classification that +you will hear people use there are + + align:start position:0% +you will hear people use there are + + + align:start position:0% +you will hear people use there are +languages out there uh Mandarin is sort + + align:start position:0% +languages out there uh Mandarin is sort + + + align:start position:0% +languages out there uh Mandarin is sort +of the the poster child for this that + + align:start position:0% +of the the poster child for this that + + + align:start position:0% +of the the poster child for this that +just are not into bound morphemes so all + + align:start position:0% +just are not into bound morphemes so all + + + align:start position:0% +just are not into bound morphemes so all +of the morphemes are are free they don't + + align:start position:0% +of the morphemes are are free they don't + + + align:start position:0% +of the morphemes are are free they don't +have to be attached to anything + + align:start position:0% +have to be attached to anything + + + align:start position:0% +have to be attached to anything +so Chinese he ate the meal consists of + + align:start position:0% +so Chinese he ate the meal consists of + + + align:start position:0% +so Chinese he ate the meal consists of +you know four freestanding words yeah + + align:start position:0% +you know four freestanding words yeah + + + align:start position:0% +you know four freestanding words yeah +um doesn't have prefixes or suffixes + + align:start position:0% +um doesn't have prefixes or suffixes + + + align:start position:0% +um doesn't have prefixes or suffixes +mostly there are a few things in + + align:start position:0% +mostly there are a few things in + + + align:start position:0% +mostly there are a few things in +Mandarin that people argue about whether + + align:start position:0% +Mandarin that people argue about whether + + + align:start position:0% +Mandarin that people argue about whether +they might be suffixes or not so like + + align:start position:0% +they might be suffixes or not so like + + + align:start position:0% +they might be suffixes or not so like +you can make pronouns plural by adding a + + align:start position:0% +you can make pronouns plural by adding a + + + align:start position:0% +you can make pronouns plural by adding a +man after them so was I and woman is we + + align:start position:0% +man after them so was I and woman is we + + + align:start position:0% +man after them so was I and woman is we +uh so you abdomen and you get a plural + + align:start position:0% +uh so you abdomen and you get a plural + + + align:start position:0% +uh so you abdomen and you get a plural +version as a candidate for uh for a + + align:start position:0% +version as a candidate for uh for a + + + align:start position:0% +version as a candidate for uh for a +bound morphine but it's certainly a + + align:start position:0% +bound morphine but it's certainly a + + + align:start position:0% +bound morphine but it's certainly a +language that doesn't have a lot of + + align:start position:0% +language that doesn't have a lot of + + + align:start position:0% +language that doesn't have a lot of +bound morphemes + + align:start position:0% +bound morphemes + + + align:start position:0% +bound morphemes +opposite extreme uh our languages like + + align:start position:0% +opposite extreme uh our languages like + + + align:start position:0% +opposite extreme uh our languages like +Mohawk or uh Wampanoag this is the + + align:start position:0% +Mohawk or uh Wampanoag this is the + + + align:start position:0% +Mohawk or uh Wampanoag this is the +language that uh spoken by the + + align:start position:0% +language that uh spoken by the + + + align:start position:0% +language that uh spoken by the +traditional owners of a lot of Eastern + + align:start position:0% +traditional owners of a lot of Eastern + + + align:start position:0% +traditional owners of a lot of Eastern +Massachusetts including arguably the + + align:start position:0% +Massachusetts including arguably the + + + align:start position:0% +Massachusetts including arguably the +place where we're standing right now + + align:start position:0% +place where we're standing right now + + + align:start position:0% +place where we're standing right now +these languages are called polysynthetic + + align:start position:0% +these languages are called polysynthetic + + + align:start position:0% +these languages are called polysynthetic +they are really really into bound + + align:start position:0% +they are really really into bound + + + align:start position:0% +they are really really into bound +morphines so uh things that would not be + + align:start position:0% +morphines so uh things that would not be + + + align:start position:0% +morphines so uh things that would not be +bound morphemes in English are bound + + align:start position:0% +bound morphemes in English are bound + + + align:start position:0% +bound morphemes in English are bound +morphemes this is an example from a + + align:start position:0% +morphemes this is an example from a + + + align:start position:0% +morphemes this is an example from a +letter that was written in the 1600s by + + align:start position:0% +letter that was written in the 1600s by + + + align:start position:0% +letter that was written in the 1600s by +a missionary to the Wampanoag on + + align:start position:0% +a missionary to the Wampanoag on + + + align:start position:0% +a missionary to the Wampanoag on +Martha's Vineyard a guy named experience + + align:start position:0% +Martha's Vineyard a guy named experience + + + align:start position:0% +Martha's Vineyard a guy named experience +Mayhew because they knew how to give + + align:start position:0% +Mayhew because they knew how to give + + + align:start position:0% +Mayhew because they knew how to give +names in the 16th 1600s he was asked + + align:start position:0% +names in the 16th 1600s he was asked + + + align:start position:0% +names in the 16th 1600s he was asked +apparently by the person he was writing + + align:start position:0% +apparently by the person he was writing + + + align:start position:0% +apparently by the person he was writing +the letter to to give him the longest + + align:start position:0% +the letter to to give him the longest + + + align:start position:0% +the letter to to give him the longest +word that he could in Wampanoag and this + + align:start position:0% +word that he could in Wampanoag and this + + + align:start position:0% +word that he could in Wampanoag and this +is what he came up with it means our + + align:start position:0% +is what he came up with it means our + + + align:start position:0% +is what he came up with it means our +very skillful mirror makers and as you + + align:start position:0% +very skillful mirror makers and as you + + + align:start position:0% +very skillful mirror makers and as you +can see it consists of lots and lots of + + align:start position:0% +can see it consists of lots and lots of + + + align:start position:0% +can see it consists of lots and lots of +morphemes all piled on top of each other + + align:start position:0% +morphemes all piled on top of each other + + + align:start position:0% +morphemes all piled on top of each other +he kind of cheated by putting mirror in + + align:start position:0% +he kind of cheated by putting mirror in + + + align:start position:0% +he kind of cheated by putting mirror in +the middle of that so mirror itself is a + + align:start position:0% +the middle of that so mirror itself is a + + + align:start position:0% +the middle of that so mirror itself is a +morphologically complex word and + + align:start position:0% +morphologically complex word and + + + align:start position:0% +morphologically complex word and +Wampanoag it means device for looking at + + align:start position:0% +Wampanoag it means device for looking at + + + align:start position:0% +Wampanoag it means device for looking at +your reflection yeah so look reflection + + align:start position:0% +your reflection yeah so look reflection + + + align:start position:0% +your reflection yeah so look reflection +device + + align:start position:0% +device + + + align:start position:0% +device +is the is the word by itself or mirror + + align:start position:0% +is the is the word by itself or mirror + + + align:start position:0% +is the is the word by itself or mirror +so he sort of gave himself a head start + + align:start position:0% +so he sort of gave himself a head start + + + align:start position:0% +so he sort of gave himself a head start +by putting that in the middle of the + + align:start position:0% +by putting that in the middle of the + + + align:start position:0% +by putting that in the middle of the +word yeah + + align:start position:0% + + + + align:start position:0% + +it's the language tends to be isolated + + align:start position:0% +it's the language tends to be isolated + + + align:start position:0% +it's the language tends to be isolated +which of these things it is + + align:start position:0% +which of these things it is + + + align:start position:0% +which of these things it is +um so + + align:start position:0% +um so + + + align:start position:0% +um so +there the question was whether there's + + align:start position:0% +there the question was whether there's + + + align:start position:0% +there the question was whether there's +any connection between like geography + + align:start position:0% +any connection between like geography + + + align:start position:0% +any connection between like geography +and whether a language is isolating or + + align:start position:0% +and whether a language is isolating or + + + align:start position:0% +and whether a language is isolating or +polysynthetic these things kind of run + + align:start position:0% +polysynthetic these things kind of run + + + align:start position:0% +polysynthetic these things kind of run +in families and language families uh so + + align:start position:0% +in families and language families uh so + + + align:start position:0% +in families and language families uh so +there are a bunch of isolating + + align:start position:0% +there are a bunch of isolating + + + align:start position:0% +there are a bunch of isolating +Polynesian languages for example uh + + align:start position:0% +Polynesian languages for example uh + + + align:start position:0% +Polynesian languages for example uh +there are a bunch of polysynthetic + + align:start position:0% +there are a bunch of polysynthetic + + + align:start position:0% +there are a bunch of polysynthetic +wampanagas Algonquian Mohawk is + + align:start position:0% +wampanagas Algonquian Mohawk is + + + align:start position:0% +wampanagas Algonquian Mohawk is +Iroquoian those language families tend + + align:start position:0% +Iroquoian those language families tend + + + align:start position:0% +Iroquoian those language families tend +to be polysynthetic + + align:start position:0% +to be polysynthetic + + + align:start position:0% +to be polysynthetic +and so you know because language + + align:start position:0% +and so you know because language + + + align:start position:0% +and so you know because language +families are confined to particular + + align:start position:0% +families are confined to particular + + + align:start position:0% +families are confined to particular +places there's some kind of connection + + align:start position:0% +places there's some kind of connection + + + align:start position:0% +places there's some kind of connection +to where you are + + align:start position:0% +to where you are + + + align:start position:0% +to where you are +um I think that might be as far as it + + align:start position:0% +um I think that might be as far as it + + + align:start position:0% +um I think that might be as far as it +goes actually yeah + + align:start position:0% + + + + align:start position:0% + +means something slightly different we'll + + align:start position:0% +means something slightly different we'll + + + align:start position:0% +means something slightly different we'll +get to a glutenative in just a second + + align:start position:0% +get to a glutenative in just a second + + + align:start position:0% +get to a glutenative in just a second +yeah that's a very good question + + align:start position:0% +yeah that's a very good question + + + align:start position:0% +yeah that's a very good question +other questions + + align:start position:0% +other questions + + + align:start position:0% +other questions +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um I think we have agglutinative coming + + align:start position:0% +um I think we have agglutinative coming + + + align:start position:0% +um I think we have agglutinative coming +up yeah so this is another again + + align:start position:0% +up yeah so this is another again + + + align:start position:0% +up yeah so this is another again +informal way of classifying languages if + + align:start position:0% +informal way of classifying languages if + + + align:start position:0% +informal way of classifying languages if +we were having tests in this class I + + align:start position:0% +we were having tests in this class I + + + align:start position:0% +we were having tests in this class I +would never test you on the meanings of + + align:start position:0% +would never test you on the meanings of + + + align:start position:0% +would never test you on the meanings of +these terms because they're fairly + + align:start position:0% +these terms because they're fairly + + + align:start position:0% +these terms because they're fairly +imprecise but they're useful for giving + + align:start position:0% +imprecise but they're useful for giving + + + align:start position:0% +imprecise but they're useful for giving +people a basic idea of what you're + + align:start position:0% +people a basic idea of what you're + + + align:start position:0% +people a basic idea of what you're +looking at + + align:start position:0% +looking at + + + align:start position:0% +looking at +agglutinative languages this is another + + align:start position:0% +agglutinative languages this is another + + + align:start position:0% +agglutinative languages this is another +way people sometimes compare languages + + align:start position:0% +way people sometimes compare languages + + + align:start position:0% +way people sometimes compare languages +gluten languages are languages in which + + align:start position:0% +gluten languages are languages in which + + + align:start position:0% +gluten languages are languages in which +there are morphemes there are typically + + align:start position:0% +there are morphemes there are typically + + + align:start position:0% +there are morphemes there are typically +a bunch of morphemes that are bound and + + align:start position:0% +a bunch of morphemes that are bound and + + + align:start position:0% +a bunch of morphemes that are bound and +they are easy to separate from each + + align:start position:0% +they are easy to separate from each + + + align:start position:0% +they are easy to separate from each +other so Turkish is the poster child's + + align:start position:0% +other so Turkish is the poster child's + + + align:start position:0% +other so Turkish is the poster child's +word in a glutinative language + + align:start position:0% +word in a glutinative language + + + align:start position:0% +word in a glutinative language +you've got a verb and then you have a + + align:start position:0% +you've got a verb and then you have a + + + align:start position:0% +you've got a verb and then you have a +bunch of suffixes on the verb and making + + align:start position:0% +bunch of suffixes on the verb and making + + + align:start position:0% +bunch of suffixes on the verb and making +the cut between one suffix and the next + + align:start position:0% +the cut between one suffix and the next + + + align:start position:0% +the cut between one suffix and the next +is pretty straightforward the there + + align:start position:0% +is pretty straightforward the there + + + align:start position:0% +is pretty straightforward the there +aren't a lot of fancy morphological + + align:start position:0% +aren't a lot of fancy morphological + + + align:start position:0% +aren't a lot of fancy morphological +changes that happen as a result of these + + align:start position:0% +changes that happen as a result of these + + + align:start position:0% +changes that happen as a result of these +morphemes coming in contact with each + + align:start position:0% +morphemes coming in contact with each + + + align:start position:0% +morphemes coming in contact with each +other and each of the morphemes has a + + align:start position:0% +other and each of the morphemes has a + + + align:start position:0% +other and each of the morphemes has a +pretty come pretty simple meaning they + + align:start position:0% +pretty come pretty simple meaning they + + + align:start position:0% +pretty come pretty simple meaning they +mean things like each other or cause or + + align:start position:0% +mean things like each other or cause or + + + align:start position:0% +mean things like each other or cause or +yeah uh yes + + align:start position:0% + + + + align:start position:0% + +so not in yeah not the kind of + + align:start position:0% +so not in yeah not the kind of + + + align:start position:0% +so not in yeah not the kind of +allomorphy that causes you to wonder + + align:start position:0% +allomorphy that causes you to wonder + + + align:start position:0% +allomorphy that causes you to wonder +where one morpheme starts and the next + + align:start position:0% +where one morpheme starts and the next + + + align:start position:0% +where one morpheme starts and the next +begins so there are languages + + align:start position:0% +begins so there are languages + + + align:start position:0% +begins so there are languages +um the polysense they're poly synthetic + + align:start position:0% +um the polysense they're poly synthetic + + + align:start position:0% +um the polysense they're poly synthetic +languages there are languages that have + + align:start position:0% +languages there are languages that have + + + align:start position:0% +languages there are languages that have +lots and lots of morphology on their + + align:start position:0% +lots and lots of morphology on their + + + align:start position:0% +lots and lots of morphology on their +verbs Navajo is a very good example + + align:start position:0% +verbs Navajo is a very good example + + + align:start position:0% +verbs Navajo is a very good example +we'll see some Navajo examples later in + + align:start position:0% +we'll see some Navajo examples later in + + + align:start position:0% +we'll see some Navajo examples later in +which there are many morphemes but they + + align:start position:0% +which there are many morphemes but they + + + align:start position:0% +which there are many morphemes but they +tend to kind of squash into each other + + align:start position:0% +tend to kind of squash into each other + + + align:start position:0% +tend to kind of squash into each other +and you have to do a lot of analysis to + + align:start position:0% +and you have to do a lot of analysis to + + + align:start position:0% +and you have to do a lot of analysis to +figure out where one starts and the next + + align:start position:0% +figure out where one starts and the next + + + align:start position:0% +figure out where one starts and the next +begins + + align:start position:0% +begins + + + align:start position:0% +begins +where one stops and the next begins did + + align:start position:0% +where one stops and the next begins did + + + align:start position:0% +where one stops and the next begins did +you have a question + + align:start position:0% +you have a question + + + align:start position:0% +you have a question +yeah okay + + align:start position:0% +yeah okay + + + align:start position:0% +yeah okay +the questions + + align:start position:0% +the questions + + + align:start position:0% +the questions +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um so uh uh agglutinative and sort of + + align:start position:0% +um so uh uh agglutinative and sort of + + + align:start position:0% +um so uh uh agglutinative and sort of +the opposite of the gluten if people + + align:start position:0% +the opposite of the gluten if people + + + align:start position:0% +the opposite of the gluten if people +talk about fusional or inflectional + + align:start position:0% +talk about fusional or inflectional + + + align:start position:0% +talk about fusional or inflectional +languages these are languages that have + + align:start position:0% +languages these are languages that have + + + align:start position:0% +languages these are languages that have +morphemes + + align:start position:0% +morphemes + + + align:start position:0% +morphemes +um and the morphemes sort of squash a + + align:start position:0% +um and the morphemes sort of squash a + + + align:start position:0% +um and the morphemes sort of squash a +bunch of bits of meaning together in one + + align:start position:0% +bunch of bits of meaning together in one + + + align:start position:0% +bunch of bits of meaning together in one +small space so these Russian nouns for + + align:start position:0% +small space so these Russian nouns for + + + align:start position:0% +small space so these Russian nouns for +example + + align:start position:0% +example + + + align:start position:0% +example +end in vowels which indicate the + + align:start position:0% +end in vowels which indicate the + + + align:start position:0% +end in vowels which indicate the +grammatical gender of the noun and also + + align:start position:0% +grammatical gender of the noun and also + + + align:start position:0% +grammatical gender of the noun and also +its number and also its case and you + + align:start position:0% +its number and also its case and you + + + align:start position:0% +its number and also its case and you +aren't aren't going to be able to divide + + align:start position:0% +aren't aren't going to be able to divide + + + align:start position:0% +aren't aren't going to be able to divide +that vowel into parts right so the ooh + + align:start position:0% +that vowel into parts right so the ooh + + + align:start position:0% +that vowel into parts right so the ooh +at the end of + + align:start position:0% +at the end of + + + align:start position:0% +at the end of +means feminine and singular and + + align:start position:0% +means feminine and singular and + + + align:start position:0% +means feminine and singular and +accusative and the U at the end of means + + align:start position:0% +accusative and the U at the end of means + + + align:start position:0% +accusative and the U at the end of means +feminine and plural and accusative and + + align:start position:0% +feminine and plural and accusative and + + + align:start position:0% +feminine and plural and accusative and +it's hopeless to try to find a part of + + align:start position:0% +it's hopeless to try to find a part of + + + align:start position:0% +it's hopeless to try to find a part of +that suffix that's the part that means + + align:start position:0% +that suffix that's the part that means + + + align:start position:0% +that suffix that's the part that means +you know singular or plural right it's + + align:start position:0% +you know singular or plural right it's + + + align:start position:0% +you know singular or plural right it's +just all in one big spot yeah + + align:start position:0% +just all in one big spot yeah + + + align:start position:0% +just all in one big spot yeah +which I mean in Hispanic say it again + + align:start position:0% +which I mean in Hispanic say it again + + + align:start position:0% +which I mean in Hispanic say it again +oh I see you're talking about like the + + align:start position:0% +oh I see you're talking about like the + + + align:start position:0% +oh I see you're talking about like the +verb endings in Spanish + + align:start position:0% + + + + align:start position:0% + +oh I see + + align:start position:0% +oh I see + + + align:start position:0% +oh I see +um so this is why I think I said so + + align:start position:0% +um so this is why I think I said so + + + align:start position:0% +um so this is why I think I said so +she's asking is this true for uh for + + align:start position:0% +she's asking is this true for uh for + + + align:start position:0% +she's asking is this true for uh for +Spanish nouns which end in endings like + + align:start position:0% +Spanish nouns which end in endings like + + + align:start position:0% +Spanish nouns which end in endings like +osanas right which indicate both gender + + align:start position:0% +osanas right which indicate both gender + + + align:start position:0% +osanas right which indicate both gender +and number sometimes and in those + + align:start position:0% +and number sometimes and in those + + + align:start position:0% +and number sometimes and in those +particular cases you could try to + + align:start position:0% +particular cases you could try to + + + align:start position:0% +particular cases you could try to +convince yourself that you know the O + + align:start position:0% +convince yourself that you know the O + + + align:start position:0% +convince yourself that you know the O +indicates masculine and the S indicates + + align:start position:0% +indicates masculine and the S indicates + + + align:start position:0% +indicates masculine and the S indicates +plural right in lots of cases this is + + align:start position:0% +plural right in lots of cases this is + + + align:start position:0% +plural right in lots of cases this is +why I said we're never going to test you + + align:start position:0% +why I said we're never going to test you + + + align:start position:0% +why I said we're never going to test you +on this kind of thing + + align:start position:0% +on this kind of thing + + + align:start position:0% +on this kind of thing +um uh because this classification is + + align:start position:0% +um uh because this classification is + + + align:start position:0% +um uh because this classification is +really a classification of how easy is + + align:start position:0% +really a classification of how easy is + + + align:start position:0% +really a classification of how easy is +it to make divisions between morphemes + + align:start position:0% +it to make divisions between morphemes + + + align:start position:0% +it to make divisions between morphemes +and make breaks in places and the answer + + align:start position:0% +and make breaks in places and the answer + + + align:start position:0% +and make breaks in places and the answer +is sometimes very easy that's Turkish + + align:start position:0% +is sometimes very easy that's Turkish + + + align:start position:0% +is sometimes very easy that's Turkish +sometimes impossible that's Russian and + + align:start position:0% +sometimes impossible that's Russian and + + + align:start position:0% +sometimes impossible that's Russian and +sort of Spanish is somewhere in the + + align:start position:0% +sort of Spanish is somewhere in the + + + align:start position:0% +sort of Spanish is somewhere in the +middle it's more maybe for that + + align:start position:0% +middle it's more maybe for that + + + align:start position:0% +middle it's more maybe for that +particular case it's more on the + + align:start position:0% +particular case it's more on the + + + align:start position:0% +particular case it's more on the +agglutinative side maybe there's a break + + align:start position:0% +agglutinative side maybe there's a break + + + align:start position:0% +agglutinative side maybe there's a break +that you can make but uh yeah so asking + + align:start position:0% +that you can make but uh yeah so asking + + + align:start position:0% +that you can make but uh yeah so asking +questions like how easy is it this is no + + align:start position:0% +questions like how easy is it this is no + + + align:start position:0% +questions like how easy is it this is no +way to do science yeah + + align:start position:0% +way to do science yeah + + + align:start position:0% +way to do science yeah +other questions yes + + align:start position:0% +other questions yes + + + align:start position:0% +other questions yes +oh uh animate where oh here uh it stands + + align:start position:0% +oh uh animate where oh here uh it stands + + + align:start position:0% +oh uh animate where oh here uh it stands +for the fact that + + align:start position:0% +for the fact that + + + align:start position:0% +for the fact that +um uh Russian masculine accusatives Take + + align:start position:0% +um uh Russian masculine accusatives Take + + + align:start position:0% +um uh Russian masculine accusatives Take +Ah only if they refer to things that are + + align:start position:0% +Ah only if they refer to things that are + + + align:start position:0% +Ah only if they refer to things that are +alive uh right so yeah + + align:start position:0% +alive uh right so yeah + + + align:start position:0% +alive uh right so yeah +um that's that's what it means + + align:start position:0% +um that's that's what it means + + + align:start position:0% +um that's that's what it means +so there's syncretism in Russian between + + align:start position:0% +so there's syncretism in Russian between + + + align:start position:0% +so there's syncretism in Russian between +the the accusative and the genitive I + + align:start position:0% +the the accusative and the genitive I + + + align:start position:0% +the the accusative and the genitive I +guess it is uh uh just for animate nouns + + align:start position:0% +guess it is uh uh just for animate nouns + + + align:start position:0% +guess it is uh uh just for animate nouns +and not for inanimate ask elements yeah + + align:start position:0% +and not for inanimate ask elements yeah + + + align:start position:0% +and not for inanimate ask elements yeah +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +any questions about this + + align:start position:0% +any questions about this + + + align:start position:0% +any questions about this +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right + + align:start position:0% +all right + + + align:start position:0% +all right +okay so I'm talking about lots of things + + align:start position:0% +okay so I'm talking about lots of things + + + align:start position:0% +okay so I'm talking about lots of things +that are language specific and I just + + align:start position:0% +that are language specific and I just + + + align:start position:0% +that are language specific and I just +wanted to to we're this is going to be a + + align:start position:0% +wanted to to we're this is going to be a + + + align:start position:0% +wanted to to we're this is going to be a +topic of conversation throughout the + + align:start position:0% +topic of conversation throughout the + + + align:start position:0% +topic of conversation throughout the +class you know uh when we are looking at + + align:start position:0% +class you know uh when we are looking at + + + align:start position:0% +class you know uh when we are looking at +things how much time are we spending + + align:start position:0% +things how much time are we spending + + + align:start position:0% +things how much time are we spending +looking at ways in which languages are + + align:start position:0% +looking at ways in which languages are + + + align:start position:0% +looking at ways in which languages are +different and how much time are we + + align:start position:0% +different and how much time are we + + + align:start position:0% +different and how much time are we +spending trying to figure out the basic + + align:start position:0% +spending trying to figure out the basic + + + align:start position:0% +spending trying to figure out the basic +rules the things that all languages have + + align:start position:0% +rules the things that all languages have + + + align:start position:0% +rules the things that all languages have +in common uh both of these are important + + align:start position:0% +in common uh both of these are important + + + align:start position:0% +in common uh both of these are important +or things for linguists to do is try to + + align:start position:0% +or things for linguists to do is try to + + + align:start position:0% +or things for linguists to do is try to +understand both the variation and the + + align:start position:0% +understand both the variation and the + + + align:start position:0% +understand both the variation and the +sort of core of uh common common thread + + align:start position:0% +sort of core of uh common common thread + + + align:start position:0% +sort of core of uh common common thread +that I'll connect all these languages + + align:start position:0% +that I'll connect all these languages + + + align:start position:0% +that I'll connect all these languages +together + + align:start position:0% +together + + + align:start position:0% +together +um I just want to try to convince you + + align:start position:0% +um I just want to try to convince you + + + align:start position:0% +um I just want to try to convince you +that even in morphology which is what + + align:start position:0% +that even in morphology which is what + + + align:start position:0% +that even in morphology which is what +we're starting with there are some + + align:start position:0% +we're starting with there are some + + + align:start position:0% +we're starting with there are some +things that uh maybe are are reliable + + align:start position:0% +things that uh maybe are are reliable + + + align:start position:0% +things that uh maybe are are reliable +cross-linguistically + + align:start position:0% +cross-linguistically + + + align:start position:0% +cross-linguistically +um so here's a Georgian verb and a + + align:start position:0% +um so here's a Georgian verb and a + + + align:start position:0% +um so here's a Georgian verb and a +Turkish verb I don't know either of + + align:start position:0% +Turkish verb I don't know either of + + + align:start position:0% +Turkish verb I don't know either of +these languages so I had to pick + + align:start position:0% +these languages so I had to pick + + + align:start position:0% +these languages so I had to pick +examples that had a different verb at + + align:start position:0% +examples that had a different verb at + + + align:start position:0% +examples that had a different verb at +the bottom so in Georgian you've got + + align:start position:0% +the bottom so in Georgian you've got + + + align:start position:0% +the bottom so in Georgian you've got +paint and in Turkish you you've got open + + align:start position:0% +paint and in Turkish you you've got open + + + align:start position:0% +paint and in Turkish you you've got open +but otherwise these verbs are the same + + align:start position:0% +but otherwise these verbs are the same + + + align:start position:0% +but otherwise these verbs are the same +so the Georgian one means I will have + + align:start position:0% +so the Georgian one means I will have + + + align:start position:0% +so the Georgian one means I will have +him paint it and the Turkish one means I + + align:start position:0% +him paint it and the Turkish one means I + + + align:start position:0% +him paint it and the Turkish one means I +had him open it okay they aren't the + + align:start position:0% +had him open it okay they aren't the + + + align:start position:0% +had him open it okay they aren't the +same they're different tenses but + + align:start position:0% +same they're different tenses but + + + align:start position:0% +same they're different tenses but +they're both uh about causing someone to + + align:start position:0% +they're both uh about causing someone to + + + align:start position:0% +they're both uh about causing someone to +do something to something there they + + align:start position:0% +do something to something there they + + + align:start position:0% +do something to something there they +have that in common + + align:start position:0% +have that in common + + + align:start position:0% +have that in common +and they have some other things and and + + align:start position:0% +and they have some other things and and + + + align:start position:0% +and they have some other things and and +they're different in other ways too so + + align:start position:0% +they're different in other ways too so + + + align:start position:0% +they're different in other ways too so +the Georgian verb uh is preceded by + + align:start position:0% +the Georgian verb uh is preceded by + + + align:start position:0% +the Georgian verb uh is preceded by +several prefixes the Turkish verb is + + align:start position:0% +several prefixes the Turkish verb is + + + align:start position:0% +several prefixes the Turkish verb is +followed by several suffixes yeah + + align:start position:0% +followed by several suffixes yeah + + + align:start position:0% +followed by several suffixes yeah +but here's what they finally have in + + align:start position:0% +but here's what they finally have in + + + align:start position:0% +but here's what they finally have in +common + + align:start position:0% +common + + + align:start position:0% +common +the red affix is merged after the blue + + align:start position:0% +the red affix is merged after the blue + + + align:start position:0% +the red affix is merged after the blue +affix yeah so the affix that means cause + + align:start position:0% +affix yeah so the affix that means cause + + + align:start position:0% +affix yeah so the affix that means cause +is the first thing that's merged with + + align:start position:0% +is the first thing that's merged with + + + align:start position:0% +is the first thing that's merged with +the verb in both of these languages and + + align:start position:0% +the verb in both of these languages and + + + align:start position:0% +the verb in both of these languages and +the affix that means uh first person + + align:start position:0% +the affix that means uh first person + + + align:start position:0% +the affix that means uh first person +singular I uh as the subject is merged + + align:start position:0% +singular I uh as the subject is merged + + + align:start position:0% +singular I uh as the subject is merged +later + + align:start position:0% +later + + + align:start position:0% +later +in both of these now in Georgian they're + + align:start position:0% +in both of these now in Georgian they're + + + align:start position:0% +in both of these now in Georgian they're +both prefixes in Turkish they're both + + align:start position:0% +both prefixes in Turkish they're both + + + align:start position:0% +both prefixes in Turkish they're both +suffixes they're not pronounced the same + + align:start position:0% +suffixes they're not pronounced the same + + + align:start position:0% +suffixes they're not pronounced the same +way right uh you know cause in Georgian + + align:start position:0% +way right uh you know cause in Georgian + + + align:start position:0% +way right uh you know cause in Georgian +is ah cause in Turkish is third + + align:start position:0% +is ah cause in Turkish is third + + + align:start position:0% +is ah cause in Turkish is third +um but they do have that property in + + align:start position:0% +um but they do have that property in + + + align:start position:0% +um but they do have that property in +common that the order in which you + + align:start position:0% +common that the order in which you + + + align:start position:0% +common that the order in which you +combine these morphemes is the same for + + align:start position:0% +combine these morphemes is the same for + + + align:start position:0% +combine these morphemes is the same for +these two otherwise fairly different + + align:start position:0% +these two otherwise fairly different + + + align:start position:0% +these two otherwise fairly different +languages + + align:start position:0% +languages + + + align:start position:0% +languages +and that's a pretty reliable thing so + + align:start position:0% +and that's a pretty reliable thing so + + + align:start position:0% +and that's a pretty reliable thing so +what's sometimes called derivational + + align:start position:0% +what's sometimes called derivational + + + align:start position:0% +what's sometimes called derivational +morphology which includes things like + + align:start position:0% +morphology which includes things like + + + align:start position:0% +morphology which includes things like +all the morphology we were talking about + + align:start position:0% +all the morphology we were talking about + + + align:start position:0% +all the morphology we were talking about +that converts things from nouns into + + align:start position:0% +that converts things from nouns into + + + align:start position:0% +that converts things from nouns into +verbs or from verbs into adjectives or + + align:start position:0% +verbs or from verbs into adjectives or + + + align:start position:0% +verbs or from verbs into adjectives or +whatever all else uh and also things + + align:start position:0% +whatever all else uh and also things + + + align:start position:0% +whatever all else uh and also things +like causative that change the number of + + align:start position:0% +like causative that change the number of + + + align:start position:0% +like causative that change the number of +participants in a verb so by adding + + align:start position:0% +participants in a verb so by adding + + + align:start position:0% +participants in a verb so by adding +someone who is causing a verb to happen + + align:start position:0% +someone who is causing a verb to happen + + + align:start position:0% +someone who is causing a verb to happen +um that type of morphology tends to be + + align:start position:0% +um that type of morphology tends to be + + + align:start position:0% +um that type of morphology tends to be +merged earlier than what's sometimes + + align:start position:0% +merged earlier than what's sometimes + + + align:start position:0% +merged earlier than what's sometimes +called inflectional morphology the kind + + align:start position:0% +called inflectional morphology the kind + + + align:start position:0% +called inflectional morphology the kind +of morphology that indicates things like + + align:start position:0% +of morphology that indicates things like + + + align:start position:0% +of morphology that indicates things like +who's doing what to whom and when + + align:start position:0% +who's doing what to whom and when + + + align:start position:0% +who's doing what to whom and when +um that's a moderately reliable fact + + align:start position:0% + + + + align:start position:0% + +or similarly there are various places + + align:start position:0% +or similarly there are various places + + + align:start position:0% +or similarly there are various places +where an a pair of Expressions can + + align:start position:0% +where an a pair of Expressions can + + + align:start position:0% +where an a pair of Expressions can +differ in all kinds of ways including + + align:start position:0% +differ in all kinds of ways including + + + align:start position:0% +differ in all kinds of ways including +you know whether you're looking at + + align:start position:0% +you know whether you're looking at + + + align:start position:0% +you know whether you're looking at +prefixes or suffixes so here's Swahili + + align:start position:0% +prefixes or suffixes so here's Swahili + + + align:start position:0% +prefixes or suffixes so here's Swahili +for you hit and German for you put and + + align:start position:0% +for you hit and German for you put and + + + align:start position:0% +for you hit and German for you put and +abstracting away from the fact that one + + align:start position:0% +abstracting away from the fact that one + + + align:start position:0% +abstracting away from the fact that one +of them is hitting and the other is + + align:start position:0% +of them is hitting and the other is + + + align:start position:0% +of them is hitting and the other is +putting in Swahili those are prefixes in + + align:start position:0% +putting in Swahili those are prefixes in + + + align:start position:0% +putting in Swahili those are prefixes in +German they're suffixes but the order in + + align:start position:0% +German they're suffixes but the order in + + + align:start position:0% +German they're suffixes but the order in +which everything is merged is the same + + align:start position:0% +which everything is merged is the same + + + align:start position:0% +which everything is merged is the same +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +or in English and Turkish in my hands + + align:start position:0% +or in English and Turkish in my hands + + + align:start position:0% +or in English and Turkish in my hands +and the Turkish version of that + + align:start position:0% + + + + align:start position:0% + +the Turkish morphemes are bound the + + align:start position:0% +the Turkish morphemes are bound the + + + align:start position:0% +the Turkish morphemes are bound the +English morphemes are free but the + + align:start position:0% +English morphemes are free but the + + + align:start position:0% +English morphemes are free but the +morphemes are being merged in the same + + align:start position:0% +morphemes are being merged in the same + + + align:start position:0% +morphemes are being merged in the same +order yeah + + align:start position:0% +order yeah + + + align:start position:0% +order yeah +so there's some hope for the idea that + + align:start position:0% +so there's some hope for the idea that + + + align:start position:0% +so there's some hope for the idea that +there is some core that these languages + + align:start position:0% +there is some core that these languages + + + align:start position:0% +there is some core that these languages +all share that we want to try to + + align:start position:0% +all share that we want to try to + + + align:start position:0% +all share that we want to try to +understand what is it that determines + + align:start position:0% +understand what is it that determines + + + align:start position:0% +understand what is it that determines +the order in which you do your merge + + align:start position:0% +the order in which you do your merge + + + align:start position:0% +the order in which you do your merge +operations if you thought I was going to + + align:start position:0% +operations if you thought I was going to + + + align:start position:0% +operations if you thought I was going to +answer that question for you today then + + align:start position:0% +answer that question for you today then + + + align:start position:0% +answer that question for you today then +I'm about to disappoint you but that's a + + align:start position:0% +I'm about to disappoint you but that's a + + + align:start position:0% +I'm about to disappoint you but that's a +question that you know we're going to + + align:start position:0% +question that you know we're going to + + + align:start position:0% +question that you know we're going to +want to keep in mind going forward yeah + + align:start position:0% +want to keep in mind going forward yeah + + + align:start position:0% +want to keep in mind going forward yeah +have anything to do with the fact that + + align:start position:0% +have anything to do with the fact that + + + align:start position:0% +have anything to do with the fact that +at least in English like there's like a + + align:start position:0% +at least in English like there's like a + + + align:start position:0% +at least in English like there's like a +certain way that you can say like you've + + align:start position:0% +certain way that you can say like you've + + + align:start position:0% +certain way that you can say like you've +got like a list of messages from you now + + align:start position:0% +got like a list of messages from you now + + + align:start position:0% +got like a list of messages from you now +you say it in like a certain order + + align:start position:0% +you say it in like a certain order + + + align:start position:0% +you say it in like a certain order +the big bad dog but not just bad big dog + + align:start position:0% +the big bad dog but not just bad big dog + + + align:start position:0% +the big bad dog but not just bad big dog +yeah yeah yeah so that's a very nice + + align:start position:0% +yeah yeah yeah so that's a very nice + + + align:start position:0% +yeah yeah yeah so that's a very nice +Point + + align:start position:0% +Point + + + align:start position:0% +Point +um uh when you have a bunch of + + align:start position:0% +um uh when you have a bunch of + + + align:start position:0% +um uh when you have a bunch of +adjectives in English they they tend to + + align:start position:0% +adjectives in English they they tend to + + + align:start position:0% +adjectives in English they they tend to +go in a particular order that's right uh + + align:start position:0% +go in a particular order that's right uh + + + align:start position:0% +go in a particular order that's right uh +um and and actually there's a very + + align:start position:0% +um and and actually there's a very + + + align:start position:0% +um and and actually there's a very +articulated order uh it's got like five + + align:start position:0% +articulated order uh it's got like five + + + align:start position:0% +articulated order uh it's got like five +slots you know for the the adjectives in + + align:start position:0% +slots you know for the the adjectives in + + + align:start position:0% +slots you know for the the adjectives in +the order that they go in + + align:start position:0% +the order that they go in + + + align:start position:0% +the order that they go in +the other cool thing about it is that + + align:start position:0% +the other cool thing about it is that + + + align:start position:0% +the other cool thing about it is that +it's + + align:start position:0% +it's + + + align:start position:0% +it's +among languages that put their + + align:start position:0% +among languages that put their + + + align:start position:0% +among languages that put their +adjectives before the noun + + align:start position:0% +adjectives before the noun + + + align:start position:0% +adjectives before the noun +if they have any rules for the order of + + align:start position:0% +if they have any rules for the order of + + + align:start position:0% +if they have any rules for the order of +the adjective that's the rule so that's + + align:start position:0% +the adjective that's the rule so that's + + + align:start position:0% +the adjective that's the rule so that's +the only kind of rule that there can be + + align:start position:0% +the only kind of rule that there can be + + + align:start position:0% +the only kind of rule that there can be +for languages that put their adjectives + + align:start position:0% +for languages that put their adjectives + + + align:start position:0% +for languages that put their adjectives +after the noun there are if they have + + align:start position:0% +after the noun there are if they have + + + align:start position:0% +after the noun there are if they have +any rules for the order there are two + + align:start position:0% +any rules for the order there are two + + + align:start position:0% +any rules for the order there are two +kinds of rules so if you number the + + align:start position:0% +kinds of rules so if you number the + + + align:start position:0% +kinds of rules so if you number the +adjectives that go before the noun in + + align:start position:0% +adjectives that go before the noun in + + + align:start position:0% +adjectives that go before the noun in +English if you say you know they go in + + align:start position:0% +English if you say you know they go in + + + align:start position:0% +English if you say you know they go in +the order one two three four five + + align:start position:0% +the order one two three four five + + + align:start position:0% +the order one two three four five +um if you put out if you're a language + + align:start position:0% +um if you put out if you're a language + + + align:start position:0% +um if you put out if you're a language +that puts your adjectives after your + + align:start position:0% +that puts your adjectives after your + + + align:start position:0% +that puts your adjectives after your +nouns uh there are only two kinds of + + align:start position:0% +nouns uh there are only two kinds of + + + align:start position:0% +nouns uh there are only two kinds of +languages like that there are languages + + align:start position:0% +languages like that there are languages + + + align:start position:0% +languages like that there are languages +in which the order is one two three four + + align:start position:0% +in which the order is one two three four + + + align:start position:0% +in which the order is one two three four +five so you get noun one two three four + + align:start position:0% +five so you get noun one two three four + + + align:start position:0% +five so you get noun one two three four +five so it'd be like you say house big + + align:start position:0% +five so it'd be like you say house big + + + align:start position:0% +five so it'd be like you say house big +black right and you can't say house + + align:start position:0% +black right and you can't say house + + + align:start position:0% +black right and you can't say house +black big you say uh so a little green + + align:start position:0% +black big you say uh so a little green + + + align:start position:0% +black big you say uh so a little green +Japanese carving knife right and in + + align:start position:0% +Japanese carving knife right and in + + + align:start position:0% +Japanese carving knife right and in +these languages you would say a knife + + align:start position:0% +these languages you would say a knife + + + align:start position:0% +these languages you would say a knife +little Japanese little green Japanese + + align:start position:0% +little Japanese little green Japanese + + + align:start position:0% +little Japanese little green Japanese +carving so you have the adjectives in + + align:start position:0% +carving so you have the adjectives in + + + align:start position:0% +carving so you have the adjectives in +the same order they'd be in English but + + align:start position:0% +the same order they'd be in English but + + + align:start position:0% +the same order they'd be in English but +after the noun that's one kind of + + align:start position:0% +after the noun that's one kind of + + + align:start position:0% +after the noun that's one kind of +adjective after the noun language and + + align:start position:0% +adjective after the noun language and + + + align:start position:0% +adjective after the noun language and +the other kind is the one that mirror + + align:start position:0% +the other kind is the one that mirror + + + align:start position:0% +the other kind is the one that mirror +has the mirror image of the adjectives + + align:start position:0% +has the mirror image of the adjectives + + + align:start position:0% +has the mirror image of the adjectives +so in the languages of the world there + + align:start position:0% +so in the languages of the world there + + + align:start position:0% +so in the languages of the world there +are I think three kinds + + align:start position:0% +are I think three kinds + + + align:start position:0% +are I think three kinds +which is kind of interesting yes + + align:start position:0% + + + + align:start position:0% + +hey good question yes + + align:start position:0% +hey good question yes + + + align:start position:0% +hey good question yes +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +very linguists working on that yes + + align:start position:0% +very linguists working on that yes + + + align:start position:0% +very linguists working on that yes +um so and that's actually basically her + + align:start position:0% +um so and that's actually basically her + + + align:start position:0% +um so and that's actually basically her +question your question from just a + + align:start position:0% +question your question from just a + + + align:start position:0% +question your question from just a +second ago right so there there are + + align:start position:0% +second ago right so there there are + + + align:start position:0% +second ago right so there there are +conditions on the ordering of the + + align:start position:0% +conditions on the ordering of the + + + align:start position:0% +conditions on the ordering of the +adjectives and yes we want to try to + + align:start position:0% +adjectives and yes we want to try to + + + align:start position:0% +adjectives and yes we want to try to +understand what those are all of you are + + align:start position:0% +understand what those are all of you are + + + align:start position:0% +understand what those are all of you are +eventually going to want to write a + + align:start position:0% +eventually going to want to write a + + + align:start position:0% +eventually going to want to write a +research proposal in which you try to + + align:start position:0% +research proposal in which you try to + + + align:start position:0% +research proposal in which you try to +tell me that you're going to figure + + align:start position:0% +tell me that you're going to figure + + + align:start position:0% +tell me that you're going to figure +something out I can give you some things + + align:start position:0% +something out I can give you some things + + + align:start position:0% +something out I can give you some things +to read that are attempting to figure + + align:start position:0% +to read that are attempting to figure + + + align:start position:0% +to read that are attempting to figure +out the answer to that question but uh + + align:start position:0% +out the answer to that question but uh + + + align:start position:0% +out the answer to that question but uh +yeah that's a that's a research topic + + align:start position:0% +yeah that's a that's a research topic + + + align:start position:0% +yeah that's a that's a research topic +other questions + + align:start position:0% + + + + align:start position:0% + +cool all right + + align:start position:0% +cool all right + + + align:start position:0% +cool all right +um + + align:start position:0% + + + + align:start position:0% + +so yeah this is just me saying again + + align:start position:0% +so yeah this is just me saying again + + + align:start position:0% +so yeah this is just me saying again +what I said uh so what those trees have + + align:start position:0% +what I said uh so what those trees have + + + align:start position:0% +what I said uh so what those trees have +in common is that if a is higher than b + + align:start position:0% +in common is that if a is higher than b + + + align:start position:0% +in common is that if a is higher than b +and one tree the same a is higher than + + align:start position:0% +and one tree the same a is higher than + + + align:start position:0% +and one tree the same a is higher than +the same B in the corresponding tree uh + + align:start position:0% +the same B in the corresponding tree uh + + + align:start position:0% +the same B in the corresponding tree uh +whereby higher we mean higher in the + + align:start position:0% +whereby higher we mean higher in the + + + align:start position:0% +whereby higher we mean higher in the +tree + + align:start position:0% +tree + + + align:start position:0% +tree +added later in the series of merge + + align:start position:0% +added later in the series of merge + + + align:start position:0% +added later in the series of merge +operations right that's what we mean + + align:start position:0% +operations right that's what we mean + + + align:start position:0% +operations right that's what we mean +um + + align:start position:0% +um + + + align:start position:0% +um +lots of questions like the question that + + align:start position:0% +lots of questions like the question that + + + align:start position:0% +lots of questions like the question that +both of you asks you know what's going + + align:start position:0% +both of you asks you know what's going + + + align:start position:0% +both of you asks you know what's going +on with order order of adjectives or how + + align:start position:0% +on with order order of adjectives or how + + + align:start position:0% +on with order order of adjectives or how +come these things have to be merged in + + align:start position:0% +come these things have to be merged in + + + align:start position:0% +come these things have to be merged in +these orders in all of the trees that + + align:start position:0% +these orders in all of the trees that + + + align:start position:0% +these orders in all of the trees that +I'm showing and I'm not offering to + + align:start position:0% +I'm showing and I'm not offering to + + + align:start position:0% +I'm showing and I'm not offering to +answer those questions for you today + + align:start position:0% +answer those questions for you today + + + align:start position:0% +answer those questions for you today +these are some of the central questions + + align:start position:0% +these are some of the central questions + + + align:start position:0% +these are some of the central questions +of syntax yeah and we'll try to + + align:start position:0% +of syntax yeah and we'll try to + + + align:start position:0% +of syntax yeah and we'll try to +understand them eventually + + align:start position:0% +understand them eventually + + + align:start position:0% +understand them eventually +okay + + align:start position:0% +okay + + + align:start position:0% +okay +yeah + + align:start position:0% + + + + align:start position:0% + +okay so we started off by saying there + + align:start position:0% +okay so we started off by saying there + + + align:start position:0% +okay so we started off by saying there +are at least two imaginable kinds of + + align:start position:0% +are at least two imaginable kinds of + + + align:start position:0% +are at least two imaginable kinds of +lexicons if we're going to make a list + + align:start position:0% +lexicons if we're going to make a list + + + align:start position:0% +lexicons if we're going to make a list +of everything you know about your + + align:start position:0% +of everything you know about your + + + align:start position:0% +of everything you know about your +language uh one that has in it entries + + align:start position:0% +language uh one that has in it entries + + + align:start position:0% +language uh one that has in it entries +like teach teacher teachers teaching + + align:start position:0% +like teach teacher teachers teaching + + + align:start position:0% +like teach teacher teachers teaching +right and mine minor miners Mining and + + align:start position:0% +right and mine minor miners Mining and + + + align:start position:0% +right and mine minor miners Mining and +so on and another one that instead has + + align:start position:0% +so on and another one that instead has + + + align:start position:0% +so on and another one that instead has +so that first lexicon consists entirely + + align:start position:0% +so that first lexicon consists entirely + + + align:start position:0% +so that first lexicon consists entirely +of words if + + align:start position:0% +of words if + + + align:start position:0% +of words if +you look at an actual you know + + align:start position:0% +you look at an actual you know + + + align:start position:0% +you look at an actual you know +dictionary that's the kind of lexicon + + align:start position:0% +dictionary that's the kind of lexicon + + + align:start position:0% +dictionary that's the kind of lexicon +you're probably used to seeing but we've + + align:start position:0% +you're probably used to seeing but we've + + + align:start position:0% +you're probably used to seeing but we've +been fooling with the idea that your + + align:start position:0% +been fooling with the idea that your + + + align:start position:0% +been fooling with the idea that your +mental lexicon is not organized that way + + align:start position:0% +mental lexicon is not organized that way + + + align:start position:0% +mental lexicon is not organized that way +um what your mental lexicon has in it is + + align:start position:0% +um what your mental lexicon has in it is + + + align:start position:0% +um what your mental lexicon has in it is +morphemes so it has teach and mine and + + align:start position:0% +morphemes so it has teach and mine and + + + align:start position:0% +morphemes so it has teach and mine and +suffixes like er and Ing and rules for + + align:start position:0% +suffixes like er and Ing and rules for + + + align:start position:0% +suffixes like er and Ing and rules for +how morphemes can be combined with each + + align:start position:0% +how morphemes can be combined with each + + + align:start position:0% +how morphemes can be combined with each +other and what the result is and what + + align:start position:0% +other and what the result is and what + + + align:start position:0% +other and what the result is and what +happens when morphemes combine with each + + align:start position:0% +happens when morphemes combine with each + + + align:start position:0% +happens when morphemes combine with each +other that's the kind of model of how + + align:start position:0% +other that's the kind of model of how + + + align:start position:0% +other that's the kind of model of how +languages put together that we've been + + align:start position:0% +languages put together that we've been + + + align:start position:0% +languages put together that we've been +playing around with yeah + + align:start position:0% +playing around with yeah + + + align:start position:0% +playing around with yeah +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right + + align:start position:0% +all right + + + align:start position:0% +all right +yes so just to give these theories you + + align:start position:0% +yes so just to give these theories you + + + align:start position:0% +yes so just to give these theories you +know names nice non-judgmental names + + align:start position:0% +know names nice non-judgmental names + + + align:start position:0% +know names nice non-judgmental names +we're going to call them the wrong + + align:start position:0% +we're going to call them the wrong + + + align:start position:0% +we're going to call them the wrong +Theory and the Right theory yeah + + align:start position:0% +Theory and the Right theory yeah + + + align:start position:0% +Theory and the Right theory yeah +um and + + align:start position:0% +um and + + + align:start position:0% +um and +um evidence that the rate theory is + + align:start position:0% +um evidence that the rate theory is + + + align:start position:0% +um evidence that the rate theory is +right uh that we that we played around + + align:start position:0% +right uh that we that we played around + + + align:start position:0% +right uh that we that we played around +with + + align:start position:0% +with + + + align:start position:0% +with +um + + align:start position:0% +um + + + align:start position:0% +um +for one thing I asked you to take pity + + align:start position:0% +for one thing I asked you to take pity + + + align:start position:0% +for one thing I asked you to take pity +on the plight of the nimurans these are + + align:start position:0% +on the plight of the nimurans these are + + + align:start position:0% +on the plight of the nimurans these are +these people in Papua New Guinea whose + + align:start position:0% +these people in Papua New Guinea whose + + + align:start position:0% +these people in Papua New Guinea whose +verbs each have like 27 000 forms if we + + align:start position:0% +verbs each have like 27 000 forms if we + + + align:start position:0% +verbs each have like 27 000 forms if we +make their lexicons have every verb form + + align:start position:0% +make their lexicons have every verb form + + + align:start position:0% +make their lexicons have every verb form +in it their lexicons are going to be + + align:start position:0% +in it their lexicons are going to be + + + align:start position:0% +in it their lexicons are going to be +very large they will have no time to do + + align:start position:0% +very large they will have no time to do + + + align:start position:0% +very large they will have no time to do +anything other than sit around and + + align:start position:0% +anything other than sit around and + + + align:start position:0% +anything other than sit around and +remember verbs + + align:start position:0% +remember verbs + + + align:start position:0% +remember verbs +um whereas if we're willing to allow + + align:start position:0% +um whereas if we're willing to allow + + + align:start position:0% +um whereas if we're willing to allow +them to break uh morphemes words into + + align:start position:0% +them to break uh morphemes words into + + + align:start position:0% +them to break uh morphemes words into +into morphemes and put those in their + + align:start position:0% +into morphemes and put those in their + + + align:start position:0% +into morphemes and put those in their +lexicons then they will have you know + + align:start position:0% +lexicons then they will have you know + + + align:start position:0% +lexicons then they will have you know +lexicons of a reasonable size and we saw + + align:start position:0% +lexicons of a reasonable size and we saw + + + align:start position:0% +lexicons of a reasonable size and we saw +lots of evidence that people manipulate + + align:start position:0% +lots of evidence that people manipulate + + + align:start position:0% +lots of evidence that people manipulate +morphemes + + align:start position:0% +morphemes + + + align:start position:0% +morphemes +um including the fact that you can apply + + align:start position:0% +um including the fact that you can apply + + + align:start position:0% +um including the fact that you can apply +morphemes to new words so if I tell you + + align:start position:0% +morphemes to new words so if I tell you + + + align:start position:0% +morphemes to new words so if I tell you +I've invented a new thing it's called a + + align:start position:0% +I've invented a new thing it's called a + + + align:start position:0% +I've invented a new thing it's called a +wug and then I show you another one then + + align:start position:0% +wug and then I show you another one then + + + align:start position:0% +wug and then I show you another one then +you will call the two things wugs + + align:start position:0% +you will call the two things wugs + + + align:start position:0% +you will call the two things wugs +there's a classic experiment by Gene + + align:start position:0% +there's a classic experiment by Gene + + + align:start position:0% +there's a classic experiment by Gene +Virgo Gleason which she did this with + + align:start position:0% +Virgo Gleason which she did this with + + + align:start position:0% +Virgo Gleason which she did this with +small children and they did what you + + align:start position:0% +small children and they did what you + + + align:start position:0% +small children and they did what you +would expect them to do + + align:start position:0% +would expect them to do + + + align:start position:0% +would expect them to do +and so on + + align:start position:0% +and so on + + + align:start position:0% +and so on +yeah good people are willing to believe + + align:start position:0% +yeah good people are willing to believe + + + align:start position:0% +yeah good people are willing to believe +in morphemes excellent + + align:start position:0% +in morphemes excellent + + + align:start position:0% +in morphemes excellent +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um I want to + + align:start position:0% +um I want to + + + align:start position:0% +um I want to +um + + align:start position:0% +um + + + align:start position:0% +um +spend some time then uh the problem set + + align:start position:0% +spend some time then uh the problem set + + + align:start position:0% +spend some time then uh the problem set +that is now finally available to you uh + + align:start position:0% +that is now finally available to you uh + + + align:start position:0% +that is now finally available to you uh +has on it a morphology problem so it + + align:start position:0% +has on it a morphology problem so it + + + align:start position:0% +has on it a morphology problem so it +gives you a bunch of data from a + + align:start position:0% +gives you a bunch of data from a + + + align:start position:0% +gives you a bunch of data from a +language language is inupyak which is a + + align:start position:0% +language language is inupyak which is a + + + align:start position:0% +language language is inupyak which is a +language spoken in the Arctic + + align:start position:0% +language spoken in the Arctic + + + align:start position:0% +language spoken in the Arctic +in Alaska and coast of Alaska + + align:start position:0% +in Alaska and coast of Alaska + + + align:start position:0% +in Alaska and coast of Alaska +and it asks you to go through and try to + + align:start position:0% +and it asks you to go through and try to + + + align:start position:0% +and it asks you to go through and try to +find all the morphemes and figure out + + align:start position:0% +find all the morphemes and figure out + + + align:start position:0% +find all the morphemes and figure out +rules for how they combine yeah + + align:start position:0% +rules for how they combine yeah + + + align:start position:0% +rules for how they combine yeah +we've already done a little bit of that + + align:start position:0% +we've already done a little bit of that + + + align:start position:0% +we've already done a little bit of that +kind of thing in this class but I wanted + + align:start position:0% +kind of thing in this class but I wanted + + + align:start position:0% +kind of thing in this class but I wanted +to do another problem like this and this + + align:start position:0% +to do another problem like this and this + + + align:start position:0% +to do another problem like this and this +problem is going to introduce some new + + align:start position:0% +problem is going to introduce some new + + + align:start position:0% +problem is going to introduce some new +sort of issues and things for you to + + align:start position:0% +sort of issues and things for you to + + + align:start position:0% +sort of issues and things for you to +think about as you're doing morphology + + align:start position:0% +think about as you're doing morphology + + + align:start position:0% +think about as you're doing morphology +so I'm going to go through this these + + align:start position:0% +so I'm going to go through this these + + + align:start position:0% +so I'm going to go through this these +data are from a language called Lardo + + align:start position:0% +data are from a language called Lardo + + + align:start position:0% +data are from a language called Lardo +which I think I've mentioned before it's + + align:start position:0% +which I think I've mentioned before it's + + + align:start position:0% +which I think I've mentioned before it's +a language spoken in Northern Australia + + align:start position:0% +a language spoken in Northern Australia + + + align:start position:0% +a language spoken in Northern Australia +which I've I've done field work on + + align:start position:0% +which I've I've done field work on + + + align:start position:0% +which I've I've done field work on +um it's a language that has uh + + align:start position:0% +um it's a language that has uh + + + align:start position:0% +um it's a language that has uh +inflection on its nouns its nouns get + + align:start position:0% +inflection on its nouns its nouns get + + + align:start position:0% +inflection on its nouns its nouns get +inflected for case so they have suffixes + + align:start position:0% +inflected for case so they have suffixes + + + align:start position:0% +inflected for case so they have suffixes +indicating case + + align:start position:0% +indicating case + + + align:start position:0% +indicating case +um and uh if you're not sure what I + + align:start position:0% +um and uh if you're not sure what I + + + align:start position:0% +um and uh if you're not sure what I +meant by that here's what I mean uh + + align:start position:0% +meant by that here's what I mean uh + + + align:start position:0% +meant by that here's what I mean uh +nouns have little markers on them + + align:start position:0% +nouns have little markers on them + + + align:start position:0% +nouns have little markers on them +telling basically whether they are the + + align:start position:0% +telling basically whether they are the + + + align:start position:0% +telling basically whether they are the +subject or the object of a verb yeah so + + align:start position:0% +subject or the object of a verb yeah so + + + align:start position:0% +subject or the object of a verb yeah so +if you're the subject of a verb you're + + align:start position:0% +if you're the subject of a verb you're + + + align:start position:0% +if you're the subject of a verb you're +in the nominative case and if you're in + + align:start position:0% +in the nominative case and if you're in + + + align:start position:0% +in the nominative case and if you're in +the object uh then you're in the + + align:start position:0% +the object uh then you're in the + + + align:start position:0% +the object uh then you're in the +accusative case uh if you study English + + align:start position:0% +accusative case uh if you study English + + + align:start position:0% +accusative case uh if you study English +does not have so much of this except on + + align:start position:0% +does not have so much of this except on + + + align:start position:0% +does not have so much of this except on +our pronouns if you study lots of other + + align:start position:0% +our pronouns if you study lots of other + + + align:start position:0% +our pronouns if you study lots of other +languages if you try to learn you know + + align:start position:0% +languages if you try to learn you know + + + align:start position:0% +languages if you try to learn you know +Russian or Japanese or Latin or many + + align:start position:0% +Russian or Japanese or Latin or many + + + align:start position:0% +Russian or Japanese or Latin or many +other languages you've had to learn + + align:start position:0% +other languages you've had to learn + + + align:start position:0% +other languages you've had to learn +about case yeah + + align:start position:0% +about case yeah + + + align:start position:0% +about case yeah +so lerdo has case + + align:start position:0% +so lerdo has case + + + align:start position:0% +so lerdo has case +here are a bunch of nouns in their + + align:start position:0% +here are a bunch of nouns in their + + + align:start position:0% +here are a bunch of nouns in their +nominative and accusative forms so + + align:start position:0% +nominative and accusative forms so + + + align:start position:0% +nominative and accusative forms so +you've got Mela which means seawater it + + align:start position:0% +you've got Mela which means seawater it + + + align:start position:0% +you've got Mela which means seawater it +also means beer I guess on the theory + + align:start position:0% +also means beer I guess on the theory + + + align:start position:0% +also means beer I guess on the theory +that it's you know they're both foamy + + align:start position:0% +that it's you know they're both foamy + + + align:start position:0% +that it's you know they're both foamy +things that make you sick if you drink + + align:start position:0% +things that make you sick if you drink + + + align:start position:0% +things that make you sick if you drink +too much of it + + align:start position:0% +too much of it + + + align:start position:0% +too much of it +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um + + align:start position:0% + + + + align:start position:0% + +in their nominative forms and then + + align:start position:0% +in their nominative forms and then + + + align:start position:0% +in their nominative forms and then +you've got their accusative forms there + + align:start position:0% +you've got their accusative forms there + + + align:start position:0% +you've got their accusative forms there +which I won't read to you + + align:start position:0% +which I won't read to you + + + align:start position:0% +which I won't read to you +what's the accusative morpheme + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +Joseph n yeah so + + align:start position:0% +Joseph n yeah so + + + align:start position:0% +Joseph n yeah so +um oh dear I'm gonna have to do this + + align:start position:0% +um oh dear I'm gonna have to do this + + + align:start position:0% +um oh dear I'm gonna have to do this +writing everything twice thing again I + + align:start position:0% +writing everything twice thing again I + + + align:start position:0% +writing everything twice thing again I +really need to learn how to + + align:start position:0% +really need to learn how to + + + align:start position:0% +really need to learn how to +manipulate the screens better so the + + align:start position:0% +manipulate the screens better so the + + + align:start position:0% +manipulate the screens better so the +accusative suffix is in + + align:start position:0% + + + + align:start position:0% + +say it again the accusative suffix is n + + align:start position:0% +say it again the accusative suffix is n + + + align:start position:0% +say it again the accusative suffix is n +does anybody find any examples through + + align:start position:0% +does anybody find any examples through + + + align:start position:0% +does anybody find any examples through +their problem for that + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% +yes + + + align:start position:0% +yes +yeah so some of them have iron right + + align:start position:0% +yeah so some of them have iron right + + + align:start position:0% +yeah so some of them have iron right +like uh tree and river and spear I think + + align:start position:0% +like uh tree and river and spear I think + + + align:start position:0% +like uh tree and river and spear I think +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +um what determines whether the suffix is + + align:start position:0% +um what determines whether the suffix is + + + align:start position:0% +um what determines whether the suffix is +n or in + + align:start position:0% +n or in + + + align:start position:0% +n or in +yes + + align:start position:0% +yes + + + align:start position:0% +yes +the last letter of the now yeah the + + align:start position:0% +the last letter of the now yeah the + + + align:start position:0% +the last letter of the now yeah the +nominative yep so + + align:start position:0% +nominative yep so + + + align:start position:0% +nominative yep so +can you be more specific when what + + align:start position:0% +can you be more specific when what + + + align:start position:0% +can you be more specific when what +determines whether it's just an N or an + + align:start position:0% +determines whether it's just an N or an + + + align:start position:0% +determines whether it's just an N or an +i n + + align:start position:0% +i n + + + align:start position:0% +i n +oun + + align:start position:0% + + + + align:start position:0% + +that's true all of these examples uh it + + align:start position:0% +that's true all of these examples uh it + + + align:start position:0% +that's true all of these examples uh it +ends in an a + + align:start position:0% + + + + align:start position:0% + +chieve yeah so we might bravely say that + + align:start position:0% +chieve yeah so we might bravely say that + + + align:start position:0% +chieve yeah so we might bravely say that +it's about vowels versus consonants and + + align:start position:0% +it's about vowels versus consonants and + + + align:start position:0% +it's about vowels versus consonants and +we'd be right but you're absolutely + + align:start position:0% +we'd be right but you're absolutely + + + align:start position:0% +we'd be right but you're absolutely +right I haven't shown you that yeah + + align:start position:0% +right I haven't shown you that yeah + + + align:start position:0% +right I haven't shown you that yeah +um so the fact is uh after a consonant + + align:start position:0% +um so the fact is uh after a consonant + + + align:start position:0% +um so the fact is uh after a consonant +you get i n and after vowel you get in + + align:start position:0% +you get i n and after vowel you get in + + + align:start position:0% +you get i n and after vowel you get in +let me say that again over here + + align:start position:0% +let me say that again over here + + + align:start position:0% +let me say that again over here +um after a consonant you get in sorry + + align:start position:0% +um after a consonant you get in sorry + + + align:start position:0% +um after a consonant you get in sorry +after a vowel you get n and after a + + align:start position:0% +after a vowel you get n and after a + + + align:start position:0% +after a vowel you get n and after a +consonant you get i n yeah okay + + align:start position:0% +consonant you get i n yeah okay + + + align:start position:0% +consonant you get i n yeah okay +good so far so good + + align:start position:0% + + + + align:start position:0% + +uh here are some more nouns so the nouns + + align:start position:0% +uh here are some more nouns so the nouns + + + align:start position:0% +uh here are some more nouns so the nouns +up here the nouns you saw before there's + + align:start position:0% +up here the nouns you saw before there's + + + align:start position:0% +up here the nouns you saw before there's +some more nouns uh rain is Wonder tip is + + align:start position:0% + + + + align:start position:0% + +and the accusatives are winning Berlin + + align:start position:0% +and the accusatives are winning Berlin + + + align:start position:0% +and the accusatives are winning Berlin +and darling + + align:start position:0% +and darling + + + align:start position:0% +and darling +that's unexpected right given our Theory + + align:start position:0% +that's unexpected right given our Theory + + + align:start position:0% +that's unexpected right given our Theory +so far + + align:start position:0% + + + + align:start position:0% + +what do you think is going on + + align:start position:0% +what do you think is going on + + + align:start position:0% +what do you think is going on +yes + + align:start position:0% + + + + align:start position:0% + +so so it's as though you're removing the + + align:start position:0% +so so it's as though you're removing the + + + align:start position:0% +so so it's as though you're removing the +D.A right at the end yeah + + align:start position:0% +D.A right at the end yeah + + + align:start position:0% +D.A right at the end yeah +yes + + align:start position:0% + + + + align:start position:0% + +problems yeah we do we have a minimal + + align:start position:0% +problems yeah we do we have a minimal + + + align:start position:0% +problems yeah we do we have a minimal +pair it was sneaky of me to put that in + + align:start position:0% +pair it was sneaky of me to put that in + + + align:start position:0% +pair it was sneaky of me to put that in +there so there's Olinda that means a + + align:start position:0% +there so there's Olinda that means a + + + align:start position:0% +there so there's Olinda that means a +type of Stingray stingray + + align:start position:0% +type of Stingray stingray + + + align:start position:0% +type of Stingray stingray +um the accusation of that is woundan and + + align:start position:0% +um the accusation of that is woundan and + + + align:start position:0% +um the accusation of that is woundan and +then there's another one down here that + + align:start position:0% +then there's another one down here that + + + align:start position:0% +then there's another one down here that +means rain and the accusative of that is + + align:start position:0% +means rain and the accusative of that is + + + align:start position:0% +means rain and the accusative of that is +one in + + align:start position:0% + + + + align:start position:0% + +so here I am asking you + + align:start position:0% +so here I am asking you + + + align:start position:0% +so here I am asking you +how do we get from the nominative to the + + align:start position:0% +how do we get from the nominative to the + + + align:start position:0% +how do we get from the nominative to the +accusative + + align:start position:0% +accusative + + + align:start position:0% +accusative +yeah + + align:start position:0% + + + + align:start position:0% + +it would be nice but no well actually + + align:start position:0% +it would be nice but no well actually + + + align:start position:0% +it would be nice but no well actually +that's an interesting way to say it + + align:start position:0% +that's an interesting way to say it + + + align:start position:0% +that's an interesting way to say it +there's a way to say what you just said + + align:start position:0% +there's a way to say what you just said + + + align:start position:0% +there's a way to say what you just said +that would be true so maybe I should + + align:start position:0% +that would be true so maybe I should + + + align:start position:0% +that would be true so maybe I should +shouldn't just say no yes + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +there are people being modified to + + align:start position:0% +there are people being modified to + + + align:start position:0% +there are people being modified to +perform + + align:start position:0% +perform + + + align:start position:0% +perform +so I think I think you and you actually + + align:start position:0% +so I think I think you and you actually + + + align:start position:0% +so I think I think you and you actually +I'm sorry I shouldn't have spoken so + + align:start position:0% +I'm sorry I shouldn't have spoken so + + + align:start position:0% +I'm sorry I shouldn't have spoken so +quickly uh are on the right track look + + align:start position:0% +quickly uh are on the right track look + + + align:start position:0% +quickly uh are on the right track look +here I am saying how can we get from the + + align:start position:0% +here I am saying how can we get from the + + + align:start position:0% +here I am saying how can we get from the +nominative to the accusative right and + + align:start position:0% +nominative to the accusative right and + + + align:start position:0% +nominative to the accusative right and +the answer is despair right that that's + + align:start position:0% +the answer is despair right that that's + + + align:start position:0% +the answer is despair right that that's +what that's what that minimal pair is + + align:start position:0% +what that's what that minimal pair is + + + align:start position:0% +what that's what that minimal pair is +meant to do we had the same thing in + + align:start position:0% +meant to do we had the same thing in + + + align:start position:0% +meant to do we had the same thing in +Polish right where + + align:start position:0% +Polish right where + + + align:start position:0% +Polish right where +um the word for lie and the word for + + align:start position:0% +um the word for lie and the word for + + + align:start position:0% +um the word for lie and the word for +something else uh were the same in the + + align:start position:0% +something else uh were the same in the + + + align:start position:0% +something else uh were the same in the +singular but different in the plural so + + align:start position:0% +singular but different in the plural so + + + align:start position:0% +singular but different in the plural so +we convinced ourselves all right we + + align:start position:0% +we convinced ourselves all right we + + + align:start position:0% +we convinced ourselves all right we +can't predict the plural from the + + align:start position:0% +can't predict the plural from the + + + align:start position:0% +can't predict the plural from the +singular + + align:start position:0% +singular + + + align:start position:0% +singular +but we can predict the singular from the + + align:start position:0% +but we can predict the singular from the + + + align:start position:0% +but we can predict the singular from the +plural that's what we decided great so + + align:start position:0% +plural that's what we decided great so + + + align:start position:0% +plural that's what we decided great so +in Polish we said some of these nouns + + align:start position:0% +in Polish we said some of these nouns + + + align:start position:0% +in Polish we said some of these nouns +underlying the end in g some of them + + align:start position:0% +underlying the end in g some of them + + + align:start position:0% +underlying the end in g some of them +underlyingly and didn't K and there's a + + align:start position:0% +underlyingly and didn't K and there's a + + + align:start position:0% +underlyingly and didn't K and there's a +general rule that g becomes k at the end + + align:start position:0% +general rule that g becomes k at the end + + + align:start position:0% +general rule that g becomes k at the end +of a word + + align:start position:0% +of a word + + + align:start position:0% +of a word +can we do something similar here yes + + align:start position:0% + + + + align:start position:0% + +could be that could be that + + align:start position:0% +could be that could be that + + + align:start position:0% +could be that could be that +um two things it isn't it's part of a + + align:start position:0% +um two things it isn't it's part of a + + + align:start position:0% +um two things it isn't it's part of a +general thing but but also but also wait + + align:start position:0% +general thing but but also but also wait + + + align:start position:0% +general thing but but also but also wait +um you're absolutely right whenever + + align:start position:0% +um you're absolutely right whenever + + + align:start position:0% +um you're absolutely right whenever +we're we're looking at a data set we + + align:start position:0% +we're we're looking at a data set we + + + align:start position:0% +we're we're looking at a data set we +could say to ourselves well you know + + align:start position:0% +could say to ourselves well you know + + + align:start position:0% +could say to ourselves well you know +what maybe this is just an exception + + align:start position:0% +what maybe this is just an exception + + + align:start position:0% +what maybe this is just an exception +maybe I shouldn't try to account for + + align:start position:0% +maybe I shouldn't try to account for + + + align:start position:0% +maybe I shouldn't try to account for +this but + + align:start position:0% +this but + + + align:start position:0% +this but +in this class you should trust me not to + + align:start position:0% +in this class you should trust me not to + + + align:start position:0% +in this class you should trust me not to +do that to you so I'm going to give you + + align:start position:0% +do that to you so I'm going to give you + + + align:start position:0% +do that to you so I'm going to give you +data sets in which you will be able to + + align:start position:0% +data sets in which you will be able to + + + align:start position:0% +data sets in which you will be able to +come up with rules that account for + + align:start position:0% +come up with rules that account for + + + align:start position:0% +come up with rules that account for +things and in life that shouldn't be + + align:start position:0% +things and in life that shouldn't be + + + align:start position:0% +things and in life that shouldn't be +your first move probably right because + + align:start position:0% +your first move probably right because + + + align:start position:0% +your first move probably right because +that's I don't want to pick on you it's + + align:start position:0% +that's I don't want to pick on you it's + + + align:start position:0% +that's I don't want to pick on you it's +a move you hear people say make a lot + + align:start position:0% +a move you hear people say make a lot + + + align:start position:0% +a move you hear people say make a lot +hey maybe this is an exception but + + align:start position:0% +hey maybe this is an exception but + + + align:start position:0% +hey maybe this is an exception but +making that your first move is kind of a + + align:start position:0% +making that your first move is kind of a + + + align:start position:0% +making that your first move is kind of a +recipe for failing to make exciting + + align:start position:0% +recipe for failing to make exciting + + + align:start position:0% +recipe for failing to make exciting +discoveries right so if you're willing + + align:start position:0% +discoveries right so if you're willing + + + align:start position:0% +discoveries right so if you're willing +to exclude certain data I'm just not + + align:start position:0% +to exclude certain data I'm just not + + + align:start position:0% +to exclude certain data I'm just not +going to account for that sometimes + + align:start position:0% +going to account for that sometimes + + + align:start position:0% +going to account for that sometimes +that's the way to actually account for + + align:start position:0% +that's the way to actually account for + + + align:start position:0% +that's the way to actually account for +everything is by being willing to + + align:start position:0% +everything is by being willing to + + + align:start position:0% +everything is by being willing to +recognize exceptions but other times + + align:start position:0% +recognize exceptions but other times + + + align:start position:0% +recognize exceptions but other times +what it does is stop you from realizing + + align:start position:0% +what it does is stop you from realizing + + + align:start position:0% +what it does is stop you from realizing +no the exceptions have a have a general + + align:start position:0% +no the exceptions have a have a general + + + align:start position:0% +no the exceptions have a have a general +character we can we can understand what + + align:start position:0% +character we can we can understand what + + + align:start position:0% +character we can we can understand what +they all are so it's worth like correct + + align:start position:0% +they all are so it's worth like correct + + + align:start position:0% +they all are so it's worth like correct +maybe that can be part of a strategy + + align:start position:0% +maybe that can be part of a strategy + + + align:start position:0% +maybe that can be part of a strategy +corralling all the exceptions into one + + align:start position:0% +corralling all the exceptions into one + + + align:start position:0% +corralling all the exceptions into one +place and then looking at them all and + + align:start position:0% +place and then looking at them all and + + + align:start position:0% +place and then looking at them all and +trying to understand what's going on + + align:start position:0% +trying to understand what's going on + + + align:start position:0% +trying to understand what's going on +in this particular case the things that + + align:start position:0% +in this particular case the things that + + + align:start position:0% +in this particular case the things that +look exceptional right now are rain tip + + align:start position:0% +look exceptional right now are rain tip + + + align:start position:0% +look exceptional right now are rain tip +and curve we had this beautiful rule on + + align:start position:0% +and curve we had this beautiful rule on + + + align:start position:0% +and curve we had this beautiful rule on +the basis of the words that were up at + + align:start position:0% +the basis of the words that were up at + + + align:start position:0% +the basis of the words that were up at +the top and now these new data are + + align:start position:0% +the top and now these new data are + + + align:start position:0% +the top and now these new data are +breaking it right we want the accusative + + align:start position:0% +breaking it right we want the accusative + + + align:start position:0% +breaking it right we want the accusative +of belda to be beldan the fact that it's + + align:start position:0% +of belda to be beldan the fact that it's + + + align:start position:0% +of belda to be beldan the fact that it's +Berlin is weird yeah + + align:start position:0% +Berlin is weird yeah + + + align:start position:0% +Berlin is weird yeah +is there a way to do the trick that we + + align:start position:0% +is there a way to do the trick that we + + + align:start position:0% +is there a way to do the trick that we +did for Polish which was to say + + align:start position:0% +did for Polish which was to say + + + align:start position:0% +did for Polish which was to say +the plural is the useful is the thing + + align:start position:0% +the plural is the useful is the thing + + + align:start position:0% +the plural is the useful is the thing +that we can use to predict the singular + + align:start position:0% +that we can use to predict the singular + + + align:start position:0% +that we can use to predict the singular +right so we'll start with the plural and + + align:start position:0% +right so we'll start with the plural and + + + align:start position:0% +right so we'll start with the plural and +then we'll figure out how to make the + + align:start position:0% +then we'll figure out how to make the + + + align:start position:0% +then we'll figure out how to make the +singular can we play that game here + + align:start position:0% + + + + align:start position:0% + +yeah is there a base form of now that we + + align:start position:0% +yeah is there a base form of now that we + + + align:start position:0% +yeah is there a base form of now that we +don't know that is you get something + + align:start position:0% +don't know that is you get something + + + align:start position:0% +don't know that is you get something +added on to that which brings it into + + align:start position:0% +added on to that which brings it into + + + align:start position:0% +added on to that which brings it into +numbers so maybe maybe that's a way to + + align:start position:0% +numbers so maybe maybe that's a way to + + + align:start position:0% +numbers so maybe maybe that's a way to +think about it so and I think this is + + align:start position:0% +think about it so and I think this is + + + align:start position:0% +think about it so and I think this is +more or less what several people have + + align:start position:0% +more or less what several people have + + + align:start position:0% +more or less what several people have +been saying what do you wish the + + align:start position:0% +been saying what do you wish the + + + align:start position:0% +been saying what do you wish the +nominative of this was + + align:start position:0% + + + + align:start position:0% + +given our rules so we wish that they + + align:start position:0% +given our rules so we wish that they + + + align:start position:0% +given our rules so we wish that they +were one Bell and Dal right + + align:start position:0% + + + + align:start position:0% + +so I'm just going to write that down + + align:start position:0% +so I'm just going to write that down + + + align:start position:0% +so I'm just going to write that down +one Bell and Barrel + + align:start position:0% +one Bell and Barrel + + + align:start position:0% +one Bell and Barrel +and then if it were that well we would + + align:start position:0% +and then if it were that well we would + + + align:start position:0% +and then if it were that well we would +be able to get the accusative + + align:start position:0% +be able to get the accusative + + + align:start position:0% +be able to get the accusative +and we would need to do something to get + + align:start position:0% +and we would need to do something to get + + + align:start position:0% +and we would need to do something to get +the the nominative yeah + + align:start position:0% + + + + align:start position:0% + +I think that would be very attractive + + align:start position:0% +I think that would be very attractive + + + align:start position:0% +I think that would be very attractive +yeah so I think a lot is raising a good + + align:start position:0% +yeah so I think a lot is raising a good + + + align:start position:0% +yeah so I think a lot is raising a good +point all of the other words that I've + + align:start position:0% +point all of the other words that I've + + + align:start position:0% +point all of the other words that I've +shown you + + align:start position:0% +shown you + + + align:start position:0% +shown you +are they're all two syllables long yeah + + align:start position:0% +are they're all two syllables long yeah + + + align:start position:0% +are they're all two syllables long yeah +these words if there were words like + + align:start position:0% +these words if there were words like + + + align:start position:0% +these words if there were words like +they would be our first Lardo + + align:start position:0% +they would be our first Lardo + + + align:start position:0% +they would be our first Lardo +monosyllables + + align:start position:0% +monosyllables + + + align:start position:0% +monosyllables +now here's the fact about lairdel it + + align:start position:0% +now here's the fact about lairdel it + + + align:start position:0% +now here's the fact about lairdel it +doesn't have monosyllables yeah + + align:start position:0% +doesn't have monosyllables yeah + + + align:start position:0% +doesn't have monosyllables yeah +all of its words are at least two + + align:start position:0% +all of its words are at least two + + + align:start position:0% +all of its words are at least two +syllables long + + align:start position:0% + + + + align:start position:0% + +so apparently I think blood is + + align:start position:0% +so apparently I think blood is + + + align:start position:0% +so apparently I think blood is +absolutely right apparently that's being + + align:start position:0% +absolutely right apparently that's being + + + align:start position:0% +absolutely right apparently that's being +enforced here yeah so indeed these words + + align:start position:0% +enforced here yeah so indeed these words + + + align:start position:0% +enforced here yeah so indeed these words +a whole bunch of people said versions of + + align:start position:0% +a whole bunch of people said versions of + + + align:start position:0% +a whole bunch of people said versions of +this let me just Channel what you all + + align:start position:0% +this let me just Channel what you all + + + align:start position:0% +this let me just Channel what you all +said these words at the end rain tip and + + align:start position:0% +said these words at the end rain tip and + + + align:start position:0% +said these words at the end rain tip and +curve they have base forms that don't + + align:start position:0% +curve they have base forms that don't + + + align:start position:0% +curve they have base forms that don't +appear anywhere in a sense their base + + align:start position:0% +appear anywhere in a sense their base + + + align:start position:0% +appear anywhere in a sense their base +forms are one Bell and that's what you + + align:start position:0% +forms are one Bell and that's what you + + + align:start position:0% +forms are one Bell and that's what you +add the accusative to by a totally + + align:start position:0% +add the accusative to by a totally + + + align:start position:0% +add the accusative to by a totally +regular rule you know they end in + + align:start position:0% +regular rule you know they end in + + + align:start position:0% +regular rule you know they end in +consonants and so the the accusative is + + align:start position:0% +consonants and so the the accusative is + + + align:start position:0% +consonants and so the the accusative is +in + + align:start position:0% +in + + + align:start position:0% +in +and then we need another rule that says + + align:start position:0% +and then we need another rule that says + + + align:start position:0% +and then we need another rule that says +um add + + align:start position:0% +um add + + + align:start position:0% +um add +da + + align:start position:0% +da + + + align:start position:0% +da +to monosyllables + + align:start position:0% + + + + align:start position:0% + +something like that yeah so if you're in + + align:start position:0% +something like that yeah so if you're in + + + align:start position:0% +something like that yeah so if you're in +danger of having a monosyllabic lairdo + + align:start position:0% +danger of having a monosyllabic lairdo + + + align:start position:0% +danger of having a monosyllabic lairdo +word + + align:start position:0% +word + + + align:start position:0% +word +can you add + + align:start position:0% +can you add + + + align:start position:0% +can you add +to monosyllables + + align:start position:0% +to monosyllables + + + align:start position:0% +to monosyllables +lerdo doesn't like words that are only + + align:start position:0% +lerdo doesn't like words that are only + + + align:start position:0% +lerdo doesn't like words that are only +one syllable long this is what's called + + align:start position:0% +one syllable long this is what's called + + + align:start position:0% +one syllable long this is what's called +a minimal word requirement they're + + align:start position:0% +a minimal word requirement they're + + + align:start position:0% +a minimal word requirement they're +cross-linguistically quite common there + + align:start position:0% +cross-linguistically quite common there + + + align:start position:0% +cross-linguistically quite common there +are a lot of languages in the world that + + align:start position:0% +are a lot of languages in the world that + + + align:start position:0% +are a lot of languages in the world that +don't like their words to be too short + + align:start position:0% +don't like their words to be too short + + + align:start position:0% +don't like their words to be too short +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right good + + align:start position:0% +all right good + + + align:start position:0% +all right good +so far so good + + align:start position:0% + + + + align:start position:0% + +right so what we want to do is posit + + align:start position:0% +right so what we want to do is posit + + + align:start position:0% +right so what we want to do is posit +underlying forms which are often the + + align:start position:0% +underlying forms which are often the + + + align:start position:0% +underlying forms which are often the +same as the nominative but not always + + align:start position:0% +same as the nominative but not always + + + align:start position:0% +same as the nominative but not always +there are also these last three that + + align:start position:0% +there are also these last three that + + + align:start position:0% +there are also these last three that +have different forms okay + + align:start position:0% + + + + align:start position:0% + +okay one is a morpheme + + align:start position:0% +okay one is a morpheme + + + align:start position:0% +okay one is a morpheme +um one dot there Stingray species is a + + align:start position:0% +um one dot there Stingray species is a + + + align:start position:0% +um one dot there Stingray species is a +morpheme + + align:start position:0% +morpheme + + + align:start position:0% +morpheme +I don't know if we want to call this a + + align:start position:0% +I don't know if we want to call this a + + + align:start position:0% +I don't know if we want to call this a +morpheme or not this is why I was + + align:start position:0% +morpheme or not this is why I was + + + align:start position:0% +morpheme or not this is why I was +reacting the way I was before it it + + align:start position:0% +reacting the way I was before it it + + + align:start position:0% +reacting the way I was before it it +doesn't mean anything right it's just + + align:start position:0% +doesn't mean anything right it's just + + + align:start position:0% +doesn't mean anything right it's just +there + + align:start position:0% +there + + + align:start position:0% +there +so the word can be long enough yeah + + align:start position:0% +so the word can be long enough yeah + + + align:start position:0% +so the word can be long enough yeah +that's all it's for uh so I think + + align:start position:0% +that's all it's for uh so I think + + + align:start position:0% +that's all it's for uh so I think +linguists would mostly not call it a + + align:start position:0% +linguists would mostly not call it a + + + align:start position:0% +linguists would mostly not call it a +morpheme yeah it's uh it's kind of like + + align:start position:0% +morpheme yeah it's uh it's kind of like + + + align:start position:0% +morpheme yeah it's uh it's kind of like +um you know we said for Polish uh if a + + align:start position:0% +um you know we said for Polish uh if a + + + align:start position:0% +um you know we said for Polish uh if a +word ends with the G the G becomes a k + + align:start position:0% +word ends with the G the G becomes a k + + + align:start position:0% +word ends with the G the G becomes a k +the change from a g to a k isn't a + + align:start position:0% +the change from a g to a k isn't a + + + align:start position:0% +the change from a g to a k isn't a +morpheme it's part of something that + + align:start position:0% +morpheme it's part of something that + + + align:start position:0% +morpheme it's part of something that +polish prefers about its words it + + align:start position:0% +polish prefers about its words it + + + align:start position:0% +polish prefers about its words it +doesn't like them to end with G Lardo + + align:start position:0% +doesn't like them to end with G Lardo + + + align:start position:0% +doesn't like them to end with G Lardo +doesn't like words to be monosyllables + + align:start position:0% +doesn't like words to be monosyllables + + + align:start position:0% +doesn't like words to be monosyllables +and this is its repair so fixes that + + align:start position:0% +and this is its repair so fixes that + + + align:start position:0% +and this is its repair so fixes that +problem + + align:start position:0% +problem + + + align:start position:0% +problem +yeah + + align:start position:0% + + + + align:start position:0% + +I don't blame you + + align:start position:0% +I don't blame you + + + align:start position:0% +I don't blame you +um + + align:start position:0% + + + + align:start position:0% + +yep but they create a honestyable more + + align:start position:0% +yep but they create a honestyable more + + + align:start position:0% +yep but they create a honestyable more +things and build all the world + + align:start position:0% +things and build all the world + + + align:start position:0% +things and build all the world +um + + align:start position:0% + + + + align:start position:0% + +yeah I totally see what you mean so let + + align:start position:0% +yeah I totally see what you mean so let + + + align:start position:0% +yeah I totally see what you mean so let +me just repeat what you just said these + + align:start position:0% +me just repeat what you just said these + + + align:start position:0% +me just repeat what you just said these +people don't like monosyllables right + + align:start position:0% +people don't like monosyllables right + + + align:start position:0% +people don't like monosyllables right +and yet + + align:start position:0% +and yet + + + align:start position:0% +and yet +their lexicon is full of monosyllables + + align:start position:0% +their lexicon is full of monosyllables + + + align:start position:0% +their lexicon is full of monosyllables +right uh it's as though I don't know + + align:start position:0% +right uh it's as though I don't know + + + align:start position:0% +right uh it's as though I don't know +somebody else gave them their lexicon + + align:start position:0% +somebody else gave them their lexicon + + + align:start position:0% +somebody else gave them their lexicon +right and then they're doing their best + + align:start position:0% +right and then they're doing their best + + + align:start position:0% +right and then they're doing their best +to to improve it in the ways that the + + align:start position:0% +to to improve it in the ways that the + + + align:start position:0% +to to improve it in the ways that the +that will make them comfortable with it + + align:start position:0% +that will make them comfortable with it + + + align:start position:0% +that will make them comfortable with it +or another way to say it maybe + + align:start position:0% +or another way to say it maybe + + + align:start position:0% +or another way to say it maybe +um when we say they don't like + + align:start position:0% +um when we say they don't like + + + align:start position:0% +um when we say they don't like +monosyllables they don't like + + align:start position:0% +monosyllables they don't like + + + align:start position:0% +monosyllables they don't like +pronouncing Mama syllables yeah + + align:start position:0% +pronouncing Mama syllables yeah + + + align:start position:0% +pronouncing Mama syllables yeah +they don't mind monosyllables in their + + align:start position:0% +they don't mind monosyllables in their + + + align:start position:0% +they don't mind monosyllables in their +lexicon but they're not willing to + + align:start position:0% +lexicon but they're not willing to + + + align:start position:0% +lexicon but they're not willing to +pronounce them that way they have to do + + align:start position:0% +pronounce them that way they have to do + + + align:start position:0% +pronounce them that way they have to do +something to them kind of like polls + + align:start position:0% +something to them kind of like polls + + + align:start position:0% +something to them kind of like polls +don't mind words that end with G as long + + align:start position:0% +don't mind words that end with G as long + + + align:start position:0% +don't mind words that end with G as long +as they're in their brains right it's + + align:start position:0% +as they're in their brains right it's + + + align:start position:0% +as they're in their brains right it's +just saying them they don't like doing + + align:start position:0% +just saying them they don't like doing + + + align:start position:0% +just saying them they don't like doing +that they have to do something to them + + align:start position:0% +that they have to do something to them + + + align:start position:0% +that they have to do something to them +first yeah + + align:start position:0% +first yeah + + + align:start position:0% +first yeah +nice Point actually this is one of many + + align:start position:0% +nice Point actually this is one of many + + + align:start position:0% +nice Point actually this is one of many +places in linguistics where you get the + + align:start position:0% +places in linguistics where you get the + + + align:start position:0% +places in linguistics where you get the +feeling that languages are designed by + + align:start position:0% +feeling that languages are designed by + + + align:start position:0% +feeling that languages are designed by +committees which have different + + align:start position:0% +committees which have different + + + align:start position:0% +committees which have different +priorities you know that there's one + + align:start position:0% +priorities you know that there's one + + + align:start position:0% +priorities you know that there's one +group of people who are like making the + + align:start position:0% +group of people who are like making the + + + align:start position:0% +group of people who are like making the +Lexicon and another group of people who + + align:start position:0% +Lexicon and another group of people who + + + align:start position:0% +Lexicon and another group of people who +are like they I imagine them taking + + align:start position:0% +are like they I imagine them taking + + + align:start position:0% +are like they I imagine them taking +reports from the first committee and + + align:start position:0% +reports from the first committee and + + + align:start position:0% +reports from the first committee and +then they're like what you gave us what + + align:start position:0% +then they're like what you gave us what + + + align:start position:0% +then they're like what you gave us what +look at all these monosyllables yeah + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um so going further into Laredo then + + align:start position:0% +um so going further into Laredo then + + + align:start position:0% +um so going further into Laredo then +here are some more words + + align:start position:0% +here are some more words + + + align:start position:0% +here are some more words +um the word for fish is Yaga the word + + align:start position:0% +um the word for fish is Yaga the word + + + align:start position:0% +um the word for fish is Yaga the word +for Strings and the word for head is + + align:start position:0% +for Strings and the word for head is + + + align:start position:0% +for Strings and the word for head is +and + + align:start position:0% +and + + + align:start position:0% +and +um the accusatives are jugging bikin + + align:start position:0% + + + + align:start position:0% + +is everyone appropriately upset by this + + align:start position:0% +is everyone appropriately upset by this + + + align:start position:0% +is everyone appropriately upset by this +what what would we have expected the + + align:start position:0% +what what would we have expected the + + + align:start position:0% +what what would we have expected the +accusative of Yaga to be + + align:start position:0% +accusative of Yaga to be + + + align:start position:0% +accusative of Yaga to be +the word for fish + + align:start position:0% +the word for fish + + + align:start position:0% +the word for fish +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +um + + align:start position:0% +um + + + align:start position:0% +um +what should we do + + align:start position:0% +what should we do + + + align:start position:0% +what should we do +yeah Joseph + + align:start position:0% + + + + align:start position:0% + +ah so + + align:start position:0% +ah so + + + align:start position:0% +ah so +um why do you ask + + align:start position:0% +um why do you ask + + + align:start position:0% +um why do you ask +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so I mean they don't right yeah guys in + + align:start position:0% +so I mean they don't right yeah guys in + + + align:start position:0% +so I mean they don't right yeah guys in +the in a in a vowel + + align:start position:0% +the in a in a vowel + + + align:start position:0% +the in a in a vowel +right yeah + + align:start position:0% + + + + align:start position:0% + +so these three if we went from the + + align:start position:0% +so these three if we went from the + + + align:start position:0% +so these three if we went from the +accusative + + align:start position:0% +accusative + + + align:start position:0% +accusative +what are these three + + align:start position:0% +what are these three + + + align:start position:0% +what are these three +if we went from the accusative right if + + align:start position:0% +if we went from the accusative right if + + + align:start position:0% +if we went from the accusative right if +we started we did the same trick we did + + align:start position:0% +we started we did the same trick we did + + + align:start position:0% +we started we did the same trick we did +with the last three and said okay + + align:start position:0% +with the last three and said okay + + + align:start position:0% +with the last three and said okay +denominative I don't understand why the + + align:start position:0% +denominative I don't understand why the + + + align:start position:0% +denominative I don't understand why the +nominative is what it is but looking + + align:start position:0% +nominative is what it is but looking + + + align:start position:0% +nominative is what it is but looking +just at the accusative I wish that the + + align:start position:0% +just at the accusative I wish that the + + + align:start position:0% +just at the accusative I wish that the +the nominee that the underlying form of + + align:start position:0% +the nominee that the underlying form of + + + align:start position:0% +the nominee that the underlying form of +fish were yuck right that would work + + align:start position:0% +fish were yuck right that would work + + + align:start position:0% +fish were yuck right that would work +yeah so our our rule for accusatives + + align:start position:0% +yeah so our our rule for accusatives + + + align:start position:0% +yeah so our our rule for accusatives +would get you the accusative of yuck it + + align:start position:0% +would get you the accusative of yuck it + + + align:start position:0% +would get you the accusative of yuck it +would be yug in and everything would be + + align:start position:0% +would be yug in and everything would be + + + align:start position:0% +would be yug in and everything would be +perfect + + align:start position:0% +perfect + + + align:start position:0% +perfect +and then the question is why isn't the + + align:start position:0% +and then the question is why isn't the + + + align:start position:0% +and then the question is why isn't the +nominative yuck to which the answer + + align:start position:0% +nominative yuck to which the answer + + + align:start position:0% +nominative yuck to which the answer +could be blood is answered it's only one + + align:start position:0% +could be blood is answered it's only one + + + align:start position:0% +could be blood is answered it's only one +syllable long + + align:start position:0% +syllable long + + + align:start position:0% +syllable long +but then why isn't the accused the + + align:start position:0% +but then why isn't the accused the + + + align:start position:0% +but then why isn't the accused the +nominative of yeah + + align:start position:0% +nominative of yeah + + + align:start position:0% +nominative of yeah +and Joseph had a suggestion about that + + align:start position:0% +and Joseph had a suggestion about that + + + align:start position:0% +and Joseph had a suggestion about that +all end in a k yeah + + align:start position:0% +all end in a k yeah + + + align:start position:0% +all end in a k yeah +yeah so maybe I've got two general rule + + align:start position:0% +yeah so maybe I've got two general rule + + + align:start position:0% +yeah so maybe I've got two general rule +here it's not add dot to monosyllables + + align:start position:0% +here it's not add dot to monosyllables + + + align:start position:0% +here it's not add dot to monosyllables +it's add da to I'll say + + align:start position:0% +it's add da to I'll say + + + align:start position:0% +it's add da to I'll say +most on the syllables + + align:start position:0% +most on the syllables + + + align:start position:0% +most on the syllables +uh + + align:start position:0% +uh + + + align:start position:0% +uh +after + + align:start position:0% +after + + + align:start position:0% +after +K yeah + + align:start position:0% +K yeah + + + align:start position:0% +K yeah +um say the same thing over here + + align:start position:0% +um say the same thing over here + + + align:start position:0% +um say the same thing over here +um Adda to most minor syllables add uh + + align:start position:0% +um Adda to most minor syllables add uh + + + align:start position:0% +um Adda to most minor syllables add uh +okay yeah + + align:start position:0% +okay yeah + + + align:start position:0% +okay yeah +okay yeah just + + align:start position:0% + + + + align:start position:0% + +you cannot have two stops in a row + + align:start position:0% +you cannot have two stops in a row + + + align:start position:0% +you cannot have two stops in a row +yukda would break that that's right yeah + + align:start position:0% +yukda would break that that's right yeah + + + align:start position:0% +yukda would break that that's right yeah +there aren't any letter words that have + + align:start position:0% +there aren't any letter words that have + + + align:start position:0% +there aren't any letter words that have +two + + align:start position:0% +two + + + align:start position:0% +two +stops in a row yeah that's true yeah + + align:start position:0% +stops in a row yeah that's true yeah + + + align:start position:0% +stops in a row yeah that's true yeah +yeah + + align:start position:0% + + + + align:start position:0% + +uh so yeah + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um I think this is the last set of + + align:start position:0% +um I think this is the last set of + + + align:start position:0% +um I think this is the last set of +layered all data I was going to show you + + align:start position:0% +layered all data I was going to show you + + + align:start position:0% +layered all data I was going to show you +if I'm remembering right + + align:start position:0% +if I'm remembering right + + + align:start position:0% +if I'm remembering right +um no it's not there are some others + + align:start position:0% +um no it's not there are some others + + + align:start position:0% +um no it's not there are some others +sorry uh panda is blood Moga is water is + + align:start position:0% +sorry uh panda is blood Moga is water is + + + align:start position:0% +sorry uh panda is blood Moga is water is +dog and Garda is a kinship term uh lerdo + + align:start position:0% +dog and Garda is a kinship term uh lerdo + + + align:start position:0% +dog and Garda is a kinship term uh lerdo +kinship terminology is + + align:start position:0% +kinship terminology is + + + align:start position:0% +kinship terminology is +um extremely uh different from ours in + + align:start position:0% +um extremely uh different from ours in + + + align:start position:0% +um extremely uh different from ours in +ways that it would take a long time to + + align:start position:0% +ways that it would take a long time to + + + align:start position:0% +ways that it would take a long time to +explain but Garda roughly means a + + align:start position:0% +explain but Garda roughly means a + + + align:start position:0% +explain but Garda roughly means a +woman's child or a man's sister's child + + align:start position:0% +woman's child or a man's sister's child + + + align:start position:0% +woman's child or a man's sister's child +yeah + + align:start position:0% + + + + align:start position:0% + +yeah no I won't try to explain that to + + align:start position:0% +yeah no I won't try to explain that to + + + align:start position:0% +yeah no I won't try to explain that to +you uh uh it's very interesting but I I + + align:start position:0% +you uh uh it's very interesting but I I + + + align:start position:0% +you uh uh it's very interesting but I I +I refuse to talk about it right now + + align:start position:0% +I refuse to talk about it right now + + + align:start position:0% +I refuse to talk about it right now +um so the accusative Ganda is gandon + + align:start position:0% +um so the accusative Ganda is gandon + + + align:start position:0% +um so the accusative Ganda is gandon +which it shouldn't be right it should be + + align:start position:0% +which it shouldn't be right it should be + + + align:start position:0% +which it shouldn't be right it should be +ganden if it were going to be anything + + align:start position:0% +ganden if it were going to be anything + + + align:start position:0% +ganden if it were going to be anything +uh do we want the underlying I mean we + + align:start position:0% +uh do we want the underlying I mean we + + + align:start position:0% +uh do we want the underlying I mean we +have a rule that adds da do we want the + + align:start position:0% +have a rule that adds da do we want the + + + align:start position:0% +have a rule that adds da do we want the +underlying form to become + + align:start position:0% + + + + align:start position:0% + +no right if the underlying form were + + align:start position:0% +no right if the underlying form were + + + align:start position:0% +no right if the underlying form were +gone what would the accusative be + + align:start position:0% +gone what would the accusative be + + + align:start position:0% +gone what would the accusative be +Gan in yeah and it's not it's yeah so we + + align:start position:0% +Gan in yeah and it's not it's yeah so we + + + align:start position:0% +Gan in yeah and it's not it's yeah so we +need another rule what's the new rule + + align:start position:0% +need another rule what's the new rule + + + align:start position:0% +need another rule what's the new rule +going to say + + align:start position:0% + + + + align:start position:0% + +yes yep + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +yep yep + + align:start position:0% + + + + align:start position:0% + +right so so we're gonna + + align:start position:0% +right so so we're gonna + + + align:start position:0% +right so so we're gonna +so we're gonna deposit underlying forms + + align:start position:0% +so we're gonna deposit underlying forms + + + align:start position:0% +so we're gonna deposit underlying forms +that's nice we're going to positive + + align:start position:0% +that's nice we're going to positive + + + align:start position:0% +that's nice we're going to positive +underlying forms like + + align:start position:0% +underlying forms like + + + align:start position:0% +underlying forms like +and then we're going to have a rule uh + + align:start position:0% +and then we're going to have a rule uh + + + align:start position:0% +and then we're going to have a rule uh +change + + align:start position:0% +change + + + align:start position:0% +change +final oh to ah yeah so underlying Google + + align:start position:0% +final oh to ah yeah so underlying Google + + + align:start position:0% +final oh to ah yeah so underlying Google +gives you the accusative the mobile + + align:start position:0% +gives you the accusative the mobile + + + align:start position:0% +gives you the accusative the mobile +takes the n + + align:start position:0% +takes the n + + + align:start position:0% +takes the n +uh and you get mugun but there's another + + align:start position:0% +uh and you get mugun but there's another + + + align:start position:0% +uh and you get mugun but there's another +rule that says change final oh to ah + + align:start position:0% +rule that says change final oh to ah + + + align:start position:0% +rule that says change final oh to ah +that uh in the nominative changes no + + align:start position:0% +that uh in the nominative changes no + + + align:start position:0% +that uh in the nominative changes no +okay good + + align:start position:0% +okay good + + + align:start position:0% +okay good +and then + + align:start position:0% +and then + + + align:start position:0% +and then +yep all right and then I think this is + + align:start position:0% +yep all right and then I think this is + + + align:start position:0% +yep all right and then I think this is +the last set of data I wanted to show + + align:start position:0% +the last set of data I wanted to show + + + align:start position:0% +the last set of data I wanted to show +you uh the word for story is not a word + + align:start position:0% +you uh the word for story is not a word + + + align:start position:0% +you uh the word for story is not a word +for Boomerang is + + align:start position:0% +for Boomerang is + + + align:start position:0% +for Boomerang is +the word for umbilical chord is but the + + align:start position:0% +the word for umbilical chord is but the + + + align:start position:0% +the word for umbilical chord is but the +accusations + + align:start position:0% + + + + align:start position:0% + +what's the underlying form of these + + align:start position:0% +what's the underlying form of these + + + align:start position:0% +what's the underlying form of these +you guys all know the drill by now it's + + align:start position:0% +you guys all know the drill by now it's + + + align:start position:0% +you guys all know the drill by now it's +like take the accusative subtract the + + align:start position:0% +like take the accusative subtract the + + + align:start position:0% +like take the accusative subtract the +accusative suffix + + align:start position:0% + + + + align:start position:0% + +so what should the accusative of uh + + align:start position:0% +so what should the accusative of uh + + + align:start position:0% +so what should the accusative of uh +umbilical cord be + + align:start position:0% +umbilical cord be + + + align:start position:0% +umbilical cord be +sorry what should the bearer form of a + + align:start position:0% +sorry what should the bearer form of a + + + align:start position:0% +sorry what should the bearer form of a +umbilical cord be + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so we'll expect + + align:start position:0% + + + + align:start position:0% + +and uh there's something that says drop + + align:start position:0% +and uh there's something that says drop + + + align:start position:0% +and uh there's something that says drop +final k + + align:start position:0% +final k + + + align:start position:0% +final k +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so + + align:start position:0% +so + + + align:start position:0% +so +we start with but in and we form the + + align:start position:0% +we start with but in and we form the + + + align:start position:0% +we start with but in and we form the +accusative off of that but if it's + + align:start position:0% +accusative off of that but if it's + + + align:start position:0% +accusative off of that but if it's +nominative we get rid of the final K yes + + align:start position:0% + + + + align:start position:0% + +what happens what + + align:start position:0% + + + + align:start position:0% + +I missed it again + + align:start position:0% + + + + align:start position:0% + +why is I think it went away oh the word + + align:start position:0% +why is I think it went away oh the word + + + align:start position:0% +why is I think it went away oh the word +for the word for string or whatever it + + align:start position:0% +for the word for string or whatever it + + + align:start position:0% +for the word for string or whatever it +was yeah which started off as book yeah + + align:start position:0% +was yeah which started off as book yeah + + + align:start position:0% +was yeah which started off as book yeah +and we asked why aren't we dropping the + + align:start position:0% +and we asked why aren't we dropping the + + + align:start position:0% +and we asked why aren't we dropping the +final K yeah you're asking exactly the + + align:start position:0% +final K yeah you're asking exactly the + + + align:start position:0% +final K yeah you're asking exactly the +right question or similarly right we + + align:start position:0% +right question or similarly right we + + + align:start position:0% +right question or similarly right we +just came up with a rule that changes + + align:start position:0% +just came up with a rule that changes + + + align:start position:0% +just came up with a rule that changes +final right but it the word for story is + + align:start position:0% +final right but it the word for story is + + + align:start position:0% +final right but it the word for story is +not + + align:start position:0% +not + + + align:start position:0% +not +yeah yeah + + align:start position:0% + + + + align:start position:0% + +so we might have to say something we + + align:start position:0% +so we might have to say something we + + + align:start position:0% +so we might have to say something we +either have to work on our rules you're + + align:start position:0% +either have to work on our rules you're + + + align:start position:0% +either have to work on our rules you're +absolutely right right and make them + + align:start position:0% +absolutely right right and make them + + + align:start position:0% +absolutely right right and make them +more specific than that that's one kind + + align:start position:0% +more specific than that that's one kind + + + align:start position:0% +more specific than that that's one kind +of thing we could do yes + + align:start position:0% + + + + align:start position:0% + +so we couldn't do that for later we + + align:start position:0% +so we couldn't do that for later we + + + align:start position:0% +so we couldn't do that for later we +could say you know what uh there are + + align:start position:0% +could say you know what uh there are + + + align:start position:0% +could say you know what uh there are +nouns that do one of these and then + + align:start position:0% +nouns that do one of these and then + + + align:start position:0% +nouns that do one of these and then +they're announced that do another set of + + align:start position:0% +they're announced that do another set of + + + align:start position:0% +they're announced that do another set of +these right so they're rules that apply + + align:start position:0% +these right so they're rules that apply + + + align:start position:0% +these right so they're rules that apply +to particular classes of nouns yeah we + + align:start position:0% +to particular classes of nouns yeah we + + + align:start position:0% +to particular classes of nouns yeah we +could say we could absolutely say that + + align:start position:0% +could say we could absolutely say that + + + align:start position:0% +could say we could absolutely say that +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +here's another thing we could do though + + align:start position:0% +here's another thing we could do though + + + align:start position:0% +here's another thing we could do though +right so here's a just to stick to the + + align:start position:0% +right so here's a just to stick to the + + + align:start position:0% +right so here's a just to stick to the +to the case that you were worried about + + align:start position:0% +to the case that you were worried about + + + align:start position:0% +to the case that you were worried about +just a second ago + + align:start position:0% +just a second ago + + + align:start position:0% +just a second ago +um + + align:start position:0% +um + + + align:start position:0% +um +what I do with my chalk I guess I took + + align:start position:0% +what I do with my chalk I guess I took + + + align:start position:0% +what I do with my chalk I guess I took +it over there + + align:start position:0% +it over there + + + align:start position:0% +it over there +um we've got words like + + align:start position:0% + + + + align:start position:0% + +that means string + + align:start position:0% +that means string + + + align:start position:0% +that means string +underlying bitter and then we've got + + align:start position:0% +underlying bitter and then we've got + + + align:start position:0% +underlying bitter and then we've got +words like underlying + + align:start position:0% + + + + align:start position:0% + +that means + + align:start position:0% +that means + + + align:start position:0% +that means +umbilical cord right and with what we do + + align:start position:0% +umbilical cord right and with what we do + + + align:start position:0% +umbilical cord right and with what we do +is add ah because uh so what we do is + + align:start position:0% +is add ah because uh so what we do is + + + align:start position:0% +is add ah because uh so what we do is +add ah but with kunduk what we do is get + + align:start position:0% +add ah but with kunduk what we do is get + + + align:start position:0% +add ah but with kunduk what we do is get +rid of the final k + + align:start position:0% +rid of the final k + + + align:start position:0% +rid of the final k +so these two words are undergoing + + align:start position:0% +so these two words are undergoing + + + align:start position:0% +so these two words are undergoing +different types of rules yeah different + + align:start position:0% +different types of rules yeah different + + + align:start position:0% +different types of rules yeah different +sets of rules or similarly uh we had a + + align:start position:0% +sets of rules or similarly uh we had a + + + align:start position:0% +sets of rules or similarly uh we had a +word + + align:start position:0% +word + + + align:start position:0% +word +here let's do blood can do uh and that + + align:start position:0% +here let's do blood can do uh and that + + + align:start position:0% +here let's do blood can do uh and that +the ooh changed ah so we got Kanda yeah + + align:start position:0% +the ooh changed ah so we got Kanda yeah + + + align:start position:0% +the ooh changed ah so we got Kanda yeah +but now we've got a word which is + + align:start position:0% +but now we've got a word which is + + + align:start position:0% +but now we've got a word which is +underlying a look + + align:start position:0% +underlying a look + + + align:start position:0% +underlying a look +and what's happening there is that + + align:start position:0% +and what's happening there is that + + + align:start position:0% +and what's happening there is that +you're dropping the final K so you've + + align:start position:0% +you're dropping the final K so you've + + + align:start position:0% +you're dropping the final K so you've +got Lalu but you don't change the final + + align:start position:0% +got Lalu but you don't change the final + + + align:start position:0% +got Lalu but you don't change the final +U to an ah + + align:start position:0% +U to an ah + + + align:start position:0% +U to an ah +so we have these rules that seem to + + align:start position:0% +so we have these rules that seem to + + + align:start position:0% +so we have these rules that seem to +apply to certain bodies of examples and + + align:start position:0% +apply to certain bodies of examples and + + + align:start position:0% +apply to certain bodies of examples and +your suggestion which seems attractive + + align:start position:0% +your suggestion which seems attractive + + + align:start position:0% +your suggestion which seems attractive +is maybe these rules need a little bit + + align:start position:0% +is maybe these rules need a little bit + + + align:start position:0% +is maybe these rules need a little bit +of work maybe we need to get them to be + + align:start position:0% +of work maybe we need to get them to be + + + align:start position:0% +of work maybe we need to get them to be +more specific so they only apply to + + align:start position:0% +more specific so they only apply to + + + align:start position:0% +more specific so they only apply to +certain kinds of things yeah + + align:start position:0% +certain kinds of things yeah + + + align:start position:0% +certain kinds of things yeah +but here's another way to think about + + align:start position:0% +but here's another way to think about + + + align:start position:0% +but here's another way to think about +this and I'll leave you with this + + align:start position:0% + + + + align:start position:0% + +so here are the rules some of the rules + + align:start position:0% + + + + align:start position:0% + +so yeah the word for head starts off as + + align:start position:0% +so yeah the word for head starts off as + + + align:start position:0% +so yeah the word for head starts off as +well and we add ah because of rule two + + align:start position:0% +well and we add ah because of rule two + + + align:start position:0% +well and we add ah because of rule two +so we get relca + + align:start position:0% +so we get relca + + + align:start position:0% +so we get relca +but this is what we're asking uh the + + align:start position:0% +but this is what we're asking uh the + + + align:start position:0% +but this is what we're asking uh the +kind of thing we're asking + + align:start position:0% +kind of thing we're asking + + + align:start position:0% +kind of thing we're asking +um you start with why don't you apply + + align:start position:0% +um you start with why don't you apply + + + align:start position:0% +um you start with why don't you apply +the rule four to get and then maybe rule + + align:start position:0% +the rule four to get and then maybe rule + + + align:start position:0% +the rule four to get and then maybe rule +one so you'd get a little da yeah + + align:start position:0% +one so you'd get a little da yeah + + + align:start position:0% +one so you'd get a little da yeah +or you start with you apply rule four so + + align:start position:0% +or you start with you apply rule four so + + + align:start position:0% +or you start with you apply rule four so +you're getting ALU why don't you then + + align:start position:0% +you're getting ALU why don't you then + + + align:start position:0% +you're getting ALU why don't you then +apply rule three to get la la yeah these + + align:start position:0% +apply rule three to get la la yeah these + + + align:start position:0% +apply rule three to get la la yeah these +are the kinds of questions that we're + + align:start position:0% +are the kinds of questions that we're + + + align:start position:0% +are the kinds of questions that we're +asking and one kind of response to this + + align:start position:0% +asking and one kind of response to this + + + align:start position:0% +asking and one kind of response to this +kind of problem that people have + + align:start position:0% +kind of problem that people have + + + align:start position:0% +kind of problem that people have +classically given is to not only have + + align:start position:0% +classically given is to not only have + + + align:start position:0% +classically given is to not only have +rules but to have the rules apply in an + + align:start position:0% +rules but to have the rules apply in an + + + align:start position:0% +rules but to have the rules apply in an +order that is to have what's called Rule + + align:start position:0% +order that is to have what's called Rule + + + align:start position:0% +order that is to have what's called Rule +ordering it's as though there's an + + align:start position:0% +ordering it's as though there's an + + + align:start position:0% +ordering it's as though there's an +assembly line between one of these + + align:start position:0% +assembly line between one of these + + + align:start position:0% +assembly line between one of these +committees and the other yeah so uh rule + + align:start position:0% +committees and the other yeah so uh rule + + + align:start position:0% +committees and the other yeah so uh rule +two and Rule three happened before rule + + align:start position:0% +two and Rule three happened before rule + + + align:start position:0% +two and Rule three happened before rule +four + + align:start position:0% +four + + + align:start position:0% +four +so uh if you are starting with + + align:start position:0% +so uh if you are starting with + + + align:start position:0% +so uh if you are starting with +the basic form for head you first apply + + align:start position:0% +the basic form for head you first apply + + + align:start position:0% +the basic form for head you first apply +rule two + + align:start position:0% +rule two + + + align:start position:0% +rule two +um and get relca having applied rule 2 + + align:start position:0% +um and get relca having applied rule 2 + + + align:start position:0% +um and get relca having applied rule 2 +which adds the ah after look you're not + + align:start position:0% +which adds the ah after look you're not + + + align:start position:0% +which adds the ah after look you're not +in any danger of applying rule three or + + align:start position:0% +in any danger of applying rule three or + + + align:start position:0% +in any danger of applying rule three or +rule four rule three never mind but rule + + align:start position:0% +rule four rule three never mind but rule + + + align:start position:0% +rule four rule three never mind but rule +four which would have gotten rid of a + + align:start position:0% +four which would have gotten rid of a + + + align:start position:0% +four which would have gotten rid of a +final K doesn't apply anymore because + + align:start position:0% +final K doesn't apply anymore because + + + align:start position:0% +final K doesn't apply anymore because +well it there isn't the final pay + + align:start position:0% +well it there isn't the final pay + + + align:start position:0% +well it there isn't the final pay +anymore yeah or naluk which is the base + + align:start position:0% +anymore yeah or naluk which is the base + + + align:start position:0% +anymore yeah or naluk which is the base +form for story + + align:start position:0% +form for story + + + align:start position:0% +form for story +um rule four happens after rule two so + + align:start position:0% +um rule four happens after rule two so + + + align:start position:0% +um rule four happens after rule two so +and Rule three so uh rule four gets rid + + align:start position:0% +and Rule three so uh rule four gets rid + + + align:start position:0% +and Rule three so uh rule four gets rid +of the K and gives you and you can + + align:start position:0% +of the K and gives you and you can + + + align:start position:0% +of the K and gives you and you can +imagine now at this point the rule three + + align:start position:0% +imagine now at this point the rule three + + + align:start position:0% +imagine now at this point the rule three +people are like hey give us that word we + + align:start position:0% +people are like hey give us that word we + + + align:start position:0% +people are like hey give us that word we +want to get rid of that ooh but it's too + + align:start position:0% +want to get rid of that ooh but it's too + + + align:start position:0% +want to get rid of that ooh but it's too +late rule three has had its time yeah + + align:start position:0% +late rule three has had its time yeah + + + align:start position:0% +late rule three has had its time yeah +um you don't get to apply it anymore so + + align:start position:0% +um you don't get to apply it anymore so + + + align:start position:0% +um you don't get to apply it anymore so +this is one way of handling these kinds + + align:start position:0% +this is one way of handling these kinds + + + align:start position:0% +this is one way of handling these kinds +of problems is to see these rules that + + align:start position:0% +of problems is to see these rules that + + + align:start position:0% +of problems is to see these rules that +change things they're not just rules + + align:start position:0% +change things they're not just rules + + + align:start position:0% +change things they're not just rules +that change things they're rules that + + align:start position:0% +that change things they're rules that + + + align:start position:0% +that change things they're rules that +apply in an order there's a series of + + align:start position:0% +apply in an order there's a series of + + + align:start position:0% +apply in an order there's a series of +processes that you apply and uh you have + + align:start position:0% +processes that you apply and uh you have + + + align:start position:0% +processes that you apply and uh you have +to apply them in one one or in the + + align:start position:0% +to apply them in one one or in the + + + align:start position:0% +to apply them in one one or in the +correct order and not in the incorrect + + align:start position:0% +correct order and not in the incorrect + + + align:start position:0% +correct order and not in the incorrect +order to get the result Joseph + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +that's that is a way to think about this + + align:start position:0% +that's that is a way to think about this + + + align:start position:0% +that's that is a way to think about this +yes a classic way we'll talk about other + + align:start position:0% +yes a classic way we'll talk about other + + + align:start position:0% +yes a classic way we'll talk about other +ways to think about this kind of problem + + align:start position:0% +ways to think about this kind of problem + + + align:start position:0% +ways to think about this kind of problem +but this is one + + align:start position:0% +but this is one + + + align:start position:0% +but this is one +all right let's stop there \ No newline at end of file diff --git a/wKMUrhlkExw.txt b/wKMUrhlkExw.txt new file mode 100644 index 0000000000000000000000000000000000000000..266ef8d225e6128feea326fe3c430e70a5d22ba7 --- /dev/null +++ b/wKMUrhlkExw.txt @@ -0,0 +1,7723 @@ +align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +down. + + align:start position:0% +down. + + + align:start position:0% +down. +Hey + + align:start position:0% +Hey + + + align:start position:0% +Hey +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +[Music] + + align:start position:0% + + + + align:start position:0% + +Hi, last time we started a discussion of + + align:start position:0% +Hi, last time we started a discussion of + + + align:start position:0% +Hi, last time we started a discussion of +the dynamics of feedback systems. Today + + align:start position:0% +the dynamics of feedback systems. Today + + + align:start position:0% +the dynamics of feedback systems. Today +we're going to extend that discussion + + align:start position:0% +we're going to extend that discussion + + + align:start position:0% +we're going to extend that discussion +and in particular begin to look at the + + align:start position:0% +and in particular begin to look at the + + + align:start position:0% +and in particular begin to look at the +issue of stability of feedback systems. + + align:start position:0% +issue of stability of feedback systems. + + + align:start position:0% +issue of stability of feedback systems. +Well, the problem really isn't + + align:start position:0% +Well, the problem really isn't + + + align:start position:0% +Well, the problem really isn't +stability. The problem is lack of + + align:start position:0% +stability. The problem is lack of + + + align:start position:0% +stability. The problem is lack of +stability or instability. And we're + + align:start position:0% +stability or instability. And we're + + + align:start position:0% +stability or instability. And we're +going to look at at how that comes about + + align:start position:0% +going to look at at how that comes about + + + align:start position:0% +going to look at at how that comes about +and how we can analyze the stability of + + align:start position:0% +and how we can analyze the stability of + + + align:start position:0% +and how we can analyze the stability of +a feedback system. + + align:start position:0% +a feedback system. + + + align:start position:0% +a feedback system. +In particular, what we have discovered + + align:start position:0% +In particular, what we have discovered + + + align:start position:0% +In particular, what we have discovered +earlier is that we generally like to + + align:start position:0% +earlier is that we generally like to + + + align:start position:0% +earlier is that we generally like to +have a large loop transmission magnitude + + align:start position:0% +have a large loop transmission magnitude + + + align:start position:0% +have a large loop transmission magnitude +at least at low frequencies in order to + + align:start position:0% +at least at low frequencies in order to + + + align:start position:0% +at least at low frequencies in order to +ensure system desensitivity. + + align:start position:0% +ensure system desensitivity. + + + align:start position:0% +ensure system desensitivity. +What we find out unfortunately is that + + align:start position:0% +What we find out unfortunately is that + + + align:start position:0% +What we find out unfortunately is that +as we when we take a feedback system and + + align:start position:0% +as we when we take a feedback system and + + + align:start position:0% +as we when we take a feedback system and +begin to increase the loop transmission + + align:start position:0% +begin to increase the loop transmission + + + align:start position:0% +begin to increase the loop transmission +magnitude, the system invariably becomes + + align:start position:0% +magnitude, the system invariably becomes + + + align:start position:0% +magnitude, the system invariably becomes +unstable. And unfortunately that very + + align:start position:0% +unstable. And unfortunately that very + + + align:start position:0% +unstable. And unfortunately that very +frequently happens before the system + + align:start position:0% +frequently happens before the system + + + align:start position:0% +frequently happens before the system +performs as well as we'd like it to. And + + align:start position:0% +performs as well as we'd like it to. And + + + align:start position:0% +performs as well as we'd like it to. And +so what we want to look at is the + + align:start position:0% +so what we want to look at is the + + + align:start position:0% +so what we want to look at is the +trade-off that generally exists between + + align:start position:0% +trade-off that generally exists between + + + align:start position:0% +trade-off that generally exists between +on the one hand large loop transmission + + align:start position:0% +on the one hand large loop transmission + + + align:start position:0% +on the one hand large loop transmission +magnitude that gives us good + + align:start position:0% +magnitude that gives us good + + + align:start position:0% +magnitude that gives us good +desensitivity possibly fast speed of + + align:start position:0% +desensitivity possibly fast speed of + + + align:start position:0% +desensitivity possibly fast speed of +response or equivalently wide bandwidth + + align:start position:0% +response or equivalently wide bandwidth + + + align:start position:0% +response or equivalently wide bandwidth +and the stability of the system. So + + align:start position:0% +and the stability of the system. So + + + align:start position:0% +and the stability of the system. So +there's almost invariably a compromise + + align:start position:0% +there's almost invariably a compromise + + + align:start position:0% +there's almost invariably a compromise +that involves those three quantities. + + align:start position:0% +that involves those three quantities. + + + align:start position:0% +that involves those three quantities. +We can get a very non-rigorous though + + align:start position:0% +We can get a very non-rigorous though + + + align:start position:0% +We can get a very non-rigorous though +somewhat physically satisfying feeling + + align:start position:0% +somewhat physically satisfying feeling + + + align:start position:0% +somewhat physically satisfying feeling +for why we might have a stability + + align:start position:0% +for why we might have a stability + + + align:start position:0% +for why we might have a stability +problem with a feedback system by + + align:start position:0% +problem with a feedback system by + + + align:start position:0% +problem with a feedback system by +considering what happens in a system + + align:start position:0% +considering what happens in a system + + + align:start position:0% +considering what happens in a system +that has large loop transmission + + align:start position:0% +that has large loop transmission + + + align:start position:0% +that has large loop transmission +magnitude. Suppose here is where we'd + + align:start position:0% +magnitude. Suppose here is where we'd + + + align:start position:0% +magnitude. Suppose here is where we'd +like the output of a system to be and + + align:start position:0% +like the output of a system to be and + + + align:start position:0% +like the output of a system to be and +here's where the output actually is. The + + align:start position:0% +here's where the output actually is. The + + + align:start position:0% +here's where the output actually is. The +system senses that there's a large error + + align:start position:0% +system senses that there's a large error + + + align:start position:0% +system senses that there's a large error +between input and output. And if it's a + + align:start position:0% +between input and output. And if it's a + + + align:start position:0% +between input and output. And if it's a +high gain system, a system with large + + align:start position:0% +high gain system, a system with large + + + align:start position:0% +high gain system, a system with large +loop transmission magnitude, it begins + + align:start position:0% +loop transmission magnitude, it begins + + + align:start position:0% +loop transmission magnitude, it begins +to drive the output in order to get it + + align:start position:0% +to drive the output in order to get it + + + align:start position:0% +to drive the output in order to get it +into better correspondence with the + + align:start position:0% +into better correspondence with the + + + align:start position:0% +into better correspondence with the +command, the value that we'd like to + + align:start position:0% +command, the value that we'd like to + + + align:start position:0% +command, the value that we'd like to +have for the output. The difficulty + + align:start position:0% +have for the output. The difficulty + + + align:start position:0% +have for the output. The difficulty +comes about in the with a high gain + + align:start position:0% +comes about in the with a high gain + + + align:start position:0% +comes about in the with a high gain +system that drive may be very pronounced + + align:start position:0% +system that drive may be very pronounced + + + align:start position:0% +system that drive may be very pronounced +very fast and the system unfortunately + + align:start position:0% +very fast and the system unfortunately + + + align:start position:0% +very fast and the system unfortunately +has sort of imperfect knowledge of the + + align:start position:0% +has sort of imperfect knowledge of the + + + align:start position:0% +has sort of imperfect knowledge of the +effect it's having on the actual error + + align:start position:0% +effect it's having on the actual error + + + align:start position:0% +effect it's having on the actual error +because of time delays associated with + + align:start position:0% +because of time delays associated with + + + align:start position:0% +because of time delays associated with +the dynamics of the elements in the loop + + align:start position:0% +the dynamics of the elements in the loop + + + align:start position:0% +the dynamics of the elements in the loop +even though the output may be changing. + + align:start position:0% +even though the output may be changing. + + + align:start position:0% +even though the output may be changing. +We may not sense that immediately + + align:start position:0% +We may not sense that immediately + + + align:start position:0% +We may not sense that immediately +because of the lowass nature of some of + + align:start position:0% +because of the lowass nature of some of + + + align:start position:0% +because of the lowass nature of some of +the elements in the loop and + + align:start position:0% +the elements in the loop and + + + align:start position:0% +the elements in the loop and +consequently the system may not stop + + align:start position:0% +consequently the system may not stop + + + align:start position:0% +consequently the system may not stop +driving soon enough. It may overshoot. + + align:start position:0% +driving soon enough. It may overshoot. + + + align:start position:0% +driving soon enough. It may overshoot. +it may drive past the point of zero + + align:start position:0% +it may drive past the point of zero + + + align:start position:0% +it may drive past the point of zero +error. In fact, if we have sufficiently + + align:start position:0% +error. In fact, if we have sufficiently + + + align:start position:0% +error. In fact, if we have sufficiently +high gain coupled with sufficiently long + + align:start position:0% +high gain coupled with sufficiently long + + + align:start position:0% +high gain coupled with sufficiently long +time delays or or the correct incorrect + + align:start position:0% +time delays or or the correct incorrect + + + align:start position:0% +time delays or or the correct incorrect +type of lowass behavior, while the error + + align:start position:0% +type of lowass behavior, while the error + + + align:start position:0% +type of lowass behavior, while the error +that we cause, the overshoot in the + + align:start position:0% +that we cause, the overshoot in the + + + align:start position:0% +that we cause, the overshoot in the +opposite direction may actually exceed + + align:start position:0% +opposite direction may actually exceed + + + align:start position:0% +opposite direction may actually exceed +our initial error. And when that + + align:start position:0% +our initial error. And when that + + + align:start position:0% +our initial error. And when that +happens, it's certainly possible for the + + align:start position:0% +happens, it's certainly possible for the + + + align:start position:0% +happens, it's certainly possible for the +system to break into to oscillation. And + + align:start position:0% +system to break into to oscillation. And + + + align:start position:0% +system to break into to oscillation. And +that's what we have to look at. + + align:start position:0% +that's what we have to look at. + + + align:start position:0% +that's what we have to look at. +The conventional definition of stability + + align:start position:0% +The conventional definition of stability + + + align:start position:0% +The conventional definition of stability +for a feedback system or for any system + + align:start position:0% +for a feedback system or for any system + + + align:start position:0% +for a feedback system or for any system +for that matter usually is made in terms + + align:start position:0% +for that matter usually is made in terms + + + align:start position:0% +for that matter usually is made in terms +of bounded input resulting in a bounded + + align:start position:0% +of bounded input resulting in a bounded + + + align:start position:0% +of bounded input resulting in a bounded +output. That is if we + + align:start position:0% +output. That is if we + + + align:start position:0% +output. That is if we +test our system with any input which is + + align:start position:0% +test our system with any input which is + + + align:start position:0% +test our system with any input which is +bounded. That's to say if the magnitude + + align:start position:0% +bounded. That's to say if the magnitude + + + align:start position:0% +bounded. That's to say if the magnitude +of the input integrated over all time is + + align:start position:0% +of the input integrated over all time is + + + align:start position:0% +of the input integrated over all time is +bounded. + + align:start position:0% +bounded. + + + align:start position:0% +bounded. +Then any one of those test inputs should + + align:start position:0% +Then any one of those test inputs should + + + align:start position:0% +Then any one of those test inputs should +yield a bounded output. In other words, + + align:start position:0% +yield a bounded output. In other words, + + + align:start position:0% +yield a bounded output. In other words, +the same measure of the output, the + + align:start position:0% +the same measure of the output, the + + + align:start position:0% +the same measure of the output, the +magnitude of the output integrated over + + align:start position:0% +magnitude of the output integrated over + + + align:start position:0% +magnitude of the output integrated over +all time should be bounded for any input + + align:start position:0% +all time should be bounded for any input + + + align:start position:0% +all time should be bounded for any input +which satisfies the top condition. And + + align:start position:0% +which satisfies the top condition. And + + + align:start position:0% +which satisfies the top condition. And +that's a mathematical definition of of + + align:start position:0% +that's a mathematical definition of of + + + align:start position:0% +that's a mathematical definition of of +stability which is adequate for either + + align:start position:0% +stability which is adequate for either + + + align:start position:0% +stability which is adequate for either +linear or nonlinear systems. In general, + + align:start position:0% +linear or nonlinear systems. In general, + + + align:start position:0% +linear or nonlinear systems. In general, +the determination of stability for + + align:start position:0% +the determination of stability for + + + align:start position:0% +the determination of stability for +nonlinear systems is a very difficult + + align:start position:0% +nonlinear systems is a very difficult + + + align:start position:0% +nonlinear systems is a very difficult +one because stability for a nonlinear + + align:start position:0% +one because stability for a nonlinear + + + align:start position:0% +one because stability for a nonlinear +system can very easily depend on the + + align:start position:0% +system can very easily depend on the + + + align:start position:0% +system can very easily depend on the +actual input that we apply. In other + + align:start position:0% +actual input that we apply. In other + + + align:start position:0% +actual input that we apply. In other +words, certain bounded inputs may result + + align:start position:0% +words, certain bounded inputs may result + + + align:start position:0% +words, certain bounded inputs may result +in a bounded output whereas other + + align:start position:0% +in a bounded output whereas other + + + align:start position:0% +in a bounded output whereas other +bounded inputs may not for a nonlinear + + align:start position:0% +bounded inputs may not for a nonlinear + + + align:start position:0% +bounded inputs may not for a nonlinear +system. The problem is in a sense much + + align:start position:0% +system. The problem is in a sense much + + + align:start position:0% +system. The problem is in a sense much +simpler for a linear system. In fact, uh + + align:start position:0% +simpler for a linear system. In fact, uh + + + align:start position:0% +simpler for a linear system. In fact, uh +the stability of a linear system can be + + align:start position:0% +the stability of a linear system can be + + + align:start position:0% +the stability of a linear system can be +determined with any single bounded test + + align:start position:0% +determined with any single bounded test + + + align:start position:0% +determined with any single bounded test +input. If the system's stable for any + + align:start position:0% +input. If the system's stable for any + + + align:start position:0% +input. If the system's stable for any +test input that's bounded, it will be + + align:start position:0% +test input that's bounded, it will be + + + align:start position:0% +test input that's bounded, it will be +demonstrate stability for any other + + align:start position:0% +demonstrate stability for any other + + + align:start position:0% +demonstrate stability for any other +bounded test input. And furthermore, we + + align:start position:0% +bounded test input. And furthermore, we + + + align:start position:0% +bounded test input. And furthermore, we +can also define the stability for a + + align:start position:0% +can also define the stability for a + + + align:start position:0% +can also define the stability for a +linear system by looking at the transfer + + align:start position:0% +linear system by looking at the transfer + + + align:start position:0% +linear system by looking at the transfer +function of the system, the closed loop + + align:start position:0% +function of the system, the closed loop + + + align:start position:0% +function of the system, the closed loop +transfer function in the case of a + + align:start position:0% +transfer function in the case of a + + + align:start position:0% +transfer function in the case of a +feedback system. And if all the poles of + + align:start position:0% +feedback system. And if all the poles of + + + align:start position:0% +feedback system. And if all the poles of +that transfer function are in the left + + align:start position:0% +that transfer function are in the left + + + align:start position:0% +that transfer function are in the left +half of the splane, in other words, if + + align:start position:0% +half of the splane, in other words, if + + + align:start position:0% +half of the splane, in other words, if +they all have negative real parts, then + + align:start position:0% +they all have negative real parts, then + + + align:start position:0% +they all have negative real parts, then +the system's stable. The reason, of + + align:start position:0% +the system's stable. The reason, of + + + align:start position:0% +the system's stable. The reason, of +course, is that when we look at the + + align:start position:0% +course, is that when we look at the + + + align:start position:0% +course, is that when we look at the +output that results for any particular + + align:start position:0% +output that results for any particular + + + align:start position:0% +output that results for any particular +input, there are terms that correspond + + align:start position:0% +input, there are terms that correspond + + + align:start position:0% +input, there are terms that correspond +really to the homogeneous solution of + + align:start position:0% +really to the homogeneous solution of + + + align:start position:0% +really to the homogeneous solution of +the system differential equation. Those + + align:start position:0% +the system differential equation. Those + + + align:start position:0% +the system differential equation. Those +terms will include only negative + + align:start position:0% +terms will include only negative + + + align:start position:0% +terms will include only negative +decaying terms uh terms with uh that + + align:start position:0% +decaying terms uh terms with uh that + + + align:start position:0% +decaying terms uh terms with uh that +decay with time. If we have all the + + align:start position:0% +decay with time. If we have all the + + + align:start position:0% +decay with time. If we have all the +poles of the system in the left half + + align:start position:0% +poles of the system in the left half + + + align:start position:0% +poles of the system in the left half +plane. Conversely, if there are one or + + align:start position:0% +plane. Conversely, if there are one or + + + align:start position:0% +plane. Conversely, if there are one or +more poles in the right half plane, why + + align:start position:0% +more poles in the right half plane, why + + + align:start position:0% +more poles in the right half plane, why +then we'll get exponentially growing + + align:start position:0% +then we'll get exponentially growing + + + align:start position:0% +then we'll get exponentially growing +terms from the homogeneous solution of + + align:start position:0% +terms from the homogeneous solution of + + + align:start position:0% +terms from the homogeneous solution of +the system equation. Consequently, the + + align:start position:0% +the system equation. Consequently, the + + + align:start position:0% +the system equation. Consequently, the +system will be unstable. There's a + + align:start position:0% +system will be unstable. There's a + + + align:start position:0% +system will be unstable. There's a +special case which has which occurs when + + align:start position:0% +special case which has which occurs when + + + align:start position:0% +special case which has which occurs when +there are poles on the axis in other + + align:start position:0% +there are poles on the axis in other + + + align:start position:0% +there are poles on the axis in other +words an integrator or a syosidal + + align:start position:0% +words an integrator or a syosidal + + + align:start position:0% +words an integrator or a syosidal +oscillator which has a pair of complex + + align:start position:0% +oscillator which has a pair of complex + + + align:start position:0% +oscillator which has a pair of complex +conjugate poles on the imaginary axis + + align:start position:0% +conjugate poles on the imaginary axis + + + align:start position:0% +conjugate poles on the imaginary axis +and there the stability at least in a + + align:start position:0% +and there the stability at least in a + + + align:start position:0% +and there the stability at least in a +bounded input bounded output sense can + + align:start position:0% +bounded input bounded output sense can + + + align:start position:0% +bounded input bounded output sense can +depend on a test input but that's sort + + align:start position:0% +depend on a test input but that's sort + + + align:start position:0% +depend on a test input but that's sort +of a pathological case and we really for + + align:start position:0% +of a pathological case and we really for + + + align:start position:0% +of a pathological case and we really for +our purposes we'll consider it unstable + + align:start position:0% +our purposes we'll consider it unstable + + + align:start position:0% +our purposes we'll consider it unstable +if we have any any poles of the system + + align:start position:0% +if we have any any poles of the system + + + align:start position:0% +if we have any any poles of the system +transfer function on the imaginary axis. + + align:start position:0% +transfer function on the imaginary axis. + + + align:start position:0% +transfer function on the imaginary axis. +Let's look at a system and see how we + + align:start position:0% +Let's look at a system and see how we + + + align:start position:0% +Let's look at a system and see how we +might get into a stability problem. + + align:start position:0% +might get into a stability problem. + + + align:start position:0% +might get into a stability problem. +Let's consider a system where all of the + + align:start position:0% +Let's consider a system where all of the + + + align:start position:0% +Let's consider a system where all of the +dynamics are concentrated in the forward + + align:start position:0% +dynamics are concentrated in the forward + + + align:start position:0% +dynamics are concentrated in the forward +path. We'll see that that doesn't make + + align:start position:0% +path. We'll see that that doesn't make + + + align:start position:0% +path. We'll see that that doesn't make +any difference. The critical thing from + + align:start position:0% +any difference. The critical thing from + + + align:start position:0% +any difference. The critical thing from +a point of view of stability is a loop + + align:start position:0% +a point of view of stability is a loop + + + align:start position:0% +a point of view of stability is a loop +transmission, not how the loop + + align:start position:0% +transmission, not how the loop + + + align:start position:0% +transmission, not how the loop +transmission is distributed between the + + align:start position:0% +transmission is distributed between the + + + align:start position:0% +transmission is distributed between the +forward path and the feedback path. + + align:start position:0% +forward path and the feedback path. + + + align:start position:0% +forward path and the feedback path. +Furthermore, we'll take our standard + + align:start position:0% +Furthermore, we'll take our standard + + + align:start position:0% +Furthermore, we'll take our standard +system and actually have a value of f of + + align:start position:0% +system and actually have a value of f of + + + align:start position:0% +system and actually have a value of f of +one. So we have a unit unity feedback + + align:start position:0% +one. So we have a unit unity feedback + + + align:start position:0% +one. So we have a unit unity feedback +system and that says that the negative + + align:start position:0% +system and that says that the negative + + + align:start position:0% +system and that says that the negative +of the loop transmission is identically + + align:start position:0% +of the loop transmission is identically + + + align:start position:0% +of the loop transmission is identically +equal to the forward path transmission a + + align:start position:0% +equal to the forward path transmission a + + + align:start position:0% +equal to the forward path transmission a +of s. + + align:start position:0% +of s. + + + align:start position:0% +of s. +Last time we looked at what happened to + + align:start position:0% +Last time we looked at what happened to + + + align:start position:0% +Last time we looked at what happened to +the closed loop transfer function for + + align:start position:0% +the closed loop transfer function for + + + align:start position:0% +the closed loop transfer function for +certain specific cases of loop + + align:start position:0% +certain specific cases of loop + + + align:start position:0% +certain specific cases of loop +transmission. In particular in this + + align:start position:0% +transmission. In particular in this + + + align:start position:0% +transmission. In particular in this +particular system if we have a forward + + align:start position:0% +particular system if we have a forward + + + align:start position:0% +particular system if we have a forward +path transfer function that's first + + align:start position:0% +path transfer function that's first + + + align:start position:0% +path transfer function that's first +order a K not over to a S + one and A + + align:start position:0% +order a K not over to a S + one and A + + + align:start position:0% +order a K not over to a S + one and A +not is much much larger than one in + + align:start position:0% +not is much much larger than one in + + + align:start position:0% +not is much much larger than one in +other words at low frequencies there's a + + align:start position:0% +other words at low frequencies there's a + + + align:start position:0% +other words at low frequencies there's a +large loop transmission magnitude + + align:start position:0% +large loop transmission magnitude + + + align:start position:0% +large loop transmission magnitude +then in fact the closed loop transfer + + align:start position:0% +then in fact the closed loop transfer + + + align:start position:0% +then in fact the closed loop transfer +function from last time is first order + + align:start position:0% +function from last time is first order + + + align:start position:0% +function from last time is first order +we'd have a one over Fnot out in front + + align:start position:0% +we'd have a one over Fnot out in front + + + align:start position:0% +we'd have a one over Fnot out in front +but in our particular system fnot is one + + align:start position:0% +but in our particular system fnot is one + + + align:start position:0% +but in our particular system fnot is one +so we simply have 1 / to a s / a kn + 1. + + align:start position:0% +so we simply have 1 / to a s / a kn + 1. + + + align:start position:0% +so we simply have 1 / to a s / a kn + 1. +And the approximation involved here is + + align:start position:0% +And the approximation involved here is + + + align:start position:0% +And the approximation involved here is +simply a term a constant term in the + + align:start position:0% +simply a term a constant term in the + + + align:start position:0% +simply a term a constant term in the +denominator which is 1 / a kn. And so to + + align:start position:0% +denominator which is 1 / a kn. And so to + + + align:start position:0% +denominator which is 1 / a kn. And so to +the extent that a kn is large, this is + + align:start position:0% +the extent that a kn is large, this is + + + align:start position:0% +the extent that a kn is large, this is +an exact expression. Well, if we examine + + align:start position:0% +an exact expression. Well, if we examine + + + align:start position:0% +an exact expression. Well, if we examine +that expression, provided both toao and + + align:start position:0% +that expression, provided both toao and + + + align:start position:0% +that expression, provided both toao and +a are negative, + + align:start position:0% +a are negative, + + + align:start position:0% +a are negative, +I'm sorry, both toao and and a are + + align:start position:0% +I'm sorry, both toao and and a are + + + align:start position:0% +I'm sorry, both toao and and a are +positive, there's no possibility of + + align:start position:0% +positive, there's no possibility of + + + align:start position:0% +positive, there's no possibility of +having a pole in the right half of the s + + align:start position:0% +having a pole in the right half of the s + + + align:start position:0% +having a pole in the right half of the s +plane. In other words, this is a system + + align:start position:0% +plane. In other words, this is a system + + + align:start position:0% +plane. In other words, this is a system +that's always stable. We can change the + + align:start position:0% +that's always stable. We can change the + + + align:start position:0% +that's always stable. We can change the +location of the closed loop pole by + + align:start position:0% +location of the closed loop pole by + + + align:start position:0% +location of the closed loop pole by +changing either tow a or a kn but + + align:start position:0% +changing either tow a or a kn but + + + align:start position:0% +changing either tow a or a kn but +providing they are both positive. In + + align:start position:0% +providing they are both positive. In + + + align:start position:0% +providing they are both positive. In +other words, providing we have a system + + align:start position:0% +other words, providing we have a system + + + align:start position:0% +other words, providing we have a system +that's negative feedback. Remember in + + align:start position:0% +that's negative feedback. Remember in + + + align:start position:0% +that's negative feedback. Remember in +our standard system notation, we + + align:start position:0% +our standard system notation, we + + + align:start position:0% +our standard system notation, we +indicate the inversion at the summing + + align:start position:0% +indicate the inversion at the summing + + + align:start position:0% +indicate the inversion at the summing +point. So providing our system is a + + align:start position:0% +point. So providing our system is a + + + align:start position:0% +point. So providing our system is a +negative feedback system which results + + align:start position:0% +negative feedback system which results + + + align:start position:0% +negative feedback system which results +with a positive value for a KN and + + align:start position:0% +with a positive value for a KN and + + + align:start position:0% +with a positive value for a KN and +providing the pole associated with the + + align:start position:0% +providing the pole associated with the + + + align:start position:0% +providing the pole associated with the +loop transmission in particular that + + align:start position:0% +loop transmission in particular that + + + align:start position:0% +loop transmission in particular that +associated with TOA is located in the + + align:start position:0% +associated with TOA is located in the + + + align:start position:0% +associated with TOA is located in the +left half plane then our system's always + + align:start position:0% +left half plane then our system's always + + + align:start position:0% +left half plane then our system's always +stable and in fact it exhibits only + + align:start position:0% +stable and in fact it exhibits only + + + align:start position:0% +stable and in fact it exhibits only +exponential responses. There's no + + align:start position:0% +exponential responses. There's no + + + align:start position:0% +exponential responses. There's no +syosoidal no oscilly response possible + + align:start position:0% +syosoidal no oscilly response possible + + + align:start position:0% +syosoidal no oscilly response possible +with a first order system. + + align:start position:0% +with a first order system. + + + align:start position:0% +with a first order system. +So that's an example of a system that's + + align:start position:0% +So that's an example of a system that's + + + align:start position:0% +So that's an example of a system that's +that's really ultimately stable. We can + + align:start position:0% +that's really ultimately stable. We can + + + align:start position:0% +that's really ultimately stable. We can +change the speed of response by + + align:start position:0% +change the speed of response by + + + align:start position:0% +change the speed of response by +modifying either to a or a KN but the + + align:start position:0% +modifying either to a or a KN but the + + + align:start position:0% +modifying either to a or a KN but the +stability is is always effectively + + align:start position:0% +stability is is always effectively + + + align:start position:0% +stability is is always effectively +ideal. + + align:start position:0% +ideal. + + + align:start position:0% +ideal. +If we look at a second order system + + align:start position:0% +If we look at a second order system + + + align:start position:0% +If we look at a second order system +where a of s is a kn over two real axis + + align:start position:0% +where a of s is a kn over two real axis + + + align:start position:0% +where a of s is a kn over two real axis +poles and again f is equal to one and we + + align:start position:0% +poles and again f is equal to one and we + + + align:start position:0% +poles and again f is equal to one and we +put on the constraint that the low + + align:start position:0% +put on the constraint that the low + + + align:start position:0% +put on the constraint that the low +frequency loop transmission magnitude is + + align:start position:0% +frequency loop transmission magnitude is + + + align:start position:0% +frequency loop transmission magnitude is +much much larger than one. Now we have + + align:start position:0% +much much larger than one. Now we have + + + align:start position:0% +much much larger than one. Now we have +the possibility of oscilly behavior and + + align:start position:0% +the possibility of oscilly behavior and + + + align:start position:0% +the possibility of oscilly behavior and +we saw this last time. uh we'd get a + + align:start position:0% +we saw this last time. uh we'd get a + + + align:start position:0% +we saw this last time. uh we'd get a +closed loop response again that's one + + align:start position:0% +closed loop response again that's one + + + align:start position:0% +closed loop response again that's one +over fn but in our case fnot is one and + + align:start position:0% +over fn but in our case fnot is one and + + + align:start position:0% +over fn but in our case fnot is one and +we then get a quadratic in the + + align:start position:0% +we then get a quadratic in the + + + align:start position:0% +we then get a quadratic in the +denominator of the closed loop response + + align:start position:0% +denominator of the closed loop response + + + align:start position:0% +denominator of the closed loop response +and certainly by appropriate choice of + + align:start position:0% +and certainly by appropriate choice of + + + align:start position:0% +and certainly by appropriate choice of +tow a tow b and a kn we can end up with + + align:start position:0% +tow a tow b and a kn we can end up with + + + align:start position:0% +tow a tow b and a kn we can end up with +a an expression that factors into two + + align:start position:0% +a an expression that factors into two + + + align:start position:0% +a an expression that factors into two +complex conjugate closed loop poles + + align:start position:0% +complex conjugate closed loop poles + + + align:start position:0% +complex conjugate closed loop poles +and under those conditions we can write + + align:start position:0% +and under those conditions we can write + + + align:start position:0% +and under those conditions we can write +our closed loop transfer function in our + + align:start position:0% +our closed loop transfer function in our + + + align:start position:0% +our closed loop transfer function in our +standard quadratic form and it will + + align:start position:0% +standard quadratic form and it will + + + align:start position:0% +standard quadratic form and it will +exhibit a damping ratio less than one. + + align:start position:0% +exhibit a damping ratio less than one. + + + align:start position:0% +exhibit a damping ratio less than one. +Well, again we looked at this last time + + align:start position:0% +Well, again we looked at this last time + + + align:start position:0% +Well, again we looked at this last time +and we saw that lower and lower values + + align:start position:0% +and we saw that lower and lower values + + + align:start position:0% +and we saw that lower and lower values +for damping ratio correspond to + + align:start position:0% +for damping ratio correspond to + + + align:start position:0% +for damping ratio correspond to +progressively more oscilly step + + align:start position:0% +progressively more oscilly step + + + align:start position:0% +progressively more oscilly step +responses or if we look at the frequency + + align:start position:0% +responses or if we look at the frequency + + + align:start position:0% +responses or if we look at the frequency +response of the system why they + + align:start position:0% +response of the system why they + + + align:start position:0% +response of the system why they +correspond to a greater and greater + + align:start position:0% +correspond to a greater and greater + + + align:start position:0% +correspond to a greater and greater +amount of resonant peaking in the + + align:start position:0% +amount of resonant peaking in the + + + align:start position:0% +amount of resonant peaking in the +frequency response. So when we have a + + align:start position:0% +frequency response. So when we have a + + + align:start position:0% +frequency response. So when we have a +second order system again if we + + align:start position:0% +second order system again if we + + + align:start position:0% +second order system again if we +constrain ourselves to the case where to + + align:start position:0% +constrain ourselves to the case where to + + + align:start position:0% +constrain ourselves to the case where to +a tow b and a kn are all positive in + + align:start position:0% +a tow b and a kn are all positive in + + + align:start position:0% +a tow b and a kn are all positive in +other words the poles associated with + + align:start position:0% +other words the poles associated with + + + align:start position:0% +other words the poles associated with +the loop transmission line the left half + + align:start position:0% +the loop transmission line the left half + + + align:start position:0% +the loop transmission line the left half +plane and we have a a negative feedback + + align:start position:0% +plane and we have a a negative feedback + + + align:start position:0% +plane and we have a a negative feedback +system signified by a kn being positive + + align:start position:0% +system signified by a kn being positive + + + align:start position:0% +system signified by a kn being positive +why we're able to get a system that has + + align:start position:0% +why we're able to get a system that has + + + align:start position:0% +why we're able to get a system that has +an arbitrarily low damping ratio by + + align:start position:0% +an arbitrarily low damping ratio by + + + align:start position:0% +an arbitrarily low damping ratio by +appropriate selection if you will of tow + + align:start position:0% +appropriate selection if you will of tow + + + align:start position:0% +appropriate selection if you will of tow +a tow b and a not but we're never able + + align:start position:0% +a tow b and a not but we're never able + + + align:start position:0% +a tow b and a not but we're never able +to get poles in the right half plane. So + + align:start position:0% +to get poles in the right half plane. So + + + align:start position:0% +to get poles in the right half plane. So +again if we start out with a system that + + align:start position:0% +again if we start out with a system that + + + align:start position:0% +again if we start out with a system that +has two energy storage elements + + align:start position:0% +has two energy storage elements + + + align:start position:0% +has two energy storage elements +resulting in two left half plane loop + + align:start position:0% +resulting in two left half plane loop + + + align:start position:0% +resulting in two left half plane loop +transmission poles why again we can get + + align:start position:0% +transmission poles why again we can get + + + align:start position:0% +transmission poles why again we can get +a system that at least in a mathematical + + align:start position:0% +a system that at least in a mathematical + + + align:start position:0% +a system that at least in a mathematical +sense in an absolute sense is always + + align:start position:0% +sense in an absolute sense is always + + + align:start position:0% +sense in an absolute sense is always +stable. The poles can have an + + align:start position:0% +stable. The poles can have an + + + align:start position:0% +stable. The poles can have an +arbitrarily small damping ratio but the + + align:start position:0% +arbitrarily small damping ratio but the + + + align:start position:0% +arbitrarily small damping ratio but the +system by this definition will be + + align:start position:0% +system by this definition will be + + + align:start position:0% +system by this definition will be +stable. + + align:start position:0% +stable. + + + align:start position:0% +stable. +The way we get into trouble is to have a + + align:start position:0% +The way we get into trouble is to have a + + + align:start position:0% +The way we get into trouble is to have a +third order or higher order negative + + align:start position:0% +third order or higher order negative + + + align:start position:0% +third order or higher order negative +feedback system. And we can demonstrate + + align:start position:0% +feedback system. And we can demonstrate + + + align:start position:0% +feedback system. And we can demonstrate +that if we look at a system which on a + + align:start position:0% +that if we look at a system which on a + + + align:start position:0% +that if we look at a system which on a +loop transmission basis has three + + align:start position:0% +loop transmission basis has three + + + align:start position:0% +loop transmission basis has three +coincident poles. In fact, we could + + align:start position:0% +coincident poles. In fact, we could + + + align:start position:0% +coincident poles. In fact, we could +demonstrate it uh with three poles in + + align:start position:0% +demonstrate it uh with three poles in + + + align:start position:0% +demonstrate it uh with three poles in +the left half plane independent of where + + align:start position:0% +the left half plane independent of where + + + align:start position:0% +the left half plane independent of where +they were located. But uh the + + align:start position:0% +they were located. But uh the + + + align:start position:0% +they were located. But uh the +mathematics is rather straightforward + + align:start position:0% +mathematics is rather straightforward + + + align:start position:0% +mathematics is rather straightforward +for a system that has three coincident + + align:start position:0% +for a system that has three coincident + + + align:start position:0% +for a system that has three coincident +real axis poles. + + align:start position:0% +real axis poles. + + + align:start position:0% +real axis poles. +So we show that by having an a of s + + align:start position:0% +So we show that by having an a of s + + + align:start position:0% +So we show that by having an a of s +that's a kn over to s + 1 quantity + + align:start position:0% +that's a kn over to s + 1 quantity + + + align:start position:0% +that's a kn over to s + 1 quantity +cubed. + + align:start position:0% +cubed. + + + align:start position:0% +cubed. +And + + align:start position:0% +And + + + align:start position:0% +And +if we expand that transfer function or + + align:start position:0% +if we expand that transfer function or + + + align:start position:0% +if we expand that transfer function or +look at the closed loop response that + + align:start position:0% +look at the closed loop response that + + + align:start position:0% +look at the closed loop response that +results again assuming that we have + + align:start position:0% +results again assuming that we have + + + align:start position:0% +results again assuming that we have +unity feedback that we have the topology + + align:start position:0% +unity feedback that we have the topology + + + align:start position:0% +unity feedback that we have the topology +we indicated earlier. Simply expanding + + align:start position:0% +we indicated earlier. Simply expanding + + + align:start position:0% +we indicated earlier. Simply expanding +out this term this expression uh + + align:start position:0% +out this term this expression uh + + + align:start position:0% +out this term this expression uh +calculating a of s as this over 1 plus + + align:start position:0% +calculating a of s as this over 1 plus + + + align:start position:0% +calculating a of s as this over 1 plus +this we end up with a closed loop + + align:start position:0% +this we end up with a closed loop + + + align:start position:0% +this we end up with a closed loop +transfer function that's a kn over to + + align:start position:0% +transfer function that's a kn over to + + + align:start position:0% +transfer function that's a kn over to +cub s cubed plus 3 to 2 s^2 + + align:start position:0% +cub s cubed plus 3 to 2 s^2 + + + align:start position:0% +cub s cubed plus 3 to 2 s^2 +plus 3 to s plus 1 + a kn is the final + + align:start position:0% +plus 3 to s plus 1 + a kn is the final + + + align:start position:0% +plus 3 to s plus 1 + a kn is the final +term. + + align:start position:0% +term. + + + align:start position:0% +term. +Now we could presumably factor that. + + align:start position:0% +Now we could presumably factor that. + + + align:start position:0% +Now we could presumably factor that. +It's not nearly as clear what the + + align:start position:0% +It's not nearly as clear what the + + + align:start position:0% +It's not nearly as clear what the +condition is to have all three poles in + + align:start position:0% +condition is to have all three poles in + + + align:start position:0% +condition is to have all three poles in +the left half plane in in this + + align:start position:0% +the left half plane in in this + + + align:start position:0% +the left half plane in in this +particular case. Certainly the condition + + align:start position:0% +particular case. Certainly the condition + + + align:start position:0% +particular case. Certainly the condition +for having all the poles in the left + + align:start position:0% +for having all the poles in the left + + + align:start position:0% +for having all the poles in the left +half plane for the first order system is + + align:start position:0% +half plane for the first order system is + + + align:start position:0% +half plane for the first order system is +obvious. As long as this coefficient is + + align:start position:0% +obvious. As long as this coefficient is + + + align:start position:0% +obvious. As long as this coefficient is +positive, we're all right. Similarly, + + align:start position:0% +positive, we're all right. Similarly, + + + align:start position:0% +positive, we're all right. Similarly, +for the second order system, as long as + + align:start position:0% +for the second order system, as long as + + + align:start position:0% +for the second order system, as long as +these two coefficients are positive, + + align:start position:0% +these two coefficients are positive, + + + align:start position:0% +these two coefficients are positive, +again, we're assured that we have both + + align:start position:0% +again, we're assured that we have both + + + align:start position:0% +again, we're assured that we have both +poles of the system in the left half + + align:start position:0% +poles of the system in the left half + + + align:start position:0% +poles of the system in the left half +plane. But there's a far more + + align:start position:0% +plane. But there's a far more + + + align:start position:0% +plane. But there's a far more +complicated relationship among the + + align:start position:0% +complicated relationship among the + + + align:start position:0% +complicated relationship among the +coefficients for the third order system. + + align:start position:0% +coefficients for the third order system. + + + align:start position:0% +coefficients for the third order system. +So we can't simply by inspection look at + + align:start position:0% +So we can't simply by inspection look at + + + align:start position:0% +So we can't simply by inspection look at +that expression and tell + + align:start position:0% +that expression and tell + + + align:start position:0% +that expression and tell +whether the system is stable or not. + + align:start position:0% +whether the system is stable or not. + + + align:start position:0% +whether the system is stable or not. +However, let's consider a special case. + + align:start position:0% +However, let's consider a special case. + + + align:start position:0% +However, let's consider a special case. +In particular, let's consider what + + align:start position:0% +In particular, let's consider what + + + align:start position:0% +In particular, let's consider what +happens + + align:start position:0% +happens + + + align:start position:0% +happens +if we pick an a of 8. In other words, if + + align:start position:0% +if we pick an a of 8. In other words, if + + + align:start position:0% +if we pick an a of 8. In other words, if +we choose this term + + align:start position:0% +we choose this term + + + align:start position:0% +we choose this term +1 + a kn to be equal to 9 + + align:start position:0% +1 + a kn to be equal to 9 + + + align:start position:0% +1 + a kn to be equal to 9 +with that choice of a kn we're able to + + align:start position:0% +with that choice of a kn we're able to + + + align:start position:0% +with that choice of a kn we're able to +factor the denominator polomial of a of + + align:start position:0% +factor the denominator polomial of a of + + + align:start position:0% +factor the denominator polomial of a of +s to find its poles. This expression + + align:start position:0% +s to find its poles. This expression + + + align:start position:0% +s to find its poles. This expression +incidentally we'll use that term uh many + + align:start position:0% +incidentally we'll use that term uh many + + + align:start position:0% +incidentally we'll use that term uh many +times is called the characteristic + + align:start position:0% +times is called the characteristic + + + align:start position:0% +times is called the characteristic +equation. One minus the loop + + align:start position:0% +equation. One minus the loop + + + align:start position:0% +equation. One minus the loop +transmission is the characteristic + + align:start position:0% +transmission is the characteristic + + + align:start position:0% +transmission is the characteristic +equation of the system. And so if we + + align:start position:0% +equation of the system. And so if we + + + align:start position:0% +equation of the system. And so if we +factor the characteristic equation, we + + align:start position:0% +factor the characteristic equation, we + + + align:start position:0% +factor the characteristic equation, we +find the closed loop poles of the + + align:start position:0% +find the closed loop poles of the + + + align:start position:0% +find the closed loop poles of the +system. And for this particular value of + + align:start position:0% +system. And for this particular value of + + + align:start position:0% +system. And for this particular value of +a KN for a KN= 8, we find that we have + + align:start position:0% +a KN for a KN= 8, we find that we have + + + align:start position:0% +a KN for a KN= 8, we find that we have +poles a single pole on the negative real + + align:start position:0% +poles a single pole on the negative real + + + align:start position:0% +poles a single pole on the negative real +axis located at s= minus3 over towo. And + + align:start position:0% +axis located at s= minus3 over towo. And + + + align:start position:0% +axis located at s= minus3 over towo. And +we have a complex conjugate pair of + + align:start position:0% +we have a complex conjugate pair of + + + align:start position:0% +we have a complex conjugate pair of +poles on the imaginary axis. They have + + align:start position:0% +poles on the imaginary axis. They have + + + align:start position:0% +poles on the imaginary axis. They have +no real part. And in fact that complex + + align:start position:0% +no real part. And in fact that complex + + + align:start position:0% +no real part. And in fact that complex +conjugate pole pair is purely imaginary. + + align:start position:0% +conjugate pole pair is purely imaginary. + + + align:start position:0% +conjugate pole pair is purely imaginary. +And so the implication is that the + + align:start position:0% +And so the implication is that the + + + align:start position:0% +And so the implication is that the +homogeneous part of the system response + + align:start position:0% +homogeneous part of the system response + + + align:start position:0% +homogeneous part of the system response +would include a constant amplitude + + align:start position:0% +would include a constant amplitude + + + align:start position:0% +would include a constant amplitude +syosoidal term. If we excited this + + align:start position:0% +syosoidal term. If we excited this + + + align:start position:0% +syosoidal term. If we excited this +system by initial conditions or excited + + align:start position:0% +system by initial conditions or excited + + + align:start position:0% +system by initial conditions or excited +its its + + align:start position:0% +its its + + + align:start position:0% +its its +unforced response, its natural response, + + align:start position:0% +unforced response, its natural response, + + + align:start position:0% +unforced response, its natural response, +why we'd find out that that response + + align:start position:0% +why we'd find out that that response + + + align:start position:0% +why we'd find out that that response +included a term that was a constant + + align:start position:0% +included a term that was a constant + + + align:start position:0% +included a term that was a constant +amplitude sinosoid or cosine because of + + align:start position:0% +amplitude sinosoid or cosine because of + + + align:start position:0% +amplitude sinosoid or cosine because of +the pair of closed loop poles with no + + align:start position:0% +the pair of closed loop poles with no + + + align:start position:0% +the pair of closed loop poles with no +real part, the pair of poles on the + + align:start position:0% +real part, the pair of poles on the + + + align:start position:0% +real part, the pair of poles on the +imaginary axis. + + align:start position:0% + + + + align:start position:0% + +Let's see if we can get some physical + + align:start position:0% +Let's see if we can get some physical + + + align:start position:0% +Let's see if we can get some physical +significance for why that might occur. + + align:start position:0% +significance for why that might occur. + + + align:start position:0% +significance for why that might occur. +Suppose we look at our loop transmission + + align:start position:0% +Suppose we look at our loop transmission + + + align:start position:0% +Suppose we look at our loop transmission +or at a of s when we pick a value of a + + align:start position:0% +or at a of s when we pick a value of a + + + align:start position:0% +or at a of s when we pick a value of a +KN equal to 8. And in particular, let's + + align:start position:0% +KN equal to 8. And in particular, let's + + + align:start position:0% +KN equal to 8. And in particular, let's +evaluate a of S at the frequency J + + align:start position:0% +evaluate a of S at the frequency J + + + align:start position:0% +evaluate a of S at the frequency J +radical 3 over to. There's something a + + align:start position:0% +radical 3 over to. There's something a + + + align:start position:0% +radical 3 over to. There's something a +little bit peculiar about that + + align:start position:0% +little bit peculiar about that + + + align:start position:0% +little bit peculiar about that +frequency. That's the frequency at which + + align:start position:0% +frequency. That's the frequency at which + + + align:start position:0% +frequency. That's the frequency at which +the closed loop poles are located for a + + align:start position:0% +the closed loop poles are located for a + + + align:start position:0% +the closed loop poles are located for a +KN= 8. So let's look and see if we can + + align:start position:0% +KN= 8. So let's look and see if we can + + + align:start position:0% +KN= 8. So let's look and see if we can +find out anything unusual about the loop + + align:start position:0% +find out anything unusual about the loop + + + align:start position:0% +find out anything unusual about the loop +transmission at the frequency s= j + + align:start position:0% +transmission at the frequency s= j + + + align:start position:0% +transmission at the frequency s= j +radical 3 over tow. In other words, for + + align:start position:0% +radical 3 over tow. In other words, for + + + align:start position:0% +radical 3 over tow. In other words, for +purely syosoidal steady state exitation + + align:start position:0% +purely syosoidal steady state exitation + + + align:start position:0% +purely syosoidal steady state exitation +at a frequency of radle 3 over to + + align:start position:0% +at a frequency of radle 3 over to + + + align:start position:0% +at a frequency of radle 3 over to +radians/s + + align:start position:0% +radians/s + + + align:start position:0% +radians/s +and with a value of a not equal to 8. + + align:start position:0% +and with a value of a not equal to 8. + + + align:start position:0% +and with a value of a not equal to 8. +Well, a of s at that frequency, which is + + align:start position:0% +Well, a of s at that frequency, which is + + + align:start position:0% +Well, a of s at that frequency, which is +identically the negative of the loop + + align:start position:0% +identically the negative of the loop + + + align:start position:0% +identically the negative of the loop +transmission, is simply 8 a kn + + align:start position:0% +transmission, is simply 8 a kn + + + align:start position:0% +transmission, is simply 8 a kn +over jle 3 + 1 quantity cubed. Notice + + align:start position:0% +over jle 3 + 1 quantity cubed. Notice + + + align:start position:0% +over jle 3 + 1 quantity cubed. Notice +that when we substitute in s= j rad 3 + + align:start position:0% +that when we substitute in s= j rad 3 + + + align:start position:0% +that when we substitute in s= j rad 3 +over to our original expression for a of + + align:start position:0% +over to our original expression for a of + + + align:start position:0% +over to our original expression for a of +s, the to cancel out. we end up with + + align:start position:0% +s, the to cancel out. we end up with + + + align:start position:0% +s, the to cancel out. we end up with +simply J radical 3 for the imaginary + + align:start position:0% +simply J radical 3 for the imaginary + + + align:start position:0% +simply J radical 3 for the imaginary +term associated with with that factor. + + align:start position:0% +term associated with with that factor. + + + align:start position:0% +term associated with with that factor. +And so our overall value for a of S is a + + align:start position:0% +And so our overall value for a of S is a + + + align:start position:0% +And so our overall value for a of S is a +KN over J radical 3 + 1 cubed. + + align:start position:0% +KN over J radical 3 + 1 cubed. + + + align:start position:0% +KN over J radical 3 + 1 cubed. +If we look at the magnitude of any of + + align:start position:0% +If we look at the magnitude of any of + + + align:start position:0% +If we look at the magnitude of any of +the individual factors in the + + align:start position:0% +the individual factors in the + + + align:start position:0% +the individual factors in the +denominator, the magnitude of J radical + + align:start position:0% +denominator, the magnitude of J radical + + + align:start position:0% +denominator, the magnitude of J radical +3 + 1 is 1/2 or the magnitude of J + + align:start position:0% +3 + 1 is 1/2 or the magnitude of J + + + align:start position:0% +3 + 1 is 1/2 or the magnitude of J +radical 3 + 1 is two. So the magnitude + + align:start position:0% +radical 3 + 1 is two. So the magnitude + + + align:start position:0% +radical 3 + 1 is two. So the magnitude +of 1 over J radical 3 + 1 is 1/2. + + align:start position:0% +of 1 over J radical 3 + 1 is 1/2. + + + align:start position:0% +of 1 over J radical 3 + 1 is 1/2. +The denominator then has a value of 8. + + align:start position:0% +The denominator then has a value of 8. + + + align:start position:0% +The denominator then has a value of 8. +The J radical 3 + 1 with a magnitude of + + align:start position:0% +The J radical 3 + 1 with a magnitude of + + + align:start position:0% +The J radical 3 + 1 with a magnitude of +2 cubed. And so the magnitude of this + + align:start position:0% +2 cubed. And so the magnitude of this + + + align:start position:0% +2 cubed. And so the magnitude of this +expression is unity at S= J radical 3. + + align:start position:0% +expression is unity at S= J radical 3. + + + align:start position:0% +expression is unity at S= J radical 3. +And furthermore, the the U + + align:start position:0% +And furthermore, the the U + + + align:start position:0% +And furthermore, the the U +angle associated with this transfer + + align:start position:0% +angle associated with this transfer + + + align:start position:0% +angle associated with this transfer +function is - 180°. We can see that by + + align:start position:0% +function is - 180°. We can see that by + + + align:start position:0% +function is - 180°. We can see that by +noticing that the angle associated with + + align:start position:0% +noticing that the angle associated with + + + align:start position:0% +noticing that the angle associated with +each of these terms is plus 60°. is the + + align:start position:0% +each of these terms is plus 60°. is the + + + align:start position:0% +each of these terms is plus 60°. is the +imaginary part is radical 3. The real + + align:start position:0% +imaginary part is radical 3. The real + + + align:start position:0% +imaginary part is radical 3. The real +part is one. If we look at the + + align:start position:0% +part is one. If we look at the + + + align:start position:0% +part is one. If we look at the +trigonometry involved, the angle + + align:start position:0% +trigonometry involved, the angle + + + align:start position:0% +trigonometry involved, the angle +associated with either any one of these + + align:start position:0% +associated with either any one of these + + + align:start position:0% +associated with either any one of these +terms is 60°. Since they're in the + + align:start position:0% +terms is 60°. Since they're in the + + + align:start position:0% +terms is 60°. Since they're in the +denominator, they contribute minus 60° + + align:start position:0% +denominator, they contribute minus 60° + + + align:start position:0% +denominator, they contribute minus 60° +per term to the overall transfer + + align:start position:0% +per term to the overall transfer + + + align:start position:0% +per term to the overall transfer +function. We have three of them. And + + align:start position:0% +function. We have three of them. And + + + align:start position:0% +function. We have three of them. And +therefore, the complex number has a + + align:start position:0% +therefore, the complex number has a + + + align:start position:0% +therefore, the complex number has a +magnitude of one at an angle of minus + + align:start position:0% +magnitude of one at an angle of minus + + + align:start position:0% +magnitude of one at an angle of minus +180°. + + align:start position:0% +180°. + + + align:start position:0% +180°. +So for purely syosoidal exitation at + + align:start position:0% +So for purely syosoidal exitation at + + + align:start position:0% +So for purely syosoidal exitation at +radical 3 radians/s + + align:start position:0% +radical 3 radians/s + + + align:start position:0% +radical 3 radians/s +a of s is equal to minus1 one at an + + align:start position:0% +a of s is equal to minus1 one at an + + + align:start position:0% +a of s is equal to minus1 one at an +angle of - 180°. + + align:start position:0% +angle of - 180°. + + + align:start position:0% +angle of - 180°. +Let's look back at our original system + + align:start position:0% +Let's look back at our original system + + + align:start position:0% +Let's look back at our original system +and see what what that implies. + + align:start position:0% +and see what what that implies. + + + align:start position:0% +and see what what that implies. +Suppose we performed an experiment where + + align:start position:0% +Suppose we performed an experiment where + + + align:start position:0% +Suppose we performed an experiment where +first of all we took the system and + + align:start position:0% +first of all we took the system and + + + align:start position:0% +first of all we took the system and +removed the input. + + align:start position:0% +removed the input. + + + align:start position:0% +removed the input. +So we eliminate VI and then we break the + + align:start position:0% +So we eliminate VI and then we break the + + + align:start position:0% +So we eliminate VI and then we break the +loop + + align:start position:0% +loop + + + align:start position:0% +loop +like this. + + align:start position:0% +like this. + + + align:start position:0% +like this. +And now we perform an experiment where + + align:start position:0% +And now we perform an experiment where + + + align:start position:0% +And now we perform an experiment where +we excite the system with a test + + align:start position:0% +we excite the system with a test + + + align:start position:0% +we excite the system with a test +generator. So what we'll do is put in a + + align:start position:0% +generator. So what we'll do is put in a + + + align:start position:0% +generator. So what we'll do is put in a +test generator here. + + align:start position:0% + + + + align:start position:0% + +Let's call it V subt. + + align:start position:0% +Let's call it V subt. + + + align:start position:0% +Let's call it V subt. +and we'll look at the signal returned by + + align:start position:0% +and we'll look at the signal returned by + + + align:start position:0% +and we'll look at the signal returned by +the loop. Observe it at this point and + + align:start position:0% +the loop. Observe it at this point and + + + align:start position:0% +the loop. Observe it at this point and +we might call that signal V subr. + + align:start position:0% +we might call that signal V subr. + + + align:start position:0% +we might call that signal V subr. +Well, let's choose a V subt as indicated + + align:start position:0% +Well, let's choose a V subt as indicated + + + align:start position:0% +Well, let's choose a V subt as indicated +earlier. In particular, let's choose V + + align:start position:0% +earlier. In particular, let's choose V + + + align:start position:0% +earlier. In particular, let's choose V +subt to be a syosoid at radical 3 over + + align:start position:0% +subt to be a syosoid at radical 3 over + + + align:start position:0% +subt to be a syosoid at radical 3 over +towal radians/s. + + align:start position:0% +towal radians/s. + + + align:start position:0% +towal radians/s. +So let's allow v subt to be some + + align:start position:0% +So let's allow v subt to be some + + + align:start position:0% +So let's allow v subt to be some +amplitude + + align:start position:0% +amplitude + + + align:start position:0% +amplitude +k + + align:start position:0% +k + + + align:start position:0% +k +time sin + + align:start position:0% +time sin + + + align:start position:0% +time sin +radle 3 divided by toao or cosine + + align:start position:0% +radle 3 divided by toao or cosine + + + align:start position:0% +radle 3 divided by toao or cosine +radical 3 / tow doesn't matter + + align:start position:0% +radical 3 / tow doesn't matter + + + align:start position:0% +radical 3 / tow doesn't matter +and let's allow the transient the + + align:start position:0% +and let's allow the transient the + + + align:start position:0% +and let's allow the transient the +startup transient to die out. So we've + + align:start position:0% +startup transient to die out. So we've + + + align:start position:0% +startup transient to die out. So we've +had this transient this signal applied + + align:start position:0% +had this transient this signal applied + + + align:start position:0% +had this transient this signal applied +for a very long period of time. + + align:start position:0% +for a very long period of time. + + + align:start position:0% +for a very long period of time. +Eventually we find out that v subr is + + align:start position:0% +Eventually we find out that v subr is + + + align:start position:0% +Eventually we find out that v subr is +identically equal to our test signal and + + align:start position:0% +identically equal to our test signal and + + + align:start position:0% +identically equal to our test signal and +the reason for that is that remember a + + align:start position:0% +the reason for that is that remember a + + + align:start position:0% +the reason for that is that remember a +of s under s syocardal steady condition + + align:start position:0% +of s under s syocardal steady condition + + + align:start position:0% +of s under s syocardal steady condition +steady state conditions with a not equal + + align:start position:0% +steady state conditions with a not equal + + + align:start position:0% +steady state conditions with a not equal +to 8 and at radical 3 over tow radians/s + + align:start position:0% +to 8 and at radical 3 over tow radians/s + + + align:start position:0% +to 8 and at radical 3 over tow radians/s +a of s is minus1. + + align:start position:0% +a of s is minus1. + + + align:start position:0% +a of s is minus1. +And so the minus1 associated with a of s + + align:start position:0% +And so the minus1 associated with a of s + + + align:start position:0% +And so the minus1 associated with a of s +combines with the minus sign at the + + align:start position:0% +combines with the minus sign at the + + + align:start position:0% +combines with the minus sign at the +summing point to give us a positive loop + + align:start position:0% +summing point to give us a positive loop + + + align:start position:0% +summing point to give us a positive loop +transmission with a magnitude of one. + + align:start position:0% +transmission with a magnitude of one. + + + align:start position:0% +transmission with a magnitude of one. +That means that the signal returned by + + align:start position:0% +That means that the signal returned by + + + align:start position:0% +That means that the signal returned by +the loop is identical to our test + + align:start position:0% +the loop is identical to our test + + + align:start position:0% +the loop is identical to our test +signal. Well, once we've done that, we + + align:start position:0% +signal. Well, once we've done that, we + + + align:start position:0% +signal. Well, once we've done that, we +can get the system started this way and + + align:start position:0% +can get the system started this way and + + + align:start position:0% +can get the system started this way and +then we can reconnect + + align:start position:0% +then we can reconnect + + + align:start position:0% +then we can reconnect +the loop and we can eliminate the test + + align:start position:0% +the loop and we can eliminate the test + + + align:start position:0% +the loop and we can eliminate the test +generator. + + align:start position:0% + + + + align:start position:0% + +And the system doesn't realize that + + align:start position:0% +And the system doesn't realize that + + + align:start position:0% +And the system doesn't realize that +we've taken away the test generator. + + align:start position:0% +we've taken away the test generator. + + + align:start position:0% +we've taken away the test generator. +It's effectively able to supply its own + + align:start position:0% +It's effectively able to supply its own + + + align:start position:0% +It's effectively able to supply its own +input. + + align:start position:0% +input. + + + align:start position:0% +input. +And so we find the possibility of + + align:start position:0% +And so we find the possibility of + + + align:start position:0% +And so we find the possibility of +maintaining a constant amplitude + + align:start position:0% +maintaining a constant amplitude + + + align:start position:0% +maintaining a constant amplitude +oscillation + + align:start position:0% +oscillation + + + align:start position:0% +oscillation +with the test generator removed. We + + align:start position:0% +with the test generator removed. We + + + align:start position:0% +with the test generator removed. We +found a way of forcing the system to + + align:start position:0% +found a way of forcing the system to + + + align:start position:0% +found a way of forcing the system to +oscillate at radical 3 over towal + + align:start position:0% +oscillate at radical 3 over towal + + + align:start position:0% +oscillate at radical 3 over towal +radians/s. + + align:start position:0% +radians/s. + + + align:start position:0% +radians/s. +So that's the physical significance + + align:start position:0% +So that's the physical significance + + + align:start position:0% +So that's the physical significance +associated with a three- pole system. + + align:start position:0% +associated with a three- pole system. + + + align:start position:0% +associated with a three- pole system. +three coincident real axis po axis poles + + align:start position:0% +three coincident real axis po axis poles + + + align:start position:0% +three coincident real axis po axis poles +when we have a a DC loop transmission + + align:start position:0% +when we have a a DC loop transmission + + + align:start position:0% +when we have a a DC loop transmission +magnitude of eight and when we test the + + align:start position:0% +magnitude of eight and when we test the + + + align:start position:0% +magnitude of eight and when we test the +system or look at the system loop + + align:start position:0% +system or look at the system loop + + + align:start position:0% +system or look at the system loop +transmission at radical 3 over towo + + align:start position:0% +transmission at radical 3 over towo + + + align:start position:0% +transmission at radical 3 over towo +radians per second I think it's worth + + align:start position:0% +radians per second I think it's worth + + + align:start position:0% +radians per second I think it's worth +cautioning at this point that + + align:start position:0% +cautioning at this point that + + + align:start position:0% +cautioning at this point that +this is a fairly simplified view or in + + align:start position:0% +this is a fairly simplified view or in + + + align:start position:0% +this is a fairly simplified view or in +fact a very simplified view of stability + + align:start position:0% +fact a very simplified view of stability + + + align:start position:0% +fact a very simplified view of stability +and the sort of test I described in + + align:start position:0% +and the sort of test I described in + + + align:start position:0% +and the sort of test I described in +other words looking for points where the + + align:start position:0% +other words looking for points where the + + + align:start position:0% +other words looking for points where the +loop transmission magnitude is precisely + + align:start position:0% +loop transmission magnitude is precisely + + + align:start position:0% +loop transmission magnitude is precisely +ly plus one is a little bit dangerous. + + align:start position:0% +ly plus one is a little bit dangerous. + + + align:start position:0% +ly plus one is a little bit dangerous. +We'll see how that goes a little bit + + align:start position:0% +We'll see how that goes a little bit + + + align:start position:0% +We'll see how that goes a little bit +further on. That's not a general test. + + align:start position:0% +further on. That's not a general test. + + + align:start position:0% +further on. That's not a general test. +The + + align:start position:0% +The + + + align:start position:0% +The +information concerning the loop + + align:start position:0% +information concerning the loop + + + align:start position:0% +information concerning the loop +transmission magnitude at only one + + align:start position:0% +transmission magnitude at only one + + + align:start position:0% +transmission magnitude at only one +frequency does not in fact give us + + align:start position:0% +frequency does not in fact give us + + + align:start position:0% +frequency does not in fact give us +complete stability information. We have + + align:start position:0% +complete stability information. We have + + + align:start position:0% +complete stability information. We have +to be a little bit careful. In this + + align:start position:0% +to be a little bit careful. In this + + + align:start position:0% +to be a little bit careful. In this +case, it does give us the correct + + align:start position:0% +case, it does give us the correct + + + align:start position:0% +case, it does give us the correct +answer. We found out by factoring the + + align:start position:0% +answer. We found out by factoring the + + + align:start position:0% +answer. We found out by factoring the +characteristic equation that there are + + align:start position:0% +characteristic equation that there are + + + align:start position:0% +characteristic equation that there are +in fact a closed loop pair of poles on + + align:start position:0% +in fact a closed loop pair of poles on + + + align:start position:0% +in fact a closed loop pair of poles on +the imaginary axis. And that's the + + align:start position:0% +the imaginary axis. And that's the + + + align:start position:0% +the imaginary axis. And that's the +result we would have concluded from the + + align:start position:0% +result we would have concluded from the + + + align:start position:0% +result we would have concluded from the +experiment I described as well. But as I + + align:start position:0% +experiment I described as well. But as I + + + align:start position:0% +experiment I described as well. But as I +say, I caution you that this isn't a + + align:start position:0% +say, I caution you that this isn't a + + + align:start position:0% +say, I caution you that this isn't a +general test. + + align:start position:0% +general test. + + + align:start position:0% +general test. +Well, we at least now see the + + align:start position:0% +Well, we at least now see the + + + align:start position:0% +Well, we at least now see the +possibility of having a system that + + align:start position:0% +possibility of having a system that + + + align:start position:0% +possibility of having a system that +behaves as a self-exited oscillator. In + + align:start position:0% +behaves as a self-exited oscillator. In + + + align:start position:0% +behaves as a self-exited oscillator. In +fact, if we examined the characteristic + + align:start position:0% +fact, if we examined the characteristic + + + align:start position:0% +fact, if we examined the characteristic +equation further and we chose any a knot + + align:start position:0% +equation further and we chose any a knot + + + align:start position:0% +equation further and we chose any a knot +that was positive but greater than 8, + + align:start position:0% +that was positive but greater than 8, + + + align:start position:0% +that was positive but greater than 8, +we'd find out that when we factored the + + align:start position:0% +we'd find out that when we factored the + + + align:start position:0% +we'd find out that when we factored the +characteristic equation, we'd actually + + align:start position:0% +characteristic equation, we'd actually + + + align:start position:0% +characteristic equation, we'd actually +get two poles with positive real parts. + + align:start position:0% +get two poles with positive real parts. + + + align:start position:0% +get two poles with positive real parts. +we'd find two poles in the right half of + + align:start position:0% +we'd find two poles in the right half of + + + align:start position:0% +we'd find two poles in the right half of +the splane. And so if we took this + + align:start position:0% +the splane. And so if we took this + + + align:start position:0% +the splane. And so if we took this +system three coincident negative left + + align:start position:0% +system three coincident negative left + + + align:start position:0% +system three coincident negative left +half plane real axis poles if we have an + + align:start position:0% +half plane real axis poles if we have an + + + align:start position:0% +half plane real axis poles if we have an +A not of anything greater than eight + + align:start position:0% +A not of anything greater than eight + + + align:start position:0% +A not of anything greater than eight +fairly low desensitivity if we choose an + + align:start position:0% +fairly low desensitivity if we choose an + + + align:start position:0% +fairly low desensitivity if we choose an +A not of only eight a loop transmission + + align:start position:0% +A not of only eight a loop transmission + + + align:start position:0% +A not of only eight a loop transmission +magnitude at DC of only eight why we'd + + align:start position:0% +magnitude at DC of only eight why we'd + + + align:start position:0% +magnitude at DC of only eight why we'd +find out that that there would in fact + + align:start position:0% +find out that that there would in fact + + + align:start position:0% +find out that that there would in fact +be poles in the right half plane. So + + align:start position:0% +be poles in the right half plane. So + + + align:start position:0% +be poles in the right half plane. So +here's a system where we really can't + + align:start position:0% +here's a system where we really can't + + + align:start position:0% +here's a system where we really can't +achieve very much desensitivity if we + + align:start position:0% +achieve very much desensitivity if we + + + align:start position:0% +achieve very much desensitivity if we +try to make a not any greater than 8. + + align:start position:0% +try to make a not any greater than 8. + + + align:start position:0% +try to make a not any greater than 8. +Why? We find out that the system becomes + + align:start position:0% +Why? We find out that the system becomes + + + align:start position:0% +Why? We find out that the system becomes +unstable. + + align:start position:0% +unstable. + + + align:start position:0% +unstable. +Well, how can we evaluate stability for + + align:start position:0% +Well, how can we evaluate stability for + + + align:start position:0% +Well, how can we evaluate stability for +arbitrary systems? And that's really + + align:start position:0% +arbitrary systems? And that's really + + + align:start position:0% +arbitrary systems? And that's really +what we're concerned about. Suppose we + + align:start position:0% +what we're concerned about. Suppose we + + + align:start position:0% +what we're concerned about. Suppose we +have systems that are third order where + + align:start position:0% +have systems that are third order where + + + align:start position:0% +have systems that are third order where +we see that the possibility of + + align:start position:0% +we see that the possibility of + + + align:start position:0% +we see that the possibility of +instability exists or even higher than + + align:start position:0% +instability exists or even higher than + + + align:start position:0% +instability exists or even higher than +third order. How do we determine the + + align:start position:0% +third order. How do we determine the + + + align:start position:0% +third order. How do we determine the +stability of those systems? + + align:start position:0% +stability of those systems? + + + align:start position:0% +stability of those systems? +In fact, I think more to the point for a + + align:start position:0% +In fact, I think more to the point for a + + + align:start position:0% +In fact, I think more to the point for a +design tool is not so much the issue of + + align:start position:0% +design tool is not so much the issue of + + + align:start position:0% +design tool is not so much the issue of +stability in a binary sense. Is the + + align:start position:0% +stability in a binary sense. Is the + + + align:start position:0% +stability in a binary sense. Is the +system stable as given by our original + + align:start position:0% +system stable as given by our original + + + align:start position:0% +system stable as given by our original +mathematical expression. Does a bound + + align:start position:0% +mathematical expression. Does a bound + + + align:start position:0% +mathematical expression. Does a bound +does a bounded input result in a bounded + + align:start position:0% +does a bounded input result in a bounded + + + align:start position:0% +does a bounded input result in a bounded +output? But very rapidly we'll get + + align:start position:0% +output? But very rapidly we'll get + + + align:start position:0% +output? But very rapidly we'll get +interested in sort of relative + + align:start position:0% +interested in sort of relative + + + align:start position:0% +interested in sort of relative +stability. We can usually solve the + + align:start position:0% +stability. We can usually solve the + + + align:start position:0% +stability. We can usually solve the +absolute stability problem. We can + + align:start position:0% +absolute stability problem. We can + + + align:start position:0% +absolute stability problem. We can +usually guarantee that the poles are in + + align:start position:0% +usually guarantee that the poles are in + + + align:start position:0% +usually guarantee that the poles are in +the left half plane by sufficient design + + align:start position:0% +the left half plane by sufficient design + + + align:start position:0% +the left half plane by sufficient design +efforts. Then we get concerned about how + + align:start position:0% +efforts. Then we get concerned about how + + + align:start position:0% +efforts. Then we get concerned about how +stable the system is. In other words, a + + align:start position:0% +stable the system is. In other words, a + + + align:start position:0% +stable the system is. In other words, a +measure of relative stability might be + + align:start position:0% +measure of relative stability might be + + + align:start position:0% +measure of relative stability might be +the damping ratio of the dominant pole + + align:start position:0% +the damping ratio of the dominant pole + + + align:start position:0% +the damping ratio of the dominant pole +pair. If we find that the closed loop + + align:start position:0% +pair. If we find that the closed loop + + + align:start position:0% +pair. If we find that the closed loop +transfer function has one pole pair + + align:start position:0% +transfer function has one pole pair + + + align:start position:0% +transfer function has one pole pair +closer to the origin than all other + + align:start position:0% +closer to the origin than all other + + + align:start position:0% +closer to the origin than all other +poles, we'll find out that that transfer + + align:start position:0% +poles, we'll find out that that transfer + + + align:start position:0% +poles, we'll find out that that transfer +function by or that pole pair by and + + align:start position:0% +function by or that pole pair by and + + + align:start position:0% +function by or that pole pair by and +large dominates the transient response + + align:start position:0% +large dominates the transient response + + + align:start position:0% +large dominates the transient response +of the system. We might be interested in + + align:start position:0% +of the system. We might be interested in + + + align:start position:0% +of the system. We might be interested in +the damping ratio associated with that + + align:start position:0% +the damping ratio associated with that + + + align:start position:0% +the damping ratio associated with that +dominant pole pair. So we're looking for + + align:start position:0% +dominant pole pair. So we're looking for + + + align:start position:0% +dominant pole pair. So we're looking for +analog measures if you will of + + align:start position:0% +analog measures if you will of + + + align:start position:0% +analog measures if you will of +stability. + + align:start position:0% +stability. + + + align:start position:0% +stability. +There are a number of ways we could + + align:start position:0% +There are a number of ways we could + + + align:start position:0% +There are a number of ways we could +proceed. One way is is to simply use + + align:start position:0% +proceed. One way is is to simply use + + + align:start position:0% +proceed. One way is is to simply use +numerical techniques. We can always + + align:start position:0% +numerical techniques. We can always + + + align:start position:0% +numerical techniques. We can always +write a closed loop transfer function + + align:start position:0% +write a closed loop transfer function + + + align:start position:0% +write a closed loop transfer function +for a linear system. And then we can use + + align:start position:0% +for a linear system. And then we can use + + + align:start position:0% +for a linear system. And then we can use +numerical methods machine computation to + + align:start position:0% +numerical methods machine computation to + + + align:start position:0% +numerical methods machine computation to +simply factor the polomial the + + align:start position:0% +simply factor the polomial the + + + align:start position:0% +simply factor the polomial the +characteristic equation. Factoring + + align:start position:0% +characteristic equation. Factoring + + + align:start position:0% +characteristic equation. Factoring +higher order polomials is a thing that + + align:start position:0% +higher order polomials is a thing that + + + align:start position:0% +higher order polomials is a thing that +people don't do very well but computers + + align:start position:0% +people don't do very well but computers + + + align:start position:0% +people don't do very well but computers +do exceedingly well and don't get bored + + align:start position:0% +do exceedingly well and don't get bored + + + align:start position:0% +do exceedingly well and don't get bored +by it and we can get the exact closed + + align:start position:0% +by it and we can get the exact closed + + + align:start position:0% +by it and we can get the exact closed +loophole locations for our system. The + + align:start position:0% +loophole locations for our system. The + + + align:start position:0% +loophole locations for our system. The +problem with that is it's very + + align:start position:0% +problem with that is it's very + + + align:start position:0% +problem with that is it's very +unsatisfying. + + align:start position:0% +unsatisfying. + + + align:start position:0% +unsatisfying. +Uh what you find out is that you go to + + align:start position:0% +Uh what you find out is that you go to + + + align:start position:0% +Uh what you find out is that you go to +the the giant mind and say where are the + + align:start position:0% +the the giant mind and say where are the + + + align:start position:0% +the the giant mind and say where are the +poles and it tells you there are three + + align:start position:0% +poles and it tells you there are three + + + align:start position:0% +poles and it tells you there are three +in the right half plane and four in the + + align:start position:0% +in the right half plane and four in the + + + align:start position:0% +in the right half plane and four in the +left half plane and now what do you ask + + align:start position:0% +left half plane and now what do you ask + + + align:start position:0% +left half plane and now what do you ask +for the next question? So you don't get + + align:start position:0% +for the next question? So you don't get + + + align:start position:0% +for the next question? So you don't get +any design insight by that process. And + + align:start position:0% +any design insight by that process. And + + + align:start position:0% +any design insight by that process. And +so the the thing we'd like to look at is + + align:start position:0% +so the the thing we'd like to look at is + + + align:start position:0% +so the the thing we'd like to look at is +some analytic method, something that we + + align:start position:0% +some analytic method, something that we + + + align:start position:0% +some analytic method, something that we +can do without really resorting to + + align:start position:0% +can do without really resorting to + + + align:start position:0% +can do without really resorting to +machine computation that maintains + + align:start position:0% +machine computation that maintains + + + align:start position:0% +machine computation that maintains +insight. I think the use of a machine to + + align:start position:0% +insight. I think the use of a machine to + + + align:start position:0% +insight. I think the use of a machine to +find exact pole locations is fine. Once + + align:start position:0% +find exact pole locations is fine. Once + + + align:start position:0% +find exact pole locations is fine. Once +we've got an idea of how the design is + + align:start position:0% +we've got an idea of how the design is + + + align:start position:0% +we've got an idea of how the design is +going, once we sort of know what we + + align:start position:0% +going, once we sort of know what we + + + align:start position:0% +going, once we sort of know what we +ought to do to make things better, if + + align:start position:0% +ought to do to make things better, if + + + align:start position:0% +ought to do to make things better, if +you will, then we we can go ahead and + + align:start position:0% +you will, then we we can go ahead and + + + align:start position:0% +you will, then we we can go ahead and +and use the machine with and and get + + align:start position:0% +and use the machine with and and get + + + align:start position:0% +and use the machine with and and get +some very useful information from it. + + align:start position:0% +some very useful information from it. + + + align:start position:0% +some very useful information from it. +But as a design tool to start a design, + + align:start position:0% +But as a design tool to start a design, + + + align:start position:0% +But as a design tool to start a design, +it's very very difficult to depend + + align:start position:0% +it's very very difficult to depend + + + align:start position:0% +it's very very difficult to depend +entirely on numerical calculations. + + align:start position:0% +entirely on numerical calculations. + + + align:start position:0% +entirely on numerical calculations. +There's also the very real possibility + + align:start position:0% +There's also the very real possibility + + + align:start position:0% +There's also the very real possibility +of the garbage in garbage out problem + + align:start position:0% +of the garbage in garbage out problem + + + align:start position:0% +of the garbage in garbage out problem +where you can easily make a mistake in + + align:start position:0% +where you can easily make a mistake in + + + align:start position:0% +where you can easily make a mistake in +your simulation. You can easily get the + + align:start position:0% +your simulation. You can easily get the + + + align:start position:0% +your simulation. You can easily get the +wrong numbers in, get totally + + align:start position:0% +wrong numbers in, get totally + + + align:start position:0% +wrong numbers in, get totally +meaningless results and not realize it + + align:start position:0% +meaningless results and not realize it + + + align:start position:0% +meaningless results and not realize it +if you don't have some sort of a hand + + align:start position:0% +if you don't have some sort of a hand + + + align:start position:0% +if you don't have some sort of a hand +check. So, we're going to look at + + align:start position:0% +check. So, we're going to look at + + + align:start position:0% +check. So, we're going to look at +techniques that hopefully allow us to + + align:start position:0% +techniques that hopefully allow us to + + + align:start position:0% +techniques that hopefully allow us to +maintain insight during the design + + align:start position:0% +maintain insight during the design + + + align:start position:0% +maintain insight during the design +process and also give us the possibility + + align:start position:0% +process and also give us the possibility + + + align:start position:0% +process and also give us the possibility +of of preventing being led astray when + + align:start position:0% +of of preventing being led astray when + + + align:start position:0% +of of preventing being led astray when +we go to get exact numerical results. + + align:start position:0% +we go to get exact numerical results. + + + align:start position:0% +we go to get exact numerical results. +One that I'll mention in passing is a + + align:start position:0% +One that I'll mention in passing is a + + + align:start position:0% +One that I'll mention in passing is a +technique known as as the Ralph test. + + align:start position:0% +technique known as as the Ralph test. + + + align:start position:0% +technique known as as the Ralph test. +And I discuss this in the text. Uh it's + + align:start position:0% +And I discuss this in the text. Uh it's + + + align:start position:0% +And I discuss this in the text. Uh it's +very boring to lecture on and so I + + align:start position:0% +very boring to lecture on and so I + + + align:start position:0% +very boring to lecture on and so I +won't. But the method is described in + + align:start position:0% +won't. But the method is described in + + + align:start position:0% +won't. But the method is described in +the text and in fact the homework + + align:start position:0% +the text and in fact the homework + + + align:start position:0% +the text and in fact the homework +problems assign assigned in conjunction + + align:start position:0% +problems assign assigned in conjunction + + + align:start position:0% +problems assign assigned in conjunction +with this lecture will force you to + + align:start position:0% +with this lecture will force you to + + + align:start position:0% +with this lecture will force you to +carry out a couple of Ralph tests. It's + + align:start position:0% +carry out a couple of Ralph tests. It's + + + align:start position:0% +carry out a couple of Ralph tests. It's +simply a mathematical method that was + + align:start position:0% +simply a mathematical method that was + + + align:start position:0% +simply a mathematical method that was +developed long before people were + + align:start position:0% +developed long before people were + + + align:start position:0% +developed long before people were +concerned about feedback systems. And + + align:start position:0% +concerned about feedback systems. And + + + align:start position:0% +concerned about feedback systems. And +what it does is take an arbitrary + + align:start position:0% +what it does is take an arbitrary + + + align:start position:0% +what it does is take an arbitrary +polomial and determine the number of + + align:start position:0% +polomial and determine the number of + + + align:start position:0% +polomial and determine the number of +roots of that polomial that have + + align:start position:0% +roots of that polomial that have + + + align:start position:0% +roots of that polomial that have +positive real parts. And so what we're + + align:start position:0% +positive real parts. And so what we're + + + align:start position:0% +positive real parts. And so what we're +able to do is apply the Ralph test to + + align:start position:0% +able to do is apply the Ralph test to + + + align:start position:0% +able to do is apply the Ralph test to +the characteristic equation of a + + align:start position:0% +the characteristic equation of a + + + align:start position:0% +the characteristic equation of a +feedback system. We can write the + + align:start position:0% +feedback system. We can write the + + + align:start position:0% +feedback system. We can write the +characteristic equation of the system, + + align:start position:0% +characteristic equation of the system, + + + align:start position:0% +characteristic equation of the system, +apply the Ralph test to it, which as I + + align:start position:0% +apply the Ralph test to it, which as I + + + align:start position:0% +apply the Ralph test to it, which as I +say is a rather simple numerical + + align:start position:0% +say is a rather simple numerical + + + align:start position:0% +say is a rather simple numerical +manipulation that doesn't require + + align:start position:0% +manipulation that doesn't require + + + align:start position:0% +manipulation that doesn't require +factoring, simply requires + + align:start position:0% +factoring, simply requires + + + align:start position:0% +factoring, simply requires +multiplications. + + align:start position:0% +multiplications. + + + align:start position:0% +multiplications. +And when we do that, we determine the + + align:start position:0% +And when we do that, we determine the + + + align:start position:0% +And when we do that, we determine the +number of roots of the characteristic + + align:start position:0% +number of roots of the characteristic + + + align:start position:0% +number of roots of the characteristic +equation that have positive real parts. + + align:start position:0% +equation that have positive real parts. + + + align:start position:0% +equation that have positive real parts. +Well, the roots of the characteristic + + align:start position:0% +Well, the roots of the characteristic + + + align:start position:0% +Well, the roots of the characteristic +equation of course are the closed loop + + align:start position:0% +equation of course are the closed loop + + + align:start position:0% +equation of course are the closed loop +poles of the system. And so we find out + + align:start position:0% +poles of the system. And so we find out + + + align:start position:0% +poles of the system. And so we find out +the number of system poles that have + + align:start position:0% +the number of system poles that have + + + align:start position:0% +the number of system poles that have +positive real parts. Except in limited + + align:start position:0% +positive real parts. Except in limited + + + align:start position:0% +positive real parts. Except in limited +cases, the Ralph method doesn't really + + align:start position:0% +cases, the Ralph method doesn't really + + + align:start position:0% +cases, the Ralph method doesn't really +give us much design information. It does + + align:start position:0% +give us much design information. It does + + + align:start position:0% +give us much design information. It does +tell us in an absolute sense, again, an + + align:start position:0% +tell us in an absolute sense, again, an + + + align:start position:0% +tell us in an absolute sense, again, an +absolute mathematical sense whether a + + align:start position:0% +absolute mathematical sense whether a + + + align:start position:0% +absolute mathematical sense whether a +system is stable or not, but it really + + align:start position:0% +system is stable or not, but it really + + + align:start position:0% +system is stable or not, but it really +doesn't give us very much design + + align:start position:0% +doesn't give us very much design + + + align:start position:0% +doesn't give us very much design +information. So aside from possibly + + align:start position:0% +information. So aside from possibly + + + align:start position:0% +information. So aside from possibly +using it for very quick checks just to + + align:start position:0% +using it for very quick checks just to + + + align:start position:0% +using it for very quick checks just to +see if we're far away from from useful + + align:start position:0% +see if we're far away from from useful + + + align:start position:0% +see if we're far away from from useful +behavior or to check possibly the + + align:start position:0% +behavior or to check possibly the + + + align:start position:0% +behavior or to check possibly the +results of a a detailed computer + + align:start position:0% +results of a a detailed computer + + + align:start position:0% +results of a a detailed computer +analysis to verify the number of of + + align:start position:0% +analysis to verify the number of of + + + align:start position:0% +analysis to verify the number of of +poles in the right half plane. We find + + align:start position:0% +poles in the right half plane. We find + + + align:start position:0% +poles in the right half plane. We find +that the Ralph method is of of limited + + align:start position:0% +that the Ralph method is of of limited + + + align:start position:0% +that the Ralph method is of of limited +usefulness as a design tool. + + align:start position:0% +usefulness as a design tool. + + + align:start position:0% +usefulness as a design tool. +We're going to look at two methods uh in + + align:start position:0% +We're going to look at two methods uh in + + + align:start position:0% +We're going to look at two methods uh in +considerable detail that allow us to + + align:start position:0% +considerable detail that allow us to + + + align:start position:0% +considerable detail that allow us to +predict something about the relative + + align:start position:0% +predict something about the relative + + + align:start position:0% +predict something about the relative +stability of a feedback system and also + + align:start position:0% +stability of a feedback system and also + + + align:start position:0% +stability of a feedback system and also +to improve the performance of a system. + + align:start position:0% +to improve the performance of a system. + + + align:start position:0% +to improve the performance of a system. +We get insight that that shows us how we + + align:start position:0% +We get insight that that shows us how we + + + align:start position:0% +We get insight that that shows us how we +might change either the forward path + + align:start position:0% +might change either the forward path + + + align:start position:0% +might change either the forward path +transfer function, the feedback path + + align:start position:0% +transfer function, the feedback path + + + align:start position:0% +transfer function, the feedback path +transfer function, something like that + + align:start position:0% +transfer function, something like that + + + align:start position:0% +transfer function, something like that +in order to improve the stability of the + + align:start position:0% +in order to improve the stability of the + + + align:start position:0% +in order to improve the stability of the +system. The first of these is called the + + align:start position:0% +system. The first of these is called the + + + align:start position:0% +system. The first of these is called the +root locus method. + + align:start position:0% + + + + align:start position:0% + +And what we do in root locus is the + + align:start position:0% +And what we do in root locus is the + + + align:start position:0% +And what we do in root locus is the +following. + + align:start position:0% +following. + + + align:start position:0% +following. +We look at a af product. Remember this + + align:start position:0% +We look at a af product. Remember this + + + align:start position:0% +We look at a af product. Remember this +is the negative of the loop transmission + + align:start position:0% +is the negative of the loop transmission + + + align:start position:0% +is the negative of the loop transmission +in our standard form. The loop + + align:start position:0% +in our standard form. The loop + + + align:start position:0% +in our standard form. The loop +transmission for our standard form + + align:start position:0% +transmission for our standard form + + + align:start position:0% +transmission for our standard form +system being minus a of s * f of s. And + + align:start position:0% +system being minus a of s * f of s. And + + + align:start position:0% +system being minus a of s * f of s. And +we'll assume that that + + align:start position:0% +we'll assume that that + + + align:start position:0% +we'll assume that that +quantity can be represented as some DC + + align:start position:0% +quantity can be represented as some DC + + + align:start position:0% +quantity can be represented as some DC +loop transmission magnitude A not Fnot + + align:start position:0% +loop transmission magnitude A not Fnot + + + align:start position:0% +loop transmission magnitude A not Fnot +and then we'll lump all the frequency + + align:start position:0% +and then we'll lump all the frequency + + + align:start position:0% +and then we'll lump all the frequency +dependent portion into a term G of S + + align:start position:0% +dependent portion into a term G of S + + + align:start position:0% +dependent portion into a term G of S +where we assume we normalize G of S or + + align:start position:0% +where we assume we normalize G of S or + + + align:start position:0% +where we assume we normalize G of S or +factor out the gain expression combine + + align:start position:0% +factor out the gain expression combine + + + align:start position:0% +factor out the gain expression combine +that a not F not so that G evaluated at + + align:start position:0% +that a not F not so that G evaluated at + + + align:start position:0% +that a not F not so that G evaluated at +S equals zero the DC gain of of the term + + align:start position:0% +S equals zero the DC gain of of the term + + + align:start position:0% +S equals zero the DC gain of of the term +G or the DC magnitude of the term G is + + align:start position:0% +G or the DC magnitude of the term G is + + + align:start position:0% +G or the DC magnitude of the term G is +unity. + + align:start position:0% +unity. + + + align:start position:0% +unity. +Hence the magnitude of the loop + + align:start position:0% +Hence the magnitude of the loop + + + align:start position:0% +Hence the magnitude of the loop +transmission at DC is simply a not f. + + align:start position:0% +transmission at DC is simply a not f. + + + align:start position:0% +transmission at DC is simply a not f. +Using that notation we find that capital + + align:start position:0% +Using that notation we find that capital + + + align:start position:0% +Using that notation we find that capital +a of s the closed loop transfer function + + align:start position:0% +a of s the closed loop transfer function + + + align:start position:0% +a of s the closed loop transfer function +is the forward path transmission a of s + + align:start position:0% +is the forward path transmission a of s + + + align:start position:0% +is the forward path transmission a of s +over 1 + a fog g of s 1 + a of s or + + align:start position:0% +over 1 + a fog g of s 1 + a of s or + + + align:start position:0% +over 1 + a fog g of s 1 + a of s or +equivalently 1 minus the loop + + align:start position:0% +equivalently 1 minus the loop + + + align:start position:0% +equivalently 1 minus the loop +transmission. + + align:start position:0% +transmission. + + + align:start position:0% +transmission. +Initially with our root locus + + align:start position:0% +Initially with our root locus + + + align:start position:0% +Initially with our root locus +manipulations, we'll only be interested + + align:start position:0% +manipulations, we'll only be interested + + + align:start position:0% +manipulations, we'll only be interested +in the pole locations, the locations of + + align:start position:0% +in the pole locations, the locations of + + + align:start position:0% +in the pole locations, the locations of +the closed loop system poles, and we + + align:start position:0% +the closed loop system poles, and we + + + align:start position:0% +the closed loop system poles, and we +won't initially be concerned about the + + align:start position:0% +won't initially be concerned about the + + + align:start position:0% +won't initially be concerned about the +location of the zeros. If all we're + + align:start position:0% +location of the zeros. If all we're + + + align:start position:0% +location of the zeros. If all we're +interested in are the pole locations, + + align:start position:0% +interested in are the pole locations, + + + align:start position:0% +interested in are the pole locations, +why we can get that by simply looking at + + align:start position:0% +why we can get that by simply looking at + + + align:start position:0% +why we can get that by simply looking at +the denominator. Recall that that for a + + align:start position:0% +the denominator. Recall that that for a + + + align:start position:0% +the denominator. Recall that that for a +system of this type, the zeros are + + align:start position:0% +system of this type, the zeros are + + + align:start position:0% +system of this type, the zeros are +dependent on how the loop transmission + + align:start position:0% +dependent on how the loop transmission + + + align:start position:0% +dependent on how the loop transmission +is distributed between A and F. But the + + align:start position:0% +is distributed between A and F. But the + + + align:start position:0% +is distributed between A and F. But the +poles of the system are dependent only + + align:start position:0% +poles of the system are dependent only + + + align:start position:0% +poles of the system are dependent only +on the afroduct. So we can consider only + + align:start position:0% +on the afroduct. So we can consider only + + + align:start position:0% +on the afroduct. So we can consider only +the characteristic equation 1 + a fnot g + + align:start position:0% +the characteristic equation 1 + a fnot g + + + align:start position:0% +the characteristic equation 1 + a fnot g +of s when we look for the system poles. + + align:start position:0% +of s when we look for the system poles. + + + align:start position:0% +of s when we look for the system poles. +And in fact uh we recognize that the + + align:start position:0% +And in fact uh we recognize that the + + + align:start position:0% +And in fact uh we recognize that the +system poles occur when the + + align:start position:0% +system poles occur when the + + + align:start position:0% +system poles occur when the +characteristic equation is equal to + + align:start position:0% +characteristic equation is equal to + + + align:start position:0% +characteristic equation is equal to +zero. In other words, if we determine + + align:start position:0% +zero. In other words, if we determine + + + align:start position:0% +zero. In other words, if we determine +the values of S for which the + + align:start position:0% +the values of S for which the + + + align:start position:0% +the values of S for which the +characteristic equation is zero, that + + align:start position:0% +characteristic equation is zero, that + + + align:start position:0% +characteristic equation is zero, that +those are the values of S for which the + + align:start position:0% +those are the values of S for which the + + + align:start position:0% +those are the values of S for which the +denominator of a closed loop transfer + + align:start position:0% +denominator of a closed loop transfer + + + align:start position:0% +denominator of a closed loop transfer +function goes to zero. Consequently, + + align:start position:0% +function goes to zero. Consequently, + + + align:start position:0% +function goes to zero. Consequently, +there the system poles. + + align:start position:0% +there the system poles. + + + align:start position:0% +there the system poles. +Well, let's see how we we might + + align:start position:0% +Well, let's see how we we might + + + align:start position:0% +Well, let's see how we we might +determine that. What one does in a root + + align:start position:0% +determine that. What one does in a root + + + align:start position:0% +determine that. What one does in a root +locus method is to determine how the + + align:start position:0% +locus method is to determine how the + + + align:start position:0% +locus method is to determine how the +poles are located as a function of first + + align:start position:0% +poles are located as a function of first + + + align:start position:0% +poles are located as a function of first +of all the poles and zeros associated + + align:start position:0% +of all the poles and zeros associated + + + align:start position:0% +of all the poles and zeros associated +with the loop transmission. In other + + align:start position:0% +with the loop transmission. In other + + + align:start position:0% +with the loop transmission. In other +words, the quantity g of s which + + align:start position:0% +words, the quantity g of s which + + + align:start position:0% +words, the quantity g of s which +includes all the frequency dependent + + align:start position:0% +includes all the frequency dependent + + + align:start position:0% +includes all the frequency dependent +portions of the loop transmission + + align:start position:0% +portions of the loop transmission + + + align:start position:0% +portions of the loop transmission +and the quantity a not fod. Certainly + + align:start position:0% +and the quantity a not fod. Certainly + + + align:start position:0% +and the quantity a not fod. Certainly +the pole locations, the closed loop pole + + align:start position:0% +the pole locations, the closed loop pole + + + align:start position:0% +the pole locations, the closed loop pole +locations given by setting the + + align:start position:0% +locations given by setting the + + + align:start position:0% +locations given by setting the +characteristic equation equal to zero + + align:start position:0% +characteristic equation equal to zero + + + align:start position:0% +characteristic equation equal to zero +are dependent both on the + + align:start position:0% +are dependent both on the + + + align:start position:0% +are dependent both on the +characteristics of g of s and on a not + + align:start position:0% +characteristics of g of s and on a not + + + align:start position:0% +characteristics of g of s and on a not +fnot. When we if we would attempt to + + align:start position:0% +fnot. When we if we would attempt to + + + align:start position:0% +fnot. When we if we would attempt to +factor this equation, we'd find out that + + align:start position:0% +factor this equation, we'd find out that + + + align:start position:0% +factor this equation, we'd find out that +that factoring would depend both on a + + align:start position:0% +that factoring would depend both on a + + + align:start position:0% +that factoring would depend both on a +not f and the specific details of g of + + align:start position:0% +not f and the specific details of g of + + + align:start position:0% +not f and the specific details of g of +s. + + align:start position:0% +s. + + + align:start position:0% +s. +Let's look at how this might go. Let's + + align:start position:0% +Let's look at how this might go. Let's + + + align:start position:0% +Let's look at how this might go. Let's +start out with an a of s f of s product + + align:start position:0% +start out with an a of s f of s product + + + align:start position:0% +start out with an a of s f of s product +that's a not fnot over two first order + + align:start position:0% +that's a not fnot over two first order + + + align:start position:0% +that's a not fnot over two first order +poles. In other words, we have a system + + align:start position:0% +poles. In other words, we have a system + + + align:start position:0% +poles. In other words, we have a system +which has a loop transmission that has + + align:start position:0% +which has a loop transmission that has + + + align:start position:0% +which has a loop transmission that has +two poles on the real axis. We've again + + align:start position:0% +two poles on the real axis. We've again + + + align:start position:0% +two poles on the real axis. We've again +looked at this before. + + align:start position:0% +looked at this before. + + + align:start position:0% +looked at this before. +The characteristic equation for such a + + align:start position:0% +The characteristic equation for such a + + + align:start position:0% +The characteristic equation for such a +system is simply 1 minus the loop + + align:start position:0% +system is simply 1 minus the loop + + + align:start position:0% +system is simply 1 minus the loop +transmission or 1 + af. And so we get 1 + + align:start position:0% +transmission or 1 + af. And so we get 1 + + + align:start position:0% +transmission or 1 + af. And so we get 1 ++ a fnot over to a s+1 * to b s + one. + + align:start position:0% ++ a fnot over to a s+1 * to b s + one. + + + align:start position:0% ++ a fnot over to a s+1 * to b s + one. +And we set that equal to zero in order + + align:start position:0% +And we set that equal to zero in order + + + align:start position:0% +And we set that equal to zero in order +to determine the poles of the system. + + align:start position:0% +to determine the poles of the system. + + + align:start position:0% +to determine the poles of the system. +If we multiply through clearer + + align:start position:0% +If we multiply through clearer + + + align:start position:0% +If we multiply through clearer +fractions, we end up with this equation. + + align:start position:0% +fractions, we end up with this equation. + + + align:start position:0% +fractions, we end up with this equation. +Tao a to b over s^ squ plus to a plus to + + align:start position:0% +Tao a to b over s^ squ plus to a plus to + + + align:start position:0% +Tao a to b over s^ squ plus to a plus to +b s + 1 + a f not equals z. + + align:start position:0% +b s + 1 + a f not equals z. + + + align:start position:0% +b s + 1 + a f not equals z. +And we can factor that by use of the + + align:start position:0% +And we can factor that by use of the + + + align:start position:0% +And we can factor that by use of the +familiar quadratic formula. Certainly + + align:start position:0% +familiar quadratic formula. Certainly + + + align:start position:0% +familiar quadratic formula. Certainly +people are perfectly capable of + + align:start position:0% +people are perfectly capable of + + + align:start position:0% +people are perfectly capable of +factoring second order equations. And + + align:start position:0% +factoring second order equations. And + + + align:start position:0% +factoring second order equations. And +when we do that we get the usual result + + align:start position:0% +when we do that we get the usual result + + + align:start position:0% +when we do that we get the usual result +in the second of the quadratic equation. + + align:start position:0% +in the second of the quadratic equation. + + + align:start position:0% +in the second of the quadratic equation. +The uh poles are the two poles are + + align:start position:0% +The uh poles are the two poles are + + + align:start position:0% +The uh poles are the two poles are +located at minus to a plus to b plus or + + align:start position:0% +located at minus to a plus to b plus or + + + align:start position:0% +located at minus to a plus to b plus or +minus the square root of this quantity + + align:start position:0% +minus the square root of this quantity + + + align:start position:0% +minus the square root of this quantity +divided by 2 to a to b. + + align:start position:0% +divided by 2 to a to b. + + + align:start position:0% +divided by 2 to a to b. +And I'd like to spend a little bit of + + align:start position:0% +And I'd like to spend a little bit of + + + align:start position:0% +And I'd like to spend a little bit of +time looking at + + align:start position:0% +time looking at + + + align:start position:0% +time looking at +that particular expression. We now have + + align:start position:0% +that particular expression. We now have + + + align:start position:0% +that particular expression. We now have +a way of finding the closed loop poles + + align:start position:0% +a way of finding the closed loop poles + + + align:start position:0% +a way of finding the closed loop poles +of the system s1 and s_ub_2 as we vary a + + align:start position:0% +of the system s1 and s_ub_2 as we vary a + + + align:start position:0% +of the system s1 and s_ub_2 as we vary a +not fnot because a not fnot appears of + + align:start position:0% +not fnot because a not fnot appears of + + + align:start position:0% +not fnot because a not fnot appears of +course in our expression for the closed + + align:start position:0% +course in our expression for the closed + + + align:start position:0% +course in our expression for the closed +loop pole locations. So we've now gotten + + align:start position:0% +loop pole locations. So we've now gotten + + + align:start position:0% +loop pole locations. So we've now gotten +the basis for our root locus method or + + align:start position:0% +the basis for our root locus method or + + + align:start position:0% +the basis for our root locus method or +what we're trying to accomplish in in + + align:start position:0% +what we're trying to accomplish in in + + + align:start position:0% +what we're trying to accomplish in in +our root locus method because what we'd + + align:start position:0% +our root locus method because what we'd + + + align:start position:0% +our root locus method because what we'd +like to do in in the root locus + + align:start position:0% +like to do in in the root locus + + + align:start position:0% +like to do in in the root locus +technique is find out where the closed + + align:start position:0% +technique is find out where the closed + + + align:start position:0% +technique is find out where the closed +loop poles lie as a function of a not + + align:start position:0% +loop poles lie as a function of a not + + + align:start position:0% +loop poles lie as a function of a not +fnot for a specified g of s. So at least + + align:start position:0% +fnot for a specified g of s. So at least + + + align:start position:0% +fnot for a specified g of s. So at least +for the second order case we're able to + + align:start position:0% +for the second order case we're able to + + + align:start position:0% +for the second order case we're able to +solve that exactly. + + align:start position:0% +solve that exactly. + + + align:start position:0% +solve that exactly. +Let me show how this information is + + align:start position:0% +Let me show how this information is + + + align:start position:0% +Let me show how this information is +normally presented. + + align:start position:0% + + + + align:start position:0% + +We normally present information + + align:start position:0% +We normally present information + + + align:start position:0% +We normally present information +concerning root locus + + align:start position:0% + + + + align:start position:0% + +analysis in terms of a a root locus + + align:start position:0% +analysis in terms of a a root locus + + + align:start position:0% +analysis in terms of a a root locus +diagram. And this is a diagram in the + + align:start position:0% +diagram. And this is a diagram in the + + + align:start position:0% +diagram. And this is a diagram in the +splane. + + align:start position:0% +splane. + + + align:start position:0% +splane. +And + + align:start position:0% + + + + align:start position:0% + +we have the usual splane coordinates, + + align:start position:0% +we have the usual splane coordinates, + + + align:start position:0% +we have the usual splane coordinates, +the imaginary axis vertically, the real + + align:start position:0% +the imaginary axis vertically, the real + + + align:start position:0% +the imaginary axis vertically, the real +axis horizontally. + + align:start position:0% +axis horizontally. + + + align:start position:0% +axis horizontally. +And we show several things. We show + + align:start position:0% +And we show several things. We show + + + align:start position:0% +And we show several things. We show +first of all the location of any loop + + align:start position:0% +first of all the location of any loop + + + align:start position:0% +first of all the location of any loop +transmission poles and zeros. In other + + align:start position:0% +transmission poles and zeros. In other + + + align:start position:0% +transmission poles and zeros. In other +words, all of the frequency dependent + + align:start position:0% +words, all of the frequency dependent + + + align:start position:0% +words, all of the frequency dependent +portions of the loop transmission are + + align:start position:0% +portions of the loop transmission are + + + align:start position:0% +portions of the loop transmission are +shown in our root locus diagram. So in + + align:start position:0% +shown in our root locus diagram. So in + + + align:start position:0% +shown in our root locus diagram. So in +in our particular second order case, we + + align:start position:0% +in our particular second order case, we + + + align:start position:0% +in our particular second order case, we +have two poles one at minus1 over to a + + align:start position:0% +have two poles one at minus1 over to a + + + align:start position:0% +have two poles one at minus1 over to a +the other one at S= minus1 over to B. + + align:start position:0% +the other one at S= minus1 over to B. + + + align:start position:0% +the other one at S= minus1 over to B. +We then draw some branches in the splane + + align:start position:0% +We then draw some branches in the splane + + + align:start position:0% +We then draw some branches in the splane +that show where the closed loop poles + + align:start position:0% +that show where the closed loop poles + + + align:start position:0% +that show where the closed loop poles +lie as a function of a not fnot. And in + + align:start position:0% +lie as a function of a not fnot. And in + + + align:start position:0% +lie as a function of a not fnot. And in +fact what we do is typically include + + align:start position:0% +fact what we do is typically include + + + align:start position:0% +fact what we do is typically include +arrows + + align:start position:0% +arrows + + + align:start position:0% +arrows +on those lines on those branches that + + align:start position:0% +on those lines on those branches that + + + align:start position:0% +on those lines on those branches that +indicate the direction of increasing a + + align:start position:0% +indicate the direction of increasing a + + + align:start position:0% +indicate the direction of increasing a +not f or a not if we have a system with + + align:start position:0% +not f or a not if we have a system with + + + align:start position:0% +not f or a not if we have a system with +unity f. uh we can determine how the + + align:start position:0% +unity f. uh we can determine how the + + + align:start position:0% +unity f. uh we can determine how the +root locus diagram has to go by looking + + align:start position:0% +root locus diagram has to go by looking + + + align:start position:0% +root locus diagram has to go by looking +at our quadratic equation. + + align:start position:0% + + + + align:start position:0% + +Let's see if we first start out for a + + align:start position:0% +Let's see if we first start out for a + + + align:start position:0% +Let's see if we first start out for a +not f equal to zero the what's + + align:start position:0% +not f equal to zero the what's + + + align:start position:0% +not f equal to zero the what's +conventionally done is to plot the loc + + align:start position:0% +conventionally done is to plot the loc + + + align:start position:0% +conventionally done is to plot the loc +roots of the characteristic equation as + + align:start position:0% +roots of the characteristic equation as + + + align:start position:0% +roots of the characteristic equation as +a not fot goes from zero to some very + + align:start position:0% +a not fot goes from zero to some very + + + align:start position:0% +a not fot goes from zero to some very +very large positive number. So we can + + align:start position:0% +very large positive number. So we can + + + align:start position:0% +very large positive number. So we can +start out looking at the root locus + + align:start position:0% +start out looking at the root locus + + + align:start position:0% +start out looking at the root locus +diagram determining the roots of the + + align:start position:0% +diagram determining the roots of the + + + align:start position:0% +diagram determining the roots of the +characteristic equation for a not f + + align:start position:0% +characteristic equation for a not f + + + align:start position:0% +characteristic equation for a not f +equal to zero. Well certainly if we + + align:start position:0% +equal to zero. Well certainly if we + + + align:start position:0% +equal to zero. Well certainly if we +factor the characteristic equation under + + align:start position:0% +factor the characteristic equation under + + + align:start position:0% +factor the characteristic equation under +those conditions we get the original + + align:start position:0% +those conditions we get the original + + + align:start position:0% +those conditions we get the original +pole locations minus one over to a minus + + align:start position:0% +pole locations minus one over to a minus + + + align:start position:0% +pole locations minus one over to a minus +one over to b and that would be the + + align:start position:0% +one over to b and that would be the + + + align:start position:0% +one over to b and that would be the +result of simply taking this general + + align:start position:0% +result of simply taking this general + + + align:start position:0% +result of simply taking this general +expression and setting a fnot equal to + + align:start position:0% +expression and setting a fnot equal to + + + align:start position:0% +expression and setting a fnot equal to +zero. + + align:start position:0% +zero. + + + align:start position:0% +zero. +As we then allow a not fot to + + align:start position:0% +As we then allow a not fot to + + + align:start position:0% +As we then allow a not fot to +increase the radic gets smaller. It + + align:start position:0% +increase the radic gets smaller. It + + + align:start position:0% +increase the radic gets smaller. It +started out as some positive number of + + align:start position:0% +started out as some positive number of + + + align:start position:0% +started out as some positive number of +course for a not fot being equal to zero + + align:start position:0% +course for a not fot being equal to zero + + + align:start position:0% +course for a not fot being equal to zero +in particular to a plus plus plus to b + + align:start position:0% +in particular to a plus plus plus to b + + + align:start position:0% +in particular to a plus plus plus to b +minus 4 to a to b which is a positive + + align:start position:0% +minus 4 to a to b which is a positive + + + align:start position:0% +minus 4 to a to b which is a positive +number. As we allow a not fnot to get + + align:start position:0% +number. As we allow a not fnot to get + + + align:start position:0% +number. As we allow a not fnot to get +bigger why this term increases in + + align:start position:0% +bigger why this term increases in + + + align:start position:0% +bigger why this term increases in +magnitude. Consequently, the radicand + + align:start position:0% +magnitude. Consequently, the radicand + + + align:start position:0% +magnitude. Consequently, the radicand +gets smaller. And what that says is that + + align:start position:0% +gets smaller. And what that says is that + + + align:start position:0% +gets smaller. And what that says is that +the separation between the two closed + + align:start position:0% +the separation between the two closed + + + align:start position:0% +the separation between the two closed +loop poles is decreasing. They start out + + align:start position:0% +loop poles is decreasing. They start out + + + align:start position:0% +loop poles is decreasing. They start out +for 0 a fnot located at at frequencies + + align:start position:0% +for 0 a fnot located at at frequencies + + + align:start position:0% +for 0 a fnot located at at frequencies +minus1 over to a and minus1 over to b + + align:start position:0% +minus1 over to a and minus1 over to b + + + align:start position:0% +minus1 over to a and minus1 over to b +and then the separation decreases as the + + align:start position:0% +and then the separation decreases as the + + + align:start position:0% +and then the separation decreases as the +as we increase a not fnot. So as we + + align:start position:0% +as we increase a not fnot. So as we + + + align:start position:0% +as we increase a not fnot. So as we +increase a not fnot the separation + + align:start position:0% +increase a not fnot the separation + + + align:start position:0% +increase a not fnot the separation +between the two closed loop poles + + align:start position:0% +between the two closed loop poles + + + align:start position:0% +between the two closed loop poles +decreases. + + align:start position:0% +decreases. + + + align:start position:0% +decreases. +They finally meet on the real axis when + + align:start position:0% +They finally meet on the real axis when + + + align:start position:0% +They finally meet on the real axis when +the radican goes to zero and therefore + + align:start position:0% +the radican goes to zero and therefore + + + align:start position:0% +the radican goes to zero and therefore +they meet at minus quantity to a plus to + + align:start position:0% +they meet at minus quantity to a plus to + + + align:start position:0% +they meet at minus quantity to a plus to +b over 2 to a to b. That's the + + align:start position:0% +b over 2 to a to b. That's the + + + align:start position:0% +b over 2 to a to b. That's the +expression that results with the radican + + align:start position:0% +expression that results with the radican + + + align:start position:0% +expression that results with the radican +zero. And if we + + align:start position:0% +zero. And if we + + + align:start position:0% +zero. And if we +work with the algebra a bit, we find out + + align:start position:0% +work with the algebra a bit, we find out + + + align:start position:0% +work with the algebra a bit, we find out +that that's the arithmetic average of + + align:start position:0% +that that's the arithmetic average of + + + align:start position:0% +that that's the arithmetic average of +the locations one over to a and one over + + align:start position:0% +the locations one over to a and one over + + + align:start position:0% +the locations one over to a and one over +to b. In other words, it's the + + align:start position:0% +to b. In other words, it's the + + + align:start position:0% +to b. In other words, it's the +arithmetic average of the openloop pole + + align:start position:0% +arithmetic average of the openloop pole + + + align:start position:0% +arithmetic average of the openloop pole +locations or the pole locations + + align:start position:0% +locations or the pole locations + + + align:start position:0% +locations or the pole locations +associated with loop transmission minus + + align:start position:0% +associated with loop transmission minus + + + align:start position:0% +associated with loop transmission minus +one/2 one over to a plus one over to B. + + align:start position:0% +one/2 one over to a plus one over to B. + + + align:start position:0% +one/2 one over to a plus one over to B. +We can go back and look at our diagram + + align:start position:0% +We can go back and look at our diagram + + + align:start position:0% +We can go back and look at our diagram +and what we've done is indicate this + + align:start position:0% +and what we've done is indicate this + + + align:start position:0% +and what we've done is indicate this +behavior in the diagram for very small + + align:start position:0% +behavior in the diagram for very small + + + align:start position:0% +behavior in the diagram for very small +values of a not Fnot. The branches start + + align:start position:0% +values of a not Fnot. The branches start + + + align:start position:0% +values of a not Fnot. The branches start +at the + + align:start position:0% +at the + + + align:start position:0% +at the +loop transmission pole locations minus + + align:start position:0% +loop transmission pole locations minus + + + align:start position:0% +loop transmission pole locations minus +one over to a minus one over to B. The + + align:start position:0% +one over to a minus one over to B. The + + + align:start position:0% +one over to a minus one over to B. The +branches come together + + align:start position:0% +branches come together + + + align:start position:0% +branches come together +and actually meet at the arithmetic mean + + align:start position:0% +and actually meet at the arithmetic mean + + + align:start position:0% +and actually meet at the arithmetic mean +at minus one/2 of 1 over to a + 1 over t + + align:start position:0% +at minus one/2 of 1 over to a + 1 over t + + + align:start position:0% +at minus one/2 of 1 over to a + 1 over t +to b + + align:start position:0% +to b + + + align:start position:0% +to b +and then branch off the axis. Notice + + align:start position:0% +and then branch off the axis. Notice + + + align:start position:0% +and then branch off the axis. Notice +that again if we go back to our original + + align:start position:0% +that again if we go back to our original + + + align:start position:0% +that again if we go back to our original +expression we had gotten up to the point + + align:start position:0% +expression we had gotten up to the point + + + align:start position:0% +expression we had gotten up to the point +where the branches had met. Beyond that + + align:start position:0% +where the branches had met. Beyond that + + + align:start position:0% +where the branches had met. Beyond that +as we increase a not fot still further y + + align:start position:0% +as we increase a not fot still further y + + + align:start position:0% +as we increase a not fot still further y +the radic becomes negative. So we pick + + align:start position:0% +the radic becomes negative. So we pick + + + align:start position:0% +the radic becomes negative. So we pick +up an imaginary component to the pole + + align:start position:0% +up an imaginary component to the pole + + + align:start position:0% +up an imaginary component to the pole +location. And for further increases in a + + align:start position:0% +location. And for further increases in a + + + align:start position:0% +location. And for further increases in a +not fnot we maintain a constant real + + align:start position:0% +not fnot we maintain a constant real + + + align:start position:0% +not fnot we maintain a constant real +part given by this value but an + + align:start position:0% +part given by this value but an + + + align:start position:0% +part given by this value but an +increasing imaginary po component + + align:start position:0% +increasing imaginary po component + + + align:start position:0% +increasing imaginary po component +because the radican gets progressively + + align:start position:0% +because the radican gets progressively + + + align:start position:0% +because the radican gets progressively +larger in magnitude although it's + + align:start position:0% +larger in magnitude although it's + + + align:start position:0% +larger in magnitude although it's +negative in sign. + + align:start position:0% +negative in sign. + + + align:start position:0% +negative in sign. +And so now we see the overall behavior + + align:start position:0% +And so now we see the overall behavior + + + align:start position:0% +And so now we see the overall behavior +of the root locus diagram. Uh again we + + align:start position:0% +of the root locus diagram. Uh again we + + + align:start position:0% +of the root locus diagram. Uh again we +start for zero a not fnot or very small + + align:start position:0% +start for zero a not fnot or very small + + + align:start position:0% +start for zero a not fnot or very small +a not fnot at the loop transmission pole + + align:start position:0% +a not fnot at the loop transmission pole + + + align:start position:0% +a not fnot at the loop transmission pole +locations for this particular case. The + + align:start position:0% +locations for this particular case. The + + + align:start position:0% +locations for this particular case. The +two branches meet at the arithmetic mean + + align:start position:0% +two branches meet at the arithmetic mean + + + align:start position:0% +two branches meet at the arithmetic mean +and then go north and south in the root + + align:start position:0% +and then go north and south in the root + + + align:start position:0% +and then go north and south in the root +locus diagram. And in particular the + + align:start position:0% +locus diagram. And in particular the + + + align:start position:0% +locus diagram. And in particular the +damping ratio associated with the + + align:start position:0% +damping ratio associated with the + + + align:start position:0% +damping ratio associated with the +complex conjugate pole pair once we have + + align:start position:0% +complex conjugate pole pair once we have + + + align:start position:0% +complex conjugate pole pair once we have +a sufficiently large value for a not + + align:start position:0% +a sufficiently large value for a not + + + align:start position:0% +a sufficiently large value for a not +fnot can get arbitrarily small because + + align:start position:0% +fnot can get arbitrarily small because + + + align:start position:0% +fnot can get arbitrarily small because +if we were interested in the damping + + align:start position:0% +if we were interested in the damping + + + align:start position:0% +if we were interested in the damping +ratio uh when the closed loop poles were + + align:start position:0% +ratio uh when the closed loop poles were + + + align:start position:0% +ratio uh when the closed loop poles were +located here remember that that would be + + align:start position:0% +located here remember that that would be + + + align:start position:0% +located here remember that that would be +related to this angle in particular + + align:start position:0% +related to this angle in particular + + + align:start position:0% +related to this angle in particular +would be the cosine of this angle and so + + align:start position:0% +would be the cosine of this angle and so + + + align:start position:0% +would be the cosine of this angle and so +uh as we increase a fnot the closed loop + + align:start position:0% +uh as we increase a fnot the closed loop + + + align:start position:0% +uh as we increase a fnot the closed loop +poles move out along these lines s the + + align:start position:0% +poles move out along these lines s the + + + align:start position:0% +poles move out along these lines s the +angle that they make with the real axis + + align:start position:0% +angle that they make with the real axis + + + align:start position:0% +angle that they make with the real axis +gets progressively larger. Consequently, + + align:start position:0% +gets progressively larger. Consequently, + + + align:start position:0% +gets progressively larger. Consequently, +the damping ratio gets smaller. This + + align:start position:0% +the damping ratio gets smaller. This + + + align:start position:0% +the damping ratio gets smaller. This +again verifies what we had said earlier + + align:start position:0% +again verifies what we had said earlier + + + align:start position:0% +again verifies what we had said earlier +where we say if we have a system that + + align:start position:0% +where we say if we have a system that + + + align:start position:0% +where we say if we have a system that +had two openloop + + align:start position:0% +had two openloop + + + align:start position:0% +had two openloop +loop transmission poles + + align:start position:0% +loop transmission poles + + + align:start position:0% +loop transmission poles +uh and is a negative feedback system and + + align:start position:0% +uh and is a negative feedback system and + + + align:start position:0% +uh and is a negative feedback system and +furthermore both of the loop + + align:start position:0% +furthermore both of the loop + + + align:start position:0% +furthermore both of the loop +transmission poles are located in the + + align:start position:0% +transmission poles are located in the + + + align:start position:0% +transmission poles are located in the +left half plane. Why we're then able to + + align:start position:0% +left half plane. Why we're then able to + + + align:start position:0% +left half plane. Why we're then able to +get an arbitrarily low damping ratio by + + align:start position:0% +get an arbitrarily low damping ratio by + + + align:start position:0% +get an arbitrarily low damping ratio by +appropriate choice of of the combination + + align:start position:0% +appropriate choice of of the combination + + + align:start position:0% +appropriate choice of of the combination +of the pole locations and the a not fot + + align:start position:0% +of the pole locations and the a not fot + + + align:start position:0% +of the pole locations and the a not fot +product and we find out that for any + + align:start position:0% +product and we find out that for any + + + align:start position:0% +product and we find out that for any +pole locations a larger a not fnot from + + align:start position:0% +pole locations a larger a not fnot from + + + align:start position:0% +pole locations a larger a not fnot from +this kind of an analysis results in a + + align:start position:0% +this kind of an analysis results in a + + + align:start position:0% +this kind of an analysis results in a +smaller damping ratio. + + align:start position:0% +smaller damping ratio. + + + align:start position:0% +smaller damping ratio. +Uh but we can never get the system to + + align:start position:0% +Uh but we can never get the system to + + + align:start position:0% +Uh but we can never get the system to +have the poles the closed loop poles lie + + align:start position:0% +have the poles the closed loop poles lie + + + align:start position:0% +have the poles the closed loop poles lie +in the right half plane. We always + + align:start position:0% +in the right half plane. We always + + + align:start position:0% +in the right half plane. We always +maintain a fixed at least once we have + + align:start position:0% +maintain a fixed at least once we have + + + align:start position:0% +maintain a fixed at least once we have +the complex conjugate situation we + + align:start position:0% +the complex conjugate situation we + + + align:start position:0% +the complex conjugate situation we +always maintain a fixed real part and + + align:start position:0% +always maintain a fixed real part and + + + align:start position:0% +always maintain a fixed real part and +that real part is negative. So we can + + align:start position:0% +that real part is negative. So we can + + + align:start position:0% +that real part is negative. So we can +never get the poles into the right half + + align:start position:0% +never get the poles into the right half + + + align:start position:0% +never get the poles into the right half +plane although we can get arbitrarily + + align:start position:0% +plane although we can get arbitrarily + + + align:start position:0% +plane although we can get arbitrarily +small damping ratios. + + align:start position:0% +small damping ratios. + + + align:start position:0% +small damping ratios. +Well this is the way one can determine a + + align:start position:0% +Well this is the way one can determine a + + + align:start position:0% +Well this is the way one can determine a +root locus diagram for a second order + + align:start position:0% +root locus diagram for a second order + + + align:start position:0% +root locus diagram for a second order +system. Certainly a root locus diagram + + align:start position:0% +system. Certainly a root locus diagram + + + align:start position:0% +system. Certainly a root locus diagram +for a first order system is trivially + + align:start position:0% +for a first order system is trivially + + + align:start position:0% +for a first order system is trivially +simple. But for a second order system, + + align:start position:0% +simple. But for a second order system, + + + align:start position:0% +simple. But for a second order system, +we can in fact calculate it fairly + + align:start position:0% +we can in fact calculate it fairly + + + align:start position:0% +we can in fact calculate it fairly +easily by hand. In fact, there is a + + align:start position:0% +easily by hand. In fact, there is a + + + align:start position:0% +easily by hand. In fact, there is a +formula that allows one to factor third + + align:start position:0% +formula that allows one to factor third + + + align:start position:0% +formula that allows one to factor third +order polomials. Uh presumably we could + + align:start position:0% +order polomials. Uh presumably we could + + + align:start position:0% +order polomials. Uh presumably we could +always do it for a higher order system + + align:start position:0% +always do it for a higher order system + + + align:start position:0% +always do it for a higher order system +by machine computation, but I've already + + align:start position:0% +by machine computation, but I've already + + + align:start position:0% +by machine computation, but I've already +badmouththed that. So what we're we + + align:start position:0% +badmouththed that. So what we're we + + + align:start position:0% +badmouththed that. So what we're we +we're really searching for is a + + align:start position:0% +we're really searching for is a + + + align:start position:0% +we're really searching for is a +technique that will allow us to + + align:start position:0% +technique that will allow us to + + + align:start position:0% +technique that will allow us to +determine rapidly and easily a root + + align:start position:0% +determine rapidly and easily a root + + + align:start position:0% +determine rapidly and easily a root +locus diagram. + + align:start position:0% +locus diagram. + + + align:start position:0% +locus diagram. +without the pain of actually having to + + align:start position:0% +without the pain of actually having to + + + align:start position:0% +without the pain of actually having to +factor the characteristic equation. + + align:start position:0% +factor the characteristic equation. + + + align:start position:0% +factor the characteristic equation. +We'll look at that the next time and and + + align:start position:0% +We'll look at that the next time and and + + + align:start position:0% +We'll look at that the next time and and +see how we can use properties associated + + align:start position:0% +see how we can use properties associated + + + align:start position:0% +see how we can use properties associated +with the loop transmission to actually + + align:start position:0% +with the loop transmission to actually + + + align:start position:0% +with the loop transmission to actually +determine the root locus diagram without + + align:start position:0% +determine the root locus diagram without + + + align:start position:0% +determine the root locus diagram without +actually having to factor the + + align:start position:0% +actually having to factor the + + + align:start position:0% +actually having to factor the +characteristic equation. Thank you. \ No newline at end of file diff --git a/wPwWtFMkxLo.txt b/wPwWtFMkxLo.txt new file mode 100644 index 0000000000000000000000000000000000000000..803e687b39346dc48c8bb8e797edb8974aa7f165 --- /dev/null +++ b/wPwWtFMkxLo.txt @@ -0,0 +1,131 @@ +Fixed-length encodings work well when all +the possible choices have the same information + +content, i.e., all the choices have an equal +probability of occurring. + +If those choices don't have the same information +content, we can do better. + +To see how, consider the expected length of +an encoding, computed by considering each + +x_i to be encoded, and weighting the length +of its encoding by p_i, the probability of + +its occurrence. + +By "doing better" we mean that we can find +encodings that have a shorter expected length + +than a fixed-length encoding. + +Ideally we'd like the expected length of the +encoding for the x_i to match the entropy + +H(X), which is the expected information content. + +We know that if x_i has a higher probability +(i.e., a larger p_i), that is has a smaller + +information content, so we'd like to use shorter +encodings. + +If x_i has a lower probability, then we'd +use a longer encoding. + +So we'll be constructing encodings where the +x_i may have different length codes - we'll + +call these variable-length encodings. + +Here's an example we've seen before. + +There are four possible choices to encode +(A, B, C, and D), each with the specified + +probability. + +The table shows a suggested encoding where +we've followed the advice from the previous + +slide: high-probability choices that convey +little information (e.g., B) are given shorter + +encodings, +while low-probability choices that convey + +more information (e.g., C or D) are given +longer encodings. + +Let's diagram this encoding as a binary tree. + +Since the symbols all appear as the leaves +of the tree, we can see that the encoding + +is unambiguous. + +Let's try decoding the following encoded data. + +We'll use the tree as follows: start at the +root of the tree and use bits from the encoded + +data to traverse the tree as directed, stopping +when we reach a leaf. + +Starting at the root, the first encoded bit +is 0, which takes us down the left branch + +to the leaf B. +So B is the first symbol of the decoded data. + +Starting at the root again, 1 takes us down +the right branch, 0 the left branch from there, + +and 0 the left branch below that, arriving +at the leaf C, the second symbol of the decoded + +data. + +Continuing on: 11 gives us A, 0 decodes as +B, 11 gives us A again, and, finally, 101 + +gives us D. +The entire decoded message is "BCABAD". + +The expected length of this encoding is easy +to compute: the length of A's encoding (2 + +bits) times its probability, plus the length +of B's encoding (1 bit) times 1/2, plus the + +contributions for C and D, each 3 times 1/12. + +This adds up to 1 and 2/3 bits. + +How did we do? + +If we had used a fixed-length encoding for +our four possible symbols, we'd have needed + +2 bits each, so we'd need 2000 bits to encode +1000 symbols. + +Using our variable-length encoding, the expected +length for 1000 symbols would be 1667. + +The lower bound on the number of bits needed +to encode 1000 symbols is 1000 times the entropy + +H(X), which is 1626 bits, so the variable-length +code got us closer to our goal, but not quite + +all the way there. + +Could another variable-length encoding have +done better? + +In general, it would be nice to have a systematic +way to generate the best-possible variable-length + +code, and that's the subject of the next video. \ No newline at end of file diff --git a/wSQaYn2h-e8.txt b/wSQaYn2h-e8.txt new file mode 100644 index 0000000000000000000000000000000000000000..b5afef95d49ea2fe2b0dd4d67a7d5dbb44513287 --- /dev/null +++ b/wSQaYn2h-e8.txt @@ -0,0 +1,747 @@ +align:start position:0% + +in the last example of the previous clip + + align:start position:0% +in the last example of the previous clip + + + align:start position:0% +in the last example of the previous clip +we have observed that the initial state + + align:start position:0% +we have observed that the initial state + + + align:start position:0% +we have observed that the initial state +of where the Markov chain starts can + + align:start position:0% +of where the Markov chain starts can + + + align:start position:0% +of where the Markov chain starts can +matter and that in some cases the + + align:start position:0% +matter and that in some cases the + + + align:start position:0% +matter and that in some cases the +influence of the initial State never + + align:start position:0% +influence of the initial State never + + + align:start position:0% +influence of the initial State never +vanishes in the long run so when we + + align:start position:0% +vanishes in the long run so when we + + + align:start position:0% +vanishes in the long run so when we +wanted to calculate the probability of + + align:start position:0% +wanted to calculate the probability of + + + align:start position:0% +wanted to calculate the probability of +ending up in state one knowing that you + + align:start position:0% +ending up in state one knowing that you + + + align:start position:0% +ending up in state one knowing that you +started instead one give you that + + align:start position:0% +started instead one give you that + + + align:start position:0% +started instead one give you that +probability and if you started in state + + align:start position:0% +probability and if you started in state + + + align:start position:0% +probability and if you started in state +three you had another long term + + align:start position:0% +three you had another long term + + + align:start position:0% +three you had another long term +probability and in case you were started + + align:start position:0% +probability and in case you were started + + + align:start position:0% +probability and in case you were started +in state two then you were equally + + align:start position:0% +in state two then you were equally + + + align:start position:0% +in state two then you were equally +likely to add up and being in state one + + align:start position:0% +likely to add up and being in state one + + + align:start position:0% +likely to add up and being in state one +or in state three we have said that this + + align:start position:0% +or in state three we have said that this + + + align:start position:0% +or in state three we have said that this +was due to the fact that some states are + + align:start position:0% +was due to the fact that some states are + + + align:start position:0% +was due to the fact that some states are +not accessible from some other states + + align:start position:0% +not accessible from some other states + + + align:start position:0% +not accessible from some other states +our goal here is to make such a + + align:start position:0% +our goal here is to make such a + + + align:start position:0% +our goal here is to make such a +statement more precise and formal in + + align:start position:0% +statement more precise and formal in + + + align:start position:0% +statement more precise and formal in +order to do so we will classify the + + align:start position:0% +order to do so we will classify the + + + align:start position:0% +order to do so we will classify the +states of a Markov chain in a transition + + align:start position:0% +states of a Markov chain in a transition + + + align:start position:0% +states of a Markov chain in a transition +diagram into two types recurrent and + + align:start position:0% +diagram into two types recurrent and + + + align:start position:0% +diagram into two types recurrent and +transient the state is set to be + + align:start position:0% +transient the state is set to be + + + align:start position:0% +transient the state is set to be +recurrent if starting from that state no + + align:start position:0% +recurrent if starting from that state no + + + align:start position:0% +recurrent if starting from that state no +matter where you go there is always a + + align:start position:0% +matter where you go there is always a + + + align:start position:0% +matter where you go there is always a +path to come back a state is said to be + + align:start position:0% +path to come back a state is said to be + + + align:start position:0% +path to come back a state is said to be +transient if it is not reckoned it means + + align:start position:0% +transient if it is not reckoned it means + + + align:start position:0% +transient if it is not reckoned it means +that starting from that state there is + + align:start position:0% +that starting from that state there is + + + align:start position:0% +that starting from that state there is +at least one place where you can go and + + align:start position:0% +at least one place where you can go and + + + align:start position:0% +at least one place where you can go and +then there will be no path back to it + + align:start position:0% +then there will be no path back to it + + + align:start position:0% +then there will be no path back to it +for example starting from state eight no + + align:start position:0% +for example starting from state eight no + + + align:start position:0% +for example starting from state eight no +matter where you go there is always a + + align:start position:0% +matter where you go there is always a + + + align:start position:0% +matter where you go there is always a +path back to eight so eight will be said + + align:start position:0% +path back to eight so eight will be said + + + align:start position:0% +path back to eight so eight will be said +to be a recurrent state for the same + + align:start position:0% +to be a recurrent state for the same + + + align:start position:0% +to be a recurrent state for the same +reason seven will also be a recurrent + + align:start position:0% +reason seven will also be a recurrent + + + align:start position:0% +reason seven will also be a recurrent +state as well as six now what about five + + align:start position:0% +state as well as six now what about five + + + align:start position:0% +state as well as six now what about five +from five the only state where you can + + align:start position:0% +from five the only state where you can + + + align:start position:0% +from five the only state where you can +go to is five itself + + align:start position:0% +go to is five itself + + + align:start position:0% +go to is five itself +so five is also a recurrent State let us + + align:start position:0% +so five is also a recurrent State let us + + + align:start position:0% +so five is also a recurrent State let us +look now at a state lat state for from + + align:start position:0% +look now at a state lat state for from + + + align:start position:0% +look now at a state lat state for from +for there is the possibility of a path + + align:start position:0% +for there is the possibility of a path + + + align:start position:0% +for there is the possibility of a path +going through to then one and then going + + align:start position:0% +going through to then one and then going + + + align:start position:0% +going through to then one and then going +to five from which there is no path back + + align:start position:0% +to five from which there is no path back + + + align:start position:0% +to five from which there is no path back +to four so four cannot be a recurrent + + align:start position:0% +to four so four cannot be a recurrent + + + align:start position:0% +to four so four cannot be a recurrent +State it is then called a transient + + align:start position:0% +State it is then called a transient + + + align:start position:0% +State it is then called a transient +State for the same reason + + align:start position:0% +State for the same reason + + + align:start position:0% +State for the same reason +starting from three there is the + + align:start position:0% +starting from three there is the + + + align:start position:0% +starting from three there is the +possibility that after doing many + + align:start position:0% +possibility that after doing many + + + align:start position:0% +possibility that after doing many +transition around here eventually you + + align:start position:0% +transition around here eventually you + + + align:start position:0% +transition around here eventually you +will end up being in either two and then + + align:start position:0% +will end up being in either two and then + + + align:start position:0% +will end up being in either two and then +go to six or you will be eventually be + + align:start position:0% +go to six or you will be eventually be + + + align:start position:0% +go to six or you will be eventually be +in one and then go to five and from five + + align:start position:0% +in one and then go to five and from five + + + align:start position:0% +in one and then go to five and from five +or from six + + align:start position:0% +or from six + + + align:start position:0% +or from six +there will be no path back to three so + + align:start position:0% +there will be no path back to three so + + + align:start position:0% +there will be no path back to three so +three is also a transient State and it + + align:start position:0% +three is also a transient State and it + + + align:start position:0% +three is also a transient State and it +is clear that for the same reason one + + align:start position:0% +is clear that for the same reason one + + + align:start position:0% +is clear that for the same reason one +will be a transient State and two will + + align:start position:0% +will be a transient State and two will + + + align:start position:0% +will be a transient State and two will +also be a transient State + + align:start position:0% +also be a transient State + + + align:start position:0% +also be a transient State +now if a state is transient like three + + align:start position:0% +now if a state is transient like three + + + align:start position:0% +now if a state is transient like three +for one or two it means that it will be + + align:start position:0% +for one or two it means that it will be + + + align:start position:0% +for one or two it means that it will be +visited only a finite number of times + + align:start position:0% +visited only a finite number of times + + + align:start position:0% +visited only a finite number of times +and in the long run + + align:start position:0% +and in the long run + + + align:start position:0% +and in the long run +the probability of being in a transient + + align:start position:0% +the probability of being in a transient + + + align:start position:0% +the probability of being in a transient +State will converge to zero the + + align:start position:0% +State will converge to zero the + + + align:start position:0% +State will converge to zero the +recurrent states of a Markov chain can + + align:start position:0% +recurrent states of a Markov chain can + + + align:start position:0% +recurrent states of a Markov chain can +be grouped in different classes here in + + align:start position:0% +be grouped in different classes here in + + + align:start position:0% +be grouped in different classes here in +this example we have to search classes + + align:start position:0% +this example we have to search classes + + + align:start position:0% +this example we have to search classes +here this is one class + + align:start position:0% + + + + align:start position:0% + +and here you have another class what is + + align:start position:0% +and here you have another class what is + + + align:start position:0% +and here you have another class what is +so special about these classes well + + align:start position:0% +so special about these classes well + + + align:start position:0% +so special about these classes well +within one class like for example in + + align:start position:0% +within one class like for example in + + + align:start position:0% +within one class like for example in +this class all recurrent states have a + + align:start position:0% +this class all recurrent states have a + + + align:start position:0% +this class all recurrent states have a +way to communicate between each other + + align:start position:0% +way to communicate between each other + + + align:start position:0% +way to communicate between each other +but there is no communication between + + align:start position:0% +but there is no communication between + + + align:start position:0% +but there is no communication between +recurrent states of different classes + + align:start position:0% +recurrent states of different classes + + + align:start position:0% +recurrent states of different classes +from that recurrent state here you have + + align:start position:0% +from that recurrent state here you have + + + align:start position:0% +from that recurrent state here you have +no communication with that recurrent + + align:start position:0% +no communication with that recurrent + + + align:start position:0% +no communication with that recurrent +state here no communication in the sense + + align:start position:0% +state here no communication in the sense + + + align:start position:0% +state here no communication in the sense +that there is no path joining that state + + align:start position:0% +that there is no path joining that state + + + align:start position:0% +that there is no path joining that state +to that state or that state to that + + align:start position:0% +to that state or that state to that + + + align:start position:0% +to that state or that state to that +state the existence of more than one + + align:start position:0% +state the existence of more than one + + + align:start position:0% +state the existence of more than one +class of recurrent States like in this + + align:start position:0% +class of recurrent States like in this + + + align:start position:0% +class of recurrent States like in this +example in a Markov chain will be the + + align:start position:0% +example in a Markov chain will be the + + + align:start position:0% +example in a Markov chain will be the +telling sign that initial states will + + align:start position:0% +telling sign that initial states will + + + align:start position:0% +telling sign that initial states will +matter in the chain it's pretty clear + + align:start position:0% +matter in the chain it's pretty clear + + + align:start position:0% +matter in the chain it's pretty clear +here that if your markov chain starts in + + align:start position:0% +here that if your markov chain starts in + + + align:start position:0% +here that if your markov chain starts in +state five you will never end up in + + align:start position:0% +state five you will never end up in + + + align:start position:0% +state five you will never end up in +state six seven or eight and if you + + align:start position:0% +state six seven or eight and if you + + + align:start position:0% +state six seven or eight and if you +start in one of the state six seven + + align:start position:0% +start in one of the state six seven + + + align:start position:0% +start in one of the state six seven +eight you will never end up in state + + align:start position:0% +eight you will never end up in state + + + align:start position:0% +eight you will never end up in state +five so depending on where you started + + align:start position:0% +five so depending on where you started + + + align:start position:0% +five so depending on where you started +the long range priority of being + + align:start position:0% +the long range priority of being + + + align:start position:0% +the long range priority of being +eventually in state six will not be the + + align:start position:0% +eventually in state six will not be the + + + align:start position:0% +eventually in state six will not be the +same \ No newline at end of file diff --git a/wWsRfu_1wvw.txt b/wWsRfu_1wvw.txt new file mode 100644 index 0000000000000000000000000000000000000000..c558a98f3440acc98ab5e94c042b4d7a869a1262 --- /dev/null +++ b/wWsRfu_1wvw.txt @@ -0,0 +1,163 @@ +align:start position:0% + +I'm Shigeru Miyagawa. I'm professor of + + align:start position:0% +I'm Shigeru Miyagawa. I'm professor of + + + align:start position:0% +I'm Shigeru Miyagawa. I'm professor of +linguistics and I also teach Japanese + + align:start position:0% +linguistics and I also teach Japanese + + + align:start position:0% +linguistics and I also teach Japanese +history here at MIT. This is my 26th + + align:start position:0% +history here at MIT. This is my 26th + + + align:start position:0% +history here at MIT. This is my 26th +year. Uh my linguistics work is on + + align:start position:0% +year. Uh my linguistics work is on + + + align:start position:0% +year. Uh my linguistics work is on +syntax. Uh more recently I have been + + align:start position:0% +syntax. Uh more recently I have been + + + align:start position:0% +syntax. Uh more recently I have been +looking at uh language evolution. + + align:start position:0% +looking at uh language evolution. + + + align:start position:0% +looking at uh language evolution. +In my uh the history class, I uh I look + + align:start position:0% +In my uh the history class, I uh I look + + + align:start position:0% +In my uh the history class, I uh I look +at modern Japanese history, something I + + align:start position:0% +at modern Japanese history, something I + + + align:start position:0% +at modern Japanese history, something I +started with John Daer, it's a very + + align:start position:0% +started with John Daer, it's a very + + + align:start position:0% +started with John Daer, it's a very +eminent pit surprise winning historian + + align:start position:0% +eminent pit surprise winning historian + + + align:start position:0% +eminent pit surprise winning historian +of modern Japan. Uh and John and I have + + align:start position:0% +of modern Japan. Uh and John and I have + + + align:start position:0% +of modern Japan. Uh and John and I have +done this incredible project visualizing + + align:start position:0% +done this incredible project visualizing + + + align:start position:0% +done this incredible project visualizing +cultures which also led to the MOO uh + + align:start position:0% +cultures which also led to the MOO uh + + + align:start position:0% +cultures which also led to the MOO uh +the EDX MOO that Harvard X and MITx did + + align:start position:0% +the EDX MOO that Harvard X and MITx did + + + align:start position:0% +the EDX MOO that Harvard X and MITx did +together visualizing Japan. + + align:start position:0% +together visualizing Japan. + + + align:start position:0% +together visualizing Japan. +uh three years ago I uh split my + + align:start position:0% +uh three years ago I uh split my + + + align:start position:0% +uh three years ago I uh split my +position between MIT and the University + + align:start position:0% +position between MIT and the University + + + align:start position:0% +position between MIT and the University +of Tokyo and at the University of Tokyo + + align:start position:0% +of Tokyo and at the University of Tokyo + + + align:start position:0% +of Tokyo and at the University of Tokyo +I'm the director of online education and + + align:start position:0% +I'm the director of online education and + + + align:start position:0% +I'm the director of online education and +there I look at uh uh MOS and also open + + align:start position:0% +there I look at uh uh MOS and also open + + + align:start position:0% +there I look at uh uh MOS and also open +courseware \ No newline at end of file diff --git a/wyoFOdR64U8.txt b/wyoFOdR64U8.txt new file mode 100644 index 0000000000000000000000000000000000000000..e12d2c71655c1f9390782017f0961584413e54be --- /dev/null +++ b/wyoFOdR64U8.txt @@ -0,0 +1,2688 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: Settle down. + +Settle down. + +Settle down. + +All right, first announcement +is the + +celebration of learning. + +Reminding you that the +celebration of learning is a + +week from today. + +Go to your assigned rooms. A +through Ha will write in here. + +This group will go +into 26-100. + +And the last group +over to 4-270. + +And you will take with you your +periodic table, table of + +constants, aid sheet, something +to write with. + +And we'll give you paper. + +You'll write on the +exam paper itself. + +And I'll say more about test +taking strategies on Monday. + +Coverage will be right +up through Monday. + +With emphasis obviously on the +material that you've had some + +time to digest. And there will +be no weekly quiz next week. + +So let's get right +into the lesson. + +Last day we looked at Louis, +who gave us the notion of + +achieving octet stability +by electron sharing. + +And that led to the concept +of covalent bonds. + +And then Pauling helped us +understand the energetics of + +covalent bonding by putting +forth the idea in a + +heteronuclear molecule +there's unequal + +sharing of the electrons. + +And out of that emerged the +concept of polar covalency and + +the definition of +electronegativity. + +And on the slide you see how +electronegativity varies + +across the periodic table. + +Electronegativity being a +measure of the pull an atom + +has for electrons within +a covalent bond. + +And as you would expect, the +non metals which are good + +electronic receptors are also +the ones that have the highest + +electronegativity. + +And the metals, over here, which +are good electron donors + +are those that have the +the lowest value of + +electronegativity. + +And Pauling was quantitative in +his formulation and gave us + +this equation that tells us how +to measure the energy of + +the x-y covalent bond. + +If x is not equal to y, then +axiomatically this is going to + +be a polar covalent bond. + +And you take the geometric +mean of the + +homonuclear bond energies. + +This is x-x bond energy +in x two. + +This is the y-y bond +energy in y two. + +You take the product square +root of which. + +And then the partial ionic +character, this is the + +contribution to unequal sharing +of the electrons. + +You take the square of +the difference in the + +electonegativities of +the two elements. + +And the 96.3 is a factor that +allows you to get the overall + +quantity in kilojoules +per mole. + +So you need these numbers +in kilojoules per mole. + +And we further had a formula +for the percent ionic + +character, which you can get by +looking at the difference + +in electronegativity. + +And then through this formula, +you end up with a scale that + +runs from 0 to 100%. + +And just by way of example, +we had a look at H-F. + +We spent a fair bit +of time on that. + +Obviously, it's a heteronuclear +molecule. + +We calculated its bond +energy and so on. + +And then to indicate +polar covalency, we + +use the dipole notation. + +The dipole shown here. + +It's just an oval. + +It's net neutral. + +But the charge is not uniformly +distributed. + +You see one end is a little +more negative. + +The other end is a little +more positive. + +Sometimes people write lowercase +Greek delta, + +indicating little bit negative +here, a little bit positive + +here, net neutral. + +There's the arrow indicating +the dipole. + +And furthermore, we argue that +this is a polar bond. + +And since this is just a +molecule with the two atoms, + +then this is also a +polar molecule. + +Which means it has a +net dipole moment. + +And I made some observations +about dipole moments and the + +ability to store energy +capacitively. + +And how you'd go about finding +a really good capacitor. + +And so that all came out of the +desire to find something + +that has a net dipole moment. + +And I want to continue +that conversation. + +And so I want to look at +some other elements. + +And what I want to look +at in particular is + +the compound methane. + +Let's look at methane from this +new found appreciation of + +polar covalency. + +So first thing I want to do is +to put it's structure up. + +We've gone through the Louis +notation and the structure. + +It forms sp3 hybrids. + +And you end up with a structure + +that looks like this. + +These are all at a 109 degrees, +symmetrically + +disposed in space. + +And we know since we have a +heteronuclear system here, + +we're going to have some +polar covalency. + +You can look up that the +electronegativity of carbon is + +2.55 electronegativity of +hydrogen is less than that + +from its position in +the periodic table. + +But to be quantitative +it's 2.2. + +So that means if I look at the +carbon hydrogen bond, carbon + +has the higher +electronegativity. + +So it's going to pull +the electrons. + +So that means that the carbon +end is going to be a little + +bit negative. + +And the hydrogen end is going +to be a little bit positive. + +So that means I've got +a dipole moment here. + +Polar bond. + +Everything is the same +as above here. + +Polar bond. + +But, I want to address +the question, is + +the molecule polar? + +So the way I interpret the +question, is it a polar + +molecule, I ask is there a +net charge displacement? + +Well, we're off to a +good start here. + +We see that we have charge +displacement on the bonds. + +But, is there a net dipole +for the molecule. + +So the way I think about that is +to say, where is the center + +of positive charge +for the molecule? + +Where's the center of +negative charge? + +So I know all the hydrogens +are a little bit positive. + +And they're all the same +distance from the nucleus. + +And I can draw a circle +that will + +capture all four hydrogens. + +Or more appropriately, +it's a sphere, right? + +These three on the bottom +don't lie in the plane. + +So the corners of the +tetrahedron lie on a sphere. + +So where is the center +of positive charge? + +The center positive charge is +right here at the center of + +the molecule. + +And where's the center of +local negative charge? + +It's on the carbon because the +carbon is the negative end of + +all the bonds. + +So the centers of positive and +negative charge for the entire + +molecule are colocated at the +center of the molecule. + +So this means no net +dipole moments. + +No net dipole moment +for the molecule. + +So this is a non +polar molecule. + +It's a non polar molecule +consisting of polar bonds. + +Non polar molecule. + +So there's two ways that I can +get a non polar molecule. + +One way is to have a homonuclear +molecule, right? + +So, homonuclear molecule. + +Homonuclear molecules + +axiomatically must be non polar. + +Because they have +equal sharing. + +So if I give you anything that's +homonuclear trivially, + +it's non polar. + +So you can look at things +like H2, P4, S8. + +These things are +all non polar. + +I don't care what +their structures + +are, it doesn't matter. + +This one here is definitely +polar. + +And then the last one here that +we're looking at, the the + +methane, is non polar because +we have spatially symmetric + +disposition of identical +polar bonds. + +So spatially symmetric, that +means there's three + +dimensional symmetry. + +Spatially symmetric disposition +of identical polar + +bonds leads to non +polar molecule. + +Because the centers of positive +and negative charge + +are colocated. + +So, now it's time to move on. + +Now I want to look at covalent +bonding from an energetic + +standpoint. + +I want to go back to energy +level diagrams. We've looked + +at energy level diagrams in +the past for atoms, single + +atoms. But now, what I want to +do is build energy level + +diagrams for molecules. + +So, for that we're going +to go back to + +the Schrodinger equation. + +I want energy level diagrams +for molecules. + +And for that I'm going to call +upon the Schrodinger equation. + +And we're not going to go +through the quantum mechanics + +in mathematical detail. + +We're going to do quantum +mechanics pictorally. + +We've got a long way. + +And in particular, what I want +to do with regard to the + +Schrodinger equation is to +recognize that we can move + +from atomic orbitals to +molecular orbitals by + +exploiting the fact that the +Schrodinger equation is a + +linear equation. + +Using the linearity property +of Schrodinger equation. + +All right, what do I +mean by linearity? + +Well, I'm going to do just +a little bit of math. + +Just enough to make you sit up +in your math classes and find + +out that there's some +utility there. + +Here's what I mean. + +Let me talk about what the +linearity principal is. + +So if I have some equation, +f of x, y, and z. + +It's a three variable +equation. + +And the equation is f +of x, y, z is k1. + +k1 could be a constant, it could +be a function, it could + +be anything. + +And let's say that it +has as its solution, + +the solution is s1. + +And then I've got a second +variant of this x, y, z. + +And it equals k2. + +So it's the same function +but it equals k2 here. + +It could be a constant, it +could be something else. + +And it has as its +solution, s2. + +If this f of x, y, z is a linear +equation, then if I'd + +give you f of x, y, z equals k1 +plus k2, you don't have to + +go and solve the equation +with impunity. + +You can write that +the solution is + +equal to s1 plus s2. + +And that doesn't hold if it's +a non linear equation. + +Just put y equals x squared. + +And if I tell you y equals one, +y equals two, and then I + +give you y equals 1 plus 2, it +doesn't equal the sum of the + +solution to that. + +You can prove it to yourself. + +So this is the fact that +superposition holds. + +You can superpose solutions +and build a library. + +So superposition holds when you +have a linear equation. + +And that's all we're going to +use in order to make equations + +for the molecular orbital. + +So that way I can write that +the wave function of a + +molecular orbital then is a +linear combination of the + +atomic orbitals. + +That's all this is doing. + +This is setting the stage for, +if you take quantum mechanics + +later, you'll go through +this in gory detail. + +But I'm saying that you know +enough now to appreciate that + +we can do what we're +about to do so. + +That means I'm just going to sum +the wave functions of the + +atomic orbitals. + +In this case, i goes from 1 to +2 because there's only two + +orbitals in a bond. + +And there will be some pre +factor here, a sub i times ci. + +And this whole business is +called linear combination of + +atomic orbitals into +molecular orbitals. + +So it's an SLI, it's a six +letter initialization. + +You know like FBI is a TLI, +it's a three letter + +initialization. + +This is an SLI, in +3L91 we go big. + +This is an SLI, six letter +initialization. + +So we're going to do +some examples here. + +And all you need to do in order +to run the examples is + +use two ideas in LCAO-MO. + +First of all, conservation +of states. + +Conservation of orbital +states. + +And the second one is, we're +going to fill the newly + +created molecular orbitals +according + +to the Aufbau principle. + +Fill MOs by Aufbau. + +If we do that, we're +in good shape. + +So let's take a look. + +So first think I want +to do is just + +rationalize this one here. + +H plus H goes to H2. + +I want to demonstrate +that there's a + +rational basis for this. + +So what I'm going to do is make +energy level diagrams. So + +there's an energy +coordinate here. + +Energy goes up in the +vertical direction. + +And out here is zero. + +And what I'm going to draw for +you is energy level diagrams + +for two atomic hydrogen +gas atoms. + +So if this is the zero, +we know that somewhere + +down here is the 1s. + +And I'm going to be complete +in my label. + +This is the 1s atomic +orbital of hydrogen. + +And over here there's +a 1s atomic + +orbital of atomic hydrogen. + +And furthermore, I've got an +electron sitting in 1s. + +Now these are at infinite +separation. + +These are far apart. + +Far, you know what that means. + +Far with quotation marks means +that they're separate quantum + +systems. So I'm not violating +the poly exclusion principal + +by having both of these +electrons sitting in the + +ground state. + +So they both have the same +set of quantum numbers. + +1, 0, 0, 1/2. + +Both of them. + +Same thing. + +Let's put it over here, +1, 0, 0, 1/2. + +So they're very, +very far apart. + +Now if I bring them close enough +together to make the + +molecule H2, what happens is I'm +going to violate the poly + +exclusion principal if I have +both of these atomic orbitals + +at the same level. + +Because I start filling them +according to Aufbau principal + +I'm going to end up with +more electrons than + +two at the same state. + +So what happens is +this splits. + +One orbitals ends up at a lower +energy and one orbital + +ends up at a higher energy than +the ground state energy + +in the atom itself. + +And so now this is called the +sigma 1s molecular orbital. + +And the one above it is +called sigma star + +1s molecular orbital. + +And sigma is at a +lower energy. + +So if electrons populate this +orbital, the system's energy + +will decrease and a +bond will form. + +So this is called a +bonding orbital. + +If electrons populate the upper +orbital, they will raise + +the energy of the system, +destabilizing it. + +And so this orbital denoted +with the star is called + +antibonding. + +It's an antibonding orbital. + +So now I've got the energy +level diagram + +for molecular hydrogen. + +So now let's go and +populate according + +to the Aufbau principal. + +I've got two electrons and they +go in spin up spin down. + +And now you can see that this +occupancy put the electrons at + +lower energy than they were by +being in the energy state of + +the atoms. + +And so I can argue that by +this diagram, I haven't + +predicted anything, but I +can use this diagram to + +rationalize that for this +reaction delta E is negative. + +And we know how negative +it is. + +It's minus 435 kilojoules +per mole. + +It's hugely negative. + +Minus 435 kilojoules per mole. + +All right. + +So, that's good. + +In fact I think I've +got some pictures. + +You can go through the whole +quantum mechanics. + +And just as is the case for a +single atoms, you can use the + +product of the wave function and +it's complex conjugate and + +so on and make plots. + +Oh by the way, this was just +making the point that you can + +pull out the electronegativity +off of the periodic table. + +It's given here. + +And the periodic table +is pretty good. + +But obviously somebody got a +little bit ahead of himself. + +They called this the first +ionization potential, which is + +the potential you'd put +across the plates in a + +gas discharge tube. + +But the unit is not +the electronvolt. + +If it's a potential, +it's a volt. + +Somebody here that put this +together seemed to think the + +electronvolt is a unit +of potential. + +And I want to make sure +that nobody in this + +class believes that. + +You got to get a little bit of +nail polish or something and + +cover up the little e there. + +Or take the nail polish, paint +over potential and write first + +ionization energy. + +One or the other, +but not this. + +This was a plot if percent +ionic characters. + +You can see that the strongly +covalent compounds down here + +have very very low +electronegativity differences + +and therefore very low +ionic character. + +And way up here are +the ionics. + +And in between is HF. + +It's almost at the cusp. + +But, can you see that +there must be a + +mistake on this diagram? + +Because this thing has got a +greater electronegativity + +difference than lithium iodide +and yet lithium iodide has a + +higher percent ionic +character. + +How can this function +zigzag like that? + +Something's wrong. + +So when you look at something, +you go wait a minute, that + +doesn't make sense. + +So I go back and I say, do +I trust anything here? + +Trust, but verify. + +Read critically. + +It's a good book. + +But, it's a big book +and there's + +going to be some mistakes. + +All right, so here's some +pictoral stuff of what we were + +just doing over here. + +So here are the two spherical 1s +orbitals and now they come + +closer and closer together +and they overlap. + +And this is what the shape +of the sigma 1s + +orbital looks like. + +It's like an oval with the +two nuclei inside. + +Here's taken from a different +text book. + +The overlap of atomic 1s atomic +and now here's the + +molecular orbital. + +Now you can also look at what +the shape of the antibonding + +orbital would be. + +This is what the shape of the +antibonding orbital would be. + +It would have two lobes with +a nodal plane in between. + +I think this is taken from +yet another book. + +Oh this is our book. + +There we go. + +1s, 1s, as there we go. + +Hydrogen molecular orbitals. + +Now look, suppose we do the +same thing for helium. + +If we do the same thing for +helium, helium starts with two + +electrons in 1s. + +And now it's going to +have four electrons. + +Two will go in the bonding +and two will go in the + +antibonding. + +And the two that go in the +antibonding raise the energy + +of the system more than the +two that go into bonding + +decrease the energy +of the system. + +There's a net increase +in energy. + +And this is the way you could +rationalize that helium exists + +as the atom in the gas phase. + +You don't see He2 +gas molecules. + +So using this energy level +diagram you can go through an + +rationalize. + +I would never ask +you to predict. + +I would say, fact, helium is +found as the atomic species in + +the gas phase. + +With the use of energy level +diagrams, rationalize. + +And that's what I would +expect you to do. + +Take this and show +that the two are + +of different stability. + +One other point to to make, +the level of 1s. + +If I wanted to put helium +on this board here. + +Not the scale, but +just roughly. + +Where would helium 1s be +relative the hydrogen 1s. + +We got three choices. + +Same level, closer to zero +energy, or more negative. + +How do you think about +the problem? + +What determines what +this energy is? + +It's the electrostatic +force of attraction. + +Is the electrostatic force of +attraction on the 1s electron + +in helium greater than or less +than it is in hydrogen? + +It's greater. + +So that means that the energy is +going to be more negative. + +And so if I were to put over +here helium, I'd put down here + +this would be 1s atomic orbital +for helium and then we + +go through the analysis. + +And why does that +come into play? + +Well you might want to do a +heteronuclear molecule. + +Suppose you wanted to do +the bonding diagram + +for hydrogen fluoride. + +So we'd have hydrogen here +and the fluorine + +and would be here. + +And all the fluorine orbitals +would be much lower and then + +they'd combine to make the +molecular orbitals. + +And I think there's something +opportunities to practice that + +in the homework. + +OK let's do one more. + +Let's do one more. + +How about lithium. + +Let's do lithium. + +I want to ask, is dilithium +stable? + +Li2. + +And this is all gas phase. + +Is dilithium stable? + +So I'll start off with +here's the zeroes. + +The zero of energy for +infinite separation. + +So this'll be a lithium +gas atom. + +And this is the putative +dilithium gas atom. + +We're going to figure out +if it's stable or not. + +So it's going to have bonding +and antibonding orbitals. + +And then this is the 1s, 2s. + +And this will be sigma 1s, +sigma star 1s, and so on. + +And then we'll have 2s atomic +orbital splitting into sigma + +and sigma star of 2s. + +And now lithium is 1s2, 2s1. + +So there's one, two, three. + +And one, two, three. + +And so now let's use +the Hund rule. + +So I've got four electrons in +the n equals one shell, and + +they populate in this manner. + +And then I've got two electrons +that go only into + +the bonding orbital. + +And according to this it appears +that lithium 2 is + +favored over atomic lithium. + +And that in fact is the case. + +That in fact is the case and so +that applies to all of the + +all of the alkalide metals. + +Because they all have the +ns1 configuration. + +So when you're driving down the +highway and you see those + +orangey yellow low pressure +sodium vapor lamps. + +What you're looking at is +emission not from atomic + +sodium but from Na2 vapor. + +And you've got the energy level +diagram to convince + +yourself of that. + +So next time you see those, +just smile, knowing that + +you're looking at disodium, +not sodium. + +OK, well so far we've only +looked at single bonds. + +Now I want to look at +multiple bonds. + +Double and triple bonds. + +So let's look at nitrogen now. + +N2. + +Remember that gave us +the the triple bond? + +We had nitrogen, one, two, +three, four, five. + +Second nitrogen, one, two, +three, four, five. + +So in order to get octet +stability, we had three pairs + +of electronic sharing. + +Which then give us a +triple bond here. + +And so what's that going +to look like? + +what's that going to look +like pictorally? + +And the way to think about that +is first of all these are + +all p orbitals. + +If we look at, this +is 2s2, 2p3. + +So 2s and these are +the 2d orbitals. + +So I've got s is filled first +and then I've got the lone + +electrons in each of +the p orbitals. + +And these things are shaped +like figure eights. + +And the p orbital, this is +the p atomic orbital. + +It has two lobes. + +Each of these zones are +just called lobes. + +Same word is earlobe. + +And this zone in the middle, +this one point in the middle, + +is called a node. + +And that's a sight of zero +electron density. + +Zero electronic density. + +And remember the electron, +even if it only has one + +electron here, the electron +can be in either a lobe. + +It can move from lobe to lobe +even though it can never be at + +the nucleus. + +And how does it get from one +lobe to the other while never + +crossing the nucleus because +it's never supposed to be in + +the nucleus? + +By behaving as a wave. The same +way that you can have a + +jump rope and you can have a +fixed point of zero motion, + +yet you can transmit energy down +the rope passed the node. + +So, let's draw these things. + +A word about how you draw, +you have to use + +the right hand rule. + +Have to use the right +hand rule. + +So when I put the coordinate +system up, it's going to have + +to conform so that the thumb +is x and they go y and z. + +And if you don't use the right +hand rule later on if you get + +into electromagnetics, you start +looking at forces and + +vectors, you're going to end up +with things moving in the + +wrong direction. + +So we conform to the +right hand rule. + +And the other thing, +and it's kind of + +nice, it's not mandatory. + +But chemists generally +like to have atoms + +bond along the z-axis. + +So that means we start with the +z-axis here, if I'm going + +to put my second nitrogen, have +them bond on the z-axis. + +And so that means if z is in +the plane of the board + +pointing to the right, then +pointing up must be y, and + +then pointing into the +board must be x. + +So I'll have, here's my px +orbital, then the py orbital, + +and the pz orbital. + +And the three of these are all +symmetrically disposed around + +the nucleus. + +And next to it at the same kind +of floral arrangement. + +I'll start with px, +py, and pz. + +And now these are going +to come close + +together and overlap. + +So I want to figure out what +those orbitals are + +going to look like. + +So let's start along +the z-axis. + +The z-axis is the easy one. + +So I've got two of these things +lying on their sides + +like infinity signs. + +We're going to do quantum +mechanics pictorally. + +Why? + +Because it's a linear +equation. + +So I can add pictural. + +So this is 2pz of one of them. + +And a 2pz of the other. + +And this is the nitrogen +atomic orbital. + +And I'm going to smear these +things and what are they going + +to look like? + +The nucleus is here, the +nucleus is where I'm + +indicating the dot. + +These two combine, very +simply, it's going + +to look like this. + +So there's one nitrogen. + +Here's the other nitrogen. + +And what's this thing? + +This is electronic density. + +And so this is our sigma bond. + +Looks a little bit different +from the case of of hydrogen, + +because hydrogen was the +blending of two s orbitals and + +s orbitals are spherically +symmetric. + +In this case, we've +got two lobes. + +But what's characteristic about +this one and hydrogen, + +hydrogen looked like +this, remember? + +This was hydrogen. + +This was H2. + +And this was a sigma bond. + +The characteristic of a sigma +bond is that when you start + +from one nucleus and you go to +the other nucleus, you move + +through unbroken electron +density. + +So there are no nodes, no +holidays, between the nitrogen + +nucleus on the left and the +nitrogen nucleus on the right. + +There is a node here, but +that's different. + +I can go from one nitrogen to +the other with unbroken + +electron density. + +That's what makes this +a sigma bond. + +So that's good. + +So this thing here is going +to be called stigma + +2p molecular orbital. + +Sigma 2p molecular orbital And +I think I've got the slide + +that shows this. + +There's some art work. + +People really get excited +about this. + +OK there's dilithium. + +Or dipotasium, disodium. + +OK so here we are. + +This is the smearing of two pz +atomic orbitals to make the + +sigma 2p bonding orbital. + +And there just for grins and +chuckles is what the + +antibonding would look like. + +But we don't care, because +it doesn't form. + +Well this is the book. + +And you know what I'm +going to say. + +I've got my little +hobby horse here. + +I don't know why they change +color on the lobes. + +Because when I look at that, it +starts conjuring up to me + +the image that one electron +stays in the blue lobe and one + +electron stays in +the yellow lobe. + +Besides, I've seen them and +they're not different colors. + +They're the same color. + +So now let's look at what +happens when we blend off of + +the z-axis. + +So let's blend the +two py orbitals. + +See what that goes like. + +OK so let's do that one. + +And that one is going +to look like this. + +We're to start with, again +figure eights. + +But now they're their side +by side, they're lateral. + +So this is 2py atomic orbital. + +2py atomic orbital. + +And then we're going to blend +them along the z-axis to give + +us, and I'm going to do +this stylized, OK? + +So there's the the two +nitrogen nuclei. + +So I put the nuclei up. + +And I'm going to smear +the upper lobes. + +So these two lobes are +going to smear. + +And I'm going to get +really stylized. + +I feel like it's France and +it's the late 1800s. + +So there it is. + +And I'm going to smear +the two bottom ones. + +And it's going to +look like this. + +So what do I have here? + +Now I have two lobes +as before. + +But if I look at the second +nucleus from the first + +nucleus, not only do I fail +to have unbroken electron + +density, I have zero +electron density. + +See, this was a nodal +point in the atom. + +With the two atoms together, +the plane orthogonal to the + +board is a nodal plane. + +There's no electron density +in the plane + +orthogonal to the board. + +Nodal plane. + +So this is definitely not a +sigma bond, this is a pi bond. + +This is a pi bond. + +And it's characterized by +smearing of atomic orbitals, + +just as the sigma bond is. + +But it has a nodal plane that +separates the two lobes. + +I think I've got some cartoon +illustrations from other books + +Here OK this is from one book. + +This is good. + +They call the px, +I call it py. + +There it is. + +And I'd go further and I'd say +that if I were to slice this + +and look at it from angle, if +we were to cut this and look + +from here, I'd venture that +you'd see something that's + +sort of figure eightish. + +Oh here's our book, bless +them with two colors. + +But anyway, there's what +it looks like. + +That's the pie. + +And then the same thing +happens with the x. + +So this is this is going +to be pi 2py. + +This is pi 2py. + +And it's a molecular orbital. + +And there's going +to be a pi 2px. + +And it's going to blend +front and back. + +So we can make a catalog. + +So we're going to do quantum +mechanics in pictures here. + +So I know that s plus s must +always make a sigma bond. + +There's no other way. + +Because I've got electron +density all around. + +Let's do it pictorally. + +That's easy. + +And this is sigma. + +We know this has to be sigma. + +What about something like HF +where the H is an s and the F + +is going to have the +one last electron + +missing in the p orbital. + +S plus p must give +sigma always. + +Because that's this cartoon. + +See there's no way that when +this smears with this, there's + +going to be zero electron +holidays from the hydrogen + +nucleus to the fluorine +nucleus. + +So you're going to end +up with something + +that looks like this. + +It starts around and gives you +something that's going to be a + +little bit asymmetric. + +So this will also be a sigma. + +So I'll just put HF here as sort +of prototypical of that. + +And then if I take p plus p +axially, on axis, that also + +gives us a sigma. + +Because that's this one, +the infinity signs. + +Two infinity signs +give us this. + +And then finally, if we get +p plus p longitudinally. + +So that will give us a pi +bond and that's the 88. + +8 plus 8 gives me, +and this is pi. + +So that's quantum mechanics. + +The math will follow. + +So now what I want to do is go +back to this energy level + +diagram and show how +these energy level + +diagrams can work. + +So here's the energy level +diagram for nitrogen, N2. + +There's two f's, two p, and the +scaffolding is in place. + +There's the energy levels. + +Now here's the molecular +orbitals and here are the + +atomic orbitals. + +And now here they +are occupied. + +So nitrogen has one, two, three, +four, five according to + +the Hund rule. + +And here is the set up +for the N2 molecules. + +So the 2s's and the 2s's +go bonding antibonding. + +Now I've got three plus +three is six. + +Two, two, two. + +Everything's paired. + +So we get the triple bond, +946 kilojoules per mole. + +Enormous energy in nitrogen. + +Enormous energy in nitrogen. + +Now, let's keep going. + +Now let's look at oxygen. + +This is the scaffolding for +oxygen and fluorine. + +And there's a little +change here. + +A little change, I'm going to +draw your attention to it. + +And you can't predict this. + +We would give you this. + +I would tell you what the energy +sequence is of the + +energy levels. + +But look here carefully, you see +in the case all nitrogen, + +the pi's lie below the sigma. + +In the case of oxygen and +fluorine the sigma + +lies below the pi's. + +These are tiny, tiny +differences. + +But, they are measurable. + +That's the little difference. + +Now let's see what happens. + +Actually here's from out text +book and it shows the stigma + +2pix slowly meandering down, +down, down, down, down. + +And somewhere between nitrogen +and oxygen it crisscrosses. + +All right, so now let's +fill oxygen. + +So oxygen is two, +four, five, six. + +So two plus two is four. + +There's the two, two, two. + +And then these last ones go +up into the antibonding. + +But look at the antibonding. + +We have, according to the Hund +rule, not two electrons in the + +first orbital, but +one and one. + +So we end up with unpaired +electrons in + +the antibonding orbital. + +So these offset the three pairs +here, and so we end up + +with a double bond. + +And its energy us 498 +kilojoules per mole. + +Substantially less +then nitrogen. + +And this energy level diagram +rationalizes that. + +And then here's for fluorine. + +If you go to fluorine it's the +same scaffolding only there's + +two more electrons. + +These are paired and you +have a single bond. + +160 kilojoules per mole. + +Now there's a property that we +get from the fact that we have + +these unpaired electrons. + +We're going back oxygen now. + +We have unpaired electrons in +the antibonding orbitals. + +We saw unpaired electrons. + +What did they do in the +Stern-Gerlach experiment? + +Changed the magnetics +substantially, right? + +We ended up with the splitting +of the silver bean. + +So this will also +have an impact. + +An impact known as +a paramagnetism. + +What's paramagnetism? + +It's shown in this +little cartoon. + +If you have a substance here +that's balanced and it is + +paramagnetic, if you engage +the magnetic field, the + +magnetic field will pull on a +substance that's paramagnetic. + +And oxygen is paramagnetic. + +Not only in a gas state, but +paramagnetic as liquid. + +And here's an illustration +from your text book. + +You may have seen this and said, +yeah a guy is pouring + +liquid oxygen, wow. + +Look carefully now. + +The boiling point of oxygen +at one atmosphere + +pressure is 90 Kelvin. + +So room temperature is +substantially higher. + +This is the equivalent of taking +water and putting it in + +an oven at about 300 degrees +celsius and watching it pour. + +It would still be liquid, +but it would be + +liquid trying to boil. + +Why doesn't it all +turned to gas? + +Because there's a time +to heat everything. + +So this is sitting at 90 Kelvin, +he pouring it down, or + +she's pouring it down, and +these are the jaw of a + +permanent magnet. + +And it's in a gravity +field, it doesn't + +keep falling, it stops. + +And it continues to boil away +and as fast as you can pour + +it, it sits between the +jaws of the magnet. + +Because it's paramagnetic. + +You can think of this +as the liquid + +equivalent of iron filings. + +If I told you that were these +were iron filings you'd say, + +yeah the iron filings go and +they stick to the magnet, + +that's what magnets do +to iron filings. + +They do the same thing +to liquid oxygen. + +And why? + +Because of this. + +This explains this. + +So we can do a lot with these +primitive little diagrams. + +Let's do one more. + +I want to do one more +of these things. + +I want to go to hybridized +systems. I want to go to a + +hybridized system. + +And I want to look +at ethylene. + +C2H4 is ethylene. + +OK, so if I told you give me +the Louis structure of + +ethylene, you just start going +according to the rule. + +So I'm going to have carbon, +carbon, hydrogen, hydrogen. + +And carbon has one, two, +three, four electrons. + +The hydrogen has one electron. + +I'll put the one electron +from hydrogen. + +And then the other carbon +over here, I'm + +going to give it dots. + +One, two, three, four. + +And then these hydrogen +each have one. + +And now let's see what +I have here. + +These hydrogens are all +isoelectronic with helium, so + +they're happy. + +And the carbon now has two, +let's see, what does he got? + +Yeah, carbon is happy. + +Two, four, six, OK good. + +So now carbon is. + +Happy as well. + +So what do we have here? + +This is the equivalent to a +carbon carbon double bond. + +So what have I learned with +the nitrogen example? + +What I learned with the nitrogen +example was, that if + +I want to make more than one +bond, I have to have a + +combination of a stigma +and a pi. + +You can only make one sigma bond +because there's no room. + +Once you've got zero electron +density between the two nuclei + +you're going to violate the +Pauli exclusion principle if + +you have another +orbital cutting + +through that same domain. + +So this means that multiple +bonds require a mix + +of sigma and pi. + +Multiple bonds require a +mix of sigma and pi. + +If you have a single bond, all +you need is the sigma. + +So let's go back to how we got +the original hybridization. + +Remember, we started with +carbon, with the box notation + +looking like this. + +Here's the 2s and the 2p's and +we started with just native + +carbon off the periodic table. + +And we have this. + +Just if we go according +to the 2s2, 2p2. + +And then in order to get +hybridization to rationalize + +methane, where we've got +four equivalent bonds. + +In that case, we hybridize +the s and all of the p's. + +We took the s and all three +of the p's to make + +the sp3 hybrid orbitals. + +And then we were able to take +these electrons and put them + +in one at a time. + +And then bring in the four +hydrogens and we end up with + +something that is + +symmetrically disposed in space. + +The carbon, hydrogen and so. + +So now I give to you ethylene +I say, well + +how do I make ethylene. + +Well, if I started with this sp3 +thing maybe I could bring + +another carbon over here. + +And I'd have three hydrogen +sticking out. + +So there's my sigma bond. + +So I'm off to the races. + +This is good. + +But now I need to build +a second bond. + +I'm going to throw away +a couple of hydrogen. + +So i'll throw this hydrogen away +and this hydrogen away. + +So I'm going to have now C2H4. + +I'm almost there. + +The only problem is, this +orbital is sticking out this + +way, this orbital is sticking +out this way. + +And I don't have the license +to bend these orbitals. + +And build a double bond. + +Because they're 109 degrees +apart and they're inflexible + +and they won't bend. + +So this hybridization technique +will not work as + +such to give me what I need +to build ethylene. + +What do I need? + +If I'm going to build a sigma +and a pi bond, I'm going to + +need to preserve one of the p +orbitals so that it can still + +be available for lateral +smearing + +Because how do I make +a pi orbital? + +I make a pi orbital +middle with an 88. + +So I need to preserve a p +orbital so that in both of the + +carbons I still have this +pi bonding capability. + +So what I'm going do is instead +of taking the s and + +all three of the p's I'm going +to take the s and only two of + +the p' s and reserve one of the +p' s to be sitting there + +for lateral smearing. + +So instead what I'm going +to do is this. + +So this is going to be an +unmixed p and this is going to + +take the s and not three +p' s but only two p 's. + +And this would be called sp2. + +And now what do I have? + +I've one, two, three. + +And how do I put three +of these in space? + +They lie symmetrically in +a plane at 120 degrees. + +And then this thing is normal +to the plane of the board. + +It's sticking out. + +Actually, I should've +maybe drawn it in + +perspective like this. + +And so now I've got +the ability to put + +two of these together. + +This'll giving me my sigma. + +And then these two things lying +on their side will smear + +with the lobes to +give me the pi. + +Now that's what gives +me the double bond. + +And here are the cartoons +that show this. + +Oh here, I took this from an old +text book, it's text book + +I had when I was your age. + +The wrote great books. + +And then I flipped +this around see. + +I did all this just for you. + +So I took this one, I flipped +the image around. + +So there are the sp2's these +are the unmixed p's. + +And you bring them close +together and bingo. + +There's the sigma. + +That's this one, p plus p +axially, that gives me the + +sigma bond. + +And then I smear those two +and that gives me the pi. + +And there's ethylene. + +You put the hydrogens here, +one, two, three, four. + +Two carbons. + +Tada. + +Isn't that cool? + +Here's from another book. + +It's looks like a Boston traffic +map, doesn't it? + +Just crazy. + +This is from our book. + +So they're showing you there's +the sigmas and the pi's. + +There we go. + +More pictures. + +OK, I'm going to take three +minutes at the end here and + +show you an example of + +electronegativity at the extreme. + +So if you take a look at the +periodic table and look at a + +compound like sodium iodide. + +If I just told you sodium +iodide, covalent or ionic? + +You'd say, ionic. + +Because you got something from +the the most metallic of the + +metals and something +from the most non + +metallic of the non metals. + +And you're right. + +And the delta chi is 1.73. + +And the covalent character +is high. + +And you end up with something +that's very polar and so on. + +Now here's a very interesting +one, if you compare cesium and + +gold, you get 1.75. + +Which is greater than what it +was for sodium and iodine. + +Now no one would argue that +sodium and iodine is covalent, + +you'd argue that's ionic. + +Well by the same metrics, cesium +and gold is as ionic. + +The plot thickens. + +Cesium, if you melt it it's +a metal, liquid metal. + +If you melt gold, it's +a liquid metal. + +But if you mix them +in equal number. + +So you make a alloy of 50 mole +percent cesium and 50 mole + +percent gold and you've got +a delta chi 1.75, you've + +essentially made a cocktail with +equal numbers of really + +good electron donors and really + +good electron acceptors. + +And guess what happens, +electron transfer. + +And the melt is not metallic, +it turns clear and colorless + +just as molten sodium +iodide would be. + +It turns into a molten salt. + +So cesium gives its +electron to gold. + +And gold becomes the +negative gold ion. + +And what color is every ion? + +It's got stable octet +configurations. + +It's got be the same color as +neon, argon, and helium. + +They are clear and colorless. + +Big drop in electrical +conductivity and a shift from + +electronic to ionic +conduction. + +Metals have electronic +conductivity, ions, what do + +ionic liquids have? + +They have like ionic +conductivity. + +Here's some data from +the literature. + +This is the log on the +connductivity as a function of + +concentration. + +So here's pure cesium +over here, here's + +pure gold over here. + +This is 600 degrees C. + +So the line stops here because +gold melts at about 1060. + +So gold is a solid beyond this +alloy concentration. + +But you can see this is roughly +what you'd get. + +So electronic conductivity up +here at about 10 to the 4 + +siemens per, this is reciprocal +ohms, but siemens + +per centimeter. + +And down here, this is very low +value ionic conductivity. + +So this is a liquid metal. + +And this is a molten solid. + +And it all happens just +when you get very + +very close to 50/50. + +So you end up with something +called cesium oride. + +And it's sorcery. + +You have one vial +of liquid metal. + +You have a second vial +of liquid metal. + +You pour then and it turns +clear and colorless. + +And the conductivity drops three +orders of magnitude all + +because of electron transfer due +to this electronegativity + +difference. + +That's so cool. + +That is so cool. + +OK, with that I'll let you go. + +We'll see you on Friday. \ No newline at end of file diff --git a/x-Ik9YAFAPo.txt b/x-Ik9YAFAPo.txt new file mode 100644 index 0000000000000000000000000000000000000000..7ce9e37c9896c2ad947faae45d5234270920ce0c --- /dev/null +++ b/x-Ik9YAFAPo.txt @@ -0,0 +1,15171 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or to view additional materials from + + align:start position:0% +or to view additional materials from + + + align:start position:0% +or to view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +All right, welcome back to 6890. Uh + + align:start position:0% +All right, welcome back to 6890. Uh + + + align:start position:0% +All right, welcome back to 6890. Uh +today we start a series of lectures on + + align:start position:0% +today we start a series of lectures on + + + align:start position:0% +today we start a series of lectures on +satisfiability. Uh we saw a little bit + + align:start position:0% +satisfiability. Uh we saw a little bit + + + align:start position:0% +satisfiability. Uh we saw a little bit +about satisfiability in the first + + align:start position:0% +about satisfiability in the first + + + align:start position:0% +about satisfiability in the first +lecture. Uh this now we're going to do + + align:start position:0% +lecture. Uh this now we're going to do + + + align:start position:0% +lecture. Uh this now we're going to do +it right and do it uh more intensely and + + align:start position:0% +it right and do it uh more intensely and + + + align:start position:0% +it right and do it uh more intensely and +see a lot of examples. Today we'll just + + align:start position:0% +see a lot of examples. Today we'll just + + + align:start position:0% +see a lot of examples. Today we'll just +see a few examples of using SAT to prove + + align:start position:0% +see a few examples of using SAT to prove + + + align:start position:0% +see a few examples of using SAT to prove +NP completeness or NP hardness. Uh but + + align:start position:0% +NP completeness or NP hardness. Uh but + + + align:start position:0% +NP completeness or NP hardness. Uh but +over the next lecture or two we will see + + align:start position:0% +over the next lecture or two we will see + + + align:start position:0% +over the next lecture or two we will see +many more examples. Um and SAT is really + + align:start position:0% +many more examples. Um and SAT is really + + + align:start position:0% +many more examples. Um and SAT is really +the most common problem that everyone + + align:start position:0% +the most common problem that everyone + + + align:start position:0% +the most common problem that everyone +uses to prove NP hardness. So this is + + align:start position:0% +uses to prove NP hardness. So this is + + + align:start position:0% +uses to prove NP hardness. So this is +the moment you've all been waiting for. + + align:start position:0% +the moment you've all been waiting for. + + + align:start position:0% +the moment you've all been waiting for. +I suppose uh this is one of the + + align:start position:0% +I suppose uh this is one of the + + + align:start position:0% +I suppose uh this is one of the +motivations for organizing this whole + + align:start position:0% +motivations for organizing this whole + + + align:start position:0% +motivations for organizing this whole +class is so we can tell you all about + + align:start position:0% +class is so we can tell you all about + + + align:start position:0% +class is so we can tell you all about +SAT. It's many variations so you get to + + align:start position:0% +SAT. It's many variations so you get to + + + align:start position:0% +SAT. It's many variations so you get to +learn them all and then see lots of + + align:start position:0% +learn them all and then see lots of + + + align:start position:0% +learn them all and then see lots of +different ways you can use SAT to + + align:start position:0% +different ways you can use SAT to + + + align:start position:0% +different ways you can use SAT to +represent your problems. So without + + align:start position:0% +represent your problems. So without + + + align:start position:0% +represent your problems. So without +further ado, let's get started. + + align:start position:0% + + + + align:start position:0% + +Um, + + align:start position:0% +Um, + + + align:start position:0% +Um, +today I'm going to + + align:start position:0% +today I'm going to + + + align:start position:0% +today I'm going to +give you a whole bunch of problems and + + align:start position:0% +give you a whole bunch of problems and + + + align:start position:0% +give you a whole bunch of problems and +definitions. Um, and then we will do + + align:start position:0% +definitions. Um, and then we will do + + + align:start position:0% +definitions. Um, and then we will do +reductions afterwards. So, there's going + + align:start position:0% +reductions afterwards. So, there's going + + + align:start position:0% +reductions afterwards. So, there's going +to be a lot of problems here. You + + align:start position:0% +to be a lot of problems here. You + + + align:start position:0% +to be a lot of problems here. You +probably will have trouble remembering + + align:start position:0% +probably will have trouble remembering + + + align:start position:0% +probably will have trouble remembering +them all. There's so many. But in + + align:start position:0% +them all. There's so many. But in + + + align:start position:0% +them all. There's so many. But in +particular, the notes serve as a useful + + align:start position:0% +particular, the notes serve as a useful + + + align:start position:0% +particular, the notes serve as a useful +reference. Like, here's all the versions + + align:start position:0% +reference. Like, here's all the versions + + + align:start position:0% +reference. Like, here's all the versions +you might care about. Here's which ones + + align:start position:0% +you might care about. Here's which ones + + + align:start position:0% +you might care about. Here's which ones +are hard, which ones are easy. Um, so + + align:start position:0% +are hard, which ones are easy. Um, so + + + align:start position:0% +are hard, which ones are easy. Um, so +with that in mind, get ready for the + + align:start position:0% +with that in mind, get ready for the + + + align:start position:0% +with that in mind, get ready for the +ride. Um so the original SAT problem is + + align:start position:0% +ride. Um so the original SAT problem is + + + align:start position:0% +ride. Um so the original SAT problem is +you're given a boolean formula formula + + align:start position:0% + + + + align:start position:0% + +uh which is like over the operators and + + align:start position:0% +uh which is like over the operators and + + + align:start position:0% +uh which is like over the operators and +or and not and in case you look at the + + align:start position:0% +or and not and in case you look at the + + + align:start position:0% +or and not and in case you look at the +literature usually and is uh the wedge + + align:start position:0% +literature usually and is uh the wedge + + + align:start position:0% +literature usually and is uh the wedge +or is the v and not is + + align:start position:0% +or is the v and not is + + + align:start position:0% +or is the v and not is +the neg I don't know the name of that + + align:start position:0% +the neg I don't know the name of that + + + align:start position:0% +the neg I don't know the name of that +symbol um and it's over + + align:start position:0% +symbol um and it's over + + + align:start position:0% +symbol um and it's over +n variables + + align:start position:0% + + + + align:start position:0% + +x1 x2 + + align:start position:0% +x1 x2 + + + align:start position:0% +x1 x2 +xn. So usually you're not given true or + + align:start position:0% +xn. So usually you're not given true or + + + align:start position:0% +xn. So usually you're not given true or +false although you can construct them by + + align:start position:0% +false although you can construct them by + + + align:start position:0% +false although you can construct them by +saying x1 and not x1 that's never true. + + align:start position:0% +saying x1 and not x1 that's never true. + + + align:start position:0% +saying x1 and not x1 that's never true. +So that's false for example then you can + + align:start position:0% +So that's false for example then you can + + + align:start position:0% +So that's false for example then you can +negate that get true. Um and the + + align:start position:0% +negate that get true. Um and the + + + align:start position:0% +negate that get true. Um and the +question is can you set the variables to + + align:start position:0% +question is can you set the variables to + + + align:start position:0% +question is can you set the variables to +make the formula true. + + align:start position:0% + + + + align:start position:0% + +So that's the general problem. This is + + align:start position:0% +So that's the general problem. This is + + + align:start position:0% +So that's the general problem. This is +the very first problem proved to be + + align:start position:0% +the very first problem proved to be + + + align:start position:0% +the very first problem proved to be +empty by uh cook and then by leaven. Uh + + align:start position:0% +empty by uh cook and then by leaven. Uh + + + align:start position:0% +empty by uh cook and then by leaven. Uh +so it's usually called the cook + + align:start position:0% +so it's usually called the cook + + + align:start position:0% +so it's usually called the cook +leavenven theorem that satisfiability is + + align:start position:0% +leavenven theorem that satisfiability is + + + align:start position:0% +leavenven theorem that satisfiability is +nplete. Um and I was looking at the + + align:start position:0% +nplete. Um and I was looking at the + + + align:start position:0% +nplete. Um and I was looking at the +paper the other day. It doesn't actually + + align:start position:0% +paper the other day. It doesn't actually + + + align:start position:0% +paper the other day. It doesn't actually +mention the notion of np in that paper. + + align:start position:0% +mention the notion of np in that paper. + + + align:start position:0% +mention the notion of np in that paper. +I think that came later but uh the + + align:start position:0% +I think that came later but uh the + + + align:start position:0% +I think that came later but uh the +notion is there. + + align:start position:0% +notion is there. + + + align:start position:0% +notion is there. +So + + align:start position:0% + + + + align:start position:0% + +give you another version uh of the same + + align:start position:0% +give you another version uh of the same + + + align:start position:0% +give you another version uh of the same +problem essentially uh called circuit. + + align:start position:0% +problem essentially uh called circuit. + + + align:start position:0% +problem essentially uh called circuit. +This is a useful perspective which we + + align:start position:0% +This is a useful perspective which we + + + align:start position:0% +This is a useful perspective which we +will see probably not till next class + + align:start position:0% +will see probably not till next class + + + align:start position:0% +will see probably not till next class +but uh another way to think about it + + align:start position:0% +but uh another way to think about it + + + align:start position:0% +but uh another way to think about it +also makes the MP completeness a little + + align:start position:0% +also makes the MP completeness a little + + + align:start position:0% +also makes the MP completeness a little +bit more intuitive. + + align:start position:0% + + + + align:start position:0% + +Okay, this is kind of the algebraic way + + align:start position:0% +Okay, this is kind of the algebraic way + + + align:start position:0% +Okay, this is kind of the algebraic way +of thinking about things. You have + + align:start position:0% +of thinking about things. You have + + + align:start position:0% +of thinking about things. You have +variables and you write operators and + + align:start position:0% +variables and you write operators and + + + align:start position:0% +variables and you write operators and +use parentheses and that sort of thing. + + align:start position:0% +use parentheses and that sort of thing. + + + align:start position:0% +use parentheses and that sort of thing. +Uh but if you're more graphically + + align:start position:0% +Uh but if you're more graphically + + + align:start position:0% +Uh but if you're more graphically +inclined, you could imagine uh you have + + align:start position:0% +inclined, you could imagine uh you have + + + align:start position:0% +inclined, you could imagine uh you have +your xis as wires. They're connected to + + align:start position:0% +your xis as wires. They're connected to + + + align:start position:0% +your xis as wires. They're connected to +gates. This is an ANDgate. Uh this is an + + align:start position:0% +gates. This is an ANDgate. Uh this is an + + + align:start position:0% +gates. This is an ANDgate. Uh this is an +orgate. This is a negation. + + align:start position:0% +orgate. This is a negation. + + + align:start position:0% +orgate. This is a negation. +Uh so + + align:start position:0% +Uh so + + + align:start position:0% +Uh so +you can imagine something like this. Um + + align:start position:0% +you can imagine something like this. Um + + + align:start position:0% +you can imagine something like this. Um +so you can generally copy your data + + align:start position:0% +so you can generally copy your data + + + align:start position:0% +so you can generally copy your data +and do various things and then this is + + align:start position:0% +and do various things and then this is + + + align:start position:0% +and do various things and then this is +sort of the output. And so this is what + + align:start position:0% +sort of the output. And so this is what + + + align:start position:0% +sort of the output. And so this is what +you might call the formula. + + align:start position:0% + + + + align:start position:0% + +It is the and of the negation of the or + + align:start position:0% +It is the and of the negation of the or + + + align:start position:0% +It is the and of the negation of the or +of x3 and the and of x1 and x2. And then + + align:start position:0% +of x3 and the and of x1 and x2. And then + + + align:start position:0% +of x3 and the and of x1 and x2. And then +pop off. It's also ended with this thing + + align:start position:0% +pop off. It's also ended with this thing + + + align:start position:0% +pop off. It's also ended with this thing +again. So the the one advantage of + + align:start position:0% +again. So the the one advantage of + + + align:start position:0% +again. So the the one advantage of +circuit set is you can reuse complex + + align:start position:0% +circuit set is you can reuse complex + + + align:start position:0% +circuit set is you can reuse complex +computations uh just by copying the + + align:start position:0% +computations uh just by copying the + + + align:start position:0% +computations uh just by copying the +signal. Normally in a formula you'd have + + align:start position:0% +signal. Normally in a formula you'd have + + + align:start position:0% +signal. Normally in a formula you'd have +to copy and paste that chunk of the + + align:start position:0% +to copy and paste that chunk of the + + + align:start position:0% +to copy and paste that chunk of the +formula. So you could imagine this lets + + align:start position:0% +formula. So you could imagine this lets + + + align:start position:0% +formula. So you could imagine this lets +you write formulas slightly more + + align:start position:0% +you write formulas slightly more + + + align:start position:0% +you write formulas slightly more +efficiently. Uh I think it doesn't. Uh + + align:start position:0% +efficiently. Uh I think it doesn't. Uh + + + align:start position:0% +efficiently. Uh I think it doesn't. Uh +you can if you reuse things you can + + align:start position:0% +you can if you reuse things you can + + + align:start position:0% +you can if you reuse things you can +always use you can always write them as + + align:start position:0% +always use you can always write them as + + + align:start position:0% +always use you can always write them as +a variable over here. But question + + align:start position:0% +a variable over here. But question + + + align:start position:0% +a variable over here. But question +what about feedback? Um does + + align:start position:0% +what about feedback? Um does + + + align:start position:0% +what about feedback? Um does +feedback is forbidden. So this should be + + align:start position:0% +feedback is forbidden. So this should be + + + align:start position:0% +feedback is forbidden. So this should be +a directed as cyclic graph. Yeah, good + + align:start position:0% +a directed as cyclic graph. Yeah, good + + + align:start position:0% +a directed as cyclic graph. Yeah, good +question. Uh so + + align:start position:0% +question. Uh so + + + align:start position:0% +question. Uh so +it's an asyclic circuit. + + align:start position:0% +it's an asyclic circuit. + + + align:start position:0% +it's an asyclic circuit. +That would be another problem which is + + align:start position:0% +That would be another problem which is + + + align:start position:0% +That would be another problem which is +harder than NP. So circuit SAT is NP + + align:start position:0% +harder than NP. So circuit SAT is NP + + + align:start position:0% +harder than NP. So circuit SAT is NP +complete when it's as cyclic. Um and you + + align:start position:0% +complete when it's as cyclic. Um and you + + + align:start position:0% +complete when it's as cyclic. Um and you +can convert between one and the other. + + align:start position:0% +can convert between one and the other. + + + align:start position:0% +can convert between one and the other. +And it's a little bit more intuitive + + align:start position:0% +And it's a little bit more intuitive + + + align:start position:0% +And it's a little bit more intuitive +that you can write arbitrary + + align:start position:0% +that you can write arbitrary + + + align:start position:0% +that you can write arbitrary +computations as a circuit. Um and then + + align:start position:0% +computations as a circuit. Um and then + + + align:start position:0% +computations as a circuit. Um and then +this is a question of whether you can uh + + align:start position:0% +this is a question of whether you can uh + + + align:start position:0% +this is a question of whether you can uh +the existence of some setting of the AIS + + align:start position:0% +the existence of some setting of the AIS + + + align:start position:0% +the existence of some setting of the AIS +is the same thing as saying uh is there + + align:start position:0% +is the same thing as saying uh is there + + + align:start position:0% +is the same thing as saying uh is there +some set of guesses that will lead me to + + align:start position:0% +some set of guesses that will lead me to + + + align:start position:0% +some set of guesses that will lead me to +a yes answer. So that is intuitively + + align:start position:0% +a yes answer. So that is intuitively + + + align:start position:0% +a yes answer. So that is intuitively +like NP and that's roughly how you prove + + align:start position:0% +like NP and that's roughly how you prove + + + align:start position:0% +like NP and that's roughly how you prove +these problems are NPMPlete. uh you + + align:start position:0% +these problems are NPMPlete. uh you + + + align:start position:0% +these problems are NPMPlete. uh you +write the computation the checking + + align:start position:0% +write the computation the checking + + + align:start position:0% +write the computation the checking +computation to see whether you your um + + align:start position:0% +computation to see whether you your um + + + align:start position:0% +computation to see whether you your um +certificate is a valid certificate as a + + align:start position:0% +certificate is a valid certificate as a + + + align:start position:0% +certificate is a valid certificate as a +circuit or as a formula and then uh the + + align:start position:0% +circuit or as a formula and then uh the + + + align:start position:0% +circuit or as a formula and then uh the +existential quantifiers on the xis let + + align:start position:0% +existential quantifiers on the xis let + + + align:start position:0% +existential quantifiers on the xis let +you do all the guessing to see whether + + align:start position:0% +you do all the guessing to see whether + + + align:start position:0% +you do all the guessing to see whether +they're uh and this is biased right it's + + align:start position:0% +they're uh and this is biased right it's + + + align:start position:0% +they're uh and this is biased right it's +trying to find a true and that's exactly + + align:start position:0% +trying to find a true and that's exactly + + + align:start position:0% +trying to find a true and that's exactly +what np does is trying to find a true + + align:start position:0% +what np does is trying to find a true + + + align:start position:0% +what np does is trying to find a true +path uh that ends up answering yes so + + align:start position:0% +path uh that ends up answering yes so + + + align:start position:0% +path uh that ends up answering yes so +yes and true are are symmetric So uh + + align:start position:0% +yes and true are are symmetric So uh + + + align:start position:0% +yes and true are are symmetric So uh +that's the extent of the complexity + + align:start position:0% +that's the extent of the complexity + + + align:start position:0% +that's the extent of the complexity +theory we'll do today. Um I'm going to + + align:start position:0% +theory we'll do today. Um I'm going to + + + align:start position:0% +theory we'll do today. Um I'm going to +give you more versions of SAT. Next one + + align:start position:0% +give you more versions of SAT. Next one + + + align:start position:0% +give you more versions of SAT. Next one +is CNFSAT. + + align:start position:0% +is CNFSAT. + + + align:start position:0% +is CNFSAT. +CNF stands for conjunctive normal form. + + align:start position:0% + + + + align:start position:0% + +I hope you all know propositional logic + + align:start position:0% +I hope you all know propositional logic + + + align:start position:0% +I hope you all know propositional logic +because we're going to be doing a bunch + + align:start position:0% +because we're going to be doing a bunch + + + align:start position:0% +because we're going to be doing a bunch +today. Uh so uh ands are also called + + align:start position:0% +today. Uh so uh ands are also called + + + align:start position:0% +today. Uh so uh ands are also called +conjunctions ors are called + + align:start position:0% +conjunctions ors are called + + + align:start position:0% +conjunctions ors are called +disjunctions. This is old terminology. + + align:start position:0% +disjunctions. This is old terminology. + + + align:start position:0% +disjunctions. This is old terminology. +Uh so conjunctive normal form means that + + align:start position:0% +Uh so conjunctive normal form means that + + + align:start position:0% +Uh so conjunctive normal form means that +your formula + + align:start position:0% +your formula + + + align:start position:0% +your formula +is an and of clauses. + + align:start position:0% + + + + align:start position:0% + +What's a clause? + + align:start position:0% +What's a clause? + + + align:start position:0% +What's a clause? +clause is going to be an or of literals. + + align:start position:0% + + + + align:start position:0% + +What's a literal? + + align:start position:0% + + + + align:start position:0% + +Literal is going to be xi or not x i. + + align:start position:0% +Literal is going to be xi or not x i. + + + align:start position:0% +Literal is going to be xi or not x i. +So these are variables. So variables are + + align:start position:0% +So these are variables. So variables are + + + align:start position:0% +So these are variables. So variables are +possible literals and negations of + + align:start position:0% +possible literals and negations of + + + align:start position:0% +possible literals and negations of +variables literal and that's it. Uh and + + align:start position:0% +variables literal and that's it. Uh and + + + align:start position:0% +variables literal and that's it. Uh and +that is CNF set. So it's a special case + + align:start position:0% +that is CNF set. So it's a special case + + + align:start position:0% +that is CNF set. So it's a special case +of SAT where your formula formula + + align:start position:0% +of SAT where your formula formula + + + align:start position:0% +of SAT where your formula formula +happens to have this uh picture and in + + align:start position:0% +happens to have this uh picture and in + + + align:start position:0% +happens to have this uh picture and in +general you can convert arbitrary + + align:start position:0% +general you can convert arbitrary + + + align:start position:0% +general you can convert arbitrary +formulas into conjunctive normal form. + + align:start position:0% +formulas into conjunctive normal form. + + + align:start position:0% +formulas into conjunctive normal form. +It's a normal form meaning it's + + align:start position:0% +It's a normal form meaning it's + + + align:start position:0% +It's a normal form meaning it's +essentially unique uh in a minimal CNF + + align:start position:0% +essentially unique uh in a minimal CNF + + + align:start position:0% +essentially unique uh in a minimal CNF +formula is unique. Uh so there's a known + + align:start position:0% +formula is unique. Uh so there's a known + + + align:start position:0% +formula is unique. Uh so there's a known +transformation to do that polinomial + + align:start position:0% +transformation to do that polinomial + + + align:start position:0% +transformation to do that polinomial +time. That's how you prove this is hard. + + align:start position:0% +time. That's how you prove this is hard. + + + align:start position:0% +time. That's how you prove this is hard. +Um another view in this picture we'll + + align:start position:0% +Um another view in this picture we'll + + + align:start position:0% +Um another view in this picture we'll +use we'll use CNFSAT a lot uh usually in + + align:start position:0% +use we'll use CNFSAT a lot uh usually in + + + align:start position:0% +use we'll use CNFSAT a lot uh usually in +even more specialized form but already + + align:start position:0% +even more specialized form but already + + + align:start position:0% +even more specialized form but already +uh one useful view which we saw uh a + + align:start position:0% +uh one useful view which we saw uh a + + + align:start position:0% +uh one useful view which we saw uh a +little bit in lecture one we'll see it + + align:start position:0% +little bit in lecture one we'll see it + + + align:start position:0% +little bit in lecture one we'll see it +again today + + align:start position:0% +again today + + + align:start position:0% +again today +is you can view such an input as a + + align:start position:0% +is you can view such an input as a + + + align:start position:0% +is you can view such an input as a +bipartite graph. + + align:start position:0% +bipartite graph. + + + align:start position:0% +bipartite graph. +You have + + align:start position:0% +You have + + + align:start position:0% +You have +uh let's say variables + + align:start position:0% + + + + align:start position:0% + +on the one side and clauses on the other + + align:start position:0% +on the one side and clauses on the other + + + align:start position:0% +on the one side and clauses on the other +side. + + align:start position:0% +side. + + + align:start position:0% +side. +And then you have two types of + + align:start position:0% +And then you have two types of + + + align:start position:0% +And then you have two types of +connections. A clause in general clause + + align:start position:0% +connections. A clause in general clause + + + align:start position:0% +connections. A clause in general clause +is going to have degree three + + align:start position:0% +is going to have degree three + + + align:start position:0% +is going to have degree three +and I don't know let's say the dashed + + align:start position:0% +and I don't know let's say the dashed + + + align:start position:0% +and I don't know let's say the dashed +edges are negated and the solid edges + + align:start position:0% +edges are negated and the solid edges + + + align:start position:0% +edges are negated and the solid edges +are not negated. So this is a clause + + align:start position:0% +are not negated. So this is a clause + + + align:start position:0% +are not negated. So this is a clause +that involves x1 or x2 or not x3 + + align:start position:0% + + + + align:start position:0% + +and in general each of these clauses is + + align:start position:0% +and in general each of these clauses is + + + align:start position:0% +and in general each of these clauses is +going to involve uh some number of + + align:start position:0% +going to involve uh some number of + + + align:start position:0% +going to involve uh some number of +variables over here. I said three but I + + align:start position:0% +variables over here. I said three but I + + + align:start position:0% +variables over here. I said three but I +haven't actually gotten to three yet. + + align:start position:0% +haven't actually gotten to three yet. + + + align:start position:0% +haven't actually gotten to three yet. +That is three setat. + + align:start position:0% +That is three setat. + + + align:start position:0% +That is three setat. +So the most common form of CNFSAT we use + + align:start position:0% +So the most common form of CNFSAT we use + + + align:start position:0% +So the most common form of CNFSAT we use +is called threesat + + align:start position:0% + + + + align:start position:0% + +where + + align:start position:0% +where + + + align:start position:0% +where +it's CNFSAT in the special case where + + align:start position:0% +it's CNFSAT in the special case where + + + align:start position:0% +it's CNFSAT in the special case where +the clause is an or of three literals + + align:start position:0% +the clause is an or of three literals + + + align:start position:0% +the clause is an or of three literals +and you can assume it's exactly three or + + align:start position:0% +and you can assume it's exactly three or + + + align:start position:0% +and you can assume it's exactly three or +at most three. Um so that's like saying + + align:start position:0% +at most three. Um so that's like saying + + + align:start position:0% +at most three. Um so that's like saying +the degree of each of the clause nodes + + align:start position:0% +the degree of each of the clause nodes + + + align:start position:0% +the degree of each of the clause nodes +here is exactly three. + + align:start position:0% +here is exactly three. + + + align:start position:0% +here is exactly three. +And that's the problem that we used in + + align:start position:0% +And that's the problem that we used in + + + align:start position:0% +And that's the problem that we used in +for proving Super Mario Brothers was + + align:start position:0% +for proving Super Mario Brothers was + + + align:start position:0% +for proving Super Mario Brothers was +hard in the first lecture. Um, so in my + + align:start position:0% +hard in the first lecture. Um, so in my + + + align:start position:0% +hard in the first lecture. Um, so in my +notes I have things nicely indented. So + + align:start position:0% +notes I have things nicely indented. So + + + align:start position:0% +notes I have things nicely indented. So +we have CNFSAT which is a special case + + align:start position:0% +we have CNFSAT which is a special case + + + align:start position:0% +we have CNFSAT which is a special case +of SAT and then threes which is a + + align:start position:0% +of SAT and then threes which is a + + + align:start position:0% +of SAT and then threes which is a +special case of CNFSAT. A special case + + align:start position:0% +special case of CNFSAT. A special case + + + align:start position:0% +special case of CNFSAT. A special case +of threes that's also hard is called + + align:start position:0% +of threes that's also hard is called + + + align:start position:0% +of threes that's also hard is called +threeat-5. I don't know that this is + + align:start position:0% +threeat-5. I don't know that this is + + + align:start position:0% +threeat-5. I don't know that this is +super standard but I found at least one + + align:start position:0% +super standard but I found at least one + + + align:start position:0% +super standard but I found at least one +paper that gives it this this name. uh + + align:start position:0% +paper that gives it this this name. uh + + + align:start position:0% +paper that gives it this this name. uh +this says that each variable + + align:start position:0% + + + + align:start position:0% + +uh occurs + + align:start position:0% +uh occurs + + + align:start position:0% +uh occurs +in less than equal to five uh clauses + + align:start position:0% +in less than equal to five uh clauses + + + align:start position:0% +in less than equal to five uh clauses +either in its positive or negated form. + + align:start position:0% +either in its positive or negated form. + + + align:start position:0% +either in its positive or negated form. +So this this is sometimes called max + + align:start position:0% +So this this is sometimes called max + + + align:start position:0% +So this this is sometimes called max +five occurrence three set um and I think + + align:start position:0% +five occurrence three set um and I think + + + align:start position:0% +five occurrence three set um and I think +you can even make them exactly five + + align:start position:0% +you can even make them exactly five + + + align:start position:0% +you can even make them exactly five +occurrences if you want uh but at most + + align:start position:0% +occurrences if you want uh but at most + + + align:start position:0% +occurrences if you want uh but at most +five occurrences is usually what you + + align:start position:0% +five occurrences is usually what you + + + align:start position:0% +five occurrences is usually what you +want. question + + align:start position:0% +want. question + + + align:start position:0% +want. question +is that tight is like three set four + + align:start position:0% +is that tight is like three set four + + + align:start position:0% +is that tight is like three set four +inde + + align:start position:0% +inde + + + align:start position:0% +inde +four I don't know uh I would guess it's + + align:start position:0% +four I don't know uh I would guess it's + + + align:start position:0% +four I don't know uh I would guess it's +tight but because there are a lot of + + align:start position:0% +tight but because there are a lot of + + + align:start position:0% +tight but because there are a lot of +people that mention five but I haven't + + align:start position:0% +people that mention five but I haven't + + + align:start position:0% +people that mention five but I haven't +seen a mention that four is polinomial + + align:start position:0% +seen a mention that four is polinomial + + + align:start position:0% +seen a mention that four is polinomial +all right so we should figure that out + + align:start position:0% +all right so we should figure that out + + + align:start position:0% +all right so we should figure that out +other questions it's probably the same + + align:start position:0% +other questions it's probably the same + + + align:start position:0% +other questions it's probably the same +one + + align:start position:0% +one + + + align:start position:0% +one +all right here's another special case of + + align:start position:0% +all right here's another special case of + + + align:start position:0% +all right here's another special case of +three set + + align:start position:0% + + + + align:start position:0% + +monitor tone three set. + + align:start position:0% +monitor tone three set. + + + align:start position:0% +monitor tone three set. +Uh this is where + + align:start position:0% + + + + align:start position:0% + +each clause + + align:start position:0% +each clause + + + align:start position:0% +each clause +is all positive + + align:start position:0% + + + + align:start position:0% + +or all negative. + + align:start position:0% + + + + align:start position:0% + +So, of course, if every clause is all + + align:start position:0% +So, of course, if every clause is all + + + align:start position:0% +So, of course, if every clause is all +positive, then + + align:start position:0% +positive, then + + + align:start position:0% +positive, then +you could set all the variables to true + + align:start position:0% +you could set all the variables to true + + + align:start position:0% +you could set all the variables to true +and you'll satisfy. If all the clauses + + align:start position:0% +and you'll satisfy. If all the clauses + + + align:start position:0% +and you'll satisfy. If all the clauses +are negative, you set all the variables + + align:start position:0% +are negative, you set all the variables + + + align:start position:0% +are negative, you set all the variables +to false and you satisfy. But if some of + + align:start position:0% +to false and you satisfy. But if some of + + + align:start position:0% +to false and you satisfy. But if some of +half the clauses are all positive, half + + align:start position:0% +half the clauses are all positive, half + + + align:start position:0% +half the clauses are all positive, half +the clauses are all negative, then + + align:start position:0% +the clauses are all negative, then + + + align:start position:0% +the clauses are all negative, then +that's hard. That's called monotone + + align:start position:0% +that's hard. That's called monotone + + + align:start position:0% +that's hard. That's called monotone +threes. I've actually not seen this + + align:start position:0% +threes. I've actually not seen this + + + align:start position:0% +threes. I've actually not seen this +used, but I imagine is helpful in a few + + align:start position:0% +used, but I imagine is helpful in a few + + + align:start position:0% +used, but I imagine is helpful in a few +situations. Um, + + align:start position:0% +situations. Um, + + + align:start position:0% +situations. Um, +this is definitely the most common. + + align:start position:0% +this is definitely the most common. + + + align:start position:0% +this is definitely the most common. +Almost every proof starts with threesat, + + align:start position:0% +Almost every proof starts with threesat, + + + align:start position:0% +Almost every proof starts with threesat, +but it's really good to know all the + + align:start position:0% +but it's really good to know all the + + + align:start position:0% +but it's really good to know all the +extra things you can assume about your + + align:start position:0% +extra things you can assume about your + + + align:start position:0% +extra things you can assume about your +threes problem and still be hard. + + align:start position:0% +threes problem and still be hard. + + + align:start position:0% +threes problem and still be hard. +Uh, I have more hard versions, but + + align:start position:0% +Uh, I have more hard versions, but + + + align:start position:0% +Uh, I have more hard versions, but +before we get there, I'm going to tell + + align:start position:0% +before we get there, I'm going to tell + + + align:start position:0% +before we get there, I'm going to tell +you about some easy versions and + + align:start position:0% +you about some easy versions and + + + align:start position:0% +you about some easy versions and +question. + + align:start position:0% +question. + + + align:start position:0% +question. +Is monotone 3AT 5? + + align:start position:0% +Is monotone 3AT 5? + + + align:start position:0% +Is monotone 3AT 5? +Another good question. Monotone 3AT 5 is + + align:start position:0% +Another good question. Monotone 3AT 5 is + + + align:start position:0% +Another good question. Monotone 3AT 5 is +that infy complete? I don't know. Um, + + align:start position:0% +that infy complete? I don't know. Um, + + + align:start position:0% +that infy complete? I don't know. Um, +partly these were done at at different + + align:start position:0% +partly these were done at at different + + + align:start position:0% +partly these were done at at different +times. Um + + align:start position:0% +times. Um + + + align:start position:0% +times. Um +monotone threesat is mentioning Gary and + + align:start position:0% +monotone threesat is mentioning Gary and + + + align:start position:0% +monotone threesat is mentioning Gary and +Johnson is done in 1978 presumably for a + + align:start position:0% +Johnson is done in 1978 presumably for a + + + align:start position:0% +Johnson is done in 1978 presumably for a +particular hardness proof. Uh threes 5 + + align:start position:0% +particular hardness proof. Uh threes 5 + + + align:start position:0% +particular hardness proof. Uh threes 5 +is probably a very old idea probably + + align:start position:0% +is probably a very old idea probably + + + align:start position:0% +is probably a very old idea probably +this idea of reducing occurrences goes + + align:start position:0% +this idea of reducing occurrences goes + + + align:start position:0% +this idea of reducing occurrences goes +to some logic thing but the earliest + + align:start position:0% +to some logic thing but the earliest + + + align:start position:0% +to some logic thing but the earliest +reference I found was 1998 + + align:start position:0% +reference I found was 1998 + + + align:start position:0% +reference I found was 1998 +and most people have forgotten about + + align:start position:0% +and most people have forgotten about + + + align:start position:0% +and most people have forgotten about +monotone 3 by then so it probably just + + align:start position:0% +monotone 3 by then so it probably just + + + align:start position:0% +monotone 3 by then so it probably just +hasn't been considered but it might be + + align:start position:0% +hasn't been considered but it might be + + + align:start position:0% +hasn't been considered but it might be +easy. Yeah, + + align:start position:0% +easy. Yeah, + + + align:start position:0% +easy. Yeah, +it + + align:start position:0% +it + + + align:start position:0% +it +limited to five variables. The + + align:start position:0% +limited to five variables. The + + + align:start position:0% +limited to five variables. The +construction to limit to five variables + + align:start position:0% +construction to limit to five variables + + + align:start position:0% +construction to limit to five variables +should I believe work with the monitor + + align:start position:0% +should I believe work with the monitor + + + align:start position:0% +should I believe work with the monitor +construction as well. + + align:start position:0% +construction as well. + + + align:start position:0% +construction as well. +Okay. Conjecture. Yes, it's hard. + + align:start position:0% +Okay. Conjecture. Yes, it's hard. + + + align:start position:0% +Okay. Conjecture. Yes, it's hard. +That's okay. + + align:start position:0% + + + + align:start position:0% + +Uh + + align:start position:0% +Uh + + + align:start position:0% +Uh +so but stay tuned for + + align:start position:0% +so but stay tuned for + + + align:start position:0% +so but stay tuned for +certain answer. Um so let me tell you + + align:start position:0% +certain answer. Um so let me tell you + + + align:start position:0% +certain answer. Um so let me tell you +some polomial time versions of SAT. uh + + align:start position:0% +some polomial time versions of SAT. uh + + + align:start position:0% +some polomial time versions of SAT. uh +the three is tight + + align:start position:0% +the three is tight + + + align:start position:0% +the three is tight +if you have the clause being an ore of + + align:start position:0% +if you have the clause being an ore of + + + align:start position:0% +if you have the clause being an ore of +two literals + + align:start position:0% +two literals + + + align:start position:0% +two literals +but otherwise you're just like threesat + + align:start position:0% +but otherwise you're just like threesat + + + align:start position:0% +but otherwise you're just like threesat +or just like cnfat I guess uh then this + + align:start position:0% +or just like cnfat I guess uh then this + + + align:start position:0% +or just like cnfat I guess uh then this +is polomial time + + align:start position:0% +is polomial time + + + align:start position:0% +is polomial time +um and let me give you a rough sketch y + + align:start position:0% +um and let me give you a rough sketch y + + + align:start position:0% +um and let me give you a rough sketch y +um so + + align:start position:0% +um so + + + align:start position:0% +um so +if you have an or of two literals that's + + align:start position:0% +if you have an or of two literals that's + + + align:start position:0% +if you have an or of two literals that's +something like x or y and uh the little + + align:start position:0% +something like x or y and uh the little + + + align:start position:0% +something like x or y and uh the little +bit of propositional logic you should + + align:start position:0% +bit of propositional logic you should + + + align:start position:0% +bit of propositional logic you should +know is the meaning of uh let's say a + + align:start position:0% +know is the meaning of uh let's say a + + + align:start position:0% +know is the meaning of uh let's say a +implies b + + align:start position:0% +implies b + + + align:start position:0% +implies b +uh saying that this should hold is and a + + align:start position:0% +uh saying that this should hold is and a + + + align:start position:0% +uh saying that this should hold is and a +and b are either true or false uh this + + align:start position:0% +and b are either true or false uh this + + + align:start position:0% +and b are either true or false uh this +is the same as saying not a or b + + align:start position:0% +is the same as saying not a or b + + + align:start position:0% +is the same as saying not a or b +okay because if a is false then the + + align:start position:0% +okay because if a is false then the + + + align:start position:0% +okay because if a is false then the +implication tells you nothing if a is + + align:start position:0% +implication tells you nothing if a is + + + align:start position:0% +implication tells you nothing if a is +true then it better be the case that b + + align:start position:0% +true then it better be the case that b + + + align:start position:0% +true then it better be the case that b +is true so either a is false in which + + align:start position:0% +is true so either a is false in which + + + align:start position:0% +is true so either a is false in which +case there's you don't have to worry + + align:start position:0% +case there's you don't have to worry + + + align:start position:0% +case there's you don't have to worry +about something or a is true and then b + + align:start position:0% +about something or a is true and then b + + + align:start position:0% +about something or a is true and then b +better be true as well so these are the + + align:start position:0% +better be true as well so these are the + + + align:start position:0% +better be true as well so these are the +maybe write triple equals for these are + + align:start position:0% +maybe write triple equals for these are + + + align:start position:0% +maybe write triple equals for these are +equivalent logical statements. Uh so we + + align:start position:0% +equivalent logical statements. Uh so we + + + align:start position:0% +equivalent logical statements. Uh so we +can apply that here and say x or y is + + align:start position:0% +can apply that here and say x or y is + + + align:start position:0% +can apply that here and say x or y is +the same thing as not x implies y or not + + align:start position:0% +the same thing as not x implies y or not + + + align:start position:0% +the same thing as not x implies y or not +y implies x. It's symmetric but this is + + align:start position:0% +y implies x. It's symmetric but this is + + + align:start position:0% +y implies x. It's symmetric but this is +now just a simple implication. If we + + align:start position:0% +now just a simple implication. If we + + + align:start position:0% +now just a simple implication. If we +ever set x to be false then y must be + + align:start position:0% +ever set x to be false then y must be + + + align:start position:0% +ever set x to be false then y must be +true. And every clause can be converted + + align:start position:0% +true. And every clause can be converted + + + align:start position:0% +true. And every clause can be converted +into such an implication. You can build + + align:start position:0% +into such an implication. You can build + + + align:start position:0% +into such an implication. You can build +a graph of all such implications. And + + align:start position:0% +a graph of all such implications. And + + + align:start position:0% +a graph of all such implications. And +then uh turns out to solve you can + + align:start position:0% +then uh turns out to solve you can + + + align:start position:0% +then uh turns out to solve you can +just pick your favorite variable x i set + + align:start position:0% +just pick your favorite variable x i set + + + align:start position:0% +just pick your favorite variable x i set +it to true follow all implications see + + align:start position:0% +it to true follow all implications see + + + align:start position:0% +it to true follow all implications see +whether you get a contradiction if you + + align:start position:0% +whether you get a contradiction if you + + + align:start position:0% +whether you get a contradiction if you +don't then the claim is there is a + + align:start position:0% +don't then the claim is there is a + + + align:start position:0% +don't then the claim is there is a +satisfying assignment where x i equals + + align:start position:0% +satisfying assignment where x i equals + + + align:start position:0% +satisfying assignment where x i equals +true. So you can try that with x i true + + align:start position:0% +true. So you can try that with x i true + + + align:start position:0% +true. So you can try that with x i true +x i false. Uh one of if there's any hope + + align:start position:0% +x i false. Uh one of if there's any hope + + + align:start position:0% +x i false. Uh one of if there's any hope +then one of them should say no + + align:start position:0% +then one of them should say no + + + align:start position:0% +then one of them should say no +contradiction and then just run with + + align:start position:0% +contradiction and then just run with + + + align:start position:0% +contradiction and then just run with +that and you can prove by induction that + + align:start position:0% +that and you can prove by induction that + + + align:start position:0% +that and you can prove by induction that +won't get stuck. Uh it won't make any uh + + align:start position:0% +won't get stuck. Uh it won't make any uh + + + align:start position:0% +won't get stuck. Uh it won't make any uh +impossible assignments unless there was + + align:start position:0% +impossible assignments unless there was + + + align:start position:0% +impossible assignments unless there was +no assignment to begin with. Uh so + + align:start position:0% +no assignment to begin with. Uh so + + + align:start position:0% +no assignment to begin with. Uh so +that's why twoat is easy and one of the + + align:start position:0% +that's why twoat is easy and one of the + + + align:start position:0% +that's why twoat is easy and one of the +situations you should be careful about. + + align:start position:0% +situations you should be careful about. + + + align:start position:0% +situations you should be careful about. +On the other hand, uh, max twoat + + align:start position:0% +On the other hand, uh, max twoat + + + align:start position:0% +On the other hand, uh, max twoat +is hard. + + align:start position:0% +is hard. + + + align:start position:0% +is hard. +So, max two setat is you're given a two + + align:start position:0% +So, max two setat is you're given a two + + + align:start position:0% +So, max two setat is you're given a two +set formula. You're given a 2 CNF + + align:start position:0% +set formula. You're given a 2 CNF + + + align:start position:0% +set formula. You're given a 2 CNF +formula. And normally we ask for an uh + + align:start position:0% +formula. And normally we ask for an uh + + + align:start position:0% +formula. And normally we ask for an uh +an assignment to the variables that + + align:start position:0% +an assignment to the variables that + + + align:start position:0% +an assignment to the variables that +satisfies all the clauses. But if you + + align:start position:0% +satisfies all the clauses. But if you + + + align:start position:0% +satisfies all the clauses. But if you +just want to satisfy K of them, uh, so + + align:start position:0% +just want to satisfy K of them, uh, so + + + align:start position:0% +just want to satisfy K of them, uh, so +satisfy + + align:start position:0% + + + + align:start position:0% + +K of the clauses. + + align:start position:0% +K of the clauses. + + + align:start position:0% +K of the clauses. +So usually you want to maximize K but + + align:start position:0% +So usually you want to maximize K but + + + align:start position:0% +So usually you want to maximize K but +let's say for a decision problem I'll + + align:start position:0% +let's say for a decision problem I'll + + + align:start position:0% +let's say for a decision problem I'll +give you K and I want to know can you + + align:start position:0% +give you K and I want to know can you + + + align:start position:0% +give you K and I want to know can you +satisfy K of the clauses that problem is + + align:start position:0% +satisfy K of the clauses that problem is + + + align:start position:0% +satisfy K of the clauses that problem is +NP hard + + align:start position:0% + + + + align:start position:0% + +so that can be useful if you can only + + align:start position:0% +so that can be useful if you can only + + + align:start position:0% +so that can be useful if you can only +represent two set clauses but you can + + align:start position:0% +represent two set clauses but you can + + + align:start position:0% +represent two set clauses but you can +somehow get a maximization thing in then + + align:start position:0% +somehow get a maximization thing in then + + + align:start position:0% +somehow get a maximization thing in then +uh you're golden again but two set alone + + align:start position:0% +uh you're golden again but two set alone + + + align:start position:0% +uh you're golden again but two set alone +is not enough uh there are some other + + align:start position:0% +is not enough uh there are some other + + + align:start position:0% +is not enough uh there are some other +easy to solve + + align:start position:0% +easy to solve + + + align:start position:0% +easy to solve +versions this is essentially general + + align:start position:0% +versions this is essentially general + + + align:start position:0% +versions this is essentially general +Generalization of TUSAT is hornsat. + + align:start position:0% + + + + align:start position:0% + +It's maybe a little bit more surprising + + align:start position:0% +It's maybe a little bit more surprising + + + align:start position:0% +It's maybe a little bit more surprising +first time you see it. + + align:start position:0% +first time you see it. + + + align:start position:0% +first time you see it. +Again, it's a special case of CNF set, + + align:start position:0% +Again, it's a special case of CNF set, + + + align:start position:0% +Again, it's a special case of CNF set, +which you can tell by my indentation. + + align:start position:0% + + + + align:start position:0% + +Each clause has at most one negative + + align:start position:0% +Each clause has at most one negative + + + align:start position:0% +Each clause has at most one negative +literal. + + align:start position:0% + + + + align:start position:0% + +Uh so that means a clause is going to + + align:start position:0% +Uh so that means a clause is going to + + + align:start position:0% +Uh so that means a clause is going to +look something like what's one negative + + align:start position:0% +look something like what's one negative + + + align:start position:0% +look something like what's one negative +sorry uh sorry horn is the other way + + align:start position:0% +sorry uh sorry horn is the other way + + + align:start position:0% +sorry uh sorry horn is the other way +around we will get that problem is also + + align:start position:0% +around we will get that problem is also + + + align:start position:0% +around we will get that problem is also +solvable but the one that's called + + align:start position:0% +solvable but the one that's called + + + align:start position:0% +solvable but the one that's called +hornsat is there's at most one positive + + align:start position:0% +hornsat is there's at most one positive + + + align:start position:0% +hornsat is there's at most one positive +literal so that means your formula is + + align:start position:0% +literal so that means your formula is + + + align:start position:0% +literal so that means your formula is +going to look something like not x or + + align:start position:0% +going to look something like not x or + + + align:start position:0% +going to look something like not x or +not y or not z or w so there's one + + align:start position:0% +not y or not z or w so there's one + + + align:start position:0% +not y or not z or w so there's one +positive the rest are all negated + + align:start position:0% +positive the rest are all negated + + + align:start position:0% +positive the rest are all negated +um And we can do some more propositional + + align:start position:0% +um And we can do some more propositional + + + align:start position:0% +um And we can do some more propositional +logic. So use Deorgan's theorem. This is + + align:start position:0% +logic. So use Deorgan's theorem. This is + + + align:start position:0% +logic. So use Deorgan's theorem. This is +the same thing as the negation of the + + align:start position:0% +the same thing as the negation of the + + + align:start position:0% +the same thing as the negation of the +and. + + align:start position:0% + + + + align:start position:0% + +Okay. And then we can apply this helpful + + align:start position:0% +Okay. And then we can apply this helpful + + + align:start position:0% +Okay. And then we can apply this helpful +rule and say this is the same thing as + + align:start position:0% +rule and say this is the same thing as + + + align:start position:0% +rule and say this is the same thing as +if X and Y and Z are true, then W better + + align:start position:0% +if X and Y and Z are true, then W better + + + align:start position:0% +if X and Y and Z are true, then W better +be true. And so you can use essentially + + align:start position:0% +be true. And so you can use essentially + + + align:start position:0% +be true. And so you can use essentially +the same algorithm. Um that you're you I + + align:start position:0% +the same algorithm. Um that you're you I + + + align:start position:0% +the same algorithm. Um that you're you I +mean slightly harder to check if if all + + align:start position:0% +mean slightly harder to check if if all + + + align:start position:0% +mean slightly harder to check if if all +three of these things are true then this + + align:start position:0% +three of these things are true then this + + + align:start position:0% +three of these things are true then this +one better be true. But it's always a + + align:start position:0% +one better be true. But it's always a + + + align:start position:0% +one better be true. But it's always a +guarantee. You know this thing must + + align:start position:0% +guarantee. You know this thing must + + + align:start position:0% +guarantee. You know this thing must +happen. Uh just like in TUAT if X happen + + align:start position:0% +happen. Uh just like in TUAT if X happen + + + align:start position:0% +happen. Uh just like in TUAT if X happen +to be set to false then you know Y must + + align:start position:0% +to be set to false then you know Y must + + + align:start position:0% +to be set to false then you know Y must +be true. So you can just follow these + + align:start position:0% +be true. So you can just follow these + + + align:start position:0% +be true. So you can just follow these +implication chains. If you get a + + align:start position:0% +implication chains. If you get a + + + align:start position:0% +implication chains. If you get a +contradiction you know you're in + + align:start position:0% +contradiction you know you're in + + + align:start position:0% +contradiction you know you're in +trouble. Um if you don't get a + + align:start position:0% +trouble. Um if you don't get a + + + align:start position:0% +trouble. Um if you don't get a +contradiction again you can improve by + + align:start position:0% +contradiction again you can improve by + + + align:start position:0% +contradiction again you can improve by +induction that all will be well and so + + align:start position:0% +induction that all will be well and so + + + align:start position:0% +induction that all will be well and so +you just make sure every time you assign + + align:start position:0% +you just make sure every time you assign + + + align:start position:0% +you just make sure every time you assign +a variable you don't get a contradiction + + align:start position:0% +a variable you don't get a contradiction + + + align:start position:0% +a variable you don't get a contradiction +and you can satisfy any horn formula. + + align:start position:0% +and you can satisfy any horn formula. + + + align:start position:0% +and you can satisfy any horn formula. +So that's cool. + + align:start position:0% + + + + align:start position:0% + +So I didn't write it on the board but + + align:start position:0% +So I didn't write it on the board but + + + align:start position:0% +So I didn't write it on the board but +this is polomally solvable. Uh there's a + + align:start position:0% +this is polomally solvable. Uh there's a + + + align:start position:0% +this is polomally solvable. Uh there's a +symmetric version which is called dual + + align:start position:0% +symmetric version which is called dual + + + align:start position:0% +symmetric version which is called dual +horn sat. + + align:start position:0% + + + + align:start position:0% + +Uh so this is same thing uh but at most + + align:start position:0% +Uh so this is same thing uh but at most + + + align:start position:0% +Uh so this is same thing uh but at most +one negative literal in each clause + + align:start position:0% +one negative literal in each clause + + + align:start position:0% +one negative literal in each clause +and uh this is also solvable in + + align:start position:0% +and uh this is also solvable in + + + align:start position:0% +and uh this is also solvable in +polinomial time because you can just + + align:start position:0% +polinomial time because you can just + + + align:start position:0% +polinomial time because you can just +negate all the variables in your formula + + align:start position:0% +negate all the variables in your formula + + + align:start position:0% +negate all the variables in your formula +and then when you get an answer you can + + align:start position:0% +and then when you get an answer you can + + + align:start position:0% +and then when you get an answer you can +negate all the variables again to get + + align:start position:0% +negate all the variables again to get + + + align:start position:0% +negate all the variables again to get +the solution to the original problem. So + + align:start position:0% +the solution to the original problem. So + + + align:start position:0% +the solution to the original problem. So +because you can solve horns, you can + + align:start position:0% +because you can solve horns, you can + + + align:start position:0% +because you can solve horns, you can +solve dual horns. + + align:start position:0% + + + + align:start position:0% + +Cool. + + align:start position:0% +Cool. + + + align:start position:0% +Cool. +One more + + align:start position:0% +One more + + + align:start position:0% +One more +bad case + + align:start position:0% +bad case + + + align:start position:0% +bad case +I'll mention. Now uh is DNFSAT. You + + align:start position:0% +I'll mention. Now uh is DNFSAT. You + + + align:start position:0% +I'll mention. Now uh is DNFSAT. You +might say well + + align:start position:0% +might say well + + + align:start position:0% +might say well +why do we make things ands of ores? What + + align:start position:0% +why do we make things ands of ores? What + + + align:start position:0% +why do we make things ands of ores? What +about ores of ands? So DNF is + + align:start position:0% +about ores of ands? So DNF is + + + align:start position:0% +about ores of ands? So DNF is +disjunctive normal form meaning the + + align:start position:0% +disjunctive normal form meaning the + + + align:start position:0% +disjunctive normal form meaning the +disjunctions are on the outside. + + align:start position:0% + + + + align:start position:0% + +So me formula + + align:start position:0% + + + + align:start position:0% + +is an and + + align:start position:0% +is an and + + + align:start position:0% +is an and +of + + align:start position:0% +of + + + align:start position:0% +of +or sorry by the way + + align:start position:0% + + + + align:start position:0% + +or of ands of literals. + + align:start position:0% +or of ands of literals. + + + align:start position:0% +or of ands of literals. +Use some shorthand not defined clauses + + align:start position:0% +Use some shorthand not defined clauses + + + align:start position:0% +Use some shorthand not defined clauses +here because we don't really use this + + align:start position:0% +here because we don't really use this + + + align:start position:0% +here because we don't really use this +problem because it's polinomial time. + + align:start position:0% +problem because it's polinomial time. + + + align:start position:0% +problem because it's polinomial time. +uh y is a polinomial time + + align:start position:0% +uh y is a polinomial time + + + align:start position:0% +uh y is a polinomial time +of the ends. + + align:start position:0% +of the ends. + + + align:start position:0% +of the ends. +Just evaluate one of the ands. If you + + align:start position:0% +Just evaluate one of the ands. If you + + + align:start position:0% +Just evaluate one of the ands. If you +it's true if any one of these is + + align:start position:0% +it's true if any one of these is + + + align:start position:0% +it's true if any one of these is +possible. So you can just check for + + align:start position:0% +possible. So you can just check for + + + align:start position:0% +possible. So you can just check for +obvious contradictions like x i and not + + align:start position:0% +obvious contradictions like x i and not + + + align:start position:0% +obvious contradictions like x i and not +x i. If that happens then that clause is + + align:start position:0% +x i. If that happens then that clause is + + + align:start position:0% +x i. If that happens then that clause is +impossible throw it away. If any clause + + align:start position:0% +impossible throw it away. If any clause + + + align:start position:0% +impossible throw it away. If any clause +has no internal contradictions then just + + align:start position:0% +has no internal contradictions then just + + + align:start position:0% +has no internal contradictions then just +satisfy the clause. Okay. So it's + + align:start position:0% +satisfy the clause. Okay. So it's + + + align:start position:0% +satisfy the clause. Okay. So it's +basically uh the answer is yes. whenever + + align:start position:0% +basically uh the answer is yes. whenever + + + align:start position:0% +basically uh the answer is yes. whenever +there is a clause could be you have the + + align:start position:0% +there is a clause could be you have the + + + align:start position:0% +there is a clause could be you have the +empty formula and no clauses. Uh so + + align:start position:0% +empty formula and no clauses. Uh so + + + align:start position:0% +empty formula and no clauses. Uh so +writing you can also write any formula + + align:start position:0% +writing you can also write any formula + + + align:start position:0% +writing you can also write any formula +into DNF it's like an enumeration of all + + align:start position:0% +into DNF it's like an enumeration of all + + + align:start position:0% +into DNF it's like an enumeration of all +the true uh possibilities but it takes + + align:start position:0% +the true uh possibilities but it takes + + + align:start position:0% +the true uh possibilities but it takes +exponential time to do so. So it's a + + align:start position:0% +exponential time to do so. So it's a + + + align:start position:0% +exponential time to do so. So it's a +funny asymmetry between and and or + + align:start position:0% +funny asymmetry between and and or + + + align:start position:0% +funny asymmetry between and and or +that's life. + + align:start position:0% +that's life. + + + align:start position:0% +that's life. +Yeah. I just want to say um for hornset + + align:start position:0% +Yeah. I just want to say um for hornset + + + align:start position:0% +Yeah. I just want to say um for hornset +um even if you don't have hornset or + + align:start position:0% +um even if you don't have hornset or + + + align:start position:0% +um even if you don't have hornset or +dual hornset you might have a formula + + align:start position:0% +dual hornset you might have a formula + + + align:start position:0% +dual hornset you might have a formula +where some renaming not necessarily all + + align:start position:0% +where some renaming not necessarily all + + + align:start position:0% +where some renaming not necessarily all +of the literals but renaming just some + + align:start position:0% +of the literals but renaming just some + + + align:start position:0% +of the literals but renaming just some +of the literals will put it in hornset + + align:start position:0% +of the literals will put it in hornset + + + align:start position:0% +of the literals will put it in hornset +and that's also that's also + + align:start position:0% +and that's also that's also + + + align:start position:0% +and that's also that's also +oh just negating some of them + + align:start position:0% +oh just negating some of them + + + align:start position:0% +oh just negating some of them +yeah like for each each time a variable + + align:start position:0% +yeah like for each each time a variable + + + align:start position:0% +yeah like for each each time a variable +occurs you have to negate all the + + align:start position:0% +occurs you have to negate all the + + + align:start position:0% +occurs you have to negate all the +instances of that variable + + align:start position:0% +instances of that variable + + + align:start position:0% +instances of that variable +but these are called renameable horn + + align:start position:0% +but these are called renameable horn + + + align:start position:0% +but these are called renameable horn +formulas and that's also do finding the + + align:start position:0% +formulas and that's also do finding the + + + align:start position:0% +formulas and that's also do finding the +renaming is linear time so + + align:start position:0% +renaming is linear time so + + + align:start position:0% +renaming is linear time so +okay so some kind of renameable horn + + align:start position:0% + + + + align:start position:0% + +And by renaming you just mean negating + + align:start position:0% +And by renaming you just mean negating + + + align:start position:0% +And by renaming you just mean negating +right? So + + align:start position:0% +right? So + + + align:start position:0% +right? So +yeah the the term used in the literature + + align:start position:0% +yeah the the term used in the literature + + + align:start position:0% +yeah the the term used in the literature +is renameable horn. So + + align:start position:0% +is renameable horn. So + + + align:start position:0% +is renameable horn. So +there exists a negation + + align:start position:0% + + + + align:start position:0% + +of uh let's say some subset of the + + align:start position:0% +of uh let's say some subset of the + + + align:start position:0% +of uh let's say some subset of the +variables x uh such that + + align:start position:0% +variables x uh such that + + + align:start position:0% +variables x uh such that +uh + + align:start position:0% + + + + align:start position:0% + +okay that's a very concise version. So + + align:start position:0% +okay that's a very concise version. So + + + align:start position:0% +okay that's a very concise version. So +you get to choose some of the variables + + align:start position:0% +you get to choose some of the variables + + + align:start position:0% +you get to choose some of the variables +to negate and make it a horn clause. + + align:start position:0% +to negate and make it a horn clause. + + + align:start position:0% +to negate and make it a horn clause. +That's also polomial time. Cool. Thank + + align:start position:0% +That's also polomial time. Cool. Thank + + + align:start position:0% +That's also polomial time. Cool. Thank +you. + + align:start position:0% + + + + align:start position:0% + +Uh you might be wondering at this point + + align:start position:0% +Uh you might be wondering at this point + + + align:start position:0% +Uh you might be wondering at this point +how am I I mean do I have to remember + + align:start position:0% +how am I I mean do I have to remember + + + align:start position:0% +how am I I mean do I have to remember +all of these? In some sense the answer + + align:start position:0% +all of these? In some sense the answer + + + align:start position:0% +all of these? In some sense the answer +is yes. But uh there is actually a + + align:start position:0% +is yes. But uh there is actually a + + + align:start position:0% +is yes. But uh there is actually a +dichotomy theorem that will tell you + + align:start position:0% +dichotomy theorem that will tell you + + + align:start position:0% +dichotomy theorem that will tell you +which versions of SAT are polinomial + + align:start position:0% +which versions of SAT are polinomial + + + align:start position:0% +which versions of SAT are polinomial +time and which versions are np hard. And + + align:start position:0% +time and which versions are np hard. And + + + align:start position:0% +time and which versions are np hard. And +we'll cover that in one more page. Um + + align:start position:0% +we'll cover that in one more page. Um + + + align:start position:0% +we'll cover that in one more page. Um +but I'm well all of these are involved + + align:start position:0% +but I'm well all of these are involved + + + align:start position:0% +but I'm well all of these are involved +in the statement of that dichotomy. So + + align:start position:0% +in the statement of that dichotomy. So + + + align:start position:0% +in the statement of that dichotomy. So +not quite all but most of them. So it's + + align:start position:0% +not quite all but most of them. So it's + + + align:start position:0% +not quite all but most of them. So it's +not exactly a shortcut. + + align:start position:0% + + + + align:start position:0% + +Uh I would say a lot of the time the + + align:start position:0% +Uh I would say a lot of the time the + + + align:start position:0% +Uh I would say a lot of the time the +problem you're working with does not + + align:start position:0% +problem you're working with does not + + + align:start position:0% +problem you're working with does not +naturally map on to ands and ors. It + + align:start position:0% +naturally map on to ands and ors. It + + + align:start position:0% +naturally map on to ands and ors. It +sort of involves bits of some sort. + + align:start position:0% +sort of involves bits of some sort. + + + align:start position:0% +sort of involves bits of some sort. +There's a zero and a one notion but they + + align:start position:0% +There's a zero and a one notion but they + + + align:start position:0% +There's a zero and a one notion but they +may not really correspond to logical + + align:start position:0% +may not really correspond to logical + + + align:start position:0% +may not really correspond to logical +notions of true or false and they may + + align:start position:0% +notions of true or false and they may + + + align:start position:0% +notions of true or false and they may +not the operations you can do on them + + align:start position:0% +not the operations you can do on them + + + align:start position:0% +not the operations you can do on them +may not correspond to and or or anything + + align:start position:0% +may not correspond to and or or anything + + + align:start position:0% +may not correspond to and or or anything +nice like that. So um the next two + + align:start position:0% +nice like that. So um the next two + + + align:start position:0% +nice like that. So um the next two +versions of SAT are in that spirit. + + align:start position:0% + + + + align:start position:0% + +So uh this is usually these days called + + align:start position:0% +So uh this is usually these days called + + + align:start position:0% +So uh this is usually these days called +one and three setat but originally it's + + align:start position:0% +one and three setat but originally it's + + + align:start position:0% +one and three setat but originally it's +called exactly one three set. + + align:start position:0% + + + + align:start position:0% + +Uh so this is going to be a little bit + + align:start position:0% +Uh so this is going to be a little bit + + + align:start position:0% +Uh so this is going to be a little bit +weirder to write down. Uh but like + + align:start position:0% +weirder to write down. Uh but like + + + align:start position:0% +weirder to write down. Uh but like +CNFSAT the formula is the and of a bunch + + align:start position:0% +CNFSAT the formula is the and of a bunch + + + align:start position:0% +CNFSAT the formula is the and of a bunch +of clauses. So that part's the same. But + + align:start position:0% +of clauses. So that part's the same. But + + + align:start position:0% +of clauses. So that part's the same. But +now we're going to make a clause + + align:start position:0% +now we're going to make a clause + + + align:start position:0% +now we're going to make a clause +to be um a relation on three variables + + align:start position:0% +to be um a relation on three variables + + + align:start position:0% +to be um a relation on three variables +which is that uh exactly + + align:start position:0% +which is that uh exactly + + + align:start position:0% +which is that uh exactly +one of uh let's say x i, xj and x k + + align:start position:0% +one of uh let's say x i, xj and x k + + + align:start position:0% +one of uh let's say x i, xj and x k +is true. + + align:start position:0% +is true. + + + align:start position:0% +is true. +So this means it could be uh true false + + align:start position:0% +So this means it could be uh true false + + + align:start position:0% +So this means it could be uh true false +false. X I is true but the other two are + + align:start position:0% +false. X I is true but the other two are + + + align:start position:0% +false. X I is true but the other two are +false. It could be XJ is true the other + + align:start position:0% +false. It could be XJ is true the other + + + align:start position:0% +false. It could be XJ is true the other +two are false. Or it could be that X K + + align:start position:0% +two are false. Or it could be that X K + + + align:start position:0% +two are false. Or it could be that X K +is true and the other two are false. But + + align:start position:0% +is true and the other two are false. But + + + align:start position:0% +is true and the other two are false. But +those are the only happy assignments. + + align:start position:0% +those are the only happy assignments. + + + align:start position:0% +those are the only happy assignments. +Question. + + align:start position:0% +Question. + + + align:start position:0% +Question. +Is it exactly one of three variables or + + align:start position:0% +Is it exactly one of three variables or + + + align:start position:0% +Is it exactly one of three variables or +three literals? + + align:start position:0% +three literals? + + + align:start position:0% +three literals? +Uh good question. Um the original + + align:start position:0% +Uh good question. Um the original + + + align:start position:0% +Uh good question. Um the original +statement is its variables. So that's + + align:start position:0% +statement is its variables. So that's + + + align:start position:0% +statement is its variables. So that's +how I wrote it. This is usually called + + align:start position:0% +how I wrote it. This is usually called + + + align:start position:0% +how I wrote it. This is usually called +monotone. These days it's usually called + + align:start position:0% +monotone. These days it's usually called + + + align:start position:0% +monotone. These days it's usually called +monotone one and three set. I don't know + + align:start position:0% +monotone one and three set. I don't know + + + align:start position:0% +monotone one and three set. I don't know +how usually exactly. Sometimes it's + + align:start position:0% +how usually exactly. Sometimes it's + + + align:start position:0% +how usually exactly. Sometimes it's +called all positive one and three set. + + align:start position:0% +called all positive one and three set. + + + align:start position:0% +called all positive one and three set. +Uh + + align:start position:0% +Uh + + + align:start position:0% +Uh +so let's say + + align:start position:0% +so let's say + + + align:start position:0% +so let's say +uh + + align:start position:0% + + + + align:start position:0% + +literal equal variables. + + align:start position:0% +literal equal variables. + + + align:start position:0% +literal equal variables. +You could of course if you want uh + + align:start position:0% +You could of course if you want uh + + + align:start position:0% +You could of course if you want uh +consider a more general version where + + align:start position:0% +consider a more general version where + + + align:start position:0% +consider a more general version where +you can have negations but you don't + + align:start position:0% +you can have negations but you don't + + + align:start position:0% +you can have negations but you don't +need to. So why bother? Uh just that + + align:start position:0% +need to. So why bother? Uh just that + + + align:start position:0% +need to. So why bother? Uh just that +fact is usually forgotten in most + + align:start position:0% +fact is usually forgotten in most + + + align:start position:0% +fact is usually forgotten in most +proofs. So you'll see in the literature + + align:start position:0% +proofs. So you'll see in the literature + + + align:start position:0% +proofs. So you'll see in the literature +a reduction for one and three setat with + + align:start position:0% +a reduction for one and three setat with + + + align:start position:0% +a reduction for one and three setat with +negations and they have a negation + + align:start position:0% +negations and they have a negation + + + align:start position:0% +negations and they have a negation +gadget. It's like you know you don't + + align:start position:0% +gadget. It's like you know you don't + + + align:start position:0% +gadget. It's like you know you don't +need to have a negation gadget. So why + + align:start position:0% +need to have a negation gadget. So why + + + align:start position:0% +need to have a negation gadget. So why +not skip it? + + align:start position:0% +not skip it? + + + align:start position:0% +not skip it? +Uh but there you go. Now I'll just + + align:start position:0% +Uh but there you go. Now I'll just + + + align:start position:0% +Uh but there you go. Now I'll just +mention I'm not a fan of the word + + align:start position:0% +mention I'm not a fan of the word + + + align:start position:0% +mention I'm not a fan of the word +monotone here because here we have + + align:start position:0% +monotone here because here we have + + + align:start position:0% +monotone here because here we have +monotone to mean all positive or all + + align:start position:0% +monotone to mean all positive or all + + + align:start position:0% +monotone to mean all positive or all +negative. Here we mean it mean all + + align:start position:0% +negative. Here we mean it mean all + + + align:start position:0% +negative. Here we mean it mean all +positive. uh not ideal reuse of + + align:start position:0% +positive. uh not ideal reuse of + + + align:start position:0% +positive. uh not ideal reuse of +terminology. I think that's why + + align:start position:0% +terminology. I think that's why + + + align:start position:0% +terminology. I think that's why +sometimes this is all positive one and + + align:start position:0% +sometimes this is all positive one and + + + align:start position:0% +sometimes this is all positive one and +three set. Anyway, it's a bit of a mess, + + align:start position:0% +three set. Anyway, it's a bit of a mess, + + + align:start position:0% +three set. Anyway, it's a bit of a mess, +but that is the state of the literature. + + align:start position:0% +but that is the state of the literature. + + + align:start position:0% +but that is the state of the literature. +So, you get it all. Um + + align:start position:0% +So, you get it all. Um + + + align:start position:0% +So, you get it all. Um +all right, here's another problem. + + align:start position:0% + + + + align:start position:0% + +Monotone not exactly 13. + + align:start position:0% + + + + align:start position:0% + +I should not add have any suspense here. + + align:start position:0% +I should not add have any suspense here. + + + align:start position:0% +I should not add have any suspense here. +This is in P. Okay, + + align:start position:0% +This is in P. Okay, + + + align:start position:0% +This is in P. Okay, +this is MP complete. This is also NP + + align:start position:0% +this is MP complete. This is also NP + + + align:start position:0% +this is MP complete. This is also NP +complete but not exactly one three is + + align:start position:0% +complete but not exactly one three is + + + align:start position:0% +complete but not exactly one three is +polomial. + + align:start position:0% +polomial. + + + align:start position:0% +polomial. +So uh I think you know what it means. Uh + + align:start position:0% +So uh I think you know what it means. Uh + + + align:start position:0% +So uh I think you know what it means. Uh +a clause specifies that again we take an + + align:start position:0% +a clause specifies that again we take an + + + align:start position:0% +a clause specifies that again we take an +and of clauses and we want zero two or + + align:start position:0% +and of clauses and we want zero two or + + + align:start position:0% +and of clauses and we want zero two or +three of three variables are true. In + + align:start position:0% +three of three variables are true. In + + + align:start position:0% +three of three variables are true. In +other words, exactly one of them is + + align:start position:0% +other words, exactly one of them is + + + align:start position:0% +other words, exactly one of them is +false. + + align:start position:0% +false. + + + align:start position:0% +false. +No, I don't mean that. Exactly one of + + align:start position:0% +No, I don't mean that. Exactly one of + + + align:start position:0% +No, I don't mean that. Exactly one of +them being false would be one and three + + align:start position:0% +them being false would be one and three + + + align:start position:0% +them being false would be one and three +set again just by negating everything + + align:start position:0% +set again just by negating everything + + + align:start position:0% +set again just by negating everything +which we're allowed to do if we want to. + + align:start position:0% +which we're allowed to do if we want to. + + + align:start position:0% +which we're allowed to do if we want to. +Uh but this is different. This is saying + + align:start position:0% +Uh but this is different. This is saying + + + align:start position:0% +Uh but this is different. This is saying +it could be everything's false or it + + align:start position:0% +it could be everything's false or it + + + align:start position:0% +it could be everything's false or it +could be one thing is false or it could + + align:start position:0% +could be one thing is false or it could + + + align:start position:0% +could be one thing is false or it could +be zero things are false + + align:start position:0% +be zero things are false + + + align:start position:0% +be zero things are false +but uh yeah but not two things are + + align:start position:0% +but uh yeah but not two things are + + + align:start position:0% +but uh yeah but not two things are +false. Okay, this turns out to be + + align:start position:0% +false. Okay, this turns out to be + + + align:start position:0% +false. Okay, this turns out to be +polomial. Um, and + + align:start position:0% +polomial. Um, and + + + align:start position:0% +polomial. Um, and +do I have a + + align:start position:0% +do I have a + + + align:start position:0% +do I have a +Oh, there's there's one funny thing here + + align:start position:0% +Oh, there's there's one funny thing here + + + align:start position:0% +Oh, there's there's one funny thing here +which is in if this is if all your + + align:start position:0% +which is in if this is if all your + + + align:start position:0% +which is in if this is if all your +clauses look like this, you can set all + + align:start position:0% +clauses look like this, you can set all + + + align:start position:0% +clauses look like this, you can set all +your variables to false. So, this is + + align:start position:0% +your variables to false. So, this is + + + align:start position:0% +your variables to false. So, this is +sort of a trivial problem, but to make + + align:start position:0% +sort of a trivial problem, but to make + + + align:start position:0% +sort of a trivial problem, but to make +it more interesting, you can say x1 + + align:start position:0% +it more interesting, you can say x1 + + + align:start position:0% +it more interesting, you can say x1 +equals true + + align:start position:0% +equals true + + + align:start position:0% +equals true +just to get you started. So, there's no + + align:start position:0% +just to get you started. So, there's no + + + align:start position:0% +just to get you started. So, there's no +trivial solution then. Uh and it turns + + align:start position:0% +trivial solution then. Uh and it turns + + + align:start position:0% +trivial solution then. Uh and it turns +still turns out this is easy because if + + align:start position:0% +still turns out this is easy because if + + + align:start position:0% +still turns out this is easy because if +you think about this long enough as I + + align:start position:0% +you think about this long enough as I + + + align:start position:0% +you think about this long enough as I +did yesterday um this will look + + align:start position:0% +did yesterday um this will look + + + align:start position:0% +did yesterday um this will look +something like + + align:start position:0% + + + + align:start position:0% + +if you have three variables uh either + + align:start position:0% +if you have three variables uh either + + + align:start position:0% +if you have three variables uh either +they're all false then fine um or if one + + align:start position:0% +they're all false then fine um or if one + + + align:start position:0% +they're all false then fine um or if one +of them is true then you better have + + align:start position:0% +of them is true then you better have + + + align:start position:0% +of them is true then you better have +another one true. That's a way of saying + + align:start position:0% +another one true. That's a way of saying + + + align:start position:0% +another one true. That's a way of saying +if there's at least one of them, there + + align:start position:0% +if there's at least one of them, there + + + align:start position:0% +if there's at least one of them, there +better be at least two. That's what we + + align:start position:0% +better be at least two. That's what we + + + align:start position:0% +better be at least two. That's what we +want. This has to be true for all shifts + + align:start position:0% +want. This has to be true for all shifts + + + align:start position:0% +want. This has to be true for all shifts +of JK. So for each of JK, if one of them + + align:start position:0% +of JK. So for each of JK, if one of them + + + align:start position:0% +of JK. So for each of JK, if one of them +is true, you want to imply the or of the + + align:start position:0% +is true, you want to imply the or of the + + + align:start position:0% +is true, you want to imply the or of the +other. And this is the same as not Xi + + align:start position:0% +other. And this is the same as not Xi + + + align:start position:0% +other. And this is the same as not Xi +or XJ or X K. Don't need the parenthesis + + align:start position:0% +or XJ or X K. Don't need the parenthesis + + + align:start position:0% +or XJ or X K. Don't need the parenthesis +because it's uh associative commutive. + + align:start position:0% +because it's uh associative commutive. + + + align:start position:0% +because it's uh associative commutive. +Um and that is a + + align:start position:0% +Um and that is a + + + align:start position:0% +Um and that is a +dual horn clause. And that's why this is + + align:start position:0% +dual horn clause. And that's why this is + + + align:start position:0% +dual horn clause. And that's why this is +polinomial + + align:start position:0% +polinomial + + + align:start position:0% +polinomial +question. + + align:start position:0% +question. + + + align:start position:0% +question. +I think I'm confused about the + + align:start position:0% +I think I'm confused about the + + + align:start position:0% +I think I'm confused about the +definition. Why can't they just all be + + align:start position:0% +definition. Why can't they just all be + + + align:start position:0% +definition. Why can't they just all be +true though? + + align:start position:0% +true though? + + + align:start position:0% +true though? +Good question. Let's say uh x2 is false. + + align:start position:0% +Good question. Let's say uh x2 is false. + + + align:start position:0% +Good question. Let's say uh x2 is false. +I'm not I should double check. I don't + + align:start position:0% +I'm not I should double check. I don't + + + align:start position:0% +I'm not I should double check. I don't +remember that in the statement of the + + align:start position:0% +remember that in the statement of the + + + align:start position:0% +remember that in the statement of the +problem. So uh we do not allow negations + + align:start position:0% +problem. So uh we do not allow negations + + + align:start position:0% +problem. So uh we do not allow negations +here. Once you allow negations, this + + align:start position:0% +here. Once you allow negations, this + + + align:start position:0% +here. Once you allow negations, this +trick won't work. But when if these + + align:start position:0% +trick won't work. But when if these + + + align:start position:0% +trick won't work. But when if these +appear all in positive form, then we can + + align:start position:0% +appear all in positive form, then we can + + + align:start position:0% +appear all in positive form, then we can +convert into the single negative and get + + align:start position:0% +convert into the single negative and get + + + align:start position:0% +convert into the single negative and get +dual horn. Question. Are you allowed to + + align:start position:0% +dual horn. Question. Are you allowed to + + + align:start position:0% +dual horn. Question. Are you allowed to +mix the 0, two, and threes or does it + + align:start position:0% +mix the 0, two, and threes or does it + + + align:start position:0% +mix the 0, two, and threes or does it +have to be all clauses have to be + + align:start position:0% +have to be all clauses have to be + + + align:start position:0% +have to be all clauses have to be +all clauses look like all clauses say 0, + + align:start position:0% +all clauses look like all clauses say 0, + + + align:start position:0% +all clauses look like all clauses say 0, +two, or three of these three variables + + align:start position:0% +two, or three of these three variables + + + align:start position:0% +two, or three of these three variables +must be true? + + align:start position:0% +must be true? + + + align:start position:0% +must be true? +You can't have a clause that says zero + + align:start position:0% +You can't have a clause that says zero + + + align:start position:0% +You can't have a clause that says zero +of these are true and two of these are + + align:start position:0% +of these are true and two of these are + + + align:start position:0% +of these are true and two of these are +true. + + align:start position:0% +true. + + + align:start position:0% +true. +No, but if you have if you have two of + + align:start position:0% +No, but if you have if you have two of + + + align:start position:0% +No, but if you have if you have two of +these clauses that give you all those + + align:start position:0% +these clauses that give you all those + + + align:start position:0% +these clauses that give you all those +choices, can you make choose one to be + + align:start position:0% +choices, can you make choose one to be + + + align:start position:0% +choices, can you make choose one to be +zero + + align:start position:0% +zero + + + align:start position:0% +zero +and then have another one be two or + + align:start position:0% +and then have another one be two or + + + align:start position:0% +and then have another one be two or +whatever? + + align:start position:0% +whatever? + + + align:start position:0% +whatever? +For each clause, it's an independent + + align:start position:0% +For each clause, it's an independent + + + align:start position:0% +For each clause, it's an independent +choice whether you have 0, two or three + + align:start position:0% +choice whether you have 0, two or three + + + align:start position:0% +choice whether you have 0, two or three +of the variables true. Yeah. So this ore + + align:start position:0% +of the variables true. Yeah. So this ore + + + align:start position:0% +of the variables true. Yeah. So this ore +is local to the clause. + + align:start position:0% +is local to the clause. + + + align:start position:0% +is local to the clause. +Other questions. + + align:start position:0% +Other questions. + + + align:start position:0% +Other questions. +So it's still an and of things that it's + + align:start position:0% +So it's still an and of things that it's + + + align:start position:0% +So it's still an and of things that it's +just we have a weirder relation. Instead + + align:start position:0% +just we have a weirder relation. Instead + + + align:start position:0% +just we have a weirder relation. Instead +of just taking the ore of of a bunch of + + align:start position:0% +of just taking the ore of of a bunch of + + + align:start position:0% +of just taking the ore of of a bunch of +things, which would be saying at least + + align:start position:0% +things, which would be saying at least + + + align:start position:0% +things, which would be saying at least +one of them is true, now we allow zero + + align:start position:0% +one of them is true, now we allow zero + + + align:start position:0% +one of them is true, now we allow zero +or two or three of them to be true. + + align:start position:0% +or two or three of them to be true. + + + align:start position:0% +or two or three of them to be true. +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +one more version. + + align:start position:0% +one more version. + + + align:start position:0% +one more version. +Then we'll get to one and a half more + + align:start position:0% +Then we'll get to one and a half more + + + align:start position:0% +Then we'll get to one and a half more +versions. + + align:start position:0% + + + + align:start position:0% + +Then we'll get to the dichotomy theorem. + + align:start position:0% + + + + align:start position:0% + +So next one is not all equal three set. + + align:start position:0% + + + + align:start position:0% + +I feel like that's about all I need to + + align:start position:0% +I feel like that's about all I need to + + + align:start position:0% +I feel like that's about all I need to +write down. uh other than the fact that + + align:start position:0% +write down. uh other than the fact that + + + align:start position:0% +write down. uh other than the fact that +it is empty + + align:start position:0% +it is empty + + + align:start position:0% +it is empty +but just in case what this means is a + + align:start position:0% +but just in case what this means is a + + + align:start position:0% +but just in case what this means is a +clause + + align:start position:0% +clause + + + align:start position:0% +clause +is something like not all equal of three + + align:start position:0% +is something like not all equal of three + + + align:start position:0% +is something like not all equal of three +variables again + + align:start position:0% + + + + align:start position:0% + +and uh this is what I'm defining is + + align:start position:0% +and uh this is what I'm defining is + + + align:start position:0% +and uh this is what I'm defining is +going to be the monotone + + align:start position:0% +going to be the monotone + + + align:start position:0% +going to be the monotone +not all equal three set which is also + + align:start position:0% +not all equal three set which is also + + + align:start position:0% +not all equal three set which is also +hard + + align:start position:0% + + + + align:start position:0% + +where uh these are variable + + align:start position:0% + + + + align:start position:0% + +not just literal. So no negations and + + align:start position:0% +not just literal. So no negations and + + + align:start position:0% +not just literal. So no negations and +monotone not all equal three set. Uh + + align:start position:0% +monotone not all equal three set. Uh + + + align:start position:0% +monotone not all equal three set. Uh +again that the original proof already + + align:start position:0% +again that the original proof already + + + align:start position:0% +again that the original proof already +had monostnicity in there. So there's no + + align:start position:0% +had monostnicity in there. So there's no + + + align:start position:0% +had monostnicity in there. So there's no +work to be done. Uh cool. So not all + + align:start position:0% +work to be done. Uh cool. So not all + + + align:start position:0% +work to be done. Uh cool. So not all +equal just means that they're not all + + align:start position:0% +equal just means that they're not all + + + align:start position:0% +equal just means that they're not all +the same values. So that means not all + + align:start position:0% +the same values. So that means not all + + + align:start position:0% +the same values. So that means not all +true and not all false. So not ttt + + align:start position:0% +true and not all false. So not ttt + + + align:start position:0% +true and not all false. So not ttt +and not fff. I really like this version + + align:start position:0% +and not fff. I really like this version + + + align:start position:0% +and not fff. I really like this version +of thet because it's completely + + align:start position:0% +of thet because it's completely + + + align:start position:0% +of thet because it's completely +symmetric between true and false. I mean + + align:start position:0% +symmetric between true and false. I mean + + + align:start position:0% +symmetric between true and false. I mean +uh not at the clause level. Every clause + + align:start position:0% +uh not at the clause level. Every clause + + + align:start position:0% +uh not at the clause level. Every clause +has to be satisfied. Those are ended + + align:start position:0% +has to be satisfied. Those are ended + + + align:start position:0% +has to be satisfied. Those are ended +together in the logical level. But the x + + align:start position:0% +together in the logical level. But the x + + + align:start position:0% +together in the logical level. But the x +i are treated completely symmetrically + + align:start position:0% +i are treated completely symmetrically + + + align:start position:0% +i are treated completely symmetrically +between true and false. You could just + + align:start position:0% +between true and false. You could just + + + align:start position:0% +between true and false. You could just +call them red and blue. There's no + + align:start position:0% +call them red and blue. There's no + + + align:start position:0% +call them red and blue. There's no +reason to think one is true, one is + + align:start position:0% +reason to think one is true, one is + + + align:start position:0% +reason to think one is true, one is +false. You just can't have them all be + + align:start position:0% +false. You just can't have them all be + + + align:start position:0% +false. You just can't have them all be +the same color within a clause. + + align:start position:0% +the same color within a clause. + + + align:start position:0% +the same color within a clause. +Okay, so you can think of it as a + + align:start position:0% +Okay, so you can think of it as a + + + align:start position:0% +Okay, so you can think of it as a +problem on hyperraphs. Three uniform + + align:start position:0% +problem on hyperraphs. Three uniform + + + align:start position:0% +problem on hyperraphs. Three uniform +hyperraphs. You have all these triples + + align:start position:0% +hyperraphs. You have all these triples + + + align:start position:0% +hyperraphs. You have all these triples +of things. You just want them to not all + + align:start position:0% +of things. You just want them to not all + + + align:start position:0% +of things. You just want them to not all +be colored the same. So it means two of + + align:start position:0% +be colored the same. So it means two of + + + align:start position:0% +be colored the same. So it means two of +one, one of the other. Two trs and one + + align:start position:0% +one, one of the other. Two trs and one + + + align:start position:0% +one, one of the other. Two trs and one +false. Two reds and one blue. Two + + align:start position:0% +false. Two reds and one blue. Two + + + align:start position:0% +false. Two reds and one blue. Two +falses, one true. They're all the those + + align:start position:0% +falses, one true. They're all the those + + + align:start position:0% +falses, one true. They're all the those +are all good cases. And these are the + + align:start position:0% +are all good cases. And these are the + + + align:start position:0% +are all good cases. And these are the +bad cases. Uh + + align:start position:0% +bad cases. Uh + + + align:start position:0% +bad cases. Uh +cool. + + align:start position:0% +cool. + + + align:start position:0% +cool. +So So this is one or two in three set. + + align:start position:0% +So So this is one or two in three set. + + + align:start position:0% +So So this is one or two in three set. +Uh yeah, you can think of this exactly + + align:start position:0% +Uh yeah, you can think of this exactly + + + align:start position:0% +Uh yeah, you can think of this exactly +one or two in three set if you want to + + align:start position:0% +one or two in three set if you want to + + + align:start position:0% +one or two in three set if you want to +phrase it in this style. Okay, so um + + align:start position:0% +phrase it in this style. Okay, so um + + + align:start position:0% +phrase it in this style. Okay, so um +ideally you should remember all of + + align:start position:0% +ideally you should remember all of + + + align:start position:0% +ideally you should remember all of +these, but I'll tell you the most + + align:start position:0% +these, but I'll tell you the most + + + align:start position:0% +these, but I'll tell you the most +important ones are regular three set, + + align:start position:0% +important ones are regular three set, + + + align:start position:0% +important ones are regular three set, +that's at least one of each thing is + + align:start position:0% +that's at least one of each thing is + + + align:start position:0% +that's at least one of each thing is +true. Exactly one three set or one and + + align:start position:0% +true. Exactly one three set or one and + + + align:start position:0% +true. Exactly one three set or one and +three set where exactly one of the + + align:start position:0% +three set where exactly one of the + + + align:start position:0% +three set where exactly one of the +things is true and adding more things + + align:start position:0% +things is true and adding more things + + + align:start position:0% +things is true and adding more things +breaks it. Uh and not all equal three + + align:start position:0% +breaks it. Uh and not all equal three + + + align:start position:0% +breaks it. Uh and not all equal three +set. Those are the three important ones + + align:start position:0% +set. Those are the three important ones + + + align:start position:0% +set. Those are the three important ones +to know from a lower bounds perspective. + + align:start position:0% +to know from a lower bounds perspective. + + + align:start position:0% +to know from a lower bounds perspective. +These others are to like be careful that + + align:start position:0% +These others are to like be careful that + + + align:start position:0% +These others are to like be careful that +you don't fall into one of these things + + align:start position:0% +you don't fall into one of these things + + + align:start position:0% +you don't fall into one of these things +that is uh polomial. + + align:start position:0% +that is uh polomial. + + + align:start position:0% +that is uh polomial. +Um so occasionally max two sat is the + + align:start position:0% +Um so occasionally max two sat is the + + + align:start position:0% +Um so occasionally max two sat is the +one other that would be useful here. But + + align:start position:0% +one other that would be useful here. But + + + align:start position:0% +one other that would be useful here. But +remember these guys they're super handy + + align:start position:0% +remember these guys they're super handy + + + align:start position:0% +remember these guys they're super handy +because what will happen when you're + + align:start position:0% +because what will happen when you're + + + align:start position:0% +because what will happen when you're +proving hardness is you you fool around + + align:start position:0% +proving hardness is you you fool around + + + align:start position:0% +proving hardness is you you fool around +and you try to find you build a gadget + + align:start position:0% +and you try to find you build a gadget + + + align:start position:0% +and you try to find you build a gadget +that has two truth two possible ways to + + align:start position:0% +that has two truth two possible ways to + + + align:start position:0% +that has two truth two possible ways to +satisfy it. Call one red and one blue or + + align:start position:0% +satisfy it. Call one red and one blue or + + + align:start position:0% +satisfy it. Call one red and one blue or +one true and one false. And then you + + align:start position:0% +one true and one false. And then you + + + align:start position:0% +one true and one false. And then you +figure you try different ways to combine + + align:start position:0% +figure you try different ways to combine + + + align:start position:0% +figure you try different ways to combine +three of them. And you're trying to get + + align:start position:0% +three of them. And you're trying to get + + + align:start position:0% +three of them. And you're trying to get +you need some other things, but you're + + align:start position:0% +you need some other things, but you're + + + align:start position:0% +you need some other things, but you're +trying to get clause gadgets. Trying to + + align:start position:0% +trying to get clause gadgets. Trying to + + + align:start position:0% +trying to get clause gadgets. Trying to +get them to uh that when you combine + + align:start position:0% +get them to uh that when you combine + + + align:start position:0% +get them to uh that when you combine +your wires in in when you combine three + + align:start position:0% +your wires in in when you combine three + + + align:start position:0% +your wires in in when you combine three +wires into a little gadget, you want + + align:start position:0% +wires into a little gadget, you want + + + align:start position:0% +wires into a little gadget, you want +them to be constrained somehow. That in + + align:start position:0% +them to be constrained somehow. That in + + + align:start position:0% +them to be constrained somehow. That in +order to be globally, okay, something + + align:start position:0% +order to be globally, okay, something + + + align:start position:0% +order to be globally, okay, something +must hold locally at those three things. + + align:start position:0% +must hold locally at those three things. + + + align:start position:0% +must hold locally at those three things. +And it might end up being a not all + + align:start position:0% +And it might end up being a not all + + + align:start position:0% +And it might end up being a not all +equal constraint. It might end up being + + align:start position:0% +equal constraint. It might end up being + + + align:start position:0% +equal constraint. It might end up being +exactly one constraint or it might end + + align:start position:0% +exactly one constraint or it might end + + + align:start position:0% +exactly one constraint or it might end +up being a threesack constraint uh with + + align:start position:0% +up being a threesack constraint uh with + + + align:start position:0% +up being a threesack constraint uh with +some negations to make it happy. Uh it + + align:start position:0% +some negations to make it happy. Uh it + + + align:start position:0% +some negations to make it happy. Uh it +should be one of those to be hard. + + align:start position:0% +should be one of those to be hard. + + + align:start position:0% +should be one of those to be hard. +Um if you fall into something like this + + align:start position:0% +Um if you fall into something like this + + + align:start position:0% +Um if you fall into something like this +then that's not good. + + align:start position:0% +then that's not good. + + + align:start position:0% +then that's not good. +Question. + + align:start position:0% +Question. + + + align:start position:0% +Question. +So let's say since this not all people + + align:start position:0% +So let's say since this not all people + + + align:start position:0% +So let's say since this not all people +thing uh let's say you call it red and + + align:start position:0% +thing uh let's say you call it red and + + + align:start position:0% +thing uh let's say you call it red and +blue. What if you add green? Uh then + + align:start position:0% +blue. What if you add green? Uh then + + + align:start position:0% +blue. What if you add green? Uh then +would would there be like uh would not + + align:start position:0% +would would there be like uh would not + + + align:start position:0% +would would there be like uh would not +all equal three sets to be empty hard or + + align:start position:0% +all equal three sets to be empty hard or + + + align:start position:0% +all equal three sets to be empty hard or +would you need like for set or + + align:start position:0% +would you need like for set or + + + align:start position:0% +would you need like for set or +something? + + align:start position:0% +something? + + + align:start position:0% +something? +Yeah. So what about turnary truth? Um + + align:start position:0% +Yeah. So what about turnary truth? Um + + + align:start position:0% +Yeah. So what about turnary truth? Um +uh I + + align:start position:0% +uh I + + + align:start position:0% +uh I +there might be a problem on that in the + + align:start position:0% +there might be a problem on that in the + + + align:start position:0% +there might be a problem on that in the +pet set. Um but in general you'd have to + + align:start position:0% +pet set. Um but in general you'd have to + + + align:start position:0% +pet set. Um but in general you'd have to +go through the work to check what which + + align:start position:0% +go through the work to check what which + + + align:start position:0% +go through the work to check what which +problems I think those are pretty + + align:start position:0% +problems I think those are pretty + + + align:start position:0% +problems I think those are pretty +uncommon. Um, so usually what you do is + + align:start position:0% +uncommon. Um, so usually what you do is + + + align:start position:0% +uncommon. Um, so usually what you do is +if you have a gadget that can be solved + + align:start position:0% +if you have a gadget that can be solved + + + align:start position:0% +if you have a gadget that can be solved +not two ways but like four ways is you + + align:start position:0% +not two ways but like four ways is you + + + align:start position:0% +not two ways but like four ways is you +call two of them true and two of them + + align:start position:0% +call two of them true and two of them + + + align:start position:0% +call two of them true and two of them +false and hope they behave more or less + + align:start position:0% +false and hope they behave more or less + + + align:start position:0% +false and hope they behave more or less +identically. So that's the most common + + align:start position:0% +identically. So that's the most common + + + align:start position:0% +identically. So that's the most common +answer practically to what we do. Uh, + + align:start position:0% +answer practically to what we do. Uh, + + + align:start position:0% +answer practically to what we do. Uh, +but certainly it's plausible with three + + align:start position:0% +but certainly it's plausible with three + + + align:start position:0% +but certainly it's plausible with three +different values. Some of these are + + align:start position:0% +different values. Some of these are + + + align:start position:0% +different values. Some of these are +going to be hard but I don't know which + + align:start position:0% +going to be hard but I don't know which + + + align:start position:0% +going to be hard but I don't know which +ones. Uh hopefully all of them but you + + align:start position:0% +ones. Uh hopefully all of them but you + + + align:start position:0% +ones. Uh hopefully all of them but you +have to be careful. And definitely the + + align:start position:0% +have to be careful. And definitely the + + + align:start position:0% +have to be careful. And definitely the +next theorem I'm going to talk about the + + align:start position:0% +next theorem I'm going to talk about the + + + align:start position:0% +next theorem I'm going to talk about the +dichotomy theorem would get more + + align:start position:0% +dichotomy theorem would get more + + + align:start position:0% +dichotomy theorem would get more +complicated with three colors + + align:start position:0% + + + + align:start position:0% + +here. Actually + + align:start position:0% + + + + align:start position:0% + +nice question. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% + + + + align:start position:0% + +let's do + + align:start position:0% + + + + align:start position:0% + +Schaefer's dichotomy theorem. + + align:start position:0% +Schaefer's dichotomy theorem. + + + align:start position:0% +Schaefer's dichotomy theorem. +This is about which + + align:start position:0% +This is about which + + + align:start position:0% +This is about which +which versions of SAT are polomial and + + align:start position:0% +which versions of SAT are polomial and + + + align:start position:0% +which versions of SAT are polomial and +which versions are MPcomplete. With the + + align:start position:0% +which versions are MPcomplete. With the + + + align:start position:0% +which versions are MPcomplete. With the +right setup, they're all every problem + + align:start position:0% +right setup, they're all every problem + + + align:start position:0% +right setup, they're all every problem +you can think of is either polomial or + + align:start position:0% +you can think of is either polomial or + + + align:start position:0% +you can think of is either polomial or +nplete. There's no things in between. + + align:start position:0% +nplete. There's no things in between. + + + align:start position:0% +nplete. There's no things in between. +These are called NP intermediate + + align:start position:0% +These are called NP intermediate + + + align:start position:0% +These are called NP intermediate +problems. So it's always going to be one + + align:start position:0% +problems. So it's always going to be one + + + align:start position:0% +problems. So it's always going to be one +extreme or the other as I'm about to set + + align:start position:0% +extreme or the other as I'm about to set + + + align:start position:0% +extreme or the other as I'm about to set +it up. Uh and there by this theorem is + + align:start position:0% +it up. Uh and there by this theorem is + + + align:start position:0% +it up. Uh and there by this theorem is +by Schaefer and in the very same paper + + align:start position:0% +by Schaefer and in the very same paper + + + align:start position:0% +by Schaefer and in the very same paper +he proves not all equal threes and one + + align:start position:0% +he proves not all equal threes and one + + + align:start position:0% +he proves not all equal threes and one +and three are hard. Those are the + + align:start position:0% +and three are hard. Those are the + + + align:start position:0% +and three are hard. Those are the +original proofs. So it's a great paper. + + align:start position:0% +original proofs. So it's a great paper. + + + align:start position:0% +original proofs. So it's a great paper. +I have looked at it many times. Uh it's + + align:start position:0% +I have looked at it many times. Uh it's + + + align:start position:0% +I have looked at it many times. Uh it's +from 1978. So long time ago, + + align:start position:0% +from 1978. So long time ago, + + + align:start position:0% +from 1978. So long time ago, +but still quite readable. + + align:start position:0% + + + + align:start position:0% + +So I don't know how many all the last + + align:start position:0% +So I don't know how many all the last + + + align:start position:0% +So I don't know how many all the last +problems we've stated have this property + + align:start position:0% +problems we've stated have this property + + + align:start position:0% +problems we've stated have this property +but I'll make it explicit again. That's + + align:start position:0% +but I'll make it explicit again. That's + + + align:start position:0% +but I'll make it explicit again. That's +uh your formula is going to be an and of + + align:start position:0% +uh your formula is going to be an and of + + + align:start position:0% +uh your formula is going to be an and of +clauses. And now we're going to allow + + align:start position:0% +clauses. And now we're going to allow + + + align:start position:0% +clauses. And now we're going to allow +general kinds of clauses. A clause is + + align:start position:0% +general kinds of clauses. A clause is + + + align:start position:0% +general kinds of clauses. A clause is +just going to be any relation on some + + align:start position:0% +just going to be any relation on some + + + align:start position:0% +just going to be any relation on some +number of variables. + + align:start position:0% + + + + align:start position:0% + +So there won't be any notion of literal + + align:start position:0% +So there won't be any notion of literal + + + align:start position:0% +So there won't be any notion of literal +here because you can put that in the + + align:start position:0% +here because you can put that in the + + + align:start position:0% +here because you can put that in the +relation. I'll call this a general + + align:start position:0% +relation. I'll call this a general + + + align:start position:0% +relation. I'll call this a general +clause. + + align:start position:0% +clause. + + + align:start position:0% +clause. +It's a + + align:start position:0% +It's a + + + align:start position:0% +It's a +relation on + + align:start position:0% +relation on + + + align:start position:0% +relation on +some variables. + + align:start position:0% + + + + align:start position:0% + +So relation is something I I give you + + align:start position:0% +So relation is something I I give you + + + align:start position:0% +So relation is something I I give you +set of truth values for those variables + + align:start position:0% +set of truth values for those variables + + + align:start position:0% +set of truth values for those variables +and it will say yes or no that's valid + + align:start position:0% +and it will say yes or no that's valid + + + align:start position:0% +and it will say yes or no that's valid +or it's invalid. You can think of a + + align:start position:0% +or it's invalid. You can think of a + + + align:start position:0% +or it's invalid. You can think of a +relation as the set of all assignments + + align:start position:0% +relation as the set of all assignments + + + align:start position:0% +relation as the set of all assignments +the variables that make it true. But you + + align:start position:0% +the variables that make it true. But you + + + align:start position:0% +the variables that make it true. But you +don't have to specify that per se. You + + align:start position:0% +don't have to specify that per se. You + + + align:start position:0% +don't have to specify that per se. You +just sort of know what it is. + + align:start position:0% + + + + align:start position:0% + +Okay. So I mean in particular if this it + + align:start position:0% +Okay. So I mean in particular if this it + + + align:start position:0% +Okay. So I mean in particular if this it +could be the or of three variables then + + align:start position:0% +could be the or of three variables then + + + align:start position:0% +could be the or of three variables then +we get three setat or it could be the + + align:start position:0% +we get three setat or it could be the + + + align:start position:0% +we get three setat or it could be the +not all equal constraint on three + + align:start position:0% +not all equal constraint on three + + + align:start position:0% +not all equal constraint on three +variables then it's not all equal three + + align:start position:0% +variables then it's not all equal three + + + align:start position:0% +variables then it's not all equal three +set and so on. + + align:start position:0% +set and so on. + + + align:start position:0% +set and so on. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +okay we are going to + + align:start position:0% +okay we are going to + + + align:start position:0% +okay we are going to +uh so the I guess sorry the relation + + align:start position:0% +uh so the I guess sorry the relation + + + align:start position:0% +uh so the I guess sorry the relation +should be given to you as a boolean + + align:start position:0% +should be given to you as a boolean + + + align:start position:0% +should be given to you as a boolean +formula. So it could be an or you can + + align:start position:0% +formula. So it could be an or you can + + + align:start position:0% +formula. So it could be an or you can +write one and three sad as a boolean + + align:start position:0% +write one and three sad as a boolean + + + align:start position:0% +write one and three sad as a boolean +formula. It's just a little tedious. You + + align:start position:0% +formula. It's just a little tedious. You + + + align:start position:0% +formula. It's just a little tedious. You +could say well it could be this or it + + align:start position:0% +could say well it could be this or it + + + align:start position:0% +could say well it could be this or it +could be this or it could be this. In + + align:start position:0% +could be this or it could be this. In + + + align:start position:0% +could be this or it could be this. In +general I'm going to assume uh that + + align:start position:0% +general I'm going to assume uh that + + + align:start position:0% +general I'm going to assume uh that +they're given to you in CNF form. Sorry + + align:start position:0% +they're given to you in CNF form. Sorry + + + align:start position:0% +they're given to you in CNF form. Sorry +that's redundant. CNF has form in it. um + + align:start position:0% +that's redundant. CNF has form in it. um + + + align:start position:0% +that's redundant. CNF has form in it. um +uh because any formula can be made into + + align:start position:0% +uh because any formula can be made into + + + align:start position:0% +uh because any formula can be made into +CNF. So now CNF is an and of ors. So + + align:start position:0% +CNF. So now CNF is an and of ors. So + + + align:start position:0% +CNF. So now CNF is an and of ors. So +this is going to be an and of what we + + align:start position:0% +this is going to be an and of what we + + + align:start position:0% +this is going to be an and of what we +might normally call clauses, but we're + + align:start position:0% +might normally call clauses, but we're + + + align:start position:0% +might normally call clauses, but we're +already in a clause. So I'm going to + + align:start position:0% +already in a clause. So I'm going to + + + align:start position:0% +already in a clause. So I'm going to +call this sub clauses. + + align:start position:0% +call this sub clauses. + + + align:start position:0% +call this sub clauses. +Starting to sound like legal, but uh + + align:start position:0% +Starting to sound like legal, but uh + + + align:start position:0% +Starting to sound like legal, but uh +that's I made up this word. It's not in + + align:start position:0% +that's I made up this word. It's not in + + + align:start position:0% +that's I made up this word. It's not in +the literature. Uh so in general, your + + align:start position:0% +the literature. Uh so in general, your + + + align:start position:0% +the literature. Uh so in general, your +formula is an and of clauses. Each one + + align:start position:0% +formula is an and of clauses. Each one + + + align:start position:0% +formula is an and of clauses. Each one +is just some relation which we're going + + align:start position:0% +is just some relation which we're going + + + align:start position:0% +is just some relation which we're going +to think of as an end of subasses. Of + + align:start position:0% +to think of as an end of subasses. Of + + + align:start position:0% +to think of as an end of subasses. Of +course, it's really just an end of all + + align:start position:0% +course, it's really just an end of all + + + align:start position:0% +course, it's really just an end of all +the things but this is trying to be + + align:start position:0% +the things but this is trying to be + + + align:start position:0% +the things but this is trying to be +general um because we're going to have + + align:start position:0% +general um because we're going to have + + + align:start position:0% +general um because we're going to have +constraints in the clauses in + + align:start position:0% +constraints in the clauses in + + + align:start position:0% +constraints in the clauses in +particular. + + align:start position:0% +particular. + + + align:start position:0% +particular. +So then claim is SAT + + align:start position:0% +So then claim is SAT + + + align:start position:0% +So then claim is SAT +uh on these types of formulas. Uh so + + align:start position:0% +uh on these types of formulas. Uh so + + + align:start position:0% +uh on these types of formulas. Uh so +here here's the difference I guess um to + + align:start position:0% +here here's the difference I guess um to + + + align:start position:0% +here here's the difference I guess um to +define the problem you specify what kind + + align:start position:0% +define the problem you specify what kind + + + align:start position:0% +define the problem you specify what kind +of relations that you allow. So in + + align:start position:0% +of relations that you allow. So in + + + align:start position:0% +of relations that you allow. So in +threes we say okay it's or of three + + align:start position:0% +threes we say okay it's or of three + + + align:start position:0% +threes we say okay it's or of three +things in cnfat it's an ore of k things + + align:start position:0% +things in cnfat it's an ore of k things + + + align:start position:0% +things in cnfat it's an ore of k things +for any k in uh not all equal three + + align:start position:0% +for any k in uh not all equal three + + + align:start position:0% +for any k in uh not all equal three +setat it's not all equal of three things + + align:start position:0% +setat it's not all equal of three things + + + align:start position:0% +setat it's not all equal of three things +uh and so on. So we give that up front + + align:start position:0% +uh and so on. So we give that up front + + + align:start position:0% +uh and so on. So we give that up front +and then the decision problem is well uh + + align:start position:0% +and then the decision problem is well uh + + + align:start position:0% +and then the decision problem is well uh +I have n variables and I can combine + + align:start position:0% +I have n variables and I can combine + + + align:start position:0% +I have n variables and I can combine +them with these clauses however I want + + align:start position:0% +them with these clauses however I want + + + align:start position:0% +them with these clauses however I want +right so that's so we need some kind of + + align:start position:0% +right so that's so we need some kind of + + + align:start position:0% +right so that's so we need some kind of +infinity right if I gave you a specific + + align:start position:0% +infinity right if I gave you a specific + + + align:start position:0% +infinity right if I gave you a specific +problem then it's not going to be hard + + align:start position:0% +problem then it's not going to be hard + + + align:start position:0% +problem then it's not going to be hard +like with these 10 variables that's + + align:start position:0% +like with these 10 variables that's + + + align:start position:0% +like with these 10 variables that's +never going to be interesting u so I + + align:start position:0% +never going to be interesting u so I + + + align:start position:0% +never going to be interesting u so I +give you the notion of what clauses are + + align:start position:0% +give you the notion of what clauses are + + + align:start position:0% +give you the notion of what clauses are +allowed what relations are permitted and + + align:start position:0% +allowed what relations are permitted and + + + align:start position:0% +allowed what relations are permitted and +then I'm I want to consider the class of + + align:start position:0% +then I'm I want to consider the class of + + + align:start position:0% +then I'm I want to consider the class of +all possible formulas you can build with + + align:start position:0% +all possible formulas you can build with + + + align:start position:0% +all possible formulas you can build with +clauses of that type. So you can think + + align:start position:0% +clauses of that type. So you can think + + + align:start position:0% +clauses of that type. So you can think +of this as really more of a clause type + + align:start position:0% +of this as really more of a clause type + + + align:start position:0% +of this as really more of a clause type +like not all equal just to be precise + + align:start position:0% +like not all equal just to be precise + + + align:start position:0% +like not all equal just to be precise +here. And then we get a version of SAT + + align:start position:0% +here. And then we get a version of SAT + + + align:start position:0% +here. And then we get a version of SAT +and + + align:start position:0% +and + + + align:start position:0% +and +it's going to be polomial + + align:start position:0% +it's going to be polomial + + + align:start position:0% +it's going to be polomial +if + + align:start position:0% +if + + + align:start position:0% +if +one of + + align:start position:0% +one of + + + align:start position:0% +one of +four cases happen. at least one any one + + align:start position:0% +four cases happen. at least one any one + + + align:start position:0% +four cases happen. at least one any one +of these will make it easy. We have seen + + align:start position:0% +of these will make it easy. We have seen + + + align:start position:0% +of these will make it easy. We have seen +almost all of these. So first one + + align:start position:0% +almost all of these. So first one + + + align:start position:0% +almost all of these. So first one +is setting all variables true + + align:start position:0% +is setting all variables true + + + align:start position:0% +is setting all variables true +satisfies the formula. + + align:start position:0% +satisfies the formula. + + + align:start position:0% +satisfies the formula. +Uh well not just the formula but all + + align:start position:0% +Uh well not just the formula but all + + + align:start position:0% +Uh well not just the formula but all +formulas of this type. So or all + + align:start position:0% +formulas of this type. So or all + + + align:start position:0% +formulas of this type. So or all +variables false + + align:start position:0% + + + + align:start position:0% + +uh satisfies + + align:start position:0% + + + + align:start position:0% + +all + + align:start position:0% +all + + + align:start position:0% +all +clauses. + + align:start position:0% + + + + align:start position:0% + +Okay, this is a statement over all + + align:start position:0% +Okay, this is a statement over all + + + align:start position:0% +Okay, this is a statement over all +formulas with this clause type, right? + + align:start position:0% +formulas with this clause type, right? + + + align:start position:0% +formulas with this clause type, right? +It's a statement about the clause types + + align:start position:0% +It's a statement about the clause types + + + align:start position:0% +It's a statement about the clause types +and it's one of the issues we were + + align:start position:0% +and it's one of the issues we were + + + align:start position:0% +and it's one of the issues we were +having with not exactly one three set + + align:start position:0% +having with not exactly one three set + + + align:start position:0% +having with not exactly one three set +because there the clause type allowed + + align:start position:0% +because there the clause type allowed + + + align:start position:0% +because there the clause type allowed +everything to be false and it also + + align:start position:0% +everything to be false and it also + + + align:start position:0% +everything to be false and it also +allowed everything to be true. So, it's + + align:start position:0% +allowed everything to be true. So, it's + + + align:start position:0% +allowed everything to be true. So, it's +doubly bad. Of course, if if you have + + align:start position:0% +doubly bad. Of course, if if you have + + + align:start position:0% +doubly bad. Of course, if if you have +clauses uh where this is true for all + + align:start position:0% +clauses uh where this is true for all + + + align:start position:0% +clauses uh where this is true for all +the you could allow different types of + + align:start position:0% +the you could allow different types of + + + align:start position:0% +the you could allow different types of +clauses. is you could have not all equal + + align:start position:0% +clauses. is you could have not all equal + + + align:start position:0% +clauses. is you could have not all equal +plus one and three set. Uh that will + + align:start position:0% +plus one and three set. Uh that will + + + align:start position:0% +plus one and three set. Uh that will +also be hard of course. Uh but if all of + + align:start position:0% +also be hard of course. Uh but if all of + + + align:start position:0% +also be hard of course. Uh but if all of +your clauses have this property then of + + align:start position:0% +your clauses have this property then of + + + align:start position:0% +your clauses have this property then of +course you just globally set the + + align:start position:0% +course you just globally set the + + + align:start position:0% +course you just globally set the +variables and you're done. + + align:start position:0% +variables and you're done. + + + align:start position:0% +variables and you're done. +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +that was the first case. + + align:start position:0% +that was the first case. + + + align:start position:0% +that was the first case. +[Applause] + + align:start position:0% + + + + align:start position:0% + +Um + + align:start position:0% +Um + + + align:start position:0% +Um +so next one is that + + align:start position:0% +so next one is that + + + align:start position:0% +so next one is that +it could be the sub clauses + + align:start position:0% +it could be the sub clauses + + + align:start position:0% +it could be the sub clauses +are all horn + + align:start position:0% + + + + align:start position:0% + +or + + align:start position:0% +or + + + align:start position:0% +or +all dual horn. + + align:start position:0% + + + + align:start position:0% + +Uh so those are two happy cases we saw + + align:start position:0% +Uh so those are two happy cases we saw + + + align:start position:0% +Uh so those are two happy cases we saw +before. I mean we can think of the + + align:start position:0% +before. I mean we can think of the + + + align:start position:0% +before. I mean we can think of the +overall problem as an and of uh the + + align:start position:0% +overall problem as an and of uh the + + + align:start position:0% +overall problem as an and of uh the +clauses which are ands of sub clauses. + + align:start position:0% +clauses which are ands of sub clauses. + + + align:start position:0% +clauses which are ands of sub clauses. +So if everything is a horn or dual horn + + align:start position:0% +So if everything is a horn or dual horn + + + align:start position:0% +So if everything is a horn or dual horn +thing then we are happy. And next case + + align:start position:0% +thing then we are happy. And next case + + + align:start position:0% +thing then we are happy. And next case +is + + align:start position:0% + + + + align:start position:0% + +the relations are all + + align:start position:0% +the relations are all + + + align:start position:0% +the relations are all +uh 2 CNF. + + align:start position:0% +uh 2 CNF. + + + align:start position:0% +uh 2 CNF. +So this would be the two set case. If + + align:start position:0% +So this would be the two set case. If + + + align:start position:0% +So this would be the two set case. If +all the relations you're working with + + align:start position:0% +all the relations you're working with + + + align:start position:0% +all the relations you're working with +are in 2CNF then when you add them + + align:start position:0% +are in 2CNF then when you add them + + + align:start position:0% +are in 2CNF then when you add them +together you still have a 2CNF formula. + + align:start position:0% +together you still have a 2CNF formula. + + + align:start position:0% +together you still have a 2CNF formula. +So you can solve it by two set. + + align:start position:0% +So you can solve it by two set. + + + align:start position:0% +So you can solve it by two set. +And so these are all things we've seen. + + align:start position:0% +And so these are all things we've seen. + + + align:start position:0% +And so these are all things we've seen. +There's one more case we haven't seen. + + align:start position:0% +There's one more case we haven't seen. + + + align:start position:0% +There's one more case we haven't seen. +Is there a question? Yeah. + + align:start position:0% +Is there a question? Yeah. + + + align:start position:0% +Is there a question? Yeah. +Uh isn't too sad just a subcase of the + + align:start position:0% +Uh isn't too sad just a subcase of the + + + align:start position:0% +Uh isn't too sad just a subcase of the +horn and horn thing because you're + + align:start position:0% +horn and horn thing because you're + + + align:start position:0% +horn and horn thing because you're +always going to have + + align:start position:0% +always going to have + + + align:start position:0% +always going to have +It's true. Too sad is a special case of + + align:start position:0% +It's true. Too sad is a special case of + + + align:start position:0% +It's true. Too sad is a special case of +horn. So + + align:start position:0% +horn. So + + + align:start position:0% +horn. So +I don't think so. + + align:start position:0% +I don't think so. + + + align:start position:0% +I don't think so. +You could have one two positives and + + align:start position:0% +You could have one two positives and + + + align:start position:0% +You could have one two positives and +another two negatives. + + align:start position:0% +another two negatives. + + + align:start position:0% +another two negatives. +Yeah. Yeah. Oh. Ah, right. Right. Right. + + align:start position:0% +Yeah. Yeah. Oh. Ah, right. Right. Right. + + + align:start position:0% +Yeah. Yeah. Oh. Ah, right. Right. Right. +So, I see. So, 2 CNF some of the clauses + + align:start position:0% +So, I see. So, 2 CNF some of the clauses + + + align:start position:0% +So, I see. So, 2 CNF some of the clauses +are going to be horn and some of them + + align:start position:0% +are going to be horn and some of them + + + align:start position:0% +are going to be horn and some of them +are dual horn I think. So, you it + + align:start position:0% +are dual horn I think. So, you it + + + align:start position:0% +are dual horn I think. So, you it +doesn't fall into this because it's not + + align:start position:0% +doesn't fall into this because it's not + + + align:start position:0% +doesn't fall into this because it's not +all one or the other. In general, those + + align:start position:0% +all one or the other. In general, those + + + align:start position:0% +all one or the other. In general, those +combinations are bad. But two set is + + align:start position:0% +combinations are bad. But two set is + + + align:start position:0% +combinations are bad. But two set is +always okay. Good question. + + align:start position:0% + + + + align:start position:0% + +Okay. Last case + + align:start position:0% + + + + align:start position:0% + +is some linear algebra. + + align:start position:0% + + + + align:start position:0% + +This is one other easy case of SAT which + + align:start position:0% +This is one other easy case of SAT which + + + align:start position:0% +This is one other easy case of SAT which +doesn't come up very often. So I didn't + + align:start position:0% +doesn't come up very often. So I didn't + + + align:start position:0% +doesn't come up very often. So I didn't +write it as a separate one. Yeah. + + align:start position:0% + + + + align:start position:0% + +Uh so imagine equations like this. I + + align:start position:0% +Uh so imagine equations like this. I + + + align:start position:0% +Uh so imagine equations like this. I +take some number of variables. I exor + + align:start position:0% +take some number of variables. I exor + + + align:start position:0% +take some number of variables. I exor +them together and I say that should be + + align:start position:0% +them together and I say that should be + + + align:start position:0% +them together and I say that should be +zero. Or similar thing I set it equal to + + align:start position:0% +zero. Or similar thing I set it equal to + + + align:start position:0% +zero. Or similar thing I set it equal to +one. Those are what I would call a + + align:start position:0% +one. Those are what I would call a + + + align:start position:0% +one. Those are what I would call a +linear equation over Z mod 2. Uh because + + align:start position:0% +linear equation over Z mod 2. Uh because + + + align:start position:0% +linear equation over Z mod 2. Uh because +in Z mod 2 the finite field and two + + align:start position:0% +in Z mod 2 the finite field and two + + + align:start position:0% +in Z mod 2 the finite field and two +elements addition becomes XOR and + + align:start position:0% +elements addition becomes XOR and + + + align:start position:0% +elements addition becomes XOR and +there's no multiplication here. So + + align:start position:0% +there's no multiplication here. So + + + align:start position:0% +there's no multiplication here. So +because it's a linear system + + align:start position:0% +because it's a linear system + + + align:start position:0% +because it's a linear system +um so we can solve these things because + + align:start position:0% +um so we can solve these things because + + + align:start position:0% +um so we can solve these things because +Z2 is a finite field. Uh we can use + + align:start position:0% +Z2 is a finite field. Uh we can use + + + align:start position:0% +Z2 is a finite field. Uh we can use +Gaussian elimination. Even if I have a + + align:start position:0% +Gaussian elimination. Even if I have a + + + align:start position:0% +Gaussian elimination. Even if I have a +whole bunch of these equations, I can + + align:start position:0% +whole bunch of these equations, I can + + + align:start position:0% +whole bunch of these equations, I can +solve them all using Gaussian + + align:start position:0% +solve them all using Gaussian + + + align:start position:0% +solve them all using Gaussian +elimination. So or determine that + + align:start position:0% +elimination. So or determine that + + + align:start position:0% +elimination. So or determine that +they're unsolvable. So that's another + + align:start position:0% +they're unsolvable. So that's another + + + align:start position:0% +they're unsolvable. So that's another +easy case for for SAT to be careful + + align:start position:0% +easy case for for SAT to be careful + + + align:start position:0% +easy case for for SAT to be careful +about uh and + + align:start position:0% +about uh and + + + align:start position:0% +about uh and +theorem is if you have one of these + + align:start position:0% +theorem is if you have one of these + + + align:start position:0% +theorem is if you have one of these +situations. So you can't mix these. If + + align:start position:0% +situations. So you can't mix these. If + + + align:start position:0% +situations. So you can't mix these. If +you have one clause of this type and + + align:start position:0% +you have one clause of this type and + + + align:start position:0% +you have one clause of this type and +another clause of this type, your + + align:start position:0% +another clause of this type, your + + + align:start position:0% +another clause of this type, your +problem will be np hard. Uh so in + + align:start position:0% +problem will be np hard. Uh so in + + + align:start position:0% +problem will be np hard. Uh so in +general we say otherwise + + align:start position:0% + + + + align:start position:0% + +SAT is NP hard. + + align:start position:0% + + + + align:start position:0% + +I guess it'll actually be MP complete + + align:start position:0% +I guess it'll actually be MP complete + + + align:start position:0% +I guess it'll actually be MP complete +here the way we set it up. Uh well + + align:start position:0% +here the way we set it up. Uh well + + + align:start position:0% +here the way we set it up. Uh well +assuming the relations are checkable. + + align:start position:0% +assuming the relations are checkable. + + + align:start position:0% +assuming the relations are checkable. +So these are the only cases. This is an + + align:start position:0% +So these are the only cases. This is an + + + align:start position:0% +So these are the only cases. This is an +easy case. This is an easy case. This is + + align:start position:0% +easy case. This is an easy case. This is + + + align:start position:0% +easy case. This is an easy case. This is +an easy case. It could be that multiple + + align:start position:0% +an easy case. It could be that multiple + + + align:start position:0% +an easy case. It could be that multiple +of these things are true. Maybe your 2 + + align:start position:0% +of these things are true. Maybe your 2 + + + align:start position:0% +of these things are true. Maybe your 2 +CNF and your all horn that will also be + + align:start position:0% +CNF and your all horn that will also be + + + align:start position:0% +CNF and your all horn that will also be +polomial of course. But if none of these + + align:start position:0% +polomial of course. But if none of these + + + align:start position:0% +polomial of course. But if none of these +individually hold then your problem is n + + align:start position:0% +individually hold then your problem is n + + + align:start position:0% +individually hold then your problem is n +hard question. + + align:start position:0% +hard question. + + + align:start position:0% +hard question. +Uh so how does this generalize for like + + align:start position:0% +Uh so how does this generalize for like + + + align:start position:0% +Uh so how does this generalize for like +non- boolean fields like I'm sure the + + align:start position:0% +non- boolean fields like I'm sure the + + + align:start position:0% +non- boolean fields like I'm sure the +last one is also still true. + + align:start position:0% +last one is also still true. + + + align:start position:0% +last one is also still true. +Yeah. So we can go back to your question + + align:start position:0% +Yeah. So we can go back to your question + + + align:start position:0% +Yeah. So we can go back to your question +about three colors and the answer is I + + align:start position:0% +about three colors and the answer is I + + + align:start position:0% +about three colors and the answer is I +don't know. As far as I know there's no + + align:start position:0% +don't know. As far as I know there's no + + + align:start position:0% +don't know. As far as I know there's no +theorem of that type but there might be + + align:start position:0% +theorem of that type but there might be + + + align:start position:0% +theorem of that type but there might be +one. It's been uh 30 years. So uh it + + align:start position:0% +one. It's been uh 30 years. So uh it + + + align:start position:0% +one. It's been uh 30 years. So uh it +wouldn't be surprising. Certainly you + + align:start position:0% +wouldn't be surprising. Certainly you + + + align:start position:0% +wouldn't be surprising. Certainly you +can some of these positive results will + + align:start position:0% +can some of these positive results will + + + align:start position:0% +can some of these positive results will +generalize. Uh but I think even this one + + align:start position:0% +generalize. Uh but I think even this one + + + align:start position:0% +generalize. Uh but I think even this one +would be a little tricky. + + align:start position:0% +would be a little tricky. + + + align:start position:0% +would be a little tricky. +Max two set doesn't fall in this + + align:start position:0% +Max two set doesn't fall in this + + + align:start position:0% +Max two set doesn't fall in this +right. So in here the goal is always to + + align:start position:0% +right. So in here the goal is always to + + + align:start position:0% +right. So in here the goal is always to +satisfy all of the clauses. It's always + + align:start position:0% +satisfy all of the clauses. It's always + + + align:start position:0% +satisfy all of the clauses. It's always +the end of all the clauses. You could + + align:start position:0% +the end of all the clauses. You could + + + align:start position:0% +the end of all the clauses. You could +imagine a maxat like theorem. My guess + + align:start position:0% +imagine a maxat like theorem. My guess + + + align:start position:0% +imagine a maxat like theorem. My guess +is most problems will be hard but uh as + + align:start position:0% +is most problems will be hard but uh as + + + align:start position:0% +is most problems will be hard but uh as +far as I know there's no such theorem. + + align:start position:0% +far as I know there's no such theorem. + + + align:start position:0% +far as I know there's no such theorem. +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +Is there any way to understand this + + align:start position:0% +Is there any way to understand this + + + align:start position:0% +Is there any way to understand this +theorem as making a geometric statement + + align:start position:0% +theorem as making a geometric statement + + + align:start position:0% +theorem as making a geometric statement +about the relation being like uh convex + + align:start position:0% +about the relation being like uh convex + + + align:start position:0% +about the relation being like uh convex +in the hyper cube or something like is + + align:start position:0% +in the hyper cube or something like is + + + align:start position:0% +in the hyper cube or something like is +there any sort of convexity property + + align:start position:0% +there any sort of convexity property + + + align:start position:0% +there any sort of convexity property +encoded in this? + + align:start position:0% +encoded in this? + + + align:start position:0% +encoded in this? +Uh + + align:start position:0% +Uh + + + align:start position:0% +Uh +I don't know. I would guess no. Um I + + align:start position:0% +I don't know. I would guess no. Um I + + + align:start position:0% +I don't know. I would guess no. Um I +know there is a more modern take on this + + align:start position:0% +know there is a more modern take on this + + + align:start position:0% +know there is a more modern take on this +that is more algebraic. Uh so it's more + + align:start position:0% +that is more algebraic. Uh so it's more + + + align:start position:0% +that is more algebraic. Uh so it's more +like if you start with these things and + + align:start position:0% +like if you start with these things and + + + align:start position:0% +like if you start with these things and +you can build up in this way. Anything + + align:start position:0% +you can build up in this way. Anything + + + align:start position:0% +you can build up in this way. Anything +you can build up in this way are the + + align:start position:0% +you can build up in this way are the + + + align:start position:0% +you can build up in this way are the +polomial solvable versions of SAT. + + align:start position:0% +polomial solvable versions of SAT. + + + align:start position:0% +polomial solvable versions of SAT. +Anything you can't build up in this way + + align:start position:0% +Anything you can't build up in this way + + + align:start position:0% +Anything you can't build up in this way +is uh is empty hard. So if you're + + align:start position:0% +is uh is empty hard. So if you're + + + align:start position:0% +is uh is empty hard. So if you're +interested in that check the Wikipedia + + align:start position:0% +interested in that check the Wikipedia + + + align:start position:0% +interested in that check the Wikipedia +page for uh Schaefer's dichotomy + + align:start position:0% +page for uh Schaefer's dichotomy + + + align:start position:0% +page for uh Schaefer's dichotomy +theorem. Uh but I don't think there's a + + align:start position:0% +theorem. Uh but I don't think there's a + + + align:start position:0% +theorem. Uh but I don't think there's a +geometric interpretation. Uh, this one + + align:start position:0% +geometric interpretation. Uh, this one + + + align:start position:0% +geometric interpretation. Uh, this one +obviously has a geometric + + align:start position:0% +obviously has a geometric + + + align:start position:0% +obviously has a geometric +interpretation, but I think the others + + align:start position:0% +interpretation, but I think the others + + + align:start position:0% +interpretation, but I think the others +not would be my guess. Yeah. + + align:start position:0% +not would be my guess. Yeah. + + + align:start position:0% +not would be my guess. Yeah. +Um, so does this say something about the + + align:start position:0% +Um, so does this say something about the + + + align:start position:0% +Um, so does this say something about the +complexity of recognizing the clauses if + + align:start position:0% +complexity of recognizing the clauses if + + + align:start position:0% +complexity of recognizing the clauses if +you interpret them as a language? + + align:start position:0% +you interpret them as a language? + + + align:start position:0% +you interpret them as a language? +If I give you the formula that specifies + + align:start position:0% +If I give you the formula that specifies + + + align:start position:0% +If I give you the formula that specifies +the types of clauses, can you determine + + align:start position:0% +the types of clauses, can you determine + + + align:start position:0% +the types of clauses, can you determine +which of these is whether any of these + + align:start position:0% +which of these is whether any of these + + + align:start position:0% +which of these is whether any of these +is the case? + + align:start position:0% +is the case? + + + align:start position:0% +is the case? +Uh, I would guess, but I don't know of + + align:start position:0% +Uh, I would guess, but I don't know of + + + align:start position:0% +Uh, I would guess, but I don't know of +such a theorem. It's another good + + align:start position:0% +such a theorem. It's another good + + + align:start position:0% +such a theorem. It's another good +question. Wow, so many so many questions + + align:start position:0% +question. Wow, so many so many questions + + + align:start position:0% +question. Wow, so many so many questions +to think about here. Um, it's definitely + + align:start position:0% +to think about here. Um, it's definitely + + + align:start position:0% +to think about here. Um, it's definitely +not explicitly mentioned that I saw in + + align:start position:0% +not explicitly mentioned that I saw in + + + align:start position:0% +not explicitly mentioned that I saw in +the Schaefer paper, but it's been around + + align:start position:0% +the Schaefer paper, but it's been around + + + align:start position:0% +the Schaefer paper, but it's been around +for a while. So, people may have thought + + align:start position:0% +for a while. So, people may have thought + + + align:start position:0% +for a while. So, people may have thought +about that more. Uh, it definitely can + + align:start position:0% +about that more. Uh, it definitely can + + + align:start position:0% +about that more. Uh, it definitely can +be a little tricky to check which things + + align:start position:0% +be a little tricky to check which things + + + align:start position:0% +be a little tricky to check which things +are of this type practically. So, uh, be + + align:start position:0% +are of this type practically. So, uh, be + + + align:start position:0% +are of this type practically. So, uh, be +nice if there's an algorithm. + + align:start position:0% +nice if there's an algorithm. + + + align:start position:0% +nice if there's an algorithm. +Uh I would say + + align:start position:0% +Uh I would say + + + align:start position:0% +Uh I would say +so again practically speaking uh uh + + align:start position:0% +so again practically speaking uh uh + + + align:start position:0% +so again practically speaking uh uh +there was one hardness proof I was + + align:start position:0% +there was one hardness proof I was + + + align:start position:0% +there was one hardness proof I was +trying to generate gadgets uh + + align:start position:0% +trying to generate gadgets uh + + + align:start position:0% +trying to generate gadgets uh +computationally. So just enumerate all + + align:start position:0% +computationally. So just enumerate all + + + align:start position:0% +computationally. So just enumerate all +possible gadgets of a certain size for + + align:start position:0% +possible gadgets of a certain size for + + + align:start position:0% +possible gadgets of a certain size for +my problem and then see what formula + + align:start position:0% +my problem and then see what formula + + + align:start position:0% +my problem and then see what formula +they were representing and then we would + + align:start position:0% +they were representing and then we would + + + align:start position:0% +they were representing and then we would +take that formula do a carno map if + + align:start position:0% +take that formula do a carno map if + + + align:start position:0% +take that formula do a carno map if +you've ever done digital logic stuff and + + align:start position:0% +you've ever done digital logic stuff and + + + align:start position:0% +you've ever done digital logic stuff and +then sort of get from that you get a + + align:start position:0% +then sort of get from that you get a + + + align:start position:0% +then sort of get from that you get a +sort of nice minimal form and then we + + align:start position:0% +sort of nice minimal form and then we + + + align:start position:0% +sort of nice minimal form and then we +would uh usually we could just look at + + align:start position:0% +would uh usually we could just look at + + + align:start position:0% +would uh usually we could just look at +the map and say oh uh that's just equals + + align:start position:0% +the map and say oh uh that's just equals + + + align:start position:0% +the map and say oh uh that's just equals +or that's not equals or something we're + + align:start position:0% +or that's not equals or something we're + + + align:start position:0% +or that's not equals or something we're +hoping for. We're dreaming for one of + + align:start position:0% +hoping for. We're dreaming for one of + + + align:start position:0% +hoping for. We're dreaming for one of +these things or threes. We never got the + + align:start position:0% +these things or threes. We never got the + + + align:start position:0% +these things or threes. We never got the +gadget we wanted. U so I think with like + + align:start position:0% +gadget we wanted. U so I think with like + + + align:start position:0% +gadget we wanted. U so I think with like +a carno map you could do this but that's + + align:start position:0% +a carno map you could do this but that's + + + align:start position:0% +a carno map you could do this but that's +exponential time. + + align:start position:0% +exponential time. + + + align:start position:0% +exponential time. +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +Uh yeah. So I don't know for sure + + align:start position:0% +Uh yeah. So I don't know for sure + + + align:start position:0% +Uh yeah. So I don't know for sure +I should probably check the algebraic + + align:start position:0% +I should probably check the algebraic + + + align:start position:0% +I should probably check the algebraic +view that might + + align:start position:0% +view that might + + + align:start position:0% +view that might +that's a clever approach though. + + align:start position:0% +that's a clever approach though. + + + align:start position:0% +that's a clever approach though. +Yeah to do things computationally. + + align:start position:0% +Yeah to do things computationally. + + + align:start position:0% +Yeah to do things computationally. +It's definitely helpful because of + + align:start position:0% +It's definitely helpful because of + + + align:start position:0% +It's definitely helpful because of +course computationally you can only look + + align:start position:0% +course computationally you can only look + + + align:start position:0% +course computationally you can only look +at small gadgets but hopefully there is + + align:start position:0% +at small gadgets but hopefully there is + + + align:start position:0% +at small gadgets but hopefully there is +a small gadget and then a nice proof. So + + align:start position:0% +a small gadget and then a nice proof. So + + + align:start position:0% +a small gadget and then a nice proof. So +why do the hard work of generating them + + align:start position:0% +why do the hard work of generating them + + + align:start position:0% +why do the hard work of generating them +yourself when the computer could do it + + align:start position:0% +yourself when the computer could do it + + + align:start position:0% +yourself when the computer could do it +for you? Doesn't work for all problems. + + align:start position:0% +for you? Doesn't work for all problems. + + + align:start position:0% +for you? Doesn't work for all problems. +It needs your problems need to be sort + + align:start position:0% +It needs your problems need to be sort + + + align:start position:0% +It needs your problems need to be sort +of locally isolatable to not worry about + + align:start position:0% +of locally isolatable to not worry about + + + align:start position:0% +of locally isolatable to not worry about +the big picture. + + align:start position:0% +the big picture. + + + align:start position:0% +the big picture. +Other questions? + + align:start position:0% +Other questions? + + + align:start position:0% +Other questions? +Cool. Um + + align:start position:0% +Cool. Um + + + align:start position:0% +Cool. Um +well that's all the versions of SAT you + + align:start position:0% +well that's all the versions of SAT you + + + align:start position:0% +well that's all the versions of SAT you +need to know. Um because here we have a + + align:start position:0% +need to know. Um because here we have a + + + align:start position:0% +need to know. Um because here we have a +universality theorem. Um there maybe + + align:start position:0% +universality theorem. Um there maybe + + + align:start position:0% +universality theorem. Um there maybe +will be another one or two that we bump + + align:start position:0% +will be another one or two that we bump + + + align:start position:0% +will be another one or two that we bump +into, but these are the the things you + + align:start position:0% +into, but these are the the things you + + + align:start position:0% +into, but these are the the things you +should all know. It's really helpful + + align:start position:0% +should all know. It's really helpful + + + align:start position:0% +should all know. It's really helpful +when doing a proof to not have to worry + + align:start position:0% +when doing a proof to not have to worry + + + align:start position:0% +when doing a proof to not have to worry +about which version of threesat you even + + align:start position:0% +about which version of threesat you even + + + align:start position:0% +about which version of threesat you even +are going to use and just know that + + align:start position:0% +are going to use and just know that + + + align:start position:0% +are going to use and just know that +these are all out here so that when you + + align:start position:0% +these are all out here so that when you + + + align:start position:0% +these are all out here so that when you +find a gadget that happens to match one + + align:start position:0% +find a gadget that happens to match one + + + align:start position:0% +find a gadget that happens to match one +of them, you say, "Oh, well, I meant to + + align:start position:0% +of them, you say, "Oh, well, I meant to + + + align:start position:0% +of them, you say, "Oh, well, I meant to +do a reduction from not all equal + + align:start position:0% +do a reduction from not all equal + + + align:start position:0% +do a reduction from not all equal +threes." Um, that that's why I wanted to + + align:start position:0% +threes." Um, that that's why I wanted to + + + align:start position:0% +threes." Um, that that's why I wanted to +tell you all these although I know it's + + align:start position:0% +tell you all these although I know it's + + + align:start position:0% +tell you all these although I know it's +a lot to take in all at once. Um, let's + + align:start position:0% +a lot to take in all at once. Um, let's + + + align:start position:0% +a lot to take in all at once. Um, let's +do some reductions finally. + + align:start position:0% + + + + align:start position:0% + +NP hardcore time. + + align:start position:0% +NP hardcore time. + + + align:start position:0% +NP hardcore time. +So, uh, + + align:start position:0% +So, uh, + + + align:start position:0% +So, uh, +the first one + + align:start position:0% +the first one + + + align:start position:0% +the first one +I had actually never seen before, um, + + align:start position:0% +I had actually never seen before, um, + + + align:start position:0% +I had actually never seen before, um, +but it's in Schaefer's paper, so I + + align:start position:0% +but it's in Schaefer's paper, so I + + + align:start position:0% +but it's in Schaefer's paper, so I +thought it would be fun to cover. + + align:start position:0% + + + + align:start position:0% + +Here's a problem which is MP hard and we + + align:start position:0% +Here's a problem which is MP hard and we + + + align:start position:0% +Here's a problem which is MP hard and we +will actually prove this one. MP hard + + align:start position:0% +will actually prove this one. MP hard + + + align:start position:0% +will actually prove this one. MP hard +two colorable perfect matching. + + align:start position:0% +two colorable perfect matching. + + + align:start position:0% +two colorable perfect matching. +Let's say you're given a planer + + align:start position:0% + + + + align:start position:0% + +three regular graph. Every vertex has + + align:start position:0% +three regular graph. Every vertex has + + + align:start position:0% +three regular graph. Every vertex has +degree three. + + align:start position:0% + + + + align:start position:0% + +And what you'd like to do is two color + + align:start position:0% +And what you'd like to do is two color + + + align:start position:0% +And what you'd like to do is two color +the vertices red and blue + + align:start position:0% + + + + align:start position:0% + +uh such that + + align:start position:0% + + + + align:start position:0% + +every vertex has exactly one + + align:start position:0% +every vertex has exactly one + + + align:start position:0% +every vertex has exactly one +neighbor of the same color. + + align:start position:0% + + + + align:start position:0% + +Okay. So, uh if you look at a vertex and + + align:start position:0% +Okay. So, uh if you look at a vertex and + + + align:start position:0% +Okay. So, uh if you look at a vertex and +it has three neighbors, + + align:start position:0% + + + + align:start position:0% + +then uh let's say we color this guy red + + align:start position:0% +then uh let's say we color this guy red + + + align:start position:0% +then uh let's say we color this guy red +should be exactly one neighbor that's + + align:start position:0% +should be exactly one neighbor that's + + + align:start position:0% +should be exactly one neighbor that's +red. And so you can think of this edge + + align:start position:0% +red. And so you can think of this edge + + + align:start position:0% +red. And so you can think of this edge +as being red. And then the red edges + + align:start position:0% +as being red. And then the red edges + + + align:start position:0% +as being red. And then the red edges +will form a perfect matching in the + + align:start position:0% +will form a perfect matching in the + + + align:start position:0% +will form a perfect matching in the +graph. Every every vertex will be + + align:start position:0% +graph. Every every vertex will be + + + align:start position:0% +graph. Every every vertex will be +instant to exactly one edge. So that's + + align:start position:0% +instant to exactly one edge. So that's + + + align:start position:0% +instant to exactly one edge. So that's +the two-colorable perfect matching. It's + + align:start position:0% +the two-colorable perfect matching. It's + + + align:start position:0% +the two-colorable perfect matching. It's +kind of well I'm sorry. The red edges + + align:start position:0% +kind of well I'm sorry. The red edges + + + align:start position:0% +kind of well I'm sorry. The red edges +form a perfect matching on the red nodes + + align:start position:0% +form a perfect matching on the red nodes + + + align:start position:0% +form a perfect matching on the red nodes +and the black or the white edges I guess + + align:start position:0% +and the black or the white edges I guess + + + align:start position:0% +and the black or the white edges I guess +form a perfect matching on the white + + align:start position:0% +form a perfect matching on the white + + + align:start position:0% +form a perfect matching on the white +nodes, black nodes, whatever. Uh so it's + + align:start position:0% +nodes, black nodes, whatever. Uh so it's + + + align:start position:0% +nodes, black nodes, whatever. Uh so it's +like two perfect matchings, one of each + + align:start position:0% +like two perfect matchings, one of each + + + align:start position:0% +like two perfect matchings, one of each +uh one in each color class. Uh so that's + + align:start position:0% +uh one in each color class. Uh so that's + + + align:start position:0% +uh one in each color class. Uh so that's +a nice problem. You can think of it as + + align:start position:0% +a nice problem. You can think of it as + + + align:start position:0% +a nice problem. You can think of it as +SAT in a sense. It's again just a local + + align:start position:0% +SAT in a sense. It's again just a local + + + align:start position:0% +SAT in a sense. It's again just a local +constraint on the nodes. Uh + + align:start position:0% +constraint on the nodes. Uh + + + align:start position:0% +constraint on the nodes. Uh +and so you can think of this as being a + + align:start position:0% +and so you can think of this as being a + + + align:start position:0% +and so you can think of this as being a +clause involving those four guys. Um I + + align:start position:0% +clause involving those four guys. Um I + + + align:start position:0% +clause involving those four guys. Um I +think if I unless I did something wrong, + + align:start position:0% +think if I unless I did something wrong, + + + align:start position:0% +think if I unless I did something wrong, +you can think of it as um to enforce + + align:start position:0% +you can think of it as um to enforce + + + align:start position:0% +you can think of it as um to enforce +or a special version of two enforce + + align:start position:0% +or a special version of two enforce + + + align:start position:0% +or a special version of two enforce +because uh + + align:start position:0% +because uh + + + align:start position:0% +because uh +right yeah so um this one if this node + + align:start position:0% +right yeah so um this one if this node + + + align:start position:0% +right yeah so um this one if this node +let's say red is true. So what we're + + align:start position:0% +let's say red is true. So what we're + + + align:start position:0% +let's say red is true. So what we're +saying is if this guy is true among + + align:start position:0% +saying is if this guy is true among + + + align:start position:0% +saying is if this guy is true among +these four nodes there should be exactly + + align:start position:0% +these four nodes there should be exactly + + + align:start position:0% +these four nodes there should be exactly +one other one that is red. On the other + + align:start position:0% +one other one that is red. On the other + + + align:start position:0% +one other one that is red. On the other +hand if this is black there should be + + align:start position:0% +hand if this is black there should be + + + align:start position:0% +hand if this is black there should be +exactly one of them that is black and so + + align:start position:0% +exactly one of them that is black and so + + + align:start position:0% +exactly one of them that is black and so +the other two should be red. So in all + + align:start position:0% +the other two should be red. So in all + + + align:start position:0% +the other two should be red. So in all +cases it's exactly two and four of them + + align:start position:0% +cases it's exactly two and four of them + + + align:start position:0% +cases it's exactly two and four of them +are red and it's symmetric between red + + align:start position:0% +are red and it's symmetric between red + + + align:start position:0% +are red and it's symmetric between red +and black. So that seems good. So this + + align:start position:0% +and black. So that seems good. So this + + + align:start position:0% +and black. So that seems good. So this +is a special case of two enforce. So in + + align:start position:0% +is a special case of two enforce. So in + + + align:start position:0% +is a special case of two enforce. So in +case you're wondering whether to enforce + + align:start position:0% +case you're wondering whether to enforce + + + align:start position:0% +case you're wondering whether to enforce +is hard uh here it is. And I have a + + align:start position:0% +is hard uh here it is. And I have a + + + align:start position:0% +is hard uh here it is. And I have a +um the original reduction by Schaefer + + align:start position:0% +um the original reduction by Schaefer + + + align:start position:0% +um the original reduction by Schaefer +here. Um do I have any notes? No, that + + align:start position:0% +here. Um do I have any notes? No, that + + + align:start position:0% +here. Um do I have any notes? No, that +would be too easy. So uh + + align:start position:0% + + + + align:start position:0% + +here's a gadget and here's another + + align:start position:0% +here's a gadget and here's another + + + align:start position:0% +here's a gadget and here's another +gadget. And then they're pasted + + align:start position:0% +gadget. And then they're pasted + + + align:start position:0% +gadget. And then they're pasted +together. So uh and I should mention + + align:start position:0% +together. So uh and I should mention + + + align:start position:0% +together. So uh and I should mention +uh so Schaefer claims that if you have a + + align:start position:0% +uh so Schaefer claims that if you have a + + + align:start position:0% +uh so Schaefer claims that if you have a +planer three regular graph, this problem + + align:start position:0% +planer three regular graph, this problem + + + align:start position:0% +planer three regular graph, this problem +is hard. But he doesn't prove it. He + + align:start position:0% +is hard. But he doesn't prove it. He + + + align:start position:0% +is hard. But he doesn't prove it. He +just should proves it for general + + align:start position:0% +just should proves it for general + + + align:start position:0% +just should proves it for general +graphs. So I'm only going to prove it + + align:start position:0% +graphs. So I'm only going to prove it + + + align:start position:0% +graphs. So I'm only going to prove it +for general graphs. Maybe we can think + + align:start position:0% +for general graphs. Maybe we can think + + + align:start position:0% +for general graphs. Maybe we can think +about the planer three regular case but + + align:start position:0% +about the planer three regular case but + + + align:start position:0% +about the planer three regular case but +not right here. So this will not this + + align:start position:0% +not right here. So this will not this + + + align:start position:0% +not right here. So this will not this +will just make a graph uh instance to + + align:start position:0% +will just make a graph uh instance to + + + align:start position:0% +will just make a graph uh instance to +that problem. So this gadget this is a + + align:start position:0% +that problem. So this gadget this is a + + + align:start position:0% +that problem. So this gadget this is a +K4 on and we're only distinguishing X Y + + align:start position:0% +K4 on and we're only distinguishing X Y + + + align:start position:0% +K4 on and we're only distinguishing X Y +and Z and it has to form there's going + + align:start position:0% +and Z and it has to form there's going + + + align:start position:0% +and Z and it has to form there's going +to be one red edge and one black edge. + + align:start position:0% +to be one red edge and one black edge. + + + align:start position:0% +to be one red edge and one black edge. +So maybe like this and like this or like + + align:start position:0% +So maybe like this and like this or like + + + align:start position:0% +So maybe like this and like this or like +this or like this. It's going to be a + + align:start position:0% +this or like this. It's going to be a + + + align:start position:0% +this or like this. It's going to be a +rotation of one of those assignments. So + + align:start position:0% +rotation of one of those assignments. So + + + align:start position:0% +rotation of one of those assignments. So +I believe the claim is X, Y, and Z just + + align:start position:0% +I believe the claim is X, Y, and Z just + + + align:start position:0% +I believe the claim is X, Y, and Z just +looking at those three vertices should + + align:start position:0% +looking at those three vertices should + + + align:start position:0% +looking at those three vertices should +be not all equal. + + align:start position:0% +be not all equal. + + + align:start position:0% +be not all equal. +Okay, if if two of them are red by + + align:start position:0% +Okay, if if two of them are red by + + + align:start position:0% +Okay, if if two of them are red by +symmetry is lots of rotational symmetry + + align:start position:0% +symmetry is lots of rotational symmetry + + + align:start position:0% +symmetry is lots of rotational symmetry +here. So maybe two of them are red and + + align:start position:0% +here. So maybe two of them are red and + + + align:start position:0% +here. So maybe two of them are red and +one is black, then this guy can be set + + align:start position:0% +one is black, then this guy can be set + + + align:start position:0% +one is black, then this guy can be set +black and you're happy. It's actually + + align:start position:0% +black and you're happy. It's actually + + + align:start position:0% +black and you're happy. It's actually +forced for that guy to be black. If two + + align:start position:0% +forced for that guy to be black. If two + + + align:start position:0% +forced for that guy to be black. If two +of them are black, then this then these + + align:start position:0% +of them are black, then this then these + + + align:start position:0% +of them are black, then this then these +two must be red. And if all three of + + align:start position:0% +two must be red. And if all three of + + + align:start position:0% +two must be red. And if all three of +these are black, you're toast because + + align:start position:0% +these are black, you're toast because + + + align:start position:0% +these are black, you're toast because +you should have two of each. Uh and if + + align:start position:0% +you should have two of each. Uh and if + + + align:start position:0% +you should have two of each. Uh and if +all three of them are are red, you're in + + align:start position:0% +all three of them are are red, you're in + + + align:start position:0% +all three of them are are red, you're in +trouble. So this is a not all equal + + align:start position:0% +trouble. So this is a not all equal + + + align:start position:0% +trouble. So this is a not all equal +clause gadget for this problem. So we're + + align:start position:0% +clause gadget for this problem. So we're + + + align:start position:0% +clause gadget for this problem. So we're +going to reduce from not all equal + + align:start position:0% +going to reduce from not all equal + + + align:start position:0% +going to reduce from not all equal +threes to two colorable perfect + + align:start position:0% +threes to two colorable perfect + + + align:start position:0% +threes to two colorable perfect +matching. So we're representing a not + + align:start position:0% +matching. So we're representing a not + + + align:start position:0% +matching. So we're representing a not +all equal clause like this. And now what + + align:start position:0% +all equal clause like this. And now what + + + align:start position:0% +all equal clause like this. And now what +we need is to the ability to copy data. + + align:start position:0% +we need is to the ability to copy data. + + + align:start position:0% +we need is to the ability to copy data. +Right? So these are three variables that + + align:start position:0% +Right? So these are three variables that + + + align:start position:0% +Right? So these are three variables that +at the moment yeah they can be red or + + align:start position:0% +at the moment yeah they can be red or + + + align:start position:0% +at the moment yeah they can be red or +blue. But what we need is that the same + + align:start position:0% +blue. But what we need is that the same + + + align:start position:0% +blue. But what we need is that the same +x i can appear in multiple clauses + + align:start position:0% +x i can appear in multiple clauses + + + align:start position:0% +x i can appear in multiple clauses +because we have a bipartite graph. If + + align:start position:0% +because we have a bipartite graph. If + + + align:start position:0% +because we have a bipartite graph. If +every variable appeared in only one + + align:start position:0% +every variable appeared in only one + + + align:start position:0% +every variable appeared in only one +clause problem would be really easy. + + align:start position:0% +clause problem would be really easy. + + + align:start position:0% +clause problem would be really easy. +So uh that's what this gadget does. The + + align:start position:0% +So uh that's what this gadget does. The + + + align:start position:0% +So uh that's what this gadget does. The +claim is this gadget copies a value. And + + align:start position:0% +claim is this gadget copies a value. And + + + align:start position:0% +claim is this gadget copies a value. And +this I think required. So it says these + + align:start position:0% +this I think required. So it says these + + + align:start position:0% +this I think required. So it says these +two guys must have the same color. And + + align:start position:0% +two guys must have the same color. And + + + align:start position:0% +two guys must have the same color. And +so what you do is you just have for each + + align:start position:0% +so what you do is you just have for each + + + align:start position:0% +so what you do is you just have for each +clause you have one of these not for + + align:start position:0% +clause you have one of these not for + + + align:start position:0% +clause you have one of these not for +each not all equal clause you have one + + align:start position:0% +each not all equal clause you have one + + + align:start position:0% +each not all equal clause you have one +of these not all equal gadgets. And then + + align:start position:0% +of these not all equal gadgets. And then + + + align:start position:0% +of these not all equal gadgets. And then +uh whenever you have two variables that + + align:start position:0% +uh whenever you have two variables that + + + align:start position:0% +uh whenever you have two variables that +are supposed to be the same thing here + + align:start position:0% +are supposed to be the same thing here + + + align:start position:0% +are supposed to be the same thing here +it's x and x and our terminology x i and + + align:start position:0% +it's x and x and our terminology x i and + + + align:start position:0% +it's x and x and our terminology x i and +x i. Then you're just going to connect + + align:start position:0% +x i. Then you're just going to connect + + + align:start position:0% +x i. Then you're just going to connect +them with this gadget and that will + + align:start position:0% +them with this gadget and that will + + + align:start position:0% +them with this gadget and that will +force them to be equal. Or over here we + + align:start position:0% +force them to be equal. Or over here we + + + align:start position:0% +force them to be equal. Or over here we +have y and y. So here's the r here is + + align:start position:0% +have y and y. So here's the r here is + + + align:start position:0% +have y and y. So here's the r here is +not all equal and our terminology be nae + + align:start position:0% +not all equal and our terminology be nae + + + align:start position:0% +not all equal and our terminology be nae +xxy and yzu. This would represent that + + align:start position:0% +xxy and yzu. This would represent that + + + align:start position:0% +xxy and yzu. This would represent that +formula. Uh so the thing to check which + + align:start position:0% +formula. Uh so the thing to check which + + + align:start position:0% +formula. Uh so the thing to check which +I will leave as an exercise because it's + + align:start position:0% +I will leave as an exercise because it's + + + align:start position:0% +I will leave as an exercise because it's +seems at least I couldn't find a clean + + align:start position:0% +seems at least I couldn't find a clean + + + align:start position:0% +seems at least I couldn't find a clean +way to do it. It seems a little bit + + align:start position:0% +way to do it. It seems a little bit + + + align:start position:0% +way to do it. It seems a little bit +tedious that this forces equality + + align:start position:0% +tedious that this forces equality + + + align:start position:0% +tedious that this forces equality +between the two ends with uh not + + align:start position:0% +between the two ends with uh not + + + align:start position:0% +between the two ends with uh not +providing any other constraints. + + align:start position:0% + + + + align:start position:0% + +So that was a simple proof, one of few + + align:start position:0% +So that was a simple proof, one of few + + + align:start position:0% +So that was a simple proof, one of few +simple proofs. Still some cases to + + align:start position:0% +simple proofs. Still some cases to + + + align:start position:0% +simple proofs. Still some cases to +check, but yeah. + + align:start position:0% +check, but yeah. + + + align:start position:0% +check, but yeah. +Um you wait, you said it was general + + align:start position:0% +Um you wait, you said it was general + + + align:start position:0% +Um you wait, you said it was general +graphs. They don't have to + + align:start position:0% +graphs. They don't have to + + + align:start position:0% +graphs. They don't have to +right. This is general graphs. Um + + align:start position:0% +right. This is general graphs. Um + + + align:start position:0% +right. This is general graphs. Um +so you might say what about planer three + + align:start position:0% +so you might say what about planer three + + + align:start position:0% +so you might say what about planer three +regular graphs. Uh planer not all equal + + align:start position:0% +regular graphs. Uh planer not all equal + + + align:start position:0% +regular graphs. Uh planer not all equal +three set. When this graph is planer uh + + align:start position:0% +three set. When this graph is planer uh + + + align:start position:0% +three set. When this graph is planer uh +when the bipartite graph is planer is + + align:start position:0% +when the bipartite graph is planer is + + + align:start position:0% +when the bipartite graph is planer is +actually easy to solve polomial. So uh + + align:start position:0% +actually easy to solve polomial. So uh + + + align:start position:0% +actually easy to solve polomial. So uh +you can't you you can't reduce from + + align:start position:0% +you can't you you can't reduce from + + + align:start position:0% +you can't you you can't reduce from +plane or not equal 3AT because it's + + align:start position:0% +plane or not equal 3AT because it's + + + align:start position:0% +plane or not equal 3AT because it's +easy. Uh but I would guess that in this + + align:start position:0% +easy. Uh but I would guess that in this + + + align:start position:0% +easy. Uh but I would guess that in this +situation and we just proved this is a + + align:start position:0% +situation and we just proved this is a + + + align:start position:0% +situation and we just proved this is a +more general problem than not equal 3AT. + + align:start position:0% +more general problem than not equal 3AT. + + + align:start position:0% +more general problem than not equal 3AT. +What we would need at this point is a + + align:start position:0% +What we would need at this point is a + + + align:start position:0% +What we would need at this point is a +crossover gadget so that when in this + + align:start position:0% +crossover gadget so that when in this + + + align:start position:0% +crossover gadget so that when in this +this thing is going to end up with + + align:start position:0% +this thing is going to end up with + + + align:start position:0% +this thing is going to end up with +crossings. If there's a gadget that just + + align:start position:0% +crossings. If there's a gadget that just + + + align:start position:0% +crossings. If there's a gadget that just +communicates the information across the + + align:start position:0% +communicates the information across the + + + align:start position:0% +communicates the information across the +crossover without any other constraints + + align:start position:0% +crossover without any other constraints + + + align:start position:0% +crossover without any other constraints +then we can just plug that in and get + + align:start position:0% +then we can just plug that in and get + + + align:start position:0% +then we can just plug that in and get +rid of all crossings. Then we have a + + align:start position:0% +rid of all crossings. Then we have a + + + align:start position:0% +rid of all crossings. Then we have a +planer graph and that would prove this + + align:start position:0% +planer graph and that would prove this + + + align:start position:0% +planer graph and that would prove this +part. And then the other part is that we + + align:start position:0% +part. And then the other part is that we + + + align:start position:0% +part. And then the other part is that we +have highderee nodes here. And so I'm + + align:start position:0% +have highderee nodes here. And so I'm + + + align:start position:0% +have highderee nodes here. And so I'm +guessing Schaefer had in mind a gadget + + align:start position:0% +guessing Schaefer had in mind a gadget + + + align:start position:0% +guessing Schaefer had in mind a gadget +that takes a high degree node and splits + + align:start position:0% +that takes a high degree node and splits + + + align:start position:0% +that takes a high degree node and splits +it up into lots of little lower degree + + align:start position:0% +it up into lots of little lower degree + + + align:start position:0% +it up into lots of little lower degree +nodes, degree three nodes that simulates + + align:start position:0% +nodes, degree three nodes that simulates + + + align:start position:0% +nodes, degree three nodes that simulates +the same effect. But I don't know either + + align:start position:0% +the same effect. But I don't know either + + + align:start position:0% +the same effect. But I don't know either +gadget. But that would be my guess on + + align:start position:0% +gadget. But that would be my guess on + + + align:start position:0% +gadget. But that would be my guess on +how to that's what you that would be the + + align:start position:0% +how to that's what you that would be the + + + align:start position:0% +how to that's what you that would be the +obvious approach of how to proceed to + + align:start position:0% +obvious approach of how to proceed to + + + align:start position:0% +obvious approach of how to proceed to +get that theorem. Yeah, + + align:start position:0% +get that theorem. Yeah, + + + align:start position:0% +get that theorem. Yeah, +the other gadget is just 1B. + + align:start position:0% +the other gadget is just 1B. + + + align:start position:0% +the other gadget is just 1B. +Split a node into degree three copies + + align:start position:0% +Split a node into degree three copies + + + align:start position:0% +Split a node into degree three copies +connected by uh that gadget. + + align:start position:0% +connected by uh that gadget. + + + align:start position:0% +connected by uh that gadget. +Okay, good. One gadget down. Now we just + + align:start position:0% +Okay, good. One gadget down. Now we just + + + align:start position:0% +Okay, good. One gadget down. Now we just +need a crossover. + + align:start position:0% +need a crossover. + + + align:start position:0% +need a crossover. +Um, other questions. + + align:start position:0% + + + + align:start position:0% + +All right. Um, I want to talk about two + + align:start position:0% +All right. Um, I want to talk about two + + + align:start position:0% +All right. Um, I want to talk about two +families of problems. Proof hardness for + + align:start position:0% +families of problems. Proof hardness for + + + align:start position:0% +families of problems. Proof hardness for +two families of problems. Next one is uh + + align:start position:0% +two families of problems. Next one is uh + + + align:start position:0% +two families of problems. Next one is uh +called Pushing Blocks. Um these come up + + align:start position:0% +called Pushing Blocks. Um these come up + + + align:start position:0% +called Pushing Blocks. Um these come up +in lots of different video games. Uh one + + align:start position:0% +in lots of different video games. Uh one + + + align:start position:0% +in lots of different video games. Uh one +of the first I think is called Sokaban. + + align:start position:0% +of the first I think is called Sokaban. + + + align:start position:0% +of the first I think is called Sokaban. +Uh this goes back to 1984. And this is I + + align:start position:0% +Uh this goes back to 1984. And this is I + + + align:start position:0% +Uh this goes back to 1984. And this is I +believe the original CGA graphics for + + align:start position:0% +believe the original CGA graphics for + + + align:start position:0% +believe the original CGA graphics for +Socabon. Um and so you may have played + + align:start position:0% +Socabon. Um and so you may have played + + + align:start position:0% +Socabon. Um and so you may have played +Socon. I think it's in Emacs and it's + + align:start position:0% +Socon. I think it's in Emacs and it's + + + align:start position:0% +Socon. I think it's in Emacs and it's +all over the place. Tons of + + align:start position:0% +all over the place. Tons of + + + align:start position:0% +all over the place. Tons of +implementations uh on it. You you are a + + align:start position:0% +implementations uh on it. You you are a + + + align:start position:0% +implementations uh on it. You you are a +warehouseman. That is what sukaban means + + align:start position:0% +warehouseman. That is what sukaban means + + + align:start position:0% +warehouseman. That is what sukaban means +literally in Japanese. And you have + + align:start position:0% +literally in Japanese. And you have + + + align:start position:0% +literally in Japanese. And you have +these boxes. They're all one by one + + align:start position:0% +these boxes. They're all one by one + + + align:start position:0% +these boxes. They're all one by one +boxes. You are one by one. There are + + align:start position:0% +boxes. You are one by one. There are + + + align:start position:0% +boxes. You are one by one. There are +some bricks which cannot be moved. Uh + + align:start position:0% +some bricks which cannot be moved. Uh + + + align:start position:0% +some bricks which cannot be moved. Uh +you have some target locations. And your + + align:start position:0% +you have some target locations. And your + + + align:start position:0% +you have some target locations. And your +poor job is to move all these boxes into + + align:start position:0% +poor job is to move all these boxes into + + + align:start position:0% +poor job is to move all these boxes into +the target locations or rather every + + align:start position:0% +the target locations or rather every + + + align:start position:0% +the target locations or rather every +target location must be covered by + + align:start position:0% +target location must be covered by + + + align:start position:0% +target location must be covered by +exactly one box. Boxes can overlap each + + align:start position:0% +exactly one box. Boxes can overlap each + + + align:start position:0% +exactly one box. Boxes can overlap each +other. You can push a box but you can + + align:start position:0% +other. You can push a box but you can + + + align:start position:0% +other. You can push a box but you can +only push one at a time because you're + + align:start position:0% +only push one at a time because you're + + + align:start position:0% +only push one at a time because you're +not that strong. So you could not, for + + align:start position:0% +not that strong. So you could not, for + + + align:start position:0% +not that strong. So you could not, for +example, push left here. But in general, + + align:start position:0% +example, push left here. But in general, + + + align:start position:0% +example, push left here. But in general, +your inputs are up, down, left, and + + align:start position:0% +your inputs are up, down, left, and + + + align:start position:0% +your inputs are up, down, left, and +right. Uh up, up, down, down, left, + + align:start position:0% +right. Uh up, up, down, down, left, + + + align:start position:0% +right. Uh up, up, down, down, left, +right, left, right. No. Um, and you + + align:start position:0% +right, left, right. No. Um, and you + + + align:start position:0% +right, left, right. No. Um, and you +can't you can only push one block at a + + align:start position:0% +can't you can only push one block at a + + + align:start position:0% +can't you can only push one block at a +time. So if you push a block into a + + align:start position:0% +time. So if you push a block into a + + + align:start position:0% +time. So if you push a block into a +corner, it's never going to move again. + + align:start position:0% +corner, it's never going to move again. + + + align:start position:0% +corner, it's never going to move again. +So often you have to hit reset. There's + + align:start position:0% +So often you have to hit reset. There's + + + align:start position:0% +So often you have to hit reset. There's +a lot of ways to get stuck, but this is + + align:start position:0% +a lot of ways to get stuck, but this is + + + align:start position:0% +a lot of ways to get stuck, but this is +a solvable instance. I think it's level + + align:start position:0% +a solvable instance. I think it's level + + + align:start position:0% +a solvable instance. I think it's level +five in the original game. + + align:start position:0% +five in the original game. + + + align:start position:0% +five in the original game. +Uh, so this got started a huge family of + + align:start position:0% +Uh, so this got started a huge family of + + + align:start position:0% +Uh, so this got started a huge family of +uh problems. There are tons of other + + align:start position:0% +uh problems. There are tons of other + + + align:start position:0% +uh problems. There are tons of other +video games that have pushing blocks + + align:start position:0% +video games that have pushing blocks + + + align:start position:0% +video games that have pushing blocks +problems. This is one in Legend of Zelda + + align:start position:0% +problems. This is one in Legend of Zelda + + + align:start position:0% +problems. This is one in Legend of Zelda +Minish Cap, which I think is a Game Boy + + align:start position:0% +Minish Cap, which I think is a Game Boy + + + align:start position:0% +Minish Cap, which I think is a Game Boy +Advance game. Uh, it's been a while + + align:start position:0% +Advance game. Uh, it's been a while + + + align:start position:0% +Advance game. Uh, it's been a while +since I played this one, but here is a + + align:start position:0% +since I played this one, but here is a + + + align:start position:0% +since I played this one, but here is a +level where you have it's it's uh in + + align:start position:0% +level where you have it's it's uh in + + + align:start position:0% +level where you have it's it's uh in +perspective a little bit, but these are + + align:start position:0% +perspective a little bit, but these are + + + align:start position:0% +perspective a little bit, but these are +this is really a 2D problem. Everything + + align:start position:0% +this is really a 2D problem. Everything + + + align:start position:0% +this is really a 2D problem. Everything +is one by one, believe me. Um, you have + + align:start position:0% +is one by one, believe me. Um, you have + + + align:start position:0% +is one by one, believe me. Um, you have +one by one blocks. You're on ice, so if + + align:start position:0% +one by one blocks. You're on ice, so if + + + align:start position:0% +one by one blocks. You're on ice, so if +you ever push a block, it will slide off + + align:start position:0% +you ever push a block, it will slide off + + + align:start position:0% +you ever push a block, it will slide off +to infinity unless it hits something + + align:start position:0% +to infinity unless it hits something + + + align:start position:0% +to infinity unless it hits something +else like a block. Um, and your goal is + + align:start position:0% +else like a block. Um, and your goal is + + + align:start position:0% +else like a block. Um, and your goal is +to get a block here. + + align:start position:0% +to get a block here. + + + align:start position:0% +to get a block here. +Okay. Anyone see how to do it? + + align:start position:0% + + + + align:start position:0% + +Can you walk? + + align:start position:0% +Can you walk? + + + align:start position:0% +Can you walk? +This is a lot like ricochet robots. + + align:start position:0% +This is a lot like ricochet robots. + + + align:start position:0% +This is a lot like ricochet robots. +Yeah. Uh, you can walk wherever you + + align:start position:0% +Yeah. Uh, you can walk wherever you + + + align:start position:0% +Yeah. Uh, you can walk wherever you +want. Uh, that there is no block. So, + + align:start position:0% +want. Uh, that there is no block. So, + + + align:start position:0% +want. Uh, that there is no block. So, +there's lots of free space in this case. + + align:start position:0% +there's lots of free space in this case. + + + align:start position:0% +there's lots of free space in this case. +So, you can push this guy down and then + + align:start position:0% +So, you can push this guy down and then + + + align:start position:0% +So, you can push this guy down and then +push it over and then push it up. It's + + align:start position:0% +push it over and then push it up. It's + + + align:start position:0% +push it over and then push it up. It's +actually not that hard. At some point I + + align:start position:0% +actually not that hard. At some point I + + + align:start position:0% +actually not that hard. At some point I +was thinking well maybe I should stack + + align:start position:0% +was thinking well maybe I should stack + + + align:start position:0% +was thinking well maybe I should stack +up three here so it ends up but no it's + + align:start position:0% +up three here so it ends up but no it's + + + align:start position:0% +up three here so it ends up but no it's +just uh three pushes and you're done. Um + + align:start position:0% +just uh three pushes and you're done. Um + + + align:start position:0% +just uh three pushes and you're done. Um +so and if you watch the YouTube video + + align:start position:0% +so and if you watch the YouTube video + + + align:start position:0% +so and if you watch the YouTube video +that's linked from this you'll see him + + align:start position:0% +that's linked from this you'll see him + + + align:start position:0% +that's linked from this you'll see him +spend like 30 minutes until he finds the + + align:start position:0% +spend like 30 minutes until he finds the + + + align:start position:0% +spend like 30 minutes until he finds the +right solution. It's in the game it's + + align:start position:0% +right solution. It's in the game it's + + + align:start position:0% +right solution. It's in the game it's +frustrating because once you push them + + align:start position:0% +frustrating because once you push them + + + align:start position:0% +frustrating because once you push them +off they disappear and you have to leave + + align:start position:0% +off they disappear and you have to leave + + + align:start position:0% +off they disappear and you have to leave +and come back. Anyway um so out of all + + align:start position:0% +and come back. Anyway um so out of all + + + align:start position:0% +and come back. Anyway um so out of all +these uh games we've defined a bunch of + + align:start position:0% +these uh games we've defined a bunch of + + + align:start position:0% +these uh games we've defined a bunch of +models. Here's one aspect of the model. + + align:start position:0% +models. Here's one aspect of the model. + + + align:start position:0% +models. Here's one aspect of the model. +Uh so we have the fixed blocks which are + + align:start position:0% +Uh so we have the fixed blocks which are + + + align:start position:0% +Uh so we have the fixed blocks which are +in red, the movable blocks which are in + + align:start position:0% +in red, the movable blocks which are in + + + align:start position:0% +in red, the movable blocks which are in +cyan here and the robot is blue. + + align:start position:0% +cyan here and the robot is blue. + + + align:start position:0% +cyan here and the robot is blue. +Everything's one by one. Uh and in one + + align:start position:0% +Everything's one by one. Uh and in one + + + align:start position:0% +Everything's one by one. Uh and in one +model which we call push, when you push + + align:start position:0% +model which we call push, when you push + + + align:start position:0% +model which we call push, when you push +a block, it moves one step. That's the + + align:start position:0% +a block, it moves one step. That's the + + + align:start position:0% +a block, it moves one step. That's the +normal model and that's like sooon. Um + + align:start position:0% +normal model and that's like sooon. Um + + + align:start position:0% +normal model and that's like sooon. Um +and I'll talk about the two in a second. + + align:start position:0% +and I'll talk about the two in a second. + + + align:start position:0% +and I'll talk about the two in a second. +Uh in push push, this is like the on ice + + align:start position:0% +Uh in push push, this is like the on ice + + + align:start position:0% +Uh in push push, this is like the on ice +version. So you're not on ice. you can + + align:start position:0% +version. So you're not on ice. you can + + + align:start position:0% +version. So you're not on ice. you can +still kind of move and then kind of + + align:start position:0% +still kind of move and then kind of + + + align:start position:0% +still kind of move and then kind of +counteract physics and just move one + + align:start position:0% +counteract physics and just move one + + + align:start position:0% +counteract physics and just move one +step. But the blocks, they'll just fly + + align:start position:0% +step. But the blocks, they'll just fly + + + align:start position:0% +step. But the blocks, they'll just fly +off until they hit something. So here, + + align:start position:0% +off until they hit something. So here, + + + align:start position:0% +off until they hit something. So here, +this block will fly until it goes there. + + align:start position:0% +this block will fly until it goes there. + + + align:start position:0% +this block will fly until it goes there. +Um uh in push push push, you're + + align:start position:0% +Um uh in push push push, you're + + + align:start position:0% +Um uh in push push push, you're +everything is so slippery that if you + + align:start position:0% +everything is so slippery that if you + + + align:start position:0% +everything is so slippery that if you +hit a block and it hits another block + + align:start position:0% +hit a block and it hits another block + + + align:start position:0% +hit a block and it hits another block +that's movable, they will all just keep + + align:start position:0% +that's movable, they will all just keep + + + align:start position:0% +that's movable, they will all just keep +going until they hit an immovable block. + + align:start position:0% +going until they hit an immovable block. + + + align:start position:0% +going until they hit an immovable block. +But you don't slip. + + align:start position:0% +But you don't slip. + + + align:start position:0% +But you don't slip. +Uh you still don't slip in any of these + + align:start position:0% +Uh you still don't slip in any of these + + + align:start position:0% +Uh you still don't slip in any of these +models. So there is another version + + align:start position:0% +models. So there is another version + + + align:start position:0% +models. So there is another version +where you slip which has not been + + align:start position:0% +where you slip which has not been + + + align:start position:0% +where you slip which has not been +considered so much although ricochet + + align:start position:0% +considered so much although ricochet + + + align:start position:0% +considered so much although ricochet +robots has been considered and that's in + + align:start position:0% +robots has been considered and that's in + + + align:start position:0% +robots has been considered and that's in +that genre. Yeah. + + align:start position:0% +that genre. Yeah. + + + align:start position:0% +that genre. Yeah. +Is there a model where the block you you + + align:start position:0% +Is there a model where the block you you + + + align:start position:0% +Is there a model where the block you you +first pushed stops and transfers its + + align:start position:0% +first pushed stops and transfers its + + + align:start position:0% +first pushed stops and transfers its +momentum to the other. + + align:start position:0% +momentum to the other. + + + align:start position:0% +momentum to the other. +Oh cool. Yeah. Conservation of momentum. + + align:start position:0% +Oh cool. Yeah. Conservation of momentum. + + + align:start position:0% +Oh cool. Yeah. Conservation of momentum. +So this one hits and the next one goes. + + align:start position:0% +So this one hits and the next one goes. + + + align:start position:0% +So this one hits and the next one goes. +That's probably pushpush. + + align:start position:0% +That's probably pushpush. + + + align:start position:0% +That's probably pushpush. +I would guess that's also hard because + + align:start position:0% +I would guess that's also hard because + + + align:start position:0% +I would guess that's also hard because +this ends up being the same proof. Um + + align:start position:0% +this ends up being the same proof. Um + + + align:start position:0% +this ends up being the same proof. Um +guessing that works but we would need to + + align:start position:0% +guessing that works but we would need to + + + align:start position:0% +guessing that works but we would need to +check. That's a good Yeah, the push push + + align:start position:0% +check. That's a good Yeah, the push push + + + align:start position:0% +check. That's a good Yeah, the push push +ricochet push. Uh um Okay, one other + + align:start position:0% +ricochet push. Uh um Okay, one other + + + align:start position:0% +ricochet push. Uh um Okay, one other +thing here is the number two. You'll + + align:start position:0% +thing here is the number two. You'll + + + align:start position:0% +thing here is the number two. You'll +notice only two blocks are moving. And + + align:start position:0% +notice only two blocks are moving. And + + + align:start position:0% +notice only two blocks are moving. And +in general, normally here, two is the + + align:start position:0% +in general, normally here, two is the + + + align:start position:0% +in general, normally here, two is the +strength of the robot, meaning you if + + align:start position:0% +strength of the robot, meaning you if + + + align:start position:0% +strength of the robot, meaning you if +they're up to two in a row, you can push + + align:start position:0% +they're up to two in a row, you can push + + + align:start position:0% +they're up to two in a row, you can push +two blocks. But once they're three in a + + align:start position:0% +two blocks. But once they're three in a + + + align:start position:0% +two blocks. But once they're three in a +row, you can't push at all. Uh the idea + + align:start position:0% +row, you can't push at all. Uh the idea + + + align:start position:0% +row, you can't push at all. Uh the idea +here is the same thing happens. So + + align:start position:0% +here is the same thing happens. So + + + align:start position:0% +here is the same thing happens. So +they're just too heavy after you get up + + align:start position:0% +they're just too heavy after you get up + + + align:start position:0% +they're just too heavy after you get up +to three of them, then they'll stop + + align:start position:0% +to three of them, then they'll stop + + + align:start position:0% +to three of them, then they'll stop +sliding. Okay? And same with push push + + align:start position:0% +sliding. Okay? And same with push push + + + align:start position:0% +sliding. Okay? And same with push push +push. + + align:start position:0% +push. + + + align:start position:0% +push. +So succubon is actually p is p p p p p p + + align:start position:0% +So succubon is actually p is p p p p p p + + + align:start position:0% +So succubon is actually p is p p p p p p +p p p p p p p p p p p p p p push one. + + align:start position:0% +p p p p p p p p p p p p p p push one. + + + align:start position:0% +p p p p p p p p p p p p p p push one. +Suckan is like push one. Uh it's a + + align:start position:0% +Suckan is like push one. Uh it's a + + + align:start position:0% +Suckan is like push one. Uh it's a +little bit more complicated as + + align:start position:0% +little bit more complicated as + + + align:start position:0% +little bit more complicated as +illustrated in this table. So succubon + + align:start position:0% +illustrated in this table. So succubon + + + align:start position:0% +illustrated in this table. So succubon +is here and there it's uh you can only + + align:start position:0% +is here and there it's uh you can only + + + align:start position:0% +is here and there it's uh you can only +push one block at a time. There are + + align:start position:0% +push one block at a time. There are + + + align:start position:0% +push one block at a time. There are +fixed blocks and in general the models + + align:start position:0% +fixed blocks and in general the models + + + align:start position:0% +fixed blocks and in general the models +that have fixed blocks are highlighted + + align:start position:0% +that have fixed blocks are highlighted + + + align:start position:0% +that have fixed blocks are highlighted +in pink here. Um, this this slide thing + + align:start position:0% +in pink here. Um, this this slide thing + + + align:start position:0% +in pink here. Um, this this slide thing +is trying to capture whether it just + + align:start position:0% +is trying to capture whether it just + + + align:start position:0% +is trying to capture whether it just +moves one step or all the way until it + + align:start position:0% +moves one step or all the way until it + + + align:start position:0% +moves one step or all the way until it +uh can't anymore. That's the max. So, + + align:start position:0% +uh can't anymore. That's the max. So, + + + align:start position:0% +uh can't anymore. That's the max. So, +there's only a couple of slide versions. + + align:start position:0% +there's only a couple of slide versions. + + + align:start position:0% +there's only a couple of slide versions. +I haven't put push push push here + + align:start position:0% +I haven't put push push push here + + + align:start position:0% +I haven't put push push push here +because that would be the only + + align:start position:0% +because that would be the only + + + align:start position:0% +because that would be the only +difference is what max means. Uh, but + + align:start position:0% +difference is what max means. Uh, but + + + align:start position:0% +difference is what max means. Uh, but +everything else you just move one step. + + align:start position:0% +everything else you just move one step. + + + align:start position:0% +everything else you just move one step. +Then the the other issue is what is the + + align:start position:0% +Then the the other issue is what is the + + + align:start position:0% +Then the the other issue is what is the +goal? I mentioned in so you have to uh + + align:start position:0% +goal? I mentioned in so you have to uh + + + align:start position:0% +goal? I mentioned in so you have to uh +cover every uh storage space with a box. + + align:start position:0% +cover every uh storage space with a box. + + + align:start position:0% +cover every uh storage space with a box. +Um, that is the only problem with that + + align:start position:0% +Um, that is the only problem with that + + + align:start position:0% +Um, that is the only problem with that +flavor in this list. Anyway, all the + + align:start position:0% +flavor in this list. Anyway, all the + + + align:start position:0% +flavor in this list. Anyway, all the +ones that are called push, the goal is + + align:start position:0% +ones that are called push, the goal is + + + align:start position:0% +ones that are called push, the goal is +just to get the robot to a destination + + align:start position:0% +just to get the robot to a destination + + + align:start position:0% +just to get the robot to a destination +like in Mario or Zelda or something. So, + + align:start position:0% +like in Mario or Zelda or something. So, + + + align:start position:0% +like in Mario or Zelda or something. So, +that's the difference between sooon and + + align:start position:0% +that's the difference between sooon and + + + align:start position:0% +that's the difference between sooon and +push one. Well, push one f I suppose is + + align:start position:0% +push one. Well, push one f I suppose is + + + align:start position:0% +push one. Well, push one f I suppose is +uh pushing one thing at a time with + + align:start position:0% +uh pushing one thing at a time with + + + align:start position:0% +uh pushing one thing at a time with +fixed blocks. That's identical to soabon + + align:start position:0% +fixed blocks. That's identical to soabon + + + align:start position:0% +fixed blocks. That's identical to soabon +except for this issue of what the goal + + align:start position:0% +except for this issue of what the goal + + + align:start position:0% +except for this issue of what the goal +is. either just to get from S to T the + + align:start position:0% +is. either just to get from S to T the + + + align:start position:0% +is. either just to get from S to T the +robot or to get all the blocks into a + + align:start position:0% +robot or to get all the blocks into a + + + align:start position:0% +robot or to get all the blocks into a +particular configuration. + + align:start position:0% +particular configuration. + + + align:start position:0% +particular configuration. +Uh + + align:start position:0% +Uh + + + align:start position:0% +Uh +okay, + + align:start position:0% +okay, + + + align:start position:0% +okay, +there are some other things here that + + align:start position:0% +there are some other things here that + + + align:start position:0% +there are some other things here that +that's we've talked about push K. Uh + + align:start position:0% +that's we've talked about push K. Uh + + + align:start position:0% +that's we've talked about push K. Uh +push star is when K is infinity. So you + + align:start position:0% +push star is when K is infinity. So you + + + align:start position:0% +push star is when K is infinity. So you +can when you push you could your + + align:start position:0% +can when you push you could your + + + align:start position:0% +can when you push you could your +arbitrary strength you can push as many + + align:start position:0% +arbitrary strength you can push as many + + + align:start position:0% +arbitrary strength you can push as many +blocks in a row as you want. Uh push + + align:start position:0% +blocks in a row as you want. Uh push + + + align:start position:0% +blocks in a row as you want. Uh push +push K push push star. Then uh we've + + align:start position:0% +push K push push star. Then uh we've + + + align:start position:0% +push K push push star. Then uh we've +talked about F. F is when you have fixed + + align:start position:0% +talked about F. F is when you have fixed + + + align:start position:0% +talked about F. F is when you have fixed +blocks. Push one F push KF. uh and push + + align:start position:0% +blocks. Push one F push KF. uh and push + + + align:start position:0% +blocks. Push one F push KF. uh and push +starf. And then there's one other + + align:start position:0% +starf. And then there's one other + + + align:start position:0% +starf. And then there's one other +variation here that's been considered + + align:start position:0% +variation here that's been considered + + + align:start position:0% +variation here that's been considered +which is the X. This is when the path + + align:start position:0% +which is the X. This is when the path + + + align:start position:0% +which is the X. This is when the path +that the robot takes must not cross + + align:start position:0% +that the robot takes must not cross + + + align:start position:0% +that the robot takes must not cross +itself, must not revisit a square. This + + align:start position:0% +itself, must not revisit a square. This + + + align:start position:0% +itself, must not revisit a square. This +is there are a lot of video games where + + align:start position:0% +is there are a lot of video games where + + + align:start position:0% +is there are a lot of video games where +after you leave a square that square + + align:start position:0% +after you leave a square that square + + + align:start position:0% +after you leave a square that square +disappears like it falls down to into + + align:start position:0% +disappears like it falls down to into + + + align:start position:0% +disappears like it falls down to into +into the abyss and so you're scared. Uh + + align:start position:0% +into the abyss and so you're scared. Uh + + + align:start position:0% +into the abyss and so you're scared. Uh +so to represent those games, uh there's + + align:start position:0% +so to represent those games, uh there's + + + align:start position:0% +so to represent those games, uh there's +another reason we did that. Uh but I'll + + align:start position:0% +another reason we did that. Uh but I'll + + + align:start position:0% +another reason we did that. Uh but I'll +get to that in a moment. There's push kx + + align:start position:0% +get to that in a moment. There's push kx + + + align:start position:0% +get to that in a moment. There's push kx +and push star x. Okay, now let's talk + + align:start position:0% +and push star x. Okay, now let's talk + + + align:start position:0% +and push star x. Okay, now let's talk +about complexity. That's this the right + + align:start position:0% +about complexity. That's this the right + + + align:start position:0% +about complexity. That's this the right +two columns here, the reference and the + + align:start position:0% +two columns here, the reference and the + + + align:start position:0% +two columns here, the reference and the +complexity. So um all of these problems + + align:start position:0% +complexity. So um all of these problems + + + align:start position:0% +complexity. So um all of these problems +are np hard. Okay, but there's this + + align:start position:0% +are np hard. Okay, but there's this + + + align:start position:0% +are np hard. Okay, but there's this +issue of are they innp or are they + + align:start position:0% +issue of are they innp or are they + + + align:start position:0% +issue of are they innp or are they +pspace complete? Question. + + align:start position:0% +pspace complete? Question. + + + align:start position:0% +pspace complete? Question. +Sorry, what did you say a fixed block + + align:start position:0% +Sorry, what did you say a fixed block + + + align:start position:0% +Sorry, what did you say a fixed block +is? + + align:start position:0% +is? + + + align:start position:0% +is? +Fixed block is a block that cannot be + + align:start position:0% +Fixed block is a block that cannot be + + + align:start position:0% +Fixed block is a block that cannot be +pushed. So it's just like glued to the + + align:start position:0% +pushed. So it's just like glued to the + + + align:start position:0% +pushed. So it's just like glued to the +ground. + + align:start position:0% +ground. + + + align:start position:0% +ground. +So this is just whether or not there are + + align:start position:0% +So this is just whether or not there are + + + align:start position:0% +So this is just whether or not there are +some blocks that are fixed, + + align:start position:0% +some blocks that are fixed, + + + align:start position:0% +some blocks that are fixed, +right? this in this these problems. This + + align:start position:0% +right? this in this these problems. This + + + align:start position:0% +right? this in this these problems. This +is a more general version than this + + align:start position:0% +is a more general version than this + + + align:start position:0% +is a more general version than this +game. Here you allow some blocks to be + + align:start position:0% +game. Here you allow some blocks to be + + + align:start position:0% +game. Here you allow some blocks to be +specified as fixed. Here everything is + + align:start position:0% +specified as fixed. Here everything is + + + align:start position:0% +specified as fixed. Here everything is +potentially movable. Although if you + + align:start position:0% +potentially movable. Although if you + + + align:start position:0% +potentially movable. Although if you +have more than K in a row, it's like a + + align:start position:0% +have more than K in a row, it's like a + + + align:start position:0% +have more than K in a row, it's like a +fixed block. Like if you have a K+1 by + + align:start position:0% +fixed block. Like if you have a K+1 by + + + align:start position:0% +fixed block. Like if you have a K+1 by +K+1 block, that's fixed effectively. But + + align:start position:0% +K+1 block, that's fixed effectively. But + + + align:start position:0% +K+1 block, that's fixed effectively. But +it you have a resolution issue that you + + align:start position:0% +it you have a resolution issue that you + + + align:start position:0% +it you have a resolution issue that you +can't make tiny fixed blocks in this + + align:start position:0% +can't make tiny fixed blocks in this + + + align:start position:0% +can't make tiny fixed blocks in this +model. And in this model, there are no + + align:start position:0% +model. And in this model, there are no + + + align:start position:0% +model. And in this model, there are no +fixed blocks whatsoever. But here you + + align:start position:0% +fixed blocks whatsoever. But here you + + + align:start position:0% +fixed blocks whatsoever. But here you +can specify some of them are fixed. + + align:start position:0% +can specify some of them are fixed. + + + align:start position:0% +can specify some of them are fixed. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Yeah, a lot of versions. + + align:start position:0% +Yeah, a lot of versions. + + + align:start position:0% +Yeah, a lot of versions. +So, push star has a boundary. Otherwise, + + align:start position:0% +So, push star has a boundary. Otherwise, + + + align:start position:0% +So, push star has a boundary. Otherwise, +you could just + + align:start position:0% +you could just + + + align:start position:0% +you could just +push star does live in a rectangular + + align:start position:0% +push star does live in a rectangular + + + align:start position:0% +push star does live in a rectangular +box. Yeah, that is the one + + align:start position:0% +box. Yeah, that is the one + + + align:start position:0% +box. Yeah, that is the one +fixed. + + align:start position:0% +fixed. + + + align:start position:0% +fixed. +You could think of that as fixed blocks + + align:start position:0% +You could think of that as fixed blocks + + + align:start position:0% +You could think of that as fixed blocks +or not. Yeah, + + align:start position:0% +or not. Yeah, + + + align:start position:0% +or not. Yeah, +if nothing is fixed, then you can just + + align:start position:0% +if nothing is fixed, then you can just + + + align:start position:0% +if nothing is fixed, then you can just +walk off to infinity. Move all the + + align:start position:0% +walk off to infinity. Move all the + + + align:start position:0% +walk off to infinity. Move all the +blocks away and then come back and find + + align:start position:0% +blocks away and then come back and find + + + align:start position:0% +blocks away and then come back and find +your destination. + + align:start position:0% +your destination. + + + align:start position:0% +your destination. +Uh, right. So, they're all empty hard. + + align:start position:0% +Uh, right. So, they're all empty hard. + + + align:start position:0% +Uh, right. So, they're all empty hard. +There's a few that are known to be + + align:start position:0% +There's a few that are known to be + + + align:start position:0% +There's a few that are known to be +pspace complete. push push with a fixed + + align:start position:0% +pspace complete. push push with a fixed + + + align:start position:0% +pspace complete. push push with a fixed +strength is pspace complete uh or with + + align:start position:0% +strength is pspace complete uh or with + + + align:start position:0% +strength is pspace complete uh or with +fixed blocks I think should also be uh + + align:start position:0% +fixed blocks I think should also be uh + + + align:start position:0% +fixed blocks I think should also be uh +pspace complete that's not written here + + align:start position:0% +pspace complete that's not written here + + + align:start position:0% +pspace complete that's not written here +but uh push push star all we know is np + + align:start position:0% +but uh push push star all we know is np + + + align:start position:0% +but uh push push star all we know is np +hardness + + align:start position:0% +hardness + + + align:start position:0% +hardness +uh push kf where k is at least two is + + align:start position:0% +uh push kf where k is at least two is + + + align:start position:0% +uh push kf where k is at least two is +known to be pspace complete but push one + + align:start position:0% +known to be pspace complete but push one + + + align:start position:0% +known to be pspace complete but push one +f or push two without the f are both + + align:start position:0% +f or push two without the f are both + + + align:start position:0% +f or push two without the f are both +open um And the reason we were + + align:start position:0% +open um And the reason we were + + + align:start position:0% +open um And the reason we were +interested in a non-crossing path is + + align:start position:0% +interested in a non-crossing path is + + + align:start position:0% +interested in a non-crossing path is +that forces the problem to be an NP + + align:start position:0% +that forces the problem to be an NP + + + align:start position:0% +that forces the problem to be an NP +because then you know the solution path + + align:start position:0% +because then you know the solution path + + + align:start position:0% +because then you know the solution path +has polinomial length can visit each + + align:start position:0% +has polinomial length can visit each + + + align:start position:0% +has polinomial length can visit each +square at most once. So uh the hard part + + align:start position:0% +square at most once. So uh the hard part + + + align:start position:0% +square at most once. So uh the hard part +here was to prove that it's still np + + align:start position:0% +here was to prove that it's still np + + + align:start position:0% +here was to prove that it's still np +hard even with non-crossing paths. We + + align:start position:0% +hard even with non-crossing paths. We + + + align:start position:0% +hard even with non-crossing paths. We +won't try to prove that today but so + + align:start position:0% +won't try to prove that today but so + + + align:start position:0% +won't try to prove that today but so +those we actually have tight bounds of + + align:start position:0% +those we actually have tight bounds of + + + align:start position:0% +those we actually have tight bounds of +npmp complete. And so bond there's a + + align:start position:0% +npmp complete. And so bond there's a + + + align:start position:0% +npmp complete. And so bond there's a +relatively old result 1998 that it's + + align:start position:0% +relatively old result 1998 that it's + + + align:start position:0% +relatively old result 1998 that it's +pspace complete. Okay let's let's do + + align:start position:0% +pspace complete. Okay let's let's do + + + align:start position:0% +pspace complete. Okay let's let's do +some reductions. So this first reduction + + align:start position:0% +some reductions. So this first reduction + + + align:start position:0% +some reductions. So this first reduction +is amazingly cool. Uh this is by Michael + + align:start position:0% +is amazingly cool. Uh this is by Michael + + + align:start position:0% +is amazingly cool. Uh this is by Michael +Hoffman 2000. Uh this is push star with + + align:start position:0% +Hoffman 2000. Uh this is push star with + + + align:start position:0% +Hoffman 2000. Uh this is push star with +a rectangular box. Okay. So you're here. + + align:start position:0% +a rectangular box. Okay. So you're here. + + + align:start position:0% +a rectangular box. Okay. So you're here. +The outlined regions are the blank + + align:start position:0% +The outlined regions are the blank + + + align:start position:0% +The outlined regions are the blank +space. Everything else is filled with a + + align:start position:0% +space. Everything else is filled with a + + + align:start position:0% +space. Everything else is filled with a +block. But every block is movable and + + align:start position:0% +block. But every block is movable and + + + align:start position:0% +block. But every block is movable and +you can push arbitrarily strongly. So + + align:start position:0% +you can push arbitrarily strongly. So + + + align:start position:0% +you can push arbitrarily strongly. So +what this is going to be variables. + + align:start position:0% +what this is going to be variables. + + + align:start position:0% +what this is going to be variables. +You're going to make some choices here. + + align:start position:0% +You're going to make some choices here. + + + align:start position:0% +You're going to make some choices here. +These are the connections between + + align:start position:0% +These are the connections between + + + align:start position:0% +These are the connections between +variables and clauses. This is a + + align:start position:0% +variables and clauses. This is a + + + align:start position:0% +variables and clauses. This is a +bipartite graph encoded in binary in the + + align:start position:0% +bipartite graph encoded in binary in the + + + align:start position:0% +bipartite graph encoded in binary in the +obvious way. There's variables here, + + align:start position:0% +obvious way. There's variables here, + + + align:start position:0% +obvious way. There's variables here, +clauses here. there's a hole exactly + + align:start position:0% +clauses here. there's a hole exactly + + + align:start position:0% +clauses here. there's a hole exactly +when that literal appears in that + + align:start position:0% +when that literal appears in that + + + align:start position:0% +when that literal appears in that +clause. Okay, there's actually two rows + + align:start position:0% +clause. Okay, there's actually two rows + + + align:start position:0% +clause. Okay, there's actually two rows +per variable, the true and the false. + + align:start position:0% +per variable, the true and the false. + + + align:start position:0% +per variable, the true and the false. +And then uh there's this gadget here to + + align:start position:0% +And then uh there's this gadget here to + + + align:start position:0% +And then uh there's this gadget here to +connect the things. And then these are + + align:start position:0% +connect the things. And then these are + + + align:start position:0% +connect the things. And then these are +the clauses where we're going to check + + align:start position:0% +the clauses where we're going to check + + + align:start position:0% +the clauses where we're going to check +that they were all set correctly. So + + align:start position:0% +that they were all set correctly. So + + + align:start position:0% +that they were all set correctly. So +let's go through it. This is the + + align:start position:0% +let's go through it. This is the + + + align:start position:0% +let's go through it. This is the +schematic diagram of what I just said. + + align:start position:0% +schematic diagram of what I just said. + + + align:start position:0% +schematic diagram of what I just said. +You're going to start here in the + + align:start position:0% +You're going to start here in the + + + align:start position:0% +You're going to start here in the +variable block. Walk through each of the + + align:start position:0% +variable block. Walk through each of the + + + align:start position:0% +variable block. Walk through each of the +variables. Here's what the variables + + align:start position:0% +variables. Here's what the variables + + + align:start position:0% +variables. Here's what the variables +look like. You have two rows, the XI row + + align:start position:0% +look like. You have two rows, the XI row + + + align:start position:0% +look like. You have two rows, the XI row +and the XI complement row. That's + + align:start position:0% +and the XI complement row. That's + + + align:start position:0% +and the XI complement row. That's +another way to write not xi. And you're + + align:start position:0% +another way to write not xi. And you're + + + align:start position:0% +another way to write not xi. And you're +going to count how many times does x i + + align:start position:0% +going to count how many times does x i + + + align:start position:0% +going to count how many times does x i +appear in any clauses in positive form, + + align:start position:0% +appear in any clauses in positive form, + + + align:start position:0% +appear in any clauses in positive form, +negative form. That's called ni and ni + + align:start position:0% +negative form. That's called ni and ni + + + align:start position:0% +negative form. That's called ni and ni +bar. And you're going to measure out + + align:start position:0% +bar. And you're going to measure out + + + align:start position:0% +bar. And you're going to measure out +these lengths. You can negate variables + + align:start position:0% +these lengths. You can negate variables + + + align:start position:0% +these lengths. You can negate variables +to make sure that ni is always bigger + + align:start position:0% +to make sure that ni is always bigger + + + align:start position:0% +to make sure that ni is always bigger +than ni bar. So do that. So in this + + align:start position:0% +than ni bar. So do that. So in this + + + align:start position:0% +than ni bar. So do that. So in this +case, ni is this big. Ni bar is this + + align:start position:0% +case, ni is this big. Ni bar is this + + + align:start position:0% +case, ni is this big. Ni bar is this +big. Measure it out. This is your blank + + align:start position:0% +big. Measure it out. This is your blank + + + align:start position:0% +big. Measure it out. This is your blank +space. And what what you're allowed what + + align:start position:0% +space. And what what you're allowed what + + + align:start position:0% +space. And what what you're allowed what +we will show you you're allowed to do is + + align:start position:0% +we will show you you're allowed to do is + + + align:start position:0% +we will show you you're allowed to do is +either move up here and move all the way + + align:start position:0% +either move up here and move all the way + + + align:start position:0% +either move up here and move all the way +over to here and then up or to move here + + align:start position:0% +over to here and then up or to move here + + + align:start position:0% +over to here and then up or to move here +and all the way over and then up. And + + align:start position:0% +and all the way over and then up. And + + + align:start position:0% +and all the way over and then up. And +this star is so that for the one block + + align:start position:0% +this star is so that for the one block + + + align:start position:0% +this star is so that for the one block +that's here could fit and then you can + + align:start position:0% +that's here could fit and then you can + + + align:start position:0% +that's here could fit and then you can +go over to this X. In general in these + + align:start position:0% +go over to this X. In general in these + + + align:start position:0% +go over to this X. In general in these +gadgets the X is your target. X marks + + align:start position:0% +gadgets the X is your target. X marks + + + align:start position:0% +gadgets the X is your target. X marks +the spot right for the gadget. And then + + align:start position:0% +the spot right for the gadget. And then + + + align:start position:0% +the spot right for the gadget. And then +there's a global X which will be at the + + align:start position:0% +there's a global X which will be at the + + + align:start position:0% +there's a global X which will be at the +end of the clauses. + + align:start position:0% +end of the clauses. + + + align:start position:0% +end of the clauses. +Uh so what does this do? Well, if you + + align:start position:0% +Uh so what does this do? Well, if you + + + align:start position:0% +Uh so what does this do? Well, if you +think about this connection block, this + + align:start position:0% +think about this connection block, this + + + align:start position:0% +think about this connection block, this +is the the bipartite graph encoded as a + + align:start position:0% +is the the bipartite graph encoded as a + + + align:start position:0% +is the the bipartite graph encoded as a +matrix. Um, there's the number of blank + + align:start position:0% +matrix. Um, there's the number of blank + + + align:start position:0% +matrix. Um, there's the number of blank +spaces over here is exactly ni. So, this + + align:start position:0% +spaces over here is exactly ni. So, this + + + align:start position:0% +spaces over here is exactly ni. So, this +is why after you push ni steps or ni bar + + align:start position:0% +is why after you push ni steps or ni bar + + + align:start position:0% +is why after you push ni steps or ni bar +steps, you'll have to stop because there + + align:start position:0% +steps, you'll have to stop because there + + + align:start position:0% +steps, you'll have to stop because there +are no blank spaces to the right of you. + + align:start position:0% +are no blank spaces to the right of you. + + + align:start position:0% +are no blank spaces to the right of you. +Then the only thing you can do is go up + + align:start position:0% +Then the only thing you can do is go up + + + align:start position:0% +Then the only thing you can do is go up +because there are no blank spaces below + + align:start position:0% +because there are no blank spaces below + + + align:start position:0% +because there are no blank spaces below +you. So, in general, these gadgets are + + align:start position:0% +you. So, in general, these gadgets are + + + align:start position:0% +you. So, in general, these gadgets are +super tight. As above you, there's + + align:start position:0% +super tight. As above you, there's + + + align:start position:0% +super tight. As above you, there's +nothing. It's all blocks. And below you + + align:start position:0% +nothing. It's all blocks. And below you + + + align:start position:0% +nothing. It's all blocks. And below you +and left of you, it's all blocks. + + align:start position:0% +and left of you, it's all blocks. + + + align:start position:0% +and left of you, it's all blocks. +There's nothing you can do. You put the + + align:start position:0% +There's nothing you can do. You put the + + + align:start position:0% +There's nothing you can do. You put the +next variable gadget here so that that + + align:start position:0% +next variable gadget here so that that + + + align:start position:0% +next variable gadget here so that that +remains true immediately to the in your + + align:start position:0% +remains true immediately to the in your + + + align:start position:0% +remains true immediately to the in your +row and in your columns you're + + align:start position:0% +row and in your columns you're + + + align:start position:0% +row and in your columns you're +completely packed. So there's the only + + align:start position:0% +completely packed. So there's the only + + + align:start position:0% +completely packed. So there's the only +choice you have is to do this or to do + + align:start position:0% +choice you have is to do this or to do + + + align:start position:0% +choice you have is to do this or to do +this and you will fill the row that you + + align:start position:0% +this and you will fill the row that you + + + align:start position:0% +this and you will fill the row that you +choose. Exactly. Okay. So that's the + + align:start position:0% +choose. Exactly. Okay. So that's the + + + align:start position:0% +choose. Exactly. Okay. So that's the +variable gadget. + + align:start position:0% +variable gadget. + + + align:start position:0% +variable gadget. +What prevents you from choosing both? + + align:start position:0% +What prevents you from choosing both? + + + align:start position:0% +What prevents you from choosing both? +Uh you could choose both or you could do + + align:start position:0% +Uh you could choose both or you could do + + + align:start position:0% +Uh you could choose both or you could do +a little bit of one and then do the + + align:start position:0% +a little bit of one and then do the + + + align:start position:0% +a little bit of one and then do the +other. That's true. Uh but as we'll see + + align:start position:0% +other. That's true. Uh but as we'll see + + + align:start position:0% +other. That's true. Uh but as we'll see +that only makes your life worse. Okay. + + align:start position:0% +that only makes your life worse. Okay. + + + align:start position:0% +that only makes your life worse. Okay. +Yeah. Good question. + + align:start position:0% +Yeah. Good question. + + + align:start position:0% +Yeah. Good question. +All right. So, next we enter the bridge + + align:start position:0% +All right. So, next we enter the bridge + + + align:start position:0% +All right. So, next we enter the bridge +gadget, which is these two pictures, and + + align:start position:0% +gadget, which is these two pictures, and + + + align:start position:0% +gadget, which is these two pictures, and +it looks like this. Uh, this is + + align:start position:0% +it looks like this. Uh, this is + + + align:start position:0% +it looks like this. Uh, this is +basically a locking mechanism. So, you + + align:start position:0% +basically a locking mechanism. So, you + + + align:start position:0% +basically a locking mechanism. So, you +start here. I'll just tell you what + + align:start position:0% +start here. I'll just tell you what + + + align:start position:0% +start here. I'll just tell you what +you're supposed to do. Uh, you walk over + + align:start position:0% +you're supposed to do. Uh, you walk over + + + align:start position:0% +you're supposed to do. Uh, you walk over +through this blank space. Uh, then you + + align:start position:0% +through this blank space. Uh, then you + + + align:start position:0% +through this blank space. Uh, then you +push all of these things down to here. + + align:start position:0% +push all of these things down to here. + + + align:start position:0% +push all of these things down to here. +Uh, so this basically, + + align:start position:0% +Uh, so this basically, + + + align:start position:0% +Uh, so this basically, +uh, prevents you from going back to + + align:start position:0% +uh, prevents you from going back to + + + align:start position:0% +uh, prevents you from going back to +where you were. So you push all that + + align:start position:0% +where you were. So you push all that + + + align:start position:0% +where you were. So you push all that +down and then you go over here and you + + align:start position:0% +down and then you go over here and you + + + align:start position:0% +down and then you go over here and you +tunnel down. Uh so I think you're moving + + align:start position:0% +tunnel down. Uh so I think you're moving + + + align:start position:0% +tunnel down. Uh so I think you're moving +these blocks over to here. It's another + + align:start position:0% +these blocks over to here. It's another + + + align:start position:0% +these blocks over to here. It's another +kind of block and then you're pushing + + align:start position:0% +kind of block and then you're pushing + + + align:start position:0% +kind of block and then you're pushing +this stuff down to here. And then you + + align:start position:0% +this stuff down to here. And then you + + + align:start position:0% +this stuff down to here. And then you +get there. So when all is said and done, + + align:start position:0% +get there. So when all is said and done, + + + align:start position:0% +get there. So when all is said and done, +this will be down here. This will be + + align:start position:0% +this will be down here. This will be + + + align:start position:0% +this will be down here. This will be +down here. This will be over here. And + + align:start position:0% +down here. This will be over here. And + + + align:start position:0% +down here. This will be over here. And +so when you're in the clause block + + align:start position:0% +so when you're in the clause block + + + align:start position:0% +so when you're in the clause block +again, you have full rows to your left, + + align:start position:0% +again, you have full rows to your left, + + + align:start position:0% +again, you have full rows to your left, +full columns above you. So there's + + align:start position:0% +full columns above you. So there's + + + align:start position:0% +full columns above you. So there's +nothing. You can't go up and you can't + + align:start position:0% +nothing. You can't go up and you can't + + + align:start position:0% +nothing. You can't go up and you can't +go left. That's the purpose of this + + align:start position:0% +go left. That's the purpose of this + + + align:start position:0% +go left. That's the purpose of this +gadget is to connect this thing to this + + align:start position:0% +gadget is to connect this thing to this + + + align:start position:0% +gadget is to connect this thing to this +thing. If there's a teleporter, it' be + + align:start position:0% +thing. If there's a teleporter, it' be + + + align:start position:0% +thing. If there's a teleporter, it' be +much easier. You could just leave these + + align:start position:0% +much easier. You could just leave these + + + align:start position:0% +much easier. You could just leave these +all filled. But we want to get up to + + align:start position:0% +all filled. But we want to get up to + + + align:start position:0% +all filled. But we want to get up to +here. Uh and then but make sure this is + + align:start position:0% +here. Uh and then but make sure this is + + + align:start position:0% +here. Uh and then but make sure this is +all filled at the end. So that's the + + align:start position:0% +all filled at the end. So that's the + + + align:start position:0% +all filled at the end. So that's the +sole purpose of this gadget. Okay. Now a + + align:start position:0% +sole purpose of this gadget. Okay. Now a + + + align:start position:0% +sole purpose of this gadget. Okay. Now a +clause. + + align:start position:0% +clause. + + + align:start position:0% +clause. +How do we do a clause again? Um so you + + align:start position:0% +How do we do a clause again? Um so you + + + align:start position:0% +How do we do a clause again? Um so you +have there's three spaces here because + + align:start position:0% +have there's three spaces here because + + + align:start position:0% +have there's three spaces here because +this is three setat. You can move down + + align:start position:0% +this is three setat. You can move down + + + align:start position:0% +this is three setat. You can move down +one here and then move over two. These + + align:start position:0% +one here and then move over two. These + + + align:start position:0% +one here and then move over two. These +two blocks go here and then you can get + + align:start position:0% +two blocks go here and then you can get + + + align:start position:0% +two blocks go here and then you can get +to the X or you can go down here and + + align:start position:0% +to the X or you can go down here and + + + align:start position:0% +to the X or you can go down here and +over and get to the X or you can go here + + align:start position:0% +over and get to the X or you can go here + + + align:start position:0% +over and get to the X or you can go here +down over and this is possible if + + align:start position:0% +down over and this is possible if + + + align:start position:0% +down over and this is possible if +there's a hole below you. This is + + align:start position:0% +there's a hole below you. This is + + + align:start position:0% +there's a hole below you. This is +possible if there's a hole below you and + + align:start position:0% +possible if there's a hole below you and + + + align:start position:0% +possible if there's a hole below you and +this is possible if there's a hole below + + align:start position:0% +this is possible if there's a hole below + + + align:start position:0% +this is possible if there's a hole below +you. These are aligned with these + + align:start position:0% +you. These are aligned with these + + + align:start position:0% +you. These are aligned with these +things. So with exact I didn't quite + + align:start position:0% +things. So with exact I didn't quite + + + align:start position:0% +things. So with exact I didn't quite +align them but these three columns are + + align:start position:0% +align them but these three columns are + + + align:start position:0% +align them but these three columns are +these three columns + + align:start position:0% +these three columns + + + align:start position:0% +these three columns +and if one of these is unfilled you'll + + align:start position:0% +and if one of these is unfilled you'll + + + align:start position:0% +and if one of these is unfilled you'll +be able to get from here to here. If + + align:start position:0% +be able to get from here to here. If + + + align:start position:0% +be able to get from here to here. If +they're all filled, you won't because it + + align:start position:0% +they're all filled, you won't because it + + + align:start position:0% +they're all filled, you won't because it +will be full columns all the way down. + + align:start position:0% +will be full columns all the way down. + + + align:start position:0% +will be full columns all the way down. +Uh + + align:start position:0% +Uh + + + align:start position:0% +Uh +so that's a clause gadget. Uh because + + align:start position:0% +so that's a clause gadget. Uh because + + + align:start position:0% +so that's a clause gadget. Uh because +things were filled when you chose that + + align:start position:0% +things were filled when you chose that + + + align:start position:0% +things were filled when you chose that +thing to be uh maybe did I get it + + align:start position:0% +thing to be uh maybe did I get it + + + align:start position:0% +thing to be uh maybe did I get it +backwards? + + align:start position:0% +backwards? + + + align:start position:0% +backwards? +So you're really choosing the the + + align:start position:0% +So you're really choosing the the + + + align:start position:0% +So you're really choosing the the +opposite, + + align:start position:0% +opposite, + + + align:start position:0% +opposite, +right? You're choosing you're you're + + align:start position:0% +right? You're choosing you're you're + + + align:start position:0% +right? You're choosing you're you're +choosing the thing to be not true uh and + + align:start position:0% +choosing the thing to be not true uh and + + + align:start position:0% +choosing the thing to be not true uh and +leaving the other one to be as true as + + align:start position:0% +leaving the other one to be as true as + + + align:start position:0% +leaving the other one to be as true as +possible by not pushing it. So it leaves + + align:start position:0% +possible by not pushing it. So it leaves + + + align:start position:0% +possible by not pushing it. So it leaves +the holes so that later you can + + align:start position:0% +the holes so that later you can + + + align:start position:0% +the holes so that later you can +traverse. + + align:start position:0% +traverse. + + + align:start position:0% +traverse. +So that's why you wouldn't want to + + align:start position:0% +So that's why you wouldn't want to + + + align:start position:0% +So that's why you wouldn't want to +choose both, + + align:start position:0% +choose both, + + + align:start position:0% +choose both, +right? If you chose both that would be + + align:start position:0% +right? If you chose both that would be + + + align:start position:0% +right? If you chose both that would be +like making them both of them not true + + align:start position:0% +like making them both of them not true + + + align:start position:0% +like making them both of them not true +and so you don't get any of the + + align:start position:0% +and so you don't get any of the + + + align:start position:0% +and so you don't get any of the +benefits. + + align:start position:0% +benefits. + + + align:start position:0% +benefits. +Okay, that's push star. + + align:start position:0% +Okay, that's push star. + + + align:start position:0% +Okay, that's push star. +Cool. + + align:start position:0% + + + + align:start position:0% + +Okay. Um let's do push push one in 3D. + + align:start position:0% +Okay. Um let's do push push one in 3D. + + + align:start position:0% +Okay. Um let's do push push one in 3D. +This is really easy. Uh this is almost + + align:start position:0% +This is really easy. Uh this is almost + + + align:start position:0% +This is really easy. Uh this is almost +like the Super Mario Brothers proof. So, + + align:start position:0% +like the Super Mario Brothers proof. So, + + + align:start position:0% +like the Super Mario Brothers proof. So, +uh, it's just old drawing style. So, um, + + align:start position:0% +uh, it's just old drawing style. So, um, + + + align:start position:0% +uh, it's just old drawing style. So, um, +and we've drawn sort of the dual graph. + + align:start position:0% +and we've drawn sort of the dual graph. + + + align:start position:0% +and we've drawn sort of the dual graph. +So, these paths are little width one + + align:start position:0% +So, these paths are little width one + + + align:start position:0% +So, these paths are little width one +tunnels that you can walk down. So, you + + align:start position:0% +tunnels that you can walk down. So, you + + + align:start position:0% +tunnels that you can walk down. So, you +start up here and you can either push + + align:start position:0% +start up here and you can either push + + + align:start position:0% +start up here and you can either push +this thing this way or this way. Um, and + + align:start position:0% +this thing this way or this way. Um, and + + + align:start position:0% +this thing this way or this way. Um, and +so you're choosing which way you'll be + + align:start position:0% +so you're choosing which way you'll be + + + align:start position:0% +so you're choosing which way you'll be +able to traverse. Either you can go the + + align:start position:0% +able to traverse. Either you can go the + + + align:start position:0% +able to traverse. Either you can go the +true way or the false way. Uh, the + + align:start position:0% +true way or the false way. Uh, the + + + align:start position:0% +true way or the false way. Uh, the +opposite of wherever you push that + + align:start position:0% +opposite of wherever you push that + + + align:start position:0% +opposite of wherever you push that +block. And so, that cuts off one of the + + align:start position:0% +block. And so, that cuts off one of the + + + align:start position:0% +block. And so, that cuts off one of the +things. Then that path is going to be + + align:start position:0% +things. Then that path is going to be + + + align:start position:0% +things. Then that path is going to be +connected to all of the clauses that it + + align:start position:0% +connected to all of the clauses that it + + + align:start position:0% +connected to all of the clauses that it +satisfies that that literal choice + + align:start position:0% +satisfies that that literal choice + + + align:start position:0% +satisfies that that literal choice +satisfies. Then there's this gadget to + + align:start position:0% +satisfies. Then there's this gadget to + + + align:start position:0% +satisfies. Then there's this gadget to +prevent you from wrapping around to the + + align:start position:0% +prevent you from wrapping around to the + + + align:start position:0% +prevent you from wrapping around to the +other side. Whichever one you come down, + + align:start position:0% +other side. Whichever one you come down, + + + align:start position:0% +other side. Whichever one you come down, +you will block off the other path. Uh + + align:start position:0% +you will block off the other path. Uh + + + align:start position:0% +you will block off the other path. Uh +and then you do that again for next + + align:start position:0% +and then you do that again for next + + + align:start position:0% +and then you do that again for next +variable, next variable, and so on. At + + align:start position:0% +variable, next variable, and so on. At + + + align:start position:0% +variable, next variable, and so on. At +the end of the last variable, you run + + align:start position:0% +the end of the last variable, you run + + + align:start position:0% +the end of the last variable, you run +through all the clauses. So how did the + + align:start position:0% +through all the clauses. So how did the + + + align:start position:0% +through all the clauses. So how did the +clauses work? Very simple. Um, if any of + + align:start position:0% +clauses work? Very simple. Um, if any of + + + align:start position:0% +clauses work? Very simple. Um, if any of +the literals that satisfy the clause uh + + align:start position:0% +the literals that satisfy the clause uh + + + align:start position:0% +the literals that satisfy the clause uh +were visitable, then you could push this + + align:start position:0% +were visitable, then you could push this + + + align:start position:0% +were visitable, then you could push this +block over. And then later when you + + align:start position:0% +block over. And then later when you + + + align:start position:0% +block over. And then later when you +visit the clause, at the end when you + + align:start position:0% +visit the clause, at the end when you + + + align:start position:0% +visit the clause, at the end when you +visit the clause and try to traverse it, + + align:start position:0% +visit the clause and try to traverse it, + + + align:start position:0% +visit the clause and try to traverse it, +if there's nothing here, when you push + + align:start position:0% +if there's nothing here, when you push + + + align:start position:0% +if there's nothing here, when you push +this block down, it will go all the way + + align:start position:0% +this block down, it will go all the way + + + align:start position:0% +this block down, it will go all the way +to the bottom and you're trapped never + + align:start position:0% +to the bottom and you're trapped never + + + align:start position:0% +to the bottom and you're trapped never +to get to the finish line down here. But + + align:start position:0% +to get to the finish line down here. But + + + align:start position:0% +to get to the finish line down here. But +if at least one of these was in then it + + align:start position:0% +if at least one of these was in then it + + + align:start position:0% +if at least one of these was in then it +will be it will block this guy and you + + align:start position:0% +will be it will block this guy and you + + + align:start position:0% +will be it will block this guy and you +can if that's true for all of the + + align:start position:0% +can if that's true for all of the + + + align:start position:0% +can if that's true for all of the +clauses then you can get to the + + align:start position:0% +clauses then you can get to the + + + align:start position:0% +clauses then you can get to the +destination. So these are just uh clause + + align:start position:0% +destination. So these are just uh clause + + + align:start position:0% +destination. So these are just uh clause +checking and uh that's very + + align:start position:0% +checking and uh that's very + + + align:start position:0% +checking and uh that's very +straightforward threescent proof. In + + align:start position:0% +straightforward threescent proof. In + + + align:start position:0% +straightforward threescent proof. In +fact the previous proof is based on this + + align:start position:0% +fact the previous proof is based on this + + + align:start position:0% +fact the previous proof is based on this +one and the next proof is based on this + + align:start position:0% +one and the next proof is based on this + + + align:start position:0% +one and the next proof is based on this +one and the Nintendo proofs are all + + align:start position:0% +one and the Nintendo proofs are all + + + align:start position:0% +one and the Nintendo proofs are all +based on this one. This is sort of the + + align:start position:0% +based on this one. This is sort of the + + + align:start position:0% +based on this one. This is sort of the +prototype. Yeah, + + align:start position:0% +prototype. Yeah, + + + align:start position:0% +prototype. Yeah, +the crossover gadget that. + + align:start position:0% +the crossover gadget that. + + + align:start position:0% +the crossover gadget that. +So, this is 3D. So, there's no + + align:start position:0% +So, this is 3D. So, there's no + + + align:start position:0% +So, this is 3D. So, there's no +crossover. + + align:start position:0% +crossover. + + + align:start position:0% +crossover. +Uh, but in 2D, we want to get a + + align:start position:0% +Uh, but in 2D, we want to get a + + + align:start position:0% +Uh, but in 2D, we want to get a +crossover. So, here's how we do 2D. And + + align:start position:0% +crossover. So, here's how we do 2D. And + + + align:start position:0% +crossover. So, here's how we do 2D. And +this will work for both push and push + + align:start position:0% +this will work for both push and push + + + align:start position:0% +this will work for both push and push +one that push and push push. Um, the + + align:start position:0% +one that push and push push. Um, the + + + align:start position:0% +one that push and push push. Um, the +only place we're using push push was + + align:start position:0% +only place we're using push push was + + + align:start position:0% +only place we're using push push was +this clause gadget. So, let's first get + + align:start position:0% +this clause gadget. So, let's first get + + + align:start position:0% +this clause gadget. So, let's first get +rid of that that aspect. Um, so here's + + align:start position:0% +rid of that that aspect. Um, so here's + + + align:start position:0% +rid of that that aspect. Um, so here's +something called a lock. And you're + + align:start position:0% +something called a lock. And you're + + + align:start position:0% +something called a lock. And you're +going to have to believe a little bit + + align:start position:0% +going to have to believe a little bit + + + align:start position:0% +going to have to believe a little bit +here, but + + align:start position:0% +here, but + + + align:start position:0% +here, but +uh your goal, let's say, is to get from + + align:start position:0% +uh your goal, let's say, is to get from + + + align:start position:0% +uh your goal, let's say, is to get from +A to B. And this is what happens if you + + align:start position:0% +A to B. And this is what happens if you + + + align:start position:0% +A to B. And this is what happens if you +try to go from A to B uh directly. There + + align:start position:0% +try to go from A to B uh directly. There + + + align:start position:0% +try to go from A to B uh directly. There +isn't much that you can move. Well, uh + + align:start position:0% +isn't much that you can move. Well, uh + + + align:start position:0% +isn't much that you can move. Well, uh +you can maybe move I down, J left, uh + + align:start position:0% +you can maybe move I down, J left, uh + + + align:start position:0% +you can maybe move I down, J left, uh +and like this. But uh + + align:start position:0% +and like this. But uh + + + align:start position:0% +and like this. But uh +yes, you can move J down uh I down, J + + align:start position:0% +yes, you can move J down uh I down, J + + + align:start position:0% +yes, you can move J down uh I down, J +left, uh E down, F left, B down, but not + + align:start position:0% +left, uh E down, F left, B down, but not + + + align:start position:0% +left, uh E down, F left, B down, but not +C left because D is in the way. Okay. + + align:start position:0% +C left because D is in the way. Okay. + + + align:start position:0% +C left because D is in the way. Okay. +Uh but so you're you can't get from A to + + align:start position:0% +Uh but so you're you can't get from A to + + + align:start position:0% +Uh but so you're you can't get from A to +B. But if you visit from U + + align:start position:0% +B. But if you visit from U + + + align:start position:0% +B. But if you visit from U +uh and you push this block out of the + + align:start position:0% +uh and you push this block out of the + + + align:start position:0% +uh and you push this block out of the +way. + + align:start position:0% +way. + + + align:start position:0% +way. +Yeah. Then you come back through A. Then + + align:start position:0% +Yeah. Then you come back through A. Then + + + align:start position:0% +Yeah. Then you come back through A. Then +you can do you can do these things. Push + + align:start position:0% +you can do you can do these things. Push + + + align:start position:0% +you can do you can do these things. Push +them all over. And then you have room to + + align:start position:0% +them all over. And then you have room to + + + align:start position:0% +them all over. And then you have room to +push C over and then A can go all the + + align:start position:0% +push C over and then A can go all the + + + align:start position:0% +push C over and then A can go all the +way down and you're through. + + align:start position:0% +way down and you're through. + + + align:start position:0% +way down and you're through. +So this unlocks the lock and then pre + + align:start position:0% +So this unlocks the lock and then pre + + + align:start position:0% +So this unlocks the lock and then pre +and then allowing A to B traversal + + align:start position:0% +and then allowing A to B traversal + + + align:start position:0% +and then allowing A to B traversal +later. + + align:start position:0% +later. + + + align:start position:0% +later. +And going backwards from V to U would + + align:start position:0% +And going backwards from V to U would + + + align:start position:0% +And going backwards from V to U would +lock it again. + + align:start position:0% +lock it again. + + + align:start position:0% +lock it again. +No, this is not a reversible gadget. + + align:start position:0% +No, this is not a reversible gadget. + + + align:start position:0% +No, this is not a reversible gadget. +Only works once. + + align:start position:0% + + + + align:start position:0% + +you can't unlock. Once L's down, it's + + align:start position:0% +you can't unlock. Once L's down, it's + + + align:start position:0% +you can't unlock. Once L's down, it's +permanently there. + + align:start position:0% +permanently there. + + + align:start position:0% +permanently there. +Uh, so now we're going to use this in a + + align:start position:0% +Uh, so now we're going to use this in a + + + align:start position:0% +Uh, so now we're going to use this in a +clause as follows. So here's the lock + + align:start position:0% +clause as follows. So here's the lock + + + align:start position:0% +clause as follows. So here's the lock +and then there's this schematic above + + align:start position:0% +and then there's this schematic above + + + align:start position:0% +and then there's this schematic above +it. So we have three possible entries. + + align:start position:0% +it. So we have three possible entries. + + + align:start position:0% +it. So we have three possible entries. +This is Xi or not XJ or XK. Um, and + + align:start position:0% +This is Xi or not XJ or XK. Um, and + + + align:start position:0% +This is Xi or not XJ or XK. Um, and +we're going to use this gadget to say, + + align:start position:0% +we're going to use this gadget to say, + + + align:start position:0% +we're going to use this gadget to say, +well, if you come down the true path + + align:start position:0% +well, if you come down the true path + + + align:start position:0% +well, if you come down the true path +from here, you're going to have to push + + align:start position:0% +from here, you're going to have to push + + + align:start position:0% +from here, you're going to have to push +this block down, which prevents you from + + align:start position:0% +this block down, which prevents you from + + + align:start position:0% +this block down, which prevents you from +using the other half of the gadget. So, + + align:start position:0% +using the other half of the gadget. So, + + + align:start position:0% +using the other half of the gadget. So, +either you move Y or you move X and you + + align:start position:0% +either you move Y or you move X and you + + + align:start position:0% +either you move Y or you move X and you +can then you can only from then on you + + align:start position:0% +can then you can only from then on you + + + align:start position:0% +can then you can only from then on you +can only do west to south traversal or + + align:start position:0% +can only do west to south traversal or + + + align:start position:0% +can only do west to south traversal or +only north to east traversal. So, it + + align:start position:0% +only north to east traversal. So, it + + + align:start position:0% +only north to east traversal. So, it +blocks the other path. So, this is + + align:start position:0% +blocks the other path. So, this is + + + align:start position:0% +blocks the other path. So, this is +because I don't want to come down here, + + align:start position:0% +because I don't want to come down here, + + + align:start position:0% +because I don't want to come down here, +unlock the lock, and then go back on a + + align:start position:0% +unlock the lock, and then go back on a + + + align:start position:0% +unlock the lock, and then go back on a +different path because that's not + + align:start position:0% +different path because that's not + + + align:start position:0% +different path because that's not +something that's necessarily true. So, + + align:start position:0% +something that's necessarily true. So, + + + align:start position:0% +something that's necessarily true. So, +as you come down one of these, you force + + align:start position:0% +as you come down one of these, you force + + + align:start position:0% +as you come down one of these, you force +these gadgets to be in a particular + + align:start position:0% +these gadgets to be in a particular + + + align:start position:0% +these gadgets to be in a particular +state that will only let you come back + + align:start position:0% +state that will only let you come back + + + align:start position:0% +state that will only let you come back +the way you came. Uh, go back the way + + align:start position:0% +the way you came. Uh, go back the way + + + align:start position:0% +the way you came. Uh, go back the way +you came. And then you can unlock the + + align:start position:0% +you came. And then you can unlock the + + + align:start position:0% +you came. And then you can unlock the +lock. And then this just connects back. + + align:start position:0% +lock. And then this just connects back. + + + align:start position:0% +lock. And then this just connects back. +Okay. Then later when we're checking the + + align:start position:0% +Okay. Then later when we're checking the + + + align:start position:0% +Okay. Then later when we're checking the +clauses, when we come through all the + + align:start position:0% +clauses, when we come through all the + + + align:start position:0% +clauses, when we come through all the +clauses to make sure that they're true, + + align:start position:0% +clauses to make sure that they're true, + + + align:start position:0% +clauses to make sure that they're true, +we're going to route those from A to B + + align:start position:0% +we're going to route those from A to B + + + align:start position:0% +we're going to route those from A to B +to A to B to A to B for all the locks. + + align:start position:0% +to A to B to A to B for all the locks. + + + align:start position:0% +to A to B to A to B for all the locks. +And if they're all unlocked, then we'll + + align:start position:0% +And if they're all unlocked, then we'll + + + align:start position:0% +And if they're all unlocked, then we'll +be able to traverse them. And otherwise, + + align:start position:0% +be able to traverse them. And otherwise, + + + align:start position:0% +be able to traverse them. And otherwise, +not. That's the idea. + + align:start position:0% +not. That's the idea. + + + align:start position:0% +not. That's the idea. +Okay. Then we have the issue of a + + align:start position:0% +Okay. Then we have the issue of a + + + align:start position:0% +Okay. Then we have the issue of a +crossover if we want to go into 2D. + + align:start position:0% +crossover if we want to go into 2D. + + + align:start position:0% +crossover if we want to go into 2D. +So we have uh here is a basic crossover + + align:start position:0% +So we have uh here is a basic crossover + + + align:start position:0% +So we have uh here is a basic crossover +in the push one model or push push one. + + align:start position:0% +in the push one model or push push one. + + + align:start position:0% +in the push one model or push push one. +If we're going to go from north to south + + align:start position:0% +If we're going to go from north to south + + + align:start position:0% +If we're going to go from north to south +then we will go okay we can push this + + align:start position:0% +then we will go okay we can push this + + + align:start position:0% +then we will go okay we can push this +down but we won't be able to go to the + + align:start position:0% +down but we won't be able to go to the + + + align:start position:0% +down but we won't be able to go to the +east then okay and we're not able to go + + align:start position:0% +east then okay and we're not able to go + + + align:start position:0% +east then okay and we're not able to go +to the west because if we push this + + align:start position:0% +to the west because if we push this + + + align:start position:0% +to the west because if we push this +block it gets stuck. So we can go north + + align:start position:0% +block it gets stuck. So we can go north + + + align:start position:0% +block it gets stuck. So we can go north +to south. That's fine. We can also go + + align:start position:0% +to south. That's fine. We can also go + + + align:start position:0% +to south. That's fine. We can also go +west to east by symmetry essentially. Uh + + align:start position:0% +west to east by symmetry essentially. Uh + + + align:start position:0% +west to east by symmetry essentially. Uh +but you can't go from west to north or + + align:start position:0% +but you can't go from west to north or + + + align:start position:0% +but you can't go from west to north or +west to south or any of the other + + align:start position:0% +west to south or any of the other + + + align:start position:0% +west to south or any of the other +combinations. This works as long as you + + align:start position:0% +combinations. This works as long as you + + + align:start position:0% +combinations. This works as long as you +do one or the other. Uh if you do if + + align:start position:0% +do one or the other. Uh if you do if + + + align:start position:0% +do one or the other. Uh if you do if +once you do west to east, you can't even + + align:start position:0% +once you do west to east, you can't even + + + align:start position:0% +once you do west to east, you can't even +do north to south. So this is why we + + align:start position:0% +do north to south. So this is why we + + + align:start position:0% +do north to south. So this is why we +call it an x over xor crossover. It's + + align:start position:0% +call it an x over xor crossover. It's + + + align:start position:0% +call it an x over xor crossover. It's +not what we want. But if we combine + + align:start position:0% +not what we want. But if we combine + + + align:start position:0% +not what we want. But if we combine +things in this way, we get a + + align:start position:0% +things in this way, we get a + + + align:start position:0% +things in this way, we get a +unidirectional crossover. Um this is one + + align:start position:0% +unidirectional crossover. Um this is one + + + align:start position:0% +unidirectional crossover. Um this is one +where I better check my notes. + + align:start position:0% +where I better check my notes. + + + align:start position:0% +where I better check my notes. +You can do one of three things. Um, you + + align:start position:0% +You can do one of three things. Um, you + + + align:start position:0% +You can do one of three things. Um, you +can do north to south if you want and + + align:start position:0% +can do north to south if you want and + + + align:start position:0% +can do north to south if you want and +then you can do west to east. + + align:start position:0% +then you can do west to east. + + + align:start position:0% +then you can do west to east. +So you could just do west to east or you + + align:start position:0% +So you could just do west to east or you + + + align:start position:0% +So you could just do west to east or you +could do north to south then west to + + align:start position:0% +could do north to south then west to + + + align:start position:0% +could do north to south then west to +east or you could just do north to + + align:start position:0% +east or you could just do north to + + + align:start position:0% +east or you could just do north to +south. Those are all possible here. So + + align:start position:0% +south. Those are all possible here. So + + + align:start position:0% +south. Those are all possible here. So +when we do north to south we prevent + + align:start position:0% +when we do north to south we prevent + + + align:start position:0% +when we do north to south we prevent +this particular thing from being + + align:start position:0% +this particular thing from being + + + align:start position:0% +this particular thing from being +traversed but we unlock this gate which + + align:start position:0% +traversed but we unlock this gate which + + + align:start position:0% +traversed but we unlock this gate which +later when we go west east will allow us + + align:start position:0% +later when we go west east will allow us + + + align:start position:0% +later when we go west east will allow us +to do it. Uh so we go here and then + + align:start position:0% +to do it. Uh so we go here and then + + + align:start position:0% +to do it. Uh so we go here and then +uh these are called + + align:start position:0% +uh these are called + + + align:start position:0% +uh these are called +uh no reverse gadgets. So once you push + + align:start position:0% +uh no reverse gadgets. So once you push + + + align:start position:0% +uh no reverse gadgets. So once you push +this block back you can never go then + + align:start position:0% +this block back you can never go then + + + align:start position:0% +this block back you can never go then +this this gadget becomes untraversible. + + align:start position:0% +this this gadget becomes untraversible. + + + align:start position:0% +this this gadget becomes untraversible. +So you come here you push this push that + + align:start position:0% +So you come here you push this push that + + + align:start position:0% +So you come here you push this push that +push that and now you can never use this + + align:start position:0% +push that and now you can never use this + + + align:start position:0% +push that and now you can never use this +gadget again. So, it's like a single-use + + align:start position:0% +gadget again. So, it's like a single-use + + + align:start position:0% +gadget again. So, it's like a single-use +thing. So, you can come here. If you + + align:start position:0% +thing. So, you can come here. If you + + + align:start position:0% +thing. So, you can come here. If you +tried to do that, you would get stuck + + align:start position:0% +tried to do that, you would get stuck + + + align:start position:0% +tried to do that, you would get stuck +because this is a lock and it hasn't + + align:start position:0% +because this is a lock and it hasn't + + + align:start position:0% +because this is a lock and it hasn't +been unlocked yet. So, instead, you've + + align:start position:0% +been unlocked yet. So, instead, you've + + + align:start position:0% +been unlocked yet. So, instead, you've +got to go over here, go through this + + align:start position:0% +got to go over here, go through this + + + align:start position:0% +got to go over here, go through this +thing, permanently destroy it, and then + + align:start position:0% +thing, permanently destroy it, and then + + + align:start position:0% +thing, permanently destroy it, and then +unlock this gadget, and then you exit. + + align:start position:0% +unlock this gadget, and then you exit. + + + align:start position:0% +unlock this gadget, and then you exit. +So, that was north to south traversal. + + align:start position:0% +So, that was north to south traversal. + + + align:start position:0% +So, that was north to south traversal. +We unlocked this gate, and we unlocked + + align:start position:0% +We unlocked this gate, and we unlocked + + + align:start position:0% +We unlocked this gate, and we unlocked +this gate. So, if you're coming west to + + align:start position:0% +this gate. So, if you're coming west to + + + align:start position:0% +this gate. So, if you're coming west to +east could be this has been done or not. + + align:start position:0% +east could be this has been done or not. + + + align:start position:0% +east could be this has been done or not. +So going west to east maybe you haven't + + align:start position:0% +So going west to east maybe you haven't + + + align:start position:0% +So going west to east maybe you haven't +visited this gadget then you can just go + + align:start position:0% +visited this gadget then you can just go + + + align:start position:0% +visited this gadget then you can just go +through here block off a later north + + align:start position:0% +through here block off a later north + + + align:start position:0% +through here block off a later north +north to south traversal that's okay + + align:start position:0% +north to south traversal that's okay + + + align:start position:0% +north to south traversal that's okay +then come over here and leave if you try + + align:start position:0% +then come over here and leave if you try + + + align:start position:0% +then come over here and leave if you try +to go here nothing happens + + align:start position:0% +to go here nothing happens + + + align:start position:0% +to go here nothing happens +okay uh or it could be this has already + + align:start position:0% +okay uh or it could be this has already + + + align:start position:0% +okay uh or it could be this has already +been done north to south and then when + + align:start position:0% +been done north to south and then when + + + align:start position:0% +been done north to south and then when +you're coming from the west this has + + align:start position:0% +you're coming from the west this has + + + align:start position:0% +you're coming from the west this has +been unlocked and so you can open this + + align:start position:0% +been unlocked and so you can open this + + + align:start position:0% +been unlocked and so you can open this +gate and come through here uh this has + + align:start position:0% +gate and come through here uh this has + + + align:start position:0% +gate and come through here uh this has +already been used so you can't go that + + align:start position:0% +already been used so you can't go that + + + align:start position:0% +already been used so you can't go that +way so instead Instead, you use this + + align:start position:0% +way so instead Instead, you use this + + + align:start position:0% +way so instead Instead, you use this +one. This has already been unlocked. So, + + align:start position:0% +one. This has already been unlocked. So, + + + align:start position:0% +one. This has already been unlocked. So, +you can get through and then you get + + align:start position:0% +you can get through and then you get + + + align:start position:0% +you can get through and then you get +out. + + align:start position:0% +out. + + + align:start position:0% +out. +So, with just a little bit of checking, + + align:start position:0% +So, with just a little bit of checking, + + + align:start position:0% +So, with just a little bit of checking, +those are the only things you can do. + + align:start position:0% +those are the only things you can do. + + + align:start position:0% +those are the only things you can do. +So, when we have this diagram, I think I + + align:start position:0% +So, when we have this diagram, I think I + + + align:start position:0% +So, when we have this diagram, I think I +have one here, variables and clauses, + + align:start position:0% +have one here, variables and clauses, + + + align:start position:0% +have one here, variables and clauses, +and you connect all the variables to all + + align:start position:0% +and you connect all the variables to all + + + align:start position:0% +and you connect all the variables to all +the clauses they're involved in. This is + + align:start position:0% +the clauses they're involved in. This is + + + align:start position:0% +the clauses they're involved in. This is +a slide from lecture one, uh, but it's + + align:start position:0% +a slide from lecture one, uh, but it's + + + align:start position:0% +a slide from lecture one, uh, but it's +the same outline. uh you can you know + + align:start position:0% +the same outline. uh you can you know + + + align:start position:0% +the same outline. uh you can you know +the order in which these crossings + + align:start position:0% +the order in which these crossings + + + align:start position:0% +the order in which these crossings +happen because you know I'm gonna ver + + align:start position:0% +happen because you know I'm gonna ver + + + align:start position:0% +happen because you know I'm gonna ver +I'm going to visit variable I before I + + align:start position:0% +I'm going to visit variable I before I + + + align:start position:0% +I'm going to visit variable I before I +visit variable J greater than I. So uh I + + align:start position:0% +visit variable J greater than I. So uh I + + + align:start position:0% +visit variable J greater than I. So uh I +know how to order and these each of + + align:start position:0% +know how to order and these each of + + + align:start position:0% +know how to order and these each of +these paths is really two paths one and + + align:start position:0% +these paths is really two paths one and + + + align:start position:0% +these paths is really two paths one and +then the other. And so uh I know whether + + align:start position:0% +then the other. And so uh I know whether + + + align:start position:0% +then the other. And so uh I know whether +I'm going to do north to south before + + align:start position:0% +I'm going to do north to south before + + + align:start position:0% +I'm going to do north to south before +west to east. If not I transpose the + + align:start position:0% +west to east. If not I transpose the + + + align:start position:0% +west to east. If not I transpose the +gadget and exchange uh north south with + + align:start position:0% +gadget and exchange uh north south with + + + align:start position:0% +gadget and exchange uh north south with +west east. And then I don't need that + + align:start position:0% +west east. And then I don't need that + + + align:start position:0% +west east. And then I don't need that +they're both visited. I don't know which + + align:start position:0% +they're both visited. I don't know which + + + align:start position:0% +they're both visited. I don't know which +ones are going to be visited, but do one + + align:start position:0% +ones are going to be visited, but do one + + + align:start position:0% +ones are going to be visited, but do one +or the other. Or if I do both, I know + + align:start position:0% +or the other. Or if I do both, I know + + + align:start position:0% +or the other. Or if I do both, I know +one will come before the other. So that + + align:start position:0% +one will come before the other. So that + + + align:start position:0% +one will come before the other. So that +kind of crossover gadget is enough for + + align:start position:0% +kind of crossover gadget is enough for + + + align:start position:0% +kind of crossover gadget is enough for +the push one and push push one. And + + align:start position:0% +the push one and push push one. And + + + align:start position:0% +the push one and push push one. And +exactly, it's exactly mimicking what we + + align:start position:0% +exactly, it's exactly mimicking what we + + + align:start position:0% +exactly, it's exactly mimicking what we +did with Super Mario Brothers. We just + + align:start position:0% +did with Super Mario Brothers. We just + + + align:start position:0% +did with Super Mario Brothers. We just +had a different variable choice and a + + align:start position:0% +had a different variable choice and a + + + align:start position:0% +had a different variable choice and a +different clause and a different + + align:start position:0% +different clause and a different + + + align:start position:0% +different clause and a different +crossover gadget. But other than that, + + align:start position:0% +crossover gadget. But other than that, + + + align:start position:0% +crossover gadget. But other than that, +it was exactly the same. The gadgets + + align:start position:0% +it was exactly the same. The gadgets + + + align:start position:0% +it was exactly the same. The gadgets +were different, but the proof structure + + align:start position:0% +were different, but the proof structure + + + align:start position:0% +were different, but the proof structure +was the same. And that's our beginning + + align:start position:0% +was the same. And that's our beginning + + + align:start position:0% +was the same. And that's our beginning +of threes reductions. We will do many + + align:start position:0% +of threes reductions. We will do many + + + align:start position:0% +of threes reductions. We will do many +more next class. \ No newline at end of file diff --git a/xHNIknabsRY.txt b/xHNIknabsRY.txt new file mode 100644 index 0000000000000000000000000000000000000000..4c333ddcc5f07a003afc858c7d9833d5e6b76797 --- /dev/null +++ b/xHNIknabsRY.txt @@ -0,0 +1,9779 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu + + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu +this class is called game design is not + + align:start position:0% +this class is called game design is not + + + align:start position:0% +this class is called game design is not +an intro class + + align:start position:0% +an intro class + + + align:start position:0% +an intro class +how many of you have taken a CMS class + + align:start position:0% +how many of you have taken a CMS class + + + align:start position:0% +how many of you have taken a CMS class +before ok about half of you alright a + + align:start position:0% +before ok about half of you alright a + + + align:start position:0% +before ok about half of you alright a +number of you haven't taken the CMS + + align:start position:0% +number of you haven't taken the CMS + + + align:start position:0% +number of you haven't taken the CMS +class before it's actually a + + align:start position:0% +class before it's actually a + + + align:start position:0% +class before it's actually a +prerequisite but I can really take as + + align:start position:0% +prerequisite but I can really take as + + + align:start position:0% +prerequisite but I can really take as +many students as can fit in here so let + + align:start position:0% +many students as can fit in here so let + + + align:start position:0% +many students as can fit in here so let +me tell you why that prerequisite exists + + align:start position:0% +me tell you why that prerequisite exists + + + align:start position:0% +me tell you why that prerequisite exists +the prerequisite exists because in a CMS + + align:start position:0% +the prerequisite exists because in a CMS + + + align:start position:0% +the prerequisite exists because in a CMS +class we typically expect people to do a + + align:start position:0% +class we typically expect people to do a + + + align:start position:0% +class we typically expect people to do a +lot of writing we expect people to + + align:start position:0% +lot of writing we expect people to + + + align:start position:0% +lot of writing we expect people to +expect their grades to depend on + + align:start position:0% +expect their grades to depend on + + + align:start position:0% +expect their grades to depend on +equality or their writing we expect + + align:start position:0% +equality or their writing we expect + + + align:start position:0% +equality or their writing we expect +people to do all the reading in class + + align:start position:0% +people to do all the reading in class + + + align:start position:0% +people to do all the reading in class +and to be able to do it before class + + align:start position:0% +and to be able to do it before class + + + align:start position:0% +and to be able to do it before class +starts so that you can actually be + + align:start position:0% +starts so that you can actually be + + + align:start position:0% +starts so that you can actually be +prepared to to have a conversation about + + align:start position:0% +prepared to to have a conversation about + + + align:start position:0% +prepared to to have a conversation about +that in class different departments even + + align:start position:0% +that in class different departments even + + + align:start position:0% +that in class different departments even +different humanities departments do + + align:start position:0% +different humanities departments do + + + align:start position:0% +different humanities departments do +things differently + + align:start position:0% +things differently + + + align:start position:0% +things differently +in CMS class if you've taken any CMS + + align:start position:0% +in CMS class if you've taken any CMS + + + align:start position:0% +in CMS class if you've taken any CMS +class none of this should sound + + align:start position:0% +class none of this should sound + + + align:start position:0% +class none of this should sound +surprising you know you've probably + + align:start position:0% +surprising you know you've probably + + + align:start position:0% +surprising you know you've probably +written way more in other CMS classes + + align:start position:0% +written way more in other CMS classes + + + align:start position:0% +written way more in other CMS classes +that you would necessarily write in this + + align:start position:0% +that you would necessarily write in this + + + align:start position:0% +that you would necessarily write in this +class you're also expected to present + + align:start position:0% +class you're also expected to present + + + align:start position:0% +class you're also expected to present +you're expected to come up in front of + + align:start position:0% +you're expected to come up in front of + + + align:start position:0% +you're expected to come up in front of +the entire class and say I talked about + + align:start position:0% +the entire class and say I talked about + + + align:start position:0% +the entire class and say I talked about +your project + + align:start position:0% +your project + + + align:start position:0% +your project +yeah I expected you should expect that + + align:start position:0% +yeah I expected you should expect that + + + align:start position:0% +yeah I expected you should expect that +your grades will depend on the quality + + align:start position:0% +your grades will depend on the quality + + + align:start position:0% +your grades will depend on the quality +of your presentation as well so one + + align:start position:0% +of your presentation as well so one + + + align:start position:0% +of your presentation as well so one +example you may you might design a + + align:start position:0% +example you may you might design a + + + align:start position:0% +example you may you might design a +perfectly good game it's like an + + align:start position:0% +perfectly good game it's like an + + + align:start position:0% +perfectly good game it's like an +extremely elegant beautiful you know a + + align:start position:0% +extremely elegant beautiful you know a + + + align:start position:0% +extremely elegant beautiful you know a +game for the ages like go something like + + align:start position:0% +game for the ages like go something like + + + align:start position:0% +game for the ages like go something like +that you designed it in this class it is + + align:start position:0% +that you designed it in this class it is + + + align:start position:0% +that you designed it in this class it is +great but if your grammar is terrible in + + align:start position:0% +great but if your grammar is terrible in + + + align:start position:0% +great but if your grammar is terrible in +your rules even though I can still read + + align:start position:0% +your rules even though I can still read + + + align:start position:0% +your rules even though I can still read +a rule then I can play the game and it + + align:start position:0% +a rule then I can play the game and it + + + align:start position:0% +a rule then I can play the game and it +says wow there's a really beautiful game + + align:start position:0% +says wow there's a really beautiful game + + + align:start position:0% +says wow there's a really beautiful game +but you're writing sucks you walk going + + align:start position:0% +but you're writing sucks you walk going + + + align:start position:0% +but you're writing sucks you walk going +to this great song based on that that's + + align:start position:0% +to this great song based on that that's + + + align:start position:0% +to this great song based on that that's +one of the things that are that you + + align:start position:0% +one of the things that are that you + + + align:start position:0% +one of the things that are that you +should expect now there is a Writing + + align:start position:0% +should expect now there is a Writing + + + align:start position:0% +should expect now there is a Writing +Center over in building 12 I think and + + align:start position:0% +Center over in building 12 I think and + + + align:start position:0% +Center over in building 12 I think and +they're going to be they're going to be + + align:start position:0% +they're going to be they're going to be + + + align:start position:0% +they're going to be they're going to be +moving in the summer but right now + + align:start position:0% +moving in the summer but right now + + + align:start position:0% +moving in the summer but right now +they're still inputting 12 definitely + + align:start position:0% +they're still inputting 12 definitely + + + align:start position:0% +they're still inputting 12 definitely +take advantage of them we are looking + + align:start position:0% +take advantage of them we are looking + + + align:start position:0% +take advantage of them we are looking +for concise writing we are looking for + + align:start position:0% +for concise writing we are looking for + + + align:start position:0% +for concise writing we are looking for +precise writing but we're not looking + + align:start position:0% +precise writing but we're not looking + + + align:start position:0% +precise writing but we're not looking +for + + align:start position:0% +for + + + align:start position:0% +for +I mean how should I put it any more + + align:start position:0% +I mean how should I put it any more + + + align:start position:0% +I mean how should I put it any more +words than it's necessary to get a point + + align:start position:0% +words than it's necessary to get a point + + + align:start position:0% +words than it's necessary to get a point +across we want things to be fast to read + + align:start position:0% +across we want things to be fast to read + + + align:start position:0% +across we want things to be fast to read +we want things to be easy for lay people + + align:start position:0% +we want things to be easy for lay people + + + align:start position:0% +we want things to be easy for lay people +to read not necessarily MIT students to + + align:start position:0% +to read not necessarily MIT students to + + + align:start position:0% +to read not necessarily MIT students to +read you are going to see examples many + + align:start position:0% +read you are going to see examples many + + + align:start position:0% +read you are going to see examples many +many examples of very fully written + + align:start position:0% +many examples of very fully written + + + align:start position:0% +many examples of very fully written +rules in this class of games are + + align:start position:0% +rules in this class of games are + + + align:start position:0% +rules in this class of games are +actually very well well made I actually + + align:start position:0% +actually very well well made I actually + + + align:start position:0% +actually very well well made I actually +kind of like this company make what + + align:start position:0% +kind of like this company make what + + + align:start position:0% +kind of like this company make what +little wooden trains toys + + align:start position:0% +little wooden trains toys + + + align:start position:0% +little wooden trains toys +if you apparently like kids settings + + align:start position:0% +if you apparently like kids settings + + + align:start position:0% +if you apparently like kids settings +they may have gotten twice from this + + align:start position:0% +they may have gotten twice from this + + + align:start position:0% +they may have gotten twice from this +company game for kids right now not for + + align:start position:0% +company game for kids right now not for + + + align:start position:0% +company game for kids right now not for +children under three years that bottom + + align:start position:0% +children under three years that bottom + + + align:start position:0% +children under three years that bottom +that's that's that's the barrier and the + + align:start position:0% +that's that's that's the barrier and the + + + align:start position:0% +that's that's that's the barrier and the +rules are written for you know in like + + align:start position:0% +rules are written for you know in like + + + align:start position:0% +rules are written for you know in like +six different languages but for kids now + + align:start position:0% +six different languages but for kids now + + + align:start position:0% +six different languages but for kids now +they still expect parents to be able to + + align:start position:0% +they still expect parents to be able to + + + align:start position:0% +they still expect parents to be able to +explain how these games oh but you know + + align:start position:0% +explain how these games oh but you know + + + align:start position:0% +explain how these games oh but you know +you can imagine like a six-year-old + + align:start position:0% +you can imagine like a six-year-old + + + align:start position:0% +you can imagine like a six-year-old +became a placate and be able to play + + align:start position:0% +became a placate and be able to play + + + align:start position:0% +became a placate and be able to play +just fine and this is actually a really + + align:start position:0% +just fine and this is actually a really + + + align:start position:0% +just fine and this is actually a really +elegant game that's kind of like where + + align:start position:0% +elegant game that's kind of like where + + + align:start position:0% +elegant game that's kind of like where +you should be aiming for with the + + align:start position:0% +you should be aiming for with the + + + align:start position:0% +you should be aiming for with the +quality of your writing try to get your + + align:start position:0% +quality of your writing try to get your + + + align:start position:0% +quality of your writing try to get your +stuff as clearly as possible as quickly + + align:start position:0% +stuff as clearly as possible as quickly + + + align:start position:0% +stuff as clearly as possible as quickly +as possible over to as well a reading + + align:start position:0% +as possible over to as well a reading + + + align:start position:0% +as possible over to as well a reading +level as possible there are a couple of + + align:start position:0% +level as possible there are a couple of + + + align:start position:0% +level as possible there are a couple of +tips that we have written and that file + + align:start position:0% +tips that we have written and that file + + + align:start position:0% +tips that we have written and that file +is up on stellar I'm not handing in that + + align:start position:0% +is up on stellar I'm not handing in that + + + align:start position:0% +is up on stellar I'm not handing in that +sheet out because you can go and and + + align:start position:0% + + + + align:start position:0% + +that's called the rule style guide I + + align:start position:0% +that's called the rule style guide I + + + align:start position:0% +that's called the rule style guide I +don't have a link for that in here I'll + + align:start position:0% +don't have a link for that in here I'll + + + align:start position:0% +don't have a link for that in here I'll +I'll just put it on top of a salad of a + + align:start position:0% +I'll just put it on top of a salad of a + + + align:start position:0% +I'll just put it on top of a salad of a +standard announcement page the rule + + align:start position:0% +standard announcement page the rule + + + align:start position:0% +standard announcement page the rule +style guide is basically a two page + + align:start position:0% +style guide is basically a two page + + + align:start position:0% +style guide is basically a two page +document that just gives you a bunch of + + align:start position:0% +document that just gives you a bunch of + + + align:start position:0% +document that just gives you a bunch of +tips on when to use bullet points versus + + align:start position:0% +tips on when to use bullet points versus + + + align:start position:0% +tips on when to use bullet points versus +numbered bullets for instance when to + + align:start position:0% +numbered bullets for instance when to + + + align:start position:0% +numbered bullets for instance when to +[Music] + + align:start position:0% + + + + align:start position:0% + +say thing think that you absolutely + + align:start position:0% +say thing think that you absolutely + + + align:start position:0% +say thing think that you absolutely +should include like a list of components + + align:start position:0% +should include like a list of components + + + align:start position:0% +should include like a list of components +in your game just so that when I when I + + align:start position:0% +in your game just so that when I when I + + + align:start position:0% +in your game just so that when I when I +get it as a + + align:start position:0% +get it as a + + + align:start position:0% +get it as a +as an instructor and Yeti assignment I + + align:start position:0% +as an instructor and Yeti assignment I + + + align:start position:0% +as an instructor and Yeti assignment I +can actually make sure that everything + + align:start position:0% +can actually make sure that everything + + + align:start position:0% +can actually make sure that everything +in your game was provided to me so that + + align:start position:0% +in your game was provided to me so that + + + align:start position:0% +in your game was provided to me so that +I can actually play the whole thing give + + align:start position:0% +I can actually play the whole thing give + + + align:start position:0% +I can actually play the whole thing give +players a way to decide who goes first + + align:start position:0% +players a way to decide who goes first + + + align:start position:0% +players a way to decide who goes first +don't just leave it up to the players as + + align:start position:0% +don't just leave it up to the players as + + + align:start position:0% +don't just leave it up to the players as +you know pick a player to go first to + + align:start position:0% +you know pick a player to go first to + + + align:start position:0% +you know pick a player to go first to +pick something silly like you know + + align:start position:0% +pick something silly like you know + + + align:start position:0% +pick something silly like you know +person who grew up closest to the scene + + align:start position:0% +person who grew up closest to the scene + + + align:start position:0% +person who grew up closest to the scene +you know that's right that's a real real + + align:start position:0% +you know that's right that's a real real + + + align:start position:0% +you know that's right that's a real real +rule from from the horror so we do + + align:start position:0% +rule from from the horror so we do + + + align:start position:0% +rule from from the horror so we do +encourage inclusive language it can be a + + align:start position:0% +encourage inclusive language it can be a + + + align:start position:0% +encourage inclusive language it can be a +little bit more verbose but instead of + + align:start position:0% +little bit more verbose but instead of + + + align:start position:0% +little bit more verbose but instead of +writing a say instead of describing all + + align:start position:0% +writing a say instead of describing all + + + align:start position:0% +writing a say instead of describing all +players as male we do appreciate it when + + align:start position:0% +players as male we do appreciate it when + + + align:start position:0% +players as male we do appreciate it when +people say he or she we is fine to be + + align:start position:0% +people say he or she we is fine to be + + + align:start position:0% +people say he or she we is fine to be +able to clip between he and she + + align:start position:0% +able to clip between he and she + + + align:start position:0% +able to clip between he and she +but of course not when you're describing + + align:start position:0% +but of course not when you're describing + + + align:start position:0% +but of course not when you're describing +the same player doing a certain rule you + + align:start position:0% +the same player doing a certain rule you + + + align:start position:0% +the same player doing a certain rule you +know they're not changing the gender the + + align:start position:0% +know they're not changing the gender the + + + align:start position:0% +know they're not changing the gender the +development of the tournament but it's a + + align:start position:0% +development of the tournament but it's a + + + align:start position:0% +development of the tournament but it's a +great way to be able to use language to + + align:start position:0% +great way to be able to use language to + + + align:start position:0% +great way to be able to use language to +describe so you're a player being you + + align:start position:0% +describe so you're a player being you + + + align:start position:0% +describe so you're a player being you +can also just say the player the player + + align:start position:0% +can also just say the player the player + + + align:start position:0% +can also just say the player the player +player + + align:start position:0% +player + + + align:start position:0% +player +it is a little bit more verbose but in + + align:start position:0% +it is a little bit more verbose but in + + + align:start position:0% +it is a little bit more verbose but in +that particular case there is a sort of + + align:start position:0% +that particular case there is a sort of + + + align:start position:0% +that particular case there is a sort of +higher goal at mine and this is that's + + align:start position:0% +higher goal at mine and this is that's + + + align:start position:0% +higher goal at mine and this is that's +to get across the point that games are + + align:start position:0% +to get across the point that games are + + + align:start position:0% +to get across the point that games are +for everyone especially the games that + + align:start position:0% +for everyone especially the games that + + + align:start position:0% +for everyone especially the games that +you're gonna be making in this class + + align:start position:0% +you're gonna be making in this class + + + align:start position:0% +you're gonna be making in this class +there's no particular reason why in this + + align:start position:0% +there's no particular reason why in this + + + align:start position:0% +there's no particular reason why in this +class you should be making a game just + + align:start position:0% +class you should be making a game just + + + align:start position:0% +class you should be making a game just +for men to play just for women to play + + align:start position:0% +for men to play just for women to play + + + align:start position:0% +for men to play just for women to play +and right now is too easy to fall into + + align:start position:0% +and right now is too easy to fall into + + + align:start position:0% +and right now is too easy to fall into +the trap but you just you just + + align:start position:0% +the trap but you just you just + + + align:start position:0% +the trap but you just you just +generalize that all the players are male + + align:start position:0% +generalize that all the players are male + + + align:start position:0% +generalize that all the players are male +and that's just bad so don't do that + + align:start position:0% +and that's just bad so don't do that + + + align:start position:0% +and that's just bad so don't do that +in fact if you if you take the effort to + + align:start position:0% +in fact if you if you take the effort to + + + align:start position:0% +in fact if you if you take the effort to +do that and you will see that reflected + + align:start position:0% +do that and you will see that reflected + + + align:start position:0% +do that and you will see that reflected +immigrants if you take the effort or to + + align:start position:0% +immigrants if you take the effort or to + + + align:start position:0% +immigrants if you take the effort or to +use inclusive language let's see what + + align:start position:0% +use inclusive language let's see what + + + align:start position:0% +use inclusive language let's see what +else + + align:start position:0% + + + + align:start position:0% + +attendance you have to attend every + + align:start position:0% +attendance you have to attend every + + + align:start position:0% +attendance you have to attend every +single class if you are sick especially + + align:start position:0% +single class if you are sick especially + + + align:start position:0% +single class if you are sick especially +if your secret something contagious or + + align:start position:0% +if your secret something contagious or + + + align:start position:0% +if your secret something contagious or +is sick to the point where you can't + + align:start position:0% +is sick to the point where you can't + + + align:start position:0% +is sick to the point where you can't +move say if you broke something and you + + align:start position:0% +move say if you broke something and you + + + align:start position:0% +move say if you broke something and you +really you should be resting + + align:start position:0% +really you should be resting + + + align:start position:0% +really you should be resting +that's fine just email us before class + + align:start position:0% +that's fine just email us before class + + + align:start position:0% +that's fine just email us before class +starts now you know if it was an + + align:start position:0% +starts now you know if it was an + + + align:start position:0% +starts now you know if it was an +accident or something and you had + + align:start position:0% +accident or something and you had + + + align:start position:0% +accident or something and you had +trouble getting to email like that + + align:start position:0% +trouble getting to email like that + + + align:start position:0% +trouble getting to email like that +that's fine you can email us after it'll + + align:start position:0% +that's fine you can email us after it'll + + + align:start position:0% +that's fine you can email us after it'll +be nice to be able to get some evidence + + align:start position:0% +be nice to be able to get some evidence + + + align:start position:0% +be nice to be able to get some evidence +from your from your doctor but you know + + align:start position:0% +from your from your doctor but you know + + + align:start position:0% +from your from your doctor but you know +which cups of chef are not going to be + + align:start position:0% +which cups of chef are not going to be + + + align:start position:0% +which cups of chef are not going to be +too too much less ticular on that things + + align:start position:0% +too too much less ticular on that things + + + align:start position:0% +too too much less ticular on that things +that I don't give or ematic exam + + align:start position:0% +that I don't give or ematic exam + + + align:start position:0% +that I don't give or ematic exam +absences include being called away for a + + align:start position:0% +absences include being called away for a + + + align:start position:0% +absences include being called away for a +job interview you know being stuck in an + + align:start position:0% +job interview you know being stuck in an + + + align:start position:0% +job interview you know being stuck in an +airport because you planned your Spring + + align:start position:0% +airport because you planned your Spring + + + align:start position:0% +airport because you planned your Spring +Break flight back too late or something + + align:start position:0% +Break flight back too late or something + + + align:start position:0% +Break flight back too late or something +like that you have three free absences + + align:start position:0% +like that you have three free absences + + + align:start position:0% +like that you have three free absences +basically you have three absences well + + align:start position:0% +basically you have three absences well + + + align:start position:0% +basically you have three absences well +you don't have to provide any excuse you + + align:start position:0% +you don't have to provide any excuse you + + + align:start position:0% +you don't have to provide any excuse you +don't have to tell me this is why you + + align:start position:0% +don't have to tell me this is why you + + + align:start position:0% +don't have to tell me this is why you +were gone and that's what I expect that + + align:start position:0% +were gone and that's what I expect that + + + align:start position:0% +were gone and that's what I expect that +you can miss about three classes and + + align:start position:0% +you can miss about three classes and + + + align:start position:0% +you can miss about three classes and +sort of I still quite satisfied that + + align:start position:0% +sort of I still quite satisfied that + + + align:start position:0% +sort of I still quite satisfied that +you've gotten everything that you need + + align:start position:0% +you've gotten everything that you need + + + align:start position:0% +you've gotten everything that you need +for the class illnesses are one of the + + align:start position:0% +for the class illnesses are one of the + + + align:start position:0% +for the class illnesses are one of the +few things that I become really really + + align:start position:0% +few things that I become really really + + + align:start position:0% +few things that I become really really +out of control I can hit people for + + align:start position:0% +out of control I can hit people for + + + align:start position:0% +out of control I can hit people for +extended periods of time and and that + + align:start position:0% +extended periods of time and and that + + + align:start position:0% +extended periods of time and and that +wasn't necessarily your fault whereas + + align:start position:0% +wasn't necessarily your fault whereas + + + align:start position:0% +wasn't necessarily your fault whereas +something like being stuck in the + + align:start position:0% +something like being stuck in the + + + align:start position:0% +something like being stuck in the +airport usually only affects you for one + + align:start position:0% +airport usually only affects you for one + + + align:start position:0% +airport usually only affects you for one +class so it's not a bad it and if you + + align:start position:0% +class so it's not a bad it and if you + + + align:start position:0% +class so it's not a bad it and if you +are planning on how many of you are + + align:start position:0% +are planning on how many of you are + + + align:start position:0% +are planning on how many of you are +seniors I didn't write the job interview + + align:start position:0% +seniors I didn't write the job interview + + + align:start position:0% +seniors I didn't write the job interview +track yeah use those save those three + + align:start position:0% +track yeah use those save those three + + + align:start position:0% +track yeah use those save those three +for things like job interviews because + + align:start position:0% +for things like job interviews because + + + align:start position:0% +for things like job interviews because +you're gonna need that and you don't + + align:start position:0% +you're gonna need that and you don't + + + align:start position:0% +you're gonna need that and you don't +have to ask for permission or anything + + align:start position:0% +have to ask for permission or anything + + + align:start position:0% +have to ask for permission or anything +just though let's go for your job + + align:start position:0% +just though let's go for your job + + + align:start position:0% +just though let's go for your job +interviews and realize that you're three + + align:start position:0% +interviews and realize that you're three + + + align:start position:0% +interviews and realize that you're three +others let's see + + align:start position:0% +others let's see + + + align:start position:0% +others let's see +what else if you do this more than three + + align:start position:0% +what else if you do this more than three + + + align:start position:0% +what else if you do this more than three +classes and it was not due to illnesses + + align:start position:0% +classes and it was not due to illnesses + + + align:start position:0% +classes and it was not due to illnesses +then you may well get a reduction in + + align:start position:0% +then you may well get a reduction in + + + align:start position:0% +then you may well get a reduction in +your internet in your grades oh I got + + align:start position:0% +your internet in your grades oh I got + + + align:start position:0% +your internet in your grades oh I got +Sudan should we drop by a full letter + + align:start position:0% +Sudan should we drop by a full letter + + + align:start position:0% +Sudan should we drop by a full letter +grade so they would have got in and B + + align:start position:0% +grade so they would have got in and B + + + align:start position:0% +grade so they would have got in and B +they gotta see based on absences alone + + align:start position:0% +they gotta see based on absences alone + + + align:start position:0% +they gotta see based on absences alone +all the assignments told them that they + + align:start position:0% +all the assignments told them that they + + + align:start position:0% +all the assignments told them that they +were going to be B average but your + + align:start position:0% +were going to be B average but your + + + align:start position:0% +were going to be B average but your +attendance was poor and it's a result of + + align:start position:0% +attendance was poor and it's a result of + + + align:start position:0% +attendance was poor and it's a result of +that usually missing for classes does it + + align:start position:0% +that usually missing for classes does it + + + align:start position:0% +that usually missing for classes does it +drop you a full letter grade but you + + align:start position:0% +drop you a full letter grade but you + + + align:start position:0% +drop you a full letter grade but you +know he really depends on how how close + + align:start position:0% +know he really depends on how how close + + + align:start position:0% +know he really depends on how how close +you were to a tip of like a b-minus and + + align:start position:0% +you were to a tip of like a b-minus and + + + align:start position:0% +you were to a tip of like a b-minus and +a c-plus before your attendance is taken + + align:start position:0% +a c-plus before your attendance is taken + + + align:start position:0% +a c-plus before your attendance is taken +into account there's a little bit more + + align:start position:0% +into account there's a little bit more + + + align:start position:0% +into account there's a little bit more +detail in syllabus about how grades are + + align:start position:0% +detail in syllabus about how grades are + + + align:start position:0% +detail in syllabus about how grades are +computed plagiarism there is I'm that's + + align:start position:0% +computed plagiarism there is I'm that's + + + align:start position:0% +computed plagiarism there is I'm that's +usually not so much of a problem when it + + align:start position:0% +usually not so much of a problem when it + + + align:start position:0% +usually not so much of a problem when it +comes to the group projects because + + align:start position:0% +comes to the group projects because + + + align:start position:0% +comes to the group projects because +you're going to be writing a lot of your + + align:start position:0% +you're going to be writing a lot of your + + + align:start position:0% +you're going to be writing a lot of your +rules and everyone is kind of like + + align:start position:0% +rules and everyone is kind of like + + + align:start position:0% +rules and everyone is kind of like +keeping an eye on what's actually being + + align:start position:0% +keeping an eye on what's actually being + + + align:start position:0% +keeping an eye on what's actually being +handed in for your assignments so still + + align:start position:0% +handed in for your assignments so still + + + align:start position:0% +handed in for your assignments so still +just keep in mind that I certainly don't + + align:start position:0% +just keep in mind that I certainly don't + + + align:start position:0% +just keep in mind that I certainly don't +want you to be copying wholesale from + + align:start position:0% +want you to be copying wholesale from + + + align:start position:0% +want you to be copying wholesale from +somebody else's rules that's that's you + + align:start position:0% +somebody else's rules that's that's you + + + align:start position:0% +somebody else's rules that's that's you +know that's not that's more than + + align:start position:0% +know that's not that's more than + + + align:start position:0% +know that's not that's more than +plagiarism that might be copyright + + align:start position:0% +plagiarism that might be copyright + + + align:start position:0% +plagiarism that might be copyright +infringement but when it comes to your + + align:start position:0% +infringement but when it comes to your + + + align:start position:0% +infringement but when it comes to your +own writing there is actually a one-page + + align:start position:0% +own writing there is actually a one-page + + + align:start position:0% +own writing there is actually a one-page +personal report for every time you hand + + align:start position:0% +personal report for every time you hand + + + align:start position:0% +personal report for every time you hand +in a team assignment that is we are + + align:start position:0% +in a team assignment that is we are + + + align:start position:0% +in a team assignment that is we are +expecting you to keep a journal of every + + align:start position:0% +expecting you to keep a journal of every + + + align:start position:0% +expecting you to keep a journal of every +team meeting personal personal journal + + align:start position:0% +team meeting personal personal journal + + + align:start position:0% +team meeting personal personal journal +about how the team meeting went what + + align:start position:0% +about how the team meeting went what + + + align:start position:0% +about how the team meeting went what +decisions you've made you know you can + + align:start position:0% +decisions you've made you know you can + + + align:start position:0% +decisions you've made you know you can +write down things like wow only half the + + align:start position:0% +write down things like wow only half the + + + align:start position:0% +write down things like wow only half the +team turned up and that meeting didn't + + align:start position:0% +team turned up and that meeting didn't + + + align:start position:0% +team turned up and that meeting didn't +really what was it really useful and + + align:start position:0% +really what was it really useful and + + + align:start position:0% +really what was it really useful and +think that these are all useful things + + align:start position:0% +think that these are all useful things + + + align:start position:0% +think that these are all useful things +to keep in mind and you get to choose + + align:start position:0% +to keep in mind and you get to choose + + + align:start position:0% +to keep in mind and you get to choose +what you what you write one write down + + align:start position:0% +what you what you write one write down + + + align:start position:0% +what you what you write one write down +here one page we report again I'm + + align:start position:0% +here one page we report again I'm + + + align:start position:0% +here one page we report again I'm +looking for something that's + + align:start position:0% +looking for something that's + + + align:start position:0% +looking for something that's +well-written reflective will be very + + align:start position:0% +well-written reflective will be very + + + align:start position:0% +well-written reflective will be very +nice it's like alright based on the + + align:start position:0% +nice it's like alright based on the + + + align:start position:0% +nice it's like alright based on the +experience of making of doing in this + + align:start position:0% +experience of making of doing in this + + + align:start position:0% +experience of making of doing in this +team assignment what would I do + + align:start position:0% +team assignment what would I do + + + align:start position:0% +team assignment what would I do +differently next time or what went well + + align:start position:0% +differently next time or what went well + + + align:start position:0% +differently next time or what went well +then I want to make sure that I do again + + align:start position:0% + + + + align:start position:0% + +next time those things are very very + + align:start position:0% +next time those things are very very + + + align:start position:0% +next time those things are very very +good to have done in your one page + + align:start position:0% +good to have done in your one page + + + align:start position:0% +good to have done in your one page +before write those on your own don't go + + align:start position:0% +before write those on your own don't go + + + align:start position:0% +before write those on your own don't go +into like a group writing session you + + align:start position:0% +into like a group writing session you + + + align:start position:0% +into like a group writing session you +can compare notes you can compare your + + align:start position:0% +can compare notes you can compare your + + + align:start position:0% +can compare notes you can compare your +notes that's fine but when actually + + align:start position:0% +notes that's fine but when actually + + + align:start position:0% +notes that's fine but when actually +comes down to writing it I want you to + + align:start position:0% +comes down to writing it I want you to + + + align:start position:0% +comes down to writing it I want you to +write it on your own let's see what else + + align:start position:0% +write it on your own let's see what else + + + align:start position:0% +write it on your own let's see what else +how many grad students in here one okay + + align:start position:0% +how many grad students in here one okay + + + align:start position:0% +how many grad students in here one okay +so residents if you're signing out for + + align:start position:0% +so residents if you're signing out for + + + align:start position:0% +so residents if you're signing out for +six oh eight there's no additional work + + align:start position:0% +six oh eight there's no additional work + + + align:start position:0% +six oh eight there's no additional work +you got signing out for eight six four + + align:start position:0% +you got signing out for eight six four + + + align:start position:0% +you got signing out for eight six four +which gives you great credit then there + + align:start position:0% +which gives you great credit then there + + + align:start position:0% +which gives you great credit then there +is additional work and that's that + + align:start position:0% +is additional work and that's that + + + align:start position:0% +is additional work and that's that +largely involves check out the games one + + align:start position:0% +largely involves check out the games one + + + align:start position:0% +largely involves check out the games one +week in advance making sure that they're + + align:start position:0% +week in advance making sure that they're + + + align:start position:0% +week in advance making sure that they're +all punched up making sure all the + + align:start position:0% +all punched up making sure all the + + + align:start position:0% +all punched up making sure all the +pieces are in there making sure you know + + align:start position:0% +pieces are in there making sure you know + + + align:start position:0% +pieces are in there making sure you know +the rules you don't actually necessarily + + align:start position:0% +the rules you don't actually necessarily + + + align:start position:0% +the rules you don't actually necessarily +have to learn the rules by reading the + + align:start position:0% +have to learn the rules by reading the + + + align:start position:0% +have to learn the rules by reading the +rules you can do it by watching let's + + align:start position:0% +rules you can do it by watching let's + + + align:start position:0% +rules you can do it by watching let's +play videos and YouTube stuff inside + + align:start position:0% +play videos and YouTube stuff inside + + + align:start position:0% +play videos and YouTube stuff inside +however it takes to learn the game you + + align:start position:0% +however it takes to learn the game you + + + align:start position:0% +however it takes to learn the game you +learn it and cut in class and you teach + + align:start position:0% +learn it and cut in class and you teach + + + align:start position:0% +learn it and cut in class and you teach +your classmates how to play this game so + + align:start position:0% +your classmates how to play this game so + + + align:start position:0% +your classmates how to play this game so +I really one can get started a little + + align:start position:0% +I really one can get started a little + + + align:start position:0% +I really one can get started a little +bit faster I'll cut and make sure that + + align:start position:0% +bit faster I'll cut and make sure that + + + align:start position:0% +bit faster I'll cut and make sure that +all the pieces are inside that's the + + align:start position:0% +all the pieces are inside that's the + + + align:start position:0% +all the pieces are inside that's the +that being said everyone should be + + align:start position:0% +that being said everyone should be + + + align:start position:0% +that being said everyone should be +looking at the rules of these games when + + align:start position:0% +looking at the rules of these games when + + + align:start position:0% +looking at the rules of these games when +during class when when you will see in + + align:start position:0% +during class when when you will see in + + + align:start position:0% +during class when when you will see in +the class schedule I actually have on + + align:start position:0% +the class schedule I actually have on + + + align:start position:0% +the class schedule I actually have on +all the games that we're going to be + + align:start position:0% +all the games that we're going to be + + + align:start position:0% +all the games that we're going to be +playing listed so that you know in case + + align:start position:0% +playing listed so that you know in case + + + align:start position:0% +playing listed so that you know in case +you the name of the game escapes you + + align:start position:0% +you the name of the game escapes you + + + align:start position:0% +you the name of the game escapes you +worry about like google it and look it + + align:start position:0% +worry about like google it and look it + + + align:start position:0% +worry about like google it and look it +up + + align:start position:0% + + + + align:start position:0% + +and you should be looking at the rules + + align:start position:0% +and you should be looking at the rules + + + align:start position:0% +and you should be looking at the rules +because you want to see how rules are + + align:start position:0% +because you want to see how rules are + + + align:start position:0% +because you want to see how rules are +written how good rules were written how + + align:start position:0% +written how good rules were written how + + + align:start position:0% +written how good rules were written how +bad rules are written and you're going + + align:start position:0% +bad rules are written and you're going + + + align:start position:0% +bad rules are written and you're going +to see again see a lot of really bad + + align:start position:0% +to see again see a lot of really bad + + + align:start position:0% +to see again see a lot of really bad +rules and you want to understand how + + align:start position:0% +rules and you want to understand how + + + align:start position:0% +rules and you want to understand how +sudden things are conveyed you know + + align:start position:0% +sudden things are conveyed you know + + + align:start position:0% +sudden things are conveyed you know +maybe it has a really elegant game + + align:start position:0% +maybe it has a really elegant game + + + align:start position:0% +maybe it has a really elegant game +mechanic that you want to try to use a + + align:start position:0% +mechanic that you want to try to use a + + + align:start position:0% +mechanic that you want to try to use a +version of that in your own game and + + align:start position:0% +version of that in your own game and + + + align:start position:0% +version of that in your own game and +then you wanna but you're you are having + + align:start position:0% +then you wanna but you're you are having + + + align:start position:0% +then you wanna but you're you are having +difficulty explaining it well look at + + align:start position:0% +difficulty explaining it well look at + + + align:start position:0% +difficulty explaining it well look at +the rules of how other board games do it + + align:start position:0% +the rules of how other board games do it + + + align:start position:0% +the rules of how other board games do it +and see when they do a better check out + + align:start position:0% +and see when they do a better check out + + + align:start position:0% +and see when they do a better check out +obvious though look at the real time + + align:start position:0% +obvious though look at the real time + + + align:start position:0% +obvious though look at the real time +what are the few people who definitely + + align:start position:0% +what are the few people who definitely + + + align:start position:0% +what are the few people who definitely +learn the game is better by watching a + + align:start position:0% +learn the game is better by watching a + + + align:start position:0% +learn the game is better by watching a +video or somebody was actually played it + + align:start position:0% +video or somebody was actually played it + + + align:start position:0% +video or somebody was actually played it +or talking to somebody who's actually + + align:start position:0% +or talking to somebody who's actually + + + align:start position:0% +or talking to somebody who's actually +played it and have + + align:start position:0% +played it and have + + + align:start position:0% +played it and have +showed to me I have trouble processing + + align:start position:0% +showed to me I have trouble processing + + + align:start position:0% +showed to me I have trouble processing +rules myself but that's why I can really + + align:start position:0% +rules myself but that's why I can really + + + align:start position:0% +rules myself but that's why I can really +appreciate well written rules when I see + + align:start position:0% +appreciate well written rules when I see + + + align:start position:0% +appreciate well written rules when I see +one + + align:start position:0% + + + + align:start position:0% + +so make sure that you are looking at the + + align:start position:0% +so make sure that you are looking at the + + + align:start position:0% +so make sure that you are looking at the +rules as I mentioned as I briefly + + align:start position:0% +rules as I mentioned as I briefly + + + align:start position:0% +rules as I mentioned as I briefly +mentioned earlier all the assignments in + + align:start position:0% +mentioned earlier all the assignments in + + + align:start position:0% +mentioned earlier all the assignments in +this class are team projects there is + + align:start position:0% +this class are team projects there is + + + align:start position:0% +this class are team projects there is +again one page individual report that + + align:start position:0% +again one page individual report that + + + align:start position:0% +again one page individual report that +you hand and usually the week after the + + align:start position:0% +you hand and usually the week after the + + + align:start position:0% +you hand and usually the week after the +assignment and that one you write + + align:start position:0% +assignment and that one you write + + + align:start position:0% +assignment and that one you write +yourself but it's all based on that team + + align:start position:0% +yourself but it's all based on that team + + + align:start position:0% +yourself but it's all based on that team +project which means you're gonna be + + align:start position:0% +project which means you're gonna be + + + align:start position:0% +project which means you're gonna be +working on teams typically of three to + + align:start position:0% +working on teams typically of three to + + + align:start position:0% +working on teams typically of three to +four people I do not recommend teams of + + align:start position:0% +four people I do not recommend teams of + + + align:start position:0% +four people I do not recommend teams of +five people in this class simply because + + align:start position:0% +five people in this class simply because + + + align:start position:0% +five people in this class simply because +once you hit five you get into certain + + align:start position:0% +once you hit five you get into certain + + + align:start position:0% +once you hit five you get into certain +communications or all the heads that + + align:start position:0% +communications or all the heads that + + + align:start position:0% +communications or all the heads that +makes it kind of counterproductive you + + align:start position:0% +makes it kind of counterproductive you + + + align:start position:0% +makes it kind of counterproductive you +can probably get about the same amount + + align:start position:0% +can probably get about the same amount + + + align:start position:0% +can probably get about the same amount +work done with four people + + align:start position:0% +work done with four people + + + align:start position:0% +work done with four people +these up side sometimes if all five + + align:start position:0% +these up side sometimes if all five + + + align:start position:0% +these up side sometimes if all five +people are living in the same living + + align:start position:0% +people are living in the same living + + + align:start position:0% +people are living in the same living +group you might be able to make it work + + align:start position:0% +group you might be able to make it work + + + align:start position:0% +group you might be able to make it work +it's still really hard to schedule a + + align:start position:0% +it's still really hard to schedule a + + + align:start position:0% +it's still really hard to schedule a +meeting with five people all at once + + align:start position:0% +meeting with five people all at once + + + align:start position:0% +meeting with five people all at once +class does end at four o'clock usually + + align:start position:0% +class does end at four o'clock usually + + + align:start position:0% +class does end at four o'clock usually +that last hour is game playing time + + align:start position:0% +that last hour is game playing time + + + align:start position:0% +that last hour is game playing time +which means it might be able to take + + align:start position:0% +which means it might be able to take + + + align:start position:0% +which means it might be able to take +take a set amount of time to meet up + + align:start position:0% +take a set amount of time to meet up + + + align:start position:0% +take a set amount of time to meet up +with your team it's even better if the + + align:start position:0% +with your team it's even better if the + + + align:start position:0% +with your team it's even better if the +hour between four and five o'clock is + + align:start position:0% +hour between four and five o'clock is + + + align:start position:0% +hour between four and five o'clock is +all free for every single member of your + + align:start position:0% +all free for every single member of your + + + align:start position:0% +all free for every single member of your +team but that's not going to be the case + + align:start position:0% +team but that's not going to be the case + + + align:start position:0% +team but that's not going to be the case +for every single team for every single + + align:start position:0% +for every single team for every single + + + align:start position:0% +for every single team for every single +project and you can switch teams between + + align:start position:0% +project and you can switch teams between + + + align:start position:0% +project and you can switch teams between +projects assignment one can be with four + + align:start position:0% +projects assignment one can be with four + + + align:start position:0% +projects assignment one can be with four +completely different group of people at + + align:start position:0% +completely different group of people at + + + align:start position:0% +completely different group of people at +home from assignment two that's fine and + + align:start position:0% +home from assignment two that's fine and + + + align:start position:0% +home from assignment two that's fine and +we're going to do team formation I think + + align:start position:0% +we're going to do team formation I think + + + align:start position:0% +we're going to do team formation I think +the schedule has it on Monday yeah + + align:start position:0% +the schedule has it on Monday yeah + + + align:start position:0% +the schedule has it on Monday yeah +because I'm not sure if this is the + + align:start position:0% +because I'm not sure if this is the + + + align:start position:0% +because I'm not sure if this is the +entire class yet so on Monday we'll + + align:start position:0% +entire class yet so on Monday we'll + + + align:start position:0% +entire class yet so on Monday we'll +actually go a little bit more into + + align:start position:0% +actually go a little bit more into + + + align:start position:0% +actually go a little bit more into +brainstorming talking a little bit about + + align:start position:0% +brainstorming talking a little bit about + + + align:start position:0% +brainstorming talking a little bit about +about what what what projects you want + + align:start position:0% +about what what what projects you want + + + align:start position:0% +about what what what projects you want +to do something teams around that and + + align:start position:0% +to do something teams around that and + + + align:start position:0% +to do something teams around that and +then you're off to the races you've only + + align:start position:0% +then you're off to the races you've only + + + align:start position:0% +then you're off to the races you've only +got like three weeks to finish this + + align:start position:0% +got like three weeks to finish this + + + align:start position:0% +got like three weeks to finish this +first game is it three weeks yeah + + align:start position:0% +first game is it three weeks yeah + + + align:start position:0% +first game is it three weeks yeah +exactly three weeks actually is less + + align:start position:0% +exactly three weeks actually is less + + + align:start position:0% +exactly three weeks actually is less +than that because you start on the + + align:start position:0% +than that because you start on the + + + align:start position:0% +than that because you start on the +Monday and then your hand + + align:start position:0% +Monday and then your hand + + + align:start position:0% +Monday and then your hand +on that third Wednesday so a very very + + align:start position:0% +on that third Wednesday so a very very + + + align:start position:0% +on that third Wednesday so a very very +short amount of time but that's okay + + align:start position:0% +short amount of time but that's okay + + + align:start position:0% +short amount of time but that's okay +because this is supposed to be your very + + align:start position:0% +because this is supposed to be your very + + + align:start position:0% +because this is supposed to be your very +very quick and dirty first assignment + + align:start position:0% +very quick and dirty first assignment + + + align:start position:0% +very quick and dirty first assignment +get it out of the way get into the + + align:start position:0% +get it out of the way get into the + + + align:start position:0% +get it out of the way get into the +groove of things we're going to spend + + align:start position:0% +groove of things we're going to spend + + + align:start position:0% +groove of things we're going to spend +most of this month just talking about + + align:start position:0% +most of this month just talking about + + + align:start position:0% +most of this month just talking about +the discipline of making games + + align:start position:0% +the discipline of making games + + + align:start position:0% +the discipline of making games +what is iterative design what is rapid + + align:start position:0% +what is iterative design what is rapid + + + align:start position:0% +what is iterative design what is rapid +prototyping what is game testing and why + + align:start position:0% +prototyping what is game testing and why + + + align:start position:0% +prototyping what is game testing and why +is it important and why you're going to + + align:start position:0% +is it important and why you're going to + + + align:start position:0% +is it important and why you're going to +be doing this over and over and over and + + align:start position:0% +be doing this over and over and over and + + + align:start position:0% +be doing this over and over and over and +over and over again all semester long + + align:start position:0% +over and over again all semester long + + + align:start position:0% +over and over again all semester long +that's the one thing that I want you to + + align:start position:0% +that's the one thing that I want you to + + + align:start position:0% +that's the one thing that I want you to +walk away from class with is by being + + align:start position:0% +walk away from class with is by being + + + align:start position:0% +walk away from class with is by being +better at iterative design who who here + + align:start position:0% +better at iterative design who who here + + + align:start position:0% +better at iterative design who who here +is familiar with some sort or like has + + align:start position:0% +is familiar with some sort or like has + + + align:start position:0% +is familiar with some sort or like has +practiced some sort of iterative design + + align:start position:0% +practiced some sort of iterative design + + + align:start position:0% +practiced some sort of iterative design +from any discipline yeah for how many of + + align:start position:0% +from any discipline yeah for how many of + + + align:start position:0% +from any discipline yeah for how many of +you are like from an engineering + + align:start position:0% +you are like from an engineering + + + align:start position:0% +you are like from an engineering +background where they participate + + align:start position:0% +background where they participate + + + align:start position:0% +background where they participate +okay just just get a sense like which + + align:start position:0% +okay just just get a sense like which + + + align:start position:0% +okay just just get a sense like which +which which sort of project kind of work + + align:start position:0% +which which sort of project kind of work + + + align:start position:0% +which which sort of project kind of work +that that came from but Becky + + align:start position:0% + + + + align:start position:0% + +yeah created dreams + + align:start position:0% + + + + align:start position:0% + +okay oh this wait about right yeah + + align:start position:0% +okay oh this wait about right yeah + + + align:start position:0% +okay oh this wait about right yeah +obviously the computer game design game + + align:start position:0% +obviously the computer game design game + + + align:start position:0% +obviously the computer game design game +class is very relevant experience here + + align:start position:0% +class is very relevant experience here + + + align:start position:0% +class is very relevant experience here +this class is of course a good + + align:start position:0% +this class is of course a good + + + align:start position:0% +this class is of course a good +prerequisite for getting into CMS 611 + + align:start position:0% +prerequisite for getting into CMS 611 + + + align:start position:0% +prerequisite for getting into CMS 611 +which is our creating video games class + + align:start position:0% +which is our creating video games class + + + align:start position:0% +which is our creating video games class +that class is a lot more about teamwork + + align:start position:0% +that class is a lot more about teamwork + + + align:start position:0% +that class is a lot more about teamwork +is a lot more about obviously software + + align:start position:0% +is a lot more about obviously software + + + align:start position:0% +is a lot more about obviously software +because it's a video games class and + + align:start position:0% +because it's a video games class and + + + align:start position:0% +because it's a video games class and +that's in that's going to be in the fall + + align:start position:0% +that's in that's going to be in the fall + + + align:start position:0% +that's in that's going to be in the fall +so so if you're interested after this + + align:start position:0% +so so if you're interested after this + + + align:start position:0% +so so if you're interested after this +class is over you might wanna check them + + align:start position:0% +class is over you might wanna check them + + + align:start position:0% +class is over you might wanna check them +out and you can talk to the students + + align:start position:0% +out and you can talk to the students + + + align:start position:0% +out and you can talk to the students +around ya who've done it before by the + + align:start position:0% +around ya who've done it before by the + + + align:start position:0% +around ya who've done it before by the +way for those people who've actually + + align:start position:0% +way for those people who've actually + + + align:start position:0% +way for those people who've actually +been in classes with me I haven't gone + + align:start position:0% +been in classes with me I haven't gone + + + align:start position:0% +been in classes with me I haven't gone +in contact I just flying right now my + + align:start position:0% +in contact I just flying right now my + + + align:start position:0% +in contact I just flying right now my +classes step in half and I threw your + + align:start position:0% +classes step in half and I threw your + + + align:start position:0% +classes step in half and I threw your +exam actually I was thinking let's see + + align:start position:0% + + + + align:start position:0% + +alright + + align:start position:0% +alright + + + align:start position:0% +alright +and the final thing that I want to talk + + align:start position:0% +and the final thing that I want to talk + + + align:start position:0% +and the final thing that I want to talk +about all the way at the end of the + + align:start position:0% +about all the way at the end of the + + + align:start position:0% +about all the way at the end of the +syllabus is this thing called a change + + align:start position:0% +syllabus is this thing called a change + + + align:start position:0% +syllabus is this thing called a change +love some of you who've done CMS 6:11 + + align:start position:0% +love some of you who've done CMS 6:11 + + + align:start position:0% +love some of you who've done CMS 6:11 +recently will find this quite familiar + + align:start position:0% +recently will find this quite familiar + + + align:start position:0% +recently will find this quite familiar +and this is again one per group not one + + align:start position:0% +and this is again one per group not one + + + align:start position:0% +and this is again one per group not one +per person your hand is at the same time + + align:start position:0% +per person your hand is at the same time + + + align:start position:0% +per person your hand is at the same time +as your hand in each assignment and what + + align:start position:0% +as your hand in each assignment and what + + + align:start position:0% +as your hand in each assignment and what +I want you to do is at the end of every + + align:start position:0% +I want you to do is at the end of every + + + align:start position:0% +I want you to do is at the end of every +time you have a design meeting whether + + align:start position:0% +time you have a design meeting whether + + + align:start position:0% +time you have a design meeting whether +you met in class or you met outside of + + align:start position:0% +you met in class or you met outside of + + + align:start position:0% +you met in class or you met outside of +class on a weekend even online or + + align:start position:0% +class on a weekend even online or + + + align:start position:0% +class on a weekend even online or +something and every time you make + + align:start position:0% +something and every time you make + + + align:start position:0% +something and every time you make +changes to your game right write down + + align:start position:0% +changes to your game right write down + + + align:start position:0% +changes to your game right write down +why those changes went down in this + + align:start position:0% +why those changes went down in this + + + align:start position:0% +why those changes went down in this +format we give you a disciple format we + + align:start position:0% +format we give you a disciple format we + + + align:start position:0% +format we give you a disciple format we +expect you to stick to it you can tweak + + align:start position:0% +expect you to stick to it you can tweak + + + align:start position:0% +expect you to stick to it you can tweak +it but we expect to see at least as much + + align:start position:0% +it but we expect to see at least as much + + + align:start position:0% +it but we expect to see at least as much +and at least this much detail what are + + align:start position:0% +and at least this much detail what are + + + align:start position:0% +and at least this much detail what are +the actions in game what are the goals + + align:start position:0% +the actions in game what are the goals + + + align:start position:0% +the actions in game what are the goals +of the player our players of course what + + align:start position:0% +of the player our players of course what + + + align:start position:0% +of the player our players of course what +are the problems that your team noticing + + align:start position:0% +are the problems that your team noticing + + + align:start position:0% +are the problems that your team noticing +after having played through this this + + align:start position:0% +after having played through this this + + + align:start position:0% +after having played through this this +game + + align:start position:0% +game + + + align:start position:0% +game +turn takes too long you know no one + + align:start position:0% +turn takes too long you know no one + + + align:start position:0% +turn takes too long you know no one +knows what to do game game takes too + + align:start position:0% +knows what to do game game takes too + + + align:start position:0% +knows what to do game game takes too +long + + align:start position:0% +long + + + align:start position:0% +long +games over too quickly get him to random + + align:start position:0% +games over too quickly get him to random + + + align:start position:0% +games over too quickly get him to random +and out about control all those things + + align:start position:0% +and out about control all those things + + + align:start position:0% +and out about control all those things +write down in problems you know these + + align:start position:0% +write down in problems you know these + + + align:start position:0% +write down in problems you know these +are these + + align:start position:0% +are these + + + align:start position:0% +are these +should be useful for you as it is for us + + align:start position:0% +should be useful for you as it is for us + + + align:start position:0% +should be useful for you as it is for us +or if somebody misses a design meeting + + align:start position:0% +or if somebody misses a design meeting + + + align:start position:0% +or if somebody misses a design meeting +or something you should be able to keep + + align:start position:0% +or something you should be able to keep + + + align:start position:0% +or something you should be able to keep +this on like a Google Doc or some + + align:start position:0% +this on like a Google Doc or some + + + align:start position:0% +this on like a Google Doc or some +publicly shared document can look it + + align:start position:0% +publicly shared document can look it + + + align:start position:0% +publicly shared document can look it +says oh that's what happened last week + + align:start position:0% +says oh that's what happened last week + + + align:start position:0% +says oh that's what happened last week +it's like oh you would change the wind + + align:start position:0% +it's like oh you would change the wind + + + align:start position:0% +it's like oh you would change the wind +condition to you know half what it was + + align:start position:0% +condition to you know half what it was + + + align:start position:0% +condition to you know half what it was +okay I guess that's what we're working + + align:start position:0% +okay I guess that's what we're working + + + align:start position:0% +okay I guess that's what we're working +with now why did you do that and this is + + align:start position:0% +with now why did you do that and this is + + + align:start position:0% +with now why did you do that and this is +oh because the game was taking too long + + align:start position:0% +oh because the game was taking too long + + + align:start position:0% +oh because the game was taking too long +that's our thing all the way expect to + + align:start position:0% +that's our thing all the way expect to + + + align:start position:0% +that's our thing all the way expect to +see that coming with your final + + align:start position:0% +see that coming with your final + + + align:start position:0% +see that coming with your final +assignment up with each five minutes all + + align:start position:0% +assignment up with each five minutes all + + + align:start position:0% +assignment up with each five minutes all +right any questions so far + + align:start position:0% + + + + align:start position:0% + +there's going to be a bunch of guest + + align:start position:0% +there's going to be a bunch of guest + + + align:start position:0% +there's going to be a bunch of guest +lectures but we haven't labeled them in + + align:start position:0% +lectures but we haven't labeled them in + + + align:start position:0% +lectures but we haven't labeled them in +here because we haven't quite scheduled + + align:start position:0% +here because we haven't quite scheduled + + + align:start position:0% +here because we haven't quite scheduled +then George this year the readings are + + align:start position:0% +then George this year the readings are + + + align:start position:0% +then George this year the readings are +the same the games are the same some + + align:start position:0% +the same the games are the same some + + + align:start position:0% +the same the games are the same some +changes might happen to this schedule on + + align:start position:0% +changes might happen to this schedule on + + + align:start position:0% +changes might happen to this schedule on +stellar our obviously make announcements + + align:start position:0% +stellar our obviously make announcements + + + align:start position:0% +stellar our obviously make announcements +week announced ment on stellar our make + + align:start position:0% +week announced ment on stellar our make + + + align:start position:0% +week announced ment on stellar our make +advancements in class I'll try to update + + align:start position:0% +advancements in class I'll try to update + + + align:start position:0% +advancements in class I'll try to update +the document on stellar with the + + align:start position:0% +the document on stellar with the + + + align:start position:0% +the document on stellar with the +schedule changes but for the most part + + align:start position:0% +schedule changes but for the most part + + + align:start position:0% +schedule changes but for the most part +assignments are not gonna change just + + align:start position:0% +assignments are not gonna change just + + + align:start position:0% +assignments are not gonna change just +some readings may get rearranged I have + + align:start position:0% +some readings may get rearranged I have + + + align:start position:0% +some readings may get rearranged I have +to point out something about readings + + align:start position:0% + + + + align:start position:0% + +individual essays but you're not gonna + + align:start position:0% +individual essays but you're not gonna + + + align:start position:0% +individual essays but you're not gonna +have to read every single one of the + + align:start position:0% +have to read every single one of the + + + align:start position:0% +have to read every single one of the +effective back like we like from from + + align:start position:0% +effective back like we like from from + + + align:start position:0% +effective back like we like from from +tabletop this is a this is actually + + align:start position:0% +tabletop this is a this is actually + + + align:start position:0% +tabletop this is a this is actually +available as a free pdf for the + + align:start position:0% +available as a free pdf for the + + + align:start position:0% +available as a free pdf for the +publisher and the link of that is on + + align:start position:0% +publisher and the link of that is on + + + align:start position:0% +publisher and the link of that is on +stellar so you don't have to buy the + + align:start position:0% +stellar so you don't have to buy the + + + align:start position:0% +stellar so you don't have to buy the +book you can download the PDF scroll + + align:start position:0% +book you can download the PDF scroll + + + align:start position:0% +book you can download the PDF scroll +down to the right reading and just for + + align:start position:0% +down to the right reading and just for + + + align:start position:0% +down to the right reading and just for +that we have one reading from this book + + align:start position:0% +that we have one reading from this book + + + align:start position:0% +that we have one reading from this book +but I actually recommend this book how + + align:start position:0% +but I actually recommend this book how + + + align:start position:0% +but I actually recommend this book how +many get hurt on the new games new you + + align:start position:0% +many get hurt on the new games new you + + + align:start position:0% +many get hurt on the new games new you +new games it's from the 60s Oh EO is the + + align:start position:0% +new games it's from the 60s Oh EO is the + + + align:start position:0% +new games it's from the 60s Oh EO is the +new games movement was something that + + align:start position:0% +new games movement was something that + + + align:start position:0% +new games movement was something that +our heart if you play with with a + + align:start position:0% +our heart if you play with with a + + + align:start position:0% +our heart if you play with with a +parachute in gym class when you're in + + align:start position:0% +parachute in gym class when you're in + + + align:start position:0% +parachute in gym class when you're in +elementary school okay you were part of + + align:start position:0% +elementary school okay you were part of + + + align:start position:0% +elementary school okay you were part of +the new games movement this was + + align:start position:0% +the new games movement this was + + + align:start position:0% +the new games movement this was +basically an activist group of game + + align:start position:0% +basically an activist group of game + + + align:start position:0% +basically an activist group of game +designers in the 60s heavily influenced + + align:start position:0% +designers in the 60s heavily influenced + + + align:start position:0% +designers in the 60s heavily influenced +by the Whole Earth Catalog if you've + + align:start position:0% +by the Whole Earth Catalog if you've + + + align:start position:0% +by the Whole Earth Catalog if you've +heard of that stupid brand yeah and + + align:start position:0% +heard of that stupid brand yeah and + + + align:start position:0% +heard of that stupid brand yeah and +basically typical counterculture but in + + align:start position:0% +basically typical counterculture but in + + + align:start position:0% +basically typical counterculture but in +the game side of things was very + + align:start position:0% +the game side of things was very + + + align:start position:0% +the game side of things was very +specifically about making games that + + align:start position:0% +specifically about making games that + + + align:start position:0% +specifically about making games that +feature different kinds of cooperative + + align:start position:0% +feature different kinds of cooperative + + + align:start position:0% +feature different kinds of cooperative +play if they were competitive they were + + align:start position:0% +play if they were competitive they were + + + align:start position:0% +play if they were competitive they were +sort of light-hearted competitive and + + align:start position:0% +sort of light-hearted competitive and + + + align:start position:0% +sort of light-hearted competitive and +we're still trying to like develop a + + align:start position:0% +we're still trying to like develop a + + + align:start position:0% +we're still trying to like develop a +sense of community + + align:start position:0% +sense of community + + + align:start position:0% +sense of community +parachute type games are very much about + + align:start position:0% +parachute type games are very much about + + + align:start position:0% +parachute type games are very much about +taking military hardware and turning + + align:start position:0% +taking military hardware and turning + + + align:start position:0% +taking military hardware and turning +them into peacetime fun activities so + + align:start position:0% +them into peacetime fun activities so + + + align:start position:0% +them into peacetime fun activities so +you know what what the parachute is + + align:start position:0% +you know what what the parachute is + + + align:start position:0% +you know what what the parachute is +something that you use to drop soldiers + + align:start position:0% +something that you use to drop soldiers + + + align:start position:0% +something that you use to drop soldiers +right so so it's a neat it's a really + + align:start position:0% +right so so it's a neat it's a really + + + align:start position:0% +right so so it's a neat it's a really +neat book + + align:start position:0% +neat book + + + align:start position:0% +neat book +because you can see like the title a + + align:start position:0% +because you can see like the title a + + + align:start position:0% +because you can see like the title a +playful path to home you know it could + + align:start position:0% +playful path to home you know it could + + + align:start position:0% +playful path to home you know it could +be some sort of New Age writing but it's + + align:start position:0% +be some sort of New Age writing but it's + + + align:start position:0% +be some sort of New Age writing but it's +actually a pretty nice treatise are a + + align:start position:0% +actually a pretty nice treatise are a + + + align:start position:0% +actually a pretty nice treatise are a +particular kind of game design there is + + align:start position:0% +particular kind of game design there is + + + align:start position:0% +particular kind of game design there is +how do you make games to bring people + + align:start position:0% +how do you make games to bring people + + + align:start position:0% +how do you make games to bring people +together which is perfectly fine goal + + align:start position:0% +together which is perfectly fine goal + + + align:start position:0% +together which is perfectly fine goal +when it comes if you want to be a game + + align:start position:0% +when it comes if you want to be a game + + + align:start position:0% +when it comes if you want to be a game +design so check it out if you're + + align:start position:0% +design so check it out if you're + + + align:start position:0% +design so check it out if you're +interested I have everyday things you + + align:start position:0% +interested I have everyday things you + + + align:start position:0% +interested I have everyday things you +should not graduate from MIT Hutton + + align:start position:0% +should not graduate from MIT Hutton + + + align:start position:0% +should not graduate from MIT Hutton +without having read this book if you + + align:start position:0% +without having read this book if you + + + align:start position:0% +without having read this book if you +design anything by chemical engineer + + align:start position:0% +design anything by chemical engineer + + + align:start position:0% +design anything by chemical engineer +software anything that's meant to be + + align:start position:0% +software anything that's meant to be + + + align:start position:0% +software anything that's meant to be +used by a human being maybe some of you + + align:start position:0% +used by a human being maybe some of you + + + align:start position:0% +used by a human being maybe some of you +who work with robots might be able to + + align:start position:0% +who work with robots might be able to + + + align:start position:0% +who work with robots might be able to +skip this but I would suggest not I + + align:start position:0% +skip this but I would suggest not I + + + align:start position:0% +skip this but I would suggest not I +think you can read this too and get a + + align:start position:0% +think you can read this too and get a + + + align:start position:0% +think you can read this too and get a +lot about usability accessibility how to + + align:start position:0% +lot about usability accessibility how to + + + align:start position:0% +lot about usability accessibility how to +make a good user interfaces we have I + + align:start position:0% +make a good user interfaces we have I + + + align:start position:0% +make a good user interfaces we have I +think two readings from here these are + + align:start position:0% +think two readings from here these are + + + align:start position:0% +think two readings from here these are +PDFs that are up on our website if these + + align:start position:0% +PDFs that are up on our website if these + + + align:start position:0% +PDFs that are up on our website if these +two fold the Oxford history of board + + align:start position:0% +two fold the Oxford history of board + + + align:start position:0% +two fold the Oxford history of board +games we actually have a lot of readings + + align:start position:0% +games we actually have a lot of readings + + + align:start position:0% +games we actually have a lot of readings +of him from here because it is relevant + + align:start position:0% +of him from here because it is relevant + + + align:start position:0% +of him from here because it is relevant +to our final assignment and what it is + + align:start position:0% +to our final assignment and what it is + + + align:start position:0% +to our final assignment and what it is +is surprisingly read about list of + + align:start position:0% +is surprisingly read about list of + + + align:start position:0% +is surprisingly read about list of +traditional board games that you maybe + + align:start position:0% +traditional board games that you maybe + + + align:start position:0% +traditional board games that you maybe +you've heard about 10% of these but but + + align:start position:0% +you've heard about 10% of these but but + + + align:start position:0% +you've heard about 10% of these but but +really it's a really interesting + + align:start position:0% +really it's a really interesting + + + align:start position:0% +really it's a really interesting +analysis and the reason why I did I + + align:start position:0% +analysis and the reason why I did I + + + align:start position:0% +analysis and the reason why I did I +prescribed this book is two reasons one + + align:start position:0% +prescribed this book is two reasons one + + + align:start position:0% +prescribed this book is two reasons one +you need this background knowledge to be + + align:start position:0% +you need this background knowledge to be + + + align:start position:0% +you need this background knowledge to be +able to execute assignment three second + + align:start position:0% +able to execute assignment three second + + + align:start position:0% +able to execute assignment three second +reason is that there is it's a good + + align:start position:0% +reason is that there is it's a good + + + align:start position:0% +reason is that there is it's a good +example of what game historical analysis + + align:start position:0% +example of what game historical analysis + + + align:start position:0% +example of what game historical analysis +looks like so if you're ever interested + + align:start position:0% +looks like so if you're ever interested + + + align:start position:0% +looks like so if you're ever interested +in going to academia and doing this sort + + align:start position:0% +in going to academia and doing this sort + + + align:start position:0% +in going to academia and doing this sort +of writing new at least now I have a + + align:start position:0% +of writing new at least now I have a + + + align:start position:0% +of writing new at least now I have a +sample of what that looks like it's not + + align:start position:0% +sample of what that looks like it's not + + + align:start position:0% +sample of what that looks like it's not +as dry and stodgy as you think it is + + align:start position:0% +as dry and stodgy as you think it is + + + align:start position:0% +as dry and stodgy as you think it is +about gameplay of the wrong so but we do + + align:start position:0% +about gameplay of the wrong so but we do + + + align:start position:0% +about gameplay of the wrong so but we do +have a lot of readings this book is + + align:start position:0% +have a lot of readings this book is + + + align:start position:0% +have a lot of readings this book is +available on reserve in the library + + align:start position:0% +available on reserve in the library + + + align:start position:0% +available on reserve in the library +we're gonna try to get more scans of + + align:start position:0% +we're gonna try to get more scans of + + + align:start position:0% +we're gonna try to get more scans of +this up on stellar but I'm not entirely + + align:start position:0% +this up on stellar but I'm not entirely + + + align:start position:0% +this up on stellar but I'm not entirely +sure what I'm legally allowed to put + + align:start position:0% +sure what I'm legally allowed to put + + + align:start position:0% +sure what I'm legally allowed to put +scans up on that many scans up + + align:start position:0% +scans up on that many scans up + + + align:start position:0% +scans up on that many scans up +but the hardcopy itself is there I don't + + align:start position:0% +but the hardcopy itself is there I don't + + + align:start position:0% +but the hardcopy itself is there I don't +think you can even buy this book anymore + + align:start position:0% +think you can even buy this book anymore + + + align:start position:0% +think you can even buy this book anymore +this book is been out of print for a + + align:start position:0% +this book is been out of print for a + + + align:start position:0% +this book is been out of print for a +really long time so I'm gonna try to be + + align:start position:0% +really long time so I'm gonna try to be + + + align:start position:0% +really long time so I'm gonna try to be +increase access to this but the best I + + align:start position:0% +increase access to this but the best I + + + align:start position:0% +increase access to this but the best I +can do right now is that it's on reserve + + align:start position:0% +can do right now is that it's on reserve + + + align:start position:0% +can do right now is that it's on reserve +in Hayden library evolution let's see + + align:start position:0% +in Hayden library evolution let's see + + + align:start position:0% +in Hayden library evolution let's see +what else finally these three books + + align:start position:0% +what else finally these three books + + + align:start position:0% +what else finally these three books +again might be familiar if you've ever + + align:start position:0% +again might be familiar if you've ever + + + align:start position:0% +again might be familiar if you've ever +taken any of the game lab classes game + + align:start position:0% +taken any of the game lab classes game + + + align:start position:0% +taken any of the game lab classes game +design workshop challenges for game + + align:start position:0% +design workshop challenges for game + + + align:start position:0% +design workshop challenges for game +designers and rules of play don't read + + align:start position:0% +designers and rules of play don't read + + + align:start position:0% +designers and rules of play don't read +the reading for today is actually + + align:start position:0% +the reading for today is actually + + + align:start position:0% +the reading for today is actually +chapter one from challenges for game + + align:start position:0% +chapter one from challenges for game + + + align:start position:0% +chapter one from challenges for game +designers all of these books are + + align:start position:0% +designers all of these books are + + + align:start position:0% +designers all of these books are +available online through MIT libraries + + align:start position:0% +available online through MIT libraries + + + align:start position:0% +available online through MIT libraries +web portal the trick is you kind of you + + align:start position:0% +web portal the trick is you kind of you + + + align:start position:0% +web portal the trick is you kind of you +need to be on a sort of MIT subnet how + + align:start position:0% +need to be on a sort of MIT subnet how + + + align:start position:0% +need to be on a sort of MIT subnet how +many of you live on campus okay you're + + align:start position:0% +many of you live on campus okay you're + + + align:start position:0% +many of you live on campus okay you're +not gonna have a problem just go to + + align:start position:0% +not gonna have a problem just go to + + + align:start position:0% +not gonna have a problem just go to +another site there is this thing called + + align:start position:0% +another site there is this thing called + + + align:start position:0% +another site there is this thing called +a books 24/7 link on this dialer you + + align:start position:0% +a books 24/7 link on this dialer you + + + align:start position:0% +a books 24/7 link on this dialer you +click on that first before you read any + + align:start position:0% +click on that first before you read any + + + align:start position:0% +click on that first before you read any +book that basically does some + + align:start position:0% +book that basically does some + + + align:start position:0% +book that basically does some +authentication to make sure that you're + + align:start position:0% +authentication to make sure that you're + + + align:start position:0% +authentication to make sure that you're +actually an MIT student if you have a + + align:start position:0% +actually an MIT student if you have a + + + align:start position:0% +actually an MIT student if you have a +browser with cookies that should work + + align:start position:0% +browser with cookies that should work + + + align:start position:0% +browser with cookies that should work +just fine and then you click the book + + align:start position:0% +just fine and then you click the book + + + align:start position:0% +just fine and then you click the book +that you want to read you'll get it + + align:start position:0% +that you want to read you'll get it + + + align:start position:0% +that you want to read you'll get it +you'll get a table of contents you jump + + align:start position:0% +you'll get a table of contents you jump + + + align:start position:0% +you'll get a table of contents you jump +to the chapter you're reading the book + + align:start position:0% +to the chapter you're reading the book + + + align:start position:0% +to the chapter you're reading the book +in HTML however if you're not on the MIT + + align:start position:0% +in HTML however if you're not on the MIT + + + align:start position:0% +in HTML however if you're not on the MIT +campus I think if you have a browser + + align:start position:0% +campus I think if you have a browser + + + align:start position:0% +campus I think if you have a browser +with cookies they're still fine but you + + align:start position:0% +with cookies they're still fine but you + + + align:start position:0% +with cookies they're still fine but you +might have better luck by actually being + + align:start position:0% +might have better luck by actually being + + + align:start position:0% +might have better luck by actually being +on MIT subnet you do exactly the same + + align:start position:0% +on MIT subnet you do exactly the same + + + align:start position:0% +on MIT subnet you do exactly the same +stuff that I said you go to stellar you + + align:start position:0% +stuff that I said you go to stellar you + + + align:start position:0% +stuff that I said you go to stellar you +click on the books waiting for seven + + align:start position:0% +click on the books waiting for seven + + + align:start position:0% +click on the books waiting for seven +think it authenticates you and can read + + align:start position:0% +think it authenticates you and can read + + + align:start position:0% +think it authenticates you and can read +you can be in the book that you can even + + align:start position:0% +you can be in the book that you can even + + + align:start position:0% +you can be in the book that you can even +print it out but if you do have trouble + + align:start position:0% +print it out but if you do have trouble + + + align:start position:0% +print it out but if you do have trouble +reading it for any reason please let me + + align:start position:0% +reading it for any reason please let me + + + align:start position:0% +reading it for any reason please let me +know because we're going to have a lot + + align:start position:0% +know because we're going to have a lot + + + align:start position:0% +know because we're going to have a lot +of readings from these three books over + + align:start position:0% +of readings from these three books over + + + align:start position:0% +of readings from these three books over +the entire semester so we let's try to + + align:start position:0% +the entire semester so we let's try to + + + align:start position:0% +the entire semester so we let's try to +fix that for you as quickly as possible + + align:start position:0% +fix that for you as quickly as possible + + + align:start position:0% +fix that for you as quickly as possible +and then you wouldn't have any more + + align:start position:0% +and then you wouldn't have any more + + + align:start position:0% +and then you wouldn't have any more +trouble with that it's free but it's a + + align:start position:0% +trouble with that it's free but it's a + + + align:start position:0% +trouble with that it's free but it's a +bit of hassle + + align:start position:0% +bit of hassle + + + align:start position:0% +bit of hassle +okay that's basically it for the + + align:start position:0% +okay that's basically it for the + + + align:start position:0% +okay that's basically it for the +formalities again any questions about + + align:start position:0% +formalities again any questions about + + + align:start position:0% +formalities again any questions about +how the class is organized how grades + + align:start position:0% +how the class is organized how grades + + + align:start position:0% +how the class is organized how grades +are assigned it is a project-based class + + align:start position:0% +are assigned it is a project-based class + + + align:start position:0% +are assigned it is a project-based class +which means your grades are going to be + + align:start position:0% +which means your grades are going to be + + + align:start position:0% +which means your grades are going to be +heavily dependent on the performance of + + align:start position:0% +heavily dependent on the performance of + + + align:start position:0% +heavily dependent on the performance of +your teammates so get along with your + + align:start position:0% +your teammates so get along with your + + + align:start position:0% +your teammates so get along with your +teammates you know try to do a good work + + align:start position:0% +teammates you know try to do a good work + + + align:start position:0% +teammates you know try to do a good work +but it's your green is not going to be + + align:start position:0% +but it's your green is not going to be + + + align:start position:0% +but it's your green is not going to be +determined by how fun your game is this + + align:start position:0% +determined by how fun your game is this + + + align:start position:0% +determined by how fun your game is this +may be coming as a surprise to some of + + align:start position:0% +may be coming as a surprise to some of + + + align:start position:0% +may be coming as a surprise to some of +you fund is one of those things that is + + align:start position:0% +you fund is one of those things that is + + + align:start position:0% +you fund is one of those things that is +really elusive even if you know what + + align:start position:0% +really elusive even if you know what + + + align:start position:0% +really elusive even if you know what +you're trying to design for you might + + align:start position:0% +you're trying to design for you might + + + align:start position:0% +you're trying to design for you might +not get there especially in the + + align:start position:0% +not get there especially in the + + + align:start position:0% +not get there especially in the +constraints of doing three projects in + + align:start position:0% +constraints of doing three projects in + + + align:start position:0% +constraints of doing three projects in +one semester and someone who's designed + + align:start position:0% +one semester and someone who's designed + + + align:start position:0% +one semester and someone who's designed +a lot of games both in MIT and outside I + + align:start position:0% +a lot of games both in MIT and outside I + + + align:start position:0% +a lot of games both in MIT and outside I +fully I fully acknowledge that you might + + align:start position:0% +fully I fully acknowledge that you might + + + align:start position:0% +fully I fully acknowledge that you might +be perfectly disciplined and do + + align:start position:0% +be perfectly disciplined and do + + + align:start position:0% +be perfectly disciplined and do +everything that I tell you and still at + + align:start position:0% +everything that I tell you and still at + + + align:start position:0% +everything that I tell you and still at +end up with a very uncommon game so I'm + + align:start position:0% +end up with a very uncommon game so I'm + + + align:start position:0% +end up with a very uncommon game so I'm +not going to grade you on the quality of + + align:start position:0% +not going to grade you on the quality of + + + align:start position:0% +not going to grade you on the quality of +that I am going to grade you on your + + align:start position:0% +that I am going to grade you on your + + + align:start position:0% +that I am going to grade you on your +ability to listen to feedback through + + align:start position:0% +ability to listen to feedback through + + + align:start position:0% +ability to listen to feedback through +feedback that we provided feedback we + + align:start position:0% +feedback that we provided feedback we + + + align:start position:0% +feedback that we provided feedback we +are getting from testers the ability to + + align:start position:0% +are getting from testers the ability to + + + align:start position:0% +are getting from testers the ability to +do things like things like regular + + align:start position:0% +do things like things like regular + + + align:start position:0% +do things like things like regular +testing sessions the ability to stick to + + align:start position:0% +testing sessions the ability to stick to + + + align:start position:0% +testing sessions the ability to stick to +the discipline of iterative design if + + align:start position:0% +the discipline of iterative design if + + + align:start position:0% +the discipline of iterative design if +you are if your game is mostly not + + align:start position:0% +you are if your game is mostly not + + + align:start position:0% +you are if your game is mostly not +playable until the last week and then + + align:start position:0% +playable until the last week and then + + + align:start position:0% +playable until the last week and then +suddenly you pull some sort of like + + align:start position:0% +suddenly you pull some sort of like + + + align:start position:0% +suddenly you pull some sort of like +marathon effort to try to get everything + + align:start position:0% +marathon effort to try to get everything + + + align:start position:0% +marathon effort to try to get everything +working together in that last week you + + align:start position:0% +working together in that last week you + + + align:start position:0% +working together in that last week you +should not expect a good grade that's + + align:start position:0% +should not expect a good grade that's + + + align:start position:0% +should not expect a good grade that's +not what I'm trying to teach you you + + align:start position:0% +not what I'm trying to teach you you + + + align:start position:0% +not what I'm trying to teach you you +should be constantly iterating on these + + align:start position:0% +should be constantly iterating on these + + + align:start position:0% +should be constantly iterating on these +games every single week but and if you + + align:start position:0% +games every single week but and if you + + + align:start position:0% +games every single week but and if you +do that you should count on a fairly + + align:start position:0% +do that you should count on a fairly + + + align:start position:0% +do that you should count on a fairly +reasonable it was fairly quickly and + + align:start position:0% +reasonable it was fairly quickly and + + + align:start position:0% +reasonable it was fairly quickly and +this is a be average class term so + + align:start position:0% +this is a be average class term so + + + align:start position:0% +this is a be average class term so +typically when I grade that's that's how + + align:start position:0% +typically when I grade that's that's how + + + align:start position:0% +typically when I grade that's that's how +it ends up I'm not actually grading on a + + align:start position:0% +it ends up I'm not actually grading on a + + + align:start position:0% +it ends up I'm not actually grading on a +curve it is possible to have an average + + align:start position:0% +curve it is possible to have an average + + + align:start position:0% +curve it is possible to have an average +class + + align:start position:0% +class + + + align:start position:0% +class +if everybody does incredibly well but + + align:start position:0% +if everybody does incredibly well but + + + align:start position:0% +if everybody does incredibly well but +typically in the past couple of years + + align:start position:0% +typically in the past couple of years + + + align:start position:0% +typically in the past couple of years +it's always be average all right so let + + align:start position:0% +it's always be average all right so let + + + align:start position:0% +it's always be average all right so let +me start with playing right now this + + align:start position:0% + + + + align:start position:0% + +quest that one + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +I've missed something up there Zambia + + align:start position:0% +I've missed something up there Zambia + + + align:start position:0% +I've missed something up there Zambia +beside Wow how the people that exclusive + + align:start position:0% +beside Wow how the people that exclusive + + + align:start position:0% +beside Wow how the people that exclusive +already I thought it an internship they + + align:start position:0% +already I thought it an internship they + + + align:start position:0% +already I thought it an internship they +just had like a bunch of board games + + align:start position:0% +just had like a bunch of board games + + + align:start position:0% +just had like a bunch of board games +okay yeah my brother played it somewhere + + align:start position:0% +okay yeah my brother played it somewhere + + + align:start position:0% +okay yeah my brother played it somewhere +and suggested to me it's very 80s game + + align:start position:0% +and suggested to me it's very 80s game + + + align:start position:0% +and suggested to me it's very 80s game +it's a game about programming + + align:start position:0% +it's a game about programming + + + align:start position:0% +it's a game about programming +programming a robust beating each other + + align:start position:0% +programming a robust beating each other + + + align:start position:0% +programming a robust beating each other +up humanity I don't this one but what's + + align:start position:0% +up humanity I don't this one but what's + + + align:start position:0% +up humanity I don't this one but what's +xx someone cast a hex oh and then + + align:start position:0% +xx someone cast a hex oh and then + + + align:start position:0% +xx someone cast a hex oh and then +whoever has the heck support of them has + + align:start position:0% +whoever has the heck support of them has + + + align:start position:0% +whoever has the heck support of them has +to deal with the hex or their cards if + + align:start position:0% +to deal with the hex or their cards if + + + align:start position:0% +to deal with the hex or their cards if +they can't then they're hexed and then + + align:start position:0% +they can't then they're hexed and then + + + align:start position:0% +they can't then they're hexed and then +they have a chance + + align:start position:0% + + + + align:start position:0% + +that's a hexagon yes it's terms they + + align:start position:0% +that's a hexagon yes it's terms they + + + align:start position:0% +that's a hexagon yes it's terms they +have and your roll lets you take actions + + align:start position:0% +have and your roll lets you take actions + + + align:start position:0% +have and your roll lets you take actions +so what you do is you lie about what + + align:start position:0% +so what you do is you lie about what + + + align:start position:0% +so what you do is you lie about what +really happens in order to take actions + + align:start position:0% +really happens in order to take actions + + + align:start position:0% +really happens in order to take actions +that you would have access to the whole + + align:start position:0% +that you would have access to the whole + + + align:start position:0% +that you would have access to the whole +thing over all the mechanics are you + + align:start position:0% +thing over all the mechanics are you + + + align:start position:0% +thing over all the mechanics are you +make money and then + + align:start position:0% +make money and then + + + align:start position:0% +make money and then +to kill other people kill someone they + + align:start position:0% +to kill other people kill someone they + + + align:start position:0% +to kill other people kill someone they +lose one of their roles so the way to + + align:start position:0% +lose one of their roles so the way to + + + align:start position:0% +lose one of their roles so the way to +killing someone or by lying and being + + align:start position:0% + + + + align:start position:0% + +okay so far like I started my task + + align:start position:0% +okay so far like I started my task + + + align:start position:0% +okay so far like I started my task +couple of people to describe the means + + align:start position:0% +couple of people to describe the means + + + align:start position:0% +couple of people to describe the means +that have come out and you can see it's + + align:start position:0% +that have come out and you can see it's + + + align:start position:0% +that have come out and you can see it's +not really been all that difficult right + + align:start position:0% +not really been all that difficult right + + + align:start position:0% +not really been all that difficult right +to say this is what's interesting about + + align:start position:0% +to say this is what's interesting about + + + align:start position:0% +to say this is what's interesting about +the game it's kind of like this game but + + align:start position:0% +the game it's kind of like this game but + + + align:start position:0% +the game it's kind of like this game but +then you've got these changes that's uh + + align:start position:0% +then you've got these changes that's uh + + + align:start position:0% +then you've got these changes that's uh +no that's that's normal where you're + + align:start position:0% +no that's that's normal where you're + + + align:start position:0% +no that's that's normal where you're +communicating you're gonna be have to do + + align:start position:0% +communicating you're gonna be have to do + + + align:start position:0% +communicating you're gonna be have to do +that multiple times this semester for + + align:start position:0% +that multiple times this semester for + + + align:start position:0% +that multiple times this semester for +your own games but often what happens is + + align:start position:0% +your own games but often what happens is + + + align:start position:0% +your own games but often what happens is +that when students come up I talk about + + align:start position:0% +that when students come up I talk about + + + align:start position:0% +that when students come up I talk about +their game you start from like ground + + align:start position:0% +their game you start from like ground + + + align:start position:0% +their game you start from like ground +like like my step one this is like well + + align:start position:0% +like like my step one this is like well + + + align:start position:0% +like like my step one this is like well +this game is a card game that has to you + + align:start position:0% +this game is a card game that has to you + + + align:start position:0% +this game is a card game that has to you +know 52 cards and it's going to be + + align:start position:0% +know 52 cards and it's going to be + + + align:start position:0% +know 52 cards and it's going to be +played with four players it's like like + + align:start position:0% +played with four players it's like like + + + align:start position:0% +played with four players it's like like +cut to the chase a little bit faster the + + align:start position:0% +cut to the chase a little bit faster the + + + align:start position:0% +cut to the chase a little bit faster the +way that you just did you know the way + + align:start position:0% +way that you just did you know the way + + + align:start position:0% +way that you just did you know the way +that you just described you know it's + + align:start position:0% +that you just described you know it's + + + align:start position:0% +that you just described you know it's +kind of like mafia but you make these + + align:start position:0% +kind of like mafia but you make these + + + align:start position:0% +kind of like mafia but you make these +changes and everything will watch those + + align:start position:0% +changes and everything will watch those + + + align:start position:0% +changes and everything will watch those +details we won't want those details the + + align:start position:0% +details we won't want those details the + + + align:start position:0% +details we won't want those details the +printing when it's written or we're + + align:start position:0% +printing when it's written or we're + + + align:start position:0% +printing when it's written or we're +actually sitting down to play when you + + align:start position:0% +actually sitting down to play when you + + + align:start position:0% +actually sitting down to play when you +sit when you're coming up here and time + + align:start position:0% +sit when you're coming up here and time + + + align:start position:0% +sit when you're coming up here and time +talking about your own game you know + + align:start position:0% +talking about your own game you know + + + align:start position:0% +talking about your own game you know +give us those elevator pitches that you + + align:start position:0% +give us those elevator pitches that you + + + align:start position:0% +give us those elevator pitches that you +just did you know it's going it is it's + + align:start position:0% +just did you know it's going it is it's + + + align:start position:0% +just did you know it's going it is it's +if you think of this game is a little + + align:start position:0% +if you think of this game is a little + + + align:start position:0% +if you think of this game is a little +bit like it's kind of like chess but + + align:start position:0% +bit like it's kind of like chess but + + + align:start position:0% +bit like it's kind of like chess but +it's going but but but with different + + align:start position:0% +it's going but but but with different + + + align:start position:0% +it's going but but but with different +pieces or something like that and then + + align:start position:0% +pieces or something like that and then + + + align:start position:0% +pieces or something like that and then +you cut it and then you can go to create + + align:start position:0% +you cut it and then you can go to create + + + align:start position:0% +you cut it and then you can go to create +a new table what your game is when you + + align:start position:0% +a new table what your game is when you + + + align:start position:0% +a new table what your game is when you +give a presentation though usually what + + align:start position:0% +give a presentation though usually what + + + align:start position:0% +give a presentation though usually what +I'm listening for isn't so much what is + + align:start position:0% +I'm listening for isn't so much what is + + + align:start position:0% +I'm listening for isn't so much what is +your game right now because I can + + align:start position:0% +your game right now because I can + + + align:start position:0% +your game right now because I can +actually read that later on but what was + + align:start position:0% +actually read that later on but what was + + + align:start position:0% +actually read that later on but what was +your game before it became the thing + + align:start position:0% +your game before it became the thing + + + align:start position:0% +your game before it became the thing +that it is now because I don't + + align:start position:0% +that it is now because I don't + + + align:start position:0% +that it is now because I don't +necessarily always see that I will see + + align:start position:0% +necessarily always see that I will see + + + align:start position:0% +necessarily always see that I will see +various play tests I may not necessarily + + align:start position:0% +various play tests I may not necessarily + + + align:start position:0% +various play tests I may not necessarily +get to every single team I want to know + + align:start position:0% +get to every single team I want to know + + + align:start position:0% +get to every single team I want to know +how you made the decisions that you did + + align:start position:0% +how you made the decisions that you did + + + align:start position:0% +how you made the decisions that you did +in order to end up before you finally + + align:start position:0% +in order to end up before you finally + + + align:start position:0% +in order to end up before you finally +some + + align:start position:0% +some + + + align:start position:0% +some +and I'll get all the details that I need + + align:start position:0% +and I'll get all the details that I need + + + align:start position:0% +and I'll get all the details that I need +from that final summation when I + + align:start position:0% +from that final summation when I + + + align:start position:0% +from that final summation when I +actually read it so when you give your + + align:start position:0% +actually read it so when you give your + + + align:start position:0% +actually read it so when you give your +presentations talk about the history of + + align:start position:0% +presentations talk about the history of + + + align:start position:0% +presentations talk about the history of +your game your tweet week history of + + align:start position:0% +your game your tweet week history of + + + align:start position:0% +your game your tweet week history of +their King before we kiss we go so these + + align:start position:0% +their King before we kiss we go so these + + + align:start position:0% +their King before we kiss we go so these +are all the games that people have been + + align:start position:0% +are all the games that people have been + + + align:start position:0% +are all the games that people have been +playing a lot of board games a lot of a + + align:start position:0% +playing a lot of board games a lot of a + + + align:start position:0% +playing a lot of board games a lot of a +couple of digital games although I can + + align:start position:0% +couple of digital games although I can + + + align:start position:0% +couple of digital games although I can +see how many of you are playing these + + align:start position:0% +see how many of you are playing these + + + align:start position:0% +see how many of you are playing these +games + + align:start position:0% +games + + + align:start position:0% +games +did you tell me any of these like board + + align:start position:0% +did you tell me any of these like board + + + align:start position:0% +did you tell me any of these like board +games are playing and digitally phone + + align:start position:0% + + + + align:start position:0% + +yeah a lot of these games actually do + + align:start position:0% +yeah a lot of these games actually do + + + align:start position:0% +yeah a lot of these games actually do +have iPhone and iOS Android phones well + + align:start position:0% +have iPhone and iOS Android phones well + + + align:start position:0% +have iPhone and iOS Android phones well +because you don't yeah all right why + + align:start position:0% +because you don't yeah all right why + + + align:start position:0% +because you don't yeah all right why +because it's more fun to you're fine to + + align:start position:0% +because it's more fun to you're fine to + + + align:start position:0% +because it's more fun to you're fine to +like guilt people into giving you you + + align:start position:0% +like guilt people into giving you you + + + align:start position:0% +like guilt people into giving you you +know trays and trays that are beneficial + + align:start position:0% +know trays and trays that are beneficial + + + align:start position:0% +know trays and trays that are beneficial +to you we often refer to that as over + + align:start position:0% +to you we often refer to that as over + + + align:start position:0% +to you we often refer to that as over +the table a talk on the whole potato + + align:start position:0% +the table a talk on the whole potato + + + align:start position:0% +the table a talk on the whole potato +over the table interaction that's + + align:start position:0% +over the table interaction that's + + + align:start position:0% +over the table interaction that's +something that you are that when you're + + align:start position:0% +something that you are that when you're + + + align:start position:0% +something that you are that when you're +designing a board game or car cave or + + align:start position:0% +designing a board game or car cave or + + + align:start position:0% +designing a board game or car cave or +even a live-action game I wouldn't say + + align:start position:0% +even a live-action game I wouldn't say + + + align:start position:0% +even a live-action game I wouldn't say +that you're allowed to design + + align:start position:0% +that you're allowed to design + + + align:start position:0% +that you're allowed to design +live-action games in this class in all + + align:start position:0% +live-action games in this class in all + + + align:start position:0% +live-action games in this class in all +games where you're not actually sitting + + align:start position:0% +games where you're not actually sitting + + + align:start position:0% +games where you're not actually sitting +down but you actually be moving around + + align:start position:0% +down but you actually be moving around + + + align:start position:0% +down but you actually be moving around +mafia kind of sits in a gray area + + align:start position:0% + + + + align:start position:0% + +oh well describe treat describe the + + align:start position:0% +oh well describe treat describe the + + + align:start position:0% +oh well describe treat describe the +tactics of cheating I thought like we + + align:start position:0% +tactics of cheating I thought like we + + + align:start position:0% +tactics of cheating I thought like we +roll it right because those are hard to + + align:start position:0% +roll it right because those are hard to + + + align:start position:0% +roll it right because those are hard to +get away with now because of the + + align:start position:0% +get away with now because of the + + + align:start position:0% +get away with now because of the +cheating because of the way how the game + + align:start position:0% +cheating because of the way how the game + + + align:start position:0% +cheating because of the way how the game +is me so you've said upgrades that you + + align:start position:0% +is me so you've said upgrades that you + + + align:start position:0% +is me so you've said upgrades that you +called that I think this week well okay + + align:start position:0% +called that I think this week well okay + + + align:start position:0% +called that I think this week well okay +so let's briefly talk about monopoly + + align:start position:0% +so let's briefly talk about monopoly + + + align:start position:0% +so let's briefly talk about monopoly +then you know it's how many people here + + align:start position:0% +then you know it's how many people here + + + align:start position:0% +then you know it's how many people here +like playing monopolies okay I ready + + align:start position:0% +like playing monopolies okay I ready + + + align:start position:0% +like playing monopolies okay I ready +please play Monopoly regularly like you + + align:start position:0% +please play Monopoly regularly like you + + + align:start position:0% +please play Monopoly regularly like you +know maybe I'm going with families or + + align:start position:0% +know maybe I'm going with families or + + + align:start position:0% +know maybe I'm going with families or +you know um what what are the good + + align:start position:0% +you know um what what are the good + + + align:start position:0% +you know um what what are the good +things about monopoly what do people + + align:start position:0% +things about monopoly what do people + + + align:start position:0% +things about monopoly what do people +like okay all right this is like real + + align:start position:0% +like okay all right this is like real + + + align:start position:0% +like okay all right this is like real +sense of my progression there right + + align:start position:0% + + + + align:start position:0% + +that's kind of like the real estate + + align:start position:0% +that's kind of like the real estate + + + align:start position:0% +that's kind of like the real estate +version I'm making Bank so these those + + align:start position:0% +version I'm making Bank so these those + + + align:start position:0% +version I'm making Bank so these those +little plastic bits mean like everything + + align:start position:0% + + + + align:start position:0% + +there's kind of like a minimum bh + + align:start position:0% +there's kind of like a minimum bh + + + align:start position:0% +there's kind of like a minimum bh +wedding like they get the basic strategy + + align:start position:0% +wedding like they get the basic strategy + + + align:start position:0% +wedding like they get the basic strategy +and then prospect is kind of my sister + + align:start position:0% +and then prospect is kind of my sister + + + align:start position:0% +and then prospect is kind of my sister +like to be I'm gonna be for some reason + + align:start position:0% +like to be I'm gonna be for some reason + + + align:start position:0% +like to be I'm gonna be for some reason +always has bail for me mmm so like she + + align:start position:0% +always has bail for me mmm so like she + + + align:start position:0% +always has bail for me mmm so like she +was about to go bankrupt and my dad made + + align:start position:0% +was about to go bankrupt and my dad made + + + align:start position:0% +was about to go bankrupt and my dad made +a deal with her that's like basically so + + align:start position:0% +a deal with her that's like basically so + + + align:start position:0% +a deal with her that's like basically so +anytime you make a profit you give me + + align:start position:0% +anytime you make a profit you give me + + + align:start position:0% +anytime you make a profit you give me +two thirds of it and I'll make sure you + + align:start position:0% +two thirds of it and I'll make sure you + + + align:start position:0% +two thirds of it and I'll make sure you +never go out I was like now I'm playing + + align:start position:0% +never go out I was like now I'm playing + + + align:start position:0% +never go out I was like now I'm playing +these two people like I don't know what + + align:start position:0% +these two people like I don't know what + + + align:start position:0% +these two people like I don't know what +I'm supposed to do anymore yeah that's + + align:start position:0% +I'm supposed to do anymore yeah that's + + + align:start position:0% +I'm supposed to do anymore yeah that's +that's called that that that situation + + align:start position:0% +that's called that that that situation + + + align:start position:0% +that's called that that that situation +has been known as has been described as + + align:start position:0% +has been known as has been described as + + + align:start position:0% +has been known as has been described as +king-making where a player who isn't + + align:start position:0% +king-making where a player who isn't + + + align:start position:0% +king-making where a player who isn't +going to win decides who's going to win + + align:start position:0% +going to win decides who's going to win + + + align:start position:0% +going to win decides who's going to win +and it can be suck if they're not the + + align:start position:0% +and it can be suck if they're not the + + + align:start position:0% +and it can be suck if they're not the +person who the more you know the game so + + align:start position:0% +person who the more you know the game so + + + align:start position:0% +person who the more you know the game so +it does allow you to it with a lot of + + align:start position:0% +it does allow you to it with a lot of + + + align:start position:0% +it does allow you to it with a lot of +strategy even though + + align:start position:0% + + + + align:start position:0% + +how many of you play Monopoly with with + + align:start position:0% +how many of you play Monopoly with with + + + align:start position:0% +how many of you play Monopoly with with +sort of open it over the table + + align:start position:0% +sort of open it over the table + + + align:start position:0% +sort of open it over the table +bargaining like yeah all the time + + align:start position:0% +bargaining like yeah all the time + + + align:start position:0% +bargaining like yeah all the time +yeah who doesn't who does it like only + + align:start position:0% +yeah who doesn't who does it like only + + + align:start position:0% +yeah who doesn't who does it like only +the rules only only the thing that you + + align:start position:0% +the rules only only the thing that you + + + align:start position:0% +the rules only only the thing that you +do but to do the other people around the + + align:start position:0% +do but to do the other people around the + + + align:start position:0% +do but to do the other people around the +table also yeah you know it's like think + + align:start position:0% +table also yeah you know it's like think + + + align:start position:0% +table also yeah you know it's like think +things like I was gonna give you money + + align:start position:0% +things like I was gonna give you money + + + align:start position:0% +things like I was gonna give you money +you know things like that there is + + align:start position:0% +you know things like that there is + + + align:start position:0% +you know things like that there is +something that a lot of people do in + + align:start position:0% +something that a lot of people do in + + + align:start position:0% +something that a lot of people do in +monopoly and that's put money in free + + align:start position:0% +monopoly and that's put money in free + + + align:start position:0% +monopoly and that's put money in free +parking yeah never do that never do that + + align:start position:0% +parking yeah never do that never do that + + + align:start position:0% +parking yeah never do that never do that +game gets four times longer because the + + align:start position:0% +game gets four times longer because the + + + align:start position:0% +game gets four times longer because the +game is designed to the rules of the + + align:start position:0% +game is designed to the rules of the + + + align:start position:0% +game is designed to the rules of the +game at nice is designed to suck money + + align:start position:0% +game at nice is designed to suck money + + + align:start position:0% +game at nice is designed to suck money +out of out of the system there are + + align:start position:0% +out of out of the system there are + + + align:start position:0% +out of out of the system there are +inflows things like to collect 200 + + align:start position:0% +inflows things like to collect 200 + + + align:start position:0% +inflows things like to collect 200 +things like the certain community chests + + align:start position:0% +things like the certain community chests + + + align:start position:0% +things like the certain community chests +and chance cards but the games also + + align:start position:0% +and chance cards but the games also + + + align:start position:0% +and chance cards but the games also +designed to take money out so that + + align:start position:0% +designed to take money out so that + + + align:start position:0% +designed to take money out so that +people go bankrupt by saying I'm now + + align:start position:0% +people go bankrupt by saying I'm now + + + align:start position:0% +people go bankrupt by saying I'm now +losing this money but I'm now putting it + + align:start position:0% +losing this money but I'm now putting it + + + align:start position:0% +losing this money but I'm now putting it +on the square and if anybody happens to + + align:start position:0% +on the square and if anybody happens to + + + align:start position:0% +on the square and if anybody happens to +let on free parking they get all this + + align:start position:0% +let on free parking they get all this + + + align:start position:0% +let on free parking they get all this +money that money hasn't actually been + + align:start position:0% +money that money hasn't actually been + + + align:start position:0% +money that money hasn't actually been +sucked out of the system it's just + + align:start position:0% +sucked out of the system it's just + + + align:start position:0% +sucked out of the system it's just +waiting to be redistributed somebody + + align:start position:0% +waiting to be redistributed somebody + + + align:start position:0% +waiting to be redistributed somebody +else and that means people take a very + + align:start position:0% +else and that means people take a very + + + align:start position:0% +else and that means people take a very +long time to go bankrupt you know anyone + + align:start position:0% +long time to go bankrupt you know anyone + + + align:start position:0% +long time to go bankrupt you know anyone +is complaining about how long in the + + align:start position:0% +is complaining about how long in the + + + align:start position:0% +is complaining about how long in the +game takes you might want to check your + + align:start position:0% +game takes you might want to check your + + + align:start position:0% +game takes you might want to check your +age to play with that rule and you are + + align:start position:0% +age to play with that rule and you are + + + align:start position:0% +age to play with that rule and you are +is and you read the rules it's not there + + align:start position:0% +is and you read the rules it's not there + + + align:start position:0% +is and you read the rules it's not there +it's not there at all it's a sort of + + align:start position:0% +it's not there at all it's a sort of + + + align:start position:0% +it's not there at all it's a sort of +thing though that does make it a lot + + align:start position:0% +thing though that does make it a lot + + + align:start position:0% +thing though that does make it a lot +easier for somebody who's about to go + + align:start position:0% +easier for somebody who's about to go + + + align:start position:0% +easier for somebody who's about to go +bankrupt to get back into the game so + + align:start position:0% +bankrupt to get back into the game so + + + align:start position:0% +bankrupt to get back into the game so +now we're back to this whole family + + align:start position:0% +now we're back to this whole family + + + align:start position:0% +now we're back to this whole family +friendly thing which is if you are not + + align:start position:0% +friendly thing which is if you are not + + + align:start position:0% +friendly thing which is if you are not +that great at playing this game or maybe + + align:start position:0% +that great at playing this game or maybe + + + align:start position:0% +that great at playing this game or maybe +even taking it that seriously useful you + + align:start position:0% +even taking it that seriously useful you + + + align:start position:0% +even taking it that seriously useful you +still stand a chance there's a couple of + + align:start position:0% +still stand a chance there's a couple of + + + align:start position:0% +still stand a chance there's a couple of +other things about Monopoly + + align:start position:0% +other things about Monopoly + + + align:start position:0% +other things about Monopoly +it's a decent game if you are if you're + + align:start position:0% +it's a decent game if you are if you're + + + align:start position:0% +it's a decent game if you are if you're +not at the table all the time say + + align:start position:0% +not at the table all the time say + + + align:start position:0% +not at the table all the time say +Thanksgiving or something and somebody + + align:start position:0% +Thanksgiving or something and somebody + + + align:start position:0% +Thanksgiving or something and somebody +is has 2's watching the game or or + + align:start position:0% +is has 2's watching the game or or + + + align:start position:0% +is has 2's watching the game or or +making sure that the turkey doesn't + + align:start position:0% +making sure that the turkey doesn't + + + align:start position:0% +making sure that the turkey doesn't +catch a fire or something again needs to + + align:start position:0% +catch a fire or something again needs to + + + align:start position:0% +catch a fire or something again needs to +like stand up and check and + + align:start position:0% +like stand up and check and + + + align:start position:0% +like stand up and check and +back to the game everything that you + + align:start position:0% +back to the game everything that you + + + align:start position:0% +back to the game everything that you +need to know about the game is right + + align:start position:0% +need to know about the game is right + + + align:start position:0% +need to know about the game is right +there in front of you and at the moment + + align:start position:0% +there in front of you and at the moment + + + align:start position:0% +there in front of you and at the moment +of time when you need to make your + + align:start position:0% +of time when you need to make your + + + align:start position:0% +of time when you need to make your +decision it's very little + + align:start position:0% +decision it's very little + + + align:start position:0% +decision it's very little +I don't except for the amount of money + + align:start position:0% +I don't except for the amount of money + + + align:start position:0% +I don't except for the amount of money +that people have and that's usually + + align:start position:0% +that people have and that's usually + + + align:start position:0% +that people have and that's usually +fairly easy to just see some people get + + align:start position:0% +fairly easy to just see some people get + + + align:start position:0% +fairly easy to just see some people get +very secretive but most people don't + + align:start position:0% + + + + align:start position:0% + +monopoly is an incredibly successful + + align:start position:0% +monopoly is an incredibly successful + + + align:start position:0% +monopoly is an incredibly successful +game I don't think this is a contentious + + align:start position:0% +game I don't think this is a contentious + + + align:start position:0% +game I don't think this is a contentious +issue it makes makes a lot of money + + align:start position:0% +issue it makes makes a lot of money + + + align:start position:0% +issue it makes makes a lot of money +a lot of people a lot of copies get sold + + align:start position:0% +a lot of people a lot of copies get sold + + + align:start position:0% +a lot of people a lot of copies get sold +and bought and there was some + + align:start position:0% +and bought and there was some + + + align:start position:0% +and bought and there was some +ambivalence here about whether it was a + + align:start position:0% +ambivalence here about whether it was a + + + align:start position:0% +ambivalence here about whether it was a +good game or not + + align:start position:0% +good game or not + + + align:start position:0% +good game or not +why does that game do well do so come + + align:start position:0% +why does that game do well do so come + + + align:start position:0% +why does that game do well do so come +I'll show you why it's is it easy + + align:start position:0% +I'll show you why it's is it easy + + + align:start position:0% +I'll show you why it's is it easy +sorry it's easy to pick up not sort of + + align:start position:0% +sorry it's easy to pick up not sort of + + + align:start position:0% +sorry it's easy to pick up not sort of +easy to win like you can take like 10 15 + + align:start position:0% +easy to win like you can take like 10 15 + + + align:start position:0% +easy to win like you can take like 10 15 +of them you play a game + + align:start position:0% +of them you play a game + + + align:start position:0% +of them you play a game +10 15 minutes to explain if you already + + align:start position:0% +10 15 minutes to explain if you already + + + align:start position:0% +10 15 minutes to explain if you already +know they already know the rules my + + align:start position:0% +know they already know the rules my + + + align:start position:0% +know they already know the rules my +chances are somebody does know the rules + + align:start position:0% +chances are somebody does know the rules + + + align:start position:0% +chances are somebody does know the rules +right somebody in that room probably has + + align:start position:0% +right somebody in that room probably has + + + align:start position:0% +right somebody in that room probably has +played cuz it's so well known right + + align:start position:0% + + + + align:start position:0% + +like yeah he didn't play without making + + align:start position:0% +like yeah he didn't play without making + + + align:start position:0% +like yeah he didn't play without making +it like roll the dice and if you can't + + align:start position:0% +it like roll the dice and if you can't + + + align:start position:0% +it like roll the dice and if you can't +afford to buy it buy it that's the + + align:start position:0% +afford to buy it buy it that's the + + + align:start position:0% +afford to buy it buy it that's the +decision making if it's not a decision + + align:start position:0% +decision making if it's not a decision + + + align:start position:0% +decision making if it's not a decision +it's a strategy + + align:start position:0% + + + + align:start position:0% + +yeah it's like no you can't afford it + + align:start position:0% +yeah it's like no you can't afford it + + + align:start position:0% +yeah it's like no you can't afford it +buy it all right so the decision make + + align:start position:0% +buy it all right so the decision make + + + align:start position:0% +buy it all right so the decision make +that that's a lot to do in the game + + align:start position:0% +that that's a lot to do in the game + + + align:start position:0% +that that's a lot to do in the game +though you roll the dice you pull cards + + align:start position:0% +though you roll the dice you pull cards + + + align:start position:0% +though you roll the dice you pull cards +out you move your little dog you know + + align:start position:0% +out you move your little dog you know + + + align:start position:0% +out you move your little dog you know +you you you you can make bargains to + + align:start position:0% +you you you you can make bargains to + + + align:start position:0% +you you you you can make bargains to +people over the table you you take your + + align:start position:0% +people over the table you you take your + + + align:start position:0% +people over the table you you take your +little houses and you put them down and + + align:start position:0% +little houses and you put them down and + + + align:start position:0% +little houses and you put them down and +you turn em into hotels and so that's a + + align:start position:0% +you turn em into hotels and so that's a + + + align:start position:0% +you turn em into hotels and so that's a +lot of like busy work that you get to do + + align:start position:0% +lot of like busy work that you get to do + + + align:start position:0% +lot of like busy work that you get to do +without having to make a single decision + + align:start position:0% +without having to make a single decision + + + align:start position:0% +without having to make a single decision +so you feel very active while you're + + align:start position:0% +so you feel very active while you're + + + align:start position:0% +so you feel very active while you're +doing it any other ideas about why I may + + align:start position:0% +doing it any other ideas about why I may + + + align:start position:0% +doing it any other ideas about why I may +be popular we talked about how how + + align:start position:0% +be popular we talked about how how + + + align:start position:0% +be popular we talked about how how +well-known it is all this oh yeah + + align:start position:0% +well-known it is all this oh yeah + + + align:start position:0% +well-known it is all this oh yeah +trivially we re skinnable + + align:start position:0% +trivially we re skinnable + + + align:start position:0% +trivially we re skinnable +all right again you can turn i have + + align:start position:0% +all right again you can turn i have + + + align:start position:0% +all right again you can turn i have +monopoly singapore somewhere it is where + + align:start position:0% +monopoly singapore somewhere it is where + + + align:start position:0% +monopoly singapore somewhere it is where +I'm from they just renamed out all the + + align:start position:0% +I'm from they just renamed out all the + + + align:start position:0% +I'm from they just renamed out all the +properties all the amounts of money are + + align:start position:0% +properties all the amounts of money are + + + align:start position:0% +properties all the amounts of money are +exactly the same I think there are some + + align:start position:0% +exactly the same I think there are some + + + align:start position:0% +exactly the same I think there are some +like warmth level regional monopolies + + align:start position:0% +like warmth level regional monopolies + + + align:start position:0% +like warmth level regional monopolies +are there where the end in the few new + + align:start position:0% +are there where the end in the few new + + + align:start position:0% +are there where the end in the few new +rules but you're right you can easily + + align:start position:0% +rules but you're right you can easily + + + align:start position:0% +rules but you're right you can easily +sell somebody who has monopoly a + + align:start position:0% +sell somebody who has monopoly a + + + align:start position:0% +sell somebody who has monopoly a +different copy of it but it's that + + align:start position:0% +different copy of it but it's that + + + align:start position:0% +different copy of it but it's that +person buying do you copy a monopoly if + + align:start position:0% +person buying do you copy a monopoly if + + + align:start position:0% +person buying do you copy a monopoly if +you already have a copy of Monopoly are + + align:start position:0% +you already have a copy of Monopoly are + + + align:start position:0% +you already have a copy of Monopoly are +you buying yourself a new copy of + + align:start position:0% +you buying yourself a new copy of + + + align:start position:0% +you buying yourself a new copy of +Monopoly + + align:start position:0% + + + + align:start position:0% + +our youth do you let us anyone actually + + align:start position:0% +our youth do you let us anyone actually + + + align:start position:0% +our youth do you let us anyone actually +pay money for that thank you getting a + + align:start position:0% +pay money for that thank you getting a + + + align:start position:0% +pay money for that thank you getting a +good gift that's the dirty little secret + + align:start position:0% +good gift that's the dirty little secret + + + align:start position:0% +good gift that's the dirty little secret +about you know all these likes them no + + align:start position:0% +about you know all these likes them no + + + align:start position:0% +about you know all these likes them no +Parker Brothers Hasbro maybe it's not + + align:start position:0% +Parker Brothers Hasbro maybe it's not + + + align:start position:0% +Parker Brothers Hasbro maybe it's not +dirty it's it's the reality on the + + align:start position:0% +dirty it's it's the reality on the + + + align:start position:0% +dirty it's it's the reality on the +majority of board games or these like + + align:start position:0% +majority of board games or these like + + + align:start position:0% +majority of board games or these like +super mega ultra perennial favorites are + + align:start position:0% +super mega ultra perennial favorites are + + + align:start position:0% +super mega ultra perennial favorites are +not bought by the people who are playing + + align:start position:0% +not bought by the people who are playing + + + align:start position:0% +not bought by the people who are playing +them they are bought by somebody else + + align:start position:0% +them they are bought by somebody else + + + align:start position:0% +them they are bought by somebody else +what given us a gift which means you can + + align:start position:0% +what given us a gift which means you can + + + align:start position:0% +what given us a gift which means you can +expect that you know they usually sell + + align:start position:0% +expect that you know they usually sell + + + align:start position:0% +expect that you know they usually sell +most of the copies and Christmas and you + + align:start position:0% +most of the copies and Christmas and you + + + align:start position:0% +most of the copies and Christmas and you +know people might get them for their + + align:start position:0% +know people might get them for their + + + align:start position:0% +know people might get them for their +birthdays and that that's the difference + + align:start position:0% +birthdays and that that's the difference + + + align:start position:0% +birthdays and that that's the difference +between you know a game that shows up in + + align:start position:0% +between you know a game that shows up in + + + align:start position:0% +between you know a game that shows up in +Target Walmart and a game that shows up + + align:start position:0% +Target Walmart and a game that shows up + + + align:start position:0% +Target Walmart and a game that shows up +in especially under the port game store + + align:start position:0% +in especially under the port game store + + + align:start position:0% +in especially under the port game store +walking up especially at the board game + + align:start position:0% +walking up especially at the board game + + + align:start position:0% +walking up especially at the board game +store which is probably under threat by + + align:start position:0% +store which is probably under threat by + + + align:start position:0% +store which is probably under threat by +companies like Amazon and you're buying + + align:start position:0% +companies like Amazon and you're buying + + + align:start position:0% +companies like Amazon and you're buying +a game for yourself you know you're + + align:start position:0% +a game for yourself you know you're + + + align:start position:0% +a game for yourself you know you're +buying special dice because a + + align:start position:0% +buying special dice because a + + + align:start position:0% +buying special dice because a +role-playing game game player or + + align:start position:0% +role-playing game game player or + + + align:start position:0% +role-playing game game player or +miniatures yeah and right next to that + + align:start position:0% +miniatures yeah and right next to that + + + align:start position:0% +miniatures yeah and right next to that +are the board games and you say hey this + + align:start position:0% +are the board games and you say hey this + + + align:start position:0% +are the board games and you say hey this +will be fun for our my next gathering + + align:start position:0% +will be fun for our my next gathering + + + align:start position:0% +will be fun for our my next gathering +either at some friends house or in my + + align:start position:0% +either at some friends house or in my + + + align:start position:0% +either at some friends house or in my +own place or something like that + + align:start position:0% +own place or something like that + + + align:start position:0% +own place or something like that +I want to play this game you buy a + + align:start position:0% +I want to play this game you buy a + + + align:start position:0% +I want to play this game you buy a +monopoly and it's usually not for your + + align:start position:0% +monopoly and it's usually not for your + + + align:start position:0% +monopoly and it's usually not for your +own collection it's usually for somebody + + align:start position:0% +own collection it's usually for somebody + + + align:start position:0% +own collection it's usually for somebody +else's then you give monopoly to + + align:start position:0% +else's then you give monopoly to + + + align:start position:0% +else's then you give monopoly to +somebody else who already has it and + + align:start position:0% +somebody else who already has it and + + + align:start position:0% +somebody else who already has it and +it's fine because you just gave them the + + align:start position:0% +it's fine because you just gave them the + + + align:start position:0% +it's fine because you just gave them the +Star Wars person if they didn't have + + align:start position:0% +Star Wars person if they didn't have + + + align:start position:0% +Star Wars person if they didn't have +that that's how you're successful I + + align:start position:0% +that that's how you're successful I + + + align:start position:0% +that that's how you're successful I +guess what I'm trying to say that not + + align:start position:0% +guess what I'm trying to say that not + + + align:start position:0% +guess what I'm trying to say that not +necessarily it doesn't really have + + align:start position:0% +necessarily it doesn't really have + + + align:start position:0% +necessarily it doesn't really have +necessarily have anything to do with how + + align:start position:0% +necessarily have anything to do with how + + + align:start position:0% +necessarily have anything to do with how +well that game is designed there are a + + align:start position:0% +well that game is designed there are a + + + align:start position:0% +well that game is designed there are a +couple of nice things that monopoly does + + align:start position:0% +couple of nice things that monopoly does + + + align:start position:0% +couple of nice things that monopoly does +about we talked about how it's + + align:start position:0% +about we talked about how it's + + + align:start position:0% +about we talked about how it's +relatively easy to learn the fact it has + + align:start position:0% +relatively easy to learn the fact it has + + + align:start position:0% +relatively easy to learn the fact it has +been around makes it very easy to teach + + align:start position:0% +been around makes it very easy to teach + + + align:start position:0% +been around makes it very easy to teach +it's very friendly to people who are + + align:start position:0% +it's very friendly to people who are + + + align:start position:0% +it's very friendly to people who are +playing on some sort of interactive + + align:start position:0% +playing on some sort of interactive + + + align:start position:0% +playing on some sort of interactive +schedule but that's not the reason that + + align:start position:0% +schedule but that's not the reason that + + + align:start position:0% +schedule but that's not the reason that +this requires a sophisticate + + align:start position:0% + + + + align:start position:0% + +from like the the snow but I feel like + + align:start position:0% +from like the the snow but I feel like + + + align:start position:0% +from like the the snow but I feel like +everyone knows but now if we assume + + align:start position:0% +everyone knows but now if we assume + + + align:start position:0% +everyone knows but now if we assume +that's true like how do you then make + + align:start position:0% +that's true like how do you then make + + + align:start position:0% +that's true like how do you then make +like a commercially successful work how + + align:start position:0% +like a commercially successful work how + + + align:start position:0% +like a commercially successful work how +much marketing money do you have + + align:start position:0% +much marketing money do you have + + + align:start position:0% +much marketing money do you have +you know I mean we've got lockers here + + align:start position:0% +you know I mean we've got lockers here + + + align:start position:0% +you know I mean we've got lockers here +that's probably one of the more + + align:start position:0% +that's probably one of the more + + + align:start position:0% +that's probably one of the more +successful recent entries and there's a + + align:start position:0% +successful recent entries and there's a + + + align:start position:0% +successful recent entries and there's a +couple of ways to be able to get family + + align:start position:0% +couple of ways to be able to get family + + + align:start position:0% +couple of ways to be able to get family +a large number of families to buy a + + align:start position:0% +a large number of families to buy a + + + align:start position:0% +a large number of families to buy a +parking if you're living in Germany + + align:start position:0% +parking if you're living in Germany + + + align:start position:0% +parking if you're living in Germany +there there is a big conference called + + align:start position:0% +there there is a big conference called + + + align:start position:0% +there there is a big conference called +the Essen spiel I believe I'm a new + + align:start position:0% +the Essen spiel I believe I'm a new + + + align:start position:0% +the Essen spiel I believe I'm a new +Magelang a language here in the town of + + align:start position:0% +Magelang a language here in the town of + + + align:start position:0% +Magelang a language here in the town of +Essen there are smaller conferences in + + align:start position:0% +Essen there are smaller conferences in + + + align:start position:0% +Essen there are smaller conferences in +places like Leipzig but what they are in + + align:start position:0% +places like Leipzig but what they are in + + + align:start position:0% +places like Leipzig but what they are in +addition to you know the vendors + + align:start position:0% +addition to you know the vendors + + + align:start position:0% +addition to you know the vendors +bringing all of your old and the new + + align:start position:0% +bringing all of your old and the new + + + align:start position:0% +bringing all of your old and the new +board game saying like this is what we + + align:start position:0% +board game saying like this is what we + + + align:start position:0% +board game saying like this is what we +have on sale we have tons and tons and + + align:start position:0% +have on sale we have tons and tons and + + + align:start position:0% +have on sale we have tons and tons and +tons of families going there trying to + + align:start position:0% +tons of families going there trying to + + + align:start position:0% +tons of families going there trying to +decide what am I in for Christmas and in + + align:start position:0% +decide what am I in for Christmas and in + + + align:start position:0% +decide what am I in for Christmas and in +Germany that it's kind of like a animal + + align:start position:0% +Germany that it's kind of like a animal + + + align:start position:0% +Germany that it's kind of like a animal +tradition for families to buy a + + align:start position:0% +tradition for families to buy a + + + align:start position:0% +tradition for families to buy a +Christmas game built on top of that + + align:start position:0% +Christmas game built on top of that + + + align:start position:0% +Christmas game built on top of that +there is this thing the shhh I I'm gonna + + align:start position:0% +there is this thing the shhh I I'm gonna + + + align:start position:0% +there is this thing the shhh I I'm gonna +mangle all the German in here the spell + + align:start position:0% +mangle all the German in here the spell + + + align:start position:0% +mangle all the German in here the spell +the spiel des jahres that's Jared oh + + align:start position:0% +the spiel des jahres that's Jared oh + + + align:start position:0% +the spiel des jahres that's Jared oh +yeah okay basically Game of the Year + + align:start position:0% +yeah okay basically Game of the Year + + + align:start position:0% +yeah okay basically Game of the Year +award that is awarded I believe at Essen + + align:start position:0% +award that is awarded I believe at Essen + + + align:start position:0% +award that is awarded I believe at Essen +they definitely do a big thing I'm not + + align:start position:0% +they definitely do a big thing I'm not + + + align:start position:0% +they definitely do a big thing I'm not +exactly sure how the timing lines up but + + align:start position:0% +exactly sure how the timing lines up but + + + align:start position:0% +exactly sure how the timing lines up but +definitely the game that happens to be + + align:start position:0% +definitely the game that happens to be + + + align:start position:0% +definitely the game that happens to be +awarded game of the year is going to be + + align:start position:0% +awarded game of the year is going to be + + + align:start position:0% +awarded game of the year is going to be +the biggest mover at the convention like + + align:start position:0% +the biggest mover at the convention like + + + align:start position:0% +the biggest mover at the convention like +as a convention is not the right word + + align:start position:0% +as a convention is not the right word + + + align:start position:0% +as a convention is not the right word +and I'm that I'm looking for + + align:start position:0% +and I'm that I'm looking for + + + align:start position:0% +and I'm that I'm looking for +it's more like a trade fair that's + + align:start position:0% +it's more like a trade fair that's + + + align:start position:0% +it's more like a trade fair that's +probably + + align:start position:0% +probably + + + align:start position:0% +probably +example I'm just lots and lots of + + align:start position:0% +example I'm just lots and lots of + + + align:start position:0% +example I'm just lots and lots of +families will go there they will buy a + + align:start position:0% +families will go there they will buy a + + + align:start position:0% +families will go there they will buy a +lot of the game of the year because a + + align:start position:0% +lot of the game of the year because a + + + align:start position:0% +lot of the game of the year because a +bunch of board game critics said this is + + align:start position:0% +bunch of board game critics said this is + + + align:start position:0% +bunch of board game critics said this is +the best new game that came out this + + align:start position:0% +the best new game that came out this + + + align:start position:0% +the best new game that came out this +past year and then once with all that + + align:start position:0% +past year and then once with all that + + + align:start position:0% +past year and then once with all that +money gets circulated back into + + align:start position:0% +money gets circulated back into + + + align:start position:0% +money gets circulated back into +marketing you see more ads you see that + + align:start position:0% +marketing you see more ads you see that + + + align:start position:0% +marketing you see more ads you see that +warrants the sticker on the side of the + + align:start position:0% +warrants the sticker on the side of the + + + align:start position:0% +warrants the sticker on the side of the +boxes you know more families buy it and + + align:start position:0% +boxes you know more families buy it and + + + align:start position:0% +boxes you know more families buy it and +that just no balls on top of each other + + align:start position:0% +that just no balls on top of each other + + + align:start position:0% +that just no balls on top of each other +right so winning sort of there are some + + align:start position:0% +right so winning sort of there are some + + + align:start position:0% +right so winning sort of there are some +of the things in the US I believe there + + align:start position:0% +of the things in the US I believe there + + + align:start position:0% +of the things in the US I believe there +are you know working eat yeah but not + + align:start position:0% +are you know working eat yeah but not + + + align:start position:0% +are you know working eat yeah but not +that many families I mean I thinking + + align:start position:0% +that many families I mean I thinking + + + align:start position:0% +that many families I mean I thinking +more like ABC News doing a top ten hot + + align:start position:0% +more like ABC News doing a top ten hot + + + align:start position:0% +more like ABC News doing a top ten hot +hot hot toys for those Christmas kind of + + align:start position:0% +hot hot toys for those Christmas kind of + + + align:start position:0% +hot hot toys for those Christmas kind of +thing right you know that's the sort of + + align:start position:0% +thing right you know that's the sort of + + + align:start position:0% +thing right you know that's the sort of +thing that bugs you up from a game that + + align:start position:0% +thing that bugs you up from a game that + + + align:start position:0% +thing that bugs you up from a game that +you buy for herself to again start + + align:start position:0% +you buy for herself to again start + + + align:start position:0% +you buy for herself to again start +buying for other people which multiplies + + align:start position:0% +buying for other people which multiplies + + + align:start position:0% +buying for other people which multiplies +how many copies actually gets gets old + + align:start position:0% +how many copies actually gets gets old + + + align:start position:0% +how many copies actually gets gets old +so that's what that's one way that's + + align:start position:0% +so that's what that's one way that's + + + align:start position:0% +so that's what that's one way that's +usually one way that happens that's not + + align:start position:0% +usually one way that happens that's not + + + align:start position:0% +usually one way that happens that's not +to say that you know again that what's + + align:start position:0% +to say that you know again that what's + + + align:start position:0% +to say that you know again that what's +called an enthusiast part but more game + + align:start position:0% +called an enthusiast part but more game + + + align:start position:0% +called an enthusiast part but more game +a game that's basically sold to people + + align:start position:0% +a game that's basically sold to people + + + align:start position:0% +a game that's basically sold to people +who are buying it for themselves + + align:start position:0% +who are buying it for themselves + + + align:start position:0% +who are buying it for themselves +can't be commercially successful it just + + align:start position:0% +can't be commercially successful it just + + + align:start position:0% +can't be commercially successful it just +means that you are you know you need to + + align:start position:0% +means that you are you know you need to + + + align:start position:0% +means that you are you know you need to +make enough money that you know you made + + align:start position:0% +make enough money that you know you made + + + align:start position:0% +make enough money that you know you made +a profit on it and a lot of these games + + align:start position:0% +a profit on it and a lot of these games + + + align:start position:0% +a profit on it and a lot of these games +all right like I think of all the games + + align:start position:0% +all right like I think of all the games + + + align:start position:0% +all right like I think of all the games +that are in part today + + align:start position:0% + + + + align:start position:0% + +let's see this is probably see if this + + align:start position:0% +let's see this is probably see if this + + + align:start position:0% +let's see this is probably see if this +one in your world this this is probably + + align:start position:0% +one in your world this this is probably + + + align:start position:0% +one in your world this this is probably +the sort of game that you will buy for + + align:start position:0% +the sort of game that you will buy for + + + align:start position:0% +the sort of game that you will buy for +families this is set and who is missing + + align:start position:0% +families this is set and who is missing + + + align:start position:0% +families this is set and who is missing +the original box but you know people + + align:start position:0% +the original box but you know people + + + align:start position:0% +the original box but you know people +kick things right okay so this is + + align:start position:0% +kick things right okay so this is + + + align:start position:0% +kick things right okay so this is +probably fits into the category of like + + align:start position:0% +probably fits into the category of like + + + align:start position:0% +probably fits into the category of like +a game that somebody in the rooms + + align:start position:0% +a game that somebody in the rooms + + + align:start position:0% +a game that somebody in the rooms +probably play it once and does kind of + + align:start position:0% +probably play it once and does kind of + + + align:start position:0% +probably play it once and does kind of +teach everybody else other play yeah + + align:start position:0% +teach everybody else other play yeah + + + align:start position:0% +teach everybody else other play yeah +okay I'm gonna keep playing with your + + align:start position:0% +okay I'm gonna keep playing with your + + + align:start position:0% +okay I'm gonna keep playing with your +family or before you came to how many of + + align:start position:0% +family or before you came to how many of + + + align:start position:0% +family or before you came to how many of +you played before you came to MIT okay + + align:start position:0% +you played before you came to MIT okay + + + align:start position:0% +you played before you came to MIT okay +high school yeah so so I think the + + align:start position:0% +high school yeah so so I think the + + + align:start position:0% +high school yeah so so I think the +reason why this is Mattel so they + + align:start position:0% +reason why this is Mattel so they + + + align:start position:0% +reason why this is Mattel so they +certainly know their marketing but I + + align:start position:0% +certainly know their marketing but I + + + align:start position:0% +certainly know their marketing but I +think the reason why discs are popular + + align:start position:0% +think the reason why discs are popular + + + align:start position:0% +think the reason why discs are popular +was again one of those top ten toys of + + align:start position:0% +was again one of those top ten toys of + + + align:start position:0% +was again one of those top ten toys of +the to buy just that Christmas when it + + align:start position:0% +the to buy just that Christmas when it + + + align:start position:0% +the to buy just that Christmas when it +was released and that's my bond markets + + align:start position:0% +was released and that's my bond markets + + + align:start position:0% +was released and that's my bond markets +really took off it's a well-designed + + align:start position:0% +really took off it's a well-designed + + + align:start position:0% +really took off it's a well-designed +game you don't get on those lists + + align:start position:0% +game you don't get on those lists + + + align:start position:0% +game you don't get on those lists +without being a long time doing but + + align:start position:0% +without being a long time doing but + + + align:start position:0% +without being a long time doing but +that's kind of that's not the reason why + + align:start position:0% +that's kind of that's not the reason why + + + align:start position:0% +that's kind of that's not the reason why +these things are successful that's kind + + align:start position:0% +these things are successful that's kind + + + align:start position:0% +these things are successful that's kind +of like the bear the bear admitted to + + align:start position:0% +of like the bear the bear admitted to + + + align:start position:0% +of like the bear the bear admitted to +even be considered so if you're in this + + align:start position:0% +even be considered so if you're in this + + + align:start position:0% +even be considered so if you're in this +class thinking that you're going to make + + align:start position:0% +class thinking that you're going to make + + + align:start position:0% +class thinking that you're going to make +a lot of money as a designer I know + + align:start position:0% +a lot of money as a designer I know + + + align:start position:0% +a lot of money as a designer I know +people in hospital I can get you in + + align:start position:0% +people in hospital I can get you in + + + align:start position:0% +people in hospital I can get you in +touch with and I think they're probably + + align:start position:0% +touch with and I think they're probably + + + align:start position:0% +touch with and I think they're probably +going to say don't expect that you you + + align:start position:0% +going to say don't expect that you you + + + align:start position:0% +going to say don't expect that you you +you you might be able to have a decent + + align:start position:0% +you you might be able to have a decent + + + align:start position:0% +you you might be able to have a decent +living working in a large company like + + align:start position:0% +living working in a large company like + + + align:start position:0% +living working in a large company like +hospira on the child which I think this + + align:start position:0% +hospira on the child which I think this + + + align:start position:0% +hospira on the child which I think this +a company yeah and but it's probably not + + align:start position:0% +a company yeah and but it's probably not + + + align:start position:0% +a company yeah and but it's probably not +because of the quality of the games that + + align:start position:0% +because of the quality of the games that + + + align:start position:0% +because of the quality of the games that +you're designing but more about your + + align:start position:0% +you're designing but more about your + + + align:start position:0% +you're designing but more about your +ability to design a game based on aspect + + align:start position:0% +ability to design a game based on aspect + + + align:start position:0% +ability to design a game based on aspect +that was handed to you based on a + + align:start position:0% +that was handed to you based on a + + + align:start position:0% +that was handed to you based on a +requirements like + + align:start position:0% +requirements like + + + align:start position:0% +requirements like +need a spa Wallis risking by Christmas + + align:start position:0% +need a spa Wallis risking by Christmas + + + align:start position:0% +need a spa Wallis risking by Christmas +design it in something like that and you + + align:start position:0% +design it in something like that and you + + + align:start position:0% +design it in something like that and you +execute that well and you know you what + + align:start position:0% +execute that well and you know you what + + + align:start position:0% +execute that well and you know you what +we get a good career in a place like + + align:start position:0% +we get a good career in a place like + + + align:start position:0% +we get a good career in a place like +Hasbro if you're designing for yourself + + align:start position:0% +Hasbro if you're designing for yourself + + + align:start position:0% +Hasbro if you're designing for yourself +you should feel very happy if you manage + + align:start position:0% +you should feel very happy if you manage + + + align:start position:0% +you should feel very happy if you manage +to make your initial investment back a + + align:start position:0% +to make your initial investment back a + + + align:start position:0% +to make your initial investment back a +lot of these a lot of people who make + + align:start position:0% +lot of these a lot of people who make + + + align:start position:0% +lot of these a lot of people who make +who sort of helped you escape designers + + align:start position:0% +who sort of helped you escape designers + + + align:start position:0% +who sort of helped you escape designers +who make incredibly good games don't + + align:start position:0% +who make incredibly good games don't + + + align:start position:0% +who make incredibly good games don't +make back the money that they initially + + align:start position:0% +make back the money that they initially + + + align:start position:0% +make back the money that they initially +invested into it and that's fine if you + + align:start position:0% +invested into it and that's fine if you + + + align:start position:0% +invested into it and that's fine if you +know if that's why that's if you went + + align:start position:0% +know if that's why that's if you went + + + align:start position:0% +know if that's why that's if you went +into that business knowing that because + + align:start position:0% +into that business knowing that because + + + align:start position:0% +into that business knowing that because +sometimes for some people it's just good + + align:start position:0% +sometimes for some people it's just good + + + align:start position:0% +sometimes for some people it's just good +enough to be able to have a game with + + align:start position:0% +enough to be able to have a game with + + + align:start position:0% +enough to be able to have a game with +your name on it you know being played by + + align:start position:0% +your name on it you know being played by + + + align:start position:0% +your name on it you know being played by +a whole bunch of people who appreciate + + align:start position:0% +a whole bunch of people who appreciate + + + align:start position:0% +a whole bunch of people who appreciate +it + + align:start position:0% +it + + + align:start position:0% +it +that's fine more likely yeah go a lot of + + align:start position:0% +that's fine more likely yeah go a lot of + + + align:start position:0% +that's fine more likely yeah go a lot of +you are going into careers I'm assuming + + align:start position:0% +you are going into careers I'm assuming + + + align:start position:0% +you are going into careers I'm assuming +there are not game design some of you + + align:start position:0% +there are not game design some of you + + + align:start position:0% +there are not game design some of you +are but but but some of you will go into + + align:start position:0% +are but but but some of you will go into + + + align:start position:0% +are but but but some of you will go into +a career that's that might benefit from + + align:start position:0% +a career that's that might benefit from + + + align:start position:0% +a career that's that might benefit from +some of the design practices that you're + + align:start position:0% +some of the design practices that you're + + + align:start position:0% +some of the design practices that you're +going to learn in this class about just + + align:start position:0% +going to learn in this class about just + + + align:start position:0% +going to learn in this class about just +iterative design although you know you + + align:start position:0% +iterative design although you know you + + + align:start position:0% +iterative design although you know you +can we talked about how that's relevant + + align:start position:0% +can we talked about how that's relevant + + + align:start position:0% +can we talked about how that's relevant +to a number of engineering disciplines + + align:start position:0% +to a number of engineering disciplines + + + align:start position:0% +to a number of engineering disciplines +but also things like you want to teach + + align:start position:0% +but also things like you want to teach + + + align:start position:0% +but also things like you want to teach +people a new system that you've designed + + align:start position:0% +people a new system that you've designed + + + align:start position:0% +people a new system that you've designed +a new system that that that's been put + + align:start position:0% +a new system that that that's been put + + + align:start position:0% +a new system that that that's been put +into practice you want to create some + + align:start position:0% +into practice you want to create some + + + align:start position:0% +into practice you want to create some +sort of team building exercise you want + + align:start position:0% +sort of team building exercise you want + + + align:start position:0% +sort of team building exercise you want +to communicate to someone how complex a + + align:start position:0% +to communicate to someone how complex a + + + align:start position:0% +to communicate to someone how complex a +certain system is that's relevant to you + + align:start position:0% +certain system is that's relevant to you + + + align:start position:0% +certain system is that's relevant to you +to to your work and your discipline + + align:start position:0% +to to your work and your discipline + + + align:start position:0% +to to your work and your discipline +there's a bunch of things that games can + + align:start position:0% +there's a bunch of things that games can + + + align:start position:0% +there's a bunch of things that games can +do to communicate ideas that might be + + align:start position:0% +do to communicate ideas that might be + + + align:start position:0% +do to communicate ideas that might be +relevant to in whatever in whatever + + align:start position:0% +relevant to in whatever in whatever + + + align:start position:0% +relevant to in whatever in whatever +career you ain't nothing so so even here + + align:start position:0% +career you ain't nothing so so even here + + + align:start position:0% +career you ain't nothing so so even here +in MIT I'm the creative director of the + + align:start position:0% +in MIT I'm the creative director of the + + + align:start position:0% +in MIT I'm the creative director of the +MIT game lab there's a bunch of + + align:start position:0% +MIT game lab there's a bunch of + + + align:start position:0% +MIT game lab there's a bunch of +different labs here in MIT who are using + + align:start position:0% +different labs here in MIT who are using + + + align:start position:0% +different labs here in MIT who are using +games for for a variety of different + + align:start position:0% +games for for a variety of different + + + align:start position:0% +games for for a variety of different +purposes I wire anyone heard of that one + + align:start position:0% +purposes I wire anyone heard of that one + + + align:start position:0% +purposes I wire anyone heard of that one +yep it's yeah over the picure Institute + + align:start position:0% +yep it's yeah over the picure Institute + + + align:start position:0% +yep it's yeah over the picure Institute +right across the street but where the + + align:start position:0% +right across the street but where the + + + align:start position:0% +right across the street but where the +train tracks run under the building + + align:start position:0% +train tracks run under the building + + + align:start position:0% +train tracks run under the building +they've got a game that's basically + + align:start position:0% +they've got a game that's basically + + + align:start position:0% +they've got a game that's basically +massively multiplayer massively single + + align:start position:0% +massively multiplayer massively single + + + align:start position:0% +massively multiplayer massively single +player really and you you solve the + + align:start position:0% +player really and you you solve the + + + align:start position:0% +player really and you you solve the +puzzle that it is like it is kind of + + align:start position:0% +puzzle that it is like it is kind of + + + align:start position:0% +puzzle that it is like it is kind of +like like people I know it's kind of + + align:start position:0% +like like people I know it's kind of + + + align:start position:0% +like like people I know it's kind of +like paint by numbers they're clicking + + align:start position:0% +like paint by numbers they're clicking + + + align:start position:0% +like paint by numbers they're clicking +and coloring a few what you're really + + align:start position:0% +and coloring a few what you're really + + + align:start position:0% +and coloring a few what you're really +doing is you're identifying neurons from + + align:start position:0% +doing is you're identifying neurons from + + + align:start position:0% +doing is you're identifying neurons from +scanning tunneling microscopes these are + + align:start position:0% +scanning tunneling microscopes these are + + + align:start position:0% +scanning tunneling microscopes these are +neurons in a mouth spread from a mouse + + align:start position:0% +neurons in a mouth spread from a mouse + + + align:start position:0% +neurons in a mouth spread from a mouse +retina and you're basically doing all + + align:start position:0% +retina and you're basically doing all + + + align:start position:0% +retina and you're basically doing all +the pattern recognition the computers + + align:start position:0% +the pattern recognition the computers + + + align:start position:0% +the pattern recognition the computers +have a tremendously difficult time to do + + align:start position:0% +have a tremendously difficult time to do + + + align:start position:0% +have a tremendously difficult time to do +what humans actually a pretty good at + + align:start position:0% +what humans actually a pretty good at + + + align:start position:0% +what humans actually a pretty good at +and that goes cumulating all of that + + align:start position:0% +and that goes cumulating all of that + + + align:start position:0% +and that goes cumulating all of that +data it's a fairly nice you know very + + align:start position:0% +data it's a fairly nice you know very + + + align:start position:0% +data it's a fairly nice you know very +cliquey minesweeper ish kind of feel to + + align:start position:0% +cliquey minesweeper ish kind of feel to + + + align:start position:0% +cliquey minesweeper ish kind of feel to +this game it's like you're just flicking + + align:start position:0% +this game it's like you're just flicking + + + align:start position:0% +this game it's like you're just flicking +things so that you find my they meet a + + align:start position:0% +things so that you find my they meet a + + + align:start position:0% +things so that you find my they meet a +nice contiguous space it's a 3d game so + + align:start position:0% +nice contiguous space it's a 3d game so + + + align:start position:0% +nice contiguous space it's a 3d game so +there's some sort of like mental hoops + + align:start position:0% +there's some sort of like mental hoops + + + align:start position:0% +there's some sort of like mental hoops +that your brain gets through and there's + + align:start position:0% +that your brain gets through and there's + + + align:start position:0% +that your brain gets through and there's +kind of a nice build Fazal feeling but + + align:start position:0% +kind of a nice build Fazal feeling but + + + align:start position:0% +kind of a nice build Fazal feeling but +what you're really doing is you're + + align:start position:0% +what you're really doing is you're + + + align:start position:0% +what you're really doing is you're +providing sebastian stone slab with a + + align:start position:0% +providing sebastian stone slab with a + + + align:start position:0% +providing sebastian stone slab with a +ton of data about how how how you're how + + align:start position:0% +ton of data about how how how you're how + + + align:start position:0% +ton of data about how how how you're how +about us i is wired which is amazing and + + align:start position:0% +about us i is wired which is amazing and + + + align:start position:0% +about us i is wired which is amazing and +i think i've got a couple of papers or + + align:start position:0% +i think i've got a couple of papers or + + + align:start position:0% +i think i've got a couple of papers or +fights it's real science anyone here + + align:start position:0% +fights it's real science anyone here + + + align:start position:0% +fights it's real science anyone here +from system to system dynamics + + align:start position:0% + + + + align:start position:0% + +engineering i think i think that i think + + align:start position:0% +engineering i think i think that i think + + + align:start position:0% +engineering i think i think that i think +there are the parent group is the + + align:start position:0% +there are the parent group is the + + + align:start position:0% +there are the parent group is the +aero-astro department but + + align:start position:0% + + + + align:start position:0% + +okay I mean it was just like a + + align:start position:0% +okay I mean it was just like a + + + align:start position:0% +okay I mean it was just like a +three-year-old or something that's that + + align:start position:0% +three-year-old or something that's that + + + align:start position:0% +three-year-old or something that's that +that's fine but I but uh systems a lot + + align:start position:0% +that's fine but I but uh systems a lot + + + align:start position:0% +that's fine but I but uh systems a lot +of system dynamics folks on campus + + align:start position:0% +of system dynamics folks on campus + + + align:start position:0% +of system dynamics folks on campus +engineering systems designed for + + align:start position:0% +engineering systems designed for + + + align:start position:0% +engineering systems designed for +instance will use games to try to teach + + align:start position:0% +instance will use games to try to teach + + + align:start position:0% +instance will use games to try to teach +clients about certain engineering + + align:start position:0% +clients about certain engineering + + + align:start position:0% +clients about certain engineering +practices so there's a group here that + + align:start position:0% +practices so there's a group here that + + + align:start position:0% +practices so there's a group here that +has a game called + + align:start position:0% +has a game called + + + align:start position:0% +has a game called +space + + align:start position:0% + + + + align:start position:0% + +yeah skirmish well yeah yeah as you + + align:start position:0% +yeah skirmish well yeah yeah as you + + + align:start position:0% +yeah skirmish well yeah yeah as you +wrong yeah yeah and I think that's + + align:start position:0% +wrong yeah yeah and I think that's + + + align:start position:0% +wrong yeah yeah and I think that's +looking for more Europe's because that + + align:start position:0% +looking for more Europe's because that + + + align:start position:0% +looking for more Europe's because that +they've turned their board game into a + + align:start position:0% +they've turned their board game into a + + + align:start position:0% +they've turned their board game into a +digital game and it keeping to keep + + align:start position:0% +digital game and it keeping to keep + + + align:start position:0% +digital game and it keeping to keep +working yeah it's kind of I was going to + + align:start position:0% +working yeah it's kind of I was going to + + + align:start position:0% +working yeah it's kind of I was going to +say a magic gathering hill but that's + + align:start position:0% +say a magic gathering hill but that's + + + align:start position:0% +say a magic gathering hill but that's +not really true and you know the way how + + align:start position:0% +not really true and you know the way how + + + align:start position:0% +not really true and you know the way how +the game has evolved but uh it's it's + + align:start position:0% +the game has evolved but uh it's it's + + + align:start position:0% +the game has evolved but uh it's it's +primarily a card game about building + + align:start position:0% +primarily a card game about building + + + align:start position:0% +primarily a card game about building +satellites marching them into space and + + align:start position:0% +satellites marching them into space and + + + align:start position:0% +satellites marching them into space and +realizing that by the time you launch + + align:start position:0% +realizing that by the time you launch + + + align:start position:0% +realizing that by the time you launch +something into space is kind of obsolete + + align:start position:0% +something into space is kind of obsolete + + + align:start position:0% +something into space is kind of obsolete +and the question is how do you design as + + align:start position:0% +and the question is how do you design as + + + align:start position:0% +and the question is how do you design as +a satellite so that they can adapt to + + align:start position:0% +a satellite so that they can adapt to + + + align:start position:0% +a satellite so that they can adapt to +changing circumstances that's you know + + align:start position:0% +changing circumstances that's you know + + + align:start position:0% +changing circumstances that's you know +that's what they will that's what + + align:start position:0% +that's what they will that's what + + + align:start position:0% +that's what they will that's what +they're teaching people from NASA from + + align:start position:0% +they're teaching people from NASA from + + + align:start position:0% +they're teaching people from NASA from +from the military about nd decided that + + align:start position:0% +from the military about nd decided that + + + align:start position:0% +from the military about nd decided that +games are the way to do it started with + + align:start position:0% +games are the way to do it started with + + + align:start position:0% +games are the way to do it started with +the parking in the digital game there's + + align:start position:0% +the parking in the digital game there's + + + align:start position:0% +the parking in the digital game there's +a very large group here in campus called + + align:start position:0% +a very large group here in campus called + + + align:start position:0% +a very large group here in campus called +the the sheller teacher education + + align:start position:0% +the the sheller teacher education + + + align:start position:0% +the the sheller teacher education +program and they design games for k-12 + + align:start position:0% +program and they design games for k-12 + + + align:start position:0% +program and they design games for k-12 +too low to freshman undergraduate level + + align:start position:0% +too low to freshman undergraduate level + + + align:start position:0% +too low to freshman undergraduate level +science math language you know how to + + align:start position:0% +science math language you know how to + + + align:start position:0% +science math language you know how to +how to better address some problems in + + align:start position:0% +how to better address some problems in + + + align:start position:0% +how to better address some problems in +curriculum in substandard class with + + align:start position:0% +curriculum in substandard class with + + + align:start position:0% +curriculum in substandard class with +curriculum so they if they start mmo's + + align:start position:0% +curriculum so they if they start mmo's + + + align:start position:0% +curriculum so they if they start mmo's +they've done puzzle games they've done a + + align:start position:0% +they've done puzzle games they've done a + + + align:start position:0% +they've done puzzle games they've done a +lot of stuff on on flash because it's + + align:start position:0% +lot of stuff on on flash because it's + + + align:start position:0% +lot of stuff on on flash because it's +very easy to get + + align:start position:0% +very easy to get + + + align:start position:0% +very easy to get +running in the school is very much + + align:start position:0% +running in the school is very much + + + align:start position:0% +running in the school is very much +harder to get a whole school allowed to + + align:start position:0% +harder to get a whole school allowed to + + + align:start position:0% +harder to get a whole school allowed to +download the piece of software and + + align:start position:0% +download the piece of software and + + + align:start position:0% +download the piece of software and +install it across 20 countries for + + align:start position:0% +install it across 20 countries for + + + align:start position:0% +install it across 20 countries for +instance all these places have Europe's + + align:start position:0% +instance all these places have Europe's + + + align:start position:0% +instance all these places have Europe's +my life has erupted so you're interested + + align:start position:0% +my life has erupted so you're interested + + + align:start position:0% +my life has erupted so you're interested +in any of these things you should + + align:start position:0% +in any of these things you should + + + align:start position:0% +in any of these things you should +definitely check them out you can ask me + + align:start position:0% +definitely check them out you can ask me + + + align:start position:0% +definitely check them out you can ask me +for four for more leads a lot of + + align:start position:0% +for four for more leads a lot of + + + align:start position:0% +for four for more leads a lot of +different and finally back to aero-astro + + align:start position:0% +different and finally back to aero-astro + + + align:start position:0% +different and finally back to aero-astro +there is a group that works with zero + + align:start position:0% +there is a group that works with zero + + + align:start position:0% +there is a group that works with zero +gravity satellites satellites they were + + align:start position:0% +gravity satellites satellites they were + + + align:start position:0% +gravity satellites satellites they were +consumer-friendly spheres yeah these + + align:start position:0% +consumer-friendly spheres yeah these + + + align:start position:0% +consumer-friendly spheres yeah these +these the little compressed air I think + + align:start position:0% +these the little compressed air I think + + + align:start position:0% +these the little compressed air I think +carbon dioxide propel spheres they look + + align:start position:0% +carbon dioxide propel spheres they look + + + align:start position:0% +carbon dioxide propel spheres they look +like gigantic dissection and it's been + + align:start position:0% +like gigantic dissection and it's been + + + align:start position:0% +like gigantic dissection and it's been +around in space and and they and they'll + + align:start position:0% +around in space and and they and they'll + + + align:start position:0% +around in space and and they and they'll +run C code and they have a high school + + align:start position:0% +run C code and they have a high school + + + align:start position:0% +run C code and they have a high school +programming competition kind of like and + + align:start position:0% +programming competition kind of like and + + + align:start position:0% +programming competition kind of like and +kind of like the FIRST Robotics + + align:start position:0% +kind of like the FIRST Robotics + + + align:start position:0% +kind of like the FIRST Robotics +tournaments think of that in zero + + align:start position:0% +tournaments think of that in zero + + + align:start position:0% +tournaments think of that in zero +gravity so it's like how do you + + align:start position:0% +gravity so it's like how do you + + + align:start position:0% +gravity so it's like how do you +accomplish this and it's a you know it's + + align:start position:0% +accomplish this and it's a you know it's + + + align:start position:0% +accomplish this and it's a you know it's +a pretty cool high school education + + align:start position:0% +a pretty cool high school education + + + align:start position:0% +a pretty cool high school education +thing to connect high school kids to + + align:start position:0% +thing to connect high school kids to + + + align:start position:0% +thing to connect high school kids to +space basically I know they are looking + + align:start position:0% +space basically I know they are looking + + + align:start position:0% +space basically I know they are looking +for your apps so you're interested in + + align:start position:0% +for your apps so you're interested in + + + align:start position:0% +for your apps so you're interested in +that you should have known you talked to + + align:start position:0% +that you should have known you talked to + + + align:start position:0% +that you should have known you talked to +me about that I'll give you the contact + + align:start position:0% +me about that I'll give you the contact + + + align:start position:0% +me about that I'll give you the contact +information so I've been yammering for + + align:start position:0% +information so I've been yammering for + + + align:start position:0% +information so I've been yammering for +about about an hour let's take a break + + align:start position:0% +about about an hour let's take a break + + + align:start position:0% +about about an hour let's take a break +stretch + + align:start position:0% +stretch + + + align:start position:0% +stretch +I'll start distributing some of these + + align:start position:0% +I'll start distributing some of these + + + align:start position:0% +I'll start distributing some of these +games but we have one more discussion + + align:start position:0% +games but we have one more discussion + + + align:start position:0% +games but we have one more discussion +topic before we go into gaming okay some + + align:start position:0% +topic before we go into gaming okay some + + + align:start position:0% +topic before we go into gaming okay some +people should probably distributor self + + align:start position:0% +people should probably distributor self + + + align:start position:0% +people should probably distributor self +up here as well bathrooms are out to the + + align:start position:0% +up here as well bathrooms are out to the + + + align:start position:0% +up here as well bathrooms are out to the +right \ No newline at end of file diff --git a/xaSL8yFgqig.txt b/xaSL8yFgqig.txt new file mode 100644 index 0000000000000000000000000000000000000000..98b9da4082d69bf4b6b863e9e7304ef199d53d8d --- /dev/null +++ b/xaSL8yFgqig.txt @@ -0,0 +1,6243 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +ok so I thought I'd begin today with as + + align:start position:0% +ok so I thought I'd begin today with as + + + align:start position:0% +ok so I thought I'd begin today with as +we're coming to the end of the sort of + + align:start position:0% +we're coming to the end of the sort of + + + align:start position:0% +we're coming to the end of the sort of +focus on linear algebra and moving on to + + align:start position:0% +focus on linear algebra and moving on to + + + align:start position:0% +focus on linear algebra and moving on to +a little probability a a little more + + align:start position:0% +a little probability a a little more + + + align:start position:0% +a little probability a a little more +optimization and a a lot of deep + + align:start position:0% +optimization and a a lot of deep + + + align:start position:0% +optimization and a a lot of deep +learning so this was like my way of + + align:start position:0% +learning so this was like my way of + + + align:start position:0% +learning so this was like my way of +review to write down the big + + align:start position:0% +review to write down the big + + + align:start position:0% +review to write down the big +factorizations of a matrix and so my + + align:start position:0% +factorizations of a matrix and so my + + + align:start position:0% +factorizations of a matrix and so my +idea and it's kind of enjoyed it as + + align:start position:0% +idea and it's kind of enjoyed it as + + + align:start position:0% +idea and it's kind of enjoyed it as +checking that a number of free + + align:start position:0% +checking that a number of free + + + align:start position:0% +checking that a number of free +parameters say in L&U or in q and r or + + align:start position:0% +parameters say in L&U or in q and r or + + + align:start position:0% +parameters say in L&U or in q and r or +every each of those that the number of + + align:start position:0% +every each of those that the number of + + + align:start position:0% +every each of those that the number of +free parameters agrees with the number + + align:start position:0% +free parameters agrees with the number + + + align:start position:0% +free parameters agrees with the number +of parameters in a itself like N squared + + align:start position:0% +of parameters in a itself like N squared + + + align:start position:0% +of parameters in a itself like N squared +usually so a usually has N squared and + + align:start position:0% +usually so a usually has N squared and + + + align:start position:0% +usually so a usually has N squared and +then can we replace a if after we've + + align:start position:0% +then can we replace a if after we've + + + align:start position:0% +then can we replace a if after we've +computed Ln you can we throw away a yes + + align:start position:0% +computed Ln you can we throw away a yes + + + align:start position:0% +computed Ln you can we throw away a yes +because all the information is in L and + + align:start position:0% +because all the information is in L and + + + align:start position:0% +because all the information is in L and +U and it fills that same n by n matrix + + align:start position:0% +U and it fills that same n by n matrix + + + align:start position:0% +U and it fills that same n by n matrix +well that's kind of obvious because L is + + align:start position:0% +well that's kind of obvious because L is + + + align:start position:0% +well that's kind of obvious because L is +a lower triangular and the diagonal all + + align:start position:0% +a lower triangular and the diagonal all + + + align:start position:0% +a lower triangular and the diagonal all +ones is not are not free parameters and + + align:start position:0% +ones is not are not free parameters and + + + align:start position:0% +ones is not are not free parameters and +U is triangular upper triangular and + + align:start position:0% +U is triangular upper triangular and + + + align:start position:0% +U is triangular upper triangular and +it's diagonal the pivots those are free + + align:start position:0% +it's diagonal the pivots those are free + + + align:start position:0% +it's diagonal the pivots those are free +parameters so that but can I just write + + align:start position:0% +parameters so that but can I just write + + + align:start position:0% +parameters so that but can I just write +down the count so so I'll go through + + align:start position:0% +down the count so so I'll go through + + + align:start position:0% +down the count so so I'll go through +each of these just quickly after I've + + align:start position:0% +each of these just quickly after I've + + + align:start position:0% +each of these just quickly after I've +figured out how these are the sort of + + align:start position:0% +figured out how these are the sort of + + + align:start position:0% +figured out how these are the sort of +the building blocks so how many free + + align:start position:0% +the building blocks so how many free + + + align:start position:0% +the building blocks so how many free +parameters are there in these two + + align:start position:0% +parameters are there in these two + + + align:start position:0% +parameters are there in these two +triangular matrices well I think the + + align:start position:0% +triangular matrices well I think the + + + align:start position:0% +triangular matrices well I think the +answer + + align:start position:0% +answer + + + align:start position:0% +answer +1/2 and n minus 1 and 1/2 and n plus 1 + + align:start position:0% +1/2 and n minus 1 and 1/2 and n plus 1 + + + align:start position:0% +1/2 and n minus 1 and 1/2 and n plus 1 +that's a familiar number that's the some + + align:start position:0% +that's a familiar number that's the some + + + align:start position:0% +that's a familiar number that's the some +of you recognize that as the sum of 1 + + align:start position:0% +of you recognize that as the sum of 1 + + + align:start position:0% +of you recognize that as the sum of 1 +plus 2 up to n and you have one free / + + align:start position:0% +plus 2 up to n and you have one free / + + + align:start position:0% +plus 2 up to n and you have one free / +in the in the upper triangular you + + align:start position:0% +in the in the upper triangular you + + + align:start position:0% +in the in the upper triangular you +you've got one free parameter up in the + + align:start position:0% +you've got one free parameter up in the + + + align:start position:0% +you've got one free parameter up in the +corner 2 in the next one and as you're + + align:start position:0% +corner 2 in the next one and as you're + + + align:start position:0% +corner 2 in the next one and as you're +coming down you end up with n on the + + align:start position:0% +coming down you end up with n on the + + + align:start position:0% +coming down you end up with n on the +main diagonal and they add up to that + + align:start position:0% +main diagonal and they add up to that + + + align:start position:0% +main diagonal and they add up to that +and you see that those two are different + + align:start position:0% +and you see that those two are different + + + align:start position:0% +and you see that those two are different +by n which is what we want okay + + align:start position:0% +by n which is what we want okay + + + align:start position:0% +by n which is what we want okay +diagonal the answers obviously in how + + align:start position:0% +diagonal the answers obviously in how + + + align:start position:0% +diagonal the answers obviously in how +about the eigenvector matrix so this is + + align:start position:0% +about the eigenvector matrix so this is + + + align:start position:0% +about the eigenvector matrix so this is +this whole exercise is like something + + align:start position:0% +this whole exercise is like something + + + align:start position:0% +this whole exercise is like something +I've never seen in a textbook in and + + align:start position:0% +I've never seen in a textbook in and + + + align:start position:0% +I've never seen in a textbook in and +it's just but for me it brings back all + + align:start position:0% +it's just but for me it brings back all + + + align:start position:0% +it's just but for me it brings back all +these key really the condensed course in + + align:start position:0% +these key really the condensed course in + + + align:start position:0% +these key really the condensed course in +linear algebra is on that top line so + + align:start position:0% +linear algebra is on that top line so + + + align:start position:0% +linear algebra is on that top line so +how many free parameters in an + + align:start position:0% +how many free parameters in an + + + align:start position:0% +how many free parameters in an +eigenvector matrix okay and of course + + align:start position:0% +eigenvector matrix okay and of course + + + align:start position:0% +eigenvector matrix okay and of course +you're sort of thinking what's the rule + + align:start position:0% +you're sort of thinking what's the rule + + + align:start position:0% +you're sort of thinking what's the rule +for free parameters so the my answer is + + align:start position:0% +for free parameters so the my answer is + + + align:start position:0% +for free parameters so the my answer is +going to be for the number of free + + align:start position:0% +going to be for the number of free + + + align:start position:0% +going to be for the number of free +parameters so this is an N by n matrix + + align:start position:0% +parameters so this is an N by n matrix + + + align:start position:0% +parameters so this is an N by n matrix +with the n eigenvectors in it but + + align:start position:0% +with the n eigenvectors in it but + + + align:start position:0% +with the n eigenvectors in it but +there's a certain freedom there and what + + align:start position:0% +there's a certain freedom there and what + + + align:start position:0% +there's a certain freedom there and what +is that what freedom do we have in + + align:start position:0% +is that what freedom do we have in + + + align:start position:0% +is that what freedom do we have in +choosing the eigenvector matrix every + + align:start position:0% +choosing the eigenvector matrix every + + + align:start position:0% +choosing the eigenvector matrix every +eigen vector can be multiplied by a + + align:start position:0% +eigen vector can be multiplied by a + + + align:start position:0% +eigen vector can be multiplied by a +scalar if x is an eigenvector so is 2x + + align:start position:0% +scalar if x is an eigenvector so is 2x + + + align:start position:0% +scalar if x is an eigenvector so is 2x +so is 3x so we could we could make a + + align:start position:0% +so is 3x so we could we could make a + + + align:start position:0% +so is 3x so we could we could make a +convention that the first component was + + align:start position:0% +convention that the first component was + + + align:start position:0% +convention that the first component was +always 1 maybe that wouldn't be the most + + align:start position:0% +always 1 maybe that wouldn't be the most + + + align:start position:0% +always 1 maybe that wouldn't be the most +intelligent convention in the world but + + align:start position:0% +intelligent convention in the world but + + + align:start position:0% +intelligent convention in the world but +it would show that that top row of ones + + align:start position:0% +it would show that that top row of ones + + + align:start position:0% +it would show that that top row of ones +were not to be counted so I get N + + align:start position:0% +were not to be counted so I get N + + + align:start position:0% +were not to be counted so I get N +squared minus n for that oh yeah well + + align:start position:0% +squared minus n for that oh yeah well + + + align:start position:0% +squared minus n for that oh yeah well +having done those + + align:start position:0% +having done those + + + align:start position:0% +having done those +- let me let me look at this at this one + + align:start position:0% +- let me let me look at this at this one + + + align:start position:0% +- let me let me look at this at this one +does that come out a total then squared + + align:start position:0% +does that come out a total then squared + + + align:start position:0% +does that come out a total then squared +yes because the eigenvector x has N + + align:start position:0% +yes because the eigenvector x has N + + + align:start position:0% +yes because the eigenvector x has N +squared minus n by this reasoning little + + align:start position:0% +squared minus n by this reasoning little + + + align:start position:0% +squared minus n by this reasoning little +hokey reasoning that I just gave and + + align:start position:0% +hokey reasoning that I just gave and + + + align:start position:0% +hokey reasoning that I just gave and +then there n more for the eigenvalue + + align:start position:0% +then there n more for the eigenvalue + + + align:start position:0% +then there n more for the eigenvalue +matrix and there's nothing left for the + + align:start position:0% +matrix and there's nothing left for the + + + align:start position:0% +matrix and there's nothing left for the +eigen the inverse because it's + + align:start position:0% +eigen the inverse because it's + + + align:start position:0% +eigen the inverse because it's +determined by x so do you see the count + + align:start position:0% +determined by x so do you see the count + + + align:start position:0% +determined by x so do you see the count +adding up to n squared for those now I + + align:start position:0% +adding up to n squared for those now I + + + align:start position:0% +adding up to n squared for those now I +left open the orthogonal one I think we + + align:start position:0% +left open the orthogonal one I think we + + + align:start position:0% +left open the orthogonal one I think we +kind of talked about that during the + + align:start position:0% +kind of talked about that during the + + + align:start position:0% +kind of talked about that during the +when we met it and it's a little less + + align:start position:0% +when we met it and it's a little less + + + align:start position:0% +when we met it and it's a little less +obvious but do you remember so I'm + + align:start position:0% +obvious but do you remember so I'm + + + align:start position:0% +obvious but do you remember so I'm +talking about an N by n orthogonal + + align:start position:0% +talking about an N by n orthogonal + + + align:start position:0% +talking about an N by n orthogonal +matrix Q so how many free parameters in + + align:start position:0% +matrix Q so how many free parameters in + + + align:start position:0% +matrix Q so how many free parameters in +column one that that column is what we + + align:start position:0% +column one that that column is what we + + + align:start position:0% +column one that that column is what we +always call Q 1 does it have end free + + align:start position:0% +always call Q 1 does it have end free + + + align:start position:0% +always call Q 1 does it have end free +parameters or is there a condition that + + align:start position:0% +parameters or is there a condition that + + + align:start position:0% +parameters or is there a condition that +that cuts that back there is a condition + + align:start position:0% +that cuts that back there is a condition + + + align:start position:0% +that cuts that back there is a condition +right and what's the condition on the + + align:start position:0% +right and what's the condition on the + + + align:start position:0% +right and what's the condition on the +first column that that removes one + + align:start position:0% +first column that that removes one + + + align:start position:0% +first column that that removes one +parameter it's normalized it's length is + + align:start position:0% +parameter it's normalized it's length is + + + align:start position:0% +parameter it's normalized it's length is +1 so I only get n minus 1 from the first + + align:start position:0% +1 so I only get n minus 1 from the first + + + align:start position:0% +1 so I only get n minus 1 from the first +column and now if I move over to the + + align:start position:0% +column and now if I move over to the + + + align:start position:0% +column and now if I move over to the +second column how many free parameters + + align:start position:0% +second column how many free parameters + + + align:start position:0% +second column how many free parameters +there again it's a unit vector but also + + align:start position:0% +there again it's a unit vector but also + + + align:start position:0% +there again it's a unit vector but also +it is orthogonal to the first so to two + + align:start position:0% +it is orthogonal to the first so to two + + + align:start position:0% +it is orthogonal to the first so to two +parameters got you two rules got imposed + + align:start position:0% +parameters got you two rules got imposed + + + align:start position:0% +parameters got you two rules got imposed +and two parameters got removed so this + + align:start position:0% +and two parameters got removed so this + + + align:start position:0% +and two parameters got removed so this +is n minus 2 and then finally whatever + + align:start position:0% +is n minus 2 and then finally whatever + + + align:start position:0% +is n minus 2 and then finally whatever +so I think that that some of these guys + + align:start position:0% +so I think that that some of these guys + + + align:start position:0% +so I think that that some of these guys +is exactly the same that we had up here + + align:start position:0% +is exactly the same that we had up here + + + align:start position:0% +is exactly the same that we had up here +I think it's also 1/2 and n minus 1 or + + align:start position:0% +I think it's also 1/2 and n minus 1 or + + + align:start position:0% +I think it's also 1/2 and n minus 1 or +1/2 n squared - Adam yeah yeah so not as + + align:start position:0% +1/2 n squared - Adam yeah yeah so not as + + + align:start position:0% +1/2 n squared - Adam yeah yeah so not as +many as you might think as the matrix is + + align:start position:0% +many as you might think as the matrix is + + + align:start position:0% +many as you might think as the matrix is +size N squared now can I use those + + align:start position:0% +size N squared now can I use those + + + align:start position:0% +size N squared now can I use those +because these are the like the building + + align:start position:0% +because these are the like the building + + + align:start position:0% +because these are the like the building +blocks can I just check these let's see + + align:start position:0% +blocks can I just check these let's see + + + align:start position:0% +blocks can I just check these let's see +just go along the list L times u so L + + align:start position:0% +just go along the list L times u so L + + + align:start position:0% +just go along the list L times u so L +had this and you had that and when I add + + align:start position:0% +had this and you had that and when I add + + + align:start position:0% +had this and you had that and when I add +those it adds up to N squared right the + + align:start position:0% +those it adds up to N squared right the + + + align:start position:0% +those it adds up to N squared right the +minus cancels the plus and the half N + + align:start position:0% +minus cancels the plus and the half N + + + align:start position:0% +minus cancels the plus and the half N +squared twice gives me N squared so good + + align:start position:0% +squared twice gives me N squared so good + + + align:start position:0% +squared twice gives me N squared so good +for that one + + align:start position:0% +for that one + + + align:start position:0% +for that one +what about Q R well R is upper + + align:start position:0% +what about Q R well R is upper + + + align:start position:0% +what about Q R well R is upper +triangular like so and then Q oh yeah we + + align:start position:0% +triangular like so and then Q oh yeah we + + + align:start position:0% +triangular like so and then Q oh yeah we +just got it right there so for Q times R + + align:start position:0% +just got it right there so for Q times R + + + align:start position:0% +just got it right there so for Q times R +it's that Plus that again adding to N + + align:start position:0% +it's that Plus that again adding to N + + + align:start position:0% +it's that Plus that again adding to N +squared good for that one and squared + + align:start position:0% +squared good for that one and squared + + + align:start position:0% +squared good for that one and squared +for that one this one we just did N + + align:start position:0% +for that one this one we just did N + + + align:start position:0% +for that one this one we just did N +squared minus N and X and on the + + align:start position:0% +squared minus N and X and on the + + + align:start position:0% +squared minus N and X and on the +diagonal total N squared what about this + + align:start position:0% +diagonal total N squared what about this + + + align:start position:0% +diagonal total N squared what about this +guy what about the Big O really + + align:start position:0% +guy what about the Big O really + + + align:start position:0% +guy what about the Big O really +fundamental one that I would normally + + align:start position:0% +fundamental one that I would normally + + + align:start position:0% +fundamental one that I would normally +write the matrix as s instead of a to + + align:start position:0% +write the matrix as s instead of a to + + + align:start position:0% +write the matrix as s instead of a to +remind us that it that the matrix here + + align:start position:0% +remind us that it that the matrix here + + + align:start position:0% +remind us that it that the matrix here +is symmetric so I'm not expecting ensk + + align:start position:0% +is symmetric so I'm not expecting ensk + + + align:start position:0% +is symmetric so I'm not expecting ensk +where'd for a symmetric me I should have + + align:start position:0% +where'd for a symmetric me I should have + + + align:start position:0% +where'd for a symmetric me I should have +put that on my list + + align:start position:0% +put that on my list + + + align:start position:0% +put that on my list +what's the count for a symmetric matrix + + align:start position:0% + + + + align:start position:0% + +s here so I'm not expecting to get N + + align:start position:0% +s here so I'm not expecting to get N + + + align:start position:0% +s here so I'm not expecting to get N +squared I'm only expecting to get the + + align:start position:0% +squared I'm only expecting to get the + + + align:start position:0% +squared I'm only expecting to get the +number of symmetric s what's the number + + align:start position:0% +number of symmetric s what's the number + + + align:start position:0% +number of symmetric s what's the number +of free parameters that I would that I + + align:start position:0% +of free parameters that I would that I + + + align:start position:0% +of free parameters that I would that I +start with that I hope will reappear in + + align:start position:0% +start with that I hope will reappear in + + + align:start position:0% +start with that I hope will reappear in +Q and lambda so how many what's the deal + + align:start position:0% +Q and lambda so how many what's the deal + + + align:start position:0% +Q and lambda so how many what's the deal +for a symmetric matrix let's see I'm + + align:start position:0% +for a symmetric matrix let's see I'm + + + align:start position:0% +for a symmetric matrix let's see I'm +free to choose is it the same count as + + align:start position:0% +free to choose is it the same count as + + + align:start position:0% +free to choose is it the same count as +this yeah because I'm free to choose the + + align:start position:0% +this yeah because I'm free to choose the + + + align:start position:0% +this yeah because I'm free to choose the +upper triangular part and the diagonal + + align:start position:0% +upper triangular part and the diagonal + + + align:start position:0% +upper triangular part and the diagonal +but I'm not free to choose the lower so + + align:start position:0% +but I'm not free to choose the lower so + + + align:start position:0% +but I'm not free to choose the lower so +so I'd say it's 1/2 n times n minus 1 + + align:start position:0% +so I'd say it's 1/2 n times n minus 1 + + + align:start position:0% +so I'd say it's 1/2 n times n minus 1 +and plus sorry diagonals in there ok so + + align:start position:0% +and plus sorry diagonals in there ok so + + + align:start position:0% +and plus sorry diagonals in there ok so +do I get that + + align:start position:0% +do I get that + + + align:start position:0% +do I get that +half of N squared plus n from these guys + + align:start position:0% +half of N squared plus n from these guys + + + align:start position:0% +half of N squared plus n from these guys +well I probably do the diagonal guy + + align:start position:0% +well I probably do the diagonal guy + + + align:start position:0% +well I probably do the diagonal guy +gives me in this gives me n and that's a + + align:start position:0% +gives me in this gives me n and that's a + + + align:start position:0% +gives me in this gives me n and that's a +Q which is my other favorite number + + align:start position:0% +Q which is my other favorite number + + + align:start position:0% +Q which is my other favorite number +there and when I add that to that that + + align:start position:0% +there and when I add that to that that + + + align:start position:0% +there and when I add that to that that +becomes a plus sign and I'm good yeah + + align:start position:0% +becomes a plus sign and I'm good yeah + + + align:start position:0% +becomes a plus sign and I'm good yeah +you see how I enjoy doing this right but + + align:start position:0% +you see how I enjoy doing this right but + + + align:start position:0% +you see how I enjoy doing this right but +I'm near the end but the last one it's + + align:start position:0% +I'm near the end but the last one it's + + + align:start position:0% +I'm near the end but the last one it's +kind of not well known okay Q time says + + align:start position:0% +kind of not well known okay Q time says + + + align:start position:0% +kind of not well known okay Q time says +do you remember that factorization + + align:start position:0% +do you remember that factorization + + + align:start position:0% +do you remember that factorization +that's a called the polar decomposition + + align:start position:0% +that's a called the polar decomposition + + + align:start position:0% +that's a called the polar decomposition +it's a it's an orthogonal times a + + align:start position:0% +it's a it's an orthogonal times a + + + align:start position:0% +it's a it's an orthogonal times a +symmetric and it is often used in + + align:start position:0% +symmetric and it is often used in + + + align:start position:0% +symmetric and it is often used in +engineering as a way to decompose a + + align:start position:0% +engineering as a way to decompose a + + + align:start position:0% +engineering as a way to decompose a +displacement or strain matrix anyway Q + + align:start position:0% +displacement or strain matrix anyway Q + + + align:start position:0% +displacement or strain matrix anyway Q +times this and it actually it is very + + align:start position:0% +times this and it actually it is very + + + align:start position:0% +times this and it actually it is very +very close to the SVD and I have friends + + align:start position:0% +very close to the SVD and I have friends + + + align:start position:0% +very close to the SVD and I have friends +who say better to compute Q s than the + + align:start position:0% +who say better to compute Q s than the + + + align:start position:0% +who say better to compute Q s than the +SVD and then just move along anyway Q + + align:start position:0% +SVD and then just move along anyway Q + + + align:start position:0% +SVD and then just move along anyway Q +times this so Q is this guy and s what's + + align:start position:0% +times this so Q is this guy and s what's + + + align:start position:0% +times this so Q is this guy and s what's +s symmetric that's this guy + + align:start position:0% +s symmetric that's this guy + + + align:start position:0% +s symmetric that's this guy +so that's Q let me write that letter Q + + align:start position:0% +so that's Q let me write that letter Q + + + align:start position:0% +so that's Q let me write that letter Q +and s so I don't lose it + + align:start position:0% +and s so I don't lose it + + + align:start position:0% +and s so I don't lose it +what are those add up to and squared + + align:start position:0% +what are those add up to and squared + + + align:start position:0% +what are those add up to and squared +happy ok so finally the SVD friendly the + + align:start position:0% +happy ok so finally the SVD friendly the + + + align:start position:0% +happy ok so finally the SVD friendly the +SVD what's the count + + align:start position:0% +SVD what's the count + + + align:start position:0% +SVD what's the count +well now I don't know I've got + + align:start position:0% +well now I don't know I've got + + + align:start position:0% +well now I don't know I've got +rectangular stuff in there so I've got + + align:start position:0% +rectangular stuff in there so I've got + + + align:start position:0% +rectangular stuff in there so I've got +to I'm ready for this one and I have to + + align:start position:0% +to I'm ready for this one and I have to + + + align:start position:0% +to I'm ready for this one and I have to +think a little bit + + align:start position:0% +think a little bit + + + align:start position:0% +think a little bit +and we may have done this so I have I + + align:start position:0% +and we may have done this so I have I + + + align:start position:0% +and we may have done this so I have I +let's suppose that M is lesser equal M + + align:start position:0% +let's suppose that M is lesser equal M + + + align:start position:0% +let's suppose that M is lesser equal M +suppose that it is yeah otherwise we + + align:start position:0% +suppose that it is yeah otherwise we + + + align:start position:0% +suppose that it is yeah otherwise we +would just transpose and look at the SVD + + align:start position:0% +would just transpose and look at the SVD + + + align:start position:0% +would just transpose and look at the SVD +so let's say M less or equal n so let's + + align:start position:0% +so let's say M less or equal n so let's + + + align:start position:0% +so let's say M less or equal n so let's +say it's got full rank and what's the + + align:start position:0% +say it's got full rank and what's the + + + align:start position:0% +say it's got full rank and what's the +largest rank that the matrix can have M + + align:start position:0% +largest rank that the matrix can have M + + + align:start position:0% +largest rank that the matrix can have M +clearly full rank M so the SVD will be M + + align:start position:0% +clearly full rank M so the SVD will be M + + + align:start position:0% +clearly full rank M so the SVD will be M +by M let's remember the the you the + + align:start position:0% +by M let's remember the the you the + + + align:start position:0% +by M let's remember the the you the +Sigma and the V transpose this will be M + + align:start position:0% +Sigma and the V transpose this will be M + + + align:start position:0% +Sigma and the V transpose this will be M +by n and this will be n by n for the + + align:start position:0% +by n and this will be n by n for the + + + align:start position:0% +by n and this will be n by n for the +full scale this VD and if the rank is + + align:start position:0% +full scale this VD and if the rank is + + + align:start position:0% +full scale this VD and if the rank is +equal to M then I really expect to get I + + align:start position:0% +equal to M then I really expect to get I + + + align:start position:0% +equal to M then I really expect to get I +expect it to add up to the total for a + + align:start position:0% +expect it to add up to the total for a + + + align:start position:0% +expect it to add up to the total for a +for a the original a has MN right it's + + align:start position:0% +for a the original a has MN right it's + + + align:start position:0% +for a the original a has MN right it's +an M by n matrix the matrix a is M by n + + align:start position:0% +an M by n matrix the matrix a is M by n + + + align:start position:0% +an M by n matrix the matrix a is M by n +with them less or equal in giving me + + align:start position:0% +with them less or equal in giving me + + + align:start position:0% +with them less or equal in giving me +these things so has MN parameters so do + + align:start position:0% +these things so has MN parameters so do + + + align:start position:0% +these things so has MN parameters so do +we get M times n from this I hope we do + + align:start position:0% +we get M times n from this I hope we do + + + align:start position:0% +we get M times n from this I hope we do +I know how many we get from Sigma what + + align:start position:0% +I know how many we get from Sigma what + + + align:start position:0% +I know how many we get from Sigma what +how many what's the count for a Sigma M + + align:start position:0% +how many what's the count for a Sigma M + + + align:start position:0% +how many what's the count for a Sigma M +and what's the count for V so that's an + + align:start position:0% +and what's the count for V so that's an + + + align:start position:0% +and what's the count for V so that's an +N by n and what's the count for you okay + + align:start position:0% +N by n and what's the count for you okay + + + align:start position:0% +N by n and what's the count for you okay +yeah they're orthogonal matrices so that + + align:start position:0% +yeah they're orthogonal matrices so that + + + align:start position:0% +yeah they're orthogonal matrices so that +I should be able to go up to that line + + align:start position:0% +I should be able to go up to that line + + + align:start position:0% +I should be able to go up to that line +this was an M by M one so that's is that + + align:start position:0% +this was an M by M one so that's is that + + + align:start position:0% +this was an M by M one so that's is that +a half and n minus one am i copying that + + align:start position:0% +a half and n minus one am i copying that + + + align:start position:0% +a half and n minus one am i copying that +correctly out of this circle there + + align:start position:0% +correctly out of this circle there + + + align:start position:0% +correctly out of this circle there +that's that's an M by M orthogonal + + align:start position:0% +that's that's an M by M orthogonal + + + align:start position:0% +that's that's an M by M orthogonal +matrix Oh + + align:start position:0% +matrix Oh + + + align:start position:0% +matrix Oh +but I have to write in that was foolish + + align:start position:0% +but I have to write in that was foolish + + + align:start position:0% +but I have to write in that was foolish +okay em em yeah because that matrix + + align:start position:0% +okay em em yeah because that matrix + + + align:start position:0% +okay em em yeah because that matrix +it's a size M so that's an M and then I + + align:start position:0% +it's a size M so that's an M and then I + + + align:start position:0% +it's a size M so that's an M and then I +have that and then I have whatever V + + align:start position:0% +have that and then I have whatever V + + + align:start position:0% +have that and then I have whatever V +transpose end by n oh what's the deal in + + align:start position:0% +transpose end by n oh what's the deal in + + + align:start position:0% +transpose end by n oh what's the deal in +there hmm + + align:start position:0% + + + + align:start position:0% + +do I want all of the 1/2 + n minus 1 Oh + + align:start position:0% + + + + align:start position:0% + +God I thought I'd got this straight + + align:start position:0% +God I thought I'd got this straight + + + align:start position:0% +God I thought I'd got this straight +does he know I meant I could subtract + + align:start position:0% +does he know I meant I could subtract + + + align:start position:0% +does he know I meant I could subtract +this from this and and find out what I + + align:start position:0% +this from this and and find out what I + + + align:start position:0% +this from this and and find out what I +should say whoa + + align:start position:0% +should say whoa + + + align:start position:0% +should say whoa +students have been known to do this too + + align:start position:0% +students have been known to do this too + + + align:start position:0% +students have been known to do this too +let's see well let's try to think anyway + + align:start position:0% +let's see well let's try to think anyway + + + align:start position:0% +let's see well let's try to think anyway +so I have this n by n submit this n by n + + align:start position:0% +so I have this n by n submit this n by n + + + align:start position:0% +so I have this n by n submit this n by n +orthogonal matrix so it's first it could + + align:start position:0% +orthogonal matrix so it's first it could + + + align:start position:0% +orthogonal matrix so it's first it could +it could be any orthogonal matrix yeah + + align:start position:0% +it could be any orthogonal matrix yeah + + + align:start position:0% +it could be any orthogonal matrix yeah +but is it only the first M columns that + + align:start position:0% +but is it only the first M columns that + + + align:start position:0% +but is it only the first M columns that +I really need the rest I could just + + align:start position:0% +I really need the rest I could just + + + align:start position:0% +I really need the rest I could just +throw away so I let me try to imagine + + align:start position:0% +throw away so I let me try to imagine + + + align:start position:0% +throw away so I let me try to imagine +that it's just the first well then I + + align:start position:0% +that it's just the first well then I + + + align:start position:0% +that it's just the first well then I +won't have any end in here so maybe I + + align:start position:0% +won't have any end in here so maybe I + + + align:start position:0% +won't have any end in here so maybe I +better take 1/2 and you know help oh oh + + align:start position:0% +better take 1/2 and you know help oh oh + + + align:start position:0% +better take 1/2 and you know help oh oh +yes of course + + align:start position:0% +yes of course + + + align:start position:0% +yes of course +ha I've got only M columns that matter + + align:start position:0% +ha I've got only M columns that matter + + + align:start position:0% +ha I've got only M columns that matter +the bait the everybody sort of now + + align:start position:0% +the bait the everybody sort of now + + + align:start position:0% +the bait the everybody sort of now +understands that SVD we've got the right + + align:start position:0% +understands that SVD we've got the right + + + align:start position:0% +understands that SVD we've got the right +the rank is am don't forget that ok then + + align:start position:0% +the rank is am don't forget that ok then + + + align:start position:0% +the rank is am don't forget that ok then +the first the the first are the first M + + align:start position:0% +the first the the first are the first M + + + align:start position:0% +the first the the first are the first M +columns of V are important those are the + + align:start position:0% +columns of V are important those are the + + + align:start position:0% +columns of V are important those are the +singular vectors that go with nonzero + + align:start position:0% +singular vectors that go with nonzero + + + align:start position:0% +singular vectors that go with nonzero +singular values that really matter so + + align:start position:0% +singular values that really matter so + + + align:start position:0% +singular values that really matter so +that's and the rest really don't matter + + align:start position:0% +that's and the rest really don't matter + + + align:start position:0% +that's and the rest really don't matter +so + + align:start position:0% +so + + + align:start position:0% +so +so I'm going to just I have to count how + + align:start position:0% +so I'm going to just I have to count how + + + align:start position:0% +so I'm going to just I have to count how +many so here sorry V the the important + + align:start position:0% +many so here sorry V the the important + + + align:start position:0% +many so here sorry V the the important +part of thee has has how many and only M + + align:start position:0% +part of thee has has how many and only M + + + align:start position:0% +part of thee has has how many and only M +columns but it's an N by n matrix and + + align:start position:0% +columns but it's an N by n matrix and + + + align:start position:0% +columns but it's an N by n matrix and +those columns are orthogonal so honor + + align:start position:0% +those columns are orthogonal so honor + + + align:start position:0% +those columns are orthogonal so honor +the answer is not MN for this guy its I + + align:start position:0% +the answer is not MN for this guy its I + + + align:start position:0% +the answer is not MN for this guy its I +have to go through this foolish + + align:start position:0% +have to go through this foolish + + + align:start position:0% +have to go through this foolish +reasoning again I have n minus 1 plus n + + align:start position:0% +reasoning again I have n minus 1 plus n + + + align:start position:0% +reasoning again I have n minus 1 plus n +minus 2 plus so on plus n minus M there + + align:start position:0% +minus 2 plus so on plus n minus M there + + + align:start position:0% +minus 2 plus so on plus n minus M there +were n minus 1 parameters in the first + + align:start position:0% +were n minus 1 parameters in the first + + + align:start position:0% +were n minus 1 parameters in the first +over thought oh vector or a unit vector + + align:start position:0% +over thought oh vector or a unit vector + + + align:start position:0% +over thought oh vector or a unit vector +n minus 2 in the second one up to n + + align:start position:0% +n minus 2 in the second one up to n + + + align:start position:0% +n minus 2 in the second one up to n +minus M in the third and then V has some + + align:start position:0% +minus M in the third and then V has some + + + align:start position:0% +minus M in the third and then V has some +more columns that are coming really from + + align:start position:0% +more columns that are coming really from + + + align:start position:0% +more columns that are coming really from +a null space that that are not are not + + align:start position:0% +a null space that that are not are not + + + align:start position:0% +a null space that that are not are not +important + + align:start position:0% +important + + + align:start position:0% +important +I believe this is the right thing to do + + align:start position:0% +I believe this is the right thing to do + + + align:start position:0% +I believe this is the right thing to do +I'm hoping you agree and now I I mean + + align:start position:0% +I'm hoping you agree and now I I mean + + + align:start position:0% +I'm hoping you agree and now I I mean +I'm hoping even more that those that up + + align:start position:0% +I'm hoping even more that those that up + + + align:start position:0% +I'm hoping even more that those that up +to M times in okay I have a half and + + align:start position:0% +to M times in okay I have a half and + + + align:start position:0% +to M times in okay I have a half and +square they have to total this thing + + align:start position:0% +square they have to total this thing + + + align:start position:0% +square they have to total this thing +okay this had m m terms + + align:start position:0% +okay this had m m terms + + + align:start position:0% +okay this had m m terms +so there's m m of these ends and then I + + align:start position:0% +so there's m m of these ends and then I + + + align:start position:0% +so there's m m of these ends and then I +have to subtract off one plus two plus + + align:start position:0% +have to subtract off one plus two plus + + + align:start position:0% +have to subtract off one plus two plus +three up to M and so what am i + + align:start position:0% +three up to M and so what am i + + + align:start position:0% +three up to M and so what am i +subtracting off what's that some one + + align:start position:0% +subtracting off what's that some one + + + align:start position:0% +subtracting off what's that some one +plus two plus three stopping at M it's + + align:start position:0% +plus two plus three stopping at M it's + + + align:start position:0% +plus two plus three stopping at M it's +one of these guys one-half is it 1/2 mm + + align:start position:0% +one of these guys one-half is it 1/2 mm + + + align:start position:0% +one of these guys one-half is it 1/2 mm +plus one yeah 1/2 m m plus 1 sorry 1/2 m + + align:start position:0% +plus one yeah 1/2 m m plus 1 sorry 1/2 m + + + align:start position:0% +plus one yeah 1/2 m m plus 1 sorry 1/2 m +m plus 1 I would supposed to enjoy this + + align:start position:0% +m plus 1 I would supposed to enjoy this + + + align:start position:0% +m plus 1 I would supposed to enjoy this +and now little nervous but okay so I + + align:start position:0% +and now little nervous but okay so I + + + align:start position:0% +and now little nervous but okay so I +believe that that + + align:start position:0% +believe that that + + + align:start position:0% +believe that that +is that okay well we have the MN that's + + align:start position:0% +is that okay well we have the MN that's + + + align:start position:0% +is that okay well we have the MN that's +a good sign that we're shooting for so + + align:start position:0% +a good sign that we're shooting for so + + + align:start position:0% +a good sign that we're shooting for so +does the rest of it add to nothing well + + align:start position:0% +does the rest of it add to nothing well + + + align:start position:0% +does the rest of it add to nothing well +I guess yeah I guess it does when I put + + align:start position:0% +I guess yeah I guess it does when I put + + + align:start position:0% +I guess yeah I guess it does when I put +these two together I have 1/2 mm plus + + align:start position:0% +these two together I have 1/2 mm plus + + + align:start position:0% +these two together I have 1/2 mm plus +one and then I'm subtracting it away + + align:start position:0% +one and then I'm subtracting it away + + + align:start position:0% +one and then I'm subtracting it away +again so I get amen + + align:start position:0% +again so I get amen + + + align:start position:0% +again so I get amen +all right well we wouldn't anything + + align:start position:0% +all right well we wouldn't anything + + + align:start position:0% +all right well we wouldn't anything +before I raise that board and consign + + align:start position:0% +before I raise that board and consign + + + align:start position:0% +before I raise that board and consign +that to history is there should I pause + + align:start position:0% +that to history is there should I pause + + + align:start position:0% +that to history is there should I pause +a little more minute this will be like + + align:start position:0% +a little more minute this will be like + + + align:start position:0% +a little more minute this will be like +I'm hoping a one-page appendix to the + + align:start position:0% +I'm hoping a one-page appendix to the + + + align:start position:0% +I'm hoping a one-page appendix to the +notes and the book and you'll see it but + + align:start position:0% +notes and the book and you'll see it but + + + align:start position:0% +notes and the book and you'll see it but +I do have one more count to do and then + + align:start position:0% +I do have one more count to do and then + + + align:start position:0% +I do have one more count to do and then +I'm good with this review and ready to + + align:start position:0% +I'm good with this review and ready to + + + align:start position:0% +I'm good with this review and ready to +move onward to the topic of saddle + + align:start position:0% +move onward to the topic of saddle + + + align:start position:0% +move onward to the topic of saddle +points and ready to move onward after + + align:start position:0% +points and ready to move onward after + + + align:start position:0% +points and ready to move onward after +that well I'll say a little bit about + + align:start position:0% +that well I'll say a little bit about + + + align:start position:0% +that well I'll say a little bit about +the next lab homework that I'm creating + + align:start position:0% +the next lab homework that I'm creating + + + align:start position:0% +the next lab homework that I'm creating +and then our next topic will be like + + align:start position:0% +and then our next topic will be like + + + align:start position:0% +and then our next topic will be like +covariance matrices it a little + + align:start position:0% +covariance matrices it a little + + + align:start position:0% +covariance matrices it a little +statistics this week and then we and we + + align:start position:0% +statistics this week and then we and we + + + align:start position:0% +statistics this week and then we and we +get a week off we could to digest it and + + align:start position:0% +get a week off we could to digest it and + + + align:start position:0% +get a week off we could to digest it and +then come back for gradient descent and + + align:start position:0% +then come back for gradient descent and + + + align:start position:0% +then come back for gradient descent and +deep learning and and those things okay + + align:start position:0% +deep learning and and those things okay + + + align:start position:0% +deep learning and and those things okay +everybody happy with that so what's my + + align:start position:0% +everybody happy with that so what's my + + + align:start position:0% +everybody happy with that so what's my +final question my final question is the + + align:start position:0% +final question my final question is the + + + align:start position:0% +final question my final question is the +SVD for for any any matrix of rank R so + + align:start position:0% +SVD for for any any matrix of rank R so + + + align:start position:0% +SVD for for any any matrix of rank R so +it's an M by n matrix but the rank is + + align:start position:0% +it's an M by n matrix but the rank is + + + align:start position:0% +it's an M by n matrix but the rank is +only R + + align:start position:0% +only R + + + align:start position:0% +only R +it's a natural question how many + + align:start position:0% +it's a natural question how many + + + align:start position:0% +it's a natural question how many +parameters are there in a in a ranked R + + align:start position:0% +parameters are there in a in a ranked R + + + align:start position:0% +parameters are there in a in a ranked R +matrix and that may be we may even have + + align:start position:0% +matrix and that may be we may even have + + + align:start position:0% +matrix and that may be we may even have +touched on this question and I have two + + align:start position:0% +touched on this question and I have two + + + align:start position:0% +touched on this question and I have two +ways to answer it and one way is the SVD + + align:start position:0% +ways to answer it and one way is the SVD + + + align:start position:0% +ways to answer it and one way is the SVD +so let me and that'll be similar to what + + align:start position:0% +so let me and that'll be similar to what + + + align:start position:0% +so let me and that'll be similar to what +I just pushed up there so if the rank is + + align:start position:0% +I just pushed up there so if the rank is + + + align:start position:0% +I just pushed up there so if the rank is +our the SVD of this typical rank our + + align:start position:0% +our the SVD of this typical rank our + + + align:start position:0% +our the SVD of this typical rank our +matrix will be u Sigma V transpose but + + align:start position:0% +matrix will be u Sigma V transpose but + + + align:start position:0% +matrix will be u Sigma V transpose but +you know this is the like the condensed + + align:start position:0% +you know this is the like the condensed + + + align:start position:0% +you know this is the like the condensed +thing where I've thrown away stuff + + align:start position:0% +thing where I've thrown away stuff + + + align:start position:0% +thing where I've thrown away stuff +that's automatically zero because if the + + align:start position:0% +that's automatically zero because if the + + + align:start position:0% +that's automatically zero because if the +rank is only our like if the rank was + + align:start position:0% +rank is only our like if the rank was + + + align:start position:0% +rank is only our like if the rank was +one suppose the rank wasn't one then I'd + + align:start position:0% +one suppose the rank wasn't one then I'd + + + align:start position:0% +one suppose the rank wasn't one then I'd +have one column times one sigma times + + align:start position:0% +have one column times one sigma times + + + align:start position:0% +have one column times one sigma times +one row right and I could do that count + + align:start position:0% +one row right and I could do that count + + + align:start position:0% +one row right and I could do that count +for R equal one now I have our columns + + align:start position:0% +for R equal one now I have our columns + + + align:start position:0% +for R equal one now I have our columns +so this is M by are there Sigma is its + + align:start position:0% +so this is M by are there Sigma is its + + + align:start position:0% +so this is M by are there Sigma is its +diagonal of course so I'm gonna get our + + align:start position:0% +diagonal of course so I'm gonna get our + + + align:start position:0% +diagonal of course so I'm gonna get our +numbers out of that and this one is now + + align:start position:0% +numbers out of that and this one is now + + + align:start position:0% +numbers out of that and this one is now +R by n in other words maybe I should + + align:start position:0% +R by n in other words maybe I should + + + align:start position:0% +R by n in other words maybe I should +like save this little bit here that was + + align:start position:0% +like save this little bit here that was + + + align:start position:0% +like save this little bit here that was +helpful + + align:start position:0% +helpful + + + align:start position:0% +helpful +but now I've got M is reduced to R so I + + align:start position:0% +but now I've got M is reduced to R so I + + + align:start position:0% +but now I've got M is reduced to R so I +believe that if I count these three I'll + + align:start position:0% +believe that if I count these three I'll + + + align:start position:0% +believe that if I count these three I'll +get the right number of parameters for a + + align:start position:0% +get the right number of parameters for a + + + align:start position:0% +get the right number of parameters for a +rank R matrix and that's not so obvious + + align:start position:0% +rank R matrix and that's not so obvious + + + align:start position:0% +rank R matrix and that's not so obvious +because the rank R matrices are not a we + + align:start position:0% +because the rank R matrices are not a we + + + align:start position:0% +because the rank R matrices are not a we +don't have a subspace if I had a rank R + + align:start position:0% +don't have a subspace if I had a rank R + + + align:start position:0% +don't have a subspace if I had a rank R +matrix to another rank R matrix + + align:start position:0% +matrix to another rank R matrix + + + align:start position:0% +matrix to another rank R matrix +well the rank could be as big as 2r and + + align:start position:0% +well the rank could be as big as 2r and + + + align:start position:0% +well the rank could be as big as 2r and +probably will be so so we you know it's + + align:start position:0% +probably will be so so we you know it's + + + align:start position:0% +probably will be so so we you know it's +just a little interesting to get your + + align:start position:0% +just a little interesting to get your + + + align:start position:0% +just a little interesting to get your +hands on matrices of rank R because + + align:start position:0% +hands on matrices of rank R because + + + align:start position:0% +hands on matrices of rank R because +they're kind of a sin like a well math + + align:start position:0% +they're kind of a sin like a well math + + + align:start position:0% +they're kind of a sin like a well math +person would call it a manifold some + + align:start position:0% +person would call it a manifold some + + + align:start position:0% +person would call it a manifold some +kind of a surface + + align:start position:0% +kind of a surface + + + align:start position:0% +kind of a surface +in matrix space yeah have you ever + + align:start position:0% +in matrix space yeah have you ever + + + align:start position:0% +in matrix space yeah have you ever +thought about matrix space so that's a + + align:start position:0% +thought about matrix space so that's a + + + align:start position:0% +thought about matrix space so that's a +vector space because we can add matrices + + align:start position:0% +vector space because we can add matrices + + + align:start position:0% +vector space because we can add matrices +we can multiply them by constants we can + + align:start position:0% +we can multiply them by constants we can + + + align:start position:0% +we can multiply them by constants we can +take the NIR combination so they're + + align:start position:0% +take the NIR combination so they're + + + align:start position:0% +take the NIR combination so they're +there we could call them vectors if we + + align:start position:0% +there we could call them vectors if we + + + align:start position:0% +there we could call them vectors if we +like that would be a vector space of M + + align:start position:0% +like that would be a vector space of M + + + align:start position:0% +like that would be a vector space of M +by n matrices what would be the + + align:start position:0% +by n matrices what would be the + + + align:start position:0% +by n matrices what would be the +dimension of that space support so the + + align:start position:0% +dimension of that space support so the + + + align:start position:0% +dimension of that space support so the +vector space of all three by four + + align:start position:0% +vector space of all three by four + + + align:start position:0% +vector space of all three by four +matrices that that has what dimension + + align:start position:0% +matrices that that has what dimension + + + align:start position:0% +matrices that that has what dimension +1212 because you've got 12 numbers to + + align:start position:0% +1212 because you've got 12 numbers to + + + align:start position:0% +1212 because you've got 12 numbers to +choose and it is a space because you're + + align:start position:0% +choose and it is a space because you're + + + align:start position:0% +choose and it is a space because you're +gonna add now if I say 3 by 4 matrices + + align:start position:0% +gonna add now if I say 3 by 4 matrices + + + align:start position:0% +gonna add now if I say 3 by 4 matrices +of Rank 2 I don't have a space anymore + + align:start position:0% +of Rank 2 I don't have a space anymore + + + align:start position:0% +of Rank 2 I don't have a space anymore +that word spaces is is priscilly asleep + + align:start position:0% +that word spaces is is priscilly asleep + + + align:start position:0% +that word spaces is is priscilly asleep +reserved for meaning vector space + + align:start position:0% +reserved for meaning vector space + + + align:start position:0% +reserved for meaning vector space +meaning I can take combinations but if I + + align:start position:0% +meaning I can take combinations but if I + + + align:start position:0% +meaning I can take combinations but if I +take a rank 2 matrix plus a rank 2 + + align:start position:0% +take a rank 2 matrix plus a rank 2 + + + align:start position:0% +take a rank 2 matrix plus a rank 2 +matrix I'm not so it's sort of a surface + + align:start position:0% +matrix I'm not so it's sort of a surface + + + align:start position:0% +matrix I'm not so it's sort of a surface +within 12 D the to the 3 by 4 matrices + + align:start position:0% +within 12 D the to the 3 by 4 matrices + + + align:start position:0% +within 12 D the to the 3 by 4 matrices +of Rank 2 and we're about to find the + + align:start position:0% +of Rank 2 and we're about to find the + + + align:start position:0% +of Rank 2 and we're about to find the +dimension of that surface does your mind + + align:start position:0% +dimension of that surface does your mind + + + align:start position:0% +dimension of that surface does your mind +sort of visualize the surface in 12 + + align:start position:0% +sort of visualize the surface in 12 + + + align:start position:0% +sort of visualize the surface in 12 +dimensions yeah well give it a shot + + align:start position:0% +dimensions yeah well give it a shot + + + align:start position:0% +dimensions yeah well give it a shot +anyway and but what that surface could + + align:start position:0% +anyway and but what that surface could + + + align:start position:0% +anyway and but what that surface could +have the 11 dimensional so to speak like + + align:start position:0% +have the 11 dimensional so to speak like + + + align:start position:0% +have the 11 dimensional so to speak like +meaning locally the it wouldn't have to + + align:start position:0% +meaning locally the it wouldn't have to + + + align:start position:0% +meaning locally the it wouldn't have to +be a plan 11 dimensional plane going + + align:start position:0% +be a plan 11 dimensional plane going + + + align:start position:0% +be a plan 11 dimensional plane going +through the origin in fact it wouldn't + + align:start position:0% +through the origin in fact it wouldn't + + + align:start position:0% +through the origin in fact it wouldn't +go through the origin because the origin + + align:start position:0% +go through the origin because the origin + + + align:start position:0% +go through the origin because the origin +won't have rank are so so it's some kind + + align:start position:0% +won't have rank are so so it's some kind + + + align:start position:0% +won't have rank are so so it's some kind +of a surface and maybe it's got some + + align:start position:0% +of a surface and maybe it's got some + + + align:start position:0% +of a surface and maybe it's got some +different pieces probably some smart + + align:start position:0% +different pieces probably some smart + + + align:start position:0% +different pieces probably some smart +person knows what that surface looks + + align:start position:0% +person knows what that surface looks + + + align:start position:0% +person knows what that surface looks +like but we're just going to find out + + align:start position:0% +like but we're just going to find out + + + align:start position:0% +like but we're just going to find out +some sense something about its number of + + align:start position:0% +some sense something about its number of + + + align:start position:0% +some sense something about its number of +parameters as local dimension well I + + align:start position:0% +parameters as local dimension well I + + + align:start position:0% +parameters as local dimension well I +know that this answer is R cuz I've got + + align:start position:0% +know that this answer is R cuz I've got + + + align:start position:0% +know that this answer is R cuz I've got +our Sigma's and this one I'm pretty good + + align:start position:0% +our Sigma's and this one I'm pretty good + + + align:start position:0% +our Sigma's and this one I'm pretty good +at but now it's not + + align:start position:0% +at but now it's not + + + align:start position:0% +at but now it's not +it's R by n so it's instead of here here + + align:start position:0% +it's R by n so it's instead of here here + + + align:start position:0% +it's R by n so it's instead of here here +our was M but now down here R is R so I + + align:start position:0% +our was M but now down here R is R so I + + + align:start position:0% +our was M but now down here R is R so I +think it's are n minus 1/2 + + align:start position:0% +think it's are n minus 1/2 + + + align:start position:0% +think it's are n minus 1/2 +what's that is that an M so now it's an + + align:start position:0% +what's that is that an M so now it's an + + + align:start position:0% +what's that is that an M so now it's an +R R plus 1 I think I think and what + + align:start position:0% +R R plus 1 I think I think and what + + + align:start position:0% +R R plus 1 I think I think and what +about the u so U is going to be similar + + align:start position:0% +about the u so U is going to be similar + + + align:start position:0% +about the u so U is going to be similar +except instead of the end here we've got + + align:start position:0% +except instead of the end here we've got + + + align:start position:0% +except instead of the end here we've got +an M I so I think we for you will will + + align:start position:0% +an M I so I think we for you will will + + + align:start position:0% +an M I so I think we for you will will +have M minus 1 plus M minus 2 plus so so + + align:start position:0% +have M minus 1 plus M minus 2 plus so so + + + align:start position:0% +have M minus 1 plus M minus 2 plus so so +let me write it here M minus 1 so you + + align:start position:0% +let me write it here M minus 1 so you + + + align:start position:0% +let me write it here M minus 1 so you +I'm talking about you here it's got our + + align:start position:0% +I'm talking about you here it's got our + + + align:start position:0% +I'm talking about you here it's got our +columns the first one has M minus 1 + + align:start position:0% +columns the first one has M minus 1 + + + align:start position:0% +columns the first one has M minus 1 +because I throw away one because it's a + + align:start position:0% +because I throw away one because it's a + + + align:start position:0% +because I throw away one because it's a +unit vector up to M minus R ours column + + align:start position:0% +unit vector up to M minus R ours column + + + align:start position:0% +unit vector up to M minus R ours column +okay and now so how what what is that + + align:start position:0% +okay and now so how what what is that + + + align:start position:0% +okay and now so how what what is that +add up to well I put all the M's + + align:start position:0% +add up to well I put all the M's + + + align:start position:0% +add up to well I put all the M's +together so that's our M let me say mr + + align:start position:0% +together so that's our M let me say mr + + + align:start position:0% +together so that's our M let me say mr +and then I'm subtracting off 1 plus 2 + + align:start position:0% +and then I'm subtracting off 1 plus 2 + + + align:start position:0% +and then I'm subtracting off 1 plus 2 +Plus 3 up to R now tell me again what + + align:start position:0% +Plus 3 up to R now tell me again what + + + align:start position:0% +Plus 3 up to R now tell me again what +that adds up to one plus two plus three + + align:start position:0% +that adds up to one plus two plus three + + + align:start position:0% +that adds up to one plus two plus three +stop at our that's what we had here and + + align:start position:0% +stop at our that's what we had here and + + + align:start position:0% +stop at our that's what we had here and +we've got it for V and we've got it + + align:start position:0% +we've got it for V and we've got it + + + align:start position:0% +we've got it for V and we've got it +again here minus 1/2 our R plus 1 you + + align:start position:0% +again here minus 1/2 our R plus 1 you + + + align:start position:0% +again here minus 1/2 our R plus 1 you +okay with that + + align:start position:0% +okay with that + + + align:start position:0% +okay with that +and now I just want to add them up so I + + align:start position:0% +and now I just want to add them up so I + + + align:start position:0% +and now I just want to add them up so I +have M R and I've n R and then I have + + align:start position:0% +have M R and I've n R and then I have + + + align:start position:0% +have M R and I've n R and then I have +two of these so let me let me get it + + align:start position:0% +two of these so let me let me get it + + + align:start position:0% +two of these so let me let me get it +here M R and n are and now I have to + + align:start position:0% +here M R and n are and now I have to + + + align:start position:0% +here M R and n are and now I have to +look at so mr check n are checked now I + + align:start position:0% +look at so mr check n are checked now I + + + align:start position:0% +look at so mr check n are checked now I +have two of these guys so they combine + + align:start position:0% +have two of these guys so they combine + + + align:start position:0% +have two of these guys so they combine +into R squared plus R and then I R + + align:start position:0% +into R squared plus R and then I R + + + align:start position:0% +into R squared plus R and then I R +squared + + align:start position:0% +squared + + + align:start position:0% +squared +yeah minus R squared + + align:start position:0% +yeah minus R squared + + + align:start position:0% +yeah minus R squared +sorry they combined into minus R squared + + align:start position:0% +sorry they combined into minus R squared + + + align:start position:0% +sorry they combined into minus R squared +plus R and then here's a are coming in + + align:start position:0% +plus R and then here's a are coming in + + + align:start position:0% +plus R and then here's a are coming in +with a plus I think we have a minus R + + align:start position:0% +with a plus I think we have a minus R + + + align:start position:0% +with a plus I think we have a minus R +squared and that is the right answer + + align:start position:0% +squared and that is the right answer + + + align:start position:0% +squared and that is the right answer +yep okay so I took a bit longer than I + + align:start position:0% +yep okay so I took a bit longer than I + + + align:start position:0% +yep okay so I took a bit longer than I +intended but it this is a number that + + align:start position:0% +intended but it this is a number that + + + align:start position:0% +intended but it this is a number that +that's sort of interesting + + align:start position:0% +that's sort of interesting + + + align:start position:0% +that's sort of interesting +I mentioned saddle points sort of like + + align:start position:0% +I mentioned saddle points sort of like + + + align:start position:0% +I mentioned saddle points sort of like +separately from maxima and minima just + + align:start position:0% +separately from maxima and minima just + + + align:start position:0% +separately from maxima and minima just +because they are definitely not as easy + + align:start position:0% +because they are definitely not as easy + + + align:start position:0% +because they are definitely not as easy +to work with you understand what I mean + + align:start position:0% +to work with you understand what I mean + + + align:start position:0% +to work with you understand what I mean +by saddle points matrices involved have + + align:start position:0% +by saddle points matrices involved have + + + align:start position:0% +by saddle points matrices involved have +are not positive definite those would go + + align:start position:0% +are not positive definite those would go + + + align:start position:0% +are not positive definite those would go +with a maximum they're not negative + + align:start position:0% +with a maximum they're not negative + + + align:start position:0% +with a maximum they're not negative +they're not negative they're not well + + align:start position:0% +they're not negative they're not well + + + align:start position:0% +they're not negative they're not well +those would go with maxima and minima + + align:start position:0% +those would go with maxima and minima + + + align:start position:0% +those would go with maxima and minima +but we're we're looking in between so + + align:start position:0% +but we're we're looking in between so + + + align:start position:0% +but we're we're looking in between so +saddle points okay well I'll get going + + align:start position:0% +saddle points okay well I'll get going + + + align:start position:0% +saddle points okay well I'll get going +on those okay I I sort of realized that + + align:start position:0% +on those okay I I sort of realized that + + + align:start position:0% +on those okay I I sort of realized that +there are two main sources of saddle + + align:start position:0% +there are two main sources of saddle + + + align:start position:0% +there are two main sources of saddle +points one of them is when I have + + align:start position:0% +points one of them is when I have + + + align:start position:0% +points one of them is when I have +problems that when I let's say I + + align:start position:0% +problems that when I let's say I + + + align:start position:0% +problems that when I let's say I +minimize so this will be the constraint + + align:start position:0% +minimize so this will be the constraint + + + align:start position:0% +minimize so this will be the constraint +saddle points have come from the + + align:start position:0% +saddle points have come from the + + + align:start position:0% +saddle points have come from the +constraint so LeBron Lagrange's gonna be + + align:start position:0% +constraint so LeBron Lagrange's gonna be + + + align:start position:0% +constraint so LeBron Lagrange's gonna be +responsible for these saddle points so + + align:start position:0% +responsible for these saddle points so + + + align:start position:0% +responsible for these saddle points so +we might have some minimum problem like + + align:start position:0% +we might have some minimum problem like + + + align:start position:0% +we might have some minimum problem like +minimize some positive definite thing + + align:start position:0% +minimize some positive definite thing + + + align:start position:0% +minimize some positive definite thing +and of course if we don't say anymore + + align:start position:0% +and of course if we don't say anymore + + + align:start position:0% +and of course if we don't say anymore +the minimum is zero right because + + align:start position:0% +the minimum is zero right because + + + align:start position:0% +the minimum is zero right because +otherwise it's positive but we're going + + align:start position:0% +otherwise it's positive but we're going + + + align:start position:0% +otherwise it's positive but we're going +to put on constraints ax equal B so this + + align:start position:0% +to put on constraints ax equal B so this + + + align:start position:0% +to put on constraints ax equal B so this +is the classical constrained + + align:start position:0% +is the classical constrained + + + align:start position:0% +is the classical constrained +optimization problem quadratic cost + + align:start position:0% +optimization problem quadratic cost + + + align:start position:0% +optimization problem quadratic cost +function linear constraints we could + + align:start position:0% +function linear constraints we could + + + align:start position:0% +function linear constraints we could +solve this exactly but let's just see + + align:start position:0% +solve this exactly but let's just see + + + align:start position:0% +solve this exactly but let's just see +where saddle point is going to rise so + + align:start position:0% +where saddle point is going to rise so + + + align:start position:0% +where saddle point is going to rise so +so there's + + align:start position:0% +so there's + + + align:start position:0% +so there's +is positive-definite but now how do we + + align:start position:0% +is positive-definite but now how do we + + + align:start position:0% +is positive-definite but now how do we +deal with that problem well the ground + + align:start position:0% +deal with that problem well the ground + + + align:start position:0% +deal with that problem well the ground +said what to do Lagaan said look at the + + align:start position:0% +said what to do Lagaan said look at the + + + align:start position:0% +said what to do Lagaan said look at the +Lagrangian okay he introduced lambda so + + align:start position:0% +Lagrangian okay he introduced lambda so + + + align:start position:0% +Lagrangian okay he introduced lambda so +this X is in this X is in n dimensions + + align:start position:0% +this X is in this X is in n dimensions + + + align:start position:0% +this X is in this X is in n dimensions +that's an N by n matrix but I have M + + align:start position:0% +that's an N by n matrix but I have M + + + align:start position:0% +that's an N by n matrix but I have M +constraints so the matrix a is M by n + + align:start position:0% + + + + align:start position:0% + +I've M constraints and then I'm going to + + align:start position:0% +I've M constraints and then I'm going to + + + align:start position:0% +I've M constraints and then I'm going to +follow the rules and introduce M lagron + + align:start position:0% +follow the rules and introduce M lagron + + + align:start position:0% +follow the rules and introduce M lagron +smalt appliers + + align:start position:0% + + + + align:start position:0% + +that's an M and then the neat part of + + align:start position:0% +that's an M and then the neat part of + + + align:start position:0% +that's an M and then the neat part of +the groan and what what is this well + + align:start position:0% +the groan and what what is this well + + + align:start position:0% +the groan and what what is this well +it's I take the function and then I + + align:start position:0% +it's I take the function and then I + + + align:start position:0% +it's I take the function and then I +introduce remember lambda is a vector + + align:start position:0% +introduce remember lambda is a vector + + + align:start position:0% +introduce remember lambda is a vector +now not just a number + + align:start position:0% +now not just a number + + + align:start position:0% +now not just a number +we had some application where it was + + align:start position:0% +we had some application where it was + + + align:start position:0% +we had some application where it was +just there was just one constraint but + + align:start position:0% +just there was just one constraint but + + + align:start position:0% +just there was just one constraint but +now I have M constraints so I take a + + align:start position:0% +now I have M constraints so I take a + + + align:start position:0% +now I have M constraints so I take a +lambda so lambda transpose times ax + + align:start position:0% +lambda so lambda transpose times ax + + + align:start position:0% +lambda so lambda transpose times ax +minus B and the plus or the minus sign + + align:start position:0% +minus B and the plus or the minus sign + + + align:start position:0% +minus B and the plus or the minus sign +here is not important I mean you can + + align:start position:0% +here is not important I mean you can + + + align:start position:0% +here is not important I mean you can +choose it because that'll determine the + + align:start position:0% +choose it because that'll determine the + + + align:start position:0% +choose it because that'll determine the +sign of lambda but either way it's + + align:start position:0% +sign of lambda but either way it's + + + align:start position:0% +sign of lambda but either way it's +correct + + align:start position:0% +correct + + + align:start position:0% +correct +okay so we've entered it we've + + align:start position:0% +okay so we've entered it we've + + + align:start position:0% +okay so we've entered it we've +introduced a function that now depends + + align:start position:0% +introduced a function that now depends + + + align:start position:0% +introduced a function that now depends +on X and also on lambda and and there's + + align:start position:0% +on X and also on lambda and and there's + + + align:start position:0% +on X and also on lambda and and there's +a and they multiply each other in and my + + align:start position:0% +a and they multiply each other in and my + + + align:start position:0% +a and they multiply each other in and my +point is that lagron says take the + + align:start position:0% +point is that lagron says take the + + + align:start position:0% +point is that lagron says take the +derivatives with respect to X and lambda + + align:start position:0% +derivatives with respect to X and lambda + + + align:start position:0% +derivatives with respect to X and lambda +so that's the cool thing that he's + + align:start position:0% +so that's the cool thing that he's + + + align:start position:0% +so that's the cool thing that he's +contributed he says if you only create + + align:start position:0% +contributed he says if you only create + + + align:start position:0% +contributed he says if you only create +my function now you can take X + + align:start position:0% +my function now you can take X + + + align:start position:0% +my function now you can take X +derivative and lambda derivative that + + align:start position:0% +derivative and lambda derivative that + + + align:start position:0% +derivative and lambda derivative that +will give you n equations for the X's + + align:start position:0% +will give you n equations for the X's + + + align:start position:0% +will give you n equations for the X's +from this one from the X derivative and + + align:start position:0% +from this one from the X derivative and + + + align:start position:0% +from this one from the X derivative and +M equations from the lambda to + + align:start position:0% +M equations from the lambda to + + + align:start position:0% +M equations from the lambda to +it'll be n plus M it'll determine the + + align:start position:0% +it'll be n plus M it'll determine the + + + align:start position:0% +it'll be n plus M it'll determine the +good X and the lambda but I'm saying it + + align:start position:0% +good X and the lambda but I'm saying it + + + align:start position:0% +good X and the lambda but I'm saying it +that's all true and all important but + + align:start position:0% +that's all true and all important but + + + align:start position:0% +that's all true and all important but +I'm saying that the X and that pair X + + align:start position:0% +I'm saying that the X and that pair X + + + align:start position:0% +I'm saying that the X and that pair X +lambda will be a saddle point of this + + align:start position:0% +lambda will be a saddle point of this + + + align:start position:0% +lambda will be a saddle point of this +function this function has saddle points + + align:start position:0% +function this function has saddle points + + + align:start position:0% +function this function has saddle points +not not a maximum okay + + align:start position:0% +not not a maximum okay + + + align:start position:0% +not not a maximum okay +let's just take the derivatives and see + + align:start position:0% +let's just take the derivatives and see + + + align:start position:0% +let's just take the derivatives and see +what we get so the derivatives with + + align:start position:0% +what we get so the derivatives with + + + align:start position:0% +what we get so the derivatives with +respect to X D by DX I'm ex is now a + + align:start position:0% +respect to X D by DX I'm ex is now a + + + align:start position:0% +respect to X D by DX I'm ex is now a +vector so I really should say the + + align:start position:0% +vector so I really should say the + + + align:start position:0% +vector so I really should say the +gradient in the X direction I get I get + + align:start position:0% +gradient in the X direction I get I get + + + align:start position:0% +gradient in the X direction I get I get +SX and here the derivative of the spec + + align:start position:0% +SX and here the derivative of the spec + + + align:start position:0% +SX and here the derivative of the spec +2x what that's that is a transpose + + align:start position:0% +2x what that's that is a transpose + + + align:start position:0% +2x what that's that is a transpose +lambda because this is the dot product + + align:start position:0% +lambda because this is the dot product + + + align:start position:0% +lambda because this is the dot product +of a transpose lambda with X you you + + align:start position:0% +of a transpose lambda with X you you + + + align:start position:0% +of a transpose lambda with X you you +know I've put parentheses around it and + + align:start position:0% +know I've put parentheses around it and + + + align:start position:0% +know I've put parentheses around it and +followed the transpose rule so that's + + align:start position:0% +followed the transpose rule so that's + + + align:start position:0% +followed the transpose rule so that's +the dot product of a transpose lambda + + align:start position:0% +the dot product of a transpose lambda + + + align:start position:0% +the dot product of a transpose lambda +with X it's linear in X so it's + + align:start position:0% +with X it's linear in X so it's + + + align:start position:0% +with X it's linear in X so it's +derivative is just a transpose lambda + + align:start position:0% +derivative is just a transpose lambda + + + align:start position:0% +derivative is just a transpose lambda +and that's and now I take the other one + + align:start position:0% +and that's and now I take the other one + + + align:start position:0% +and that's and now I take the other one +the the lambda derivative the lambda + + align:start position:0% +the the lambda derivative the lambda + + + align:start position:0% +the the lambda derivative the lambda +derivative this doesn't depend on lambda + + align:start position:0% +derivative this doesn't depend on lambda + + + align:start position:0% +derivative this doesn't depend on lambda +the lambda derivative is just a X minus + + align:start position:0% +the lambda derivative is just a X minus + + + align:start position:0% +the lambda derivative is just a X minus +B it brings back the constraints so + + align:start position:0% +B it brings back the constraints so + + + align:start position:0% +B it brings back the constraints so +that's pretty simple no it doesn't even + + align:start position:0% +that's pretty simple no it doesn't even + + + align:start position:0% +that's pretty simple no it doesn't even +require much thought because you just + + align:start position:0% +require much thought because you just + + + align:start position:0% +require much thought because you just +know the constraints are coming back and + + align:start position:0% +know the constraints are coming back and + + + align:start position:0% +know the constraints are coming back and +of course B should be put over on this + + align:start position:0% +of course B should be put over on this + + + align:start position:0% +of course B should be put over on this +side because it's a constant so there we + + align:start position:0% +side because it's a constant so there we + + + align:start position:0% +side because it's a constant so there we +see to a block we see a important very + + align:start position:0% +see to a block we see a important very + + + align:start position:0% +see to a block we see a important very +important class of problems and the + + align:start position:0% +important class of problems and the + + + align:start position:0% +important class of problems and the +matrix we're seeing we could write this + + align:start position:0% +matrix we're seeing we could write this + + + align:start position:0% +matrix we're seeing we could write this +in block matrix form s minus a transpose + + align:start position:0% +in block matrix form s minus a transpose + + + align:start position:0% +in block matrix form s minus a transpose +oh I'm going to change that to a plus + + align:start position:0% +oh I'm going to change that to a plus + + + align:start position:0% +oh I'm going to change that to a plus +because I'm more of a plus person okay a + + align:start position:0% +because I'm more of a plus person okay a + + + align:start position:0% +because I'm more of a plus person okay a +transpose + + align:start position:0% +transpose + + + align:start position:0% +transpose +and a yeah yeah when I when I took the + + align:start position:0% +and a yeah yeah when I when I took the + + + align:start position:0% +and a yeah yeah when I when I took the +derivative this break the lambda I + + align:start position:0% +derivative this break the lambda I + + + align:start position:0% +derivative this break the lambda I +didn't put the minus sign in here and I + + align:start position:0% +didn't put the minus sign in here and I + + + align:start position:0% +didn't put the minus sign in here and I +didn't want to so let's make it a plus a + + align:start position:0% +didn't want to so let's make it a plus a + + + align:start position:0% +didn't want to so let's make it a plus a +and then there's no nothing there and + + align:start position:0% +and then there's no nothing there and + + + align:start position:0% +and then there's no nothing there and +the X and the lambda and the zero and + + align:start position:0% +the X and the lambda and the zero and + + + align:start position:0% +the X and the lambda and the zero and +the B that is the model of a constrained + + align:start position:0% +the B that is the model of a constrained + + + align:start position:0% +the B that is the model of a constrained +minimum a minimum problem with + + align:start position:0% +minimum a minimum problem with + + + align:start position:0% +minimum a minimum problem with +constraints it's a model because the + + align:start position:0% +constraints it's a model because the + + + align:start position:0% +constraints it's a model because the +function here is quadratic and the + + align:start position:0% +function here is quadratic and the + + + align:start position:0% +function here is quadratic and the +constraints are linear it's a you know + + align:start position:0% +constraints are linear it's a you know + + + align:start position:0% +constraints are linear it's a you know +it's in in course six it's everywhere + + align:start position:0% +it's in in course six it's everywhere + + + align:start position:0% +it's in in course six it's everywhere +constant constantly appearing as the + + align:start position:0% +constant constantly appearing as the + + + align:start position:0% +constant constantly appearing as the +simplest model okay and my point today + + align:start position:0% +simplest model okay and my point today + + + align:start position:0% +simplest model okay and my point today +is just that solution X lambda that that + + align:start position:0% +is just that solution X lambda that that + + + align:start position:0% +is just that solution X lambda that that +that total solution the the X together + + align:start position:0% +that total solution the the X together + + + align:start position:0% +that total solution the the X together +with a lambda that that is a saddle + + align:start position:0% +with a lambda that that is a saddle + + + align:start position:0% +with a lambda that that is a saddle +point of the lagrangian function l it's + + align:start position:0% +point of the lagrangian function l it's + + + align:start position:0% +point of the lagrangian function l it's +a saddle point not a minimum it's sort + + align:start position:0% +a saddle point not a minimum it's sort + + + align:start position:0% +a saddle point not a minimum it's sort +of a minimum in the X direction because + + align:start position:0% +of a minimum in the X direction because + + + align:start position:0% +of a minimum in the X direction because +this is positive definite that makes + + align:start position:0% +this is positive definite that makes + + + align:start position:0% +this is positive definite that makes +that makes that as a function of X it's + + align:start position:0% +that makes that as a function of X it's + + + align:start position:0% +that makes that as a function of X it's +going up but somehow the appearance of + + align:start position:0% +going up but somehow the appearance of + + + align:start position:0% +going up but somehow the appearance of +lambda makes this matrix indefinite it + + align:start position:0% +lambda makes this matrix indefinite it + + + align:start position:0% +lambda makes this matrix indefinite it +starts positive definite but it has this + + align:start position:0% +starts positive definite but it has this + + + align:start position:0% +starts positive definite but it has this +a transpose a and that zero + + align:start position:0% +a transpose a and that zero + + + align:start position:0% +a transpose a and that zero +it couldn't be Popeye look at that + + align:start position:0% +it couldn't be Popeye look at that + + + align:start position:0% +it couldn't be Popeye look at that +matrix I see it's not positive definite + + align:start position:0% +matrix I see it's not positive definite + + + align:start position:0% +matrix I see it's not positive definite +what do I see him why do I say that + + align:start position:0% +what do I see him why do I say that + + + align:start position:0% +what do I see him why do I say that +immediately when I look at that matrix + + align:start position:0% +immediately when I look at that matrix + + + align:start position:0% +immediately when I look at that matrix +it's not a positive definite matrix + + align:start position:0% +it's not a positive definite matrix + + + align:start position:0% +it's not a positive definite matrix +because when I see that zero on the + + align:start position:0% +because when I see that zero on the + + + align:start position:0% +because when I see that zero on the +diagonal that shoots positive definitely + + align:start position:0% +diagonal that shoots positive definitely + + + align:start position:0% +diagonal that shoots positive definitely +couldn't be take take as an example s + + align:start position:0% +couldn't be take take as an example s + + + align:start position:0% +couldn't be take take as an example s +equal three 1 and 1 0 take that matrix + + align:start position:0% +equal three 1 and 1 0 take that matrix + + + align:start position:0% +equal three 1 and 1 0 take that matrix +just random smell I made it to buy 2 + + align:start position:0% +just random smell I made it to buy 2 + + + align:start position:0% +just random smell I made it to buy 2 +instead of size n plus in do you see how + + align:start position:0% +instead of size n plus in do you see how + + + align:start position:0% +instead of size n plus in do you see how +do I know that the eigenvalues of that + + align:start position:0% +do I know that the eigenvalues of that + + + align:start position:0% +do I know that the eigenvalues of that +matrix one is plus and one is minus the + + align:start position:0% +matrix one is plus and one is minus the + + + align:start position:0% +matrix one is plus and one is minus the +determinant is negative so that tells me + + align:start position:0% +determinant is negative so that tells me + + + align:start position:0% +determinant is negative so that tells me +right away that one is plus and one is - + + align:start position:0% +right away that one is plus and one is - + + + align:start position:0% +right away that one is plus and one is - +thanks yes yes determinant is negative + + align:start position:0% +thanks yes yes determinant is negative + + + align:start position:0% +thanks yes yes determinant is negative +and somehow here the determinant is + + align:start position:0% +and somehow here the determinant is + + + align:start position:0% +and somehow here the determinant is +similar calculation would produce a + + align:start position:0% +similar calculation would produce a + + + align:start position:0% +similar calculation would produce a +transpose a or something with the - cuz + + align:start position:0% +transpose a or something with the - cuz + + + align:start position:0% +transpose a or something with the - cuz +I'm going this way well I could I could + + align:start position:0% +I'm going this way well I could I could + + + align:start position:0% +I'm going this way well I could I could +do better than that but you saw the + + align:start position:0% +do better than that but you saw the + + + align:start position:0% +do better than that but you saw the +point that that matrix that simple + + align:start position:0% +point that that matrix that simple + + + align:start position:0% +point that that matrix that simple +example of this is has eigenvalues are + + align:start position:0% +example of this is has eigenvalues are + + + align:start position:0% +example of this is has eigenvalues are +both signs let me just quickly say and + + align:start position:0% +both signs let me just quickly say and + + + align:start position:0% +both signs let me just quickly say and +I'll put it in the notes or in that + + align:start position:0% +I'll put it in the notes or in that + + + align:start position:0% +I'll put it in the notes or in that +chapter I guess it all this is coming is + + align:start position:0% +chapter I guess it all this is coming is + + + align:start position:0% +chapter I guess it all this is coming is +still 3.2 the that was originally 4.2 + + align:start position:0% +still 3.2 the that was originally 4.2 + + + align:start position:0% +still 3.2 the that was originally 4.2 +and and you'll see it so what do I want + + align:start position:0% +and and you'll see it so what do I want + + + align:start position:0% +and and you'll see it so what do I want +to say I'd like to say that that example + + align:start position:0% +to say I'd like to say that that example + + + align:start position:0% +to say I'd like to say that that example +is pretty convincing to me that that + + align:start position:0% +is pretty convincing to me that that + + + align:start position:0% +is pretty convincing to me that that +these KKT matrices if if you talk to + + align:start position:0% +these KKT matrices if if you talk to + + + align:start position:0% +these KKT matrices if if you talk to +people in in optimization that's kirusha + + align:start position:0% +people in in optimization that's kirusha + + + align:start position:0% +people in in optimization that's kirusha +kuhn and tucker three famous guys and + + align:start position:0% +kuhn and tucker three famous guys and + + + align:start position:0% +kuhn and tucker three famous guys and +these are the KKT conditions that that + + align:start position:0% +these are the KKT conditions that that + + + align:start position:0% +these are the KKT conditions that that +they derived following lagrosse right + + align:start position:0% +they derived following lagrosse right + + + align:start position:0% +they derived following lagrosse right +and my point is yeah and this is a + + align:start position:0% +and my point is yeah and this is a + + + align:start position:0% +and my point is yeah and this is a +typical sort so it's it's an indefinite + + align:start position:0% +typical sort so it's it's an indefinite + + + align:start position:0% +typical sort so it's it's an indefinite +matrix I believe it has that one if I do + + align:start position:0% +matrix I believe it has that one if I do + + + align:start position:0% +matrix I believe it has that one if I do +elimination yeah tell me this this is a + + align:start position:0% +elimination yeah tell me this this is a + + + align:start position:0% +elimination yeah tell me this this is a +good way to look at it suppose I do + + align:start position:0% +good way to look at it suppose I do + + + align:start position:0% +good way to look at it suppose I do +elimination on on this one or on this + + align:start position:0% +elimination on on this one or on this + + + align:start position:0% +elimination on on this one or on this +one well suppose + + align:start position:0% +one well suppose + + + align:start position:0% +one well suppose +I do elimination there what is the first + + align:start position:0% +I do elimination there what is the first + + + align:start position:0% +I do elimination there what is the first +pivot three positive so now let me turn + + align:start position:0% +pivot three positive so now let me turn + + + align:start position:0% +pivot three positive so now let me turn +down to here what if I do elimination on + + align:start position:0% +down to here what if I do elimination on + + + align:start position:0% +down to here what if I do elimination on +this block matrix then I start up here + + align:start position:0% +this block matrix then I start up here + + + align:start position:0% +this block matrix then I start up here +and I and that first pivot is positive + + align:start position:0% +and I and that first pivot is positive + + + align:start position:0% +and I and that first pivot is positive +again right this is s is a positive + + align:start position:0% +again right this is s is a positive + + + align:start position:0% +again right this is s is a positive +definite matrix don't forget + + align:start position:0% +definite matrix don't forget + + + align:start position:0% +definite matrix don't forget +in fact the first n pivots will all be + + align:start position:0% +in fact the first n pivots will all be + + + align:start position:0% +in fact the first n pivots will all be +positive because the first and pivot + + align:start position:0% +positive because the first and pivot + + + align:start position:0% +positive because the first and pivot +search you're working away in this + + align:start position:0% +search you're working away in this + + + align:start position:0% +search you're working away in this +corner and if you only if you're only + + align:start position:0% +corner and if you only if you're only + + + align:start position:0% +corner and if you only if you're only +thinking about the first n this corner + + align:start position:0% +thinking about the first n this corner + + + align:start position:0% +thinking about the first n this corner +is size n by n then you you don't even + + align:start position:0% +is size n by n then you you don't even + + + align:start position:0% +is size n by n then you you don't even +see a you're doing some subtractions and + + align:start position:0% +see a you're doing some subtractions and + + + align:start position:0% +see a you're doing some subtractions and +I'll do those but the pivots themselves + + align:start position:0% +I'll do those but the pivots themselves + + + align:start position:0% +I'll do those but the pivots themselves +are coming all coming from s and S is + + align:start position:0% +are coming all coming from s and S is + + + align:start position:0% +are coming all coming from s and S is +positive definite so we know that one of + + align:start position:0% +positive definite so we know that one of + + + align:start position:0% +positive definite so we know that one of +the tests for a positive definite matrix + + align:start position:0% +the tests for a positive definite matrix + + + align:start position:0% +the tests for a positive definite matrix +is all pivots are positive so I think + + align:start position:0% +is all pivots are positive so I think + + + align:start position:0% +is all pivots are positive so I think +all n of the first pivots will be + + align:start position:0% +all n of the first pivots will be + + + align:start position:0% +all n of the first pivots will be +positive and and when we use them let's + + align:start position:0% +positive and and when we use them let's + + + align:start position:0% +positive and and when we use them let's +just see what happens when we use them + + align:start position:0% +just see what happens when we use them + + + align:start position:0% +just see what happens when we use them +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +so so here's the KKT matrix that I start + + align:start position:0% +so so here's the KKT matrix that I start + + + align:start position:0% +so so here's the KKT matrix that I start +with and what do I end up with well + + align:start position:0% +with and what do I end up with well + + + align:start position:0% +with and what do I end up with well +really what I'm doing is I'm multiplying + + align:start position:0% +really what I'm doing is I'm multiplying + + + align:start position:0% +really what I'm doing is I'm multiplying +that block row by something to and + + align:start position:0% +that block row by something to and + + + align:start position:0% +that block row by something to and +subtracting to kill that a I'm so the + + align:start position:0% +subtracting to kill that a I'm so the + + + align:start position:0% +subtracting to kill that a I'm so the +these rows well near enough let me let + + align:start position:0% +these rows well near enough let me let + + + align:start position:0% +these rows well near enough let me let +me do block elimination block + + align:start position:0% +me do block elimination block + + + align:start position:0% +me do block elimination block +elimination is like easier I don't have + + align:start position:0% +elimination is like easier I don't have + + + align:start position:0% +elimination is like easier I don't have +to write down all little tiny numbers so + + align:start position:0% +to write down all little tiny numbers so + + + align:start position:0% +to write down all little tiny numbers so +I just want to multiply this row by + + align:start position:0% +I just want to multiply this row by + + + align:start position:0% +I just want to multiply this row by +something tell me what and subtract from + + align:start position:0% +something tell me what and subtract from + + + align:start position:0% +something tell me what and subtract from +this second row except I suppose there + + align:start position:0% +this second row except I suppose there + + + align:start position:0% +this second row except I suppose there +are numbers or letters I guess they are + + align:start position:0% +are numbers or letters I guess they are + + + align:start position:0% +are numbers or letters I guess they are +letters what do I multiply that first + + align:start position:0% +letters what do I multiply that first + + + align:start position:0% +letters what do I multiply that first +row by and subtract + + align:start position:0% + + + + align:start position:0% + +let's see if these were just little tiny + + align:start position:0% +let's see if these were just little tiny + + + align:start position:0% +let's see if these were just little tiny +numbers as like in 3 1 1 0 what do I + + align:start position:0% +numbers as like in 3 1 1 0 what do I + + + align:start position:0% +numbers as like in 3 1 1 0 what do I +multiply that row by and subtract from + + align:start position:0% +multiply that row by and subtract from + + + align:start position:0% +multiply that row by and subtract from +this I multiply by a / s right I do + + align:start position:0% +this I multiply by a / s right I do + + + align:start position:0% +this I multiply by a / s right I do +multiplied by a / s which puts an A + + align:start position:0% +multiplied by a / s which puts an A + + + align:start position:0% +multiplied by a / s which puts an A +there then I subtract so here I'll + + align:start position:0% +there then I subtract so here I'll + + + align:start position:0% +there then I subtract so here I'll +multiply by a / s but I these are + + align:start position:0% +multiply by a / s but I these are + + + align:start position:0% +multiply by a / s but I these are +matrices so while I multiply by s by a + + align:start position:0% +matrices so while I multiply by s by a + + + align:start position:0% +matrices so while I multiply by s by a +SN I'm multiplying by a s inverse times + + align:start position:0% +SN I'm multiplying by a s inverse times + + + align:start position:0% +SN I'm multiplying by a s inverse times +this s I get a and then I subtract and I + + align:start position:0% +this s I get a and then I subtract and I + + + align:start position:0% +this s I get a and then I subtract and I +get to 0 and when I multiply by this guy + + align:start position:0% +get to 0 and when I multiply by this guy + + + align:start position:0% +get to 0 and when I multiply by this guy +and subtract I get minus because I'm + + align:start position:0% +and subtract I get minus because I'm + + + align:start position:0% +and subtract I get minus because I'm +subtracting this thing - a s inverse a + + align:start position:0% +subtracting this thing - a s inverse a + + + align:start position:0% +subtracting this thing - a s inverse a +transpose that was block elimination + + align:start position:0% +transpose that was block elimination + + + align:start position:0% +transpose that was block elimination +which just in other words it's just I + + align:start position:0% +which just in other words it's just I + + + align:start position:0% +which just in other words it's just I +you've learned about 2 by 2 matrices you + + align:start position:0% +you've learned about 2 by 2 matrices you + + + align:start position:0% +you've learned about 2 by 2 matrices you +know 3x plus 4y equals 7 and stuff now + + align:start position:0% +know 3x plus 4y equals 7 and stuff now + + + align:start position:0% +know 3x plus 4y equals 7 and stuff now +I'm just doing it with with with blocks + + align:start position:0% +I'm just doing it with with with blocks + + + align:start position:0% +I'm just doing it with with with blocks +instead of single numbers but you see + + align:start position:0% +instead of single numbers but you see + + + align:start position:0% +instead of single numbers but you see +this produced those positive pivots and + + align:start position:0% +this produced those positive pivots and + + + align:start position:0% +this produced those positive pivots and +what can you tell me about that matrix + + align:start position:0% +what can you tell me about that matrix + + + align:start position:0% +what can you tell me about that matrix +what what kind of what can you tell me + + align:start position:0% +what what kind of what can you tell me + + + align:start position:0% +what what kind of what can you tell me +about the signs or the eigenvalues or + + align:start position:0% +about the signs or the eigenvalues or + + + align:start position:0% +about the signs or the eigenvalues or +whatever of this matrix suppose this was + + align:start position:0% +whatever of this matrix suppose this was + + + align:start position:0% +whatever of this matrix suppose this was +the identity what could you tell me + + align:start position:0% +the identity what could you tell me + + + align:start position:0% +the identity what could you tell me +about - a a transpose + + align:start position:0% +about - a a transpose + + + align:start position:0% +about - a a transpose +- a a transpose a my voice should + + align:start position:0% +- a a transpose a my voice should + + + align:start position:0% +- a a transpose a my voice should +emphasize that - it's that matrix there + + align:start position:0% +emphasize that - it's that matrix there + + + align:start position:0% +emphasize that - it's that matrix there +is negative definite so although the + + align:start position:0% +is negative definite so although the + + + align:start position:0% +is negative definite so although the +next set of mm pivots that come from + + align:start position:0% +next set of mm pivots that come from + + + align:start position:0% +next set of mm pivots that come from +here we'll all be negative so I get M + + align:start position:0% +here we'll all be negative so I get M + + + align:start position:0% +here we'll all be negative so I get M +rather n n+ + n- pivots + + align:start position:0% +rather n n+ + n- pivots + + + align:start position:0% +rather n n+ + n- pivots +and and then I remember that the pivots + + align:start position:0% +and and then I remember that the pivots + + + align:start position:0% +and and then I remember that the pivots +actually have the same sign as the + + align:start position:0% +actually have the same sign as the + + + align:start position:0% +actually have the same sign as the +eigenvalues that's just a beautiful fact + + align:start position:0% +eigenvalues that's just a beautiful fact + + + align:start position:0% +eigenvalues that's just a beautiful fact +we know that for for positive definite + + align:start position:0% +we know that for for positive definite + + + align:start position:0% +we know that for for positive definite +ones the eigenvalues are all positive + + align:start position:0% +ones the eigenvalues are all positive + + + align:start position:0% +ones the eigenvalues are all positive +the pivots are all positive but it's + + align:start position:0% +the pivots are all positive but it's + + + align:start position:0% +the pivots are all positive but it's +even better than that that if we have + + align:start position:0% +even better than that that if we have + + + align:start position:0% +even better than that that if we have +some mixture for the signs of the pivots + + align:start position:0% +some mixture for the signs of the pivots + + + align:start position:0% +some mixture for the signs of the pivots +that tells us the signs of the + + align:start position:0% +that tells us the signs of the + + + align:start position:0% +that tells us the signs of the +eigenvalues that's really neat fact so + + align:start position:0% +eigenvalues that's really neat fact so + + + align:start position:0% +eigenvalues that's really neat fact so +I'll just write that down signs plus and + + align:start position:0% +I'll just write that down signs plus and + + + align:start position:0% +I'll just write that down signs plus and +minus signs of pivots give us the plus + + align:start position:0% +minus signs of pivots give us the plus + + + align:start position:0% +minus signs of pivots give us the plus +or minus signs of the I ganache + + align:start position:0% +or minus signs of the I ganache + + + align:start position:0% +or minus signs of the I ganache +so I've sneaked sneaked in a nice matrix + + align:start position:0% +so I've sneaked sneaked in a nice matrix + + + align:start position:0% +so I've sneaked sneaked in a nice matrix +theorem that prefer for symmetric + + align:start position:0% +theorem that prefer for symmetric + + + align:start position:0% +theorem that prefer for symmetric +matrices this is symmetric matrices okay + + align:start position:0% + + + + align:start position:0% + +that's what I wanted to say about + + align:start position:0% + + + + align:start position:0% + +constraints and saddle points coming + + align:start position:0% +constraints and saddle points coming + + + align:start position:0% +constraints and saddle points coming +from there and then I want to say + + align:start position:0% +from there and then I want to say + + + align:start position:0% +from there and then I want to say +something about constraints and not + + align:start position:0% +something about constraints and not + + + align:start position:0% +something about constraints and not +constraints now I'm going to look at the + + align:start position:0% +constraints now I'm going to look at the + + + align:start position:0% +constraints now I'm going to look at the +second source of of saddle points so + + align:start position:0% +second source of of saddle points so + + + align:start position:0% +second source of of saddle points so +these are the saddles from this + + align:start position:0% +these are the saddles from this + + + align:start position:0% +these are the saddles from this +remarkable function that we know so I + + align:start position:0% +remarkable function that we know so I + + + align:start position:0% +remarkable function that we know so I +now have a symmetric matrix S could be + + align:start position:0% +now have a symmetric matrix S could be + + + align:start position:0% +now have a symmetric matrix S could be +even positive definite usually it is + + align:start position:0% +even positive definite usually it is + + + align:start position:0% +even positive definite usually it is +here do you know what the name for R is + + align:start position:0% +here do you know what the name for R is + + + align:start position:0% +here do you know what the name for R is +it's a ratio or a quotient it's named + + align:start position:0% +it's a ratio or a quotient it's named + + + align:start position:0% +it's a ratio or a quotient it's named +after somebody starting with our who's + + align:start position:0% +after somebody starting with our who's + + + align:start position:0% +after somebody starting with our who's +that really right it's a Rayleigh + + align:start position:0% +that really right it's a Rayleigh + + + align:start position:0% +that really right it's a Rayleigh +quotient + + align:start position:0% + + + + align:start position:0% + +and what is the largest value possible + + align:start position:0% +and what is the largest value possible + + + align:start position:0% +and what is the largest value possible +value of the Rayleigh quotient we've + + align:start position:0% +value of the Rayleigh quotient we've + + + align:start position:0% +value of the Rayleigh quotient we've +seen this idea it is the maximum value + + align:start position:0% +seen this idea it is the maximum value + + + align:start position:0% +seen this idea it is the maximum value +of that Rayleigh quotient of that ratio + + align:start position:0% +of that Rayleigh quotient of that ratio + + + align:start position:0% +of that Rayleigh quotient of that ratio +is is lambda max right lambda one the + + align:start position:0% +is is lambda max right lambda one the + + + align:start position:0% +is is lambda max right lambda one the +biggest one and the exit does it is the + + align:start position:0% +biggest one and the exit does it is the + + + align:start position:0% +biggest one and the exit does it is the +eigenvector right so max is is lambda 1 + + align:start position:0% +eigenvector right so max is is lambda 1 + + + align:start position:0% +eigenvector right so max is is lambda 1 +and at X equal Q because Q 1 transpose s + + align:start position:0% +and at X equal Q because Q 1 transpose s + + + align:start position:0% +and at X equal Q because Q 1 transpose s +Q 1 over Q 1 transpose Q 1 so I'm + + align:start position:0% +Q 1 over Q 1 transpose Q 1 so I'm + + + align:start position:0% +Q 1 over Q 1 transpose Q 1 so I'm +plugging in this winner and s Q 1 is + + align:start position:0% +plugging in this winner and s Q 1 is + + + align:start position:0% +plugging in this winner and s Q 1 is +lambda 1 Q 1 right it's the first + + align:start position:0% +lambda 1 Q 1 right it's the first + + + align:start position:0% +lambda 1 Q 1 right it's the first +eigenvector and so a lambda 1 comes out + + align:start position:0% +eigenvector and so a lambda 1 comes out + + + align:start position:0% +eigenvector and so a lambda 1 comes out +so I get lambda 1 I know everything + + align:start position:0% +so I get lambda 1 I know everything + + + align:start position:0% +so I get lambda 1 I know everything +about that and what I know is if I put + + align:start position:0% +about that and what I know is if I put + + + align:start position:0% +about that and what I know is if I put +in any X where do I know if I put in any + + align:start position:0% +in any X where do I know if I put in any + + + align:start position:0% +in any X where do I know if I put in any +X whatever and look at this number what + + align:start position:0% +X whatever and look at this number what + + + align:start position:0% +X whatever and look at this number what +do I know about that number it's smaller + + align:start position:0% +do I know about that number it's smaller + + + align:start position:0% +do I know about that number it's smaller +than lambda 1 or it might hit lambda 1 + + align:start position:0% +than lambda 1 or it might hit lambda 1 + + + align:start position:0% +than lambda 1 or it might hit lambda 1 +but it's not bigger that's why Maxima + + align:start position:0% +but it's not bigger that's why Maxima + + + align:start position:0% +but it's not bigger that's why Maxima +are easy you put in any vector and you + + align:start position:0% +are easy you put in any vector and you + + + align:start position:0% +are easy you put in any vector and you +know what's happening you know it + + align:start position:0% +know what's happening you know it + + + align:start position:0% +know what's happening you know it +doesn't it's it's not above the max + + align:start position:0% +doesn't it's it's not above the max + + + align:start position:0% +doesn't it's it's not above the max +obviously and what about the min what's + + align:start position:0% +obviously and what about the min what's + + + align:start position:0% +obviously and what about the min what's +that's equally simple of course it's at + + align:start position:0% +that's equally simple of course it's at + + + align:start position:0% +that's equally simple of course it's at +the bottom so what would be the minimum + + align:start position:0% +the bottom so what would be the minimum + + + align:start position:0% +the bottom so what would be the minimum +of that really of that quotient if I was + + align:start position:0% +of that really of that quotient if I was + + + align:start position:0% +of that really of that quotient if I was +looking for + + align:start position:0% +looking for + + + align:start position:0% +looking for +what eigen vector and eigen value will I + + align:start position:0% +what eigen vector and eigen value will I + + + align:start position:0% +what eigen vector and eigen value will I +find when I look at the bottom of this I + + align:start position:0% +find when I look at the bottom of this I + + + align:start position:0% +find when I look at the bottom of this I +will find lambda and the last guy lambda + + align:start position:0% +will find lambda and the last guy lambda + + + align:start position:0% +will find lambda and the last guy lambda +min + + align:start position:0% + + + + align:start position:0% + +and the I think where the X will be its + + align:start position:0% +and the I think where the X will be its + + + align:start position:0% +and the I think where the X will be its +eigenvector and again this stuff will + + align:start position:0% +eigenvector and again this stuff will + + + align:start position:0% +eigenvector and again this stuff will +equal lambda n so that's easy I know + + align:start position:0% +equal lambda n so that's easy I know + + + align:start position:0% +equal lambda n so that's easy I know +that if I put in any vector whatever + + align:start position:0% + + + + align:start position:0% + +just choose any vector in n dimensions + + align:start position:0% +just choose any vector in n dimensions + + + align:start position:0% +just choose any vector in n dimensions +and compute R of X what do I now also + + align:start position:0% +and compute R of X what do I now also + + + align:start position:0% +and compute R of X what do I now also +know about our that our of that vector + + align:start position:0% +know about our that our of that vector + + + align:start position:0% +know about our that our of that vector +it's greater than lambda and below the + + align:start position:0% +it's greater than lambda and below the + + + align:start position:0% +it's greater than lambda and below the +max above the men but now if I put in + + align:start position:0% +max above the men but now if I put in + + + align:start position:0% +max above the men but now if I put in +now what about the other lambdas well + + align:start position:0% +now what about the other lambdas well + + + align:start position:0% +now what about the other lambdas well +the point is that those are saddle + + align:start position:0% +the point is that those are saddle + + + align:start position:0% +the point is that those are saddle +points the beautiful thing about this + + align:start position:0% +points the beautiful thing about this + + + align:start position:0% +points the beautiful thing about this +Rayleigh quotient is its derivative + + align:start position:0% +Rayleigh quotient is its derivative + + + align:start position:0% +Rayleigh quotient is its derivative +equals 0 right at the saddle point at T + + align:start position:0% +equals 0 right at the saddle point at T + + + align:start position:0% +equals 0 right at the saddle point at T +at the eigenvectors and and its value at + + align:start position:0% +at the eigenvectors and and its value at + + + align:start position:0% +at the eigenvectors and and its value at +the eigenvectors is the eigenvalue so so + + align:start position:0% +the eigenvectors is the eigenvalue so so + + + align:start position:0% +the eigenvectors is the eigenvalue so so +i have you see what i'm saying i have + + align:start position:0% +i have you see what i'm saying i have + + + align:start position:0% +i have you see what i'm saying i have +lambda 1 here a max lambda and here a + + align:start position:0% +lambda 1 here a max lambda and here a + + + align:start position:0% +lambda 1 here a max lambda and here a +min and in between i have a bunch of + + align:start position:0% +min and in between i have a bunch of + + + align:start position:0% +min and in between i have a bunch of +other lambdas which are saddle points + + align:start position:0% +other lambdas which are saddle points + + + align:start position:0% +other lambdas which are saddle points +and if i put an x in to the 2 r of x and + + align:start position:0% +and if i put an x in to the 2 r of x and + + + align:start position:0% +and if i put an x in to the 2 r of x and +look to see what happens i have no idea + + align:start position:0% +look to see what happens i have no idea + + + align:start position:0% +look to see what happens i have no idea +whether I'm on this side the below it or + + align:start position:0% +whether I'm on this side the below it or + + + align:start position:0% +whether I'm on this side the below it or +this side above lambda I so the saddle + + align:start position:0% +this side above lambda I so the saddle + + + align:start position:0% +this side above lambda I so the saddle +points are more difficult and take a + + align:start position:0% +points are more difficult and take a + + + align:start position:0% +points are more difficult and take a +little more patience so that's the other + + align:start position:0% +little more patience so that's the other + + + align:start position:0% +little more patience so that's the other +source of saddle points and I so these + + align:start position:0% +source of saddle points and I so these + + + align:start position:0% +source of saddle points and I so these +are so let me just emphasize again what + + align:start position:0% +are so let me just emphasize again what + + + align:start position:0% +are so let me just emphasize again what +I'm saying at lambda at X equal Q K I + + align:start position:0% +I'm saying at lambda at X equal Q K I + + + align:start position:0% +I'm saying at lambda at X equal Q K I +have some number the + + align:start position:0% +have some number the + + + align:start position:0% +have some number the +our ex has some number of positive + + align:start position:0% +our ex has some number of positive + + + align:start position:0% +our ex has some number of positive +eigenvalues and some number of negative + + align:start position:0% +eigenvalues and some number of negative + + + align:start position:0% +eigenvalues and some number of negative +ones for the things above and below QK + + align:start position:0% +ones for the things above and below QK + + + align:start position:0% +ones for the things above and below QK +okay I've run out of time to to follow + + align:start position:0% +okay I've run out of time to to follow + + + align:start position:0% +okay I've run out of time to to follow +up on the saddle point part of that on + + align:start position:0% +up on the saddle point part of that on + + + align:start position:0% +up on the saddle point part of that on +the details of this picture I might + + align:start position:0% +the details of this picture I might + + + align:start position:0% +the details of this picture I might +that'll be in the notes and I might come + + align:start position:0% +that'll be in the notes and I might come + + + align:start position:0% +that'll be in the notes and I might come +back to it at the very start of next + + align:start position:0% +back to it at the very start of next + + + align:start position:0% +back to it at the very start of next +time but I will before that you will + + align:start position:0% +time but I will before that you will + + + align:start position:0% +time but I will before that you will +have the lab number three and then I + + align:start position:0% +have the lab number three and then I + + + align:start position:0% +have the lab number three and then I +think we should discuss it because I + + align:start position:0% +think we should discuss it because I + + + align:start position:0% +think we should discuss it because I +haven't done this lab it's it's intended + + align:start position:0% +haven't done this lab it's it's intended + + + align:start position:0% +haven't done this lab it's it's intended +to give you some feeling for overfitting + + align:start position:0% +to give you some feeling for overfitting + + + align:start position:0% +to give you some feeling for overfitting +and also intended to give you a little + + align:start position:0% +and also intended to give you a little + + + align:start position:0% +and also intended to give you a little +introduction to deep learning and so + + align:start position:0% +introduction to deep learning and so + + + align:start position:0% +introduction to deep learning and so +I'll get it to you and we can talk about + + align:start position:0% +I'll get it to you and we can talk about + + + align:start position:0% +I'll get it to you and we can talk about +it Wednesday and again it won't be due + + align:start position:0% +it Wednesday and again it won't be due + + + align:start position:0% +it Wednesday and again it won't be due +until the Wednesday after break okay + + align:start position:0% +until the Wednesday after break okay + + + align:start position:0% +until the Wednesday after break okay +thanks so I'll see you Wednesday \ No newline at end of file diff --git a/xrypSZU8cBE.txt b/xrypSZU8cBE.txt new file mode 100644 index 0000000000000000000000000000000000000000..68af65d4d4c9b5637212f42263ffba0b3bc261cf --- /dev/null +++ b/xrypSZU8cBE.txt @@ -0,0 +1,8107 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common license. Your support + + align:start position:0% +a Creative Common license. Your support + + + align:start position:0% +a Creative Common license. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or to view additional materials from + + align:start position:0% +or to view additional materials from + + + align:start position:0% +or to view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +Okay, so today we have a new topic and + + align:start position:0% +Okay, so today we have a new topic and + + + align:start position:0% +Okay, so today we have a new topic and +we're going to start to learn about + + align:start position:0% +we're going to start to learn about + + + align:start position:0% +we're going to start to learn about +vector fields + + align:start position:0% +vector fields + + + align:start position:0% +vector fields +and line integrals. + + align:start position:0% +and line integrals. + + + align:start position:0% +and line integrals. +So + + align:start position:0% + + + + align:start position:0% + +last week we've been doing double + + align:start position:0% +last week we've been doing double + + + align:start position:0% +last week we've been doing double +integrals. For today we just forget all + + align:start position:0% +integrals. For today we just forget all + + + align:start position:0% +integrals. For today we just forget all +of that. But don't actually forget it, + + align:start position:0% +of that. But don't actually forget it, + + + align:start position:0% +of that. But don't actually forget it, +you know, put it away in a corner of + + align:start position:0% +you know, put it away in a corner of + + + align:start position:0% +you know, put it away in a corner of +your mind. It's going to come back next + + align:start position:0% +your mind. It's going to come back next + + + align:start position:0% +your mind. It's going to come back next +week. But what we do today, we're going + + align:start position:0% +week. But what we do today, we're going + + + align:start position:0% +week. But what we do today, we're going +to do line integrals. And these are + + align:start position:0% +to do line integrals. And these are + + + align:start position:0% +to do line integrals. And these are +completely different things. So it helps + + align:start position:0% +completely different things. So it helps + + + align:start position:0% +completely different things. So it helps +actually if you don't think of double + + align:start position:0% +actually if you don't think of double + + + align:start position:0% +actually if you don't think of double +integrals at all while doing line + + align:start position:0% +integrals at all while doing line + + + align:start position:0% +integrals at all while doing line +integrals. + + align:start position:0% +integrals. + + + align:start position:0% +integrals. +So anyway, let's start with vector + + align:start position:0% +So anyway, let's start with vector + + + align:start position:0% +So anyway, let's start with vector +fields. So what's a vector field? + + align:start position:0% +fields. So what's a vector field? + + + align:start position:0% +fields. So what's a vector field? +Well, a vector field is something that's + + align:start position:0% +Well, a vector field is something that's + + + align:start position:0% +Well, a vector field is something that's +of a form + + align:start position:0% +of a form + + + align:start position:0% +of a form +well it's a vector but where m and n the + + align:start position:0% +well it's a vector but where m and n the + + + align:start position:0% +well it's a vector but where m and n the +components + + align:start position:0% + + + + align:start position:0% + +actually depend on x and y on the point + + align:start position:0% +actually depend on x and y on the point + + + align:start position:0% +actually depend on x and y on the point +where you are. So they are functions + + align:start position:0% + + + + align:start position:0% + +of x and y. + + align:start position:0% +of x and y. + + + align:start position:0% +of x and y. +So what that means concretely is that at + + align:start position:0% +So what that means concretely is that at + + + align:start position:0% +So what that means concretely is that at +any point in at every point in the plane + + align:start position:0% +any point in at every point in the plane + + + align:start position:0% +any point in at every point in the plane +you have a vector. Okay. So in a corn + + align:start position:0% +you have a vector. Okay. So in a corn + + + align:start position:0% +you have a vector. Okay. So in a corn +field at everywhere you have corn in a + + align:start position:0% +field at everywhere you have corn in a + + + align:start position:0% +field at everywhere you have corn in a +vector field everywhere you have a + + align:start position:0% +vector field everywhere you have a + + + align:start position:0% +vector field everywhere you have a +vector. + + align:start position:0% +vector. + + + align:start position:0% +vector. +That's how it works. Okay. So + + align:start position:0% +That's how it works. Okay. So + + + align:start position:0% +That's how it works. Okay. So +a good example of a vector field. I + + align:start position:0% +a good example of a vector field. I + + + align:start position:0% +a good example of a vector field. I +don't know if you've seen these maps + + align:start position:0% +don't know if you've seen these maps + + + align:start position:0% +don't know if you've seen these maps +that show the wind + + align:start position:0% +that show the wind + + + align:start position:0% +that show the wind +but so here's some cool images done by + + align:start position:0% +but so here's some cool images done by + + + align:start position:0% +but so here's some cool images done by +NAZA. So, actually that's + + align:start position:0% +NAZA. So, actually that's + + + align:start position:0% +NAZA. So, actually that's +that's a picture of the wind patterns um + + align:start position:0% +that's a picture of the wind patterns um + + + align:start position:0% +that's a picture of the wind patterns um +of the coast of California with Santa + + align:start position:0% +of the coast of California with Santa + + + align:start position:0% +of the coast of California with Santa +Ana winds in case you're wondering + + align:start position:0% +Ana winds in case you're wondering + + + align:start position:0% +Ana winds in case you're wondering +what's been going on recently. Uh so you + + align:start position:0% +what's been going on recently. Uh so you + + + align:start position:0% +what's been going on recently. Uh so you +have all of these vectors that show you + + align:start position:0% +have all of these vectors that show you + + + align:start position:0% +have all of these vectors that show you +the velocity of the air + + align:start position:0% +the velocity of the air + + + align:start position:0% +the velocity of the air +basically at every point. I mean, of + + align:start position:0% +basically at every point. I mean, of + + + align:start position:0% +basically at every point. I mean, of +course, you don't draw it at every point + + align:start position:0% +course, you don't draw it at every point + + + align:start position:0% +course, you don't draw it at every point +because, you know, if you draw a vector + + align:start position:0% +because, you know, if you draw a vector + + + align:start position:0% +because, you know, if you draw a vector +at absolutely all the points of a plane, + + align:start position:0% +at absolutely all the points of a plane, + + + align:start position:0% +at absolutely all the points of a plane, +then you just fill up everything and you + + align:start position:0% +then you just fill up everything and you + + + align:start position:0% +then you just fill up everything and you +wouldn't see anything. So you just, you + + align:start position:0% +wouldn't see anything. So you just, you + + + align:start position:0% +wouldn't see anything. So you just, you +know, choose points and you draw the + + align:start position:0% +know, choose points and you draw the + + + align:start position:0% +know, choose points and you draw the +vectors at those points. So here's + + align:start position:0% +vectors at those points. So here's + + + align:start position:0% +vectors at those points. So here's +another cool image of upside down. + + align:start position:0% +another cool image of upside down. + + + align:start position:0% +another cool image of upside down. +That's a hurricane of the coast of + + align:start position:0% +That's a hurricane of the coast of + + + align:start position:0% +That's a hurricane of the coast of +Mexico with the winds spiraling around + + align:start position:0% +Mexico with the winds spiraling around + + + align:start position:0% +Mexico with the winds spiraling around +the hurricane. + + align:start position:0% +the hurricane. + + + align:start position:0% +the hurricane. +So + + align:start position:0% +So + + + align:start position:0% +So +anyway, it's kind of hard to see, you + + align:start position:0% +anyway, it's kind of hard to see, you + + + align:start position:0% +anyway, it's kind of hard to see, you +know, you don't really see all the + + align:start position:0% +know, you don't really see all the + + + align:start position:0% +know, you don't really see all the +vectors. Actually, I guess the autofocus + + align:start position:0% +vectors. Actually, I guess the autofocus + + + align:start position:0% +vectors. Actually, I guess the autofocus +is having trouble with it. + + align:start position:0% + + + + align:start position:0% + +Yeah, I can't really do it. So, I guess + + align:start position:0% +Yeah, I can't really do it. So, I guess + + + align:start position:0% +Yeah, I can't really do it. So, I guess +I'll go back to the previous one. + + align:start position:0% +I'll go back to the previous one. + + + align:start position:0% +I'll go back to the previous one. +But, um, + + align:start position:0% + + + + align:start position:0% + +okay. + + align:start position:0% +okay. + + + align:start position:0% +okay. +So, anyway, a vector field + + align:start position:0% +So, anyway, a vector field + + + align:start position:0% +So, anyway, a vector field +is something where at each point + + align:start position:0% + + + + align:start position:0% + +In the plane we have + + align:start position:0% +In the plane we have + + + align:start position:0% +In the plane we have +a vector f + + align:start position:0% + + + + align:start position:0% + +that depends on x and y. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% +So + + + align:start position:0% +So +this occurs in real life when you look + + align:start position:0% +this occurs in real life when you look + + + align:start position:0% +this occurs in real life when you look +at velocity fields in a fluid. For + + align:start position:0% +at velocity fields in a fluid. For + + + align:start position:0% +at velocity fields in a fluid. For +example, the wind. That's what these + + align:start position:0% +example, the wind. That's what these + + + align:start position:0% +example, the wind. That's what these +pictures show. You know, at every point + + align:start position:0% +pictures show. You know, at every point + + + align:start position:0% +pictures show. You know, at every point +you have a velocity of a fluid that's + + align:start position:0% +you have a velocity of a fluid that's + + + align:start position:0% +you have a velocity of a fluid that's +moving. Another example is force fields. + + align:start position:0% +moving. Another example is force fields. + + + align:start position:0% +moving. Another example is force fields. +So now force fields are not something + + align:start position:0% +So now force fields are not something + + + align:start position:0% +So now force fields are not something +out of Star Wars. Okay? It's just you + + align:start position:0% +out of Star Wars. Okay? It's just you + + + align:start position:0% +out of Star Wars. Okay? It's just you +know if you look at gravitational + + align:start position:0% +know if you look at gravitational + + + align:start position:0% +know if you look at gravitational +attraction you know you know that if you + + align:start position:0% +attraction you know you know that if you + + + align:start position:0% +attraction you know you know that if you +have a mass somewhere well it will be + + align:start position:0% +have a mass somewhere well it will be + + + align:start position:0% +have a mass somewhere well it will be +attracted to fall down because of a + + align:start position:0% +attracted to fall down because of a + + + align:start position:0% +attracted to fall down because of a +gravity field of the earth which means + + align:start position:0% +gravity field of the earth which means + + + align:start position:0% +gravity field of the earth which means +that at every point you have a vector + + align:start position:0% +that at every point you have a vector + + + align:start position:0% +that at every point you have a vector +that's pointing down and same thing in + + align:start position:0% +that's pointing down and same thing in + + + align:start position:0% +that's pointing down and same thing in +space you have the gravitational field + + align:start position:0% +space you have the gravitational field + + + align:start position:0% +space you have the gravitational field +of planets stars and so on. So that's + + align:start position:0% +of planets stars and so on. So that's + + + align:start position:0% +of planets stars and so on. So that's +also an example of a vector field + + align:start position:0% +also an example of a vector field + + + align:start position:0% +also an example of a vector field +because wherever you go you would have + + align:start position:0% +because wherever you go you would have + + + align:start position:0% +because wherever you go you would have +that vector and what it is depends on + + align:start position:0% +that vector and what it is depends on + + + align:start position:0% +that vector and what it is depends on +where you are. + + align:start position:0% +where you are. + + + align:start position:0% +where you are. +So the examples from the real world + + align:start position:0% +So the examples from the real world + + + align:start position:0% +So the examples from the real world +are things like velocity + + align:start position:0% +are things like velocity + + + align:start position:0% +are things like velocity +in a fluid + + align:start position:0% + + + + align:start position:0% + +or + + align:start position:0% +or + + + align:start position:0% +or +force field + + align:start position:0% + + + + align:start position:0% + +where you have a force that depends on + + align:start position:0% +where you have a force that depends on + + + align:start position:0% +where you have a force that depends on +the point where you are. So we're going + + align:start position:0% +the point where you are. So we're going + + + align:start position:0% +the point where you are. So we're going +to try to study vector fields + + align:start position:0% +to try to study vector fields + + + align:start position:0% +to try to study vector fields +mathematically. So we won't really care + + align:start position:0% +mathematically. So we won't really care + + + align:start position:0% +mathematically. So we won't really care +what they are most of the time. But as + + align:start position:0% +what they are most of the time. But as + + + align:start position:0% +what they are most of the time. But as +we'll explore with them define + + align:start position:0% +we'll explore with them define + + + align:start position:0% +we'll explore with them define +quantities and so on, we'll very often + + align:start position:0% +quantities and so on, we'll very often + + + align:start position:0% +quantities and so on, we'll very often +use these motivations to justify why we + + align:start position:0% +use these motivations to justify why we + + + align:start position:0% +use these motivations to justify why we +would care about certain quantities. + + align:start position:0% +would care about certain quantities. + + + align:start position:0% +would care about certain quantities. +Okay, so the first thing we have to + + align:start position:0% +Okay, so the first thing we have to + + + align:start position:0% +Okay, so the first thing we have to +figure out is how do we draw a vector + + align:start position:0% +figure out is how do we draw a vector + + + align:start position:0% +figure out is how do we draw a vector +field? You know, how do you generate a + + align:start position:0% +field? You know, how do you generate a + + + align:start position:0% +field? You know, how do you generate a +plot like that? + + align:start position:0% +plot like that? + + + align:start position:0% +plot like that? +So + + align:start position:0% + + + + align:start position:0% + +let's practice drawing a few vector + + align:start position:0% +let's practice drawing a few vector + + + align:start position:0% +let's practice drawing a few vector +fields. Well, + + align:start position:0% +fields. Well, + + + align:start position:0% +fields. Well, +let's start with let's say our very + + align:start position:0% +let's start with let's say our very + + + align:start position:0% +let's start with let's say our very +first vector field will be just 2 I + J. + + align:start position:0% +first vector field will be just 2 I + J. + + + align:start position:0% +first vector field will be just 2 I + J. +So it's kind of a silly vector field + + align:start position:0% +So it's kind of a silly vector field + + + align:start position:0% +So it's kind of a silly vector field +because it doesn't actually depend on X + + align:start position:0% +because it doesn't actually depend on X + + + align:start position:0% +because it doesn't actually depend on X +and Y. So that means it's the same + + align:start position:0% +and Y. So that means it's the same + + + align:start position:0% +and Y. So that means it's the same +vector everywhere. + + align:start position:0% +vector everywhere. + + + align:start position:0% +vector everywhere. +Okay. So + + align:start position:0% +Okay. So + + + align:start position:0% +Okay. So +I take picture of a plane and I take the + + align:start position:0% +I take picture of a plane and I take the + + + align:start position:0% +I take picture of a plane and I take the +vector 2 comma 1. I guess it points in + + align:start position:0% +vector 2 comma 1. I guess it points in + + + align:start position:0% +vector 2 comma 1. I guess it points in +that direction. It's two units to the + + align:start position:0% +that direction. It's two units to the + + + align:start position:0% +that direction. It's two units to the +right, one up. And I just put that + + align:start position:0% +right, one up. And I just put that + + + align:start position:0% +right, one up. And I just put that +vector everywhere. + + align:start position:0% +vector everywhere. + + + align:start position:0% +vector everywhere. +Okay. So you know, + + align:start position:0% +Okay. So you know, + + + align:start position:0% +Okay. So you know, +you just put it at a few points all over + + align:start position:0% +you just put it at a few points all over + + + align:start position:0% +you just put it at a few points all over +the place and when you think you have + + align:start position:0% +the place and when you think you have + + + align:start position:0% +the place and when you think you have +enough so that you understand what's + + align:start position:0% +enough so that you understand what's + + + align:start position:0% +enough so that you understand what's +going on, then you stop. + + align:start position:0% +going on, then you stop. + + + align:start position:0% +going on, then you stop. +So here probably we don't need that + + align:start position:0% +So here probably we don't need that + + + align:start position:0% +So here probably we don't need that +many. I mean here I think we get the + + align:start position:0% +many. I mean here I think we get the + + + align:start position:0% +many. I mean here I think we get the +picture. Okay. + + align:start position:0% + + + + align:start position:0% + +So everywhere we have a vector 2 one. + + align:start position:0% + + + + align:start position:0% + +Now let's try to look at slightly more + + align:start position:0% +Now let's try to look at slightly more + + + align:start position:0% +Now let's try to look at slightly more +interesting examples. Okay. Let's say I + + align:start position:0% +interesting examples. Okay. Let's say I + + + align:start position:0% +interesting examples. Okay. Let's say I +give you the vector field X times I hat. + + align:start position:0% +give you the vector field X times I hat. + + + align:start position:0% +give you the vector field X times I hat. +Okay. So there's no J component. + + align:start position:0% + + + + align:start position:0% + +So, how would you draw that? Maybe I + + align:start position:0% +So, how would you draw that? Maybe I + + + align:start position:0% +So, how would you draw that? Maybe I +don't need that much. + + align:start position:0% + + + + align:start position:0% + +Well, + + align:start position:0% + + + + align:start position:0% + +so first of all, we know that this guy + + align:start position:0% +so first of all, we know that this guy + + + align:start position:0% +so first of all, we know that this guy +is only in the I direction. So, it's + + align:start position:0% +is only in the I direction. So, it's + + + align:start position:0% +is only in the I direction. So, it's +always horizontal, right? It doesn't + + align:start position:0% +always horizontal, right? It doesn't + + + align:start position:0% +always horizontal, right? It doesn't +have a J component. So, everywhere it + + align:start position:0% +have a J component. So, everywhere it + + + align:start position:0% +have a J component. So, everywhere it +will be a horizontal vector. Now, the + + align:start position:0% +will be a horizontal vector. Now, the + + + align:start position:0% +will be a horizontal vector. Now, the +question is how long is it? Well, how + + align:start position:0% +question is how long is it? Well, how + + + align:start position:0% +question is how long is it? Well, how +long it is depends on X. So for example, + + align:start position:0% +long it is depends on X. So for example, + + + align:start position:0% +long it is depends on X. So for example, +if x is zero, then this will be actually + + align:start position:0% +if x is zero, then this will be actually + + + align:start position:0% +if x is zero, then this will be actually +the zero vector. + + align:start position:0% +the zero vector. + + + align:start position:0% +the zero vector. +So x is zero, that's here. See on the y- + + align:start position:0% +So x is zero, that's here. See on the y- + + + align:start position:0% +So x is zero, that's here. See on the y- +axis, maybe I should take a different + + align:start position:0% +axis, maybe I should take a different + + + align:start position:0% +axis, maybe I should take a different +color. + + align:start position:0% +color. + + + align:start position:0% +color. +So if I'm on the y- axis, I actually + + align:start position:0% +So if I'm on the y- axis, I actually + + + align:start position:0% +So if I'm on the y- axis, I actually +have the zero vector. + + align:start position:0% +have the zero vector. + + + align:start position:0% +have the zero vector. +Now if x becomes positive small, then I + + align:start position:0% +Now if x becomes positive small, then I + + + align:start position:0% +Now if x becomes positive small, then I +will have actually a small positive + + align:start position:0% +will have actually a small positive + + + align:start position:0% +will have actually a small positive +multiple of i. So I will be going a + + align:start position:0% +multiple of i. So I will be going a + + + align:start position:0% +multiple of i. So I will be going a +little bit to the right. + + align:start position:0% +little bit to the right. + + + align:start position:0% +little bit to the right. +And then if I increase x then this guy + + align:start position:0% +And then if I increase x then this guy + + + align:start position:0% +And then if I increase x then this guy +becomes larger. So I get a longer vector + + align:start position:0% +becomes larger. So I get a longer vector + + + align:start position:0% +becomes larger. So I get a longer vector +to the right. + + align:start position:0% +to the right. + + + align:start position:0% +to the right. +If x is negative then my vector field + + align:start position:0% +If x is negative then my vector field + + + align:start position:0% +If x is negative then my vector field +points to the left instead. So + + align:start position:0% + + + + align:start position:0% + +it looks something like that. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Any questions about that picture? + + align:start position:0% +Any questions about that picture? + + + align:start position:0% +Any questions about that picture? +No. Okay. So, usually we're not going to + + align:start position:0% +No. Okay. So, usually we're not going to + + + align:start position:0% +No. Okay. So, usually we're not going to +try to have, you know, very accurate, + + align:start position:0% +try to have, you know, very accurate, + + + align:start position:0% +try to have, you know, very accurate, +you know, we won't actually take time to + + align:start position:0% +you know, we won't actually take time to + + + align:start position:0% +you know, we won't actually take time to +plot a vector field very carefully. I if + + align:start position:0% +plot a vector field very carefully. I if + + + align:start position:0% +plot a vector field very carefully. I if +we need to, computers can do it for us. + + align:start position:0% +we need to, computers can do it for us. + + + align:start position:0% +we need to, computers can do it for us. +Um, but it's useful to have an idea of + + align:start position:0% +Um, but it's useful to have an idea of + + + align:start position:0% +Um, but it's useful to have an idea of +what the vector field does roughly. You + + align:start position:0% +what the vector field does roughly. You + + + align:start position:0% +what the vector field does roughly. You +know, whether it's getting larger and + + align:start position:0% +know, whether it's getting larger and + + + align:start position:0% +know, whether it's getting larger and +larger, in what direction it's pointing, + + align:start position:0% +larger, in what direction it's pointing, + + + align:start position:0% +larger, in what direction it's pointing, +what are the general features? + + align:start position:0% +what are the general features? + + + align:start position:0% +what are the general features? +So just to you know do a couple more + + align:start position:0% + + + + align:start position:0% + +and actually you'll see very quickly + + align:start position:0% +and actually you'll see very quickly + + + align:start position:0% +and actually you'll see very quickly +that the examples I take in lecture are + + align:start position:0% +that the examples I take in lecture are + + + align:start position:0% +that the examples I take in lecture are +pretty much always the same ones. So you + + align:start position:0% +pretty much always the same ones. So you + + + align:start position:0% +pretty much always the same ones. So you +know + + align:start position:0% +know + + + align:start position:0% +know +we'll be playing a lot with these + + align:start position:0% +we'll be playing a lot with these + + + align:start position:0% +we'll be playing a lot with these +particular vector fields just because + + align:start position:0% +particular vector fields just because + + + align:start position:0% +particular vector fields just because +they're good examples. + + align:start position:0% +they're good examples. + + + align:start position:0% +they're good examples. +So let's say I give you X I plus YJ. So + + align:start position:0% +So let's say I give you X I plus YJ. So + + + align:start position:0% +So let's say I give you X I plus YJ. So +that one has an interesting geometric + + align:start position:0% +that one has an interesting geometric + + + align:start position:0% +that one has an interesting geometric +signification the significance + + align:start position:0% +signification the significance + + + align:start position:0% +signification the significance +if I take a point XY + + align:start position:0% + + + + align:start position:0% + +you know so there I want to take the + + align:start position:0% +you know so there I want to take the + + + align:start position:0% +you know so there I want to take the +vector XY + + align:start position:0% +vector XY + + + align:start position:0% +vector XY +how do I do that well it's the same as + + align:start position:0% +how do I do that well it's the same as + + + align:start position:0% +how do I do that well it's the same as +the vector from the origin to this point + + align:start position:0% +the vector from the origin to this point + + + align:start position:0% +the vector from the origin to this point +so I take this vector and I copy it so + + align:start position:0% +so I take this vector and I copy it so + + + align:start position:0% +so I take this vector and I copy it so +that it starts at my given point okay so + + align:start position:0% +that it starts at my given point okay so + + + align:start position:0% +that it starts at my given point okay so +it looks like that and you know same + + align:start position:0% +it looks like that and you know same + + + align:start position:0% +it looks like that and you know same +thing at every point. + + align:start position:0% + + + + align:start position:0% + +Oops. So, it's a vector field that's + + align:start position:0% +Oops. So, it's a vector field that's + + + align:start position:0% +Oops. So, it's a vector field that's +pointing radially + + align:start position:0% +pointing radially + + + align:start position:0% +pointing radially +away from the origin + + align:start position:0% +away from the origin + + + align:start position:0% +away from the origin +and its magnitude increases with + + align:start position:0% +and its magnitude increases with + + + align:start position:0% +and its magnitude increases with +distance from the origin. + + align:start position:0% + + + + align:start position:0% + +Okay? So, you don't have to draw, you + + align:start position:0% +Okay? So, you don't have to draw, you + + + align:start position:0% +Okay? So, you don't have to draw, you +know, as many as me. Uh + + align:start position:0% +know, as many as me. Uh + + + align:start position:0% +know, as many as me. Uh +but so the idea is this vector field + + align:start position:0% +but so the idea is this vector field + + + align:start position:0% +but so the idea is this vector field +everywhere points away from the origin + + align:start position:0% +everywhere points away from the origin + + + align:start position:0% +everywhere points away from the origin +and its magnitude is equal to the + + align:start position:0% +and its magnitude is equal to the + + + align:start position:0% +and its magnitude is equal to the +distance from the origin. + + align:start position:0% + + + + align:start position:0% + +So you know if this were for example + + align:start position:0% +So you know if this were for example + + + align:start position:0% +So you know if this were for example +velocity fields well that would tell you + + align:start position:0% +velocity fields well that would tell you + + + align:start position:0% +velocity fields well that would tell you +you know you would see visually what's + + align:start position:0% +you know you would see visually what's + + + align:start position:0% +you know you would see visually what's +happening to your fluid like here maybe + + align:start position:0% +happening to your fluid like here maybe + + + align:start position:0% +happening to your fluid like here maybe +you have a source at the origin that's + + align:start position:0% +you have a source at the origin that's + + + align:start position:0% +you have a source at the origin that's +spewing fluid out and it's flowing all + + align:start position:0% +spewing fluid out and it's flowing all + + + align:start position:0% +spewing fluid out and it's flowing all +the way away from that. + + align:start position:0% + + + + align:start position:0% + +Okay, let's do just a last one. + + align:start position:0% + + + + align:start position:0% + +Let's say I give you + + align:start position:0% +Let's say I give you + + + align:start position:0% +Let's say I give you +minus y comma x. + + align:start position:0% +minus y comma x. + + + align:start position:0% +minus y comma x. +What does that look like? + + align:start position:0% +What does that look like? + + + align:start position:0% +What does that look like? +That's that's an interesting one + + align:start position:0% +That's that's an interesting one + + + align:start position:0% +That's that's an interesting one +actually. It's + + align:start position:0% + + + + align:start position:0% + +a nice one. So, let's see. So let's say + + align:start position:0% +a nice one. So, let's see. So let's say + + + align:start position:0% +a nice one. So, let's see. So let's say +that I have a point xy here. + + align:start position:0% +that I have a point xy here. + + + align:start position:0% +that I have a point xy here. +Okay. So + + align:start position:0% +Okay. So + + + align:start position:0% +Okay. So +this vector here is x comm y. But the + + align:start position:0% +this vector here is x comm y. But the + + + align:start position:0% +this vector here is x comm y. But the +vector I want is - y comma x. So what + + align:start position:0% +vector I want is - y comma x. So what + + + align:start position:0% +vector I want is - y comma x. So what +does that look like compared to + + align:start position:0% +does that look like compared to + + + align:start position:0% +does that look like compared to +yeah it's perpendicular to the position + + align:start position:0% +yeah it's perpendicular to the position + + + align:start position:0% +yeah it's perpendicular to the position +to this vector. Okay. If I rotate this + + align:start position:0% +to this vector. Okay. If I rotate this + + + align:start position:0% +to this vector. Okay. If I rotate this +vector. So let me maybe draw a picture + + align:start position:0% +vector. So let me maybe draw a picture + + + align:start position:0% +vector. So let me maybe draw a picture +on the side. + + align:start position:0% +on the side. + + + align:start position:0% +on the side. +If I take the vector xy, + + align:start position:0% +If I take the vector xy, + + + align:start position:0% +If I take the vector xy, +then the vector with components - y and + + align:start position:0% +then the vector with components - y and + + + align:start position:0% +then the vector with components - y and +x is going to be like this + + align:start position:0% +x is going to be like this + + + align:start position:0% +x is going to be like this +is the vector that I get by rotating by + + align:start position:0% +is the vector that I get by rotating by + + + align:start position:0% +is the vector that I get by rotating by +90° counterclockwise. + + align:start position:0% + + + + align:start position:0% + +And of course, I don't want to put that + + align:start position:0% +And of course, I don't want to put that + + + align:start position:0% +And of course, I don't want to put that +vector at the origin. I want to put it + + align:start position:0% +vector at the origin. I want to put it + + + align:start position:0% +vector at the origin. I want to put it +at the point xy. Okay. So in fact what I + + align:start position:0% +at the point xy. Okay. So in fact what I + + + align:start position:0% +at the point xy. Okay. So in fact what I +will draw is something like this. + + align:start position:0% +will draw is something like this. + + + align:start position:0% +will draw is something like this. +Okay. And similarly here it would be + + align:start position:0% +Okay. And similarly here it would be + + + align:start position:0% +Okay. And similarly here it would be +like that like that. + + align:start position:0% + + + + align:start position:0% + +And if I'm closer to the origin then it + + align:start position:0% +And if I'm closer to the origin then it + + + align:start position:0% +And if I'm closer to the origin then it +looks a bit the same but it's shorter. + + align:start position:0% + + + + align:start position:0% + +Okay. And at the origin it's zero. And + + align:start position:0% +Okay. And at the origin it's zero. And + + + align:start position:0% +Okay. And at the origin it's zero. And +when I'm further away, it becomes even + + align:start position:0% +when I'm further away, it becomes even + + + align:start position:0% +when I'm further away, it becomes even +larger. So see this vector field, if it + + align:start position:0% +larger. So see this vector field, if it + + + align:start position:0% +larger. So see this vector field, if it +was the motion of a fluid, it would + + align:start position:0% +was the motion of a fluid, it would + + + align:start position:0% +was the motion of a fluid, it would +correspond to a fluid that's just going + + align:start position:0% +correspond to a fluid that's just going + + + align:start position:0% +correspond to a fluid that's just going +around the origin in circles rotating at + + align:start position:0% +around the origin in circles rotating at + + + align:start position:0% +around the origin in circles rotating at +uniform speed. + + align:start position:0% +uniform speed. + + + align:start position:0% +uniform speed. +Okay, so + + align:start position:0% +Okay, so + + + align:start position:0% +Okay, so +this is actually the velocity field + + align:start position:0% + + + + align:start position:0% + +for + + align:start position:0% +for + + + align:start position:0% +for +uniform rotation. + + align:start position:0% + + + + align:start position:0% + +And if you figure out, you know, how + + align:start position:0% +And if you figure out, you know, how + + + align:start position:0% +And if you figure out, you know, how +long does it take for a piece, a + + align:start position:0% +long does it take for a piece, a + + + align:start position:0% +long does it take for a piece, a +particle of fluid to go all the way + + align:start position:0% +particle of fluid to go all the way + + + align:start position:0% +particle of fluid to go all the way +around, well, that will be actually 2 pi + + align:start position:0% +around, well, that will be actually 2 pi + + + align:start position:0% +around, well, that will be actually 2 pi +because the length of a circle is 2 pi + + align:start position:0% +because the length of a circle is 2 pi + + + align:start position:0% +because the length of a circle is 2 pi +times the radius. So that's actually at + + align:start position:0% +times the radius. So that's actually at + + + align:start position:0% +times the radius. So that's actually at +unit angular velocity, + + align:start position:0% + + + + align:start position:0% + +one rad per second or per unit time. + + align:start position:0% + + + + align:start position:0% + +Okay, so that's why this guy comes up + + align:start position:0% +Okay, so that's why this guy comes up + + + align:start position:0% +Okay, so that's why this guy comes up +quite a lot in real life. + + align:start position:0% + + + + align:start position:0% + +Okay, and you know, you can imagine lots + + align:start position:0% +Okay, and you know, you can imagine lots + + + align:start position:0% +Okay, and you know, you can imagine lots +of variations on these. Of course, you + + align:start position:0% +of variations on these. Of course, you + + + align:start position:0% +of variations on these. Of course, you +can also imagine vector fields given by + + align:start position:0% +can also imagine vector fields given by + + + align:start position:0% +can also imagine vector fields given by +much more complicated formulas and then + + align:start position:0% +much more complicated formulas and then + + + align:start position:0% +much more complicated formulas and then +you'll have a hard time drawing them. So + + align:start position:0% +you'll have a hard time drawing them. So + + + align:start position:0% +you'll have a hard time drawing them. So +maybe you'll use a computer or maybe + + align:start position:0% +maybe you'll use a computer or maybe + + + align:start position:0% +maybe you'll use a computer or maybe +you'll just give up and just do whatever + + align:start position:0% +you'll just give up and just do whatever + + + align:start position:0% +you'll just give up and just do whatever +calculation you have to do without + + align:start position:0% +calculation you have to do without + + + align:start position:0% +calculation you have to do without +trying to visualize the vector field. + + align:start position:0% +trying to visualize the vector field. + + + align:start position:0% +trying to visualize the vector field. +But if you have a nice simple one, then + + align:start position:0% +But if you have a nice simple one, then + + + align:start position:0% +But if you have a nice simple one, then +it's worth doing it because sometimes it + + align:start position:0% +it's worth doing it because sometimes it + + + align:start position:0% +it's worth doing it because sometimes it +will give you insight about what we're + + align:start position:0% +will give you insight about what we're + + + align:start position:0% +will give you insight about what we're +going to compute next. + + align:start position:0% + + + + align:start position:0% + +Okay. Any questions first about these + + align:start position:0% +Okay. Any questions first about these + + + align:start position:0% +Okay. Any questions first about these +pictures? + + align:start position:0% + + + + align:start position:0% + +No. + + align:start position:0% + + + + align:start position:0% + +Okay. Oh, yes. + + align:start position:0% + + + + align:start position:0% + +Sorry. + + align:start position:0% + + + + align:start position:0% + +y and you're asking if it should be y + + align:start position:0% +y and you're asking if it should be y + + + align:start position:0% +y and you're asking if it should be y +and + + align:start position:0% +and + + + align:start position:0% +and +uh so yx I think would be the other way + + align:start position:0% +uh so yx I think would be the other way + + + align:start position:0% +uh so yx I think would be the other way +around. See for example if I + + align:start position:0% +around. See for example if I + + + align:start position:0% +around. See for example if I +if I'm at this point then y is positive + + align:start position:0% +if I'm at this point then y is positive + + + align:start position:0% +if I'm at this point then y is positive +and x is zero. So if I take yx + + align:start position:0% +and x is zero. So if I take yx + + + align:start position:0% +and x is zero. So if I take yx +I guess a positive first component and + + align:start position:0% +I guess a positive first component and + + + align:start position:0% +I guess a positive first component and +zero for the second one. So yx would be + + align:start position:0% +zero for the second one. So yx would be + + + align:start position:0% +zero for the second one. So yx would be +rotation at unit speed in the opposite + + align:start position:0% +rotation at unit speed in the opposite + + + align:start position:0% +rotation at unit speed in the opposite +direction. Okay. So yeah, and there's a + + align:start position:0% +direction. Okay. So yeah, and there's a + + + align:start position:0% +direction. Okay. So yeah, and there's a +lot of tweaks you can do to it. But so + + align:start position:0% +lot of tweaks you can do to it. But so + + + align:start position:0% +lot of tweaks you can do to it. But so +if you flip the signs, you get rotation + + align:start position:0% +if you flip the signs, you get rotation + + + align:start position:0% +if you flip the signs, you get rotation +in the other direction. + + align:start position:0% + + + + align:start position:0% + +Uh yes, + + align:start position:0% + + + + align:start position:0% + +how do I know? + + align:start position:0% +how do I know? + + + align:start position:0% +how do I know? +H how do I know that it's at unit + + align:start position:0% +H how do I know that it's at unit + + + align:start position:0% +H how do I know that it's at unit +angular velocity? Well, that's because + + align:start position:0% +angular velocity? Well, that's because + + + align:start position:0% +angular velocity? Well, that's because +if my angular velocity is one, then that + + align:start position:0% +if my angular velocity is one, then that + + + align:start position:0% +if my angular velocity is one, then that +means that the speed, the actual speed + + align:start position:0% +means that the speed, the actual speed + + + align:start position:0% +means that the speed, the actual speed +is equal to the distance from the + + align:start position:0% +is equal to the distance from the + + + align:start position:0% +is equal to the distance from the +origin, + + align:start position:0% +origin, + + + align:start position:0% +origin, +right? Because the length, I mean the + + align:start position:0% +right? Because the length, I mean the + + + align:start position:0% +right? Because the length, I mean the +arc length on a circle of a certain + + align:start position:0% +arc length on a circle of a certain + + + align:start position:0% +arc length on a circle of a certain +radius is equal to the radius times the + + align:start position:0% +radius is equal to the radius times the + + + align:start position:0% +radius is equal to the radius times the +angle. So if the angle varies at rate + + align:start position:0% +angle. So if the angle varies at rate + + + align:start position:0% +angle. So if the angle varies at rate +one, then I travel at speed equal to the + + align:start position:0% +one, then I travel at speed equal to the + + + align:start position:0% +one, then I travel at speed equal to the +radius. And that's what I do here. The + + align:start position:0% +radius. And that's what I do here. The + + + align:start position:0% +radius. And that's what I do here. The +length of this vector is equal to the + + align:start position:0% +length of this vector is equal to the + + + align:start position:0% +length of this vector is equal to the +distance from the origin. + + align:start position:0% +distance from the origin. + + + align:start position:0% +distance from the origin. +I mean, it's not obvious on the picture, + + align:start position:0% +I mean, it's not obvious on the picture, + + + align:start position:0% +I mean, it's not obvious on the picture, +but really the vector that I put here is + + align:start position:0% +but really the vector that I put here is + + + align:start position:0% +but really the vector that I put here is +the same as this vector rotated. So, it + + align:start position:0% +the same as this vector rotated. So, it + + + align:start position:0% +the same as this vector rotated. So, it +has the same length. So, that's why the + + align:start position:0% +has the same length. So, that's why the + + + align:start position:0% +has the same length. So, that's why the +angular velocity is one. It doesn't + + align:start position:0% +angular velocity is one. It doesn't + + + align:start position:0% +angular velocity is one. It doesn't +really matter much anyway. But, + + align:start position:0% + + + + align:start position:0% + +okay. + + align:start position:0% +okay. + + + align:start position:0% +okay. +So, now what are we going to do with + + align:start position:0% +So, now what are we going to do with + + + align:start position:0% +So, now what are we going to do with +vector fields? Well, we're going to do a + + align:start position:0% +vector fields? Well, we're going to do a + + + align:start position:0% +vector fields? Well, we're going to do a +lot of things, but uh let's, you know, + + align:start position:0% + + + + align:start position:0% + +let's start somewhere. So, one thing you + + align:start position:0% +let's start somewhere. So, one thing you + + + align:start position:0% +let's start somewhere. So, one thing you +might want to do with a vector field is + + align:start position:0% +might want to do with a vector field is + + + align:start position:0% +might want to do with a vector field is +so I'm going to think for now of the + + align:start position:0% +so I'm going to think for now of the + + + align:start position:0% +so I'm going to think for now of the +situation where we have a force. Okay? + + align:start position:0% +situation where we have a force. Okay? + + + align:start position:0% +situation where we have a force. Okay? +So + + align:start position:0% +So + + + align:start position:0% +So +if you have a force + + align:start position:0% +if you have a force + + + align:start position:0% +if you have a force +exerted on a particle and that particle + + align:start position:0% +exerted on a particle and that particle + + + align:start position:0% +exerted on a particle and that particle +moves on some trajectory + + align:start position:0% +moves on some trajectory + + + align:start position:0% +moves on some trajectory +then probably you've seen in physics + + align:start position:0% +then probably you've seen in physics + + + align:start position:0% +then probably you've seen in physics +that the work done by the force + + align:start position:0% +that the work done by the force + + + align:start position:0% +that the work done by the force +corresponds to the force dot product + + align:start position:0% +corresponds to the force dot product + + + align:start position:0% +corresponds to the force dot product +with the the displacement vector how + + align:start position:0% +with the the displacement vector how + + + align:start position:0% +with the the displacement vector how +much you have moved your particle. + + align:start position:0% +much you have moved your particle. + + + align:start position:0% +much you have moved your particle. +And of course if you do just a you know + + align:start position:0% +And of course if you do just a you know + + + align:start position:0% +And of course if you do just a you know +straight line trajectory or if the force + + align:start position:0% +straight line trajectory or if the force + + + align:start position:0% +straight line trajectory or if the force +is constant that works well but if + + align:start position:0% +is constant that works well but if + + + align:start position:0% +is constant that works well but if +you're moving on a complicated + + align:start position:0% +you're moving on a complicated + + + align:start position:0% +you're moving on a complicated +trajectory and the force keeps changing + + align:start position:0% +trajectory and the force keeps changing + + + align:start position:0% +trajectory and the force keeps changing +then actually you want to integrate that + + align:start position:0% +then actually you want to integrate that + + + align:start position:0% +then actually you want to integrate that +over time. So + + align:start position:0% + + + + align:start position:0% + +okay so we're going to the first + + align:start position:0% +okay so we're going to the first + + + align:start position:0% +okay so we're going to the first +thing we'll do is learn how to compute + + align:start position:0% +thing we'll do is learn how to compute + + + align:start position:0% +thing we'll do is learn how to compute +the work done by a vector field. And + + align:start position:0% +the work done by a vector field. And + + + align:start position:0% +the work done by a vector field. And +mathematically that's called + + align:start position:0% +mathematically that's called + + + align:start position:0% +mathematically that's called +a line integral. + + align:start position:0% + + + + align:start position:0% + +Okay. So physically remember the work + + align:start position:0% +Okay. So physically remember the work + + + align:start position:0% +Okay. So physically remember the work +done by a force is the force times the + + align:start position:0% +done by a force is the force times the + + + align:start position:0% +done by a force is the force times the +distance. + + align:start position:0% +distance. + + + align:start position:0% +distance. +And more precisely, + + align:start position:0% +And more precisely, + + + align:start position:0% +And more precisely, +it's actually + + align:start position:0% +it's actually + + + align:start position:0% +it's actually +the dotproduct between the force as a + + align:start position:0% +the dotproduct between the force as a + + + align:start position:0% +the dotproduct between the force as a +vector and + + align:start position:0% +vector and + + + align:start position:0% +vector and +the displacement vector + + align:start position:0% +the displacement vector + + + align:start position:0% +the displacement vector +for a small motion. So say that you know + + align:start position:0% +for a small motion. So say that you know + + + align:start position:0% +for a small motion. So say that you know +your point is moving from here to here. + + align:start position:0% +your point is moving from here to here. + + + align:start position:0% +your point is moving from here to here. +You have the displacement + + align:start position:0% +You have the displacement + + + align:start position:0% +You have the displacement +delta R. That's just the change in the + + align:start position:0% +delta R. That's just the change in the + + + align:start position:0% +delta R. That's just the change in the +position vector. That's the vector from + + align:start position:0% +position vector. That's the vector from + + + align:start position:0% +position vector. That's the vector from +the old position to the new position. + + align:start position:0% +the old position to the new position. + + + align:start position:0% +the old position to the new position. +And then you have your force that's + + align:start position:0% +And then you have your force that's + + + align:start position:0% +And then you have your force that's +being exerted and you do the dot product + + align:start position:0% +being exerted and you do the dot product + + + align:start position:0% +being exerted and you do the dot product +between them and that will give you the + + align:start position:0% +between them and that will give you the + + + align:start position:0% +between them and that will give you the +work of the force during this motion. + + align:start position:0% +work of the force during this motion. + + + align:start position:0% +work of the force during this motion. +And the physical significance of this + + align:start position:0% +And the physical significance of this + + + align:start position:0% +And the physical significance of this +well the work tells you basically how + + align:start position:0% +well the work tells you basically how + + + align:start position:0% +well the work tells you basically how +much energy you have to provide to + + align:start position:0% +much energy you have to provide to + + + align:start position:0% +much energy you have to provide to +actually perform this motion. Okay, just + + align:start position:0% +actually perform this motion. Okay, just + + + align:start position:0% +actually perform this motion. Okay, just +in case you haven't seen this in 801 + + align:start position:0% +in case you haven't seen this in 801 + + + align:start position:0% +in case you haven't seen this in 801 +yet. I'm hoping all of you have heard + + align:start position:0% +yet. I'm hoping all of you have heard + + + align:start position:0% +yet. I'm hoping all of you have heard +about work somewhere. But in case it's + + align:start position:0% +about work somewhere. But in case it's + + + align:start position:0% +about work somewhere. But in case it's +completely mysterious, that's the amount + + align:start position:0% +completely mysterious, that's the amount + + + align:start position:0% +completely mysterious, that's the amount +of energy you have to provide. Sorry, + + align:start position:0% +of energy you have to provide. Sorry, + + + align:start position:0% +of energy you have to provide. Sorry, +actually no, that's the amount of energy + + align:start position:0% +actually no, that's the amount of energy + + + align:start position:0% +actually no, that's the amount of energy +provided by the force. Sorry. Right. So + + align:start position:0% +provided by the force. Sorry. Right. So + + + align:start position:0% +provided by the force. Sorry. Right. So +if the force goes along the motion, it + + align:start position:0% +if the force goes along the motion, it + + + align:start position:0% +if the force goes along the motion, it +actually pushes the particle. It + + align:start position:0% +actually pushes the particle. It + + + align:start position:0% +actually pushes the particle. It +provides energy to it to do that motion. + + align:start position:0% +provides energy to it to do that motion. + + + align:start position:0% +provides energy to it to do that motion. +And conversely, if you're trying to go + + align:start position:0% +And conversely, if you're trying to go + + + align:start position:0% +And conversely, if you're trying to go +against the force, then you have to + + align:start position:0% +against the force, then you have to + + + align:start position:0% +against the force, then you have to +provide energy to the particle to be + + align:start position:0% +provide energy to the particle to be + + + align:start position:0% +provide energy to the particle to be +able to do that. + + align:start position:0% +able to do that. + + + align:start position:0% +able to do that. +So in particular the work you know if + + align:start position:0% +So in particular the work you know if + + + align:start position:0% +So in particular the work you know if +this is the only force that's taking + + align:start position:0% +this is the only force that's taking + + + align:start position:0% +this is the only force that's taking +place then the work will be the + + align:start position:0% +place then the work will be the + + + align:start position:0% +place then the work will be the +variation in kinetic energy of a + + align:start position:0% +variation in kinetic energy of a + + + align:start position:0% +variation in kinetic energy of a +particle along the motion. + + align:start position:0% +particle along the motion. + + + align:start position:0% +particle along the motion. +So now that's a good description for a + + align:start position:0% +So now that's a good description for a + + + align:start position:0% +So now that's a good description for a +small motion but let's say that my + + align:start position:0% +small motion but let's say that my + + + align:start position:0% +small motion but let's say that my +particle is not just doing that but you + + align:start position:0% +particle is not just doing that but you + + + align:start position:0% +particle is not just doing that but you +know it's doing you know something + + align:start position:0% +know it's doing you know something + + + align:start position:0% +know it's doing you know something +complicated + + align:start position:0% +complicated + + + align:start position:0% +complicated +and my force keeps changing. So somehow + + align:start position:0% +and my force keeps changing. So somehow + + + align:start position:0% +and my force keeps changing. So somehow +maybe you know I have a different force + + align:start position:0% +maybe you know I have a different force + + + align:start position:0% +maybe you know I have a different force +at every point. + + align:start position:0% + + + + align:start position:0% + +So then I want to find the total work + + align:start position:0% +So then I want to find the total work + + + align:start position:0% +So then I want to find the total work +done along the motion. Well, what I have + + align:start position:0% +done along the motion. Well, what I have + + + align:start position:0% +done along the motion. Well, what I have +to do is I have to cut my trajectory + + align:start position:0% +to do is I have to cut my trajectory + + + align:start position:0% +to do is I have to cut my trajectory +into these little pieces, you know, and + + align:start position:0% +into these little pieces, you know, and + + + align:start position:0% +into these little pieces, you know, and +for each of them I have a vector along + + align:start position:0% +for each of them I have a vector along + + + align:start position:0% +for each of them I have a vector along +the trajectory. I have the force. I do + + align:start position:0% +the trajectory. I have the force. I do + + + align:start position:0% +the trajectory. I have the force. I do +the dot product and I sum them together. + + align:start position:0% + + + + align:start position:0% + +And of course the actual answer + + align:start position:0% +And of course the actual answer + + + align:start position:0% +And of course the actual answer +well to get the actual answer I should + + align:start position:0% +well to get the actual answer I should + + + align:start position:0% +well to get the actual answer I should +actually cut into smaller and smaller + + align:start position:0% +actually cut into smaller and smaller + + + align:start position:0% +actually cut into smaller and smaller +pieces and sum all of the small + + align:start position:0% +pieces and sum all of the small + + + align:start position:0% +pieces and sum all of the small +contributions to work. So in fact it's + + align:start position:0% +contributions to work. So in fact it's + + + align:start position:0% +contributions to work. So in fact it's +going to be an integral. + + align:start position:0% + + + + align:start position:0% + +Okay. So + + align:start position:0% +Okay. So + + + align:start position:0% +Okay. So +along + + align:start position:0% +along + + + align:start position:0% +along +some trajectory + + align:start position:0% + + + + align:start position:0% + +let's call C the trajectory for curve. + + align:start position:0% +let's call C the trajectory for curve. + + + align:start position:0% +let's call C the trajectory for curve. +you know, it's some curve. And here, um, + + align:start position:0% +you know, it's some curve. And here, um, + + + align:start position:0% +you know, it's some curve. And here, um, +the work + + align:start position:0% + + + + align:start position:0% + +adds up to an integral, + + align:start position:0% + + + + align:start position:0% + +which well, we write this using the + + align:start position:0% +which well, we write this using the + + + align:start position:0% +which well, we write this using the +notation integral along C of F. DL. + + align:start position:0% +notation integral along C of F. DL. + + + align:start position:0% +notation integral along C of F. DL. +Okay. So we have to decode this + + align:start position:0% +Okay. So we have to decode this + + + align:start position:0% +Okay. So we have to decode this +notation. + + align:start position:0% +notation. + + + align:start position:0% +notation. +So + + align:start position:0% +So + + + align:start position:0% +So +one way to decode this is to say it's a + + align:start position:0% +one way to decode this is to say it's a + + + align:start position:0% +one way to decode this is to say it's a +limit as we cut + + align:start position:0% + + + + align:start position:0% + +into smaller and smaller pieces + + align:start position:0% +into smaller and smaller pieces + + + align:start position:0% +into smaller and smaller pieces +of the sum over each piece of the + + align:start position:0% +of the sum over each piece of the + + + align:start position:0% +of the sum over each piece of the +trajectory of the force at the given + + align:start position:0% +trajectory of the force at the given + + + align:start position:0% +trajectory of the force at the given +point. Dot product with + + align:start position:0% +point. Dot product with + + + align:start position:0% +point. Dot product with +that small vector along the trajectory + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +well that's not how we're going to + + align:start position:0% +well that's not how we're going to + + + align:start position:0% +well that's not how we're going to +compute it. You know to compute it we do + + align:start position:0% +compute it. You know to compute it we do + + + align:start position:0% +compute it. You know to compute it we do +things differently. So how can we + + align:start position:0% +things differently. So how can we + + + align:start position:0% +things differently. So how can we +actually compute it? Well + + align:start position:0% +actually compute it? Well + + + align:start position:0% +actually compute it? Well +what we can do is say that actually we + + align:start position:0% +what we can do is say that actually we + + + align:start position:0% +what we can do is say that actually we +are cutting things + + align:start position:0% +are cutting things + + + align:start position:0% +are cutting things +into know small time intervals. So the + + align:start position:0% +into know small time intervals. So the + + + align:start position:0% +into know small time intervals. So the +way that we split our trajectory is we + + align:start position:0% +way that we split our trajectory is we + + + align:start position:0% +way that we split our trajectory is we +just take you know a picture every say + + align:start position:0% +just take you know a picture every say + + + align:start position:0% +just take you know a picture every say +millisecond. + + align:start position:0% +millisecond. + + + align:start position:0% +millisecond. +So every millisecond we have a new + + align:start position:0% +So every millisecond we have a new + + + align:start position:0% +So every millisecond we have a new +position and the motion you know the + + align:start position:0% +position and the motion you know the + + + align:start position:0% +position and the motion you know the +amount by which you have moved during + + align:start position:0% +amount by which you have moved during + + + align:start position:0% +amount by which you have moved during +each small time interval is basically + + align:start position:0% +each small time interval is basically + + + align:start position:0% +each small time interval is basically +the velocity vector times the amount of + + align:start position:0% +the velocity vector times the amount of + + + align:start position:0% +the velocity vector times the amount of +time. + + align:start position:0% +time. + + + align:start position:0% +time. +So + + align:start position:0% +So + + + align:start position:0% +So +in fact + + align:start position:0% +in fact + + + align:start position:0% +in fact +let me just rewrite this as you know you + + align:start position:0% +let me just rewrite this as you know you + + + align:start position:0% +let me just rewrite this as you know you +do the dot product between the force and + + align:start position:0% +do the dot product between the force and + + + align:start position:0% +do the dot product between the force and +how much you have moved. + + align:start position:0% + + + + align:start position:0% + +Well, if I just rewrite it this way, + + align:start position:0% +Well, if I just rewrite it this way, + + + align:start position:0% +Well, if I just rewrite it this way, +nothing's happened. But what this thing + + align:start position:0% +nothing's happened. But what this thing + + + align:start position:0% +nothing's happened. But what this thing +is actually is the velocity vector + + align:start position:0% + + + + align:start position:0% + +drdt. + + align:start position:0% + + + + align:start position:0% + +So what I'm trying to say is that I can + + align:start position:0% +So what I'm trying to say is that I can + + + align:start position:0% +So what I'm trying to say is that I can +actually compute my integral by + + align:start position:0% +actually compute my integral by + + + align:start position:0% +actually compute my integral by +integrating + + align:start position:0% +integrating + + + align:start position:0% +integrating +f dotproduct with + + align:start position:0% +f dotproduct with + + + align:start position:0% +f dotproduct with +drdt + + align:start position:0% +drdt + + + align:start position:0% +drdt +over time from time you know whatever + + align:start position:0% +over time from time you know whatever + + + align:start position:0% +over time from time you know whatever +the initial time + + align:start position:0% +the initial time + + + align:start position:0% +the initial time +to whatever the final time is I + + align:start position:0% +to whatever the final time is I + + + align:start position:0% +to whatever the final time is I +integrate f dotproduct velocity dt + + align:start position:0% +integrate f dotproduct velocity dt + + + align:start position:0% +integrate f dotproduct velocity dt +and of + + align:start position:0% +and of + + + align:start position:0% +and of +I mean here when I say f I mean f at the + + align:start position:0% +I mean here when I say f I mean f at the + + + align:start position:0% +I mean here when I say f I mean f at the +point on the trajectory at time t + + align:start position:0% +point on the trajectory at time t + + + align:start position:0% +point on the trajectory at time t +right this guy depends on x and y + + align:start position:0% +right this guy depends on x and y + + + align:start position:0% +right this guy depends on x and y +therefore it depends on t + + align:start position:0% + + + + align:start position:0% + +okay I see a lot of confused faces so + + align:start position:0% +okay I see a lot of confused faces so + + + align:start position:0% +okay I see a lot of confused faces so +let's do an example and then I will ask + + align:start position:0% +let's do an example and then I will ask + + + align:start position:0% +let's do an example and then I will ask +you oh okay + + align:start position:0% + + + + align:start position:0% + +so now yes that would be probably um + + align:start position:0% +so now yes that would be probably um + + + align:start position:0% +so now yes that would be probably um +yeah so here I need to put a limit as + + align:start position:0% +yeah so here I need to put a limit as + + + align:start position:0% +yeah so here I need to put a limit as +delta t tends to zero. I cut my + + align:start position:0% +delta t tends to zero. I cut my + + + align:start position:0% +delta t tends to zero. I cut my +trajectory into smaller and smaller time + + align:start position:0% +trajectory into smaller and smaller time + + + align:start position:0% +trajectory into smaller and smaller time +intervals. For each time interval, I + + align:start position:0% +intervals. For each time interval, I + + + align:start position:0% +intervals. For each time interval, I +have a small + + align:start position:0% +have a small + + + align:start position:0% +have a small +motion which is essentially velocity + + align:start position:0% +motion which is essentially velocity + + + align:start position:0% +motion which is essentially velocity +times delta t. And then I dot that with + + align:start position:0% +times delta t. And then I dot that with + + + align:start position:0% +times delta t. And then I dot that with +a force and I sum them. + + align:start position:0% + + + + align:start position:0% + +Okay. So let's do an example. + + align:start position:0% + + + + align:start position:0% + +Let's say that we do + + align:start position:0% +Let's say that we do + + + align:start position:0% +Let's say that we do +we want to find the work of this force. + + align:start position:0% +we want to find the work of this force. + + + align:start position:0% +we want to find the work of this force. +So I guess that's the last example that + + align:start position:0% +So I guess that's the last example that + + + align:start position:0% +So I guess that's the last example that +we had. Okay. So it's a force field that + + align:start position:0% +we had. Okay. So it's a force field that + + + align:start position:0% +we had. Okay. So it's a force field that +tries to make everything can rotate + + align:start position:0% +tries to make everything can rotate + + + align:start position:0% +tries to make everything can rotate +somehow. Your force points along these + + align:start position:0% +somehow. Your force points along these + + + align:start position:0% +somehow. Your force points along these +circles. + + align:start position:0% +circles. + + + align:start position:0% +circles. +And let's say that our trajectory, our + + align:start position:0% +And let's say that our trajectory, our + + + align:start position:0% +And let's say that our trajectory, our +particle is moving + + align:start position:0% +particle is moving + + + align:start position:0% +particle is moving +along the parametric curve + + align:start position:0% +along the parametric curve + + + align:start position:0% +along the parametric curve +x= t, y= t ^2 + + align:start position:0% +x= t, y= t ^2 + + + align:start position:0% +x= t, y= t ^2 +for t going from 0 to 1. + + align:start position:0% +for t going from 0 to 1. + + + align:start position:0% +for t going from 0 to 1. +Okay, so + + align:start position:0% +Okay, so + + + align:start position:0% +Okay, so +what that looks like? Well, maybe I + + align:start position:0% +what that looks like? Well, maybe I + + + align:start position:0% +what that looks like? Well, maybe I +should draw a new picture. + + align:start position:0% +should draw a new picture. + + + align:start position:0% +should draw a new picture. +So our vector field + + align:start position:0% + + + + align:start position:0% + +Oh well, whatever. And our trajectory, + + align:start position:0% +Oh well, whatever. And our trajectory, + + + align:start position:0% +Oh well, whatever. And our trajectory, +if you try to plot this, when you see y + + align:start position:0% +if you try to plot this, when you see y + + + align:start position:0% +if you try to plot this, when you see y +is actually x squ. So it's a piece of + + align:start position:0% +is actually x squ. So it's a piece of + + + align:start position:0% +is actually x squ. So it's a piece of +parabola + + align:start position:0% +parabola + + + align:start position:0% +parabola +that goes from the origin to 1 one. + + align:start position:0% +that goes from the origin to 1 one. + + + align:start position:0% +that goes from the origin to 1 one. +Okay, that's what our curve looks like. + + align:start position:0% +Okay, that's what our curve looks like. + + + align:start position:0% +Okay, that's what our curve looks like. +Okay, so we're trying to find the work + + align:start position:0% +Okay, so we're trying to find the work + + + align:start position:0% +Okay, so we're trying to find the work +done by our force along this trajectory. + + align:start position:0% +done by our force along this trajectory. + + + align:start position:0% +done by our force along this trajectory. +I should point out I mean you know if + + align:start position:0% +I should point out I mean you know if + + + align:start position:0% +I should point out I mean you know if +you're asking me how did you get this + + align:start position:0% +you're asking me how did you get this + + + align:start position:0% +you're asking me how did you get this +that's actually the wrong question I + + align:start position:0% +that's actually the wrong question I + + + align:start position:0% +that's actually the wrong question I +didn't you know this is all part of the + + align:start position:0% +didn't you know this is all part of the + + + align:start position:0% +didn't you know this is all part of the +data I have a force and I have a + + align:start position:0% +data I have a force and I have a + + + align:start position:0% +data I have a force and I have a +trajectory and I want to find what's the + + align:start position:0% +trajectory and I want to find what's the + + + align:start position:0% +trajectory and I want to find what's the +work done along that trajectory these + + align:start position:0% +work done along that trajectory these + + + align:start position:0% +work done along that trajectory these +two guys I can choose completely + + align:start position:0% +two guys I can choose completely + + + align:start position:0% +two guys I can choose completely +independently of each other + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +the integral along C of FD dr + + align:start position:0% +the integral along C of FD dr + + + align:start position:0% +the integral along C of FD dr +will be well it's the integral from time + + align:start position:0% +will be well it's the integral from time + + + align:start position:0% +will be well it's the integral from time +0 to time 1 of f dot the velocity vector + + align:start position:0% +0 to time 1 of f dot the velocity vector + + + align:start position:0% +0 to time 1 of f dot the velocity vector +drdt + + align:start position:0% +drdt + + + align:start position:0% +drdt +* dt. + + align:start position:0% +* dt. + + + align:start position:0% +* dt. +So that will be the integral from 0 to + + align:start position:0% +So that will be the integral from 0 to + + + align:start position:0% +So that will be the integral from 0 to +one of + + align:start position:0% +one of + + + align:start position:0% +one of +okay let's try to figure it out. So what + + align:start position:0% +okay let's try to figure it out. So what + + + align:start position:0% +okay let's try to figure it out. So what +is f? + + align:start position:0% + + + + align:start position:0% + +f + + align:start position:0% +f + + + align:start position:0% +f +at a point xy is minus y comma x. But if + + align:start position:0% +at a point xy is minus y comma x. But if + + + align:start position:0% +at a point xy is minus y comma x. But if +I take the point where I am at time t, + + align:start position:0% +I take the point where I am at time t, + + + align:start position:0% +I take the point where I am at time t, +then x is t and y is t ^2. Okay. So here + + align:start position:0% +then x is t and y is t ^2. Okay. So here + + + align:start position:0% +then x is t and y is t ^2. Okay. So here +I plug x= t, y = t ^2. That will give me + + align:start position:0% +I plug x= t, y = t ^2. That will give me + + + align:start position:0% +I plug x= t, y = t ^2. That will give me +t ^2 and t. Okay. So here I will put t + + align:start position:0% +t ^2 and t. Okay. So here I will put t + + + align:start position:0% +t ^2 and t. Okay. So here I will put t +^2 t + + align:start position:0% +^2 t + + + align:start position:0% +^2 t +dot product. What is the velocity + + align:start position:0% +dot product. What is the velocity + + + align:start position:0% +dot product. What is the velocity +vector? + + align:start position:0% +vector? + + + align:start position:0% +vector? +Well, dx dt + + align:start position:0% +Well, dx dt + + + align:start position:0% +Well, dx dt +is just one. dy dt + + align:start position:0% +is just one. dy dt + + + align:start position:0% +is just one. dy dt +is 2t. So the velocity vector is 1 and + + align:start position:0% +is 2t. So the velocity vector is 1 and + + + align:start position:0% +is 2t. So the velocity vector is 1 and +2t + + align:start position:0% +2t + + + align:start position:0% +2t +dt. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So now we have to continue + + align:start position:0% +So now we have to continue + + + align:start position:0% +So now we have to continue +calculation. We get integral from 0 to 1 + + align:start position:0% +calculation. We get integral from 0 to 1 + + + align:start position:0% +calculation. We get integral from 0 to 1 +of what is this dot product? Well, it's + + align:start position:0% +of what is this dot product? Well, it's + + + align:start position:0% +of what is this dot product? Well, it's +- t ^2 + 2 t ^2. I get t ^2. Well, maybe + + align:start position:0% +- t ^2 + 2 t ^2. I get t ^2. Well, maybe + + + align:start position:0% +- t ^2 + 2 t ^2. I get t ^2. Well, maybe +I'll write it t ^2 + 2t ^2 dt. That ends + + align:start position:0% +I'll write it t ^2 + 2t ^2 dt. That ends + + + align:start position:0% +I'll write it t ^2 + 2t ^2 dt. That ends +up being integral from 0 to 1 of t ^2 + + align:start position:0% +up being integral from 0 to 1 of t ^2 + + + align:start position:0% +up being integral from 0 to 1 of t ^2 +dt, which you all know how to integrate + + align:start position:0% +dt, which you all know how to integrate + + + align:start position:0% +dt, which you all know how to integrate +and get 1/3. + + align:start position:0% +and get 1/3. + + + align:start position:0% +and get 1/3. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So that's the work done by the force + + align:start position:0% +So that's the work done by the force + + + align:start position:0% +So that's the work done by the force +along this curve. Yes. How did you get + + align:start position:0% +along this curve. Yes. How did you get + + + align:start position:0% +along this curve. Yes. How did you get +the t? + + align:start position:0% +the t? + + + align:start position:0% +the t? +Well, I got it by just taking the dot + + align:start position:0% +Well, I got it by just taking the dot + + + align:start position:0% +Well, I got it by just taking the dot +product between the force and the + + align:start position:0% +product between the force and the + + + align:start position:0% +product between the force and the +velocity. + + align:start position:0% +velocity. + + + align:start position:0% +velocity. +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +sorry. That's in case you're wondering, + + align:start position:0% +sorry. That's in case you're wondering, + + + align:start position:0% +sorry. That's in case you're wondering, +things go like this. + + align:start position:0% + + + + align:start position:0% + +Okay, any questions on how we did this + + align:start position:0% +Okay, any questions on how we did this + + + align:start position:0% +Okay, any questions on how we did this +calculation? + + align:start position:0% + + + + align:start position:0% + +No. Yes. + + align:start position:0% + + + + align:start position:0% + +Ah, why can't you just do fdr? Well, + + align:start position:0% +Ah, why can't you just do fdr? Well, + + + align:start position:0% +Ah, why can't you just do fdr? Well, +soon we'll be able to. We don't know yet + + align:start position:0% +soon we'll be able to. We don't know yet + + + align:start position:0% +soon we'll be able to. We don't know yet +what dr means or how to use it as a + + align:start position:0% +what dr means or how to use it as a + + + align:start position:0% +what dr means or how to use it as a +symbol. Okay, because + + align:start position:0% +symbol. Okay, because + + + align:start position:0% +symbol. Okay, because +you know we haven't said yet. I mean, + + align:start position:0% +you know we haven't said yet. I mean, + + + align:start position:0% +you know we haven't said yet. I mean, +see this is a d vector r. That's kind of + + align:start position:0% +see this is a d vector r. That's kind of + + + align:start position:0% +see this is a d vector r. That's kind of +a strange + + align:start position:0% +a strange + + + align:start position:0% +a strange +thing to have. I mean, certainly R is + + align:start position:0% +thing to have. I mean, certainly R is + + + align:start position:0% +thing to have. I mean, certainly R is +not a usual variable. + + align:start position:0% +not a usual variable. + + + align:start position:0% +not a usual variable. +I mean, we have to be careful about, you + + align:start position:0% +I mean, we have to be careful about, you + + + align:start position:0% +I mean, we have to be careful about, you +know, what are the rules? What does this + + align:start position:0% +know, what are the rules? What does this + + + align:start position:0% +know, what are the rules? What does this +symbol mean? So, I mean, we're going to + + align:start position:0% +symbol mean? So, I mean, we're going to + + + align:start position:0% +symbol mean? So, I mean, we're going to +see that right now. And then we can do + + align:start position:0% +see that right now. And then we can do + + + align:start position:0% +see that right now. And then we can do +it actually in a slightly more efficient + + align:start position:0% +it actually in a slightly more efficient + + + align:start position:0% +it actually in a slightly more efficient +way. + + align:start position:0% +way. + + + align:start position:0% +way. +But you can't just use I mean, R is not + + align:start position:0% +But you can't just use I mean, R is not + + + align:start position:0% +But you can't just use I mean, R is not +a scalar quantity. R is a position + + align:start position:0% +a scalar quantity. R is a position + + + align:start position:0% +a scalar quantity. R is a position +vector, right? So, you can't integrate F + + align:start position:0% +vector, right? So, you can't integrate F + + + align:start position:0% +vector, right? So, you can't integrate F +with respect to R. We don't know how to + + align:start position:0% +with respect to R. We don't know how to + + + align:start position:0% +with respect to R. We don't know how to +do that. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So, oh yes, sorry, I can't see people up + + align:start position:0% +So, oh yes, sorry, I can't see people up + + + align:start position:0% +So, oh yes, sorry, I can't see people up +there because of the spotlights, but + + align:start position:0% +there because of the spotlights, but + + + align:start position:0% +there because of the spotlights, but +yes, + + align:start position:0% +yes, + + + align:start position:0% +yes, +if I were to do + + align:start position:0% + + + + align:start position:0% + +I still can't hear you. Sorry. + + align:start position:0% + + + + align:start position:0% + +Mhm. Okay. So question is if I took a + + align:start position:0% +Mhm. Okay. So question is if I took a + + + align:start position:0% +Mhm. Okay. So question is if I took a +different trajectory from the origin to + + align:start position:0% +different trajectory from the origin to + + + align:start position:0% +different trajectory from the origin to +that point one one would happen. Well + + align:start position:0% +that point one one would happen. Well + + + align:start position:0% +that point one one would happen. Well +the answer is I would get something + + align:start position:0% +the answer is I would get something + + + align:start position:0% +the answer is I would get something +different. + + align:start position:0% +different. + + + align:start position:0% +different. +Okay. So for example let me try to + + align:start position:0% +Okay. So for example let me try to + + + align:start position:0% +Okay. So for example let me try to +convince you of that. For example, say + + align:start position:0% +convince you of that. For example, say + + + align:start position:0% +convince you of that. For example, say +that I chose + + align:start position:0% + + + + align:start position:0% + +say I chose to instead go like this and + + align:start position:0% +say I chose to instead go like this and + + + align:start position:0% +say I chose to instead go like this and +then around like that. Then you know + + align:start position:0% +then around like that. Then you know + + + align:start position:0% +then around like that. Then you know +first I wouldn't do any work because + + align:start position:0% +first I wouldn't do any work because + + + align:start position:0% +first I wouldn't do any work because +here the force is perpendicular to my + + align:start position:0% +here the force is perpendicular to my + + + align:start position:0% +here the force is perpendicular to my +motion and then I would be going against + + align:start position:0% +motion and then I would be going against + + + align:start position:0% +motion and then I would be going against +the force all the way around. So I + + align:start position:0% +the force all the way around. So I + + + align:start position:0% +the force all the way around. So I +should get something that's negative. + + align:start position:0% +should get something that's negative. + + + align:start position:0% +should get something that's negative. +Okay, even if you don't see that, just + + align:start position:0% +Okay, even if you don't see that, just + + + align:start position:0% +Okay, even if you don't see that, just +you know accept at face value what I'm + + align:start position:0% +you know accept at face value what I'm + + + align:start position:0% +you know accept at face value what I'm +going to say now the value of a line + + align:start position:0% +going to say now the value of a line + + + align:start position:0% +going to say now the value of a line +integral in general depends on how we + + align:start position:0% +integral in general depends on how we + + + align:start position:0% +integral in general depends on how we +got from point A to point B and that's + + align:start position:0% +got from point A to point B and that's + + + align:start position:0% +got from point A to point B and that's +why we have to compute it by using the + + align:start position:0% +why we have to compute it by using the + + + align:start position:0% +why we have to compute it by using the +parametric equation for the curve. It + + align:start position:0% +parametric equation for the curve. It + + + align:start position:0% +parametric equation for the curve. It +really depends on what curve you choose. + + align:start position:0% + + + + align:start position:0% + +Okay, any other questions? Oh, yes. + + align:start position:0% + + + + align:start position:0% + +Ah, so yes. What happens when the force + + align:start position:0% +Ah, so yes. What happens when the force + + + align:start position:0% +Ah, so yes. What happens when the force +infllects the trajectory? Well, then + + align:start position:0% +infllects the trajectory? Well, then + + + align:start position:0% +infllects the trajectory? Well, then +actually you'd have to solve a + + align:start position:0% +actually you'd have to solve a + + + align:start position:0% +actually you'd have to solve a +differential equation telling you how + + align:start position:0% +differential equation telling you how + + + align:start position:0% +differential equation telling you how +the particle moves to find what the + + align:start position:0% +the particle moves to find what the + + + align:start position:0% +the particle moves to find what the +trajectory is. Uh so that's something + + align:start position:0% +trajectory is. Uh so that's something + + + align:start position:0% +trajectory is. Uh so that's something +that would you know be a very useful + + align:start position:0% +that would you know be a very useful + + + align:start position:0% +that would you know be a very useful +topic and that's probably more like what + + align:start position:0% +topic and that's probably more like what + + + align:start position:0% +topic and that's probably more like what +you will do in 1803 although maybe you + + align:start position:0% +you will do in 1803 although maybe you + + + align:start position:0% +you will do in 1803 although maybe you +actually know how to do it in this case. + + align:start position:0% +actually know how to do it in this case. + + + align:start position:0% +actually know how to do it in this case. +Uh so what we're trying to develop here + + align:start position:0% +Uh so what we're trying to develop here + + + align:start position:0% +Uh so what we're trying to develop here +is a method to figure out if we know + + align:start position:0% +is a method to figure out if we know + + + align:start position:0% +is a method to figure out if we know +what the trajectory is what the work + + align:start position:0% +what the trajectory is what the work + + + align:start position:0% +what the trajectory is what the work +will be. It doesn't tell us what the + + align:start position:0% +will be. It doesn't tell us what the + + + align:start position:0% +will be. It doesn't tell us what the +trajectory will be. But of course we + + align:start position:0% +trajectory will be. But of course we + + + align:start position:0% +trajectory will be. But of course we +could also find that. + + align:start position:0% +could also find that. + + + align:start position:0% +could also find that. +But here see I'm not assuming for + + align:start position:0% +But here see I'm not assuming for + + + align:start position:0% +But here see I'm not assuming for +example that the particle is moving just + + align:start position:0% +example that the particle is moving just + + + align:start position:0% +example that the particle is moving just +based on that force. Maybe actually I'm + + align:start position:0% +based on that force. Maybe actually I'm + + + align:start position:0% +based on that force. Maybe actually I'm +here to, you know, hold it in my hand + + align:start position:0% +here to, you know, hold it in my hand + + + align:start position:0% +here to, you know, hold it in my hand +and force it to go where it's going. Or + + align:start position:0% +and force it to go where it's going. Or + + + align:start position:0% +and force it to go where it's going. Or +maybe there's some rail that's taking it + + align:start position:0% +maybe there's some rail that's taking it + + + align:start position:0% +maybe there's some rail that's taking it +on that trajectory or whatever. So I can + + align:start position:0% +on that trajectory or whatever. So I can + + + align:start position:0% +on that trajectory or whatever. So I can +really do it along any trajectory. And + + align:start position:0% +really do it along any trajectory. And + + + align:start position:0% +really do it along any trajectory. And +if I wanted to, if I knew that it's the + + align:start position:0% +if I wanted to, if I knew that it's the + + + align:start position:0% +if I wanted to, if I knew that it's the +case, then I could try to find the + + align:start position:0% +case, then I could try to find the + + + align:start position:0% +case, then I could try to find the +trajectory based on what the force is. + + align:start position:0% +trajectory based on what the force is. + + + align:start position:0% +trajectory based on what the force is. +But that's not what we are doing here. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So + + align:start position:0% + + + + align:start position:0% + +next + + align:start position:0% +next + + + align:start position:0% +next +okay so let's try to make sense I mean + + align:start position:0% +okay so let's try to make sense I mean + + + align:start position:0% +okay so let's try to make sense I mean +you asked a while ago and just a few + + align:start position:0% +you asked a while ago and just a few + + + align:start position:0% +you asked a while ago and just a few +minutes ago what what can we do directly + + align:start position:0% +minutes ago what what can we do directly + + + align:start position:0% +minutes ago what what can we do directly +with dr so dr see becomes somehow a + + align:start position:0% +with dr so dr see becomes somehow a + + + align:start position:0% +with dr so dr see becomes somehow a +vector I mean when I replace it by drdt + + align:start position:0% +vector I mean when I replace it by drdt + + + align:start position:0% +vector I mean when I replace it by drdt +* dt it becomes something that's a + + align:start position:0% +* dt it becomes something that's a + + + align:start position:0% +* dt it becomes something that's a +vector but with a dt next to it So + + align:start position:0% +vector but with a dt next to it So + + + align:start position:0% +vector but with a dt next to it So +in fact + + align:start position:0% + + + + align:start position:0% + +well it's not really new but uh let's + + align:start position:0% +well it's not really new but uh let's + + + align:start position:0% +well it's not really new but uh let's +see another another way to do it. + + align:start position:0% + + + + align:start position:0% + +Let's say that our force has components + + align:start position:0% +Let's say that our force has components + + + align:start position:0% +Let's say that our force has components +m and n. + + align:start position:0% +m and n. + + + align:start position:0% +m and n. +I claim that we can write symbolically + + align:start position:0% +I claim that we can write symbolically + + + align:start position:0% +I claim that we can write symbolically +vector dr stands for it's a vector whose + + align:start position:0% +vector dr stands for it's a vector whose + + + align:start position:0% +vector dr stands for it's a vector whose +components are dx and dy. + + align:start position:0% +components are dx and dy. + + + align:start position:0% +components are dx and dy. +Okay. So now that's a strange kind of + + align:start position:0% +Okay. So now that's a strange kind of + + + align:start position:0% +Okay. So now that's a strange kind of +vector. I mean it's not a real vector of + + align:start position:0% +vector. I mean it's not a real vector of + + + align:start position:0% +vector. I mean it's not a real vector of +course but as a notation it's a pretty + + align:start position:0% +course but as a notation it's a pretty + + + align:start position:0% +course but as a notation it's a pretty +good notation + + align:start position:0% +good notation + + + align:start position:0% +good notation +because it tells us that fd dr + + align:start position:0% +because it tells us that fd dr + + + align:start position:0% +because it tells us that fd dr +is + + align:start position:0% +is + + + align:start position:0% +is +m dx plus n dy. + + align:start position:0% +m dx plus n dy. + + + align:start position:0% +m dx plus n dy. +And so in fact + + align:start position:0% +And so in fact + + + align:start position:0% +And so in fact +we'll very often write instead of fdr + + align:start position:0% +we'll very often write instead of fdr + + + align:start position:0% +we'll very often write instead of fdr +line integral along c we'll write the + + align:start position:0% +line integral along c we'll write the + + + align:start position:0% +line integral along c we'll write the +line integral along c of m dx + + align:start position:0% +line integral along c of m dx + + + align:start position:0% +line integral along c of m dx +plus n dy. + + align:start position:0% +plus n dy. + + + align:start position:0% +plus n dy. +And so in this language of course what + + align:start position:0% +And so in this language of course what + + + align:start position:0% +And so in this language of course what +we're integrating now rather than a + + align:start position:0% +we're integrating now rather than a + + + align:start position:0% +we're integrating now rather than a +vector field becomes a differential. But + + align:start position:0% +vector field becomes a differential. But + + + align:start position:0% +vector field becomes a differential. But +you should think of the two as being + + align:start position:0% +you should think of the two as being + + + align:start position:0% +you should think of the two as being +pretty much the same thing right? It's + + align:start position:0% +pretty much the same thing right? It's + + + align:start position:0% +pretty much the same thing right? It's +like when you compare the gradient of a + + align:start position:0% +like when you compare the gradient of a + + + align:start position:0% +like when you compare the gradient of a +function and it's differential. They are + + align:start position:0% +function and it's differential. They are + + + align:start position:0% +function and it's differential. They are +different notations but they have the + + align:start position:0% +different notations but they have the + + + align:start position:0% +different notations but they have the +same content. + + align:start position:0% + + + + align:start position:0% + +Okay. So now there still remains the + + align:start position:0% +Okay. So now there still remains the + + + align:start position:0% +Okay. So now there still remains the +question how do we compute this kind of + + align:start position:0% +question how do we compute this kind of + + + align:start position:0% +question how do we compute this kind of +integral because it's more subtle than + + align:start position:0% +integral because it's more subtle than + + + align:start position:0% +integral because it's more subtle than +the notation suggests right because m + + align:start position:0% +the notation suggests right because m + + + align:start position:0% +the notation suggests right because m +and n both depend on x and y. And if you + + align:start position:0% +and n both depend on x and y. And if you + + + align:start position:0% +and n both depend on x and y. And if you +just integrate it with respect to x + + align:start position:0% +just integrate it with respect to x + + + align:start position:0% +just integrate it with respect to x +you'd be left with y's in there. And you + + align:start position:0% +you'd be left with y's in there. And you + + + align:start position:0% +you'd be left with y's in there. And you +don't want to be left with y's. You want + + align:start position:0% +don't want to be left with y's. You want + + + align:start position:0% +don't want to be left with y's. You want +a number at the end. And see the catch + + align:start position:0% +a number at the end. And see the catch + + + align:start position:0% +a number at the end. And see the catch +is along the curve X and Y are actually + + align:start position:0% +is along the curve X and Y are actually + + + align:start position:0% +is along the curve X and Y are actually +related to each other. So + + align:start position:0% +related to each other. So + + + align:start position:0% +related to each other. So +whenever we write this we have two + + align:start position:0% +whenever we write this we have two + + + align:start position:0% +whenever we write this we have two +variables X and Y but in fact along the + + align:start position:0% +variables X and Y but in fact along the + + + align:start position:0% +variables X and Y but in fact along the +curve C we have only one parameter could + + align:start position:0% +curve C we have only one parameter could + + + align:start position:0% +curve C we have only one parameter could +be X could be Y could be time whatever + + align:start position:0% +be X could be Y could be time whatever + + + align:start position:0% +be X could be Y could be time whatever +you want but we have to actually express + + align:start position:0% +you want but we have to actually express + + + align:start position:0% +you want but we have to actually express +everything in terms of that one + + align:start position:0% +everything in terms of that one + + + align:start position:0% +everything in terms of that one +parameter and then we get a usual single + + align:start position:0% +parameter and then we get a usual single + + + align:start position:0% +parameter and then we get a usual single +variable integral. + + align:start position:0% +variable integral. + + + align:start position:0% +variable integral. +Okay. So how do we evaluate things in + + align:start position:0% +Okay. So how do we evaluate things in + + + align:start position:0% +Okay. So how do we evaluate things in +this language? Well, we do it by + + align:start position:0% +this language? Well, we do it by + + + align:start position:0% +this language? Well, we do it by +substituting a parameter into + + align:start position:0% +substituting a parameter into + + + align:start position:0% +substituting a parameter into +everything. + + align:start position:0% + + + + align:start position:0% + +Okay, so + + align:start position:0% +Okay, so + + + align:start position:0% +Okay, so +the method to evaluate + + align:start position:0% + + + + align:start position:0% + +is to express + + align:start position:0% +is to express + + + align:start position:0% +is to express +X and Y in terms of a single variable. + + align:start position:0% + + + + align:start position:0% + +and then + + align:start position:0% +and then + + + align:start position:0% +and then +substitute that variable. + + align:start position:0% + + + + align:start position:0% + +Okay, so let's for example redo the one + + align:start position:0% +Okay, so let's for example redo the one + + + align:start position:0% +Okay, so let's for example redo the one +we had up there just using this new + + align:start position:0% +we had up there just using this new + + + align:start position:0% +we had up there just using this new +notations. You'll see it's the same + + align:start position:0% +notations. You'll see it's the same + + + align:start position:0% +notations. You'll see it's the same +calculation but with different + + align:start position:0% +calculation but with different + + + align:start position:0% +calculation but with different +notations. + + align:start position:0% +notations. + + + align:start position:0% +notations. +So + + align:start position:0% + + + + align:start position:0% + +in that example that we had + + align:start position:0% +in that example that we had + + + align:start position:0% +in that example that we had +our vector field f + + align:start position:0% +our vector field f + + + align:start position:0% +our vector field f +was + + align:start position:0% +was + + + align:start position:0% +was +- y comma x. So what we're integrating + + align:start position:0% +- y comma x. So what we're integrating + + + align:start position:0% +- y comma x. So what we're integrating +is - ydx + + align:start position:0% +is - ydx + + + align:start position:0% +is - ydx +plus x dy. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +And see if we have just this we don't + + align:start position:0% +And see if we have just this we don't + + + align:start position:0% +And see if we have just this we don't +know how to integrate that. I mean, + + align:start position:0% +know how to integrate that. I mean, + + + align:start position:0% +know how to integrate that. I mean, +well, you could try to come up with like + + align:start position:0% +well, you could try to come up with like + + + align:start position:0% +well, you could try to come up with like +negativexy or something like that, but + + align:start position:0% +negativexy or something like that, but + + + align:start position:0% +negativexy or something like that, but +that actually doesn't make sense. It + + align:start position:0% +that actually doesn't make sense. It + + + align:start position:0% +that actually doesn't make sense. It +doesn't work. + + align:start position:0% +doesn't work. + + + align:start position:0% +doesn't work. +So, + + align:start position:0% +So, + + + align:start position:0% +So, +what we'll do + + align:start position:0% +what we'll do + + + align:start position:0% +what we'll do +is we'll actually have to express + + align:start position:0% +is we'll actually have to express + + + align:start position:0% +is we'll actually have to express +everything + + align:start position:0% + + + + align:start position:0% + +in terms of a same variable because it's + + align:start position:0% +in terms of a same variable because it's + + + align:start position:0% +in terms of a same variable because it's +a single integral. We should have only + + align:start position:0% +a single integral. We should have only + + + align:start position:0% +a single integral. We should have only +one variable. + + align:start position:0% +one variable. + + + align:start position:0% +one variable. +and what that variable will be. Well, if + + align:start position:0% +and what that variable will be. Well, if + + + align:start position:0% +and what that variable will be. Well, if +we just do it the same way, that would + + align:start position:0% +we just do it the same way, that would + + + align:start position:0% +we just do it the same way, that would +just be T. + + align:start position:0% + + + + align:start position:0% + +So, how do we express everything in + + align:start position:0% +So, how do we express everything in + + + align:start position:0% +So, how do we express everything in +terms of t? + + align:start position:0% + + + + align:start position:0% + +Well, we use the parametric equation. We + + align:start position:0% +Well, we use the parametric equation. We + + + align:start position:0% +Well, we use the parametric equation. We +know that x is t and y is t ^2. + + align:start position:0% +know that x is t and y is t ^2. + + + align:start position:0% +know that x is t and y is t ^2. +Okay, so we know what to do with these + + align:start position:0% +Okay, so we know what to do with these + + + align:start position:0% +Okay, so we know what to do with these +two guys. What about dx and dy? Well, + + align:start position:0% +two guys. What about dx and dy? Well, + + + align:start position:0% +two guys. What about dx and dy? Well, +it's easy. We just differentiate. + + align:start position:0% +it's easy. We just differentiate. + + + align:start position:0% +it's easy. We just differentiate. +dx becomes dt. + + align:start position:0% +dx becomes dt. + + + align:start position:0% +dx becomes dt. +dy becomes 2t dt. + + align:start position:0% + + + + align:start position:0% + +Okay, I'm just saying in a different + + align:start position:0% +Okay, I'm just saying in a different + + + align:start position:0% +Okay, I'm just saying in a different +language what I said over there with + + align:start position:0% +language what I said over there with + + + align:start position:0% +language what I said over there with +dxdt equals 1, dydt equals 2t. It's the + + align:start position:0% +dxdt equals 1, dydt equals 2t. It's the + + + align:start position:0% +dxdt equals 1, dydt equals 2t. It's the +same thing but written slightly + + align:start position:0% +same thing but written slightly + + + align:start position:0% +same thing but written slightly +differently. + + align:start position:0% +differently. + + + align:start position:0% +differently. +So now, + + align:start position:0% +So now, + + + align:start position:0% +So now, +so I'm going to do it again. Um I'm + + align:start position:0% +so I'm going to do it again. Um I'm + + + align:start position:0% +so I'm going to do it again. Um I'm +going to switch from one bot to the next + + align:start position:0% +going to switch from one bot to the next + + + align:start position:0% +going to switch from one bot to the next +one. + + align:start position:0% +one. + + + align:start position:0% +one. +My integral becomes the integral / c of + + align:start position:0% +My integral becomes the integral / c of + + + align:start position:0% +My integral becomes the integral / c of +- y is minus t ^2 dt + + align:start position:0% +- y is minus t ^2 dt + + + align:start position:0% +- y is minus t ^2 dt +plus x is t * dy is 2t dt. + + align:start position:0% +plus x is t * dy is 2t dt. + + + align:start position:0% +plus x is t * dy is 2t dt. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +And now that I have only t left, it's + + align:start position:0% +And now that I have only t left, it's + + + align:start position:0% +And now that I have only t left, it's +fine to say, oh, I have a usual single + + align:start position:0% +fine to say, oh, I have a usual single + + + align:start position:0% +fine to say, oh, I have a usual single +variable integral over a variable t that + + align:start position:0% +variable integral over a variable t that + + + align:start position:0% +variable integral over a variable t that +goes from 0 to one. So now I can say + + align:start position:0% +goes from 0 to one. So now I can say + + + align:start position:0% +goes from 0 to one. So now I can say +yes, this is the integral from 0 to 1 of + + align:start position:0% +yes, this is the integral from 0 to 1 of + + + align:start position:0% +yes, this is the integral from 0 to 1 of +that stuff. Well, I can simplify a bit + + align:start position:0% +that stuff. Well, I can simplify a bit + + + align:start position:0% +that stuff. Well, I can simplify a bit +becomes just t ^2 dt and I can compute + + align:start position:0% +becomes just t ^2 dt and I can compute + + + align:start position:0% +becomes just t ^2 dt and I can compute +it. + + align:start position:0% +it. + + + align:start position:0% +it. +Uh I have negative t ^2 and then I have + + align:start position:0% +Uh I have negative t ^2 and then I have + + + align:start position:0% +Uh I have negative t ^2 and then I have +plus 2 t^2. So I end up with positive + + align:start position:0% +plus 2 t^2. So I end up with positive + + + align:start position:0% +plus 2 t^2. So I end up with positive +t^2. + + align:start position:0% +t^2. + + + align:start position:0% +t^2. +Okay, it's the same as up there. + + align:start position:0% + + + + align:start position:0% + +Okay, any questions? + + align:start position:0% +Okay, any questions? + + + align:start position:0% +Okay, any questions? +Yes. + + align:start position:0% + + + + align:start position:0% + +Uh when no when when you do dy so what + + align:start position:0% +Uh when no when when you do dy so what + + + align:start position:0% +Uh when no when when you do dy so what +is dy? dy is the derivative of y. It's + + align:start position:0% +is dy? dy is the derivative of y. It's + + + align:start position:0% +is dy? dy is the derivative of y. It's +the differential of y. y is t ^2. So I + + align:start position:0% +the differential of y. y is t ^2. So I + + + align:start position:0% +the differential of y. y is t ^2. So I +get 2t ddt. Okay, so I plug dt for dx, I + + align:start position:0% +get 2t ddt. Okay, so I plug dt for dx, I + + + align:start position:0% +get 2t ddt. Okay, so I plug dt for dx, I +plug 2tdt for dy and so on. + + align:start position:0% + + + + align:start position:0% + +Okay, and that's the general method. So + + align:start position:0% +Okay, and that's the general method. So + + + align:start position:0% +Okay, and that's the general method. So +if you are given a curve, then you first + + align:start position:0% +if you are given a curve, then you first + + + align:start position:0% +if you are given a curve, then you first +have to figure out how do you express x + + align:start position:0% +have to figure out how do you express x + + + align:start position:0% +have to figure out how do you express x +and y in terms of the same thing. + + align:start position:0% +and y in terms of the same thing. + + + align:start position:0% +and y in terms of the same thing. +And you get to choose in general what + + align:start position:0% +And you get to choose in general what + + + align:start position:0% +And you get to choose in general what +parameter we use. Okay, you choose to + + align:start position:0% +parameter we use. Okay, you choose to + + + align:start position:0% +parameter we use. Okay, you choose to +parameterize your curve in whatever way + + align:start position:0% +parameterize your curve in whatever way + + + align:start position:0% +parameterize your curve in whatever way +you want. So + + align:start position:0% + + + + align:start position:0% + +the note that I want to make is that + + align:start position:0% + + + + align:start position:0% + +this line integral depends + + align:start position:0% +this line integral depends + + + align:start position:0% +this line integral depends +on the trajectory + + align:start position:0% + + + + align:start position:0% + +C but not + + align:start position:0% +C but not + + + align:start position:0% +C but not +on the parameter. ization. + + align:start position:0% + + + + align:start position:0% + +Okay. So you can choose whichever + + align:start position:0% +Okay. So you can choose whichever + + + align:start position:0% +Okay. So you can choose whichever +variable you want. So for example + + align:start position:0% +variable you want. So for example + + + align:start position:0% +variable you want. So for example +what you could do + + align:start position:0% +what you could do + + + align:start position:0% +what you could do +is you know when you know that you have + + align:start position:0% +is you know when you know that you have + + + align:start position:0% +is you know when you know that you have +that trajectory you could also choose to + + align:start position:0% +that trajectory you could also choose to + + + align:start position:0% +that trajectory you could also choose to +parameterize it as x= + + align:start position:0% +parameterize it as x= + + + align:start position:0% +parameterize it as x= +say I don't know x= sin theta and y = + + align:start position:0% +say I don't know x= sin theta and y = + + + align:start position:0% +say I don't know x= sin theta and y = +sin square theta because y is x^2 where + + align:start position:0% +sin square theta because y is x^2 where + + + align:start position:0% +sin square theta because y is x^2 where +theta goes from 0 to pi / 2 and then you + + align:start position:0% +theta goes from 0 to pi / 2 and then you + + + align:start position:0% +theta goes from 0 to pi / 2 and then you +could get dx and dy in terms of d theta + + align:start position:0% +could get dx and dy in terms of d theta + + + align:start position:0% +could get dx and dy in terms of d theta +and you'd be able to do it with a lot of + + align:start position:0% +and you'd be able to do it with a lot of + + + align:start position:0% +and you'd be able to do it with a lot of +trig and you would get the same answer. + + align:start position:0% +trig and you would get the same answer. + + + align:start position:0% +trig and you would get the same answer. +So that would be a harder way to get the + + align:start position:0% +So that would be a harder way to get the + + + align:start position:0% +So that would be a harder way to get the +same thing. Okay. So what you should do + + align:start position:0% +same thing. Okay. So what you should do + + + align:start position:0% +same thing. Okay. So what you should do +in practice is use you know the most + + align:start position:0% +in practice is use you know the most + + + align:start position:0% +in practice is use you know the most +reasonable way to parameterize your your + + align:start position:0% +reasonable way to parameterize your your + + + align:start position:0% +reasonable way to parameterize your your +curve. If you know that here you have a + + align:start position:0% +curve. If you know that here you have a + + + align:start position:0% +curve. If you know that here you have a +piece of parabola y= x^2 there's no way + + align:start position:0% +piece of parabola y= x^2 there's no way + + + align:start position:0% +piece of parabola y= x^2 there's no way +you will put s and sin^ squ. You know + + align:start position:0% +you will put s and sin^ squ. You know + + + align:start position:0% +you will put s and sin^ squ. You know +you could set I mean x= t y= t square is + + align:start position:0% +you could set I mean x= t y= t square is + + + align:start position:0% +you could set I mean x= t y= t square is +very reasonable. You can even take a + + align:start position:0% +very reasonable. You can even take a + + + align:start position:0% +very reasonable. You can even take a +small shortcut and say that your + + align:start position:0% +small shortcut and say that your + + + align:start position:0% +small shortcut and say that your +variable will be just x. So that means x + + align:start position:0% +variable will be just x. So that means x + + + align:start position:0% +variable will be just x. So that means x +you just keep it you know as it is and + + align:start position:0% +you just keep it you know as it is and + + + align:start position:0% +you just keep it you know as it is and +then when you have y you set y = x^2 d y + + align:start position:0% +then when you have y you set y = x^2 d y + + + align:start position:0% +then when you have y you set y = x^2 d y += 2x dx and then you have an integral + + align:start position:0% += 2x dx and then you have an integral + + + align:start position:0% += 2x dx and then you have an integral +over x that works. + + align:start position:0% + + + + align:start position:0% + +Okay. So this one is + + align:start position:0% +Okay. So this one is + + + align:start position:0% +Okay. So this one is +not practical + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% +but + + + align:start position:0% +but +You know, you get to choose. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +So now let me tell you a bit more about + + align:start position:0% +So now let me tell you a bit more about + + + align:start position:0% +So now let me tell you a bit more about +the geometry. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% +So + + + align:start position:0% +So +we've said + + align:start position:0% +we've said + + + align:start position:0% +we've said +you know here's how we compute it in + + align:start position:0% +you know here's how we compute it in + + + align:start position:0% +you know here's how we compute it in +general and that's the general method + + align:start position:0% +general and that's the general method + + + align:start position:0% +general and that's the general method +for computing a line integral for work. + + align:start position:0% +for computing a line integral for work. + + + align:start position:0% +for computing a line integral for work. +You can always do this. Try to find a + + align:start position:0% +You can always do this. Try to find a + + + align:start position:0% +You can always do this. Try to find a +parameter the simplest one express + + align:start position:0% +parameter the simplest one express + + + align:start position:0% +parameter the simplest one express +everything in terms of that variable and + + align:start position:0% +everything in terms of that variable and + + + align:start position:0% +everything in terms of that variable and +then you have an integral to compute. + + align:start position:0% +then you have an integral to compute. + + + align:start position:0% +then you have an integral to compute. +But sometimes you can actually save a + + align:start position:0% +But sometimes you can actually save a + + + align:start position:0% +But sometimes you can actually save a +lot of work by just thinking + + align:start position:0% +lot of work by just thinking + + + align:start position:0% +lot of work by just thinking +geometrically about what this all does. + + align:start position:0% +geometrically about what this all does. + + + align:start position:0% +geometrically about what this all does. +Okay. So let me tell you about + + align:start position:0% +Okay. So let me tell you about + + + align:start position:0% +Okay. So let me tell you about +the geometric + + align:start position:0% +the geometric + + + align:start position:0% +the geometric +approach. + + align:start position:0% + + + + align:start position:0% + +So so + + align:start position:0% +So so + + + align:start position:0% +So so +one thing I want to remind you of first + + align:start position:0% +one thing I want to remind you of first + + + align:start position:0% +one thing I want to remind you of first +is what is this vector dr? Well what is + + align:start position:0% +is what is this vector dr? Well what is + + + align:start position:0% +is what is this vector dr? Well what is +vector delta r? + + align:start position:0% +vector delta r? + + + align:start position:0% +vector delta r? +You know if I take a very small piece of + + align:start position:0% +You know if I take a very small piece of + + + align:start position:0% +You know if I take a very small piece of +a trajectory + + align:start position:0% +a trajectory + + + align:start position:0% +a trajectory +then my vector delta r will be tangent + + align:start position:0% +then my vector delta r will be tangent + + + align:start position:0% +then my vector delta r will be tangent +to the trajectory. + + align:start position:0% +to the trajectory. + + + align:start position:0% +to the trajectory. +So it will be going in the same + + align:start position:0% +So it will be going in the same + + + align:start position:0% +So it will be going in the same +direction as the unit tangent vector t. + + align:start position:0% +direction as the unit tangent vector t. + + + align:start position:0% +direction as the unit tangent vector t. +And what is its length? Well, its length + + align:start position:0% +And what is its length? Well, its length + + + align:start position:0% +And what is its length? Well, its length +is the arc length along the trajectory + + align:start position:0% +is the arc length along the trajectory + + + align:start position:0% +is the arc length along the trajectory +which is what we called delta s. + + align:start position:0% +which is what we called delta s. + + + align:start position:0% +which is what we called delta s. +Remember s was distance along the + + align:start position:0% +Remember s was distance along the + + + align:start position:0% +Remember s was distance along the +trajectory. + + align:start position:0% +trajectory. + + + align:start position:0% +trajectory. +So + + align:start position:0% +So + + + align:start position:0% +So +we can write vector dr. So we said it's + + align:start position:0% +we can write vector dr. So we said it's + + + align:start position:0% +we can write vector dr. So we said it's +dx comma dy but that's also t * ds. + + align:start position:0% + + + + align:start position:0% + +It's a vector whose direction is tangent + + align:start position:0% +It's a vector whose direction is tangent + + + align:start position:0% +It's a vector whose direction is tangent +to the curve and whose length element is + + align:start position:0% +to the curve and whose length element is + + + align:start position:0% +to the curve and whose length element is +actually the arklength element. + + align:start position:0% +actually the arklength element. + + + align:start position:0% +actually the arklength element. +I mean if you you know if you don't like + + align:start position:0% +I mean if you you know if you don't like + + + align:start position:0% +I mean if you you know if you don't like +this notation think about + + align:start position:0% + + + + align:start position:0% + +divide everything by dt + + align:start position:0% +divide everything by dt + + + align:start position:0% +divide everything by dt +then what we're saying is d rdt that's a + + align:start position:0% +then what we're saying is d rdt that's a + + + align:start position:0% +then what we're saying is d rdt that's a +velocity vector while in coordinates the + + align:start position:0% +velocity vector while in coordinates the + + + align:start position:0% +velocity vector while in coordinates the +velocity vector is dxdt + + align:start position:0% +velocity vector is dxdt + + + align:start position:0% +velocity vector is dxdt +dydt + + align:start position:0% +dydt + + + align:start position:0% +dydt +but more geometrically + + align:start position:0% +but more geometrically + + + align:start position:0% +but more geometrically +the direction of a velocity vector is + + align:start position:0% +the direction of a velocity vector is + + + align:start position:0% +the direction of a velocity vector is +tangent to the trajectory and its + + align:start position:0% +tangent to the trajectory and its + + + align:start position:0% +tangent to the trajectory and its +magnitude is speed dst. + + align:start position:0% + + + + align:start position:0% + +Okay, so that's really the same thing. + + align:start position:0% + + + + align:start position:0% + +Okay, so + + align:start position:0% +Okay, so + + + align:start position:0% +Okay, so +if I say this, that means + + align:start position:0% +if I say this, that means + + + align:start position:0% +if I say this, that means +that my line integral + + align:start position:0% + + + + align:start position:0% + +f + + align:start position:0% +f + + + align:start position:0% +f +well I said I can write it as integral + + align:start position:0% +well I said I can write it as integral + + + align:start position:0% +well I said I can write it as integral +of m dx plus n dy. That's what's that's + + align:start position:0% +of m dx plus n dy. That's what's that's + + + align:start position:0% +of m dx plus n dy. That's what's that's +what I will do if I want to actually + + align:start position:0% +what I will do if I want to actually + + + align:start position:0% +what I will do if I want to actually +compute it by computing the integral. + + align:start position:0% +compute it by computing the integral. + + + align:start position:0% +compute it by computing the integral. +But if instead I want to think about it + + align:start position:0% +But if instead I want to think about it + + + align:start position:0% +But if instead I want to think about it +geometrically, I could rewrite it as ft + + align:start position:0% +geometrically, I could rewrite it as ft + + + align:start position:0% +geometrically, I could rewrite it as ft +ds. + + align:start position:0% + + + + align:start position:0% + +Okay. So now you can think of this you + + align:start position:0% +Okay. So now you can think of this you + + + align:start position:0% +Okay. So now you can think of this you +know ft t is a scalar quantity. It's the + + align:start position:0% +know ft t is a scalar quantity. It's the + + + align:start position:0% +know ft t is a scalar quantity. It's the +tangent component of my force. So I take + + align:start position:0% +tangent component of my force. So I take + + + align:start position:0% +tangent component of my force. So I take +my force and I project it to the tangent + + align:start position:0% +my force and I project it to the tangent + + + align:start position:0% +my force and I project it to the tangent +direction to the trajectory and then I + + align:start position:0% +direction to the trajectory and then I + + + align:start position:0% +direction to the trajectory and then I +integrate that along the curve. + + align:start position:0% +integrate that along the curve. + + + align:start position:0% +integrate that along the curve. +It's still the same thing. + + align:start position:0% + + + + align:start position:0% + +And sometimes it's easier to do it this + + align:start position:0% +And sometimes it's easier to do it this + + + align:start position:0% +And sometimes it's easier to do it this +way. So here's an example. + + align:start position:0% + + + + align:start position:0% + +Let's say so you know this is bound to + + align:start position:0% +Let's say so you know this is bound to + + + align:start position:0% +Let's say so you know this is bound to +be easier only when the field and the + + align:start position:0% +be easier only when the field and the + + + align:start position:0% +be easier only when the field and the +curve are relatively simple and have a + + align:start position:0% +curve are relatively simple and have a + + + align:start position:0% +curve are relatively simple and have a +geometric relation to each other. you + + align:start position:0% +geometric relation to each other. you + + + align:start position:0% +geometric relation to each other. you +know, if I give you an evil formula + + align:start position:0% +know, if I give you an evil formula + + + align:start position:0% +know, if I give you an evil formula +with, you know, x cub + y to the 5th or + + align:start position:0% +with, you know, x cub + y to the 5th or + + + align:start position:0% +with, you know, x cub + y to the 5th or +whatever, there's very little chance + + align:start position:0% +whatever, there's very little chance + + + align:start position:0% +whatever, there's very little chance +that you will be able to simplify it + + align:start position:0% +that you will be able to simplify it + + + align:start position:0% +that you will be able to simplify it +that way. But let's say that I'm doing + + align:start position:0% +that way. But let's say that I'm doing + + + align:start position:0% +that way. But let's say that I'm doing +say my trajectory is just a circle of + + align:start position:0% +say my trajectory is just a circle of + + + align:start position:0% +say my trajectory is just a circle of +radius a + + align:start position:0% +radius a + + + align:start position:0% +radius a +centered at the origin. + + align:start position:0% +centered at the origin. + + + align:start position:0% +centered at the origin. +Let's say I'm doing that + + align:start position:0% +Let's say I'm doing that + + + align:start position:0% +Let's say I'm doing that +counterclockwise. + + align:start position:0% + + + + align:start position:0% + +And let's say that my vector field + + align:start position:0% +And let's say that my vector field + + + align:start position:0% +And let's say that my vector field +is x i + yj. + + align:start position:0% +is x i + yj. + + + align:start position:0% +is x i + yj. +Okay. So what does that look like? + + align:start position:0% +Okay. So what does that look like? + + + align:start position:0% +Okay. So what does that look like? +Well, + + align:start position:0% +Well, + + + align:start position:0% +Well, +so my trajectory is just this circle. + + align:start position:0% +so my trajectory is just this circle. + + + align:start position:0% +so my trajectory is just this circle. +My vector field, remember x i plus y, + + align:start position:0% +My vector field, remember x i plus y, + + + align:start position:0% +My vector field, remember x i plus y, +that's the one that's pointing radially + + align:start position:0% +that's the one that's pointing radially + + + align:start position:0% +that's the one that's pointing radially +from the origin. + + align:start position:0% + + + + align:start position:0% + +So hopefully if you have good physics + + align:start position:0% +So hopefully if you have good physics + + + align:start position:0% +So hopefully if you have good physics +intuition here, you already know what + + align:start position:0% +intuition here, you already know what + + + align:start position:0% +intuition here, you already know what +the work is going to be, right? It's + + align:start position:0% +the work is going to be, right? It's + + + align:start position:0% +the work is going to be, right? It's +going to be + + align:start position:0% +going to be + + + align:start position:0% +going to be +zero because the force is perpendicular + + align:start position:0% +zero because the force is perpendicular + + + align:start position:0% +zero because the force is perpendicular +to the motion. + + align:start position:0% +to the motion. + + + align:start position:0% +to the motion. +Well, + + align:start position:0% + + + + align:start position:0% + +now we can say it directly by saying + + align:start position:0% +now we can say it directly by saying + + + align:start position:0% +now we can say it directly by saying +well if we take any point of a circle + + align:start position:0% +well if we take any point of a circle + + + align:start position:0% +well if we take any point of a circle +sorry + + align:start position:0% +sorry + + + align:start position:0% +sorry +so you know if you have any point of a + + align:start position:0% +so you know if you have any point of a + + + align:start position:0% +so you know if you have any point of a +circle then the tangent vector + + align:start position:0% +circle then the tangent vector + + + align:start position:0% +circle then the tangent vector +to the circle will be tangent well it's + + align:start position:0% +to the circle will be tangent well it's + + + align:start position:0% +to the circle will be tangent well it's +tangent to the circle so that means it's + + align:start position:0% +tangent to the circle so that means it's + + + align:start position:0% +tangent to the circle so that means it's +perpendicular to the radial direction + + align:start position:0% +perpendicular to the radial direction + + + align:start position:0% +perpendicular to the radial direction +while the force is pointing + + align:start position:0% +while the force is pointing + + + align:start position:0% +while the force is pointing +in the radial direction. So you have a + + align:start position:0% +in the radial direction. So you have a + + + align:start position:0% +in the radial direction. So you have a +right angle between them. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% +So + + + align:start position:0% +So +f is perpendicular to t. + + align:start position:0% +f is perpendicular to t. + + + align:start position:0% +f is perpendicular to t. +So f t is zero. And the line integral of + + align:start position:0% +So f t is zero. And the line integral of + + + align:start position:0% +So f t is zero. And the line integral of +ft t ds is just zero. + + align:start position:0% +ft t ds is just zero. + + + align:start position:0% +ft t ds is just zero. +See that's much easier than writing well + + align:start position:0% +See that's much easier than writing well + + + align:start position:0% +See that's much easier than writing well +this is integral of x dx + y d y what do + + align:start position:0% +this is integral of x dx + y d y what do + + + align:start position:0% +this is integral of x dx + y d y what do +we do? Well we probably we set x= a + + align:start position:0% +we do? Well we probably we set x= a + + + align:start position:0% +we do? Well we probably we set x= a +cosine theta y= a sin theta. We get a + + align:start position:0% +cosine theta y= a sin theta. We get a + + + align:start position:0% +cosine theta y= a sin theta. We get a +bunch of trick things. Oh it cancels out + + align:start position:0% +bunch of trick things. Oh it cancels out + + + align:start position:0% +bunch of trick things. Oh it cancels out +to zero. It's not much harder but we + + align:start position:0% +to zero. It's not much harder but we + + + align:start position:0% +to zero. It's not much harder but we +saved time by not even thinking about + + align:start position:0% +saved time by not even thinking about + + + align:start position:0% +saved time by not even thinking about +how to parameterize things. + + align:start position:0% +how to parameterize things. + + + align:start position:0% +how to parameterize things. +Let's just do a last one. That was first + + align:start position:0% +Let's just do a last one. That was first + + + align:start position:0% +Let's just do a last one. That was first +one. + + align:start position:0% +one. + + + align:start position:0% +one. +Let's say now that I take the same curve + + align:start position:0% +Let's say now that I take the same curve + + + align:start position:0% +Let's say now that I take the same curve +C, + + align:start position:0% + + + + align:start position:0% + +but now my vector field is the one that + + align:start position:0% +but now my vector field is the one that + + + align:start position:0% +but now my vector field is the one that +rotates + + align:start position:0% + + + + align:start position:0% + +- Yi + XJ. + + align:start position:0% +- Yi + XJ. + + + align:start position:0% +- Yi + XJ. +Okay. So + + align:start position:0% +Okay. So + + + align:start position:0% +Okay. So +that means + + align:start position:0% + + + + align:start position:0% + +along my circle + + align:start position:0% + + + + align:start position:0% + +the tension vector goes like this + + align:start position:0% +the tension vector goes like this + + + align:start position:0% +the tension vector goes like this +and my vector field is also going + + align:start position:0% +and my vector field is also going + + + align:start position:0% +and my vector field is also going +around. So in fact at this point the + + align:start position:0% +around. So in fact at this point the + + + align:start position:0% +around. So in fact at this point the +vector field will also be going in the + + align:start position:0% +vector field will also be going in the + + + align:start position:0% +vector field will also be going in the +same direction. + + align:start position:0% + + + + align:start position:0% + +Okay, so now + + align:start position:0% +Okay, so now + + + align:start position:0% +Okay, so now +F is actually parallel to the tangent + + align:start position:0% +F is actually parallel to the tangent + + + align:start position:0% +F is actually parallel to the tangent +direction. So that means that the dot + + align:start position:0% +direction. So that means that the dot + + + align:start position:0% +direction. So that means that the dot +product F dot T, remember that's the + + align:start position:0% +product F dot T, remember that's the + + + align:start position:0% +product F dot T, remember that's the +component of F in this direction that + + align:start position:0% +component of F in this direction that + + + align:start position:0% +component of F in this direction that +will be the same as the length of F, + + align:start position:0% +will be the same as the length of F, + + + align:start position:0% +will be the same as the length of F, +right? But what's the length of F on + + align:start position:0% +right? But what's the length of F on + + + align:start position:0% +right? But what's the length of F on +this circle if this radius is A? It's + + align:start position:0% +this circle if this radius is A? It's + + + align:start position:0% +this circle if this radius is A? It's +just going to be a. That's what we said + + align:start position:0% +just going to be a. That's what we said + + + align:start position:0% +just going to be a. That's what we said +earlier about this vector field. + + align:start position:0% +earlier about this vector field. + + + align:start position:0% +earlier about this vector field. +So at every point this dot product is a. + + align:start position:0% +So at every point this dot product is a. + + + align:start position:0% +So at every point this dot product is a. +Now we know how to integrate that quite + + align:start position:0% +Now we know how to integrate that quite + + + align:start position:0% +Now we know how to integrate that quite +quickly + + align:start position:0% + + + + align:start position:0% + +because that becomes the integral of a + + align:start position:0% +because that becomes the integral of a + + + align:start position:0% +because that becomes the integral of a +ds. But a is a constant so we can take + + align:start position:0% +ds. But a is a constant so we can take + + + align:start position:0% +ds. But a is a constant so we can take +it out. And now what do we get when we + + align:start position:0% +it out. And now what do we get when we + + + align:start position:0% +it out. And now what do we get when we +integrate ds along c? Well, we should + + align:start position:0% +integrate ds along c? Well, we should + + + align:start position:0% +integrate ds along c? Well, we should +get the total length of the curve. + + align:start position:0% +get the total length of the curve. + + + align:start position:0% +get the total length of the curve. +Right? If we sum all the little pieces + + align:start position:0% +Right? If we sum all the little pieces + + + align:start position:0% +Right? If we sum all the little pieces +of arc length, + + align:start position:0% + + + + align:start position:0% + +but we know that the length of a circle + + align:start position:0% +but we know that the length of a circle + + + align:start position:0% +but we know that the length of a circle +of radius a is 2 pi a. So we get 2 pi a^ + + align:start position:0% +of radius a is 2 pi a. So we get 2 pi a^ + + + align:start position:0% +of radius a is 2 pi a. So we get 2 pi a^ +2. + + align:start position:0% +2. + + + align:start position:0% +2. +If we were to compute that + + align:start position:0% + + + + align:start position:0% + +by hand, + + align:start position:0% +by hand, + + + align:start position:0% +by hand, +well, what would we do? We'd set So, we + + align:start position:0% +well, what would we do? We'd set So, we + + + align:start position:0% +well, what would we do? We'd set So, we +would be computing integral of minus y + + align:start position:0% +would be computing integral of minus y + + + align:start position:0% +would be computing integral of minus y +dx + x d y. We'd probably set since + + align:start position:0% +dx + x d y. We'd probably set since + + + align:start position:0% +dx + x d y. We'd probably set since +we're on a circle x= a cos theta y = a + + align:start position:0% +we're on a circle x= a cos theta y = a + + + align:start position:0% +we're on a circle x= a cos theta y = a +sin theta + + align:start position:0% +sin theta + + + align:start position:0% +sin theta +for theta between 0 and 2 pi. + + align:start position:0% +for theta between 0 and 2 pi. + + + align:start position:0% +for theta between 0 and 2 pi. +So then we would get dx and dy out of + + align:start position:0% +So then we would get dx and dy out of + + + align:start position:0% +So then we would get dx and dy out of +these. + + align:start position:0% + + + + align:start position:0% + +So y is + + align:start position:0% +So y is + + + align:start position:0% +So y is +a sin theta. dx is a sin theta d theta. + + align:start position:0% +a sin theta. dx is a sin theta d theta. + + + align:start position:0% +a sin theta. dx is a sin theta d theta. +If you differentiate a cosine plus a cos + + align:start position:0% +If you differentiate a cosine plus a cos + + + align:start position:0% +If you differentiate a cosine plus a cos +theta + + align:start position:0% +theta + + + align:start position:0% +theta +a cos theta d theta. + + align:start position:0% +a cos theta d theta. + + + align:start position:0% +a cos theta d theta. +Well, you'll just end up with integral + + align:start position:0% +Well, you'll just end up with integral + + + align:start position:0% +Well, you'll just end up with integral +from 0 to 2 pi of a^ 2 * sin square + + align:start position:0% +from 0 to 2 pi of a^ 2 * sin square + + + align:start position:0% +from 0 to 2 pi of a^ 2 * sin square +theta plus cosine square theta d theta + + align:start position:0% +theta plus cosine square theta d theta + + + align:start position:0% +theta plus cosine square theta d theta +that becomes just one and you get the + + align:start position:0% +that becomes just one and you get the + + + align:start position:0% +that becomes just one and you get the +same answer. It took about the same + + align:start position:0% +same answer. It took about the same + + + align:start position:0% +same answer. It took about the same +amount of time because I did this one + + align:start position:0% +amount of time because I did this one + + + align:start position:0% +amount of time because I did this one +rushing very quickly. Okay, but normally + + align:start position:0% +rushing very quickly. Okay, but normally + + + align:start position:0% +rushing very quickly. Okay, but normally +it takes about you know at least twice + + align:start position:0% +it takes about you know at least twice + + + align:start position:0% +it takes about you know at least twice +the amount of time to do it with a + + align:start position:0% +the amount of time to do it with a + + + align:start position:0% +the amount of time to do it with a +calculation. So that tells you sometimes + + align:start position:0% +calculation. So that tells you sometimes + + + align:start position:0% +calculation. So that tells you sometimes +it's worth thinking geometrically. \ No newline at end of file diff --git a/yEbr410E2RE.txt b/yEbr410E2RE.txt new file mode 100644 index 0000000000000000000000000000000000000000..1321e95941727baaa4adae63f31b65e3ab95c1dc --- /dev/null +++ b/yEbr410E2RE.txt @@ -0,0 +1,8107 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license + + align:start position:0% +a Creative Commons license + + + align:start position:0% +a Creative Commons license +your support will help MIT + + align:start position:0% +your support will help MIT + + + align:start position:0% +your support will help MIT +OpenCourseWare continue to offer high + + align:start position:0% +OpenCourseWare continue to offer high + + + align:start position:0% +OpenCourseWare continue to offer high +quality educational resources for free + + align:start position:0% +quality educational resources for free + + + align:start position:0% +quality educational resources for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu + + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu +well a scientist who approaches a + + align:start position:0% +well a scientist who approaches a + + + align:start position:0% +well a scientist who approaches a +complex phenomena or when an engineer + + align:start position:0% +complex phenomena or when an engineer + + + align:start position:0% +complex phenomena or when an engineer +looks at a different difficult problem + + align:start position:0% +looks at a different difficult problem + + + align:start position:0% +looks at a different difficult problem +the user will break it up into pieces + + align:start position:0% +the user will break it up into pieces + + + align:start position:0% +the user will break it up into pieces +and try to understand them + + align:start position:0% +and try to understand them + + + align:start position:0% +and try to understand them +this phenomena and solve them separately + + align:start position:0% +this phenomena and solve them separately + + + align:start position:0% +this phenomena and solve them separately +and the staining intelligence is one + + align:start position:0% +and the staining intelligence is one + + + align:start position:0% +and the staining intelligence is one +such very very complex in fact + + align:start position:0% +such very very complex in fact + + + align:start position:0% +such very very complex in fact +extraordinary complex problem and over + + align:start position:0% +extraordinary complex problem and over + + + align:start position:0% +extraordinary complex problem and over +the years this divide and conquer + + align:start position:0% +the years this divide and conquer + + + align:start position:0% +the years this divide and conquer +approach produced a number of very + + align:start position:0% +approach produced a number of very + + + align:start position:0% +approach produced a number of very +successful fields like computer vision + + align:start position:0% +successful fields like computer vision + + + align:start position:0% +successful fields like computer vision +natural language processing cognitive + + align:start position:0% +natural language processing cognitive + + + align:start position:0% +natural language processing cognitive +science neuroscience machine vision and + + align:start position:0% +science neuroscience machine vision and + + + align:start position:0% +science neuroscience machine vision and +so on but we need to remember that most + + align:start position:0% +so on but we need to remember that most + + + align:start position:0% +so on but we need to remember that most +cognitive tasks that humans perform + + align:start position:0% +cognitive tasks that humans perform + + + align:start position:0% +cognitive tasks that humans perform +actually go across modalities they span + + align:start position:0% +actually go across modalities they span + + + align:start position:0% +actually go across modalities they span +these established fields and the goal of + + align:start position:0% +these established fields and the goal of + + + align:start position:0% +these established fields and the goal of +our trust is to bring together + + align:start position:0% +our trust is to bring together + + + align:start position:0% +our trust is to bring together +techniques from all these fields create + + align:start position:0% +techniques from all these fields create + + + align:start position:0% +techniques from all these fields create +new models and for solving intelligence + + align:start position:0% +new models and for solving intelligence + + + align:start position:0% +new models and for solving intelligence +tasks and we also would like to + + align:start position:0% +tasks and we also would like to + + + align:start position:0% +tasks and we also would like to +understand how these tasks operate in + + align:start position:0% +understand how these tasks operate in + + + align:start position:0% +understand how these tasks operate in +the brain so I will start with one task + + align:start position:0% +the brain so I will start with one task + + + align:start position:0% +the brain so I will start with one task +which is scene recognition well it does + + align:start position:0% +which is scene recognition well it does + + + align:start position:0% +which is scene recognition well it does +scene recognition involve well machine + + align:start position:0% +scene recognition involve well machine + + + align:start position:0% +scene recognition involve well machine +in order to recognize the scene a + + align:start position:0% +in order to recognize the scene a + + + align:start position:0% +in order to recognize the scene a +machine needs to do some type of + + align:start position:0% +machine needs to do some type of + + + align:start position:0% +machine needs to do some type of +verification is that a streetlamp + + align:start position:0% + + + + align:start position:0% + +it needs to the detection are there + + align:start position:0% +it needs to the detection are there + + + align:start position:0% +it needs to the detection are there +people in the scene it needs to do + + align:start position:0% +people in the scene it needs to do + + + align:start position:0% +people in the scene it needs to do +identification is this particular + + align:start position:0% +identification is this particular + + + align:start position:0% +identification is this particular +building potala palace somewhere in + + align:start position:0% +building potala palace somewhere in + + + align:start position:0% +building potala palace somewhere in +Tibet into the object catalyzation look + + align:start position:0% +Tibet into the object catalyzation look + + + align:start position:0% +Tibet into the object catalyzation look +at this image and tell me where a + + align:start position:0% +at this image and tell me where a + + + align:start position:0% +at this image and tell me where a +mountain squeeze building streetlamps + + align:start position:0% +mountain squeeze building streetlamps + + + align:start position:0% +mountain squeeze building streetlamps +vendors people and so forth we should + + align:start position:0% +vendors people and so forth we should + + + align:start position:0% +vendors people and so forth we should +also be able to recognize activity what + + align:start position:0% +also be able to recognize activity what + + + align:start position:0% +also be able to recognize activity what +is this person doing or what are these + + align:start position:0% +is this person doing or what are these + + + align:start position:0% +is this person doing or what are these +two guys doing here well currently our + + align:start position:0% +two guys doing here well currently our + + + align:start position:0% +two guys doing here well currently our +machines are pretty bad and all of these + + align:start position:0% +machines are pretty bad and all of these + + + align:start position:0% +machines are pretty bad and all of these +tasks I understand that there has been + + align:start position:0% +tasks I understand that there has been + + + align:start position:0% +tasks I understand that there has been +quite a lot of progress recently made in + + align:start position:0% +quite a lot of progress recently made in + + + align:start position:0% +quite a lot of progress recently made in +machine learning and I also seen some + + align:start position:0% +machine learning and I also seen some + + + align:start position:0% +machine learning and I also seen some +claims that machines perform better than + + align:start position:0% +claims that machines perform better than + + + align:start position:0% +claims that machines perform better than +humans in some visual tasks however I + + align:start position:0% +humans in some visual tasks however I + + + align:start position:0% +humans in some visual tasks however I +think we should take these claims of the + + align:start position:0% +think we should take these claims of the + + + align:start position:0% +think we should take these claims of the +grain of salt first there is nothing + + align:start position:0% +grain of salt first there is nothing + + + align:start position:0% +grain of salt first there is nothing +amazing about machines doing certain + + align:start position:0% +amazing about machines doing certain + + + align:start position:0% +amazing about machines doing certain +things better than humans people did it + + align:start position:0% +things better than humans people did it + + + align:start position:0% +things better than humans people did it +over millenia humans need the tools to + + align:start position:0% +over millenia humans need the tools to + + + align:start position:0% +over millenia humans need the tools to +be built pyramids they build tools to + + align:start position:0% +be built pyramids they build tools to + + + align:start position:0% +be built pyramids they build tools to +carry heavy things to live them to go + + align:start position:0% +carry heavy things to live them to go + + + align:start position:0% +carry heavy things to live them to go +faster and so on well you'll tell me no + + align:start position:0% +faster and so on well you'll tell me no + + + align:start position:0% +faster and so on well you'll tell me no +no we need we are talking about + + align:start position:0% +no we need we are talking about + + + align:start position:0% +no we need we are talking about +intelligent tasks well for $5.00 you can + + align:start position:0% +intelligent tasks well for $5.00 you can + + + align:start position:0% +intelligent tasks well for $5.00 you can +buy a calculator that multiplies numbers + + align:start position:0% +buy a calculator that multiplies numbers + + + align:start position:0% +buy a calculator that multiplies numbers +much better than you do for $100 you can + + align:start position:0% +much better than you do for $100 you can + + + align:start position:0% +much better than you do for $100 you can +build a gadget that has a huge lookup + + align:start position:0% +build a gadget that has a huge lookup + + + align:start position:0% +build a gadget that has a huge lookup +table and plays just much better than + + align:start position:0% +table and plays just much better than + + + align:start position:0% +table and plays just much better than +any of you + + align:start position:0% + + + + align:start position:0% + +so when you hear that the computer can + + align:start position:0% +so when you hear that the computer can + + + align:start position:0% +so when you hear that the computer can +distinguish between 20 breeds of dogs or + + align:start position:0% +distinguish between 20 breeds of dogs or + + + align:start position:0% +distinguish between 20 breeds of dogs or +something like that better than you do I + + align:start position:0% +something like that better than you do I + + + align:start position:0% +something like that better than you do I +don't think you should assume that the + + align:start position:0% +don't think you should assume that the + + + align:start position:0% +don't think you should assume that the +vision problem is solved well understand + + align:start position:0% +vision problem is solved well understand + + + align:start position:0% +vision problem is solved well understand +I'm not saying that because we have a + + align:start position:0% +I'm not saying that because we have a + + + align:start position:0% +I'm not saying that because we have a +dramatically better solution not at all + + align:start position:0% +dramatically better solution not at all + + + align:start position:0% +dramatically better solution not at all +my point is that the problems of real + + align:start position:0% +my point is that the problems of real + + + align:start position:0% +my point is that the problems of real +visual understanding and real language + + align:start position:0% +visual understanding and real language + + + align:start position:0% +visual understanding and real language +understanding I extraordinary heart and + + align:start position:0% +understanding I extraordinary heart and + + + align:start position:0% +understanding I extraordinary heart and +we need to be patient and try to + + align:start position:0% +we need to be patient and try to + + + align:start position:0% +we need to be patient and try to +understand why and eventually find + + align:start position:0% +understand why and eventually find + + + align:start position:0% +understand why and eventually find +better solutions so back to visual + + align:start position:0% +better solutions so back to visual + + + align:start position:0% +better solutions so back to visual +understanding problem so as I said + + align:start position:0% +understanding problem so as I said + + + align:start position:0% +understanding problem so as I said +machines are bad at these things but + + align:start position:0% +machines are bad at these things but + + + align:start position:0% +machines are bad at these things but +humans are absolutely awesome you have + + align:start position:0% +humans are absolutely awesome you have + + + align:start position:0% +humans are absolutely awesome you have +absolutely no trouble to do verification + + align:start position:0% +absolutely no trouble to do verification + + + align:start position:0% +absolutely no trouble to do verification +detection identification categorization + + align:start position:0% +detection identification categorization + + + align:start position:0% +detection identification categorization +you could do much more than that you + + align:start position:0% +you could do much more than that you + + + align:start position:0% +you could do much more than that you +could recognize spatial and temporal or + + align:start position:0% +could recognize spatial and temporal or + + + align:start position:0% +could recognize spatial and temporal or +relationship between objects you can do + + align:start position:0% +relationship between objects you can do + + + align:start position:0% +relationship between objects you can do +event recognition you can explain things + + align:start position:0% +event recognition you can explain things + + + align:start position:0% +event recognition you can explain things +you can look at that image that I showed + + align:start position:0% +you can look at that image that I showed + + + align:start position:0% +you can look at that image that I showed +you and and tell me what past events + + align:start position:0% +you and and tell me what past events + + + align:start position:0% +you and and tell me what past events +caused the scene to look like it is you + + align:start position:0% +caused the scene to look like it is you + + + align:start position:0% +caused the scene to look like it is you +can look at that scene and say what + + align:start position:0% +can look at that scene and say what + + + align:start position:0% +can look at that scene and say what +future events might occur in that scene + + align:start position:0% +future events might occur in that scene + + + align:start position:0% +future events might occur in that scene +you can fill gaps you can hallucinate + + align:start position:0% +you can fill gaps you can hallucinate + + + align:start position:0% +you can fill gaps you can hallucinate +things you could tell me what objects + + align:start position:0% +things you could tell me what objects + + + align:start position:0% +things you could tell me what objects +which were occluded in that scene which + + align:start position:0% +which were occluded in that scene which + + + align:start position:0% +which were occluded in that scene which +I've barely seen actually there might be + + align:start position:0% +I've barely seen actually there might be + + + align:start position:0% +I've barely seen actually there might be +present there and what events not + + align:start position:0% +present there and what events not + + + align:start position:0% +present there and what events not +visible in the scene could have occurred + + align:start position:0% + + + + align:start position:0% + +so why are machines are falling short + + align:start position:0% + + + + align:start position:0% + +well in part our visual system is tuned + + align:start position:0% +well in part our visual system is tuned + + + align:start position:0% +well in part our visual system is tuned +to process structures typically found in + + align:start position:0% +to process structures typically found in + + + align:start position:0% +to process structures typically found in +the world but our machines have no idea + + align:start position:0% +the world but our machines have no idea + + + align:start position:0% +the world but our machines have no idea +they don't know enough about the world + + align:start position:0% +they don't know enough about the world + + + align:start position:0% +they don't know enough about the world +and they don't know what structures in + + align:start position:0% +and they don't know what structures in + + + align:start position:0% +and they don't know what structures in +events make sense and typically happen + + align:start position:0% +events make sense and typically happen + + + align:start position:0% +events make sense and typically happen +in the world so I will show you a blurry + + align:start position:0% +in the world so I will show you a blurry + + + align:start position:0% +in the world so I will show you a blurry +video and one day if well the some of + + align:start position:0% +video and one day if well the some of + + + align:start position:0% +video and one day if well the some of +you who didn't see it but you could + + align:start position:0% +you who didn't see it but you could + + + align:start position:0% +you who didn't see it but you could +figure out what's going on + + align:start position:0% + + + + align:start position:0% + +who have not seen this video could you + + align:start position:0% +who have not seen this video could you + + + align:start position:0% +who have not seen this video could you +tell me what you saw + + align:start position:0% + + + + align:start position:0% + +right well this is amazing it was almost + + align:start position:0% +right well this is amazing it was almost + + + align:start position:0% +right well this is amazing it was almost +no pixels there and you still recognize + + align:start position:0% +no pixels there and you still recognize + + + align:start position:0% +no pixels there and you still recognize +what's going on well because you know + + align:start position:0% +what's going on well because you know + + + align:start position:0% +what's going on well because you know +what typically happens in the world well + + align:start position:0% +what typically happens in the world well + + + align:start position:0% +what typically happens in the world well +of course it was sort of a joke and + + align:start position:0% +of course it was sort of a joke and + + + align:start position:0% +of course it was sort of a joke and +people sometimes make mistakes - so + + align:start position:0% +people sometimes make mistakes - so + + + align:start position:0% +people sometimes make mistakes - so +here's the unblurred video but all jokes + + align:start position:0% +here's the unblurred video but all jokes + + + align:start position:0% +here's the unblurred video but all jokes +Oh jokes aside though it would have be + + align:start position:0% +Oh jokes aside though it would have be + + + align:start position:0% +Oh jokes aside though it would have be +the extraordinary if our machines could + + align:start position:0% +the extraordinary if our machines could + + + align:start position:0% +the extraordinary if our machines could +make mistakes such like this + + align:start position:0% +make mistakes such like this + + + align:start position:0% +make mistakes such like this +not even close well so we may want to + + align:start position:0% +not even close well so we may want to + + + align:start position:0% +not even close well so we may want to +ask ourselves questions how is this + + align:start position:0% +ask ourselves questions how is this + + + align:start position:0% +ask ourselves questions how is this +knowledge that you seem to have is + + align:start position:0% +knowledge that you seem to have is + + + align:start position:0% +knowledge that you seem to have is +obtained and how can we pass this + + align:start position:0% +obtained and how can we pass this + + + align:start position:0% +obtained and how can we pass this +knowledge to our computers and how can + + align:start position:0% +knowledge to our computers and how can + + + align:start position:0% +knowledge to our computers and how can +be determined whether this computer + + align:start position:0% +be determined whether this computer + + + align:start position:0% +be determined whether this computer +knowledge is correct our partial answer + + align:start position:0% +knowledge is correct our partial answer + + + align:start position:0% +knowledge is correct our partial answer +is using language and I bolded the word + + align:start position:0% +is using language and I bolded the word + + + align:start position:0% +is using language and I bolded the word +partial here because clearly there are + + align:start position:0% +partial here because clearly there are + + + align:start position:0% +partial here because clearly there are +many other ways humans obtain knowledge + + align:start position:0% +many other ways humans obtain knowledge + + + align:start position:0% +many other ways humans obtain knowledge +about the world but today I will be + + align:start position:0% +about the world but today I will be + + + align:start position:0% +about the world but today I will be +talking about language and and show you + + align:start position:0% +talking about language and and show you + + + align:start position:0% +talking about language and and show you +what is needed to give knowledge to the + + align:start position:0% +what is needed to give knowledge to the + + + align:start position:0% +what is needed to give knowledge to the +machine so we have a proposal we would + + align:start position:0% +machine so we have a proposal we would + + + align:start position:0% +machine so we have a proposal we would +like to create a knowledge base that + + align:start position:0% +like to create a knowledge base that + + + align:start position:0% +like to create a knowledge base that +contains descriptions of objects their + + align:start position:0% +contains descriptions of objects their + + + align:start position:0% +contains descriptions of objects their +properties relations between them as + + align:start position:0% +properties relations between them as + + + align:start position:0% +properties relations between them as +they typically found in the world and we + + align:start position:0% +they typically found in the world and we + + + align:start position:0% +they typically found in the world and we +want to make this knowledge base + + align:start position:0% +want to make this knowledge base + + + align:start position:0% +want to make this knowledge base +available to a senior cognition system + + align:start position:0% +available to a senior cognition system + + + align:start position:0% +available to a senior cognition system +and to test the performance of the + + align:start position:0% +and to test the performance of the + + + align:start position:0% +and to test the performance of the +system we will ask natural language + + align:start position:0% +system we will ask natural language + + + align:start position:0% +system we will ask natural language +questions one of our students decided to + + align:start position:0% +questions one of our students decided to + + + align:start position:0% +questions one of our students decided to +see what questions people actually ask + + align:start position:0% +see what questions people actually ask + + + align:start position:0% +see what questions people actually ask +and he set up Amazon torque experiment + + align:start position:0% +and he set up Amazon torque experiment + + + align:start position:0% +and he set up Amazon torque experiment +where he showed people hundreds of + + align:start position:0% +where he showed people hundreds of + + + align:start position:0% +where he showed people hundreds of +images and asked them to + + align:start position:0% +images and asked them to + + + align:start position:0% +images and asked them to +right down generate questions about + + align:start position:0% +right down generate questions about + + + align:start position:0% +right down generate questions about +these images and I'll show you a couple + + align:start position:0% + + + + align:start position:0% + +here's a scene in here the question that + + align:start position:0% +here's a scene in here the question that + + + align:start position:0% +here's a scene in here the question that +people ask you know how many men in the + + align:start position:0% +people ask you know how many men in the + + + align:start position:0% +people ask you know how many men in the +picture what's in the cart what does the + + align:start position:0% +picture what's in the cart what does the + + + align:start position:0% +picture what's in the cart what does the +number on the sign say is there any + + align:start position:0% +number on the sign say is there any + + + align:start position:0% +number on the sign say is there any +luggage the color shot of some lady + + align:start position:0% +luggage the color shot of some lady + + + align:start position:0% +luggage the color shot of some lady +another example who is winning yellow or + + align:start position:0% +another example who is winning yellow or + + + align:start position:0% +another example who is winning yellow or +red well the answer is of course red but + + align:start position:0% +red well the answer is of course red but + + + align:start position:0% +red well the answer is of course red but +how did you do that + + align:start position:0% +how did you do that + + + align:start position:0% +how did you do that +well you need to know that this is a + + align:start position:0% +well you need to know that this is a + + + align:start position:0% +well you need to know that this is a +sporting event which all of you do that + + align:start position:0% +sporting event which all of you do that + + + align:start position:0% +sporting event which all of you do that +it involves in this particular sporting + + align:start position:0% +it involves in this particular sporting + + + align:start position:0% +it involves in this particular sporting +event winners and losers that you do it + + align:start position:0% +event winners and losers that you do it + + + align:start position:0% +event winners and losers that you do it +needs to know that this sort of + + align:start position:0% +needs to know that this sort of + + + align:start position:0% +needs to know that this sort of +shorthand yellow and red means people + + align:start position:0% +shorthand yellow and red means people + + + align:start position:0% +shorthand yellow and red means people +wearing these colors rather than colors + + align:start position:0% +wearing these colors rather than colors + + + align:start position:0% +wearing these colors rather than colors +themselves you need to know that to pay + + align:start position:0% +themselves you need to know that to pay + + + align:start position:0% +themselves you need to know that to pay +no attention to people wearing red or + + align:start position:0% +no attention to people wearing red or + + + align:start position:0% +no attention to people wearing red or +maybe blue in the audience and you also + + align:start position:0% +maybe blue in the audience and you also + + + align:start position:0% +maybe blue in the audience and you also +need to know that a participant on the + + align:start position:0% +need to know that a participant on the + + + align:start position:0% +need to know that a participant on the +floor is likely a loser not a winner + + align:start position:0% +floor is likely a loser not a winner + + + align:start position:0% +floor is likely a loser not a winner +it's a lot of knowledge so back to our + + align:start position:0% +it's a lot of knowledge so back to our + + + align:start position:0% +it's a lot of knowledge so back to our +proposal we want to try to give at least + + align:start position:0% +proposal we want to try to give at least + + + align:start position:0% +proposal we want to try to give at least +some of that knowledge using language + + align:start position:0% +some of that knowledge using language + + + align:start position:0% +some of that knowledge using language +and for that of course we need tools and + + align:start position:0% +and for that of course we need tools and + + + align:start position:0% +and for that of course we need tools and +over the years we built a system called + + align:start position:0% +over the years we built a system called + + + align:start position:0% +over the years we built a system called +start which in fact contains some tools + + align:start position:0% +start which in fact contains some tools + + + align:start position:0% +start which in fact contains some tools +that could be helpful for this task and + + align:start position:0% +that could be helpful for this task and + + + align:start position:0% +that could be helpful for this task and +I could we'll be happy to share the API + + align:start position:0% +I could we'll be happy to share the API + + + align:start position:0% +I could we'll be happy to share the API +with you so that you could use the + + align:start position:0% +with you so that you could use the + + + align:start position:0% +with you so that you could use the +system or maybe try to hear what to do + + align:start position:0% +system or maybe try to hear what to do + + + align:start position:0% +system or maybe try to hear what to do +with the knowledge that you give it so + + align:start position:0% +with the knowledge that you give it so + + + align:start position:0% +with the knowledge that you give it so +there are only three tools on the slide + + align:start position:0% +there are only three tools on the slide + + + align:start position:0% +there are only three tools on the slide +so one is going from language to + + align:start position:0% +so one is going from language to + + + align:start position:0% +so one is going from language to +structure so in order to provide machine + + align:start position:0% +structure so in order to provide machine + + + align:start position:0% +structure so in order to provide machine +with knowledge we give them shin a bunch + + align:start position:0% +with knowledge we give them shin a bunch + + + align:start position:0% +with knowledge we give them shin a bunch +of sentences stacks paragraphs and that + + align:start position:0% +of sentences stacks paragraphs and that + + + align:start position:0% +of sentences stacks paragraphs and that +will be converted into some kind of + + align:start position:0% +will be converted into some kind of + + + align:start position:0% +will be converted into some kind of +semantic representation and I'll show + + align:start position:0% +semantic representation and I'll show + + + align:start position:0% +semantic representation and I'll show +some details of that we want to go the + + align:start position:0% +some details of that we want to go the + + + align:start position:0% +some details of that we want to go the +other direction we want a machine to + + align:start position:0% +other direction we want a machine to + + + align:start position:0% +other direction we want a machine to +explain what it does or describe it + + align:start position:0% +explain what it does or describe it + + + align:start position:0% +explain what it does or describe it +knowledge using language + + align:start position:0% +knowledge using language + + + align:start position:0% +knowledge using language +have a generator that does that that + + align:start position:0% +have a generator that does that that + + + align:start position:0% +have a generator that does that that +goes from semantic representation to + + align:start position:0% +goes from semantic representation to + + + align:start position:0% +goes from semantic representation to +language and we want to test the machine + + align:start position:0% +language and we want to test the machine + + + align:start position:0% +language and we want to test the machine +because it's very important to know + + align:start position:0% +because it's very important to know + + + align:start position:0% +because it's very important to know +whether what you told machine the + + align:start position:0% +whether what you told machine the + + + align:start position:0% +whether what you told machine the +machine is actually it understood you + + align:start position:0% +machine is actually it understood you + + + align:start position:0% +machine is actually it understood you +correctly we want to ask questions give + + align:start position:0% +correctly we want to ask questions give + + + align:start position:0% +correctly we want to ask questions give +queries those will be converted in + + align:start position:0% +queries those will be converted in + + + align:start position:0% +queries those will be converted in +semantic representations that will be + + align:start position:0% +semantic representations that will be + + + align:start position:0% +semantic representations that will be +matched against random she knows and the + + align:start position:0% +matched against random she knows and the + + + align:start position:0% +matched against random she knows and the +computer will either give you a language + + align:start position:0% +computer will either give you a language + + + align:start position:0% +computer will either give you a language +response or perform some actions which + + align:start position:0% +response or perform some actions which + + + align:start position:0% +response or perform some actions which +will indicate that you understood what + + align:start position:0% +will indicate that you understood what + + + align:start position:0% +will indicate that you understood what +what you asked so we will go through + + align:start position:0% +what you asked so we will go through + + + align:start position:0% +what you asked so we will go through +these tools and I will describe you the + + align:start position:0% +these tools and I will describe you the + + + align:start position:0% +these tools and I will describe you the +start system in details but I just want + + align:start position:0% +start system in details but I just want + + + align:start position:0% +start system in details but I just want +you to remember that this is a + + align:start position:0% +you to remember that this is a + + + align:start position:0% +you to remember that this is a +discipline and engineering enterprise + + align:start position:0% +discipline and engineering enterprise + + + align:start position:0% +discipline and engineering enterprise +and these are the tools that I want to + + align:start position:0% +and these are the tools that I want to + + + align:start position:0% +and these are the tools that I want to +give you and other people so that you + + align:start position:0% +give you and other people so that you + + + align:start position:0% +give you and other people so that you +could start thinking Keeper about human + + align:start position:0% +could start thinking Keeper about human + + + align:start position:0% +could start thinking Keeper about human +abilities and metallic lipstick vision + + align:start position:0% +abilities and metallic lipstick vision + + + align:start position:0% +abilities and metallic lipstick vision +and language and and others some of the + + align:start position:0% +and language and and others some of the + + + align:start position:0% +and language and and others some of the +building blocks of the start system we + + align:start position:0% +building blocks of the start system we + + + align:start position:0% +building blocks of the start system we +need to parse a language we need to come + + align:start position:0% +need to parse a language we need to come + + + align:start position:0% +need to parse a language we need to come +up with semantic representation generate + + align:start position:0% +up with semantic representation generate + + + align:start position:0% +up with semantic representation generate +match reply and and so forth so let's + + align:start position:0% +match reply and and so forth so let's + + + align:start position:0% +match reply and and so forth so let's +very quickly go through that most of you + + align:start position:0% +very quickly go through that most of you + + + align:start position:0% +very quickly go through that most of you +are somewhere in middle school learned + + align:start position:0% +are somewhere in middle school learned + + + align:start position:0% +are somewhere in middle school learned +about parse trees linguist loved and + + align:start position:0% +about parse trees linguist loved and + + + align:start position:0% +about parse trees linguist loved and +read beautiful this is an example of a + + align:start position:0% +read beautiful this is an example of a + + + align:start position:0% +read beautiful this is an example of a +sentence from Tom Sawyer Tom greeted his + + align:start position:0% +sentence from Tom Sawyer Tom greeted his + + + align:start position:0% +sentence from Tom Sawyer Tom greeted his +aunt who was sitting by an open window + + align:start position:0% +aunt who was sitting by an open window + + + align:start position:0% +aunt who was sitting by an open window +in the pleasant in your world apartment + + align:start position:0% +in the pleasant in your world apartment + + + align:start position:0% +in the pleasant in your world apartment +and linguist liked to argue but exactly + + align:start position:0% +and linguist liked to argue but exactly + + + align:start position:0% +and linguist liked to argue but exactly +the representations but pretty much most + + align:start position:0% +the representations but pretty much most + + + align:start position:0% +the representations but pretty much most +of them will agree that something like + + align:start position:0% +of them will agree that something like + + + align:start position:0% +of them will agree that something like +that represents the structure syntactic + + align:start position:0% +that represents the structure syntactic + + + align:start position:0% +that represents the structure syntactic +structure of the sentence well they're + + align:start position:0% +structure of the sentence well they're + + + align:start position:0% +structure of the sentence well they're +beautiful and nice but they're really + + align:start position:0% +beautiful and nice but they're really + + + align:start position:0% +beautiful and nice but they're really +horrible if you want to store them if + + align:start position:0% +horrible if you want to store them if + + + align:start position:0% +horrible if you want to store them if +you want to match them if you want to + + align:start position:0% +you want to match them if you want to + + + align:start position:0% +you want to match them if you want to +retrieve from them and so we use the + + align:start position:0% +retrieve from them and so we use the + + + align:start position:0% +retrieve from them and so we use the +information found in parse trees but we + + align:start position:0% +information found in parse trees but we + + + align:start position:0% +information found in parse trees but we +developed a different representation + + align:start position:0% +developed a different representation + + + align:start position:0% +developed a different representation +which we called toward an expression + + align:start position:0% +which we called toward an expression + + + align:start position:0% +which we called toward an expression +representation which is a more semantic + + align:start position:0% +representation which is a more semantic + + + align:start position:0% +representation which is a more semantic +representation + + align:start position:0% +representation + + + align:start position:0% +representation +language it is syntax driven but it + + align:start position:0% +language it is syntax driven but it + + + align:start position:0% +language it is syntax driven but it +highlights semantic relations which + + align:start position:0% +highlights semantic relations which + + + align:start position:0% +highlights semantic relations which +humans find important and it also of + + align:start position:0% +humans find important and it also of + + + align:start position:0% +humans find important and it also of +because we give this knowledge to + + align:start position:0% +because we give this knowledge to + + + align:start position:0% +because we give this knowledge to +computers we made it very efficient for + + align:start position:0% +computers we made it very efficient for + + + align:start position:0% +computers we made it very efficient for +indexing for matching and for retrieval + + align:start position:0% +indexing for matching and for retrieval + + + align:start position:0% +indexing for matching and for retrieval +it's also reversible and I explained in + + align:start position:0% +it's also reversible and I explained in + + + align:start position:0% +it's also reversible and I explained in +a second what I mean by that we + + align:start position:0% +a second what I mean by that we + + + align:start position:0% +a second what I mean by that we +implemented it as a nest that subject + + align:start position:0% +implemented it as a nest that subject + + + align:start position:0% +implemented it as a nest that subject +relation object set of tuples so here is + + align:start position:0% +relation object set of tuples so here is + + + align:start position:0% +relation object set of tuples so here is +a different sentence say you have a + + align:start position:0% +a different sentence say you have a + + + align:start position:0% +a different sentence say you have a +image you may recognize one of the + + align:start position:0% +image you may recognize one of the + + + align:start position:0% +image you may recognize one of the +characters there in the back it's Andre + + align:start position:0% +characters there in the back it's Andre + + + align:start position:0% +characters there in the back it's Andre +Barbeau and say you want to describe in + + align:start position:0% +Barbeau and say you want to describe in + + + align:start position:0% +Barbeau and say you want to describe in +language what you see here you say + + align:start position:0% +language what you see here you say + + + align:start position:0% +language what you see here you say +something like the person who picked up + + align:start position:0% +something like the person who picked up + + + align:start position:0% +something like the person who picked up +the yellow lemon placed it in the ball + + align:start position:0% +the yellow lemon placed it in the ball + + + align:start position:0% +the yellow lemon placed it in the ball +on the table using the structure + + align:start position:0% +on the table using the structure + + + align:start position:0% +on the table using the structure +subjective Asian object structure you + + align:start position:0% +subjective Asian object structure you + + + align:start position:0% +subjective Asian object structure you +could first place in the sentence you + + align:start position:0% +could first place in the sentence you + + + align:start position:0% +could first place in the sentence you +could create this same expression you + + align:start position:0% +could create this same expression you + + + align:start position:0% +could create this same expression you +could see person picked up lemon that + + align:start position:0% +could see person picked up lemon that + + + align:start position:0% +could see person picked up lemon that +same person placed that lemon in the + + align:start position:0% +same person placed that lemon in the + + + align:start position:0% +same person placed that lemon in the +ball on the table and that lemon happens + + align:start position:0% +ball on the table and that lemon happens + + + align:start position:0% +ball on the table and that lemon happens +to be yellow to make it a little bit + + align:start position:0% +to be yellow to make it a little bit + + + align:start position:0% +to be yellow to make it a little bit +more easy for you to see what's going on + + align:start position:0% +more easy for you to see what's going on + + + align:start position:0% +more easy for you to see what's going on +and convenient for for humans and + + align:start position:0% +and convenient for for humans and + + + align:start position:0% +and convenient for for humans and +machines we created a sort of + + align:start position:0% +machines we created a sort of + + + align:start position:0% +machines we created a sort of +topologically equivalent linearization + + align:start position:0% +topologically equivalent linearization + + + align:start position:0% +topologically equivalent linearization +of that graph that knowledge graph and + + align:start position:0% +of that graph that knowledge graph and + + + align:start position:0% +of that graph that knowledge graph and +as a set of triples they're a little bit + + align:start position:0% +as a set of triples they're a little bit + + + align:start position:0% +as a set of triples they're a little bit +misleading here I just did it for + + align:start position:0% +misleading here I just did it for + + + align:start position:0% +misleading here I just did it for +simplicity but all the words here of + + align:start position:0% +simplicity but all the words here of + + + align:start position:0% +simplicity but all the words here of +course need to have an index because if + + align:start position:0% +course need to have an index because if + + + align:start position:0% +course need to have an index because if +you have say a tall person and a short + + align:start position:0% +you have say a tall person and a short + + + align:start position:0% +you have say a tall person and a short +person or then you will have to + + align:start position:0% +person or then you will have to + + + align:start position:0% +person or then you will have to +distinguish between them so you need + + align:start position:0% +distinguish between them so you need + + + align:start position:0% +distinguish between them so you need +indices but for simplicity I didn't show + + align:start position:0% +indices but for simplicity I didn't show + + + align:start position:0% +indices but for simplicity I didn't show +them here and when the verbs also have + + align:start position:0% +them here and when the verbs also have + + + align:start position:0% +them here and when the verbs also have +indices so that when you use the same + + align:start position:0% +indices so that when you use the same + + + align:start position:0% +indices so that when you use the same +word place here that is the relation + + align:start position:0% +word place here that is the relation + + + align:start position:0% +word place here that is the relation +that ripple that happened to be in the + + align:start position:0% +that ripple that happened to be in the + + + align:start position:0% +that ripple that happened to be in the +ball that the person plays the lemon + + align:start position:0% +ball that the person plays the lemon + + + align:start position:0% +ball that the person plays the lemon +interval + + align:start position:0% +interval + + + align:start position:0% +interval +so this is our presentation and when we + + align:start position:0% +so this is our presentation and when we + + + align:start position:0% +so this is our presentation and when we +distinguished at least three types of + + align:start position:0% +distinguished at least three types of + + + align:start position:0% +distinguished at least three types of +toning expressions so the first type you + + align:start position:0% +toning expressions so the first type you + + + align:start position:0% +toning expressions so the first type you +you see it here syntactic structure of + + align:start position:0% +you see it here syntactic structure of + + + align:start position:0% +you see it here syntactic structure of +of a sentence we also have syntactic + + align:start position:0% +of a sentence we also have syntactic + + + align:start position:0% +of a sentence we also have syntactic +features the fact that the sitting was + + align:start position:0% +features the fact that the sitting was + + + align:start position:0% +features the fact that the sitting was +it was past tense + + align:start position:0% +it was past tense + + + align:start position:0% +it was past tense +she was was sitting it said here that + + align:start position:0% +she was was sitting it said here that + + + align:start position:0% +she was was sitting it said here that +it's a progressive tense was sitting + + align:start position:0% +it's a progressive tense was sitting + + + align:start position:0% +it's a progressive tense was sitting +that and also what kind of articles + + align:start position:0% +that and also what kind of articles + + + align:start position:0% +that and also what kind of articles +things have the window were heard and an + + align:start position:0% +things have the window were heard and an + + + align:start position:0% +things have the window were heard and an +article an indefinite article and also + + align:start position:0% +article an indefinite article and also + + + align:start position:0% +article an indefinite article and also +the lexical features that don't change + + align:start position:0% +the lexical features that don't change + + + align:start position:0% +the lexical features that don't change +from sentence to sentence the fact that + + align:start position:0% +from sentence to sentence the fact that + + + align:start position:0% +from sentence to sentence the fact that +tom is a proper noun and so forth well I + + align:start position:0% +tom is a proper noun and so forth well I + + + align:start position:0% +tom is a proper noun and so forth well I +told you that our presentation is + + align:start position:0% + + + + align:start position:0% + +irreversible well we need to be able to + + align:start position:0% +irreversible well we need to be able to + + + align:start position:0% +irreversible well we need to be able to +teach machines to talk to us and there + + align:start position:0% +teach machines to talk to us and there + + + align:start position:0% +teach machines to talk to us and there +are many reasons to do that some of them + + align:start position:0% +are many reasons to do that some of them + + + align:start position:0% +are many reasons to do that some of them +are shown on the slide we want your + + align:start position:0% +are shown on the slide we want your + + + align:start position:0% +are shown on the slide we want your +robot or your computer to explain what + + align:start position:0% +robot or your computer to explain what + + + align:start position:0% +robot or your computer to explain what +it does some very motley you want your + + align:start position:0% +it does some very motley you want your + + + align:start position:0% +it does some very motley you want your +machine your robot to answer questions + + align:start position:0% +machine your robot to answer questions + + + align:start position:0% +machine your robot to answer questions +which are complex and the robot may want + + align:start position:0% +which are complex and the robot may want + + + align:start position:0% +which are complex and the robot may want +to ask you about it to for clarification + + align:start position:0% +to ask you about it to for clarification + + + align:start position:0% +to ask you about it to for clarification +you want to keep track of conversation + + align:start position:0% +you want to keep track of conversation + + + align:start position:0% +you want to keep track of conversation +history instead engage in mix initiative + + align:start position:0% +history instead engage in mix initiative + + + align:start position:0% +history instead engage in mix initiative +dialogue or for related information so + + align:start position:0% +dialogue or for related information so + + + align:start position:0% +dialogue or for related information so +all these things need to happen in a + + align:start position:0% +all these things need to happen in a + + + align:start position:0% +all these things need to happen in a +dialogue and therefore your computer + + align:start position:0% +dialogue and therefore your computer + + + align:start position:0% +dialogue and therefore your computer +must be able to speak to you in a + + align:start position:0% +must be able to speak to you in a + + + align:start position:0% +must be able to speak to you in a +language that you understand + + align:start position:0% +language that you understand + + + align:start position:0% +language that you understand +in fact I I find that the biggest + + align:start position:0% +in fact I I find that the biggest + + + align:start position:0% +in fact I I find that the biggest +problem with learning systems that we + + align:start position:0% +problem with learning systems that we + + + align:start position:0% +problem with learning systems that we +have today is that some of them work and + + align:start position:0% +have today is that some of them work and + + + align:start position:0% +have today is that some of them work and +what cuatro Bosley and sometimes give + + align:start position:0% +what cuatro Bosley and sometimes give + + + align:start position:0% +what cuatro Bosley and sometimes give +you good results but you have no idea + + align:start position:0% +you good results but you have no idea + + + align:start position:0% +you good results but you have no idea +why you press a button you say aha here + + align:start position:0% +why you press a button you say aha here + + + align:start position:0% +why you press a button you say aha here +is the number and put it in the paper + + align:start position:0% +is the number and put it in the paper + + + align:start position:0% +is the number and put it in the paper +but more recently people started looking + + align:start position:0% +but more recently people started looking + + + align:start position:0% +but more recently people started looking +at wide + + align:start position:0% +at wide + + + align:start position:0% +at wide +what it does but again it's done by + + align:start position:0% +what it does but again it's done by + + + align:start position:0% +what it does but again it's done by +numbers it would be really wonderful if + + align:start position:0% +numbers it would be really wonderful if + + + align:start position:0% +numbers it would be really wonderful if +our learning system could tell us why + + align:start position:0% +our learning system could tell us why + + + align:start position:0% +our learning system could tell us why +they came up with their conclusions so + + align:start position:0% +they came up with their conclusions so + + + align:start position:0% +they came up with their conclusions so +we need language and so we created an + + align:start position:0% +we need language and so we created an + + + align:start position:0% +we need language and so we created an +ability of sound generator that goes + + align:start position:0% +ability of sound generator that goes + + + align:start position:0% +ability of sound generator that goes +from those same expressions and create + + align:start position:0% +from those same expressions and create + + + align:start position:0% +from those same expressions and create +natural language this is why we call + + align:start position:0% +natural language this is why we call + + + align:start position:0% +natural language this is why we call +this representation reversible so giving + + align:start position:0% +this representation reversible so giving + + + align:start position:0% +this representation reversible so giving +a set of tonal expressions the machine + + align:start position:0% +a set of tonal expressions the machine + + + align:start position:0% +a set of tonal expressions the machine +will create a sentence the person who + + align:start position:0% +will create a sentence the person who + + + align:start position:0% +will create a sentence the person who +picked up the yellow lemon placed it in + + align:start position:0% +picked up the yellow lemon placed it in + + + align:start position:0% +picked up the yellow lemon placed it in +the bowl on the table but of course this + + align:start position:0% +the bowl on the table but of course this + + + align:start position:0% +the bowl on the table but of course this +little bit silly just parroting the same + + align:start position:0% +little bit silly just parroting the same + + + align:start position:0% +little bit silly just parroting the same +sentence back you want the machine for + + align:start position:0% +sentence back you want the machine for + + + align:start position:0% +sentence back you want the machine for +example if I said ask you a question or + + align:start position:0% +example if I said ask you a question or + + + align:start position:0% +example if I said ask you a question or +indicate a negative statement or + + align:start position:0% +indicate a negative statement or + + + align:start position:0% +indicate a negative statement or +rephrase it from different pieces that + + align:start position:0% +rephrase it from different pieces that + + + align:start position:0% +rephrase it from different pieces that +it knows about so in fact our generator + + align:start position:0% +it knows about so in fact our generator + + + align:start position:0% +it knows about so in fact our generator +is very flexible so here is an example + + align:start position:0% +is very flexible so here is an example + + + align:start position:0% +is very flexible so here is an example +where by say observing the world robot + + align:start position:0% +where by say observing the world robot + + + align:start position:0% +where by say observing the world robot +adds more information to this + + align:start position:0% +adds more information to this + + + align:start position:0% +adds more information to this +representation and indicated here in + + align:start position:0% +representation and indicated here in + + + align:start position:0% +representation and indicated here in +blue and now from the original sentence + + align:start position:0% +blue and now from the original sentence + + + align:start position:0% +blue and now from the original sentence +about which was the person who picked up + + align:start position:0% +about which was the person who picked up + + + align:start position:0% +about which was the person who picked up +the yellow lemon place it in the ball + + align:start position:0% +the yellow lemon place it in the ball + + + align:start position:0% +the yellow lemon place it in the ball +the machine by just adding a couple of + + align:start position:0% +the machine by just adding a couple of + + + align:start position:0% +the machine by just adding a couple of +new relations the generator will be able + + align:start position:0% +new relations the generator will be able + + + align:start position:0% +new relations the generator will be able +to ask a question of the human will the + + align:start position:0% +to ask a question of the human will the + + + align:start position:0% +to ask a question of the human will the +person who plays the yellow lemon in a + + align:start position:0% +person who plays the yellow lemon in a + + + align:start position:0% +person who plays the yellow lemon in a +ball on the table pick it up soon and + + align:start position:0% +ball on the table pick it up soon and + + + align:start position:0% +ball on the table pick it up soon and +and so forth all right so we talked + + align:start position:0% +and so forth all right so we talked + + + align:start position:0% +and so forth all right so we talked +about parse trees about semantic + + align:start position:0% +about parse trees about semantic + + + align:start position:0% +about parse trees about semantic +representation about generation so what + + align:start position:0% +representation about generation so what + + + align:start position:0% +representation about generation so what +do we do with that let's supposing that + + align:start position:0% +do we do with that let's supposing that + + + align:start position:0% +do we do with that let's supposing that +you gave some knowledge to a machine + + align:start position:0% +you gave some knowledge to a machine + + + align:start position:0% +you gave some knowledge to a machine +here that Tom Sawyer assertion and + + align:start position:0% +here that Tom Sawyer assertion and + + + align:start position:0% +here that Tom Sawyer assertion and +somebody asked you was anyone sitting by + + align:start position:0% +somebody asked you was anyone sitting by + + + align:start position:0% +somebody asked you was anyone sitting by +an open window well what needs to happen + + align:start position:0% +an open window well what needs to happen + + + align:start position:0% +an open window well what needs to happen +is this question needs to be converted + + align:start position:0% +is this question needs to be converted + + + align:start position:0% +is this question needs to be converted +into ternary presentation as I indicated + + align:start position:0% +into ternary presentation as I indicated + + + align:start position:0% +into ternary presentation as I indicated +and the knowledge base we assumed had + + align:start position:0% +and the knowledge base we assumed had + + + align:start position:0% +and the knowledge base we assumed had +the knowledge from the region + + align:start position:0% +the knowledge from the region + + + align:start position:0% +the knowledge from the region +social plus million other assertions of + + align:start position:0% +social plus million other assertions of + + + align:start position:0% +social plus million other assertions of +course so we would need to match the + + align:start position:0% +course so we would need to match the + + + align:start position:0% +course so we would need to match the +representation of the query with the + + align:start position:0% +representation of the query with the + + + align:start position:0% +representation of the query with the +knowledge base and the Machine will say + + align:start position:0% +knowledge base and the Machine will say + + + align:start position:0% +knowledge base and the Machine will say +AHA here is the match well this is very + + align:start position:0% +AHA here is the match well this is very + + + align:start position:0% +AHA here is the match well this is very +simple here if you think you know window + + align:start position:0% +simple here if you think you know window + + + align:start position:0% +simple here if you think you know window +needs to open two window open - OH - + + align:start position:0% +needs to open two window open - OH - + + + align:start position:0% +needs to open two window open - OH - +match window open open and sit and sit + + align:start position:0% +match window open open and sit and sit + + + align:start position:0% +match window open open and sit and sit +and then the word anyone which sort of a + + align:start position:0% +and then the word anyone which sort of a + + + align:start position:0% +and then the word anyone which sort of a +matching and the world needs to match on + + align:start position:0% +matching and the world needs to match on + + + align:start position:0% +matching and the world needs to match on +but in reality of course people ask + + align:start position:0% +but in reality of course people ask + + + align:start position:0% +but in reality of course people ask +questions which are not that closely + + align:start position:0% +questions which are not that closely + + + align:start position:0% +questions which are not that closely +follow what the machine knows and so for + + align:start position:0% +follow what the machine knows and so for + + + align:start position:0% +follow what the machine knows and so for +our major needs to be much more + + align:start position:0% +our major needs to be much more + + + align:start position:0% +our major needs to be much more +sophisticated this is just a graphical + + align:start position:0% +sophisticated this is just a graphical + + + align:start position:0% +sophisticated this is just a graphical +effect knowledge graph representation of + + align:start position:0% +effect knowledge graph representation of + + + align:start position:0% +effect knowledge graph representation of +that match so start distinguishes things + + align:start position:0% +that match so start distinguishes things + + + align:start position:0% +that match so start distinguishes things +like Torme matching which as I showed + + align:start position:0% +like Torme matching which as I showed + + + align:start position:0% +like Torme matching which as I showed +could be a lexical match of course if + + align:start position:0% +could be a lexical match of course if + + + align:start position:0% +could be a lexical match of course if +nose anonyme it knows - aamir happen + + align:start position:0% +nose anonyme it knows - aamir happen + + + align:start position:0% +nose anonyme it knows - aamir happen +amis when goes one way it's like a car + + align:start position:0% +amis when goes one way it's like a car + + + align:start position:0% +amis when goes one way it's like a car +is a vehicle and as you can imagine the + + align:start position:0% +is a vehicle and as you can imagine the + + + align:start position:0% +is a vehicle and as you can imagine the +match also needs to go one way if I say + + align:start position:0% +match also needs to go one way if I say + + + align:start position:0% +match also needs to go one way if I say +about a car it also means that I bought + + align:start position:0% +about a car it also means that I bought + + + align:start position:0% +about a car it also means that I bought +a vehicle but if I say about the vehicle + + align:start position:0% +a vehicle but if I say about the vehicle + + + align:start position:0% +a vehicle but if I say about the vehicle +it's not true that I bought the car + + align:start position:0% +it's not true that I bought the car + + + align:start position:0% +it's not true that I bought the car +because if I may have bought a truck but + + align:start position:0% +because if I may have bought a truck but + + + align:start position:0% +because if I may have bought a truck but +it's aside so it's pretty easy to do + + align:start position:0% +it's aside so it's pretty easy to do + + + align:start position:0% +it's aside so it's pretty easy to do +matching on the level of terms of words + + align:start position:0% +matching on the level of terms of words + + + align:start position:0% +matching on the level of terms of words +but a much more complex problem is to + + align:start position:0% +but a much more complex problem is to + + + align:start position:0% +but a much more complex problem is to +mention the level of the structure and I + + align:start position:0% +mention the level of the structure and I + + + align:start position:0% +mention the level of the structure and I +will show you some examples of this + + align:start position:0% +will show you some examples of this + + + align:start position:0% +will show you some examples of this +problem well by now you must have + + align:start position:0% +problem well by now you must have + + + align:start position:0% +problem well by now you must have +figured out I love to stare at English + + align:start position:0% +figured out I love to stare at English + + + align:start position:0% +figured out I love to stare at English +sentences I hope you do a little bit if + + align:start position:0% +sentences I hope you do a little bit if + + + align:start position:0% +sentences I hope you do a little bit if +not please try so so here let's consider + + align:start position:0% +not please try so so here let's consider + + + align:start position:0% +not please try so so here let's consider +a couple of verbs so here's a verb + + align:start position:0% +a couple of verbs so here's a verb + + + align:start position:0% +a couple of verbs so here's a verb +surprise let's consider these two + + align:start position:0% +surprise let's consider these two + + + align:start position:0% +surprise let's consider these two +sentences the patient surprised the + + align:start position:0% +sentences the patient surprised the + + + align:start position:0% +sentences the patient surprised the +doctor with his fast recovery or the + + align:start position:0% +doctor with his fast recovery or the + + + align:start position:0% +doctor with his fast recovery or the +patient faster recovery surprised the + + align:start position:0% +patient faster recovery surprised the + + + align:start position:0% +patient faster recovery surprised the +doctor now for you were used to + + align:start position:0% +doctor now for you were used to + + + align:start position:0% +doctor now for you were used to +understanding language so quickly it's + + align:start position:0% +understanding language so quickly it's + + + align:start position:0% +understanding language so quickly it's +even hard to hear what's different about + + align:start position:0% +even hard to hear what's different about + + + align:start position:0% +even hard to hear what's different about +the sentences + + align:start position:0% +the sentences + + + align:start position:0% +the sentences +but if you actually do the parsing you + + align:start position:0% +but if you actually do the parsing you + + + align:start position:0% +but if you actually do the parsing you +will see that the pastor is a + + align:start position:0% +will see that the pastor is a + + + align:start position:0% +will see that the pastor is a +dramatically different and therefore our + + align:start position:0% +dramatically different and therefore our + + + align:start position:0% +dramatically different and therefore our +turn their presentations will be very + + align:start position:0% +turn their presentations will be very + + + align:start position:0% +turn their presentations will be very +different so we need to find a way to + + align:start position:0% +different so we need to find a way to + + + align:start position:0% +different so we need to find a way to +tell the Machine yeah that's the same + + align:start position:0% +tell the Machine yeah that's the same + + + align:start position:0% +tell the Machine yeah that's the same +thing and the linguists call these + + align:start position:0% +thing and the linguists call these + + + align:start position:0% +thing and the linguists call these +things syntactic alternations well in a + + align:start position:0% +things syntactic alternations well in a + + + align:start position:0% +things syntactic alternations well in a +different verb like load here's a + + align:start position:0% +different verb like load here's a + + + align:start position:0% +different verb like load here's a +different alternation the crane loaded + + align:start position:0% +different alternation the crane loaded + + + align:start position:0% +different alternation the crane loaded +the ship with containers or the crane + + align:start position:0% +the ship with containers or the crane + + + align:start position:0% +the ship with containers or the crane +loaded containers onto the ship again + + align:start position:0% +loaded containers onto the ship again + + + align:start position:0% +loaded containers onto the ship again +means the same thing pretty much but the + + align:start position:0% +means the same thing pretty much but the + + + align:start position:0% +means the same thing pretty much but the +surface representation is different the + + align:start position:0% +surface representation is different the + + + align:start position:0% +surface representation is different the +next one is in terms of a question did + + align:start position:0% +next one is in terms of a question did + + + align:start position:0% +next one is in terms of a question did +Iran provide Syria with weapons or did + + align:start position:0% +Iran provide Syria with weapons or did + + + align:start position:0% +Iran provide Syria with weapons or did +the run provide weapons to Syria let's + + align:start position:0% +the run provide weapons to Syria let's + + + align:start position:0% +the run provide weapons to Syria let's +see if it's true for every verb in the + + align:start position:0% +see if it's true for every verb in the + + + align:start position:0% +see if it's true for every verb in the +universe so let's try to look at the say + + align:start position:0% +universe so let's try to look at the say + + + align:start position:0% +universe so let's try to look at the say +surprise alternation and use it with a + + align:start position:0% +surprise alternation and use it with a + + + align:start position:0% +surprise alternation and use it with a +load verb or the other way around so I + + align:start position:0% +load verb or the other way around so I + + + align:start position:0% +load verb or the other way around so I +hope you bearing with me so linguist put + + align:start position:0% +hope you bearing with me so linguist put + + + align:start position:0% +hope you bearing with me so linguist put +stars in front of bad sentences and so + + align:start position:0% +stars in front of bad sentences and so + + + align:start position:0% +stars in front of bad sentences and so +here I tried to use the word surprise + + align:start position:0% +here I tried to use the word surprise + + + align:start position:0% +here I tried to use the word surprise +with the alternation which Lord allows + + align:start position:0% +with the alternation which Lord allows + + + align:start position:0% +with the alternation which Lord allows +you to do he used the same on too and it + + align:start position:0% +you to do he used the same on too and it + + + align:start position:0% +you to do he used the same on too and it +says the patient surprised fast recovery + + align:start position:0% +says the patient surprised fast recovery + + + align:start position:0% +says the patient surprised fast recovery +on to the doctor it makes absolutely no + + align:start position:0% +on to the doctor it makes absolutely no + + + align:start position:0% +on to the doctor it makes absolutely no +sense here I try to do surprise + + align:start position:0% +sense here I try to do surprise + + + align:start position:0% +sense here I try to do surprise +alternation for the word load and it + + align:start position:0% +alternation for the word load and it + + + align:start position:0% +alternation for the word load and it +says the cranes containers loaded the + + align:start position:0% +says the cranes containers loaded the + + + align:start position:0% +says the cranes containers loaded the +ship again complete gibberish and they + + align:start position:0% +ship again complete gibberish and they + + + align:start position:0% +ship again complete gibberish and they +same below did the runs weapon weapons + + align:start position:0% +same below did the runs weapon weapons + + + align:start position:0% +same below did the runs weapon weapons +provide Syria so it looks like a really + + align:start position:0% +provide Syria so it looks like a really + + + align:start position:0% +provide Syria so it looks like a really +horrible story every English verbs it + + align:start position:0% +horrible story every English verbs it + + + align:start position:0% +horrible story every English verbs it +looks like has a different way of saying + + align:start position:0% +looks like has a different way of saying + + + align:start position:0% +looks like has a different way of saying +expressing these sort of nations but + + align:start position:0% +expressing these sort of nations but + + + align:start position:0% +expressing these sort of nations but +fortunately this is not the case let's + + align:start position:0% +fortunately this is not the case let's + + + align:start position:0% +fortunately this is not the case let's +go back to the word surprise + + align:start position:0% + + + + align:start position:0% + +well let's look at verbs similar to the + + align:start position:0% +well let's look at verbs similar to the + + + align:start position:0% +well let's look at verbs similar to the +word surprise so you could use the same + + align:start position:0% +word surprise so you could use the same + + + align:start position:0% +word surprise so you could use the same +alternation with the word confused you + + align:start position:0% +alternation with the word confused you + + + align:start position:0% +alternation with the word confused you +can say the patient confused the doctor + + align:start position:0% +can say the patient confused the doctor + + + align:start position:0% +can say the patient confused the doctor +with slow recovery which will convert + + align:start position:0% +with slow recovery which will convert + + + align:start position:0% +with slow recovery which will convert +into the patient slow recovery confuse + + align:start position:0% +into the patient slow recovery confuse + + + align:start position:0% +into the patient slow recovery confuse +the doctor you can say the same thing + + align:start position:0% +the doctor you can say the same thing + + + align:start position:0% +the doctor you can say the same thing +with anger disappoint embarrass frighten + + align:start position:0% +with anger disappoint embarrass frighten + + + align:start position:0% +with anger disappoint embarrass frighten +impress please threaten what is really + + align:start position:0% +impress please threaten what is really + + + align:start position:0% +impress please threaten what is really +amazing about it and and very + + align:start position:0% +amazing about it and and very + + + align:start position:0% +amazing about it and and very +interesting that this syntactic + + align:start position:0% +interesting that this syntactic + + + align:start position:0% +interesting that this syntactic +alternation works the same way for verbs + + align:start position:0% +alternation works the same way for verbs + + + align:start position:0% +alternation works the same way for verbs +of the same meaning of the same + + align:start position:0% +of the same meaning of the same + + + align:start position:0% +of the same meaning of the same +semantics class and this particular + + align:start position:0% +semantics class and this particular + + + align:start position:0% +semantics class and this particular +class link is called emotional reaction + + align:start position:0% +class link is called emotional reaction + + + align:start position:0% +class link is called emotional reaction +verbs and it's a it's a large semantic + + align:start position:0% +verbs and it's a it's a large semantic + + + align:start position:0% +verbs and it's a it's a large semantic +class for about 300 verbs and they all + + align:start position:0% +class for about 300 verbs and they all + + + align:start position:0% +class for about 300 verbs and they all +behave identically from the point of + + align:start position:0% +behave identically from the point of + + + align:start position:0% +behave identically from the point of +view of that alternations and it's true + + align:start position:0% +view of that alternations and it's true + + + align:start position:0% +view of that alternations and it's true +for all now the alternation that I + + align:start position:0% +for all now the alternation that I + + + align:start position:0% +for all now the alternation that I +showed you so that's of course is good + + align:start position:0% +showed you so that's of course is good + + + align:start position:0% +showed you so that's of course is good +news because it makes interesting + + align:start position:0% +news because it makes interesting + + + align:start position:0% +news because it makes interesting +connection between syntax and semantics + + align:start position:0% +connection between syntax and semantics + + + align:start position:0% +connection between syntax and semantics +but it also allows to build the lexicon + + align:start position:0% +but it also allows to build the lexicon + + + align:start position:0% +but it also allows to build the lexicon +that are more compact and easy to deal + + align:start position:0% +that are more compact and easy to deal + + + align:start position:0% +that are more compact and easy to deal +with and one can imagine creating this + + align:start position:0% +with and one can imagine creating this + + + align:start position:0% +with and one can imagine creating this +verb membership automatically by looking + + align:start position:0% +verb membership automatically by looking + + + align:start position:0% +verb membership automatically by looking +at large corpus and this is how + + align:start position:0% +at large corpus and this is how + + + align:start position:0% +at large corpus and this is how +presumably children know these were + + align:start position:0% +presumably children know these were + + + align:start position:0% +presumably children know these were +classes and these automations alright so + + align:start position:0% +classes and these automations alright so + + + align:start position:0% +classes and these automations alright so +now that you know how to match and it's + + align:start position:0% +now that you know how to match and it's + + + align:start position:0% +now that you know how to match and it's +not as trivial match only like I showed + + align:start position:0% +not as trivial match only like I showed + + + align:start position:0% +not as trivial match only like I showed +here but the most sophisticated mesh on + + align:start position:0% +here but the most sophisticated mesh on + + + align:start position:0% +here but the most sophisticated mesh on +the level of structure as well let's see + + align:start position:0% +the level of structure as well let's see + + + align:start position:0% +the level of structure as well let's see +what we can do after the match happens + + align:start position:0% +what we can do after the match happens + + + align:start position:0% +what we can do after the match happens +so here's the same sentence and the same + + align:start position:0% +so here's the same sentence and the same + + + align:start position:0% +so here's the same sentence and the same +question was anybody sitting by an open + + align:start position:0% +question was anybody sitting by an open + + + align:start position:0% +question was anybody sitting by an open +window we retrieved the structure and + + align:start position:0% +window we retrieved the structure and + + + align:start position:0% +window we retrieved the structure and +then we could sell our generator go and + + align:start position:0% +then we could sell our generator go and + + + align:start position:0% +then we could sell our generator go and +generate the sentence and it will do + + align:start position:0% +generate the sentence and it will do + + + align:start position:0% +generate the sentence and it will do +that Tom's aunt was sitting by an open + + align:start position:0% +that Tom's aunt was sitting by an open + + + align:start position:0% +that Tom's aunt was sitting by an open +window in a pleasant rearward apartment + + align:start position:0% +window in a pleasant rearward apartment + + + align:start position:0% +window in a pleasant rearward apartment +well it's not as interesting it's sort + + align:start position:0% +well it's not as interesting it's sort + + + align:start position:0% +well it's not as interesting it's sort +of parroting the same thing you know I + + align:start position:0% +of parroting the same thing you know I + + + align:start position:0% +of parroting the same thing you know I +tell it ABC and it told me back ABC if I + + align:start position:0% +tell it ABC and it told me back ABC if I + + + align:start position:0% +tell it ABC and it told me back ABC if I +ask you know who B he or something like + + align:start position:0% +ask you know who B he or something like + + + align:start position:0% +ask you know who B he or something like +that + + align:start position:0% +that + + + align:start position:0% +that +if you want to build a question + + align:start position:0% +if you want to build a question + + + align:start position:0% +if you want to build a question +answering system we wanted to be able to + + align:start position:0% +answering system we wanted to be able to + + + align:start position:0% +answering system we wanted to be able to +in response to a question understand it + + align:start position:0% +in response to a question understand it + + + align:start position:0% +in response to a question understand it +go somewhere find the right answer and + + align:start position:0% +go somewhere find the right answer and + + + align:start position:0% +go somewhere find the right answer and +give it back to you and we built that + + align:start position:0% +give it back to you and we built that + + + align:start position:0% +give it back to you and we built that +and we do it by a general way of looking + + align:start position:0% +and we do it by a general way of looking + + + align:start position:0% +and we do it by a general way of looking +at it our system can execute a procedure + + align:start position:0% +at it our system can execute a procedure + + + align:start position:0% +at it our system can execute a procedure +in response to a match that to obtain + + align:start position:0% +in response to a match that to obtain + + + align:start position:0% +in response to a match that to obtain +the answer from the data source so an + + align:start position:0% +the answer from the data source so an + + + align:start position:0% +the answer from the data source so an +example is here and I can show you some + + align:start position:0% +example is here and I can show you some + + + align:start position:0% +example is here and I can show you some +screenshots so in fact if you like it we + + align:start position:0% +screenshots so in fact if you like it we + + + align:start position:0% +screenshots so in fact if you like it we +can play with the system life and you'll + + align:start position:0% +can play with the system life and you'll + + + align:start position:0% +can play with the system life and you'll +see what it does so it executes a + + align:start position:0% +see what it does so it executes a + + + align:start position:0% +see what it does so it executes a +procedure to obtain an answer from the + + align:start position:0% +procedure to obtain an answer from the + + + align:start position:0% +procedure to obtain an answer from the +data source if you say we directly over + + align:start position:0% +data source if you say we directly over + + + align:start position:0% +data source if you say we directly over +the world some match will happen between + + align:start position:0% +the world some match will happen between + + + align:start position:0% +the world some match will happen between +what you know what you ask and what the + + align:start position:0% +what you know what you ask and what the + + + align:start position:0% +what you know what you ask and what the +system knows some script will get + + align:start position:0% +system knows some script will get + + + align:start position:0% +system knows some script will get +executed and the Machine will go to some + + align:start position:0% +executed and the Machine will go to some + + + align:start position:0% +executed and the Machine will go to some +data source find the answer and give it + + align:start position:0% +data source find the answer and give it + + + align:start position:0% +data source find the answer and give it +back to you so how this is done well in + + align:start position:0% +back to you so how this is done well in + + + align:start position:0% +back to you so how this is done well in +order to explain that I need two more + + align:start position:0% +order to explain that I need two more + + + align:start position:0% +order to explain that I need two more +ideas one is a match of language + + align:start position:0% +ideas one is a match of language + + + align:start position:0% +ideas one is a match of language +annotation ready + + align:start position:0% +annotation ready + + + align:start position:0% +annotation ready +so annotations sentences and phrases + + align:start position:0% +so annotations sentences and phrases + + + align:start position:0% +so annotations sentences and phrases +that describe the content of retrievable + + align:start position:0% +that describe the content of retrievable + + + align:start position:0% +that describe the content of retrievable +information segment this is a graphic + + align:start position:0% +information segment this is a graphic + + + align:start position:0% +information segment this is a graphic +sort of an acute way so this sentence + + align:start position:0% +sort of an acute way so this sentence + + + align:start position:0% +sort of an acute way so this sentence +level of phrase level labels on some + + align:start position:0% +level of phrase level labels on some + + + align:start position:0% +level of phrase level labels on some +data and they described retrievable + + align:start position:0% +data and they described retrievable + + + align:start position:0% +data and they described retrievable +information segments annotations are + + align:start position:0% +information segments annotations are + + + align:start position:0% +information segments annotations are +then matched again submitted queries and + + align:start position:0% +then matched again submitted queries and + + + align:start position:0% +then matched again submitted queries and +a successful match results in either + + align:start position:0% +a successful match results in either + + + align:start position:0% +a successful match results in either +retrieval of that information or some + + align:start position:0% +retrieval of that information or some + + + align:start position:0% +retrieval of that information or some +procedure to retrieve that information + + align:start position:0% +procedure to retrieve that information + + + align:start position:0% +procedure to retrieve that information +and the special case of this procedure + + align:start position:0% +and the special case of this procedure + + + align:start position:0% +and the special case of this procedure +is done using our object prop of the + + align:start position:0% +is done using our object prop of the + + + align:start position:0% +is done using our object prop of the +property value data model this technique + + align:start position:0% +property value data model this technique + + + align:start position:0% +property value data model this technique +can connect language to arbitrary + + align:start position:0% +can connect language to arbitrary + + + align:start position:0% +can connect language to arbitrary +procedures but as I said let's consider + + align:start position:0% +procedures but as I said let's consider + + + align:start position:0% +procedures but as I said let's consider +a lot of semi structured information + + align:start position:0% +a lot of semi structured information + + + align:start position:0% +a lot of semi structured information +sources available on the web that can be + + align:start position:0% +sources available on the web that can be + + + align:start position:0% +sources available on the web that can be +modeled using this object property value + + align:start position:0% +modeled using this object property value + + + align:start position:0% +modeled using this object property value +model well what are these + + align:start position:0% +model well what are these + + + align:start position:0% +model well what are these +what kind of repositories have this + + align:start position:0% +what kind of repositories have this + + + align:start position:0% +what kind of repositories have this +property if you think about that almost + + align:start position:0% +property if you think about that almost + + + align:start position:0% +property if you think about that almost +anything that humans create on the web + + align:start position:0% +anything that humans create on the web + + + align:start position:0% +anything that humans create on the web +which is semi structured is like that if + + align:start position:0% +which is semi structured is like that if + + + align:start position:0% +which is semi structured is like that if +you have a site that has a bunch of + + align:start position:0% +you have a site that has a bunch of + + + align:start position:0% +you have a site that has a bunch of +countries this properties like + + align:start position:0% +countries this properties like + + + align:start position:0% +countries this properties like +populations areas capitals birth rates + + align:start position:0% +populations areas capitals birth rates + + + align:start position:0% +populations areas capitals birth rates +and so forth the country is an object + + align:start position:0% +and so forth the country is an object + + + align:start position:0% +and so forth the country is an object +the world population is a property and + + align:start position:0% +the world population is a property and + + + align:start position:0% +the world population is a property and +value is the actual value of that + + align:start position:0% +value is the actual value of that + + + align:start position:0% +value is the actual value of that +property you can have people with their + + align:start position:0% +property you can have people with their + + + align:start position:0% +property you can have people with their +birth dates you can have cities with the + + align:start position:0% +birth dates you can have cities with the + + + align:start position:0% +birth dates you can have cities with the +maps and elevations and so forth so in a + + align:start position:0% +maps and elevations and so forth so in a + + + align:start position:0% +maps and elevations and so forth so in a +sense this object property value model + + align:start position:0% +sense this object property value model + + + align:start position:0% +sense this object property value model +makes it possible to view and use large + + align:start position:0% +makes it possible to view and use large + + + align:start position:0% +makes it possible to view and use large +segments of the web as a database and + + align:start position:0% +segments of the web as a database and + + + align:start position:0% +segments of the web as a database and +schematically here how start using this + + align:start position:0% +schematically here how start using this + + + align:start position:0% +schematically here how start using this +model user ask the language part of the + + align:start position:0% +model user ask the language part of the + + + align:start position:0% +model user ask the language part of the +system a question this amidst understand + + align:start position:0% +system a question this amidst understand + + + align:start position:0% +system a question this amidst understand +the question understands where the + + align:start position:0% +the question understands where the + + + align:start position:0% +the question understands where the +question might be found and what is the + + align:start position:0% +question might be found and what is the + + + align:start position:0% +question might be found and what is the +object and property implicit in the + + align:start position:0% +object and property implicit in the + + + align:start position:0% +object and property implicit in the +question after start does that it says + + align:start position:0% +question after start does that it says + + + align:start position:0% +question after start does that it says +it has a friend called omni base and it + + align:start position:0% +it has a friend called omni base and it + + + align:start position:0% +it has a friend called omni base and it +says go get it go to this site go for + + align:start position:0% +says go get it go to this site go for + + + align:start position:0% +says go get it go to this site go for +that symbol called France and go get the + + align:start position:0% +that symbol called France and go get the + + + align:start position:0% +that symbol called France and go get the +population and it will go to some World + + align:start position:0% +population and it will go to some World + + + align:start position:0% +population and it will go to some World +Factbook and get app activation so this + + align:start position:0% +Factbook and get app activation so this + + + align:start position:0% +Factbook and get app activation so this +is how the system works + + align:start position:0% +is how the system works + + + align:start position:0% +is how the system works +and here's an example of such a question + + align:start position:0% +and here's an example of such a question + + + align:start position:0% +and here's an example of such a question +here the question is just a screenshot + + align:start position:0% +here the question is just a screenshot + + + align:start position:0% +here the question is just a screenshot +does Russia border on Moldova the system + + align:start position:0% +does Russia border on Moldova the system + + + align:start position:0% +does Russia border on Moldova the system +says aha he you want to find out what + + align:start position:0% +says aha he you want to find out what + + + align:start position:0% +says aha he you want to find out what +country's border Moldova and find out + + align:start position:0% +country's border Moldova and find out + + + align:start position:0% +country's border Moldova and find out +whether Russia is among them and then it + + align:start position:0% +whether Russia is among them and then it + + + align:start position:0% +whether Russia is among them and then it +actually checks that and it tells you + + align:start position:0% +actually checks that and it tells you + + + align:start position:0% +actually checks that and it tells you +know Russia does not border Moldova + + align:start position:0% +know Russia does not border Moldova + + + align:start position:0% +know Russia does not border Moldova +because it doesn't find Russia in in + + align:start position:0% +because it doesn't find Russia in in + + + align:start position:0% +because it doesn't find Russia in in +this response and just for comparison if + + align:start position:0% +this response and just for comparison if + + + align:start position:0% +this response and just for comparison if +you ask the same question of a search + + align:start position:0% +you ask the same question of a search + + + align:start position:0% +you ask the same question of a search +engine it will give you 24 million + + align:start position:0% +engine it will give you 24 million + + + align:start position:0% +engine it will give you 24 million +results today maybe 240 million results + + align:start position:0% +results today maybe 240 million results + + + align:start position:0% +results today maybe 240 million results +and none of them really answer the + + align:start position:0% +and none of them really answer the + + + align:start position:0% +and none of them really answer the +question + + align:start position:0% + + + + align:start position:0% + +well I just want to tell you that the + + align:start position:0% +well I just want to tell you that the + + + align:start position:0% +well I just want to tell you that the +ability to understand something really + + align:start position:0% +ability to understand something really + + + align:start position:0% +ability to understand something really +helps in this case the ability to + + align:start position:0% +helps in this case the ability to + + + align:start position:0% +helps in this case the ability to +understand language gives you a lot of + + align:start position:0% +understand language gives you a lot of + + + align:start position:0% +understand language gives you a lot of +power if you you can do a lot by trying + + align:start position:0% +power if you you can do a lot by trying + + + align:start position:0% +power if you you can do a lot by trying +to the key words in it can achieve a lot + + align:start position:0% +to the key words in it can achieve a lot + + + align:start position:0% +to the key words in it can achieve a lot +of documents and this is how a lot of + + align:start position:0% +of documents and this is how a lot of + + + align:start position:0% +of documents and this is how a lot of +pretty much modern system modern systems + + align:start position:0% +pretty much modern system modern systems + + + align:start position:0% +pretty much modern system modern systems +work but if you want to do some a little + + align:start position:0% +work but if you want to do some a little + + + align:start position:0% +work but if you want to do some a little +bit more complex it would be nice to + + align:start position:0% +bit more complex it would be nice to + + + align:start position:0% +bit more complex it would be nice to +understand some so here's an example of + + align:start position:0% +understand some so here's an example of + + + align:start position:0% +understand some so here's an example of +a complex question who is the president + + align:start position:0% +a complex question who is the president + + + align:start position:0% +a complex question who is the president +of the fourth largest country married to + + align:start position:0% +of the fourth largest country married to + + + align:start position:0% +of the fourth largest country married to +well if you can analyze this question in + + align:start position:0% +well if you can analyze this question in + + + align:start position:0% +well if you can analyze this question in +two pieces then you can very quickly + + align:start position:0% +two pieces then you can very quickly + + + align:start position:0% +two pieces then you can very quickly +figure out that right away just throwing + + align:start position:0% +figure out that right away just throwing + + + align:start position:0% +figure out that right away just throwing +the pieces on your knowledge base he + + align:start position:0% +the pieces on your knowledge base he + + + align:start position:0% +the pieces on your knowledge base he +could not resolve it but we built a very + + align:start position:0% +could not resolve it but we built a very + + + align:start position:0% +could not resolve it but we built a very +nice impractical based algorithms that + + align:start position:0% +nice impractical based algorithms that + + + align:start position:0% +nice impractical based algorithms that +allows us to resolve the complex + + align:start position:0% +allows us to resolve the complex + + + align:start position:0% +allows us to resolve the complex +questions into subsets of simpler + + align:start position:0% +questions into subsets of simpler + + + align:start position:0% +questions into subsets of simpler +questions and understand in which order + + align:start position:0% +questions and understand in which order + + + align:start position:0% +questions and understand in which order +to ask them so the machine will say Oh + + align:start position:0% +to ask them so the machine will say Oh + + + align:start position:0% +to ask them so the machine will say Oh +first I need to find out what the first + + align:start position:0% +first I need to find out what the first + + + align:start position:0% +first I need to find out what the first +largest country then who its president + + align:start position:0% +largest country then who its president + + + align:start position:0% +largest country then who its president +is and only them who he is married to + + align:start position:0% +is and only them who he is married to + + + align:start position:0% +is and only them who he is married to +and very quickly this is how schema + + align:start position:0% +and very quickly this is how schema + + + align:start position:0% +and very quickly this is how schema +schematically it's done this is sort of + + align:start position:0% +schematically it's done this is sort of + + + align:start position:0% +schematically it's done this is sort of +an under the hood the turn expression + + align:start position:0% +an under the hood the turn expression + + + align:start position:0% +an under the hood the turn expression +representation of the question then she + + align:start position:0% +representation of the question then she + + + align:start position:0% +representation of the question then she +says oh too hard let's first find out + + align:start position:0% +says oh too hard let's first find out + + + align:start position:0% +says oh too hard let's first find out +what the largest fourth largest country + + align:start position:0% +what the largest fourth largest country + + + align:start position:0% +what the largest fourth largest country +is it's China then let's find out it's + + align:start position:0% +is it's China then let's find out it's + + + align:start position:0% +is it's China then let's find out it's +still hard so let's go night with the + + align:start position:0% +still hard so let's go night with the + + + align:start position:0% +still hard so let's go night with the +president of Chinese found the name and + + align:start position:0% +president of Chinese found the name and + + + align:start position:0% +president of Chinese found the name and +then the next is just a lookup table who + + align:start position:0% +then the next is just a lookup table who + + + align:start position:0% +then the next is just a lookup table who +is he married to it gives you gives you + + align:start position:0% +is he married to it gives you gives you + + + align:start position:0% +is he married to it gives you gives you +an immense + + align:start position:0% + + + + align:start position:0% + +some other examples in what city was the + + align:start position:0% +some other examples in what city was the + + + align:start position:0% +some other examples in what city was the +first president of the is born and finds + + align:start position:0% +first president of the is born and finds + + + align:start position:0% +first president of the is born and finds +that if James Monroe and gives you the + + align:start position:0% +that if James Monroe and gives you the + + + align:start position:0% +that if James Monroe and gives you the +city what book did the water one piece + + align:start position:0% +city what book did the water one piece + + + align:start position:0% +city what book did the water one piece +right finds the Tolstoy and finds his + + align:start position:0% +right finds the Tolstoy and finds his + + + align:start position:0% +right finds the Tolstoy and finds his +books of different sources so the + + align:start position:0% +books of different sources so the + + + align:start position:0% +books of different sources so the +technologies that I described of the + + align:start position:0% +technologies that I described of the + + + align:start position:0% +technologies that I described of the +property value data model our toner + + align:start position:0% +property value data model our toner + + + align:start position:0% +property value data model our toner +expression representation complex + + align:start position:0% +expression representation complex + + + align:start position:0% +expression representation complex +question answering the annotation + + align:start position:0% +question answering the annotation + + + align:start position:0% +question answering the annotation +national regeneration representation + + align:start position:0% +national regeneration representation + + + align:start position:0% +national regeneration representation +they all the years inspired a bunch of + + align:start position:0% +they all the years inspired a bunch of + + + align:start position:0% +they all the years inspired a bunch of +companies budget technologists of + + align:start position:0% +companies budget technologists of + + + align:start position:0% +companies budget technologists of +starting with as Jeeves + + align:start position:0% +starting with as Jeeves + + + align:start position:0% +starting with as Jeeves +who I guess existed before you guys were + + align:start position:0% +who I guess existed before you guys were + + + align:start position:0% +who I guess existed before you guys were +even born to wall from alpha who pretty + + align:start position:0% +even born to wall from alpha who pretty + + + align:start position:0% +even born to wall from alpha who pretty +much took very wholesale to more + + align:start position:0% +much took very wholesale to more + + + align:start position:0% +much took very wholesale to more +recently Google QA started doing really + + align:start position:0% +recently Google QA started doing really + + + align:start position:0% +recently Google QA started doing really +wonderful things using this idea that + + align:start position:0% +wonderful things using this idea that + + + align:start position:0% +wonderful things using this idea that +everybody have idea that you should go + + align:start position:0% +everybody have idea that you should go + + + align:start position:0% +everybody have idea that you should go +from surface to a question you have a + + align:start position:0% +from surface to a question you have a + + + align:start position:0% +from surface to a question you have a +question you throw a question on to the + + align:start position:0% +question you throw a question on to the + + + align:start position:0% +question you throw a question on to the +web and you get some answer but it + + align:start position:0% +web and you get some answer but it + + + align:start position:0% +web and you get some answer but it +doesn't work with high precision so the + + align:start position:0% +doesn't work with high precision so the + + + align:start position:0% +doesn't work with high precision so the +idea that you need to curate knowledge + + align:start position:0% +idea that you need to curate knowledge + + + align:start position:0% +idea that you need to curate knowledge +and build some huge repository of + + align:start position:0% +and build some huge repository of + + + align:start position:0% +and build some huge repository of +knowledge was picked up by these + + align:start position:0% +knowledge was picked up by these + + + align:start position:0% +knowledge was picked up by these +companies to certainly now all these + + align:start position:0% +companies to certainly now all these + + + align:start position:0% +companies to certainly now all these +companies though quite decent question + + align:start position:0% +companies though quite decent question + + + align:start position:0% +companies though quite decent question +answering the same is true for Watson + + align:start position:0% +answering the same is true for Watson + + + align:start position:0% +answering the same is true for Watson +and Siri and I I was involved in some of + + align:start position:0% +and Siri and I I was involved in some of + + + align:start position:0% +and Siri and I I was involved in some of +these things so I will show you let's + + align:start position:0% +these things so I will show you let's + + + align:start position:0% +these things so I will show you let's +see right so let's start with this I + + align:start position:0% + + + + align:start position:0% + +about ten years ago we on top of start + + align:start position:0% +about ten years ago we on top of start + + + align:start position:0% +about ten years ago we on top of start +we build a system + + align:start position:0% +we build a system + + + align:start position:0% +we build a system +that was connected to a cellphone again + + align:start position:0% +that was connected to a cellphone again + + + align:start position:0% +that was connected to a cellphone again +I don't know how many of you remember + + align:start position:0% +I don't know how many of you remember + + + align:start position:0% +I don't know how many of you remember +the world without smartphones but that + + align:start position:0% +the world without smartphones but that + + + align:start position:0% +the world without smartphones but that +was when smartphones wasn't there there + + align:start position:0% +was when smartphones wasn't there there + + + align:start position:0% +was when smartphones wasn't there there +was no such thing as iPhone + + align:start position:0% +was no such thing as iPhone + + + align:start position:0% +was no such thing as iPhone +so there's vanilla phone that all they + + align:start position:0% +so there's vanilla phone that all they + + + align:start position:0% +so there's vanilla phone that all they +did that made phone calls of course it + + align:start position:0% +did that made phone calls of course it + + + align:start position:0% +did that made phone calls of course it +also had a camera and then a text but it + + align:start position:0% +also had a camera and then a text but it + + + align:start position:0% +also had a camera and then a text but it +really didn't do much more and we + + align:start position:0% +really didn't do much more and we + + + align:start position:0% +really didn't do much more and we +decided it's time to connect it to + + align:start position:0% +decided it's time to connect it to + + + align:start position:0% +decided it's time to connect it to +language so we convinced a company to + + align:start position:0% +language so we convinced a company to + + + align:start position:0% +language so we convinced a company to +find us to do that and we built + + align:start position:0% +find us to do that and we built + + + align:start position:0% +find us to do that and we built +something visual start mobile and this + + align:start position:0% +something visual start mobile and this + + + align:start position:0% +something visual start mobile and this +is an intelligent phone assistance which + + align:start position:0% +is an intelligent phone assistance which + + + align:start position:0% +is an intelligent phone assistance which +could at the time retrieve + + align:start position:0% +could at the time retrieve + + + align:start position:0% +could at the time retrieve +general-purpose information provide + + align:start position:0% +general-purpose information provide + + + align:start position:0% +general-purpose information provide +access to computational services perform + + align:start position:0% +access to computational services perform + + + align:start position:0% +access to computational services perform +action on another phone trigger + + align:start position:0% +action on another phone trigger + + + align:start position:0% +action on another phone trigger +apparatus like a camera on the phone we + + align:start position:0% +apparatus like a camera on the phone we + + + align:start position:0% +apparatus like a camera on the phone we +receive instructions and we have a + + align:start position:0% +receive instructions and we have a + + + align:start position:0% +receive instructions and we have a +talking about YouTube we have a video + + align:start position:0% +talking about YouTube we have a video + + + align:start position:0% +talking about YouTube we have a video +that shows the system in action that + + align:start position:0% +that shows the system in action that + + + align:start position:0% +that shows the system in action that +video is quite old is from beginning of + + align:start position:0% +video is quite old is from beginning of + + + align:start position:0% +video is quite old is from beginning of +206 and at the time we did not connect + + align:start position:0% +206 and at the time we did not connect + + + align:start position:0% +206 and at the time we did not connect +to speech but you could see what it does + + align:start position:0% +to speech but you could see what it does + + + align:start position:0% +to speech but you could see what it does +by the user what typing in questions of + + align:start position:0% +by the user what typing in questions of + + + align:start position:0% +by the user what typing in questions of +the system in depth in that particular + + align:start position:0% +the system in depth in that particular + + + align:start position:0% +the system in depth in that particular +video so there's no narration so if you + + align:start position:0% +video so there's no narration so if you + + + align:start position:0% +video so there's no narration so if you +read the captions you figure out what is + + align:start position:0% +read the captions you figure out what is + + + align:start position:0% +read the captions you figure out what is +going on + + align:start position:0% + + + + align:start position:0% + +so here's my former student who actually + + align:start position:0% +so here's my former student who actually + + + align:start position:0% +so here's my former student who actually +went to Google to transition our + + align:start position:0% +went to Google to transition our + + + align:start position:0% +went to Google to transition our +technology eventually and he's not sure + + align:start position:0% +technology eventually and he's not sure + + + align:start position:0% +technology eventually and he's not sure +well he needs to take his coat or not + + align:start position:0% + + + + align:start position:0% + +yeah this is very dated of course + + align:start position:0% +yeah this is very dated of course + + + align:start position:0% +yeah this is very dated of course +because now the temperature is always + + align:start position:0% +because now the temperature is always + + + align:start position:0% +because now the temperature is always +uniform but again that was 10 years ago + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +is any sound + + align:start position:0% + + + + align:start position:0% + +alright those are you know Cambridge no + + align:start position:0% +alright those are you know Cambridge no + + + align:start position:0% +alright those are you know Cambridge no +that station + + align:start position:0% + + + + align:start position:0% + +well anyway the GPS just came came about + + align:start position:0% +well anyway the GPS just came came about + + + align:start position:0% +well anyway the GPS just came came about +and we were lucky to connect it and so + + align:start position:0% +and we were lucky to connect it and so + + + align:start position:0% +and we were lucky to connect it and so +now the guy gets the map and knows were + + align:start position:0% +now the guy gets the map and knows were + + + align:start position:0% +now the guy gets the map and knows were +to find where he needs to go + + align:start position:0% +to find where he needs to go + + + align:start position:0% +to find where he needs to go +so this is our status center for those + + align:start position:0% +so this is our status center for those + + + align:start position:0% +so this is our status center for those +who haven't seen it this is where Cecil + + align:start position:0% +who haven't seen it this is where Cecil + + + align:start position:0% +who haven't seen it this is where Cecil +is again it's dated because right now + + align:start position:0% +is again it's dated because right now + + + align:start position:0% +is again it's dated because right now +this loan is a huge building but it + + align:start position:0% +this loan is a huge building but it + + + align:start position:0% +this loan is a huge building but it +wasn't there at the time oh it says here + + align:start position:0% +wasn't there at the time oh it says here + + + align:start position:0% +wasn't there at the time oh it says here +trying to reach my mother I don't know + + align:start position:0% +trying to reach my mother I don't know + + + align:start position:0% +trying to reach my mother I don't know +why it shows you the stuff he's worried + + align:start position:0% +why it shows you the stuff he's worried + + + align:start position:0% +why it shows you the stuff he's worried +about his mother and so he decides to + + align:start position:0% +about his mother and so he decides to + + + align:start position:0% +about his mother and so he decides to +tell her remind my mother to take her + + align:start position:0% +tell her remind my mother to take her + + + align:start position:0% +tell her remind my mother to take her +medicine at 3:00 p.m. and we'll see what + + align:start position:0% +medicine at 3:00 p.m. and we'll see what + + + align:start position:0% +medicine at 3:00 p.m. and we'll see what +happens with that later + + align:start position:0% + + + + align:start position:0% + +take a high-resolution picture using + + align:start position:0% +take a high-resolution picture using + + + align:start position:0% +take a high-resolution picture using +flash in 10 seconds I don't think any + + align:start position:0% +flash in 10 seconds I don't think any + + + align:start position:0% +flash in 10 seconds I don't think any +phones can do it even today for some + + align:start position:0% +phones can do it even today for some + + + align:start position:0% +phones can do it even today for some +reason I don't know why it's so hard + + align:start position:0% +reason I don't know why it's so hard + + + align:start position:0% +reason I don't know why it's so hard +right for selfie very good yeah alright + + align:start position:0% +right for selfie very good yeah alright + + + align:start position:0% +right for selfie very good yeah alright +so his friend this busy and he wants to + + align:start position:0% +so his friend this busy and he wants to + + + align:start position:0% +so his friend this busy and he wants to +entertain himself I guess but he doesn't + + align:start position:0% +entertain himself I guess but he doesn't + + + align:start position:0% +entertain himself I guess but he doesn't +quite know how to do it + + align:start position:0% + + + + align:start position:0% + +how do use the radio rifles + + align:start position:0% + + + + align:start position:0% + +well + + align:start position:0% + + + + align:start position:0% + +all right now you know + + align:start position:0% + + + + align:start position:0% + +alright alright mother's house + + align:start position:0% + + + + align:start position:0% + +right so exactly so a delayed action + + align:start position:0% +right so exactly so a delayed action + + + align:start position:0% +right so exactly so a delayed action +happened on her phone so we inserted the + + align:start position:0% +happened on her phone so we inserted the + + + align:start position:0% +happened on her phone so we inserted the +thing on her phone and that she got this + + align:start position:0% +thing on her phone and that she got this + + + align:start position:0% +thing on her phone and that she got this +warning and it's my staff they all turn + + align:start position:0% +warning and it's my staff they all turn + + + align:start position:0% +warning and it's my staff they all turn +out to be very good actors + + align:start position:0% +out to be very good actors + + + align:start position:0% +out to be very good actors +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +all right so this is the last thing + + align:start position:0% +all right so this is the last thing + + + align:start position:0% +all right so this is the last thing +traveling she is going back he now has a + + align:start position:0% +traveling she is going back he now has a + + + align:start position:0% +traveling she is going back he now has a +car and this is the last thing that I'll + + align:start position:0% +car and this is the last thing that I'll + + + align:start position:0% +car and this is the last thing that I'll +show you + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +how do I get from here to feed + + align:start position:0% +how do I get from here to feed + + + align:start position:0% +how do I get from here to feed +house well if you think about it this is + + align:start position:0% +house well if you think about it this is + + + align:start position:0% +house well if you think about it this is +a very hard question you need to know + + align:start position:0% +a very hard question you need to know + + + align:start position:0% +a very hard question you need to know +that here is here and go to GPS and find + + align:start position:0% +that here is here and go to GPS and find + + + align:start position:0% +that here is here and go to GPS and find +the location you need to know Sidda cos + + align:start position:0% +the location you need to know Sidda cos + + + align:start position:0% +the location you need to know Sidda cos +house for me list of contacts and him to + + align:start position:0% +house for me list of contacts and him to + + + align:start position:0% +house for me list of contacts and him to +go there and you need to then send it to + + align:start position:0% +go there and you need to then send it to + + + align:start position:0% +go there and you need to then send it to +in that case we send it I believe it was + + align:start position:0% +in that case we send it I believe it was + + + align:start position:0% +in that case we send it I believe it was +MapQuest I don't even know if it exists + + align:start position:0% +MapQuest I don't even know if it exists + + + align:start position:0% +MapQuest I don't even know if it exists +now to to actually give the directions + + align:start position:0% +now to to actually give the directions + + + align:start position:0% +now to to actually give the directions +well anyway so so well we it was a + + align:start position:0% +well anyway so so well we it was a + + + align:start position:0% +well anyway so so well we it was a +little bit of a sad story actually so we + + align:start position:0% +little bit of a sad story actually so we + + + align:start position:0% +little bit of a sad story actually so we +build the system the company that I + + align:start position:0% +build the system the company that I + + + align:start position:0% +build the system the company that I +mentioned was Noah Kia we showed them + + align:start position:0% +mentioned was Noah Kia we showed them + + + align:start position:0% +mentioned was Noah Kia we showed them +the demo they were very excited but they + + align:start position:0% +the demo they were very excited but they + + + align:start position:0% +the demo they were very excited but they +said well can we put start on on the + + align:start position:0% +said well can we put start on on the + + + align:start position:0% +said well can we put start on on the +phone because in that application the + + align:start position:0% +phone because in that application the + + + align:start position:0% +phone because in that application the +signals were sent to MIT from the phone + + align:start position:0% +signals were sent to MIT from the phone + + + align:start position:0% +signals were sent to MIT from the phone +and the answer was sending back to the + + align:start position:0% +and the answer was sending back to the + + + align:start position:0% +and the answer was sending back to the +phone I said well it doesn't seem right + + align:start position:0% +phone I said well it doesn't seem right + + + align:start position:0% +phone I said well it doesn't seem right +start is large and there was no there is + + align:start position:0% +start is large and there was no there is + + + align:start position:0% +start is large and there was no there is +still internet that could take care of + + align:start position:0% +still internet that could take care of + + + align:start position:0% +still internet that could take care of +that they say no no no how big is your + + align:start position:0% +that they say no no no how big is your + + + align:start position:0% +that they say no no no how big is your +system can you talk to the company to + + align:start position:0% +system can you talk to the company to + + + align:start position:0% +system can you talk to the company to +put it to a list compiler to put it on + + align:start position:0% +put it to a list compiler to put it on + + + align:start position:0% +put it to a list compiler to put it on +our chip and so forth we need to know + + align:start position:0% +our chip and so forth we need to know + + + align:start position:0% +our chip and so forth we need to know +how phone unfortunately the word cloud + + align:start position:0% +how phone unfortunately the word cloud + + + align:start position:0% +how phone unfortunately the word cloud +hadn't been invented yet maybe I would + + align:start position:0% +hadn't been invented yet maybe I would + + + align:start position:0% +hadn't been invented yet maybe I would +have been more eloquent and explaining + + align:start position:0% +have been more eloquent and explaining + + + align:start position:0% +have been more eloquent and explaining +to them why they don't need to have the + + align:start position:0% +to them why they don't need to have the + + + align:start position:0% +to them why they don't need to have the +system on the phone and so they didn't + + align:start position:0% +system on the phone and so they didn't + + + align:start position:0% +system on the phone and so they didn't +want to use it the way it is we wrote a + + align:start position:0% +want to use it the way it is we wrote a + + + align:start position:0% +want to use it the way it is we wrote a +paper showed it to them say do something + + align:start position:0% +paper showed it to them say do something + + + align:start position:0% +paper showed it to them say do something +about this it will be too late and right + + align:start position:0% +about this it will be too late and right + + + align:start position:0% +about this it will be too late and right +at that time Apple released its first + + align:start position:0% +at that time Apple released its first + + + align:start position:0% +at that time Apple released its first +iPhone so I go to like senior vice + + align:start position:0% +iPhone so I go to like senior vice + + + align:start position:0% +iPhone so I go to like senior vice +president and say look these guys ahead + + align:start position:0% +president and say look these guys ahead + + + align:start position:0% +president and say look these guys ahead +of you you should do some about it + + align:start position:0% +of you you should do some about it + + + align:start position:0% +of you you should do some about it +because they will do what I gave you + + align:start position:0% +because they will do what I gave you + + + align:start position:0% +because they will do what I gave you +he asked me how many iPhones did Apple + + align:start position:0% +he asked me how many iPhones did Apple + + + align:start position:0% +he asked me how many iPhones did Apple +sell last month I said I read some like + + align:start position:0% +sell last month I said I read some like + + + align:start position:0% +sell last month I said I read some like +a couple of thousand and he starts + + align:start position:0% +a couple of thousand and he starts + + + align:start position:0% +a couple of thousand and he starts +laughing hysterically he said we my + + align:start position:0% +laughing hysterically he said we my + + + align:start position:0% +laughing hysterically he said we my +company ships 1 million phones every day + + align:start position:0% +company ships 1 million phones every day + + + align:start position:0% +company ships 1 million phones every day +why do we care about Apple yourself well + + align:start position:0% +why do we care about Apple yourself well + + + align:start position:0% +why do we care about Apple yourself well +so we gave this talk that was September + + align:start position:0% +so we gave this talk that was September + + + align:start position:0% +so we gave this talk that was September +207 by then in December somebody started + + align:start position:0% +207 by then in December somebody started + + + align:start position:0% +207 by then in December somebody started +a company called Siri and then two years + + align:start position:0% +a company called Siri and then two years + + + align:start position:0% +a company called Siri and then two years +later a seer was bought by Apple and the + + align:start position:0% +later a seer was bought by Apple and the + + + align:start position:0% +later a seer was bought by Apple and the +rest is history + + align:start position:0% +rest is history + + + align:start position:0% +rest is history +and Nokia was so pretty much in a yard + + align:start position:0% +and Nokia was so pretty much in a yard + + + align:start position:0% +and Nokia was so pretty much in a yard +sale and doesn't exist anymore so be + + align:start position:0% +sale and doesn't exist anymore so be + + + align:start position:0% +sale and doesn't exist anymore so be +visionary don't don't think that you + + align:start position:0% +visionary don't don't think that you + + + align:start position:0% +visionary don't don't think that you +know what you are doing all the time + + align:start position:0% +know what you are doing all the time + + + align:start position:0% +know what you are doing all the time +yeah people often ask me to say V words + + align:start position:0% +yeah people often ask me to say V words + + + align:start position:0% +yeah people often ask me to say V words +about jeopardy the question that the IBM + + align:start position:0% +about jeopardy the question that the IBM + + + align:start position:0% +about jeopardy the question that the IBM +team was hoping to answer was actually a + + align:start position:0% +team was hoping to answer was actually a + + + align:start position:0% +team was hoping to answer was actually a +very important question can we create a + + align:start position:0% +very important question can we create a + + + align:start position:0% +very important question can we create a +computer system to compete against the + + align:start position:0% +computer system to compete against the + + + align:start position:0% +computer system to compete against the +best human in a task which is normally + + align:start position:0% +best human in a task which is normally + + + align:start position:0% +best human in a task which is normally +thought to require higher level of human + + align:start position:0% +thought to require higher level of human + + + align:start position:0% +thought to require higher level of human +intelligence I was involved with them + + align:start position:0% +intelligence I was involved with them + + + align:start position:0% +intelligence I was involved with them +from the very beginning for various + + align:start position:0% +from the very beginning for various + + + align:start position:0% +from the very beginning for various +reasons which I will not go into they + + align:start position:0% +reasons which I will not go into they + + + align:start position:0% +reasons which I will not go into they +put together wonderful team some really + + align:start position:0% +put together wonderful team some really + + + align:start position:0% +put together wonderful team some really +good people very devoted people they + + align:start position:0% +good people very devoted people they + + + align:start position:0% +good people very devoted people they +spent four or five years of their life + + align:start position:0% +spent four or five years of their life + + + align:start position:0% +spent four or five years of their life +pretty much totally devoted to that and + + align:start position:0% +pretty much totally devoted to that and + + + align:start position:0% +pretty much totally devoted to that and +and they build a system and these are + + align:start position:0% +and they build a system and these are + + + align:start position:0% +and they build a system and these are +the kind of I guess I don't know if many + + align:start position:0% +the kind of I guess I don't know if many + + + align:start position:0% +the kind of I guess I don't know if many +of you know what jeopardy is but pretty + + align:start position:0% +of you know what jeopardy is but pretty + + + align:start position:0% +of you know what jeopardy is but pretty +much people asked a question which for + + align:start position:0% +much people asked a question which for + + + align:start position:0% +much people asked a question which for +various reasons is formulated not as a + + align:start position:0% +various reasons is formulated not as a + + + align:start position:0% +various reasons is formulated not as a +question but but as an assertion with + + align:start position:0% +question but but as an assertion with + + + align:start position:0% +question but but as an assertion with +this demonstrative like these that are + + align:start position:0% +this demonstrative like these that are + + + align:start position:0% +this demonstrative like these that are +pronouns and you need to give an answer + + align:start position:0% +pronouns and you need to give an answer + + + align:start position:0% +pronouns and you need to give an answer +which they call the question for some + + align:start position:0% +which they call the question for some + + + align:start position:0% +which they call the question for some +reason as a gimmick you have to say what + + align:start position:0% +reason as a gimmick you have to say what + + + align:start position:0% +reason as a gimmick you have to say what +is envelope instead of envelope but + + align:start position:0% +is envelope instead of envelope but + + + align:start position:0% +is envelope instead of envelope but +let's stop it + + align:start position:0% +let's stop it + + + align:start position:0% +let's stop it +it doesn't matter and this is very hard + + align:start position:0% +it doesn't matter and this is very hard + + + align:start position:0% +it doesn't matter and this is very hard +to push one of these paper products is + + align:start position:0% +to push one of these paper products is + + + align:start position:0% +to push one of these paper products is +to stretch the establish limits and you + + align:start position:0% +to stretch the establish limits and you + + + align:start position:0% +to stretch the establish limits and you +need to figure out that to push the + + align:start position:0% +need to figure out that to push the + + + align:start position:0% +need to figure out that to push the +envelopes me and stretch + + align:start position:0% +envelopes me and stretch + + + align:start position:0% +envelopes me and stretch +establish limits this is an idiom for + + align:start position:0% +establish limits this is an idiom for + + + align:start position:0% +establish limits this is an idiom for +those of you who are not native and the + + align:start position:0% +those of you who are not native and the + + + align:start position:0% +those of you who are not native and the +answer is envelope a simple question is + + align:start position:0% +answer is envelope a simple question is + + + align:start position:0% +answer is envelope a simple question is +the chapel's of these colleges were + + align:start position:0% +the chapel's of these colleges were + + + align:start position:0% +the chapel's of these colleges were +designed by this architect and you need + + align:start position:0% +designed by this architect and you need + + + align:start position:0% +designed by this architect and you need +to figure out that Christopher Wren is + + align:start position:0% +to figure out that Christopher Wren is + + + align:start position:0% +to figure out that Christopher Wren is +the answer of course many questions + + align:start position:0% +the answer of course many questions + + + align:start position:0% +the answer of course many questions +involves question decomposition so + + align:start position:0% +involves question decomposition so + + + align:start position:0% +involves question decomposition so +here's an example of a real question of + + align:start position:0% +here's an example of a real question of + + + align:start position:0% +here's an example of a real question of +the four countries in the world that the + + align:start position:0% +the four countries in the world that the + + + align:start position:0% +the four countries in the world that the +u.s. does not have diplomatic relations + + align:start position:0% +u.s. does not have diplomatic relations + + + align:start position:0% +u.s. does not have diplomatic relations +with the one that's farthest north so + + align:start position:0% +with the one that's farthest north so + + + align:start position:0% +with the one that's farthest north so +pretty much asking which several + + align:start position:0% +pretty much asking which several + + + align:start position:0% +pretty much asking which several +questions one is the sort of inner sub + + align:start position:0% +questions one is the sort of inner sub + + + align:start position:0% +questions one is the sort of inner sub +question the four countries in the world + + align:start position:0% +question the four countries in the world + + + align:start position:0% +question the four countries in the world +that the US doesn't have relations with + + align:start position:0% +that the US doesn't have relations with + + + align:start position:0% +that the US doesn't have relations with +and the outer sub question is of now + + align:start position:0% +and the outer sub question is of now + + + align:start position:0% +and the outer sub question is of now +that you know the answer of these four + + align:start position:0% +that you know the answer of these four + + + align:start position:0% +that you know the answer of these four +countries which is the father snores you + + align:start position:0% +countries which is the father snores you + + + align:start position:0% +countries which is the father snores you +do a little bit of arithmetic and you + + align:start position:0% +do a little bit of arithmetic and you + + + align:start position:0% +do a little bit of arithmetic and you +find the answer is North Korea and of + + align:start position:0% +find the answer is North Korea and of + + + align:start position:0% +find the answer is North Korea and of +course this is very similar to what + + align:start position:0% +course this is very similar to what + + + align:start position:0% +course this is very similar to what +started years before is pretty much you + + align:start position:0% +started years before is pretty much you + + + align:start position:0% +started years before is pretty much you +decompose the question and you solve + + align:start position:0% +decompose the question and you solve + + + align:start position:0% +decompose the question and you solve +them separately as I showed you a few + + align:start position:0% +them separately as I showed you a few + + + align:start position:0% +them separately as I showed you a few +minutes ago so so what son actually took + + align:start position:0% +minutes ago so so what son actually took + + + align:start position:0% +minutes ago so so what son actually took +a bunch of ideas from start the tone + + align:start position:0% +a bunch of ideas from start the tone + + + align:start position:0% +a bunch of ideas from start the tone +expressing the presentation the natural + + align:start position:0% +expressing the presentation the natural + + + align:start position:0% +expressing the presentation the natural +language annotations idea the object + + align:start position:0% +language annotations idea the object + + + align:start position:0% +language annotations idea the object +property value data model and the + + align:start position:0% +property value data model and the + + + align:start position:0% +property value data model and the +question the competition model and + + align:start position:0% +question the competition model and + + + align:start position:0% +question the competition model and +applied them when they could really + + align:start position:0% +applied them when they could really + + + align:start position:0% +applied them when they could really +analyze and tactically the question + + align:start position:0% +analyze and tactically the question + + + align:start position:0% +analyze and tactically the question +where the question was not too + + align:start position:0% +where the question was not too + + + align:start position:0% +where the question was not too +convoluted and when there was a semi + + align:start position:0% +convoluted and when there was a semi + + + align:start position:0% +convoluted and when there was a semi +structured resource or several resources + + align:start position:0% +structured resource or several resources + + + align:start position:0% +structured resource or several resources +to find an answer but many questions of + + align:start position:0% +to find an answer but many questions of + + + align:start position:0% +to find an answer but many questions of +course we're not like that and + + align:start position:0% +course we're not like that and + + + align:start position:0% +course we're not like that and +stretching the envelope is one example + + align:start position:0% +stretching the envelope is one example + + + align:start position:0% +stretching the envelope is one example +and so what's in use some statistical + + align:start position:0% +and so what's in use some statistical + + + align:start position:0% +and so what's in use some statistical +machine learning approaches and they did + + align:start position:0% +machine learning approaches and they did + + + align:start position:0% +machine learning approaches and they did +quite a good job of looking at a lot of + + align:start position:0% +quite a good job of looking at a lot of + + + align:start position:0% +quite a good job of looking at a lot of +data to resolve + + align:start position:0% +data to resolve + + + align:start position:0% +data to resolve +announcer equations the pipeline is + + align:start position:0% +announcer equations the pipeline is + + + align:start position:0% +announcer equations the pipeline is +really miles long + + align:start position:0% +really miles long + + + align:start position:0% +really miles long +because each of these bullets has three + + align:start position:0% +because each of these bullets has three + + + align:start position:0% +because each of these bullets has three +which a bunch of bullets with a bunch of + + align:start position:0% +which a bunch of bullets with a bunch of + + + align:start position:0% +which a bunch of bullets with a bunch of +bullets that the task that they were + + align:start position:0% +bullets that the task that they were + + + align:start position:0% +bullets that the task that they were +doing but on a very high level they + + align:start position:0% +doing but on a very high level they + + + align:start position:0% +doing but on a very high level they +needed to content acquisition pretty + + align:start position:0% +needed to content acquisition pretty + + + align:start position:0% +needed to content acquisition pretty +much all right there was a problem the + + align:start position:0% +much all right there was a problem the + + + align:start position:0% +much all right there was a problem the +company Jeopardy told them there is no + + align:start position:0% +company Jeopardy told them there is no + + + align:start position:0% +company Jeopardy told them there is no +the web could not be part of that + + align:start position:0% +the web could not be part of that + + + align:start position:0% +the web could not be part of that +because everything that Google knows + + align:start position:0% +because everything that Google knows + + + align:start position:0% +because everything that Google knows +everything so what is that you guys are + + align:start position:0% +everything so what is that you guys are + + + align:start position:0% +everything so what is that you guys are +doing so they had so what would you do + + align:start position:0% +doing so they had so what would you do + + + align:start position:0% +doing so they had so what would you do +if somebody tells you you cannot use the + + align:start position:0% +if somebody tells you you cannot use the + + + align:start position:0% +if somebody tells you you cannot use the +web what's that well you pretty much + + align:start position:0% +web what's that well you pretty much + + + align:start position:0% +web what's that well you pretty much +bring the bat the web and put it in a + + align:start position:0% +bring the bat the web and put it in a + + + align:start position:0% +bring the bat the web and put it in a +box and this is what IBM did they took + + align:start position:0% +box and this is what IBM did they took + + + align:start position:0% +box and this is what IBM did they took +every repository into a positive every + + align:start position:0% +every repository into a positive every + + + align:start position:0% +every repository into a positive every +database every encyclopedia every + + align:start position:0% +database every encyclopedia every + + + align:start position:0% +database every encyclopedia every +newspaper collection forgot what the + + align:start position:0% +newspaper collection forgot what the + + + align:start position:0% +newspaper collection forgot what the +blog's existed at the time and just had + + align:start position:0% +blog's existed at the time and just had + + + align:start position:0% +blog's existed at the time and just had +a lot of clusters and a lot of memory + + align:start position:0% +a lot of clusters and a lot of memory + + + align:start position:0% +a lot of clusters and a lot of memory +and everything was there so now they + + align:start position:0% +and everything was there so now they + + + align:start position:0% +and everything was there so now they +could tell the company know well we are + + align:start position:0% +could tell the company know well we are + + + align:start position:0% +could tell the company know well we are +smart without the world so that was the + + align:start position:0% +smart without the world so that was the + + + align:start position:0% +smart without the world so that was the +first thing then they actually there's + + align:start position:0% +first thing then they actually there's + + + align:start position:0% +first thing then they actually there's +some wonderful nature and it's + + align:start position:0% +some wonderful nature and it's + + + align:start position:0% +some wonderful nature and it's +processing people do so they did + + align:start position:0% +processing people do so they did + + + align:start position:0% +processing people do so they did +question-answering they search the + + align:start position:0% +question-answering they search the + + + align:start position:0% +question-answering they search the +documents so what they really did they + + align:start position:0% +documents so what they really did they + + + align:start position:0% +documents so what they really did they +would took the clue they call it they + + align:start position:0% +would took the clue they call it they + + + align:start position:0% +would took the clue they call it they +the question throw it on not the web but + + align:start position:0% +the question throw it on not the web but + + + align:start position:0% +the question throw it on not the web but +on their web find tens of thousands of + + align:start position:0% +on their web find tens of thousands of + + + align:start position:0% +on their web find tens of thousands of +documents that even closely match these + + align:start position:0% +documents that even closely match these + + + align:start position:0% +documents that even closely match these +keywords and then the real work just + + align:start position:0% +keywords and then the real work just + + + align:start position:0% +keywords and then the real work just +started they had this kind of filtering + + align:start position:0% +started they had this kind of filtering + + + align:start position:0% +started they had this kind of filtering +that kind of filtering this kind of + + align:start position:0% +that kind of filtering this kind of + + + align:start position:0% +that kind of filtering this kind of +answer generation that can they would + + align:start position:0% +answer generation that can they would + + + align:start position:0% +answer generation that can they would +their what score it they will obtain new + + align:start position:0% +their what score it they will obtain new + + + align:start position:0% +their what score it they will obtain new +evidence they will do it again they will + + align:start position:0% +evidence they will do it again they will + + + align:start position:0% +evidence they will do it again they will +do ranking and they will decide how + + align:start position:0% +do ranking and they will decide how + + + align:start position:0% +do ranking and they will decide how +confident they are about that and then + + align:start position:0% +confident they are about that and then + + + align:start position:0% +confident they are about that and then +they will decide whether it's worse how + + align:start position:0% +they will decide whether it's worse how + + + align:start position:0% +they will decide whether it's worse how +much they spend in care-a-lot of time + + align:start position:0% +much they spend in care-a-lot of time + + + align:start position:0% +much they spend in care-a-lot of time +figuring out how much to money I don't + + align:start position:0% +figuring out how much to money I don't + + + align:start position:0% +figuring out how much to money I don't +actually know much about jeopardy but + + align:start position:0% +actually know much about jeopardy but + + + align:start position:0% +actually know much about jeopardy but +depends we have to tell them how good + + align:start position:0% +depends we have to tell them how good + + + align:start position:0% +depends we have to tell them how good +you answer well you could come you need + + align:start position:0% +you answer well you could come you need + + + align:start position:0% +you answer well you could come you need +to cover the number of how expensive you + + align:start position:0% +to cover the number of how expensive you + + + align:start position:0% +to cover the number of how expensive you +how much you make if you win and how + + align:start position:0% +how much you make if you win and how + + + align:start position:0% +how much you make if you win and how +much you lose if you + + align:start position:0% +much you lose if you + + + align:start position:0% +much you lose if you +Louis and so they did it all and they + + align:start position:0% +Louis and so they did it all and they + + + align:start position:0% +Louis and so they did it all and they +they really did a wonderful they build a + + align:start position:0% +they really did a wonderful they build a + + + align:start position:0% +they really did a wonderful they build a +wonderful system in the beginning when I + + align:start position:0% +wonderful system in the beginning when I + + + align:start position:0% +wonderful system in the beginning when I +started going there that was very very + + align:start position:0% +started going there that was very very + + + align:start position:0% +started going there that was very very +slow it it ran on a single processor and + + align:start position:0% +slow it it ran on a single processor and + + + align:start position:0% +slow it it ran on a single processor and +really took two hours to do that to do + + align:start position:0% +really took two hours to do that to do + + + align:start position:0% +really took two hours to do that to do +this pipeline but that if you think + + align:start position:0% +this pipeline but that if you think + + + align:start position:0% +this pipeline but that if you think +about it is a very profitable problem + + align:start position:0% +about it is a very profitable problem + + + align:start position:0% +about it is a very profitable problem +you could send it all to in that case I + + align:start position:0% +you could send it all to in that case I + + + align:start position:0% +you could send it all to in that case I +think by the end it was like several + + align:start position:0% +think by the end it was like several + + + align:start position:0% +think by the end it was like several +thousand course and they easily use the + + align:start position:0% +thousand course and they easily use the + + + align:start position:0% +thousand course and they easily use the +time to three seconds which was passable + + align:start position:0% +time to three seconds which was passable + + + align:start position:0% +time to three seconds which was passable +and doable for for the computation and + + align:start position:0% +and doable for for the computation and + + + align:start position:0% +and doable for for the computation and +so they want as you all know they it's a + + align:start position:0% +so they want as you all know they it's a + + + align:start position:0% +so they want as you all know they it's a +great system that melds the + + align:start position:0% +great system that melds the + + + align:start position:0% +great system that melds the +state-of-the-art in natural language and + + align:start position:0% +state-of-the-art in natural language and + + + align:start position:0% +state-of-the-art in natural language and +QA and information retrieval machine + + align:start position:0% +QA and information retrieval machine + + + align:start position:0% +QA and information retrieval machine +learning it's a great piece of + + align:start position:0% +learning it's a great piece of + + + align:start position:0% +learning it's a great piece of +engineering it we ignite it I know + + align:start position:0% +engineering it we ignite it I know + + + align:start position:0% +engineering it we ignite it I know +doubts about the public interest in AI + + align:start position:0% +doubts about the public interest in AI + + + align:start position:0% +doubts about the public interest in AI +it brought talented new talented people + + align:start position:0% +it brought talented new talented people + + + align:start position:0% +it brought talented new talented people +we now field so this is all great news + + align:start position:0% + + + + align:start position:0% + +but let's look at some of the blunders + + align:start position:0% +but let's look at some of the blunders + + + align:start position:0% +but let's look at some of the blunders +that occurred well both before the + + align:start position:0% +that occurred well both before the + + + align:start position:0% +that occurred well both before the +computation and after I had a whole + + align:start position:0% +computation and after I had a whole + + + align:start position:0% +computation and after I had a whole +bunch a collection of those I'll just + + align:start position:0% +bunch a collection of those I'll just + + + align:start position:0% +bunch a collection of those I'll just +show you a couple this actually happened + + align:start position:0% +show you a couple this actually happened + + + align:start position:0% +show you a couple this actually happened +before the computation so they fixed the + + align:start position:0% +before the computation so they fixed the + + + align:start position:0% +before the computation so they fixed the +problem so the question was again it's + + align:start position:0% +problem so the question was again it's + + + align:start position:0% +problem so the question was again it's +called a clue in a category letters in + + align:start position:0% +called a clue in a category letters in + + + align:start position:0% +called a clue in a category letters in +the late 40s a mother wrote to this + + align:start position:0% +the late 40s a mother wrote to this + + + align:start position:0% +the late 40s a mother wrote to this +artist that his picture number nine + + align:start position:0% +artist that his picture number nine + + + align:start position:0% +artist that his picture number nine +looked like her son's finger paintings + + align:start position:0% +looked like her son's finger paintings + + + align:start position:0% +looked like her son's finger paintings +well so those who quick adept I'm sure + + align:start position:0% +well so those who quick adept I'm sure + + + align:start position:0% +well so those who quick adept I'm sure +you know that it Jackson Pollock but + + align:start position:0% +you know that it Jackson Pollock but + + + align:start position:0% +you know that it Jackson Pollock but +Watson's and Rembrandt for some stupid + + align:start position:0% +Watson's and Rembrandt for some stupid + + + align:start position:0% +Watson's and Rembrandt for some stupid +reasons it failed to recognize that late + + align:start position:0% +reasons it failed to recognize that late + + + align:start position:0% +reasons it failed to recognize that late +43 for to 1940s rather we thought it's + + align:start position:0% +43 for to 1940s rather we thought it's + + + align:start position:0% +43 for to 1940s rather we thought it's +maybe previous centuries and apparently + + align:start position:0% +maybe previous centuries and apparently + + + align:start position:0% +maybe previous centuries and apparently +the it has something to do with number + + align:start position:0% +the it has something to do with number + + + align:start position:0% +the it has something to do with number +nine + + align:start position:0% +nine + + + align:start position:0% +nine +that wasn't a bunch of documents related + + align:start position:0% +that wasn't a bunch of documents related + + + align:start position:0% +that wasn't a bunch of documents related +to Rembrandt and so it said remembered + + align:start position:0% +to Rembrandt and so it said remembered + + + align:start position:0% +to Rembrandt and so it said remembered +another more famous blunder because that + + align:start position:0% +another more famous blunder because that + + + align:start position:0% +another more famous blunder because that +happened at the computation the category + + align:start position:0% +happened at the computation the category + + + align:start position:0% +happened at the computation the category +was us CD and the question was if which + + align:start position:0% +was us CD and the question was if which + + + align:start position:0% +was us CD and the question was if which +is the city's largest airport is named + + align:start position:0% +is the city's largest airport is named + + + align:start position:0% +is the city's largest airport is named +for a World War two hero and its second + + align:start position:0% +for a World War two hero and its second + + + align:start position:0% +for a World War two hero and its second +largest for a world world to battle and + + align:start position:0% +largest for a world world to battle and + + + align:start position:0% +largest for a world world to battle and +again those of you quicker that will + + align:start position:0% +again those of you quicker that will + + + align:start position:0% +again those of you quicker that will +know that in Chicago the resist O'Hare + + align:start position:0% +know that in Chicago the resist O'Hare + + + align:start position:0% +know that in Chicago the resist O'Hare +Airport and he happened to be a famous + + align:start position:0% +Airport and he happened to be a famous + + + align:start position:0% +Airport and he happened to be a famous +hero for the world and the second + + align:start position:0% +hero for the world and the second + + + align:start position:0% +hero for the world and the second +Airport called me the way which is a + + align:start position:0% +Airport called me the way which is a + + + align:start position:0% +Airport called me the way which is a +famous battle in the Second World War + + align:start position:0% +famous battle in the Second World War + + + align:start position:0% +famous battle in the Second World War +and what some press of the button and + + align:start position:0% +and what some press of the button and + + + align:start position:0% +and what some press of the button and +says Toronto and they're sort of gas in + + align:start position:0% +says Toronto and they're sort of gas in + + + align:start position:0% +says Toronto and they're sort of gas in +in the audience and also an elect ends + + align:start position:0% +in the audience and also an elect ends + + + align:start position:0% +in the audience and also an elect ends +of millions or hundreds of millions + + align:start position:0% +of millions or hundreds of millions + + + align:start position:0% +of millions or hundreds of millions +television sets sets around the world + + align:start position:0% +television sets sets around the world + + + align:start position:0% +television sets sets around the world +and again there are some stupid reasons + + align:start position:0% +and again there are some stupid reasons + + + align:start position:0% +and again there are some stupid reasons +what some did machine learning as I said + + align:start position:0% +what some did machine learning as I said + + + align:start position:0% +what some did machine learning as I said +and it's the test we figured out the the + + align:start position:0% +and it's the test we figured out the the + + + align:start position:0% +and it's the test we figured out the the +category part of the clue which in this + + align:start position:0% +category part of the clue which in this + + + align:start position:0% +category part of the clue which in this +case insists it's a US city it might not + + align:start position:0% +case insists it's a US city it might not + + + align:start position:0% +case insists it's a US city it might not +be that important so you should pay less + + align:start position:0% +be that important so you should pay less + + + align:start position:0% +be that important so you should pay less +attention to it it also knew that + + align:start position:0% +attention to it it also knew that + + + align:start position:0% +attention to it it also knew that +Toronto team plane and baseball is a + + align:start position:0% +Toronto team plane and baseball is a + + + align:start position:0% +Toronto team plane and baseball is a +true yes in the US baseball league and + + align:start position:0% +true yes in the US baseball league and + + + align:start position:0% +true yes in the US baseball league and +that in fact one of Toronto Airport is + + align:start position:0% +that in fact one of Toronto Airport is + + + align:start position:0% +that in fact one of Toronto Airport is +named for a hero although it's what what + + align:start position:0% +named for a hero although it's what what + + + align:start position:0% +named for a hero although it's what what +one hero so it put it all together and + + align:start position:0% +one hero so it put it all together and + + + align:start position:0% +one hero so it put it all together and +said Toronto in any case it won't anyway + + align:start position:0% +said Toronto in any case it won't anyway + + + align:start position:0% +said Toronto in any case it won't anyway +because it did an amazing job and + + align:start position:0% +because it did an amazing job and + + + align:start position:0% +because it did an amazing job and +answering many more questions and but a + + align:start position:0% +answering many more questions and but a + + + align:start position:0% +answering many more questions and but a +question to us is whether this is what + + align:start position:0% +question to us is whether this is what + + + align:start position:0% +question to us is whether this is what +we should all be striving for I'm + + align:start position:0% +we should all be striving for I'm + + + align:start position:0% +we should all be striving for I'm +certainly all in favor of building + + align:start position:0% +certainly all in favor of building + + + align:start position:0% +certainly all in favor of building +awesome systems and they did and I + + align:start position:0% +awesome systems and they did and I + + + align:start position:0% +awesome systems and they did and I +explained to you why I think it's good + + align:start position:0% +explained to you why I think it's good + + + align:start position:0% +explained to you why I think it's good +but iBM has not created a machine that + + align:start position:0% +but iBM has not created a machine that + + + align:start position:0% +but iBM has not created a machine that +things like us and what's in success + + align:start position:0% +things like us and what's in success + + + align:start position:0% +things like us and what's in success +didn't bring us even for an inch closer + + align:start position:0% +didn't bring us even for an inch closer + + + align:start position:0% +didn't bring us even for an inch closer +to understanding human intelligence + + align:start position:0% + + + + align:start position:0% + +the positive news of course is that + + align:start position:0% +the positive news of course is that + + + align:start position:0% +the positive news of course is that +what's those blunders should remind us + + align:start position:0% +what's those blunders should remind us + + + align:start position:0% +what's those blunders should remind us +that the problem is waiting to be solved + + align:start position:0% +that the problem is waiting to be solved + + + align:start position:0% +that the problem is waiting to be solved +and I you guys and in good positions to + + align:start position:0% +and I you guys and in good positions to + + + align:start position:0% +and I you guys and in good positions to +to try to do that and that should be our + + align:start position:0% +to try to do that and that should be our + + + align:start position:0% +to try to do that and that should be our +next big challenge + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/yl8bygSTGTE.txt b/yl8bygSTGTE.txt new file mode 100644 index 0000000000000000000000000000000000000000..b2291c7940026ac40e40f6fd6f4e7b0aad46b6c8 --- /dev/null +++ b/yl8bygSTGTE.txt @@ -0,0 +1,9856 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mit.edu. + + align:start position:0% + + + + align:start position:0% + +So, molecules + + align:start position:0% +So, molecules + + + align:start position:0% +So, molecules +have three kinds of uh structures. + + align:start position:0% +have three kinds of uh structures. + + + align:start position:0% +have three kinds of uh structures. +electronic, vibrational, and rotational. + + align:start position:0% +electronic, vibrational, and rotational. + + + align:start position:0% +electronic, vibrational, and rotational. +And my goal is to give you a sense of + + align:start position:0% +And my goal is to give you a sense of + + + align:start position:0% +And my goal is to give you a sense of +how do we predict each kind of uh + + align:start position:0% +how do we predict each kind of uh + + + align:start position:0% +how do we predict each kind of uh +structure? Not how do we calculate it + + align:start position:0% +structure? Not how do we calculate it + + + align:start position:0% +structure? Not how do we calculate it +but how do you have it in your head so + + align:start position:0% +but how do you have it in your head so + + + align:start position:0% +but how do you have it in your head so +that you know what are the the expected + + align:start position:0% +that you know what are the the expected + + + align:start position:0% +that you know what are the the expected +patterns and how do you use one pattern + + align:start position:0% +patterns and how do you use one pattern + + + align:start position:0% +patterns and how do you use one pattern +to uh help you with a decision about + + align:start position:0% +to uh help you with a decision about + + + align:start position:0% +to uh help you with a decision about +what another pattern means. So + + align:start position:0% +what another pattern means. So + + + align:start position:0% +what another pattern means. So +electronic structure is a combination of + + align:start position:0% +electronic structure is a combination of + + + align:start position:0% +electronic structure is a combination of +big stuff and small stuff. + + align:start position:0% +big stuff and small stuff. + + + align:start position:0% +big stuff and small stuff. +The big stuff is basically the spectrum + + align:start position:0% +The big stuff is basically the spectrum + + + align:start position:0% +The big stuff is basically the spectrum +of hydrogen or the spectrum of H2 plus + + align:start position:0% +of hydrogen or the spectrum of H2 plus + + + align:start position:0% +of hydrogen or the spectrum of H2 plus +molecular ion. Uh that these are + + align:start position:0% +molecular ion. Uh that these are + + + align:start position:0% +molecular ion. Uh that these are +patterns one kind of pattern that is uh + + align:start position:0% +patterns one kind of pattern that is uh + + + align:start position:0% +patterns one kind of pattern that is uh +uh possible to remember but the more + + align:start position:0% +uh possible to remember but the more + + + align:start position:0% +uh possible to remember but the more +electrons we have the more complicated + + align:start position:0% +electrons we have the more complicated + + + align:start position:0% +electrons we have the more complicated +that will be. But it's useful to have a + + align:start position:0% +that will be. But it's useful to have a + + + align:start position:0% +that will be. But it's useful to have a +simple picture of what it ought to be + + align:start position:0% +simple picture of what it ought to be + + + align:start position:0% +simple picture of what it ought to be +and how it gets disguised. But there are + + align:start position:0% +and how it gets disguised. But there are + + + align:start position:0% +and how it gets disguised. But there are +little things too that also provide + + align:start position:0% +little things too that also provide + + + align:start position:0% +little things too that also provide +crucial clues what the electronic + + align:start position:0% +crucial clues what the electronic + + + align:start position:0% +crucial clues what the electronic +structure is like fine structure + + align:start position:0% +structure is like fine structure + + + align:start position:0% +structure is like fine structure +hyperfine structure spin orbit spin spin + + align:start position:0% +hyperfine structure spin orbit spin spin + + + align:start position:0% +hyperfine structure spin orbit spin spin +spin rotation things where uh the + + align:start position:0% +spin rotation things where uh the + + + align:start position:0% +spin rotation things where uh the +spectrum gets a little complicated but + + align:start position:0% +spectrum gets a little complicated but + + + align:start position:0% +spectrum gets a little complicated but +it's really small splittings and often + + align:start position:0% +it's really small splittings and often + + + align:start position:0% +it's really small splittings and often +they tell you a lot more about the + + align:start position:0% +they tell you a lot more about the + + + align:start position:0% +they tell you a lot more about the +nature of the states you're looking at + + align:start position:0% +nature of the states you're looking at + + + align:start position:0% +nature of the states you're looking at +than the big stuff. And so you want to + + align:start position:0% +than the big stuff. And so you want to + + + align:start position:0% +than the big stuff. And so you want to +be able to to deal with both. And so I'm + + align:start position:0% +be able to to deal with both. And so I'm + + + align:start position:0% +be able to to deal with both. And so I'm +going to present my unique view of + + align:start position:0% +going to present my unique view of + + + align:start position:0% +going to present my unique view of +atomic spectra + + align:start position:0% +atomic spectra + + + align:start position:0% +atomic spectra +uh with the view of making it useful to + + align:start position:0% +uh with the view of making it useful to + + + align:start position:0% +uh with the view of making it useful to +you for understanding what you're going + + align:start position:0% +you for understanding what you're going + + + align:start position:0% +you for understanding what you're going +to encounter in molecular spectrum. So + + align:start position:0% +to encounter in molecular spectrum. So + + + align:start position:0% +to encounter in molecular spectrum. So +Bob, can I ask one quick question now? + + align:start position:0% +Bob, can I ask one quick question now? + + + align:start position:0% +Bob, can I ask one quick question now? +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +So we talk about electronic, vibrational + + align:start position:0% +So we talk about electronic, vibrational + + + align:start position:0% +So we talk about electronic, vibrational +and rotational structure. + + align:start position:0% +and rotational structure. + + + align:start position:0% +and rotational structure. +Yes. + + align:start position:0% +Yes. + + + align:start position:0% +Yes. +And typically only these three. And by + + align:start position:0% +And typically only these three. And by + + + align:start position:0% +And typically only these three. And by +electronic structure we really mean like + + align:start position:0% +electronic structure we really mean like + + + align:start position:0% +electronic structure we really mean like +veence electronic structure. So it + + align:start position:0% +veence electronic structure. So it + + + align:start position:0% +veence electronic structure. So it +basically right so so I is the reason we + + align:start position:0% +basically right so so I is the reason we + + + align:start position:0% +basically right so so I is the reason we +don't talk about spectra of core + + align:start position:0% +don't talk about spectra of core + + + align:start position:0% +don't talk about spectra of core +electrons because it's experimentally + + align:start position:0% +electrons because it's experimentally + + + align:start position:0% +electrons because it's experimentally +hard to make X-rays or is it because + + align:start position:0% +hard to make X-rays or is it because + + + align:start position:0% +hard to make X-rays or is it because +it's really really not as interesting + + align:start position:0% +it's really really not as interesting + + + align:start position:0% +it's really really not as interesting +and similarly do we not talk about like + + align:start position:0% +and similarly do we not talk about like + + + align:start position:0% +and similarly do we not talk about like +the the nuclear magnetic resonance type + + align:start position:0% +the the nuclear magnetic resonance type + + + align:start position:0% +the the nuclear magnetic resonance type +spectra because it doesn't really affect + + align:start position:0% +spectra because it doesn't really affect + + + align:start position:0% +spectra because it doesn't really affect +these other motions or because you know + + align:start position:0% +these other motions or because you know + + + align:start position:0% +these other motions or because you know +you need a big magnet. The simple + + align:start position:0% +you need a big magnet. The simple + + + align:start position:0% +you need a big magnet. The simple +answer, we don't talk about them because + + align:start position:0% +answer, we don't talk about them because + + + align:start position:0% +answer, we don't talk about them because +I don't know them. It's not like as well + + align:start position:0% +I don't know them. It's not like as well + + + align:start position:0% +I don't know them. It's not like as well +as I know these other things. The core + + align:start position:0% +as I know these other things. The core + + + align:start position:0% +as I know these other things. The core +structure we when we excite to uh very + + align:start position:0% +structure we when we excite to uh very + + + align:start position:0% +structure we when we excite to uh very +highly excited electronic states by + + align:start position:0% +highly excited electronic states by + + + align:start position:0% +highly excited electronic states by +opening up the core, + + align:start position:0% +opening up the core, + + + align:start position:0% +opening up the core, +the molecule is never stable and so you + + align:start position:0% +the molecule is never stable and so you + + + align:start position:0% +the molecule is never stable and so you +end up having continu. + + align:start position:0% +end up having continu. + + + align:start position:0% +end up having continu. +Mhm. Uh but in some ways the core + + align:start position:0% +Mhm. Uh but in some ways the core + + + align:start position:0% +Mhm. Uh but in some ways the core +structure is simpler because the cores + + align:start position:0% +structure is simpler because the cores + + + align:start position:0% +structure is simpler because the cores +are really they don't know they're in a + + align:start position:0% +are really they don't know they're in a + + + align:start position:0% +are really they don't know they're in a +molecule or they only know they're in a + + align:start position:0% +molecule or they only know they're in a + + + align:start position:0% +molecule or they only know they're in a +particular molecule through fine + + align:start position:0% +particular molecule through fine + + + align:start position:0% +particular molecule through fine +structures. And so they are wonderful + + align:start position:0% +structures. And so they are wonderful + + + align:start position:0% +structures. And so they are wonderful +probes of the chemical nature of a + + align:start position:0% +probes of the chemical nature of a + + + align:start position:0% +probes of the chemical nature of a +particular the chemical environment of a + + align:start position:0% +particular the chemical environment of a + + + align:start position:0% +particular the chemical environment of a +particular atom and that uh that is + + align:start position:0% +particular atom and that uh that is + + + align:start position:0% +particular atom and that uh that is +useful but it's it's not complicated in + + align:start position:0% +useful but it's it's not complicated in + + + align:start position:0% +useful but it's it's not complicated in +the sense that assigning a spectrum is + + align:start position:0% +the sense that assigning a spectrum is + + + align:start position:0% +the sense that assigning a spectrum is +complicated. Basically, you know, where + + align:start position:0% +complicated. Basically, you know, where + + + align:start position:0% +complicated. Basically, you know, where +each shell has its uh spectra and and + + align:start position:0% +each shell has its uh spectra and and + + + align:start position:0% +each shell has its uh spectra and and +each atom has its different end shells + + align:start position:0% +each atom has its different end shells + + + align:start position:0% +each atom has its different end shells +at different energies. And so it it's + + align:start position:0% +at different energies. And so it it's + + + align:start position:0% +at different energies. And so it it's +not you don't need me to help you to + + align:start position:0% +not you don't need me to help you to + + + align:start position:0% +not you don't need me to help you to +assign such spectrum. Those are very + + align:start position:0% +assign such spectrum. Those are very + + + align:start position:0% +assign such spectrum. Those are very +easy. It's the kind of spectra that most + + align:start position:0% +easy. It's the kind of spectra that most + + + align:start position:0% +easy. It's the kind of spectra that most +people who uh are not physical chemists + + align:start position:0% +people who uh are not physical chemists + + + align:start position:0% +people who uh are not physical chemists +think all spectra would be things that + + align:start position:0% +think all spectra would be things that + + + align:start position:0% +think all spectra would be things that +are very very low resolution, very + + align:start position:0% +are very very low resolution, very + + + align:start position:0% +are very very low resolution, very +simple to interpret and have direct + + align:start position:0% +simple to interpret and have direct + + + align:start position:0% +simple to interpret and have direct +chemical significance. + + align:start position:0% +chemical significance. + + + align:start position:0% +chemical significance. +NMR is of great importance usually for + + align:start position:0% +NMR is of great importance usually for + + + align:start position:0% +NMR is of great importance usually for +larger molecules where uh uh you you + + align:start position:0% +larger molecules where uh uh you you + + + align:start position:0% +larger molecules where uh uh you you +want to know what's connected to what. + + align:start position:0% +want to know what's connected to what. + + + align:start position:0% +want to know what's connected to what. +uh the kind of thing that I'm talking to + + align:start position:0% +uh the kind of thing that I'm talking to + + + align:start position:0% +uh the kind of thing that I'm talking to +you about is you know pretty much which + + align:start position:0% +you about is you know pretty much which + + + align:start position:0% +you about is you know pretty much which +what the uh bonded network is and you + + align:start position:0% +what the uh bonded network is and you + + + align:start position:0% +what the uh bonded network is and you +have some ideas about what the structure + + align:start position:0% +have some ideas about what the structure + + + align:start position:0% +have some ideas about what the structure +of the molecule would be. There may be + + align:start position:0% +of the molecule would be. There may be + + + align:start position:0% +of the molecule would be. There may be +times when you have spectra of different + + align:start position:0% +times when you have spectra of different + + + align:start position:0% +times when you have spectra of different +molecules and you'd like to sort them + + align:start position:0% +molecules and you'd like to sort them + + + align:start position:0% +molecules and you'd like to sort them +out according to which is which and in + + align:start position:0% +out according to which is which and in + + + align:start position:0% +out according to which is which and in +that sense NMR might be of use but + + align:start position:0% +that sense NMR might be of use but + + + align:start position:0% +that sense NMR might be of use but +usually you nobody does NMR in the gas + + align:start position:0% +usually you nobody does NMR in the gas + + + align:start position:0% +usually you nobody does NMR in the gas +phase + + align:start position:0% +phase + + + align:start position:0% +phase +because it need it's a magnetic dipole + + align:start position:0% +because it need it's a magnetic dipole + + + align:start position:0% +because it need it's a magnetic dipole +transition you need it's weak and you + + align:start position:0% +transition you need it's weak and you + + + align:start position:0% +transition you need it's weak and you +need a lot of uh uh molecules in order + + align:start position:0% +need a lot of uh uh molecules in order + + + align:start position:0% +need a lot of uh uh molecules in order +to get an NMR spectrum so I think the + + align:start position:0% +to get an NMR spectrum so I think the + + + align:start position:0% +to get an NMR spectrum so I think the +communities who use F core structure. + + align:start position:0% +communities who use F core structure. + + + align:start position:0% +communities who use F core structure. +Mhm. + + align:start position:0% +Mhm. + + + align:start position:0% +Mhm. +Uh and and NMR are different from the + + align:start position:0% +Uh and and NMR are different from the + + + align:start position:0% +Uh and and NMR are different from the +physical chemists mostly that are are + + align:start position:0% +physical chemists mostly that are are + + + align:start position:0% +physical chemists mostly that are are +going to be concerned with the spectra + + align:start position:0% +going to be concerned with the spectra + + + align:start position:0% +going to be concerned with the spectra +of smallish molecules in the gas phase. + + align:start position:0% +of smallish molecules in the gas phase. + + + align:start position:0% +of smallish molecules in the gas phase. +But that was a really good question. + + align:start position:0% +But that was a really good question. + + + align:start position:0% +But that was a really good question. +Okay. So, uh + + align:start position:0% + + + + align:start position:0% + +we want to ask two questions when we + + align:start position:0% +we want to ask two questions when we + + + align:start position:0% +we want to ask two questions when we +approach a spectrum. + + align:start position:0% +approach a spectrum. + + + align:start position:0% +approach a spectrum. +What do we expect and when should we be + + align:start position:0% +What do we expect and when should we be + + + align:start position:0% +What do we expect and when should we be +surprised? + + align:start position:0% +surprised? + + + align:start position:0% +surprised? +Because if the spectrum is entirely what + + align:start position:0% +Because if the spectrum is entirely what + + + align:start position:0% +Because if the spectrum is entirely what +we expect, well then there isn't really + + align:start position:0% +we expect, well then there isn't really + + + align:start position:0% +we expect, well then there isn't really +any challenge and there isn't anything + + align:start position:0% +any challenge and there isn't anything + + + align:start position:0% +any challenge and there isn't anything +new. But if we're surprised, you need to + + align:start position:0% +new. But if we're surprised, you need to + + + align:start position:0% +new. But if we're surprised, you need to +know you should be surprised and that + + align:start position:0% +know you should be surprised and that + + + align:start position:0% +know you should be surprised and that +the molecule is telling you something + + align:start position:0% +the molecule is telling you something + + + align:start position:0% +the molecule is telling you something +that it's worth figuring out because + + align:start position:0% +that it's worth figuring out because + + + align:start position:0% +that it's worth figuring out because +it's violating some rule or it's it's + + align:start position:0% +it's violating some rule or it's it's + + + align:start position:0% +it's violating some rule or it's it's +doing something really neat. And so + + align:start position:0% +doing something really neat. And so + + + align:start position:0% +doing something really neat. And so +being surprised is good. And so what uh + + align:start position:0% +being surprised is good. And so what uh + + + align:start position:0% +being surprised is good. And so what uh +I'm going to begin talking about + + align:start position:0% +I'm going to begin talking about + + + align:start position:0% +I'm going to begin talking about +patterns + + align:start position:0% +patterns + + + align:start position:0% +patterns +of levels + + align:start position:0% +of levels + + + align:start position:0% +of levels +transitions + + align:start position:0% + + + + align:start position:0% + +and we're going to talk about good + + align:start position:0% +and we're going to talk about good + + + align:start position:0% +and we're going to talk about good +quantum numbers + + align:start position:0% + + + + align:start position:0% + +and things like that. Okay. But the the + + align:start position:0% +and things like that. Okay. But the the + + + align:start position:0% +and things like that. Okay. But the the +way we're going to start we're going to + + align:start position:0% +way we're going to start we're going to + + + align:start position:0% +way we're going to start we're going to +talk about one electron atoms. + + align:start position:0% +talk about one electron atoms. + + + align:start position:0% +talk about one electron atoms. +In other words, hydrogen atom, helium + + align:start position:0% +In other words, hydrogen atom, helium + + + align:start position:0% +In other words, hydrogen atom, helium +plus ion, lithium 2 plus ion. And these + + align:start position:0% +plus ion, lithium 2 plus ion. And these + + + align:start position:0% +plus ion, lithium 2 plus ion. And these +are all really simple things. Uh but + + align:start position:0% +are all really simple things. Uh but + + + align:start position:0% +are all really simple things. Uh but +they illustrate that electronic + + align:start position:0% +they illustrate that electronic + + + align:start position:0% +they illustrate that electronic +structure doesn't have to be a telephone + + align:start position:0% +structure doesn't have to be a telephone + + + align:start position:0% +structure doesn't have to be a telephone +direct. It can be just a bunch of + + align:start position:0% +direct. It can be just a bunch of + + + align:start position:0% +direct. It can be just a bunch of +related things and if you know one, you + + align:start position:0% +related things and if you know one, you + + + align:start position:0% +related things and if you know one, you +know the others. + + align:start position:0% +know the others. + + + align:start position:0% +know the others. +And uh and then life gets more + + align:start position:0% +And uh and then life gets more + + + align:start position:0% +And uh and then life gets more +complicated when we go beyond one + + align:start position:0% +complicated when we go beyond one + + + align:start position:0% +complicated when we go beyond one +electron out. So we're going to talk + + align:start position:0% +electron out. So we're going to talk + + + align:start position:0% +electron out. So we're going to talk +about molecular atoms, the terms in the + + align:start position:0% +about molecular atoms, the terms in the + + + align:start position:0% +about molecular atoms, the terms in the +Hamiltonian, the basis functions we use + + align:start position:0% +Hamiltonian, the basis functions we use + + + align:start position:0% +Hamiltonian, the basis functions we use +to express the Hamiltonian, + + align:start position:0% +to express the Hamiltonian, + + + align:start position:0% +to express the Hamiltonian, +various kinds of scaling rules that tell + + align:start position:0% +various kinds of scaling rules that tell + + + align:start position:0% +various kinds of scaling rules that tell +you how uh properties depend on quantum + + align:start position:0% +you how uh properties depend on quantum + + + align:start position:0% +you how uh properties depend on quantum +numbers, some notation + + align:start position:0% +numbers, some notation + + + align:start position:0% +numbers, some notation +and uh transition propensity rules. For + + align:start position:0% +and uh transition propensity rules. For + + + align:start position:0% +and uh transition propensity rules. For +example, we have the atomic angular + + align:start position:0% +example, we have the atomic angular + + + align:start position:0% +example, we have the atomic angular +momentum J and for a transition we and + + align:start position:0% +momentum J and for a transition we and + + + align:start position:0% +momentum J and for a transition we and +the atomic orbital angular momentum L. + + align:start position:0% +the atomic orbital angular momentum L. + + + align:start position:0% +the atomic orbital angular momentum L. +Uh the propensity rule uh says that + + align:start position:0% +Uh the propensity rule uh says that + + + align:start position:0% +Uh the propensity rule uh says that +delta J ought to be equal to delta J + + align:start position:0% +delta J ought to be equal to delta J + + + align:start position:0% +delta J ought to be equal to delta J +delta L. J changes by + one, L changes + + align:start position:0% +delta L. J changes by + one, L changes + + + align:start position:0% +delta L. J changes by + one, L changes +by plus one. You can have things + + align:start position:0% +by plus one. You can have things + + + align:start position:0% +by plus one. You can have things +violating propensity rules, but the + + align:start position:0% +violating propensity rules, but the + + + align:start position:0% +violating propensity rules, but the +stronger transitions are this. And you + + align:start position:0% +stronger transitions are this. And you + + + align:start position:0% +stronger transitions are this. And you +get that from a vector model. + + align:start position:0% +get that from a vector model. + + + align:start position:0% +get that from a vector model. +And I'll I'll introduce you to a vector + + align:start position:0% +And I'll I'll introduce you to a vector + + + align:start position:0% +And I'll I'll introduce you to a vector +model uh + + align:start position:0% +model uh + + + align:start position:0% +model uh +which uh is the beginning of using these + + align:start position:0% +which uh is the beginning of using these + + + align:start position:0% +which uh is the beginning of using these +precessing vectors or uh uh things that + + align:start position:0% +precessing vectors or uh uh things that + + + align:start position:0% +precessing vectors or uh uh things that +usually when they when you start to see + + align:start position:0% +usually when they when you start to see + + + align:start position:0% +usually when they when you start to see +them you say I want out of this room + + align:start position:0% +them you say I want out of this room + + + align:start position:0% +them you say I want out of this room +because I don't really know what these + + align:start position:0% +because I don't really know what these + + + align:start position:0% +because I don't really know what these +vectors are and why why I'm forced to + + align:start position:0% +vectors are and why why I'm forced to + + + align:start position:0% +vectors are and why why I'm forced to +memorize these things. Okay. So after we + + align:start position:0% +memorize these things. Okay. So after we + + + align:start position:0% +memorize these things. Okay. So after we +do one electron we'll do alkali + + align:start position:0% + + + + align:start position:0% + +atoms + + align:start position:0% +atoms + + + align:start position:0% +atoms +and those are atoms with one electron + + align:start position:0% +and those are atoms with one electron + + + align:start position:0% +and those are atoms with one electron +outside of a closed shell and they + + align:start position:0% +outside of a closed shell and they + + + align:start position:0% +outside of a closed shell and they +differ from the one electron atoms in an + + align:start position:0% +differ from the one electron atoms in an + + + align:start position:0% +differ from the one electron atoms in an +important way a simple way and that's + + align:start position:0% +important way a simple way and that's + + + align:start position:0% +important way a simple way and that's +the first step into complexity + + align:start position:0% +the first step into complexity + + + align:start position:0% +the first step into complexity +and uh we'll eventually get to many + + align:start position:0% +and uh we'll eventually get to many + + + align:start position:0% +and uh we'll eventually get to many +electron atoms and then we have to do + + align:start position:0% +electron atoms and then we have to do + + + align:start position:0% +electron atoms and then we have to do +more work to relate what you see in the + + align:start position:0% +more work to relate what you see in the + + + align:start position:0% +more work to relate what you see in the +spectrum + + align:start position:0% +spectrum + + + align:start position:0% +spectrum +to uh the things you'd like to + + align:start position:0% +to uh the things you'd like to + + + align:start position:0% +to uh the things you'd like to +understand. + + align:start position:0% + + + + align:start position:0% + +And once we get to alike like atoms, uh + + align:start position:0% +And once we get to alike like atoms, uh + + + align:start position:0% +And once we get to alike like atoms, uh +there's going to be a little bit of + + align:start position:0% +there's going to be a little bit of + + + align:start position:0% +there's going to be a little bit of +quantum + + align:start position:0% +quantum + + + align:start position:0% +quantum +defect + + align:start position:0% + + + + align:start position:0% + +theory. + + align:start position:0% +theory. + + + align:start position:0% +theory. +It's a topic I'm going to come back to + + align:start position:0% +It's a topic I'm going to come back to + + + align:start position:0% +It's a topic I'm going to come back to +repeatedly in in increasing + + align:start position:0% +repeatedly in in increasing + + + align:start position:0% +repeatedly in in increasing +uh sophistication. + + align:start position:0% +uh sophistication. + + + align:start position:0% +uh sophistication. +Basically, as chemists, we know about + + align:start position:0% +Basically, as chemists, we know about + + + align:start position:0% +Basically, as chemists, we know about +quantum mechanics a little bit. We know + + align:start position:0% +quantum mechanics a little bit. We know + + + align:start position:0% +quantum mechanics a little bit. We know +about Hamiltonians. + + align:start position:0% +about Hamiltonians. + + + align:start position:0% +about Hamiltonians. +And most of my approach to the problem + + align:start position:0% +And most of my approach to the problem + + + align:start position:0% +And most of my approach to the problem +is in terms of effective Hamiltonians, + + align:start position:0% +is in terms of effective Hamiltonians, + + + align:start position:0% +is in terms of effective Hamiltonians, +which are just a toy version of the real + + align:start position:0% +which are just a toy version of the real + + + align:start position:0% +which are just a toy version of the real +thing. + + align:start position:0% +thing. + + + align:start position:0% +thing. +There is another approach which is more + + align:start position:0% +There is another approach which is more + + + align:start position:0% +There is another approach which is more +of a physicist approach which is + + align:start position:0% +of a physicist approach which is + + + align:start position:0% +of a physicist approach which is +scattering and there is a way of using + + align:start position:0% +scattering and there is a way of using + + + align:start position:0% +scattering and there is a way of using +scattering to learn about the structure + + align:start position:0% +scattering to learn about the structure + + + align:start position:0% +scattering to learn about the structure +of things and that's where quantum + + align:start position:0% +of things and that's where quantum + + + align:start position:0% +of things and that's where quantum +defect theory comes in and it's more + + align:start position:0% +defect theory comes in and it's more + + + align:start position:0% +defect theory comes in and it's more +powerful for certain classes of problems + + align:start position:0% +powerful for certain classes of problems + + + align:start position:0% +powerful for certain classes of problems +and we see that + + align:start position:0% +and we see that + + + align:start position:0% +and we see that +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +bottom of page one + + align:start position:0% +bottom of page one + + + align:start position:0% +bottom of page one +the one electron atoms are called + + align:start position:0% +the one electron atoms are called + + + align:start position:0% +the one electron atoms are called +hydrogenic + + align:start position:0% +hydrogenic + + + align:start position:0% +hydrogenic +So the Hamiltonian is a function of + + align:start position:0% +So the Hamiltonian is a function of + + + align:start position:0% +So the Hamiltonian is a function of +spherical polar coordinates + + align:start position:0% +spherical polar coordinates + + + align:start position:0% +spherical polar coordinates +and spin coordinates which are just + + align:start position:0% +and spin coordinates which are just + + + align:start position:0% +and spin coordinates which are just +something that uh we don't really know + + align:start position:0% +something that uh we don't really know + + + align:start position:0% +something that uh we don't really know +what they are but so uh it's a central + + align:start position:0% +what they are but so uh it's a central + + + align:start position:0% +what they are but so uh it's a central +force problem and central force problems + + align:start position:0% +force problem and central force problems + + + align:start position:0% +force problem and central force problems +are all related and the Hamiltonian + + align:start position:0% +are all related and the Hamiltonian + + + align:start position:0% +are all related and the Hamiltonian +is + + align:start position:0% + + + + align:start position:0% + +expressed in this + + align:start position:0% + + + + align:start position:0% + +In this way we have z^2 + + align:start position:0% +In this way we have z^2 + + + align:start position:0% +In this way we have z^2 +r cubed 2^2 + + align:start position:0% +r cubed 2^2 + + + align:start position:0% +r cubed 2^2 +c^2. + + align:start position:0% + + + + align:start position:0% + +So this is the kinetic energy. This is + + align:start position:0% +So this is the kinetic energy. This is + + + align:start position:0% +So this is the kinetic energy. This is +the potential energy. And this is my + + align:start position:0% +the potential energy. And this is my + + + align:start position:0% +the potential energy. And this is my +very good friend spin. It's an example + + align:start position:0% +very good friend spin. It's an example + + + align:start position:0% +very good friend spin. It's an example +of small stuff that helps you a lot in + + align:start position:0% +of small stuff that helps you a lot in + + + align:start position:0% +of small stuff that helps you a lot in +understanding what's going on. So, it's + + align:start position:0% +understanding what's going on. So, it's + + + align:start position:0% +understanding what's going on. So, it's +it's perhaps an extra level of + + align:start position:0% +it's perhaps an extra level of + + + align:start position:0% +it's perhaps an extra level of +complexity, but it's it's something that + + align:start position:0% +complexity, but it's it's something that + + + align:start position:0% +complexity, but it's it's something that +we uh care about. Now, one of the neat + + align:start position:0% +we uh care about. Now, one of the neat + + + align:start position:0% +we uh care about. Now, one of the neat +things you notice right away is this is + + align:start position:0% +things you notice right away is this is + + + align:start position:0% +things you notice right away is this is +1 / r cubed. + + align:start position:0% +1 / r cubed. + + + align:start position:0% +1 / r cubed. +And so that actually turns out to be a + + align:start position:0% +And so that actually turns out to be a + + + align:start position:0% +And so that actually turns out to be a +very important simplification because it + + align:start position:0% +very important simplification because it + + + align:start position:0% +very important simplification because it +says spin orbit whatever that is happens + + align:start position:0% +says spin orbit whatever that is happens + + + align:start position:0% +says spin orbit whatever that is happens +near the nucleus and we don't care that + + align:start position:0% +near the nucleus and we don't care that + + + align:start position:0% +near the nucleus and we don't care that +much about what's going on outside. + + align:start position:0% +much about what's going on outside. + + + align:start position:0% +much about what's going on outside. +So it is if it's happening near the + + align:start position:0% +So it is if it's happening near the + + + align:start position:0% +So it is if it's happening near the +nucleus it's where things are pretty + + align:start position:0% +nucleus it's where things are pretty + + + align:start position:0% +nucleus it's where things are pretty +simple + + align:start position:0% +simple + + + align:start position:0% +simple +and so this is why it's such a valuable + + align:start position:0% +and so this is why it's such a valuable + + + align:start position:0% +and so this is why it's such a valuable +probe. Okay. Kinetic energy. Well, there + + align:start position:0% +probe. Okay. Kinetic energy. Well, there + + + align:start position:0% +probe. Okay. Kinetic energy. Well, there +are some things a lot of things in the + + align:start position:0% +are some things a lot of things in the + + + align:start position:0% +are some things a lot of things in the +kinetic energy and one of them is + + align:start position:0% +kinetic energy and one of them is + + + align:start position:0% +kinetic energy and one of them is +angular momentum. + + align:start position:0% + + + + align:start position:0% + +So we have orbital angular momentum + + align:start position:0% +So we have orbital angular momentum + + + align:start position:0% +So we have orbital angular momentum +that's included in here. And when we + + align:start position:0% +that's included in here. And when we + + + align:start position:0% +that's included in here. And when we +write a basis set which includes L as + + align:start position:0% +write a basis set which includes L as + + + align:start position:0% +write a basis set which includes L as +one of the quantum numbers that part of + + align:start position:0% +one of the quantum numbers that part of + + + align:start position:0% +one of the quantum numbers that part of +the angular momentum has this form. We + + align:start position:0% +the angular momentum has this form. We + + + align:start position:0% +the angular momentum has this form. We +still have uh uh + + align:start position:0% +still have uh uh + + + align:start position:0% +still have uh uh +we still have r 2 as as a variable but + + align:start position:0% +we still have r 2 as as a variable but + + + align:start position:0% +we still have r 2 as as a variable but +this is now a quantum number and this + + align:start position:0% +this is now a quantum number and this + + + align:start position:0% +this is now a quantum number and this +has taken the l that taken the uh the + + align:start position:0% +has taken the l that taken the uh the + + + align:start position:0% +has taken the l that taken the uh the +angular part of the problem out and we + + align:start position:0% +angular part of the problem out and we + + + align:start position:0% +angular part of the problem out and we +have now something that although it + + align:start position:0% +have now something that although it + + + align:start position:0% +have now something that although it +comes from the kinetic energy we stick + + align:start position:0% +comes from the kinetic energy we stick + + + align:start position:0% +comes from the kinetic energy we stick +it into this the potential energy and we + + align:start position:0% +it into this the potential energy and we + + + align:start position:0% +it into this the potential energy and we +say we have + + align:start position:0% +say we have + + + align:start position:0% +say we have +an effective potential + + align:start position:0% +an effective potential + + + align:start position:0% +an effective potential +which is a function of r alone. And so + + align:start position:0% +which is a function of r alone. And so + + + align:start position:0% +which is a function of r alone. And so +it's a it's a central force problem + + align:start position:0% +it's a it's a central force problem + + + align:start position:0% +it's a it's a central force problem +which has been dressed up with something + + align:start position:0% +which has been dressed up with something + + + align:start position:0% +which has been dressed up with something +that has some angular momentum + + align:start position:0% +that has some angular momentum + + + align:start position:0% +that has some angular momentum +dependence. + + align:start position:0% + + + + align:start position:0% + +And so we say this generates a + + align:start position:0% +And so we say this generates a + + + align:start position:0% +And so we say this generates a +centrifugal barrier. Why is it barrier? + + align:start position:0% +centrifugal barrier. Why is it barrier? + + + align:start position:0% +centrifugal barrier. Why is it barrier? +Because it's a positive and as r gets + + align:start position:0% +Because it's a positive and as r gets + + + align:start position:0% +Because it's a positive and as r gets +small this gets big. + + align:start position:0% +small this gets big. + + + align:start position:0% +small this gets big. +And so it's a barrier that keeps the + + align:start position:0% +And so it's a barrier that keeps the + + + align:start position:0% +And so it's a barrier that keeps the +electron from getting in close to the + + align:start position:0% +electron from getting in close to the + + + align:start position:0% +electron from getting in close to the +nucleus. + + align:start position:0% +nucleus. + + + align:start position:0% +nucleus. +And uh you would Yes. Okay. + + align:start position:0% + + + + align:start position:0% + +So we have a central force problem and + + align:start position:0% +So we have a central force problem and + + + align:start position:0% +So we have a central force problem and +the wave function + + align:start position:0% + + + + align:start position:0% + +can be written as a product of two + + align:start position:0% +can be written as a product of two + + + align:start position:0% +can be written as a product of two +factors. + + align:start position:0% + + + + align:start position:0% + +an angular factor and a radial factor. + + align:start position:0% +an angular factor and a radial factor. + + + align:start position:0% +an angular factor and a radial factor. +Now for all central problems you get the + + align:start position:0% +Now for all central problems you get the + + + align:start position:0% +Now for all central problems you get the +same angular factor set uh and and so + + align:start position:0% +same angular factor set uh and and so + + + align:start position:0% +same angular factor set uh and and so +this is universal and this radial factor + + align:start position:0% +this is universal and this radial factor + + + align:start position:0% +this is universal and this radial factor +is uh unique to the particular atom but + + align:start position:0% +is uh unique to the particular atom but + + + align:start position:0% +is uh unique to the particular atom but +not when you have one electron atoms + + align:start position:0% +not when you have one electron atoms + + + align:start position:0% +not when you have one electron atoms +it's basically the same thing. It's only + + align:start position:0% +it's basically the same thing. It's only + + + align:start position:0% +it's basically the same thing. It's only +scaled by the charge on the atom. + + align:start position:0% +scaled by the charge on the atom. + + + align:start position:0% +scaled by the charge on the atom. +So uh this for one electron atoms this + + align:start position:0% +So uh this for one electron atoms this + + + align:start position:0% +So uh this for one electron atoms this +is universal. But generally the wave + + align:start position:0% +is universal. But generally the wave + + + align:start position:0% +is universal. But generally the wave +function is divided into a universal + + align:start position:0% +function is divided into a universal + + + align:start position:0% +function is divided into a universal +angular momentum factor + + align:start position:0% +angular momentum factor + + + align:start position:0% +angular momentum factor +and a system specific radial factor + + align:start position:0% +and a system specific radial factor + + + align:start position:0% +and a system specific radial factor +which is where all the interesting stuff + + align:start position:0% +which is where all the interesting stuff + + + align:start position:0% +which is where all the interesting stuff +is but a lot of the manipulations get + + align:start position:0% +is but a lot of the manipulations get + + + align:start position:0% +is but a lot of the manipulations get +down here. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So + + align:start position:0% +So + + + align:start position:0% +So +C is charge of a nucleus. Yes. + + align:start position:0% +C is charge of a nucleus. Yes. + + + align:start position:0% +C is charge of a nucleus. Yes. +Um could you just remind me how we + + align:start position:0% +Um could you just remind me how we + + + align:start position:0% +Um could you just remind me how we +actually include like that spin orbit + + align:start position:0% +actually include like that spin orbit + + + align:start position:0% +actually include like that spin orbit +term into the Hamiltonian because I + + align:start position:0% +term into the Hamiltonian because I + + + align:start position:0% +term into the Hamiltonian because I +guess I I'm still thinking like + + align:start position:0% +guess I I'm still thinking like + + + align:start position:0% +guess I I'm still thinking like +potential energy and kinetic energy. + + align:start position:0% +potential energy and kinetic energy. + + + align:start position:0% +potential energy and kinetic energy. +Well, okay. The Hamiltonian is the + + align:start position:0% +Well, okay. The Hamiltonian is the + + + align:start position:0% +Well, okay. The Hamiltonian is the +energy + + align:start position:0% +energy + + + align:start position:0% +energy +and so anything that contributes the + + align:start position:0% +and so anything that contributes the + + + align:start position:0% +and so anything that contributes the +energy of a state gets put into the + + align:start position:0% +energy of a state gets put into the + + + align:start position:0% +energy of a state gets put into the +Hamiltonian. So, uh, you're right to say + + align:start position:0% +Hamiltonian. So, uh, you're right to say + + + align:start position:0% +Hamiltonian. So, uh, you're right to say +I I know where this comes from. + + align:start position:0% +I I know where this comes from. + + + align:start position:0% +I I know where this comes from. +Uh, this has to do it's actually a + + align:start position:0% +Uh, this has to do it's actually a + + + align:start position:0% +Uh, this has to do it's actually a +relativistic effect. Uh, but the + + align:start position:0% +relativistic effect. Uh, but the + + + align:start position:0% +relativistic effect. Uh, but the +convenient thing is that it behaves as L + + align:start position:0% +convenient thing is that it behaves as L + + + align:start position:0% +convenient thing is that it behaves as L +do S, the orbital angular the spin and + + align:start position:0% +do S, the orbital angular the spin and + + + align:start position:0% +do S, the orbital angular the spin and +it's the angular momentum and the spin + + align:start position:0% +it's the angular momentum and the spin + + + align:start position:0% +it's the angular momentum and the spin +of the same electron. + + align:start position:0% +of the same electron. + + + align:start position:0% +of the same electron. +And so I'm not going to derive these + + align:start position:0% +And so I'm not going to derive these + + + align:start position:0% +And so I'm not going to derive these +things. I'm going to tell you uh because + + align:start position:0% +things. I'm going to tell you uh because + + + align:start position:0% +things. I'm going to tell you uh because +you know many courses you see the + + align:start position:0% +you know many courses you see the + + + align:start position:0% +you know many courses you see the +lengthy derivations and you don't see + + align:start position:0% +lengthy derivations and you don't see + + + align:start position:0% +lengthy derivations and you don't see +what they're for. So this is just a + + align:start position:0% +what they're for. So this is just a + + + align:start position:0% +what they're for. So this is just a +contribution to the energy that happens + + align:start position:0% +contribution to the energy that happens + + + align:start position:0% +contribution to the energy that happens +for atoms and molecules. There are other + + align:start position:0% +for atoms and molecules. There are other + + + align:start position:0% +for atoms and molecules. There are other +smaller contributions like hyperfine + + align:start position:0% +smaller contributions like hyperfine + + + align:start position:0% +smaller contributions like hyperfine +where you have the electron with its + + align:start position:0% +where you have the electron with its + + + align:start position:0% +where you have the electron with its +orbital and spin angular momentum and + + align:start position:0% +orbital and spin angular momentum and + + + align:start position:0% +orbital and spin angular momentum and +interacts with the the angular momentum + + align:start position:0% +interacts with the the angular momentum + + + align:start position:0% +interacts with the the angular momentum +of the nucleus. + + align:start position:0% +of the nucleus. + + + align:start position:0% +of the nucleus. +That's well that's not that's easy. + + align:start position:0% +That's well that's not that's easy. + + + align:start position:0% +That's well that's not that's easy. +Can can we think about this as a like + + align:start position:0% +Can can we think about this as a like + + + align:start position:0% +Can can we think about this as a like +potential energy of the uh spin being in + + align:start position:0% +potential energy of the uh spin being in + + + align:start position:0% +potential energy of the uh spin being in +the magnetic field created by its own + + align:start position:0% +the magnetic field created by its own + + + align:start position:0% +the magnetic field created by its own +rotation. sol you can do that but it's a + + align:start position:0% +rotation. sol you can do that but it's a + + + align:start position:0% +rotation. sol you can do that but it's a +little bit dangerous because you know we + + align:start position:0% +little bit dangerous because you know we + + + align:start position:0% +little bit dangerous because you know we +associate a magnetic dipole with the + + align:start position:0% +associate a magnetic dipole with the + + + align:start position:0% +associate a magnetic dipole with the +orbital angular momentum and with the + + align:start position:0% +orbital angular momentum and with the + + + align:start position:0% +orbital angular momentum and with the +spin and so this looks like a dipole + + align:start position:0% +spin and so this looks like a dipole + + + align:start position:0% +spin and so this looks like a dipole +dipole interaction but it isn't quite + + align:start position:0% +dipole interaction but it isn't quite + + + align:start position:0% +dipole interaction but it isn't quite +because uh the uh + + align:start position:0% +because uh the uh + + + align:start position:0% +because uh the uh +the uh + + align:start position:0% +the uh + + + align:start position:0% +the uh +when it's a relativistic effect has to + + align:start position:0% +when it's a relativistic effect has to + + + align:start position:0% +when it's a relativistic effect has to +do with the electron moving very fast + + align:start position:0% +do with the electron moving very fast + + + align:start position:0% +do with the electron moving very fast +near the nucleus and I can't really + + align:start position:0% +near the nucleus and I can't really + + + align:start position:0% +near the nucleus and I can't really +explain it any better than that and it + + align:start position:0% +explain it any better than that and it + + + align:start position:0% +explain it any better than that and it +scales with the nuclear charge + + align:start position:0% +scales with the nuclear charge + + + align:start position:0% +scales with the nuclear charge +and a simple dipole dipole interaction + + align:start position:0% +and a simple dipole dipole interaction + + + align:start position:0% +and a simple dipole dipole interaction +wouldn't do that. So but if you think of + + align:start position:0% +wouldn't do that. So but if you think of + + + align:start position:0% +wouldn't do that. So but if you think of +it as two magnetic dlesoles interacting + + align:start position:0% +it as two magnetic dlesoles interacting + + + align:start position:0% +it as two magnetic dlesoles interacting +you get the operator form but not the + + align:start position:0% +you get the operator form but not the + + + align:start position:0% +you get the operator form but not the +magnitude and that's okay. + + align:start position:0% +magnitude and that's okay. + + + align:start position:0% +magnitude and that's okay. +So there, you know, we're always + + align:start position:0% +So there, you know, we're always + + + align:start position:0% +So there, you know, we're always +sticking terms into the Hamilton because + + align:start position:0% +sticking terms into the Hamilton because + + + align:start position:0% +sticking terms into the Hamilton because +we need them or we're taking them out + + align:start position:0% +we need them or we're taking them out + + + align:start position:0% +we need them or we're taking them out +because we just assume they weren't + + align:start position:0% +because we just assume they weren't + + + align:start position:0% +because we just assume they weren't +there. But this is a really good + + align:start position:0% +there. But this is a really good + + + align:start position:0% +there. But this is a really good +question. Okay, so now um I have to + + align:start position:0% +question. Okay, so now um I have to + + + align:start position:0% +question. Okay, so now um I have to +define some things. This is the charge + + align:start position:0% +define some things. This is the charge + + + align:start position:0% +define some things. This is the charge +on the nucleus. And so for hydrogen it's + + align:start position:0% +on the nucleus. And so for hydrogen it's + + + align:start position:0% +on the nucleus. And so for hydrogen it's +one and for helium plus it's two. And uh + + align:start position:0% +one and for helium plus it's two. And uh + + + align:start position:0% +one and for helium plus it's two. And uh +uh I want to make a distinction. You + + align:start position:0% +uh I want to make a distinction. You + + + align:start position:0% +uh I want to make a distinction. You +might have a particle + + align:start position:0% +might have a particle + + + align:start position:0% +might have a particle +uh well for one electron systems it is + + align:start position:0% +uh well for one electron systems it is + + + align:start position:0% +uh well for one electron systems it is +the charge on the nucleus but for many + + align:start position:0% +the charge on the nucleus but for many + + + align:start position:0% +the charge on the nucleus but for many +electron alkalike systems it is not uh + + align:start position:0% +electron alkalike systems it is not uh + + + align:start position:0% +electron alkalike systems it is not uh +necessarily either an integer or the + + align:start position:0% +necessarily either an integer or the + + + align:start position:0% +necessarily either an integer or the +charge on either the ion core + + align:start position:0% +charge on either the ion core + + + align:start position:0% +charge on either the ion core +or the nucleus itself. And so this is + + align:start position:0% +or the nucleus itself. And so this is + + + align:start position:0% +or the nucleus itself. And so this is +this turns into a budge factor in a few + + align:start position:0% +this turns into a budge factor in a few + + + align:start position:0% +this turns into a budge factor in a few +minutes. But for one electron systems + + align:start position:0% +minutes. But for one electron systems + + + align:start position:0% +minutes. But for one electron systems +it's not a budge factor. This is the + + align:start position:0% +it's not a budge factor. This is the + + + align:start position:0% +it's not a budge factor. This is the +reduced mass. And the reduced mass is + + align:start position:0% +reduced mass. And the reduced mass is + + + align:start position:0% +reduced mass. And the reduced mass is +the mass of the nucleus + + align:start position:0% +the mass of the nucleus + + + align:start position:0% +the mass of the nucleus +times the mass of the electron over the + + align:start position:0% +times the mass of the electron over the + + + align:start position:0% +times the mass of the electron over the +mass of the electron plus the mass of + + align:start position:0% +mass of the electron plus the mass of + + + align:start position:0% +mass of the electron plus the mass of +the nucleus. + + align:start position:0% +the nucleus. + + + align:start position:0% +the nucleus. +Now this is always really small compared + + align:start position:0% +Now this is always really small compared + + + align:start position:0% +Now this is always really small compared +to this. + + align:start position:0% +to this. + + + align:start position:0% +to this. +And so if if you throw that away, + + align:start position:0% +And so if if you throw that away, + + + align:start position:0% +And so if if you throw that away, +this becomes just the mass of the + + align:start position:0% +this becomes just the mass of the + + + align:start position:0% +this becomes just the mass of the +electrons. + + align:start position:0% +electrons. + + + align:start position:0% +electrons. +Okay? So this reduced mass factor is + + align:start position:0% +Okay? So this reduced mass factor is + + + align:start position:0% +Okay? So this reduced mass factor is +almost exactly the mass of the electron + + align:start position:0% +almost exactly the mass of the electron + + + align:start position:0% +almost exactly the mass of the electron +but it isn't exactly because this is not + + align:start position:0% +but it isn't exactly because this is not + + + align:start position:0% +but it isn't exactly because this is not +zero. And so if you change the uh + + align:start position:0% +zero. And so if you change the uh + + + align:start position:0% +zero. And so if you change the uh +nuclear mass from one to 200 to 100 to + + align:start position:0% +nuclear mass from one to 200 to 100 to + + + align:start position:0% +nuclear mass from one to 200 to 100 to +200 you can do that uh there will be a + + align:start position:0% +200 you can do that uh there will be a + + + align:start position:0% +200 you can do that uh there will be a +very very small effect on this reduced + + align:start position:0% +very very small effect on this reduced + + + align:start position:0% +very very small effect on this reduced +mass. And one of the neat things is okay + + align:start position:0% +mass. And one of the neat things is okay + + + align:start position:0% +mass. And one of the neat things is okay +that's going to change the energy levels + + align:start position:0% +that's going to change the energy levels + + + align:start position:0% +that's going to change the energy levels +by an amount that's proportional to how + + align:start position:0% +by an amount that's proportional to how + + + align:start position:0% +by an amount that's proportional to how +much the reduced mass has changed. + + align:start position:0% +much the reduced mass has changed. + + + align:start position:0% +much the reduced mass has changed. +And so it changes maybe by a part in a + + align:start position:0% +And so it changes maybe by a part in a + + + align:start position:0% +And so it changes maybe by a part in a +thousand. Well, that's pretty small. But + + align:start position:0% +thousand. Well, that's pretty small. But + + + align:start position:0% +thousand. Well, that's pretty small. But +in electronic spectroscopy, we measure + + align:start position:0% +in electronic spectroscopy, we measure + + + align:start position:0% +in electronic spectroscopy, we measure +things typically to a part in a million. + + align:start position:0% +things typically to a part in a million. + + + align:start position:0% +things typically to a part in a million. +So it starts to make a significant + + align:start position:0% +So it starts to make a significant + + + align:start position:0% +So it starts to make a significant +difference one atom versus another. + + align:start position:0% +difference one atom versus another. + + + align:start position:0% +difference one atom versus another. +So it's not it's not uh it's not just + + align:start position:0% +So it's not it's not uh it's not just + + + align:start position:0% +So it's not it's not uh it's not just +the mass of the electron uh but it's + + align:start position:0% +the mass of the electron uh but it's + + + align:start position:0% +the mass of the electron uh but it's +so there's a little bit of stuff there. + + align:start position:0% +so there's a little bit of stuff there. + + + align:start position:0% +so there's a little bit of stuff there. +Okay. Now um + + align:start position:0% + + + + align:start position:0% + +we have two choices of basis sets + + align:start position:0% + + + + align:start position:0% + +and and + + align:start position:0% + + + + align:start position:0% + +in which we can look at this problem and + + align:start position:0% +in which we can look at this problem and + + + align:start position:0% +in which we can look at this problem and +this thing here + + align:start position:0% +this thing here + + + align:start position:0% +this thing here +uh is the reason why we talk about basis + + align:start position:0% +uh is the reason why we talk about basis + + + align:start position:0% +uh is the reason why we talk about basis +sets and a choice of basis sets and that + + align:start position:0% +sets and a choice of basis sets and that + + + align:start position:0% +sets and a choice of basis sets and that +there's one good choice and one not such + + align:start position:0% +there's one good choice and one not such + + + align:start position:0% +there's one good choice and one not such +a good choice. And so the uncoupled + + align:start position:0% +a good choice. And so the uncoupled + + + align:start position:0% +a good choice. And so the uncoupled +basis set is uh written as + + align:start position:0% +basis set is uh written as + + + align:start position:0% +basis set is uh written as +L M L S M and the coupled one is uh + + align:start position:0% +L M L S M and the coupled one is uh + + + align:start position:0% +L M L S M and the coupled one is uh +written as L SJ + + align:start position:0% +written as L SJ + + + align:start position:0% +written as L SJ +MJ. + + align:start position:0% + + + + align:start position:0% + +So what is this? These are shortorthhand + + align:start position:0% +So what is this? These are shortorthhand + + + align:start position:0% +So what is this? These are shortorthhand +for igen values of operators that + + align:start position:0% +for igen values of operators that + + + align:start position:0% +for igen values of operators that +commute with the exact well commute with + + align:start position:0% +commute with the exact well commute with + + + align:start position:0% +commute with the exact well commute with +each other and they commute with the + + align:start position:0% +each other and they commute with the + + + align:start position:0% +each other and they commute with the +zero order Hamiltonian if they're going + + align:start position:0% +zero order Hamiltonian if they're going + + + align:start position:0% +zero order Hamiltonian if they're going +to be basis functions. So + + align:start position:0% +to be basis functions. So + + + align:start position:0% +to be basis functions. So +the angular momentum total angular + + align:start position:0% +the angular momentum total angular + + + align:start position:0% +the angular momentum total angular +momentum orbital angular momentum l^2 + + align:start position:0% +momentum orbital angular momentum l^2 + + + align:start position:0% +momentum orbital angular momentum l^2 +gives you lz + + align:start position:0% +gives you lz + + + align:start position:0% +gives you lz +gives you ml etc and j + + align:start position:0% +gives you ml etc and j + + + align:start position:0% +gives you ml etc and j +is the vector sum of l and s. + + align:start position:0% +is the vector sum of l and s. + + + align:start position:0% +is the vector sum of l and s. +So we have these angular random things. + + align:start position:0% +So we have these angular random things. + + + align:start position:0% +So we have these angular random things. +These are this is an igen function of L + + align:start position:0% +These are this is an igen function of L + + + align:start position:0% +These are this is an igen function of L +squ where the value of the + + align:start position:0% +squ where the value of the + + + align:start position:0% +squ where the value of the +igen value of L^2 is LL + one. + + align:start position:0% +igen value of L^2 is LL + one. + + + align:start position:0% +igen value of L^2 is LL + one. +So we don't write LL + one in here. We + + align:start position:0% +So we don't write LL + one in here. We + + + align:start position:0% +So we don't write LL + one in here. We +write L because it's takes less space + + align:start position:0% +write L because it's takes less space + + + align:start position:0% +write L because it's takes less space +and it's not it's unambiguous. And the + + align:start position:0% +and it's not it's unambiguous. And the + + + align:start position:0% +and it's not it's unambiguous. And the +igen value for L subZ is M subL. LZ + + align:start position:0% +igen value for L subZ is M subL. LZ + + + align:start position:0% +igen value for L subZ is M subL. LZ +operating on this gives the function + + align:start position:0% +operating on this gives the function + + + align:start position:0% +operating on this gives the function +back times M subL. + + align:start position:0% +back times M subL. + + + align:start position:0% +back times M subL. +So we have these building blocks + + align:start position:0% +So we have these building blocks + + + align:start position:0% +So we have these building blocks +and with them whenever we see any + + align:start position:0% +and with them whenever we see any + + + align:start position:0% +and with them whenever we see any +angular momentum in this problem we can + + align:start position:0% +angular momentum in this problem we can + + + align:start position:0% +angular momentum in this problem we can +work out what that what the contribution + + align:start position:0% +work out what that what the contribution + + + align:start position:0% +work out what that what the contribution +of that is to the energy level formula. + + align:start position:0% + + + + align:start position:0% + +So L+ + + align:start position:0% +So L+ + + + align:start position:0% +So L+ +so we can write um + + align:start position:0% +so we can write um + + + align:start position:0% +so we can write um +we can write the components of L as LZ + + align:start position:0% +we can write the components of L as LZ + + + align:start position:0% +we can write the components of L as LZ +plus LX plus L Y and but we like uh to + + align:start position:0% +plus LX plus L Y and but we like uh to + + + align:start position:0% +plus LX plus L Y and but we like uh to +write things as uh in terms of these + + align:start position:0% +write things as uh in terms of these + + + align:start position:0% +write things as uh in terms of these +raising and lowering operators because + + align:start position:0% +raising and lowering operators because + + + align:start position:0% +raising and lowering operators because +they're neat + + align:start position:0% +they're neat + + + align:start position:0% +they're neat +because they're analogous to the + + align:start position:0% +because they're analogous to the + + + align:start position:0% +because they're analogous to the +creation annihilation operators we had + + align:start position:0% +creation annihilation operators we had + + + align:start position:0% +creation annihilation operators we had +with harmonic oscillators and so L+ plus + + align:start position:0% +with harmonic oscillators and so L+ plus + + + align:start position:0% +with harmonic oscillators and so L+ plus +is L X + L Y + + align:start position:0% +is L X + L Y + + + align:start position:0% +is L X + L Y +I Y + + align:start position:0% +I Y + + + align:start position:0% +I Y +and L minus is LX minus L I L Y + + align:start position:0% +and L minus is LX minus L I L Y + + + align:start position:0% +and L minus is LX minus L I L Y +and L do + + align:start position:0% +and L do + + + align:start position:0% +and L do +S + + align:start position:0% +S + + + align:start position:0% +S +is L Z S + + align:start position:0% +is L Z S + + + align:start position:0% +is L Z S ++ 12 + + align:start position:0% ++ 12 + + + align:start position:0% ++ 12 +L + S - L - S + + + align:start position:0% +L + S - L - S + + + + align:start position:0% +L + S - L - S + +Now, with quantum mechanical operators, + + align:start position:0% +Now, with quantum mechanical operators, + + + align:start position:0% +Now, with quantum mechanical operators, +you do have to worry about computation, + + align:start position:0% +you do have to worry about computation, + + + align:start position:0% +you do have to worry about computation, +but I just got through saying that these + + align:start position:0% +but I just got through saying that these + + + align:start position:0% +but I just got through saying that these +come from mutually commuting operators + + align:start position:0% +come from mutually commuting operators + + + align:start position:0% +come from mutually commuting operators +and okay, well, L+ is not one of them, + + align:start position:0% +and okay, well, L+ is not one of them, + + + align:start position:0% +and okay, well, L+ is not one of them, +but L L and S do commute and the + + align:start position:0% +but L L and S do commute and the + + + align:start position:0% +but L L and S do commute and the +components of L and S do commute because + + align:start position:0% +components of L and S do commute because + + + align:start position:0% +components of L and S do commute because +they're operate on different particles. + + align:start position:0% +they're operate on different particles. + + + align:start position:0% +they're operate on different particles. +So, uh we don't have to worry about the + + align:start position:0% +So, uh we don't have to worry about the + + + align:start position:0% +So, uh we don't have to worry about the +order. We don't have to symmetriize and + + align:start position:0% +order. We don't have to symmetriize and + + + align:start position:0% +order. We don't have to symmetriize and +L+ operating on LML. + + align:start position:0% +L+ operating on LML. + + + align:start position:0% +L+ operating on LML. +It only operates on the LML part, not + + align:start position:0% +It only operates on the LML part, not + + + align:start position:0% +It only operates on the LML part, not +the SMS part gives back L+1 + + align:start position:0% +the SMS part gives back L+1 + + + align:start position:0% +the SMS part gives back L+1 +minus. Now, it's just like harmonic + + align:start position:0% +minus. Now, it's just like harmonic + + + align:start position:0% +minus. Now, it's just like harmonic +oscillators in a second. The non-zero + + align:start position:0% +oscillators in a second. The non-zero + + + align:start position:0% +oscillators in a second. The non-zero +matrix elements of L+ always are between + + align:start position:0% +matrix elements of L+ always are between + + + align:start position:0% +matrix elements of L+ always are between +one value of M subl and over here one + + align:start position:0% +one value of M subl and over here one + + + align:start position:0% +one value of M subl and over here one +higher. + + align:start position:0% +higher. + + + align:start position:0% +higher. +And so what goes in here is the product + + align:start position:0% +And so what goes in here is the product + + + align:start position:0% +And so what goes in here is the product +of the two values of M subL that occur + + align:start position:0% +of the two values of M subL that occur + + + align:start position:0% +of the two values of M subL that occur +in a non-zero matrix element. So you + + align:start position:0% +in a non-zero matrix element. So you + + + align:start position:0% +in a non-zero matrix element. So you +don't have to remember anything if you + + align:start position:0% +don't have to remember anything if you + + + align:start position:0% +don't have to remember anything if you +know how to write you know L M M sub L+ + + align:start position:0% +know how to write you know L M M sub L+ + + + align:start position:0% +know how to write you know L M M sub L+ +increases M subL by one + + align:start position:0% +increases M subL by one + + + align:start position:0% +increases M subL by one +and so uh you have ML over here and ML + + + align:start position:0% +and so uh you have ML over here and ML + + + + align:start position:0% +and so uh you have ML over here and ML + +one over here if it were a matrix + + align:start position:0% +one over here if it were a matrix + + + align:start position:0% +one over here if it were a matrix +element. And so you have uh m l + + align:start position:0% +element. And so you have uh m l + + + align:start position:0% +element. And so you have uh m l +ml + + align:start position:0% +ml + + + align:start position:0% +ml ++ one minus row time ml. + + align:start position:0% + + + + align:start position:0% + +Okay. So this is a little bit more + + align:start position:0% +Okay. So this is a little bit more + + + align:start position:0% +Okay. So this is a little bit more +complicated than a dagger and a but the + + align:start position:0% +complicated than a dagger and a but the + + + align:start position:0% +complicated than a dagger and a but the +important thing is the thing you don't + + align:start position:0% +important thing is the thing you don't + + + align:start position:0% +important thing is the thing you don't +know automatically is uh which two + + align:start position:0% +know automatically is uh which two + + + align:start position:0% +know automatically is uh which two +values of m subl you put in here and now + + align:start position:0% +values of m subl you put in here and now + + + align:start position:0% +values of m subl you put in here and now +you do know that and now if we write + + align:start position:0% +you do know that and now if we write + + + align:start position:0% +you do know that and now if we write +this we know immediately that it's going + + align:start position:0% +this we know immediately that it's going + + + align:start position:0% +this we know immediately that it's going +to this be plus or minus one + + align:start position:0% +to this be plus or minus one + + + align:start position:0% +to this be plus or minus one +okay so the important thing is if you're + + align:start position:0% +okay so the important thing is if you're + + + align:start position:0% +okay so the important thing is if you're +going to have insights into this stuff. + + align:start position:0% +going to have insights into this stuff. + + + align:start position:0% +going to have insights into this stuff. +You don't want to be constantly looking + + align:start position:0% +You don't want to be constantly looking + + + align:start position:0% +You don't want to be constantly looking +it up in a book. You want it to be hard, + + align:start position:0% +it up in a book. You want it to be hard, + + + align:start position:0% +it up in a book. You want it to be hard, +you know, the stuff you need to be + + align:start position:0% +you know, the stuff you need to be + + + align:start position:0% +you know, the stuff you need to be +hardwired. So, what has to be hardwired? + + align:start position:0% +hardwired. So, what has to be hardwired? + + + align:start position:0% +hardwired. So, what has to be hardwired? +Selection rules. + + align:start position:0% +Selection rules. + + + align:start position:0% +Selection rules. +L+ raises M subl. S+ raises M subs. + + align:start position:0% +L+ raises M subl. S+ raises M subs. + + + align:start position:0% +L+ raises M subl. S+ raises M subs. +They change the value by one. Uh L+ and + + align:start position:0% +They change the value by one. Uh L+ and + + + align:start position:0% +They change the value by one. Uh L+ and +S+ LZ, SZ, none of them change the value + + align:start position:0% +S+ LZ, SZ, none of them change the value + + + align:start position:0% +S+ LZ, SZ, none of them change the value +of L. + + align:start position:0% +of L. + + + align:start position:0% +of L. +And the matrix element or the thing you + + align:start position:0% +And the matrix element or the thing you + + + align:start position:0% +And the matrix element or the thing you +get is the the product of the initial + + align:start position:0% +get is the the product of the initial + + + align:start position:0% +get is the the product of the initial +and final quantum numbers. Nothing to + + align:start position:0% +and final quantum numbers. Nothing to + + + align:start position:0% +and final quantum numbers. Nothing to +remember beyond that. I mean that's + + align:start position:0% +remember beyond that. I mean that's + + + align:start position:0% +remember beyond that. I mean that's +pretty simple. + + align:start position:0% +pretty simple. + + + align:start position:0% +pretty simple. +Okay. So we have these two basis sets + + align:start position:0% +Okay. So we have these two basis sets + + + align:start position:0% +Okay. So we have these two basis sets +and the only angular momentum in this + + align:start position:0% +and the only angular momentum in this + + + align:start position:0% +and the only angular momentum in this +problem. Well there actually is two bits + + align:start position:0% +problem. Well there actually is two bits + + + align:start position:0% +problem. Well there actually is two bits +of angular momentum. I said we get this. + + align:start position:0% +of angular momentum. I said we get this. + + + align:start position:0% +of angular momentum. I said we get this. +Well that came from L squ. Well, L squ + + align:start position:0% +Well that came from L squ. Well, L squ + + + align:start position:0% +Well that came from L squ. Well, L squ +operating on L ML is L squ L L + one. + + align:start position:0% +operating on L ML is L squ L L + one. + + + align:start position:0% +operating on L ML is L squ L L + one. +Okay. So I I did that without even + + align:start position:0% +Okay. So I I did that without even + + + align:start position:0% +Okay. So I I did that without even +breathing. But so there was some angular + + align:start position:0% +breathing. But so there was some angular + + + align:start position:0% +breathing. But so there was some angular +momentum that came from the uh uh + + align:start position:0% +momentum that came from the uh uh + + + align:start position:0% +momentum that came from the uh uh +kinetic energy term. + + align:start position:0% +kinetic energy term. + + + align:start position:0% +kinetic energy term. +But the important angular moment is up + + align:start position:0% +But the important angular moment is up + + + align:start position:0% +But the important angular moment is up +here. + + align:start position:0% +here. + + + align:start position:0% +here. +And so I've written L dos S in this form + + align:start position:0% +And so I've written L dos S in this form + + + align:start position:0% +And so I've written L dos S in this form +which is the way we normally do it even + + align:start position:0% +which is the way we normally do it even + + + align:start position:0% +which is the way we normally do it even +though everybody knows the dotproduct of + + align:start position:0% +though everybody knows the dotproduct of + + + align:start position:0% +though everybody knows the dotproduct of +two vectors is uh the zz XX Y term and + + align:start position:0% +two vectors is uh the zz XX Y term and + + + align:start position:0% +two vectors is uh the zz XX Y term and +but if you write it in this way you get + + align:start position:0% +but if you write it in this way you get + + + align:start position:0% +but if you write it in this way you get +the plus minus minus plus and the ZZ + + align:start position:0% +the plus minus minus plus and the ZZ + + + align:start position:0% +the plus minus minus plus and the ZZ +term. + + align:start position:0% +term. + + + align:start position:0% +term. +Okay. And so + + align:start position:0% +Okay. And so + + + align:start position:0% +Okay. And so +we can uh we have L doss and so we can + + align:start position:0% +we can uh we have L doss and so we can + + + align:start position:0% +we can uh we have L doss and so we can +write L dos two different ways. We can + + align:start position:0% +write L dos two different ways. We can + + + align:start position:0% +write L dos two different ways. We can +write L doss this way + + align:start position:0% +write L doss this way + + + align:start position:0% +write L doss this way +and we can also do a trick + + align:start position:0% +and we can also do a trick + + + align:start position:0% +and we can also do a trick +and the trick uh + + align:start position:0% + + + + align:start position:0% + +J is equal to L + S. These this is + + align:start position:0% +J is equal to L + S. These this is + + + align:start position:0% +J is equal to L + S. These this is +vector. Now J^2 is equal to L + S^2. + + align:start position:0% +vector. Now J^2 is equal to L + S^2. + + + align:start position:0% +vector. Now J^2 is equal to L + S^2. +And so that's equal to L2 + 2 L S + + align:start position:0% + + + + align:start position:0% + ++ S 2. And so rearranging we have J^2 - + + align:start position:0% ++ S 2. And so rearranging we have J^2 - + + + align:start position:0% ++ S 2. And so rearranging we have J^2 - +L^2 - S^2 + + align:start position:0% +L^2 - S^2 + + + align:start position:0% +L^2 - S^2 +* a half is equal to L S. + + align:start position:0% +* a half is equal to L S. + + + align:start position:0% +* a half is equal to L S. +So if we're operating in the J the L SJ + + align:start position:0% +So if we're operating in the J the L SJ + + + align:start position:0% +So if we're operating in the J the L SJ +MJ basis set this thing operating on + + align:start position:0% +MJ basis set this thing operating on + + + align:start position:0% +MJ basis set this thing operating on +that F + + align:start position:0% + + + + align:start position:0% + +lus + + align:start position:0% +lus + + + align:start position:0% +lus + + align:start position:0% + + + align:start position:0% +that gives well these are these are the + + align:start position:0% +that gives well these are these are the + + + align:start position:0% +that gives well these are these are the +operators for which we have quantum + + align:start position:0% +operators for which we have quantum + + + align:start position:0% +operators for which we have quantum +numbers here. So that means no work and + + align:start position:0% +numbers here. So that means no work and + + + align:start position:0% +numbers here. So that means no work and +we have 1/2. I'm suppressing the h bar + + align:start position:0% +we have 1/2. I'm suppressing the h bar + + + align:start position:0% +we have 1/2. I'm suppressing the h bar +squares. + + align:start position:0% +squares. + + + align:start position:0% +squares. +Angular momentum operators always give + + align:start position:0% +Angular momentum operators always give + + + align:start position:0% +Angular momentum operators always give +you an h bar for every power of the + + align:start position:0% +you an h bar for every power of the + + + align:start position:0% +you an h bar for every power of the +operator. And why keep them? You just + + align:start position:0% +operator. And why keep them? You just + + + align:start position:0% +operator. And why keep them? You just +absorb them in confidence. Uh okay. And + + align:start position:0% +absorb them in confidence. Uh okay. And + + + align:start position:0% +absorb them in confidence. Uh okay. And +so we get J + 1 - L L + 1 - S S + 1 + + align:start position:0% +so we get J + 1 - L L + 1 - S S + 1 + + + align:start position:0% +so we get J + 1 - L L + 1 - S S + 1 +times L SJ M. So the spin orbit operator + + align:start position:0% +times L SJ M. So the spin orbit operator + + + align:start position:0% +times L SJ M. So the spin orbit operator +the angular momentum part of the spin + + align:start position:0% +the angular momentum part of the spin + + + align:start position:0% +the angular momentum part of the spin +orbit operator gives this nice compact + + align:start position:0% +orbit operator gives this nice compact + + + align:start position:0% +orbit operator gives this nice compact +thing and it's exclusively diagonal. + + align:start position:0% +thing and it's exclusively diagonal. + + + align:start position:0% +thing and it's exclusively diagonal. +Whereas + + align:start position:0% +Whereas + + + align:start position:0% +Whereas +this guy this other form well this is + + align:start position:0% +this guy this other form well this is + + + align:start position:0% +this guy this other form well this is +diagonal in the m subls and m subs but + + align:start position:0% +diagonal in the m subls and m subs but + + + align:start position:0% +diagonal in the m subls and m subs but +this is not. + + align:start position:0% +this is not. + + + align:start position:0% +this is not. +So if you would like to write down an + + align:start position:0% +So if you would like to write down an + + + align:start position:0% +So if you would like to write down an +operator and convert the Hamiltonian to + + align:start position:0% +operator and convert the Hamiltonian to + + + align:start position:0% +operator and convert the Hamiltonian to +a formula you'd like to have the form of + + align:start position:0% +a formula you'd like to have the form of + + + align:start position:0% +a formula you'd like to have the form of +the operator be such that we just get a + + align:start position:0% +the operator be such that we just get a + + + align:start position:0% +the operator be such that we just get a +formula. No off diagonal matrix + + align:start position:0% +formula. No off diagonal matrix + + + align:start position:0% +formula. No off diagonal matrix +elements. no work. + + align:start position:0% +elements. no work. + + + align:start position:0% +elements. no work. +And so when you have spin orbit, it's + + align:start position:0% +And so when you have spin orbit, it's + + + align:start position:0% +And so when you have spin orbit, it's +usually preferable to use this coupled + + align:start position:0% +usually preferable to use this coupled + + + align:start position:0% +usually preferable to use this coupled +LSJMJ basis rather than the uncoupled + + align:start position:0% +LSJMJ basis rather than the uncoupled + + + align:start position:0% +LSJMJ basis rather than the uncoupled +one. But there are many advantages for + + align:start position:0% +one. But there are many advantages for + + + align:start position:0% +one. But there are many advantages for +using the uncoupled basis. And it's, you + + align:start position:0% +using the uncoupled basis. And it's, you + + + align:start position:0% +using the uncoupled basis. And it's, you +know, it all comes out in the wash. You + + align:start position:0% +know, it all comes out in the wash. You + + + align:start position:0% +know, it all comes out in the wash. You +do transformations between basis sets. + + align:start position:0% +do transformations between basis sets. + + + align:start position:0% +do transformations between basis sets. +I'm going to teach you about that, too. + + align:start position:0% +I'm going to teach you about that, too. + + + align:start position:0% +I'm going to teach you about that, too. +But right now you know the example is + + align:start position:0% +But right now you know the example is + + + align:start position:0% +But right now you know the example is +there are two choices of basis set. One + + align:start position:0% + + + + align:start position:0% + +uh for one the Hamiltonian is completely + + align:start position:0% +uh for one the Hamiltonian is completely + + + align:start position:0% +uh for one the Hamiltonian is completely +diagonal + + align:start position:0% +diagonal + + + align:start position:0% +diagonal +for the other the spin orbit is off + + align:start position:0% +for the other the spin orbit is off + + + align:start position:0% +for the other the spin orbit is off +diagonal and in an innocuous way but it + + align:start position:0% +diagonal and in an innocuous way but it + + + align:start position:0% +diagonal and in an innocuous way but it +still leads to work you have to do. + + align:start position:0% +still leads to work you have to do. + + + align:start position:0% +still leads to work you have to do. +Okay. Please ask me questions about this + + align:start position:0% +Okay. Please ask me questions about this + + + align:start position:0% +Okay. Please ask me questions about this +uh as it's going by. Can I ask you about + + align:start position:0% +uh as it's going by. Can I ask you about + + + align:start position:0% +uh as it's going by. Can I ask you about +the H bars again? + + align:start position:0% +the H bars again? + + + align:start position:0% +the H bars again? +Yes. + + align:start position:0% +Yes. + + + align:start position:0% +Yes. +So with each H bar has units. + + align:start position:0% +So with each H bar has units. + + + align:start position:0% +So with each H bar has units. +H bar has units, right? + + align:start position:0% +H bar has units, right? + + + align:start position:0% +H bar has units, right? +So every time you apply those operators, + + align:start position:0% +So every time you apply those operators, + + + align:start position:0% +So every time you apply those operators, +you not only get some quantity of + + align:start position:0% +you not only get some quantity of + + + align:start position:0% +you not only get some quantity of +angular momentum, but you get + + align:start position:0% +angular momentum, but you get + + + align:start position:0% +angular momentum, but you get +But remember last time I talked about we + + align:start position:0% +But remember last time I talked about we + + + align:start position:0% +But remember last time I talked about we +had some matrix element expressed in + + align:start position:0% +had some matrix element expressed in + + + align:start position:0% +had some matrix element expressed in +terms of quantum numbers. + + align:start position:0% +terms of quantum numbers. + + + align:start position:0% +terms of quantum numbers. +Mhm. + + align:start position:0% +Mhm. + + + align:start position:0% +Mhm. +And trash. + + align:start position:0% +And trash. + + + align:start position:0% +And trash. +Mhm. And you can + + align:start position:0% +Mhm. And you can + + + align:start position:0% +Mhm. And you can +we care about the value of the trash, + + align:start position:0% +we care about the value of the trash, + + + align:start position:0% +we care about the value of the trash, +right? + + align:start position:0% +right? + + + align:start position:0% +right? +But that's a separate bookkeeping + + align:start position:0% +But that's a separate bookkeeping + + + align:start position:0% +But that's a separate bookkeeping +matter. And that this is too remember + + align:start position:0% +matter. And that this is too remember + + + align:start position:0% +matter. And that this is too remember +the Hamiltonian generally has energy + + align:start position:0% +the Hamiltonian generally has energy + + + align:start position:0% +the Hamiltonian generally has energy +units, but if you're a spectroscopal + + align:start position:0% +units, but if you're a spectroscopal + + + align:start position:0% +units, but if you're a spectroscopal +centimeter unit, + + align:start position:0% +centimeter unit, + + + align:start position:0% +centimeter unit, +so you got a factor of HC also. + + align:start position:0% +so you got a factor of HC also. + + + align:start position:0% +so you got a factor of HC also. +Mhm. + + align:start position:0% +Mhm. + + + align:start position:0% +Mhm. +So why not just stick all the stuff that + + align:start position:0% +So why not just stick all the stuff that + + + align:start position:0% +So why not just stick all the stuff that +you don't care about into the constant, + + align:start position:0% +you don't care about into the constant, + + + align:start position:0% +you don't care about into the constant, +the spin orbit constant or whatever it + + align:start position:0% +the spin orbit constant or whatever it + + + align:start position:0% +the spin orbit constant or whatever it +is that you're going to be manipulating. + + align:start position:0% +is that you're going to be manipulating. + + + align:start position:0% +is that you're going to be manipulating. +Okay. So if you apply the operators + + align:start position:0% +Okay. So if you apply the operators + + + align:start position:0% +Okay. So if you apply the operators +though different numbers of times, + + align:start position:0% +though different numbers of times, + + + align:start position:0% +though different numbers of times, +you end up with different units. + + align:start position:0% +you end up with different units. + + + align:start position:0% +you end up with different units. +Well, not really because + + align:start position:0% +Well, not really because + + + align:start position:0% +Well, not really because +Okay. So so that that's what I'm asking. + + align:start position:0% +Okay. So so that that's what I'm asking. + + + align:start position:0% +Okay. So so that that's what I'm asking. +How do you get around + + align:start position:0% +How do you get around + + + align:start position:0% +How do you get around +all of these terms have dimension of + + align:start position:0% +all of these terms have dimension of + + + align:start position:0% +all of these terms have dimension of +energy? + + align:start position:0% +energy? + + + align:start position:0% +energy? +Mhm. + + align:start position:0% +Mhm. + + + align:start position:0% +Mhm. +And so + + align:start position:0% +And so + + + align:start position:0% +And so +uh uh you notice that I had an L squ. + + align:start position:0% +uh uh you notice that I had an L squ. + + + align:start position:0% +uh uh you notice that I had an L squ. +Mhm. + + align:start position:0% +Mhm. + + + align:start position:0% +Mhm. +that came from the centrifugal barrier + + align:start position:0% +that came from the centrifugal barrier + + + align:start position:0% +that came from the centrifugal barrier +that has dimensions of energy + + align:start position:0% +that has dimensions of energy + + + align:start position:0% +that has dimensions of energy +when you divide it by + + align:start position:0% +when you divide it by + + + align:start position:0% +when you divide it by +uh 2 m r^ 2 + + align:start position:0% +uh 2 m r^ 2 + + + align:start position:0% +uh 2 m r^ 2 +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and spin arbit l dos s + + align:start position:0% +and spin arbit l dos s + + + align:start position:0% +and spin arbit l dos s +multiplied by the that has units of + + align:start position:0% +multiplied by the that has units of + + + align:start position:0% +multiplied by the that has units of +energy we always have products of two + + align:start position:0% +energy we always have products of two + + + align:start position:0% +energy we always have products of two +angular momentum + + align:start position:0% +angular momentum + + + align:start position:0% +angular momentum +and the only time you have one angular + + align:start position:0% +and the only time you have one angular + + + align:start position:0% +and the only time you have one angular +momentum by itself is for this to say + + align:start position:0% +momentum by itself is for this to say + + + align:start position:0% +momentum by itself is for this to say +this zon interaction + + align:start position:0% +this zon interaction + + + align:start position:0% +this zon interaction +but then you have uh a vector the the + + align:start position:0% +but then you have uh a vector the the + + + align:start position:0% +but then you have uh a vector the the +field + + align:start position:0% +field + + + align:start position:0% +field +uh dotted into the angular momentum and + + align:start position:0% +uh dotted into the angular momentum and + + + align:start position:0% +uh dotted into the angular momentum and +so it all works out and so you know + + align:start position:0% +so it all works out and so you know + + + align:start position:0% +so it all works out and so you know +people like to use atomic units where h + + align:start position:0% +people like to use atomic units where h + + + align:start position:0% +people like to use atomic units where h +bar is one and then you have to just + + align:start position:0% +bar is one and then you have to just + + + align:start position:0% +bar is one and then you have to just +take it on face and people haven't + + align:start position:0% +take it on face and people haven't + + + align:start position:0% +take it on face and people haven't +haven't given you a a bum formula which + + align:start position:0% +haven't given you a a bum formula which + + + align:start position:0% +haven't given you a a bum formula which +doesn't have the right stuff in it + + align:start position:0% +doesn't have the right stuff in it + + + align:start position:0% +doesn't have the right stuff in it +because you can't check anymore + + align:start position:0% +because you can't check anymore + + + align:start position:0% +because you can't check anymore +but angular man always give you a factor + + align:start position:0% +but angular man always give you a factor + + + align:start position:0% +but angular man always give you a factor +base h bar for every + + align:start position:0% +base h bar for every + + + align:start position:0% +base h bar for every +uh every time you so this gives you one + + align:start position:0% +uh every time you so this gives you one + + + align:start position:0% +uh every time you so this gives you one +h bar and this gives you h bar squared + + align:start position:0% +h bar and this gives you h bar squared + + + align:start position:0% +h bar and this gives you h bar squared +and uh you can always reconstruct things + + align:start position:0% +and uh you can always reconstruct things + + + align:start position:0% +and uh you can always reconstruct things +but I you know I just don't like to + + align:start position:0% +but I you know I just don't like to + + + align:start position:0% +but I you know I just don't like to +write h bar a lot of times + + align:start position:0% +write h bar a lot of times + + + align:start position:0% +write h bar a lot of times +okay so + + align:start position:0% + + + + align:start position:0% + +another way of saying some of the stuff + + align:start position:0% +another way of saying some of the stuff + + + align:start position:0% +another way of saying some of the stuff +that I uh + + align:start position:0% + + + + align:start position:0% + +uh said before we have this operator LS + + align:start position:0% +uh said before we have this operator LS + + + align:start position:0% +uh said before we have this operator LS +which we need from the spin orbit and we + + align:start position:0% +which we need from the spin orbit and we + + + align:start position:0% +which we need from the spin orbit and we +can write a computation rule + + align:start position:0% +can write a computation rule + + + align:start position:0% +can write a computation rule +uh and we know that LS + + align:start position:0% +uh and we know that LS + + + align:start position:0% +uh and we know that LS +commutes with L squ + + align:start position:0% +commutes with L squ + + + align:start position:0% +commutes with L squ +and J squ + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +and it commutes with JZ. + + align:start position:0% +and it commutes with JZ. + + + align:start position:0% +and it commutes with JZ. +So, + + align:start position:0% +So, + + + align:start position:0% +So, +so you can have + + align:start position:0% +so you can have + + + align:start position:0% +so you can have +this, + + align:start position:0% +this, + + + align:start position:0% +this, +this is going to be diagonal in a + + align:start position:0% +this is going to be diagonal in a + + + align:start position:0% +this is going to be diagonal in a +representation where you have L², S², + + align:start position:0% +representation where you have L², S², + + + align:start position:0% +representation where you have L², S², +J^2 and JZ. But L do S commuting with LZ + + align:start position:0% +J^2 and JZ. But L do S commuting with LZ + + + align:start position:0% +J^2 and JZ. But L do S commuting with LZ +is not zero + + align:start position:0% + + + + align:start position:0% + +because you're going to get an L+ and an + + align:start position:0% +because you're going to get an L+ and an + + + align:start position:0% +because you're going to get an L+ and an +LZ and the computation rules for angular + + align:start position:0% +LZ and the computation rules for angular + + + align:start position:0% +LZ and the computation rules for angular +momentum says well that's too damn bad. + + align:start position:0% +momentum says well that's too damn bad. + + + align:start position:0% +momentum says well that's too damn bad. +You you know they don't commute and the + + align:start position:0% +You you know they don't commute and the + + + align:start position:0% +You you know they don't commute and the +S doesn't help you. + + align:start position:0% +S doesn't help you. + + + align:start position:0% +S doesn't help you. +So, uh, + + align:start position:0% +So, uh, + + + align:start position:0% +So, uh, +you if you're going to get diagonal + + align:start position:0% +you if you're going to get diagonal + + + align:start position:0% +you if you're going to get diagonal +matrix elements in some basis set, it's + + align:start position:0% +matrix elements in some basis set, it's + + + align:start position:0% +matrix elements in some basis set, it's +because the operator commutes with all + + align:start position:0% +because the operator commutes with all + + + align:start position:0% +because the operator commutes with all +of the quantum numbers or all of the + + align:start position:0% +of the quantum numbers or all of the + + + align:start position:0% +of the quantum numbers or all of the +operators that correspond with the + + align:start position:0% +operators that correspond with the + + + align:start position:0% +operators that correspond with the +quantum numbers in that basis set. + + align:start position:0% + + + + align:start position:0% + +Are we all okay? + + align:start position:0% + + + + align:start position:0% + +All right. Next is a a handy dandy + + align:start position:0% +All right. Next is a a handy dandy + + + align:start position:0% +All right. Next is a a handy dandy +formula for all the energy levels + + align:start position:0% +formula for all the energy levels + + + align:start position:0% +formula for all the energy levels +of one electron + + align:start position:0% +of one electron + + + align:start position:0% +of one electron +atoms. + + align:start position:0% +atoms. + + + align:start position:0% +atoms. +And the reason I give this formula is + + align:start position:0% +And the reason I give this formula is + + + align:start position:0% +And the reason I give this formula is +not because you don't know it or + + align:start position:0% +not because you don't know it or + + + align:start position:0% +not because you don't know it or +couldn't, you know, couldn't figure it + + align:start position:0% +couldn't, you know, couldn't figure it + + + align:start position:0% +couldn't, you know, couldn't figure it +out, but because it gives you an idea of + + align:start position:0% +out, but because it gives you an idea of + + + align:start position:0% +out, but because it gives you an idea of +how things are built. And as soon as we + + align:start position:0% +how things are built. And as soon as we + + + align:start position:0% +how things are built. And as soon as we +go from one electron system to more than + + align:start position:0% +go from one electron system to more than + + + align:start position:0% +go from one electron system to more than +one electron system, we're going to have + + align:start position:0% +one electron system, we're going to have + + + align:start position:0% +one electron system, we're going to have +to make each of these terms a little + + align:start position:0% +to make each of these terms a little + + + align:start position:0% +to make each of these terms a little +more complicated. But the insight comes + + align:start position:0% +more complicated. But the insight comes + + + align:start position:0% +more complicated. But the insight comes +in seeing how you get back to this one + + align:start position:0% +in seeing how you get back to this one + + + align:start position:0% +in seeing how you get back to this one +electron picture. + + align:start position:0% + + + + align:start position:0% + +Okay. So we have energy levels or matrix + + align:start position:0% +Okay. So we have energy levels or matrix + + + align:start position:0% +Okay. So we have energy levels or matrix +elements of the Hamiltonian. So we have + + align:start position:0% +elements of the Hamiltonian. So we have + + + align:start position:0% +elements of the Hamiltonian. So we have +quantum numbers. The principal quantum + + align:start position:0% +quantum numbers. The principal quantum + + + align:start position:0% +quantum numbers. The principal quantum +number orbital angular momentum quantum + + align:start position:0% +number orbital angular momentum quantum + + + align:start position:0% +number orbital angular momentum quantum +number the spin J MJ. We decided that + + align:start position:0% +number the spin J MJ. We decided that + + + align:start position:0% +number the spin J MJ. We decided that +was a better basis set than the other + + align:start position:0% +was a better basis set than the other + + + align:start position:0% +was a better basis set than the other +the uncoupled basis. I actually like the + + align:start position:0% +the uncoupled basis. I actually like the + + + align:start position:0% +the uncoupled basis. I actually like the +uncoupled basis because + + align:start position:0% +uncoupled basis because + + + align:start position:0% +uncoupled basis because +for doing simple algebra using creation + + align:start position:0% +for doing simple algebra using creation + + + align:start position:0% +for doing simple algebra using creation +using latter operators it's always more + + align:start position:0% +using latter operators it's always more + + + align:start position:0% +using latter operators it's always more +convenient to have an operator a a + + align:start position:0% +convenient to have an operator a a + + + align:start position:0% +convenient to have an operator a a +magnitude and a projection for each + + align:start position:0% +magnitude and a projection for each + + + align:start position:0% +magnitude and a projection for each +operator L and LZ S and SC but you can + + align:start position:0% +operator L and LZ S and SC but you can + + + align:start position:0% +operator L and LZ S and SC but you can +do much more as soon as you give that up + + align:start position:0% +do much more as soon as you give that up + + + align:start position:0% +do much more as soon as you give that up +as soon as you have three magnitudes in + + align:start position:0% +as soon as you have three magnitudes in + + + align:start position:0% +as soon as you have three magnitudes in +one projection you have to do angular + + align:start position:0% +one projection you have to do angular + + + align:start position:0% +one projection you have to do angular +momentum transformations, + + align:start position:0% +momentum transformations, + + + align:start position:0% +momentum transformations, +3J coefficients, which we'll get to + + align:start position:0% +3J coefficients, which we'll get to + + + align:start position:0% +3J coefficients, which we'll get to +sometime. + + align:start position:0% +sometime. + + + align:start position:0% +sometime. +So, but I like to always use tools that + + align:start position:0% +So, but I like to always use tools that + + + align:start position:0% +So, but I like to always use tools that +I can do in my head rather than having + + align:start position:0% +I can do in my head rather than having + + + align:start position:0% +I can do in my head rather than having +to look at a book. + + align:start position:0% +to look at a book. + + + align:start position:0% +to look at a book. +And sometimes I waste a lot of time + + align:start position:0% +And sometimes I waste a lot of time + + + align:start position:0% +And sometimes I waste a lot of time +doing that, but usually it's a good + + align:start position:0% +doing that, but usually it's a good + + + align:start position:0% +doing that, but usually it's a good +idea. So h over C and uh N ls M U + + align:start position:0% + + + + align:start position:0% + +okay so these are the matrix elements + + align:start position:0% +okay so these are the matrix elements + + + align:start position:0% +okay so these are the matrix elements +that we're going to care about the + + align:start position:0% +that we're going to care about the + + + align:start position:0% +that we're going to care about the +energy and so uh the first thing that we + + align:start position:0% +energy and so uh the first thing that we + + + align:start position:0% +energy and so uh the first thing that we +know is that the the Hamiltonian for a + + align:start position:0% +know is that the the Hamiltonian for a + + + align:start position:0% +know is that the the Hamiltonian for a +spherical object is spherical. + + align:start position:0% +spherical object is spherical. + + + align:start position:0% +spherical object is spherical. +is totally symmetric. That means it + + align:start position:0% +is totally symmetric. That means it + + + align:start position:0% +is totally symmetric. That means it +cannot change any angle moment. + + align:start position:0% +cannot change any angle moment. + + + align:start position:0% +cannot change any angle moment. +Therefore, we immediately write down uh + + align:start position:0% +Therefore, we immediately write down uh + + + align:start position:0% +Therefore, we immediately write down uh +L prime L S prime S + + align:start position:0% +L prime L S prime S + + + align:start position:0% +L prime L S prime S +prime J. And uh it's a scalar. It can't + + align:start position:0% +prime J. And uh it's a scalar. It can't + + + align:start position:0% +prime J. And uh it's a scalar. It can't +even change the projection quantum + + align:start position:0% +even change the projection quantum + + + align:start position:0% +even change the projection quantum +numbers. + + align:start position:0% + + + + align:start position:0% + +So, and uh we're going to set the zero + + align:start position:0% +So, and uh we're going to set the zero + + + align:start position:0% +So, and uh we're going to set the zero +of energy at the uh dissociation energy. + + align:start position:0% +of energy at the uh dissociation energy. + + + align:start position:0% +of energy at the uh dissociation energy. +So, we're going to have a minus sign + + align:start position:0% +So, we're going to have a minus sign + + + align:start position:0% +So, we're going to have a minus sign +here because everything is lower than + + align:start position:0% +here because everything is lower than + + + align:start position:0% +here because everything is lower than +that. And now this all multiplies + + align:start position:0% +that. And now this all multiplies + + + align:start position:0% +that. And now this all multiplies +a factor. + + align:start position:0% +a factor. + + + align:start position:0% +a factor. +We have mu over me, the reduced mass + + align:start position:0% +We have mu over me, the reduced mass + + + align:start position:0% +We have mu over me, the reduced mass +over the mass. Now remember this is + + align:start position:0% +over the mass. Now remember this is + + + align:start position:0% +over the mass. Now remember this is +almost equal to me. So this is almost + + align:start position:0% +almost equal to me. So this is almost + + + align:start position:0% +almost equal to me. So this is almost +one but it isn't quite one. And then + + align:start position:0% +one but it isn't quite one. And then + + + align:start position:0% +one but it isn't quite one. And then +that multiplies + + align:start position:0% +that multiplies + + + align:start position:0% +that multiplies +uh 109,000 + + align:start position:0% +uh 109,000 + + + align:start position:0% +uh 109,000 +737. There's some more digits but I + + align:start position:0% +737. There's some more digits but I + + + align:start position:0% +737. There's some more digits but I +remember 109 737. It's you know I know + + align:start position:0% +remember 109 737. It's you know I know + + + align:start position:0% +remember 109 737. It's you know I know +that and the you know the telephone + + align:start position:0% +that and the you know the telephone + + + align:start position:0% +that and the you know the telephone +number of the house I lived in when I + + align:start position:0% +number of the house I lived in when I + + + align:start position:0% +number of the house I lived in when I +was five. But uh uh but this one I think + + align:start position:0% +was five. But uh uh but this one I think + + + align:start position:0% +was five. But uh uh but this one I think +I know I'll never forget. + + align:start position:0% +I know I'll never forget. + + + align:start position:0% +I know I'll never forget. +Um so um so this is the Rber constant + + align:start position:0% +Um so um so this is the Rber constant + + + align:start position:0% +Um so um so this is the Rber constant +and this is the big stuff in the + + align:start position:0% +and this is the big stuff in the + + + align:start position:0% +and this is the big stuff in the +electronic structure of uh atoms. So + + align:start position:0% +electronic structure of uh atoms. So + + + align:start position:0% +electronic structure of uh atoms. So +this is about one this is 100,000 wave + + align:start position:0% +this is about one this is 100,000 wave + + + align:start position:0% +this is about one this is 100,000 wave +numbers and this is the charge over the + + align:start position:0% +numbers and this is the charge over the + + + align:start position:0% +numbers and this is the charge over the +principal quantum number L E A L + + align:start position:0% +principal quantum number L E A L + + + align:start position:0% +principal quantum number L E A L +principle + + align:start position:0% + + + + align:start position:0% + +it's like nuclear and nuclear you know + + align:start position:0% +it's like nuclear and nuclear you know + + + align:start position:0% +it's like nuclear and nuclear you know +if you get it wrong you're an idiot + + align:start position:0% + + + + align:start position:0% + +and the next term is the spin and that + + align:start position:0% +and the next term is the spin and that + + + align:start position:0% +and the next term is the spin and that +has a scale factor + + align:start position:0% +has a scale factor + + + align:start position:0% +has a scale factor +and it goes to the charge to the fourth + + align:start position:0% +and it goes to the charge to the fourth + + + align:start position:0% +and it goes to the charge to the fourth +power and the principal quantum number + + align:start position:0% +power and the principal quantum number + + + align:start position:0% +power and the principal quantum number +to the fourth power and n over j + + + align:start position:0% +to the fourth power and n over j + + + + align:start position:0% +to the fourth power and n over j + +I don't normally work in these in in + + align:start position:0% +I don't normally work in these in in + + + align:start position:0% +I don't normally work in these in in +this + + align:start position:0% +this + + + align:start position:0% +this +in this way I have to look that up but + + align:start position:0% +in this way I have to look that up but + + + align:start position:0% +in this way I have to look that up but +notice we have an n here and an n 4th + + align:start position:0% +notice we have an n here and an n 4th + + + align:start position:0% +notice we have an n here and an n 4th +here and so this is overall n 1 / n + + align:start position:0% +here and so this is overall n 1 / n + + + align:start position:0% +here and so this is overall n 1 / n +cubed and almost everything in uh uh + + align:start position:0% +cubed and almost everything in uh uh + + + align:start position:0% +cubed and almost everything in uh uh +Ridberg land which is really hydrogen + + align:start position:0% +Ridberg land which is really hydrogen + + + align:start position:0% +Ridberg land which is really hydrogen +atom goes as 1 / n cubed or 1 / n^ the + + align:start position:0% +atom goes as 1 / n cubed or 1 / n^ the + + + align:start position:0% +atom goes as 1 / n cubed or 1 / n^ the +three halves depending on whether you're + + align:start position:0% +three halves depending on whether you're + + + align:start position:0% +three halves depending on whether you're +talking about uh an amplitude or a thing + + align:start position:0% +talking about uh an amplitude or a thing + + + align:start position:0% +talking about uh an amplitude or a thing +an energy or an expectation value. So we + + align:start position:0% +an energy or an expectation value. So we + + + align:start position:0% +an energy or an expectation value. So we +have that and then we have uh + + align:start position:0% +have that and then we have uh + + + align:start position:0% +have that and then we have uh +that's it. So this is E N + + align:start position:0% +that's it. So this is E N + + + align:start position:0% +that's it. So this is E N +L J + + align:start position:0% +L J + + + align:start position:0% +L J +and uh I guess we lost something off the + + align:start position:0% +and uh I guess we lost something off the + + + align:start position:0% +and uh I guess we lost something off the +stage Z mu. + + align:start position:0% +stage Z mu. + + + align:start position:0% +stage Z mu. +So this is the universal formula for the + + align:start position:0% +So this is the universal formula for the + + + align:start position:0% +So this is the universal formula for the +energy levels of a one electron atom. + + align:start position:0% +energy levels of a one electron atom. + + + align:start position:0% +energy levels of a one electron atom. +Big deal. Uh it it's you know the + + align:start position:0% +Big deal. Uh it it's you know the + + + align:start position:0% +Big deal. Uh it it's you know the +energies are determined by N L and J. uh + + align:start position:0% +energies are determined by N L and J. uh + + + align:start position:0% +energies are determined by N L and J. uh +except that L is gone through electron + + align:start position:0% +except that L is gone through electron + + + align:start position:0% +except that L is gone through electron +atoms because of a surprising symmetry. + + align:start position:0% +atoms because of a surprising symmetry. + + + align:start position:0% +atoms because of a surprising symmetry. +You would have expected it not to be + + align:start position:0% +You would have expected it not to be + + + align:start position:0% +You would have expected it not to be +gone uh but there's a cancellation and + + align:start position:0% +gone uh but there's a cancellation and + + + align:start position:0% +gone uh but there's a cancellation and +uh uh and so then there's a weak + + align:start position:0% +uh uh and so then there's a weak + + + align:start position:0% +uh uh and so then there's a weak +dependence on the charge on the well not + + align:start position:0% +dependence on the charge on the well not + + + align:start position:0% +dependence on the charge on the well not +a weak dependence a charge on the + + align:start position:0% +a weak dependence a charge on the + + + align:start position:0% +a weak dependence a charge on the +nucleus and a dependence on the medium. + + align:start position:0% +nucleus and a dependence on the medium. + + + align:start position:0% +nucleus and a dependence on the medium. +Okay. So the these are the energy levels + + align:start position:0% +Okay. So the these are the energy levels + + + align:start position:0% +Okay. So the these are the energy levels +for a one electron atom. We have the big + + align:start position:0% +for a one electron atom. We have the big + + + align:start position:0% +for a one electron atom. We have the big +thing and we have the small thing. And + + align:start position:0% +thing and we have the small thing. And + + + align:start position:0% +thing and we have the small thing. And +we have a weaker scaling with the + + align:start position:0% +we have a weaker scaling with the + + + align:start position:0% +we have a weaker scaling with the +principal quantum number and a stronger + + align:start position:0% +principal quantum number and a stronger + + + align:start position:0% +principal quantum number and a stronger +scaling with the principal. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +So we have the energy levels + + align:start position:0% +So we have the energy levels + + + align:start position:0% +So we have the energy levels +and uh and each of the energy levels is + + align:start position:0% +and uh and each of the energy levels is + + + align:start position:0% +and uh and each of the energy levels is +is a state. So, and the the states have + + align:start position:0% +is a state. So, and the the states have + + + align:start position:0% +is a state. So, and the the states have +names and so + + align:start position:0% +names and so + + + align:start position:0% +names and so +we label the states of a u one electron + + align:start position:0% +we label the states of a u one electron + + + align:start position:0% +we label the states of a u one electron +atom + + align:start position:0% +atom + + + align:start position:0% +atom +um + + align:start position:0% +um + + + align:start position:0% +um +like this. + + align:start position:0% + + + + align:start position:0% + +So this is the multiplicity 2s + 1. This + + align:start position:0% +So this is the multiplicity 2s + 1. This + + + align:start position:0% +So this is the multiplicity 2s + 1. This +is the principal quantum number. This is + + align:start position:0% +is the principal quantum number. This is + + + align:start position:0% +is the principal quantum number. This is +J and this is an interesting pneummonic + + align:start position:0% +J and this is an interesting pneummonic + + + align:start position:0% +J and this is an interesting pneummonic +uh for L. The values of L can be 0 1 2 3 + + align:start position:0% +uh for L. The values of L can be 0 1 2 3 + + + align:start position:0% +uh for L. The values of L can be 0 1 2 3 +4 5 6 S B F G H I + + align:start position:0% +4 5 6 S B F G H I + + + align:start position:0% +4 5 6 S B F G H I +K. + + align:start position:0% +K. + + + align:start position:0% +K. +Why don't we put J there? Because we use + + align:start position:0% +Why don't we put J there? Because we use + + + align:start position:0% +Why don't we put J there? Because we use +J for something else. + + align:start position:0% +J for something else. + + + align:start position:0% +J for something else. +So, but everything in spectroscopy uses + + align:start position:0% +So, but everything in spectroscopy uses + + + align:start position:0% +So, but everything in spectroscopy uses +the alphabet except occasionally you + + align:start position:0% +the alphabet except occasionally you + + + align:start position:0% +the alphabet except occasionally you +have to make a a glitch. Okay. So, + + align:start position:0% +have to make a a glitch. Okay. So, + + + align:start position:0% +have to make a a glitch. Okay. So, +so if you're at L equals 8, would that + + align:start position:0% +so if you're at L equals 8, would that + + + align:start position:0% +so if you're at L equals 8, would that +also skip out on? + + align:start position:0% +also skip out on? + + + align:start position:0% +also skip out on? +No. No. For some reason, J is excluded, + + align:start position:0% +No. No. For some reason, J is excluded, + + + align:start position:0% +No. No. For some reason, J is excluded, +but you have L states. + + align:start position:0% +but you have L states. + + + align:start position:0% +but you have L states. +I don't know why. + + align:start position:0% +I don't know why. + + + align:start position:0% +I don't know why. +Um so + + align:start position:0% +Um so + + + align:start position:0% +Um so +we uh we generally use lowercase letters + + align:start position:0% +we uh we generally use lowercase letters + + + align:start position:0% +we uh we generally use lowercase letters +for one electron + + align:start position:0% +for one electron + + + align:start position:0% +for one electron +and uh uppercase letters when there's + + align:start position:0% +and uh uppercase letters when there's + + + align:start position:0% +and uh uppercase letters when there's +more than one electron and so that this + + align:start position:0% +more than one electron and so that this + + + align:start position:0% +more than one electron and so that this +is enough to completely specify a state + + align:start position:0% +is enough to completely specify a state + + + align:start position:0% +is enough to completely specify a state +and uh uh okay + + align:start position:0% + + + + align:start position:0% + +so we could have a spin orbit splitting + + align:start position:0% +so we could have a spin orbit splitting + + + align:start position:0% +so we could have a spin orbit splitting +which would be two delta P 3s minus the + + align:start position:0% +which would be two delta P 3s minus the + + + align:start position:0% +which would be two delta P 3s minus the +energy of 2 delta P 1/2 + + align:start position:0% +energy of 2 delta P 1/2 + + + align:start position:0% +energy of 2 delta P 1/2 +and uh those scale according to the Z Z + + align:start position:0% +and uh those scale according to the Z Z + + + align:start position:0% +and uh those scale according to the Z Z +to the 4th and so the value of that + + align:start position:0% +to the 4th and so the value of that + + + align:start position:0% +to the 4th and so the value of that +splitting for hydrogen here's some more + + align:start position:0% +splitting for hydrogen here's some more + + + align:start position:0% +splitting for hydrogen here's some more +notation + + align:start position:0% + + + + align:start position:0% + +so this This is called the first + + align:start position:0% +so this This is called the first + + + align:start position:0% +so this This is called the first +spectrum of hydrogen + + align:start position:0% +spectrum of hydrogen + + + align:start position:0% +spectrum of hydrogen +and that's the neutral. This is called + + align:start position:0% +and that's the neutral. This is called + + + align:start position:0% +and that's the neutral. This is called +the third spectrum of lithium. The first + + align:start position:0% +the third spectrum of lithium. The first + + + align:start position:0% +the third spectrum of lithium. The first +spectrum of lithium would be lithium + + align:start position:0% +spectrum of lithium would be lithium + + + align:start position:0% +spectrum of lithium would be lithium +neutral. Second would be lithium plus + + align:start position:0% +neutral. Second would be lithium plus + + + align:start position:0% +neutral. Second would be lithium plus +one and the third would be lithium + + align:start position:0% +one and the third would be lithium + + + align:start position:0% +one and the third would be lithium +plus2. And this unfortunately disagrees + + align:start position:0% +plus2. And this unfortunately disagrees + + + align:start position:0% +plus2. And this unfortunately disagrees +with the way chemists label things. + + align:start position:0% +with the way chemists label things. + + + align:start position:0% +with the way chemists label things. +So you just have to be careful to find + + align:start position:0% +So you just have to be careful to find + + + align:start position:0% +So you just have to be careful to find +out whether uh the uh the + + align:start position:0% +out whether uh the uh the + + + align:start position:0% +out whether uh the uh the +atomic spectra uh labeling scheme is + + align:start position:0% +atomic spectra uh labeling scheme is + + + align:start position:0% +atomic spectra uh labeling scheme is +used or the chemist scheme. Okay. Now + + align:start position:0% +used or the chemist scheme. Okay. Now + + + align:start position:0% +used or the chemist scheme. Okay. Now +the spin orbit splitting for the the two + + align:start position:0% +the spin orbit splitting for the the two + + + align:start position:0% +the spin orbit splitting for the the two +WP state in hydrogen is 0.37 wave + + align:start position:0% +WP state in hydrogen is 0.37 wave + + + align:start position:0% +WP state in hydrogen is 0.37 wave +numbers. For lithium it's 30 wave + + align:start position:0% +numbers. For lithium it's 30 wave + + + align:start position:0% +numbers. For lithium it's 30 wave +numbers and for sodium it's 5400. + + align:start position:0% +numbers and for sodium it's 5400. + + + align:start position:0% +numbers and for sodium it's 5400. +And it's just reflecting the Z to the + + align:start position:0% +And it's just reflecting the Z to the + + + align:start position:0% +And it's just reflecting the Z to the +4th scale. + + align:start position:0% + + + + align:start position:0% + +And since it's determined near the + + align:start position:0% +And since it's determined near the + + + align:start position:0% +And since it's determined near the +nucleus, + + align:start position:0% +nucleus, + + + align:start position:0% +nucleus, +it's a kind of us universal measure of + + align:start position:0% +it's a kind of us universal measure of + + + align:start position:0% +it's a kind of us universal measure of +what is this orbital that is open shell + + align:start position:0% +what is this orbital that is open shell + + + align:start position:0% +what is this orbital that is open shell +that's giving us this thing. And so it + + align:start position:0% +that's giving us this thing. And so it + + + align:start position:0% +that's giving us this thing. And so it +turns out to be a very very useful uh + + align:start position:0% +turns out to be a very very useful uh + + + align:start position:0% +turns out to be a very very useful uh +signpost for what state is this? What + + align:start position:0% +signpost for what state is this? What + + + align:start position:0% +signpost for what state is this? What +are the the the orbitals that are + + align:start position:0% +are the the the orbitals that are + + + align:start position:0% +are the the the orbitals that are +involved in generating this state? And + + align:start position:0% +involved in generating this state? And + + + align:start position:0% +involved in generating this state? And +so um + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% +So + + + align:start position:0% +So +um if we have one electron wave + + align:start position:0% +um if we have one electron wave + + + align:start position:0% +um if we have one electron wave +functions + + align:start position:0% +functions + + + align:start position:0% +functions +uh + + align:start position:0% +uh + + + align:start position:0% +uh +practically anything we care about can + + align:start position:0% +practically anything we care about can + + + align:start position:0% +practically anything we care about can +be written as some function of the + + align:start position:0% +be written as some function of the + + + align:start position:0% +be written as some function of the +quantum numbers. So if we have uh an off + + align:start position:0% +quantum numbers. So if we have uh an off + + + align:start position:0% +quantum numbers. So if we have uh an off +diagonal matrix element, one can write + + align:start position:0% +diagonal matrix element, one can write + + + align:start position:0% +diagonal matrix element, one can write +uh remember spin can only have value of + + align:start position:0% +uh remember spin can only have value of + + + align:start position:0% +uh remember spin can only have value of +a half. So it's silly to write it as + + align:start position:0% +a half. So it's silly to write it as + + + align:start position:0% +a half. So it's silly to write it as +prime. But uh so anyway, you could you + + align:start position:0% +prime. But uh so anyway, you could you + + + align:start position:0% +prime. But uh so anyway, you could you +could write any quantity as an explicit + + align:start position:0% +could write any quantity as an explicit + + + align:start position:0% +could write any quantity as an explicit +function of the quantum numbers + + align:start position:0% +function of the quantum numbers + + + align:start position:0% +function of the quantum numbers +especially n + + align:start position:0% +especially n + + + align:start position:0% +especially n +and and so now what I'm going to talk + + align:start position:0% +and and so now what I'm going to talk + + + align:start position:0% +and and so now what I'm going to talk +about is some of these formulas for how + + align:start position:0% +about is some of these formulas for how + + + align:start position:0% +about is some of these formulas for how +things behave. + + align:start position:0% + + + + align:start position:0% + +And one of the things you care most + + align:start position:0% +And one of the things you care most + + + align:start position:0% +And one of the things you care most +about is the coordinate is the uh + + align:start position:0% +about is the coordinate is the uh + + + align:start position:0% +about is the coordinate is the uh +coordinate of the electron relative to + + align:start position:0% +coordinate of the electron relative to + + + align:start position:0% +coordinate of the electron relative to +the nucleus. + + align:start position:0% +the nucleus. + + + align:start position:0% +the nucleus. +Okay, this is the coordinate of the + + align:start position:0% +Okay, this is the coordinate of the + + + align:start position:0% +Okay, this is the coordinate of the +electron. + + align:start position:0% +electron. + + + align:start position:0% +electron. +It operates on spatial coordinates. It + + align:start position:0% +It operates on spatial coordinates. It + + + align:start position:0% +It operates on spatial coordinates. It +doesn't operate on spin. So immediately + + align:start position:0% +doesn't operate on spin. So immediately + + + align:start position:0% +doesn't operate on spin. So immediately +if I write down an operator that is some + + align:start position:0% +if I write down an operator that is some + + + align:start position:0% +if I write down an operator that is some +function of r, it's not going to do + + align:start position:0% +function of r, it's not going to do + + + align:start position:0% +function of r, it's not going to do +anything to the spin part. the spin is + + align:start position:0% +anything to the spin part. the spin is + + + align:start position:0% +anything to the spin part. the spin is +acting like a scalar relative to this. + + align:start position:0% +acting like a scalar relative to this. + + + align:start position:0% +acting like a scalar relative to this. +It's just a constant. It doesn't see it. + + align:start position:0% +It's just a constant. It doesn't see it. + + + align:start position:0% +It's just a constant. It doesn't see it. +So, uh r only operates on uh spatial not + + align:start position:0% +So, uh r only operates on uh spatial not + + + align:start position:0% +So, uh r only operates on uh spatial not +uh uh spin coordinates. + + align:start position:0% +uh uh spin coordinates. + + + align:start position:0% +uh uh spin coordinates. +Now, you know about scalers and vectors + + align:start position:0% +Now, you know about scalers and vectors + + + align:start position:0% +Now, you know about scalers and vectors +and tensors. If you don't know, let me + + align:start position:0% +and tensors. If you don't know, let me + + + align:start position:0% +and tensors. If you don't know, let me +just tell you a scaler is like a + + align:start position:0% +just tell you a scaler is like a + + + align:start position:0% +just tell you a scaler is like a +constant. It doesn't have any angular + + align:start position:0% +constant. It doesn't have any angular + + + align:start position:0% +constant. It doesn't have any angular +event. It's just a number. And uh if you + + align:start position:0% +event. It's just a number. And uh if you + + + align:start position:0% +event. It's just a number. And uh if you +have some angular momentum + + align:start position:0% +have some angular momentum + + + align:start position:0% +have some angular momentum +representation, one of the things about + + align:start position:0% +representation, one of the things about + + + align:start position:0% +representation, one of the things about +it is that it doesn't care which uh + + align:start position:0% +it is that it doesn't care which uh + + + align:start position:0% +it is that it doesn't care which uh +which projection quantum number you've + + align:start position:0% +which projection quantum number you've + + + align:start position:0% +which projection quantum number you've +got. It when you calculate its + + align:start position:0% +got. It when you calculate its + + + align:start position:0% +got. It when you calculate its +expectation value, it's going to have + + align:start position:0% +expectation value, it's going to have + + + align:start position:0% +expectation value, it's going to have +the same expectation value independent + + align:start position:0% +the same expectation value independent + + + align:start position:0% +the same expectation value independent +of projection quantum number. + + align:start position:0% +of projection quantum number. + + + align:start position:0% +of projection quantum number. +A vector is you know has three + + align:start position:0% +A vector is you know has three + + + align:start position:0% +A vector is you know has three +components uh and we can understand + + align:start position:0% +components uh and we can understand + + + align:start position:0% +components uh and we can understand +vectors. You can imagine going to + + align:start position:0% +vectors. You can imagine going to + + + align:start position:0% +vectors. You can imagine going to +something which we call a second brain + + align:start position:0% +something which we call a second brain + + + align:start position:0% +something which we call a second brain +tensor + + align:start position:0% +tensor + + + align:start position:0% +tensor +and that's sort of like a d orbital. Uh + + align:start position:0% +and that's sort of like a d orbital. Uh + + + align:start position:0% +and that's sort of like a d orbital. Uh +and uh we can classify all operators + + align:start position:0% +and uh we can classify all operators + + + align:start position:0% +and uh we can classify all operators +according to their tensorial rank and + + align:start position:0% +according to their tensorial rank and + + + align:start position:0% +according to their tensorial rank and +that's called spherical tensor algebra. + + align:start position:0% +that's called spherical tensor algebra. + + + align:start position:0% +that's called spherical tensor algebra. +And this is useful because the tensorial + + align:start position:0% +And this is useful because the tensorial + + + align:start position:0% +And this is useful because the tensorial +rank is just like an angular momentum. + + align:start position:0% +rank is just like an angular momentum. + + + align:start position:0% +rank is just like an angular momentum. +And so if you're coupling an angular + + align:start position:0% +And so if you're coupling an angular + + + align:start position:0% +And so if you're coupling an angular +momentum of one to an angular momentum + + align:start position:0% +momentum of one to an angular momentum + + + align:start position:0% +momentum of one to an angular momentum +of two, there are certain formulas for + + align:start position:0% +of two, there are certain formulas for + + + align:start position:0% +of two, there are certain formulas for +how to do that. And so it's very useful + + align:start position:0% +how to do that. And so it's very useful + + + align:start position:0% +how to do that. And so it's very useful +to look at an operator and say, "Oh, I + + align:start position:0% +to look at an operator and say, "Oh, I + + + align:start position:0% +to look at an operator and say, "Oh, I +know it's tensorial rank. Well, this is + + align:start position:0% +know it's tensorial rank. Well, this is + + + align:start position:0% +know it's tensorial rank. Well, this is +one. It's like an angular momentum of + + align:start position:0% +one. It's like an angular momentum of + + + align:start position:0% +one. It's like an angular momentum of +one. It couples to other angular + + align:start position:0% +one. It couples to other angular + + + align:start position:0% +one. It couples to other angular +momentum." And in a sense they can + + align:start position:0% +momentum." And in a sense they can + + + align:start position:0% +momentum." And in a sense they can +change their the the total angular + + align:start position:0% +change their the the total angular + + + align:start position:0% +change their the the total angular +momentum by plus or minus one or zero + + align:start position:0% +momentum by plus or minus one or zero + + + align:start position:0% +momentum by plus or minus one or zero +because you can tell that this is like a + + align:start position:0% +because you can tell that this is like a + + + align:start position:0% +because you can tell that this is like a +vector and we know vectors are rank one. + + align:start position:0% +vector and we know vectors are rank one. + + + align:start position:0% +vector and we know vectors are rank one. +Okay. And we'll you'll see eventually + + align:start position:0% +Okay. And we'll you'll see eventually + + + align:start position:0% +Okay. And we'll you'll see eventually +things with higher tensorial rank. + + align:start position:0% +things with higher tensorial rank. + + + align:start position:0% +things with higher tensorial rank. +Okay. Another thing about this is if we + + align:start position:0% +Okay. Another thing about this is if we + + + align:start position:0% +Okay. Another thing about this is if we +ask well what happens to r this vector + + align:start position:0% +ask well what happens to r this vector + + + align:start position:0% +ask well what happens to r this vector +if we invert through the origin it + + align:start position:0% +if we invert through the origin it + + + align:start position:0% +if we invert through the origin it +changes sign that means it has odd par + + align:start position:0% +changes sign that means it has odd par + + + align:start position:0% +changes sign that means it has odd par +is an important quantum number two and + + align:start position:0% +is an important quantum number two and + + + align:start position:0% +is an important quantum number two and +so by writing this down you know it does + + align:start position:0% +so by writing this down you know it does + + + align:start position:0% +so by writing this down you know it does +not operate on spin it has odd par if it + + align:start position:0% +not operate on spin it has odd par if it + + + align:start position:0% +not operate on spin it has odd par if it +looks like an angular moment of one and + + align:start position:0% +looks like an angular moment of one and + + + align:start position:0% +looks like an angular moment of one and +so that tells you a lot about its it's + + align:start position:0% +so that tells you a lot about its it's + + + align:start position:0% +so that tells you a lot about its it's +uh uh nonzero matrix elements. + + align:start position:0% +uh uh nonzero matrix elements. + + + align:start position:0% +uh uh nonzero matrix elements. +So the matrix elements of this have uh + + align:start position:0% +So the matrix elements of this have uh + + + align:start position:0% +So the matrix elements of this have uh +selection rules + + align:start position:0% + + + + align:start position:0% + +and uh the reason it can't change L by + + align:start position:0% +and uh the reason it can't change L by + + + align:start position:0% +and uh the reason it can't change L by +one is because it has odd parity and if + + align:start position:0% +one is because it has odd parity and if + + + align:start position:0% +one is because it has odd parity and if +you I mean the reason it can't change L + + align:start position:0% +you I mean the reason it can't change L + + + align:start position:0% +you I mean the reason it can't change L +by zero is it has odd parity. If you + + align:start position:0% +by zero is it has odd parity. If you + + + align:start position:0% +by zero is it has odd parity. If you +take the same L twice that's got even + + align:start position:0% +take the same L twice that's got even + + + align:start position:0% +take the same L twice that's got even +parity and so the integral is going to + + align:start position:0% +parity and so the integral is going to + + + align:start position:0% +parity and so the integral is going to +be zero. + + align:start position:0% +be zero. + + + align:start position:0% +be zero. +So R by alone will just will change L by + + align:start position:0% +So R by alone will just will change L by + + + align:start position:0% +So R by alone will just will change L by +one. uh it can't change s + + align:start position:0% +one. uh it can't change s + + + align:start position:0% +one. uh it can't change s +uh + + align:start position:0% +uh + + + align:start position:0% +uh +surprisingly it can change j by zero or + + align:start position:0% +surprisingly it can change j by zero or + + + align:start position:0% +surprisingly it can change j by zero or +plus or minus one and that comes from + + align:start position:0% +plus or minus one and that comes from + + + align:start position:0% +plus or minus one and that comes from +vector addition between these things and + + align:start position:0% +vector addition between these things and + + + align:start position:0% +vector addition between these things and +like that it can't change m subs + + align:start position:0% +like that it can't change m subs + + + align:start position:0% +like that it can't change m subs +and + + align:start position:0% +and + + + align:start position:0% +and +it can change m subj + + align:start position:0% + + + + align:start position:0% + +and uh + + align:start position:0% + + + + align:start position:0% + +N is not an angular momentum and so you + + align:start position:0% +N is not an angular momentum and so you + + + align:start position:0% +N is not an angular momentum and so you +can have any change in M + + align:start position:0% +can have any change in M + + + align:start position:0% +can have any change in M +uh for this kind of an operator. Okay. + + align:start position:0% +uh for this kind of an operator. Okay. + + + align:start position:0% +uh for this kind of an operator. Okay. +So now + + align:start position:0% +So now + + + align:start position:0% +So now +for hydrogenic functions there are there + + align:start position:0% +for hydrogenic functions there are there + + + align:start position:0% +for hydrogenic functions there are there +are two kinds of matrix elements of R + + align:start position:0% +are two kinds of matrix elements of R + + + align:start position:0% +are two kinds of matrix elements of R +that we care about. One would be the + + align:start position:0% +that we care about. One would be the + + + align:start position:0% +that we care about. One would be the +operator that enables you to have a + + align:start position:0% +operator that enables you to have a + + + align:start position:0% +operator that enables you to have a +absorption of a photon the electric + + align:start position:0% +absorption of a photon the electric + + + align:start position:0% +absorption of a photon the electric +dipole operator. + + align:start position:0% +dipole operator. + + + align:start position:0% +dipole operator. +So + + align:start position:0% +So + + + align:start position:0% +So +in continent shortly which is a + + align:start position:0% +in continent shortly which is a + + + align:start position:0% +in continent shortly which is a +wonderful book just because it's filled + + align:start position:0% +wonderful book just because it's filled + + + align:start position:0% +wonderful book just because it's filled +with formulas which for many many cases + + align:start position:0% +with formulas which for many many cases + + + align:start position:0% +with formulas which for many many cases +and it's also filled with obscure + + align:start position:0% +and it's also filled with obscure + + + align:start position:0% +and it's also filled with obscure +derivations which you mostly don't want + + align:start position:0% +derivations which you mostly don't want + + + align:start position:0% +derivations which you mostly don't want +to look at. So you just look at the + + align:start position:0% +to look at. So you just look at the + + + align:start position:0% +to look at. So you just look at the +formulas and it's organized in a very + + align:start position:0% +formulas and it's organized in a very + + + align:start position:0% +formulas and it's organized in a very +transparent way. Uh uh so one of the + + align:start position:0% +transparent way. Uh uh so one of the + + + align:start position:0% +transparent way. Uh uh so one of the +formulas is the thing that tells you + + align:start position:0% +formulas is the thing that tells you + + + align:start position:0% +formulas is the thing that tells you +about the transition from the ground + + align:start position:0% +about the transition from the ground + + + align:start position:0% +about the transition from the ground +state of any hydrogenic system to any + + align:start position:0% +state of any hydrogenic system to any + + + align:start position:0% +state of any hydrogenic system to any +possible excited state. Since we're + + align:start position:0% +possible excited state. Since we're + + + align:start position:0% +possible excited state. Since we're +starting in S and L can only change by + + align:start position:0% +starting in S and L can only change by + + + align:start position:0% +starting in S and L can only change by +one, it's NP. + + align:start position:0% +one, it's NP. + + + align:start position:0% +one, it's NP. +So these are this is the uh transition + + align:start position:0% +So these are this is the uh transition + + + align:start position:0% +So these are this is the uh transition +moment squared. This is what determines + + align:start position:0% +moment squared. This is what determines + + + align:start position:0% +moment squared. This is what determines +the intensity of transitions. Uh and + + align:start position:0% +the intensity of transitions. Uh and + + + align:start position:0% +the intensity of transitions. Uh and +only transitions from S to P are + + align:start position:0% +only transitions from S to P are + + + align:start position:0% +only transitions from S to P are +allowed. Uh and this has the uh uh + + align:start position:0% +allowed. Uh and this has the uh uh + + + align:start position:0% +allowed. Uh and this has the uh uh +magnitude + + align:start position:0% +magnitude + + + align:start position:0% +magnitude +N^ 7 N -1 to the 2 N - 5 power. You + + align:start position:0% +N^ 7 N -1 to the 2 N - 5 power. You + + + align:start position:0% +N^ 7 N -1 to the 2 N - 5 power. You +know, you can derive these things, but + + align:start position:0% +know, you can derive these things, but + + + align:start position:0% +know, you can derive these things, but +you got to be nuts to do it because + + align:start position:0% +you got to be nuts to do it because + + + align:start position:0% +you got to be nuts to do it because +they've already been done. uh n +1 + + align:start position:0% +they've already been done. uh n +1 + + + align:start position:0% +they've already been done. uh n +1 +to the 2 n to the minus 2 n - 5. + + align:start position:0% +to the 2 n to the minus 2 n - 5. + + + align:start position:0% +to the 2 n to the minus 2 n - 5. +Uh + + align:start position:0% +Uh + + + align:start position:0% +Uh +and so when you look at this and you say + + align:start position:0% +and so when you look at this and you say + + + align:start position:0% +and so when you look at this and you say +well at least they're both just about n + + align:start position:0% +well at least they're both just about n + + + align:start position:0% +well at least they're both just about n +and we so we get n^ the minus 10 n 10 n + + align:start position:0% + + + + align:start position:0% +10 n 10 n 10 n 10 n 10 n 10 n 10 n 10 n +10 7 we get 10^ theus 3 which is what + + align:start position:0% +10 7 we get 10^ theus 3 which is what + + + align:start position:0% +10 7 we get 10^ theus 3 which is what +you sort of expect for transitions among + + align:start position:0% +you sort of expect for transitions among + + + align:start position:0% +you sort of expect for transitions among +electron + + align:start position:0% +electron + + + align:start position:0% +electron +from one from n= 1 to n and I'll soon + + align:start position:0% +from one from n= 1 to n and I'll soon + + + align:start position:0% +from one from n= 1 to n and I'll soon +explain this nus 3 is the source of the + + align:start position:0% +explain this nus 3 is the source of the + + + align:start position:0% +explain this nus 3 is the source of the +nus 3 scaling factor in rubric. Uh I + + align:start position:0% +nus 3 scaling factor in rubric. Uh I + + + align:start position:0% +nus 3 scaling factor in rubric. Uh I +won't do that today. So then in another + + align:start position:0% +won't do that today. So then in another + + + align:start position:0% +won't do that today. So then in another +table and that's uh expectation values + + align:start position:0% +table and that's uh expectation values + + + align:start position:0% +table and that's uh expectation values +of the scalar quantity uh magnitude of r + + align:start position:0% +of the scalar quantity uh magnitude of r + + + align:start position:0% +of the scalar quantity uh magnitude of r +not the vector to the k power and we + + align:start position:0% +not the vector to the k power and we + + + align:start position:0% +not the vector to the k power and we +have the radial factors uh r. + + align:start position:0% + + + + align:start position:0% + +So this integral + + align:start position:0% +So this integral + + + align:start position:0% +So this integral +uh that also can be tabulated and + + align:start position:0% +uh that also can be tabulated and + + + align:start position:0% +uh that also can be tabulated and +there's something very interesting about + + align:start position:0% +there's something very interesting about + + + align:start position:0% +there's something very interesting about +that. I'm not going to write it down on + + align:start position:0% +that. I'm not going to write it down on + + + align:start position:0% +that. I'm not going to write it down on +the board. It's in the notes. Uh what + + align:start position:0% +the board. It's in the notes. Uh what + + + align:start position:0% +the board. It's in the notes. Uh what +you discover is that + + align:start position:0% +you discover is that + + + align:start position:0% +you discover is that +when when + + align:start position:0% +when when + + + align:start position:0% +when when +so when k is minus one that's the the uh + + align:start position:0% +so when k is minus one that's the the uh + + + align:start position:0% +so when k is minus one that's the the uh +uh the rberg formula that's the energy + + align:start position:0% +uh the rberg formula that's the energy + + + align:start position:0% +uh the rberg formula that's the energy +levels of redberg states. So this is + + align:start position:0% +levels of redberg states. So this is + + + align:start position:0% +levels of redberg states. So this is +going to go as n^ squ + + align:start position:0% +going to go as n^ squ + + + align:start position:0% +going to go as n^ squ +when k is minus2 + + align:start position:0% +when k is minus2 + + + align:start position:0% +when k is minus2 +that's the centrifugal barrier and it's + + align:start position:0% +that's the centrifugal barrier and it's + + + align:start position:0% +that's the centrifugal barrier and it's +also the interaction of electron with a + + align:start position:0% +also the interaction of electron with a + + + align:start position:0% +also the interaction of electron with a +dipole. If there were a point dipole on + + align:start position:0% +dipole. If there were a point dipole on + + + align:start position:0% +dipole. If there were a point dipole on +the nucleus, this would describe that + + align:start position:0% +the nucleus, this would describe that + + + align:start position:0% +the nucleus, this would describe that +when you get k is minus3 + + align:start position:0% +when you get k is minus3 + + + align:start position:0% +when you get k is minus3 +that's uh um + + align:start position:0% +that's uh um + + + align:start position:0% +that's uh um +spin orbit. + + align:start position:0% +spin orbit. + + + align:start position:0% +spin orbit. +And it turns out for k of minus3 and all + + align:start position:0% +And it turns out for k of minus3 and all + + + align:start position:0% +And it turns out for k of minus3 and all +small all other values of k smaller than + + align:start position:0% +small all other values of k smaller than + + + align:start position:0% +small all other values of k smaller than +three you get basically an n to the + + align:start position:0% +three you get basically an n to the + + + align:start position:0% +three you get basically an n to the +minus3. + + align:start position:0% +minus3. + + + align:start position:0% +minus3. +You see for example in the k uh k is + + align:start position:0% +You see for example in the k uh k is + + + align:start position:0% +You see for example in the k uh k is +minus4 you get an n^2 in the numerator + + align:start position:0% +minus4 you get an n^2 in the numerator + + + align:start position:0% +minus4 you get an n^2 in the numerator +and an n to the five in the denominator + + align:start position:0% +and an n to the five in the denominator + + + align:start position:0% +and an n to the five in the denominator +that's 10us 3. + + align:start position:0% +that's 10us 3. + + + align:start position:0% +that's 10us 3. +So for everything of higher negative + + align:start position:0% +So for everything of higher negative + + + align:start position:0% +So for everything of higher negative +power than three uh you get this + + align:start position:0% +power than three uh you get this + + + align:start position:0% +power than three uh you get this +basically it's telling you all it cares + + align:start position:0% +basically it's telling you all it cares + + + align:start position:0% +basically it's telling you all it cares +about is what is the amplitude of the + + align:start position:0% +about is what is the amplitude of the + + + align:start position:0% +about is what is the amplitude of the +wave function near the nucleus. + + align:start position:0% +wave function near the nucleus. + + + align:start position:0% +wave function near the nucleus. +And the amplitude of the wave function + + align:start position:0% +And the amplitude of the wave function + + + align:start position:0% +And the amplitude of the wave function +near the nucleus scales as n minus3 + + align:start position:0% +near the nucleus scales as n minus3 + + + align:start position:0% +near the nucleus scales as n minus3 +halves as I will prove next time. And + + align:start position:0% +halves as I will prove next time. And + + + align:start position:0% +halves as I will prove next time. And +that's where you get this universal nus + + align:start position:0% +that's where you get this universal nus + + + align:start position:0% +that's where you get this universal nus +3. + + align:start position:0% +3. + + + align:start position:0% +3. +You never knew that. You never find that + + align:start position:0% +You never knew that. You never find that + + + align:start position:0% +You never knew that. You never find that +in a book. Okay. Um what time is it? + + align:start position:0% +in a book. Okay. Um what time is it? + + + align:start position:0% +in a book. Okay. Um what time is it? +It's time to quit. Uh let me just do one + + align:start position:0% +It's time to quit. Uh let me just do one + + + align:start position:0% +It's time to quit. Uh let me just do one +more thing. + + align:start position:0% + + + + align:start position:0% + +Let's talk about the vector model for a + + align:start position:0% +Let's talk about the vector model for a + + + align:start position:0% +Let's talk about the vector model for a +second or a vector model. + + align:start position:0% + + + + align:start position:0% + +Suppose we have J here and L here and S + + align:start position:0% +Suppose we have J here and L here and S + + + align:start position:0% +Suppose we have J here and L here and S +here. So L + S is J. + + align:start position:0% +here. So L + S is J. + + + align:start position:0% +here. So L + S is J. +Now suppose we stick a photon in uh and + + align:start position:0% +Now suppose we stick a photon in uh and + + + align:start position:0% +Now suppose we stick a photon in uh and +remember the photon only knows about L. + + align:start position:0% +remember the photon only knows about L. + + + align:start position:0% +remember the photon only knows about L. +So we have a choice. We can put a photon + + align:start position:0% +So we have a choice. We can put a photon + + + align:start position:0% +So we have a choice. We can put a photon +in with its angular momentum because + + align:start position:0% +in with its angular momentum because + + + align:start position:0% +in with its angular momentum because +it's like an angular momentum of one + + align:start position:0% +it's like an angular momentum of one + + + align:start position:0% +it's like an angular momentum of one +pointing parallel to L. + + align:start position:0% +pointing parallel to L. + + + align:start position:0% +pointing parallel to L. +So we could do that. + + align:start position:0% + + + + align:start position:0% + +And uh what does that do? Well, it it + + align:start position:0% +And uh what does that do? Well, it it + + + align:start position:0% +And uh what does that do? Well, it it +shifts S up by one and up and so it + + align:start position:0% +shifts S up by one and up and so it + + + align:start position:0% +shifts S up by one and up and so it +increases J by one. Propensity rule. + + align:start position:0% +increases J by one. Propensity rule. + + + align:start position:0% +increases J by one. Propensity rule. +Now, if we do this, if we put in the + + align:start position:0% +Now, if we do this, if we put in the + + + align:start position:0% +Now, if we do this, if we put in the +photon perpendicular to L, well, that + + align:start position:0% +photon perpendicular to L, well, that + + + align:start position:0% +photon perpendicular to L, well, that +doesn't shift S up. + + align:start position:0% +doesn't shift S up. + + + align:start position:0% +doesn't shift S up. +Mhm. + + align:start position:0% +Mhm. + + + align:start position:0% +Mhm. +And J doesn't change. So this simple + + align:start position:0% +And J doesn't change. So this simple + + + align:start position:0% +And J doesn't change. So this simple +diagram as long as L is long compared to + + align:start position:0% +diagram as long as L is long compared to + + + align:start position:0% +diagram as long as L is long compared to +S + + align:start position:0% +S + + + align:start position:0% +S +uh you you get this very strong + + align:start position:0% +uh you you get this very strong + + + align:start position:0% +uh you you get this very strong +propensity rule and so you can you can + + align:start position:0% +propensity rule and so you can you can + + + align:start position:0% +propensity rule and so you can you can +understand why delta J is approximately + + align:start position:0% +understand why delta J is approximately + + + align:start position:0% +understand why delta J is approximately +equal to delta L for transitions. + + align:start position:0% +equal to delta L for transitions. + + + align:start position:0% +equal to delta L for transitions. +There are other more complicated uses of + + align:start position:0% +There are other more complicated uses of + + + align:start position:0% +There are other more complicated uses of +these vectors but that's one of the + + align:start position:0% +these vectors but that's one of the + + + align:start position:0% +these vectors but that's one of the +nicest simplest ones. Okay. And so um + + align:start position:0% +nicest simplest ones. Okay. And so um + + + align:start position:0% +nicest simplest ones. Okay. And so um +I'm going to stop now and tomorrow + + align:start position:0% +I'm going to stop now and tomorrow + + + align:start position:0% +I'm going to stop now and tomorrow +morning I will do a little bit of + + align:start position:0% +morning I will do a little bit of + + + align:start position:0% +morning I will do a little bit of +explanation of the n the minus3 halves + + align:start position:0% +explanation of the n the minus3 halves + + + align:start position:0% +explanation of the n the minus3 halves +amplitude factor for the amplitude of + + align:start position:0% +amplitude factor for the amplitude of + + + align:start position:0% +amplitude factor for the amplitude of +the wave function near the eye core. + + align:start position:0% +the wave function near the eye core. + + + align:start position:0% +the wave function near the eye core. +That's beginning of quantity theory say. + + align:start position:0% +That's beginning of quantity theory say. + + + align:start position:0% +That's beginning of quantity theory say. +So, I'm looking at the notes on uh page + + align:start position:0% +So, I'm looking at the notes on uh page + + + align:start position:0% +So, I'm looking at the notes on uh page +three, and at the very bottom, there's + + align:start position:0% +three, and at the very bottom, there's + + + align:start position:0% +three, and at the very bottom, there's +the H1 and lithium 3 and sodium 11 + + align:start position:0% +the H1 and lithium 3 and sodium 11 + + + align:start position:0% +the H1 and lithium 3 and sodium 11 +energy levels. + + align:start position:0% +energy levels. + + + align:start position:0% +energy levels. +And you say that it obeys the Z to the + + align:start position:0% +And you say that it obeys the Z to the + + + align:start position:0% +And you say that it obeys the Z to the +4th scaling relationship very + + align:start position:0% +4th scaling relationship very + + + align:start position:0% +4th scaling relationship very +accurately. + + align:start position:0% +accurately. + + + align:start position:0% +accurately. +I didn't say that. I said it ought to. + + align:start position:0% +I didn't say that. I said it ought to. + + + align:start position:0% +I didn't say that. I said it ought to. +Does it or + + align:start position:0% +Does it or + + + align:start position:0% +Does it or +Okay. So, so this is sort of curiosity. + + align:start position:0% +Okay. So, so this is sort of curiosity. + + + align:start position:0% +Okay. So, so this is sort of curiosity. +So the um exact relationship for the + + align:start position:0% +So the um exact relationship for the + + + align:start position:0% +So the um exact relationship for the +first two should be 1 to 81. It's + + align:start position:0% +first two should be 1 to 81. It's + + + align:start position:0% +first two should be 1 to 81. It's +actually 1 to 81.967. + + align:start position:0% +actually 1 to 81.967. + + + align:start position:0% +actually 1 to 81.967. +So basically 1 to 82. + + align:start position:0% +So basically 1 to 82. + + + align:start position:0% +So basically 1 to 82. +Well, but 30 is I just wrote 30 down. I + + align:start position:0% +Well, but 30 is I just wrote 30 down. I + + + align:start position:0% +Well, but 30 is I just wrote 30 down. I +don't even know how I got that 30 + + align:start position:0% +don't even know how I got that 30 + + + align:start position:0% +don't even know how I got that 30 +whether. + + align:start position:0% +whether. + + + align:start position:0% +whether. +Oh, really? Okay. + + align:start position:0% +Oh, really? Okay. + + + align:start position:0% +Oh, really? Okay. +Rounded it off. + + align:start position:0% +Rounded it off. + + + align:start position:0% +Rounded it off. +How many significant figures is that + + align:start position:0% +How many significant figures is that + + + align:start position:0% +How many significant figures is that +man? + + align:start position:0% +man? + + + align:start position:0% +man? +All right. All right. So So maybe I'll + + align:start position:0% +All right. All right. So So maybe I'll + + + align:start position:0% +All right. All right. So So maybe I'll +look it up tonight, but And then the + + align:start position:0% +look it up tonight, but And then the + + + align:start position:0% +look it up tonight, but And then the +other one should be 180 and it's 180.75. + + align:start position:0% +other one should be 180 and it's 180.75. + + + align:start position:0% +other one should be 180 and it's 180.75. +So I was just curious + + align:start position:0% +So I was just curious + + + align:start position:0% +So I was just curious +where did I get these numbers? + + align:start position:0% +where did I get these numbers? + + + align:start position:0% +where did I get these numbers? +Well, that was one thing, but also if it + + align:start position:0% +Well, that was one thing, but also if it + + + align:start position:0% +Well, that was one thing, but also if it +doesn't obey it exactly, where else is + + align:start position:0% +doesn't obey it exactly, where else is + + + align:start position:0% +doesn't obey it exactly, where else is +it coming from? Like what what else + + align:start position:0% +it coming from? Like what what else + + + align:start position:0% +it coming from? Like what what else +could be changing? Cuz even if you if + + align:start position:0% +could be changing? Cuz even if you if + + + align:start position:0% +could be changing? Cuz even if you if +you wiggle around the wave numbers a + + align:start position:0% +you wiggle around the wave numbers a + + + align:start position:0% +you wiggle around the wave numbers a +little bit, + + align:start position:0% +little bit, + + + align:start position:0% +little bit, +there's there's still some deviation. So + + align:start position:0% +there's there's still some deviation. So + + + align:start position:0% +there's there's still some deviation. So +is it is it coming from + + align:start position:0% + + + + align:start position:0% + +isotopic effects because you're + + align:start position:0% +isotopic effects because you're + + + align:start position:0% +isotopic effects because you're +measuring you know not just one isotope + + align:start position:0% +measuring you know not just one isotope + + + align:start position:0% +measuring you know not just one isotope +of sodium but a few like what's the + + align:start position:0% +of sodium but a few like what's the + + + align:start position:0% +of sodium but a few like what's the +dominant other thing other than next to + + align:start position:0% +dominant other thing other than next to + + + align:start position:0% +dominant other thing other than next to +the + + align:start position:0% +the + + + align:start position:0% +the +I think relativistic effects + + align:start position:0% +I think relativistic effects + + + align:start position:0% +I think relativistic effects +the I said spin orbit is relativistic + + align:start position:0% +the I said spin orbit is relativistic + + + align:start position:0% +the I said spin orbit is relativistic +but there's several levels of + + align:start position:0% +but there's several levels of + + + align:start position:0% +but there's several levels of +relativistic one is just saying the + + align:start position:0% +relativistic one is just saying the + + + align:start position:0% +relativistic one is just saying the +interaction between this uh this moving + + align:start position:0% +interaction between this uh this moving + + + align:start position:0% +interaction between this uh this moving +magnetic dipole near this charge + + align:start position:0% +magnetic dipole near this charge + + + align:start position:0% +magnetic dipole near this charge +uh that produces an interaction that's + + align:start position:0% +uh that produces an interaction that's + + + align:start position:0% +uh that produces an interaction that's +looks like a dipole dipole interaction. + + align:start position:0% +looks like a dipole dipole interaction. + + + align:start position:0% +looks like a dipole dipole interaction. +Mhm. + + align:start position:0% +Mhm. + + + align:start position:0% +Mhm. +Uh but there is also a contraction of + + align:start position:0% +Uh but there is also a contraction of + + + align:start position:0% +Uh but there is also a contraction of +the + + align:start position:0% +the + + + align:start position:0% +the +thing is is spinning. Yeah. + + align:start position:0% +thing is is spinning. Yeah. + + + align:start position:0% +thing is is spinning. Yeah. +And and so there's it probably the + + align:start position:0% +And and so there's it probably the + + + align:start position:0% +And and so there's it probably the +deviations would probably be of + + align:start position:0% +deviations would probably be of + + + align:start position:0% +deviations would probably be of +relativistic origin. Now, I've been + + align:start position:0% +relativistic origin. Now, I've been + + + align:start position:0% +relativistic origin. Now, I've been +teaching this course for a very long + + align:start position:0% +teaching this course for a very long + + + align:start position:0% +teaching this course for a very long +time, and I don't know where I got those + + align:start position:0% +time, and I don't know where I got those + + + align:start position:0% +time, and I don't know where I got those +numbers. + + align:start position:0% +numbers. + + + align:start position:0% +numbers. +I probably multiplied + + align:start position:0% +I probably multiplied + + + align:start position:0% +I probably multiplied +uh uh Z to the 4 and rounded it off. + + align:start position:0% +uh uh Z to the 4 and rounded it off. + + + align:start position:0% +uh uh Z to the 4 and rounded it off. +And that's pretty good for a one + + align:start position:0% +And that's pretty good for a one + + + align:start position:0% +And that's pretty good for a one +electron system. So, you know, that's + + align:start position:0% +electron system. So, you know, that's + + + align:start position:0% +electron system. So, you know, that's +safe. + + align:start position:0% +safe. + + + align:start position:0% +safe. +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +And you know, you got to be a little bit + + align:start position:0% +And you know, you got to be a little bit + + + align:start position:0% +And you know, you got to be a little bit +crazy to think that sodium with one + + align:start position:0% +crazy to think that sodium with one + + + align:start position:0% +crazy to think that sodium with one +electron is going to be relativistic. + + align:start position:0% +electron is going to be relativistic. + + + align:start position:0% +electron is going to be relativistic. +So I I think I used the formula. I + + align:start position:0% +So I I think I used the formula. I + + + align:start position:0% +So I I think I used the formula. I +didn't look them up. + + align:start position:0% +didn't look them up. + + + align:start position:0% +didn't look them up. +So with your selection rules there, is + + align:start position:0% +So with your selection rules there, is + + + align:start position:0% +So with your selection rules there, is +it worth noting that J prime equals 0 + + align:start position:0% +it worth noting that J prime equals 0 + + + align:start position:0% +it worth noting that J prime equals 0 +and J equals 0 is excluded? + + align:start position:0% + + + + align:start position:0% + +I mean it's kind of a minor point. + + align:start position:0% +I mean it's kind of a minor point. + + + align:start position:0% +I mean it's kind of a minor point. +Oh, but you can get that from this. + + align:start position:0% +Oh, but you can get that from this. + + + align:start position:0% +Oh, but you can get that from this. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +But is it okay? + + align:start position:0% +But is it okay? + + + align:start position:0% +But is it okay? +um + + align:start position:0% +um + + + align:start position:0% +um +you can't have a transition of a vector + + align:start position:0% +you can't have a transition of a vector + + + align:start position:0% +you can't have a transition of a vector +operator, + + align:start position:0% +operator, + + + align:start position:0% +operator, +right? + + align:start position:0% +right? + + + align:start position:0% +right? +Uh so you you have a system which got no + + align:start position:0% +Uh so you you have a system which got no + + + align:start position:0% +Uh so you you have a system which got no +angular momentum. You stick an angular + + align:start position:0% +angular momentum. You stick an angular + + + align:start position:0% +angular momentum. You stick an angular +momentum in it. + + align:start position:0% +momentum in it. + + + align:start position:0% +momentum in it. +It's got to have something. + + align:start position:0% +It's got to have something. + + + align:start position:0% +It's got to have something. +It's going to have an angular momentum. + + align:start position:0% +It's going to have an angular momentum. + + + align:start position:0% +It's going to have an angular momentum. +So this J equals 0 to J equals0 + + align:start position:0% +So this J equals 0 to J equals0 + + + align:start position:0% +So this J equals 0 to J equals0 +transition has to be forbidden, + + align:start position:0% +transition has to be forbidden, + + + align:start position:0% +transition has to be forbidden, +right? + + align:start position:0% +right? + + + align:start position:0% +right? +For electric dipoles. + + align:start position:0% +For electric dipoles. + + + align:start position:0% +For electric dipoles. +Yes. + + align:start position:0% + + + + align:start position:0% + +Does that vector model hold? So that + + align:start position:0% +Does that vector model hold? So that + + + align:start position:0% +Does that vector model hold? So that +vector model is true when L is large. + + align:start position:0% +vector model is true when L is large. + + + align:start position:0% +vector model is true when L is large. +I said that I but when I said it I + + align:start position:0% +I said that I but when I said it I + + + align:start position:0% +I said that I but when I said it I +thought well how do I where did they + + align:start position:0% +thought well how do I where did they + + + align:start position:0% +thought well how do I where did they +okay + + align:start position:0% +okay + + + align:start position:0% +okay +it was my memory + + align:start position:0% +it was my memory + + + align:start position:0% +it was my memory +unchecked which you know could be wrong + + align:start position:0% +unchecked which you know could be wrong + + + align:start position:0% +unchecked which you know could be wrong +but I think + + align:start position:0% +but I think + + + align:start position:0% +but I think +but when but when L is + + align:start position:0% +but when but when L is + + + align:start position:0% +but when but when L is +you know if it's like an S or a P + + align:start position:0% +you know if it's like an S or a P + + + align:start position:0% +you know if it's like an S or a P +orbital then that propensity rule does + + align:start position:0% +orbital then that propensity rule does + + + align:start position:0% +orbital then that propensity rule does +not hold as well + + align:start position:0% +not hold as well + + + align:start position:0% +not hold as well +when L and S are about the same length + + align:start position:0% +when L and S are about the same length + + + align:start position:0% +when L and S are about the same length +I think that uh uh it the relative uh uh + + align:start position:0% +I think that uh uh it the relative uh uh + + + align:start position:0% +I think that uh uh it the relative uh uh +intensity of propensity rule + + align:start position:0% +intensity of propensity rule + + + align:start position:0% +intensity of propensity rule +uh violating a propensity rule obeying + + align:start position:0% +uh violating a propensity rule obeying + + + align:start position:0% +uh violating a propensity rule obeying +transitions are about the same. + + align:start position:0% +transitions are about the same. + + + align:start position:0% +transitions are about the same. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Okay. And you don't really need this + + align:start position:0% +Okay. And you don't really need this + + + align:start position:0% +Okay. And you don't really need this +because + + align:start position:0% +because + + + align:start position:0% +because +uh we can also derive these formulas + + align:start position:0% +uh we can also derive these formulas + + + align:start position:0% +uh we can also derive these formulas +using angular momentum coupling. And so + + align:start position:0% +using angular momentum coupling. And so + + + align:start position:0% +using angular momentum coupling. And so +the matrix the explicit dependence of + + align:start position:0% +the matrix the explicit dependence of + + + align:start position:0% +the matrix the explicit dependence of +the transition probability + + align:start position:0% +the transition probability + + + align:start position:0% +the transition probability +uh on uh J L and S that can be worked + + align:start position:0% +uh on uh J L and S that can be worked + + + align:start position:0% +uh on uh J L and S that can be worked +out in a universal sense. So but it's + + align:start position:0% +out in a universal sense. So but it's + + + align:start position:0% +out in a universal sense. So but it's +nice to be able to to say okay what's + + align:start position:0% +nice to be able to to say okay what's + + + align:start position:0% +nice to be able to to say okay what's +this trying to do and uh so any but I + + align:start position:0% +this trying to do and uh so any but I + + + align:start position:0% +this trying to do and uh so any but I +must admit I made that statement without + + align:start position:0% +must admit I made that statement without + + + align:start position:0% +must admit I made that statement without +working it out but I'm pretty sure it + + align:start position:0% +working it out but I'm pretty sure it + + + align:start position:0% +working it out but I'm pretty sure it +was correct. It is correct. + + align:start position:0% + + + + align:start position:0% + +Are we + + align:start position:0% +Are we + + + align:start position:0% +Are we +content? So, tomorrow morning early I + + align:start position:0% +content? So, tomorrow morning early I + + + align:start position:0% +content? So, tomorrow morning early I +will attempt to uh finish talk about + + align:start position:0% +will attempt to uh finish talk about + + + align:start position:0% +will attempt to uh finish talk about +alkali like uh spectra and uh uh begin + + align:start position:0% +alkali like uh spectra and uh uh begin + + + align:start position:0% +alkali like uh spectra and uh uh begin +bringing in some of the concepts of + + align:start position:0% +bringing in some of the concepts of + + + align:start position:0% +bringing in some of the concepts of +photo detector. + + align:start position:0% +photo detector. + + + align:start position:0% +photo detector. +See you then. \ No newline at end of file diff --git a/yv0KsBKJzKY.txt b/yv0KsBKJzKY.txt new file mode 100644 index 0000000000000000000000000000000000000000..bd521cdb4c12325c9057bf22b1d9bd20852986d7 --- /dev/null +++ b/yv0KsBKJzKY.txt @@ -0,0 +1,9699 @@ +align:start position:0% + +so after doing aslm in the first part of + + align:start position:0% +so after doing aslm in the first part of + + + align:start position:0% +so after doing aslm in the first part of +the course and where we took prices + + align:start position:0% +the course and where we took prices + + + align:start position:0% +the course and where we took prices +completely sticky and output was fully + + align:start position:0% +completely sticky and output was fully + + + align:start position:0% +completely sticky and output was fully +determined by aggregate demand uh we + + align:start position:0% +determined by aggregate demand uh we + + + align:start position:0% +determined by aggregate demand uh we +said well that minates in the very very + + align:start position:0% +said well that minates in the very very + + + align:start position:0% +said well that minates in the very very +short run but but over time at some + + align:start position:0% +short run but but over time at some + + + align:start position:0% +short run but but over time at some +point the supply side start showing up + + align:start position:0% +point the supply side start showing up + + + align:start position:0% +point the supply side start showing up +there are constraints the labor market + + align:start position:0% +there are constraints the labor market + + + align:start position:0% +there are constraints the labor market +gets very tight and so on and and so we + + align:start position:0% +gets very tight and so on and and so we + + + align:start position:0% +gets very tight and so on and and so we +added a block that started from wage + + align:start position:0% +added a block that started from wage + + + align:start position:0% +added a block that started from wage +determination and then we look at the + + align:start position:0% +determination and then we look at the + + + align:start position:0% +determination and then we look at the +impact of wages on + + align:start position:0% +impact of wages on + + + align:start position:0% +impact of wages on +prices and then we related inflation + + align:start position:0% +prices and then we related inflation + + + align:start position:0% +prices and then we related inflation +rate use that to relate inflation rate + + align:start position:0% +rate use that to relate inflation rate + + + align:start position:0% +rate use that to relate inflation rate +to economic activity so output above or + + align:start position:0% +to economic activity so output above or + + + align:start position:0% +to economic activity so output above or +below the potential output or or the + + align:start position:0% +below the potential output or or the + + + align:start position:0% +below the potential output or or the +natural level of output and things of + + align:start position:0% +natural level of output and things of + + + align:start position:0% +natural level of output and things of +that kind so remember the starting point + + align:start position:0% +that kind so remember the starting point + + + align:start position:0% +that kind so remember the starting point +was a um a wage + + align:start position:0% +was a um a wage + + + align:start position:0% +was a um a wage +demand equations so what what workers + + align:start position:0% +demand equations so what what workers + + + align:start position:0% +demand equations so what what workers +demand for a wage this period depends on + + align:start position:0% +demand for a wage this period depends on + + + align:start position:0% +demand for a wage this period depends on +how what's the price level they expect + + align:start position:0% +how what's the price level they expect + + + align:start position:0% +how what's the price level they expect +for the period because they set the wage + + align:start position:0% +for the period because they set the wage + + + align:start position:0% +for the period because they set the wage +today and they have to leave through the + + align:start position:0% +today and they have to leave through the + + + align:start position:0% +today and they have to leave through the +year or to whatever is the Contracting + + align:start position:0% +year or to whatever is the Contracting + + + align:start position:0% +year or to whatever is the Contracting +period H with that nominal wage so + + align:start position:0% +period H with that nominal wage so + + + align:start position:0% +period H with that nominal wage so +naturally if if they expect higher price + + align:start position:0% +naturally if if they expect higher price + + + align:start position:0% +naturally if if they expect higher price +level in the future they're going to + + align:start position:0% +level in the future they're going to + + + align:start position:0% +level in the future they're going to +demand the higher nominal wage today and + + align:start position:0% +demand the higher nominal wage today and + + + align:start position:0% +demand the higher nominal wage today and +then we said that's a funion that is + + align:start position:0% +then we said that's a funion that is + + + align:start position:0% +then we said that's a funion that is +also going to be decreasing in the level + + align:start position:0% +also going to be decreasing in the level + + + align:start position:0% +also going to be decreasing in the level +of unemployment because the obviously + + align:start position:0% +of unemployment because the obviously + + + align:start position:0% +of unemployment because the obviously +that weakens bargaining for power for + + align:start position:0% +that weakens bargaining for power for + + + align:start position:0% +that weakens bargaining for power for +workers or makes makes actually becoming + + align:start position:0% +workers or makes makes actually becoming + + + align:start position:0% +workers or makes makes actually becoming +unemployed or not having a job H more + + align:start position:0% +unemployed or not having a job H more + + + align:start position:0% +unemployed or not having a job H more +costly because it's very difficult to + + align:start position:0% +costly because it's very difficult to + + + align:start position:0% +costly because it's very difficult to +exit out of unemployment and then we + + align:start position:0% +exit out of unemployment and then we + + + align:start position:0% +exit out of unemployment and then we +made us an normalization this function + + align:start position:0% +made us an normalization this function + + + align:start position:0% +made us an normalization this function +also an increasing function on this + + align:start position:0% +also an increasing function on this + + + align:start position:0% +also an increasing function on this +variable Z which captures a bunch of + + align:start position:0% +variable Z which captures a bunch of + + + align:start position:0% +variable Z which captures a bunch of +Labor Market institutions including wage + + align:start position:0% +Labor Market institutions including wage + + + align:start position:0% +Labor Market institutions including wage +labor bargaining power so more + + align:start position:0% +labor bargaining power so more + + + align:start position:0% +labor bargaining power so more +bargaining power means that for any + + align:start position:0% +bargaining power means that for any + + + align:start position:0% +bargaining power means that for any +given level of unemployment workers + + align:start position:0% +given level of unemployment workers + + + align:start position:0% +given level of unemployment workers +would tend to demand a higher wage okay + + align:start position:0% +would tend to demand a higher wage okay + + + align:start position:0% +would tend to demand a higher wage okay +so that's what the Z variable was all + + align:start position:0% +so that's what the Z variable was all + + + align:start position:0% +so that's what the Z variable was all +about then we wanted to go from wages to + + align:start position:0% +about then we wanted to go from wages to + + + align:start position:0% +about then we wanted to go from wages to +prices H because the ultimate goal was + + align:start position:0% +prices H because the ultimate goal was + + + align:start position:0% +prices H because the ultimate goal was +to bring inflation into the picture and + + align:start position:0% +to bring inflation into the picture and + + + align:start position:0% +to bring inflation into the picture and +and for that we have to produce a we we + + align:start position:0% +and for that we have to produce a we we + + + align:start position:0% +and for that we have to produce a we we +introduce a production function H + + align:start position:0% +introduce a production function H + + + align:start position:0% +introduce a production function H +because uh in particular out we made + + align:start position:0% +because uh in particular out we made + + + align:start position:0% +because uh in particular out we made +output a function of employment and and + + align:start position:0% +output a function of employment and and + + + align:start position:0% +output a function of employment and and +that very naturally will connect wage + + align:start position:0% +that very naturally will connect wage + + + align:start position:0% +that very naturally will connect wage +pressure to price pressure because you + + align:start position:0% +pressure to price pressure because you + + + align:start position:0% +pressure to price pressure because you +know you need labor to produce output so + + align:start position:0% +know you need labor to produce output so + + + align:start position:0% +know you need labor to produce output so +the labor market is very tight that + + align:start position:0% +the labor market is very tight that + + + align:start position:0% +the labor market is very tight that +means also it's going to be more + + align:start position:0% +means also it's going to be more + + + align:start position:0% +means also it's going to be more +expensive to produce output and we + + align:start position:0% +expensive to produce output and we + + + align:start position:0% +expensive to produce output and we +simplifi this production function a lot + + align:start position:0% +simplifi this production function a lot + + + align:start position:0% +simplifi this production function a lot +we made it output equal to employment + + align:start position:0% +we made it output equal to employment + + + align:start position:0% +we made it output equal to employment +and that meant also that one unit of + + align:start position:0% +and that meant also that one unit of + + + align:start position:0% +and that meant also that one unit of +Labor in order to produce one extra unit + + align:start position:0% +Labor in order to produce one extra unit + + + align:start position:0% +Labor in order to produce one extra unit +of output you need one extra unit of + + align:start position:0% +of output you need one extra unit of + + + align:start position:0% +of output you need one extra unit of +label which means you need to pay a wage + + align:start position:0% +label which means you need to pay a wage + + + align:start position:0% +label which means you need to pay a wage +okay one one one unit of the wage and so + + align:start position:0% +okay one one one unit of the wage and so + + + align:start position:0% +okay one one one unit of the wage and so +then we said suppose that the price + + align:start position:0% +then we said suppose that the price + + + align:start position:0% +then we said suppose that the price +setting from the side of the firms + + align:start position:0% +setting from the side of the firms + + + align:start position:0% +setting from the side of the firms +simply takes this cost which is the wage + + align:start position:0% +simply takes this cost which is the wage + + + align:start position:0% +simply takes this cost which is the wage +and adds a markup to it to pay for a + + align:start position:0% +and adds a markup to it to pay for a + + + align:start position:0% +and adds a markup to it to pay for a +bunch of other things that we haven't + + align:start position:0% +bunch of other things that we haven't + + + align:start position:0% +bunch of other things that we haven't +introduced in this model okay so the + + align:start position:0% +introduced in this model okay so the + + + align:start position:0% +introduced in this model okay so the +price charged by firms is equal to the + + align:start position:0% +price charged by firms is equal to the + + + align:start position:0% +price charged by firms is equal to the +wage times one plus some positive + + align:start position:0% +wage times one plus some positive + + + align:start position:0% +wage times one plus some positive +numbers 8.2 or something like that so + + align:start position:0% +numbers 8.2 or something like that so + + + align:start position:0% +numbers 8.2 or something like that so +1.2 H and we can write rewrite this + + align:start position:0% +1.2 H and we can write rewrite this + + + align:start position:0% +1.2 H and we can write rewrite this +price setting equation as a wage the + + align:start position:0% +price setting equation as a wage the + + + align:start position:0% +price setting equation as a wage the +real wage the firms are willing to offer + + align:start position:0% +real wage the firms are willing to offer + + + align:start position:0% +real wage the firms are willing to offer +and it's just equal to that okay so when + + align:start position:0% +and it's just equal to that okay so when + + + align:start position:0% +and it's just equal to that okay so when +the markup goes up that means the real + + align:start position:0% +the markup goes up that means the real + + + align:start position:0% +the markup goes up that means the real +wage the firms are willing to offer is + + align:start position:0% +wage the firms are willing to offer is + + + align:start position:0% +wage the firms are willing to offer is +lower than + + align:start position:0% + + + + align:start position:0% + +otherwise okay that took us to the + + align:start position:0% +otherwise okay that took us to the + + + align:start position:0% +otherwise okay that took us to the +concept of the natural rate of + + align:start position:0% +concept of the natural rate of + + + align:start position:0% +concept of the natural rate of +unemployment and and and what the + + align:start position:0% +unemployment and and and what the + + + align:start position:0% +unemployment and and and what the +natural what I said no is there's + + align:start position:0% +natural what I said no is there's + + + align:start position:0% +natural what I said no is there's +nothing natural about the natural rate + + align:start position:0% +nothing natural about the natural rate + + + align:start position:0% +nothing natural about the natural rate +of unemployment it's simply a definition + + align:start position:0% +of unemployment it's simply a definition + + + align:start position:0% +of unemployment it's simply a definition +that says that's an employment that + + align:start position:0% +that says that's an employment that + + + align:start position:0% +that says that's an employment that +results when the price expected price is + + align:start position:0% +results when the price expected price is + + + align:start position:0% +results when the price expected price is +equal to the actual price that's that's + + align:start position:0% +equal to the actual price that's that's + + + align:start position:0% +equal to the actual price that's that's +what that's all that that is and if when + + align:start position:0% +what that's all that that is and if when + + + align:start position:0% +what that's all that that is and if when +when we have that condition then we can + + align:start position:0% +when we have that condition then we can + + + align:start position:0% +when we have that condition then we can +think of the real wage demanded by work + + align:start position:0% +think of the real wage demanded by work + + + align:start position:0% +think of the real wage demanded by work +because I can replace expected price for + + align:start position:0% +because I can replace expected price for + + + align:start position:0% +because I can replace expected price for +actual price and divide both sides by + + align:start position:0% +actual price and divide both sides by + + + align:start position:0% +actual price and divide both sides by +price so the actual wage demanded by + + align:start position:0% +price so the actual wage demanded by + + + align:start position:0% +price so the actual wage demanded by +workers is equal to a function of the + + align:start position:0% +workers is equal to a function of the + + + align:start position:0% +workers is equal to a function of the +natural rate of unemployment and I stick + + align:start position:0% +natural rate of unemployment and I stick + + + align:start position:0% +natural rate of unemployment and I stick +the end there precisely because I + + align:start position:0% +the end there precisely because I + + + align:start position:0% +the end there precisely because I +replace expected price or P for no other + + align:start position:0% +replace expected price or P for no other + + + align:start position:0% +replace expected price or P for no other +reason okay but now we have two + + align:start position:0% +reason okay but now we have two + + + align:start position:0% +reason okay but now we have two +equations for the real wage the real + + align:start position:0% +equations for the real wage the real + + + align:start position:0% +equations for the real wage the real +wage that firms are willing to pay and + + align:start position:0% +wage that firms are willing to pay and + + + align:start position:0% +wage that firms are willing to pay and +the real weight of workers need to + + align:start position:0% +the real weight of workers need to + + + align:start position:0% +the real weight of workers need to +demand and we can make them both equal + + align:start position:0% +demand and we can make them both equal + + + align:start position:0% +demand and we can make them both equal +and that determines the natural rate of + + align:start position:0% +and that determines the natural rate of + + + align:start position:0% +and that determines the natural rate of +unemployment okay so remember this from + + align:start position:0% +unemployment okay so remember this from + + + align:start position:0% +unemployment okay so remember this from +the point of view of the firm this is + + align:start position:0% +the point of view of the firm this is + + + align:start position:0% +the point of view of the firm this is +equal to one over one plus a marup the + + align:start position:0% +equal to one over one plus a marup the + + + align:start position:0% +equal to one over one plus a marup the +only endogenous variable the marup is a + + align:start position:0% +only endogenous variable the marup is a + + + align:start position:0% +only endogenous variable the marup is a +constant the Z is also a parameter is + + align:start position:0% +constant the Z is also a parameter is + + + align:start position:0% +constant the Z is also a parameter is +exogenous and so from the here we can + + align:start position:0% +exogenous and so from the here we can + + + align:start position:0% +exogenous and so from the here we can +solve the natural rate of unemployment 1 + + align:start position:0% +solve the natural rate of unemployment 1 + + + align:start position:0% +solve the natural rate of unemployment 1 +over 1 plus M and we can solve the + + align:start position:0% +over 1 plus M and we can solve the + + + align:start position:0% +over 1 plus M and we can solve the +natural rate of unemployment and if you + + align:start position:0% +natural rate of unemployment and if you + + + align:start position:0% +natural rate of unemployment and if you +do the algebra right you you're going to + + align:start position:0% +do the algebra right you you're going to + + + align:start position:0% +do the algebra right you you're going to +get to a point like that that pins down + + align:start position:0% +get to a point like that that pins down + + + align:start position:0% +get to a point like that that pins down +natural rate of unemployment again there + + align:start position:0% +natural rate of unemployment again there + + + align:start position:0% +natural rate of unemployment again there +is nothing natural about the natural + + align:start position:0% +is nothing natural about the natural + + + align:start position:0% +is nothing natural about the natural +rate of unemployment it depends on a + + align:start position:0% +rate of unemployment it depends on a + + + align:start position:0% +rate of unemployment it depends on a +bunch of parameters okay which for + + align:start position:0% +bunch of parameters okay which for + + + align:start position:0% +bunch of parameters okay which for +example it clearly depends on the markup + + align:start position:0% +example it clearly depends on the markup + + + align:start position:0% +example it clearly depends on the markup +it depends on things that we took as + + align:start position:0% +it depends on things that we took as + + + align:start position:0% +it depends on things that we took as +constant here as given here all the + + align:start position:0% +constant here as given here all the + + + align:start position:0% +constant here as given here all the +things that wear in Z those are part of + + align:start position:0% +things that wear in Z those are part of + + + align:start position:0% +things that wear in Z those are part of +that and so we then we look at things + + align:start position:0% +that and so we then we look at things + + + align:start position:0% +that and so we then we look at things +that change and that's just done with + + align:start position:0% +that change and that's just done with + + + align:start position:0% +that change and that's just done with +equations we look at things that change + + align:start position:0% +equations we look at things that change + + + align:start position:0% +equations we look at things that change +the natural rate of unemployment that's + + align:start position:0% +the natural rate of unemployment that's + + + align:start position:0% +the natural rate of unemployment that's +one example if bargaining Power by + + align:start position:0% +one example if bargaining Power by + + + align:start position:0% +one example if bargaining Power by +workers goes up they're going to demand + + align:start position:0% +workers goes up they're going to demand + + + align:start position:0% +workers goes up they're going to demand +a higher wage at the initial natural + + align:start position:0% +a higher wage at the initial natural + + + align:start position:0% +a higher wage at the initial natural +rate of unemployment well that obviously + + align:start position:0% +rate of unemployment well that obviously + + + align:start position:0% +rate of unemployment well that obviously +that higher wage is inconsistent with + + align:start position:0% +that higher wage is inconsistent with + + + align:start position:0% +that higher wage is inconsistent with +what firms are willing to pay the only + + align:start position:0% +what firms are willing to pay the only + + + align:start position:0% +what firms are willing to pay the only +way equilibrium can be restor in this + + align:start position:0% +way equilibrium can be restor in this + + + align:start position:0% +way equilibrium can be restor in this +model that's the medium run equilibrium + + align:start position:0% +model that's the medium run equilibrium + + + align:start position:0% +model that's the medium run equilibrium +is for the natural rate of unemployment + + align:start position:0% +is for the natural rate of unemployment + + + align:start position:0% +is for the natural rate of unemployment +to rise to un Prime okay + + align:start position:0% +to rise to un Prime okay + + + align:start position:0% +to rise to un Prime okay +so there you have it nothing natural the + + align:start position:0% +so there you have it nothing natural the + + + align:start position:0% +so there you have it nothing natural the +natural rate of employ is not constant + + align:start position:0% +natural rate of employ is not constant + + + align:start position:0% +natural rate of employ is not constant +it depends on institutional parameters + + align:start position:0% +it depends on institutional parameters + + + align:start position:0% +it depends on institutional parameters +such as bargaining power another example + + align:start position:0% +such as bargaining power another example + + + align:start position:0% +such as bargaining power another example +is markups it depends on markups as well + + align:start position:0% +is markups it depends on markups as well + + + align:start position:0% +is markups it depends on markups as well +the degree of competition if you will in + + align:start position:0% +the degree of competition if you will in + + + align:start position:0% +the degree of competition if you will in +the Goods Market if if we are in some + + align:start position:0% +the Goods Market if if we are in some + + + align:start position:0% +the Goods Market if if we are in some +equilibrium like this one and now + + align:start position:0% +equilibrium like this one and now + + + align:start position:0% +equilibrium like this one and now +suddenly firms for whatever + + align:start position:0% +suddenly firms for whatever + + + align:start position:0% +suddenly firms for whatever +reason choose or need to charge a higher + + align:start position:0% +reason choose or need to charge a higher + + + align:start position:0% +reason choose or need to charge a higher +markup that h means that that at this + + align:start position:0% +markup that h means that that at this + + + align:start position:0% +markup that h means that that at this +level of unemploy the wage that workers + + align:start position:0% +level of unemploy the wage that workers + + + align:start position:0% +level of unemploy the wage that workers +would demand is higher than the wage + + align:start position:0% +would demand is higher than the wage + + + align:start position:0% +would demand is higher than the wage +that firms are willing to pay the real + + align:start position:0% +that firms are willing to pay the real + + + align:start position:0% +that firms are willing to pay the real +wage and the only thing that can clear + + align:start position:0% +wage and the only thing that can clear + + + align:start position:0% +wage and the only thing that can clear +the market in this case here in the + + align:start position:0% +the market in this case here in the + + + align:start position:0% +the market in this case here in the +medium run is for the natural rate of + + align:start position:0% +medium run is for the natural rate of + + + align:start position:0% +medium run is for the natural rate of +unemployment to rise okay so here we got + + align:start position:0% +unemployment to rise okay so here we got + + + align:start position:0% +unemployment to rise okay so here we got +two experiments where we move some + + align:start position:0% +two experiments where we move some + + + align:start position:0% +two experiments where we move some +parameter one the bargaining power of + + align:start position:0% +parameter one the bargaining power of + + + align:start position:0% +parameter one the bargaining power of +workers and the other one the the markup + + align:start position:0% +workers and the other one the the markup + + + align:start position:0% +workers and the other one the the markup +of the firms and both increase the + + align:start position:0% +of the firms and both increase the + + + align:start position:0% +of the firms and both increase the +natural rate of unemployment + + align:start position:0% +natural rate of unemployment + + + align:start position:0% +natural rate of unemployment +good The Next Step was + + align:start position:0% +good The Next Step was + + + align:start position:0% +good The Next Step was +to look at things that happen outside + + align:start position:0% +to look at things that happen outside + + + align:start position:0% +to look at things that happen outside +the natural rate of unemployment and + + align:start position:0% +the natural rate of unemployment and + + + align:start position:0% +the natural rate of unemployment and +particular what happens to prices there + + align:start position:0% +particular what happens to prices there + + + align:start position:0% +particular what happens to prices there +okay we look so what we did is we took + + align:start position:0% +okay we look so what we did is we took + + + align:start position:0% +okay we look so what we did is we took +the we went back to the + + align:start position:0% +the we went back to the + + + align:start position:0% +the we went back to the +model with the expected price here that + + align:start position:0% +model with the expected price here that + + + align:start position:0% +model with the expected price here that +means an employment that comes out from + + align:start position:0% +means an employment that comes out from + + + align:start position:0% +means an employment that comes out from +this equilibrium is not is not going to + + align:start position:0% +this equilibrium is not is not going to + + + align:start position:0% +this equilibrium is not is not going to +be necessarily the natural rate of an + + align:start position:0% +be necessarily the natural rate of an + + + align:start position:0% +be necessarily the natural rate of an +employment that will be the case only if + + align:start position:0% +employment that will be the case only if + + + align:start position:0% +employment that will be the case only if +P happens to be equal to p h then we + + align:start position:0% +P happens to be equal to p h then we + + + align:start position:0% +P happens to be equal to p h then we +simplify this function f here for + + align:start position:0% +simplify this function f here for + + + align:start position:0% +simplify this function f here for +something linear like this very simple + + align:start position:0% +something linear like this very simple + + + align:start position:0% +something linear like this very simple +but again decreasing in unemployment + + align:start position:0% +but again decreasing in unemployment + + + align:start position:0% +but again decreasing in unemployment +increasing in this institutional + + align:start position:0% +increasing in this institutional + + + align:start position:0% +increasing in this institutional +parameters + + align:start position:0% +parameters + + + align:start position:0% +parameters +z h we replace this wage here from this + + align:start position:0% +z h we replace this wage here from this + + + align:start position:0% +z h we replace this wage here from this +expression here and rearrange so we got + + align:start position:0% +expression here and rearrange so we got + + + align:start position:0% +expression here and rearrange so we got +this + + align:start position:0% +this + + + align:start position:0% +this +here okay and the next step was just to + + align:start position:0% +here okay and the next step was just to + + + align:start position:0% +here okay and the next step was just to +go from here to rate of inflation and we + + align:start position:0% +go from here to rate of inflation and we + + + align:start position:0% +go from here to rate of inflation and we +did it through a SE several steps and + + align:start position:0% +did it through a SE several steps and + + + align:start position:0% +did it through a SE several steps and +approximations and we ended up with what + + align:start position:0% +approximations and we ended up with what + + + align:start position:0% +approximations and we ended up with what +is known as the Philips curve okay so + + align:start position:0% +is known as the Philips curve okay so + + + align:start position:0% +is known as the Philips curve okay so +this say inflation is increasing an + + align:start position:0% +this say inflation is increasing an + + + align:start position:0% +this say inflation is increasing an +expected inflation on these + + align:start position:0% +expected inflation on these + + + align:start position:0% +expected inflation on these +institutional parameters if the markups + + align:start position:0% +institutional parameters if the markups + + + align:start position:0% +institutional parameters if the markups +go up that will tend to + + align:start position:0% +go up that will tend to + + + align:start position:0% +go up that will tend to +increase inflation H if bargaining Power + + align:start position:0% +increase inflation H if bargaining Power + + + align:start position:0% +increase inflation H if bargaining Power +by workers go up then that's the same + + align:start position:0% +by workers go up then that's the same + + + align:start position:0% +by workers go up then that's the same +but most importantly is negatively + + align:start position:0% +but most importantly is negatively + + + align:start position:0% +but most importantly is negatively +related to unemployment and that's the + + align:start position:0% +related to unemployment and that's the + + + align:start position:0% +related to unemployment and that's the +reason that today nowadays you know + + align:start position:0% +reason that today nowadays you know + + + align:start position:0% +reason that today nowadays you know +there's lots of discussion about the + + align:start position:0% +there's lots of discussion about the + + + align:start position:0% +there's lots of discussion about the +tightness in the labor market and and + + align:start position:0% +tightness in the labor market and and + + + align:start position:0% +tightness in the labor market and and +whether that's really necessary do we + + align:start position:0% +whether that's really necessary do we + + + align:start position:0% +whether that's really necessary do we +need to cause a recession a situation + + align:start position:0% +need to cause a recession a situation + + + align:start position:0% +need to cause a recession a situation +where an employment goes up a lot in + + align:start position:0% +where an employment goes up a lot in + + + align:start position:0% +where an employment goes up a lot in +order to really finally bring down + + align:start position:0% +order to really finally bring down + + + align:start position:0% +order to really finally bring down +inflation yeah that's was + + align:start position:0% +inflation yeah that's was + + + align:start position:0% +inflation yeah that's was +question is + + align:start position:0% +question is + + + align:start position:0% +question is +alha oh remember that I made up this + + align:start position:0% +alha oh remember that I made up this + + + align:start position:0% +alha oh remember that I made up this +function we said this function is + + align:start position:0% +function we said this function is + + + align:start position:0% +function we said this function is +decreasing + + align:start position:0% +decreasing + + + align:start position:0% +decreasing +unemployment I just + + align:start position:0% +unemployment I just + + + align:start position:0% +unemployment I just +uh replace that function for that + + align:start position:0% +uh replace that function for that + + + align:start position:0% +uh replace that function for that +okay so it's a sensitivity of wage + + align:start position:0% +okay so it's a sensitivity of wage + + + align:start position:0% +okay so it's a sensitivity of wage +Demand by workers to their employment + + align:start position:0% +Demand by workers to their employment + + + align:start position:0% +Demand by workers to their employment +rate Alpha that is very high means that + + align:start position:0% +rate Alpha that is very high means that + + + align:start position:0% +rate Alpha that is very high means that +wage demand is very sensitive very + + align:start position:0% +wage demand is very sensitive very + + + align:start position:0% +wage demand is very sensitive very +responsive to unemployment y intuition + + align:start position:0% +responsive to unemployment y intuition + + + align:start position:0% +responsive to unemployment y intuition +for like an expected price like could + + align:start position:0% +for like an expected price like could + + + align:start position:0% +for like an expected price like could +you connect that back to like I don't + + align:start position:0% +you connect that back to like I don't + + + align:start position:0% +you connect that back to like I don't +know some sort of like a commodity or + + align:start position:0% +know some sort of like a commodity or + + + align:start position:0% +know some sort of like a commodity or +something or so what is the intuition + + align:start position:0% +something or so what is the intuition + + + align:start position:0% +something or so what is the intuition +for for this yeah like just like a price + + align:start position:0% +for for this yeah like just like a price + + + align:start position:0% +for for this yeah like just like a price +feels tactile but like an expected price + + align:start position:0% +feels tactile but like an expected price + + + align:start position:0% +feels tactile but like an expected price +I don't well I mean imagine that workers + + align:start position:0% +I don't well I mean imagine that workers + + + align:start position:0% +I don't well I mean imagine that workers +and firms bargain for a wage that will + + align:start position:0% +and firms bargain for a wage that will + + + align:start position:0% +and firms bargain for a wage that will +live through the year you're buying by + + align:start position:0% +live through the year you're buying by + + + align:start position:0% +live through the year you're buying by +you're bargaining for the wage nominal + + align:start position:0% +you're bargaining for the wage nominal + + + align:start position:0% +you're bargaining for the wage nominal +wage today you don't set a real wage you + + align:start position:0% +wage today you don't set a real wage you + + + align:start position:0% +wage today you don't set a real wage you +set the nominal wage say $100 whatever + + align:start position:0% +set the nominal wage say $100 whatever + + + align:start position:0% +set the nominal wage say $100 whatever +well the wage demand will depend a lot + + align:start position:0% +well the wage demand will depend a lot + + + align:start position:0% +well the wage demand will depend a lot +on on what I expect inflation to be + + align:start position:0% +on on what I expect inflation to be + + + align:start position:0% +on on what I expect inflation to be +during this period if I expect inflation + + align:start position:0% +during this period if I expect inflation + + + align:start position:0% +during this period if I expect inflation +to be 10% you're very likely to demand a + + align:start position:0% +to be 10% you're very likely to demand a + + + align:start position:0% +to be 10% you're very likely to demand a +higher nominal wage because you have to + + align:start position:0% +higher nominal wage because you have to + + + align:start position:0% +higher nominal wage because you have to +leave an average with higher prices so + + align:start position:0% +leave an average with higher prices so + + + align:start position:0% +leave an average with higher prices so +that's that's the role of that is the + + align:start position:0% +that's that's the role of that is the + + + align:start position:0% +that's that's the role of that is the +price I mean I I would prefer and there + + align:start position:0% +price I mean I I would prefer and there + + + align:start position:0% +price I mean I I would prefer and there +are countries where that's done to set + + align:start position:0% +are countries where that's done to set + + + align:start position:0% +are countries where that's done to set +my wage in real terms so I don't need to + + align:start position:0% +my wage in real terms so I don't need to + + + align:start position:0% +my wage in real terms so I don't need to +worry about that but in practice you in + + align:start position:0% +worry about that but in practice you in + + + align:start position:0% +worry about that but in practice you in +economies with low inflation like the US + + align:start position:0% +economies with low inflation like the US + + + align:start position:0% +economies with low inflation like the US +you don't do that you you get a nominal + + align:start position:0% +you don't do that you you get a nominal + + + align:start position:0% +you don't do that you you get a nominal +wage and you have to leave for a year or + + align:start position:0% +wage and you have to leave for a year or + + + align:start position:0% +wage and you have to leave for a year or +until the next negotiation for your wage + + align:start position:0% +until the next negotiation for your wage + + + align:start position:0% +until the next negotiation for your wage +contract with that level of of wages + + align:start position:0% + + + + align:start position:0% + +okay with the interest rate or with the + + align:start position:0% +okay with the interest rate or with the + + + align:start position:0% +okay with the interest rate or with the +the inflation rate whereas the I guess + + align:start position:0% +the inflation rate whereas the I guess + + + align:start position:0% +the inflation rate whereas the I guess +the regular price is defined by the wage + + align:start position:0% +the regular price is defined by the wage + + + align:start position:0% +the regular price is defined by the wage +is depend on the market no no they're + + align:start position:0% +is depend on the market no no they're + + + align:start position:0% +is depend on the market no no they're +both the same but one is the only thing + + align:start position:0% +both the same but one is the only thing + + + align:start position:0% +both the same but one is the only thing +is + + align:start position:0% +is + + + align:start position:0% +is +that this price here is not sort of the + + align:start position:0% +that this price here is not sort of the + + + align:start position:0% +that this price here is not sort of the +current is what you really expect the + + align:start position:0% +current is what you really expect the + + + align:start position:0% +current is what you really expect the +price to be during the year is that is + + align:start position:0% +price to be during the year is that is + + + align:start position:0% +price to be during the year is that is +this is here just because at the moment + + align:start position:0% +this is here just because at the moment + + + align:start position:0% +this is here just because at the moment +in which you set the wage you don't know + + align:start position:0% +in which you set the wage you don't know + + + align:start position:0% +in which you set the wage you don't know +the price you're going to face as a as a + + align:start position:0% +the price you're going to face as a as a + + + align:start position:0% +the price you're going to face as a as a +worker but it's it's the price so you + + align:start position:0% +worker but it's it's the price so you + + + align:start position:0% +worker but it's it's the price so you +don't know the price that you're going + + align:start position:0% +don't know the price that you're going + + + align:start position:0% +don't know the price that you're going +to actually face so the only the best + + align:start position:0% +to actually face so the only the best + + + align:start position:0% +to actually face so the only the best +you can do is calculate well I think + + align:start position:0% +you can do is calculate well I think + + + align:start position:0% +you can do is calculate well I think +inflation is going to be 10% so give me + + align:start position:0% +inflation is going to be 10% so give me + + + align:start position:0% +inflation is going to be 10% so give me +know what I would have had in mind with + + align:start position:0% +know what I would have had in mind with + + + align:start position:0% +know what I would have had in mind with +inflation equal to zero plus 5% so on + + align:start position:0% +inflation equal to zero plus 5% so on + + + align:start position:0% +inflation equal to zero plus 5% so on +average I'm about right that's sort of + + align:start position:0% +average I'm about right that's sort of + + + align:start position:0% +average I'm about right that's sort of +the + + align:start position:0% +the + + + align:start position:0% +the +logic but this expected price is meant + + align:start position:0% +logic but this expected price is meant + + + align:start position:0% +logic but this expected price is meant +to be your best proxy you have at the + + align:start position:0% +to be your best proxy you have at the + + + align:start position:0% +to be your best proxy you have at the +moment in which you're bargaining for + + align:start position:0% +moment in which you're bargaining for + + + align:start position:0% +moment in which you're bargaining for +your wage for what the actual price will + + align:start position:0% +your wage for what the actual price will + + + align:start position:0% +your wage for what the actual price will +be during the life of that particular + + align:start position:0% +be during the life of that particular + + + align:start position:0% +be during the life of that particular +wage + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +um okay so we end up with that that that + + align:start position:0% +um okay so we end up with that that that + + + align:start position:0% +um okay so we end up with that that that +uh Philips curve here importantly this + + align:start position:0% +uh Philips curve here importantly this + + + align:start position:0% +uh Philips curve here importantly this +an decreasing function of + + align:start position:0% +an decreasing function of + + + align:start position:0% +an decreasing function of +unemployment er um and then we' made + + align:start position:0% +unemployment er um and then we' made + + + align:start position:0% +unemployment er um and then we' made +different assumptions about expectations + + align:start position:0% +different assumptions about expectations + + + align:start position:0% +different assumptions about expectations +if expected inflation for example is a + + align:start position:0% +if expected inflation for example is a + + + align:start position:0% +if expected inflation for example is a +constant that's when we say expected + + align:start position:0% +constant that's when we say expected + + + align:start position:0% +constant that's when we say expected +infl inflation is very well anchored + + align:start position:0% +infl inflation is very well anchored + + + align:start position:0% +infl inflation is very well anchored +then you get a Philips curve that looks + + align:start position:0% +then you get a Philips curve that looks + + + align:start position:0% +then you get a Philips curve that looks +like this in which inflation it has a + + align:start position:0% +like this in which inflation it has a + + + align:start position:0% +like this in which inflation it has a +constant here and it's decreasing on the + + align:start position:0% +constant here and it's decreasing on the + + + align:start position:0% +constant here and it's decreasing on the +rate of unemployment and and during the + + align:start position:0% +rate of unemployment and and during the + + + align:start position:0% +rate of unemployment and and during the +60s H that that relationship sort of + + align:start position:0% +60s H that that relationship sort of + + + align:start position:0% +60s H that that relationship sort of +held fairly well it was a downward slope + + align:start position:0% +held fairly well it was a downward slope + + + align:start position:0% +held fairly well it was a downward slope +in relationship it got to be steeper and + + align:start position:0% +in relationship it got to be steeper and + + + align:start position:0% +in relationship it got to be steeper and +steeper as we moved into higher and + + align:start position:0% +steeper as we moved into higher and + + + align:start position:0% +steeper as we moved into higher and +higher inflation levels and then I said + + align:start position:0% +higher inflation levels and then I said + + + align:start position:0% +higher inflation levels and then I said +but in the 70s the whole thing broke + + align:start position:0% +but in the 70s the whole thing broke + + + align:start position:0% +but in the 70s the whole thing broke +loose you nothing like a downward + + align:start position:0% +loose you nothing like a downward + + + align:start position:0% +loose you nothing like a downward +sloping curve here that happened for two + + align:start position:0% +sloping curve here that happened for two + + + align:start position:0% +sloping curve here that happened for two +reasons there were some cause push + + align:start position:0% +reasons there were some cause push + + + align:start position:0% +reasons there were some cause push +shocks you can think of lots of shocks + + align:start position:0% +shocks you can think of lots of shocks + + + align:start position:0% +shocks you can think of lots of shocks +to M but more interesting H expected + + align:start position:0% +to M but more interesting H expected + + + align:start position:0% +to M but more interesting H expected +inflation became an anchor and then we + + align:start position:0% +inflation became an anchor and then we + + + align:start position:0% +inflation became an anchor and then we +changed then H the expected inflation + + align:start position:0% +changed then H the expected inflation + + + align:start position:0% +changed then H the expected inflation +mod for rather than being a constant + + align:start position:0% +mod for rather than being a constant + + + align:start position:0% +mod for rather than being a constant +being the some weighted average like + + align:start position:0% +being the some weighted average like + + + align:start position:0% +being the some weighted average like +this and we said look during the + + align:start position:0% +this and we said look during the + + + align:start position:0% +this and we said look during the +70s essentially that that Theta was + + align:start position:0% +70s essentially that that Theta was + + + align:start position:0% +70s essentially that that Theta was +equal to one okay so inflation expected + + align:start position:0% +equal to one okay so inflation expected + + + align:start position:0% +equal to one okay so inflation expected +inflation was really whatever was + + align:start position:0% +inflation was really whatever was + + + align:start position:0% +inflation was really whatever was +inflation last year people expected that + + align:start position:0% +inflation last year people expected that + + + align:start position:0% +inflation last year people expected that +level of inflation to stay the next year + + align:start position:0% +level of inflation to stay the next year + + + align:start position:0% +level of inflation to stay the next year +rather than going back to that whatever + + align:start position:0% +rather than going back to that whatever + + + align:start position:0% +rather than going back to that whatever +was the constant or inflation Target or + + align:start position:0% +was the constant or inflation Target or + + + align:start position:0% +was the constant or inflation Target or +historical constant pi and and that + + align:start position:0% +historical constant pi and and that + + + align:start position:0% +historical constant pi and and that +meant that the the during that period + + align:start position:0% +meant that the the during that period + + + align:start position:0% +meant that the the during that period +really the Philips curve looked more + + align:start position:0% +really the Philips curve looked more + + + align:start position:0% +really the Philips curve looked more +like a relationship of the change in the + + align:start position:0% +like a relationship of the change in the + + + align:start position:0% +like a relationship of the change in the +inflation rate as a decrease in function + + align:start position:0% +inflation rate as a decrease in function + + + align:start position:0% +inflation rate as a decrease in function +of unemployment so that means that when + + align:start position:0% +of unemployment so that means that when + + + align:start position:0% +of unemployment so that means that when +you increase an employment here you + + align:start position:0% +you increase an employment here you + + + align:start position:0% +you increase an employment here you +reduce a rate at which unemployment is + + align:start position:0% +reduce a rate at which unemployment is + + + align:start position:0% +reduce a rate at which unemployment is +inflation is rising okay that's the goal + + align:start position:0% +inflation is rising okay that's the goal + + + align:start position:0% +inflation is rising okay that's the goal +of + + align:start position:0% +of + + + align:start position:0% +of +the situation in in a case in + + align:start position:0% +the situation in in a case in + + + align:start position:0% +the situation in in a case in +which expected inflation is an an anchor + + align:start position:0% +which expected inflation is an an anchor + + + align:start position:0% +which expected inflation is an an anchor +and the last step we had there is we + + align:start position:0% +and the last step we had there is we + + + align:start position:0% +and the last step we had there is we +replace we notice we said well what + + align:start position:0% +replace we notice we said well what + + + align:start position:0% +replace we notice we said well what +happens if we stick in here the natural + + align:start position:0% +happens if we stick in here the natural + + + align:start position:0% +happens if we stick in here the natural +rate of unemployment then that will give + + align:start position:0% +rate of unemployment then that will give + + + align:start position:0% +rate of unemployment then that will give +us that will happen only when expected + + align:start position:0% +us that will happen only when expected + + + align:start position:0% +us that will happen only when expected +price is equal to actual prices so that + + align:start position:0% +price is equal to actual prices so that + + + align:start position:0% +price is equal to actual prices so that +means that when inflation is equal to + + align:start position:0% +means that when inflation is equal to + + + align:start position:0% +means that when inflation is equal to +expected inflation from here we can + + align:start position:0% +expected inflation from here we can + + + align:start position:0% +expected inflation from here we can +solve the natural rate of unemployment + + align:start position:0% +solve the natural rate of unemployment + + + align:start position:0% +solve the natural rate of unemployment +as a function of these structural + + align:start position:0% +as a function of these structural + + + align:start position:0% +as a function of these structural +parameters and once we have that we + + align:start position:0% +parameters and once we have that we + + + align:start position:0% +parameters and once we have that we +could go back to our Philips curve and + + align:start position:0% +could go back to our Philips curve and + + + align:start position:0% +could go back to our Philips curve and +rewrite it in this way okay so you can + + align:start position:0% +rewrite it in this way okay so you can + + + align:start position:0% +rewrite it in this way okay so you can +think of the Philips curve in this way + + align:start position:0% +think of the Philips curve in this way + + + align:start position:0% +think of the Philips curve in this way +and this is the the the way you + + align:start position:0% +and this is the the the way you + + + align:start position:0% +and this is the the the way you +typically we typically write it down in + + align:start position:0% +typically we typically write it down in + + + align:start position:0% +typically we typically write it down in +which it says H inflation is decreasing + + align:start position:0% +which it says H inflation is decreasing + + + align:start position:0% +which it says H inflation is decreasing +in the unemployment + + align:start position:0% +in the unemployment + + + align:start position:0% +in the unemployment +Gap + + align:start position:0% +Gap + + + align:start position:0% +Gap +so so if the unemployment is above the + + align:start position:0% +so so if the unemployment is above the + + + align:start position:0% +so so if the unemployment is above the +natural rate of unemployment that means + + align:start position:0% +natural rate of unemployment that means + + + align:start position:0% +natural rate of unemployment that means +inflation will tend to be below expected + + align:start position:0% +inflation will tend to be below expected + + + align:start position:0% +inflation will tend to be below expected +inflation if expected inflation happen + + align:start position:0% +inflation if expected inflation happen + + + align:start position:0% +inflation if expected inflation happen +to be equal to lag inflation that means + + align:start position:0% +to be equal to lag inflation that means + + + align:start position:0% +to be equal to lag inflation that means +if an employment is above the natural + + align:start position:0% +if an employment is above the natural + + + align:start position:0% +if an employment is above the natural +rate of unemployment then inflation will + + align:start position:0% +rate of unemployment then inflation will + + + align:start position:0% +rate of unemployment then inflation will +be falling + + align:start position:0% +be falling + + + align:start position:0% +be falling +okay any questions good you need to know + + align:start position:0% +okay any questions good you need to know + + + align:start position:0% +okay any questions good you need to know +this + + align:start position:0% + + + + align:start position:0% + +okay how to derive these things I mean + + align:start position:0% +okay how to derive these things I mean + + + align:start position:0% +okay how to derive these things I mean +not so much yeah you should know how to + + align:start position:0% +not so much yeah you should know how to + + + align:start position:0% +not so much yeah you should know how to +WR but you need to understand this + + align:start position:0% +WR but you need to understand this + + + align:start position:0% +WR but you need to understand this +relationship between the out the + + align:start position:0% +relationship between the out the + + + align:start position:0% +relationship between the out the +unemployment Gap and + + align:start position:0% + + + + align:start position:0% + +inflation relative to spected + + align:start position:0% +inflation relative to spected + + + align:start position:0% +inflation relative to spected +inflation yep + + align:start position:0% +inflation yep + + + align:start position:0% +inflation yep +unor versus de unored inflation expected + + align:start position:0% +unor versus de unored inflation expected + + + align:start position:0% +unor versus de unored inflation expected +inflation it's just a statement + + align:start position:0% +inflation it's just a statement + + + align:start position:0% +inflation it's just a statement +about ER what is the model we have H for + + align:start position:0% +about ER what is the model we have H for + + + align:start position:0% +about ER what is the model we have H for +expected + + align:start position:0% +expected + + + align:start position:0% +expected +inflation + + align:start position:0% +inflation + + + align:start position:0% +inflation +so suppose we have the following model + + align:start position:0% +so suppose we have the following model + + + align:start position:0% +so suppose we have the following model +for expected inflation one minus Theta + + align:start position:0% +for expected inflation one minus Theta + + + align:start position:0% +for expected inflation one minus Theta +Theta some number between Z and one + + align:start position:0% +Theta some number between Z and one + + + align:start position:0% +Theta some number between Z and one +times a constant + + align:start position:0% +times a constant + + + align:start position:0% +times a constant +inflation plus something that is a + + align:start position:0% +inflation plus something that is a + + + align:start position:0% +inflation plus something that is a +function of plus Thea times whatever is + + align:start position:0% +function of plus Thea times whatever is + + + align:start position:0% +function of plus Thea times whatever is +previous + + align:start position:0% +previous + + + align:start position:0% +previous +inflation central banks try to set a + + align:start position:0% +inflation central banks try to set a + + + align:start position:0% +inflation central banks try to set a +target for the inflation rate in the US + + align:start position:0% +target for the inflation rate in the US + + + align:start position:0% +target for the inflation rate in the US +is around 2% and ideally people will + + align:start position:0% +is around 2% and ideally people will + + + align:start position:0% +is around 2% and ideally people will +tend to believe they may see an tempor + + align:start position:0% +tend to believe they may see an tempor + + + align:start position:0% +tend to believe they may see an tempor +inflation that that is above say 2% but + + align:start position:0% +inflation that that is above say 2% but + + + align:start position:0% +inflation that that is above say 2% but +as long as as as people expect that to + + align:start position:0% +as long as as as people expect that to + + + align:start position:0% +as long as as as people expect that to +be undone in the in the in the next + + align:start position:0% +be undone in the in the in the next + + + align:start position:0% +be undone in the in the in the next +period then inflations we say they're + + align:start position:0% +period then inflations we say they're + + + align:start position:0% +period then inflations we say they're +very well anchored so that's a case in + + align:start position:0% +very well anchored so that's a case in + + + align:start position:0% +very well anchored so that's a case in +which very well anchored means th equal + + align:start position:0% +which very well anchored means th equal + + + align:start position:0% +which very well anchored means th equal +to Z here and you always sticking there + + align:start position:0% +to Z here and you always sticking there + + + align:start position:0% +to Z here and you always sticking there +in the case of the US at 2% and and + + align:start position:0% +in the case of the US at 2% and and + + + align:start position:0% +in the case of the US at 2% and and +there's a lot of there's a lot of that's + + align:start position:0% +there's a lot of there's a lot of that's + + + align:start position:0% +there's a lot of there's a lot of that's +the way the econom is behaving right now + + align:start position:0% +the way the econom is behaving right now + + + align:start position:0% +the way the econom is behaving right now +inflation today is 5% but if you ask + + align:start position:0% +inflation today is 5% but if you ask + + + align:start position:0% +inflation today is 5% but if you ask +people what do you expect inflation to + + align:start position:0% +people what do you expect inflation to + + + align:start position:0% +people what do you expect inflation to +be two and two years from now people + + align:start position:0% +be two and two years from now people + + + align:start position:0% +be two and two years from now people +tell you me look around 2% two and a + + align:start position:0% +tell you me look around 2% two and a + + + align:start position:0% +tell you me look around 2% two and a +half percent or so unanchor expectation + + align:start position:0% +half percent or so unanchor expectation + + + align:start position:0% +half percent or so unanchor expectation +is when when you don't have that anchor + + align:start position:0% +is when when you don't have that anchor + + + align:start position:0% +is when when you don't have that anchor +that 2% that the FED told you is + + align:start position:0% +that 2% that the FED told you is + + + align:start position:0% +that 2% that the FED told you is +whatever was the previous inflation + + align:start position:0% +whatever was the previous inflation + + + align:start position:0% +whatever was the previous inflation +that's what people extrapolate will be + + align:start position:0% +that's what people extrapolate will be + + + align:start position:0% +that's what people extrapolate will be +inflation for Next Period and that's a + + align:start position:0% +inflation for Next Period and that's a + + + align:start position:0% +inflation for Next Period and that's a +lot harder when you get into an + + align:start position:0% +lot harder when you get into an + + + align:start position:0% +lot harder when you get into an +inflationary episode in that context is + + align:start position:0% +inflationary episode in that context is + + + align:start position:0% +inflationary episode in that context is +very difficult because you at 5% people + + align:start position:0% +very difficult because you at 5% people + + + align:start position:0% +very difficult because you at 5% people +are still expecting 5% for next year so + + align:start position:0% +are still expecting 5% for next year so + + + align:start position:0% +are still expecting 5% for next year so +you need to is much harder to bring + + align:start position:0% +you need to is much harder to bring + + + align:start position:0% +you need to is much harder to bring +inflation down you need to create much + + align:start position:0% +inflation down you need to create much + + + align:start position:0% +inflation down you need to create much +more unemployment to bring inflation + + align:start position:0% +more unemployment to bring inflation + + + align:start position:0% +more unemployment to bring inflation +back to the 2% 2% Target okay that's + + align:start position:0% +back to the 2% 2% Target okay that's + + + align:start position:0% +back to the 2% 2% Target okay that's +that's what it means to an so anchor + + align:start position:0% +that's what it means to an so anchor + + + align:start position:0% +that's what it means to an so anchor +means Theta very close to zero an anchor + + align:start position:0% +means Theta very close to zero an anchor + + + align:start position:0% +means Theta very close to zero an anchor +Theta very close to one that's a a + + align:start position:0% +Theta very close to one that's a a + + + align:start position:0% +Theta very close to one that's a a +formal definition + + align:start position:0% + + + + align:start position:0% + +we then move + + align:start position:0% +we then move + + + align:start position:0% +we then move +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +to what I think is probably the most + + align:start position:0% +to what I think is probably the most + + + align:start position:0% +to what I think is probably the most +important model you'll see in this + + align:start position:0% +important model you'll see in this + + + align:start position:0% +important model you'll see in this +course which is the islm PC which is + + align:start position:0% +course which is the islm PC which is + + + align:start position:0% +course which is the islm PC which is +just the islm plus the Philips curve and + + align:start position:0% +just the islm plus the Philips curve and + + + align:start position:0% +just the islm plus the Philips curve and +that allow us to talk about the short + + align:start position:0% +that allow us to talk about the short + + + align:start position:0% +that allow us to talk about the short +run which is what we did in the slm and + + align:start position:0% +run which is what we did in the slm and + + + align:start position:0% +run which is what we did in the slm and +then all the way to the medium Run Okay + + align:start position:0% +then all the way to the medium Run Okay + + + align:start position:0% +then all the way to the medium Run Okay +in medium understood as when you go back + + align:start position:0% +in medium understood as when you go back + + + align:start position:0% +in medium understood as when you go back +to the Natural rate of unemployment + + align:start position:0% +to the Natural rate of unemployment + + + align:start position:0% +to the Natural rate of unemployment +natural level of output and so on + + align:start position:0% +natural level of output and so on + + + align:start position:0% +natural level of output and so on +oh we got a banking crisis there but + + align:start position:0% + + + + align:start position:0% + +that's + + align:start position:0% +that's + + + align:start position:0% +that's +oh this you may find useful here here I + + align:start position:0% +oh this you may find useful here here I + + + align:start position:0% +oh this you may find useful here here I +was trying to explain the banking crisis + + align:start position:0% +was trying to explain the banking crisis + + + align:start position:0% +was trying to explain the banking crisis +and and so and I said we have a model + + align:start position:0% +and and so and I said we have a model + + + align:start position:0% +and and so and I said we have a model +for that already remember we had this x + + align:start position:0% +for that already remember we had this x + + + align:start position:0% +for that already remember we had this x +this spreads in the investment function + + align:start position:0% +this spreads in the investment function + + + align:start position:0% +this spreads in the investment function +I said well you can think of a negative + + align:start position:0% +I said well you can think of a negative + + + align:start position:0% +I said well you can think of a negative +Financial shock something like a a + + align:start position:0% +Financial shock something like a a + + + align:start position:0% +Financial shock something like a a +credit spread shock as an increasing X + + align:start position:0% +credit spread shock as an increasing X + + + align:start position:0% +credit spread shock as an increasing X +and that will shift to left okay just + + align:start position:0% +and that will shift to left okay just + + + align:start position:0% +and that will shift to left okay just +saying + + align:start position:0% +saying + + + align:start position:0% +saying +good + + align:start position:0% +good + + + align:start position:0% +good +uh islm PC model was just going back to + + align:start position:0% +uh islm PC model was just going back to + + + align:start position:0% +uh islm PC model was just going back to +the islm model we're going to simplify + + align:start position:0% +the islm model we're going to simplify + + + align:start position:0% +the islm model we're going to simplify +things by not by just assuming that the + + align:start position:0% +things by not by just assuming that the + + + align:start position:0% +things by not by just assuming that the +Central Bank sets the real interest rate + + align:start position:0% +Central Bank sets the real interest rate + + + align:start position:0% +Central Bank sets the real interest rate +and the real interest rate is that okay + + align:start position:0% +and the real interest rate is that okay + + + align:start position:0% +and the real interest rate is that okay +ER and uh and to that we added a Philips + + align:start position:0% +ER and uh and to that we added a Philips + + + align:start position:0% +ER and uh and to that we added a Philips +curve but we didn't like that Philips + + align:start position:0% +curve but we didn't like that Philips + + + align:start position:0% +curve but we didn't like that Philips +curve because you know we have + + align:start position:0% +curve because you know we have + + + align:start position:0% +curve because you know we have +everything is a function of output here + + align:start position:0% +everything is a function of output here + + + align:start position:0% +everything is a function of output here +and interest rate and now we have + + align:start position:0% +and interest rate and now we have + + + align:start position:0% +and interest rate and now we have +inflation and then employment rate so + + align:start position:0% +inflation and then employment rate so + + + align:start position:0% +inflation and then employment rate so +yet another variable to carry around so + + align:start position:0% +yet another variable to carry around so + + + align:start position:0% +yet another variable to carry around so +we went from H the output Gap to an + + align:start position:0% +we went from H the output Gap to an + + + align:start position:0% +we went from H the output Gap to an +employment R an employment gap to an + + align:start position:0% +employment R an employment gap to an + + + align:start position:0% +employment R an employment gap to an +output Gap and and we did that just by + + align:start position:0% +output Gap and and we did that just by + + + align:start position:0% +output Gap and and we did that just by +noticing that output is equal to the + + align:start position:0% +noticing that output is equal to the + + + align:start position:0% +noticing that output is equal to the +labor force time one minus unemployment + + align:start position:0% +labor force time one minus unemployment + + + align:start position:0% +labor force time one minus unemployment +rate equivalently similar you can Define + + align:start position:0% +rate equivalently similar you can Define + + + align:start position:0% +rate equivalently similar you can Define +potential output or the natural output + + align:start position:0% +potential output or the natural output + + + align:start position:0% +potential output or the natural output +level as employment Time 1 minus the + + align:start position:0% +level as employment Time 1 minus the + + + align:start position:0% +level as employment Time 1 minus the +natural rate of unemployment subtract + + align:start position:0% +natural rate of unemployment subtract + + + align:start position:0% +natural rate of unemployment subtract +these two no and I you get that the + + align:start position:0% +these two no and I you get that the + + + align:start position:0% +these two no and I you get that the +output Gap is equal to minus L times the + + align:start position:0% +output Gap is equal to minus L times the + + + align:start position:0% +output Gap is equal to minus L times the +unemployment Gap and so we replace this + + align:start position:0% +unemployment Gap and so we replace this + + + align:start position:0% +unemployment Gap and so we replace this +for that expression divided by L and we + + align:start position:0% +for that expression divided by L and we + + + align:start position:0% +for that expression divided by L and we +end up with a Philips curve written in + + align:start position:0% +end up with a Philips curve written in + + + align:start position:0% +end up with a Philips curve written in +the form of an increasing function of + + align:start position:0% +the form of an increasing function of + + + align:start position:0% +the form of an increasing function of +the output Gap so when the output Gap is + + align:start position:0% +the output Gap so when the output Gap is + + + align:start position:0% +the output Gap so when the output Gap is +positive then inflation will exceed + + align:start position:0% +positive then inflation will exceed + + + align:start position:0% +positive then inflation will exceed +expected inflation if expected inflation + + align:start position:0% +expected inflation if expected inflation + + + align:start position:0% +expected inflation if expected inflation +is an anchor that is expected inflation + + align:start position:0% +is an anchor that is expected inflation + + + align:start position:0% +is an anchor that is expected inflation +is equal to lag inflation then that + + align:start position:0% +is equal to lag inflation then that + + + align:start position:0% +is equal to lag inflation then that +means that a positive output Gap leads + + align:start position:0% +means that a positive output Gap leads + + + align:start position:0% +means that a positive output Gap leads +to an increase in inflation inflation R + + align:start position:0% +to an increase in inflation inflation R + + + align:start position:0% +to an increase in inflation inflation R +okay so we look at an example here H you + + align:start position:0% +okay so we look at an example here H you + + + align:start position:0% +okay so we look at an example here H you +know this is the type of but now we're + + align:start position:0% +know this is the type of but now we're + + + align:start position:0% +know this is the type of but now we're +going to have the real interest rate + + align:start position:0% +going to have the real interest rate + + + align:start position:0% +going to have the real interest rate +here just makes it simpler to think + + align:start position:0% +here just makes it simpler to think + + + align:start position:0% +here just makes it simpler to think +about Central monetary policy in terms + + align:start position:0% +about Central monetary policy in terms + + + align:start position:0% +about Central monetary policy in terms +of the real interest rate otherwise too + + align:start position:0% +of the real interest rate otherwise too + + + align:start position:0% +of the real interest rate otherwise too +many things move at once so this is what + + align:start position:0% +many things move at once so this is what + + + align:start position:0% +many things move at once so this is what +we had done for quiz one here you have + + align:start position:0% +we had done for quiz one here you have + + + align:start position:0% +we had done for quiz one here you have +some particular equilibrium the islm + + align:start position:0% +some particular equilibrium the islm + + + align:start position:0% +some particular equilibrium the islm +with this real interest rate we + + align:start position:0% +with this real interest rate we + + + align:start position:0% +with this real interest rate we +got some equilibrium output equal to Y + + align:start position:0% +got some equilibrium output equal to Y + + + align:start position:0% +got some equilibrium output equal to Y +the new part the contribution of this + + align:start position:0% +the new part the contribution of this + + + align:start position:0% +the new part the contribution of this +block of the course is that now we need + + align:start position:0% +block of the course is that now we need + + + align:start position:0% +block of the course is that now we need +to also check whether this Y is is + + align:start position:0% +to also check whether this Y is is + + + align:start position:0% +to also check whether this Y is is +consistent with potential output or not + + align:start position:0% +consistent with potential output or not + + + align:start position:0% +consistent with potential output or not +with natural level of output and that + + align:start position:0% +with natural level of output and that + + + align:start position:0% +with natural level of output and that +for that we need to uh see whether this + + align:start position:0% +for that we need to uh see whether this + + + align:start position:0% +for that we need to uh see whether this +level of output H is consider again is + + align:start position:0% +level of output H is consider again is + + + align:start position:0% +level of output H is consider again is +above or below the natural rate of + + align:start position:0% +above or below the natural rate of + + + align:start position:0% +above or below the natural rate of +output and for that we need to look at + + align:start position:0% +output and for that we need to look at + + + align:start position:0% +output and for that we need to look at +the Philips curve okay okay and in this + + align:start position:0% +the Philips curve okay okay and in this + + + align:start position:0% +the Philips curve okay okay and in this +particular case that's not the the case + + align:start position:0% +particular case that's not the the case + + + align:start position:0% +particular case that's not the the case +because output is above the natural rate + + align:start position:0% +because output is above the natural rate + + + align:start position:0% +because output is above the natural rate +of output you put now given that + + align:start position:0% +of output you put now given that + + + align:start position:0% +of output you put now given that +observation you you put right draw here + + align:start position:0% +observation you you put right draw here + + + align:start position:0% +observation you you put right draw here +the the Philips curve you know that + + align:start position:0% +the the Philips curve you know that + + + align:start position:0% +the the Philips curve you know that +because output is above the natural rate + + align:start position:0% +because output is above the natural rate + + + align:start position:0% +because output is above the natural rate +of output the natural level of output + + align:start position:0% +of output the natural level of output + + + align:start position:0% +of output the natural level of output +that means inflation is above expected + + align:start position:0% +that means inflation is above expected + + + align:start position:0% +that means inflation is above expected +inflation if expected inflation happens + + align:start position:0% +inflation if expected inflation happens + + + align:start position:0% +inflation if expected inflation happens +to be an anchor equal to Pi minus one + + align:start position:0% +to be an anchor equal to Pi minus one + + + align:start position:0% +to be an anchor equal to Pi minus one +that means that at this output Gap that + + align:start position:0% +that means that at this output Gap that + + + align:start position:0% +that means that at this output Gap that +there's an inflation that is rising okay + + align:start position:0% +there's an inflation that is rising okay + + + align:start position:0% +there's an inflation that is rising okay +H now inflation Rising means the central + + align:start position:0% +H now inflation Rising means the central + + + align:start position:0% +H now inflation Rising means the central +bank will have to react and the way we + + align:start position:0% +bank will have to react and the way we + + + align:start position:0% +bank will have to react and the way we +so you'll have to do something up here + + align:start position:0% +so you'll have to do something up here + + + align:start position:0% +so you'll have to do something up here +you need to bring output down and how + + align:start position:0% +you need to bring output down and how + + + align:start position:0% +you need to bring output down and how +can you bring output + + align:start position:0% +can you bring output + + + align:start position:0% +can you bring output +down so so this economy is is engaging + + align:start position:0% +down so so this economy is is engaging + + + align:start position:0% +down so so this economy is is engaging +in an inflationary spiral actually given + + align:start position:0% +in an inflationary spiral actually given + + + align:start position:0% +in an inflationary spiral actually given +this mod of expectation how do you stop + + align:start position:0% + + + + align:start position:0% + +that if you are the fed and you you + + align:start position:0% +that if you are the fed and you you + + + align:start position:0% +that if you are the fed and you you +raise the interest rate no because you + + align:start position:0% +raise the interest rate no because you + + + align:start position:0% +raise the interest rate no because you +need to bring the L back so the + + align:start position:0% +need to bring the L back so the + + + align:start position:0% +need to bring the L back so the +equilibrium level of output you need + + align:start position:0% +equilibrium level of output you need + + + align:start position:0% +equilibrium level of output you need +increase the real rate up to a point in + + align:start position:0% +increase the real rate up to a point in + + + align:start position:0% +increase the real rate up to a point in +which um the level equilibrium level of + + align:start position:0% +which um the level equilibrium level of + + + align:start position:0% +which um the level equilibrium level of +output is equal to the Natural rate of + + align:start position:0% +output is equal to the Natural rate of + + + align:start position:0% +output is equal to the Natural rate of +output um and you may have to do more + + align:start position:0% +output um and you may have to do more + + + align:start position:0% +output um and you may have to do more +than that if inflation was an anchor and + + align:start position:0% +than that if inflation was an anchor and + + + align:start position:0% +than that if inflation was an anchor and +you find yourself with 5% inflation you + + align:start position:0% +you find yourself with 5% inflation you + + + align:start position:0% +you find yourself with 5% inflation you +may have to temporarily actually to + + align:start position:0% +may have to temporarily actually to + + + align:start position:0% +may have to temporarily actually to +bring inflation back down to 2% you may + + align:start position:0% +bring inflation back down to 2% you may + + + align:start position:0% +bring inflation back down to 2% you may +have to overshoot raise interest rate a + + align:start position:0% +have to overshoot raise interest rate a + + + align:start position:0% +have to overshoot raise interest rate a +lot generate a negative output gap for a + + align:start position:0% +lot generate a negative output gap for a + + + align:start position:0% +lot generate a negative output gap for a +while and then once you reach the level + + align:start position:0% +while and then once you reach the level + + + align:start position:0% +while and then once you reach the level +of inflation you like the 2% then you + + align:start position:0% +of inflation you like the 2% then you + + + align:start position:0% +of inflation you like the 2% then you +can go back uh to the Natural level of + + align:start position:0% +can go back uh to the Natural level of + + + align:start position:0% +can go back uh to the Natural level of +output okay so that's the reason central + + align:start position:0% +output okay so that's the reason central + + + align:start position:0% +output okay so that's the reason central +banks worry a lot about unanchor + + align:start position:0% +banks worry a lot about unanchor + + + align:start position:0% +banks worry a lot about unanchor +expectations because then they know that + + align:start position:0% +expectations because then they know that + + + align:start position:0% +expectations because then they know that +they find themselves an inflation above + + align:start position:0% +they find themselves an inflation above + + + align:start position:0% +they find themselves an inflation above +their target is not going to be enough + + align:start position:0% +their target is not going to be enough + + + align:start position:0% +their target is not going to be enough +to bring the output Gap to zero they're + + align:start position:0% +to bring the output Gap to zero they're + + + align:start position:0% +to bring the output Gap to zero they're +going to have to overshoot in the way + + align:start position:0% +going to have to overshoot in the way + + + align:start position:0% +going to have to overshoot in the way +down in order to re re-anchor expect + + align:start position:0% +down in order to re re-anchor expect + + + align:start position:0% +down in order to re re-anchor expect +well in order to bring inflation back + + align:start position:0% +well in order to bring inflation back + + + align:start position:0% +well in order to bring inflation back +down to the Target of + + align:start position:0% +down to the Target of + + + align:start position:0% +down to the Target of +2% but in any event even if inflation + + align:start position:0% +2% but in any event even if inflation + + + align:start position:0% +2% but in any event even if inflation +are expect well anchor you still have to + + align:start position:0% +are expect well anchor you still have to + + + align:start position:0% +are expect well anchor you still have to +bring output down because at the very + + align:start position:0% +bring output down because at the very + + + align:start position:0% +bring output down because at the very +least you need to close this pos + + align:start position:0% +least you need to close this pos + + + align:start position:0% +least you need to close this pos +positive output Gap and that if you're + + align:start position:0% +positive output Gap and that if you're + + + align:start position:0% +positive output Gap and that if you're +the FED in the US or any Central Bank + + align:start position:0% +the FED in the US or any Central Bank + + + align:start position:0% +the FED in the US or any Central Bank +you do it by increasing the real + + align:start position:0% +you do it by increasing the real + + + align:start position:0% +you do it by increasing the real +interest rate now in practice central + + align:start position:0% +interest rate now in practice central + + + align:start position:0% +interest rate now in practice central +banks really don't control the real + + align:start position:0% +banks really don't control the real + + + align:start position:0% +banks really don't control the real +interest they control the nominal + + align:start position:0% +interest they control the nominal + + + align:start position:0% +interest they control the nominal +interest ratees so there's a little + + align:start position:0% +interest ratees so there's a little + + + align:start position:0% +interest ratees so there's a little +fight there between inflation and and + + align:start position:0% +fight there between inflation and and + + + align:start position:0% +fight there between inflation and and +what they do to the nominal interest + + align:start position:0% +what they do to the nominal interest + + + align:start position:0% +what they do to the nominal interest +rate but let's ignore that complication + + align:start position:0% +rate but let's ignore that complication + + + align:start position:0% +rate but let's ignore that complication +for now okay now H suppose that the FED + + align:start position:0% +for now okay now H suppose that the FED + + + align:start position:0% +for now okay now H suppose that the FED +is is is in vacation + + align:start position:0% +is is is in vacation + + + align:start position:0% +is is is in vacation +and and and so and and somebody someone + + align:start position:0% +and and and so and and somebody someone + + + align:start position:0% +and and and so and and somebody someone +else you know decides in the government + + align:start position:0% +else you know decides in the government + + + align:start position:0% +else you know decides in the government +decides that no we cannot have this very + + align:start position:0% +decides that no we cannot have this very + + + align:start position:0% +decides that no we cannot have this very +high level of inflation so what else + + align:start position:0% +high level of inflation so what else + + + align:start position:0% +high level of inflation so what else +could you + + align:start position:0% + + + + align:start position:0% + +do and you're not the FED fed in + + align:start position:0% +do and you're not the FED fed in + + + align:start position:0% +do and you're not the FED fed in +vacation who else can make + + align:start position:0% +vacation who else can make + + + align:start position:0% +vacation who else can make +policy the government the central + + align:start position:0% +policy the government the central + + + align:start position:0% +policy the government the central +government the treasury and so on no + + align:start position:0% +government the treasury and so on no + + + align:start position:0% +government the treasury and so on no +what is the instrument they have what do + + align:start position:0% +what is the instrument they have what do + + + align:start position:0% +what is the instrument they have what do +they need to do + + align:start position:0% +they need to do + + + align:start position:0% +they need to do +the problem they have is output is too + + align:start position:0% +the problem they have is output is too + + + align:start position:0% +the problem they have is output is too +high and that's what is leading to lots + + align:start position:0% +high and that's what is leading to lots + + + align:start position:0% +high and that's what is leading to lots +of inflation so + + align:start position:0% +of inflation so + + + align:start position:0% +of inflation so +what do you think they should + + align:start position:0% + + + + align:start position:0% + +do c govern expend raise taxes something + + align:start position:0% +do c govern expend raise taxes something + + + align:start position:0% +do c govern expend raise taxes something +of that kind okay but they need a fiscal + + align:start position:0% +of that kind okay but they need a fiscal + + + align:start position:0% +of that kind okay but they need a fiscal +contraction because that will bring the + + align:start position:0% +contraction because that will bring the + + + align:start position:0% +contraction because that will bring the +yes down and so equilibrium + + align:start position:0% +yes down and so equilibrium + + + align:start position:0% +yes down and so equilibrium +output will be lower okay so that's an + + align:start position:0% +output will be lower okay so that's an + + + align:start position:0% +output will be lower okay so that's an +alternative you have you should know + + align:start position:0% +alternative you have you should know + + + align:start position:0% +alternative you have you should know +this + + align:start position:0% + + + + align:start position:0% + +and here I just did what we just + + align:start position:0% +and here I just did what we just + + + align:start position:0% +and here I just did what we just +discussed just in in a steps these + + align:start position:0% +discussed just in in a steps these + + + align:start position:0% +discussed just in in a steps these +things happen slowly the F doesn't hike + + align:start position:0% +things happen slowly the F doesn't hike + + + align:start position:0% +things happen slowly the F doesn't hike +interest rate in one shot and so on it + + align:start position:0% +interest rate in one shot and so on it + + + align:start position:0% +interest rate in one shot and so on it +takes a while before you get to the + + align:start position:0% +takes a while before you get to the + + + align:start position:0% +takes a while before you get to the +final + + align:start position:0% + + + + align:start position:0% + +equilibrium oh I I show you the + + align:start position:0% +equilibrium oh I I show you the + + + align:start position:0% +equilibrium oh I I show you the +deflationary spiral said sometimes + + align:start position:0% +deflationary spiral said sometimes + + + align:start position:0% +deflationary spiral said sometimes +things can get very + + align:start position:0% +things can get very + + + align:start position:0% +things can get very +complicated ER because you may hit the + + align:start position:0% +complicated ER because you may hit the + + + align:start position:0% +complicated ER because you may hit the +zero lower bound the FED can bring the + + align:start position:0% +zero lower bound the FED can bring the + + + align:start position:0% +zero lower bound the FED can bring the +nominal interest R to zero but if + + align:start position:0% +nominal interest R to zero but if + + + align:start position:0% +nominal interest R to zero but if +inflation is already low that may not + + align:start position:0% +inflation is already low that may not + + + align:start position:0% +inflation is already low that may not +give you the real interest that you need + + align:start position:0% +give you the real interest that you need + + + align:start position:0% +give you the real interest that you need +in order to get output equal to the + + align:start position:0% +in order to get output equal to the + + + align:start position:0% +in order to get output equal to the +Natural rate of output I me here was one + + align:start position:0% +Natural rate of output I me here was one + + + align:start position:0% +Natural rate of output I me here was one +example in which you need a negative + + align:start position:0% +example in which you need a negative + + + align:start position:0% +example in which you need a negative +real interest rate to get output to be + + align:start position:0% +real interest rate to get output to be + + + align:start position:0% +real interest rate to get output to be +equal to Natural rate of output but that + + align:start position:0% +equal to Natural rate of output but that + + + align:start position:0% +equal to Natural rate of output but that +may not happen because you you you hit + + align:start position:0% +may not happen because you you you hit + + + align:start position:0% +may not happen because you you you hit +the zero lower bound H and so at that + + align:start position:0% +the zero lower bound H and so at that + + + align:start position:0% +the zero lower bound H and so at that +point the problem you have is that and + + align:start position:0% +point the problem you have is that and + + + align:start position:0% +point the problem you have is that and +that's was the trag tragedy of Japan for + + align:start position:0% +that's was the trag tragedy of Japan for + + + align:start position:0% +that's was the trag tragedy of Japan for +so long is that not + + align:start position:0% +so long is that not + + + align:start position:0% +so long is that not +only you cannot bring the interest rate + + align:start position:0% +only you cannot bring the interest rate + + + align:start position:0% +only you cannot bring the interest rate +the nominal interest rate below zero but + + align:start position:0% +the nominal interest rate below zero but + + + align:start position:0% +the nominal interest rate below zero but +you start getting into deflationary + + align:start position:0% +you start getting into deflationary + + + align:start position:0% +you start getting into deflationary +inflation below expectation and + + align:start position:0% +inflation below expectation and + + + align:start position:0% +inflation below expectation and +expectation goes to number very close to + + align:start position:0% +expectation goes to number very close to + + + align:start position:0% +expectation goes to number very close to +zero because of an anchor deflation + + align:start position:0% +zero because of an anchor deflation + + + align:start position:0% +zero because of an anchor deflation +expectations then you start getting + + align:start position:0% +expectations then you start getting + + + align:start position:0% +expectations then you start getting +negative expected inflation and when you + + align:start position:0% +negative expected inflation and when you + + + align:start position:0% +negative expected inflation and when you +get Negative expected inflation even if + + align:start position:0% +get Negative expected inflation even if + + + align:start position:0% +get Negative expected inflation even if +you're at the zero lower Bound in the + + align:start position:0% +you're at the zero lower Bound in the + + + align:start position:0% +you're at the zero lower Bound in the +nominal interest rate that means a + + align:start position:0% +nominal interest rate that means a + + + align:start position:0% +nominal interest rate that means a +positive real interest rate so + + align:start position:0% +positive real interest rate so + + + align:start position:0% +positive real interest rate so +effectively you're increasing interest + + align:start position:0% +effectively you're increasing interest + + + align:start position:0% +effectively you're increasing interest +rate at the same time and that can be a + + align:start position:0% +rate at the same time and that can be a + + + align:start position:0% +rate at the same time and that can be a +very complicated thing to get out of + + align:start position:0% +very complicated thing to get out of + + + align:start position:0% +very complicated thing to get out of +again that's what happened to Japan for + + align:start position:0% +again that's what happened to Japan for + + + align:start position:0% +again that's what happened to Japan for +a long + + align:start position:0% +a long + + + align:start position:0% +a long +time what would you do if as a + + align:start position:0% +time what would you do if as a + + + align:start position:0% +time what would you do if as a +government if you fall into a situation + + align:start position:0% +government if you fall into a situation + + + align:start position:0% +government if you fall into a situation +like + + align:start position:0% + + + + align:start position:0% + +that and Japan did a lot of + + align:start position:0% +that and Japan did a lot of + + + align:start position:0% +that and Japan did a lot of +that well you can do lots of things but + + align:start position:0% +that well you can do lots of things but + + + align:start position:0% +that well you can do lots of things but +but in particular of the kind of things + + align:start position:0% +but in particular of the kind of things + + + align:start position:0% +but in particular of the kind of things +you know what what would you do if you + + align:start position:0% +you know what what would you do if you + + + align:start position:0% +you know what what would you do if you +are in a situation like this in which + + align:start position:0% +are in a situation like this in which + + + align:start position:0% +are in a situation like this in which +the zero lower bound is binding and and + + align:start position:0% +the zero lower bound is binding and and + + + align:start position:0% +the zero lower bound is binding and and +inflation is actually falling here I had + + align:start position:0% +inflation is actually falling here I had + + + align:start position:0% +inflation is actually falling here I had +a benign case in which inflation + + align:start position:0% +a benign case in which inflation + + + align:start position:0% +a benign case in which inflation +expectation was well anchor that's not + + align:start position:0% +expectation was well anchor that's not + + + align:start position:0% +expectation was well anchor that's not +what happened to Japan after they + + align:start position:0% +what happened to Japan after they + + + align:start position:0% +what happened to Japan after they +experienced a long period of + + align:start position:0% +experienced a long period of + + + align:start position:0% +experienced a long period of +deflationary forces the then the people + + align:start position:0% +deflationary forces the then the people + + + align:start position:0% +deflationary forces the then the people +began to expect more deflation more + + align:start position:0% +began to expect more deflation more + + + align:start position:0% +began to expect more deflation more +deflation and so on so what else can you + + align:start position:0% + + + + align:start position:0% + +do let me give you a hint Japan is one + + align:start position:0% +do let me give you a hint Japan is one + + + align:start position:0% +do let me give you a hint Japan is one +of the countries has the highest levels + + align:start position:0% +of the countries has the highest levels + + + align:start position:0% +of the countries has the highest levels +of public debt + + align:start position:0% +of public debt + + + align:start position:0% +of public debt +how do you accumulate public + + align:start position:0% +how do you accumulate public + + + align:start position:0% +how do you accumulate public +debt yeah you you need to borrow a lot + + align:start position:0% +debt yeah you you need to borrow a lot + + + align:start position:0% +debt yeah you you need to borrow a lot +you have big fiscal deficit so that's + + align:start position:0% +you have big fiscal deficit so that's + + + align:start position:0% +you have big fiscal deficit so that's +the way you can fight this you know you + + align:start position:0% +the way you can fight this you know you + + + align:start position:0% +the way you can fight this you know you +can shift the yes to the right by having + + align:start position:0% +can shift the yes to the right by having + + + align:start position:0% +can shift the yes to the right by having +an expansionary fiscal policy that's the + + align:start position:0% +an expansionary fiscal policy that's the + + + align:start position:0% +an expansionary fiscal policy that's the +only tool really you have you lose the + + align:start position:0% +only tool really you have you lose the + + + align:start position:0% +only tool really you have you lose the +power of monetary policy against the + + align:start position:0% +power of monetary policy against the + + + align:start position:0% +power of monetary policy against the +zero lower bound but you still have + + align:start position:0% +zero lower bound but you still have + + + align:start position:0% +zero lower bound but you still have +fiscal policy and they did a lot of + + align:start position:0% +fiscal policy and they did a lot of + + + align:start position:0% +fiscal policy and they did a lot of +fiscal policy + + align:start position:0% + + + + align:start position:0% + +not + + align:start position:0% +not + + + align:start position:0% +not +interesting this is this is interesting + + align:start position:0% +interesting this is this is interesting + + + align:start position:0% +interesting this is this is interesting +ER that's a different kind of shock + + align:start position:0% +ER that's a different kind of shock + + + align:start position:0% +ER that's a different kind of shock +suppose you are at your medium run + + align:start position:0% +suppose you are at your medium run + + + align:start position:0% +suppose you are at your medium run +equilibrium and then all of a sudden + + align:start position:0% +equilibrium and then all of a sudden + + + align:start position:0% +equilibrium and then all of a sudden +markups go up perhaps for example + + align:start position:0% +markups go up perhaps for example + + + align:start position:0% +markups go up perhaps for example +because the price of oil went up a lot + + align:start position:0% +because the price of oil went up a lot + + + align:start position:0% +because the price of oil went up a lot +and something like that so then what you + + align:start position:0% +and something like that so then what you + + + align:start position:0% +and something like that so then what you +then that's a different kind of shock + + align:start position:0% +then that's a different kind of shock + + + align:start position:0% +then that's a different kind of shock +from the previous one from from any + + align:start position:0% +from the previous one from from any + + + align:start position:0% +from the previous one from from any +fiscal sh or anything like that that's + + align:start position:0% +fiscal sh or anything like that that's + + + align:start position:0% +fiscal sh or anything like that that's +an aggregate demand this is an agre + + align:start position:0% +an aggregate demand this is an agre + + + align:start position:0% +an aggregate demand this is an agre +supply problem because the first thing I + + align:start position:0% +supply problem because the first thing I + + + align:start position:0% +supply problem because the first thing I +know of a permanent at least change in m + + align:start position:0% +know of a permanent at least change in m + + + align:start position:0% +know of a permanent at least change in m +is that the natural rate of unemployment + + align:start position:0% +is that the natural rate of unemployment + + + align:start position:0% +is that the natural rate of unemployment +has to + + align:start position:0% +has to + + + align:start position:0% +has to +rise if the natural rate of unemployment + + align:start position:0% +rise if the natural rate of unemployment + + + align:start position:0% +rise if the natural rate of unemployment +has to rise that mean my Philips Curve + + align:start position:0% +has to rise that mean my Philips Curve + + + align:start position:0% +has to rise that mean my Philips Curve +will shift + + align:start position:0% +will shift + + + align:start position:0% +will shift +now okay in that particular case I know + + align:start position:0% +now okay in that particular case I know + + + align:start position:0% +now okay in that particular case I know +the Philips Curve will shift to the left + + align:start position:0% +the Philips Curve will shift to the left + + + align:start position:0% +the Philips Curve will shift to the left +how do I know that well because I know + + align:start position:0% +how do I know that well because I know + + + align:start position:0% +how do I know that well because I know +that that the natural rate of + + align:start position:0% +that that the natural rate of + + + align:start position:0% +that that the natural rate of +unemployment went up which means the + + align:start position:0% +unemployment went up which means the + + + align:start position:0% +unemployment went up which means the +natural rate of natural level of output + + align:start position:0% +natural rate of natural level of output + + + align:start position:0% +natural rate of natural level of output +has to come down and the natural level + + align:start position:0% +has to come down and the natural level + + + align:start position:0% +has to come down and the natural level +of output coming down means simply that + + align:start position:0% +of output coming down means simply that + + + align:start position:0% +of output coming down means simply that +that the level at which is expected + + align:start position:0% +that the level at which is expected + + + align:start position:0% +that the level at which is expected +inflation and inflation are + + align:start position:0% +inflation and inflation are + + + align:start position:0% +inflation and inflation are +equal happens at a lower level of output + + align:start position:0% +equal happens at a lower level of output + + + align:start position:0% +equal happens at a lower level of output +so the Philips can move to the left so + + align:start position:0% +so the Philips can move to the left so + + + align:start position:0% +so the Philips can move to the left so +suppose you were in this equilibrium + + align:start position:0% +suppose you were in this equilibrium + + + align:start position:0% +suppose you were in this equilibrium +here I'm doing for the case of an anchor + + align:start position:0% +here I'm doing for the case of an anchor + + + align:start position:0% +here I'm doing for the case of an anchor +expectations but the same logic goes for + + align:start position:0% +expectations but the same logic goes for + + + align:start position:0% +expectations but the same logic goes for +the case of anchor expectation ER so + + align:start position:0% +the case of anchor expectation ER so + + + align:start position:0% +the case of anchor expectation ER so +suppose you were at some equilibrium + + align:start position:0% +suppose you were at some equilibrium + + + align:start position:0% +suppose you were at some equilibrium +like this it was your medium run + + align:start position:0% +like this it was your medium run + + + align:start position:0% +like this it was your medium run +equilibrium but now the price of energy + + align:start position:0% +equilibrium but now the price of energy + + + align:start position:0% +equilibrium but now the price of energy +goes up a lot and and and you expect + + align:start position:0% +goes up a lot and and and you expect + + + align:start position:0% +goes up a lot and and and you expect +that to last for a while that means the + + align:start position:0% +that to last for a while that means the + + + align:start position:0% +that to last for a while that means the +Philips curve moves up so that means + + align:start position:0% +Philips curve moves up so that means + + + align:start position:0% +Philips curve moves up so that means +that if output with output at this level + + align:start position:0% +that if output with output at this level + + + align:start position:0% +that if output with output at this level +now you get you have a problem because + + align:start position:0% +now you get you have a problem because + + + align:start position:0% +now you get you have a problem because +you start getting inflation out of this + + align:start position:0% +you start getting inflation out of this + + + align:start position:0% +you start getting inflation out of this +okay because this this level of output + + align:start position:0% +okay because this this level of output + + + align:start position:0% +okay because this this level of output +is too high relative to the new level of + + align:start position:0% +is too high relative to the new level of + + + align:start position:0% +is too high relative to the new level of +the natural the new level of natural + + align:start position:0% +the natural the new level of natural + + + align:start position:0% +the natural the new level of natural +level of output so you have a positive + + align:start position:0% +level of output so you have a positive + + + align:start position:0% +level of output so you have a positive +output Gap positive output Gap means + + align:start position:0% +output Gap positive output Gap means + + + align:start position:0% +output Gap positive output Gap means +inflation above expected inflation if + + align:start position:0% +inflation above expected inflation if + + + align:start position:0% +inflation above expected inflation if +you have an anchor expectations means + + align:start position:0% +you have an anchor expectations means + + + align:start position:0% +you have an anchor expectations means +inflation starts + + align:start position:0% +inflation starts + + + align:start position:0% +inflation starts +rising + + align:start position:0% +rising + + + align:start position:0% +rising +up so that means the FED now needs to + + align:start position:0% +up so that means the FED now needs to + + + align:start position:0% +up so that means the FED now needs to +react to that and needs to tighten + + align:start position:0% +react to that and needs to tighten + + + align:start position:0% +react to that and needs to tighten +interest rate in order to to go to a new + + align:start position:0% +interest rate in order to to go to a new + + + align:start position:0% +interest rate in order to to go to a new +level of H natural level of output okay + + align:start position:0% +level of H natural level of output okay + + + align:start position:0% +level of H natural level of output okay +and that's the response but if the F + + align:start position:0% +and that's the response but if the F + + + align:start position:0% +and that's the response but if the F +that's not react and a little bit of + + align:start position:0% +that's not react and a little bit of + + + align:start position:0% +that's not react and a little bit of +this is what happened we had some Supply + + align:start position:0% +this is what happened we had some Supply + + + align:start position:0% +this is what happened we had some Supply +shocks and so on that were considered to + + align:start position:0% +shocks and so on that were considered to + + + align:start position:0% +shocks and so on that were considered to +be temporary well they weren't as + + align:start position:0% +be temporary well they weren't as + + + align:start position:0% +be temporary well they weren't as +temporary so there was no reaction but + + align:start position:0% +temporary so there was no reaction but + + + align:start position:0% +temporary so there was no reaction but +it turns out that that they lasted a lot + + align:start position:0% +it turns out that that they lasted a lot + + + align:start position:0% +it turns out that that they lasted a lot +longer than the fair expected and so so + + align:start position:0% +longer than the fair expected and so so + + + align:start position:0% +longer than the fair expected and so so +so now they had to catch up + + align:start position:0% +so now they had to catch up + + + align:start position:0% +so now they had to catch up +okay that was part of the reason we got + + align:start position:0% +okay that was part of the reason we got + + + align:start position:0% +okay that was part of the reason we got +into a high inflation episode + + align:start position:0% +into a high inflation episode + + + align:start position:0% +into a high inflation episode +that was the main reason in + + align:start position:0% +that was the main reason in + + + align:start position:0% +that was the main reason in +Europe the US is a mixture of aggregate + + align:start position:0% +Europe the US is a mixture of aggregate + + + align:start position:0% +Europe the US is a mixture of aggregate +demand lots of fiscal policy and so on + + align:start position:0% +demand lots of fiscal policy and so on + + + align:start position:0% +demand lots of fiscal policy and so on +and ER and supply side in Europe was + + align:start position:0% +and ER and supply side in Europe was + + + align:start position:0% +and ER and supply side in Europe was +very much a story of this + + align:start position:0% + + + + align:start position:0% + +kind well a financial Panic you need to + + align:start position:0% +kind well a financial Panic you need to + + + align:start position:0% +kind well a financial Panic you need to +upset it with a decline in in in real + + align:start position:0% +upset it with a decline in in in real + + + align:start position:0% +upset it with a decline in in in real +interest rate and a little bit of that + + align:start position:0% +interest rate and a little bit of that + + + align:start position:0% +interest rate and a little bit of that +has been happening it's not the FED that + + align:start position:0% +has been happening it's not the FED that + + + align:start position:0% +has been happening it's not the FED that +has cut their rates but but the markets + + align:start position:0% +has cut their rates but but the markets + + + align:start position:0% +has cut their rates but but the markets +have anticipated the FED will not raise + + align:start position:0% +have anticipated the FED will not raise + + + align:start position:0% +have anticipated the FED will not raise +interest rate as much as they expected + + align:start position:0% +interest rate as much as they expected + + + align:start position:0% +interest rate as much as they expected +before we got we got into this banking + + align:start position:0% +before we got we got into this banking + + + align:start position:0% +before we got we got into this banking +mess so we had already sort of studied + + align:start position:0% +mess so we had already sort of studied + + + align:start position:0% +mess so we had already sort of studied +the short run the medium run and now we + + align:start position:0% +the short run the medium run and now we + + + align:start position:0% +the short run the medium run and now we +want to look at the long run okay and + + align:start position:0% +want to look at the long run okay and + + + align:start position:0% +want to look at the long run okay and +that's what economic growth is about + + align:start position:0% +that's what economic growth is about + + + align:start position:0% +that's what economic growth is about +economic growth Theory and facts and so + + align:start position:0% + + + + align:start position:0% + +on let me go to so one of the things I + + align:start position:0% +on let me go to so one of the things I + + + align:start position:0% +on let me go to so one of the things I +I highlighted is that we tend to + + align:start position:0% +I highlighted is that we tend to + + + align:start position:0% +I highlighted is that we tend to +see among countries that are fairly + + align:start position:0% +see among countries that are fairly + + + align:start position:0% +see among countries that are fairly +similar + + align:start position:0% + + + + align:start position:0% + +along education and variables like that + + align:start position:0% +along education and variables like that + + + align:start position:0% +along education and variables like that +systems economic systems and political + + align:start position:0% +systems economic systems and political + + + align:start position:0% +systems economic systems and political +systems and so on you tend to find + + align:start position:0% +systems and so on you tend to find + + + align:start position:0% +systems and so on you tend to find +relationship like this that is countries + + align:start position:0% +relationship like this that is countries + + + align:start position:0% +relationship like this that is countries +with a lower per capita income at the + + align:start position:0% +with a lower per capita income at the + + + align:start position:0% +with a lower per capita income at the +beginning of the sample tend to grow + + align:start position:0% +beginning of the sample tend to grow + + + align:start position:0% +beginning of the sample tend to grow +faster in the sample and that captures + + align:start position:0% +faster in the sample and that captures + + + align:start position:0% +faster in the sample and that captures +very much the idea that there's a + + align:start position:0% +very much the idea that there's a + + + align:start position:0% +very much the idea that there's a +convergence there's a force towards + + align:start position:0% +convergence there's a force towards + + + align:start position:0% +convergence there's a force towards +convergence of H income per capita if + + align:start position:0% +convergence of H income per capita if + + + align:start position:0% +convergence of H income per capita if +you will okay that's another + + align:start position:0% +you will okay that's another + + + align:start position:0% +you will okay that's another +illustration of that phenomenon lots of + + align:start position:0% +illustration of that phenomenon lots of + + + align:start position:0% +illustration of that phenomenon lots of +dispersion here ER 70 years later a lot + + align:start position:0% +dispersion here ER 70 years later a lot + + + align:start position:0% +dispersion here ER 70 years later a lot +less + + align:start position:0% +less + + + align:start position:0% +less +dispersion but we also said that some + + align:start position:0% +dispersion but we also said that some + + + align:start position:0% +dispersion but we also said that some +countries that do not match that and but + + align:start position:0% +countries that do not match that and but + + + align:start position:0% +countries that do not match that and but +we focus most of what we did in + + align:start position:0% +we focus most of what we did in + + + align:start position:0% +we focus most of what we did in +growth on understanding this process the + + align:start position:0% +growth on understanding this process the + + + align:start position:0% +growth on understanding this process the +process of convergence and how it + + align:start position:0% +process of convergence and how it + + + align:start position:0% +process of convergence and how it +happened with without technological + + align:start position:0% +happened with without technological + + + align:start position:0% +happened with without technological +progress and so on and then we spent a + + align:start position:0% +progress and so on and then we spent a + + + align:start position:0% +progress and so on and then we spent a +little bit of a lecture say at most 10 + + align:start position:0% +little bit of a lecture say at most 10 + + + align:start position:0% +little bit of a lecture say at most 10 +10 points worth in a quiz or seven + + align:start position:0% +10 points worth in a quiz or seven + + + align:start position:0% +10 points worth in a quiz or seven +points talking about sort of anomalies + + align:start position:0% +points talking about sort of anomalies + + + align:start position:0% +points talking about sort of anomalies +and things like that no five points or + + align:start position:0% + + + + align:start position:0% + +something so the key ER object here one + + align:start position:0% +something so the key ER object here one + + + align:start position:0% +something so the key ER object here one +of the key objects there there are a + + align:start position:0% +of the key objects there there are a + + + align:start position:0% +of the key objects there there are a +couple but but one of them was well now + + align:start position:0% +couple but but one of them was well now + + + align:start position:0% +couple but but one of them was well now +we need to be a little bit more serious + + align:start position:0% +we need to be a little bit more serious + + + align:start position:0% +we need to be a little bit more serious +about the production function we said + + align:start position:0% +about the production function we said + + + align:start position:0% +about the production function we said +because for the short it's okay to take + + align:start position:0% +because for the short it's okay to take + + + align:start position:0% +because for the short it's okay to take +Capital as given and just worry about + + align:start position:0% +Capital as given and just worry about + + + align:start position:0% +Capital as given and just worry about +most of the fluctuation in output will + + align:start position:0% +most of the fluctuation in output will + + + align:start position:0% +most of the fluctuation in output will +come from fluctuations in + + align:start position:0% +come from fluctuations in + + + align:start position:0% +come from fluctuations in +employment that's not so over long + + align:start position:0% +employment that's not so over long + + + align:start position:0% +employment that's not so over long +periods of time capital accumulation + + align:start position:0% +periods of time capital accumulation + + + align:start position:0% +periods of time capital accumulation +plays a huge role and so we need to be + + align:start position:0% +plays a huge role and so we need to be + + + align:start position:0% +plays a huge role and so we need to be +explicit about the fact that Capital + + align:start position:0% +explicit about the fact that Capital + + + align:start position:0% +explicit about the fact that Capital +matters a lot for production + + align:start position:0% +matters a lot for production + + + align:start position:0% +matters a lot for production +okay and so we postulated a production + + align:start position:0% +okay and so we postulated a production + + + align:start position:0% +okay and so we postulated a production +function like this output as increas + + align:start position:0% +function like this output as increas + + + align:start position:0% +function like this output as increas +increasing function of cap and of + + align:start position:0% +increasing function of cap and of + + + align:start position:0% +increasing function of cap and of +capital and labor and now we said for + + align:start position:0% +capital and labor and now we said for + + + align:start position:0% +capital and labor and now we said for +this part of the course we're not going + + align:start position:0% +this part of the course we're not going + + + align:start position:0% +this part of the course we're not going +to worry about unemployment and so on + + align:start position:0% +to worry about unemployment and so on + + + align:start position:0% +to worry about unemployment and so on +employment labor force population + + align:start position:0% +employment labor force population + + + align:start position:0% +employment labor force population +they're all the same for us here for + + align:start position:0% +they're all the same for us here for + + + align:start position:0% +they're all the same for us here for +this part of the course and then said + + align:start position:0% +this part of the course and then said + + + align:start position:0% +this part of the course and then said +this production function has some + + align:start position:0% +this production function has some + + + align:start position:0% +this production function has some +important + + align:start position:0% +important + + + align:start position:0% +important +properties one is it has constant + + align:start position:0% +properties one is it has constant + + + align:start position:0% +properties one is it has constant +returns to scale things change quite a + + align:start position:0% +returns to scale things change quite a + + + align:start position:0% +returns to scale things change quite a +bit if you don't have constant return to + + align:start position:0% +bit if you don't have constant return to + + + align:start position:0% +bit if you don't have constant return to +scale so we have constant return to + + align:start position:0% +scale so we have constant return to + + + align:start position:0% +scale so we have constant return to +scale which means you should know this + + align:start position:0% +scale which means you should know this + + + align:start position:0% +scale which means you should know this +that if you scale all output all input + + align:start position:0% +that if you scale all output all input + + + align:start position:0% +that if you scale all output all input +all the factors of Productions by the + + align:start position:0% +all the factors of Productions by the + + + align:start position:0% +all the factors of Productions by the +same factor output Also Rises by the + + align:start position:0% +same factor output Also Rises by the + + + align:start position:0% +same factor output Also Rises by the +same factor okay so a production + + align:start position:0% +same factor okay so a production + + + align:start position:0% +same factor okay so a production +function we use a lot was aob Douglas + + align:start position:0% +function we use a lot was aob Douglas + + + align:start position:0% +function we use a lot was aob Douglas +you know output equal square root of K * + + align:start position:0% +you know output equal square root of K * + + + align:start position:0% +you know output equal square root of K * +the square root of n well the sum of + + align:start position:0% +the square root of n well the sum of + + + align:start position:0% +the square root of n well the sum of +those exponents is one so that's a a + + align:start position:0% +those exponents is one so that's a a + + + align:start position:0% +those exponents is one so that's a a +production function with constant return + + align:start position:0% +production function with constant return + + + align:start position:0% +production function with constant return +to scale okay so anything that has the + + align:start position:0% +to scale okay so anything that has the + + + align:start position:0% +to scale okay so anything that has the +exponents add up to one then you're + + align:start position:0% +exponents add up to one then you're + + + align:start position:0% +exponents add up to one then you're +that's a constant return to scale + + align:start position:0% +that's a constant return to scale + + + align:start position:0% +that's a constant return to scale +technology but importantly and it also + + align:start position:0% +technology but importantly and it also + + + align:start position:0% +technology but importantly and it also +has decreasing returns with each of its + + align:start position:0% +has decreasing returns with each of its + + + align:start position:0% +has decreasing returns with each of its +factor of production + + align:start position:0% +factor of production + + + align:start position:0% +factor of production +that means as you rather than moving + + align:start position:0% +that means as you rather than moving + + + align:start position:0% +that means as you rather than moving +both factors of production up you move + + align:start position:0% +both factors of production up you move + + + align:start position:0% +both factors of production up you move +only one well you're going to increase + + align:start position:0% +only one well you're going to increase + + + align:start position:0% +only one well you're going to increase +output but as just keep increasing that + + align:start position:0% +output but as just keep increasing that + + + align:start position:0% +output but as just keep increasing that +factor alone you're going to increase + + align:start position:0% +factor alone you're going to increase + + + align:start position:0% +factor alone you're going to increase +output by less and less and less and + + align:start position:0% +output by less and less and less and + + + align:start position:0% +output by less and less and less and +less because essentially has fewer and + + align:start position:0% +less because essentially has fewer and + + + align:start position:0% +less because essentially has fewer and +fewer of the + + align:start position:0% +fewer of the + + + align:start position:0% +fewer of the +other factor of production to work with + + align:start position:0% +other factor of production to work with + + + align:start position:0% +other factor of production to work with +okay and so that's decreasing returns to + + align:start position:0% +okay and so that's decreasing returns to + + + align:start position:0% +okay and so that's decreasing returns to +Capital or labor I mean if you fix the + + align:start position:0% +Capital or labor I mean if you fix the + + + align:start position:0% +Capital or labor I mean if you fix the +other factor of production you move up + + align:start position:0% +other factor of production you move up + + + align:start position:0% +other factor of production you move up +it's going to increase at a decreasing + + align:start position:0% +it's going to increase at a decreasing + + + align:start position:0% +it's going to increase at a decreasing +rate so one normalization that we start + + align:start position:0% +rate so one normalization that we start + + + align:start position:0% +rate so one normalization that we start +with was well a scaling Factor could be + + align:start position:0% +with was well a scaling Factor could be + + + align:start position:0% +with was well a scaling Factor could be +a population one over population okay + + align:start position:0% +a population one over population okay + + + align:start position:0% +a population one over population okay +that's a scaling factor and if I do that + + align:start position:0% +that's a scaling factor and if I do that + + + align:start position:0% +that's a scaling factor and if I do that +I multiply both everything by one / n + + align:start position:0% +I multiply both everything by one / n + + + align:start position:0% +I multiply both everything by one / n +would go into output per person is an + + align:start position:0% +would go into output per person is an + + + align:start position:0% +would go into output per person is an +increasing function of a increasing + + align:start position:0% +increasing function of a increasing + + + align:start position:0% +increasing function of a increasing +function but at a increasing rate of + + align:start position:0% +function but at a increasing rate of + + + align:start position:0% +function but at a increasing rate of +capital per person okay we plot that + + align:start position:0% +capital per person okay we plot that + + + align:start position:0% +capital per person okay we plot that +function here and and this conc is + + align:start position:0% +function here and and this conc is + + + align:start position:0% +function here and and this conc is +increasing but it's concave that shows + + align:start position:0% +increasing but it's concave that shows + + + align:start position:0% +increasing but it's concave that shows +the decreasing returns of capital no h + + align:start position:0% +the decreasing returns of capital no h + + + align:start position:0% +the decreasing returns of capital no h +and we got that function there then the + + align:start position:0% +and we got that function there then the + + + align:start position:0% +and we got that function there then the +SEC uh and we talk + + align:start position:0% +SEC uh and we talk + + + align:start position:0% +SEC uh and we talk +well we said H so so so when you move in + + align:start position:0% +well we said H so so so when you move in + + + align:start position:0% +well we said H so so so when you move in +this you can increase output per person + + align:start position:0% +this you can increase output per person + + + align:start position:0% +this you can increase output per person +per per person by simply increasing + + align:start position:0% +per per person by simply increasing + + + align:start position:0% +per per person by simply increasing +Capital per person and the more you + + align:start position:0% +Capital per person and the more you + + + align:start position:0% +Capital per person and the more you +increase Capital per person output will + + align:start position:0% +increase Capital per person output will + + + align:start position:0% +increase Capital per person output will +increase more and more but but but at a + + align:start position:0% +increase more and more but but but at a + + + align:start position:0% +increase more and more but but but at a +decreasing rate you can see that moving + + align:start position:0% +decreasing rate you can see that moving + + + align:start position:0% +decreasing rate you can see that moving +a the distance between A and B is the + + align:start position:0% +a the distance between A and B is the + + + align:start position:0% +a the distance between A and B is the +same as the distance between C and D + + align:start position:0% +same as the distance between C and D + + + align:start position:0% +same as the distance between C and D +however the increasing output when you + + align:start position:0% +however the increasing output when you + + + align:start position:0% +however the increasing output when you +go from A to B is enormous compar when + + align:start position:0% +go from A to B is enormous compar when + + + align:start position:0% +go from A to B is enormous compar when +compare with the increasing output that + + align:start position:0% +compare with the increasing output that + + + align:start position:0% +compare with the increasing output that +you get from the increasing capitals + + align:start position:0% +you get from the increasing capitals + + + align:start position:0% +you get from the increasing capitals +over per per person from C to D okay + + align:start position:0% +over per per person from C to D okay + + + align:start position:0% +over per per person from C to D okay +decreasing returns this there is another + + align:start position:0% +decreasing returns this there is another + + + align:start position:0% +decreasing returns this there is another +way of of increasing output per person + + align:start position:0% +way of of increasing output per person + + + align:start position:0% +way of of increasing output per person +which is with technological progress + + align:start position:0% +which is with technological progress + + + align:start position:0% +which is with technological progress +when the function f shifting up over + + align:start position:0% +when the function f shifting up over + + + align:start position:0% +when the function f shifting up over +time and we split the two main lectures + + align:start position:0% +time and we split the two main lectures + + + align:start position:0% +time and we split the two main lectures +in grow both into one part one in which + + align:start position:0% +in grow both into one part one in which + + + align:start position:0% +in grow both into one part one in which +we just we shut down the second Channel + + align:start position:0% +we just we shut down the second Channel + + + align:start position:0% +we just we shut down the second Channel +and then the second important lecture + + align:start position:0% +and then the second important lecture + + + align:start position:0% +and then the second important lecture +here had we focus on this channel so + + align:start position:0% +here had we focus on this channel so + + + align:start position:0% +here had we focus on this channel so +that's a that's what we + + align:start position:0% + + + + align:start position:0% + +have so let's go to when I shut down + + align:start position:0% +have so let's go to when I shut down + + + align:start position:0% +have so let's go to when I shut down +this channel for now and focus on on the + + align:start position:0% +this channel for now and focus on on the + + + align:start position:0% +this channel for now and focus on on the +case without technological progress + + align:start position:0% +case without technological progress + + + align:start position:0% +case without technological progress +first okay so so we put things together + + align:start position:0% +first okay so so we put things together + + + align:start position:0% +first okay so so we put things together +we said this is comes from the previous + + align:start position:0% +we said this is comes from the previous + + + align:start position:0% +we said this is comes from the previous +lecture we can write a output per + + align:start position:0% +lecture we can write a output per + + + align:start position:0% +lecture we can write a output per +uh per person as an increasing function + + align:start position:0% +uh per person as an increasing function + + + align:start position:0% +uh per person as an increasing function +of um Capital per person second key + + align:start position:0% +of um Capital per person second key + + + align:start position:0% +of um Capital per person second key +equation is well this is a proper it has + + align:start position:0% +equation is well this is a proper it has + + + align:start position:0% +equation is well this is a proper it has +to be if you in a closed economy no over + + align:start position:0% +to be if you in a closed economy no over + + + align:start position:0% +to be if you in a closed economy no over +expenditure or anything like we could + + align:start position:0% +expenditure or anything like we could + + + align:start position:0% +expenditure or anything like we could +add that but it's not important for the + + align:start position:0% +add that but it's not important for the + + + align:start position:0% +add that but it's not important for the +message then investment has to be equal + + align:start position:0% +message then investment has to be equal + + + align:start position:0% +message then investment has to be equal +so investment is going to be very + + align:start position:0% +so investment is going to be very + + + align:start position:0% +so investment is going to be very +important here because it's what will + + align:start position:0% +important here because it's what will + + + align:start position:0% +important here because it's what will +make the Capital stock grow but there + + align:start position:0% +make the Capital stock grow but there + + + align:start position:0% +make the Capital stock grow but there +has to be funed fing for that and the + + align:start position:0% +has to be funed fing for that and the + + + align:start position:0% +has to be funed fing for that and the +funding come from saving okay and we + + align:start position:0% +funding come from saving okay and we + + + align:start position:0% +funding come from saving okay and we +simplify things by assuming that the + + align:start position:0% +simplify things by assuming that the + + + align:start position:0% +simplify things by assuming that the +saving function is just proportional to + + align:start position:0% +saving function is just proportional to + + + align:start position:0% +saving function is just proportional to +the level of output which is reasonable + + align:start position:0% +the level of output which is reasonable + + + align:start position:0% +the level of output which is reasonable +when you think about long run all these + + align:start position:0% +when you think about long run all these + + + align:start position:0% +when you think about long run all these +things scale up when you're thinking + + align:start position:0% +things scale up when you're thinking + + + align:start position:0% +things scale up when you're thinking +about very shortterm no we have some + + align:start position:0% +about very shortterm no we have some + + + align:start position:0% +about very shortterm no we have some +constants and so on floating around but + + align:start position:0% +constants and so on floating around but + + + align:start position:0% +constants and so on floating around but +but but over the long run things do + + align:start position:0% +but but over the long run things do + + + align:start position:0% +but but over the long run things do +scale up and so we can write investment + + align:start position:0% +scale up and so we can write investment + + + align:start position:0% +scale up and so we can write investment +in equilibrium investment has to be + + align:start position:0% +in equilibrium investment has to be + + + align:start position:0% +in equilibrium investment has to be +equal to saving saving is proportional + + align:start position:0% +equal to saving saving is proportional + + + align:start position:0% +equal to saving saving is proportional +to Output so we get that investment in + + align:start position:0% +to Output so we get that investment in + + + align:start position:0% +to Output so we get that investment in +this economy is increasing in output + + align:start position:0% +this economy is increasing in output + + + align:start position:0% +this economy is increasing in output +this is an constant somewhere between + + align:start position:0% +this is an constant somewhere between + + + align:start position:0% +this is an constant somewhere between +zero and one okay and the last key + + align:start position:0% +zero and one okay and the last key + + + align:start position:0% +zero and one okay and the last key +equation here is the capital + + align:start position:0% +equation here is the capital + + + align:start position:0% +equation here is the capital +accumulation equation the capital + + align:start position:0% +accumulation equation the capital + + + align:start position:0% +accumulation equation the capital +accumulation equation says that Capital + + align:start position:0% +accumulation equation says that Capital + + + align:start position:0% +accumulation equation says that Capital +t+ One is equal to Capital today minus + + align:start position:0% +t+ One is equal to Capital today minus + + + align:start position:0% +t+ One is equal to Capital today minus +the depreciation some a fraction of the + + align:start position:0% +the depreciation some a fraction of the + + + align:start position:0% +the depreciation some a fraction of the +machines break down in every period but + + align:start position:0% +machines break down in every period but + + + align:start position:0% +machines break down in every period but +plus the new investment plus I okay and + + align:start position:0% +plus the new investment plus I okay and + + + align:start position:0% +plus the new investment plus I okay and +we rote things and replace the saving + + align:start position:0% +we rote things and replace the saving + + + align:start position:0% +we rote things and replace the saving +function and so on and we end up in in + + align:start position:0% +function and so on and we end up in in + + + align:start position:0% +function and so on and we end up in in +in qu an expression like this that says + + align:start position:0% +in qu an expression like this that says + + + align:start position:0% +in qu an expression like this that says +Capital per person here grows with + + align:start position:0% +Capital per person here grows with + + + align:start position:0% +Capital per person here grows with +investment which is funded by savings + + align:start position:0% +investment which is funded by savings + + + align:start position:0% +investment which is funded by savings +which is an increasing function of + + align:start position:0% +which is an increasing function of + + + align:start position:0% +which is an increasing function of +output which in turn is an increasing + + align:start position:0% +output which in turn is an increasing + + + align:start position:0% +output which in turn is an increasing +function of capital per person minus + + align:start position:0% +function of capital per person minus + + + align:start position:0% +function of capital per person minus +whatever is the depreciation and what we + + align:start position:0% +whatever is the depreciation and what we + + + align:start position:0% +whatever is the depreciation and what we +did then the the start diagram in in in + + align:start position:0% +did then the the start diagram in in in + + + align:start position:0% +did then the the start diagram in in in +the solo model is is we plot this + + align:start position:0% +the solo model is is we plot this + + + align:start position:0% +the solo model is is we plot this +function and that function we know that + + align:start position:0% +function and that function we know that + + + align:start position:0% +function and that function we know that +the state state is when these two things + + align:start position:0% +the state state is when these two things + + + align:start position:0% +the state state is when these two things +are equal that pins down the K star of + + align:start position:0% +are equal that pins down the K star of + + + align:start position:0% +are equal that pins down the K star of +over n k Over N start of this economy + + align:start position:0% +over n k Over N start of this economy + + + align:start position:0% +over n k Over N start of this economy +but we also know that to the left of + + align:start position:0% +but we also know that to the left of + + + align:start position:0% +but we also know that to the left of +that point in in capital + + align:start position:0% +that point in in capital + + + align:start position:0% +that point in in capital +space this term is greater than that and + + align:start position:0% +space this term is greater than that and + + + align:start position:0% +space this term is greater than that and +therefore H the Capital stock is rising + + align:start position:0% +therefore H the Capital stock is rising + + + align:start position:0% +therefore H the Capital stock is rising +to the right we get that this term is + + align:start position:0% +to the right we get that this term is + + + align:start position:0% +to the right we get that this term is +greater than that and therefore the + + align:start position:0% +greater than that and therefore the + + + align:start position:0% +greater than that and therefore the +Capital stock is falling okay and that's + + align:start position:0% +Capital stock is falling okay and that's + + + align:start position:0% +Capital stock is falling okay and that's +what we have in this diagram so that's + + align:start position:0% +what we have in this diagram so that's + + + align:start position:0% +what we have in this diagram so that's +the state of the economy when when the + + align:start position:0% +the state of the economy when when the + + + align:start position:0% +the state of the economy when when the +depreciation per worker which is the + + align:start position:0% +depreciation per worker which is the + + + align:start position:0% +depreciation per worker which is the +require in the minimum in you need to + + align:start position:0% +require in the minimum in you need to + + + align:start position:0% +require in the minimum in you need to +keep the Capital stock constant is + + align:start position:0% +keep the Capital stock constant is + + + align:start position:0% +keep the Capital stock constant is +whatever is depreciation per worker no + + align:start position:0% +whatever is depreciation per worker no + + + align:start position:0% +whatever is depreciation per worker no +anything else you do it will grow the + + align:start position:0% +anything else you do it will grow the + + + align:start position:0% +anything else you do it will grow the +stock of capital anything less you do + + align:start position:0% +stock of capital anything less you do + + + align:start position:0% +stock of capital anything less you do +you're not maintaining enough of your + + align:start position:0% +you're not maintaining enough of your + + + align:start position:0% +you're not maintaining enough of your +Capital stock is declining and that's + + align:start position:0% +Capital stock is declining and that's + + + align:start position:0% +Capital stock is declining and that's +exactly what happens here that's State + + align:start position:0% +exactly what happens here that's State + + + align:start position:0% +exactly what happens here that's State +you have Capital below that then then uh + + align:start position:0% +you have Capital below that then then uh + + + align:start position:0% +you have Capital below that then then uh +Capital stock will be rising because you + + align:start position:0% +Capital stock will be rising because you + + + align:start position:0% +Capital stock will be rising because you +have lots of saving and therefore lots + + align:start position:0% +have lots of saving and therefore lots + + + align:start position:0% +have lots of saving and therefore lots +of investment relative to what you need + + align:start position:0% +of investment relative to what you need + + + align:start position:0% +of investment relative to what you need +in order to maintain the stock of the + + align:start position:0% +in order to maintain the stock of the + + + align:start position:0% +in order to maintain the stock of the +small stock of capital you have until + + align:start position:0% +small stock of capital you have until + + + align:start position:0% +small stock of capital you have until +you reach a c state + + align:start position:0% + + + + align:start position:0% + +and the and you know the this model + + align:start position:0% +and the and you know the this model + + + align:start position:0% +and the and you know the this model +alone can explain really the that + + align:start position:0% +alone can explain really the that + + + align:start position:0% +alone can explain really the that +pattern we have that that you know that + + align:start position:0% +pattern we have that that you know that + + + align:start position:0% +pattern we have that that you know that +the poorer economies tended to grow + + align:start position:0% +the poorer economies tended to grow + + + align:start position:0% +the poorer economies tended to grow +faster than the Richer economies if you + + align:start position:0% +faster than the Richer economies if you + + + align:start position:0% +faster than the Richer economies if you +think of poorer economies as economies + + align:start position:0% +think of poorer economies as economies + + + align:start position:0% +think of poorer economies as economies +that are otherwise similar but that have + + align:start position:0% +that are otherwise similar but that have + + + align:start position:0% +that are otherwise similar but that have +low a low stock of capital to start with + + align:start position:0% +low a low stock of capital to start with + + + align:start position:0% +low a low stock of capital to start with +well those economies are going to be to + + align:start position:0% +well those economies are going to be to + + + align:start position:0% +well those economies are going to be to +the left of the stady state and + + align:start position:0% +the left of the stady state and + + + align:start position:0% +the left of the stady state and +therefore they're going to tend to grow + + align:start position:0% +therefore they're going to tend to grow + + + align:start position:0% +therefore they're going to tend to grow +at whatever is the steady state rate of + + align:start position:0% +at whatever is the steady state rate of + + + align:start position:0% +at whatever is the steady state rate of +growth plus this catching up growth okay + + align:start position:0% +growth plus this catching up growth okay + + + align:start position:0% +growth plus this catching up growth okay +and so this is a very powerful little + + align:start position:0% +and so this is a very powerful little + + + align:start position:0% +and so this is a very powerful little +model it can explain a lot of that those + + align:start position:0% +model it can explain a lot of that those + + + align:start position:0% +model it can explain a lot of that those +convergence the convergence that we saw + + align:start position:0% +convergence the convergence that we saw + + + align:start position:0% +convergence the convergence that we saw +in in the data + + align:start position:0% +in in the data + + + align:start position:0% +in in the data +okay do you understand + + align:start position:0% +okay do you understand + + + align:start position:0% +okay do you understand +this this is + + align:start position:0% + + + + align:start position:0% + +important + + align:start position:0% +important + + + align:start position:0% +important +okay then we did some experiments what + + align:start position:0% +okay then we did some experiments what + + + align:start position:0% +okay then we did some experiments what +happens if you increase the saving rate + + align:start position:0% +happens if you increase the saving rate + + + align:start position:0% +happens if you increase the saving rate +at the time when solo was writing this + + align:start position:0% +at the time when solo was writing this + + + align:start position:0% +at the time when solo was writing this +model many people said that what was + + align:start position:0% +model many people said that what was + + + align:start position:0% +model many people said that what was +behind growth was saving well in this + + align:start position:0% +behind growth was saving well in this + + + align:start position:0% +behind growth was saving well in this +model we show that indeed if a saving + + align:start position:0% +model we show that indeed if a saving + + + align:start position:0% +model we show that indeed if a saving +rate Rises then you at any given level + + align:start position:0% +rate Rises then you at any given level + + + align:start position:0% +rate Rises then you at any given level +of capital suppose that was the oldest + + align:start position:0% +of capital suppose that was the oldest + + + align:start position:0% +of capital suppose that was the oldest +state if now the saving rate Rises that + + align:start position:0% +state if now the saving rate Rises that + + + align:start position:0% +state if now the saving rate Rises that +will increase H increase investment + + align:start position:0% +will increase H increase investment + + + align:start position:0% +will increase H increase investment +above what you need to maintain that + + align:start position:0% +above what you need to maintain that + + + align:start position:0% +above what you need to maintain that +level of the stock of capital so the + + align:start position:0% +level of the stock of capital so the + + + align:start position:0% +level of the stock of capital so the +stock stock of capital going to start + + align:start position:0% +stock stock of capital going to start + + + align:start position:0% +stock stock of capital going to start +growing when that happens output per + + align:start position:0% +growing when that happens output per + + + align:start position:0% +growing when that happens output per +capita will grow faster than in a state + + align:start position:0% +capita will grow faster than in a state + + + align:start position:0% +capita will grow faster than in a state +state because you're going to go be + + align:start position:0% +state because you're going to go be + + + align:start position:0% +state because you're going to go be +going from here to there but eventually + + align:start position:0% +going from here to there but eventually + + + align:start position:0% +going from here to there but eventually +you'll converge to the same whole rate + + align:start position:0% +you'll converge to the same whole rate + + + align:start position:0% +you'll converge to the same whole rate +of growth so the point here is that the + + align:start position:0% +of growth so the point here is that the + + + align:start position:0% +of growth so the point here is that the +saving rate cannot change per se does + + align:start position:0% +saving rate cannot change per se does + + + align:start position:0% +saving rate cannot change per se does +not change the rate of growth in the + + align:start position:0% +not change the rate of growth in the + + + align:start position:0% +not change the rate of growth in the +long run but it gives you transitional + + align:start position:0% +long run but it gives you transitional + + + align:start position:0% +long run but it gives you transitional +growth and a lot of the the Asian + + align:start position:0% +growth and a lot of the the Asian + + + align:start position:0% +growth and a lot of the the Asian +Miracle of the very fast rates of growth + + align:start position:0% +Miracle of the very fast rates of growth + + + align:start position:0% +Miracle of the very fast rates of growth +from the 60s and 70s and 80s has to do + + align:start position:0% +from the 60s and 70s and 80s has to do + + + align:start position:0% +from the 60s and 70s and 80s has to do +with this kind of thing very sudden + + align:start position:0% +with this kind of thing very sudden + + + align:start position:0% +with this kind of thing very sudden +increasing saving rates plus other + + align:start position:0% +increasing saving rates plus other + + + align:start position:0% +increasing saving rates plus other +institutional changes and so on but High + + align:start position:0% +institutional changes and so on but High + + + align:start position:0% +institutional changes and so on but High +increase in the saving rate that also Le + + align:start position:0% +increase in the saving rate that also Le + + + align:start position:0% +increase in the saving rate that also Le +led to very fast growth okay so again + + align:start position:0% +led to very fast growth okay so again + + + align:start position:0% +led to very fast growth okay so again +this little model can explain a lot as + + align:start position:0% +this little model can explain a lot as + + + align:start position:0% +this little model can explain a lot as +well it can explain when you see those + + align:start position:0% +well it can explain when you see those + + + align:start position:0% +well it can explain when you see those +growth Miracles often is associated to + + align:start position:0% +growth Miracles often is associated to + + + align:start position:0% +growth Miracles often is associated to +some for some + + align:start position:0% +some for some + + + align:start position:0% +some for some +reason varies a lot across different + + align:start position:0% +reason varies a lot across different + + + align:start position:0% +reason varies a lot across different +scenarios the saving rate went up quite + + align:start position:0% +scenarios the saving rate went up quite + + + align:start position:0% +scenarios the saving rate went up quite +a + + align:start position:0% +a + + + align:start position:0% +a +bit but point is so that gives you very + + align:start position:0% +bit but point is so that gives you very + + + align:start position:0% +bit but point is so that gives you very +fast growth in the short term but + + align:start position:0% +fast growth in the short term but + + + align:start position:0% +fast growth in the short term but +eventually pets out + + align:start position:0% +eventually pets out + + + align:start position:0% +eventually pets out +okay so the the the next thing we all + + align:start position:0% +okay so the the the next thing we all + + + align:start position:0% +okay so the the the next thing we all +that we did for a fixed population it + + align:start position:0% +that we did for a fixed population it + + + align:start position:0% +that we did for a fixed population it +said well so suppose now the population + + align:start position:0% +said well so suppose now the population + + + align:start position:0% +said well so suppose now the population +is + + align:start position:0% +is + + + align:start position:0% +is +growing H I said the diagram we had + + align:start position:0% +growing H I said the diagram we had + + + align:start position:0% +growing H I said the diagram we had +before would be very unpleasant because + + align:start position:0% +before would be very unpleasant because + + + align:start position:0% +before would be very unpleasant because +all these curves would be shifting so + + align:start position:0% +all these curves would be shifting so + + + align:start position:0% +all these curves would be shifting so +what we need well what we need to do is + + align:start position:0% +what we need well what we need to do is + + + align:start position:0% +what we need well what we need to do is +divide not by a constant we need to + + align:start position:0% +divide not by a constant we need to + + + align:start position:0% +divide not by a constant we need to +divide by whatever is the population at + + align:start position:0% +divide by whatever is the population at + + + align:start position:0% +divide by whatever is the population at +that point in time and that will give us + + align:start position:0% +that point in time and that will give us + + + align:start position:0% +that point in time and that will give us +the same diagram we had with one little + + align:start position:0% +the same diagram we had with one little + + + align:start position:0% +the same diagram we had with one little +twist so I went through sort of a little + + align:start position:0% +twist so I went through sort of a little + + + align:start position:0% +twist so I went through sort of a little +algebra here to arrive to a capital + + align:start position:0% +algebra here to arrive to a capital + + + align:start position:0% +algebra here to arrive to a capital +accumulation equation Capital per person + + align:start position:0% +accumulation equation Capital per person + + + align:start position:0% +accumulation equation Capital per person +equ an equation for the change in the + + align:start position:0% +equ an equation for the change in the + + + align:start position:0% +equ an equation for the change in the +capital per person which is very similar + + align:start position:0% +capital per person which is very similar + + + align:start position:0% +capital per person which is very similar +to what we had the only difference is + + align:start position:0% +to what we had the only difference is + + + align:start position:0% +to what we had the only difference is +that the required capital investment + + align:start position:0% +that the required capital investment + + + align:start position:0% +that the required capital investment +required to maintain the stock of + + align:start position:0% +required to maintain the stock of + + + align:start position:0% +required to maintain the stock of +capital per person has an extra term + + align:start position:0% +capital per person has an extra term + + + align:start position:0% +capital per person has an extra term +here + + align:start position:0% +here + + + align:start position:0% +here +GM and I said that GM so let's think + + align:start position:0% +GM and I said that GM so let's think + + + align:start position:0% +GM and I said that GM so let's think +about this + + align:start position:0% +about this + + + align:start position:0% +about this +term so Delta so think of this as the + + align:start position:0% +term so Delta so think of this as the + + + align:start position:0% +term so Delta so think of this as the +required + + align:start position:0% +required + + + align:start position:0% +required +investment in order to maintain the + + align:start position:0% +investment in order to maintain the + + + align:start position:0% +investment in order to maintain the +stock of capital where it + + align:start position:0% +stock of capital where it + + + align:start position:0% +stock of capital where it +was ER if if h this Delta comes from the + + align:start position:0% +was ER if if h this Delta comes from the + + + align:start position:0% +was ER if if h this Delta comes from the +fact that well you have a stock of + + align:start position:0% +fact that well you have a stock of + + + align:start position:0% +fact that well you have a stock of +capital you lose a fraction of that well + + align:start position:0% +capital you lose a fraction of that well + + + align:start position:0% +capital you lose a fraction of that well +you need an investment equal to that + + align:start position:0% +you need an investment equal to that + + + align:start position:0% +you need an investment equal to that +fraction that you lost in order to + + align:start position:0% +fraction that you lost in order to + + + align:start position:0% +fraction that you lost in order to +maintain the stock of capital the same + + align:start position:0% +maintain the stock of capital the same + + + align:start position:0% +maintain the stock of capital the same +that's that's that's that's + + align:start position:0% +that's that's that's that's + + + align:start position:0% +that's that's that's that's +clear but that's not enough to maintain + + align:start position:0% +clear but that's not enough to maintain + + + align:start position:0% +clear but that's not enough to maintain +the capital per person constant if if + + align:start position:0% +the capital per person constant if if + + + align:start position:0% +the capital per person constant if if +per person is rising population is + + align:start position:0% +per person is rising population is + + + align:start position:0% +per person is rising population is +rising because even if you maintain the + + align:start position:0% +rising because even if you maintain the + + + align:start position:0% +rising because even if you maintain the +stock of capital constant the + + align:start position:0% +stock of capital constant the + + + align:start position:0% +stock of capital constant the +denominator is rising at the rate of + + align:start position:0% +denominator is rising at the rate of + + + align:start position:0% +denominator is rising at the rate of +population growth + + align:start position:0% +population growth + + + align:start position:0% +population growth +so in order to maintain the capital per + + align:start position:0% +so in order to maintain the capital per + + + align:start position:0% +so in order to maintain the capital per +person constant you need to deal with + + align:start position:0% +person constant you need to deal with + + + align:start position:0% +person constant you need to deal with +the growth of denominator as well and + + align:start position:0% +the growth of denominator as well and + + + align:start position:0% +the growth of denominator as well and +that means you need a little you need + + align:start position:0% +that means you need a little you need + + + align:start position:0% +that means you need a little you need +also investment to match the increase in + + align:start position:0% +also investment to match the increase in + + + align:start position:0% +also investment to match the increase in +population so they can keep the capital + + align:start position:0% +population so they can keep the capital + + + align:start position:0% +population so they can keep the capital +per person constant okay so that's a + + align:start position:0% +per person constant okay so that's a + + + align:start position:0% +per person constant okay so that's a +that's a modification so in terms of our + + align:start position:0% +that's a modification so in terms of our + + + align:start position:0% +that's a modification so in terms of our +diagram all that happened here I have + + align:start position:0% +diagram all that happened here I have + + + align:start position:0% +diagram all that happened here I have +technological progress as well set it to + + align:start position:0% +technological progress as well set it to + + + align:start position:0% +technological progress as well set it to +zero for now all that happened relative + + align:start position:0% +zero for now all that happened relative + + + align:start position:0% +zero for now all that happened relative +to the previous diagram is that now this + + align:start position:0% +to the previous diagram is that now this + + + align:start position:0% +to the previous diagram is that now this +I rotated this curve up upward a little + + align:start position:0% +I rotated this curve up upward a little + + + align:start position:0% +I rotated this curve up upward a little +bit okay + + align:start position:0% + + + + align:start position:0% + +GN but then you conduct analysis exactly + + align:start position:0% +GN but then you conduct analysis exactly + + + align:start position:0% +GN but then you conduct analysis exactly +in the same way the only thing that is + + align:start position:0% +in the same way the only thing that is + + + align:start position:0% +in the same way the only thing that is +different now is that in the previous + + align:start position:0% +different now is that in the previous + + + align:start position:0% +different now is that in the previous +model we had that the rate of growth the + + align:start position:0% +model we had that the rate of growth the + + + align:start position:0% +model we had that the rate of growth the +stady state rate of growth was equal to + + align:start position:0% +stady state rate of growth was equal to + + + align:start position:0% +stady state rate of growth was equal to +zero and the state state rate of growth + + align:start position:0% +zero and the state state rate of growth + + + align:start position:0% +zero and the state state rate of growth +of output per person was also equal to + + align:start position:0% +of output per person was also equal to + + + align:start position:0% +of output per person was also equal to +zero population was not growing output + + align:start position:0% +zero population was not growing output + + + align:start position:0% +zero population was not growing output +was not growing the ratio wasn't growing + + align:start position:0% +was not growing the ratio wasn't growing + + + align:start position:0% +was not growing the ratio wasn't growing +either here is still the case that in a + + align:start position:0% +either here is still the case that in a + + + align:start position:0% +either here is still the case that in a +steady state output per person is is not + + align:start position:0% +steady state output per person is is not + + + align:start position:0% +steady state output per person is is not +growing okay but that also means since + + align:start position:0% +growing okay but that also means since + + + align:start position:0% +growing okay but that also means since +population is growing at the rate GN or + + align:start position:0% +population is growing at the rate GN or + + + align:start position:0% +population is growing at the rate GN or +N I don't know how I call it here H that + + align:start position:0% +N I don't know how I call it here H that + + + align:start position:0% +N I don't know how I call it here H that +means output must be also growing at the + + align:start position:0% +means output must be also growing at the + + + align:start position:0% +means output must be also growing at the +rate GN that's what will keep output per + + align:start position:0% +rate GN that's what will keep output per + + + align:start position:0% +rate GN that's what will keep output per +person not growing okay so so for the + + align:start position:0% +person not growing okay so so for the + + + align:start position:0% +person not growing okay so so for the +output itself a very important factor in + + align:start position:0% +output itself a very important factor in + + + align:start position:0% +output itself a very important factor in +in in in in the in growth is population + + align:start position:0% +in in in in the in growth is population + + + align:start position:0% +in in in in the in growth is population +growth and if you look at rates of + + align:start position:0% +growth and if you look at rates of + + + align:start position:0% +growth and if you look at rates of +growth in general in the world s + + align:start position:0% +growth in general in the world s + + + align:start position:0% +growth in general in the world s +certainly in the developed World H + + align:start position:0% +certainly in the developed World H + + + align:start position:0% +certainly in the developed World H +they're falling for a variety of reasons + + align:start position:0% +they're falling for a variety of reasons + + + align:start position:0% +they're falling for a variety of reasons +and one of them is because population + + align:start position:0% +and one of them is because population + + + align:start position:0% +and one of them is because population +growth is + + align:start position:0% +growth is + + + align:start position:0% +growth is +falling okay but per person that doesn't + + align:start position:0% +falling okay but per person that doesn't + + + align:start position:0% +falling okay but per person that doesn't +make a difference but but but for the + + align:start position:0% +make a difference but but but for the + + + align:start position:0% +make a difference but but but for the +level the rate of growth it does and + + align:start position:0% +level the rate of growth it does and + + + align:start position:0% +level the rate of growth it does and +then we we added technological progress + + align:start position:0% +then we we added technological progress + + + align:start position:0% +then we we added technological progress +which we model as a effective as + + align:start position:0% +which we model as a effective as + + + align:start position:0% +which we model as a effective as +enhancing labor so having a better + + align:start position:0% +enhancing labor so having a better + + + align:start position:0% +enhancing labor so having a better +technology means is as you had more + + align:start position:0% +technology means is as you had more + + + align:start position:0% +technology means is as you had more +workers so for any given level of + + align:start position:0% +workers so for any given level of + + + align:start position:0% +workers so for any given level of +workers having a better technology we + + align:start position:0% +workers having a better technology we + + + align:start position:0% +workers having a better technology we +model it as having more workers okay and + + align:start position:0% +model it as having more workers okay and + + + align:start position:0% +model it as having more workers okay and +you can model it exactly that way you + + align:start position:0% +you can model it exactly that way you + + + align:start position:0% +you can model it exactly that way you +can use exactly the same diagram we had + + align:start position:0% +can use exactly the same diagram we had + + + align:start position:0% +can use exactly the same diagram we had +before but now we will divide our + + align:start position:0% +before but now we will divide our + + + align:start position:0% +before but now we will divide our +scaling Factor rather than being one + + align:start position:0% +scaling Factor rather than being one + + + align:start position:0% +scaling Factor rather than being one +over population is going to be one over + + align:start position:0% +over population is going to be one over + + + align:start position:0% +over population is going to be one over +effective population effective workers + + align:start position:0% +effective population effective workers + + + align:start position:0% +effective population effective workers +one over again and you conduct exactly + + align:start position:0% +one over again and you conduct exactly + + + align:start position:0% +one over again and you conduct exactly +the same analysis you do exactly the + + align:start position:0% +the same analysis you do exactly the + + + align:start position:0% +the same analysis you do exactly the +same approximations I did before H but + + align:start position:0% +same approximations I did before H but + + + align:start position:0% +same approximations I did before H but +the difference now is + + align:start position:0% +the difference now is + + + align:start position:0% +the difference now is +that ER is that here you have a rather + + align:start position:0% +that ER is that here you have a rather + + + align:start position:0% +that ER is that here you have a rather +than GN you have + + align:start position:0% +than GN you have + + + align:start position:0% +than GN you have +G why is that well because if I want to + + align:start position:0% +G why is that well because if I want to + + + align:start position:0% +G why is that well because if I want to +maintain the capital per effective + + align:start position:0% +maintain the capital per effective + + + align:start position:0% +maintain the capital per effective +worker constant then I need to First + + align:start position:0% +worker constant then I need to First + + + align:start position:0% +worker constant then I need to First +make up for the depreciation of the + + align:start position:0% +make up for the depreciation of the + + + align:start position:0% +make up for the depreciation of the +stock of capital that's I have to + + align:start position:0% +stock of capital that's I have to + + + align:start position:0% +stock of capital that's I have to +stabilize the numerator but then I have + + align:start position:0% +stabilize the numerator but then I have + + + align:start position:0% +stabilize the numerator but then I have +to take into account that the + + align:start position:0% +to take into account that the + + + align:start position:0% +to take into account that the +denominator is growing for two reasons + + align:start position:0% +denominator is growing for two reasons + + + align:start position:0% +denominator is growing for two reasons +because population is growing and + + align:start position:0% +because population is growing and + + + align:start position:0% +because population is growing and +because technology is growing and in + + align:start position:0% +because technology is growing and in + + + align:start position:0% +because technology is growing and in +order to maintain the ratio constant I'm + + align:start position:0% +order to maintain the ratio constant I'm + + + align:start position:0% +order to maintain the ratio constant I'm +going to have to investment so so to + + align:start position:0% +going to have to investment so so to + + + align:start position:0% +going to have to investment so so to +maintain that ratio constant and that's + + align:start position:0% +maintain that ratio constant and that's + + + align:start position:0% +maintain that ratio constant and that's +the reason now we + + align:start position:0% +the reason now we + + + align:start position:0% +the reason now we +have this this line here rotates even + + align:start position:0% +have this this line here rotates even + + + align:start position:0% +have this this line here rotates even +further and we get Delta plus GA plus GN + + align:start position:0% + + + + align:start position:0% + +okay and you should play with these + + align:start position:0% +okay and you should play with these + + + align:start position:0% +okay and you should play with these +things what happen in this diagram if I + + align:start position:0% +things what happen in this diagram if I + + + align:start position:0% +things what happen in this diagram if I +you know if I increase GA or stuff like + + align:start position:0% + + + + align:start position:0% + +that and notice that here now still you + + align:start position:0% +that and notice that here now still you + + + align:start position:0% +that and notice that here now still you +have a steady state but it's a steady + + align:start position:0% +have a steady state but it's a steady + + + align:start position:0% +have a steady state but it's a steady +state in the space of output per + + align:start position:0% +state in the space of output per + + + align:start position:0% +state in the space of output per +effective worker in capital per + + align:start position:0% +effective worker in capital per + + + align:start position:0% +effective worker in capital per +effective worker that means for example + + align:start position:0% +effective worker that means for example + + + align:start position:0% +effective worker that means for example +that so that means that these quantities + + align:start position:0% +that so that means that these quantities + + + align:start position:0% +that so that means that these quantities +are not growing in the stady state but + + align:start position:0% +are not growing in the stady state but + + + align:start position:0% +are not growing in the stady state but +output will be growing at which rate in + + align:start position:0% +output will be growing at which rate in + + + align:start position:0% +output will be growing at which rate in +the stady state in any state state here + + align:start position:0% +the stady state in any state state here + + + align:start position:0% +the stady state in any state state here +what is the rate of growth of + + align:start position:0% + + + + align:start position:0% + +output if output Over N is constant in + + align:start position:0% +output if output Over N is constant in + + + align:start position:0% +output if output Over N is constant in +in the today + + align:start position:0% +in the today + + + align:start position:0% +in the today +State how can that happen output has to + + align:start position:0% +State how can that happen output has to + + + align:start position:0% +State how can that happen output has to +be growing at which rate at the same + + align:start position:0% +be growing at which rate at the same + + + align:start position:0% +be growing at which rate at the same +rate as the + + align:start position:0% +rate as the + + + align:start position:0% +rate as the +denominator so it's GA plus + + align:start position:0% + + + + align:start position:0% + +GN what about that's a tricker question + + align:start position:0% +GN what about that's a tricker question + + + align:start position:0% +GN what about that's a tricker question +what happens to Output per person in + + align:start position:0% +what happens to Output per person in + + + align:start position:0% +what happens to Output per person in +this stady state what rate is it growing + + align:start position:0% +this stady state what rate is it growing + + + align:start position:0% +this stady state what rate is it growing +at output per + + align:start position:0% + + + + align:start position:0% + +person sorry somebody said the right + + align:start position:0% +person sorry somebody said the right + + + align:start position:0% +person sorry somebody said the right +thing but ga exactly I want to keep this + + align:start position:0% +thing but ga exactly I want to keep this + + + align:start position:0% +thing but ga exactly I want to keep this +ratio constant I'm asking the question + + align:start position:0% +ratio constant I'm asking the question + + + align:start position:0% +ratio constant I'm asking the question +at which Pace does this need to rise in + + align:start position:0% +at which Pace does this need to rise in + + + align:start position:0% +at which Pace does this need to rise in +order to maintain this constant well at + + align:start position:0% +order to maintain this constant well at + + + align:start position:0% +order to maintain this constant well at +the same rate as a is growing + + align:start position:0% + + + + align:start position:0% + +good here we also did we asked the + + align:start position:0% +good here we also did we asked the + + + align:start position:0% +good here we also did we asked the +question well could it be that here if + + align:start position:0% +question well could it be that here if + + + align:start position:0% +question well could it be that here if +we change the saving rate we get some + + align:start position:0% +we change the saving rate we get some + + + align:start position:0% +we change the saving rate we get some +extra kick in the long run and the + + align:start position:0% +extra kick in the long run and the + + + align:start position:0% +extra kick in the long run and the +answer is no for the same logic as we + + align:start position:0% +answer is no for the same logic as we + + + align:start position:0% +answer is no for the same logic as we +had before you're going to get + + align:start position:0% +had before you're going to get + + + align:start position:0% +had before you're going to get +transitional growth but you're + + align:start position:0% +transitional growth but you're + + + align:start position:0% +transitional growth but you're +eventually you're going to convert to a + + align:start position:0% +eventually you're going to convert to a + + + align:start position:0% +eventually you're going to convert to a +stady state and the rate of growth in + + align:start position:0% +stady state and the rate of growth in + + + align:start position:0% +stady state and the rate of growth in +the long run is not going to be a + + align:start position:0% +the long run is not going to be a + + + align:start position:0% +the long run is not going to be a +function of the saving rate is going to + + align:start position:0% +function of the saving rate is going to + + + align:start position:0% +function of the saving rate is going to +be equal to GA plus GN + + align:start position:0% +be equal to GA plus GN + + + align:start position:0% +be equal to GA plus GN +okay + + align:start position:0% + + + + align:start position:0% + +good do here measuring technological + + align:start position:0% +good do here measuring technological + + + align:start position:0% +good do here measuring technological +progress blah blah told you the story of + + align:start position:0% +progress blah blah told you the story of + + + align:start position:0% +progress blah blah told you the story of +China + + align:start position:0% + + + + align:start position:0% + +good oh we run out of time so let me + + align:start position:0% +good oh we run out of time so let me + + + align:start position:0% +good oh we run out of time so let me +just say the the the last thing uh that + + align:start position:0% +just say the the the last thing uh that + + + align:start position:0% +just say the the the last thing uh that +I want to say so the last thing we + + align:start position:0% +I want to say so the last thing we + + + align:start position:0% +I want to say so the last thing we +discussed you say well what happen if + + align:start position:0% +discussed you say well what happen if + + + align:start position:0% +discussed you say well what happen if +you add education to this and and try to + + align:start position:0% +you add education to this and and try to + + + align:start position:0% +you add education to this and and try to +no I make what am I doing yeah I + + align:start position:0% +no I make what am I doing yeah I + + + align:start position:0% +no I make what am I doing yeah I +expanded the model a little bit I had + + align:start position:0% +expanded the model a little bit I had + + + align:start position:0% +expanded the model a little bit I had +education and said does this change + + align:start position:0% +education and said does this change + + + align:start position:0% +education and said does this change +conclusions a lot I said no not really I + + align:start position:0% +conclusions a lot I said no not really I + + + align:start position:0% +conclusions a lot I said no not really I +mean it it doesn't change the conclusion + + align:start position:0% +mean it it doesn't change the conclusion + + + align:start position:0% +mean it it doesn't change the conclusion +with respect to the long run it affects + + align:start position:0% +with respect to the long run it affects + + + align:start position:0% +with respect to the long run it affects +the level of output per capita if you + + align:start position:0% +the level of output per capita if you + + + align:start position:0% +the level of output per capita if you +have more education but it want a che + + align:start position:0% +have more education but it want a che + + + align:start position:0% +have more education but it want a che +affect the rate of growth in the long + + align:start position:0% +affect the rate of growth in the long + + + align:start position:0% +affect the rate of growth in the long +run and the last point I made is that + + align:start position:0% +run and the last point I made is that + + + align:start position:0% +run and the last point I made is that +look H in this model if you expand it + + align:start position:0% +look H in this model if you expand it + + + align:start position:0% +look H in this model if you expand it +and you try to assume the technology the + + align:start position:0% +and you try to assume the technology the + + + align:start position:0% +and you try to assume the technology the +technology is the same and the rate of + + align:start position:0% +technology is the same and the rate of + + + align:start position:0% +technology is the same and the rate of +technological progress is the same + + align:start position:0% +technological progress is the same + + + align:start position:0% +technological progress is the same +across the world you stick those + + align:start position:0% +across the world you stick those + + + align:start position:0% +across the world you stick those +parameters in the mod population growth + + align:start position:0% +parameters in the mod population growth + + + align:start position:0% +parameters in the mod population growth +education levels and all that then you + + align:start position:0% +education levels and all that then you + + + align:start position:0% +education levels and all that then you +don't explain the amount of inequality + + align:start position:0% +don't explain the amount of inequality + + + align:start position:0% +don't explain the amount of inequality +we see in the world the world will look + + align:start position:0% +we see in the world the world will look + + + align:start position:0% +we see in the world the world will look +a lot flatter if if it was just H + + align:start position:0% +a lot flatter if if it was just H + + + align:start position:0% +a lot flatter if if it was just H +differences in population growth + + align:start position:0% +differences in population growth + + + align:start position:0% +differences in population growth +depreciation + + align:start position:0% +depreciation + + + align:start position:0% +depreciation +education level and things like that but + + align:start position:0% +education level and things like that but + + + align:start position:0% +education level and things like that but +with the same technology so if you want + + align:start position:0% +with the same technology so if you want + + + align:start position:0% +with the same technology so if you want +to account for so this model the + + align:start position:0% +to account for so this model the + + + align:start position:0% +to account for so this model the +mod doesn't produce enough + + align:start position:0% +mod doesn't produce enough + + + align:start position:0% +mod doesn't produce enough +inequality in the world you need to add + + align:start position:0% +inequality in the world you need to add + + + align:start position:0% +inequality in the world you need to add +something else that explains that we + + align:start position:0% +something else that explains that we + + + align:start position:0% +something else that explains that we +have some countries in Africa that are + + align:start position:0% +have some countries in Africa that are + + + align:start position:0% +have some countries in Africa that are +not growing that they're growing at a + + align:start position:0% +not growing that they're growing at a + + + align:start position:0% +not growing that they're growing at a +very low levels rate and we said that + + align:start position:0% +very low levels rate and we said that + + + align:start position:0% +very low levels rate and we said that +something else technology for whatever + + align:start position:0% +something else technology for whatever + + + align:start position:0% +something else technology for whatever +reason it happens that there's a pocket + + align:start position:0% +reason it happens that there's a pocket + + + align:start position:0% +reason it happens that there's a pocket +of countries that that seem to have a + + align:start position:0% +of countries that that seem to have a + + + align:start position:0% +of countries that that seem to have a +lower sort of permanently lower level of + + align:start position:0% +lower sort of permanently lower level of + + + align:start position:0% +lower sort of permanently lower level of +technology and both level and growth + + align:start position:0% +technology and both level and growth + + + align:start position:0% +technology and both level and growth +rate and that's what explains sort of a + + align:start position:0% +rate and that's what explains sort of a + + + align:start position:0% +rate and that's what explains sort of a +subset of countries that are sort of + + align:start position:0% +subset of countries that are sort of + + + align:start position:0% +subset of countries that are sort of +seem stack they are not consistent with + + align:start position:0% +seem stack they are not consistent with + + + align:start position:0% +seem stack they are not consistent with +this convergence type thing so that's + + align:start position:0% +this convergence type thing so that's + + + align:start position:0% +this convergence type thing so that's +the reason it's called conditional + + align:start position:0% +the reason it's called conditional + + + align:start position:0% +the reason it's called conditional +convergence those countries themselves + + align:start position:0% +convergence those countries themselves + + + align:start position:0% +convergence those countries themselves +are converging to something but they're + + align:start position:0% +are converging to something but they're + + + align:start position:0% +are converging to something but they're +converging to something much lower and + + align:start position:0% +converging to something much lower and + + + align:start position:0% +converging to something much lower and +with much lower rate of growth than most + + align:start position:0% +with much lower rate of growth than most + + + align:start position:0% +with much lower rate of growth than most +of the rest of the world but for the + + align:start position:0% +of the rest of the world but for the + + + align:start position:0% +of the rest of the world but for the +final lesson is for the average country + + align:start position:0% +final lesson is for the average country + + + align:start position:0% +final lesson is for the average country +on + + align:start position:0% +on + + + align:start position:0% +on +average it's clear that poorer countries + + align:start position:0% +average it's clear that poorer countries + + + align:start position:0% +average it's clear that poorer countries +grow faster than richer countries that's + + align:start position:0% +grow faster than richer countries that's + + + align:start position:0% +grow faster than richer countries that's +a that's that's a dominant Force but you + + align:start position:0% +a that's that's a dominant Force but you + + + align:start position:0% +a that's that's a dominant Force but you +need a little more if you want to + + align:start position:0% +need a little more if you want to + + + align:start position:0% +need a little more if you want to +explain certain pockets of the world + + align:start position:0% +explain certain pockets of the world + + + align:start position:0% +explain certain pockets of the world +okay \ No newline at end of file diff --git a/z0lJ2k0sl1g.txt b/z0lJ2k0sl1g.txt new file mode 100644 index 0000000000000000000000000000000000000000..01b044e848dfc42bcbd2971e6c91259124bc65b6 --- /dev/null +++ b/z0lJ2k0sl1g.txt @@ -0,0 +1,13035 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +All right, let's get started. + + align:start position:0% +All right, let's get started. + + + align:start position:0% +All right, let's get started. +Today we're going to continue the theme + + align:start position:0% +Today we're going to continue the theme + + + align:start position:0% +Today we're going to continue the theme +of randomization and data structures. + + align:start position:0% +of randomization and data structures. + + + align:start position:0% +of randomization and data structures. +Last time we saw skip listless. Skip + + align:start position:0% +Last time we saw skip listless. Skip + + + align:start position:0% +Last time we saw skip listless. Skip +list uh solve the predecessor successor + + align:start position:0% +list uh solve the predecessor successor + + + align:start position:0% +list uh solve the predecessor successor +problem. You can search for an item and + + align:start position:0% +problem. You can search for an item and + + + align:start position:0% +problem. You can search for an item and +if it's not there, you get the closest + + align:start position:0% +if it's not there, you get the closest + + + align:start position:0% +if it's not there, you get the closest +item on either side in login with high + + align:start position:0% +item on either side in login with high + + + align:start position:0% +item on either side in login with high +probability. Um but we already knew how + + align:start position:0% +probability. Um but we already knew how + + + align:start position:0% +probability. Um but we already knew how +to do that deterministically. + + align:start position:0% +to do that deterministically. + + + align:start position:0% +to do that deterministically. +Today we're going to solve a slightly + + align:start position:0% +Today we're going to solve a slightly + + + align:start position:0% +Today we're going to solve a slightly +different problem, the dictionary + + align:start position:0% +different problem, the dictionary + + + align:start position:0% +different problem, the dictionary +problem uh with hashts. Something you + + align:start position:0% +problem uh with hashts. Something you + + + align:start position:0% +problem uh with hashts. Something you +already think you know, but uh we're + + align:start position:0% +already think you know, but uh we're + + + align:start position:0% +already think you know, but uh we're +going to show you how much you didn't + + align:start position:0% +going to show you how much you didn't + + + align:start position:0% +going to show you how much you didn't +know, but after today you will know. + + align:start position:0% +know, but after today you will know. + + + align:start position:0% +know, but after today you will know. +And we're going to get constant time uh + + align:start position:0% +And we're going to get constant time uh + + + align:start position:0% +And we're going to get constant time uh +not with high probability. That's hard, + + align:start position:0% +not with high probability. That's hard, + + + align:start position:0% +not with high probability. That's hard, +but we'll do constant expected time. So + + align:start position:0% +but we'll do constant expected time. So + + + align:start position:0% +but we'll do constant expected time. So +uh that's in some sense better. It's + + align:start position:0% +uh that's in some sense better. It's + + + align:start position:0% +uh that's in some sense better. It's +going to solve a weaker problem, but + + align:start position:0% +going to solve a weaker problem, but + + + align:start position:0% +going to solve a weaker problem, but +we're going to get a tighter bound + + align:start position:0% +we're going to get a tighter bound + + + align:start position:0% +we're going to get a tighter bound +constant instead of logarithmic. Um, so + + align:start position:0% +constant instead of logarithmic. Um, so + + + align:start position:0% +constant instead of logarithmic. Um, so +for starters, let me remind you uh what + + align:start position:0% +for starters, let me remind you uh what + + + align:start position:0% +for starters, let me remind you uh what +problem we're solving and the basics of + + align:start position:0% +problem we're solving and the basics of + + + align:start position:0% +problem we're solving and the basics of +hashing which you learned in 6006. + + align:start position:0% + + + + align:start position:0% + +I'm going to give this problem a name + + align:start position:0% +I'm going to give this problem a name + + + align:start position:0% +I'm going to give this problem a name +because it's important. And we often + + align:start position:0% +because it's important. And we often + + + align:start position:0% +because it's important. And we often +forget to distinguish between uh two + + align:start position:0% +forget to distinguish between uh two + + + align:start position:0% +forget to distinguish between uh two +types of things. Um + + align:start position:0% +types of things. Um + + + align:start position:0% +types of things. Um +it's kind of an old term, but I would + + align:start position:0% +it's kind of an old term, but I would + + + align:start position:0% +it's kind of an old term, but I would +call this an abstract data type. + + align:start position:0% +call this an abstract data type. + + + align:start position:0% +call this an abstract data type. +This is just the uh problem + + align:start position:0% +This is just the uh problem + + + align:start position:0% +This is just the uh problem +specification of what you're trying to + + align:start position:0% +specification of what you're trying to + + + align:start position:0% +specification of what you're trying to +do. Uh you might call this an interface + + align:start position:0% +do. Uh you might call this an interface + + + align:start position:0% +do. Uh you might call this an interface +or something. This is a problem + + align:start position:0% +or something. This is a problem + + + align:start position:0% +or something. This is a problem +statement versus the data structure is + + align:start position:0% +statement versus the data structure is + + + align:start position:0% +statement versus the data structure is +how you actually solve it. that hashts + + align:start position:0% +how you actually solve it. that hashts + + + align:start position:0% +how you actually solve it. that hashts +are the data structure, dictionary is + + align:start position:0% +are the data structure, dictionary is + + + align:start position:0% +are the data structure, dictionary is +the problem or the abstract data type. + + align:start position:0% +the problem or the abstract data type. + + + align:start position:0% +the problem or the abstract data type. +Uh so what we're trying to do today uh + + align:start position:0% +Uh so what we're trying to do today uh + + + align:start position:0% +Uh so what we're trying to do today uh +as in most data structures is maintain a + + align:start position:0% +as in most data structures is maintain a + + + align:start position:0% +as in most data structures is maintain a +dynamic set of items. + + align:start position:0% +dynamic set of items. + + + align:start position:0% +dynamic set of items. +Uh and here I'm going to distinguish + + align:start position:0% +Uh and here I'm going to distinguish + + + align:start position:0% +Uh and here I'm going to distinguish +between the items and their keys. + + align:start position:0% +between the items and their keys. + + + align:start position:0% +between the items and their keys. +Each item has a key and normally think + + align:start position:0% +Each item has a key and normally think + + + align:start position:0% +Each item has a key and normally think +of there also being a value like in + + align:start position:0% +of there also being a value like in + + + align:start position:0% +of there also being a value like in +Python. Uh, but we're just worrying + + align:start position:0% +Python. Uh, but we're just worrying + + + align:start position:0% +Python. Uh, but we're just worrying +about the keys and moving the items + + align:start position:0% +about the keys and moving the items + + + align:start position:0% +about the keys and moving the items +around. Uh, and we want to support three + + align:start position:0% +around. Uh, and we want to support three + + + align:start position:0% +around. Uh, and we want to support three +operations. + + align:start position:0% +operations. + + + align:start position:0% +operations. +Uh, we want to be able to insert an + + align:start position:0% +Uh, we want to be able to insert an + + + align:start position:0% +Uh, we want to be able to insert an +item, + + align:start position:0% + + + + align:start position:0% + +uh, delete an item, + + align:start position:0% + + + + align:start position:0% + +and search for an item. + + align:start position:0% + + + + align:start position:0% + +But search is going to be different from + + align:start position:0% +But search is going to be different from + + + align:start position:0% +But search is going to be different from +uh what we know from AVL trees or skip + + align:start position:0% +uh what we know from AVL trees or skip + + + align:start position:0% +uh what we know from AVL trees or skip +list or even venom DOS. Uh that was a + + align:start position:0% +list or even venom DOS. Uh that was a + + + align:start position:0% +list or even venom DOS. Uh that was a +predecessor successor search. Here we + + align:start position:0% +predecessor successor search. Here we + + + align:start position:0% +predecessor successor search. Here we +just want to know uh sorry you're not + + align:start position:0% +just want to know uh sorry you're not + + + align:start position:0% +just want to know uh sorry you're not +searching for an item. Usually you're + + align:start position:0% +searching for an item. Usually you're + + + align:start position:0% +searching for an item. Usually you're +searching for just a key. + + align:start position:0% + + + + align:start position:0% + +Here you just want to know is there any + + align:start position:0% +Here you just want to know is there any + + + align:start position:0% +Here you just want to know is there any +item with that key and return it. + + align:start position:0% + + + + align:start position:0% + +This is often called an exact search + + align:start position:0% +This is often called an exact search + + + align:start position:0% +This is often called an exact search +because if the key is not in there, you + + align:start position:0% +because if the key is not in there, you + + + align:start position:0% +because if the key is not in there, you +learn absolutely nothing. You don't you + + align:start position:0% +learn absolutely nothing. You don't you + + + align:start position:0% +learn absolutely nothing. You don't you +can't find the nearest key. And for + + align:start position:0% +can't find the nearest key. And for + + + align:start position:0% +can't find the nearest key. And for +whatever reason, this is called a + + align:start position:0% +whatever reason, this is called a + + + align:start position:0% +whatever reason, this is called a +dictionary problem. That's unlike a real + + align:start position:0% +dictionary problem. That's unlike a real + + + align:start position:0% +dictionary problem. That's unlike a real +dictionary. Usually, when you search for + + align:start position:0% +dictionary. Usually, when you search for + + + align:start position:0% +dictionary. Usually, when you search for +a word, you do find its neighbors. here + + align:start position:0% +a word, you do find its neighbors. here + + + align:start position:0% +a word, you do find its neighbors. here +uh we're just going to either if the key + + align:start position:0% +uh we're just going to either if the key + + + align:start position:0% +uh we're just going to either if the key +is there we find the item otherwise not + + align:start position:0% +is there we find the item otherwise not + + + align:start position:0% +is there we find the item otherwise not +and this is exactly uh what a Python + + align:start position:0% +and this is exactly uh what a Python + + + align:start position:0% +and this is exactly uh what a Python +dictionary implements + + align:start position:0% +dictionary implements + + + align:start position:0% +dictionary implements +uh so I guess that's why Python + + align:start position:0% +uh so I guess that's why Python + + + align:start position:0% +uh so I guess that's why Python +dictionaries are called uh dicts + + align:start position:0% +dictionaries are called uh dicts + + + align:start position:0% +dictionaries are called uh dicts +so + + align:start position:0% +so + + + align:start position:0% +so +uh today I'm going to assume all items + + align:start position:0% +uh today I'm going to assume all items + + + align:start position:0% +uh today I'm going to assume all items +have distinct keys so in the insertion I + + align:start position:0% +have distinct keys so in the insertion I + + + align:start position:0% +have distinct keys so in the insertion I +will assume uh key + + align:start position:0% +will assume uh key + + + align:start position:0% +will assume uh key +is not already in the + + align:start position:0% + + + + align:start position:0% + +uh with a little bit of work you can + + align:start position:0% +uh with a little bit of work you can + + + align:start position:0% +uh with a little bit of work you can +allow there to be allow inserting an + + align:start position:0% +allow there to be allow inserting an + + + align:start position:0% +allow there to be allow inserting an +item with an existing key and you just + + align:start position:0% +item with an existing key and you just + + + align:start position:0% +item with an existing key and you just +overwrite that that existing item but I + + align:start position:0% +overwrite that that existing item but I + + + align:start position:0% +overwrite that that existing item but I +don't want to worry about that here + + align:start position:0% +don't want to worry about that here + + + align:start position:0% +don't want to worry about that here +right so we could of course solve this + + align:start position:0% +right so we could of course solve this + + + align:start position:0% +right so we could of course solve this +using an AVL tree and in login time uh + + align:start position:0% +using an AVL tree and in login time uh + + + align:start position:0% +using an AVL tree and in login time uh +but our goal is to do better because + + align:start position:0% +but our goal is to do better because + + + align:start position:0% +but our goal is to do better because +it's a an easier problem + + align:start position:0% +it's a an easier problem + + + align:start position:0% +it's a an easier problem +and I'm going to remind you of the + + align:start position:0% +and I'm going to remind you of the + + + align:start position:0% +and I'm going to remind you of the +simplest way you learned to do this + + align:start position:0% +simplest way you learned to do this + + + align:start position:0% +simplest way you learned to do this +which was hashing with chaining + + align:start position:0% + + + + align:start position:0% + +in 006 and the catch is you didn't + + align:start position:0% +in 006 and the catch is you didn't + + + align:start position:0% +in 006 and the catch is you didn't +really analyze this in 006 + + align:start position:0% + + + + align:start position:0% + +so we're getting constant + + align:start position:0% + + + + align:start position:0% + +time per operation + + align:start position:0% + + + + align:start position:0% + +that's going to be expected + + align:start position:0% + + + + align:start position:0% + +or something uh and linear space + + align:start position:0% + + + + align:start position:0% + +and the remember the uh variables we + + align:start position:0% +and the remember the uh variables we + + + align:start position:0% +and the remember the uh variables we +care about there's uh u n and m so u is + + align:start position:0% +care about there's uh u n and m so u is + + + align:start position:0% +care about there's uh u n and m so u is +the size of the universe this is the all + + align:start position:0% +the size of the universe this is the all + + + align:start position:0% +the size of the universe this is the all +possible keys the space of all possible + + align:start position:0% +possible keys the space of all possible + + + align:start position:0% +possible keys the space of all possible +keys + + align:start position:0% + + + + align:start position:0% + +n is the size of your the set you're + + align:start position:0% +n is the size of your the set you're + + + align:start position:0% +n is the size of your the set you're +currently ly storing. So that's the + + align:start position:0% +currently ly storing. So that's the + + + align:start position:0% +currently ly storing. So that's the +number of items or keys uh currently in + + align:start position:0% +number of items or keys uh currently in + + + align:start position:0% +number of items or keys uh currently in +the data structure. + + align:start position:0% + + + + align:start position:0% + +Uh and then m is the size of your table. + + align:start position:0% +Uh and then m is the size of your table. + + + align:start position:0% +Uh and then m is the size of your table. +So I'll say it's the number of slots in + + align:start position:0% +So I'll say it's the number of slots in + + + align:start position:0% +So I'll say it's the number of slots in +the table. + + align:start position:0% + + + + align:start position:0% + +So you remember the picture you have a + + align:start position:0% +So you remember the picture you have a + + + align:start position:0% +So you remember the picture you have a +table + + align:start position:0% +table + + + align:start position:0% +table +of slots + + align:start position:0% +of slots + + + align:start position:0% +of slots +uh say 0 to n minus one each of them is + + align:start position:0% +uh say 0 to n minus one each of them is + + + align:start position:0% +uh say 0 to n minus one each of them is +a pointer to a linked list. + + align:start position:0% +a pointer to a linked list. + + + align:start position:0% +a pointer to a linked list. +Um and if you have let's say over here + + align:start position:0% +Um and if you have let's say over here + + + align:start position:0% +Um and if you have let's say over here +is your universe of all possible keys. + + align:start position:0% +is your universe of all possible keys. + + + align:start position:0% +is your universe of all possible keys. +Uh then we have a hash function which + + align:start position:0% +Uh then we have a hash function which + + + align:start position:0% +Uh then we have a hash function which +maps each universe item uh into one of + + align:start position:0% +maps each universe item uh into one of + + + align:start position:0% +maps each universe item uh into one of +these slots and then the linked list + + align:start position:0% +these slots and then the linked list + + + align:start position:0% +these slots and then the linked list +here is storing all of the items that + + align:start position:0% +here is storing all of the items that + + + align:start position:0% +here is storing all of the items that +hash to that slot. + + align:start position:0% +hash to that slot. + + + align:start position:0% +hash to that slot. +All right. So + + align:start position:0% +All right. So + + + align:start position:0% +All right. So +uh yeah + + align:start position:0% + + + + align:start position:0% + +so we have a hash function which maps + + align:start position:0% +so we have a hash function which maps + + + align:start position:0% +so we have a hash function which maps +the universe. I'm going to assume the + + align:start position:0% +the universe. I'm going to assume the + + + align:start position:0% +the universe. I'm going to assume the +universe has already been mapped into + + align:start position:0% +universe has already been mapped into + + + align:start position:0% +universe has already been mapped into +integers 0 to u minus one and it maps to + + align:start position:0% +integers 0 to u minus one and it maps to + + + align:start position:0% +integers 0 to u minus one and it maps to +slots. + + align:start position:0% + + + + align:start position:0% + +Okay. And when we do hashing with + + align:start position:0% +Okay. And when we do hashing with + + + align:start position:0% +Okay. And when we do hashing with +chaining + + align:start position:0% +chaining + + + align:start position:0% +chaining +think I mentioned this last week the + + align:start position:0% +think I mentioned this last week the + + + align:start position:0% +think I mentioned this last week the +bounds you get + + align:start position:0% + + + + align:start position:0% + +we achieve + + align:start position:0% + + + + align:start position:0% + +bound of uh 1 + alpha where alpha is the + + align:start position:0% +bound of uh 1 + alpha where alpha is the + + + align:start position:0% +bound of uh 1 + alpha where alpha is the +load factor n / m the average number of + + align:start position:0% +load factor n / m the average number of + + + align:start position:0% +load factor n / m the average number of +items you'd expect to hash to a slot. + + align:start position:0% +items you'd expect to hash to a slot. + + + align:start position:0% +items you'd expect to hash to a slot. +It's the number of items divided by a + + align:start position:0% +It's the number of items divided by a + + + align:start position:0% +It's the number of items divided by a +number of slots. + + align:start position:0% +number of slots. + + + align:start position:0% +number of slots. +Okay. Um and you proved this in 66, but + + align:start position:0% +Okay. Um and you proved this in 66, but + + + align:start position:0% +Okay. Um and you proved this in 66, but +you assumed uh something called + + align:start position:0% +you assumed uh something called + + + align:start position:0% +you assumed uh something called +simple uniform hashing. + + align:start position:0% + + + + align:start position:0% + +Simple uniform hashing is an assumption + + align:start position:0% +Simple uniform hashing is an assumption + + + align:start position:0% +Simple uniform hashing is an assumption +uh I think invented for CLRS. It makes + + align:start position:0% +uh I think invented for CLRS. It makes + + + align:start position:0% +uh I think invented for CLRS. It makes +the analysis very simple but it's also + + align:start position:0% +the analysis very simple but it's also + + + align:start position:0% +the analysis very simple but it's also +basically cheating. So today our goal is + + align:start position:0% +basically cheating. So today our goal is + + + align:start position:0% +basically cheating. So today our goal is +to not cheat. It's nice as a warm-up but + + align:start position:0% +to not cheat. It's nice as a warm-up but + + + align:start position:0% +to not cheat. It's nice as a warm-up but +we don't like cheating. So um you may + + align:start position:0% +we don't like cheating. So um you may + + + align:start position:0% +we don't like cheating. So um you may +recall the the the + + align:start position:0% + + + + align:start position:0% + +assumption is about the hash function. + + align:start position:0% +assumption is about the hash function. + + + align:start position:0% +assumption is about the hash function. +You want a good hash function + + align:start position:0% +You want a good hash function + + + align:start position:0% +You want a good hash function +and good means + + align:start position:0% + + + + align:start position:0% + +this. I want the probability of two + + align:start position:0% +this. I want the probability of two + + + align:start position:0% +this. I want the probability of two +distinct keys mapping to the same slot + + align:start position:0% +distinct keys mapping to the same slot + + + align:start position:0% +distinct keys mapping to the same slot +to be one over m. There are m slots. If + + align:start position:0% +to be one over m. There are m slots. If + + + align:start position:0% +to be one over m. There are m slots. If +everything was completely random, if h + + align:start position:0% +everything was completely random, if h + + + align:start position:0% +everything was completely random, if h +was basically choosing a random number + + align:start position:0% +was basically choosing a random number + + + align:start position:0% +was basically choosing a random number +for every key, uh then that's what we + + align:start position:0% +for every key, uh then that's what we + + + align:start position:0% +for every key, uh then that's what we +would expect to happen. So this is like + + align:start position:0% +would expect to happen. So this is like + + + align:start position:0% +would expect to happen. So this is like +the idealized scenario. Now we can't + + align:start position:0% +the idealized scenario. Now we can't + + + align:start position:0% +the idealized scenario. Now we can't +have a hash function choosing an arbit a + + align:start position:0% +have a hash function choosing an arbit a + + + align:start position:0% +have a hash function choosing an arbit a +random number for every key because it + + align:start position:0% +random number for every key because it + + + align:start position:0% +random number for every key because it +has to choose the same value if you give + + align:start position:0% +has to choose the same value if you give + + + align:start position:0% +has to choose the same value if you give +it the same key. So it has to be some + + align:start position:0% +it the same key. So it has to be some + + + align:start position:0% +it the same key. So it has to be some +kind of deterministic strategy or at + + align:start position:0% +kind of deterministic strategy or at + + + align:start position:0% +kind of deterministic strategy or at +least repeatable strategy where if you + + align:start position:0% +least repeatable strategy where if you + + + align:start position:0% +least repeatable strategy where if you +plug in the same key you get the same + + align:start position:0% +plug in the same key you get the same + + + align:start position:0% +plug in the same key you get the same +thing. Uh so really what this assumption + + align:start position:0% +thing. Uh so really what this assumption + + + align:start position:0% +thing. Uh so really what this assumption +is saying is that uh the keys that you + + align:start position:0% +is saying is that uh the keys that you + + + align:start position:0% +is saying is that uh the keys that you +give are + + align:start position:0% +give are + + + align:start position:0% +give are +uh in some sense random. If I give you + + align:start position:0% +uh in some sense random. If I give you + + + align:start position:0% +uh in some sense random. If I give you +random keys and I have a not too crazy + + align:start position:0% +random keys and I have a not too crazy + + + align:start position:0% +random keys and I have a not too crazy +hash function, then this will be true. + + align:start position:0% +hash function, then this will be true. + + + align:start position:0% +hash function, then this will be true. +Uh but I don't like assuming anything + + align:start position:0% +Uh but I don't like assuming anything + + + align:start position:0% +Uh but I don't like assuming anything +about the keys. Maybe I want my keys to + + align:start position:0% +about the keys. Maybe I want my keys to + + + align:start position:0% +about the keys. Maybe I want my keys to +be worst case. + + align:start position:0% +be worst case. + + + align:start position:0% +be worst case. +Maybe uh and there are lots of examples + + align:start position:0% +Maybe uh and there are lots of examples + + + align:start position:0% +Maybe uh and there are lots of examples +in in the real world where uh you apply + + align:start position:0% +in in the real world where uh you apply + + + align:start position:0% +in in the real world where uh you apply +some hash function. It turns out your + + align:start position:0% +some hash function. It turns out your + + + align:start position:0% +some hash function. It turns out your +data has some very particular structure + + align:start position:0% +data has some very particular structure + + + align:start position:0% +data has some very particular structure +and if you choose a bad hash function + + align:start position:0% +and if you choose a bad hash function + + + align:start position:0% +and if you choose a bad hash function +then uh your hash table gets really + + align:start position:0% +then uh your hash table gets really + + + align:start position:0% +then uh your hash table gets really +really slow. Maybe everything hashes to + + align:start position:0% +really slow. Maybe everything hashes to + + + align:start position:0% +really slow. Maybe everything hashes to +the same slot. + + align:start position:0% +the same slot. + + + align:start position:0% +the same slot. +Uh or you know say you take well yeah + + align:start position:0% +Uh or you know say you take well yeah + + + align:start position:0% +Uh or you know say you take well yeah +lots of examples of that. Uh we want to + + align:start position:0% +lots of examples of that. Uh we want to + + + align:start position:0% +lots of examples of that. Uh we want to +avoid that. After today you will know + + align:start position:0% +avoid that. After today you will know + + + align:start position:0% +avoid that. After today you will know +how to achieve uh constant expected time + + align:start position:0% +how to achieve uh constant expected time + + + align:start position:0% +how to achieve uh constant expected time +no matter what your keys are for worst + + align:start position:0% +no matter what your keys are for worst + + + align:start position:0% +no matter what your keys are for worst +case keys. Okay. But it's going to take + + align:start position:0% +case keys. Okay. But it's going to take + + + align:start position:0% +case keys. Okay. But it's going to take +some work to do that. + + align:start position:0% +some work to do that. + + + align:start position:0% +some work to do that. +So this assumption requires + + align:start position:0% + + + + align:start position:0% + +assuming that the keys are random + + align:start position:0% + + + + align:start position:0% + +and this is what we would call an + + align:start position:0% +and this is what we would call an + + + align:start position:0% +and this is what we would call an +average case analysis. + + align:start position:0% + + + + align:start position:0% + +You might think that average case + + align:start position:0% +You might think that average case + + + align:start position:0% +You might think that average case +analysis is necessary for randomized + + align:start position:0% +analysis is necessary for randomized + + + align:start position:0% +analysis is necessary for randomized +algorithms, but that's not true. Uh, and + + align:start position:0% +algorithms, but that's not true. Uh, and + + + align:start position:0% +algorithms, but that's not true. Uh, and +we saw that last week with quicksort. + + align:start position:0% +we saw that last week with quicksort. + + + align:start position:0% +we saw that last week with quicksort. +Quicksort, if you say, uh, I will always + + align:start position:0% +Quicksort, if you say, uh, I will always + + + align:start position:0% +Quicksort, if you say, uh, I will always +choose a of one to be my partition + + align:start position:0% +choose a of one to be my partition + + + align:start position:0% +choose a of one to be my partition +element. That's what the textbook calls + + align:start position:0% +element. That's what the textbook calls + + + align:start position:0% +element. That's what the textbook calls +basic quicksort. Uh, then for an average + + align:start position:0% +basic quicksort. Uh, then for an average + + + align:start position:0% +basic quicksort. Uh, then for an average +input, that will do really well. If you + + align:start position:0% +input, that will do really well. If you + + + align:start position:0% +input, that will do really well. If you +have a a a uniform random permutation of + + align:start position:0% +have a a a uniform random permutation of + + + align:start position:0% +have a a a uniform random permutation of +items and you sort with the method of + + align:start position:0% +items and you sort with the method of + + + align:start position:0% +items and you sort with the method of +always choosing the first item as your + + align:start position:0% +always choosing the first item as your + + + align:start position:0% +always choosing the first item as your +partition uh then that will be n login + + align:start position:0% +partition uh then that will be n login + + + align:start position:0% +partition uh then that will be n login +uh on average if your data is average + + align:start position:0% +uh on average if your data is average + + + align:start position:0% +uh on average if your data is average +but we saw you could avoid that + + align:start position:0% +but we saw you could avoid that + + + align:start position:0% +but we saw you could avoid that +assumption by choosing a random pivot. + + align:start position:0% +assumption by choosing a random pivot. + + + align:start position:0% +assumption by choosing a random pivot. +If you choose a random pivot then you + + align:start position:0% +If you choose a random pivot then you + + + align:start position:0% +If you choose a random pivot then you +don't need to assume anything about the + + align:start position:0% +don't need to assume anything about the + + + align:start position:0% +don't need to assume anything about the +input. You just need to assume that the + + align:start position:0% +input. You just need to assume that the + + + align:start position:0% +input. You just need to assume that the +pivots are random. So there's a big + + align:start position:0% +pivots are random. So there's a big + + + align:start position:0% +pivots are random. So there's a big +difference between assuming your inputs + + align:start position:0% +difference between assuming your inputs + + + align:start position:0% +difference between assuming your inputs +are random versus assuming your coin + + align:start position:0% +are random versus assuming your coin + + + align:start position:0% +are random versus assuming your coin +flips are random. It's pretty reasonable + + align:start position:0% +flips are random. It's pretty reasonable + + + align:start position:0% +flips are random. It's pretty reasonable +to assume you uh can flip coins + + align:start position:0% +to assume you uh can flip coins + + + align:start position:0% +to assume you uh can flip coins +uh if you've got enough dexterity in + + align:start position:0% +uh if you've got enough dexterity in + + + align:start position:0% +uh if you've got enough dexterity in +your thumb then you can do it. Uh but + + align:start position:0% +your thumb then you can do it. Uh but + + + align:start position:0% +your thumb then you can do it. Uh but +it's not so reasonable to assume that + + align:start position:0% +it's not so reasonable to assume that + + + align:start position:0% +it's not so reasonable to assume that +your input is random. So we'd like to + + align:start position:0% +your input is random. So we'd like to + + + align:start position:0% +your input is random. So we'd like to +avoid uh average case analysis whenever + + align:start position:0% +avoid uh average case analysis whenever + + + align:start position:0% +avoid uh average case analysis whenever +we can and that's the goal of today. So + + align:start position:0% +we can and that's the goal of today. So + + + align:start position:0% +we can and that's the goal of today. So +what you saw in 006 was essentially + + align:start position:0% +what you saw in 006 was essentially + + + align:start position:0% +what you saw in 006 was essentially +assuming the inputs are random. We're + + align:start position:0% +assuming the inputs are random. We're + + + align:start position:0% +assuming the inputs are random. We're +going to get rid of that unreasonable + + align:start position:0% +going to get rid of that unreasonable + + + align:start position:0% +going to get rid of that unreasonable +assumption today. + + align:start position:0% +assumption today. + + + align:start position:0% +assumption today. +Okay, + + align:start position:0% + + + + align:start position:0% + +so that's uh in some sense review from + + align:start position:0% +so that's uh in some sense review from + + + align:start position:0% +so that's uh in some sense review from +006. I'm going to take a brief pause and + + align:start position:0% +006. I'm going to take a brief pause and + + + align:start position:0% +006. I'm going to take a brief pause and +tell you about the etmology of the word + + align:start position:0% +tell you about the etmology of the word + + + align:start position:0% +tell you about the etmology of the word +hash in case you're curious. Um hash is + + align:start position:0% +hash in case you're curious. Um hash is + + + align:start position:0% +hash in case you're curious. Um hash is +a English word since the uh 1650s, + + align:start position:0% + + + + align:start position:0% + +so it's pretty old. Um it means uh + + align:start position:0% +so it's pretty old. Um it means uh + + + align:start position:0% +so it's pretty old. Um it means uh +literally cut into small pieces. It's + + align:start position:0% +literally cut into small pieces. It's + + + align:start position:0% +literally cut into small pieces. It's +usually used in a culinary sense. Uh + + align:start position:0% +usually used in a culinary sense. Uh + + + align:start position:0% +usually used in a culinary sense. Uh +like these days you have corn beef hash + + align:start position:0% +like these days you have corn beef hash + + + align:start position:0% +like these days you have corn beef hash +or something. + + align:start position:0% +or something. + + + align:start position:0% +or something. +Put the definition over here. + + align:start position:0% + + + + align:start position:0% + +Uh it comes from French. + + align:start position:0% + + + + align:start position:0% + +uh hashe + + align:start position:0% + + + + align:start position:0% + +uh which means uh + + align:start position:0% +uh which means uh + + + align:start position:0% +uh which means uh +to chop up. + + align:start position:0% +to chop up. + + + align:start position:0% +to chop up. +Okay. Uh you know it in English from the + + align:start position:0% +Okay. Uh you know it in English from the + + + align:start position:0% +Okay. Uh you know it in English from the +word hatchet. + + align:start position:0% +word hatchet. + + + align:start position:0% +word hatchet. +So it's the same derivation + + align:start position:0% + + + + align:start position:0% + +and it comes from old French. + + align:start position:0% + + + + align:start position:0% + +uh I don't actually know whether that's + + align:start position:0% +uh I don't actually know whether that's + + + align:start position:0% +uh I don't actually know whether that's +hashe or hash but uh + + align:start position:0% + + + + align:start position:0% + +uh which means axe. + + align:start position:0% +uh which means axe. + + + align:start position:0% +uh which means axe. +Okay, so you can see the derivation. Um + + align:start position:0% +Okay, so you can see the derivation. Um + + + align:start position:0% +Okay, so you can see the derivation. Um +that's if you look this up in OED or + + align:start position:0% +that's if you look this up in OED or + + + align:start position:0% +that's if you look this up in OED or +what or pick your favorite dictionary or + + align:start position:0% +what or pick your favorite dictionary or + + + align:start position:0% +what or pick your favorite dictionary or +even Google uh that's what you find. But + + align:start position:0% +even Google uh that's what you find. But + + + align:start position:0% +even Google uh that's what you find. But +in fact uh there's a a new prevailing + + align:start position:0% +in fact uh there's a a new prevailing + + + align:start position:0% +in fact uh there's a a new prevailing +theory that in fact hash comes from uh + + align:start position:0% +theory that in fact hash comes from uh + + + align:start position:0% +theory that in fact hash comes from uh +another language + + align:start position:0% + + + + align:start position:0% + +uh which is Vulcan + + align:start position:0% +uh which is Vulcan + + + align:start position:0% +uh which is Vulcan +uh la ash I mean you could see the + + align:start position:0% +uh la ash I mean you could see the + + + align:start position:0% +uh la ash I mean you could see the +derivation right uh actually means axe + + align:start position:0% +derivation right uh actually means axe + + + align:start position:0% +derivation right uh actually means axe +so maybe French got it from Vulcan or + + align:start position:0% +so maybe French got it from Vulcan or + + + align:start position:0% +so maybe French got it from Vulcan or +vice versa but I think I think that's + + align:start position:0% +vice versa but I think I think that's + + + align:start position:0% +vice versa but I think I think that's +pretty clear uh live long and prosper + + align:start position:0% +pretty clear uh live long and prosper + + + align:start position:0% +pretty clear uh live long and prosper +and uh farewell to Spock + + align:start position:0% + + + + align:start position:0% + +sad news of last week. + + align:start position:0% +sad news of last week. + + + align:start position:0% +sad news of last week. +Okay, so enough about hashing. We'll + + align:start position:0% +Okay, so enough about hashing. We'll + + + align:start position:0% +Okay, so enough about hashing. We'll +come back to that in a little bit. Uh, + + align:start position:0% +come back to that in a little bit. Uh, + + + align:start position:0% +come back to that in a little bit. Uh, +but hash functions essentially take up + + align:start position:0% +but hash functions essentially take up + + + align:start position:0% +but hash functions essentially take up +this idea of taking your key, chopping + + align:start position:0% +this idea of taking your key, chopping + + + align:start position:0% +this idea of taking your key, chopping +up into pieces, and mixing it like in a + + align:start position:0% +up into pieces, and mixing it like in a + + + align:start position:0% +up into pieces, and mixing it like in a +good dish. + + align:start position:0% +good dish. + + + align:start position:0% +good dish. +All right, so uh we're going to cover + + align:start position:0% +All right, so uh we're going to cover + + + align:start position:0% +All right, so uh we're going to cover +two ways to get uh strong constant time + + align:start position:0% +two ways to get uh strong constant time + + + align:start position:0% +two ways to get uh strong constant time +bounds. Uh what the probably the most + + align:start position:0% +bounds. Uh what the probably the most + + + align:start position:0% +bounds. Uh what the probably the most +useful one is called universal hashing. + + align:start position:0% +useful one is called universal hashing. + + + align:start position:0% +useful one is called universal hashing. +We'll spend most of our time on that. Uh + + align:start position:0% +We'll spend most of our time on that. Uh + + + align:start position:0% +We'll spend most of our time on that. Uh +but the theoretically cooler one is + + align:start position:0% +but the theoretically cooler one is + + + align:start position:0% +but the theoretically cooler one is +called perfect hashing. Universal + + align:start position:0% +called perfect hashing. Universal + + + align:start position:0% +called perfect hashing. Universal +hashing, we're going to guarantee there + + align:start position:0% +hashing, we're going to guarantee there + + + align:start position:0% +hashing, we're going to guarantee there +are very few conflicts in expectation. + + align:start position:0% +are very few conflicts in expectation. + + + align:start position:0% +are very few conflicts in expectation. +Perfect hashing, we're going to + + align:start position:0% +Perfect hashing, we're going to + + + align:start position:0% +Perfect hashing, we're going to +guarantee there are zero conflicts. Uh + + align:start position:0% +guarantee there are zero conflicts. Uh + + + align:start position:0% +guarantee there are zero conflicts. Uh +the catch is uh at least in its obvious + + align:start position:0% +the catch is uh at least in its obvious + + + align:start position:0% +the catch is uh at least in its obvious +form, it only works for static sets. If + + align:start position:0% +form, it only works for static sets. If + + + align:start position:0% +form, it only works for static sets. If +you're if you uh forbid insert and + + align:start position:0% +you're if you uh forbid insert and + + + align:start position:0% +you're if you uh forbid insert and +delete and just want to do search, then + + align:start position:0% +delete and just want to do search, then + + + align:start position:0% +delete and just want to do search, then +perfect hashing is a good method. So + + align:start position:0% +perfect hashing is a good method. So + + + align:start position:0% +perfect hashing is a good method. So +like if you're actually storing a + + align:start position:0% +like if you're actually storing a + + + align:start position:0% +like if you're actually storing a +dictionary um like the OED, you know, + + align:start position:0% +dictionary um like the OED, you know, + + + align:start position:0% +dictionary um like the OED, you know, +English doesn't change that quickly. So + + align:start position:0% +English doesn't change that quickly. So + + + align:start position:0% +English doesn't change that quickly. So +you can afford to recomputee your data + + align:start position:0% +you can afford to recomputee your data + + + align:start position:0% +you can afford to recomputee your data +structure whenever you release a new + + align:start position:0% +structure whenever you release a new + + + align:start position:0% +structure whenever you release a new +addition. All right. Uh but let's start + + align:start position:0% +addition. All right. Uh but let's start + + + align:start position:0% +addition. All right. Uh but let's start +with universal hashing. This is a nice + + align:start position:0% +with universal hashing. This is a nice + + + align:start position:0% +with universal hashing. This is a nice +powerful technique. + + align:start position:0% +powerful technique. + + + align:start position:0% +powerful technique. +It works for dynamic data. Insert, + + align:start position:0% +It works for dynamic data. Insert, + + + align:start position:0% +It works for dynamic data. Insert, +delete, and search will be constant + + align:start position:0% +delete, and search will be constant + + + align:start position:0% +delete, and search will be constant +expected time with no assumptions about + + align:start position:0% +expected time with no assumptions about + + + align:start position:0% +expected time with no assumptions about +the input. So it will not be average + + align:start position:0% +the input. So it will not be average + + + align:start position:0% +the input. So it will not be average +case. that's in some sense worst case + + align:start position:0% +case. that's in some sense worst case + + + align:start position:0% +case. that's in some sense worst case +but randomized. + + align:start position:0% + + + + align:start position:0% + +So the idea is we need to do something + + align:start position:0% +So the idea is we need to do something + + + align:start position:0% +So the idea is we need to do something +random. If you just say well I choose + + align:start position:0% +random. If you just say well I choose + + + align:start position:0% +random. If you just say well I choose +one hash function once and for all and I + + align:start position:0% +one hash function once and for all and I + + + align:start position:0% +one hash function once and for all and I +use that for my table. Okay, maybe my + + align:start position:0% +use that for my table. Okay, maybe my + + + align:start position:0% +use that for my table. Okay, maybe my +table doubles in size. I change the hash + + align:start position:0% +table doubles in size. I change the hash + + + align:start position:0% +table doubles in size. I change the hash +function. But um there's no randomness + + align:start position:0% +function. But um there's no randomness + + + align:start position:0% +function. But um there's no randomness +there. What we we need to introduce + + align:start position:0% +there. What we we need to introduce + + + align:start position:0% +there. What we we need to introduce +randomness somehow into this data + + align:start position:0% +randomness somehow into this data + + + align:start position:0% +randomness somehow into this data +structure. And uh the way we're going to + + align:start position:0% +structure. And uh the way we're going to + + + align:start position:0% +structure. And uh the way we're going to +do that is in how we choose the hash + + align:start position:0% +do that is in how we choose the hash + + + align:start position:0% +do that is in how we choose the hash +function. + + align:start position:0% +function. + + + align:start position:0% +function. +We're going to choose our hash function + + align:start position:0% +We're going to choose our hash function + + + align:start position:0% +We're going to choose our hash function +uh randomly + + align:start position:0% + + + + align:start position:0% + +from some set of hash functions call it + + align:start position:0% +from some set of hash functions call it + + + align:start position:0% +from some set of hash functions call it +capital H. + + align:start position:0% +capital H. + + + align:start position:0% +capital H. +This is going to be a universal hash + + align:start position:0% +This is going to be a universal hash + + + align:start position:0% +This is going to be a universal hash +family. We're going to imagine there are + + align:start position:0% +family. We're going to imagine there are + + + align:start position:0% +family. We're going to imagine there are +many possible hash functions we could + + align:start position:0% +many possible hash functions we could + + + align:start position:0% +many possible hash functions we could +choose. If we choose one of them + + align:start position:0% +choose. If we choose one of them + + + align:start position:0% +choose. If we choose one of them +uniformly at random, that's a random + + align:start position:0% +uniformly at random, that's a random + + + align:start position:0% +uniformly at random, that's a random +choice. And that randomness is going to + + align:start position:0% +choice. And that randomness is going to + + + align:start position:0% +choice. And that randomness is going to +be enough that we no longer need to + + align:start position:0% +be enough that we no longer need to + + + align:start position:0% +be enough that we no longer need to +assume anything about the keys. + + align:start position:0% +assume anything about the keys. + + + align:start position:0% +assume anything about the keys. +So + + align:start position:0% +So + + + align:start position:0% +So +uh for that to work we need some + + align:start position:0% +uh for that to work we need some + + + align:start position:0% +uh for that to work we need some +assumption about capital H. You know + + align:start position:0% +assumption about capital H. You know + + + align:start position:0% +assumption about capital H. You know +maybe it's just a set of one hash + + align:start position:0% +maybe it's just a set of one hash + + + align:start position:0% +maybe it's just a set of one hash +function that wouldn't add much + + align:start position:0% +function that wouldn't add much + + + align:start position:0% +function that wouldn't add much +randomness. Two also would not add much + + align:start position:0% +randomness. Two also would not add much + + + align:start position:0% +randomness. Two also would not add much +randomness. We need a lot of them. And + + align:start position:0% +randomness. We need a lot of them. And + + + align:start position:0% +randomness. We need a lot of them. And +so we're going to require H to have this + + align:start position:0% +so we're going to require H to have this + + + align:start position:0% +so we're going to require H to have this +property + + align:start position:0% +property + + + align:start position:0% +property +and we're going to call it the property + + align:start position:0% +and we're going to call it the property + + + align:start position:0% +and we're going to call it the property +universality. + + align:start position:0% +universality. + + + align:start position:0% +universality. +Uh generally you call it a universal + + align:start position:0% +Uh generally you call it a universal + + + align:start position:0% +Uh generally you call it a universal +hash family + + align:start position:0% + + + + align:start position:0% + +just a set of hash functions. + + align:start position:0% +just a set of hash functions. + + + align:start position:0% +just a set of hash functions. +What we want is that um + + align:start position:0% +What we want is that um + + + align:start position:0% +What we want is that um +so we're choosing our hash function + + align:start position:0% +so we're choosing our hash function + + + align:start position:0% +so we're choosing our hash function +little h from big h and among those + + align:start position:0% +little h from big h and among those + + + align:start position:0% +little h from big h and among those +choices we want the probability + + align:start position:0% +choices we want the probability + + + align:start position:0% +choices we want the probability +that two keys hash to the same value to + + align:start position:0% +that two keys hash to the same value to + + + align:start position:0% +that two keys hash to the same value to +be small + + align:start position:0% + + + + align:start position:0% + +I'll Okay. + + align:start position:0% + + + + align:start position:0% + +And this is very similar looking to + + align:start position:0% +And this is very similar looking to + + + align:start position:0% +And this is very similar looking to +universal sorry to simple uniform + + align:start position:0% +universal sorry to simple uniform + + + align:start position:0% +universal sorry to simple uniform +hashing looks almost the same here + + align:start position:0% +hashing looks almost the same here + + + align:start position:0% +hashing looks almost the same here +except I switched from K1 and K2 to K + + align:start position:0% +except I switched from K1 and K2 to K + + + align:start position:0% +except I switched from K1 and K2 to K +and K prime but same thing. Um but what + + align:start position:0% +and K prime but same thing. Um but what + + + align:start position:0% +and K prime but same thing. Um but what +we're taking the probability over what's + + align:start position:0% +we're taking the probability over what's + + + align:start position:0% +we're taking the probability over what's +we're assuming is random is different + + align:start position:0% +we're assuming is random is different + + + align:start position:0% +we're assuming is random is different +here. We're assuming K1 and K2 are + + align:start position:0% +here. We're assuming K1 and K2 are + + + align:start position:0% +here. We're assuming K1 and K2 are +random because H was fixed. This was an + + align:start position:0% +random because H was fixed. This was an + + + align:start position:0% +random because H was fixed. This was an +assumption about uh the inputs over + + align:start position:0% +assumption about uh the inputs over + + + align:start position:0% +assumption about uh the inputs over +here. We're thinking of K and K prime as + + align:start position:0% +here. We're thinking of K and K prime as + + + align:start position:0% +here. We're thinking of K and K prime as +being fixed. This has to work for every + + align:start position:0% +being fixed. This has to work for every + + + align:start position:0% +being fixed. This has to work for every +pair of distinct keys. And the + + align:start position:0% +pair of distinct keys. And the + + + align:start position:0% +pair of distinct keys. And the +probability we're considering is the + + align:start position:0% +probability we're considering is the + + + align:start position:0% +probability we're considering is the +distribution of H. So we're trying all + + align:start position:0% +distribution of H. So we're trying all + + + align:start position:0% +distribution of H. So we're trying all +the different H's or we're trying them + + align:start position:0% +the different H's or we're trying them + + + align:start position:0% +the different H's or we're trying them +trying little H uniformly at random. We + + align:start position:0% +trying little H uniformly at random. We + + + align:start position:0% +trying little H uniformly at random. We +want the probability that a random H + + align:start position:0% +want the probability that a random H + + + align:start position:0% +want the probability that a random H +makes K and K prime collide to be at + + align:start position:0% +makes K and K prime collide to be at + + + align:start position:0% +makes K and K prime collide to be at +most 1 over M. Okay. The other + + align:start position:0% +most 1 over M. Okay. The other + + + align:start position:0% +most 1 over M. Okay. The other +difference is we switch from equals to + + align:start position:0% +difference is we switch from equals to + + + align:start position:0% +difference is we switch from equals to +at most. Um doesn't I mean less would be + + align:start position:0% +at most. Um doesn't I mean less would be + + + align:start position:0% +at most. Um doesn't I mean less would be +better and there are ways to make it + + align:start position:0% +better and there are ways to make it + + + align:start position:0% +better and there are ways to make it +less for a couple pairs but it doesn't + + align:start position:0% +less for a couple pairs but it doesn't + + + align:start position:0% +less for a couple pairs but it doesn't +really matter. Um but of course anything + + align:start position:0% +really matter. Um but of course anything + + + align:start position:0% +really matter. Um but of course anything +less than or equal to 1 / m will be just + + align:start position:0% +less than or equal to 1 / m will be just + + + align:start position:0% +less than or equal to 1 / m will be just +as good. + + align:start position:0% +as good. + + + align:start position:0% +as good. +So this is an assumption about capital + + align:start position:0% +So this is an assumption about capital + + + align:start position:0% +So this is an assumption about capital +h. We will see how to achieve this + + align:start position:0% +h. We will see how to achieve this + + + align:start position:0% +h. We will see how to achieve this +assumption in a little bit. Let me first + + align:start position:0% +assumption in a little bit. Let me first + + + align:start position:0% +assumption in a little bit. Let me first +uh prove to you that this is enough. Uh + + align:start position:0% +uh prove to you that this is enough. Uh + + + align:start position:0% +uh prove to you that this is enough. Uh +it's going to be basically the same as + + align:start position:0% +it's going to be basically the same as + + + align:start position:0% +it's going to be basically the same as +uh the 006 analysis, but it's worth + + align:start position:0% +uh the 006 analysis, but it's worth + + + align:start position:0% +uh the 006 analysis, but it's worth +repeating just so we are sure + + align:start position:0% +repeating just so we are sure + + + align:start position:0% +repeating just so we are sure +everything's okay + + align:start position:0% + + + + align:start position:0% + +and so I can be more precise about + + align:start position:0% +and so I can be more precise about + + + align:start position:0% +and so I can be more precise about +what we're assuming. + + align:start position:0% + + + + align:start position:0% + +The key difference between this theorem + + align:start position:0% +The key difference between this theorem + + + align:start position:0% +The key difference between this theorem +and the 006 theorem is we get to assume + + align:start position:0% +and the 006 theorem is we get to assume + + + align:start position:0% +and the 006 theorem is we get to assume +we get to make no assumptions about the + + align:start position:0% +we get to make no assumptions about the + + + align:start position:0% +we get to make no assumptions about the +keys. They are arbitrary. You get to + + align:start position:0% +keys. They are arbitrary. You get to + + + align:start position:0% +keys. They are arbitrary. You get to +choose them however you want. But then I + + align:start position:0% +choose them however you want. But then I + + + align:start position:0% +choose them however you want. But then I +choose a random hash function without + + align:start position:0% +choose a random hash function without + + + align:start position:0% +choose a random hash function without +the hash function cannot depend on these + + align:start position:0% +the hash function cannot depend on these + + + align:start position:0% +the hash function cannot depend on these +keys. But it's going to be random. And I + + align:start position:0% +keys. But it's going to be random. And I + + + align:start position:0% +keys. But it's going to be random. And I +choose the hash function after you + + align:start position:0% +choose the hash function after you + + + align:start position:0% +choose the hash function after you +choose the keys. That's uh important. + + align:start position:0% + + + + align:start position:0% + +So we're going to choose a random little + + align:start position:0% +So we're going to choose a random little + + + align:start position:0% +So we're going to choose a random little +h in big h and we're assuming uh big h + + align:start position:0% +h in big h and we're assuming uh big h + + + align:start position:0% +h in big h and we're assuming uh big h +is universal. + + align:start position:0% + + + + align:start position:0% + +Then + + align:start position:0% +Then + + + align:start position:0% +Then +the expected number of keys in a slot + + align:start position:0% + + + + align:start position:0% + +among those n keys + + align:start position:0% + + + + align:start position:0% + +is at most uh 1 plus alpha. + + align:start position:0% +is at most uh 1 plus alpha. + + + align:start position:0% +is at most uh 1 plus alpha. +Alpha is n / m. So this is exactly what + + align:start position:0% +Alpha is n / m. So this is exactly what + + + align:start position:0% +Alpha is n / m. So this is exactly what +we had over here. uh here we're talking + + align:start position:0% +we had over here. uh here we're talking + + + align:start position:0% +we had over here. uh here we're talking +about time bound but the time bound + + align:start position:0% +about time bound but the time bound + + + align:start position:0% +about time bound but the time bound +followed because the length of each + + align:start position:0% +followed because the length of each + + + align:start position:0% +followed because the length of each +chain uh was expected to be 1 plus alpha + + align:start position:0% +chain uh was expected to be 1 plus alpha + + + align:start position:0% +chain uh was expected to be 1 plus alpha +and here the expectation is over the + + align:start position:0% +and here the expectation is over the + + + align:start position:0% +and here the expectation is over the +choice of h right not assuming anything + + align:start position:0% +choice of h right not assuming anything + + + align:start position:0% +choice of h right not assuming anything +about the keys + + align:start position:0% +about the keys + + + align:start position:0% +about the keys +so uh let's prove this theorem + + align:start position:0% + + + + align:start position:0% + +it's pretty easy but uh I'm going to + + align:start position:0% +it's pretty easy but uh I'm going to + + + align:start position:0% +it's pretty easy but uh I'm going to +introduce some analysis techniques that + + align:start position:0% +introduce some analysis techniques that + + + align:start position:0% +introduce some analysis techniques that +we will use for uh more interesting + + align:start position:0% +we will use for uh more interesting + + + align:start position:0% +we will use for uh more interesting +things. + + align:start position:0% +things. + + + align:start position:0% +things. +So, let's uh give the keys a name. + + align:start position:0% +So, let's uh give the keys a name. + + + align:start position:0% +So, let's uh give the keys a name. +I'll just call them + + align:start position:0% +I'll just call them + + + align:start position:0% +I'll just call them +uh K0 + + align:start position:0% +uh K0 + + + align:start position:0% +uh K0 +up to I'll be lazy. Use K1 up to KN. + + align:start position:0% + + + + align:start position:0% + +Okay. And + + align:start position:0% + + + + align:start position:0% + +I just want to compute that expectation. + + align:start position:0% + + + + align:start position:0% + +So I want to compute um + + align:start position:0% + + + + align:start position:0% + +let's say the number of keys + + align:start position:0% +let's say the number of keys + + + align:start position:0% +let's say the number of keys +colliding with one of those keys let's + + align:start position:0% +colliding with one of those keys let's + + + align:start position:0% +colliding with one of those keys let's +say uh ki + + align:start position:0% + + + + align:start position:0% + +So uh this is of course the size of the + + align:start position:0% +So uh this is of course the size of the + + + align:start position:0% +So uh this is of course the size of the +slot that ki happens to go. This is + + align:start position:0% +slot that ki happens to go. This is + + + align:start position:0% +slot that ki happens to go. This is +going to work for all i. And so if I can + + align:start position:0% +going to work for all i. And so if I can + + + align:start position:0% +going to work for all i. And so if I can +say that this is at most one over alpha + + align:start position:0% +say that this is at most one over alpha + + + align:start position:0% +say that this is at most one over alpha +for each i then I have my theorem. Okay + + align:start position:0% +for each i then I have my theorem. Okay + + + align:start position:0% +for each i then I have my theorem. Okay +just another way to talk about it. Now + + align:start position:0% +just another way to talk about it. Now + + + align:start position:0% +just another way to talk about it. Now +the number of keys colliding with ki + + align:start position:0% +the number of keys colliding with ki + + + align:start position:0% +the number of keys colliding with ki +here's a general trick. If whenever you + + align:start position:0% +here's a general trick. If whenever you + + + align:start position:0% +here's a general trick. If whenever you +want to count something in expectation a + + align:start position:0% +want to count something in expectation a + + + align:start position:0% +want to count something in expectation a +very helpful tool is indicator random + + align:start position:0% +very helpful tool is indicator random + + + align:start position:0% +very helpful tool is indicator random +variables. + + align:start position:0% +variables. + + + align:start position:0% +variables. +Let's let's name all of the different + + align:start position:0% +Let's let's name all of the different + + + align:start position:0% +Let's let's name all of the different +events that we want to count and then + + align:start position:0% +events that we want to count and then + + + align:start position:0% +events that we want to count and then +we're basically summing those variables. + + align:start position:0% +we're basically summing those variables. + + + align:start position:0% +we're basically summing those variables. +So I'm going to say uh I'm going to use + + align:start position:0% +So I'm going to say uh I'm going to use + + + align:start position:0% +So I'm going to say uh I'm going to use +I capital I I J to be an indicator + + align:start position:0% +I capital I I J to be an indicator + + + align:start position:0% +I capital I I J to be an indicator +random variable. It's going to be one or + + align:start position:0% +random variable. It's going to be one or + + + align:start position:0% +random variable. It's going to be one or +zero. One if uh + + align:start position:0% +zero. One if uh + + + align:start position:0% +zero. One if uh +hash function of + + align:start position:0% +hash function of + + + align:start position:0% +hash function of +AI equals the hash function of KJ. So + + align:start position:0% +AI equals the hash function of KJ. So + + + align:start position:0% +AI equals the hash function of KJ. So +there's a collision between KI and KJ + + align:start position:0% +there's a collision between KI and KJ + + + align:start position:0% +there's a collision between KI and KJ +and zero if they hash to different + + align:start position:0% +and zero if they hash to different + + + align:start position:0% +and zero if they hash to different +slots. + + align:start position:0% +slots. + + + align:start position:0% +slots. +Okay. Now this is it's a random variable + + align:start position:0% +Okay. Now this is it's a random variable + + + align:start position:0% +Okay. Now this is it's a random variable +because it depends on H and H is a + + align:start position:0% +because it depends on H and H is a + + + align:start position:0% +because it depends on H and H is a +random thing. KI and KJ are not random. + + align:start position:0% +random thing. KI and KJ are not random. + + + align:start position:0% +random thing. KI and KJ are not random. +They're they're given to you. And then I + + align:start position:0% +They're they're given to you. And then I + + + align:start position:0% +They're they're given to you. And then I +want to know uh when does H map those + + align:start position:0% +want to know uh when does H map those + + + align:start position:0% +want to know uh when does H map those +two uh keys to the same slot. And so + + align:start position:0% +two uh keys to the same slot. And so + + + align:start position:0% +two uh keys to the same slot. And so +this number is really just the sum of + + align:start position:0% +this number is really just the sum of + + + align:start position:0% +this number is really just the sum of +iig j over all j. Right? This is the + + align:start position:0% +iig j over all j. Right? This is the + + + align:start position:0% +iig j over all j. Right? This is the +same thing. + + align:start position:0% +same thing. + + + align:start position:0% +same thing. +The the number in here is the sum for j + + align:start position:0% +The the number in here is the sum for j + + + align:start position:0% +The the number in here is the sum for j +not equal to i + + align:start position:0% +not equal to i + + + align:start position:0% +not equal to i +of i i i j because we get a one every + + align:start position:0% +of i i i j because we get a one every + + + align:start position:0% +of i i i j because we get a one every +time they collide zero otherwise. So + + align:start position:0% +time they collide zero otherwise. So + + + align:start position:0% +time they collide zero otherwise. So +that counts how many collide. + + align:start position:0% +that counts how many collide. + + + align:start position:0% +that counts how many collide. +Once we have it in this notation, we can + + align:start position:0% +Once we have it in this notation, we can + + + align:start position:0% +Once we have it in this notation, we can +use all the great uh lemas and theorems + + align:start position:0% +use all the great uh lemas and theorems + + + align:start position:0% +use all the great uh lemas and theorems +about uh in this case e expectation. Uh + + align:start position:0% +about uh in this case e expectation. Uh + + + align:start position:0% +about uh in this case e expectation. Uh +what should I use here? + + align:start position:0% + + + + align:start position:0% + +What's a good uh how can I simplify this + + align:start position:0% +What's a good uh how can I simplify this + + + align:start position:0% +What's a good uh how can I simplify this +formula? + + align:start position:0% +formula? + + + align:start position:0% +formula? +Linearity of expectation. Thank you. + + align:start position:0% + + + + align:start position:0% + +If you don't know all these things, read + + align:start position:0% +If you don't know all these things, read + + + align:start position:0% +If you don't know all these things, read +the probability appendex in the + + align:start position:0% +the probability appendex in the + + + align:start position:0% +the probability appendex in the +textbook. + + align:start position:0% +textbook. + + + align:start position:0% +textbook. +So we want to + + align:start position:0% +So we want to + + + align:start position:0% +So we want to +talk about expectation of the simplest + + align:start position:0% +talk about expectation of the simplest + + + align:start position:0% +talk about expectation of the simplest +thing possible. So linearity lets us put + + align:start position:0% +thing possible. So linearity lets us put + + + align:start position:0% +thing possible. So linearity lets us put +the e inside the sum + + align:start position:0% +the e inside the sum + + + align:start position:0% +the e inside the sum +without uh losing anything. Now the + + align:start position:0% +without uh losing anything. Now the + + + align:start position:0% +without uh losing anything. Now the +expectation + + align:start position:0% +expectation + + + align:start position:0% +expectation +of an indicator random variable is + + align:start position:0% +of an indicator random variable is + + + align:start position:0% +of an indicator random variable is +pretty simple because the zeros don't + + align:start position:0% +pretty simple because the zeros don't + + + align:start position:0% +pretty simple because the zeros don't +contribute to the expectation. The ones + + align:start position:0% +contribute to the expectation. The ones + + + align:start position:0% +contribute to the expectation. The ones +contribute one. So this is the same + + align:start position:0% +contribute one. So this is the same + + + align:start position:0% +contribute one. So this is the same +thing as just the probability of this + + align:start position:0% +thing as just the probability of this + + + align:start position:0% +thing as just the probability of this +being one. Okay. So we get uh sum of j + + align:start position:0% +being one. Okay. So we get uh sum of j + + + align:start position:0% +being one. Okay. So we get uh sum of j +not equal to i of the probability that i + + align:start position:0% +not equal to i of the probability that i + + + align:start position:0% +not equal to i of the probability that i +i j equals 1. + + align:start position:0% +i j equals 1. + + + align:start position:0% +i j equals 1. +And the probability that iig equals 1. + + align:start position:0% +And the probability that iig equals 1. + + + align:start position:0% +And the probability that iig equals 1. +Well, that's the probability that this + + align:start position:0% +Well, that's the probability that this + + + align:start position:0% +Well, that's the probability that this +happens. + + align:start position:0% +happens. + + + align:start position:0% +happens. +And what's the probability that that + + align:start position:0% +And what's the probability that that + + + align:start position:0% +And what's the probability that that +happens? Uh at most one over m by + + align:start position:0% +happens? Uh at most one over m by + + + align:start position:0% +happens? Uh at most one over m by +universality. + + align:start position:0% +universality. + + + align:start position:0% +universality. +So I'm gonna I'll write it out. + + align:start position:0% +So I'm gonna I'll write it out. + + + align:start position:0% +So I'm gonna I'll write it out. +This is sum j not equal to i. + + align:start position:0% +This is sum j not equal to i. + + + align:start position:0% +This is sum j not equal to i. +Probability that h maps k i and kj to + + align:start position:0% +Probability that h maps k i and kj to + + + align:start position:0% +Probability that h maps k i and kj to +the same slot. + + align:start position:0% +the same slot. + + + align:start position:0% +the same slot. +So that's because it's an indicator. + + align:start position:0% +So that's because it's an indicator. + + + align:start position:0% +So that's because it's an indicator. +Sorry, that's the definition of iig. And + + align:start position:0% +Sorry, that's the definition of iig. And + + + align:start position:0% +Sorry, that's the definition of iig. And +uh this is at most sum j not equal to i + + align:start position:0% +uh this is at most sum j not equal to i + + + align:start position:0% +uh this is at most sum j not equal to i +of 1 / m by universality. So here's + + align:start position:0% +of 1 / m by universality. So here's + + + align:start position:0% +of 1 / m by universality. So here's +where we're using it. + + align:start position:0% + + + + align:start position:0% + +uh and sum of j not equal to i. Well, + + align:start position:0% +uh and sum of j not equal to i. Well, + + + align:start position:0% +uh and sum of j not equal to i. Well, +that's that's basically n. + + align:start position:0% + + + + align:start position:0% + +Uh + + align:start position:0% +Uh + + + align:start position:0% +Uh +but I made a mistake here slightly off + + align:start position:0% +but I made a mistake here slightly off + + + align:start position:0% +but I made a mistake here slightly off +um from here. Yeah. So this this uh line + + align:start position:0% +um from here. Yeah. So this this uh line + + + align:start position:0% +um from here. Yeah. So this this uh line +is wrong. Sorry, let me fix it. Uh + + align:start position:0% +is wrong. Sorry, let me fix it. Uh + + + align:start position:0% +is wrong. Sorry, let me fix it. Uh +because this assumption only works when + + align:start position:0% +because this assumption only works when + + + align:start position:0% +because this assumption only works when +the keys are distinct. + + align:start position:0% +the keys are distinct. + + + align:start position:0% +the keys are distinct. +So uh in fact + + align:start position:0% +So uh in fact + + + align:start position:0% +So uh in fact +yeah how did I get J? Yeah. + + align:start position:0% + + + + align:start position:0% + +Yeah sorry + + align:start position:0% +Yeah sorry + + + align:start position:0% +Yeah sorry +this should have been this uh actually + + align:start position:0% +this should have been this uh actually + + + align:start position:0% +this should have been this uh actually +everything I said is true but uh if you + + align:start position:0% +everything I said is true but uh if you + + + align:start position:0% +everything I said is true but uh if you +want to count the number of keys I + + align:start position:0% +want to count the number of keys I + + + align:start position:0% +want to count the number of keys I +really wanted to count the total number + + align:start position:0% +really wanted to count the total number + + + align:start position:0% +really wanted to count the total number +of keys that hash the same place as uh + + align:start position:0% +of keys that hash the same place as uh + + + align:start position:0% +of keys that hash the same place as uh +ki. So there's one more which is ki + + align:start position:0% +ki. So there's one more which is ki + + + align:start position:0% +ki. So there's one more which is ki +itself always hashes to wherever ki + + align:start position:0% +itself always hashes to wherever ki + + + align:start position:0% +itself always hashes to wherever ki +hashes. Okay. So I did a summation of j + + align:start position:0% +hashes. Okay. So I did a summation of j + + + align:start position:0% +hashes. Okay. So I did a summation of j +not equal to i but I should also have a + + align:start position:0% +not equal to i but I should also have a + + + align:start position:0% +not equal to i but I should also have a +plus i I I + + align:start position:0% +plus i I I + + + align:start position:0% +plus i I I +captain. + + align:start position:0% +captain. + + + align:start position:0% +captain. +So uh there's the case when i hashing to + + align:start position:0% +So uh there's the case when i hashing to + + + align:start position:0% +So uh there's the case when i hashing to +the same place uh which of course is + + align:start position:0% +the same place uh which of course is + + + align:start position:0% +the same place uh which of course is +always going to happen. So you get um + + align:start position:0% +always going to happen. So you get um + + + align:start position:0% +always going to happen. So you get um +basically plus one everywhere. + + align:start position:0% +basically plus one everywhere. + + + align:start position:0% +basically plus one everywhere. +Okay. So that's makes me happier because + + align:start position:0% +Okay. So that's makes me happier because + + + align:start position:0% +Okay. So that's makes me happier because +then I actually get what the theorem + + align:start position:0% +then I actually get what the theorem + + + align:start position:0% +then I actually get what the theorem +said which was one plus alpha. There's + + align:start position:0% +said which was one plus alpha. There's + + + align:start position:0% +said which was one plus alpha. There's +always going to be the one guy hashing + + align:start position:0% +always going to be the one guy hashing + + + align:start position:0% +always going to be the one guy hashing +there when I assume that ki hash to + + align:start position:0% +there when I assume that ki hash to + + + align:start position:0% +there when I assume that ki hash to +wherever it does. + + align:start position:0% +wherever it does. + + + align:start position:0% +wherever it does. +Okay. So this tells you that if we could + + align:start position:0% +Okay. So this tells you that if we could + + + align:start position:0% +Okay. So this tells you that if we could +find a universal hash family then we're + + align:start position:0% +find a universal hash family then we're + + + align:start position:0% +find a universal hash family then we're +guaranteed insert delete and search cost + + align:start position:0% +guaranteed insert delete and search cost + + + align:start position:0% +guaranteed insert delete and search cost +uh order one plus alpha in expectation. + + align:start position:0% +uh order one plus alpha in expectation. + + + align:start position:0% +uh order one plus alpha in expectation. +And the expectation is only over the + + align:start position:0% +And the expectation is only over the + + + align:start position:0% +And the expectation is only over the +choice of h not over the inputs. I think + + align:start position:0% +choice of h not over the inputs. I think + + + align:start position:0% +choice of h not over the inputs. I think +I've stressed that enough times. Uh but + + align:start position:0% +I've stressed that enough times. Uh but + + + align:start position:0% +I've stressed that enough times. Uh but +the remaining question is can we + + align:start position:0% +the remaining question is can we + + + align:start position:0% +the remaining question is can we +actually design a universal hash family? + + align:start position:0% +actually design a universal hash family? + + + align:start position:0% +actually design a universal hash family? +Are there any universal hash families? + + align:start position:0% +Are there any universal hash families? + + + align:start position:0% +Are there any universal hash families? +Uh + + align:start position:0% + + + + align:start position:0% + +yes, as you might expect there are. + + align:start position:0% +yes, as you might expect there are. + + + align:start position:0% +yes, as you might expect there are. +Otherwise this wouldn't be very + + align:start position:0% +Otherwise this wouldn't be very + + + align:start position:0% +Otherwise this wouldn't be very +interesting. + + align:start position:0% + + + + align:start position:0% + +Okay, let me give you an example of a + + align:start position:0% +Okay, let me give you an example of a + + + align:start position:0% +Okay, let me give you an example of a +bad universal hash family. + + align:start position:0% +bad universal hash family. + + + align:start position:0% +bad universal hash family. +Sort of an oxymoron, but uh it's + + align:start position:0% +Sort of an oxymoron, but uh it's + + + align:start position:0% +Sort of an oxymoron, but uh it's +possible. + + align:start position:0% + + + + align:start position:0% + +Uh bad. Uh here's a hash family that's + + align:start position:0% +Uh bad. Uh here's a hash family that's + + + align:start position:0% +Uh bad. Uh here's a hash family that's +universal. H is the set of all hash + + align:start position:0% +universal. H is the set of all hash + + + align:start position:0% +universal. H is the set of all hash +functions. + + align:start position:0% +functions. + + + align:start position:0% +functions. +H from 01 + + align:start position:0% +H from 01 + + + align:start position:0% +H from 01 +to U minus one. + + align:start position:0% + + + + align:start position:0% + +This is what's normally called uniform + + align:start position:0% +This is what's normally called uniform + + + align:start position:0% +This is what's normally called uniform +hashing. It makes analysis really easy + + align:start position:0% +hashing. It makes analysis really easy + + + align:start position:0% +hashing. It makes analysis really easy +uh because uh you get to assume I mean + + align:start position:0% +uh because uh you get to assume I mean + + + align:start position:0% +uh because uh you get to assume I mean +this says a ahead of time for every + + align:start position:0% +this says a ahead of time for every + + + align:start position:0% +this says a ahead of time for every +universe item I'm going to choose a + + align:start position:0% +universe item I'm going to choose a + + + align:start position:0% +universe item I'm going to choose a +random slot to put it + + align:start position:0% +random slot to put it + + + align:start position:0% +random slot to put it +and then just I'll just remember that. + + align:start position:0% +and then just I'll just remember that. + + + align:start position:0% +and then just I'll just remember that. +And so whenever you give me a key, I'll + + align:start position:0% +And so whenever you give me a key, I'll + + + align:start position:0% +And so whenever you give me a key, I'll +just map it via H and I get a consistent + + align:start position:0% +just map it via H and I get a consistent + + + align:start position:0% +just map it via H and I get a consistent +slot. And definitely it's universal. + + align:start position:0% +slot. And definitely it's universal. + + + align:start position:0% +slot. And definitely it's universal. +What's bad about this hash function? + + align:start position:0% +What's bad about this hash function? + + + align:start position:0% +What's bad about this hash function? +Many things, but + + align:start position:0% + + + + align:start position:0% + +sorry. + + align:start position:0% +sorry. + + + align:start position:0% +sorry. +That's just as hard as the problem. + + align:start position:0% +That's just as hard as the problem. + + + align:start position:0% +That's just as hard as the problem. +Sort of the I'm begging the question. + + align:start position:0% +Sort of the I'm begging the question. + + + align:start position:0% +Sort of the I'm begging the question. +It's just as hard as the problem I'm + + align:start position:0% +It's just as hard as the problem I'm + + + align:start position:0% +It's just as hard as the problem I'm +solving. And what algorithmically what + + align:start position:0% +solving. And what algorithmically what + + + align:start position:0% +solving. And what algorithmically what +goes wrong here? + + align:start position:0% +goes wrong here? + + + align:start position:0% +goes wrong here? +They're two things I guess. + + align:start position:0% + + + + align:start position:0% + +Yeah, + + align:start position:0% +Yeah, + + + align:start position:0% +Yeah, +it's not deterministic. + + align:start position:0% +it's not deterministic. + + + align:start position:0% +it's not deterministic. +It's not deterministic. Um, that's okay + + align:start position:0% +It's not deterministic. Um, that's okay + + + align:start position:0% +It's not deterministic. Um, that's okay +because we're allowing randomiz + + align:start position:0% +because we're allowing randomiz + + + align:start position:0% +because we're allowing randomiz +randomization in this algorithm. So, uh, + + align:start position:0% +randomization in this algorithm. So, uh, + + + align:start position:0% +randomization in this algorithm. So, uh, +I mean, how I would compute this is for + + align:start position:0% +I mean, how I would compute this is for + + + align:start position:0% +I mean, how I would compute this is for +I would do a for loop over all universe + + align:start position:0% +I would do a for loop over all universe + + + align:start position:0% +I would do a for loop over all universe +items and I assume I have a way to + + align:start position:0% +items and I assume I have a way to + + + align:start position:0% +items and I assume I have a way to +generate a random number between 0 and n + + align:start position:0% +generate a random number between 0 and n + + + align:start position:0% +generate a random number between 0 and n +minus one. That's legitimate, but + + align:start position:0% +minus one. That's legitimate, but + + + align:start position:0% +minus one. That's legitimate, but +there's something bad about that + + align:start position:0% +there's something bad about that + + + align:start position:0% +there's something bad about that +algorithm. + + align:start position:0% +algorithm. + + + align:start position:0% +algorithm. +It's not consistent. + + align:start position:0% +It's not consistent. + + + align:start position:0% +It's not consistent. +Not consistent. It is consistent. If I + + align:start position:0% +Not consistent. It is consistent. If I + + + align:start position:0% +Not consistent. It is consistent. If I +premputee for every universe item where + + align:start position:0% +premputee for every universe item where + + + align:start position:0% +premputee for every universe item where +to map it, that's good. Uh, so all these + + align:start position:0% +to map it, that's good. Uh, so all these + + + align:start position:0% +to map it, that's good. Uh, so all these +things are actually okay. + + align:start position:0% +things are actually okay. + + + align:start position:0% +things are actually okay. +It takes too much time. + + align:start position:0% +It takes too much time. + + + align:start position:0% +It takes too much time. +It takes too much time and space. Yeah. + + align:start position:0% +It takes too much time and space. Yeah. + + + align:start position:0% +It takes too much time and space. Yeah. +Uh, that's + + align:start position:0% +Uh, that's + + + align:start position:0% +Uh, that's +the the bad thing. It's hard to isolate + + align:start position:0% +the the bad thing. It's hard to isolate + + + align:start position:0% +the the bad thing. It's hard to isolate +in a bad thing. What is so bad about it? + + align:start position:0% +in a bad thing. What is so bad about it? + + + align:start position:0% +in a bad thing. What is so bad about it? +But um + + align:start position:0% +But um + + + align:start position:0% +But um +we need U time to to compute all those + + align:start position:0% +we need U time to to compute all those + + + align:start position:0% +we need U time to to compute all those +random numbers and we need U space to + + align:start position:0% +random numbers and we need U space to + + + align:start position:0% +random numbers and we need U space to +store that hash function. In order to + + align:start position:0% +store that hash function. In order to + + + align:start position:0% +store that hash function. In order to +get consistency, we have to uh Whoops. + + align:start position:0% +get consistency, we have to uh Whoops. + + + align:start position:0% +get consistency, we have to uh Whoops. +Good catch. In order to get consistency, + + align:start position:0% +Good catch. In order to get consistency, + + + align:start position:0% +Good catch. In order to get consistency, +we need to keep track of all those hash + + align:start position:0% +we need to keep track of all those hash + + + align:start position:0% +we need to keep track of all those hash +function values. Uh and that's that's + + align:start position:0% +function values. Uh and that's that's + + + align:start position:0% +function values. Uh and that's that's +not good. + + align:start position:0% +not good. + + + align:start position:0% +not good. +You could try to not store them all, you + + align:start position:0% +You could try to not store them all, you + + + align:start position:0% +You could try to not store them all, you +know, use a hash table, but you can't + + align:start position:0% +know, use a hash table, but you can't + + + align:start position:0% +know, use a hash table, but you can't +use a hash table to store a hash + + align:start position:0% +use a hash table to store a hash + + + align:start position:0% +use a hash table to store a hash +function. That would be that would be + + align:start position:0% +function. That would be that would be + + + align:start position:0% +function. That would be that would be +infinite recursion. Um, so but you know, + + align:start position:0% +infinite recursion. Um, so but you know, + + + align:start position:0% +infinite recursion. Um, so but you know, +at least they're out there. So the + + align:start position:0% +at least they're out there. So the + + + align:start position:0% +at least they're out there. So the +challenge is to find an efficient hash + + align:start position:0% +challenge is to find an efficient hash + + + align:start position:0% +challenge is to find an efficient hash +family that doesn't take much space to + + align:start position:0% +family that doesn't take much space to + + + align:start position:0% +family that doesn't take much space to +store and doesn't take much time to + + align:start position:0% +store and doesn't take much time to + + + align:start position:0% +store and doesn't take much time to +compute. Okay, we're allowing + + align:start position:0% +compute. Okay, we're allowing + + + align:start position:0% +compute. Okay, we're allowing +randomness, + + align:start position:0% +randomness, + + + align:start position:0% +randomness, +but + + align:start position:0% + + + + align:start position:0% + +But we don't want too much randomness. + + align:start position:0% +But we don't want too much randomness. + + + align:start position:0% +But we don't want too much randomness. +We can't afford U units of time of + + align:start position:0% +We can't afford U units of time of + + + align:start position:0% +We can't afford U units of time of +randomness. I mean, U could be huge. + + align:start position:0% +randomness. I mean, U could be huge. + + + align:start position:0% +randomness. I mean, U could be huge. +We're only doing N operations probably + + align:start position:0% +We're only doing N operations probably + + + align:start position:0% +We're only doing N operations probably +on this hash table. You could be way + + align:start position:0% +on this hash table. You could be way + + + align:start position:0% +on this hash table. You could be way +bigger than N. We don't want to have to + + align:start position:0% +bigger than N. We don't want to have to + + + align:start position:0% +bigger than N. We don't want to have to +premp compute this giant table and then + + align:start position:0% +premp compute this giant table and then + + + align:start position:0% +premp compute this giant table and then +use it for like five steps. That would + + align:start position:0% +use it for like five steps. That would + + + align:start position:0% +use it for like five steps. That would +be really, really slow, even amortized. + + align:start position:0% +be really, really slow, even amortized. + + + align:start position:0% +be really, really slow, even amortized. +So, um, here's one that I will analyze. + + align:start position:0% +So, um, here's one that I will analyze. + + + align:start position:0% +So, um, here's one that I will analyze. +And there's another one in the textbook + + align:start position:0% +And there's another one in the textbook + + + align:start position:0% +And there's another one in the textbook +which I'll mention. + + align:start position:0% + + + + align:start position:0% + +This one's a little bit simpler to + + align:start position:0% +This one's a little bit simpler to + + + align:start position:0% +This one's a little bit simpler to +analyze. + + align:start position:0% +analyze. + + + align:start position:0% +analyze. +We're going to need a little bit of + + align:start position:0% +We're going to need a little bit of + + + align:start position:0% +We're going to need a little bit of +number theory, just prime numbers. Uh, + + align:start position:0% +number theory, just prime numbers. Uh, + + + align:start position:0% +number theory, just prime numbers. Uh, +and you + + align:start position:0% +and you + + + align:start position:0% +and you +probably heard of the idea of your hasht + + align:start position:0% +probably heard of the idea of your hasht + + + align:start position:0% +probably heard of the idea of your hasht +size being prime here. You'll see why + + align:start position:0% +size being prime here. You'll see why + + + align:start position:0% +size being prime here. You'll see why +that's useful, at least for this family. + + align:start position:0% +that's useful, at least for this family. + + + align:start position:0% +that's useful, at least for this family. +You don't always need primality, but + + align:start position:0% +You don't always need primality, but + + + align:start position:0% +You don't always need primality, but +it's going to make this family work. So + + align:start position:0% +it's going to make this family work. So + + + align:start position:0% +it's going to make this family work. So +I'm going to assume that my table size + + align:start position:0% +I'm going to assume that my table size + + + align:start position:0% +I'm going to assume that my table size +is prime. Now really my table size is + + align:start position:0% +is prime. Now really my table size is + + + align:start position:0% +is prime. Now really my table size is +doubling. Uh so that's a little awkward + + align:start position:0% +doubling. Uh so that's a little awkward + + + align:start position:0% +doubling. Uh so that's a little awkward +but luckily there are algorithms given a + + align:start position:0% +but luckily there are algorithms given a + + + align:start position:0% +but luckily there are algorithms given a +number to find a nearby prime number. + + align:start position:0% +number to find a nearby prime number. + + + align:start position:0% +number to find a nearby prime number. +We're not going to cover that here. Uh + + align:start position:0% +We're not going to cover that here. Uh + + + align:start position:0% +We're not going to cover that here. Uh +but that's an algorithmic number theory + + align:start position:0% +but that's an algorithmic number theory + + + align:start position:0% +but that's an algorithmic number theory +thing. Uh and in poly logarithmic time I + + align:start position:0% +thing. Uh and in poly logarithmic time I + + + align:start position:0% +thing. Uh and in poly logarithmic time I +guess you can uh find a nearby prime + + align:start position:0% +guess you can uh find a nearby prime + + + align:start position:0% +guess you can uh find a nearby prime +number. So you want it to be a power of + + align:start position:0% +number. So you want it to be a power of + + + align:start position:0% +number. So you want it to be a power of +two and you'll just uh look around for + + align:start position:0% +two and you'll just uh look around for + + + align:start position:0% +two and you'll just uh look around for +nearby prime numbers. And then we have a + + align:start position:0% +nearby prime numbers. And then we have a + + + align:start position:0% +nearby prime numbers. And then we have a +prime that's about the same size. So + + align:start position:0% +prime that's about the same size. So + + + align:start position:0% +prime that's about the same size. So +that will work just as well for from a + + align:start position:0% +that will work just as well for from a + + + align:start position:0% +that will work just as well for from a +table doubling perspective. + + align:start position:0% +table doubling perspective. + + + align:start position:0% +table doubling perspective. +Okay. Then furthermore, + + align:start position:0% + + + + align:start position:0% + +uh for convenience, I'm going to assume + + align:start position:0% +uh for convenience, I'm going to assume + + + align:start position:0% +uh for convenience, I'm going to assume +that u is an integer power of m. + + align:start position:0% + + + + align:start position:0% + +I want my universe to be a power of that + + align:start position:0% +I want my universe to be a power of that + + + align:start position:0% +I want my universe to be a power of that +prime. Um, I mean, if it isn't, just + + align:start position:0% +prime. Um, I mean, if it isn't, just + + + align:start position:0% +prime. Um, I mean, if it isn't, just +make you a little bigger. It's okay if + + align:start position:0% +make you a little bigger. It's okay if + + + align:start position:0% +make you a little bigger. It's okay if +you gets bigger as long as it covers all + + align:start position:0% +you gets bigger as long as it covers all + + + align:start position:0% +you gets bigger as long as it covers all +of the same items. Okay. Now, once I + + align:start position:0% +of the same items. Okay. Now, once I + + + align:start position:0% +of the same items. Okay. Now, once I +view my universe as a power of the table + + align:start position:0% +view my universe as a power of the table + + + align:start position:0% +view my universe as a power of the table +size, a natural thing to do is take my + + align:start position:0% +size, a natural thing to do is take my + + + align:start position:0% +size, a natural thing to do is take my +uh universe items to take my input + + align:start position:0% +uh universe items to take my input + + + align:start position:0% +uh universe items to take my input +integers and think of them in base m. + + align:start position:0% +integers and think of them in base m. + + + align:start position:0% +integers and think of them in base m. +So, that's what I'm what I'm going to + + align:start position:0% +So, that's what I'm what I'm going to + + + align:start position:0% +So, that's what I'm what I'm going to +do. I'm going to view a key + + align:start position:0% +do. I'm going to view a key + + + align:start position:0% +do. I'm going to view a key +k in base m. Whenever I have a key, I + + align:start position:0% +k in base m. Whenever I have a key, I + + + align:start position:0% +k in base m. Whenever I have a key, I +can think of it as a vector of sub keys + + align:start position:0% +can think of it as a vector of sub keys + + + align:start position:0% +can think of it as a vector of sub keys +k1 + + align:start position:0% +k1 + + + align:start position:0% +k1 +up to k uh r minus one. + + align:start position:0% +up to k uh r minus one. + + + align:start position:0% +up to k uh r minus one. +There are digits in base m because of + + align:start position:0% +There are digits in base m because of + + + align:start position:0% +There are digits in base m because of +this relation. uh and I don't even care + + align:start position:0% +this relation. uh and I don't even care + + + align:start position:0% +this relation. uh and I don't even care +which is the least significant and which + + align:start position:0% +which is the least significant and which + + + align:start position:0% +which is the least significant and which +is the most significant that won't + + align:start position:0% +is the most significant that won't + + + align:start position:0% +is the most significant that won't +matter. So whatever whichever order you + + align:start position:0% +matter. So whatever whichever order you + + + align:start position:0% +matter. So whatever whichever order you +want to think of it um and each of the + + align:start position:0% +want to think of it um and each of the + + + align:start position:0% +want to think of it um and each of the +kis here I guess is between zero and m + + align:start position:0% +kis here I guess is between zero and m + + + align:start position:0% +kis here I guess is between zero and m +minus one. + + align:start position:0% + + + + align:start position:0% + +So, + + align:start position:0% +So, + + + align:start position:0% +So, +so far so good. + + align:start position:0% + + + + align:start position:0% + +So, uh with this perspective, the basm + + align:start position:0% +So, uh with this perspective, the basm + + + align:start position:0% +So, uh with this perspective, the basm +perspective, I can define a dotproduct + + align:start position:0% +perspective, I can define a dotproduct + + + align:start position:0% +perspective, I can define a dotproduct +hash function + + align:start position:0% +hash function + + + align:start position:0% +hash function +as follows. It's going to be + + align:start position:0% +as follows. It's going to be + + + align:start position:0% +as follows. It's going to be +parameterized by another key. I'll call + + align:start position:0% +parameterized by another key. I'll call + + + align:start position:0% +parameterized by another key. I'll call +it a + + align:start position:0% +it a + + + align:start position:0% +it a +which we can think of again as a vector. + + align:start position:0% + + + + align:start position:0% + +I want to define + + align:start position:0% +I want to define + + + align:start position:0% +I want to define +h sub a of k. So this is parameterized + + align:start position:0% +h sub a of k. So this is parameterized + + + align:start position:0% +h sub a of k. So this is parameterized +by a but it's a function of a given key + + align:start position:0% +by a but it's a function of a given key + + + align:start position:0% +by a but it's a function of a given key +k as the dotproduct of those two vectors + + align:start position:0% +k as the dotproduct of those two vectors + + + align:start position:0% +k as the dotproduct of those two vectors +mod m. + + align:start position:0% + + + + align:start position:0% + +Uh so remember dotproduct is just the + + align:start position:0% +Uh so remember dotproduct is just the + + + align:start position:0% +Uh so remember dotproduct is just the +sum from i = 0 to r minus one of a i * + + align:start position:0% +sum from i = 0 to r minus one of a i * + + + align:start position:0% +sum from i = 0 to r minus one of a i * +ki. + + align:start position:0% +ki. + + + align:start position:0% +ki. +I want to do all of that modulo m. + + align:start position:0% +I want to do all of that modulo m. + + + align:start position:0% +I want to do all of that modulo m. +We'll worry about uh how long this takes + + align:start position:0% +We'll worry about uh how long this takes + + + align:start position:0% +We'll worry about uh how long this takes +to compute in a moment I guess. Um maybe + + align:start position:0% +to compute in a moment I guess. Um maybe + + + align:start position:0% +to compute in a moment I guess. Um maybe +very soon. + + align:start position:0% +very soon. + + + align:start position:0% +very soon. +But the hash family H is just all of + + align:start position:0% +But the hash family H is just all of + + + align:start position:0% +But the hash family H is just all of +these HAS's for all possible choices of + + align:start position:0% +these HAS's for all possible choices of + + + align:start position:0% +these HAS's for all possible choices of +A. + + align:start position:0% + + + + align:start position:0% + +A was a key. So it comes from uh the + + align:start position:0% +A was a key. So it comes from uh the + + + align:start position:0% +A was a key. So it comes from uh the +universe U. + + align:start position:0% + + + + align:start position:0% + +And so what that means is uh to do + + align:start position:0% +And so what that means is uh to do + + + align:start position:0% +And so what that means is uh to do +universal hashing, I want to choose one + + align:start position:0% +universal hashing, I want to choose one + + + align:start position:0% +universal hashing, I want to choose one +of these HA uniformly at random. How do + + align:start position:0% +of these HA uniformly at random. How do + + + align:start position:0% +of these HA uniformly at random. How do +I do that? I just choose a uniformly at + + align:start position:0% +I do that? I just choose a uniformly at + + + align:start position:0% +I do that? I just choose a uniformly at +random. Pretty easy. It's one random + + align:start position:0% +random. Pretty easy. It's one random + + + align:start position:0% +random. Pretty easy. It's one random +value from one random key. So that + + align:start position:0% +value from one random key. So that + + + align:start position:0% +value from one random key. So that +should take constant time and constant + + align:start position:0% +should take constant time and constant + + + align:start position:0% +should take constant time and constant +space. Store one number. + + align:start position:0% +space. Store one number. + + + align:start position:0% +space. Store one number. +Okay. In general, we're in a world + + align:start position:0% +Okay. In general, we're in a world + + + align:start position:0% +Okay. In general, we're in a world +called the word RAM model. + + align:start position:0% +called the word RAM model. + + + align:start position:0% +called the word RAM model. +This is actually uh I guess M stands for + + align:start position:0% +This is actually uh I guess M stands for + + + align:start position:0% +This is actually uh I guess M stands for +model. So I shouldn't write model. Uh + + align:start position:0% +model. So I shouldn't write model. Uh + + + align:start position:0% +model. So I shouldn't write model. Uh +random access machine. uh and which you + + align:start position:0% +random access machine. uh and which you + + + align:start position:0% +random access machine. uh and which you +may have heard of. The word RAM assumes + + align:start position:0% +may have heard of. The word RAM assumes + + + align:start position:0% +may have heard of. The word RAM assumes +that uh we're you know in general we're + + align:start position:0% +that uh we're you know in general we're + + + align:start position:0% +that uh we're you know in general we're +manipulating integers + + align:start position:0% +manipulating integers + + + align:start position:0% +manipulating integers +and the integers fit in a word + + align:start position:0% +and the integers fit in a word + + + align:start position:0% +and the integers fit in a word +and the computational assumption is that + + align:start position:0% +and the computational assumption is that + + + align:start position:0% +and the computational assumption is that +manipulating um a constant number of + + align:start position:0% +manipulating um a constant number of + + + align:start position:0% +manipulating um a constant number of +words and doing essentially any + + align:start position:0% +words and doing essentially any + + + align:start position:0% +words and doing essentially any +operation you want on a constant number + + align:start position:0% +operation you want on a constant number + + + align:start position:0% +operation you want on a constant number +of words uh takes constant time. + + align:start position:0% + + + + align:start position:0% + +And the other part of the word RAM model + + align:start position:0% +And the other part of the word RAM model + + + align:start position:0% +And the other part of the word RAM model +is to assume that the things you care + + align:start position:0% +is to assume that the things you care + + + align:start position:0% +is to assume that the things you care +about fit in a word. + + align:start position:0% + + + + align:start position:0% + +Say uh individual data values. Uh here + + align:start position:0% +Say uh individual data values. Uh here + + + align:start position:0% +Say uh individual data values. Uh here +we're talking about keys + + align:start position:0% + + + + align:start position:0% + +fit in a word. + + align:start position:0% +fit in a word. + + + align:start position:0% +fit in a word. +uh this is what you need to assume say + + align:start position:0% +uh this is what you need to assume say + + + align:start position:0% +uh this is what you need to assume say +in venom debose that you can compute + + align:start position:0% +in venom debose that you can compute + + + align:start position:0% +in venom debose that you can compute +high of x in constant time or low of x + + align:start position:0% +high of x in constant time or low of x + + + align:start position:0% +high of x in constant time or low of x +in constant time here I'm going to use + + align:start position:0% +in constant time here I'm going to use + + + align:start position:0% +in constant time here I'm going to use +it to assume that we can compute h sub a + + align:start position:0% +it to assume that we can compute h sub a + + + align:start position:0% +it to assume that we can compute h sub a +of k in constant time uh in practice + + align:start position:0% +of k in constant time uh in practice + + + align:start position:0% +of k in constant time uh in practice +this would be done by implementing this + + align:start position:0% +this would be done by implementing this + + + align:start position:0% +this would be done by implementing this +computation this dotproduct computation + + align:start position:0% +computation this dotproduct computation + + + align:start position:0% +computation this dotproduct computation +in hardware and the reason you know a + + align:start position:0% +in hardware and the reason you know a + + + align:start position:0% +in hardware and the reason you know a +64-bit edition on a modern processor or + + align:start position:0% +64-bit edition on a modern processor or + + + align:start position:0% +64-bit edition on a modern processor or +32-bit on most phones takes constant + + align:start position:0% +32-bit on most phones takes constant + + + align:start position:0% +32-bit on most phones takes constant +time is because there's hardware that's + + align:start position:0% +time is because there's hardware that's + + + align:start position:0% +time is because there's hardware that's +designed to do that really fast. And in + + align:start position:0% +designed to do that really fast. And in + + + align:start position:0% +designed to do that really fast. And in +general, we're assuming uh that the + + align:start position:0% +general, we're assuming uh that the + + + align:start position:0% +general, we're assuming uh that the +things we care about fit in a single + + align:start position:0% +things we care about fit in a single + + + align:start position:0% +things we care about fit in a single +word. Uh and we're assuming random + + align:start position:0% +word. Uh and we're assuming random + + + align:start position:0% +word. Uh and we're assuming random +access and that we can have arrays. + + align:start position:0% +access and that we can have arrays. + + + align:start position:0% +access and that we can have arrays. +That's what we need in order to store a + + align:start position:0% +That's what we need in order to store a + + + align:start position:0% +That's what we need in order to store a +table. And same thing in Vano Devos, we + + align:start position:0% +table. And same thing in Vano Devos, we + + + align:start position:0% +table. And same thing in Vano Devos, we +needed to assume we had arrays. + + align:start position:0% +needed to assume we had arrays. + + + align:start position:0% +needed to assume we had arrays. +Okay. So, um I think this operation is + + align:start position:0% +Okay. So, um I think this operation is + + + align:start position:0% +Okay. So, um I think this operation is +actually pretty uh exists in Intel + + align:start position:0% +actually pretty uh exists in Intel + + + align:start position:0% +actually pretty uh exists in Intel +architectures in some form. Uh but it's + + align:start position:0% +architectures in some form. Uh but it's + + + align:start position:0% +architectures in some form. Uh but it's +certainly not a normal operation. If + + align:start position:0% +certainly not a normal operation. If + + + align:start position:0% +certainly not a normal operation. If +you're going to do this explicitly, + + align:start position:0% +you're going to do this explicitly, + + + align:start position:0% +you're going to do this explicitly, +adding up and multiplying things, this + + align:start position:0% +adding up and multiplying things, this + + + align:start position:0% +adding up and multiplying things, this +would be r is the log base m of u. So + + align:start position:0% +would be r is the log base m of u. So + + + align:start position:0% +would be r is the log base m of u. So +it's kind of logish time. Um maybe I'll + + align:start position:0% +it's kind of logish time. Um maybe I'll + + + align:start position:0% +it's kind of logish time. Um maybe I'll +mention another hash family + + align:start position:0% +mention another hash family + + + align:start position:0% +mention another hash family +that's more obviously computable, + + align:start position:0% + + + + align:start position:0% + +but I won't analyze here. It's analyzed + + align:start position:0% +but I won't analyze here. It's analyzed + + + align:start position:0% +but I won't analyze here. It's analyzed +in the textbook though, so if you're + + align:start position:0% +in the textbook though, so if you're + + + align:start position:0% +in the textbook though, so if you're +curious, you can check it out there. Um + + align:start position:0% +curious, you can check it out there. Um + + + align:start position:0% +curious, you can check it out there. Um +let's call this + + align:start position:0% +let's call this + + + align:start position:0% +let's call this +Just another + + align:start position:0% + + + + align:start position:0% + +bit weird because it has two mods. You + + align:start position:0% +bit weird because it has two mods. You + + + align:start position:0% +bit weird because it has two mods. You +take mod p and then mod m. But the com + + align:start position:0% +take mod p and then mod m. But the com + + + align:start position:0% +take mod p and then mod m. But the com +the main computation is very simple. You + + align:start position:0% +the main computation is very simple. You + + + align:start position:0% +the main computation is very simple. You +choose a uniformly random value a you + + align:start position:0% +choose a uniformly random value a you + + + align:start position:0% +choose a uniformly random value a you +multiply it by your key in usual binary + + align:start position:0% +multiply it by your key in usual binary + + + align:start position:0% +multiply it by your key in usual binary +multiplication um instead of dotproduct + + align:start position:0% +multiplication um instead of dotproduct + + + align:start position:0% +multiplication um instead of dotproduct +and then you add another uniformly + + align:start position:0% +and then you add another uniformly + + + align:start position:0% +and then you add another uniformly +random key. This is also universal. Uh + + align:start position:0% +random key. This is also universal. Uh + + + align:start position:0% +random key. This is also universal. Uh +so capital H is uh hab for all A and B + + align:start position:0% +so capital H is uh hab for all A and B + + + align:start position:0% +so capital H is uh hab for all A and B +that are keys. + + align:start position:0% + + + + align:start position:0% + +Okay. Okay. So if you're not happy with + + align:start position:0% +Okay. Okay. So if you're not happy with + + + align:start position:0% +Okay. Okay. So if you're not happy with +this assumption that you can compute + + align:start position:0% +this assumption that you can compute + + + align:start position:0% +this assumption that you can compute +this in constant time, you should be + + align:start position:0% +this in constant time, you should be + + + align:start position:0% +this in constant time, you should be +happy with this assumption. If you + + align:start position:0% +happy with this assumption. If you + + + align:start position:0% +happy with this assumption. If you +believe in addition and multiplication + + align:start position:0% +believe in addition and multiplication + + + align:start position:0% +believe in addition and multiplication +and division being constant time, then + + align:start position:0% +and division being constant time, then + + + align:start position:0% +and division being constant time, then +this will be constant time. + + align:start position:0% +this will be constant time. + + + align:start position:0% +this will be constant time. +Okay. Uh so both of these families are + + align:start position:0% +Okay. Uh so both of these families are + + + align:start position:0% +Okay. Uh so both of these families are +universal. I'm going to prove that this + + align:start position:0% +universal. I'm going to prove that this + + + align:start position:0% +universal. I'm going to prove that this +one is universal because a little bit + + align:start position:0% +one is universal because a little bit + + + align:start position:0% +one is universal because a little bit +easier. Yeah. + + align:start position:0% +easier. Yeah. + + + align:start position:0% +easier. Yeah. +Ah okay. Right. What is P? uh P just has + + align:start position:0% +Ah okay. Right. What is P? uh P just has + + + align:start position:0% +Ah okay. Right. What is P? uh P just has +to be bigger than M and it should be + + align:start position:0% +to be bigger than M and it should be + + + align:start position:0% +to be bigger than M and it should be +prime. It's not random. You can just + + align:start position:0% +prime. It's not random. You can just + + + align:start position:0% +prime. It's not random. You can just +choose one prime that's bigger than your + + align:start position:0% +choose one prime that's bigger than your + + + align:start position:0% +choose one prime that's bigger than your +table size and this will work. + + align:start position:0% + + + + align:start position:0% + +Uh I am um + + align:start position:0% +Uh I am um + + + align:start position:0% +Uh I am um +I forget whether you have to assume that + + align:start position:0% +I forget whether you have to assume that + + + align:start position:0% +I forget whether you have to assume that +M is prime. I have to check. + + align:start position:0% +M is prime. I have to check. + + + align:start position:0% +M is prime. I have to check. +I'm guessing not, but don't quote me on + + align:start position:0% +I'm guessing not, but don't quote me on + + + align:start position:0% +I'm guessing not, but don't quote me on +that. Uh that was check the section on + + align:start position:0% +that. Uh that was check the section on + + + align:start position:0% +that. Uh that was check the section on +the textbook. + + align:start position:0% +the textbook. + + + align:start position:0% +the textbook. +Okay, so good, easy to compute. + + align:start position:0% +Okay, so good, easy to compute. + + + align:start position:0% +Okay, so good, easy to compute. +The analysis is simpler, but it's a + + align:start position:0% +The analysis is simpler, but it's a + + + align:start position:0% +The analysis is simpler, but it's a +little bit easier here. Essentially, + + align:start position:0% +little bit easier here. Essentially, + + + align:start position:0% +little bit easier here. Essentially, +this is very much like uh products, but + + align:start position:0% +this is very much like uh products, but + + + align:start position:0% +this is very much like uh products, but +there's no carries here from one uh when + + align:start position:0% +there's no carries here from one uh when + + + align:start position:0% +there's no carries here from one uh when +we do the dot productduct instead of + + align:start position:0% +we do the dot productduct instead of + + + align:start position:0% +we do the dot productduct instead of +just multiplying in base m. If we + + align:start position:0% +just multiplying in base m. If we + + + align:start position:0% +just multiplying in base m. If we +multiply it in base m, that would give + + align:start position:0% +multiply it in base m, that would give + + + align:start position:0% +multiply it in base m, that would give +the same thing as multiplying in base 2. + + align:start position:0% +the same thing as multiplying in base 2. + + + align:start position:0% +the same thing as multiplying in base 2. +uh but we get carries from one msized + + align:start position:0% +uh but we get carries from one msized + + + align:start position:0% +uh but we get carries from one msized +digit to the next one and that's just + + align:start position:0% +digit to the next one and that's just + + + align:start position:0% +digit to the next one and that's just +more annoying to think about. So here + + align:start position:0% +more annoying to think about. So here + + + align:start position:0% +more annoying to think about. So here +we're essentially getting rid of carries + + align:start position:0% +we're essentially getting rid of carries + + + align:start position:0% +we're essentially getting rid of carries +uh so it's in some sense even easier to + + align:start position:0% +uh so it's in some sense even easier to + + + align:start position:0% +uh so it's in some sense even easier to +compute and + + align:start position:0% +compute and + + + align:start position:0% +compute and +in both cases it's universal. + + align:start position:0% + + + + align:start position:0% + +Okay. So + + align:start position:0% + + + + align:start position:0% + +we want to prove this property that if + + align:start position:0% +we want to prove this property that if + + + align:start position:0% +we want to prove this property that if +we choose a random A + + align:start position:0% +we choose a random A + + + align:start position:0% +we choose a random A +then the probability of two keys K and K + + align:start position:0% +then the probability of two keys K and K + + + align:start position:0% +then the probability of two keys K and K +prime which are distinct mapping via H + + align:start position:0% +prime which are distinct mapping via H + + + align:start position:0% +prime which are distinct mapping via H +to the same value is at most 1 over M. + + align:start position:0% +to the same value is at most 1 over M. + + + align:start position:0% +to the same value is at most 1 over M. +So let's prove that. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% + + + + align:start position:0% + +we're given two keys. We have no control + + align:start position:0% +we're given two keys. We have no control + + + align:start position:0% +we're given two keys. We have no control +over them because this has to work for + + align:start position:0% +over them because this has to work for + + + align:start position:0% +over them because this has to work for +all keys that are distinct. + + align:start position:0% + + + + align:start position:0% + +The only thing we know is that they're + + align:start position:0% +The only thing we know is that they're + + + align:start position:0% +The only thing we know is that they're +distinct. Now, if two keys are distinct, + + align:start position:0% +distinct. Now, if two keys are distinct, + + + align:start position:0% +distinct. Now, if two keys are distinct, +then their vectors must be distinct. If + + align:start position:0% +then their vectors must be distinct. If + + + align:start position:0% +then their vectors must be distinct. If +two vectors are distinct, that means at + + align:start position:0% +two vectors are distinct, that means at + + + align:start position:0% +two vectors are distinct, that means at +least one item must be different. Should + + align:start position:0% +least one item must be different. Should + + + align:start position:0% +least one item must be different. Should +sound familiar. Um, + + align:start position:0% + + + + align:start position:0% + +so this was like in the matrix + + align:start position:0% +so this was like in the matrix + + + align:start position:0% +so this was like in the matrix +multiplication verification algorithm + + align:start position:0% +multiplication verification algorithm + + + align:start position:0% +multiplication verification algorithm +that taught taught. Um so + + align:start position:0% +that taught taught. Um so + + + align:start position:0% +that taught taught. Um so +uh + + align:start position:0% + + + + align:start position:0% + +k and k prime differ in some digit. + + align:start position:0% + + + + align:start position:0% + +Let's call that digit + + align:start position:0% +Let's call that digit + + + align:start position:0% +Let's call that digit +d. + + align:start position:0% +d. + + + align:start position:0% +d. +So uh k subd is different from k subd + + align:start position:0% +So uh k subd is different from k subd + + + align:start position:0% +So uh k subd is different from k subd +prime. + + align:start position:0% +prime. + + + align:start position:0% +prime. +Okay. And I want to compute + + align:start position:0% +Okay. And I want to compute + + + align:start position:0% +Okay. And I want to compute +this probability. + + align:start position:0% +this probability. + + + align:start position:0% +this probability. +Rewrite it. + + align:start position:0% + + + + align:start position:0% + +The probability is over a. I'm choosing + + align:start position:0% +The probability is over a. I'm choosing + + + align:start position:0% +The probability is over a. I'm choosing +a uniformly at random. I want to know + + align:start position:0% +a uniformly at random. I want to know + + + align:start position:0% +a uniformly at random. I want to know +the probability that that maps K and K + + align:start position:0% +the probability that that maps K and K + + + align:start position:0% +the probability that that maps K and K +prime to the same slot. + + align:start position:0% +prime to the same slot. + + + align:start position:0% +prime to the same slot. +Okay. So let me just uh write out the + + align:start position:0% +Okay. So let me just uh write out the + + + align:start position:0% +Okay. So let me just uh write out the +definition. + + align:start position:0% +definition. + + + align:start position:0% +definition. +It's probability over a that the + + align:start position:0% +It's probability over a that the + + + align:start position:0% +It's probability over a that the +dotproduct + + align:start position:0% +dotproduct + + + align:start position:0% +dotproduct +of a and k + + align:start position:0% + + + + align:start position:0% + +uh is the same thing as when I do the + + align:start position:0% +uh is the same thing as when I do the + + + align:start position:0% +uh is the same thing as when I do the +dotproduct with k prime. + + align:start position:0% + + + + align:start position:0% + +uh mod m + + align:start position:0% +uh mod m + + + align:start position:0% +uh mod m +these two val sums should come out the + + align:start position:0% +these two val sums should come out the + + + align:start position:0% +these two val sums should come out the +same mod m. + + align:start position:0% +same mod m. + + + align:start position:0% +same mod m. +Okay. Uh so let me move this this part + + align:start position:0% +Okay. Uh so let me move this this part + + + align:start position:0% +Okay. Uh so let me move this this part +over to this side. Uh because in both + + align:start position:0% +over to this side. Uh because in both + + + align:start position:0% +over to this side. Uh because in both +cases we have the same AI. So I can + + align:start position:0% +cases we have the same AI. So I can + + + align:start position:0% +cases we have the same AI. So I can +group terms and say this is the + + align:start position:0% +group terms and say this is the + + + align:start position:0% +group terms and say this is the +probability + + align:start position:0% + + + + align:start position:0% + +Probability sum over i = 0 to r -1 of a + + align:start position:0% +Probability sum over i = 0 to r -1 of a + + + align:start position:0% +Probability sum over i = 0 to r -1 of a +i * k i - k i prime + + align:start position:0% +i * k i - k i prime + + + align:start position:0% +i * k i - k i prime +equals z + + align:start position:0% + + + + align:start position:0% + +modulo m + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +Okay. No pun intended. Uh now + + align:start position:0% +Okay. No pun intended. Uh now + + + align:start position:0% +Okay. No pun intended. Uh now +we care about this digit D. D is a place + + align:start position:0% +we care about this digit D. D is a place + + + align:start position:0% +we care about this digit D. D is a place +where we know that this is non zero. So + + align:start position:0% +where we know that this is non zero. So + + + align:start position:0% +where we know that this is non zero. So +let me separate out the terms for D and + + align:start position:0% +let me separate out the terms for D and + + + align:start position:0% +let me separate out the terms for D and +everything but D. + + align:start position:0% +everything but D. + + + align:start position:0% +everything but D. +So this is the same as probability + + align:start position:0% +So this is the same as probability + + + align:start position:0% +So this is the same as probability +of let's do the d term first. So we have + + align:start position:0% +of let's do the d term first. So we have + + + align:start position:0% +of let's do the d term first. So we have +a d time k d minus k d prime + + align:start position:0% +a d time k d minus k d prime + + + align:start position:0% +a d time k d minus k d prime +that's one term. I'm going to write the + + align:start position:0% +that's one term. I'm going to write the + + + align:start position:0% +that's one term. I'm going to write the +summation of uh i not equal to d + + align:start position:0% +summation of uh i not equal to d + + + align:start position:0% +summation of uh i not equal to d +of + + align:start position:0% +of + + + align:start position:0% +of +a + + align:start position:0% +a + + + align:start position:0% +a +i k i minus k i prime. These ones, some + + align:start position:0% +i k i minus k i prime. These ones, some + + + align:start position:0% +i k i minus k i prime. These ones, some +of them might be zero, some are not. Uh, + + align:start position:0% +of them might be zero, some are not. Uh, + + + align:start position:0% +of them might be zero, some are not. Uh, +we're not going to worry about it. It's + + align:start position:0% +we're not going to worry about it. It's + + + align:start position:0% +we're not going to worry about it. It's +enough to just isolate one term that is + + align:start position:0% +enough to just isolate one term that is + + + align:start position:0% +enough to just isolate one term that is +non zero. + + align:start position:0% + + + + align:start position:0% + +Right? So, this thing we know does not + + align:start position:0% +Right? So, this thing we know does not + + + align:start position:0% +Right? So, this thing we know does not +equal zero. + + align:start position:0% + + + + align:start position:0% + +Cool. Uh, here's where I'm going to use + + align:start position:0% +Cool. Uh, here's where I'm going to use + + + align:start position:0% +Cool. Uh, here's where I'm going to use +a little bit of number theory. I haven't + + align:start position:0% +a little bit of number theory. I haven't + + + align:start position:0% +a little bit of number theory. I haven't +yet used that m is prime. + + align:start position:0% +yet used that m is prime. + + + align:start position:0% +yet used that m is prime. +I required uh m is prime because when + + align:start position:0% +I required uh m is prime because when + + + align:start position:0% +I required uh m is prime because when +you're working modulo m you have + + align:start position:0% +you're working modulo m you have + + + align:start position:0% +you're working modulo m you have +multiplicative inverses + + align:start position:0% +multiplicative inverses + + + align:start position:0% +multiplicative inverses +because this is not zero there's + + align:start position:0% +because this is not zero there's + + + align:start position:0% +because this is not zero there's +something I can multiply on both sides + + align:start position:0% +something I can multiply on both sides + + + align:start position:0% +something I can multiply on both sides +and get um + + align:start position:0% +and get um + + + align:start position:0% +and get um +this to cancel out and become one for + + align:start position:0% +this to cancel out and become one for + + + align:start position:0% +this to cancel out and become one for +every value x there's a value y such + + align:start position:0% +every value x there's a value y such + + + align:start position:0% +every value x there's a value y such +that x * y equals 1 modulo m and you can + + align:start position:0% +that x * y equals 1 modulo m and you can + + + align:start position:0% +that x * y equals 1 modulo m and you can +even compute it in constant time in a + + align:start position:0% +even compute it in constant time in a + + + align:start position:0% +even compute it in constant time in a +reasonable model. + + align:start position:0% +reasonable model. + + + align:start position:0% +reasonable model. +So uh + + align:start position:0% + + + + align:start position:0% + +then I can say I want the probability + + align:start position:0% +then I can say I want the probability + + + align:start position:0% +then I can say I want the probability +that a d + + align:start position:0% + + + + align:start position:0% + +is minus + + align:start position:0% +is minus + + + align:start position:0% +is minus +k d minus k d prime inverse. This is the + + align:start position:0% +k d minus k d prime inverse. This is the + + + align:start position:0% +k d minus k d prime inverse. This is the +multiplicative inverse I was talking + + align:start position:0% +multiplicative inverse I was talking + + + align:start position:0% +multiplicative inverse I was talking +about. And then this sum i not equal to + + align:start position:0% +about. And then this sum i not equal to + + + align:start position:0% +about. And then this sum i not equal to +d of whatever. I don't actually care + + align:start position:0% +d of whatever. I don't actually care + + + align:start position:0% +d of whatever. I don't actually care +what this is too much. + + align:start position:0% + + + + align:start position:0% + +I've already done the equals part. Still + + align:start position:0% +I've already done the equals part. Still + + + align:start position:0% +I've already done the equals part. Still +need to write mod m. + + align:start position:0% +need to write mod m. + + + align:start position:0% +need to write mod m. +Okay. The point is this is all about a + + align:start position:0% +Okay. The point is this is all about a + + + align:start position:0% +Okay. The point is this is all about a +d. + + align:start position:0% +d. + + + align:start position:0% +d. +Okay. And remember we're choosing a + + align:start position:0% +Okay. And remember we're choosing a + + + align:start position:0% +Okay. And remember we're choosing a +uniformly at random. That's the same + + align:start position:0% +uniformly at random. That's the same + + + align:start position:0% +uniformly at random. That's the same +thing as choosing each of the AIS + + align:start position:0% +thing as choosing each of the AIS + + + align:start position:0% +thing as choosing each of the AIS +independently uniformly at random. + + align:start position:0% +independently uniformly at random. + + + align:start position:0% +independently uniformly at random. +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +Is the second line over there isolated? + + align:start position:0% + + + + align:start position:0% + +This + + align:start position:0% +This + + + align:start position:0% +This +which uh this one + + align:start position:0% +which uh this one + + + align:start position:0% +which uh this one +this + + align:start position:0% +this + + + align:start position:0% +this +that the one below that + + align:start position:0% +that the one below that + + + align:start position:0% +that the one below that +yes + + align:start position:0% +yes + + + align:start position:0% +yes +is that is that line isolating D or + + align:start position:0% +is that is that line isolating D or + + + align:start position:0% +is that is that line isolating D or +No, I haven't isolated D yet. This is + + align:start position:0% +No, I haven't isolated D yet. This is + + + align:start position:0% +No, I haven't isolated D yet. This is +all the terms and then to going from + + align:start position:0% +all the terms and then to going from + + + align:start position:0% +all the terms and then to going from +this line to this one I'm just pulling + + align:start position:0% +this line to this one I'm just pulling + + + align:start position:0% +this line to this one I'm just pulling +out the the i equals d term. + + align:start position:0% +out the the i equals d term. + + + align:start position:0% +out the the i equals d term. +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +se that's this term and then separating + + align:start position:0% +se that's this term and then separating + + + align:start position:0% +se that's this term and then separating +out the i not equal to d. + + align:start position:0% +out the i not equal to d. + + + align:start position:0% +out the i not equal to d. +Right. This this sum is just the same as + + align:start position:0% +Right. This this sum is just the same as + + + align:start position:0% +Right. This this sum is just the same as +that sum but I've done the d term + + align:start position:0% +that sum but I've done the d term + + + align:start position:0% +that sum but I've done the d term +explicitly. + + align:start position:0% +explicitly. + + + align:start position:0% +explicitly. +Sure. + + align:start position:0% +Sure. + + + align:start position:0% +Sure. +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +Okay. So, uh I've done all this + + align:start position:0% +Okay. So, uh I've done all this + + + align:start position:0% +Okay. So, uh I've done all this +rewriting because I know that ad is + + align:start position:0% +rewriting because I know that ad is + + + align:start position:0% +rewriting because I know that ad is +chosen uniformly at random. And here we + + align:start position:0% +chosen uniformly at random. And here we + + + align:start position:0% +chosen uniformly at random. And here we +have this thing this monstrosity + + align:start position:0% +have this thing this monstrosity + + + align:start position:0% +have this thing this monstrosity +but it does not depend on a d. In fact + + align:start position:0% +but it does not depend on a d. In fact + + + align:start position:0% +but it does not depend on a d. In fact +it is independent of a d. I'm going to + + align:start position:0% +it is independent of a d. I'm going to + + + align:start position:0% +it is independent of a d. I'm going to +write this as a function of k and k + + align:start position:0% +write this as a function of k and k + + + align:start position:0% +write this as a function of k and k +prime because those are given to us and + + align:start position:0% +prime because those are given to us and + + + align:start position:0% +prime because those are given to us and +fixed. And then it's also a function of + + align:start position:0% +fixed. And then it's also a function of + + + align:start position:0% +fixed. And then it's also a function of +a z and a1 everything except d. Uh so a + + align:start position:0% +a z and a1 everything except d. Uh so a + + + align:start position:0% +a z and a1 everything except d. Uh so a +d minus one a d + one and so on up to a + + align:start position:0% +d minus one a d + one and so on up to a + + + align:start position:0% +d minus one a d + one and so on up to a +r minus one. This is awkward to write + + align:start position:0% +r minus one. This is awkward to write + + + align:start position:0% +r minus one. This is awkward to write +but everything except a d appears here + + align:start position:0% +but everything except a d appears here + + + align:start position:0% +but everything except a d appears here +because we have i not equal to d and and + + align:start position:0% +because we have i not equal to d and and + + + align:start position:0% +because we have i not equal to d and and +these a i's are random variables but + + align:start position:0% +these a i's are random variables but + + + align:start position:0% +these a i's are random variables but +we're assuming that they're all chosen + + align:start position:0% +we're assuming that they're all chosen + + + align:start position:0% +we're assuming that they're all chosen +independently from each other. So I + + align:start position:0% +independently from each other. So I + + + align:start position:0% +independently from each other. So I +don't really care what's going on in + + align:start position:0% +don't really care what's going on in + + + align:start position:0% +don't really care what's going on in +this function. It's something. And if I + + align:start position:0% +this function. It's something. And if I + + + align:start position:0% +this function. It's something. And if I +rewrite this probability, this is + + align:start position:0% +rewrite this probability, this is + + + align:start position:0% +rewrite this probability, this is +probability over the choice of a + + align:start position:0% +probability over the choice of a + + + align:start position:0% +probability over the choice of a +I can separate out the choice of all + + align:start position:0% +I can separate out the choice of all + + + align:start position:0% +I can separate out the choice of all +these things + + align:start position:0% +these things + + + align:start position:0% +these things +from uh the choice of a d. And this is + + align:start position:0% +from uh the choice of a d. And this is + + + align:start position:0% +from uh the choice of a d. And this is +just a useful formula. Uh I'm going to + + align:start position:0% +just a useful formula. Uh I'm going to + + + align:start position:0% +just a useful formula. Uh I'm going to +write a uh not equal to d. All the other + + align:start position:0% +write a uh not equal to d. All the other + + + align:start position:0% +write a uh not equal to d. All the other +um maybe I'll write a sub i not equal to + + align:start position:0% +um maybe I'll write a sub i not equal to + + + align:start position:0% +um maybe I'll write a sub i not equal to +d. all the choices of those guys + + align:start position:0% +d. all the choices of those guys + + + align:start position:0% +d. all the choices of those guys +separately from the probability over + + align:start position:0% +separately from the probability over + + + align:start position:0% +separately from the probability over +choosing a d + + align:start position:0% +choosing a d + + + align:start position:0% +choosing a d +of a d equal to this function. + + align:start position:0% + + + + align:start position:0% + +Okay, if you just think about the + + align:start position:0% +Okay, if you just think about the + + + align:start position:0% +Okay, if you just think about the +definition of expectation, um this is + + align:start position:0% +definition of expectation, um this is + + + align:start position:0% +definition of expectation, um this is +doing the same thing. We're thinking of + + align:start position:0% +doing the same thing. We're thinking of + + + align:start position:0% +doing the same thing. We're thinking of +first choosing the AI's where I is not + + align:start position:0% +first choosing the AI's where I is not + + + align:start position:0% +first choosing the AI's where I is not +equal to D and then we choose A D and + + align:start position:0% +equal to D and then we choose A D and + + + align:start position:0% +equal to D and then we choose A D and +this computation will come out the same + + align:start position:0% +this computation will come out the same + + + align:start position:0% +this computation will come out the same +as that. + + align:start position:0% + + + + align:start position:0% + +Okay. Uh but this is the probability of + + align:start position:0% +Okay. Uh but this is the probability of + + + align:start position:0% +Okay. Uh but this is the probability of +a uniformly random number equaling + + align:start position:0% +a uniformly random number equaling + + + align:start position:0% +a uniformly random number equaling +something. + + align:start position:0% +something. + + + align:start position:0% +something. +So uh we just need to think about uh + + align:start position:0% +So uh we just need to think about uh + + + align:start position:0% +So uh we just need to think about uh +sorry important that would be pretty + + align:start position:0% +sorry important that would be pretty + + + align:start position:0% +sorry important that would be pretty +pretty unlikely that would be one over u + + align:start position:0% +pretty unlikely that would be one over u + + + align:start position:0% +pretty unlikely that would be one over u +but this is all working modulo m okay so + + align:start position:0% +but this is all working modulo m okay so + + + align:start position:0% +but this is all working modulo m okay so +if I just take a uniformly random + + align:start position:0% +if I just take a uniformly random + + + align:start position:0% +if I just take a uniformly random +integer and the chance of it hitting any + + align:start position:0% +integer and the chance of it hitting any + + + align:start position:0% +integer and the chance of it hitting any +particular value mod m is 1 over m + + align:start position:0% + + + + align:start position:0% + +and that's universality. + + align:start position:0% + + + + align:start position:0% + +Yes. So in this case we get exactly 1 + + align:start position:0% +Yes. So in this case we get exactly 1 + + + align:start position:0% +Yes. So in this case we get exactly 1 +over m no less than or equal to + + align:start position:0% +over m no less than or equal to + + + align:start position:0% +over m no less than or equal to +sorry I should have written it's the + + align:start position:0% +sorry I should have written it's the + + + align:start position:0% +sorry I should have written it's the +expectation of 1 over m but that's one + + align:start position:0% +expectation of 1 over m but that's one + + + align:start position:0% +expectation of 1 over m but that's one +over m because one over m has no random + + align:start position:0% +over m because one over m has no random + + + align:start position:0% +over m because one over m has no random +parts in it. + + align:start position:0% +parts in it. + + + align:start position:0% +parts in it. +Yeah. How do we know that this + + align:start position:0% +Yeah. How do we know that this + + + align:start position:0% +Yeah. How do we know that this +expression doesn't have any biases in + + align:start position:0% +expression doesn't have any biases in + + + align:start position:0% +expression doesn't have any biases in +the sense that it doesn't give more more + + align:start position:0% +the sense that it doesn't give more more + + + align:start position:0% +the sense that it doesn't give more more +like if you give it a uniform + + align:start position:0% +like if you give it a uniform + + + align:start position:0% +like if you give it a uniform +distribution of numbers, it doesn't spit + + align:start position:0% +distribution of numbers, it doesn't spit + + + align:start position:0% +distribution of numbers, it doesn't spit +out more numbers than others and that + + align:start position:0% +out more numbers than others and that + + + align:start position:0% +out more numbers than others and that +could potentially + + align:start position:0% +could potentially + + + align:start position:0% +could potentially +Oh, so you're asking how do we know that + + align:start position:0% +Oh, so you're asking how do we know that + + + align:start position:0% +Oh, so you're asking how do we know that +this hash family doesn't prefer some + + align:start position:0% +this hash family doesn't prefer some + + + align:start position:0% +this hash family doesn't prefer some +slots over others? I guess + + align:start position:0% +slots over others? I guess + + + align:start position:0% +slots over others? I guess +or like after after the equal sign like + + align:start position:0% +or like after after the equal sign like + + + align:start position:0% +or like after after the equal sign like +the the in this middle line in the + + align:start position:0% +the the in this middle line in the + + + align:start position:0% +the the in this middle line in the +middle. + + align:start position:0% +middle. + + + align:start position:0% +middle. +This one. + + align:start position:0% +This one. + + + align:start position:0% +This one. +Oh, this one. + + align:start position:0% +Oh, this one. + + + align:start position:0% +Oh, this one. +Middle board here. + + align:start position:0% +Middle board here. + + + align:start position:0% +Middle board here. +Yes. + + align:start position:0% +Yes. + + + align:start position:0% +Yes. +So, how do we know that random + + align:start position:0% +So, how do we know that random + + + align:start position:0% +So, how do we know that random +variables? It won't it won't prefer + + align:start position:0% +variables? It won't it won't prefer + + + align:start position:0% +variables? It won't it won't prefer +certain numbers over others. + + align:start position:0% +certain numbers over others. + + + align:start position:0% +certain numbers over others. +So, this function may prefer some + + align:start position:0% +So, this function may prefer some + + + align:start position:0% +So, this function may prefer some +numbers over others, but it doesn't + + align:start position:0% +numbers over others, but it doesn't + + + align:start position:0% +numbers over others, but it doesn't +matter. All we need is that this + + align:start position:0% +matter. All we need is that this + + + align:start position:0% +matter. All we need is that this +function is independent of our choice of + + align:start position:0% +function is independent of our choice of + + + align:start position:0% +function is independent of our choice of +ad. So you can think of this function. + + align:start position:0% +ad. So you can think of this function. + + + align:start position:0% +ad. So you can think of this function. +You choose all of these random actually + + align:start position:0% +You choose all of these random actually + + + align:start position:0% +You choose all of these random actually +K and K prime are not random but you + + align:start position:0% +K and K prime are not random but you + + + align:start position:0% +K and K prime are not random but you +choose all these random numbers. Then + + align:start position:0% +choose all these random numbers. Then + + + align:start position:0% +choose all these random numbers. Then +you evaluate your F. Maybe it always + + align:start position:0% +you evaluate your F. Maybe it always + + + align:start position:0% +you evaluate your F. Maybe it always +comes out to five. Who knows? It could + + align:start position:0% +comes out to five. Who knows? It could + + + align:start position:0% +comes out to five. Who knows? It could +be super biased. But then you choose AD + + align:start position:0% +be super biased. But then you choose AD + + + align:start position:0% +be super biased. But then you choose AD +uniformly at random. So you're I mean + + align:start position:0% +uniformly at random. So you're I mean + + + align:start position:0% +uniformly at random. So you're I mean +the chance of AD equaling five is the + + align:start position:0% +the chance of AD equaling five is the + + + align:start position:0% +the chance of AD equaling five is the +same of the chance of AD equaling three. + + align:start position:0% +same of the chance of AD equaling three. + + + align:start position:0% +same of the chance of AD equaling three. +Uh so in all cases you get the + + align:start position:0% +Uh so in all cases you get the + + + align:start position:0% +Uh so in all cases you get the +probability is 1 over M. What we need is + + align:start position:0% +probability is 1 over M. What we need is + + + align:start position:0% +probability is 1 over M. What we need is +independence. We need that the A D is + + align:start position:0% +independence. We need that the A D is + + + align:start position:0% +independence. We need that the A D is +chosen independently from the other AIS. + + align:start position:0% +chosen independently from the other AIS. + + + align:start position:0% +chosen independently from the other AIS. +But we don't need to know anything about + + align:start position:0% +But we don't need to know anything about + + + align:start position:0% +But we don't need to know anything about +f other than it doesn't depend on AD. + + align:start position:0% +f other than it doesn't depend on AD. + + + align:start position:0% +f other than it doesn't depend on AD. +Yeah. So, and we made it not depend on + + align:start position:0% +Yeah. So, and we made it not depend on + + + align:start position:0% +Yeah. So, and we made it not depend on +AD because I I isolated AD by pulling it + + align:start position:0% +AD because I I isolated AD by pulling it + + + align:start position:0% +AD because I I isolated AD by pulling it +out of that summation. So, we know + + align:start position:0% +out of that summation. So, we know + + + align:start position:0% +out of that summation. So, we know +there's no ADS over here. Good question. + + align:start position:0% +there's no ADS over here. Good question. + + + align:start position:0% +there's no ADS over here. Good question. +Get a bonus Frisbee for question. + + align:start position:0% +Get a bonus Frisbee for question. + + + align:start position:0% +Get a bonus Frisbee for question. +Uh, all right. That ends universal + + align:start position:0% +Uh, all right. That ends universal + + + align:start position:0% +Uh, all right. That ends universal +hashing. + + align:start position:0% +hashing. + + + align:start position:0% +hashing. +Any more questions? So at this point we + + align:start position:0% +Any more questions? So at this point we + + + align:start position:0% +Any more questions? So at this point we +have at least one universal hash family. + + align:start position:0% +have at least one universal hash family. + + + align:start position:0% +have at least one universal hash family. +So we're just choosing in this case a + + align:start position:0% +So we're just choosing in this case a + + + align:start position:0% +So we're just choosing in this case a +uniformly at random. In the other method + + align:start position:0% +uniformly at random. In the other method + + + align:start position:0% +uniformly at random. In the other method +we choose a and b uniformly at random. + + align:start position:0% +we choose a and b uniformly at random. + + + align:start position:0% +we choose a and b uniformly at random. +And then uh then we build our hash table + + align:start position:0% +And then uh then we build our hash table + + + align:start position:0% +And then uh then we build our hash table +and the the hash function depends on m. + + align:start position:0% +and the the hash function depends on m. + + + align:start position:0% +and the the hash function depends on m. +So also every time we double our table + + align:start position:0% +So also every time we double our table + + + align:start position:0% +So also every time we double our table +size we're going to have to choose a new + + align:start position:0% +size we're going to have to choose a new + + + align:start position:0% +size we're going to have to choose a new +hash function for the new value of m. Um + + align:start position:0% +hash function for the new value of m. Um + + + align:start position:0% +hash function for the new value of m. Um +and that's about it. So this will give + + align:start position:0% +and that's about it. So this will give + + + align:start position:0% +and that's about it. So this will give +us constant expected time uh or in + + align:start position:0% +us constant expected time uh or in + + + align:start position:0% +us constant expected time uh or in +general on one plus alpha if you're not + + align:start position:0% +general on one plus alpha if you're not + + + align:start position:0% +general on one plus alpha if you're not +doing table doubling uh for insert + + align:start position:0% +doing table doubling uh for insert + + + align:start position:0% +doing table doubling uh for insert +delete and exact search + + align:start position:0% +delete and exact search + + + align:start position:0% +delete and exact search +just building on the hashing with + + align:start position:0% +just building on the hashing with + + + align:start position:0% +just building on the hashing with +chaining + + align:start position:0% +chaining + + + align:start position:0% +chaining +and so this is a good method question + + align:start position:0% + + + + align:start position:0% + +uh yeah well so um I I wanted to isolate + + align:start position:0% +uh yeah well so um I I wanted to isolate + + + align:start position:0% +uh yeah well so um I I wanted to isolate +it is the overall probability ability of + + align:start position:0% +it is the overall probability ability of + + + align:start position:0% +it is the overall probability ability of +this happening. I rewrote it this way + + align:start position:0% +this happening. I rewrote it this way + + + align:start position:0% +this happening. I rewrote it this way +because I wanted to think about first + + align:start position:0% +because I wanted to think about first + + + align:start position:0% +because I wanted to think about first +choosing the AIS where I does not equal + + align:start position:0% +choosing the AIS where I does not equal + + + align:start position:0% +choosing the AIS where I does not equal +D and then choosing A. So this + + align:start position:0% +D and then choosing A. So this + + + align:start position:0% +D and then choosing A. So this +probability was supposed to be only over + + align:start position:0% +probability was supposed to be only over + + + align:start position:0% +probability was supposed to be only over +the choice of AD. And you have to do + + align:start position:0% +the choice of AD. And you have to do + + + align:start position:0% +the choice of AD. And you have to do +something with the other AIS because + + align:start position:0% +something with the other AIS because + + + align:start position:0% +something with the other AIS because +they're random. You can't just say + + align:start position:0% +they're random. You can't just say + + + align:start position:0% +they're random. You can't just say +what's the probability of AD equaling a + + align:start position:0% +what's the probability of AD equaling a + + + align:start position:0% +what's the probability of AD equaling a +random variable. That's a little + + align:start position:0% +random variable. That's a little + + + align:start position:0% +random variable. That's a little +sketchy. I wanted to have no random + + align:start position:0% +sketchy. I wanted to have no random + + + align:start position:0% +sketchy. I wanted to have no random +variables overall. So I have to kind of + + align:start position:0% +variables overall. So I have to kind of + + + align:start position:0% +variables overall. So I have to kind of +bind those variables with something. And + + align:start position:0% +bind those variables with something. And + + + align:start position:0% +bind those variables with something. And +I just want to add them. I just want to + + align:start position:0% +I just want to add them. I just want to + + + align:start position:0% +I just want to add them. I just want to +see what the this doesn't really affect + + align:start position:0% +see what the this doesn't really affect + + + align:start position:0% +see what the this doesn't really affect +very much but to make this algebraically + + align:start position:0% +very much but to make this algebraically + + + align:start position:0% +very much but to make this algebraically +correct I need to say what the AI's I + + align:start position:0% +correct I need to say what the AI's I + + + align:start position:0% +correct I need to say what the AI's I +not equal to D are doing + + align:start position:0% +not equal to D are doing + + + align:start position:0% +not equal to D are doing +other questions + + align:start position:0% +other questions + + + align:start position:0% +other questions +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +I'm a bit confused about your definition + + align:start position:0% + + + + align:start position:0% + +uh yeah sorry this is a funny notion of + + align:start position:0% +uh yeah sorry this is a funny notion of + + + align:start position:0% +uh yeah sorry this is a funny notion of +colliding I just mean I want to count + + align:start position:0% +colliding I just mean I want to count + + + align:start position:0% +colliding I just mean I want to count +the number of keys that hash to the same + + align:start position:0% +the number of keys that hash to the same + + + align:start position:0% +the number of keys that hash to the same +slot as KI. + + align:start position:0% +slot as KI. + + + align:start position:0% +slot as KI. +So it's not necessarily like a + + align:start position:0% +So it's not necessarily like a + + + align:start position:0% +So it's not necessarily like a +collision. + + align:start position:0% +collision. + + + align:start position:0% +collision. +You may not call it a collision when it + + align:start position:0% +You may not call it a collision when it + + + align:start position:0% +You may not call it a collision when it +collides with itself. Yeah. Uh whatever + + align:start position:0% +collides with itself. Yeah. Uh whatever + + + align:start position:0% +collides with itself. Yeah. Uh whatever +you want to call it, + + align:start position:0% +you want to call it, + + + align:start position:0% +you want to call it, +but I just mean hashing to the same slot + + align:start position:0% +but I just mean hashing to the same slot + + + align:start position:0% +but I just mean hashing to the same slot +as KI. Yeah. Just because I want to + + align:start position:0% +as KI. Yeah. Just because I want to + + + align:start position:0% +as KI. Yeah. Just because I want to +count the total length of the chain. I + + align:start position:0% +count the total length of the chain. I + + + align:start position:0% +count the total length of the chain. I +don't want to count number of collisions + + align:start position:0% +don't want to count number of collisions + + + align:start position:0% +don't want to count number of collisions +in the chain. Yeah, sorry. Probably poor + + align:start position:0% +in the chain. Yeah, sorry. Probably poor + + + align:start position:0% +in the chain. Yeah, sorry. Probably poor +choice of word. + + align:start position:0% + + + + align:start position:0% + +Uh, we're hashing + + align:start position:0% +Uh, we're hashing + + + align:start position:0% +Uh, we're hashing +because we're taking our key, we're + + align:start position:0% +because we're taking our key, we're + + + align:start position:0% +because we're taking our key, we're +cutting it up into little bits, and then + + align:start position:0% +cutting it up into little bits, and then + + + align:start position:0% +cutting it up into little bits, and then +we're mixing them up just like a good + + align:start position:0% +we're mixing them up just like a good + + + align:start position:0% +we're mixing them up just like a good +corn beef hash or something. + + align:start position:0% +corn beef hash or something. + + + align:start position:0% +corn beef hash or something. +All right, let's move on to perfect + + align:start position:0% +All right, let's move on to perfect + + + align:start position:0% +All right, let's move on to perfect +hashing. This is uh more exciting, I + + align:start position:0% +hashing. This is uh more exciting, I + + + align:start position:0% +hashing. This is uh more exciting, I +would say. Even cooler. This was uh cool + + align:start position:0% +would say. Even cooler. This was uh cool + + + align:start position:0% +would say. Even cooler. This was uh cool +from a probability perspective. + + align:start position:0% +from a probability perspective. + + + align:start position:0% +from a probability perspective. +Depending on your notion of cool, uh, + + align:start position:0% +Depending on your notion of cool, uh, + + + align:start position:0% +Depending on your notion of cool, uh, +this method will be cool from a data + + align:start position:0% +this method will be cool from a data + + + align:start position:0% +this method will be cool from a data +structures perspective and a probability + + align:start position:0% +structures perspective and a probability + + + align:start position:0% +structures perspective and a probability +perspective. + + align:start position:0% + + + + align:start position:0% + +But it uh so far our data structures are + + align:start position:0% +But it uh so far our data structures are + + + align:start position:0% +But it uh so far our data structures are +what we know from 006. Now we're going + + align:start position:0% +what we know from 006. Now we're going + + + align:start position:0% +what we know from 006. Now we're going +to go uh up a level literally we're + + align:start position:0% +to go uh up a level literally we're + + + align:start position:0% +to go uh up a level literally we're +going to have two levels. Um so here + + align:start position:0% +going to have two levels. Um so here + + + align:start position:0% +going to have two levels. Um so here +we're solving you can actually make this + + align:start position:0% +we're solving you can actually make this + + + align:start position:0% +we're solving you can actually make this +data structure dynamic but we're going + + align:start position:0% +data structure dynamic but we're going + + + align:start position:0% +data structure dynamic but we're going +to solve the static dictionary problem + + align:start position:0% + + + + align:start position:0% + +which is uh when you have no inserts and + + align:start position:0% +which is uh when you have no inserts and + + + align:start position:0% +which is uh when you have no inserts and +deletes you're given the keys up front + + align:start position:0% + + + + align:start position:0% + +you're given n keys you want to build a + + align:start position:0% +you're given n keys you want to build a + + + align:start position:0% +you're given n keys you want to build a +table + + align:start position:0% +table + + + align:start position:0% +table +that supports search + + align:start position:0% + + + + align:start position:0% + +and that's it. You want search uh to be + + align:start position:0% +and that's it. You want search uh to be + + + align:start position:0% +and that's it. You want search uh to be +constant time and perfect hashing + + align:start position:0% + + + + align:start position:0% + +also known as FKS hashing because it + + align:start position:0% +also known as FKS hashing because it + + + align:start position:0% +also known as FKS hashing because it +invented by Fredman Klo and Seamaretti + + align:start position:0% +invented by Fredman Klo and Seamaretti + + + align:start position:0% +invented by Fredman Klo and Seamaretti +1984. + + align:start position:0% +1984. + + + align:start position:0% +1984. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +what we will achieve is + + align:start position:0% +what we will achieve is + + + align:start position:0% +what we will achieve is +constant time worst case + + align:start position:0% + + + + align:start position:0% + +for search. + + align:start position:0% + + + + align:start position:0% + +So that's a little better because here + + align:start position:0% +So that's a little better because here + + + align:start position:0% +So that's a little better because here +we're just doing constant expected time + + align:start position:0% +we're just doing constant expected time + + + align:start position:0% +we're just doing constant expected time +for search, but it's worse and that we + + align:start position:0% +for search, but it's worse and that we + + + align:start position:0% +for search, but it's worse and that we +have to know the keys up in advance. + + align:start position:0% +have to know the keys up in advance. + + + align:start position:0% +have to know the keys up in advance. +Um, we're going to take linear space + + align:start position:0% +Um, we're going to take linear space + + + align:start position:0% +Um, we're going to take linear space +in the worst case. + + align:start position:0% + + + + align:start position:0% + +Uh, and then the the remaining question + + align:start position:0% +Uh, and then the the remaining question + + + align:start position:0% +Uh, and then the the remaining question +is how long does it take you to build + + align:start position:0% +is how long does it take you to build + + + align:start position:0% +is how long does it take you to build +this data structure? And for now, I'll + + align:start position:0% +this data structure? And for now, I'll + + + align:start position:0% +this data structure? And for now, I'll +just say it's polomial time. It's + + align:start position:0% +just say it's polomial time. It's + + + align:start position:0% +just say it's polomial time. It's +actually going to be nearly linear. + + align:start position:0% + + + + align:start position:0% + +Uh and this is also an expected bound uh + + align:start position:0% +Uh and this is also an expected bound uh + + + align:start position:0% +Uh and this is also an expected bound uh +actually + + align:start position:0% +actually + + + align:start position:0% +actually +with high probability can be a little + + align:start position:0% +with high probability can be a little + + + align:start position:0% +with high probability can be a little +more strong here. + + align:start position:0% +more strong here. + + + align:start position:0% +more strong here. +So it's going to take us a little bit of + + align:start position:0% +So it's going to take us a little bit of + + + align:start position:0% +So it's going to take us a little bit of +time to build this structure but once + + align:start position:0% +time to build this structure but once + + + align:start position:0% +time to build this structure but once +you have it you have the the perfect + + align:start position:0% +you have it you have the the perfect + + + align:start position:0% +you have it you have the the perfect +scenario. There's going to be in some + + align:start position:0% +scenario. There's going to be in some + + + align:start position:0% +scenario. There's going to be in some +sense no collisions in our hash table. + + align:start position:0% +sense no collisions in our hash table. + + + align:start position:0% +sense no collisions in our hash table. +So it be constant times for search and + + align:start position:0% +So it be constant times for search and + + + align:start position:0% +So it be constant times for search and +linear space. So that part's great. The + + align:start position:0% +linear space. So that part's great. The + + + align:start position:0% +linear space. So that part's great. The +only catch is it's uh static, + + align:start position:0% +only catch is it's uh static, + + + align:start position:0% +only catch is it's uh static, +but + + align:start position:0% +but + + + align:start position:0% +but +beggars can't be choosers, I guess. + + align:start position:0% +beggars can't be choosers, I guess. + + + align:start position:0% +beggars can't be choosers, I guess. +All right. + + align:start position:0% + + + + align:start position:0% + +I'm not sure who's begging in that + + align:start position:0% +I'm not sure who's begging in that + + + align:start position:0% +I'm not sure who's begging in that +analogy, but + + align:start position:0% + + + + align:start position:0% + +the keys who want to be stored. I don't + + align:start position:0% +the keys who want to be stored. I don't + + + align:start position:0% +the keys who want to be stored. I don't +know. Um, all right. So big idea for uh + + align:start position:0% +know. Um, all right. So big idea for uh + + + align:start position:0% +know. Um, all right. So big idea for uh +perfect hashing is to use two levels. + + align:start position:0% + + + + align:start position:0% + +So uh let me draw a picture. We have our + + align:start position:0% +So uh let me draw a picture. We have our + + + align:start position:0% +So uh let me draw a picture. We have our +universe + + align:start position:0% +universe + + + align:start position:0% +universe +and we're mapping that via hash function + + align:start position:0% +and we're mapping that via hash function + + + align:start position:0% +and we're mapping that via hash function +h1 into a table. Look familiar? Exactly + + align:start position:0% +h1 into a table. Look familiar? Exactly + + + align:start position:0% +h1 into a table. Look familiar? Exactly +the diagram I drew before. Okay. Okay, + + align:start position:0% +the diagram I drew before. Okay. Okay, + + + align:start position:0% +the diagram I drew before. Okay. Okay, +it's going to have some table size m + + align:start position:0% +it's going to have some table size m + + + align:start position:0% +it's going to have some table size m +and we're going to assume that m or + + align:start position:0% +and we're going to assume that m or + + + align:start position:0% +and we're going to assume that m or +we're going to set m to be within a + + align:start position:0% +we're going to set m to be within a + + + align:start position:0% +we're going to set m to be within a +constant factor of n. + + align:start position:0% +constant factor of n. + + + align:start position:0% +constant factor of n. +So right now it looks exactly like + + align:start position:0% +So right now it looks exactly like + + + align:start position:0% +So right now it looks exactly like +regular and this is going to be a + + align:start position:0% +regular and this is going to be a + + + align:start position:0% +regular and this is going to be a +universal h1 is chosen from a universal + + align:start position:0% +universal h1 is chosen from a universal + + + align:start position:0% +universal h1 is chosen from a universal +hash family. So uh you know universal + + align:start position:0% +hash family. So uh you know universal + + + align:start position:0% +hash family. So uh you know universal +hashing applies. The trouble is we're + + align:start position:0% +hashing applies. The trouble is we're + + + align:start position:0% +hashing applies. The trouble is we're +going to get some lists here and we + + align:start position:0% +going to get some lists here and we + + + align:start position:0% +going to get some lists here and we +don't we don't want to store the the uh + + align:start position:0% +don't we don't want to store the the uh + + + align:start position:0% +don't we don't want to store the the uh +set of colliding elements the set of + + align:start position:0% +set of colliding elements the set of + + + align:start position:0% +set of colliding elements the set of +elements to hash to that place with a + + align:start position:0% +elements to hash to that place with a + + + align:start position:0% +elements to hash to that place with a +linked list because link lists are slow. + + align:start position:0% +linked list because link lists are slow. + + + align:start position:0% +linked list because link lists are slow. +Instead we're going to store them using + + align:start position:0% +Instead we're going to store them using + + + align:start position:0% +Instead we're going to store them using +a hash table. + + align:start position:0% +a hash table. + + + align:start position:0% +a hash table. +Sounds crazy + + align:start position:0% +Sounds crazy + + + align:start position:0% +Sounds crazy +but uh + + align:start position:0% +but uh + + + align:start position:0% +but uh +we're going to have so this is position + + align:start position:0% +we're going to have so this is position + + + align:start position:0% +we're going to have so this is position +one. This is going to be H2 comma one. + + align:start position:0% +one. This is going to be H2 comma one. + + + align:start position:0% +one. This is going to be H2 comma one. +It's going to be another hash function + + align:start position:0% +It's going to be another hash function + + + align:start position:0% +It's going to be another hash function +H2 comma 0 that maps to some other hash + + align:start position:0% +H2 comma 0 that maps to some other hash + + + align:start position:0% +H2 comma 0 that maps to some other hash +table. These hash tables are going to be + + align:start position:0% +table. These hash tables are going to be + + + align:start position:0% +table. These hash tables are going to be +of varying sizes. Some of them will be + + align:start position:0% +of varying sizes. Some of them will be + + + align:start position:0% +of varying sizes. Some of them will be +of size zero because nothing hashes + + align:start position:0% +of size zero because nothing hashes + + + align:start position:0% +of size zero because nothing hashes +there. Um but in general each of these + + align:start position:0% +there. Um but in general each of these + + + align:start position:0% +there. Um but in general each of these +slots is going to map instead of to a + + align:start position:0% +slots is going to map instead of to a + + + align:start position:0% +slots is going to map instead of to a +linked list to a hash table. Okay. So + + align:start position:0% +linked list to a hash table. Okay. So + + + align:start position:0% +linked list to a hash table. Okay. So +this would be h 2, m minus one. + + align:start position:0% +this would be h 2, m minus one. + + + align:start position:0% +this would be h 2, m minus one. +I'm going to guarantee in the second + + align:start position:0% +I'm going to guarantee in the second + + + align:start position:0% +I'm going to guarantee in the second +level of hashing there are zero + + align:start position:0% +level of hashing there are zero + + + align:start position:0% +level of hashing there are zero +collisions. + + align:start position:0% + + + + align:start position:0% + +Uh let that sink in a little bit. Um let + + align:start position:0% +Uh let that sink in a little bit. Um let + + + align:start position:0% +Uh let that sink in a little bit. Um let +me write down a little more carefully + + align:start position:0% +me write down a little more carefully + + + align:start position:0% +me write down a little more carefully +what I'm doing. + + align:start position:0% + + + + align:start position:0% + +So H1 is picked from a universal hash + + align:start position:0% +So H1 is picked from a universal hash + + + align:start position:0% +So H1 is picked from a universal hash +family + + align:start position:0% + + + + align:start position:0% + +uh where m is theta theta n. + + align:start position:0% +uh where m is theta theta n. + + + align:start position:0% +uh where m is theta theta n. +Uh I want to put a theta. I mean, I + + align:start position:0% +Uh I want to put a theta. I mean, I + + + align:start position:0% +Uh I want to put a theta. I mean, I +could say M equals N, but sometimes we + + align:start position:0% +could say M equals N, but sometimes we + + + align:start position:0% +could say M equals N, but sometimes we +require M to be a prime. So, I'm going + + align:start position:0% +require M to be a prime. So, I'm going + + + align:start position:0% +require M to be a prime. So, I'm going +to give you some slop in how you choose + + align:start position:0% +to give you some slop in how you choose + + + align:start position:0% +to give you some slop in how you choose +M. So, it can be prime or whatever you + + align:start position:0% +M. So, it can be prime or whatever you + + + align:start position:0% +M. So, it can be prime or whatever you +want. + + align:start position:0% +want. + + + align:start position:0% +want. +Okay. And then at the first level, we're + + align:start position:0% +Okay. And then at the first level, we're + + + align:start position:0% +Okay. And then at the first level, we're +basically doing hashing with chaining. + + align:start position:0% +basically doing hashing with chaining. + + + align:start position:0% +basically doing hashing with chaining. +And now, uh, + + align:start position:0% + + + + align:start position:0% + +I want to look at each slot in that hash + + align:start position:0% +I want to look at each slot in that hash + + + align:start position:0% +I want to look at each slot in that hash +table. So between zero and n minus one + + align:start position:0% + + + + align:start position:0% + +I'm going to let l j be the number of + + align:start position:0% +I'm going to let l j be the number of + + + align:start position:0% +I'm going to let l j be the number of +keys that hash that's the length of the + + align:start position:0% +keys that hash that's the length of the + + + align:start position:0% +keys that hash that's the length of the +list that would go there. It's going to + + align:start position:0% +list that would go there. It's going to + + + align:start position:0% +list that would go there. It's going to +be the number of keys among just the n + + align:start position:0% +be the number of keys among just the n + + + align:start position:0% +be the number of keys among just the n +keys. + + align:start position:0% +keys. + + + align:start position:0% +keys. +Uh, + + align:start position:0% + + + + align:start position:0% + +number of keys hashing to slot J. + + align:start position:0% +number of keys hashing to slot J. + + + align:start position:0% +number of keys hashing to slot J. +So now the big question is if I have LJ + + align:start position:0% +So now the big question is if I have LJ + + + align:start position:0% +So now the big question is if I have LJ +keys here, how big do I make that table? + + align:start position:0% +keys here, how big do I make that table? + + + align:start position:0% +keys here, how big do I make that table? +You might say, well, I make it theta LJ. + + align:start position:0% +You might say, well, I make it theta LJ. + + + align:start position:0% +You might say, well, I make it theta LJ. +That's what I always do. But that's not + + align:start position:0% +That's what I always do. But that's not + + + align:start position:0% +That's what I always do. But that's not +what I'm going to do. That wouldn't + + align:start position:0% +what I'm going to do. That wouldn't + + + align:start position:0% +what I'm going to do. That wouldn't +help. We'd get exactly I think the same + + align:start position:0% +help. We'd get exactly I think the same + + + align:start position:0% +help. We'd get exactly I think the same +number of collisions if we did that more + + align:start position:0% +number of collisions if we did that more + + + align:start position:0% +number of collisions if we did that more +or less in expectation. So we're going + + align:start position:0% +or less in expectation. So we're going + + + align:start position:0% +or less in expectation. So we're going +to do something else. + + align:start position:0% +to do something else. + + + align:start position:0% +to do something else. +We're going to pick a universal hash + + align:start position:0% +We're going to pick a universal hash + + + align:start position:0% +We're going to pick a universal hash +pick a hash function from a universal + + align:start position:0% +pick a hash function from a universal + + + align:start position:0% +pick a hash function from a universal +family H2, J. + + align:start position:0% +family H2, J. + + + align:start position:0% +family H2, J. +It again maps the same universe. + + align:start position:0% + + + + align:start position:0% + +The key thing is the size of the hash + + align:start position:0% +The key thing is the size of the hash + + + align:start position:0% +The key thing is the size of the hash +table I'm going to choose which is LJ + + align:start position:0% +table I'm going to choose which is LJ + + + align:start position:0% +table I'm going to choose which is LJ +squared. + + align:start position:0% + + + + align:start position:0% + +So uh if there are you know three + + align:start position:0% +So uh if there are you know three + + + align:start position:0% +So uh if there are you know three +elements that happen to hash to this + + align:start position:0% +elements that happen to hash to this + + + align:start position:0% +elements that happen to hash to this +slot this table will have size nine. + + align:start position:0% +slot this table will have size nine. + + + align:start position:0% +slot this table will have size nine. +So it's mostly empty only square root + + align:start position:0% +So it's mostly empty only square root + + + align:start position:0% +So it's mostly empty only square root +fraction if that's a word uh if that's a + + align:start position:0% +fraction if that's a word uh if that's a + + + align:start position:0% +fraction if that's a word uh if that's a +phrase will be full most of it's empty y + + align:start position:0% +phrase will be full most of it's empty y + + + align:start position:0% +phrase will be full most of it's empty y +squared + + align:start position:0% +squared + + + align:start position:0% +squared +any ideas + + align:start position:0% +any ideas + + + align:start position:0% +any ideas +I claim this will guarantee zero + + align:start position:0% +I claim this will guarantee zero + + + align:start position:0% +I claim this will guarantee zero +collisions with decent chance. Yeah. + + align:start position:0% +collisions with decent chance. Yeah. + + + align:start position:0% +collisions with decent chance. Yeah. +With one probability + + align:start position:0% +With one probability + + + align:start position:0% +With one probability +with one half probability I'm going to + + align:start position:0% +with one half probability I'm going to + + + align:start position:0% +with one half probability I'm going to +end up with no collisions. Why? What's + + align:start position:0% +end up with no collisions. Why? What's + + + align:start position:0% +end up with no collisions. Why? What's +it called? + + align:start position:0% + + + + align:start position:0% + +Markov inequality would prove it. Uh but + + align:start position:0% +Markov inequality would prove it. Uh but + + + align:start position:0% +Markov inequality would prove it. Uh but +it's uh more commonly known as the whoa + + align:start position:0% +it's uh more commonly known as the whoa + + + align:start position:0% +it's uh more commonly known as the whoa +as the birthday paradox. Yeah. So the + + align:start position:0% +as the birthday paradox. Yeah. So the + + + align:start position:0% +as the birthday paradox. Yeah. So the +the whole name of the game here is the + + align:start position:0% +the whole name of the game here is the + + + align:start position:0% +the whole name of the game here is the +birthday paradox. If I have uh how's it + + align:start position:0% +birthday paradox. If I have uh how's it + + + align:start position:0% +birthday paradox. If I have uh how's it +go? If I have n squared people with n + + align:start position:0% +go? If I have n squared people with n + + + align:start position:0% +go? If I have n squared people with n +possible birthdays, then is that the + + align:start position:0% +possible birthdays, then is that the + + + align:start position:0% +possible birthdays, then is that the +right way? No, less. If I have n people + + align:start position:0% +right way? No, less. If I have n people + + + align:start position:0% +right way? No, less. If I have n people +and n squared possible birthdays, the + + align:start position:0% +and n squared possible birthdays, the + + + align:start position:0% +and n squared possible birthdays, the +probability of getting a collision, a + + align:start position:0% +probability of getting a collision, a + + + align:start position:0% +probability of getting a collision, a +shared birthday is 1/2. Normally, we + + align:start position:0% +shared birthday is 1/2. Normally, we + + + align:start position:0% +shared birthday is 1/2. Normally, we +think of that as a a funny thing. You + + align:start position:0% +think of that as a a funny thing. You + + + align:start position:0% +think of that as a a funny thing. You +know, if I choose a fair number of + + align:start position:0% +know, if I choose a fair number of + + + align:start position:0% +know, if I choose a fair number of +people, then I get uh immediately a + + align:start position:0% +people, then I get uh immediately a + + + align:start position:0% +people, then I get uh immediately a +collision. I'm going to do it the + + align:start position:0% +collision. I'm going to do it the + + + align:start position:0% +collision. I'm going to do it the +opposite way. I'm going to guarantee + + align:start position:0% +opposite way. I'm going to guarantee + + + align:start position:0% +opposite way. I'm going to guarantee +that there's so many birthdays that no + + align:start position:0% +that there's so many birthdays that no + + + align:start position:0% +that there's so many birthdays that no +two of them will collide with + + align:start position:0% +two of them will collide with + + + align:start position:0% +two of them will collide with +probability of half. Now half's not + + align:start position:0% +probability of half. Now half's not + + + align:start position:0% +probability of half. Now half's not +great. We're going to fix that. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +So actually I haven't given you the + + align:start position:0% +So actually I haven't given you the + + + align:start position:0% +So actually I haven't given you the +whole algorithm yet. Uh there are two + + align:start position:0% +whole algorithm yet. Uh there are two + + + align:start position:0% +whole algorithm yet. Uh there are two +steps one and two but there are also two + + align:start position:0% +steps one and two but there are also two + + + align:start position:0% +steps one and two but there are also two +other steps 1.5 and 2.5. So, + + align:start position:0% +other steps 1.5 and 2.5. So, + + + align:start position:0% +other steps 1.5 and 2.5. So, +but that's this is the right idea and + + align:start position:0% +but that's this is the right idea and + + + align:start position:0% +but that's this is the right idea and +this will make things work in + + align:start position:0% +this will make things work in + + + align:start position:0% +this will make things work in +expectation but I'm going to tweak it a + + align:start position:0% +expectation but I'm going to tweak it a + + + align:start position:0% +expectation but I'm going to tweak it a +little bit. Uh + + align:start position:0% +little bit. Uh + + + align:start position:0% +little bit. Uh +so first let me tell you step 1.5 it + + align:start position:0% +so first let me tell you step 1.5 it + + + align:start position:0% +so first let me tell you step 1.5 it +fits in between the two. Um I want that + + align:start position:0% +fits in between the two. Um I want that + + + align:start position:0% +fits in between the two. Um I want that +the space uh of this data structure is + + align:start position:0% +the space uh of this data structure is + + + align:start position:0% +the space uh of this data structure is +linear. + + align:start position:0% +linear. + + + align:start position:0% +linear. +So I need to make sure it is. If the sum + + align:start position:0% +So I need to make sure it is. If the sum + + + align:start position:0% +So I need to make sure it is. If the sum +j = 0 to n minus one of lj^2 + + align:start position:0% + + + + align:start position:0% + +is bigger than some constant times n. + + align:start position:0% +is bigger than some constant times n. + + + align:start position:0% +is bigger than some constant times n. +We'll figure out what the constant is + + align:start position:0% +We'll figure out what the constant is + + + align:start position:0% +We'll figure out what the constant is +later. Then + + align:start position:0% +later. Then + + + align:start position:0% +later. Then +uh redo step one. + + align:start position:0% +uh redo step one. + + + align:start position:0% +uh redo step one. +Okay. So after I do step one, I know how + + align:start position:0% +Okay. So after I do step one, I know how + + + align:start position:0% +Okay. So after I do step one, I know how +big all these tables are going to be. If + + align:start position:0% +big all these tables are going to be. If + + + align:start position:0% +big all these tables are going to be. If +the sum of those squares is bigger than + + align:start position:0% +the sum of those squares is bigger than + + + align:start position:0% +the sum of those squares is bigger than +linear, start over. Okay. Okay, I need + + align:start position:0% +linear, start over. Okay. Okay, I need + + + align:start position:0% +linear, start over. Okay. Okay, I need +to prove that this this will only have + + align:start position:0% +to prove that this this will only have + + + align:start position:0% +to prove that this this will only have +to take this will happen um expected + + align:start position:0% +to take this will happen um expected + + + align:start position:0% +to take this will happen um expected +constant number of times login times + + align:start position:0% +constant number of times login times + + + align:start position:0% +constant number of times login times +with high probability. Uh in fact why + + align:start position:0% +with high probability. Uh in fact why + + + align:start position:0% +with high probability. Uh in fact why +don't we + + align:start position:0% +don't we + + + align:start position:0% +don't we +yeah let's worry about that later. + + align:start position:0% +yeah let's worry about that later. + + + align:start position:0% +yeah let's worry about that later. +Okay, let me first tell you step 2.5 + + align:start position:0% +Okay, let me first tell you step 2.5 + + + align:start position:0% +Okay, let me first tell you step 2.5 +which is I want there to be zero + + align:start position:0% +which is I want there to be zero + + + align:start position:0% +which is I want there to be zero +collisions in each of these tables. It's + + align:start position:0% +collisions in each of these tables. It's + + + align:start position:0% +collisions in each of these tables. It's +only going to happen with probability a + + align:start position:0% +only going to happen with probability a + + + align:start position:0% +only going to happen with probability a +half. So if it doesn't happen just try + + align:start position:0% +half. So if it doesn't happen just try + + + align:start position:0% +half. So if it doesn't happen just try +again. + + align:start position:0% +again. + + + align:start position:0% +again. +So 2.5 + + align:start position:0% + + + + align:start position:0% + +is while + + align:start position:0% +is while + + + align:start position:0% +is while +there's some hash function H2J that maps + + align:start position:0% +there's some hash function H2J that maps + + + align:start position:0% +there's some hash function H2J that maps +two keys that we're given + + align:start position:0% + + + + align:start position:0% + +to the same slot at the second level. + + align:start position:0% + + + + align:start position:0% + +uh this is + + align:start position:0% +uh this is + + + align:start position:0% +uh this is +for some + + align:start position:0% +for some + + + align:start position:0% +for some +uh j + + align:start position:0% +uh j + + + align:start position:0% +uh j +and + + align:start position:0% +and + + + align:start position:0% +and +let's say k i different from k i prime + + align:start position:0% +let's say k i different from k i prime + + + align:start position:0% +let's say k i different from k i prime +but they map to the same place by the + + align:start position:0% +but they map to the same place by the + + + align:start position:0% +but they map to the same place by the +first hash function. + + align:start position:0% + + + + align:start position:0% + +Okay. So if two keys mapped to the same + + align:start position:0% +Okay. So if two keys mapped to the same + + + align:start position:0% +Okay. So if two keys mapped to the same +uh secondary table and there's a + + align:start position:0% +uh secondary table and there's a + + + align:start position:0% +uh secondary table and there's a +conflict uh then I'm just going to redo + + align:start position:0% +conflict uh then I'm just going to redo + + + align:start position:0% +conflict uh then I'm just going to redo +um that construction. So I'm going to + + align:start position:0% +um that construction. So I'm going to + + + align:start position:0% +um that construction. So I'm going to +repick H2J. + + align:start position:0% +repick H2J. + + + align:start position:0% +repick H2J. +H2J was a random choice. So um if I get + + align:start position:0% +H2J was a random choice. So um if I get + + + align:start position:0% +H2J was a random choice. So um if I get +a bad choice, I'll just try another one. + + align:start position:0% +a bad choice, I'll just try another one. + + + align:start position:0% +a bad choice, I'll just try another one. +Just keep randomly choosing the A or + + align:start position:0% +Just keep randomly choosing the A or + + + align:start position:0% +Just keep randomly choosing the A or +randomly choosing this hash function + + align:start position:0% +randomly choosing this hash function + + + align:start position:0% +randomly choosing this hash function +until there are zero collisions at that + + align:start position:0% +until there are zero collisions at that + + + align:start position:0% +until there are zero collisions at that +in that secondary table. I'm going to do + + align:start position:0% +in that secondary table. I'm going to do + + + align:start position:0% +in that secondary table. I'm going to do +this for each table. So, we worry about + + align:start position:0% +this for each table. So, we worry about + + + align:start position:0% +this for each table. So, we worry about +how long these will take, but I claim + + align:start position:0% +how long these will take, but I claim + + + align:start position:0% +how long these will take, but I claim +expected constant number of trials. + + align:start position:0% +expected constant number of trials. + + + align:start position:0% +expected constant number of trials. +So, let's do the second one first. + + align:start position:0% + + + + align:start position:0% + +Just write uh after we do this while + + align:start position:0% +Just write uh after we do this while + + + align:start position:0% +Just write uh after we do this while +loop, there are no collisions + + align:start position:0% +loop, there are no collisions + + + align:start position:0% +loop, there are no collisions +with the proper notion of the word + + align:start position:0% +with the proper notion of the word + + + align:start position:0% +with the proper notion of the word +collision, which is two different keys + + align:start position:0% +collision, which is two different keys + + + align:start position:0% +collision, which is two different keys +mapping to the same value. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% + + + + align:start position:0% + +uh at this point we've guaranteed that + + align:start position:0% +uh at this point we've guaranteed that + + + align:start position:0% +uh at this point we've guaranteed that +searches are constant time worst case + + align:start position:0% +searches are constant time worst case + + + align:start position:0% +searches are constant time worst case +after we do all these four steps because + + align:start position:0% +after we do all these four steps because + + + align:start position:0% +after we do all these four steps because +uh we apply H1 we figure out which slot + + align:start position:0% +uh we apply H1 we figure out which slot + + + align:start position:0% +uh we apply H1 we figure out which slot +we fit in then we say it's slot J then + + align:start position:0% +we fit in then we say it's slot J then + + + align:start position:0% +we fit in then we say it's slot J then +we apply H2 2J. And if your item's in + + align:start position:0% +we apply H2 2J. And if your item's in + + + align:start position:0% +we apply H2 2J. And if your item's in +this in the overall table, it should be + + align:start position:0% +this in the overall table, it should be + + + align:start position:0% +this in the overall table, it should be +in that secondary table. Because there + + align:start position:0% +in that secondary table. Because there + + + align:start position:0% +in that secondary table. Because there +are no collisions, you can see is that + + align:start position:0% +are no collisions, you can see is that + + + align:start position:0% +are no collisions, you can see is that +one item the one I'm looking for. If so, + + align:start position:0% +one item the one I'm looking for. If so, + + + align:start position:0% +one item the one I'm looking for. If so, +return it. If not, it's not anywhere. If + + align:start position:0% +return it. If not, it's not anywhere. If + + + align:start position:0% +return it. If not, it's not anywhere. If +there are no collisions, then I don't + + align:start position:0% +there are no collisions, then I don't + + + align:start position:0% +there are no collisions, then I don't +need I don't need chains coming out of + + align:start position:0% +need I don't need chains coming out of + + + align:start position:0% +need I don't need chains coming out of +here because it's just a single item. + + align:start position:0% +here because it's just a single item. + + + align:start position:0% +here because it's just a single item. +Okay, the big question. So, constant + + align:start position:0% +Okay, the big question. So, constant + + + align:start position:0% +Okay, the big question. So, constant +worst case space because 1.5 guarantees + + align:start position:0% +worst case space because 1.5 guarantees + + + align:start position:0% +worst case space because 1.5 guarantees +that constant worst case time for + + align:start position:0% +that constant worst case time for + + + align:start position:0% +that constant worst case time for +search. Uh the big question is how long + + align:start position:0% +search. Uh the big question is how long + + + align:start position:0% +search. Uh the big question is how long +does it take to build? How many times do + + align:start position:0% +does it take to build? How many times do + + + align:start position:0% +does it take to build? How many times do +we have to redo uh steps one and two + + align:start position:0% +we have to redo uh steps one and two + + + align:start position:0% +we have to redo uh steps one and two +before we get a decent before we get a + + align:start position:0% +before we get a decent before we get a + + + align:start position:0% +before we get a decent before we get a +perfect hasht. + + align:start position:0% +perfect hasht. + + + align:start position:0% +perfect hasht. +Okay. So uh let me remind you of the + + align:start position:0% +Okay. So uh let me remind you of the + + + align:start position:0% +Okay. So uh let me remind you of the +birthday paradox how why it works here. + + align:start position:0% + + + + align:start position:0% + +As uh mentioned earlier, this is going + + align:start position:0% +As uh mentioned earlier, this is going + + + align:start position:0% +As uh mentioned earlier, this is going +to be a union bound. + + align:start position:0% +to be a union bound. + + + align:start position:0% +to be a union bound. +We want to know the probability of + + align:start position:0% +We want to know the probability of + + + align:start position:0% +We want to know the probability of +collision at that second level. Well, + + align:start position:0% +collision at that second level. Well, + + + align:start position:0% +collision at that second level. Well, +that's at most the sum of all possible + + align:start position:0% +that's at most the sum of all possible + + + align:start position:0% +that's at most the sum of all possible +collisions, probabilities of collisions. + + align:start position:0% +collisions, probabilities of collisions. + + + align:start position:0% +collisions, probabilities of collisions. +So I'm going to say the sum overall i + + align:start position:0% +So I'm going to say the sum overall i + + + align:start position:0% +So I'm going to say the sum overall i +not equal to i j of the probability + + align:start position:0% +not equal to i j of the probability + + + align:start position:0% +not equal to i j of the probability +uh now this is over our choice of the + + align:start position:0% +uh now this is over our choice of the + + + align:start position:0% +uh now this is over our choice of the +hash function h2j + + align:start position:0% +hash function h2j + + + align:start position:0% +hash function h2j +of h2j + + align:start position:0% +of h2j + + + align:start position:0% +of h2j +of ki equaling h2 j of ki prime. + + align:start position:0% +of ki equaling h2 j of ki prime. + + + align:start position:0% +of ki equaling h2 j of ki prime. +So union bound says of course the + + align:start position:0% +So union bound says of course the + + + align:start position:0% +So union bound says of course the +probability of any of any of them + + align:start position:0% +probability of any of any of them + + + align:start position:0% +probability of any of any of them +happening we don't know about + + align:start position:0% +happening we don't know about + + + align:start position:0% +happening we don't know about +interdependence or whatnot uh but + + align:start position:0% +interdependence or whatnot uh but + + + align:start position:0% +interdependence or whatnot uh but +certainly at most the sum of each of + + align:start position:0% +certainly at most the sum of each of + + + align:start position:0% +certainly at most the sum of each of +these possible events + + align:start position:0% +these possible events + + + align:start position:0% +these possible events +uh there are a lot of possible events + + align:start position:0% +uh there are a lot of possible events + + + align:start position:0% +uh there are a lot of possible events +there are if there's li things they're + + align:start position:0% +there are if there's li things they're + + + align:start position:0% +there are if there's li things they're +going to be li choose two possible + + align:start position:0% +going to be li choose two possible + + + align:start position:0% +going to be li choose two possible +collisions we have to worry about we + + align:start position:0% +collisions we have to worry about we + + + align:start position:0% +collisions we have to worry about we +know I is not equal I prime um + + align:start position:0% +know I is not equal I prime um + + + align:start position:0% +know I is not equal I prime um +so the number of terms here is li + + align:start position:0% + + + + align:start position:0% + +Uh, and what's this probability? + + align:start position:0% + + + + align:start position:0% + +One over LI + + align:start position:0% + + + + align:start position:0% + +at most because we're assuming H2J is a + + align:start position:0% +at most because we're assuming H2J is a + + + align:start position:0% +at most because we're assuming H2J is a +universal hash function. So the + + align:start position:0% +universal hash function. So the + + + align:start position:0% +universal hash function. So the +probability of choosing sorry + + align:start position:0% +probability of choosing sorry + + + align:start position:0% +probability of choosing sorry +LI squ the size of the table uh one over + + align:start position:0% +LI squ the size of the table uh one over + + + align:start position:0% +LI squ the size of the table uh one over +M but M in this case the size of our + + align:start position:0% +M but M in this case the size of our + + + align:start position:0% +M but M in this case the size of our +table is LI squ. So uh the probability + + align:start position:0% +table is LI squ. So uh the probability + + + align:start position:0% +table is LI squ. So uh the probability +that we choose a good hash function in + + align:start position:0% +that we choose a good hash function in + + + align:start position:0% +that we choose a good hash function in +that these particular keys don't hit is + + align:start position:0% +that these particular keys don't hit is + + + align:start position:0% +that these particular keys don't hit is +at most 1 over li. This is basically li + + align:start position:0% +at most 1 over li. This is basically li + + + align:start position:0% +at most 1 over li. This is basically li +over two and so this is at most 12. This + + align:start position:0% +over two and so this is at most 12. This + + + align:start position:0% +over two and so this is at most 12. This +is slightly less than li over two. So + + align:start position:0% +is slightly less than li over two. So + + + align:start position:0% +is slightly less than li over two. So +this is at most a half and this is + + align:start position:0% +this is at most a half and this is + + + align:start position:0% +this is at most a half and this is +basically a birthday paradox in this + + align:start position:0% +basically a birthday paradox in this + + + align:start position:0% +basically a birthday paradox in this +particular case. That means there's a + + align:start position:0% +particular case. That means there's a + + + align:start position:0% +particular case. That means there's a +probability of at least a half that + + align:start position:0% +probability of at least a half that + + + align:start position:0% +probability of at least a half that +there are zero collisions in one of + + align:start position:0% +there are zero collisions in one of + + + align:start position:0% +there are zero collisions in one of +these tables. So that means I'm + + align:start position:0% +these tables. So that means I'm + + + align:start position:0% +these tables. So that means I'm +basically flipping a fair coin. If I + + align:start position:0% +basically flipping a fair coin. If I + + + align:start position:0% +basically flipping a fair coin. If I +ever get a heads, I'm happy. Each time I + + align:start position:0% +ever get a heads, I'm happy. Each time I + + + align:start position:0% +ever get a heads, I'm happy. Each time I +get a tails, I have to reflip. Should + + align:start position:0% +get a tails, I have to reflip. Should + + + align:start position:0% +get a tails, I have to reflip. Should +sound familiar from last time. Uh so + + align:start position:0% +sound familiar from last time. Uh so + + + align:start position:0% +sound familiar from last time. Uh so +this is um two expected + + align:start position:0% +this is um two expected + + + align:start position:0% +this is um two expected +trials + + align:start position:0% + + + + align:start position:0% + +uh or login with high probability. + + align:start position:0% + + + + align:start position:0% + +Uh we proved login with high + + align:start position:0% +Uh we proved login with high + + + align:start position:0% +Uh we proved login with high +probability. Uh that's the same as + + align:start position:0% +probability. Uh that's the same as + + + align:start position:0% +probability. Uh that's the same as +saying the number of levels in a skip + + align:start position:0% +saying the number of levels in a skip + + + align:start position:0% +saying the number of levels in a skip +list is login with high probability. How + + align:start position:0% +list is login with high probability. How + + + align:start position:0% +list is login with high probability. How +many times do I have to flip a coin + + align:start position:0% +many times do I have to flip a coin + + + align:start position:0% +many times do I have to flip a coin +before I get a heads? Definitely at most + + align:start position:0% +before I get a heads? Definitely at most + + + align:start position:0% +before I get a heads? Definitely at most +login. + + align:start position:0% + + + + align:start position:0% + +Okay. Uh now we have to do this for each + + align:start position:0% +Okay. Uh now we have to do this for each + + + align:start position:0% +Okay. Uh now we have to do this for each +secondary table. There are m= theta n + + align:start position:0% +secondary table. There are m= theta n + + + align:start position:0% +secondary table. There are m= theta n +secondary tables. Uh and + + align:start position:0% + + + + align:start position:0% + +yeah uh there's a slight question of how + + align:start position:0% +yeah uh there's a slight question of how + + + align:start position:0% +yeah uh there's a slight question of how +big are the secondary tables? If a if + + align:start position:0% +big are the secondary tables? If a if + + + align:start position:0% +big are the secondary tables? If a if +one of these tables is like linear size + + align:start position:0% +one of these tables is like linear size + + + align:start position:0% +one of these tables is like linear size +then I have to spend linear time for a + + align:start position:0% +then I have to spend linear time for a + + + align:start position:0% +then I have to spend linear time for a +trial and then I multiply that by the + + align:start position:0% +trial and then I multiply that by the + + + align:start position:0% +trial and then I multiply that by the +number of trials and also the number of + + align:start position:0% +number of trials and also the number of + + + align:start position:0% +number of trials and also the number of +different things that would be like n + + align:start position:0% +different things that would be like n + + + align:start position:0% +different things that would be like n +squ n. But you know a secondary table + + align:start position:0% +squ n. But you know a secondary table + + + align:start position:0% +squ n. But you know a secondary table +better not have linear size. Uh I mean a + + align:start position:0% +better not have linear size. Uh I mean a + + + align:start position:0% +better not have linear size. Uh I mean a +linear number of li equal n that would + + align:start position:0% +linear number of li equal n that would + + + align:start position:0% +linear number of li equal n that would +be bad because n li squar is n squ and + + align:start position:0% +be bad because n li squar is n squ and + + + align:start position:0% +be bad because n li squar is n squ and +we guaranteed that we had linear space. + + align:start position:0% +we guaranteed that we had linear space. + + + align:start position:0% +we guaranteed that we had linear space. +Um so in fact you can prove uh with + + align:start position:0% +Um so in fact you can prove uh with + + + align:start position:0% +Um so in fact you can prove uh with +another + + align:start position:0% +another + + + align:start position:0% +another +churnoff bound let me put this over here + + align:start position:0% + + + + align:start position:0% + +that all the li are pretty small not + + align:start position:0% +that all the li are pretty small not + + + align:start position:0% +that all the li are pretty small not +constant + + align:start position:0% +constant + + + align:start position:0% +constant +but + + align:start position:0% +but + + + align:start position:0% +but +logarithmic + + align:start position:0% +logarithmic + + + align:start position:0% +logarithmic +so uh li is order log n + + align:start position:0% +so uh li is order log n + + + align:start position:0% +so uh li is order log n +with high probability + + align:start position:0% +with high probability + + + align:start position:0% +with high probability +for each i and therefore for all i. So I + + align:start position:0% +for each i and therefore for all i. So I + + + align:start position:0% +for each i and therefore for all i. So I +can just change the alpha in my one + + align:start position:0% +can just change the alpha in my one + + + align:start position:0% +can just change the alpha in my one +minus one over n and to the alpha and + + align:start position:0% +minus one over n and to the alpha and + + + align:start position:0% +minus one over n and to the alpha and +get that for all i uh this happens. In + + align:start position:0% +get that for all i uh this happens. In + + + align:start position:0% +get that for all i uh this happens. In +fact the right answer is log over log + + align:start position:0% +fact the right answer is log over log + + + align:start position:0% +fact the right answer is log over log +log if you want to do some really messy + + align:start position:0% +log if you want to do some really messy + + + align:start position:0% +log if you want to do some really messy +analysis but uh we just logarithmic fine + + align:start position:0% +analysis but uh we just logarithmic fine + + + align:start position:0% +analysis but uh we just logarithmic fine +for us. So what this means is uh we're + + align:start position:0% +for us. So what this means is uh we're + + + align:start position:0% +for us. So what this means is uh we're +doing n different things for each of + + align:start position:0% +doing n different things for each of + + + align:start position:0% +doing n different things for each of +them with high probability li is of size + + align:start position:0% +them with high probability li is of size + + + align:start position:0% +them with high probability li is of size +log n and then maybe we'll have to do + + align:start position:0% +log n and then maybe we'll have to do + + + align:start position:0% +log n and then maybe we'll have to do +like login trials repeating until we get + + align:start position:0% +like login trials repeating until we get + + + align:start position:0% +like login trials repeating until we get +a good hash function there. And so the + + align:start position:0% +a good hash function there. And so the + + + align:start position:0% +a good hash function there. And so the +total build time for steps two and 2.5 + + align:start position:0% +total build time for steps two and 2.5 + + + align:start position:0% +total build time for steps two and 2.5 +is going to be uh n at most n* log squar + + align:start position:0% +is going to be uh n at most n* log squar + + + align:start position:0% +is going to be uh n at most n* log squar +n. You can prove a tighter bound but + + align:start position:0% +n. You can prove a tighter bound but + + + align:start position:0% +n. You can prove a tighter bound but +that's it's polomial. That's all I + + align:start position:0% +that's it's polomial. That's all I + + + align:start position:0% +that's it's polomial. That's all I +wanted to go for and it's almost linear. + + align:start position:0% +wanted to go for and it's almost linear. + + + align:start position:0% +wanted to go for and it's almost linear. +So I'm left with one thing to analyze + + align:start position:0% +So I'm left with one thing to analyze + + + align:start position:0% +So I'm left with one thing to analyze +which is step 1.5. This to me is maybe + + align:start position:0% +which is step 1.5. This to me is maybe + + + align:start position:0% +which is step 1.5. This to me is maybe +the most surprising thing that it works + + align:start position:0% +the most surprising thing that it works + + + align:start position:0% +the most surprising thing that it works +out. Uh I mean here we we designed we + + align:start position:0% +out. Uh I mean here we we designed we + + + align:start position:0% +out. Uh I mean here we we designed we +did this Liy to LII squared so that + + align:start position:0% +did this Liy to LII squared so that + + + align:start position:0% +did this Liy to LII squared so that +birthday paradox would happen. That's + + align:start position:0% +birthday paradox would happen. That's + + + align:start position:0% +birthday paradox would happen. That's +this is not surprising. I it's a cool + + align:start position:0% +this is not surprising. I it's a cool + + + align:start position:0% +this is not surprising. I it's a cool +idea but once you have the idea it's not + + align:start position:0% +idea but once you have the idea it's not + + + align:start position:0% +idea but once you have the idea it's not +surprising that it works. Uh what's a + + align:start position:0% +surprising that it works. Uh what's a + + + align:start position:0% +surprising that it works. Uh what's a +little more surprising is that squaring + + align:start position:0% +little more surprising is that squaring + + + align:start position:0% +little more surprising is that squaring +is okay from a space perspective. 1.5 + + align:start position:0% +is okay from a space perspective. 1.5 + + + align:start position:0% +is okay from a space perspective. 1.5 +says we're going to have to rebuild that + + align:start position:0% +says we're going to have to rebuild that + + + align:start position:0% +says we're going to have to rebuild that +first table until the sum of these + + align:start position:0% +first table until the sum of these + + + align:start position:0% +first table until the sum of these +squared lengths is at most linear. I can + + align:start position:0% +squared lengths is at most linear. I can + + + align:start position:0% +squared lengths is at most linear. I can +guarantee that each of these is + + align:start position:0% +guarantee that each of these is + + + align:start position:0% +guarantee that each of these is +logarithmic. So the sum of the squares + + align:start position:0% +logarithmic. So the sum of the squares + + + align:start position:0% +logarithmic. So the sum of the squares +is at most like n log 2 n. But I claim I + + align:start position:0% +is at most like n log 2 n. But I claim I + + + align:start position:0% +is at most like n log 2 n. But I claim I +can get linear. + + align:start position:0% +can get linear. + + + align:start position:0% +can get linear. +Okay, let's do that. + + align:start position:0% +Okay, let's do that. + + + align:start position:0% +Okay, let's do that. +So for step 1.5 + + align:start position:0% +So for step 1.5 + + + align:start position:0% +So for step 1.5 +we're looking at what is the expectation + + align:start position:0% +we're looking at what is the expectation + + + align:start position:0% +we're looking at what is the expectation +of the sum of the LJ squares being more + + align:start position:0% +of the sum of the LJ squares being more + + + align:start position:0% +of the sum of the LJ squares being more +than linear. Oh sorry expectation um + + align:start position:0% +than linear. Oh sorry expectation um + + + align:start position:0% +than linear. Oh sorry expectation um +let's first compute the expectation then + + align:start position:0% +let's first compute the expectation then + + + align:start position:0% +let's first compute the expectation then +we'll talk about a tailbound um which is + + align:start position:0% +we'll talk about a tailbound um which is + + + align:start position:0% +we'll talk about a tailbound um which is +the probability that we're much bigger + + align:start position:0% +the probability that we're much bigger + + + align:start position:0% +the probability that we're much bigger +than the expectation. First thing is I + + align:start position:0% +than the expectation. First thing is I + + + align:start position:0% +than the expectation. First thing is I +claim the expectation is linear. + + align:start position:0% +claim the expectation is linear. + + + align:start position:0% +claim the expectation is linear. +So uh again whenever we're counting + + align:start position:0% +So uh again whenever we're counting + + + align:start position:0% +So uh again whenever we're counting +something I mean this is basically the + + align:start position:0% +something I mean this is basically the + + + align:start position:0% +something I mean this is basically the +total number of pairs of items that + + align:start position:0% +total number of pairs of items that + + + align:start position:0% +total number of pairs of items that +collide at the first level + + align:start position:0% +collide at the first level + + + align:start position:0% +collide at the first level +right uh with double counting. So I mean + + align:start position:0% +right uh with double counting. So I mean + + + align:start position:0% +right uh with double counting. So I mean +if you think of LJ and then I make a + + align:start position:0% +if you think of LJ and then I make a + + + align:start position:0% +if you think of LJ and then I make a +complete graph on those uh LJ items + + align:start position:0% +complete graph on those uh LJ items + + + align:start position:0% +complete graph on those uh LJ items +that's going to have like square number + + align:start position:0% +that's going to have like square number + + + align:start position:0% +that's going to have like square number +of edges. So if I also multiply by two. + + align:start position:0% +of edges. So if I also multiply by two. + + + align:start position:0% +of edges. So if I also multiply by two. +So this is the same thing as counting + + align:start position:0% +So this is the same thing as counting + + + align:start position:0% +So this is the same thing as counting +how many pairs of items map to the same + + align:start position:0% +how many pairs of items map to the same + + + align:start position:0% +how many pairs of items map to the same +spot the same slot. + + align:start position:0% +spot the same slot. + + + align:start position:0% +spot the same slot. +So this is going to and that I can write + + align:start position:0% +So this is going to and that I can write + + + align:start position:0% +So this is going to and that I can write +as an indicator random variable which + + align:start position:0% +as an indicator random variable which + + + align:start position:0% +as an indicator random variable which +lets me use linearity of expectation + + align:start position:0% +lets me use linearity of expectation + + + align:start position:0% +lets me use linearity of expectation +which makes me happy because then + + align:start position:0% +which makes me happy because then + + + align:start position:0% +which makes me happy because then +everything's simple. + + align:start position:0% +everything's simple. + + + align:start position:0% +everything's simple. +So I'm going to write I I J + + align:start position:0% +So I'm going to write I I J + + + align:start position:0% +So I'm going to write I I J +this is going to be uh one if H1 of I + + align:start position:0% +this is going to be uh one if H1 of I + + + align:start position:0% +this is going to be uh one if H1 of I +sorry of KI I guess + + align:start position:0% +sorry of KI I guess + + + align:start position:0% +sorry of KI I guess +equals H1 of KJ + + align:start position:0% +equals H1 of KJ + + + align:start position:0% +equals H1 of KJ +and it's going to be zero if H1 oh + + align:start position:0% +and it's going to be zero if H1 oh + + + align:start position:0% +and it's going to be zero if H1 oh +otherwise + + align:start position:0% + + + + align:start position:0% + +right this is the total number of + + align:start position:0% +right this is the total number of + + + align:start position:0% +right this is the total number of +pairways colliding items including I + + align:start position:0% +pairways colliding items including I + + + align:start position:0% +pairways colliding items including I +versus I. + + align:start position:0% +versus I. + + + align:start position:0% +versus I. +Uh and so like if LI equals 1, LI squ is + + align:start position:0% +Uh and so like if LI equals 1, LI squ is + + + align:start position:0% +Uh and so like if LI equals 1, LI squ is +also one. There's one item colliding + + align:start position:0% +also one. There's one item colliding + + + align:start position:0% +also one. There's one item colliding +with itself. So this actually works + + align:start position:0% +with itself. So this actually works + + + align:start position:0% +with itself. So this actually works +exactly. + + align:start position:0% +exactly. + + + align:start position:0% +exactly. +All right, with the wrong definition of + + align:start position:0% +All right, with the wrong definition of + + + align:start position:0% +All right, with the wrong definition of +colliding if you bear with me. Uh so uh + + align:start position:0% +colliding if you bear with me. Uh so uh + + + align:start position:0% +colliding if you bear with me. Uh so uh +now we can use linear of expectation and + + align:start position:0% +now we can use linear of expectation and + + + align:start position:0% +now we can use linear of expectation and +put the E in here. So this is sum i = 1 + + align:start position:0% +put the E in here. So this is sum i = 1 + + + align:start position:0% +put the E in here. So this is sum i = 1 +to n sum j = 1 to n of the expectation + + align:start position:0% +to n sum j = 1 to n of the expectation + + + align:start position:0% +to n sum j = 1 to n of the expectation +of iig. + + align:start position:0% +of iig. + + + align:start position:0% +of iig. +But we know uh the expectation of iig is + + align:start position:0% +But we know uh the expectation of iig is + + + align:start position:0% +But we know uh the expectation of iig is +the probability of it equaling one + + align:start position:0% +the probability of it equaling one + + + align:start position:0% +the probability of it equaling one +because it's an indicator random + + align:start position:0% +because it's an indicator random + + + align:start position:0% +because it's an indicator random +variable. Probability of this happening + + align:start position:0% +variable. Probability of this happening + + + align:start position:0% +variable. Probability of this happening +over our choice of h1 is at most one + + align:start position:0% +over our choice of h1 is at most one + + + align:start position:0% +over our choice of h1 is at most one +over m by universality. Here it actually + + align:start position:0% +over m by universality. Here it actually + + + align:start position:0% +over m by universality. Here it actually +is m because we're at the first level. + + align:start position:0% +is m because we're at the first level. + + + align:start position:0% +is m because we're at the first level. +So this is at most 1 / m + + align:start position:0% +So this is at most 1 / m + + + align:start position:0% +So this is at most 1 / m +which is theta n + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% + + + + align:start position:0% + +uh when i does not equal j. So uh it's a + + align:start position:0% +uh when i does not equal j. So uh it's a + + + align:start position:0% +uh when i does not equal j. So uh it's a +little bit annoying. I do have to + + align:start position:0% +little bit annoying. I do have to + + + align:start position:0% +little bit annoying. I do have to +separate out the uh the i terms from the + + align:start position:0% +separate out the uh the i terms from the + + + align:start position:0% +separate out the uh the i terms from the +i and different i not equal to j terms. + + align:start position:0% +i and different i not equal to j terms. + + + align:start position:0% +i and different i not equal to j terms. +But there's only I mean it's basically + + align:start position:0% +But there's only I mean it's basically + + + align:start position:0% +But there's only I mean it's basically +the diagonal of this matrix. there's n + + align:start position:0% +the diagonal of this matrix. there's n + + + align:start position:0% +the diagonal of this matrix. there's n +things that will always collide with + + align:start position:0% +things that will always collide with + + + align:start position:0% +things that will always collide with +themselves. So we're going to get like n + + align:start position:0% +themselves. So we're going to get like n + + + align:start position:0% +themselves. So we're going to get like n +plus + + align:start position:0% +plus + + + align:start position:0% +plus +uh the number of i not equal to j pairs + + align:start position:0% +uh the number of i not equal to j pairs + + + align:start position:0% +uh the number of i not equal to j pairs +double counted. So it's like 2 * n + + align:start position:0% +double counted. So it's like 2 * n + + + align:start position:0% +double counted. So it's like 2 * n +choose 2. Uh but we get to divide by m. + + align:start position:0% +choose 2. Uh but we get to divide by m. + + + align:start position:0% +choose 2. Uh but we get to divide by m. +So this is like n^2 over n. So we get uh + + align:start position:0% +So this is like n^2 over n. So we get uh + + + align:start position:0% +So this is like n^2 over n. So we get uh +order n. + + align:start position:0% +order n. + + + align:start position:0% +order n. +Okay. So that's that's not well that's + + align:start position:0% +Okay. So that's that's not well that's + + + align:start position:0% +Okay. So that's that's not well that's +cool. expected space is linear. This is + + align:start position:0% +cool. expected space is linear. This is + + + align:start position:0% +cool. expected space is linear. This is +what makes everything work. + + align:start position:0% + + + + align:start position:0% + +Uh last class was about getting with + + align:start position:0% +Uh last class was about getting with + + + align:start position:0% +Uh last class was about getting with +high probability bounds when we were + + align:start position:0% +high probability bounds when we were + + + align:start position:0% +high probability bounds when we were +working with logs. + + align:start position:0% +working with logs. + + + align:start position:0% +working with logs. +When you want to get that something is + + align:start position:0% +When you want to get that something is + + + align:start position:0% +When you want to get that something is +log with high probability, you have to + + align:start position:0% +log with high probability, you have to + + + align:start position:0% +log with high probability, you have to +use with respect to n you have to use a + + align:start position:0% +use with respect to n you have to use a + + + align:start position:0% +use with respect to n you have to use a +choff bound. But this is about now I + + align:start position:0% +choff bound. But this is about now I + + + align:start position:0% +choff bound. But this is about now I +want to show that the space is linear + + align:start position:0% +want to show that the space is linear + + + align:start position:0% +want to show that the space is linear +with high probability. Linear is + + align:start position:0% +with high probability. Linear is + + + align:start position:0% +with high probability. Linear is +actually really easy. You can use a much + + align:start position:0% +actually really easy. You can use a much + + + align:start position:0% +actually really easy. You can use a much +weaker bound called Marov inequality. So + + align:start position:0% +weaker bound called Marov inequality. So + + + align:start position:0% +weaker bound called Marov inequality. So +I want to claim that the probability of + + align:start position:0% +I want to claim that the probability of + + + align:start position:0% +I want to claim that the probability of +H1 + + align:start position:0% +H1 + + + align:start position:0% +H1 +uh + + align:start position:0% +uh + + + align:start position:0% +uh +of this thing + + align:start position:0% +of this thing + + + align:start position:0% +of this thing +uh + + align:start position:0% +uh + + + align:start position:0% +uh +LJ squares being bigger than some + + align:start position:0% +LJ squares being bigger than some + + + align:start position:0% +LJ squares being bigger than some +constant times N is at most uh the + + align:start position:0% +constant times N is at most uh the + + + align:start position:0% +constant times N is at most uh the +expectation of that thing divided by + + align:start position:0% +expectation of that thing divided by + + + align:start position:0% +expectation of that thing divided by +CN. + + align:start position:0% +CN. + + + align:start position:0% +CN. +This is Marov's inequality holds for any + + align:start position:0% +This is Marov's inequality holds for any + + + align:start position:0% +This is Marov's inequality holds for any +thing here. by just repeating it over + + align:start position:0% +thing here. by just repeating it over + + + align:start position:0% +thing here. by just repeating it over +here. + + align:start position:0% + + + + align:start position:0% + +Okay, so this is nice because we know + + align:start position:0% +Okay, so this is nice because we know + + + align:start position:0% +Okay, so this is nice because we know +that this expectation + + align:start position:0% +that this expectation + + + align:start position:0% +that this expectation +is linear. + + align:start position:0% +is linear. + + + align:start position:0% +is linear. +So we're getting like a linear function + + align:start position:0% +So we're getting like a linear function + + + align:start position:0% +So we're getting like a linear function +divided by CN. + + align:start position:0% +divided by CN. + + + align:start position:0% +divided by CN. +Remember, we get to choose C. The step + + align:start position:0% +Remember, we get to choose C. The step + + + align:start position:0% +Remember, we get to choose C. The step +said if it's bigger than some constant + + align:start position:0% +said if it's bigger than some constant + + + align:start position:0% +said if it's bigger than some constant +times N, then we're redoing the thing. + + align:start position:0% +times N, then we're redoing the thing. + + + align:start position:0% +times N, then we're redoing the thing. +So I can choose C to be 100, whatever. + + align:start position:0% +So I can choose C to be 100, whatever. + + + align:start position:0% +So I can choose C to be 100, whatever. +I'm going to choose it to be twice this + + align:start position:0% +I'm going to choose it to be twice this + + + align:start position:0% +I'm going to choose it to be twice this +constant. And then this is at most a + + align:start position:0% +constant. And then this is at most a + + + align:start position:0% +constant. And then this is at most a +half. + + align:start position:0% +half. + + + align:start position:0% +half. +Okay, so the probability of my space + + align:start position:0% +Okay, so the probability of my space + + + align:start position:0% +Okay, so the probability of my space +being too big is at most a half. We're + + align:start position:0% +being too big is at most a half. We're + + + align:start position:0% +being too big is at most a half. We're +back to coin flipping. Every time I flip + + align:start position:0% +back to coin flipping. Every time I flip + + + align:start position:0% +back to coin flipping. Every time I flip +a coin, if I get a heads, I have the + + align:start position:0% +a coin, if I get a heads, I have the + + + align:start position:0% +a coin, if I get a heads, I have the +right amount of space at less than CN + + align:start position:0% +right amount of space at less than CN + + + align:start position:0% +right amount of space at less than CN +time space. + + align:start position:0% +time space. + + + align:start position:0% +time space. +Uh less than C * N space. Um if I get a + + align:start position:0% +Uh less than C * N space. Um if I get a + + + align:start position:0% +Uh less than C * N space. Um if I get a +tails, I try again. So the expected + + align:start position:0% +tails, I try again. So the expected + + + align:start position:0% +tails, I try again. So the expected +number of trials is two at most. not + + align:start position:0% +number of trials is two at most. not + + + align:start position:0% +number of trials is two at most. not +trails trials + + align:start position:0% +trails trials + + + align:start position:0% +trails trials +and uh it's also login trials with high + + align:start position:0% +and uh it's also login trials with high + + + align:start position:0% +and uh it's also login trials with high +probability + + align:start position:0% + + + + align:start position:0% + +how much time do I spend for each trial + + align:start position:0% +how much time do I spend for each trial + + + align:start position:0% +how much time do I spend for each trial +linear time I choose one hash function I + + align:start position:0% +linear time I choose one hash function I + + + align:start position:0% +linear time I choose one hash function I +hash all the items I count the number of + + align:start position:0% +hash all the items I count the number of + + + align:start position:0% +hash all the items I count the number of +collisions squared or number the sum of + + align:start position:0% +collisions squared or number the sum of + + + align:start position:0% +collisions squared or number the sum of +LJ squ that takes linear time to do and + + align:start position:0% +LJ squ that takes linear time to do and + + + align:start position:0% +LJ squ that takes linear time to do and +so the total work I'm doing for these + + align:start position:0% +so the total work I'm doing for these + + + align:start position:0% +so the total work I'm doing for these +steps is n log n. + + align:start position:0% + + + + align:start position:0% + +So n log n to do step one and one prime. + + align:start position:0% +So n log n to do step one and one prime. + + + align:start position:0% +So n log n to do step one and one prime. +N log squ n to step to do steps two and + + align:start position:0% +N log squ n to step to do steps two and + + + align:start position:0% +N log squ n to step to do steps two and +two prime overall n poly log or polomial + + align:start position:0% +two prime overall n poly log or polomial + + + align:start position:0% +two prime overall n poly log or polomial +time. Uh and we get guaranteed no + + align:start position:0% +time. Uh and we get guaranteed no + + + align:start position:0% +time. Uh and we get guaranteed no +collisions for static data. Uh constant + + align:start position:0% +collisions for static data. Uh constant + + + align:start position:0% +collisions for static data. Uh constant +worst case search and linear worstase + + align:start position:0% +worst case search and linear worstase + + + align:start position:0% +worst case search and linear worstase +space. This is kind of surprising that + + align:start position:0% +space. This is kind of surprising that + + + align:start position:0% +space. This is kind of surprising that +this works out, but everything's nice. + + align:start position:0% + + + + align:start position:0% + +Now you know hashing. \ No newline at end of file diff --git a/zLGHH9Rwvlw.txt b/zLGHH9Rwvlw.txt new file mode 100644 index 0000000000000000000000000000000000000000..f830819c2382e27edf42740fd23ec3e989365f4a --- /dev/null +++ b/zLGHH9Rwvlw.txt @@ -0,0 +1,81 @@ +PROFESSOR: So let's begin with +trying to introduce you to + +biochemistry. + +So I'm going to be thinking +atoms and molecules for a + +little bit. + +Let's begin by thinking about +the composition of a cell, so + +that's the basic unit of life. + +It's about 60% hydrogen, 20% +oxygen, 12% carbon, 5% + +nitrogen, and then there's +a bunch of other stuff-- + +phosphates, sulfur, magnesium, +manganese, et cetera. + +But that's not very helpful +way of studying biology. + +It's interesting and is relevant +in some contexts, but + +that's the atomic composition. + +If we look instead at the +molecular composition of a + +cell, then things start +to get interesting. + +Cells are about somewhere in +the ballpark of 80% water. + +Water's going to be +very important-- + +I'm going to be talking +about that. + +But of the remainder, then about +50% is protein, about + +15% are these molecules we call +nucleic acids, and that + +means DNA and RNA, which most of +you have probably heard of. + +We'll be talking about those +in great detail. + +15% are carbohydrate-- + +and in fact, we will talk +about those today-- + +and about 10% fall in the +category of molecules known as + +lipids, which we'll be talking +about in another day or two. + +And then there's a bunch of +other things-- vitamins and + +other things that happen, but +you can sort of see the big + +classes of proteins that make +up most of a cell are + +proteins, nucleic acids, +carbohydrates, and lipids. \ No newline at end of file diff --git a/zgk93CwMVk8.txt b/zgk93CwMVk8.txt new file mode 100644 index 0000000000000000000000000000000000000000..af651ca8cda5e7e5bcfcda16a0cf95e5d8755e03 --- /dev/null +++ b/zgk93CwMVk8.txt @@ -0,0 +1,7155 @@ +align:start position:0% + +so so far we haven't really done much + + align:start position:0% +so so far we haven't really done much + + + align:start position:0% +so so far we haven't really done much +with data structures outside of Python + + align:start position:0% +with data structures outside of Python + + + align:start position:0% +with data structures outside of Python +lists we looked at two dimensional lists + + align:start position:0% +lists we looked at two dimensional lists + + + align:start position:0% +lists we looked at two dimensional lists +but you know there's still lists and so + + align:start position:0% +but you know there's still lists and so + + + align:start position:0% +but you know there's still lists and so +this particular puzzle that we're going + + align:start position:0% +this particular puzzle that we're going + + + align:start position:0% +this particular puzzle that we're going +to do today I has a graph structure + + align:start position:0% +to do today I has a graph structure + + + align:start position:0% +to do today I has a graph structure +associated with it so for the first time + + align:start position:0% +associated with it so for the first time + + + align:start position:0% +associated with it so for the first time +at least in this class we'll be looking + + align:start position:0% +at least in this class we'll be looking + + + align:start position:0% +at least in this class we'll be looking +at traversing graphs and I we're gonna + + align:start position:0% +at traversing graphs and I we're gonna + + + align:start position:0% +at traversing graphs and I we're gonna +do this in a recursive way and also + + align:start position:0% +do this in a recursive way and also + + + align:start position:0% +do this in a recursive way and also +we'll have a graph representation by + + align:start position:0% +we'll have a graph representation by + + + align:start position:0% +we'll have a graph representation by +using dictionaries so most of you have + + align:start position:0% +using dictionaries so most of you have + + + align:start position:0% +using dictionaries so most of you have +probably seen dictionaries if you + + align:start position:0% +probably seen dictionaries if you + + + align:start position:0% +probably seen dictionaries if you +haven't I'm going to explain them + + align:start position:0% +haven't I'm going to explain them + + + align:start position:0% +haven't I'm going to explain them +they're essentially ways that you can + + align:start position:0% +they're essentially ways that you can + + + align:start position:0% +they're essentially ways that you can +index into lists not just using nonzero + + align:start position:0% +index into lists not just using nonzero + + + align:start position:0% +index into lists not just using nonzero +integers you know indices 0 through n or + + align:start position:0% +integers you know indices 0 through n or + + + align:start position:0% +integers you know indices 0 through n or +what-have-you but things like strings or + + align:start position:0% +what-have-you but things like strings or + + + align:start position:0% +what-have-you but things like strings or +tuples and so they're just more general + + align:start position:0% +tuples and so they're just more general + + + align:start position:0% +tuples and so they're just more general +and they're more general data structure + + align:start position:0% +and they're more general data structure + + + align:start position:0% +and they're more general data structure +then then Python lists and so they're + + align:start position:0% +then then Python lists and so they're + + + align:start position:0% +then then Python lists and so they're +very convenient I when when it comes to + + align:start position:0% +very convenient I when when it comes to + + + align:start position:0% +very convenient I when when it comes to +representing graphs and traversing + + align:start position:0% +representing graphs and traversing + + + align:start position:0% +representing graphs and traversing +graphs so the puzzle we can look at is + + align:start position:0% +graphs so the puzzle we can look at is + + + align:start position:0% +graphs so the puzzle we can look at is +as always a little bit contrived it's + + align:start position:0% +as always a little bit contrived it's + + + align:start position:0% +as always a little bit contrived it's +about a weakened dinner scheduling so + + align:start position:0% +about a weakened dinner scheduling so + + + align:start position:0% +about a weakened dinner scheduling so +you have a bunch of friends and let me + + align:start position:0% +you have a bunch of friends and let me + + + align:start position:0% +you have a bunch of friends and let me +draw your social network here or + + align:start position:0% +draw your social network here or + + + align:start position:0% +draw your social network here or +someone's social network so we won't + + align:start position:0% +someone's social network so we won't + + + align:start position:0% +someone's social network so we won't +name names but each node in this graph + + align:start position:0% +name names but each node in this graph + + + align:start position:0% +name names but each node in this graph +represents a friend and a couple more + + align:start position:0% + + + + align:start position:0% + +and so that's the set of friends a + + align:start position:0% +and so that's the set of friends a + + + align:start position:0% +and so that's the set of friends a +through H and it won't be particularly + + align:start position:0% +through H and it won't be particularly + + + align:start position:0% +through H and it won't be particularly +interesting as a graph if it just had + + align:start position:0% +interesting as a graph if it just had + + + align:start position:0% +interesting as a graph if it just had +nodes you want to add edges to it + + align:start position:0% +nodes you want to add edges to it + + + align:start position:0% +nodes you want to add edges to it +what are these edges represent well you + + align:start position:0% +what are these edges represent well you + + + align:start position:0% +what are these edges represent well you +like all of your friends but your + + align:start position:0% +like all of your friends but your + + + align:start position:0% +like all of your friends but your +friends don't necessarily like each + + align:start position:0% +friends don't necessarily like each + + + align:start position:0% +friends don't necessarily like each +other and so an edge between nodes so + + align:start position:0% +other and so an edge between nodes so + + + align:start position:0% +other and so an edge between nodes so +nodes are friends and an edge between a + + align:start position:0% +nodes are friends and an edge between a + + + align:start position:0% +nodes are friends and an edge between a +pair of nodes implies a dislike + + align:start position:0% +pair of nodes implies a dislike + + + align:start position:0% +pair of nodes implies a dislike +relationship all right I'm so be dislike + + align:start position:0% +relationship all right I'm so be dislike + + + align:start position:0% +relationship all right I'm so be dislike +see and it's symmetric you could argue + + align:start position:0% +see and it's symmetric you could argue + + + align:start position:0% +see and it's symmetric you could argue +that dislikes is not necessarily + + align:start position:0% +that dislikes is not necessarily + + + align:start position:0% +that dislikes is not necessarily +symmetric but we'll just call it that + + align:start position:0% +symmetric but we'll just call it that + + + align:start position:0% +symmetric but we'll just call it that +that implies that C dislikes B as well + + align:start position:0% +that implies that C dislikes B as well + + + align:start position:0% +that implies that C dislikes B as well +so this is not necessarily a directed + + align:start position:0% +so this is not necessarily a directed + + + align:start position:0% +so this is not necessarily a directed +graph some of the time especially when + + align:start position:0% +graph some of the time especially when + + + align:start position:0% +graph some of the time especially when +you're doing route planning going from + + align:start position:0% +you're doing route planning going from + + + align:start position:0% +you're doing route planning going from +point A to point B you have to take into + + align:start position:0% +point A to point B you have to take into + + + align:start position:0% +point A to point B you have to take into +account one way streets and so you'd + + align:start position:0% +account one way streets and so you'd + + + align:start position:0% +account one way streets and so you'd +have directed graphs but many a time + + align:start position:0% +have directed graphs but many a time + + + align:start position:0% +have directed graphs but many a time +you're you can get away with undirected + + align:start position:0% +you're you can get away with undirected + + + align:start position:0% +you're you can get away with undirected +graphs so you just the existence of an + + align:start position:0% +graphs so you just the existence of an + + + align:start position:0% +graphs so you just the existence of an +edge between B and C implies that in a + + align:start position:0% +edge between B and C implies that in a + + + align:start position:0% +edge between B and C implies that in a +traversal you can get from B to C or C + + align:start position:0% +traversal you can get from B to C or C + + + align:start position:0% +traversal you can get from B to C or C +to B and it there's no direction there + + align:start position:0% +to B and it there's no direction there + + + align:start position:0% +to B and it there's no direction there +and so I'm gonna fill in the rest of + + align:start position:0% +and so I'm gonna fill in the rest of + + + align:start position:0% +and so I'm gonna fill in the rest of +this and then get to the question that + + align:start position:0% +this and then get to the question that + + + align:start position:0% +this and then get to the question that +we want to answer and so that's your + + align:start position:0% +we want to answer and so that's your + + + align:start position:0% +we want to answer and so that's your +your friend graph and it also has these + + align:start position:0% +your friend graph and it also has these + + + align:start position:0% +your friend graph and it also has these +six or seven dislike relationships and + + align:start position:0% +six or seven dislike relationships and + + + align:start position:0% +six or seven dislike relationships and +your job is to well keep all your + + align:start position:0% +your job is to well keep all your + + + align:start position:0% +your job is to well keep all your +friends happy i and at the way you're + + align:start position:0% +friends happy i and at the way you're + + + align:start position:0% +friends happy i and at the way you're +going to do that is by is by having a + + align:start position:0% +going to do that is by is by having a + + + align:start position:0% +going to do that is by is by having a +couple of parties on the weekend so this + + align:start position:0% +couple of parties on the weekend so this + + + align:start position:0% +couple of parties on the weekend so this +is a regular weekend you know let's call + + align:start position:0% +is a regular weekend you know let's call + + + align:start position:0% +is a regular weekend you know let's call +it the Friday and Saturday Friday and + + align:start position:0% +it the Friday and Saturday Friday and + + + align:start position:0% +it the Friday and Saturday Friday and +Saturday night parties and that the only + + align:start position:0% +Saturday night parties and that the only + + + align:start position:0% +Saturday night parties and that the only +constraint are actually there's two + + align:start position:0% +constraint are actually there's two + + + align:start position:0% +constraint are actually there's two +constraints there's the two constraints + + align:start position:0% +constraints there's the two constraints + + + align:start position:0% +constraints there's the two constraints +that you need to fall + + align:start position:0% +that you need to fall + + + align:start position:0% +that you need to fall +are satisfied then you have these two + + align:start position:0% +are satisfied then you have these two + + + align:start position:0% +are satisfied then you have these two +parties so you have your Friday party in + + align:start position:0% +parties so you have your Friday party in + + + align:start position:0% +parties so you have your Friday party in +your Saturday party is you can't leave + + align:start position:0% +your Saturday party is you can't leave + + + align:start position:0% +your Saturday party is you can't leave +anybody out right so you effectively the + + align:start position:0% +anybody out right so you effectively the + + + align:start position:0% +anybody out right so you effectively the +constraint is on each friend comes to + + align:start position:0% + + + + align:start position:0% + +exactly one party no one gets left out + + align:start position:0% +exactly one party no one gets left out + + + align:start position:0% +exactly one party no one gets left out +no one comes to both so that's fair and + + align:start position:0% +no one comes to both so that's fair and + + + align:start position:0% +no one comes to both so that's fair and +then the second constraint as you can + + align:start position:0% +then the second constraint as you can + + + align:start position:0% +then the second constraint as you can +probably guess is no pair of friends who + + align:start position:0% +probably guess is no pair of friends who + + + align:start position:0% +probably guess is no pair of friends who +dislike each other they're not friendly + + align:start position:0% +dislike each other they're not friendly + + + align:start position:0% +dislike each other they're not friendly +they're your friends can be invited on + + align:start position:0% +they're your friends can be invited on + + + align:start position:0% +they're your friends can be invited on +the same day + + align:start position:0% + + + + align:start position:0% + +and so you want an algorithm that is + + align:start position:0% +and so you want an algorithm that is + + + align:start position:0% +and so you want an algorithm that is +going to give you a schedule and + + align:start position:0% +going to give you a schedule and + + + align:start position:0% +going to give you a schedule and +obviously the schedule is not + + align:start position:0% +obviously the schedule is not + + + align:start position:0% +obviously the schedule is not +necessarily unique I mean if you had a + + align:start position:0% +necessarily unique I mean if you had a + + + align:start position:0% +necessarily unique I mean if you had a +bunch of happy-go-lucky low overhead + + align:start position:0% +bunch of happy-go-lucky low overhead + + + align:start position:0% +bunch of happy-go-lucky low overhead +friends you know they all like each + + align:start position:0% +friends you know they all like each + + + align:start position:0% +friends you know they all like each +other and you can just randomly break + + align:start position:0% +other and you can just randomly break + + + align:start position:0% +other and you can just randomly break +them up into two groups you can think of + + align:start position:0% +them up into two groups you can think of + + + align:start position:0% +them up into two groups you can think of +it as a partition a partition this is a + + align:start position:0% +it as a partition a partition this is a + + + align:start position:0% +it as a partition a partition this is a +grouping where then you have anything at + + align:start position:0% +grouping where then you have anything at + + + align:start position:0% +grouping where then you have anything at +a set of nodes for example and you + + align:start position:0% +a set of nodes for example and you + + + align:start position:0% +a set of nodes for example and you +partition it you're essentially saying + + align:start position:0% +partition it you're essentially saying + + + align:start position:0% +partition it you're essentially saying +you're breaking it up into two groups + + align:start position:0% +you're breaking it up into two groups + + + align:start position:0% +you're breaking it up into two groups +such that each node is in exactly one + + align:start position:0% +such that each node is in exactly one + + + align:start position:0% +such that each node is in exactly one +group and each node and then you have + + align:start position:0% +group and each node and then you have + + + align:start position:0% +group and each node and then you have +another property associated with the + + align:start position:0% +another property associated with the + + + align:start position:0% +another property associated with the +partition that corresponds to the edges + + align:start position:0% +partition that corresponds to the edges + + + align:start position:0% +partition that corresponds to the edges +between these nodes but we'll get to + + align:start position:0% +between these nodes but we'll get to + + + align:start position:0% +between these nodes but we'll get to +that in just just a minute + + align:start position:0% +that in just just a minute + + + align:start position:0% +that in just just a minute +yeah go ahead buddy so so the purpose of + + align:start position:0% +yeah go ahead buddy so so the purpose of + + + align:start position:0% +yeah go ahead buddy so so the purpose of +this puzzle is to determine whether you + + align:start position:0% +this puzzle is to determine whether you + + + align:start position:0% +this puzzle is to determine whether you +can actually do this or not + + align:start position:0% +can actually do this or not + + + align:start position:0% +can actually do this or not +and so you are certainly welcome to when + + align:start position:0% +and so you are certainly welcome to when + + + align:start position:0% +and so you are certainly welcome to when +you write a computer program or when we + + align:start position:0% +you write a computer program or when we + + + align:start position:0% +you write a computer program or when we +write a computer program here it might + + align:start position:0% +write a computer program here it might + + + align:start position:0% +write a computer program here it might +say no can do you know find a different + + align:start position:0% +say no can do you know find a different + + + align:start position:0% +say no can do you know find a different +set of friends or maybe identify a + + align:start position:0% +set of friends or maybe identify a + + + align:start position:0% +set of friends or maybe identify a +problem case you know this one person + + align:start position:0% +problem case you know this one person + + + align:start position:0% +problem case you know this one person +who dislikes + + align:start position:0% +who dislikes + + + align:start position:0% +who dislikes +all of your other friends maybe you + + align:start position:0% +all of your other friends maybe you + + + align:start position:0% +all of your other friends maybe you +should drop that person right and so so + + align:start position:0% +should drop that person right and so so + + + align:start position:0% +should drop that person right and so so +you can imagine that I that you would + + align:start position:0% +you can imagine that I that you would + + + align:start position:0% +you can imagine that I that you would +not necessarily be able to satisfy these + + align:start position:0% +not necessarily be able to satisfy these + + + align:start position:0% +not necessarily be able to satisfy these +two constraints for all graphs right and + + align:start position:0% +two constraints for all graphs right and + + + align:start position:0% +two constraints for all graphs right and +so that's really the essence of the + + align:start position:0% +so that's really the essence of the + + + align:start position:0% +so that's really the essence of the +puzzle for what kind of graphs and this + + align:start position:0% +puzzle for what kind of graphs and this + + + align:start position:0% +puzzle for what kind of graphs and this +it turns out they're a fairly famous + + align:start position:0% +it turns out they're a fairly famous + + + align:start position:0% +it turns out they're a fairly famous +kind of graph that's does this puzzle + + align:start position:0% +kind of graph that's does this puzzle + + + align:start position:0% +kind of graph that's does this puzzle +have a solution right and so you you you + + align:start position:0% +have a solution right and so you you you + + + align:start position:0% +have a solution right and so you you you +have to look at this and you kind of go + + align:start position:0% +have to look at this and you kind of go + + + align:start position:0% +have to look at this and you kind of go +and the first thing that occurred to you + + align:start position:0% +and the first thing that occurred to you + + + align:start position:0% +and the first thing that occurred to you +was hey if I had if + + align:start position:0% +was hey if I had if + + + align:start position:0% +was hey if I had if +gah if I invite f1 Friday I have to + + align:start position:0% +gah if I invite f1 Friday I have to + + + align:start position:0% +gah if I invite f1 Friday I have to +invite G and H on Saturday but then G + + align:start position:0% +invite G and H on Saturday but then G + + + align:start position:0% +invite G and H on Saturday but then G +and H don't like each other right so + + align:start position:0% +and H don't like each other right so + + + align:start position:0% +and H don't like each other right so +that's a problem right and so in this + + align:start position:0% +that's a problem right and so in this + + + align:start position:0% +that's a problem right and so in this +particular case you've identified this + + align:start position:0% +particular case you've identified this + + + align:start position:0% +particular case you've identified this +cycle that indicates that this problem + + align:start position:0% +cycle that indicates that this problem + + + align:start position:0% +cycle that indicates that this problem +is not solvable but let's say that + + align:start position:0% +is not solvable but let's say that + + + align:start position:0% +is not solvable but let's say that +somehow you've located G and you past + + align:start position:0% +somehow you've located G and you past + + + align:start position:0% +somehow you've located G and you past +they've patched up alright so so you end + + align:start position:0% +they've patched up alright so so you end + + + align:start position:0% +they've patched up alright so so you end +up having you know fairly complex graph + + align:start position:0% +up having you know fairly complex graph + + + align:start position:0% +up having you know fairly complex graph +structure that looks like this right and + + align:start position:0% +structure that looks like this right and + + + align:start position:0% +structure that looks like this right and +now what happens now is there is there a + + align:start position:0% +now what happens now is there is there a + + + align:start position:0% +now what happens now is there is there a +solution to this problem this particular + + align:start position:0% +solution to this problem this particular + + + align:start position:0% +solution to this problem this particular +puzzle I mean a can come on any day so + + align:start position:0% +puzzle I mean a can come on any day so + + + align:start position:0% +puzzle I mean a can come on any day so +let's ignore a I is easy + + align:start position:0% +let's ignore a I is easy + + + align:start position:0% +let's ignore a I is easy +suppose you invite you could try and + + align:start position:0% +suppose you invite you could try and + + + align:start position:0% +suppose you invite you could try and +figure this out by saying let's let's go + + align:start position:0% +figure this out by saying let's let's go + + + align:start position:0% +figure this out by saying let's let's go +ahead and invite invite be on on Friday + + align:start position:0% +ahead and invite invite be on on Friday + + + align:start position:0% +ahead and invite invite be on on Friday +so what does that imply that immediately + + align:start position:0% +so what does that imply that immediately + + + align:start position:0% +so what does that imply that immediately +implies that C is on Saturday right what + + align:start position:0% +implies that C is on Saturday right what + + + align:start position:0% +implies that C is on Saturday right what +does that imply D is on Friday right so + + align:start position:0% +does that imply D is on Friday right so + + + align:start position:0% +does that imply D is on Friday right so +you see you see how this is going to go + + align:start position:0% +you see you see how this is going to go + + + align:start position:0% +you see you see how this is going to go +what does that imply enf are on are on + + align:start position:0% +what does that imply enf are on are on + + + align:start position:0% +what does that imply enf are on are on +Saturday so I have e and F on Saturday + + align:start position:0% +Saturday so I have e and F on Saturday + + + align:start position:0% +Saturday so I have e and F on Saturday +ok and then what does that imply the FFF + + align:start position:0% +ok and then what does that imply the FFF + + + align:start position:0% +ok and then what does that imply the FFF +being on Saturday implies that G H and I + + align:start position:0% +being on Saturday implies that G H and I + + + align:start position:0% +being on Saturday implies that G H and I +have to be on on Friday right and then I + + align:start position:0% +have to be on on Friday right and then I + + + align:start position:0% +have to be on on Friday right and then I +don't forget a so let's just take a in + + align:start position:0% +don't forget a so let's just take a in + + + align:start position:0% +don't forget a so let's just take a in +here to even things out + + align:start position:0% +here to even things out + + + align:start position:0% +here to even things out +all right and so so we kind of did an + + align:start position:0% +all right and so so we kind of did an + + + align:start position:0% +all right and so so we kind of did an +algorithm here we executed an algorithm + + align:start position:0% +algorithm here we executed an algorithm + + + align:start position:0% +algorithm here we executed an algorithm +right and it it turns out that as graphs + + align:start position:0% +right and it it turns out that as graphs + + + align:start position:0% +right and it it turns out that as graphs +that can be partitioned in this manner + + align:start position:0% +that can be partitioned in this manner + + + align:start position:0% +that can be partitioned in this manner +are have a special name are they called + + align:start position:0% +are have a special name are they called + + + align:start position:0% +are have a special name are they called +up bipartite graphs + + align:start position:0% +up bipartite graphs + + + align:start position:0% +up bipartite graphs +bipartite graphs I'll write it out and + + align:start position:0% +bipartite graphs I'll write it out and + + + align:start position:0% +bipartite graphs I'll write it out and +the the reason they call bipartite + + align:start position:0% +the the reason they call bipartite + + + align:start position:0% +the the reason they call bipartite +graphs is if you have a bipartite graph + + align:start position:0% +graphs is if you have a bipartite graph + + + align:start position:0% +graphs is if you have a bipartite graph +you can always draw it in this fashion + + align:start position:0% + + + + align:start position:0% + +where you have a c EF and then you have + + align:start position:0% +where you have a c EF and then you have + + + align:start position:0% +where you have a c EF and then you have +B D G H I such that you never see edges + + align:start position:0% +B D G H I such that you never see edges + + + align:start position:0% +B D G H I such that you never see edges +like this or like that all the edges go + + align:start position:0% +like this or like that all the edges go + + + align:start position:0% +like this or like that all the edges go +from left to right or right to left + + align:start position:0% +from left to right or right to left + + + align:start position:0% +from left to right or right to left +they're undirected okay so that's really + + align:start position:0% +they're undirected okay so that's really + + + align:start position:0% +they're undirected okay so that's really +a a bipartite graph and if I draw this + + align:start position:0% +a a bipartite graph and if I draw this + + + align:start position:0% +a a bipartite graph and if I draw this +out oh don't need that C goes to B and D + + align:start position:0% +out oh don't need that C goes to B and D + + + align:start position:0% +out oh don't need that C goes to B and D +it goes nowhere he goes to D and F goes + + align:start position:0% +it goes nowhere he goes to D and F goes + + + align:start position:0% +it goes nowhere he goes to D and F goes +to a bunch of different places yeah so + + align:start position:0% +to a bunch of different places yeah so + + + align:start position:0% +to a bunch of different places yeah so +you're allowed to have this would still + + align:start position:0% +you're allowed to have this would still + + + align:start position:0% +you're allowed to have this would still +be about I want this is not the graph + + align:start position:0% +be about I want this is not the graph + + + align:start position:0% +be about I want this is not the graph +that we had but it's not that the edges + + align:start position:0% +that we had but it's not that the edges + + + align:start position:0% +that we had but it's not that the edges +can't be crossing edges okay they just + + align:start position:0% +can't be crossing edges okay they just + + + align:start position:0% +can't be crossing edges okay they just +all have to go from left to right you + + align:start position:0% +all have to go from left to right you + + + align:start position:0% +all have to go from left to right you +just can't have an edge between a and C + + align:start position:0% +just can't have an edge between a and C + + + align:start position:0% +just can't have an edge between a and C +or C and a you can't have an edge + + align:start position:0% +or C and a you can't have an edge + + + align:start position:0% +or C and a you can't have an edge +between D and H etc right so you you + + align:start position:0% +between D and H etc right so you you + + + align:start position:0% +between D and H etc right so you you +want you have to be able to separate out + + align:start position:0% +want you have to be able to separate out + + + align:start position:0% +want you have to be able to separate out +the nodes such that and they're no edges + + align:start position:0% +the nodes such that and they're no edges + + + align:start position:0% +the nodes such that and they're no edges +in this set of nodes you know it's just + + align:start position:0% +in this set of nodes you know it's just + + + align:start position:0% +in this set of nodes you know it's just +between these set of nodes and no edges + + align:start position:0% +between these set of nodes and no edges + + + align:start position:0% +between these set of nodes and no edges +between that set of nodes and this is + + align:start position:0% +between that set of nodes and this is + + + align:start position:0% +between that set of nodes and this is +just a topological property that I + + align:start position:0% +just a topological property that I + + + align:start position:0% +just a topological property that I +cursed wants to bipartite graphs and + + align:start position:0% +cursed wants to bipartite graphs and + + + align:start position:0% +cursed wants to bipartite graphs and +there's another property that + + align:start position:0% +there's another property that + + + align:start position:0% +there's another property that +essentially is equivalent to our puzzle + + align:start position:0% +essentially is equivalent to our puzzle + + + align:start position:0% +essentially is equivalent to our puzzle +which says bipartite graphs are + + align:start position:0% +which says bipartite graphs are + + + align:start position:0% +which says bipartite graphs are +two colorable and it's obvious as to why + + align:start position:0% +two colorable and it's obvious as to why + + + align:start position:0% +two colorable and it's obvious as to why +I buy but bipartite graph is two + + align:start position:0% +I buy but bipartite graph is two + + + align:start position:0% +I buy but bipartite graph is two +colorable and what does it mean to be + + align:start position:0% +colorable and what does it mean to be + + + align:start position:0% +colorable and what does it mean to be +two colorable well you need to color + + align:start position:0% +two colorable well you need to color + + + align:start position:0% +two colorable well you need to color +each node with two colors in this case + + align:start position:0% +each node with two colors in this case + + + align:start position:0% +each node with two colors in this case +Friday and Saturday such that no pair of + + align:start position:0% +Friday and Saturday such that no pair of + + + align:start position:0% +Friday and Saturday such that no pair of +nodes with an edge between them have the + + align:start position:0% +nodes with an edge between them have the + + + align:start position:0% +nodes with an edge between them have the +same color so exactly equivalent to what + + align:start position:0% +same color so exactly equivalent to what + + + align:start position:0% +same color so exactly equivalent to what +we've talked about here so our goal now + + align:start position:0% +we've talked about here so our goal now + + + align:start position:0% +we've talked about here so our goal now +is to discover whether a bipartite graph + + align:start position:0% +is to discover whether a bipartite graph + + + align:start position:0% +is to discover whether a bipartite graph +I've already given graph excuse me is + + align:start position:0% +I've already given graph excuse me is + + + align:start position:0% +I've already given graph excuse me is +bipartite or not once you know that a + + align:start position:0% +bipartite or not once you know that a + + + align:start position:0% +bipartite or not once you know that a +graph is bipartite you know it's two + + align:start position:0% +graph is bipartite you know it's two + + + align:start position:0% +graph is bipartite you know it's two +colorable you know it's a solution to + + align:start position:0% +colorable you know it's a solution to + + + align:start position:0% +colorable you know it's a solution to +our to our problem to our puzzle problem + + align:start position:0% +our to our problem to our puzzle problem + + + align:start position:0% +our to our problem to our puzzle problem +okay and of course in order to do this + + align:start position:0% +okay and of course in order to do this + + + align:start position:0% +okay and of course in order to do this +and if you had a graph but you had + + align:start position:0% +and if you had a graph but you had + + + align:start position:0% +and if you had a graph but you had +thousands of friends and perhaps tens of + + align:start position:0% +thousands of friends and perhaps tens of + + + align:start position:0% +thousands of friends and perhaps tens of +thousands of edges and you need to + + align:start position:0% +thousands of edges and you need to + + + align:start position:0% +thousands of edges and you need to +discover it's not your dinner problem + + align:start position:0% +discover it's not your dinner problem + + + align:start position:0% +discover it's not your dinner problem +maybe but you need to discover whether + + align:start position:0% +maybe but you need to discover whether + + + align:start position:0% +maybe but you need to discover whether +the graph is two colorable or not then + + align:start position:0% +the graph is two colorable or not then + + + align:start position:0% +the graph is two colorable or not then +you need to write a computer program for + + align:start position:0% +you need to write a computer program for + + + align:start position:0% +you need to write a computer program for +this you need a graph representation you + + align:start position:0% +this you need a graph representation you + + + align:start position:0% +this you need a graph representation you +need to do this traversal etc etc go + + align:start position:0% +need to do this traversal etc etc go + + + align:start position:0% +need to do this traversal etc etc go +ahead Josh I guess they're equivalent + + align:start position:0% +ahead Josh I guess they're equivalent + + + align:start position:0% +ahead Josh I guess they're equivalent +different definitions absolutely right + + align:start position:0% +different definitions absolutely right + + + align:start position:0% +different definitions absolutely right +because that what would happen is if you + + align:start position:0% +because that what would happen is if you + + + align:start position:0% +because that what would happen is if you +can color it then it means that you can + + align:start position:0% +can color it then it means that you can + + + align:start position:0% +can color it then it means that you can +take all of the red colors you read + + align:start position:0% +take all of the red colors you read + + + align:start position:0% +take all of the red colors you read +could be equivalent to Friday and and in + + align:start position:0% +could be equivalent to Friday and and in + + + align:start position:0% +could be equivalent to Friday and and in +blue could be equivalent to Saturday and + + align:start position:0% +blue could be equivalent to Saturday and + + + align:start position:0% +blue could be equivalent to Saturday and +all of the red colors could be placed on + + align:start position:0% +all of the red colors could be placed on + + + align:start position:0% +all of the red colors could be placed on +the left and and the the blue on the + + align:start position:0% +the left and and the the blue on the + + + align:start position:0% +the left and and the the blue on the +right buddy + + align:start position:0% + + + + align:start position:0% + +yes that's that that's that there's + + align:start position:0% +yes that's that that's that there's + + + align:start position:0% +yes that's that that's that there's +always pathological cases and they're + + align:start position:0% +always pathological cases and they're + + + align:start position:0% +always pathological cases and they're +usually things that get swept under the + + align:start position:0% +usually things that get swept under the + + + align:start position:0% +usually things that get swept under the +rug but one colorable is is it is + + align:start position:0% +rug but one colorable is is it is + + + align:start position:0% +rug but one colorable is is it is +considered too colorable you can color + + align:start position:0% +considered too colorable you can color + + + align:start position:0% +considered too colorable you can color +it with two colors that's really what it + + align:start position:0% +it with two colors that's really what it + + + align:start position:0% +it with two colors that's really what it +is let's talk about cycles to get a + + align:start position:0% +is let's talk about cycles to get a + + + align:start position:0% +is let's talk about cycles to get a +sense for this property so immediately I + + align:start position:0% +sense for this property so immediately I + + + align:start position:0% +sense for this property so immediately I +think you recognize that when you have + + align:start position:0% +think you recognize that when you have + + + align:start position:0% +think you recognize that when you have +something like I figured what it was + + align:start position:0% +something like I figured what it was + + + align:start position:0% +something like I figured what it was +exactly f GI or F G H whatever that if + + align:start position:0% +exactly f GI or F G H whatever that if + + + align:start position:0% +exactly f GI or F G H whatever that if +you had a cycle like this + + align:start position:0% +you had a cycle like this + + + align:start position:0% +you had a cycle like this +that a graph is not bipartite right the + + align:start position:0% +that a graph is not bipartite right the + + + align:start position:0% +that a graph is not bipartite right the +three cycle is not bipartite is any + + align:start position:0% +three cycle is not bipartite is any + + + align:start position:0% +three cycle is not bipartite is any +cycle a problem if I have a cycle in the + + align:start position:0% +cycle a problem if I have a cycle in the + + + align:start position:0% +cycle a problem if I have a cycle in the +graph which means that I can go from one + + align:start position:0% +graph which means that I can go from one + + + align:start position:0% +graph which means that I can go from one +node back to the same node through a + + align:start position:0% +node back to the same node through a + + + align:start position:0% +node back to the same node through a +sequence of edges and obviously + + align:start position:0% +sequence of edges and obviously + + + align:start position:0% +sequence of edges and obviously +traversing nodes do I have a problem is + + align:start position:0% +traversing nodes do I have a problem is + + + align:start position:0% +traversing nodes do I have a problem is +that it can be immediately declared that + + align:start position:0% +that it can be immediately declared that + + + align:start position:0% +that it can be immediately declared that +the graph is not bipartite + + align:start position:0% +the graph is not bipartite + + + align:start position:0% +the graph is not bipartite +yeah go ahead Julia why not + + align:start position:0% + + + + align:start position:0% + +ah yeah that's exactly what I wanted to + + align:start position:0% +ah yeah that's exactly what I wanted to + + + align:start position:0% +ah yeah that's exactly what I wanted to +bring up so if I had something like ABCD + + align:start position:0% +bring up so if I had something like ABCD + + + align:start position:0% +bring up so if I had something like ABCD +right + + align:start position:0% +right + + + align:start position:0% +right +that's clearly a a cyclic graph and I I + + align:start position:0% +that's clearly a a cyclic graph and I I + + + align:start position:0% +that's clearly a a cyclic graph and I I +could put um a and C out here and V and + + align:start position:0% +could put um a and C out here and V and + + + align:start position:0% +could put um a and C out here and V and +D up here and clearly there's no edge + + align:start position:0% +D up here and clearly there's no edge + + + align:start position:0% +D up here and clearly there's no edge +between a and C there's no edge between + + align:start position:0% +between a and C there's no edge between + + + align:start position:0% +between a and C there's no edge between +B and D there's an edge between a and B + + align:start position:0% +B and D there's an edge between a and B + + + align:start position:0% +B and D there's an edge between a and B +there's an edge between C and D and + + align:start position:0% +there's an edge between C and D and + + + align:start position:0% +there's an edge between C and D and +there's also an edge between a and G and + + align:start position:0% +there's also an edge between a and G and + + + align:start position:0% +there's also an edge between a and G and +C and B so as I mentioned you're allowed + + align:start position:0% +C and B so as I mentioned you're allowed + + + align:start position:0% +C and B so as I mentioned you're allowed +crossing edges right they all have to go + + align:start position:0% +crossing edges right they all have to go + + + align:start position:0% +crossing edges right they all have to go +from left to right or right to left + + align:start position:0% +from left to right or right to left + + + align:start position:0% +from left to right or right to left +whichever way you're looking at it so + + align:start position:0% +whichever way you're looking at it so + + + align:start position:0% +whichever way you're looking at it so +interesting enough and this is two + + align:start position:0% +interesting enough and this is two + + + align:start position:0% +interesting enough and this is two +colorable on but when you get to when + + align:start position:0% +colorable on but when you get to when + + + align:start position:0% +colorable on but when you get to when +you get to odd cycles so I'll draw one + + align:start position:0% +you get to odd cycles so I'll draw one + + + align:start position:0% +you get to odd cycles so I'll draw one +out here in the middle and let's say I + + align:start position:0% +out here in the middle and let's say I + + + align:start position:0% +out here in the middle and let's say I +want a mark these nodes the names but + + align:start position:0% +want a mark these nodes the names but + + + align:start position:0% +want a mark these nodes the names but +let's say that you have a five cycle now + + align:start position:0% +let's say that you have a five cycle now + + + align:start position:0% +let's say that you have a five cycle now +right if you have a five cycle think + + align:start position:0% +right if you have a five cycle think + + + align:start position:0% +right if you have a five cycle think +about it you you you're going to go + + align:start position:0% +about it you you you're going to go + + + align:start position:0% +about it you you you're going to go +color this red so let me just go ahead + + align:start position:0% +color this red so let me just go ahead + + + align:start position:0% +color this red so let me just go ahead +and say this is red which means this + + align:start position:0% +and say this is red which means this + + + align:start position:0% +and say this is red which means this +needs to be blue that needs to be blue + + align:start position:0% +needs to be blue that needs to be blue + + + align:start position:0% +needs to be blue that needs to be blue +this blue implies this needs to be red + + align:start position:0% +this blue implies this needs to be red + + + align:start position:0% +this blue implies this needs to be red + now implies that this needs to be + + align:start position:0% + now implies that this needs to be + + + align:start position:0% + now implies that this needs to be +blue and it's like whoops that's a + + align:start position:0% +blue and it's like whoops that's a + + + align:start position:0% +blue and it's like whoops that's a +problem right so interestingly enough + + align:start position:0% +problem right so interestingly enough + + + align:start position:0% +problem right so interestingly enough +the odd evenness or the parody of a + + align:start position:0% +the odd evenness or the parody of a + + + align:start position:0% +the odd evenness or the parody of a +cycle determines whether a graph is + + align:start position:0% +cycle determines whether a graph is + + + align:start position:0% +cycle determines whether a graph is +bipartite or not it doesn't mean that + + align:start position:0% +bipartite or not it doesn't mean that + + + align:start position:0% +bipartite or not it doesn't mean that +that I that a graph that only has four + + align:start position:0% +that I that a graph that only has four + + + align:start position:0% +that I that a graph that only has four +cycles in it is is is necessarily + + align:start position:0% +cycles in it is is is necessarily + + + align:start position:0% +cycles in it is is is necessarily +bipartite because they they could be + + align:start position:0% +bipartite because they they could be + + + align:start position:0% +bipartite because they they could be +other reasons for it not to be not to be + + align:start position:0% +other reasons for it not to be not to be + + + align:start position:0% +other reasons for it not to be not to be +bipartite because you know you don't + + align:start position:0% +bipartite because you know you don't + + + align:start position:0% +bipartite because you know you don't +know but the other cycles in the graph + + align:start position:0% +know but the other cycles in the graph + + + align:start position:0% +know but the other cycles in the graph +they could be you say it's only up to + + align:start position:0% +they could be you say it's only up to + + + align:start position:0% +they could be you say it's only up to +four cycles well there could be a three + + align:start position:0% +four cycles well there could be a three + + + align:start position:0% +four cycles well there could be a three +cycle in it and and things get pretty + + align:start position:0% +cycle in it and and things get pretty + + + align:start position:0% +cycle in it and and things get pretty +complicated when you have things like + + align:start position:0% +complicated when you have things like + + + align:start position:0% +complicated when you have things like +like that there's a lot of cycles in + + align:start position:0% +like that there's a lot of cycles in + + + align:start position:0% +like that there's a lot of cycles in +here this is a cycle like that there's a + + align:start position:0% +here this is a cycle like that there's a + + + align:start position:0% +here this is a cycle like that there's a +cycle like this and the moment you put + + align:start position:0% +cycle like this and the moment you put + + + align:start position:0% +cycle like this and the moment you put +an edge in here now you're saying this + + align:start position:0% +an edge in here now you're saying this + + + align:start position:0% +an edge in here now you're saying this +goes over here it goes like this + + align:start position:0% +goes over here it goes like this + + + align:start position:0% +goes over here it goes like this +there's a three cycle here but even if + + align:start position:0% +there's a three cycle here but even if + + + align:start position:0% +there's a three cycle here but even if +this didn't exist there would be a five + + align:start position:0% +this didn't exist there would be a five + + + align:start position:0% +this didn't exist there would be a five +cycle etc etc so there's a lot of cycles + + align:start position:0% +cycle etc etc so there's a lot of cycles + + + align:start position:0% +cycle etc etc so there's a lot of cycles +and graphs right and your algorithm + + align:start position:0% +and graphs right and your algorithm + + + align:start position:0% +and graphs right and your algorithm +essentially needs to ensure that for + + align:start position:0% +essentially needs to ensure that for + + + align:start position:0% +essentially needs to ensure that for +that every cycle is an even cycle okay + + align:start position:0% +that every cycle is an even cycle okay + + + align:start position:0% +that every cycle is an even cycle okay +and that is exactly equivalent to + + align:start position:0% +and that is exactly equivalent to + + + align:start position:0% +and that is exactly equivalent to +coloring it with two colors okay so um + + align:start position:0% +coloring it with two colors okay so um + + + align:start position:0% +coloring it with two colors okay so um +we I obviously need to have a way of + + align:start position:0% +we I obviously need to have a way of + + + align:start position:0% +we I obviously need to have a way of +stopping here in the sense that when you + + align:start position:0% +stopping here in the sense that when you + + + align:start position:0% +stopping here in the sense that when you +have a cycle you you you're going to + + align:start position:0% +have a cycle you you you're going to + + + align:start position:0% +have a cycle you you you're going to +come back and the cycle may may be fine + + align:start position:0% +come back and the cycle may may be fine + + + align:start position:0% +come back and the cycle may may be fine +because it's an even cycle but you + + align:start position:0% +because it's an even cycle but you + + + align:start position:0% +because it's an even cycle but you +obviously can't keep going around the + + align:start position:0% +obviously can't keep going around the + + + align:start position:0% +obviously can't keep going around the +cycle without terminating in a computer + + align:start position:0% +cycle without terminating in a computer + + + align:start position:0% +cycle without terminating in a computer +program so we if we're going to have to + + align:start position:0% +program so we if we're going to have to + + + align:start position:0% +program so we if we're going to have to +do a recursive search which has + + align:start position:0% +do a recursive search which has + + + align:start position:0% +do a recursive search which has +interesting termination conditions you + + align:start position:0% +interesting termination conditions you + + + align:start position:0% +interesting termination conditions you +know as opposed to the + + align:start position:0% +know as opposed to the + + + align:start position:0% +know as opposed to the +divide-and-conquer I or even the + + align:start position:0% +divide-and-conquer I or even the + + + align:start position:0% +divide-and-conquer I or even the +iterative enumeration that we did where + + align:start position:0% +iterative enumeration that we did where + + + align:start position:0% +iterative enumeration that we did where +it was pretty clear what the termination + + align:start position:0% +it was pretty clear what the termination + + + align:start position:0% +it was pretty clear what the termination +condition was that the base case was + + align:start position:0% +condition was that the base case was + + + align:start position:0% +condition was that the base case was +fairly straightforward because you came + + align:start position:0% +fairly straightforward because you came + + + align:start position:0% +fairly straightforward because you came +down to a list of length one or you had + + align:start position:0% +down to a list of length one or you had + + + align:start position:0% +down to a list of length one or you had +something where you broke things up to + + align:start position:0% +something where you broke things up to + + + align:start position:0% +something where you broke things up to +the point where you had really small + + align:start position:0% +the point where you had really small + + + align:start position:0% +the point where you had really small +problems and that corresponded to your + + align:start position:0% +problems and that corresponded to your + + + align:start position:0% +problems and that corresponded to your +base case right but cycle detection + + align:start position:0% +base case right but cycle detection + + + align:start position:0% +base case right but cycle detection +especially when you're doing recursive + + align:start position:0% +especially when you're doing recursive + + + align:start position:0% +especially when you're doing recursive +traversal can be pretty tricky right and + + align:start position:0% +traversal can be pretty tricky right and + + + align:start position:0% +traversal can be pretty tricky right and +we also of course as I said initially we + + align:start position:0% +we also of course as I said initially we + + + align:start position:0% +we also of course as I said initially we +have to be able to to represent this + + align:start position:0% +have to be able to to represent this + + + align:start position:0% +have to be able to to represent this +graph structure right um you could + + align:start position:0% +graph structure right um you could + + + align:start position:0% +graph structure right um you could +represent it as a matrix right there's + + align:start position:0% +represent it as a matrix right there's + + + align:start position:0% +represent it as a matrix right there's +you could say well I hate dictionaries I + + align:start position:0% +you could say well I hate dictionaries I + + + align:start position:0% +you could say well I hate dictionaries I +I love lists and that's all I'm gonna + + align:start position:0% +I love lists and that's all I'm gonna + + + align:start position:0% +I love lists and that's all I'm gonna +use for the rest of my life right not a + + align:start position:0% +use for the rest of my life right not a + + + align:start position:0% +use for the rest of my life right not a +good idea but if you did that uh you + + align:start position:0% +good idea but if you did that uh you + + + align:start position:0% +good idea but if you did that uh you +could certainly represent the graphs as + + align:start position:0% +could certainly represent the graphs as + + + align:start position:0% +could certainly represent the graphs as +a as a matrix or a two dimensional list + + align:start position:0% +a as a matrix or a two dimensional list + + + align:start position:0% +a as a matrix or a two dimensional list +it's called an adjacency matrix + + align:start position:0% +it's called an adjacency matrix + + + align:start position:0% +it's called an adjacency matrix +representation and + + align:start position:0% +representation and + + + align:start position:0% +representation and +want to write it out but effectively + + align:start position:0% +want to write it out but effectively + + + align:start position:0% +want to write it out but effectively +your rows are all the nodes and your + + align:start position:0% +your rows are all the nodes and your + + + align:start position:0% +your rows are all the nodes and your +columns are all the nodes and you you + + align:start position:0% +columns are all the nodes and you you + + + align:start position:0% +columns are all the nodes and you you +have a 1 or a 0 in the appropriate + + align:start position:0% +have a 1 or a 0 in the appropriate + + + align:start position:0% +have a 1 or a 0 in the appropriate +location based on whether there's an + + align:start position:0% +location based on whether there's an + + + align:start position:0% +location based on whether there's an +edge between the row node and the column + + align:start position:0% +edge between the row node and the column + + + align:start position:0% +edge between the row node and the column +no right and you can certainly do that + + align:start position:0% +no right and you can certainly do that + + + align:start position:0% +no right and you can certainly do that +and it's most for most cases in most + + align:start position:0% +and it's most for most cases in most + + + align:start position:0% +and it's most for most cases in most +cases it's a painful representation I do + + align:start position:0% +cases it's a painful representation I do + + + align:start position:0% +cases it's a painful representation I do +deal with eye graphs are much easier to + + align:start position:0% +deal with eye graphs are much easier to + + + align:start position:0% +deal with eye graphs are much easier to +deal with many especially when you want + + align:start position:0% +deal with many especially when you want + + + align:start position:0% +deal with many especially when you want +to do traversal so we'll stick with the + + align:start position:0% +to do traversal so we'll stick with the + + + align:start position:0% +to do traversal so we'll stick with the +graph structure all right um so let's + + align:start position:0% +graph structure all right um so let's + + + align:start position:0% +graph structure all right um so let's +talk algorithms I want to take a + + align:start position:0% +talk algorithms I want to take a + + + align:start position:0% +talk algorithms I want to take a +slightly different example it's similar + + align:start position:0% +slightly different example it's similar + + + align:start position:0% +slightly different example it's similar +to what we have here but and I want to + + align:start position:0% +to what we have here but and I want to + + + align:start position:0% +to what we have here but and I want to +talk about exactly how and an algorithm + + align:start position:0% +talk about exactly how and an algorithm + + + align:start position:0% +talk about exactly how and an algorithm +would work and we kind of did that so + + align:start position:0% +would work and we kind of did that so + + + align:start position:0% +would work and we kind of did that so +actually let's run it on this one and + + align:start position:0% +actually let's run it on this one and + + + align:start position:0% +actually let's run it on this one and +then I'll write out what the pseudocode + + align:start position:0% +then I'll write out what the pseudocode + + + align:start position:0% +then I'll write out what the pseudocode +for the algorithm would be I'm gonna + + align:start position:0% +for the algorithm would be I'm gonna + + + align:start position:0% +for the algorithm would be I'm gonna +ignore a here you could imagine that + + align:start position:0% +ignore a here you could imagine that + + + align:start position:0% +ignore a here you could imagine that +this particular algorithm would be run + + align:start position:0% +this particular algorithm would be run + + + align:start position:0% +this particular algorithm would be run +on this degenerate case that corresponds + + align:start position:0% +on this degenerate case that corresponds + + + align:start position:0% +on this degenerate case that corresponds +to a and you'd end up coloring this red + + align:start position:0% +to a and you'd end up coloring this red + + + align:start position:0% +to a and you'd end up coloring this red +or blue so I'm just gonna go ahead and + + align:start position:0% +or blue so I'm just gonna go ahead and + + + align:start position:0% +or blue so I'm just gonna go ahead and +and color this red and I'm not done with + + align:start position:0% +and color this red and I'm not done with + + + align:start position:0% +and color this red and I'm not done with +my problem but I'm done with the + + align:start position:0% +my problem but I'm done with the + + + align:start position:0% +my problem but I'm done with the +particular graph that corresponds to a + + align:start position:0% +particular graph that corresponds to a + + + align:start position:0% +particular graph that corresponds to a +because a can't reach any other node in + + align:start position:0% +because a can't reach any other node in + + + align:start position:0% +because a can't reach any other node in +the graph so you ought to be a little + + align:start position:0% +the graph so you ought to be a little + + + align:start position:0% +the graph so you ought to be a little +bit careful and the code I'm going to + + align:start position:0% +bit careful and the code I'm going to + + + align:start position:0% +bit careful and the code I'm going to +show you would need to be generalized to + + align:start position:0% +show you would need to be generalized to + + + align:start position:0% +show you would need to be generalized to +take into account this this forest of + + align:start position:0% +take into account this this forest of + + + align:start position:0% +take into account this this forest of +graphs okay because there's really a + + align:start position:0% +graphs okay because there's really a + + + align:start position:0% +graphs okay because there's really a +bunch of different graphs that are + + align:start position:0% +bunch of different graphs that are + + + align:start position:0% +bunch of different graphs that are +disconnected that are part of the + + align:start position:0% +disconnected that are part of the + + + align:start position:0% +disconnected that are part of the +overall problem but if I start with B + + align:start position:0% +overall problem but if I start with B + + + align:start position:0% +overall problem but if I start with B +then I get connectivity to all of the + + align:start position:0% +then I get connectivity to all of the + + + align:start position:0% +then I get connectivity to all of the +remaining edges and so I'm good there so + + align:start position:0% +remaining edges and so I'm good there so + + + align:start position:0% +remaining edges and so I'm good there so +let me go ahead and color this red and + + align:start position:0% +let me go ahead and color this red and + + + align:start position:0% +let me go ahead and color this red and +so the way we described it we we say I'm + + align:start position:0% +so the way we described it we we say I'm + + + align:start position:0% +so the way we described it we we say I'm +going to look for the neighbors of B and + + align:start position:0% +going to look for the neighbors of B and + + + align:start position:0% +going to look for the neighbors of B and +so B is connected to just see in this + + align:start position:0% +so B is connected to just see in this + + + align:start position:0% +so B is connected to just see in this +case and when I when I traverse an edge + + align:start position:0% +case and when I when I traverse an edge + + + align:start position:0% +case and when I when I traverse an edge +what do I do with respect to the color + + align:start position:0% + + + + align:start position:0% + +I flipped the color right I changed the + + align:start position:0% +I flipped the color right I changed the + + + align:start position:0% +I flipped the color right I changed the +color there's only two colors so I can + + align:start position:0% +color there's only two colors so I can + + + align:start position:0% +color there's only two colors so I can +think of it as flipping the color right + + align:start position:0% +think of it as flipping the color right + + + align:start position:0% +think of it as flipping the color right +so I go then I Traverse an edge I need + + align:start position:0% +so I go then I Traverse an edge I need + + + align:start position:0% +so I go then I Traverse an edge I need +to flip the color to do to blue right + + align:start position:0% +to flip the color to do to blue right + + + align:start position:0% +to flip the color to do to blue right +and then I get to see and when I get to + + align:start position:0% +and then I get to see and when I get to + + + align:start position:0% +and then I get to see and when I get to +see I then start traversing edges but + + align:start position:0% +see I then start traversing edges but + + + align:start position:0% +see I then start traversing edges but +when I traverse an edge I need to flip + + align:start position:0% +when I traverse an edge I need to flip + + + align:start position:0% +when I traverse an edge I need to flip +the color so this goes to are in the + + align:start position:0% +the color so this goes to are in the + + + align:start position:0% +the color so this goes to are in the +case of D I can go to two different + + align:start position:0% +case of D I can go to two different + + + align:start position:0% +case of D I can go to two different +places and so I need to go ahead and + + align:start position:0% +places and so I need to go ahead and + + + align:start position:0% +places and so I need to go ahead and +Traverse to E and just for the heck of + + align:start position:0% +Traverse to E and just for the heck of + + + align:start position:0% +Traverse to E and just for the heck of +it I'm gonna add another edge there + + align:start position:0% +it I'm gonna add another edge there + + + align:start position:0% +it I'm gonna add another edge there +right because now you're going to see + + align:start position:0% +right because now you're going to see + + + align:start position:0% +right because now you're going to see +how Y the code is gonna get a little + + align:start position:0% +how Y the code is gonna get a little + + + align:start position:0% +how Y the code is gonna get a little +more complicated with respect to the + + align:start position:0% +more complicated with respect to the + + + align:start position:0% +more complicated with respect to the +termination condition that I described + + align:start position:0% +termination condition that I described + + + align:start position:0% +termination condition that I described +to you and the checks that we need to + + align:start position:0% +to you and the checks that we need to + + + align:start position:0% +to you and the checks that we need to +perform with respect to the fact that we + + align:start position:0% +perform with respect to the fact that we + + + align:start position:0% +perform with respect to the fact that we +wanted this graph to be 2 colorable okay + + align:start position:0% +wanted this graph to be 2 colorable okay + + + align:start position:0% +wanted this graph to be 2 colorable okay +so when I write the way the way this + + align:start position:0% +so when I write the way the way this + + + align:start position:0% +so when I write the way the way this +code is going to work is is I'm gonna + + align:start position:0% +code is going to work is is I'm gonna + + + align:start position:0% +code is going to work is is I'm gonna +get to D and and with that color red and + + align:start position:0% +get to D and and with that color red and + + + align:start position:0% +get to D and and with that color red and +I'm gonna now see for the first time + + align:start position:0% +I'm gonna now see for the first time + + + align:start position:0% +I'm gonna now see for the first time +this is an interesting case for the + + align:start position:0% +this is an interesting case for the + + + align:start position:0% +this is an interesting case for the +first time I'm gonna see that D has two + + align:start position:0% +first time I'm gonna see that D has two + + + align:start position:0% +first time I'm gonna see that D has two +neighbors okay now I need to traverse + + align:start position:0% +neighbors okay now I need to traverse + + + align:start position:0% +neighbors okay now I need to traverse +both of these edges that correspond to + + align:start position:0% +both of these edges that correspond to + + + align:start position:0% +both of these edges that correspond to +these two neighbors in sequence I'm + + align:start position:0% +these two neighbors in sequence I'm + + + align:start position:0% +these two neighbors in sequence I'm +gonna pick one and go with that and then + + align:start position:0% +gonna pick one and go with that and then + + + align:start position:0% +gonna pick one and go with that and then +I'm gonna pick the other one + + align:start position:0% +I'm gonna pick the other one + + + align:start position:0% +I'm gonna pick the other one +right in general there's two strategies + + align:start position:0% +right in general there's two strategies + + + align:start position:0% +right in general there's two strategies +that you can follow and one of which is + + align:start position:0% +that you can follow and one of which is + + + align:start position:0% +that you can follow and one of which is +called depth-first search and the other + + align:start position:0% +called depth-first search and the other + + + align:start position:0% +called depth-first search and the other +is called breadth-first search okay so + + align:start position:0% +is called breadth-first search okay so + + + align:start position:0% +is called breadth-first search okay so +I'm not gonna you're gonna see + + align:start position:0% +I'm not gonna you're gonna see + + + align:start position:0% +I'm not gonna you're gonna see +effectively a depth-first algorithm and + + align:start position:0% +effectively a depth-first algorithm and + + + align:start position:0% +effectively a depth-first algorithm and +I'm happy to tell you about + + align:start position:0% +I'm happy to tell you about + + + align:start position:0% +I'm happy to tell you about +breadth-first in detail offline but i'll + + align:start position:0% +breadth-first in detail offline but i'll + + + align:start position:0% +breadth-first in detail offline but i'll +mention what the difference is here so + + align:start position:0% +mention what the difference is here so + + + align:start position:0% +mention what the difference is here so +you get a sense of what the differences + + align:start position:0% +you get a sense of what the differences + + + align:start position:0% +you get a sense of what the differences +are and they're two fundamental search + + align:start position:0% +are and they're two fundamental search + + + align:start position:0% +are and they're two fundamental search +techniques traversal techniques and the + + align:start position:0% +techniques traversal techniques and the + + + align:start position:0% +techniques traversal techniques and the +depth first technique says I'm going to + + align:start position:0% +depth first technique says I'm going to + + + align:start position:0% +depth first technique says I'm going to +I take D and I'm gonna pick one of its + + align:start position:0% +I take D and I'm gonna pick one of its + + + align:start position:0% +I take D and I'm gonna pick one of its +neighbors and I'm going to go ahead and + + align:start position:0% +neighbors and I'm going to go ahead and + + + align:start position:0% +neighbors and I'm going to go ahead and +say that effectively that that's the + + align:start position:0% +say that effectively that that's the + + + align:start position:0% +say that effectively that that's the +only only neighbor and I'm going to + + align:start position:0% +only only neighbor and I'm going to + + + align:start position:0% +only only neighbor and I'm going to +explore everything that I can get to + + align:start position:0% +explore everything that I can get to + + + align:start position:0% +explore everything that I can get to +from that neighbor and then once I'm all + + align:start position:0% +from that neighbor and then once I'm all + + + align:start position:0% +from that neighbor and then once I'm all +done and there's some termination + + align:start position:0% +done and there's some termination + + + align:start position:0% +done and there's some termination +condition that happens I'm going to come + + align:start position:0% +condition that happens I'm going to come + + + align:start position:0% +condition that happens I'm going to come +back and I'm going to look at this other + + align:start position:0% +back and I'm going to look at this other + + + align:start position:0% +back and I'm going to look at this other +neighbor just wanting to ask + + align:start position:0% +neighbor just wanting to ask + + + align:start position:0% +neighbor just wanting to ask +so so what would happen here in + + align:start position:0% +so so what would happen here in + + + align:start position:0% +so so what would happen here in +depth-first search is the following D + + align:start position:0% +depth-first search is the following D + + + align:start position:0% +depth-first search is the following D +would go to e and when I go through an + + align:start position:0% +would go to e and when I go through an + + + align:start position:0% +would go to e and when I go through an +edge I need to flip the color right so I + + align:start position:0% +edge I need to flip the color right so I + + + align:start position:0% +edge I need to flip the color right so I +get a B here at this point unlike what + + align:start position:0% +get a B here at this point unlike what + + + align:start position:0% +get a B here at this point unlike what +we did early on when we did this + + align:start position:0% +we did early on when we did this + + + align:start position:0% +we did early on when we did this +particular example or something similar + + align:start position:0% +particular example or something similar + + + align:start position:0% +particular example or something similar +I what I did was when I saw our here + + align:start position:0% +I what I did was when I saw our here + + + align:start position:0% +I what I did was when I saw our here +I colored F N and E both blue that's + + align:start position:0% +I colored F N and E both blue that's + + + align:start position:0% +I colored F N and E both blue that's +effectively what I did remember that + + align:start position:0% +effectively what I did remember that + + + align:start position:0% +effectively what I did remember that +right but now I'm actually doing + + align:start position:0% +right but now I'm actually doing + + + align:start position:0% +right but now I'm actually doing +something different right this is a + + align:start position:0% +something different right this is a + + + align:start position:0% +something different right this is a +different execution corresponding to + + align:start position:0% +different execution corresponding to + + + align:start position:0% +different execution corresponding to +depth-first search right when I looked + + align:start position:0% +depth-first search right when I looked + + + align:start position:0% +depth-first search right when I looked +at all of my neighbors including the F + + align:start position:0% +at all of my neighbors including the F + + + align:start position:0% +at all of my neighbors including the F +case I remember we we had some color for + + align:start position:0% +case I remember we we had some color for + + + align:start position:0% +case I remember we we had some color for +this and then we immediately took G H + + align:start position:0% +this and then we immediately took G H + + + align:start position:0% +this and then we immediately took G H +and I and we colored them right that is + + align:start position:0% +and I and we colored them right that is + + + align:start position:0% +and I and we colored them right that is +breadth-first search okay that is + + align:start position:0% +breadth-first search okay that is + + + align:start position:0% +breadth-first search okay that is +looking at taking one step in all + + align:start position:0% +looking at taking one step in all + + + align:start position:0% +looking at taking one step in all +directions that you can take and + + align:start position:0% +directions that you can take and + + + align:start position:0% +directions that you can take and +essentially it's a frontier based + + align:start position:0% +essentially it's a frontier based + + + align:start position:0% +essentially it's a frontier based +approach where I'm taking the the + + align:start position:0% +approach where I'm taking the the + + + align:start position:0% +approach where I'm taking the the +frontier of my neighbors and pushing it + + align:start position:0% +frontier of my neighbors and pushing it + + + align:start position:0% +frontier of my neighbors and pushing it +outward one step at a time right + + align:start position:0% +outward one step at a time right + + + align:start position:0% +outward one step at a time right +contrast that with what we're doing here + + align:start position:0% +contrast that with what we're doing here + + + align:start position:0% +contrast that with what we're doing here +you are going to take this a the + + align:start position:0% +you are going to take this a the + + + align:start position:0% +you are going to take this a the +neighbor EE corresponding to D and then + + align:start position:0% +neighbor EE corresponding to D and then + + + align:start position:0% +neighbor EE corresponding to D and then +you're not going to go to F you're in + + align:start position:0% +you're not going to go to F you're in + + + align:start position:0% +you're not going to go to F you're in +fact going to go ahead and pick one of + + align:start position:0% +fact going to go ahead and pick one of + + + align:start position:0% +fact going to go ahead and pick one of +the neighbors of E right and you might + + align:start position:0% +the neighbors of E right and you might + + + align:start position:0% +the neighbors of E right and you might +even have in your representation E's + + align:start position:0% +even have in your representation E's + + + align:start position:0% +even have in your representation E's +neighbor being D because you know yeah D + + align:start position:0% +neighbor being D because you know yeah D + + + align:start position:0% +neighbor being D because you know yeah D +has a as a neighbor and so does e having + + align:start position:0% +has a as a neighbor and so does e having + + + align:start position:0% +has a as a neighbor and so does e having +has D as a neighbor but you'll say oh + + align:start position:0% +has D as a neighbor but you'll say oh + + + align:start position:0% +has D as a neighbor but you'll say oh +look look I don't need to go look at G + + align:start position:0% +look look I don't need to go look at G + + + align:start position:0% +look look I don't need to go look at G +now in my depth-first search because D + + align:start position:0% +now in my depth-first search because D + + + align:start position:0% +now in my depth-first search because D +is already been colored right so you + + align:start position:0% +is already been colored right so you + + + align:start position:0% +is already been colored right so you +check that and then you say oh what has + + align:start position:0% +check that and then you say oh what has + + + align:start position:0% +check that and then you say oh what has +not been colored I has not been colored + + align:start position:0% +not been colored I has not been colored + + + align:start position:0% +not been colored I has not been colored +and and when I traverse an edge I need + + align:start position:0% +and and when I traverse an edge I need + + + align:start position:0% +and and when I traverse an edge I need +to flip the color and I'm gonna go ahead + + align:start position:0% +to flip the color and I'm gonna go ahead + + + align:start position:0% +to flip the color and I'm gonna go ahead +and put our in here alright and it's not + + align:start position:0% +and put our in here alright and it's not + + + align:start position:0% +and put our in here alright and it's not +that you even go back to 2f now from D + + align:start position:0% +that you even go back to 2f now from D + + + align:start position:0% +that you even go back to 2f now from D +you don't go back to D at this point you + + align:start position:0% +you don't go back to D at this point you + + + align:start position:0% +you don't go back to D at this point you +now look at I and you do another + + align:start position:0% +now look at I and you do another + + + align:start position:0% +now look at I and you do another +recursion corresponding to I and you say + + align:start position:0% +recursion corresponding to I and you say + + + align:start position:0% +recursion corresponding to I and you say +okay what about eyes neighbors well II + + align:start position:0% +okay what about eyes neighbors well II + + + align:start position:0% +okay what about eyes neighbors well II +may be first but you've already done + + align:start position:0% +may be first but you've already done + + + align:start position:0% +may be first but you've already done +with the I'm gonna go ahead and I'm + + align:start position:0% +with the I'm gonna go ahead and I'm + + + align:start position:0% +with the I'm gonna go ahead and I'm +gonna get to F and you do the flip and + + align:start position:0% +gonna get to F and you do the flip and + + + align:start position:0% +gonna get to F and you do the flip and +you get B over here right I'm + + align:start position:0% +you get B over here right I'm + + + align:start position:0% +you get B over here right I'm +you still don't go go back to 2d um you + + align:start position:0% +you still don't go go back to 2d um you + + + align:start position:0% +you still don't go go back to 2d um you +look at F and you say I'm going to now + + align:start position:0% +look at F and you say I'm going to now + + + align:start position:0% +look at F and you say I'm going to now +look at the the neighbors of F and maybe + + align:start position:0% +look at the the neighbors of F and maybe + + + align:start position:0% +look at the the neighbors of F and maybe +you'll get a CH and you say this is our + + align:start position:0% +you'll get a CH and you say this is our + + + align:start position:0% +you'll get a CH and you say this is our +then you go back and now for the first + + align:start position:0% +then you go back and now for the first + + + align:start position:0% +then you go back and now for the first +time you're going to look at exhausting + + align:start position:0% +time you're going to look at exhausting + + + align:start position:0% +time you're going to look at exhausting +the neighbors of a node that you've + + align:start position:0% +the neighbors of a node that you've + + + align:start position:0% +the neighbors of a node that you've +actually reached and you've gone to one + + align:start position:0% +actually reached and you've gone to one + + + align:start position:0% +actually reached and you've gone to one +neighbor for and so so at this point you + + align:start position:0% +neighbor for and so so at this point you + + + align:start position:0% +neighbor for and so so at this point you +go and you make this R so now you come + + align:start position:0% +go and you make this R so now you come + + + align:start position:0% +go and you make this R so now you come +back and you say I have i exhausted F's + + align:start position:0% +back and you say I have i exhausted F's + + + align:start position:0% +back and you say I have i exhausted F's +neighbors and yes in the sense that all + + align:start position:0% +neighbors and yes in the sense that all + + + align:start position:0% +neighbors and yes in the sense that all +the neighbors that I needed to look at + + align:start position:0% +the neighbors that I needed to look at + + + align:start position:0% +the neighbors that I needed to look at +because they didn't have colors have + + align:start position:0% +because they didn't have colors have + + + align:start position:0% +because they didn't have colors have +been exhausted and of course F had D and + + align:start position:0% +been exhausted and of course F had D and + + + align:start position:0% +been exhausted and of course F had D and +I as neighbors and they already had + + align:start position:0% +I as neighbors and they already had + + + align:start position:0% +I as neighbors and they already had +colors so I'm cool with that right I + + align:start position:0% +colors so I'm cool with that right I + + + align:start position:0% +colors so I'm cool with that right I +don't need to and your I don't need to + + align:start position:0% +don't need to and your I don't need to + + + align:start position:0% +don't need to and your I don't need to +touch them + + align:start position:0% +touch them + + + align:start position:0% +touch them +now at this point I'm popping up because + + align:start position:0% +now at this point I'm popping up because + + + align:start position:0% +now at this point I'm popping up because +of exhausted F's neighbors I'm going to + + align:start position:0% +of exhausted F's neighbors I'm going to + + + align:start position:0% +of exhausted F's neighbors I'm going to +go back to where I came from + + align:start position:0% +go back to where I came from + + + align:start position:0% +go back to where I came from +how did I get to F I did not get to F + + align:start position:0% +how did I get to F I did not get to F + + + align:start position:0% +how did I get to F I did not get to F +from D I actually got to F from I right + + align:start position:0% +from D I actually got to F from I right + + + align:start position:0% +from D I actually got to F from I right +so I'm going to go to I but the fact of + + align:start position:0% +so I'm going to go to I but the fact of + + + align:start position:0% +so I'm going to go to I but the fact of +the matter is that I is done because I + + align:start position:0% +the matter is that I is done because I + + + align:start position:0% +the matter is that I is done because I +didn't have to deal with E and I've + + align:start position:0% +didn't have to deal with E and I've + + + align:start position:0% +didn't have to deal with E and I've +already I'm already done with F then I + + align:start position:0% +already I'm already done with F then I + + + align:start position:0% +already I'm already done with F then I +go back to e same thing right then + + align:start position:0% +go back to e same thing right then + + + align:start position:0% +go back to e same thing right then +finally I get back to D and I say oh now + + align:start position:0% +finally I get back to D and I say oh now + + + align:start position:0% +finally I get back to D and I say oh now +I need to go look at F and I go and I + + align:start position:0% +I need to go look at F and I go and I + + + align:start position:0% +I need to go look at F and I go and I +say Oh F is already colored so therefore + + align:start position:0% +say Oh F is already colored so therefore + + + align:start position:0% +say Oh F is already colored so therefore +I'm done this is the simplest + + align:start position:0% +I'm done this is the simplest + + + align:start position:0% +I'm done this is the simplest +representation that I can think of for a + + align:start position:0% +representation that I can think of for a + + + align:start position:0% +representation that I can think of for a +graph that's also very efficient so I + + align:start position:0% +graph that's also very efficient so I + + + align:start position:0% +graph that's also very efficient so I +messed with this graph quite a bit so I + + align:start position:0% +messed with this graph quite a bit so I + + + align:start position:0% +messed with this graph quite a bit so I +want to claim that that dictionary + + align:start position:0% +want to claim that that dictionary + + + align:start position:0% +want to claim that that dictionary +representation that says graph equals + + align:start position:0% +representation that says graph equals + + + align:start position:0% +representation that says graph equals +open curly brackets and then eventually + + align:start position:0% +open curly brackets and then eventually + + + align:start position:0% +open curly brackets and then eventually +close curly brackets corresponds to that + + align:start position:0% +close curly brackets corresponds to that + + + align:start position:0% +close curly brackets corresponds to that +but it's kind of roughly corresponds to + + align:start position:0% +but it's kind of roughly corresponds to + + + align:start position:0% +but it's kind of roughly corresponds to +that right and I can certainly write out + + align:start position:0% +that right and I can certainly write out + + + align:start position:0% +that right and I can certainly write out +any graph representation in Python for + + align:start position:0% +any graph representation in Python for + + + align:start position:0% +any graph representation in Python for +for any topological representation that + + align:start position:0% +for any topological representation that + + + align:start position:0% +for any topological representation that +you give me but if you look at what + + align:start position:0% +you give me but if you look at what + + + align:start position:0% +you give me but if you look at what +what's up there the important thing is I + + align:start position:0% +what's up there the important thing is I + + + align:start position:0% +what's up there the important thing is I +want to show you or tell you about + + align:start position:0% + + + + align:start position:0% + +the constituents of this rep so graph is + + align:start position:0% +the constituents of this rep so graph is + + + align:start position:0% +the constituents of this rep so graph is +a dictionary okay a dictionary is a set + + align:start position:0% +a dictionary okay a dictionary is a set + + + align:start position:0% +a dictionary okay a dictionary is a set +of key value pairs you represent sets in + + align:start position:0% +of key value pairs you represent sets in + + + align:start position:0% +of key value pairs you represent sets in +Python using curly brackets right and + + align:start position:0% +Python using curly brackets right and + + + align:start position:0% +Python using curly brackets right and +each of the key value pairs is + + align:start position:0% +each of the key value pairs is + + + align:start position:0% +each of the key value pairs is +represented using some key : + + align:start position:0% +represented using some key : + + + align:start position:0% +represented using some key : +Val and you see a set of key value pairs + + align:start position:0% +Val and you see a set of key value pairs + + + align:start position:0% +Val and you see a set of key value pairs +because you see these commas between + + align:start position:0% +because you see these commas between + + + align:start position:0% +because you see these commas between +them and so what you see here is the key + + align:start position:0% +them and so what you see here is the key + + + align:start position:0% +them and so what you see here is the key +and the keys could be strings they could + + align:start position:0% +and the keys could be strings they could + + + align:start position:0% +and the keys could be strings they could +be tuples um you you could have many + + align:start position:0% +be tuples um you you could have many + + + align:start position:0% +be tuples um you you could have many +possibilities for keys and the key comes + + align:start position:0% +possibilities for keys and the key comes + + + align:start position:0% +possibilities for keys and the key comes +first and in this case the key is the is + + align:start position:0% +first and in this case the key is the is + + + align:start position:0% +first and in this case the key is the is +the string B okay and so that represents + + align:start position:0% +the string B okay and so that represents + + + align:start position:0% +the string B okay and so that represents +the name of the node RB and the value is + + align:start position:0% +the name of the node RB and the value is + + + align:start position:0% +the name of the node RB and the value is +it is usually a list and in this case + + align:start position:0% +it is usually a list and in this case + + + align:start position:0% +it is usually a list and in this case +you have a list that has a single entry + + align:start position:0% +you have a list that has a single entry + + + align:start position:0% +you have a list that has a single entry +in it because B only has one edge that + + align:start position:0% +in it because B only has one edge that + + + align:start position:0% +in it because B only has one edge that +goes to C right and so a more + + align:start position:0% +goes to C right and so a more + + + align:start position:0% +goes to C right and so a more +interesting case as you can see up there + + align:start position:0% +interesting case as you can see up there + + + align:start position:0% +interesting case as you can see up there +is D and D connects to C F and E and so + + align:start position:0% +is D and D connects to C F and E and so + + + align:start position:0% +is D and D connects to C F and E and so +you see D with C a and F right so that's + + align:start position:0% +you see D with C a and F right so that's + + + align:start position:0% +you see D with C a and F right so that's +exactly what the point here is right + + align:start position:0% +exactly what the point here is right + + + align:start position:0% +exactly what the point here is right +this algorithm would run differently if + + align:start position:0% +this algorithm would run differently if + + + align:start position:0% +this algorithm would run differently if +you had a representation that was + + align:start position:0% +you had a representation that was + + + align:start position:0% +you had a representation that was +equivalent from a topological standpoint + + align:start position:0% +equivalent from a topological standpoint + + + align:start position:0% +equivalent from a topological standpoint +there's no order in the topology but i + + align:start position:0% +there's no order in the topology but i + + + align:start position:0% +there's no order in the topology but i +chose c EF i you know it got typed + + align:start position:0% +chose c EF i you know it got typed + + + align:start position:0% +chose c EF i you know it got typed +somewhere c EF and so the order of + + align:start position:0% +somewhere c EF and so the order of + + + align:start position:0% +somewhere c EF and so the order of +neighbors is c followed by e followed by + + align:start position:0% +neighbors is c followed by e followed by + + + align:start position:0% +neighbors is c followed by e followed by +F now that is if you took this list of + + align:start position:0% +F now that is if you took this list of + + + align:start position:0% +F now that is if you took this list of +neighbors and you went from 0 1 2 in + + align:start position:0% +neighbors and you went from 0 1 2 in + + + align:start position:0% +neighbors and you went from 0 1 2 in +terms of indices of that list there's + + align:start position:0% +terms of indices of that list there's + + + align:start position:0% +terms of indices of that list there's +nothing that's stopping you from going + + align:start position:0% +nothing that's stopping you from going + + + align:start position:0% +nothing that's stopping you from going +to 1 0 in which case you would go FEC + + align:start position:0% +to 1 0 in which case you would go FEC + + + align:start position:0% +to 1 0 in which case you would go FEC +right or you could do some you know + + align:start position:0% +right or you could do some you know + + + align:start position:0% +right or you could do some you know +crazy random ordering for the list + + align:start position:0% +crazy random ordering for the list + + + align:start position:0% +crazy random ordering for the list +itself right + + align:start position:0% +itself right + + + align:start position:0% +itself right +entirely up to you right it's + + align:start position:0% +entirely up to you right it's + + + align:start position:0% +entirely up to you right it's +deterministic it's entirely up to you + + align:start position:0% +deterministic it's entirely up to you + + + align:start position:0% +deterministic it's entirely up to you +but now you see how the order of the + + align:start position:0% +but now you see how the order of the + + + align:start position:0% +but now you see how the order of the +values that corresponds to these lists + + align:start position:0% +values that corresponds to these lists + + + align:start position:0% +values that corresponds to these lists +that give you the neighbors for every + + align:start position:0% +that give you the neighbors for every + + + align:start position:0% +that give you the neighbors for every +node affects the execution of the + + align:start position:0% +node affects the execution of the + + + align:start position:0% +node affects the execution of the +algorithm right now you do not want the + + align:start position:0% +algorithm right now you do not want the + + + align:start position:0% +algorithm right now you do not want the +result of the algorithm yes or no this + + align:start position:0% +result of the algorithm yes or no this + + + align:start position:0% +result of the algorithm yes or no this +graph is bipartite or not to be affected + + align:start position:0% +graph is bipartite or not to be affected + + + align:start position:0% +graph is bipartite or not to be affected +by the order that you see there right + + align:start position:0% +by the order that you see there right + + + align:start position:0% +by the order that you see there right +because when I draw a graph like this I + + align:start position:0% +because when I draw a graph like this I + + + align:start position:0% +because when I draw a graph like this I +mean this graph is effectively something + + align:start position:0% +mean this graph is effectively something + + + align:start position:0% +mean this graph is effectively something +that doesn't have order you can't really + + align:start position:0% +that doesn't have order you can't really + + + align:start position:0% +that doesn't have order you can't really +say anything about the order of G H and + + align:start position:0% +say anything about the order of G H and + + + align:start position:0% +say anything about the order of G H and +I in relation to F I mean there felt + + align:start position:0% +I in relation to F I mean there felt + + + align:start position:0% +I in relation to F I mean there felt +that want us to the kind of the left of + + align:start position:0% +that want us to the kind of the left of + + + align:start position:0% +that want us to the kind of the left of +it they're all two of them at the bottom + + align:start position:0% +it they're all two of them at the bottom + + + align:start position:0% +it they're all two of them at the bottom +but that's not what this is about and so + + align:start position:0% +but that's not what this is about and so + + + align:start position:0% +but that's not what this is about and so +obviously that graph regardless of + + align:start position:0% +obviously that graph regardless of + + + align:start position:0% +obviously that graph regardless of +whether I drew it like this all right I + + align:start position:0% +whether I drew it like this all right I + + + align:start position:0% +whether I drew it like this all right I +you know I drew it like that should be + + align:start position:0% +you know I drew it like that should be + + + align:start position:0% +you know I drew it like that should be +by pie chart both of those graphs that + + align:start position:0% +by pie chart both of those graphs that + + + align:start position:0% +by pie chart both of those graphs that +right that correspond to H and G with + + align:start position:0% +right that correspond to H and G with + + + align:start position:0% +right that correspond to H and G with +their name slip are either bipartite or + + align:start position:0% +their name slip are either bipartite or + + + align:start position:0% +their name slip are either bipartite or +not bipartite right so you absolutely + + align:start position:0% +not bipartite right so you absolutely + + + align:start position:0% +not bipartite right so you absolutely +cannot have the algorithm being affected + + align:start position:0% +cannot have the algorithm being affected + + + align:start position:0% +cannot have the algorithm being affected +by the order in which you see CEF or + + align:start position:0% +by the order in which you see CEF or + + + align:start position:0% +by the order in which you see CEF or +what have you that make sense so you can + + align:start position:0% +what have you that make sense so you can + + + align:start position:0% +what have you that make sense so you can +do a lot of operations on dictionaries + + align:start position:0% +do a lot of operations on dictionaries + + + align:start position:0% +do a lot of operations on dictionaries +it's probably something that you want to + + align:start position:0% +it's probably something that you want to + + + align:start position:0% +it's probably something that you want to +look at by looking at the code that we + + align:start position:0% +look at by looking at the code that we + + + align:start position:0% +look at by looking at the code that we +have here and and looking at the code + + align:start position:0% +have here and and looking at the code + + + align:start position:0% +have here and and looking at the code +from from graph analysis algorithms and + + align:start position:0% +from from graph analysis algorithms and + + + align:start position:0% +from from graph analysis algorithms and +I'm happy to point you to other + + align:start position:0% +I'm happy to point you to other + + + align:start position:0% +I'm happy to point you to other +literature but the way you access a + + align:start position:0% +literature but the way you access a + + + align:start position:0% +literature but the way you access a +dictionary is looks a lot like accessing + + align:start position:0% +dictionary is looks a lot like accessing + + + align:start position:0% +dictionary is looks a lot like accessing +the list so you can say something like + + align:start position:0% +the list so you can say something like + + + align:start position:0% +the list so you can say something like +graph a and then you say something like + + align:start position:0% +graph a and then you say something like + + + align:start position:0% +graph a and then you say something like +graph a if a is not a key in the graph + + align:start position:0% +graph a if a is not a key in the graph + + + align:start position:0% +graph a if a is not a key in the graph +it would give you an error okay and but + + align:start position:0% +it would give you an error okay and but + + + align:start position:0% +it would give you an error okay and but +you can you can you can certainly get + + align:start position:0% +you can you can you can certainly get + + + align:start position:0% +you can you can you can certainly get +values back and you can also assign + + align:start position:0% +values back and you can also assign + + + align:start position:0% +values back and you can also assign +values so graph a B would give it you + + align:start position:0% +values so graph a B would give it you + + + align:start position:0% +values so graph a B would give it you +would give you + + align:start position:0% +would give you + + + align:start position:0% +would give you +at this list see and you can go off and + + align:start position:0% +at this list see and you can go off and + + + align:start position:0% +at this list see and you can go off and +you can say something like graph a b dot + + align:start position:0% +you can say something like graph a b dot + + + align:start position:0% +you can say something like graph a b dot +append i and you could say d and if you + + align:start position:0% +append i and you could say d and if you + + + align:start position:0% +append i and you could say d and if you +did that if you did graph a b dot append + + align:start position:0% +did that if you did graph a b dot append + + + align:start position:0% +did that if you did graph a b dot append +d then that's effectively are taking + + align:start position:0% +d then that's effectively are taking + + + align:start position:0% +d then that's effectively are taking +this and adding adding d to it so you + + align:start position:0% +this and adding adding d to it so you + + + align:start position:0% +this and adding adding d to it so you +could mutate the graph if you wanted you + + align:start position:0% +could mutate the graph if you wanted you + + + align:start position:0% +could mutate the graph if you wanted you +don't have to do that i in our code for + + align:start position:0% +don't have to do that i in our code for + + + align:start position:0% +don't have to do that i in our code for +a bipartite graph checking because we're + + align:start position:0% +a bipartite graph checking because we're + + + align:start position:0% +a bipartite graph checking because we're +not mutating the graph we're just + + align:start position:0% +not mutating the graph we're just + + + align:start position:0% +not mutating the graph we're just +reversing the graph but you could + + align:start position:0% +reversing the graph but you could + + + align:start position:0% +reversing the graph but you could +certainly do that + + align:start position:0% +certainly do that + + + align:start position:0% +certainly do that +so the dictionaries are a pretty cool + + align:start position:0% +so the dictionaries are a pretty cool + + + align:start position:0% +so the dictionaries are a pretty cool +representation encourage you to learn + + align:start position:0% +representation encourage you to learn + + + align:start position:0% +representation encourage you to learn +about them and they're useful in in many + + align:start position:0% +about them and they're useful in in many + + + align:start position:0% +about them and they're useful in in many +instances i clearly they replace lists + + align:start position:0% +instances i clearly they replace lists + + + align:start position:0% +instances i clearly they replace lists +because you can certainly have keys as + + align:start position:0% +because you can certainly have keys as + + + align:start position:0% +because you can certainly have keys as +integers right you can also have + + align:start position:0% +integers right you can also have + + + align:start position:0% +integers right you can also have +negative numbers as keys there's nothing + + align:start position:0% +negative numbers as keys there's nothing + + + align:start position:0% +negative numbers as keys there's nothing +that's stopping you from doing that and + + align:start position:0% +that's stopping you from doing that and + + + align:start position:0% +that's stopping you from doing that and +you don't have to represent the negative + + align:start position:0% +you don't have to represent the negative + + + align:start position:0% +you don't have to represent the negative +number on as as a string i mean you + + align:start position:0% +number on as as a string i mean you + + + align:start position:0% +number on as as a string i mean you +could just have keys that are that go + + align:start position:0% +could just have keys that are that go + + + align:start position:0% +could just have keys that are that go +from minus 22 to 27 what have you um so + + align:start position:0% +from minus 22 to 27 what have you um so + + + align:start position:0% +from minus 22 to 27 what have you um so +hopefully you have some sense of what + + align:start position:0% +hopefully you have some sense of what + + + align:start position:0% +hopefully you have some sense of what +this code is going to look like both + + align:start position:0% +this code is going to look like both + + + align:start position:0% +this code is going to look like both +from a standpoint of the algorithm which + + align:start position:0% +from a standpoint of the algorithm which + + + align:start position:0% +from a standpoint of the algorithm which +we executed a few times and from the + + align:start position:0% +we executed a few times and from the + + + align:start position:0% +we executed a few times and from the +standpoint of this structure the + + align:start position:0% +standpoint of this structure the + + + align:start position:0% +standpoint of this structure the +representation of the graph right so + + align:start position:0% +representation of the graph right so + + + align:start position:0% +representation of the graph right so +let's take a look and at about ten lines + + align:start position:0% +let's take a look and at about ten lines + + + align:start position:0% +let's take a look and at about ten lines +of code that corresponds to bipartite + + align:start position:0% +of code that corresponds to bipartite + + + align:start position:0% +of code that corresponds to bipartite +graph coloring so it fits on a screen + + align:start position:0% +graph coloring so it fits on a screen + + + align:start position:0% +graph coloring so it fits on a screen +okay and so this is a pretty tight code + + align:start position:0% +okay and so this is a pretty tight code + + + align:start position:0% +okay and so this is a pretty tight code +it does exactly what we wanted to do in + + align:start position:0% +it does exactly what we wanted to do in + + + align:start position:0% +it does exactly what we wanted to do in +the sense of it's going to determine + + align:start position:0% +the sense of it's going to determine + + + align:start position:0% +the sense of it's going to determine +whether a graph is bipartite or not and + + align:start position:0% +whether a graph is bipartite or not and + + + align:start position:0% +whether a graph is bipartite or not and +it has a bunch of arguments a graph is + + align:start position:0% +it has a bunch of arguments a graph is + + + align:start position:0% +it has a bunch of arguments a graph is +what you imagined it to be + + align:start position:0% +what you imagined it to be + + + align:start position:0% +what you imagined it to be +it's the input graph we have to start + + align:start position:0% +it's the input graph we have to start + + + align:start position:0% +it's the input graph we have to start +from somewhere this graph has a list of + + align:start position:0% +from somewhere this graph has a list of + + + align:start position:0% +from somewhere this graph has a list of +key value pairs the keys happen to be + + align:start position:0% +key value pairs the keys happen to be + + + align:start position:0% +key value pairs the keys happen to be +the nodes you should never depend on the + + align:start position:0% +the nodes you should never depend on the + + + align:start position:0% +the nodes you should never depend on the +keys being stored in a particular order + + align:start position:0% +keys being stored in a particular order + + + align:start position:0% +keys being stored in a particular order +um these ways of saying you know you can + + align:start position:0% +um these ways of saying you know you can + + + align:start position:0% +um these ways of saying you know you can +say things like graph keys + + align:start position:0% + + + + align:start position:0% + +and this is going to give you back a + + align:start position:0% +and this is going to give you back a + + + align:start position:0% +and this is going to give you back a +list of keys and it's possible that when + + align:start position:0% +list of keys and it's possible that when + + + align:start position:0% +list of keys and it's possible that when +you say graphed our keys at one point in + + align:start position:0% +you say graphed our keys at one point in + + + align:start position:0% +you say graphed our keys at one point in +the program you get the keys in a + + align:start position:0% +the program you get the keys in a + + + align:start position:0% +the program you get the keys in a +particular order and when you say it at + + align:start position:0% +particular order and when you say it at + + + align:start position:0% +particular order and when you say it at +a different part of the program you get + + align:start position:0% +a different part of the program you get + + + align:start position:0% +a different part of the program you get +the keys in a different order okay but + + align:start position:0% +the keys in a different order okay but + + + align:start position:0% +the keys in a different order okay but +all the keys won't change if there's no + + align:start position:0% +all the keys won't change if there's no + + + align:start position:0% +all the keys won't change if there's no +bugs in your program you'll get the same + + align:start position:0% +bugs in your program you'll get the same + + + align:start position:0% +bugs in your program you'll get the same +set of keys but they may be in different + + align:start position:0% +set of keys but they may be in different + + + align:start position:0% +set of keys but they may be in different +order all right so you obviously want to + + align:start position:0% +order all right so you obviously want to + + + align:start position:0% +order all right so you obviously want to +start a bit some node in the graph and + + align:start position:0% +start a bit some node in the graph and + + + align:start position:0% +start a bit some node in the graph and +you're going to color it with a + + align:start position:0% +you're going to color it with a + + + align:start position:0% +you're going to color it with a +particular color call it red I think I + + align:start position:0% +particular color call it red I think I + + + align:start position:0% +particular color call it red I think I +had shaded than hatched here so sha + + align:start position:0% +had shaded than hatched here so sha + + + align:start position:0% +had shaded than hatched here so sha +stands for shaded and hatch stands for + + align:start position:0% +stands for shaded and hatch stands for + + + align:start position:0% +stands for shaded and hatch stands for +hatched but you can use what you want so + + align:start position:0% +hatched but you can use what you want so + + + align:start position:0% +hatched but you can use what you want so +if you see the invocation here bipartite + + align:start position:0% +if you see the invocation here bipartite + + + align:start position:0% +if you see the invocation here bipartite +graph color graph three starts with a + + align:start position:0% +graph color graph three starts with a + + + align:start position:0% +graph color graph three starts with a +node this is an its coloring as a + + align:start position:0% +node this is an its coloring as a + + + align:start position:0% +node this is an its coloring as a +dictionary and so we are also + + align:start position:0% +dictionary and so we are also + + + align:start position:0% +dictionary and so we are also +representing not only the graph as a + + align:start position:0% +representing not only the graph as a + + + align:start position:0% +representing not only the graph as a +dictionary but we're also representing + + align:start position:0% +dictionary but we're also representing + + + align:start position:0% +dictionary but we're also representing +the mapping that we get namely the node + + align:start position:0% +the mapping that we get namely the node + + + align:start position:0% +the mapping that we get namely the node +B was colored with red so B is up is is + + align:start position:0% +B was colored with red so B is up is is + + + align:start position:0% +B was colored with red so B is up is is +a key in this coloring dictionary and + + align:start position:0% +a key in this coloring dictionary and + + + align:start position:0% +a key in this coloring dictionary and +our red is is the color that's the value + + align:start position:0% +our red is is the color that's the value + + + align:start position:0% +our red is is the color that's the value +right so you can represent mappings key + + align:start position:0% +right so you can represent mappings key + + + align:start position:0% +right so you can represent mappings key +values or mappings right so so that the + + align:start position:0% +values or mappings right so so that the + + + align:start position:0% +values or mappings right so so that the +coloring of a node is also a dictionary + + align:start position:0% +coloring of a node is also a dictionary + + + align:start position:0% +coloring of a node is also a dictionary +right and so that's essentially what we + + align:start position:0% +right and so that's essentially what we + + + align:start position:0% +right and so that's essentially what we +have so I'm going to start with it with + + align:start position:0% +have so I'm going to start with it with + + + align:start position:0% +have so I'm going to start with it with +none of the nodes are colored so that's + + align:start position:0% +none of the nodes are colored so that's + + + align:start position:0% +none of the nodes are colored so that's +why this is Mt and I'm going to start + + align:start position:0% +why this is Mt and I'm going to start + + + align:start position:0% +why this is Mt and I'm going to start +with a and I'm going to start with the + + align:start position:0% +with a and I'm going to start with the + + + align:start position:0% +with a and I'm going to start with the +color shaded which means that a is going + + align:start position:0% +color shaded which means that a is going + + + align:start position:0% +color shaded which means that a is going +to be colored shaded or a is going to be + + align:start position:0% +to be colored shaded or a is going to be + + + align:start position:0% +to be colored shaded or a is going to be +shade + + align:start position:0% +shade + + + align:start position:0% +shade +okay and this is gonna return true or + + align:start position:0% +okay and this is gonna return true or + + + align:start position:0% +okay and this is gonna return true or +false depending on whether I the graph + + align:start position:0% +false depending on whether I the graph + + + align:start position:0% +false depending on whether I the graph +is bipartite or not and if it's true + + align:start position:0% +is bipartite or not and if it's true + + + align:start position:0% +is bipartite or not and if it's true +then I'm going to get something + + align:start position:0% +then I'm going to get something + + + align:start position:0% +then I'm going to get something +interesting with respect to the mapping + + align:start position:0% +interesting with respect to the mapping + + + align:start position:0% +interesting with respect to the mapping +of nodes to colors that's my dictionary + + align:start position:0% +of nodes to colors that's my dictionary + + + align:start position:0% +of nodes to colors that's my dictionary +coloring and otherwise I get false back + + align:start position:0% +coloring and otherwise I get false back + + + align:start position:0% +coloring and otherwise I get false back +which an empty dictionary because then I + + align:start position:0% +which an empty dictionary because then I + + + align:start position:0% +which an empty dictionary because then I +have something that's false I mean you + + align:start position:0% +have something that's false I mean you + + + align:start position:0% +have something that's false I mean you +could imagine saying well there's a + + align:start position:0% +could imagine saying well there's a + + + align:start position:0% +could imagine saying well there's a +problem case here you you you can color + + align:start position:0% +problem case here you you you can color + + + align:start position:0% +problem case here you you you can color +all of these different nodes but I'm + + align:start position:0% +all of these different nodes but I'm + + + align:start position:0% +all of these different nodes but I'm +just kind of stuck here because of that + + align:start position:0% +just kind of stuck here because of that + + + align:start position:0% +just kind of stuck here because of that +five cycle but it that's kind of + + align:start position:0% +five cycle but it that's kind of + + + align:start position:0% +five cycle but it that's kind of +indeterminate in terms of what the + + align:start position:0% +indeterminate in terms of what the + + + align:start position:0% +indeterminate in terms of what the +colors need to be and so unless you were + + align:start position:0% +colors need to be and so unless you were + + + align:start position:0% +colors need to be and so unless you were +actually going to go off and mutate the + + align:start position:0% +actually going to go off and mutate the + + + align:start position:0% +actually going to go off and mutate the +graph and remove a node and and say this + + align:start position:0% +graph and remove a node and and say this + + + align:start position:0% +graph and remove a node and and say this +is the friend you want to dump today and + + align:start position:0% +is the friend you want to dump today and + + + align:start position:0% +is the friend you want to dump today and +then the rest of them are going to be + + align:start position:0% +then the rest of them are going to be + + + align:start position:0% +then the rest of them are going to be +invited for dinner in that case you + + align:start position:0% +invited for dinner in that case you + + + align:start position:0% +invited for dinner in that case you +could obviously return a coloring + + align:start position:0% +could obviously return a coloring + + + align:start position:0% +could obviously return a coloring +dictionary even in this case of the + + align:start position:0% +dictionary even in this case of the + + + align:start position:0% +dictionary even in this case of the +graph original graph not being bipartite + + align:start position:0% +graph original graph not being bipartite + + + align:start position:0% +graph original graph not being bipartite +but most of the time you're probably in + + align:start position:0% +but most of the time you're probably in + + + align:start position:0% +but most of the time you're probably in +a situation where if it's not bipartite + + align:start position:0% +a situation where if it's not bipartite + + + align:start position:0% +a situation where if it's not bipartite +you don't return anything other than + + align:start position:0% +you don't return anything other than + + + align:start position:0% +you don't return anything other than +false all right so let's take a look at + + align:start position:0% +false all right so let's take a look at + + + align:start position:0% +false all right so let's take a look at +what each of these things do and then + + align:start position:0% +what each of these things do and then + + + align:start position:0% +what each of these things do and then +you'll also get a sense of how we + + align:start position:0% +you'll also get a sense of how we + + + align:start position:0% +you'll also get a sense of how we +manipulate dictionary structures so I'm + + align:start position:0% +manipulate dictionary structures so I'm + + + align:start position:0% +manipulate dictionary structures so I'm +just going to explain very quickly each + + align:start position:0% +just going to explain very quickly each + + + align:start position:0% +just going to explain very quickly each +line of code here so this pair of lines + + align:start position:0% +line of code here so this pair of lines + + + align:start position:0% +line of code here so this pair of lines +of this pair of lines of code + + align:start position:0% +of this pair of lines of code + + + align:start position:0% +of this pair of lines of code +essentially say something like well if + + align:start position:0% +essentially say something like well if + + + align:start position:0% +essentially say something like well if +you've given me a starting node is just + + align:start position:0% +you've given me a starting node is just + + + align:start position:0% +you've given me a starting node is just +a check on the input if the starting + + align:start position:0% +a check on the input if the starting + + + align:start position:0% +a check on the input if the starting +node is not in the graph it's not a key + + align:start position:0% +node is not in the graph it's not a key + + + align:start position:0% +node is not in the graph it's not a key +in the graph then I'm throwing up my + + align:start position:0% +in the graph then I'm throwing up my + + + align:start position:0% +in the graph then I'm throwing up my +hands here this is not a graph it's not + + align:start position:0% +hands here this is not a graph it's not + + + align:start position:0% +hands here this is not a graph it's not +a bipartite graph I can't give you a + + align:start position:0% +a bipartite graph I can't give you a + + + align:start position:0% +a bipartite graph I can't give you a +coloring right so easy check not much + + align:start position:0% +coloring right so easy check not much + + + align:start position:0% +coloring right so easy check not much +there this is an interesting check on + + align:start position:0% +there this is an interesting check on + + + align:start position:0% +there this is an interesting check on +this essentially is going to check to + + align:start position:0% +this essentially is going to check to + + + align:start position:0% +this essentially is going to check to +see whether on the particular node that + + align:start position:0% +see whether on the particular node that + + + align:start position:0% +see whether on the particular node that +you have this is going to be done + + align:start position:0% +you have this is going to be done + + + align:start position:0% +you have this is going to be done +recursively so anytime you arrive at a + + align:start position:0% +recursively so anytime you arrive at a + + + align:start position:0% +recursively so anytime you arrive at a +node you have to check whether there's + + align:start position:0% +node you have to check whether there's + + + align:start position:0% +node you have to check whether there's +already a color there or not + + align:start position:0% +already a color there or not + + + align:start position:0% +already a color there or not +if there's no color then you move + + align:start position:0% +if there's no color then you move + + + align:start position:0% +if there's no color then you move +forward and you color it and you also + + align:start position:0% +forward and you color it and you also + + + align:start position:0% +forward and you color it and you also +move forward in the sense that you'll + + align:start position:0% +move forward in the sense that you'll + + + align:start position:0% +move forward in the sense that you'll +probably I go ahead and if it has + + align:start position:0% +probably I go ahead and if it has + + + align:start position:0% +probably I go ahead and if it has +neighbors you will Traverse their + + align:start position:0% +neighbors you will Traverse their + + + align:start position:0% +neighbors you will Traverse their +neighbors right but if it has a color if + + align:start position:0% +neighbors right but if it has a color if + + + align:start position:0% +neighbors right but if it has a color if +it's already in coloring that means it + + align:start position:0% +it's already in coloring that means it + + + align:start position:0% +it's already in coloring that means it +already has a color right because the + + align:start position:0% +already has a color right because the + + + align:start position:0% +already has a color right because the +keys that correspond to the coloring + + align:start position:0% +keys that correspond to the coloring + + + align:start position:0% +keys that correspond to the coloring +dictionary are exactly the same in the + + align:start position:0% +dictionary are exactly the same in the + + + align:start position:0% +dictionary are exactly the same in the +sense that they're their graph nodes and + + align:start position:0% +sense that they're their graph nodes and + + + align:start position:0% +sense that they're their graph nodes and +they're also in the graph dictionary + + align:start position:0% +they're also in the graph dictionary + + + align:start position:0% +they're also in the graph dictionary +right the mappings are F was completely + + align:start position:0% +right the mappings are F was completely + + + align:start position:0% +right the mappings are F was completely +different and the coloring dictionary is + + align:start position:0% +different and the coloring dictionary is + + + align:start position:0% +different and the coloring dictionary is +being grown as we speak or as we execute + + align:start position:0% +being grown as we speak or as we execute + + + align:start position:0% +being grown as we speak or as we execute +but the the graph dictionary is actually + + align:start position:0% +but the the graph dictionary is actually + + + align:start position:0% +but the the graph dictionary is actually +not mutated it's static okay and so this + + align:start position:0% +not mutated it's static okay and so this + + + align:start position:0% +not mutated it's static okay and so this +check here says that I'm going to go + + align:start position:0% +check here says that I'm going to go + + + align:start position:0% +check here says that I'm going to go +ahead and if it's not in coloring + + align:start position:0% +ahead and if it's not in coloring + + + align:start position:0% +ahead and if it's not in coloring +great I'm going to go ahead and whatever + + align:start position:0% +great I'm going to go ahead and whatever + + + align:start position:0% +great I'm going to go ahead and whatever +color I have I'm gonna go ahead and + + align:start position:0% +color I have I'm gonna go ahead and + + + align:start position:0% +color I have I'm gonna go ahead and +color it with that right that's what + + align:start position:0% +color it with that right that's what + + + align:start position:0% +color it with that right that's what +coloring start equals color does it just + + align:start position:0% +coloring start equals color does it just + + + align:start position:0% +coloring start equals color does it just +colors the note okay and then that + + align:start position:0% +colors the note okay and then that + + + align:start position:0% +colors the note okay and then that +effectively is adding the key value pair + + align:start position:0% +effectively is adding the key value pair + + + align:start position:0% +effectively is adding the key value pair +a start comma color to the coloring + + align:start position:0% +a start comma color to the coloring + + + align:start position:0% +a start comma color to the coloring +dictionary right that's what it does + + align:start position:0% +dictionary right that's what it does + + + align:start position:0% +dictionary right that's what it does +otherwise um well I got two cases here + + align:start position:0% +otherwise um well I got two cases here + + + align:start position:0% +otherwise um well I got two cases here +right this thing has already been + + align:start position:0% +right this thing has already been + + + align:start position:0% +right this thing has already been +colored but I have two cases um I want + + align:start position:0% +colored but I have two cases um I want + + + align:start position:0% +colored but I have two cases um I want +to color it with something different + + align:start position:0% +to color it with something different + + + align:start position:0% +to color it with something different +from what it's already been colored + + align:start position:0% +from what it's already been colored + + + align:start position:0% +from what it's already been colored +that's the problem that's a problem + + align:start position:0% +that's the problem that's a problem + + + align:start position:0% +that's the problem that's a problem +that's exactly when we get a five cycle + + align:start position:0% +that's exactly when we get a five cycle + + + align:start position:0% +that's exactly when we get a five cycle +and we throw up our hands so we're done + + align:start position:0% +and we throw up our hands so we're done + + + align:start position:0% +and we throw up our hands so we're done +here we just say doesn't matter what + + align:start position:0% +here we just say doesn't matter what + + + align:start position:0% +here we just say doesn't matter what +we've colored so far it's all garbage + + align:start position:0% +we've colored so far it's all garbage + + + align:start position:0% +we've colored so far it's all garbage +you know this thing can be colored with + + align:start position:0% +you know this thing can be colored with + + + align:start position:0% +you know this thing can be colored with +two colors given the constraints I have + + align:start position:0% +two colors given the constraints I have + + + align:start position:0% +two colors given the constraints I have +so I'm just going to return false and an + + align:start position:0% +so I'm just going to return false and an + + + align:start position:0% +so I'm just going to return false and an +empty dictionary right so anything that + + align:start position:0% +empty dictionary right so anything that + + + align:start position:0% +empty dictionary right so anything that +coloring had in it I mean it's gone + + align:start position:0% +coloring had in it I mean it's gone + + + align:start position:0% +coloring had in it I mean it's gone +right because it's bogus otherwise at + + align:start position:0% +right because it's bogus otherwise at + + + align:start position:0% +right because it's bogus otherwise at +this recursion would say oh well I'm + + align:start position:0% +this recursion would say oh well I'm + + + align:start position:0% +this recursion would say oh well I'm +going to return true for for this thing + + align:start position:0% +going to return true for for this thing + + + align:start position:0% +going to return true for for this thing +here and I'm going to it's it has been + + align:start position:0% +here and I'm going to it's it has been + + + align:start position:0% +here and I'm going to it's it has been +colored which means that you know have + + align:start position:0% +colored which means that you know have + + + align:start position:0% +colored which means that you know have +it I don't want to do any more work on + + align:start position:0% +it I don't want to do any more work on + + + align:start position:0% +it I don't want to do any more work on +it I mean I got this node here it's + + align:start position:0% +it I mean I got this node here it's + + + align:start position:0% +it I mean I got this node here it's +already you know was already colored and + + align:start position:0% +already you know was already colored and + + + align:start position:0% +already you know was already colored and +was consistently colored so if I don't + + align:start position:0% +was consistently colored so if I don't + + + align:start position:0% +was consistently colored so if I don't +want to get into infinite loops I better + + align:start position:0% +want to get into infinite loops I better + + + align:start position:0% +want to get into infinite loops I better +not you know start traversing nodes from + + align:start position:0% +not you know start traversing nodes from + + + align:start position:0% +not you know start traversing nodes from +this node because we've already seen it + + align:start position:0% +this node because we've already seen it + + + align:start position:0% +this node because we've already seen it +before + + align:start position:0% +before + + + align:start position:0% +before +right so the fact that it's already + + align:start position:0% +right so the fact that it's already + + + align:start position:0% +right so the fact that it's already +colored correctly is a termination + + align:start position:0% +colored correctly is a termination + + + align:start position:0% +colored correctly is a termination +condition this is important I'm that it + + align:start position:0% +condition this is important I'm that it + + + align:start position:0% +condition this is important I'm that it +says that I don't want to keep repeating + + align:start position:0% +says that I don't want to keep repeating + + + align:start position:0% +says that I don't want to keep repeating +myself that is like going through the + + align:start position:0% +myself that is like going through the + + + align:start position:0% +myself that is like going through the +cycle over and over right if you didn't + + align:start position:0% +cycle over and over right if you didn't + + + align:start position:0% +cycle over and over right if you didn't +have that right that makes sense yeah + + align:start position:0% +have that right that makes sense yeah + + + align:start position:0% +have that right that makes sense yeah +that's important + + align:start position:0% +that's important + + + align:start position:0% +that's important +so now well this is a flip so this is + + align:start position:0% +so now well this is a flip so this is + + + align:start position:0% +so now well this is a flip so this is +this there's no recursion there's no + + align:start position:0% +this there's no recursion there's no + + + align:start position:0% +this there's no recursion there's no +procedure calls here this is just + + align:start position:0% +procedure calls here this is just + + + align:start position:0% +procedure calls here this is just +flipping the color that make sense so + + align:start position:0% +flipping the color that make sense so + + + align:start position:0% +flipping the color that make sense so +now at the last part which is at the the + + align:start position:0% +now at the last part which is at the the + + + align:start position:0% +now at the last part which is at the the +part where I'm actually doing + + align:start position:0% +part where I'm actually doing + + + align:start position:0% +part where I'm actually doing +depth-first search is the part which + + align:start position:0% +depth-first search is the part which + + + align:start position:0% +depth-first search is the part which +says okay I got to the point now where + + align:start position:0% +says okay I got to the point now where + + + align:start position:0% +says okay I got to the point now where +I'm essentially the the haven't done any + + align:start position:0% +I'm essentially the the haven't done any + + + align:start position:0% +I'm essentially the the haven't done any +returns here right I've colored + + align:start position:0% +returns here right I've colored + + + align:start position:0% +returns here right I've colored +with with color and and I've flipped the + + align:start position:0% +with with color and and I've flipped the + + + align:start position:0% +with with color and and I've flipped the +color right so these two lines are + + align:start position:0% +color right so these two lines are + + + align:start position:0% +color right so these two lines are +excuted no returns + + align:start position:0% +excuted no returns + + + align:start position:0% +excuted no returns +these lines are executed and now I I've + + align:start position:0% +these lines are executed and now I I've + + + align:start position:0% +these lines are executed and now I I've +clearly already colored starred and I + + align:start position:0% +clearly already colored starred and I + + + align:start position:0% +clearly already colored starred and I +flipped the color and I'm going to go + + align:start position:0% +flipped the color and I'm going to go + + + align:start position:0% +flipped the color and I'm going to go +ahead and make the recursive call + + align:start position:0% +ahead and make the recursive call + + + align:start position:0% +ahead and make the recursive call +corresponding to the the neighbors of + + align:start position:0% +corresponding to the the neighbors of + + + align:start position:0% +corresponding to the the neighbors of +start and all I have to do to look at + + align:start position:0% +start and all I have to do to look at + + + align:start position:0% +start and all I have to do to look at +the neighbors of start is to return the + + align:start position:0% +the neighbors of start is to return the + + + align:start position:0% +the neighbors of start is to return the +list corresponding to the value of graph + + align:start position:0% +list corresponding to the value of graph + + + align:start position:0% +list corresponding to the value of graph +start remember I said graph a or graph + + align:start position:0% +start remember I said graph a or graph + + + align:start position:0% +start remember I said graph a or graph +start is going to give you this this + + align:start position:0% +start is going to give you this this + + + align:start position:0% +start is going to give you this this +list and I can go ahead and and append + + align:start position:0% +list and I can go ahead and and append + + + align:start position:0% +list and I can go ahead and and append +to it and I'm not gonna mutate but I + + align:start position:0% +to it and I'm not gonna mutate but I + + + align:start position:0% +to it and I'm not gonna mutate but I +could have done that and so that is + + align:start position:0% +could have done that and so that is + + + align:start position:0% +could have done that and so that is +going to give me my list and I'm just + + align:start position:0% +going to give me my list and I'm just + + + align:start position:0% +going to give me my list and I'm just +going to go through and you mer ate that + + align:start position:0% +going to go through and you mer ate that + + + align:start position:0% +going to go through and you mer ate that +list in whatever order that it came to + + align:start position:0% +list in whatever order that it came to + + + align:start position:0% +list in whatever order that it came to +me and start with I'm gonna call the + + align:start position:0% +me and start with I'm gonna call the + + + align:start position:0% +me and start with I'm gonna call the +first element vertex because that's also + + align:start position:0% +first element vertex because that's also + + + align:start position:0% +first element vertex because that's also +a vertex or node synonymous and I'm + + align:start position:0% +a vertex or node synonymous and I'm + + + align:start position:0% +a vertex or node synonymous and I'm +gonna send in vertex here graph stays + + align:start position:0% +gonna send in vertex here graph stays + + + align:start position:0% +gonna send in vertex here graph stays +the same vertex stays the same I've + + align:start position:0% +the same vertex stays the same I've + + + align:start position:0% +the same vertex stays the same I've +modified coloring so I want to pass that + + align:start position:0% +modified coloring so I want to pass that + + + align:start position:0% +modified coloring so I want to pass that +over and obviously I'm gonna pass new + + align:start position:0% +over and obviously I'm gonna pass new + + + align:start position:0% +over and obviously I'm gonna pass new +color here because I've done the flip + + align:start position:0% +color here because I've done the flip + + + align:start position:0% +color here because I've done the flip +right and if I ever I get something + + align:start position:0% +right and if I ever I get something + + + align:start position:0% +right and if I ever I get something +that's false + + align:start position:0% +that's false + + + align:start position:0% +that's false +that means I've founded an odd cycle and + + align:start position:0% +that means I've founded an odd cycle and + + + align:start position:0% +that means I've founded an odd cycle and +I return false and then if everything + + align:start position:0% +I return false and then if everything + + + align:start position:0% +I return false and then if everything +works out I return true in the coloring + + align:start position:0% +works out I return true in the coloring + + + align:start position:0% +works out I return true in the coloring +okay so if I go ahead and run that if my + + align:start position:0% +okay so if I go ahead and run that if my + + + align:start position:0% +okay so if I go ahead and run that if my +machine hasn't gone to sleep doesn't do + + align:start position:0% +machine hasn't gone to sleep doesn't do + + + align:start position:0% +machine hasn't gone to sleep doesn't do +very much you know the first graph it + + align:start position:0% +very much you know the first graph it + + + align:start position:0% +very much you know the first graph it +was not colorable I'd you can check + + align:start position:0% +was not colorable I'd you can check + + + align:start position:0% +was not colorable I'd you can check +these results by yourself but this is + + align:start position:0% +these results by yourself but this is + + + align:start position:0% +these results by yourself but this is +more the reason I'm putting this up is + + align:start position:0% +more the reason I'm putting this up is + + + align:start position:0% +more the reason I'm putting this up is +to give you a sense of what the coloring + + align:start position:0% +to give you a sense of what the coloring + + + align:start position:0% +to give you a sense of what the coloring +dictionary looks like right so just so + + align:start position:0% +dictionary looks like right so just so + + + align:start position:0% +dictionary looks like right so just so +you get some more exposure to these + + align:start position:0% +you get some more exposure to these + + + align:start position:0% +you get some more exposure to these +things so in this case you get a + + align:start position:0% +things so in this case you get a + + + align:start position:0% +things so in this case you get a +non-empty coloring dictionary for the + + align:start position:0% +non-empty coloring dictionary for the + + + align:start position:0% +non-empty coloring dictionary for the +second run so I ran it four times on + + align:start position:0% +second run so I ran it four times on + + + align:start position:0% +second run so I ran it four times on +four different graphs you get a non + + align:start position:0% +four different graphs you get a non + + + align:start position:0% +four different graphs you get a non +empty coloring dictionary it's true the + + align:start position:0% +empty coloring dictionary it's true the + + + align:start position:0% +empty coloring dictionary it's true the +graph is bipartite and notice that the + + align:start position:0% +graph is bipartite and notice that the + + + align:start position:0% +graph is bipartite and notice that the +order in which this coloring dictionary + + align:start position:0% +order in which this coloring dictionary + + + align:start position:0% +order in which this coloring dictionary +was was what was created was certainly a + + align:start position:0% +was was what was created was certainly a + + + align:start position:0% +was was what was created was certainly a +function of the execution of the + + align:start position:0% +function of the execution of the + + + align:start position:0% +function of the execution of the +algorithm but I this order might + + align:start position:0% +algorithm but I this order might + + + align:start position:0% +algorithm but I this order might +actually change if I keep running this + + align:start position:0% +actually change if I keep running this + + + align:start position:0% +actually change if I keep running this +algorithm and if my machine had + + align:start position:0% +algorithm and if my machine had + + + align:start position:0% +algorithm and if my machine had +different loads and so on and so forth + + align:start position:0% +different loads and so on and so forth + + + align:start position:0% +different loads and so on and so forth +but it + + align:start position:0% +but it + + + align:start position:0% +but it +you would always get true for any graph + + align:start position:0% +you would always get true for any graph + + + align:start position:0% +you would always get true for any graph +representation that is bipartite or two + + align:start position:0% +representation that is bipartite or two + + + align:start position:0% +representation that is bipartite or two +colorable but you you you have no + + align:start position:0% +colorable but you you you have no + + + align:start position:0% +colorable but you you you have no +control over whether f hat comes first + + align:start position:0% +control over whether f hat comes first + + + align:start position:0% +control over whether f hat comes first +or a hat comes first those could be + + align:start position:0% +or a hat comes first those could be + + + align:start position:0% +or a hat comes first those could be +flipped alright + + align:start position:0% +flipped alright + + + align:start position:0% +flipped alright +so never depend on the order of keys in + + align:start position:0% +so never depend on the order of keys in + + + align:start position:0% +so never depend on the order of keys in +a dictionary okay + + align:start position:0% +a dictionary okay + + + align:start position:0% +a dictionary okay +but certainly the existence of keys in a + + align:start position:0% +but certainly the existence of keys in a + + + align:start position:0% +but certainly the existence of keys in a +dictionary you can or the nonexistence + + align:start position:0% +dictionary you can or the nonexistence + + + align:start position:0% +dictionary you can or the nonexistence +you can depend on alright good so that's + + align:start position:0% +you can depend on alright good so that's + + + align:start position:0% +you can depend on alright good so that's +really all I had to say any questions + + align:start position:0% + + + + align:start position:0% + +all right excellent I want credit for + + align:start position:0% +all right excellent I want credit for + + + align:start position:0% +all right excellent I want credit for +finishing one minute early \ No newline at end of file diff --git a/zhk9xLjrmi4.txt b/zhk9xLjrmi4.txt new file mode 100644 index 0000000000000000000000000000000000000000..e6e13673ad00807be9e642e887ed0b0f0b4bfae2 --- /dev/null +++ b/zhk9xLjrmi4.txt @@ -0,0 +1,11432 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or to view additional materials from + + align:start position:0% +or to view additional materials from + + + align:start position:0% +or to view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +All right, let's get started. Today's + + align:start position:0% +All right, let's get started. Today's + + + align:start position:0% +All right, let's get started. Today's +all about Lrange will method. We will + + align:start position:0% +all about Lrange will method. We will + + + align:start position:0% +all about Lrange will method. We will +talk a lot about what we really mean by + + align:start position:0% +talk a lot about what we really mean by + + + align:start position:0% +talk a lot about what we really mean by +generalized coordinates and generalized + + align:start position:0% +generalized coordinates and generalized + + + align:start position:0% +generalized coordinates and generalized +forces + + align:start position:0% +forces + + + align:start position:0% +forces +and then do a number of application + + align:start position:0% +and then do a number of application + + + align:start position:0% +and then do a number of application +examples. + + align:start position:0% +examples. + + + align:start position:0% +examples. +There's a + + align:start position:0% +There's a + + + align:start position:0% +There's a +set of notes on stellar on the Lrange + + align:start position:0% +set of notes on stellar on the Lrange + + + align:start position:0% +set of notes on stellar on the Lrange +method. It's about 10 pages long and I + + align:start position:0% +method. It's about 10 pages long and I + + + align:start position:0% +method. It's about 10 pages long and I +highly recommend you + + align:start position:0% +highly recommend you + + + align:start position:0% +highly recommend you +you read them. They're they're they're + + align:start position:0% +you read them. They're they're they're + + + align:start position:0% +you read them. They're they're they're +not somehow up with the notes associated + + align:start position:0% +not somehow up with the notes associated + + + align:start position:0% +not somehow up with the notes associated +with lecture notes. They're kind of in a + + align:start position:0% +with lecture notes. They're kind of in a + + + align:start position:0% +with lecture notes. They're kind of in a +way down at the bottom. So, you have to + + align:start position:0% +way down at the bottom. So, you have to + + + align:start position:0% +way down at the bottom. So, you have to +scroll all the way down in the stellar + + align:start position:0% +scroll all the way down in the stellar + + + align:start position:0% +scroll all the way down in the stellar +website to find them. + + align:start position:0% +website to find them. + + + align:start position:0% +website to find them. +The uh there's our second quiz is + + align:start position:0% +The uh there's our second quiz is + + + align:start position:0% +The uh there's our second quiz is +November 8th. That's a week from next + + align:start position:0% +November 8th. That's a week from next + + + align:start position:0% +November 8th. That's a week from next +Tuesday. Okay. Pretty much same format + + align:start position:0% +Tuesday. Okay. Pretty much same format + + + align:start position:0% +Tuesday. Okay. Pretty much same format +as the first one. Okay. + + align:start position:0% +as the first one. Okay. + + + align:start position:0% +as the first one. Okay. +So let's talk about how to use lrange + + align:start position:0% +So let's talk about how to use lrange + + + align:start position:0% +So let's talk about how to use lrange +equations. + + align:start position:0% + + + + align:start position:0% + +So I defined what's called the lrangeian + + align:start position:0% +So I defined what's called the lrangeian + + + align:start position:0% +So I defined what's called the lrangeian +last time. + + align:start position:0% +last time. + + + align:start position:0% +last time. +T minus v the kinetic energy minus the + + align:start position:0% +T minus v the kinetic energy minus the + + + align:start position:0% +T minus v the kinetic energy minus the +potential energy of the entire system. + + align:start position:0% +potential energy of the entire system. + + + align:start position:0% +potential energy of the entire system. +Total kinetic and total potential energy + + align:start position:0% +Total kinetic and total potential energy + + + align:start position:0% +Total kinetic and total potential energy +expressions. + + align:start position:0% +expressions. + + + align:start position:0% +expressions. +Then we have some quantities + + align:start position:0% +Then we have some quantities + + + align:start position:0% +Then we have some quantities +QJs. + + align:start position:0% +QJs. + + + align:start position:0% +QJs. +These are defined as the generalized + + align:start position:0% +These are defined as the generalized + + + align:start position:0% +These are defined as the generalized +forces + + align:start position:0% +forces + + + align:start position:0% +forces +generalized discoordinates I should say + + align:start position:0% + + + + align:start position:0% + +and the capital Q subjs are the + + align:start position:0% +and the capital Q subjs are the + + + align:start position:0% +and the capital Q subjs are the +generalized forces. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +And the lrangege + + align:start position:0% +And the lrangege + + + align:start position:0% +And the lrangege +equation + + align:start position:0% +equation + + + align:start position:0% +equation +says that d by dt the time derivative + + align:start position:0% +says that d by dt the time derivative + + + align:start position:0% +says that d by dt the time derivative +of the partial of l with respect to + + align:start position:0% +of the partial of l with respect to + + + align:start position:0% +of the partial of l with respect to +the q j dots the velocities + + align:start position:0% + + + + align:start position:0% + +minus the partial + + align:start position:0% +minus the partial + + + align:start position:0% +minus the partial +minus the partial derivative of L with + + align:start position:0% +minus the partial derivative of L with + + + align:start position:0% +minus the partial derivative of L with +respect to the + + align:start position:0% +respect to the + + + align:start position:0% +respect to the +generalized displacements + + align:start position:0% +generalized displacements + + + align:start position:0% +generalized displacements +equals the generalized forces. And in + + align:start position:0% +equals the generalized forces. And in + + + align:start position:0% +equals the generalized forces. And in +for a typical system, you'll have a + + align:start position:0% +for a typical system, you'll have a + + + align:start position:0% +for a typical system, you'll have a +number of degrees of freedom like say + + align:start position:0% +number of degrees of freedom like say + + + align:start position:0% +number of degrees of freedom like say +three. And if you have three degrees of + + align:start position:0% +three. And if you have three degrees of + + + align:start position:0% +three. And if you have three degrees of +freedom, you need three equations of + + align:start position:0% +freedom, you need three equations of + + + align:start position:0% +freedom, you need three equations of +motion. And so that you're the J's will + + align:start position:0% +motion. And so that you're the J's will + + + align:start position:0% +motion. And so that you're the J's will +go from one to three in that case. So + + align:start position:0% +go from one to three in that case. So + + + align:start position:0% +go from one to three in that case. So +the J's here refer to an indicy that + + align:start position:0% +the J's here refer to an indicy that + + + align:start position:0% +the J's here refer to an indicy that +gives you the number of equations that + + align:start position:0% +gives you the number of equations that + + + align:start position:0% +gives you the number of equations that +you need. So you do this calculation for + + align:start position:0% +you need. So you do this calculation for + + + align:start position:0% +you need. So you do this calculation for +coordinate one again for coordinate two + + align:start position:0% +coordinate one again for coordinate two + + + align:start position:0% +coordinate one again for coordinate two +again for coordinate three and you get + + align:start position:0% +again for coordinate three and you get + + + align:start position:0% +again for coordinate three and you get +then three equations of motion. Okay. So + + align:start position:0% +then three equations of motion. Okay. So + + + align:start position:0% +then three equations of motion. Okay. So +this + + align:start position:0% +this + + + align:start position:0% +this +is a little + + align:start position:0% +is a little + + + align:start position:0% +is a little +a little obscure. I like to let's just + + align:start position:0% +a little obscure. I like to let's just + + + align:start position:0% +a little obscure. I like to let's just +plug in + + align:start position:0% + + + + align:start position:0% + +for L= T minus V and just put it in here + + align:start position:0% +for L= T minus V and just put it in here + + + align:start position:0% +for L= T minus V and just put it in here +and see what happens. + + align:start position:0% + + + + align:start position:0% + +You get d by + + align:start position:0% +You get d by + + + align:start position:0% +You get d by +dt + + align:start position:0% +dt + + + align:start position:0% +dt +of + + align:start position:0% + + + + align:start position:0% + +the partial of t with respect to q j dot + + align:start position:0% +the partial of t with respect to q j dot + + + align:start position:0% +the partial of t with respect to q j dot +minus d by dt + + align:start position:0% +minus d by dt + + + align:start position:0% +minus d by dt +of the partial of v with respect to q j + + align:start position:0% +of the partial of v with respect to q j + + + align:start position:0% +of the partial of v with respect to q j +dot + + align:start position:0% + + + + align:start position:0% + +plus + + align:start position:0% + + + + align:start position:0% + +I'll organize it this way + + align:start position:0% + + + + align:start position:0% + +minus the partial of T with respect to Q + + align:start position:0% +minus the partial of T with respect to Q + + + align:start position:0% +minus the partial of T with respect to Q +J + + align:start position:0% +J + + + align:start position:0% +J +plus the partial of V with respect to QJ + + align:start position:0% +plus the partial of V with respect to QJ + + + align:start position:0% +plus the partial of V with respect to QJ +equals capital QJ. + + align:start position:0% +equals capital QJ. + + + align:start position:0% +equals capital QJ. +Now when we first talked about + + align:start position:0% +Now when we first talked about + + + align:start position:0% +Now when we first talked about +potential energy a few days ago, we said + + align:start position:0% +potential energy a few days ago, we said + + + align:start position:0% +potential energy a few days ago, we said +that for mechanical systems the + + align:start position:0% +that for mechanical systems the + + + align:start position:0% +that for mechanical systems the +potential energy is not a function of + + align:start position:0% +potential energy is not a function of + + + align:start position:0% +potential energy is not a function of +time or + + align:start position:0% +time or + + + align:start position:0% +time or +anybody remember velocity. + + align:start position:0% +anybody remember velocity. + + + align:start position:0% +anybody remember velocity. +So if the potential energy is not a + + align:start position:0% +So if the potential energy is not a + + + align:start position:0% +So if the potential energy is not a +function of time velocity, what will + + align:start position:0% +function of time velocity, what will + + + align:start position:0% +function of time velocity, what will +happen to this term? + + align:start position:0% +happen to this term? + + + align:start position:0% +happen to this term? +Goes this goes away. So this is zero + + align:start position:0% +Goes this goes away. So this is zero + + + align:start position:0% +Goes this goes away. So this is zero +for + + align:start position:0% +for + + + align:start position:0% +for +mechanical + + align:start position:0% + + + + align:start position:0% + +systems. + + align:start position:0% +systems. + + + align:start position:0% +systems. +You know, if you start getting into + + align:start position:0% +You know, if you start getting into + + + align:start position:0% +You know, if you start getting into +electrons moving in magnetic fields, + + align:start position:0% +electrons moving in magnetic fields, + + + align:start position:0% +electrons moving in magnetic fields, +then you start having potential energies + + align:start position:0% +then you start having potential energies + + + align:start position:0% +then you start having potential energies +involving + + align:start position:0% +involving + + + align:start position:0% +involving +velocities. But for mechanical systems, + + align:start position:0% +velocities. But for mechanical systems, + + + align:start position:0% +velocities. But for mechanical systems, +this term's zero. And I think the + + align:start position:0% +this term's zero. And I think the + + + align:start position:0% +this term's zero. And I think the +bookkeeping though, so this is the form + + align:start position:0% +bookkeeping though, so this is the form + + + align:start position:0% +bookkeeping though, so this is the form +of lrange equations that I write down + + align:start position:0% +of lrange equations that I write down + + + align:start position:0% +of lrange equations that I write down +when I'm doing problems. I don't write + + align:start position:0% +when I'm doing problems. I don't write + + + align:start position:0% +when I'm doing problems. I don't write +this. Mathematicians + + align:start position:0% +this. Mathematicians + + + align:start position:0% +this. Mathematicians +like you know elegance + + align:start position:0% +like you know elegance + + + align:start position:0% +like you know elegance +and this comes down to this beautifully + + align:start position:0% +and this comes down to this beautifully + + + align:start position:0% +and this comes down to this beautifully +elegant simple looking formula but I'm + + align:start position:0% +elegant simple looking formula but I'm + + + align:start position:0% +elegant simple looking formula but I'm +an engineer and I like it to be + + align:start position:0% +an engineer and I like it to be + + + align:start position:0% +an engineer and I like it to be +efficient you know and and practically + + align:start position:0% +efficient you know and and practically + + + align:start position:0% +efficient you know and and practically +useful. This is the practically useful + + align:start position:0% +useful. This is the practically useful + + + align:start position:0% +useful. This is the practically useful +form of lrange equations. So you just + + align:start position:0% +form of lrange equations. So you just + + + align:start position:0% +form of lrange equations. So you just +use what you need potent kinetic energy + + align:start position:0% +use what you need potent kinetic energy + + + align:start position:0% +use what you need potent kinetic energy +here kinetic energy there potential + + align:start position:0% +here kinetic energy there potential + + + align:start position:0% +here kinetic energy there potential +energy there. And I number these. + + align:start position:0% +energy there. And I number these. + + + align:start position:0% +energy there. And I number these. +There's a lot of bookkeeping in Lrange. + + align:start position:0% +There's a lot of bookkeeping in Lrange. + + + align:start position:0% +There's a lot of bookkeeping in Lrange. +So I call it term one, term two, term + + align:start position:0% +So I call it term one, term two, term + + + align:start position:0% +So I call it term one, term two, term +three, and term four because you have to + + align:start position:0% +three, and term four because you have to + + + align:start position:0% +three, and term four because you have to +grind through this quite a few times. + + align:start position:0% +grind through this quite a few times. + + + align:start position:0% +grind through this quite a few times. +And so when you do, basically, you take + + align:start position:0% +And so when you do, basically, you take + + + align:start position:0% +And so when you do, basically, you take +one the results of 1 + 2 + 3 = 4. And + + align:start position:0% +one the results of 1 + 2 + 3 = 4. And + + + align:start position:0% +one the results of 1 + 2 + 3 = 4. And +you do that uh j times + + align:start position:0% +you do that uh j times + + + align:start position:0% +you do that uh j times +to get the equations you're after. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +So a little now we need to talk a little + + align:start position:0% +So a little now we need to talk a little + + + align:start position:0% +So a little now we need to talk a little +bit about what we mean by generalized + + align:start position:0% +bit about what we mean by generalized + + + align:start position:0% +bit about what we mean by generalized +coordinates. + + align:start position:0% +coordinates. + + + align:start position:0% +coordinates. +QJ + + align:start position:0% + + + + align:start position:0% + +general. What you know what's this word + + align:start position:0% +general. What you know what's this word + + + align:start position:0% +general. What you know what's this word +generalized mean? Generalized just means + + align:start position:0% +generalized mean? Generalized just means + + + align:start position:0% +generalized mean? Generalized just means +it doesn't have to be cartisian. + + align:start position:0% + + + + align:start position:0% + +Not necessarily cartisian as in xyz. + + align:start position:0% +Not necessarily cartisian as in xyz. + + + align:start position:0% +Not necessarily cartisian as in xyz. +You have a lot of liberty in how you + + align:start position:0% +You have a lot of liberty in how you + + + align:start position:0% +You have a lot of liberty in how you +choose coordinates. Not necessarily + + align:start position:0% +choose coordinates. Not necessarily + + + align:start position:0% +choose coordinates. Not necessarily +cartisian. Uh not + + align:start position:0% + + + + align:start position:0% + +even um inertial. + + align:start position:0% + + + + align:start position:0% + +They do have to satisfy certain + + align:start position:0% +They do have to satisfy certain + + + align:start position:0% +They do have to satisfy certain +requirements. The coordinates they must + + align:start position:0% +requirements. The coordinates they must + + + align:start position:0% +requirements. The coordinates they must +be + + align:start position:0% + + + + align:start position:0% + +what we call independent. + + align:start position:0% + + + + align:start position:0% + +They must be complete + + align:start position:0% + + + + align:start position:0% + +and so they must be independent and + + align:start position:0% +and so they must be independent and + + + align:start position:0% +and so they must be independent and +complete and the system + + align:start position:0% + + + + align:start position:0% + +must be holic. + + align:start position:0% + + + + align:start position:0% + +Now I'll get to that in a minute. So we + + align:start position:0% +Now I'll get to that in a minute. So we + + + align:start position:0% +Now I'll get to that in a minute. So we +need to you need to understand what it + + align:start position:0% +need to you need to understand what it + + + align:start position:0% +need to you need to understand what it +means to be independent, complete and + + align:start position:0% +means to be independent, complete and + + + align:start position:0% +means to be independent, complete and +whole and + + align:start position:0% + + + + align:start position:0% + +so what do we mean by independent? + + align:start position:0% +so what do we mean by independent? + + + align:start position:0% +so what do we mean by independent? +So if you have a multiple degree of + + align:start position:0% +So if you have a multiple degree of + + + align:start position:0% +So if you have a multiple degree of +freedom system and you fix all but one + + align:start position:0% +freedom system and you fix all but one + + + align:start position:0% +freedom system and you fix all but one +of the coordinates, you say system can't + + align:start position:0% +of the coordinates, you say system can't + + + align:start position:0% +of the coordinates, you say system can't +move in in all but one of its + + align:start position:0% +move in in all but one of its + + + align:start position:0% +move in in all but one of its +coordinates, that last degree of freedom + + align:start position:0% +coordinates, that last degree of freedom + + + align:start position:0% +coordinates, that last degree of freedom +still has to have a complete range of + + align:start position:0% +still has to have a complete range of + + + align:start position:0% +still has to have a complete range of +motion. So if you have a double pendulum + + align:start position:0% +motion. So if you have a double pendulum + + + align:start position:0% +motion. So if you have a double pendulum +and you grab the first mass, the second + + align:start position:0% +and you grab the first mass, the second + + + align:start position:0% +and you grab the first mass, the second +mass can still move. It takes two angles + + align:start position:0% +mass can still move. It takes two angles + + + align:start position:0% +mass can still move. It takes two angles +to define your double pendulum. + + align:start position:0% +to define your double pendulum. + + + align:start position:0% +to define your double pendulum. +So independent + + align:start position:0% + + + + align:start position:0% + +when you fix + + align:start position:0% +when you fix + + + align:start position:0% +when you fix +all but + + align:start position:0% +all but + + + align:start position:0% +all but +one + + align:start position:0% +one + + + align:start position:0% +one +coordinate. + + align:start position:0% + + + + align:start position:0% + +still + + align:start position:0% +still + + + align:start position:0% +still +have a + + align:start position:0% + + + + align:start position:0% + +continuous + + align:start position:0% + + + + align:start position:0% + +range of movement + + align:start position:0% + + + + align:start position:0% + +in essentially in the free + + align:start position:0% +in essentially in the free + + + align:start position:0% +in essentially in the free +coordinate. + + align:start position:0% + + + + align:start position:0% + +And that's independence. + + align:start position:0% +And that's independence. + + + align:start position:0% +And that's independence. +And we'll just we'll just kind of use + + align:start position:0% +And we'll just we'll just kind of use + + + align:start position:0% +And we'll just we'll just kind of use +the we'll we'll uh + + align:start position:0% +the we'll we'll uh + + + align:start position:0% +the we'll we'll uh +do this by example mostly. and complete + + align:start position:0% +do this by example mostly. and complete + + + align:start position:0% +do this by example mostly. and complete +the to complete really means it's + + align:start position:0% +the to complete really means it's + + + align:start position:0% +the to complete really means it's +capable of locating all parts of the + + align:start position:0% +capable of locating all parts of the + + + align:start position:0% +capable of locating all parts of the +system + + align:start position:0% +system + + + align:start position:0% +system +at all times. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +So let's think about let's look at the + + align:start position:0% +So let's think about let's look at the + + + align:start position:0% +So let's think about let's look at the +system here. It's double pendulum. + + align:start position:0% + + + + align:start position:0% + +It's a simple one just made out of two + + align:start position:0% +It's a simple one just made out of two + + + align:start position:0% +It's a simple one just made out of two +particles. + + align:start position:0% +particles. + + + align:start position:0% +particles. +and strings. I should have didn't bring + + align:start position:0% +and strings. I should have didn't bring + + + align:start position:0% +and strings. I should have didn't bring +one today. + + align:start position:0% +one today. + + + align:start position:0% +one today. +And I could I need to pick some + + align:start position:0% +And I could I need to pick some + + + align:start position:0% +And I could I need to pick some +coordinates to describe this. + + align:start position:0% +coordinates to describe this. + + + align:start position:0% +coordinates to describe this. +Okay. And we'll put this in a uh we'll + + align:start position:0% +Okay. And we'll put this in a uh we'll + + + align:start position:0% +Okay. And we'll put this in a uh we'll +use some cartisian coordinates here. Say + + align:start position:0% +use some cartisian coordinates here. Say + + + align:start position:0% +use some cartisian coordinates here. Say +an x and a y. And here's particle one. + + align:start position:0% +an x and a y. And here's particle one. + + + align:start position:0% +an x and a y. And here's particle one. +And I could choose to describe this + + align:start position:0% +And I could choose to describe this + + + align:start position:0% +And I could choose to describe this +system co uh xy coordinates. And I'll + + align:start position:0% +system co uh xy coordinates. And I'll + + + align:start position:0% +system co uh xy coordinates. And I'll +specify the location of the system with + + align:start position:0% +specify the location of the system with + + + align:start position:0% +specify the location of the system with +coordinates x1 and y1. Two values to + + align:start position:0% +coordinates x1 and y1. Two values to + + + align:start position:0% +coordinates x1 and y1. Two values to +specify the location of that. And I'm + + align:start position:0% +specify the location of that. And I'm + + + align:start position:0% +specify the location of that. And I'm +down here. I'm going to pick two more + + align:start position:0% +down here. I'm going to pick two more + + + align:start position:0% +down here. I'm going to pick two more +values x2 and y2 + + align:start position:0% +values x2 and y2 + + + align:start position:0% +values x2 and y2 +to describe the uh so these are the x1 + + align:start position:0% +to describe the uh so these are the x1 + + + align:start position:0% +to describe the uh so these are the x1 +is a different coordinate from x2. x1 is + + align:start position:0% +is a different coordinate from x2. x1 is + + + align:start position:0% +is a different coordinate from x2. x1 is +the x position of particle one. x2 is + + align:start position:0% +the x position of particle one. x2 is + + + align:start position:0% +the x position of particle one. x2 is +the x position of particle 2. Y1 and y2. + + align:start position:0% +the x position of particle 2. Y1 and y2. + + + align:start position:0% +the x position of particle 2. Y1 and y2. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So, how many coordinates do I have to + + align:start position:0% +So, how many coordinates do I have to + + + align:start position:0% +So, how many coordinates do I have to +describe this system? + + align:start position:0% + + + + align:start position:0% + +How many have I used? + + align:start position:0% +How many have I used? + + + align:start position:0% +How many have I used? +Four. Right. How many degrees of freedom + + align:start position:0% +Four. Right. How many degrees of freedom + + + align:start position:0% +Four. Right. How many degrees of freedom +do you think this problem has? + + align:start position:0% +do you think this problem has? + + + align:start position:0% +do you think this problem has? +Two. Right. So, there's something + + align:start position:0% +Two. Right. So, there's something + + + align:start position:0% +Two. Right. So, there's something +already a little out of whack here. Um, + + align:start position:0% +already a little out of whack here. Um, + + + align:start position:0% +already a little out of whack here. Um, +okay. + + align:start position:0% +okay. + + + align:start position:0% +okay. +But the point is these aren't + + align:start position:0% +But the point is these aren't + + + align:start position:0% +But the point is these aren't +independent. You'll find you just do a + + align:start position:0% +independent. You'll find you just do a + + + align:start position:0% +independent. You'll find you just do a +test, you find that these aren't + + align:start position:0% +test, you find that these aren't + + + align:start position:0% +test, you find that these aren't +independent. If I fix x1 and x2 systems + + align:start position:0% +independent. If I fix x1 and x2 systems + + + align:start position:0% +independent. If I fix x1 and x2 systems +doesn't move + + align:start position:0% +doesn't move + + + align:start position:0% +doesn't move +right. + + align:start position:0% +right. + + + align:start position:0% +right. +I say this has got to be one and this + + align:start position:0% +I say this has got to be one and this + + + align:start position:0% +I say this has got to be one and this +has got to be three. It this system is + + align:start position:0% +has got to be three. It this system is + + + align:start position:0% +has got to be three. It this system is +now frozen. + + align:start position:0% +now frozen. + + + align:start position:0% +now frozen. +So this system of core coordinates is + + align:start position:0% +So this system of core coordinates is + + + align:start position:0% +So this system of core coordinates is +not independent. + + align:start position:0% + + + + align:start position:0% + +What do we say independent? When you fix + + align:start position:0% +What do we say independent? When you fix + + + align:start position:0% +What do we say independent? When you fix +all but one coordinate, you still have + + align:start position:0% +all but one coordinate, you still have + + + align:start position:0% +all but one coordinate, you still have +continuous range of movement of the + + align:start position:0% +continuous range of movement of the + + + align:start position:0% +continuous range of movement of the +final one. I can fix only just two of + + align:start position:0% +final one. I can fix only just two of + + + align:start position:0% +final one. I can fix only just two of +these and I've frozen the system. I + + align:start position:0% +these and I've frozen the system. I + + + align:start position:0% +these and I've frozen the system. I +don't even have to go to the extent of + + align:start position:0% +don't even have to go to the extent of + + + align:start position:0% +don't even have to go to the extent of +fixing three. + + align:start position:0% +fixing three. + + + align:start position:0% +fixing three. +I'm assuming the strings are of fixed + + align:start position:0% +I'm assuming the strings are of fixed + + + align:start position:0% +I'm assuming the strings are of fixed +length. You can't change the string + + align:start position:0% +length. You can't change the string + + + align:start position:0% +length. You can't change the string +length. Okay. So, this is not a very + + align:start position:0% +length. Okay. So, this is not a very + + + align:start position:0% +length. Okay. So, this is not a very +good choice of coordinates. And we had a + + align:start position:0% +good choice of coordinates. And we had a + + + align:start position:0% +good choice of coordinates. And we had a +hint that it might not be because it's + + align:start position:0% +hint that it might not be because it's + + + align:start position:0% +hint that it might not be because it's +more than we ought to use. We only + + align:start position:0% +more than we ought to use. We only + + + align:start position:0% +more than we ought to use. We only +really need two. Okay. Okay. So, and + + align:start position:0% +really need two. Okay. Okay. So, and + + + align:start position:0% +really need two. Okay. Okay. So, and +then if we choose these angles F1 + + align:start position:0% +then if we choose these angles F1 + + + align:start position:0% +then if we choose these angles F1 +and F2, + + align:start position:0% +and F2, + + + align:start position:0% +and F2, +let's do the test with that. Are those + + align:start position:0% +let's do the test with that. Are those + + + align:start position:0% +let's do the test with that. Are those +independent? So, if those are the + + align:start position:0% +independent? So, if those are the + + + align:start position:0% +independent? So, if those are the +coordinates of the system, if you fix + + align:start position:0% +coordinates of the system, if you fix + + + align:start position:0% +coordinates of the system, if you fix +F1, is there still free and continuous + + align:start position:0% +F1, is there still free and continuous + + + align:start position:0% +F1, is there still free and continuous +movement of F2 of the system? Sure. And + + align:start position:0% +movement of F2 of the system? Sure. And + + + align:start position:0% +movement of F2 of the system? Sure. And +if you fix V2, which means you can + + align:start position:0% +if you fix V2, which means you can + + + align:start position:0% +if you fix V2, which means you can +require this angle stay rigid like that + + align:start position:0% +require this angle stay rigid like that + + + align:start position:0% +require this angle stay rigid like that +and move F1, well, the whole system will + + align:start position:0% +and move F1, well, the whole system will + + + align:start position:0% +and move F1, well, the whole system will +still move. So Fe1 and Fe2 are a system + + align:start position:0% +still move. So Fe1 and Fe2 are a system + + + align:start position:0% +still move. So Fe1 and Fe2 are a system +which satisfies the independence + + align:start position:0% +which satisfies the independence + + + align:start position:0% +which satisfies the independence +requirement complete. They're both + + align:start position:0% +requirement complete. They're both + + + align:start position:0% +requirement complete. They're both +systems are complete. They're both + + align:start position:0% +systems are complete. They're both + + + align:start position:0% +systems are complete. They're both +capable of locating all points at all + + align:start position:0% +capable of locating all points at all + + + align:start position:0% +capable of locating all points at all +times. + + align:start position:0% +times. + + + align:start position:0% +times. +Okay? But + + align:start position:0% +Okay? But + + + align:start position:0% +Okay? But +only the pair f1 and f2 in this example + + align:start position:0% +only the pair f1 and f2 in this example + + + align:start position:0% +only the pair f1 and f2 in this example +are both independent and complete. + + align:start position:0% +are both independent and complete. + + + align:start position:0% +are both independent and complete. +Now the third + + align:start position:0% +Now the third + + + align:start position:0% +Now the third +requirement is this thing thing called + + align:start position:0% +requirement is this thing thing called + + + align:start position:0% +requirement is this thing thing called +hol holomicity. + + align:start position:0% +hol holomicity. + + + align:start position:0% +hol holomicity. +And what holen what it means to be + + align:start position:0% +And what holen what it means to be + + + align:start position:0% +And what holen what it means to be +holomic + + align:start position:0% +holomic + + + align:start position:0% +holomic +is that the system the number of degrees + + align:start position:0% +is that the system the number of degrees + + + align:start position:0% +is that the system the number of degrees +of freedom required + + align:start position:0% +of freedom required + + + align:start position:0% +of freedom required +is equal to the number of number of + + align:start position:0% +is equal to the number of number of + + + align:start position:0% +is equal to the number of number of +coordinates required to completely + + align:start position:0% +coordinates required to completely + + + align:start position:0% +coordinates required to completely +describe the motion. Now, most of the + + align:start position:0% +describe the motion. Now, most of the + + + align:start position:0% +describe the motion. Now, most of the +time, every example we've ever done so + + align:start position:0% +time, every example we've ever done so + + + align:start position:0% +time, every example we've ever done so +far in this class satisfies that. We + + align:start position:0% +far in this class satisfies that. We + + + align:start position:0% +far in this class satisfies that. We +pick V1 and V2, and that's all the + + align:start position:0% +pick V1 and V2, and that's all the + + + align:start position:0% +pick V1 and V2, and that's all the +coordinates we need to completely + + align:start position:0% +coordinates we need to completely + + + align:start position:0% +coordinates we need to completely +describe the motion. Let me see if I can + + align:start position:0% +describe the motion. Let me see if I can + + + align:start position:0% +describe the motion. Let me see if I can +figure out a uh a counter example. + + align:start position:0% + + + + align:start position:0% + +So, I did I I didn't write down this + + align:start position:0% +So, I did I I didn't write down this + + + align:start position:0% +So, I did I I didn't write down this +definition. So, holomic + + align:start position:0% + + + + align:start position:0% + +And if the answer to this question is + + align:start position:0% +And if the answer to this question is + + + align:start position:0% +And if the answer to this question is +no, you cannot use lrange equations. + + align:start position:0% +no, you cannot use lrange equations. + + + align:start position:0% +no, you cannot use lrange equations. +So let's see if I can show you an + + align:start position:0% +So let's see if I can show you an + + + align:start position:0% +So let's see if I can show you an +example of a system in which + + align:start position:0% + + + + align:start position:0% + +You need more coordinates than you have + + align:start position:0% +You need more coordinates than you have + + + align:start position:0% +You need more coordinates than you have +degrees of freedom. I've got a ball. + + align:start position:0% +degrees of freedom. I've got a ball. + + + align:start position:0% +degrees of freedom. I've got a ball. +It's on the X. This is an XY plane. + + align:start position:0% +It's on the X. This is an XY plane. + + + align:start position:0% +It's on the X. This is an XY plane. +And the I'm not going to allow it to + + align:start position:0% +And the I'm not going to allow it to + + + align:start position:0% +And the I'm not going to allow it to +translate in Z. + + align:start position:0% +translate in Z. + + + align:start position:0% +translate in Z. +And I'm not going to allow it to rotate + + align:start position:0% +And I'm not going to allow it to rotate + + + align:start position:0% +And I'm not going to allow it to rotate +about the Z-axis. + + align:start position:0% +about the Z-axis. + + + align:start position:0% +about the Z-axis. +So I'm constru. + + align:start position:0% +So I'm constru. + + + align:start position:0% +So I'm constru. +So this is one rigid body. How how many + + align:start position:0% +So this is one rigid body. How how many + + + align:start position:0% +So this is one rigid body. How how many +general how many degrees of freedom does + + align:start position:0% +general how many degrees of freedom does + + + align:start position:0% +general how many degrees of freedom does +it have? + + align:start position:0% +it have? + + + align:start position:0% +it have? +Six. Okay. I'm going to constrain it. So + + align:start position:0% +Six. Okay. I'm going to constrain it. So + + + align:start position:0% +Six. Okay. I'm going to constrain it. So +no Z motion. Five. No Z rotation. Four. + + align:start position:0% +no Z motion. Five. No Z rotation. Four. + + + align:start position:0% +no Z motion. Five. No Z rotation. Four. +I'm not it's is not going to allow it to + + align:start position:0% +I'm not it's is not going to allow it to + + + align:start position:0% +I'm not it's is not going to allow it to +slip. This is X and that's Y. I'm not + + align:start position:0% +slip. This is X and that's Y. I'm not + + + align:start position:0% +slip. This is X and that's Y. I'm not +going to allow it to slip in the X. + + align:start position:0% +going to allow it to slip in the X. + + + align:start position:0% +going to allow it to slip in the X. +So now I've got another that's one. Now + + align:start position:0% +So now I've got another that's one. Now + + + align:start position:0% +So now I've got another that's one. Now +I'm down to three. And I'm not going to + + align:start position:0% +I'm down to three. And I'm not going to + + + align:start position:0% +I'm down to three. And I'm not going to +allow it to slip in the y + + align:start position:0% +allow it to slip in the y + + + align:start position:0% +allow it to slip in the y +two. So that by our calculus of how many + + align:start position:0% +two. So that by our calculus of how many + + + align:start position:0% +two. So that by our calculus of how many +degrees of freedom you need, we're down + + align:start position:0% +degrees of freedom you need, we're down + + + align:start position:0% +degrees of freedom you need, we're down +to two. We should be able to describe + + align:start position:0% +to two. We should be able to describe + + + align:start position:0% +to two. We should be able to describe +completely describe the motion of this + + align:start position:0% +completely describe the motion of this + + + align:start position:0% +completely describe the motion of this +system with two coordinates. Okay. So + + align:start position:0% +system with two coordinates. Okay. So + + + align:start position:0% +system with two coordinates. Okay. So +I've got this put this piece of tape on + + align:start position:0% +I've got this put this piece of tape on + + + align:start position:0% +I've got this put this piece of tape on +the top and it's pointing + + align:start position:0% +the top and it's pointing + + + align:start position:0% +the top and it's pointing +diagonally + + align:start position:0% +diagonally + + + align:start position:0% +diagonally +that way. And I'm going to roll this + + align:start position:0% +that way. And I'm going to roll this + + + align:start position:0% +that way. And I'm going to roll this +ball + + align:start position:0% +ball + + + align:start position:0% +ball +like this. + + align:start position:0% +like this. + + + align:start position:0% +like this. +until it shows up again. So, it's right + + align:start position:0% +until it shows up again. So, it's right + + + align:start position:0% +until it shows up again. So, it's right +on top just the way it started. + + align:start position:0% +on top just the way it started. + + + align:start position:0% +on top just the way it started. +Okay. Now, start off the same way again. + + align:start position:0% +Okay. Now, start off the same way again. + + + align:start position:0% +Okay. Now, start off the same way again. +I'm going to roll first this way + + align:start position:0% +I'm going to roll first this way + + + align:start position:0% +I'm going to roll first this way +and then I'm going to roll this way to + + align:start position:0% +and then I'm going to roll this way to + + + align:start position:0% +and then I'm going to roll this way to +the same place. + + align:start position:0% +the same place. + + + align:start position:0% +the same place. +Where's the stripe? + + align:start position:0% +Where's the stripe? + + + align:start position:0% +Where's the stripe? +It's in the back. + + align:start position:0% + + + + align:start position:0% + +So, I've gone to the same position, + + align:start position:0% +So, I've gone to the same position, + + + align:start position:0% +So, I've gone to the same position, +but I've ended up with the ball not in + + align:start position:0% +but I've ended up with the ball not in + + + align:start position:0% +but I've ended up with the ball not in +the same orientation as it was. I went + + align:start position:0% +the same orientation as it was. I went + + + align:start position:0% +the same orientation as it was. I went +by two different paths + + align:start position:0% + + + + align:start position:0% + +and the ball comes out over here rather + + align:start position:0% +and the ball comes out over here rather + + + align:start position:0% +and the ball comes out over here rather +than up there where it started. Okay. So + + align:start position:0% +than up there where it started. Okay. So + + + align:start position:0% +than up there where it started. Okay. So +this system actually to actually + + align:start position:0% +this system actually to actually + + + align:start position:0% +this system actually to actually +describe where the ball is at any place + + align:start position:0% +describe where the ball is at any place + + + align:start position:0% +describe where the ball is at any place +out here having gotten there by running + + align:start position:0% +out here having gotten there by running + + + align:start position:0% +out here having gotten there by running +around rolling around without slipping + + align:start position:0% +around rolling around without slipping + + + align:start position:0% +around rolling around without slipping +and without Z rotation. + + align:start position:0% +and without Z rotation. + + + align:start position:0% +and without Z rotation. +How many coordinates do you think it'll + + align:start position:0% +How many coordinates do you think it'll + + + align:start position:0% +How many coordinates do you think it'll +take to actually specify where that + + align:start position:0% +take to actually specify where that + + + align:start position:0% +take to actually specify where that +stripe is arbit at any arbitrary place + + align:start position:0% +stripe is arbit at any arbitrary place + + + align:start position:0% +stripe is arbit at any arbitrary place +that it's gotten to on the plane? + + align:start position:0% + + + + align:start position:0% + +Name them. + + align:start position:0% +Name them. + + + align:start position:0% +Name them. +distance + + align:start position:0% +distance + + + align:start position:0% +distance +rotation. + + align:start position:0% +rotation. + + + align:start position:0% +rotation. +So you got in order to actually fully + + align:start position:0% +So you got in order to actually fully + + + align:start position:0% +So you got in order to actually fully +describe it, you got to say where it is + + align:start position:0% +describe it, you got to say where it is + + + align:start position:0% +describe it, you got to say where it is +x and y and you actually have to say + + align:start position:0% +x and y and you actually have to say + + + align:start position:0% +x and y and you actually have to say +some kind of theta and fe rotations that + + align:start position:0% +some kind of theta and fe rotations that + + + align:start position:0% +some kind of theta and fe rotations that +it's gone through so that you know where + + align:start position:0% +it's gone through so that you know where + + + align:start position:0% +it's gone through so that you know where +this is. Okay. So this system is not + + align:start position:0% +this is. Okay. So this system is not + + + align:start position:0% +this is. Okay. So this system is not +holomic + + align:start position:0% +holomic + + + align:start position:0% +holomic +and holomic. It has to be holomic in + + align:start position:0% +and holomic. It has to be holomic in + + + align:start position:0% +and holomic. It has to be holomic in +order to + + align:start position:0% +order to + + + align:start position:0% +order to +be in order to use lrron's equations. + + align:start position:0% +be in order to use lrron's equations. + + + align:start position:0% +be in order to use lrron's equations. +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +so when you go to do Lrange problems, + + align:start position:0% +so when you go to do Lrange problems, + + + align:start position:0% +so when you go to do Lrange problems, +you need to test for your coordinates + + align:start position:0% +you need to test for your coordinates + + + align:start position:0% +you need to test for your coordinates +complete, independent, and holomic. And + + align:start position:0% +complete, independent, and holomic. And + + + align:start position:0% +complete, independent, and holomic. And +you get pretty good at it. So + + align:start position:0% + + + + align:start position:0% + +So here's my lrangee equations + + align:start position:0% +So here's my lrangee equations + + + align:start position:0% +So here's my lrangee equations +and I've itemize these four calcula calc + + align:start position:0% +and I've itemize these four calcula calc + + + align:start position:0% +and I've itemize these four calcula calc +calculations you have to do column 1 2 3 + + align:start position:0% +calculations you have to do column 1 2 3 + + + align:start position:0% +calculations you have to do column 1 2 3 +and four. Okay. And so what I just want + + align:start position:0% +and four. Okay. And so what I just want + + + align:start position:0% +and four. Okay. And so what I just want +what I want to write out is just to show + + align:start position:0% +what I want to write out is just to show + + + align:start position:0% +what I want to write out is just to show +you just to get you to adapt a + + align:start position:0% +you just to get you to adapt a + + + align:start position:0% +you just to get you to adapt a +systematic approach to doing lrange. So, + + align:start position:0% + + + + align:start position:0% + +left hand side. So, the left hand side + + align:start position:0% +left hand side. So, the left hand side + + + align:start position:0% +left hand side. So, the left hand side +of your equations of motion is + + align:start position:0% +of your equations of motion is + + + align:start position:0% +of your equations of motion is +everything with T and V. The right hand + + align:start position:0% +everything with T and V. The right hand + + + align:start position:0% +everything with T and V. The right hand +side is has these generalized forces + + align:start position:0% +side is has these generalized forces + + + align:start position:0% +side is has these generalized forces +that you have to deal with. And the + + align:start position:0% +that you have to deal with. And the + + + align:start position:0% +that you have to deal with. And the +generalized forces are the + + align:start position:0% +generalized forces are the + + + align:start position:0% +generalized forces are the +non-conservative forces in the system. + + align:start position:0% +non-conservative forces in the system. + + + align:start position:0% +non-conservative forces in the system. +Okay. So, this is going to get a little + + align:start position:0% +Okay. So, this is going to get a little + + + align:start position:0% +Okay. So, this is going to get a little +bit cookbook, but it's I think you + + align:start position:0% +bit cookbook, but it's I think you + + + align:start position:0% +bit cookbook, but it's I think you +appropriate for the moment here. So step + + align:start position:0% +appropriate for the moment here. So step + + + align:start position:0% +appropriate for the moment here. So step +one, + + align:start position:0% + + + + align:start position:0% + +determine the number of degrees of + + align:start position:0% +determine the number of degrees of + + + align:start position:0% +determine the number of degrees of +freedom that you need + + align:start position:0% + + + + align:start position:0% + +and choose + + align:start position:0% + + + + align:start position:0% + +your delta J's. Those are your not + + align:start position:0% +your delta J's. Those are your not + + + align:start position:0% +your delta J's. Those are your not +deltas, excuse me, just qjs. + + align:start position:0% +deltas, excuse me, just qjs. + + + align:start position:0% +deltas, excuse me, just qjs. +Choose your coordinates. You find the + + align:start position:0% +Choose your coordinates. You find the + + + align:start position:0% +Choose your coordinates. You find the +number of degrees of freedom and choose + + align:start position:0% +number of degrees of freedom and choose + + + align:start position:0% +number of degrees of freedom and choose +the coordinates you're going to use. + + align:start position:0% +the coordinates you're going to use. + + + align:start position:0% +the coordinates you're going to use. +Basically + + align:start position:0% + + + + align:start position:0% + +verify + + align:start position:0% + + + + align:start position:0% + +complete + + align:start position:0% + + + + align:start position:0% + +independent + + align:start position:0% + + + + align:start position:0% + +Polomic + + align:start position:0% + + + + align:start position:0% + +three. + + align:start position:0% + + + + align:start position:0% + +Compute T and V for every rigid body in + + align:start position:0% +Compute T and V for every rigid body in + + + align:start position:0% +Compute T and V for every rigid body in +the system. Compute your kinetic and + + align:start position:0% +the system. Compute your kinetic and + + + align:start position:0% +the system. Compute your kinetic and +potential energies. + + align:start position:0% + + + + align:start position:0% + +One, two, + + align:start position:0% +One, two, + + + align:start position:0% +One, two, +three + + align:start position:0% + + + + align:start position:0% + +for each + + align:start position:0% +for each + + + align:start position:0% +for each +qj. So for every coordinate you have, + + align:start position:0% +qj. So for every coordinate you have, + + + align:start position:0% +qj. So for every coordinate you have, +you have to go through these + + align:start position:0% +you have to go through these + + + align:start position:0% +you have to go through these +computations. 1 2 3 4 for every + + align:start position:0% +computations. 1 2 3 4 for every + + + align:start position:0% +computations. 1 2 3 4 for every +coordinate. + + align:start position:0% +coordinate. + + + align:start position:0% +coordinate. +And this is your left hand side. + + align:start position:0% + + + + align:start position:0% + +And if you don't have any external + + align:start position:0% +And if you don't have any external + + + align:start position:0% +And if you don't have any external +forces, any non-conservative external + + align:start position:0% +forces, any non-conservative external + + + align:start position:0% +forces, any non-conservative external +forces, then 1 2 1 plus 2 plus 3 equals + + align:start position:0% +forces, then 1 2 1 plus 2 plus 3 equals + + + align:start position:0% +forces, then 1 2 1 plus 2 plus 3 equals +zero. But if you have non-conservative + + align:start position:0% +zero. But if you have non-conservative + + + align:start position:0% +zero. But if you have non-conservative +forces, then you have to compute the + + align:start position:0% +forces, then you have to compute the + + + align:start position:0% +forces, then you have to compute the +right hand side. So the right hand side. + + align:start position:0% + + + + align:start position:0% + +So for + + align:start position:0% + + + + align:start position:0% + +each qj each generalized coordinate + + align:start position:0% +each qj each generalized coordinate + + + align:start position:0% +each qj each generalized coordinate +you need to find + + align:start position:0% +you need to find + + + align:start position:0% +you need to find +the generalized force + + align:start position:0% + + + + align:start position:0% + +that essentially goes with it. + + align:start position:0% + + + + align:start position:0% + +And you do this by computing + + align:start position:0% + + + + align:start position:0% + +the virtual work + + align:start position:0% + + + + align:start position:0% + +delta W. I'll put the little NC up here + + align:start position:0% +delta W. I'll put the little NC up here + + + align:start position:0% +delta W. I'll put the little NC up here +to remind you these are for the + + align:start position:0% +to remind you these are for the + + + align:start position:0% +to remind you these are for the +non-conservative forces. The delta W + + align:start position:0% +non-conservative forces. The delta W + + + align:start position:0% +non-conservative forces. The delta W +associated + + align:start position:0% + + + + align:start position:0% + +with the + + align:start position:0% + + + + align:start position:0% + +virtual displacement + + align:start position:0% + + + + align:start position:0% + +delta qj. So for every generalized + + align:start position:0% +delta qj. So for every generalized + + + align:start position:0% +delta qj. So for every generalized +coordinate you have, you're going to try + + align:start position:0% +coordinate you have, you're going to try + + + align:start position:0% +coordinate you have, you're going to try +out this little delta c delta of motion + + align:start position:0% +out this little delta c delta of motion + + + align:start position:0% +out this little delta c delta of motion +in that coordinate and figure out how + + align:start position:0% +in that coordinate and figure out how + + + align:start position:0% +in that coordinate and figure out how +much um + + align:start position:0% +much um + + + align:start position:0% +much um +virtual work you've done. So so delta wj + + align:start position:0% +virtual work you've done. So so delta wj + + + align:start position:0% +virtual work you've done. So so delta wj +is going to be qj + + align:start position:0% +is going to be qj + + + align:start position:0% +is going to be qj +delta j. So whatever this is the thing + + align:start position:0% +delta j. So whatever this is the thing + + + align:start position:0% +delta j. So whatever this is the thing +you're looking for. + + align:start position:0% +you're looking for. + + + align:start position:0% +you're looking for. +And it's going to be a function of all + + align:start position:0% +And it's going to be a function of all + + + align:start position:0% +And it's going to be a function of all +those external + + align:start position:0% +those external + + + align:start position:0% +those external +non-conservative forces acting through a + + align:start position:0% +non-conservative forces acting through a + + + align:start position:0% +non-conservative forces acting through a +little virtual displacement. A little + + align:start position:0% +little virtual displacement. A little + + + align:start position:0% +little virtual displacement. A little +bit of work will be done. Mostly I'm + + align:start position:0% +bit of work will be done. Mostly I'm + + + align:start position:0% +bit of work will be done. Mostly I'm +going to teach you how to do this by by + + align:start position:0% +going to teach you how to do this by by + + + align:start position:0% +going to teach you how to do this by by +example. + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +So let's quickly do + + align:start position:0% +So let's quickly do + + + align:start position:0% +So let's quickly do +a really simple trivial system. + + align:start position:0% +a really simple trivial system. + + + align:start position:0% +a really simple trivial system. +Our mass spring + + align:start position:0% + + + + align:start position:0% + +dash pot system single degree of freedom + + align:start position:0% +dash pot system single degree of freedom + + + align:start position:0% +dash pot system single degree of freedom +m k b + + align:start position:0% +m k b + + + align:start position:0% +m k b +it's going to take one coordinate to + + align:start position:0% +it's going to take one coordinate to + + + align:start position:0% +it's going to take one coordinate to +describe the motion. + + align:start position:0% +describe the motion. + + + align:start position:0% +describe the motion. +X happens to be cartisian. + + align:start position:0% +X happens to be cartisian. + + + align:start position:0% +X happens to be cartisian. +There'll be one generalized coordinate. + + align:start position:0% +There'll be one generalized coordinate. + + + align:start position:0% +There'll be one generalized coordinate. +So Q + + align:start position:0% +So Q + + + align:start position:0% +So Q +J = Q1 + + align:start position:0% +J = Q1 + + + align:start position:0% +J = Q1 +equals QX in this case. It's our X + + align:start position:0% +equals QX in this case. It's our X + + + align:start position:0% +equals QX in this case. It's our X +coordinate. Actually I should just call + + align:start position:0% +coordinate. Actually I should just call + + + align:start position:0% +coordinate. Actually I should just call +it X. That's our generalized coordinate + + align:start position:0% +it X. That's our generalized coordinate + + + align:start position:0% +it X. That's our generalized coordinate +for this problem. Is it complete? Yep. + + align:start position:0% +for this problem. Is it complete? Yep. + + + align:start position:0% +for this problem. Is it complete? Yep. +Is it independent? Yes. Is it whole? No + + align:start position:0% +Is it independent? Yes. Is it whole? No + + + align:start position:0% +Is it independent? Yes. Is it whole? No +problem. Okay, + + align:start position:0% +problem. Okay, + + + align:start position:0% +problem. Okay, +we need t + + align:start position:0% + + + + align:start position:0% + +m x dot squared. We need v and + + align:start position:0% +m x dot squared. We need v and + + + align:start position:0% +m x dot squared. We need v and +we have 12 k x^2 for the spring + + align:start position:0% +we have 12 k x^2 for the spring + + + align:start position:0% +we have 12 k x^2 for the spring +minus + + align:start position:0% + + + + align:start position:0% + +mgx for the gravitational potential + + align:start position:0% +mgx for the gravitational potential + + + align:start position:0% +mgx for the gravitational potential +energy. + + align:start position:0% +energy. + + + align:start position:0% +energy. +And now we can start + + align:start position:0% +And now we can start + + + align:start position:0% +And now we can start +and we have some external + + align:start position:0% +and we have some external + + + align:start position:0% +and we have some external +non-conservative forces. What are they + + align:start position:0% +non-conservative forces. What are they + + + align:start position:0% +non-conservative forces. What are they +fi non-conservative? + + align:start position:0% + + + + align:start position:0% + +And I think I'll better I'm going to put + + align:start position:0% +And I think I'll better I'm going to put + + + align:start position:0% +And I think I'll better I'm going to put +an excitation on here too. Some f of t. + + align:start position:0% +an excitation on here too. Some f of t. + + + align:start position:0% +an excitation on here too. Some f of t. +So what are the non-conservative forces + + align:start position:0% +So what are the non-conservative forces + + + align:start position:0% +So what are the non-conservative forces +Jonathan? Pardon? + + align:start position:0% +Jonathan? Pardon? + + + align:start position:0% +Jonathan? Pardon? +K. It's not K, but + + align:start position:0% +K. It's not K, but + + + align:start position:0% +K. It's not K, but +oh, I wrote my mistake. Sorry about + + align:start position:0% +oh, I wrote my mistake. Sorry about + + + align:start position:0% +oh, I wrote my mistake. Sorry about +you're correct. I'm just uh my brain is + + align:start position:0% +you're correct. I'm just uh my brain is + + + align:start position:0% +you're correct. I'm just uh my brain is +getting ahead of my writing here. That's + + align:start position:0% +getting ahead of my writing here. That's + + + align:start position:0% +getting ahead of my writing here. That's +normally B and this would be K. I'm not + + align:start position:0% +normally B and this would be K. I'm not + + + align:start position:0% +normally B and this would be K. I'm not +trying to really mess you up there. So, + + align:start position:0% +trying to really mess you up there. So, + + + align:start position:0% +trying to really mess you up there. So, +what would that it would be Bx dot, + + align:start position:0% +what would that it would be Bx dot, + + + align:start position:0% +what would that it would be Bx dot, +right? Okay. Right. And is there + + align:start position:0% +right? Okay. Right. And is there + + + align:start position:0% +right? Okay. Right. And is there +anything else? + + align:start position:0% +anything else? + + + align:start position:0% +anything else? +Are there any other non-conservative + + align:start position:0% +Are there any other non-conservative + + + align:start position:0% +Are there any other non-conservative +forces? Things that can put energy into + + align:start position:0% +forces? Things that can put energy into + + + align:start position:0% +forces? Things that can put energy into +or out of the system? + + align:start position:0% + + + + align:start position:0% + +So the damper can certainly extract + + align:start position:0% +So the damper can certainly extract + + + align:start position:0% +So the damper can certainly extract +energy. + + align:start position:0% +energy. + + + align:start position:0% +energy. +F. + + align:start position:0% +F. + + + align:start position:0% +F. +Yeah, the forcef that external it might + + align:start position:0% +Yeah, the forcef that external it might + + + align:start position:0% +Yeah, the forcef that external it might +be, you know, something that's making it + + align:start position:0% +be, you know, something that's making it + + + align:start position:0% +be, you know, something that's making it +vibrate or whatever, but it's an + + align:start position:0% +vibrate or whatever, but it's an + + + align:start position:0% +vibrate or whatever, but it's an +external force and it could do work on + + align:start position:0% +external force and it could do work on + + + align:start position:0% +external force and it could do work on +the system and it's not necessarily a + + align:start position:0% +the system and it's not necessarily a + + + align:start position:0% +the system and it's not necessarily a +it's not a potential. It's not a spring + + align:start position:0% +it's not a potential. It's not a spring + + + align:start position:0% +it's not a potential. It's not a spring +and it's not a it's not gravity. + + align:start position:0% +and it's not a it's not gravity. + + + align:start position:0% +and it's not a it's not gravity. +It's coming up and somebody's shaking it + + align:start position:0% +It's coming up and somebody's shaking it + + + align:start position:0% +It's coming up and somebody's shaking it +or something like that. So F is also + + align:start position:0% +or something like that. So F is also + + + align:start position:0% +or something like that. So F is also +non-conservative. So the + + align:start position:0% +non-conservative. So the + + + align:start position:0% +non-conservative. So the +non-conservative forces in this thing + + align:start position:0% +non-conservative forces in this thing + + + align:start position:0% +non-conservative forces in this thing +are uh F in the + + align:start position:0% +are uh F in the + + + align:start position:0% +are uh F in the +I direction and minus Bx dot in the I + + align:start position:0% +I direction and minus Bx dot in the I + + + align:start position:0% +I direction and minus Bx dot in the I +direction. And we could in our normal + + align:start position:0% +direction. And we could in our normal + + + align:start position:0% +direction. And we could in our normal +approach using Newton, we'd draw a free + + align:start position:0% +approach using Newton, we'd draw a free + + + align:start position:0% +approach using Newton, we'd draw a free +body diagram and we we'd identify a BX + + align:start position:0% +body diagram and we we'd identify a BX + + + align:start position:0% +body diagram and we we'd identify a BX +dot on it and an F on it, but we'd also + + align:start position:0% +dot on it and an F on it, but we'd also + + + align:start position:0% +dot on it and an F on it, but we'd also +have our kx on it. + + align:start position:0% +have our kx on it. + + + align:start position:0% +have our kx on it. +That would be what our free body diagram + + align:start position:0% +That would be what our free body diagram + + + align:start position:0% +That would be what our free body diagram +would look like. And the non that's a + + align:start position:0% +would look like. And the non that's a + + + align:start position:0% +would look like. And the non that's a +conservative force. Oops. And we need an + + align:start position:0% +conservative force. Oops. And we need an + + + align:start position:0% +conservative force. Oops. And we need an +mg. + + align:start position:0% +mg. + + + align:start position:0% +mg. +So we have two conservative forces kx + + align:start position:0% +So we have two conservative forces kx + + + align:start position:0% +So we have two conservative forces kx +and mg. And we have two non-conservative + + align:start position:0% +and mg. And we have two non-conservative + + + align:start position:0% +and mg. And we have two non-conservative +forces bx dot and f. So in this case the + + align:start position:0% +forces bx dot and f. So in this case the + + + align:start position:0% +forces bx dot and f. So in this case the +non-con sum of the non-conservative + + align:start position:0% +non-con sum of the non-conservative + + + align:start position:0% +non-con sum of the non-conservative +forces is f in the i direction minus bx + + align:start position:0% +forces is f in the i direction minus bx + + + align:start position:0% +forces is f in the i direction minus bx +in the i x dot in the i direction. + + align:start position:0% +in the i x dot in the i direction. + + + align:start position:0% +in the i x dot in the i direction. +So let's + + align:start position:0% +So let's + + + align:start position:0% +So let's +do our calculus here. So 1 d by dt of + + align:start position:0% +do our calculus here. So 1 d by dt of + + + align:start position:0% +do our calculus here. So 1 d by dt of +the partial of t which is 12 m x dot + + align:start position:0% +the partial of t which is 12 m x dot + + + align:start position:0% +the partial of t which is 12 m x dot +squared with respect to x dot. + + align:start position:0% +squared with respect to x dot. + + + align:start position:0% +squared with respect to x dot. +So that gives me the derivative of x + + align:start position:0% +So that gives me the derivative of x + + + align:start position:0% +So that gives me the derivative of x +dot^2 with respect to x dot gives me a 2 + + align:start position:0% +dot^2 with respect to x dot gives me a 2 + + + align:start position:0% +dot^2 with respect to x dot gives me a 2 +mx dot. So this is d by dt + + align:start position:0% +mx dot. So this is d by dt + + + align:start position:0% +mx dot. So this is d by dt +of mx dot but that's m x dot. And as you + + align:start position:0% +of mx dot but that's m x dot. And as you + + + align:start position:0% +of mx dot but that's m x dot. And as you +might expect when you're trying to drive + + align:start position:0% +might expect when you're trying to drive + + + align:start position:0% +might expect when you're trying to drive +equation of motion you're probably going + + align:start position:0% +equation of motion you're probably going + + + align:start position:0% +equation of motion you're probably going +to end up with an mx dot in the result + + align:start position:0% +to end up with an mx dot in the result + + + align:start position:0% +to end up with an mx dot in the result +and it always comes out of these dydt + + align:start position:0% +and it always comes out of these dydt + + + align:start position:0% +and it always comes out of these dydt +expressions. + + align:start position:0% +expressions. + + + align:start position:0% +expressions. +Okay. So that's term one. + + align:start position:0% +Okay. So that's term one. + + + align:start position:0% +Okay. So that's term one. +term two in this problem minus t with + + align:start position:0% +term two in this problem minus t with + + + align:start position:0% +term two in this problem minus t with +respect to x in this case + + align:start position:0% +respect to x in this case + + + align:start position:0% +respect to x in this case +is t a function of x + + align:start position:0% + + + + align:start position:0% + +say 12 mx dot squared but so is t a + + align:start position:0% +say 12 mx dot squared but so is t a + + + align:start position:0% +say 12 mx dot squared but so is t a +function of displacement x it's a + + align:start position:0% +function of displacement x it's a + + + align:start position:0% +function of displacement x it's a +function of velocity in the x direction + + align:start position:0% +function of velocity in the x direction + + + align:start position:0% +function of velocity in the x direction +but is it a function of displacement + + align:start position:0% +but is it a function of displacement + + + align:start position:0% +but is it a function of displacement +no so this term is + + align:start position:0% +no so this term is + + + align:start position:0% +no so this term is +zero + + align:start position:0% +zero + + + align:start position:0% +zero +three our third term + + align:start position:0% +three our third term + + + align:start position:0% +three our third term +partial of v + + align:start position:0% +partial of v + + + align:start position:0% +partial of v +with respect to x ah well where's v half + + align:start position:0% +with respect to x ah well where's v half + + + align:start position:0% +with respect to x ah well where's v half +kx^2 the derivative of this is kx minus + + align:start position:0% +kx^2 the derivative of this is kx minus + + + align:start position:0% +kx^2 the derivative of this is kx minus +mg + + align:start position:0% + + + + align:start position:0% + +okay and we sum those + + align:start position:0% + + + + align:start position:0% + +So we get mx dot plus + + align:start position:0% + + + + align:start position:0% + +kx - mg equals and on the right hand + + align:start position:0% +kx - mg equals and on the right hand + + + align:start position:0% +kx - mg equals and on the right hand +side this is four. + + align:start position:0% +side this is four. + + + align:start position:0% +side this is four. +Now we need to do four for the right + + align:start position:0% +Now we need to do four for the right + + + align:start position:0% +Now we need to do four for the right +hand side + + align:start position:0% +hand side + + + align:start position:0% +hand side +and four is really the summation + + align:start position:0% + + + + align:start position:0% + +of the FIS the individual forces dotted + + align:start position:0% +of the FIS the individual forces dotted + + + align:start position:0% +of the FIS the individual forces dotted +with + + align:start position:0% +with + + + align:start position:0% +with +dr. + + align:start position:0% +dr. + + + align:start position:0% +dr. +These are both vectors. + + align:start position:0% + + + + align:start position:0% + +dr is the movement. little bit of work + + align:start position:0% +dr is the movement. little bit of work + + + align:start position:0% +dr is the movement. little bit of work +and it's going to be a delta quantity + + align:start position:0% +and it's going to be a delta quantity + + + align:start position:0% +and it's going to be a delta quantity +like delta x and f of the applied forces + + align:start position:0% +like delta x and f of the applied forces + + + align:start position:0% +like delta x and f of the applied forces +and you need to sum these up. So this dr + + align:start position:0% +and you need to sum these up. So this dr + + + align:start position:0% +and you need to sum these up. So this dr +in general is going to be a function of + + align:start position:0% +in general is going to be a function of + + + align:start position:0% +in general is going to be a function of +the delta + + align:start position:0% +the delta + + + align:start position:0% +the delta +j's the virtual displacements in all the + + align:start position:0% +j's the virtual displacements in all the + + + align:start position:0% +j's the virtual displacements in all the +possible degrees of freedom of the + + align:start position:0% +possible degrees of freedom of the + + + align:start position:0% +possible degrees of freedom of the +system. We do them one at a time. This + + align:start position:0% +system. We do them one at a time. This + + + align:start position:0% +system. We do them one at a time. This +case we only have one so it's trivial + + align:start position:0% +case we only have one so it's trivial + + + align:start position:0% +case we only have one so it's trivial +but this could be you know delta 1 2 3 4 + + align:start position:0% +but this could be you know delta 1 2 3 4 + + + align:start position:0% +but this could be you know delta 1 2 3 4 +and each one of them might do some work + + align:start position:0% +and each one of them might do some work + + + align:start position:0% +and each one of them might do some work +when f moves through it but work is f + + align:start position:0% +when f moves through it but work is f + + + align:start position:0% +when f moves through it but work is f +dot the displacement so it's the + + align:start position:0% +dot the displacement so it's the + + + align:start position:0% +dot the displacement so it's the +component of the force in the direction + + align:start position:0% +component of the force in the direction + + + align:start position:0% +component of the force in the direction +of the movement the dotproduct that + + align:start position:0% +of the movement the dotproduct that + + + align:start position:0% +of the movement the dotproduct that +gives you this little bit of virtual + + align:start position:0% +gives you this little bit of virtual + + + align:start position:0% +gives you this little bit of virtual +work okay so in this problem this is + + align:start position:0% +work okay so in this problem this is + + + align:start position:0% +work okay so in this problem this is +going to be equal two, + + align:start position:0% + + + + align:start position:0% + +we actually have an f of t some function + + align:start position:0% +we actually have an f of t some function + + + align:start position:0% +we actually have an f of t some function +of time in the i direction minus b x dot + + align:start position:0% +of time in the i direction minus b x dot + + + align:start position:0% +of time in the i direction minus b x dot +in the i direction + + align:start position:0% +in the i direction + + + align:start position:0% +in the i direction +dotted with delta + + align:start position:0% +dotted with delta + + + align:start position:0% +dotted with delta +x which is our virtual displacement in + + align:start position:0% +x which is our virtual displacement in + + + align:start position:0% +x which is our virtual displacement in +our single generalized coordinate. And + + align:start position:0% +our single generalized coordinate. And + + + align:start position:0% +our single generalized coordinate. And +this whole thing is going to be equal to + + align:start position:0% +this whole thing is going to be equal to + + + align:start position:0% +this whole thing is going to be equal to +q x delta x. + + align:start position:0% + + + + align:start position:0% + +So you figure out the virtual work + + align:start position:0% +So you figure out the virtual work + + + align:start position:0% +So you figure out the virtual work +that's done. + + align:start position:0% +that's done. + + + align:start position:0% +that's done. +So delta. So if you do this dotproduct, + + align:start position:0% +So delta. So if you do this dotproduct, + + + align:start position:0% +So delta. So if you do this dotproduct, +this is also in the ihat direction. into + + align:start position:0% +this is also in the ihat direction. into + + + align:start position:0% +this is also in the ihat direction. into +I do I I do I you just get ones because + + align:start position:0% +I do I I do I you just get ones because + + + align:start position:0% +I do I I do I you just get ones because +the forces are in the same direction as + + align:start position:0% +the forces are in the same direction as + + + align:start position:0% +the forces are in the same direction as +the dis as the displacement + + align:start position:0% +the dis as the displacement + + + align:start position:0% +the dis as the displacement +you're going to get an FT f of t delta x + + align:start position:0% +you're going to get an FT f of t delta x + + + align:start position:0% +you're going to get an FT f of t delta x +is one of the little bits of virtual + + align:start position:0% +is one of the little bits of virtual + + + align:start position:0% +is one of the little bits of virtual +work and you'll get a minus bx dot delta + + align:start position:0% +work and you'll get a minus bx dot delta + + + align:start position:0% +work and you'll get a minus bx dot delta +x + + align:start position:0% +x + + + align:start position:0% +x +and that together those two pieces added + + align:start position:0% +and that together those two pieces added + + + align:start position:0% +and that together those two pieces added +together + + align:start position:0% +together + + + align:start position:0% +together +are the generalized force times delta x + + align:start position:0% +are the generalized force times delta x + + + align:start position:0% +are the generalized force times delta x +This total here gives you delta w + + align:start position:0% +This total here gives you delta w + + + align:start position:0% +This total here gives you delta w +non-conservative for in this case + + align:start position:0% +non-conservative for in this case + + + align:start position:0% +non-conservative for in this case +coordinate x. + + align:start position:0% +coordinate x. + + + align:start position:0% +coordinate x. +So we need to we're trying to solve for + + align:start position:0% +So we need to we're trying to solve for + + + align:start position:0% +So we need to we're trying to solve for +the what goes on the right hand side. We + + align:start position:0% +the what goes on the right hand side. We + + + align:start position:0% +the what goes on the right hand side. We +need the qx. + + align:start position:0% +need the qx. + + + align:start position:0% +need the qx. +So we have here you notice what'll + + align:start position:0% +So we have here you notice what'll + + + align:start position:0% +So we have here you notice what'll +happen. you'll divide, it'll cancel out + + align:start position:0% +happen. you'll divide, it'll cancel out + + + align:start position:0% +happen. you'll divide, it'll cancel out +the delta x's that result. + + align:start position:0% +the delta x's that result. + + + align:start position:0% +the delta x's that result. +And in this case, what you're left with + + align:start position:0% +And in this case, what you're left with + + + align:start position:0% +And in this case, what you're left with +is + + align:start position:0% + + + + align:start position:0% + +qx + + align:start position:0% +qx + + + align:start position:0% +qx += f of t minus bx dot. + + align:start position:0% += f of t minus bx dot. + + + align:start position:0% += f of t minus bx dot. +So this is number four. + + align:start position:0% + + + + align:start position:0% + +So qx delta x is the bit of virtual work + + align:start position:0% +So qx delta x is the bit of virtual work + + + align:start position:0% +So qx delta x is the bit of virtual work +that's done what goes into our equation + + align:start position:0% +that's done what goes into our equation + + + align:start position:0% +that's done what goes into our equation +of motion is the qx part and we got it + + align:start position:0% +of motion is the qx part and we got it + + + align:start position:0% +of motion is the qx part and we got it +by computing the virtual work done by + + align:start position:0% +by computing the virtual work done by + + + align:start position:0% +by computing the virtual work done by +the applied external non-conservative + + align:start position:0% +the applied external non-conservative + + + align:start position:0% +the applied external non-conservative +forces as we imagine them going through + + align:start position:0% +forces as we imagine them going through + + + align:start position:0% +forces as we imagine them going through +delta x + + align:start position:0% +delta x + + + align:start position:0% +delta x +and we're done. And you have the + + align:start position:0% +and we're done. And you have the + + + align:start position:0% +and we're done. And you have the +complete equation of motion for a single + + align:start position:0% +complete equation of motion for a single + + + align:start position:0% +complete equation of motion for a single +degree of freedom system. You could + + align:start position:0% +degree of freedom system. You could + + + align:start position:0% +degree of freedom system. You could +rearrange it a little bit. mx dot plus + + align:start position:0% +rearrange it a little bit. mx dot plus + + + align:start position:0% +rearrange it a little bit. mx dot plus +bx dot plus kx equals mg plus f of t if + + align:start position:0% +bx dot plus kx equals mg plus f of t if + + + align:start position:0% +bx dot plus kx equals mg plus f of t if +you will. So it's the same thing you + + align:start position:0% +you will. So it's the same thing you + + + align:start position:0% +you will. So it's the same thing you +would have gotten from saying from using + + align:start position:0% +would have gotten from saying from using + + + align:start position:0% +would have gotten from saying from using +Newton in a you know in a trivial kind + + align:start position:0% +Newton in a you know in a trivial kind + + + align:start position:0% +Newton in a you know in a trivial kind +of example but it helps define each of + + align:start position:0% +of example but it helps define each of + + + align:start position:0% +of example but it helps define each of +the steps + + align:start position:0% +the steps + + + align:start position:0% +the steps +things that we said were required. + + align:start position:0% + + + + align:start position:0% + +Okay. So, we're going to go from there + + align:start position:0% +Okay. So, we're going to go from there + + + align:start position:0% +Okay. So, we're going to go from there +to a much harder problem. + + align:start position:0% +to a much harder problem. + + + align:start position:0% +to a much harder problem. +So, any issues or questions about + + align:start position:0% +So, any issues or questions about + + + align:start position:0% +So, any issues or questions about +definitions, + + align:start position:0% +definitions, + + + align:start position:0% +definitions, +procedure? + + align:start position:0% +procedure? + + + align:start position:0% +procedure? +So, when you start getting into multiple + + align:start position:0% +So, when you start getting into multiple + + + align:start position:0% +So, when you start getting into multiple +degrees of freedom, you need to set up a + + align:start position:0% +degrees of freedom, you need to set up a + + + align:start position:0% +degrees of freedom, you need to set up a +careful bookkeeping. + + align:start position:0% +careful bookkeeping. + + + align:start position:0% +careful bookkeeping. +So, I I do I just do this myself. Then I + + align:start position:0% +So, I I do I just do this myself. Then I + + + align:start position:0% +So, I I do I just do this myself. Then I +I top of the page, I identify my + + align:start position:0% +I top of the page, I identify my + + + align:start position:0% +I top of the page, I identify my +coordinates. + + align:start position:0% +coordinates. + + + align:start position:0% +coordinates. +I write down t, write down v. Then I + + align:start position:0% +I write down t, write down v. Then I + + + align:start position:0% +I write down t, write down v. Then I +say, okay, coordinate one, + + align:start position:0% +say, okay, coordinate one, + + + align:start position:0% +say, okay, coordinate one, +one, two, three, four equation. Then I + + align:start position:0% +one, two, three, four equation. Then I + + + align:start position:0% +one, two, three, four equation. Then I +start with a coordinate two. Calculus + + align:start position:0% +start with a coordinate two. Calculus + + + align:start position:0% +start with a coordinate two. Calculus +for one, two, three, and four and so + + align:start position:0% +for one, two, three, and four and so + + + align:start position:0% +for one, two, three, and four and so +forth till you get to the end. Okay, + + align:start position:0% +forth till you get to the end. Okay, + + + align:start position:0% +forth till you get to the end. Okay, +questions. Yeah. + + align:start position:0% +questions. Yeah. + + + align:start position:0% +questions. Yeah. +on the line. + + align:start position:0% +on the line. + + + align:start position:0% +on the line. +Um, what's that thing? + + align:start position:0% + + + + align:start position:0% + +Oh, I these are functions of the of the + + align:start position:0% +Oh, I these are functions of the of the + + + align:start position:0% +Oh, I these are functions of the of the +delta J's. this this DR where it comes + + align:start position:0% +delta J's. this this DR where it comes + + + align:start position:0% +delta J's. this this DR where it comes +from the work that's being done in the + + align:start position:0% +from the work that's being done in the + + + align:start position:0% +from the work that's being done in the +virtual displacement around a dynamic + + align:start position:0% +virtual displacement around a dynamic + + + align:start position:0% +virtual displacement around a dynamic +equilibri equilibrium position for the + + align:start position:0% +equilibri equilibrium position for the + + + align:start position:0% +equilibri equilibrium position for the +system is a little movement of the + + align:start position:0% +system is a little movement of the + + + align:start position:0% +system is a little movement of the +system Dr. + + align:start position:0% +system Dr. + + + align:start position:0% +system Dr. +and we express it it's expressed in + + align:start position:0% +and we express it it's expressed in + + + align:start position:0% +and we express it it's expressed in +terms of the generalized a virtual + + align:start position:0% +terms of the generalized a virtual + + + align:start position:0% +terms of the generalized a virtual +displacement of the generalized + + align:start position:0% +displacement of the generalized + + + align:start position:0% +displacement of the generalized +coordinates of the system. So where the + + align:start position:0% +coordinates of the system. So where the + + + align:start position:0% +coordinates of the system. So where the +dr comes from is going to be delta in + + align:start position:0% +dr comes from is going to be delta in + + + align:start position:0% +dr comes from is going to be delta in +this case it's only delta x + + align:start position:0% +this case it's only delta x + + + align:start position:0% +this case it's only delta x +and in the next problem we're going to + + align:start position:0% +and in the next problem we're going to + + + align:start position:0% +and in the next problem we're going to +do the force in the problem is not in + + align:start position:0% +do the force in the problem is not in + + + align:start position:0% +do the force in the problem is not in +exactly the same direction as the delta + + align:start position:0% +exactly the same direction as the delta + + + align:start position:0% +exactly the same direction as the delta +x's and delta thetas and so forth. So + + align:start position:0% +x's and delta thetas and so forth. So + + + align:start position:0% +x's and delta thetas and so forth. So +when you do the dotproduct only that + + align:start position:0% +when you do the dotproduct only that + + + align:start position:0% +when you do the dotproduct only that +component of the force that's in the + + align:start position:0% +component of the force that's in the + + + align:start position:0% +component of the force that's in the +direction of the virtual displacement + + align:start position:0% +direction of the virtual displacement + + + align:start position:0% +direction of the virtual displacement +does work and you you account for that. + + align:start position:0% +does work and you you account for that. + + + align:start position:0% +does work and you you account for that. +So let's let's uh look into a more + + align:start position:0% +So let's let's uh look into a more + + + align:start position:0% +So let's let's uh look into a more +difficult problem. + + align:start position:0% +difficult problem. + + + align:start position:0% +difficult problem. +So the problem is this. I tried to I I + + align:start position:0% +So the problem is this. I tried to I I + + + align:start position:0% +So the problem is this. I tried to I I +tried to fix this up before I came to + + align:start position:0% +tried to fix this up before I came to + + + align:start position:0% +tried to fix this up before I came to +class and I really didn't really quite + + align:start position:0% +class and I really didn't really quite + + + align:start position:0% +class and I really didn't really quite +have the the uh parts and pieces I + + align:start position:0% +have the the uh parts and pieces I + + + align:start position:0% +have the the uh parts and pieces I +needed, but this is a piece of just a + + align:start position:0% +needed, but this is a piece of just a + + + align:start position:0% +needed, but this is a piece of just a +piece of steel pipe here. It's a sleeve + + align:start position:0% +piece of steel pipe here. It's a sleeve + + + align:start position:0% +piece of steel pipe here. It's a sleeve +on the outside of this rod. + + align:start position:0% +on the outside of this rod. + + + align:start position:0% +on the outside of this rod. +And I've got a + + align:start position:0% +And I've got a + + + align:start position:0% +And I've got a +spring that's on the outside connected + + align:start position:0% +spring that's on the outside connected + + + align:start position:0% +spring that's on the outside connected +to this piece. And so it can do this. + + align:start position:0% + + + + align:start position:0% + +Okay. And it's also though a pendulum. + + align:start position:0% +Okay. And it's also though a pendulum. + + + align:start position:0% +Okay. And it's also though a pendulum. +So the system I really want to look at + + align:start position:0% +So the system I really want to look at + + + align:start position:0% +So the system I really want to look at +is this system. + + align:start position:0% + + + + align:start position:0% + +So as it swings back and forth, the + + align:start position:0% +So as it swings back and forth, the + + + align:start position:0% +So as it swings back and forth, the +thing slides up and down. + + align:start position:0% +thing slides up and down. + + + align:start position:0% +thing slides up and down. +So this has multiple sources of kinetic + + align:start position:0% +So this has multiple sources of kinetic + + + align:start position:0% +So this has multiple sources of kinetic +energy, multiple forms of potential + + align:start position:0% +energy, multiple forms of potential + + + align:start position:0% +energy, multiple forms of potential +energy. Okay? And I'll for the purpose + + align:start position:0% +energy. Okay? And I'll for the purpose + + + align:start position:0% +energy. Okay? And I'll for the purpose +of the problem, I'm going to say that + + align:start position:0% +of the problem, I'm going to say that + + + align:start position:0% +of the problem, I'm going to say that +there's a force that's always horizontal + + align:start position:0% +there's a force that's always horizontal + + + align:start position:0% +there's a force that's always horizontal +acting on this mass pushing this system + + align:start position:0% +acting on this mass pushing this system + + + align:start position:0% +acting on this mass pushing this system +back and forth. Some F cosine omega t + + align:start position:0% +back and forth. Some F cosine omega t + + + align:start position:0% +back and forth. Some F cosine omega t +always horizontal. And I want to drive + + align:start position:0% +always horizontal. And I want to drive + + + align:start position:0% +always horizontal. And I want to drive +the equations of motion of the system. + + align:start position:0% + + + + align:start position:0% + +So, is it a planer motion problem? + + align:start position:0% + + + + align:start position:0% + +All right. How many rigid bodies + + align:start position:0% +All right. How many rigid bodies + + + align:start position:0% +All right. How many rigid bodies +involved? + + align:start position:0% + + + + align:start position:0% + +Okay. So, you know, for so there's two + + align:start position:0% +Okay. So, you know, for so there's two + + + align:start position:0% +Okay. So, you know, for so there's two +there's two rigid bodies. Each could + + align:start position:0% +there's two rigid bodies. Each could + + + align:start position:0% +there's two rigid bodies. Each could +have possibly six degrees of freedom. + + align:start position:0% +have possibly six degrees of freedom. + + + align:start position:0% +have possibly six degrees of freedom. +But when you say it's uh planer motion, + + align:start position:0% +But when you say it's uh planer motion, + + + align:start position:0% +But when you say it's uh planer motion, +you're actually immediately confining + + align:start position:0% +you're actually immediately confining + + + align:start position:0% +you're actually immediately confining +each rigid body to three. Each rigid + + align:start position:0% +each rigid body to three. Each rigid + + + align:start position:0% +each rigid body to three. Each rigid +body can move X and Y and rotate in Z. + + align:start position:0% +body can move X and Y and rotate in Z. + + + align:start position:0% +body can move X and Y and rotate in Z. +So the number when you thread out now + + align:start position:0% +So the number when you thread out now + + + align:start position:0% +So the number when you thread out now +say this is planer motion you've just + + align:start position:0% +say this is planer motion you've just + + + align:start position:0% +say this is planer motion you've just +said each rigid body has max three. So + + align:start position:0% +said each rigid body has max three. So + + + align:start position:0% +said each rigid body has max three. So +this has a maximum of six possible + + align:start position:0% +this has a maximum of six possible + + + align:start position:0% +this has a maximum of six possible +right? No the other where the other + + align:start position:0% +right? No the other where the other + + + align:start position:0% +right? No the other where the other +three disappear too is no Z deflection + + align:start position:0% +three disappear too is no Z deflection + + + align:start position:0% +three disappear too is no Z deflection +and no rotation in the X or Y. Okay. So + + align:start position:0% +and no rotation in the X or Y. Okay. So + + + align:start position:0% +and no rotation in the X or Y. Okay. So +we have a possible uh + + align:start position:0% +we have a possible uh + + + align:start position:0% +we have a possible uh +possible maximum six. How many degrees + + align:start position:0% +possible maximum six. How many degrees + + + align:start position:0% +possible maximum six. How many degrees +of freedom does this problem have? How + + align:start position:0% +of freedom does this problem have? How + + + align:start position:0% +of freedom does this problem have? How +many coordinates will we need to + + align:start position:0% +many coordinates will we need to + + + align:start position:0% +many coordinates will we need to +completely describe the motion of the + + align:start position:0% +completely describe the motion of the + + + align:start position:0% +completely describe the motion of the +system? So, come up. So, think about + + align:start position:0% +system? So, come up. So, think about + + + align:start position:0% +system? So, come up. So, think about +that. Talk to a neighbor. Decide on the + + align:start position:0% +that. Talk to a neighbor. Decide on the + + + align:start position:0% +that. Talk to a neighbor. Decide on the +coordinates that we need to use for this + + align:start position:0% +coordinates that we need to use for this + + + align:start position:0% +coordinates that we need to use for this +system. And while I'm drawing it, + + align:start position:0% + + + + align:start position:0% + +Okay. What do you decide? How many? + + align:start position:0% +Okay. What do you decide? How many? + + + align:start position:0% +Okay. What do you decide? How many? +Two. All right. What would you + + align:start position:0% +Two. All right. What would you + + + align:start position:0% +Two. All right. What would you +recommend? + + align:start position:0% + + + + align:start position:0% + +What would you choose? + + align:start position:0% + + + + align:start position:0% + +Pardon? + + align:start position:0% +Pardon? + + + align:start position:0% +Pardon? +The angle. + + align:start position:0% +The angle. + + + align:start position:0% +The angle. +an angle and a deflection of what I'm + + align:start position:0% +an angle and a deflection of what I'm + + + align:start position:0% +an angle and a deflection of what I'm +calling M2 here. + + align:start position:0% +calling M2 here. + + + align:start position:0% +calling M2 here. +Okay, so this is M2, the rod is M1, + + align:start position:0% + + + + align:start position:0% + +and he's suggesting an angle + + align:start position:0% +and he's suggesting an angle + + + align:start position:0% +and he's suggesting an angle +theta, and + + align:start position:0% + + + + align:start position:0% + +a deflection, + + align:start position:0% +a deflection, + + + align:start position:0% +a deflection, +which I'll call X1. And I've attached to + + align:start position:0% +which I'll call X1. And I've attached to + + + align:start position:0% +which I'll call X1. And I've attached to +this + + align:start position:0% +this + + + align:start position:0% +this +bar, the rod, I'm calling it, a rotating + + align:start position:0% +bar, the rod, I'm calling it, a rotating + + + align:start position:0% +bar, the rod, I'm calling it, a rotating +coordinate system, x1 + + align:start position:0% +coordinate system, x1 + + + align:start position:0% +coordinate system, x1 +y1 + + align:start position:0% +y1 + + + align:start position:0% +y1 +about point a. So a x1 y1 is my rotating + + align:start position:0% +about point a. So a x1 y1 is my rotating + + + align:start position:0% +about point a. So a x1 y1 is my rotating +coordinate system attached to this rod. + + align:start position:0% +coordinate system attached to this rod. + + + align:start position:0% +coordinate system attached to this rod. +Okay. So, I'm going to locate the + + align:start position:0% +Okay. So, I'm going to locate the + + + align:start position:0% +Okay. So, I'm going to locate the +position of this by some value x1 + + align:start position:0% +position of this by some value x1 + + + align:start position:0% +position of this by some value x1 +measured from point A and + + align:start position:0% +measured from point A and + + + align:start position:0% +measured from point A and +locate the position of the rod itself by + + align:start position:0% +locate the position of the rod itself by + + + align:start position:0% +locate the position of the rod itself by +an angle theta. Good. + + align:start position:0% +an angle theta. Good. + + + align:start position:0% +an angle theta. Good. +Is it complete? So, if you freeze one, + + align:start position:0% +Is it complete? So, if you freeze one, + + + align:start position:0% +Is it complete? So, if you freeze one, +do you still have uh complete? Does it + + align:start position:0% +do you still have uh complete? Does it + + + align:start position:0% +do you still have uh complete? Does it +again? Can you describe the motion at + + align:start position:0% +again? Can you describe the motion at + + + align:start position:0% +again? Can you describe the motion at +any possible position? + + align:start position:0% +any possible position? + + + align:start position:0% +any possible position? +Those two things. Yes. Is it + + align:start position:0% +Those two things. Yes. Is it + + + align:start position:0% +Those two things. Yes. Is it +independent? + + align:start position:0% +independent? + + + align:start position:0% +independent? +If you freeze x, can theta still move? + + align:start position:0% +If you freeze x, can theta still move? + + + align:start position:0% +If you freeze x, can theta still move? +If three is the can the x still move + + align:start position:0% +If three is the can the x still move + + + align:start position:0% +If three is the can the x still move +okay is it whole and + + align:start position:0% +okay is it whole and + + + align:start position:0% +okay is it whole and +right two equals you know you need two + + align:start position:0% +right two equals you know you need two + + + align:start position:0% +right two equals you know you need two +we got two and they're independent and + + align:start position:0% +we got two and they're independent and + + + align:start position:0% +we got two and they're independent and +complete good so now the harder work + + align:start position:0% +complete good so now the harder work + + + align:start position:0% +complete good so now the harder work +starts so I'm going to give us the mass + + align:start position:0% +starts so I'm going to give us the mass + + + align:start position:0% +starts so I'm going to give us the mass +of the rod the mass moment of inertia of + + align:start position:0% +of the rod the mass moment of inertia of + + + align:start position:0% +of the rod the mass moment of inertia of +the rod about the zaxis about with + + align:start position:0% +the rod about the zaxis about with + + + align:start position:0% +the rod about the zaxis about with +respect to a the length of the rod is l1 + + align:start position:0% +respect to a the length of the rod is l1 + + + align:start position:0% +respect to a the length of the rod is l1 +the sleeve mass m2 gi iz with respect to + + align:start position:0% +the sleeve mass m2 gi iz with respect to + + + align:start position:0% +the sleeve mass m2 gi iz with respect to +its G. So it has a G. They there's also + + align:start position:0% +its G. So it has a G. They there's also + + + align:start position:0% +its G. So it has a G. They there's also +I better call it G2. + + align:start position:0% +I better call it G2. + + + align:start position:0% +I better call it G2. +That's the G of the sleeve. There's also + + align:start position:0% +That's the G of the sleeve. There's also + + + align:start position:0% +That's the G of the sleeve. There's also +a G1, + + align:start position:0% +a G1, + + + align:start position:0% +a G1, +a uh center of mass for the rod and a + + align:start position:0% +a uh center of mass for the rod and a + + + align:start position:0% +a uh center of mass for the rod and a +center of mass for the sleeve. We those + + align:start position:0% +center of mass for the sleeve. We those + + + align:start position:0% +center of mass for the sleeve. We those +are properties we'll need to know and + + align:start position:0% +are properties we'll need to know and + + + align:start position:0% +are properties we'll need to know and +I'll give them to you. + + align:start position:0% +I'll give them to you. + + + align:start position:0% +I'll give them to you. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So we need + + align:start position:0% +So we need + + + align:start position:0% +So we need +to come up with expressions for + + align:start position:0% +to come up with expressions for + + + align:start position:0% +to come up with expressions for +potential energy + + align:start position:0% +potential energy + + + align:start position:0% +potential energy +and kinetic energy. So this this problem + + align:start position:0% +and kinetic energy. So this this problem + + + align:start position:0% +and kinetic energy. So this this problem +the connect potential energy is a little + + align:start position:0% +the connect potential energy is a little + + + align:start position:0% +the connect potential energy is a little +messy because you have to pick + + align:start position:0% +messy because you have to pick + + + align:start position:0% +messy because you have to pick +references you have to account for the + + align:start position:0% +references you have to account for the + + + align:start position:0% +references you have to account for the +unstretched length of the spring. + + align:start position:0% +unstretched length of the spring. + + + align:start position:0% +unstretched length of the spring. +Right? So uh + + align:start position:0% +Right? So uh + + + align:start position:0% +Right? So uh +call L0 is the unstretched + + align:start position:0% + + + + align:start position:0% + +spring + + align:start position:0% +spring + + + align:start position:0% +spring +length + + align:start position:0% + + + + align:start position:0% + +give it we know that also. So I propose + + align:start position:0% +give it we know that also. So I propose + + + align:start position:0% +give it we know that also. So I propose +that the potential energy look like 1/2 + + align:start position:0% +that the potential energy look like 1/2 + + + align:start position:0% +that the potential energy look like 1/2 +for the spring. Anyway, one half the + + align:start position:0% +for the spring. Anyway, one half the + + + align:start position:0% +for the spring. Anyway, one half the +amount that it stretches in a movement + + align:start position:0% +amount that it stretches in a movement + + + align:start position:0% +amount that it stretches in a movement +x1. + + align:start position:0% +x1. + + + align:start position:0% +x1. +The amount that it stretches then should + + align:start position:0% +The amount that it stretches then should + + + align:start position:0% +The amount that it stretches then should +be whatever that x1 position is. And + + align:start position:0% +be whatever that x1 position is. And + + + align:start position:0% +be whatever that x1 position is. And +that x1 position and I have just I drew + + align:start position:0% +that x1 position and I have just I drew + + + align:start position:0% +that x1 position and I have just I drew +it slightly + + align:start position:0% + + + + align:start position:0% + +incorrectly. I'm going to use X1 to + + align:start position:0% +incorrectly. I'm going to use X1 to + + + align:start position:0% +incorrectly. I'm going to use X1 to +locate the center of mass, which is + + align:start position:0% +locate the center of mass, which is + + + align:start position:0% +locate the center of mass, which is +always a good practice. So, here's the + + align:start position:0% +always a good practice. So, here's the + + + align:start position:0% +always a good practice. So, here's the +center of mass. So, my X1 goes to the + + align:start position:0% +center of mass. So, my X1 goes to the + + + align:start position:0% +center of mass. So, my X1 goes to the +center of mass. + + align:start position:0% +center of mass. + + + align:start position:0% +center of mass. +Okay, that's X1. + + align:start position:0% +Okay, that's X1. + + + align:start position:0% +Okay, that's X1. +So, that the that's the total distance. + + align:start position:0% +So, that the that's the total distance. + + + align:start position:0% +So, that the that's the total distance. +And from that we need to subtract L0 the + + align:start position:0% +And from that we need to subtract L0 the + + + align:start position:0% +And from that we need to subtract L0 the +unstretched length of the spring and we + + align:start position:0% +unstretched length of the spring and we + + + align:start position:0% +unstretched length of the spring and we +need to subtract half the length of the + + align:start position:0% +need to subtract half the length of the + + + align:start position:0% +need to subtract half the length of the +body because it's going that that's that + + align:start position:0% +body because it's going that that's that + + + align:start position:0% +body because it's going that that's that +extra bit here. Okay. So this is the + + align:start position:0% +extra bit here. Okay. So this is the + + + align:start position:0% +extra bit here. Okay. So this is the +amount that the string is actually + + align:start position:0% +amount that the string is actually + + + align:start position:0% +amount that the string is actually +stretched + + align:start position:0% +stretched + + + align:start position:0% +stretched +when you go through a motion when + + align:start position:0% +when you go through a motion when + + + align:start position:0% +when you go through a motion when +there's motion when the coordinate is x1 + + align:start position:0% +there's motion when the coordinate is x1 + + + align:start position:0% +there's motion when the coordinate is x1 +and you got to square that and that + + align:start position:0% +and you got to square that and that + + + align:start position:0% +and you got to square that and that +would be the kinetic excuse me the + + align:start position:0% +would be the kinetic excuse me the + + + align:start position:0% +would be the kinetic excuse me the +potential energy stored in the spring. + + align:start position:0% +potential energy stored in the spring. + + + align:start position:0% +potential energy stored in the spring. +Then we got to do the same thing for the + + align:start position:0% +Then we got to do the same thing for the + + + align:start position:0% +Then we got to do the same thing for the +uh potential energy. You have two + + align:start position:0% +uh potential energy. You have two + + + align:start position:0% +uh potential energy. You have two +sources of potential energy and they and + + align:start position:0% +sources of potential energy and they and + + + align:start position:0% +sources of potential energy and they and +due to gravity and they are + + align:start position:0% + + + + align:start position:0% + +two objects, right? Two potential + + align:start position:0% +two objects, right? Two potential + + + align:start position:0% +two objects, right? Two potential +energy. So, why don't you take a minute + + align:start position:0% +energy. So, why don't you take a minute + + + align:start position:0% +energy. So, why don't you take a minute +and tell me the potential energy + + align:start position:0% +and tell me the potential energy + + + align:start position:0% +and tell me the potential energy +associated with the rod? + + align:start position:0% + + + + align:start position:0% + +So, the rod has a center of mass and the + + align:start position:0% +So, the rod has a center of mass and the + + + align:start position:0% +So, the rod has a center of mass and the +center it's a pendulum basically. So, + + align:start position:0% +center it's a pendulum basically. So, + + + align:start position:0% +center it's a pendulum basically. So, +it's the same as all the pendulum + + align:start position:0% +it's the same as all the pendulum + + + align:start position:0% +it's the same as all the pendulum +problems you've ever seen. + + align:start position:0% +problems you've ever seen. + + + align:start position:0% +problems you've ever seen. +And I would recommend that we use as our + + align:start position:0% +And I would recommend that we use as our + + + align:start position:0% +And I would recommend that we use as our +reference position its static + + align:start position:0% +reference position its static + + + align:start position:0% +reference position its static +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +position hanging straight down. And I'm + + align:start position:0% +position hanging straight down. And I'm + + + align:start position:0% +position hanging straight down. And I'm +going I'll tell you in advance I'm going + + align:start position:0% +going I'll tell you in advance I'm going + + + align:start position:0% +going I'll tell you in advance I'm going +to use the unstretched spring position + + align:start position:0% +to use the unstretched spring position + + + align:start position:0% +to use the unstretched spring position +this time. I just stay with that. That's + + align:start position:0% +this time. I just stay with that. That's + + + align:start position:0% +this time. I just stay with that. That's +where it's going to start from. That's + + align:start position:0% +where it's going to start from. That's + + + align:start position:0% +where it's going to start from. That's +my reference for potential energy. But + + align:start position:0% +my reference for potential energy. But + + + align:start position:0% +my reference for potential energy. But +does this does the the unstretched + + align:start position:0% +does this does the the unstretched + + + align:start position:0% +does this does the the unstretched +spring position have anything to do with + + align:start position:0% +spring position have anything to do with + + + align:start position:0% +spring position have anything to do with +the potential energy of the rod? No. + + align:start position:0% +the potential energy of the rod? No. + + + align:start position:0% +the potential energy of the rod? No. +Okay. So it's reference position is just + + align:start position:0% +Okay. So it's reference position is just + + + align:start position:0% +Okay. So it's reference position is just +hanging straight down. So figure it out. + + align:start position:0% +hanging straight down. So figure it out. + + + align:start position:0% +hanging straight down. So figure it out. +What's the give me a potential energy + + align:start position:0% +What's the give me a potential energy + + + align:start position:0% +What's the give me a potential energy +expression for just the rod part. + + align:start position:0% +expression for just the rod part. + + + align:start position:0% +expression for just the rod part. +Think about that. + + align:start position:0% + + + + align:start position:0% + +So I'm going to remind you about + + align:start position:0% +So I'm going to remind you about + + + align:start position:0% +So I'm going to remind you about +something about potential energy. + + align:start position:0% +something about potential energy. + + + align:start position:0% +something about potential energy. +potential energy. One of the + + align:start position:0% +potential energy. One of the + + + align:start position:0% +potential energy. One of the +requirements about it is the change in + + align:start position:0% +requirements about it is the change in + + + align:start position:0% +requirements about it is the change in +potential energy from one position to + + align:start position:0% +potential energy from one position to + + + align:start position:0% +potential energy from one position to +another is path independent. + + align:start position:0% +another is path independent. + + + align:start position:0% +another is path independent. +So you don't actually ever have to do + + align:start position:0% +So you don't actually ever have to do + + + align:start position:0% +So you don't actually ever have to do +the integral of you know minus mg dr. + + align:start position:0% +the integral of you know minus mg dr. + + + align:start position:0% +the integral of you know minus mg dr. +You don't have to do the integral. You + + align:start position:0% +You don't have to do the integral. You + + + align:start position:0% +You don't have to do the integral. You +just have to account for the change in + + align:start position:0% +just have to account for the change in + + + align:start position:0% +just have to account for the change in +height between its starting position and + + align:start position:0% +height between its starting position and + + + align:start position:0% +height between its starting position and +it's some other position. + + align:start position:0% + + + + align:start position:0% + +Spend a minute or two thinking about + + align:start position:0% +Spend a minute or two thinking about + + + align:start position:0% +Spend a minute or two thinking about +that. Work it out. You got a question? + + align:start position:0% +that. Work it out. You got a question? + + + align:start position:0% +that. Work it out. You got a question? +Okay. + + align:start position:0% + + + + align:start position:0% + +Can you talk talk to a neighbor, check + + align:start position:0% +Can you talk talk to a neighbor, check + + + align:start position:0% +Can you talk talk to a neighbor, check +your ideas and then + + align:start position:0% + + + + align:start position:0% + +So, you have a suggestion for me, + + align:start position:0% +So, you have a suggestion for me, + + + align:start position:0% +So, you have a suggestion for me, +ladies? + + align:start position:0% +ladies? + + + align:start position:0% +ladies? +Huh? + + align:start position:0% + + + + align:start position:0% + +Okay. Um + + align:start position:0% +Okay. Um + + + align:start position:0% +Okay. Um +any anybody want to make an improvement + + align:start position:0% +any anybody want to make an improvement + + + align:start position:0% +any anybody want to make an improvement +on that or like they like it improvement + + align:start position:0% + + + + align:start position:0% + +1us cosine theta. So let's put that up + + align:start position:0% +1us cosine theta. So let's put that up + + + align:start position:0% +1us cosine theta. So let's put that up +and let's figure out if if we need that. + + align:start position:0% +and let's figure out if if we need that. + + + align:start position:0% +and let's figure out if if we need that. +So could be co we've have a a bid for + + align:start position:0% +So could be co we've have a a bid for + + + align:start position:0% +So could be co we've have a a bid for +cosine theta and 1 minus cosine theta. + + align:start position:0% +cosine theta and 1 minus cosine theta. + + + align:start position:0% +cosine theta and 1 minus cosine theta. +So you need to have a potential energy + + align:start position:0% +So you need to have a potential energy + + + align:start position:0% +So you need to have a potential energy +at the reference and you need to have a + + align:start position:0% +at the reference and you need to have a + + + align:start position:0% +at the reference and you need to have a +potential energy at the final point. And + + align:start position:0% +potential energy at the final point. And + + + align:start position:0% +potential energy at the final point. And +the difference between the two is a + + align:start position:0% +the difference between the two is a + + + align:start position:0% +the difference between the two is a +change in potential energy here. Okay. + + align:start position:0% +change in potential energy here. Okay. + + + align:start position:0% +change in potential energy here. Okay. +So what's the reference potential energy + + align:start position:0% +So what's the reference potential energy + + + align:start position:0% +So what's the reference potential energy +is mg l1 over2 when it hangs straight + + align:start position:0% +is mg l1 over2 when it hangs straight + + + align:start position:0% +is mg l1 over2 when it hangs straight +down. And then when it moves up to this + + align:start position:0% +down. And then when it moves up to this + + + align:start position:0% +down. And then when it moves up to this +other position, this is the the L1 over2 + + align:start position:0% +other position, this is the the L1 over2 + + + align:start position:0% +other position, this is the the L1 over2 +times this is delta H. + + align:start position:0% +times this is delta H. + + + align:start position:0% +times this is delta H. +This is the change in height that it + + align:start position:0% +This is the change in height that it + + + align:start position:0% +This is the change in height that it +goes through. So you need the one minus, + + align:start position:0% +goes through. So you need the one minus, + + + align:start position:0% +goes through. So you need the one minus, +right? And why is it uh + + align:start position:0% + + + + align:start position:0% + +and do we have the signs right? + + align:start position:0% +and do we have the signs right? + + + align:start position:0% +and do we have the signs right? +Yeah. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +So, now we need another term. And I'll + + align:start position:0% +So, now we need another term. And I'll + + + align:start position:0% +So, now we need another term. And I'll +write this one down. We need a It's a + + align:start position:0% +write this one down. We need a It's a + + + align:start position:0% +write this one down. We need a It's a +little This one's a little messier. We + + align:start position:0% +little This one's a little messier. We + + + align:start position:0% +little This one's a little messier. We +need a potential energy term due to + + align:start position:0% +need a potential energy term due to + + + align:start position:0% +need a potential energy term due to +gravity for the sleeve. + + align:start position:0% +gravity for the sleeve. + + + align:start position:0% +gravity for the sleeve. +And that's going to mimic this. You're + + align:start position:0% +And that's going to mimic this. You're + + + align:start position:0% +And that's going to mimic this. You're +going to have a term here plus m2g. + + align:start position:0% + + + + align:start position:0% + +And its reference, I'm just going to do + + align:start position:0% +And its reference, I'm just going to do + + + align:start position:0% +And its reference, I'm just going to do +it as a reference amount minus the final + + align:start position:0% +it as a reference amount minus the final + + + align:start position:0% +it as a reference amount minus the final +amount. The reference will be at the + + align:start position:0% +amount. The reference will be at the + + + align:start position:0% +amount. The reference will be at the +initial + + align:start position:0% +initial + + + align:start position:0% +initial +location of its center of mass which is + + align:start position:0% +location of its center of mass which is + + + align:start position:0% +location of its center of mass which is +L0 + L2 / 2 + + align:start position:0% +L0 + L2 / 2 + + + align:start position:0% +L0 + L2 / 2 +minus M2 + + align:start position:0% +minus M2 + + + align:start position:0% +minus M2 +G + + align:start position:0% +G + + + align:start position:0% +G +X1 + + align:start position:0% +X1 + + + align:start position:0% +X1 +cosine + + align:start position:0% +cosine + + + align:start position:0% +cosine +theta. + + align:start position:0% + + + + align:start position:0% + +Okay, because this this one gets a + + align:start position:0% +Okay, because this this one gets a + + + align:start position:0% +Okay, because this this one gets a +little messier because you got this + + align:start position:0% +little messier because you got this + + + align:start position:0% +little messier because you got this +thing. it can move up and down the + + align:start position:0% +thing. it can move up and down the + + + align:start position:0% +thing. it can move up and down the +sleeve + + align:start position:0% +sleeve + + + align:start position:0% +sleeve +and if that moves you've lost your + + align:start position:0% +and if that moves you've lost your + + + align:start position:0% +and if that moves you've lost your +reference. So you can't do this as a + + align:start position:0% +reference. So you can't do this as a + + + align:start position:0% +reference. So you can't do this as a +concise little term like this. You have + + align:start position:0% +concise little term like this. You have + + + align:start position:0% +concise little term like this. You have +to separate out the reference and then + + align:start position:0% +to separate out the reference and then + + + align:start position:0% +to separate out the reference and then +this is the final + + align:start position:0% +this is the final + + + align:start position:0% +this is the final +and and the L0 plus L2. This quantity + + align:start position:0% +and and the L0 plus L2. This quantity + + + align:start position:0% +and and the L0 plus L2. This quantity +here is the initial starting height. + + align:start position:0% +here is the initial starting height. + + + align:start position:0% +here is the initial starting height. +This X1 cosine theta is the finishing + + align:start position:0% +This X1 cosine theta is the finishing + + + align:start position:0% +This X1 cosine theta is the finishing +height. And the difference between the + + align:start position:0% +height. And the difference between the + + + align:start position:0% +height. And the difference between the +two gives you the change in the + + align:start position:0% +two gives you the change in the + + + align:start position:0% +two gives you the change in the +potential energy. So this is your + + align:start position:0% +potential energy. So this is your + + + align:start position:0% +potential energy. So this is your +potential energy expression. This plus + + align:start position:0% +potential energy expression. This plus + + + align:start position:0% +potential energy expression. This plus +this plus these. All right. + + align:start position:0% + + + + align:start position:0% + +So what about T? We got to be able to + + align:start position:0% +So what about T? We got to be able to + + + align:start position:0% +So what about T? We got to be able to +write it. Kinetic energy is generally + + align:start position:0% +write it. Kinetic energy is generally + + + align:start position:0% +write it. Kinetic energy is generally +easier. Got to account for all the parts + + align:start position:0% +easier. Got to account for all the parts + + + align:start position:0% +easier. Got to account for all the parts +and pieces. So we have two chunks. And + + align:start position:0% +and pieces. So we have two chunks. And + + + align:start position:0% +and pieces. So we have two chunks. And +we're going to have rotational kinetic + + align:start position:0% +we're going to have rotational kinetic + + + align:start position:0% +we're going to have rotational kinetic +energy associated with a rod. rotational + + align:start position:0% +energy associated with a rod. rotational + + + align:start position:0% +energy associated with a rod. rotational +kinetic energy associated with the + + align:start position:0% +kinetic energy associated with the + + + align:start position:0% +kinetic energy associated with the +sleeve, but also some translational + + align:start position:0% +sleeve, but also some translational + + + align:start position:0% +sleeve, but also some translational +kinetic energy associated with the + + align:start position:0% +kinetic energy associated with the + + + align:start position:0% +kinetic energy associated with the +sleeve. Right? And I'll write these + + align:start position:0% +sleeve. Right? And I'll write these + + + align:start position:0% +sleeve. Right? And I'll write these +terms down. + + align:start position:0% +terms down. + + + align:start position:0% +terms down. +I' when I've made make the problem go a + + align:start position:0% +I' when I've made make the problem go a + + + align:start position:0% +I' when I've made make the problem go a +little faster here. + + align:start position:0% + + + + align:start position:0% + +12 IZ about a + + align:start position:0% +12 IZ about a + + + align:start position:0% +12 IZ about a +for that's the first that's the rod + + align:start position:0% + + + + align:start position:0% + +plus a half + + align:start position:0% + + + + align:start position:0% + +i z + + align:start position:0% +i z + + + align:start position:0% +i z +for the sleeve about g + + align:start position:0% +for the sleeve about g + + + align:start position:0% +for the sleeve about g +we'll discuss why the difference here + + align:start position:0% +we'll discuss why the difference here + + + align:start position:0% +we'll discuss why the difference here +and + + align:start position:0% +and + + + align:start position:0% +and +that's theta dot squared + + align:start position:0% + + + + align:start position:0% + +now for the + + align:start position:0% + + + + align:start position:0% + +kinetic energy that comes from + + align:start position:0% +kinetic energy that comes from + + + align:start position:0% +kinetic energy that comes from +translation of the center of mass + + align:start position:0% +translation of the center of mass + + + align:start position:0% +translation of the center of mass +because I'm broken up I've accounted for + + align:start position:0% +because I'm broken up I've accounted for + + + align:start position:0% +because I'm broken up I've accounted for +this is a + + align:start position:0% +this is a + + + align:start position:0% +this is a +let me start over this system is pinned + + align:start position:0% +let me start over this system is pinned + + + align:start position:0% +let me start over this system is pinned +about a + + align:start position:0% +about a + + + align:start position:0% +about a +and and + + align:start position:0% +and and + + + align:start position:0% +and and +the rod is just simply pinned at a and + + align:start position:0% +the rod is just simply pinned at a and + + + align:start position:0% +the rod is just simply pinned at a and +that The last lecture I put up these + + align:start position:0% +that The last lecture I put up these + + + align:start position:0% +that The last lecture I put up these +different conditions and simplifications + + align:start position:0% +different conditions and simplifications + + + align:start position:0% +different conditions and simplifications +you can account for a something about a + + align:start position:0% +you can account for a something about a + + + align:start position:0% +you can account for a something about a +fixed pin by computing mass moment of + + align:start position:0% +fixed pin by computing mass moment of + + + align:start position:0% +fixed pin by computing mass moment of +inertia about a it's basically a + + align:start position:0% +inertia about a it's basically a + + + align:start position:0% +inertia about a it's basically a +parallel axis theorem argument times 12 + + align:start position:0% +parallel axis theorem argument times 12 + + + align:start position:0% +parallel axis theorem argument times 12 +times that time theta dot squared. So + + align:start position:0% +times that time theta dot squared. So + + + align:start position:0% +times that time theta dot squared. So +this gives you all of the kinetic energy + + align:start position:0% +this gives you all of the kinetic energy + + + align:start position:0% +this gives you all of the kinetic energy +in one go with the rod. But for the + + align:start position:0% +in one go with the rod. But for the + + + align:start position:0% +in one go with the rod. But for the +sliding mass because its position is + + align:start position:0% +sliding mass because its position is + + + align:start position:0% +sliding mass because its position is +changing, you can't do that. You have to + + align:start position:0% +changing, you can't do that. You have to + + + align:start position:0% +changing, you can't do that. You have to +account for the two components of its + + align:start position:0% +account for the two components of its + + + align:start position:0% +account for the two components of its +kinetic energy separately. This accounts + + align:start position:0% +kinetic energy separately. This accounts + + + align:start position:0% +kinetic energy separately. This accounts +for rotation about G even though G is + + align:start position:0% +for rotation about G even though G is + + + align:start position:0% +for rotation about G even though G is +moving + + align:start position:0% +moving + + + align:start position:0% +moving +that accounts for that energy. This + + align:start position:0% +that accounts for that energy. This + + + align:start position:0% +that accounts for that energy. This +accounts for because it's only a + + align:start position:0% +accounts for because it's only a + + + align:start position:0% +accounts for because it's only a +function of theta dot. It's not a + + align:start position:0% +function of theta dot. It's not a + + + align:start position:0% +function of theta dot. It's not a +function of that position X. This + + align:start position:0% +function of that position X. This + + + align:start position:0% +function of that position X. This +account this term is going to account + + align:start position:0% +account this term is going to account + + + align:start position:0% +account this term is going to account +for then the kinetic energy associated + + align:start position:0% +for then the kinetic energy associated + + + align:start position:0% +for then the kinetic energy associated +with the movement of the center of mass. + + align:start position:0% +with the movement of the center of mass. + + + align:start position:0% +with the movement of the center of mass. +So we need a VG2 + + align:start position:0% +So we need a VG2 + + + align:start position:0% +So we need a VG2 +in the inertial frame dot VG2. + + align:start position:0% + + + + align:start position:0% + +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +these being vectors and does that get + + align:start position:0% +these being vectors and does that get + + + align:start position:0% +these being vectors and does that get +everything? I think that does. So VGO + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% + + + + align:start position:0% + +it certainly has a component that is its + + align:start position:0% +it certainly has a component that is its + + + align:start position:0% +it certainly has a component that is its +speed sliding up and down the rod right + + align:start position:0% +speed sliding up and down the rod right + + + align:start position:0% +speed sliding up and down the rod right +and that's in the ihat direction + + align:start position:0% +and that's in the ihat direction + + + align:start position:0% +and that's in the ihat direction +but it has another component due to what + + align:start position:0% +but it has another component due to what + + + align:start position:0% +but it has another component due to what +and can you tell me what it is + + align:start position:0% +and can you tell me what it is + + + align:start position:0% +and can you tell me what it is +it's contribution to its speed due to + + align:start position:0% +it's contribution to its speed due to + + + align:start position:0% +it's contribution to its speed due to +its + + align:start position:0% +its + + + align:start position:0% +its +rotation + + align:start position:0% + + + + align:start position:0% + +It's got a theta dot. Yep. It's got + + align:start position:0% +It's got a theta dot. Yep. It's got + + + align:start position:0% +It's got a theta dot. Yep. It's got +needs an R, right? + + align:start position:0% + + + + align:start position:0% + +Yeah. So, this would be an X1 plus + + align:start position:0% + + + + align:start position:0% + +Uh no actually I made x1 go right to the + + align:start position:0% +Uh no actually I made x1 go right to the + + + align:start position:0% +Uh no actually I made x1 go right to the +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so just x1 + + align:start position:0% +so just x1 + + + align:start position:0% +so just x1 +theta dot in what direction? + + align:start position:0% +theta dot in what direction? + + + align:start position:0% +theta dot in what direction? +Yeah. So j hat here right the moving + + align:start position:0% +Yeah. So j hat here right the moving + + + align:start position:0% +Yeah. So j hat here right the moving +it's actually that's the moving + + align:start position:0% +it's actually that's the moving + + + align:start position:0% +it's actually that's the moving +coordinate system unit vector in the y + + align:start position:0% +coordinate system unit vector in the y + + + align:start position:0% +coordinate system unit vector in the y +direction. And so we do the dot do the + + align:start position:0% +direction. And so we do the dot do the + + + align:start position:0% +direction. And so we do the dot do the +dotproduct you get this times itself i + + align:start position:0% +dotproduct you get this times itself i + + + align:start position:0% +dotproduct you get this times itself i +do i and j.j J you get that uh this + + align:start position:0% +do i and j.j J you get that uh this + + + align:start position:0% +do i and j.j J you get that uh this +quantity here is + + align:start position:0% +quantity here is + + + align:start position:0% +quantity here is + + align:start position:0% + + + align:start position:0% +m2 + + align:start position:0% +m2 + + + align:start position:0% +m2 +x dot squared plus x it's an x1 I guess + + align:start position:0% +x dot squared plus x it's an x1 I guess + + + align:start position:0% +x dot squared plus x it's an x1 I guess +x1^ 2ar theta dot squared that's the + + align:start position:0% +x1^ 2ar theta dot squared that's the + + + align:start position:0% +x1^ 2ar theta dot squared that's the +kinetic energy of accounting for the + + align:start position:0% +kinetic energy of accounting for the + + + align:start position:0% +kinetic energy of accounting for the +velocity of the center of mass. So now + + align:start position:0% +velocity of the center of mass. So now + + + align:start position:0% +velocity of the center of mass. So now +we have our entire kinetic energy + + align:start position:0% +we have our entire kinetic energy + + + align:start position:0% +we have our entire kinetic energy +expression. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +So now we have how many coordinates? + + align:start position:0% +So now we have how many coordinates? + + + align:start position:0% +So now we have how many coordinates? +Two, right? How many times we have to + + align:start position:0% +Two, right? How many times we have to + + + align:start position:0% +Two, right? How many times we have to +turn the crank and go through the lrange + + align:start position:0% +turn the crank and go through the lrange + + + align:start position:0% +turn the crank and go through the lrange +in says something. You got to go through + + align:start position:0% +in says something. You got to go through + + + align:start position:0% +in says something. You got to go through +it twice. So + + align:start position:0% +it twice. So + + + align:start position:0% +it twice. So +let's apply + + align:start position:0% + + + + align:start position:0% + +the garage here + + align:start position:0% + + + + align:start position:0% + +and we'll just do number one first. So + + align:start position:0% +and we'll just do number one first. So + + + align:start position:0% +and we'll just do number one first. So +and let's and let's see which one do I + + align:start position:0% +and let's and let's see which one do I + + + align:start position:0% +and let's and let's see which one do I +have on my paper first. I guess we'll do + + align:start position:0% +have on my paper first. I guess we'll do + + + align:start position:0% +have on my paper first. I guess we'll do +the x1 equation. This is delta x1. So + + align:start position:0% +the x1 equation. This is delta x1. So + + + align:start position:0% +the x1 equation. This is delta x1. So +this is generalized coordinate x1 and we + + align:start position:0% +this is generalized coordinate x1 and we + + + align:start position:0% +this is generalized coordinate x1 and we +need to do term one which is then d by + + align:start position:0% +need to do term one which is then d by + + + align:start position:0% +need to do term one which is then d by +dt + + align:start position:0% +dt + + + align:start position:0% +dt +of + + align:start position:0% +of + + + align:start position:0% +of +partial of t with respect to x1 + + align:start position:0% +partial of t with respect to x1 + + + align:start position:0% +partial of t with respect to x1 +dot. + + align:start position:0% +dot. + + + align:start position:0% +dot. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So we look at this and say well we got + + align:start position:0% +So we look at this and say well we got + + + align:start position:0% +So we look at this and say well we got +to go is this a function is this term a + + align:start position:0% +to go is this a function is this term a + + + align:start position:0% +to go is this a function is this term a +function of x of x? Nothing. Do you get + + align:start position:0% +function of x of x? Nothing. Do you get + + + align:start position:0% +function of x of x? Nothing. Do you get +nothing from there? Uh is this term a + + align:start position:0% +nothing from there? Uh is this term a + + + align:start position:0% +nothing from there? Uh is this term a +function of x? Yeah, it's down here. So + + align:start position:0% +function of x? Yeah, it's down here. So + + + align:start position:0% +function of x? Yeah, it's down here. So +we just this we only have to take the + + align:start position:0% +we just this we only have to take the + + + align:start position:0% +we just this we only have to take the +derivative of this. We have to do that + + align:start position:0% +derivative of this. We have to do that + + + align:start position:0% +derivative of this. We have to do that +job. Okay. So the derivative of this + + align:start position:0% +job. Okay. So the derivative of this + + + align:start position:0% +job. Okay. So the derivative of this +with respect to x dot + + align:start position:0% +with respect to x dot + + + align:start position:0% +with respect to x dot +you get a 2x + + align:start position:0% +you get a 2x + + + align:start position:0% +you get a 2x +dot here. Do you get anything from here? + + align:start position:0% +dot here. Do you get anything from here? + + + align:start position:0% +dot here. Do you get anything from here? +When you do this with derative with + + align:start position:0% +When you do this with derative with + + + align:start position:0% +When you do this with derative with +respect to x dot you only get a + + align:start position:0% +respect to x dot you only get a + + + align:start position:0% +respect to x dot you only get a +contribution from here. The two cancels + + align:start position:0% +contribution from here. The two cancels + + + align:start position:0% +contribution from here. The two cancels +that. And so this should look like m2 + + align:start position:0% +that. And so this should look like m2 + + + align:start position:0% +that. And so this should look like m2 +x1 + + align:start position:0% +x1 + + + align:start position:0% +x1 +dot but d bydt. And I I won't do this do + + align:start position:0% +dot but d bydt. And I I won't do this do + + + align:start position:0% +dot but d bydt. And I I won't do this do +this once in two steps here. So you see + + align:start position:0% +this once in two steps here. So you see + + + align:start position:0% +this once in two steps here. So you see +where what happens. You get an m2 x1 + + align:start position:0% +where what happens. You get an m2 x1 + + + align:start position:0% +where what happens. You get an m2 x1 +double dot out of that. + + align:start position:0% +double dot out of that. + + + align:start position:0% +double dot out of that. +Okay. + + align:start position:0% + + + + align:start position:0% + +Let's So, we've gotten the first first + + align:start position:0% +Let's So, we've gotten the first first + + + align:start position:0% +Let's So, we've gotten the first first +piece of this. We got a couple to go, + + align:start position:0% +piece of this. We got a couple to go, + + + align:start position:0% +piece of this. We got a couple to go, +but I want you you know a lot about + + align:start position:0% +but I want you you know a lot about + + + align:start position:0% +but I want you you know a lot about +Newton's laws and you know a lot about + + align:start position:0% +Newton's laws and you know a lot about + + + align:start position:0% +Newton's laws and you know a lot about +calculating equations of motion now + + align:start position:0% +calculating equations of motion now + + + align:start position:0% +calculating equations of motion now +using sum of torqus and all that all + + align:start position:0% +using sum of torqus and all that all + + + align:start position:0% +using sum of torqus and all that all +that stuff, right? So, this is just + + align:start position:0% +that stuff, right? So, this is just + + + align:start position:0% +that stuff, right? So, this is just +something moving has angular it has + + align:start position:0% +something moving has angular it has + + + align:start position:0% +something moving has angular it has +circular motion has translational + + align:start position:0% +circular motion has translational + + + align:start position:0% +circular motion has translational +motion. What other accelerations + + align:start position:0% +motion. What other accelerations + + + align:start position:0% +motion. What other accelerations +had better appear in this equation of + + align:start position:0% +had better appear in this equation of + + + align:start position:0% +had better appear in this equation of +motion? + + align:start position:0% +motion? + + + align:start position:0% +motion? +And we're get we you know which equation + + align:start position:0% +And we're get we you know which equation + + + align:start position:0% +And we're get we you know which equation +are we getting? + + align:start position:0% +are we getting? + + + align:start position:0% +are we getting? +There's going to be two equations and + + align:start position:0% +There's going to be two equations and + + + align:start position:0% +There's going to be two equations and +they have sort of physical significance + + align:start position:0% +they have sort of physical significance + + + align:start position:0% +they have sort of physical significance +to it. What equation is this beginning + + align:start position:0% +to it. What equation is this beginning + + + align:start position:0% +to it. What equation is this beginning +to look like + + align:start position:0% +to look like + + + align:start position:0% +to look like +just physically? What movement is being + + align:start position:0% +just physically? What movement is being + + + align:start position:0% +just physically? What movement is being +accounted for here? + + align:start position:0% +accounted for here? + + + align:start position:0% +accounted for here? +Looks like translation in the x + + align:start position:0% +Looks like translation in the x + + + align:start position:0% +Looks like translation in the x +direction. It's this thing sliding. It's + + align:start position:0% +direction. It's this thing sliding. It's + + + align:start position:0% +direction. It's this thing sliding. It's +this part of the motion sliding up and + + align:start position:0% +this part of the motion sliding up and + + + align:start position:0% +this part of the motion sliding up and +down there. You're writing an equation + + align:start position:0% +down there. You're writing an equation + + + align:start position:0% +down there. You're writing an equation +of motion. And mx dot has units of what? + + align:start position:0% + + + + align:start position:0% + +torque + + align:start position:0% +torque + + + align:start position:0% +torque +force. So this is a force equation. This + + align:start position:0% +force. So this is a force equation. This + + + align:start position:0% +force. So this is a force equation. This +is just F= ma is what this what this is + + align:start position:0% +is just F= ma is what this what this is + + + align:start position:0% +is just F= ma is what this what this is +going to show us. Remember the direct + + align:start position:0% +going to show us. Remember the direct + + + align:start position:0% +going to show us. Remember the direct +method has to give you the same answer + + align:start position:0% +method has to give you the same answer + + + align:start position:0% +method has to give you the same answer +as Lrange. + + align:start position:0% +as Lrange. + + + align:start position:0% +as Lrange. +So + + align:start position:0% +So + + + align:start position:0% +So +we're getting a force equation. It's + + align:start position:0% +we're getting a force equation. It's + + + align:start position:0% +we're getting a force equation. It's +describing mx dot. What other what other + + align:start position:0% +describing mx dot. What other what other + + + align:start position:0% +describing mx dot. What other what other +acceleration terms do you expect to + + align:start position:0% +acceleration terms do you expect to + + + align:start position:0% +acceleration terms do you expect to +appear in this from what you know? Yeah. + + align:start position:0% +appear in this from what you know? Yeah. + + + align:start position:0% +appear in this from what you know? Yeah. +A centripal term. You believe there + + align:start position:0% +A centripal term. You believe there + + + align:start position:0% +A centripal term. You believe there +ought to be a centrial term in this + + align:start position:0% +ought to be a centrial term in this + + + align:start position:0% +ought to be a centrial term in this +answer. + + align:start position:0% +answer. + + + align:start position:0% +answer. +Why? + + align:start position:0% +Why? + + + align:start position:0% +Why? +Because it's got circular motion + + align:start position:0% +Because it's got circular motion + + + align:start position:0% +Because it's got circular motion +involved for sure. Any others? Is there + + align:start position:0% +involved for sure. Any others? Is there + + + align:start position:0% +involved for sure. Any others? Is there +any corololis in this? + + align:start position:0% +any corololis in this? + + + align:start position:0% +any corololis in this? +In this direction? Which direction are + + align:start position:0% +In this direction? Which direction are + + + align:start position:0% +In this direction? Which direction are +we working in? + + align:start position:0% +we working in? + + + align:start position:0% +we working in? +Is there corololis acceleration in the x + + align:start position:0% +Is there corololis acceleration in the x + + + align:start position:0% +Is there corololis acceleration in the x +direction? This by the way these + + align:start position:0% +direction? This by the way these + + + align:start position:0% +direction? This by the way these +equations, do we have any jks in here? + + align:start position:0% +equations, do we have any jks in here? + + + align:start position:0% +equations, do we have any jks in here? +These are pure scalar equations. No + + align:start position:0% +These are pure scalar equations. No + + + align:start position:0% +These are pure scalar equations. No +vector, no unit vectors involved. So + + align:start position:0% +vector, no unit vectors involved. So + + + align:start position:0% +vector, no unit vectors involved. So +this equation only describe motion in + + align:start position:0% +this equation only describe motion in + + + align:start position:0% +this equation only describe motion in +the x. + + align:start position:0% + + + + align:start position:0% + +So will there be a corololis force in + + align:start position:0% +So will there be a corololis force in + + + align:start position:0% +So will there be a corololis force in +this acceleration in this problem? Will + + align:start position:0% +this acceleration in this problem? Will + + + align:start position:0% +this acceleration in this problem? Will +there be an orarian acceleration in this + + align:start position:0% +there be an orarian acceleration in this + + + align:start position:0% +there be an orarian acceleration in this +equation of motion? The reason I'm going + + align:start position:0% +equation of motion? The reason I'm going + + + align:start position:0% +equation of motion? The reason I'm going +through this, I want you to start + + align:start position:0% +through this, I want you to start + + + align:start position:0% +through this, I want you to start +developing your own intuition about + + align:start position:0% +developing your own intuition about + + + align:start position:0% +developing your own intuition about +whether or not when you get the get it + + align:start position:0% +whether or not when you get the get it + + + align:start position:0% +whether or not when you get the get it +at the end, it's got everything it ought + + align:start position:0% +at the end, it's got everything it ought + + + align:start position:0% +at the end, it's got everything it ought +to have and doesn't have stuff it + + align:start position:0% +to have and doesn't have stuff it + + + align:start position:0% +to have and doesn't have stuff it +shouldn't have. Right? Okay, so the + + align:start position:0% +shouldn't have. Right? Okay, so the + + + align:start position:0% +shouldn't have. Right? Okay, so the +you're forecasting that we better get a + + align:start position:0% +you're forecasting that we better get a + + + align:start position:0% +you're forecasting that we better get a +centripal term. Well, let's see what + + align:start position:0% +centripal term. Well, let's see what + + + align:start position:0% +centripal term. Well, let's see what +happens. So that was number one. + + align:start position:0% +happens. So that was number one. + + + align:start position:0% +happens. So that was number one. +Number two here is + + align:start position:0% +Number two here is + + + align:start position:0% +Number two here is +our + + align:start position:0% + + + + align:start position:0% + +dt by + + align:start position:0% +dt by + + + align:start position:0% +dt by +minus dp + + align:start position:0% +minus dp + + + align:start position:0% +minus dp +minus the derivative of the with respect + + align:start position:0% +minus the derivative of the with respect + + + align:start position:0% +minus the derivative of the with respect +to x in this case. So we go here x1 + + align:start position:0% +to x in this case. So we go here x1 + + + align:start position:0% +to x in this case. So we go here x1 +we've been calling it. Is this a + + align:start position:0% +we've been calling it. Is this a + + + align:start position:0% +we've been calling it. Is this a +function of x? This piece? Nope. It's x + + align:start position:0% +function of x? This piece? Nope. It's x + + + align:start position:0% +function of x? This piece? Nope. It's x +dot. How about this one? Right. Take + + align:start position:0% +dot. How about this one? Right. Take + + + align:start position:0% +dot. How about this one? Right. Take +this derivative you get 2x. + + align:start position:0% +this derivative you get 2x. + + + align:start position:0% +this derivative you get 2x. +So this fellow is going to give us minus + + align:start position:0% +So this fellow is going to give us minus + + + align:start position:0% +So this fellow is going to give us minus +m2 + + align:start position:0% + + + + align:start position:0% + +x1 + + align:start position:0% +x1 + + + align:start position:0% +x1 +theta dot squared. + + align:start position:0% +theta dot squared. + + + align:start position:0% +theta dot squared. +H. What's that look like? + + align:start position:0% +H. What's that look like? + + + align:start position:0% +H. What's that look like? +There it is. There's your centrial term + + align:start position:0% +There it is. There's your centrial term + + + align:start position:0% +There it is. There's your centrial term +that you're expecting to get. Okay. And + + align:start position:0% +that you're expecting to get. Okay. And + + + align:start position:0% +that you're expecting to get. Okay. And +step three + + align:start position:0% +step three + + + align:start position:0% +step three +is plus partial of V with respect to X, + + align:start position:0% +is plus partial of V with respect to X, + + + align:start position:0% +is plus partial of V with respect to X, +right? This case with respect to X. And + + align:start position:0% +right? This case with respect to X. And + + + align:start position:0% +right? This case with respect to X. And +where's our potential energy expression? + + align:start position:0% +where's our potential energy expression? + + + align:start position:0% +where's our potential energy expression? +Well, it's up here. And + + align:start position:0% + + + + align:start position:0% + +where are the X dependencies in it? + + align:start position:0% +where are the X dependencies in it? + + + align:start position:0% +where are the X dependencies in it? +There is no x in that term and no x in + + align:start position:0% +There is no x in that term and no x in + + + align:start position:0% +There is no x in that term and no x in +that term. But we have x's in both of + + align:start position:0% +that term. But we have x's in both of + + + align:start position:0% +that term. But we have x's in both of +these other terms. Right? So when we + + align:start position:0% +these other terms. Right? So when we + + + align:start position:0% +these other terms. Right? So when we +grind through this, I'll write down what + + align:start position:0% +grind through this, I'll write down what + + + align:start position:0% +grind through this, I'll write down what +we uh come up with. We get a certainly a + + align:start position:0% +we uh come up with. We get a certainly a + + + align:start position:0% +we uh come up with. We get a certainly a +spring term. K x1 - l0 minus l + + align:start position:0% +spring term. K x1 - l0 minus l + + + align:start position:0% +spring term. K x1 - l0 minus l +2 over 2. So that's the spring piece. + + align:start position:0% +2 over 2. So that's the spring piece. + + + align:start position:0% +2 over 2. So that's the spring piece. +When you take the derivative, + + align:start position:0% +When you take the derivative, + + + align:start position:0% +When you take the derivative, +the two cancels the half and the + + align:start position:0% +the two cancels the half and the + + + align:start position:0% +the two cancels the half and the +derivative of parts inside just gives + + align:start position:0% +derivative of parts inside just gives + + + align:start position:0% +derivative of parts inside just gives +you one. So that's the first piece of + + align:start position:0% +you one. So that's the first piece of + + + align:start position:0% +you one. So that's the first piece of +the potential energy expression. And the + + align:start position:0% +the potential energy expression. And the + + + align:start position:0% +the potential energy expression. And the +second piece is only going to come from + + align:start position:0% +second piece is only going to come from + + + align:start position:0% +second piece is only going to come from +here. The derivative of this with + + align:start position:0% +here. The derivative of this with + + + align:start position:0% +here. The derivative of this with +respect to x1 is just mg m2 g cosine + + align:start position:0% +respect to x1 is just mg m2 g cosine + + + align:start position:0% +respect to x1 is just mg m2 g cosine +theta + + align:start position:0% +theta + + + align:start position:0% +theta +minus + + align:start position:0% + + + + align:start position:0% + +and you add those bits together, you end + + align:start position:0% +and you add those bits together, you end + + + align:start position:0% +and you add those bits together, you end +up with + + align:start position:0% +up with + + + align:start position:0% +up with +m_sub_2 x1 dot + + align:start position:0% +m_sub_2 x1 dot + + + align:start position:0% +m_sub_2 x1 dot +minus m_sub_2 + + align:start position:0% +minus m_sub_2 + + + align:start position:0% +minus m_sub_2 +x1 theta dot + + align:start position:0% +x1 theta dot + + + align:start position:0% +x1 theta dot +squared + + align:start position:0% +squared + + + align:start position:0% +squared ++ k + + align:start position:0% ++ k + + + align:start position:0% ++ k +x1 - l0 - l2 / 2 + + align:start position:0% +x1 - l0 - l2 / 2 + + + align:start position:0% +x1 - l0 - l2 / 2 +- m 2 g cosine + + align:start position:0% +- m 2 g cosine + + + align:start position:0% +- m 2 g cosine +theta. So those are the three terms 1 + + align:start position:0% +theta. So those are the three terms 1 + + + align:start position:0% +theta. So those are the three terms 1 +plus 2 + 3 that go on the left hand side + + align:start position:0% +plus 2 + 3 that go on the left hand side + + + align:start position:0% +plus 2 + 3 that go on the left hand side +and they're going to equal my q + + align:start position:0% +and they're going to equal my q + + + align:start position:0% +and they're going to equal my q +x that I find. But I still now have to + + align:start position:0% +x that I find. But I still now have to + + + align:start position:0% +x that I find. But I still now have to +find what the generalized force is in + + align:start position:0% +find what the generalized force is in + + + align:start position:0% +find what the generalized force is in +the x direction. + + align:start position:0% + + + + align:start position:0% + +Since all is left to do for this problem + + align:start position:0% +Since all is left to do for this problem + + + align:start position:0% +Since all is left to do for this problem +is to find Q subx, the generalized force + + align:start position:0% +is to find Q subx, the generalized force + + + align:start position:0% +is to find Q subx, the generalized force +that goes on the right hand side. So now + + align:start position:0% +that goes on the right hand side. So now + + + align:start position:0% +that goes on the right hand side. So now +let's draw a little little diagram here + + align:start position:0% +let's draw a little little diagram here + + + align:start position:0% +let's draw a little little diagram here +of my system. + + align:start position:0% +of my system. + + + align:start position:0% +of my system. +And at the end of the sleeve, so here's + + align:start position:0% +And at the end of the sleeve, so here's + + + align:start position:0% +And at the end of the sleeve, so here's +my sleeve, + + align:start position:0% +my sleeve, + + + align:start position:0% +my sleeve, +I've applied this force. + + align:start position:0% + + + + align:start position:0% + +This is F of T. + + align:start position:0% +This is F of T. + + + align:start position:0% +This is F of T. +Maybe it's some F kn cosine + + align:start position:0% +Maybe it's some F kn cosine + + + align:start position:0% +Maybe it's some F kn cosine +omega t. It's an oscilly force, external + + align:start position:0% +omega t. It's an oscilly force, external + + + align:start position:0% +omega t. It's an oscilly force, external +force. + + align:start position:0% +force. + + + align:start position:0% +force. +Make it vibrate. + + align:start position:0% + + + + align:start position:0% + +And I need to know the virtual work done + + align:start position:0% +And I need to know the virtual work done + + + align:start position:0% +And I need to know the virtual work done +making that force go through a + + align:start position:0% +making that force go through a + + + align:start position:0% +making that force go through a +displacement in what direction? + + align:start position:0% + + + + align:start position:0% + +So this equation is the x1 equation, + + align:start position:0% +So this equation is the x1 equation, + + + align:start position:0% +So this equation is the x1 equation, +right? And so the virtual displacement + + align:start position:0% +right? And so the virtual displacement + + + align:start position:0% +right? And so the virtual displacement +I'm talking about is delta x1. + + align:start position:0% +I'm talking about is delta x1. + + + align:start position:0% +I'm talking about is delta x1. +And the amount of work that it does is + + align:start position:0% +And the amount of work that it does is + + + align:start position:0% +And the amount of work that it does is +delta x1 times the component of this + + align:start position:0% +delta x1 times the component of this + + + align:start position:0% +delta x1 times the component of this +force that's in its direction. So + + align:start position:0% +force that's in its direction. So + + + align:start position:0% +force that's in its direction. So +I'm going to take + + align:start position:0% +I'm going to take + + + align:start position:0% +I'm going to take +this force and break it up into two + + align:start position:0% +this force and break it up into two + + + align:start position:0% +this force and break it up into two +components. + + align:start position:0% +components. + + + align:start position:0% +components. +And if + + align:start position:0% + + + + align:start position:0% + +this is my theta, this is also theta. + + align:start position:0% + + + + align:start position:0% + +So this will be f not I'll leave out the + + align:start position:0% +So this will be f not I'll leave out the + + + align:start position:0% +So this will be f not I'll leave out the +cosine omega t here. + + align:start position:0% +cosine omega t here. + + + align:start position:0% +cosine omega t here. +It's a function of time. But this side + + align:start position:0% +It's a function of time. But this side + + + align:start position:0% +It's a function of time. But this side +then is cosine theta i. + + align:start position:0% +then is cosine theta i. + + + align:start position:0% +then is cosine theta i. +No. Hey, I got this wrong. I drew this + + align:start position:0% +No. Hey, I got this wrong. I drew this + + + align:start position:0% +No. Hey, I got this wrong. I drew this +wrong. I'm sorry. This is theta. This is + + align:start position:0% +wrong. I'm sorry. This is theta. This is + + + align:start position:0% +wrong. I'm sorry. This is theta. This is +going to be sine + + align:start position:0% +going to be sine + + + align:start position:0% +going to be sine +this side is sine theta + + align:start position:0% +this side is sine theta + + + align:start position:0% +this side is sine theta +in the i direction and this piece + + align:start position:0% +in the i direction and this piece + + + align:start position:0% +in the i direction and this piece +is f of t + + align:start position:0% +is f of t + + + align:start position:0% +is f of t +cosine theta in the j. + + align:start position:0% +cosine theta in the j. + + + align:start position:0% +cosine theta in the j. +So I break it up in two parts + + align:start position:0% +So I break it up in two parts + + + align:start position:0% +So I break it up in two parts +and the virtual work associated with X1 + + align:start position:0% +and the virtual work associated with X1 + + + align:start position:0% +and the virtual work associated with X1 +is the thing I'm looking for qx + + align:start position:0% +is the thing I'm looking for qx + + + align:start position:0% +is the thing I'm looking for qx +dotted with delta x1 + + align:start position:0% +dotted with delta x1 + + + align:start position:0% +dotted with delta x1 +and that is f + + align:start position:0% +and that is f + + + align:start position:0% +and that is f +of t here the vector dotted with dr my + + align:start position:0% +of t here the vector dotted with dr my + + + align:start position:0% +of t here the vector dotted with dr my +little displacement. But in this case, + + align:start position:0% +little displacement. But in this case, + + + align:start position:0% +little displacement. But in this case, +this then all works out to be f + + align:start position:0% +this then all works out to be f + + + align:start position:0% +this then all works out to be f +not + + align:start position:0% + + + + align:start position:0% + +cosine omega t. + + align:start position:0% +cosine omega t. + + + align:start position:0% +cosine omega t. +And it has + + align:start position:0% +And it has + + + align:start position:0% +And it has +sin theta i plus cos theta j components + + align:start position:0% +sin theta i plus cos theta j components + + + align:start position:0% +sin theta i plus cos theta j components +dotted with delta x in the i. + + align:start position:0% +dotted with delta x in the i. + + + align:start position:0% +dotted with delta x in the i. +So you're only going to get i.j gives + + align:start position:0% +So you're only going to get i.j gives + + + align:start position:0% +So you're only going to get i.j gives +you zero. I do i gives you one. So + + align:start position:0% +you zero. I do i gives you one. So + + + align:start position:0% +you zero. I do i gives you one. So +you're going to get one piece out of + + align:start position:0% +you're going to get one piece out of + + + align:start position:0% +you're going to get one piece out of +this. This says then that qx + + align:start position:0% +this. This says then that qx + + + align:start position:0% +this. This says then that qx +equals f cosine omega t + + align:start position:0% +equals f cosine omega t + + + align:start position:0% +equals f cosine omega t +sin + + align:start position:0% + + + + align:start position:0% + +theta + + align:start position:0% +theta + + + align:start position:0% +theta +and that's + + align:start position:0% +and that's + + + align:start position:0% +and that's +and to start with you know you have a + + align:start position:0% +and to start with you know you have a + + + align:start position:0% +and to start with you know you have a +delta x here and a delta x here and + + align:start position:0% +delta x here and a delta x here and + + + align:start position:0% +delta x here and a delta x here and +that's gives you the delta virtual work + + align:start position:0% +that's gives you the delta virtual work + + + align:start position:0% +that's gives you the delta virtual work +then to solve to find that you need I + + align:start position:0% +then to solve to find that you need I + + + align:start position:0% +then to solve to find that you need I +need personally when I do these problems + + align:start position:0% +need personally when I do these problems + + + align:start position:0% +need personally when I do these problems +I have to think in terms of that little + + align:start position:0% +I have to think in terms of that little + + + align:start position:0% +I have to think in terms of that little +virtual deflection and I actually figure + + align:start position:0% +virtual deflection and I actually figure + + + align:start position:0% +virtual deflection and I actually figure +out what's the virtual work done and + + align:start position:0% +out what's the virtual work done and + + + align:start position:0% +out what's the virtual work done and +then at the end I take this out and this + + align:start position:0% +then at the end I take this out and this + + + align:start position:0% +then at the end I take this out and this +is the qx that I'm looking for. So my + + align:start position:0% +is the qx that I'm looking for. So my + + + align:start position:0% +is the qx that I'm looking for. So my +final equation of motion says this + + align:start position:0% +final equation of motion says this + + + align:start position:0% +final equation of motion says this +equals + + align:start position:0% + + + + align:start position:0% + +fot cosine omega t + + align:start position:0% +fot cosine omega t + + + align:start position:0% +fot cosine omega t +sin theta. That's your equation of + + align:start position:0% +sin theta. That's your equation of + + + align:start position:0% +sin theta. That's your equation of +motion in the x1 direction. + + align:start position:0% +motion in the x1 direction. + + + align:start position:0% +motion in the x1 direction. +[Applause] + + align:start position:0% + + + + align:start position:0% + +So once on when you finish one of these + + align:start position:0% +So once on when you finish one of these + + + align:start position:0% +So once on when you finish one of these +you need to ask yourself does this make + + align:start position:0% +you need to ask yourself does this make + + + align:start position:0% +you need to ask yourself does this make +sense? You know, does this jive with my + + align:start position:0% +sense? You know, does this jive with my + + + align:start position:0% +sense? You know, does this jive with my +understanding of Newtonian physics? + + align:start position:0% + + + + align:start position:0% + +Better have a linear acceleration term + + align:start position:0% +Better have a linear acceleration term + + + align:start position:0% +Better have a linear acceleration term +because that's what it's doing. You have + + align:start position:0% +because that's what it's doing. You have + + + align:start position:0% +because that's what it's doing. You have +another an acceleration term in the same + + align:start position:0% +another an acceleration term in the same + + + align:start position:0% +another an acceleration term in the same +direction due to centrial + + align:start position:0% +direction due to centrial + + + align:start position:0% +direction due to centrial +a spring force for sure and a component + + align:start position:0% +a spring force for sure and a component + + + align:start position:0% +a spring force for sure and a component +of gravity in the direction of motion + + align:start position:0% +of gravity in the direction of motion + + + align:start position:0% +of gravity in the direction of motion +down the up and down the slide equal to + + align:start position:0% +down the up and down the slide equal to + + + align:start position:0% +down the up and down the slide equal to +any external forces in that direction. + + align:start position:0% +any external forces in that direction. + + + align:start position:0% +any external forces in that direction. +So, it makes pretty good sense. Okay. + + align:start position:0% +So, it makes pretty good sense. Okay. + + + align:start position:0% +So, it makes pretty good sense. Okay. +Now also another test you can do is does + + align:start position:0% +Now also another test you can do is does + + + align:start position:0% +Now also another test you can do is does +it satisfy the laws of statics + + align:start position:0% +it satisfy the laws of statics + + + align:start position:0% +it satisfy the laws of statics +that's another check you can perform + + align:start position:0% +that's another check you can perform + + + align:start position:0% +that's another check you can perform +this what's does this thing at static + + align:start position:0% +this what's does this thing at static + + + align:start position:0% +this what's does this thing at static +equilibrium tell the truth at static + + align:start position:0% +equilibrium tell the truth at static + + + align:start position:0% +equilibrium tell the truth at static +equilibrium all time derivatives are + + align:start position:0% +equilibrium all time derivatives are + + + align:start position:0% +equilibrium all time derivatives are +zero so this would be zero this would be + + align:start position:0% +zero so this would be zero this would be + + + align:start position:0% +zero so this would be zero this would be +zero you know at static equilibrium + + align:start position:0% +zero you know at static equilibrium + + + align:start position:0% +zero you know at static equilibrium +hangs down so cosine theta is one static + + align:start position:0% +hangs down so cosine theta is one static + + + align:start position:0% +hangs down so cosine theta is one static +you don't have any time dependent forces + + align:start position:0% +you don't have any time dependent forces + + + align:start position:0% +you don't have any time dependent forces +that's zero so the static part of this + + align:start position:0% +that's zero so the static part of this + + + align:start position:0% +that's zero so the static part of this +says that + + align:start position:0% + + + + align:start position:0% + +says that k + + align:start position:0% +says that k + + + align:start position:0% +says that k +x1 - l0 - l2 / 2 equ= + + align:start position:0% +x1 - l0 - l2 / 2 equ= + + + align:start position:0% +x1 - l0 - l2 / 2 equ= +m2 g cosine and that's cosine theta is + + align:start position:0% +m2 g cosine and that's cosine theta is + + + align:start position:0% +m2 g cosine and that's cosine theta is +1. So it's m2g + + align:start position:0% +1. So it's m2g + + + align:start position:0% +1. So it's m2g +and you could figure out then this must + + align:start position:0% +and you could figure out then this must + + + align:start position:0% +and you could figure out then this must +be k * something. This is the x this is + + align:start position:0% +be k * something. This is the x this is + + + align:start position:0% +be k * something. This is the x this is +the amount that the spring stretches the + + align:start position:0% +the amount that the spring stretches the + + + align:start position:0% +the amount that the spring stretches the +static stretch of the spring so that + + align:start position:0% +static stretch of the spring so that + + + align:start position:0% +static stretch of the spring so that +it's equal to the spring has an equal + + align:start position:0% +it's equal to the spring has an equal + + + align:start position:0% +it's equal to the spring has an equal +opposite force to the weight of the + + align:start position:0% +opposite force to the weight of the + + + align:start position:0% +opposite force to the weight of the +thing m2g. So that's another check you + + align:start position:0% +thing m2g. So that's another check you + + + align:start position:0% +thing m2g. So that's another check you +can do when doing the problems. + + align:start position:0% +can do when doing the problems. + + + align:start position:0% +can do when doing the problems. +Okay. So I want you there's I'll I'll + + align:start position:0% +Okay. So I want you there's I'll I'll + + + align:start position:0% +Okay. So I want you there's I'll I'll +write up the final the other one. We + + align:start position:0% +write up the final the other one. We + + + align:start position:0% +write up the final the other one. We +have one more equation to go right got + + align:start position:0% +have one more equation to go right got + + + align:start position:0% +have one more equation to go right got +to do all the derivatives with respect + + align:start position:0% +to do all the derivatives with respect + + + align:start position:0% +to do all the derivatives with respect +to theta. + + align:start position:0% +to theta. + + + align:start position:0% +to theta. +So do you take a minute to decide how + + align:start position:0% +So do you take a minute to decide how + + + align:start position:0% +So do you take a minute to decide how +many terms how many acceleration terms + + align:start position:0% +many terms how many acceleration terms + + + align:start position:0% +many terms how many acceleration terms +and what acceleration terms do you + + align:start position:0% +and what acceleration terms do you + + + align:start position:0% +and what acceleration terms do you +expect to see come out of this second + + align:start position:0% +expect to see come out of this second + + + align:start position:0% +expect to see come out of this second +equation of motion? Because now we're + + align:start position:0% +equation of motion? Because now we're + + + align:start position:0% +equation of motion? Because now we're +talking about which motion + + align:start position:0% +talking about which motion + + + align:start position:0% +talking about which motion +swinging motion and what's its + + align:start position:0% +swinging motion and what's its + + + align:start position:0% +swinging motion and what's its +direction? It's you know in in Newtonian + + align:start position:0% +direction? It's you know in in Newtonian + + + align:start position:0% +direction? It's you know in in Newtonian +sense it would have a vector direction. + + align:start position:0% +sense it would have a vector direction. + + + align:start position:0% +sense it would have a vector direction. +It's in the in what we call J here. + + align:start position:0% +It's in the in what we call J here. + + + align:start position:0% +It's in the in what we call J here. +Okay. So you're about to get the J + + align:start position:0% +Okay. So you're about to get the J + + + align:start position:0% +Okay. So you're about to get the J +equation. What ex what terms do you + + align:start position:0% +equation. What ex what terms do you + + + align:start position:0% +equation. What ex what terms do you +expect to find in it? + + align:start position:0% + + + + align:start position:0% + +Talk to your neighbors and sort this + + align:start position:0% +Talk to your neighbors and sort this + + + align:start position:0% +Talk to your neighbors and sort this +out. Tell me what the basically tell me + + align:start position:0% +out. Tell me what the basically tell me + + + align:start position:0% +out. Tell me what the basically tell me +what the answer is going to be. + + align:start position:0% + + + + align:start position:0% + +What do you think? + + align:start position:0% + + + + align:start position:0% + +What are we going to get? + + align:start position:0% +What are we going to get? + + + align:start position:0% +What are we going to get? +Um, we were debating about whether or + + align:start position:0% +Um, we were debating about whether or + + + align:start position:0% +Um, we were debating about whether or +not it was going to be like speeding up. + + align:start position:0% + + + + align:start position:0% + +So it's it it is a pendulum just a weird + + align:start position:0% +So it's it it is a pendulum just a weird + + + align:start position:0% +So it's it it is a pendulum just a weird +pendulum. So is there + + align:start position:0% +pendulum. So is there + + + align:start position:0% +pendulum. So is there +does does the theta change speed? + + align:start position:0% +does does the theta change speed? + + + align:start position:0% +does does the theta change speed? +Sure. When it gets up the top it swing + + align:start position:0% +Sure. When it gets up the top it swing + + + align:start position:0% +Sure. When it gets up the top it swing +at zero all the way down it's maximum + + align:start position:0% +at zero all the way down it's maximum + + + align:start position:0% +at zero all the way down it's maximum +speed. So what terms do you what terms + + align:start position:0% +speed. So what terms do you what terms + + + align:start position:0% +speed. So what terms do you what terms +does that imply that you're going to get + + align:start position:0% +does that imply that you're going to get + + + align:start position:0% +does that imply that you're going to get +part? Well maybe maybe not. + + align:start position:0% +part? Well maybe maybe not. + + + align:start position:0% +part? Well maybe maybe not. +Yeah, + + align:start position:0% +Yeah, + + + align:start position:0% +Yeah, +you're going to get an orarian, which + + align:start position:0% +you're going to get an orarian, which + + + align:start position:0% +you're going to get an orarian, which +means you got a theta dot term. You're + + align:start position:0% +means you got a theta dot term. You're + + + align:start position:0% +means you got a theta dot term. You're +you're expecting a theta dot term to + + align:start position:0% +you're expecting a theta dot term to + + + align:start position:0% +you're expecting a theta dot term to +show up. Okay. What else? + + align:start position:0% + + + + align:start position:0% + +Will you get a Corololis term? + + align:start position:0% +Will you get a Corololis term? + + + align:start position:0% +Will you get a Corololis term? +Do you expect a Corololis term? + + align:start position:0% +Do you expect a Corololis term? + + + align:start position:0% +Do you expect a Corololis term? +Something looks like X do theta dot. + + align:start position:0% + + + + align:start position:0% + +Yeah, the thing is sliding up and down + + align:start position:0% +Yeah, the thing is sliding up and down + + + align:start position:0% +Yeah, the thing is sliding up and down +the sleeve. It has a nonzero value of x + + align:start position:0% +the sleeve. It has a nonzero value of x + + + align:start position:0% +the sleeve. It has a nonzero value of x +dot. Anytime you got things moving + + align:start position:0% +dot. Anytime you got things moving + + + align:start position:0% +dot. Anytime you got things moving +radially while something is swinging + + align:start position:0% +radially while something is swinging + + + align:start position:0% +radially while something is swinging +in a circle, you will get corololis + + align:start position:0% +in a circle, you will get corololis + + + align:start position:0% +in a circle, you will get corololis +forces. It means the angular momentum of + + align:start position:0% +forces. It means the angular momentum of + + + align:start position:0% +forces. It means the angular momentum of +that thing is changing and it takes + + align:start position:0% +that thing is changing and it takes + + + align:start position:0% +that thing is changing and it takes +forces to make that happen. So here's + + align:start position:0% +forces to make that happen. So here's + + + align:start position:0% +forces to make that happen. So here's +what this uh + + align:start position:0% +what this uh + + + align:start position:0% +what this uh +answer looks like. + + align:start position:0% + + + + align:start position:0% + +That's the one term. + + align:start position:0% +That's the one term. + + + align:start position:0% +That's the one term. +The two piece gives you + + align:start position:0% +The two piece gives you + + + align:start position:0% +The two piece gives you +zero. + + align:start position:0% + + + + align:start position:0% + +It's not a function of of uh x in the + + align:start position:0% +It's not a function of of uh x in the + + + align:start position:0% +It's not a function of of uh x in the +three piece. The potential energy piece + + align:start position:0% +three piece. The potential energy piece + + + align:start position:0% +three piece. The potential energy piece +gives you m2 g x1 + + align:start position:0% +gives you m2 g x1 + + + align:start position:0% +gives you m2 g x1 +sin theta + + align:start position:0% +sin theta + + + align:start position:0% +sin theta +plus m1 g l1 / 2 + + align:start position:0% +plus m1 g l1 / 2 + + + align:start position:0% +plus m1 g l1 / 2 +sin theta. + + align:start position:0% +sin theta. + + + align:start position:0% +sin theta. +And the fourth piece, the Q theta. + + align:start position:0% +And the fourth piece, the Q theta. + + + align:start position:0% +And the fourth piece, the Q theta. +Well, that's just going to be the + + align:start position:0% +Well, that's just going to be the + + + align:start position:0% +Well, that's just going to be the +virtual work done. + + align:start position:0% + + + + align:start position:0% + +There's a tricky bit to this one. Now, + + align:start position:0% +There's a tricky bit to this one. Now, + + + align:start position:0% +There's a tricky bit to this one. Now, +there's virtual work, but which + + align:start position:0% +there's virtual work, but which + + + align:start position:0% +there's virtual work, but which +direction? So, we have an F dot a DR. + + align:start position:0% +direction? So, we have an F dot a DR. + + + align:start position:0% +direction? So, we have an F dot a DR. +The only F we have is this. + + align:start position:0% +The only F we have is this. + + + align:start position:0% +The only F we have is this. +What's the DR? What direction is it? + + align:start position:0% + + + + align:start position:0% + +This is the theta coordinate. What + + align:start position:0% +This is the theta coordinate. What + + + align:start position:0% +This is the theta coordinate. What +direction does that give you? + + align:start position:0% +direction does that give you? + + + align:start position:0% +direction does that give you? +Displacements. F dot dr is a + + align:start position:0% +Displacements. F dot dr is a + + + align:start position:0% +Displacements. F dot dr is a +displacement, not an angle. To get the + + align:start position:0% +displacement, not an angle. To get the + + + align:start position:0% +displacement, not an angle. To get the +work done, you got to move a force + + align:start position:0% +work done, you got to move a force + + + align:start position:0% +work done, you got to move a force +through a distance. So the distance + + align:start position:0% +through a distance. So the distance + + + align:start position:0% +through a distance. So the distance +first of all is in what direction? When + + align:start position:0% +first of all is in what direction? When + + + align:start position:0% +first of all is in what direction? When +theta moves + + align:start position:0% +theta moves + + + align:start position:0% +theta moves +j little j hat, right? And how much if + + align:start position:0% +j little j hat, right? And how much if + + + align:start position:0% +j little j hat, right? And how much if +now if you get a virtual deflection of + + align:start position:0% +now if you get a virtual deflection of + + + align:start position:0% +now if you get a virtual deflection of +delta theta what's the virtual + + align:start position:0% +delta theta what's the virtual + + + align:start position:0% +delta theta what's the virtual +displacement you get a virtual change in + + align:start position:0% +displacement you get a virtual change in + + + align:start position:0% +displacement you get a virtual change in +angle delta theta but is that the + + align:start position:0% +angle delta theta but is that the + + + align:start position:0% +angle delta theta but is that the +virtual displacement + + align:start position:0% + + + + align:start position:0% + +what's the displacement of this point + + align:start position:0% +what's the displacement of this point + + + align:start position:0% +what's the displacement of this point +here in the J direction given a virtual + + align:start position:0% +here in the J direction given a virtual + + + align:start position:0% +here in the J direction given a virtual +displacement delta theta think that + + align:start position:0% + + + + align:start position:0% + +Can't quite hear it. + + align:start position:0% +Can't quite hear it. + + + align:start position:0% +Can't quite hear it. +X1 delta theta will give you the motion + + align:start position:0% +X1 delta theta will give you the motion + + + align:start position:0% +X1 delta theta will give you the motion +the displacement at the center of mass + + align:start position:0% +the displacement at the center of mass + + + align:start position:0% +the displacement at the center of mass +in that direction. + + align:start position:0% +in that direction. + + + align:start position:0% +in that direction. +X1 comes from here to here. So X1 delta + + align:start position:0% +X1 comes from here to here. So X1 delta + + + align:start position:0% +X1 comes from here to here. So X1 delta +theta will give you a little + + align:start position:0% +theta will give you a little + + + align:start position:0% +theta will give you a little +displacement in that direction. But is + + align:start position:0% +displacement in that direction. But is + + + align:start position:0% +displacement in that direction. But is +that the delta that is that the + + align:start position:0% +that the delta that is that the + + + align:start position:0% +that the delta that is that the +displacement we care about? We need the + + align:start position:0% +displacement we care about? We need the + + + align:start position:0% +displacement we care about? We need the +displacement here. So you're close. + + align:start position:0% + + + + align:start position:0% + +So we're going to get some force dot + + align:start position:0% +So we're going to get some force dot + + + align:start position:0% +So we're going to get some force dot +a displacement dr. + + align:start position:0% +a displacement dr. + + + align:start position:0% +a displacement dr. +And that's going to be our force. This + + align:start position:0% +And that's going to be our force. This + + + align:start position:0% +And that's going to be our force. This +guy with its I and J components I and J + + align:start position:0% +guy with its I and J components I and J + + + align:start position:0% +guy with its I and J components I and J +terms. But this term out here is + + align:start position:0% +terms. But this term out here is + + + align:start position:0% +terms. But this term out here is +x1 + + align:start position:0% +x1 + + + align:start position:0% +x1 +plus l2 over 2 to get to the end. And + + align:start position:0% +plus l2 over 2 to get to the end. And + + + align:start position:0% +plus l2 over 2 to get to the end. And +it's in the j + + align:start position:0% +it's in the j + + + align:start position:0% +it's in the j +direction. So it's a length times a and + + align:start position:0% +direction. So it's a length times a and + + + align:start position:0% +direction. So it's a length times a and +and you need the delta + + align:start position:0% + + + + align:start position:0% + +this this quantity and you need a delta + + align:start position:0% +this this quantity and you need a delta + + + align:start position:0% +this this quantity and you need a delta +theta + + align:start position:0% +theta + + + align:start position:0% +theta +delta theta. This is the term. This is + + align:start position:0% +delta theta. This is the term. This is + + + align:start position:0% +delta theta. This is the term. This is +the dr + + align:start position:0% +the dr + + + align:start position:0% +the dr +for this system. An angle, a virtual + + align:start position:0% +for this system. An angle, a virtual + + + align:start position:0% +for this system. An angle, a virtual +deflection and angle times a moment arm + + align:start position:0% +deflection and angle times a moment arm + + + align:start position:0% +deflection and angle times a moment arm +gives you a distance. It's in the uh J + + align:start position:0% +gives you a distance. It's in the uh J + + + align:start position:0% +gives you a distance. It's in the uh J +hat direction + + align:start position:0% +hat direction + + + align:start position:0% +hat direction +dotted with the same force. Breaking the + + align:start position:0% +dotted with the same force. Breaking the + + + align:start position:0% +dotted with the same force. Breaking the +force up into its I and J components. It + + align:start position:0% +force up into its I and J components. It + + + align:start position:0% +force up into its I and J components. It +had a sin theta I cos theta J. So this + + align:start position:0% +had a sin theta I cos theta J. So this + + + align:start position:0% +had a sin theta I cos theta J. So this +is going to give me a f cosine omega t + + align:start position:0% +is going to give me a f cosine omega t + + + align:start position:0% +is going to give me a f cosine omega t +cos theta j.j J + + align:start position:0% + + + + align:start position:0% + +Fnot + + align:start position:0% +Fnot + + + align:start position:0% +Fnot +cossine omega t + + align:start position:0% +cossine omega t + + + align:start position:0% +cossine omega t +cos + + align:start position:0% +cos + + + align:start position:0% +cos +theta + + align:start position:0% + + + + align:start position:0% + +x1 + l2 over 2 delta theta is the delta + + align:start position:0% +x1 + l2 over 2 delta theta is the delta + + + align:start position:0% +x1 + l2 over 2 delta theta is the delta +w that's the work and the virtual equal + + align:start position:0% +w that's the work and the virtual equal + + + align:start position:0% +w that's the work and the virtual equal +the generalized force Q theta is this + + align:start position:0% +the generalized force Q theta is this + + + align:start position:0% +the generalized force Q theta is this +part of it. So + + align:start position:0% +part of it. So + + + align:start position:0% +part of it. So +this plus this plus this equals that on + + align:start position:0% +this plus this plus this equals that on + + + align:start position:0% +this plus this plus this equals that on +the right hand side. So this is part + + align:start position:0% +the right hand side. So this is part + + + align:start position:0% +the right hand side. So this is part +four. + + align:start position:0% +four. + + + align:start position:0% +four. +So this let's look at it. Yeah. + + align:start position:0% + + + + align:start position:0% + +So f of t you know I I I just I didn't + + align:start position:0% +So f of t you know I I I just I didn't + + + align:start position:0% +So f of t you know I I I just I didn't +want to write it all out. It this thing + + align:start position:0% +want to write it all out. It this thing + + + align:start position:0% +want to write it all out. It this thing +breaks into an i and a j piece which is + + align:start position:0% +breaks into an i and a j piece which is + + + align:start position:0% +breaks into an i and a j piece which is +written over there. This is the sin + + align:start position:0% +written over there. This is the sin + + + align:start position:0% +written over there. This is the sin +theta i cos theta j term + + align:start position:0% + + + + align:start position:0% + +which I pulled out which I brought back + + align:start position:0% +which I pulled out which I brought back + + + align:start position:0% +which I pulled out which I brought back +from over there and that and we dot it + + align:start position:0% +from over there and that and we dot it + + + align:start position:0% +from over there and that and we dot it +with the dr that we care about which is + + align:start position:0% +with the dr that we care about which is + + + align:start position:0% +with the dr that we care about which is +x1 this length times that angle in the j + + align:start position:0% +x1 this length times that angle in the j + + + align:start position:0% +x1 this length times that angle in the j +direction. a J dot. We only pick up the + + align:start position:0% +direction. a J dot. We only pick up the + + + align:start position:0% +direction. a J dot. We only pick up the +J piece of this and that gives us this + + align:start position:0% +J piece of this and that gives us this + + + align:start position:0% +J piece of this and that gives us this +cosine theta term. + + align:start position:0% +cosine theta term. + + + align:start position:0% +cosine theta term. +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +let's look quickly. This is a rotational + + align:start position:0% +let's look quickly. This is a rotational + + + align:start position:0% +let's look quickly. This is a rotational +thing. It has units of is it force? Is + + align:start position:0% +thing. It has units of is it force? Is + + + align:start position:0% +thing. It has units of is it force? Is +this equation a force equation? + + align:start position:0% + + + + align:start position:0% + +I theta dot has units of what? + + align:start position:0% +I theta dot has units of what? + + + align:start position:0% +I theta dot has units of what? +Torque. This is a torque equation. This + + align:start position:0% +Torque. This is a torque equation. This + + + align:start position:0% +Torque. This is a torque equation. This +is the the uh + + align:start position:0% +is the the uh + + + align:start position:0% +is the the uh +total mass moment of inertia izz with + + align:start position:0% +total mass moment of inertia izz with + + + align:start position:0% +total mass moment of inertia izz with +respect to a for this system such that + + align:start position:0% +respect to a for this system such that + + + align:start position:0% +respect to a for this system such that +the orilarian acceleration the torque it + + align:start position:0% +the orilarian acceleration the torque it + + + align:start position:0% +the orilarian acceleration the torque it +takes to make that happen is the sum of + + align:start position:0% +takes to make that happen is the sum of + + + align:start position:0% +takes to make that happen is the sum of +the mass moment of inertia of the rod + + align:start position:0% +the mass moment of inertia of the rod + + + align:start position:0% +the mass moment of inertia of the rod +plus the mass moment of inertia of g + + align:start position:0% +plus the mass moment of inertia of g + + + align:start position:0% +plus the mass moment of inertia of g +plus m2x1^2 which is looks a lot like + + align:start position:0% +plus m2x1^2 which is looks a lot like + + + align:start position:0% +plus m2x1^2 which is looks a lot like +the parallel axis theorem. This is IZA + + align:start position:0% +the parallel axis theorem. This is IZA + + + align:start position:0% +the parallel axis theorem. This is IZA +for the moving mass. There's your + + align:start position:0% +for the moving mass. There's your + + + align:start position:0% +for the moving mass. There's your +corololis term + + align:start position:0% + + + + align:start position:0% + +and here's your potential terms and + + align:start position:0% +and here's your potential terms and + + + align:start position:0% +and here's your potential terms and +there's your external force. + + align:start position:0% +there's your external force. + + + align:start position:0% +there's your external force. +Okay, + + align:start position:0% + + + + align:start position:0% + +talk more about these things in + + align:start position:0% +talk more about these things in + + + align:start position:0% +talk more about these things in +recitation. \ No newline at end of file